LMFDB - Embedded newform 256.2.m.a.101.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [256,2,Mod(5,256)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(256, base_ring=CyclotomicField(64))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("256.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 256 = 2^{8} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	256.m (of order $64$, degree $32$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.04417029174$
Analytic rank:	$0$
Dimension:	$992$
Relative dimension:	$31$ over $\Q(\zeta_{64})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{64}]$

Embedding invariants

Embedding label			101.10
Character	$\chi$	$=$	256.101
Dual form			256.2.m.a.109.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.648839 - 1.25659i) q^{2} +(0.0594759 - 0.0148979i) q^{3} +(-1.15801 + 1.63064i) q^{4} +(0.188276 + 0.0890481i) q^{5} +(-0.0573108 - 0.0650702i) q^{6} +(1.26794 + 4.17983i) q^{7} +(2.80041 + 0.397118i) q^{8} +(-2.64245 + 1.41242i) q^{9} +O(q^{10})$	\(q+(-0.648839 - 1.25659i) q^{2} +(0.0594759 - 0.0148979i) q^{3} +(-1.15801 + 1.63064i) q^{4} +(0.188276 + 0.0890481i) q^{5} +(-0.0573108 - 0.0650702i) q^{6} +(1.26794 + 4.17983i) q^{7} +(2.80041 + 0.397118i) q^{8} +(-2.64245 + 1.41242i) q^{9} +(-0.0102646 - 0.294363i) q^{10} +(-4.53471 + 0.672661i) q^{11} +(-0.0445807 + 0.114236i) q^{12} +(-1.16000 + 3.24198i) q^{13} +(4.42963 - 4.30531i) q^{14} +(0.0125245 + 0.00249129i) q^{15} +(-1.31800 - 3.77662i) q^{16} +(6.40887 - 1.27480i) q^{17} +(3.48935 + 2.40403i) q^{18} +(3.76962 + 3.41659i) q^{19} +(-0.363233 + 0.203893i) q^{20} +(0.137683 + 0.229709i) q^{21} +(3.78756 + 5.26180i) q^{22} +(1.15707 - 0.113962i) q^{23} +(0.172473 - 0.0181014i) q^{24} +(-3.14445 - 3.83152i) q^{25} +(4.82647 - 0.645886i) q^{26} +(-0.272410 + 0.246898i) q^{27} +(-8.28411 - 2.77275i) q^{28} +(-2.97315 - 4.00883i) q^{29} +(-0.00499590 - 0.0173546i) q^{30} +(6.05937 + 2.50987i) q^{31} +(-3.89047 + 4.10661i) q^{32} +(-0.259685 + 0.107565i) q^{33} +(-5.76023 - 7.22615i) q^{34} +(-0.133483 + 0.899871i) q^{35} +(0.756842 - 5.94450i) q^{36} +(0.295776 - 6.02065i) q^{37} +(1.84735 - 6.95367i) q^{38} +(-0.0206931 + 0.210101i) q^{39} +(0.491889 + 0.324139i) q^{40} +(-3.07022 + 3.74107i) q^{41} +(0.199316 - 0.322054i) q^{42} +(-2.50492 + 10.0002i) q^{43} +(4.15439 - 8.17345i) q^{44} +(-0.623284 + 0.0306200i) q^{45} +(-0.893958 - 1.38002i) q^{46} +(4.78914 + 3.20000i) q^{47} +(-0.134653 - 0.204982i) q^{48} +(-10.0430 + 6.71054i) q^{49} +(-2.77439 + 6.43731i) q^{50} +(0.362181 - 0.171299i) q^{51} +(-3.94322 - 5.64580i) q^{52} +(3.64723 - 4.91773i) q^{53} +(0.487000 + 0.182110i) q^{54} +(-0.913678 - 0.277161i) q^{55} +(1.89086 + 12.2088i) q^{56} +(0.275102 + 0.147045i) q^{57} +(-3.10834 + 6.33711i) q^{58} +(-1.46355 - 4.09036i) q^{59} +(-0.0185660 + 0.0175381i) q^{60} +(6.15559 - 10.2700i) q^{61} +(-0.777687 - 9.24261i) q^{62} +(-9.25413 - 9.25413i) q^{63} +(7.68459 + 2.22419i) q^{64} +(-0.507092 + 0.507092i) q^{65} +(0.303658 + 0.256524i) q^{66} +(-10.4645 - 6.27217i) q^{67} +(-5.34281 + 11.9268i) q^{68} +(0.0671202 - 0.0240160i) q^{69} +(1.21737 - 0.416139i) q^{70} +(-0.884166 + 1.65416i) q^{71} +(-7.96084 + 2.90599i) q^{72} +(-4.16236 + 13.7215i) q^{73} +(-7.75738 + 3.53477i) q^{74} +(-0.244101 - 0.181037i) q^{75} +(-9.93652 + 2.19046i) q^{76} +(-8.56134 - 18.1014i) q^{77} +(0.277436 - 0.110319i) q^{78} +(4.91460 + 7.35522i) q^{79} +(0.0881520 - 0.828414i) q^{80} +(4.98134 - 7.45511i) q^{81} +(6.69306 + 1.43064i) q^{82} +(0.263258 + 5.35873i) q^{83} +(-0.534013 - 0.0414956i) q^{84} +(1.32016 + 0.330682i) q^{85} +(14.1914 - 3.34088i) q^{86} +(-0.236554 - 0.194135i) q^{87} +(-12.9662 + 0.0829103i) q^{88} +(11.0729 + 1.09058i) q^{89} +(0.442888 + 0.763342i) q^{90} +(-15.0217 - 0.737970i) q^{91} +(-1.15408 + 2.01874i) q^{92} +(0.397778 + 0.0590048i) q^{93} +(0.913692 - 8.09425i) q^{94} +(0.405490 + 0.978940i) q^{95} +(-0.170210 + 0.302204i) q^{96} +(2.30908 - 5.57462i) q^{97} +(14.9487 + 8.26586i) q^{98} +(11.0327 - 8.18238i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 992 q - 32 q^{2} - 32 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 32 q^{7} - 32 q^{8} - 32 q^{9}+O(q^{10}) $ 992 * q - 32 * q^2 - 32 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 32 * q^8 - 32 * q^9	\( 992 q - 32 q^{2} - 32 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 32 q^{7} - 32 q^{8} - 32 q^{9} - 32 q^{10} - 32 q^{11} - 32 q^{12} - 32 q^{13} - 32 q^{14} - 32 q^{15} - 32 q^{16} - 32 q^{17} - 32 q^{18} - 32 q^{19} - 32 q^{20} - 32 q^{21} - 32 q^{22} - 32 q^{23} - 32 q^{24} - 32 q^{25} - 32 q^{26} - 32 q^{27} - 32 q^{28} - 32 q^{29} - 32 q^{30} - 32 q^{31} - 32 q^{32} - 32 q^{33} - 32 q^{34} - 32 q^{35} - 32 q^{36} - 32 q^{37} - 32 q^{38} - 32 q^{39} - 32 q^{40} - 32 q^{41} - 32 q^{42} - 32 q^{43} - 32 q^{44} - 32 q^{45} - 32 q^{46} - 32 q^{47} - 32 q^{48} - 32 q^{49} - 32 q^{50} - 32 q^{51} - 32 q^{52} - 32 q^{53} - 32 q^{54} - 32 q^{55} - 32 q^{56} - 32 q^{57} - 32 q^{58} - 32 q^{59} - 32 q^{60} - 32 q^{61} - 32 q^{62} - 32 q^{63} - 32 q^{64} - 32 q^{65} - 32 q^{66} - 32 q^{67} - 32 q^{68} - 32 q^{69} - 32 q^{70} - 32 q^{71} - 32 q^{72} - 32 q^{73} - 32 q^{74} - 32 q^{75} - 32 q^{76} - 32 q^{77} - 32 q^{78} - 32 q^{79} - 32 q^{80} - 32 q^{81} - 32 q^{82} - 32 q^{83} - 32 q^{84} - 32 q^{85} - 32 q^{86} - 32 q^{87} - 32 q^{88} - 32 q^{89} - 32 q^{90} - 32 q^{91} - 32 q^{92} - 32 q^{93} - 32 q^{94} - 32 q^{95} - 32 q^{96} - 32 q^{97} - 32 q^{98} - 32 q^{99}+O(q^{100}) \) 992 * q - 32 * q^2 - 32 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 32 * q^8 - 32 * q^9 - 32 * q^10 - 32 * q^11 - 32 * q^12 - 32 * q^13 - 32 * q^14 - 32 * q^15 - 32 * q^16 - 32 * q^17 - 32 * q^18 - 32 * q^19 - 32 * q^20 - 32 * q^21 - 32 * q^22 - 32 * q^23 - 32 * q^24 - 32 * q^25 - 32 * q^26 - 32 * q^27 - 32 * q^28 - 32 * q^29 - 32 * q^30 - 32 * q^31 - 32 * q^32 - 32 * q^33 - 32 * q^34 - 32 * q^35 - 32 * q^36 - 32 * q^37 - 32 * q^38 - 32 * q^39 - 32 * q^40 - 32 * q^41 - 32 * q^42 - 32 * q^43 - 32 * q^44 - 32 * q^45 - 32 * q^46 - 32 * q^47 - 32 * q^48 - 32 * q^49 - 32 * q^50 - 32 * q^51 - 32 * q^52 - 32 * q^53 - 32 * q^54 - 32 * q^55 - 32 * q^56 - 32 * q^57 - 32 * q^58 - 32 * q^59 - 32 * q^60 - 32 * q^61 - 32 * q^62 - 32 * q^63 - 32 * q^64 - 32 * q^65 - 32 * q^66 - 32 * q^67 - 32 * q^68 - 32 * q^69 - 32 * q^70 - 32 * q^71 - 32 * q^72 - 32 * q^73 - 32 * q^74 - 32 * q^75 - 32 * q^76 - 32 * q^77 - 32 * q^78 - 32 * q^79 - 32 * q^80 - 32 * q^81 - 32 * q^82 - 32 * q^83 - 32 * q^84 - 32 * q^85 - 32 * q^86 - 32 * q^87 - 32 * q^88 - 32 * q^89 - 32 * q^90 - 32 * q^91 - 32 * q^92 - 32 * q^93 - 32 * q^94 - 32 * q^95 - 32 * q^96 - 32 * q^97 - 32 * q^98 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/256\mathbb{Z}\right)^\times$.

$n$	$5$	$255$
$\chi(n)$	$e\left(\frac{9}{64}\right)$	$1$

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 $

$2$	−0.648839	−	1.25659i	−0.458799	−	0.888540i
$2$	−0.648839	−	1.25659i	−0.458799	−	0.888540i
$3$	0.0594759	−	0.0148979i	0.0343384	−	0.00860133i	−0.225773	−	0.974180i	$-0.572491\pi$
$3$	0.0594759	−	0.0148979i	0.0343384	−	0.00860133i	0.260111	+	0.965579i	$0.416241\pi$
$4$	−1.15801	+	1.63064i	−0.579007	+	0.815322i
$5$	0.188276	+	0.0890481i	0.0841998	+	0.0398235i	0.469191	−	0.883097i	$-0.344546\pi$
$5$	0.188276	+	0.0890481i	0.0841998	+	0.0398235i	−0.384991	+	0.922920i	$0.625796\pi$
$6$	−0.0573108	−	0.0650702i	−0.0233970	−	0.0265648i
$7$	1.26794	+	4.17983i	0.479235	+	1.57983i	0.779776	+	0.626058i	$0.215333\pi$
$7$	1.26794	+	4.17983i	0.479235	+	1.57983i	−0.300541	+	0.953769i	$0.597167\pi$
$8$	2.80041	+	0.397118i	0.990095	+	0.140402i
$9$	−2.64245	+	1.41242i	−0.880816	+	0.470806i
$10$	−0.0102646	−	0.294363i	−0.00324595	−	0.0930859i
$11$	−4.53471	+	0.672661i	−1.36727	+	0.202815i	−0.789682	−	0.613516i	$-0.789755\pi$
$11$	−4.53471	+	0.672661i	−1.36727	+	0.202815i	−0.577585	+	0.816331i	$0.696005\pi$
$12$	−0.0445807	+	0.114236i	−0.0128693	+	0.0329771i
$13$	−1.16000	+	3.24198i	−0.321726	+	0.899163i	0.666411	+	0.745585i	$0.267830\pi$
$13$	−1.16000	+	3.24198i	−0.321726	+	0.899163i	−0.988137	+	0.153578i	$0.950920\pi$
$14$	4.42963	−	4.30531i	1.18387	−	1.15064i
$15$	0.0125245	+	0.00249129i	0.00323382	+	0.000643247i
$16$	−1.31800	−	3.77662i	−0.329501	−	0.944155i
$17$	6.40887	−	1.27480i	1.55438	−	0.309185i	0.658188	−	0.752854i	$-0.271323\pi$
$17$	6.40887	−	1.27480i	1.55438	−	0.309185i	0.896191	+	0.443668i	$0.146323\pi$
$18$	3.48935	+	2.40403i	0.822447	+	0.566635i
$19$	3.76962	+	3.41659i	0.864811	+	0.783819i	0.977748	−	0.209783i	$-0.0672759\pi$
$19$	3.76962	+	3.41659i	0.864811	+	0.783819i	−0.112937	+	0.993602i	$0.536026\pi$
$20$	−0.363233	+	0.203893i	−0.0812213	+	0.0455918i
$21$	0.137683	+	0.229709i	0.0300448	+	0.0501267i
$22$	3.78756	+	5.26180i	0.807510	+	1.12182i
$23$	1.15707	−	0.113962i	0.241266	−	0.0237627i	0.0233389	−	0.999728i	$-0.492570\pi$
$23$	1.15707	−	0.113962i	0.241266	−	0.0237627i	0.217928	+	0.975965i	$0.430070\pi$
$24$	0.172473	−	0.0181014i	0.0352059	−	0.00369493i
$25$	−3.14445	−	3.83152i	−0.628890	−	0.766304i
$26$	4.82647	−	0.645886i	0.946550	−	0.126669i
$27$	−0.272410	+	0.246898i	−0.0524254	+	0.0475156i
$28$	−8.28411	−	2.77275i	−1.56555	−	0.524000i
$29$	−2.97315	−	4.00883i	−0.552100	−	0.744421i	0.435709	−	0.900087i	$-0.356498\pi$
$29$	−2.97315	−	4.00883i	−0.552100	−	0.744421i	−0.987810	+	0.155666i	$0.950248\pi$
$30$	−0.00499590	−	0.0173546i	−0.000912123	−	0.00316850i
$31$	6.05937	+	2.50987i	1.08829	+	0.450786i	0.853412	−	0.521238i	$-0.174529\pi$
$31$	6.05937	+	2.50987i	1.08829	+	0.450786i	0.234882	+	0.972024i	$0.424529\pi$
$32$	−3.89047	+	4.10661i	−0.687745	+	0.725952i
$33$	−0.259685	+	0.107565i	−0.0452053	+	0.0187247i
$34$	−5.76023	−	7.22615i	−0.987871	−	1.23927i
$35$	−0.133483	+	0.899871i	−0.0225628	+	0.152106i
$36$	0.756842	−	5.94450i	0.126140	−	0.990749i
$37$	0.295776	−	6.02065i	0.0486252	−	0.989789i	−0.843254	−	0.537515i	$-0.819363\pi$
$37$	0.295776	−	6.02065i	0.0486252	−	0.989789i	0.891879	−	0.452274i	$-0.149387\pi$
$38$	1.84735	−	6.95367i	0.299680	−	1.12803i
$39$	−0.0206931	+	0.210101i	−0.00331356	+	0.0336431i
$40$	0.491889	+	0.324139i	0.0777744	+	0.0512509i
$41$	−3.07022	+	3.74107i	−0.479488	+	0.584257i	−0.955430	−	0.295219i	$-0.904607\pi$
