LMFDB - Embedded newform 175.2.x.a.108.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [175,2,Mod(3,175)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("175.3"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(175, base_ring=CyclotomicField(60)) chi = DirichletCharacter(H, H._module([21, 10])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	175.x (of order $60$, degree $16$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.39738203537$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$18$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			108.11
Character	$\chi$	$=$	175.108
Dual form			175.2.x.a.47.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0218036 + 0.416038i) q^{2} +(-0.968728 - 0.784461i) q^{3} +(1.81643 - 0.190915i) q^{4} +(-1.17429 + 1.90291i) q^{5} +(0.305244 - 0.420132i) q^{6} +(2.40197 + 1.10931i) q^{7} +(0.249376 + 1.57450i) q^{8} +(-0.300679 - 1.41458i) q^{9} +(-0.817285 - 0.447058i) q^{10} +(4.07495 + 0.866158i) q^{11} +(-1.90939 - 1.23997i) q^{12} +(-0.207137 - 0.406529i) q^{13} +(-0.409142 + 1.02350i) q^{14} +(2.63032 - 0.922217i) q^{15} +(2.92344 - 0.621395i) q^{16} +(1.05776 + 0.406038i) q^{17} +(0.581965 - 0.155937i) q^{18} +(-0.0282868 + 0.269131i) q^{19} +(-1.76972 + 3.68069i) q^{20} +(-1.45664 - 2.95886i) q^{21} +(-0.271506 + 1.71422i) q^{22} +(-8.97950 + 0.470596i) q^{23} +(0.993556 - 1.72089i) q^{24} +(-2.24210 - 4.46911i) q^{25} +(0.164615 - 0.0950407i) q^{26} +(-2.51613 + 4.93819i) q^{27} +(4.57479 + 1.55641i) q^{28} +(1.26059 + 1.73505i) q^{29} +(0.441028 + 1.07420i) q^{30} +(-2.76313 - 6.20610i) q^{31} +(1.14745 + 4.28233i) q^{32} +(-3.26806 - 4.03571i) q^{33} +(-0.145864 + 0.448923i) q^{34} +(-4.93150 + 3.26807i) q^{35} +(-0.816228 - 2.51209i) q^{36} +(0.997003 - 1.53525i) q^{37} +(-0.112586 - 0.00590036i) q^{38} +(-0.118247 + 0.556307i) q^{39} +(-3.28897 - 1.37438i) q^{40} +(-6.60977 - 2.14764i) q^{41} +(1.19924 - 0.670533i) q^{42} +(-6.90254 - 6.90254i) q^{43} +(7.56724 + 0.795349i) q^{44} +(3.04490 + 1.08896i) q^{45} +(-0.391571 - 3.72555i) q^{46} +(0.00617944 + 0.0160980i) q^{47} +(-3.31947 - 1.69136i) q^{48} +(4.53888 + 5.32903i) q^{49} +(1.81043 - 1.03024i) q^{50} +(-0.706165 - 1.22311i) q^{51} +(-0.453863 - 0.698887i) q^{52} +(4.26257 - 5.26384i) q^{53} +(-2.10934 - 0.939137i) q^{54} +(-6.43338 + 6.73714i) q^{55} +(-1.14761 + 4.05853i) q^{56} +(0.238525 - 0.238525i) q^{57} +(-0.694362 + 0.562283i) q^{58} +(-7.19184 - 7.98735i) q^{59} +(4.60173 - 2.17731i) q^{60} +(8.00447 + 7.20725i) q^{61} +(2.52173 - 1.28488i) q^{62} +(0.846987 - 3.73133i) q^{63} +(3.92834 - 1.27640i) q^{64} +(1.01683 + 0.0832196i) q^{65} +(1.60775 - 1.44763i) q^{66} +(-0.673817 + 1.75535i) q^{67} +(1.99887 + 0.535597i) q^{68} +(9.06786 + 6.58819i) q^{69} +(-1.46717 - 1.98044i) q^{70} +(-7.24631 + 5.26475i) q^{71} +(2.15228 - 0.826184i) q^{72} +(4.36826 - 2.83678i) q^{73} +(0.660461 + 0.381317i) q^{74} +(-1.33386 + 6.08820i) q^{75} +0.494259i q^{76} +(8.82706 + 6.60086i) q^{77} +(-0.234023 - 0.0370656i) q^{78} +(-6.01516 + 13.5103i) q^{79} +(-2.25049 + 6.29272i) q^{80} +(2.34780 - 1.04531i) q^{81} +(0.749384 - 2.79674i) q^{82} +(13.2680 - 2.10145i) q^{83} +(-3.21079 - 5.09648i) q^{84} +(-2.01477 + 1.53602i) q^{85} +(2.72122 - 3.02222i) q^{86} +(0.139912 - 2.66968i) q^{87} +(-0.347569 + 6.63202i) q^{88} +(2.73357 - 3.03594i) q^{89} +(-0.386660 + 1.29054i) q^{90} +(-0.0465702 - 1.20625i) q^{91} +(-16.2208 + 2.56912i) q^{92} +(-2.19171 + 8.17959i) q^{93} +(-0.00656264 + 0.00292188i) q^{94} +(-0.478915 - 0.369864i) q^{95} +(2.24775 - 5.04854i) q^{96} +(-8.19248 - 1.29756i) q^{97} +(-2.11812 + 2.00454i) q^{98} -6.02480i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22}+ \cdots + 222 q^{98}+O(q^{100}) $ 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9 - 36 * q^10 - 6 * q^11 - 36 * q^12 - 20 * q^14 - 28 * q^15 - 30 * q^16 - 42 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 + 32 * q^22 - 40 * q^23 + 2 * q^25 - 48 * q^26 + 22 * q^28 - 58 * q^30 - 18 * q^31 + 8 * q^32 - 30 * q^33 - 2 * q^35 + 40 * q^36 - 10 * q^37 + 72 * q^38 + 30 * q^39 - 48 * q^40 + 6 * q^42 - 108 * q^43 - 10 * q^44 + 186 * q^45 - 6 * q^46 - 54 * q^47 - 248 * q^50 - 16 * q^51 + 216 * q^52 + 50 * q^53 - 30 * q^54 + 4 * q^56 - 216 * q^57 - 4 * q^58 + 90 * q^59 + 96 * q^60 - 18 * q^61 - 66 * q^63 - 100 * q^64 + 14 * q^65 - 90 * q^66 + 4 * q^67 + 342 * q^68 - 60 * q^70 - 24 * q^71 + 58 * q^72 - 6 * q^73 + 216 * q^75 - 80 * q^77 - 132 * q^78 - 10 * q^79 - 6 * q^80 - 10 * q^81 + 216 * q^82 + 20 * q^84 - 48 * q^85 - 6 * q^86 - 48 * q^87 - 122 * q^88 + 120 * q^89 - 12 * q^91 - 4 * q^92 + 106 * q^93 - 30 * q^94 - 98 * q^95 - 90 * q^96 + 222 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{20}\right)$

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 $

$2$	0.0218036	+	0.416038i	0.0154175	+	0.294183i	0.995446	+	0.0953265i	$0.0303895\pi$
$2$	0.0218036	+	0.416038i	0.0154175	+	0.294183i	−0.980029	+	0.198857i	$0.936277\pi$
$3$	−0.968728	−	0.784461i	−0.559296	−	0.452909i	0.307517	−	0.951543i	$-0.400502\pi$
$3$	−0.968728	−	0.784461i	−0.559296	−	0.452909i	−0.866813	+	0.498634i	$0.833835\pi$
$4$	1.81643	−	0.190915i	0.908216	−	0.0954573i
$5$	−1.17429	+	1.90291i	−0.525157	+	0.851005i
$5$	−1.17429	+	1.90291i	−0.525157	+	0.851005i
$6$	0.305244	−	0.420132i	0.124615	−	0.171518i
$7$	2.40197	+	1.10931i	0.907858	+	0.419279i
$7$	2.40197	+	1.10931i	0.907858	+	0.419279i
$8$	0.249376	+	1.57450i	0.0881679	+	0.556670i
$9$	−0.300679	−	1.41458i	−0.100226	−	0.471528i
$10$	−0.817285	−	0.447058i	−0.258448	−	0.141372i
$11$	4.07495	+	0.866158i	1.22864	+	0.261157i	0.776114	−	0.630592i	$-0.217188\pi$
$11$	4.07495	+	0.866158i	1.22864	+	0.261157i	0.452531	+	0.891749i	$0.350521\pi$
$12$	−1.90939	−	1.23997i	−0.551194	−	0.357950i
$13$	−0.207137	−	0.406529i	−0.0574495	−	0.112751i	0.860497	−	0.509456i	$-0.170153\pi$
$13$	−0.207137	−	0.406529i	−0.0574495	−	0.112751i	−0.917946	+	0.396705i	$0.870153\pi$
$14$	−0.409142	+	1.02350i	−0.109348	+	0.273541i
$15$	2.63032	−	0.922217i	0.679146	−	0.238115i
$16$	2.92344	−	0.621395i	0.730859	−	0.155349i
$17$	1.05776	+	0.406038i	0.256545	+	0.0984786i	0.483242	−	0.875487i	$-0.339459\pi$
$17$	1.05776	+	0.406038i	0.256545	+	0.0984786i	−0.226696	+	0.973965i	$0.572793\pi$
$18$	0.581965	−	0.155937i	0.137170	−	0.0367547i
$19$	−0.0282868	+	0.269131i	−0.00648944	+	0.0617429i	−0.997287	−	0.0736066i	$-0.976549\pi$
$19$	−0.0282868	+	0.269131i	−0.00648944	+	0.0617429i	0.990798	+	0.135350i	$0.0432157\pi$
$20$	−1.76972	+	3.68069i	−0.395721	+	0.823027i
$21$	−1.45664	−	2.95886i	−0.317866	−	0.645677i
$22$	−0.271506	+	1.71422i	−0.0578853	+	0.365473i
$23$	−8.97950	+	0.470596i	−1.87236	+	0.0981260i	−0.954395	−	0.298546i	$-0.903498\pi$
$23$	−8.97950	+	0.470596i	−1.87236	+	0.0981260i	−0.917961	+	0.396672i	$0.870165\pi$
$24$	0.993556	−	1.72089i	0.202809	−	0.351275i
$25$	−2.24210	−	4.46911i	−0.448420	−	0.893823i
$26$	0.164615	−	0.0950407i	0.0322837	−	0.0186390i
$27$	−2.51613	+	4.93819i	−0.484230	+	0.950356i
$28$	4.57479	+	1.55641i	0.864554	+	0.294134i
$29$	1.26059	+	1.73505i	0.234085	+	0.322191i	0.909858	−	0.414919i	$-0.136190\pi$
$29$	1.26059	+	1.73505i	0.234085	+	0.322191i	−0.675773	+	0.737110i	$0.736190\pi$
$30$	0.441028	+	1.07420i	0.0805203	+	0.196122i
$31$	−2.76313	−	6.20610i	−0.496273	−	1.11465i	−0.971984	−	0.235046i	$-0.924476\pi$
$31$	−2.76313	−	6.20610i	−0.496273	−	1.11465i	0.475711	−	0.879602i	$-0.342191\pi$
$32$	1.14745	+	4.28233i	0.202842	+	0.757016i
$33$	−3.26806	−	4.03571i	−0.568896	−	0.702528i
$34$	−0.145864	+	0.448923i	−0.0250155	+	0.0769897i
$35$	−4.93150	+	3.26807i	−0.833576	+	0.552405i
$36$	−0.816228	−	2.51209i	−0.136038	−	0.418682i
$37$	0.997003	−	1.53525i	0.163906	−	0.252394i	−0.747168	−	0.664635i	$-0.768587\pi$
$37$	0.997003	−	1.53525i	0.163906	−	0.252394i	0.911075	+	0.412241i	$0.135254\pi$
$38$	−0.112586	−	0.00590036i	−0.0182638	−	0.000957164i
$39$	−0.118247	+	0.556307i	−0.0189346	+	0.0890804i
$40$	−3.28897	−	1.37438i	−0.520031	−	0.217308i
$41$	−6.60977	−	2.14764i	−1.03227	−	0.335406i	−0.256584	−	0.966522i	$-0.582597\pi$
$41$	−6.60977	−	2.14764i	−1.03227	−	0.335406i	−0.775688	+	0.631116i	$0.782597\pi$
$42$	1.19924	−	0.670533i	0.185047	−	0.103466i
$43$	−6.90254	−	6.90254i	−1.05263	−	1.05263i	−0.998536	−	0.0540922i	$-0.982774\pi$
$43$	−6.90254	−	6.90254i	−1.05263	−	1.05263i	−0.0540922	−	0.998536i	$-0.517226\pi$
$44$	7.56724	+	0.795349i	1.14080	+	0.119903i
$45$	3.04490	+	1.08896i	0.453908	+	0.162333i
$46$	−0.391571	−	3.72555i	−0.0577341	−	0.549303i
$47$	0.00617944	+	0.0160980i	0.000901364	+	0.00234813i	0.934030	−	0.357194i	$-0.116266\pi$
$47$	0.00617944	+	0.0160980i	0.000901364	+	0.00234813i	−0.933129	+	0.359542i	$0.882933\pi$
$48$	−3.31947	−	1.69136i	−0.479125	−	0.244126i
$49$	4.53888	+	5.32903i	0.648411	+	0.761291i
$50$	1.81043	−	1.03024i	0.256034	−	0.145698i
$51$	−0.706165	−	1.22311i	−0.0988829	−	0.171270i
$52$	−0.453863	−	0.698887i	−0.0629394	−	0.0969182i
$53$	4.26257	−	5.26384i	0.585510	−	0.723044i	−0.395182	−	0.918603i	$-0.629319\pi$
$53$	4.26257	−	5.26384i	0.585510	−	0.723044i	0.980692	+	0.195558i	$0.0626519\pi$
$54$	−2.10934	−	0.939137i	−0.287044	−	0.127800i
$55$	−6.43338	+	6.73714i	−0.867477	+	0.908435i
$56$	−1.14761	+	4.05853i	−0.153356	+	0.542344i
$57$	0.238525	−	0.238525i	0.0315934	−	0.0315934i
$58$	−0.694362	+	0.562283i	−0.0911742	+	0.0738314i
$59$	−7.19184	−	7.98735i	−0.936298	−	1.03986i	−0.999124	−	0.0418399i	$-0.986678\pi$
$59$	−7.19184	−	7.98735i	−0.936298	−	1.03986i	0.0628262	−	0.998024i	$-0.479989\pi$
$60$	4.60173	−	2.17731i	0.594081	−	0.281090i
$61$	8.00447	+	7.20725i	1.02487	+	0.922794i	0.997045	−	0.0768188i	$-0.0244763\pi$
$61$	8.00447	+	7.20725i	1.02487	+	0.922794i	0.0278217	+	0.999613i	$0.491143\pi$
$62$	2.52173	−	1.28488i	0.320259	−	0.163180i
$63$	0.846987	−	3.73133i	0.106710	−	0.470103i
