LMFDB - Embedded newform 80.10.q.a.29.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [80,10,Mod(29,80)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(80, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 3, 2])) N = Newforms(chi, 10, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("80.29"); S:= CuspForms(chi, 10); N := Newforms(S);

Level:	$ N $	$=$	$ 80 = 2^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	80.q (of order $4$, 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:	$41.2028668931$
Analytic rank:	$0$
Dimension:	$212$
Relative dimension:	$106$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			29.3
Character	$\chi$	$=$	80.29
Dual form			80.10.q.a.69.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-22.5970 + 1.17210i) q^{2} +(-90.3471 + 90.3471i) q^{3} +(509.252 - 52.9719i) q^{4} +(-476.958 + 1313.63i) q^{5} +(1935.68 - 2147.47i) q^{6} -6610.86 q^{7} +(-11445.5 + 1793.90i) q^{8} +3357.81i q^{9} +(9238.12 - 30243.3i) q^{10} +(28452.0 - 28452.0i) q^{11} +(-41223.6 + 50795.3i) q^{12} +(-13430.1 + 13430.1i) q^{13} +(149386. - 7748.57i) q^{14} +(-75591.3 - 161775. i) q^{15} +(256532. - 53952.1i) q^{16} -123388. i q^{17} +(-3935.69 - 75876.7i) q^{18} +(-208703. - 208703. i) q^{19} +(-173306. + 694237. i) q^{20} +(597272. - 597272. i) q^{21} +(-609582. + 676279. i) q^{22} -2.14093e6 q^{23} +(871994. - 1.19614e6i) q^{24} +(-1.49815e6 - 1.25310e6i) q^{25} +(287739. - 319222. i) q^{26} +(-2.08167e6 - 2.08167e6i) q^{27} +(-3.36660e6 + 350190. i) q^{28} +(-2.14474e6 - 2.14474e6i) q^{29} +(1.89776e6 + 3.56703e6i) q^{30} +2.76699e6 q^{31} +(-5.73363e6 + 1.51984e6i) q^{32} +5.14111e6i q^{33} +(144623. + 2.78821e6i) q^{34} +(3.15310e6 - 8.68426e6i) q^{35} +(177870. + 1.70998e6i) q^{36} +(8.34988e6 + 8.34988e6i) q^{37} +(4.96069e6 + 4.47145e6i) q^{38} -2.42674e6i q^{39} +(3.10249e6 - 1.58908e7i) q^{40} -6.08621e6i q^{41} +(-1.27965e7 + 1.41966e7i) q^{42} +(-8.06652e6 - 8.06652e6i) q^{43} +(1.29821e7 - 1.59964e7i) q^{44} +(-4.41094e6 - 1.60154e6i) q^{45} +(4.83787e7 - 2.50938e6i) q^{46} +2.85542e6i q^{47} +(-1.83025e7 + 2.80513e7i) q^{48} +3.34986e6 q^{49} +(3.53225e7 + 2.65603e7i) q^{50} +(1.11478e7 + 1.11478e7i) q^{51} +(-6.12790e6 + 7.55073e6i) q^{52} +(4.98951e7 + 4.98951e7i) q^{53} +(4.94795e7 + 4.45997e7i) q^{54} +(2.38051e7 + 5.09459e7i) q^{55} +(7.56646e7 - 1.18592e7i) q^{56} +3.77114e7 q^{57} +(5.09787e7 + 4.59510e7i) q^{58} +(3.45208e7 - 3.45208e7i) q^{59} +(-4.70646e7 - 7.83800e7i) q^{60} +(3.08085e7 + 3.08085e7i) q^{61} +(-6.25258e7 + 3.24318e6i) q^{62} -2.21980e7i q^{63} +(1.27782e8 - 4.10642e7i) q^{64} +(-1.12367e7 - 2.40479e7i) q^{65} +(-6.02588e6 - 1.16174e8i) q^{66} +(9.71331e7 - 9.71331e7i) q^{67} +(-6.53610e6 - 6.28357e7i) q^{68} +(1.93427e8 - 1.93427e8i) q^{69} +(-6.10720e7 + 1.99934e8i) q^{70} +2.49958e8i q^{71} +(-6.02359e6 - 3.84319e7i) q^{72} -2.42611e7 q^{73} +(-1.98469e8 - 1.78896e8i) q^{74} +(2.48567e8 - 2.21396e7i) q^{75} +(-1.17338e8 - 9.52271e7i) q^{76} +(-1.88092e8 + 1.88092e8i) q^{77} +(2.84438e6 + 5.48372e7i) q^{78} +3.84466e8 q^{79} +(-5.14815e7 + 3.62722e8i) q^{80} +3.10054e8 q^{81} +(7.13363e6 + 1.37530e8i) q^{82} +(7.99529e6 - 7.99529e6i) q^{83} +(2.72523e8 - 3.35801e8i) q^{84} +(1.62087e8 + 5.88509e7i) q^{85} +(1.91734e8 + 1.72825e8i) q^{86} +3.87543e8 q^{87} +(-2.74607e8 + 3.76687e8i) q^{88} +5.63203e8i q^{89} +(1.01551e8 + 3.10199e7i) q^{90} +(8.87846e7 - 8.87846e7i) q^{91} +(-1.09027e9 + 1.13409e8i) q^{92} +(-2.49989e8 + 2.49989e8i) q^{93} +(-3.34683e6 - 6.45239e7i) q^{94} +(3.73702e8 - 1.74617e8i) q^{95} +(3.80703e8 - 6.55329e8i) q^{96} +3.36205e8i q^{97} +(-7.56970e7 + 3.92637e6i) q^{98} +(9.55365e7 + 9.55365e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 212 q - 4 q^{4} - 2 q^{5} - 4 q^{6} + 17812 q^{10} - 4 q^{11} + 108500 q^{14} - 4 q^{15} - 534208 q^{16} + 480884 q^{19} + 2372984 q^{20} - 78736 q^{21} - 4888112 q^{24} - 7927240 q^{26} - 4 q^{29} - 34132064 q^{30}+ \cdots + 771348172 q^{99}+O(q^{100}) $ 212 * q - 4 * q^4 - 2 * q^5 - 4 * q^6 + 17812 * q^10 - 4 * q^11 + 108500 * q^14 - 4 * q^15 - 534208 * q^16 + 480884 * q^19 + 2372984 * q^20 - 78736 * q^21 - 4888112 * q^24 - 7927240 * q^26 - 4 * q^29 - 34132064 * q^30 + 22164496 * q^31 - 32890400 * q^34 + 15214056 * q^35 - 72152684 * q^36 + 40955304 * q^40 - 63499328 * q^44 + 3945614 * q^45 + 13956012 * q^46 + 1083782580 * q^49 - 119678604 * q^50 + 90093056 * q^51 + 6659032 * q^54 - 74344568 * q^56 - 144037620 * q^59 - 106324752 * q^60 - 90121108 * q^61 + 74046704 * q^64 - 62806092 * q^65 + 1419462624 * q^66 - 382438912 * q^69 - 127364260 * q^70 + 2153363568 * q^74 + 119613476 * q^75 + 1579189648 * q^76 + 423438896 * q^79 + 425390872 * q^80 - 7748409788 * q^81 + 4494494704 * q^84 + 3906248 * q^85 + 2482762604 * q^86 - 3409730584 * q^90 + 1231623152 * q^91 + 3948740348 * q^94 - 2480993260 * q^95 - 464870984 * q^96 + 771348172 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/80\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$	−22.5970	+	1.17210i	−0.998657	+	0.0517999i
$2$	−22.5970	+	1.17210i	−0.998657	+	0.0517999i
$3$	−90.3471	+	90.3471i	−0.643974	+	0.643974i	−0.951530	−	0.307556i	$-0.900489\pi$
$3$	−90.3471	+	90.3471i	−0.643974	+	0.643974i	0.307556	+	0.951530i	$0.400489\pi$
$4$	509.252	−	52.9719i	0.994634	−	0.103461i
$5$	−476.958	+	1313.63i	−0.341283	+	0.939961i
$5$	−476.958	+	1313.63i	−0.341283	+	0.939961i
$6$	1935.68	−	2147.47i	0.609752	−	0.676467i
$7$	−6610.86			−1.04068			−0.520339	−	0.853959i	$-0.674195\pi$
$7$	−6610.86			−1.04068			−0.520339	+	0.853959i	$0.674195\pi$
$8$	−11445.5	+	1793.90i	−0.987939	+	0.154844i
$9$			3357.81i			0.170595i
$10$	9238.12	−	30243.3i	0.292135	−	0.956377i
$11$	28452.0	−	28452.0i	0.585930	−	0.585930i	−0.350597	−	0.936526i	$-0.614021\pi$
$11$	28452.0	−	28452.0i	0.585930	−	0.585930i	0.936526	+	0.350597i	$0.114021\pi$
$12$	−41223.6	+	50795.3i	−0.573892	+	0.707144i
$13$	−13430.1	+	13430.1i	−0.130417	+	0.130417i	−0.769302	−	0.638885i	$-0.779396\pi$
$13$	−13430.1	+	13430.1i	−0.130417	+	0.130417i	0.638885	+	0.769302i	$0.279396\pi$
$14$	149386.	−	7748.57i	1.03928	−	0.0539071i
$15$	−75591.3	−	161775.i	−0.385533	−	0.825088i
$16$	256532.	−	53952.1i	0.978592	−	0.205811i
$17$		−	123388.i		−	0.358305i	−0.983821	−	0.179153i	$-0.942664\pi$
$17$		−	123388.i		−	0.358305i	0.983821	−	0.179153i	$-0.0573356\pi$
$18$	−3935.69	−	75876.7i	−0.00883679	−	0.170366i
$19$	−208703.	−	208703.i	−0.367399	−	0.367399i	0.499129	−	0.866528i	$-0.333653\pi$
$19$	−208703.	−	208703.i	−0.367399	−	0.367399i	−0.866528	+	0.499129i	$0.833653\pi$
$20$	−173306.	+	694237.i	−0.242203	+	0.970226i
$21$	597272.	−	597272.i	0.670170	−	0.670170i
$22$	−609582.	+	676279.i	−0.554792	+	0.615494i
$23$	−2.14093e6			−1.59524			−0.797622	−	0.603158i	$-0.793909\pi$
$23$	−2.14093e6			−1.59524			−0.797622	+	0.603158i	$0.793909\pi$
$24$	871994.	−	1.19614e6i	0.536492	−	0.735922i
$25$	−1.49815e6	−	1.25310e6i	−0.767052	−	0.641585i
$26$	287739.	−	319222.i	0.123486	−	0.136998i
$27$	−2.08167e6	−	2.08167e6i	−0.753833	−	0.753833i
$28$	−3.36660e6	+	350190.i	−1.03509	+	0.107669i
$29$	−2.14474e6	−	2.14474e6i	−0.563099	−	0.563099i	0.367088	−	0.930186i	$-0.380355\pi$
$29$	−2.14474e6	−	2.14474e6i	−0.563099	−	0.563099i	−0.930186	+	0.367088i	$0.880355\pi$
$30$	1.89776e6	+	3.56703e6i	0.427755	+	0.804010i
$31$	2.76699e6			0.538121			0.269061	−	0.963123i	$-0.413287\pi$
$31$	2.76699e6			0.538121			0.269061	+	0.963123i	$0.413287\pi$
$32$	−5.73363e6	+	1.51984e6i	−0.966617	+	0.256226i
$33$			5.14111e6i			0.754647i
$34$	144623.	+	2.78821e6i	0.0185602	+	0.357824i
$35$	3.15310e6	−	8.68426e6i	0.355166	−	0.978197i
$36$	177870.	+	1.70998e6i	0.0176498	+	0.169679i
$37$	8.34988e6	+	8.34988e6i	0.732441	+	0.732441i	0.971103	−	0.238662i	$-0.0767088\pi$
$37$	8.34988e6	+	8.34988e6i	0.732441	+	0.732441i	−0.238662	+	0.971103i	$0.576709\pi$
$38$	4.96069e6	+	4.47145e6i	0.385937	+	0.347874i
$39$		−	2.42674e6i		−	0.167970i
$40$	3.10249e6	−	1.58908e7i	0.191620	−	0.981469i
$41$		−	6.08621e6i		−	0.336372i	−0.985755	−	0.168186i	$-0.946209\pi$
$41$		−	6.08621e6i		−	0.336372i	0.985755	−	0.168186i	$-0.0537909\pi$
$42$	−1.27965e7	+	1.41966e7i	−0.634556	+	0.703985i
$43$	−8.06652e6	−	8.06652e6i	−0.359814	−	0.359814i	0.503930	−	0.863744i	$-0.331887\pi$
$43$	−8.06652e6	−	8.06652e6i	−0.359814	−	0.359814i	−0.863744	+	0.503930i	$0.831887\pi$
$44$	1.29821e7	−	1.59964e7i	0.522165	−	0.643406i
$45$	−4.41094e6	−	1.60154e6i	−0.160352	−	0.0582211i
$46$	4.83787e7	−	2.50938e6i	1.59310	−	0.0826335i
$47$			2.85542e6i			0.0853550i	0.999089	+	0.0426775i	$0.0135888\pi$
$47$			2.85542e6i			0.0853550i	−0.999089	+	0.0426775i	$0.986411\pi$
$48$	−1.83025e7	+	2.80513e7i	−0.497651	+	0.762725i
$49$	3.34986e6			0.0830127
$50$	3.53225e7	+	2.65603e7i	0.799256	+	0.600991i
$51$	1.11478e7	+	1.11478e7i	0.230739	+	0.230739i
$52$	−6.12790e6	+	7.55073e6i	−0.116224	+	0.143210i
$53$	4.98951e7	+	4.98951e7i	0.868594	+	0.868594i	0.992317	−	0.123723i	$-0.0394834\pi$
$53$	4.98951e7	+	4.98951e7i	0.868594	+	0.868594i	−0.123723	+	0.992317i	$0.539483\pi$
$54$	4.94795e7	+	4.45997e7i	0.791869	+	0.713772i
$55$	2.38051e7	+	5.09459e7i	0.350783	+	0.750719i
$56$	7.56646e7	−	1.18592e7i	1.02813	−	0.161143i
$57$	3.77114e7			0.473190
$58$	5.09787e7	+	4.59510e7i	0.591511	+	0.533174i
$59$	3.45208e7	−	3.45208e7i	0.370892	−	0.370892i	−0.496910	−	0.867802i	$-0.665532\pi$
$59$	3.45208e7	−	3.45208e7i	0.370892	−	0.370892i	0.867802	+	0.496910i	$0.165532\pi$
$60$	−4.70646e7	−	7.83800e7i	−0.468828	−	0.780773i
$61$	3.08085e7	+	3.08085e7i	0.284896	+	0.284896i	0.835058	−	0.550162i	$-0.185434\pi$
$61$	3.08085e7	+	3.08085e7i	0.284896	+	0.284896i	−0.550162	+	0.835058i	$0.685434\pi$
$62$	−6.25258e7	+	3.24318e6i	−0.537399	+	0.0278746i
$63$		−	2.21980e7i		−	0.177534i
