LMFDB - Embedded newform 164.2.o.b.111.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [164,2,Mod(7,164)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(164, base_ring=CyclotomicField(40))

chi = DirichletCharacter(H, H._module([20, 39]))

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

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

chi := DirichletCharacter("164.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 164 = 2^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	164.o (of order $40$, 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:	$1.30954659315$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$18$ over $\Q(\zeta_{40})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{40}]$

Embedding invariants

Embedding label			111.17
Character	$\chi$	$=$	164.111
Dual form			164.2.o.b.99.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.37854 + 0.315653i) q^{2} +(-1.89955 - 0.786819i) q^{3} +(1.80073 + 0.870280i) q^{4} +(2.17460 - 1.10802i) q^{5} +(-2.37024 - 1.68426i) q^{6} +(-0.151929 - 0.247926i) q^{7} +(2.20766 + 1.76812i) q^{8} +(0.867885 + 0.867885i) q^{9} +O(q^{10})$	\(q+(1.37854 + 0.315653i) q^{2} +(-1.89955 - 0.786819i) q^{3} +(1.80073 + 0.870280i) q^{4} +(2.17460 - 1.10802i) q^{5} +(-2.37024 - 1.68426i) q^{6} +(-0.151929 - 0.247926i) q^{7} +(2.20766 + 1.76812i) q^{8} +(0.867885 + 0.867885i) q^{9} +(3.34752 - 0.841019i) q^{10} +(2.25578 + 0.177534i) q^{11} +(-2.73582 - 3.06999i) q^{12} +(-0.172173 - 0.717151i) q^{13} +(-0.131182 - 0.389733i) q^{14} +(-5.00258 + 0.393711i) q^{15} +(2.48523 + 3.13427i) q^{16} +(-3.59606 + 3.07132i) q^{17} +(0.922460 + 1.47036i) q^{18} +(-3.49324 - 0.838652i) q^{19} +(4.88015 - 0.102720i) q^{20} +(0.0935244 + 0.590490i) q^{21} +(3.05364 + 0.956783i) q^{22} +(-2.94903 + 2.14260i) q^{23} +(-2.80237 - 5.09566i) q^{24} +(0.562277 - 0.773908i) q^{25} +(-0.0109752 - 1.04297i) q^{26} +(1.39474 + 3.36719i) q^{27} +(-0.0578181 - 0.578669i) q^{28} +(-3.88263 - 3.31608i) q^{29} +(-7.02051 - 1.03634i) q^{30} +(-2.10889 - 6.49051i) q^{31} +(2.43663 + 5.10518i) q^{32} +(-4.14529 - 2.11213i) q^{33} +(-5.92677 + 3.09882i) q^{34} +(-0.605093 - 0.370801i) q^{35} +(0.807520 + 2.31812i) q^{36} +(-3.56006 + 10.9567i) q^{37} +(-4.55083 - 2.25877i) q^{38} +(-0.237218 + 1.49773i) q^{39} +(6.75989 + 1.39883i) q^{40} +(-5.78230 - 2.75045i) q^{41} +(-0.0574633 + 0.843533i) q^{42} +(9.67140 + 1.53180i) q^{43} +(3.90754 + 2.28285i) q^{44} +(2.84894 + 0.925675i) q^{45} +(-4.74167 + 2.02278i) q^{46} +(-0.192743 + 0.314528i) q^{47} +(-2.25471 - 7.90913i) q^{48} +(3.13955 - 6.16171i) q^{49} +(1.01941 - 0.889376i) q^{50} +(9.24747 - 3.00469i) q^{51} +(0.314086 - 1.44123i) q^{52} +(5.01498 - 5.87179i) q^{53} +(0.859829 + 5.08205i) q^{54} +(5.10215 - 2.11338i) q^{55} +(0.102954 - 0.815966i) q^{56} +(5.97571 + 4.34161i) q^{57} +(-4.30562 - 5.79690i) q^{58} +(3.42355 + 4.71211i) q^{59} +(-9.35091 - 3.64467i) q^{60} +(9.82955 - 1.55685i) q^{61} +(-0.858436 - 9.61308i) q^{62} +(0.0833142 - 0.347029i) q^{63} +(1.74752 + 7.80680i) q^{64} +(-1.16902 - 1.36875i) q^{65} +(-5.04773 - 4.22012i) q^{66} +(0.538603 + 6.84360i) q^{67} +(-9.14843 + 2.40104i) q^{68} +(7.28768 - 1.74962i) q^{69} +(-0.717098 - 0.702163i) q^{70} +(0.568673 - 7.22567i) q^{71} +(0.381472 + 3.45052i) q^{72} +(-5.96949 + 5.96949i) q^{73} +(-8.36621 + 13.9805i) q^{74} +(-1.67700 + 1.02767i) q^{75} +(-5.56050 - 4.55028i) q^{76} +(-0.298705 - 0.586241i) q^{77} +(-0.799778 + 1.98980i) q^{78} +(-5.14027 + 12.4097i) q^{79} +(8.87721 + 4.06212i) q^{80} -11.1757i q^{81} +(-7.10292 - 5.61680i) q^{82} -17.9188i q^{83} +(-0.345479 + 1.14470i) q^{84} +(-4.41693 + 10.6634i) q^{85} +(12.8489 + 5.16445i) q^{86} +(4.76610 + 9.35399i) q^{87} +(4.66610 + 4.38043i) q^{88} +(-2.99682 + 1.83645i) q^{89} +(3.63517 + 2.17535i) q^{90} +(-0.151643 + 0.151643i) q^{91} +(-7.17506 + 1.29175i) q^{92} +(-1.10091 + 13.9884i) q^{93} +(-0.364985 + 0.372748i) q^{94} +(-8.52565 + 2.04683i) q^{95} +(-0.611655 - 11.6147i) q^{96} +(-0.792616 - 10.0711i) q^{97} +(6.27295 - 7.50313i) q^{98} +(1.80368 + 2.11184i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 12 q^{2} - 20 q^{4} - 32 q^{5} - 28 q^{6} - 24 q^{8} - 40 q^{9}+O(q^{10}) $ 288 * q - 12 * q^2 - 20 * q^4 - 32 * q^5 - 28 * q^6 - 24 * q^8 - 40 * q^9	$ 288 q - 12 q^{2} - 20 q^{4} - 32 q^{5} - 28 q^{6} - 24 q^{8} - 40 q^{9} - 12 q^{10} - 8 q^{12} - 24 q^{13} - 4 q^{14} - 28 q^{16} - 12 q^{18} - 44 q^{20} - 32 q^{21} - 40 q^{22} + 8 q^{24} - 40 q^{25} + 4 q^{26} - 48 q^{29} - 44 q^{30} + 108 q^{32} - 72 q^{33} + 12 q^{34} - 20 q^{36} - 24 q^{37} + 56 q^{38} + 8 q^{41} - 112 q^{42} - 40 q^{45} - 48 q^{46} - 68 q^{48} - 16 q^{49} - 60 q^{50} - 124 q^{52} - 64 q^{53} + 64 q^{54} - 84 q^{56} - 24 q^{57} + 40 q^{60} - 8 q^{61} - 44 q^{62} - 20 q^{64} + 64 q^{65} + 60 q^{66} - 28 q^{68} - 8 q^{69} + 128 q^{70} + 160 q^{72} - 32 q^{73} + 80 q^{74} + 288 q^{76} - 32 q^{77} + 116 q^{78} + 176 q^{80} + 212 q^{82} + 152 q^{84} - 56 q^{85} + 180 q^{86} + 144 q^{88} - 72 q^{89} + 224 q^{90} + 36 q^{92} - 8 q^{93} + 52 q^{94} + 136 q^{96} - 88 q^{97} + 104 q^{98}+O(q^{100}) $ 288 * q - 12 * q^2 - 20 * q^4 - 32 * q^5 - 28 * q^6 - 24 * q^8 - 40 * q^9 - 12 * q^10 - 8 * q^12 - 24 * q^13 - 4 * q^14 - 28 * q^16 - 12 * q^18 - 44 * q^20 - 32 * q^21 - 40 * q^22 + 8 * q^24 - 40 * q^25 + 4 * q^26 - 48 * q^29 - 44 * q^30 + 108 * q^32 - 72 * q^33 + 12 * q^34 - 20 * q^36 - 24 * q^37 + 56 * q^38 + 8 * q^41 - 112 * q^42 - 40 * q^45 - 48 * q^46 - 68 * q^48 - 16 * q^49 - 60 * q^50 - 124 * q^52 - 64 * q^53 + 64 * q^54 - 84 * q^56 - 24 * q^57 + 40 * q^60 - 8 * q^61 - 44 * q^62 - 20 * q^64 + 64 * q^65 + 60 * q^66 - 28 * q^68 - 8 * q^69 + 128 * q^70 + 160 * q^72 - 32 * q^73 + 80 * q^74 + 288 * q^76 - 32 * q^77 + 116 * q^78 + 176 * q^80 + 212 * q^82 + 152 * q^84 - 56 * q^85 + 180 * q^86 + 144 * q^88 - 72 * q^89 + 224 * q^90 + 36 * q^92 - 8 * q^93 + 52 * q^94 + 136 * q^96 - 88 * q^97 + 104 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/164\mathbb{Z}\right)^\times$.

$n$	$83$	$129$
$\chi(n)$	$-1$	$e\left(\frac{7}{40}\right)$

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 $

$2$	1.37854	+	0.315653i	0.974773	+	0.223201i
$2$	1.37854	+	0.315653i	0.974773	+	0.223201i
$3$	−1.89955	−	0.786819i	−1.09671	−	0.454270i	−0.240365	−	0.970682i	$-0.577267\pi$
$3$	−1.89955	−	0.786819i	−1.09671	−	0.454270i	−0.856340	+	0.516412i	$0.827267\pi$
$4$	1.80073	+	0.870280i	0.900363	+	0.435140i
$5$	2.17460	−	1.10802i	0.972513	−	0.495520i	0.105832	−	0.994384i	$-0.466249\pi$
$5$	2.17460	−	1.10802i	0.972513	−	0.495520i	0.866680	+	0.498864i	$0.166249\pi$
$6$	−2.37024	−	1.68426i	−0.967645	−	0.687596i
$7$	−0.151929	−	0.247926i	−0.0574240	−	0.0937074i	0.822640	−	0.568563i	$-0.192500\pi$
$7$	−0.151929	−	0.247926i	−0.0574240	−	0.0937074i	−0.880064	+	0.474855i	$0.842500\pi$
$8$	2.20766	+	1.76812i	0.780526	+	0.625124i
$9$	0.867885	+	0.867885i	0.289295	+	0.289295i
$10$	3.34752	−	0.841019i	1.05858	−	0.265954i
$11$	2.25578	+	0.177534i	0.680144	+	0.0535285i	0.413825	−	0.910356i	$-0.364192\pi$
$11$	2.25578	+	0.177534i	0.680144	+	0.0535285i	0.266319	+	0.963885i	$0.414192\pi$
$12$	−2.73582	−	3.06999i	−0.789762	−	0.886228i
$13$	−0.172173	−	0.717151i	−0.0477521	−	0.198902i	0.943395	−	0.331672i	$-0.107613\pi$
$13$	−0.172173	−	0.717151i	−0.0477521	−	0.198902i	−0.991147	+	0.132770i	$0.957613\pi$
$14$	−0.131182	−	0.389733i	−0.0350597	−	0.104160i
$15$	−5.00258	+	0.393711i	−1.29166	+	0.101656i
$16$	2.48523	+	3.13427i	0.621307	+	0.783567i
$17$	−3.59606	+	3.07132i	−0.872172	+	0.744906i	−0.968122	−	0.250481i	$-0.919411\pi$
$17$	−3.59606	+	3.07132i	−0.872172	+	0.744906i	0.0959492	+	0.995386i	$0.469411\pi$
$18$	0.922460	+	1.47036i	0.217426	+	0.346567i
$19$	−3.49324	−	0.838652i	−0.801404	−	0.192400i	−0.188000	−	0.982169i	$-0.560200\pi$
$19$	−3.49324	−	0.838652i	−0.801404	−	0.192400i	−0.613404	+	0.789769i	$0.710200\pi$
$20$	4.88015	−	0.102720i	1.09123	−	0.0229688i
$21$	0.0935244	+	0.590490i	0.0204087	+	0.128855i
$22$	3.05364	+	0.956783i	0.651038	+	0.203987i
$23$	−2.94903	+	2.14260i	−0.614916	+	0.446763i	−0.851142	−	0.524935i	$-0.824089\pi$
$23$	−2.94903	+	2.14260i	−0.614916	+	0.446763i	0.236226	+	0.971698i	$0.424089\pi$
$24$	−2.80237	−	5.09566i	−0.572031	−	1.04015i
$25$	0.562277	−	0.773908i	0.112455	−	0.154782i
$26$	−0.0109752	−	1.04297i	−0.00215242	−	0.204542i
$27$	1.39474	+	3.36719i	0.268417	+	0.648016i
$28$	−0.0578181	−	0.578669i	−0.0109266	−	0.109358i
$29$	−3.88263	−	3.31608i	−0.720986	−	0.615781i	0.211334	−	0.977414i	$-0.432219\pi$
$29$	−3.88263	−	3.31608i	−0.720986	−	0.615781i	−0.932320	+	0.361633i	$0.882219\pi$
$30$	−7.02051	−	1.03634i	−1.28176	−	0.189208i
$31$	−2.10889	−	6.49051i	−0.378768	−	1.16573i	−0.940901	−	0.338682i	$-0.890019\pi$
$31$	−2.10889	−	6.49051i	−0.378768	−	1.16573i	0.562133	−	0.827047i	$-0.309981\pi$
$32$	2.43663	+	5.10518i	0.430740	+	0.902476i
$33$	−4.14529	−	2.11213i	−0.721602	−	0.367674i
$34$	−5.92677	+	3.09882i	−1.01643	+	0.531444i
$35$	−0.605093	−	0.370801i	−0.102279	−	0.0626769i
$36$	0.807520	+	2.31812i	0.134587	+	0.386354i
$37$	−3.56006	+	10.9567i	−0.585271	+	1.80128i	0.0129099	+	0.999917i	$0.495891\pi$
$37$	−3.56006	+	10.9567i	−0.585271	+	1.80128i	−0.598181	+	0.801361i	$0.704109\pi$
$38$	−4.55083	−	2.25877i	−0.738243	−	0.366420i
$39$	−0.237218	+	1.49773i	−0.0379852	+	0.239829i
$40$	6.75989	+	1.39883i	1.06883	+	0.221175i
$41$	−5.78230	−	2.75045i	−0.903044	−	0.429548i
$41$	−5.78230	−	2.75045i	−0.903044	−	0.429548i
$42$	−0.0574633	+	0.843533i	−0.00886678	+	0.130160i
$43$	9.67140	+	1.53180i	1.47487	+	0.233597i	0.841504	−	0.540251i	$-0.181671\pi$
$43$	9.67140	+	1.53180i	1.47487	+	0.233597i	0.633371	+	0.773848i	$0.281671\pi$
$44$	3.90754	+	2.28285i	0.589084	+	0.344153i
$45$	2.84894	+	0.925675i	0.424694	+	0.137992i
$46$	−4.74167	+	2.02278i	−0.699121	+	0.298242i
$47$	−0.192743	+	0.314528i	−0.0281144	+	0.0458786i	−0.866389	−	0.499370i	$-0.833565\pi$