$64$	3.92834	−	1.27640i	0.491043	−	0.159549i
$65$	1.01683	+	0.0832196i	0.126122	+	0.0103221i
$66$	1.60775	−	1.44763i	0.197901	−	0.178191i
$67$	−0.673817	+	1.75535i	−0.0823199	+	0.214451i	−0.968562	−	0.248771i	$-0.919973\pi$
$67$	−0.673817	+	1.75535i	−0.0823199	+	0.214451i	0.886242	+	0.463222i	$0.153307\pi$
$68$	1.99887	+	0.535597i	0.242399	+	0.0649507i
$69$	9.06786	+	6.58819i	1.09164	+	0.793125i
$70$	−1.46717	−	1.98044i	−0.175360	−	0.236707i
$71$	−7.24631	+	5.26475i	−0.859979	+	0.624811i	−0.927879	−	0.372881i	$-0.878370\pi$
$71$	−7.24631	+	5.26475i	−0.859979	+	0.624811i	0.0679005	+	0.997692i	$0.478370\pi$
$72$	2.15228	−	0.826184i	0.253649	−	0.0973667i
$73$	4.36826	−	2.83678i	0.511267	−	0.332020i	−0.263088	−	0.964772i	$-0.584741\pi$
$73$	4.36826	−	2.83678i	0.511267	−	0.332020i	0.774355	+	0.632751i	$0.218074\pi$
$74$	0.660461	+	0.381317i	0.0767770	+	0.0443272i
$75$	−1.33386	+	6.08820i	−0.154020	+	0.703005i
$76$			0.494259i			0.0566954i
$77$	8.82706	+	6.60086i	1.00594	+	0.752237i
$78$	−0.234023	−	0.0370656i	−0.0264979	−	0.00419685i
$79$	−6.01516	+	13.5103i	−0.676758	+	1.52002i	0.168521	+	0.985698i	$0.446101\pi$
$79$	−6.01516	+	13.5103i	−0.676758	+	1.52002i	−0.845279	+	0.534326i	$0.820566\pi$
$80$	−2.25049	+	6.29272i	−0.251613	+	0.703547i
$81$	2.34780	−	1.04531i	0.260866	−	0.116145i
$82$	0.749384	−	2.79674i	0.0827557	−	0.308848i
$83$	13.2680	−	2.10145i	1.45635	−	0.230664i	0.622487	−	0.782630i	$-0.286122\pi$
$83$	13.2680	−	2.10145i	1.45635	−	0.230664i	0.833866	+	0.551967i	$0.186122\pi$
$84$	−3.21079	−	5.09648i	−0.350325	−	0.556072i
$85$	−2.01477	+	1.53602i	−0.218532	+	0.166605i
$86$	2.72122	−	3.02222i	0.293437	−	0.325894i
$87$	0.139912	−	2.66968i	0.0150001	−	0.286219i
$88$	−0.347569	+	6.63202i	−0.0370510	+	0.706976i
$89$	2.73357	−	3.03594i	0.289758	−	0.321809i	−0.580637	−	0.814162i	$-0.697197\pi$
$89$	2.73357	−	3.03594i	0.289758	−	0.321809i	0.870395	+	0.492353i	$0.163863\pi$
$90$	−0.386660	+	1.29054i	−0.0407575	+	0.136035i
$91$	−0.0465702	−	1.20625i	−0.00488189	−	0.126449i
$92$	−16.2208	+	2.56912i	−1.69114	+	0.267850i
$93$	−2.19171	+	8.17959i	−0.227270	+	0.848184i
$94$	−0.00656264	+	0.00292188i	−0.000676885	+	0.000301369i
$95$	−0.478915	−	0.369864i	−0.0491356	−	0.0379473i
$96$	2.24775	−	5.04854i	0.229411	−	0.515264i
$97$	−8.19248	−	1.29756i	−0.831820	−	0.131747i	−0.274022	−	0.961724i	$-0.588354\pi$
$97$	−8.19248	−	1.29756i	−0.831820	−	0.131747i	−0.557799	+	0.829976i	$0.688354\pi$
$98$	−2.11812	+	2.00454i	−0.213962	+	0.202489i
$99$		−	6.02480i		−	0.605515i
$100$	−4.92584	−	7.68979i	−0.492584	−	0.768979i
$101$	−4.33946	−	2.50539i	−0.431793	−	0.249296i	0.268317	−	0.963331i	$-0.413532\pi$
$101$	−4.33946	−	2.50539i	−0.431793	−	0.249296i	−0.700110	+	0.714035i	$0.746866\pi$
$102$	0.493465	−	0.320460i	0.0488603	−	0.0317303i
$103$	−4.32474	+	1.66011i	−0.426130	+	0.163576i	−0.561975	−	0.827154i	$-0.689958\pi$
$103$	−4.32474	+	1.66011i	−0.426130	+	0.163576i	0.135845	+	0.990730i	$0.456625\pi$
$104$	0.588426	−	0.427516i	0.0576999	−	0.0419214i
$105$	7.34096	+	0.702698i	0.716404	+	0.0685763i
$106$	2.28290	+	1.65862i	0.221735	+	0.161100i
$107$	7.29067	+	1.95353i	0.704816	+	0.188855i	0.593387	−	0.804918i	$-0.297791\pi$
$107$	7.29067	+	1.95353i	0.704816	+	0.188855i	0.111429	+	0.993772i	$0.464457\pi$
$108$	−3.62761	+	9.45026i	−0.349067	+	0.909351i
$109$	11.4498	−	10.3094i	1.09669	−	0.987466i	0.0967224	−	0.995311i	$-0.469164\pi$
$109$	11.4498	−	10.3094i	1.09669	−	0.987466i	0.999969	+	0.00784584i	$0.00249743\pi$
$110$	−2.94318	−	2.52964i	−0.280621	−	0.241191i
$111$	−2.17017	+	0.705131i	−0.205983	+	0.0669280i
$112$	7.71131	+	1.75042i	0.728650	+	0.165399i
$113$	2.97293	−	1.51479i	0.279670	−	0.142499i	−0.308530	−	0.951215i	$-0.599837\pi$
$113$	2.97293	−	1.51479i	0.279670	−	0.142499i	0.588200	+	0.808716i	$0.299837\pi$
$114$	0.104436	+	0.0940348i	0.00978135	+	0.00880716i
$115$	9.64901	−	17.6398i	0.899775	−	1.64492i
$116$	2.62102	+	2.91094i	0.243356	+	0.270274i
$117$	−0.512788	+	0.415248i	−0.0474073	+	0.0383897i
$118$	3.16623	−	3.16623i	0.291475	−	0.291475i
$119$	2.09029	+	2.14867i	0.191617	+	0.196969i
$120$	2.10797	+	3.91146i	0.192431	+	0.357066i
$121$	5.80602	+	2.58501i	0.527820	+	0.235001i
$122$	−2.82396	+	3.48731i	−0.255670	+	0.315726i
$123$	4.71833	+	7.26559i	0.425437	+	0.655116i
$124$	−6.20388	−	10.7454i	−0.557125	−	0.964968i
$125$	11.1372	+	0.981511i	0.996139	+	0.0877890i
$126$	1.57084	+	0.271022i	0.139942	+	0.0241446i
$127$	1.22792	+	0.625655i	0.108960	+	0.0555179i	0.507621	−	0.861580i	$-0.330525\pi$
$127$	1.22792	+	0.625655i	0.108960	+	0.0555179i	−0.398661	+	0.917098i	$0.630525\pi$
$128$	3.79425	+	9.88437i	0.335368	+	0.873663i
$129$	1.27192	+	12.1015i	0.111986	+	1.06547i
$130$	−0.0124520	+	0.424852i	−0.00109212	+	0.0372620i
$131$	3.81824	+	0.401313i	0.333601	+	0.0350629i	0.269848	−	0.962903i	$-0.413026\pi$
$131$	3.81824	+	0.401313i	0.333601	+	0.0350629i	0.0637526	+	0.997966i	$0.479693\pi$
$132$	−6.70668	−	6.70668i	−0.583741	−	0.583741i
$133$	−0.366493	+	0.615065i	−0.0317790	+	0.0533329i
$134$	−0.744985	−	0.242060i	−0.0643569	−	0.0209108i
$135$	−6.44225	−	10.5868i	−0.554461	−	0.911168i
$136$	−0.375525	+	1.76671i	−0.0322010	+	0.151494i
$137$	−3.14349	−	0.164743i	−0.268567	−	0.0140750i	−0.0824226	−	0.996597i	$-0.526266\pi$
$137$	−3.14349	−	0.164743i	−0.268567	−	0.0140750i	−0.186144	+	0.982522i	$0.559599\pi$
$138$	−2.54322	+	3.91622i	−0.216494	+	0.333371i
$139$	−2.03657	−	6.26792i	−0.172740	−	0.531638i	0.826783	−	0.562520i	$-0.190168\pi$
$139$	−2.03657	−	6.26792i	−0.172740	−	0.531638i	−0.999523	+	0.0308825i	$0.990168\pi$
$140$	−8.33381	+	6.87772i	−0.704336	+	0.581274i
$141$	0.00664205	−	0.0204421i	0.000559361	−	0.00172154i
$142$	−2.34833	−	2.89995i	−0.197068	−	0.243358i
$143$	−0.491955	−	1.83600i	−0.0411394	−	0.153534i
$144$	−1.75803	−	3.94861i	−0.146503	−	0.329050i
$145$	−4.78193	+	0.361334i	−0.397118	+	0.0300072i
$146$	1.27545	+	1.75551i	0.105557	+	0.145287i
$147$	−0.216520	−	8.72296i	−0.0178583	−	0.719457i
$148$	1.51789	−	2.97902i	0.124770	−	0.244874i
$149$	−13.4928	+	7.79005i	−1.10537	+	0.638186i	−0.937626	−	0.347645i	$-0.886982\pi$
$149$	−13.4928	+	7.79005i	−1.10537	+	0.638186i	−0.167744	+	0.985831i	$0.553648\pi$
$150$	−2.56200	−	0.422190i	−0.209187	−	0.0344717i
$151$	−8.07317	+	13.9831i	−0.656985	+	1.13793i	0.324407	+	0.945918i	$0.394835\pi$
$151$	−8.07317	+	13.9831i	−0.656985	+	1.13793i	−0.981392	+	0.192014i	$0.938498\pi$
$152$	−0.430801	+	0.0225773i	−0.0349426	+	0.00183126i
$153$	0.256327	−	1.61838i	0.0207228	−	0.130839i
$154$	−2.55374	+	3.81632i	−0.205787	+	0.307528i
$155$	15.0543	+	2.02976i	1.20919	+	0.163034i
$156$	−0.108580	+	1.03307i	−0.00869335	+	0.0827117i
$157$	11.9442	−	3.20043i	0.953248	−	0.255422i	0.251508	−	0.967855i	$-0.419073\pi$
$157$	11.9442	−	3.20043i	0.953248	−	0.255422i	0.701740	+	0.712433i	$0.252407\pi$
$158$	−5.75194	−	2.20796i	−0.457599	−	0.175656i
$159$	−8.25855	+	1.75541i	−0.654946	+	0.139213i
$160$	−9.49630	−	2.84520i	−0.750749	−	0.224933i
$161$	−22.0905	−	8.83067i	−1.74097	−	0.695954i
$162$	0.486077	+	0.953980i	0.0381898	+	0.0749518i
$163$	−4.64205	−	3.01458i	−0.363594	−	0.236120i	0.349892	−	0.936790i	$-0.386218\pi$
$163$	−4.64205	−	3.01458i	−0.363594	−	0.236120i	−0.713486	+	0.700669i	$0.752885\pi$
$164$	−12.4162	−	2.63915i	−0.969543	−	0.206083i
$165$	11.5172	−	1.47972i	0.896614	−	0.115196i
$166$	1.16357	+	5.47417i	0.0903107	+	0.424878i
$167$	−3.45892	−	21.8387i	−0.267659	−	1.68993i	−0.645260	−	0.763963i	$-0.723251\pi$
$167$	−3.45892	−	21.8387i	−0.267659	−	1.68993i	0.377601	−	0.925968i	$-0.376749\pi$
$168$	4.29548	−	3.03136i	0.331404	−	0.233874i
$169$	7.51885	−	10.3488i	0.578373	−	0.796062i
$170$	−0.682972	−	0.804730i	−0.0523816	−	0.0617199i
$171$	0.389214	−	0.0409080i	0.0297639	−	0.00312832i
$172$	−13.8558	−	11.2202i	−1.05649	−	0.855532i
$173$	0.201439	+	3.84369i	0.0153152	+	0.292231i	0.995540	+	0.0943426i	$0.0300749\pi$
$173$	0.201439	+	3.84369i	0.0153152	+	0.292231i	−0.980225	+	0.197888i	$0.936592\pi$
$174$	1.11374			0.0844322
$175$	−0.427833	−	13.2218i	−0.0323411	−	0.999477i
$176$	12.4511			0.938536
$177$	0.701179	+	13.3793i	0.0527038	+	1.00565i
$178$	1.32267	+	1.07108i	0.0991382	+	0.0802805i
$179$	−22.2457	+	2.33811i	−1.66272	+	0.174759i	−0.888727	−	0.458437i	$-0.848409\pi$
$179$	−22.2457	+	2.33811i	−1.66272	+	0.174759i	−0.773992	+	0.633196i	$0.781743\pi$
$180$	5.73876	+	1.39671i	0.427742	+	0.104105i
$181$	−12.0280	+	16.5551i	−0.894031	+	1.23053i	0.0783022	+	0.996930i	$0.475050\pi$
$181$	−12.0280	+	16.5551i	−0.894031	+	1.23053i	−0.972333	+	0.233598i	$0.924950\pi$
$182$	0.500829	−	0.0456756i	0.0371239	−	0.00338570i
$183$	−2.10035	−	13.2611i	−0.155262	−	0.980286i
$184$	−2.98023	−	14.0209i	−0.219706	−	1.03363i
$185$	1.75067	+	3.70003i	0.128712	+	0.272031i
$186$	−3.45081	−	0.733492i	−0.253025	−	0.0537822i
$187$	3.95865	+	2.57078i	0.289485	+	0.187994i
$188$	0.0142979	+	0.0280612i	0.00104278	+	0.00204657i
$189$	−11.5216	+	9.07020i	−0.838076	+	0.659760i
$190$	0.143436	−	0.207311i	0.0104059	−	0.0150399i
$191$	4.94671	−	1.05145i	0.357931	−	0.0760806i	−0.0254365	−	0.999676i	$-0.508098\pi$
$191$	4.94671	−	1.05145i	0.357931	−	0.0760806i	0.383368	+	0.923596i	$0.374764\pi$
$192$	−4.80678	−	1.84515i	−0.346899	−	0.133162i
$193$	−9.13540	+	2.44782i	−0.657581	+	0.176198i	−0.572154	−	0.820146i	$-0.693892\pi$
$193$	−9.13540	+	2.44782i	−0.657581	+	0.176198i	−0.0854268	+	0.996344i	$0.527225\pi$
$194$	0.361209	−	3.43667i	0.0259333	−	0.246739i
$195$	−0.919745	−	0.878277i	−0.0658643	−	0.0628947i
$196$	9.26195	+	8.81329i	0.661568	+	0.629521i
$197$	−2.31321	+	14.6050i	−0.164809	+	1.04056i	0.757140	+	0.653253i	$0.226596\pi$
$197$	−2.31321	+	14.6050i	−0.164809	+	1.04056i	−0.921949	+	0.387311i	$0.873404\pi$
$198$	2.50655	−	0.131363i	0.178132	−	0.00933553i
$199$	−9.48990	+	16.4370i	−0.672721	+	1.16519i	0.304408	+	0.952542i	$0.401541\pi$