$64$	1.27782e8	−	4.10642e7i	0.952047	−	0.305952i
$65$	−1.12367e7	−	2.40479e7i	−0.0780778	−	0.167096i
$66$	−6.02588e6	−	1.16174e8i	−0.0390906	−	0.753634i
$67$	9.71331e7	−	9.71331e7i	0.588885	−	0.588885i	−0.348445	−	0.937329i	$-0.613290\pi$
$67$	9.71331e7	−	9.71331e7i	0.588885	−	0.588885i	0.937329	+	0.348445i	$0.113290\pi$
$68$	−6.53610e6	−	6.28357e7i	−0.0370705	−	0.356382i
$69$	1.93427e8	−	1.93427e8i	1.02730	−	1.02730i
$70$	−6.10720e7	+	1.99934e8i	−0.304019	+	0.995281i
$71$			2.49958e8i			1.16736i	0.811984	+	0.583680i	$0.198388\pi$
$71$			2.49958e8i			1.16736i	−0.811984	+	0.583680i	$0.801612\pi$
$72$	−6.02359e6	−	3.84319e7i	−0.0264155	−	0.168537i
$73$	−2.42611e7			−0.0999903			−0.0499952	−	0.998749i	$-0.515921\pi$
$73$	−2.42611e7			−0.0999903			−0.0499952	+	0.998749i	$0.515921\pi$
$74$	−1.98469e8	−	1.78896e8i	−0.769398	−	0.693517i
$75$	2.48567e8	−	2.21396e7i	0.907126	−	0.0807969i
$76$	−1.17338e8	−	9.52271e7i	−0.403438	−	0.327416i
$77$	−1.88092e8	+	1.88092e8i	−0.609765	+	0.609765i
$78$	2.84438e6	+	5.48372e7i	0.00870085	+	0.167745i
$79$	3.84466e8			1.11055			0.555273	−	0.831668i	$-0.312614\pi$
$79$	3.84466e8			1.11055			0.555273	+	0.831668i	$0.312614\pi$
$80$	−5.14815e7	+	3.62722e8i	−0.140523	+	0.990077i
$81$	3.10054e8			0.800303
$82$	7.13363e6	+	1.37530e8i	0.0174240	+	0.335920i
$83$	7.99529e6	−	7.99529e6i	0.0184920	−	0.0184920i	−0.697800	−	0.716292i	$-0.745838\pi$
$83$	7.99529e6	−	7.99529e6i	0.0184920	−	0.0184920i	0.716292	+	0.697800i	$0.245838\pi$
$84$	2.72523e8	−	3.35801e8i	0.597238	−	0.735910i
$85$	1.62087e8	+	5.88509e7i	0.336793	+	0.122284i
$86$	1.91734e8	+	1.72825e8i	0.377970	+	0.340693i
$87$	3.87543e8			0.725242
$88$	−2.74607e8	+	3.76687e8i	−0.488135	+	0.669590i
$89$			5.63203e8i			0.951502i	0.879580	+	0.475751i	$0.157824\pi$
$89$			5.63203e8i			0.951502i	−0.879580	+	0.475751i	$0.842176\pi$
$90$	1.01551e8	+	3.10199e7i	0.163153	+	0.0498367i
$91$	8.87846e7	−	8.87846e7i	0.135722	−	0.135722i
$92$	−1.09027e9	+	1.13409e8i	−1.58668	+	0.165045i
$93$	−2.49989e8	+	2.49989e8i	−0.346536	+	0.346536i
$94$	−3.34683e6	−	6.45239e7i	−0.00442138	−	0.0852404i
$95$	3.73702e8	−	1.74617e8i	0.470727	−	0.219953i
$96$	3.80703e8	−	6.55329e8i	0.457474	−	0.787479i
$97$			3.36205e8i			0.385595i	0.981239	+	0.192798i	$0.0617561\pi$
$97$			3.36205e8i			0.385595i	−0.981239	+	0.192798i	$0.938244\pi$
$98$	−7.56970e7	+	3.92637e6i	−0.0829013	+	0.00430005i
$99$	9.55365e7	+	9.55365e7i	0.0999565	+	0.0999565i
$100$	−8.29314e8	−	5.58783e8i	−0.829314	−	0.558783i
$101$	−1.38365e9	+	1.38365e9i	−1.32306	+	1.32306i	−0.411783	+	0.911282i	$0.635094\pi$
$101$	−1.38365e9	+	1.38365e9i	−1.32306	+	1.32306i	−0.911282	+	0.411783i	$0.864906\pi$
$102$	−2.64972e8	−	2.38840e8i	−0.242382	−	0.218477i
$103$	2.13553e9			1.86956			0.934778	−	0.355233i	$-0.115598\pi$
$103$	2.13553e9			1.86956			0.934778	+	0.355233i	$0.115598\pi$
$104$	1.29622e8	−	1.77807e8i	0.108650	−	0.149038i
$105$	4.99724e8	+	1.06947e9i	0.401216	+	0.858652i
$106$	−1.18596e9	−	1.06900e9i	−0.912421	−	0.822435i
$107$	−1.17183e9	−	1.17183e9i	−0.864245	−	0.864245i	0.127583	−	0.991828i	$-0.459278\pi$
$107$	−1.17183e9	−	1.17183e9i	−0.864245	−	0.864245i	−0.991828	+	0.127583i	$0.959278\pi$
$108$	−1.17037e9	−	9.49825e8i	−0.827779	−	0.671795i
$109$	−1.67856e9	−	1.67856e9i	−1.13899	−	1.13899i	−0.988632	−	0.150355i	$-0.951958\pi$
$109$	−1.67856e9	−	1.67856e9i	−1.13899	−	1.13899i	−0.150355	−	0.988632i	$-0.548042\pi$
$110$	−5.97639e8	−	1.12332e9i	−0.389199	−	0.731540i
$111$	−1.50877e9			−0.943346
$112$	−1.69590e9	+	3.56670e8i	−1.01840	+	0.214183i
$113$		−	9.42979e8i		−	0.544063i	−0.962288	−	0.272031i	$-0.912305\pi$
$113$		−	9.42979e8i		−	0.544063i	0.962288	−	0.272031i	$-0.0876954\pi$
$114$	−8.52166e8	+	4.42015e7i	−0.472555	+	0.0245112i
$115$	1.02113e9	−	2.81240e9i	0.544430	−	1.49947i
$116$	−1.20583e9	−	9.78605e8i	−0.618335	−	0.501818i
$117$	−4.50958e7	−	4.50958e7i	−0.0222485	−	0.0222485i
$118$	−7.39607e8	+	8.20530e8i	−0.351182	+	0.389606i
$119$			8.15701e8i			0.372881i
$120$	1.15539e9	+	1.71599e9i	0.508642	+	0.755439i
$121$			7.38917e8i			0.313373i
$122$	−7.32290e8	−	6.60069e8i	−0.299271	−	0.269756i
$123$	5.49871e8	+	5.49871e8i	0.216615	+	0.216615i
$124$	1.40910e9	−	1.46573e8i	0.535233	−	0.0556744i
$125$	2.36066e9	−	1.37034e9i	0.864847	−	0.502036i
$126$	2.60183e7	+	5.01610e8i	0.00919626	+	0.177296i
$127$		−	9.15566e8i		−	0.312301i	−0.987733	−	0.156150i	$-0.950092\pi$
$127$		−	9.15566e8i		−	0.312301i	0.987733	−	0.156150i	$-0.0499084\pi$
$128$	−2.83935e9	+	1.07770e9i	−0.934920	+	0.354857i
$129$	1.45757e9			0.463422
$130$	2.82102e8	+	5.30240e8i	0.0866285	+	0.162827i
$131$	1.96128e9	+	1.96128e9i	0.581861	+	0.581861i	0.935414	−	0.353554i	$-0.115027\pi$
$131$	1.96128e9	+	1.96128e9i	0.581861	+	0.581861i	−0.353554	+	0.935414i	$0.615027\pi$
$132$	2.72334e8	+	2.61812e9i	0.0780763	+	0.750597i
$133$	1.37971e9	+	1.37971e9i	0.382344	+	0.382344i
$134$	−2.08107e9	+	2.30877e9i	−0.557590	+	0.618598i
$135$	3.72742e9	−	1.74169e9i	0.965843	−	0.451303i
$136$	2.21346e8	+	1.41224e9i	0.0554813	+	0.353984i
$137$	3.77261e9			0.914955			0.457478	−	0.889221i	$-0.348753\pi$
$137$	3.77261e9			0.914955			0.457478	+	0.889221i	$0.348753\pi$
$138$	−4.14416e9	+	4.59759e9i	−0.972703	+	1.07913i
$139$	−4.25943e9	+	4.25943e9i	−0.967799	+	0.967799i	−0.999497	−	0.0316982i	$-0.989908\pi$
$139$	−4.25943e9	+	4.25943e9i	−0.967799	+	0.967799i	0.0316982	+	0.999497i	$0.489908\pi$
$140$	1.14570e9	−	4.58950e9i	0.252055	−	1.00969i
$141$	−2.57978e8	−	2.57978e8i	−0.0549664	−	0.0549664i
$142$	−2.92975e8	−	5.64831e9i	−0.0604691	−	1.16579i
$143$			7.64227e8i			0.152830i
$144$	1.81161e8	+	8.61387e8i	0.0351103	+	0.166943i
$145$	3.84036e9	−	1.79446e9i	0.721467	−	0.337114i
$146$	5.48230e8	−	2.84364e7i	0.0998561	−	0.00517949i
$147$	−3.02650e8	+	3.02650e8i	−0.0534580	+	0.0534580i
$148$	4.69451e9	+	3.80989e9i	0.804289	+	0.652731i
$149$	−6.60453e9	+	6.60453e9i	−1.09775	+	1.09775i	−0.103077	+	0.994673i	$0.532869\pi$
$149$	−6.60453e9	+	6.60453e9i	−1.09775	+	1.09775i	−0.994673	+	0.103077i	$0.967131\pi$
$150$	−5.59092e9	+	7.91635e8i	−0.901723	+	0.127677i
$151$		−	1.04237e10i		−	1.63164i	−0.578304	−	0.815821i	$-0.696285\pi$
$151$		−	1.04237e10i		−	1.63164i	0.578304	−	0.815821i	$-0.303715\pi$
$152$	2.76311e9	+	2.01432e9i	0.419857	+	0.306078i
$153$	4.14314e8			0.0611249
$154$	4.02986e9	−	4.47079e9i	0.577360	−	0.640532i
$155$	−1.31974e9	+	3.63481e9i	−0.183652	+	0.505813i
$156$	−1.28549e8	−	1.23582e9i	−0.0173783	−	0.167069i
$157$	1.00146e10	−	1.00146e10i	1.31549	−	1.31549i	0.398180	−	0.917307i	$-0.369642\pi$
$157$	1.00146e10	−	1.00146e10i	1.31549	−	1.31549i	0.917307	−	0.398180i	$-0.130358\pi$
$158$	−8.68780e9	+	4.50632e8i	−1.10905	+	0.0575261i
$159$	−9.01576e9			−1.11870
$160$	7.38185e8	−	8.25679e9i	0.0890482	−	0.996027i
$161$	1.41534e10			1.66014
$162$	−7.00630e9	+	3.63413e8i	−0.799228	+	0.0414556i
$163$	−4.52494e9	+	4.52494e9i	−0.502075	+	0.502075i	−0.912082	−	0.410007i	$-0.865526\pi$
$163$	−4.52494e9	+	4.52494e9i	−0.502075	+	0.502075i	0.410007	+	0.912082i	$0.365526\pi$
$164$	−3.22398e8	−	3.09942e9i	−0.0348013	−	0.334567i
$165$	−6.75354e9	−	2.45209e9i	−0.709338	−	0.257548i
$166$	−1.71299e8	+	1.90041e8i	−0.0175093	+	0.0194250i
$167$	6.24644e9			0.621454			0.310727	−	0.950499i	$-0.399428\pi$
$167$	6.24644e9			0.621454			0.310727	+	0.950499i	$0.399428\pi$
$168$	−5.76463e9	+	7.90753e9i	−0.558316	+	0.765859i
$169$			1.02438e10i			0.965983i
$170$	−3.73166e9	−	1.13987e9i	−0.342675	−	0.104674i
$171$	7.00786e8	−	7.00786e8i	0.0626763	−	0.0626763i
$172$	−4.53520e9	−	3.68060e9i	−0.395110	−	0.320657i
$173$	−6.95006e9	+	6.95006e9i	−0.589904	+	0.589904i	−0.937605	−	0.347702i	$-0.886962\pi$
$173$	−6.95006e9	+	6.95006e9i	−0.589904	+	0.589904i	0.347702	+	0.937605i	$0.386962\pi$
$174$	−8.75732e9	+	4.54238e8i	−0.724268	+	0.0375675i
$175$	9.90404e9	+	8.28405e9i	0.798254	+	0.667684i
$176$	5.76380e9	−	8.83389e9i	0.452795	−	0.693977i
$177$			6.23771e9i			0.477689i
$178$	−6.60129e8	−	1.27267e10i	−0.0492877	−	0.950225i
$179$	1.23397e8	+	1.23397e8i	0.00898390	+	0.00898390i	0.711584	−	0.702601i	$-0.247978\pi$
$179$	1.23397e8	+	1.23397e8i	0.00898390	+	0.00898390i	−0.702601	+	0.711584i	$0.747978\pi$
$180$	−2.33112e9	−	5.81930e8i	−0.165515	−	0.0413185i
$181$	1.33893e10	−	1.33893e10i	0.927267	−	0.927267i	−0.0702616	−	0.997529i	$-0.522383\pi$
$181$	1.33893e10	−	1.33893e10i	0.927267	−	0.927267i	0.997529	+	0.0702616i	$0.0223834\pi$
$182$	−1.90220e9	+	2.11033e9i	−0.128510	+	0.142571i
$183$	−5.56691e9			−0.366931
$184$	2.45040e10	−	3.84062e9i	1.57600	−	0.247014i
$185$	−1.49512e10	+	6.98615e9i	−0.938435	+	0.438496i
$186$	5.35601e9	−	5.94203e9i	0.328120	−	0.364021i
$187$	−3.51064e9	−	3.51064e9i	−0.209942	−	0.209942i
$188$	1.51257e8	+	1.45413e9i	0.00883089	+	0.0848969i
$189$	1.37616e10	+	1.37616e10i	0.784498	+	0.784498i
$190$	−8.23989e9	+	4.38384e9i	−0.458702	+	0.244042i
$191$	2.99659e10			1.62921			0.814605	−	0.580016i	$-0.196954\pi$
$191$	2.99659e10			1.62921			0.814605	+	0.580016i	$0.196954\pi$
$192$	−7.83466e9	+	1.52547e10i	−0.416068	+	0.810119i
$193$			1.63185e10i			0.846589i	0.905992	+	0.423295i	$0.139127\pi$
$193$			1.63185e10i			0.846589i	−0.905992	+	0.423295i	$0.860873\pi$
$194$	−3.94066e8	−	7.59725e9i	−0.0199738	−	0.385078i
$195$	3.18785e9	+	1.15745e9i	0.157886	+	0.0573255i
$196$	1.70593e9	−	1.77448e8i	0.0825672	−	0.00858855i
$197$	1.13986e10	+	1.13986e10i	0.539205	+	0.539205i	0.923295	−	0.384091i	$-0.125485\pi$
$197$	1.13986e10	+	1.13986e10i	0.539205	+	0.539205i	−0.384091	+	0.923295i	$0.625485\pi$
$198$	−2.27082e9	−	2.04686e9i	−0.105000	−	0.0946446i
$199$		−	4.03062e10i		−	1.82194i	−0.412478	−	0.910968i	$-0.635337\pi$
$199$		−	4.03062e10i		−	1.82194i	0.412478	−	0.910968i	$-0.364663\pi$
$200$	1.93950e10	+	1.16548e10i	0.857146	+	0.515074i
