LMFDB - Embedded newform 21.30.e.b.4.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [21,30,Mod(4,21)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(21, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

N = Newforms(chi, 30, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("21.4");

S:= CuspForms(chi, 30);

N := Newforms(S);

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 30 $
Character orbit:	$[\chi]$	$=$	21.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$111.883889004$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			4.11
Character	$\chi$	$=$	21.4
Dual form			21.30.e.b.16.11

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3938.62 + 6821.90i) q^{2} +(-2.39148e6 + 4.14217e6i) q^{3} +(2.37410e8 - 4.11206e8i) q^{4} +(1.52926e8 + 2.64876e8i) q^{5} -3.76766e10 q^{6} +(1.72284e12 + 5.01708e11i) q^{7} +7.96934e12 q^{8} +(-1.14384e13 - 1.98119e13i) q^{9} +O(q^{10})$	\(q+(3938.62 + 6821.90i) q^{2} +(-2.39148e6 + 4.14217e6i) q^{3} +(2.37410e8 - 4.11206e8i) q^{4} +(1.52926e8 + 2.64876e8i) q^{5} -3.76766e10 q^{6} +(1.72284e12 + 5.01708e11i) q^{7} +7.96934e12 q^{8} +(-1.14384e13 - 1.98119e13i) q^{9} +(-1.20464e12 + 2.08649e12i) q^{10} +(9.83650e13 - 1.70373e14i) q^{11} +(1.13552e15 + 1.96679e15i) q^{12} -1.06270e16 q^{13} +(3.36304e15 + 1.37291e16i) q^{14} -1.46288e15 q^{15} +(-9.60703e16 - 1.66399e17i) q^{16} +(-5.25246e17 + 9.09752e17i) q^{17} +(9.01031e16 - 1.56063e17i) q^{18} +(1.20245e18 + 2.08271e18i) q^{19} +1.45225e17 q^{20} +(-6.19832e18 + 5.93649e18i) q^{21} +1.54969e18 q^{22} +(-7.87629e18 - 1.36421e19i) q^{23} +(-1.90585e19 + 3.30104e19i) q^{24} +(9.30855e19 - 1.61229e20i) q^{25} +(-4.18559e19 - 7.24966e19i) q^{26} +1.09419e20 q^{27} +(6.15326e20 - 5.89334e20i) q^{28} -2.50410e21 q^{29} +(-5.76174e18 - 9.97963e18i) q^{30} +(-3.67834e21 + 6.37108e21i) q^{31} +(2.89602e21 - 5.01606e21i) q^{32} +(4.70477e20 + 8.14890e20i) q^{33} -8.27498e21 q^{34} +(1.30578e20 + 5.33064e20i) q^{35} -1.08624e22 q^{36} +(-3.97497e21 - 6.88484e21i) q^{37} +(-9.47202e21 + 1.64060e22i) q^{38} +(2.54144e22 - 4.40191e22i) q^{39} +(1.21872e21 + 2.11089e21i) q^{40} +1.73435e23 q^{41} +(-6.49110e22 - 1.89027e22i) q^{42} +4.31663e23 q^{43} +(-4.67057e22 - 8.08966e22i) q^{44} +(3.49846e21 - 6.05951e21i) q^{45} +(6.20434e22 - 1.07462e23i) q^{46} +(1.17047e24 + 2.02732e24i) q^{47} +9.19002e23 q^{48} +(2.71648e24 + 1.72873e24i) q^{49} +1.46651e24 q^{50} +(-2.51223e24 - 4.35132e24i) q^{51} +(-2.52297e24 + 4.36991e24i) q^{52} +(2.60973e24 - 4.52018e24i) q^{53} +(4.30960e23 + 7.46445e23i) q^{54} +6.01703e22 q^{55} +(1.37299e25 + 3.99828e24i) q^{56} -1.15026e25 q^{57} +(-9.86270e24 - 1.70827e25i) q^{58} +(-2.68539e25 + 4.65123e25i) q^{59} +(-3.47303e23 + 6.01546e23i) q^{60} +(-9.55124e24 - 1.65432e25i) q^{61} -5.79504e25 q^{62} +(-9.76680e24 - 3.98715e25i) q^{63} -5.75293e25 q^{64} +(-1.62515e24 - 2.81485e24i) q^{65} +(-3.70606e24 + 6.41909e24i) q^{66} +(-8.80507e25 + 1.52508e26i) q^{67} +(2.49397e26 + 4.31968e26i) q^{68} +7.53441e25 q^{69} +(-3.12221e24 + 2.99033e24i) q^{70} +9.89497e25 q^{71} +(-9.11564e25 - 1.57888e26i) q^{72} +(3.63932e26 - 6.30349e26i) q^{73} +(3.13118e25 - 5.42336e25i) q^{74} +(4.45225e26 + 7.71152e26i) q^{75} +1.14190e27 q^{76} +(2.54945e26 - 2.44176e26i) q^{77} +4.00391e26 q^{78} +(8.41980e26 + 1.45835e27i) q^{79} +(2.93833e25 - 5.08934e25i) q^{80} +(-2.61674e26 + 4.53232e26i) q^{81} +(6.83097e26 + 1.18316e27i) q^{82} -1.14084e28 q^{83} +(9.69580e26 + 3.95817e27i) q^{84} -3.21295e26 q^{85} +(1.70016e27 + 2.94476e27i) q^{86} +(5.98851e27 - 1.03724e28i) q^{87} +(7.83904e26 - 1.35776e27i) q^{88} +(-1.10267e27 - 1.90989e27i) q^{89} +5.51165e25 q^{90} +(-1.83088e28 - 5.33168e27i) q^{91} -7.47963e27 q^{92} +(-1.75934e28 - 3.04727e28i) q^{93} +(-9.22009e27 + 1.59697e28i) q^{94} +(-3.67773e26 + 6.37002e26i) q^{95} +(1.38516e28 + 2.39916e28i) q^{96} +7.92305e28 q^{97} +(-1.09401e27 + 2.53404e28i) q^{98} -4.50055e27 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 7743 q^{2} - 95659380 q^{3} - 5985454645 q^{4} + 14215352760 q^{5} + 74069057934 q^{6} - 368001036334 q^{7} + 49989480496086 q^{8} - 457535849099220 q^{9}+O(q^{10}) $ 40 * q - 7743 * q^2 - 95659380 * q^3 - 5985454645 * q^4 + 14215352760 * q^5 + 74069057934 * q^6 - 368001036334 * q^7 + 49989480496086 * q^8 - 457535849099220 * q^9	$ 40 q - 7743 q^{2} - 95659380 q^{3} - 5985454645 q^{4} + 14215352760 q^{5} + 74069057934 q^{6} - 368001036334 q^{7} + 49989480496086 q^{8} - 457535849099220 q^{9} - 167879133295903 q^{10} - 31\!\cdots\!14 q^{11}+ \cdots + 14\!\cdots\!08 q^{99}+O(q^{100}) $ 40 * q - 7743 * q^2 - 95659380 * q^3 - 5985454645 * q^4 + 14215352760 * q^5 + 74069057934 * q^6 - 368001036334 * q^7 + 49989480496086 * q^8 - 457535849099220 * q^9 - 167879133295903 * q^10 - 3154300361224314 * q^11 - 28628244017941005 * q^12 + 27686480502978220 * q^13 - 214257133773063450 * q^14 - 135983183150288880 * q^15 - 1764048935658629353 * q^16 + 41802108452009436 * q^17 - 177135003978763023 * q^18 - 7235175939726809174 * q^19 - 2944336803535185762 * q^20 + 9048396870023397228 * q^21 + 89086825354637664038 * q^22 + 44902952138264019852 * q^23 - 119549067769441979667 * q^24 - 856461315876501170374 * q^25 + 740598921837346265154 * q^26 + 4376759565260494368360 * q^27 + 837334611372858240643 * q^28 + 3042539991157763918664 * q^29 - 802960690301171876007 * q^30 - 7171021288148722128918 * q^31 - 3221069809618281449199 * q^32 - 15086920844424695908266 * q^33 - 40988792924743489638864 * q^34 + 22734956365007065015692 * q^35 + 273856007324494541487690 * q^36 - 32961210550052530362042 * q^37 - 21824144763887061483774 * q^38 - 66211788982424616967590 * q^39 - 561274593219911517352413 * q^40 - 407158367720211769052760 * q^41 + 261768399564896960899059 * q^42 - 742478352427516947522676 * q^43 - 860699497136335577636151 * q^44 + 325201674764577027042360 * q^45 - 3603590382443692607483880 * q^46 + 5088913555222492904989956 * q^47 + 16874782747476437555778114 * q^48 - 1107011263686123128490044 * q^49 + 20047363110221889541650996 * q^50 + 199938188860599120095484 * q^51 - 15020364113616852849255436 * q^52 + 4503823724603073528076524 * q^53 - 847231232845300197355287 * q^54 - 26118327809723981533730792 * q^55 + 23391818796605514251144607 * q^56 + 69211244458518393496315212 * q^57 - 19344263089875691399511041 * q^58 - 107339818359767325079738806 * q^59 + 7041335828433941954443689 * q^60 - 55695583344240438158518844 * q^61 + 595684893227471470626855138 * q^62 - 34859518397595458196656958 * q^63 + 2556323224325113131258620002 * q^64 + 116576686276646946961533216 * q^65 - 213049761989822976663084411 * q^66 - 395633506213215660680479214 * q^67 - 341809314919360918295601216 * q^68 - 429538856171601041535001176 * q^69 + 3114247010513527110020739673 * q^70 - 357045698249607322103230392 * q^71 - 571799485120140136045891323 * q^72 + 1563411738231613398537297906 * q^73 - 2560064971236623546640897774 * q^74 - 4096427923536512926362560406 * q^75 + 24051365932177387567037871800 * q^76 - 788772365883171194224066980 * q^77 - 7084523369162900456994724452 * q^78 + 5677690363343606232557230766 * q^79 - 3948631034904977500881109899 * q^80 - 10466952660547210744270230420 * q^81 - 14901652274869047200277511964 * q^82 + 21293945454157612982870988948 * q^83 - 13769091913378092591470544324 * q^84 + 8900456942787328180094572008 * q^85 - 1540767080130988487092741200 * q^86 - 7276187229483929466144216708 * q^87 - 63208209978831072085072879725 * q^88 - 11757157651476935757967358112 * q^89 + 7681072179858211493226649566 * q^90 - 1529257930272663641703478390 * q^91 + 158106912155564585073501217248 * q^92 - 34298772519555405332228797542 * q^93 - 133188762499886306919098285406 * q^94 - 159842963957338542634753903584 * q^95 - 15406277046240142004793891831 * q^96 - 390739421663203813144382175132 * q^97 + 239765305290895114544854004019 * q^98 + 144320549408674286727326243508 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/21\mathbb{Z}\right)^\times$.

$n$	$8$	$10$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	3938.62	+	6821.90i	0.169985	+	0.294422i	0.938414	−	0.345512i	$-0.112295\pi$
$2$	3938.62	+	6821.90i	0.169985	+	0.294422i	−0.768430	+	0.639934i	$0.778962\pi$
$3$	−2.39148e6	+	4.14217e6i	−0.288675	+	0.500000i
$3$	−2.39148e6	+	4.14217e6i	−0.288675	+	0.500000i
$4$	2.37410e8	−	4.11206e8i	0.442210	−	0.765931i
$5$	1.52926e8	+	2.64876e8i	0.0112051	+	0.0194078i	0.871574	−	0.490265i	$-0.163100\pi$
$5$	1.52926e8	+	2.64876e8i	0.0112051	+	0.0194078i	−0.860368	+	0.509673i	$0.829767\pi$
$6$	−3.76766e10			−0.196281
$7$	1.72284e12	+	5.01708e11i	0.960118	+	0.279595i
$7$	1.72284e12	+	5.01708e11i	0.960118	+	0.279595i
$8$	7.96934e12			0.640645
$9$	−1.14384e13	−	1.98119e13i	−0.166667	−	0.288675i
$10$	−1.20464e12	+	2.08649e12i	−0.00380940	+	0.00659807i
$11$	9.83650e13	−	1.70373e14i	0.0780992	−	0.135272i	−0.824331	−	0.566109i	$-0.808448\pi$
$11$	9.83650e13	−	1.70373e14i	0.0780992	−	0.135272i	0.902430	+	0.430837i	$0.141782\pi$
$12$	1.13552e15	+	1.96679e15i	0.255310	+	0.442210i
$13$	−1.06270e16			−0.748573			−0.374286	−	0.927313i	$-0.622112\pi$
$13$	−1.06270e16			−0.748573			−0.374286	+	0.927313i	$0.622112\pi$
$14$	3.36304e15	+	1.37291e16i	0.0808863	+	0.330207i
$15$	−1.46288e15			−0.0129386
$16$	−9.60703e16	−	1.66399e17i	−0.333311	−	0.577311i
$17$	−5.25246e17	+	9.09752e17i	−0.756577	+	1.31043i	0.188010	+	0.982167i	$0.439796\pi$
$17$	−5.25246e17	+	9.09752e17i	−0.756577	+	1.31043i	−0.944587	+	0.328263i	$0.893537\pi$
$18$	9.01031e16	−	1.56063e17i	0.0566615	−	0.0981406i
$19$	1.20245e18	+	2.08271e18i	0.345256	+	0.598001i	0.985400	−	0.170254i	$-0.0544588\pi$
$19$	1.20245e18	+	2.08271e18i	0.345256	+	0.598001i	−0.640144	+	0.768255i	$0.721125\pi$
$20$	1.45225e17			0.0198201
$21$	−6.19832e18	+	5.93649e18i	−0.416960	+	0.399347i
$22$	1.54969e18			0.0531027
$23$	−7.87629e18	−	1.36421e19i	−0.141667	−	0.245374i	0.786458	−	0.617644i	$-0.211913\pi$
$23$	−7.87629e18	−	1.36421e19i	−0.141667	−	0.245374i	−0.928124	+	0.372270i	$0.878579\pi$
$24$	−1.90585e19	+	3.30104e19i	−0.184938	+	0.320323i
$25$	9.30855e19	−	1.61229e20i	0.499749	−	0.865590i
$26$	−4.18559e19	−	7.24966e19i	−0.127246	−	0.220396i
$27$	1.09419e20			0.192450
$28$	6.15326e20	−	5.89334e20i	0.638725	−	0.611744i
$29$	−2.50410e21			−1.56272			−0.781358	−	0.624083i	$-0.785473\pi$
$29$	−2.50410e21			−1.56272			−0.781358	+	0.624083i	$0.785473\pi$
