LMFDB - Embedded newform 7.24.c.a.2.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [7,24,Mod(2,7)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("7.2"); S:= CuspForms(chi, 24); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(7, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 24, names="a")

Level:	$ N $	$=$	$ 7 $
Weight:	$ k $	$=$	$ 24 $
Character orbit:	$[\chi]$	$=$	7.c (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$23.4642826142$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			2.5
Character	$\chi$	$=$	7.2
Dual form			7.24.c.a.4.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1256.79 + 2176.82i) q^{2} +(-192681. - 333734. i) q^{3} +(1.03526e6 + 1.79313e6i) q^{4} +(-3.60011e7 + 6.23558e7i) q^{5} +9.68640e8 q^{6} +(-1.43544e9 - 5.03073e9i) q^{7} -2.62899e10 q^{8} +(-2.71807e10 + 4.70783e10i) q^{9} +(-9.04917e10 - 1.56736e11i) q^{10} +(-4.63271e11 - 8.02408e11i) q^{11} +(3.98951e11 - 6.91004e11i) q^{12} +5.15744e12 q^{13} +(1.27551e13 + 3.19787e12i) q^{14} +2.77470e13 q^{15} +(2.43564e13 - 4.21866e13i) q^{16} +(-1.22537e13 - 2.12240e13i) q^{17} +(-6.83207e13 - 1.18335e14i) q^{18} +(-2.66191e14 + 4.61056e14i) q^{19} -1.49082e14 q^{20} +(-1.40234e15 + 1.44838e15i) q^{21} +2.32894e15 q^{22} +(-5.87256e14 + 1.01716e15i) q^{23} +(5.06557e15 + 8.77382e15i) q^{24} +(3.36830e15 + 5.83407e15i) q^{25} +(-6.48182e15 + 1.12268e16i) q^{26} -1.53305e16 q^{27} +(7.53468e15 - 7.78205e15i) q^{28} +6.90610e16 q^{29} +(-3.48721e16 + 6.04003e16i) q^{30} +(1.39206e17 + 2.41113e17i) q^{31} +(-4.90458e16 - 8.49499e16i) q^{32} +(-1.78527e17 + 3.09218e17i) q^{33} +6.16013e16 q^{34} +(3.65373e17 + 9.16039e16i) q^{35} -1.12556e17 q^{36} +(-7.19796e17 + 1.24672e18i) q^{37} +(-6.69092e17 - 1.15890e18i) q^{38} +(-9.93743e17 - 1.72121e18i) q^{39} +(9.46464e17 - 1.63932e18i) q^{40} +1.70772e18 q^{41} +(-1.39043e18 - 4.87297e18i) q^{42} +6.33058e18 q^{43} +(9.59212e17 - 1.66140e18i) q^{44} +(-1.95707e18 - 3.38974e18i) q^{45} +(-1.47612e18 - 2.55671e18i) q^{46} +(6.77549e18 - 1.17355e19i) q^{47} -1.87721e19 q^{48} +(-2.32478e19 + 1.44426e19i) q^{49} -1.69330e19 q^{50} +(-4.72212e18 + 8.17895e18i) q^{51} +(5.33930e18 + 9.24795e18i) q^{52} +(3.50799e19 + 6.07601e19i) q^{53} +(1.92672e19 - 3.33717e19i) q^{54} +6.67130e19 q^{55} +(3.77376e19 + 1.32257e20i) q^{56} +2.05160e20 q^{57} +(-8.67952e19 + 1.50334e20i) q^{58} +(-1.19815e20 - 2.07526e20i) q^{59} +(2.87254e19 + 4.97538e19i) q^{60} +(-6.89142e19 + 1.19363e20i) q^{61} -6.99813e20 q^{62} +(2.75854e20 + 6.91604e19i) q^{63} +6.55194e20 q^{64} +(-1.85674e20 + 3.21596e20i) q^{65} +(-4.48742e20 - 7.77245e20i) q^{66} +(-3.39382e20 - 5.87827e20i) q^{67} +(2.53716e19 - 4.39448e19i) q^{68} +4.52614e20 q^{69} +(-6.58602e20 + 6.80225e20i) q^{70} +2.14404e21 q^{71} +(7.14576e20 - 1.23768e21i) q^{72} +(-1.53774e21 - 2.66344e21i) q^{73} +(-1.80927e21 - 3.13374e21i) q^{74} +(1.29802e21 - 2.24824e21i) q^{75} -1.10231e21 q^{76} +(-3.37170e21 + 3.48240e21i) q^{77} +4.99571e21 q^{78} +(-3.40862e21 + 5.90391e21i) q^{79} +(1.75372e21 + 3.03753e21i) q^{80} +(5.51277e21 + 9.54839e21i) q^{81} +(-2.14625e21 + 3.71741e21i) q^{82} +8.36785e21 q^{83} +(-4.04893e21 - 1.01512e21i) q^{84} +1.76459e21 q^{85} +(-7.95622e21 + 1.37806e22i) q^{86} +(-1.33068e22 - 2.30480e22i) q^{87} +(1.21793e22 + 2.10952e22i) q^{88} +(-1.70799e22 + 2.95832e22i) q^{89} +9.83849e21 q^{90} +(-7.40321e21 - 2.59457e22i) q^{91} -2.43186e21 q^{92} +(5.36450e22 - 9.29158e22i) q^{93} +(1.70307e22 + 2.94981e22i) q^{94} +(-1.91663e22 - 3.31970e22i) q^{95} +(-1.89004e22 + 3.27365e22i) q^{96} -1.21614e22 q^{97} +(-2.22153e21 - 6.87577e22i) q^{98} +5.03680e22 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 966 q^{2} - 177148 q^{3} - 55357148 q^{4} - 74771022 q^{5} + 3009216508 q^{6} + 654254272 q^{7} + 50444801232 q^{8} - 336909608980 q^{9} - 334296297894 q^{10} + 1355476566108 q^{11} - 4984668058916 q^{12}+ \cdots - 46\!\cdots\!68 q^{99}+O(q^{100}) $ 28 * q + 966 * q^2 - 177148 * q^3 - 55357148 * q^4 - 74771022 * q^5 + 3009216508 * q^6 + 654254272 * q^7 + 50444801232 * q^8 - 336909608980 * q^9 - 334296297894 * q^10 + 1355476566108 * q^11 - 4984668058916 * q^12 - 854080437112 * q^13 - 43134424917234 * q^14 + 77341621307888 * q^15 - 160538324156336 * q^16 - 130193896130514 * q^17 + 110632655983108 * q^18 - 214771980430396 * q^19 - 96438878562936 * q^20 - 3455509877919050 * q^21 + 15069544565754252 * q^22 + 6685548913560552 * q^23 - 31330599354826008 * q^24 - 9156874000789424 * q^25 - 48260478025970868 * q^26 + 16955244397080056 * q^27 + 45364719181029388 * q^28 - 230797950910889208 * q^29 + 4149727265170942 * q^30 + 94821366637509632 * q^31 - 989053585410677472 * q^32 + 471925265098792298 * q^33 + 409331438407832700 * q^34 + 991848218293906764 * q^35 + 323097285821290960 * q^36 + 228196281955951106 * q^37 + 846979764807573006 * q^38 - 4289472930557071768 * q^39 - 10645750240235319192 * q^40 + 25326139004865203064 * q^41 - 8224906244908771096 * q^42 - 854479038224841232 * q^43 + 11572396920387558444 * q^44 - 9362992784223924004 * q^45 - 33418566325741763586 * q^46 - 61615364375433533424 * q^47 + 317023259856261797920 * q^48 - 52662871130642447108 * q^49 - 186545340785228725104 * q^50 + 84287583500847206172 * q^51 - 90603352071153943672 * q^52 - 282093764343878671758 * q^53 + 13895299932605385046 * q^54 + 474892685489135665440 * q^55 + 228268901501348771616 * q^56 - 850914722748570925564 * q^57 + 339998979132364080060 * q^58 - 283820607003252730116 * q^59 - 701673169918628967164 * q^60 - 870322613357668504870 * q^61 + 564486602904139969932 * q^62 - 999989531155067147576 * q^63 + 4248282134320804279168 * q^64 + 384582138286683330588 * q^65 - 157008004213679191250 * q^66 + 1414046473258733295716 * q^67 + 435228382363177447884 * q^68 - 5326254705815467337364 * q^69 + 4483423880974817421510 * q^70 + 426436671912495312096 * q^71 - 10118884230376615693104 * q^72 + 5942494661268692359862 * q^73 + 13389833203328450370642 * q^74 + 14120811240771906960232 * q^75 - 45841052995588797879688 * q^76 + 2861961524728931175726 * q^77 + 14402574434410352321656 * q^78 - 3444345943288433723680 * q^79 - 8255607259451726029008 * q^80 + 2565358457232096585122 * q^81 + 34656759475287179918772 * q^82 + 12170751598086155609808 * q^83 - 30272689833547903395556 * q^84 - 15360706479116717074524 * q^85 + 743687862046869712056 * q^86 - 7978312766181293835640 * q^87 - 2867657955669848060664 * q^88 - 68609868120257601678426 * q^89 + 34663480073027193102856 * q^90 - 4728467461925451365632 * q^91 - 15501695671963373778696 * q^92 + 50628291689744906093838 * q^93 + 18415808745499513811142 * q^94 - 113148862333982926479168 * q^95 - 150237583048546245409696 * q^96 + 460377553176923245905944 * q^97 + 318336375165209650855326 * q^98 - 468278480109509528565568 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/7\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1256.79	+	2176.82i	−0.433928	+	0.751586i	−0.997207	−	0.0746810i	$-0.976206\pi$
$2$	−1256.79	+	2176.82i	−0.433928	+	0.751586i	0.563279	+	0.826267i	$0.309539\pi$
$3$	−192681.	−	333734.i	−0.627979	−	1.08769i	−0.987957	−	0.154731i	$-0.950549\pi$
$3$	−192681.	−	333734.i	−0.627979	−	1.08769i	0.359977	−	0.932961i	$-0.382784\pi$
$4$	1.03526e6	+	1.79313e6i	0.123413	+	0.213757i
$5$	−3.60011e7	+	6.23558e7i	−0.329732	+	0.571112i	−0.982459	−	0.186481i	$-0.940292\pi$
$5$	−3.60011e7	+	6.23558e7i	−0.329732	+	0.571112i	0.652727	+	0.757593i	$0.273625\pi$
$6$	9.68640e8			1.08999
$7$	−1.43544e9	−	5.03073e9i	−0.274384	−	0.961620i
$7$	−1.43544e9	−	5.03073e9i	−0.274384	−	0.961620i
$8$	−2.62899e10			−1.08207
$9$	−2.71807e10	+	4.70783e10i	−0.288716	+	0.500071i
$10$	−9.04917e10	−	1.56736e11i	−0.286160	−	0.495643i
$11$	−4.63271e11	−	8.02408e11i	−0.489575	−	0.847968i	0.510354	−	0.859965i	$-0.329515\pi$
$11$	−4.63271e11	−	8.02408e11i	−0.489575	−	0.847968i	−0.999928	+	0.0119968i	$0.996181\pi$
$12$	3.98951e11	−	6.91004e11i	0.155001	−	0.268470i
$13$	5.15744e12			0.798153			0.399076	−	0.916918i	$-0.369331\pi$
$13$	5.15744e12			0.798153			0.399076	+	0.916918i	$0.369331\pi$
$14$	1.27551e13	+	3.19787e12i	0.841803	+	0.211051i
$15$	2.77470e13			0.828259
$16$	2.43564e13	−	4.21866e13i	0.346126	−	0.599507i
$17$	−1.22537e13	−	2.12240e13i	−0.0867171	−	0.150198i	0.819405	−	0.573216i	$-0.194304\pi$
$17$	−1.22537e13	−	2.12240e13i	−0.0867171	−	0.150198i	−0.906122	+	0.423017i	$0.860971\pi$
$18$	−6.83207e13	−	1.18335e14i	−0.250564	−	0.433990i
$19$	−2.66191e14	+	4.61056e14i	−0.524235	+	0.908002i	0.475366	+	0.879788i	$0.342315\pi$
$19$	−2.66191e14	+	4.61056e14i	−0.524235	+	0.908002i	−0.999602	+	0.0282146i	$0.991018\pi$
$20$	−1.49082e14			−0.162773
$21$	−1.40234e15	+	1.44838e15i	−0.873640	+	0.902323i
$22$	2.32894e15			0.849761
$23$	−5.87256e14	+	1.01716e15i	−0.128516	+	0.222596i	−0.923102	−	0.384555i	$-0.874355\pi$
$23$	−5.87256e14	+	1.01716e15i	−0.128516	+	0.222596i	0.794586	+	0.607152i	$0.207688\pi$
$24$	5.06557e15	+	8.77382e15i	0.679515	+	1.17695i
$25$	3.36830e15	+	5.83407e15i	0.282554	+	0.489398i
$26$	−6.48182e15	+	1.12268e16i	−0.346341	+	0.599880i
$27$	−1.53305e16			−0.530728
$28$	7.53468e15	−	7.78205e15i	0.171691	−	0.177328i
$29$	6.90610e16			1.05113			0.525564	−	0.850754i	$-0.323854\pi$
$29$	6.90610e16			1.05113			0.525564	+	0.850754i	$0.323854\pi$
$30$	−3.48721e16	+	6.04003e16i	−0.359405	+	0.622508i
$31$	1.39206e17	+	2.41113e17i	0.984011	+	1.70436i	0.646252	+	0.763124i	$0.276335\pi$
$31$	1.39206e17	+	2.41113e17i	0.984011	+	1.70436i	0.337758	+	0.941233i	$0.390331\pi$
$32$	−4.90458e16	−	8.49499e16i	−0.240645	−	0.416810i
$33$	−1.78527e17	+	3.09218e17i	−0.614885	+	1.06501i
$34$	6.16013e16			0.150516
$35$	3.65373e17	+	9.16039e16i	0.639666	+	0.160373i
$36$	−1.12556e17			−0.142525
$37$	−7.19796e17	+	1.24672e18i	−0.665104	+	1.15199i	0.314153	+	0.949372i	$0.398280\pi$
$37$	−7.19796e17	+	1.24672e18i	−0.665104	+	1.15199i	−0.979257	+	0.202622i	$0.935054\pi$
$38$	−6.69092e17	−	1.15890e18i	−0.454961	−	0.788016i
$39$	−9.93743e17	−	1.72121e18i	−0.501223	−	0.868144i
