LMFDB - Embedded newform 930.2.bs.a.107.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(107,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([30, 15, 44]))

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

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

chi := DirichletCharacter("930.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.bs (of order $60$, degree $16$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$1024$
Relative dimension:	$64$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			107.19
Character	$\chi$	$=$	930.107
Dual form			930.2.bs.a.113.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.453990 - 0.891007i) q^{2} +(0.546386 + 1.64361i) q^{3} +(-0.587785 + 0.809017i) q^{4} +(0.869573 - 2.06006i) q^{5} +(1.21642 - 1.23302i) q^{6} +(-1.46148 + 1.18348i) q^{7} +(0.987688 + 0.156434i) q^{8} +(-2.40292 + 1.79610i) q^{9} +O(q^{10})$	\(q+(-0.453990 - 0.891007i) q^{2} +(0.546386 + 1.64361i) q^{3} +(-0.587785 + 0.809017i) q^{4} +(0.869573 - 2.06006i) q^{5} +(1.21642 - 1.23302i) q^{6} +(-1.46148 + 1.18348i) q^{7} +(0.987688 + 0.156434i) q^{8} +(-2.40292 + 1.79610i) q^{9} +(-2.23030 + 0.160452i) q^{10} +(-2.27542 - 5.11067i) q^{11} +(-1.65087 - 0.524055i) q^{12} +(2.17373 - 1.41163i) q^{13} +(1.71799 + 0.764897i) q^{14} +(3.86106 + 0.303653i) q^{15} +(-0.309017 - 0.951057i) q^{16} +(3.31125 - 1.27107i) q^{17} +(2.69124 + 1.32561i) q^{18} +(-0.0578930 - 0.272365i) q^{19} +(1.15550 + 1.91437i) q^{20} +(-2.74372 - 1.75546i) q^{21} +(-3.52062 + 4.34761i) q^{22} +(-3.18267 - 0.504085i) q^{23} +(0.282542 + 1.70885i) q^{24} +(-3.48768 - 3.58274i) q^{25} +(-2.24463 - 1.29594i) q^{26} +(-4.26501 - 2.96811i) q^{27} +(-0.0984214 - 1.87799i) q^{28} +(1.22397 - 3.76699i) q^{29} +(-1.48233 - 3.57809i) q^{30} +(1.90951 - 5.23008i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(7.15670 - 6.53230i) q^{33} +(-2.63581 - 2.37329i) q^{34} +(1.16718 + 4.03985i) q^{35} +(-0.0406684 - 2.99972i) q^{36} +(0.0690470 - 0.257687i) q^{37} +(-0.216396 + 0.175234i) q^{38} +(3.50787 + 2.80147i) q^{39} +(1.18113 - 1.89866i) q^{40} +(-1.12525 + 1.01318i) q^{41} +(-0.318509 + 3.24163i) q^{42} +(4.25034 - 6.54494i) q^{43} +(5.47208 + 1.16313i) q^{44} +(1.61054 + 6.51200i) q^{45} +(0.995758 + 3.06463i) q^{46} +(5.51393 + 2.80949i) q^{47} +(1.39433 - 1.02755i) q^{48} +(-0.720093 + 3.38777i) q^{49} +(-1.60887 + 4.73408i) q^{50} +(3.89837 + 4.74791i) q^{51} +(-0.135648 + 2.58832i) q^{52} +(6.25914 - 7.72939i) q^{53} +(-0.708334 + 5.14765i) q^{54} +(-12.5069 + 0.243390i) q^{55} +(-1.62862 + 0.940285i) q^{56} +(0.416031 - 0.243970i) q^{57} +(-3.91208 + 0.619613i) q^{58} +(-2.93702 + 3.26189i) q^{59} +(-2.51514 + 2.94518i) q^{60} +7.95083 q^{61} +(-5.52694 + 0.673025i) q^{62} +(1.38617 - 5.46877i) q^{63} +(0.951057 + 0.309017i) q^{64} +(-1.01784 - 5.70552i) q^{65} +(-9.06940 - 3.41107i) q^{66} +(-1.78599 + 0.478553i) q^{67} +(-0.917986 + 3.42597i) q^{68} +(-0.910447 - 5.50650i) q^{69} +(3.06965 - 2.87402i) q^{70} +(-3.77466 + 0.396732i) q^{71} +(-2.65431 + 1.39808i) q^{72} +(-0.0858084 + 0.223539i) q^{73} +(-0.260947 + 0.0554661i) q^{74} +(3.98302 - 7.68996i) q^{75} +(0.254377 + 0.113256i) q^{76} +(9.37385 + 4.77622i) q^{77} +(0.903582 - 4.39738i) q^{78} +(-1.93164 + 4.33854i) q^{79} +(-2.22795 - 0.190420i) q^{80} +(2.54808 - 8.63176i) q^{81} +(1.41360 + 0.542630i) q^{82} +(0.907457 - 17.3153i) q^{83} +(3.03292 - 1.18788i) q^{84} +(0.260896 - 7.92665i) q^{85} +(-7.76120 - 0.815735i) q^{86} +(6.86023 - 0.0465013i) q^{87} +(-1.44792 - 5.40370i) q^{88} +(-9.57872 - 6.95935i) q^{89} +(5.07106 - 4.39139i) q^{90} +(-1.50621 + 4.63564i) q^{91} +(2.27854 - 2.27854i) q^{92} +(9.63956 + 0.280843i) q^{93} -6.18843i q^{94} +(-0.611431 - 0.117579i) q^{95} +(-1.54856 - 0.775856i) q^{96} +(-0.266810 - 1.68457i) q^{97} +(3.34544 - 0.896408i) q^{98} +(14.6469 + 8.19368i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1024 q - 8 q^{3} + 24 q^{7}+O(q^{10}) $ 1024 * q - 8 * q^3 + 24 * q^7	$ 1024 q - 8 q^{3} + 24 q^{7} + 8 q^{10} + 8 q^{12} - 8 q^{15} + 256 q^{16} + 44 q^{22} + 16 q^{25} - 20 q^{27} + 4 q^{28} + 48 q^{30} - 32 q^{31} - 52 q^{33} + 112 q^{37} + 12 q^{42} + 40 q^{45} + 24 q^{46} - 12 q^{48} + 16 q^{51} - 20 q^{55} - 40 q^{57} - 56 q^{58} - 12 q^{60} + 32 q^{61} + 224 q^{63} - 32 q^{66} + 24 q^{67} - 24 q^{70} - 88 q^{73} + 224 q^{75} - 96 q^{76} - 32 q^{78} + 48 q^{81} - 24 q^{85} + 20 q^{87} - 36 q^{88} + 8 q^{90} - 80 q^{91} - 252 q^{93} - 32 q^{97}+O(q^{100}) $ 1024 * q - 8 * q^3 + 24 * q^7 + 8 * q^10 + 8 * q^12 - 8 * q^15 + 256 * q^16 + 44 * q^22 + 16 * q^25 - 20 * q^27 + 4 * q^28 + 48 * q^30 - 32 * q^31 - 52 * q^33 + 112 * q^37 + 12 * q^42 + 40 * q^45 + 24 * q^46 - 12 * q^48 + 16 * q^51 - 20 * q^55 - 40 * q^57 - 56 * q^58 - 12 * q^60 + 32 * q^61 + 224 * q^63 - 32 * q^66 + 24 * q^67 - 24 * q^70 - 88 * q^73 + 224 * q^75 - 96 * q^76 - 32 * q^78 + 48 * q^81 - 24 * q^85 + 20 * q^87 - 36 * q^88 + 8 * q^90 - 80 * q^91 - 252 * q^93 - 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{11}{15}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.453990	−	0.891007i	−0.321020	−	0.630037i
$2$	−0.453990	−	0.891007i	−0.321020	−	0.630037i
$3$	0.546386	+	1.64361i	0.315456	+	0.948940i
$3$	0.546386	+	1.64361i	0.315456	+	0.948940i
$4$	−0.587785	+	0.809017i	−0.293893	+	0.404508i
$5$	0.869573	−	2.06006i	0.388885	−	0.921286i
$5$	0.869573	−	2.06006i	0.388885	−	0.921286i
$6$	1.21642	−	1.23302i	0.496599	−	0.503378i
$7$	−1.46148	+	1.18348i	−0.552387	+	0.447314i	−0.864429	−	0.502754i	$-0.832320\pi$
$7$	−1.46148	+	1.18348i	−0.552387	+	0.447314i	0.312043	+	0.950068i	$0.398987\pi$
$8$	0.987688	+	0.156434i	0.349201	+	0.0553079i
$9$	−2.40292	+	1.79610i	−0.800975	+	0.598698i
$10$	−2.23030	+	0.160452i	−0.705284	+	0.0507393i
$11$	−2.27542	−	5.11067i	−0.686064	−	1.54092i	−0.833901	−	0.551913i	$-0.813898\pi$
$11$	−2.27542	−	5.11067i	−0.686064	−	1.54092i	0.147837	−	0.989012i	$-0.452769\pi$
$12$	−1.65087	−	0.524055i	−0.476565	−	0.151282i
$13$	2.17373	−	1.41163i	0.602883	−	0.391517i	−0.206801	−	0.978383i	$-0.566305\pi$
$13$	2.17373	−	1.41163i	0.602883	−	0.391517i	0.809684	+	0.586866i	$0.199639\pi$
$14$	1.71799	+	0.764897i	0.459151	+	0.204427i
$15$	3.86106	+	0.303653i	0.996922	+	0.0784029i
$16$	−0.309017	−	0.951057i	−0.0772542	−	0.237764i
$17$	3.31125	−	1.27107i	0.803096	−	0.308280i	0.0780227	−	0.996952i	$-0.475139\pi$
$17$	3.31125	−	1.27107i	0.803096	−	0.308280i	0.725073	+	0.688672i	$0.241806\pi$
$18$	2.69124	+	1.32561i	0.634331	+	0.312449i
$19$	−0.0578930	−	0.272365i	−0.0132816	−	0.0624849i	0.971008	−	0.239048i	$-0.0768353\pi$
$19$	−0.0578930	−	0.272365i	−0.0132816	−	0.0624849i	−0.984289	+	0.176563i	$0.943502\pi$
$20$	1.15550	+	1.91437i	0.258378	+	0.428067i
$21$	−2.74372	−	1.75546i	−0.598728	−	0.383074i
$22$	−3.52062	+	4.34761i	−0.750599	+	0.926913i
$23$	−3.18267	−	0.504085i	−0.663632	−	0.105109i	−0.184474	−	0.982837i	$-0.559058\pi$
$23$	−3.18267	−	0.504085i	−0.663632	−	0.105109i	−0.479159	+	0.877728i	$0.659058\pi$
$24$	0.282542	+	1.70885i	0.0576736	+	0.348818i
$25$	−3.48768	−	3.58274i	−0.697537	−	0.716549i
$26$	−2.24463	−	1.29594i	−0.440207	−	0.254154i
$27$	−4.26501	−	2.96811i	−0.820801	−	0.571214i
$28$	−0.0984214	−	1.87799i	−0.0185999	−	0.354907i
$29$	1.22397	−	3.76699i	0.227285	−	0.699513i	−0.770766	−	0.637118i	$-0.780126\pi$
$29$	1.22397	−	3.76699i	0.227285	−	0.699513i	0.998052	−	0.0623944i	$-0.0198737\pi$
$30$	−1.48233	−	3.57809i	−0.270635	−	0.653266i
$31$	1.90951	−	5.23008i	0.342958	−	0.939351i
$31$	1.90951	−	5.23008i	0.342958	−	0.939351i
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	7.15670	−	6.53230i	1.24582	−	1.13713i
$34$	−2.63581	−	2.37329i	−0.452037	−	0.407016i
$35$	1.16718	+	4.03985i	0.197289	+	0.682860i
$36$	−0.0406684	−	2.99972i	−0.00677807	−	0.499954i
$37$	0.0690470	−	0.257687i	0.0113513	−	0.0423634i	−0.960018	−	0.279939i	$-0.909686\pi$
$37$	0.0690470	−	0.257687i	0.0113513	−	0.0423634i	0.971369	+	0.237575i	$0.0763526\pi$
$38$	−0.216396	+	0.175234i	−0.0351041	+	0.0284268i
$39$	3.50787	+	2.80147i	0.561709	+	0.448593i
$40$	1.18113	−	1.89866i	0.186753	−	0.300205i
$41$	−1.12525	+	1.01318i	−0.175734	+	0.158232i	−0.752304	−	0.658816i	$-0.771058\pi$
$41$	−1.12525	+	1.01318i	−0.175734	+	0.158232i	0.576570	+	0.817048i	$0.304391\pi$
$42$	−0.318509	+	3.24163i	−0.0491471	+	0.500195i
$43$	4.25034	−	6.54494i	0.648170	−	0.998094i	−0.349948	−	0.936769i	$-0.613801\pi$
$43$	4.25034	−	6.54494i	0.648170	−	0.998094i	0.998118	−	0.0613252i	$-0.0195327\pi$
$44$	5.47208	+	1.16313i	0.824946	+	0.175348i
$45$	1.61054	+	6.51200i	0.240086	+	0.970752i
$46$	0.995758	+	3.06463i	0.146817	+	0.451855i
$47$	5.51393	+	2.80949i	0.804289	+	0.409806i	0.807264	−	0.590190i	$-0.200947\pi$
$47$	5.51393	+	2.80949i	0.804289	+	0.409806i	−0.00297549	+	0.999996i	$0.500947\pi$
$48$	1.39433	−	1.02755i	0.201254	−	0.148314i
$49$	−0.720093	+	3.38777i	−0.102870	+	0.483967i
$50$	−1.60887	+	4.73408i	−0.227529	+	0.669500i
$51$	3.89837	+	4.74791i	0.545880	+	0.664841i
$52$	−0.135648	+	2.58832i	−0.0188110	+	0.358935i
$53$	6.25914	−	7.72939i	0.859758	−	1.06171i	−0.137701	−	0.990474i	$-0.543971\pi$
$53$	6.25914	−	7.72939i	0.859758	−	1.06171i	0.997459	−	0.0712394i	$-0.0226954\pi$
$54$	−0.708334	+	5.14765i	−0.0963921	+	0.700506i
$55$	−12.5069	+	0.243390i	−1.68643	+	0.0328187i
$56$	−1.62862	+	0.940285i	−0.217634	+	0.125651i
$57$	0.416031	−	0.243970i	0.0551047	−	0.0323147i
$58$	−3.91208	+	0.619613i	−0.513682	+	0.0813592i
$59$	−2.93702	+	3.26189i	−0.382367	+	0.424662i	−0.903349	−	0.428906i	$-0.858899\pi$
$59$	−2.93702	+	3.26189i	−0.382367	+	0.424662i	0.520982	+	0.853568i	$0.325566\pi$
$60$	−2.51514	+	2.94518i	−0.324703	+	0.380221i
$61$	7.95083			1.01800			0.509000	−	0.860767i	$-0.330015\pi$
$61$	7.95083			1.01800			0.509000	+	0.860767i	$0.330015\pi$