$47$	−0.192743	+	0.314528i	−0.0281144	+	0.0458786i	0.838274	+	0.545249i	$0.183565\pi$
$48$	−2.25471	−	7.90913i	−0.325439	−	1.14158i
$49$	3.13955	−	6.16171i	0.448507	−	0.880244i
$50$	1.01941	−	0.889376i	0.144166	−	0.125777i
$51$	9.24747	−	3.00469i	1.29490	−	0.420740i
$52$	0.314086	−	1.44123i	0.0435559	−	0.199863i
$53$	5.01498	−	5.87179i	0.688861	−	0.806553i	−0.300229	−	0.953867i	$-0.597063\pi$
$53$	5.01498	−	5.87179i	0.688861	−	0.806553i	0.989090	+	0.147315i	$0.0470630\pi$
$54$	0.859829	+	5.08205i	0.117008	+	0.691579i
$55$	5.10215	−	2.11338i	0.687973	−	0.284968i
$56$	0.102954	−	0.815966i	0.0137579	−	0.109038i
$57$	5.97571	+	4.34161i	0.791502	+	0.575060i
$58$	−4.30562	−	5.79690i	−0.565355	−	0.761171i
$59$	3.42355	+	4.71211i	0.445708	+	0.613465i	0.971469	−	0.237168i	$-0.0762192\pi$
$59$	3.42355	+	4.71211i	0.445708	+	0.613465i	−0.525760	+	0.850633i	$0.676219\pi$
$60$	−9.35091	−	3.64467i	−1.20720	−	0.470525i
$61$	9.82955	−	1.55685i	1.25855	−	0.199334i	0.508698	−	0.860945i	$-0.330127\pi$
$61$	9.82955	−	1.55685i	1.25855	−	0.199334i	0.749847	+	0.661611i	$0.230127\pi$
$62$	−0.858436	−	9.61308i	−0.109021	−	1.22086i
$63$	0.0833142	−	0.347029i	0.0104966	−	0.0437215i
$64$	1.74752	+	7.80680i	0.218440	+	0.975850i
$65$	−1.16902	−	1.36875i	−0.144999	−	0.169772i
$66$	−5.04773	−	4.22012i	−0.621332	−	0.519461i
$67$	0.538603	+	6.84360i	0.0658008	+	0.836079i	0.937935	+	0.346812i	$0.112736\pi$
$67$	0.538603	+	6.84360i	0.0658008	+	0.836079i	−0.872134	+	0.489267i	$0.837264\pi$
$68$	−9.14843	+	2.40104i	−1.10941	+	0.291168i
$69$	7.28768	−	1.74962i	0.877333	−	0.210629i
$70$	−0.717098	−	0.702163i	−0.0857096	−	0.0839245i
$71$	0.568673	−	7.22567i	0.0674890	−	0.857530i	−0.866258	−	0.499597i	$-0.833482\pi$
$71$	0.568673	−	7.22567i	0.0674890	−	0.857530i	0.933747	−	0.357933i	$-0.116518\pi$
$72$	0.381472	+	3.45052i	0.0449569	+	0.406647i
$73$	−5.96949	+	5.96949i	−0.698675	+	0.698675i	−0.964125	−	0.265449i	$-0.914480\pi$
$73$	−5.96949	+	5.96949i	−0.698675	+	0.698675i	0.265449	+	0.964125i	$0.414480\pi$
$74$	−8.36621	+	13.9805i	−0.972552	+	1.62520i
$75$	−1.67700	+	1.02767i	−0.193643	+	0.118665i
$76$	−5.56050	−	4.55028i	−0.637833	−	0.521953i
$77$	−0.298705	−	0.586241i	−0.0340406	−	0.0668084i
$78$	−0.799778	+	1.98980i	−0.0905570	+	0.225301i
$79$	−5.14027	+	12.4097i	−0.578325	+	1.39620i	0.315989	+	0.948763i	$0.397664\pi$
$79$	−5.14027	+	12.4097i	−0.578325	+	1.39620i	−0.894315	+	0.447438i	$0.852336\pi$
$80$	8.87721	+	4.06212i	0.992502	+	0.454159i
$81$		−	11.1757i		−	1.24174i
$82$	−7.10292	−	5.61680i	−0.784387	−	0.620272i
$83$		−	17.9188i		−	1.96684i	−0.181338	−	0.983421i	$-0.558043\pi$
$83$		−	17.9188i		−	1.96684i	0.181338	−	0.983421i	$-0.441957\pi$
$84$	−0.345479	+	1.14470i	−0.0376949	+	0.124897i
$85$	−4.41693	+	10.6634i	−0.479083	+	1.15661i
$86$	12.8489	+	5.16445i	1.38553	+	0.556897i
$87$	4.76610	+	9.35399i	0.510979	+	1.00285i
$88$	4.66610	+	4.38043i	0.497408	+	0.466955i
$89$	−2.99682	+	1.83645i	−0.317662	+	0.194663i	−0.672184	−	0.740384i	$-0.734644\pi$
$89$	−2.99682	+	1.83645i	−0.317662	+	0.194663i	0.354522	+	0.935048i	$0.384644\pi$
$90$	3.63517	+	2.17535i	0.383180	+	0.229302i
$91$	−0.151643	+	0.151643i	−0.0158965	+	0.0158965i
$92$	−7.17506	+	1.29175i	−0.748052	+	0.134674i
$93$	−1.10091	+	13.9884i	−0.114159	+	1.45052i
$94$	−0.364985	+	0.372748i	−0.0376453	+	0.0384460i
$95$	−8.52565	+	2.04683i	−0.874713	+	0.210000i
$96$	−0.611655	−	11.6147i	−0.0624268	−	1.18542i
$97$	−0.792616	−	10.0711i	−0.0804780	−	1.02257i	−0.896061	−	0.443930i	$-0.853584\pi$
$97$	−0.792616	−	10.0711i	−0.0804780	−	1.02257i	0.815583	−	0.578639i	$-0.196416\pi$
$98$	6.27295	−	7.50313i	0.633663	−	0.757931i
$99$	1.80368	+	2.11184i	0.181277	+	0.212248i
$100$	1.68602	−	0.904258i	0.168602	−	0.0904258i
$101$	0.226638	−	0.944016i	0.0225514	−	0.0939331i	−0.959959	−	0.280139i	$-0.909619\pi$
$101$	0.226638	−	0.944016i	0.0225514	−	0.0939331i	0.982511	+	0.186206i	$0.0596193\pi$
$102$	13.6964	−	1.22307i	1.35615	−	0.121102i
$103$	6.47555	−	1.02563i	0.638055	−	0.101058i	0.170978	−	0.985275i	$-0.445307\pi$
$103$	6.47555	−	1.02563i	0.638055	−	0.101058i	0.467077	+	0.884217i	$0.345307\pi$
$104$	0.887908	−	1.88765i	0.0870666	−	0.185099i
$105$	0.857651	+	1.18045i	0.0836981	+	0.115201i
$106$	8.76679	−	6.51148i	0.851506	−	0.632451i
$107$	−9.30718	−	6.76206i	−0.899759	−	0.653713i	0.0386448	−	0.999253i	$-0.487696\pi$
$107$	−9.30718	−	6.76206i	−0.899759	−	0.653713i	−0.938404	+	0.345540i	$0.887696\pi$
$108$	−0.418860	+	7.27720i	−0.0403048	+	0.700249i
$109$	13.8838	−	5.75086i	1.32983	−	0.550833i	0.399222	−	0.916854i	$-0.369280\pi$
$109$	13.8838	−	5.75086i	1.32983	−	0.550833i	0.930606	+	0.366021i	$0.119280\pi$
$110$	7.70059	−	1.30286i	0.734223	−	0.124223i
$111$	15.3835	−	18.0118i	1.46014	−	1.70960i
$112$	0.399489	−	1.09234i	0.0377482	−	0.103217i
$113$	−3.69950	+	1.20204i	−0.348020	+	0.113079i	−0.477811	−	0.878463i	$-0.658569\pi$
$113$	−3.69950	+	1.20204i	−0.348020	+	0.113079i	0.129791	+	0.991541i	$0.458569\pi$
$114$	6.86729	+	7.87132i	0.643181	+	0.737217i
$115$	−4.03895	+	7.92688i	−0.376634	+	0.739186i
$116$	−4.10564	−	9.35033i	−0.381199	−	0.868156i
$117$	0.472978	−	0.771830i	0.0437268	−	0.0713557i
$118$	3.23209	+	7.57647i	0.297538	+	0.697471i
$119$	1.30781	+	0.424933i	0.119887	+	0.0389536i
$120$	−11.7401	−	7.97596i	−1.07172	−	0.728103i
$121$	−5.80753	−	0.919822i	−0.527957	−	0.0836202i
$122$	14.0418	+	0.956560i	1.27129	+	0.0866029i
$123$	8.81966	+	9.77425i	0.795242	+	0.881314i
$124$	1.85102	−	13.5229i	0.166226	−	1.21440i
$125$	−1.54375	+	9.74688i	−0.138078	+	0.871787i
$126$	0.224393	−	0.452093i	0.0199905	−	0.0402757i
$127$	0.858054	−	2.64082i	0.0761400	−	0.234335i	−0.905742	−	0.423830i	$-0.860685\pi$
$127$	0.858054	−	2.64082i	0.0761400	−	0.234335i	0.981882	+	0.189496i	$0.0606853\pi$
$128$	−0.0552221	+	11.3136i	−0.00488099	+	0.999988i
$129$	−17.1661	−	10.5194i	−1.51139	−	0.926179i
$130$	−1.17949	−	2.25588i	−0.103448	−	0.197853i
$131$	−10.2609	−	5.22817i	−0.896496	−	0.456787i	−0.0558912	−	0.998437i	$-0.517800\pi$
$131$	−10.2609	−	5.22817i	−0.896496	−	0.456787i	−0.840604	+	0.541650i	$0.817800\pi$
$132$	−5.62638	−	7.41092i	−0.489714	−	0.645038i
$133$	0.322802	+	0.993482i	0.0279905	+	0.0861458i
$134$	−1.41772	+	9.60416i	−0.122472	+	0.829673i
$135$	6.76390	+	5.77692i	0.582144	+	0.497198i
$136$	−13.3693	+	0.422184i	−1.14641	+	0.0362020i
$137$	−1.00341	−	2.42244i	−0.0857269	−	0.206963i	0.875202	−	0.483757i	$-0.160728\pi$
$137$	−1.00341	−	2.42244i	−0.0857269	−	0.206963i	−0.960929	+	0.276794i	$0.910728\pi$
$138$	10.5986	−	0.111530i	0.902213	−	0.00949405i
$139$	2.57427	−	3.54318i	0.218347	−	0.300528i	−0.685766	−	0.727822i	$-0.740533\pi$
$139$	2.57427	−	3.54318i	0.218347	−	0.300528i	0.904113	+	0.427293i	$0.140533\pi$
$140$	−0.766906	−	1.19431i	−0.0648154	−	0.100938i
$141$	0.613601	−	0.445807i	0.0516745	−	0.0375438i
$142$	3.06474	−	9.78135i	0.257188	−	0.820833i
$143$	−0.261066	−	1.64830i	−0.0218314	−	0.137838i
$144$	−0.563294	+	4.87707i	−0.0469412	+	0.406423i
$145$	−12.1175	−	2.90914i	−1.00630	−	0.241591i
$146$	−10.1134	+	6.34487i	−0.836994	+	0.525105i
$147$	−10.8119	+	9.23422i	−0.891749	+	0.761626i
$148$	−15.9461	+	16.6318i	−1.31076	+	1.36713i
$149$	14.8071	−	1.16535i	1.21305	−	0.0954690i	0.544256	−	0.838919i	$-0.316812\pi$
$149$	14.8071	−	1.16535i	1.21305	−	0.0954690i	0.668792	+	0.743450i	$0.266812\pi$
$150$	−2.63619	+	0.887325i	−0.215244	+	0.0724498i
$151$	2.52688	+	10.5252i	0.205635	+	0.856530i	0.975796	+	0.218681i	$0.0701755\pi$
$151$	2.52688	+	10.5252i	0.205635	+	0.856530i	−0.770162	+	0.637849i	$0.779824\pi$
$152$	−6.22905	−	8.02791i	−0.505242	−	0.651150i
$153$	−5.78652	−	0.455409i	−0.467812	−	0.0368176i
$154$	−0.226726	−	0.902442i	−0.0182701	−	0.0727208i
$155$	−11.7776	−	11.7776i	−0.945999	−	0.945999i
$156$	−1.73061	+	2.49056i	−0.138560	+	0.199404i
$157$	11.2634	+	18.3803i	0.898920	+	1.46690i	0.884251	+	0.467012i	$0.154669\pi$
$157$	11.2634	+	18.3803i	0.898920	+	1.46690i	0.0146689	+	0.999892i	$0.495331\pi$
$158$	−11.0032	+	15.4847i	−0.875369	+	1.23190i
$159$	−14.1463	+	7.20787i	−1.12187	+	0.571622i
$160$	10.9553	+	8.40191i	0.866095	+	0.664229i
$161$	0.979252	+	0.405619i	0.0771759	+	0.0319673i
$162$	3.52764	−	15.4061i	0.277158	−	1.21042i
$163$	0.656933			0.0514550			0.0257275	−	0.999669i	$-0.491810\pi$
$163$	0.656933			0.0514550			0.0257275	+	0.999669i	$0.491810\pi$
$164$	−8.01868	−	9.98503i	−0.626154	−	0.779700i
$165$	−11.3546			−0.883957
$166$	5.65612	−	24.7017i	0.439000	−	1.91722i
$167$	−4.25114	−	1.76088i	−0.328963	−	0.136261i	0.212088	−	0.977250i	$-0.431974\pi$
$167$	−4.25114	−	1.76088i	−0.328963	−	0.136261i	−0.541051	+	0.840990i	$0.681974\pi$
$168$	−0.837585	+	1.46896i	−0.0646211	+	0.113333i
$169$	11.0984	−	5.65493i	0.853725	−	0.434995i
$170$	−9.45484	+	13.3057i	−0.725153	+	1.02050i
$171$	−2.30387	−	3.75958i	−0.176182	−	0.287502i
$172$	16.0824	+	11.1752i	1.22628	+	0.852099i
$173$	0.259172	+	0.259172i	0.0197045	+	0.0197045i	0.716890	−	0.697186i	$-0.245565\pi$
$173$	0.259172	+	0.259172i	0.0197045	+	0.0197045i	−0.697186	+	0.716890i	$0.745565\pi$
$174$	3.61762	+	14.3992i	0.274251	+	1.09160i
$175$	−0.277299	−	0.0218239i	−0.0209618	−	0.00164973i
$176$	5.04970	+	7.51145i	0.380635	+	0.566197i
$177$	−2.79562	−	11.6446i	−0.210132	−	0.875262i
$178$	−4.71090	+	1.58566i	−0.353097	+	0.118850i
$179$	−22.0289	+	1.73371i	−1.64651	+	0.129583i	−0.867505	−	0.497429i	$-0.834278\pi$
$179$	−22.0289	+	1.73371i	−1.64651	+	0.129583i	−0.779009	+	0.627012i	$0.784278\pi$
$180$	4.32456	+	4.14626i	0.322333	+	0.309044i
$181$	11.2209	−	9.58354i	0.834041	−	0.712339i	−0.126050	−	0.992024i	$-0.540230\pi$
$181$	11.2209	−	9.58354i	0.834041	−	0.712339i	0.960092	+	0.279685i	$0.0902301\pi$
$182$	−0.256911	+	0.161178i	−0.0190435	+	0.0119473i
$183$	−19.8967	−	4.77677i	−1.47081	−	0.353109i
$184$	−10.2988	−	0.484110i	−0.759240	−	0.0356891i
$185$	4.39852	+	27.7712i	0.323386	+	2.04178i
$186$	−5.93311	+	18.9360i	−0.435037	+	1.38845i
$187$	−8.65720	+	6.28982i	−0.633077	+	0.459957i
$188$	−0.620804	+	0.398638i	−0.0452768	+	0.0290737i