$30$	−5.76174e18	−	9.97963e18i	−0.00219936	−	0.00380940i
$31$	−3.67834e21	+	6.37108e21i	−0.872786	+	1.51171i	−0.0136825	+	0.999906i	$0.504355\pi$
$31$	−3.67834e21	+	6.37108e21i	−0.872786	+	1.51171i	−0.859103	+	0.511803i	$0.828978\pi$
$32$	2.89602e21	−	5.01606e21i	0.433638	−	0.751083i
$33$	4.70477e20	+	8.14890e20i	0.0450906	+	0.0780992i
$34$	−8.27498e21			−0.514426
$35$	1.30578e20	+	5.33064e20i	0.00533191	+	0.0217667i
$36$	−1.08624e22			−0.294807
$37$	−3.97497e21	−	6.88484e21i	−0.0725118	−	0.125594i	0.827490	−	0.561481i	$-0.189768\pi$
$37$	−3.97497e21	−	6.88484e21i	−0.0725118	−	0.125594i	−0.900002	+	0.435887i	$0.856435\pi$
$38$	−9.47202e21	+	1.64060e22i	−0.117376	+	0.203302i
$39$	2.54144e22	−	4.40191e22i	0.216094	−	0.374286i
$40$	1.21872e21	+	2.11089e21i	0.00717851	+	0.0124335i
$41$	1.73435e23			0.714121			0.357061	−	0.934081i	$-0.383779\pi$
$41$	1.73435e23			0.714121			0.357061	+	0.934081i	$0.383779\pi$
$42$	−6.49110e22	−	1.89027e22i	−0.188453	−	0.0548793i
$43$	4.31663e23			0.890948			0.445474	−	0.895295i	$-0.353035\pi$
$43$	4.31663e23			0.890948			0.445474	+	0.895295i	$0.353035\pi$
$44$	−4.67057e22	−	8.08966e22i	−0.0690726	−	0.119637i
$45$	3.49846e21	−	6.05951e21i	0.00373504	−	0.00646928i
$46$	6.20434e22	−	1.07462e23i	0.0481623	−	0.0834196i
$47$	1.17047e24	+	2.02732e24i	0.665184	+	1.15213i	0.979235	+	0.202726i	$0.0649802\pi$
$47$	1.17047e24	+	2.02732e24i	0.665184	+	1.15213i	−0.314052	+	0.949406i	$0.601686\pi$
$48$	9.19002e23			0.384874
$49$	2.71648e24	+	1.72873e24i	0.843653	+	0.536889i
$50$	1.46651e24			0.339798
$51$	−2.51223e24	−	4.35132e24i	−0.436810	−	0.756577i
$52$	−2.52297e24	+	4.36991e24i	−0.331027	+	0.573355i
$53$	2.60973e24	−	4.52018e24i	0.259774	−	0.449941i	−0.706407	−	0.707805i	$-0.749685\pi$
$53$	2.60973e24	−	4.52018e24i	0.259774	−	0.449941i	0.966181	+	0.257864i	$0.0830187\pi$
$54$	4.30960e23	+	7.46445e23i	0.0327135	+	0.0566615i
$55$	6.01703e22			0.00350045
$56$	1.37299e25	+	3.99828e24i	0.615095	+	0.179121i
$57$	−1.15026e25			−0.398667
$58$	−9.86270e24	−	1.70827e25i	−0.265638	−	0.460098i
$59$	−2.68539e25	+	4.65123e25i	−0.564485	+	0.977717i	0.432612	+	0.901580i	$0.357592\pi$
$59$	−2.68539e25	+	4.65123e25i	−0.564485	+	0.977717i	−0.997097	+	0.0761372i	$0.975741\pi$
$60$	−3.47303e23	+	6.01546e23i	−0.00572157	+	0.00991005i
$61$	−9.55124e24	−	1.65432e25i	−0.123816	−	0.214456i	0.797453	−	0.603381i	$-0.206180\pi$
$61$	−9.55124e24	−	1.65432e25i	−0.123816	−	0.214456i	−0.921270	+	0.388925i	$0.872847\pi$
$62$	−5.79504e25			−0.593440
$63$	−9.76680e24	−	3.98715e25i	−0.0793075	−	0.323761i
$64$	−5.75293e25			−0.371774
$65$	−1.62515e24	−	2.81485e24i	−0.00838785	−	0.0145282i
$66$	−3.70606e24	+	6.41909e24i	−0.0153294	+	0.0265513i
$67$	−8.80507e25	+	1.52508e26i	−0.292852	+	0.507234i	−0.974483	−	0.224462i	$-0.927938\pi$
$67$	−8.80507e25	+	1.52508e26i	−0.292852	+	0.507234i	0.681631	+	0.731696i	$0.261271\pi$
$68$	2.49397e26	+	4.31968e26i	0.669133	+	1.15897i
$69$	7.53441e25			0.163583
$70$	−3.12221e24	+	2.99033e24i	−0.00550226	+	0.00526984i
$71$	9.89497e25			0.141961			0.0709804	−	0.997478i	$-0.477387\pi$
$71$	9.89497e25			0.141961			0.0709804	+	0.997478i	$0.477387\pi$
$72$	−9.11564e25	−	1.57888e26i	−0.106774	−	0.184938i
$73$	3.63932e26	−	6.30349e26i	0.349011	−	0.604504i	−0.637063	−	0.770811i	$-0.719851\pi$
$73$	3.63932e26	−	6.30349e26i	0.349011	−	0.604504i	0.986074	+	0.166307i	$0.0531844\pi$
$74$	3.13118e25	−	5.42336e25i	0.0246518	−	0.0426981i
$75$	4.45225e26	+	7.71152e26i	0.288530	+	0.499749i
$76$	1.14190e27			0.610703
$77$	2.54945e26	−	2.44176e26i	0.112806	−	0.108041i
$78$	4.00391e26			0.146931
$79$	8.41980e26	+	1.45835e27i	0.256867	+	0.444907i	0.965401	−	0.260770i	$-0.0839763\pi$
$79$	8.41980e26	+	1.45835e27i	0.256867	+	0.444907i	−0.708534	+	0.705677i	$0.750643\pi$
$80$	2.93833e25	−	5.08934e25i	0.00746958	−	0.0129377i
$81$	−2.61674e26	+	4.53232e26i	−0.0555556	+	0.0962250i
$82$	6.83097e26	+	1.18316e27i	0.121390	+	0.210253i
$83$	−1.14084e28			−1.70057			−0.850284	−	0.526323i	$-0.823570\pi$
$83$	−1.14084e28			−1.70057			−0.850284	+	0.526323i	$0.823570\pi$
$84$	9.69580e26	+	3.95817e27i	0.121488	+	0.495958i
$85$	−3.21295e26			−0.0339102
$86$	1.70016e27	+	2.94476e27i	0.151447	+	0.262315i
$87$	5.98851e27	−	1.03724e28i	0.451117	−	0.781358i
$88$	7.83904e26	−	1.35776e27i	0.0500339	−	0.0866612i
$89$	−1.10267e27	−	1.90989e27i	−0.0597436	−	0.103479i	0.834607	−	0.550846i	$-0.185695\pi$
$89$	−1.10267e27	−	1.90989e27i	−0.0597436	−	0.103479i	−0.894350	+	0.447367i	$0.852362\pi$
$90$	5.51165e25			0.00253960
$91$	−1.83088e28	−	5.33168e27i	−0.718718	−	0.209297i
$92$	−7.47963e27			−0.250586
$93$	−1.75934e28	−	3.04727e28i	−0.503903	−	0.872786i
$94$	−9.22009e27	+	1.59697e28i	−0.226142	+	0.391689i
$95$	−3.67773e26	+	6.37002e26i	−0.00773727	+	0.0134013i
$96$	1.38516e28	+	2.39916e28i	0.250361	+	0.433638i
$97$	7.92305e28			1.23226			0.616130	−	0.787645i	$-0.288700\pi$
$97$	7.92305e28			1.23226			0.616130	+	0.787645i	$0.288700\pi$
$98$	−1.09401e27	+	2.53404e28i	−0.0146637	+	0.339653i
$99$	−4.50055e27			−0.0520661
$100$	−4.41988e28	−	7.65546e28i	−0.441988	−	0.765546i
$101$	−1.13318e29	+	1.96273e29i	−0.980935	+	1.69903i	−0.322167	+	0.946683i	$0.604411\pi$
$101$	−1.13318e29	+	1.96273e29i	−0.980935	+	1.69903i	−0.658768	+	0.752346i	$0.728922\pi$
$102$	1.97895e28	−	3.42764e28i	0.148502	−	0.257213i
$103$	−4.10552e28	−	7.11097e28i	−0.267441	−	0.463222i	0.700759	−	0.713398i	$-0.252845\pi$
$103$	−4.10552e28	−	7.11097e28i	−0.267441	−	0.463222i	−0.968200	+	0.250176i	$0.919511\pi$
$104$	−8.46905e28			−0.479569
$105$	−2.52032e27	−	7.33940e26i	−0.0124226	−	0.00361756i
$106$	4.11150e28			0.176630
$107$	5.13809e28	+	8.89944e28i	0.192636	+	0.333655i	0.946123	−	0.323808i	$-0.104963\pi$
$107$	5.13809e28	+	8.89944e28i	0.192636	+	0.333655i	−0.753487	+	0.657463i	$0.771630\pi$
$108$	2.59772e28	−	4.49938e28i	0.0851034	−	0.147403i
$109$	−2.35918e29	+	4.08623e29i	−0.676204	+	1.17122i	0.299912	+	0.953967i	$0.403043\pi$
$109$	−2.35918e29	+	4.08623e29i	−0.676204	+	1.17122i	−0.976115	+	0.217252i	$0.930291\pi$
$110$	2.36988e26	+	4.10476e26i	0.000595022	+	0.00103061i
$111$	3.80243e28			0.0837294
$112$	−8.20307e28	−	3.34878e29i	−0.158604	−	0.647479i
$113$	2.26808e29			0.385496			0.192748	−	0.981248i	$-0.438260\pi$
$113$	2.26808e29			0.385496			0.192748	+	0.981248i	$0.438260\pi$
$114$	−4.53044e28	−	7.84695e28i	−0.0677673	−	0.117376i
$115$	2.40898e27	−	4.17248e27i	0.00317479	−	0.00549889i
$116$	−5.94498e29	+	1.02970e30i	−0.691050	+	1.19693i
$117$	1.21556e29	+	2.10542e29i	0.124762	+	0.216094i
$118$	−4.23069e29			−0.383815
$119$	−1.36135e30	+	1.30384e30i	−1.09279	+	1.04663i
$120$	−1.16582e28			−0.00828903
$121$	7.73803e29	+	1.34027e30i	0.487801	+	0.844896i
$122$	7.52375e28	−	1.30315e29i	0.0420937	−	0.0729084i
$123$	−4.14768e29	+	7.18400e29i	−0.206149	+	0.357061i
$124$	1.74655e30	+	3.02511e30i	0.771910	+	1.33699i
$125$	1.13910e29			0.0448093
$126$	2.33532e29	−	2.23667e29i	0.0818414	−	0.0783843i
$127$	−4.60306e30			−1.43844			−0.719222	−	0.694780i	$-0.755502\pi$
$127$	−4.60306e30			−1.43844			−0.719222	+	0.694780i	$0.755502\pi$
$128$	−1.78138e30	−	3.08543e30i	−0.496834	−	0.860541i
$129$	−1.03232e30	+	1.78802e30i	−0.257194	+	0.445474i
$130$	1.28017e28	−	2.21733e28i	0.00285161	−	0.00493914i
$131$	−3.90971e28	−	6.77182e28i	−0.00779311	−	0.0134981i	0.862103	−	0.506734i	$-0.169147\pi$
$131$	−3.90971e28	−	6.77182e28i	−0.00779311	−	0.0134981i	−0.869896	+	0.493236i	$0.835814\pi$
$132$	4.46783e29			0.0797582
$133$	1.02673e30	+	4.19147e30i	0.164288	+	0.670683i
$134$	−1.38719e30			−0.199121
$135$	1.67330e28	+	2.89825e28i	0.00215643	+	0.00373504i
$136$	−4.18586e30	+	7.25012e30i	−0.484697	+	0.839520i
$137$	−6.66779e30	+	1.15489e31i	−0.694278	+	1.20253i	0.276145	+	0.961116i	$0.410943\pi$
$137$	−6.66779e30	+	1.15489e31i	−0.694278	+	1.20253i	−0.970423	+	0.241409i	$0.922390\pi$
$138$	2.96752e29	+	5.13989e29i	0.0278065	+	0.0481623i
$139$	−1.89717e31			−1.60101			−0.800503	−	0.599329i	$-0.795434\pi$
$139$	−1.89717e31			−1.60101			−0.800503	+	0.599329i	$0.795434\pi$
$140$	2.50200e29	+	7.28604e28i	0.0190296	+	0.00554160i
$141$	−1.11967e31			−0.768088
$142$	3.89726e29	+	6.75025e29i	0.0241312	+	0.0417964i
$143$	−1.04533e30	+	1.81056e30i	−0.0584630	+	0.101261i
$144$	−2.19778e30	+	3.80667e30i	−0.111104	+	0.192437i
$145$	−3.82942e29	−	6.63275e29i	−0.0175104	−	0.0303290i
$146$	5.73356e30			0.237306
$147$	−1.36571e31	+	7.11791e30i	−0.511986	+	0.266840i
$148$	−3.77479e30			−0.128262
$149$	4.73803e30	+	8.20651e30i	0.146015	+	0.252905i	0.929751	−	0.368189i	$-0.120022\pi$
$149$	4.73803e30	+	8.20651e30i	0.146015	+	0.252905i	−0.783736	+	0.621094i	$0.786689\pi$
$150$	−3.50715e30	+	6.07456e30i	−0.0980914	+	0.169899i
$151$	7.23217e30	−	1.25265e31i	0.183697	−	0.318173i	−0.759439	−	0.650578i	$-0.774527\pi$
$151$	7.23217e30	−	1.25265e31i	0.183697	−	0.318173i	0.943137	+	0.332405i	$0.107860\pi$
$152$	9.58276e30	+	1.65978e31i	0.221186	+	0.383106i
$153$	2.40319e31			0.504385
$154$	2.66988e30	+	7.77492e29i	0.0509848	+	0.0148472i
$155$	−2.25006e30			−0.0391187
$156$	−1.20673e31	−	2.09011e31i	−0.191118	−	0.331027i
$157$	−3.15735e31	+	5.46869e31i	−0.455803	+	0.789474i	−0.998734	−	0.0503030i	$-0.983981\pi$
$157$	−3.15735e31	+	5.46869e31i	−0.455803	+	0.789474i	0.542931	+	0.839777i	$0.317315\pi$
$158$	−6.63248e30	+	1.14878e31i	−0.0873270	+	0.151255i
$159$	1.24823e31	+	2.16199e31i	0.149980	+	0.259774i
$160$	1.77151e30			0.0194359
$161$	−6.72525e30	−	2.74549e31i	−0.0674114	−	0.275197i
$162$	−4.12254e30			−0.0377744
$163$	1.05478e32	+	1.82692e32i	0.883975	+	1.53109i	0.846884	+	0.531777i	$0.178476\pi$
$163$	1.05478e32	+	1.82692e32i	0.883975	+	1.53109i	0.0370903	+	0.999312i	$0.488191\pi$
$164$	4.11753e31	−	7.13177e31i	0.315792	−	0.546968i
$165$	−1.43896e29	+	2.49236e29i	−0.00101049	+	0.00175022i
$166$	−4.49336e31	−	7.78272e31i	−0.289070	−	0.500685i
$167$	−2.61673e32			−1.54301			−0.771507	−	0.636221i	$-0.780497\pi$
$167$	−2.61673e32			−1.54301			−0.771507	+	0.636221i	$0.780497\pi$
$168$	−4.93965e31	+	4.73099e31i	−0.267123	+	0.255840i
$169$	−8.86040e31			−0.439639
$170$	−1.26546e30	−	2.19184e30i	−0.00576420	−	0.00998390i
$171$	2.75083e31	−	4.76457e31i	0.115085	−	0.199334i
$172$	1.02481e32	−	1.77502e32i	0.393986	−	0.682405i
$173$	5.03734e31	+	8.72494e31i	0.178046	+	0.308385i	0.941211	−	0.337818i	$-0.109689\pi$
$173$	5.03734e31	+	8.72494e31i	0.178046	+	0.308385i	−0.763165	+	0.646204i	$0.776356\pi$