$62$	−5.52694	+	0.673025i	−0.701922	+	0.0854742i
$63$	1.38617	−	5.46877i	0.174642	−	0.689000i
$64$	0.951057	+	0.309017i	0.118882	+	0.0386271i
$65$	−1.01784	−	5.70552i	−0.126247	−	0.707683i
$66$	−9.06940	−	3.41107i	−1.11637	−	0.419873i
$67$	−1.78599	+	0.478553i	−0.218193	+	0.0584646i	−0.366259	−	0.930513i	$-0.619362\pi$
$67$	−1.78599	+	0.478553i	−0.218193	+	0.0584646i	0.148067	+	0.988977i	$0.452695\pi$
$68$	−0.917986	+	3.42597i	−0.111322	+	0.415460i
$69$	−0.910447	−	5.50650i	−0.109605	−	0.662905i
$70$	3.06965	−	2.87402i	0.366893	−	0.343511i
$71$	−3.77466	+	0.396732i	−0.447969	+	0.0470835i	−0.325828	−	0.945429i	$-0.605643\pi$
$71$	−3.77466	+	0.396732i	−0.447969	+	0.0470835i	−0.122142	+	0.992513i	$0.538976\pi$
$72$	−2.65431	+	1.39808i	−0.312814	+	0.164766i
$73$	−0.0858084	+	0.223539i	−0.0100431	+	0.0261632i	−0.938510	−	0.345251i	$-0.887794\pi$
$73$	−0.0858084	+	0.223539i	−0.0100431	+	0.0261632i	0.928467	+	0.371414i	$0.121127\pi$
$74$	−0.260947	+	0.0554661i	−0.0303345	+	0.00644780i
$75$	3.98302	−	7.68996i	0.459919	−	0.887961i
$76$	0.254377	+	0.113256i	0.0291790	+	0.0129913i
$77$	9.37385	+	4.77622i	1.06825	+	0.544300i
$78$	0.903582	−	4.39738i	0.102311	−	0.497905i
$79$	−1.93164	+	4.33854i	−0.217327	+	0.488124i	−0.989004	−	0.147891i	$-0.952752\pi$
$79$	−1.93164	+	4.33854i	−0.217327	+	0.488124i	0.771677	+	0.636015i	$0.219418\pi$
$80$	−2.22795	−	0.190420i	−0.249092	−	0.0212896i
$81$	2.54808	−	8.63176i	0.283120	−	0.959084i
$82$	1.41360	+	0.542630i	0.156106	+	0.0599235i
$83$	0.907457	−	17.3153i	0.0996063	−	1.90060i	−0.257100	−	0.966385i	$-0.582767\pi$
$83$	0.907457	−	17.3153i	0.0996063	−	1.90060i	0.356706	−	0.934217i	$-0.383900\pi$
$84$	3.03292	−	1.18788i	0.330918	−	0.129608i
$85$	0.260896	−	7.92665i	0.0282982	−	0.859766i
$86$	−7.76120	−	0.815735i	−0.836912	−	0.0879629i
$87$	6.86023	−	0.0465013i	0.735494	−	0.00498546i
$88$	−1.44792	−	5.40370i	−0.154349	−	0.576037i
$89$	−9.57872	−	6.95935i	−1.01534	−	0.737689i	−0.0500194	−	0.998748i	$-0.515928\pi$
$89$	−9.57872	−	6.95935i	−1.01534	−	0.737689i	−0.965323	+	0.261059i	$0.915928\pi$
$90$	5.07106	−	4.39139i	0.534537	−	0.462893i
$91$	−1.50621	+	4.63564i	−0.157894	+	0.485947i
$92$	2.27854	−	2.27854i	0.237554	−	0.237554i
$93$	9.63956	+	0.280843i	0.999576	+	0.0291221i
$94$		−	6.18843i		−	0.638287i
$95$	−0.611431	−	0.117579i	−0.0627315	−	0.0120633i
$96$	−1.54856	−	0.775856i	−0.158050	−	0.0791855i
$97$	−0.266810	−	1.68457i	−0.0270905	−	0.171042i	0.970434	−	0.241368i	$-0.0775961\pi$
$97$	−0.266810	−	1.68457i	−0.0270905	−	0.171042i	−0.997524	+	0.0703257i	$0.977596\pi$
$98$	3.34544	−	0.896408i	0.337941	−	0.0905509i
$99$	14.6469	+	8.19368i	1.47207	+	0.823496i
$100$	4.94851	−	0.715712i	0.494851	−	0.0715712i
$101$	1.43067	+	1.96915i	0.142357	+	0.195938i	0.874242	−	0.485491i	$-0.161359\pi$
$101$	1.43067	+	1.96915i	0.142357	+	0.195938i	−0.731885	+	0.681429i	$0.761359\pi$
$102$	2.46060	−	5.62898i	0.243636	−	0.557352i
$103$	−19.3996	−	1.01669i	−1.91150	−	0.100178i	−0.940579	−	0.339575i	$-0.889717\pi$
$103$	−19.3996	−	1.01669i	−1.91150	−	0.100178i	−0.970922	+	0.239397i	$0.923050\pi$
$104$	2.36779	−	1.05421i	0.232181	−	0.103374i
$105$	−6.00222	+	4.12571i	−0.585757	+	0.402628i
$106$	−9.72852	−	2.06786i	−0.944918	−	0.200848i
$107$	−0.726422	+	0.278847i	−0.0702259	+	0.0269572i	−0.393227	−	0.919441i	$-0.628641\pi$
$107$	−0.726422	+	0.278847i	−0.0702259	+	0.0269572i	0.323001	+	0.946398i	$0.395308\pi$
$108$	4.90816	−	1.70585i	0.472288	−	0.164146i
$109$	3.18900	−	1.03617i	0.305451	−	0.0992470i	−0.152281	−	0.988337i	$-0.548662\pi$
$109$	3.18900	−	1.03617i	0.305451	−	0.0992470i	0.457732	+	0.889090i	$0.348662\pi$
$110$	5.89489	+	11.0333i	0.562055	+	1.05198i
$111$	0.461264	−	0.0273101i	0.0437812	−	0.00259216i
$112$	1.57718	+	1.02423i	0.149029	+	0.0967808i
$113$	16.4730	+	6.32340i	1.54965	+	0.594855i	0.974736	−	0.223359i	$-0.0717022\pi$
$113$	16.4730	+	6.32340i	1.54965	+	0.594855i	0.574914	+	0.818214i	$0.305035\pi$
$114$	−0.406253	−	0.259926i	−0.0380491	−	0.0243443i
$115$	−3.80601	+	6.11815i	−0.354912	+	0.570520i
$116$	2.32813	+	3.20439i	0.216161	+	0.297520i
$117$	−2.68787	+	7.29627i	−0.248494	+	0.674540i
$118$	4.23974	+	1.13604i	0.390300	+	0.104581i
$119$	−3.33503	+	5.77644i	−0.305722	+	0.529525i
$120$	3.76602	+	0.903918i	0.343789	+	0.0825160i
$121$	−13.5810	+	15.0832i	−1.23464	+	1.37120i
$122$	−3.60960	−	7.08425i	−0.326798	−	0.641377i
$123$	−2.28009	−	1.29588i	−0.205589	−	0.116846i
$124$	3.10885	+	4.61899i	0.279183	+	0.414798i
$125$	−10.4135	+	4.06938i	−0.931408	+	0.363976i
$126$	−5.50202	+	1.24768i	−0.490159	+	0.111152i
$127$	−15.2434	+	0.798875i	−1.35264	+	0.0708887i	−0.714825	−	0.699303i	$-0.753494\pi$
$127$	−15.2434	+	0.798875i	−1.35264	+	0.0708887i	−0.637812	+	0.770192i	$0.720160\pi$
$128$	−0.156434	−	0.987688i	−0.0138270	−	0.0873001i
$129$	13.0797	+	3.40984i	1.15160	+	0.300219i
$130$	−4.62157	+	3.49715i	−0.405339	+	0.306720i
$131$	−4.30962	−	0.452959i	−0.376533	−	0.0395753i	−0.0856282	−	0.996327i	$-0.527290\pi$
$131$	−4.30962	−	0.452959i	−0.376533	−	0.0395753i	−0.290905	+	0.956752i	$0.593956\pi$
$132$	1.07814	+	9.62949i	0.0938401	+	0.838139i
$133$	0.406949	+	0.329541i	0.0352869	+	0.0285748i
$134$	1.23721	+	1.37407i	0.106879	+	0.118701i
$135$	−9.82323	+	6.20518i	−0.845449	+	0.534057i
$136$	3.46932	−	0.737427i	0.297492	−	0.0632338i
$137$	17.5383	−	11.3895i	1.49840	−	0.973069i	0.504421	−	0.863458i	$-0.331706\pi$
$137$	17.5383	−	11.3895i	1.49840	−	0.973069i	0.993974	−	0.109612i	$-0.0349607\pi$
$138$	−4.49299	+	3.31111i	−0.382469	+	0.281861i
$139$	−6.12988	+	1.99172i	−0.519930	+	0.168935i	−0.557213	−	0.830369i	$-0.688129\pi$
$139$	−6.12988	+	1.99172i	−0.519930	+	0.168935i	0.0372837	+	0.999305i	$0.488129\pi$
$140$	−3.95436	−	1.43030i	−0.334204	−	0.120882i
$141$	−1.60497	+	10.5978i	−0.135163	+	0.892498i
$142$	2.06715	+	3.18313i	0.173471	+	0.267122i
$143$	−12.1605	−	7.89714i	−1.01691	−	0.660392i
$144$	2.45073	+	1.73029i	0.204228	+	0.144191i
$145$	−6.69589	−	5.79712i	−0.556063	−	0.481425i
$146$	0.238131	−	0.0250285i	0.0197078	−	0.00207138i
$147$	−5.96163	+	0.667478i	−0.491707	+	0.0550527i
$148$	0.167888	+	0.207325i	0.0138003	+	0.0170420i
$149$	0.713723	+	1.23621i	0.0584705	+	0.101274i	0.893779	−	0.448508i	$-0.148044\pi$
$149$	0.713723	+	1.23621i	0.0584705	+	0.101274i	−0.835309	+	0.549782i	$0.814711\pi$
$150$	−8.66006	−	0.0577257i	−0.707091	−	0.00471328i
$151$	14.2913	+	10.3833i	1.16301	+	0.844977i	0.990156	−	0.139970i	$-0.0447006\pi$
$151$	14.2913	+	10.3833i	1.16301	+	0.844977i	0.172856	+	0.984947i	$0.444701\pi$
$152$	−0.0145730	−	0.278069i	−0.00118202	−	0.0225543i
$153$	−5.67372	+	9.00160i	−0.458693	+	0.727736i
$154$		−	10.5205i		−	0.847768i
$155$	−9.11382	−	8.48164i	−0.732040	−	0.681262i
$156$	−4.32831	+	1.19127i	−0.346542	+	0.0953779i
$157$	12.5390	−	6.38892i	1.00072	−	0.509891i	0.124712	−	0.992193i	$-0.460199\pi$
$157$	12.5390	−	6.38892i	1.00072	−	0.509891i	0.876005	+	0.482302i	$0.160199\pi$
$158$	4.74262	−	0.248550i	0.377303	−	0.0197736i
$159$	16.1240	+	6.06436i	1.27872	+	0.480935i
$160$	0.841800	+	2.07156i	0.0665502	+	0.163771i
$161$	5.24798	−	3.02992i	0.413598	−	0.238791i
$162$	−8.84776	+	1.64838i	−0.695146	+	0.129509i
$163$	−1.60849	+	10.1556i	−0.125987	+	0.795448i	0.841077	+	0.540915i	$0.181922\pi$
$163$	−1.60849	+	10.1556i	−0.125987	+	0.795448i	−0.967064	+	0.254533i	$0.918078\pi$
$164$	−0.158274	−	1.50588i	−0.0123591	−	0.117589i
$165$	−7.23365	−	20.4235i	−0.563139	−	1.58997i
$166$	−15.8400	+	7.05243i	−1.22942	+	0.547375i
$167$	−7.85748	+	12.0995i	−0.608030	+	0.936284i	0.391838	+	0.920034i	$0.371839\pi$
$167$	−7.85748	+	12.0995i	−0.608030	+	0.936284i	−0.999868	+	0.0162497i	$0.994827\pi$
$168$	−2.43532	−	2.16306i	−0.187889	−	0.166884i
$169$	−2.55520	+	5.73908i	−0.196554	+	0.441468i
$170$	−7.18114	+	3.36617i	−0.550769	+	0.258173i
$171$	0.628307	+	0.550492i	0.0480478	+	0.0420972i
$172$	2.79669	+	7.28561i	0.213245	+	0.555523i
$173$	−7.81354	−	12.0318i	−0.594052	−	0.914760i	−1.00000		0.000863891i	$-0.999725\pi$
$173$	−7.81354	−	12.0318i	−0.594052	−	0.914760i	0.405947	−	0.913896i	$-0.366942\pi$
$174$	−3.15591	−	6.09140i	−0.239249	−	0.461788i
$175$	9.33728	+	1.10849i	0.705832	+	0.0837941i
$176$	−4.15739	+	3.74333i	−0.313375	+	0.282164i
$177$	−6.96603	−	3.04507i	−0.523599	−	0.228881i
$178$	−1.85218	+	11.6942i	−0.138826	+	0.876516i
$179$	−1.76936	+	16.8344i	−0.132248	+	1.25826i	0.704115	+	0.710086i	$0.251344\pi$
$179$	−1.76936	+	16.8344i	−0.132248	+	1.25826i	−0.836364	+	0.548175i	$0.815323\pi$
$180$	−6.21497	−	2.52470i	−0.463237	−	0.188180i
$181$	2.44709	−	4.23849i	0.181891	−	0.315044i	−0.760633	−	0.649182i	$-0.775112\pi$
$181$	2.44709	−	4.23849i	0.181891	−	0.315044i	0.942524	+	0.334137i	$0.108445\pi$
$182$	4.81419	−	0.762492i	0.356851	−	0.0565197i
$183$	4.34423	+	13.0681i	0.321135	+	0.966021i
$184$	−3.06463	−	0.995758i	−0.225927	−	0.0734083i
$185$	−0.470809	−	0.366318i	−0.0346145	−	0.0269323i
$186$	−4.12604	−	8.71641i	−0.302536	−	0.639118i
$187$	−14.0305	−	14.0305i	−1.02601	−	1.02601i
$188$	−5.51393	+	2.80949i	−0.402144	+	0.204903i
$189$	9.74592	−	0.709728i	0.708911	−	0.0516251i
$190$	0.172821	+	0.598169i	0.0125377	+	0.0433957i
$191$	−4.66247	−	2.69188i	−0.337364	−	0.194777i	0.321742	−	0.946828i	$-0.395732\pi$
$191$	−4.66247	−	2.69188i	−0.337364	−	0.194777i	−0.659106	+	0.752050i	$0.729065\pi$
$192$	0.0117402	+	1.73201i	0.000847278	+	0.124997i
$193$	15.9017	+	19.6370i	1.14463	+	1.41350i	0.895516	+	0.445030i	$0.146807\pi$
$193$	15.9017	+	19.6370i	1.14463	+	1.41350i	0.249116	+	0.968474i	$0.419860\pi$
$194$	−1.37984	+	1.00251i	−0.0990665	+	0.0719760i
$195$	8.82154	−	4.79035i	0.631723	−	0.343044i
$196$	−2.31750	−	2.57385i	−0.165536	−	0.183846i
$197$	−0.515529	+	1.34300i	−0.0367299	+	0.0956848i	−0.950719	−	0.310055i	$-0.899653\pi$
$197$	−0.515529	+	1.34300i	−0.0367299	+	0.0956848i	0.913989	+	0.405739i	$0.132986\pi$
