LMFDB - Embedded newform 21.30.e.b.4.19

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			4.19
Character	$\chi$	$=$	21.4
Dual form			21.30.e.b.16.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(19476.8 + 33734.8i) q^{2} +(-2.39148e6 + 4.14217e6i) q^{3} +(-4.90254e8 + 8.49146e8i) q^{4} +(-7.17536e9 - 1.24281e10i) q^{5} -1.86314e11 q^{6} +(7.19771e11 - 1.64373e12i) q^{7} -1.72813e13 q^{8} +(-1.14384e13 - 1.98119e13i) q^{9} +O(q^{10})$	\(q+(19476.8 + 33734.8i) q^{2} +(-2.39148e6 + 4.14217e6i) q^{3} +(-4.90254e8 + 8.49146e8i) q^{4} +(-7.17536e9 - 1.24281e10i) q^{5} -1.86314e11 q^{6} +(7.19771e11 - 1.64373e12i) q^{7} -1.72813e13 q^{8} +(-1.14384e13 - 1.98119e13i) q^{9} +(2.79506e14 - 4.84119e14i) q^{10} +(-1.40872e14 + 2.43998e14i) q^{11} +(-2.34487e15 - 4.06144e15i) q^{12} +8.46772e15 q^{13} +(6.94695e16 - 7.73318e15i) q^{14} +6.86391e16 q^{15} +(-7.33803e16 - 1.27098e17i) q^{16} +(-1.44235e17 + 2.49823e17i) q^{17} +(4.45566e17 - 7.71743e17i) q^{18} +(1.56555e18 + 2.71162e18i) q^{19} +1.40710e19 q^{20} +(5.08728e18 + 6.91236e18i) q^{21} -1.09750e19 q^{22} +(-2.23951e19 - 3.87894e19i) q^{23} +(4.13279e19 - 7.15820e19i) q^{24} +(-9.83944e18 + 1.70424e19i) q^{25} +(1.64924e20 + 2.85657e20i) q^{26} +1.09419e20 q^{27} +(1.04289e21 + 1.41703e21i) q^{28} -3.23964e19 q^{29} +(1.33687e21 + 2.31552e21i) q^{30} +(-1.62364e21 + 2.81222e21i) q^{31} +(-1.78048e21 + 3.08389e21i) q^{32} +(-6.73788e20 - 1.16704e21i) q^{33} -1.12370e22 q^{34} +(-2.55930e22 + 2.84895e21i) q^{35} +2.24309e22 q^{36} +(3.13440e22 + 5.42894e22i) q^{37} +(-6.09839e22 + 1.05627e23i) q^{38} +(-2.02504e22 + 3.50747e22i) q^{39} +(1.23999e23 + 2.14773e23i) q^{40} -2.97932e23 q^{41} +(-1.34103e23 + 3.06249e23i) q^{42} +6.95562e23 q^{43} +(-1.38127e23 - 2.39242e23i) q^{44} +(-1.64149e23 + 2.84315e23i) q^{45} +(8.72367e23 - 1.51098e24i) q^{46} +(-1.46647e24 - 2.54001e24i) q^{47} +7.01951e23 q^{48} +(-2.18376e24 - 2.36621e24i) q^{49} -7.66562e23 q^{50} +(-6.89874e23 - 1.19490e24i) q^{51} +(-4.15134e24 + 7.19032e24i) q^{52} +(-2.30142e24 + 3.98618e24i) q^{53} +(2.13113e24 + 3.69122e24i) q^{54} +4.04324e24 q^{55} +(-1.24386e25 + 2.84057e25i) q^{56} -1.49760e25 q^{57} +(-6.30978e23 - 1.09289e24i) q^{58} +(-3.45043e25 + 5.97632e25i) q^{59} +(-3.36506e25 + 5.82846e25i) q^{60} +(1.72557e25 + 2.98877e25i) q^{61} -1.26493e26 q^{62} +(-4.07983e25 + 4.54157e24i) q^{63} -2.17504e26 q^{64} +(-6.07590e25 - 1.05238e26i) q^{65} +(2.62465e25 - 4.54602e25i) q^{66} +(-1.75118e26 + 3.03314e26i) q^{67} +(-1.41424e26 - 2.44954e26i) q^{68} +2.14230e26 q^{69} +(-5.94578e26 - 8.07886e26i) q^{70} +3.05578e26 q^{71} +(1.97670e26 + 3.42375e26i) q^{72} +(-1.62640e25 + 2.81700e25i) q^{73} +(-1.22096e27 + 2.11477e27i) q^{74} +(-4.70617e25 - 8.15133e25i) q^{75} -3.07008e27 q^{76} +(2.99670e26 + 4.07178e26i) q^{77} -1.57765e27 q^{78} +(1.37937e27 + 2.38914e27i) q^{79} +(-1.05306e27 + 1.82395e27i) q^{80} +(-2.61674e26 + 4.53232e26i) q^{81} +(-5.80275e27 - 1.00507e28i) q^{82} +5.71829e27 q^{83} +(-8.36366e27 + 9.31022e26i) q^{84} +4.13977e27 q^{85} +(1.35473e28 + 2.34646e28i) q^{86} +(7.74756e25 - 1.34192e26i) q^{87} +(2.43445e27 - 4.21660e27i) q^{88} +(1.15680e28 + 2.00364e28i) q^{89} -1.27884e28 q^{90} +(6.09482e27 - 1.39186e28i) q^{91} +4.39171e28 q^{92} +(-7.76580e27 - 1.34508e28i) q^{93} +(5.71244e28 - 9.89423e28i) q^{94} +(2.24668e28 - 3.89137e28i) q^{95} +(-8.51600e27 - 1.47502e28i) q^{96} -6.09189e28 q^{97} +(3.72909e28 - 1.19755e29i) q^{98} +6.44542e27 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 $

$2$	19476.8	+	33734.8i	0.840586	+	1.45594i	0.889400	+	0.457130i	$0.151123\pi$
$2$	19476.8	+	33734.8i	0.840586	+	1.45594i	−0.0488138	+	0.998808i	$0.515544\pi$
$3$	−2.39148e6	+	4.14217e6i	−0.288675	+	0.500000i
$3$	−2.39148e6	+	4.14217e6i	−0.288675	+	0.500000i
$4$	−4.90254e8	+	8.49146e8i	−0.913170	+	1.58166i
$5$	−7.17536e9	−	1.24281e10i	−0.525750	−	0.910625i	−0.999550	−	0.0299927i	$-0.990452\pi$
$5$	−7.17536e9	−	1.24281e10i	−0.525750	−	0.910625i	0.473801	−	0.880632i	$-0.342882\pi$
$6$	−1.86314e11			−0.970625
$7$	7.19771e11	−	1.64373e12i	0.401119	−	0.916026i
$7$	7.19771e11	−	1.64373e12i	0.401119	−	0.916026i
$8$	−1.72813e13			−1.38922
$9$	−1.14384e13	−	1.98119e13i	−0.166667	−	0.288675i
$10$	2.79506e14	−	4.84119e14i	0.883875	−	1.53092i
$11$	−1.40872e14	+	2.43998e14i	−0.111849	+	0.193728i	−0.916516	−	0.399999i	$-0.869011\pi$
$11$	−1.40872e14	+	2.43998e14i	−0.111849	+	0.193728i	0.804667	+	0.593727i	$0.202344\pi$
$12$	−2.34487e15	−	4.06144e15i	−0.527219	−	0.913170i
$13$	8.46772e15			0.596469			0.298234	−	0.954493i	$-0.403602\pi$
$13$	8.46772e15			0.596469			0.298234	+	0.954493i	$0.403602\pi$
$14$	6.94695e16	−	7.73318e15i	1.67085	−	0.185995i
$15$	6.86391e16			0.607083
$16$	−7.33803e16	−	1.27098e17i	−0.254589	−	0.440961i
$17$	−1.44235e17	+	2.49823e17i	−0.207760	+	0.359852i	−0.951009	−	0.309164i	$-0.899951\pi$
$17$	−1.44235e17	+	2.49823e17i	−0.207760	+	0.359852i	0.743248	+	0.669016i	$0.233284\pi$
$18$	4.45566e17	−	7.71743e17i	0.280195	−	0.485313i
$19$	1.56555e18	+	2.71162e18i	0.449511	+	0.778577i	0.998354	−	0.0573490i	$-0.0182648\pi$
$19$	1.56555e18	+	2.71162e18i	0.449511	+	0.778577i	−0.548843	+	0.835926i	$0.684931\pi$
$20$	1.40710e19			1.92039
$21$	5.08728e18	+	6.91236e18i	0.342220	+	0.464993i
$22$	−1.09750e19			−0.376075
$23$	−2.23951e19	−	3.87894e19i	−0.402808	−	0.697685i	0.591255	−	0.806485i	$-0.298633\pi$
$23$	−2.23951e19	−	3.87894e19i	−0.402808	−	0.697685i	−0.994064	+	0.108800i	$0.965299\pi$
$24$	4.13279e19	−	7.15820e19i	0.401033	−	0.694610i
$25$	−9.83944e18	+	1.70424e19i	−0.0528251	+	0.0914957i
$26$	1.64924e20	+	2.85657e20i	0.501383	+	0.868422i
$27$	1.09419e20			0.192450
$28$	1.04289e21	+	1.41703e21i	1.08255	+	1.47092i
$29$	−3.23964e19			−0.0202174			−0.0101087	−	0.999949i	$-0.503218\pi$
$29$	−3.23964e19			−0.0202174			−0.0101087	+	0.999949i	$0.503218\pi$
$30$	1.33687e21	+	2.31552e21i	0.510306	+	0.883875i
$31$	−1.62364e21	+	2.81222e21i	−0.385251	+	0.667275i	−0.991804	−	0.127769i	$-0.959219\pi$
$31$	−1.62364e21	+	2.81222e21i	−0.385251	+	0.667275i	0.606553	+	0.795043i	$0.292552\pi$
$32$	−1.78048e21	+	3.08389e21i	−0.266602	+	0.461768i
$33$	−6.73788e20	−	1.16704e21i	−0.0645760	−	0.111849i
$34$	−1.12370e22			−0.698562
$35$	−2.55930e22	+	2.84895e21i	−1.04504	+	0.116332i
$36$	2.24309e22			0.608780
$37$	3.13440e22	+	5.42894e22i	0.571781	+	0.990353i	0.996383	+	0.0849732i	$0.0270805\pi$
$37$	3.13440e22	+	5.42894e22i	0.571781	+	0.990353i	−0.424603	+	0.905380i	$0.639586\pi$
$38$	−6.09839e22	+	1.05627e23i	−0.755706	+	1.30892i
$39$	−2.02504e22	+	3.50747e22i	−0.172186	+	0.298234i
$40$	1.23999e23	+	2.14773e23i	0.730382	+	1.26506i
$41$	−2.97932e23			−1.22674			−0.613368	−	0.789797i	$-0.710186\pi$
$41$	−2.97932e23			−1.22674			−0.613368	+	0.789797i	$0.710186\pi$
$42$	−1.34103e23	+	3.06249e23i	−0.389336	+	0.889118i
$43$	6.95562e23			1.43563			0.717816	−	0.696233i	$-0.245142\pi$
$43$	6.95562e23			1.43563			0.717816	+	0.696233i	$0.245142\pi$
$44$	−1.38127e23	−	2.39242e23i	−0.204274	−	0.353813i
$45$	−1.64149e23	+	2.84315e23i	−0.175250	+	0.303542i
$46$	8.72367e23	−	1.51098e24i	0.677190	−	1.17293i
$47$	−1.46647e24	−	2.54001e24i	−0.833404	−	1.44350i	−0.895324	−	0.445416i	$-0.853056\pi$
$47$	−1.46647e24	−	2.54001e24i	−0.833404	−	1.44350i	0.0619199	−	0.998081i	$-0.480278\pi$
$48$	7.01951e23			0.293974
$49$	−2.18376e24	−	2.36621e24i	−0.678208	−	0.734870i
$50$	−7.66562e23			−0.177616
$51$	−6.89874e23	−	1.19490e24i	−0.119951	−	0.207760i
$52$	−4.15134e24	+	7.19032e24i	−0.544677	+	0.943409i
$53$	−2.30142e24	+	3.98618e24i	−0.229085	+	0.396787i	−0.957537	−	0.288310i	$-0.906907\pi$
$53$	−2.30142e24	+	3.98618e24i	−0.229085	+	0.396787i	0.728452	+	0.685097i	$0.240240\pi$
$54$	2.13113e24	+	3.69122e24i	0.161771	+	0.280195i
$55$	4.04324e24			0.235218
$56$	−1.24386e25	+	2.84057e25i	−0.557242	+	1.27256i
$57$	−1.49760e25			−0.519051
$58$	−6.30978e23	−	1.09289e24i	−0.0169945	−	0.0294353i
$59$	−3.45043e25	+	5.97632e25i	−0.725302	+	1.25626i	0.233548	+	0.972345i	$0.424967\pi$
$59$	−3.45043e25	+	5.97632e25i	−0.725302	+	1.25626i	−0.958850	+	0.283915i	$0.908367\pi$
$60$	−3.36506e25	+	5.82846e25i	−0.554370	+	0.960197i
$61$	1.72557e25	+	2.98877e25i	0.223692	+	0.387445i	0.955926	−	0.293607i	$-0.0948558\pi$
$61$	1.72557e25	+	2.98877e25i	0.223692	+	0.387445i	−0.732234	+	0.681053i	$0.761522\pi$
$62$	−1.26493e26			−1.29535
$63$	−4.07983e25	+	4.54157e24i	−0.331287	+	0.0368780i
$64$	−2.17504e26			−1.40559
$65$	−6.07590e25	−	1.05238e26i	−0.313593	−	0.543159i
$66$	2.62465e25	−	4.54602e25i	0.108563	−	0.188037i
$67$	−1.75118e26	+	3.03314e26i	−0.582434	+	1.00880i	0.412756	+	0.910841i	$0.364566\pi$
$67$	−1.75118e26	+	3.03314e26i	−0.582434	+	1.00880i	−0.995190	+	0.0979632i	$0.968767\pi$
$68$	−1.41424e26	−	2.44954e26i	−0.379441	−	0.657211i
$69$	2.14230e26			0.465123
$70$	−5.94578e26	−	8.07886e26i	−1.04782	−	1.42373i
$71$	3.05578e26			0.438405			0.219202	−	0.975679i	$-0.429654\pi$
$71$	3.05578e26			0.438405			0.219202	+	0.975679i	$0.429654\pi$
$72$	1.97670e26	+	3.42375e26i	0.231537	+	0.401033i
$73$	−1.62640e25	+	2.81700e25i	−0.0155971	+	0.0270151i	−0.873719	−	0.486432i	$-0.838298\pi$
$73$	−1.62640e25	+	2.81700e25i	−0.0155971	+	0.0270151i	0.858121	+	0.513447i	$0.171632\pi$