$174$	9.43460e31			0.306732
$175$	2.41262e32	−	2.31070e32i	0.721833	−	0.691342i
$176$	−3.77998e31			−0.104125
$177$	−1.28441e32	−	2.22467e32i	−0.325906	−	0.564485i
$178$	8.68603e30	−	1.50446e31i	0.0203110	−	0.0351797i
$179$	−4.41839e31	+	7.65288e31i	−0.0952566	+	0.164989i	−0.909716	−	0.415232i	$-0.863701\pi$
$179$	−4.41839e31	+	7.65288e31i	−0.0952566	+	0.164989i	0.814459	+	0.580221i	$0.197034\pi$
$180$	−1.66114e30	−	2.87718e30i	−0.00330335	−	0.00572157i
$181$	5.59356e32			1.02648			0.513238	−	0.858246i	$-0.328446\pi$
$181$	5.59356e32			1.02648			0.513238	+	0.858246i	$0.328446\pi$
$182$	−3.57392e31	−	1.45900e32i	−0.0605493	−	0.247184i
$183$	9.13666e31			0.142971
$184$	−6.27688e31	−	1.08719e32i	−0.0907581	−	0.157198i
$185$	1.21575e30	−	2.10575e30i	0.00162501	−	0.00281459i
$186$	1.38588e32	−	2.40041e32i	0.171311	−	0.296720i
$187$	1.03332e32	+	1.78976e32i	0.118176	+	0.204687i
$188$	1.11153e33			1.17661
$189$	1.88512e32	+	5.48964e31i	0.184775	+	0.0538081i
$190$	−5.79408e30			−0.00526087
$191$	−3.62012e32	−	6.27024e32i	−0.304607	−	0.527594i	0.672567	−	0.740036i	$-0.265192\pi$
$191$	−3.62012e32	−	6.27024e32i	−0.304607	−	0.527594i	−0.977174	+	0.212442i	$0.931858\pi$
$192$	1.37580e32	−	2.38296e32i	0.107322	−	0.185887i
$193$	1.15608e33	−	2.00239e33i	0.836388	−	1.44867i	−0.0565067	−	0.998402i	$-0.517996\pi$
$193$	1.15608e33	−	2.00239e33i	0.836388	−	1.44867i	0.892895	−	0.450265i	$-0.148670\pi$
$194$	3.12059e32	+	5.40502e32i	0.209465	+	0.362804i
$195$	1.55461e31			0.00968546
$196$	1.35578e33	−	7.06617e32i	0.784292	−	0.408762i
$197$	2.06327e33			1.10866			0.554328	−	0.832298i	$-0.312975\pi$
$197$	2.06327e33			1.10866			0.554328	+	0.832298i	$0.312975\pi$
$198$	−1.77260e31	−	3.07023e31i	−0.00885044	−	0.0153294i
$199$	5.75748e32	−	9.97225e32i	0.267216	−	0.462832i	−0.700926	−	0.713234i	$-0.747230\pi$
$199$	5.75748e32	−	9.97225e32i	0.267216	−	0.462832i	0.968142	+	0.250402i	$0.0805629\pi$
$200$	7.41830e32	−	1.28489e33i	0.320162	−	0.554536i
$201$	−4.21144e32	−	7.29442e32i	−0.169078	−	0.292852i
$202$	−1.78527e33			−0.666975
$203$	−4.31417e33	−	1.25633e33i	−1.50039	−	0.436928i
$204$	−2.38572e33			−0.772648
$205$	2.65228e31	+	4.59389e31i	0.00800182	+	0.0138596i
$206$	3.23402e32	−	5.60148e32i	0.0909217	−	0.157481i
$207$	−1.80184e32	+	3.12088e32i	−0.0472222	+	0.0817913i
$208$	1.02094e33	+	1.76833e33i	0.249507	+	0.432159i
$209$	4.73117e32			0.107857
$210$	−4.91973e30	−	2.00841e31i	−0.00104655	−	0.00427240i
$211$	2.17380e33			0.431643			0.215821	−	0.976433i	$-0.430757\pi$
$211$	2.17380e33			0.431643			0.215821	+	0.976433i	$0.430757\pi$
$212$	−1.23915e33	−	2.14627e33i	−0.229749	−	0.397938i
$213$	−2.36637e32	+	4.09867e32i	−0.0409806	+	0.0709804i
$214$	−4.04740e32	+	7.01031e32i	−0.0654903	+	0.113432i
$215$	6.60126e31	+	1.14337e32i	0.00998318	+	0.0172914i
$216$	8.71997e32			0.123292
$217$	−9.53363e33	+	9.13092e33i	−1.26064	+	1.20739i
$218$	−3.71677e33			−0.459777
$219$	1.74068e33	+	3.01494e33i	0.201501	+	0.349011i
$220$	1.42850e31	−	2.47424e31i	0.00154793	−	0.00268110i
$221$	5.58181e33	−	9.66798e33i	0.566353	−	0.980952i
$222$	1.49763e32	+	2.59398e32i	0.0142327	+	0.0246518i
$223$	2.05824e34			1.83263			0.916317	−	0.400453i	$-0.131147\pi$
$223$	2.05824e34			1.83263			0.916317	+	0.400453i	$0.131147\pi$
$224$	7.50599e33	−	7.18893e33i	0.626343	−	0.599885i
$225$	−4.25899e33			−0.333166
$226$	8.93310e32	+	1.54726e33i	0.0655284	+	0.113499i
$227$	−1.11265e34	+	1.92716e34i	−0.765567	+	1.32600i	0.174380	+	0.984678i	$0.444208\pi$
$227$	−1.11265e34	+	1.92716e34i	−0.765567	+	1.32600i	−0.939946	+	0.341322i	$0.889125\pi$
$228$	−2.73083e33	+	4.72994e33i	−0.176295	+	0.305351i
$229$	3.42781e33	+	5.93713e33i	0.207683	+	0.359718i	0.950984	−	0.309239i	$-0.100074\pi$
$229$	3.42781e33	+	5.93713e33i	0.207683	+	0.359718i	−0.743301	+	0.668957i	$0.766741\pi$
$230$	3.79523e31			0.00215866
$231$	4.01722e32	+	1.63997e33i	0.0214561	+	0.0875916i
$232$	−1.99560e34			−1.00115
$233$	9.18849e33	+	1.59149e34i	0.433095	+	0.750143i	0.997138	−	0.0756027i	$-0.0240881\pi$
$233$	9.18849e33	+	1.59149e34i	0.433095	+	0.750143i	−0.564043	+	0.825746i	$0.690755\pi$
$234$	−9.57530e32	+	1.65849e33i	−0.0424153	+	0.0734654i
$235$	−3.57991e32	+	6.20059e32i	−0.0149069	+	0.0258196i
$236$	1.27508e34	+	2.20850e34i	0.499243	+	0.864714i
$237$	−8.05433e33			−0.296605
$238$	−1.42565e34	−	4.15162e33i	−0.493909	−	0.143831i
$239$	−3.43452e34			−1.11969			−0.559844	−	0.828598i	$-0.689139\pi$
$239$	−3.43452e34			−1.11969			−0.559844	+	0.828598i	$0.689139\pi$
$240$	1.40540e32	+	2.43422e32i	0.00431256	+	0.00746958i
$241$	−1.11937e34	+	1.93881e34i	−0.323391	+	0.560129i	−0.981185	−	0.193068i	$-0.938156\pi$
$241$	−1.11937e34	+	1.93881e34i	−0.323391	+	0.560129i	0.657795	+	0.753197i	$0.271489\pi$
$242$	−6.09544e33	+	1.05576e34i	−0.165837	+	0.287239i
$243$	−1.25158e33	−	2.16780e33i	−0.0320750	−	0.0555556i
$244$	−9.07024e33			−0.219011
$245$	−4.24776e31	+	9.83899e32i	−0.000966610	+	0.0223894i
$246$	−6.53446e33			−0.140169
$247$	−1.27785e34	−	2.21331e34i	−0.258449	−	0.447647i
$248$	−2.93140e34	+	5.07733e34i	−0.559146	+	0.968469i
$249$	2.72831e34	−	4.72558e34i	0.490912	−	0.850284i
$250$	4.48650e32	+	7.77084e32i	0.00761688	+	0.0131928i
$251$	−4.31203e34			−0.690897			−0.345448	−	0.938438i	$-0.612273\pi$
$251$	−4.31203e34			−0.690897			−0.345448	+	0.938438i	$0.612273\pi$
$252$	−1.87142e34	−	5.44973e33i	−0.283050	−	0.0824266i
$253$	−3.09900e33			−0.0442562
$254$	−1.81297e34	−	3.14016e34i	−0.244513	−	0.423510i
$255$	7.68373e32	−	1.33086e33i	0.00978902	−	0.0169551i
$256$	−1.41056e33	+	2.44317e33i	−0.0169790	+	0.0294086i
$257$	2.06844e34	+	3.58265e34i	0.235295	+	0.407543i	0.959358	−	0.282190i	$-0.0910610\pi$
$257$	2.06844e34	+	3.58265e34i	0.235295	+	0.407543i	−0.724063	+	0.689734i	$0.757728\pi$
$258$	−1.62636e34			−0.174876
$259$	−3.39407e33	−	1.38558e34i	−0.0345044	−	0.140859i
$260$	−1.54331e33			−0.0148368
$261$	2.86429e34	+	4.96109e34i	0.260453	+	0.451117i
$262$	3.07978e32	−	5.33433e32i	0.00264942	−	0.00458893i
$263$	1.15921e34	−	2.00781e34i	0.0943635	−	0.163442i	−0.814979	−	0.579490i	$-0.803252\pi$
$263$	1.15921e34	−	2.00781e34i	0.0943635	−	0.163442i	0.909343	+	0.416048i	$0.136585\pi$
$264$	3.74939e33	+	6.49413e33i	0.0288871	+	0.0500339i
$265$	1.59638e33			0.0116432
$266$	−2.45499e34	+	2.35128e34i	−0.169537	+	0.162376i
$267$	1.05481e34			0.0689860
$268$	4.18082e34	+	7.24139e34i	0.259004	+	0.448609i
$269$	−6.48936e32	+	1.12399e33i	−0.00380885	+	0.00659712i	−0.867924	−	0.496698i	$-0.834546\pi$
$269$	−6.48936e32	+	1.12399e33i	−0.00380885	+	0.00659712i	0.864115	+	0.503295i	$0.167879\pi$
$270$	−1.31810e32	+	2.28302e32i	−0.000733119	+	0.00126980i
$271$	5.23732e34	+	9.07130e34i	0.276092	+	0.478206i	0.970410	−	0.241463i	$-0.0776271\pi$
$271$	5.23732e34	+	9.07130e34i	0.276092	+	0.478206i	−0.694318	+	0.719668i	$0.744294\pi$
$272$	2.01842e35			1.00870
$273$	6.58698e34	−	6.30874e34i	0.312125	−	0.298940i
$274$	−1.05048e35			−0.472066
$275$	−1.83127e34	−	3.17185e34i	−0.0780600	−	0.135204i
$276$	1.78874e34	−	3.09819e34i	0.0723380	−	0.125293i
$277$	2.60351e35	−	4.50942e35i	0.999087	−	1.73047i	0.462537	−	0.886600i	$-0.346939\pi$
$277$	2.60351e35	−	4.50942e35i	0.999087	−	1.73047i	0.536549	−	0.843869i	$-0.319728\pi$
$278$	−7.47226e34	−	1.29423e35i	−0.272146	−	0.471371i
$279$	1.68297e35			0.581857
$280$	1.04062e33	+	4.24817e33i	0.00341586	+	0.0139447i
$281$	9.26977e34			0.288953			0.144477	−	0.989508i	$-0.453850\pi$
$281$	9.26977e34			0.288953			0.144477	+	0.989508i	$0.453850\pi$
$282$	−4.40994e34	−	7.63824e34i	−0.130563	−	0.226142i
$283$	−1.10729e35	+	1.91788e35i	−0.311428	+	0.539409i	−0.978672	−	0.205430i	$-0.934141\pi$
$283$	−1.10729e35	+	1.91788e35i	−0.311428	+	0.539409i	0.667244	+	0.744839i	$0.267474\pi$
$284$	2.34917e34	−	4.06887e34i	0.0627766	−	0.108732i
$285$	−1.75905e33	−	3.04676e33i	−0.00446711	−	0.00773727i
$286$	−1.64686e34			−0.0397512
$287$	2.98802e35	+	8.70140e34i	0.685641	+	0.199665i
$288$	−1.32503e35			−0.289092
$289$	−3.10782e35	−	5.38290e35i	−0.644817	−	1.11686i
$290$	3.01653e33	−	5.22478e33i	0.00595301	−	0.0103109i
$291$	−1.89478e35	+	3.28186e35i	−0.355723	+	0.616130i
$292$	−1.72802e35	−	2.99302e35i	−0.308672	−	0.534636i
$293$	9.67872e35			1.64527			0.822636	−	0.568569i	$-0.192503\pi$
$293$	9.67872e35			1.64527			0.822636	+	0.568569i	$0.192503\pi$
$294$	−1.02348e35	−	6.51327e34i	−0.165593	−	0.105381i
$295$	−1.64266e34			−0.0253005
$296$	−3.16779e34	−	5.48676e34i	−0.0464543	−	0.0804612i
$297$	1.07630e34	−	1.86421e34i	0.0150302	−	0.0260331i
$298$	−3.73227e34	+	6.46447e34i	−0.0496406	+	0.0859800i
$299$	8.37017e34	+	1.44976e35i	0.106048	+	0.183680i
$300$	4.22803e35			0.510364
$301$	7.43688e35	+	2.16569e35i	0.855415	+	0.249105i
$302$	1.13939e35			0.124903
$303$	−5.41998e35	−	9.38768e35i	−0.566343	−	0.980935i
$304$	2.31040e35	−	4.00173e35i	0.230155	−	0.398640i
$305$	2.92127e33	−	5.05979e33i	0.00277475	−	0.00480601i
$306$	9.46525e34	+	1.63943e35i	0.0857376	+	0.148502i
$307$	−1.16306e36			−1.00483			−0.502417	−	0.864625i	$-0.667556\pi$
$307$	−1.16306e36			−1.00483			−0.502417	+	0.864625i	$0.667556\pi$
$308$	−3.98801e34	−	1.62805e35i	−0.0328679	−	0.134178i
$309$	3.92731e35			0.308814
$310$	−8.86214e33	−	1.53497e34i	−0.00664957	−	0.0115174i
$311$	6.83016e35	−	1.18302e36i	0.489108	−	0.847160i	−0.510813	−	0.859692i	$-0.670656\pi$
$311$	6.83016e35	−	1.18302e36i	0.489108	−	0.847160i	0.999921	+	0.0125314i	$0.00398898\pi$
$312$	2.02536e35	−	3.50803e35i	0.138440	−	0.239785i
$313$	−3.02968e35	−	5.24757e35i	−0.197699	−	0.342425i	0.750083	−	0.661344i	$-0.230014\pi$
$313$	−3.02968e35	−	5.24757e35i	−0.197699	−	0.342425i	−0.947782	+	0.318919i	$0.896680\pi$
$314$	−4.97424e35			−0.309918
$315$	9.06741e33	−	8.68439e33i	0.00539486	−	0.00516698i
$316$	7.99578e35			0.454358
$317$	8.38691e35	+	1.45266e36i	0.455242	+	0.788503i	0.998702	−	0.0509323i	$-0.0162193\pi$
$317$	8.38691e35	+	1.45266e36i	0.455242	+	0.788503i	−0.543460	+	0.839435i	$0.682886\pi$
$318$	−9.83258e34	+	1.70305e35i	−0.0509887	+	0.0883151i
$319$	−2.46316e35	+	4.26631e35i	−0.122047	+	0.211392i
$320$	−8.79774e33	−	1.52381e34i	−0.00416578	−	0.00721534i
$321$	−4.91507e35			−0.222437
$322$	1.60806e35	−	1.54013e35i	0.0695652	−	0.0666267i
$323$	−2.52633e36			−1.04485
$324$	1.24248e35	+	2.15204e35i	0.0491345	+	0.0851034i
$325$	−9.89224e35	+	1.71339e36i	−0.374098	+	0.647958i
$326$	−8.30873e35	+	1.43911e36i	−0.300524	+	0.520523i