$41$	−3.07022	+	3.74107i	−0.479488	+	0.584257i	0.475942	+	0.879477i	$0.342107\pi$
$42$	0.199316	−	0.322054i	0.0307551	−	0.0496941i
$43$	−2.50492	+	10.0002i	−0.381997	+	1.52502i	0.408620	+	0.912705i	$0.366010\pi$
$43$	−2.50492	+	10.0002i	−0.381997	+	1.52502i	−0.790616	+	0.612312i	$0.790240\pi$
$44$	4.15439	−	8.17345i	0.626298	−	1.23219i
$45$	−0.623284	+	0.0306200i	−0.0929137	+	0.00456456i
$46$	−0.893958	−	1.38002i	−0.131807	−	0.203473i
$47$	4.78914	+	3.20000i	0.698568	+	0.466768i	0.853457	−	0.521164i	$-0.174502\pi$
$47$	4.78914	+	3.20000i	0.698568	+	0.466768i	−0.154889	+	0.987932i	$0.549502\pi$
$48$	−0.134653	−	0.204982i	−0.0194355	−	0.0295867i
$49$	−10.0430	+	6.71054i	−1.43472	+	0.958648i
$50$	−2.77439	+	6.43731i	−0.392358	+	0.910373i
$51$	0.362181	−	0.171299i	0.0507155	−	0.0239867i
$52$	−3.94322	−	5.64580i	−0.546826	−	0.782932i
$53$	3.64723	−	4.91773i	0.500986	−	0.675502i	−0.478250	−	0.878224i	$-0.658729\pi$
$53$	3.64723	−	4.91773i	0.500986	−	0.675502i	0.979236	+	0.202722i	$0.0649788\pi$
$54$	0.487000	+	0.182110i	0.0662723	+	0.0247820i
$55$	−0.913678	−	0.277161i	−0.123200	−	0.0373724i
$56$	1.89086	+	12.2088i	0.252677	+	1.63146i
$57$	0.275102	+	0.147045i	0.0364381	+	0.0194766i
$58$	−3.10834	+	6.33711i	−0.408145	+	0.832103i
$59$	−1.46355	−	4.09036i	−0.190538	−	0.532519i	0.807843	−	0.589398i	$-0.200635\pi$
$59$	−1.46355	−	4.09036i	−0.190538	−	0.532519i	−0.998381	+	0.0568791i	$0.981885\pi$
$60$	−0.0185660	+	0.0175381i	−0.00239686	+	0.00226416i
$61$	6.15559	−	10.2700i	0.788143	−	1.31494i	−0.156777	−	0.987634i	$-0.550110\pi$
$61$	6.15559	−	10.2700i	0.788143	−	1.31494i	0.944920	−	0.327303i	$-0.106140\pi$
$62$	−0.777687	−	9.24261i	−0.0987664	−	1.17381i
$63$	−9.25413	−	9.25413i	−1.16591	−	1.16591i
$64$	7.68459	+	2.22419i	0.960574	+	0.278023i
$65$	−0.507092	+	0.507092i	−0.0628971	+	0.0628971i
$66$	0.303658	+	0.256524i	0.0373777	+	0.0315759i
$67$	−10.4645	−	6.27217i	−1.27844	−	0.766268i	−0.296423	−	0.955057i	$-0.595794\pi$
$67$	−10.4645	−	6.27217i	−1.27844	−	0.766268i	−0.982018	+	0.188789i	$0.939544\pi$
$68$	−5.34281	+	11.9268i	−0.647911	+	1.44634i
$69$	0.0671202	−	0.0240160i	0.00808032	−	0.00289118i
$70$	1.21737	−	0.416139i	0.145504	−	0.0497381i
$71$	−0.884166	+	1.65416i	−0.104931	+	0.196312i	−0.928908	−	0.370312i	$-0.879251\pi$
$71$	−0.884166	+	1.65416i	−0.104931	+	0.196312i	0.823976	+	0.566624i	$0.191751\pi$
$72$	−7.96084	+	2.90599i	−0.938194	+	0.342474i
$73$	−4.16236	+	13.7215i	−0.487168	+	1.60598i	0.276939	+	0.960887i	$0.410680\pi$
$73$	−4.16236	+	13.7215i	−0.487168	+	1.60598i	−0.764107	+	0.645090i	$0.776820\pi$
$74$	−7.75738	+	3.53477i	−0.901777	+	0.410909i
$75$	−0.244101	−	0.181037i	−0.0281863	−	0.0209044i
$76$	−9.93652	+	2.19046i	−1.13980	+	0.251263i
$77$	−8.56134	−	18.1014i	−0.975655	−	2.06285i
$78$	0.277436	−	0.110319i	0.0314135	−	0.0124912i
$79$	4.91460	+	7.35522i	0.552936	+	0.827527i	0.997676	−	0.0681322i	$-0.0217040\pi$
$79$	4.91460	+	7.35522i	0.552936	+	0.827527i	−0.444740	+	0.895660i	$0.646704\pi$
$80$	0.0881520	−	0.828414i	0.00985569	−	0.0926195i
$81$	4.98134	−	7.45511i	0.553483	−	0.828345i
$82$	6.69306	+	1.43064i	0.739125	+	0.157987i
$83$	0.263258	+	5.35873i	0.0288963	+	0.588197i	0.968963	+	0.247206i	$0.0795126\pi$
$83$	0.263258	+	5.35873i	0.0288963	+	0.588197i	−0.940067	+	0.340991i	$0.889237\pi$
$84$	−0.534013	−	0.0414956i	−0.0582656	−	0.00452755i
$85$	1.32016	+	0.330682i	0.143191	+	0.0358675i
$86$	14.1914	−	3.34088i	1.53030	−	0.360256i
$87$	−0.236554	−	0.194135i	−0.0253613	−	0.0208134i
$88$	−12.9662	+	0.0829103i	−1.38220	+	0.00883827i
$89$	11.0729	+	1.09058i	1.17372	+	0.115602i	0.666022	−	0.745932i	$-0.267996\pi$
$89$	11.0729	+	1.09058i	1.17372	+	0.115602i	0.507700	+	0.861534i	$0.330496\pi$
$90$	0.442888	+	0.763342i	0.0466845	+	0.0804633i
$91$	−15.0217	−	0.737970i	−1.57470	−	0.0773603i
$92$	−1.15408	+	2.01874i	−0.120321	+	0.210469i
$93$	0.397778	+	0.0590048i	0.0412477	+	0.00611851i
$94$	0.913692	−	8.09425i	0.0942401	−	0.834858i
$95$	0.405490	+	0.978940i	0.0416024	+	0.100437i
$96$	−0.170210	+	0.302204i	−0.0173719	+	0.0308436i
$97$	2.30908	−	5.57462i	0.234452	−	0.566017i	−0.762239	−	0.647295i	$-0.775900\pi$
$97$	2.30908	−	5.57462i	0.234452	−	0.566017i	0.996691	+	0.0812779i	$0.0259001\pi$
$98$	14.9487	+	8.26586i	1.51004	+	0.834978i
$99$	11.0327	−	8.18238i	1.10882	−	0.822360i
$100$	9.88917	−	0.690519i	0.988917	−	0.0690519i
$101$	6.46308	+	7.13091i	0.643101	+	0.709552i	0.972044	−	0.234797i	$-0.0754426\pi$
$101$	6.46308	+	7.13091i	0.643101	+	0.709552i	−0.328944	+	0.944350i	$0.606693\pi$
$102$	−0.450249	−	0.343966i	−0.0445813	−	0.0340577i
$103$	9.49415	−	7.79165i	0.935487	−	0.767734i	−0.0373318	−	0.999303i	$-0.511886\pi$
$103$	9.49415	−	7.79165i	0.935487	−	0.767734i	0.972819	+	0.231569i	$0.0743859\pi$
$104$	−4.53592	+	8.61821i	−0.444783	+	0.845085i
$105$	0.00546718	+	0.0555092i	0.000533543	+	0.00541715i
$106$	−8.54601	−	1.39225i	−0.830062	−	0.135227i
$107$	11.1009	−	6.65359i	1.07316	−	0.643227i	0.135498	−	0.990778i	$-0.456736\pi$
$107$	11.1009	−	6.65359i	1.07316	−	0.643227i	0.937661	+	0.347550i	$0.112986\pi$
$108$	−0.0871483	−	0.730117i	−0.00838585	−	0.0702555i
$109$	−4.56259	+	5.03404i	−0.437017	+	0.482173i	−0.919141	−	0.393929i	$-0.871115\pi$
$109$	−4.56259	+	5.03404i	−0.437017	+	0.482173i	0.482124	+	0.876103i	$0.339865\pi$
$110$	0.244554	+	1.32795i	0.0233173	+	0.126615i
$111$	−0.0721038	−	0.362490i	−0.00684379	−	0.0344060i
$112$	14.1145	−	10.2976i	1.33369	−	0.973027i
$113$	0.906296	−	4.55626i	0.0852572	−	0.428617i	−0.914456	−	0.404684i	$-0.867381\pi$
$113$	0.906296	−	4.55626i	0.0852572	−	0.428617i	0.999714	−	0.0239323i	$-0.00761862\pi$
$114$	0.00627770	−	0.441097i	0.000587960	−	0.0413126i
$115$	0.227998	+	0.0815789i	0.0212609	+	0.00760727i
$116$	9.97993	−	0.205868i	0.926613	−	0.0191144i
$117$	−1.51379	−	10.2052i	−0.139950	−	0.943467i
$118$	−4.19027	+	4.49306i	−0.385746	+	0.413620i
$119$	13.4545	+	25.1716i	1.23337	+	2.30748i
$120$	0.0340845	+	0.0119503i	0.00311148	+	0.00109091i
$121$	9.58479	−	2.90751i	0.871344	−	0.264319i
$122$	−16.8991	−	1.07146i	−1.52997	−	0.0970052i
$123$	−0.126870	+	0.268244i	−0.0114395	+	0.0241867i
$124$	−11.1095	+	6.97420i	−0.997666	+	0.626302i
$125$	−0.503867	−	2.01155i	−0.0450672	−	0.179918i
$126$	−5.62416	+	17.6330i	−0.501040	+	1.57088i
$127$		−	17.6776i		−	1.56863i	−0.620363	−	0.784315i	$-0.713015\pi$
$127$		−	17.6776i		−	1.56863i	0.620363	−	0.784315i	$-0.286985\pi$
$128$	−2.19119	−	11.0995i	−0.193675	−	0.981066i
$129$			0.632089i			0.0556523i
$130$	0.966226	+	0.308183i	0.0847437	+	0.0270295i
$131$	2.57634	+	10.2853i	0.225096	+	0.898634i	0.972243	+	0.233975i	$0.0751733\pi$
$131$	2.57634	+	10.2853i	0.225096	+	0.898634i	−0.747147	+	0.664659i	$0.768577\pi$
$132$	0.125319	−	0.548015i	0.0109076	−	0.0476986i
$133$	−9.50111	+	20.0884i	−0.823850	+	1.74189i
$134$	−1.09175	+	17.2192i	−0.0943128	+	1.48751i
$135$	−0.0732743	+	0.0222275i	−0.00630645	+	0.00191304i
$136$	18.4537	−	1.02489i	1.58239	−	0.0878839i
$137$	−2.36151	−	4.41808i	−0.201757	−	0.377462i	0.760612	−	0.649207i	$-0.224899\pi$
$137$	−2.36151	−	4.41808i	−0.201757	−	0.377462i	−0.962369	+	0.271745i	$0.912399\pi$
$138$	−0.0737284	−	0.0687597i	−0.00627617	−	0.00585322i
$139$	−0.805829	−	5.43246i	−0.0683495	−	0.460775i	−0.996148	−	0.0876922i	$-0.972051\pi$
$139$	−0.805829	−	5.43246i	−0.0683495	−	0.460775i	0.927798	−	0.373083i	$-0.121699\pi$
$140$	−1.31279	−	1.25973i	−0.110951	−	0.106466i
$141$	0.332512	+	0.118975i	0.0280025	+	0.0100195i
$142$	2.65227	+	0.0377472i	0.222574	+	0.00316767i
$143$	3.07950	−	15.4817i	0.257521	−	1.29465i
$144$	8.81692	+	8.11795i	0.734744	+	0.676496i
$145$	−0.202795	−	1.01952i	−0.0168412	−	0.0846667i
$146$	19.9429	−	3.67267i	1.65049	−	0.303952i
$147$	−0.497345	+	0.548736i	−0.0410203	+	0.0452589i
$148$	9.47503	+	7.45431i	0.778843	+	0.612740i
$149$	4.95009	−	2.96697i	0.405527	−	0.243064i	−0.296768	−	0.954950i	$-0.595909\pi$
$149$	4.95009	−	2.96697i	0.405527	−	0.243064i	0.702295	+	0.711886i	$0.252159\pi$
$150$	−0.0691068	+	0.424197i	−0.00564255	+	0.0346356i
$151$	0.476061	+	4.83353i	0.0387413	+	0.393347i	0.994928	+	0.100589i	$0.0320728\pi$
$151$	0.476061	+	4.83353i	0.0387413	+	0.393347i	−0.956187	+	0.292757i	$0.905427\pi$
$152$	9.19970	+	11.0648i	0.746194	+	0.897476i
$153$	−15.1346	+	12.4206i	−1.22356	+	1.00415i
$154$	−17.1911	+	22.5030i	−1.38530	+	1.81334i
$155$	0.917336	+	1.01212i	0.0736822	+	0.0812958i
$156$	−0.318637	−	0.277043i	−0.0255114	−	0.0221812i
$157$	3.63613	−	2.69674i	0.290195	−	0.215223i	−0.440801	−	0.897605i	$-0.645306\pi$
$157$	3.63613	−	2.69674i	0.290195	−	0.215223i	0.730996	+	0.682381i	$0.239056\pi$
$158$	6.05368	−	10.9480i	0.481605	−	0.870975i
$159$	0.143659	−	0.346822i	0.0113929	−	0.0275048i
$160$	−1.09817	+	0.426737i	−0.0868180	+	0.0337366i
$161$	1.94344	+	4.69187i	0.153164	+	0.369772i
$162$	−12.6001	−	1.42232i	−0.989955	−	0.111748i
$163$	−4.49243	−	0.666389i	−0.351874	−	0.0521956i	−0.0315462	−	0.999502i	$-0.510043\pi$
$163$	−4.49243	−	0.666389i	−0.351874	−	0.0521956i	−0.320328	+	0.947307i	$0.603793\pi$
$164$	−2.54500	−	9.33865i	−0.198731	−	0.729226i
$165$	−0.0584710	−	0.00287249i	−0.00455196	−	0.000223623i
$166$	6.56290	−	3.80776i	0.509380	−	0.295540i
$167$	−3.97157	−	0.391166i	−0.307329	−	0.0302693i	−0.0568231	−	0.998384i	$-0.518097\pi$
$167$	−3.97157	−	0.391166i	−0.307329	−	0.0302693i	−0.250506	+	0.968115i	$0.580597\pi$
$168$	0.294346	+	0.697957i	0.0227093	+	0.0538486i
$169$	0.884313	+	0.725737i	0.0680241	+	0.0558259i
$170$	−0.441040	−	1.87345i	−0.0338262	−	0.143687i
$171$	−14.7867	−	3.70387i	−1.13077	−	0.283242i
$172$	−13.4060	−	15.6650i	−1.02220	−	1.19445i
$173$	−0.276655	−	5.63144i	−0.0210337	−	0.428150i	−0.986101	−	0.166148i	$-0.946867\pi$
$173$	−0.276655	−	5.63144i	−0.0210337	−	0.428150i	0.965067	−	0.262002i	$-0.0843829\pi$
$174$	−0.0904615	+	0.423213i	−0.00685787	+	0.0320837i
$175$	12.0281	−	18.0014i	0.909242	−	1.36078i
$176$	8.51715	+	16.2393i	0.642004	+	1.22408i
$177$	−0.147984	−	0.221474i	−0.0111232	−	0.0166470i
$178$	−5.81411	−	14.6216i	−0.435786	−	1.09594i
$179$	−1.96900	−	4.16309i	−0.147170	−	0.311164i	0.816915	−	0.576757i	$-0.195682\pi$
$179$	−1.96900	−	4.16309i	−0.147170	−	0.311164i	−0.964085	+	0.265593i	$0.914432\pi$
$180$	0.671842	−	1.05181i	0.0500761	−	0.0783975i
$181$	11.3521	+	8.41930i	0.843796	+	0.625801i	0.928801	−	0.370579i	$-0.120841\pi$