$198$	0.651072	−	16.7703i	0.0462697	−	1.19182i
$199$	−4.60789	+	21.6784i	−0.326644	+	1.53674i	0.441970	+	0.897030i	$0.354280\pi$
$199$	−4.60789	+	21.6784i	−0.326644	+	1.53674i	−0.768615	+	0.639712i	$0.779054\pi$
$200$	−2.88428	−	4.08423i	−0.203949	−	0.288799i
$201$	−1.76239	−	2.67399i	−0.124310	−	0.188609i
$202$	1.10502	−	2.16872i	0.0777487	−	0.152590i
$203$	2.66936	+	6.95392i	0.187352	+	0.488069i
$204$	−6.13254	+	0.363091i	−0.429364	+	0.0254214i
$205$	1.10872	+	3.19911i	0.0774364	+	0.223435i
$206$	7.90136	+	17.7468i	0.550514	+	1.23647i
$207$	8.55310	−	4.50510i	0.594481	−	0.313126i
$208$	−2.01426	−	1.63112i	−0.139664	−	0.113098i
$209$	−1.26024	+	0.915617i	−0.0871725	+	0.0633346i
$210$	6.40099	+	3.47499i	0.441710	+	0.239797i
$211$	−8.59207	−	14.8819i	−0.591503	−	1.02451i	−0.994030	−	0.109105i	$-0.965202\pi$
$211$	−8.59207	−	14.8819i	−0.591503	−	1.02451i	0.402527	−	0.915408i	$-0.368132\pi$
$212$	2.57418	+	9.60697i	0.176795	+	0.659809i
$213$	−2.71449	−	5.98730i	−0.185994	−	0.410243i
$214$	0.578244	+	0.520653i	0.0395279	+	0.0355911i
$215$	−9.78699	−	14.4472i	−0.667467	−	0.985294i
$216$	−3.74818	−	3.59877i	−0.255032	−	0.244865i
$217$	3.39900	+	9.90352i	0.230739	+	0.672295i
$218$	−2.37101	−	2.37101i	−0.160585	−	0.160585i
$219$	−0.414295	−	0.0188973i	−0.0279955	−	0.00127696i
$220$	7.15448	−	10.2614i	0.482355	−	0.691822i
$221$	5.40346	−	7.43723i	0.363476	−	0.500282i
$222$	−0.233743	−	0.398590i	−0.0156878	−	0.0267516i
$223$	3.51814	+	0.942682i	0.235592	+	0.0631266i	0.374683	−	0.927153i	$-0.377752\pi$
$223$	3.51814	+	0.942682i	0.235592	+	0.0631266i	−0.139091	+	0.990280i	$0.544418\pi$
$224$	0.196573	−	1.87027i	0.0131341	−	0.124963i
$225$	14.8156	+	2.34485i	0.987706	+	0.156323i
$226$	−1.84440	−	17.5483i	−0.122688	−	1.16730i
$227$	24.7996	+	1.29969i	1.64600	+	0.0862634i	0.852645	−	0.522490i	$-0.174997\pi$
$227$	24.7996	+	1.29969i	1.64600	+	0.0862634i	0.793359	+	0.608754i	$0.208330\pi$
$228$	−0.0471607	+	0.479979i	−0.00312329	+	0.0317874i
$229$	4.94918	+	23.2841i	0.327051	+	1.53866i	0.767602	+	0.640927i	$0.221450\pi$
$229$	4.94918	+	23.2841i	0.327051	+	1.53866i	−0.440550	+	0.897728i	$0.645217\pi$
$230$	7.17920	+	0.613599i	0.473382	+	0.0404595i
$231$	−2.72850	+	18.0166i	−0.179522	+	1.18541i
$232$	1.79819	−	3.52914i	0.118057	−	0.231699i
$233$	−0.741134	+	1.45456i	−0.0485533	+	0.0952912i	−0.914008	−	0.405695i	$-0.867029\pi$
$233$	−0.741134	+	1.45456i	−0.0485533	+	0.0952912i	0.865455	+	0.500987i	$0.167029\pi$
$234$	7.72129	−	0.917528i	0.504756	−	0.0599807i
$235$	10.5825	−	8.91596i	0.690324	−	0.581613i
$236$	−0.912587	−	4.29339i	−0.0594044	−	0.279476i
$237$	−8.18631	−	0.804353i	−0.531758	−	0.0522483i
$238$	6.66092	+	0.349084i	0.431763	+	0.0226277i
$239$	2.83503	+	26.9735i	0.183383	+	1.74477i	0.569204	+	0.822196i	$0.307252\pi$
$239$	2.83503	+	26.9735i	0.183383	+	1.74477i	−0.385821	+	0.922574i	$0.626082\pi$
$240$	−0.904342	−	3.76592i	−0.0583750	−	0.243089i
$241$	−2.04090	+	19.4179i	−0.131466	+	1.25081i	0.707532	+	0.706681i	$0.249808\pi$
$241$	−2.04090	+	19.4179i	−0.131466	+	1.25081i	−0.838998	+	0.544134i	$0.816858\pi$
$242$	19.6049	+	5.25311i	1.26025	+	0.337683i
$243$	15.5795	−	0.528213i	0.999426	−	0.0338849i
$244$	−4.67338	+	6.43236i	−0.299183	+	0.411790i
$245$	6.35283	+	4.42935i	0.405868	+	0.282981i
$246$	−0.119502	+	2.61990i	−0.00761916	+	0.167038i
$247$	−0.510324	−	0.510324i	−0.0324711	−	0.0324711i
$248$	2.70416	−	4.86698i	0.171715	−	0.309054i
$249$	28.9555	−	7.96934i	1.83498	−	0.505036i
$250$	8.35345	+	7.43100i	0.528319	+	0.469978i
$251$	1.54099	+	1.38752i	0.0972667	+	0.0875794i	0.716330	−	0.697762i	$-0.245821\pi$
$251$	1.54099	+	1.38752i	0.0972667	+	0.0875794i	−0.619063	+	0.785341i	$0.712487\pi$
$252$	3.60955	+	4.33590i	0.227380	+	0.273136i
$253$	4.66569	+	17.4126i	0.293329	+	1.09472i
$254$	7.63218	+	13.2193i	0.478886	+	0.829454i
$255$	13.1709	−	3.90220i	0.824793	−	0.244365i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−16.4848	−	13.3491i	−1.02829	−	0.832695i	−0.0422369	−	0.999108i	$-0.513448\pi$
$257$	−16.4848	−	13.3491i	−1.02829	−	0.832695i	−0.986056	+	0.166412i	$0.946782\pi$
$258$	−2.89986	−	13.2021i	−0.180538	−	0.821927i
$259$	0.204057	+	0.458319i	0.0126795	+	0.0284786i
$260$	5.21413	+	2.53018i	0.323367	+	0.156915i
$261$	3.82477	+	11.2502i	0.236747	+	0.696367i
$262$	1.55294	+	4.04554i	0.0959408	+	0.249934i
$263$	−3.76245	+	7.38423i	−0.232003	+	0.455331i	−0.977431	−	0.211255i	$-0.932245\pi$
$263$	−3.76245	+	7.38423i	−0.232003	+	0.455331i	0.745428	+	0.666586i	$0.232245\pi$
$264$	8.09047	−	5.33233i	0.497934	−	0.328182i
$265$	−10.4802	−	19.6155i	−0.643795	−	1.20497i
$266$	0.108872	−	0.512202i	0.00667537	−	0.0314051i
$267$	6.20479	−	19.5462i	0.379727	−	1.19621i
$268$	0.662618	−	1.72618i	0.0404758	−	0.105443i
$269$	−16.2056	−	17.9982i	−0.988074	−	1.09737i	−0.995246	−	0.0973934i	$-0.968949\pi$
$269$	−16.2056	−	17.9982i	−0.988074	−	1.09737i	0.00717167	−	0.999974i	$-0.497717\pi$
$270$	9.98851	+	5.93547i	0.607881	+	0.361221i
$271$	20.1117	−	14.6120i	1.22170	−	0.887618i	0.225461	−	0.974252i	$-0.427611\pi$
$271$	20.1117	−	14.6120i	1.22170	−	0.887618i	0.996240	+	0.0866339i	$0.0276110\pi$
$272$	−2.23209	−	2.75640i	−0.135340	−	0.167131i
$273$	−8.44216	+	0.0572242i	−0.510943	+	0.00346336i
$274$	−18.1103	−	10.4560i	−1.09408	−	0.631670i
$275$	−10.3743	+	25.9766i	−0.625593	+	1.56645i
$276$	4.99000	+	2.50007i	0.300363	+	0.150487i
$277$	−8.97818	+	4.57461i	−0.539447	+	0.274862i	−0.702413	−	0.711770i	$-0.747894\pi$
$277$	−8.97818	+	4.57461i	−0.539447	+	0.274862i	0.162966	+	0.986632i	$0.447894\pi$
$278$	4.55754	+	4.55754i	0.273343	+	0.273343i
$279$	4.80533	+	15.9972i	0.287687	+	0.957724i
$280$	0.520837	+	4.17270i	0.0311259	+	0.249367i
$281$	−1.79739	−	0.584009i	−0.107224	−	0.0348390i	0.254914	−	0.966964i	$-0.417953\pi$
$281$	−1.79739	−	0.584009i	−0.107224	−	0.0348390i	−0.362137	+	0.932125i	$0.617953\pi$
$282$	10.1714	−	3.38127i	0.605696	−	0.201352i
$283$	22.9985	−	3.64261i	1.36712	−	0.216531i	0.570642	−	0.821199i	$-0.306694\pi$
$283$	22.9985	−	3.64261i	1.36712	−	0.216531i	0.796478	+	0.604668i	$0.206694\pi$
$284$	1.89772	−	3.28695i	0.112609	−	0.195045i
$285$	−0.140824	−	1.06920i	−0.00834169	−	0.0633339i
$286$	−1.51564	+	14.4203i	−0.0896216	+	0.852692i
$287$	0.445448	−	2.81245i	0.0262939	−	0.166013i
$288$	0.429093	−	2.96915i	0.0252845	−	0.174959i
$289$	−3.28472	+	2.95757i	−0.193219	+	0.173975i
$290$	−2.12540	+	8.59792i	−0.124808	+	0.504887i
$291$	2.62300	−	1.35896i	0.153763	−	0.0796637i
$292$	−0.130410	−	0.200813i	−0.00763165	−	0.0117517i
$293$	0.914046	+	2.38117i	0.0533992	+	0.139110i	0.957685	−	0.287817i	$-0.0929296\pi$
$293$	0.914046	+	2.38117i	0.0533992	+	0.139110i	−0.904286	+	0.426927i	$0.859596\pi$
$294$	3.30125	+	5.00882i	0.192533	+	0.292121i
$295$	4.16573	+	8.88688i	0.242538	+	0.517414i
$296$	0.108508	−	0.243713i	0.00630690	−	0.0141655i
$297$	−5.46437	+	28.5507i	−0.317075	+	1.65668i
$298$	0.777443	−	1.19716i	0.0450361	−	0.0693495i
$299$	−7.62984	+	3.39702i	−0.441245	+	0.196455i
$300$	3.88015	+	7.74238i	0.224021	+	0.447006i
$301$	1.53405	+	14.5955i	0.0884210	+	0.841269i
$302$	2.76342	−	17.4476i	0.159017	−	1.00399i
$303$	−2.45482	+	3.42739i	−0.141026	+	0.196898i
$304$	−0.241145	+	0.139225i	−0.0138306	+	0.00798511i
$305$	6.91383	−	16.3792i	0.395885	−	0.937869i
$306$	10.5963	+	0.968677i	0.605750	+	0.0553756i
$307$	18.2104	−	0.954368i	1.03932	−	0.0544687i	0.474970	−	0.880002i	$-0.342459\pi$
$307$	18.2104	−	0.954368i	1.03932	−	0.0544687i	0.564354	+	0.825533i	$0.309125\pi$
$308$	−9.37385	+	4.77622i	−0.534125	+	0.272150i
$309$	−8.92864	−	32.4410i	−0.507933	−	1.84550i
$310$	−3.41961	+	11.9711i	−0.194221	+	0.679911i
$311$		−	7.80395i		−	0.442522i	−0.975215	−	0.221261i	$-0.928983\pi$
$311$		−	7.80395i		−	0.442522i	0.975215	−	0.221261i	$-0.0710172\pi$
$312$	3.02644	+	3.31573i	0.171338	+	0.187716i
$313$	−1.10291	−	21.0448i	−0.0623401	−	1.18952i	−0.833368	−	0.552719i	$-0.813590\pi$
$313$	−1.10291	−	21.0448i	−0.0623401	−	1.18952i	0.771028	−	0.636802i	$-0.219743\pi$
$314$	−11.3851	−	8.27178i	−0.642500	−	0.466804i
$315$	−10.0606	−	7.61110i	−0.566851	−	0.428837i
$316$	−2.37456	−	4.11287i	−0.133580	−	0.231367i
$317$	3.44915	+	4.25934i	0.193724	+	0.239229i	0.864747	−	0.502207i	$-0.167479\pi$
$317$	3.44915	+	4.25934i	0.193724	+	0.239229i	−0.671024	+	0.741436i	$0.734145\pi$
$318$	−1.91677	−	17.1198i	−0.107487	−	0.960029i
$319$	−22.0369	+	2.31617i	−1.23383	+	0.129681i
$320$	1.46361	−	1.69052i	0.0818181	−	0.0945029i
$321$	−0.855224	−	1.04160i	−0.0477340	−	0.0581363i
$322$	−5.08221	−	3.30043i	−0.283220	−	0.183926i
$323$	−0.537893	−	0.828283i	−0.0299292	−	0.0460869i
$324$	5.48551	+	7.13506i	0.304751	+	0.396392i
$325$	−12.6388	−	2.86457i	−0.701074	−	0.158898i
$326$	9.77895	−	3.17737i	0.541606	−	0.175978i
$327$	3.44549	+	4.67533i	0.190536	+	0.258546i
$328$	−1.26989	+	0.824676i	−0.0701180	+	0.0455351i
$329$	−11.3835	+	2.41963i	−0.627590	+	0.133398i
$330$	−14.9135	+	15.7173i	−0.820961	+	0.865210i
$331$	−7.32140	−	8.13124i	−0.402421	−	0.446933i	0.507540	−	0.861628i	$-0.330555\pi$
$331$	−7.32140	−	8.13124i	−0.402421	−	0.446933i	−0.909960	+	0.414695i	$0.863888\pi$
$332$	13.4750	+	10.9118i	0.739536	+	0.598864i
$333$	0.296915	+	0.743217i	0.0162709	+	0.0407280i
$334$	14.3479	+	1.50803i	0.785083	+	0.0825155i
$335$	−0.567197	+	4.09537i	−0.0309893	+	0.223754i
$336$	−0.821691	+	3.15190i	−0.0448269	+	0.171950i
$337$	−1.79001	−	11.3017i	−0.0975080	−	0.615641i	−0.987250	−	0.159177i	$-0.949116\pi$
$337$	−1.79001	−	11.3017i	−0.0975080	−	0.615641i	0.889742	−	0.456464i	$-0.150884\pi$
$338$	6.27359	−	0.328785i	0.341239	−	0.0178836i
$339$	−1.39258	+	30.5303i	−0.0756347	+	1.65818i
$340$	6.25945	+	4.87024i	0.339466	+	0.264126i
$341$	−31.0742	+	2.14176i	−1.68276	+	0.115983i
$342$	0.205246	−	0.809743i	0.0110985	−	0.0437859i