$327$	−1.12839e36	−	1.95443e36i	−0.390406	−	0.676204i
$328$	1.38217e36			0.457498
$329$	9.99420e35	+	4.07998e36i	0.316525	+	1.29217i
$330$	−2.26702e33			−0.000687072
$331$	−1.55106e36	−	2.68651e36i	−0.449906	−	0.779260i	0.548474	−	0.836168i	$-0.315209\pi$
$331$	−1.55106e36	−	2.68651e36i	−0.449906	−	0.779260i	−0.998379	+	0.0569082i	$0.981876\pi$
$332$	−2.70848e36	+	4.69122e36i	−0.752009	+	1.30252i
$333$	−9.09345e34	+	1.57503e35i	−0.0241706	+	0.0418647i
$334$	−1.03063e36	−	1.78511e36i	−0.262289	−	0.454297i
$335$	−5.38610e34			−0.0131258
$336$	1.58330e36	+	4.61071e35i	0.369525	+	0.107609i
$337$	−8.23194e35			−0.184022			−0.0920108	−	0.995758i	$-0.529329\pi$
$337$	−8.23194e35			−0.184022			−0.0920108	+	0.995758i	$0.529329\pi$
$338$	−3.48978e35	−	6.04447e35i	−0.0747318	−	0.129439i
$339$	−5.42407e35	+	9.39477e35i	−0.111283	+	0.192748i
$340$	−7.62787e34	+	1.32119e35i	−0.0149954	+	0.0259728i
$341$	7.23640e35	+	1.25338e36i	0.136328	+	0.236127i
$342$	4.33379e35			0.0782509
$343$	3.81276e36	+	4.34122e36i	0.659895	+	0.751358i
$344$	3.44007e36			0.570781
$345$	1.15221e34	+	1.99568e34i	0.00183296	+	0.00317479i
$346$	−3.96804e35	+	6.87285e35i	−0.0605303	+	0.104842i
$347$	−5.24157e36	+	9.07866e36i	−0.766803	+	1.32814i	0.172485	+	0.985012i	$0.444820\pi$
$347$	−5.24157e36	+	9.07866e36i	−0.766803	+	1.32814i	−0.939288	+	0.343130i	$0.888513\pi$
$348$	−2.84346e36	−	4.92502e36i	−0.398978	−	0.691050i
$349$	−5.76978e36			−0.776588			−0.388294	−	0.921536i	$-0.626936\pi$
$349$	−5.76978e36			−0.776588			−0.388294	+	0.921536i	$0.626936\pi$
$350$	2.52658e36	+	7.35762e35i	0.326247	+	0.0950060i
$351$	−1.16280e36			−0.144063
$352$	−5.69735e35	−	9.86809e35i	−0.0677336	−	0.117318i
$353$	−5.09666e36	+	8.82767e36i	−0.581504	+	1.00719i	0.413798	+	0.910369i	$0.364202\pi$
$353$	−5.09666e36	+	8.82767e36i	−0.581504	+	1.00719i	−0.995301	+	0.0968249i	$0.969131\pi$
$354$	1.01176e36	−	1.75243e36i	0.110798	−	0.191908i
$355$	1.51320e34	+	2.62094e34i	0.00159069	+	0.00275515i
$356$	−1.04714e36			−0.105677
$357$	−2.14510e36	−	8.75705e36i	−0.207854	−	0.848533i
$358$	−6.96095e35			−0.0647686
$359$	7.29365e36	+	1.26330e37i	0.651742	+	1.12885i	0.982700	+	0.185204i	$0.0592946\pi$
$359$	7.29365e36	+	1.26330e37i	0.651742	+	1.12885i	−0.330959	+	0.943645i	$0.607372\pi$
$360$	2.78804e34	−	4.82903e34i	0.00239284	−	0.00414451i
$361$	3.17312e36	−	5.49601e36i	0.261597	−	0.453099i
$362$	2.20309e36	+	3.81587e36i	0.174485	+	0.302217i
$363$	−7.40215e36			−0.563264
$364$	−6.53910e36	+	6.26288e36i	−0.478132	+	0.457935i
$365$	2.22619e35			0.0156428
$366$	3.59859e35	+	6.23293e35i	0.0243028	+	0.0420937i
$367$	6.90262e36	−	1.19557e37i	0.448081	−	0.776099i	−0.550180	−	0.835046i	$-0.685441\pi$
$367$	6.90262e36	−	1.19557e37i	0.448081	−	0.776099i	0.998261	+	0.0589472i	$0.0187744\pi$
$368$	−1.51335e36	+	2.62121e36i	−0.0944381	+	0.163572i
$369$	−1.98382e36	−	3.43608e36i	−0.119020	−	0.206149i
$370$	1.91536e34			0.00110490
$371$	6.76397e36	−	6.47825e36i	0.375215	−	0.359365i
$372$	−1.67074e37			−0.891325
$373$	−1.40845e37	−	2.43951e37i	−0.722710	−	1.25177i	−0.959910	−	0.280310i	$-0.909563\pi$
$373$	−1.40845e37	−	2.43951e37i	−0.722710	−	1.25177i	0.237199	−	0.971461i	$-0.423771\pi$
$374$	−8.13968e35	+	1.40983e36i	−0.0401762	+	0.0695873i
$375$	−2.72415e35	+	4.71836e35i	−0.0129353	+	0.0224046i
$376$	9.32788e36	+	1.61564e37i	0.426147	+	0.738108i
$377$	2.66112e37			1.16981
$378$	3.67980e35	+	1.50223e36i	0.0155666	+	0.0635483i
$379$	5.40080e36			0.219882			0.109941	−	0.993938i	$-0.464934\pi$
$379$	5.40080e36			0.219882			0.109941	+	0.993938i	$0.464934\pi$
$380$	1.74626e35	+	3.02461e35i	0.00684300	+	0.0118524i
$381$	1.10082e37	−	1.90667e37i	0.415243	−	0.719222i
$382$	2.85166e36	−	4.93922e36i	0.103557	−	0.179366i
$383$	−1.09628e37	−	1.89881e37i	−0.383299	−	0.663893i	0.608233	−	0.793759i	$-0.291879\pi$
$383$	−1.09628e37	−	1.89881e37i	−0.383299	−	0.663893i	−0.991532	+	0.129866i	$0.958545\pi$
$384$	1.70405e37			0.573694
$385$	1.03664e35	+	3.01879e34i	0.00336084	+	0.000978708i
$386$	1.82135e37			0.568692
$387$	−4.93753e36	−	8.55206e36i	−0.148491	−	0.257194i
$388$	1.88101e37	−	3.25801e37i	0.544918	−	0.943826i
$389$	5.69687e36	−	9.86727e36i	0.158989	−	0.275377i	−0.775515	−	0.631329i	$-0.782510\pi$
$389$	5.69687e36	−	9.86727e36i	0.158989	−	0.275377i	0.934504	+	0.355952i	$0.115843\pi$
$390$	6.12303e34	+	1.06054e35i	0.00164638	+	0.00285161i
$391$	1.65479e37			0.428727
$392$	2.16486e37	+	1.37768e37i	0.540482	+	0.343955i
$393$	3.74001e35			0.00899871
$394$	8.12646e36	+	1.40754e37i	0.188454	+	0.326413i
$395$	−2.57522e35	+	4.46040e35i	−0.00575646	+	0.00997049i
$396$	−1.06848e36	+	1.85065e36i	−0.0230242	+	0.0398791i
$397$	−2.54268e37	−	4.40404e37i	−0.528237	−	0.914933i	−0.999458	−	0.0329178i	$-0.989520\pi$
$397$	−2.54268e37	−	4.40404e37i	−0.528237	−	0.914933i	0.471221	−	0.882015i	$-0.343813\pi$
$398$	9.07062e36			0.181691
$399$	−1.98172e37	−	5.77094e36i	−0.382767	−	0.111465i
$400$	−3.57710e37			−0.666287
$401$	2.44719e37	+	4.23866e37i	0.439617	+	0.761439i	0.997660	−	0.0683734i	$-0.0217809\pi$
$401$	2.44719e37	+	4.23866e37i	0.439617	+	0.761439i	−0.558043	+	0.829812i	$0.688448\pi$
$402$	3.31745e36	−	5.74600e36i	0.0574813	−	0.0995606i
$403$	3.90899e37	−	6.77057e37i	0.653344	−	1.13162i
$404$	5.38058e37	+	9.31944e37i	0.867559	+	1.50266i
$405$	−1.60067e35			−0.00249003
$406$	−8.42137e36	−	3.43790e37i	−0.126402	−	0.516019i
$407$	−1.56399e36			−0.0226524
$408$	−2.00208e37	−	3.46771e37i	−0.279840	−	0.484697i
$409$	1.19838e37	−	2.07565e37i	0.161661	−	0.280005i	−0.773803	−	0.633426i	$-0.781648\pi$
$409$	1.19838e37	−	2.07565e37i	0.161661	−	0.280005i	0.935465	+	0.353421i	$0.114982\pi$
$410$	−2.08927e35	+	3.61872e35i	−0.00272037	+	0.00471182i
$411$	−3.18918e37	−	5.52383e37i	−0.400842	−	0.694278i
$412$	−3.89876e37			−0.473061
$413$	−6.96006e37	+	6.66606e37i	−0.815338	+	0.780897i
$414$	−2.83871e36			−0.0321082
$415$	−1.74465e36	−	3.02182e36i	−0.0190551	−	0.0330044i
$416$	−3.07762e37	+	5.33059e37i	−0.324610	+	0.562240i
$417$	4.53706e37	−	7.85843e37i	0.462170	−	0.800503i
$418$	1.86343e36	+	3.22756e36i	0.0183340	+	0.0317554i
$419$	7.22119e37			0.686287			0.343143	−	0.939283i	$-0.388508\pi$
$419$	7.22119e37			0.686287			0.343143	+	0.939283i	$0.388508\pi$
$420$	−9.00149e35	+	8.62126e35i	−0.00826418	+	0.00791509i
$421$	−9.20991e37			−0.816893			−0.408446	−	0.912782i	$-0.633929\pi$
$421$	−9.20991e37			−0.816893			−0.408446	+	0.912782i	$0.633929\pi$
$422$	8.56179e36	+	1.48295e37i	0.0733726	+	0.127085i
$423$	2.67766e37	−	4.63785e37i	0.221728	−	0.384044i
$424$	2.07978e37	−	3.60229e37i	0.166423	−	0.288253i
$425$	9.77855e37	+	1.69369e38i	0.756197	+	1.30977i
$426$	−3.72809e36			−0.0278643
$427$	−8.15543e36	−	3.32934e37i	−0.0589173	−	0.240521i
$428$	4.87934e37			0.340742
$429$	−4.99978e36	−	8.65987e36i	−0.0337536	−	0.0584630i
$430$	−5.19997e35	+	9.00662e35i	−0.00339397	+	0.00587854i
$431$	−1.15434e38	+	1.99937e38i	−0.728472	+	1.26175i	0.229057	+	0.973413i	$0.426436\pi$
$431$	−1.15434e38	+	1.99937e38i	−0.728472	+	1.26175i	−0.957529	+	0.288337i	$0.906898\pi$
$432$	−1.05119e37	−	1.82072e37i	−0.0641457	−	0.111104i
$433$	−1.30623e38			−0.770807			−0.385404	−	0.922748i	$-0.625938\pi$
$433$	−1.30623e38			−0.770807			−0.385404	+	0.922748i	$0.625938\pi$
$434$	−9.98396e37	−	2.90742e37i	−0.569773	−	0.165923i
$435$	3.66320e36			0.0202193
$436$	1.12019e38	+	1.94022e38i	0.598049	+	1.03585i
$437$	1.89417e37	−	3.28080e37i	0.0978225	−	0.169434i
$438$	−1.37117e37	+	2.37494e37i	−0.0685043	+	0.118653i
$439$	−6.85399e37	−	1.18715e38i	−0.331290	−	0.573811i	0.651475	−	0.758670i	$-0.274150\pi$
$439$	−6.85399e37	−	1.18715e38i	−0.331290	−	0.573811i	−0.982765	+	0.184859i	$0.940817\pi$
$440$	4.79518e35			0.00224254
$441$	3.17719e36	−	7.35926e37i	0.0143775	−	0.333023i
$442$	8.79386e37			0.385085
$443$	2.24382e38	+	3.88642e38i	0.950900	+	1.64701i	0.743484	+	0.668753i	$0.233172\pi$
$443$	2.24382e38	+	3.88642e38i	0.950900	+	1.64701i	0.207415	+	0.978253i	$0.433495\pi$
$444$	9.02734e36	−	1.56358e37i	0.0370260	−	0.0641309i
$445$	3.37255e35	−	5.84143e35i	0.00133887	−	0.00231899i
$446$	8.10664e37	+	1.40411e38i	0.311520	+	0.539568i
$447$	−4.53237e37			−0.168603
$448$	−9.91141e37	−	2.88629e37i	−0.356947	−	0.103946i
$449$	−3.18653e38			−1.11108			−0.555541	−	0.831489i	$-0.687489\pi$
$449$	−3.18653e38			−1.11108			−0.555541	+	0.831489i	$0.687489\pi$
$450$	−1.67746e37	−	2.90544e37i	−0.0566331	−	0.0980914i
$451$	1.70600e37	−	2.95488e37i	0.0557723	−	0.0966005i
$452$	5.38464e37	−	9.32647e37i	0.170471	−	0.295264i
$453$	3.45912e37	+	5.99138e37i	0.106058	+	0.183697i
$454$	−1.75292e38			−0.520538
$455$	−1.38766e36	−	5.66490e36i	−0.00399132	−	0.0162940i
$456$	−9.16681e37			−0.255404
$457$	−1.64849e38	−	2.85526e38i	−0.444939	−	0.770657i	0.553109	−	0.833109i	$-0.313441\pi$
$457$	−1.64849e38	−	2.85526e38i	−0.444939	−	0.770657i	−0.998048	+	0.0624522i	$0.980108\pi$
$458$	−2.70017e37	+	4.67683e37i	−0.0706060	+	0.122293i
$459$	−5.74718e37	+	9.95442e37i	−0.145603	+	0.252192i
$460$	−1.14383e36	−	1.98117e36i	−0.00280785	−	0.00486334i
$461$	−1.31743e38			−0.313374			−0.156687	−	0.987648i	$-0.550081\pi$
$461$	−1.31743e38			−0.313374			−0.156687	+	0.987648i	$0.550081\pi$
$462$	−9.60548e36	+	9.19973e36i	−0.0221417	+	0.0212064i
$463$	−5.36753e38			−1.19909			−0.599543	−	0.800343i	$-0.704651\pi$
$463$	−5.36753e38			−1.19909			−0.599543	+	0.800343i	$0.704651\pi$
$464$	2.40569e38	+	4.16678e38i	0.520870	+	0.902174i
$465$	5.38098e36	−	9.32013e36i	0.0112926	−	0.0195593i
$466$	−7.23800e37	+	1.25366e38i	−0.147239	+	0.255025i
$467$	−2.50534e38	−	4.33937e38i	−0.494051	−	0.855721i	0.505926	−	0.862577i	$-0.331151\pi$
$467$	−2.50534e38	−	4.33937e38i	−0.494051	−	0.855721i	−0.999976	+	0.00685612i	$0.997818\pi$
$468$	1.15435e38			0.220685
$469$	−2.28212e38	+	2.18572e38i	−0.422993	+	0.405125i
$470$	−5.63997e36			−0.0101358
$471$	−1.51015e38	−	2.61566e38i	−0.263158	−	0.455803i
$472$	−2.14008e38	+	3.70672e38i	−0.361635	+	0.626370i
$473$	4.24605e37	−	7.35438e37i	0.0695823	−	0.120520i
$474$	−3.17230e37	−	5.49458e37i	−0.0504183	−	0.0873270i
$475$	4.47724e38			0.690165
$476$	2.12950e38	+	8.69339e38i	0.318403	+	1.29984i
$477$	−1.19404e38			−0.173182
$478$	−1.35273e38	−	2.34300e38i	−0.190330	−	0.329661i
$479$	3.17355e38	−	5.49675e38i	0.433192	−	0.750311i	−0.563954	−	0.825806i	$-0.690720\pi$
$479$	3.17355e38	−	5.49675e38i	0.433192	−	0.750311i	0.997146	+	0.0754954i	$0.0240538\pi$