$181$	11.3521	+	8.41930i	0.843796	+	0.625801i	−0.0850054	+	0.996380i	$0.527091\pi$
$182$	8.81936	+	19.3549i	0.653735	+	1.43468i
$183$	0.213108	−	0.702522i	0.0157534	−	0.0519319i
$184$	3.28554	+	0.140355i	0.242213	+	0.0103471i
$185$	0.591815	−	1.10721i	0.0435111	−	0.0814036i
$186$	−0.183949	−	0.538127i	−0.0134878	−	0.0394574i
$187$	−28.2049	+	10.0919i	−2.06254	+	0.737990i
$188$	−10.7640	+	4.10373i	−0.785042	+	0.299296i
$189$	−1.37739	−	0.825578i	−0.100191	−	0.0600519i
$190$	0.967024	−	1.14471i	0.0701553	−	0.0830459i
$191$	0.483398	−	0.483398i	0.0349774	−	0.0349774i	−0.689402	−	0.724379i	$-0.742127\pi$
$191$	0.483398	−	0.483398i	0.0349774	−	0.0349774i	0.724379	+	0.689402i	$0.242127\pi$
$192$	0.490184	+	0.0178009i	0.0353760	+	0.00128467i
$193$	15.1589	+	15.1589i	1.09116	+	1.09116i	0.995405	+	0.0957585i	$0.0305276\pi$
$193$	15.1589	+	15.1589i	1.09116	+	1.09116i	0.0957585	+	0.995405i	$0.469472\pi$
$194$	−8.50322	+	0.715473i	−0.610495	+	0.0513680i
$195$	−0.0226051	+	0.0377144i	−0.00161879	+	0.00270078i
$196$	0.687474	−	24.1475i	0.0491053	−	1.72482i
$197$	1.52566	+	4.26393i	0.108699	+	0.303793i	0.983560	−	0.180581i	$-0.0577977\pi$
$197$	1.52566	+	4.26393i	0.108699	+	0.303793i	−0.874861	+	0.484373i	$0.839048\pi$
$198$	−17.4403	−	8.55443i	−1.23943	−	0.607937i
$199$	5.44811	+	2.91208i	0.386206	+	0.206432i	0.653061	−	0.757305i	$-0.273484\pi$
$199$	5.44811	+	2.91208i	0.386206	+	0.206432i	−0.266855	+	0.963737i	$0.585984\pi$
$200$	−7.28418	−	11.9785i	−0.515069	−	0.847011i
$201$	−0.715827	−	0.217144i	−0.0504905	−	0.0153161i
$202$	4.76710	−	12.7482i	0.335412	−	0.896963i
$203$	12.9865	−	17.5102i	0.911471	−	1.22898i
$204$	−0.140083	+	0.788956i	−0.00980781	+	0.0552379i
$205$	−0.911185	+	0.430959i	−0.0636399	+	0.0300995i
$206$	−15.9511	−	6.87469i	−1.11136	−	0.478982i
$207$	−2.89655	+	1.93541i	−0.201324	+	0.134520i
$208$	13.7726	+	0.107935i	0.954958	+	0.00748395i
$209$	−19.3924	−	12.9576i	−1.34140	−	0.896293i
$210$	0.0662048	−	0.0428866i	0.00456857	−	0.00295945i
$211$	−1.32951	+	0.0653148i	−0.0915275	+	0.00449646i	−0.0947799	−	0.995498i	$-0.530215\pi$
$211$	−1.32951	+	0.0653148i	−0.0915275	+	0.00449646i	0.00325239	+	0.999995i	$0.498965\pi$
$212$	3.79551	+	11.6421i	0.260677	+	0.799586i
$213$	−0.0279430	+	0.111555i	−0.00191462	+	0.00764361i
$214$	−15.5635	−	9.63206i	−1.06390	−	0.658434i
$215$	−1.36212	+	1.65974i	−0.0928956	+	0.113194i
$216$	−0.860909	+	0.583238i	−0.0585774	+	0.0396843i
$217$	−2.80794	+	28.5095i	−0.190615	+	1.93535i
$218$	9.28609	+	2.46700i	0.628933	+	0.167086i
$219$	−0.0431387	+	0.878107i	−0.00291504	+	0.0593370i
$220$	1.51000	−	1.16893i	0.101804	−	0.0788091i
$221$	−3.30139	+	22.2562i	−0.222076	+	1.49711i
$222$	−0.408716	+	0.325802i	−0.0274312	+	0.0218664i
$223$	−13.9435	+	5.77559i	−0.933727	+	0.386762i	−0.797091	−	0.603859i	$-0.793629\pi$
$223$	−13.9435	+	5.77559i	−0.933727	+	0.386762i	−0.136636	+	0.990621i	$0.543629\pi$
$224$	−22.0978	−	11.0546i	−1.47647	−	0.738617i
$225$	13.7208	+	5.68332i	0.914717	+	0.378888i
$226$	−6.31337	+	1.81744i	−0.419959	+	0.120894i
$227$	−12.1129	−	16.3324i	−0.803964	−	1.08402i	−0.994745	−	0.102388i	$-0.967352\pi$
$227$	−12.1129	−	16.3324i	−0.803964	−	1.08402i	0.190780	−	0.981633i	$-0.438898\pi$
$228$	−0.558350	+	0.278313i	−0.0369776	+	0.0184317i
$229$	5.33176	−	4.83243i	0.352333	−	0.319336i	−0.476135	−	0.879372i	$-0.657963\pi$
$229$	5.33176	−	4.83243i	0.352333	−	0.319336i	0.828468	+	0.560036i	$0.189213\pi$
$230$	−0.0454231	−	0.339430i	−0.00299511	−	0.0223814i
$231$	−0.778867	−	0.949052i	−0.0512457	−	0.0624431i
$232$	−6.73406	−	12.4071i	−0.442113	−	0.814563i
$233$	−13.5867	+	1.33817i	−0.890095	+	0.0876667i	−0.532718	−	0.846293i	$-0.678829\pi$
$233$	−13.5867	+	1.33817i	−0.890095	+	0.0876667i	−0.357378	+	0.933960i	$0.616329\pi$
$234$	−11.8414	+	8.52372i	−0.774100	+	0.557213i
$235$	0.616728	+	1.02895i	0.0402309	+	0.0671212i
$236$	8.36473	+	2.35016i	0.544498	+	0.152982i
$237$	0.401878	+	0.364241i	0.0261048	+	0.0236600i
$238$	22.9005	−	33.2391i	1.48442	−	2.15457i
$239$	−15.1210	+	3.00776i	−0.978097	+	0.194556i	−0.658156	−	0.752882i	$-0.728663\pi$
$239$	−15.1210	+	3.00776i	−0.978097	+	0.194556i	−0.319941	+	0.947437i	$0.603663\pi$
$240$	−0.00709875	−	0.0505840i	−0.000458222	−	0.00326518i
$241$	12.7273	+	2.53162i	0.819838	+	0.163076i	0.587153	−	0.809476i	$-0.300249\pi$
$241$	12.7273	+	2.53162i	0.819838	+	0.163076i	0.232685	+	0.972552i	$0.425249\pi$
$242$	−9.87253	−	10.1576i	−0.634630	−	0.652955i
$243$	0.556776	−	1.55609i	0.0357172	−	0.0998230i
$244$	9.61843	+	21.9304i	0.615757	+	1.40395i
$245$	−2.48843	+	0.369123i	−0.158980	+	0.0235824i
$246$	0.419389	−	0.0146243i	0.0267393	−	0.000932411i
$247$	−15.4493	+	8.25780i	−0.983012	+	0.525431i
$248$	15.9720	+	9.43495i	1.01422	+	0.599120i
$249$	0.0954915	+	0.314793i	0.00605153	+	0.0199492i
$250$	−2.20075	+	1.93832i	−0.139188	+	0.122590i
$251$	5.41621	+	2.56167i	0.341868	+	0.161691i	0.590776	−	0.806836i	$-0.298822\pi$
$251$	5.41621	+	2.56167i	0.341868	+	0.161691i	−0.248908	+	0.968527i	$0.580072\pi$
$252$	25.8066	−	4.37378i	1.62566	−	0.275522i
$253$	−5.17034	+	1.29510i	−0.325056	+	0.0814224i
$254$	−22.2134	+	11.4699i	−1.39379	+	0.719685i
$255$	0.0834440			0.00522547
$256$	−12.5257	+	9.95520i	−0.782858	+	0.622200i
$257$	−9.69787			−0.604937			−0.302468	−	0.953159i	$-0.597811\pi$
$257$	−9.69787			−0.604937			−0.302468	+	0.953159i	$0.597811\pi$
$258$	0.794274	−	0.410124i	0.0494493	−	0.0255332i
$259$	25.5403	−	6.39752i	1.58700	−	0.397523i
$260$	−0.239667	−	1.41411i	−0.0148635	−	0.0876992i
$261$	13.5185	+	6.39379i	0.836777	+	0.395766i
$262$	11.2528	−	9.91093i	0.695199	−	0.612299i
$263$	−2.63184	−	8.67603i	−0.162286	−	0.534987i	0.837651	−	0.546206i	$-0.183929\pi$
$263$	−2.63184	−	8.67603i	−0.162286	−	0.534987i	−0.999937	+	0.0112197i	$0.996429\pi$
$264$	−0.769940	+	0.198100i	−0.0473865	+	0.0121922i
$265$	1.12460	−	0.601113i	0.0690838	−	0.0369261i
$266$	31.4075	−	1.09519i	1.92572	−	0.0671506i
$267$	0.674816	−	0.100100i	0.0412981	−	0.00612599i
$268$	22.3457	−	9.80059i	1.36498	−	0.598666i
$269$	5.97228	−	16.6914i	0.364136	−	1.01769i	−0.610132	−	0.792300i	$-0.708884\pi$
$269$	5.97228	−	16.6914i	0.364136	−	1.01769i	0.974268	−	0.225392i	$-0.0723664\pi$
$270$	0.0754740	+	0.0776534i	0.00459320	+	0.00472583i
$271$	17.3281	+	3.44677i	1.05261	+	0.209376i	0.690926	−	0.722926i	$-0.257203\pi$
$271$	17.3281	+	3.44677i	1.05261	+	0.209376i	0.361681	+	0.932302i	$0.382203\pi$
$272$	−13.2614	−	22.5237i	−0.804088	−	1.36570i
$273$	−0.904424	+	0.179901i	−0.0547383	+	0.0108881i
$274$	−4.01945	+	5.83406i	−0.242824	+	0.352449i
$275$	16.8365	+	15.2597i	1.01528	+	0.920194i
$276$	−0.0385646	+	0.137260i	−0.00232132	+	0.00826208i
$277$	0.743442	+	1.24036i	0.0446691	+	0.0745259i	0.879253	−	0.476354i	$-0.158042\pi$
$277$	0.743442	+	1.24036i	0.0446691	+	0.0745259i	−0.834584	+	0.550880i	$0.814292\pi$
$278$	−6.30349	+	4.53738i	−0.378058	+	0.272134i
$279$	−19.5565	+	1.92615i	−1.17082	+	0.115316i
$280$	−0.731163	+	2.46700i	−0.0436953	+	0.147431i
$281$	−10.1677	−	12.3894i	−0.606555	−	0.739089i	0.375679	−	0.926750i	$-0.377410\pi$
$281$	−10.1677	−	12.3894i	−0.606555	−	0.739089i	−0.982234	+	0.187660i	$0.939910\pi$
$282$	−0.0662449	−	0.495025i	−0.00394483	−	0.0294783i
$283$	−8.27901	+	7.50366i	−0.492136	+	0.446046i	−0.879513	−	0.475875i	$-0.842131\pi$
$283$	−8.27901	+	7.50366i	−0.492136	+	0.446046i	0.387377	+	0.921922i	$0.373381\pi$
$284$	−1.67347	−	3.35730i	−0.0993020	−	0.199219i
$285$	0.0387011	+	0.0521824i	0.00229245	+	0.00309102i
$286$	−21.4522	+	6.17549i	−1.26850	+	0.365164i
$287$	−19.5299	−	8.08955i	−1.15281	−	0.477511i
$288$	4.48014	−	16.3465i	0.263995	−	0.963225i
$289$	23.7425	−	9.83448i	1.39662	−	0.578499i
$290$	−1.14953	+	0.916336i	−0.0675030	+	0.0538091i
$291$	0.0542845	−	0.365956i	0.00318221	−	0.0214527i
$292$	−17.5548	−	22.6770i	−1.02732	−	1.32707i
$293$	−0.425140	+	8.65392i	−0.0248369	+	0.505567i	0.953859	+	0.300254i	$0.0970714\pi$
$293$	−0.425140	+	8.65392i	−0.0248369	+	0.505567i	−0.978696	+	0.205313i	$0.934179\pi$
$294$	1.01223	+	0.268915i	0.0590345	+	0.0156835i
$295$	0.0886860	−	0.900444i	0.00516350	−	0.0524259i
$296$	3.21920	−	16.7428i	0.187112	−	0.973158i
$297$	1.06922	−	1.30285i	0.0620427	−	0.0755992i
$298$	−6.94006	−	4.29512i	−0.402027	−	0.248810i
$299$	−0.972741	+	3.88340i	−0.0562551	+	0.224583i
$300$	0.577880	−	0.188397i	0.0333639	−	0.0108771i
$301$	−44.9752	+	2.20949i	−2.59233	+	0.127353i
$302$	5.76485	−	3.73439i	0.331730	−	0.214890i
$303$	0.490634	+	0.327831i	0.0281862	+	0.0188334i
$304$	7.93478	−	18.7395i	0.455091	−	1.07478i
$305$	2.07348	−	1.38545i	0.118727	−	0.0793307i
$306$	25.4274	+	10.9589i	1.45359	+	0.626477i
$307$	11.3741	−	5.37956i	0.649156	−	0.307028i	−0.0744669	−	0.997223i	$-0.523726\pi$
$307$	11.3741	−	5.37956i	0.649156	−	0.307028i	0.723623	+	0.690196i	$0.242476\pi$
$308$	39.4312	+	7.00122i	2.24680	+	0.398932i
$309$	0.448594	−	0.604859i	0.0255196	−	0.0344092i
$310$	0.676617	−	1.80942i	0.0384293	−	0.102768i
$311$	−5.67430	−	1.72128i	−0.321760	−	0.0976049i	0.125273	−	0.992122i	$-0.460019\pi$
$311$	−5.67430	−	1.72128i	−0.321760	−	0.0976049i	−0.447033	+	0.894517i	$0.647519\pi$
$312$	−0.141384	+	0.580152i	−0.00800431	+	0.0328446i
$313$	−9.39120	−	5.01970i	−0.530822	−	0.283730i	0.184132	−	0.982901i	$-0.441052\pi$
$313$	−9.39120	−	5.01970i	−0.530822	−	0.283730i	−0.714954	+	0.699171i	$0.753552\pi$
$314$	−5.74795	−	2.81936i	−0.324375	−	0.159106i
$315$	−0.918271	−	2.56640i	−0.0517387	−	0.144600i
$316$	−17.6849	−	0.503486i	−0.994856	−	0.0283233i
$317$	−4.10830	+	6.85428i	−0.230745	+	0.384975i	−0.951224	−	0.308502i	$-0.900172\pi$
$317$	−4.10830	+	6.85428i	−0.230745	+	0.384975i	0.720479	+	0.693477i	$0.243922\pi$
$318$	−0.529023	+	0.0445128i	−0.0296662	+	0.00249615i
$319$	16.1790	+	16.1790i	0.905848	+	0.905848i
$320$	1.24877	+	1.10306i	0.0698083	+	0.0616630i
$321$	0.561108	−	0.561108i	0.0313180	−	0.0313180i
$322$	4.63476	−	5.48637i	0.258285	−	0.305743i
$323$	28.5145	+	17.0909i	1.58659	+	0.950965i
$324$	6.38816	+	16.7559i	0.354898	+	0.930885i
$325$	16.0693	−	5.74967i	0.891362	−	0.318934i
$326$	2.07749	+	6.07750i	0.115062	+	0.336602i
$327$	−0.196367	+	0.367377i	−0.0108591	+	0.0203160i
$328$	−10.0835	+	9.25730i	−0.556769	+	0.511149i
$329$	−7.30313	+	24.0752i	−0.402634	+	1.32731i
$330$	0.0343287	+	0.0753376i	0.00188973	+	0.00414720i
