LMFDB - Embedded newform 875.2.bb.c.243.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [875,2,Mod(82,875)] 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("875.82"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(875, base_ring=CyclotomicField(60)) chi = DirichletCharacter(H, H._module([27, 50])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 875 = 5^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	875.bb (of order $60$, degree $16$, not minimal)

Newform invariants

comment:select newform

sage:traces = [288,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$6.98691017686$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$18$ over $\Q(\zeta_{60})$
Twist minimal:	no (minimal twist has level 175)
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			243.16
Character	$\chi$	$=$	875.243
Dual form			875.2.bb.c.857.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.08800 + 0.109427i) q^{2} +(0.522748 + 0.645540i) q^{3} +(2.35872 + 0.247911i) q^{4} +(1.02086 + 1.40509i) q^{6} +(1.53148 - 2.15744i) q^{7} +(0.767632 + 0.121581i) q^{8} +(0.480279 - 2.25953i) q^{9} +(1.02734 - 0.218367i) q^{11} +(1.07298 + 1.65224i) q^{12} +(4.08239 + 2.08008i) q^{13} +(3.43382 - 4.33715i) q^{14} +(-3.05026 - 0.648353i) q^{16} +(0.808289 + 2.10566i) q^{17} +(1.25008 - 4.66535i) q^{18} +(-0.520869 - 4.95574i) q^{19} +(2.19329 - 0.139164i) q^{21} +(2.16897 - 0.343531i) q^{22} +(-0.325733 + 6.21536i) q^{23} +(0.322792 + 0.559093i) q^{24} +(8.29642 + 4.78994i) q^{26} +(3.93004 - 2.00245i) q^{27} +(4.14720 - 4.70913i) q^{28} +(-0.743348 + 1.02313i) q^{29} +(-4.14336 + 9.30613i) q^{31} +(-7.79943 - 2.08985i) q^{32} +(0.678002 + 0.549035i) q^{33} +(1.45729 + 4.48507i) q^{34} +(1.69301 - 5.21054i) q^{36} +(-5.27200 + 3.42368i) q^{37} +(-0.545281 - 10.4046i) q^{38} +(0.791286 + 3.72271i) q^{39} +(5.32280 - 1.72948i) q^{41} +(4.59482 - 0.0505673i) q^{42} +(-4.80861 - 4.80861i) q^{43} +(2.47733 - 0.260378i) q^{44} +(-1.36026 + 12.9420i) q^{46} +(-0.292218 - 0.112172i) q^{47} +(-1.17598 - 2.30799i) q^{48} +(-2.30911 - 6.60818i) q^{49} +(-0.936759 + 1.62251i) q^{51} +(9.11355 + 5.91841i) q^{52} +(0.217690 - 0.176281i) q^{53} +(8.42504 - 3.75107i) q^{54} +(1.43792 - 1.46992i) q^{56} +(2.92684 - 2.92684i) q^{57} +(-1.66407 + 2.05495i) q^{58} +(4.60084 - 5.10975i) q^{59} +(-3.94111 + 3.54859i) q^{61} +(-9.66967 + 18.9778i) q^{62} +(-4.13927 - 4.49661i) q^{63} +(-10.1249 - 3.28979i) q^{64} +(1.35559 + 1.22058i) q^{66} +(-11.4671 + 4.40181i) q^{67} +(1.38451 + 5.16706i) q^{68} +(-4.18254 + 3.03879i) q^{69} +(-1.66579 - 1.21027i) q^{71} +(0.643393 - 1.67610i) q^{72} +(0.705919 - 1.08702i) q^{73} +(-11.3826 + 6.57173i) q^{74} -11.8183i q^{76} +(1.10223 - 2.55084i) q^{77} +(1.24484 + 7.85959i) q^{78} +(4.40735 + 9.89907i) q^{79} +(-2.98382 - 1.32848i) q^{81} +(11.3033 - 3.02870i) q^{82} +(-0.579789 + 3.66064i) q^{83} +(5.20787 + 0.215495i) q^{84} +(-9.51417 - 10.5666i) q^{86} +(-1.04906 + 0.0549787i) q^{87} +(0.815165 - 0.0427210i) q^{88} +(-7.09604 - 7.88095i) q^{89} +(10.7398 - 5.62191i) q^{91} +(-2.30917 + 14.5795i) q^{92} +(-8.17341 + 2.19006i) q^{93} +(-0.597877 - 0.266192i) q^{94} +(-2.72805 - 6.12730i) q^{96} +(-0.775456 - 4.89604i) q^{97} +(-4.09830 - 14.0505i) q^{98} -2.42618i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q + 8 q^{2} + 24 q^{3} - 10 q^{4} + 10 q^{7} + 36 q^{8} - 10 q^{9} - 6 q^{11} + 36 q^{12} - 20 q^{14} - 30 q^{16} + 42 q^{17} + 14 q^{18} - 30 q^{19} - 12 q^{21} - 32 q^{22} + 40 q^{23} - 48 q^{26}+ \cdots - 222 q^{98}+O(q^{100}) $ 288 * q + 8 * q^2 + 24 * q^3 - 10 * q^4 + 10 * q^7 + 36 * q^8 - 10 * q^9 - 6 * q^11 + 36 * q^12 - 20 * q^14 - 30 * q^16 + 42 * q^17 + 14 * q^18 - 30 * q^19 - 12 * q^21 - 32 * q^22 + 40 * q^23 - 48 * q^26 - 22 * q^28 - 18 * q^31 - 8 * q^32 + 30 * q^33 + 40 * q^36 + 10 * q^37 - 72 * q^38 + 30 * q^39 - 6 * q^42 + 108 * q^43 - 10 * q^44 - 6 * q^46 + 54 * q^47 - 16 * q^51 - 216 * q^52 - 50 * q^53 - 30 * q^54 + 4 * q^56 + 216 * q^57 + 4 * q^58 + 90 * q^59 - 18 * q^61 + 66 * q^63 - 100 * q^64 - 90 * q^66 - 4 * q^67 - 342 * q^68 - 24 * q^71 - 58 * q^72 + 6 * q^73 + 80 * q^77 + 132 * q^78 - 10 * q^79 - 10 * q^81 - 216 * q^82 + 20 * q^84 - 6 * q^86 + 48 * q^87 + 122 * q^88 + 120 * q^89 - 12 * q^91 + 4 * q^92 - 106 * q^93 - 30 * q^94 - 90 * q^96 - 222 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/875\mathbb{Z}\right)^\times$.