$480$	−4.23654e36	+	7.33790e36i	−0.00561065	+	0.00971793i
$481$	4.22422e37	+	7.31656e37i	0.0542803	+	0.0940163i
$482$	−1.76351e38			−0.219886
$483$	1.29806e38	+	3.78007e37i	0.157059	+	0.0457369i
$484$	7.34834e38			0.862843
$485$	1.21164e37	+	2.09862e37i	0.0138076	+	0.0239155i
$486$	9.85899e36	−	1.70763e37i	0.0109045	−	0.0188872i
$487$	−2.15352e38	+	3.73000e38i	−0.231195	+	0.400441i	−0.958160	−	0.286233i	$-0.907597\pi$
$487$	−2.15352e38	+	3.73000e38i	−0.231195	+	0.400441i	0.726965	+	0.686674i	$0.240930\pi$
$488$	−7.61171e37	−	1.31839e38i	−0.0793222	−	0.137390i
$489$	−1.00899e39			−1.02073
$490$	−6.87936e36	+	3.58543e36i	−0.00675624	+	0.00352126i
$491$	1.73868e39			1.65782			0.828912	−	0.559378i	$-0.188960\pi$
$491$	1.73868e39			1.65782			0.828912	+	0.559378i	$0.188960\pi$
$492$	1.96940e38	+	3.41110e38i	0.182323	+	0.315792i
$493$	1.31527e39	−	2.27811e39i	1.18232	−	2.04783i
$494$	1.00660e38	−	1.74348e38i	0.0878647	−	0.152186i
$495$	−6.88252e35	−	1.19209e36i	−0.000583408	−	0.00101049i
$496$	1.41352e39			1.16364
$497$	1.70475e38	+	4.96439e37i	0.136299	+	0.0396916i
$498$	4.29832e38			0.333790
$499$	3.07936e38	+	5.33361e38i	0.232275	+	0.402312i	0.958477	−	0.285169i	$-0.0920497\pi$
$499$	3.07936e38	+	5.33361e38i	0.232275	+	0.402312i	−0.726202	+	0.687481i	$0.758716\pi$
$500$	2.70434e37	−	4.68406e37i	0.0198151	−	0.0343208i
$501$	6.25787e38	−	1.08389e39i	0.445430	−	0.771507i
$502$	−1.69835e38	−	2.94162e38i	−0.117442	−	0.203415i
$503$	2.38033e38			0.159919			0.0799597	−	0.996798i	$-0.474521\pi$
$503$	2.38033e38			0.159919			0.0799597	+	0.996798i	$0.474521\pi$
$504$	−7.78349e37	−	3.17750e38i	−0.0508080	−	0.207416i
$505$	−6.93173e37			−0.0439660
$506$	−1.22058e37	−	2.11411e37i	−0.00752288	−	0.0130300i
$507$	2.11895e38	−	3.67013e38i	0.126913	−	0.219819i
$508$	−1.09281e39	+	1.89281e39i	−0.636095	+	1.10175i
$509$	−6.72826e38	−	1.16537e39i	−0.380623	−	0.659258i	0.610529	−	0.791994i	$-0.290957\pi$
$509$	−6.72826e38	−	1.16537e39i	−0.380623	−	0.659258i	−0.991151	+	0.132736i	$0.957624\pi$
$510$	1.21053e37			0.00665593
$511$	9.43249e38	−	9.03405e38i	0.504108	−	0.482814i
$512$	−1.93496e39			−1.00521
$513$	1.31571e38	+	2.27888e38i	0.0664445	+	0.115085i
$514$	−1.62936e38	+	2.82214e38i	−0.0799931	+	0.138552i
$515$	1.25568e37	−	2.17491e37i	0.00599342	−	0.0103809i
$516$	4.90164e38	+	8.48989e38i	0.227468	+	0.393986i
$517$	4.60534e38			0.207801
$518$	8.11548e37	−	7.77267e37i	0.0356068	−	0.0341027i
$519$	−4.81869e38			−0.205590
$520$	−1.29514e37	−	2.24325e37i	−0.00537364	−	0.00930741i
$521$	3.72617e38	−	6.45392e38i	0.150354	−	0.260421i	−0.781003	−	0.624527i	$-0.785292\pi$
$521$	3.72617e38	−	6.45392e38i	0.150354	−	0.260421i	0.931358	+	0.364105i	$0.118625\pi$
$522$	−2.25627e38	+	3.90797e38i	−0.0885459	+	0.153366i
$523$	−1.48426e39	−	2.57081e39i	−0.566545	−	0.981285i	−0.996904	−	0.0786271i	$-0.974946\pi$
$523$	−1.48426e39	−	2.57081e39i	−0.566545	−	0.981285i	0.430359	−	0.902658i	$-0.358387\pi$
$524$	−3.71282e37			−0.0137848
$525$	3.80160e38	+	1.55195e39i	0.137296	+	0.560490i
$526$	1.82628e38			0.0641613
$527$	−3.86407e39	−	6.69276e39i	−1.32066	−	2.28745i
$528$	9.03977e37	−	1.56573e38i	0.0300584	−	0.0520626i
$529$	1.42146e39	−	2.46204e39i	0.459861	−	0.796503i
$530$	6.28755e36	+	1.08904e37i	0.00197916	+	0.00342801i
$531$	1.22866e39			0.376324
$532$	1.96731e39	+	5.72899e38i	0.586347	+	0.170750i
$533$	−1.84311e39			−0.534572
$534$	4.15450e37	+	7.19580e37i	0.0117266	+	0.0203110i
$535$	−1.57150e37	+	2.72191e37i	−0.00431702	+	0.00747730i
$536$	−7.01706e38	+	1.21539e39i	−0.187614	+	0.324957i
$537$	−2.11330e38	−	3.66035e38i	−0.0549964	−	0.0952566i
$538$	−1.02237e37			−0.00258978
$539$	5.61736e38	−	2.92769e38i	0.138515	−	0.0721919i
$540$	1.58903e37			0.00381438
$541$	1.83588e39	+	3.17984e39i	0.429026	+	0.743095i	0.996787	−	0.0800986i	$-0.0255235\pi$
$541$	1.83588e39	+	3.17984e39i	0.429026	+	0.743095i	−0.567761	+	0.823194i	$0.692190\pi$
$542$	−4.12556e38	+	7.14569e38i	−0.0938629	+	0.162575i
$543$	−1.33769e39	+	2.31695e39i	−0.296318	+	0.513238i
$544$	3.04225e39	+	5.26932e39i	0.656161	+	1.13650i
$545$	−1.44312e38			−0.0303078
$546$	6.89812e38	+	2.00880e38i	0.141071	+	0.0410811i
$547$	−3.78526e39			−0.753840			−0.376920	−	0.926246i	$-0.623017\pi$
$547$	−3.78526e39			−0.753840			−0.376920	+	0.926246i	$0.623017\pi$
$548$	3.16600e39	+	5.48367e39i	0.614034	+	1.06354i
$549$	−2.18502e38	+	3.78456e38i	−0.0412720	+	0.0714853i
$550$	1.44254e38	−	2.49855e38i	0.0265380	−	0.0459652i
$551$	−3.01106e39	−	5.21531e39i	−0.539537	−	0.934506i
$552$	6.00442e38			0.104798
$553$	7.18934e38	+	2.93494e39i	0.122229	+	0.498982i
$554$	4.10170e39			0.679317
$555$	5.81491e36	+	1.00717e37i	0.000938198	+	0.00162501i
$556$	−4.50408e39	+	7.80130e39i	−0.707981	+	1.22626i
$557$	4.31398e39	−	7.47203e39i	0.660660	−	1.14430i	−0.319783	−	0.947491i	$-0.603610\pi$
$557$	4.31398e39	−	7.47203e39i	0.660660	−	1.14430i	0.980443	−	0.196805i	$-0.0630566\pi$
$558$	6.62860e38	+	1.14811e39i	0.0989067	+	0.171311i
$559$	−4.58730e39			−0.666939
$560$	7.61565e37	−	7.29396e37i	0.0107890	−	0.0103332i
$561$	−9.88464e38			−0.136458
$562$	3.65101e38	+	6.32374e38i	0.0491176	+	0.0850741i
$563$	−3.50257e39	+	6.06663e39i	−0.459214	+	0.795382i	−0.998920	−	0.0464716i	$-0.985202\pi$
$563$	−3.50257e39	+	6.06663e39i	−0.459214	+	0.795382i	0.539705	+	0.841854i	$0.318536\pi$
$564$	−2.65820e39	+	4.60413e39i	−0.339657	+	0.588303i
$565$	3.46848e37	+	6.00759e37i	0.00431954	+	0.00748166i
$566$	−1.74448e39			−0.211752
$567$	−6.78214e38	+	6.49565e38i	−0.0802439	+	0.0768543i
$568$	7.88564e38			0.0909465
$569$	−3.80942e39	−	6.59810e39i	−0.428283	−	0.741808i	0.568438	−	0.822726i	$-0.307548\pi$
$569$	−3.80942e39	−	6.59810e39i	−0.428283	−	0.741808i	−0.996721	+	0.0809186i	$0.974215\pi$
$570$	1.38565e37	−	2.40001e37i	0.00151868	−	0.00263043i
$571$	−4.35613e39	+	7.54505e39i	−0.465455	+	0.806192i	−0.999222	−	0.0394400i	$-0.987443\pi$
$571$	−4.35613e39	+	7.54505e39i	−0.465455	+	0.806192i	0.533767	+	0.845632i	$0.320776\pi$
$572$	4.96343e38	+	8.59692e38i	0.0517059	+	0.0895572i
$573$	3.46299e39			0.351730
$574$	5.83270e38	+	2.38111e39i	0.0577627	+	0.235808i
$575$	−2.93267e39			−0.283191
$576$	6.58043e38	+	1.13976e39i	0.0619624	+	0.107322i
$577$	−8.26901e38	+	1.43223e39i	−0.0759284	+	0.131512i	−0.901490	−	0.432801i	$-0.857525\pi$
$577$	−8.26901e38	+	1.43223e39i	−0.0759284	+	0.131512i	0.825561	+	0.564313i	$0.190859\pi$
$578$	2.44810e39	−	4.24024e39i	0.219218	−	0.379697i
$579$	5.52951e39	+	9.57739e39i	0.482889	+	0.836388i
$580$	−3.63657e38			−0.0309732
$581$	−1.96550e40	−	5.72371e39i	−1.63275	−	0.475471i
$582$	−2.98514e39			−0.241869
$583$	−5.13412e38	−	8.89256e38i	−0.0405763	−	0.0702801i
$584$	2.90030e39	−	5.02346e39i	0.223592	−	0.387273i
$585$	−3.71783e37	+	6.43947e37i	−0.00279595	+	0.00484273i
$586$	3.81208e39	+	6.60272e39i	0.279671	+	0.484404i
$587$	3.39973e39			0.243328			0.121664	−	0.992571i	$-0.461177\pi$
$587$	3.39973e39			0.243328			0.121664	+	0.992571i	$0.461177\pi$
$588$	−3.15409e38	+	7.30576e39i	−0.0220243	+	0.510145i
$589$	−1.76921e40			−1.20534
$590$	−6.46983e37	−	1.12061e38i	−0.00430070	−	0.00744903i
$591$	−4.93429e39	+	8.54644e39i	−0.320041	+	0.554328i
$592$	−7.63752e38	+	1.32286e39i	−0.0483379	+	0.0837237i
$593$	−1.04810e40	−	1.81536e40i	−0.647306	−	1.12117i	−0.983764	−	0.179468i	$-0.942562\pi$
$593$	−1.04810e40	−	1.81536e40i	−0.647306	−	1.12117i	0.336458	−	0.941698i	$-0.390771\pi$
$594$	1.69566e38			0.0102196
$595$	−5.53542e38	−	1.61196e38i	−0.0325578	−	0.00948111i
$596$	4.49942e39			0.258277
$597$	2.75379e39	+	4.76970e39i	0.154277	+	0.267216i
$598$	−6.59339e38	+	1.14201e39i	−0.0360530	+	0.0624456i
$599$	6.08115e39	−	1.05329e40i	0.324561	−	0.562156i	−0.656862	−	0.754011i	$-0.728117\pi$
$599$	6.08115e39	−	1.05329e40i	0.324561	−	0.562156i	0.981423	+	0.191854i	$0.0614501\pi$
$600$	3.54815e39	+	6.14557e39i	0.184845	+	0.320162i
$601$	1.92245e40			0.977630			0.488815	−	0.872388i	$-0.337429\pi$
$601$	1.92245e40			0.977630			0.488815	+	0.872388i	$0.337429\pi$
$602$	1.45170e39	+	5.92635e39i	0.0720655	+	0.294197i
$603$	4.02863e39			0.195235
$604$	−3.43398e39	−	5.94782e39i	−0.162466	−	0.281399i
$605$	−2.36670e38	+	4.09924e38i	−0.0109317	+	0.0189343i
$606$	4.26945e39	−	7.39491e39i	0.192539	−	0.333488i
$607$	7.30536e39	+	1.26533e40i	0.321666	+	0.557143i	0.980832	−	0.194855i	$-0.0624237\pi$
$607$	7.30536e39	+	1.26533e40i	0.321666	+	0.557143i	−0.659166	+	0.751998i	$0.729090\pi$
$608$	1.39293e40			0.598864
$609$	1.55212e40	−	1.48656e40i	0.651590	−	0.624066i
$610$	4.60231e37			0.00188666
$611$	−1.24387e40	−	2.15444e40i	−0.497939	−	0.862455i
$612$	5.70541e39	−	9.88205e39i	0.223044	−	0.386324i
$613$	1.13223e40	−	1.96108e40i	0.432273	−	0.748719i	−0.564796	−	0.825231i	$-0.691045\pi$
$613$	1.13223e40	−	1.96108e40i	0.432273	−	0.748719i	0.997069	+	0.0765121i	$0.0243784\pi$
$614$	−4.58084e39	−	7.93425e39i	−0.170806	−	0.295845i
$615$	−2.53716e38			−0.00923971
$616$	2.03175e39	−	1.94592e39i	0.0722685	−	0.0692158i
$617$	4.12231e39			0.143221			0.0716103	−	0.997433i	$-0.477186\pi$
$617$	4.12231e39			0.143221			0.0716103	+	0.997433i	$0.477186\pi$
$618$	1.54682e39	+	2.67917e39i	0.0524937	+	0.0909217i
$619$	9.54610e39	−	1.65343e40i	0.316455	−	0.548116i	−0.663291	−	0.748362i	$-0.730841\pi$
$619$	9.54610e39	−	1.65343e40i	0.316455	−	0.548116i	0.979746	+	0.200246i	$0.0641741\pi$
$620$	−5.34186e38	+	9.25238e38i	−0.0172987	+	0.0299622i
$621$	−8.61815e38	−	1.49271e39i	−0.0272638	−	0.0472222i
$622$	1.07606e40			0.332563
$623$	−9.41529e38	−	3.84366e39i	−0.0284287	−	0.116056i
$624$	−9.76628e39			−0.288106
$625$	−1.73211e40	−	3.00010e40i	−0.499247	−	0.864721i
$626$	2.38656e39	−	4.13364e39i	0.0672115	−	0.116414i
$627$	−1.13145e39	+	1.95973e39i	−0.0311356	+	0.0539284i
$628$	1.49917e40	+	2.59664e40i	0.403122	+	0.698228i
$629$	8.35133e39			0.219443
$630$	9.49571e37	+	2.76524e37i	0.00243831	+	0.000710059i
$631$	3.87215e40			0.971687			0.485843	−	0.874046i	$-0.338513\pi$
$631$	3.87215e40			0.971687			0.485843	+	0.874046i	$0.338513\pi$
$632$	6.71002e39	+	1.16221e40i	0.164561	+	0.285028i
$633$	−5.19861e39	+	9.00426e39i	−0.124605	+	0.215821i
$634$	−6.60658e39	+	1.14429e40i	−0.154768	+	0.268067i
$635$	−7.03929e38	−	1.21924e39i	−0.0161180	−	0.0279171i
$636$	1.18536e40			0.265292
$637$	−2.88682e40	−	1.83713e40i	−0.631536	−	0.401900i
$638$	−3.88058e39			−0.0829844
$639$	−1.13183e39	−	1.96038e39i	−0.0236601	−	0.0409806i
$640$	5.44838e38	−	9.43687e38i	0.0111342	−	0.0192850i
