LMFDB - Embedded newform 946.2.t.a.7.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [946,2,Mod(7,946)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(946, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([21, 25]))

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

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

chi := DirichletCharacter("946.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 946 = 2 \cdot 11 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	946.t (of order $30$, degree $8$, 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:	$7.55384803121$
Analytic rank:	$0$
Dimension:	$176$
Relative dimension:	$22$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			7.3
Character	$\chi$	$=$	946.7
Dual form			946.2.t.a.811.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 - 0.587785i) q^{2} +(-0.599378 - 2.81985i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.127711 - 0.286844i) q^{5} +(-1.17256 + 2.63361i) q^{6} +(3.11044 + 0.661144i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-4.85168 + 2.16011i) q^{9} +O(q^{10})$	\(q+(-0.809017 - 0.587785i) q^{2} +(-0.599378 - 2.81985i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.127711 - 0.286844i) q^{5} +(-1.17256 + 2.63361i) q^{6} +(3.11044 + 0.661144i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-4.85168 + 2.16011i) q^{9} +(-0.271923 + 0.156995i) q^{10} +(3.13600 - 1.07958i) q^{11} +(2.49662 - 1.44142i) q^{12} +(1.17548 + 2.64016i) q^{13} +(-2.12779 - 2.36315i) q^{14} +(-0.885406 - 0.188199i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(7.42941 - 0.780862i) q^{17} +(5.19477 + 1.10418i) q^{18} +(-1.27012 + 0.269973i) q^{19} +(0.312270 + 0.0328209i) q^{20} -9.16725i q^{21} +(-3.17164 - 0.969902i) q^{22} +(-2.18242 - 3.78006i) q^{23} +(-2.86706 - 0.301340i) q^{24} +(3.27968 + 3.64246i) q^{25} +(0.600868 - 2.82686i) q^{26} +(3.91568 + 5.38947i) q^{27} +(0.332393 + 3.16251i) q^{28} +(9.62705 + 2.04629i) q^{29} +(0.605688 + 0.672684i) q^{30} +(0.635488 - 6.04627i) q^{31} +1.00000 q^{32} +(-4.92389 - 8.19599i) q^{33} +(-6.46949 - 3.73516i) q^{34} +(0.586883 - 0.807776i) q^{35} +(-3.55363 - 3.94671i) q^{36} +(-1.41861 - 1.27732i) q^{37} +(1.18624 + 0.528146i) q^{38} +(6.74031 - 4.89712i) q^{39} +(-0.233340 - 0.210100i) q^{40} +(1.74761 + 0.567834i) q^{41} +(-5.38838 + 7.41646i) q^{42} +(-4.39467 + 4.86691i) q^{43} +(1.99582 + 2.64891i) q^{44} +1.66755i q^{45} +(-0.456250 + 4.34093i) q^{46} +(-0.926431 + 2.85126i) q^{47} +(2.14237 + 1.92900i) q^{48} +(2.84290 + 1.26574i) q^{49} +(-0.512337 - 4.87456i) q^{50} +(-6.65494 - 20.4818i) q^{51} +(-2.14770 + 1.93380i) q^{52} +(-0.691492 + 6.57911i) q^{53} -6.66176i q^{54} +(0.0908331 - 1.03742i) q^{55} +(1.58996 - 2.75390i) q^{56} +(1.52257 + 3.41974i) q^{57} +(-6.58567 - 7.31412i) q^{58} +(-0.160277 - 0.493281i) q^{59} +(-0.0946177 - 0.900227i) q^{60} +(0.302938 + 2.88226i) q^{61} +(-4.06803 + 4.51800i) q^{62} +(-16.5190 + 3.51122i) q^{63} +(-0.809017 - 0.587785i) q^{64} +0.907436 q^{65} +(-0.833969 + 9.52489i) q^{66} +(-3.33950 - 5.78418i) q^{67} +(3.03846 + 6.82448i) q^{68} +(-9.35112 + 8.41979i) q^{69} +(-0.949597 + 0.308543i) q^{70} +(0.316345 - 0.0332492i) q^{71} +(0.555132 + 5.28173i) q^{72} +(-6.91963 - 1.47081i) q^{73} +(0.396888 + 1.86721i) q^{74} +(8.30542 - 11.4314i) q^{75} +(-0.649248 - 1.12453i) q^{76} +(10.4681 - 1.28460i) q^{77} -8.33149 q^{78} +(-4.04832 - 9.09267i) q^{79} +(0.0652822 + 0.307129i) q^{80} +(2.18964 - 2.43185i) q^{81} +(-1.08009 - 1.48661i) q^{82} +(-4.86173 + 10.9196i) q^{83} +(8.71858 - 2.83284i) q^{84} +(0.724833 - 2.23081i) q^{85} +(6.41607 - 1.35429i) q^{86} -28.3734i q^{87} +(-0.0576587 - 3.31612i) q^{88} +(-9.95045 + 5.74490i) q^{89} +(0.980159 - 1.34907i) q^{90} +(1.91072 + 8.98922i) q^{91} +(2.92065 - 3.24371i) q^{92} +(-17.4305 + 1.83202i) q^{93} +(2.42543 - 1.76218i) q^{94} +(-0.0847687 + 0.398805i) q^{95} +(-0.599378 - 2.81985i) q^{96} +(-9.58839 - 6.96637i) q^{97} +(-1.55597 - 2.69502i) q^{98} +(-12.8829 + 12.0119i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q - 44 q^{2} - 44 q^{4} - 5 q^{6} - 15 q^{7} - 44 q^{8} - 20 q^{9}+O(q^{10}) $ 176 * q - 44 * q^2 - 44 * q^4 - 5 * q^6 - 15 * q^7 - 44 * q^8 - 20 * q^9	$ 176 q - 44 q^{2} - 44 q^{4} - 5 q^{6} - 15 q^{7} - 44 q^{8} - 20 q^{9} - 5 q^{11} - 5 q^{13} + 15 q^{14} + 41 q^{15} - 44 q^{16} - 2 q^{17} - 25 q^{18} + 34 q^{19} + 5 q^{22} - 4 q^{23} + 5 q^{24} - 24 q^{25} + 20 q^{26} - 60 q^{27} - 3 q^{29} - 49 q^{30} + 40 q^{31} + 176 q^{32} - 47 q^{33} + 3 q^{34} - 60 q^{35} - 25 q^{36} - 8 q^{37} + 14 q^{38} + 12 q^{39} - 19 q^{43} - 10 q^{44} + 26 q^{46} - 4 q^{47} - 21 q^{49} + 6 q^{50} + 45 q^{51} - 20 q^{52} - 27 q^{53} + 68 q^{55} + 71 q^{57} - 3 q^{58} - 21 q^{59} + 6 q^{60} + 30 q^{61} + 71 q^{63} - 44 q^{64} - 16 q^{65} + 43 q^{66} - 3 q^{67} + 8 q^{68} - 42 q^{69} + 3 q^{71} - 20 q^{72} - 19 q^{73} - 28 q^{74} + 9 q^{76} + 38 q^{77} + 92 q^{78} + 32 q^{79} - 23 q^{81} - 5 q^{82} - 26 q^{83} + 2 q^{85} + 36 q^{86} + 5 q^{88} + 57 q^{89} + 30 q^{91} + 6 q^{92} - 10 q^{93} + 6 q^{94} - 58 q^{95} - 37 q^{97} - 106 q^{98} - 119 q^{99}+O(q^{100}) $ 176 * q - 44 * q^2 - 44 * q^4 - 5 * q^6 - 15 * q^7 - 44 * q^8 - 20 * q^9 - 5 * q^11 - 5 * q^13 + 15 * q^14 + 41 * q^15 - 44 * q^16 - 2 * q^17 - 25 * q^18 + 34 * q^19 + 5 * q^22 - 4 * q^23 + 5 * q^24 - 24 * q^25 + 20 * q^26 - 60 * q^27 - 3 * q^29 - 49 * q^30 + 40 * q^31 + 176 * q^32 - 47 * q^33 + 3 * q^34 - 60 * q^35 - 25 * q^36 - 8 * q^37 + 14 * q^38 + 12 * q^39 - 19 * q^43 - 10 * q^44 + 26 * q^46 - 4 * q^47 - 21 * q^49 + 6 * q^50 + 45 * q^51 - 20 * q^52 - 27 * q^53 + 68 * q^55 + 71 * q^57 - 3 * q^58 - 21 * q^59 + 6 * q^60 + 30 * q^61 + 71 * q^63 - 44 * q^64 - 16 * q^65 + 43 * q^66 - 3 * q^67 + 8 * q^68 - 42 * q^69 + 3 * q^71 - 20 * q^72 - 19 * q^73 - 28 * q^74 + 9 * q^76 + 38 * q^77 + 92 * q^78 + 32 * q^79 - 23 * q^81 - 5 * q^82 - 26 * q^83 + 2 * q^85 + 36 * q^86 + 5 * q^88 + 57 * q^89 + 30 * q^91 + 6 * q^92 - 10 * q^93 + 6 * q^94 - 58 * q^95 - 37 * q^97 - 106 * q^98 - 119 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/946\mathbb{Z}\right)^\times$.

$n$	$89$	$431$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{10}\right)$

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 $

$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$3$	−0.599378	−	2.81985i	−0.346051	−	1.62804i	−0.715374	−	0.698742i	$-0.753744\pi$
$3$	−0.599378	−	2.81985i	−0.346051	−	1.62804i	0.369323	−	0.929301i	$-0.379590\pi$
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	0.127711	−	0.286844i	0.0571142	−	0.128281i	−0.882734	−	0.469873i	$-0.844300\pi$
$5$	0.127711	−	0.286844i	0.0571142	−	0.128281i	0.939848	+	0.341593i	$0.110966\pi$
$6$	−1.17256	+	2.63361i	−0.478696	+	1.07517i
$7$	3.11044	+	0.661144i	1.17564	+	0.249889i	0.753999	−	0.656876i	$-0.228122\pi$
$7$	3.11044	+	0.661144i	1.17564	+	0.249889i	0.421637	+	0.906765i	$0.361456\pi$
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$	−4.85168	+	2.16011i	−1.61723	+	0.720035i
$10$	−0.271923	+	0.156995i	−0.0859897	+	0.0496462i
$11$	3.13600	−	1.07958i	0.945541	−	0.325504i
$11$	3.13600	−	1.07958i	0.945541	−	0.325504i
$12$	2.49662	−	1.44142i	0.720712	−	0.416104i
$13$	1.17548	+	2.64016i	0.326018	+	0.732249i	0.999979	−	0.00651827i	$-0.00207484\pi$
$13$	1.17548	+	2.64016i	0.326018	+	0.732249i	−0.673960	+	0.738767i	$0.735408\pi$
$14$	−2.12779	−	2.36315i	−0.568675	−	0.631578i
$15$	−0.885406	−	0.188199i	−0.228611	−	0.0485927i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	7.42941	−	0.780862i	1.80190	−	0.189387i	0.856683	−	0.515843i	$-0.172521\pi$
$17$	7.42941	−	0.780862i	1.80190	−	0.189387i	0.945212	+	0.326456i	$0.105855\pi$
$18$	5.19477	+	1.10418i	1.22442	+	0.260258i
$19$	−1.27012	+	0.269973i	−0.291386	+	0.0619359i	−0.351285	−	0.936268i	$-0.614255\pi$
$19$	−1.27012	+	0.269973i	−0.291386	+	0.0619359i	0.0598996	+	0.998204i	$0.480922\pi$
$20$	0.312270	+	0.0328209i	0.0698257	+	0.00733897i
$21$		−	9.16725i		−	2.00046i
$22$	−3.17164	−	0.969902i	−0.676196	−	0.206784i
$23$	−2.18242	−	3.78006i	−0.455066	−	0.788197i	0.543626	−	0.839328i	$-0.317051\pi$
$23$	−2.18242	−	3.78006i	−0.455066	−	0.788197i	−0.998692	+	0.0511302i	$0.983718\pi$
$24$	−2.86706	−	0.301340i	−0.585236	−	0.0615107i
$25$	3.27968	+	3.64246i	0.655937	+	0.728492i
$26$	0.600868	−	2.82686i	0.117840	−	0.554394i
$27$	3.91568	+	5.38947i	0.753573	+	1.03720i
$28$	0.332393	+	3.16251i	0.0628164	+	0.597658i
$29$	9.62705	+	2.04629i	1.78770	+	0.379987i	0.978287	−	0.207255i	$-0.0664529\pi$
$29$	9.62705	+	2.04629i	1.78770	+	0.379987i	0.809412	+	0.587242i	$0.199786\pi$
$30$	0.605688	+	0.672684i	0.110583	+	0.122815i
$31$	0.635488	−	6.04627i	0.114137	−	1.08594i	−0.776152	−	0.630546i	$-0.782831\pi$
$31$	0.635488	−	6.04627i	0.114137	−	1.08594i	0.890289	−	0.455396i	$-0.150502\pi$
$32$	1.00000			0.176777
$33$	−4.92389	−	8.19599i	−0.857140	−	1.42674i
$34$	−6.46949	−	3.73516i	−1.10951	−	0.640575i
$35$	0.586883	−	0.807776i	0.0992014	−	0.136539i
$36$	−3.55363	−	3.94671i	−0.592272	−	0.657785i
$37$	−1.41861	−	1.27732i	−0.233218	−	0.209990i	0.544233	−	0.838934i	$-0.316821\pi$
$37$	−1.41861	−	1.27732i	−0.233218	−	0.209990i	−0.777451	+	0.628944i	$0.783488\pi$
$38$	1.18624	+	0.528146i	0.192433	+	0.0856766i
$39$	6.74031	−	4.89712i	1.07931	−	0.784167i
$40$	−0.233340	−	0.210100i	−0.0368943	−	0.0332198i
$41$	1.74761	+	0.567834i	0.272932	+	0.0886808i	0.442285	−	0.896875i	$-0.354168\pi$
$41$	1.74761	+	0.567834i	0.272932	+	0.0886808i	−0.169354	+	0.985555i	$0.554168\pi$
$42$	−5.38838	+	7.41646i	−0.831445	+	1.14439i
$43$	−4.39467	+	4.86691i	−0.670181	+	0.742197i
$43$	−4.39467	+	4.86691i	−0.670181	+	0.742197i
$44$	1.99582	+	2.64891i	0.300880	+	0.399338i
$45$			1.66755i			0.248583i
$46$	−0.456250	+	4.34093i	−0.0672704	+	0.640035i
$47$	−0.926431	+	2.85126i	−0.135134	+	0.415899i	−0.995611	−	0.0935900i	$-0.970166\pi$