$201$			1.75514e10i			0.758453i
$202$	2.96447e10	−	3.28882e10i	1.25275	−	1.38982i
$203$	1.41786e10	+	1.41786e10i	0.586005	+	0.586005i
$204$	6.26754e9	+	5.08650e9i	0.253373	+	0.205629i
$205$	7.99506e9	+	2.90286e9i	0.316176	+	0.114798i
$206$	−4.82567e10	+	2.50305e9i	−1.86705	+	0.0968428i
$207$		−	7.18885e9i		−	0.272140i
$208$	−2.72067e9	+	4.16984e9i	−0.100784	+	0.154466i
$209$	−1.18760e10			−0.430540
$210$	−1.25458e10	−	2.35811e10i	−0.445155	−	0.836716i
$211$	−3.67509e10	−	3.67509e10i	−1.27643	−	1.27643i	−0.942651	−	0.333779i	$-0.891676\pi$
$211$	−3.67509e10	−	3.67509e10i	−1.27643	−	1.27643i	−0.333779	−	0.942651i	$-0.608324\pi$
$212$	2.80523e10	+	2.27662e10i	0.953798	+	0.774067i
$213$	−2.25830e10	−	2.25830e10i	−0.751749	−	0.751749i
$214$	2.78533e10	+	2.51063e10i	0.907852	+	0.818317i
$215$	1.44439e10	−	6.74908e9i	0.461010	−	0.215413i
$216$	2.75601e10	+	2.00915e10i	0.861467	+	0.628014i
$217$	−1.82922e10			−0.560011
$218$	3.98980e10	+	3.59631e10i	1.19646	+	1.07846i
$219$	2.19192e9	−	2.19192e9i	0.0643912	−	0.0643912i
$220$	1.48215e10	+	2.46833e10i	0.426570	+	0.710398i
$221$	1.65712e9	+	1.65712e9i	0.0467291	+	0.0467291i
$222$	3.40938e10	−	1.76843e9i	0.942079	−	0.0488652i
$223$		−	2.17225e10i		−	0.588218i	−0.955772	−	0.294109i	$-0.904977\pi$
$223$		−	2.17225e10i		−	0.588218i	0.955772	−	0.294109i	$-0.0950228\pi$
$224$	3.79042e10	−	1.00474e10i	1.00594	−	0.266649i
$225$	4.20767e9	−	5.03050e9i	0.109451	−	0.130855i
$226$	1.10526e9	+	2.13085e10i	0.0281824	+	0.543332i
$227$	1.11931e10	−	1.11931e10i	0.279790	−	0.279790i	−0.553235	−	0.833025i	$-0.686607\pi$
$227$	1.11931e10	−	1.11931e10i	0.279790	−	0.279790i	0.833025	+	0.553235i	$0.186607\pi$
$228$	1.92046e10	−	1.99764e9i	0.470651	−	0.0489566i
$229$	−3.92734e10	+	3.92734e10i	−0.943711	+	0.943711i	−0.998498	−	0.0547875i	$-0.982552\pi$
$229$	−3.92734e10	+	3.92734e10i	−0.943711	+	0.943711i	0.0547875	+	0.998498i	$0.482552\pi$
$230$	−1.97782e10	+	6.47488e10i	−0.466027	+	1.52565i
$231$		−	3.39871e10i		−	0.785345i
$232$	2.83951e10	+	2.07002e10i	0.643499	+	0.469115i
$233$	−4.01720e10			−0.892938			−0.446469	−	0.894799i	$-0.647319\pi$
$233$	−4.01720e10			−0.892938			−0.446469	+	0.894799i	$0.647319\pi$
$234$	1.07189e9	+	9.66175e8i	0.0233711	+	0.0210661i
$235$	−3.75097e9	−	1.36191e9i	−0.0802303	−	0.0291302i
$236$	1.57512e10	−	1.94084e10i	0.330529	−	0.407274i
$237$	−3.47354e10	+	3.47354e10i	−0.715162	+	0.715162i
$238$	−9.56082e8	−	1.84324e10i	−0.0193152	−	0.372380i
$239$	−5.78988e10			−1.14783			−0.573917	−	0.818913i	$-0.694577\pi$
$239$	−5.78988e10			−1.14783			−0.573917	+	0.818913i	$0.694577\pi$
$240$	−2.81197e10	−	3.74221e10i	−0.547091	−	0.728077i
$241$	−1.25105e10			−0.238890			−0.119445	−	0.992841i	$-0.538112\pi$
$241$	−1.25105e10			−0.238890			−0.119445	+	0.992841i	$0.538112\pi$
$242$	−8.66083e8	−	1.66973e10i	−0.0162327	−	0.312952i
$243$	1.29611e10	−	1.29611e10i	0.238458	−	0.238458i
$244$	1.73213e10	+	1.40573e10i	0.312842	+	0.253891i
$245$	−1.59774e9	+	4.40050e9i	−0.0283308	+	0.0780287i
$246$	−1.30700e10	−	1.17810e10i	−0.227545	−	0.205103i
$247$	5.60581e9			0.0958301
$248$	−3.16696e10	+	4.96371e9i	−0.531631	+	0.0833247i
$249$			1.44470e9i			0.0238167i
$250$	−5.17378e10	+	3.37327e10i	−0.837680	+	0.546161i
$251$	4.74131e10	−	4.74131e10i	0.753992	−	0.753992i	−0.221230	−	0.975222i	$-0.571007\pi$
$251$	4.74131e10	−	4.74131e10i	0.753992	−	0.753992i	0.975222	+	0.221230i	$0.0710071\pi$
$252$	−1.17587e9	−	1.13044e10i	−0.0183678	−	0.176582i
$253$	−6.09137e10	+	6.09137e10i	−0.934701	+	0.934701i
$254$	1.07313e9	+	2.06891e10i	0.0161771	+	0.311881i
$255$	−1.99611e10	+	9.32707e9i	−0.295633	+	0.138138i
$256$	6.28978e10	−	2.76809e10i	0.915284	−	0.402810i
$257$		−	4.75665e10i		−	0.680145i	−0.940399	−	0.340073i	$-0.889548\pi$
$257$		−	4.75665e10i		−	0.680145i	0.940399	−	0.340073i	$-0.110452\pi$
$258$	−3.29368e10	+	1.70842e9i	−0.462800	+	0.0240052i
$259$	−5.51999e10	−	5.51999e10i	−0.762236	−	0.762236i
$260$	−6.99616e9	−	1.16512e10i	−0.0949466	−	0.158121i
$261$	7.20165e9	−	7.20165e9i	0.0960616	−	0.0960616i
$262$	−4.66179e10	−	4.20203e10i	−0.611220	−	0.550939i
$263$	1.23976e10			0.159785			0.0798926	−	0.996803i	$-0.474542\pi$
$263$	1.23976e10			0.159785			0.0798926	+	0.996803i	$0.474542\pi$
$264$	−9.22264e9	−	5.88426e10i	−0.116852	−	0.745545i
$265$	−8.93418e10	+	4.17461e10i	−1.11288	+	0.520007i
$266$	−3.27944e10	−	2.95601e10i	−0.401636	−	0.362025i
$267$	−5.08837e10	−	5.08837e10i	−0.612743	−	0.612743i
$268$	4.43199e10	−	5.46106e10i	0.524798	−	0.646651i
$269$	−1.07452e10	−	1.07452e10i	−0.125120	−	0.125120i	0.641774	−	0.766894i	$-0.278199\pi$
$269$	−1.07452e10	−	1.07452e10i	−0.125120	−	0.125120i	−0.766894	+	0.641774i	$0.778199\pi$
$270$	−8.21873e10	+	4.37258e10i	−0.941169	+	0.500727i
$271$	−1.54900e10			−0.174457			−0.0872286	−	0.996188i	$-0.527801\pi$
$271$	−1.54900e10			−0.174457			−0.0872286	+	0.996188i	$0.527801\pi$
$272$	−6.65705e9	−	3.16530e10i	−0.0737431	−	0.350634i
$273$			1.60429e10i			0.174803i
$274$	−8.52499e10	+	4.42187e9i	−0.913727	+	0.0473946i
$275$	−7.82784e10	+	6.97219e9i	−0.825362	+	0.0735143i
$276$	8.82568e10	−	1.08749e11i	0.915498	−	1.12807i
$277$	−4.94867e9	−	4.94867e9i	−0.0505044	−	0.0505044i	0.681404	−	0.731908i	$-0.261370\pi$
$277$	−4.94867e9	−	4.94867e9i	−0.0505044	−	0.0505044i	−0.731908	+	0.681404i	$0.761370\pi$
$278$	9.12581e10	−	1.01243e11i	0.916368	−	1.01663i
$279$			9.29104e9i			0.0918006i
$280$	−2.05101e10	+	1.05052e11i	−0.199415	+	1.02139i
$281$			1.29628e10i			0.124028i	0.998075	+	0.0620140i	$0.0197523\pi$
$281$			1.29628e10i			0.124028i	−0.998075	+	0.0620140i	$0.980248\pi$
$282$	6.13192e9	+	5.52717e9i	0.0577399	+	0.0520454i
$283$	−5.45226e10	−	5.45226e10i	−0.505286	−	0.505286i	0.407790	−	0.913076i	$-0.366300\pi$
$283$	−5.45226e10	−	5.45226e10i	−0.505286	−	0.505286i	−0.913076	+	0.407790i	$0.866300\pi$
$284$	1.32407e10	+	1.27292e11i	0.120776	+	1.16109i
$285$	−1.79868e10	+	4.95390e10i	−0.161492	+	0.444780i
$286$	−8.95748e8	−	1.72693e10i	−0.00791660	−	0.152625i
$287$			4.02351e10i			0.350055i
$288$	−5.10334e9	−	1.92525e10i	−0.0437107	−	0.164900i
$289$	1.03363e11			0.871617
$290$	−8.46776e10	+	4.50507e10i	−0.703036	+	0.374034i
$291$	−3.03752e10	−	3.03752e10i	−0.248314	−	0.248314i
$292$	−1.23550e10	+	1.28516e9i	−0.0994537	+	0.0103451i
$293$	8.13711e10	+	8.13711e10i	0.645009	+	0.645009i	0.951783	−	0.306774i	$-0.0992494\pi$
$293$	8.13711e10	+	8.13711e10i	0.645009	+	0.645009i	−0.306774	+	0.951783i	$0.599249\pi$
$294$	6.48426e9	−	7.19373e9i	0.0506171	−	0.0561554i
$295$	2.88828e10	+	6.18127e10i	0.222044	+	0.475203i
$296$	−1.10547e11	−	8.05898e10i	−0.837021	−	0.610193i
$297$	−1.18455e11			−0.883386
$298$	1.41502e11	−	1.56984e11i	1.03941	−	1.15314i
$299$	2.87529e10	−	2.87529e10i	0.208047	−	0.208047i
$300$	1.25410e11	−	2.44417e10i	0.893898	−	0.174215i
$301$	5.33267e10	+	5.33267e10i	0.374451	+	0.374451i
$302$	1.22176e10	+	2.35544e11i	0.0845189	+	1.62945i
$303$		−	2.50018e11i		−	1.70404i
$304$	−6.47990e10	−	4.22790e10i	−0.435148	−	0.283919i
$305$	−5.51654e10	+	2.57767e10i	−0.365021	+	0.170561i
$306$	−9.36228e9	+	4.85617e8i	−0.0610429	+	0.00316627i
$307$	−6.65622e10	+	6.65622e10i	−0.427666	+	0.427666i	−0.887833	−	0.460166i	$-0.847790\pi$
$307$	−6.65622e10	+	6.65622e10i	−0.427666	+	0.427666i	0.460166	+	0.887833i	$0.347790\pi$
$308$	−8.58228e10	+	1.05750e11i	−0.543406	+	0.669579i
$309$	−1.92939e11	+	1.92939e11i	−1.20395	+	1.20395i
$310$	2.55618e10	−	8.36829e10i	0.157204	−	0.514647i
$311$		−	7.45836e10i		−	0.452087i	−0.974117	−	0.226043i	$-0.927421\pi$
$311$		−	7.45836e10i		−	0.452087i	0.974117	−	0.226043i	$-0.0725791\pi$
$312$	4.35334e9	+	2.77753e10i	0.0260092	+	0.165945i
$313$	2.09830e11			1.23571			0.617857	−	0.786291i	$-0.288001\pi$
$313$	2.09830e11			1.23571			0.617857	+	0.786291i	$0.288001\pi$
$314$	−2.14563e11	+	2.38039e11i	−1.24558	+	1.38186i
$315$	2.91601e10	+	1.05875e10i	0.166875	+	0.0605895i
$316$	1.95790e11	−	2.03659e10i	1.10459	−	0.114898i
$317$	−1.01880e11	+	1.01880e11i	−0.566661	+	0.566661i	−0.931192	−	0.364530i	$-0.881230\pi$
$317$	−1.01880e11	+	1.01880e11i	−0.566661	+	0.566661i	0.364530	+	0.931192i	$0.381230\pi$
$318$	2.03729e11	−	1.05673e10i	1.11720	−	0.0579487i
$319$	−1.22044e11			−0.659872
$320$	−7.00302e9	+	1.87444e11i	−0.0373345	+	0.999303i
$321$	2.11742e11			1.11310
$322$	−3.19825e11	+	1.65892e10i	−1.65791	+	0.0859949i
$323$	−2.57515e10	+	2.57515e10i	−0.131641	+	0.131641i
$324$	1.57896e11	−	1.64241e10i	0.796008	−	0.0827999i
$325$	3.69495e10	−	3.29106e9i	0.183710	−	0.0163629i
$326$	9.69466e10	−	1.07554e11i	0.475394	−	0.527409i
$327$	3.03307e11			1.46696
$328$	1.09181e10	+	6.96598e10i	0.0520851	+	0.332315i
$329$		−	1.88768e10i		−	0.0888271i
$330$	1.55484e11	+	4.74942e10i	0.721727	+	0.220459i
$331$	3.07930e11	−	3.07930e11i	1.41002	−	1.41002i	0.650620	−	0.759404i	$-0.274509\pi$
$331$	3.07930e11	−	3.07930e11i	1.41002	−	1.41002i	0.759404	−	0.650620i	$-0.225491\pi$
$332$	3.64810e9	−	4.49515e9i	0.0164795	−	0.0203059i
$333$	−2.80374e10	+	2.80374e10i	−0.124950	+	0.124950i
$334$	−1.41151e11	+	7.32144e9i	−0.620619	+	0.0321912i
$335$	8.12690e10	+	1.73926e11i	0.352552	+	0.754505i
$336$	1.20995e11	−	1.85443e11i	0.517895	−	0.793752i
$337$		−	3.51647e11i		−	1.48516i	−0.669759	−	0.742579i	$-0.733603\pi$
$337$		−	3.51647e11i		−	1.48516i	0.669759	−	0.742579i	$-0.266397\pi$
$338$	−1.20067e10	−	2.31479e11i	−0.0500378	−	0.964686i
$339$	8.51953e10	+	8.51953e10i	0.350362	+	0.350362i
$340$	8.56606e10	+	2.13839e10i	0.347637	+	0.0867825i
$341$	7.87264e10	−	7.87264e10i	0.315301	−	0.315301i
$342$	−1.50143e10	+	1.66571e10i	−0.0593455	+	0.0658387i
$343$	2.44627e11			0.954289
$344$	1.06796e11	+	7.78549e10i	0.411190	+	0.299760i
$345$	1.61836e11	+	3.46348e11i	0.615019	+	1.31622i
$346$	1.48905e11	−	1.65197e11i	0.558555	−	0.619669i
