LMFDB - Embedded newform 21.30.e.b.4.14

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			4.14
Character	$\chi$	$=$	21.4
Dual form			21.30.e.b.16.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(7798.16 + 13506.8i) q^{2} +(-2.39148e6 + 4.14217e6i) q^{3} +(1.46813e8 - 2.54287e8i) q^{4} +(5.50788e9 + 9.53994e9i) q^{5} -7.45967e10 q^{6} +(-9.07383e11 + 1.54808e12i) q^{7} +1.29527e13 q^{8} +(-1.14384e13 - 1.98119e13i) q^{9} +O(q^{10})$	\(q+(7798.16 + 13506.8i) q^{2} +(-2.39148e6 + 4.14217e6i) q^{3} +(1.46813e8 - 2.54287e8i) q^{4} +(5.50788e9 + 9.53994e9i) q^{5} -7.45967e10 q^{6} +(-9.07383e11 + 1.54808e12i) q^{7} +1.29527e13 q^{8} +(-1.14384e13 - 1.98119e13i) q^{9} +(-8.59027e13 + 1.48788e14i) q^{10} +(3.33258e14 - 5.77219e14i) q^{11} +(7.02202e14 + 1.21625e15i) q^{12} +1.64328e16 q^{13} +(-2.79856e16 - 1.83641e14i) q^{14} -5.26881e16 q^{15} +(2.21875e16 + 3.84299e16i) q^{16} +(4.16061e17 - 7.20639e17i) q^{17} +(1.78397e17 - 3.08992e17i) q^{18} +(7.32936e17 + 1.26948e18i) q^{19} +3.23451e18 q^{20} +(-4.24244e18 - 7.46075e18i) q^{21} +1.03952e19 q^{22} +(-5.23590e19 - 9.06884e19i) q^{23} +(-3.09762e19 + 5.36523e19i) q^{24} +(3.24587e19 - 5.62201e19i) q^{25} +(1.28145e20 + 2.21954e20i) q^{26} +1.09419e20 q^{27} +(2.60443e20 + 4.58015e20i) q^{28} +1.93767e21 q^{29} +(-4.10870e20 - 7.11648e20i) q^{30} +(-2.56775e21 + 4.44747e21i) q^{31} +(3.13092e21 - 5.42291e21i) q^{32} +(1.59396e21 + 2.76082e21i) q^{33} +1.29780e22 q^{34} +(-1.97664e22 - 1.29707e20i) q^{35} -6.71722e21 q^{36} +(-3.46428e22 - 6.00031e22i) q^{37} +(-1.14311e22 + 1.97992e22i) q^{38} +(-3.92987e22 + 6.80673e22i) q^{39} +(7.13419e22 + 1.23568e23i) q^{40} -3.06990e23 q^{41} +(6.76877e22 - 1.15482e23i) q^{42} +7.58853e23 q^{43} +(-9.78531e22 - 1.69487e23i) q^{44} +(1.26003e23 - 2.18243e23i) q^{45} +(8.16607e23 - 1.41441e24i) q^{46} +(-1.02540e24 - 1.77605e24i) q^{47} -2.12244e23 q^{48} +(-1.57322e24 - 2.80941e24i) q^{49} +1.01247e24 q^{50} +(1.99001e24 + 3.44679e24i) q^{51} +(2.41254e24 - 4.17864e24i) q^{52} +(2.42337e24 - 4.19741e24i) q^{53} +(8.53266e23 + 1.47790e24i) q^{54} +7.34218e24 q^{55} +(-1.17530e25 + 2.00518e25i) q^{56} -7.01122e24 q^{57} +(1.51103e25 + 2.61717e25i) q^{58} +(2.13008e25 - 3.68941e25i) q^{59} +(-7.73529e24 + 1.33979e25i) q^{60} +(2.52540e24 + 4.37412e24i) q^{61} -8.00948e25 q^{62} +(4.10495e25 + 2.69366e23i) q^{63} +1.21485e26 q^{64} +(9.05097e25 + 1.56767e26i) q^{65} +(-2.48599e25 + 4.30586e25i) q^{66} +(2.06921e26 - 3.58398e26i) q^{67} +(-1.22166e26 - 2.11598e26i) q^{68} +5.00863e26 q^{69} +(-1.52389e26 - 2.67992e26i) q^{70} +7.25060e26 q^{71} +(-1.48158e26 - 2.56617e26i) q^{72} +(-5.75575e26 + 9.96925e26i) q^{73} +(5.40300e26 - 9.35827e26i) q^{74} +(1.55249e26 + 2.68899e26i) q^{75} +4.30418e26 q^{76} +(5.91191e26 + 1.03967e27i) q^{77} -1.22583e27 q^{78} +(-2.95293e27 - 5.11463e27i) q^{79} +(-2.44412e26 + 4.23335e26i) q^{80} +(-2.61674e26 + 4.53232e26i) q^{81} +(-2.39396e27 - 4.14645e27i) q^{82} +4.79018e27 q^{83} +(-2.52002e27 - 1.65364e25i) q^{84} +9.16647e27 q^{85} +(5.91766e27 + 1.02497e28i) q^{86} +(-4.63391e27 + 8.02617e27i) q^{87} +(4.31658e27 - 7.47654e27i) q^{88} +(1.04375e28 + 1.80782e28i) q^{89} +3.93036e27 q^{90} +(-1.49108e28 + 2.54393e28i) q^{91} -3.07479e28 q^{92} +(-1.22815e28 - 2.12721e28i) q^{93} +(1.59925e28 - 2.76998e28i) q^{94} +(-8.07385e27 + 1.39843e28i) q^{95} +(1.49751e28 + 2.59376e28i) q^{96} -3.75413e28 q^{97} +(2.56779e28 - 4.31574e28i) q^{98} -1.52477e28 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 $

$2$	7798.16	+	13506.8i	0.336556	+	0.582932i	0.983782	−	0.179366i	$-0.0574046\pi$
$2$	7798.16	+	13506.8i	0.336556	+	0.582932i	−0.647227	+	0.762298i	$0.724071\pi$
$3$	−2.39148e6	+	4.14217e6i	−0.288675	+	0.500000i
$3$	−2.39148e6	+	4.14217e6i	−0.288675	+	0.500000i
$4$	1.46813e8	−	2.54287e8i	0.273460	−	0.473647i
$5$	5.50788e9	+	9.53994e9i	0.403571	+	0.699005i	0.994154	−	0.107972i	$-0.0344356\pi$
$5$	5.50788e9	+	9.53994e9i	0.403571	+	0.699005i	−0.590583	+	0.806977i	$0.701102\pi$
$6$	−7.45967e10			−0.388621
$7$	−9.07383e11	+	1.54808e12i	−0.505672	+	0.862726i
$7$	−9.07383e11	+	1.54808e12i	−0.505672	+	0.862726i
$8$	1.29527e13			1.04125
$9$	−1.14384e13	−	1.98119e13i	−0.166667	−	0.288675i
$10$	−8.59027e13	+	1.48788e14i	−0.271648	+	0.470508i
$11$	3.33258e14	−	5.77219e14i	0.264598	−	0.458297i	−0.702860	−	0.711328i	$-0.748094\pi$
$11$	3.33258e14	−	5.77219e14i	0.264598	−	0.458297i	0.967458	+	0.253031i	$0.0814275\pi$
$12$	7.02202e14	+	1.21625e15i	0.157882	+	0.273460i
$13$	1.64328e16			1.15753			0.578764	−	0.815495i	$-0.303535\pi$
$13$	1.64328e16			1.15753			0.578764	+	0.815495i	$0.303535\pi$
$14$	−2.79856e16	−	1.83641e14i	−0.673097	−	0.00441686i
$15$	−5.26881e16			−0.466003
$16$	2.21875e16	+	3.84299e16i	0.0769784	+	0.133330i
$17$	4.16061e17	−	7.20639e17i	0.599305	−	1.03803i	−0.393619	−	0.919274i	$-0.628777\pi$
$17$	4.16061e17	−	7.20639e17i	0.599305	−	1.03803i	0.992924	−	0.118753i	$-0.0378896\pi$
$18$	1.78397e17	−	3.08992e17i	0.112185	−	0.194311i
$19$	7.32936e17	+	1.26948e18i	0.210445	+	0.364502i	0.951854	−	0.306552i	$-0.0991753\pi$
$19$	7.32936e17	+	1.26948e18i	0.210445	+	0.364502i	−0.741409	+	0.671054i	$0.765842\pi$
$20$	3.23451e18			0.441443
$21$	−4.24244e18	−	7.46075e18i	−0.285388	−	0.501883i
$22$	1.03952e19			0.356208
$23$	−5.23590e19	−	9.06884e19i	−0.941755	−	1.63117i	−0.762123	−	0.647433i	$-0.775843\pi$
$23$	−5.23590e19	−	9.06884e19i	−0.941755	−	1.63117i	−0.179632	−	0.983734i	$-0.557491\pi$
$24$	−3.09762e19	+	5.36523e19i	−0.300583	+	0.520625i
$25$	3.24587e19	−	5.62201e19i	0.174261	−	0.301829i
$26$	1.28145e20	+	2.21954e20i	0.389573	+	0.674760i
$27$	1.09419e20			0.192450
$28$	2.60443e20	+	4.58015e20i	0.270347	+	0.475432i
$29$	1.93767e21			1.20923			0.604615	−	0.796518i	$-0.293327\pi$
$29$	1.93767e21			1.20923			0.604615	+	0.796518i	$0.293327\pi$
$30$	−4.10870e20	−	7.11648e20i	−0.156836	−	0.271648i
$31$	−2.56775e21	+	4.44747e21i	−0.609267	+	1.05528i	0.382094	+	0.924123i	$0.375203\pi$
$31$	−2.56775e21	+	4.44747e21i	−0.609267	+	1.05528i	−0.991361	+	0.131158i	$0.958130\pi$
$32$	3.13092e21	−	5.42291e21i	0.468810	−	0.812003i
$33$	1.59396e21	+	2.76082e21i	0.152766	+	0.264598i
$34$	1.29780e22			0.806798
$35$	−1.97664e22	−	1.29707e20i	−0.807124	−	0.00529634i
$36$	−6.71722e21			−0.182307
$37$	−3.46428e22	−	6.00031e22i	−0.631958	−	1.09458i	−0.987151	−	0.159790i	$-0.948918\pi$
$37$	−3.46428e22	−	6.00031e22i	−0.631958	−	1.09458i	0.355193	−	0.934793i	$-0.384415\pi$
$38$	−1.14311e22	+	1.97992e22i	−0.141653	+	0.245350i
$39$	−3.92987e22	+	6.80673e22i	−0.334150	+	0.578764i
$40$	7.13419e22	+	1.23568e23i	0.420218	+	0.727839i
$41$	−3.06990e23			−1.26403			−0.632016	−	0.774955i	$-0.717772\pi$
$41$	−3.06990e23			−1.26403			−0.632016	+	0.774955i	$0.717772\pi$
$42$	6.76877e22	−	1.15482e23i	0.196515	−	0.335273i
$43$	7.58853e23			1.56627			0.783133	−	0.621855i	$-0.213621\pi$
$43$	7.58853e23			1.56627			0.783133	+	0.621855i	$0.213621\pi$
$44$	−9.78531e22	−	1.69487e23i	−0.144714	−	0.250652i
$45$	1.26003e23	−	2.18243e23i	0.134524	−	0.233002i
$46$	8.16607e23	−	1.41441e24i	0.633906	−	1.09796i
$47$	−1.02540e24	−	1.77605e24i	−0.582740	−	1.00934i	−0.995153	−	0.0983382i	$-0.968647\pi$
$47$	−1.02540e24	−	1.77605e24i	−0.582740	−	1.00934i	0.412413	−	0.910997i	$-0.364686\pi$
$48$	−2.12244e23			−0.0888870
$49$	−1.57322e24	−	2.80941e24i	−0.488592	−	0.872513i
$50$	1.01247e24			0.234594
$51$	1.99001e24	+	3.44679e24i	0.346009	+	0.599305i
$52$	2.41254e24	−	4.17864e24i	0.316538	−	0.548260i
$53$	2.42337e24	−	4.19741e24i	0.241224	−	0.417812i	−0.719839	−	0.694141i	$-0.755785\pi$
$53$	2.42337e24	−	4.19741e24i	0.241224	−	0.417812i	0.961063	+	0.276329i	$0.0891179\pi$
$54$	8.53266e23	+	1.47790e24i	0.0647702	+	0.112185i
$55$	7.34218e24			0.427136
$56$	−1.17530e25	+	2.00518e25i	−0.526531	+	0.898314i
$57$	−7.01122e24			−0.243001
$58$	1.51103e25	+	2.61717e25i	0.406974	+	0.704899i
$59$	2.13008e25	−	3.68941e25i	0.447757	−	0.775538i	−0.550483	−	0.834847i	$-0.685556\pi$
$59$	2.13008e25	−	3.68941e25i	0.447757	−	0.775538i	0.998240	+	0.0593086i	$0.0188896\pi$
$60$	−7.73529e24	+	1.33979e25i	−0.127433	+	0.220721i
$61$	2.52540e24	+	4.37412e24i	0.0327376	+	0.0567032i	0.881930	−	0.471380i	$-0.156244\pi$
$61$	2.52540e24	+	4.37412e24i	0.0327376	+	0.0567032i	−0.849192	+	0.528084i	$0.822911\pi$
$62$	−8.00948e25			−0.820210
$63$	4.10495e25	+	2.69366e23i	0.333326	+	0.00218728i
$64$	1.21485e26			0.785080
$65$	9.05097e25	+	1.56767e26i	0.467145	+	0.809119i
$66$	−2.48599e25	+	4.30586e25i	−0.102828	+	0.178104i
$67$	2.06921e26	−	3.58398e26i	0.688209	−	1.19201i	−0.284208	−	0.958763i	$-0.591731\pi$
$67$	2.06921e26	−	3.58398e26i	0.688209	−	1.19201i	0.972417	−	0.233250i	$-0.0749359\pi$
$68$	−1.22166e26	−	2.11598e26i	−0.327772	−	0.567718i
$69$	5.00863e26			1.08744
$70$	−1.52389e26	−	2.67992e26i	−0.268555	−	0.472281i
$71$	7.25060e26			1.04023			0.520113	−	0.854097i	$-0.325890\pi$
$71$	7.25060e26			1.04023			0.520113	+	0.854097i	$0.325890\pi$
$72$	−1.48158e26	−	2.56617e26i	−0.173542	−	0.300583i
$73$	−5.75575e26	+	9.96925e26i	−0.551976	+	0.956051i	0.446155	+	0.894956i	$0.352793\pi$
$73$	−5.75575e26	+	9.96925e26i	−0.551976	+	0.956051i	−0.998132	+	0.0610958i	$0.980540\pi$
$74$	5.40300e26	−	9.35827e26i	0.425378	−	0.736776i