$47$	−0.926431	+	2.85126i	−0.135134	+	0.415899i	0.860477	+	0.509489i	$0.170166\pi$
$48$	2.14237	+	1.92900i	0.309225	+	0.278428i
$49$	2.84290	+	1.26574i	0.406128	+	0.180820i
$50$	−0.512337	−	4.87456i	−0.0724554	−	0.689367i
$51$	−6.65494	−	20.4818i	−0.931878	−	2.86803i
$52$	−2.14770	+	1.93380i	−0.297833	+	0.268170i
$53$	−0.691492	+	6.57911i	−0.0949837	+	0.903710i	0.838454	+	0.544972i	$0.183460\pi$
$53$	−0.691492	+	6.57911i	−0.0949837	+	0.903710i	−0.933438	+	0.358738i	$0.883207\pi$
$54$		−	6.66176i		−	0.906550i
$55$	0.0908331	−	1.03742i	0.0122479	−	0.139885i
$56$	1.58996	−	2.75390i	0.212468	−	0.368005i
$57$	1.52257	+	3.41974i	0.201669	+	0.452955i
$58$	−6.58567	−	7.31412i	−0.864740	−	0.960392i
$59$	−0.160277	−	0.493281i	−0.0208663	−	0.0642197i	0.940081	−	0.340951i	$-0.110749\pi$
$59$	−0.160277	−	0.493281i	−0.0208663	−	0.0642197i	−0.960947	+	0.276731i	$0.910749\pi$
$60$	−0.0946177	−	0.900227i	−0.0122151	−	0.116219i
$61$	0.302938	+	2.88226i	0.0387872	+	0.369035i	0.996648	+	0.0818040i	$0.0260682\pi$
$61$	0.302938	+	2.88226i	0.0387872	+	0.369035i	−0.957861	+	0.287231i	$0.907265\pi$
$62$	−4.06803	+	4.51800i	−0.516640	+	0.573787i
$63$	−16.5190	+	3.51122i	−2.08120	+	0.442372i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	0.907436			0.112554
$66$	−0.833969	+	9.52489i	−0.102655	+	1.17243i
$67$	−3.33950	−	5.78418i	−0.407985	−	0.706650i	0.586679	−	0.809819i	$-0.300435\pi$
$67$	−3.33950	−	5.78418i	−0.407985	−	0.706650i	−0.994664	+	0.103169i	$0.967102\pi$
$68$	3.03846	+	6.82448i	0.368467	+	0.827590i
$69$	−9.35112	+	8.41979i	−1.12574	+	1.01362i
$70$	−0.949597	+	0.308543i	−0.113499	+	0.0368779i
$71$	0.316345	−	0.0332492i	0.0375432	−	0.00394595i	−0.0857382	−	0.996318i	$-0.527325\pi$
$71$	0.316345	−	0.0332492i	0.0375432	−	0.00394595i	0.123281	+	0.992372i	$0.460658\pi$
$72$	0.555132	+	5.28173i	0.0654230	+	0.622458i
$73$	−6.91963	−	1.47081i	−0.809882	−	0.172146i	−0.215682	−	0.976464i	$-0.569198\pi$
$73$	−6.91963	−	1.47081i	−0.809882	−	0.172146i	−0.594199	+	0.804318i	$0.702531\pi$
$74$	0.396888	+	1.86721i	0.0461373	+	0.217059i
$75$	8.30542	−	11.4314i	0.959028	−	1.31999i
$76$	−0.649248	−	1.12453i	−0.0744739	−	0.128993i
$77$	10.4681	−	1.28460i	1.19295	−	0.146394i
$78$	−8.33149			−0.943355
$79$	−4.04832	−	9.09267i	−0.455472	−	1.02301i	−0.984657	−	0.174500i	$-0.944169\pi$
$79$	−4.04832	−	9.09267i	−0.455472	−	1.02301i	0.529186	−	0.848506i	$-0.322497\pi$
$80$	0.0652822	+	0.307129i	0.00729877	+	0.0343380i
$81$	2.18964	−	2.43185i	0.243294	−	0.270205i
$82$	−1.08009	−	1.48661i	−0.119275	−	0.164169i
$83$	−4.86173	+	10.9196i	−0.533644	+	1.19858i	0.422681	+	0.906279i	$0.361089\pi$
$83$	−4.86173	+	10.9196i	−0.533644	+	1.19858i	−0.956325	+	0.292306i	$0.905577\pi$
$84$	8.71858	−	2.83284i	0.951275	−	0.309088i
$85$	0.724833	−	2.23081i	0.0786192	−	0.241965i
$86$	6.41607	−	1.35429i	0.691862	−	0.146037i
$87$		−	28.3734i		−	3.04194i
$88$	−0.0576587	−	3.31612i	−0.00614644	−	0.353500i
$89$	−9.95045	+	5.74490i	−1.05475	+	0.608958i	−0.923974	−	0.382455i	$-0.875079\pi$
$89$	−9.95045	+	5.74490i	−1.05475	+	0.608958i	−0.130772	+	0.991413i	$0.541745\pi$
$90$	0.980159	−	1.34907i	0.103318	−	0.142205i
$91$	1.91072	+	8.98922i	0.200298	+	0.942326i
$92$	2.92065	−	3.24371i	0.304499	−	0.338180i
$93$	−17.4305	+	1.83202i	−1.80746	+	0.189971i
$94$	2.42543	−	1.76218i	0.250164	−	0.181755i
$95$	−0.0847687	+	0.398805i	−0.00869708	+	0.0409166i
$96$	−0.599378	−	2.81985i	−0.0611738	−	0.287800i
$97$	−9.58839	−	6.96637i	−0.973553	−	0.707328i	−0.0172945	−	0.999850i	$-0.505505\pi$
$97$	−9.58839	−	6.96637i	−0.973553	−	0.707328i	−0.956259	+	0.292523i	$0.905505\pi$
$98$	−1.55597	−	2.69502i	−0.157177	−	0.272238i
$99$	−12.8829	+	12.0119i	−1.29478	+	1.20724i
$100$	−2.45071	+	4.24475i	−0.245071	+	0.424475i
$101$	−6.27513	−	14.0942i	−0.624399	−	1.40242i	−0.897749	−	0.440508i	$-0.854798\pi$
$101$	−6.27513	−	14.0942i	−0.624399	−	1.40242i	0.273350	−	0.961915i	$-0.411868\pi$
$102$	−6.65494	+	20.4818i	−0.658937	+	2.02800i
$103$	−0.509032	−	0.108198i	−0.0501564	−	0.0106611i	0.182765	−	0.983157i	$-0.441495\pi$
$103$	−0.509032	−	0.108198i	−0.0501564	−	0.0106611i	−0.232922	+	0.972496i	$0.574829\pi$
$104$	2.87419	−	0.302089i	0.281837	−	0.0296223i
$105$	−2.62957	−	1.17076i	−0.256620	−	0.114255i
$106$	4.42653	−	4.91616i	0.429943	−	0.477500i
$107$	−18.3763	−	5.97081i	−1.77650	−	0.577220i	−0.777817	−	0.628491i	$-0.783673\pi$
$107$	−18.3763	−	5.97081i	−1.77650	−	0.577220i	−0.998685	+	0.0512710i	$0.983673\pi$
$108$	−3.91568	+	5.38947i	−0.376787	+	0.518602i
$109$	−4.86599	+	2.80938i	−0.466078	+	0.269090i	−0.714596	−	0.699537i	$-0.753390\pi$
$109$	−4.86599	+	2.80938i	−0.466078	+	0.269090i	0.248519	+	0.968627i	$0.420056\pi$
$110$	−0.683265	+	0.785899i	−0.0651467	+	0.0749325i
$111$	−2.75158	+	4.76587i	−0.261168	+	0.452356i
$112$	−2.90501	+	1.29339i	−0.274497	+	0.122214i
$113$	18.7775	+	6.10117i	1.76643	+	0.573949i	0.997834	−	0.0657794i	$-0.0209533\pi$
$113$	18.7775	+	6.10117i	1.76643	+	0.573949i	0.768601	+	0.639729i	$0.220953\pi$
$114$	0.778290	−	3.66157i	0.0728936	−	0.342937i
$115$	−1.36301	+	0.143258i	−0.127101	+	0.0133589i
$116$	1.02878	+	9.78821i	0.0955200	+	0.908812i
$117$	−11.4061	−	10.2701i	−1.05449	−	0.949468i
$118$	−0.160277	+	0.493281i	−0.0147547	+	0.0454102i
$119$	23.6250	+	2.48308i	2.16570	+	0.227624i
$120$	−0.452593	+	0.783914i	−0.0413159	+	0.0715612i
$121$	8.66903	−	6.77110i	0.788094	−	0.615555i
$122$	1.44907	−	2.50986i	0.131192	−	0.227232i
$123$	0.553727	−	5.26836i	0.0499279	−	0.475032i
$124$	5.94672	−	1.26401i	0.534031	−	0.113512i
$125$	2.95678	−	0.960716i	0.264463	−	0.0859291i
$126$	15.4280	+	6.86898i	1.37443	+	0.611938i
$127$	5.13892	+	7.07312i	0.456006	+	0.627638i	0.973674	−	0.227943i	$-0.0732000\pi$
$127$	5.13892	+	7.07312i	0.456006	+	0.627638i	−0.517669	+	0.855581i	$0.673200\pi$
$128$	0.309017	+	0.951057i	0.0273135	+	0.0840623i
$129$	16.3581	+	9.47521i	1.44025	+	0.834245i
$130$	−0.734132	−	0.533378i	−0.0643876	−	0.0467803i
$131$	13.1462			1.14859			0.574294	−	0.818649i	$-0.305277\pi$
$131$	13.1462			1.14859			0.574294	+	0.818649i	$0.305277\pi$
$132$	6.27329	−	7.21560i	0.546019	−	0.628038i
$133$	−4.12912			−0.358040
$134$	−0.698145	+	6.64241i	−0.0603106	+	0.573817i
$135$	2.04602	−	0.434894i	0.176093	−	0.0374297i
$136$	1.55317	−	7.30708i	0.133183	−	0.626577i
$137$	0.136019	+	0.187214i	0.0116209	+	0.0159948i	0.814788	−	0.579759i	$-0.196853\pi$
$137$	0.136019	+	0.187214i	0.0116209	+	0.0159948i	−0.803167	+	0.595754i	$0.796853\pi$
$138$	12.5142	−	1.31530i	1.06528	−	0.111966i
$139$	7.30970	+	6.58168i	0.620000	+	0.558251i	0.918132	−	0.396274i	$-0.129697\pi$
$139$	7.30970	+	6.58168i	0.620000	+	0.558251i	−0.298132	+	0.954525i	$0.596364\pi$
$140$	0.949597	+	0.308543i	0.0802556	+	0.0260766i
$141$	8.59542	+	0.903415i	0.723865	+	0.0760813i
$142$	−0.275472	−	0.159044i	−0.0231171	−	0.0133466i
$143$	6.53655	+	7.01054i	0.546614	+	0.586251i
$144$	2.65541	−	4.59931i	0.221284	−	0.383276i
$145$	1.81645	−	2.50013i	0.150848	−	0.207624i
$146$	4.73358	+	5.25717i	0.391754	+	0.435087i
$147$	1.86523	−	8.77521i	0.153841	−	0.723767i
$148$	0.776431	−	1.74389i	0.0638222	−	0.143347i
$149$	7.35045	+	3.27263i	0.602173	+	0.268105i	0.685098	−	0.728451i	$-0.259760\pi$
$149$	7.35045	+	3.27263i	0.602173	+	0.268105i	−0.0829249	+	0.996556i	$0.526426\pi$
$150$	−13.4385	+	4.36642i	−1.09725	+	0.356517i
$151$	4.69252	−	14.4421i	0.381872	−	1.17528i	−0.556852	−	0.830612i	$-0.687991\pi$
$151$	4.69252	−	14.4421i	0.381872	−	1.17528i	0.938724	−	0.344670i	$-0.112009\pi$
$152$	−0.135730	+	1.29138i	−0.0110091	+	0.104745i
$153$	−34.3583	+	19.8368i	−2.77771	+	1.60371i
$154$	−9.22394	−	5.11373i	−0.743286	−	0.412076i
$155$	−1.65318	−	0.954462i	−0.132786	−	0.0766642i
$156$	6.74031	+	4.89712i	0.539657	+	0.392084i
$157$	−10.8987	+	9.81321i	−0.869809	+	0.783180i	−0.977485	−	0.211007i	$-0.932326\pi$
$157$	−10.8987	+	9.81321i	−0.869809	+	0.783180i	0.107676	+	0.994186i	$0.465659\pi$
$158$	−2.06938	+	9.73567i	−0.164631	+	0.774528i
$159$	18.9666	−	1.99347i	1.50415	−	0.158092i
$160$	0.127711	−	0.286844i	0.0100965	−	0.0226770i
$161$	−4.28912	−	13.2005i	−0.338030	−	1.04035i
$162$	−3.20086	+	0.680364i	−0.251483	+	0.0534545i
$163$	−0.724624	−	1.62753i	−0.0567569	−	0.127478i	0.882941	−	0.469484i	$-0.155560\pi$
$163$	−0.724624	−	1.62753i	−0.0567569	−	0.127478i	−0.939698	+	0.342006i	$0.888894\pi$
$164$			1.83755i			0.143489i
$165$	−2.97981	+	0.365670i	−0.231978	+	0.0284674i
$166$	10.3516	−	5.97651i	0.803441	−	0.463867i
$167$	−3.49605	−	0.367450i	−0.270532	−	0.0284341i	−0.0317091	−	0.999497i	$-0.510095\pi$
$167$	−3.49605	−	0.367450i	−0.270532	−	0.0284341i	−0.238823	+	0.971063i	$0.576762\pi$
$168$	−8.71858	−	2.83284i	−0.672653	−	0.218558i
$169$	3.10999	−	3.45399i	0.239230	−	0.265691i
$170$	−1.89764	+	1.37871i	−0.145542	+	0.105743i
$171$	5.57905	−	4.05342i	0.426640	−	0.309972i
$172$	−5.98674	−	2.67562i	−0.456485	−	0.204014i
$173$	−17.1671	−	5.57793i	−1.30519	−	0.424082i	−0.427807	−	0.903870i	$-0.640714\pi$
$173$	−17.1671	−	5.57793i	−1.30519	−	0.424082i	−0.877384	+	0.479788i	$0.840714\pi$
$174$	−16.6774	+	22.9545i	−1.26431	+	1.74018i
$175$	7.79307	+	13.4980i	0.589100	+	1.02035i
$176$	−1.90252	+	2.71669i	−0.143408	+	0.204778i
$177$	−1.29491	+	0.747619i	−0.0973317	+	0.0561945i
$178$	11.4268	+	1.20101i	0.856479	+	0.0900195i
$179$	9.66397	−	8.70148i	0.722319	−	0.650379i	−0.223638	−	0.974672i	$-0.571793\pi$
$179$	9.66397	−	8.70148i	0.722319	−	0.650379i	0.945957	+	0.324293i	$0.105127\pi$
$180$	−1.58593	+	0.515300i	−0.118208	+	0.0384082i
$181$	−0.763336	−	7.26265i	−0.0567383	−	0.539829i	−0.985563	−	0.169309i	$-0.945846\pi$
$181$	−0.763336	−	7.26265i	−0.0567383	−	0.539829i	0.928825	−	0.370520i	$-0.120820\pi$
$182$	3.73793	−	8.39552i	0.277074	−	0.622318i
$183$	7.94597	−	2.58180i	0.587383	−	0.190852i
$184$	−4.26946	+	0.907501i	−0.314749	+	0.0669019i
$185$	−0.547565	+	0.243791i	−0.0402577	+	0.0179239i
$186$	15.1784	+	8.76324i	1.11293	+	0.642552i