$343$	−8.93329	−	17.5326i	−0.482352	−	0.946670i
$344$	5.22186	−	5.79946i	0.281544	−	0.312686i
$345$	−12.1354	−	2.91273i	−0.653349	−	0.156816i
$346$	−7.17313	+	12.4242i	−0.385630	+	0.667931i
$347$	3.42690	+	0.918236i	0.183966	+	0.0492935i	0.349626	−	0.936889i	$-0.386309\pi$
$347$	3.42690	+	0.918236i	0.183966	+	0.0492935i	−0.165660	+	0.986183i	$0.552975\pi$
$348$	−3.99472	+	5.57738i	−0.214140	+	0.298979i
$349$	−21.6233	−	29.7620i	−1.15747	−	1.59312i	−0.720154	−	0.693815i	$-0.755929\pi$
$349$	−21.6233	−	29.7620i	−1.15747	−	1.59312i	−0.437317	−	0.899307i	$-0.644071\pi$
$350$	−3.25136	−	8.82283i	−0.173793	−	0.471600i
$351$	−13.4609	−	0.431232i	−0.718487	−	0.0230175i
$352$	5.22275	+	2.00483i	0.278374	+	0.106858i
$353$	4.32538	+	2.80894i	0.230217	+	0.149505i	0.654593	−	0.755981i	$-0.272840\pi$
$353$	4.32538	+	2.80894i	0.230217	+	0.149505i	−0.424376	+	0.905486i	$0.639507\pi$
$354$	0.449336	+	7.58920i	0.0238819	+	0.403362i
$355$	−2.46505	+	8.12100i	−0.130831	+	0.431018i
$356$	11.2605	−	3.65875i	0.596803	−	0.193913i
$357$	−11.3164	−	2.32533i	−0.598930	−	0.123069i
$358$	15.8028	−	6.06613i	0.835204	−	0.320605i
$359$	−14.4960	−	3.08122i	−0.765070	−	0.162621i	−0.191182	−	0.981555i	$-0.561232\pi$
$359$	−14.4960	−	3.08122i	−0.765070	−	0.162621i	−0.573888	+	0.818934i	$0.694565\pi$
$360$	0.572014	+	6.68377i	0.0301478	+	0.352266i
$361$	17.2865	−	7.69646i	0.909817	−	0.405077i
$362$	−4.88748	−	0.256142i	−0.256880	−	0.0134625i
$363$	−32.2114	−	14.0806i	−1.69066	−	0.739041i
$364$	−2.86498	−	3.94331i	−0.150166	−	0.206685i
$365$	0.385886	+	0.371154i	0.0201982	+	0.0194271i
$366$	9.67152	−	9.80352i	0.505538	−	0.512438i
$367$	28.6049	−	7.66467i	1.49317	−	0.400092i	0.582361	−	0.812931i	$-0.302129\pi$
$367$	28.6049	−	7.66467i	1.49317	−	0.400092i	0.910804	+	0.412838i	$0.135463\pi$
$368$	0.504085	+	3.18267i	0.0262773	+	0.165908i
$369$	0.884121	−	4.45564i	0.0460255	−	0.231951i
$370$	−0.112649	+	0.585799i	−0.00585637	+	0.0304542i
$371$			18.7039i			0.971058i
$372$	−5.89320	+	7.63349i	−0.305548	+	0.395778i
$373$	−16.7107	+	16.7107i	−0.865248	+	0.865248i	−0.991942	−	0.126694i	$-0.959563\pi$
$373$	−16.7107	+	16.7107i	−0.865248	+	0.865248i	0.126694	+	0.991942i	$0.459563\pi$
$374$	−6.13155	+	18.8710i	−0.317055	+	0.975794i
$375$	−12.3783	−	14.8922i	−0.639210	−	0.769032i
$376$	5.00654	+	3.63747i	0.258193	+	0.187588i
$377$	−2.65704	−	9.91620i	−0.136844	−	0.510710i
$378$	−5.05693	−	8.36147i	−0.260100	−	0.430068i
$379$	23.3237	+	2.45142i	1.19806	+	0.125921i	0.682469	−	0.730914i	$-0.260906\pi$
$379$	23.3237	+	2.45142i	1.19806	+	0.125921i	0.515590	+	0.856835i	$0.327573\pi$
$380$	0.454513	−	0.425547i	0.0233160	−	0.0218301i
$381$	−9.64185	−	24.6178i	−0.493967	−	1.26121i
$382$	−0.281764	+	5.37638i	−0.0144163	+	0.275079i
$383$	3.59625	+	1.38047i	0.183760	+	0.0705388i	0.448508	−	0.893779i	$-0.351956\pi$
$383$	3.59625	+	1.38047i	0.183760	+	0.0705388i	−0.264748	+	0.964318i	$0.585289\pi$
$384$	1.53790	−	0.796777i	0.0784808	−	0.0406604i
$385$	17.9905	−	15.1574i	0.916883	−	0.772494i
$386$	10.2775	−	23.0836i	0.523109	−	1.17492i
$387$	1.54211	+	23.3610i	0.0783898	+	1.18751i
$388$	1.51968	+	0.774313i	0.0771498	+	0.0393098i
$389$	−20.6907	−	9.21211i	−1.04906	−	0.467072i	−0.191521	−	0.981489i	$-0.561342\pi$
$389$	−20.6907	−	9.21211i	−1.04906	−	0.467072i	−0.857541	+	0.514416i	$0.828009\pi$
$390$	−8.27312	−	5.68527i	−0.418926	−	0.287885i
$391$	−11.1793	+	2.37624i	−0.565363	+	0.120172i
$392$	−1.24119	+	3.23341i	−0.0626896	+	0.163312i
$393$	−1.61023	−	7.33084i	−0.0812253	−	0.369792i
$394$	1.43067	−	0.150369i	0.0720760	−	0.00757549i
$395$	7.25795	+	7.75198i	0.365187	+	0.390045i
$396$	−15.2381	+	7.03347i	−0.765742	+	0.353445i
$397$	−1.36218	+	5.08371i	−0.0683657	+	0.255144i	−0.991647	−	0.128980i	$-0.958830\pi$
$397$	−1.36218	+	5.08371i	−0.0683657	+	0.255144i	0.923282	+	0.384124i	$0.125496\pi$
$398$	21.4075	−	5.73613i	1.07306	−	0.287526i
$399$	−0.319286	+	0.848922i	−0.0159843	+	0.0424993i
$400$	−2.32964	+	4.42411i	−0.116482	+	0.221206i
$401$	23.7532	+	7.71790i	1.18618	+	0.385413i	0.834659	−	0.550767i	$-0.185665\pi$
$401$	23.7532	+	7.71790i	1.18618	+	0.385413i	0.351521	+	0.936180i	$0.385665\pi$
$402$	−1.58243	+	2.78427i	−0.0789247	+	0.138867i
$403$	−3.23222	−	14.0643i	−0.161008	−	0.700593i
$404$	−2.43401			−0.121096
$405$	−15.5662	−	12.7552i	−0.773490	−	0.633809i
$406$	4.98412	−	5.53543i	0.247358	−	0.274719i
$407$	−1.47406	+	0.233469i	−0.0730666	+	0.0115726i
$408$	3.10763	+	5.29930i	0.153851	+	0.262354i
$409$	−2.77882	+	1.60435i	−0.137404	+	0.0793300i	−0.567126	−	0.823631i	$-0.691945\pi$
$409$	−2.77882	+	1.60435i	−0.137404	+	0.0793300i	0.429722	+	0.902961i	$0.358611\pi$
$410$	2.34708	−	2.44024i	0.115914	−	0.120515i
$411$	28.3026	+	22.6031i	1.39606	+	1.11493i
$412$	12.2253	−	15.0970i	0.602299	−	0.743777i
$413$	0.432001	−	8.24308i	0.0212574	−	0.405615i
$414$	−7.89710	−	5.57559i	−0.388121	−	0.274025i
$415$	−34.8814	−	16.9263i	−1.71226	−	0.830881i
$416$	−0.538880	+	2.53523i	−0.0264208	+	0.124300i
$417$	−6.62290	−	8.98690i	−0.324325	−	0.440090i
$418$	1.38796	+	0.707199i	0.0678872	+	0.0345903i
$419$	0.186078	+	0.572689i	0.00909050	+	0.0279777i	0.955499	−	0.294995i	$-0.0953179\pi$
$419$	0.186078	+	0.572689i	0.00909050	+	0.0279777i	−0.946408	+	0.322972i	$0.895318\pi$
$420$	0.190248	−	7.28093i	0.00928313	−	0.355273i
$421$	−6.68970	−	1.42194i	−0.326036	−	0.0693011i	0.0419859	−	0.999118i	$-0.486632\pi$
$421$	−6.68970	−	1.42194i	−0.326036	−	0.0693011i	−0.368022	+	0.929817i	$0.619965\pi$
$422$	−9.35916	+	14.4118i	−0.455597	+	0.701557i
$423$	−18.2957	+	3.15256i	−0.889565	+	0.153283i
$424$	7.39122	−	6.65508i	0.358949	−	0.323199i
$425$	−16.1025	−	7.43027i	−0.781086	−	0.360421i
$426$	−4.10237	+	5.13681i	−0.198760	+	0.248879i
$427$	−11.6200	+	9.40966i	−0.562330	+	0.455366i
$428$	0.201388	−	0.751590i	0.00973446	−	0.0363295i
$429$	6.33549	−	24.3021i	0.305880	−	1.17332i
$430$	−8.42939	+	15.2792i	−0.406501	+	0.736828i
$431$	5.39381	+	4.85661i	0.259811	+	0.233935i	0.788733	−	0.614735i	$-0.210737\pi$
$431$	5.39381	+	4.85661i	0.259811	+	0.233935i	−0.528923	+	0.848670i	$0.677404\pi$
$432$	−1.50488	+	4.97346i	−0.0724037	+	0.239286i
$433$	3.91045	−	3.91045i	0.187924	−	0.187924i	−0.606874	−	0.794798i	$-0.707577\pi$
$433$	3.91045	−	3.91045i	0.187924	−	0.187924i	0.794798	+	0.606874i	$0.207577\pi$
$434$	7.28098	−	7.52464i	0.349498	−	0.361194i
$435$	5.86968	−	14.1729i	0.281430	−	0.679539i
$436$	−1.03617	+	3.18900i	−0.0496235	+	0.152725i
$437$	0.0469590	+	0.896032i	0.00224636	+	0.0428630i
$438$	0.171249	+	0.377719i	0.00818257	+	0.0180481i
$439$	18.6650	+	10.7762i	0.890832	+	0.514322i	0.874215	−	0.485540i	$-0.161377\pi$
$439$	18.6650	+	10.7762i	0.890832	+	0.514322i	0.0166177	+	0.999862i	$0.494710\pi$
$440$	−12.3910	−	1.71612i	−0.590719	−	0.0818128i
$441$	−4.35443	−	9.43391i	−0.207354	−	0.449234i
$442$	−9.07974	−	1.43809i	−0.431879	−	0.0684029i
$443$	18.9428	−	23.3924i	0.899997	−	1.11140i	−0.0932792	−	0.995640i	$-0.529735\pi$
$443$	18.9428	−	23.3924i	0.899997	−	1.11140i	0.993277	−	0.115764i	$-0.0369317\pi$
$444$	−0.249030	+	0.389223i	−0.0118184	+	0.0184717i
$445$	−22.6661	+	13.6811i	−1.07447	+	0.648545i
$446$	−0.757265	−	3.56265i	−0.0358575	−	0.168696i
$447$	−1.64187	+	1.84853i	−0.0776579	+	0.0874325i
$448$	−1.75566	+	0.673936i	−0.0829473	+	0.0318405i
$449$	7.65266	+	23.5525i	0.361151	+	1.11151i	0.952356	+	0.304988i	$0.0986525\pi$
$449$	7.65266	+	23.5525i	0.361151	+	1.11151i	−0.591205	+	0.806521i	$0.701347\pi$
$450$	−4.63686	−	14.2653i	−0.218584	−	0.672474i
$451$	7.73843	+	3.44537i	0.364388	+	0.162236i
$452$	−14.7983	+	9.61015i	−0.696055	+	0.452023i
$453$	−9.25746	+	29.1627i	−0.434953	+	1.37018i
$454$	−10.1007	−	22.6866i	−0.474051	−	1.06474i
$455$	8.23992	+	7.13391i	0.386294	+	0.334443i
$456$	0.449074	−	0.175885i	0.0210298	−	0.00823658i
$457$	2.70725	+	0.428787i	0.126640	+	0.0200578i	0.219433	−	0.975628i	$-0.429579\pi$
$457$	2.70725	+	0.428787i	0.126640	+	0.0200578i	−0.0927927	+	0.995685i	$0.529579\pi$
$458$	18.4994	−	14.9805i	0.864419	−	0.699993i
$459$	−17.8952	−	4.40704i	−0.835275	−	0.205703i
$460$	−2.71257	−	6.67528i	−0.126474	−	0.311237i
$461$	−10.3554	+	14.2529i	−0.482297	+	0.663825i	−0.978944	−	0.204128i	$-0.934564\pi$
$461$	−10.3554	+	14.2529i	−0.482297	+	0.663825i	0.496647	+	0.867952i	$0.334564\pi$
$462$	17.2917	−	5.74827i	0.804481	−	0.267434i
$463$	3.67307	+	7.20881i	0.170702	+	0.335022i	0.960470	−	0.278384i	$-0.0897989\pi$
$463$	3.67307	+	7.20881i	0.170702	+	0.335022i	−0.789768	+	0.613406i	$0.789799\pi$
$464$	−3.96085			−0.183878
$465$	8.96086	−	19.6138i	0.415550	−	0.909570i
$466$	1.63249			0.0756235
$467$	−5.50618	−	10.8065i	−0.254796	−	0.500065i	0.727808	−	0.685781i	$-0.240539\pi$
$467$	−5.50618	−	10.8065i	−0.254796	−	0.500065i	−0.982603	+	0.185717i	$0.940539\pi$
$468$	−4.32292	−	6.46317i	−0.199827	−	0.298760i
$469$	2.04382	−	2.81308i	0.0943748	−	0.129896i
$470$	−12.7485	−	5.38129i	−0.588045	−	0.248220i
$471$	17.3520	+	17.1184i	0.799539	+	0.788772i
$472$	−3.41113	+	2.76228i	−0.157010	+	0.127144i
$473$	−43.1203	−	6.82959i	−1.98267	−	0.314025i
$474$	2.99982	+	7.65922i	0.137786	+	0.351800i
$475$	−0.773903	+	1.15734i	−0.0355091	+	0.0531024i
$476$	−2.71296	−	6.09340i	−0.124348	−	0.279291i
$477$	−1.15751	+	29.8151i	−0.0529986	+	1.36514i
$478$	22.7465	−	14.7717i	1.04040	−	0.675644i
$479$	−31.9722	−	14.2349i	−1.46085	−	0.650411i	−0.486137	−	0.873883i	$-0.661594\pi$
$479$	−31.9722	−	14.2349i	−1.46085	−	0.650411i	−0.974710	+	0.223472i	$0.928261\pi$
$480$	−2.94490	+	2.51547i	−0.134416	+	0.114815i
$481$	−0.213670	−	0.657610i	−0.00974253	−	0.0299844i
$482$	18.2280	−	6.99707i	0.830263	−	0.318708i
$483$	7.84744	+	6.97013i	0.357071	+	0.317152i
$484$	−4.21987	−	19.8529i	−0.191812	−	0.902406i
$485$	−3.70233	−	0.915215i	−0.168114	−	0.0415578i
$486$	−7.54359	−	13.6416i	−0.342184	−	0.618797i