$74$	−1.22096e27	+	2.11477e27i	−0.961262	+	1.66495i
$75$	−4.70617e25	−	8.15133e25i	−0.0304986	−	0.0528251i
$76$	−3.07008e27			−1.64192
$77$	2.99670e26	+	4.07178e26i	0.132595	+	0.180165i
$78$	−1.57765e27			−0.578948
$79$	1.37937e27	+	2.38914e27i	0.420811	+	0.728867i	0.996019	−	0.0891407i	$-0.0284121\pi$
$79$	1.37937e27	+	2.38914e27i	0.420811	+	0.728867i	−0.575208	+	0.818007i	$0.695079\pi$
$80$	−1.05306e27	+	1.82395e27i	−0.267700	+	0.463670i
$81$	−2.61674e26	+	4.53232e26i	−0.0555556	+	0.0962250i
$82$	−5.80275e27	−	1.00507e28i	−1.03118	−	1.78605i
$83$	5.71829e27			0.852381			0.426190	−	0.904634i	$-0.359855\pi$
$83$	5.71829e27			0.852381			0.426190	+	0.904634i	$0.359855\pi$
$84$	−8.36366e27	+	9.31022e26i	−1.04796	+	0.116657i
$85$	4.13977e27			0.436920
$86$	1.35473e28	+	2.34646e28i	1.20677	+	2.09019i
$87$	7.74756e25	−	1.34192e26i	0.00583627	−	0.0101087i
$88$	2.43445e27	−	4.21660e27i	0.155383	−	0.269131i
$89$	1.15680e28	+	2.00364e28i	0.626763	+	1.08559i	0.988197	+	0.153188i	$0.0489539\pi$
$89$	1.15680e28	+	2.00364e28i	0.626763	+	1.08559i	−0.361434	+	0.932398i	$0.617713\pi$
$90$	−1.27884e28			−0.589250
$91$	6.09482e27	−	1.39186e28i	0.239255	−	0.546381i
$92$	4.39171e28			1.47133
$93$	−7.76580e27	−	1.34508e28i	−0.222425	−	0.385251i
$94$	5.71244e28	−	9.89423e28i	1.40110	−	2.42677i
$95$	2.24668e28	−	3.89137e28i	0.472661	−	0.818673i
$96$	−8.51600e27	−	1.47502e28i	−0.153923	−	0.266602i
$97$	−6.09189e28			−0.947462			−0.473731	−	0.880670i	$-0.657093\pi$
$97$	−6.09189e28			−0.947462			−0.473731	+	0.880670i	$0.657093\pi$
$98$	3.72909e28	−	1.19755e29i	0.499833	−	1.60515i
$99$	6.44542e27			0.0745660
$100$	−9.64766e27	−	1.67102e28i	−0.0964766	−	0.167102i
$101$	2.67942e28	−	4.64089e28i	0.231943	−	0.401737i	−0.726437	−	0.687233i	$-0.758825\pi$
$101$	2.67942e28	−	4.64089e28i	0.231943	−	0.401737i	0.958380	+	0.285496i	$0.0921584\pi$
$102$	2.68730e28	−	4.65455e28i	0.201657	−	0.349281i
$103$	2.41133e27	+	4.17655e27i	0.0157079	+	0.0272068i	0.873772	−	0.486335i	$-0.161666\pi$
$103$	2.41133e27	+	4.17655e27i	0.0157079	+	0.0272068i	−0.858065	+	0.513542i	$0.828333\pi$
$104$	−1.46333e29			−0.828626
$105$	4.94044e28	−	1.12824e29i	0.243512	−	0.556104i
$106$	−1.79297e29			−0.770263
$107$	1.75600e29	+	3.04148e29i	0.658355	+	1.14030i	0.981041	+	0.193798i	$0.0620806\pi$
$107$	1.75600e29	+	3.04148e29i	0.658355	+	1.14030i	−0.322687	+	0.946506i	$0.604586\pi$
$108$	−5.36431e28	+	9.29126e28i	−0.175740	+	0.304390i
$109$	−1.58267e29	+	2.74127e29i	−0.453635	+	0.785720i	−0.998609	−	0.0527339i	$-0.983206\pi$
$109$	−1.58267e29	+	2.74127e29i	−0.453635	+	0.785720i	0.544973	+	0.838453i	$0.316540\pi$
$110$	7.87493e28	+	1.36398e29i	0.197721	+	0.342463i
$111$	−2.99835e29			−0.660235
$112$	−2.61732e29	+	2.91353e28i	−0.506052	+	0.0563325i
$113$	7.13643e28			0.121295			0.0606476	−	0.998159i	$-0.480683\pi$
$113$	7.13643e28			0.121295			0.0606476	+	0.998159i	$0.480683\pi$
$114$	−2.91684e29	−	5.05212e29i	−0.436307	−	0.755706i
$115$	−3.21385e29	+	5.56656e29i	−0.423553	+	0.733615i
$116$	1.58825e28	−	2.75093e28i	0.0184620	−	0.0319771i
$117$	−9.68571e28	−	1.67761e29i	−0.0994115	−	0.172186i
$118$	−2.68813e30			−2.43872
$119$	3.06824e29	+	4.16899e29i	0.246297	+	0.334657i
$120$	−1.18617e30			−0.843372
$121$	7.53465e29	+	1.30504e30i	0.474980	+	0.822689i
$122$	−6.72171e29	+	1.16423e30i	−0.376064	+	0.651363i
$123$	7.12499e29	−	1.23409e30i	0.354128	−	0.613368i
$124$	−1.59199e30	−	2.75741e30i	−0.703600	−	1.21867i
$125$	−2.39063e30			−0.940408
$126$	−9.47829e29	−	1.28787e30i	−0.332167	−	0.451334i
$127$	−5.35079e30			−1.67211			−0.836053	−	0.548648i	$-0.815143\pi$
$127$	−5.35079e30			−1.67211			−0.836053	+	0.548648i	$0.815143\pi$
$128$	−3.28038e30	−	5.68179e30i	−0.914914	−	1.58468i
$129$	−1.66343e30	+	2.88114e30i	−0.414431	+	0.717816i
$130$	2.36678e30	−	4.09938e30i	0.527204	−	0.913144i
$131$	−3.85429e30	−	6.67582e30i	−0.768264	−	1.33067i	−0.938504	−	0.345269i	$-0.887788\pi$
$131$	−3.85429e30	−	6.67582e30i	−0.768264	−	1.33067i	0.170240	−	0.985403i	$-0.445546\pi$
$132$	1.32131e30			0.235876
$133$	5.58400e30	−	6.21597e29i	0.893504	−	0.0994626i
$134$	−1.36429e31			−1.95834
$135$	−7.85121e29	−	1.35987e30i	−0.101181	−	0.175250i
$136$	2.49257e30	−	4.31726e30i	0.288625	−	0.499913i
$137$	−4.16343e30	+	7.21128e30i	−0.433514	+	0.750869i	−0.997173	−	0.0751388i	$-0.976060\pi$
$137$	−4.16343e30	+	7.21128e30i	−0.433514	+	0.750869i	0.563659	+	0.826008i	$0.309393\pi$
$138$	4.17251e30	+	7.22699e30i	0.390976	+	0.677190i
$139$	1.10768e31			0.934756			0.467378	−	0.884058i	$-0.345199\pi$
$139$	1.10768e31			0.934756			0.467378	+	0.884058i	$0.345199\pi$
$140$	1.01279e31	−	2.31289e31i	0.770306	−	1.75913i
$141$	1.40282e31			0.962332
$142$	5.95167e30	+	1.03086e31i	0.368517	+	0.638290i
$143$	−1.19287e30	+	2.06611e30i	−0.0667144	+	0.115553i
$144$	−1.67871e30	+	2.90760e30i	−0.0848630	+	0.146987i
$145$	2.32456e29	+	4.02626e29i	0.0106293	+	0.0184105i
$146$	−1.26708e30			−0.0524430
$147$	1.50237e31	−	3.38677e30i	0.563217	−	0.126965i
$148$	−6.14661e31			−2.08853
$149$	−2.75404e31	−	4.77013e31i	−0.848729	−	1.47004i	−0.882343	−	0.470606i	$-0.844035\pi$
$149$	−2.75404e31	−	4.77013e31i	−0.848729	−	1.47004i	0.0336149	−	0.999435i	$-0.489298\pi$
$150$	1.83322e30	−	3.17523e30i	0.0512734	−	0.0888081i
$151$	−7.07460e30	+	1.22536e31i	−0.179695	+	0.311241i	−0.941776	−	0.336241i	$-0.890844\pi$
$151$	−7.07460e30	+	1.22536e31i	−0.179695	+	0.311241i	0.762081	+	0.647482i	$0.224178\pi$
$152$	−2.70548e31	−	4.68602e31i	−0.624470	−	1.08161i
$153$	6.59929e30			0.138507
$154$	−7.89946e30	+	1.80398e31i	−0.150851	+	0.344494i
$155$	4.66007e31			0.810183
$156$	−1.98557e31	−	3.43911e31i	−0.314470	−	0.544677i
$157$	3.60046e31	−	6.23618e31i	0.519773	−	0.900273i	−0.479963	−	0.877289i	$-0.659350\pi$
$157$	3.60046e31	−	6.23618e31i	0.519773	−	0.900273i	0.999736	−	0.0229840i	$-0.00731667\pi$
$158$	−5.37313e31	+	9.30654e31i	−0.707456	+	1.22535i
$159$	−1.10076e31	−	1.90658e31i	−0.132262	−	0.229085i
$160$	5.11025e31			0.560664
$161$	−7.98784e31	+	8.89187e30i	−0.800671	+	0.0891287i
$162$	−2.03863e31			−0.186797
$163$	−2.00235e30	−	3.46817e30i	−0.0167811	−	0.0290656i	0.857513	−	0.514462i	$-0.172008\pi$
$163$	−2.00235e30	−	3.46817e30i	−0.0167811	−	0.0290656i	−0.874294	+	0.485397i	$0.838675\pi$
$164$	1.46062e32	−	2.52987e32i	1.12022	−	1.94027i
$165$	−9.66935e30	+	1.67478e31i	−0.0679016	+	0.117609i
$166$	1.11374e32	+	1.92905e32i	0.716499	+	1.24101i
$167$	−1.93707e32			−1.14224			−0.571118	−	0.820868i	$-0.693490\pi$
$167$	−1.93707e32			−1.14224			−0.571118	+	0.820868i	$0.693490\pi$
$168$	−8.79146e31	−	1.19454e32i	−0.475419	−	0.645978i
$169$	−1.29836e32			−0.644225
$170$	8.06294e31	+	1.39654e32i	0.367269	+	0.636128i
$171$	3.58148e31	−	6.20331e31i	0.149837	−	0.259526i
$172$	−3.41002e32	+	5.90633e32i	−1.31098	+	2.27068i
$173$	1.49013e32	+	2.58099e32i	0.526692	+	0.912258i	0.999516	+	0.0311007i	$0.00990126\pi$
$173$	1.49013e32	+	2.58099e32i	0.526692	+	0.912258i	−0.472824	+	0.881157i	$0.656765\pi$
$174$	6.03590e30			0.0196236
$175$	2.09309e31	+	2.84400e31i	0.0626233	+	0.0850898i
$176$	4.13490e31			0.113902
$177$	−1.65033e32	−	2.85845e32i	−0.418753	−	0.725302i
$178$	−4.50615e32	+	7.80488e32i	−1.05370	+	1.82506i
$179$	−2.34630e32	+	4.06391e32i	−0.505842	+	0.876144i	0.494135	+	0.869385i	$0.335485\pi$
$179$	−2.34630e32	+	4.06391e32i	−0.505842	+	0.876144i	−0.999977	+	0.00675883i	$0.997849\pi$
$180$	−1.60950e32	−	2.78773e32i	−0.320066	−	0.554370i
$181$	−7.37973e31			−0.135426			−0.0677129	−	0.997705i	$-0.521570\pi$
$181$	−7.37973e31			−0.135426			−0.0677129	+	0.997705i	$0.521570\pi$
$182$	5.88248e32	−	6.54823e31i	0.996611	−	0.110940i
$183$	−1.65067e32			−0.258297
$184$	3.87015e32	+	6.70330e32i	0.559590	+	0.969238i
$185$	4.49809e32	−	7.79092e32i	0.601227	−	1.04136i
$186$	3.02505e32	−	5.23955e32i	0.373935	−	0.647674i
$187$	−4.06376e31	−	7.03864e31i	−0.0464756	−	0.0804981i
$188$	2.87578e33			3.04416
$189$	7.87566e31	−	1.79855e32i	0.0771953	−	0.176289i
$190$	1.75033e33			1.58925
$191$	2.01809e32	+	3.49543e32i	0.169807	+	0.294115i	0.938352	−	0.345681i	$-0.112352\pi$
$191$	2.01809e32	+	3.49543e32i	0.169807	+	0.294115i	−0.768545	+	0.639796i	$0.779019\pi$
$192$	5.20157e32	−	9.00939e32i	0.405758	−	0.702793i
$193$	−9.51113e32	+	1.64738e33i	−0.688099	+	1.19182i	0.284353	+	0.958720i	$0.408221\pi$
$193$	−9.51113e32	+	1.64738e33i	−0.688099	+	1.19182i	−0.972452	+	0.233103i	$0.925112\pi$
$194$	−1.18650e33	−	2.05508e33i	−0.796423	−	1.37945i
$195$	5.81216e32			0.362106
$196$	3.07986e33	−	6.94288e32i	1.78163	−	0.401630i
$197$	1.51598e33			0.814579			0.407290	−	0.913299i	$-0.366474\pi$
$197$	1.51598e33			0.814579			0.407290	+	0.913299i	$0.366474\pi$
$198$	1.25536e32	+	2.17435e32i	0.0626791	+	0.108563i
$199$	−1.79116e33	+	3.10238e33i	−0.831313	+	1.43988i	0.0656836	+	0.997841i	$0.479077\pi$
$199$	−1.79116e33	+	3.10238e33i	−0.831313	+	1.43988i	−0.896997	+	0.442037i	$0.854256\pi$
$200$	1.70038e32	−	2.94515e32i	0.0733857	−	0.127108i
$201$	−8.37585e32	−	1.45074e33i	−0.336268	−	0.582434i
$202$	2.08746e33			0.779872
$203$	−2.33180e31	+	5.32509e31i	−0.00810959	+	0.0185197i
$204$	1.35285e33			0.438141
$205$	2.13777e33	+	3.70273e33i	0.644956	+	1.11710i
$206$	−9.39300e31	+	1.62692e32i	−0.0264076	+	0.0457394i
$207$	−5.12327e32	+	8.87377e32i	−0.134269	+	0.232562i