$331$	−8.46814	−	6.28040i	−0.465451	−	0.345202i	0.337421	−	0.941354i	$-0.390446\pi$
$331$	−8.46814	−	6.28040i	−0.465451	−	0.345202i	−0.802872	+	0.596152i	$0.796696\pi$
$332$	−9.04305	−	5.77621i	−0.496302	−	0.317011i
$333$	7.72211	+	16.3270i	0.423169	+	0.894715i
$334$	2.08538	+	5.24442i	0.114107	+	0.286962i
$335$	−1.41169	−	2.11274i	−0.0771289	−	0.115432i
$336$	0.686059	−	0.822733i	0.0374276	−	0.0448838i
$337$	3.43506	−	5.14093i	0.187120	−	0.280044i	−0.726035	−	0.687658i	$-0.758639\pi$
$337$	3.43506	−	5.14093i	0.187120	−	0.280044i	0.913154	+	0.407614i	$0.133639\pi$
$338$	0.338174	−	1.58210i	0.0183942	−	0.0860550i
$339$	−0.0139761	−	0.284489i	−0.000759076	−	0.0154513i
$340$	−2.06799	+	1.76977i	−0.112152	+	0.0959794i
$341$	−29.1658	−	7.30564i	−1.57941	−	0.395623i
$342$	4.93995	+	20.9839i	0.267122	+	1.13468i
$343$	−17.1478	−	14.0728i	−0.925892	−	0.759860i
$344$	−10.9861	+	27.0099i	−0.592329	+	1.45628i
$345$	0.0147757	+	0.00145528i	0.000795498	+	7.83497e-5i
$346$	−6.89688	+	4.00154i	−0.370778	+	0.215124i
$347$	7.72518	+	0.379514i	0.414709	+	0.0203734i	0.255353	−	0.966848i	$-0.417808\pi$
$347$	7.72518	+	0.379514i	0.414709	+	0.0203734i	0.159356	+	0.987221i	$0.449058\pi$
$348$	0.590498	−	0.160925i	0.0316540	−	0.00862646i
$349$	23.4426	+	3.47738i	1.25485	+	0.186140i	0.740863	−	0.671656i	$-0.234417\pi$
$349$	23.4426	+	3.47738i	1.25485	+	0.186140i	0.513990	+	0.857796i	$0.328167\pi$
$350$	−30.4246	−	3.43438i	−1.62626	−	0.183575i
$351$	−0.484444	−	1.16955i	−0.0258577	−	0.0624260i
$352$	14.8798	−	21.2392i	0.793097	−	1.13206i
$353$	−7.72967	+	18.6611i	−0.411409	+	0.993229i	0.573351	+	0.819310i	$0.305643\pi$
$353$	−7.72967	+	18.6611i	−0.411409	+	0.993229i	−0.984760	+	0.173919i	$0.944357\pi$
$354$	−0.182283	+	0.329655i	−0.00968822	+	0.0175210i
$355$	−0.313767	+	0.232706i	−0.0166530	+	0.0123507i
$356$	−14.6009	+	16.7930i	−0.773846	+	0.890028i
$357$	1.17522	+	1.29666i	0.0621994	+	0.0686265i
$358$	−3.95372	+	5.17539i	−0.208961	+	0.273528i
$359$	21.4938	−	17.6395i	1.13440	−	0.930977i	0.136183	−	0.990684i	$-0.456517\pi$
$359$	21.4938	−	17.6395i	1.13440	−	0.930977i	0.998216	+	0.0597066i	$0.0190165\pi$
$360$	−1.75761	−	0.161769i	−0.0926342	−	0.00852597i
$361$	0.674663	+	6.84997i	0.0355086	+	0.360525i
$362$	3.21387	−	19.7277i	0.168917	−	1.03686i
$363$	0.526748	−	0.315721i	0.0276471	−	0.0165710i
$364$	18.5987	−	23.6405i	0.974839	−	1.23910i
$365$	−2.00555	+	2.21278i	−0.104975	+	0.115822i
$366$	−1.02105	+	0.188036i	−0.0533712	+	0.00982879i
$367$	−0.318332	−	1.60037i	−0.0166168	−	0.0835384i	0.971587	−	0.236683i	$-0.0760601\pi$
$367$	−0.318332	−	1.60037i	−0.0166168	−	0.0835384i	−0.988204	+	0.153144i	$0.951060\pi$
$368$	−1.95542	−	4.21963i	−0.101933	−	0.219963i
$369$	2.82894	−	14.2220i	0.147269	−	0.740369i
$370$	−1.77530	−	0.0252660i	−0.0922932	−	0.00131352i
$371$	25.1797	+	9.00945i	1.30727	+	0.467747i
$372$	−0.556849	+	0.580306i	−0.0288713	+	0.0300875i
$373$	4.05302	+	27.3233i	0.209858	+	1.41475i	0.796372	+	0.604807i	$0.206750\pi$
$373$	4.05302	+	27.3233i	0.209858	+	1.41475i	−0.586515	+	0.809939i	$0.699500\pi$
$374$	30.9817	+	28.8938i	1.60203	+	1.49406i
$375$	−0.0599358	−	0.112132i	−0.00309507	−	0.00579047i
$376$	12.1408	+	10.8632i	0.626113	+	0.560225i
$377$	16.4454	−	4.98865i	0.846981	−	0.256929i
$378$	−0.143702	+	2.26648i	−0.00739124	+	0.116575i
$379$	−10.5112	+	22.2242i	−0.539926	+	1.14158i	0.431034	+	0.902336i	$0.358149\pi$
$379$	−10.5112	+	22.2242i	−0.539926	+	1.14158i	−0.970960	+	0.239242i	$0.923101\pi$
$380$	−2.06587	−	0.472417i	−0.105977	−	0.0242345i
$381$	−0.263359	−	1.05139i	−0.0134923	−	0.0538643i
$382$	−0.921078	−	0.293783i	−0.0471265	−	0.0150313i
$383$		−	12.3079i		−	0.628905i	−0.949273	−	0.314452i	$-0.898179\pi$
$383$		−	12.3079i		−	0.628905i	0.949273	−	0.314452i	$-0.101821\pi$
$384$	−0.295682	−	0.627508i	−0.0150890	−	0.0320224i
$385$		−	4.17044i		−	0.212546i
$386$	9.21278	−	28.8842i	0.468918	−	1.47017i
$387$	−7.50534	−	29.9630i	−0.381518	−	1.52311i
$388$	6.41628	+	10.2208i	0.325737	+	0.518882i
$389$	−12.9146	+	27.3055i	−0.654794	+	1.38445i	0.254002	+	0.967204i	$0.418253\pi$
$389$	−12.9146	+	27.3055i	−0.654794	+	1.38445i	−0.908796	+	0.417241i	$0.862997\pi$
$390$	0.0620585	+	0.00393470i	0.00314245	+	0.000199241i
$391$	7.27025	−	2.20541i	0.367673	−	0.111532i
$392$	−30.7895	+	14.8040i	−1.55510	+	0.747714i
$393$	0.306461	+	0.573347i	0.0154589	+	0.0289216i
$394$	4.36809	−	4.68373i	0.220061	−	0.235963i
$395$	0.270335	+	1.82245i	0.0136020	+	0.0916975i
$396$	0.566568	+	27.4657i	0.0284711	+	1.38020i
$397$	11.1676	+	3.99582i	0.560485	+	0.200545i	0.601864	−	0.798599i	$-0.294425\pi$
$397$	11.1676	+	3.99582i	0.560485	+	0.200545i	−0.0413788	+	0.999144i	$0.513175\pi$
$398$	0.124323	−	8.73549i	0.00623177	−	0.437870i
$399$	−0.265811	+	1.33632i	−0.0133072	+	0.0668998i
$400$	−10.3258	+	16.9253i	−0.516290	+	0.846267i
$401$	−4.92208	−	24.7450i	−0.245797	−	1.23571i	−0.884606	−	0.466340i	$-0.845572\pi$
$401$	−4.92208	−	24.7450i	−0.245797	−	1.23571i	0.638809	−	0.769366i	$-0.279428\pi$
$402$	0.191597	+	1.04039i	0.00955599	+	0.0518899i
$403$	−15.1658	+	16.7329i	−0.755462	+	0.833524i
$404$	−19.1123	+	2.28129i	−0.950874	+	0.113498i
$405$	1.60173	−	0.960042i	0.0795907	−	0.0477048i
$406$	−30.4292	−	4.95728i	−1.51018	−	0.246026i
$407$	2.70860	+	27.5009i	0.134260	+	1.36317i
$408$	1.08228	−	0.335879i	0.0535809	−	0.0166285i
$409$	19.0907	−	15.6673i	0.943975	−	0.774700i	−0.0304216	−	0.999537i	$-0.509685\pi$
$409$	19.0907	−	15.6673i	0.943975	−	0.774700i	0.974396	+	0.224837i	$0.0721850\pi$
$410$	1.13275	+	0.865359i	0.0559425	+	0.0427371i
$411$	−0.206273	−	0.227587i	−0.0101747	−	0.0112261i
$412$	1.71104	+	24.5044i	0.0842970	+	1.20725i
$413$	15.2413	−	11.3037i	0.749975	−	0.556220i
$414$	4.31140	+	2.38399i	0.211894	+	0.117167i
$415$	−0.427620	+	1.03237i	−0.0209910	+	0.0506768i
$416$	−8.80058	−	17.3765i	−0.431484	−	0.851952i
$417$	−0.128860	−	0.311095i	−0.00631029	−	0.0152344i
$418$	−3.69975	+	32.7755i	−0.180961	+	1.60310i
$419$	−37.1617	−	5.51242i	−1.81547	−	0.269299i	−0.849431	−	0.527700i	$-0.823054\pi$
$419$	−37.1617	−	5.51242i	−1.81547	−	0.269299i	−0.966038	+	0.258401i	$0.916804\pi$
$420$	−0.0968469	−	0.0553655i	−0.00472565	−	0.00270156i
$421$	9.43512	+	0.463518i	0.459840	+	0.0225905i	0.277670	−	0.960677i	$-0.410438\pi$
$421$	9.43512	+	0.463518i	0.459840	+	0.0225905i	0.182170	+	0.983267i	$0.441688\pi$
$422$	0.944715	+	1.62827i	0.0459880	+	0.0792629i
$423$	−17.1748	−	1.69157i	−0.835067	−	0.0822469i
$424$	12.1667	−	12.3233i	0.590866	−	0.598471i
$425$	−25.0368	−	20.5472i	−1.21446	−	0.996684i
$426$	0.158309	−	0.0372683i	0.00767008	−	0.00180566i
$427$	50.7317	+	12.7076i	2.45508	+	0.614965i
$428$	−2.00530	+	25.8065i	−0.0969299	+	1.24740i
$429$	−0.0474893	−	0.966667i	−0.00229281	−	0.0466711i
$430$	2.96941	+	0.634709i	0.143197	+	0.0306084i
$431$	−21.2949	+	31.8701i	−1.02574	+	1.53513i	−0.193201	+	0.981159i	$0.561887\pi$
$431$	−21.2949	+	31.8701i	−1.02574	+	1.53513i	−0.832538	+	0.553968i	$0.813113\pi$
$432$	1.29148	+	0.703378i	0.0621364	+	0.0338413i
$433$	−6.03542	−	9.03264i	−0.290044	−	0.434081i	0.657621	−	0.753349i	$-0.271563\pi$
$433$	−6.03542	−	9.03264i	−0.290044	−	0.434081i	−0.947664	+	0.319268i	$0.896563\pi$
$434$	37.6465	−	14.9697i	1.80709	−	0.718567i
$435$	−0.0272502	−	0.0576157i	−0.00130655	−	0.00276246i
$436$	−2.92519	−	13.2694i	−0.140091	−	0.635491i
$437$	4.75109	+	3.52365i	0.227275	+	0.168559i
$438$	1.13141	−	0.515543i	0.0540607	−	0.0246336i
$439$	−0.748838	+	2.46859i	−0.0357401	+	0.117819i	−0.972995	−	0.230824i	$-0.925858\pi$
$439$	−0.748838	+	2.46859i	−0.0357401	+	0.117819i	0.937255	+	0.348644i	$0.113358\pi$
$440$	−2.44861	−	1.13900i	−0.116733	−	0.0542999i
$441$	17.0601	−	31.9172i	0.812386	−	1.51987i
$442$	30.1089	−	10.2922i	1.43213	−	0.489550i
$443$	−18.6569	+	6.67554i	−0.886415	+	0.317164i	−0.740439	−	0.672124i	$-0.765382\pi$
$443$	−18.6569	+	6.67554i	−0.886415	+	0.317164i	−0.145976	+	0.989288i	$0.546632\pi$
$444$	0.674590	+	0.302193i	0.0320146	+	0.0143415i
$445$	1.98765	+	1.19135i	0.0942235	+	0.0564754i
$446$	16.3046	+	13.7738i	0.772047	+	0.652208i
$447$	0.250209	−	0.250209i	0.0118345	−	0.0118345i
$448$	0.446861	+	34.9404i	0.0211122	+	1.65078i
$449$	−22.0169	−	22.0169i	−1.03904	−	1.03904i	−0.999206	−	0.0398339i	$-0.987317\pi$
$449$	−22.0169	−	22.0169i	−1.03904	−	1.03904i	−0.0398339	−	0.999206i	$-0.512683\pi$
$450$	−1.76098	−	20.9289i	−0.0830136	−	0.986596i
$451$	11.4061	−	19.0299i	0.537092	−	0.896083i
$452$	6.38013	+	6.75406i	0.300096	+	0.317684i
$453$	0.100324	+	0.280386i	0.00471362	+	0.0131737i
$454$	−12.6637	+	25.8181i	−0.594338	+	1.21170i
$455$	−2.76252	−	1.47660i	−0.129509	−	0.0692240i
$456$	0.712003	+	0.521034i	0.0333426	+	0.0243997i
$457$	12.9572	+	3.93052i	0.606112	+	0.183862i	0.578399	−	0.815754i	$-0.303678\pi$
$457$	12.9572	+	3.93052i	0.606112	+	0.183862i	0.0277129	+	0.999616i	$0.491178\pi$
$458$	−9.53181	−	3.56434i	−0.445392	−	0.166551i
$459$	−1.43110	+	1.92961i	−0.0667978	+	0.0900665i
$460$	−0.397051	+	0.277314i	−0.0185126	+	0.0129298i
$461$	−18.9833	+	8.97845i	−0.884143	+	0.418168i	−0.815015	−	0.579440i	$-0.803271\pi$
$461$	−18.9833	+	8.97845i	−0.884143	+	0.418168i	−0.0691274	+	0.997608i	$0.522021\pi$
$462$	−0.687206	+	1.59450i	−0.0319717	+	0.0741827i
$463$	9.43010	−	6.30099i	0.438254	−	0.292832i	−0.316803	−	0.948491i	$-0.602609\pi$
$463$	9.43010	−	6.30099i	0.438254	−	0.292832i	0.755057	+	0.655660i	$0.227609\pi$
$464$	−11.2212	+	16.5121i	−0.520932	+	0.766556i
$465$	0.0696380	+	0.0465306i	0.00322938	+	0.00215780i
$466$	10.4971	+	16.2046i	0.486270	+	0.750664i
$467$	−7.71145	+	0.378839i	−0.356843	+	0.0175306i	−0.226700	−	0.973965i	$-0.572794\pi$
$467$	−7.71145	+	0.378839i	−0.356843	+	0.0175306i	−0.130143	+	0.991495i	$0.541544\pi$
$468$	18.3940	+	9.34927i	0.850262	+	0.432170i
$469$	12.9483	−	51.6925i	0.597897	−	2.38694i
$470$	0.892804	−	1.44259i	0.0411820	−	0.0665419i
$471$	0.176086	−	0.214562i	0.00811363	−	0.00988648i
$472$	−2.47419	−	12.0359i	−0.113884	−	0.553996i
$473$	4.63235	−	47.0330i	0.212995	−	2.16258i
$474$	0.196946	−	0.741328i	0.00904602	−	0.0340503i
$475$	1.23734	−	25.1867i	0.0567731	−	1.15564i
$476$	−56.6265	−	7.20958i	−2.59547	−	0.330451i
$477$	−2.69174	+	18.1463i	−0.123246	+	0.830860i
$478$	13.5906	+	17.0493i	0.621620	+	0.779817i
$479$	14.8313	−	6.14335i	0.677662	−	0.280697i	−0.0171874	−	0.999852i	$-0.505471\pi$