$189$	0.622914	−	0.857368i	0.0453103	−	0.0623643i
$190$	−12.3990	+	0.130476i	−0.899519	+	0.00946570i
$191$	−4.50224	−	10.8694i	−0.325771	−	0.786480i	−0.998897	−	0.0469524i	$-0.985049\pi$
$191$	−4.50224	−	10.8694i	−0.325771	−	0.786480i	0.673127	−	0.739527i	$-0.264951\pi$
$192$	2.82304	−	16.2044i	0.203735	−	1.16945i
$193$	2.04104	+	1.74321i	0.146917	+	0.125479i	0.719869	−	0.694110i	$-0.244202\pi$
$193$	2.04104	+	1.74321i	0.146917	+	0.125479i	−0.572952	+	0.819589i	$0.694202\pi$
$194$	2.08634	−	14.1336i	0.149791	−	1.01474i
$195$	1.14366	+	3.51982i	0.0818990	+	0.252059i
$196$	11.0159	−	8.36327i	0.786848	−	0.597376i
$197$	−10.4301	−	5.31442i	−0.743116	−	0.378636i	0.0410751	−	0.999156i	$-0.486922\pi$
$197$	−10.4301	−	5.31442i	−0.743116	−	0.378636i	−0.784191	+	0.620520i	$0.786922\pi$
$198$	1.81983	+	3.48059i	0.129330	+	0.247354i
$199$	7.60047	+	4.65758i	0.538783	+	0.330167i	0.765126	−	0.643881i	$-0.222677\pi$
$199$	7.60047	+	4.65758i	0.538783	+	0.330167i	−0.226342	+	0.974048i	$0.572677\pi$
$200$	2.60968	−	0.714354i	0.184532	−	0.0505124i
$201$	4.36157	−	13.4235i	0.307642	−	0.946823i
$202$	0.610411	−	1.22982i	0.0429484	−	0.0865300i
$203$	−0.232258	+	1.46642i	−0.0163013	+	0.102922i
$204$	19.2671	+	2.63727i	1.34897	+	0.184646i
$205$	−15.6218	+	0.425740i	−1.09107	+	0.0297350i
$206$	9.25053	+	0.630166i	0.644515	+	0.0439058i
$207$	−4.41895	−	0.699893i	−0.307138	−	0.0486459i
$208$	1.81986	−	2.32192i	0.126184	−	0.160996i
$209$	−7.73110	−	2.51199i	−0.534771	−	0.173758i
$210$	0.809688	+	1.89802i	0.0558738	+	0.130976i
$211$	8.20287	−	13.3859i	0.564709	−	0.921521i	−0.435068	−	0.900397i	$-0.643276\pi$
$211$	8.20287	−	13.3859i	0.564709	−	0.921521i	0.999777	−	0.0211233i	$-0.00672424\pi$
$212$	14.1407	−	6.20905i	0.971188	−	0.426439i
$213$	−6.76552	+	13.2781i	−0.463566	+	0.909799i
$214$	−10.6958	−	12.2596i	−0.731151	−	0.838049i
$215$	22.7287	−	7.38501i	1.55009	−	0.503654i
$216$	−2.87449	+	9.89967i	−0.195584	+	0.673587i
$217$	−1.28876	+	1.50895i	−0.0874870	+	0.102434i
$218$	20.9546	−	3.54530i	1.41923	−	0.240118i
$219$	16.0362	−	6.64243i	1.08363	−	0.448854i
$220$	11.0268	+	0.634679i	0.743427	+	0.0427901i
$221$	2.82175	+	2.05012i	0.189811	+	0.137906i
$222$	26.8922	−	19.9740i	1.80489	−	1.34057i
$223$	1.92414	+	2.64835i	0.128850	+	0.177347i	0.868568	−	0.495570i	$-0.165041\pi$
$223$	1.92414	+	2.64835i	0.128850	+	0.177347i	−0.739718	+	0.672917i	$0.765041\pi$
$224$	0.895511	−	1.37973i	0.0598339	−	0.0921873i
$225$	1.15965	−	0.183671i	0.0773103	−	0.0122448i
$226$	−5.47933	+	0.489297i	−0.364479	+	0.0325476i
$227$	0.655915	−	2.73208i	0.0435346	−	0.181335i	−0.946366	−	0.323096i	$-0.895276\pi$
$227$	0.655915	−	2.73208i	0.0435346	−	0.181335i	0.989901	+	0.141761i	$0.0452764\pi$
$228$	6.98221	+	13.0186i	0.462408	+	0.862177i
$229$	3.43774	+	4.02508i	0.227172	+	0.265985i	0.862272	−	0.506446i	$-0.169041\pi$
$229$	3.43774	+	4.02508i	0.227172	+	0.265985i	−0.635100	+	0.772430i	$0.719041\pi$
$230$	−8.06998	+	9.65259i	−0.532119	+	0.636473i
$231$	0.106139	+	1.34862i	0.00698342	+	0.0887327i
$232$	−2.70831	−	14.1857i	−0.177809	−	0.931338i
$233$	20.3212	−	4.87869i	1.33129	−	0.319613i	0.495471	−	0.868625i	$-0.334996\pi$
$233$	20.3212	−	4.87869i	1.33129	−	0.319613i	0.835815	+	0.549011i	$0.184996\pi$
$234$	0.895649	−	0.914699i	0.0585504	−	0.0597957i
$235$	−0.0706376	+	0.897536i	−0.00460789	+	0.0585488i
$236$	2.06402	+	11.4647i	0.134356	+	0.746286i
$237$	19.5284	−	19.5284i	1.26851	−	1.26851i
$238$	1.66873	+	0.998601i	0.108168	+	0.0647297i
$239$	−7.59076	+	4.65162i	−0.491005	+	0.300888i	−0.745874	−	0.666087i	$-0.767968\pi$
$239$	−7.59076	+	4.65162i	−0.491005	+	0.300888i	0.254869	+	0.966976i	$0.417968\pi$
$240$	−13.6665	−	14.7010i	−0.882171	−	0.948943i
$241$	1.83618	+	3.60371i	0.118279	+	0.232135i	0.942554	−	0.334055i	$-0.108417\pi$
$241$	1.83618	+	3.60371i	0.118279	+	0.232135i	−0.824275	+	0.566190i	$0.808417\pi$
$242$	−7.71555	−	3.10118i	−0.495974	−	0.199351i
$243$	−4.60903	+	11.1272i	−0.295669	+	0.713809i
$244$	19.0552	+	5.75100i	1.21989	+	0.368170i
$245$		−	16.8780i		−	1.07829i
$246$	9.07295	+	16.2581i	0.578470	+	1.03658i
$247$			2.64957i			0.168588i
$248$	6.82026	−	18.0576i	0.433087	−	1.14666i
$249$	−14.0988	+	34.0376i	−0.893478	+	2.15705i
$250$	−5.20476	+	12.9491i	−0.329178	+	0.818975i
$251$	5.59483	+	10.9805i	0.353143	+	0.693081i	0.997426	−	0.0717056i	$-0.0228442\pi$
$251$	5.59483	+	10.9805i	0.353143	+	0.693081i	−0.644283	+	0.764787i	$0.722844\pi$
$252$	0.452038	−	0.552397i	0.0284757	−	0.0347977i
$253$	−7.03277	+	4.30969i	−0.442146	+	0.270948i
$254$	2.01644	−	3.36962i	0.126523	−	0.211429i
$255$	16.7803	−	16.7803i	1.05083	−	1.05083i
$256$	−3.64729	+	15.5787i	−0.227956	+	0.973671i
$257$	−1.15727	+	14.7046i	−0.0721888	+	0.917245i	0.849066	+	0.528286i	$0.177165\pi$
$257$	−1.15727	+	14.7046i	−0.0721888	+	0.917245i	−0.921255	+	0.388959i	$0.872835\pi$
$258$	−20.3436	−	19.9199i	−1.26653	−	1.24016i
$259$	3.25735	−	0.782019i	0.202402	−	0.0485923i
$260$	−0.913894	−	3.48212i	−0.0566773	−	0.215952i
$261$	−0.491701	−	6.24765i	−0.0304355	−	0.386720i
$262$	−12.4947	−	10.4461i	−0.771924	−	0.645362i
$263$	10.7317	+	12.5652i	0.661745	+	0.774804i	0.985194	−	0.171442i	$-0.0548425\pi$
$263$	10.7317	+	12.5652i	0.661745	+	0.774804i	−0.323449	+	0.946246i	$0.604842\pi$
$264$	−5.41689	−	11.9922i	−0.333386	−	0.738070i
$265$	4.39956	−	18.3255i	0.270263	−	1.12573i
$266$	0.131398	+	1.47144i	0.00805654	+	0.0902201i
$267$	7.13756	−	1.13048i	0.436811	−	0.0691841i
$268$	−4.98597	+	12.7922i	−0.304566	+	0.781407i
$269$	−2.19602	−	3.02256i	−0.133894	−	0.184289i	0.736806	−	0.676105i	$-0.236333\pi$
$269$	−2.19602	−	3.02256i	−0.133894	−	0.184289i	−0.870699	+	0.491816i	$0.836333\pi$
$270$	7.50078	+	10.0987i	0.456483	+	0.614590i
$271$	17.5084	+	12.7206i	1.06356	+	0.772721i	0.974744	−	0.223327i	$-0.0716918\pi$
$271$	17.5084	+	12.7206i	1.06356	+	0.772721i	0.0888156	+	0.996048i	$0.471692\pi$
$272$	−18.5634	−	3.63808i	−1.12557	−	0.220591i
$273$	0.407368	−	0.168737i	0.0246550	−	0.0102124i
$274$	−0.618582	−	3.65615i	−0.0373699	−	0.220876i
$275$	1.40577	−	1.64595i	0.0847712	−	0.0992543i
$276$	14.6458	+	3.19174i	0.881571	+	0.192120i
$277$	−11.8965	+	3.86542i	−0.714794	+	0.232251i	−0.643764	−	0.765224i	$-0.722628\pi$
$277$	−11.8965	+	3.86542i	−0.714794	+	0.232251i	−0.0710291	+	0.997474i	$0.522628\pi$
$278$	4.66714	−	4.07182i	0.279916	−	0.244212i
$279$	3.80273	−	7.46328i	0.227664	−	0.446815i
$280$	−0.680219	−	1.88848i	−0.0406508	−	0.112858i
$281$	−2.68519	+	4.38183i	−0.160185	+	0.261398i	−0.922656	−	0.385624i	$-0.873986\pi$
$281$	−2.68519	+	4.38183i	−0.160185	+	0.261398i	0.762471	+	0.647023i	$0.223986\pi$
$282$	0.986592	−	0.420876i	0.0587507	−	0.0250628i
$283$	−25.8064	−	8.38500i	−1.53403	−	0.498436i	−0.584308	−	0.811532i	$-0.698634\pi$
$283$	−25.8064	−	8.38500i	−1.53403	−	0.498436i	−0.949722	+	0.313096i	$0.898634\pi$
$284$	7.31238	−	12.5166i	0.433910	−	0.742721i
$285$	17.8054	+	2.82010i	1.05470	+	0.167048i
$286$	0.160404	−	2.35465i	0.00948490	−	0.139234i
$287$	0.196593	+	1.85146i	0.0116045	+	0.109288i
$288$	−2.31599	+	6.54542i	−0.136471	+	0.385693i
$289$	0.839220	−	5.29863i	0.0493659	−	0.311684i
$290$	−15.7861	−	7.83528i	−0.926990	−	0.460103i
$291$	−6.41856	+	19.7543i	−0.376262	+	1.15802i
$292$	−15.9445	+	5.55429i	−0.933083	+	0.325040i
$293$	−12.4889	−	7.65319i	−0.729608	−	0.447104i	0.107456	−	0.994210i	$-0.465730\pi$
$293$	−12.4889	−	7.65319i	−0.729608	−	0.447104i	−0.837064	+	0.547105i	$0.815730\pi$
$294$	−17.8194	+	9.31690i	−1.03925	+	0.543373i
$295$	12.6660	+	6.45363i	0.737441	+	0.375745i
$296$	−27.2322	+	17.8942i	−1.58284	+	1.04008i
$297$	2.54843	+	7.84327i	0.147875	+	0.455113i
$298$	20.7800	+	3.06745i	1.20375	+	0.177693i
$299$	2.04431	+	1.74601i	0.118225	+	0.100974i
$300$	−3.91417	+	0.391087i	−0.225985	+	0.0225794i
$301$	−1.08960	−	2.63052i	−0.0628034	−	0.151621i
$302$	0.161077	+	15.3070i	0.00926893	+	0.880820i
$303$	−1.17328	+	1.61488i	−0.0674032	+	0.0927726i
$304$	−6.05293	−	13.0330i	−0.347159	−	0.747493i
$305$	19.6504	−	14.2768i	1.12518	−	0.817489i
$306$	−7.83318	−	2.45433i	−0.447793	−	0.140305i
$307$	−4.31516	−	27.2448i	−0.246279	−	1.55494i	−0.732291	−	0.680992i	$-0.761549\pi$
$307$	−4.31516	−	27.2448i	−0.246279	−	1.55494i	0.486012	−	0.873952i	$-0.338451\pi$
$308$	−0.0276917	−	1.31562i	−0.00157788	−	0.0749642i
$309$	−13.1076	−	3.14686i	−0.745666	−	0.179019i
$310$	−12.5182	−	19.9535i	−0.710986	−	1.13328i
$311$	7.24224	−	6.18546i	0.410670	−	0.350745i	−0.419987	−	0.907530i	$-0.637965\pi$
$311$	7.24224	−	6.18546i	0.410670	−	0.350745i	0.830657	+	0.556785i	$0.187965\pi$
$312$	−3.17186	+	2.88706i	−0.179571	+	0.163447i
$313$	8.64147	−	0.680098i	0.488445	−	0.0384414i	0.168154	−	0.985761i	$-0.446219\pi$
$313$	8.64147	−	0.680098i	0.488445	−	0.0384414i	0.320291	+	0.947319i	$0.396219\pi$
$314$	9.72527	+	28.8932i	0.548829	+	1.63054i
$315$	−0.203338	−	0.846964i	−0.0114568	−	0.0477210i
$316$	−20.0561	+	17.8730i	−1.12825	+	1.00544i
$317$	26.2869	+	2.06882i	1.47642	+	0.116197i	0.790939	−	0.611895i	$-0.209593\pi$
$317$	26.2869	+	2.06882i	1.47642	+	0.116197i	0.685480	+	0.728092i	$0.259593\pi$
$318$	−21.7763	+	5.47101i	−1.22116	+	0.306799i
$319$	−8.16966	−	8.16966i	−0.457413	−	0.457413i
$320$	12.4502	+	15.0404i	0.695989	+	0.840785i
$321$	12.3589	+	20.1679i	0.689809	+	1.12567i
$322$	1.22190	+	0.868266i	0.0680938	+	0.0483865i
$323$	15.1377	−	7.71303i	0.842282	−	0.429164i
$324$	9.72596	−	20.1243i	0.540331	−	1.11802i
$325$	−0.651818	−	0.269992i	−0.0361564	−	0.0149765i
$326$	0.905606	+	0.207363i	0.0501569	+	0.0114848i
$327$	−30.8979			−1.70866
$328$	−7.90223	−	16.2958i	−0.436328	−	0.899788i
$329$	0.107263			0.00591360
$330$	−15.6528	−	3.58413i	−0.861657	−	0.197300i
$331$	11.4203	+	4.73045i	0.627717	+	0.260009i	0.673783	−	0.738929i	$-0.264668\pi$
$331$	11.4203	+	4.73045i	0.627717	+	0.260009i	−0.0460657	+	0.998938i	$0.514668\pi$
$332$	15.5943	−	32.2668i	0.855851	−	1.77087i
$333$	−12.5989	+	6.41947i	−0.690416	+	0.351785i