$347$	2.51722e11	+	2.51722e11i	0.932049	+	0.932049i	0.997834	−	0.0657852i	$-0.0209552\pi$
$347$	2.51722e11	+	2.51722e11i	0.932049	+	0.932049i	−0.0657852	+	0.997834i	$0.520955\pi$
$348$	1.97357e11	−	2.05289e10i	0.721350	−	0.0750340i
$349$	2.74537e11	+	2.74537e11i	0.990575	+	0.990575i	0.999956	−	0.00938134i	$-0.00298622\pi$
$349$	2.74537e11	+	2.74537e11i	0.990575	+	0.990575i	−0.00938134	+	0.999956i	$0.502986\pi$
$350$	−2.33512e11	−	1.75586e11i	−0.831769	−	0.625439i
$351$	5.59141e10			0.196625
$352$	−1.19891e11	+	2.06375e11i	−0.416239	+	0.716500i
$353$		−	3.40373e11i		−	1.16673i	−0.812211	−	0.583364i	$-0.801736\pi$
$353$		−	3.40373e11i		−	1.16673i	0.812211	−	0.583364i	$-0.198264\pi$
$354$	−7.31121e9	−	1.40954e11i	−0.0247443	−	0.477048i
$355$	−3.28354e11	−	1.19219e11i	−1.09727	−	0.398400i
$356$	2.98339e10	+	2.86812e11i	0.0984431	+	0.946396i
$357$	−7.36962e10	−	7.36962e10i	−0.240125	−	0.240125i
$358$	−2.93303e9	−	2.64377e9i	−0.00943720	−	0.00850647i
$359$			2.35669e11i			0.748821i	0.927263	+	0.374411i	$0.122155\pi$
$359$			2.35669e11i			0.748821i	−0.927263	+	0.374411i	$0.877845\pi$
$360$	5.33585e10	+	1.04176e10i	0.167433	+	0.0326893i
$361$		−	2.35574e11i		−	0.730036i
$362$	−2.86865e11	+	3.18252e11i	−0.877990	+	0.974054i
$363$	−6.67590e10	−	6.67590e10i	−0.201804	−	0.201804i
$364$	4.05107e10	−	4.99168e10i	0.120952	−	0.149036i
$365$	1.15715e10	−	3.18703e10i	0.0341250	−	0.0939870i
$366$	1.25796e11	−	6.52496e9i	0.366438	−	0.0190070i
$367$		−	3.59611e10i		−	0.103475i	−0.998661	−	0.0517375i	$-0.983524\pi$
$367$		−	3.59611e10i		−	0.103475i	0.998661	−	0.0517375i	$-0.0164759\pi$
$368$	−5.49217e11	+	1.15508e11i	−1.56109	+	0.328319i
$369$	2.04364e10			0.0573832
$370$	3.29665e11	−	1.75391e11i	0.914461	−	0.486518i
$371$	−3.29850e11	−	3.29850e11i	−0.903927	−	0.903927i
$372$	−1.14065e11	+	1.40550e11i	−0.308824	+	0.380529i
$373$	5.05252e11	+	5.05252e11i	1.35151	+	1.35151i	0.883977	+	0.467530i	$0.154856\pi$
$373$	5.05252e11	+	5.05252e11i	1.35151	+	1.35151i	0.467530	+	0.883977i	$0.345144\pi$
$374$	8.34448e10	+	7.52152e10i	0.220535	+	0.198785i
$375$	−8.94725e10	+	3.37086e11i	−0.233641	+	0.880237i
$376$	−5.12233e9	−	3.26817e10i	−0.0132167	−	0.0843255i
$377$	5.76083e10			0.146875
$378$	−3.27102e11	−	2.94842e11i	−0.824082	−	0.742808i
$379$	2.53658e11	−	2.53658e11i	0.631499	−	0.631499i	−0.316945	−	0.948444i	$-0.602657\pi$
$379$	2.53658e11	−	2.53658e11i	0.631499	−	0.631499i	0.948444	+	0.316945i	$0.102657\pi$
$380$	1.81059e11	−	1.08720e11i	0.445445	−	0.267475i
$381$	8.27187e10	+	8.27187e10i	0.201114	+	0.201114i
$382$	−6.77140e11	+	3.51230e10i	−1.62702	+	0.0843929i
$383$			1.53518e10i			0.0364557i	0.999834	+	0.0182279i	$0.00580243\pi$
$383$			1.53518e10i			0.0364557i	−0.999834	+	0.0182279i	$0.994198\pi$
$384$	1.59160e11	−	3.53895e11i	0.373546	−	0.830584i
$385$	−1.57372e11	−	3.36796e11i	−0.365052	−	0.781257i
$386$	−1.91269e10	−	3.68750e11i	−0.0438532	−	0.845453i
$387$	2.70859e10	−	2.70859e10i	0.0613824	−	0.0613824i
$388$	1.78094e10	+	1.71213e11i	0.0398940	+	0.383526i
$389$	3.38544e10	−	3.38544e10i	0.0749621	−	0.0749621i	−0.668632	−	0.743594i	$-0.733120\pi$
$389$	3.38544e10	−	3.38544e10i	0.0749621	−	0.0749621i	0.743594	+	0.668632i	$0.233120\pi$
$390$	−7.33927e10	−	2.24185e10i	−0.160643	−	0.0490701i
$391$			2.64165e11i			0.571584i
$392$	−3.83409e10	+	6.00932e9i	−0.0820115	+	0.0128540i
$393$	−3.54392e11			−0.749406
$394$	−2.70935e11	−	2.44214e11i	−0.566412	−	0.510550i
$395$	−1.83374e11	+	5.05048e11i	−0.379010	+	1.04387i
$396$	5.37129e10	+	4.35914e10i	0.109762	+	0.0890785i
$397$	5.22634e11	−	5.22634e11i	1.05594	−	1.05594i	0.0576041	−	0.998340i	$-0.481654\pi$
$397$	5.22634e11	−	5.22634e11i	1.05594	−	1.05594i	0.998340	−	0.0576041i	$-0.0183461\pi$
$398$	4.72428e10	+	9.10801e11i	0.0943761	+	1.81949i
$399$	−2.49305e11			−0.492439
$400$	−4.51930e11	−	2.40631e11i	−0.882676	−	0.469983i
$401$	−4.00444e11			−0.773379			−0.386689	−	0.922210i	$-0.626381\pi$
$401$	−4.00444e11			−0.773379			−0.386689	+	0.922210i	$0.626381\pi$
$402$	−2.05719e10	−	3.96609e11i	−0.0392878	−	0.757435i
$403$	−3.71610e10	+	3.71610e10i	−0.0701802	+	0.0701802i
$404$	−6.31334e11	+	7.77923e11i	−1.17908	+	1.45285i
$405$	−1.47883e11	+	4.07297e11i	−0.273130	+	0.752253i
$406$	−3.37013e11	−	3.03776e11i	−0.615573	−	0.554863i
$407$	4.75141e11			0.858318
$408$	−1.47590e11	−	1.07594e11i	−0.263685	−	0.192228i
$409$		−	7.17445e11i		−	1.26775i	−0.773436	−	0.633875i	$-0.781463\pi$
$409$		−	7.17445e11i		−	1.26775i	0.773436	−	0.633875i	$-0.218537\pi$
$410$	−1.84067e11	−	5.62252e10i	−0.321698	−	0.0982660i
$411$	−3.40845e11	+	3.40845e11i	−0.589208	+	0.589208i
$412$	1.08752e12	−	1.13123e11i	1.85952	−	0.193426i
$413$	−2.28212e11	+	2.28212e11i	−0.385979	+	0.385979i
$414$	8.42603e9	+	1.62447e11i	0.0140968	+	0.271775i
$415$	6.68948e9	+	1.43163e10i	0.0110707	+	0.0236927i
$416$	5.65916e10	−	9.74148e10i	0.0926472	−	0.159480i
$417$		−	7.69655e11i		−	1.24648i
$418$	2.68363e11	−	1.39199e10i	0.429962	−	0.0223019i
$419$	6.35142e11	+	6.35142e11i	1.00672	+	1.00672i	0.999977	+	0.00674057i	$0.00214561\pi$
$419$	6.35142e11	+	6.35142e11i	1.00672	+	1.00672i	0.00674057	+	0.999977i	$0.497854\pi$
$420$	3.11137e11	+	5.18159e11i	0.487899	+	0.812534i
$421$	4.04997e11	−	4.04997e11i	0.628322	−	0.628322i	−0.319324	−	0.947646i	$-0.603456\pi$
$421$	4.04997e11	−	4.04997e11i	0.628322	−	0.628322i	0.947646	+	0.319324i	$0.103456\pi$
$422$	8.73538e11	+	7.87386e11i	1.34084	+	1.20860i
$423$	−9.58796e9			−0.0145611
$424$	−6.60582e11	−	4.81568e11i	−0.992614	−	0.723621i
$425$	−1.54617e11	+	1.84854e11i	−0.229883	+	0.274839i
$426$	5.36778e11	+	4.83839e11i	0.789681	+	0.711799i
$427$	−2.03670e11	−	2.03670e11i	−0.296485	−	0.296485i
$428$	−6.58830e11	−	5.34682e11i	−0.949022	−	0.770192i
$429$	−6.90456e10	−	6.90456e10i	−0.0984189	−	0.0984189i
$430$	−3.18478e11	+	1.69439e11i	−0.449233	+	0.239004i
$431$	1.06744e12			1.49004			0.745020	−	0.667042i	$-0.232440\pi$
$431$	1.06744e12			1.49004			0.745020	+	0.667042i	$0.232440\pi$
$432$	−6.46325e11	−	4.21704e11i	−0.892841	−	0.582547i
$433$			9.00507e11i			1.23110i	0.788100	+	0.615548i	$0.211065\pi$
$433$			9.00507e11i			1.23110i	−0.788100	+	0.615548i	$0.788935\pi$
$434$	4.13349e11	−	2.14402e10i	0.559259	−	0.0290085i
$435$	−1.84841e11	+	5.09090e11i	−0.247513	+	0.681699i
$436$	−9.43730e11	−	7.65896e11i	−1.25072	−	1.01503i
$437$	4.46819e11	+	4.46819e11i	0.586091	+	0.586091i
$438$	−4.69618e10	+	5.21001e10i	−0.0609693	+	0.0676402i
$439$		−	8.47539e10i		−	0.108910i	−0.998516	−	0.0544552i	$-0.982658\pi$
$439$		−	8.47539e10i		−	0.108910i	0.998516	−	0.0544552i	$-0.0173422\pi$
$440$	−3.63854e11	−	5.40398e11i	−0.462796	−	0.687348i
$441$			1.12482e10i			0.0141615i
$442$	−3.93882e10	−	3.55036e10i	−0.0490869	−	0.0442458i
$443$	−1.08556e12	−	1.08556e12i	−1.33918	−	1.33918i	−0.896855	−	0.442325i	$-0.854154\pi$
$443$	−1.08556e12	−	1.08556e12i	−1.33918	−	1.33918i	−0.442325	−	0.896855i	$-0.645846\pi$
$444$	−7.68347e11	+	7.99226e10i	−0.938283	+	0.0975992i
$445$	−7.39843e11	−	2.68624e11i	−0.894374	−	0.324732i
$446$	2.54609e10	+	4.90864e11i	0.0304696	+	0.587428i
$447$		−	1.19340e12i		−	1.41385i
$448$	−8.44746e11	+	2.71470e11i	−0.990775	+	0.318398i
$449$	9.53555e11			1.10723			0.553614	−	0.832773i	$-0.313248\pi$
$449$	9.53555e11			1.10723			0.553614	+	0.832773i	$0.313248\pi$
$450$	−8.91846e10	+	1.18606e11i	−0.102526	+	0.136349i
$451$	−1.73165e11	−	1.73165e11i	−0.197090	−	0.197090i
$452$	−4.99513e10	−	4.80214e11i	−0.0562891	−	0.541143i
$453$	9.41749e11	+	9.41749e11i	1.05074	+	1.05074i
$454$	−2.39811e11	+	2.66049e11i	−0.264921	+	0.293908i
$455$	7.42840e10	+	1.58977e11i	0.0812539	+	0.173893i
$456$	−4.31626e11	+	6.76506e10i	−0.467483	+	0.0732706i
$457$	6.84025e11			0.733582			0.366791	−	0.930303i	$-0.380456\pi$
$457$	6.84025e11			0.733582			0.366791	+	0.930303i	$0.380456\pi$
$458$	8.41430e11	−	9.33495e11i	0.893560	−	0.991328i
$459$	−2.56853e11	+	2.56853e11i	−0.270102	+	0.270102i
$460$	3.71036e11	−	1.48631e12i	0.386373	−	1.54775i
$461$	−8.54779e11	−	8.54779e11i	−0.881454	−	0.881454i	0.112229	−	0.993682i	$-0.464201\pi$
$461$	−8.54779e11	−	8.54779e11i	−0.881454	−	0.881454i	−0.993682	+	0.112229i	$0.964201\pi$
$462$	3.98363e10	+	7.68009e11i	0.0406808	+	0.784291i
$463$		−	6.03598e11i		−	0.610426i	−0.952284	−	0.305213i	$-0.901272\pi$
$463$		−	6.03598e11i		−	0.610426i	0.952284	−	0.305213i	$-0.0987277\pi$
$464$	−6.65909e11	−	4.34482e11i	−0.666936	−	0.435152i
$465$	−2.09160e11	−	4.47629e11i	−0.207463	−	0.443997i
$466$	9.07768e11	−	4.70855e10i	0.891740	−	0.0462541i
$467$	−1.24451e11	+	1.24451e11i	−0.121080	+	0.121080i	−0.765050	−	0.643971i	$-0.777286\pi$
$467$	−1.24451e11	+	1.24451e11i	−0.121080	+	0.121080i	0.643971	+	0.765050i	$0.277286\pi$
$468$	−2.53540e10	−	2.05763e10i	−0.0244309	−	0.0198272i
$469$	−6.42133e11	+	6.42133e11i	−0.612840	+	0.612840i
$470$	8.63572e10	+	2.63787e10i	0.0816316	+	0.0249352i
$471$			1.80959e12i			1.69428i
$472$	−3.33181e11	+	4.57035e11i	−0.308988	+	0.423849i
$473$	−4.59017e11			−0.421652
$474$	7.44204e11	−	8.25630e11i	0.677157	−	0.751248i
$475$	5.11429e10	+	5.74193e11i	0.0460961	+	0.517531i
$476$	4.32092e10	+	4.15398e11i	0.0385785	+	0.370880i
$477$	−1.67539e11	+	1.67539e11i	−0.148177	+	0.148177i
$478$	1.30834e12	−	6.78631e10i	1.14629	−	0.0594577i
$479$	4.99498e11			0.433535			0.216767	−	0.976223i	$-0.430449\pi$
$479$	4.99498e11			0.433535			0.216767	+	0.976223i	$0.430449\pi$
$480$	6.79284e11	+	8.12669e11i	0.584071	+	0.698761i
$481$	−2.24280e11			−0.191046
$482$	2.82701e11	−	1.46635e10i	0.238570	−	0.0123745i
$483$	−1.27872e12	+	1.27872e12i	−1.06909	+	1.06909i
$484$	3.91418e10	+	3.76295e11i	0.0324218	+	0.311691i
$485$	−4.41651e11	−	1.60356e11i	−0.362445	−	0.131597i
$486$	−2.77690e11	+	3.08073e11i	−0.225786	+	0.250490i
$487$	1.87971e12			1.51430			0.757148	−	0.653244i	$-0.226592\pi$