$40$	9.46464e17	−	1.63932e18i	0.356791	−	0.617981i
$41$	1.70772e18			0.484621			0.242311	−	0.970199i	$-0.422095\pi$
$41$	1.70772e18			0.484621			0.242311	+	0.970199i	$0.422095\pi$
$42$	−1.39043e18	−	4.87297e18i	−0.299076	−	1.04816i
$43$	6.33058e18			1.03886			0.519429	−	0.854513i	$-0.326145\pi$
$43$	6.33058e18			1.03886			0.519429	+	0.854513i	$0.326145\pi$
$44$	9.59212e17	−	1.66140e18i	0.120840	−	0.209300i
$45$	−1.95707e18	−	3.38974e18i	−0.190398	−	0.329779i
$46$	−1.47612e18	−	2.55671e18i	−0.111534	−	0.193182i
$47$	6.77549e18	−	1.17355e19i	0.399775	−	0.692430i	−0.593923	−	0.804522i	$-0.702422\pi$
$47$	6.77549e18	−	1.17355e19i	0.399775	−	0.692430i	0.993698	+	0.112092i	$0.0357550\pi$
$48$	−1.87721e19			−0.869439
$49$	−2.32478e19	+	1.44426e19i	−0.849427	+	0.527706i
$50$	−1.69330e19			−0.490432
$51$	−4.72212e18	+	8.17895e18i	−0.108913	+	0.188643i
$52$	5.33930e18	+	9.24795e18i	0.0985023	+	0.170611i
$53$	3.50799e19	+	6.07601e19i	0.519859	+	0.900422i	0.999734	+	0.0230846i	$0.00734872\pi$
$53$	3.50799e19	+	6.07601e19i	0.519859	+	0.900422i	−0.479875	+	0.877337i	$0.659318\pi$
$54$	1.92672e19	−	3.33717e19i	0.230298	−	0.398887i
$55$	6.67130e19			0.645713
$56$	3.77376e19	+	1.32257e20i	0.296901	+	1.04054i
$57$	2.05160e20			1.31684
$58$	−8.67952e19	+	1.50334e20i	−0.456114	+	0.790013i
$59$	−1.19815e20	−	2.07526e20i	−0.517267	−	0.895932i	−0.999799	−	0.0200540i	$-0.993616\pi$
$59$	−1.19815e20	−	2.07526e20i	−0.517267	−	0.895932i	0.482532	−	0.875878i	$-0.339717\pi$
$60$	2.87254e19	+	4.97538e19i	0.102218	+	0.177046i
$61$	−6.89142e19	+	1.19363e20i	−0.202776	+	0.351218i	−0.949422	−	0.314004i	$-0.898330\pi$
$61$	−6.89142e19	+	1.19363e20i	−0.202776	+	0.351218i	0.746646	+	0.665221i	$0.231663\pi$
$62$	−6.99813e20			−1.70796
$63$	2.75854e20	+	6.91604e19i	0.560097	+	0.140424i
$64$	6.55194e20			1.10994
$65$	−1.85674e20	+	3.21596e20i	−0.263176	+	0.455835i
$66$	−4.48742e20	−	7.77245e20i	−0.533632	−	0.924278i
$67$	−3.39382e20	−	5.87827e20i	−0.339491	−	0.588016i	0.644846	−	0.764313i	$-0.276922\pi$
$67$	−3.39382e20	−	5.87827e20i	−0.339491	−	0.588016i	−0.984337	+	0.176296i	$0.943588\pi$
$68$	2.53716e19	−	4.39448e19i	0.0214040	−	0.0370728i
$69$	4.52614e20			0.322822
$70$	−6.58602e20	+	6.80225e20i	−0.398103	+	0.411173i
$71$	2.14404e21			1.10093			0.550467	−	0.834857i	$-0.314450\pi$
$71$	2.14404e21			1.10093			0.550467	+	0.834857i	$0.314450\pi$
$72$	7.14576e20	−	1.23768e21i	0.312410	−	0.541109i
$73$	−1.53774e21	−	2.66344e21i	−0.573679	−	0.993642i	−0.996184	−	0.0872808i	$-0.972182\pi$
$73$	−1.53774e21	−	2.66344e21i	−0.573679	−	0.993642i	0.422504	−	0.906361i	$-0.361151\pi$
$74$	−1.80927e21	−	3.13374e21i	−0.577215	−	0.999766i
$75$	1.29802e21	−	2.24824e21i	0.354876	−	0.614663i
$76$	−1.10231e21			−0.258789
$77$	−3.37170e21	+	3.48240e21i	−0.681092	+	0.703453i
$78$	4.99571e21			0.869980
$79$	−3.40862e21	+	5.90391e21i	−0.512705	+	0.888031i	0.487186	+	0.873298i	$0.338023\pi$
$79$	−3.40862e21	+	5.90391e21i	−0.512705	+	0.888031i	−0.999891	+	0.0147333i	$0.995310\pi$
$80$	1.75372e21	+	3.03753e21i	0.228257	+	0.395353i
$81$	5.51277e21	+	9.54839e21i	0.622002	+	1.07734i
$82$	−2.14625e21	+	3.71741e21i	−0.210291	+	0.364234i
$83$	8.36785e21			0.713208			0.356604	−	0.934256i	$-0.383935\pi$
$83$	8.36785e21			0.713208			0.356604	+	0.934256i	$0.383935\pi$
$84$	−4.04893e21	−	1.01512e21i	−0.300696	−	0.0753887i
$85$	1.76459e21			0.114373
$86$	−7.95622e21	+	1.37806e22i	−0.450790	+	0.780791i
$87$	−1.33068e22	−	2.30480e22i	−0.660087	−	1.14330i
$88$	1.21793e22	+	2.10952e22i	0.529752	+	0.917557i
$89$	−1.70799e22	+	2.95832e22i	−0.652378	+	1.12995i	0.330166	+	0.943923i	$0.392895\pi$
$89$	−1.70799e22	+	2.95832e22i	−0.652378	+	1.12995i	−0.982544	+	0.186029i	$0.940438\pi$
$90$	9.83849e21			0.330476
$91$	−7.40321e21	−	2.59457e22i	−0.219000	−	0.767520i
$92$	−2.43186e21			−0.0634422
$93$	5.36450e22	−	9.29158e22i	1.23588	−	2.14060i
$94$	1.70307e22	+	2.94981e22i	0.346947	+	0.600930i
$95$	−1.91663e22	−	3.31970e22i	−0.345714	−	0.598795i
$96$	−1.89004e22	+	3.27365e22i	−0.302241	+	0.523496i
$97$	−1.21614e22			−0.172626			−0.0863131	−	0.996268i	$-0.527509\pi$
$97$	−1.21614e22			−0.172626			−0.0863131	+	0.996268i	$0.527509\pi$
$98$	−2.22153e21	−	6.87577e22i	−0.0280254	−	0.867404i
$99$	5.03680e22			0.565392
$100$	−6.97415e21	+	1.20796e22i	−0.0697415	+	0.120796i
$101$	−9.45961e21	−	1.63845e22i	−0.0843680	−	0.146130i	0.820754	−	0.571282i	$-0.193554\pi$
$101$	−9.45961e21	−	1.63845e22i	−0.0843680	−	0.146130i	−0.905122	+	0.425153i	$0.860220\pi$
$102$	−1.18694e22	−	2.05584e22i	−0.0945209	−	0.163715i
$103$	−7.52216e22	+	1.30288e23i	−0.535445	+	0.927418i	0.463697	+	0.885994i	$0.346523\pi$
$103$	−7.52216e22	+	1.30288e23i	−0.535445	+	0.927418i	−0.999142	+	0.0414238i	$0.986811\pi$
$104$	−1.35588e23			−0.863653
$105$	−3.98292e22	−	1.39588e23i	−0.227261	−	0.796471i
$106$	−1.76352e23			−0.902325
$107$	1.45520e23	−	2.52047e23i	0.668357	−	1.15763i	−0.310007	−	0.950734i	$-0.600331\pi$
$107$	1.45520e23	−	2.52047e23i	0.668357	−	1.15763i	0.978364	−	0.206893i	$-0.0663353\pi$
$108$	−1.58710e22	−	2.74894e22i	−0.0654986	−	0.113447i
$109$	2.46138e23	+	4.26324e23i	0.913638	+	1.58247i	0.808883	+	0.587969i	$0.200072\pi$
$109$	2.46138e23	+	4.26324e23i	0.913638	+	1.58247i	0.104755	+	0.994498i	$0.466594\pi$
$110$	−8.38443e22	+	1.45223e23i	−0.280193	+	0.485309i
$111$	5.54765e23			1.67069
$112$	−2.47192e23	−	6.19743e22i	−0.671470	−	0.168347i
$113$	4.47921e23			1.09850			0.549249	−	0.835659i	$-0.314914\pi$
$113$	4.47921e23			1.09850			0.549249	+	0.835659i	$0.314914\pi$
$114$	−2.57843e23	+	4.46597e23i	−0.571412	+	0.989715i
$115$	−4.22838e22	−	7.32376e22i	−0.0847517	−	0.146794i
$116$	7.14962e22	+	1.23835e23i	0.129723	+	0.224686i
$117$	−1.40183e23	+	2.42804e23i	−0.230440	+	0.399133i
$118$	6.02331e23			0.897826
$119$	−8.91829e22	+	9.21109e22i	−0.120640	+	0.124601i
$120$	−7.29464e23			−0.896230
$121$	1.84759e22	−	3.20012e22i	0.0206336	−	0.0357384i
$122$	−1.73221e23	−	3.00028e23i	−0.175980	−	0.304806i
$123$	−3.29046e23	−	5.69924e23i	−0.304332	−	0.527118i
$124$	−2.88230e23	+	4.99229e23i	−0.242879	+	0.420679i
$125$	−1.34338e24			−1.03213
$126$	−4.97241e23	+	5.13566e23i	−0.348583	+	0.360027i
$127$	2.53761e24			1.62436			0.812181	−	0.583406i	$-0.198280\pi$
$127$	2.53761e24			1.62436			0.812181	+	0.583406i	$0.198280\pi$
$128$	−4.12016e23	+	7.13632e23i	−0.240990	+	0.417407i
$129$	−1.21979e24	−	2.11273e24i	−0.652382	−	1.12996i
$130$	−4.66706e23	−	8.08358e23i	−0.228399	−	0.395599i
$131$	1.99590e24	−	3.45700e24i	0.894373	−	1.54910i	0.0597940	−	0.998211i	$-0.480956\pi$
$131$	1.99590e24	−	3.45700e24i	0.894373	−	1.54910i	0.834579	−	0.550889i	$-0.185711\pi$
$132$	−7.39290e23			−0.303539
$133$	2.70155e24	+	6.77315e23i	1.01700	+	0.254975i
$134$	1.70613e24			0.589259
$135$	5.51913e23	−	9.55942e23i	0.174998	−	0.303105i
$136$	3.22148e23	+	5.57977e23i	0.0938335	+	0.162524i
$137$	−9.86402e23	−	1.70850e24i	−0.264099	−	0.457434i	0.703228	−	0.710965i	$-0.251741\pi$
$137$	−9.86402e23	−	1.70850e24i	−0.264099	−	0.457434i	−0.967327	+	0.253531i	$0.918408\pi$
$138$	−5.68840e23	+	9.85260e23i	−0.140082	+	0.242628i
$139$	−2.25247e24			−0.510493			−0.255246	−	0.966876i	$-0.582157\pi$
$139$	−2.25247e24			−0.510493			−0.255246	+	0.966876i	$0.582157\pi$
$140$	2.13999e23	+	7.49993e23i	0.0446621	+	0.156525i
$141$	−5.22204e24			−1.00420
$142$	−2.69461e24	+	4.66719e24i	−0.477726	+	0.827446i
$143$	−2.38929e24	−	4.13837e24i	−0.390755	−	0.676808i
$144$	1.32405e24	+	2.29332e24i	0.199864	+	0.346175i
$145$	−2.48627e24	+	4.30635e24i	−0.346591	+	0.600312i
$146$	7.73045e24			0.995742
$147$	9.29941e24	+	4.97574e24i	1.10740	+	0.592527i
$148$	−2.98071e24			−0.328330
$149$	−6.08612e24	+	1.05415e25i	−0.620438	+	1.07463i	0.368967	+	0.929443i	$0.379712\pi$
$149$	−6.08612e24	+	1.05415e25i	−0.620438	+	1.07463i	−0.989404	+	0.145187i	$0.953622\pi$
$150$	3.26268e24	+	5.65112e24i	0.307981	+	0.533439i
$151$	8.97018e24	+	1.55368e25i	0.784451	+	1.35871i	0.929326	+	0.369260i	$0.120389\pi$
$151$	8.97018e24	+	1.55368e25i	0.784451	+	1.35871i	−0.144875	+	0.989450i	$0.546278\pi$
$152$	6.99812e24	−	1.21211e25i	0.567257	−	0.982518i
$153$	1.33225e24			0.100146
$154$	−3.34305e24	−	1.17162e25i	−0.233160	−	0.817147i
$155$	−2.00463e25			−1.29784
$156$	2.05757e24	−	3.56381e24i	0.123715	−	0.214280i
$157$	3.83190e24	+	6.63705e24i	0.214076	+	0.370791i	0.952986	−	0.303013i	$-0.0979926\pi$
$157$	3.83190e24	+	6.63705e24i	0.214076	+	0.370791i	−0.738910	+	0.673804i	$0.764659\pi$
$158$	−8.56785e24	−	1.48400e25i	−0.444954	−	0.770684i
$159$	1.35185e25	−	2.34147e25i	0.652921	−	1.13089i
$160$	7.06282e24			0.317394
$161$	5.96002e24	+	1.49426e24i	0.249316	+	0.0625069i
$162$	−2.77136e25			−1.07962
$163$	2.32964e24	−	4.03506e24i	0.0845536	−	0.146451i	−0.820647	−	0.571435i	$-0.806387\pi$
$163$	2.32964e24	−	4.03506e24i	0.0845536	−	0.146451i	0.905201	+	0.424984i	$0.139720\pi$
$164$	1.76794e24	+	3.06216e24i	0.0598084	+	0.103591i
$165$	−1.28544e25	−	2.22644e25i	−0.405495	−	0.702337i
$166$	−1.05166e25	+	1.82153e25i	−0.309481	+	0.536036i
$167$	1.36410e25			0.374634			0.187317	−	0.982300i	$-0.440021\pi$
$167$	1.36410e25			0.374634			0.187317	+	0.982300i	$0.440021\pi$
$168$	3.68674e25	−	3.80778e25i	0.945335	−	0.976372i
$169$	−1.51547e25			−0.362952
$170$	−2.21772e24	+	3.84120e24i	−0.0496299	+	0.0859615i
$171$	−1.44705e25	−	2.50636e25i	−0.302710	−	0.524310i
$172$	6.55381e24	+	1.13515e25i	0.128208	+	0.222064i
$173$	−4.35682e25	+	7.54624e25i	−0.797333	+	1.38102i	0.124015	+	0.992280i	$0.460423\pi$
$173$	−4.35682e25	+	7.54624e25i	−0.797333	+	1.38102i	−0.921347	+	0.388740i	$0.872910\pi$
$174$	6.68953e25			1.14572
$175$	2.45147e25	−	2.53195e25i	0.393087	−	0.405992i
$176$	−4.51345e25			−0.677817
$177$	−4.61724e25	+	7.99729e25i	−0.649666	+	1.12525i
$178$	−4.29316e25	−	7.43597e25i	−0.566170	−	0.980636i
$179$	4.02665e24	+	6.97436e24i	0.0497891	+	0.0862372i	0.889846	−	0.456261i	$-0.150812\pi$
$179$	4.02665e24	+	6.97436e24i	0.0497891	+	0.0862372i	−0.840057	+	0.542498i	$0.817478\pi$
$180$	4.05215e24	−	7.01854e24i	0.0469950	−	0.0813978i
$181$	−5.91500e24			−0.0643652			−0.0321826	−	0.999482i	$-0.510246\pi$