$187$	22.4556	−	10.4694i	1.64212	−	0.765597i
$188$	−2.99799			−0.218651
$189$	8.61627	+	19.3525i	0.626741	+	1.40768i
$190$	0.302991	−	0.272814i	0.0219813	−	0.0197920i
$191$	12.4275	+	11.1898i	0.899222	+	0.809663i	0.982384	−	0.186873i	$-0.0598352\pi$
$191$	12.4275	+	11.1898i	0.899222	+	0.809663i	−0.0831620	+	0.996536i	$0.526502\pi$
$192$	−1.17256	+	2.63361i	−0.0846223	+	0.190065i
$193$	0.272866	+	0.375567i	0.0196413	+	0.0270339i	0.818725	−	0.574186i	$-0.194681\pi$
$193$	0.272866	+	0.375567i	0.0196413	+	0.0270339i	−0.799083	+	0.601220i	$0.794681\pi$
$194$	3.66244	+	11.2718i	0.262948	+	0.809270i
$195$	−0.543898	−	2.55884i	−0.0389493	−	0.183242i
$196$	−0.325286	+	3.09489i	−0.0232347	+	0.221064i
$197$	−17.4556	−	10.0780i	−1.24366	−	0.718026i	−0.273821	−	0.961781i	$-0.588288\pi$
$197$	−17.4556	−	10.0780i	−1.24366	−	0.718026i	−0.969837	+	0.243754i	$0.921621\pi$
$198$	17.4829	−	2.14542i	1.24245	−	0.152469i
$199$			6.79065i			0.481376i	0.970603	+	0.240688i	$0.0773731\pi$
$199$			6.79065i			0.481376i	−0.970603	+	0.240688i	$0.922627\pi$
$200$	4.47766	−	1.99358i	0.316618	−	0.140968i
$201$	−14.3089	+	12.8838i	−1.00927	+	0.908754i
$202$	−3.20766	+	15.0909i	−0.225690	+	1.06179i
$203$	28.5915	+	12.7297i	2.00673	+	0.893452i
$204$	17.4229	−	12.6584i	1.21984	−	0.886268i
$205$	0.386070	−	0.428774i	0.0269643	−	0.0299469i
$206$	0.348218	+	0.386735i	0.0242615	+	0.0269451i
$207$	18.7537	+	13.6254i	1.30347	+	0.947030i
$208$	−2.50283	−	1.44501i	−0.173540	−	0.100193i
$209$	−3.69165	+	2.21783i	−0.255357	+	0.153410i
$210$	1.43921	+	2.49279i	0.0993151	+	0.172019i
$211$	0.478970	+	0.347992i	0.0329736	+	0.0239567i	0.604150	−	0.796871i	$-0.293513\pi$
$211$	0.478970	+	0.347992i	0.0329736	+	0.0239567i	−0.571176	+	0.820827i	$0.693513\pi$
$212$	−6.47079	+	1.37541i	−0.444415	+	0.0944634i
$213$	−0.283368	−	0.872117i	−0.0194161	−	0.0597565i
$214$	11.3572	+	15.6318i	0.776360	+	1.06857i
$215$	0.834797	+	1.88215i	0.0569327	+	0.128361i
$216$	6.33571	−	2.05860i	0.431090	−	0.140070i
$217$	5.97410	−	18.3864i	0.405548	−	1.24815i
$218$	5.58798	+	0.587321i	0.378466	+	0.0397784i
$219$			20.3939i			1.37809i
$220$	1.01471	−	0.234192i	0.0684119	−	0.0157893i
$221$	10.7947	+	18.6969i	0.726129	+	1.25769i
$222$	5.02738	−	2.23833i	0.337416	−	0.150227i
$223$	−0.347981	−	0.113066i	−0.0233025	−	0.00757145i	0.297343	−	0.954771i	$-0.403900\pi$
$223$	−0.347981	−	0.113066i	−0.0233025	−	0.00757145i	−0.320645	+	0.947199i	$0.603900\pi$
$224$	3.11044	+	0.661144i	0.207825	+	0.0441746i
$225$	−23.7801	−	10.5876i	−1.58534	−	0.705838i
$226$	−11.6051	−	15.9731i	−0.771960	−	1.06251i
$227$	9.30913	−	10.3388i	0.617869	−	0.686213i	−0.350264	−	0.936651i	$-0.613908\pi$
$227$	9.30913	−	10.3388i	0.617869	−	0.686213i	0.968133	+	0.250438i	$0.0805748\pi$
$228$	−2.78187	+	2.50480i	−0.184234	+	0.165885i
$229$	−22.3552	+	9.95316i	−1.47727	+	0.657723i	−0.977978	−	0.208710i	$-0.933074\pi$
$229$	−22.3552	+	9.95316i	−1.47727	+	0.657723i	−0.499293	+	0.866433i	$0.666407\pi$
$230$	1.18690	+	0.685258i	0.0782620	+	0.0451846i
$231$	−9.89674	−	28.7485i	−0.651158	−	1.89151i
$232$	4.92106	−	8.52353i	0.323084	−	0.559597i
$233$	22.9331	−	10.2105i	1.50240	−	0.668910i	0.519737	−	0.854326i	$-0.326030\pi$
$233$	22.9331	−	10.2105i	1.50240	−	0.668910i	0.982660	+	0.185416i	$0.0593633\pi$
$234$	3.19111	+	15.0130i	0.208609	+	0.981429i
$235$	0.699552	+	0.629880i	0.0456338	+	0.0410888i
$236$	0.419610	−	0.304864i	0.0273143	−	0.0198450i
$237$	−23.2135	+	16.8656i	−1.50788	+	1.09554i
$238$	−17.6535	−	15.8953i	−1.14431	−	1.03034i
$239$	−4.72828	−	22.2448i	−0.305847	−	1.43890i	−0.815620	−	0.578588i	$-0.803604\pi$
$239$	−4.72828	−	22.2448i	−0.305847	−	1.43890i	0.509773	−	0.860309i	$-0.329729\pi$
$240$	0.826929	−	0.368172i	0.0533780	−	0.0237654i
$241$	−12.4708	+	21.6001i	−0.803316	+	1.39138i	0.114106	+	0.993469i	$0.463600\pi$
$241$	−12.4708	+	21.6001i	−0.803316	+	1.39138i	−0.917422	+	0.397916i	$0.869734\pi$
$242$	−10.9934	+	0.382407i	−0.706679	+	0.0245820i
$243$	9.13788	+	5.27576i	0.586195	+	0.338440i
$244$	−2.64758	+	1.17878i	−0.169494	+	0.0754635i
$245$	0.726140	−	0.653820i	0.0463914	−	0.0417710i
$246$	−3.54464	+	3.93672i	−0.225998	+	0.250996i
$247$	−2.20577	−	3.03598i	−0.140350	−	0.193175i
$248$	−5.55396	−	2.47278i	−0.352677	−	0.157022i
$249$	33.7058	+	7.16438i	2.13602	+	0.454024i
$250$	−2.95678	−	0.960716i	−0.187003	−	0.0607610i
$251$	−8.10009	+	3.60639i	−0.511273	+	0.227634i	−0.646124	−	0.763232i	$-0.723611\pi$
$251$	−8.10009	+	3.60639i	−0.511273	+	0.227634i	0.134851	+	0.990866i	$0.456945\pi$
$252$	−8.44402	−	14.6255i	−0.531923	−	0.921318i
$253$	−10.9249	−	9.49820i	−0.686845	−	0.597147i
$254$		−	8.74286i		−	0.548576i
$255$	−6.72499	−	0.706825i	−0.421135	−	0.0442631i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	27.1959	−	8.83649i	1.69643	−	0.551205i	0.708450	−	0.705761i	$-0.249395\pi$
$257$	27.1959	−	8.83649i	1.69643	−	0.551205i	0.987984	+	0.154556i	$0.0493946\pi$
$258$	−7.66455	−	17.2806i	−0.477174	−	1.07584i
$259$	−3.56800	−	4.91094i	−0.221705	−	0.305151i
$260$	0.280413	+	0.863023i	0.0173905	+	0.0535224i
$261$	−51.1276	+	10.8675i	−3.16472	+	0.672681i
$262$	−10.6355	−	7.72714i	−0.657063	−	0.477384i
$263$	−7.87912	−	13.6470i	−0.485847	−	0.841512i	0.514020	−	0.857778i	$-0.328156\pi$
$263$	−7.87912	−	13.6470i	−0.485847	−	0.841512i	−0.999868	+	0.0162657i	$0.994822\pi$
$264$	−9.31642	+	2.15020i	−0.573386	+	0.132336i
$265$	1.79887	+	1.03858i	0.110504	+	0.0637992i
$266$	3.34053	+	2.42704i	0.204821	+	0.148811i
$267$	22.1638	+	24.6154i	1.35641	+	1.50644i
$268$	4.46912	−	4.96346i	0.272995	−	0.303192i
$269$	−14.1983	+	10.3157i	−0.865688	+	0.628959i	−0.929427	−	0.369007i	$-0.879698\pi$
$269$	−14.1983	+	10.3157i	−0.865688	+	0.628959i	0.0637382	+	0.997967i	$0.479698\pi$
$270$	−1.91089	−	0.850781i	−0.116293	−	0.0517769i
$271$	−3.06194	+	14.4053i	−0.185999	+	0.875058i	0.781838	+	0.623482i	$0.214282\pi$
$271$	−3.06194	+	14.4053i	−0.185999	+	0.875058i	−0.967837	+	0.251577i	$0.919051\pi$
$272$	−5.55154	+	4.99863i	−0.336611	+	0.303086i
$273$	24.2030	−	10.7759i	1.46483	−	0.652186i
$274$		−	0.231409i		−	0.0139800i
$275$	14.2174	+	7.88209i	0.857342	+	0.475308i
$276$	−10.8973	−	6.29159i	−0.655943	−	0.378709i
$277$	−2.18126	+	20.7533i	−0.131059	+	1.24695i	0.709296	+	0.704911i	$0.249013\pi$
$277$	−2.18126	+	20.7533i	−0.131059	+	1.24695i	−0.840355	+	0.542036i	$0.817653\pi$
$278$	−2.04505	−	9.62122i	−0.122654	−	0.577043i
$279$	9.97739	+	30.7073i	0.597331	+	1.83840i
$280$	−0.586883	−	0.807776i	−0.0350730	−	0.0482738i
$281$	−7.04146	+	15.8154i	−0.420058	+	0.943466i	0.572297	+	0.820047i	$0.306053\pi$
$281$	−7.04146	+	15.8154i	−0.420058	+	0.943466i	−0.992355	+	0.123419i	$0.960614\pi$
$282$	−6.42283	−	5.78314i	−0.382474	−	0.344381i
$283$	−10.8823	+	9.79846i	−0.646885	+	0.582458i	−0.925872	−	0.377837i	$-0.876668\pi$
$283$	−10.8823	+	9.79846i	−0.646885	+	0.582458i	0.278987	+	0.960295i	$0.410001\pi$
$284$	0.129378	+	0.290587i	0.00767716	+	0.0172432i
$285$	1.17538			0.0696235
$286$	−1.16749	−	9.51374i	−0.0690349	−	0.562559i
$287$	5.06043	+	2.92164i	0.298708	+	0.172459i
$288$	−4.85168	+	2.16011i	−0.285888	+	0.127285i
$289$	37.9578	−	8.06818i	2.23281	−	0.474599i
$290$	−2.93908	+	0.954964i	−0.172589	+	0.0560774i
$291$	−13.8971	+	31.2133i	−0.814661	+	1.82976i
$292$	−0.739457	−	7.03547i	−0.0432735	−	0.411720i
$293$	−1.63759	+	0.532085i	−0.0956691	+	0.0310848i	−0.356460	−	0.934310i	$-0.616017\pi$
$293$	−1.63759	+	0.532085i	−0.0956691	+	0.0310848i	0.260791	+	0.965395i	$0.416017\pi$
$294$	−6.66694	+	6.00294i	−0.388824	+	0.350099i
$295$	−0.161964	−	0.0170231i	−0.00942991	−	0.000991123i
$296$	−1.65318	+	0.954464i	−0.0960891	+	0.0554771i
$297$	18.0979	+	12.6741i	1.05015	+	0.735428i
$298$	−4.02304	−	6.96810i	−0.233048	−	0.403651i
$299$	7.41459	−	10.2053i	0.428797	−	0.590188i
$300$	13.4385	+	4.36642i	0.775870	+	0.252095i
$301$	−16.8871	+	12.2327i	−0.973356	+	0.705083i
$302$	−12.2852	+	8.92571i	−0.706933	+	0.513617i
$303$	−35.9823	+	26.1427i	−2.06713	+	1.50186i
$304$	0.868863	−	0.964971i	0.0498327	−	0.0553449i
$305$	0.865447	+	0.281201i	0.0495554	+	0.0161015i
$306$	39.4563	+	4.14702i	2.25556	+	0.237069i
$307$	16.6472	−	9.61127i	0.950107	−	0.548544i	0.0569927	−	0.998375i	$-0.481849\pi$
$307$	16.6472	−	9.61127i	0.950107	−	0.548544i	0.893114	+	0.449830i	$0.148516\pi$
$308$	4.45655	+	9.55879i	0.253936	+	0.544663i
$309$			1.50025i			0.0853460i
$310$	0.776429	+	1.74389i	0.0440982	+	0.0990462i
$311$	5.10728	−	1.08558i	0.289607	−	0.0615579i	−0.0608173	−	0.998149i	$-0.519371\pi$
$311$	5.10728	−	1.08558i	0.289607	−	0.0615579i	0.350424	+	0.936591i	$0.386037\pi$
$312$	−2.57457	−	7.92371i	−0.145756	−	0.448592i
$313$	0.423762	−	0.951784i	0.0239524	−	0.0537980i	−0.901173	−	0.433459i	$-0.857293\pi$
$313$	0.423762	−	0.951784i	0.0239524	−	0.0537980i	0.925126	+	0.379661i	$0.123959\pi$
$314$	14.5853	−	1.53297i	0.823095	−	0.0865107i
$315$	−1.10249	+	5.18680i	−0.0621181	+	0.292243i
$316$	7.39665	−	6.65997i	0.416094	−	0.374653i
$317$	−1.04243	−	0.757373i	−0.0585490	−	0.0425383i	0.558126	−	0.829756i	$-0.311521\pi$
$317$	−1.04243	−	0.757373i	−0.0585490	−	0.0425383i	−0.616675	+	0.787218i	$0.711521\pi$
$318$	−16.5160	−	9.53553i	−0.926172	−	0.534726i
$319$	32.3996	−	3.97594i	1.81403	−	0.222610i
$320$	−0.271923	+	0.156995i	−0.0152010	+	0.00877629i
$321$	−5.82248	+	55.3972i	−0.324979	+	3.09197i
$322$	−4.28912	+	13.2005i	−0.239023	+	0.735637i
$323$	−9.22543	+	2.99752i	−0.513317	+	0.166787i
$324$	2.98946	+	1.33099i	0.166081	+	0.0739441i
$325$	−5.76149	+	12.9405i	−0.319590	+	0.717811i
$326$	−0.370406	+	1.74262i	−0.0205149	+	0.0965150i
$327$	10.8386	+	12.0375i	0.599377	+	0.665675i
$328$	1.08009	−	1.48661i	0.0596377	−	0.0820843i
$329$	−4.76670	+	8.25617i	−0.262797	+	0.455178i
$330$	2.62565	+	1.45565i	0.144537	+	0.0801312i
$331$	−12.3746	−	7.14447i	−0.680169	−	0.392696i	0.119750	−	0.992804i	$-0.461791\pi$
$331$	−12.3746	−	7.14447i	−0.680169	−	0.392696i	−0.799919	+	0.600108i	$0.795124\pi$