$334$	−5.30452	−	3.76932i	−0.290250	−	0.206248i
$335$	8.75407	+	14.2853i	0.478286	+	0.780491i
$336$	−1.61832	+	1.76063i	−0.0882868	+	0.0960503i
$337$	−21.7249	−	21.7249i	−1.18343	−	1.18343i	−0.978850	−	0.204581i	$-0.934417\pi$
$337$	−21.7249	−	21.7249i	−1.18343	−	1.18343i	−0.204581	−	0.978850i	$-0.565583\pi$
$338$	17.0846	−	4.29227i	0.929279	−	0.233469i
$339$	7.97318	+	0.627503i	0.433044	+	0.0340813i
$340$	−17.2338	+	15.3579i	−0.934635	+	0.832900i
$341$	−3.60492	−	15.0156i	−0.195217	−	0.813139i
$342$	−1.98925	−	5.90995i	−0.107566	−	0.319573i
$343$	−4.03379	+	0.317466i	−0.217804	+	0.0171416i
$344$	18.6428	+	20.4819i	1.00515	+	1.10431i
$345$	13.9092	−	11.8796i	0.748847	−	0.639575i
$346$	0.275470	+	0.439087i	0.0148094	+	0.0236055i
$347$	28.8505	+	6.92638i	1.54877	+	0.371828i	0.915570	−	0.402158i	$-0.131740\pi$
$347$	28.8505	+	6.92638i	1.54877	+	0.371828i	0.633203	+	0.773986i	$0.281740\pi$
$348$	0.441846	+	20.9918i	0.0236854	+	1.12528i
$349$	1.81376	+	11.4517i	0.0970885	+	0.612993i	0.987474	+	0.157785i	$0.0504352\pi$
$349$	1.81376	+	11.4517i	0.0970885	+	0.612993i	−0.890385	+	0.455208i	$0.849565\pi$
$350$	−0.375378	−	0.117615i	−0.0200648	−	0.00628681i
$351$	2.17465	−	1.57997i	0.116074	−	0.0843328i
$352$	4.59018	+	11.9488i	0.244657	+	0.636871i
$353$	−11.7349	+	16.1517i	−0.624584	+	0.859666i	−0.997677	−	0.0681279i	$-0.978297\pi$
$353$	−11.7349	+	16.1517i	−0.624584	+	0.859666i	0.373092	+	0.927794i	$0.378297\pi$
$354$	−0.178208	−	16.9350i	−0.00947164	−	0.900083i
$355$	−6.76952	−	16.3431i	−0.359289	−	0.867400i
$356$	−6.99467	+	0.698878i	−0.370717	+	0.0370404i
$357$	−2.14990	−	1.83619i	−0.113785	−	0.0971816i
$358$	−30.9148	−	4.56350i	−1.63390	−	0.241189i
$359$	−1.95037	−	6.00262i	−0.102936	−	0.316806i	0.886304	−	0.463104i	$-0.153264\pi$
$359$	−1.95037	−	6.00262i	−0.102936	−	0.316806i	−0.989241	+	0.146298i	$0.953264\pi$
$360$	4.65278	+	7.08083i	0.245223	+	0.373192i
$361$	−5.42975	−	2.76659i	−0.285776	−	0.145610i
$362$	18.4935	−	9.66935i	0.971995	−	0.508209i
$363$	10.3080	+	6.31672i	0.541027	+	0.331542i
$364$	−0.405038	+	0.141095i	−0.0212298	+	0.00739540i
$365$	−6.36698	+	19.5956i	−0.333263	+	1.02568i
$366$	−25.9205	−	12.8654i	−1.35489	−	0.672486i
$367$	−3.74901	+	23.6703i	−0.195697	+	1.23558i	0.672777	+	0.739845i	$0.265101\pi$
$367$	−3.74901	+	23.6703i	−0.195697	+	1.23558i	−0.868474	+	0.495735i	$0.834899\pi$
$368$	−14.0445	−	3.91822i	−0.732120	−	0.204252i
$369$	−2.63130	−	7.40544i	−0.136980	−	0.385512i
$370$	−2.70255	+	39.6720i	−0.140499	+	2.06245i
$371$	−2.21770	−	0.351249i	−0.115137	−	0.0182359i
$372$	−14.1562	+	24.2311i	−0.733965	+	1.25632i
$373$	−27.8045	−	9.03424i	−1.43966	−	0.467775i	−0.517872	−	0.855458i	$-0.673276\pi$
$373$	−27.8045	−	9.03424i	−1.43966	−	0.467775i	−0.921793	+	0.387683i	$0.873276\pi$
$374$	−13.9197	+	5.93808i	−0.719769	+	0.307051i
$375$	10.6015	−	17.3000i	0.547458	−	0.893370i
$376$	−0.981633	+	0.353578i	−0.0506238	+	0.0182344i
$377$	−1.70965	+	3.35537i	−0.0880513	+	0.172810i
$378$	1.12934	−	0.985288i	0.0580870	−	0.0506777i
$379$	4.53376	−	1.47311i	0.232883	−	0.0756684i	−0.190250	−	0.981736i	$-0.560930\pi$
$379$	4.53376	−	1.47311i	0.232883	−	0.0756684i	0.423134	+	0.906067i	$0.360930\pi$
$380$	−17.1337	−	3.73392i	−0.878939	−	0.191546i
$381$	−3.70776	+	4.34123i	−0.189955	+	0.222408i
$382$	−2.77555	−	16.4050i	−0.142009	−	0.839351i
$383$	−16.0324	+	6.64084i	−0.819217	+	0.339331i	−0.752625	−	0.658449i	$-0.771213\pi$
$383$	−16.0324	+	6.64084i	−0.819217	+	0.339331i	−0.0665922	+	0.997780i	$0.521213\pi$
$384$	9.00664	−	21.4472i	0.459618	−	1.09448i
$385$	−1.29913	−	0.943873i	−0.0662098	−	0.0481042i
$386$	2.26339	+	3.04734i	0.115204	+	0.155106i
$387$	7.06423	+	9.72309i	0.359095	+	0.494252i
$388$	7.33743	−	18.8252i	0.372501	−	0.955703i
$389$	9.32220	−	1.47649i	0.472654	−	0.0748611i	0.0844367	−	0.996429i	$-0.473091\pi$
$389$	9.32220	−	1.47649i	0.472654	−	0.0748611i	0.388217	+	0.921568i	$0.373091\pi$
$390$	0.465532	+	5.21320i	0.0235731	+	0.263980i
$391$	4.02429	−	16.7624i	0.203517	−	0.847709i
$392$	17.8257	−	8.05187i	0.900333	−	0.406681i
$393$	15.3774	+	18.0046i	0.775687	+	0.908213i
$394$	−12.7008	−	10.6184i	−0.639857	−	0.534948i
$395$	2.57211	+	32.6817i	0.129417	+	1.64439i
$396$	1.41004	+	5.37255i	0.0708574	+	0.269981i
$397$	−12.4991	+	3.00077i	−0.627311	+	0.150604i	−0.534622	−	0.845091i	$-0.679546\pi$
$397$	−12.4991	+	3.00077i	−0.627311	+	0.150604i	−0.0926888	+	0.995695i	$0.529546\pi$
$398$	9.00735	+	8.81975i	0.451498	+	0.442094i
$399$	0.168513	−	2.14116i	0.00843618	−	0.107192i
$400$	3.82302	−	0.161009i	0.191151	−	0.00805045i
$401$	−9.63914	+	9.63914i	−0.481356	+	0.481356i	−0.905564	−	0.424209i	$-0.860552\pi$
$401$	−9.63914	+	9.63914i	−0.481356	+	0.481356i	0.424209	+	0.905564i	$0.360552\pi$
$402$	10.2498	−	17.1281i	0.511212	−	0.854272i
$403$	−4.29158	+	2.62988i	−0.213779	+	0.131004i
$404$	1.22967	−	1.50268i	0.0611784	−	0.0747609i
$405$	−12.3828	−	24.3027i	−0.615308	−	1.20761i
$406$	−0.783055	+	1.94820i	−0.0388624	+	0.0966874i
$407$	−9.97593	+	24.0840i	−0.494488	+	1.19380i
$408$	25.7279	+	9.71729i	1.27372	+	0.481078i
$409$		−	12.7998i		−	0.632908i	−0.948608	−	0.316454i	$-0.897508\pi$
$409$		−	12.7998i		−	0.632908i	0.948608	−	0.316454i	$-0.102492\pi$
$410$	−21.6696	−	4.34416i	−1.07018	−	0.214543i
$411$			5.39104i			0.265921i
$412$	12.5533	+	3.78867i	0.618455	+	0.186654i
$413$	0.648119	−	1.56470i	0.0318918	−	0.0769937i
$414$	−5.87076	−	2.35968i	−0.288532	−	0.115972i
$415$	−19.8543	−	38.9663i	−0.974609	−	1.91278i
$416$	3.24166	−	2.62641i	0.158935	−	0.128770i
$417$	−7.67779	+	4.70496i	−0.375983	+	0.230403i
$418$	−9.86469	−	5.90321i	−0.482498	−	0.288736i
$419$	5.93402	−	5.93402i	0.289896	−	0.289896i	−0.547143	−	0.837039i	$-0.684285\pi$
$419$	5.93402	−	5.93402i	0.289896	−	0.289896i	0.837039	+	0.547143i	$0.184285\pi$
$420$	0.517068	+	2.87207i	0.0252303	+	0.140143i
$421$	−0.140476	+	1.78492i	−0.00684640	+	0.0869917i	−0.999391	−	0.0348885i	$-0.988892\pi$
$421$	−0.140476	+	1.78492i	−0.00684640	+	0.0869917i	0.992545	+	0.121880i	$0.0388924\pi$
$422$	15.5332	−	15.8636i	0.756147	−	0.772230i
$423$	−0.440252	+	0.105695i	−0.0214058	+	0.00513908i
$424$	21.4534	−	4.09584i	1.04187	−	0.198911i
$425$	0.354941	+	4.50996i	0.0172172	+	0.218765i
$426$	−13.5178	+	16.1688i	−0.654939	+	0.783379i
$427$	−1.87938	−	2.20047i	−0.0909497	−	0.106488i
$428$	−10.8748	−	20.2765i	−0.525653	−	0.980100i
$429$	−0.801010	+	3.33645i	−0.0386731	+	0.161085i
$430$	33.6635	−	3.00611i	1.62340	−	0.144967i
$431$	9.64926	−	1.52829i	0.464788	−	0.0736152i	0.0803516	−	0.996767i	$-0.474396\pi$
$431$	9.64926	−	1.52829i	0.464788	−	0.0736152i	0.384437	+	0.923151i	$0.374396\pi$
$432$	−7.08745	+	12.7397i	−0.340995	+	0.612940i
$433$	−3.12812	−	4.30549i	−0.150328	−	0.206909i	0.727211	−	0.686414i	$-0.240816\pi$
$433$	−3.12812	−	4.30549i	−0.150328	−	0.206909i	−0.877539	+	0.479505i	$0.840816\pi$
$434$	−2.25291	+	1.67334i	−0.108143	+	0.0803228i
$435$	20.7287	+	15.0603i	0.993867	+	0.722087i
$436$	30.0058	+	1.72707i	1.43702	+	0.0827117i
$437$	12.0986	−	5.01139i	0.578753	−	0.239727i
$438$	24.2032	−	4.09494i	1.15648	−	0.195664i
$439$	−18.4150	+	21.5613i	−0.878902	+	1.02906i	0.120437	+	0.992721i	$0.461570\pi$
$439$	−18.4150	+	21.5613i	−0.878902	+	1.02906i	−0.999339	+	0.0363414i	$0.988430\pi$
$440$	15.0005	+	4.35558i	0.715121	+	0.207644i
$441$	8.07242	−	2.62289i	0.384401	−	0.124899i
$442$	3.24275	+	3.71686i	0.154242	+	0.176793i
$443$	10.2807	−	20.1771i	0.488452	−	0.958641i	−0.506870	−	0.862023i	$-0.669197\pi$
$443$	10.2807	−	20.1771i	0.488452	−	0.958641i	0.995322	−	0.0966180i	$-0.0308025\pi$
$444$	43.3767	−	19.0463i	2.05857	−	0.903897i
$445$	−4.48207	+	7.31408i	−0.212471	+	0.346721i
$446$	1.81654	+	4.25821i	0.0860155	+	0.201632i
$447$	−29.0438	−	9.43691i	−1.37373	−	0.446350i
$448$	1.67001	−	1.61934i	0.0789007	−	0.0765066i
$449$	0.871440	+	0.138023i	0.0411258	+	0.00651369i	0.176963	−	0.984217i	$-0.443373\pi$
$449$	0.871440	+	0.138023i	0.0411258	+	0.00651369i	−0.135838	+	0.990731i	$0.543373\pi$
$450$	1.65660	+	0.112851i	0.0780930	+	0.00531987i
$451$	−12.5553	−	7.23098i	−0.591207	−	0.340494i
$452$	−7.70790	−	1.05505i	−0.362549	−	0.0496256i
$453$	3.48151	−	21.9814i	0.163575	−	1.03278i
$454$	1.76659	−	3.55923i	0.0829103	−	0.167043i
$455$	−0.161740	+	0.497785i	−0.00758249	+	0.0233365i
$456$	5.51586	+	20.1506i	0.258304	+	0.943636i
$457$	−1.25519	−	0.769179i	−0.0587151	−	0.0359807i	0.492831	−	0.870125i	$-0.335962\pi$
$457$	−1.25519	−	0.769179i	−0.0587151	−	0.0359807i	−0.551546	+	0.834144i	$0.685962\pi$
$458$	3.46852	+	6.63385i	0.162073	+	0.309979i
$459$	−15.3573	−	7.82493i	−0.716817	−	0.365237i
$460$	−14.1716	+	10.7591i	−0.660756	+	0.501647i
$461$	6.01179	+	18.5024i	0.279997	+	0.861742i	0.987854	+	0.155386i	$0.0496622\pi$
$461$	6.01179	+	18.5024i	0.279997	+	0.861742i	−0.707857	+	0.706356i	$0.750338\pi$
$462$	−0.279381	+	1.89263i	−0.0129980	+	0.0880529i
$463$	22.9826	+	19.6290i	1.06809	+	0.912236i	0.996365	−	0.0851886i	$-0.0271493\pi$
$463$	22.9826	+	19.6290i	1.06809	+	0.912236i	0.0717260	+	0.997424i	$0.477149\pi$
$464$	0.744271	−	20.4104i	0.0345519	−	0.947530i
$465$	13.1053	+	31.6390i	0.607743	+	1.46722i
$466$	29.5535	−	0.310993i	1.36904	−	0.0144065i
$467$	−0.0916952	+	0.126208i	−0.00424315	+	0.00584019i	−0.811133	−	0.584861i	$-0.801149\pi$
$467$	−0.0916952	+	0.126208i	−0.00424315	+	0.00584019i	0.806890	+	0.590702i	$0.201149\pi$
$468$	1.52341	−	0.978231i	0.0704197	−	0.0452188i
$469$	1.61488	−	1.17328i	0.0745682	−	0.0541770i
$470$	−0.380687	+	1.21499i	−0.0175598	+	0.0560432i
$471$	−6.93352	−	43.7765i	−0.319480	−	2.01711i
$472$	−0.773535	+	16.4560i	−0.0356048	+	0.757448i
$473$	21.5446	+	5.17241i	0.990624	+	0.237828i
$474$	33.0848	−	20.7564i	1.51964	−	0.953373i
$475$	−2.61321	+	2.23189i	−0.119902	+	0.102406i
$476$	1.98520	+	1.90335i	0.0909913	+	0.0872398i
$477$	9.44846	−	0.743610i	0.432615	−	0.0340476i
$478$	−11.9324	+	4.01638i	−0.545777	+	0.183705i
$479$	−3.81124	−	15.8750i	−0.174140	−	0.725346i	−0.989274	−	0.146073i	$-0.953337\pi$