$199$	−9.48990	+	16.4370i	−0.672721	+	1.16519i	−0.977129	+	0.212645i	$0.931792\pi$
$200$	6.47750	−	4.64468i	0.458028	−	0.328429i
$201$	2.02975	−	1.17188i	0.143168	−	0.0826579i
$202$	0.947721	−	1.86001i	0.0666814	−	0.130870i
$203$	1.10319	+	5.56591i	0.0774285	+	0.390650i
$204$	−1.51621	−	2.08689i	−0.106156	−	0.146111i
$205$	11.8485	−	10.0558i	0.827537	−	0.702329i
$206$	−0.784965	−	1.76306i	−0.0546911	−	0.122838i
$207$	3.36565	+	12.5608i	0.233929	+	0.873034i
$208$	−0.858167	−	1.05975i	−0.0595032	−	0.0734803i
$209$	−0.348378	+	1.07220i	−0.0240978	+	0.0741654i
$210$	−0.132289	+	3.06944i	−0.00912884	+	0.211811i
$211$	5.14512	+	15.8351i	0.354205	+	1.09013i	0.956469	+	0.291834i	$0.0942654\pi$
$211$	5.14512	+	15.8351i	0.354205	+	1.09013i	−0.602264	+	0.798297i	$0.705735\pi$
$212$	6.73773	−	10.3752i	0.462749	−	0.712571i
$213$	11.1497	+	0.584331i	0.763965	+	0.0400377i
$214$	−0.653779	+	3.07579i	−0.0446914	+	0.210257i
$215$	21.2405	−	5.02933i	1.44859	−	0.342997i
$216$	−8.40265	−	2.73019i	−0.571728	−	0.185766i
$217$	0.247518	−	17.9720i	0.0168026	−	1.22002i
$218$	4.53877	+	4.53877i	0.307404	+	0.307404i
$219$	−6.45701	−	0.678659i	−0.436324	−	0.0458595i
$220$	−10.3996	+	13.4658i	−0.701140	+	0.907862i
$221$	−0.0540359	−	0.514117i	−0.00363485	−	0.0345833i
$222$	−0.340679	−	0.887498i	−0.0228649	−	0.0595650i
$223$	17.4430	+	8.88764i	1.16807	+	0.595160i	0.926895	−	0.375322i	$-0.122468\pi$
$223$	17.4430	+	8.88764i	1.16807	+	0.595160i	0.241173	+	0.970482i	$0.422468\pi$
$224$	−1.99429	+	11.5589i	−0.133249	+	0.772310i
$225$	−5.64779	+	4.51541i	−0.376519	+	0.301027i
$226$	0.695029	+	1.20383i	0.0462326	+	0.0800773i
$227$	0.135147	+	0.208109i	0.00897005	+	0.0138127i	0.843127	−	0.537714i	$-0.180712\pi$
$227$	0.135147	+	0.208109i	0.00897005	+	0.0138127i	−0.834157	+	0.551527i	$0.814045\pi$
$228$	0.387727	−	0.478802i	0.0256778	−	0.0317095i
$229$	24.3629	+	10.8470i	1.60994	+	0.716793i	0.997291	−	0.0735590i	$-0.0234357\pi$
$229$	24.3629	+	10.8470i	1.60994	+	0.716793i	0.612653	+	0.790352i	$0.290102\pi$
$230$	7.54919	+	3.62974i	0.497779	+	0.239338i
$231$	−3.37291	−	13.3189i	−0.221921	−	0.876321i
$232$	−2.41748	+	2.41748i	−0.158715	+	0.158715i
$233$	10.8149	−	8.75776i	0.708510	−	0.573740i	−0.205879	−	0.978577i	$-0.566005\pi$
$233$	10.8149	−	8.75776i	0.708510	−	0.573740i	0.914389	+	0.404838i	$0.132672\pi$
$234$	−0.183939	−	0.204285i	−0.0120245	−	0.0133546i
$235$	−0.0378894	−	0.00714477i	−0.00247163	−	0.000466073i
$236$	−14.5884	−	13.1354i	−0.949623	−	0.855045i
$237$	16.4253	−	8.36912i	1.06694	−	0.543633i
$238$	−0.848354	+	0.916490i	−0.0549906	+	0.0594072i
$239$	7.25153	−	2.35616i	0.469062	−	0.152408i	−0.0649425	−	0.997889i	$-0.520686\pi$
$239$	7.25153	−	2.35616i	0.469062	−	0.152408i	0.534005	+	0.845481i	$0.320686\pi$
$240$	7.11651	−	4.33051i	0.459369	−	0.279533i
$241$	5.00322	−	4.50492i	0.322286	−	0.290187i	−0.492067	−	0.870557i	$-0.663759\pi$
$241$	5.00322	−	4.50492i	0.322286	−	0.290187i	0.814353	+	0.580370i	$0.197092\pi$
$242$	−0.948869	+	2.47189i	−0.0609956	+	0.158899i
$243$	12.9659	+	3.47419i	0.831761	+	0.222870i
$244$	15.9155	+	11.5633i	1.01889	+	0.740265i
$245$	−15.4706	+	2.37924i	−0.988380	+	0.152004i
$246$	−2.91988	+	2.12142i	−0.186165	+	0.135257i
$247$	0.115269	−	0.0442476i	0.00733439	−	0.00281541i
$248$	9.08245	−	5.89821i	0.576736	−	0.374537i
$249$	−14.5016	−	8.37250i	−0.919001	−	0.530586i
$250$	−0.165515	+	4.65489i	−0.0104681	+	0.294401i
$251$		−	8.11241i		−	0.512051i	−0.966670	−	0.256025i	$-0.917587\pi$
$251$		−	8.11241i		−	0.512051i	0.966670	−	0.256025i	$-0.0824130\pi$
$252$	0.826129	−	6.93941i	0.0520412	−	0.437141i
$253$	−36.9987	−	5.86001i	−2.32609	−	0.368416i
$254$	−0.233523	+	0.524501i	−0.0146525	+	0.0329101i
$255$	3.15671	+	0.0925204i	0.197681	+	0.00579385i
$256$	3.51726	−	1.56598i	0.219829	−	0.0978740i
$257$	−1.82750	+	6.82034i	−0.113997	+	0.425441i	−0.999210	−	0.0397443i	$-0.987346\pi$
$257$	−1.82750	+	6.82034i	−0.113997	+	0.425441i	0.885213	+	0.465185i	$0.154012\pi$
$258$	−5.00694	+	0.793021i	−0.311718	+	0.0493713i
$259$	4.09783	−	2.58164i	0.254627	−	0.160415i
$260$	1.86288	−	0.0429641i	0.115531	−	0.00266452i
$261$	2.07534	−	2.30490i	0.128461	−	0.142670i
$262$	−0.0837100	+	1.59728i	−0.00517162	+	0.0986804i
$263$	−0.0448976	+	0.856698i	−0.00276851	+	0.0528263i	−0.999664	−	0.0259045i	$-0.991753\pi$
$263$	−0.0448976	+	0.856698i	−0.00276851	+	0.0528263i	0.996896	+	0.0787308i	$0.0250867\pi$
$264$	5.53926	−	6.15197i	0.340918	−	0.378628i
$265$	5.01111	+	14.2925i	0.307830	+	0.877984i
$266$	−0.263881	−	0.139064i	−0.0161796	−	0.00852658i
$267$	−5.02967	+	0.796621i	−0.307811	+	0.0487524i
$268$	−0.888820	+	3.31712i	−0.0542933	+	0.202625i
$269$	24.3017	−	10.8198i	1.48170	−	0.659695i	0.502867	−	0.864364i	$-0.332278\pi$
$269$	24.3017	−	10.8198i	1.48170	−	0.659695i	0.978831	+	0.204669i	$0.0656117\pi$
$270$	4.26405	−	2.91105i	0.259502	−	0.177161i
$271$	−9.34332	+	20.9854i	−0.567566	+	1.27477i	0.370665	+	0.928766i	$0.379130\pi$
$271$	−9.34332	+	20.9854i	−0.567566	+	1.27477i	−0.938232	+	0.346008i	$0.887537\pi$
$272$	3.34461	+	0.529735i	0.202797	+	0.0321199i
$273$	−0.901140	+	1.20506i	−0.0545395	+	0.0729335i
$274$		−	1.31140i		−	0.0792248i
$275$	−5.26550	−	20.1534i	−0.317522	−	1.21530i
$276$	17.7289	+	10.2358i	1.06716	+	0.616123i
$277$	6.69430	−	4.34733i	0.402222	−	0.261206i	−0.327637	−	0.944804i	$-0.606252\pi$
$277$	6.69430	−	4.34733i	0.402222	−	0.261206i	0.729859	+	0.683598i	$0.239586\pi$
$278$	2.56329	−	0.983954i	0.153736	−	0.0590136i
$279$	−7.94823	+	5.77473i	−0.475848	+	0.345724i
$280$	−6.37538	−	6.94968i	−0.381002	−	0.415323i
$281$	3.83031	+	2.78288i	0.228497	+	0.166013i	0.696143	−	0.717903i	$-0.254898\pi$
$281$	3.83031	+	2.78288i	0.228497	+	0.166013i	−0.467646	+	0.883916i	$0.654898\pi$
$282$	0.00864952	+	0.00231763i	0.000515071	+	0.000138013i
$283$	−10.6888	+	27.8452i	−0.635382	+	1.65523i	0.114314	+	0.993445i	$0.463533\pi$
$283$	−10.6888	+	27.8452i	−0.635382	+	1.65523i	−0.749696	+	0.661782i	$0.769800\pi$
$284$	−12.1573	+	10.9465i	−0.721403	+	0.649555i
$285$	0.173794	+	0.733988i	0.0102947	+	0.0434777i
$286$	0.753120	−	0.244703i	0.0445329	−	0.0144696i
$287$	−13.4940	−	12.4908i	−0.796528	−	0.737310i
$288$	5.71270	−	2.91077i	0.336624	−	0.171519i
$289$	−11.6795	−	10.5162i	−0.687027	−	0.618602i
$290$	−0.254592	−	1.98159i	−0.0149502	−	0.116363i
$291$	6.91840	+	7.68366i	0.405564	+	0.450424i
$292$	7.39307	−	5.98679i	0.432647	−	0.350350i
$293$	18.8350	−	18.8350i	1.10035	−	1.10035i	0.105985	−	0.994368i	$-0.466200\pi$
$293$	18.8350	−	18.8350i	1.10035	−	1.10035i	0.994368	−	0.105985i	$-0.0337997\pi$
$294$	3.62436	−	0.280273i	0.211377	−	0.0163458i
$295$	23.6445	−	4.30596i	1.37663	−	0.250703i
$296$	2.66588	+	1.18693i	0.154951	+	0.0689888i
$297$	−14.5304	+	17.9435i	−0.843139	+	1.04119i
$298$	−3.53515	−	5.44365i	−0.204786	−	0.315342i
$299$	2.05130	+	3.55295i	0.118630	+	0.205473i
$300$	−1.26053	+	11.3134i	−0.0727769	+	0.653182i
$301$	−8.92263	−	24.2367i	−0.514292	−	1.39698i
$302$	−5.99354	−	3.05386i	−0.344890	−	0.175730i
$303$	2.23838	+	5.83118i	0.128592	+	0.334992i
$304$	0.0845422	+	0.804365i	0.00484883	+	0.0461335i
$305$	−23.1143	+	6.76836i	−1.32352	+	0.387555i
$306$	0.678898	+	0.0713550i	0.0388100	+	0.00407910i
$307$	−14.2537	−	14.2537i	−0.813499	−	0.813499i	0.171658	−	0.985157i	$-0.445088\pi$
$307$	−14.2537	−	14.2537i	−0.813499	−	0.813499i	−0.985157	+	0.171658i	$0.945088\pi$
$308$	17.2940	+	10.3048i	0.985415	+	0.587170i
$309$	5.49180	+	1.78439i	0.312417	+	0.101511i
$310$	−0.516216	+	6.30743i	−0.0293191	+	0.358238i
$311$	−3.86372	+	18.1774i	−0.219092	+	1.03074i	0.721817	+	0.692084i	$0.243307\pi$
$311$	−3.86372	+	18.1774i	−0.219092	+	1.03074i	−0.940909	+	0.338661i	$0.890026\pi$
$312$	−0.905394	−	0.0474497i	−0.0512579	−	0.00268631i
$313$	−3.55735	+	5.47784i	−0.201073	+	0.309626i	−0.924795	−	0.380466i	$-0.875763\pi$
$313$	−3.55735	+	5.47784i	−0.201073	+	0.309626i	0.723721	+	0.690092i	$0.242430\pi$
$314$	1.59193	+	4.89945i	0.0898376	+	0.276492i
$315$	6.10576	+	5.99339i	0.344021	+	0.337689i
$316$	−8.34682	+	25.6889i	−0.469545	+	1.44511i
$317$	6.91379	+	8.53782i	0.388317	+	0.479532i	0.933393	−	0.358855i	$-0.116833\pi$
$317$	6.91379	+	8.53782i	0.388317	+	0.479532i	−0.545076	+	0.838387i	$0.683499\pi$
$318$	−0.910383	−	3.39760i	−0.0510518	−	0.190528i
$319$	3.63401	+	8.16212i	0.203466	+	0.456991i
$320$	−2.18414	+	8.97412i	−0.122097	+	0.501668i
$321$	−5.53021	−	7.61168i	−0.308666	−	0.424843i
$322$	3.19224	−	9.38302i	0.177897	−	0.522895i
$323$	−0.139198	+	0.273192i	−0.00774519	+	0.0152008i
$324$	4.06505	−	2.34695i	0.225836	−	0.130386i
$325$	−1.35240	+	1.83720i	−0.0750178	+	0.101909i
$326$	1.15297	−	1.99700i	0.0638570	−	0.110604i
$327$	−19.1791	+	1.00513i	−1.06061	+	0.0555840i
$328$	1.73315	−	10.9427i	0.0956970	−	0.604207i
$329$	−0.00301481	+	0.0455217i	−0.000166212	+	0.00250969i
$330$	0.866737	+	4.75934i	0.0477123	+	0.261993i
$331$	−0.240946	+	2.29245i	−0.0132436	+	0.126004i	−0.999146	−	0.0413163i	$-0.986845\pi$
$331$	−0.240946	+	2.29245i	−0.0132436	+	0.126004i	0.985903	+	0.167321i	$0.0535115\pi$
$332$	23.6992	−	6.35019i	1.30066	−	0.348512i
$333$	−2.47152	−	0.948728i	−0.135438	−	0.0519900i
$334$	9.01032	−	1.91520i	0.493023	−	0.104795i
$335$	−2.54902	−	3.34350i	−0.139268	−	0.182675i
$336$	−6.09703	−	7.74490i	−0.332620	−	0.422519i
$337$	−7.10695	−	13.9482i	−0.387140	−	0.759806i	0.612387	−	0.790558i	$-0.290210\pi$
$337$	−7.10695	−	13.9482i	−0.387140	−	0.759806i	−0.999527	+	0.0307527i	$0.990210\pi$
$338$	4.46943	+	2.90248i	0.243105	+	0.157874i
$339$	−4.06826	−	0.864734i	−0.220957	−	0.0469659i
$340$	−3.36644	+	3.17473i	−0.182571	+	0.172174i
$341$	−5.88418	−	27.6829i	−0.318646	−	1.49911i
$342$	0.0255056	+	0.161036i	0.00137918	+	0.00870782i
$343$	4.99069	+	17.8352i	0.269472	+	0.963008i
$344$	9.14673	−	12.5894i	0.493159	−	0.678775i
$345$	−23.1850	+	9.51887i	−1.24824	+	0.512479i