$75$	1.55249e26	+	2.68899e26i	0.100610	+	0.174261i
$76$	4.30418e26			0.230194
$77$	5.91191e26	+	1.03967e27i	0.261585	+	0.460023i
$78$	−1.22583e27			−0.449840
$79$	−2.95293e27	−	5.11463e27i	−0.900867	−	1.56035i	−0.826372	−	0.563125i	$-0.809599\pi$
$79$	−2.95293e27	−	5.11463e27i	−0.900867	−	1.56035i	−0.0744950	−	0.997221i	$-0.523734\pi$
$80$	−2.44412e26	+	4.23335e26i	−0.0621325	+	0.107617i
$81$	−2.61674e26	+	4.53232e26i	−0.0555556	+	0.0962250i
$82$	−2.39396e27	−	4.14645e27i	−0.425417	−	0.736845i
$83$	4.79018e27			0.714035			0.357018	−	0.934098i	$-0.383794\pi$
$83$	4.79018e27			0.714035			0.357018	+	0.934098i	$0.383794\pi$
$84$	−2.52002e27	−	1.65364e25i	−0.315758	−	0.00207200i
$85$	9.16647e27			0.967448
$86$	5.91766e27	+	1.02497e28i	0.527136	+	0.913026i
$87$	−4.63391e27	+	8.02617e27i	−0.349075	+	0.604615i
$88$	4.31658e27	−	7.47654e27i	0.275513	−	0.477202i
$89$	1.04375e28	+	1.80782e28i	0.565510	+	0.979493i	0.997002	+	0.0773757i	$0.0246541\pi$
$89$	1.04375e28	+	1.80782e28i	0.565510	+	0.979493i	−0.431492	+	0.902117i	$0.642013\pi$
$90$	3.93036e27			0.181099
$91$	−1.49108e28	+	2.54393e28i	−0.585330	+	0.998630i
$92$	−3.07479e28			−1.03013
$93$	−1.22815e28	−	2.12721e28i	−0.351761	−	0.609267i
$94$	1.59925e28	−	2.76998e28i	0.392249	−	0.679395i
$95$	−8.07385e27	+	1.39843e28i	−0.169859	+	0.294204i
$96$	1.49751e28	+	2.59376e28i	0.270668	+	0.468810i
$97$	−3.75413e28			−0.583874			−0.291937	−	0.956438i	$-0.594300\pi$
$97$	−3.75413e28			−0.583874			−0.291937	+	0.956438i	$0.594300\pi$
$98$	2.56779e28	−	4.31574e28i	0.344177	−	0.578465i
$99$	−1.52477e28			−0.176399
$100$	−9.53071e27	−	1.65077e28i	−0.0953071	−	0.165077i
$101$	−6.15420e28	+	1.06594e29i	−0.532736	+	0.922725i	0.466534	+	0.884503i	$0.345503\pi$
$101$	−6.15420e28	+	1.06594e29i	−0.532736	+	0.922725i	−0.999269	+	0.0382217i	$0.987831\pi$
$102$	−3.10368e28	+	5.37573e28i	−0.232903	+	0.403399i
$103$	1.00684e29	+	1.74389e29i	0.655873	+	1.13600i	0.981674	+	0.190566i	$0.0610325\pi$
$103$	1.00684e29	+	1.74389e29i	0.655873	+	1.13600i	−0.325802	+	0.945438i	$0.605634\pi$
$104$	2.12848e29			1.20528
$105$	4.78082e28	−	8.15655e28i	0.235645	−	0.402033i
$106$	7.55914e28			0.324741
$107$	−1.07056e29	−	1.85426e29i	−0.401370	−	0.695192i	0.592522	−	0.805554i	$-0.298132\pi$
$107$	−1.07056e29	−	1.85426e29i	−0.401370	−	0.695192i	−0.993891	+	0.110362i	$0.964799\pi$
$108$	1.60641e28	−	2.78239e28i	0.0526275	−	0.0911535i
$109$	−2.68147e29	+	4.64444e29i	−0.768579	+	1.33122i	0.169755	+	0.985486i	$0.445702\pi$
$109$	−2.68147e29	+	4.64444e29i	−0.768579	+	1.33122i	−0.938334	+	0.345731i	$0.887631\pi$
$110$	5.72555e28	+	9.91694e28i	0.143755	+	0.248991i
$111$	3.31391e29			0.729722
$112$	−7.96252e28	−	5.22500e26i	−0.153953	−	0.00101024i
$113$	8.64303e29			1.46902			0.734512	−	0.678596i	$-0.237411\pi$
$113$	8.64303e29			1.46902			0.734512	+	0.678596i	$0.237411\pi$
$114$	−5.46746e28	−	9.46992e28i	−0.0817834	−	0.141653i
$115$	5.76775e29	−	9.99003e29i	0.760129	−	1.31658i
$116$	2.84475e29	−	4.92725e29i	0.330677	−	0.572749i
$117$	−1.87964e29	−	3.25564e29i	−0.192921	−	0.334150i
$118$	6.64429e29			0.602781
$119$	7.38083e29	+	1.29799e30i	0.592481	+	1.04194i
$120$	−6.82452e29			−0.485226
$121$	5.71033e29	+	9.89059e29i	0.359976	+	0.623497i
$122$	−3.93869e28	+	6.82201e28i	−0.0220361	+	0.0381676i
$123$	7.34162e29	−	1.27161e30i	0.364895	−	0.632016i
$124$	7.53957e29	+	1.30589e30i	0.333221	+	0.577156i
$125$	2.76696e30			1.08845
$126$	3.16472e29	+	5.56547e29i	0.110908	+	0.195043i
$127$	5.06077e30			1.58148			0.790738	−	0.612155i	$-0.209697\pi$
$127$	5.06077e30			1.58148			0.790738	+	0.612155i	$0.209697\pi$
$128$	−7.33538e29	−	1.27052e30i	−0.204587	−	0.354355i
$129$	−1.81479e30	+	3.14330e30i	−0.452142	+	0.783133i
$130$	−1.41162e30	+	2.44499e30i	−0.314441	+	0.544627i
$131$	2.46848e30	+	4.27554e30i	0.492036	+	0.852231i	0.999958	−	0.00917198i	$-0.00291957\pi$
$131$	2.46848e30	+	4.27554e30i	0.492036	+	0.852231i	−0.507922	+	0.861403i	$0.669586\pi$
$132$	9.36056e29			0.167101
$133$	−2.63032e30	−	1.72601e28i	−0.420881	−	0.00276182i
$134$	6.45441e30			0.926482
$135$	6.02667e29	+	1.04385e30i	0.0776672	+	0.134524i
$136$	5.38911e30	−	9.33422e30i	0.624026	−	1.08085i
$137$	−4.09515e30	+	7.09300e30i	−0.426404	+	0.738553i	−0.996550	−	0.0829897i	$-0.973553\pi$
$137$	−4.09515e30	+	7.09300e30i	−0.426404	+	0.738553i	0.570146	+	0.821543i	$0.306886\pi$
$138$	3.90581e30	+	6.76506e30i	0.365986	+	0.633906i
$139$	9.80496e30			0.827430			0.413715	−	0.910406i	$-0.364231\pi$
$139$	9.80496e30			0.827430			0.413715	+	0.910406i	$0.364231\pi$
$140$	−2.93494e30	+	5.00730e30i	−0.223225	+	0.380844i
$141$	9.80892e30			0.672890
$142$	5.65413e30	+	9.79325e30i	0.350094	+	0.606381i
$143$	5.47634e30	−	9.48530e30i	0.306280	−	0.530492i
$144$	5.07579e29	−	8.79153e29i	0.0256595	−	0.0444435i
$145$	1.06725e31	+	1.84853e31i	0.488010	+	0.845258i
$146$	−1.79537e31			−0.743084
$147$	1.53994e31	+	2.02110e29i	0.577301	+	0.00757681i
$148$	−2.03440e31			−0.691262
$149$	1.45351e31	+	2.51755e31i	0.447936	+	0.775848i	0.998252	−	0.0591090i	$-0.0188259\pi$
$149$	1.45351e31	+	2.51755e31i	0.447936	+	0.775848i	−0.550316	+	0.834957i	$0.685493\pi$
$150$	−2.42131e30	+	4.19383e30i	−0.0677216	+	0.117297i
$151$	1.33977e31	−	2.32055e31i	0.340303	−	0.589422i	−0.644186	−	0.764869i	$-0.722804\pi$
$151$	1.33977e31	−	2.32055e31i	0.340303	−	0.589422i	0.984489	+	0.175447i	$0.0561371\pi$
$152$	9.49349e30	+	1.64432e31i	0.219126	+	0.379537i
$153$	−1.90363e31			−0.399537
$154$	−9.43241e30	+	1.60926e31i	−0.180124	+	0.307310i
$155$	−5.65714e31			−0.983530
$156$	1.15391e31	+	1.99863e31i	0.182753	+	0.316538i
$157$	8.53573e30	−	1.47843e31i	0.123224	−	0.213430i	−0.797813	−	0.602905i	$-0.794010\pi$
$157$	8.53573e30	−	1.47843e31i	0.123224	−	0.213430i	0.921037	+	0.389474i	$0.127343\pi$
$158$	4.60548e31	−	7.97693e31i	0.606384	−	1.05029i
$159$	1.15909e31	+	2.00761e31i	0.139271	+	0.241224i
$160$	6.89789e31			0.756792
$161$	1.87903e32	+	1.23302e30i	1.88347	+	0.0123593i
$162$	−8.16229e30			−0.0747902
$163$	−8.10093e31	−	1.40312e32i	−0.678914	−	1.17591i	−0.975308	−	0.220848i	$-0.929118\pi$
$163$	−8.10093e31	−	1.40312e32i	−0.678914	−	1.17591i	0.296394	−	0.955066i	$-0.404216\pi$
$164$	−4.50701e31	+	7.80637e31i	−0.345663	+	0.598706i
$165$	−1.75587e31	+	3.04126e31i	−0.123303	+	0.213568i
$166$	3.73546e31	+	6.47001e31i	0.240313	+	0.416234i
$167$	−1.16039e32			−0.684250			−0.342125	−	0.939655i	$-0.611147\pi$
$167$	−1.16039e32			−0.684250			−0.342125	+	0.939655i	$0.611147\pi$
$168$	−5.49510e31	−	9.66368e31i	−0.297160	−	0.522586i
$169$	6.84974e31			0.339873
$170$	7.14816e31	+	1.23810e32i	0.325600	+	0.563956i
$171$	1.67672e31	−	2.90417e31i	0.0701484	−	0.121501i
$172$	1.11409e32	−	1.92967e32i	0.428312	−	0.741857i
$173$	1.76246e31	+	3.05267e31i	0.0622946	+	0.107897i	0.895491	−	0.445080i	$-0.146825\pi$
$173$	1.76246e31	+	3.05267e31i	0.0622946	+	0.107897i	−0.833196	+	0.552978i	$0.813492\pi$
$174$	−1.44544e32			−0.469933
$175$	5.75809e31	+	1.01262e32i	0.172277	+	0.302966i
$176$	2.95766e31			0.0814732
$177$	1.01881e32	+	1.76463e32i	0.258513	+	0.447757i
$178$	−1.62786e32	+	2.81954e32i	−0.380652	+	0.659308i
$179$	−1.77165e31	+	3.06858e31i	−0.0381952	+	0.0661560i	−0.884491	−	0.466557i	$-0.845494\pi$
$179$	−1.77165e31	+	3.06858e31i	−0.0381952	+	0.0661560i	0.846296	+	0.532713i	$0.178828\pi$
$180$	−3.69977e31	−	6.40818e31i	−0.0735738	−	0.127433i
$181$	−6.46103e32			−1.18567			−0.592833	−	0.805325i	$-0.701991\pi$
$181$	−6.46103e32			−1.18567			−0.592833	+	0.805325i	$0.701991\pi$
$182$	−4.59880e32	−	3.01773e30i	−0.779129	−	0.00511264i
$183$	−2.41578e31			−0.0378021
$184$	−6.78190e32	−	1.17466e33i	−0.980602	−	1.69845i
$185$	3.81617e32	−	6.60980e32i	0.510079	−	0.883483i
$186$	1.91545e32	−	3.31767e32i	0.236774	−	0.410105i
$187$	−2.77311e32	−	4.80317e32i	−0.317150	−	0.549319i
$188$	−6.02168e32			−0.637425
$189$	−9.92849e31	+	1.69390e32i	−0.0973166	+	0.166032i
$190$	−2.51845e32			−0.228668
$191$	1.03634e32	+	1.79500e32i	0.0872005	+	0.151036i	0.906327	−	0.422578i	$-0.138875\pi$
$191$	1.03634e32	+	1.79500e32i	0.0872005	+	0.151036i	−0.819126	+	0.573613i	$0.805541\pi$
$192$	−2.90530e32	+	5.03213e32i	−0.226633	+	0.392540i
$193$	2.28027e32	−	3.94955e32i	0.164970	−	0.285737i	−0.771674	−	0.636018i	$-0.780580\pi$
$193$	2.28027e32	−	3.94955e32i	0.164970	−	0.285737i	0.936645	+	0.350281i	$0.113914\pi$
$194$	−2.92753e32	−	5.07063e32i	−0.196506	−	0.340358i
$195$	−8.65810e32			−0.539412
$196$	−9.45366e32	−	1.24075e31i	−0.546874	−	0.00717747i
$197$	−2.17949e33			−1.17110			−0.585552	−	0.810635i	$-0.699122\pi$
$197$	−2.17949e33			−1.17110			−0.585552	+	0.810635i	$0.699122\pi$
$198$	−1.18904e32	−	2.05948e32i	−0.0593679	−	0.102828i
$199$	8.46752e32	−	1.46662e33i	0.392995	−	0.680687i	−0.599848	−	0.800114i	$-0.704772\pi$
$199$	8.46752e32	−	1.46662e33i	0.392995	−	0.680687i	0.992843	+	0.119427i	$0.0381057\pi$
$200$	4.20427e32	−	7.28201e32i	0.181450	−	0.314280i
$201$	9.89697e32	+	1.71421e33i	0.397337	+	0.688209i
$202$	−1.91966e33			−0.717181
$203$	−1.75821e33	+	2.99968e33i	−0.611474	+	1.04323i
$204$	1.16864e33			0.378479
$205$	−1.69086e33	−	2.92866e33i	−0.510127	−	0.883565i
$206$	−1.57029e33	+	2.71983e33i	−0.441475	+	0.764658i
$207$	−1.19781e33	+	2.07466e33i	−0.313918	+	0.543722i
$208$	3.64602e32	+	6.31509e32i	0.0891047	+	0.154334i