$479$	14.8313	−	6.14335i	0.677662	−	0.280697i	0.694849	+	0.719156i	$0.255471\pi$
$480$	−0.0589571	+	0.0417411i	−0.00269101	+	0.00190521i
$481$	19.1757	+	7.94284i	0.874338	+	0.362162i
$482$	−5.07678	−	17.6356i	−0.231241	−	0.803278i
$483$	0.185487	+	0.250100i	0.00843995	+	0.0113800i
$484$	−6.35820	+	18.9963i	−0.289009	+	0.863469i
$485$	0.931156	−	0.843950i	0.0422816	−	0.0383218i
$486$	−2.31661	+	0.310013i	−0.105084	+	0.0140625i
$487$	15.4594	+	18.8373i	0.700531	+	0.853599i	0.994771	−	0.102132i	$-0.0325665\pi$
$487$	15.4594	+	18.8373i	0.700531	+	0.853599i	−0.294240	+	0.955732i	$0.595067\pi$
$488$	21.3166	−	26.3157i	0.964956	−	1.19125i
$489$	−0.277119	+	0.0272939i	−0.0125318	+	0.00123427i
$490$	2.07842	+	2.88742i	0.0938936	+	0.130440i
$491$	4.80492	+	8.01653i	0.216843	+	0.361781i	0.946859	−	0.321649i	$-0.104237\pi$
$491$	4.80492	+	8.01653i	0.216843	+	0.361781i	−0.730016	+	0.683430i	$0.760487\pi$
$492$	−0.290493	−	0.517509i	−0.0130964	−	0.0233311i
$493$	−24.1650	−	21.9019i	−1.08834	−	0.986411i
$494$	20.4007	+	14.0553i	0.917871	+	0.632379i
$495$	2.80582	−	0.558111i	0.126112	−	0.0250852i
$496$	1.49257	−	26.1919i	0.0670182	−	1.17605i
$497$	−8.03517	−	1.59829i	−0.360427	−	0.0716933i
$498$	0.333606	−	0.324244i	0.0149493	−	0.0145297i
$499$	−1.08120	+	3.02176i	−0.0484013	+	0.135272i	−0.963312	−	0.268383i	$-0.913511\pi$
$499$	−1.08120	+	3.02176i	−0.0484013	+	0.135272i	0.914911	+	0.403656i	$0.132261\pi$
$500$	3.86360	+	1.50778i	0.172786	+	0.0674297i
$501$	−0.242040	+	0.0359033i	−0.0108136	+	0.00160404i
$502$	−0.295285	−	8.46804i	−0.0131792	−	0.377947i
$503$	1.64852	−	0.881152i	0.0735039	−	0.0392886i	−0.434235	−	0.900799i	$-0.642981\pi$
$503$	1.64852	−	0.881152i	0.0735039	−	0.0392886i	0.507739	+	0.861511i	$0.330481\pi$
$504$	−22.2404	−	29.5903i	−0.990665	−	1.31806i
$505$	0.581852	+	1.91811i	0.0258921	+	0.0853547i
$506$	4.98212	+	5.65666i	0.221482	+	0.251469i
$507$	0.0634073	+	0.0299894i	0.00281602	+	0.00133188i
$508$	28.8258	+	20.4709i	1.27894	+	0.908248i
$509$	40.0264	−	10.0261i	1.77414	−	0.444398i	0.788748	−	0.614716i	$-0.210729\pi$
$509$	40.0264	−	10.0261i	1.77414	−	0.444398i	0.985389	+	0.170318i	$0.0544794\pi$
$510$	−0.0541418	−	0.104855i	−0.00239744	−	0.00464304i
$511$	−62.6311			−2.77063
$512$	20.6368	+	9.28033i	0.912024	+	0.410136i
$513$	−1.87043			−0.0825817
$514$	6.29236	+	12.1862i	0.277544	+	0.537511i
$515$	2.48136	−	0.621548i	0.109342	−	0.0273887i
$516$	−1.03071	−	0.731968i	−0.0453746	−	0.0322231i
$517$	−23.8699	−	11.2896i	−1.04980	−	0.496516i
$518$	−24.6106	−	27.9426i	−1.08133	−	1.22773i
$519$	−0.100351	−	0.330813i	−0.00440492	−	0.0145211i
$520$	−1.62144	+	1.21869i	−0.0711049	+	0.0534431i
$521$	18.6490	−	9.96811i	0.817029	−	0.436711i	−0.00926042	−	0.999957i	$-0.502948\pi$
$521$	18.6490	−	9.96811i	0.817029	−	0.436711i	0.826289	+	0.563246i	$0.190448\pi$
$522$	−0.737014	−	21.1358i	−0.0322582	−	0.925087i
$523$	6.31456	−	0.936676i	0.276116	−	0.0409580i	−0.00723623	−	0.999974i	$-0.502303\pi$
$523$	6.31456	−	0.936676i	0.276116	−	0.0409580i	0.283352	+	0.959016i	$0.408553\pi$
$524$	−19.7552	−	7.70947i	−0.863009	−	0.336790i
$525$	0.447201	−	1.24984i	0.0195175	−	0.0545476i
$526$	−9.19452	+	8.93648i	−0.400900	+	0.389649i
$527$	42.0333	+	8.36094i	1.83100	+	0.364208i
$528$	0.748497	+	0.838960i	0.0325742	+	0.0365110i
$529$	−21.2322	+	4.22335i	−0.923140	+	0.183624i
$530$	−1.48504	−	1.02313i	−0.0645058	−	0.0444421i
$531$	9.64466	+	8.74141i	0.418542	+	0.379345i
$532$	−21.7546	−	38.7556i	−0.943182	−	1.68027i
$533$	−8.56703	−	14.2932i	−0.371079	−	0.619108i
$534$	−0.563631	−	0.783016i	−0.0243907	−	0.0338844i
$535$	2.68252	−	0.264205i	0.115975	−	0.0114226i
$536$	−26.8141	−	21.7203i	−1.15819	−	0.938174i
$537$	−0.179129	−	0.218270i	−0.00773000	−	0.00941903i
$538$	−24.8492	+	3.32536i	−1.07133	+	0.143366i
$539$	41.0283	−	37.1859i	1.76721	−	1.60171i
$540$	0.0486076	−	0.145224i	0.00209174	−	0.00624945i
$541$	−2.12326	−	2.86289i	−0.0912863	−	0.123085i	0.755203	−	0.655491i	$-0.227538\pi$
$541$	−2.12326	−	2.86289i	−0.0912863	−	0.123085i	−0.846489	+	0.532405i	$0.821288\pi$
$542$	−6.91198	−	24.0106i	−0.296895	−	1.03134i
$543$	0.800607	+	0.331622i	0.0343573	+	0.0142313i
$544$	−19.6984	+	31.2783i	−0.844563	+	1.34105i
$545$	−1.30730	+	0.541501i	−0.0559985	+	0.0231954i
$546$	0.812888	+	1.01976i	0.0347884	+	0.0436417i
$547$	−2.16801	+	14.6155i	−0.0926974	+	0.624915i	0.892182	+	0.451676i	$0.149174\pi$
$547$	−2.16801	+	14.6155i	−0.0926974	+	0.624915i	−0.984880	+	0.173240i	$0.944576\pi$
$548$	9.93898	+	1.26541i	0.424572	+	0.0540557i
$549$	−1.76032	+	35.8322i	−0.0751287	+	1.52928i
$550$	8.25094	−	31.0576i	0.351821	−	1.32430i
$551$	2.48886	−	25.2698i	0.106029	−	1.07653i
$552$	0.197501	−	0.0406000i	0.00840621	−	0.00172805i
$553$	−24.5122	+	29.8682i	−1.04236	+	1.27012i
$554$	1.07624	−	1.73899i	0.0457251	−	0.0738827i
$555$	0.0187036	−	0.0746690i	0.000793924	−	0.00316952i
$556$	9.79157	+	4.97684i	0.415255	+	0.211065i
$557$	−8.62282	+	0.423612i	−0.365361	+	0.0179490i	−0.230920	−	0.972973i	$-0.574174\pi$
$557$	−8.62282	+	0.423612i	−0.365361	+	0.0179490i	−0.134440	+	0.990922i	$0.542924\pi$
$558$	15.1094	+	23.3247i	0.639633	+	0.987414i
$559$	−29.5147	−	19.7211i	−1.24834	−	0.834114i
$560$	3.57440	−	0.681918i	0.151046	−	0.0288163i
$561$	−1.52716	+	1.02042i	−0.0644768	+	0.0430820i
$562$	−8.97112	+	20.8153i	−0.378424	+	0.878042i
$563$	−7.91247	+	3.74232i	−0.333471	+	0.157720i	−0.586955	−	0.809620i	$-0.699673\pi$
$563$	−7.91247	+	3.74232i	−0.333471	+	0.157720i	0.253484	+	0.967340i	$0.418423\pi$
$564$	−0.579059	+	0.404434i	−0.0243828	+	0.0170297i
$565$	0.576360	−	0.777132i	0.0242477	−	0.0326942i
$566$	14.8007	+	5.53461i	0.622121	+	0.232637i
$567$	37.4771	+	11.3686i	1.57389	+	0.477435i
$568$	−3.13292	+	4.28120i	−0.131455	+	0.179635i
$569$	16.9840	+	9.07814i	0.712006	+	0.380575i	0.787287	−	0.616587i	$-0.211485\pi$
$569$	16.9840	+	9.07814i	0.712006	+	0.380575i	−0.0752803	+	0.997162i	$0.523985\pi$
$570$	0.0404608	−	0.0824892i	0.00169472	−	0.00345509i
$571$	−0.372973	−	1.04239i	−0.0156084	−	0.0436227i	0.933487	−	0.358611i	$-0.116749\pi$
$571$	−0.372973	−	1.04239i	−0.0156084	−	0.0436227i	−0.949096	+	0.314988i	$0.897999\pi$
$572$	21.6791	+	22.9496i	0.906447	+	0.959572i
$573$	0.0215489	−	0.0359521i	0.000900218	−	0.00150192i
$574$	2.50656	+	29.7898i	0.104622	+	1.24340i
$575$	−4.07500	−	4.07500i	−0.169939	−	0.169939i
$576$	−23.4476	+	4.97656i	−0.976984	+	0.207357i
$577$	−5.72861	+	5.72861i	−0.238485	+	0.238485i	−0.816223	−	0.577738i	$-0.803936\pi$
$577$	−5.72861	+	5.72861i	−0.238485	+	0.238485i	0.577738	+	0.816223i	$0.303936\pi$
$578$	−27.7630	−	23.4535i	−1.15479	−	0.975538i
$579$	1.12743	+	0.675754i	0.0468543	+	0.0280834i
$580$	1.89732	+	0.849934i	0.0787818	+	0.0352916i
$581$	−22.0648	+	7.89491i	−0.915402	+	0.327536i
$582$	−0.495077	+	0.169234i	−0.0205216	+	0.00701496i
$583$	−13.2312	+	24.7538i	−0.547980	+	1.02520i
$584$	−17.1054	+	36.7728i	−0.707825	+	1.52167i
$585$	0.623739	−	2.05619i	0.0257884	−	0.0850131i
$586$	11.1502	−	5.08078i	0.460612	−	0.209885i
$587$	8.17923	+	6.06613i	0.337593	+	0.250376i	0.751193	−	0.660083i	$-0.229479\pi$
$587$	8.17923	+	6.06613i	0.337593	+	0.250376i	−0.413600	+	0.910459i	$0.635729\pi$
$588$	−0.318860	−	1.44644i	−0.0131496	−	0.0596500i
$589$	14.2663	+	30.1636i	0.587834	+	1.24287i
$590$	−1.18903	+	0.472802i	−0.0489515	+	0.0194650i
$591$	0.154264	+	0.230872i	0.00634556	+	0.00949680i
$592$	−23.1276	+	6.81821i	−0.950537	+	0.280227i
$593$	−7.39551	+	11.0682i	−0.303697	+	0.454515i	−0.951658	−	0.307159i	$-0.900622\pi$
$593$	−7.39551	+	11.0682i	−0.303697	+	0.454515i	0.647961	+	0.761673i	$0.275622\pi$
$594$	−2.33090	−	0.498229i	−0.0956380	−	0.0204426i
$595$	0.291682	+	5.93732i	0.0119578	+	0.243406i
$596$	−0.894204	+	11.5076i	−0.0366280	+	0.471371i
$597$	0.367415	+	0.0920327i	0.0150373	+	0.00376665i
$598$	5.51098	−	1.29737i	0.225361	−	0.0530535i
$599$	−17.1578	−	14.0811i	−0.701049	−	0.575336i	0.214897	−	0.976637i	$-0.431058\pi$
$599$	−17.1578	−	14.0811i	−0.701049	−	0.575336i	−0.915946	+	0.401300i	$0.868558\pi$
$600$	−0.611689	−	0.603916i	−0.0249721	−	0.0246547i
$601$	−9.64790	−	0.950236i	−0.393546	−	0.0387609i	−0.100691	−	0.994918i	$-0.532105\pi$
$601$	−9.64790	−	0.950236i	−0.393546	−	0.0387609i	−0.292855	+	0.956157i	$0.594605\pi$
$602$	31.9581	+	55.0816i	1.30252	+	2.24496i
$603$	36.5108	+	1.79366i	1.48683	+	0.0730435i
$604$	−8.43305	−	4.82101i	−0.343136	−	0.196164i
$605$	2.06350	+	0.306091i	0.0838931	+	0.0124444i
$606$	0.0936051	−	0.829233i	0.00380245	−	0.0336853i
$607$	−15.6095	−	37.6847i	−0.633570	−	1.52957i	−0.835104	−	0.550092i	$-0.814593\pi$
$607$	−15.6095	−	37.6847i	−0.633570	−	1.52957i	0.201534	−	0.979482i	$-0.435407\pi$
$608$	−28.6962	+	2.18821i	−1.16378	+	0.0887435i
$609$	0.511515	−	1.23491i	0.0207276	−	0.0500410i
$610$	−3.08629	−	1.70656i	−0.124960	−	0.0690967i
$611$	−15.9297	+	11.8143i	−0.644447	+	0.477955i
$612$	−2.72756	−	39.0623i	−0.110255	−	1.57900i
$613$	−31.2098	−	34.4347i	−1.26055	−	1.39080i	−0.886059	−	0.463573i	$-0.846567\pi$
$613$	−31.2098	−	34.4347i	−1.26055	−	1.39080i	−0.374492	−	0.927230i	$-0.622183\pi$
$614$	−14.1399	−	10.8021i	−0.570639	−	0.435937i
$615$	−0.0477732	+	0.0392064i	−0.00192640	+	0.00158096i
$616$	−16.7869	−	54.0913i	−0.676362	−	2.17940i
$617$	−4.61260	−	46.8325i	−0.185696	−	1.88541i	−0.411758	−	0.911293i	$-0.635085\pi$
$617$	−4.61260	−	46.8325i	−0.185696	−	1.88541i	0.226061	−	0.974113i	$-0.427415\pi$
$618$	−1.05112	−	0.171240i	−0.0422823	−	0.00688829i
$619$	−1.79173	+	1.07392i	−0.0720157	+	0.0431646i	−0.549657	−	0.835390i	$-0.685242\pi$
$619$	−1.79173	+	1.07392i	−0.0720157	+	0.0431646i	0.477642	+	0.878555i	$0.341492\pi$
$620$	−2.71270	+	0.323794i	−0.108945	+	0.0130039i
$621$	−0.287062	+	0.316724i	−0.0115194	+	0.0127097i
$622$	1.51877	+	8.24708i	0.0608973	+	0.330678i
$623$	9.48126	+	47.6655i	0.379859	+	1.90968i
$624$	0.820746	−	0.198764i	0.0328561	−	0.00795692i
$625$	−4.75069	+	23.8833i	−0.190027	+	0.955333i
$626$	−0.214303	+	15.0578i	−0.00856527	+	0.601832i
$627$	−1.34642	−	0.481756i	−0.0537708	−	0.0192395i
$628$	0.186729	+	9.05210i	0.00745129	+	0.361218i
$629$	−5.77956	−	38.9626i	−0.230446	−	1.55354i
$630$	−2.62909	+	2.81907i	−0.104745	+	0.112314i
$631$	−5.12384	−	9.58602i	−0.203977	−	0.381614i	0.759045	−	0.651039i	$-0.225666\pi$
$631$	−5.12384	−	9.58602i	−0.203977	−	0.381614i	−0.963021	+	0.269425i	$0.913166\pi$