$487$	26.5182	−	32.7473i	1.20166	−	1.48392i	0.369636	−	0.929177i	$-0.379482\pi$
$487$	26.5182	−	32.7473i	1.20166	−	1.48392i	0.832020	−	0.554745i	$-0.187184\pi$
$488$	7.85295	+	1.24378i	0.355486	+	0.0563035i
$489$	−17.5707	+	2.90515i	−0.794576	+	0.131375i
$490$	1.06245	−	7.67130i	0.0479967	−	0.346554i
$491$	11.2284	+	6.48270i	0.506729	+	0.292560i	0.731488	−	0.681854i	$-0.238826\pi$
$491$	11.2284	+	6.48270i	0.506729	+	0.292560i	−0.224759	+	0.974414i	$0.572160\pi$
$492$	2.38860	−	1.08293i	0.107686	−	0.0488223i
$493$	−0.735239	−	14.0292i	−0.0331135	−	0.631843i
$494$	−0.223020	+	0.686384i	−0.0100341	+	0.0308819i
$495$	29.6160	−	23.0485i	1.33114	−	1.03595i
$496$	−5.56418	−	0.199865i	−0.249839	−	0.00897419i
$497$	5.04705	−	5.04705i	0.226391	−	0.226391i
$498$	−20.2462	−	22.1815i	−0.907256	−	0.993977i
$499$	−14.7302	−	13.2631i	−0.659414	−	0.593739i	0.269963	−	0.962871i	$-0.412988\pi$
$499$	−14.7302	−	13.2631i	−0.659414	−	0.593739i	−0.929377	+	0.369132i	$0.879655\pi$
$500$	2.82868	−	10.8166i	0.126503	−	0.483732i
$501$	−24.1800	−	6.30367i	−1.08028	−	0.281627i
$502$	0.536691	−	2.00296i	0.0239537	−	0.0893963i
$503$	−31.0492	+	25.1431i	−1.38441	+	1.12108i	−0.406128	+	0.913816i	$0.633121\pi$
$503$	−31.0492	+	25.1431i	−1.38441	+	1.12108i	−0.978286	+	0.207260i	$0.933545\pi$
$504$	2.22461	−	5.18459i	0.0990921	−	0.230940i
$505$	5.30065	−	1.23495i	0.235876	−	0.0549545i
$506$	13.3965	−	12.0623i	0.595549	−	0.536235i
$507$	−10.8289	−	1.06401i	−0.480931	−	0.0472542i
$508$	8.31357	−	12.8018i	0.368855	−	0.567987i
$509$	21.9883	+	4.67377i	0.974616	+	0.207161i	0.667581	−	0.744537i	$-0.267330\pi$
$509$	21.9883	+	4.67377i	0.974616	+	0.207161i	0.307035	+	0.951698i	$0.400663\pi$
$510$	−9.45635	−	9.96379i	−0.418734	−	0.441204i
$511$	−0.139147	−	0.428249i	−0.00615549	−	0.0189446i
$512$	0.891007	+	0.453990i	0.0393773	+	0.0200637i
$513$	−0.561497	+	1.33347i	−0.0247907	+	0.0588743i
$514$	−4.41022	+	20.7484i	−0.194526	+	0.915174i
$515$	−18.9638	+	39.0803i	−0.835646	+	1.72208i
$516$	−10.4467	+	8.57743i	−0.459888	+	0.377600i
$517$	1.81187	−	34.5726i	0.0796861	−	1.52050i
$518$	0.315726	−	0.389889i	0.0138722	−	0.0171307i
$519$	15.5064	−	19.4164i	0.680655	−	0.852287i
$520$	−0.112764	−	5.79450i	−0.00494501	−	0.254106i
$521$	20.5809	−	11.8824i	0.901667	−	0.520578i	0.0239263	−	0.999714i	$-0.492383\pi$
$521$	20.5809	−	11.8824i	0.901667	−	0.520578i	0.877741	+	0.479136i	$0.159050\pi$
$522$	8.28755	−	8.51536i	0.362736	−	0.372707i
$523$	23.4309	−	3.71109i	1.02456	−	0.162275i	0.378534	−	0.925588i	$-0.376428\pi$
$523$	23.4309	−	3.71109i	1.02456	−	0.162275i	0.646029	+	0.763313i	$0.276428\pi$
$524$	2.89958	−	3.22031i	0.126669	−	0.140680i
$525$	3.27983	+	15.9525i	0.143144	+	0.696226i
$526$	8.28751			0.361353
$527$	−0.324945	−	19.7452i	−0.0141548	−	0.860115i
$528$	−8.42413	−	4.78784i	−0.366613	−	0.208364i
$529$	−11.9990	−	3.89872i	−0.521696	−	0.169509i
$530$	−12.7196	+	18.2432i	−0.552503	+	0.792433i
$531$	1.19877	−	13.1132i	0.0520220	−	0.569066i
$532$	−0.505802	+	0.135529i	−0.0219293	+	0.00587594i
$533$	−1.01574	+	3.79081i	−0.0439968	+	0.164198i
$534$	−20.2327	+	3.34528i	−0.875555	+	0.144764i
$535$	−0.0572354	+	1.73895i	−0.00247450	+	0.0751814i
$536$	−1.83886	+	0.193272i	−0.0794266	+	0.00834807i
$537$	−28.6359	+	6.28992i	−1.23573	+	0.271430i
$538$	−8.67929	+	22.6103i	−0.374191	+	0.974800i
$539$	18.9523	−	4.02843i	0.816333	−	0.173517i
$540$	0.753853	−	11.5945i	0.0324407	−	0.498946i
$541$	−2.72780	−	1.21450i	−0.117277	−	0.0522153i	0.347259	−	0.937769i	$-0.387112\pi$
$541$	−2.72780	−	1.21450i	−0.117277	−	0.0522153i	−0.464537	+	0.885554i	$0.653779\pi$
$542$	−22.1500	−	11.2860i	−0.951422	−	0.484774i
$543$	8.30349	+	1.70622i	0.356337	+	0.0732209i
$544$	−1.44262	+	3.24019i	−0.0618520	+	0.138922i
$545$	0.638501	−	7.47055i	0.0273504	−	0.320003i
$546$	3.88365	+	7.49604i	0.166205	+	0.320801i
$547$	5.93775	+	2.27929i	0.253880	+	0.0974553i	0.481980	−	0.876182i	$-0.339918\pi$
$547$	5.93775	+	2.27929i	0.253880	+	0.0974553i	−0.228100	+	0.973638i	$0.573251\pi$
$548$	−1.09445	+	20.8833i	−0.0467525	+	0.892092i
$549$	−19.1052	+	14.2805i	−0.815392	+	0.609475i
$550$	27.8552	−	2.54959i	1.18775	−	0.108715i
$551$	−1.09686	−	0.115284i	−0.0467277	−	0.00491128i
$552$	−0.0378310	−	5.58113i	−0.00161020	−	0.237549i
$553$	−2.31153	−	8.62675i	−0.0982963	−	0.366847i
$554$	8.15202	+	5.92279i	0.346346	+	0.251635i
$555$	0.344842	−	0.973978i	0.0146377	−	0.0413431i
$556$	1.99172	−	6.12988i	0.0844677	−	0.259965i
$557$	10.2352	−	10.2352i	0.433677	−	0.433677i	−0.456200	−	0.889877i	$-0.650790\pi$
$557$	10.2352	−	10.2352i	0.433677	−	0.433677i	0.889877	+	0.456200i	$0.150790\pi$
$558$	12.0720	−	11.5441i	0.511048	−	0.488702i
$559$		−	20.2268i		−	0.855504i
$560$	3.48145	−	2.35844i	0.147118	−	0.0996621i
$561$	15.3946	−	30.7267i	0.649961	−	1.29728i
$562$	0.295644	+	1.86662i	0.0124710	+	0.0787388i
$563$	12.2941	−	3.29418i	0.518132	−	0.138833i	0.00972985	−	0.999953i	$-0.496903\pi$
$563$	12.2941	−	3.29418i	0.518132	−	0.138833i	0.508403	+	0.861119i	$0.330236\pi$
$564$	−7.63044	−	7.52769i	−0.321300	−	0.316973i
$565$	27.3511	−	28.4367i	1.15067	−	1.19634i
$566$	−13.6867	−	18.8381i	−0.575295	−	0.791825i
$567$	6.49156	+	15.6307i	0.272620	+	0.656429i
$568$	−3.79025	−	0.198638i	−0.159035	−	0.00833468i
$569$	13.4446	−	5.98594i	0.563628	−	0.250944i	−0.105086	−	0.994463i	$-0.533512\pi$
$569$	13.4446	−	5.98594i	0.563628	−	0.250944i	0.668714	+	0.743520i	$0.266845\pi$
$570$	−0.888730	+	0.610881i	−0.0372248	+	0.0255870i
$571$	−26.0776	−	5.54297i	−1.09131	−	0.231966i	−0.373102	−	0.927790i	$-0.621706\pi$
$571$	−26.0776	−	5.54297i	−1.09131	−	0.231966i	−0.718212	+	0.695824i	$0.755039\pi$
$572$	13.5367	−	5.19625i	0.565998	−	0.217266i
$573$	1.87689	−	9.13410i	0.0784083	−	0.381582i
$574$	−2.70814	+	0.879927i	−0.113035	+	0.0367274i
$575$	9.29414	+	13.1608i	0.387592	+	0.548842i
$576$	−2.84034	+	0.965644i	−0.118348	+	0.0402352i
$577$	35.9204	+	23.3270i	1.49539	+	0.971116i	0.994402	+	0.105660i	$0.0336955\pi$
$577$	35.9204	+	23.3270i	1.49539	+	0.971116i	0.500985	+	0.865456i	$0.332971\pi$
$578$	4.12644	+	1.58399i	0.171637	+	0.0658854i
$579$	−23.5871	+	36.8657i	−0.980248	+	1.53209i
$580$	8.62572	−	2.00963i	0.358163	−	0.0834452i
$581$	19.1661	+	26.3799i	0.795144	+	1.09442i
$582$	−2.40166	−	1.72016i	−0.0995520	−	0.0713028i
$583$	−53.7445	−	14.4008i	−2.22587	−	0.596420i
$584$	−0.119721	+	0.207363i	−0.00495410	+	0.00858075i
$585$	12.6934	+	11.8818i	0.524809	+	0.491252i
$586$	1.70667	−	1.89545i	0.0705019	−	0.0783003i
$587$	16.6658	+	32.7085i	0.687872	+	1.35003i	0.925529	+	0.378676i	$0.123621\pi$
$587$	16.6658	+	32.7085i	0.687872	+	1.35003i	−0.237657	+	0.971349i	$0.576379\pi$
$588$	2.96416	−	5.21539i	0.122240	−	0.215079i
$589$	−1.53504	−	0.217298i	−0.0632503	−	0.00895362i
$590$	6.02706	−	7.74625i	0.248130	−	0.318908i
$591$	−2.48905	−	0.113533i	−0.102386	−	0.00467014i
$592$	−0.266411	+	0.0139620i	−0.0109494	+	0.000573836i
$593$	0.192679	+	1.21653i	0.00791240	+	0.0499569i	0.991329	−	0.131406i	$-0.0419491\pi$
$593$	0.192679	+	1.21653i	0.00791240	+	0.0499569i	−0.983416	+	0.181363i	$0.941949\pi$
$594$	27.9197	−	8.09298i	1.14556	−	0.332059i
$595$	8.99975	+	11.8934i	0.368954	+	0.487582i
$596$	−1.41963	−	0.149209i	−0.0581502	−	0.00611183i
$597$	−38.1486	+	4.27121i	−1.56132	+	0.174809i
$598$	6.49064	+	5.25602i	0.265422	+	0.214935i
$599$	−7.22238	−	8.02127i	−0.295098	−	0.327740i	0.577303	−	0.816530i	$-0.304105\pi$
$599$	−7.22238	−	8.02127i	−0.295098	−	0.327740i	−0.872402	+	0.488790i	$0.837438\pi$
$600$	5.13696	−	6.97221i	0.209715	−	0.284639i
$601$	33.5028	−	7.12125i	1.36661	−	0.290482i	0.534535	−	0.845146i	$-0.320487\pi$
$601$	33.5028	−	7.12125i	1.36661	−	0.290482i	0.832074	+	0.554664i	$0.187153\pi$
$602$	12.3082	−	7.99305i	0.501646	−	0.325773i
$603$	3.43206	−	4.35773i	0.139764	−	0.177460i
$604$	−16.8005	+	5.45880i	−0.683601	+	0.222115i
$605$	19.2626	+	41.0936i	0.783138	+	1.67069i
$606$	4.16829	+	0.631261i	0.169325	+	0.0256432i
$607$	−10.2832	−	15.8347i	−0.417381	−	0.642711i	0.565970	−	0.824426i	$-0.308502\pi$
$607$	−10.2832	−	15.8347i	−0.417381	−	0.642711i	−0.983351	+	0.181715i	$0.941835\pi$
$608$	0.233528	+	0.151655i	0.00947081	+	0.00615042i
$609$	−9.97104	+	8.18692i	−0.404047	+	0.331751i
$610$	−17.7328	+	1.27572i	−0.717979	+	0.0516526i
$611$	15.9517	−	1.67659i	0.645338	−	0.0678278i
$612$	−3.94752	−	9.88114i	−0.159569	−	0.399421i
$613$	28.0704	+	34.6640i	1.13375	+	1.40007i	0.904380	+	0.426728i	$0.140334\pi$
$613$	28.0704	+	34.6640i	1.13375	+	1.40007i	0.229372	+	0.973339i	$0.426333\pi$
$614$	−9.11771	−	15.7923i	−0.367961	−	0.637327i
$615$	−4.65231	+	3.57026i	−0.187599	+	0.143967i
$616$	8.51128	+	6.18381i	0.342929	+	0.249153i
$617$	−1.71308	−	32.6875i	−0.0689660	−	1.31595i	−0.785702	−	0.618606i	$-0.787698\pi$
$617$	−1.71308	−	32.6875i	−0.0689660	−	1.31595i	0.716736	−	0.697345i	$-0.245635\pi$
$618$	−24.8516	+	22.6834i	−0.999677	+	0.912459i
$619$		−	6.30627i		−	0.253470i	−0.991937	−	0.126735i	$-0.959550\pi$
$619$		−	6.30627i		−	0.253470i	0.991937	−	0.126735i	$-0.0404498\pi$
$620$	12.2188	−	2.38786i	0.490717	−	0.0958986i
$621$	12.0779	+	11.5965i	0.484671	+	0.465350i
$622$	−6.95337	+	3.54292i	−0.278805	+	0.142058i
$623$	22.2353	−	1.16530i	0.890840	−	0.0466870i
$624$	1.58036	−	4.20189i	0.0632650	−	0.168210i
$625$	−0.672115	+	24.9910i	−0.0268846	+	0.999639i
$626$	−18.2503	+	10.5368i	−0.729429	+	0.421136i
$627$	−2.19350	−	1.57106i	−0.0875998	−	0.0627422i
$628$	−2.20147	+	13.8995i	−0.0878482	+	0.554652i
$629$	−0.0989061	−	0.941028i	−0.00394364	−	0.0375213i
$630$	−2.21412	+	12.4194i	−0.0882125	+	0.494802i
$631$	25.4967	−	11.3519i	1.01501	−	0.451910i	0.169304	−	0.985564i	$-0.445848\pi$
$631$	25.4967	−	11.3519i	1.01501	−	0.451910i	0.845703	+	0.533654i	$0.179181\pi$
$632$	−2.58656	+	3.98295i	−0.102888	+	0.158433i