$479$	−3.81124	−	15.8750i	−0.174140	−	0.725346i	0.815134	−	0.579273i	$-0.196663\pi$
$480$	−14.1994	−	24.5797i	−0.648112	−	1.12191i
$481$	8.47059	+	0.666650i	0.386226	+	0.0303966i
$482$	1.39372	+	5.54744i	0.0634822	+	0.252679i
$483$	−1.54099	−	1.54099i	−0.0701174	−	0.0701174i
$484$	−9.65727	−	6.71052i	−0.438967	−	0.305024i
$485$	−12.8826	−	21.0225i	−0.584969	−	0.954583i
$486$	−9.86605	+	13.8844i	−0.447533	+	0.629808i
$487$	−25.7199	+	13.1049i	−1.16548	+	0.593841i	−0.926171	−	0.377103i	$-0.876920\pi$
$487$	−25.7199	+	13.1049i	−1.16548	+	0.593841i	−0.239307	+	0.970944i	$0.576920\pi$
$488$	24.4530	+	13.9428i	1.10694	+	0.631162i
$489$	−1.24788	−	0.516888i	−0.0564310	−	0.0233745i
$490$	5.32758	−	23.2669i	0.240676	−	1.05109i
$491$	−37.0349			−1.67136			−0.835681	−	0.549215i	$-0.814927\pi$
$491$	−37.0349			−1.67136			−0.835681	+	0.549215i	$0.814927\pi$
$492$	7.37547	+	25.2763i	0.332512	+	1.13954i
$493$	24.1469			1.08752
$494$	−0.836347	+	3.65253i	−0.0376290	+	0.164335i
$495$	6.26224	+	2.59391i	0.281467	+	0.116587i
$496$	15.1019	−	22.7402i	0.678096	−	1.02107i
$497$	−1.87783	+	0.956804i	−0.0842323	+	0.0429185i
$498$	−30.1799	+	42.4717i	−1.35239	+	1.90320i
$499$	−5.26662	−	8.59434i	−0.235766	−	0.384736i	0.712773	−	0.701395i	$-0.247439\pi$
$499$	−5.26662	−	8.59434i	−0.235766	−	0.384736i	−0.948539	+	0.316659i	$0.897439\pi$
$500$	−11.2624	+	16.2080i	−0.503669	+	0.724842i
$501$	6.68975	+	6.68975i	0.298876	+	0.298876i
$502$	4.24665	+	16.9030i	0.189537	+	0.754418i
$503$	−37.4758	−	2.94941i	−1.67096	−	0.131508i	−0.792678	−	0.609641i	$-0.791314\pi$
$503$	−37.4758	−	2.94941i	−1.67096	−	0.131508i	−0.878287	+	0.478133i	$0.841314\pi$
$504$	0.797517	−	0.618812i	0.0355242	−	0.0275641i
$505$	−0.553137	−	2.30398i	−0.0246143	−	0.102526i
$506$	−11.0553	+	3.72114i	−0.491468	+	0.165425i
$507$	−25.5314	+	2.00937i	−1.13389	+	0.0892391i
$508$	3.84337	−	4.00864i	0.170522	−	0.177855i
$509$	−22.9070	+	19.5644i	−1.01534	+	0.867178i	−0.991179	−	0.132530i	$-0.957690\pi$
$509$	−22.9070	+	19.5644i	−1.01534	+	0.867178i	−0.0241562	+	0.999708i	$0.507690\pi$
$510$	28.4291	−	17.8355i	1.25886	−	0.789771i
$511$	2.38693	+	0.573052i	0.105592	+	0.0253503i
$512$	−9.94541	+	20.3246i	−0.439529	+	0.898228i
$513$	−2.04824	−	12.9321i	−0.0904322	−	0.570966i
$514$	−6.23689	+	19.9055i	−0.275097	+	0.877993i
$515$	12.9454	−	9.40535i	0.570440	−	0.414449i
$516$	−21.7566	−	33.8818i	−0.957780	−	1.49156i
$517$	−0.490626	+	0.675288i	−0.0215777	+	0.0296991i
$518$	4.73722	−	0.0498501i	0.208141	−	0.00219029i
$519$	−0.288389	−	0.696232i	−0.0126589	−	0.0305612i
$520$	−0.160694	−	5.08870i	−0.00704689	−	0.223154i
$521$	−23.3587	−	19.9502i	−1.02336	−	0.874034i	−0.0312655	−	0.999511i	$-0.509954\pi$
$521$	−23.3587	−	19.9502i	−1.02336	−	0.874034i	−0.992096	+	0.125477i	$0.959954\pi$
$522$	1.29426	−	8.76782i	0.0566484	−	0.383757i
$523$	12.0480	+	37.0799i	0.526822	+	1.62139i	0.760684	+	0.649122i	$0.224864\pi$
$523$	12.0480	+	37.0799i	0.526822	+	1.62139i	−0.233862	+	0.972270i	$0.575136\pi$
$524$	−13.9270	−	18.3443i	−0.608405	−	0.801375i
$525$	0.509571	+	0.259640i	0.0222395	+	0.0113316i
$526$	10.8278	+	20.7091i	0.472114	+	0.902960i
$527$	27.5182	+	16.8631i	1.19871	+	0.734570i
$528$	−3.68200	−	18.2416i	−0.160238	−	0.793862i
$529$	−3.00132	+	9.23711i	−0.130492	+	0.401613i
$530$	11.8495	−	23.8736i	0.514708	−	1.03700i
$531$	−1.11832	+	7.06082i	−0.0485311	+	0.306413i
$532$	−0.283329	+	2.06992i	−0.0122839	+	0.0897423i
$533$	−0.976934	+	4.62034i	−0.0423157	+	0.200129i
$534$	10.1962	+	0.694589i	0.441234	+	0.0300578i
$535$	−27.7319	−	4.39230i	−1.19896	−	0.189896i
$536$	−10.9112	+	16.0606i	−0.471293	+	0.693714i
$537$	43.2090	+	14.0395i	1.86461	+	0.605848i
$538$	−2.07321	−	4.85989i	−0.0893825	−	0.209525i
$539$	8.17606	−	13.3421i	0.352168	−	0.574685i
$540$	7.15240	+	16.2891i	0.307790	+	0.700973i
$541$	9.71975	−	19.0761i	0.417885	−	0.820145i	−0.582091	−	0.813124i	$-0.697765\pi$
$541$	9.71975	−	19.0761i	0.417885	−	0.820145i	0.999975	−	0.00702084i	$-0.00223482\pi$
$542$	20.1207	+	23.0624i	0.864256	+	0.990614i
$543$	−28.8551	+	9.37560i	−1.23829	+	0.402345i
$544$	−24.4419	−	10.8748i	−1.04794	−	0.466254i
$545$	23.8198	−	27.8893i	1.02033	−	1.19465i
$546$	0.614834	−	0.104023i	0.0263125	−	0.00445179i
$547$	−7.06464	+	2.92627i	−0.302062	+	0.125118i	−0.528566	−	0.848892i	$-0.677270\pi$
$547$	−7.06464	+	2.92627i	−0.302062	+	0.125118i	0.226504	+	0.974010i	$0.427270\pi$
$548$	0.301338	−	5.23539i	0.0128725	−	0.223645i
$549$	9.88208	+	7.17975i	0.421757	+	0.306424i
$550$	2.45746	−	1.82526i	0.104786	−	0.0778294i
$551$	10.7819	+	14.8400i	0.459325	+	0.632207i
$552$	19.1822	+	9.02291i	0.816450	+	0.384041i
$553$	3.85765	−	0.610992i	0.164044	−	0.0259820i
$554$	−17.6199	+	1.57344i	−0.748600	+	0.0668490i
$555$	13.4957	−	56.2136i	0.572860	−	2.38613i
$556$	7.71911	−	4.13996i	0.327363	−	0.175573i
$557$	−18.9353	−	22.1704i	−0.802315	−	0.939390i	0.196842	−	0.980435i	$-0.436931\pi$
$557$	−18.9353	−	22.1704i	−0.802315	−	0.939390i	−0.999157	+	0.0410451i	$0.986931\pi$
$558$	7.59802	−	9.08806i	0.321650	−	0.384728i
$559$	−0.566620	−	7.19959i	−0.0239655	−	0.304510i
$560$	−0.341602	−	2.81805i	−0.0144353	−	0.119084i
$561$	21.3937	−	5.13618i	0.903244	−	0.216850i
$562$	−5.08478	+	5.19293i	−0.214488	+	0.219050i
$563$	−3.33166	+	42.3327i	−0.140413	+	1.78411i	0.374856	+	0.927083i	$0.377692\pi$
$563$	−3.33166	+	42.3327i	−0.140413	+	1.78411i	−0.515268	+	0.857029i	$0.672308\pi$
$564$	1.49290	−	0.268772i	0.0628626	−	0.0113174i
$565$	−6.71307	+	6.71307i	−0.282421	+	0.282421i
$566$	−32.9283	−	19.7049i	−1.38408	−	0.828258i
$567$	−2.77074	+	1.69791i	−0.116360	+	0.0713057i
$568$	14.0313	−	14.9463i	0.588739	−	0.627135i
$569$	9.45361	+	18.5537i	0.396316	+	0.777814i	0.999809	−	0.0195547i	$-0.00622485\pi$
$569$	9.45361	+	18.5537i	0.396316	+	0.777814i	−0.603493	+	0.797368i	$0.706225\pi$
$570$	23.6552	+	9.50793i	0.990807	+	0.398244i
$571$	14.1492	−	34.1591i	0.592125	−	1.42952i	−0.289322	−	0.957232i	$-0.593430\pi$
$571$	14.1492	−	34.1591i	0.592125	−	1.42952i	0.881447	−	0.472284i	$-0.156570\pi$
$572$	0.964378	−	3.19534i	0.0403227	−	0.133604i
$573$			24.1893i			1.01052i
$574$	−0.313410	+	2.61436i	−0.0130815	+	0.109121i
$575$			3.48702i			0.145419i
$576$	−5.25876	+	8.29205i	−0.219115	+	0.345502i
$577$	6.23450	−	15.0514i	0.259546	−	0.626599i	−0.739363	−	0.673307i	$-0.764873\pi$
$577$	6.23450	−	15.0514i	0.259546	−	0.626599i	0.998909	+	0.0467085i	$0.0148732\pi$
$578$	2.82943	−	7.03945i	0.117689	−	0.292803i
$579$	−2.50546	−	4.91724i	−0.104123	−	0.204354i
$580$	−19.2884	−	15.7841i	−0.800909	−	0.655401i
$581$	−4.44254	+	2.72239i	−0.184308	+	0.112944i
$582$	−15.0837	+	25.2060i	−0.625240	+	1.04482i
$583$	12.3552	−	12.3552i	0.511699	−	0.511699i
$584$	−23.7333	+	2.62384i	−0.982093	+	0.108575i
$585$	0.173340	−	2.20249i	0.00716672	−	0.0910619i
$586$	−14.8006	−	14.4924i	−0.611408	−	0.598674i
$587$	1.63907	−	0.393506i	0.0676517	−	0.0162417i	−0.199478	−	0.979902i	$-0.563925\pi$
$587$	1.63907	−	0.393506i	0.0676517	−	0.0162417i	0.267130	+	0.963661i	$0.413925\pi$
$588$	−27.5056	+	7.21894i	−1.13431	+	0.297704i
$589$	1.92359	+	24.4415i	0.0792601	+	1.00709i
$590$	15.4234	+	12.8946i	0.634971	+	0.530863i
$591$	15.6311	+	18.3016i	0.642976	+	0.752828i
$592$	−43.1890	+	16.0718i	−1.77506	+	0.660547i
$593$	6.94892	−	28.9443i	0.285358	−	1.18860i	−0.626938	−	0.779069i	$-0.715692\pi$
$593$	6.94892	−	28.9443i	0.285358	−	1.18860i	0.912296	−	0.409532i	$-0.134308\pi$
$594$	1.03735	+	11.6167i	0.0425631	+	0.476637i
$595$	3.31480	−	0.525013i	0.135894	−	0.0215234i
$596$	27.6778	+	10.7879i	1.13373	+	0.441889i
$597$	−10.7728	−	14.8275i	−0.440902	−	0.606849i
$598$	2.26702	+	3.05223i	0.0927055	+	0.124815i
$599$	14.1710	+	10.2959i	0.579013	+	0.420678i	0.838368	−	0.545104i	$-0.183510\pi$
$599$	14.1710	+	10.2959i	0.579013	+	0.420678i	−0.259355	+	0.965782i	$0.583510\pi$
$600$	−5.51928	−	0.696394i	−0.225324	−	0.0284302i
$601$	−22.0707	+	9.14196i	−0.900281	+	0.372908i	−0.784328	−	0.620346i	$-0.786992\pi$
$601$	−22.0707	+	9.14196i	−0.900281	+	0.372908i	−0.115953	+	0.993255i	$0.536992\pi$
$602$	−0.671717	−	3.97021i	−0.0273771	−	0.161813i
$603$	−5.47201	+	6.40690i	−0.222837	+	0.260909i
$604$	−4.60966	+	21.1521i	−0.187564	+	0.860668i
$605$	−13.6483	+	4.43459i	−0.554880	+	0.180292i
$606$	−2.12715	+	1.85582i	−0.0864097	+	0.0753877i
$607$	1.53146	−	3.00567i	0.0621602	−	0.121996i	−0.857836	−	0.513923i	$-0.828192\pi$
$607$	1.53146	−	3.00567i	0.0621602	−	0.121996i	0.919996	+	0.391927i	$0.128192\pi$
$608$	−4.23027	−	19.8771i	−0.171560	−	0.806122i
$609$	1.59499	−	2.60279i	0.0646323	−	0.105470i
$610$	31.5953	−	13.4784i	1.27926	−	0.545726i
$611$	0.258749	+	0.0840726i	0.0104679	+	0.00340121i
$612$	−10.0236	−	5.85596i	−0.405180	−	0.236713i
$613$	24.6754	+	3.90820i	0.996630	+	0.157851i	0.633380	−	0.773841i	$-0.281667\pi$
$613$	24.6754	+	3.90820i	0.996630	+	0.157851i	0.363250	+	0.931692i	$0.381667\pi$
$614$	2.65132	−	38.9201i	0.106999	−	1.57069i
$615$	30.0093	+	11.4828i	1.21009	+	0.463031i
$616$	0.377105	−	1.82237i	0.0151940	−	0.0734252i
$617$	−3.78107	+	23.8727i	−0.152220	+	0.961079i	0.786798	+	0.617211i	$0.211737\pi$
$617$	−3.78107	+	23.8727i	−0.152220	+	0.961079i	−0.939018	+	0.343868i	$0.888263\pi$
$618$	−17.0760	−	8.47553i	−0.686898	−	0.340936i
$619$	−12.9832	+	39.9581i	−0.521838	+	1.60605i	0.248648	+	0.968594i	$0.420014\pi$
$619$	−12.9832	+	39.9581i	−0.521838	+	1.60605i	−0.770486	+	0.637457i	$0.779986\pi$
$620$	−10.9584	−	31.4580i	−0.440101	−	1.26338i
$621$	−11.3277	−	6.94160i	−0.454564	−	0.278557i
$622$	11.9362	−	6.24084i	0.478596	−	0.250235i
$623$	0.910610	+	0.463979i	0.0364828	+	0.0185889i
$624$	−5.28384	+	2.97870i	−0.211523	+	0.119244i
$625$	8.92068	+	27.4550i	0.356827	+	1.09820i
$626$	12.1273	+	1.79017i	0.484703	+	0.0715495i
$627$	12.7091	+	10.8546i	0.507554	+	0.433492i
$628$	4.28640	+	42.9001i	0.171046	+	1.71190i
$629$	−20.8495	−	50.3352i	−0.831325	−	2.00700i
$630$	−0.0129618	−	1.23175i	−0.000516412	−	0.0490743i
$631$	26.4520	−	36.4080i	1.05304	−	1.44938i	0.166891	−	0.985975i	$-0.446627\pi$