$181$	−5.91500e24			−0.0643652			−0.0321826	+	0.999482i	$0.510246\pi$
$182$	6.57835e25	+	1.64928e25i	0.671887	+	0.168451i
$183$	5.31139e25			0.509356
$184$	1.54389e25	−	2.67409e25i	0.139063	−	0.240864i
$185$	−5.18269e25	−	8.97669e25i	−0.438612	−	0.759699i
$186$	1.34841e26	+	2.33551e26i	1.07256	+	1.85773i
$187$	−1.13536e25	+	1.96649e25i	−0.0849089	+	0.147067i
$188$	2.80576e25			0.197349
$189$	2.20060e25	+	7.71234e25i	0.145623	+	0.510359i
$190$	9.63522e25			0.600060
$191$	−1.40185e26	+	2.42808e26i	−0.821900	+	1.42357i	0.0823653	+	0.996602i	$0.473753\pi$
$191$	−1.40185e26	+	2.42808e26i	−0.821900	+	1.42357i	−0.904265	+	0.426971i	$0.859581\pi$
$192$	−1.26244e26	−	2.18661e26i	−0.697021	−	1.20728i
$193$	2.52111e25	+	4.36669e25i	0.131124	+	0.227114i	0.924110	−	0.382126i	$-0.124808\pi$
$193$	2.52111e25	+	4.36669e25i	0.131124	+	0.227114i	−0.792986	+	0.609240i	$0.791475\pi$
$194$	1.52843e25	−	2.64731e25i	0.0749074	−	0.129743i
$195$	1.43103e26			0.661077
$196$	−4.99650e25	−	2.67343e25i	−0.217631	−	0.116446i
$197$	2.81161e25			0.115503			0.0577514	−	0.998331i	$-0.481607\pi$
$197$	2.81161e25			0.115503			0.0577514	+	0.998331i	$0.481607\pi$
$198$	−6.33020e25	+	1.09642e26i	−0.245340	+	0.424941i
$199$	−2.32799e26	−	4.03220e26i	−0.851474	−	1.47480i	−0.879878	−	0.475200i	$-0.842376\pi$
$199$	−2.32799e26	−	4.03220e26i	−0.851474	−	1.47480i	0.0284034	−	0.999597i	$-0.490958\pi$
$200$	−8.85523e25	−	1.53377e26i	−0.305742	−	0.529560i
$201$	−1.30785e26	+	2.26527e26i	−0.426387	+	0.738524i
$202$	4.75550e25			0.146439
$203$	−9.91330e25	−	3.47427e26i	−0.288412	−	1.01079i
$204$	−1.95545e25			−0.0537651
$205$	−6.14798e25	+	1.06486e26i	−0.159795	+	0.276773i
$206$	−1.89076e26	−	3.27489e26i	−0.464689	−	0.804865i
$207$	−3.19240e25	−	5.52940e25i	−0.0742094	−	0.128534i
$208$	1.25617e26	−	2.17575e26i	0.276261	−	0.478498i
$209$	4.93273e26			1.02661
$210$	3.53915e26	+	8.87312e25i	0.697231	+	0.174805i
$211$	5.35197e26			0.998310			0.499155	−	0.866513i	$-0.333644\pi$
$211$	5.35197e26			0.998310			0.499155	+	0.866513i	$0.333644\pi$
$212$	−7.26337e25	+	1.25805e26i	−0.128314	+	0.222247i
$213$	−4.13116e26	−	7.15538e26i	−0.691364	−	1.19748i
$214$	3.65775e26	+	6.33541e26i	0.580037	+	1.00465i
$215$	−2.27908e26	+	3.94748e26i	−0.342545	+	0.593305i
$216$	4.03036e26			0.574282
$217$	1.01315e27	−	1.04641e27i	1.36895	−	1.41389i
$218$	−1.23738e27			−1.58581
$219$	−5.92587e26	+	1.02639e27i	−0.720517	+	1.24797i
$220$	6.90654e25	+	1.19625e26i	0.0796893	+	0.138026i
$221$	−6.31978e25	−	1.09462e26i	−0.0692134	−	0.119881i
$222$	−6.97224e26	+	1.20763e27i	−0.724958	+	1.25566i
$223$	1.49821e26			0.147934			0.0739669	−	0.997261i	$-0.476434\pi$
$223$	1.49821e26			0.147934			0.0739669	+	0.997261i	$0.476434\pi$
$224$	−3.56958e26	+	3.68677e26i	−0.334784	+	0.345775i
$225$	−3.66211e26			−0.326311
$226$	−5.62942e26	+	9.75044e26i	−0.476669	+	0.825615i
$227$	3.72936e26	+	6.45945e26i	0.300149	+	0.519874i	0.976170	−	0.217009i	$-0.0696302\pi$
$227$	3.72936e26	+	6.45945e26i	0.300149	+	0.519874i	−0.676020	+	0.736883i	$0.736297\pi$
$228$	2.12394e26	+	3.67878e26i	0.162514	+	0.281483i
$229$	2.59157e26	−	4.48873e26i	0.188562	−	0.326599i	−0.756209	−	0.654330i	$-0.772951\pi$
$229$	2.59157e26	−	4.48873e26i	0.188562	−	0.326599i	0.944771	+	0.327731i	$0.106284\pi$
$230$	2.12567e26			0.147105
$231$	1.81186e27	+	4.54258e26i	1.19285	+	0.299064i
$232$	−1.81560e27			−1.13739
$233$	1.27542e27	−	2.20910e27i	0.760434	−	1.31711i	−0.182192	−	0.983263i	$-0.558319\pi$
$233$	1.27542e27	−	2.20910e27i	0.760434	−	1.31711i	0.942627	−	0.333848i	$-0.108347\pi$
$234$	−3.52360e26	−	6.10306e26i	−0.199988	−	0.346390i
$235$	4.87850e26	+	8.44981e26i	0.263637	+	0.456632i
$236$	2.48081e26	−	4.29688e26i	0.127675	−	0.221139i
$237$	2.62711e27			1.28787
$238$	−8.84251e25	−	3.09900e26i	−0.0412991	−	0.144739i
$239$	−4.16431e27			−1.85339			−0.926696	−	0.375811i	$-0.877364\pi$
$239$	−4.16431e27			−1.85339			−0.926696	+	0.375811i	$0.877364\pi$
$240$	6.75817e26	−	1.17055e27i	0.286682	−	0.496547i
$241$	1.40508e27	+	2.43368e27i	0.568207	+	0.984163i	0.996743	+	0.0806388i	$0.0256960\pi$
$241$	1.40508e27	+	2.43368e27i	0.568207	+	0.984163i	−0.428536	+	0.903525i	$0.640971\pi$
$242$	4.64407e25	+	8.04377e25i	0.0179070	+	0.0310158i
$243$	1.40279e27	−	2.42970e27i	0.515845	−	0.893470i
$244$	−2.85377e26			−0.100100
$245$	−6.36364e25	−	1.96958e27i	−0.0212959	−	0.659120i
$246$	1.65417e27			0.528233
$247$	−1.37286e27	+	2.37787e27i	−0.418420	+	0.724725i
$248$	−3.65972e27	−	6.33882e27i	−1.06476	−	1.84423i
$249$	−1.61233e27	−	2.79264e27i	−0.447880	−	0.775750i
$250$	1.68835e27	−	2.92431e27i	0.447871	−	0.775735i
$251$	−5.49506e27			−1.39227			−0.696136	−	0.717909i	$-0.745099\pi$
$251$	−5.49506e27			−1.39227			−0.696136	+	0.717909i	$0.745099\pi$
$252$	1.61568e26	+	5.66241e26i	0.0391065	+	0.137055i
$253$	1.08823e27			0.251673
$254$	−3.18925e27	+	5.52394e27i	−0.704856	+	1.22085i
$255$	−3.40003e26	−	5.88903e26i	−0.0718242	−	0.124403i
$256$	1.71245e27	+	2.96605e27i	0.345827	+	0.598989i
$257$	−2.91522e27	+	5.04931e27i	−0.562912	+	0.974992i	0.434329	+	0.900755i	$0.356986\pi$
$257$	−2.91522e27	+	5.04931e27i	−0.562912	+	0.974992i	−0.997241	+	0.0742377i	$0.976348\pi$
$258$	6.13206e27			1.13235
$259$	7.30516e27	+	1.83150e27i	1.29028	+	0.323490i
$260$	−7.68883e26			−0.129917
$261$	−1.87712e27	+	3.25127e27i	−0.303478	+	0.525639i
$262$	5.01685e27	+	8.68944e27i	0.776187	+	1.34440i
$263$	−5.53407e27	−	9.58529e27i	−0.819509	−	1.41943i	−0.906045	−	0.423182i	$-0.860913\pi$
$263$	−5.53407e27	−	9.58529e27i	−0.819509	−	1.41943i	0.0865358	−	0.996249i	$-0.472420\pi$
$264$	4.69346e27	−	8.12931e27i	0.665346	−	1.15241i
$265$	−5.05165e27			−0.685656
$266$	−4.86968e27	+	5.02955e27i	−0.632938	+	0.653718i
$267$	1.31639e28			1.63872
$268$	7.02699e26	−	1.21711e27i	0.0837952	−	0.145137i
$269$	−7.94041e26	−	1.37532e27i	−0.0907177	−	0.157128i	0.817096	−	0.576502i	$-0.195583\pi$
$269$	−7.94041e26	−	1.37532e27i	−0.0907177	−	0.157128i	−0.907813	+	0.419375i	$0.862249\pi$
$270$	1.38728e27	+	2.40284e27i	0.151873	+	0.263052i
$271$	−3.77388e27	+	6.53655e27i	−0.395951	+	0.685807i	−0.993222	−	0.116232i	$-0.962918\pi$
$271$	−3.77388e27	+	6.53655e27i	−0.395951	+	0.685807i	0.597271	+	0.802039i	$0.296252\pi$
$272$	−1.19383e27			−0.120060
$273$	−7.23250e27	+	7.46996e27i	−0.697298	+	0.720191i
$274$	4.95880e27			0.458401
$275$	3.12087e27	−	5.40551e27i	0.276662	−	0.479193i
$276$	4.68573e26	+	8.11593e26i	0.0398404	+	0.0690055i
$277$	3.57489e27	+	6.19189e27i	0.291571	+	0.505017i	0.974181	−	0.225766i	$-0.0724886\pi$
$277$	3.57489e27	+	6.19189e27i	0.291571	+	0.505017i	−0.682610	+	0.730783i	$0.739155\pi$
$278$	2.83089e27	−	4.90324e27i	0.221517	−	0.383679i
$279$	−1.51349e28			−1.13640
$280$	−9.60559e27	−	2.40825e27i	−0.692161	−	0.173534i
$281$	−1.73530e27			−0.120019			−0.0600097	−	0.998198i	$-0.519113\pi$
$281$	−1.73530e27			−0.120019			−0.0600097	+	0.998198i	$0.519113\pi$
$282$	6.56301e27	−	1.13675e28i	0.435751	−	0.754743i
$283$	2.46788e27	+	4.27449e27i	0.157319	+	0.272484i	0.933901	−	0.357532i	$-0.116382\pi$
$283$	2.46788e27	+	4.27449e27i	0.157319	+	0.272484i	−0.776582	+	0.630016i	$0.783048\pi$
$284$	2.21964e27	+	3.84453e27i	0.135869	+	0.235333i
$285$	−7.38599e27	+	1.27929e28i	−0.434203	+	0.752061i
$286$	1.20114e28			0.678239
$287$	−2.45133e27	−	8.59108e27i	−0.132972	−	0.466021i
$288$	5.33239e27			0.277913
$289$	9.68348e27	−	1.67723e28i	0.484960	−	0.839976i
$290$	−6.24945e27	−	1.08244e28i	−0.300791	−	0.520985i
$291$	2.34327e27	+	4.05866e27i	0.108406	+	0.187764i
$292$	3.18392e27	−	5.51471e27i	0.141599	−	0.245256i
$293$	−2.34613e28			−1.00317			−0.501586	−	0.865108i	$-0.667250\pi$
$293$	−2.34613e28			−1.00317			−0.501586	+	0.865108i	$0.667250\pi$
$294$	−2.25187e28	+	1.39897e28i	−0.925869	+	0.575195i
$295$	1.72540e28			0.682237
$296$	1.89233e28	−	3.27762e28i	0.719686	−	1.24653i
$297$	7.10215e27	+	1.23013e28i	0.259831	+	0.450040i
$298$	−1.52979e28	−	2.64968e28i	−0.538451	−	0.932624i
$299$	−3.02874e27	+	5.24594e27i	−0.102575	+	0.177666i
$300$	5.37516e27			0.175185
$301$	−9.08718e27	−	3.18475e28i	−0.285046	−	0.998988i
$302$	−4.50945e28			−1.36158
$303$	−3.64538e27	+	6.31399e27i	−0.105963	+	0.183533i
$304$	1.29669e28	+	2.24593e28i	0.362903	+	0.628566i
$305$	−4.96198e27	−	8.59439e27i	−0.133723	−	0.231615i
$306$	−1.67436e27	+	2.90008e27i	−0.0434564	+	0.0752686i
$307$	3.49585e28			0.873900			0.436950	−	0.899486i	$-0.356059\pi$
$307$	3.49585e28			0.873900			0.436950	+	0.899486i	$0.356059\pi$
$308$	−9.73497e27	−	2.44069e27i	−0.234424	−	0.0587732i
$309$	5.79752e28			1.34499
$310$	2.51940e28	−	4.36374e28i	0.563169	−	0.975437i
$311$	4.43458e28	+	7.68092e28i	0.955230	+	1.65451i	0.733841	+	0.679322i	$0.237726\pi$
$311$	4.43458e28	+	7.68092e28i	0.955230	+	1.65451i	0.221389	+	0.975186i	$0.428941\pi$
$312$	2.61254e28	+	4.52505e28i	0.542356	+	0.939389i
$313$	−2.93874e28	+	5.09005e28i	−0.588033	+	1.01850i	0.406457	+	0.913670i	$0.366764\pi$
$313$	−2.93874e28	+	5.09005e28i	−0.588033	+	1.01850i	−0.994490	+	0.104833i	$0.966569\pi$
$314$	−1.92636e28			−0.371575
$315$	−1.42436e28	+	1.47113e28i	−0.264880	+	0.273576i
$316$	−1.41153e28			−0.253098
$317$	−5.54611e27	+	9.60614e27i	−0.0958974	+	0.166099i	−0.909983	−	0.414646i	$-0.863905\pi$
$317$	−5.54611e27	+	9.60614e27i	−0.0958974	+	0.166099i	0.814085	+	0.580745i	$0.197239\pi$
$318$	3.39798e28	+	5.88547e28i	0.566642	+	0.981452i
$319$	−3.19939e28	−	5.54151e28i	−0.514606	−	0.891323i
$320$	−2.35877e28	+	4.08551e28i	−0.365983	+	0.633902i
$321$	−1.12156e29			−1.67886
$322$	−1.07432e28	+	1.10959e28i	−0.155165	+	0.160259i
$323$	1.30473e28			0.181841
$324$	−1.14143e28	+	1.97702e28i	−0.153526	+	0.265915i
$325$	1.73718e28	+	3.00889e28i	0.225521	+	0.390614i
$326$	5.85575e27	+	1.01425e28i	0.0733804	+	0.127099i
$327$	9.48525e28	−	1.64289e29i	1.14749	−	1.98751i
$328$	−4.48957e28			−0.524392
$329$	−6.87639e28	−	1.72401e28i	−0.775546	−	0.194440i
$330$	6.46209e28			0.703822
$331$	2.04359e28	−	3.53960e28i	0.214967	−	0.372333i	−0.738295	−	0.674477i	$-0.764369\pi$
$331$	2.04359e28	−	3.53960e28i	0.214967	−	0.372333i	0.953262	+	0.302144i	$0.0977023\pi$