$633$	19.7655	−	22.2533i	0.785608	−	0.884490i
$634$	2.22922	−	5.00692i	0.0885337	−	0.198850i
$635$	−11.6096	+	32.0971i	−0.460712	+	1.27373i
$636$	−14.3836	+	9.48007i	−0.570348	+	0.375909i
$637$	3.21701	+	8.38059i	0.127463	+	0.332051i
$638$	12.0683	+	18.5835i	0.477787	+	0.735727i
$639$	8.35764	−	7.73296i	0.330623	−	0.305911i
$640$	−2.17073	−	0.536603i	−0.0858055	−	0.0212111i
$641$	20.8141	−	18.7411i	0.822107	−	0.740228i	−0.146397	−	0.989226i	$-0.546768\pi$
$641$	20.8141	−	18.7411i	0.822107	−	0.740228i	0.968504	+	0.248997i	$0.0801011\pi$
$642$	−0.539807	+	1.23489i	−0.0213045	+	0.0487371i
$643$	−6.06594	+	38.2989i	−0.239217	+	1.51036i	0.516969	+	0.856004i	$0.327060\pi$
$643$	−6.06594	+	38.2989i	−0.239217	+	1.51036i	−0.756187	+	0.654356i	$0.772940\pi$
$644$	−0.633426	+	6.02664i	−0.0249605	+	0.237483i
$645$	18.3982	−	23.9798i	0.724428	−	0.944204i
$646$	−0.493807	+	0.855299i	−0.0194286	+	0.0336513i
$647$	−35.2296	+	5.57983i	−1.38502	+	0.219366i	−0.804051	−	0.594560i	$-0.797326\pi$
$647$	−35.2296	+	5.57983i	−1.38502	+	0.219366i	−0.580969	+	0.813926i	$0.697326\pi$
$648$	3.86702	−	8.12688i	0.151911	−	0.319254i
$649$	23.3534	+	7.58797i	0.916700	+	0.297854i
$650$	3.18554	+	12.5617i	0.124947	+	0.492712i
$651$	−14.4204	+	10.9978i	−0.565179	+	0.431037i
$652$	−7.27061	−	7.27061i	−0.284739	−	0.284739i
$653$	8.93738	−	4.55382i	0.349747	−	0.178205i	−0.270287	−	0.962780i	$-0.587119\pi$
$653$	8.93738	−	4.55382i	0.349747	−	0.178205i	0.620034	+	0.784575i	$0.287119\pi$
$654$	2.60153	−	5.19251i	0.101728	−	0.203043i
$655$	−4.68066	+	8.48419i	−0.182888	+	0.331505i
$656$	1.31131	+	0.757085i	0.0511981	+	0.0295592i
$657$	−0.195306	−	0.691266i	−0.00761959	−	0.0269689i
$658$	7.32389	+	9.04425i	0.285515	+	0.352581i
$659$	20.8326	−	15.1358i	0.811524	−	0.589607i	−0.102748	−	0.994707i	$-0.532763\pi$
$659$	20.8326	−	15.1358i	0.811524	−	0.589607i	0.914272	+	0.405100i	$0.132763\pi$
$660$	20.7748	+	6.15251i	0.808659	+	0.239486i
$661$	−6.89896	−	7.66207i	−0.268338	−	0.298020i	0.593883	−	0.804551i	$-0.297594\pi$
$661$	−6.89896	−	7.66207i	−0.268338	−	0.298020i	−0.862222	+	0.506531i	$0.830927\pi$
$662$	−3.92114	+	10.2149i	−0.152399	+	0.397014i
$663$	15.1763	+	4.81760i	0.589399	+	0.187100i
$664$	3.60499	−	16.9602i	0.139901	−	0.658182i
$665$	1.03274	−	0.551779i	0.0400481	−	0.0213971i
$666$	0.527414	−	0.601967i	0.0204369	−	0.0233257i
$667$	−5.79437	+	11.3721i	−0.224359	+	0.440329i
$668$	−5.17015	−	13.4687i	−0.200039	−	0.521120i
$669$	0.372858	+	6.29752i	0.0144155	+	0.243476i
$670$	3.90651	−	1.35388i	0.150921	−	0.0523051i
$671$	−18.0915	−	40.6341i	−0.698413	−	1.56866i
$672$	3.18140	−	0.698799i	0.122725	−	0.0269568i
$673$	−29.2946	−	23.7223i	−1.12923	−	0.914429i	−0.132179	−	0.991226i	$-0.542197\pi$
$673$	−29.2946	−	23.7223i	−1.12923	−	0.914429i	−0.997047	+	0.0767973i	$0.975531\pi$
$674$	−9.25722	+	6.72576i	−0.356575	+	0.259067i
$675$	4.24102	+	25.6323i	0.163237	+	0.986587i
$676$	−3.14110	−	5.44055i	−0.120812	−	0.209252i
$677$	3.60651	+	13.4597i	0.138609	+	0.517297i	0.999957	+	0.00928094i	$0.00295426\pi$
$677$	3.60651	+	13.4597i	0.138609	+	0.517297i	−0.861348	+	0.508016i	$0.830379\pi$
$678$	27.8349	−	12.6196i	1.06899	−	0.484655i
$679$	2.38360	+	2.14620i	0.0914741	+	0.0823636i
$680$	1.49769	−	7.78825i	0.0574336	−	0.298666i
$681$	11.4140	+	41.4710i	0.437384	+	1.58917i
$682$	16.0157	+	26.7149i	0.613273	+	1.02297i
$683$	27.9881	+	27.9881i	1.07094	+	1.07094i	0.997284	+	0.0736512i	$0.0234652\pi$
$683$	27.9881	+	27.9881i	1.07094	+	1.07094i	0.0736512	+	0.997284i	$0.476535\pi$
$684$	−0.814667	+	0.184740i	−0.0311496	+	0.00706370i
$685$	−8.21220	−	46.0339i	−0.313772	−	1.75886i
$686$	−11.5660	+	15.9192i	−0.441592	+	0.607799i
$687$	−35.5658	+	20.8566i	−1.35692	+	0.795731i
$688$	−7.53804	−	2.01981i	−0.287385	−	0.0770046i
$689$	2.69458	−	25.6372i	0.102655	−	0.976699i
$690$	2.91410	+	12.1351i	0.110938	+	0.461975i
$691$	−0.842997	−	8.02059i	−0.0320691	−	0.305117i	−0.998786	−	0.0492674i	$-0.984311\pi$
$691$	−0.842997	−	8.02059i	−0.0320691	−	0.305117i	0.966716	−	0.255850i	$-0.0823553\pi$
$692$	14.3266	+	0.750826i	0.544616	+	0.0285421i
$693$	−31.1032	+	5.35945i	−1.18151	+	0.203589i
$694$	−0.737627	−	3.47026i	−0.0279999	−	0.131729i
$695$	−1.22732	+	14.3599i	−0.0465550	+	0.544701i
$696$	6.78305	+	1.02725i	0.257111	+	0.0389377i
$697$	−2.43816	+	4.78515i	−0.0923517	+	0.181251i
$698$	−16.7013	+	32.7782i	−0.632154	+	1.24067i
$699$	−2.79567	−	0.423387i	−0.105742	−	0.0160139i
$700$	−6.38511	+	6.90247i	−0.241334	+	0.260889i
$701$	−8.23381	−	38.7370i	−0.310987	−	1.46308i	−0.804819	−	0.593520i	$-0.797738\pi$
$701$	−8.23381	−	38.7370i	−0.310987	−	1.46308i	0.493832	−	0.869557i	$-0.335596\pi$
$702$	5.72687	+	12.1895i	0.216147	+	0.460062i
$703$	−0.0741823	−	0.00388773i	−0.00279784	−	0.000146629i
$704$	−0.584766	−	5.56368i	−0.0220392	−	0.209689i
$705$	20.4365	+	12.5219i	0.769683	+	0.471603i
$706$	0.539098	−	5.12918i	0.0202892	−	0.193039i
$707$	−4.42135	−	1.18470i	−0.166282	−	0.0445552i
$708$	6.55804	−	3.84579i	0.246466	−	0.144534i
$709$	26.6405	−	36.6675i	1.00050	−	1.37708i	0.0754881	−	0.997147i	$-0.475949\pi$
$709$	26.6405	−	36.6675i	1.00050	−	1.37708i	0.925016	−	0.379929i	$-0.124051\pi$
$710$	8.35497	−	1.49048i	0.313557	−	0.0559368i
$711$	−3.15084	−	13.8946i	−0.118166	−	0.521089i
$712$	−8.37211	−	8.37211i	−0.313758	−	0.313758i
$713$	−8.71374	+	15.6831i	−0.326332	+	0.587336i
$714$	3.06568	+	11.1387i	0.114730	+	0.416855i
$715$	−26.8430	+	18.1843i	−1.00387	+	0.680053i
$716$	−12.5793	−	11.3264i	−0.470110	−	0.423289i
$717$	−42.7849	+	19.3976i	−1.59783	+	0.724418i
$718$	3.83566	+	14.3149i	0.143146	+	0.534227i
$719$	−16.4346	−	28.4655i	−0.612907	−	1.06159i	−0.990748	−	0.135715i	$-0.956667\pi$
$719$	−16.4346	−	28.4655i	−0.612907	−	1.06159i	0.377841	−	0.925870i	$-0.376666\pi$
$720$	5.69560	−	3.54404i	0.212262	−	0.132078i
$721$	29.5553	−	21.4732i	1.10070	−	0.799704i
$722$	−14.7055	−	11.9083i	−0.547283	−	0.443181i
$723$	−33.0306	+	7.25521i	−1.22842	+	0.269824i
$724$	1.99064	+	4.47106i	0.0739817	+	0.166166i
$725$	−17.7650	+	8.75290i	−0.659775	+	0.325075i
$726$	2.07776	+	35.0931i	0.0771130	+	1.30243i
$727$	2.10971	+	5.49597i	0.0782447	+	0.203834i	0.967123	−	0.254309i	$-0.0818480\pi$
$727$	2.10971	+	5.49597i	0.0782447	+	0.203834i	−0.888878	+	0.458143i	$0.848515\pi$
$728$	−2.21284	+	4.34294i	−0.0820133	+	0.160960i
$729$	9.38061	+	25.3181i	0.347430	+	0.937706i
$730$	0.155512	−	0.512327i	0.00575575	−	0.0189621i
$731$	5.75484	−	27.0744i	0.212850	−	1.00138i
$732$	−13.1258	−	4.16668i	−0.485143	−	0.154005i
$733$	−11.0093	+	28.6802i	−0.406638	+	1.05933i	0.565465	+	0.824772i	$0.308697\pi$
$733$	−11.0093	+	28.6802i	−0.406638	+	1.05933i	−0.972103	+	0.234556i	$0.924637\pi$
$734$	−19.8156	−	22.0075i	−0.731408	−	0.812311i
$735$	−3.80903	+	12.8617i	−0.140498	+	0.474412i
$736$	2.60693	−	1.89404i	0.0960927	−	0.0698154i
$737$	6.50959	+	8.03867i	0.239784	+	0.296108i
$738$	−4.37139	+	1.23506i	−0.160913	+	0.0454632i
$739$	34.7545	+	20.0655i	1.27847	+	0.738122i	0.976566	−	0.215218i	$-0.0690461\pi$
$739$	34.7545	+	20.0655i	1.27847	+	0.738122i	0.301899	+	0.953340i	$0.402379\pi$
$740$	0.573092	−	0.165576i	0.0210673	−	0.00608668i
$741$	0.559941	−	1.11761i	0.0205699	−	0.0410564i
$742$	16.6653	−	8.49139i	0.611802	−	0.311729i
$743$	−11.3232	−	11.3232i	−0.415410	−	0.415410i	0.468208	−	0.883618i	$-0.344900\pi$
$743$	−11.3232	−	11.3232i	−0.415410	−	0.415410i	−0.883618	+	0.468208i	$0.844900\pi$
$744$	9.47695	+	1.78535i	0.347442	+	0.0654539i
$745$	3.16729	−	0.395341i	0.116041	−	0.0144842i
$746$	22.4759	+	7.30285i	0.822900	+	0.267376i
$747$	28.9194	+	43.2372i	1.05810	+	1.58197i
$748$	19.5978	−	3.10399i	0.716567	−	0.113493i
$749$	0.731639	−	1.26724i	0.0267335	−	0.0463038i
$750$	−7.64948	+	17.7900i	−0.279319	+	0.649600i
$751$	−4.47262	+	42.5541i	−0.163208	+	1.55282i	0.539894	+	0.841733i	$0.318464\pi$
$751$	−4.47262	+	42.5541i	−0.163208	+	1.55282i	−0.703102	+	0.711089i	$0.748202\pi$
$752$	0.968083	−	6.11224i	0.0353024	−	0.222890i
$753$	−1.43856	+	3.29092i	−0.0524241	+	0.119928i
$754$	−7.62913	+	6.86930i	−0.277837	+	0.250165i
$755$	33.8175	−	20.4120i	1.23074	−	0.742868i
$756$	−5.15433	+	8.30178i	−0.187461	+	0.301933i
$757$	14.3016	+	22.0225i	0.519801	+	0.800423i	0.996921	−	0.0784153i	$-0.0249860\pi$
$757$	14.3016	+	22.0225i	0.519801	+	0.800423i	−0.477120	+	0.878838i	$0.658319\pi$
$758$	−8.40451	−	21.8945i	−0.305266	−	0.795244i
$759$	−26.0703	+	17.1826i	−0.946290	+	0.623688i
$760$	−0.585510	−	0.211780i	−0.0212387	−	0.00768206i
$761$	6.15933	−	13.8341i	0.223275	−	0.501485i	−0.766823	−	0.641858i	$-0.778164\pi$
$761$	6.15933	−	13.8341i	0.223275	−	0.501485i	0.990099	+	0.140374i	$0.0448304\pi$
$762$	−17.5573	+	19.7672i	−0.636035	+	0.716091i
$763$	−3.43437	+	5.28846i	−0.124332	+	0.191455i
$764$	4.91830	−	2.18977i	0.177938	−	0.0792231i
$765$	13.6101	+	19.5157i	0.492075	+	0.705593i
$766$	−0.402655	−	3.83100i	−0.0145485	−	0.138420i
$767$	−1.77968	+	11.2364i	−0.0642604	+	0.405724i
$768$	−1.40813	−	1.00855i	−0.0508114	−	0.0363930i
$769$	26.1422	−	15.0932i	0.942714	−	0.544276i	0.0519036	−	0.998652i	$-0.483471\pi$
$769$	26.1422	−	15.0932i	0.942714	−	0.544276i	0.890810	+	0.454376i	$0.150138\pi$
$770$	−21.6729	−	9.14836i	−0.781037	−	0.329684i
$771$	12.9337	−	34.3884i	0.465796	−	1.23847i
$772$	−25.2335	+	1.32243i	−0.908173	+	0.0475953i
$773$	−11.8262	+	6.02575i	−0.425359	+	0.216731i	−0.653547	−	0.756886i	$-0.726720\pi$
$773$	−11.8262	+	6.02575i	−0.425359	+	0.216731i	0.228188	+	0.973617i	$0.426720\pi$
$774$	20.1147	−	11.9797i	0.723008	−	0.430602i
$775$	−25.3978	+	11.3996i	−0.912316	+	0.409486i
$776$		−	1.70557i		−	0.0612264i
$777$	−0.641805	+	0.585810i	−0.0230246	+	0.0210158i
$778$	1.18535	+	22.6178i	0.0424968	+	0.810887i
$779$	0.341099	+	0.247823i	0.0122211	+	0.00887917i
$780$	−1.30970	+	9.95247i	−0.0468947	+	0.356356i