$332$	−11.8875	−	1.24943i	−0.652413	−	0.0685714i
$333$	9.64179	+	3.13281i	0.528367	+	0.171677i
$334$	2.61238	+	2.35220i	0.142943	+	0.128707i
$335$	−2.08565	+	0.219211i	−0.113951	+	0.0119768i
$336$	5.38838	+	7.41646i	0.293960	+	0.404601i
$337$	5.63182	−	26.4956i	0.306785	−	1.44331i	−0.506901	−	0.862004i	$-0.669209\pi$
$337$	5.63182	−	26.4956i	0.306785	−	1.44331i	0.813686	−	0.581305i	$-0.197458\pi$
$338$	−4.54624	+	0.966332i	−0.247283	+	0.0525615i
$339$	5.94959	−	56.6066i	0.323137	−	3.07445i
$340$	2.34561			0.127208
$341$	−4.53451	−	19.6472i	−0.245557	−	1.06395i
$342$	−6.89608			−0.372897
$343$	−10.0025	−	7.26723i	−0.540083	−	0.392394i
$344$	3.27068	+	5.68354i	0.176343	+	0.306436i
$345$	1.22092	+	3.75762i	0.0657323	+	0.202303i
$346$	10.6099	+	14.6032i	0.570389	+	0.785074i
$347$	−15.2762	−	6.80141i	−0.820070	−	0.365119i	−0.0465701	−	0.998915i	$-0.514829\pi$
$347$	−15.2762	−	6.80141i	−0.820070	−	0.365119i	−0.773500	+	0.633796i	$0.781496\pi$
$348$	26.9847	−	8.76785i	1.44653	−	0.470006i
$349$	2.65221	−	0.563745i	0.141970	−	0.0301766i	−0.136379	−	0.990657i	$-0.543546\pi$
$349$	2.65221	−	0.563745i	0.141970	−	0.0301766i	0.278348	+	0.960480i	$0.410213\pi$
$350$	1.62919	−	15.5007i	0.0870841	−	0.828550i
$351$	−9.62629	+	16.6732i	−0.513814	+	0.889951i
$352$	3.13600	−	1.07958i	0.167150	−	0.0575416i
$353$	12.5036	−	21.6569i	0.665501	−	1.15268i	−0.313649	−	0.949539i	$-0.601551\pi$
$353$	12.5036	−	21.6569i	0.665501	−	1.15268i	0.979149	−	0.203142i	$-0.0651152\pi$
$354$	1.48705	+	0.156295i	0.0790356	+	0.00830698i
$355$	0.0308635	−	0.0949879i	0.00163806	−	0.00504144i
$356$	−8.53858	−	7.68817i	−0.452544	−	0.407472i
$357$	−7.15836	−	68.1072i	−0.378861	−	3.60462i
$358$	−12.9329	+	1.35930i	−0.683526	+	0.0718415i
$359$	−5.46733	+	25.7218i	−0.288555	+	1.35754i	0.560025	+	0.828476i	$0.310792\pi$
$359$	−5.46733	+	25.7218i	−0.288555	+	1.35754i	−0.848580	+	0.529068i	$0.822542\pi$
$360$	1.58593	+	0.515300i	0.0835858	+	0.0271587i
$361$	−15.8170	+	7.04220i	−0.832476	+	0.370642i
$362$	−3.65133	+	6.32429i	−0.191910	+	0.332397i
$363$	−24.2895	−	20.3869i	−1.27487	−	1.07004i
$364$	−7.95881	+	4.59502i	−0.417155	+	0.240845i
$365$	−1.30561	+	1.79702i	−0.0683387	+	0.0940601i
$366$	−7.94597	−	2.58180i	−0.415342	−	0.134953i
$367$	−10.1291	+	11.2495i	−0.528735	+	0.587219i	−0.947051	−	0.321082i	$-0.895954\pi$
$367$	−10.1291	+	11.2495i	−0.528735	+	0.587219i	0.418317	+	0.908301i	$0.362620\pi$
$368$	3.98748	+	1.77534i	0.207862	+	0.0925460i
$369$	−9.70544	+	1.02008i	−0.505245	+	0.0531034i
$370$	0.586286	+	0.124619i	0.0304796	+	0.00647863i
$371$	−6.50058	+	20.0067i	−0.337493	+	1.03870i
$372$	−7.12866	−	16.0112i	−0.369604	−	0.830144i
$373$	−7.12325	+	12.3378i	−0.368828	+	0.638829i	−0.989383	−	0.145335i	$-0.953574\pi$
$373$	−7.12325	+	12.3378i	−0.368828	+	0.638829i	0.620555	+	0.784163i	$0.286907\pi$
$374$	−24.3207	−	4.72918i	−1.25760	−	0.244540i
$375$	−4.48131	−	7.76185i	−0.231414	−	0.400820i
$376$	2.42543	+	1.76218i	0.125082	+	0.0908773i
$377$	5.91382	+	27.8223i	0.304577	+	1.43292i
$378$	4.40438	−	20.7210i	0.226537	−	1.06577i
$379$	−11.0045	+	7.99523i	−0.565263	+	0.410687i	−0.833381	−	0.552699i	$-0.813598\pi$
$379$	−11.0045	+	7.99523i	−0.565263	+	0.410687i	0.268119	+	0.963386i	$0.413598\pi$
$380$	−0.405481	+	0.0426178i	−0.0208008	+	0.00218625i
$381$	16.8650	−	18.7305i	0.864020	−	0.959591i
$382$	−3.47688	−	16.3574i	−0.177892	−	0.836918i
$383$	1.69079	−	2.32717i	0.0863954	−	0.118913i	−0.763632	−	0.645652i	$-0.776586\pi$
$383$	1.69079	−	2.32717i	0.0863954	−	0.118913i	0.850027	+	0.526739i	$0.176586\pi$
$384$	2.49662	−	1.44142i	0.127405	−	0.0735574i
$385$	0.968414	−	3.16677i	0.0493549	−	0.161394i
$386$		−	0.464227i		−	0.0236285i
$387$	10.8085	−	33.1057i	0.549426	−	1.68286i
$388$	3.66244	−	11.2718i	0.185932	−	0.572240i
$389$	−29.8746	+	9.70686i	−1.51470	+	0.492157i	−0.944266	−	0.329183i	$-0.893227\pi$
$389$	−29.8746	+	9.70686i	−1.51470	+	0.492157i	−0.570439	+	0.821340i	$0.693227\pi$
$390$	−1.06402	+	2.38984i	−0.0538790	+	0.121014i
$391$	−19.1658	−	26.3794i	−0.969255	−	1.33407i
$392$	2.08229	−	2.31262i	0.105172	−	0.116805i
$393$	−7.87954	−	37.0703i	−0.397470	−	1.86995i
$394$	8.19817	+	18.4134i	0.413018	+	0.927653i
$395$	−3.12520			−0.157246
$396$	−15.4050	−	8.54048i	−0.774129	−	0.429175i
$397$	0.733183	+	1.26991i	0.0367974	+	0.0637349i	0.883838	−	0.467794i	$-0.154951\pi$
$397$	0.733183	+	1.26991i	0.0367974	+	0.0637349i	−0.847040	+	0.531529i	$0.821618\pi$
$398$	3.99144	−	5.49375i	0.200073	−	0.275377i
$399$	2.47491	+	11.6435i	0.123900	+	0.582905i
$400$	−4.79430	−	1.01906i	−0.239715	−	0.0509530i
$401$	0.518547	+	4.93364i	0.0258950	+	0.246374i	0.999811	+	0.0194636i	$0.00619586\pi$
$401$	0.518547	+	4.93364i	0.0258950	+	0.246374i	−0.973916	+	0.226911i	$0.927137\pi$
$402$	19.1491	−	2.01265i	0.955069	−	0.100382i
$403$	16.7101	−	5.42945i	0.832390	−	0.270460i
$404$	11.4652	−	10.3233i	0.570417	−	0.513606i
$405$	−0.417919	−	0.938661i	−0.0207665	−	0.0466424i
$406$	−15.6486	−	27.1042i	−0.776628	−	1.34516i
$407$	−5.82773	−	2.47419i	−0.288870	−	0.122641i
$408$	−21.5358			−1.06618
$409$	23.1247	+	16.8011i	1.14344	+	0.830759i	0.987595	−	0.157023i	$-0.0501896\pi$
$409$	23.1247	+	16.8011i	1.14344	+	0.830759i	0.155846	+	0.987781i	$0.450190\pi$
$410$	−0.564364	+	0.119959i	−0.0278720	+	0.00592437i
$411$	0.446389	−	0.495766i	0.0220188	−	0.0244543i
$412$	−0.0543970	−	0.517553i	−0.00267995	−	0.0254980i
$413$	−0.172401	−	1.64029i	−0.00848330	−	0.0807132i
$414$	−7.16329	−	22.0463i	−0.352056	−	1.08352i
$415$	2.51133	+	2.78912i	0.123276	+	0.136912i
$416$	1.17548	+	2.64016i	0.0576324	+	0.129445i
$417$	14.1781	−	24.5572i	0.694304	−	1.20257i
$418$	4.29021	+	0.375637i	0.209841	+	0.0183730i
$419$			5.12134i			0.250194i	0.992145	+	0.125097i	$0.0399242\pi$
$419$			5.12134i			0.250194i	−0.992145	+	0.125097i	$0.960076\pi$
$420$	0.300877	−	2.86266i	0.0146813	−	0.139683i
$421$	11.0098	−	9.91325i	0.536584	−	0.483142i	−0.355710	−	0.934596i	$-0.615761\pi$
$421$	11.0098	−	9.91325i	0.536584	−	0.483142i	0.892295	+	0.451454i	$0.149094\pi$
$422$	−0.182950	−	0.563063i	−0.00890587	−	0.0274095i
$423$	−1.66428	−	15.8346i	−0.0809202	−	0.769904i
$424$	6.04342	+	2.69070i	0.293494	+	0.130672i
$425$	27.2104	+	24.5003i	1.31990	+	1.18844i
$426$	−0.283368	+	0.872117i	−0.0137292	+	0.0422542i
$427$	−0.963319	+	9.16537i	−0.0466183	+	0.443543i
$428$		−	19.3220i		−	0.933962i
$429$	15.8508	−	22.6341i	0.765285	−	1.09278i
$430$	0.430933	−	2.01337i	0.0207814	−	0.0970933i
$431$	21.0090	−	28.9165i	1.01197	−	1.39286i	0.0942862	−	0.995545i	$-0.469943\pi$
$431$	21.0090	−	28.9165i	1.01197	−	1.39286i	0.917684	−	0.397312i	$-0.130057\pi$
$432$	−6.33571	−	2.05860i	−0.304827	−	0.0990442i
$433$	−4.00142	−	3.60289i	−0.192296	−	0.173144i	0.567359	−	0.823471i	$-0.307965\pi$
$433$	−4.00142	−	3.60289i	−0.192296	−	0.173144i	−0.759655	+	0.650327i	$0.774632\pi$
$434$	−15.6404	+	11.3634i	−0.750763	+	0.545461i
$435$	−8.13873	−	3.62360i	−0.390222	−	0.173738i
$436$	−4.17556	−	3.75969i	−0.199973	−	0.180056i
$437$	3.79245	+	4.21194i	0.181417	+	0.201484i
$438$	11.9872	−	16.4990i	0.572773	−	0.788354i
$439$	−34.7440	−	20.0594i	−1.65824	−	0.957384i	−0.973528	−	0.228570i	$-0.926595\pi$
$439$	−34.7440	−	20.0594i	−1.65824	−	0.957384i	−0.684711	−	0.728815i	$-0.740072\pi$
$440$	−0.958574	−	0.406967i	−0.0456982	−	0.0194014i
$441$	−16.5270			−0.786998
$442$	2.25670	−	21.4711i	0.107340	−	1.02128i
$443$	−24.5971	−	27.3179i	−1.16864	−	1.29791i	−0.946429	−	0.322913i	$-0.895338\pi$
$443$	−24.5971	−	27.3179i	−1.16864	−	1.29791i	−0.222216	−	0.974998i	$-0.571329\pi$
$444$	−5.38289	−	1.14417i	−0.255461	−	0.0542999i
$445$	0.377105	+	3.58792i	0.0178765	+	0.170084i
$446$	0.215064	+	0.296010i	0.0101836	+	0.0140165i
$447$	4.82264	−	22.6887i	0.228103	−	1.07314i
$448$	−2.12779	−	2.36315i	−0.100528	−	0.111648i
$449$	25.0759	+	2.63559i	1.18341	+	0.124381i	0.675719	−	0.737160i	$-0.263833\pi$
$449$	25.0759	+	2.63559i	1.18341	+	0.124381i	0.507688	+	0.861541i	$0.330500\pi$
$450$	13.0153	+	22.5431i	0.613545	+	1.06269i
$451$	6.09354	−	0.105951i	0.286934	−	0.00498903i
$452$			19.7438i			0.928670i
$453$	−43.5372	−	4.57594i	−2.04556	−	0.214997i
$454$	−13.6083	+	2.89252i	−0.638667	+	0.135753i
$455$	2.82253	+	0.599946i	0.132322	+	0.0281259i
$456$	3.72286	−	0.391289i	0.174339	−	0.0183238i
$457$	−22.4092	+	16.2812i	−1.04826	+	0.761603i	−0.971880	−	0.235476i	$-0.924335\pi$
$457$	−22.4092	+	16.2812i	−1.04826	+	0.761603i	−0.0763762	+	0.997079i	$0.524335\pi$
$458$	23.9360	+	5.08776i	1.11846	+	0.237735i
$459$	33.2996	+	36.9830i	1.55429	+	1.72622i
$460$	−0.557439	−	1.25203i	−0.0259907	−	0.0583761i
$461$	25.2304	−	14.5668i	1.17510	−	0.678443i	0.220222	−	0.975450i	$-0.429322\pi$
$461$	25.2304	−	14.5668i	1.17510	−	0.678443i	0.954875	+	0.297007i	$0.0959885\pi$
$462$	−8.89134	+	29.0752i	−0.413662	+	1.35270i
$463$	8.55545	−	4.93949i	0.397605	−	0.229558i	−0.287845	−	0.957677i	$-0.592939\pi$
$463$	8.55545	−	4.93949i	0.397605	−	0.229558i	0.685450	+	0.728119i	$0.259605\pi$
$464$	−8.99123	+	4.00315i	−0.417407	+	0.185842i
$465$	−1.70056	+	5.23380i	−0.0788618	+	0.242712i
$466$	−24.5548	−	5.21929i	−1.13748	−	0.241779i
$467$	−4.44972	+	9.99424i	−0.205909	+	0.462478i	−0.986749	−	0.162252i	$-0.948124\pi$
$467$	−4.44972	+	9.99424i	−0.205909	+	0.462478i	0.780841	+	0.624730i	$0.214791\pi$
$468$	6.24274	−	14.0214i	0.288571	−	0.648141i
$469$	−6.56313	−	20.1992i	−0.303057	−	0.932714i
$470$	−0.195716	−	0.920770i	−0.00902769	−	0.0424719i
$471$	34.2042	+	24.8508i	1.57605	+	1.14507i
$472$	−0.518666			−0.0238736
$473$	−8.52751	+	20.0070i	−0.392095	+	0.919925i
$474$	28.6935			1.31794
$475$	−5.14896	−	3.74094i	−0.236250	−	0.171646i
$476$	4.93896	+	23.2360i	0.226377	+	1.06502i
$477$	−10.8567	−	33.4134i	−0.497093	−	1.52990i
$478$	−9.24991	+	20.7756i	−0.423081	+	0.950255i
$479$	−6.91297	+	15.5268i	−0.315862	+	0.709437i	−0.999798	−	0.0201047i	$-0.993600\pi$
$479$	−6.91297	+	15.5268i	−0.315862	+	0.709437i	0.683936	+	0.729542i	$0.260267\pi$