$209$	9.77026e32			0.222733
$210$	1.47451e33	+	9.67570e30i	0.313666	+	0.00205827i
$211$	2.58849e33			0.513986			0.256993	−	0.966413i	$-0.417268\pi$
$211$	2.58849e33			0.513986			0.256993	+	0.966413i	$0.417268\pi$
$212$	−7.11565e32	−	1.23247e33i	−0.131930	−	0.228510i
$213$	−1.73397e33	+	3.00332e33i	−0.300288	+	0.520113i
$214$	1.66967e33	−	2.89196e33i	0.270166	−	0.467942i
$215$	4.17968e33	+	7.23941e33i	0.632099	+	1.09483i
$216$	1.41727e33			0.200389
$217$	−4.55513e33	−	8.01065e33i	−0.602330	−	1.05926i
$218$	−8.36420e33			−1.03468
$219$	−2.75296e33	−	4.76826e33i	−0.318684	−	0.551976i
$220$	1.07793e33	−	1.86702e33i	0.116805	−	0.202312i
$221$	6.83703e33	−	1.18421e34i	0.693713	−	1.20155i
$222$	2.58424e33	+	4.47603e33i	0.245592	+	0.425378i
$223$	6.22780e33			0.554516			0.277258	−	0.960795i	$-0.410574\pi$
$223$	6.22780e33			0.554516			0.277258	+	0.960795i	$0.410574\pi$
$224$	5.55417e33	+	9.76757e33i	0.463472	+	0.815062i
$225$	−1.48510e33			−0.116174
$226$	6.73997e33	+	1.16740e34i	0.494408	+	0.856340i
$227$	8.69861e33	−	1.50664e34i	0.598515	−	1.03666i	−0.394526	−	0.918885i	$-0.629091\pi$
$227$	8.69861e33	−	1.50664e34i	0.598515	−	1.03666i	0.993041	−	0.117773i	$-0.0375755\pi$
$228$	−1.02934e33	+	1.78287e33i	−0.0664512	+	0.115097i
$229$	−2.86536e33	−	4.96295e33i	−0.173606	−	0.300694i	0.766072	−	0.642755i	$-0.222209\pi$
$229$	−2.86536e33	−	4.96295e33i	−0.173606	−	0.300694i	−0.939678	+	0.342060i	$0.888875\pi$
$230$	1.79911e34			1.02330
$231$	−5.72032e33	−	3.75367e31i	−0.305525	−	0.00200485i
$232$	2.50981e34			1.25911
$233$	7.82283e33	+	1.35495e34i	0.368725	+	0.638651i	0.989367	−	0.145444i	$-0.0464610\pi$
$233$	7.82283e33	+	1.35495e34i	0.368725	+	0.638651i	−0.620641	+	0.784095i	$0.713128\pi$
$234$	2.93155e33	−	5.07760e33i	0.129858	−	0.224920i
$235$	1.12956e34	−	1.95645e34i	0.470354	−	0.814676i
$236$	−6.25448e33	−	1.08331e34i	−0.244888	−	0.424158i
$237$	2.82476e34			1.04023
$238$	−1.17761e34	+	2.00911e34i	−0.407975	+	0.696046i
$239$	−8.58106e33			−0.279751			−0.139875	−	0.990169i	$-0.544670\pi$
$239$	−8.58106e33			−0.279751			−0.139875	+	0.990169i	$0.544670\pi$
$240$	−1.16902e33	−	2.02480e33i	−0.0358722	−	0.0621325i
$241$	−2.52531e34	+	4.37397e34i	−0.729572	+	1.26365i	0.227493	+	0.973780i	$0.426947\pi$
$241$	−2.52531e34	+	4.37397e34i	−0.729572	+	1.26365i	−0.957064	+	0.289875i	$0.906386\pi$
$242$	−8.90601e33	+	1.54257e34i	−0.242304	+	0.419683i
$243$	−1.25158e33	−	2.16780e33i	−0.0320750	−	0.0555556i
$244$	1.48304e33			0.0358098
$245$	1.81365e34	−	3.04823e34i	0.412709	−	0.693649i
$246$	2.29004e34			0.491230
$247$	1.20442e34	+	2.08611e34i	0.243596	+	0.421921i
$248$	−3.32592e34	+	5.76067e34i	−0.634400	+	1.09881i
$249$	−1.14556e34	+	1.98418e34i	−0.206124	+	0.357018i
$250$	2.15772e34	+	3.73728e34i	0.366324	+	0.634491i
$251$	2.49017e34			0.398988			0.199494	−	0.979899i	$-0.436070\pi$
$251$	2.49017e34			0.398988			0.199494	+	0.979899i	$0.436070\pi$
$252$	6.09509e33	−	1.03988e34i	0.0921875	−	0.157281i
$253$	−6.97962e34			−0.996745
$254$	3.94647e34	+	6.83548e34i	0.532255	+	0.921892i
$255$	−2.19215e34	+	3.79691e34i	−0.279278	+	0.483724i
$256$	4.40514e34	−	7.62993e34i	0.530250	−	0.918419i
$257$	−1.11145e32	−	1.92509e32i	−0.00126433	−	0.00218988i	0.865393	−	0.501095i	$-0.167069\pi$
$257$	−1.11145e32	−	1.92509e32i	−0.00126433	−	0.00218988i	−0.866657	+	0.498905i	$0.833736\pi$
$258$	−5.66079e34			−0.608684
$259$	1.24324e35	+	8.15814e32i	1.26389	+	0.00829363i
$260$	5.31520e34			0.510983
$261$	−2.21638e34	−	3.83889e34i	−0.201538	−	0.349075i
$262$	−3.84993e34	+	6.66827e34i	−0.331195	+	0.573647i
$263$	7.96280e33	−	1.37920e34i	0.0648198	−	0.112271i	−0.831794	−	0.555084i	$-0.812686\pi$
$263$	7.96280e33	−	1.37920e34i	0.0648198	−	0.112271i	0.896614	+	0.442813i	$0.146019\pi$
$264$	2.06461e34	+	3.57601e34i	0.159067	+	0.275513i
$265$	5.33907e34			0.389404
$266$	−2.02785e34	−	3.56618e34i	−0.140040	−	0.246274i
$267$	−9.98443e34			−0.652995
$268$	−6.07574e34	−	1.05235e35i	−0.376396	−	0.651936i
$269$	9.32233e34	−	1.61468e35i	0.547163	−	0.947714i	−0.451305	−	0.892370i	$-0.649041\pi$
$269$	9.32233e34	−	1.61468e35i	0.547163	−	0.947714i	0.998467	−	0.0553437i	$-0.0176255\pi$
$270$	−9.39939e33	+	1.62802e34i	−0.0522787	+	0.0905494i
$271$	−8.29130e34	−	1.43609e35i	−0.437087	−	0.757057i	0.560377	−	0.828238i	$-0.310656\pi$
$271$	−8.29130e34	−	1.43609e35i	−0.437087	−	0.757057i	−0.997463	+	0.0711813i	$0.977323\pi$
$272$	3.69254e34			0.184534
$273$	−6.97150e34	−	1.22601e35i	−0.330345	−	0.580945i
$274$	−1.27738e35			−0.574035
$275$	−2.16342e34	−	3.74715e34i	−0.0922183	−	0.159727i
$276$	7.35332e34	−	1.27363e35i	0.297373	−	0.515065i
$277$	−1.40538e35	+	2.43419e35i	−0.539308	+	0.934109i	0.459633	+	0.888109i	$0.347981\pi$
$277$	−1.40538e35	+	2.43419e35i	−0.539308	+	0.934109i	−0.998941	+	0.0460002i	$0.985353\pi$
$278$	7.64606e34	+	1.32434e35i	0.278476	+	0.482335i
$279$	1.17484e35			0.406178
$280$	−2.56028e35	−	1.68005e33i	−0.840418	−	0.00551482i
$281$	−5.02564e35			−1.56657			−0.783285	−	0.621663i	$-0.786457\pi$
$281$	−5.02564e35			−1.56657			−0.783285	+	0.621663i	$0.786457\pi$
$282$	7.64915e34	+	1.32487e35i	0.226465	+	0.392249i
$283$	−4.61704e34	+	7.99695e34i	−0.129855	+	0.224916i	−0.923620	−	0.383308i	$-0.874785\pi$
$283$	−4.61704e34	+	7.99695e34i	−0.129855	+	0.224916i	0.793765	+	0.608225i	$0.208118\pi$
$284$	1.06448e35	−	1.84374e35i	0.284461	−	0.492701i
$285$	−3.86170e34	−	6.68866e34i	−0.0980681	−	0.169859i
$286$	1.70822e35			0.412321
$287$	2.78557e35	−	4.75246e35i	0.639186	−	1.09051i
$288$	−1.43251e35			−0.312540
$289$	−1.05230e35	−	1.82263e35i	−0.218333	−	0.378164i
$290$	−1.66451e35	+	2.88302e35i	−0.328485	+	0.568953i
$291$	8.97794e34	−	1.55502e35i	0.168550	−	0.291937i
$292$	1.69004e35	+	2.92723e35i	0.301887	+	0.522884i
$293$	−3.20589e34			−0.0544965			−0.0272482	−	0.999629i	$-0.508674\pi$
$293$	−3.20589e34			−0.0544965			−0.0272482	+	0.999629i	$0.508674\pi$
$294$	1.17357e35	+	2.09573e35i	0.189877	+	0.339077i
$295$	4.69290e35			0.722807
$296$	−4.48717e35	−	7.77201e35i	−0.658026	−	1.13973i
$297$	3.64647e34	−	6.31587e34i	0.0509219	−	0.0881993i
$298$	−2.26693e35	+	3.92644e35i	−0.301511	+	0.522232i
$299$	−8.60403e35	−	1.49026e36i	−1.09011	−	1.88812i
$300$	9.11702e34			0.110051
$301$	−6.88570e35	+	1.17477e36i	−0.792016	+	1.35126i
$302$	4.17910e35			0.458123
$303$	−2.94353e35	−	5.09835e35i	−0.307575	−	0.532736i
$304$	−3.25240e34	+	5.63333e34i	−0.0323994	+	0.0561175i
$305$	−2.78192e34	+	4.81842e34i	−0.0264239	+	0.0457675i
$306$	−1.48448e35	−	2.57119e35i	−0.134466	−	0.232903i
$307$	5.69289e34			0.0491843			0.0245921	−	0.999698i	$-0.492171\pi$
$307$	5.69289e34			0.0491843			0.0245921	+	0.999698i	$0.492171\pi$
$308$	3.51169e35	+	2.30437e33i	0.289422	+	0.00189918i
$309$	−9.63134e35			−0.757336
$310$	−4.41153e35	−	7.64099e35i	−0.331013	−	0.573331i
$311$	−7.79118e35	+	1.34947e36i	−0.557927	+	0.966358i	0.439742	+	0.898124i	$0.355070\pi$
$311$	−7.79118e35	+	1.34947e36i	−0.557927	+	0.966358i	−0.997669	+	0.0682340i	$0.978264\pi$
$312$	−5.09024e35	+	8.81655e35i	−0.347934	+	0.602639i
$313$	4.60184e35	+	7.97062e35i	0.300288	+	0.520115i	0.976201	−	0.216867i	$-0.0695838\pi$
$313$	4.60184e35	+	7.97062e35i	0.300288	+	0.520115i	−0.675913	+	0.736982i	$0.736250\pi$
$314$	2.66252e35			0.165887
$315$	2.23526e35	+	3.93093e35i	0.132992	+	0.233879i
$316$	−1.73411e36			−0.985405
$317$	1.84965e35	+	3.20369e35i	0.100399	+	0.173896i	0.911849	−	0.410525i	$-0.134655\pi$
$317$	1.84965e35	+	3.20369e35i	0.100399	+	0.173896i	−0.811450	+	0.584422i	$0.801321\pi$
$318$	−1.80776e35	+	3.13113e35i	−0.0937447	+	0.162371i
$319$	6.45744e35	−	1.11846e36i	0.319960	−	0.554186i
$320$	6.69126e35	+	1.15896e36i	0.316835	+	0.548775i
$321$	1.02409e36			0.463462
$322$	1.44864e36	+	2.54758e36i	0.626688	+	1.10209i
$323$	1.21979e36			0.504483
$324$	7.68342e34	+	1.33081e35i	0.0303845	+	0.0526275i
$325$	5.33386e35	−	9.23851e35i	0.201712	−	0.349376i
$326$	1.26345e36	−	2.18835e36i	0.456985	−	0.791521i
$327$	−1.28254e36	−	2.22142e36i	−0.443739	−	0.768579i
$328$	−3.97634e36			−1.31617
$329$	3.67990e36	+	2.41475e34i	1.16545	+	0.00764771i
$330$	−5.47702e35			−0.165994
$331$	1.45773e35	+	2.52487e35i	0.0422837	+	0.0732375i	0.886393	−	0.462934i	$-0.153203\pi$
$331$	1.45773e35	+	2.52487e35i	0.0422837	+	0.0732375i	−0.844109	+	0.536172i	$0.819870\pi$
$332$	7.03261e35	−	1.21808e36i	0.195260	−	0.338201i
$333$	−7.92516e35	+	1.37268e36i	−0.210653	+	0.364861i
$334$	−9.04889e35	−	1.56731e36i	−0.230288	−	0.398871i
$335$	4.55879e36			1.11096
$336$	1.92587e35	−	3.28572e35i	0.0449477	−	0.0766851i
$337$	3.15056e36			0.704295			0.352147	−	0.935945i	$-0.385452\pi$
$337$	3.15056e36			0.704295			0.352147	+	0.935945i	$0.385452\pi$
$338$	5.34154e35	+	9.25181e35i	0.114386	+	0.198123i
$339$	−2.06697e36	+	3.58009e36i	−0.424070	+	0.734512i
$340$	1.34576e36	−	2.33092e36i	0.264559	−	0.458229i
$341$	1.71144e36	+	2.96431e36i	0.322422	+	0.558451i
$342$	5.23014e35			0.0944354
$343$	5.77671e36	+	1.13733e35i	0.999806	+	0.0196844i
$344$	9.82919e36			1.63087
$345$	2.75870e36	+	4.77820e36i	0.438861	+	0.760129i
$346$	−2.74878e35	+	4.76103e35i	−0.0419312	+	0.0726270i
$347$	2.06772e35	−	3.58139e35i	0.0302492	−	0.0523932i	−0.850504	−	0.525968i	$-0.823703\pi$
$347$	2.06772e35	−	3.58139e35i	0.0302492	−	0.0523932i	0.880754	+	0.473575i	$0.157037\pi$