$n$	$127$	$626$
$\chi(n)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	2.08800	+	0.109427i	1.47644	+	0.0773768i	0.773465	−	0.633839i	$-0.218522\pi$
$2$	2.08800	+	0.109427i	1.47644	+	0.0773768i	0.702973	+	0.711216i	$0.251855\pi$
$3$	0.522748	+	0.645540i	0.301809	+	0.372703i	0.905377	−	0.424609i	$-0.139588\pi$
$3$	0.522748	+	0.645540i	0.301809	+	0.372703i	−0.603568	+	0.797311i	$0.706255\pi$
$4$	2.35872	+	0.247911i	1.17936	+	0.123956i
$5$		0			0
$5$		0			0
$6$	1.02086	+	1.40509i	0.416763	+	0.573625i
$7$	1.53148	−	2.15744i	0.578847	−	0.815436i
$7$	1.53148	−	2.15744i	0.578847	−	0.815436i
$8$	0.767632	+	0.121581i	0.271399	+	0.0429853i
$9$	0.480279	−	2.25953i	0.160093	−	0.753178i
$10$		0			0
$11$	1.02734	−	0.218367i	0.309753	−	0.0658401i	−0.0504122	−	0.998728i	$-0.516054\pi$
$11$	1.02734	−	0.218367i	0.309753	−	0.0658401i	0.360166	+	0.932888i	$0.382720\pi$
$12$	1.07298	+	1.65224i	0.309742	+	0.476961i
$13$	4.08239	+	2.08008i	1.13225	+	0.576911i	0.916698	−	0.399580i	$-0.130844\pi$
$13$	4.08239	+	2.08008i	1.13225	+	0.576911i	0.215554	+	0.976492i	$0.430844\pi$
$14$	3.43382	−	4.33715i	0.917727	−	1.15915i
$15$		0			0
$16$	−3.05026	−	0.648353i	−0.762565	−	0.162088i
$17$	0.808289	+	2.10566i	0.196039	+	0.510699i	0.996000	−	0.0893531i	$-0.0284800\pi$
$17$	0.808289	+	2.10566i	0.196039	+	0.510699i	−0.799961	+	0.600052i	$0.795147\pi$
$18$	1.25008	−	4.66535i	0.294646	−	1.09963i
$19$	−0.520869	−	4.95574i	−0.119496	−	1.13692i	−0.875790	−	0.482693i	$-0.839659\pi$
$19$	−0.520869	−	4.95574i	−0.119496	−	1.13692i	0.756294	−	0.654232i	$-0.227008\pi$
$20$		0			0
$21$	2.19329	−	0.139164i	0.478616	−	0.0303680i
$22$	2.16897	−	0.343531i	0.462426	−	0.0732411i
$23$	−0.325733	+	6.21536i	−0.0679201	+	1.29599i	0.725884	+	0.687818i	$0.241431\pi$
$23$	−0.325733	+	6.21536i	−0.0679201	+	1.29599i	−0.793804	+	0.608174i	$0.791902\pi$
$24$	0.322792	+	0.559093i	0.0658897	+	0.114124i
$25$		0			0
$26$	8.29642	+	4.78994i	1.62706	+	0.939384i
$27$	3.93004	−	2.00245i	0.756336	−	0.385373i
$28$	4.14720	−	4.70913i	0.783747	−	0.889942i
$29$	−0.743348	+	1.02313i	−0.138036	+	0.189991i	−0.872439	−	0.488724i	$-0.837463\pi$
$29$	−0.743348	+	1.02313i	−0.138036	+	0.189991i	0.734402	+	0.678714i	$0.237463\pi$
$30$		0			0
$31$	−4.14336	+	9.30613i	−0.744169	+	1.67143i	−0.00310567	+	0.999995i	$0.500989\pi$
$31$	−4.14336	+	9.30613i	−0.744169	+	1.67143i	−0.741063	+	0.671435i	$0.765678\pi$
$32$	−7.79943	−	2.08985i	−1.37876	−	0.369437i
$33$	0.678002	+	0.549035i	0.118025	+	0.0955748i
$34$	1.45729	+	4.48507i	0.249923	+	0.769184i
$35$		0			0
$36$	1.69301	−	5.21054i	0.282168	−	0.868424i
$37$	−5.27200	+	3.42368i	−0.866712	+	0.562849i	−0.899652	−	0.436608i	$-0.856180\pi$
$37$	−5.27200	+	3.42368i	−0.866712	+	0.562849i	0.0329402	+	0.999457i	$0.489513\pi$
$38$	−0.545281	−	10.4046i	−0.0884562	−	1.68785i
$39$	0.791286	+	3.72271i	0.126707	+	0.596110i
$40$		0			0
$41$	5.32280	−	1.72948i	0.831282	−	0.270100i	0.137697	−	0.990474i	$-0.456030\pi$
$41$	5.32280	−	1.72948i	0.831282	−	0.270100i	0.693585	+	0.720374i	$0.256030\pi$
$42$	4.59482	−	0.0505673i	0.708997	−	0.00780270i
$43$	−4.80861	−	4.80861i	−0.733306	−	0.733306i	0.237968	−	0.971273i	$-0.423519\pi$
$43$	−4.80861	−	4.80861i	−0.733306	−	0.733306i	−0.971273	+	0.237968i	$0.923519\pi$
$44$	2.47733	−	0.260378i	0.373472	−	0.0392535i
$45$		0			0
$46$	−1.36026	+	12.9420i	−0.200559	+	1.90820i
$47$	−0.292218	−	0.112172i	−0.0426244	−	0.0163620i	0.336962	−	0.941518i	$-0.390600\pi$
$47$	−0.292218	−	0.112172i	−0.0426244	−	0.0163620i	−0.379587	+	0.925156i	$0.623934\pi$
$48$	−1.17598	−	2.30799i	−0.169738	−	0.333130i
$49$	−2.30911	−	6.60818i	−0.329873	−	0.944025i
$50$		0			0
$51$	−0.936759	+	1.62251i	−0.131172	+	0.227197i
$52$	9.11355	+	5.91841i	1.26382	+	0.820736i
$53$	0.217690	−	0.176281i	0.0299020	−	0.0242141i	−0.614253	−	0.789109i	$-0.710543\pi$
$53$	0.217690	−	0.176281i	0.0299020	−	0.0242141i	0.644155	+	0.764895i	$0.277209\pi$
$54$	8.42504	−	3.75107i	1.14650	−	0.510456i
$55$		0			0
$56$	1.43792	−	1.46992i	0.192150	−	0.196426i
$57$	2.92684	−	2.92684i	0.387670	−	0.387670i
$58$	−1.66407	+	2.05495i	−0.218503	+	0.269829i
$59$	4.60084	−	5.10975i	0.598978	−	0.665232i	−0.365064	−	0.930982i	$-0.618953\pi$
$59$	4.60084	−	5.10975i	0.598978	−	0.665232i	0.964042	+	0.265750i	$0.0856196\pi$
$60$		0			0
$61$	−3.94111	+	3.54859i	−0.504607	+	0.454350i	−0.881690	−	0.471829i	$-0.843594\pi$
$61$	−3.94111	+	3.54859i	−0.504607	+	0.454350i	0.377083	+	0.926180i	$0.376927\pi$