$208$	−6.21363e32	−	1.07623e33i	−0.151854	−	0.263019i
$209$	−8.82173e32			−0.201110
$210$	4.76833e33	−	5.30798e32i	1.01435	−	0.112914i
$211$	6.04159e33			1.19965			0.599826	−	0.800130i	$-0.295236\pi$
$211$	6.04159e33			1.19965			0.599826	+	0.800130i	$0.295236\pi$
$212$	−2.25657e33	−	3.90849e33i	−0.418387	−	0.724668i
$213$	−7.30784e32	+	1.26575e33i	−0.126557	+	0.219202i
$214$	−6.84025e33	+	1.18477e34i	−1.10681	+	1.91705i
$215$	−4.99091e33	−	8.64451e33i	−0.754783	−	1.30732i
$216$	−1.89090e33			−0.267355
$217$	3.45387e33	+	4.69297e33i	0.456710	+	0.620556i
$218$	−1.23301e34			−1.52528
$219$	−7.77901e31	−	1.34736e32i	−0.00900502	−	0.0155971i
$220$	−1.98222e33	+	3.43330e33i	−0.214794	+	0.372034i
$221$	−1.22135e33	+	2.11543e33i	−0.123923	+	0.214640i
$222$	−5.83982e33	−	1.01149e34i	−0.554985	−	0.961262i
$223$	−1.53726e34			−1.36876			−0.684379	−	0.729126i	$-0.739927\pi$
$223$	−1.53726e34			−1.36876			−0.684379	+	0.729126i	$0.739927\pi$
$224$	3.78753e33	+	5.14632e33i	0.316053	+	0.429438i
$225$	4.50190e32			0.0352167
$226$	1.38995e33	+	2.40746e33i	0.101959	+	0.176598i
$227$	6.36863e33	−	1.10308e34i	0.438199	−	0.758983i	−0.559352	−	0.828930i	$-0.688950\pi$
$227$	6.36863e33	−	1.10308e34i	0.438199	−	0.758983i	0.997551	+	0.0699475i	$0.0222832\pi$
$228$	7.34204e33	−	1.27168e34i	0.473982	−	0.820961i
$229$	−1.27011e33	−	2.19990e33i	−0.0769534	−	0.133287i	0.824981	−	0.565161i	$-0.191186\pi$
$229$	−1.27011e33	−	2.19990e33i	−0.0769534	−	0.133287i	−0.901934	+	0.431874i	$0.857853\pi$
$230$	−2.50382e34			−1.42413
$231$	−2.40326e33	+	2.67525e32i	−0.128359	+	0.0142886i
$232$	5.59852e32			0.0280865
$233$	−3.49053e33	−	6.04577e33i	−0.164524	−	0.284965i	0.771962	−	0.635669i	$-0.219276\pi$
$233$	−3.49053e33	−	6.04577e33i	−0.164524	−	0.284965i	−0.936486	+	0.350704i	$0.885942\pi$
$234$	3.77293e33	−	6.53490e33i	0.167128	−	0.289474i
$235$	−2.10450e34	+	3.64510e34i	−0.876323	+	1.51784i
$236$	−3.38318e34	−	5.85983e34i	−1.32465	−	2.29436i
$237$	−1.31950e34			−0.485911
$238$	−8.08805e33	+	1.84705e34i	−0.280206	+	0.639901i
$239$	5.31235e34			1.73188			0.865938	−	0.500151i	$-0.166722\pi$
$239$	5.31235e34			1.73188			0.865938	+	0.500151i	$0.166722\pi$
$240$	−5.03675e33	−	8.72391e33i	−0.154557	−	0.267700i
$241$	−5.87604e33	+	1.01776e34i	−0.169761	+	0.294035i	−0.938336	−	0.345725i	$-0.887633\pi$
$241$	−5.87604e33	+	1.01776e34i	−0.169761	+	0.294035i	0.768575	+	0.639760i	$0.220966\pi$
$242$	−2.93501e34	+	5.08359e34i	−0.798523	+	1.38308i
$243$	−1.25158e33	−	2.16780e33i	−0.0320750	−	0.0555556i
$244$	−3.38387e34			−0.817074
$245$	−1.37382e34	+	4.41185e34i	−0.312624	+	1.00395i
$246$	5.55088e34			1.19070
$247$	1.32567e34	+	2.29612e34i	0.268120	+	0.464397i
$248$	2.80585e34	−	4.85987e34i	0.535199	−	0.926991i
$249$	−1.36752e34	+	2.36861e34i	−0.246061	+	0.426190i
$250$	−4.65617e34	−	8.06472e34i	−0.790494	−	1.36918i
$251$	8.26725e34			1.32462			0.662312	−	0.749228i	$-0.269576\pi$
$251$	8.26725e34			1.32462			0.662312	+	0.749228i	$0.269576\pi$
$252$	1.61451e34	−	3.68702e34i	0.244193	−	0.557658i
$253$	1.26194e34			0.180215
$254$	−1.04216e35	−	1.80508e35i	−1.40555	−	2.43448i
$255$	−9.90019e33	+	1.71476e34i	−0.126128	+	0.218460i
$256$	6.93969e34	−	1.20199e35i	0.835335	−	1.44684i
$257$	6.36288e34	+	1.10208e35i	0.723808	+	1.25367i	0.959463	+	0.281836i	$0.0909434\pi$
$257$	6.36288e34	+	1.10208e35i	0.723808	+	1.25367i	−0.235654	+	0.971837i	$0.575723\pi$
$258$	−1.29593e35			−1.39346
$259$	1.11797e35	−	1.24450e34i	1.13654	−	0.126517i
$260$	1.19149e35			1.14546
$261$	3.70563e32	+	6.41834e32i	0.00336957	+	0.00583627i
$262$	1.50138e35	−	2.60047e35i	1.29158	−	2.23709i
$263$	−7.82370e34	+	1.35510e35i	−0.636874	+	1.10310i	0.349240	+	0.937033i	$0.386440\pi$
$263$	−7.82370e34	+	1.35510e35i	−0.636874	+	1.10310i	−0.986115	+	0.166065i	$0.946894\pi$
$264$	1.16439e34	+	2.01679e34i	0.0897103	+	0.155383i
$265$	6.60542e34			0.481765
$266$	1.29728e35	+	1.76268e35i	0.895878	+	1.21728i
$267$	−1.10659e35			−0.723723
$268$	−1.71705e35	−	2.97402e35i	−1.06372	−	1.84242i
$269$	−8.18514e34	+	1.41771e35i	−0.480416	+	0.832106i	−0.999748	−	0.0224674i	$-0.992848\pi$
$269$	−8.18514e34	+	1.41771e35i	−0.480416	+	0.832106i	0.519331	+	0.854573i	$0.326181\pi$
$270$	3.05833e34	−	5.29718e34i	0.170102	−	0.294625i
$271$	−9.23140e34	−	1.59892e35i	−0.486645	−	0.842895i	0.513237	−	0.858247i	$-0.328446\pi$
$271$	−9.23140e34	−	1.59892e35i	−0.486645	−	0.842895i	−0.999882	+	0.0153525i	$0.995113\pi$
$272$	4.23362e34			0.211574
$273$	4.30776e34	+	5.85319e34i	0.204124	+	0.277354i
$274$	−3.24361e35			−1.45762
$275$	−2.77221e33	−	4.80161e33i	−0.0118169	−	0.0204674i
$276$	−1.05027e35	+	1.81912e35i	−0.424737	+	0.735665i
$277$	−1.77116e35	+	3.06774e35i	−0.679676	+	1.17723i	0.295403	+	0.955373i	$0.404546\pi$
$277$	−1.77116e35	+	3.06774e35i	−0.679676	+	1.17723i	−0.975079	+	0.221860i	$0.928787\pi$
$278$	2.15740e35	+	3.73672e35i	0.785743	+	1.36095i
$279$	7.42871e34			0.256834
$280$	4.42280e35	−	4.92335e34i	1.45180	−	0.161610i
$281$	−1.87038e35			−0.583027			−0.291513	−	0.956567i	$-0.594159\pi$
$281$	−1.87038e35			−0.583027			−0.291513	+	0.956567i	$0.594159\pi$
$282$	2.73224e35	+	4.73238e35i	0.808923	+	1.40110i
$283$	−2.90488e35	+	5.03140e35i	−0.817005	+	1.41509i	0.0908736	+	0.995862i	$0.471034\pi$
$283$	−2.90488e35	+	5.03140e35i	−0.817005	+	1.41509i	−0.907879	+	0.419232i	$0.862299\pi$
$284$	−1.49811e35	+	2.59480e35i	−0.400338	+	0.693406i
$285$	1.07458e35	+	1.86123e35i	0.272891	+	0.472661i
$286$	−9.29329e34			−0.224317
$287$	−2.14443e35	+	4.89718e35i	−0.492067	+	1.12372i
$288$	8.14636e34			0.177735
$289$	1.99377e35	+	3.45330e35i	0.413671	+	0.716500i
$290$	−9.05500e33	+	1.56837e34i	−0.0178697	+	0.0309512i
$291$	1.45687e35	−	2.52337e35i	0.273509	−	0.473731i
$292$	−1.59470e34	−	2.76210e34i	−0.0284857	−	0.0493387i
$293$	−7.65355e35			−1.30101			−0.650507	−	0.759500i	$-0.725444\pi$
$293$	−7.65355e35			−1.30101			−0.650507	+	0.759500i	$0.725444\pi$
$294$	4.06865e35	+	4.40858e35i	0.658286	+	0.713284i
$295$	9.90323e35			1.52531
$296$	−5.41664e35	−	9.38190e35i	−0.794329	−	1.37582i
$297$	−1.54141e34	+	2.66980e34i	−0.0215253	+	0.0372830i
$298$	1.07280e36	−	1.85814e36i	1.42686	−	2.47139i
$299$	−1.89635e35	−	3.28458e35i	−0.240263	−	0.416147i
$300$	9.22889e34			0.111402
$301$	5.00645e35	−	1.14331e36i	0.575859	−	1.31508i
$302$	−5.51162e35			−0.604197
$303$	1.28156e35	+	2.21972e35i	0.133912	+	0.231943i
$304$	2.29761e35	−	3.97959e35i	0.228881	−	0.396434i
$305$	2.47632e35	−	4.28911e35i	0.235212	−	0.407398i
$306$	1.28533e35	+	2.22626e35i	0.116427	+	0.201657i
$307$	8.95386e35			0.773578			0.386789	−	0.922168i	$-0.373584\pi$
$307$	8.95386e35			0.773578			0.386789	+	0.922168i	$0.373584\pi$
$308$	−4.92668e35	+	5.48426e34i	−0.406040	+	0.0451994i
$309$	−2.30667e34			−0.0181379
$310$	9.07632e35	+	1.57206e36i	0.681028	+	1.17958i
$311$	2.32951e35	−	4.03483e35i	0.166816	−	0.288935i	−0.770482	−	0.637461i	$-0.779985\pi$
$311$	2.32951e35	−	4.03483e35i	0.166816	−	0.288935i	0.937299	+	0.348527i	$0.113318\pi$
$312$	3.49953e35	−	6.06136e35i	0.239204	−	0.414313i
$313$	3.23823e35	+	5.60879e35i	0.211308	+	0.365996i	0.952124	−	0.305712i	$-0.0988944\pi$
$313$	3.23823e35	+	5.60879e35i	0.211308	+	0.365996i	−0.740816	+	0.671708i	$0.765561\pi$
$314$	2.80502e36			1.74765
$315$	3.49186e35	+	4.74458e35i	0.207756	+	0.282290i
$316$	−2.70497e36			−1.53709
$317$	9.81618e35	+	1.70021e36i	0.532823	+	0.922877i	0.999265	+	0.0383253i	$0.0122023\pi$
$317$	9.81618e35	+	1.70021e36i	0.532823	+	0.922877i	−0.466442	+	0.884552i	$0.654464\pi$
$318$	4.28787e35	−	7.42681e35i	0.222356	−	0.385131i
$319$	4.56376e33	−	7.90467e33i	0.00226130	−	0.00391669i
$320$	1.56067e36	+	2.70316e36i	0.738986	+	1.27996i
$321$	−1.67978e36			−0.760202
$322$	−1.85574e36	−	2.52150e36i	−0.802799	−	1.09081i
$323$	−9.03234e35			−0.373563
$324$	−2.56573e35	−	4.44398e35i	−0.101463	−	0.175740i
$325$	−8.33176e34	+	1.44310e35i	−0.0315085	+	0.0545743i
$326$	7.79986e34	−	1.35097e35i	0.0282118	−	0.0488643i
$327$	−7.56988e35	−	1.31114e36i	−0.261907	−	0.453635i
$328$	5.14864e36			1.70421
$329$	−5.23060e36	+	5.82257e35i	−1.65658	+	0.184406i
$330$	−7.53311e35			−0.228309
$331$	1.01769e35	+	1.76269e35i	0.0295195	+	0.0511292i	0.880408	−	0.474218i	$-0.157269\pi$
$331$	1.01769e35	+	1.76269e35i	0.0295195	+	0.0511292i	−0.850888	+	0.525347i	$0.823936\pi$
$332$	−2.80342e36	+	4.85566e36i	−0.778368	+	1.34817i
$333$	7.17050e35	−	1.24197e36i	0.190594	−	0.330118i
$334$	−3.77279e36	−	6.53466e36i	−0.960148	−	1.66303i
$335$	5.02615e36			1.22486
$336$	5.05244e35	−	1.15382e36i	0.117918	−	0.269288i
$337$	−5.43974e36			−1.21603			−0.608015	−	0.793925i	$-0.708034\pi$
$337$	−5.43974e36			−1.21603			−0.608015	+	0.793925i	$0.708034\pi$
$338$	−2.52878e36	−	4.37998e36i	−0.541527	−	0.937951i
$339$	−1.70667e35	+	2.95603e35i	−0.0350149	+	0.0606476i
$340$	−2.02954e36	+	3.51527e36i	−0.398982	+	0.691057i
$341$	−4.57451e35	−	7.92328e35i	−0.0861799	−	0.149268i
$342$	2.79023e36			0.503804
$343$	−5.46122e36	+	1.88638e36i	−0.945202	+	0.326486i
$344$	−1.20202e37			−1.99441
$345$	−1.53718e36	−	2.66247e36i	−0.244538	−	0.423553i
$346$	−5.80460e36	+	1.00539e37i	−0.885460	+	1.53366i
$347$	3.23051e36	−	5.59541e36i	0.472600	−	0.818568i	−0.526908	−	0.849922i	$-0.676649\pi$