$348$	1.36064e36	+	2.35669e36i	0.190916	+	0.330677i
$349$	−9.32663e36			−1.25533			−0.627663	−	0.778486i	$-0.715988\pi$
$349$	−9.32663e36			−1.25533			−0.627663	+	0.778486i	$0.715988\pi$
$350$	−9.18699e35	+	1.56739e36i	−0.118628	+	0.202391i
$351$	1.79806e36			0.222767
$352$	−2.08680e36	−	3.61445e36i	−0.248092	−	0.429708i
$353$	3.38290e36	−	5.85936e36i	0.385972	−	0.668524i	−0.605931	−	0.795517i	$-0.707199\pi$
$353$	3.38290e36	−	5.85936e36i	0.385972	−	0.668524i	0.991904	+	0.126993i	$0.0405327\pi$
$354$	−1.58897e36	+	2.75218e36i	−0.174008	+	0.301391i
$355$	3.99355e36	+	6.91703e36i	0.419805	+	0.727124i
$356$	6.12943e36			0.618579
$357$	−7.14162e36	−	4.68633e34i	−0.692003	−	0.00454092i
$358$	−5.52623e35			−0.0514192
$359$	1.54111e36	+	2.66927e36i	0.137709	+	0.238519i	0.926629	−	0.375977i	$-0.122693\pi$
$359$	1.54111e36	+	2.66927e36i	0.137709	+	0.238519i	−0.788920	+	0.614496i	$0.789359\pi$
$360$	1.63207e36	−	2.82684e36i	0.140073	−	0.242613i
$361$	4.99052e36	−	8.64384e36i	0.411426	−	0.712610i
$362$	−5.03842e36	−	8.72679e36i	−0.399043	−	0.691163i
$363$	−5.46247e36			−0.415664
$364$	4.27979e36	+	7.52645e36i	0.312934	+	0.550326i
$365$	−1.26808e37			−0.891046
$366$	−1.88386e35	−	3.26295e35i	−0.0127225	−	0.0220361i
$367$	−5.07246e36	+	8.78576e36i	−0.329276	+	0.570324i	−0.982368	−	0.186955i	$-0.940138\pi$
$367$	−5.07246e36	+	8.78576e36i	−0.329276	+	0.570324i	0.653092	+	0.757279i	$0.273471\pi$
$368$	2.32343e36	−	4.02430e36i	0.144989	−	0.251129i
$369$	3.51147e36	+	6.08205e36i	0.210672	+	0.364895i
$370$	1.19036e37			0.686681
$371$	4.29901e36	+	7.56024e36i	0.238477	+	0.419386i
$372$	−7.21231e36			−0.384770
$373$	−2.84993e35	−	4.93623e35i	−0.0146237	−	0.0253289i	0.858621	−	0.512611i	$-0.171322\pi$
$373$	−2.84993e35	−	4.93623e35i	−0.0146237	−	0.0253289i	−0.873245	+	0.487282i	$0.837988\pi$
$374$	4.32503e36	−	7.49118e36i	0.213477	−	0.369753i
$375$	−6.61715e36	+	1.14612e37i	−0.314208	+	0.544224i
$376$	−1.32817e37	−	2.30046e37i	−0.606778	−	1.05097i
$377$	3.18413e37			1.39972
$378$	−3.06215e36	−	2.00938e34i	−0.129538	−	0.000850025i
$379$	−3.92856e37			−1.59943			−0.799714	−	0.600381i	$-0.795016\pi$
$379$	−3.92856e37			−1.59943			−0.799714	+	0.600381i	$0.795016\pi$
$380$	2.37069e36	+	4.10616e36i	0.0928994	+	0.160907i
$381$	−1.21027e37	+	2.09626e37i	−0.456533	+	0.790738i
$382$	−1.61631e36	+	2.79953e36i	−0.0586957	+	0.101664i
$383$	−1.95150e37	−	3.38010e37i	−0.682317	−	1.18181i	−0.974272	−	0.225376i	$-0.927639\pi$
$383$	−1.95150e37	−	3.38010e37i	−0.682317	−	1.18181i	0.291954	−	0.956432i	$-0.405694\pi$
$384$	7.01698e36			0.236237
$385$	−6.66217e36	+	1.13663e37i	−0.215991	+	0.368501i
$386$	7.11278e36			0.222087
$387$	−8.68007e36	−	1.50343e37i	−0.261044	−	0.452142i
$388$	−5.51154e36	+	9.54628e36i	−0.159666	+	0.276550i
$389$	5.05878e35	−	8.76207e35i	0.0141181	−	0.0244533i	−0.858880	−	0.512177i	$-0.828839\pi$
$389$	5.05878e35	−	8.76207e35i	0.0141181	−	0.0244533i	0.872998	+	0.487724i	$0.162173\pi$
$390$	−6.75173e36	−	1.16943e37i	−0.181542	−	0.314441i
$391$	−8.71382e37			−2.25759
$392$	−2.03774e37	−	3.63894e37i	−0.508746	−	0.908504i
$393$	−2.36134e37			−0.568154
$394$	−1.69960e37	−	2.94380e37i	−0.394142	−	0.682673i
$395$	3.25288e37	−	5.63415e37i	0.727127	−	1.25942i
$396$	−2.23856e36	+	3.87731e36i	−0.0482380	+	0.0835507i
$397$	2.79794e37	+	4.84617e37i	0.581267	+	1.00678i	0.995330	+	0.0965356i	$0.0307762\pi$
$397$	2.79794e37	+	4.84617e37i	0.581267	+	1.00678i	−0.414062	+	0.910248i	$0.635891\pi$
$398$	2.64124e37			0.529059
$399$	6.36186e36	−	1.08540e37i	0.122879	−	0.209643i
$400$	2.88071e36			0.0536574
$401$	−7.13235e36	−	1.23536e37i	−0.128127	−	0.221922i	0.794824	−	0.606840i	$-0.207563\pi$
$401$	−7.13235e36	−	1.23536e37i	−0.128127	−	0.221922i	−0.922951	+	0.384918i	$0.874230\pi$
$402$	−1.54356e37	+	2.67353e37i	−0.267452	+	0.463241i
$403$	−4.21952e37	+	7.30842e37i	−0.705244	+	1.22152i
$404$	1.80703e37	+	3.12987e37i	0.291364	+	0.504658i
$405$	−5.76508e36			−0.0896824
$406$	−5.42268e37	−	3.55836e35i	−0.813929	−	0.00534100i
$407$	−4.61799e37			−0.668858
$408$	2.57760e37	+	4.46453e37i	0.360282	+	0.624026i
$409$	6.51917e37	−	1.12915e38i	0.879436	−	1.52323i	0.0274755	−	0.999622i	$-0.491253\pi$
$409$	6.51917e37	−	1.12915e38i	0.879436	−	1.52323i	0.851961	−	0.523606i	$-0.175413\pi$
$410$	2.63713e37	−	4.56764e37i	0.343372	−	0.594738i
$411$	−1.95870e37	−	3.39256e37i	−0.246184	−	0.426404i
$412$	5.91267e37			0.717421
$413$	3.77872e37	+	6.64526e37i	0.442659	+	0.778460i
$414$	−3.73627e37			−0.422604
$415$	2.63838e37	+	4.56980e37i	0.288164	+	0.499114i
$416$	5.14496e37	−	8.91133e37i	0.542661	−	0.939917i
$417$	−2.34484e37	+	4.06138e37i	−0.238858	+	0.413715i
$418$	7.61900e36	+	1.31965e37i	0.0749622	+	0.129838i
$419$	1.86689e38			1.77426			0.887128	−	0.461523i	$-0.152697\pi$
$419$	1.86689e38			1.77426			0.887128	+	0.461523i	$0.152697\pi$
$420$	−1.37222e37	−	2.41319e37i	−0.125982	−	0.221553i
$421$	−8.55234e37			−0.758568			−0.379284	−	0.925280i	$-0.623830\pi$
$421$	−8.55234e37			−0.758568			−0.379284	+	0.925280i	$0.623830\pi$
$422$	2.01855e37	+	3.49622e37i	0.172985	+	0.299619i
$423$	−2.34579e37	+	4.06302e37i	−0.194247	+	0.336445i
$424$	3.13892e37	−	5.43677e37i	0.251174	−	0.435047i
$425$	−2.70096e37	−	4.67820e37i	−0.208871	−	0.361776i
$426$	−5.40871e37			−0.404254
$427$	−9.06300e36	−	5.94713e34i	−0.0654738	−	0.000429639i
$428$	−6.28686e37			−0.439035
$429$	2.61932e37	+	4.53679e37i	0.176831	+	0.306280i
$430$	−6.51875e37	+	1.12908e38i	−0.425473	+	0.736941i
$431$	8.97214e37	−	1.55402e38i	0.566208	−	0.980700i	−0.430729	−	0.902482i	$-0.641743\pi$
$431$	8.97214e37	−	1.55402e38i	0.566208	−	0.980700i	0.996936	−	0.0782189i	$-0.0249233\pi$
$432$	2.42773e36	+	4.20496e36i	0.0148145	+	0.0256595i
$433$	−1.30851e38			−0.772153			−0.386076	−	0.922467i	$-0.626170\pi$
$433$	−1.30851e38			−0.772153			−0.386076	+	0.922467i	$0.626170\pi$
$434$	7.26766e37	−	1.23993e38i	0.414757	−	0.707616i
$435$	−1.02092e38			−0.563506
$436$	7.87348e37	+	1.36373e38i	0.420352	+	0.728070i
$437$	7.67516e37	−	1.32938e38i	0.396375	−	0.686542i
$438$	4.29360e37	−	7.43673e37i	0.214510	−	0.371542i
$439$	−1.12339e37	−	1.94576e37i	−0.0542992	−	0.0940490i	0.837598	−	0.546287i	$-0.183959\pi$
$439$	−1.12339e37	−	1.94576e37i	−0.0542992	−	0.0940490i	−0.891897	+	0.452238i	$0.850626\pi$
$440$	9.51010e37			0.444755
$441$	−3.76646e37	+	6.33036e37i	−0.170441	+	0.286463i
$442$	2.13265e38			0.933892
$443$	1.29836e38	+	2.24883e38i	0.550228	+	0.953022i	0.998258	+	0.0590039i	$0.0187924\pi$
$443$	1.29836e38	+	2.24883e38i	0.550228	+	0.953022i	−0.448030	+	0.894019i	$0.647874\pi$
$444$	4.86525e37	−	8.42686e37i	0.199550	−	0.345631i
$445$	−1.14977e38	+	1.99146e38i	−0.456447	+	0.790589i
$446$	4.85654e37	+	8.41177e37i	0.186626	+	0.323245i
$447$	−1.39041e38			−0.517232
$448$	−1.10234e38	+	1.88069e38i	−0.396993	+	0.677309i
$449$	4.56649e38			1.59225			0.796124	−	0.605134i	$-0.206880\pi$
$449$	4.56649e38			1.59225			0.796124	+	0.605134i	$0.206880\pi$
$450$	−1.15811e37	−	2.00590e37i	−0.0390991	−	0.0677216i
$451$	−1.02307e38	+	1.77200e38i	−0.334460	+	0.579302i
$452$	1.26891e38	−	2.19781e38i	0.401720	−	0.695799i
$453$	6.40809e37	+	1.10991e38i	0.196474	+	0.340303i
$454$	2.71332e38			0.805734
$455$	−3.24816e38	−	2.13144e36i	−0.934270	−	0.00613067i
$456$	−9.08142e37			−0.253025
$457$	3.59837e38	+	6.23256e38i	0.971228	+	1.68222i	0.691859	+	0.722032i	$0.256792\pi$
$457$	3.59837e38	+	6.23256e38i	0.971228	+	1.68222i	0.279369	+	0.960184i	$0.409875\pi$
$458$	4.46890e37	−	7.74037e37i	0.116856	−	0.202401i
$459$	4.55250e37	−	7.88516e37i	0.115336	−	0.199768i
$460$	−1.69356e38	−	2.93333e38i	−0.415731	−	0.720066i
$461$	−2.26588e38			−0.538981			−0.269491	−	0.963003i	$-0.586855\pi$
$461$	−2.26588e38			−0.538981			−0.269491	+	0.963003i	$0.586855\pi$
$462$	−4.41009e37	−	7.75559e37i	−0.101657	−	0.178775i
$463$	−6.70455e38			−1.49777			−0.748885	−	0.662699i	$-0.769411\pi$
$463$	−6.70455e38			−1.49777			−0.748885	+	0.662699i	$0.769411\pi$
$464$	4.29921e37	+	7.44645e37i	0.0930846	+	0.161227i
$465$	1.35290e38	−	2.34329e38i	0.283921	−	0.491765i
$466$	−1.22007e38	+	2.11323e38i	−0.248193	+	0.429883i
$467$	1.67466e38	+	2.90059e38i	0.330241	+	0.571994i	0.982559	−	0.185951i	$-0.0595367\pi$
$467$	1.67466e38	+	2.90059e38i	0.330241	+	0.571994i	−0.652318	+	0.757945i	$0.726203\pi$
$468$	−1.10382e38			−0.211026
$469$	3.67073e38	+	6.45535e38i	0.680372	+	1.19650i
$470$	3.52339e38			0.633201
$471$	4.08261e37	+	7.07130e37i	0.0711435	+	0.123224i
$472$	2.75903e38	−	4.77878e38i	0.466227	−	0.807529i
$473$	2.52894e38	−	4.38025e38i	0.414430	−	0.717814i
$474$	2.20279e38	+	3.81534e38i	0.350096	+	0.606384i
$475$	9.51605e37			0.146690
$476$	4.38423e38	+	2.87693e36i	0.655531	+	0.00430159i
$477$	−1.10878e38			−0.160816
$478$	−6.69164e37	−	1.15903e38i	−0.0941517	−	0.163076i
$479$	2.59893e38	−	4.50148e38i	0.354756	−	0.614456i	−0.632320	−	0.774707i	$-0.717897\pi$
$479$	2.59893e38	−	4.50148e38i	0.354756	−	0.614456i	0.987076	+	0.160252i	$0.0512306\pi$
$480$	−1.64962e38	+	2.85723e38i	−0.218467	+	0.378396i
$481$	−5.69277e38	−	9.86016e38i	−0.731509	−	1.26701i
$482$	−7.87711e38			−0.982166
$483$	−4.54474e38	+	7.75378e38i	−0.549890	+	0.938166i
$484$	3.35340e38			0.393757
$485$	−2.06773e38	−	3.58141e38i	−0.235634	−	0.408131i