$332$	8.66292e27	+	1.50046e28i	0.0880189	+	0.152453i
$333$	−3.91291e28	−	6.77735e28i	−0.384053	−	0.665199i
$334$	−1.71439e28	+	2.96941e28i	−0.162564	+	0.281570i
$335$	4.88725e28			0.447764
$336$	2.69463e28	+	9.44375e28i	0.238560	+	0.836071i
$337$	4.89238e28			0.418578			0.209289	−	0.977854i	$-0.432885\pi$
$337$	4.89238e28			0.418578			0.209289	+	0.977854i	$0.432885\pi$
$338$	1.90463e28	−	3.29891e28i	0.157495	−	0.272790i
$339$	−8.63060e28	−	1.49486e29i	−0.689834	−	1.19483i
$340$	1.82681e27	+	3.16413e27i	0.0141152	+	0.0244482i
$341$	1.28980e29	−	2.23401e29i	0.963493	−	1.66882i
$342$	7.27454e28			0.525418
$343$	1.06028e29	+	9.62217e28i	0.740521	+	0.672033i
$344$	−1.66430e29			−1.12411
$345$	−1.62946e28	+	2.82231e28i	−0.106445	+	0.184368i
$346$	−1.09512e29	−	1.89681e29i	−0.691970	−	1.19853i
$347$	6.57880e28	+	1.13948e29i	0.402122	+	0.696495i	0.993982	−	0.109545i	$-0.0349395\pi$
$347$	6.57880e28	+	1.13948e29i	0.402122	+	0.696495i	−0.591860	+	0.806041i	$0.701606\pi$
$348$	2.75520e28	−	4.77214e28i	0.162926	−	0.282197i
$349$	−1.32383e29			−0.757426			−0.378713	−	0.925514i	$-0.623633\pi$
$349$	−1.32383e29			−0.757426			−0.378713	+	0.925514i	$0.623633\pi$
$350$	2.43063e28	+	8.51854e28i	0.134567	+	0.471610i
$351$	−7.90660e28			−0.423602
$352$	−4.54430e28	+	7.87095e28i	−0.235628	+	0.408119i
$353$	7.88093e28	+	1.36502e29i	0.395520	+	0.685060i	0.993167	−	0.116699i	$-0.0372311\pi$
$353$	7.88093e28	+	1.36502e29i	0.395520	+	0.685060i	−0.597648	+	0.801759i	$0.703898\pi$
$354$	−1.16058e29	−	2.01018e29i	−0.563816	−	0.976559i
$355$	−7.71878e28	+	1.33693e29i	−0.363013	+	0.628757i
$356$	−7.07285e28			−0.322047
$357$	4.79244e28	+	1.20153e28i	0.211287	+	0.0529725i
$358$	−2.02426e28			−0.0864195
$359$	−8.69951e28	+	1.50680e29i	−0.359674	+	0.622973i	−0.987906	−	0.155053i	$-0.950445\pi$
$359$	−8.69951e28	+	1.50680e29i	−0.359674	+	0.622973i	0.628233	+	0.778026i	$0.283779\pi$
$360$	5.14510e28	+	8.91158e28i	0.206023	+	0.356842i
$361$	−1.28001e28	−	2.21705e28i	−0.0496457	−	0.0859888i
$362$	7.43392e27	−	1.28759e28i	0.0279299	−	0.0483760i
$363$	−1.42399e28			−0.0518298
$364$	3.88597e28	−	4.01355e28i	0.137036	−	0.141535i
$365$	2.21441e29			0.756641
$366$	−6.67531e28	+	1.15620e29i	−0.221024	+	0.382824i
$367$	1.61471e29	+	2.79677e29i	0.518127	+	0.897422i	0.999778	+	0.0210588i	$0.00670373\pi$
$367$	1.61471e29	+	2.79677e29i	0.518127	+	0.897422i	−0.481652	+	0.876363i	$0.659963\pi$
$368$	2.86069e28	+	4.95487e28i	0.0889655	+	0.154093i
$369$	−4.64169e28	+	8.03965e28i	−0.139918	+	0.242345i
$370$	2.60542e29			0.761305
$371$	2.55313e29	−	2.63695e29i	0.723223	−	0.746967i
$372$	2.22146e29			0.610092
$373$	−5.85410e27	+	1.01396e28i	−0.0155887	+	0.0270004i	−0.873715	−	0.486439i	$-0.838296\pi$
$373$	−5.85410e27	+	1.01396e28i	−0.0155887	+	0.0270004i	0.858126	+	0.513439i	$0.171629\pi$
$374$	−2.85381e28	−	4.94294e28i	−0.0736887	−	0.127633i
$375$	2.58845e29	+	4.48333e29i	0.648157	+	1.12264i
$376$	−1.78127e29	+	3.08524e29i	−0.432582	+	0.749255i
$377$	3.56178e29			0.838961
$378$	−1.95541e29	−	4.90248e28i	−0.446768	−	0.112011i
$379$	−5.49051e29			−1.21692			−0.608460	−	0.793585i	$-0.708212\pi$
$379$	−5.49051e29			−1.21692			−0.608460	+	0.793585i	$0.708212\pi$
$380$	3.96843e28	−	6.87352e28i	0.0853311	−	0.147798i
$381$	−4.88951e29	−	8.46888e29i	−1.02007	−	1.76680i
$382$	−3.52367e29	−	6.10318e29i	−0.713291	−	1.23546i
$383$	−2.96333e28	+	5.13264e28i	−0.0582096	+	0.100822i	−0.893662	−	0.448741i	$-0.851873\pi$
$383$	−2.96333e28	+	5.13264e28i	−0.0582096	+	0.100822i	0.835452	+	0.549563i	$0.185206\pi$
$384$	3.17551e29			0.605347
$385$	−9.57626e28	−	3.35615e29i	−0.177173	−	0.620931i
$386$	−1.26740e29			−0.227594
$387$	−1.72069e29	+	2.98033e29i	−0.299935	+	0.519503i
$388$	−1.25902e28	−	2.18068e28i	−0.0213043	−	0.0369001i
$389$	3.65788e29	+	6.33563e29i	0.600909	+	1.04081i	0.992684	+	0.120744i	$0.0385281\pi$
$389$	3.65788e29	+	6.33563e29i	0.600909	+	1.04081i	−0.391774	+	0.920061i	$0.628139\pi$
$390$	−1.79851e29	+	3.11511e29i	−0.286860	+	0.496856i
$391$	2.87843e28			0.0445782
$392$	6.11181e29	−	3.79695e29i	0.919136	−	0.571012i
$393$	−1.53829e30			−2.24659
$394$	−3.53360e28	+	6.12037e28i	−0.0501199	+	0.0868103i
$395$	−2.45429e29	−	4.25095e29i	−0.338110	−	0.585624i
$396$	5.21440e28	+	9.03161e28i	0.0697766	+	0.120857i
$397$	1.02737e29	−	1.77945e29i	0.133547	−	0.231310i	−0.791494	−	0.611176i	$-0.790697\pi$
$397$	1.02737e29	−	1.77945e29i	0.133547	−	0.231310i	0.925041	+	0.379866i	$0.124030\pi$
$398$	1.17032e30			1.47791
$399$	−2.94495e29	−	1.03210e30i	−0.361318	−	1.26630i
$400$	3.28160e29			0.391197
$401$	1.57683e29	−	2.73114e29i	0.182652	−	0.316362i	−0.760131	−	0.649770i	$-0.774865\pi$
$401$	1.57683e29	−	2.73114e29i	0.182652	−	0.316362i	0.942783	+	0.333408i	$0.108199\pi$
$402$	−3.28739e29	−	5.69393e29i	−0.370043	−	0.640933i
$403$	7.17949e29	+	1.24352e30i	0.785391	+	1.36034i
$404$	1.95864e28	−	3.39246e28i	0.0208242	−	0.0360685i
$405$	−7.93863e29			−0.820376
$406$	8.80878e29	+	2.20848e29i	0.884843	+	0.221842i
$407$	1.33384e30			1.30247
$408$	1.24144e29	−	2.15023e29i	0.117851	−	0.204124i
$409$	−4.78957e29	−	8.29579e29i	−0.442058	−	0.765666i	0.555784	−	0.831326i	$-0.312418\pi$
$409$	−4.78957e29	−	8.29579e29i	−0.442058	−	0.765666i	−0.997842	+	0.0656602i	$0.979085\pi$
$410$	−1.54534e29	−	2.67661e29i	−0.138679	−	0.240199i
$411$	−3.80123e29	+	6.58392e29i	−0.331698	+	0.574518i
$412$	−3.11496e29			−0.264323
$413$	−8.72021e29	+	9.00651e29i	−0.719617	+	0.743243i
$414$	1.60487e29			0.128806
$415$	−3.01252e29	+	5.21784e29i	−0.235167	+	0.407322i
$416$	−2.52951e29	−	4.38124e29i	−0.192072	−	0.332678i
$417$	4.34010e29	+	7.51727e29i	0.320579	+	0.555259i
$418$	−6.19941e29	+	1.07377e30i	−0.445475	+	0.771585i
$419$	5.13468e29			0.358965			0.179483	−	0.983761i	$-0.442558\pi$
$419$	5.13468e29			0.358965			0.179483	+	0.983761i	$0.442558\pi$
$420$	2.09064e29	−	2.15928e29i	0.142205	−	0.146873i
$421$	2.43397e28			0.0161091			0.00805456	−	0.999968i	$-0.497436\pi$
$421$	2.43397e28			0.0161091			0.00805456	+	0.999968i	$0.497436\pi$
$422$	−6.72630e29	+	1.16503e30i	−0.433195	+	0.750315i
$423$	3.68324e29	+	6.37957e29i	0.230843	+	0.399831i
$424$	−9.22245e29	−	1.59737e30i	−0.562521	−	0.974315i
$425$	8.25484e28	−	1.42978e29i	0.0490045	−	0.0848783i
$426$	2.07680e30			1.20001
$427$	6.99405e29	+	1.75350e29i	0.393376	+	0.0986248i
$428$	6.02604e29			0.329935
$429$	−9.20744e29	+	1.59478e30i	−0.490772	+	0.850043i
$430$	−5.72865e29	−	9.92232e29i	−0.297280	−	0.514903i
$431$	7.28887e29	+	1.26247e30i	0.368274	+	0.637870i	0.989296	−	0.145924i	$-0.0466154\pi$
$431$	7.28887e29	+	1.26247e30i	0.368274	+	0.637870i	−0.621022	+	0.783794i	$0.713282\pi$
$432$	−3.73395e29	+	6.46739e29i	−0.183699	+	0.318175i
$433$	−2.75821e30			−1.32135			−0.660673	−	0.750673i	$-0.729729\pi$
$433$	−2.75821e30			−1.32135			−0.660673	+	0.750673i	$0.729729\pi$
$434$	1.00454e30	+	3.52057e30i	0.468636	+	1.64241i
$435$	1.91623e30			0.870607
$436$	−5.09635e29	+	8.82713e29i	−0.225509	+	0.390593i
$437$	−3.12644e29	−	5.41516e29i	−0.134745	−	0.233386i
$438$	−1.48951e30	−	2.57991e30i	−0.625306	−	1.08306i
$439$	1.72439e30	−	2.98673e30i	0.705170	−	1.22139i	−0.261460	−	0.965214i	$-0.584204\pi$
$439$	1.72439e30	−	2.98673e30i	0.705170	−	1.22139i	0.966630	−	0.256176i	$-0.0824628\pi$
$440$	−1.75388e30			−0.698704
$441$	−4.80451e28	−	1.48702e30i	−0.0186469	−	0.577131i
$442$	3.17705e29			0.120135
$443$	7.89024e29	−	1.36663e30i	0.290702	−	0.503510i	−0.683274	−	0.730162i	$-0.739445\pi$
$443$	7.89024e29	−	1.36663e30i	0.290702	−	0.503510i	0.973976	+	0.226652i	$0.0727780\pi$
$444$	5.74327e29	+	9.94764e29i	0.206184	+	0.357122i
$445$	−1.22979e30	−	2.13006e30i	−0.430220	−	0.745162i
$446$	−1.88294e29	+	3.26134e29i	−0.0641926	+	0.111185i
$447$	4.69072e30			1.55849
$448$	−9.40493e29	−	3.29611e30i	−0.304550	−	1.06734i
$449$	−3.99683e30			−1.26149			−0.630743	−	0.775992i	$-0.717250\pi$
$449$	−3.99683e30			−1.26149			−0.630743	+	0.775992i	$0.717250\pi$
$450$	4.60250e29	−	7.97177e29i	0.141596	−	0.245251i
$451$	−7.91136e29	−	1.37029e30i	−0.237258	−	0.410943i
$452$	4.63715e29	+	8.03178e29i	0.135569	+	0.234812i
$453$	3.45677e30	−	5.98730e30i	0.985239	−	1.70648i
$454$	−1.87481e30			−0.520973
$455$	1.88439e30	+	4.72442e29i	0.510551	+	0.128002i
$456$	−5.39363e30			−1.42490
$457$	−8.23404e29	+	1.42618e30i	−0.212118	+	0.367398i	−0.952377	−	0.304923i	$-0.901369\pi$
$457$	−8.23404e29	+	1.42618e30i	−0.212118	+	0.367398i	0.740259	+	0.672321i	$0.234703\pi$
$458$	6.51412e29	+	1.12828e30i	0.163645	+	0.283441i
$459$	1.87855e29	+	3.25374e29i	0.0460231	+	0.0797144i
$460$	8.75495e28	−	1.51640e29i	0.0209189	−	0.0362326i
$461$	−2.18794e30			−0.509888			−0.254944	−	0.966956i	$-0.582057\pi$
$461$	−2.18794e30			−0.509888			−0.254944	+	0.966956i	$0.582057\pi$
$462$	−3.26597e30	+	3.37319e30i	−0.742385	+	0.766758i
$463$	5.94749e30			1.31872			0.659360	−	0.751827i	$-0.270827\pi$
$463$	5.94749e30			1.31872			0.659360	+	0.751827i	$0.270827\pi$
$464$	1.68208e30	−	2.91345e30i	0.363823	−	0.630159i
$465$	3.86256e30	+	6.69015e30i	0.815016	+	1.41165i
$466$	3.20588e30	+	5.55275e30i	0.659948	+	1.14306i
$467$	1.05326e30	−	1.82430e30i	0.211539	−	0.366397i	−0.740657	−	0.671883i	$-0.765486\pi$
$467$	1.05326e30	−	1.82430e30i	0.211539	−	0.366397i	0.952196	+	0.305487i	$0.0988191\pi$
$468$	−5.80503e29			−0.113757
$469$	−2.47004e30	+	2.55113e30i	−0.472298	+	0.487804i
$470$	−2.45250e30			−0.457598
$471$	1.47667e30	−	2.55767e30i	0.268871	−	0.465698i
$472$	3.14993e30	+	5.45584e30i	0.559716	+	0.969457i
$473$	−2.93277e30	−	5.07971e30i	−0.508599	−	0.880919i
$474$	−3.30173e30	+	5.71877e30i	−0.558844	+	0.967947i
$475$	−3.58644e30			−0.592499
$476$	−2.57494e29	−	6.45573e28i	−0.0415229	−	0.0104103i
$477$	−3.81397e30			−0.600366
$478$	5.23367e30	−	9.06497e30i	0.804239	−	1.39298i
$479$	4.06649e30	+	7.04337e30i	0.610044	+	1.05663i	0.991232	+	0.132130i	$0.0421818\pi$
$479$	4.06649e30	+	7.04337e30i	0.610044	+	1.05663i	−0.381188	+	0.924498i	$0.624485\pi$
$480$	−1.36087e30	−	2.35710e30i	−0.199317	−	0.345227i
$481$	−3.71231e30	+	6.42991e30i	−0.530855	+	0.919468i