$641$	−1.72272e39	+	2.98384e39i	−0.0344171	+	0.0596121i	−0.882721	−	0.469898i	$-0.844291\pi$
$641$	−1.72272e39	+	2.98384e39i	−0.0344171	+	0.0596121i	0.848304	+	0.529510i	$0.177624\pi$
$642$	−1.93586e39	−	3.35301e39i	−0.0378108	−	0.0654903i
$643$	−2.23385e40			−0.426574			−0.213287	−	0.976990i	$-0.568417\pi$
$643$	−2.23385e40			−0.426574			−0.213287	+	0.976990i	$0.568417\pi$
$644$	−1.28863e40	−	3.75259e39i	−0.240592	−	0.0700626i
$645$	−6.31472e38			−0.0115276
$646$	−9.95028e39	−	1.72344e40i	−0.177608	−	0.307627i
$647$	1.47321e40	−	2.55168e40i	0.257131	−	0.445363i	−0.708341	−	0.705870i	$-0.750556\pi$
$647$	1.47321e40	−	2.55168e40i	0.257131	−	0.445363i	0.965472	+	0.260507i	$0.0838896\pi$
$648$	−2.08537e39	+	3.61196e39i	−0.0355914	+	0.0616461i
$649$	5.28296e39	+	9.15036e39i	0.0881717	+	0.152718i
$650$	−1.55847e40			−0.254364
$651$	−1.50223e40	−	6.13264e40i	−0.239780	−	0.978866i
$652$	1.00166e41			1.56361
$653$	3.06873e40	+	5.31520e40i	0.468509	+	0.811481i	0.999352	−	0.0359891i	$-0.0114582\pi$
$653$	3.06873e40	+	5.31520e40i	0.468509	+	0.811481i	−0.530844	+	0.847470i	$0.678125\pi$
$654$	8.88861e39	−	1.53955e40i	0.132726	−	0.229888i
$655$	1.19579e37	−	2.07118e37i	0.000174646	−	0.000302495i
$656$	−1.66620e40	−	2.88594e40i	−0.238024	−	0.412270i
$657$	−1.66512e40			−0.232674
$658$	−2.38969e40	+	2.28875e40i	−0.326637	+	0.312840i
$659$	8.28239e40			1.10743			0.553716	−	0.832705i	$-0.313209\pi$
$659$	8.28239e40			1.10743			0.553716	+	0.832705i	$0.313209\pi$
$660$	6.83249e37	+	1.18342e38i	0.000893700	+	0.00154793i
$661$	3.20030e40	−	5.54308e40i	0.409515	−	0.709300i	−0.585321	−	0.810802i	$-0.699031\pi$
$661$	3.20030e40	−	5.54308e40i	0.409515	−	0.709300i	0.994835	+	0.101502i	$0.0323648\pi$
$662$	1.22181e40	−	2.11623e40i	0.152954	−	0.264924i
$663$	2.66976e40	+	4.62417e40i	0.326984	+	0.566353i
$664$	−9.09178e40			−1.08946
$665$	−9.53205e38	+	9.12941e38i	−0.0111756	+	0.0107036i
$666$	−1.43263e39			−0.0164345
$667$	1.97230e40	+	3.41612e40i	0.221385	+	0.383450i
$668$	−6.21237e40	+	1.07601e41i	−0.682337	+	1.18184i
$669$	−4.92225e40	+	8.52559e40i	−0.529036	+	0.916317i
$670$	−2.12138e38	−	3.67434e38i	−0.00223118	−	0.00386451i
$671$	−3.75803e39			−0.0386798
$672$	1.18273e40	+	4.82833e40i	0.119133	+	0.486343i
$673$	−9.94995e40			−0.980850			−0.490425	−	0.871483i	$-0.663158\pi$
$673$	−9.94995e40			−0.980850			−0.490425	+	0.871483i	$0.663158\pi$
$674$	−3.24225e39	−	5.61574e39i	−0.0312808	−	0.0541800i
$675$	1.01853e40	−	1.76415e40i	0.0961767	−	0.166583i
$676$	−2.10355e40	+	3.64345e40i	−0.194413	+	0.336733i
$677$	−3.09443e40	−	5.35972e40i	−0.279927	−	0.484849i	0.691439	−	0.722435i	$-0.256977\pi$
$677$	−3.09443e40	−	5.35972e40i	−0.279927	−	0.484849i	−0.971366	+	0.237586i	$0.923644\pi$
$678$	−8.54535e39			−0.0756657
$679$	1.36502e41	+	3.97506e40i	1.18311	+	0.344534i
$680$	−2.56051e39			−0.0217244
$681$	−5.32176e40	−	9.21756e40i	−0.442000	−	0.765567i
$682$	−5.70029e39	+	9.87320e39i	−0.0463472	+	0.0802758i
$683$	−6.97008e40	+	1.20725e41i	−0.554801	+	0.960944i	0.443118	+	0.896464i	$0.353872\pi$
$683$	−6.97008e40	+	1.20725e41i	−0.554801	+	0.960944i	−0.997919	+	0.0644807i	$0.979461\pi$
$684$	−1.30615e40	−	2.26231e40i	−0.101784	−	0.176295i
$685$	−4.07872e39			−0.0311179
$686$	−1.45983e40	+	4.31087e40i	−0.109044	+	0.322007i
$687$	−3.27902e40			−0.239812
$688$	−4.14700e40	−	7.18281e40i	−0.296962	−	0.514354i
$689$	−2.77337e40	+	4.80362e40i	−0.194460	+	0.336814i
$690$	−9.07623e37	+	1.57205e38i	−0.000623151	+	0.00107933i
$691$	3.80872e40	+	6.59690e40i	0.256064	+	0.443515i	0.965184	−	0.261572i	$-0.0842410\pi$
$691$	3.80872e40	+	6.59690e40i	0.256064	+	0.443515i	−0.709120	+	0.705087i	$0.750908\pi$
$692$	4.78366e40			0.314936
$693$	−7.75375e39	−	2.25796e39i	−0.0499896	−	0.0145574i
$694$	−8.25783e40			−0.521379
$695$	−2.90128e39	−	5.02516e39i	−0.0179395	−	0.0310721i
$696$	4.77245e40	−	8.26612e40i	0.289006	−	0.500573i
$697$	−9.10962e40	+	1.57783e41i	−0.540288	+	0.935806i
$698$	−2.27250e40	−	3.93609e40i	−0.132008	−	0.228645i
$699$	−8.78965e40			−0.500095
$700$	−3.77397e40	−	1.54067e41i	−0.210318	−	0.858593i
$701$	3.13960e41			1.71381			0.856905	−	0.515474i	$-0.172384\pi$
$701$	3.13960e41			1.71381			0.856905	+	0.515474i	$0.172384\pi$
$702$	−4.57984e39	−	7.93251e39i	−0.0244885	−	0.0424153i
$703$	9.55942e39	−	1.65574e40i	0.0500702	−	0.0867241i
$704$	−5.65887e39	+	9.80145e39i	−0.0290353	+	0.0502906i
$705$	−1.71226e39	−	2.96572e39i	−0.00860653	−	0.0149069i
$706$	−8.02953e40			−0.395387
$707$	−2.93702e41	+	2.81295e41i	−1.41685	+	1.35700i
$708$	−1.21973e41			−0.576476
$709$	4.71350e39	+	8.16403e39i	0.0218260	+	0.0378037i	0.876732	−	0.480979i	$-0.159719\pi$
$709$	4.71350e39	+	8.16403e39i	0.0218260	+	0.0378037i	−0.854906	+	0.518783i	$0.826385\pi$
$710$	−1.19199e38	+	2.06458e38i	−0.000540785	+	0.000936668i
$711$	1.92618e40	−	3.33624e40i	0.0856225	−	0.148302i
$712$	−8.78757e39	−	1.52205e40i	−0.0382745	−	0.0662933i
$713$	1.15887e41			0.494579
$714$	5.12910e40	−	4.91244e40i	0.214495	−	0.205434i
$715$	−6.39433e38			−0.00262034
$716$	2.09794e40	+	3.63374e40i	0.0842470	+	0.145920i
$717$	8.21361e40	−	1.42264e41i	0.323226	−	0.559844i
$718$	−5.74539e40	+	9.95130e40i	−0.221572	+	0.383774i
$719$	2.21062e41	+	3.82890e41i	0.835497	+	1.44712i	0.893626	+	0.448813i	$0.148153\pi$
$719$	2.21062e41	+	3.82890e41i	0.835497	+	1.44712i	−0.0581290	+	0.998309i	$0.518513\pi$
$720$	−1.34439e39			−0.00497972
$721$	−3.50554e40	−	1.43109e41i	−0.127261	−	0.519523i
$722$	4.99910e40			0.177870
$723$	−5.35392e40	−	9.27327e40i	−0.186710	−	0.323391i
$724$	1.32797e41	−	2.30011e41i	0.453918	−	0.786210i
$725$	−2.33095e41	+	4.03733e41i	−0.780966	+	1.35267i
$726$	−2.91543e40	−	5.04967e40i	−0.0957462	−	0.165837i
$727$	2.30350e41			0.741548			0.370774	−	0.928723i	$-0.379092\pi$
$727$	2.30350e41			0.741548			0.370774	+	0.928723i	$0.379092\pi$
$728$	−1.45909e41	−	4.24899e40i	−0.460443	−	0.134085i
$729$	1.19725e40			0.0370370
$730$	8.76812e38	+	1.51868e39i	0.00265904	+	0.00460559i
$731$	−2.26729e41	+	3.92706e41i	−0.674071	+	1.16752i
$732$	2.16913e40	−	3.75705e40i	0.0632231	−	0.109506i
$733$	−2.28537e41	−	3.95837e41i	−0.653053	−	1.13112i	−0.982378	−	0.186904i	$-0.940155\pi$
$733$	−2.28537e41	−	3.95837e41i	−0.653053	−	1.13112i	0.329325	−	0.944217i	$-0.393179\pi$
$734$	1.08747e41			0.304667
$735$	−3.97390e39	−	2.52893e39i	−0.0109157	−	0.00694657i
$736$	−9.12396e40			−0.245728
$737$	1.73222e40	+	3.00029e40i	0.0457430	+	0.0792292i
$738$	1.56271e40	−	2.70669e40i	0.0404632	−	0.0700843i
$739$	1.08475e41	−	1.87885e41i	0.275414	−	0.477032i	−0.694825	−	0.719179i	$-0.744518\pi$
$739$	1.08475e41	−	1.87885e41i	0.275414	−	0.477032i	0.970240	+	0.242147i	$0.0778516\pi$
$740$	−5.77264e38	−	9.99850e38i	−0.00143719	−	0.00248929i
$741$	1.22239e41			0.298431
$742$	7.08347e40	+	2.06277e40i	0.169586	+	0.0493849i
$743$	7.36319e41			1.72873			0.864367	−	0.502861i	$-0.167719\pi$
$743$	7.36319e41			1.72873			0.864367	+	0.502861i	$0.167719\pi$
$744$	−1.40208e41	−	2.42847e41i	−0.322823	−	0.559146i
$745$	−1.44914e39	+	2.50998e39i	−0.00327223	+	0.00566767i
$746$	1.10947e41	−	1.92166e41i	0.245699	−	0.425564i
$747$	1.30494e41	+	2.26023e41i	0.283428	+	0.490912i
$748$	9.81278e40			0.209035
$749$	4.38722e40	+	1.79102e41i	0.0916649	+	0.374208i
$750$	−4.29175e39			−0.00879522
$751$	−3.93104e41	−	6.80876e41i	−0.790185	−	1.36864i	−0.925852	−	0.377885i	$-0.876651\pi$
$751$	−3.93104e41	−	6.80876e41i	−0.790185	−	1.36864i	0.135668	−	0.990754i	$-0.456682\pi$
$752$	2.24895e41	−	3.89529e41i	0.443426	−	0.768036i
$753$	1.03122e41	−	1.78612e41i	0.199445	−	0.345448i
$754$	1.04811e41	+	1.81539e41i	0.198849	+	0.344417i
$755$	4.42395e39			0.00823341
$756$	6.73283e40	−	6.44843e40i	0.122923	−	0.117730i
$757$	8.86824e40			0.158835			0.0794177	−	0.996841i	$-0.474694\pi$
$757$	8.86824e40			0.158835			0.0794177	+	0.996841i	$0.474694\pi$
$758$	2.12717e40	+	3.68437e40i	0.0373766	+	0.0647381i
$759$	7.41122e39	−	1.28366e40i	0.0127757	−	0.0221281i
$760$	−2.93091e39	+	5.07648e39i	−0.00495684	+	0.00858550i
$761$	−2.75696e41	−	4.77520e41i	−0.457460	−	0.792345i	0.541366	−	0.840787i	$-0.317907\pi$
$761$	−2.75696e41	−	4.77520e41i	−0.457460	−	0.792345i	−0.998826	+	0.0484427i	$0.984574\pi$
$762$	1.73428e41			0.282340
$763$	−6.11460e41	+	5.85631e41i	−0.976702	+	0.935445i
$764$	−3.43781e41			−0.538801
$765$	3.67510e39	+	6.36546e39i	0.00565169	+	0.00978902i
$766$	8.63563e40	−	1.49574e41i	0.130310	−	0.225703i
$767$	2.85377e41	−	4.94288e41i	0.422558	−	0.731893i
$768$	−6.74668e39	−	1.16856e40i	−0.00980285	−	0.0169790i
$769$	1.07480e42			1.53249			0.766244	−	0.642550i	$-0.222123\pi$
$769$	1.07480e42			1.53249			0.766244	+	0.642550i	$0.222123\pi$
$770$	2.02355e38	+	8.26085e38i	0.000283138	+	0.00115587i
$771$	−1.97866e41			−0.271696
$772$	−5.48931e41	−	9.50777e41i	−0.739719	−	1.28123i
$773$	−3.15993e41	+	5.47316e41i	−0.417902	+	0.723828i	−0.995728	−	0.0923319i	$-0.970568\pi$
$773$	−3.15993e41	+	5.47316e41i	−0.417902	+	0.723828i	0.577826	+	0.816160i	$0.303901\pi$
$774$	3.88942e40	−	6.73667e40i	0.0504825	−	0.0874382i
$775$	6.84801e41	+	1.18611e42i	0.872347	+	1.51095i
$776$	6.31414e41			0.789441
$777$	6.55099e40	+	1.90771e40i	0.0803901	+	0.0234103i
$778$	8.97513e40			0.108103
$779$	2.08548e41	+	3.61216e41i	0.246555	+	0.427045i
$780$	3.69080e39	−	6.39266e39i	0.00428301	−	0.00741839i
$781$	9.73319e39	−	1.68584e40i	0.0110870	−	0.0192033i
$782$	6.51761e40	+	1.12888e41i	0.0728770	+	0.126227i
$783$	−2.73996e41			−0.300745
$784$	2.66850e40	−	6.18099e41i	0.0287530	−	0.666001i
$785$	−1.93136e40			−0.0204293
$786$	1.47305e39	+	2.55139e39i	0.00152964	+	0.00264942i
$787$	4.62473e41	−	8.01026e41i	0.471468	−	0.816607i	−0.527999	−	0.849245i	$-0.677058\pi$
$787$	4.62473e41	−	8.01026e41i	0.471468	−	0.816607i	0.999467	+	0.0326381i	$0.0103909\pi$
$788$	4.89842e41	−	8.48431e41i	0.490259	−	0.849154i
$789$	5.54447e40	+	9.60330e40i	0.0544808	+	0.0943635i
$790$	−4.05712e39			−0.00391404
$791$	3.90754e41	+	1.13791e41i	0.370122	+	0.107783i
$792$	−3.58664e40			−0.0333559
$793$	1.01502e41	+	1.75806e41i	0.0926854	+	0.160536i
$794$	2.00293e41	−	3.46917e41i	0.179584	−	0.311049i
$795$	−3.81773e39	+	6.61250e39i	−0.00336110	+	0.00582160i
$796$	−2.73377e41	−	4.73502e41i	−0.236332	−	0.409338i
$797$	8.38811e41			0.712063			0.356031	−	0.934474i	$-0.384130\pi$
$797$	8.38811e41			0.712063			0.356031	+	0.934474i	$0.384130\pi$
$798$	−3.86836e40	−	1.57920e41i	−0.0322467	−	0.131643i