$486$	1.95200e37	−	3.38096e37i	0.0215901	−	0.0373951i
$487$	−1.75775e38	+	3.04451e38i	−0.188706	+	0.326849i	−0.944819	−	0.327592i	$-0.893763\pi$
$487$	−1.75775e38	+	3.04451e38i	−0.188706	+	0.326849i	0.756113	+	0.654441i	$0.227096\pi$
$488$	3.27107e37	+	5.66566e37i	0.0340881	+	0.0590422i
$489$	7.74930e38			0.783942
$490$	5.53150e38	+	7.25984e36i	0.543250	+	0.00712991i
$491$	−1.54175e39			−1.47005			−0.735026	−	0.678039i	$-0.762830\pi$
$491$	−1.54175e39			−1.47005			−0.735026	+	0.678039i	$0.762830\pi$
$492$	−2.15569e38	−	3.73376e38i	−0.199569	−	0.345663i
$493$	8.06190e38	−	1.39636e39i	0.724698	−	1.25521i
$494$	−1.87845e38	+	3.25356e38i	−0.163967	+	0.284000i
$495$	−8.39827e37	−	1.45462e38i	−0.0711893	−	0.123303i
$496$	−2.27888e38			−0.187602
$497$	−6.57907e38	+	1.12245e39i	−0.526014	+	0.897431i
$498$	−3.57332e38			−0.277489
$499$	−1.01641e39	−	1.76047e39i	−0.766672	−	1.32791i	−0.939358	−	0.342937i	$-0.888578\pi$
$499$	−1.01641e39	−	1.76047e39i	−0.766672	−	1.32791i	0.172687	−	0.984977i	$-0.444755\pi$
$500$	4.06226e38	−	7.03604e38i	0.297648	−	0.515541i
$501$	2.77505e38	−	4.80653e38i	0.197526	−	0.342125i
$502$	1.94187e38	+	3.36342e38i	0.134282	+	0.232583i
$503$	7.94800e38			0.533976			0.266988	−	0.963700i	$-0.413972\pi$
$503$	7.94800e38			0.533976			0.266988	+	0.963700i	$0.413972\pi$
$504$	5.31701e38	+	3.48902e36i	0.347076	+	0.00227751i
$505$	−1.35586e39			−0.859986
$506$	−5.44281e38	−	9.42723e38i	−0.335460	−	0.581034i
$507$	−1.63811e38	+	2.83728e38i	−0.0981130	+	0.169937i
$508$	7.42986e38	−	1.28689e39i	0.432471	−	0.749062i
$509$	−1.08887e39	−	1.88598e39i	−0.615981	−	1.06691i	−0.990211	−	0.139575i	$-0.955426\pi$
$509$	−1.08887e39	−	1.88598e39i	−0.615981	−	1.06691i	0.374230	−	0.927336i	$-0.377907\pi$
$510$	−6.83788e38			−0.375971
$511$	−1.02106e39	−	1.79563e39i	−0.545691	−	0.959653i
$512$	5.86449e38			0.304660
$513$	8.01971e37	+	1.38905e38i	0.0405002	+	0.0701484i
$514$	1.73345e36	−	3.00242e36i	0.000851033	−	0.00147403i
$515$	−1.10911e39	+	1.92103e39i	−0.529382	+	0.916917i
$516$	5.32868e38	+	9.22955e38i	0.247286	+	0.428312i
$517$	−1.36689e39			−0.616767
$518$	9.58480e38	+	1.68558e39i	0.420534	+	0.739552i
$519$	−1.68596e38			−0.0719316
$520$	1.17234e39	+	2.03056e39i	0.486415	+	0.842495i
$521$	−2.07265e39	+	3.58993e39i	−0.836332	+	1.44857i	0.0566094	+	0.998396i	$0.481971\pi$
$521$	−2.07265e39	+	3.58993e39i	−0.836332	+	1.44857i	−0.892941	+	0.450173i	$0.851362\pi$
$522$	3.45674e38	−	5.98726e38i	0.135658	−	0.234966i
$523$	−1.50020e39	−	2.59843e39i	−0.572632	−	0.991828i	−0.996294	−	0.0860077i	$-0.972589\pi$
$523$	−1.50020e39	−	2.59843e39i	−0.572632	−	0.991828i	0.423662	−	0.905820i	$-0.360744\pi$
$524$	1.44962e39			0.538209
$525$	−5.57148e38	−	3.65600e36i	−0.201215	−	0.00132037i
$526$	2.48381e38			0.0872619
$527$	2.13668e39	+	3.70084e39i	0.730274	+	1.26487i
$528$	−7.07320e37	+	1.22512e38i	−0.0235193	+	0.0407366i
$529$	−3.93740e39	+	6.81978e39i	−1.27380	+	2.20629i
$530$	4.16349e38	+	7.21137e38i	0.131056	+	0.226996i
$531$	−9.74590e38			−0.298505
$532$	−3.90554e38	+	6.66323e38i	−0.116402	+	0.198594i
$533$	−5.04469e39			−1.46315
$534$	−7.78601e38	−	1.34858e39i	−0.219769	−	0.380652i
$535$	1.17930e39	−	2.04261e39i	0.323962	−	0.561119i
$536$	2.68018e39	−	4.64222e39i	0.716597	−	1.24118i
$537$	−8.47374e37	−	1.46769e38i	−0.0220520	−	0.0381952i
$538$	2.90788e39			0.736603
$539$	−2.14593e39	−	2.81644e37i	−0.529150	−	0.00694486i
$540$	3.53917e38			0.0849557
$541$	3.73639e38	+	6.47161e38i	0.0873155	+	0.151235i	0.906376	−	0.422473i	$-0.138838\pi$
$541$	3.73639e38	+	6.47161e38i	0.0873155	+	0.151235i	−0.819060	+	0.573708i	$0.805505\pi$
$542$	1.29314e39	−	2.23978e39i	0.294208	−	0.509584i
$543$	1.54515e39	−	2.67627e39i	0.342273	−	0.592833i
$544$	−2.60531e39	−	4.51252e39i	−0.561920	−	0.973275i
$545$	−5.90768e39			−1.24070
$546$	1.11230e39	−	1.89769e39i	0.227472	−	0.388089i
$547$	2.00150e39			0.398602			0.199301	−	0.979938i	$-0.436133\pi$
$547$	2.00150e39			0.398602			0.199301	+	0.979938i	$0.436133\pi$
$548$	1.20244e39	+	2.08269e39i	0.233209	+	0.403930i
$549$	5.77730e37	−	1.00066e38i	0.0109125	−	0.0189011i
$550$	3.37414e38	−	5.84418e38i	0.0620732	−	0.107514i
$551$	1.42019e39	+	2.45984e39i	0.254477	+	0.440766i
$552$	6.48752e39			1.13230
$553$	1.05973e40	+	6.95395e37i	1.80169	+	0.0118227i
$554$	−4.38375e39			−0.726029
$555$	1.82526e39	+	3.16145e39i	0.294494	+	0.510079i
$556$	1.43950e39	−	2.49328e39i	0.226269	−	0.391910i
$557$	−5.39383e38	+	9.34238e38i	−0.0826032	+	0.143073i	−0.904367	−	0.426755i	$-0.859657\pi$
$557$	−5.39383e38	+	9.34238e38i	−0.0826032	+	0.143073i	0.821764	+	0.569828i	$0.192990\pi$
$558$	9.16156e38	+	1.58683e39i	0.136702	+	0.236774i
$559$	1.24701e40			1.81300
$560$	−4.33582e38	−	7.62497e38i	−0.0614250	−	0.108022i
$561$	2.65274e39			0.366213
$562$	−3.91907e39	−	6.78803e39i	−0.527238	−	0.913203i
$563$	−2.89780e39	+	5.01913e39i	−0.379924	+	0.658047i	−0.991051	−	0.133485i	$-0.957383\pi$
$563$	−2.89780e39	+	5.01913e39i	−0.379924	+	0.658047i	0.611127	+	0.791532i	$0.290716\pi$
$564$	1.44008e39	−	2.49429e39i	0.184009	−	0.318713i
$565$	4.76048e39	+	8.24540e39i	0.592855	+	1.02685i
$566$	−1.44018e39			−0.174814
$567$	−4.64203e38	−	8.16348e38i	−0.0549229	−	0.0965875i
$568$	9.39148e39			1.08314
$569$	2.66605e38	+	4.61774e38i	0.0299737	+	0.0519160i	0.880623	−	0.473817i	$-0.157124\pi$
$569$	2.66605e38	+	4.61774e38i	0.0299737	+	0.0519160i	−0.850649	+	0.525733i	$0.823791\pi$
$570$	6.02283e38	−	1.04318e39i	0.0660108	−	0.114334i
$571$	−2.01986e39	+	3.49850e39i	−0.215823	+	0.373816i	−0.953527	−	0.301308i	$-0.902577\pi$
$571$	−2.01986e39	+	3.49850e39i	−0.215823	+	0.373816i	0.737704	+	0.675124i	$0.235910\pi$
$572$	−1.60800e39	−	2.78513e39i	−0.167511	−	0.290137i
$573$	−9.91358e38			−0.100690
$574$	8.59129e39	+	5.63760e37i	0.850816	+	0.00558305i
$575$	−6.79802e39			−0.656445
$576$	−1.38960e39	−	2.40685e39i	−0.130847	−	0.226633i
$577$	−7.39010e39	+	1.28000e40i	−0.678580	+	1.17533i	0.296829	+	0.954931i	$0.404071\pi$
$577$	−7.39010e39	+	1.28000e40i	−0.678580	+	1.17533i	−0.975409	+	0.220404i	$0.929262\pi$
$578$	1.64119e39	−	2.84263e39i	0.146962	−	0.254546i
$579$	1.09065e39	+	1.88906e39i	0.0952457	+	0.164970i
$580$	6.26743e39			0.533806
$581$	−4.34653e39	+	7.41560e39i	−0.361068	+	0.616017i
$582$	2.80045e39			0.226906
$583$	−1.61522e39	−	2.79764e39i	−0.127655	−	0.221104i
$584$	−7.45525e39	+	1.29129e40i	−0.574746	+	0.995489i
$585$	2.07057e39	−	3.58634e39i	0.155715	−	0.269706i
$586$	−2.50000e38	−	4.33013e38i	−0.0183411	−	0.0317677i
$587$	2.36675e40			1.69395			0.846974	−	0.531635i	$-0.178422\pi$
$587$	2.36675e40			1.69395			0.846974	+	0.531635i	$0.178422\pi$
$588$	2.31222e39	−	3.88620e39i	0.161458	−	0.271365i
$589$	−7.52798e39			−0.512869
$590$	3.65960e39	+	6.33861e39i	0.243265	+	0.421347i
$591$	5.21222e39	−	9.02784e39i	0.338068	−	0.585552i
$592$	1.53727e39	−	2.66264e39i	0.0972942	−	0.168518i
$593$	−4.83486e39	−	8.37423e39i	−0.298601	−	0.517192i	0.677215	−	0.735785i	$-0.263187\pi$
$593$	−4.83486e39	−	8.37423e39i	−0.298601	−	0.517192i	−0.975816	+	0.218593i	$0.929853\pi$
$594$	1.13743e39			0.0685522
$595$	−8.31749e39	+	1.41905e40i	−0.489211	+	0.834642i
$596$	8.53574e39			0.489971
$597$	4.04999e39	+	7.01479e39i	0.226896	+	0.392995i
$598$	1.34191e40	−	2.32426e40i	0.733764	−	1.27092i
$599$	−8.18376e39	+	1.41747e40i	−0.436781	+	0.756527i	−0.997439	−	0.0715203i	$-0.977215\pi$
$599$	−8.18376e39	+	1.41747e40i	−0.436781	+	0.756527i	0.560658	+	0.828047i	$0.310548\pi$
$600$	2.01089e39	+	3.48296e39i	0.104760	+	0.181450i
$601$	−3.45425e40			−1.75660			−0.878302	−	0.478107i	$-0.841323\pi$
$601$	−3.45425e40			−1.75660			−0.878302	+	0.478107i	$0.841323\pi$
$602$	−2.12369e40	−	1.39357e38i	−1.05425	−	0.00691797i
$603$	−9.46738e39			−0.458806
$604$	−3.93392e39	−	6.81375e39i	−0.186119	−	0.322367i
$605$	−6.29037e39	+	1.08952e40i	−0.290552	+	0.503250i
$606$	4.59083e39	−	7.95155e39i	0.207032	−	0.358590i
$607$	5.44657e39	+	9.43374e39i	0.239821	+	0.415382i	0.960663	−	0.277718i	$-0.0895779\pi$
$607$	5.44657e39	+	9.43374e39i	0.239821	+	0.415382i	−0.720842	+	0.693100i	$0.756245\pi$
$608$	9.17905e39			0.394635
$609$	−8.22045e39	−	1.44565e40i	−0.345100	−	0.606893i
$610$	−8.67754e38			−0.0355725
$611$	−1.68502e40	−	2.91853e40i	−0.674538	−	1.16833i
$612$	−2.79477e39	+	4.84069e39i	−0.109257	+	0.189239i
$613$	1.28086e40	−	2.21852e40i	0.489019	−	0.847005i	−0.510901	−	0.859639i	$-0.670688\pi$
$613$	1.28086e40	−	2.21852e40i	0.489019	−	0.847005i	0.999920	+	0.0126340i	$0.00402165\pi$
$614$	4.43940e38	+	7.68927e38i	0.0165533	+	0.0286711i
$615$	1.61747e40			0.589043
$616$	7.65752e39	+	1.34665e40i	0.272375	+	0.478999i
$617$	−4.94405e39			−0.171770			−0.0858851	−	0.996305i	$-0.527372\pi$
$617$	−4.94405e39			−0.171770			−0.0858851	+	0.996305i	$0.527372\pi$
$618$	−7.51067e39	−	1.30089e40i	−0.254886	−	0.441475i
$619$	−4.86889e39	+	8.43317e39i	−0.161405	+	0.279561i	−0.935373	−	0.353664i	$-0.884936\pi$
$619$	−4.86889e39	+	8.43317e39i	−0.161405	+	0.279561i	0.773968	+	0.633225i	$0.218269\pi$
$620$	−8.30542e39	+	1.43854e40i	−0.268957	+	0.465846i
$621$	−5.72907e39	−	9.92304e39i	−0.181241	−	0.313918i
$622$	−2.43027e40			−0.751094
$623$	−3.74574e40	−	2.45795e38i	−1.13100	−	0.00742159i
$624$	−3.48776e39			−0.102889
$625$	9.19420e39	+	1.59248e40i	0.265005	+	0.459002i