$62$	−9.66967	+	18.9778i	−1.22805	+	2.41018i
$63$	−4.13927	−	4.49661i	−0.521499	−	0.566520i
$64$	−10.1249	−	3.28979i	−1.26562	−	0.411224i
$65$		0			0
$66$	1.35559	+	1.22058i	0.166861	+	0.150243i
$67$	−11.4671	+	4.40181i	−1.40093	+	0.537767i	−0.937382	−	0.348304i	$-0.886758\pi$
$67$	−11.4671	+	4.40181i	−1.40093	+	0.537767i	−0.463550	+	0.886071i	$0.653425\pi$
$68$	1.38451	+	5.16706i	0.167896	+	0.626598i
$69$	−4.18254	+	3.03879i	−0.503518	+	0.365827i
$70$		0			0
$71$	−1.66579	−	1.21027i	−0.197693	−	0.143632i	0.484535	−	0.874772i	$-0.338989\pi$
$71$	−1.66579	−	1.21027i	−0.197693	−	0.143632i	−0.682228	+	0.731140i	$0.738989\pi$
$72$	0.643393	−	1.67610i	0.0758246	−	0.197530i
$73$	0.705919	−	1.08702i	0.0826215	−	0.127226i	−0.794944	−	0.606683i	$-0.792500\pi$
$73$	0.705919	−	1.08702i	0.0826215	−	0.127226i	0.877565	+	0.479457i	$0.159166\pi$
$74$	−11.3826	+	6.57173i	−1.32320	+	0.763948i
$75$		0			0
$76$		−	11.8183i		−	1.35566i
$77$	1.10223	−	2.55084i	0.125611	−	0.290696i
$78$	1.24484	+	7.85959i	0.140950	+	0.889924i
$79$	4.40735	+	9.89907i	0.495865	+	1.11373i	0.972133	+	0.234431i	$0.0753228\pi$
$79$	4.40735	+	9.89907i	0.495865	+	1.11373i	−0.476267	+	0.879301i	$0.658011\pi$
$80$		0			0
$81$	−2.98382	−	1.32848i	−0.331536	−	0.147609i
$82$	11.3033	−	3.02870i	1.24824	−	0.334464i
$83$	−0.579789	+	3.66064i	−0.0636401	+	0.401808i	0.935220	+	0.354068i	$0.115202\pi$
$83$	−0.579789	+	3.66064i	−0.0636401	+	0.401808i	−0.998860	+	0.0477399i	$0.984798\pi$
$84$	5.20787	+	0.215495i	0.568225	+	0.0235124i
$85$		0			0
$86$	−9.51417	−	10.5666i	−1.02594	−	1.13942i
$87$	−1.04906	+	0.0549787i	−0.112471	+	0.00589433i
$88$	0.815165	−	0.0427210i	0.0868968	−	0.00455407i
$89$	−7.09604	−	7.88095i	−0.752179	−	0.835379i	0.238565	−	0.971127i	$-0.423323\pi$
$89$	−7.09604	−	7.88095i	−0.752179	−	0.835379i	−0.990743	+	0.135747i	$0.956656\pi$
$90$		0			0
$91$	10.7398	−	5.62191i	1.12584	−	0.589337i
$92$	−2.30917	+	14.5795i	−0.240748	+	1.52002i
$93$	−8.17341	+	2.19006i	−0.847543	+	0.227098i
$94$	−0.597877	−	0.266192i	−0.0616663	−	0.0274556i
$95$		0			0
$96$	−2.72805	−	6.12730i	−0.278431	−	0.625365i
$97$	−0.775456	−	4.89604i	−0.0787356	−	0.497117i	−0.995269	−	0.0971587i	$-0.969025\pi$
$97$	−0.775456	−	4.89604i	−0.0787356	−	0.497117i	0.916533	−	0.399958i	$-0.130975\pi$
$98$	−4.09830	−	14.0505i	−0.413991	−	1.41932i
$99$		−	2.42618i		−	0.243840i
$100$		0			0
$101$	13.1637	−	7.60006i	1.30984	−	0.756234i	0.327767	−	0.944758i	$-0.393704\pi$
$101$	13.1637	−	7.60006i	1.30984	−	0.756234i	0.982069	+	0.188524i	$0.0603704\pi$
$102$	−2.13350	+	3.28530i	−0.211248	+	0.325293i
$103$	−2.43305	+	6.33830i	−0.239735	+	0.624532i	−0.999676	−	0.0254609i	$-0.991895\pi$
$103$	−2.43305	+	6.33830i	−0.239735	+	0.624532i	0.759941	+	0.649993i	$0.225228\pi$
$104$	2.88088	+	2.09308i	0.282493	+	0.205243i
$105$		0			0
$106$	0.473825	−	0.344254i	0.0460220	−	0.0334369i
$107$	−5.09063	−	18.9985i	−0.492130	−	1.83665i	−0.545546	−	0.838081i	$-0.683678\pi$
$107$	−5.09063	−	18.9985i	−0.492130	−	1.83665i	0.0534166	−	0.998572i	$-0.482989\pi$
$108$	9.76629	−	3.74893i	0.939762	−	0.360741i
$109$	14.2080	+	12.7930i	1.36088	+	1.22535i	0.949455	+	0.313903i	$0.101637\pi$
$109$	14.2080	+	12.7930i	1.36088	+	1.22535i	0.411428	+	0.911442i	$0.365030\pi$
$110$		0			0
$111$	−4.96605	−	1.61357i	−0.471356	−	0.153153i
$112$	−6.07021	+	5.58782i	−0.573581	+	0.527999i
$113$	−3.96233	+	7.77652i	−0.372745	+	0.731553i	−0.998838	−	0.0481952i	$-0.984653\pi$
$113$	−3.96233	+	7.77652i	−0.372745	+	0.731553i	0.626093	+	0.779748i	$0.284653\pi$
$114$	6.43152	−	5.79097i	0.602367	−	0.542374i
$115$		0			0
$116$	−2.00700	+	2.22900i	−0.186345	+	0.206957i
$117$	6.66071	−	8.22529i	0.615783	−	0.760428i
$118$	10.1657	−	10.1657i	0.935827	−	0.935827i
$119$	5.78073	+	1.48096i	0.529919	+	0.135759i
$120$		0			0
$121$	−9.04127	+	4.02543i	−0.821933	+	0.365948i
$122$	−8.61734	+	6.97819i	−0.780177	+	0.631775i
$123$	3.89893	+	2.53200i	0.351555	+	0.228303i
$124$	−12.0801	+	20.9234i	−1.08483	+	1.87897i
$125$		0			0
$126$	−8.15074	−	9.84188i	−0.726126	−	0.876784i
$127$	−5.89827	−	11.5760i	−0.523386	−	1.02720i	−0.989777	−	0.142625i	$-0.954446\pi$
$127$	−5.89827	−	11.5760i	−0.523386	−	1.02720i	0.466390	−	0.884579i	$-0.345554\pi$
$128$	−5.70438	−	2.18971i	−0.504201	−	0.193544i
$129$	0.590458	−	5.61783i	0.0519869	−	0.494623i
$130$		0			0
$131$	3.52330	−	0.370314i	0.307832	−	0.0323545i	0.0506472	−	0.998717i	$-0.483872\pi$