$346$	−1.59473	+	0.167613i	−0.0857332	+	0.00901092i
$347$	2.82138	+	2.28471i	0.151460	+	0.122650i	0.702055	−	0.712123i	$-0.252266\pi$
$347$	2.82138	+	2.28471i	0.151460	+	0.122650i	−0.550596	+	0.834772i	$0.685599\pi$
$348$	−0.255540	−	4.87599i	−0.0136984	−	0.261381i
$349$	10.3897			0.556148			0.278074	−	0.960560i	$-0.410304\pi$
$349$	10.3897			0.556148			0.278074	+	0.960560i	$0.410304\pi$
$350$	5.49146	−	0.466279i	0.293531	−	0.0249236i
$351$	2.52870			0.134972
$352$	0.966618	+	18.4442i	0.0515209	+	0.983077i
$353$	2.77310	+	2.24561i	0.147597	+	0.119522i	0.700275	−	0.713873i	$-0.253061\pi$
$353$	2.77310	+	2.24561i	0.147597	+	0.119522i	−0.552678	+	0.833395i	$0.686394\pi$
$354$	−5.55100	+	0.583434i	−0.295032	+	0.0310092i
$355$	−1.50908	−	19.9714i	−0.0800939	−	1.05997i
$356$	4.38575	−	6.03646i	0.232444	−	0.319932i
$357$	−0.339376	−	3.72123i	−0.0179617	−	0.196949i
$358$	−1.45778	−	9.20406i	−0.0770460	−	0.486450i
$359$	−4.21953	−	19.8513i	−0.222698	−	1.04771i	−0.937392	−	0.348276i	$-0.886767\pi$
$359$	−4.21953	−	19.8513i	−0.222698	−	1.04771i	0.714694	−	0.699437i	$-0.246566\pi$
$360$	−0.955246	+	5.06577i	−0.0503459	+	0.266989i
$361$	18.5132	+	3.93510i	0.974378	+	0.207110i
$362$	−7.14979	−	4.64313i	−0.375784	−	0.244037i
$363$	−3.59662	−	7.05877i	−0.188774	−	0.370489i
$364$	−0.314882	−	2.18218i	−0.0165043	−	0.114377i
$365$	0.268539	+	11.6436i	0.0140560	+	0.609454i
$366$	5.47131	−	1.16296i	0.285990	−	0.0607890i
$367$	22.2752	+	8.55064i	1.16275	+	0.446340i	0.861775	−	0.507291i	$-0.169353\pi$
$367$	22.2752	+	8.55064i	1.16275	+	0.446340i	0.300980	+	0.953630i	$0.402686\pi$
$368$	−25.9586	+	6.95558i	−1.35318	+	0.362585i
$369$	−1.05060	+	9.99583i	−0.0546922	+	0.520362i
$370$	−1.50118	+	0.809019i	−0.0780427	+	0.0420589i
$371$	16.0778	−	7.91506i	0.834716	−	0.410930i
$372$	−2.41950	+	15.2761i	−0.125445	+	0.792029i
$373$	−7.17306	+	0.375924i	−0.371407	+	0.0194646i	−0.237127	−	0.971479i	$-0.576206\pi$
$373$	−7.17306	+	0.375924i	−0.371407	+	0.0194646i	−0.134280	+	0.990943i	$0.542872\pi$
$374$	−0.983227	+	1.70300i	−0.0508415	+	0.0880600i
$375$	−10.0189	−	9.68749i	−0.517376	−	0.500260i
$376$	−0.0238053	+	0.0137440i	−0.00122767	+	0.000708793i
$377$	0.444235	−	0.871859i	0.0228792	−	0.0449030i
$378$	−4.02476	−	4.59568i	−0.207011	−	0.236376i
$379$	−12.3615	−	17.0141i	−0.634966	−	0.873956i	0.363368	−	0.931646i	$-0.381627\pi$
$379$	−12.3615	−	17.0141i	−0.634966	−	0.873956i	−0.998335	+	0.0576896i	$0.981627\pi$
$380$	−0.940528	−	0.580401i	−0.0482481	−	0.0297740i
$381$	−0.698716	−	1.56934i	−0.0357963	−	0.0803998i
$382$	0.545301	+	2.03509i	0.0279000	+	0.104124i
$383$	−17.4744	−	21.5791i	−0.892900	−	1.10264i	−0.994175	−	0.107781i	$-0.965626\pi$
$383$	−17.4744	−	21.5791i	−0.892900	−	1.10264i	0.101275	−	0.994858i	$-0.467708\pi$
$384$	4.07830	−	12.5517i	0.208120	−	0.640527i
$385$	−22.9263	+	9.04577i	−1.16843	+	0.461015i
$386$	−1.21757	−	3.74730i	−0.0619728	−	0.190733i
$387$	−7.68878	+	11.8397i	−0.390843	+	0.601845i
$388$	−15.1288	−	0.792867i	−0.768049	−	0.0402517i
$389$	3.20459	−	15.0764i	0.162479	−	0.764404i	−0.819146	−	0.573585i	$-0.805552\pi$
$389$	3.20459	−	15.0764i	0.162479	−	0.764404i	0.981625	−	0.190819i	$-0.0611145\pi$
$390$	0.345343	−	0.401798i	0.0174871	−	0.0203458i
$391$	−9.68928	−	3.14824i	−0.490008	−	0.159213i
$392$	−7.25868	+	8.47540i	−0.366619	+	0.428072i
$393$	−3.38402	−	3.38402i	−0.170701	−	0.170701i
$394$	−6.12668	−	0.643940i	−0.308658	−	0.0324412i
$395$	−18.6452	−	27.3112i	−0.938144	−	1.37418i
$396$	−1.15022	−	10.9436i	−0.0578009	−	0.549939i
$397$	7.78738	+	20.2868i	0.390837	+	1.01817i	0.977983	+	0.208685i	$0.0669183\pi$
$397$	7.78738	+	20.2868i	0.390837	+	1.01817i	−0.587145	+	0.809481i	$0.699748\pi$
$398$	−7.04532	−	3.58977i	−0.353150	−	0.179939i
$399$	0.837527	−	0.308332i	0.0419288	−	0.0154359i
$400$	−9.33173	−	11.6719i	−0.466586	−	0.583597i
$401$	−4.12035	−	7.13665i	−0.205760	−	0.356387i	0.744614	−	0.667495i	$-0.232633\pi$
$401$	−4.12035	−	7.13665i	−0.205760	−	0.356387i	−0.950375	+	0.311107i	$0.899300\pi$
$402$	0.531802	+	0.818903i	0.0265239	+	0.0408431i
$403$	−1.95061	+	2.40881i	−0.0971670	+	0.119991i
$404$	−8.36065	−	3.72240i	−0.415958	−	0.185196i
$405$	−0.767866	+	5.69512i	−0.0381556	+	0.282993i
$406$	−2.29158	+	0.580324i	−0.113729	+	0.0288010i
$407$	5.39251	−	5.39251i	0.267297	−	0.267297i
$408$	1.74969	−	1.41687i	0.0866228	−	0.0701457i
$409$	6.97282	+	7.74410i	0.344784	+	0.382921i	0.890450	−	0.455082i	$-0.150390\pi$
$409$	6.97282	+	7.74410i	0.344784	+	0.382921i	−0.545666	+	0.838003i	$0.683723\pi$
$410$	4.44194	+	4.71018i	0.219372	+	0.232619i
$411$	2.91595	+	2.62554i	0.143833	+	0.129508i
$412$	−7.53866	+	3.84114i	−0.371403	+	0.189239i
$413$	−8.41413	−	27.1633i	−0.414032	−	1.33662i
$414$	−5.15237	+	1.67411i	−0.253225	+	0.0822779i
$415$	−11.5816	+	27.7155i	−0.568518	+	1.36050i
$416$	1.50321	−	1.35350i	0.0737011	−	0.0663608i
$417$	−2.94405	+	7.66952i	−0.144171	+	0.375578i
$418$	−0.453670	−	0.121561i	−0.0221897	−	0.00594572i
$419$	22.9552	+	16.6779i	1.12143	+	0.814769i	0.984426	−	0.175801i	$-0.0562515\pi$
$419$	22.9552	+	16.6779i	1.12143	+	0.814769i	0.137008	+	0.990570i	$0.456251\pi$
$420$	13.4685	−	0.125094i	0.657196	−	0.00610396i
$421$	−1.40395	+	1.02003i	−0.0684242	+	0.0497131i	−0.621472	−	0.783437i	$-0.713465\pi$
$421$	−1.40395	+	1.02003i	−0.0684242	+	0.0497131i	0.553047	+	0.833150i	$0.313465\pi$
$422$	−6.47580	+	2.48583i	−0.315237	+	0.121008i
$423$	0.0209140	−	0.0135817i	0.00101687	−	0.000660364i
$424$	9.35091	+	5.39875i	0.454120	+	0.262187i
$425$	−0.556987	−	5.63765i	−0.0270178	−	0.273466i
$426$			4.65144i			0.225363i
$427$	11.2314	+	26.1910i	0.543525	+	1.26747i
$428$	13.6160	+	2.15656i	0.658152	+	0.104241i
$429$	−0.963700	+	2.16451i	−0.0465279	+	0.104503i
$430$	2.55551	+	8.72718i	0.123238	+	0.420862i
$431$	11.3650	−	5.06003i	0.547434	−	0.243733i	−0.114334	−	0.993442i	$-0.536473\pi$
$431$	11.3650	−	5.06003i	0.547434	−	0.243733i	0.661767	+	0.749709i	$0.269807\pi$
$432$	−4.28719	+	16.0000i	−0.206267	+	0.769800i
$433$	−19.2299	+	3.04572i	−0.924130	+	0.146368i	−0.600325	−	0.799756i	$-0.704962\pi$
$433$	−19.2299	+	3.04572i	−0.924130	+	0.146368i	−0.323805	+	0.946124i	$0.604962\pi$
$434$	7.48243	−	0.288878i	0.359168	−	0.0138666i
$435$	4.91584	+	3.40120i	0.235697	+	0.163075i
$436$	18.8295	−	20.9123i	0.901772	−	1.00152i
$437$	0.127350	−	2.42998i	0.00609196	−	0.116242i
$438$	0.141562	−	2.70116i	0.00676408	−	0.129066i
$439$	−4.34107	+	4.82125i	−0.207188	+	0.230106i	−0.837779	−	0.546010i	$-0.816146\pi$
$439$	−4.34107	+	4.82125i	−0.207188	+	0.230106i	0.630591	+	0.776116i	$0.282813\pi$
$440$	−12.2120	−	8.44928i	−0.582183	−	0.402804i
$441$	6.17362	−	8.02295i	0.293982	−	0.382045i
$442$	0.212714	−	0.0336906i	0.0101178	−	0.00160250i
$443$	−5.41131	+	20.1953i	−0.257099	+	0.959506i	0.709812	+	0.704391i	$0.248780\pi$
$443$	−5.41131	+	20.1953i	−0.257099	+	0.959506i	−0.966911	+	0.255115i	$0.917887\pi$
$444$	−3.80734	+	1.69514i	−0.180689	+	0.0804477i
$445$	2.56711	+	8.76680i	0.121693	+	0.415586i
$446$	−3.31727	+	7.45072i	−0.157078	+	0.352802i
$447$	19.1818	+	3.03810i	0.907269	+	0.143697i
$448$	10.8517	+	1.29188i	0.512692	+	0.0610355i
$449$			10.1728i			0.480082i	0.970763	+	0.240041i	$0.0771610\pi$
$449$			10.1728i			0.480082i	−0.970763	+	0.240041i	$0.922839\pi$
$450$	−2.00172	−	2.25124i	−0.0943622	−	0.106124i
$451$	−25.0743	−	14.4767i	−1.18070	−	0.681679i
$452$	5.11094	−	3.31908i	0.240398	−	0.156116i
$453$	18.7899	−	7.21278i	0.882828	−	0.338886i
$454$	−0.0836345	+	0.0607640i	−0.00392516	+	0.00285180i
$455$	2.35006	+	1.32786i	0.110173	+	0.0622511i
$456$	0.435041	+	0.316075i	0.0203726	+	0.0148016i
$457$	23.4285	+	6.27766i	1.09594	+	0.293656i	0.761111	−	0.648622i	$-0.224654\pi$
$457$	23.4285	+	6.27766i	1.09594	+	0.293656i	0.334830	+	0.942278i	$0.391321\pi$
$458$	−3.98158	+	10.3724i	−0.186047	+	0.484670i
$459$	−4.66657	+	4.20180i	−0.217817	+	0.196123i
$460$	14.1591	−	33.8836i	0.660170	−	1.57983i
$461$	9.74059	−	3.16491i	0.453664	−	0.147405i	−0.0732669	−	0.997312i	$-0.523342\pi$
$461$	9.74059	−	3.16491i	0.453664	−	0.147405i	0.526931	+	0.849908i	$0.323342\pi$
$462$	5.46763	−	1.69366i	0.254377	−	0.0787962i
$463$	−2.27633	+	1.15985i	−0.105790	+	0.0539027i	−0.506085	−	0.862484i	$-0.668908\pi$
$463$	−2.27633	+	1.15985i	−0.105790	+	0.0539027i	0.400295	+	0.916386i	$0.368908\pi$
$464$	4.76340	+	4.28899i	0.221135	+	0.199111i
$465$	−12.9913	−	13.7758i	−0.602457	−	0.638838i
$466$	3.87936	+	4.30847i	0.179708	+	0.199586i
$467$	−8.84219	+	7.16027i	−0.409168	+	0.331338i	−0.811707	−	0.584065i	$-0.801461\pi$
$467$	−8.84219	+	7.16027i	−0.409168	+	0.331338i	0.402539	+	0.915403i	$0.368128\pi$
$468$	−0.852168	+	0.852168i	−0.0393915	+	0.0393915i
$469$	−3.56571	+	3.46883i	−0.164649	+	0.160176i
$470$	0.00214637	−	0.0159192i	9.90045e−5	−	0.000734299i
$471$	−14.0813	−	6.26938i	−0.648830	−	0.288878i
$472$	10.7826	−	13.3154i	0.496310	−	0.612892i
$473$	−22.1489	−	34.1062i	−1.01841	−	1.56821i
$474$	3.84000	+	6.65108i	0.176377	+	0.305494i
$475$	1.26620	−	0.477003i	0.0580972	−	0.0218864i
$476$	4.20709	+	3.50385i	0.192831	+	0.160599i
$477$	−8.72782	−	4.44704i	−0.399619	−	0.203616i
$478$	1.13836	+	2.96554i	0.0520675	+	0.135641i
$479$	−1.96621	−	18.7072i	−0.0898383	−	0.854754i	−0.942930	−	0.332992i	$-0.891942\pi$
$479$	−1.96621	−	18.7072i	−0.0898383	−	0.854754i	0.853091	−	0.521762i	$-0.174725\pi$
$480$	6.96739	+	10.2057i	0.318016	+	0.465824i
$481$	−0.830641	−	0.0873039i	−0.0378740	−	0.00398071i
$482$	1.98331	+	1.98331i	0.0903371	+	0.0903371i
$483$	14.4724	+	25.8836i	0.658516	+	1.17775i
$484$	11.0398	+	3.58703i	0.501807	+	0.163047i
$485$	12.0895	−	14.0658i	0.548954	−	0.638696i
$486$	−1.16269	+	5.47004i	−0.0527408	+	0.248126i
$487$	2.14494	+	0.112412i	0.0971966	+	0.00509386i	0.100872	−	0.994899i	$-0.467837\pi$
$487$	2.14494	+	0.112412i	0.0971966	+	0.00509386i	−0.00367567	+	0.999993i	$0.501170\pi$