$626$	−7.17717e39	+	1.24312e40i	−0.202128	+	0.350095i
$627$	−2.33654e39	+	4.04701e39i	−0.0642976	+	0.111367i
$628$	−2.50631e39	−	4.34106e39i	−0.0673939	−	0.116730i
$629$	−5.76541e40			−1.51494
$630$	−3.56634e39	+	6.08452e39i	−0.0915766	+	0.156239i
$631$	6.58480e40			1.65241			0.826204	−	0.563372i	$-0.190496\pi$
$631$	6.58480e40			1.65241			0.826204	+	0.563372i	$0.190496\pi$
$632$	−3.82484e40	−	6.62482e40i	−0.938028	−	1.62471i
$633$	−6.19034e39	+	1.07220e40i	−0.148375	+	0.256993i
$634$	−2.88477e39	+	4.99657e39i	−0.0675799	+	0.117052i
$635$	2.78741e40	+	4.82794e40i	0.638237	+	1.10546i
$636$	6.80679e39			0.152340
$637$	−2.58523e40	−	4.61663e40i	−0.565559	−	1.00996i
$638$	2.01424e40			0.430737
$639$	−8.29353e39	−	1.43648e40i	−0.173371	−	0.300288i
$640$	8.08048e39	−	1.39958e40i	0.165131	−	0.286015i
$641$	1.46014e40	−	2.52903e40i	0.291711	−	0.505257i	−0.682504	−	0.730882i	$-0.739109\pi$
$641$	1.46014e40	−	2.52903e40i	0.291711	−	0.505257i	0.974214	+	0.225625i	$0.0724423\pi$
$642$	7.98599e39	+	1.38321e40i	0.155981	+	0.270166i
$643$	−6.70587e40			−1.28055			−0.640274	−	0.768146i	$-0.721179\pi$
$643$	−6.70587e40			−1.28055			−0.640274	+	0.768146i	$0.721179\pi$
$644$	2.79001e40	−	4.76003e40i	0.520908	−	0.888720i
$645$	−3.99825e40			−0.729885
$646$	9.51208e39	+	1.64754e40i	0.169787	+	0.294079i
$647$	3.50790e39	−	6.07586e39i	0.0612259	−	0.106046i	−0.833788	−	0.552085i	$-0.813832\pi$
$647$	3.50790e39	−	6.07586e39i	0.0612259	−	0.106046i	0.895014	+	0.446039i	$0.147166\pi$
$648$	−3.38938e39	+	5.87058e39i	−0.0578472	+	0.100194i
$649$	−1.41973e40	−	2.45905e40i	−0.236951	−	0.410411i
$650$	1.66377e40			0.271550
$651$	4.40750e40	+	2.89220e38i	0.703506	+	0.00461640i
$652$	−4.75729e40			−0.742625
$653$	3.56338e40	+	6.17196e40i	0.544028	+	0.942284i	0.998667	+	0.0516086i	$0.0164348\pi$
$653$	3.56338e40	+	6.17196e40i	0.544028	+	0.942284i	−0.454639	+	0.890676i	$0.650232\pi$
$654$	2.00029e40	−	3.46460e40i	0.298686	−	0.517339i
$655$	−2.71923e40	+	4.70984e40i	−0.397143	+	0.687871i
$656$	−6.81134e39	−	1.17976e40i	−0.0973032	−	0.168534i
$657$	2.63346e40			0.367984
$658$	2.83703e40	+	4.98920e40i	0.387782	+	0.681954i
$659$	7.51671e40			1.00505			0.502527	−	0.864562i	$-0.332404\pi$
$659$	7.51671e40			1.00505			0.502527	+	0.864562i	$0.332404\pi$
$660$	5.15569e39	+	8.92992e39i	0.0674372	+	0.116805i
$661$	2.09941e40	−	3.63629e40i	0.268644	−	0.465305i	−0.699868	−	0.714272i	$-0.746758\pi$
$661$	2.09941e40	−	3.63629e40i	0.268644	−	0.465305i	0.968512	+	0.248968i	$0.0800912\pi$
$662$	−2.27353e39	+	3.93787e39i	−0.0284616	+	0.0492970i
$663$	3.27013e40	+	5.66403e40i	0.400515	+	0.693713i
$664$	6.20457e40			0.743489
$665$	−1.43228e40	−	2.51881e40i	−0.167925	−	0.295313i
$666$	−2.47207e40			−0.283585
$667$	−1.01455e41	−	1.75724e41i	−1.13880	−	1.97246i
$668$	−1.70360e40	+	2.95072e40i	−0.187115	+	0.324093i
$669$	−1.48937e40	+	2.57966e40i	−0.160075	+	0.277258i
$670$	3.55502e40	+	6.15747e40i	0.373901	+	0.647616i
$671$	3.36643e39			0.0346492
$672$	−5.37417e40	−	3.52653e38i	−0.541324	−	0.00355216i
$673$	1.22560e41			1.20817			0.604087	−	0.796918i	$-0.293538\pi$
$673$	1.22560e41			1.20817			0.604087	+	0.796918i	$0.293538\pi$
$674$	2.45686e40	+	4.25540e40i	0.237034	+	0.410556i
$675$	3.55160e39	−	6.15154e39i	0.0335366	−	0.0580871i
$676$	1.00563e40	−	1.74180e40i	0.0929419	−	0.160980i
$677$	−5.64538e39	−	9.77809e39i	−0.0510690	−	0.0884542i	0.839361	−	0.543575i	$-0.182930\pi$
$677$	−5.64538e39	−	9.77809e39i	−0.0510690	−	0.0884542i	−0.890430	+	0.455120i	$0.849596\pi$
$678$	−6.44741e40			−0.570893
$679$	3.40643e40	−	5.81170e40i	0.295249	−	0.503723i
$680$	1.18730e41			1.00736
$681$	4.16052e40	+	7.20623e40i	0.345553	+	0.598515i
$682$	−2.66922e40	+	4.62323e40i	−0.217026	+	0.375899i
$683$	−2.04128e40	+	3.53560e40i	−0.162481	+	0.281425i	−0.935758	−	0.352643i	$-0.885283\pi$
$683$	−2.04128e40	+	3.53560e40i	−0.162481	+	0.281425i	0.773277	+	0.634069i	$0.218616\pi$
$684$	−4.92329e39	−	8.52739e39i	−0.0383656	−	0.0664512i
$685$	−9.02224e40			−0.688337
$686$	4.35115e40	+	7.89118e40i	0.325016	+	0.589444i
$687$	2.74098e40			0.200463
$688$	1.68371e40	+	2.91627e40i	0.120569	+	0.208831i
$689$	3.98227e40	−	6.89750e40i	0.279224	−	0.483630i
$690$	−4.30255e40	+	7.45223e40i	−0.295402	+	0.511652i
$691$	−2.68348e40	−	4.64793e40i	−0.180413	−	0.312484i	0.761608	−	0.648038i	$-0.224410\pi$
$691$	−2.68348e40	−	4.64793e40i	−0.180413	−	0.312484i	−0.942021	+	0.335553i	$0.891077\pi$
$692$	1.03501e40			0.0681404
$693$	1.38355e40	−	2.36048e40i	0.0891998	−	0.152184i
$694$	6.44976e39			0.0407222
$695$	5.40046e40	+	9.35387e40i	0.333927	+	0.578378i
$696$	−6.00216e40	+	1.03960e41i	−0.363474	+	0.629556i
$697$	−1.27727e41	+	2.21229e41i	−0.757541	+	1.31210i
$698$	−7.27306e40	−	1.25973e41i	−0.422487	−	0.731769i
$699$	−7.48327e40			−0.425767
$700$	3.42033e40	+	2.24442e38i	0.190610	+	0.00125078i
$701$	1.22269e41			0.667428			0.333714	−	0.942674i	$-0.391698\pi$
$701$	1.22269e41			0.667428			0.333714	+	0.942674i	$0.391698\pi$
$702$	1.40215e40	+	2.42860e40i	0.0749734	+	0.129858i
$703$	5.07819e40	−	8.79569e40i	0.265985	−	0.460699i
$704$	4.04859e40	−	7.01236e40i	0.207730	−	0.359800i
$705$	5.40264e40	+	9.35765e40i	0.271559	+	0.470354i
$706$	1.05522e41			0.519605
$707$	−1.09174e41	−	1.91994e41i	−0.526669	−	0.926201i
$708$	5.98299e40			0.282772
$709$	−4.45861e40	−	7.72254e40i	−0.206457	−	0.357593i	0.744139	−	0.668025i	$-0.232860\pi$
$709$	−4.45861e40	−	7.72254e40i	−0.206457	−	0.357593i	−0.950596	+	0.310431i	$0.899527\pi$
$710$	−6.22846e40	+	1.07880e41i	−0.282576	+	0.489435i
$711$	−6.75536e40	+	1.17006e41i	−0.300289	+	0.520116i
$712$	1.35193e41	+	2.34162e41i	0.588838	+	1.01990i
$713$	5.37779e41			2.29512
$714$	−5.50585e40	−	9.68260e40i	−0.230251	−	0.404919i
$715$	1.20652e41			0.494422
$716$	5.20202e39	+	9.01016e39i	0.0208897	+	0.0361821i
$717$	2.05215e40	−	3.55442e40i	0.0807571	−	0.139875i
$718$	−2.40356e40	+	4.16308e40i	−0.0926936	+	0.160550i
$719$	−1.77406e40	−	3.07276e40i	−0.0670501	−	0.116134i	0.830551	−	0.556942i	$-0.188025\pi$
$719$	−1.77406e40	−	3.07276e40i	−0.0670501	−	0.116134i	−0.897602	+	0.440808i	$0.854692\pi$
$720$	1.11827e40			0.0414216
$721$	−3.61328e41	−	2.37103e39i	−1.31172	−	0.00860748i
$722$	1.55667e41			0.553871
$723$	−1.20785e41	−	2.09206e41i	−0.421218	−	0.729572i
$724$	−9.48563e40	+	1.64296e41i	−0.324233	+	0.561588i
$725$	6.28942e40	−	1.08936e41i	0.210722	−	0.364981i
$726$	−4.25972e40	−	7.37805e40i	−0.139894	−	0.242304i
$727$	5.54331e41			1.78452			0.892258	−	0.451527i	$-0.149120\pi$
$727$	5.54331e41			1.78452			0.892258	+	0.451527i	$0.149120\pi$
$728$	−1.93135e41	+	3.29507e41i	−0.609475	+	1.03982i
$729$	1.19725e40			0.0370370
$730$	−9.88869e40	−	1.71277e41i	−0.299887	−	0.519419i
$731$	3.15729e41	−	5.46859e41i	0.938670	−	1.62582i
$732$	−3.54668e39	+	6.14302e39i	−0.0103374	+	0.0179049i
$733$	−4.46798e40	−	7.73877e40i	−0.127674	−	0.221138i	0.795101	−	0.606477i	$-0.207418\pi$
$733$	−4.46798e40	−	7.73877e40i	−0.127674	−	0.221138i	−0.922775	+	0.385339i	$0.874085\pi$
$734$	−1.58223e41			−0.443280
$735$	8.28899e40	+	1.48022e41i	0.227685	+	0.406594i
$736$	−6.55727e41			−1.76602
$737$	−1.37916e41	−	2.38878e41i	−0.364197	−	0.630808i
$738$	−5.47660e40	+	9.48575e40i	−0.141806	+	0.245615i
$739$	−2.03803e41	+	3.52998e41i	−0.517448	+	0.896247i	0.482346	+	0.875981i	$0.339785\pi$
$739$	−2.03803e41	+	3.52998e41i	−0.517448	+	0.896247i	−0.999795	+	0.0202660i	$0.993549\pi$
$740$	−1.12053e41	−	1.94081e41i	−0.278973	−	0.483195i
$741$	−1.15214e41			−0.281281
$742$	−6.85903e40	+	1.17022e41i	−0.164213	+	0.280163i
$743$	3.23620e41			0.759797			0.379899	−	0.925028i	$-0.375959\pi$
$743$	3.23620e41			0.759797			0.379899	+	0.925028i	$0.375959\pi$
$744$	−1.59078e41	−	2.75531e41i	−0.366271	−	0.634400i
$745$	−1.60115e41	+	2.77327e41i	−0.361548	+	0.626219i
$746$	4.44484e39	−	7.69870e39i	0.00984336	−	0.0170492i
$747$	−5.47920e40	−	9.49025e40i	−0.119006	−	0.206124i
$748$	−1.62851e41			−0.346911
$749$	3.84195e41	+	2.52108e39i	0.802722	+	0.00526746i
$750$	−2.06406e41			−0.422994
$751$	9.44602e40	+	1.63610e41i	0.189876	+	0.328875i	0.945209	−	0.326467i	$-0.105858\pi$
$751$	9.44602e40	+	1.63610e41i	0.189876	+	0.328875i	−0.755333	+	0.655341i	$0.772525\pi$
$752$	4.55022e40	−	7.88121e40i	0.0897167	−	0.155394i
$753$	−5.95520e40	+	1.03147e41i	−0.115178	+	0.199494i
$754$	2.48303e41	+	4.30074e41i	0.471084	+	0.815941i
$755$	2.95173e41			0.549345
$756$	2.84974e40	+	5.01155e40i	0.0520282	+	0.0914968i
$757$	−1.29429e41			−0.231815			−0.115907	−	0.993260i	$-0.536978\pi$
$757$	−1.29429e41			−0.231815			−0.115907	+	0.993260i	$0.536978\pi$
$758$	−3.06355e41	−	5.30623e41i	−0.538297	−	0.932358i
$759$	1.66916e41	−	2.89108e41i	0.287735	−	0.498372i
$760$	−1.04578e41	+	1.81135e41i	−0.176866	+	0.306340i
$761$	1.24150e41	+	2.15035e41i	0.206001	+	0.356805i	0.950451	−	0.310873i	$-0.100622\pi$
$761$	1.24150e41	+	2.15035e41i	0.206001	+	0.356805i	−0.744450	+	0.667678i	$0.767288\pi$
$762$	−3.77517e41			−0.614595
$763$	−4.75686e41	−	8.36542e41i	−0.759827	−	1.33623i
$764$	6.08593e40			0.0953836
$765$	−1.04850e41	−	1.81605e41i	−0.161241	−	0.279278i
$766$	3.04362e41	−	5.27171e41i	0.459276	−	0.795489i
$767$	3.50032e41	−	6.06272e41i	0.518292	−	0.897708i
$768$	2.10697e41	+	3.64937e41i	0.306140	+	0.530250i
$769$	−6.44060e41			−0.918320			−0.459160	−	0.888354i	$-0.651850\pi$