$632$	10.8420	+	22.5493i	0.431272	+	0.896964i
$633$	−0.0781010	+	0.0236917i	−0.00310423	+	0.000941659i
$634$	11.2786	+	0.715100i	0.447931	+	0.0284003i
$635$	1.57415	−	3.32827i	0.0624684	−	0.132078i
$636$	0.399185	+	0.635881i	0.0158287	+	0.0252143i
$637$	−10.1055	−	40.3435i	−0.400395	−	1.59847i
$638$	9.83270	−	30.8278i	0.389280	−	1.22048i
$639$		−	5.61984i		−	0.222317i
$640$	0.575840	−	2.28489i	0.0227621	−	0.0903183i
$641$		−	21.9032i		−	0.865126i	−0.901604	−	0.432563i	$-0.857609\pi$
$641$		−	21.9032i		−	0.865126i	0.901604	−	0.432563i	$-0.142391\pi$
$642$	−1.06915	−	0.341011i	−0.0421960	−	0.0134586i
$643$	−1.62471	−	6.48620i	−0.0640723	−	0.255791i	0.929527	−	0.368754i	$-0.120216\pi$
$643$	−1.62471	−	6.48620i	−0.0640723	−	0.255791i	−0.993599	+	0.112964i	$0.963966\pi$
$644$	−9.90131	−	2.26420i	−0.390166	−	0.0892221i
$645$	−0.0562863	+	0.119007i	−0.00221627	+	0.00468591i
$646$	2.97489	−	46.9202i	0.117045	−	1.84605i
$647$	−41.4054	+	12.5602i	−1.62782	+	0.493793i	−0.966576	−	0.256382i	$-0.917470\pi$
$647$	−41.4054	+	12.5602i	−1.62782	+	0.493793i	−0.661240	+	0.750174i	$0.729970\pi$
$648$	16.9104	−	18.8992i	0.664302	−	0.742430i
$649$	9.38821	+	17.5641i	0.368520	+	0.689452i
$650$	−17.6513	−	16.4618i	−0.692342	−	0.645684i
$651$	0.257728	+	1.73746i	0.0101011	+	0.0680964i
$652$	6.28894	−	6.55387i	0.246294	−	0.256669i
$653$	16.8920	+	6.04405i	0.661035	+	0.236522i	0.645968	−	0.763364i	$-0.276454\pi$
$653$	16.8920	+	6.04405i	0.661035	+	0.236522i	0.0150667	+	0.999886i	$0.495204\pi$
$654$	0.589051	+	0.00838338i	0.0230337	+	0.000327816i
$655$	−0.430825	+	2.16591i	−0.0168337	+	0.0846289i
$656$	18.1752	+	6.66431i	0.709621	+	0.260197i
$657$	−8.38163	−	42.1373i	−0.326998	−	1.64393i
$658$	34.9911	−	6.44392i	1.36409	−	0.251210i
$659$	−10.7768	+	11.8903i	−0.419804	+	0.463182i	−0.913730	−	0.406322i	$-0.866811\pi$
$659$	−10.7768	+	11.8903i	−0.419804	+	0.463182i	0.493926	+	0.869504i	$0.335561\pi$
$660$	0.0723943	−	0.0920190i	0.00281794	−	0.00358183i
$661$	−20.9383	+	12.5500i	−0.814407	+	0.488137i	−0.859677	−	0.510838i	$-0.829335\pi$
$661$	−20.9383	+	12.5500i	−0.814407	+	0.488137i	0.0452697	+	0.998975i	$0.485585\pi$
$662$	−2.39740	+	14.7159i	−0.0931775	+	0.571950i
$663$	0.135218	+	1.37289i	0.00525143	+	0.0533186i
$664$	−1.39082	+	15.1112i	−0.0539743	+	0.586428i
$665$	−3.57767	+	2.93612i	−0.138736	+	0.113858i
$666$	15.5059	−	20.2971i	0.600841	−	0.786497i
$667$	−3.89701	−	4.29969i	−0.150893	−	0.166484i
$668$	5.23699	−	6.02325i	0.202625	−	0.233046i
$669$	−0.743259	+	0.551238i	−0.0287360	+	0.0213121i
$670$	−1.73888	+	3.14474i	−0.0671790	+	0.121492i
$671$	−21.0056	+	50.7120i	−0.810913	+	1.95772i
$672$	−1.47898	−	0.328271i	−0.0570528	−	0.0126633i
$673$	−12.4159	−	29.9747i	−0.478599	−	1.15544i	−0.960266	−	0.279086i	$-0.909969\pi$
$673$	−12.4159	−	29.9747i	−0.478599	−	1.15544i	0.481667	−	0.876354i	$-0.340031\pi$
$674$	−8.68882	−	0.980808i	−0.334681	−	0.0377793i
$675$	1.80258	+	0.267387i	0.0693812	+	0.0102917i
$676$	−2.20747	+	0.601586i	−0.0849026	+	0.0231379i
$677$	20.0580	+	0.985386i	0.770891	+	0.0378715i	0.430712	−	0.902489i	$-0.358262\pi$
$677$	20.0580	+	0.985386i	0.770891	+	0.0378715i	0.340179	+	0.940361i	$0.389512\pi$
$678$	−0.348417	+	0.202150i	−0.0133809	+	0.00776353i
$679$	26.2288	+	2.58331i	1.00657	+	0.0991382i
$680$	3.56566	+	1.45030i	0.136737	+	0.0556166i
$681$	−0.963747	−	0.790927i	−0.0369309	−	0.0303084i
$682$	9.74373	+	41.3895i	0.373107	+	1.58488i
$683$	24.5813	+	6.15728i	0.940576	+	0.235602i	0.682802	−	0.730603i	$-0.260761\pi$
$683$	24.5813	+	6.15728i	0.940576	+	0.235602i	0.257774	+	0.966205i	$0.417011\pi$
$684$	23.1629	−	19.8227i	0.885655	−	0.757939i
$685$	−0.0511955	−	1.04211i	−0.00195608	−	0.0398169i
$686$	−6.55754	+	30.6786i	−0.250368	+	1.17132i
$687$	0.245118	−	0.366845i	0.00935183	−	0.0139960i
$688$	41.0685	−	3.72017i	1.56572	−	0.141830i
$689$	11.7124	+	17.5288i	0.446206	+	0.667794i
$690$	−0.00775839	−	0.0195112i	−0.000295357	−	0.000742779i
$691$	3.24777	+	6.86683i	0.123551	+	0.261226i	0.956279	−	0.292456i	$-0.0944723\pi$
$691$	3.24777	+	6.86683i	0.123551	+	0.261226i	−0.832728	+	0.553682i	$0.813222\pi$
$692$	9.50324	+	6.07016i	0.361259	+	0.230753i
$693$	48.1897	+	35.7399i	1.83057	+	1.35765i
$694$	−4.53551	−	9.95360i	−0.172166	−	0.377833i
$695$	0.332031	−	1.09456i	0.0125947	−	0.0415191i
$696$	−0.585354	−	0.637597i	−0.0221878	−	0.0241681i
$697$	−14.9075	+	27.8900i	−0.564662	+	1.05641i
$698$	−10.8409	−	31.7139i	−0.410333	−	1.20039i
$699$	−0.788146	+	0.282003i	−0.0298104	+	0.0106663i
$700$	15.4251	+	40.4595i	0.583014	+	1.52923i
$701$	−31.3076	−	18.7650i	−1.18247	−	0.708746i	−0.218782	−	0.975774i	$-0.570209\pi$
$701$	−31.3076	−	18.7650i	−1.18247	−	0.708746i	−0.963689	+	0.267028i	$0.913959\pi$
$702$	−1.15531	+	1.36760i	−0.0436045	+	0.0516166i
$703$	21.6850	−	21.6850i	0.817867	−	0.817867i
$704$	−36.3435	−	4.91692i	−1.36975	−	0.185313i
$705$	0.0520096	+	0.0520096i	0.00195880	+	0.00195880i
$706$	28.4645	−	2.39505i	1.07128	−	0.0901388i
$707$	−21.6112	+	36.0562i	−0.812774	+	1.35603i
$708$	0.532512	+	0.0151605i	0.0200130	+	0.000569767i
$709$	9.34931	+	26.1296i	0.351121	+	0.981316i	0.979152	+	0.203129i	$0.0651109\pi$
$709$	9.34931	+	26.1296i	0.351121	+	0.981316i	−0.628031	+	0.778188i	$0.716139\pi$
$710$	0.495999	+	0.243287i	0.0186145	+	0.00913039i
$711$	−23.3752	−	12.4943i	−0.876640	−	0.468574i
$712$	30.5755	+	7.45132i	1.14587	+	0.279250i
$713$	7.29716	+	2.21357i	0.273281	+	0.0828988i
$714$	0.866832	−	2.31809i	0.0324404	−	0.0867525i
$715$	1.95842	−	2.64062i	0.0732406	−	0.0987535i
$716$	9.06865	+	1.61019i	0.338912	+	0.0601756i
$717$	−0.854526	+	0.404161i	−0.0319129	+	0.0150937i
$718$	−36.1116	−	15.5636i	−1.34767	−	0.580828i
$719$	−7.06205	+	4.71871i	−0.263370	+	0.175978i	−0.680243	−	0.732986i	$-0.738126\pi$
$719$	−7.06205	+	4.71871i	−0.263370	+	0.175978i	0.416873	+	0.908965i	$0.363126\pi$
$720$	0.937130	+	2.31355i	0.0349248	+	0.0862209i
$721$	44.6058	+	29.8046i	1.66121	+	1.10998i
$722$	8.16982	−	5.29230i	0.304049	−	0.196959i
$723$	0.794684	−	0.0390403i	0.0295546	−	0.00145192i
$724$	−26.8748	+	8.76158i	−0.998794	+	0.325622i
$725$	−6.01100	+	23.9972i	−0.223243	+	0.891235i
$726$	−0.738505	−	0.457052i	−0.0274085	−	0.0169628i
$727$	−8.69905	+	10.5998i	−0.322630	+	0.393126i	−0.908917	−	0.416978i	$-0.863089\pi$
$727$	−8.69905	+	10.5998i	−0.322630	+	0.393126i	0.586287	+	0.810104i	$0.300589\pi$
$728$	−41.7739	−	8.03202i	−1.54824	−	0.297686i
$729$	−2.62659	+	26.6682i	−0.0972810	+	0.987710i
$730$	4.08182	+	1.08440i	0.151075	+	0.0401355i
$731$	−3.30542	+	67.2833i	−0.122255	+	2.48856i
$732$	0.898782	+	1.16103i	0.0332199	+	0.0429130i
$733$	0.486630	−	3.28060i	0.0179741	−	0.121172i	−0.978332	−	0.207041i	$-0.933617\pi$
$733$	0.486630	−	3.28060i	0.0179741	−	0.121172i	0.996306	+	0.0858692i	$0.0273667\pi$
$734$	−1.80445	+	1.43839i	−0.0666034	+	0.0530920i
$735$	−0.142502	+	0.0590263i	−0.00525627	+	0.00217722i
$736$	−4.03357	+	5.19501i	−0.148679	+	0.191491i
$737$	51.6725	+	21.4034i	1.90338	+	0.788406i
$738$	−19.7067	+	5.67301i	−0.725414	+	0.208826i
$739$	15.5930	+	21.0247i	0.573597	+	0.773406i	0.990789	−	0.135412i	$-0.0432359\pi$
$739$	15.5930	+	21.0247i	0.573597	+	0.773406i	−0.417192	+	0.908818i	$0.636986\pi$
$740$	1.12013	+	2.24720i	0.0411769	+	0.0826089i
$741$	−0.795834	+	0.721302i	−0.0292357	+	0.0264977i
$742$	−5.01646	−	37.4862i	−0.184160	−	1.37616i
$743$	−12.5827	−	15.3321i	−0.461615	−	0.562480i	0.489226	−	0.872157i	$-0.337279\pi$
$743$	−12.5827	−	15.3321i	−0.461615	−	0.562480i	−0.950842	+	0.309677i	$0.899779\pi$
$744$	1.09051	+	0.323202i	0.0399800	+	0.0118492i
$745$	1.19619	−	0.117814i	0.0438249	−	0.00431638i
$746$	31.7043	−	22.8214i	1.16078	−	0.835550i
$747$	−8.26442	−	13.7883i	−0.302379	−	0.504489i
$748$	16.2054	−	57.6786i	0.592528	−	2.10894i
$749$	41.8861	+	37.9633i	1.53048	+	1.38715i
$750$	−0.102015	+	0.148070i	−0.00372505	+	0.00540676i
$751$	10.6066	−	2.10978i	0.387039	−	0.0769868i	0.00226432	−	0.999997i	$-0.499279\pi$
$751$	10.6066	−	2.10978i	0.387039	−	0.0769868i	0.384774	+	0.923011i	$0.374279\pi$
$752$	5.77308	−	22.3044i	0.210523	−	0.813357i
$753$	0.360297	+	0.0716676i	0.0131300	+	0.00261171i
$754$	−16.9391	−	17.4282i	−0.616885	−	0.634698i
$755$	−0.340785	+	0.952431i	−0.0124025	+	0.0346625i
$756$	2.94127	−	1.29001i	0.106973	−	0.0469171i
$757$	33.9294	−	5.03296i	1.23319	−	0.182926i	0.501857	−	0.864951i	$-0.332650\pi$
$757$	33.9294	−	5.03296i	1.23319	−	0.182926i	0.731329	+	0.682025i	$0.238900\pi$
$758$	34.7467	−	1.21163i	1.26206	−	0.0440085i
$759$	−0.288216	+	0.154055i	−0.0104616	+	0.00559183i
$760$	0.746784	+	2.90246i	0.0270887	+	0.105283i
$761$	−14.9153	−	49.1692i	−0.540680	−	1.78238i	−0.618928	−	0.785448i	$-0.712433\pi$
$761$	−14.9153	−	49.1692i	−0.540680	−	1.78238i	0.0782483	−	0.996934i	$-0.475067\pi$
$762$	−1.15028	+	1.01312i	−0.0416703	+	0.0367013i
$763$	−26.8265	−	12.6880i	−0.971185	−	0.459336i
$764$	0.228468	+	1.34803i	0.00826569	+	0.0487701i
$765$	−3.95551	+	0.990804i	−0.143012	+	0.0358226i
$766$	−15.4659	+	7.98586i	−0.558807	+	0.288541i
$767$	14.9586			0.540122
$768$	−0.596667	+	0.778702i	−0.0215304	+	0.0280990i
$769$	−3.67279			−0.132444			−0.0662221	−	0.997805i	$-0.521095\pi$
$769$	−3.67279			−0.132444			−0.0662221	+	0.997805i	$0.521095\pi$
$770$	−5.24052	+	2.70595i	−0.188855	+	0.0975156i
$771$	−0.576790	+	0.144478i	−0.0207726	+	0.00520326i
$772$	−42.2731	+	7.16456i	−1.52144	+	0.257858i
$773$	−18.7294	−	8.85833i	−0.673649	−	0.318612i	0.0599438	−	0.998202i	$-0.480908\pi$
$773$	−18.7294	−	8.85833i	−0.673649	−	0.318612i	−0.733592	+	0.679590i	$0.762158\pi$
$774$	−32.7813	+	28.8723i	−1.17830	+	1.03779i
$775$	−9.43673	−	31.1087i	−0.338978	−	1.11746i
$776$	8.68017	−	14.6943i	0.311600	−	0.527493i
$777$	1.42372	−	0.760996i	0.0510758	−	0.0273006i
$778$	42.6912	−	1.48866i	1.53055	−	0.0533711i
$779$	−24.3553	+	3.61276i	−0.872618	+	0.129441i
$780$	−0.0353217	−	0.0805348i	−0.00126472	−	0.00288361i
$781$	2.89675	−	8.09587i	0.103654	−	0.289693i
$782$	−7.48851	−	7.70474i	−0.267789	−	0.275521i
$783$	1.79969	+	0.357981i	0.0643157	+	0.0127932i
$784$	38.5799	+	29.0842i	1.37785	+	1.03872i
$785$	0.924737	−	0.183942i	0.0330053	−	0.00656516i
$786$	0.521616	−	0.757104i	0.0186054	−	0.0270050i
$787$	−4.78216	−	4.33430i	−0.170466	−	0.154501i	0.581868	−	0.813283i	$-0.302322\pi$