$799$	−2.45914e42			−2.01305
$800$	−5.39155e41	−	9.33844e41i	−0.433420	−	0.750706i
$801$	−2.52256e40	+	4.36921e40i	−0.0199145	+	0.0344930i
$802$	−1.92771e41	+	3.33889e41i	−0.149456	+	0.258866i
$803$	−7.15963e40	−	1.24008e41i	−0.0545149	−	0.0944226i
$804$	−3.99935e41			−0.299072
$805$	6.24367e39	−	5.97993e39i	0.00458563	−	0.00439193i
$806$	6.15842e41			0.444233
$807$	−3.10384e39	−	5.37601e39i	−0.00219904	−	0.00380885i
$808$	−9.03072e41	+	1.56417e42i	−0.628431	+	1.08847i
$809$	−6.61214e41	+	1.14526e42i	−0.451948	+	0.782797i	−0.998507	−	0.0546235i	$-0.982604\pi$
$809$	−6.61214e41	+	1.14526e42i	−0.451948	+	0.782797i	0.546559	+	0.837421i	$0.315937\pi$
$810$	−6.30444e38	−	1.09196e39i	−0.000423266	−	0.000733119i
$811$	1.02365e42			0.675068			0.337534	−	0.941313i	$-0.390407\pi$
$811$	1.02365e42			0.675068			0.337534	+	0.941313i	$0.390407\pi$
$812$	−1.54084e42	+	1.47575e42i	−0.998146	+	0.955983i
$813$	−5.00999e41			−0.318804
$814$	−6.15997e39	−	1.06694e40i	−0.00385057	−	0.00666938i
$815$	−3.22606e40	+	5.58769e40i	−0.0198101	+	0.0343121i
$816$	−4.82702e41	+	8.36064e41i	−0.291187	+	0.504350i
$817$	5.19055e41	+	8.99029e41i	0.307605	+	0.532787i
$818$	1.88798e41			0.109920
$819$	1.03792e41	+	4.23717e41i	0.0593675	+	0.242359i
$820$	2.51871e40			0.0141540
$821$	−9.54584e41	−	1.65339e42i	−0.527034	−	0.912849i	−0.999504	−	0.0315026i	$-0.989971\pi$
$821$	−9.54584e41	−	1.65339e42i	−0.527034	−	0.912849i	0.472470	−	0.881347i	$-0.343363\pi$
$822$	2.51220e41	−	4.35125e41i	0.136274	−	0.236033i
$823$	−1.66316e42	+	2.88068e42i	−0.886415	+	1.53532i	−0.0423312	+	0.999104i	$0.513478\pi$
$823$	−1.66316e42	+	2.88068e42i	−0.886415	+	1.53532i	−0.844084	+	0.536212i	$0.819855\pi$
$824$	−3.27183e41	−	5.66697e41i	−0.171335	−	0.296761i
$825$	1.75178e41			0.0901359
$826$	−7.28883e41	−	2.12257e41i	−0.368508	−	0.107313i
$827$	−2.33991e42			−1.16243			−0.581217	−	0.813748i	$-0.697423\pi$
$827$	−2.33991e42			−1.16243			−0.581217	+	0.813748i	$0.697423\pi$
$828$	8.55550e40	+	1.48186e41i	0.0417643	+	0.0723380i
$829$	7.17966e41	−	1.24355e42i	0.344400	−	0.596518i	−0.640845	−	0.767671i	$-0.721416\pi$
$829$	7.17966e41	−	1.24355e42i	0.344400	−	0.596518i	0.985245	+	0.171152i	$0.0547491\pi$
$830$	1.37430e40	−	2.38036e40i	0.00647814	−	0.0112205i
$831$	1.24525e42	+	2.15684e42i	0.576823	+	0.999087i
$832$	6.11367e41			0.278300
$833$	−2.99954e42	+	1.56332e42i	−1.34184	+	0.699351i
$834$	7.14791e41			0.314247
$835$	−4.00166e40	−	6.93108e40i	−0.0172897	−	0.0299466i
$836$	1.12323e41	−	1.94549e41i	0.0476954	−	0.0826109i
$837$	−4.02480e41	+	6.97117e41i	−0.167968	+	0.290929i
$838$	2.84416e41	+	4.92622e41i	0.116658	+	0.202058i
$839$	2.12368e42			0.856132			0.428066	−	0.903748i	$-0.359195\pi$
$839$	2.12368e42			0.856132			0.428066	+	0.903748i	$0.359195\pi$
$840$	−2.00853e40	−	5.84902e39i	−0.00795844	−	0.00231757i
$841$	3.70282e42			1.44208
$842$	−3.62744e41	−	6.28291e41i	−0.138859	−	0.240511i
$843$	−2.21685e41	+	3.83970e41i	−0.0834136	+	0.144477i
$844$	5.16082e41	−	8.93881e41i	0.190877	−	0.330609i
$845$	−1.35499e40	−	2.34691e40i	−0.00492621	−	0.00853244i
$846$	4.21852e41			0.150761
$847$	6.60721e41	+	2.69729e42i	0.232118	+	0.947587i
$848$	−1.00287e42			−0.346341
$849$	−5.29613e41	−	9.17316e41i	−0.179803	−	0.311428i
$850$	−7.70280e41	+	1.33416e42i	−0.257084	+	0.445282i
$851$	−6.26159e40	+	1.08454e41i	−0.0205450	+	0.0355850i
$852$	1.12360e41	+	1.94613e41i	0.0362441	+	0.0627766i
$853$	1.08274e42			0.343370			0.171685	−	0.985152i	$-0.445079\pi$
$853$	1.08274e42			0.343370			0.171685	+	0.985152i	$0.445079\pi$
$854$	1.95003e41	−	1.86766e41i	0.0607997	−	0.0582315i
$855$	1.68269e40			0.00515818
$856$	4.09472e41	+	7.09226e41i	0.123411	+	0.213755i
$857$	1.13345e42	−	1.96320e42i	0.335878	−	0.581758i	−0.647775	−	0.761832i	$-0.724300\pi$
$857$	1.13345e42	−	1.96320e42i	0.335878	−	0.581758i	0.983653	+	0.180074i	$0.0576337\pi$
$858$	3.93845e40	−	6.82160e40i	0.0114752	−	0.0198756i
$859$	1.31987e41	+	2.28609e41i	0.0378122	+	0.0654926i	0.884312	−	0.466896i	$-0.154628\pi$
$859$	1.31987e41	+	2.28609e41i	0.0378122	+	0.0654926i	−0.846500	+	0.532389i	$0.821294\pi$
$860$	6.26882e40			0.0176587
$861$	−1.07501e42	+	1.02960e42i	−0.297760	+	0.285182i
$862$	−1.81860e42			−0.495316
$863$	−2.79702e42	−	4.84458e42i	−0.749098	−	1.29748i	−0.948255	−	0.317509i	$-0.897154\pi$
$863$	−2.79702e42	−	4.84458e42i	−0.749098	−	1.29748i	0.199157	−	0.979968i	$-0.436180\pi$
$864$	3.16880e41	−	5.48852e41i	0.0834536	−	0.144546i
$865$	−1.54068e40	+	2.66854e40i	−0.00399006	+	0.00691099i
$866$	−5.14475e41	−	8.91098e41i	−0.131025	−	0.226942i
$867$	2.97292e42			0.744571
$868$	1.49131e42	+	6.08806e42i	0.367310	+	1.49949i
$869$	3.31285e41			0.0802446
$870$	1.44280e40	+	2.49900e40i	0.00343697	+	0.00595301i
$871$	9.35719e41	−	1.62071e42i	0.219221	−	0.379702i
$872$	−1.88011e42	+	3.25645e42i	−0.433207	+	0.750336i
$873$	−9.06270e41	−	1.56971e42i	−0.205377	−	0.355723i
$874$	2.98417e41			0.0665133
$875$	1.96250e41	+	5.71497e40i	0.0430222	+	0.0125284i
$876$	1.65301e42			0.356424
$877$	−2.52312e42	−	4.37017e42i	−0.535110	−	0.926839i	−0.999158	−	0.0410282i	$-0.986937\pi$
$877$	−2.52312e42	−	4.37017e42i	−0.535110	−	0.926839i	0.464048	−	0.885810i	$-0.346397\pi$
$878$	5.39906e41	−	9.35145e41i	0.112628	−	0.195078i
$879$	−2.31465e42	+	4.00909e42i	−0.474949	+	0.822636i
$880$	−5.78058e39	−	1.00123e40i	−0.00116674	−	0.00202085i
$881$	2.29927e42			0.456499			0.228249	−	0.973603i	$-0.426700\pi$
$881$	2.29927e42			0.456499			0.228249	+	0.973603i	$0.426700\pi$
$882$	5.14555e41	−	2.68179e41i	0.100493	−	0.0523757i
$883$	6.24484e42			1.19975			0.599876	−	0.800093i	$-0.295217\pi$
$883$	6.24484e42			1.19975			0.599876	+	0.800093i	$0.295217\pi$
$884$	−2.65036e42	−	4.59055e42i	−0.500894	−	0.867575i
$885$	3.92841e40	−	6.80420e40i	0.00730363	−	0.0126503i
$886$	−1.76752e42	+	3.06143e42i	−0.323277	+	0.559931i
$887$	−4.02565e42	−	6.97263e42i	−0.724342	−	1.25460i	−0.959244	−	0.282578i	$-0.908810\pi$
$887$	−4.02565e42	−	6.97263e42i	−0.724342	−	1.25460i	0.234902	−	0.972019i	$-0.424523\pi$
$888$	3.03028e41			0.0536408
$889$	−7.93037e42	−	2.30939e42i	−1.38108	−	0.402182i
$890$	5.31328e39			0.000910349
$891$	5.14791e40	+	8.91644e40i	0.00867769	+	0.0150302i
$892$	4.88647e42	−	8.46362e42i	0.810410	−	1.40367i
$893$	−2.81487e42	+	4.87550e42i	−0.459317	+	0.795561i
$894$	−1.78513e41	−	3.09194e41i	−0.0286600	−	0.0496406i
$895$	−2.70275e40			−0.00426945
$896$	−1.52105e42	−	6.20946e42i	−0.236416	−	0.965134i
$897$	−8.00685e41			−0.122454
$898$	−1.25505e42	−	2.17382e42i	−0.188867	−	0.327127i
$899$	9.21093e42	−	1.59538e43i	1.36392	−	2.36237i
$900$	−1.01113e42	+	1.75132e42i	−0.147329	+	0.255182i
$901$	2.74150e42	+	4.74841e42i	0.393078	+	0.680830i
$902$	2.68771e41			0.0379217
$903$	−2.67559e42	+	2.56257e42i	−0.371489	+	0.355797i
$904$	1.80751e42			0.246966
$905$	8.55401e40	+	1.48160e41i	0.0115018	+	0.0199217i
$906$	−2.72484e41	+	4.71956e41i	−0.0360563	+	0.0624514i
$907$	1.81405e42	−	3.14202e42i	0.236234	−	0.409169i	−0.723397	−	0.690433i	$-0.757420\pi$
$907$	1.81405e42	−	3.14202e42i	0.236234	−	0.409169i	0.959631	+	0.281263i	$0.0907534\pi$
$908$	5.28308e42	+	9.15056e42i	0.677083	+	1.17274i
$909$	5.18472e42			0.653957
$910$	3.31799e40	−	3.17784e40i	0.00411884	−	0.00394486i
$911$	1.09095e43			1.33288			0.666438	−	0.745560i	$-0.267818\pi$
$911$	1.09095e43			1.33288			0.666438	+	0.745560i	$0.267818\pi$
$912$	1.10506e42	+	1.91402e42i	0.132880	+	0.230155i
$913$	−1.12219e42	+	1.94369e42i	−0.132813	+	0.230039i
$914$	1.29855e42	−	2.24916e42i	0.151265	−	0.261999i
$915$	1.39723e40	+	2.42008e40i	0.00160200	+	0.00277475i
$916$	3.25518e42			0.367359
$917$	−3.33835e40	−	1.36283e41i	−0.00370831	−	0.0151387i
$918$	−9.05440e41			−0.0990013
$919$	−1.99801e42	−	3.46066e42i	−0.215042	−	0.372463i	0.738244	−	0.674534i	$-0.235655\pi$
$919$	−1.99801e42	−	3.46066e42i	−0.215042	−	0.372463i	−0.953286	+	0.302071i	$0.902322\pi$
$920$	1.91980e40	−	3.32519e40i	0.00203391	−	0.00352284i
$921$	2.78143e42	−	4.81758e42i	0.290071	−	0.502417i
$922$	−5.18885e41	−	8.98736e41i	−0.0532688	−	0.0922643i
$923$	−1.05154e42			−0.106268
$924$	7.69739e41	+	2.24155e41i	0.0765772	+	0.0223000i
$925$	−1.48005e42			−0.144951
$926$	−2.11407e42	−	3.66167e42i	−0.203826	−	0.353037i
$927$	−9.39211e41	+	1.62676e42i	−0.0891471	+	0.154407i
$928$	−7.25192e42	+	1.25607e43i	−0.677653	+	1.17373i
$929$	−4.18949e41	−	7.25640e41i	−0.0385419	−	0.0667565i	0.846111	−	0.533007i	$-0.178938\pi$
$929$	−4.18949e41	−	7.25640e41i	−0.0385419	−	0.0667565i	−0.884653	+	0.466250i	$0.845605\pi$
$930$	8.47746e40			0.00767827
$931$	−3.34000e41	+	7.73637e42i	−0.0297835	+	0.689869i
$932$	8.72576e42			0.766077
$933$	3.26684e42	+	5.65834e42i	0.282387	+	0.489108i
$934$	1.97352e42	−	3.41823e42i	0.167962	−	0.290919i
$935$	−3.16042e40	+	5.47401e40i	−0.00264836	+	0.00458709i
$936$	9.68724e41	+	1.67788e42i	0.0799282	+	0.138440i
$937$	1.71876e43			1.39634			0.698170	−	0.715932i	$-0.253998\pi$
$937$	1.71876e43			1.39634			0.698170	+	0.715932i	$0.253998\pi$
$938$	−2.38992e42	−	6.95966e41i	−0.191180	−	0.0556733i
$939$	2.89818e42			0.228283
$940$	1.69981e41	+	2.94416e41i	0.0131840	+	0.0228354i
$941$	4.40690e41	−	7.63298e41i	0.0336577	−	0.0582968i	−0.848706	−	0.528865i	$-0.822618\pi$
$941$	4.40690e41	−	7.63298e41i	0.0336577	−	0.0582968i	0.882364	+	0.470568i	$0.155951\pi$
$942$	1.18958e42	−	2.06042e42i	0.0894657	−	0.154959i
$943$	−1.36603e42	−	2.36603e42i	−0.101167	−	0.175227i
$944$	1.03194e43			0.752596
$945$	1.42877e40	+	5.83274e40i	0.00102613	+	0.00418901i
$946$	6.68944e41			0.0473117
$947$	−1.10906e43	−	1.92095e43i	−0.772467	−	1.33795i	−0.936207	−	0.351448i	$-0.885689\pi$
$947$	−1.10906e43	−	1.92095e43i	−0.772467	−	1.33795i	0.163741	−	0.986503i	$-0.447644\pi$
$948$	−1.91218e42	+	3.31199e42i	−0.131162	+	0.227179i
$949$	−3.86752e42	+	6.69875e42i	−0.261260	+	0.452515i
$950$	1.76342e42	+	3.05432e42i	0.117317	+	0.203200i
$951$	−8.02287e42			−0.525669
$952$	−1.08490e43	+	1.03908e43i	−0.700092	+	0.670520i
$953$	−2.32428e43			−1.47721			−0.738605	−	0.674139i	$-0.764515\pi$
$953$	−2.32428e43			−1.47721			−0.738605	+	0.674139i	$0.764515\pi$
$954$	−4.70289e41	−	8.14565e41i	−0.0294384	−	0.0509887i
$955$	1.10722e41	−	1.91777e41i	0.00682632	−	0.0118235i
$956$	−8.15390e42	+	1.41230e43i	−0.495138	+	0.857603i
$957$	−1.17812e42	−	2.04056e42i	−0.0704638	−	0.122047i
$958$	4.99977e42			0.294544
$959$	−1.72818e43	+	1.65518e43i	−1.00281	+	0.960449i