$631$	26.4520	−	36.4080i	1.05304	−	1.44938i	0.886146	−	0.463406i	$-0.153373\pi$
$632$	−33.2898	+	18.3078i	−1.32420	+	0.728245i
$633$	−26.1140	+	18.9729i	−1.03794	+	0.754107i
$634$	35.5844	+	11.1495i	1.41324	+	0.442803i
$635$	−1.06014	−	6.69348i	−0.0420705	−	0.265622i
$636$	−31.7464	+	0.668213i	−1.25883	+	0.0264964i
$637$	−4.95942	−	1.19065i	−0.196499	−	0.0471753i
$638$	−8.68339	−	13.8410i	−0.343779	−	0.547969i
$639$	6.76459	−	5.77751i	0.267603	−	0.228555i
$640$	12.4155	+	24.6637i	0.490767	+	0.974920i
$641$	−47.0127	+	3.69998i	−1.85689	+	0.146140i	−0.957021	−	0.290019i	$-0.906338\pi$
$641$	−47.0127	+	3.69998i	−1.85689	+	0.146140i	−0.899869	+	0.436159i	$0.856338\pi$
$642$	10.6712	+	31.7034i	0.421157	+	1.25123i
$643$	1.71006	+	7.12290i	0.0674381	+	0.280900i	0.995892	−	0.0905474i	$-0.0288617\pi$
$643$	1.71006	+	7.12290i	0.0674381	+	0.280900i	−0.928454	+	0.371447i	$0.878862\pi$
$644$	1.41036	+	1.58263i	0.0555761	+	0.0623645i
$645$	−48.9850	−	3.85521i	−1.92878	−	0.151799i
$646$	23.3025	−	5.85443i	0.916823	−	0.230340i
$647$	−0.0265675	−	0.0265675i	−0.00104448	−	0.00104448i	0.706584	−	0.707629i	$-0.250235\pi$
$647$	−0.0265675	−	0.0265675i	−0.00104448	−	0.00104448i	−0.707629	+	0.706584i	$0.750235\pi$
$648$	19.7599	−	24.6721i	0.776242	−	0.969211i
$649$	6.88623	+	11.2373i	0.270308	+	0.441103i
$650$	−0.813331	−	0.577942i	−0.0319015	−	0.0226688i
$651$	3.63534	−	1.85230i	0.142480	−	0.0725974i
$652$	1.18296	+	0.571716i	0.0463282	+	0.0223901i
$653$	−17.4289	−	7.21929i	−0.682046	−	0.282513i	0.0146358	−	0.999893i	$-0.495341\pi$
$653$	−17.4289	−	7.21929i	−0.682046	−	0.282513i	−0.696682	+	0.717380i	$0.745341\pi$
$654$	−42.5939	−	9.75303i	−1.66555	−	0.381373i
$655$	−28.1062			−1.09820
$656$	−5.74968	−	24.9588i	−0.224487	−	0.974477i
$657$	−10.3616			−0.404246
$658$	0.147866	+	0.0338580i	0.00576442	+	0.00131992i
$659$	36.3086	+	15.0395i	1.41438	+	0.585856i	0.953442	−	0.301577i	$-0.0975129\pi$
$659$	36.3086	+	15.0395i	1.41438	+	0.585856i	0.460938	+	0.887432i	$0.347513\pi$
$660$	−20.4466	−	9.88170i	−0.795882	−	0.384645i
$661$	−23.0082	+	11.7233i	−0.894916	+	0.455983i	−0.840049	−	0.542511i	$-0.817474\pi$
$661$	−23.0082	+	11.7233i	−0.894916	+	0.455983i	−0.0548677	+	0.998494i	$0.517474\pi$
$662$	14.2501	+	10.1260i	0.553847	+	0.393556i
$663$	−3.74698	−	6.11451i	−0.145520	−	0.237468i
$664$	31.6825	−	39.5586i	1.22952	−	1.53517i
$665$	1.80276	+	1.80276i	0.0699081	+	0.0699081i
$666$	−19.3944	+	4.87258i	−0.751517	+	0.188809i
$667$	18.5550	+	1.46031i	0.718454	+	0.0565436i
$668$	−6.12268	−	6.87054i	−0.236893	−	0.265829i
$669$	−1.57123	−	6.54463i	−0.0607471	−	0.253030i
$670$	7.55858	+	22.4561i	0.292014	+	0.867555i
$671$	22.4497	−	1.76683i	0.866663	−	0.0682078i
$672$	−2.78667	+	1.91626i	−0.107498	+	0.0739215i
$673$	0.943611	−	0.805920i	0.0363735	−	0.0310659i	−0.631076	−	0.775721i	$-0.717386\pi$
$673$	0.943611	−	0.805920i	0.0363735	−	0.0310659i	0.667449	+	0.744655i	$0.267386\pi$
$674$	−23.0910	−	36.8061i	−0.889433	−	1.41772i
$675$	3.39013	+	0.813897i	0.130486	+	0.0313269i
$676$	24.9066	−	0.524246i	0.957946	−	0.0201633i
$677$	−4.59243	−	28.9954i	−0.176501	−	1.11439i	−0.903766	−	0.428028i	$-0.859209\pi$
$677$	−4.59243	−	28.9954i	−0.176501	−	1.11439i	0.727264	−	0.686357i	$-0.240791\pi$
$678$	10.7932	+	3.38180i	0.414512	+	0.129877i
$679$	−2.37648	+	1.72661i	−0.0912009	+	0.0662614i
$680$	−28.6052	+	15.7315i	−1.09696	+	0.603276i
$681$	−3.39560	+	4.67364i	−0.130120	+	0.179094i
$682$	−0.229797	−	21.8374i	−0.00879938	−	0.836198i
$683$	−15.1451	−	36.5636i	−0.579512	−	1.39907i	−0.893251	−	0.449557i	$-0.851582\pi$
$683$	−15.1451	−	36.5636i	−0.579512	−	1.39907i	0.313739	−	0.949509i	$-0.398418\pi$
$684$	−0.876759	−	8.77499i	−0.0335237	−	0.335520i
$685$	−4.86612	−	4.15605i	−0.185925	−	0.158795i
$686$	−5.66094	−	0.835641i	−0.216136	−	0.0319049i
$687$	−3.36315	−	10.3507i	−0.128312	−	0.394904i
$688$	19.2346	+	34.1197i	0.733311	+	1.30080i
$689$	−5.07440	−	2.58554i	−0.193319	−	0.0985012i
$690$	22.9242	−	11.9860i	0.872709	−	0.456297i
$691$	25.9505	+	15.9025i	0.987205	+	0.604960i	0.919643	−	0.392755i	$-0.128478\pi$
$691$	25.9505	+	15.9025i	0.987205	+	0.604960i	0.0675617	+	0.997715i	$0.478478\pi$
$692$	0.241146	+	0.692251i	0.00916699	+	0.0263154i
$693$	0.249548	−	0.768031i	0.00947956	−	0.0291751i
$694$	37.5851	+	18.6550i	1.42671	+	0.708135i
$695$	1.67212	−	10.5573i	0.0634271	−	0.400463i
$696$	−6.01703	+	29.0774i	−0.228075	+	1.10218i
$697$	29.2410	−	7.86854i	1.10758	−	0.298042i
$698$	−1.11441	+	16.3590i	−0.0421812	+	0.619199i
$699$	−42.4398	−	6.72180i	−1.60522	−	0.254242i
$700$	−0.480346	−	0.280626i	−0.0181554	−	0.0106067i
$701$	30.6582	+	9.96146i	1.15795	+	0.376239i	0.824131	−	0.566400i	$-0.191664\pi$
$701$	30.6582	+	9.96146i	1.15795	+	0.376239i	0.333814	+	0.942639i	$0.391664\pi$
$702$	3.49656	−	1.49162i	0.131969	−	0.0562975i
$703$	21.6250	−	35.2889i	0.815604	−	1.33094i
$704$	2.55606	+	17.9207i	0.0963350	+	0.675412i
$705$	0.840378	−	1.64933i	0.0316505	−	0.0621175i
$706$	−21.2753	+	18.5615i	−0.800706	+	0.698571i
$707$	−0.268480	+	0.0872343i	−0.0100972	+	0.00328078i
$708$	5.09991	−	23.4017i	0.191666	−	0.879490i
$709$	−13.9148	+	16.2921i	−0.522581	+	0.611864i	−0.957439	−	0.288635i	$-0.906799\pi$
$709$	−13.9148	+	16.2921i	−0.522581	+	0.611864i	0.434858	+	0.900499i	$0.356799\pi$
$710$	−4.17329	−	24.6663i	−0.156621	−	0.925712i
$711$	−15.2314	+	6.30903i	−0.571220	+	0.236607i
$712$	−9.86301	−	1.24446i	−0.369632	−	0.0466383i
$713$	20.1257	+	14.6222i	0.753715	+	0.547606i
$714$	−2.38412	−	3.20988i	−0.0892235	−	0.120127i
$715$	−2.39406	−	3.29514i	−0.0895328	−	0.123231i
$716$	−41.1768	−	16.0493i	−1.53885	−	0.599792i
$717$	18.0790	−	2.86343i	0.675173	−	0.106937i
$718$	−0.793907	−	8.89046i	−0.0296284	−	0.331789i
$719$	−4.32379	+	18.0099i	−0.161250	+	0.671655i	0.831912	+	0.554908i	$0.187247\pi$
$719$	−4.32379	+	18.0099i	−0.161250	+	0.671655i	−0.993162	+	0.116747i	$0.962753\pi$
$720$	4.17894	+	11.2298i	0.155740	+	0.418512i
$721$	−1.23811	−	1.44964i	−0.0461095	−	0.0539873i
$722$	−6.61182	−	5.52777i	−0.246066	−	0.205722i
$723$	−0.652450	−	8.29016i	−0.0242649	−	0.308314i
$724$	28.5461	−	7.49202i	1.06091	−	0.278439i
$725$	−4.74946	+	1.14024i	−0.176390	+	0.0423476i
$726$	12.2160	+	11.9616i	0.453378	+	0.443936i
$727$	−4.10639	+	52.1767i	−0.152298	+	1.93513i	0.163990	+	0.986462i	$0.447564\pi$
$727$	−4.10639	+	52.1767i	−0.152298	+	1.93513i	−0.316287	+	0.948663i	$0.602436\pi$
$728$	−0.602897	+	0.0666533i	−0.0223448	+	0.00247033i
$729$	−6.19703	+	6.19703i	−0.229520	+	0.229520i
$730$	−14.9625	+	25.0034i	−0.553788	+	0.925418i
$731$	−39.4836	+	24.1956i	−1.46035	+	0.894906i
$732$	−31.6713	−	25.9173i	−1.17061	−	0.957932i
$733$	8.46001	+	16.6037i	0.312477	+	0.613272i	0.992819	−	0.119623i	$-0.0381687\pi$
$733$	8.46001	+	16.6037i	0.312477	+	0.613272i	−0.680342	+	0.732895i	$0.738169\pi$
$734$	−12.6398	+	31.4470i	−0.466542	+	1.16073i
$735$	−13.2799	+	32.0605i	−0.489836	+	1.18257i
$736$	−18.1241	−	9.83461i	−0.668062	−	0.362509i
$737$			15.5333i			0.572176i
$738$	−1.28978	−	11.0393i	−0.0474776	−	0.406361i
$739$		−	14.2463i		−	0.524057i	−0.965060	−	0.262029i	$-0.915608\pi$
$739$		−	14.2463i		−	0.524057i	0.965060	−	0.262029i	$-0.0843915\pi$
$740$	−16.2482	+	53.8363i	−0.597294	+	1.97906i
$741$	2.08473	−	5.03299i	0.0765846	−	0.184892i
$742$	−2.94630	−	1.18423i	−0.108162	−	0.0434745i
$743$	2.74553	+	5.38841i	0.100724	+	0.197682i	0.935869	−	0.352348i	$-0.114617\pi$
$743$	2.74553	+	5.38841i	0.100724	+	0.197682i	−0.835145	+	0.550029i	$0.814617\pi$
$744$	−27.1635	+	28.9350i	−0.995862	+	1.06081i
$745$	30.9084	−	18.9407i	1.13240	−	0.693934i
$746$	−35.4779	−	21.2306i	−1.29894	−	0.777309i
$747$	15.5514	−	15.5514i	0.568997	−	0.568997i
$748$	−21.0631	+	3.79206i	−0.770145	+	0.138652i
$749$	−0.262459	+	3.33485i	−0.00959003	+	0.121853i
$750$	20.0753	−	20.5023i	0.733047	−	0.748639i
$751$	47.1673	−	11.3239i	1.72116	−	0.413214i	0.751905	−	0.659271i	$-0.229135\pi$
$751$	47.1673	−	11.3239i	1.72116	−	0.413214i	0.969255	+	0.246057i	$0.0791350\pi$
$752$	−1.46482	+	0.177565i	−0.0534167	+	0.00647512i
$753$	−1.98801	−	25.2601i	−0.0724472	−	0.920528i
$754$	−3.41595	+	4.08585i	−0.124401	+	0.148798i
$755$	17.1571	+	20.0884i	0.624410	+	0.731090i
$756$	1.86785	−	1.00177i	0.0679329	−	0.0364342i
$757$	−0.156917	+	0.653606i	−0.00570325	+	0.0237557i	−0.975149	−	0.221550i	$-0.928888\pi$
$757$	−0.156917	+	0.653606i	−0.00570325	+	0.0237557i	0.969446	+	0.245306i	$0.0788884\pi$
$758$	6.71494	−	0.599636i	0.243898	−	0.0217797i
$759$	16.7500	−	2.65295i	0.607988	−	0.0962958i
$760$	−22.4408	−	10.5557i	−0.814012	−	0.382894i
$761$	27.4449	+	37.7747i	0.994877	+	1.36933i	0.928416	+	0.371542i	$0.121171\pi$
$761$	27.4449	+	37.7747i	0.994877	+	1.36933i	0.0664610	+	0.997789i	$0.478829\pi$
$762$	−6.48161	+	4.81418i	−0.234804	+	0.174399i
$763$	−3.53515	−	2.56844i	−0.127981	−	0.0929837i
$764$	1.35209	−	23.4910i	0.0489169	−	0.849873i
$765$	−13.0880	+	5.42122i	−0.473197	+	0.196005i
$766$	−24.1974	+	4.09395i	−0.874289	+	0.147921i
$767$	2.78985	−	3.26650i	0.100736	−	0.117946i
$768$	19.1859	−	26.7228i	0.692311	−	0.964277i
$769$	23.9215	−	7.77255i	0.862630	−	0.280285i	0.155903	−	0.987772i	$-0.450171\pi$
$769$	23.9215	−	7.77255i	0.862630	−	0.280285i	0.706726	+	0.707487i	$0.250171\pi$
$770$	−1.49296	−	1.71124i	−0.0538026	−	0.0616687i
$771$	13.7681	−	27.0215i	0.495847	−	0.973155i
$772$	2.15827	+	4.91532i	0.0776778	+	0.176906i
$773$	6.79762	−	11.0927i	0.244493	−	0.398977i	−0.706728	−	0.707485i	$-0.749830\pi$
$773$	6.79762	−	11.0927i	0.244493	−	0.398977i	0.951222	+	0.308508i	$0.0998297\pi$
$774$	6.66918	+	15.6335i	0.239719	+	0.561934i
$775$	−6.20884	−	2.01737i	−0.223028	−	0.0724662i
$776$	16.0571	−	23.6351i	0.576418	−	0.848450i
$777$	−6.80280	−	1.07746i	−0.244049	−	0.0386536i
$778$	13.3170	+	0.907187i	0.477439	+	0.0325242i
$779$	17.8923	+	14.4573i	0.641058	+	0.517987i
$780$	−1.00381	+	7.33353i	−0.0359422	+	0.262582i
$781$	2.56561	−	16.1986i	0.0918046	−	0.579631i