$480$	−0.885406	−	0.188199i	−0.0404130	−	0.00859006i
$481$	1.70479	−	5.24682i	0.0777320	−	0.239234i
$482$	22.7853	−	10.1447i	1.03784	−	0.462077i
$483$	−34.6528	+	20.0068i	−1.57676	+	0.910341i
$484$	9.11858	+	6.15236i	0.414481	+	0.279653i
$485$	−3.22281	+	1.86069i	−0.146340	+	0.0844895i
$486$	−4.29169	−	9.63928i	−0.194675	−	0.437247i
$487$	8.75916	+	9.72804i	0.396916	+	0.440819i	0.908165	−	0.418613i	$-0.137484\pi$
$487$	8.75916	+	9.72804i	0.396916	+	0.440819i	−0.511249	+	0.859433i	$0.670817\pi$
$488$	2.83480	+	0.602556i	0.128326	+	0.0272764i
$489$	−4.15508	+	3.01884i	−0.187899	+	0.136517i
$490$	−0.971765	+	0.102137i	−0.0438999	+	0.00461406i
$491$	18.3417	+	3.89865i	0.827749	+	0.175943i	0.602258	−	0.798302i	$-0.294268\pi$
$491$	18.3417	+	3.89865i	0.827749	+	0.175943i	0.225491	+	0.974245i	$0.427601\pi$
$492$	5.18162	−	1.10139i	0.233606	−	0.0496544i
$493$	73.1211	+	7.68534i	3.29321	+	0.346130i
$494$			3.75268i			0.168841i
$495$	1.80024	+	5.22943i	0.0809148	+	0.235045i
$496$	3.03979	+	5.26506i	0.136490	+	0.236408i
$497$	1.00595	+	0.105730i	0.0451232	+	0.00474264i
$498$	−23.0574	−	25.6078i	−1.03323	−	1.14752i
$499$	−3.03437	+	14.2756i	−0.135837	+	0.639064i	0.856566	+	0.516037i	$0.172593\pi$
$499$	−3.03437	+	14.2756i	−0.135837	+	0.639064i	−0.992403	+	0.123027i	$0.960740\pi$
$500$	1.82739	+	2.51519i	0.0817234	+	0.112483i
$501$	1.05930	+	10.0786i	0.0473261	+	0.450278i
$502$	8.67290	+	1.84348i	0.387090	+	0.0822786i
$503$	19.3097	+	21.4456i	0.860979	+	0.956214i	0.999416	−	0.0341575i	$-0.0108748\pi$
$503$	19.3097	+	21.4456i	0.860979	+	0.956214i	−0.138438	+	0.990371i	$0.544208\pi$
$504$	−1.76528	+	16.7955i	−0.0786318	+	0.748132i
$505$	−4.84424			−0.215566
$506$	3.25556	+	14.1057i	0.144727	+	0.627076i
$507$	−11.6038	−	6.69946i	−0.515343	−	0.297533i
$508$	−5.13892	+	7.07312i	−0.228003	+	0.313819i
$509$	−11.2321	−	12.4745i	−0.497852	−	0.552921i	0.440881	−	0.897566i	$-0.354666\pi$
$509$	−11.2321	−	12.4745i	−0.497852	−	0.552921i	−0.938733	+	0.344645i	$0.887999\pi$
$510$	5.02517	+	4.52469i	0.222518	+	0.200356i
$511$	−20.5507	−	9.14975i	−0.909108	−	0.404761i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	−6.42840	−	5.78816i	−0.283821	−	0.255553i
$514$	−27.1959	−	8.83649i	−1.19956	−	0.389761i
$515$	−0.0960450	+	0.132195i	−0.00423225	+	0.00582519i
$516$	−3.95654	+	18.4854i	−0.174177	+	0.813776i
$517$	0.172860	+	9.94172i	0.00760239	+	0.437236i
$518$			6.07025i			0.266711i
$519$	−5.43935	+	51.7520i	−0.238761	+	2.27166i
$520$	0.280413	−	0.863023i	0.0122969	−	0.0378461i
$521$	5.32144	+	4.79145i	0.233136	+	0.209917i	0.777416	−	0.628987i	$-0.216530\pi$
$521$	5.32144	+	4.79145i	0.233136	+	0.209917i	−0.544279	+	0.838904i	$0.683197\pi$
$522$	47.7508	+	21.2600i	2.09000	+	0.930527i
$523$	−1.82399	−	17.3541i	−0.0797576	−	0.758843i	−0.959179	−	0.282799i	$-0.908737\pi$
$523$	−1.82399	−	17.3541i	−0.0797576	−	0.758843i	0.879422	−	0.476044i	$-0.157930\pi$
$524$	4.06240	+	12.5028i	0.177467	+	0.546186i
$525$	33.3913	−	30.0657i	1.45732	−	1.31217i
$526$	−1.64718	+	15.6719i	−0.0718207	+	0.683328i
$527$		−	45.4164i		−	1.97837i
$528$	8.80100	+	3.73651i	0.383014	+	0.162611i
$529$	1.97409	−	3.41922i	0.0858300	−	0.148662i
$530$	−0.844854	−	1.89757i	−0.0366981	−	0.0824253i
$531$	1.84315	+	2.04703i	0.0799859	+	0.0888334i
$532$	−1.27597	−	3.92703i	−0.0553203	−	0.170258i
$533$	0.555104	+	5.28146i	0.0240442	+	0.228765i
$534$	−3.46233	−	32.9419i	−0.149830	−	1.42554i
$535$	−4.05955	+	4.50859i	−0.175510	+	0.194923i
$536$	−6.53304	+	1.38864i	−0.282185	+	0.0599802i
$537$	−30.3293	−	22.0355i	−1.30880	−	0.950902i
$538$	17.5501			0.756639
$539$	10.2818	+	0.900242i	0.442869	+	0.0387762i
$540$	1.04586	+	1.81149i	0.0450067	+	0.0779540i
$541$	7.53389	+	16.9214i	0.323907	+	0.727508i	0.999956	−	0.00934886i	$-0.00297588\pi$
$541$	7.53389	+	16.9214i	0.323907	+	0.727508i	−0.676049	+	0.736857i	$0.736309\pi$
$542$	10.9444	−	9.85435i	0.470101	−	0.423281i
$543$	−20.0221	+	6.50557i	−0.859230	+	0.279181i
$544$	7.42941	−	0.780862i	0.318533	−	0.0334792i
$545$	0.184413	+	1.75457i	0.00789938	+	0.0751576i
$546$	−25.9146	−	5.50831i	−1.10904	−	0.235734i
$547$	0.723654	+	3.40452i	0.0309412	+	0.145567i	0.990907	−	0.134552i	$-0.0429595\pi$
$547$	0.723654	+	3.40452i	0.0309412	+	0.145567i	−0.959965	+	0.280119i	$0.909626\pi$
$548$	−0.136019	+	0.187214i	−0.00581045	+	0.00799739i
$549$	−7.69574	−	13.3294i	−0.328446	−	0.568885i
$550$	−6.86914	−	14.7335i	−0.292901	−	0.628240i
$551$	−12.7800			−0.544445
$552$	5.11804	+	11.4953i	0.217838	+	0.489273i
$553$	−6.58048	−	30.9587i	−0.279830	−	1.31650i
$554$	13.9632	−	15.5077i	0.593239	−	0.658859i
$555$	1.01565	+	1.39793i	0.0431121	+	0.0593387i
$556$	−4.00073	+	8.98579i	−0.169669	+	0.381082i
$557$	2.35670	−	0.765738i	0.0998566	−	0.0324454i	−0.258663	−	0.965968i	$-0.583282\pi$
$557$	2.35670	−	0.765738i	0.0998566	−	0.0324454i	0.358519	+	0.933522i	$0.383282\pi$
$558$	9.97739	−	30.7073i	0.422377	−	1.29994i
$559$	−18.0153	−	5.88171i	−0.761965	−	0.248770i
$560$			0.998465i			0.0421929i
$561$	−42.9816	−	57.0465i	−1.81468	−	2.40850i
$562$	14.9927	−	8.65604i	0.632429	−	0.365133i
$563$	−22.4492	+	30.8986i	−0.946120	+	1.30222i	0.00710964	+	0.999975i	$0.497737\pi$
$563$	−22.4492	+	30.8986i	−0.946120	+	1.30222i	−0.953229	+	0.302248i	$0.902263\pi$
$564$	1.79693	+	8.45390i	0.0756645	+	0.355974i
$565$	4.14818	−	4.60702i	0.174515	−	0.193819i
$566$	14.5633	−	1.53067i	0.612143	−	0.0643388i
$567$	8.41855	−	6.11644i	0.353546	−	0.256866i
$568$	0.0661341	−	0.311136i	0.00277492	−	0.0130550i
$569$	3.19168	+	15.0157i	0.133802	+	0.629490i	0.993027	+	0.117891i	$0.0376134\pi$
$569$	3.19168	+	15.0157i	0.133802	+	0.629490i	−0.859224	+	0.511599i	$0.829053\pi$
$570$	−0.950903	−	0.690871i	−0.0398289	−	0.0289374i
$571$	0.385705	+	0.668060i	0.0161412	+	0.0279574i	0.873983	−	0.485956i	$-0.161529\pi$
$571$	0.385705	+	0.668060i	0.0161412	+	0.0279574i	−0.857842	+	0.513914i	$0.828195\pi$
$572$	−4.64752	+	8.38301i	−0.194322	+	0.350511i
$573$	24.1047	−	41.7506i	1.00699	−	1.74416i
$574$	−2.37668	−	5.33810i	−0.0992005	−	0.222808i
$575$	6.61107	−	20.3468i	0.275701	−	0.848519i
$576$	5.19477	+	1.10418i	0.216449	+	0.0460076i
$577$	−44.4333	+	4.67013i	−1.84978	+	0.194420i	−0.963315	−	0.268372i	$-0.913514\pi$
$577$	−44.4333	+	4.67013i	−1.84978	+	0.194420i	−0.886467	+	0.462792i	$0.846848\pi$
$578$	−35.4509	−	15.7837i	−1.47456	−	0.656517i
$579$	0.895495	−	0.994548i	0.0372155	−	0.0413320i
$580$	2.93908	+	0.954964i	0.122039	+	0.0396527i
$581$	−22.3416	+	30.7505i	−0.926884	+	1.27575i
$582$	29.5897	−	17.0836i	1.22653	−	0.708139i
$583$	4.93412	+	21.3786i	0.204350	+	0.885412i
$584$	−3.53711	+	6.12646i	−0.146367	+	0.253515i
$585$	−4.40259	+	1.96016i	−0.182025	+	0.0810426i
$586$	1.63759	+	0.532085i	0.0676482	+	0.0219802i
$587$	5.99749	−	28.2160i	0.247543	−	1.16460i	−0.662168	−	0.749355i	$-0.730364\pi$
$587$	5.99749	−	28.2160i	0.247543	−	1.16460i	0.909711	−	0.415242i	$-0.136303\pi$
$588$	8.92211	−	0.937751i	0.367942	−	0.0386722i
$589$	0.825179	+	7.85105i	0.0340009	+	0.323497i
$590$	0.121026	+	0.108972i	0.00498255	+	0.00448631i
$591$	−17.9559	+	55.2627i	−0.738608	+	2.27320i
$592$	1.89847	+	0.199537i	0.0780266	+	0.00820093i
$593$	3.55635	−	6.15979i	0.146042	−	0.252952i	−0.783719	−	0.621115i	$-0.786680\pi$
$593$	3.55635	−	6.15979i	0.146042	−	0.252952i	0.929761	+	0.368163i	$0.120013\pi$
$594$	−7.19187	−	20.8913i	−0.295086	−	0.857180i
$595$	3.72943	−	6.45957i	0.152892	−	0.264816i
$596$	−0.841044	+	8.00200i	−0.0344505	+	0.327775i
$597$	19.1486	−	4.07017i	0.783701	−	0.166581i
$598$	−11.9971	+	3.89808i	−0.490596	+	0.159404i
$599$	29.5956	+	13.1768i	1.20924	+	0.538389i	0.909529	−	0.415640i	$-0.136442\pi$
$599$	29.5956	+	13.1768i	1.20924	+	0.538389i	0.299713	+	0.954029i	$0.403109\pi$
$600$	−8.30542	−	11.4314i	−0.339067	−	0.466686i
$601$	−10.8709	−	33.4571i	−0.443432	−	1.36474i	−0.884194	−	0.467119i	$-0.845292\pi$
$601$	−10.8709	−	33.4571i	−0.443432	−	1.36474i	0.440763	−	0.897624i	$-0.354708\pi$
$602$	20.8522	+	0.0295001i	0.849871	+	0.00120233i
$603$	28.6966	+	20.8493i	1.16862	+	0.849050i
$604$	15.1853			0.617882
$605$	−0.835118	−	3.35141i	−0.0339524	−	0.136254i
$606$	44.4766			1.80674
$607$	−4.12143	+	39.2128i	−0.167284	+	1.59160i	0.512830	+	0.858490i	$0.328597\pi$
$607$	−4.12143	+	39.2128i	−0.167284	+	1.59160i	−0.680114	+	0.733107i	$0.738070\pi$
$608$	−1.27012	+	0.269973i	−0.0515102	+	0.0109488i
$609$	18.7589	−	88.2536i	0.760148	−	3.57622i
$610$	−0.534876	−	0.736193i	−0.0216565	−	0.0298076i
$611$	−8.61679	+	0.905661i	−0.348598	+	0.0366391i
$612$	−29.4832	−	26.5468i	−1.19179	−	1.07309i
$613$	12.9646	+	4.21247i	0.523637	+	0.170140i	0.558895	−	0.829238i	$-0.311225\pi$
$613$	12.9646	+	4.21247i	0.523637	+	0.170140i	−0.0352584	+	0.999378i	$0.511225\pi$
$614$	−19.1172	−	2.00930i	−0.771509	−	0.0810889i
$615$	−1.44048	−	0.831662i	−0.0580858	−	0.0335359i
$616$	2.01309	−	10.3527i	0.0811098	−	0.417123i
$617$	−20.9313	+	36.2541i	−0.842662	+	1.45953i	0.0449743	+	0.998988i	$0.485679\pi$
$617$	−20.9313	+	36.2541i	−0.842662	+	1.45953i	−0.887636	+	0.460545i	$0.847654\pi$
$618$	0.881822	−	1.21372i	0.0354721	−	0.0488232i
$619$	−4.02976	−	4.47550i	−0.161970	−	0.179886i	0.656697	−	0.754155i	$-0.271953\pi$
$619$	−4.02976	−	4.47550i	−0.161970	−	0.179886i	−0.818667	+	0.574269i	$0.805286\pi$
$620$	0.396888	−	1.86721i	0.0159394	−	0.0749889i
$621$	11.8269	−	26.5636i	0.474596	−	1.06596i
$622$	−4.76996	−	2.12372i	−0.191258	−	0.0851536i
$623$	−34.7485	+	11.2905i	−1.39217	+	0.452343i
$624$	−2.57457	+	7.92371i	−0.103065	+	0.317202i
$625$	−2.45965	+	23.4020i	−0.0983858	+	0.936079i
$626$	−0.902275	+	0.520929i	−0.0360622	+	0.0208205i
$627$	8.46663	+	9.08059i	0.338125	+	0.362644i
$628$	−12.7008	−	7.33281i	−0.506817	−	0.292611i
$629$	−11.5368	−	8.38200i	−0.460004	−	0.334212i
$630$	3.94065	−	3.54818i	0.156999	−	0.141363i
$631$	−0.0753043	+	0.354279i	−0.00299782	+	0.0141036i	−0.979621	−	0.200854i	$-0.935628\pi$