$347$	3.23051e36	−	5.59541e36i	0.472600	−	0.818568i	0.999508	+	0.0313546i	$0.00998213\pi$
$348$	7.59655e34	+	1.31576e35i	0.0106590	+	0.0184620i
$349$	1.39545e37			1.87822			0.939111	−	0.343614i	$-0.111651\pi$
$349$	1.39545e37			1.87822			0.939111	+	0.343614i	$0.111651\pi$
$350$	−5.51749e35	+	1.26002e36i	−0.0712451	+	0.162701i
$351$	9.26529e35			0.114790
$352$	−5.01642e35	−	8.68870e35i	−0.0596383	−	0.103297i
$353$	−1.39343e36	+	2.41349e36i	−0.158983	+	0.275367i	−0.934502	−	0.355957i	$-0.884155\pi$
$353$	−1.39343e36	+	2.41349e36i	−0.158983	+	0.275367i	0.775519	+	0.631324i	$0.217488\pi$
$354$	6.42862e36	−	1.11347e37i	0.703996	−	1.21936i
$355$	−2.19263e36	−	3.79775e36i	−0.230491	−	0.399222i
$356$	−2.26851e37			−2.28936
$357$	−2.46063e36	+	2.73912e35i	−0.238428	+	0.0265412i
$358$	−1.82794e37			−1.70081
$359$	−6.30013e36	−	1.09122e37i	−0.562964	−	0.975082i	−0.997236	−	0.0742999i	$-0.976328\pi$
$359$	−6.30013e36	−	1.09122e37i	−0.562964	−	0.975082i	0.434272	−	0.900782i	$-0.357006\pi$
$360$	2.83671e36	−	4.91333e36i	0.243461	−	0.421686i
$361$	1.16300e36	−	2.01437e36i	0.0958790	−	0.166067i
$362$	−1.43733e36	−	2.48954e36i	−0.113837	−	0.197171i
$363$	−7.20760e36			−0.548459
$364$	8.83091e36	+	1.19990e37i	0.645707	+	0.877358i
$365$	4.66800e35			0.0328008
$366$	−3.21497e36	−	5.56850e36i	−0.217121	−	0.376064i
$367$	5.83102e35	−	1.00996e36i	0.0378518	−	0.0655613i	−0.846479	−	0.532422i	$-0.821282\pi$
$367$	5.83102e35	−	1.00996e36i	0.0378518	−	0.0655613i	0.884331	+	0.466861i	$0.154615\pi$
$368$	−3.28671e36	+	5.69275e36i	−0.205101	+	0.355246i
$369$	3.40786e36	+	5.90259e36i	0.204456	+	0.354128i
$370$	3.50433e37			2.02153
$371$	4.89570e36	+	6.65205e36i	0.271577	+	0.369006i
$372$	1.52289e37			0.812447
$373$	1.82284e37	+	3.15724e37i	0.935340	+	1.62006i	0.774027	+	0.633153i	$0.218240\pi$
$373$	1.82284e37	+	3.15724e37i	0.935340	+	1.62006i	0.161313	+	0.986903i	$0.448427\pi$
$374$	1.58298e36	−	2.74180e36i	0.0781334	−	0.135331i
$375$	5.71714e36	−	9.90238e36i	0.271472	−	0.470204i
$376$	2.53425e37	+	4.38946e37i	1.15778	+	2.00534i
$377$	−2.74324e35			−0.0120591
$378$	7.60129e36	−	8.46156e35i	0.321556	−	0.0357948i
$379$	1.98325e37			0.807435			0.403718	−	0.914884i	$-0.367718\pi$
$379$	1.98325e37			0.807435			0.403718	+	0.914884i	$0.367718\pi$
$380$	2.20289e37	+	3.81552e37i	0.863239	+	1.49517i
$381$	1.27963e37	−	2.21639e37i	0.482696	−	0.836053i
$382$	−7.86117e36	+	1.36160e37i	−0.285475	+	0.494458i
$383$	−2.43503e37	−	4.21760e37i	−0.851378	−	1.47463i	−0.879965	−	0.475039i	$-0.842434\pi$
$383$	−2.43503e37	−	4.21760e37i	−0.851378	−	1.47463i	0.0285864	−	0.999591i	$-0.490899\pi$
$384$	3.13800e37			1.05645
$385$	2.91021e36	−	6.64598e36i	0.0943504	−	0.215466i
$386$	−7.40985e37			−2.31363
$387$	−7.95611e36	−	1.37804e37i	−0.239272	−	0.414431i
$388$	2.98658e37	−	5.17290e37i	0.865194	−	1.49856i
$389$	2.97098e37	−	5.14589e37i	0.829145	−	1.43612i	−0.0695651	−	0.997577i	$-0.522161\pi$
$389$	2.97098e37	−	5.14589e37i	0.829145	−	1.43612i	0.898710	−	0.438544i	$-0.144506\pi$
$390$	1.13202e37	+	1.96072e37i	0.304381	+	0.527204i
$391$	1.29207e37			0.334751
$392$	3.77382e37	+	4.08912e37i	0.942180	+	1.02090i
$393$	3.68699e37			0.887115
$394$	2.95264e37	+	5.11413e37i	0.684724	+	1.18598i
$395$	1.97949e37	−	3.42858e37i	0.442483	−	0.766403i
$396$	−3.15989e36	+	5.47310e36i	−0.0680914	+	0.117938i
$397$	−4.10303e37	−	7.10666e37i	−0.852398	−	1.47640i	−0.879038	−	0.476752i	$-0.841814\pi$
$397$	−4.10303e37	−	7.10666e37i	−0.852398	−	1.47640i	0.0266397	−	0.999645i	$-0.491519\pi$
$398$	−1.39544e38			−2.79516
$399$	−1.07793e37	+	2.46164e37i	−0.208201	+	0.475464i
$400$	2.88808e36			0.0537947
$401$	2.30070e37	+	3.98493e37i	0.413301	+	0.715858i	0.995248	−	0.0973683i	$-0.0310425\pi$
$401$	2.30070e37	+	3.98493e37i	0.413301	+	0.715858i	−0.581948	+	0.813226i	$0.697709\pi$
$402$	3.26269e37	−	5.65115e37i	0.565325	−	0.979171i
$403$	−1.37485e37	+	2.38131e37i	−0.229790	+	0.398009i
$404$	2.62720e37	+	4.55044e37i	0.423607	+	0.733708i
$405$	7.51042e36			0.116833
$406$	−2.25057e36	+	2.50527e35i	−0.0337803	+	0.00376034i
$407$	−1.76620e37			−0.255812
$408$	1.19219e37	+	2.06493e37i	0.166638	+	0.288625i
$409$	2.98992e37	−	5.17870e37i	0.403341	−	0.698607i	−0.590786	−	0.806828i	$-0.701182\pi$
$409$	2.98992e37	−	5.17870e37i	0.403341	−	0.698607i	0.994127	+	0.108222i	$0.0345156\pi$
$410$	−8.32737e37	+	1.44234e38i	−1.08428	+	1.87803i
$411$	−1.99136e37	−	3.44913e37i	−0.250290	−	0.433514i
$412$	−4.72867e36			−0.0573758
$413$	7.33991e37	+	9.97314e37i	0.859835	+	1.16830i
$414$	−3.99139e37			−0.451460
$415$	−4.10308e37	−	7.10674e37i	−0.448139	−	0.776199i
$416$	−1.50766e37	+	2.61135e37i	−0.159020	+	0.275430i
$417$	−2.64899e37	+	4.58819e37i	−0.269841	+	0.467378i
$418$	−1.71819e37	−	2.97599e37i	−0.169050	−	0.292803i
$419$	−5.90326e37			−0.561034			−0.280517	−	0.959849i	$-0.590506\pi$
$419$	−5.90326e37			−0.561034			−0.280517	+	0.959849i	$0.590506\pi$
$420$	7.15831e37	+	9.72639e37i	0.657198	+	0.892971i
$421$	2.14740e36			0.0190468			0.00952340	−	0.999955i	$-0.496969\pi$
$421$	2.14740e36			0.0190468			0.00952340	+	0.999955i	$0.496969\pi$
$422$	1.17671e38	+	2.03812e38i	1.00841	+	1.74662i
$423$	−3.35482e37	+	5.81072e37i	−0.277801	+	0.481166i
$424$	3.97716e37	−	6.88864e37i	0.318249	−	0.551224i
$425$	−2.83839e36	−	4.91624e36i	−0.0219499	−	0.0380184i
$426$	−5.69333e37			−0.425527
$427$	6.15474e37	−	6.85130e36i	0.444637	−	0.0494959i
$428$	−3.44355e38			−2.40476
$429$	−5.70545e36	−	9.88213e36i	−0.0385176	−	0.0667144i
$430$	1.94414e38	−	3.36734e38i	1.26892	−	2.19783i
$431$	−1.02041e38	+	1.76740e38i	−0.643952	+	1.11536i	0.340591	+	0.940212i	$0.389373\pi$
$431$	−1.02041e38	+	1.76740e38i	−0.643952	+	1.11536i	−0.984543	+	0.175145i	$0.943960\pi$
$432$	−8.02919e36	−	1.39070e37i	−0.0489957	−	0.0848630i
$433$	−1.90029e37			−0.112136			−0.0560681	−	0.998427i	$-0.517856\pi$
$433$	−1.90029e37			−0.112136			−0.0560681	+	0.998427i	$0.517856\pi$
$434$	−9.10458e37	+	2.07919e38i	−0.519588	+	1.18657i
$435$	−2.22366e36			−0.0122737
$436$	−1.55182e38	−	2.68784e38i	−0.828492	−	1.43499i
$437$	7.01213e37	−	1.21454e38i	0.362134	−	0.627235i
$438$	3.03020e36	−	5.24846e36i	0.0151390	−	0.0262215i
$439$	−1.17805e38	−	2.04044e38i	−0.569414	−	0.986254i	−0.996624	−	0.0821016i	$-0.973837\pi$
$439$	−1.17805e38	−	2.04044e38i	−0.569414	−	0.986254i	0.427210	−	0.904152i	$-0.359497\pi$
$440$	−6.98724e37			−0.326770
$441$	−2.19004e37	+	7.03302e37i	−0.0991042	+	0.318260i
$442$	−9.51515e37			−0.416670
$443$	−2.50502e37	−	4.33883e37i	−0.106159	−	0.183873i	0.808052	−	0.589111i	$-0.200522\pi$
$443$	−2.50502e37	−	4.33883e37i	−0.106159	−	0.183873i	−0.914211	+	0.405238i	$0.867189\pi$
$444$	1.46995e38	−	2.54603e38i	0.602907	−	1.04427i
$445$	1.66009e38	−	2.87536e38i	0.659041	−	1.14149i
$446$	−2.99409e38	−	5.18591e38i	−1.15056	−	1.99283i
$447$	2.63449e38			0.980027
$448$	−1.56553e38	+	3.57517e38i	−0.563807	+	1.28755i
$449$	4.36088e38			1.52055			0.760277	−	0.649598i	$-0.225063\pi$
$449$	4.36088e38			1.52055			0.760277	+	0.649598i	$0.225063\pi$
$450$	8.76824e36	+	1.51870e37i	0.0296027	+	0.0512734i
$451$	4.19704e37	−	7.26948e37i	0.137209	−	0.237653i
$452$	−3.49867e37	+	6.05987e37i	−0.110763	+	0.191847i
$453$	−3.38376e37	−	5.86084e37i	−0.103747	−	0.179695i
$454$	4.96162e38			1.47338
$455$	−2.16714e38	+	2.41241e37i	−0.623336	+	0.0693882i
$456$	2.58804e38			0.721076
$457$	2.17029e38	+	3.75905e38i	0.585777	+	1.01460i	0.994778	+	0.102061i	$0.0325438\pi$
$457$	2.17029e38	+	3.75905e38i	0.585777	+	1.01460i	−0.409001	+	0.912534i	$0.634123\pi$
$458$	4.94754e37	−	8.56939e37i	0.129372	−	0.224079i
$459$	−1.57821e37	+	2.73354e37i	−0.0399835	+	0.0692535i
$460$	−3.15121e38	−	5.45806e38i	−0.773551	−	1.33983i
$461$	2.84477e38			0.676680			0.338340	−	0.941024i	$-0.390135\pi$
$461$	2.84477e38			0.676680			0.338340	+	0.941024i	$0.390135\pi$
$462$	−5.58327e37	−	7.58629e37i	−0.128700	−	0.174872i
$463$	−6.77785e38			−1.51414			−0.757072	−	0.653331i	$-0.773371\pi$
$463$	−6.77785e38			−1.51414			−0.757072	+	0.653331i	$0.773371\pi$
$464$	2.37726e36	+	4.11753e36i	0.00514714	+	0.00891510i
$465$	−1.11445e38	+	1.93028e38i	−0.233880	+	0.405091i
$466$	1.35969e38	−	2.35504e38i	0.276594	−	0.479075i
$467$	8.50420e37	+	1.47297e38i	0.167702	+	0.290469i	0.937612	−	0.347684i	$-0.113032\pi$
$467$	8.50420e37	+	1.47297e38i	0.167702	+	0.290469i	−0.769909	+	0.638153i	$0.779699\pi$
$468$	1.89938e38			0.363118
$469$	3.72519e38	+	5.06163e38i	0.690466	+	0.938175i
$470$	−1.63955e39			−2.94650
$471$	1.72209e38	+	2.98275e38i	0.300091	+	0.519773i
$472$	5.96278e38	−	1.03278e39i	1.00760	−	1.74522i
$473$	−9.79855e37	+	1.69716e38i	−0.160574	+	0.278122i
$474$	−2.56995e38	−	4.45129e38i	−0.408450	−	0.707456i
$475$	−6.16167e37			−0.0949819
$476$	−5.04430e38	+	5.61519e37i	−0.754224	+	0.0839583i
$477$	1.05298e38			0.152723
$478$	1.03467e39	+	1.79211e39i	1.45579	+	2.52151i
$479$	2.38913e38	−	4.13809e38i	0.326118	−	0.564852i	−0.655620	−	0.755091i	$-0.727593\pi$
$479$	2.38913e38	−	4.13809e38i	0.326118	−	0.564852i	0.981738	+	0.190239i	$0.0609261\pi$
$480$	−1.22211e38	+	2.11675e38i	−0.161850	+	0.280332i
$481$	2.65412e38	+	4.59707e38i	0.341049	+	0.590715i
$482$	−4.57786e38			−0.570795
$483$	1.54196e38	−	3.52135e38i	0.186570	−	0.426065i
$484$	−1.47756e39			−1.73495
$485$	4.37115e38	+	7.57106e38i	0.498128	+	0.862782i