$488$	−9.35170	+	14.4004i	−0.423332	+	0.651874i
$489$	2.13206	+	6.56182i	0.0964153	+	0.296736i
$490$	−1.32717	−	6.38448i	−0.0599554	−	0.288421i
$491$	0.270800	−	0.833436i	0.0122210	−	0.0376124i	−0.944760	−	0.327763i	$-0.893705\pi$
$491$	0.270800	−	0.833436i	0.0122210	−	0.0376124i	0.956981	+	0.290150i	$0.0937053\pi$
$492$	9.95762	+	12.2966i	0.448924	+	0.554375i
$493$	0.628909	+	2.34712i	0.0283246	+	0.105709i
$494$	0.0209220	+	0.0469915i	0.000941324	+	0.00211425i
$495$	11.4646	+	7.07484i	0.515297	+	0.317991i
$496$	−11.9343	−	16.4261i	−0.535865	−	0.737555i
$497$	−23.2456	+	4.60737i	−1.04271	+	0.206669i
$498$	3.16709	−	6.21576i	0.141921	−	0.278535i
$499$	17.9979	−	10.3911i	0.805696	−	0.465169i	−0.0397630	−	0.999209i	$-0.512660\pi$
$499$	17.9979	−	10.3911i	0.805696	−	0.465169i	0.845459	+	0.534040i	$0.179327\pi$
$500$	20.4173	−	0.343402i	0.913089	−	0.0153574i
$501$	−13.7809	+	23.8692i	−0.615684	+	1.06640i
$502$	3.37507	−	0.176880i	0.150637	−	0.00789453i
$503$	5.98936	−	37.8153i	0.267052	−	1.68610i	−0.381055	−	0.924553i	$-0.624439\pi$
$503$	5.98936	−	37.8153i	0.267052	−	1.68610i	0.648107	−	0.761549i	$-0.275561\pi$
$504$	6.08620	+	0.403077i	0.271101	+	0.0179545i
$505$	9.86329	−	5.31554i	0.438911	−	0.236539i
$506$	1.63128	−	15.5206i	0.0725194	−	0.689976i
$507$	−15.4020	+	4.12694i	−0.684025	+	0.183284i
$508$	2.34987	+	0.902032i	0.104259	+	0.0400212i
$509$	−31.3220	+	6.65770i	−1.38832	+	0.295097i	−0.840643	−	0.541590i	$-0.817822\pi$
$509$	−31.3220	+	6.65770i	−1.38832	+	0.295097i	−0.547680	+	0.836688i	$0.684489\pi$
$510$	0.0303358	+	1.31533i	0.00134329	+	0.0582438i
$511$	13.6393	−	1.96811i	0.603366	−	0.0870641i
$512$	10.3415	+	20.2964i	0.457035	+	0.896982i
$513$	−1.25785	−	0.816856i	−0.0555354	−	0.0360651i
$514$	−2.87737	−	0.611603i	−0.126915	−	0.0269767i
$515$	1.91945	−	10.1790i	0.0845810	−	0.448542i
$516$	4.62069	+	21.7387i	0.203415	+	0.956991i
$517$	0.0112375	+	0.0709510i	0.000494226	+	0.00312042i
$518$	1.16341	+	1.64856i	0.0511171	+	0.0724338i
$519$	2.82009	−	3.88151i	0.123788	−	0.170380i
$520$	0.122543	+	1.62175i	0.00537386	+	0.0711182i
$521$	21.8823	−	2.29992i	0.958682	−	0.100761i	0.387755	−	0.921763i	$-0.373251\pi$
$521$	21.8823	−	2.29992i	0.958682	−	0.100761i	0.570927	+	0.821001i	$0.306584\pi$
$522$	1.00418	+	0.813166i	0.0439516	+	0.0355913i
$523$	0.730500	+	13.9388i	0.0319426	+	0.609500i	0.966965	+	0.254911i	$0.0820461\pi$
$523$	0.730500	+	13.9388i	0.0319426	+	0.609500i	−0.935022	+	0.354590i	$0.884621\pi$
$524$	7.01218			0.306329
$525$	−9.95756	+	13.1440i	−0.434583	+	0.573651i
$526$	−0.357398			−0.0155833
$527$	−0.402834	−	7.68652i	−0.0175477	−	0.334830i
$528$	−12.0617	−	9.76739i	−0.524919	−	0.425071i
$529$	57.5360	−	6.04728i	2.50157	−	0.262925i
$530$	−5.83698	+	2.39644i	−0.253542	+	0.104095i
$531$	−9.13634	+	12.5751i	−0.396484	+	0.545713i
$532$	−0.548285	+	1.18719i	−0.0237712	+	0.0514713i
$533$	0.496047	+	3.13192i	0.0214862	+	0.135659i
$534$	−0.441090	−	2.07516i	−0.0190878	−	0.0898011i
$535$	−12.2787	+	11.5795i	−0.530855	+	0.500624i
$536$	−2.93184	−	0.623182i	−0.126636	−	0.0269174i
$537$	23.3842	+	15.1858i	1.00910	+	0.655318i
$538$	5.03131	+	9.87450i	0.216915	+	0.425720i
$539$	13.8799	+	25.6470i	0.597851	+	1.10469i
$540$	−13.7231	−	18.0003i	−0.590548	−	0.774610i
$541$	3.29560	−	0.700502i	0.141689	−	0.0301169i	−0.136521	−	0.990637i	$-0.543592\pi$
$541$	3.29560	−	0.700502i	0.141689	−	0.0301169i	0.278210	+	0.960520i	$0.410259\pi$
$542$	−8.93445	−	3.42962i	−0.383768	−	0.147315i
$543$	24.6386	−	6.60190i	1.05734	−	0.283315i
$544$	−0.525059	+	4.99560i	−0.0225117	+	0.214185i
$545$	6.17256	+	33.8941i	0.264403	+	1.45186i
$546$	−0.520998	−	0.348634i	−0.0222967	−	0.0149201i
$547$	4.46548	−	28.1940i	0.190930	−	1.20549i	−0.686985	−	0.726671i	$-0.741066\pi$
$547$	4.46548	−	28.1940i	0.190930	−	1.20549i	0.877916	−	0.478815i	$-0.158934\pi$
$548$	−5.74139	+	0.300893i	−0.245260	+	0.0128535i
$549$	7.78849	−	13.4901i	0.332405	−	0.575742i
$550$	8.26979	−	2.63007i	0.352625	−	0.112146i
$551$	−0.502614	+	0.290185i	−0.0214121	+	0.0123623i
$552$	−8.11180	+	15.9203i	−0.345261	+	0.677613i
$553$	−29.4352	+	25.7785i	−1.25171	+	1.09621i
$554$	1.95461	+	2.69030i	0.0830436	+	0.114300i
$555$	1.20660	−	4.95765i	0.0512174	−	0.210441i
$556$	−4.89593	−	10.9964i	−0.207634	−	0.466353i
$557$	7.56621	+	28.2375i	0.320591	+	1.19646i	0.918671	+	0.395024i	$0.129264\pi$
$557$	7.56621	+	28.2375i	0.320591	+	1.19646i	−0.598080	+	0.801436i	$0.704070\pi$
$558$	−2.57581	−	3.18086i	−0.109043	−	0.134656i
$559$	−1.37631	+	4.23586i	−0.0582119	+	0.179158i
$560$	−12.3862	+	12.6184i	−0.523411	+	0.533225i
$561$	−1.81818	−	5.59579i	−0.0767637	−	0.236254i
$562$	−1.07427	+	1.65423i	−0.0453154	+	0.0697796i
$563$	14.2010	+	0.744245i	0.598502	+	0.0313662i	0.349182	−	0.937055i	$-0.386460\pi$
$563$	14.2010	+	0.744245i	0.598502	+	0.0313662i	0.249320	+	0.968421i	$0.419793\pi$
$564$	0.00816212	−	0.0383998i	0.000343687	−	0.00161692i
$565$	−0.608582	+	7.43601i	−0.0256032	+	0.312835i
$566$	−11.8177	−	3.83981i	−0.496736	−	0.161399i
$567$	6.79889	+	0.0936370i	0.285526	+	0.00393238i
$568$	−10.0964	−	10.0964i	−0.423636	−	0.423636i
$569$	−30.5666	−	3.21268i	−1.28142	−	0.134683i	−0.560764	−	0.827976i	$-0.689492\pi$
$569$	−30.5666	−	3.21268i	−1.28142	−	0.134683i	−0.720656	+	0.693293i	$0.756159\pi$
$570$	−0.301577	+	0.0883085i	−0.0126317	+	0.00369884i
$571$	−3.43192	−	32.6526i	−0.143621	−	1.36647i	−0.794490	−	0.607277i	$-0.792262\pi$
$571$	−3.43192	−	32.6526i	−0.143621	−	1.36647i	0.650869	−	0.759190i	$-0.274405\pi$
$572$	−1.24412	−	3.24105i	−0.0520194	−	0.135515i
$573$	−5.61684	−	2.86192i	−0.234647	−	0.119559i
$574$	4.90244	−	5.88638i	0.204624	−	0.245693i
$575$	22.2361	+	39.0753i	0.927310	+	1.62955i
$576$	−2.98674	−	5.17318i	−0.124447	−	0.215549i
$577$	−22.3621	−	34.4347i	−0.930948	−	1.43353i	−0.900920	−	0.433985i	$-0.857107\pi$
$577$	−22.3621	−	34.4347i	−0.930948	−	1.43353i	−0.0300281	−	0.999549i	$-0.509560\pi$
$578$	4.12050	−	5.08839i	0.171390	−	0.211649i
$579$	10.7699	+	4.79509i	0.447584	+	0.199277i
$580$	−8.61707	+	1.56928i	−0.357804	+	0.0651608i
$581$	34.2004	+	9.67069i	1.41887	+	0.401208i
$582$	−3.04585	+	3.04585i	−0.126255	+	0.126255i
$583$	21.9291	−	17.7578i	0.908211	−	0.735455i
$584$	5.55586	+	6.17041i	0.229903	+	0.255333i
$585$	−0.188017	−	1.46341i	−0.00777355	−	0.0605045i
$586$	8.24675	+	7.42541i	0.340670	+	0.306741i
$587$	−21.1676	+	10.7855i	−0.873682	+	0.445163i	−0.832524	−	0.553989i	$-0.813105\pi$
$587$	−21.1676	+	10.7855i	−0.873682	+	0.445163i	−0.0411584	+	0.999153i	$0.513105\pi$
$588$	−2.05863	−	15.8033i	−0.0848967	−	0.651718i
$589$	1.74841	−	0.568094i	0.0720422	−	0.0234079i
$590$	2.30698	+	9.74311i	0.0949768	+	0.401117i
$591$	13.6979	−	12.3337i	0.563458	−	0.507339i
$592$	1.96068	−	5.10774i	0.0805833	−	0.209927i
$593$	−17.4687	−	4.68072i	−0.717353	−	0.192214i	−0.118363	−	0.992970i	$-0.537765\pi$
$593$	−17.4687	−	4.68072i	−0.717353	−	0.192214i	−0.598990	+	0.800756i	$0.704431\pi$
$594$	−7.78201	−	5.65396i	−0.319300	−	0.231985i
$595$	−6.54333	+	1.45447i	−0.268250	+	0.0596275i
$596$	−23.0215	+	16.7261i	−0.942996	+	0.685126i
$597$	22.0873	−	8.47852i	0.903973	−	0.347003i
$598$	−1.43344	+	0.930885i	−0.0586176	+	0.0380667i
$599$	−4.39041	−	2.53480i	−0.179387	−	0.103569i	0.407617	−	0.913153i	$-0.366360\pi$
$599$	−4.39041	−	2.53480i	−0.179387	−	0.103569i	−0.587005	+	0.809583i	$0.699693\pi$
$600$	−9.91851	−	0.581905i	−0.404921	−	0.0237562i
$601$			14.7165i			0.600300i	0.953892	+	0.300150i	$0.0970368\pi$
$601$			14.7165i			0.600300i	−0.953892	+	0.300150i	$0.902963\pi$
$602$	9.88885	−	4.24060i	0.403039	−	0.172834i
$603$	2.68570	+	0.425373i	0.109370	+	0.0173225i
$604$	−11.9948	+	26.9407i	−0.488060	+	1.09620i
$605$	−11.7370	+	8.01277i	−0.477175	+	0.325766i
$606$	−2.37719	+	1.05839i	−0.0965666	+	0.0429942i
$607$	8.91332	−	33.2650i	0.361781	−	1.35018i	−0.509952	−	0.860203i	$-0.670337\pi$
$607$	8.91332	−	33.2650i	0.361781	−	1.35018i	0.871733	−	0.489981i	$-0.162996\pi$
$608$	−1.18497	+	0.187680i	−0.0480567	+	0.00761144i
$609$	3.29755	−	6.25726i	0.133624	−	0.253557i
$610$	−3.31987	−	9.46883i	−0.134418	−	0.383382i
$611$	0.00526432	−	0.00584662i	0.000212971	−	0.000236529i
$612$	0.156627	−	2.98862i	0.00633127	−	0.120808i
$613$	−0.497101	+	9.48524i	−0.0200777	+	0.383105i	0.970047	+	0.242917i	$0.0781042\pi$
$613$	−0.497101	+	9.48524i	−0.0200777	+	0.383105i	−0.990125	+	0.140189i	$0.955229\pi$
$614$	5.61928	−	6.24084i	0.226776	−	0.251860i
$615$	−19.3664	+	0.446652i	−0.780928	+	0.0180107i
$616$	−8.19180	+	15.5443i	−0.330057	+	0.626299i
$617$	8.90288	−	1.41008i	0.358416	−	0.0567676i	0.0253702	−	0.999678i	$-0.491924\pi$
$617$	8.90288	−	1.41008i	0.358416	−	0.0567676i	0.333046	+	0.942911i	$0.391924\pi$
$618$	−0.622634	+	2.32370i	−0.0250460	+	0.0934730i
$619$	4.75420	−	2.11671i	0.191087	−	0.0850776i	−0.308962	−	0.951074i	$-0.599982\pi$
$619$	4.75420	−	2.11671i	0.191087	−	0.0850776i	0.500050	+	0.865997i	$0.333315\pi$
$620$	27.7327	+	0.812820i	1.11377	+	0.0326436i
$621$	20.2697	−	45.5266i	0.813397	−	1.82692i
$622$	−7.64672	−	1.21112i	−0.306606	−	0.0485616i
$623$	9.93374	−	4.25985i	0.397987	−	0.170667i
$624$			1.69981i			0.0680467i
$625$	−14.9460	+	20.0404i	−0.597838	+	0.801617i
$626$	−2.35655	−	1.36056i	−0.0941868	−	0.0543788i
$627$	1.17858	−	0.765378i	0.0470679	−	0.0305663i
$628$	21.0848	−	8.09368i	0.841373	−	0.322973i
$629$	1.67796	−	1.21911i	0.0669048	−	0.0486092i
$630$	−2.36035	+	2.67091i	−0.0940385	+	0.106411i
$631$	21.0020	+	15.2589i	0.836078	+	0.607446i	0.921272	−	0.388918i	$-0.127151\pi$
$631$	21.0020	+	15.2589i	0.836078	+	0.607446i	−0.0851944	+	0.996364i	$0.527151\pi$
$632$	−22.7720	−	6.10173i	−0.905820	−	0.242714i
$633$	7.43776	−	19.3760i	0.295624	−	0.770128i
$634$	−3.40131	+	3.06256i	−0.135083	+	0.121630i
$635$	−2.63249	+	1.60191i	−0.104467	+	0.0635699i