$487$	1.87971e12			1.51430			0.757148	+	0.653244i	$0.226592\pi$
$488$	−4.07886e11	−	2.97351e11i	−0.325574	−	0.237345i
$489$		−	8.17631e11i		−	0.646647i
$490$	3.09464e10	−	1.01311e11i	0.0242509	−	0.0793914i
$491$	−6.98307e11	+	6.98307e11i	−0.542225	+	0.542225i	−0.924181	−	0.381955i	$-0.875251\pi$
$491$	−6.98307e11	+	6.98307e11i	−0.542225	+	0.542225i	0.381955	+	0.924181i	$0.375251\pi$
$492$	3.09151e11	+	2.50896e11i	0.237863	+	0.193041i
$493$	−2.64636e11	+	2.64636e11i	−0.201761	+	0.201761i
$494$	−1.26675e11	+	6.57056e9i	−0.0957015	+	0.00496399i
$495$	−1.71067e11	+	7.99332e10i	−0.128069	+	0.0598417i
$496$	7.09821e11	−	1.49285e11i	0.526601	−	0.110751i
$497$		−	1.65244e12i		−	1.21485i
$498$	−1.69333e9	−	3.26460e10i	−0.00123370	−	0.0237847i
$499$	−1.97046e11	−	1.97046e11i	−0.142271	−	0.142271i	0.632384	−	0.774655i	$-0.282076\pi$
$499$	−1.97046e11	−	1.97046e11i	−0.142271	−	0.142271i	−0.774655	+	0.632384i	$0.782076\pi$
$500$	1.12958e12	−	8.22900e11i	0.808265	−	0.588819i
$501$	−5.64348e11	+	5.64348e11i	−0.400200	+	0.400200i
$502$	−1.01582e12	+	1.12697e12i	−0.713923	+	0.792036i
$503$	−7.46670e10			−0.0520083			−0.0260042	−	0.999662i	$-0.508278\pi$
$503$	−7.46670e10			−0.0520083			−0.0260042	+	0.999662i	$0.508278\pi$
$504$	3.98211e10	+	2.54068e11i	0.0274901	+	0.175393i
$505$	−1.15767e12	−	2.47756e12i	−0.792089	−	1.69517i
$506$	1.30507e12	−	1.44787e12i	0.885029	−	0.981864i
$507$	−9.25494e11	−	9.25494e11i	−0.622068	−	0.622068i
$508$	−4.84992e10	−	4.66254e11i	−0.0323108	−	0.310625i
$509$	−1.56501e12	−	1.56501e12i	−1.03344	−	1.03344i	−0.999421	−	0.0340202i	$-0.989169\pi$
$509$	−1.56501e12	−	1.56501e12i	−1.03344	−	1.03344i	−0.0340202	−	0.999421i	$-0.510831\pi$
$510$	4.40129e11	−	2.34160e11i	0.288081	−	0.153267i
$511$	1.60387e11			0.104058
$512$	−1.38886e12	+	6.99228e11i	−0.893189	+	0.449681i
$513$			8.68902e11i			0.553914i
$514$	5.57525e10	+	1.07486e12i	0.0352315	+	0.679232i
$515$	−1.01856e12	+	2.80531e12i	−0.638048	+	1.75731i
$516$	7.42273e11	−	7.72104e10i	0.460935	−	0.0479460i
$517$	8.12422e10	+	8.12422e10i	0.0500120	+	0.0500120i
$518$	1.31205e12	+	1.18265e12i	0.800696	+	0.721729i
$519$		−	1.25583e12i		−	0.759765i
$520$	1.71749e11	+	2.55082e11i	0.103010	+	0.152991i
$521$			2.01619e9i			0.00119884i	1.00000		0.000599421i	$0.000190802\pi$
$521$			2.01619e9i			0.00119884i	−1.00000		0.000599421i	$0.999809\pi$
$522$	−1.54295e11	+	1.71177e11i	−0.0909567	+	0.100909i
$523$	−6.97115e11	−	6.97115e11i	−0.407424	−	0.407424i	0.473415	−	0.880839i	$-0.343021\pi$
$523$	−6.97115e11	−	6.97115e11i	−0.407424	−	0.407424i	−0.880839	+	0.473415i	$0.843021\pi$
$524$	1.10268e12	+	8.94894e11i	0.638938	+	0.518538i
$525$	−1.64324e12	+	1.46362e11i	−0.944027	+	0.0840837i
$526$	−2.80149e11	+	1.45312e10i	−0.159571	+	0.00827685i
$527$		−	3.41414e11i		−	0.192812i
$528$	2.77374e11	+	1.31886e12i	0.155315	+	0.738491i
$529$	2.78243e12			1.54480
$530$	1.96993e12	−	1.04806e12i	1.08445	−	0.576956i
$531$	1.15915e11	+	1.15915e11i	0.0632722	+	0.0632722i
$532$	7.75705e11	+	6.29533e11i	0.419850	+	0.340735i
$533$	8.17385e10	+	8.17385e10i	0.0438686	+	0.0438686i
$534$	1.20946e12	+	1.09018e12i	0.643660	+	0.580180i
$535$	2.09827e12	−	9.80441e11i	1.10731	−	0.517404i
$536$	−9.37490e11	+	1.28598e12i	−0.490597	+	0.672967i
$537$	−2.22971e10			−0.0115708
$538$	2.55403e11	+	2.30215e11i	0.131434	+	0.118471i
$539$	9.53102e10	−	9.53102e10i	0.0486396	−	0.0486396i
$540$	1.80594e12	−	1.08441e12i	0.913968	−	0.548807i
$541$	−1.72298e12	−	1.72298e12i	−0.864756	−	0.864756i	0.127130	−	0.991886i	$-0.459423\pi$
$541$	−1.72298e12	−	1.72298e12i	−0.864756	−	0.864756i	−0.991886	+	0.127130i	$0.959423\pi$
$542$	3.50028e11	−	1.81558e10i	0.174223	−	0.00903687i
$543$			2.41937e12i			1.19427i
$544$	1.87530e11	+	7.07461e11i	0.0918070	+	0.346344i
$545$	3.00563e12	−	1.40442e12i	1.45932	−	0.681886i
$546$	−1.88038e10	−	3.62521e11i	−0.00905479	−	0.174569i
$547$	−1.68937e12	+	1.68937e12i	−0.806831	+	0.806831i	−0.984153	−	0.177322i	$-0.943257\pi$
$547$	−1.68937e12	+	1.68937e12i	−0.806831	+	0.806831i	0.177322	+	0.984153i	$0.443257\pi$
$548$	1.92121e12	−	1.99842e11i	0.910045	−	0.0946619i
$549$	−1.03449e11	+	1.03449e11i	−0.0486017	+	0.0486017i
$550$	1.76069e12	−	2.49301e11i	0.820446	−	0.116169i
$551$			8.95229e11i			0.413763i
$552$	−1.86688e12	+	2.56086e12i	−0.855835	+	1.17398i
$553$	−2.54165e12			−1.15572
$554$	1.17626e11	+	1.06025e11i	0.0530528	+	0.0478205i
$555$	7.19622e11	−	1.98198e12i	0.321948	−	0.886708i
$556$	−1.94350e12	+	2.39476e12i	−0.862476	+	1.06273i
$557$	1.69911e12	−	1.69911e12i	0.747951	−	0.747951i	−0.226143	−	0.974094i	$-0.572612\pi$
$557$	1.69911e12	−	1.69911e12i	0.747951	−	0.747951i	0.974094	+	0.226143i	$0.0726118\pi$
$558$	−1.08900e10	−	2.09950e11i	−0.00475526	−	0.0916773i
$559$	2.16669e11			0.0938519
$560$	3.40337e11	−	2.39791e12i	0.146239	−	1.03035i
$561$	6.34351e11			0.270394
$562$	−1.51937e10	−	2.92921e11i	−0.00642464	−	0.123862i
$563$	−1.62686e12	+	1.62686e12i	−0.682435	+	0.682435i	−0.960548	−	0.278113i	$-0.910291\pi$
$563$	−1.62686e12	+	1.62686e12i	−0.682435	+	0.682435i	0.278113	+	0.960548i	$0.410291\pi$
$564$	−1.45042e11	−	1.17711e11i	−0.0603583	−	0.0489846i
$565$	1.23873e12	+	4.49761e11i	0.511397	+	0.185679i
$566$	1.29596e12	+	1.16814e12i	0.530782	+	0.478434i
$567$	−2.04972e12			−0.832858
$568$	−4.48400e11	−	2.86090e12i	−0.180758	−	1.15328i
$569$			1.22274e12i			0.489021i	0.969647	+	0.244511i	$0.0786273\pi$
$569$			1.22274e12i			0.489021i	−0.969647	+	0.244511i	$0.921373\pi$
$570$	3.48383e11	−	1.14052e12i	0.138236	−	0.452549i
$571$	1.41415e12	−	1.41415e12i	0.556714	−	0.556714i	−0.371657	−	0.928370i	$-0.621210\pi$
$571$	1.41415e12	−	1.41415e12i	0.556714	−	0.556714i	0.928370	+	0.371657i	$0.121210\pi$
$572$	4.04825e10	+	3.89184e11i	0.0158120	+	0.152010i
$573$	−2.70733e12	+	2.70733e12i	−1.04917	+	1.04917i
$574$	−4.71594e10	−	9.09194e11i	−0.0181328	−	0.349585i
$575$	3.20743e12	+	2.68279e12i	1.22363	+	1.02349i
$576$	1.37886e11	+	4.29067e11i	0.0521938	+	0.162414i
$577$		−	4.33891e12i		−	1.62963i	−0.579720	−	0.814815i	$-0.696838\pi$
$577$		−	4.33891e12i		−	1.62963i	0.579720	−	0.814815i	$-0.303162\pi$
$578$	−2.33570e12	+	1.21152e11i	−0.870447	+	0.0451497i
$579$	−1.47433e12	−	1.47433e12i	−0.545182	−	0.545182i
$580$	1.86066e12	−	1.11726e12i	0.682717	−	0.409949i
$581$	−5.28558e10	+	5.28558e10i	−0.0192442	+	0.0192442i
$582$	7.21992e11	+	6.50786e11i	0.260843	+	0.235118i
$583$	2.83923e12			1.01787
$584$	2.77681e11	−	4.35221e10i	0.0987843	−	0.0154829i
$585$	8.07482e10	−	3.77306e10i	0.0285057	−	0.0133196i
$586$	−1.93412e12	−	1.74337e12i	−0.677554	−	0.610732i
$587$	−2.97694e12	−	2.97694e12i	−1.03490	−	1.03490i	−0.999369	−	0.0355329i	$-0.988687\pi$
$587$	−2.97694e12	−	2.97694e12i	−1.03490	−	1.03490i	−0.0355329	−	0.999369i	$-0.511313\pi$
$588$	−1.38093e11	+	1.70157e11i	−0.0476403	+	0.0587020i
$589$	−5.77479e11	−	5.77479e11i	−0.197705	−	0.197705i
$590$	−7.25116e11	−	1.36293e12i	−0.246362	−	0.463063i
$591$	−2.05966e12			−0.694468
$592$	2.59251e12	+	1.69152e12i	0.867505	+	0.566016i
$593$		−	4.30634e12i		−	1.43009i	−0.699080	−	0.715043i	$-0.746407\pi$
$593$		−	4.30634e12i		−	1.43009i	0.699080	−	0.715043i	$-0.253593\pi$
$594$	2.67674e12	−	1.38841e11i	0.882200	−	0.0457593i
$595$	−1.07153e12	−	3.89055e11i	−0.350493	−	0.127258i
$596$	−3.01352e12	+	3.71323e12i	−0.978286	+	1.20543i
$597$	3.64155e12	+	3.64155e12i	1.17328	+	1.17328i
$598$	−6.16030e11	+	6.83432e11i	−0.196991	+	0.218545i
$599$			4.89201e12i			1.55262i	0.630349	+	0.776312i	$0.282912\pi$
$599$			4.89201e12i			1.55262i	−0.630349	+	0.776312i	$0.717088\pi$
$600$	−2.80526e12	+	6.99304e11i	−0.883674	+	0.220285i
$601$		−	2.14268e10i		−	0.00669919i	−0.999994	−	0.00334960i	$-0.998934\pi$
$601$		−	2.14268e10i		−	0.00669919i	0.999994	−	0.00334960i	$-0.00106621\pi$
$602$	−1.26753e12	−	1.14252e12i	−0.393345	−	0.354552i
$603$	3.26155e11	+	3.26155e11i	0.100461	+	0.100461i
$604$	−5.52162e11	−	5.30828e12i	−0.168811	−	1.62289i
$605$	−9.70667e11	−	3.52432e11i	−0.294558	−	0.106949i
$606$	2.93046e11	+	5.64967e12i	0.0882690	+	1.70175i
$607$		−	2.19254e12i		−	0.655538i	−0.944758	−	0.327769i	$-0.893703\pi$
$607$		−	2.19254e12i		−	0.655538i	0.944758	−	0.327769i	$-0.106297\pi$
$608$	1.51382e12	+	8.79430e11i	0.449271	+	0.260997i
$609$	−2.56199e12			−0.754744
$610$	1.21636e12	−	6.47137e11i	0.355696	−	0.189240i
$611$	−3.83485e10	−	3.83485e10i	−0.0111318	−	0.0111318i
$612$	2.10991e11	−	2.19470e10i	0.0607969	−	0.00632403i
$613$	2.42295e12	+	2.42295e12i	0.693063	+	0.693063i	0.962905	−	0.269842i	$-0.0869714\pi$
$613$	2.42295e12	+	2.42295e12i	0.693063	+	0.693063i	−0.269842	+	0.962905i	$0.586971\pi$
$614$	1.42609e12	−	1.58213e12i	0.404939	−	0.449245i
$615$	−9.84595e11	+	4.60065e11i	−0.277536	+	0.129682i
$616$	1.81539e12	−	2.49023e12i	0.507992	−	0.696829i
$617$	2.77112e11			0.0769789			0.0384895	−	0.999259i	$-0.487745\pi$
$617$	2.77112e11			0.0769789			0.0384895	+	0.999259i	$0.487745\pi$
$618$	4.13371e12	−	4.58599e12i	1.13996	−	1.26469i
$619$	−2.71094e12	+	2.71094e12i	−0.742185	+	0.742185i	−0.972998	−	0.230813i	$-0.925862\pi$
$619$	−2.71094e12	+	2.71094e12i	−0.742185	+	0.742185i	0.230813	+	0.972998i	$0.425862\pi$
$620$	−4.79536e11	+	1.92095e12i	−0.130334	+	0.522099i
$621$	4.45671e12	+	4.45671e12i	1.20255	+	1.20255i
$622$	8.74193e10	+	1.68537e12i	0.0234180	+	0.451480i
$623$		−	3.72325e12i		−	0.990208i
$624$	−1.30928e11	−	6.22537e11i	−0.0345702	−	0.164375i
$625$	6.74195e11	+	3.75465e12i	0.176736	+	0.984258i
$626$	−4.74153e12	+	2.45941e11i	−1.23405	+	0.0640098i
$627$	1.07296e12	−	1.07296e12i	0.277256	−	0.277256i
$628$	4.56948e12	−	5.63047e12i	1.17233	−	1.44453i
$629$	1.03028e12	−	1.03028e12i	0.262437	−	0.262437i
$630$	−6.71342e11	−	2.05068e11i	−0.169790	−	0.0518640i
$631$			6.09430e12i			1.53035i	0.643820	+	0.765177i	$0.277349\pi$