$631$	−0.0753043	+	0.354279i	−0.00299782	+	0.0141036i	0.976623	+	0.214958i	$0.0689615\pi$
$632$	−9.89865	+	1.04039i	−0.393747	+	0.0413845i
$633$	0.694202	−	1.55920i	0.0275920	−	0.0619727i
$634$	0.398175	+	1.22546i	0.0158135	+	0.0486691i
$635$	2.68518	−	0.570753i	0.106558	−	0.0226496i
$636$	7.75690	+	17.4223i	0.307581	+	0.690838i
$637$			8.99356i			0.356338i
$638$	−28.5488	−	15.8274i	−1.13026	−	0.626613i
$639$	−1.46298	+	0.844653i	−0.0578746	+	0.0334139i
$640$	0.312270	+	0.0328209i	0.0123436	+	0.00129736i
$641$	33.2878	+	10.8159i	1.31479	+	0.427201i	0.880703	−	0.473670i	$-0.157071\pi$
$641$	33.2878	+	10.8159i	1.31479	+	0.427201i	0.434087	+	0.900871i	$0.357071\pi$
$642$	37.2721	−	41.3949i	1.47101	−	1.63373i
$643$	−24.2177	+	17.5952i	−0.955052	+	0.693886i	−0.951996	−	0.306110i	$-0.900973\pi$
$643$	−24.2177	+	17.5952i	−0.955052	+	0.693886i	−0.00305557	+	0.999995i	$0.500973\pi$
$644$	11.2291	−	8.15838i	0.442487	−	0.321485i
$645$	4.80701	−	3.48212i	0.189276	−	0.137108i
$646$	9.22543	+	2.99752i	0.362970	+	0.117936i
$647$	22.5841	−	31.0843i	0.887872	−	1.22205i	−0.0863053	−	0.996269i	$-0.527506\pi$
$647$	22.5841	−	31.0843i	0.887872	−	1.22205i	0.974178	−	0.225783i	$-0.0724939\pi$
$648$	−1.63619	−	2.83396i	−0.0642754	−	0.111328i
$649$	−1.03516	−	1.37390i	−0.0406337	−	0.0539303i
$650$	12.2674	−	7.08258i	0.481167	−	0.277802i
$651$	−55.4277	−	5.82568i	−2.17238	−	0.228326i
$652$	1.32395	−	1.19209i	0.0518500	−	0.0466860i
$653$	−7.42729	+	2.41327i	−0.290652	+	0.0944387i	−0.450714	−	0.892668i	$-0.648831\pi$
$653$	−7.42729	+	2.41327i	−0.290652	+	0.0944387i	0.160062	+	0.987107i	$0.448831\pi$
$654$	−1.69316	−	16.1093i	−0.0662077	−	0.629924i
$655$	1.67892	−	3.77091i	0.0656007	−	0.147342i
$656$	−1.74761	+	0.567834i	−0.0682329	+	0.0221702i
$657$	36.7489	−	7.81123i	1.43371	−	0.304745i
$658$	8.70920	−	3.87759i	0.339520	−	0.151164i
$659$	16.6333	+	9.60324i	0.647942	+	0.374089i	0.787667	−	0.616101i	$-0.211289\pi$
$659$	16.6333	+	9.60324i	0.647942	+	0.374089i	−0.139726	+	0.990190i	$0.544622\pi$
$660$	−1.26858	−	2.72097i	−0.0493796	−	0.105914i
$661$	−10.9404			−0.425531			−0.212766	−	0.977103i	$-0.568247\pi$
$661$	−10.9404			−0.425531			−0.212766	+	0.977103i	$0.568247\pi$
$662$	5.81184	+	13.0536i	0.225883	+	0.507343i
$663$	46.2525	−	41.6460i	1.79630	−	1.61740i
$664$	8.88282	+	7.99813i	0.344720	+	0.310388i
$665$	−0.527335	+	1.18441i	−0.0204492	+	0.0459296i
$666$	−5.95895	−	8.20179i	−0.230905	−	0.317813i
$667$	−13.2752	−	40.8567i	−0.514016	−	1.58198i
$668$	−0.730873	−	3.43849i	−0.0282783	−	0.133039i
$669$	−0.110257	+	1.04902i	−0.00426278	+	0.0405576i
$670$	1.81618	+	1.04857i	0.0701650	+	0.0405098i
$671$	4.06163	+	8.71173i	0.156797	+	0.336313i
$672$		−	9.16725i		−	0.353634i
$673$	−10.6458	+	4.73982i	−0.410366	+	0.182707i	−0.601528	−	0.798852i	$-0.705441\pi$
$673$	−10.6458	+	4.73982i	−0.410366	+	0.182707i	0.191162	+	0.981558i	$0.438774\pi$
$674$	−20.1300	+	18.1251i	−0.775378	+	0.698153i
$675$	−6.78873	+	31.9385i	−0.261298	+	1.22931i
$676$	4.24598	+	1.89043i	0.163307	+	0.0727089i
$677$	−30.2345	+	21.9667i	−1.16201	+	0.844248i	−0.990031	−	0.140853i	$-0.955016\pi$
$677$	−30.2345	+	21.9667i	−1.16201	+	0.844248i	−0.171977	+	0.985101i	$0.555016\pi$
$678$	−38.0858	+	42.2986i	−1.46268	+	1.62447i
$679$	−25.2183	−	28.0078i	−0.967790	−	1.07484i
$680$	−1.89764	−	1.37871i	−0.0727711	−	0.0528713i
$681$	−34.7337	−	20.0535i	−1.33100	−	0.768452i
$682$	−7.87982	+	18.5602i	−0.301734	+	0.710707i
$683$	18.6214	+	32.2533i	0.712530	+	1.23414i	0.963905	+	0.266248i	$0.0857841\pi$
$683$	18.6214	+	32.2533i	0.712530	+	1.23414i	−0.251375	+	0.967890i	$0.580883\pi$
$684$	5.57905	+	4.05342i	0.213320	+	0.154986i
$685$	0.0710724	−	0.0151069i	0.00271554	−	0.000577205i
$686$	3.82061	+	11.7586i	0.145872	+	0.448946i
$687$	41.4656	+	57.0726i	1.58201	+	2.17745i
$688$	0.694664	−	6.52054i	0.0264838	−	0.248593i
$689$	−18.1827	+	5.90793i	−0.692707	+	0.225074i
$690$	1.22092	−	3.75762i	0.0464798	−	0.143050i
$691$	4.97828	+	0.523238i	0.189383	+	0.0199049i	0.198745	−	0.980051i	$-0.436313\pi$
$691$	4.97828	+	0.523238i	0.189383	+	0.0199049i	−0.00936223	+	0.999956i	$0.502980\pi$
$692$		−	18.0506i		−	0.686180i
$693$	−48.0130	+	28.8447i	−1.82386	+	1.09572i
$694$	8.36095	+	14.4816i	0.317377	+	0.549714i
$695$	2.82145	−	1.25619i	0.107024	−	0.0476500i
$696$	−26.9847	−	8.76785i	−1.02285	−	0.332345i
$697$	13.4271	+	2.85403i	0.508589	+	0.108104i
$698$	−2.47705	−	1.10285i	−0.0937576	−	0.0417436i
$699$	−42.5376	−	58.5480i	−1.60892	−	2.21449i
$700$	−10.4292	+	11.5828i	−0.394185	+	0.437787i
$701$	−28.3421	+	25.5193i	−1.07047	+	0.963852i	−0.999435	−	0.0336216i	$-0.989296\pi$
$701$	−28.3421	+	25.5193i	−1.07047	+	0.963852i	−0.0710320	+	0.997474i	$0.522629\pi$
$702$	17.5881	−	7.83073i	0.663821	−	0.295552i
$703$	2.14665	+	1.23937i	0.0809623	+	0.0467436i
$704$	−3.17164	−	0.969902i	−0.119536	−	0.0365546i
$705$	1.35687	−	2.35017i	0.0511027	−	0.0885125i
$706$	−22.8453	+	10.1714i	−0.859792	+	0.382804i
$707$	−10.2001	−	47.9878i	−0.383615	−	1.80477i
$708$	−1.11118	−	1.00051i	−0.0417606	−	0.0376014i
$709$	4.15768	−	3.02073i	0.156145	−	0.113446i	−0.506969	−	0.861964i	$-0.669234\pi$
$709$	4.15768	−	3.02073i	0.156145	−	0.113446i	0.663114	+	0.748518i	$0.269234\pi$
$710$	−0.0808016	+	0.0587058i	−0.00303243	+	0.00220319i
$711$	39.2823	+	35.3699i	1.47320	+	1.32648i
$712$	2.38886	+	11.2387i	0.0895264	+	0.421189i
$713$	−24.2422	+	10.7933i	−0.907876	+	0.404212i
$714$	−34.2412	+	59.3075i	−1.28144	+	2.21953i
$715$	2.84572	−	0.979646i	0.106424	−	0.0366367i
$716$	11.2619	+	6.50208i	0.420878	+	0.242994i
$717$	−59.8930	+	26.6661i	−2.23675	+	0.995863i
$718$	19.5420	−	17.5957i	0.729303	−	0.656667i
$719$	−21.4288	+	23.7991i	−0.799161	+	0.887558i	−0.995671	−	0.0929437i	$-0.970372\pi$
$719$	−21.4288	+	23.7991i	−0.799161	+	0.887558i	0.196511	+	0.980502i	$0.437039\pi$
$720$	−0.980159	−	1.34907i	−0.0365284	−	0.0502770i
$721$	−1.51178	−	0.673087i	−0.0563015	−	0.0250671i
$722$	16.9356	+	3.59976i	0.630276	+	0.133969i
$723$	68.3838	+	22.2192i	2.54322	+	0.826343i
$724$	6.67131	−	2.97026i	0.247937	−	0.110389i
$725$	24.1201	+	41.7773i	0.895800	+	1.55157i
$726$	7.66750	+	30.7704i	0.284568	+	1.14200i
$727$		−	9.33270i		−	0.346131i	−0.984910	−	0.173065i	$-0.944633\pi$
$727$		−	9.33270i		−	0.346131i	0.984910	−	0.173065i	$-0.0553672\pi$
$728$	9.13970	+	0.960621i	0.338740	+	0.0356030i
$729$	12.4335	−	38.2663i	0.460499	−	1.41727i
$730$	2.11252	−	0.686399i	0.0781879	−	0.0254048i
$731$	−28.8494	+	39.5899i	−1.06703	+	1.46429i
$732$	4.91088	+	6.75924i	0.181511	+	0.249829i
$733$	1.21787	+	3.74821i	0.0449830	+	0.138443i	0.971026	−	0.238976i	$-0.0768116\pi$
$733$	1.21787	+	3.74821i	0.0449830	+	0.138443i	−0.926043	+	0.377419i	$0.876812\pi$
$734$	14.8069	−	3.14730i	0.546533	−	0.116169i
$735$	−2.27891	−	1.65572i	−0.0840588	−	0.0610723i
$736$	−2.18242	−	3.78006i	−0.0804450	−	0.139335i
$737$	−16.7171	−	14.5340i	−0.615784	−	0.535366i
$738$	8.45146	+	4.87945i	0.311103	+	0.179615i
$739$	0.756472	+	0.549609i	0.0278273	+	0.0202177i	0.601612	−	0.798788i	$-0.294525\pi$
$739$	0.756472	+	0.549609i	0.0278273	+	0.0202177i	−0.573785	+	0.819006i	$0.694525\pi$
$740$	−0.401066	−	0.445429i	−0.0147435	−	0.0163743i
$741$	−7.23892	+	8.03964i	−0.265928	+	0.295344i
$742$	17.0187	−	12.3648i	0.624778	−	0.453928i
$743$	−31.9979	−	14.2464i	−1.17389	−	0.522650i	−0.275266	−	0.961368i	$-0.588766\pi$
$743$	−31.9979	−	14.2464i	−1.17389	−	0.522650i	−0.898625	+	0.438718i	$0.855433\pi$
$744$	−3.64396	+	17.1435i	−0.133594	+	0.628511i
$745$	1.87747	−	1.69048i	0.0687852	−	0.0619345i
$746$	13.0148	−	5.79457i	0.476507	−	0.212154i
$747$		−	63.4804i		−	2.32263i
$748$	16.8962	+	18.1214i	0.617785	+	0.662583i
$749$	−53.2107	−	30.7212i	−1.94428	−	1.12253i
$750$	−0.936849	+	8.91352i	−0.0342089	+	0.325476i
$751$	4.55130	+	21.4122i	0.166079	+	0.781342i	0.979783	+	0.200062i	$0.0641144\pi$
$751$	4.55130	+	21.4122i	0.166079	+	0.781342i	−0.813704	+	0.581280i	$0.802552\pi$
$752$	−0.926431	−	2.85126i	−0.0337835	−	0.103975i
$753$	15.0245	+	20.6795i	0.547524	+	0.753602i
$754$	11.5692	−	25.9848i	0.421325	−	0.946311i
$755$	−3.54335	−	3.19044i	−0.128956	−	0.116112i
$756$	−15.7427	+	14.1748i	−0.572557	+	0.515532i
$757$	13.2388	+	29.7347i	0.481171	+	1.08073i	0.977181	+	0.212411i	$0.0681314\pi$
$757$	13.2388	+	29.7347i	0.481171	+	1.08073i	−0.496010	+	0.868317i	$0.665202\pi$
$758$	13.6023			0.494058
$759$	−20.2354	+	36.4997i	−0.734497	+	1.32486i
$760$	0.353091	+	0.203857i	0.0128080	+	0.00739468i
$761$	25.6536	−	11.4217i	0.929942	−	0.414037i	0.114859	−	0.993382i	$-0.463358\pi$
$761$	25.6536	−	11.4217i	0.929942	−	0.414037i	0.815082	+	0.579345i	$0.196692\pi$
$762$	−24.6536	+	5.24028i	−0.893105	+	0.189835i
$763$	−16.9928	+	5.52129i	−0.615180	+	0.199884i
$764$	−6.80179	+	15.2771i	−0.246080	+	0.552705i
$765$	1.30212	+	12.3889i	0.0470783	+	0.447921i
$766$	−2.73576	+	0.888901i	−0.0988469	+	0.0321173i
$767$	1.11394	−	1.00300i	0.0402221	−	0.0362161i
$768$	−2.86706	−	0.301340i	−0.103456	−	0.0108737i
$769$	−9.70035	+	5.60050i	−0.349804	+	0.201959i	−0.664599	−	0.747200i	$-0.731398\pi$
$769$	−9.70035	+	5.60050i	−0.349804	+	0.201959i	0.314795	+	0.949160i	$0.398064\pi$
$770$	−2.64484	+	1.99275i	−0.0953136	+	0.0718138i
$771$	−41.2182	−	71.3921i	−1.48444	−	2.57112i
$772$	−0.272866	+	0.375567i	−0.00982065	+	0.0135170i
$773$	−18.6336	−	6.05444i	−0.670205	−	0.217763i	−0.0459033	−	0.998946i	$-0.514617\pi$
$773$	−18.6336	−	6.05444i	−0.670205	−	0.217763i	−0.624302	+	0.781183i	$0.714617\pi$
$774$	−28.2033	+	20.4300i	−1.01375	+	0.734340i
$775$	24.1075	−	17.5151i	0.865966	−	0.629161i
$776$	−9.58839	+	6.96637i	−0.344203	+	0.250078i
$777$	−11.7095	+	13.0048i	−0.420077	+	0.466543i
$778$	29.8746	+	9.70686i	1.07106	+	0.348008i
$779$	−2.37298	−	0.249410i	−0.0850209	−	0.00893605i
$780$	2.26553	−	1.30800i	0.0811188	−	0.0468340i
$781$	0.956163	−	0.445787i	0.0342142	−	0.0159515i
$782$			32.6068i			1.16602i