$769$	−6.44060e41			−0.918320			−0.459160	+	0.888354i	$0.651850\pi$
$770$	−2.05475e41	−	1.34833e39i	−0.287504	−	0.00188660i
$771$	1.06320e39			0.00145992
$772$	−6.69548e40	−	1.15969e41i	−0.0902258	−	0.156276i
$773$	−2.50960e41	+	4.34676e41i	−0.331896	+	0.574862i	−0.982884	−	0.184227i	$-0.941022\pi$
$773$	−2.50960e41	+	4.34676e41i	−0.331896	+	0.574862i	0.650987	+	0.759089i	$0.274355\pi$
$774$	1.35377e41	−	2.34480e41i	0.175712	−	0.304342i
$775$	1.66691e41	+	2.88718e41i	0.212343	+	0.367789i
$776$	−4.86260e41			−0.607959
$777$	−3.00698e41	+	5.13021e41i	−0.369000	+	0.629550i
$778$	1.57797e40			0.0190061
$779$	−2.25004e41	−	3.89718e41i	−0.266009	−	0.460742i
$780$	−1.27112e41	+	2.20165e41i	−0.147508	+	0.255491i
$781$	2.41632e41	−	4.18519e41i	0.275242	−	0.476733i
$782$	−6.79517e41	−	1.17696e42i	−0.759806	−	1.31602i
$783$	2.12018e41			0.232717
$784$	7.30594e40	−	1.22792e41i	0.0787215	−	0.132309i
$785$	1.88055e41			0.198919
$786$	−1.84141e41	−	3.18941e41i	−0.191216	−	0.331195i
$787$	−7.08452e40	+	1.22707e41i	−0.0722232	+	0.125094i	−0.899875	−	0.436147i	$-0.856343\pi$
$787$	−7.08452e40	+	1.22707e41i	−0.0722232	+	0.125094i	0.827652	+	0.561241i	$0.189676\pi$
$788$	−3.19978e41	+	5.54218e41i	−0.320250	+	0.554690i
$789$	3.80858e40	+	6.59666e40i	0.0374237	+	0.0648198i
$790$	1.01466e42			0.978875
$791$	−7.84254e41	+	1.33801e42i	−0.742844	+	1.26736i
$792$	−1.97499e41			−0.183675
$793$	4.14992e40	+	7.18788e40i	0.0378947	+	0.0656356i
$794$	−4.36375e41	+	7.55824e41i	−0.391258	+	0.677678i
$795$	−1.27683e41	+	2.21153e41i	−0.112411	+	0.194702i
$796$	−2.48628e41	−	4.30637e41i	−0.214937	−	0.372282i
$797$	8.89368e40			0.0754981			0.0377490	−	0.999287i	$-0.487981\pi$
$797$	8.89368e40			0.0754981			0.0377490	+	0.999287i	$0.487981\pi$
$798$	1.96213e41	+	1.28755e39i	0.163563	+	0.00107330i
$799$	−1.70652e42			−1.39696
$800$	−2.03251e41	−	3.52041e41i	−0.163391	−	0.283001i
$801$	2.38776e41	−	4.13572e41i	0.188503	−	0.326498i
$802$	1.11238e41	−	1.92670e41i	0.0862435	−	0.149378i
$803$	3.83630e41	+	6.64466e41i	0.292104	+	0.505938i
$804$	5.81201e41			0.434624
$805$	1.02318e42	+	1.79937e42i	0.751474	+	1.32154i
$806$	−1.31618e42			−0.949416
$807$	4.45884e41	+	7.72294e41i	0.315905	+	0.547163i
$808$	−7.97134e41	+	1.38068e42i	−0.554711	+	0.960788i
$809$	7.56512e40	−	1.31032e41i	0.0517085	−	0.0895618i	−0.839013	−	0.544112i	$-0.816867\pi$
$809$	7.56512e40	−	1.31032e41i	0.0517085	−	0.0895618i	0.890721	+	0.454550i	$0.150200\pi$
$810$	−4.49570e40	−	7.78678e40i	−0.0301831	−	0.0522787i
$811$	2.44731e42			1.61394			0.806968	−	0.590595i	$-0.201107\pi$
$811$	2.44731e42			1.61394			0.806968	+	0.590595i	$0.201107\pi$
$812$	5.04652e41	+	8.87482e41i	0.326911	+	0.574906i
$813$	7.93140e41			0.504704
$814$	−3.60118e41	−	6.23743e41i	−0.225108	−	0.389899i
$815$	8.92380e41	−	1.54565e42i	0.547980	−	0.949129i
$816$	−8.83066e40	+	1.52952e41i	−0.0532704	+	0.0922671i
$817$	5.56191e41	+	9.63351e41i	0.329613	+	0.570906i
$818$	2.03350e42			1.18392
$819$	6.74556e41	+	4.42643e39i	0.385835	+	0.00253185i
$820$	−9.92963e41			−0.557998
$821$	−5.70388e41	−	9.87941e41i	−0.314916	−	0.545451i	0.664504	−	0.747285i	$-0.268643\pi$
$821$	−5.70388e41	−	9.87941e41i	−0.314916	−	0.545451i	−0.979420	+	0.201834i	$0.935310\pi$
$822$	3.05484e41	−	5.29115e41i	0.165710	−	0.287017i
$823$	9.21922e41	−	1.59682e42i	0.491356	−	0.851054i	−0.508594	−	0.861006i	$-0.669835\pi$
$823$	9.21922e41	−	1.59682e42i	0.491356	−	0.851054i	0.999950	+	0.00995232i	$0.00316797\pi$
$824$	1.30412e42	+	2.25881e42i	0.682927	+	1.18287i
$825$	2.06951e41			0.106484
$826$	−6.02891e41	+	1.02859e42i	−0.304809	+	0.520035i
$827$	2.46894e42			1.22654			0.613269	−	0.789874i	$-0.289854\pi$
$827$	2.46894e42			1.22654			0.613269	+	0.789874i	$0.289854\pi$
$828$	3.51707e41	+	6.09174e41i	0.171688	+	0.297373i
$829$	1.57993e42	−	2.73652e42i	0.757875	−	1.31268i	−0.186057	−	0.982539i	$-0.559571\pi$
$829$	1.57993e42	−	2.73652e42i	0.757875	−	1.31268i	0.943932	−	0.330139i	$-0.107096\pi$
$830$	−4.11490e41	+	7.12721e41i	−0.193966	+	0.335960i
$831$	−6.72189e41	−	1.16426e42i	−0.311370	−	0.539308i
$832$	1.99634e42			0.908753
$833$	−2.67913e42	−	3.51623e40i	−1.19851	−	0.0157299i
$834$	−7.31418e41			−0.321557
$835$	−6.39128e41	−	1.10700e42i	−0.276143	−	0.478294i
$836$	1.43440e41	−	2.48446e41i	0.0609087	−	0.105497i
$837$	−2.80960e41	+	4.86638e41i	−0.117254	+	0.203089i
$838$	1.45583e42	+	2.52158e42i	0.597136	+	1.03427i
$839$	9.17769e41			0.369986			0.184993	−	0.982740i	$-0.440774\pi$
$839$	9.17769e41			0.369986			0.184993	+	0.982740i	$0.440774\pi$
$840$	6.19245e41	−	1.05649e42i	0.245365	−	0.418617i
$841$	1.18688e42			0.462238
$842$	−6.66925e41	−	1.15515e42i	−0.255301	−	0.442194i
$843$	1.20187e42	−	2.08171e42i	0.452230	−	0.783285i
$844$	3.80024e41	−	6.58221e41i	0.140555	−	0.243448i
$845$	3.77276e41	+	6.53461e41i	0.137163	+	0.237573i
$846$	−7.31713e41			−0.261499
$847$	−2.04929e42	−	1.34474e40i	−0.719937	−	0.00472422i
$848$	2.15075e41			0.0742761
$849$	−2.20832e41	−	3.82491e41i	−0.0749721	−	0.129855i
$850$	4.21250e41	−	7.29627e41i	0.140594	−	0.243515i
$851$	−3.62772e42	+	6.28340e42i	−1.19030	+	2.06166i
$852$	5.09139e41	+	8.81854e41i	0.164234	+	0.284461i
$853$	2.49876e42			0.792434			0.396217	−	0.918157i	$-0.370323\pi$
$853$	2.49876e42			0.792434			0.396217	+	0.918157i	$0.370323\pi$
$854$	−6.98714e40	−	1.22876e41i	−0.0217851	−	0.0383114i
$855$	3.69408e41			0.113239
$856$	−1.38666e42	−	2.40176e42i	−0.417926	−	0.723869i
$857$	5.35074e41	−	9.26775e41i	0.158559	−	0.274633i	−0.775790	−	0.630991i	$-0.782648\pi$
$857$	5.35074e41	−	9.26775e41i	0.158559	−	0.274633i	0.934349	+	0.356358i	$0.115982\pi$
$858$	−4.08517e41	+	7.07572e41i	−0.119027	+	0.206160i
$859$	−1.54277e42	−	2.67215e42i	−0.441977	−	0.765527i	0.555859	−	0.831277i	$-0.312389\pi$
$859$	−1.54277e42	−	2.67215e42i	−0.441977	−	0.765527i	−0.997836	+	0.0657499i	$0.979056\pi$
$860$	2.45452e42			0.691416
$861$	1.30239e42	+	2.29038e42i	0.360740	+	0.634397i
$862$	2.79865e42			0.762242
$863$	1.98596e42	+	3.43979e42i	0.531882	+	0.921246i	0.999307	+	0.0372137i	$0.0118482\pi$
$863$	1.98596e42	+	3.43979e42i	0.531882	+	0.921246i	−0.467426	+	0.884032i	$0.654818\pi$
$864$	3.42582e41	−	5.93369e41i	0.0902225	−	0.156270i
$865$	−1.94148e41	+	3.36275e41i	−0.0502805	+	0.0870884i
$866$	−1.02040e42	−	1.76738e42i	−0.259873	−	0.450112i
$867$	1.00662e42			0.252109
$868$	−2.70576e42	−	1.77552e40i	−0.666428	−	0.00437309i
$869$	−3.93635e42			−0.953469
$870$	−7.96131e41	−	1.37894e42i	−0.189651	−	0.328485i
$871$	3.40028e42	−	5.88946e42i	0.796621	−	1.37979i
$872$	−3.47322e42	+	6.01580e42i	−0.800283	+	1.38613i
$873$	4.29412e41	+	7.43763e41i	0.0973123	+	0.168550i
$874$	2.39408e42			0.533610
$875$	−2.51069e42	+	4.28349e42i	−0.550398	+	0.939033i
$876$	−1.61668e42			−0.348590
$877$	−3.35591e42	−	5.81261e42i	−0.711731	−	1.23275i	−0.964207	−	0.265152i	$-0.914578\pi$
$877$	−3.35591e42	−	5.81261e42i	−0.711731	−	1.23275i	0.252475	−	0.967603i	$-0.418755\pi$
$878$	1.75207e41	−	3.03467e41i	0.0365494	−	0.0633055i
$879$	7.66684e40	−	1.32794e41i	0.0157318	−	0.0272482i
$880$	1.62905e41	+	2.82159e41i	0.0328802	+	0.0569502i
$881$	−2.16213e42			−0.429271			−0.214635	−	0.976694i	$-0.568856\pi$
$881$	−2.16213e42			−0.429271			−0.214635	+	0.976694i	$0.568856\pi$
$882$	−1.14874e42	−	1.50767e40i	−0.224351	−	0.00294451i
$883$	−2.83893e42			−0.545411			−0.272706	−	0.962097i	$-0.587919\pi$
$883$	−2.83893e42			−0.545411			−0.272706	+	0.962097i	$0.587919\pi$
$884$	−2.00753e42	−	3.47714e42i	−0.379406	−	0.657150i
$885$	−1.12230e42	+	1.94388e42i	−0.208656	+	0.361403i
$886$	−2.02497e42	+	3.50735e42i	−0.370365	+	0.641490i
$887$	−2.17290e42	−	3.76357e42i	−0.390973	−	0.677185i	0.601605	−	0.798794i	$-0.294528\pi$
$887$	−2.17290e42	−	3.76357e42i	−0.390973	−	0.677185i	−0.992578	+	0.121608i	$0.961195\pi$
$888$	4.29240e42			0.759823
$889$	−4.59205e42	+	7.83449e42i	−0.799708	+	1.36438i
$890$	−3.58643e42			−0.614479
$891$	1.74410e41	+	3.02086e41i	0.0293998	+	0.0509219i
$892$	9.14322e41	−	1.58365e42i	0.151638	−	0.262645i
$893$	1.50311e42	−	2.60346e42i	0.245270	−	0.424819i
$894$	−1.08427e42	−	1.87801e42i	−0.174077	−	0.301511i
$895$	−3.90321e41			−0.0616578
$896$	2.63248e42	+	1.72743e40i	0.409165	+	0.00268494i
$897$	8.23056e42			1.25875
$898$	3.56102e42	+	6.16787e42i	0.535880	+	0.928172i
$899$	−4.97545e42	+	8.61773e42i	−0.736745	+	1.27608i
$900$	−2.18032e41	+	3.77643e41i	−0.0317690	+	0.0550256i
$901$	−2.01654e42	−	3.49276e42i	−0.289133	−	0.500794i
$902$	−3.19122e42			−0.450258
$903$	−3.21939e42	−	5.66162e42i	−0.446993	−	0.786083i
$904$	1.11950e43			1.52962
$905$	−3.55866e42	−	6.16378e42i	−0.478501	−	0.828787i
$906$	−9.99426e41	+	1.73106e42i	−0.132249	+	0.229062i
$907$	−4.06401e42	+	7.03908e42i	−0.529236	+	0.916664i	0.470182	+	0.882569i	$0.344188\pi$
$907$	−4.06401e42	+	7.03908e42i	−0.529236	+	0.916664i	−0.999419	+	0.0340948i	$0.989145\pi$
$908$	−2.55414e42	−	4.42389e42i	−0.327340	−	0.566970i
$909$	2.81577e42			0.355157
$910$	−2.50418e42	−	4.40385e42i	−0.310860	−	0.546679i
$911$	−1.21602e43			−1.48567			−0.742836	−	0.669474i	$-0.766520\pi$
$911$	−1.21602e43			−1.48567			−0.742836	+	0.669474i	$0.766520\pi$
$912$	−1.55562e41	−	2.69440e41i	−0.0187058	−	0.0323994i
$913$	1.59636e42	−	2.76499e42i	0.188932	−	0.327240i