$486$	4.87534e37	−	8.44434e37i	0.0539236	−	0.0933985i
$487$	1.65020e38	−	2.85823e38i	0.177161	−	0.306851i	−0.763746	−	0.645517i	$-0.776642\pi$
$487$	1.65020e38	−	2.85823e38i	0.177161	−	0.306851i	0.940907	+	0.338665i	$0.109975\pi$
$488$	−2.98200e38	−	5.16498e38i	−0.310757	−	0.538247i
$489$	1.91543e37			0.0193771
$490$	−1.75590e39	+	3.95830e38i	−1.72448	+	0.388746i
$491$	−1.78162e39			−1.69877			−0.849383	−	0.527778i	$-0.823025\pi$
$491$	−1.78162e39			−1.69877			−0.849383	+	0.527778i	$0.823025\pi$
$492$	6.98612e38	+	1.21003e39i	0.646758	+	1.12022i
$493$	4.67272e36	−	8.09338e36i	0.00420038	−	0.00727528i
$494$	−5.16394e38	+	8.94421e38i	−0.450755	+	0.780731i
$495$	−4.62482e37	−	8.01043e37i	−0.0392030	−	0.0679016i
$496$	4.76571e38			0.392323
$497$	2.19946e38	−	5.02286e38i	0.175852	−	0.401590i
$498$	−1.06539e39			−0.827342
$499$	6.28550e38	+	1.08868e39i	0.474113	+	0.821189i	0.999561	−	0.0296376i	$-0.00943533\pi$
$499$	6.28550e38	+	1.08868e39i	0.474113	+	0.821189i	−0.525447	+	0.850826i	$0.676102\pi$
$500$	1.17201e39	−	2.02999e39i	0.858752	−	1.48740i
$501$	4.63247e38	−	8.02367e38i	0.329735	−	0.571118i
$502$	1.61020e39	+	2.78894e39i	1.11346	+	1.92857i
$503$	2.43798e39			1.63793			0.818963	−	0.573846i	$-0.194549\pi$
$503$	2.43798e39			1.63793			0.818963	+	0.573846i	$0.194549\pi$
$504$	7.05047e38	−	7.84841e37i	0.460231	−	0.0512317i
$505$	−7.69033e38			−0.487775
$506$	2.45785e38	+	4.25712e38i	0.151486	+	0.262382i
$507$	3.10501e38	−	5.37803e38i	0.185972	−	0.322112i
$508$	2.62325e39	−	4.54360e39i	1.52692	−	2.64470i
$509$	3.26422e38	+	5.65379e38i	0.184659	+	0.319839i	0.943462	−	0.331482i	$-0.107549\pi$
$509$	3.26422e38	+	5.65379e38i	0.184659	+	0.319839i	−0.758802	+	0.651321i	$0.774215\pi$
$510$	−7.71295e38			−0.424085
$511$	3.45975e37	+	4.70095e37i	0.0184902	+	0.0251236i
$512$	1.88423e39			0.978856
$513$	1.71301e38	+	2.96703e38i	0.0865085	+	0.149837i
$514$	−2.47857e39	+	4.29301e39i	−1.21685	+	2.10764i
$515$	3.46044e37	−	5.99365e37i	0.0165168	−	0.0286080i
$516$	−1.63100e39	−	2.82498e39i	−0.756893	−	1.31098i
$517$	8.26343e38			0.372861
$518$	2.59728e39	+	3.52907e39i	1.13956	+	1.54838i
$519$	−1.42545e39			−0.608172
$520$	1.04999e39	+	1.81864e39i	0.435650	+	0.754568i
$521$	9.90335e38	−	1.71531e39i	0.399609	−	0.692143i	−0.594069	−	0.804414i	$-0.702479\pi$
$521$	9.90335e38	−	1.71531e39i	0.399609	−	0.692143i	0.993678	+	0.112271i	$0.0358126\pi$
$522$	−1.44348e37	+	2.50017e37i	−0.00566483	+	0.00981178i
$523$	1.57275e39	+	2.72409e39i	0.600324	+	1.03979i	0.992772	+	0.120018i	$0.0382951\pi$
$523$	1.57275e39	+	2.72409e39i	0.600324	+	1.03979i	−0.392448	+	0.919774i	$0.628372\pi$
$524$	7.55833e39			2.80622
$525$	−1.67859e38	+	1.86857e37i	−0.0606227	+	0.00674837i
$526$	−6.09522e39			−2.14139
$527$	−4.68372e38	−	8.11244e38i	−0.160080	−	0.277267i
$528$	−9.88855e37	+	1.71275e38i	−0.0328807	+	0.0569510i
$529$	5.42452e38	−	9.39554e38i	0.175491	−	0.303959i
$530$	1.28652e39	+	2.22832e39i	0.404965	+	0.701420i
$531$	1.57869e39			0.483535
$532$	−2.20975e39	+	5.04637e39i	−0.658605	+	1.50404i
$533$	−2.52280e39			−0.731710
$534$	−2.15528e39	−	3.73305e39i	−0.608352	−	1.05370i
$535$	2.51999e39	−	4.36475e39i	0.692259	−	1.19903i
$536$	3.02626e39	−	5.24164e39i	0.809128	−	1.40145i
$537$	−1.12223e39	−	1.94376e39i	−0.292048	−	0.505842i
$538$	−6.37680e39			−1.61533
$539$	8.84984e38	−	1.99500e38i	0.218222	−	0.0491934i
$540$	1.53964e39			0.369580
$541$	−1.13375e39	−	1.96372e39i	−0.264946	−	0.458900i	0.702603	−	0.711582i	$-0.252021\pi$
$541$	−1.13375e39	−	1.96372e39i	−0.264946	−	0.458900i	−0.967550	+	0.252682i	$0.918688\pi$
$542$	3.59596e39	−	6.22838e39i	0.818135	−	1.41705i
$543$	1.76485e38	−	3.05681e38i	0.0390940	−	0.0677129i
$544$	−5.13618e38	−	8.89613e38i	−0.110779	−	0.191874i
$545$	4.54250e39			0.953994
$546$	−1.13555e39	+	2.59323e39i	−0.232227	+	0.530331i
$547$	5.74906e39			1.14493			0.572467	−	0.819928i	$-0.305987\pi$
$547$	5.74906e39			1.14493			0.572467	+	0.819928i	$0.305987\pi$
$548$	−4.08228e39	−	7.07072e39i	−0.791745	−	1.37134i
$549$	3.94755e38	−	6.83736e38i	0.0745639	−	0.129148i
$550$	1.07987e38	−	1.87040e38i	0.0198662	−	0.0344092i
$551$	−5.07183e37	−	8.78468e37i	−0.00908797	−	0.0157408i
$552$	−3.70216e39			−0.646158
$553$	4.91992e39	−	5.47673e38i	0.836456	−	0.0931122i
$554$	−1.37986e40			−2.28530
$555$	2.15142e39	+	3.72637e39i	0.347118	+	0.601227i
$556$	−5.43043e39	+	9.40578e39i	−0.853591	+	1.47846i
$557$	−1.16883e39	+	2.02448e39i	−0.179000	+	0.310036i	−0.941538	−	0.336906i	$-0.890619\pi$
$557$	−1.16883e39	+	2.02448e39i	−0.179000	+	0.310036i	0.762539	+	0.646943i	$0.223953\pi$
$558$	1.44687e39	+	2.50606e39i	0.215891	+	0.373935i
$559$	5.88982e39			0.856310
$560$	2.24012e39	+	3.04377e39i	0.317354	+	0.431207i
$561$	3.88737e38			0.0536654
$562$	−3.64290e39	−	6.30969e39i	−0.490084	−	0.848850i
$563$	2.21393e39	−	3.83464e39i	0.290264	−	0.502751i	−0.683608	−	0.729849i	$-0.739590\pi$
$563$	2.21393e39	−	3.83464e39i	0.290264	−	0.502751i	0.973872	+	0.227098i	$0.0729237\pi$
$564$	−6.87739e39	+	1.19120e40i	−0.878772	+	1.52208i
$565$	−5.12065e38	−	8.86923e38i	−0.0637709	−	0.110454i
$566$	−2.26311e40			−2.74705
$567$	5.56645e38	+	7.56344e38i	0.0658603	+	0.0894880i
$568$	−5.28077e39			−0.609041
$569$	−3.07796e39	−	5.33119e39i	−0.346047	−	0.599372i	0.639496	−	0.768794i	$-0.279143\pi$
$569$	−3.07796e39	−	5.33119e39i	−0.346047	−	0.599372i	−0.985543	+	0.169423i	$0.945810\pi$
$570$	−4.18588e39	+	7.25015e39i	−0.458776	+	0.794624i
$571$	5.87350e38	−	1.01732e39i	0.0627586	−	0.108701i	−0.832939	−	0.553365i	$-0.813344\pi$
$571$	5.87350e38	−	1.01732e39i	0.0627586	−	0.108701i	0.895698	+	0.444664i	$0.146677\pi$
$572$	−1.16962e39	−	2.02584e39i	−0.121843	−	0.211039i
$573$	−1.93049e39			−0.196077
$574$	−2.06972e40	+	2.30396e39i	−2.04969	+	0.228167i
$575$	8.81419e38			0.0851136
$576$	2.48790e39	+	4.30916e39i	0.234264	+	0.405758i
$577$	8.21643e38	−	1.42313e39i	0.0754456	−	0.130676i	−0.825834	−	0.563913i	$-0.809295\pi$
$577$	8.21643e38	−	1.42313e39i	0.0754456	−	0.130676i	0.901280	+	0.433237i	$0.142629\pi$
$578$	−7.76643e39	+	1.34518e40i	−0.695453	+	1.20456i
$579$	−4.54914e39	−	7.87935e39i	−0.397274	−	0.688099i
$580$	−4.55851e38			−0.0388255
$581$	4.11586e39	−	9.39930e39i	0.341906	−	0.780803i
$582$	1.13500e40			0.919630
$583$	−6.48414e38	−	1.12309e39i	−0.0512458	−	0.0887604i
$584$	2.81062e38	−	4.86814e38i	0.0216679	−	0.0375299i
$585$	−1.38997e39	+	2.40750e39i	−0.104531	+	0.181053i
$586$	−1.49066e40	−	2.58191e40i	−1.09362	−	1.89420i
$587$	1.65031e39			0.118117			0.0590584	−	0.998255i	$-0.481190\pi$
$587$	1.65031e39			0.118117			0.0590584	+	0.998255i	$0.481190\pi$
$588$	−4.48958e39	+	1.44177e40i	−0.313498	+	1.00676i
$589$	−1.01676e40			−0.692699
$590$	1.92883e40	+	3.34083e40i	1.28215	+	2.22075i
$591$	−3.62544e39	+	6.27945e39i	−0.235149	+	0.407290i
$592$	4.60006e39	−	7.96754e39i	0.291138	−	0.504266i
$593$	−5.13860e39	−	8.90032e39i	−0.317360	−	0.549683i	0.662577	−	0.748994i	$-0.269463\pi$
$593$	−5.13860e39	−	8.90032e39i	−0.317360	−	0.549683i	−0.979936	+	0.199311i	$0.936130\pi$
$594$	−1.20087e39			−0.0723756
$595$	2.97969e39	−	6.80465e39i	0.175257	−	0.400230i
$596$	5.40071e40			3.10013
$597$	−8.56706e39	−	1.48386e40i	−0.479959	−	0.831313i
$598$	7.38696e39	−	1.27946e40i	0.403923	−	0.699615i
$599$	4.77847e39	−	8.27655e39i	0.255035	−	0.441733i	−0.709870	−	0.704333i	$-0.751246\pi$
$599$	4.77847e39	−	8.27655e39i	0.255035	−	0.441733i	0.964905	+	0.262599i	$0.0845797\pi$
$600$	8.13287e38	+	1.40865e39i	0.0423692	+	0.0733857i
$601$	2.30032e40			1.16979			0.584895	−	0.811109i	$-0.301136\pi$
$601$	2.30032e40			1.16979			0.584895	+	0.811109i	$0.301136\pi$
$602$	4.83204e40	−	5.37890e39i	2.39873	−	0.267020i
$603$	8.01228e39			0.388289
$604$	−6.93671e39	−	1.20147e40i	−0.328184	−	0.568432i
$605$	1.08128e40	−	1.87283e40i	0.499441	−	0.865056i
$606$	−4.99213e39	+	8.64662e39i	−0.225130	+	0.389936i
$607$	−1.76284e40	−	3.05333e40i	−0.776206	−	1.34443i	−0.934114	−	0.356975i	$-0.883808\pi$
$607$	−1.76284e40	−	3.05333e40i	−0.776206	−	1.34443i	0.157908	−	0.987454i	$-0.449525\pi$
$608$	−1.11498e40			−0.479363
$609$	−1.64810e38	−	2.23936e38i	−0.00691881	−	0.00940097i
$610$	1.92923e40			0.790863
$611$	−1.24177e40	−	2.15081e40i	−0.497099	−	0.861001i
$612$	−3.23533e39	+	5.60376e39i	−0.126480	+	0.219070i
$613$	1.03027e40	−	1.78447e40i	0.393344	−	0.681291i	−0.599544	−	0.800341i	$-0.704652\pi$
$613$	1.03027e40	−	1.78447e40i	0.393344	−	0.681291i	0.992888	+	0.119050i	$0.0379849\pi$
$614$	1.74392e40	+	3.02056e40i	0.650259	+	1.12628i
$615$	−2.04498e40			−0.744731
$616$	−5.17868e39	−	7.03656e39i	−0.184204	−	0.250288i
$617$	1.69251e40			0.588025			0.294012	−	0.955802i	$-0.405009\pi$
$617$	1.69251e40			0.588025			0.294012	+	0.955802i	$0.405009\pi$
$618$	−4.49264e38	−	7.78148e38i	−0.0152465	−	0.0264076i
$619$	−1.30965e40	+	2.26839e40i	−0.434152	+	0.751974i	−0.997226	−	0.0744329i	$-0.976285\pi$
$619$	−1.30965e40	+	2.26839e40i	−0.434152	+	0.751974i	0.563074	+	0.826407i	$0.309619\pi$
$620$	−2.28462e40	+	3.95708e40i	−0.739834	+	1.28143i
$621$	−2.45044e39	−	4.24429e39i	−0.0775205	−	0.134269i
$622$	1.81485e40			0.560894
$623$	4.12606e40	−	4.59303e39i	1.24583	−	0.138683i
$624$	5.94392e39			0.175346
$625$	1.89863e40	+	3.28853e40i	0.547244	+	0.947855i