$482$	−7.06359e30			−0.986244
$483$	−6.49700e29	−	2.27698e30i	−0.0885770	−	0.310432i
$484$	7.65096e28			0.0101858
$485$	4.37822e29	−	7.58330e29i	0.0569204	−	0.0985890i
$486$	3.52602e30	+	6.10724e30i	0.447679	+	0.775403i
$487$	2.67960e30	+	4.64121e30i	0.332267	+	0.575504i	0.982956	−	0.183841i	$-0.0588531\pi$
$487$	2.67960e30	+	4.64121e30i	0.332267	+	0.575504i	−0.650689	+	0.759345i	$0.725520\pi$
$488$	1.81175e30	−	3.13803e30i	0.219416	−	0.380040i
$489$	−1.79552e30			−0.212392
$490$	4.36741e30	+	2.33683e30i	0.504626	+	0.270005i
$491$	7.21743e30			0.814602			0.407301	−	0.913294i	$-0.366470\pi$
$491$	7.21743e30			0.814602			0.407301	+	0.913294i	$0.366470\pi$
$492$	6.81297e29	−	1.18004e30i	0.0751169	−	0.130106i
$493$	−8.46253e29	−	1.46575e30i	−0.0911508	−	0.157878i
$494$	−3.45080e30	−	5.97696e30i	−0.363128	−	0.628957i
$495$	−1.81330e30	+	3.14073e30i	−0.186428	+	0.322902i
$496$	1.35623e31			1.36237
$497$	−3.07764e30	−	1.07861e31i	−0.302078	−	1.05868i
$498$	8.10544e30			0.777390
$499$	3.51540e29	−	6.08886e29i	0.0329472	−	0.0570663i	−0.849082	−	0.528262i	$-0.822844\pi$
$499$	3.51540e29	−	6.08886e29i	0.0329472	−	0.0570663i	0.882029	+	0.471195i	$0.156177\pi$
$500$	−1.39075e30	−	2.40886e30i	−0.127378	−	0.220626i
$501$	−2.62837e30	−	4.55247e30i	−0.235262	−	0.407487i
$502$	6.90613e30	−	1.19618e31i	0.604146	−	1.04641i
$503$	−1.27287e31			−1.08831			−0.544155	−	0.838984i	$-0.683150\pi$
$503$	−1.27287e31			−1.08831			−0.544155	+	0.838984i	$0.683150\pi$
$504$	−7.25217e30	−	1.81822e30i	−0.606062	−	0.151948i
$505$	1.36223e30			0.111275
$506$	−1.36768e30	+	2.36890e30i	−0.109208	+	0.189154i
$507$	2.92002e30	+	5.05763e30i	0.227927	+	0.394780i
$508$	2.62709e30	+	4.55026e30i	0.200467	+	0.347219i
$509$	−4.47569e30	+	7.75213e30i	−0.333892	+	0.578318i	−0.983271	−	0.182147i	$-0.941695\pi$
$509$	−4.47569e30	+	7.75213e30i	−0.333892	+	0.578318i	0.649379	+	0.760465i	$0.275029\pi$
$510$	1.70925e30			0.124666
$511$	−1.11917e31	+	1.15592e31i	−0.798098	+	0.824301i
$512$	−1.55212e31			−1.08224
$513$	4.08082e30	−	7.06819e30i	0.278226	−	0.481902i
$514$	−7.32764e30	−	1.26918e31i	−0.488527	−	0.846153i
$515$	−5.41613e30	−	9.38101e30i	−0.353106	−	0.611598i
$516$	2.52559e30	−	4.37446e30i	0.161025	−	0.278903i
$517$	−1.25555e31			−0.782878
$518$	−1.31679e31	+	1.36002e31i	−0.803017	+	0.829381i
$519$	3.35791e31			2.00283
$520$	4.88134e30	−	8.45472e30i	0.284774	−	0.493243i
$521$	−1.34827e31	−	2.33527e31i	−0.769382	−	1.33261i	−0.937898	−	0.346911i	$-0.887231\pi$
$521$	−1.34827e31	−	2.33527e31i	−0.769382	−	1.33261i	0.168516	−	0.985699i	$-0.446103\pi$
$522$	−4.71830e30	−	8.17233e30i	−0.263375	−	0.456179i
$523$	−8.30353e30	+	1.43821e31i	−0.453412	+	0.785333i	−0.998595	−	0.0529837i	$-0.983127\pi$
$523$	−8.30353e30	+	1.43821e31i	−0.453412	+	0.785333i	0.545183	+	0.838317i	$0.316460\pi$
$524$	8.26511e30			0.441508
$525$	−1.31735e31	−	3.30278e30i	−0.688445	−	0.172602i
$526$	2.78207e31			1.42243
$527$	3.41159e30	−	5.90904e30i	0.170661	−	0.295594i
$528$	8.69657e30	+	1.50629e31i	0.425655	+	0.737257i
$529$	9.75049e30	+	1.68884e31i	0.466967	+	0.808811i
$530$	6.34887e30	−	1.09966e31i	0.297525	−	0.515329i
$531$	1.30266e31			0.597373
$532$	1.58230e30	+	5.54541e30i	0.0710076	+	0.248857i
$533$	8.80747e30			0.386802
$534$	−1.65442e31	+	2.86555e31i	−0.711087	+	1.23164i
$535$	1.04777e31	+	1.81480e31i	0.440757	+	0.763413i
$536$	8.92231e30	+	1.54539e31i	0.367352	+	0.636272i
$537$	1.55172e30	−	2.68766e30i	0.0625330	−	0.108310i
$538$	3.99177e30			0.157460
$539$	2.23589e31	+	1.19633e31i	0.863335	+	0.461936i
$540$	2.28550e30			0.0863879
$541$	2.93771e30	−	5.08827e30i	0.108703	−	0.188279i	−0.806542	−	0.591177i	$-0.798664\pi$
$541$	2.93771e30	−	5.08827e30i	0.108703	−	0.188279i	0.915245	+	0.402898i	$0.131997\pi$
$542$	−9.48595e30	−	1.64301e31i	−0.343628	−	0.595182i
$543$	1.13971e30	+	1.97404e30i	0.0404200	+	0.0700096i
$544$	−1.20199e30	+	2.08190e30i	−0.0417361	+	0.0722891i
$545$	−3.54450e31			−1.20502
$546$	−7.17105e30	−	2.51321e31i	−0.238708	−	0.836590i
$547$	−4.88371e31			−1.59183			−0.795913	−	0.605411i	$-0.793009\pi$
$547$	−4.88371e31			−1.59183			−0.795913	+	0.605411i	$0.793009\pi$
$548$	2.04237e30	−	3.53749e30i	0.0651865	−	0.112906i
$549$	−3.74627e30	−	6.48872e30i	−0.117089	−	0.202804i
$550$	7.84456e30	+	1.35872e31i	0.240103	+	0.415871i
$551$	−1.83834e31	+	3.18410e31i	−0.551039	+	0.954427i
$552$	−1.18991e31			−0.349314
$553$	3.45939e31	+	8.67316e30i	0.994627	+	0.249367i
$554$	−1.79715e31			−0.506084
$555$	−1.99722e31	+	3.45928e31i	−0.550879	+	0.954150i
$556$	−2.33190e30	−	4.03897e30i	−0.0630013	−	0.109122i
$557$	−3.53825e30	−	6.12843e30i	−0.0936383	−	0.162186i	0.815401	−	0.578896i	$-0.196516\pi$
$557$	−3.53825e30	−	6.12843e30i	−0.0936383	−	0.162186i	−0.909039	+	0.416710i	$0.863183\pi$
$558$	1.90214e31	−	3.29460e31i	0.493115	−	0.854101i
$559$	3.26496e31			0.829168
$560$	1.27636e31	−	1.31827e31i	0.317550	−	0.327975i
$561$	8.75047e30			0.213284
$562$	2.18091e30	−	3.77744e30i	0.0520798	−	0.0902049i
$563$	7.29040e30	+	1.26273e31i	0.170571	+	0.295437i	0.938620	−	0.344954i	$-0.112105\pi$
$563$	7.29040e30	+	1.26273e31i	0.170571	+	0.295437i	−0.768049	+	0.640391i	$0.778772\pi$
$564$	−5.40618e30	−	9.36378e30i	−0.123931	−	0.214655i
$565$	−1.61256e31	+	2.79304e31i	−0.362209	+	0.627365i
$566$	−1.24064e31			−0.273060
$567$	4.01221e31	−	4.14394e31i	0.865324	−	0.893734i
$568$	−5.63665e31			−1.19128
$569$	1.06226e31	−	1.83989e31i	0.220009	−	0.381067i	−0.734801	−	0.678282i	$-0.762725\pi$
$569$	1.06226e31	−	1.83989e31i	0.220009	−	0.381067i	0.954810	+	0.297216i	$0.0960580\pi$
$570$	−1.85653e31	−	3.21560e31i	−0.376826	−	0.652681i
$571$	−3.67470e31	−	6.36477e31i	−0.730983	−	1.26610i	−0.956464	−	0.291852i	$-0.905729\pi$
$571$	−3.67470e31	−	6.36477e31i	−0.730983	−	1.26610i	0.225481	−	0.974248i	$-0.427605\pi$
$572$	4.94708e30	−	8.56860e30i	0.0964484	−	0.167054i
$573$	1.08044e32			2.06455
$574$	2.17821e31	+	5.46106e30i	0.407955	+	0.102280i
$575$	−7.91223e30			−0.145251
$576$	−1.78086e31	+	3.08454e31i	−0.320458	+	0.555050i
$577$	−2.75822e31	−	4.77737e31i	−0.486527	−	0.842689i	0.513353	−	0.858177i	$-0.328403\pi$
$577$	−2.75822e31	−	4.77737e31i	−0.486527	−	0.842689i	−0.999880	+	0.0154883i	$0.995070\pi$
$578$	2.43402e31	+	4.21585e31i	0.420876	+	0.728978i
$579$	9.71542e30	−	1.68276e31i	0.164687	−	0.285246i
$580$	−1.02958e31			−0.171095
$581$	−1.20116e31	−	4.20964e31i	−0.195692	−	0.685835i
$582$	−1.17800e31			−0.188161
$583$	3.25029e31	−	5.62967e31i	0.509019	−	0.881647i
$584$	4.04269e31	+	7.00214e31i	0.620758	+	1.07519i
$585$	−1.00935e31	−	1.74824e31i	−0.151966	−	0.263214i
$586$	2.94860e31	−	5.10712e31i	0.435304	−	0.753969i
$587$	4.14937e30			0.0600681			0.0300340	−	0.999549i	$-0.490438\pi$
$587$	4.14937e30			0.0600681			0.0300340	+	0.999549i	$0.490438\pi$
$588$	7.05195e29	+	2.18262e31i	0.0100108	+	0.309841i
$589$	−1.48222e32			−2.06341
$590$	−2.16846e31	+	3.75588e31i	−0.296042	+	0.512760i
$591$	−5.41744e30	−	9.38328e30i	−0.0725334	−	0.125632i
$592$	3.50633e31	+	6.07315e31i	0.460420	+	0.797470i
$593$	1.19047e31	−	2.06195e31i	0.153316	−	0.265551i	−0.779128	−	0.626864i	$-0.784338\pi$
$593$	1.19047e31	−	2.06195e31i	0.153316	−	0.265551i	0.932445	+	0.361313i	$0.117671\pi$
$594$	−3.57036e31			−0.450991
$595$	−2.53296e30	−	8.87716e30i	−0.0313822	−	0.109984i
$596$	−2.52029e31			−0.306280
$597$	−8.97122e31	+	1.55386e32i	−1.06942	+	1.85228i
$598$	−7.61299e30	−	1.31861e31i	−0.0890208	−	0.154189i
$599$	2.97662e31	+	5.15566e31i	0.341440	+	0.591392i	0.984700	−	0.174256i	$-0.0557519\pi$
$599$	2.97662e31	+	5.15566e31i	0.341440	+	0.591392i	−0.643260	+	0.765648i	$0.722419\pi$
$600$	−3.41247e31	+	5.91058e31i	−0.383999	+	0.665106i
$601$	1.13077e32			1.24830			0.624150	−	0.781304i	$-0.285445\pi$
$601$	1.13077e32			1.24830			0.624150	+	0.781304i	$0.285445\pi$
$602$	8.07470e31	+	2.02444e31i	0.874514	+	0.219253i
$603$	3.68985e31			0.392066
$604$	−1.85730e31	+	3.21693e31i	−0.193623	+	0.335364i
$605$	1.33031e30	+	2.30416e30i	0.0136071	+	0.0235682i
$606$	−9.16296e30	−	1.58707e31i	−0.0919604	−	0.159280i
$607$	1.96633e31	−	3.40578e31i	0.193636	−	0.335388i	−0.752816	−	0.658231i	$-0.771305\pi$
$607$	1.96633e31	−	3.40578e31i	0.193636	−	0.335388i	0.946453	+	0.322843i	$0.104639\pi$
$608$	5.22222e31			0.504619
$609$	−9.68472e31	+	1.00027e32i	−0.918308	+	0.948457i
$610$	2.49446e31			0.232105
$611$	3.49442e31	−	6.05251e31i	0.319081	−	0.552665i
$612$	1.37923e30	+	2.38890e30i	0.0123594	+	0.0214070i
$613$	3.98636e31	+	6.90457e31i	0.350575	+	0.607214i	0.986350	−	0.164661i	$-0.0526529\pi$
$613$	3.98636e31	+	6.90457e31i	0.350575	+	0.607214i	−0.635775	+	0.771874i	$0.719320\pi$
$614$	−4.39355e31	+	7.60986e31i	−0.379210	+	0.656811i
$615$	4.73841e31			0.401392
$616$	8.86416e31	−	9.15518e31i	0.736986	−	0.761182i
$617$	1.31619e32			1.07409			0.537044	−	0.843554i	$-0.319541\pi$
$617$	1.31619e32			1.07409			0.537044	+	0.843554i	$0.319541\pi$
$618$	−7.28627e31	+	1.26202e32i	−0.583630	+	1.01088i
$619$	−9.73069e31	−	1.68541e32i	−0.765070	−	1.32514i	−0.940209	−	0.340597i	$-0.889371\pi$
$619$	−9.73069e31	−	1.68541e32i	−0.765070	−	1.32514i	0.175139	−	0.984544i	$-0.443962\pi$
$620$	−2.07532e31	−	3.59456e31i	−0.160170	−	0.277422i
$621$	9.00291e30	−	1.55935e31i	0.0682071	−	0.118138i
$622$	−2.22933e32			−1.65800
$623$	1.73342e32	+	4.34593e31i	1.26559	+	0.317300i
$624$	−9.68162e31			−0.693945
$625$	8.21001e30	−	1.42201e31i	0.0577728	−	0.100065i
$626$	−7.38677e31	−	1.27943e32i	−0.510328	−	0.883914i
$627$	−9.50446e31	−	1.64622e32i	−0.644689	−	1.11663i
$628$	−7.93404e30	+	1.37422e31i	−0.0528395	+	0.0915207i
$629$	3.52807e31			0.230704
$630$	−1.41226e31	−	4.94948e31i	−0.0906771	−	0.317792i
$631$	2.09276e32			1.31941			0.659707	−	0.751523i	$-0.270680\pi$
$631$	2.09276e32			1.31941			0.659707	+	0.751523i	$0.270680\pi$
$632$	8.96123e31	−	1.55213e32i	0.554780	−	0.960908i
$633$	−1.03123e32	−	1.78613e32i	−0.626918	−	1.08585i
$634$	−1.39406e31	−	2.41458e31i	−0.0832252	−	0.144150i
$635$	−9.13569e31	+	1.58235e32i	−0.535604	+	0.927693i
$636$	5.59806e31			0.322315
$637$	−1.19899e32	+	7.44871e31i	−0.677973	+	0.421190i