$960$	8.41586e40			0.00481023
$961$	−1.81795e43	−	3.14877e43i	−1.02351	−	1.77277i
$962$	−3.32752e41	+	5.76343e41i	−0.0184536	+	0.0319626i
$963$	1.17543e42	−	2.03591e42i	0.0642120	−	0.111218i
$964$	5.31500e42	+	9.20585e42i	0.286013	+	0.495390i
$965$	7.07181e41			0.0374873
$966$	2.53385e41	+	1.03441e42i	0.0132316	+	0.0540161i
$967$	−2.96276e42			−0.152410			−0.0762048	−	0.997092i	$-0.524280\pi$
$967$	−2.96276e42			−0.152410			−0.0762048	+	0.997092i	$0.524280\pi$
$968$	6.16670e42	+	1.06810e43i	0.312507	+	0.541279i
$969$	6.04169e42	−	1.04645e43i	0.301622	−	0.522425i
$970$	−9.54440e40	+	1.65314e41i	−0.00469417	+	0.00813053i
$971$	1.56342e43	+	2.70793e43i	0.757527	+	1.31207i	0.944108	+	0.329635i	$0.106926\pi$
$971$	1.56342e43	+	2.70793e43i	0.757527	+	1.31207i	−0.186582	+	0.982439i	$0.559741\pi$
$972$	−1.18855e42			−0.0567356
$973$	−3.26854e43	−	9.51828e42i	−1.53715	−	0.447633i
$974$	−3.39276e42			−0.157198
$975$	−4.73143e42	−	8.19507e42i	−0.215986	−	0.374098i
$976$	−1.83518e42	+	3.17863e42i	−0.0825385	+	0.142961i
$977$	−1.50140e43	+	2.60050e43i	−0.665312	+	1.15235i	0.313889	+	0.949460i	$0.398368\pi$
$977$	−1.50140e43	+	2.60050e43i	−0.665312	+	1.15235i	−0.979201	+	0.202894i	$0.934965\pi$
$978$	−3.97404e42	−	6.88324e42i	−0.173508	−	0.300524i
$979$	−4.33858e41			−0.0186637
$980$	3.94501e41	+	2.51055e41i	0.0167213	+	0.0106412i
$981$	1.07941e43			0.450802
$982$	6.84802e42	+	1.18611e43i	0.281805	+	0.488100i
$983$	−1.38209e42	+	2.39384e42i	−0.0560414	+	0.0970666i	−0.892685	−	0.450681i	$-0.851181\pi$
$983$	−1.38209e42	+	2.39384e42i	−0.0560414	+	0.0970666i	0.836644	+	0.547748i	$0.184515\pi$
$984$	−3.30543e42	+	5.72517e42i	−0.132068	+	0.228749i
$985$	3.15529e41	+	5.46512e41i	0.0124226	+	0.0215166i
$986$	2.07214e43			0.803902
$987$	−1.92901e43	−	5.61745e42i	−0.737455	−	0.214754i
$988$	−1.21350e43			−0.457156
$989$	−3.39990e42	−	5.88880e42i	−0.126218	−	0.218615i
$990$	5.42153e39	−	9.39037e39i	0.000198341	−	0.000343536i
$991$	2.84451e42	−	4.92683e42i	0.102551	−	0.177623i	−0.810184	−	0.586176i	$-0.800633\pi$
$991$	2.84451e42	−	4.92683e42i	0.102551	−	0.177623i	0.912735	+	0.408552i	$0.133966\pi$
$992$	2.13051e43	+	3.69016e43i	0.756946	+	1.31107i
$993$	1.48373e43			0.519506
$994$	3.32772e41	+	1.35849e42i	0.0114827	+	0.0468764i
$995$	3.52188e41			0.0119768
$996$	−1.29546e43	−	2.24380e43i	−0.434173	−	0.752009i
$997$	−3.27735e41	+	5.67654e41i	−0.0108254	+	0.0187501i	−0.871387	−	0.490596i	$-0.836779\pi$
$997$	−3.27735e41	+	5.67654e41i	−0.0108254	+	0.0187501i	0.860562	+	0.509346i	$0.170113\pi$
$998$	−2.42569e42	+	4.20141e42i	−0.0789664	+	0.136774i
$999$	−4.34937e41	−	7.53333e41i	−0.0139549	−	0.0241706i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.30.e.b.4.11	✓	40
7.2	even	3	inner	21.30.e.b.16.11	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.30.e.b.4.11	✓	40	1.1	even	1	trivial
21.30.e.b.16.11	yes	40	7.2	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 30 \)
Character orbit:	\([\chi]\)	\(=\)	21.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(3938.62 + 6821.90i) q^{2} +(-2.39148e6 + 4.14217e6i) q^{3} +(2.37410e8 - 4.11206e8i) q^{4} +(1.52926e8 + 2.64876e8i) q^{5} -3.76766e10 q^{6} +(1.72284e12 + 5.01708e11i) q^{7} +7.96934e12 q^{8} +(-1.14384e13 - 1.98119e13i) q^{9} +O(q^{10})\)	\(q+(3938.62 + 6821.90i) q^{2} +(-2.39148e6 + 4.14217e6i) q^{3} +(2.37410e8 - 4.11206e8i) q^{4} +(1.52926e8 + 2.64876e8i) q^{5} -3.76766e10 q^{6} +(1.72284e12 + 5.01708e11i) q^{7} +7.96934e12 q^{8} +(-1.14384e13 - 1.98119e13i) q^{9} +(-1.20464e12 + 2.08649e12i) q^{10} +(9.83650e13 - 1.70373e14i) q^{11} +(1.13552e15 + 1.96679e15i) q^{12} -1.06270e16 q^{13} +(3.36304e15 + 1.37291e16i) q^{14} -1.46288e15 q^{15} +(-9.60703e16 - 1.66399e17i) q^{16} +(-5.25246e17 + 9.09752e17i) q^{17} +(9.01031e16 - 1.56063e17i) q^{18} +(1.20245e18 + 2.08271e18i) q^{19} +1.45225e17 q^{20} +(-6.19832e18 + 5.93649e18i) q^{21} +1.54969e18 q^{22} +(-7.87629e18 - 1.36421e19i) q^{23} +(-1.90585e19 + 3.30104e19i) q^{24} +(9.30855e19 - 1.61229e20i) q^{25} +(-4.18559e19 - 7.24966e19i) q^{26} +1.09419e20 q^{27} +(6.15326e20 - 5.89334e20i) q^{28} -2.50410e21 q^{29} +(-5.76174e18 - 9.97963e18i) q^{30} +(-3.67834e21 + 6.37108e21i) q^{31} +(2.89602e21 - 5.01606e21i) q^{32} +(4.70477e20 + 8.14890e20i) q^{33} -8.27498e21 q^{34} +(1.30578e20 + 5.33064e20i) q^{35} -1.08624e22 q^{36} +(-3.97497e21 - 6.88484e21i) q^{37} +(-9.47202e21 + 1.64060e22i) q^{38} +(2.54144e22 - 4.40191e22i) q^{39} +(1.21872e21 + 2.11089e21i) q^{40} +1.73435e23 q^{41} +(-6.49110e22 - 1.89027e22i) q^{42} +4.31663e23 q^{43} +(-4.67057e22 - 8.08966e22i) q^{44} +(3.49846e21 - 6.05951e21i) q^{45} +(6.20434e22 - 1.07462e23i) q^{46} +(1.17047e24 + 2.02732e24i) q^{47} +9.19002e23 q^{48} +(2.71648e24 + 1.72873e24i) q^{49} +1.46651e24 q^{50} +(-2.51223e24 - 4.35132e24i) q^{51} +(-2.52297e24 + 4.36991e24i) q^{52} +(2.60973e24 - 4.52018e24i) q^{53} +(4.30960e23 + 7.46445e23i) q^{54} +6.01703e22 q^{55} +(1.37299e25 + 3.99828e24i) q^{56} -1.15026e25 q^{57} +(-9.86270e24 - 1.70827e25i) q^{58} +(-2.68539e25 + 4.65123e25i) q^{59} +(-3.47303e23 + 6.01546e23i) q^{60} +(-9.55124e24 - 1.65432e25i) q^{61} -5.79504e25 q^{62} +(-9.76680e24 - 3.98715e25i) q^{63} -5.75293e25 q^{64} +(-1.62515e24 - 2.81485e24i) q^{65} +(-3.70606e24 + 6.41909e24i) q^{66} +(-8.80507e25 + 1.52508e26i) q^{67} +(2.49397e26 + 4.31968e26i) q^{68} +7.53441e25 q^{69} +(-3.12221e24 + 2.99033e24i) q^{70} +9.89497e25 q^{71} +(-9.11564e25 - 1.57888e26i) q^{72} +(3.63932e26 - 6.30349e26i) q^{73} +(3.13118e25 - 5.42336e25i) q^{74} +(4.45225e26 + 7.71152e26i) q^{75} +1.14190e27 q^{76} +(2.54945e26 - 2.44176e26i) q^{77} +4.00391e26 q^{78} +(8.41980e26 + 1.45835e27i) q^{79} +(2.93833e25 - 5.08934e25i) q^{80} +(-2.61674e26 + 4.53232e26i) q^{81} +(6.83097e26 + 1.18316e27i) q^{82} -1.14084e28 q^{83} +(9.69580e26 + 3.95817e27i) q^{84} -3.21295e26 q^{85} +(1.70016e27 + 2.94476e27i) q^{86} +(5.98851e27 - 1.03724e28i) q^{87} +(7.83904e26 - 1.35776e27i) q^{88} +(-1.10267e27 - 1.90989e27i) q^{89} +5.51165e25 q^{90} +(-1.83088e28 - 5.33168e27i) q^{91} -7.47963e27 q^{92} +(-1.75934e28 - 3.04727e28i) q^{93} +(-9.22009e27 + 1.59697e28i) q^{94} +(-3.67773e26 + 6.37002e26i) q^{95} +(1.38516e28 + 2.39916e28i) q^{96} +7.92305e28 q^{97} +(-1.09401e27 + 2.53404e28i) q^{98} -4.50055e27 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 7743 q^{2} - 95659380 q^{3} - 5985454645 q^{4} + 14215352760 q^{5} + 74069057934 q^{6} - 368001036334 q^{7} + 49989480496086 q^{8} - 457535849099220 q^{9}+O(q^{10}) \) 40 * q - 7743 * q^2 - 95659380 * q^3 - 5985454645 * q^4 + 14215352760 * q^5 + 74069057934 * q^6 - 368001036334 * q^7 + 49989480496086 * q^8 - 457535849099220 * q^9	\( 40 q - 7743 q^{2} - 95659380 q^{3} - 5985454645 q^{4} + 14215352760 q^{5} + 74069057934 q^{6} - 368001036334 q^{7} + 49989480496086 q^{8} - 457535849099220 q^{9} - 167879133295903 q^{10} - 31\!\cdots\!14 q^{11}+ \cdots + 14\!\cdots\!08 q^{99}+O(q^{100}) \) 40 * q - 7743 * q^2 - 95659380 * q^3 - 5985454645 * q^4 + 14215352760 * q^5 + 74069057934 * q^6 - 368001036334 * q^7 + 49989480496086 * q^8 - 457535849099220 * q^9 - 167879133295903 * q^10 - 3154300361224314 * q^11 - 28628244017941005 * q^12 + 27686480502978220 * q^13 - 214257133773063450 * q^14 - 135983183150288880 * q^15 - 1764048935658629353 * q^16 + 41802108452009436 * q^17 - 177135003978763023 * q^18 - 7235175939726809174 * q^19 - 2944336803535185762 * q^20 + 9048396870023397228 * q^21 + 89086825354637664038 * q^22 + 44902952138264019852 * q^23 - 119549067769441979667 * q^24 - 856461315876501170374 * q^25 + 740598921837346265154 * q^26 + 4376759565260494368360 * q^27 + 837334611372858240643 * q^28 + 3042539991157763918664 * q^29 - 802960690301171876007 * q^30 - 7171021288148722128918 * q^31 - 3221069809618281449199 * q^32 - 15086920844424695908266 * q^33 - 40988792924743489638864 * q^34 + 22734956365007065015692 * q^35 + 273856007324494541487690 * q^36 - 32961210550052530362042 * q^37 - 21824144763887061483774 * q^38 - 66211788982424616967590 * q^39 - 561274593219911517352413 * q^40 - 407158367720211769052760 * q^41 + 261768399564896960899059 * q^42 - 742478352427516947522676 * q^43 - 860699497136335577636151 * q^44 + 325201674764577027042360 * q^45 - 3603590382443692607483880 * q^46 + 5088913555222492904989956 * q^47 + 16874782747476437555778114 * q^48 - 1107011263686123128490044 * q^49 + 20047363110221889541650996 * q^50 + 199938188860599120095484 * q^51 - 15020364113616852849255436 * q^52 + 4503823724603073528076524 * q^53 - 847231232845300197355287 * q^54 - 26118327809723981533730792 * q^55 + 23391818796605514251144607 * q^56 + 69211244458518393496315212 * q^57 - 19344263089875691399511041 * q^58 - 107339818359767325079738806 * q^59 + 7041335828433941954443689 * q^60 - 55695583344240438158518844 * q^61 + 595684893227471470626855138 * q^62 - 34859518397595458196656958 * q^63 + 2556323224325113131258620002 * q^64 + 116576686276646946961533216 * q^65 - 213049761989822976663084411 * q^66 - 395633506213215660680479214 * q^67 - 341809314919360918295601216 * q^68 - 429538856171601041535001176 * q^69 + 3114247010513527110020739673 * q^70 - 357045698249607322103230392 * q^71 - 571799485120140136045891323 * q^72 + 1563411738231613398537297906 * q^73 - 2560064971236623546640897774 * q^74 - 4096427923536512926362560406 * q^75 + 24051365932177387567037871800 * q^76 - 788772365883171194224066980 * q^77 - 7084523369162900456994724452 * q^78 + 5677690363343606232557230766 * q^79 - 3948631034904977500881109899 * q^80 - 10466952660547210744270230420 * q^81 - 14901652274869047200277511964 * q^82 + 21293945454157612982870988948 * q^83 - 13769091913378092591470544324 * q^84 + 8900456942787328180094572008 * q^85 - 1540767080130988487092741200 * q^86 - 7276187229483929466144216708 * q^87 - 63208209978831072085072879725 * q^88 - 11757157651476935757967358112 * q^89 + 7681072179858211493226649566 * q^90 - 1529257930272663641703478390 * q^91 + 158106912155564585073501217248 * q^92 - 34298772519555405332228797542 * q^93 - 133188762499886306919098285406 * q^94 - 159842963957338542634753903584 * q^95 - 15406277046240142004793891831 * q^96 - 390739421663203813144382175132 * q^97 + 239765305290895114544854004019 * q^98 + 144320549408674286727326243508 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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