$626$	−1.26141e40	+	2.18482e40i	−0.355245	+	0.615302i
$627$	2.10970e39	−	3.65411e39i	0.0580553	−	0.100555i
$628$	3.53029e40	+	6.11463e40i	0.949282	+	1.64420i
$629$	−1.80837e40			−0.475174
$630$	−9.20472e39	+	2.10206e40i	−0.236359	+	0.539769i
$631$	3.87257e40			0.971793			0.485896	−	0.874016i	$-0.338493\pi$
$631$	3.87257e40			0.971793			0.485896	+	0.874016i	$0.338493\pi$
$632$	−2.38372e40	−	4.12873e40i	−0.584600	−	1.01256i
$633$	−1.44484e40	+	2.50253e40i	−0.346310	+	0.599826i
$634$	−3.82375e40	+	6.62293e40i	−0.895768	+	1.55152i
$635$	3.83939e40	+	6.65001e40i	0.879109	+	1.52266i
$636$	2.15862e40			0.483112
$637$	−1.84915e40	−	2.00364e40i	−0.404530	−	0.438327i
$638$	3.55550e38			0.00760327
$639$	−3.49532e39	−	6.05407e39i	−0.0730675	−	0.126557i
$640$	−4.70759e40	+	8.15379e40i	−0.962031	+	1.66629i
$641$	−2.03722e39	+	3.52856e39i	−0.0407001	+	0.0704947i	−0.885658	−	0.464338i	$-0.846292\pi$
$641$	−2.03722e39	+	3.52856e39i	−0.0407001	+	0.0704947i	0.844958	+	0.534833i	$0.179626\pi$
$642$	−3.27167e40	−	5.66670e40i	−0.639016	−	1.10681i
$643$	7.97537e40			1.52297			0.761486	−	0.648181i	$-0.224470\pi$
$643$	7.97537e40			1.52297			0.761486	+	0.648181i	$0.224470\pi$
$644$	3.16103e40	−	7.21877e40i	0.590178	−	1.34778i
$645$	4.77427e40			0.871548
$646$	−1.75921e40	−	3.04704e40i	−0.314012	−	0.543884i
$647$	−2.34651e40	+	4.06427e40i	−0.409553	+	0.709366i	−0.994840	−	0.101460i	$-0.967648\pi$
$647$	−2.34651e40	+	4.06427e40i	−0.409553	+	0.709366i	0.585287	+	0.810826i	$0.300982\pi$
$648$	4.52206e39	−	7.83243e39i	0.0771789	−	0.133678i
$649$	−9.72140e39	−	1.68380e40i	−0.162249	−	0.281023i
$650$	−6.49103e39			−0.105942
$651$	−2.76990e40	+	3.08338e39i	−0.442119	+	0.0492156i
$652$	3.92664e39			0.0612958
$653$	−9.53995e39	−	1.65237e40i	−0.145648	−	0.252270i	0.783966	−	0.620803i	$-0.213193\pi$
$653$	−9.53995e39	−	1.65237e40i	−0.145648	−	0.252270i	−0.929615	+	0.368533i	$0.879860\pi$
$654$	2.94874e40	−	5.10736e40i	0.440310	−	0.762639i
$655$	−5.53118e40	+	9.58029e40i	−0.807829	+	1.39920i
$656$	2.18623e40	+	3.78666e40i	0.312313	+	0.540943i
$657$	7.44135e38			0.0103981
$658$	−1.21518e41	−	1.65113e41i	−1.66098	−	2.25686i
$659$	−9.95267e40			−1.33076			−0.665382	−	0.746503i	$-0.731731\pi$
$659$	−9.95267e40			−1.33076			−0.665382	+	0.746503i	$0.731731\pi$
$660$	−9.48089e39	−	1.64214e40i	−0.124011	−	0.214794i
$661$	−4.78857e40	+	8.29404e40i	−0.612752	+	1.06132i	0.378023	+	0.925796i	$0.376604\pi$
$661$	−4.78857e40	+	8.29404e40i	−0.612752	+	1.06132i	−0.990775	+	0.135521i	$0.956729\pi$
$662$	−3.96425e39	+	6.86629e39i	−0.0496273	+	0.0859570i
$663$	−5.84166e39	−	1.01180e40i	−0.0715468	−	0.123923i
$664$	−9.88193e40			−1.18414
$665$	−4.77925e40	−	6.49383e40i	−0.560332	−	0.761354i
$666$	5.58633e40			0.640841
$667$	7.25520e38	+	1.25664e39i	0.00814376	+	0.0141054i
$668$	9.49656e40	−	1.64485e41i	1.04306	−	1.80663i
$669$	3.67633e40	−	6.36760e40i	0.395127	−	0.684379i
$670$	9.78931e40	+	1.69556e41i	1.02960	+	1.78332i
$671$	−9.72341e39			−0.100079
$672$	−3.03748e40	+	3.38124e39i	−0.305956	+	0.0340582i
$673$	1.46094e41			1.44017			0.720086	−	0.693884i	$-0.244102\pi$
$673$	1.46094e41			1.44017			0.720086	+	0.693884i	$0.244102\pi$
$674$	−1.05949e41	−	1.83508e41i	−1.02218	−	1.77047i
$675$	−1.07662e39	+	1.86476e39i	−0.0101662	+	0.0176084i
$676$	6.36526e40	−	1.10250e41i	0.588287	−	1.01894i
$677$	4.53224e40	+	7.85007e40i	0.409994	+	0.710130i	0.994889	−	0.100979i	$-0.0321976\pi$
$677$	4.53224e40	+	7.85007e40i	0.409994	+	0.710130i	−0.584895	+	0.811109i	$0.698864\pi$
$678$	−1.32962e40			−0.117732
$679$	−4.38477e40	+	1.00134e41i	−0.380045	+	0.867900i
$680$	−7.15405e40			−0.606978
$681$	3.04610e40	+	5.27600e40i	0.252994	+	0.438199i
$682$	1.78193e40	−	3.08640e40i	0.144883	−	0.250945i
$683$	−9.70434e40	+	1.68084e41i	−0.772442	+	1.33791i	0.163780	+	0.986497i	$0.447631\pi$
$683$	−9.70434e40	+	1.68084e41i	−0.772442	+	1.33791i	−0.936221	+	0.351411i	$0.885702\pi$
$684$	3.51168e40	+	6.08240e40i	0.273654	+	0.473982i
$685$	1.19497e41			0.911680
$686$	−1.70003e41	−	1.47492e41i	−1.26987	−	1.10172i
$687$	1.21498e40			0.0888581
$688$	−5.10405e40	−	8.84048e40i	−0.365496	−	0.633058i
$689$	−1.94878e40	+	3.37539e40i	−0.136642	+	0.236671i
$690$	5.98785e40	−	1.03713e41i	0.411111	−	0.712065i
$691$	4.43524e40	+	7.68207e40i	0.298185	+	0.516472i	0.975721	−	0.219018i	$-0.0702854\pi$
$691$	4.43524e40	+	7.68207e40i	0.298185	+	0.516472i	−0.677536	+	0.735490i	$0.736952\pi$
$692$	−2.92218e41			−1.92384
$693$	4.63922e39	−	1.05945e40i	0.0299098	−	0.0683044i
$694$	2.51680e41			1.58904
$695$	−7.94798e40	−	1.37663e41i	−0.491448	−	0.851212i
$696$	−1.33888e39	+	2.31900e39i	−0.00810787	+	0.0140432i
$697$	4.29723e40	−	7.44303e40i	0.254867	−	0.441443i
$698$	2.71790e41	+	4.70753e41i	1.57881	+	2.73457i
$699$	3.33902e40			0.189976
$700$	−3.44111e40	+	3.83056e39i	−0.191769	+	0.0213472i
$701$	−1.73950e41			−0.949540			−0.474770	−	0.880110i	$-0.657469\pi$
$701$	−1.73950e41			−0.949540			−0.474770	+	0.880110i	$0.657469\pi$
$702$	1.80458e40	+	3.12562e40i	0.0964913	+	0.167128i
$703$	−9.81414e40	+	1.69986e41i	−0.514044	+	0.890350i
$704$	3.06403e40	−	5.30705e40i	0.157213	−	0.272301i
$705$	−1.00657e41	−	1.74344e41i	−0.505945	−	0.876323i
$706$	−1.08558e41			−0.534557
$707$	−5.69979e40	−	7.74462e40i	−0.274965	−	0.373610i
$708$	3.23632e41			1.52957
$709$	1.17723e41	+	2.03902e41i	0.545117	+	0.944170i	0.998600	+	0.0529047i	$0.0168479\pi$
$709$	1.17723e41	+	2.03902e41i	0.545117	+	0.944170i	−0.453483	+	0.891265i	$0.649819\pi$
$710$	8.54107e40	−	1.47936e41i	0.387495	−	0.671162i
$711$	3.15555e40	−	5.46558e40i	0.140270	−	0.242956i
$712$	−1.99910e41	−	3.46254e41i	−0.870712	−	1.50812i
$713$	1.45446e41			0.620730
$714$	−5.71656e40	−	7.76740e40i	−0.239062	−	0.324827i
$715$	3.42370e40			0.140300
$716$	−2.30057e41	−	3.98470e41i	−0.923839	−	1.60014i
$717$	−1.27044e41	+	2.20047e41i	−0.499950	+	0.865938i
$718$	2.45413e41	−	4.25067e41i	0.946439	−	1.63928i
$719$	7.67018e40	+	1.32851e41i	0.289892	+	0.502108i	0.973784	−	0.227476i	$-0.0730472\pi$
$719$	7.67018e40	+	1.32851e41i	0.289892	+	0.502108i	−0.683892	+	0.729584i	$0.739714\pi$
$720$	4.81813e40			0.178467
$721$	8.60071e39	−	9.57410e38i	0.0312229	−	0.00347565i
$722$	9.06056e40			0.322378
$723$	−2.81049e40	−	4.86792e40i	−0.0980116	−	0.169761i
$724$	3.61795e40	−	6.26647e40i	0.123667	−	0.214197i
$725$	3.18763e38	−	5.52113e38i	0.00106799	−	0.00184981i
$726$	−1.40381e41	−	2.43147e41i	−0.461027	−	0.798523i
$727$	−3.73425e41			−1.20214			−0.601069	−	0.799197i	$-0.705258\pi$
$727$	−3.73425e41			−1.20214			−0.601069	+	0.799197i	$0.705258\pi$
$728$	−1.05326e41	+	2.40531e41i	−0.332377	+	0.759043i
$729$	1.19725e40			0.0370370
$730$	9.09176e39	+	1.57474e40i	0.0275719	+	0.0477559i
$731$	−1.00325e41	+	1.73768e41i	−0.298268	+	0.516615i
$732$	8.09248e40	−	1.40166e41i	0.235869	−	0.408537i
$733$	−1.75851e41	−	3.04583e41i	−0.502501	−	0.870357i	−0.999996	−	0.00289040i	$-0.999080\pi$
$733$	−1.75851e41	−	3.04583e41i	−0.502501	−	0.870357i	0.497495	−	0.867467i	$-0.334253\pi$
$734$	4.54278e40			0.127271
$735$	−1.49892e41	−	1.62415e41i	−0.411729	−	0.446127i
$736$	1.59496e41			0.429558
$737$	−4.93386e40	−	8.54570e40i	−0.130289	−	0.225668i
$738$	−1.32748e41	+	2.29927e41i	−0.343726	+	0.595350i
$739$	1.85916e41	−	3.22016e41i	0.472033	−	0.817585i	−0.527455	−	0.849583i	$-0.676854\pi$
$739$	1.85916e41	−	3.22016e41i	0.472033	−	0.817585i	0.999488	+	0.0319982i	$0.0101871\pi$
$740$	4.41042e41	+	7.63907e41i	1.09804	+	1.90187i
$741$	−1.26812e41			−0.309598
$742$	−1.29053e41	+	2.94716e41i	−0.308967	+	0.705581i
$743$	−4.82701e41			−1.13329			−0.566644	−	0.823962i	$-0.691759\pi$
$743$	−4.82701e41			−1.13329			−0.566644	+	0.823962i	$0.691759\pi$
$744$	1.34203e41	+	2.32446e41i	0.308997	+	0.535199i
$745$	−3.95224e41	+	6.84549e41i	−0.892437	+	1.54575i
$746$	−7.10059e41	+	1.22986e42i	−1.57247	+	2.72359i
$747$	−6.54080e40	−	1.13290e41i	−0.142063	−	0.246061i
$748$	7.96911e40			0.169760
$749$	6.26328e41	−	6.97213e40i	1.30863	−	0.145673i
$750$	4.45406e41			0.912784
$751$	−2.16415e41	−	3.74842e41i	−0.435019	−	0.753476i	0.562278	−	0.826948i	$-0.309925\pi$
$751$	−2.16415e41	−	3.74842e41i	−0.435019	−	0.753476i	−0.997297	+	0.0734728i	$0.976592\pi$
$752$	−2.15220e41	+	3.72773e41i	−0.424351	+	0.734997i
$753$	−1.97710e41	+	3.42444e41i	−0.382386	+	0.662312i
$754$	−5.34294e39	−	9.25425e39i	−0.0101367	−	0.0175573i
$755$	2.03051e41			0.377898
$756$	1.14112e41	+	1.55050e41i	0.208337	+	0.283079i
$757$	3.23870e41			0.580069			0.290035	−	0.957016i	$-0.406333\pi$
$757$	3.23870e41			0.580069			0.290035	+	0.957016i	$0.406333\pi$
$758$	3.86272e41	+	6.69043e41i	0.678719	+	1.17558i
$759$	−3.01791e40	+	5.22717e40i	−0.0520235	+	0.0901074i
$760$	−3.88256e41	+	6.72478e41i	−0.656630	+	1.13732i
$761$	−2.71322e41	−	4.69943e41i	−0.450202	−	0.779773i	0.548196	−	0.836350i	$-0.315315\pi$
$761$	−2.71322e41	−	4.69943e41i	−0.450202	−	0.779773i	−0.998398	+	0.0565771i	$0.981981\pi$
$762$	9.96925e41			1.62299
$763$	3.36673e41	+	4.57457e41i	0.537778	+	0.730709i
$764$	−3.95751e41			−0.620252
$765$	−4.73523e40	−	8.20166e40i	−0.0728200	−	0.126128i
$766$	9.48532e41	−	1.64291e42i	1.43131	−	2.47911i
$767$	−2.92173e41	+	5.06058e41i	−0.432620	+	0.749320i
$768$	3.31923e41	+	5.74908e41i	0.482281	+	0.835335i
$769$	7.92528e41			1.13001			0.565005	−	0.825087i	$-0.308874\pi$