$638$	1.60839e32			0.893208
$639$	−5.82764e31	+	1.00938e32i	−0.317858	+	0.550545i
$640$	−2.96660e31	−	5.13831e31i	−0.158924	−	0.275265i
$641$	1.28039e32	+	2.21770e32i	0.673714	+	1.16691i	0.976843	+	0.213957i	$0.0686352\pi$
$641$	1.28039e32	+	2.21770e32i	0.673714	+	1.16691i	−0.303129	+	0.952949i	$0.598031\pi$
$642$	1.40956e32	−	2.44143e32i	0.728503	−	1.26180i
$643$	−1.90581e32			−0.967507			−0.483754	−	0.875204i	$-0.660727\pi$
$643$	−1.90581e32			−0.967507			−0.483754	+	0.875204i	$0.660727\pi$
$644$	3.49079e30	+	1.22340e31i	0.0174075	+	0.0610073i
$645$	1.75655e32			0.860444
$646$	−1.63977e31	+	2.84016e31i	−0.0789058	+	0.136669i
$647$	5.86875e31	+	1.01650e32i	0.277426	+	0.480515i	0.970744	−	0.240116i	$-0.0771855\pi$
$647$	5.86875e31	+	1.01650e32i	0.277426	+	0.480515i	−0.693319	+	0.720631i	$0.743852\pi$
$648$	−1.44930e32	−	2.51026e32i	−0.673047	−	1.16575i
$649$	−1.11014e32	+	1.92282e32i	−0.506481	+	0.877251i
$650$	−8.73310e31			−0.391440
$651$	−5.44439e32	−	1.36498e32i	−2.39755	−	0.601099i
$652$	9.64717e30			0.0417400
$653$	2.15935e32	−	3.74010e32i	0.917954	−	1.58994i	0.115436	−	0.993315i	$-0.463174\pi$
$653$	2.15935e32	−	3.74010e32i	0.917954	−	1.58994i	0.802518	−	0.596628i	$-0.203493\pi$
$654$	2.38419e32	+	4.12954e32i	0.995858	+	1.72488i
$655$	1.43709e32	+	2.48912e32i	0.589806	+	1.02157i
$656$	4.15940e31	−	7.20429e31i	0.167740	−	0.290534i
$657$	1.67187e32			0.662522
$658$	1.23950e32	−	1.28020e32i	0.482670	−	0.498516i
$659$	−4.05209e32			−1.55059			−0.775295	−	0.631600i	$-0.782399\pi$
$659$	−4.05209e32			−1.55059			−0.775295	+	0.631600i	$0.782399\pi$
$660$	2.66152e31	−	4.60990e31i	0.100086	−	0.173355i
$661$	4.86881e31	+	8.43303e31i	0.179931	+	0.311650i	0.941857	−	0.336015i	$-0.109079\pi$
$661$	4.86881e31	+	8.43303e31i	0.179931	+	0.311650i	−0.761926	+	0.647665i	$0.775746\pi$
$662$	5.13672e31	+	8.89706e31i	0.186560	+	0.323132i
$663$	−2.43541e31	+	4.21825e31i	−0.0869292	+	0.150566i
$664$	−2.19990e32			−0.771737
$665$	−1.39493e32	+	1.44073e32i	−0.480955	+	0.496745i
$666$	1.96708e32			0.666605
$667$	−4.05565e31	+	7.02459e31i	−0.135087	+	0.233978i
$668$	1.41220e31	+	2.44601e31i	0.0462346	+	0.0800808i
$669$	−2.88678e31	−	5.00004e31i	−0.0928994	−	0.160906i
$670$	−6.14225e31	+	1.06387e32i	−0.194298	+	0.336533i
$671$	1.27704e32			0.397095
$672$	1.91819e32	+	4.80917e31i	0.586334	+	0.147002i
$673$	−3.34090e31			−0.100390			−0.0501949	−	0.998739i	$-0.515984\pi$
$673$	−3.34090e31			−0.100390			−0.0501949	+	0.998739i	$0.515984\pi$
$674$	−6.14869e31	+	1.06498e32i	−0.181633	+	0.314597i
$675$	−5.16376e31	−	8.94390e31i	−0.149959	−	0.259737i
$676$	−1.56891e31	−	2.71742e31i	−0.0447930	−	0.0775837i
$677$	7.14381e31	−	1.23734e32i	0.200521	−	0.347313i	−0.748175	−	0.663501i	$-0.769070\pi$
$677$	7.14381e31	−	1.23734e32i	0.200521	−	0.347313i	0.948696	+	0.316188i	$0.102403\pi$
$678$	4.33874e32			1.19735
$679$	1.74569e31	+	6.11805e31i	0.0473658	+	0.166001i
$680$	−4.63907e31			−0.123760
$681$	1.43716e32	−	2.48923e32i	0.376975	−	0.652940i
$682$	3.24203e32	+	5.61536e32i	0.836174	+	1.44830i
$683$	−4.00502e31	−	6.93689e31i	−0.101570	−	0.175925i	0.810762	−	0.585377i	$-0.199053\pi$
$683$	−4.00502e31	−	6.93689e31i	−0.101570	−	0.175925i	−0.912332	+	0.409452i	$0.865720\pi$
$684$	2.99614e31	−	5.18948e31i	0.0747167	−	0.129413i
$685$	1.42046e32			0.348328
$686$	−3.42712e32	+	1.09874e32i	−0.826423	+	0.264951i
$687$	−1.99739e32			−0.473653
$688$	1.54190e32	−	2.67066e32i	0.359576	−	0.622804i
$689$	1.80922e32	+	3.13367e32i	0.414927	+	0.718674i
$690$	−4.09578e31	−	7.09409e31i	−0.0923787	−	0.160005i
$691$	−3.03339e32	+	5.25398e32i	−0.672868	+	1.16544i	0.304219	+	0.952602i	$0.401605\pi$
$691$	−3.03339e32	+	5.25398e32i	−0.672868	+	1.16544i	−0.977087	+	0.212840i	$0.931729\pi$
$692$	−1.80418e32			−0.393604
$693$	−7.23003e31	−	2.53388e32i	−0.155134	−	0.543693i
$694$	−3.30727e32			−0.697968
$695$	8.10916e31	−	1.40455e32i	0.168326	−	0.291549i
$696$	3.49833e32	+	6.05929e32i	0.714257	+	1.23713i
$697$	−2.09259e31	−	3.62447e31i	−0.0420249	−	0.0727893i
$698$	1.66378e32	−	2.88175e32i	0.328668	−	0.569270i
$699$	−9.83003e32			−1.91015
$700$	7.07801e31	+	1.77455e31i	0.135296	+	0.0339205i
$701$	5.03914e32			0.947544			0.473772	−	0.880648i	$-0.342892\pi$
$701$	5.03914e32			0.947544			0.473772	+	0.880648i	$0.342892\pi$
$702$	9.93693e31	−	1.72113e32i	0.183813	−	0.318373i
$703$	−3.83206e32	−	6.63732e32i	−0.697343	−	1.20783i
$704$	−3.03532e32	−	5.25733e32i	−0.543400	−	0.941196i
$705$	1.87999e32	−	3.25624e32i	0.331117	−	0.573511i
$706$	−3.96187e32			−0.686509
$707$	−6.88475e31	+	7.11078e31i	−0.117372	+	0.121226i
$708$	−1.91202e32			−0.320708
$709$	9.78040e31	−	1.69402e32i	0.161408	−	0.279567i	−0.773966	−	0.633227i	$-0.781730\pi$
$709$	9.78040e31	−	1.69402e32i	0.161408	−	0.279567i	0.935374	+	0.353660i	$0.115063\pi$
$710$	−1.94018e32	−	3.36048e32i	−0.315043	−	0.545671i
$711$	−1.85297e32	−	3.20944e32i	−0.296052	−	0.512778i
$712$	4.49027e32	−	7.77738e32i	0.705916	−	1.22268i
$713$	−3.27000e32			−0.505845
$714$	−8.63861e31	+	8.92223e31i	−0.131497	+	0.135814i
$715$	3.44069e32			0.515378
$716$	−8.33727e30	+	1.44406e31i	−0.0122892	+	0.0212855i
$717$	8.02385e32	+	1.38977e33i	1.16389	+	2.01592i
$718$	−2.18669e32	−	3.78746e32i	−0.312145	−	0.540651i
$719$	−1.80677e32	+	3.12942e32i	−0.253817	+	0.439624i	−0.964574	−	0.263814i	$-0.915020\pi$
$719$	−1.80677e32	+	3.12942e32i	−0.253817	+	0.439624i	0.710756	+	0.703438i	$0.248353\pi$
$720$	−1.90669e32			−0.263606
$721$	7.63419e32	+	1.91399e32i	1.03874	+	0.260427i
$722$	6.43483e31			0.0861706
$723$	5.41467e32	−	9.37849e32i	0.713644	−	1.23607i
$724$	−6.12358e30	−	1.06063e31i	−0.00794349	−	0.0137585i
$725$	2.32618e32	+	4.02907e32i	0.297000	+	0.514420i
$726$	1.78965e31	−	3.09977e31i	0.0224904	−	0.0389545i
$727$	5.93026e32			0.733547			0.366773	−	0.930310i	$-0.380462\pi$
$727$	5.93026e32			0.733547			0.366773	+	0.930310i	$0.380462\pi$
$728$	1.94629e32	+	6.82109e32i	0.236972	+	0.830507i
$729$	−4.31845e31			−0.0517561
$730$	−2.78305e32	+	4.82038e32i	−0.328328	+	0.568681i
$731$	−7.75731e31	−	1.34360e32i	−0.0900868	−	0.156035i
$732$	5.49868e31	+	9.52400e31i	0.0628610	+	0.108878i
$733$	6.00071e32	−	1.03935e33i	0.675316	−	1.16968i	−0.301061	−	0.953605i	$-0.597341\pi$
$733$	6.00071e32	−	1.03935e33i	0.675316	−	1.16968i	0.976377	−	0.216076i	$-0.0693259\pi$
$734$	−8.11743e32			−0.899319
$735$	−6.45055e32	+	4.00740e32i	−0.703546	+	0.437077i
$736$	1.15210e32			0.123707
$737$	−3.14451e32	+	5.44646e32i	−0.332413	+	0.575756i
$738$	−1.16673e32	−	2.02083e32i	−0.121429	−	0.210321i
$739$	−9.92797e31	−	1.71957e32i	−0.101730	−	0.176202i	0.810667	−	0.585507i	$-0.199104\pi$
$739$	−9.92797e31	−	1.71957e32i	−0.101730	−	0.176202i	−0.912398	+	0.409305i	$0.865771\pi$
$740$	1.07309e32	−	1.85864e32i	0.108261	−	0.187513i
$741$	1.05810e33			1.05104
$742$	2.53143e32	+	8.87180e32i	0.247583	+	0.867694i
$743$	9.02149e32			0.868774			0.434387	−	0.900726i	$-0.356965\pi$
$743$	9.02149e32			0.868774			0.434387	+	0.900726i	$0.356965\pi$
$744$	−1.41032e33	+	2.44274e33i	−1.33730	+	2.31627i
$745$	−4.38214e32	−	7.59009e32i	−0.409156	−	0.708679i
$746$	−1.47148e31	−	2.54867e31i	−0.0135287	−	0.0234324i
$747$	−2.27444e32	+	3.93944e32i	−0.205915	+	0.356654i
$748$	−4.70156e31			−0.0419154
$749$	−1.47687e33	−	3.70271e32i	−1.29658	−	0.325071i
$750$	−1.30126e33			−1.12501
$751$	−1.98676e32	+	3.44117e32i	−0.169155	+	0.292986i	−0.938123	−	0.346302i	$-0.887437\pi$
$751$	−1.98676e32	+	3.44117e32i	−0.169155	+	0.292986i	0.768968	+	0.639288i	$0.220771\pi$
$752$	−3.30053e32	−	5.71669e32i	−0.276745	−	0.479336i
$753$	1.05880e33	+	1.83389e33i	0.874319	+	1.51436i
$754$	−4.47641e32	+	7.75337e32i	−0.364049	+	0.630551i
$755$	−1.29175e33			−1.03463
$756$	−1.15510e32	+	1.19302e32i	−0.0911211	+	0.0941127i
$757$	8.67116e32			0.673712			0.336856	−	0.941556i	$-0.390636\pi$
$757$	8.67116e32			0.673712			0.336856	+	0.941556i	$0.390636\pi$
$758$	6.90042e32	−	1.19519e33i	0.528055	−	0.914619i
$759$	−2.09683e32	−	3.63181e32i	−0.158045	−	0.273743i
$760$	5.03880e32	+	8.72746e32i	0.374085	+	0.647935i
$761$	−1.08069e32	+	1.87180e32i	−0.0790272	+	0.136879i	−0.902830	−	0.429997i	$-0.858515\pi$
$761$	−1.08069e32	+	1.87180e32i	−0.0790272	+	0.136879i	0.823803	+	0.566876i	$0.191848\pi$
$762$	2.45803e33			1.77054
$763$	1.79140e33	−	1.85022e33i	1.27105	−	1.31278i
$764$	−5.80514e32			−0.405732
$765$	−4.79626e31	+	8.30737e31i	−0.0330215	+	0.0571949i
$766$	−7.44857e31	−	1.29013e32i	−0.0505176	−	0.0874990i
$767$	−6.17941e32	−	1.07031e33i	−0.412858	−	0.715091i
$768$	6.59915e32	−	1.14301e33i	0.434344	−	0.752306i
$769$	7.41782e32			0.480976			0.240488	−	0.970652i	$-0.422693\pi$
$769$	7.41782e32			0.480976			0.240488	+	0.970652i	$0.422693\pi$
$770$	8.50929e32	+	2.13339e32i	0.543563	+	0.136279i
$771$	2.24684e33			1.41399
$772$	−5.22002e31	+	9.04134e31i	−0.0323648	+	0.0560575i
$773$	−4.01971e32	−	6.96234e32i	−0.245545	−	0.425296i	0.716740	−	0.697341i	$-0.245633\pi$
$773$	−4.01971e32	−	6.96234e32i	−0.245545	−	0.425296i	−0.962285	+	0.272045i	$0.912300\pi$
$774$	−4.32510e32	−	7.49130e32i	−0.260301	−	0.450854i
$775$	−9.37779e32	+	1.62428e33i	−0.556072	+	0.963145i
$776$	3.19720e32			0.186793
$777$	−7.96333e32	−	2.79088e33i	−0.458409	−	1.60657i
$778$	−1.83887e33			−1.04301
$779$	−4.54579e32	+	7.87354e32i	−0.254056	+	0.440037i
$780$	1.48150e32	+	2.56603e32i	0.0815854	+	0.141310i
$781$	−9.93270e32	−	1.72039e33i	−0.538989	−	0.933557i
$782$	−3.61758e31	+	6.26583e31i	−0.0193437	+	0.0335043i
$783$	−1.05874e33			−0.557863
$784$	4.30530e31	+	1.33251e33i	0.0223547	+	0.691890i
$785$	−5.51811e32			−0.282351
$786$	1.93331e33	−	3.34859e33i	0.974859	−	1.68851i
$787$	−1.07011e33	−	1.85348e33i	−0.531762	−	0.921039i	−0.999313	−	0.0370729i	$-0.988197\pi$
$787$	−1.07011e33	−	1.85348e33i	−0.531762	−	0.921039i	0.467550	−	0.883967i	$-0.345137\pi$
$788$	2.91075e31	+	5.04156e31i	0.0142545	+	0.0246896i
$789$	−2.13263e33	+	3.69382e33i	−1.02927	+	1.78275i
$790$	1.23381e33			0.586862
$791$	−6.42964e32	−	2.25337e33i	−0.301410	−	1.05634i
$792$	−1.32417e33			−0.611791