$636$	−14.6660	+	4.76526i	−0.581543	+	0.188955i
$637$	1.22624	−	2.94903i	0.0485854	−	0.116845i
$638$	−3.31652	+	1.68985i	−0.131302	+	0.0669018i
$639$	9.62625	+	8.66751i	0.380809	+	0.342882i
$640$	−23.2646	−	4.38697i	−0.919613	−	0.173410i
$641$	−6.75345	−	7.50047i	−0.266745	−	0.296251i	0.594860	−	0.803829i	$-0.297207\pi$
$641$	−6.75345	−	7.50047i	−0.266745	−	0.296251i	−0.861606	+	0.507578i	$0.830541\pi$
$642$	3.04617	−	2.46674i	0.120223	−	0.0973545i
$643$	−21.1590	+	21.1590i	−0.834431	+	0.834431i	−0.988119	−	0.153688i	$-0.950885\pi$
$643$	−21.1590	+	21.1590i	−0.834431	+	0.834431i	0.153688	+	0.988119i	$0.450885\pi$
$644$	−41.8118	−	11.8229i	−1.64761	−	0.465888i
$645$	−24.5215	−	11.7903i	−0.965535	−	0.464241i
$646$	−0.116693	−	0.0519551i	−0.00459123	−	0.00204415i
$647$	−0.672477	+	0.830440i	−0.0264378	+	0.0326480i	−0.790193	−	0.612858i	$-0.790020\pi$
$647$	−0.672477	+	0.830440i	−0.0264378	+	0.0326480i	0.763756	+	0.645506i	$0.223353\pi$
$648$	2.23132	+	3.43593i	0.0876545	+	0.134976i
$649$	−22.3881	−	38.7774i	−0.878811	−	1.52214i
$650$	−0.793832	−	0.522593i	−0.0311366	−	0.0204978i
$651$	−14.3381	+	17.2158i	−0.561954	+	0.674741i
$652$	−9.00750	−	4.58955i	−0.352761	−	0.179741i
$653$	10.6733	+	27.8050i	0.417680	+	1.08809i	0.967513	+	0.252820i	$0.0813580\pi$
$653$	10.6733	+	27.8050i	0.417680	+	1.08809i	−0.549833	+	0.835275i	$0.685309\pi$
$654$	−0.836347	−	7.95731i	−0.0327038	−	0.311156i
$655$	−5.24736	+	6.79449i	−0.205031	+	0.265483i
$656$	−20.6578	−	2.17122i	−0.806550	−	0.0847718i
$657$	−5.32632	−	5.32632i	−0.207799	−	0.207799i
$658$	−0.0190045		0.000261738i	−0.000740873		1.02036e-5i
$659$	−8.35402	−	2.71439i	−0.325426	−	0.105737i	0.141748	−	0.989903i	$-0.454728\pi$
$659$	−8.35402	−	2.71439i	−0.325426	−	0.105737i	−0.467174	+	0.884165i	$0.654728\pi$
$660$	20.6377	−	4.88661i	0.803323	−	0.190211i
$661$	−2.27662	+	10.7107i	−0.0885503	+	0.416596i	0.911436	+	0.411441i	$0.134974\pi$
$661$	−2.27662	+	10.7107i	−0.0885503	+	0.416596i	−0.999987	+	0.00515533i	$0.998359\pi$
$662$	−0.959000	−	0.0502590i	−0.0372726	−	0.00195337i
$663$	−0.350959	+	0.540429i	−0.0136301	+	0.0209885i
$664$	6.61746	+	20.3664i	0.256807	+	0.790371i
$665$	−0.740043	−	1.41966i	−0.0286976	−	0.0550522i
$666$	0.340819	−	1.04893i	0.0132065	−	0.0406453i
$667$	−12.1360	−	14.9867i	−0.469906	−	0.580286i
$668$	−10.4522	−	39.0082i	−0.404408	−	1.50927i
$669$	−9.92550	−	22.2930i	−0.383742	−	0.861898i
$670$	1.33544	−	1.13339i	0.0515927	−	0.0437866i
$671$	26.3752	+	36.3024i	1.01820	+	1.40144i
$672$	10.9994	−	9.63297i	0.424311	−	0.371600i
$673$	−12.8993	+	25.3164i	−0.497233	+	0.975875i	0.496910	+	0.867802i	$0.334468\pi$
$673$	−12.8993	+	25.3164i	−0.497233	+	0.975875i	−0.994143	+	0.108073i	$0.965532\pi$
$674$	5.64801	−	3.26088i	0.217553	−	0.125604i
$675$	27.7108	+	0.172961i	1.06659	+	0.00665728i
$676$	11.6817	−	20.2334i	0.449297	−	0.778206i
$677$	−12.5912	+	0.659879i	−0.483921	+	0.0253612i	−0.292737	−	0.956193i	$-0.594566\pi$
$677$	−12.5912	+	0.659879i	−0.483921	+	0.0253612i	−0.191184	+	0.981554i	$0.561233\pi$
$678$	0.271060	−	1.71140i	0.0104100	−	0.0657260i
$679$	−18.2387	−	12.2047i	−0.699936	−	0.468372i
$680$	−2.92090	−	2.78921i	−0.112012	−	0.106961i
$681$	0.0323320	−	0.307619i	0.00123897	−	0.0117880i
$682$	11.3888	−	3.05163i	0.436101	−	0.116853i
$683$	31.6148	+	12.1358i	1.20971	+	0.464363i	0.877835	−	0.478962i	$-0.158987\pi$
$683$	31.6148	+	12.1358i	1.20971	+	0.464363i	0.331871	+	0.943325i	$0.392320\pi$
$684$	0.699171	−	0.148613i	0.0267335	−	0.00568237i
$685$	4.00485	−	5.78831i	0.153017	−	0.221160i
$686$	−7.31129	+	2.46519i	−0.279146	+	0.0941213i
$687$	−15.0919	−	29.6196i	−0.575793	−	1.13006i
$688$	−24.4683	−	15.8899i	−0.932847	−	0.605798i
$689$	−3.02284	−	0.642525i	−0.115161	−	0.0244783i
$690$	−4.46573	−	9.43828i	−0.170007	−	0.359309i
$691$	3.90436	+	18.3686i	0.148529	+	0.698774i	0.987884	+	0.155191i	$0.0495994\pi$
$691$	3.90436	+	18.3686i	0.148529	+	0.698774i	−0.839355	+	0.543583i	$0.817067\pi$
$692$	1.09972	+	6.94335i	0.0418050	+	0.263946i
$693$	6.68335	−	14.4714i	0.253880	−	0.549722i
$694$	−0.889009	+	1.22362i	−0.0337463	+	0.0464478i
$695$	14.3188	+	3.48493i	0.543142	+	0.132191i
$696$	4.23830	−	0.445463i	0.160652	−	0.0168852i
$697$	−6.11955	−	4.95551i	−0.231794	−	0.187703i
$698$	0.226533	+	4.32251i	0.00857441	+	0.163609i
$699$	−17.3468			−0.656118
$700$	−3.30137	−	23.9349i	−0.124780	−	0.904654i
$701$	3.28420			0.124042			0.0620212	−	0.998075i	$-0.480245\pi$
$701$	3.28420			0.124042			0.0620212	+	0.998075i	$0.480245\pi$
$702$	0.0551349	+	1.05204i	0.00208093	+	0.0397066i
$703$	0.384982	+	0.311752i	0.0145199	+	0.0117580i
$704$	17.1134	−	1.79869i	0.644984	−	0.0677906i
$705$	0.0310998	+	0.0366441i	0.00117128	+	0.00138010i
$706$	−0.873797	+	1.20268i	−0.0328858	+	0.0452634i
$707$	−7.64399	−	10.8317i	−0.287482	−	0.407366i
$708$	3.82795	+	24.1687i	0.143863	+	0.908315i
$709$	4.94321	+	23.2560i	0.185646	+	0.873396i	0.968076	+	0.250657i	$0.0806467\pi$
$709$	4.94321	+	23.2560i	0.185646	+	0.873396i	−0.782430	+	0.622739i	$0.786020\pi$
$710$	8.27594	−	1.06328i	0.310591	−	0.0399044i
$711$	20.9200	+	4.44669i	0.784563	+	0.166764i
$712$	5.46178	+	3.54692i	0.204689	+	0.132927i
$713$	27.7321	+	54.4274i	1.03858	+	2.03832i
$714$	1.54077	−	0.222330i	0.0576620	−	0.00832047i
$715$	4.07143	+	1.21985i	0.152263	+	0.0456197i
$716$	−39.9613	+	8.49404i	−1.49343	+	0.317437i
$717$	−8.87308	−	3.40606i	−0.331371	−	0.127201i
$718$	8.16690	−	2.18832i	0.304786	−	0.0816672i
$719$	−1.48731	+	14.1508i	−0.0554673	+	0.527736i	0.931145	+	0.364650i	$0.118811\pi$
$719$	−1.48731	+	14.1508i	−0.0554673	+	0.527736i	−0.986612	+	0.163086i	$0.947855\pi$
$720$	9.57826	+	1.29142i	0.356961	+	0.0481285i
$721$	−12.2295	−	0.809932i	−0.455449	−	0.0301635i
$722$	−1.23350	+	7.78798i	−0.0459059	+	0.289839i
$723$	−8.38070	+	0.439214i	−0.311681	+	0.0163345i
$724$	−18.6874	+	32.3675i	−0.694510	+	1.20293i
$725$	4.92777	−	9.52387i	0.183013	−	0.353708i
$726$	2.85829	−	1.65024i	0.106081	−	0.0612460i
$727$	17.4611	−	34.2694i	0.647597	−	1.27098i	−0.300737	−	0.953707i	$-0.597233\pi$
$727$	17.4611	−	34.2694i	0.647597	−	1.27098i	0.948334	−	0.317273i	$-0.102767\pi$
$728$	1.88763	−	0.374135i	0.0699600	−	0.0138664i
$729$	−14.3668	−	19.7742i	−0.532105	−	0.732379i
$730$	−4.83832	+	0.365595i	−0.179074	+	0.0135313i
$731$	−4.49857	−	10.1040i	−0.166386	−	0.373708i
$732$	−6.34686	−	23.6868i	−0.234587	−	0.875490i
$733$	−30.8545	−	38.1021i	−1.13964	−	1.40733i	−0.899681	−	0.436548i	$-0.856201\pi$
$733$	−30.8545	−	38.1021i	−1.13964	−	1.40733i	−0.239954	−	0.970784i	$-0.577132\pi$
$734$	−3.07171	+	9.45375i	−0.113379	+	0.348944i
$735$	16.8532	+	9.83123i	0.621640	+	0.362630i
$736$	−12.3187	−	37.9132i	−0.454075	−	1.39750i
$737$	−4.26619	+	6.56935i	−0.157147	+	0.241985i
$738$	−4.18155	−	0.219146i	−0.153925	−	0.00806687i
$739$	2.32460	−	10.9364i	0.0855116	−	0.402301i	−0.914486	−	0.404618i	$-0.867404\pi$
$739$	2.32460	−	10.9364i	0.0855116	−	0.402301i	0.999997	+	0.00231771i	$0.000737750\pi$
$740$	3.88636	+	6.38662i	0.142865	+	0.234777i
$741$	−0.146375	−	0.0475601i	−0.00537721	−	0.00174716i
$742$	3.64352	+	6.51639i	0.133758	+	0.239224i
$743$	13.0550	+	13.0550i	0.478941	+	0.478941i	0.904793	−	0.425852i	$-0.140026\pi$
$743$	13.0550	+	13.0550i	0.478941	+	0.478941i	−0.425852	+	0.904793i	$0.640026\pi$
$744$	−13.4253	−	1.41106i	−0.492197	−	0.0517320i
$745$	1.02064	−	34.8232i	0.0373933	−	1.27582i
$746$	−0.312797	−	2.97607i	−0.0114523	−	0.108962i
$747$	−6.96209	−	18.1369i	−0.254729	−	0.663593i
$748$	7.68141	+	3.91387i	0.280860	+	0.143105i
$749$	15.3449	+	12.7799i	0.560690	+	0.466967i
$750$	3.81191	−	4.37948i	0.139191	−	0.159916i
$751$	23.9092	+	41.4119i	0.872458	+	1.51114i	0.859446	+	0.511227i	$0.170809\pi$
$751$	23.9092	+	41.4119i	0.872458	+	1.51114i	0.0130124	+	0.999915i	$0.495858\pi$
$752$	0.0280684	+	0.0432216i	0.00102355	+	0.00157613i
$753$	−6.36386	+	7.85872i	−0.231912	+	0.286388i
$754$	0.372413	+	0.165809i	0.0135625	+	0.00603840i
$755$	−17.1284	−	31.7827i	−0.623366	−	1.15669i
$756$	−19.1966	+	18.6751i	−0.698175	+	0.679205i
$757$	−25.0469	+	25.0469i	−0.910346	+	0.910346i	−0.996299	−	0.0859530i	$-0.972607\pi$
$757$	−25.0469	+	25.0469i	−0.910346	+	0.910346i	0.0859530	+	0.996299i	$0.472607\pi$
$758$	6.80899	−	5.51381i	0.247314	−	0.200271i
$759$	31.2447	+	34.7008i	1.13411	+	1.25956i
$760$	0.462922	−	0.846287i	0.0167919	−	0.0306981i
$761$	−0.127252	−	0.114578i	−0.00461286	−	0.00415344i	0.666821	−	0.745218i	$-0.267655\pi$
$761$	−0.127252	−	0.114578i	−0.00461286	−	0.00415344i	−0.671434	+	0.741065i	$0.734321\pi$
$762$	0.637671	−	0.324910i	0.0231004	−	0.0117702i
$763$	38.9384	−	12.0616i	1.40966	−	0.436659i
$764$	8.78462	−	2.85429i	0.317816	−	0.103265i
$765$	2.77863	+	2.38821i	0.100462	+	0.0863460i
$766$	8.59671	−	7.74051i	0.310612	−	0.279676i
$767$	−1.75739	+	4.57817i	−0.0634559	+	0.165308i
$768$	−4.63572	−	1.24214i	−0.167277	−	0.0448218i
$769$	−27.2261	−	19.7809i	−0.981797	−	0.713317i	−0.0236871	−	0.999719i	$-0.507541\pi$
$769$	−27.2261	−	19.7809i	−0.981797	−	0.713317i	−0.958109	+	0.286403i	$0.907541\pi$
$770$	−4.26326	−	9.34098i	−0.153637	−	0.336626i
$771$	7.12064	−	5.17345i	0.256444	−	0.186317i
$772$	−16.1265	+	6.19039i	−0.580406	+	0.222797i
$773$	−31.2203	+	20.2747i	−1.12292	+	0.729230i	−0.966041	−	0.258388i	$-0.916809\pi$
$773$	−31.2203	+	20.2747i	−1.12292	+	0.729230i	−0.156875	+	0.987619i	$0.550142\pi$
$774$	−5.09340	−	2.94068i	−0.183078	−	0.105700i
$775$	−21.5405	+	26.2635i	−0.773759	+	0.943411i
$776$		−	13.2227i		−	0.474666i
$777$	−5.99488	−	0.713684i	−0.215065	−	0.0256033i
$778$	6.34223	+	1.00451i	0.227380	+	0.0360135i
$779$	0.764967	−	1.71814i	0.0274078	−	0.0615589i
$780$	−1.83833	−	1.41974i	−0.0658227	−	0.0508347i
$781$	−34.0885	+	15.1772i	−1.21978	+	0.543082i
$782$	1.09852	−	4.09975i	0.0392832	−	0.146607i
$783$	−11.7398	+	1.85941i	−0.419547	+	0.0664497i
$784$	16.5805	+	12.7586i	0.592162	+	0.455666i