$769$	7.92528e41			1.13001			0.565005	+	0.825087i	$0.308874\pi$
$770$	2.80882e41	−	3.12671e40i	0.393015	−	0.0437494i
$771$	−6.08669e41			−0.835782
$772$	−9.32574e41	−	1.61527e42i	−1.25670	−	2.17667i
$773$	3.16342e41	−	5.47920e41i	0.418363	−	0.724627i	−0.577412	−	0.816453i	$-0.695937\pi$
$773$	3.16342e41	−	5.47920e41i	0.418363	−	0.724627i	0.995775	+	0.0918264i	$0.0292705\pi$
$774$	3.09919e41	−	5.36795e41i	0.402258	−	0.696730i
$775$	−3.19513e40	−	5.53413e40i	−0.0407019	−	0.0704977i
$776$	1.05276e42			1.31623
$777$	−2.15812e41	+	4.92846e41i	−0.264833	+	0.604793i
$778$	2.31460e42			2.78787
$779$	−4.66428e41	−	8.07877e41i	−0.551432	−	0.955108i
$780$	−2.84944e41	+	4.93537e41i	−0.330665	+	0.572728i
$781$	−4.30474e40	+	7.45603e40i	−0.0490351	+	0.0849313i
$782$	2.51653e41	+	4.35875e41i	0.281387	+	0.487376i
$783$	−3.54478e39			−0.00389085
$784$	−1.40497e41	+	4.51186e41i	−0.151385	+	0.486153i
$785$	−1.03339e42			−1.09308
$786$	7.18107e41	+	1.24380e42i	0.745696	+	1.29158i
$787$	7.53833e41	−	1.30568e42i	0.768496	−	1.33107i	−0.169882	−	0.985464i	$-0.554339\pi$
$787$	7.53833e41	−	1.30568e42i	0.768496	−	1.33107i	0.938378	−	0.345610i	$-0.112328\pi$
$788$	−7.43216e41	+	1.28729e42i	−0.743849	+	1.28839i
$789$	−3.74205e41	−	6.48142e41i	−0.367700	−	0.636874i
$790$	1.54217e42			1.48778
$791$	5.13660e40	−	1.17303e41i	0.0486538	−	0.111110i
$792$	−1.11385e41			−0.103589
$793$	1.46116e41	+	2.53081e41i	0.133425	+	0.231099i
$794$	1.59828e42	−	2.76830e42i	1.43303	−	2.48208i
$795$	−1.57968e41	+	2.73608e41i	−0.139074	+	0.240883i
$796$	−1.75625e42	−	3.04191e42i	−1.51826	−	2.62971i
$797$	−1.09546e42			−0.929931			−0.464966	−	0.885329i	$-0.653933\pi$
$797$	−1.09546e42			−0.929931			−0.464966	+	0.885329i	$0.653933\pi$
$798$	−1.04038e42	+	1.15812e41i	−0.867257	+	0.0965409i
$799$	8.46070e41			0.692593
$800$	−3.50379e40	−	6.06875e40i	−0.0281666	−	0.0487859i
$801$	2.64639e41	−	4.58368e41i	0.208921	−	0.361862i
$802$	−8.96204e41	+	1.55227e42i	−0.694830	+	1.20348i
$803$	−4.58229e39	−	7.93676e39i	−0.00348905	−	0.00604321i
$804$	1.64252e42			1.22828
$805$	6.83666e41	+	9.28934e41i	0.502115	+	0.682252i
$806$	−1.07111e42			−0.772634
$807$	−3.91493e41	−	6.78085e41i	−0.277369	−	0.480416i
$808$	−4.63038e41	+	8.02006e41i	−0.322220	+	0.558101i
$809$	1.70977e41	−	2.96141e41i	0.116865	−	0.202416i	−0.801659	−	0.597782i	$-0.796049\pi$
$809$	1.70977e41	−	2.96141e41i	0.116865	−	0.202416i	0.918524	+	0.395366i	$0.129382\pi$
$810$	1.46279e41	+	2.53362e41i	0.0982084	+	0.170102i
$811$	−1.22554e42			−0.808214			−0.404107	−	0.914712i	$-0.632418\pi$
$811$	−1.22554e42			−0.808214			−0.404107	+	0.914712i	$0.632418\pi$
$812$	−3.37860e40	−	4.59069e40i	−0.0218864	−	0.0297382i
$813$	8.83070e41			0.561930
$814$	−3.43999e41	−	5.95824e41i	−0.215032	−	0.372447i
$815$	−2.87351e40	+	4.97707e40i	−0.0176453	+	0.0305625i
$816$	−1.01246e41	+	1.75364e41i	−0.0610762	+	0.105787i
$817$	1.08894e42	+	1.88610e42i	0.645333	+	1.11775i
$818$	2.32936e42			1.35617
$819$	−3.45469e41	+	3.84567e40i	−0.197602	+	0.0219966i
$820$	−4.19220e42			−2.35582
$821$	−8.22739e41	−	1.42503e42i	−0.454241	−	0.786769i	0.544403	−	0.838824i	$-0.316756\pi$
$821$	−8.22739e41	−	1.42503e42i	−0.454241	−	0.786769i	−0.998644	+	0.0520550i	$0.983423\pi$
$822$	7.75705e41	−	1.34356e42i	0.420780	−	0.728812i
$823$	−9.13145e41	+	1.58161e42i	−0.486678	+	0.842952i	−0.999883	−	0.0153149i	$-0.995125\pi$
$823$	−9.13145e41	+	1.58161e42i	−0.486678	+	0.842952i	0.513204	+	0.858266i	$0.328458\pi$
$824$	−4.16709e40	−	7.21761e40i	−0.0218217	−	0.0377963i
$825$	2.65188e40			0.0136449
$826$	−1.93484e42	+	4.41855e42i	−0.978214	+	2.23393i
$827$	−3.80184e42			−1.88870			−0.944351	−	0.328939i	$-0.893309\pi$
$827$	−3.80184e42			−1.88870			−0.944351	+	0.328939i	$0.893309\pi$
$828$	−5.02341e41	−	8.70081e41i	−0.245222	−	0.424737i
$829$	−1.17723e41	+	2.03903e41i	−0.0564705	+	0.0978097i	−0.892879	−	0.450297i	$-0.851318\pi$
$829$	−1.17723e41	+	2.03903e41i	−0.0564705	+	0.0978097i	0.836408	+	0.548107i	$0.184651\pi$
$830$	1.59830e42	−	2.76833e42i	0.753398	−	1.30492i
$831$	−8.47141e41	−	1.46729e42i	−0.392411	−	0.679676i
$832$	−1.84176e42			−0.838388
$833$	9.06111e41	−	2.04263e41i	0.405349	−	0.0913772i
$834$	−2.06375e42			−0.907298
$835$	1.38992e42	+	2.40741e42i	0.600530	+	1.04015i
$836$	4.32489e41	−	7.49093e41i	0.183647	−	0.318086i
$837$	−1.77657e41	+	3.07710e41i	−0.0741416	+	0.128417i
$838$	−1.14977e42	−	1.99145e42i	−0.471597	−	0.816830i
$839$	−2.12201e42			−0.855459			−0.427730	−	0.903907i	$-0.640686\pi$
$839$	−2.12201e42			−0.855459			−0.427730	+	0.903907i	$0.640686\pi$
$840$	−8.53772e41	+	1.94974e42i	−0.338292	+	0.772551i
$841$	−2.56664e42			−0.999591
$842$	4.18244e40	+	7.24420e40i	0.0160105	+	0.0277310i
$843$	4.47299e41	−	7.74744e41i	0.168305	−	0.291513i
$844$	−2.96191e42	+	5.13019e42i	−1.09549	+	1.89744i
$845$	9.31620e41	+	1.61361e42i	0.338701	+	0.586647i
$846$	−2.61365e42			−0.934063
$847$	2.68745e42	−	2.99160e41i	0.944128	−	0.105098i
$848$	6.75517e41			0.233290
$849$	−1.38940e42	−	2.40650e42i	−0.471698	−	0.817005i
$850$	1.10565e41	−	1.91505e41i	0.0369016	−	0.0639154i
$851$	1.40390e42	−	2.43163e42i	0.460636	−	0.797845i
$852$	−7.16540e41	−	1.24108e42i	−0.231135	−	0.400338i
$853$	5.63122e42			1.78584			0.892918	−	0.450220i	$-0.148654\pi$
$853$	5.63122e42			1.78584			0.892918	+	0.450220i	$0.148654\pi$
$854$	1.42987e42	+	1.94285e42i	0.445819	+	0.605758i
$855$	−1.02794e42			−0.315107
$856$	−3.03459e42	−	5.25607e42i	−0.914599	−	1.58413i
$857$	3.55769e41	−	6.16211e41i	0.105426	−	0.182603i	−0.808486	−	0.588515i	$-0.799713\pi$
$857$	3.55769e41	−	6.16211e41i	0.105426	−	0.182603i	0.913912	+	0.405912i	$0.133046\pi$
$858$	2.22248e41	−	3.84944e41i	0.0647547	−	0.112158i
$859$	1.53515e42	+	2.65896e42i	0.439795	+	0.761747i	0.997673	−	0.0681756i	$-0.0217178\pi$
$859$	1.53515e42	+	2.65896e42i	0.439795	+	0.761747i	−0.557878	+	0.829923i	$0.688384\pi$
$860$	9.78726e42			2.75698
$861$	−1.51566e42	−	2.05941e42i	−0.419814	−	0.570424i
$862$	−7.94970e42			−2.16519
$863$	1.92767e42	+	3.33883e42i	0.516270	+	0.894206i	0.999822	+	0.0188903i	$0.00601332\pi$
$863$	1.92767e42	+	3.33883e42i	0.516270	+	0.894206i	−0.483551	+	0.875316i	$0.660653\pi$
$864$	−1.94819e41	+	3.37436e41i	−0.0513076	+	0.0888674i
$865$	2.13845e42	−	3.70391e42i	0.553816	−	0.959238i
$866$	−3.70116e41	−	6.41060e41i	−0.0942602	−	0.163263i
$867$	−1.90722e42			−0.477666
$868$	−5.67829e42	+	6.32093e41i	−1.39856	+	0.155684i
$869$	−7.77260e41			−0.188269
$870$	−4.33098e40	−	7.50147e40i	−0.0103171	−	0.0178697i
$871$	−1.48285e42	+	2.56837e42i	−0.347404	+	0.601721i
$872$	2.73506e42	−	4.73726e42i	0.630199	−	1.09154i
$873$	6.96814e41	+	1.20692e42i	0.157910	+	0.273509i
$874$	5.46295e42			1.21762
$875$	−1.72070e42	+	3.92953e42i	−0.377215	+	0.861438i
$876$	1.52548e41			0.0328925
$877$	9.92513e41	+	1.71908e42i	0.210495	+	0.364588i	0.951870	−	0.306503i	$-0.0991591\pi$
$877$	9.92513e41	+	1.71908e42i	0.210495	+	0.364588i	−0.741374	+	0.671092i	$0.765826\pi$
$878$	4.58892e42	−	7.94825e42i	0.957283	−	1.65806i
$879$	1.83033e42	−	3.17023e42i	0.375571	−	0.650507i
$880$	−2.96694e41	−	5.13889e41i	−0.0598839	−	0.103722i
$881$	−2.03255e38			−4.03544e−5			−2.01772e−5	−	1.00000i	$-0.500006\pi$
$881$	−2.03255e38			−4.03544e−5			−2.01772e−5		1.00000i	$0.500006\pi$
$882$	−2.79912e42	+	6.31001e41i	−0.546672	+	0.123236i
$883$	6.33316e42			1.21672			0.608359	−	0.793662i	$-0.291828\pi$
$883$	6.33316e42			1.21672			0.608359	+	0.793662i	$0.291828\pi$
$884$	−1.19754e42	−	2.07420e42i	−0.226325	−	0.392006i
$885$	−2.36834e42	+	4.10209e42i	−0.440319	+	0.762654i
$886$	9.75796e41	−	1.69013e42i	0.178472	−	0.309123i
$887$	2.39279e41	+	4.14443e41i	0.0430538	+	0.0745714i	0.886749	−	0.462251i	$-0.152958\pi$
$887$	2.39279e41	+	4.14443e41i	0.0430538	+	0.0745714i	−0.843695	+	0.536822i	$0.819625\pi$
$888$	5.18153e42			0.917212
$889$	−3.85134e42	+	8.79523e42i	−0.670713	+	1.53169i
$890$	1.29333e43			2.21592
$891$	−7.37252e40	−	1.27696e41i	−0.0124277	−	0.0215253i
$892$	7.53649e42	−	1.30536e43i	1.24991	−	2.16491i
$893$	4.59169e42	−	7.95303e42i	0.749249	−	1.29774i
$894$	5.13115e42	+	8.88741e42i	0.823797	+	1.42686i
$895$	6.73423e42			1.06378
$896$	−1.17004e43	+	1.30246e42i	−1.81859	+	0.202441i
$897$	1.81404e42			0.277431
$898$	8.49359e42	+	1.47113e43i	1.27816	+	2.21383i
$899$	5.26000e40	−	9.11059e40i	0.00778879	−	0.0134906i
$900$	−2.20707e41	+	3.82276e41i	−0.0321589	+	0.0557008i
$901$	−6.63894e41	−	1.14990e42i	−0.0951896	−	0.164873i
$902$	3.26979e42			0.461344
$903$	3.53852e42	+	4.80798e42i	0.491302	+	0.667559i
$904$	−1.23327e42			−0.168506
$905$	5.29523e41	+	9.17160e41i	0.0712000	+	0.123322i
$906$	1.31809e42	−	2.28301e42i	0.174417	−	0.302098i
$907$	−4.29576e42	+	7.44047e42i	−0.559415	+	0.968935i	0.438131	+	0.898911i	$0.355641\pi$
$907$	−4.29576e42	+	7.44047e42i	−0.559415	+	0.968935i	−0.997545	+	0.0700234i	$0.977693\pi$
$908$	6.24450e42	+	1.08158e43i	0.800300	+	1.38616i
$909$	−1.22593e42			−0.154629
$910$	−5.03472e42	−	6.84095e42i	−0.624993	−	0.849212i
$911$	−1.15733e42			−0.141397			−0.0706986	−	0.997498i	$-0.522523\pi$
$911$	−1.15733e42			−0.141397			−0.0706986	+	0.997498i	$0.522523\pi$
$912$	1.09894e42	+	1.90342e42i	0.132145	+	0.228881i
$913$	−8.05549e41	+	1.39525e42i	−0.0953379	+	0.165130i