$793$	−3.55421e32	+	6.15607e32i	−0.161846	+	0.280325i
$794$	2.58237e32	+	4.47279e32i	0.115900	+	0.200744i
$795$	9.73360e32	+	1.68591e33i	0.430578	+	0.745782i
$796$	4.82017e32	−	8.34877e32i	0.210166	−	0.364018i
$797$	9.61312e31			0.0413136			0.0206568	−	0.999787i	$-0.493424\pi$
$797$	9.61312e31			0.0413136			0.0206568	+	0.999787i	$0.493424\pi$
$798$	2.61683e33	+	6.56075e32i	1.10852	+	0.277920i
$799$	−3.32099e32			−0.138669
$800$	3.30403e32	−	5.72274e32i	0.135991	−	0.235542i
$801$	−9.28484e32	−	1.60818e33i	−0.376704	−	0.652471i
$802$	3.96348e32	+	6.86494e32i	0.158515	+	0.274557i
$803$	−1.42478e33	+	2.46779e33i	−0.561718	+	0.972923i
$804$	−5.41588e32			−0.210487
$805$	−3.07743e32	+	3.17847e32i	−0.117906	+	0.121777i
$806$	−3.60925e33			−1.36321
$807$	−3.05994e32	+	5.29997e32i	−0.113938	+	0.197346i
$808$	2.48692e32	+	4.30747e32i	0.0912917	+	0.158122i
$809$	1.85324e33	+	3.20990e33i	0.670691	+	1.16167i	0.977708	+	0.209967i	$0.0673358\pi$
$809$	1.85324e33	+	3.20990e33i	0.670691	+	1.16167i	−0.307017	+	0.951704i	$0.599331\pi$
$810$	9.97719e32	−	1.72810e33i	0.355984	−	0.616582i
$811$	3.98885e33			1.40316			0.701580	−	0.712590i	$-0.252478\pi$
$811$	3.98885e33			1.40316			0.701580	+	0.712590i	$0.252478\pi$
$812$	5.20352e32	−	5.37436e32i	0.180469	−	0.186394i
$813$	2.90863e33			0.994596
$814$	−1.67636e33	+	2.90354e33i	−0.565179	+	0.978920i
$815$	1.67740e32	+	2.90533e32i	0.0557600	+	0.0965792i
$816$	2.30028e32	+	3.98420e32i	0.0753952	+	0.130588i
$817$	−1.68514e33	+	2.91875e33i	−0.544607	+	0.943286i
$818$	2.40780e33			0.767285
$819$	1.42270e33	+	3.56691e32i	0.447043	+	0.112080i
$820$	−2.54591e32			−0.0788830
$821$	−2.11043e33	+	3.65537e33i	−0.644799	+	1.11682i	0.339549	+	0.940588i	$0.389726\pi$
$821$	−2.11043e33	+	3.65537e33i	−0.644799	+	1.11682i	−0.984348	+	0.176236i	$0.943608\pi$
$822$	−9.55469e32	−	1.65492e33i	−0.287866	−	0.498599i
$823$	2.46502e33	+	4.26955e33i	0.732357	+	1.26848i	0.955873	+	0.293779i	$0.0949131\pi$
$823$	2.46502e33	+	4.26955e33i	0.732357	+	1.26848i	−0.223516	+	0.974700i	$0.571754\pi$
$824$	1.97757e33	−	3.42525e33i	0.579386	−	1.00353i
$825$	−2.40534e33			−0.694953
$826$	−8.64611e32	−	3.03017e33i	−0.246349	−	0.863368i
$827$	−6.03766e32			−0.169651			−0.0848253	−	0.996396i	$-0.527033\pi$
$827$	−6.03766e32			−0.169651			−0.0848253	+	0.996396i	$0.527033\pi$
$828$	6.60994e31	−	1.14488e32i	0.0183168	−	0.0317256i
$829$	−2.15662e33	−	3.73537e33i	−0.589381	−	1.02084i	−0.994314	−	0.106491i	$-0.966039\pi$
$829$	−2.15662e33	−	3.73537e33i	−0.589381	−	1.02084i	0.404933	−	0.914346i	$-0.367295\pi$
$830$	−7.57221e32	−	1.31155e33i	−0.204091	−	0.353497i
$831$	1.37763e33	−	2.38612e33i	0.366202	−	0.634280i
$832$	3.37913e33			0.885904
$833$	5.91402e32	+	3.16435e32i	0.152920	+	0.0818215i
$834$	−2.18184e33			−0.556433
$835$	−4.91092e32	+	8.50596e32i	−0.123529	+	0.213958i
$836$	5.10667e32	+	8.84501e32i	0.126697	+	0.219445i
$837$	−2.13410e33	−	3.69637e33i	−0.522242	−	0.904549i
$838$	−6.45322e32	+	1.11773e33i	−0.155765	+	0.269793i
$839$	−2.82182e33			−0.671842			−0.335921	−	0.941890i	$-0.609047\pi$
$839$	−2.82182e33			−0.671842			−0.335921	+	0.941890i	$0.609047\pi$
$840$	1.04710e33	+	3.66974e33i	0.245911	+	0.861833i
$841$	4.52701e32			0.104871
$842$	−3.05899e31	+	5.29833e31i	−0.00699020	+	0.0121074i
$843$	3.34360e32	+	5.79128e32i	0.0753697	+	0.130544i
$844$	5.54069e32	+	9.59676e32i	0.123204	+	0.213396i
$845$	5.45585e32	−	9.44981e32i	0.119677	−	0.207287i
$846$	−1.85163e33			−0.400677
$847$	−1.87511e32	−	4.70115e31i	−0.0400283	−	0.0100356i
$848$	3.41768e33			0.719746
$849$	9.51029e32	−	1.64723e33i	0.197586	−	0.342228i
$850$	2.07492e32	+	3.59387e32i	0.0425288	+	0.0736621i
$851$	−8.45410e32	−	1.46429e33i	−0.170953	−	0.296100i
$852$	8.55367e32	−	1.48154e33i	0.170646	−	0.295568i
$853$	−8.25823e32			−0.162545			−0.0812724	−	0.996692i	$-0.525898\pi$
$853$	−8.25823e32			−0.162545			−0.0812724	+	0.996692i	$0.525898\pi$
$854$	−1.26071e33	+	1.30210e33i	−0.244822	+	0.252860i
$855$	2.08381e33			0.399253
$856$	−3.82569e33	+	6.62629e33i	−0.723205	+	1.25263i
$857$	1.27436e33	+	2.20726e33i	0.237692	+	0.411694i	0.960052	−	0.279823i	$-0.0902759\pi$
$857$	1.27436e33	+	2.20726e33i	0.237692	+	0.411694i	−0.722360	+	0.691517i	$0.756943\pi$
$858$	−2.31436e33	−	4.00860e33i	−0.425920	−	0.737715i
$859$	2.21380e33	−	3.83442e33i	0.401992	−	0.696270i	−0.591974	−	0.805957i	$-0.701651\pi$
$859$	2.21380e33	−	3.83442e33i	0.401992	−	0.696270i	0.993966	+	0.109686i	$0.0349847\pi$
$860$	−9.43778e32			−0.169098
$861$	−2.39481e33	+	2.47343e33i	−0.423384	+	0.437284i
$862$	−3.66423e33			−0.639218
$863$	5.59729e33	−	9.69479e33i	0.963505	−	1.66884i	0.249925	−	0.968265i	$-0.419594\pi$
$863$	5.59729e33	−	9.69479e33i	0.963505	−	1.66884i	0.713580	−	0.700574i	$-0.247073\pi$
$864$	7.51895e32	+	1.30232e33i	0.127717	+	0.221213i
$865$	−3.13701e33	−	5.43346e33i	−0.525812	−	0.910733i
$866$	3.46649e33	−	6.00414e33i	0.573370	−	0.993105i
$867$	−7.46330e33			−1.21818
$868$	2.92523e33	+	7.33394e32i	0.471175	+	0.118130i
$869$	6.31646e33			1.00403
$870$	−2.40830e33	+	4.17130e33i	−0.377781	+	0.654335i
$871$	−1.75034e33	−	3.03168e33i	−0.270966	−	0.469327i
$872$	−6.47094e33	−	1.12080e34i	−0.988616	−	1.71233i
$873$	3.30553e32	−	5.72535e32i	0.0498400	−	0.0863254i
$874$	1.57171e33			0.233879
$875$	1.92835e33	+	6.75820e33i	0.283200	+	0.992519i
$876$	−2.45393e33			−0.355684
$877$	−3.02240e33	+	5.23495e33i	−0.432371	+	0.748889i	−0.997077	−	0.0764036i	$-0.975656\pi$
$877$	−3.02240e33	+	5.23495e33i	−0.432371	+	0.748889i	0.564706	+	0.825292i	$0.308990\pi$
$878$	4.33440e33	+	7.50740e33i	0.611986	+	1.05999i
$879$	4.52056e33	+	7.82984e33i	0.629971	+	1.09114i
$880$	1.62489e33	−	2.81439e33i	0.223498	−	0.387110i
$881$	7.67902e33			1.04252			0.521258	−	0.853399i	$-0.325463\pi$
$881$	7.67902e33			1.04252			0.521258	+	0.853399i	$0.325463\pi$
$882$	3.29737e33	+	1.76429e33i	0.441855	+	0.236419i
$883$	−1.70686e33			−0.225762			−0.112881	−	0.993609i	$-0.536008\pi$
$883$	−1.70686e33			−0.225762			−0.112881	+	0.993609i	$0.536008\pi$
$884$	1.30852e32	−	2.26643e32i	0.0170837	−	0.0295898i
$885$	−3.32452e33	−	5.75823e33i	−0.428431	−	0.742064i
$886$	1.98328e33	+	3.43513e33i	0.252287	+	0.436974i
$887$	−3.19634e33	+	5.53623e33i	−0.401358	+	0.695172i	−0.993890	−	0.110375i	$-0.964795\pi$
$887$	−3.19634e33	+	5.53623e33i	−0.401358	+	0.695172i	0.592532	+	0.805547i	$0.298128\pi$
$888$	−1.45847e34			−1.80779
$889$	−3.64260e33	−	1.27660e34i	−0.445698	−	1.56202i
$890$	6.18234e33			0.746738
$891$	5.10780e33	−	8.84698e33i	0.609033	−	1.05488i
$892$	1.55104e32	+	2.68648e32i	0.0182569	+	0.0316219i
$893$	3.60714e33	+	6.24776e33i	0.419152	+	0.725993i
$894$	−5.89526e33	+	1.02109e34i	−0.676272	+	1.17134i
$895$	−5.79855e32			−0.0656681
$896$	4.18151e33	+	1.04836e33i	0.467511	+	0.117211i
$897$	2.33433e33			0.257661
$898$	5.02317e33	−	8.70039e33i	0.547394	−	0.948114i
$899$	9.61374e33	+	1.66515e34i	1.03432	+	1.79150i
$900$	−3.79124e32	−	6.56662e32i	−0.0402710	−	0.0697514i
$901$	8.59716e32	−	1.48907e33i	0.0901612	−	0.156164i
$902$	3.97717e33			0.411812
$903$	−8.87765e33	+	9.16912e33i	−0.907588	+	0.937386i
$904$	−1.17758e34			−1.18865
$905$	2.12947e32	−	3.68834e32i	0.0212233	−	0.0367598i
$906$	8.68887e33	+	1.50496e34i	0.855045	+	1.48098i
$907$	8.02264e33	+	1.38956e34i	0.779531	+	1.35019i	0.932212	+	0.361913i	$0.117876\pi$
$907$	8.02264e33	+	1.38956e34i	0.779531	+	1.35019i	−0.152681	+	0.988276i	$0.548791\pi$
$908$	−7.72173e32	+	1.33744e33i	−0.0740845	+	0.128318i
$909$	1.02847e33			0.0974336
$910$	−3.39670e33	+	3.50822e33i	−0.317747	+	0.328179i
$911$	−2.12344e33			−0.196146			−0.0980730	−	0.995179i	$-0.531268\pi$
$911$	−2.12344e33			−0.196146			−0.0980730	+	0.995179i	$0.531268\pi$
$912$	4.99696e33	−	8.65500e33i	0.455791	−	0.789453i
$913$	−3.87658e33	−	6.71443e33i	−0.349168	−	0.604777i
$914$	−2.06969e33	−	3.58481e33i	−0.184088	−	0.318849i
$915$	−1.91216e33	+	3.31196e33i	−0.167951	+	0.290899i
$916$	1.07318e33			0.0930840
$917$	−2.02562e34	−	5.07851e33i	−1.73505	−	0.435000i
$918$	−9.44376e32			−0.0798829
$919$	3.73462e33	−	6.46855e33i	0.311974	−	0.540354i	−0.666816	−	0.745222i	$-0.732343\pi$
$919$	3.73462e33	−	6.46855e33i	0.311974	−	0.540354i	0.978790	+	0.204868i	$0.0656766\pi$
$920$	1.11163e33	+	1.92541e33i	0.0917069	+	0.158841i
$921$	−6.73586e33	−	1.16668e34i	−0.548791	−	0.950534i
$922$	2.74978e33	−	4.76276e33i	0.221255	−	0.383224i
$923$	1.10578e34			0.878714
$924$	1.06121e33	+	3.71917e33i	0.0832861	+	0.291889i
$925$	−9.69797e33			−0.751711
$926$	−7.47475e33	+	1.29466e34i	−0.572230	+	0.991131i
$927$	−4.08915e33	−	7.08261e33i	−0.309183	−	0.535521i
$928$	−3.38715e33	−	5.86672e33i	−0.252949	−	0.438121i
$929$	−6.31465e32	+	1.09373e33i	−0.0465767	+	0.0806731i	−0.888374	−	0.459121i	$-0.848165\pi$
$929$	−6.31465e32	+	1.09373e33i	−0.0465767	+	0.0806731i	0.841797	+	0.539794i	$0.181498\pi$
$930$	−1.94177e34			−1.41463
$931$	−4.70525e32	−	1.45630e34i	−0.0338580	−	1.04792i
$932$	5.28159e33			0.375389
$933$	1.70892e34	−	2.95994e34i	1.19973	−	2.07799i
$934$	2.64745e33	+	4.58552e33i	0.183586	+	0.317979i
$935$	−8.17481e32	−	1.41592e33i	−0.0559944	−	0.0969851i
$936$	3.68538e33	−	6.38327e33i	0.249351	−	0.431888i
$937$	7.33696e33			0.490355			0.245178	−	0.969478i	$-0.421154\pi$
$937$	7.33696e33			0.490355			0.245178	+	0.969478i	$0.421154\pi$
$938$	−2.44905e33	−	8.58307e33i	−0.161683	−	0.566644i
$939$	2.26496e34			1.47709
$940$	−1.01011e33	+	1.74955e33i	−0.0650723	+	0.112709i
$941$	1.16906e34	+	2.02487e34i	0.743971	+	1.28859i	0.950674	+	0.310191i	$0.100393\pi$
$941$	1.16906e34	+	2.02487e34i	0.743971	+	1.28859i	−0.206704	+	0.978404i	$0.566274\pi$
$942$	3.71173e33	+	6.42891e33i	0.233341	+	0.404159i
$943$	−1.00287e33	+	1.73702e33i	−0.0622816	+	0.107875i
$944$	−1.16731e34			−0.716157
$945$	−5.60133e33	−	1.40433e33i	−0.339489	−	0.0851144i
$946$	1.47435e34			0.882781
$947$	5.02701e33	−	8.70704e33i	0.297362	−	0.515046i	−0.678170	−	0.734905i	$-0.737227\pi$
$947$	5.02701e33	−	8.70704e33i	0.297362	−	0.515046i	0.975532	+	0.219859i	$0.0705599\pi$
$948$	2.71975e33	+	4.71075e33i	0.158940	+	0.275292i
$949$	−7.93079e33	−	1.37365e34i	−0.457884	−	0.793078i