$785$	−7.93576	+	26.4868i	−0.283239	+	0.945356i
$786$	1.33410	−	1.48166i	0.0475856	−	0.0528492i
$787$	−1.78893	+	34.1349i	−0.0637685	+	1.21678i	0.760028	+	0.649890i	$0.225185\pi$
$787$	−1.78893	+	34.1349i	−0.0637685	+	1.21678i	−0.823796	+	0.566886i	$0.808148\pi$
$788$	−1.41347	+	26.9706i	−0.0503528	+	0.960789i
$789$	0.715540	−	0.794687i	0.0254739	−	0.0282916i
$790$	10.9560	−	8.35261i	0.389796	−	0.297173i
$791$	8.82125	−	0.340566i	0.313648	−	0.0121091i
$792$	9.48606	−	1.50244i	0.337072	−	0.0533870i
$793$	1.27194	−	4.74694i	0.0451679	−	0.168569i
$794$	−8.27029	+	3.68217i	−0.293502	+	0.130675i
$795$	6.35753	−	17.7766i	0.225478	−	0.630471i
$796$	−14.0997	+	31.6684i	−0.499750	+	1.12246i
$797$	22.0892	+	3.49859i	0.782441	+	0.123926i	0.534860	−	0.844941i	$-0.320364\pi$
$797$	22.0892	+	3.49859i	0.782441	+	0.123926i	0.247581	+	0.968867i	$0.420364\pi$
$798$	0.146539	+	0.341720i	0.00518741	+	0.0120968i
$799$			0.0195370i			0.000691168i
$800$	16.5655	−	14.7295i	0.585680	−	0.520766i
$801$	−5.11653	−	2.95403i	−0.180784	−	0.104375i
$802$	2.87928	−	1.86983i	0.101671	−	0.0660259i
$803$	20.2576	−	7.77616i	0.714875	−	0.274415i
$804$	3.46318	−	2.51615i	0.122137	−	0.0887376i
$805$	42.7445	−	31.6664i	1.50655	−	1.11609i
$806$	−1.04469	−	0.759008i	−0.0367975	−	0.0267349i
$807$	−32.0294	−	8.58226i	−1.12749	−	0.302110i
$808$	2.86258	−	7.45727i	0.100705	−	0.262346i
$809$	4.18403	−	3.76732i	0.147103	−	0.132452i	−0.592294	−	0.805722i	$-0.701778\pi$
$809$	4.18403	−	3.76732i	0.147103	−	0.132452i	0.739397	+	0.673270i	$0.235111\pi$
$810$	−2.38613	−	0.195287i	−0.0838400	−	0.00686169i
$811$	−19.3958	+	6.30209i	−0.681080	+	0.221296i	−0.629068	−	0.777350i	$-0.716563\pi$
$811$	−19.3958	+	6.30209i	−0.681080	+	0.221296i	−0.0520120	+	0.998646i	$0.516563\pi$
$812$	3.06648	+	9.89949i	0.107612	+	0.347404i
$813$	25.5134	−	12.9997i	0.894793	−	0.455920i
$814$	2.36107	+	2.12591i	0.0827553	+	0.0745132i
$815$	11.1876	−	5.29340i	0.391883	−	0.185420i
$816$	−2.82447	−	3.13689i	−0.0988761	−	0.109813i
$817$	2.05294	−	1.66244i	0.0718233	−	0.0581614i
$818$	−3.06981	+	3.06981i	−0.107333	+	0.107333i
$819$	−1.69234	+	0.428571i	−0.0591350	+	0.0149755i
$820$	19.6022	−	20.5278i	0.684540	−	0.716860i
$821$	18.3211	+	8.15710i	0.639412	+	0.284685i	0.700722	−	0.713434i	$-0.252861\pi$
$821$	18.3211	+	8.15710i	0.639412	+	0.284685i	−0.0613100	+	0.998119i	$0.519528\pi$
$822$	−1.02874	+	1.27039i	−0.0358816	+	0.0443101i
$823$	14.1680	+	21.8168i	0.493866	+	0.760487i	0.994451	−	0.105201i	$-0.0335485\pi$
$823$	14.1680	+	21.8168i	0.493866	+	0.760487i	−0.500585	+	0.865687i	$0.666882\pi$
$824$	−3.69234	−	6.39532i	−0.128629	−	0.222792i
$825$	−10.7087	+	23.6538i	−0.372831	+	0.823519i
$826$	11.1175	−	4.09286i	0.386827	−	0.142409i
$827$	24.2154	+	12.3384i	0.842052	+	0.429047i	0.821135	−	0.570734i	$-0.193341\pi$
$827$	24.2154	+	12.3384i	0.842052	+	0.429047i	0.0209175	+	0.999781i	$0.493341\pi$
$828$	8.51150	+	22.1732i	0.295795	+	0.770573i
$829$	−2.51274	−	23.9071i	−0.0872712	−	0.830330i	−0.947357	−	0.320180i	$-0.896257\pi$
$829$	−2.51274	−	23.9071i	−0.0872712	−	0.830330i	0.860086	−	0.510150i	$-0.170410\pi$
$830$	−11.7832	−	4.21408i	−0.409001	−	0.146273i
$831$	−9.89527	−	1.04003i	−0.343263	−	0.0360784i
$832$	−1.33260	−	1.33260i	−0.0461995	−	0.0461995i
$833$	2.63727	+	7.47981i	0.0913761	+	0.259160i
$834$	−3.25500	−	1.05761i	−0.112712	−	0.0366222i
$835$	45.6188	+	19.0629i	1.57870	+	0.659700i
$836$	−0.428106	+	2.01408i	−0.0148064	+	0.0696585i
$837$	37.5993	+	1.97050i	1.29962	+	0.0681103i
$838$	−6.43814	+	9.91386i	−0.222402	+	0.342469i
$839$	−17.2942	−	53.2260i	−0.597061	−	1.83757i	−0.544187	−	0.838964i	$-0.683162\pi$
$839$	−17.2942	−	53.2260i	−0.597061	−	1.83757i	−0.0528742	−	0.998601i	$-0.516838\pi$
$840$	0.724264	+	11.7336i	0.0249895	+	0.404847i
$841$	7.54017	−	23.2063i	0.260006	−	0.800216i
$842$	−0.454981	−	0.561855i	−0.0156797	−	0.0193628i
$843$	−1.52747	−	5.70059i	−0.0526088	−	0.196339i
$844$	12.3689	+	27.7810i	0.425755	+	0.956262i
$845$	10.8635	+	26.4601i	0.373717	+	0.910256i
$846$	0.00610649	+	0.00840487i	0.000209946	+	0.000288965i
$847$	11.0783	+	12.6498i	0.380655	+	0.434651i
$848$	9.19043	−	18.0372i	0.315601	−	0.619401i
$849$	32.1980	−	18.5895i	1.10503	−	0.637991i
$850$	2.33333	−	0.354649i	0.0800326	−	0.0121644i
$851$	−8.23011	+	14.2550i	−0.282125	+	0.488654i
$852$	20.3642	−	1.06724i	0.697667	−	0.0365632i
$853$	−2.04369	+	12.9033i	−0.0699745	+	0.441802i	0.927681	+	0.373373i	$0.121799\pi$
$853$	−2.04369	+	12.9033i	−0.0699745	+	0.441802i	−0.997656	+	0.0684291i	$0.978201\pi$
$854$	−10.6516	+	5.24374i	−0.364489	+	0.179437i
$855$	−0.379205	+	0.788676i	−0.0129685	+	0.0269721i
$856$	−1.25771	+	11.9663i	−0.0429877	+	0.409001i
$857$	−37.7085	+	10.1040i	−1.28810	+	0.345145i	−0.836938	−	0.547298i	$-0.815656\pi$
$857$	−37.7085	+	10.1040i	−1.28810	+	0.345145i	−0.451161	+	0.892443i	$0.648990\pi$
$858$	−0.921529	−	0.353742i	−0.0314605	−	0.0120765i
$859$	−23.0972	+	4.90947i	−0.788068	+	0.167509i	−0.584330	−	0.811516i	$-0.698642\pi$
$859$	−23.0972	+	4.90947i	−0.788068	+	0.167509i	−0.203738	+	0.979025i	$0.565309\pi$
$860$	37.6217	−	13.1905i	1.28289	−	0.449794i
$861$	3.27349	+	22.6858i	0.111560	+	0.773129i
$862$	2.35296	+	4.61795i	0.0801423	+	0.157288i
$863$	−38.1066	−	24.7467i	−1.29716	−	0.842389i	−0.303290	−	0.952898i	$-0.598085\pi$
$863$	−38.1066	−	24.7467i	−1.29716	−	0.842389i	−0.993875	+	0.110510i	$0.964752\pi$
$864$	−24.0341	−	5.10860i	−0.817657	−	0.173798i
$865$	−7.55073	−	4.13028i	−0.256733	−	0.140434i
$866$	−1.68642	−	7.93396i	−0.0573067	−	0.269607i
$867$	3.06465	+	19.3495i	0.104081	+	0.657142i
$868$	−2.98152	−	32.6922i	−0.101199	−	1.10964i
$869$	−36.2135	+	49.8436i	−1.22846	+	1.69083i
$870$	−1.30785	+	2.11934i	−0.0443401	+	0.0718522i
$871$	0.853175	−	0.0896723i	0.0289087	−	0.00303843i
$872$	19.0875	+	15.4568i	0.646386	+	0.523433i
$873$	0.627798	+	11.9791i	0.0212478	+	0.405431i
$874$	1.01374			0.0342902
$875$	25.6623	+	14.7121i	0.867544	+	0.497360i
$876$	−11.8583			−0.400654
$877$	−3.01192	−	57.4708i	−0.101705	−	1.94065i	−0.286921	−	0.957954i	$-0.592632\pi$
$877$	−3.01192	−	57.4708i	−0.101705	−	1.94065i	0.185216	−	0.982698i	$-0.440701\pi$
$878$	−2.10047	−	1.70093i	−0.0708875	−	0.0574036i
$879$	−33.0213	+	3.47068i	−1.11378	+	0.117063i
$880$	−14.6211	+	23.6933i	−0.492879	+	0.798699i
$881$	10.2302	−	14.0806i	0.344663	−	0.474388i	−0.601133	−	0.799149i	$-0.705284\pi$
$881$	10.2302	−	14.0806i	0.344663	−	0.474388i	0.945796	+	0.324761i	$0.105284\pi$
$882$	3.47246	+	2.39353i	0.116924	+	0.0805944i
$883$	0.0821037	+	0.518382i	0.00276301	+	0.0174450i	0.989031	−	0.147706i	$-0.0471889\pi$
$883$	0.0821037	+	0.518382i	0.00276301	+	0.0174450i	−0.986268	+	0.165151i	$0.947189\pi$
$884$	−0.196305	−	0.923543i	−0.00660246	−	0.0310621i
$885$	−26.2829	−	14.3768i	−0.883490	−	0.483272i
$886$	−8.51999	−	1.81098i	−0.286235	−	0.0608410i
$887$	−27.2167	−	17.6747i	−0.913848	−	0.593460i	−0.000214834	−	1.00000i	$-0.500068\pi$
$887$	−27.2167	−	17.6747i	−0.913848	−	0.593460i	−0.913633	+	0.406540i	$0.866735\pi$
$888$	−1.65142	−	3.24109i	−0.0554180	−	0.108764i
$889$	2.25537	+	2.86494i	0.0756427	+	0.0960869i
$890$	−3.59135	+	1.25916i	−0.120382	+	0.0422073i
$891$	10.4726	−	2.22601i	0.350844	−	0.0745742i
$892$	33.3807	+	12.8137i	1.11767	+	0.429033i
$893$	−0.00450727	+	0.00120772i	−0.000150830	+	4.04148e-5i
$894$	−0.845732	+	8.04660i	−0.0282855	+	0.269119i
$895$	21.6736	−	45.0770i	0.724467	−	1.50676i
$896$	−1.85113	+	27.9509i	−0.0618420	+	0.933774i
$897$	0.800001	−	5.05101i	0.0267113	−	0.168648i
$898$	−4.23226	+	0.221803i	−0.141232	+	0.00740167i
$899$	7.28472	−	12.6175i	0.242959	−	0.420818i
$900$	−9.39676	+	9.28018i	−0.313225	+	0.309339i
$901$	6.64612	−	3.83714i	0.221414	−	0.127834i
$902$	5.47613	−	10.7475i	0.182335	−	0.357853i
$903$	−10.3691	+	30.4782i	−0.345063	+	1.01425i
$904$	3.12641	+	4.30314i	0.103983	+	0.143120i
$905$	−17.3785	−	42.3285i	−0.577679	−	1.40705i
$906$	3.41048	+	7.66006i	0.113306	+	0.254488i
$907$	−3.10385	−	11.5837i	−0.103062	−	0.384631i	0.895056	−	0.445953i	$-0.147135\pi$
$907$	−3.10385	−	11.5837i	−0.103062	−	0.384631i	−0.998118	+	0.0613217i	$0.980468\pi$
$908$	0.285217	+	0.352214i	0.00946527	+	0.0116886i
$909$	−2.23930	+	6.89185i	−0.0742729	+	0.228588i
$910$	−0.501201	+	1.00667i	−0.0166147	+	0.0333707i
$911$	1.11500	+	3.43163i	0.0369417	+	0.113695i	0.967827	−	0.251617i	$-0.0809623\pi$
$911$	1.11500	+	3.43163i	0.0369417	+	0.113695i	−0.930885	+	0.365312i	$0.880962\pi$
$912$	0.549094	−	0.845531i	0.0181823	−	0.0279983i
$913$	55.8867	+	2.92890i	1.84958	+	0.0969324i
$914$	−2.10092	+	9.88404i	−0.0694922	+	0.326935i
$915$	27.7010	+	11.5755i	0.915765	+	0.382675i
$916$	46.3243	+	15.0517i	1.53060	+	0.497322i
$917$	8.72609	+	5.19954i	0.288161	+	0.171704i
$918$	−1.84985	−	1.84985i	−0.0610543	−	0.0610543i
$919$	−45.5683	−	4.78943i	−1.50316	−	0.157989i	−0.683125	−	0.730301i	$-0.739380\pi$
$919$	−45.5683	−	4.78943i	−1.50316	−	0.157989i	−0.820035	+	0.572313i	$0.806046\pi$
$920$	30.1801	+	10.7934i	0.995007	+	0.355849i
$921$	2.62649	+	24.9894i	0.0865457	+	0.823427i
$922$	1.52910	+	3.98345i	0.0503583	+	0.131188i
$923$	3.64125	+	1.85531i	0.119853	+	0.0610683i
$924$	−8.66944	−	23.5490i	−0.285204	−	0.774704i
$925$	−9.09659	−	1.01353i	−0.299094	−	0.0333248i
$926$	−0.532173	−	0.921751i	−0.0174883	−	0.0302906i
$927$	3.64873	+	5.61855i	0.119840	+	0.184538i
$928$	−5.98360	+	7.38913i	−0.196421	+	0.242560i
$929$	13.1562	+	5.85752i	0.431641	+	0.192179i	0.611044	−	0.791597i	$-0.290750\pi$
$929$	13.1562	+	5.85752i	0.431641	+	0.192179i	−0.179403	+	0.983776i	$0.557417\pi$
$930$	5.44800	−	5.70523i	0.178647	−	0.187082i
$931$	−1.56260	+	1.07081i	−0.0512121	+	0.0350944i
$932$	17.9726	−	17.9726i	0.588712	−	0.588712i
$933$	18.0023	−	14.5780i	0.589370	−	0.477262i
$934$	−3.17173	−	3.52257i	−0.103782	−	0.115262i
$935$	−9.54053	+	4.51411i	−0.312009	+	0.147627i