$787$	−4.78216	−	4.33430i	−0.170466	−	0.154501i	−0.752334	+	0.658782i	$0.771072\pi$
$788$	−8.71969	−	2.44989i	−0.310626	−	0.0872737i
$789$	−0.285786	−	0.476805i	−0.0101743	−	0.0169747i
$790$	2.11466	−	1.52218i	0.0752363	−	0.0541567i
$791$	20.1935	−	1.98889i	0.717999	−	0.0707167i
$792$	34.1453	−	18.5327i	1.21330	−	0.658533i
$793$	26.1546	+	31.8694i	0.928776	+	1.13172i
$794$	−2.22487	−	16.6257i	−0.0789578	−	0.590023i
$795$	0.0579314	−	0.0525060i	0.00205461	−	0.00186219i
$796$	−11.0576	+	5.51171i	−0.391925	+	0.195357i
$797$	31.7936	+	42.8687i	1.12619	+	1.51849i	0.825184	+	0.564865i	$0.191072\pi$
$797$	31.7936	+	42.8687i	1.12619	+	1.51849i	0.301004	+	0.953623i	$0.402678\pi$
$798$	1.85167	−	0.533044i	0.0655485	−	0.0188696i
$799$	34.7723	+	14.4032i	1.23016	+	0.509548i
$800$	27.9679	+	1.99343i	0.988816	+	0.0704784i
$801$	−30.7999	+	12.7577i	−1.08826	+	0.450772i
$802$	−27.9006	+	22.2405i	−0.985203	+	0.785341i
$803$	9.64522	−	65.0228i	0.340372	−	2.29460i
$804$	1.18302	−	0.915804i	0.0417220	−	0.0322979i
$805$	−0.0518990	+	1.05643i	−0.00182920	+	0.0372342i
$806$	30.8665	+	8.20017i	1.08722	+	0.288839i
$807$	0.106539	−	1.08171i	0.00375035	−	0.0380780i
$808$	15.2675	+	22.5361i	0.537108	+	0.792817i
$809$	6.12954	−	7.46887i	0.215503	−	0.262591i	−0.654027	−	0.756471i	$-0.726922\pi$
$809$	6.12954	−	7.46887i	0.215503	−	0.262591i	0.869530	+	0.493880i	$0.164422\pi$
$810$	−2.24564	−	1.38980i	−0.0789038	−	0.0488326i
$811$	−3.60475	+	14.3910i	−0.126580	+	0.505335i	0.873257	+	0.487260i	$0.162004\pi$
$811$	−3.60475	+	14.3910i	−0.126580	+	0.505335i	−0.999837	+	0.0180747i	$0.994246\pi$
$812$	13.5144	+	41.4534i	0.474263	+	1.45473i
$813$	1.08195	−	0.0531529i	0.0379458	−	0.00186416i
$814$	32.7998	−	21.2472i	1.14963	−	0.744715i
$815$	−0.786478	−	0.525508i	−0.0275491	−	0.0184077i
$816$	−1.12429	−	1.14205i	−0.0393579	−	0.0399797i
$817$	−43.6092	+	29.1387i	−1.52569	+	1.01943i
$818$	−32.0742	−	13.8235i	−1.12145	−	0.483328i
$819$	40.7364	−	19.2669i	1.42345	−	0.673240i
$820$	0.352426	−	1.98488i	0.0123072	−	0.0693149i
$821$	19.3407	−	26.0780i	0.674997	−	0.910128i	−0.324362	−	0.945933i	$-0.605150\pi$
$821$	19.3407	−	26.0780i	0.674997	−	0.910128i	0.999359	+	0.0358052i	$0.0113996\pi$
$822$	−0.152145	+	0.406868i	−0.00530666	+	0.0141911i
$823$	35.6816	+	10.8239i	1.24378	+	0.377297i	0.842520	−	0.538665i	$-0.181071\pi$
$823$	35.6816	+	10.8239i	1.24378	+	0.377297i	0.401263	+	0.915963i	$0.368571\pi$
$824$	29.6817	−	18.0495i	1.03401	−	0.628785i
$825$	1.22870	+	0.656755i	0.0427779	+	0.0228653i
$826$	−24.0932	−	11.8177i	−0.838311	−	0.411190i
$827$	−10.3012	−	28.7899i	−0.358207	−	1.00112i	−0.976564	−	0.215225i	$-0.930951\pi$
$827$	−10.3012	−	28.7899i	−0.358207	−	1.00112i	0.618357	−	0.785897i	$-0.287799\pi$
$828$	0.198277	−	6.96447i	0.00689060	−	0.242032i
$829$	−8.84339	+	14.7543i	−0.307143	+	0.512438i	−0.972138	−	0.234411i	$-0.924684\pi$
$829$	−8.84339	+	14.7543i	−0.307143	+	0.512438i	0.664994	+	0.746849i	$0.268434\pi$
$830$	1.57471	−	0.132499i	0.0546591	−	0.00459909i
$831$	0.0626956	+	0.0626956i	0.00217489	+	0.00217489i
$832$	−16.1249	+	22.3332i	−0.559030	+	0.774265i
$833$	−55.8098	+	55.8098i	−1.93370	+	1.93370i
$834$	−0.307308	+	0.363774i	−0.0106412	+	0.0125965i
$835$	−0.712921	−	0.427308i	−0.0246716	−	0.0147876i
$836$	43.5858	−	16.6170i	1.50745	−	0.574711i
$837$	−2.27032	+	0.812333i	−0.0784737	+	0.0280783i
$838$	17.1852	+	50.2735i	0.593651	+	1.73667i
$839$	1.83275	−	3.42884i	0.0632737	−	0.118377i	−0.848296	−	0.529522i	$-0.822371\pi$
$839$	1.83275	−	3.42884i	0.0632737	−	0.118377i	0.911570	+	0.411146i	$0.134871\pi$
$840$	−0.00673337	+	0.157620i	−0.000232323	+	0.00543840i
$841$	1.18716	−	3.91355i	0.0409367	−	0.134950i
$842$	−5.53943	−	12.1568i	−0.190901	−	0.418951i
$843$	−0.789310	−	0.585392i	−0.0271853	−	0.0201620i
$844$	1.43309	−	2.24360i	0.0493290	−	0.0772279i
$845$	0.101870	+	0.215386i	0.00350443	+	0.00740949i
$846$	9.01808	+	22.6791i	0.310048	+	0.779725i
$847$	24.3058	+	36.3762i	0.835158	+	1.24990i
$848$	−23.3795	−	7.29264i	−0.802854	−	0.250430i
$849$	−0.380612	+	0.569627i	−0.0130626	+	0.0195495i
$850$	−9.57441	+	44.7927i	−0.328400	+	1.53638i
$851$	−0.343890	−	7.00004i	−0.0117884	−	0.239958i
$852$	−0.149548	−	0.174747i	−0.00512342	−	0.00598674i
$853$	−34.3656	−	8.60815i	−1.17666	−	0.294737i	−0.395140	−	0.918621i	$-0.629304\pi$
$853$	−34.3656	−	8.60815i	−1.17666	−	0.294737i	−0.781517	+	0.623884i	$0.785554\pi$
$854$	−16.9485	−	71.9939i	−0.579966	−	2.46358i
$855$	−2.45416	−	2.01408i	−0.0839305	−	0.0688800i
$856$	33.7292	−	14.2244i	1.15284	−	0.486181i
$857$	−3.58887	−	0.353473i	−0.122593	−	0.0120744i	0.0365343	−	0.999332i	$-0.488368\pi$
$857$	−3.58887	−	0.353473i	−0.122593	−	0.0120744i	−0.159128	+	0.987258i	$0.550868\pi$
$858$	−1.18389	+	0.686886i	−0.0404172	+	0.0234499i
$859$	−15.6656	−	0.769602i	−0.534504	−	0.0262585i	−0.219973	−	0.975506i	$-0.570597\pi$
$859$	−15.6656	−	0.769602i	−0.534504	−	0.0262585i	−0.314530	+	0.949247i	$0.601847\pi$
$860$	−1.12910	−	4.14314i	−0.0385020	−	0.141280i
$861$	−1.28208	−	0.190178i	−0.0436930	−	0.00648125i
$862$	53.8644	+	6.08031i	1.83463	+	0.207096i
$863$	20.9030	+	50.4644i	0.711548	+	1.71783i	0.696097	+	0.717948i	$0.254918\pi$
$863$	20.9030	+	50.4644i	0.711548	+	1.71783i	0.0154509	+	0.999881i	$0.495082\pi$
$864$	0.0458916	−	2.07923i	0.00156126	−	0.0707370i
$865$	0.449381	−	1.08490i	0.0152794	−	0.0368878i
$866$	−7.43427	+	13.4448i	−0.252627	+	0.456871i
$867$	1.26559	−	0.938629i	0.0429818	−	0.0318775i
$868$	−43.2372	−	37.5931i	−1.46757	−	1.27599i
$869$	−27.2339	−	30.0480i	−0.923846	−	1.01931i
$870$	−0.0547181	+	0.0716256i	−0.00185512	+	0.00242833i
$871$	32.4730	−	26.6499i	1.10031	−	0.902998i
$872$	−14.7762	+	12.2855i	−0.500386	+	0.416039i
$873$	1.77206	+	17.9920i	0.0599752	+	0.608939i
$874$	1.34507	−	8.25643i	0.0454977	−	0.279278i
$875$	7.76906	−	4.65659i	0.262642	−	0.157422i
$876$	−1.38193	−	1.08721i	−0.0466910	−	0.0367333i
$877$	4.05621	−	4.47534i	0.136969	−	0.151122i	−0.668604	−	0.743619i	$-0.733108\pi$
$877$	4.05621	−	4.47534i	0.136969	−	0.151122i	0.805573	+	0.592497i	$0.201858\pi$
$878$	3.58787	−	0.660739i	0.121085	−	0.0222988i
$879$	0.103640	+	0.521033i	0.00349569	+	0.0175740i
$880$	0.157498	+	3.81592i	0.00530926	+	0.128635i
$881$	−3.11207	+	15.6454i	−0.104848	+	0.527107i	0.892287	+	0.451468i	$0.149100\pi$
$881$	−3.11207	+	15.6454i	−0.104848	+	0.527107i	−0.997135	+	0.0756389i	$0.975900\pi$
$882$	−51.1760	−	0.728336i	−1.72318	−	0.0245244i
$883$	−55.7403	−	19.9442i	−1.87581	−	0.671175i	−0.967497	−	0.252884i	$-0.918621\pi$
$883$	−55.7403	−	19.9442i	−1.87581	−	0.671175i	−0.908313	−	0.418292i	$-0.862629\pi$
$884$	−32.4689	−	31.1564i	−1.09205	−	1.04790i
$885$	−0.00814008	−	0.0548760i	−0.000273626	−	0.00184464i
$886$	20.4937	+	19.1126i	0.688499	+	0.642101i
$887$	−16.7947	−	31.4206i	−0.563910	−	1.05500i	−0.988728	−	0.149722i	$-0.952162\pi$
$887$	−16.7947	−	31.4206i	−0.563910	−	1.05500i	0.424819	−	0.905279i	$-0.360338\pi$
$888$	−0.0579687	−	1.04375i	−0.00194530	−	0.0350261i
$889$	73.8892	−	22.4140i	2.47816	−	0.751743i
$890$	0.207369	−	3.27064i	0.00695103	−	0.109632i
$891$	−17.5742	+	37.1575i	−0.588758	+	1.24482i
$892$	6.72886	−	29.4251i	0.225299	−	0.985227i
$893$	7.12016	+	28.4253i	0.238267	+	0.951216i
$894$	−0.476755	−	0.152064i	−0.0159451	−	0.00508577i
$895$		−	0.959148i		−	0.0320608i
$896$	43.6157	−	23.2323i	1.45710	−	0.776135i
$897$			0.245461i			0.00819569i
$898$	−13.3807	+	41.9515i	−0.446519	+	1.39994i
$899$	−7.95376	−	31.7532i	−0.265273	−	1.05903i
$900$	−25.1563	+	15.7923i	−0.838544	+	0.526410i
$901$	17.1055	−	36.1666i	0.569867	−	1.20488i
$902$	−31.3134	−	1.98537i	−1.04262	−	0.0661056i
$903$	−2.64203	+	0.801450i	−0.0879211	+	0.0266706i
$904$	4.34737	−	12.3995i	0.144592	−	0.412401i
$905$	1.38761	+	2.59604i	0.0461258	+	0.0862953i
$906$	0.287235	−	0.307991i	0.00954274	−	0.0102323i
$907$	−3.79661	−	25.5947i	−0.126064	−	0.849857i	−0.956288	−	0.292426i	$-0.905537\pi$
$907$	−3.79661	−	25.5947i	−0.126064	−	0.849857i	0.830224	−	0.557430i	$-0.188213\pi$
$908$	40.6593	−	0.838730i	1.34933	−	0.0278342i
$909$	−27.1502	−	9.71450i	−0.900515	−	0.322209i
$910$	−0.0630395	+	4.42942i	−0.00208974	+	0.146834i
$911$	0.756394	−	3.80265i	0.0250605	−	0.125987i	−0.966230	−	0.257681i	$-0.917042\pi$
$911$	0.756394	−	3.80265i	0.0250605	−	0.125987i	0.991290	+	0.131694i	$0.0420416\pi$
$912$	0.192748	−	1.23276i	0.00638252	−	0.0408208i
$913$	−4.79841	−	24.1232i	−0.158804	−	0.798362i
$914$	−3.46810	−	18.8321i	−0.114715	−	0.622911i
$915$	0.102681	−	0.113291i	0.00339454	−	0.00374530i
$916$	1.70571	+	14.2902i	0.0563583	+	0.472162i
$917$	−39.7243	+	23.8098i	−1.31181	+	0.786270i
$918$	3.35327	+	0.546288i	0.110674	+	0.0180302i
$919$	−5.25989	−	53.4046i	−0.173508	−	1.76165i	−0.549934	−	0.835208i	$-0.685347\pi$
$919$	−5.25989	−	53.4046i	−0.173508	−	1.76165i	0.376426	−	0.926447i	$-0.377153\pi$
$920$	0.606091	+	0.318996i	0.0199822	+	0.0105170i
$921$	0.596342	−	0.489405i	0.0196501	−	0.0161265i
$922$	23.5993	+	18.0286i	0.777203	+	0.593741i
$923$	−4.33711	−	4.78527i	−0.142758	−	0.157509i
$924$	2.44951	−	0.171039i	0.0805829	−	0.00562677i
$925$	−23.9983	+	17.7984i	−0.789059	+	0.585206i
$926$	−14.0364	−	7.76139i	−0.461263	−	0.255055i
$927$	−14.0827	+	33.9987i	−0.462538	+	1.11667i
$928$	28.0297	+	3.38670i	0.920118	+	0.111174i
$929$	18.6713	+	45.0766i	0.612586	+	1.47891i	0.860149	+	0.510042i	$0.170370\pi$
$929$	18.6713	+	45.0766i	0.612586	+	1.47891i	−0.247563	+	0.968872i	$0.579630\pi$
$930$	0.0132858	−	0.117697i	0.000435659	−	0.00385943i
$931$	−60.7856	−	9.01669i	−1.99217	−	0.295510i
$932$	13.5515	−	23.7047i	0.443895	−	0.776474i
$933$	−0.363128	−	0.0178393i	−0.0118883	−	0.000584033i
$934$	5.47954	+	9.44429i	0.179296	+	0.309027i
$935$	−6.20897	−	0.611530i	−0.203055	−	0.0199992i
$936$	−0.186586	−	29.1798i	−0.00609875	−	0.953771i
$937$	−43.8637	−	35.9980i	−1.43296	−	1.17600i	−0.954618	−	0.297832i	$-0.903737\pi$
$937$	−43.8637	−	35.9980i	−1.43296	−	1.17600i	−0.478346	−	0.878172i	$-0.658763\pi$
$938$	−73.3574	+	17.2695i	−2.39520	+	0.563869i
$939$	−0.633333	−	0.158642i	−0.0206680	−	0.00517707i
$940$	−2.39203	−	0.185873i	−0.0780194	−	0.00606252i
$941$	1.65567	+	33.7019i	0.0539732	+	1.09865i	0.861154	+	0.508345i	$0.169742\pi$
$941$	1.65567	+	33.7019i	0.0539732	+	1.09865i	−0.807181	+	0.590305i	$0.799008\pi$
$942$	−0.383867	−	0.0820514i	−0.0125071	−	0.00267338i