$782$	10.8387	−	21.8372i	0.387592	−	0.780898i
$783$	5.75063	−	17.6986i	0.205511	−	0.632497i
$784$	27.1150	−	5.47306i	0.968391	−	0.195466i
$785$	44.8591	+	27.4897i	1.60109	+	0.981150i
$786$	15.5151	+	29.6739i	0.553405	+	1.05843i
$787$	0.453538	+	0.231089i	0.0161669	+	0.00823744i	0.462055	−	0.886851i	$-0.347112\pi$
$787$	0.453538	+	0.231089i	0.0161669	+	0.00823744i	−0.445888	+	0.895089i	$0.647112\pi$
$788$	−14.1568	−	18.6469i	−0.504314	−	0.664269i
$789$	−10.4989	−	32.3122i	−0.373769	−	1.15034i
$790$	−6.77035	+	45.8648i	−0.240878	+	1.63180i
$791$	0.860081	+	0.734579i	0.0305810	+	0.0261186i
$792$	0.247934	+	7.85134i	0.00880995	+	0.278985i
$793$	−2.80888	−	6.78123i	−0.0997461	−	0.240808i
$794$	−18.1777	+	0.191285i	−0.645101	+	0.00678844i
$795$	−22.7761	+	31.3486i	−0.807783	+	1.11182i
$796$	9.63298	+	15.0016i	0.341432	+	0.531716i
$797$	11.2863	−	8.20000i	0.399782	−	0.290459i	−0.369670	−	0.929163i	$-0.620529\pi$
$797$	11.2863	−	8.20000i	0.399782	−	0.290459i	0.769452	+	0.638704i	$0.220529\pi$
$798$	0.908164	−	2.89847i	0.0321487	−	0.102605i
$799$	−0.272902	−	1.72304i	−0.00965458	−	0.0609566i
$800$	5.32100	+	0.984794i	0.188126	+	0.0348177i
$801$	−4.19472	−	1.00706i	−0.148213	−	0.0355828i
$802$	−16.3305	+	10.2453i	−0.576651	+	0.361773i
$803$	−14.5257	+	12.4061i	−0.512599	+	0.437801i
$804$	19.5362	−	20.3763i	0.688990	−	0.718618i
$805$	2.57892	−	0.202965i	0.0908949	−	0.00715359i
$806$	−6.74623	+	2.27074i	−0.237626	+	0.0799833i
$807$	1.79324	+	7.46938i	0.0631250	+	0.262935i
$808$	2.16947	−	1.68334i	0.0763218	−	0.0592198i
$809$	5.43015	+	0.427362i	0.190914	+	0.0150252i	0.173556	−	0.984824i	$-0.444474\pi$
$809$	5.43015	+	0.427362i	0.190914	+	0.0150252i	0.0173584	+	0.999849i	$0.494474\pi$
$810$	−9.39896	−	37.4108i	−0.330246	−	1.31448i
$811$	−22.9728	−	22.9728i	−0.806686	−	0.806686i	0.177445	−	0.984131i	$-0.443217\pi$
$811$	−22.9728	−	22.9728i	−0.806686	−	0.806686i	−0.984131	+	0.177445i	$0.943217\pi$
$812$	−1.69443	+	2.43849i	−0.0594627	+	0.0855741i
$813$	−23.2493	−	37.9393i	−0.815387	−	1.33059i
$814$	−21.3544	+	30.0518i	−0.748471	+	1.05331i
$815$	1.42857	−	0.727893i	0.0500406	−	0.0254970i
$816$	32.3996	+	21.5167i	1.13421	+	0.753237i
$817$	−32.4999	−	13.4619i	−1.13703	−	0.470972i
$818$	4.04029	−	17.6450i	0.141266	−	0.616942i
$819$	−0.263216			−0.00919753
$820$	−28.5010	−	12.8287i	−0.995299	−	0.447996i
$821$	6.50682			0.227090			0.113545	−	0.993533i	$-0.463779\pi$
$821$	6.50682			0.227090			0.113545	+	0.993533i	$0.463779\pi$
$822$	−1.70170	+	7.43175i	−0.0593537	+	0.259212i
$823$	13.5219	+	5.60097i	0.471345	+	0.195237i	0.605696	−	0.795696i	$-0.292895\pi$
$823$	13.5219	+	5.60097i	0.471345	+	0.195237i	−0.134351	+	0.990934i	$0.542895\pi$
$824$	16.1092	+	9.18530i	0.561192	+	0.319985i
$825$	−3.96539	+	2.02047i	−0.138057	+	0.0703437i
$826$	1.38736	−	1.95241i	0.0482723	−	0.0679331i
$827$	−5.23184	−	8.53759i	−0.181929	−	0.296881i	0.748655	−	0.662960i	$-0.230700\pi$
$827$	−5.23184	−	8.53759i	−0.181929	−	0.296881i	−0.930584	+	0.366079i	$0.880700\pi$
$828$	−7.34821	−	5.10604i	−0.255368	−	0.177447i
$829$	13.7966	+	13.7966i	0.479174	+	0.479174i	0.904868	−	0.425693i	$-0.139970\pi$
$829$	13.7966	+	13.7966i	0.479174	+	0.479174i	−0.425693	+	0.904868i	$0.639970\pi$
$830$	−15.0700	−	59.9835i	−0.523089	−	2.08206i
$831$	25.6394	+	2.01787i	0.889423	+	0.0699991i
$832$	5.29778	−	2.59736i	0.183667	−	0.0900471i
$833$	7.63461	+	31.8005i	0.264524	+	1.10182i
$834$	−12.0693	+	4.06243i	−0.417924	+	0.140671i
$835$	−11.1956	+	0.881115i	−0.387441	+	0.0304922i
$836$	−11.7355	−	11.2516i	−0.405879	−	0.389145i
$837$	18.9134	−	16.1536i	0.653744	−	0.558350i
$838$	10.0534	−	6.30717i	0.347287	−	0.217878i
$839$	41.2186	+	9.89572i	1.42303	+	0.341638i	0.870628	−	0.491942i	$-0.163713\pi$
$839$	41.2186	+	9.89572i	1.42303	+	0.341638i	0.552398	+	0.833581i	$0.313713\pi$
$840$	−0.193782	+	4.12247i	−0.00668612	+	0.142239i
$841$	−0.458164	−	2.89273i	−0.0157987	−	0.0997494i
$842$	−0.757068	+	2.41624i	−0.0260903	+	0.0832690i
$843$	8.54837	−	6.21075i	0.294421	−	0.213910i
$844$	26.4206	−	16.9655i	0.909433	−	0.583976i
$845$	17.8689	−	24.5945i	0.614710	−	0.846075i
$846$	−0.640267	+	0.00673758i	−0.0220128	+	0.000231643i
$847$	0.654287	+	1.57959i	0.0224816	+	0.0542753i
$848$	30.8672	+	1.12558i	1.05998	+	0.0386525i
$849$	42.4230	+	36.2327i	1.45595	+	1.24350i
$850$	−0.934284	+	6.32918i	−0.0320457	+	0.217089i
$851$	−12.9772	−	39.9396i	−0.444851	−	1.36911i
$852$	−23.7385	+	18.0223i	−0.813267	+	0.617433i
$853$	33.7127	+	17.1775i	1.15430	+	0.588145i	0.923024	−	0.384743i	$-0.125710\pi$
$853$	33.7127	+	17.1775i	1.15430	+	0.588145i	0.231276	+	0.972888i	$0.425710\pi$
$854$	−1.89621	−	3.62667i	−0.0648870	−	0.124102i
$855$	−9.17569	−	5.62287i	−0.313802	−	0.192298i
$856$	−8.59097	−	31.3845i	−0.293633	−	1.07270i
$857$	6.07893	−	18.7090i	0.207652	−	0.639088i	−0.791942	−	0.610597i	$-0.790930\pi$
$857$	6.07893	−	18.7090i	0.207652	−	0.639088i	0.999594	−	0.0284913i	$-0.00907029\pi$
$858$	−2.15738	+	4.34657i	−0.0736518	+	0.148390i
$859$	−1.12277	+	7.08887i	−0.0383083	+	0.241869i	−0.999411	−	0.0343229i	$-0.989073\pi$
$859$	−1.12277	+	7.08887i	−0.0383083	+	0.241869i	0.961102	+	0.276192i	$0.0890725\pi$
$860$	47.3552	+	6.48197i	1.61480	+	0.221033i
$861$	1.08333	−	3.67162i	0.0369197	−	0.125129i
$862$	13.7843	+	0.939014i	0.469494	+	0.0319830i
$863$	39.9087	+	6.32092i	1.35851	+	0.215167i	0.792822	−	0.609453i	$-0.208611\pi$
$863$	39.9087	+	6.32092i	1.35851	+	0.215167i	0.565687	+	0.824620i	$0.308611\pi$
$864$	−13.7916	+	15.3250i	−0.469201	+	0.521367i
$865$	0.850764	+	0.276430i	0.0289269	+	0.00939890i
$866$	−2.95319	−	6.92267i	−0.100353	−	0.235242i
$867$	−5.76320	+	9.40470i	−0.195729	+	0.319400i
$868$	−3.63392	+	1.59562i	−0.123343	+	0.0541588i
$869$	−13.7985	+	27.0810i	−0.468081	+	0.918661i
$870$	23.8215	+	27.3043i	0.807624	+	0.925702i
$871$	4.81516	−	1.56454i	0.163155	−	0.0530124i
$872$	40.8189	+	11.8523i	1.38230	+	0.401368i
$873$	8.05269	−	9.42849i	0.272542	−	0.319106i
$874$	18.2602	−	3.08943i	0.617660	−	0.104502i
$875$	2.65105	−	1.09810i	0.0896219	−	0.0371226i
$876$	34.6576	+	1.99482i	1.17097	+	0.0673987i
$877$	−1.38885	−	1.00906i	−0.0468981	−	0.0340734i	0.564089	−	0.825714i	$-0.309227\pi$
$877$	−1.38885	−	1.00906i	−0.0468981	−	0.0340734i	−0.610987	+	0.791640i	$0.709227\pi$
$878$	−32.1917	+	23.9102i	−1.08642	+	0.806930i
$879$	17.7016	+	24.3641i	0.597059	+	0.821781i
$880$	19.3039	+	10.7393i	0.650734	+	0.362021i
$881$	−27.9079	+	4.42018i	−0.940242	+	0.148920i	−0.607698	−	0.794168i	$-0.707907\pi$
$881$	−27.9079	+	4.42018i	−0.940242	+	0.148920i	−0.332544	+	0.943088i	$0.607907\pi$
$882$	11.9560	−	1.06766i	0.402581	−	0.0359500i
$883$	11.6735	−	48.6235i	0.392843	−	1.63631i	−0.329055	−	0.944311i	$-0.606730\pi$
$883$	11.6735	−	48.6235i	0.392843	−	1.63631i	0.721898	−	0.692000i	$-0.243270\pi$
$884$	3.29702	+	6.14741i	0.110891	+	0.206760i
$885$	−18.9818	−	22.2248i	−0.638066	−	0.747079i
$886$	20.5413	−	24.5697i	0.690099	−	0.825434i
$887$	−3.62118	−	46.0114i	−0.121587	−	1.54491i	−0.690996	−	0.722859i	$-0.742828\pi$
$887$	−3.62118	−	46.0114i	−0.121587	−	1.54491i	0.569409	−	0.822055i	$-0.307172\pi$
$888$	65.8084	−	12.5640i	2.20839	−	0.421620i
$889$	−0.785093	+	0.188484i	−0.0263312	+	0.00632155i
$890$	−8.48741	+	8.66794i	−0.284499	+	0.290550i
$891$	1.98406	−	25.2099i	0.0664686	−	0.844564i
$892$	1.16004	+	6.44350i	0.0388411	+	0.215744i
$893$	0.937076	−	0.937076i	0.0313581	−	0.0313581i
$894$	−37.0592	−	22.1769i	−1.23944	−	0.741707i
$895$	−45.9831	+	28.1785i	−1.53704	+	0.941902i
$896$	2.81332	−	1.70517i	0.0939865	−	0.0569659i
$897$	−2.50948	−	4.92513i	−0.0837890	−	0.164445i
$898$	1.15774	+	0.465342i	0.0386344	+	0.0155287i
$899$	−13.3350	+	32.1935i	−0.444747	+	1.07371i
$900$	2.24807	+	0.678482i	0.0749355	+	0.0226161i
$901$			36.5180i			1.21659i
$902$	−15.0255	−	13.9313i	−0.500294	−	0.463862i
$903$			5.85412i			0.194813i
$904$	−10.2926	−	3.88746i	−0.342326	−	0.129295i
$905$	13.7823	−	33.2733i	0.458138	−	1.10604i
$906$	11.7379	−	29.2032i	0.389965	−	0.970211i
$907$	−8.92210	−	17.5106i	−0.296253	−	0.581430i	0.694119	−	0.719861i	$-0.255794\pi$
$907$	−8.92210	−	17.5106i	−0.296253	−	0.581430i	−0.990372	+	0.138430i	$0.955794\pi$
$908$	3.55880	−	4.34890i	0.118103	−	0.144323i
$909$	1.01599	−	0.622601i	0.0336984	−	0.0206504i
$910$	−0.380092	+	0.635161i	−0.0125999	+	0.0210554i
$911$	−8.96435	+	8.96435i	−0.297002	+	0.297002i	−0.839838	−	0.542836i	$-0.817350\pi$
$911$	−8.96435	+	8.96435i	−0.297002	+	0.297002i	0.542836	+	0.839838i	$0.317350\pi$
$912$	1.24323	+	29.5194i	0.0411674	+	0.977484i
$913$	3.18119	−	40.4209i	0.105282	−	1.33774i
$914$	−1.48753	−	1.45655i	−0.0492030	−	0.0481782i
$915$	−48.5602	+	11.6583i	−1.60535	+	0.385410i
$916$	2.68749	+	10.2399i	0.0887970	+	0.338334i
$917$	0.262726	+	3.33825i	0.00867598	+	0.110239i
$918$	−18.7006	−	15.6345i	−0.617212	−	0.516017i
$919$	−37.1616	−	43.5106i	−1.22585	−	1.43528i	−0.864335	−	0.502916i	$-0.832260\pi$
$919$	−37.1616	−	43.5106i	−1.22585	−	1.43528i	−0.361513	−	0.932367i	$-0.617740\pi$
$920$	−22.9323	+	10.3585i	−0.756055	+	0.341510i
$921$	−13.2399	+	55.1481i	−0.436269	+	1.81719i
$922$	2.44713	+	27.4039i	0.0805919	+	0.902498i
$923$	−5.27981	+	0.836239i	−0.173787	+	0.0275252i
$924$	−0.982550	+	2.52087i	−0.0323235	+	0.0829304i
$925$	6.47777	+	8.91589i	0.212988	+	0.293153i
$926$	25.4864	+	34.3138i	0.837534	+	1.12762i
$927$	6.51016	+	4.72991i	0.213822	+	0.155350i
$928$	7.46862	−	27.9016i	0.245170	−	0.915914i
$929$	−34.6933	+	14.3704i	−1.13825	+	0.471479i	−0.870578	−	0.492031i	$-0.836255\pi$
$929$	−34.6933	+	14.3704i	−1.13825	+	0.471479i	−0.267673	+	0.963510i	$0.586255\pi$
$930$	8.07917	+	47.7522i	0.264926	+	1.56586i
$931$	−16.1347	+	18.8913i	−0.528794	+	0.619139i
$932$	40.8387	+	8.89994i	1.33772	+	0.291527i
$933$	−18.6238	+	6.05125i	−0.609717	+	0.198109i
$934$	−0.166243	+	0.145038i	−0.00543964	+	0.00474578i
$935$	−11.8568	+	23.2702i	−0.387757	+	0.761017i
$936$	2.40886	−	0.867657i	0.0787361	−	0.0283603i