$131$	3.52330	−	0.370314i	0.307832	−	0.0323545i	0.257185	+	0.966362i	$0.417205\pi$
$132$	1.46310	+	1.46310i	0.127347	+	0.127347i
$133$	−11.4894	−	6.46590i	−0.996260	−	0.560664i
$134$	−24.4250	+	7.93617i	−2.11000	+	0.685580i
$135$		0			0
$136$	0.364459	+	1.71465i	0.0312521	+	0.147030i
$137$	−0.396425	−	7.56424i	−0.0338689	−	0.646257i	−0.961841	−	0.273608i	$-0.911783\pi$
$137$	−0.396425	−	7.56424i	−0.0338689	−	0.646257i	0.927972	−	0.372649i	$-0.121550\pi$
$138$	−9.06566	+	5.88731i	−0.771720	+	0.501161i
$139$	−2.73221	+	8.40888i	−0.231743	+	0.713232i	0.765794	+	0.643086i	$0.222346\pi$
$139$	−2.73221	+	8.40888i	−0.231743	+	0.713232i	−0.997537	+	0.0701455i	$0.977654\pi$
$140$		0			0
$141$	−0.0803449	−	0.247276i	−0.00676626	−	0.0208244i
$142$	−3.34573	−	2.70932i	−0.280767	−	0.227361i
$143$	4.64821	+	1.24548i	0.388703	+	0.104153i
$144$	−2.92995	+	6.58078i	−0.244163	+	0.548398i
$145$		0			0
$146$	1.59291	−	2.19245i	0.131830	−	0.181448i
$147$	3.05876	−	4.94503i	0.252282	−	0.407859i
$148$	−13.2839	+	6.76851i	−1.09193	+	0.556368i
$149$	−1.52475	−	0.880317i	−0.124913	−	0.0721183i	0.436242	−	0.899830i	$-0.356309\pi$
$149$	−1.52475	−	0.880317i	−0.124913	−	0.0721183i	−0.561154	+	0.827711i	$0.689643\pi$
$150$		0			0
$151$	−3.13479	−	5.42962i	−0.255106	−	0.441856i	0.709819	−	0.704385i	$-0.248777\pi$
$151$	−3.13479	−	5.42962i	−0.255106	−	0.441856i	−0.964924	+	0.262529i	$0.915444\pi$
$152$	0.202688	−	3.86751i	0.0164401	−	0.313697i
$153$	5.14602	−	0.815050i	0.416031	−	0.0658929i
$154$	2.58060	−	5.20554i	0.207950	−	0.419474i
$155$		0			0
$156$	0.943520	+	8.97699i	0.0755420	+	0.718735i
$157$	−2.79709	+	10.4389i	−0.223232	+	0.833115i	0.759872	+	0.650072i	$0.225261\pi$
$157$	−2.79709	+	10.4389i	−0.223232	+	0.833115i	−0.983105	+	0.183043i	$0.941405\pi$
$158$	8.11931	+	21.1515i	0.645937	+	1.68272i
$159$	0.227593	+	0.0483765i	0.0180493	+	0.00383650i
$160$		0			0
$161$	12.9104	+	10.2215i	1.01748	+	0.805565i
$162$	−6.08485	−	3.10038i	−0.478071	−	0.243589i
$163$	3.03858	+	4.67900i	0.238000	+	0.366488i	0.937407	−	0.348236i	$-0.113219\pi$
$163$	3.03858	+	4.67900i	0.238000	+	0.366488i	−0.699407	+	0.714724i	$0.746552\pi$
$164$	12.9838	−	2.75978i	1.01386	−	0.215503i
$165$		0			0
$166$	−1.61117	+	7.57998i	−0.125051	+	0.588320i
$167$	10.3561	+	1.64024i	0.801379	+	0.126926i	0.543673	−	0.839297i	$-0.317033\pi$
$167$	10.3561	+	1.64024i	0.801379	+	0.126926i	0.257706	+	0.966223i	$0.417033\pi$
$168$	1.70056	+	0.159836i	0.131201	+	0.0123316i
$169$	4.69799	+	6.46623i	0.361384	+	0.497402i
$170$		0			0
$171$	−11.4478	−	1.20322i	−0.875437	−	0.0920122i
$172$	−10.1500	−	12.5343i	−0.773934	−	0.955729i
$173$	13.7091	+	0.718462i	1.04228	+	0.0546236i	0.565785	−	0.824553i	$-0.308573\pi$
$173$	13.7091	+	0.718462i	1.04228	+	0.0546236i	0.476496	+	0.879177i	$0.341907\pi$
$174$	−2.19644			−0.166512
$175$		0			0
$176$	−3.27522			−0.246879
$177$	5.70362	+	0.298914i	0.428710	+	0.0224678i
$178$	−13.9541	−	17.2319i	−1.04591	−	1.29159i
$179$	1.60078	+	0.168248i	0.119648	+	0.0125755i	0.164163	−	0.986433i	$-0.447508\pi$
$179$	1.60078	+	0.168248i	0.119648	+	0.0125755i	−0.0445154	+	0.999009i	$0.514174\pi$
$180$		0			0
$181$	−2.04450	−	2.81402i	−0.151967	−	0.209164i	0.726245	−	0.687436i	$-0.241264\pi$
$181$	−2.04450	−	2.81402i	−0.151967	−	0.209164i	−0.878212	+	0.478271i	$0.841264\pi$
$182$	23.0398	−	10.5633i	1.70783	−	0.783005i
$183$	−4.35096	−	0.689125i	−0.321632	−	0.0509416i
$184$	−1.00571	+	4.73150i	−0.0741421	+	0.348811i
$185$		0			0
$186$	−17.3057	+	3.67844i	−1.26892	+	0.269717i
$187$	1.29019	+	1.98672i	0.0943481	+	0.145283i
$188$	−0.661452	−	0.337027i	−0.0482414	−	0.0245802i
$189$	1.69861	−	11.5456i	0.123556	−	0.839816i
$190$		0			0
$191$	2.89987	+	0.616386i	0.209827	+	0.0446001i	0.311626	−	0.950205i	$-0.399126\pi$
$191$	2.89987	+	0.616386i	0.209827	+	0.0446001i	−0.101799	+	0.994805i	$0.532460\pi$
$192$	−3.16910	−	8.25579i	−0.228710	−	0.595810i
$193$	−4.41207	+	16.4661i	−0.317588	+	1.18525i	0.603968	+	0.797009i	$0.293586\pi$
$193$	−4.41207	+	16.4661i	−0.317588	+	1.18525i	−0.921556	+	0.388246i	$0.873081\pi$
$194$	−1.08339	−	10.3078i	−0.0777829	−	0.740055i
$195$		0			0
$196$	−3.80830	−	16.1593i	−0.272022	−	1.15424i
$197$	−19.1171	+	3.02785i	−1.36204	+	0.215725i	−0.794320	−	0.607499i	$-0.792173\pi$
$197$	−19.1171	+	3.02785i	−1.36204	+	0.215725i	−0.567716	+	0.823225i	$0.692173\pi$
$198$	0.265490	−	5.06585i	0.0188676	−	0.360015i