$631$			6.09430e12i			1.53035i	−0.643820	+	0.765177i	$0.722651\pi$
$632$	−4.40041e12	+	6.89694e11i	−1.09715	+	0.171961i
$633$	6.64068e12			1.64398
$634$	2.18278e12	−	2.42161e12i	0.536547	−	0.595253i
$635$	1.20272e12	+	4.36686e11i	0.293550	+	0.106583i
$636$	−4.59130e12	+	4.77582e11i	−1.11270	+	0.115742i
$637$	−4.49890e10	+	4.49890e10i	−0.0108263	+	0.0108263i
$638$	2.75784e12	−	1.43048e11i	0.658987	−	0.0341813i
$639$	−8.39313e11			−0.199145
$640$	−6.14554e10	−	4.24389e12i	−0.0144794	−	0.999895i
$641$	−1.72377e12			−0.403291			−0.201646	−	0.979459i	$-0.564629\pi$
$641$	−1.72377e12			−0.403291			−0.201646	+	0.979459i	$0.564629\pi$
$642$	−4.78475e12	+	2.48183e11i	−1.11161	+	0.0576586i
$643$	−8.18804e11	+	8.18804e11i	−0.188899	+	0.188899i	−0.795220	−	0.606321i	$-0.792645\pi$
$643$	−8.18804e11	+	8.18804e11i	−0.188899	+	0.188899i	0.606321	+	0.795220i	$0.292645\pi$
$644$	7.20765e12	−	7.49732e11i	1.65123	−	0.171759i
$645$	−6.95201e11	+	1.91472e12i	−0.158158	+	0.435599i
$646$	5.51724e11	−	6.12090e11i	0.124645	−	0.138283i
$647$	4.76086e12			1.06811			0.534055	−	0.845450i	$-0.320668\pi$
$647$	4.76086e12			1.06811			0.534055	+	0.845450i	$0.320668\pi$
$648$	−3.54872e12	+	5.56206e11i	−0.790650	+	0.123922i
$649$		−	1.96437e12i		−	0.434633i
$650$	−8.31092e11	+	1.17677e11i	−0.182616	+	0.0258571i
$651$	1.65265e12	−	1.65265e12i	0.360633	−	0.360633i
$652$	−2.06464e12	+	2.54403e12i	−0.447436	+	0.551326i
$653$	2.26798e12	−	2.26798e12i	0.488125	−	0.488125i	−0.419589	−	0.907714i	$-0.637826\pi$
$653$	2.26798e12	−	2.26798e12i	0.488125	−	0.488125i	0.907714	+	0.419589i	$0.137826\pi$
$654$	−6.85383e12	+	3.55505e11i	−1.46499	+	0.0759882i
$655$	−3.51185e12	+	1.64096e12i	−0.745505	+	0.348347i
$656$	−3.28364e11	−	1.56131e12i	−0.0692290	−	0.329171i
$657$		−	8.14644e10i		−	0.0170578i
$658$	2.21254e10	+	4.26559e11i	0.00460124	+	0.0887079i
$659$	−3.45812e12	−	3.45812e12i	−0.714258	−	0.714258i	0.253165	−	0.967423i	$-0.418528\pi$
$659$	−3.45812e12	−	3.45812e12i	−0.714258	−	0.714258i	−0.967423	+	0.253165i	$0.918528\pi$
$660$	−3.56915e12	−	8.90986e11i	−0.732178	−	0.182778i
$661$	−1.14879e12	+	1.14879e12i	−0.234064	+	0.234064i	−0.814387	−	0.580323i	$-0.802926\pi$
$661$	−1.14879e12	+	1.14879e12i	−0.234064	+	0.234064i	0.580323	+	0.814387i	$0.302926\pi$
$662$	−6.59739e12	+	7.31924e12i	−1.33509	+	1.48117i
$663$	−2.99431e11			−0.0601847
$664$	−7.71674e10	+	1.05853e11i	−0.0154056	+	0.0211323i
$665$	−2.47049e12	+	1.15437e12i	−0.489876	+	0.228901i
$666$	6.00699e11	−	6.66424e11i	0.118310	−	0.131255i
$667$	4.59175e12	+	4.59175e12i	0.898280	+	0.898280i
$668$	3.18102e12	−	3.30886e11i	0.618119	−	0.0642960i
$669$	1.96257e12	+	1.96257e12i	0.378797	+	0.378797i
$670$	−2.04030e12	−	3.83495e12i	−0.391162	−	0.735230i
$671$	1.75312e12			0.333858
$672$	−2.51678e12	+	4.33229e12i	−0.476083	+	0.819513i
$673$		−	4.72216e12i		−	0.887304i	−0.896199	−	0.443652i	$-0.853683\pi$
$673$		−	4.72216e12i		−	0.887304i	0.896199	−	0.443652i	$-0.146317\pi$
$674$	4.12165e11	+	7.94618e12i	0.0769310	+	1.48316i
$675$	5.10115e11	+	5.72718e12i	0.0945804	+	1.06188i
$676$	5.42631e11	+	5.21666e12i	0.0999413	+	0.960799i
$677$	−5.04820e12	−	5.04820e12i	−0.923608	−	0.923608i	0.0736742	−	0.997282i	$-0.476528\pi$
$677$	−5.04820e12	−	5.04820e12i	−0.923608	−	0.923608i	−0.997282	+	0.0736742i	$0.976528\pi$
$678$	−2.02502e12	−	1.82531e12i	−0.368041	−	0.331743i
$679$		−	2.22261e12i		−	0.401281i
$680$	−1.96074e12	−	3.82811e11i	−0.351665	−	0.0686584i
$681$			2.02252e12i			0.360355i
$682$	−1.68671e12	+	1.87126e12i	−0.298545	+	0.331210i
$683$	6.30210e11	+	6.30210e11i	0.110813	+	0.110813i	0.760339	−	0.649526i	$-0.225033\pi$
$683$	6.30210e11	+	6.30210e11i	0.110813	+	0.110813i	−0.649526	+	0.760339i	$0.725033\pi$
$684$	3.19755e11	−	3.93999e11i	0.0558554	−	0.0688244i
$685$	−1.79938e12	+	4.95584e12i	−0.312259	+	0.860022i
$686$	−5.52784e12	+	2.86726e11i	−0.953008	+	0.0494321i
$687$		−	7.09647e12i		−	1.21545i
$688$	−2.50453e12	−	1.63412e12i	−0.426165	−	0.278058i
$689$	−1.34019e12			−0.226559
$690$	−4.06296e12	−	7.63676e12i	−0.682373	−	1.28259i
$691$	−6.38702e12	−	6.38702e12i	−1.06573	−	1.06573i	−0.997682	−	0.0680484i	$-0.978323\pi$
$691$	−6.38702e12	−	6.38702e12i	−1.06573	−	1.06573i	−0.0680484	−	0.997682i	$-0.521677\pi$
$692$	−3.17118e12	+	3.90749e12i	−0.525706	+	0.647770i
$693$	−6.31578e11	−	6.31578e11i	−0.104023	−	0.104023i
$694$	−5.98322e12	−	5.39313e12i	−0.979077	−	0.882517i
$695$	−3.56377e12	−	7.62691e12i	−0.579399	−	1.23999i
$696$	−4.43562e12	+	6.95213e11i	−0.716495	+	0.112299i
$697$	−7.50966e11			−0.120524
$698$	−6.52552e12	−	5.88195e12i	−1.04056	−	0.937933i
$699$	3.62942e12	−	3.62942e12i	0.575029	−	0.575029i
$700$	5.48248e12	+	3.69403e12i	0.863050	+	0.581513i
$701$	1.41707e12	+	1.41707e12i	0.221646	+	0.221646i	0.809191	−	0.587545i	$-0.199906\pi$
$701$	1.41707e12	+	1.41707e12i	0.221646	+	0.221646i	−0.587545	+	0.809191i	$0.699906\pi$
$702$	−1.26349e12	+	6.55368e10i	−0.196361	+	0.0101852i
$703$		−	3.48529e12i		−	0.538196i
$704$	2.46728e12	−	4.80400e12i	0.378566	−	0.737099i
$705$	4.61934e11	−	2.15845e11i	0.0704254	−	0.0329071i
$706$	3.98951e11	+	7.69143e12i	0.0604363	+	1.16516i
$707$	9.14714e12	−	9.14714e12i	1.37689	−	1.37689i
$708$	3.30423e11	+	3.17657e12i	0.0494221	+	0.475126i
$709$	−5.11888e11	+	5.11888e11i	−0.0760794	+	0.0760794i	−0.744123	−	0.668043i	$-0.767132\pi$
$709$	−5.11888e11	+	5.11888e11i	−0.0760794	+	0.0760794i	0.668043	+	0.744123i	$0.267132\pi$
$710$	7.55956e12	+	2.30914e12i	1.11644	+	0.341027i
$711$			1.29097e12i			0.189453i
$712$	−1.01033e12	−	6.44614e12i	−0.147334	−	0.940026i
$713$	−5.92393e12			−0.858435
$714$	1.75170e12	+	1.57894e12i	0.252242	+	0.227365i
$715$	−1.00391e12	−	3.64504e11i	−0.143655	−	0.0521585i
$716$	6.93766e10	+	5.63035e10i	0.00986517	+	0.00800621i
$717$	5.23099e12	−	5.23099e12i	0.739176	−	0.739176i
$718$	−2.76228e11	−	5.32543e12i	−0.0387889	−	0.747816i
$719$	−2.19742e12			−0.306644			−0.153322	−	0.988176i	$-0.548997\pi$
$719$	−2.19742e12			−0.306644			−0.153322	+	0.988176i	$0.548997\pi$
$720$	−1.21795e12	−	1.72865e11i	−0.168902	−	0.0239724i
$721$	−1.41177e13			−1.94561
$722$	2.76115e11	+	5.32327e12i	0.0378158	+	0.729056i
$723$	1.13029e12	−	1.13029e12i	0.153839	−	0.153839i
$724$	6.10928e12	−	7.52780e12i	0.826355	−	1.01823i
$725$	5.25572e11	+	5.90072e12i	0.0706498	+	0.793202i
$726$	1.58680e12	+	1.43031e12i	0.211986	+	0.191080i
$727$	1.22831e13			1.63081			0.815404	−	0.578892i	$-0.196515\pi$
$727$	1.22831e13			1.63081			0.815404	+	0.578892i	$0.196515\pi$
$728$	−8.56914e11	+	1.17546e12i	−0.113070	+	0.155101i
$729$			8.44478e12i			1.10742i
$730$	−2.24127e11	+	7.33736e11i	−0.0292107	+	0.0956285i
$731$	−9.95313e11	+	9.95313e11i	−0.128923	+	0.128923i
$732$	−2.83496e12	+	2.94890e11i	−0.364962	+	0.0379629i
$733$	−5.45608e12	+	5.45608e12i	−0.698092	+	0.698092i	−0.963999	−	0.265907i	$-0.914329\pi$
$733$	−5.45608e12	+	5.45608e12i	−0.698092	+	0.698092i	0.265907	+	0.963999i	$0.414329\pi$
$734$	4.21499e10	+	8.12614e11i	0.00535999	+	0.103336i
$735$	−2.53220e11	−	5.41923e11i	−0.0320041	−	0.0684928i
$736$	1.22753e13	−	3.25387e12i	1.54199	−	0.408742i
$737$		−	5.52726e12i		−	0.690090i
$738$	−4.61801e11	+	2.39534e10i	−0.0573062	+	0.00297245i
$739$	−5.88631e12	−	5.88631e12i	−0.726011	−	0.726011i	0.243812	−	0.969823i	$-0.421602\pi$
$739$	−5.88631e12	−	5.88631e12i	−0.726011	−	0.726011i	−0.969823	+	0.243812i	$0.921602\pi$
$740$	−7.24388e12	+	4.34971e12i	−0.888032	+	0.533234i
$741$	−5.06469e11	+	5.06469e11i	−0.0617121	+	0.0617121i
$742$	7.84024e12	+	7.06701e12i	0.949537	+	0.855890i
$743$	6.12807e12			0.737690			0.368845	−	0.929491i	$-0.379753\pi$
$743$	6.12807e12			0.737690			0.368845	+	0.929491i	$0.379753\pi$
$744$	2.41280e12	−	3.30971e12i	0.288698	−	0.396015i
$745$	−5.52586e12	−	1.18260e13i	−0.657198	−	1.40649i
$746$	−1.20094e13	−	1.08250e13i	−1.41970	−	1.27969i
$747$	2.68467e10	+	2.68467e10i	0.00315463	+	0.00315463i
$748$	−1.97376e12	−	1.60183e12i	−0.230536	−	0.187094i
$749$	7.74679e12	+	7.74679e12i	0.899402	+	0.899402i
$750$	1.62672e12	−	7.72201e12i	0.187731	−	0.891158i
$751$	3.02022e12			0.346465			0.173232	−	0.984881i	$-0.444579\pi$
$751$	3.02022e12			0.346465			0.173232	+	0.984881i	$0.444579\pi$
$752$	1.54056e11	+	7.32505e11i	0.0175670	+	0.0835277i
$753$			8.56727e12i			0.971102i
$754$	−1.30178e12	+	6.75226e10i	−0.146678	+	0.00760813i
$755$	1.36929e13	+	4.97166e12i	1.53368	+	0.556852i
$756$	7.73712e12	+	6.27916e12i	0.861453	+	0.699123i
$757$	2.79523e12	+	2.79523e12i	0.309376	+	0.309376i	0.844667	−	0.535292i	$-0.179798\pi$
$757$	2.79523e12	+	2.79523e12i	0.309376	+	0.309376i	−0.535292	+	0.844667i	$0.679798\pi$
$758$	−5.43461e12	+	6.02924e12i	−0.597939	+	0.663363i
$759$		−	1.10067e13i		−	1.20385i
$760$	−3.96396e12	+	2.66897e12i	−0.430991	+	0.290190i
$761$			1.02246e13i			1.10513i	0.833469	+	0.552566i	$0.186351\pi$
$761$			1.02246e13i			1.10513i	−0.833469	+	0.552566i	$0.813649\pi$
$762$	−1.96615e12	−	1.77224e12i	−0.211261	−	0.190426i
$763$	1.10968e13	+	1.10968e13i	1.18532	+	1.18532i
$764$	1.52602e13	−	1.58735e12i	1.62047	−	0.168559i
$765$	−1.97610e11	+	5.44258e11i	−0.0208609	+	0.0574550i
$766$	−1.79939e10	−	3.46906e11i	−0.00188840	−	0.0364068i
$767$			9.27237e11i			0.0967412i
$768$	−3.18175e12	+	8.18352e12i	−0.330020	+	0.848818i
$769$	1.40886e13			1.45278			0.726389	−	0.687284i	$-0.241197\pi$
$769$	1.40886e13			1.45278			0.726389	+	0.687284i	$0.241197\pi$
$770$	3.95091e12	+	7.42614e12i	0.405031	+	0.761299i
$771$	4.29749e12	+	4.29749e12i	0.437996	+	0.437996i
$772$	8.64423e11	+	8.31024e12i	0.0875887	+	0.842046i
$773$	−3.21910e12	−	3.21910e12i	−0.324285	−	0.324285i	0.526123	−	0.850408i	$-0.323645\pi$
$773$	−3.21910e12	−	3.21910e12i	−0.324285	−	0.324285i	−0.850408	+	0.526123i	$0.823645\pi$
$774$	−5.80314e11	+	6.43808e11i	−0.0581204	+	0.0644796i