$914$	−8.45404e42	+	1.46428e43i	−0.984792	+	1.70571i
$915$	1.18442e42	+	2.05147e42i	0.135799	+	0.235212i
$916$	2.49071e42			0.281086
$917$	−1.37474e43	+	1.53033e42i	−1.52710	+	0.169992i
$918$	−1.22954e42			−0.134438
$919$	−7.93419e42	−	1.37424e43i	−0.853941	−	1.47907i	−0.877624	−	0.479349i	$-0.840873\pi$
$919$	−7.93419e42	−	1.37424e43i	−0.853941	−	1.47907i	0.0236835	−	0.999720i	$-0.492461\pi$
$920$	5.55395e42	−	9.61972e42i	0.588408	−	1.01915i
$921$	−2.14130e42	+	3.70884e42i	−0.223313	+	0.386789i
$922$	5.54069e42	+	9.59676e42i	0.568808	+	0.985204i
$923$	2.58754e42			0.261495
$924$	9.51041e41	−	2.17187e42i	0.0946141	−	0.216068i
$925$	−1.23363e42			−0.120817
$926$	−1.32011e43	−	2.28649e43i	−1.27277	−	2.20450i
$927$	5.51636e40	−	9.55461e40i	0.00523596	−	0.00906894i
$928$	5.76814e40	−	9.99070e40i	0.00539001	−	0.00933578i
$929$	−3.16089e42	−	5.47482e42i	−0.290791	−	0.503665i	0.683206	−	0.730226i	$-0.260585\pi$
$929$	−3.16089e42	−	5.47482e42i	−0.290791	−	0.503665i	−0.973997	+	0.226561i	$0.927252\pi$
$930$	−8.68235e42			−0.786384
$931$	2.99747e42	−	9.62597e42i	0.267291	−	0.858369i
$932$	6.84499e42			0.600955
$933$	1.11420e42	+	1.92985e42i	0.0963115	+	0.166816i
$934$	−3.31269e42	+	5.73775e42i	−0.281936	+	0.488328i
$935$	−5.83179e41	+	1.01010e42i	−0.0488690	+	0.0846436i
$936$	1.67381e42	+	2.89913e42i	0.138104	+	0.239204i
$937$	−2.51380e42			−0.204224			−0.102112	−	0.994773i	$-0.532560\pi$
$937$	−2.51380e42			−0.204224			−0.102112	+	0.994773i	$0.532560\pi$
$938$	−9.81980e42	+	2.24253e43i	−0.785528	+	1.79389i
$939$	−3.09768e42			−0.243997
$940$	−2.06348e43	−	3.57405e43i	−1.60046	−	2.77208i
$941$	1.98302e42	−	3.43469e42i	0.151453	−	0.262324i	−0.780309	−	0.625394i	$-0.784938\pi$
$941$	1.98302e42	−	3.43469e42i	0.151453	−	0.262324i	0.931762	+	0.363070i	$0.118271\pi$
$942$	−6.70815e42	+	1.16189e43i	−0.504504	+	0.873827i
$943$	6.67220e42	+	1.15566e43i	0.494140	+	0.855875i
$944$	1.01277e43			0.738615
$945$	−2.80036e42	+	3.11729e41i	−0.201119	+	0.0223880i
$946$	−7.63377e42			−0.539905
$947$	1.02222e43	+	1.77054e43i	0.711985	+	1.23319i	0.964111	+	0.265499i	$0.0855368\pi$
$947$	1.02222e43	+	1.77054e43i	0.711985	+	1.23319i	−0.252126	+	0.967694i	$0.581130\pi$
$948$	6.46888e42	−	1.12044e43i	0.443720	−	0.768545i
$949$	−1.37719e41	+	2.38536e41i	−0.00930321	+	0.0161136i
$950$	−1.20009e42	−	2.07862e42i	−0.0798405	−	0.138288i
$951$	−9.39010e42			−0.615251
$952$	−5.30232e42	−	7.20455e42i	−0.342161	−	0.464912i
$953$	9.06402e42			0.576068			0.288034	−	0.957620i	$-0.406998\pi$
$953$	9.06402e42			0.576068			0.288034	+	0.957620i	$0.406998\pi$
$954$	2.05087e42	+	3.55222e42i	0.128377	+	0.222356i
$955$	2.89610e42	−	5.01620e42i	0.178552	−	0.309261i
$956$	−2.60440e43	+	4.51096e43i	−1.58150	+	2.73923i
$957$	2.18283e40	+	3.78078e40i	0.00130556	+	0.00226130i
$958$	1.86130e43			1.09652
$959$	8.85665e42	+	1.20340e43i	0.513925	+	0.698298i
$960$	−1.49293e43			−0.853308
$961$	3.60856e42	+	6.25021e42i	0.203163	+	0.351889i
$962$	−1.03387e43	+	1.79072e43i	−0.573363	+	0.993093i
$963$	4.01717e42	−	6.95794e42i	0.219452	−	0.380101i
$964$	−5.76151e42	−	9.97923e42i	−0.310041	−	0.537007i
$965$	2.72983e43			1.44707
$966$	1.48824e43	−	1.65668e42i	0.777152	−	0.0865106i
$967$	2.35225e43			1.21004			0.605020	−	0.796211i	$-0.293165\pi$
$967$	2.35225e43			1.21004			0.605020	+	0.796211i	$0.293165\pi$
$968$	−1.30208e43	−	2.25527e43i	−0.659851	−	1.14290i
$969$	2.16007e42	−	3.74135e42i	0.107838	−	0.186781i
$970$	−1.70272e43	+	2.94920e43i	−0.837438	+	1.45049i
$971$	−1.66387e43	−	2.88190e43i	−0.806194	−	1.39637i	−0.915482	−	0.402359i	$-0.868191\pi$
$971$	−1.66387e43	−	2.88190e43i	−0.806194	−	1.39637i	0.109288	−	0.994010i	$-0.465143\pi$
$972$	2.45437e42			0.117160
$973$	7.97273e42	−	1.82072e43i	0.374948	−	0.856261i
$974$	1.28562e43			0.595675
$975$	−3.98505e41	−	6.90232e41i	−0.0181914	−	0.0315085i
$976$	2.53246e42	−	4.38634e42i	0.113899	−	0.197279i
$977$	3.50261e42	−	6.06669e42i	0.155210	−	0.268832i	−0.777925	−	0.628357i	$-0.783728\pi$
$977$	3.50261e42	−	6.06669e42i	0.155210	−	0.268832i	0.933136	+	0.359525i	$0.117061\pi$
$978$	3.73065e41	+	6.46167e41i	0.0162881	+	0.0282118i
$979$	−6.51845e42			−0.280411
$980$	−3.07278e43	−	3.32950e43i	−1.30243	−	1.41124i
$981$	7.24130e42			0.302424
$982$	−3.47002e43	−	6.01025e43i	−1.42796	−	2.47330i
$983$	1.26652e42	−	2.19368e42i	0.0513555	−	0.0889504i	−0.839205	−	0.543815i	$-0.816979\pi$
$983$	1.26652e42	−	2.19368e42i	0.0513555	−	0.0889504i	0.890560	+	0.454865i	$0.150313\pi$
$984$	−1.23129e43	+	2.13266e43i	−0.491962	+	0.852103i
$985$	−1.08777e43	−	1.88408e43i	−0.428265	−	0.741776i
$986$	3.64038e41			0.0141231
$987$	1.00971e43	−	2.30585e43i	0.386009	−	0.881521i
$988$	−2.59966e43			−0.979355
$989$	−1.55772e43	−	2.69804e43i	−0.578285	−	1.00162i
$990$	1.80153e42	−	3.12035e42i	0.0659070	−	0.114154i
$991$	2.08206e43	−	3.60624e43i	0.750629	−	1.30013i	−0.196889	−	0.980426i	$-0.563084\pi$
$991$	2.08206e43	−	3.60624e43i	0.750629	−	1.30013i	0.947518	−	0.319702i	$-0.103583\pi$
$992$	−5.78172e42	−	1.00142e43i	−0.205418	−	0.355794i
$993$	−9.73513e41			−0.0340861
$994$	2.12283e43	−	2.36308e42i	0.732510	−	0.0815411i
$995$	5.14089e43			1.74825
$996$	−1.34086e43	−	2.32245e43i	−0.449391	−	0.778368i
$997$	−3.62858e42	+	6.28489e42i	−0.119855	+	0.207595i	−0.919710	−	0.392598i	$-0.871576\pi$
$997$	−3.62858e42	+	6.28489e42i	−0.119855	+	0.207595i	0.799855	+	0.600193i	$0.204910\pi$
$998$	−2.44843e43	+	4.24080e43i	−0.797066	+	1.38056i
$999$	3.42963e42	+	5.94029e42i	0.110039	+	0.190594i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.30.e.b.4.19	✓	40
7.2	even	3	inner	21.30.e.b.16.19	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.30.e.b.4.19	✓	40	1.1	even	1	trivial
21.30.e.b.16.19	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)

\(f(q)\)	\(=\)	\(q+(19476.8 + 33734.8i) q^{2} +(-2.39148e6 + 4.14217e6i) q^{3} +(-4.90254e8 + 8.49146e8i) q^{4} +(-7.17536e9 - 1.24281e10i) q^{5} -1.86314e11 q^{6} +(7.19771e11 - 1.64373e12i) q^{7} -1.72813e13 q^{8} +(-1.14384e13 - 1.98119e13i) q^{9} +O(q^{10})\)	\(q+(19476.8 + 33734.8i) q^{2} +(-2.39148e6 + 4.14217e6i) q^{3} +(-4.90254e8 + 8.49146e8i) q^{4} +(-7.17536e9 - 1.24281e10i) q^{5} -1.86314e11 q^{6} +(7.19771e11 - 1.64373e12i) q^{7} -1.72813e13 q^{8} +(-1.14384e13 - 1.98119e13i) q^{9} +(2.79506e14 - 4.84119e14i) q^{10} +(-1.40872e14 + 2.43998e14i) q^{11} +(-2.34487e15 - 4.06144e15i) q^{12} +8.46772e15 q^{13} +(6.94695e16 - 7.73318e15i) q^{14} +6.86391e16 q^{15} +(-7.33803e16 - 1.27098e17i) q^{16} +(-1.44235e17 + 2.49823e17i) q^{17} +(4.45566e17 - 7.71743e17i) q^{18} +(1.56555e18 + 2.71162e18i) q^{19} +1.40710e19 q^{20} +(5.08728e18 + 6.91236e18i) q^{21} -1.09750e19 q^{22} +(-2.23951e19 - 3.87894e19i) q^{23} +(4.13279e19 - 7.15820e19i) q^{24} +(-9.83944e18 + 1.70424e19i) q^{25} +(1.64924e20 + 2.85657e20i) q^{26} +1.09419e20 q^{27} +(1.04289e21 + 1.41703e21i) q^{28} -3.23964e19 q^{29} +(1.33687e21 + 2.31552e21i) q^{30} +(-1.62364e21 + 2.81222e21i) q^{31} +(-1.78048e21 + 3.08389e21i) q^{32} +(-6.73788e20 - 1.16704e21i) q^{33} -1.12370e22 q^{34} +(-2.55930e22 + 2.84895e21i) q^{35} +2.24309e22 q^{36} +(3.13440e22 + 5.42894e22i) q^{37} +(-6.09839e22 + 1.05627e23i) q^{38} +(-2.02504e22 + 3.50747e22i) q^{39} +(1.23999e23 + 2.14773e23i) q^{40} -2.97932e23 q^{41} +(-1.34103e23 + 3.06249e23i) q^{42} +6.95562e23 q^{43} +(-1.38127e23 - 2.39242e23i) q^{44} +(-1.64149e23 + 2.84315e23i) q^{45} +(8.72367e23 - 1.51098e24i) q^{46} +(-1.46647e24 - 2.54001e24i) q^{47} +7.01951e23 q^{48} +(-2.18376e24 - 2.36621e24i) q^{49} -7.66562e23 q^{50} +(-6.89874e23 - 1.19490e24i) q^{51} +(-4.15134e24 + 7.19032e24i) q^{52} +(-2.30142e24 + 3.98618e24i) q^{53} +(2.13113e24 + 3.69122e24i) q^{54} +4.04324e24 q^{55} +(-1.24386e25 + 2.84057e25i) q^{56} -1.49760e25 q^{57} +(-6.30978e23 - 1.09289e24i) q^{58} +(-3.45043e25 + 5.97632e25i) q^{59} +(-3.36506e25 + 5.82846e25i) q^{60} +(1.72557e25 + 2.98877e25i) q^{61} -1.26493e26 q^{62} +(-4.07983e25 + 4.54157e24i) q^{63} -2.17504e26 q^{64} +(-6.07590e25 - 1.05238e26i) q^{65} +(2.62465e25 - 4.54602e25i) q^{66} +(-1.75118e26 + 3.03314e26i) q^{67} +(-1.41424e26 - 2.44954e26i) q^{68} +2.14230e26 q^{69} +(-5.94578e26 - 8.07886e26i) q^{70} +3.05578e26 q^{71} +(1.97670e26 + 3.42375e26i) q^{72} +(-1.62640e25 + 2.81700e25i) q^{73} +(-1.22096e27 + 2.11477e27i) q^{74} +(-4.70617e25 - 8.15133e25i) q^{75} -3.07008e27 q^{76} +(2.99670e26 + 4.07178e26i) q^{77} -1.57765e27 q^{78} +(1.37937e27 + 2.38914e27i) q^{79} +(-1.05306e27 + 1.82395e27i) q^{80} +(-2.61674e26 + 4.53232e26i) q^{81} +(-5.80275e27 - 1.00507e28i) q^{82} +5.71829e27 q^{83} +(-8.36366e27 + 9.31022e26i) q^{84} +4.13977e27 q^{85} +(1.35473e28 + 2.34646e28i) q^{86} +(7.74756e25 - 1.34192e26i) q^{87} +(2.43445e27 - 4.21660e27i) q^{88} +(1.15680e28 + 2.00364e28i) q^{89} -1.27884e28 q^{90} +(6.09482e27 - 1.39186e28i) q^{91} +4.39171e28 q^{92} +(-7.76580e27 - 1.34508e28i) q^{93} +(5.71244e28 - 9.89423e28i) q^{94} +(2.24668e28 - 3.89137e28i) q^{95} +(-8.51600e27 - 1.47502e28i) q^{96} -6.09189e28 q^{97} +(3.72909e28 - 1.19755e29i) q^{98} +6.44542e27 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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Database

Properties

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