$781$	10.6165	+	18.3883i	0.379888	+	0.657985i
$782$	7.19256	+	8.88207i	0.257205	+	0.317622i
$783$	−16.4011	+	12.4334i	−0.586127	+	0.444332i
$784$	3.44448	−	0.362030i	0.123017	−	0.0129296i
$785$	−2.25800	−	31.3866i	−0.0805916	−	1.12024i
$786$	−5.80080	+	4.76286i	−0.206908	+	0.169885i
$787$	−18.3345	−	11.9066i	−0.653555	−	0.424424i	0.174818	−	0.984601i	$-0.444066\pi$
$787$	−18.3345	−	11.9066i	−0.653555	−	0.424424i	−0.828373	+	0.560177i	$0.810733\pi$
$788$	−0.783489	−	1.20647i	−0.0279106	−	0.0429786i
$789$	−14.1926	−	2.14937i	−0.505269	−	0.0765196i
$790$	3.61203	−	9.98621i	0.128510	−	0.355293i
$791$	−31.5586	+	10.2540i	−1.12209	+	0.364590i
$792$	13.1848	+	10.3841i	0.468501	+	0.368982i
$793$	17.2829	−	11.2237i	0.613735	−	0.398564i
$794$	5.14803	−	1.09425i	0.182697	−	0.0388334i
$795$	26.5140	−	27.9430i	0.940353	−	0.991037i
$796$	−14.8298	−	16.4701i	−0.525627	−	0.583767i
$797$	−13.2425	−	10.7236i	−0.469073	−	0.379848i	0.365441	−	0.930834i	$-0.380918\pi$
$797$	−13.2425	−	10.7236i	−0.469073	−	0.379848i	−0.834514	+	0.550987i	$0.814252\pi$
$798$	0.901348	−	0.100917i	0.0319074	−	0.00357243i
$799$	21.8290	+	2.29432i	0.772256	+	0.0811673i
$800$	4.99955	+	0.0672175i	0.176761	+	0.00237650i
$801$	35.5166	−	0.481512i	1.25492	−	0.0170134i
$802$	−3.90705	−	24.6681i	−0.137963	−	0.871062i
$803$	1.33768	−	0.0701049i	0.0472058	−	0.00247395i
$804$	3.19922	+	0.145926i	0.112828	+	0.00514643i
$805$	−1.67831	−	13.4459i	−0.0591528	−	0.473905i
$806$	−11.0640	+	9.26499i	−0.389712	+	0.326345i
$807$	20.7275	−	36.4697i	0.729642	−	1.28379i
$808$	1.10502	+	2.16872i	0.0388743	+	0.0762952i
$809$	−1.77514	+	1.97149i	−0.0624105	+	0.0693139i	−0.773542	−	0.633746i	$-0.781517\pi$
$809$	−1.77514	+	1.97149i	−0.0624105	+	0.0693139i	0.711131	+	0.703060i	$0.248183\pi$
$810$	−4.29802	+	19.6603i	−0.151017	+	0.690792i
$811$	−19.6228	+	33.9877i	−0.689049	+	1.19347i	0.283097	+	0.959091i	$0.408638\pi$
$811$	−19.6228	+	33.9877i	−0.689049	+	1.19347i	−0.972146	+	0.234377i	$0.924695\pi$
$812$	−7.19485	−	1.92785i	−0.252490	−	0.0676544i
$813$	35.0053	+	25.0721i	1.22769	+	0.879317i
$814$	0.877233	+	1.20741i	0.0307470	+	0.0423196i
$815$	19.5224	+	12.1446i	0.683841	+	0.425408i
$816$	3.31087	−	5.17475i	0.115904	−	0.181153i
$817$	−2.02868	−	0.778738i	−0.0709745	−	0.0272446i
$818$	2.69104	+	1.74758i	0.0940901	+	0.0611028i
$819$	−4.70674	−	13.8444i	−0.164467	−	0.483762i
$820$	−3.23982	−	0.983416i	−0.113140	−	0.0343424i
$821$	−34.9009	+	11.3400i	−1.21805	+	0.395769i	−0.846372	−	0.532593i	$-0.821218\pi$
$821$	−34.9009	+	11.3400i	−1.21805	+	0.395769i	−0.371679	+	0.928361i	$0.621218\pi$
$822$	7.29037	−	35.4794i	0.254281	−	1.23748i
$823$	39.1470	−	15.0271i	1.36458	−	0.523813i	0.437682	−	0.899130i	$-0.355800\pi$
$823$	39.1470	−	15.0271i	1.36458	−	0.523813i	0.926896	+	0.375317i	$0.122466\pi$
$824$	−19.0017	−	4.03894i	−0.661957	−	0.140703i
$825$	−48.3639	−	2.85802i	−1.68381	−	0.0995036i
$826$	−7.54076	+	3.35736i	−0.262377	+	0.116818i
$827$	10.3464	+	0.542229i	0.359778	+	0.0188552i	0.231369	−	0.972866i	$-0.425680\pi$
$827$	10.3464	+	0.542229i	0.359778	+	0.0188552i	0.128409	+	0.991721i	$0.459013\pi$
$828$	−1.38268	+	9.56763i	−0.0480515	+	0.332498i
$829$	11.4531	+	15.7638i	0.397782	+	0.547500i	0.960186	−	0.279363i	$-0.0901233\pi$
$829$	11.4531	+	15.7638i	0.397782	+	0.547500i	−0.562404	+	0.826863i	$0.690123\pi$
$830$	0.754364	+	38.7640i	0.0261844	+	1.34552i
$831$	−12.4244	−	12.2571i	−0.430999	−	0.425196i
$832$	2.50356	−	0.670826i	0.0867952	−	0.0232567i
$833$	1.92168	+	12.1330i	0.0665824	+	0.420385i
$834$	−5.00065	+	9.98101i	−0.173158	+	0.345614i
$835$	18.0929	+	26.7082i	0.626132	+	0.924276i
$836$		−	1.55774i		−	0.0538756i
$837$	−23.6675	+	16.6387i	−0.818070	+	0.575118i
$838$	0.425792	−	0.425792i	0.0147087	−	0.0147087i
$839$	14.2791	−	43.9466i	0.492969	−	1.51720i	−0.327128	−	0.944980i	$-0.606081\pi$
$839$	14.2791	−	43.9466i	0.492969	−	1.51720i	0.820097	−	0.572224i	$-0.193919\pi$
$840$	−6.57373	+	3.13596i	−0.226815	+	0.108201i
$841$	10.7694	+	7.82441i	0.371358	+	0.269807i
$842$	1.77010	+	6.60612i	0.0610018	+	0.227662i
$843$	−0.0221878	−	3.27331i	−0.000764187	−	0.112739i
$844$	17.0900	+	1.79623i	0.588263	+	0.0618289i
$845$	9.60090	+	10.2544i	0.330281	+	0.352763i
$846$	11.1150	+	14.8703i	0.382142	+	0.511252i
$847$	1.99761	−	38.1166i	0.0686386	−	1.30970i
$848$	−9.28527	−	3.56428i	−0.318857	−	0.122398i
$849$	18.5531	+	35.8104i	0.636741	+	1.22901i
$850$	0.689967	+	17.7207i	0.0236657	+	0.607815i
$851$	−0.349650	+	0.785326i	−0.0119858	+	0.0269206i
$852$	6.43937	+	1.32318i	0.220609	+	0.0453312i
$853$	−9.04852	−	4.61045i	−0.309815	−	0.157859i	0.292169	−	0.956367i	$-0.405623\pi$
$853$	−9.04852	−	4.61045i	−0.309815	−	0.157859i	−0.601984	+	0.798508i	$0.705623\pi$
$854$	13.6594	+	6.08157i	0.467416	+	0.208107i
$855$	1.68040	−	0.815656i	0.0574686	−	0.0278948i
$856$	−0.761100	+	0.161777i	−0.0260139	+	0.00552942i
$857$	16.7873	−	43.7324i	0.573442	−	1.49387i	−0.273334	−	0.961919i	$-0.588126\pi$
$857$	16.7873	−	43.7324i	0.573442	−	1.49387i	0.846776	−	0.531949i	$-0.178540\pi$
$858$	−24.5296	+	5.38795i	−0.837426	+	0.183942i
$859$	57.2381	−	6.01597i	1.95294	−	0.205262i	0.956643	−	0.291262i	$-0.0940750\pi$
$859$	57.2381	−	6.01597i	1.95294	−	0.205262i	0.996295	+	0.0859994i	$0.0274083\pi$
$860$	17.4407	+	0.574040i	0.594723	+	0.0195746i
$861$	4.86596	−	0.804539i	0.165831	−	0.0274186i
$862$	1.87853	−	7.01077i	0.0639830	−	0.238788i
$863$	−1.38577	+	0.371315i	−0.0471721	+	0.0126397i	−0.282328	−	0.959318i	$-0.591107\pi$
$863$	−1.38577	+	0.371315i	−0.0471721	+	0.0126397i	0.235156	+	0.971958i	$0.424440\pi$
$864$	5.11459	−	0.917044i	0.174002	−	0.0311985i
$865$	−31.5806	+	5.63382i	−1.07377	+	0.191556i
$866$	−5.25954	−	1.70893i	−0.178726	−	0.0580717i
$867$	−6.65582	−	3.78282i	−0.226044	−	0.128471i
$868$	−10.0100	−	3.07129i	−0.339761	−	0.104246i
$869$	26.5682			0.901263
$870$	−15.2929	+	1.20445i	−0.518479	+	0.0408346i
$871$	−3.20670	+	3.56140i	−0.108655	+	0.120674i
$872$	3.31183	−	0.524543i	0.112153	−	0.0177633i
$873$	3.66678	+	3.56868i	0.124102	+	0.120782i
$874$	0.777051	−	0.448631i	0.0262842	−	0.0151752i
$875$	10.4030	−	18.2714i	0.351686	−	0.617687i
$876$	0.258805	−	0.324064i	0.00874421	−	0.0109491i
$877$	−11.3553	+	14.0227i	−0.383443	+	0.473512i	−0.931926	−	0.362649i	$-0.881872\pi$
$877$	−11.3553	+	14.0227i	−0.383443	+	0.473512i	0.548483	+	0.836162i	$0.315206\pi$
$878$	1.12797	−	21.5230i	0.0380672	−	0.726365i
$879$	−3.41430	+	2.80338i	−0.115162	+	0.0945556i
$880$	4.09633	+	11.8196i	0.138087	+	0.398438i
$881$	4.50375	−	21.1885i	0.151735	−	0.713857i	−0.834833	−	0.550504i	$-0.814436\pi$
$881$	4.50375	−	21.1885i	0.151735	−	0.713857i	0.986568	−	0.163353i	$-0.0522311\pi$
$882$	−6.42881	+	8.16273i	−0.216469	+	0.274853i
$883$	−16.1160	−	8.21149i	−0.542345	−	0.276339i	0.161281	−	0.986908i	$-0.448437\pi$
$883$	−16.1160	−	8.21149i	−0.542345	−	0.276339i	−0.703627	+	0.710570i	$0.748437\pi$
$884$	2.84077	+	8.74298i	0.0955454	+	0.294058i
$885$	−12.3305	+	11.7025i	−0.414485	+	0.393376i
$886$	−29.4426	−	6.25821i	−0.989143	−	0.210249i
$887$	−8.58098	+	13.2136i	−0.288121	+	0.443668i	−0.952861	−	0.303407i	$-0.901876\pi$
$887$	−8.58098	+	13.2136i	−0.288121	+	0.443668i	0.664740	+	0.747075i	$0.268542\pi$
$888$	0.459857	+	0.0451836i	0.0154318	+	0.00151626i
$889$	21.3325	−	19.2079i	0.715469	−	0.644211i
$890$	22.4801	+	13.9845i	0.753534	+	0.468763i
$891$	−49.9120	+	6.61843i	−1.67212	+	0.221726i
$892$	−2.83055	+	2.29214i	−0.0947739	+	0.0767464i
$893$	0.445989	−	1.66445i	0.0149244	−	0.0556988i
$894$	2.39245	+	0.623705i	0.0800154	+	0.0208598i
$895$	33.1412	+	18.2837i	1.10779	+	0.611157i
$896$	1.39754	+	1.25835i	0.0466884	+	0.0420384i
$897$	−9.75223	−	10.6844i	−0.325617	−	0.356742i
$898$	17.5112	−	17.5112i	0.584355	−	0.584355i
$899$	−17.3645	−	13.5946i	−0.579138	−	0.453404i
$900$	−10.6054	+	10.6078i	−0.353514	+	0.353593i
$901$	10.9010	−	33.5497i	0.363164	−	1.11770i
$902$	−0.443325	−	8.45915i	−0.0147611	−	0.281659i
$903$	−23.1511	+	10.4962i	−0.770421	+	0.349290i
$904$	15.2810	+	8.82249i	0.508239	+	0.293432i
$905$	−6.60361	−	8.72683i	−0.219511	−	0.290090i
$906$	30.1869	−	4.99112i	1.00289	−	0.165819i
$907$	−8.69650	−	1.37739i	−0.288763	−	0.0457355i	0.0103727	−	0.999946i	$-0.496698\pi$
$907$	−8.69650	−	1.37739i	−0.288763	−	0.0457355i	−0.299135	+	0.954211i	$0.596698\pi$
$908$	−15.6283	+	19.2993i	−0.518643	+	0.640471i
$909$	−6.97459	−	2.16210i	−0.231332	−	0.0717123i
$910$	2.61551	−	10.5805i	0.0867033	−	0.350742i
$911$	−11.4583	−	53.9069i	−0.379629	−	1.78601i	−0.588952	−	0.808168i	$-0.700459\pi$
$911$	−11.4583	−	53.9069i	−0.379629	−	1.78601i	0.209323	−	0.977847i	$-0.432874\pi$
$912$	−0.360590	−	0.320278i	−0.0119403	−	0.0106055i
$913$	−90.5576	+	34.7618i	−2.99702	+	1.15045i
$914$	−0.847015	−	2.60685i	−0.0280168	−	0.0862268i
$915$	30.6987	+	2.41430i	1.01487	+	0.0798142i
$916$	−21.7463	−	9.68206i	−0.718517	−	0.319904i
$917$	6.83448	−	4.43837i	0.225695	−	0.146568i
$918$	4.19754	+	17.9455i	0.138540	+	0.592289i
$919$	−0.946474	−	2.12582i	−0.0312213	−	0.0701242i	0.897262	−	0.441499i	$-0.145553\pi$
$919$	−0.946474	−	2.12582i	−0.0312213	−	0.0701242i	−0.928483	+	0.371375i	$0.878886\pi$
$920$	−4.71624	+	5.44743i	−0.155490	+	0.179596i
$921$	11.5185	+	29.4094i	0.379549	+	0.969074i
$922$	17.4007	+	2.75600i	0.573061	+	0.0907639i
$923$	−7.64503	+	6.19082i	−0.251639	+	0.203773i
$924$	−12.9720	−	12.7973i	−0.426747	−	0.421001i
$925$	−1.16404	+	0.651353i	−0.0382734	+	0.0214163i
$926$	4.75555	−	6.54546i	0.156277	−	0.215097i
$927$	48.4419	−	32.4005i	1.59104	−	1.06417i
$928$	1.79819	+	3.52914i	0.0590284	+	0.115850i
$929$	−13.1614			−0.431813			−0.215906	−	0.976414i	$-0.569271\pi$
$929$	−13.1614			−0.431813			−0.215906	+	0.976414i	$0.569271\pi$
$930$	−21.5442	+	0.920317i	−0.706463	+	0.0301784i
$931$	0.964400			0.0316069
$932$	−0.741134	−	1.45456i	−0.0242766	−	0.0476456i