$950$	4.50741e33	−	7.80706e33i	0.257102	−	0.445314i
$951$	4.27453e33			0.240886
$952$	2.34461e33	−	2.42158e33i	0.130540	−	0.134826i
$953$	5.87817e33			0.323351			0.161675	−	0.986844i	$-0.448310\pi$
$953$	5.87817e33			0.323351			0.161675	+	0.986844i	$0.448310\pi$
$954$	4.79336e33	−	8.30235e33i	0.260516	−	0.451227i
$955$	−1.00937e34	−	1.74827e34i	−0.542013	−	0.938795i
$956$	−4.31115e33	−	7.46713e33i	−0.228732	−	0.396176i
$957$	−1.23293e34	+	2.13549e34i	−0.646324	+	1.11947i
$958$	−2.04429e34			−1.05886
$959$	−7.17907e33	+	7.41477e33i	−0.367413	+	0.379476i
$960$	1.81797e34			0.919320
$961$	−2.87502e34	+	4.97968e34i	−1.43655	+	2.48818i
$962$	−9.33119e33	−	1.61621e34i	−0.460706	−	0.797966i
$963$	7.91064e33	+	1.37016e34i	0.385931	+	0.668451i
$964$	−2.90926e33	+	5.03899e33i	−0.140248	+	0.242917i
$965$	−3.63051e33			−0.172943
$966$	5.77312e33	+	1.44740e33i	0.271752	+	0.0681320i
$967$	2.63145e33			0.122402			0.0612012	−	0.998125i	$-0.480507\pi$
$967$	2.63145e33			0.122402			0.0612012	+	0.998125i	$0.480507\pi$
$968$	−4.85729e32	+	8.41308e32i	−0.0223269	+	0.0386713i
$969$	−2.51397e33	−	4.35432e33i	−0.114192	−	0.197787i
$970$	1.10050e33	+	1.90612e33i	0.0493987	+	0.0855611i
$971$	−9.17536e33	+	1.58922e34i	−0.407007	+	0.704957i	−0.994553	−	0.104234i	$-0.966761\pi$
$971$	−9.17536e33	+	1.58922e34i	−0.407007	+	0.704957i	0.587546	+	0.809191i	$0.300094\pi$
$972$	5.80900e33			0.254648
$973$	3.23329e33	+	1.13316e34i	0.140071	+	0.490900i
$974$	−1.34708e34			−0.576720
$975$	6.69446e33	−	1.15951e34i	0.283245	−	0.490595i
$976$	3.35701e33	+	5.81451e33i	0.140372	+	0.243131i
$977$	2.23997e33	+	3.87974e33i	0.0925666	+	0.160330i	0.908590	−	0.417688i	$-0.137160\pi$
$977$	2.23997e33	+	3.87974e33i	0.0925666	+	0.160330i	−0.816024	+	0.578018i	$0.803826\pi$
$978$	2.25659e33	−	3.90852e33i	0.0921627	−	0.159631i
$979$	3.16504e34			1.27755
$980$	3.46583e33	−	2.15314e33i	0.138263	−	0.0858960i
$981$	−2.67608e34			−1.05513
$982$	−9.07079e33	+	1.57111e34i	−0.353479	+	0.612243i
$983$	−9.31151e33	−	1.61280e34i	−0.358637	−	0.621177i	0.629097	−	0.777327i	$-0.283425\pi$
$983$	−9.31151e33	−	1.61280e34i	−0.358637	−	0.621177i	−0.987733	+	0.156150i	$0.950092\pi$
$984$	8.65057e33	+	1.49832e34i	0.329307	+	0.570377i
$985$	−1.01221e33	+	1.75320e33i	−0.0380850	+	0.0659651i
$986$	4.25425e33			0.158212
$987$	7.49594e33	+	2.62707e34i	0.275536	+	0.965660i
$988$	−5.68509e33			−0.206554
$989$	−3.71768e33	+	6.43920e33i	−0.133510	+	0.231246i
$990$	−4.55788e33	−	7.89448e33i	−0.161793	−	0.280233i
$991$	7.23734e33	+	1.25354e34i	0.253941	+	0.439838i	0.964607	−	0.263691i	$-0.0849399\pi$
$991$	7.23734e33	+	1.25354e34i	0.253941	+	0.439838i	−0.710667	+	0.703529i	$0.751607\pi$
$992$	1.36550e34	−	2.36511e34i	0.473595	−	0.820291i
$993$	−1.57505e34			−0.539979
$994$	2.73473e34	+	6.85635e33i	0.926770	+	0.232354i
$995$	3.35242e34			1.12303
$996$	3.33837e33	−	5.78222e33i	0.110548	−	0.191475i
$997$	1.44200e33	+	2.49762e33i	0.0472032	+	0.0817583i	0.888662	−	0.458564i	$-0.151636\pi$
$997$	1.44200e33	+	2.49762e33i	0.0472032	+	0.0817583i	−0.841458	+	0.540322i	$0.818303\pi$
$998$	8.83625e32	+	1.53048e33i	0.0285935	+	0.0495253i
$999$	1.10348e34	−	1.91128e34i	0.352989	−	0.611395i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7.24.c.a.2.5	✓	28
7.2	even	3		49.24.a.g.1.10		14
7.4	even	3	inner	7.24.c.a.4.5	yes	28
7.5	odd	6		49.24.a.f.1.10		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.24.c.a.2.5	✓	28	1.1	even	1	trivial
7.24.c.a.4.5	yes	28	7.4	even	3	inner
49.24.a.f.1.10		14	7.5	odd	6
49.24.a.g.1.10		14	7.2	even	3

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 7 \)
Weight:	\( k \)	\(=\)	\( 24 \)
Character orbit:	\([\chi]\)	\(=\)	7.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1256.79 + 2176.82i) q^{2} +(-192681. - 333734. i) q^{3} +(1.03526e6 + 1.79313e6i) q^{4} +(-3.60011e7 + 6.23558e7i) q^{5} +9.68640e8 q^{6} +(-1.43544e9 - 5.03073e9i) q^{7} -2.62899e10 q^{8} +(-2.71807e10 + 4.70783e10i) q^{9} +(-9.04917e10 - 1.56736e11i) q^{10} +(-4.63271e11 - 8.02408e11i) q^{11} +(3.98951e11 - 6.91004e11i) q^{12} +5.15744e12 q^{13} +(1.27551e13 + 3.19787e12i) q^{14} +2.77470e13 q^{15} +(2.43564e13 - 4.21866e13i) q^{16} +(-1.22537e13 - 2.12240e13i) q^{17} +(-6.83207e13 - 1.18335e14i) q^{18} +(-2.66191e14 + 4.61056e14i) q^{19} -1.49082e14 q^{20} +(-1.40234e15 + 1.44838e15i) q^{21} +2.32894e15 q^{22} +(-5.87256e14 + 1.01716e15i) q^{23} +(5.06557e15 + 8.77382e15i) q^{24} +(3.36830e15 + 5.83407e15i) q^{25} +(-6.48182e15 + 1.12268e16i) q^{26} -1.53305e16 q^{27} +(7.53468e15 - 7.78205e15i) q^{28} +6.90610e16 q^{29} +(-3.48721e16 + 6.04003e16i) q^{30} +(1.39206e17 + 2.41113e17i) q^{31} +(-4.90458e16 - 8.49499e16i) q^{32} +(-1.78527e17 + 3.09218e17i) q^{33} +6.16013e16 q^{34} +(3.65373e17 + 9.16039e16i) q^{35} -1.12556e17 q^{36} +(-7.19796e17 + 1.24672e18i) q^{37} +(-6.69092e17 - 1.15890e18i) q^{38} +(-9.93743e17 - 1.72121e18i) q^{39} +(9.46464e17 - 1.63932e18i) q^{40} +1.70772e18 q^{41} +(-1.39043e18 - 4.87297e18i) q^{42} +6.33058e18 q^{43} +(9.59212e17 - 1.66140e18i) q^{44} +(-1.95707e18 - 3.38974e18i) q^{45} +(-1.47612e18 - 2.55671e18i) q^{46} +(6.77549e18 - 1.17355e19i) q^{47} -1.87721e19 q^{48} +(-2.32478e19 + 1.44426e19i) q^{49} -1.69330e19 q^{50} +(-4.72212e18 + 8.17895e18i) q^{51} +(5.33930e18 + 9.24795e18i) q^{52} +(3.50799e19 + 6.07601e19i) q^{53} +(1.92672e19 - 3.33717e19i) q^{54} +6.67130e19 q^{55} +(3.77376e19 + 1.32257e20i) q^{56} +2.05160e20 q^{57} +(-8.67952e19 + 1.50334e20i) q^{58} +(-1.19815e20 - 2.07526e20i) q^{59} +(2.87254e19 + 4.97538e19i) q^{60} +(-6.89142e19 + 1.19363e20i) q^{61} -6.99813e20 q^{62} +(2.75854e20 + 6.91604e19i) q^{63} +6.55194e20 q^{64} +(-1.85674e20 + 3.21596e20i) q^{65} +(-4.48742e20 - 7.77245e20i) q^{66} +(-3.39382e20 - 5.87827e20i) q^{67} +(2.53716e19 - 4.39448e19i) q^{68} +4.52614e20 q^{69} +(-6.58602e20 + 6.80225e20i) q^{70} +2.14404e21 q^{71} +(7.14576e20 - 1.23768e21i) q^{72} +(-1.53774e21 - 2.66344e21i) q^{73} +(-1.80927e21 - 3.13374e21i) q^{74} +(1.29802e21 - 2.24824e21i) q^{75} -1.10231e21 q^{76} +(-3.37170e21 + 3.48240e21i) q^{77} +4.99571e21 q^{78} +(-3.40862e21 + 5.90391e21i) q^{79} +(1.75372e21 + 3.03753e21i) q^{80} +(5.51277e21 + 9.54839e21i) q^{81} +(-2.14625e21 + 3.71741e21i) q^{82} +8.36785e21 q^{83} +(-4.04893e21 - 1.01512e21i) q^{84} +1.76459e21 q^{85} +(-7.95622e21 + 1.37806e22i) q^{86} +(-1.33068e22 - 2.30480e22i) q^{87} +(1.21793e22 + 2.10952e22i) q^{88} +(-1.70799e22 + 2.95832e22i) q^{89} +9.83849e21 q^{90} +(-7.40321e21 - 2.59457e22i) q^{91} -2.43186e21 q^{92} +(5.36450e22 - 9.29158e22i) q^{93} +(1.70307e22 + 2.94981e22i) q^{94} +(-1.91663e22 - 3.31970e22i) q^{95} +(-1.89004e22 + 3.27365e22i) q^{96} -1.21614e22 q^{97} +(-2.22153e21 - 6.87577e22i) q^{98} +5.03680e22 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 966 q^{2} - 177148 q^{3} - 55357148 q^{4} - 74771022 q^{5} + 3009216508 q^{6} + 654254272 q^{7} + 50444801232 q^{8} - 336909608980 q^{9} - 334296297894 q^{10} + 1355476566108 q^{11} - 4984668058916 q^{12}+ \cdots - 46\!\cdots\!68 q^{99}+O(q^{100}) \) 28 * q + 966 * q^2 - 177148 * q^3 - 55357148 * q^4 - 74771022 * q^5 + 3009216508 * q^6 + 654254272 * q^7 + 50444801232 * q^8 - 336909608980 * q^9 - 334296297894 * q^10 + 1355476566108 * q^11 - 4984668058916 * q^12 - 854080437112 * q^13 - 43134424917234 * q^14 + 77341621307888 * q^15 - 160538324156336 * q^16 - 130193896130514 * q^17 + 110632655983108 * q^18 - 214771980430396 * q^19 - 96438878562936 * q^20 - 3455509877919050 * q^21 + 15069544565754252 * q^22 + 6685548913560552 * q^23 - 31330599354826008 * q^24 - 9156874000789424 * q^25 - 48260478025970868 * q^26 + 16955244397080056 * q^27 + 45364719181029388 * q^28 - 230797950910889208 * q^29 + 4149727265170942 * q^30 + 94821366637509632 * q^31 - 989053585410677472 * q^32 + 471925265098792298 * q^33 + 409331438407832700 * q^34 + 991848218293906764 * q^35 + 323097285821290960 * q^36 + 228196281955951106 * q^37 + 846979764807573006 * q^38 - 4289472930557071768 * q^39 - 10645750240235319192 * q^40 + 25326139004865203064 * q^41 - 8224906244908771096 * q^42 - 854479038224841232 * q^43 + 11572396920387558444 * q^44 - 9362992784223924004 * q^45 - 33418566325741763586 * q^46 - 61615364375433533424 * q^47 + 317023259856261797920 * q^48 - 52662871130642447108 * q^49 - 186545340785228725104 * q^50 + 84287583500847206172 * q^51 - 90603352071153943672 * q^52 - 282093764343878671758 * q^53 + 13895299932605385046 * q^54 + 474892685489135665440 * q^55 + 228268901501348771616 * q^56 - 850914722748570925564 * q^57 + 339998979132364080060 * q^58 - 283820607003252730116 * q^59 - 701673169918628967164 * q^60 - 870322613357668504870 * q^61 + 564486602904139969932 * q^62 - 999989531155067147576 * q^63 + 4248282134320804279168 * q^64 + 384582138286683330588 * q^65 - 157008004213679191250 * q^66 + 1414046473258733295716 * q^67 + 435228382363177447884 * q^68 - 5326254705815467337364 * q^69 + 4483423880974817421510 * q^70 + 426436671912495312096 * q^71 - 10118884230376615693104 * q^72 + 5942494661268692359862 * q^73 + 13389833203328450370642 * q^74 + 14120811240771906960232 * q^75 - 45841052995588797879688 * q^76 + 2861961524728931175726 * q^77 + 14402574434410352321656 * q^78 - 3444345943288433723680 * q^79 - 8255607259451726029008 * q^80 + 2565358457232096585122 * q^81 + 34656759475287179918772 * q^82 + 12170751598086155609808 * q^83 - 30272689833547903395556 * q^84 - 15360706479116717074524 * q^85 + 743687862046869712056 * q^86 - 7978312766181293835640 * q^87 - 2867657955669848060664 * q^88 - 68609868120257601678426 * q^89 + 34663480073027193102856 * q^90 - 4728467461925451365632 * q^91 - 15501695671963373778696 * q^92 + 50628291689744906093838 * q^93 + 18415808745499513811142 * q^94 - 113148862333982926479168 * q^95 - 150237583048546245409696 * q^96 + 460377553176923245905944 * q^97 + 318336375165209650855326 * q^98 - 468278480109509528565568 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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