$199$	−0.0959424	−	0.166177i	−0.00680118	−	0.0117800i	0.862605	−	0.505878i	$-0.168832\pi$
$199$	−0.0959424	−	0.166177i	−0.00680118	−	0.0117800i	−0.869406	+	0.494098i	$0.835498\pi$
$200$		0			0
$201$	−8.83596	−	5.10144i	−0.623240	−	0.359828i
$202$	28.3174	−	14.4284i	1.99241	−	1.01518i
$203$	1.06892	+	3.17064i	0.0750234	+	0.222535i
$204$	−2.61179	+	3.59482i	−0.182862	+	0.251688i
$205$		0			0
$206$	−5.77378	+	12.9681i	−0.402278	+	0.903532i
$207$	13.8874	+	3.72111i	0.965239	+	0.258635i
$208$	−11.1037	−	8.99163i	−0.769906	−	0.623457i
$209$	−1.61728	−	4.97747i	−0.111869	−	0.344299i
$210$		0			0
$211$	1.96658	−	6.05250i	0.135385	−	0.416671i	−0.860265	−	0.509847i	$-0.829702\pi$
$211$	1.96658	−	6.05250i	0.135385	−	0.416671i	0.995650	+	0.0931759i	$0.0297019\pi$
$212$	0.557171	−	0.361831i	0.0382666	−	0.0248507i
$213$	−0.0895123	−	1.70800i	−0.00613328	−	0.117030i
$214$	−8.55027	−	40.2259i	−0.584485	−	2.74978i
$215$		0			0
$216$	3.26028	−	1.05933i	0.221834	−	0.0720783i
$217$	13.7319	+	23.1912i	0.932185	+	1.57432i
$218$	28.2665	+	28.2665i	1.91445	+	1.91445i
$219$	1.07073	−	0.112538i	0.0723533	−	0.00760464i
$220$		0			0
$221$	−1.08020	+	10.2775i	−0.0726624	+	0.691337i
$222$	−10.1925	−	3.91254i	−0.684078	−	0.262593i
$223$	6.05349	+	11.8807i	0.405372	+	0.795587i	0.999964	−	0.00843996i	$-0.00268655\pi$
$223$	6.05349	+	11.8807i	0.405372	+	0.795587i	−0.594592	+	0.804027i	$0.702687\pi$
$224$	−16.4534	+	13.6262i	−1.09934	+	0.910441i
$225$		0			0
$226$	−9.12431	+	15.8038i	−0.606940	+	1.05125i
$227$	4.06947	+	2.64274i	0.270100	+	0.175405i	0.672581	−	0.740023i	$-0.265185\pi$
$227$	4.06947	+	2.64274i	0.270100	+	0.175405i	−0.402481	+	0.915428i	$0.631852\pi$
$228$	7.62920	−	6.17801i	0.505256	−	0.409149i
$229$	−6.10856	+	2.71971i	−0.403665	+	0.179723i	−0.598518	−	0.801109i	$-0.704244\pi$
$229$	−6.10856	+	2.71971i	−0.403665	+	0.179723i	0.194853	+	0.980832i	$0.437577\pi$
$230$		0			0
$231$	2.22286	−	0.621911i	0.146254	−	0.0409187i
$232$	−0.695011	+	0.695011i	−0.0456297	+	0.0456297i
$233$	5.43374	−	6.71012i	0.355976	−	0.439594i	−0.567428	−	0.823423i	$-0.692061\pi$
$233$	5.43374	−	6.71012i	0.355976	−	0.439594i	0.923404	+	0.383829i	$0.125395\pi$
$234$	14.8076	−	16.4455i	0.968004	−	1.07508i
$235$		0			0
$236$	12.1189	−	10.9119i	0.788870	−	0.710302i
$237$	−4.08631	+	8.01983i	−0.265434	+	0.520944i
$238$	11.9081	+	3.72480i	0.771887	+	0.241443i
$239$	−18.2461	−	5.92852i	−1.18024	−	0.383484i	−0.347785	−	0.937574i	$-0.613066\pi$
$239$	−18.2461	−	5.92852i	−1.18024	−	0.383484i	−0.832457	+	0.554090i	$0.813066\pi$
$240$		0			0
$241$	19.2863	+	17.3654i	1.24234	+	1.11861i	0.988478	+	0.151366i	$0.0483671\pi$
$241$	19.2863	+	17.3654i	1.24234	+	1.11861i	0.253861	+	0.967241i	$0.418300\pi$
$242$	−19.3186	+	7.41573i	−1.24185	+	0.476701i
$243$	−4.12698	−	15.4021i	−0.264746	−	0.988046i
$244$	−10.1757	+	7.39308i	−0.651433	+	0.473294i
$245$		0			0
$246$	7.86390	+	5.71346i	0.501384	+	0.364277i
$247$	8.18196	−	21.3147i	0.520606	−	1.35622i
$248$	−4.31202	+	6.63993i	−0.273814	+	0.421636i
$249$	−2.66617	+	1.53932i	−0.168962	+	0.0975502i
$250$		0			0
$251$			15.4133i			0.972880i	0.873714	+	0.486440i	$0.161705\pi$
$251$			15.4133i			0.972880i	−0.873714	+	0.486440i	$0.838295\pi$
$252$	−8.64862	−	11.6324i	−0.544812	−	0.732774i
$253$	1.02259	+	6.45639i	0.0642898	+	0.405910i
$254$	−11.0488	−	24.8161i	−0.693266	−	1.55710i
$255$		0			0
$256$	7.78009	+	3.46392i	0.486256	+	0.216495i
$257$	−29.5275	+	7.91188i	−1.84188	+	0.493529i	−0.999006	−	0.0445856i	$-0.985803\pi$
$257$	−29.5275	+	7.91188i	−1.84188	+	0.493529i	−0.842871	+	0.538115i	$0.819137\pi$
$258$	1.84762	−	11.6654i	0.115028	−	0.726257i
$259$	−0.687603	+	16.6173i	−0.0427256	+	1.03255i
$260$		0			0
$261$	1.95479	+	2.17101i	0.120998	+	0.134382i
$262$	7.39718	−	0.387670i	0.456999	−	0.0239503i
$263$	0.407151	−	0.0213379i	0.0251060	−	0.00131575i	−0.0397788	−	0.999209i	$-0.512665\pi$
$263$	0.407151	−	0.0213379i	0.0251060	−	0.00131575i	0.0648848	+	0.997893i	$0.479332\pi$
$264$	0.453704	+	0.503889i	0.0279235	+	0.0310122i
$265$		0			0
$266$	−23.2824	−	14.7580i	−1.42753	−	0.904873i
$267$	1.37803	−	8.70053i	0.0843340	−	0.532464i
$268$	−28.1390	+	7.53982i	−1.71886	+	0.460568i
$269$	17.4978	+	7.79051i	1.06686	+	0.474996i	0.863625	−	0.504134i	$-0.168188\pi$
$269$	17.4978	+	7.79051i	1.06686	+	0.474996i	0.203233	+	0.979130i	$0.434855\pi$
$270$		0			0
$271$	−7.85265	−	17.6373i	−0.477015	−	1.07139i	−0.978504	−	0.206228i	$-0.933881\pi$