$933$	12.8267	−	4.26397i	0.419927	−	0.139596i
$934$	−7.12890	+	9.81209i	−0.233265	+	0.321061i
$935$	−41.1042	+	16.7031i	−1.34425	+	0.546249i
$936$	−3.79616	+	6.78596i	−0.124082	+	0.221806i
$937$	−31.6933	+	25.6647i	−1.03538	+	0.838430i	−0.987052	−	0.160401i	$-0.948721\pi$
$937$	−31.6933	+	25.6647i	−1.03538	+	0.838430i	−0.0483235	+	0.998832i	$0.515388\pi$
$938$	−3.43434	−	0.543946i	−0.112135	−	0.0177605i
$939$	33.9868	−	13.3113i	1.10912	−	0.434399i
$940$	0.992943	+	13.8021i	0.0323862	+	0.450174i
$941$	−12.6964	−	28.5166i	−0.413891	−	0.929616i	−0.993406	−	0.114653i	$-0.963424\pi$
$941$	−12.6964	−	28.5166i	−0.413891	−	0.929616i	0.579514	−	0.814962i	$-0.303242\pi$
$942$	7.37492	−	23.2323i	0.240288	−	0.756950i
$943$	4.09202	−	2.65739i	0.133255	−	0.0865365i
$944$	4.00983	+	1.78529i	0.130509	+	0.0581062i
$945$	7.01271	−	20.6943i	0.228124	−	0.673187i
$946$	13.4910	+	41.5211i	0.438631	+	1.34997i
$947$	−0.482122	+	0.185069i	−0.0156668	+	0.00601394i	−0.366189	−	0.930541i	$-0.619338\pi$
$947$	−0.482122	+	0.185069i	−0.0156668	+	0.00601394i	0.350522	+	0.936555i	$0.386004\pi$
$948$	5.46253	−	6.15008i	0.177415	−	0.199745i
$949$	0.129031	+	0.607042i	0.00418851	+	0.0197054i
$950$	1.38254	+	0.164131i	0.0448556	+	0.00532511i
$951$	−5.11614	+	7.99631i	−0.165902	+	0.259298i
$952$	−4.19760	+	5.18361i	−0.136045	+	0.168002i
$953$	36.9996	+	5.86016i	1.19853	+	0.189829i	0.723617	−	0.690202i	$-0.242478\pi$
$953$	36.9996	+	5.86016i	1.19853	+	0.189829i	0.474917	+	0.880031i	$0.342478\pi$
$954$	27.0910	−	12.5044i	0.877103	−	0.404846i
$955$	−9.59978	+	7.26417i	−0.310642	+	0.235063i
$956$	−23.4884	−	13.5610i	−0.759669	−	0.438595i
$957$	−15.8475	−	34.9546i	−0.512278	−	1.12992i
$958$	1.83165	+	34.9500i	0.0591779	+	1.12918i
$959$	−12.1525	+	37.4017i	−0.392426	+	1.20776i
$960$	3.57825	+	1.48193i	0.115488	+	0.0478289i
$961$	−23.7076	−	19.9738i	−0.764760	−	0.644315i
$962$	−0.488930	+	0.488930i	−0.0157637	+	0.0157637i
$963$	1.24470	−	1.97477i	0.0401099	−	0.0636361i
$964$	−14.5098	−	13.0647i	−0.467328	−	0.420784i
$965$	54.2811	−	15.6827i	1.74737	−	0.504844i
$966$	2.64777	−	10.1565i	0.0851906	−	0.326780i
$967$	3.20451	−	11.9594i	0.103050	−	0.384589i	−0.895066	−	0.445933i	$-0.852872\pi$
$967$	3.20451	−	11.9594i	0.103050	−	0.384589i	0.998117	+	0.0613441i	$0.0195387\pi$
$968$	−15.7733	+	12.7730i	−0.506974	+	0.410539i
$969$	1.06748	−	1.33665i	0.0342924	−	0.0429394i
$970$	0.865360	+	3.71430i	0.0277850	+	0.119259i
$971$	−13.0010	+	11.7061i	−0.417221	+	0.375668i	−0.850837	−	0.525430i	$-0.823904\pi$
$971$	−13.0010	+	11.7061i	−0.417221	+	0.375668i	0.433615	+	0.901098i	$0.357238\pi$
$972$	−8.73007	+	12.9146i	−0.280017	+	0.414235i
$973$	6.60152	−	10.1655i	0.211635	−	0.325889i
$974$	−41.2171	−	8.76096i	−1.32068	−	0.280719i
$975$	−2.19742	−	22.3384i	−0.0703739	−	0.715403i
$976$	−2.45694	−	7.56169i	−0.0786448	−	0.242044i
$977$	23.5609	+	12.0049i	0.753779	+	0.384070i	0.788265	−	0.615336i	$-0.210979\pi$
$977$	23.5609	+	12.0049i	0.753779	+	0.384070i	−0.0344862	+	0.999405i	$0.510979\pi$
$978$	10.5655	+	14.3367i	0.337846	+	0.458438i
$979$	−13.7713	+	64.7891i	−0.440134	+	2.07067i
$980$	−7.31752	+	2.53604i	−0.233750	+	0.0810110i
$981$	−5.80187	+	8.21758i	−0.185239	+	0.262367i
$982$	0.678556	−	12.9476i	0.0216536	−	0.413175i
$983$	−27.1372	+	33.5117i	−0.865543	+	1.06886i	0.131447	+	0.991323i	$0.458038\pi$
$983$	−27.1372	+	33.5117i	−0.865543	+	1.06886i	−0.996990	+	0.0775336i	$0.975295\pi$
$984$	−2.04930	−	1.63662i	−0.0653293	−	0.0521734i
$985$	2.31837	+	2.22986i	0.0738693	+	0.0710492i
$986$	−12.1663	+	7.02422i	−0.387454	+	0.223697i
$987$	−10.1967	−	17.3879i	−0.324564	−	0.553464i
$988$	0.712822	−	0.112900i	0.0226779	−	0.00359182i
$989$	−16.8266	+	18.6879i	−0.535055	+	0.594239i
$990$	−33.9817	−	15.9243i	−1.08001	−	0.506107i
$991$	5.77086			0.183317			0.0916586	−	0.995790i	$-0.470783\pi$
$991$	5.77086			0.183317			0.0916586	+	0.995790i	$0.470783\pi$
$992$	2.34800	+	5.04845i	0.0745491	+	0.160289i
$993$	9.36429	−	16.4763i	0.297167	−	0.522861i
$994$	−6.78827	−	2.20564i	−0.215311	−	0.0699587i
$995$	40.6519	+	28.3435i	1.28875	+	0.898549i
$996$	−10.5723	+	28.1097i	−0.334995	+	0.890691i
$997$	30.1734	−	8.08494i	0.955601	−	0.256053i	0.252864	−	0.967502i	$-0.418628\pi$
$997$	30.1734	−	8.08494i	0.955601	−	0.256053i	0.702737	+	0.711449i	$0.251961\pi$
$998$	−5.13016	+	19.1460i	−0.162392	+	0.606057i
$999$	−1.05933	+	0.894097i	−0.0335157	+	0.0282880i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bs.a.107.19	✓	1024
3.2	odd	2	inner	930.2.bs.a.107.46	yes	1024
5.3	odd	4	inner	930.2.bs.a.293.3	yes	1024
15.8	even	4	inner	930.2.bs.a.293.35	yes	1024
31.20	even	15	inner	930.2.bs.a.857.35	yes	1024
93.20	odd	30	inner	930.2.bs.a.857.3	yes	1024
155.113	odd	60	inner	930.2.bs.a.113.46	yes	1024
465.113	even	60	inner	930.2.bs.a.113.19	yes	1024

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bs.a.107.19	✓	1024	1.1	even	1	trivial
930.2.bs.a.107.46	yes	1024	3.2	odd	2	inner
930.2.bs.a.113.19	yes	1024	465.113	even	60	inner
930.2.bs.a.113.46	yes	1024	155.113	odd	60	inner
930.2.bs.a.293.3	yes	1024	5.3	odd	4	inner
930.2.bs.a.293.35	yes	1024	15.8	even	4	inner
930.2.bs.a.857.3	yes	1024	93.20	odd	30	inner
930.2.bs.a.857.35	yes	1024	31.20	even	15	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.bs (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.453990 - 0.891007i) q^{2} +(0.546386 + 1.64361i) q^{3} +(-0.587785 + 0.809017i) q^{4} +(0.869573 - 2.06006i) q^{5} +(1.21642 - 1.23302i) q^{6} +(-1.46148 + 1.18348i) q^{7} +(0.987688 + 0.156434i) q^{8} +(-2.40292 + 1.79610i) q^{9} +O(q^{10})\)	\(q+(-0.453990 - 0.891007i) q^{2} +(0.546386 + 1.64361i) q^{3} +(-0.587785 + 0.809017i) q^{4} +(0.869573 - 2.06006i) q^{5} +(1.21642 - 1.23302i) q^{6} +(-1.46148 + 1.18348i) q^{7} +(0.987688 + 0.156434i) q^{8} +(-2.40292 + 1.79610i) q^{9} +(-2.23030 + 0.160452i) q^{10} +(-2.27542 - 5.11067i) q^{11} +(-1.65087 - 0.524055i) q^{12} +(2.17373 - 1.41163i) q^{13} +(1.71799 + 0.764897i) q^{14} +(3.86106 + 0.303653i) q^{15} +(-0.309017 - 0.951057i) q^{16} +(3.31125 - 1.27107i) q^{17} +(2.69124 + 1.32561i) q^{18} +(-0.0578930 - 0.272365i) q^{19} +(1.15550 + 1.91437i) q^{20} +(-2.74372 - 1.75546i) q^{21} +(-3.52062 + 4.34761i) q^{22} +(-3.18267 - 0.504085i) q^{23} +(0.282542 + 1.70885i) q^{24} +(-3.48768 - 3.58274i) q^{25} +(-2.24463 - 1.29594i) q^{26} +(-4.26501 - 2.96811i) q^{27} +(-0.0984214 - 1.87799i) q^{28} +(1.22397 - 3.76699i) q^{29} +(-1.48233 - 3.57809i) q^{30} +(1.90951 - 5.23008i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(7.15670 - 6.53230i) q^{33} +(-2.63581 - 2.37329i) q^{34} +(1.16718 + 4.03985i) q^{35} +(-0.0406684 - 2.99972i) q^{36} +(0.0690470 - 0.257687i) q^{37} +(-0.216396 + 0.175234i) q^{38} +(3.50787 + 2.80147i) q^{39} +(1.18113 - 1.89866i) q^{40} +(-1.12525 + 1.01318i) q^{41} +(-0.318509 + 3.24163i) q^{42} +(4.25034 - 6.54494i) q^{43} +(5.47208 + 1.16313i) q^{44} +(1.61054 + 6.51200i) q^{45} +(0.995758 + 3.06463i) q^{46} +(5.51393 + 2.80949i) q^{47} +(1.39433 - 1.02755i) q^{48} +(-0.720093 + 3.38777i) q^{49} +(-1.60887 + 4.73408i) q^{50} +(3.89837 + 4.74791i) q^{51} +(-0.135648 + 2.58832i) q^{52} +(6.25914 - 7.72939i) q^{53} +(-0.708334 + 5.14765i) q^{54} +(-12.5069 + 0.243390i) q^{55} +(-1.62862 + 0.940285i) q^{56} +(0.416031 - 0.243970i) q^{57} +(-3.91208 + 0.619613i) q^{58} +(-2.93702 + 3.26189i) q^{59} +(-2.51514 + 2.94518i) q^{60} +7.95083 q^{61} +(-5.52694 + 0.673025i) q^{62} +(1.38617 - 5.46877i) q^{63} +(0.951057 + 0.309017i) q^{64} +(-1.01784 - 5.70552i) q^{65} +(-9.06940 - 3.41107i) q^{66} +(-1.78599 + 0.478553i) q^{67} +(-0.917986 + 3.42597i) q^{68} +(-0.910447 - 5.50650i) q^{69} +(3.06965 - 2.87402i) q^{70} +(-3.77466 + 0.396732i) q^{71} +(-2.65431 + 1.39808i) q^{72} +(-0.0858084 + 0.223539i) q^{73} +(-0.260947 + 0.0554661i) q^{74} +(3.98302 - 7.68996i) q^{75} +(0.254377 + 0.113256i) q^{76} +(9.37385 + 4.77622i) q^{77} +(0.903582 - 4.39738i) q^{78} +(-1.93164 + 4.33854i) q^{79} +(-2.22795 - 0.190420i) q^{80} +(2.54808 - 8.63176i) q^{81} +(1.41360 + 0.542630i) q^{82} +(0.907457 - 17.3153i) q^{83} +(3.03292 - 1.18788i) q^{84} +(0.260896 - 7.92665i) q^{85} +(-7.76120 - 0.815735i) q^{86} +(6.86023 - 0.0465013i) q^{87} +(-1.44792 - 5.40370i) q^{88} +(-9.57872 - 6.95935i) q^{89} +(5.07106 - 4.39139i) q^{90} +(-1.50621 + 4.63564i) q^{91} +(2.27854 - 2.27854i) q^{92} +(9.63956 + 0.280843i) q^{93} -6.18843i q^{94} +(-0.611431 - 0.117579i) q^{95} +(-1.54856 - 0.775856i) q^{96} +(-0.266810 - 1.68457i) q^{97} +(3.34544 - 0.896408i) q^{98} +(14.6469 + 8.19368i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1024 q - 8 q^{3} + 24 q^{7}+O(q^{10}) \) 1024 * q - 8 * q^3 + 24 * q^7	\( 1024 q - 8 q^{3} + 24 q^{7} + 8 q^{10} + 8 q^{12} - 8 q^{15} + 256 q^{16} + 44 q^{22} + 16 q^{25} - 20 q^{27} + 4 q^{28} + 48 q^{30} - 32 q^{31} - 52 q^{33} + 112 q^{37} + 12 q^{42} + 40 q^{45} + 24 q^{46} - 12 q^{48} + 16 q^{51} - 20 q^{55} - 40 q^{57} - 56 q^{58} - 12 q^{60} + 32 q^{61} + 224 q^{63} - 32 q^{66} + 24 q^{67} - 24 q^{70} - 88 q^{73} + 224 q^{75} - 96 q^{76} - 32 q^{78} + 48 q^{81} - 24 q^{85} + 20 q^{87} - 36 q^{88} + 8 q^{90} - 80 q^{91} - 252 q^{93} - 32 q^{97}+O(q^{100}) \) 1024 * q - 8 * q^3 + 24 * q^7 + 8 * q^10 + 8 * q^12 - 8 * q^15 + 256 * q^16 + 44 * q^22 + 16 * q^25 - 20 * q^27 + 4 * q^28 + 48 * q^30 - 32 * q^31 - 52 * q^33 + 112 * q^37 + 12 * q^42 + 40 * q^45 + 24 * q^46 - 12 * q^48 + 16 * q^51 - 20 * q^55 - 40 * q^57 - 56 * q^58 - 12 * q^60 + 32 * q^61 + 224 * q^63 - 32 * q^66 + 24 * q^67 - 24 * q^70 - 88 * q^73 + 224 * q^75 - 96 * q^76 - 32 * q^78 + 48 * q^81 - 24 * q^85 + 20 * q^87 - 36 * q^88 + 8 * q^90 - 80 * q^91 - 252 * q^93 - 32 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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