$783$	26.6680	+	59.8974i	0.953037	+	2.14056i
$784$	−3.04394	+	0.647009i	−0.108712	+	0.0231075i
$785$	1.42298	+	4.37948i	0.0507883	+	0.156310i
$786$	−15.4147	+	34.6220i	−0.549824	+	1.23493i
$787$	53.0496	−	5.57573i	1.89101	−	0.198753i	0.913095	−	0.407747i	$-0.133685\pi$
$787$	53.0496	−	5.57573i	1.89101	−	0.198753i	0.977917	+	0.208993i	$0.0670186\pi$
$788$	4.19066	−	19.7155i	0.149286	−	0.702336i
$789$	−33.7601	+	30.3977i	−1.20189	+	1.08219i
$790$	2.52834	+	1.83694i	0.0899542	+	0.0653555i
$791$	54.3724	+	31.3919i	1.93326	+	1.11617i
$792$	7.44292	+	15.9642i	0.264473	+	0.567264i
$793$	−7.25353	+	4.18783i	−0.257580	+	0.148714i
$794$	0.153277	−	1.45833i	0.00543959	−	0.0517543i
$795$	1.85043	−	5.69504i	0.0656280	−	0.201982i
$796$	−6.45829	+	2.09843i	−0.228908	+	0.0743767i
$797$	−40.6795	−	18.1117i	−1.44094	−	0.641549i	−0.470394	−	0.882457i	$-0.655888\pi$
$797$	−40.6795	−	18.1117i	−1.44094	−	0.641549i	−0.970548	+	0.240908i	$0.922555\pi$
$798$	4.84165	−	10.8745i	0.171392	−	0.384954i
$799$	−4.65639	+	21.9066i	−0.164731	+	0.775000i
$800$	3.27968	+	3.64246i	0.115954	+	0.128780i
$801$	35.8668	−	49.3664i	1.26729	−	1.74428i
$802$	2.48041	−	4.29619i	0.0875863	−	0.151704i
$803$	−23.2878	+	2.85779i	−0.821810	+	0.100849i
$804$	−16.6749	−	9.62727i	−0.588079	−	0.339528i
$805$	−4.33427	−	0.455550i	−0.152763	−	0.0160560i
$806$	−16.7101	−	5.42945i	−0.588589	−	0.191244i
$807$	37.5989	+	33.8542i	1.32355	+	1.19173i
$808$	−15.3435	+	1.61266i	−0.539782	+	0.0567334i
$809$	9.28990	+	12.7864i	0.326615	+	0.449547i	0.940473	−	0.339870i	$-0.110383\pi$
$809$	9.28990	+	12.7864i	0.326615	+	0.449547i	−0.613857	+	0.789417i	$0.710383\pi$
$810$	−0.213628	+	1.00504i	−0.00750611	+	0.0353135i
$811$	−13.9910	+	2.97389i	−0.491292	+	0.104427i	−0.446895	−	0.894587i	$-0.647470\pi$
$811$	−13.9910	+	2.97389i	−0.491292	+	0.104427i	−0.0443974	+	0.999014i	$0.514137\pi$
$812$	−3.27145	+	31.1258i	−0.114805	+	1.09230i
$813$	42.4560			1.48900
$814$	3.26044	+	5.42711i	0.114278	+	0.190220i
$815$	−0.559391			−0.0195946
$816$	17.4229	+	12.6584i	0.609922	+	0.443134i
$817$	4.26783	−	7.36801i	0.149313	−	0.257774i
$818$	−8.83284	−	27.1847i	−0.308833	−	0.950490i
$819$	−28.6879	−	39.4855i	−1.00243	−	1.37973i
$820$	0.527091	+	0.234676i	0.0184068	+	0.00819524i
$821$	27.9832	−	9.09228i	0.976619	−	0.317323i	0.223134	−	0.974788i	$-0.428371\pi$
$821$	27.9832	−	9.09228i	0.976619	−	0.317323i	0.753485	+	0.657465i	$0.228371\pi$
$822$	−0.652540	+	0.138702i	−0.0227600	+	0.00483778i
$823$	−4.69650	+	44.6842i	−0.163710	+	1.55759i	0.536652	+	0.843804i	$0.319689\pi$
$823$	−4.69650	+	44.6842i	−0.163710	+	1.55759i	−0.700361	+	0.713789i	$0.746978\pi$
$824$	−0.260202	+	0.450683i	−0.00906456	+	0.0157003i
$825$	13.7047	−	44.8153i	0.477138	−	1.56027i
$826$	−0.824661	+	1.42835i	−0.0286936	+	0.0496988i
$827$	27.8736	+	2.92963i	0.969259	+	0.101873i	0.575907	−	0.817515i	$-0.304649\pi$
$827$	27.8736	+	2.92963i	0.969259	+	0.101873i	0.393351	+	0.919388i	$0.371316\pi$
$828$	−7.16329	+	22.0463i	−0.248941	+	0.766163i
$829$	3.88628	+	3.49923i	0.134976	+	0.121533i	0.733854	−	0.679307i	$-0.237720\pi$
$829$	3.88628	+	3.49923i	0.134976	+	0.121533i	−0.598878	+	0.800841i	$0.704386\pi$
$830$	−0.392309	−	3.73257i	−0.0136172	−	0.129559i
$831$	59.8288	−	6.28826i	2.07544	−	0.218137i
$832$	0.600868	−	2.82686i	0.0208314	−	0.0980039i
$833$	22.1094	+	7.18378i	0.766046	+	0.248903i
$834$	−25.9047	+	11.5335i	−0.897005	+	0.399373i
$835$	−0.551885	+	0.955894i	−0.0190988	+	0.0330801i
$836$	−3.25006	−	2.82562i	−0.112406	−	0.0977261i
$837$	35.0746	−	20.2503i	1.21235	−	0.699953i
$838$	3.01025	−	4.14325i	0.103987	−	0.143126i
$839$	36.8109	+	11.9606i	1.27085	+	0.412926i	0.865350	−	0.501167i	$-0.167096\pi$
$839$	36.8109	+	11.9606i	1.27085	+	0.412926i	0.405504	+	0.914093i	$0.367096\pi$
$840$	−1.92604	+	2.13909i	−0.0664548	+	0.0738055i
$841$	62.0000	+	27.6042i	2.13793	+	0.951868i
$842$	−14.7340	+	1.54860i	−0.507766	+	0.0533684i
$843$	48.8175	+	10.3765i	1.68136	+	0.357385i
$844$	−0.182950	+	0.563063i	−0.00629740	+	0.0193814i
$845$	−0.593576	−	1.33319i	−0.0204196	−	0.0458633i
$846$	−7.96091	+	13.7887i	−0.273702	+	0.474065i
$847$	31.4412	−	15.3296i	1.08033	−	0.526732i
$848$	−3.30767	−	5.72906i	−0.113586	−	0.196737i
$849$	34.1528	+	24.8135i	1.17212	+	0.851596i
$850$	−7.61272	−	35.8150i	−0.261114	−	1.22844i
$851$	−1.73235	+	8.15008i	−0.0593843	+	0.279381i
$852$	0.741867	−	0.538998i	0.0254159	−	0.0184658i
$853$	−19.8863	+	2.09014i	−0.680895	+	0.0715650i	−0.438661	−	0.898653i	$-0.644547\pi$
$853$	−19.8863	+	2.09014i	−0.680895	+	0.0715650i	−0.242235	+	0.970218i	$0.577880\pi$
$854$	6.16661	−	6.84872i	0.211017	−	0.234358i
$855$	−0.450191	−	2.11798i	−0.0153962	−	0.0724335i
$856$	−11.3572	+	15.6318i	−0.388180	+	0.534284i
$857$	−17.2592	+	9.96463i	−0.589565	+	0.340385i	−0.764925	−	0.644119i	$-0.777224\pi$
$857$	−17.2592	+	9.96463i	−0.589565	+	0.340385i	0.175361	+	0.984504i	$0.443891\pi$
$858$	−26.1276	+	8.99446i	−0.891980	+	0.307066i
$859$		−	14.2947i		−	0.487730i	−0.969809	−	0.243865i	$-0.921585\pi$
$859$		−	14.2947i		−	0.487730i	0.969809	−	0.243865i	$-0.0784154\pi$
$860$	−1.53206	+	1.37555i	−0.0522428	+	0.0469060i
$861$	5.20548	−	16.0208i	0.177402	−	0.545988i
$862$	−33.9933	+	11.0451i	−1.15782	+	0.376198i
$863$	−9.08142	+	20.3972i	−0.309135	+	0.694329i	−0.999578	−	0.0290581i	$-0.990749\pi$
$863$	−9.08142	+	20.3972i	−0.309135	+	0.694329i	0.690442	+	0.723387i	$0.257416\pi$
$864$	3.91568	+	5.38947i	0.133214	+	0.183354i
$865$	−3.79243	+	4.21192i	−0.128946	+	0.143210i
$866$	1.11949	+	5.26677i	0.0380417	+	0.178972i
$867$	−45.5022	−	102.200i	−1.54533	−	3.47088i
$868$	19.3326			0.656191
$869$	−22.5118	−	24.1442i	−0.763659	−	0.819036i
$870$	4.45448	+	7.71538i	0.151021	+	0.261576i
$871$	11.3457	−	15.6160i	0.384434	−	0.529127i
$872$	1.16821	+	5.49598i	0.0395605	+	0.186117i
$873$	61.5679	+	13.0867i	2.08376	+	0.442916i
$874$	−0.592439	−	5.63668i	−0.0200395	−	0.190663i
$875$	9.83206	−	1.03339i	0.332384	−	0.0349350i
$876$	−19.3958	+	6.30207i	−0.655322	+	0.212927i
$877$	−21.4308	+	19.2964i	−0.723666	+	0.651592i	−0.946292	−	0.323312i	$-0.895204\pi$
$877$	−21.4308	+	19.2964i	−0.723666	+	0.651592i	0.222626	+	0.974904i	$0.428537\pi$
$878$	16.3178	+	36.6504i	0.550700	+	1.23689i
$879$	2.48194	+	4.29884i	0.0837137	+	0.144996i
$880$	0.536294	+	0.892679i	0.0180785	+	0.0300922i
$881$	33.7044			1.13553			0.567765	−	0.823191i	$-0.307808\pi$
$881$	33.7044			1.13553			0.567765	+	0.823191i	$0.307808\pi$
$882$	13.3706	+	9.71430i	0.450211	+	0.327098i
$883$	−37.3210	+	7.93282i	−1.25595	+	0.266961i	−0.787382	−	0.616466i	$-0.788564\pi$
$883$	−37.3210	+	7.93282i	−1.25595	+	0.266961i	−0.468570	+	0.883426i	$0.655231\pi$
$884$	−14.4461	+	16.0440i	−0.485875	+	0.539619i
$885$	0.0490750	+	0.466918i	0.00164964	+	0.0156953i
$886$	3.84245	+	36.5584i	0.129090	+	1.22820i
$887$	−6.64750	−	20.4589i	−0.223201	−	0.686942i	−0.998469	−	0.0553101i	$-0.982385\pi$
$887$	−6.64750	−	20.4589i	−0.223201	−	0.686942i	0.775268	−	0.631632i	$-0.217615\pi$
$888$	3.68233	+	4.08964i	0.123571	+	0.137239i
$889$	11.3080	+	25.3981i	0.379257	+	0.851824i
$890$	1.80384	−	3.12434i	0.0604648	−	0.104728i
$891$	4.24137	−	9.99016i	0.142091	−	0.334683i
$892$		−	0.365889i		−	0.0122509i
$893$	0.406917	−	3.87156i	0.0136170	−	0.129557i
$894$	−17.2377	+	15.5209i	−0.576515	+	0.519097i
$895$	−1.26177	−	3.88333i	−0.0421763	−	0.129805i
$896$	0.332393	+	3.16251i	0.0111045	+	0.105652i
$897$	−33.2216	−	14.7912i	−1.10924	−	0.493864i
$898$	−18.7377	−	16.8715i	−0.625285	−	0.563009i
$899$	18.4903	−	56.9073i	0.616686	−	1.89797i
$900$	2.72093	−	25.8879i	0.0906977	−	0.862931i
$901$			49.4188i			1.64638i
$902$	−4.99206	−	3.49598i	−0.166217	−	0.116403i
$903$	44.6162	+	40.2871i	1.48474	+	1.34067i
$904$	11.6051	−	15.9731i	0.385980	−	0.531256i
$905$	−2.18074	−	0.708564i	−0.0724901	−	0.0235535i
$906$	32.5327	+	29.2925i	1.08083	+	0.973180i
$907$	−4.35281	+	3.16250i	−0.144533	+	0.105009i	−0.657702	−	0.753278i	$-0.728471\pi$
$907$	−4.35281	+	3.16250i	−0.144533	+	0.105009i	0.513169	+	0.858287i	$0.328471\pi$
$908$	12.7095	+	5.65863i	0.421779	+	0.187788i
$909$	60.8898	+	54.8255i	2.01959	+	1.81845i
$910$	−1.93083	−	2.14441i	−0.0640064	−	0.0710864i
$911$	11.0291	−	15.1803i	0.365411	−	0.502945i	−0.586236	−	0.810141i	$-0.699391\pi$
$911$	11.0291	−	15.1803i	0.365411	−	0.502945i	0.951646	+	0.307196i	$0.0993907\pi$
$912$	−3.24185	−	1.87168i	−0.107348	−	0.0619777i
$913$	−3.45785	+	39.4926i	−0.114438	+	1.30701i
$914$	27.6992			0.916210
$915$	0.274215	−	2.60898i	0.00906526	−	0.0862502i
$916$	−16.3741	−	18.1853i	−0.541017	−	0.600860i
$917$	40.8904	+	8.69153i	1.35032	+	0.287019i
$918$	−5.20191	−	49.4929i	−0.171689	−	1.63351i
$919$	−3.61142	−	4.97069i	−0.119130	−	0.163968i	0.745287	−	0.666743i	$-0.232312\pi$
$919$	−3.61142	−	4.97069i	−0.119130	−	0.163968i	−0.864417	+	0.502775i	$0.832312\pi$
$920$	−0.284946	+	1.34057i	−0.00939440	+	0.0441972i
$921$	−37.0804	−	41.1819i	−1.22184	−	1.35699i
$922$	−28.9740	−	3.04529i	−0.954207	−	0.100291i
$923$	0.459639	+	0.796118i	0.0151292	+	0.0262045i
$924$	24.2832	−	18.2961i	0.798859	−	0.601899i
$925$		−	9.35643i		−	0.307638i
$926$	−9.82486	−	1.03263i	−0.322865	−	0.0339345i
$927$	2.70338	−	0.574621i	0.0887905	−	0.0188730i
$928$	9.62705	+	2.04629i	0.316023	+	0.0671729i
$929$	24.6594	−	2.59181i	0.809050	−	0.0850346i	0.309034	−	0.951051i	$-0.399994\pi$
$929$	24.6594	−	2.59181i	0.809050	−	0.0850346i	0.500016	+	0.866016i	$0.333328\pi$
$930$	4.45214	−	3.23467i	0.145991	−	0.106069i
$931$	−3.95254	−	0.840138i	−0.129539	−	0.0275344i
$932$	16.7975	+	18.6555i	0.550219	+	0.611080i
$933$	−6.12238	−	13.7511i	−0.200438	−	0.450190i
$934$	9.47437	−	5.47003i	0.310011	−	0.178985i
$935$	−0.135245	−	7.77833i	−0.00442297	−	0.254379i
$936$	−13.2921	+	7.67418i	−0.434465	+	0.250839i
$937$	15.9481	−	7.10055i	0.521002	−	0.231965i	−0.129349	−	0.991599i	$-0.541289\pi$
$937$	15.9481	−	7.10055i	0.521002	−	0.231965i	0.650351	+	0.759634i	$0.274622\pi$