$271$	−7.85265	−	17.6373i	−0.477015	−	1.07139i	0.501489	−	0.865164i	$-0.332786\pi$
$272$	−1.10028	−	6.94688i	−0.0667141	−	0.421216i
$273$	9.24337	+	3.99411i	0.559434	+	0.241735i
$274$		−	15.8375i		−	0.956779i
$275$		0			0
$276$	−10.6188	+	6.13076i	−0.639176	+	0.369028i
$277$	4.16515	−	6.41377i	0.250260	−	0.385366i	−0.691106	−	0.722753i	$-0.742876\pi$
$277$	4.16515	−	6.41377i	0.250260	−	0.385366i	0.941366	+	0.337387i	$0.109543\pi$
$278$	−6.62501	+	17.2587i	−0.397342	+	1.03511i
$279$	19.0376	+	13.8316i	1.13975	+	0.828076i
$280$		0			0
$281$	15.1432	−	11.0022i	0.903367	−	0.656334i	−0.0359618	−	0.999353i	$-0.511449\pi$
$281$	15.1432	−	11.0022i	0.903367	−	0.656334i	0.939329	+	0.343019i	$0.111449\pi$
$282$	−0.140701	−	0.525104i	−0.00837864	−	0.0312695i
$283$	−2.66042	+	1.02124i	−0.158145	+	0.0607063i	−0.436153	−	0.899873i	$-0.643659\pi$
$283$	−2.66042	+	1.02124i	−0.158145	+	0.0607063i	0.278008	+	0.960579i	$0.410326\pi$
$284$	−3.62909	−	3.26765i	−0.215347	−	0.193899i
$285$		0			0
$286$	9.56917	+	3.10921i	0.565837	+	0.183852i
$287$	4.42053	−	14.1323i	0.260936	−	0.834204i
$288$	−8.46799	+	16.6194i	−0.498981	+	0.979305i
$289$	8.85297	−	7.97125i	0.520763	−	0.468897i
$290$		0			0
$291$	2.75522	−	3.05998i	0.161514	−	0.179379i
$292$	1.93455	−	2.38897i	0.113211	−	0.139804i
$293$	−0.584948	+	0.584948i	−0.0341730	+	0.0341730i	−0.723987	−	0.689814i	$-0.757692\pi$
$293$	−0.584948	+	0.584948i	−0.0341730	+	0.0341730i	0.689814	+	0.723987i	$0.257692\pi$
$294$	6.92781	−	9.99051i	0.404038	−	0.582658i
$295$		0			0
$296$	−4.46321	+	1.98715i	−0.259419	+	0.115501i
$297$	3.60020	−	2.91538i	0.208905	−	0.169168i
$298$	−3.08735	−	2.00495i	−0.178845	−	0.116144i
$299$	−14.2582	+	24.6960i	−0.824575	+	1.42821i
$300$		0			0
$301$	−17.7386	+	3.00998i	−1.02244	+	0.173492i
$302$	−5.95129	−	11.6801i	−0.342458	−	0.672112i
$303$	11.7874	+	4.52477i	0.677170	+	0.259941i
$304$	−1.62428	+	15.4540i	−0.0931589	+	0.886348i
$305$		0			0
$306$	10.8341	−	1.13871i	0.619343	−	0.0650956i
$307$	10.4006	+	10.4006i	0.593593	+	0.593593i	0.938600	−	0.345007i	$-0.112123\pi$
$307$	10.4006	+	10.4006i	0.593593	+	0.593593i	−0.345007	+	0.938600i	$0.612123\pi$
$308$	3.23225	−	5.74347i	0.184174	−	0.327264i
$309$	−5.36350	+	1.74271i	−0.305119	+	0.0991391i
$310$		0			0
$311$	−2.47049	−	11.6228i	−0.140089	−	0.659066i	−0.991012	−	0.133776i	$-0.957290\pi$
$311$	−2.47049	−	11.6228i	−0.140089	−	0.659066i	0.850923	−	0.525291i	$-0.176043\pi$
$312$	0.154806	+	2.95387i	0.00876416	+	0.167230i
$313$	8.44819	−	5.48632i	0.477520	−	0.310105i	−0.283342	−	0.959019i	$-0.591443\pi$
$313$	8.44819	−	5.48632i	0.477520	−	0.310105i	0.760862	+	0.648914i	$0.224777\pi$
$314$	−6.98263	+	21.4903i	−0.394053	+	1.21277i
$315$		0			0
$316$	7.94161	+	24.4418i	0.446750	+	1.37496i
$317$	−14.6927	−	11.8979i	−0.825223	−	0.668252i	0.120684	−	0.992691i	$-0.461491\pi$
$317$	−14.6927	−	11.8979i	−0.825223	−	0.668252i	−0.945907	+	0.324439i	$0.894825\pi$
$318$	0.469921	+	0.125915i	0.0263519	+	0.00706096i
$319$	−0.540250	+	1.21342i	−0.0302482	+	0.0679386i
$320$		0			0
$321$	9.60316	−	13.2176i	0.535996	−	0.737736i
$322$	25.8384	+	22.7552i	1.43992	+	1.26810i
$323$	10.0141	−	5.10245i	0.557200	−	0.283908i
$324$	−6.70866	−	3.87325i	−0.372703	−	0.215180i
$325$		0			0
$326$	5.83254	+	10.1023i	0.323035	+	0.559512i
$327$	−0.831154	+	15.8594i	−0.0459629	+	0.877024i
$328$	4.29622	−	0.680455i	0.237219	−	0.0375719i
$329$	−0.689532	+	0.458654i	−0.0380152	+	0.0252864i
$330$		0			0
$331$	−3.25235	−	30.9441i	−0.178766	−	1.70084i	−0.604998	−	0.796227i	$-0.706826\pi$
$331$	−3.25235	−	30.9441i	−0.178766	−	1.70084i	0.426232	−	0.904614i	$-0.359841\pi$
$332$	−2.27508	+	8.49070i	−0.124861	+	0.465988i
$333$	5.20388	+	13.5566i	0.285171	+	0.742896i
$334$	21.4440	+	4.55807i	1.17336	+	0.249406i
$335$		0			0
$336$	−6.78035	−	0.997543i	−0.369898	−	0.0544204i
$337$	31.0198	+	15.8054i	1.68976	+	0.860974i	0.989060	+	0.147514i	$0.0471271\pi$
$337$	31.0198	+	15.8054i	1.68976	+	0.860974i	0.700696	+	0.713460i	$0.252873\pi$
$338$	9.10181	+	14.0156i	0.495073	+	0.762346i
$339$	−7.09135	+	1.50731i	−0.385149	+	0.0818660i
$340$		0			0
$341$	−2.22447	+	10.4653i	−0.120462	+	0.566727i
$342$	−23.7714	−	3.76502i	−1.28541	−	0.203589i
$343$	−17.7931	−	5.13855i	−0.960738	−	0.277456i
$344$	−3.10660	−	4.27587i	−0.167497	−	0.230540i
$345$		0			0
$346$	28.5459	+	3.00029i	1.53464	+	0.161297i
$347$	16.9534	+	20.9357i	0.910107	+	1.12389i	0.991872	+	0.127237i	$0.0406109\pi$