$936$	−0.781685	−	0.703833i	−0.0255502	−	0.0230055i
$937$	−28.8746	+	14.7123i	−0.943291	+	0.480631i	−0.856816	−	0.515623i	$-0.827561\pi$
$937$	−28.8746	+	14.7123i	−0.943291	+	0.480631i	−0.0864758	+	0.996254i	$0.527561\pi$
$938$	−1.52091	−	1.40784i	−0.0496595	−	0.0459676i
$939$	7.74326	−	2.51594i	0.252692	−	0.0821045i
$940$	−0.0701876	−	0.00574433i	−0.00228927	−	0.000187360i
$941$	−4.57408	+	4.11852i	−0.149111	+	0.134260i	−0.740310	−	0.672266i	$-0.765321\pi$
$941$	−4.57408	+	4.11852i	−0.149111	+	0.134260i	0.591199	+	0.806525i	$0.298655\pi$
$942$	2.30128	−	5.99503i	0.0749797	−	0.195329i
$943$	60.3631	+	16.1742i	1.96569	+	0.526706i
$944$	−25.9882	−	18.8815i	−0.845843	−	0.614541i
$945$	−3.73003	−	32.5756i	−0.121338	−	1.05968i
$946$	13.7066	−	9.95840i	0.445639	−	0.323776i
$947$	14.2853	−	5.48362i	0.464211	−	0.178194i	−0.115010	−	0.993364i	$-0.536690\pi$
$947$	14.2853	−	5.48362i	0.464211	−	0.178194i	0.579221	+	0.815170i	$0.303357\pi$
$948$	28.2377	−	18.3378i	0.917118	−	0.595583i
$949$	−2.05807	−	1.18822i	−0.0668076	−	0.0385714i
$950$	0.226059	+	0.516387i	0.00733432	+	0.0167538i
$951$		−	13.6944i		−	0.444072i
$952$	−2.86182	+	3.82700i	−0.0927521	+	0.124034i
$953$	−18.0615	−	2.86067i	−0.585070	−	0.0926660i	−0.143120	−	0.989705i	$-0.545713\pi$
$953$	−18.0615	−	2.86067i	−0.585070	−	0.0926660i	−0.441951	+	0.897039i	$0.645713\pi$
$954$	1.65984	−	3.72806i	0.0537393	−	0.120701i
$955$	−3.80803	+	10.6478i	−0.123225	+	0.344556i
$956$	12.7221	−	5.66423i	0.411461	−	0.183194i
$957$	2.88250	−	10.7576i	0.0931778	−	0.347744i
$958$	7.74004	−	1.22590i	0.250069	−	0.0396071i
$959$	−7.36781	−	3.88280i	−0.237919	−	0.125382i
$960$	9.15568	−	6.98011i	0.295498	−	0.225282i
$961$	−10.1377	+	11.2591i	−0.327023	+	0.363195i
$962$	0.0182107	−	0.347482i	0.000587138	−	0.0112033i
$963$	0.571279	−	10.9007i	0.0184092	−	0.351269i
$964$	8.22795	−	9.13807i	0.265005	−	0.294317i
$965$	6.06960	−	20.2583i	0.195387	−	0.652137i
$966$	−10.4530	+	6.58541i	−0.336321	+	0.211882i
$967$	5.84954	−	0.926476i	0.188108	−	0.0297934i	−0.0616694	−	0.998097i	$-0.519642\pi$
$967$	5.84954	−	0.926476i	0.188108	−	0.0297934i	0.249778	+	0.968303i	$0.419642\pi$
$968$	−2.62221	+	9.78623i	−0.0842811	+	0.314541i
$969$	0.349153	−	0.155453i	0.0112164	−	0.00499387i
$970$	6.11550	+	4.72299i	0.196357	+	0.151646i
$971$	−15.2816	+	34.3230i	−0.490410	+	1.10148i	0.483665	+	0.875253i	$0.339305\pi$
$971$	−15.2816	+	34.3230i	−0.490410	+	1.10148i	−0.974075	+	0.226225i	$0.927362\pi$
$972$	24.2149	+	3.83526i	0.776693	+	0.123016i
$973$	2.06127	−	17.3145i	0.0660814	−	0.555078i
$974$			0.894828i			0.0286721i
$975$	2.75132	−	0.718839i	0.0881128	−	0.0230213i
$976$	27.8791	+	16.0960i	0.892388	+	0.515220i
$977$	−6.19741	+	4.02464i	−0.198273	+	0.128760i	−0.639957	−	0.768411i	$-0.721048\pi$
$977$	−6.19741	+	4.02464i	−0.198273	+	0.128760i	0.441684	+	0.897171i	$0.354381\pi$
$978$	−2.68348	+	1.03009i	−0.0858082	+	0.0329387i
$979$	13.7688	−	10.0036i	0.440053	−	0.319717i
$980$	−27.6470	+	7.27529i	−0.883152	+	0.232401i
$981$	−18.0263	−	13.0969i	−0.575535	−	0.418151i
$982$	0.352645	+	0.0944910i	0.0112534	+	0.00301533i
$983$	−17.7922	+	46.3503i	−0.567484	+	1.47835i	0.286518	+	0.958075i	$0.407502\pi$
$983$	−17.7922	+	46.3503i	−0.567484	+	1.47835i	−0.854001	+	0.520271i	$0.825831\pi$
$984$	−10.2630	+	9.24088i	−0.327174	+	0.294588i
$985$	−25.0756	−	21.5523i	−0.798975	−	0.686713i
$986$	−0.962779	+	0.312826i	−0.0306611	+	0.00996240i
$987$	0.0386306	−	0.0417332i	0.00122962	−	0.00132838i
$988$	0.200931	−	0.102379i	0.00639246	−	0.00325712i
$989$	65.2297	+	58.7331i	2.07418	+	1.86760i
$990$	−2.69343	+	4.92398i	−0.0856029	+	0.156494i
$991$	−24.7481	−	27.4856i	−0.786149	−	0.873107i	0.208328	−	0.978059i	$-0.433198\pi$
$991$	−24.7481	−	27.4856i	−0.786149	−	0.873107i	−0.994477	+	0.104952i	$0.966531\pi$
$992$	23.4060	−	18.9538i	0.743141	−	0.601784i
$993$	2.03175	−	2.03175i	0.0644756	−	0.0644756i
$994$	−2.42368	−	9.57060i	−0.0768745	−	0.303561i
$995$	−20.1342	−	37.3601i	−0.638296	−	1.18440i
$996$	−27.9396	−	12.4395i	−0.885300	−	0.394161i
$997$	−4.61687	+	5.70135i	−0.146218	+	0.180564i	−0.844993	−	0.534778i	$-0.820395\pi$
$997$	−4.61687	+	5.70135i	−0.146218	+	0.180564i	0.698775	+	0.715341i	$0.253729\pi$
$998$	4.71550	+	7.26124i	0.149267	+	0.229851i
$999$	5.07277	+	8.78629i	0.160495	+	0.277986i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.2.x.a.108.11	yes	288
5.2	odd	4		875.2.bb.b.857.8		288
5.3	odd	4		875.2.bb.a.857.11		288
5.4	even	2		875.2.bb.c.143.8		288
7.5	odd	6	inner	175.2.x.a.33.11	✓	288
25.3	odd	20		875.2.bb.c.507.8		288
25.4	even	10		875.2.bb.a.493.8		288
25.21	even	5		875.2.bb.b.493.11		288
25.22	odd	20	inner	175.2.x.a.122.11	yes	288
35.12	even	12		875.2.bb.b.607.11		288
35.19	odd	6		875.2.bb.c.768.8		288
35.33	even	12		875.2.bb.a.607.8		288
175.47	even	60	inner	175.2.x.a.47.11	yes	288
175.54	odd	30		875.2.bb.a.243.11		288
175.96	odd	30		875.2.bb.b.243.8		288
175.103	even	60		875.2.bb.c.257.8		288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.33.11	✓	288	7.5	odd	6	inner
175.2.x.a.47.11	yes	288	175.47	even	60	inner
175.2.x.a.108.11	yes	288	1.1	even	1	trivial
175.2.x.a.122.11	yes	288	25.22	odd	20	inner
875.2.bb.a.243.11		288	175.54	odd	30
875.2.bb.a.493.8		288	25.4	even	10
875.2.bb.a.607.8		288	35.33	even	12
875.2.bb.a.857.11		288	5.3	odd	4
875.2.bb.b.243.8		288	175.96	odd	30
875.2.bb.b.493.11		288	25.21	even	5
875.2.bb.b.607.11		288	35.12	even	12
875.2.bb.b.857.8		288	5.2	odd	4
875.2.bb.c.143.8		288	5.4	even	2
875.2.bb.c.257.8		288	175.103	even	60
875.2.bb.c.507.8		288	25.3	odd	20
875.2.bb.c.768.8		288	35.19	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	175.x (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0218036 + 0.416038i) q^{2} +(-0.968728 - 0.784461i) q^{3} +(1.81643 - 0.190915i) q^{4} +(-1.17429 + 1.90291i) q^{5} +(0.305244 - 0.420132i) q^{6} +(2.40197 + 1.10931i) q^{7} +(0.249376 + 1.57450i) q^{8} +(-0.300679 - 1.41458i) q^{9} +(-0.817285 - 0.447058i) q^{10} +(4.07495 + 0.866158i) q^{11} +(-1.90939 - 1.23997i) q^{12} +(-0.207137 - 0.406529i) q^{13} +(-0.409142 + 1.02350i) q^{14} +(2.63032 - 0.922217i) q^{15} +(2.92344 - 0.621395i) q^{16} +(1.05776 + 0.406038i) q^{17} +(0.581965 - 0.155937i) q^{18} +(-0.0282868 + 0.269131i) q^{19} +(-1.76972 + 3.68069i) q^{20} +(-1.45664 - 2.95886i) q^{21} +(-0.271506 + 1.71422i) q^{22} +(-8.97950 + 0.470596i) q^{23} +(0.993556 - 1.72089i) q^{24} +(-2.24210 - 4.46911i) q^{25} +(0.164615 - 0.0950407i) q^{26} +(-2.51613 + 4.93819i) q^{27} +(4.57479 + 1.55641i) q^{28} +(1.26059 + 1.73505i) q^{29} +(0.441028 + 1.07420i) q^{30} +(-2.76313 - 6.20610i) q^{31} +(1.14745 + 4.28233i) q^{32} +(-3.26806 - 4.03571i) q^{33} +(-0.145864 + 0.448923i) q^{34} +(-4.93150 + 3.26807i) q^{35} +(-0.816228 - 2.51209i) q^{36} +(0.997003 - 1.53525i) q^{37} +(-0.112586 - 0.00590036i) q^{38} +(-0.118247 + 0.556307i) q^{39} +(-3.28897 - 1.37438i) q^{40} +(-6.60977 - 2.14764i) q^{41} +(1.19924 - 0.670533i) q^{42} +(-6.90254 - 6.90254i) q^{43} +(7.56724 + 0.795349i) q^{44} +(3.04490 + 1.08896i) q^{45} +(-0.391571 - 3.72555i) q^{46} +(0.00617944 + 0.0160980i) q^{47} +(-3.31947 - 1.69136i) q^{48} +(4.53888 + 5.32903i) q^{49} +(1.81043 - 1.03024i) q^{50} +(-0.706165 - 1.22311i) q^{51} +(-0.453863 - 0.698887i) q^{52} +(4.26257 - 5.26384i) q^{53} +(-2.10934 - 0.939137i) q^{54} +(-6.43338 + 6.73714i) q^{55} +(-1.14761 + 4.05853i) q^{56} +(0.238525 - 0.238525i) q^{57} +(-0.694362 + 0.562283i) q^{58} +(-7.19184 - 7.98735i) q^{59} +(4.60173 - 2.17731i) q^{60} +(8.00447 + 7.20725i) q^{61} +(2.52173 - 1.28488i) q^{62} +(0.846987 - 3.73133i) q^{63} +(3.92834 - 1.27640i) q^{64} +(1.01683 + 0.0832196i) q^{65} +(1.60775 - 1.44763i) q^{66} +(-0.673817 + 1.75535i) q^{67} +(1.99887 + 0.535597i) q^{68} +(9.06786 + 6.58819i) q^{69} +(-1.46717 - 1.98044i) q^{70} +(-7.24631 + 5.26475i) q^{71} +(2.15228 - 0.826184i) q^{72} +(4.36826 - 2.83678i) q^{73} +(0.660461 + 0.381317i) q^{74} +(-1.33386 + 6.08820i) q^{75} +0.494259i q^{76} +(8.82706 + 6.60086i) q^{77} +(-0.234023 - 0.0370656i) q^{78} +(-6.01516 + 13.5103i) q^{79} +(-2.25049 + 6.29272i) q^{80} +(2.34780 - 1.04531i) q^{81} +(0.749384 - 2.79674i) q^{82} +(13.2680 - 2.10145i) q^{83} +(-3.21079 - 5.09648i) q^{84} +(-2.01477 + 1.53602i) q^{85} +(2.72122 - 3.02222i) q^{86} +(0.139912 - 2.66968i) q^{87} +(-0.347569 + 6.63202i) q^{88} +(2.73357 - 3.03594i) q^{89} +(-0.386660 + 1.29054i) q^{90} +(-0.0465702 - 1.20625i) q^{91} +(-16.2208 + 2.56912i) q^{92} +(-2.19171 + 8.17959i) q^{93} +(-0.00656264 + 0.00292188i) q^{94} +(-0.478915 - 0.369864i) q^{95} +(2.24775 - 5.04854i) q^{96} +(-8.19248 - 1.29756i) q^{97} +(-2.11812 + 2.00454i) q^{98} -6.02480i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22}+ \cdots + 222 q^{98}+O(q^{100}) \) 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9 - 36 * q^10 - 6 * q^11 - 36 * q^12 - 20 * q^14 - 28 * q^15 - 30 * q^16 - 42 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 + 32 * q^22 - 40 * q^23 + 2 * q^25 - 48 * q^26 + 22 * q^28 - 58 * q^30 - 18 * q^31 + 8 * q^32 - 30 * q^33 - 2 * q^35 + 40 * q^36 - 10 * q^37 + 72 * q^38 + 30 * q^39 - 48 * q^40 + 6 * q^42 - 108 * q^43 - 10 * q^44 + 186 * q^45 - 6 * q^46 - 54 * q^47 - 248 * q^50 - 16 * q^51 + 216 * q^52 + 50 * q^53 - 30 * q^54 + 4 * q^56 - 216 * q^57 - 4 * q^58 + 90 * q^59 + 96 * q^60 - 18 * q^61 - 66 * q^63 - 100 * q^64 + 14 * q^65 - 90 * q^66 + 4 * q^67 + 342 * q^68 - 60 * q^70 - 24 * q^71 + 58 * q^72 - 6 * q^73 + 216 * q^75 - 80 * q^77 - 132 * q^78 - 10 * q^79 - 6 * q^80 - 10 * q^81 + 216 * q^82 + 20 * q^84 - 48 * q^85 - 6 * q^86 - 48 * q^87 - 122 * q^88 + 120 * q^89 - 12 * q^91 - 4 * q^92 + 106 * q^93 - 30 * q^94 - 98 * q^95 - 90 * q^96 + 222 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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