$938$	−6.56313	+	20.1992i	−0.214294	+	0.659528i
$939$	−2.93788	−	0.624467i	−0.0958743	−	0.0203787i
$940$	−0.382878	+	0.859957i	−0.0124881	+	0.0280487i
$941$	21.7743	−	48.9060i	0.709823	−	1.59429i	−0.0913239	−	0.995821i	$-0.529110\pi$
$941$	21.7743	−	48.9060i	0.709823	−	1.59429i	0.801147	−	0.598468i	$-0.204223\pi$
$942$	−13.0649	−	40.2095i	−0.425676	−	1.31010i
$943$	−1.66758	−	7.84534i	−0.0543038	−	0.255479i
$944$	0.419610	+	0.304864i	0.0136571	+	0.00992249i
$945$	6.65153			0.216374
$946$	18.6587	−	11.1737i	0.606648	−	0.363288i
$947$	28.2240			0.917158			0.458579	−	0.888654i	$-0.348359\pi$
$947$	28.2240			0.917158			0.458579	+	0.888654i	$0.348359\pi$
$948$	−23.2135	−	16.8656i	−0.753940	−	0.547770i
$949$	−4.25068	−	19.9979i	−0.137983	−	0.649158i
$950$	1.96673	+	6.05296i	0.0638090	+	0.196384i
$951$	−1.51087	+	3.39347i	−0.0489933	+	0.110041i
$952$	9.66207	−	21.7014i	0.313150	−	0.703345i
$953$	−53.0738	−	11.2812i	−1.71923	−	0.365433i	−0.760408	−	0.649446i	$-0.775001\pi$
$953$	−53.0738	−	11.2812i	−1.71923	−	0.365433i	−0.958821	+	0.284012i	$0.908334\pi$
$954$	−10.8567	+	33.4134i	−0.351498	+	1.08180i
$955$	4.79685	−	2.13570i	0.155222	−	0.0691095i
$956$	19.6949	−	11.3709i	0.636980	−	0.367761i
$957$	−30.6312	−	88.9790i	−0.990166	−	2.87628i
$958$	14.7191	−	8.49809i	0.475554	−	0.274561i
$959$	0.299303	+	0.672246i	0.00966501	+	0.0217080i
$960$	0.605688	+	0.672684i	0.0195485	+	0.0217108i
$961$	−5.83091	−	1.23940i	−0.188094	−	0.0399806i
$962$	−4.46321	+	3.24271i	−0.143900	+	0.104549i
$963$	102.053	−	10.7262i	3.28862	−	0.345648i
$964$	−24.3966	−	5.18566i	−0.785762	−	0.167019i
$965$	0.142577	−	0.0303057i	0.00458973	−	0.000975576i
$966$	39.7944	+	4.18256i	1.28036	+	0.134572i
$967$			22.0387i			0.708718i	0.935109	+	0.354359i	$0.115301\pi$
$967$			22.0387i			0.708718i	−0.935109	+	0.354359i	$0.884699\pi$
$968$	−3.76082	−	10.3371i	−0.120877	−	0.332248i
$969$	13.9821	+	24.2177i	0.449170	+	0.777985i
$970$	3.70099	+	0.388990i	0.118832	+	0.0124897i
$971$	−1.05787	−	1.17489i	−0.0339488	−	0.0377040i	0.725931	−	0.687767i	$-0.241409\pi$
$971$	−1.05787	−	1.17489i	−0.0339488	−	0.0377040i	−0.759880	+	0.650063i	$0.774742\pi$
$972$	−2.19378	+	10.3209i	−0.0703656	+	0.331044i
$973$	18.3849	+	25.3047i	0.589394	+	0.811231i
$974$	−1.36832	−	13.0187i	−0.0438437	−	0.417145i
$975$	39.9437	+	8.49029i	1.27922	+	0.271907i
$976$	−1.93923	−	2.15373i	−0.0620733	−	0.0689393i
$977$	1.07537	−	10.2315i	0.0344042	−	0.327334i	−0.963760	−	0.266770i	$-0.914043\pi$
$977$	1.07537	−	10.2315i	0.0344042	−	0.327334i	0.998164	−	0.0605638i	$-0.0192899\pi$
$978$	5.13596			0.164230
$979$	−25.0026	+	28.7583i	−0.799087	+	0.919118i
$980$	0.846209	+	0.488559i	0.0270312	+	0.0156064i
$981$	17.5397	−	24.1413i	0.559998	−	0.770772i
$982$	−12.5472	−	13.9350i	−0.400396	−	0.444685i
$983$	−44.7521	−	40.2950i	−1.42737	−	1.28521i	−0.900218	−	0.435440i	$-0.856593\pi$
$983$	−44.7521	−	40.2950i	−1.42737	−	1.28521i	−0.527153	−	0.849770i	$-0.676741\pi$
$984$	−4.83940	−	2.15464i	−0.154274	−	0.0686874i
$985$	−5.12008	+	3.71996i	−0.163139	+	0.118528i
$986$	−54.6389	−	49.1971i	−1.74006	−	1.56675i
$987$	26.1382	+	8.49283i	0.831990	+	0.270330i
$988$	2.20577	−	3.03598i	0.0701748	−	0.0965873i
$989$	27.9883	+	5.99048i	0.889975	+	0.190486i
$990$	1.61736	−	5.28885i	0.0514029	−	0.168091i
$991$			42.6466i			1.35471i	0.735655	+	0.677356i	$0.236874\pi$
$991$			42.6466i			1.35471i	−0.735655	+	0.677356i	$0.763126\pi$
$992$	0.635488	−	6.04627i	0.0201768	−	0.191969i
$993$	−12.7293	+	39.1768i	−0.403952	+	1.24324i
$994$	−0.751687	−	0.676822i	−0.0238421	−	0.0214675i
$995$	1.94786	+	0.867242i	0.0617512	+	0.0274934i
$996$	3.60192	+	34.2700i	0.114131	+	1.08589i
$997$	1.35238	+	4.16221i	0.0428304	+	0.131818i	0.970185	−	0.242365i	$-0.0779231\pi$
$997$	1.35238	+	4.16221i	0.0428304	+	0.131818i	−0.927355	+	0.374183i	$0.877923\pi$
$998$	10.8459	−	9.76565i	0.343319	−	0.309126i
$999$	1.32927	−	12.6471i	0.0420562	−	0.400138i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	946.2.t.a.7.3	✓	176
11.8	odd	10		946.2.t.b.437.20	yes	176
43.37	odd	6		946.2.t.b.381.20	yes	176
473.338	even	30	inner	946.2.t.a.811.3	yes	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
946.2.t.a.7.3	✓	176	1.1	even	1	trivial
946.2.t.a.811.3	yes	176	473.338	even	30	inner
946.2.t.b.381.20	yes	176	43.37	odd	6
946.2.t.b.437.20	yes	176	11.8	odd	10

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:	\( N \)	\(=\)	\( 946 = 2 \cdot 11 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	946.t (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 - 0.587785i) q^{2} +(-0.599378 - 2.81985i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.127711 - 0.286844i) q^{5} +(-1.17256 + 2.63361i) q^{6} +(3.11044 + 0.661144i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-4.85168 + 2.16011i) q^{9} +O(q^{10})\)	\(q+(-0.809017 - 0.587785i) q^{2} +(-0.599378 - 2.81985i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.127711 - 0.286844i) q^{5} +(-1.17256 + 2.63361i) q^{6} +(3.11044 + 0.661144i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-4.85168 + 2.16011i) q^{9} +(-0.271923 + 0.156995i) q^{10} +(3.13600 - 1.07958i) q^{11} +(2.49662 - 1.44142i) q^{12} +(1.17548 + 2.64016i) q^{13} +(-2.12779 - 2.36315i) q^{14} +(-0.885406 - 0.188199i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(7.42941 - 0.780862i) q^{17} +(5.19477 + 1.10418i) q^{18} +(-1.27012 + 0.269973i) q^{19} +(0.312270 + 0.0328209i) q^{20} -9.16725i q^{21} +(-3.17164 - 0.969902i) q^{22} +(-2.18242 - 3.78006i) q^{23} +(-2.86706 - 0.301340i) q^{24} +(3.27968 + 3.64246i) q^{25} +(0.600868 - 2.82686i) q^{26} +(3.91568 + 5.38947i) q^{27} +(0.332393 + 3.16251i) q^{28} +(9.62705 + 2.04629i) q^{29} +(0.605688 + 0.672684i) q^{30} +(0.635488 - 6.04627i) q^{31} +1.00000 q^{32} +(-4.92389 - 8.19599i) q^{33} +(-6.46949 - 3.73516i) q^{34} +(0.586883 - 0.807776i) q^{35} +(-3.55363 - 3.94671i) q^{36} +(-1.41861 - 1.27732i) q^{37} +(1.18624 + 0.528146i) q^{38} +(6.74031 - 4.89712i) q^{39} +(-0.233340 - 0.210100i) q^{40} +(1.74761 + 0.567834i) q^{41} +(-5.38838 + 7.41646i) q^{42} +(-4.39467 + 4.86691i) q^{43} +(1.99582 + 2.64891i) q^{44} +1.66755i q^{45} +(-0.456250 + 4.34093i) q^{46} +(-0.926431 + 2.85126i) q^{47} +(2.14237 + 1.92900i) q^{48} +(2.84290 + 1.26574i) q^{49} +(-0.512337 - 4.87456i) q^{50} +(-6.65494 - 20.4818i) q^{51} +(-2.14770 + 1.93380i) q^{52} +(-0.691492 + 6.57911i) q^{53} -6.66176i q^{54} +(0.0908331 - 1.03742i) q^{55} +(1.58996 - 2.75390i) q^{56} +(1.52257 + 3.41974i) q^{57} +(-6.58567 - 7.31412i) q^{58} +(-0.160277 - 0.493281i) q^{59} +(-0.0946177 - 0.900227i) q^{60} +(0.302938 + 2.88226i) q^{61} +(-4.06803 + 4.51800i) q^{62} +(-16.5190 + 3.51122i) q^{63} +(-0.809017 - 0.587785i) q^{64} +0.907436 q^{65} +(-0.833969 + 9.52489i) q^{66} +(-3.33950 - 5.78418i) q^{67} +(3.03846 + 6.82448i) q^{68} +(-9.35112 + 8.41979i) q^{69} +(-0.949597 + 0.308543i) q^{70} +(0.316345 - 0.0332492i) q^{71} +(0.555132 + 5.28173i) q^{72} +(-6.91963 - 1.47081i) q^{73} +(0.396888 + 1.86721i) q^{74} +(8.30542 - 11.4314i) q^{75} +(-0.649248 - 1.12453i) q^{76} +(10.4681 - 1.28460i) q^{77} -8.33149 q^{78} +(-4.04832 - 9.09267i) q^{79} +(0.0652822 + 0.307129i) q^{80} +(2.18964 - 2.43185i) q^{81} +(-1.08009 - 1.48661i) q^{82} +(-4.86173 + 10.9196i) q^{83} +(8.71858 - 2.83284i) q^{84} +(0.724833 - 2.23081i) q^{85} +(6.41607 - 1.35429i) q^{86} -28.3734i q^{87} +(-0.0576587 - 3.31612i) q^{88} +(-9.95045 + 5.74490i) q^{89} +(0.980159 - 1.34907i) q^{90} +(1.91072 + 8.98922i) q^{91} +(2.92065 - 3.24371i) q^{92} +(-17.4305 + 1.83202i) q^{93} +(2.42543 - 1.76218i) q^{94} +(-0.0847687 + 0.398805i) q^{95} +(-0.599378 - 2.81985i) q^{96} +(-9.58839 - 6.96637i) q^{97} +(-1.55597 - 2.69502i) q^{98} +(-12.8829 + 12.0119i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q - 44 q^{2} - 44 q^{4} - 5 q^{6} - 15 q^{7} - 44 q^{8} - 20 q^{9}+O(q^{10}) \) 176 * q - 44 * q^2 - 44 * q^4 - 5 * q^6 - 15 * q^7 - 44 * q^8 - 20 * q^9	\( 176 q - 44 q^{2} - 44 q^{4} - 5 q^{6} - 15 q^{7} - 44 q^{8} - 20 q^{9} - 5 q^{11} - 5 q^{13} + 15 q^{14} + 41 q^{15} - 44 q^{16} - 2 q^{17} - 25 q^{18} + 34 q^{19} + 5 q^{22} - 4 q^{23} + 5 q^{24} - 24 q^{25} + 20 q^{26} - 60 q^{27} - 3 q^{29} - 49 q^{30} + 40 q^{31} + 176 q^{32} - 47 q^{33} + 3 q^{34} - 60 q^{35} - 25 q^{36} - 8 q^{37} + 14 q^{38} + 12 q^{39} - 19 q^{43} - 10 q^{44} + 26 q^{46} - 4 q^{47} - 21 q^{49} + 6 q^{50} + 45 q^{51} - 20 q^{52} - 27 q^{53} + 68 q^{55} + 71 q^{57} - 3 q^{58} - 21 q^{59} + 6 q^{60} + 30 q^{61} + 71 q^{63} - 44 q^{64} - 16 q^{65} + 43 q^{66} - 3 q^{67} + 8 q^{68} - 42 q^{69} + 3 q^{71} - 20 q^{72} - 19 q^{73} - 28 q^{74} + 9 q^{76} + 38 q^{77} + 92 q^{78} + 32 q^{79} - 23 q^{81} - 5 q^{82} - 26 q^{83} + 2 q^{85} + 36 q^{86} + 5 q^{88} + 57 q^{89} + 30 q^{91} + 6 q^{92} - 10 q^{93} + 6 q^{94} - 58 q^{95} - 37 q^{97} - 106 q^{98} - 119 q^{99}+O(q^{100}) \) 176 * q - 44 * q^2 - 44 * q^4 - 5 * q^6 - 15 * q^7 - 44 * q^8 - 20 * q^9 - 5 * q^11 - 5 * q^13 + 15 * q^14 + 41 * q^15 - 44 * q^16 - 2 * q^17 - 25 * q^18 + 34 * q^19 + 5 * q^22 - 4 * q^23 + 5 * q^24 - 24 * q^25 + 20 * q^26 - 60 * q^27 - 3 * q^29 - 49 * q^30 + 40 * q^31 + 176 * q^32 - 47 * q^33 + 3 * q^34 - 60 * q^35 - 25 * q^36 - 8 * q^37 + 14 * q^38 + 12 * q^39 - 19 * q^43 - 10 * q^44 + 26 * q^46 - 4 * q^47 - 21 * q^49 + 6 * q^50 + 45 * q^51 - 20 * q^52 - 27 * q^53 + 68 * q^55 + 71 * q^57 - 3 * q^58 - 21 * q^59 + 6 * q^60 + 30 * q^61 + 71 * q^63 - 44 * q^64 - 16 * q^65 + 43 * q^66 - 3 * q^67 + 8 * q^68 - 42 * q^69 + 3 * q^71 - 20 * q^72 - 19 * q^73 - 28 * q^74 + 9 * q^76 + 38 * q^77 + 92 * q^78 + 32 * q^79 - 23 * q^81 - 5 * q^82 - 26 * q^83 + 2 * q^85 + 36 * q^86 + 5 * q^88 + 57 * q^89 + 30 * q^91 + 6 * q^92 - 10 * q^93 + 6 * q^94 - 58 * q^95 - 37 * q^97 - 106 * q^98 - 119 * q^99

Introduction

L-functions

Modular forms

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