$347$	16.9534	+	20.9357i	0.910107	+	1.12389i	−0.0817651	+	0.996652i	$0.526056\pi$
$348$	−2.48806	−	0.130394i	−0.133374	−	0.00698983i
$349$	28.9278			1.54847			0.774236	−	0.632897i	$-0.218134\pi$
$349$	28.9278			1.54847			0.774236	+	0.632897i	$0.218134\pi$
$350$		0			0
$351$	20.2092			1.07869
$352$	−8.46898	−	0.443841i	−0.451398	−	0.0236568i
$353$	7.34270	+	9.06748i	0.390813	+	0.482613i	0.934140	−	0.356908i	$-0.116169\pi$
$353$	7.34270	+	9.06748i	0.390813	+	0.482613i	−0.543327	+	0.839521i	$0.682836\pi$
$354$	11.8764	+	1.24826i	0.631226	+	0.0663445i
$355$		0			0
$356$	−14.7838	−	20.3482i	−0.783540	−	1.07845i
$357$	2.06585	+	4.50586i	0.109336	+	0.238475i
$358$	3.32401	+	0.526471i	0.175679	+	0.0278248i
$359$	0.925593	−	4.35457i	0.0488509	−	0.229826i	−0.946949	−	0.321385i	$-0.895852\pi$
$359$	0.925593	−	4.35457i	0.0488509	−	0.229826i	0.995800	+	0.0915592i	$0.0291851\pi$
$360$		0			0
$361$	−5.70326	+	1.21227i	−0.300172	+	0.0638034i
$362$	−3.96099	−	6.09939i	−0.208185	−	0.320577i
$363$	−7.32488	−	3.73221i	−0.384456	−	0.195890i
$364$	26.7259	−	10.5980i	1.40082	−	0.555486i
$365$		0			0
$366$	−9.00939	−	1.91501i	−0.470928	−	0.100099i
$367$	−9.20390	−	23.9770i	−0.480440	−	1.25159i	−0.933007	−	0.359858i	$-0.882825\pi$
$367$	−9.20390	−	23.9770i	−0.480440	−	1.25159i	0.452567	−	0.891730i	$-0.350508\pi$
$368$	5.02332	−	18.7473i	0.261858	−	0.977269i
$369$	−1.35140	−	12.8577i	−0.0703510	−	0.669345i
$370$		0			0
$371$	−0.0469289	−	0.739625i	−0.00243643	−	0.0383994i
$372$	−19.8217	+	3.13945i	−1.02771	+	0.162773i
$373$	1.87432	−	35.7641i	0.0970485	−	1.85180i	−0.325606	−	0.945506i	$-0.605568\pi$
$373$	1.87432	−	35.7641i	0.0970485	−	1.85180i	0.422655	−	0.906291i	$-0.361098\pi$
$374$	2.47652	+	4.28945i	0.128058	+	0.221802i
$375$		0			0
$376$	−0.210678	−	0.121635i	−0.0108649	−	0.00627285i
$377$	−5.16284	+	2.63060i	−0.265900	+	0.135483i
$378$	4.81010	−	23.9212i	0.247405	−	1.23038i
$379$	−13.3436	+	18.3659i	−0.685416	+	0.943394i	−0.999983	−	0.00584095i	$-0.998141\pi$
$379$	−13.3436	+	18.3659i	−0.685416	+	0.943394i	0.314567	+	0.949235i	$0.398141\pi$
$380$		0			0
$381$	4.38946	−	9.85889i	0.224879	−	0.505086i
$382$	5.98747	+	1.60434i	0.306346	+	0.0820850i
$383$	−16.9050	−	13.6894i	−0.863806	−	0.699496i	0.0912802	−	0.995825i	$-0.470904\pi$
$383$	−16.9050	−	13.6894i	−0.863806	−	0.699496i	−0.955086	+	0.296329i	$0.904237\pi$
$384$	−1.56841	−	4.82707i	−0.0800375	−	0.246330i
$385$		0			0
$386$	−11.0142	+	33.8984i	−0.560610	+	1.72538i
$387$	−13.1747	+	8.55574i	−0.669707	+	0.434913i
$388$	−0.615300	−	11.7406i	−0.0312371	−	0.596040i
$389$	2.70252	+	12.7143i	0.137023	+	0.644643i	0.992027	+	0.126022i	$0.0402210\pi$
$389$	2.70252	+	12.7143i	0.137023	+	0.644643i	−0.855004	+	0.518621i	$0.826446\pi$
$390$		0			0
$391$	−13.3507	+	4.33792i	−0.675176	+	0.219378i
$392$	−0.969118	−	5.35339i	−0.0489478	−	0.270387i
$393$	2.08085	+	2.08085i	0.104965	+	0.104965i
$394$	−40.2478	+	4.23021i	−2.02765	+	0.213115i
$395$		0			0
$396$	0.601477	−	5.72267i	0.0302254	−	0.287575i
$397$	4.46102	+	1.71242i	0.223892	+	0.0859441i	0.467728	−	0.883872i	$-0.345073\pi$
$397$	4.46102	+	1.71242i	0.223892	+	0.0859441i	−0.243836	+	0.969816i	$0.578406\pi$
$398$	−0.182143	−	0.357476i	−0.00913002	−	0.0179187i
$399$	−1.83208	−	10.7969i	−0.0917187	−	0.540522i
$400$		0			0
$401$	7.58351	−	13.1350i	0.378702	−	0.655932i	−0.612171	−	0.790725i	$-0.709704\pi$
$401$	7.58351	−	13.1350i	0.378702	−	0.655932i	0.990874	+	0.134793i	$0.0430370\pi$
$402$	−17.8912	−	11.6187i	−0.892333	−	0.579488i
$403$	−36.2724	+	29.3728i	−1.80685	+	1.46316i
$404$	32.9336	−	14.6630i	1.63851	−	0.729511i
$405$		0			0
$406$	1.88495	+	6.73726i	0.0935484	+	0.334365i
$407$	−4.66850	+	4.66850i	−0.231409	+	0.231409i
$408$	−0.916352	+	1.13160i	−0.0453662	+	0.0560226i
$409$	6.87712	−	7.63781i	0.340052	−	0.377666i	−0.548728	−	0.836001i	$-0.684888\pi$
$409$	6.87712	−	7.63781i	0.340052	−	0.377666i	0.888779	+	0.458336i	$0.151554\pi$
$410$		0			0
$411$	4.67579	−	4.21010i	0.230640	−	0.207669i
$412$	−7.31021	+	14.3471i	−0.360148	+	0.706831i
$413$	−3.97787	−	17.7515i	−0.195738	−	0.873496i
$414$	28.5896	+	9.28933i	1.40510	+	0.456546i
$415$		0			0
$416$	−27.4933	−	24.7551i	−1.34797	−	1.21372i
$417$	−6.85652	+	2.63197i	−0.335765	+	0.128888i
$418$	−2.83220	−	10.5699i	−0.138528	−	0.516992i
$419$	−14.4852	+	10.5241i	−0.707648	+	0.514137i	−0.882414	−	0.470473i	$-0.844083\pi$
$419$	−14.4852	+	10.5241i	−0.707648	+	0.514137i	0.174766	+	0.984610i	$0.444083\pi$