$937$	−13.0455	+	21.2884i	−0.426179	+	0.695461i	−0.991600	−	0.129342i	$-0.958714\pi$
$937$	−13.0455	+	21.2884i	−0.426179	+	0.695461i	0.565421	+	0.824802i	$0.308714\pi$
$938$	2.59652	−	1.10766i	0.0847793	−	0.0361665i
$939$	−16.9500	−	5.50739i	−0.553143	−	0.179727i
$940$	−0.908306	+	1.55474i	−0.0296257	+	0.0507101i
$941$	−20.8663	−	3.30489i	−0.680221	−	0.107736i	−0.193243	−	0.981151i	$-0.561901\pi$
$941$	−20.8663	−	3.30489i	−0.680221	−	0.107736i	−0.486978	+	0.873414i	$0.661901\pi$
$942$	4.26010	−	62.5361i	0.138801	−	2.03754i
$943$	22.9453	−	4.27798i	0.747202	−	0.139310i
$944$	−6.26073	+	22.4410i	−0.203769	+	0.730392i
$945$	0.404614	−	2.55463i	0.0131621	−	0.0831023i
$946$	28.0674	+	13.9310i	0.912550	+	0.452936i
$947$	−3.48177	+	10.7158i	−0.113142	+	0.348216i	−0.991555	−	0.129687i	$-0.958603\pi$
$947$	−3.48177	+	10.7158i	−0.113142	+	0.348216i	0.878413	+	0.477903i	$0.158603\pi$
$948$	52.1604	−	18.1701i	1.69409	−	0.590138i
$949$	5.30880	+	3.25324i	0.172331	+	0.105605i
$950$	−4.30691	+	2.25188i	−0.139735	+	0.0730605i
$951$	−48.3055	−	24.6129i	−1.56641	−	0.798127i
$952$	2.13587	+	3.25047i	0.0692239	+	0.105348i
$953$	−16.5406	−	50.9066i	−0.535801	−	1.64903i	−0.741912	−	0.670498i	$-0.766081\pi$
$953$	−16.5406	−	50.9066i	−0.535801	−	1.64903i	0.206110	−	0.978529i	$-0.433919\pi$
$954$	13.2598	+	1.95735i	0.429301	+	0.0633714i
$955$	−21.8340	−	18.6480i	−0.706532	−	0.603436i
$956$	−17.7171	+	1.77022i	−0.573011	+	0.0572528i
$957$	9.09063	+	21.9467i	0.293858	+	0.709437i
$958$	−0.242949	−	23.0873i	−0.00784932	−	0.745915i
$959$	−0.448139	+	0.616811i	−0.0144712	+	0.0199179i
$960$	−11.8157	−	38.3661i	−0.381351	−	1.23826i
$961$	−12.5997	+	9.15422i	−0.406442	+	0.295297i
$962$	11.4666	+	3.59277i	0.369697	+	0.115836i
$963$	−2.20887	−	13.9463i	−0.0711798	−	0.449412i
$964$	0.170225	+	8.08728i	0.00548258	+	0.260474i
$965$	6.36996	+	1.52929i	0.205056	+	0.0492296i
$966$	−1.63789	−	2.61073i	−0.0526983	−	0.0839988i
$967$	1.58521	−	1.35390i	0.0509769	−	0.0435384i	−0.623595	−	0.781748i	$-0.714328\pi$
$967$	1.58521	−	1.35390i	0.0509769	−	0.0435384i	0.674572	+	0.738209i	$0.264328\pi$
$968$	−11.1947	−	12.2990i	−0.359811	−	0.395306i
$969$	−34.8235	+	2.74067i	−1.11869	+	0.0880430i
$970$	−11.1233	−	33.0468i	−0.357148	−	1.06107i
$971$	10.5807	+	44.0717i	0.339551	+	1.41433i	0.837174	+	0.546937i	$0.184206\pi$
$971$	10.5807	+	44.0717i	0.339551	+	1.41433i	−0.497624	+	0.867393i	$0.665794\pi$
$972$	−17.9834	+	16.0259i	−0.576816	+	0.514029i
$973$	−1.26955	−	0.0999161i	−0.0407001	−	0.00320316i
$974$	−39.5924	+	9.94706i	−1.26862	+	0.318724i
$975$	1.02573	+	1.02573i	0.0328495	+	0.0328495i
$976$	29.3083	+	26.9393i	0.938134	+	0.862308i
$977$	−17.1641	−	28.0093i	−0.549129	−	0.896097i	−0.999994	−	0.00350453i	$-0.998884\pi$
$977$	−17.1641	−	28.0093i	−0.549129	−	0.896097i	0.450865	−	0.892592i	$-0.351116\pi$
$978$	−1.55709	−	1.10645i	−0.0497902	−	0.0353802i
$979$	−7.08620	+	3.61060i	−0.226476	+	0.115395i
$980$	14.6885	−	30.3926i	0.469208	−	0.970855i
$981$	17.0406	+	7.05846i	0.544066	+	0.225359i
$982$	−51.0540	−	11.6902i	−1.62920	−	0.373049i
$983$	−44.5658			−1.42143			−0.710714	−	0.703481i	$-0.751628\pi$
$983$	−44.5658			−1.42143			−0.710714	+	0.703481i	$0.751628\pi$
$984$	2.18880	+	37.1724i	0.0697763	+	1.18501i
$985$	−28.5699			−0.910311
$986$	33.2874	+	7.62206i	1.06009	+	0.242736i
$987$	−0.203752	−	0.0843966i	−0.00648548	−	0.00268637i
$988$	−2.30587	+	4.77115i	−0.0733595	+	0.151791i
$989$	−31.8033	+	16.2046i	−1.01129	+	0.515276i
$990$	7.81396	+	5.55249i	0.248344	+	0.176470i
$991$	−2.04923	−	3.34405i	−0.0650961	−	0.106227i	0.818436	−	0.574597i	$-0.194841\pi$
$991$	−2.04923	−	3.34405i	−0.0650961	−	0.106227i	−0.883532	+	0.468370i	$0.844841\pi$
$992$	27.9966	−	26.5812i	0.888892	−	0.843955i
$993$	−17.9714	−	17.9714i	−0.570307	−	0.570307i
$994$	−2.89068	+	0.726244i	−0.0916868	+	0.0230351i
$995$	21.6887	+	1.70694i	0.687578	+	0.0541135i
$996$	−55.0104	+	49.0225i	−1.74307	+	1.55334i
$997$	10.8693	+	45.2739i	0.344234	+	1.43384i	0.829027	+	0.559209i	$0.188895\pi$
$997$	10.8693	+	45.2739i	0.344234	+	1.43384i	−0.484792	+	0.874629i	$0.661105\pi$
$998$	−4.54739	−	13.5100i	−0.143945	−	0.427653i
$999$	−41.8588	+	3.29436i	−1.32435	+	0.104229i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	164.2.o.b.111.17	yes	288
4.3	odd	2	inner	164.2.o.b.111.1	yes	288
41.17	odd	40	inner	164.2.o.b.99.1	✓	288
164.99	even	40	inner	164.2.o.b.99.17	yes	288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
164.2.o.b.99.1	✓	288	41.17	odd	40	inner
164.2.o.b.99.17	yes	288	164.99	even	40	inner
164.2.o.b.111.1	yes	288	4.3	odd	2	inner
164.2.o.b.111.17	yes	288	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 164 = 2^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	164.o (of order \(40\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(1.37854 + 0.315653i) q^{2} +(-1.89955 - 0.786819i) q^{3} +(1.80073 + 0.870280i) q^{4} +(2.17460 - 1.10802i) q^{5} +(-2.37024 - 1.68426i) q^{6} +(-0.151929 - 0.247926i) q^{7} +(2.20766 + 1.76812i) q^{8} +(0.867885 + 0.867885i) q^{9} +O(q^{10})\)	\(q+(1.37854 + 0.315653i) q^{2} +(-1.89955 - 0.786819i) q^{3} +(1.80073 + 0.870280i) q^{4} +(2.17460 - 1.10802i) q^{5} +(-2.37024 - 1.68426i) q^{6} +(-0.151929 - 0.247926i) q^{7} +(2.20766 + 1.76812i) q^{8} +(0.867885 + 0.867885i) q^{9} +(3.34752 - 0.841019i) q^{10} +(2.25578 + 0.177534i) q^{11} +(-2.73582 - 3.06999i) q^{12} +(-0.172173 - 0.717151i) q^{13} +(-0.131182 - 0.389733i) q^{14} +(-5.00258 + 0.393711i) q^{15} +(2.48523 + 3.13427i) q^{16} +(-3.59606 + 3.07132i) q^{17} +(0.922460 + 1.47036i) q^{18} +(-3.49324 - 0.838652i) q^{19} +(4.88015 - 0.102720i) q^{20} +(0.0935244 + 0.590490i) q^{21} +(3.05364 + 0.956783i) q^{22} +(-2.94903 + 2.14260i) q^{23} +(-2.80237 - 5.09566i) q^{24} +(0.562277 - 0.773908i) q^{25} +(-0.0109752 - 1.04297i) q^{26} +(1.39474 + 3.36719i) q^{27} +(-0.0578181 - 0.578669i) q^{28} +(-3.88263 - 3.31608i) q^{29} +(-7.02051 - 1.03634i) q^{30} +(-2.10889 - 6.49051i) q^{31} +(2.43663 + 5.10518i) q^{32} +(-4.14529 - 2.11213i) q^{33} +(-5.92677 + 3.09882i) q^{34} +(-0.605093 - 0.370801i) q^{35} +(0.807520 + 2.31812i) q^{36} +(-3.56006 + 10.9567i) q^{37} +(-4.55083 - 2.25877i) q^{38} +(-0.237218 + 1.49773i) q^{39} +(6.75989 + 1.39883i) q^{40} +(-5.78230 - 2.75045i) q^{41} +(-0.0574633 + 0.843533i) q^{42} +(9.67140 + 1.53180i) q^{43} +(3.90754 + 2.28285i) q^{44} +(2.84894 + 0.925675i) q^{45} +(-4.74167 + 2.02278i) q^{46} +(-0.192743 + 0.314528i) q^{47} +(-2.25471 - 7.90913i) q^{48} +(3.13955 - 6.16171i) q^{49} +(1.01941 - 0.889376i) q^{50} +(9.24747 - 3.00469i) q^{51} +(0.314086 - 1.44123i) q^{52} +(5.01498 - 5.87179i) q^{53} +(0.859829 + 5.08205i) q^{54} +(5.10215 - 2.11338i) q^{55} +(0.102954 - 0.815966i) q^{56} +(5.97571 + 4.34161i) q^{57} +(-4.30562 - 5.79690i) q^{58} +(3.42355 + 4.71211i) q^{59} +(-9.35091 - 3.64467i) q^{60} +(9.82955 - 1.55685i) q^{61} +(-0.858436 - 9.61308i) q^{62} +(0.0833142 - 0.347029i) q^{63} +(1.74752 + 7.80680i) q^{64} +(-1.16902 - 1.36875i) q^{65} +(-5.04773 - 4.22012i) q^{66} +(0.538603 + 6.84360i) q^{67} +(-9.14843 + 2.40104i) q^{68} +(7.28768 - 1.74962i) q^{69} +(-0.717098 - 0.702163i) q^{70} +(0.568673 - 7.22567i) q^{71} +(0.381472 + 3.45052i) q^{72} +(-5.96949 + 5.96949i) q^{73} +(-8.36621 + 13.9805i) q^{74} +(-1.67700 + 1.02767i) q^{75} +(-5.56050 - 4.55028i) q^{76} +(-0.298705 - 0.586241i) q^{77} +(-0.799778 + 1.98980i) q^{78} +(-5.14027 + 12.4097i) q^{79} +(8.87721 + 4.06212i) q^{80} -11.1757i q^{81} +(-7.10292 - 5.61680i) q^{82} -17.9188i q^{83} +(-0.345479 + 1.14470i) q^{84} +(-4.41693 + 10.6634i) q^{85} +(12.8489 + 5.16445i) q^{86} +(4.76610 + 9.35399i) q^{87} +(4.66610 + 4.38043i) q^{88} +(-2.99682 + 1.83645i) q^{89} +(3.63517 + 2.17535i) q^{90} +(-0.151643 + 0.151643i) q^{91} +(-7.17506 + 1.29175i) q^{92} +(-1.10091 + 13.9884i) q^{93} +(-0.364985 + 0.372748i) q^{94} +(-8.52565 + 2.04683i) q^{95} +(-0.611655 - 11.6147i) q^{96} +(-0.792616 - 10.0711i) q^{97} +(6.27295 - 7.50313i) q^{98} +(1.80368 + 2.11184i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 12 q^{2} - 20 q^{4} - 32 q^{5} - 28 q^{6} - 24 q^{8} - 40 q^{9}+O(q^{10}) \) 288 * q - 12 * q^2 - 20 * q^4 - 32 * q^5 - 28 * q^6 - 24 * q^8 - 40 * q^9	\( 288 q - 12 q^{2} - 20 q^{4} - 32 q^{5} - 28 q^{6} - 24 q^{8} - 40 q^{9} - 12 q^{10} - 8 q^{12} - 24 q^{13} - 4 q^{14} - 28 q^{16} - 12 q^{18} - 44 q^{20} - 32 q^{21} - 40 q^{22} + 8 q^{24} - 40 q^{25} + 4 q^{26} - 48 q^{29} - 44 q^{30} + 108 q^{32} - 72 q^{33} + 12 q^{34} - 20 q^{36} - 24 q^{37} + 56 q^{38} + 8 q^{41} - 112 q^{42} - 40 q^{45} - 48 q^{46} - 68 q^{48} - 16 q^{49} - 60 q^{50} - 124 q^{52} - 64 q^{53} + 64 q^{54} - 84 q^{56} - 24 q^{57} + 40 q^{60} - 8 q^{61} - 44 q^{62} - 20 q^{64} + 64 q^{65} + 60 q^{66} - 28 q^{68} - 8 q^{69} + 128 q^{70} + 160 q^{72} - 32 q^{73} + 80 q^{74} + 288 q^{76} - 32 q^{77} + 116 q^{78} + 176 q^{80} + 212 q^{82} + 152 q^{84} - 56 q^{85} + 180 q^{86} + 144 q^{88} - 72 q^{89} + 224 q^{90} + 36 q^{92} - 8 q^{93} + 52 q^{94} + 136 q^{96} - 88 q^{97} + 104 q^{98}+O(q^{100}) \) 288 * q - 12 * q^2 - 20 * q^4 - 32 * q^5 - 28 * q^6 - 24 * q^8 - 40 * q^9 - 12 * q^10 - 8 * q^12 - 24 * q^13 - 4 * q^14 - 28 * q^16 - 12 * q^18 - 44 * q^20 - 32 * q^21 - 40 * q^22 + 8 * q^24 - 40 * q^25 + 4 * q^26 - 48 * q^29 - 44 * q^30 + 108 * q^32 - 72 * q^33 + 12 * q^34 - 20 * q^36 - 24 * q^37 + 56 * q^38 + 8 * q^41 - 112 * q^42 - 40 * q^45 - 48 * q^46 - 68 * q^48 - 16 * q^49 - 60 * q^50 - 124 * q^52 - 64 * q^53 + 64 * q^54 - 84 * q^56 - 24 * q^57 + 40 * q^60 - 8 * q^61 - 44 * q^62 - 20 * q^64 + 64 * q^65 + 60 * q^66 - 28 * q^68 - 8 * q^69 + 128 * q^70 + 160 * q^72 - 32 * q^73 + 80 * q^74 + 288 * q^76 - 32 * q^77 + 116 * q^78 + 176 * q^80 + 212 * q^82 + 152 * q^84 - 56 * q^85 + 180 * q^86 + 144 * q^88 - 72 * q^89 + 224 * q^90 + 36 * q^92 - 8 * q^93 + 52 * q^94 + 136 * q^96 - 88 * q^97 + 104 * q^98

Introduction

L-functions

Modular forms

Varieties

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