$914$	−5.61213e42	+	9.72050e42i	−0.653745	+	1.13232i
$915$	−1.33058e41	−	2.30464e41i	−0.0152558	−	0.0264239i
$916$	−1.68269e42			−0.189897
$917$	−8.85876e42	−	5.81311e40i	−0.984050	−	0.00645733i
$918$	1.42004e42			0.155268
$919$	−4.80421e42	−	8.32113e42i	−0.517067	−	0.895586i	−0.999804	−	0.0198208i	$-0.993690\pi$
$919$	−4.80421e42	−	8.32113e42i	−0.517067	−	0.895586i	0.482736	−	0.875766i	$-0.339643\pi$
$920$	7.47078e42	−	1.29398e43i	0.791485	−	1.37089i
$921$	−1.36145e41	+	2.35809e41i	−0.0141983	+	0.0245921i
$922$	−1.76697e42	−	3.06048e42i	−0.181397	−	0.314189i
$923$	1.19147e43			1.20409
$924$	−8.49361e41	+	1.44909e42i	−0.0844985	+	0.144163i
$925$	−4.49784e42			−0.440503
$926$	−5.22832e42	−	9.05571e42i	−0.504083	−	0.873098i
$927$	2.30332e42	−	3.98947e42i	0.218624	−	0.378668i
$928$	6.06669e42	−	1.05078e43i	0.566899	−	0.981899i
$929$	5.64394e42	+	9.77559e42i	0.519224	+	0.899322i	0.999750	+	0.0223419i	$0.00711225\pi$
$929$	5.64394e42	+	9.77559e42i	0.519224	+	0.899322i	−0.480526	+	0.876980i	$0.659554\pi$
$930$	4.22004e42			0.382221
$931$	2.41343e42	−	4.05629e42i	0.215211	−	0.361708i
$932$	4.59397e42			0.403327
$933$	−3.72650e42	−	6.45448e42i	−0.322119	−	0.557927i
$934$	−2.61185e42	+	4.52385e42i	−0.222289	+	0.385016i
$935$	3.05480e42	−	5.29106e42i	0.255985	−	0.443378i
$936$	−2.43464e42	−	4.21693e42i	−0.200880	−	0.347934i
$937$	−5.67553e42			−0.461086			−0.230543	−	0.973062i	$-0.574050\pi$
$937$	−5.67553e42			−0.461086			−0.230543	+	0.973062i	$0.574050\pi$
$938$	−5.85662e42	+	9.99197e42i	−0.468496	+	0.799300i
$939$	−4.40209e42			−0.346743
$940$	−3.31667e42	−	5.74465e42i	−0.257246	−	0.445563i
$941$	9.88699e42	−	1.71248e43i	0.755118	−	1.30790i	−0.190198	−	0.981746i	$-0.560913\pi$
$941$	9.88699e42	−	1.71248e43i	0.755118	−	1.30790i	0.945316	−	0.326156i	$-0.105754\pi$
$942$	−6.36737e41	+	1.10286e42i	−0.0478875	+	0.0829436i
$943$	1.60737e43	+	2.78404e43i	1.19041	+	2.06185i
$944$	1.89045e42			0.137870
$945$	−2.16282e42	−	1.41924e40i	−0.155331	−	0.00101928i
$946$	7.88842e42			0.557916
$947$	4.61762e42	+	7.99795e42i	0.321620	+	0.557062i	0.980822	−	0.194903i	$-0.0624393\pi$
$947$	4.61762e42	+	7.99795e42i	0.321620	+	0.557062i	−0.659202	+	0.751966i	$0.729106\pi$
$948$	4.14711e42	−	7.18300e42i	0.284462	−	0.492703i
$949$	−9.45829e42	+	1.63822e43i	−0.638929	+	1.10666i
$950$	7.42077e41	+	1.28531e42i	0.0493693	+	0.0855101i
$951$	−1.76936e42			−0.115931
$952$	9.56016e42	+	1.68125e43i	0.616921	+	1.08492i
$953$	2.06029e43			1.30943			0.654713	−	0.755878i	$-0.272790\pi$
$953$	2.06029e43			1.30943			0.654713	+	0.755878i	$0.272790\pi$
$954$	−8.64644e41	−	1.49761e42i	−0.0541235	−	0.0937447i
$955$	−1.14161e42	+	1.97733e42i	−0.0703832	+	0.121907i
$956$	−1.25981e42	+	2.18205e42i	−0.0765007	+	0.132503i
$957$	3.08857e42	+	5.34956e42i	0.184729	+	0.319960i
$958$	8.10675e42			0.477581
$959$	−7.26470e42	−	1.27757e43i	−0.421549	−	0.741336i
$960$	−6.40082e42			−0.365850
$961$	−4.30572e42	−	7.45772e42i	−0.242413	−	0.419872i
$962$	8.87862e42	−	1.53782e43i	0.492387	−	0.852840i
$963$	−2.44909e42	+	4.24194e42i	−0.133790	+	0.231731i
$964$	7.41497e42	+	1.28431e43i	0.399018	+	0.691119i
$965$	5.02379e42			0.266309
$966$	−1.40169e43	−	9.19791e40i	−0.731956	−	0.00480309i
$967$	6.21303e42			0.319609			0.159805	−	0.987149i	$-0.448914\pi$
$967$	6.21303e42			0.319609			0.159805	+	0.987149i	$0.448914\pi$
$968$	7.39642e42	+	1.28110e43i	0.374825	+	0.649216i
$969$	−2.91710e42	+	5.05256e42i	−0.145632	+	0.252242i
$970$	3.22490e42	−	5.58568e42i	0.158608	−	0.274717i
$971$	1.65275e43	+	2.86265e43i	0.800809	+	1.38704i	0.919084	+	0.394062i	$0.128930\pi$
$971$	1.65275e43	+	2.86265e43i	0.800809	+	1.38704i	−0.118275	+	0.992981i	$0.537736\pi$
$972$	−7.34991e41			−0.0350850
$973$	−8.89685e42	+	1.51789e43i	−0.418408	+	0.713845i
$974$	−5.48288e42			−0.254041
$975$	2.55117e42	+	4.41875e42i	0.116459	+	0.201712i
$976$	−1.12065e41	+	1.94101e41i	−0.00504018	+	0.00872984i
$977$	−8.89029e42	+	1.53984e43i	−0.393953	+	0.682347i	−0.992967	−	0.118392i	$-0.962226\pi$
$977$	−8.89029e42	+	1.53984e43i	−0.393953	+	0.682347i	0.599014	+	0.800739i	$0.295560\pi$
$978$	6.04303e42	+	1.04668e43i	0.263840	+	0.456985i
$979$	1.39135e43			0.598531
$980$	−5.08860e42	−	9.08707e42i	−0.215685	−	0.385164i
$981$	1.22687e43			0.512386
$982$	−1.20228e43	−	2.08241e43i	−0.494754	−	0.856940i
$983$	−9.77181e42	+	1.69253e43i	−0.396231	+	0.686293i	−0.993258	−	0.115929i	$-0.963016\pi$
$983$	−9.77181e42	+	1.69253e43i	−0.396231	+	0.686293i	0.597026	+	0.802222i	$0.296349\pi$
$984$	9.50937e42	−	1.64707e43i	0.379947	−	0.658087i
$985$	−1.20044e43	−	2.07922e43i	−0.472623	−	0.818607i
$986$	2.51472e43			0.975605
$987$	−8.90044e42	+	1.51850e43i	−0.340262	+	0.580520i
$988$	7.07295e42			0.266456
$989$	−3.97328e43	−	6.88192e43i	−1.47504	−	2.55484i
$990$	1.30982e42	−	2.26868e42i	0.0479183	−	0.0829970i
$991$	−2.57232e43	+	4.45540e43i	−0.927380	+	1.60627i	−0.139692	+	0.990195i	$0.544611\pi$
$991$	−2.57232e43	+	4.45540e43i	−0.927380	+	1.60627i	−0.787688	+	0.616075i	$0.788722\pi$
$992$	1.60788e43	+	2.78493e43i	0.571261	+	0.989454i
$993$	−1.39446e42			−0.0488250
$994$	−2.02912e43	−	1.33151e41i	−0.700174	−	0.00459454i
$995$	1.86553e43			0.634405
$996$	3.36367e42	+	5.82605e42i	0.112734	+	0.195260i
$997$	−7.76254e42	+	1.34451e43i	−0.256404	+	0.444104i	−0.965276	−	0.261233i	$-0.915871\pi$
$997$	−7.76254e42	+	1.34451e43i	−0.256404	+	0.444104i	0.708872	+	0.705337i	$0.249204\pi$
$998$	1.58522e43	−	2.74568e43i	0.516056	−	0.893834i
$999$	−3.79058e42	−	6.56548e42i	−0.121620	−	0.210653i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.30.e.b.4.14	✓	40
7.2	even	3	inner	21.30.e.b.16.14	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.30.e.b.4.14	✓	40	1.1	even	1	trivial
21.30.e.b.16.14	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)

\(f(q)\)	\(=\)	\(q+(7798.16 + 13506.8i) q^{2} +(-2.39148e6 + 4.14217e6i) q^{3} +(1.46813e8 - 2.54287e8i) q^{4} +(5.50788e9 + 9.53994e9i) q^{5} -7.45967e10 q^{6} +(-9.07383e11 + 1.54808e12i) q^{7} +1.29527e13 q^{8} +(-1.14384e13 - 1.98119e13i) q^{9} +O(q^{10})\)	\(q+(7798.16 + 13506.8i) q^{2} +(-2.39148e6 + 4.14217e6i) q^{3} +(1.46813e8 - 2.54287e8i) q^{4} +(5.50788e9 + 9.53994e9i) q^{5} -7.45967e10 q^{6} +(-9.07383e11 + 1.54808e12i) q^{7} +1.29527e13 q^{8} +(-1.14384e13 - 1.98119e13i) q^{9} +(-8.59027e13 + 1.48788e14i) q^{10} +(3.33258e14 - 5.77219e14i) q^{11} +(7.02202e14 + 1.21625e15i) q^{12} +1.64328e16 q^{13} +(-2.79856e16 - 1.83641e14i) q^{14} -5.26881e16 q^{15} +(2.21875e16 + 3.84299e16i) q^{16} +(4.16061e17 - 7.20639e17i) q^{17} +(1.78397e17 - 3.08992e17i) q^{18} +(7.32936e17 + 1.26948e18i) q^{19} +3.23451e18 q^{20} +(-4.24244e18 - 7.46075e18i) q^{21} +1.03952e19 q^{22} +(-5.23590e19 - 9.06884e19i) q^{23} +(-3.09762e19 + 5.36523e19i) q^{24} +(3.24587e19 - 5.62201e19i) q^{25} +(1.28145e20 + 2.21954e20i) q^{26} +1.09419e20 q^{27} +(2.60443e20 + 4.58015e20i) q^{28} +1.93767e21 q^{29} +(-4.10870e20 - 7.11648e20i) q^{30} +(-2.56775e21 + 4.44747e21i) q^{31} +(3.13092e21 - 5.42291e21i) q^{32} +(1.59396e21 + 2.76082e21i) q^{33} +1.29780e22 q^{34} +(-1.97664e22 - 1.29707e20i) q^{35} -6.71722e21 q^{36} +(-3.46428e22 - 6.00031e22i) q^{37} +(-1.14311e22 + 1.97992e22i) q^{38} +(-3.92987e22 + 6.80673e22i) q^{39} +(7.13419e22 + 1.23568e23i) q^{40} -3.06990e23 q^{41} +(6.76877e22 - 1.15482e23i) q^{42} +7.58853e23 q^{43} +(-9.78531e22 - 1.69487e23i) q^{44} +(1.26003e23 - 2.18243e23i) q^{45} +(8.16607e23 - 1.41441e24i) q^{46} +(-1.02540e24 - 1.77605e24i) q^{47} -2.12244e23 q^{48} +(-1.57322e24 - 2.80941e24i) q^{49} +1.01247e24 q^{50} +(1.99001e24 + 3.44679e24i) q^{51} +(2.41254e24 - 4.17864e24i) q^{52} +(2.42337e24 - 4.19741e24i) q^{53} +(8.53266e23 + 1.47790e24i) q^{54} +7.34218e24 q^{55} +(-1.17530e25 + 2.00518e25i) q^{56} -7.01122e24 q^{57} +(1.51103e25 + 2.61717e25i) q^{58} +(2.13008e25 - 3.68941e25i) q^{59} +(-7.73529e24 + 1.33979e25i) q^{60} +(2.52540e24 + 4.37412e24i) q^{61} -8.00948e25 q^{62} +(4.10495e25 + 2.69366e23i) q^{63} +1.21485e26 q^{64} +(9.05097e25 + 1.56767e26i) q^{65} +(-2.48599e25 + 4.30586e25i) q^{66} +(2.06921e26 - 3.58398e26i) q^{67} +(-1.22166e26 - 2.11598e26i) q^{68} +5.00863e26 q^{69} +(-1.52389e26 - 2.67992e26i) q^{70} +7.25060e26 q^{71} +(-1.48158e26 - 2.56617e26i) q^{72} +(-5.75575e26 + 9.96925e26i) q^{73} +(5.40300e26 - 9.35827e26i) q^{74} +(1.55249e26 + 2.68899e26i) q^{75} +4.30418e26 q^{76} +(5.91191e26 + 1.03967e27i) q^{77} -1.22583e27 q^{78} +(-2.95293e27 - 5.11463e27i) q^{79} +(-2.44412e26 + 4.23335e26i) q^{80} +(-2.61674e26 + 4.53232e26i) q^{81} +(-2.39396e27 - 4.14645e27i) q^{82} +4.79018e27 q^{83} +(-2.52002e27 - 1.65364e25i) q^{84} +9.16647e27 q^{85} +(5.91766e27 + 1.02497e28i) q^{86} +(-4.63391e27 + 8.02617e27i) q^{87} +(4.31658e27 - 7.47654e27i) q^{88} +(1.04375e28 + 1.80782e28i) q^{89} +3.93036e27 q^{90} +(-1.49108e28 + 2.54393e28i) q^{91} -3.07479e28 q^{92} +(-1.22815e28 - 2.12721e28i) q^{93} +(1.59925e28 - 2.76998e28i) q^{94} +(-8.07385e27 + 1.39843e28i) q^{95} +(1.49751e28 + 2.59376e28i) q^{96} -3.75413e28 q^{97} +(2.56779e28 - 4.31574e28i) q^{98} -1.52477e28 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

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Groups

Database

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