$775$	−4.14536e12	−	3.46731e12i	−0.412767	−	0.345251i
$776$	−6.03119e11	−	3.84804e12i	−0.0597070	−	0.380945i
$777$	9.97430e12			0.981720
$778$	−7.25329e11	+	8.04690e11i	−0.0709785	+	0.0787445i
$779$	−1.27021e12	+	1.27021e12i	−0.123583	+	0.123583i
$780$	1.68473e12	+	4.20569e11i	0.162969	+	0.0406829i
$781$	7.11180e12	+	7.11180e12i	0.683991	+	0.683991i
$782$	−3.09627e11	−	5.96935e12i	−0.0296080	−	0.570817i
$783$			8.92930e12i			0.848964i
$784$	8.59347e11	−	1.80732e11i	0.0812355	−	0.0170849i
$785$	8.37901e12	+	1.79321e13i	0.787552	+	1.68546i
$786$	8.00821e12	−	4.15382e11i	0.748400	−	0.0388192i
$787$	5.59318e12	−	5.59318e12i	0.519724	−	0.519724i	−0.397764	−	0.917488i	$-0.630214\pi$
$787$	5.59318e12	−	5.59318e12i	0.519724	−	0.519724i	0.917488	+	0.397764i	$0.130214\pi$
$788$	6.40857e12	+	5.20096e12i	0.592098	+	0.480525i
$789$	−1.12009e12	+	1.12009e12i	−0.102897	+	0.102897i
$790$	3.55175e12	−	1.16275e13i	0.324429	−	1.06210i
$791$			6.23390e12i			0.566194i
$792$	−1.26485e12	−	9.22081e11i	−0.114229	−	0.0832733i
$793$	−8.27522e11			−0.0743105
$794$	−1.11974e13	+	1.24226e13i	−0.999828	+	1.10922i
$795$	4.30014e12	−	1.18434e13i	0.381795	−	1.05154i
$796$	−2.13510e12	−	2.05260e13i	−0.188499	−	1.81216i
$797$	−2.51881e12	+	2.51881e12i	−0.221122	+	0.221122i	−0.808971	−	0.587849i	$-0.799975\pi$
$797$	−2.51881e12	+	2.51881e12i	−0.221122	+	0.221122i	0.587849	+	0.808971i	$0.299975\pi$
$798$	5.63355e12	−	2.92210e11i	0.491778	−	0.0255083i
$799$	3.52324e11			0.0305831
$800$	1.04943e13	+	4.90784e12i	0.905836	+	0.423629i
$801$	−1.89113e12			−0.162321
$802$	9.04885e12	−	4.69360e11i	0.772341	−	0.0400609i
$803$	−6.90277e11	+	6.90277e11i	−0.0585873	+	0.0585873i
$804$	9.29729e11	+	8.93808e12i	0.0784701	+	0.754383i
$805$	−6.75057e12	+	1.85924e13i	−0.566577	+	1.56046i
$806$	7.96172e11	−	8.83285e11i	0.0664506	−	0.0737213i
$807$	1.94159e12			0.161149
$808$	1.33545e13	−	1.83188e13i	1.10224	−	1.51198i
$809$			1.57107e13i			1.28952i	0.764386	+	0.644759i	$0.223042\pi$
$809$			1.57107e13i			1.28952i	−0.764386	+	0.644759i	$0.776958\pi$
$810$	2.86431e12	−	9.37705e12i	0.233797	−	0.765391i
$811$	6.32003e12	−	6.32003e12i	0.513010	−	0.513010i	−0.402438	−	0.915447i	$-0.631837\pi$
$811$	6.32003e12	−	6.32003e12i	0.513010	−	0.513010i	0.915447	+	0.402438i	$0.131837\pi$
$812$	7.97155e12	+	6.46942e12i	0.643489	+	0.522232i
$813$	1.39947e12	−	1.39947e12i	0.112346	−	0.112346i
$814$	−1.07368e13	+	5.56912e11i	−0.857165	+	0.0444608i
$815$	−3.78592e12	−	8.10233e12i	−0.300581	−	0.643281i
$816$	3.46120e12	+	2.25831e12i	0.273288	+	0.178311i
$817$			3.36702e12i			0.264391i
$818$	8.40915e11	+	1.62121e13i	0.0656693	+	1.26605i
$819$	2.98122e11	+	2.98122e11i	0.0231535	+	0.0231535i
$820$	4.22527e12	+	1.05478e12i	0.326357	+	0.0814702i
$821$	1.52310e13	−	1.52310e13i	1.17000	−	1.17000i	0.187786	−	0.982210i	$-0.439869\pi$
$821$	1.52310e13	−	1.52310e13i	1.17000	−	1.17000i	0.982210	−	0.187786i	$-0.0601310\pi$
$822$	7.30258e12	−	8.10158e12i	0.557896	−	0.618937i
$823$	−1.98451e13			−1.50784			−0.753918	−	0.656968i	$-0.771838\pi$
$823$	−1.98451e13			−1.50784			−0.753918	+	0.656968i	$0.771838\pi$
$824$	−2.44422e13	+	3.83093e12i	−1.84701	+	0.289489i
$825$	6.44230e12	−	7.70214e12i	0.484171	−	0.578853i
$826$	4.88944e12	−	5.42441e12i	0.365467	−	0.405455i
$827$	−6.13949e12	−	6.13949e12i	−0.456412	−	0.456412i	0.441064	−	0.897476i	$-0.354601\pi$
$827$	−6.13949e12	−	6.13949e12i	−0.456412	−	0.456412i	−0.897476	+	0.441064i	$0.854601\pi$
$828$	−3.80807e11	−	3.66094e12i	−0.0281558	−	0.270680i
$829$	3.70206e12	+	3.70206e12i	0.272237	+	0.272237i	0.830000	−	0.557763i	$-0.188340\pi$
$829$	3.70206e12	+	3.70206e12i	0.272237	+	0.272237i	−0.557763	+	0.830000i	$0.688340\pi$
$830$	−1.67942e11	−	3.15665e11i	−0.0122831	−	0.0230874i
$831$	8.94196e11			0.0650471
$832$	−1.16462e12	+	2.26762e12i	−0.0842618	+	0.164065i
$833$		−	4.13333e11i		−	0.0297439i
$834$	9.02111e11	+	1.73919e13i	0.0645673	+	1.24480i
$835$	−2.97929e12	+	8.20555e12i	−0.212092	+	0.584142i
$836$	−6.04790e12	+	6.29096e11i	−0.428229	+	0.0445439i
$837$	−5.75996e12	−	5.75996e12i	−0.405653	−	0.405653i
$838$	−1.50968e13	−	1.36079e13i	−1.05751	−	0.953218i
$839$		−	1.84663e13i		−	1.28662i	−0.765604	−	0.643312i	$-0.777560\pi$
$839$		−	1.84663e13i		−	1.28662i	0.765604	−	0.643312i	$-0.222440\pi$
$840$	−7.63811e12	−	1.13442e13i	−0.529333	−	0.786170i
$841$		−	5.30729e12i		−	0.365840i
$842$	−8.67703e12	+	9.62642e12i	−0.594931	+	0.660025i
$843$	−1.17115e12	−	1.17115e12i	−0.0798708	−	0.0798708i
$844$	−2.06623e13	−	1.67687e13i	−1.40164	−	1.13752i
$845$	−1.34566e13	−	4.88584e12i	−0.907986	−	0.329674i
$846$	2.16659e11	−	1.12380e10i	0.0145416	−	0.000754264i
$847$		−	4.88487e12i		−	0.326120i
$848$	1.54916e13	+	1.01077e13i	1.02876	+	0.671233i
$849$	9.85191e12			0.650783
$850$	3.27722e12	−	4.35837e12i	0.215338	−	0.286377i
$851$	−1.78765e13	−	1.78765e13i	−1.16842	−	1.16842i
$852$	−1.26967e13	−	1.03042e13i	−0.825491	−	0.669938i
$853$	−2.09777e13	−	2.09777e13i	−1.35671	−	1.35671i	−0.877936	−	0.478778i	$-0.841080\pi$
$853$	−2.09777e13	−	2.09777e13i	−1.35671	−	1.35671i	−0.478778	−	0.877936i	$-0.658920\pi$
$854$	4.84107e12	+	4.36363e12i	0.311445	+	0.280729i
$855$	5.86332e11	+	1.25482e12i	0.0375229	+	0.0803036i
$856$	1.55143e13	+	1.13100e13i	0.987644	+	0.719998i
$857$	−1.98908e13			−1.25962			−0.629809	−	0.776750i	$-0.716867\pi$
$857$	−1.98908e13			−1.25962			−0.629809	+	0.776750i	$0.716867\pi$
$858$	1.64116e12	+	1.47930e12i	0.103385	+	0.0931887i
$859$	−2.66262e12	+	2.66262e12i	−0.166856	+	0.166856i	−0.785596	−	0.618740i	$-0.787643\pi$
$859$	−2.66262e12	+	2.66262e12i	−0.166856	+	0.166856i	0.618740	+	0.785596i	$0.287643\pi$
$860$	6.99806e12	−	4.20210e12i	0.436249	−	0.261953i
$861$	−3.63512e12	−	3.63512e12i	−0.225426	−	0.225426i
$862$	−2.41211e13	+	1.25115e12i	−1.48804	+	0.0771839i
$863$			2.98867e13i			1.83413i	0.398739	+	0.917064i	$0.369448\pi$
$863$			2.98867e13i			1.83413i	−0.398739	+	0.917064i	$0.630552\pi$
$864$	1.50993e13	+	8.77171e12i	0.921819	+	0.535516i
$865$	−5.81495e12	−	1.24447e13i	−0.353162	−	0.755810i
$866$	−1.05548e12	−	2.03488e13i	−0.0637706	−	1.22944i
$867$	−9.33857e12	+	9.33857e12i	−0.561299	+	0.561299i
$868$	−9.31534e12	+	9.68971e11i	−0.557006	+	0.0579392i
$869$	1.09388e13	−	1.09388e13i	0.650701	−	0.650701i
$870$	3.58017e12	−	1.17206e13i	0.211869	−	0.693605i
$871$			2.60902e12i			0.153601i
$872$	2.22232e13	+	1.62008e13i	1.30161	+	0.948885i
$873$	−1.12892e12			−0.0657805
$874$	−1.06205e13	−	9.57306e12i	−0.615663	−	0.554944i
$875$	−1.56060e13	+	9.05916e12i	−0.900028	+	0.522458i
$876$	1.00013e12	−	1.23235e12i	0.0573837	−	0.0707076i
$877$	−2.63201e12	+	2.63201e12i	−0.150241	+	0.150241i	−0.778226	−	0.627985i	$-0.783880\pi$
$877$	−2.63201e12	+	2.63201e12i	−0.150241	+	0.150241i	0.627985	+	0.778226i	$0.283880\pi$
$878$	9.93399e10	+	1.91519e12i	0.00564155	+	0.108764i
$879$	−1.47033e13			−0.830738
$880$	8.85541e12	+	1.17849e13i	0.497779	+	0.662452i
$881$	−6.41548e12			−0.358788			−0.179394	−	0.983777i	$-0.557414\pi$
$881$	−6.41548e12			−0.358788			−0.179394	+	0.983777i	$0.557414\pi$
$882$	−1.31840e10	−	2.54176e11i	−0.000733565	−	0.0141425i
$883$	−1.99904e12	+	1.99904e12i	−0.110662	+	0.110662i	−0.760270	−	0.649608i	$-0.774933\pi$
$883$	−1.99904e12	+	1.99904e12i	−0.110662	+	0.110662i	0.649608	+	0.760270i	$0.274933\pi$
$884$	9.31670e11	+	7.56109e11i	0.0513130	+	0.0416437i
$885$	−8.19407e12	−	2.97513e12i	−0.449009	−	0.163027i
$886$	2.58029e13	+	2.32582e13i	1.40675	+	1.26801i
$887$	−2.75521e13			−1.49451			−0.747253	−	0.664539i	$-0.768628\pi$
$887$	−2.75521e13			−1.49451			−0.747253	+	0.664539i	$0.768628\pi$
$888$	1.72687e13	−	2.70659e12i	0.931968	−	0.146071i
$889$			6.05268e12i			0.325005i
$890$	1.70331e13	+	5.20294e12i	0.909995	+	0.277967i
$891$	8.82164e12	−	8.82164e12i	0.468921	−	0.468921i
$892$	−1.15068e12	−	1.10622e13i	−0.0608574	−	0.585061i
$893$	5.95934e11	−	5.95934e11i	0.0313593	−	0.0313593i
$894$	1.39878e12	+	2.69673e13i	0.0732371	+	1.41195i
$895$	−2.20953e11	+	1.03243e11i	−0.0115106	+	0.00537846i
$896$	1.87706e13	−	7.12454e12i	0.972952	−	0.369293i
$897$			5.19548e12i			0.267954i
$898$	−2.15475e13	+	1.11766e12i	−1.10574	+	0.0573543i
$899$	−5.93449e12	−	5.93449e12i	−0.303015	−	0.303015i
$900$	1.87629e12	−	2.78468e12i	0.0953254	−	0.141477i
$901$	6.15646e12	−	6.15646e12i	0.311222	−	0.311222i
$902$	4.11598e12	+	3.71004e12i	0.207035	+	0.186616i
$903$	−9.63581e12			−0.482274
$904$	1.69161e12	+	1.07929e13i	0.0842447	+	0.537501i
$905$	1.12025e13	+	2.39748e13i	0.555134	+	1.18806i
$906$	−2.23846e13	−	2.01769e13i	−1.10375	−	0.994897i
$907$	1.18946e11	+	1.18946e11i	0.00583605	+	0.00583605i	0.710019	−	0.704183i	$-0.248686\pi$
$907$	1.18946e11	+	1.18946e11i	0.00583605	+	0.00583605i	−0.704183	+	0.710019i	$0.748686\pi$
$908$	5.10718e12	−	6.29301e12i	0.249341	−	0.307236i
$909$	−4.64605e12	−	4.64605e12i	−0.225708	−	0.225708i
$910$	−1.86494e12	−	3.50534e12i	−0.0901524	−	0.169451i
$911$	3.84164e12			0.184792			0.0923962	−	0.995722i	$-0.470547\pi$
$911$	3.84164e12			0.184792			0.0923962	+	0.995722i	$0.470547\pi$
$912$	9.67418e12	−	2.03461e12i	0.463060	−	0.0973878i
$913$		−	4.54964e11i		−	0.0216700i
$914$	−1.54569e13	+	8.01744e11i	−0.732597	+	0.0379995i
$915$	2.65518e12	−	7.31288e12i	0.125227	−	0.344900i
$916$	−1.79197e13	+	2.20805e13i	−0.841009	+	1.03628i
$917$	−1.29658e13	−	1.29658e13i	−0.605530	−	0.605530i
$918$	5.50307e12	−	6.10518e12i	0.255748	−	0.283731i
$919$			4.54500e12i			0.210191i	0.994462	+	0.105095i	$0.0335148\pi$
$919$			4.54500e12i			0.210191i	−0.994462	+	0.105095i	$0.966485\pi$
$920$	−6.64222e12	+	3.40212e13i	−0.305681	+	1.56568i
$921$		−	1.20274e13i		−	0.550812i
$922$	2.03174e13	+	1.83136e13i	0.925930	+	0.834611i
$923$	−3.35696e12	−	3.35696e12i	−0.152244	−	0.152244i
$924$	−1.80036e12	−	1.73080e13i	−0.0812524	−	0.781131i