$943$	−3.12613	+	4.67858i	−0.101801	+	0.152356i
$944$	−13.5188	+	10.9184i	−0.439998	+	0.355363i
$945$	−0.185815	−	0.278091i	−0.00604455	−	0.00904630i
$946$	−62.1066	+	24.6959i	−2.01926	+	0.802934i
$947$	−8.69522	−	18.3845i	−0.282557	−	0.597416i	0.711933	−	0.702247i	$-0.247820\pi$
$947$	−8.69522	−	18.3845i	−0.282557	−	0.597416i	−0.994490	+	0.104831i	$0.966570\pi$
$948$	−1.05933	+	0.233524i	−0.0344054	+	0.00758450i
$949$	−39.6564	−	29.4112i	−1.28730	−	0.954727i
$950$	−32.4520	+	14.7873i	−1.05288	+	0.479763i
$951$	−0.142230	+	0.468870i	−0.00461213	+	0.0152041i
$952$	27.6820	+	75.8339i	0.897180	+	2.45779i
$953$	−15.6013	+	29.1880i	−0.505376	+	0.945491i	0.491823	+	0.870695i	$0.336331\pi$
$953$	−15.6013	+	29.1880i	−0.505376	+	0.945491i	−0.997199	+	0.0747963i	$0.976169\pi$
$954$	24.5488	−	8.39160i	0.794798	−	0.271688i
$955$	0.134058	−	0.0479667i	0.00433802	−	0.00155217i
$956$	12.6058	−	28.1400i	0.407700	−	0.910113i
$957$	1.20329	+	0.721225i	0.0388969	+	0.0233139i
$958$	−17.3428	−	14.6508i	−0.560321	−	0.473346i
$959$	15.4726	−	15.4726i	0.499635	−	0.499635i
$960$	0.0907049	+	0.0470014i	0.00292749	+	0.00151697i
$961$	8.49614	+	8.49614i	0.274069	+	0.274069i
$962$	−2.46110	−	29.2496i	−0.0793491	−	0.943044i
$963$	−19.9358	+	33.2608i	−0.642421	+	1.07182i
$964$	−18.8666	+	17.8221i	−0.607652	+	0.574010i
$965$	1.50419	+	4.20394i	0.0484217	+	0.135330i
$966$	0.193921	−	0.395355i	0.00623931	−	0.0127203i
$967$	39.6363	+	21.1861i	1.27462	+	0.681297i	0.963151	−	0.268960i	$-0.0866798\pi$
$967$	39.6363	+	21.1861i	1.27462	+	0.681297i	0.311466	+	0.950257i	$0.399180\pi$
$968$	27.9960	−	4.33594i	0.899824	−	0.139362i
$969$	1.95054	+	0.591691i	0.0626605	+	0.0190079i
$970$	−1.66467	−	0.622489i	−0.0534492	−	0.0199869i
$971$	21.5208	−	29.0174i	0.690634	−	0.931212i	−0.309170	−	0.951007i	$-0.600051\pi$
$971$	21.5208	−	29.0174i	0.690634	−	0.931212i	0.999804	+	0.0197948i	$0.00630129\pi$
$972$	1.89267	+	2.70988i	0.0607074	+	0.0869193i
$973$	21.6850	−	10.2562i	0.695189	−	0.328800i
$974$	13.6400	−	31.6484i	0.437055	−	1.01408i
$975$	0.870075	−	0.581366i	0.0278647	−	0.0186186i
$976$	−46.8989	−	9.71146i	−1.50120	−	0.310856i
$977$	6.74459	+	4.50659i	0.215779	+	0.144179i	0.658763	−	0.752351i	$-0.271080\pi$
$977$	6.74459	+	4.50659i	0.215779	+	0.144179i	−0.442984	+	0.896530i	$0.646080\pi$
$978$	0.214103	+	0.330515i	0.00684625	+	0.0105687i
$979$	−50.9459	+	2.50281i	−1.62824	+	0.0799902i
$980$	2.27973	−	4.48519i	0.0728232	−	0.143274i
$981$	4.94623	−	19.7465i	0.157921	−	0.630456i
$982$	6.95583	−	11.2392i	0.221970	−	0.358659i
$983$	−5.22253	+	6.36367i	−0.166573	+	0.202970i	−0.849606	−	0.527418i	$-0.823160\pi$
$983$	−5.22253	+	6.36367i	−0.166573	+	0.202970i	0.683033	+	0.730387i	$0.260660\pi$
$984$	−0.461812	+	0.700810i	−0.0147220	+	0.0223410i
$985$	−0.0924494	+	0.938655i	−0.00294568	+	0.0299080i
$986$	−11.8424	+	44.5762i	−0.377138	+	1.41960i
$987$	−0.0756895	+	1.54069i	−0.00240922	+	0.0490408i
$988$	4.42493	−	34.7549i	0.140776	−	1.10570i
$989$	−1.75874	+	11.8564i	−0.0559245	+	0.377013i
$990$	−2.52184	−	3.16362i	−0.0801493	−	0.100547i
$991$	−0.461741	+	0.191259i	−0.0146677	+	0.00607555i	−0.390005	−	0.920813i	$-0.627527\pi$
$991$	−0.461741	+	0.191259i	−0.0146677	+	0.00607555i	0.375338	+	0.926888i	$0.377527\pi$
$992$	−33.8809	+	15.1188i	−1.07572	+	0.480023i
$993$	−0.597215	−	0.247375i	−0.0189520	−	0.00785019i
$994$	3.20514	+	11.1339i	0.101661	+	0.353146i
$995$	0.766436	+	1.03342i	0.0242977	+	0.0327616i
$996$	−0.623897	−	0.208823i	−0.0197689	−	0.00661680i
$997$	25.1397	−	22.7853i	0.796183	−	0.721618i	−0.168308	−	0.985735i	$-0.553830\pi$
$997$	25.1397	−	22.7853i	0.796183	−	0.721618i	0.964491	+	0.264116i	$0.0850802\pi$
$998$	4.49862	−	0.602013i	0.142401	−	0.0190564i
$999$	1.40592	+	1.71312i	0.0444813	+	0.0542006i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	256.2.m.a.101.10	✓	992
256.109	even	64	inner	256.2.m.a.109.10	yes	992

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
256.2.m.a.101.10	✓	992	1.1	even	1	trivial
256.2.m.a.109.10	yes	992	256.109	even	64	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 256 = 2^{8} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	256.m (of order \(64\), degree \(32\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.648839 - 1.25659i) q^{2} +(0.0594759 - 0.0148979i) q^{3} +(-1.15801 + 1.63064i) q^{4} +(0.188276 + 0.0890481i) q^{5} +(-0.0573108 - 0.0650702i) q^{6} +(1.26794 + 4.17983i) q^{7} +(2.80041 + 0.397118i) q^{8} +(-2.64245 + 1.41242i) q^{9} +O(q^{10})\)	\(q+(-0.648839 - 1.25659i) q^{2} +(0.0594759 - 0.0148979i) q^{3} +(-1.15801 + 1.63064i) q^{4} +(0.188276 + 0.0890481i) q^{5} +(-0.0573108 - 0.0650702i) q^{6} +(1.26794 + 4.17983i) q^{7} +(2.80041 + 0.397118i) q^{8} +(-2.64245 + 1.41242i) q^{9} +(-0.0102646 - 0.294363i) q^{10} +(-4.53471 + 0.672661i) q^{11} +(-0.0445807 + 0.114236i) q^{12} +(-1.16000 + 3.24198i) q^{13} +(4.42963 - 4.30531i) q^{14} +(0.0125245 + 0.00249129i) q^{15} +(-1.31800 - 3.77662i) q^{16} +(6.40887 - 1.27480i) q^{17} +(3.48935 + 2.40403i) q^{18} +(3.76962 + 3.41659i) q^{19} +(-0.363233 + 0.203893i) q^{20} +(0.137683 + 0.229709i) q^{21} +(3.78756 + 5.26180i) q^{22} +(1.15707 - 0.113962i) q^{23} +(0.172473 - 0.0181014i) q^{24} +(-3.14445 - 3.83152i) q^{25} +(4.82647 - 0.645886i) q^{26} +(-0.272410 + 0.246898i) q^{27} +(-8.28411 - 2.77275i) q^{28} +(-2.97315 - 4.00883i) q^{29} +(-0.00499590 - 0.0173546i) q^{30} +(6.05937 + 2.50987i) q^{31} +(-3.89047 + 4.10661i) q^{32} +(-0.259685 + 0.107565i) q^{33} +(-5.76023 - 7.22615i) q^{34} +(-0.133483 + 0.899871i) q^{35} +(0.756842 - 5.94450i) q^{36} +(0.295776 - 6.02065i) q^{37} +(1.84735 - 6.95367i) q^{38} +(-0.0206931 + 0.210101i) q^{39} +(0.491889 + 0.324139i) q^{40} +(-3.07022 + 3.74107i) q^{41} +(0.199316 - 0.322054i) q^{42} +(-2.50492 + 10.0002i) q^{43} +(4.15439 - 8.17345i) q^{44} +(-0.623284 + 0.0306200i) q^{45} +(-0.893958 - 1.38002i) q^{46} +(4.78914 + 3.20000i) q^{47} +(-0.134653 - 0.204982i) q^{48} +(-10.0430 + 6.71054i) q^{49} +(-2.77439 + 6.43731i) q^{50} +(0.362181 - 0.171299i) q^{51} +(-3.94322 - 5.64580i) q^{52} +(3.64723 - 4.91773i) q^{53} +(0.487000 + 0.182110i) q^{54} +(-0.913678 - 0.277161i) q^{55} +(1.89086 + 12.2088i) q^{56} +(0.275102 + 0.147045i) q^{57} +(-3.10834 + 6.33711i) q^{58} +(-1.46355 - 4.09036i) q^{59} +(-0.0185660 + 0.0175381i) q^{60} +(6.15559 - 10.2700i) q^{61} +(-0.777687 - 9.24261i) q^{62} +(-9.25413 - 9.25413i) q^{63} +(7.68459 + 2.22419i) q^{64} +(-0.507092 + 0.507092i) q^{65} +(0.303658 + 0.256524i) q^{66} +(-10.4645 - 6.27217i) q^{67} +(-5.34281 + 11.9268i) q^{68} +(0.0671202 - 0.0240160i) q^{69} +(1.21737 - 0.416139i) q^{70} +(-0.884166 + 1.65416i) q^{71} +(-7.96084 + 2.90599i) q^{72} +(-4.16236 + 13.7215i) q^{73} +(-7.75738 + 3.53477i) q^{74} +(-0.244101 - 0.181037i) q^{75} +(-9.93652 + 2.19046i) q^{76} +(-8.56134 - 18.1014i) q^{77} +(0.277436 - 0.110319i) q^{78} +(4.91460 + 7.35522i) q^{79} +(0.0881520 - 0.828414i) q^{80} +(4.98134 - 7.45511i) q^{81} +(6.69306 + 1.43064i) q^{82} +(0.263258 + 5.35873i) q^{83} +(-0.534013 - 0.0414956i) q^{84} +(1.32016 + 0.330682i) q^{85} +(14.1914 - 3.34088i) q^{86} +(-0.236554 - 0.194135i) q^{87} +(-12.9662 + 0.0829103i) q^{88} +(11.0729 + 1.09058i) q^{89} +(0.442888 + 0.763342i) q^{90} +(-15.0217 - 0.737970i) q^{91} +(-1.15408 + 2.01874i) q^{92} +(0.397778 + 0.0590048i) q^{93} +(0.913692 - 8.09425i) q^{94} +(0.405490 + 0.978940i) q^{95} +(-0.170210 + 0.302204i) q^{96} +(2.30908 - 5.57462i) q^{97} +(14.9487 + 8.26586i) q^{98} +(11.0327 - 8.18238i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 992 q - 32 q^{2} - 32 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 32 q^{7} - 32 q^{8} - 32 q^{9}+O(q^{10}) \) 992 * q - 32 * q^2 - 32 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 32 * q^8 - 32 * q^9	\( 992 q - 32 q^{2} - 32 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 32 q^{7} - 32 q^{8} - 32 q^{9} - 32 q^{10} - 32 q^{11} - 32 q^{12} - 32 q^{13} - 32 q^{14} - 32 q^{15} - 32 q^{16} - 32 q^{17} - 32 q^{18} - 32 q^{19} - 32 q^{20} - 32 q^{21} - 32 q^{22} - 32 q^{23} - 32 q^{24} - 32 q^{25} - 32 q^{26} - 32 q^{27} - 32 q^{28} - 32 q^{29} - 32 q^{30} - 32 q^{31} - 32 q^{32} - 32 q^{33} - 32 q^{34} - 32 q^{35} - 32 q^{36} - 32 q^{37} - 32 q^{38} - 32 q^{39} - 32 q^{40} - 32 q^{41} - 32 q^{42} - 32 q^{43} - 32 q^{44} - 32 q^{45} - 32 q^{46} - 32 q^{47} - 32 q^{48} - 32 q^{49} - 32 q^{50} - 32 q^{51} - 32 q^{52} - 32 q^{53} - 32 q^{54} - 32 q^{55} - 32 q^{56} - 32 q^{57} - 32 q^{58} - 32 q^{59} - 32 q^{60} - 32 q^{61} - 32 q^{62} - 32 q^{63} - 32 q^{64} - 32 q^{65} - 32 q^{66} - 32 q^{67} - 32 q^{68} - 32 q^{69} - 32 q^{70} - 32 q^{71} - 32 q^{72} - 32 q^{73} - 32 q^{74} - 32 q^{75} - 32 q^{76} - 32 q^{77} - 32 q^{78} - 32 q^{79} - 32 q^{80} - 32 q^{81} - 32 q^{82} - 32 q^{83} - 32 q^{84} - 32 q^{85} - 32 q^{86} - 32 q^{87} - 32 q^{88} - 32 q^{89} - 32 q^{90} - 32 q^{91} - 32 q^{92} - 32 q^{93} - 32 q^{94} - 32 q^{95} - 32 q^{96} - 32 q^{97} - 32 q^{98} - 32 q^{99}+O(q^{100}) \) 992 * q - 32 * q^2 - 32 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 32 * q^8 - 32 * q^9 - 32 * q^10 - 32 * q^11 - 32 * q^12 - 32 * q^13 - 32 * q^14 - 32 * q^15 - 32 * q^16 - 32 * q^17 - 32 * q^18 - 32 * q^19 - 32 * q^20 - 32 * q^21 - 32 * q^22 - 32 * q^23 - 32 * q^24 - 32 * q^25 - 32 * q^26 - 32 * q^27 - 32 * q^28 - 32 * q^29 - 32 * q^30 - 32 * q^31 - 32 * q^32 - 32 * q^33 - 32 * q^34 - 32 * q^35 - 32 * q^36 - 32 * q^37 - 32 * q^38 - 32 * q^39 - 32 * q^40 - 32 * q^41 - 32 * q^42 - 32 * q^43 - 32 * q^44 - 32 * q^45 - 32 * q^46 - 32 * q^47 - 32 * q^48 - 32 * q^49 - 32 * q^50 - 32 * q^51 - 32 * q^52 - 32 * q^53 - 32 * q^54 - 32 * q^55 - 32 * q^56 - 32 * q^57 - 32 * q^58 - 32 * q^59 - 32 * q^60 - 32 * q^61 - 32 * q^62 - 32 * q^63 - 32 * q^64 - 32 * q^65 - 32 * q^66 - 32 * q^67 - 32 * q^68 - 32 * q^69 - 32 * q^70 - 32 * q^71 - 32 * q^72 - 32 * q^73 - 32 * q^74 - 32 * q^75 - 32 * q^76 - 32 * q^77 - 32 * q^78 - 32 * q^79 - 32 * q^80 - 32 * q^81 - 32 * q^82 - 32 * q^83 - 32 * q^84 - 32 * q^85 - 32 * q^86 - 32 * q^87 - 32 * q^88 - 32 * q^89 - 32 * q^90 - 32 * q^91 - 32 * q^92 - 32 * q^93 - 32 * q^94 - 32 * q^95 - 32 * q^96 - 32 * q^97 - 32 * q^98 - 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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