$925$	−2.04615e12	−	2.29726e13i	−0.0918965	−	1.03174i
$926$	7.07476e11	+	1.36395e13i	0.0316200	+	0.609607i
$927$			7.17072e12i			0.318936i
$928$	1.55568e13	+	9.03750e12i	0.688581	+	0.400020i
$929$	4.76787e12			0.210017			0.105008	−	0.994471i	$-0.466513\pi$
$929$	4.76787e12			0.210017			0.105008	+	0.994471i	$0.466513\pi$
$930$	5.25107e12	+	9.86994e12i	0.230184	+	0.432654i
$931$	−6.99126e11	−	6.99126e11i	−0.0304988	−	0.0304988i
$932$	−2.04577e13	+	2.12798e12i	−0.888146	+	0.0923840i
$933$	6.73841e12	+	6.73841e12i	0.291132	+	0.291132i
$934$	2.66635e12	−	2.95808e12i	0.114645	−	0.127189i
$935$	6.28612e12	−	2.93727e12i	0.268986	−	0.125687i
$936$	5.97042e11	+	4.35247e11i	0.0254252	+	0.0185351i
$937$	2.33452e13			0.989394			0.494697	−	0.869065i	$-0.335279\pi$
$937$	2.33452e13			0.989394			0.494697	+	0.869065i	$0.335279\pi$
$938$	1.37577e13	−	1.52629e13i	0.580272	−	0.643762i
$939$	−1.89575e13	+	1.89575e13i	−0.795768	+	0.795768i
$940$	−1.98233e12	−	4.94861e11i	−0.0828136	−	0.0206732i
$941$	−1.59903e13	−	1.59903e13i	−0.664819	−	0.664819i	0.291693	−	0.956512i	$-0.405781\pi$
$941$	−1.59903e13	−	1.59903e13i	−0.664819	−	0.664819i	−0.956512	+	0.291693i	$0.905781\pi$
$942$	−2.12101e12	−	4.08913e13i	−0.0877635	−	1.69201i
$943$			1.30301e13i			0.536595i
$944$	6.99322e12	−	1.07182e13i	0.286618	−	0.439285i
$945$	−2.46415e13	+	1.15140e13i	−1.00513	+	0.469661i
$946$	1.03724e13	−	5.38013e11i	0.421086	−	0.0218415i
$947$	1.87432e13	−	1.87432e13i	0.757302	−	0.757302i	−0.218529	−	0.975831i	$-0.570126\pi$
$947$	1.87432e13	−	1.87432e13i	0.757302	−	0.757302i	0.975831	+	0.218529i	$0.0701257\pi$
$948$	−1.58491e13	+	1.95291e13i	−0.637333	+	0.785316i
$949$	3.25830e11	−	3.25830e11i	0.0130404	−	0.0130404i
$950$	−1.82869e12	−	1.29151e13i	−0.0728423	−	0.514449i
$951$		−	1.84092e13i		−	0.729830i
$952$	−1.46329e12	−	9.33612e12i	−0.0577382	−	0.368383i
$953$	−8.83675e12			−0.347036			−0.173518	−	0.984831i	$-0.555513\pi$
$953$	−8.83675e12			−0.347036			−0.173518	+	0.984831i	$0.555513\pi$
$954$	3.58950e12	−	3.98225e12i	0.140303	−	0.155654i
$955$	−1.42925e13	+	3.93642e13i	−0.556022	+	1.53139i
$956$	−2.94851e13	+	3.06701e12i	−1.14167	+	0.118756i
$957$	1.10264e13	−	1.10264e13i	0.424941	−	0.424941i
$958$	−1.12872e13	+	5.85461e11i	−0.432953	+	0.0224571i
$959$	−2.49402e13			−0.952175
$960$	−1.63023e13	−	1.75677e13i	−0.619483	−	0.667568i
$961$	−1.87834e13			−0.710426
$962$	5.06806e12	−	2.62878e11i	0.190789	−	0.00989614i
$963$	3.93478e12	−	3.93478e12i	0.147436	−	0.147436i
$964$	−6.37101e12	+	6.62706e11i	−0.237608	+	0.0247158i
$965$	−2.14366e13	−	7.78324e12i	−0.795761	−	0.288927i
$966$	2.73964e13	−	3.03940e13i	1.01227	−	1.12303i
$967$	−1.61739e13			−0.594835			−0.297418	−	0.954748i	$-0.596125\pi$
$967$	−1.61739e13			−0.594835			−0.297418	+	0.954748i	$0.596125\pi$
$968$	−1.32554e12	−	8.45728e12i	−0.0485238	−	0.309593i
$969$		−	4.65314e12i		−	0.169547i
$970$	1.01680e13	+	3.10591e12i	0.368775	+	0.112646i
$971$	5.55047e12	−	5.55047e12i	0.200375	−	0.200375i	−0.599786	−	0.800161i	$-0.704748\pi$
$971$	5.55047e12	−	5.55047e12i	0.200375	−	0.200375i	0.800161	+	0.599786i	$0.204748\pi$
$972$	5.91388e12	−	7.28703e12i	0.212508	−	0.261850i
$973$	2.81585e13	−	2.81585e13i	1.00717	−	1.00717i
$974$	−4.24759e13	+	2.20320e12i	−1.51226	+	0.0784403i
$975$	−3.04094e12	+	3.63562e12i	−0.107767	+	0.128842i
$976$	9.56554e12	+	6.24117e12i	0.337431	+	0.220162i
$977$			1.67525e13i			0.588241i	0.955768	+	0.294120i	$0.0950266\pi$
$977$			1.67525e13i			0.588241i	−0.955768	+	0.294120i	$0.904973\pi$
$978$	9.58343e11	+	1.84760e13i	0.0334963	+	0.645779i
$979$	1.60242e13	+	1.60242e13i	0.557513	+	0.557513i
$980$	−5.80552e11	+	2.32560e12i	−0.0201059	+	0.0805411i
$981$	5.63631e12	−	5.63631e12i	0.194305	−	0.194305i
$982$	1.49612e13	−	1.65982e13i	0.513410	−	0.569585i
$983$	4.78839e12			0.163568			0.0817840	−	0.996650i	$-0.473938\pi$
$983$	4.78839e12			0.163568			0.0817840	+	0.996650i	$0.473938\pi$
$984$	−7.27997e12	−	5.30714e12i	−0.247544	−	0.180461i
$985$	−2.04103e13	+	9.53695e12i	−0.690853	+	0.322810i
$986$	5.66981e12	−	6.29017e12i	0.191039	−	0.211941i
$987$	1.70546e12	+	1.70546e12i	0.0572024	+	0.0572024i
$988$	2.85477e12	−	2.96950e11i	0.0953159	−	0.00991465i
$989$	1.72699e13	+	1.72699e13i	0.573992	+	0.573992i
$990$	3.77192e12	−	2.00676e12i	0.124797	−	0.0663953i
$991$	4.67123e13			1.53851			0.769254	−	0.638943i	$-0.220628\pi$
$991$	4.67123e13			1.53851			0.769254	+	0.638943i	$0.220628\pi$
$992$	−1.58649e13	+	4.20538e12i	−0.520157	+	0.137880i
$993$			5.56412e13i			1.81604i
$994$	1.93682e12	+	3.73402e13i	0.0629289	+	1.21322i
$995$	5.29476e13	+	1.92244e13i	1.71255	+	0.621796i
$996$	7.65286e10	+	7.35718e11i	0.00246409	+	0.0236889i
$997$	2.31525e13	+	2.31525e13i	0.742111	+	0.742111i	0.972984	−	0.230873i	$-0.0741581\pi$
$997$	2.31525e13	+	2.31525e13i	0.742111	+	0.742111i	−0.230873	+	0.972984i	$0.574158\pi$
$998$	4.68362e12	+	4.22170e12i	0.149449	+	0.134710i
$999$		−	3.47634e13i		−	1.10428i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.10.q.a.29.3	✓	212
5.4	even	2	inner	80.10.q.a.29.104	yes	212
16.5	even	4	inner	80.10.q.a.69.104	yes	212
80.69	even	4	inner	80.10.q.a.69.3	yes	212

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.10.q.a.29.3	✓	212	1.1	even	1	trivial
80.10.q.a.29.104	yes	212	5.4	even	2	inner
80.10.q.a.69.3	yes	212	80.69	even	4	inner
80.10.q.a.69.104	yes	212	16.5	even	4	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	80.q (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-22.5970 + 1.17210i) q^{2} +(-90.3471 + 90.3471i) q^{3} +(509.252 - 52.9719i) q^{4} +(-476.958 + 1313.63i) q^{5} +(1935.68 - 2147.47i) q^{6} -6610.86 q^{7} +(-11445.5 + 1793.90i) q^{8} +3357.81i q^{9} +(9238.12 - 30243.3i) q^{10} +(28452.0 - 28452.0i) q^{11} +(-41223.6 + 50795.3i) q^{12} +(-13430.1 + 13430.1i) q^{13} +(149386. - 7748.57i) q^{14} +(-75591.3 - 161775. i) q^{15} +(256532. - 53952.1i) q^{16} -123388. i q^{17} +(-3935.69 - 75876.7i) q^{18} +(-208703. - 208703. i) q^{19} +(-173306. + 694237. i) q^{20} +(597272. - 597272. i) q^{21} +(-609582. + 676279. i) q^{22} -2.14093e6 q^{23} +(871994. - 1.19614e6i) q^{24} +(-1.49815e6 - 1.25310e6i) q^{25} +(287739. - 319222. i) q^{26} +(-2.08167e6 - 2.08167e6i) q^{27} +(-3.36660e6 + 350190. i) q^{28} +(-2.14474e6 - 2.14474e6i) q^{29} +(1.89776e6 + 3.56703e6i) q^{30} +2.76699e6 q^{31} +(-5.73363e6 + 1.51984e6i) q^{32} +5.14111e6i q^{33} +(144623. + 2.78821e6i) q^{34} +(3.15310e6 - 8.68426e6i) q^{35} +(177870. + 1.70998e6i) q^{36} +(8.34988e6 + 8.34988e6i) q^{37} +(4.96069e6 + 4.47145e6i) q^{38} -2.42674e6i q^{39} +(3.10249e6 - 1.58908e7i) q^{40} -6.08621e6i q^{41} +(-1.27965e7 + 1.41966e7i) q^{42} +(-8.06652e6 - 8.06652e6i) q^{43} +(1.29821e7 - 1.59964e7i) q^{44} +(-4.41094e6 - 1.60154e6i) q^{45} +(4.83787e7 - 2.50938e6i) q^{46} +2.85542e6i q^{47} +(-1.83025e7 + 2.80513e7i) q^{48} +3.34986e6 q^{49} +(3.53225e7 + 2.65603e7i) q^{50} +(1.11478e7 + 1.11478e7i) q^{51} +(-6.12790e6 + 7.55073e6i) q^{52} +(4.98951e7 + 4.98951e7i) q^{53} +(4.94795e7 + 4.45997e7i) q^{54} +(2.38051e7 + 5.09459e7i) q^{55} +(7.56646e7 - 1.18592e7i) q^{56} +3.77114e7 q^{57} +(5.09787e7 + 4.59510e7i) q^{58} +(3.45208e7 - 3.45208e7i) q^{59} +(-4.70646e7 - 7.83800e7i) q^{60} +(3.08085e7 + 3.08085e7i) q^{61} +(-6.25258e7 + 3.24318e6i) q^{62} -2.21980e7i q^{63} +(1.27782e8 - 4.10642e7i) q^{64} +(-1.12367e7 - 2.40479e7i) q^{65} +(-6.02588e6 - 1.16174e8i) q^{66} +(9.71331e7 - 9.71331e7i) q^{67} +(-6.53610e6 - 6.28357e7i) q^{68} +(1.93427e8 - 1.93427e8i) q^{69} +(-6.10720e7 + 1.99934e8i) q^{70} +2.49958e8i q^{71} +(-6.02359e6 - 3.84319e7i) q^{72} -2.42611e7 q^{73} +(-1.98469e8 - 1.78896e8i) q^{74} +(2.48567e8 - 2.21396e7i) q^{75} +(-1.17338e8 - 9.52271e7i) q^{76} +(-1.88092e8 + 1.88092e8i) q^{77} +(2.84438e6 + 5.48372e7i) q^{78} +3.84466e8 q^{79} +(-5.14815e7 + 3.62722e8i) q^{80} +3.10054e8 q^{81} +(7.13363e6 + 1.37530e8i) q^{82} +(7.99529e6 - 7.99529e6i) q^{83} +(2.72523e8 - 3.35801e8i) q^{84} +(1.62087e8 + 5.88509e7i) q^{85} +(1.91734e8 + 1.72825e8i) q^{86} +3.87543e8 q^{87} +(-2.74607e8 + 3.76687e8i) q^{88} +5.63203e8i q^{89} +(1.01551e8 + 3.10199e7i) q^{90} +(8.87846e7 - 8.87846e7i) q^{91} +(-1.09027e9 + 1.13409e8i) q^{92} +(-2.49989e8 + 2.49989e8i) q^{93} +(-3.34683e6 - 6.45239e7i) q^{94} +(3.73702e8 - 1.74617e8i) q^{95} +(3.80703e8 - 6.55329e8i) q^{96} +3.36205e8i q^{97} +(-7.56970e7 + 3.92637e6i) q^{98} +(9.55365e7 + 9.55365e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 212 q - 4 q^{4} - 2 q^{5} - 4 q^{6} + 17812 q^{10} - 4 q^{11} + 108500 q^{14} - 4 q^{15} - 534208 q^{16} + 480884 q^{19} + 2372984 q^{20} - 78736 q^{21} - 4888112 q^{24} - 7927240 q^{26} - 4 q^{29} - 34132064 q^{30}+ \cdots + 771348172 q^{99}+O(q^{100}) \) 212 * q - 4 * q^4 - 2 * q^5 - 4 * q^6 + 17812 * q^10 - 4 * q^11 + 108500 * q^14 - 4 * q^15 - 534208 * q^16 + 480884 * q^19 + 2372984 * q^20 - 78736 * q^21 - 4888112 * q^24 - 7927240 * q^26 - 4 * q^29 - 34132064 * q^30 + 22164496 * q^31 - 32890400 * q^34 + 15214056 * q^35 - 72152684 * q^36 + 40955304 * q^40 - 63499328 * q^44 + 3945614 * q^45 + 13956012 * q^46 + 1083782580 * q^49 - 119678604 * q^50 + 90093056 * q^51 + 6659032 * q^54 - 74344568 * q^56 - 144037620 * q^59 - 106324752 * q^60 - 90121108 * q^61 + 74046704 * q^64 - 62806092 * q^65 + 1419462624 * q^66 - 382438912 * q^69 - 127364260 * q^70 + 2153363568 * q^74 + 119613476 * q^75 + 1579189648 * q^76 + 423438896 * q^79 + 425390872 * q^80 - 7748409788 * q^81 + 4494494704 * q^84 + 3906248 * q^85 + 2482762604 * q^86 - 3409730584 * q^90 + 1231623152 * q^91 + 3948740348 * q^94 - 2480993260 * q^95 - 464870984 * q^96 + 771348172 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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