$420$		0			0
$421$	13.5865	+	9.87120i	0.662168	+	0.481093i	0.867394	−	0.497621i	$-0.165793\pi$
$421$	13.5865	+	9.87120i	0.662168	+	0.481093i	−0.205227	+	0.978714i	$0.565793\pi$
$422$	4.76852	−	12.4224i	0.232128	−	0.604714i
$423$	−0.393803	+	0.606403i	−0.0191473	+	0.0294843i
$424$	0.188538	−	0.108852i	0.00915621	−	0.00528634i
$425$		0			0
$426$		−	3.57609i		−	0.173262i
$427$	1.62013	+	13.9373i	0.0784036	+	0.674474i
$428$	−7.29743	−	46.0741i	−0.352734	−	2.22708i
$429$	1.62583	+	3.65168i	0.0784959	+	0.176305i
$430$		0			0
$431$	−8.17166	−	3.63826i	−0.393615	−	0.175249i	0.200378	−	0.979719i	$-0.435783\pi$
$431$	−8.17166	−	3.63826i	−0.393615	−	0.175249i	−0.593993	+	0.804470i	$0.702449\pi$
$432$	−13.2859	+	3.55996i	−0.639220	+	0.171278i
$433$	2.75652	−	17.4040i	0.132470	−	0.836382i	−0.828552	−	0.559912i	$-0.810835\pi$
$433$	2.75652	−	17.4040i	0.132470	−	0.836382i	0.961022	−	0.276471i	$-0.0891649\pi$
$434$	26.1345	+	49.9259i	1.25450	+	2.39652i
$435$		0			0
$436$	30.3413	+	33.6974i	1.45308	+	1.61381i
$437$	30.9714	−	1.62314i	1.48156	−	0.0776454i
$438$	2.24800	−	0.117813i	0.107414	−	0.00562931i
$439$	−18.3365	−	20.3647i	−0.875151	−	0.971954i	0.124644	−	0.992202i	$-0.460221\pi$
$439$	−18.3365	−	20.3647i	−0.875151	−	0.971954i	−0.999795	+	0.0202474i	$0.993555\pi$
$440$		0			0
$441$	−16.0404	+	2.04375i	−0.763829	+	0.0973212i
$442$	−3.38010	+	21.3411i	−0.160775	+	1.01509i
$443$	10.7062	−	2.86872i	0.508667	−	0.136297i	0.00464732	−	0.999989i	$-0.498521\pi$
$443$	10.7062	−	2.86872i	0.508667	−	0.136297i	0.504019	+	0.863692i	$0.331854\pi$
$444$	−11.3135	−	5.03709i	−0.536914	−	0.239050i
$445$		0			0
$446$	11.3396	+	25.4692i	0.536947	+	1.20600i
$447$	−0.228782	−	1.44447i	−0.0108210	−	0.0683212i
$448$	−22.6037	+	16.8057i	−1.06793	+	0.793995i
$449$		−	40.1154i		−	1.89316i	−0.322465	−	0.946581i	$-0.604511\pi$
$449$		−	40.1154i		−	1.89316i	0.322465	−	0.946581i	$-0.395489\pi$
$450$		0			0
$451$	5.09064	−	2.93909i	0.239709	−	0.138396i
$452$	−11.2739	+	17.3603i	−0.530281	+	0.816561i
$453$	1.86633	−	4.86195i	0.0876878	−	0.228434i
$454$	8.20786	+	5.96336i	0.385214	+	0.279874i
$455$		0			0
$456$	2.60259	−	1.89089i	0.121877	−	0.0885490i
$457$	8.79489	+	32.8230i	0.411408	+	1.53539i	0.791924	+	0.610620i	$0.209080\pi$
$457$	8.79489	+	32.8230i	0.411408	+	1.53539i	−0.380516	+	0.924774i	$0.624254\pi$
$458$	−13.0523	+	5.01030i	−0.609893	+	0.234116i
$459$	7.39310	+	6.65678i	0.345081	+	0.310712i
$460$		0			0
$461$	30.0506	+	9.76402i	1.39959	+	0.454756i	0.909060	−	0.416666i	$-0.136802\pi$
$461$	30.0506	+	9.76402i	1.39959	+	0.454756i	0.490535	+	0.871422i	$0.336802\pi$
$462$	4.70938	−	1.05531i	0.219100	−	0.0490973i
$463$	8.64582	−	16.9684i	0.401805	−	0.788587i	−0.598113	−	0.801412i	$-0.704082\pi$
$463$	8.64582	−	16.9684i	0.401805	−	0.788587i	0.999918	+	0.0128250i	$0.00408243\pi$
$464$	2.93076	−	2.63886i	0.136057	−	0.122506i
$465$		0			0
$466$	12.0799	−	13.4161i	0.559592	−	0.621489i
$467$	−3.74989	+	4.63073i	−0.173524	+	0.214285i	−0.856487	−	0.516169i	$-0.827358\pi$
$467$	−3.74989	+	4.63073i	−0.173524	+	0.214285i	0.682963	+	0.730453i	$0.260691\pi$
$468$	17.7499	−	17.7499i	0.820489	−	0.820489i
$469$	−8.06506	+	31.4810i	−0.372410	+	1.45366i
$470$		0			0
$471$	−8.20090	+	3.65128i	−0.377877	+	0.168242i
$472$	4.15300	−	3.36303i	0.191157	−	0.154796i
$473$	−5.99009	−	3.89001i	−0.275425	−	0.178863i
$474$	−9.40980	+	16.2982i	−0.432206	+	0.748603i
$475$		0			0
$476$	13.2680	+	4.92627i	0.608137	+	0.225795i
$477$	−0.293762	−	0.576541i	−0.0134505	−	0.0263980i
$478$	−37.4491	−	14.3754i	−1.71288	−	0.657513i
$479$	2.17952	−	20.7367i	0.0995846	−	0.947484i	−0.824646	−	0.565649i	$-0.808626\pi$
$479$	2.17952	−	20.7367i	0.0995846	−	0.947484i	0.924231	−	0.381835i	$-0.124708\pi$
$480$		0			0
$481$	−28.6439	+	3.01060i	−1.30605	+	0.137271i
$482$	38.3695	+	38.3695i	1.74768	+	1.74768i
$483$	0.150524	+	13.6774i	0.00684907	+	0.622345i
$484$	−22.3238	+	7.25343i	−1.01472	+	0.329701i
$485$		0			0
$486$	−6.93172	−	32.6112i	−0.314429	−	1.47927i
$487$	−1.53608	−	29.3101i	−0.0696064	−	1.32817i	−0.780627	−	0.624997i	$-0.785100\pi$
$487$	−1.53608	−	29.3101i	−0.0696064	−	1.32817i	0.711021	−	0.703171i	$-0.248233\pi$
$488$	−3.45676	+	2.24485i	−0.156480	+	0.101619i
$489$	−1.43207	+	4.40746i	−0.0647605	+	0.199312i
$490$		0			0
$491$	−5.56395	−	17.1241i	−0.251097	−	0.772798i	−0.994574	−	0.104036i	$-0.966824\pi$
$491$	−5.56395	−	17.1241i	−0.251097	−	0.772798i	0.743476	−	0.668762i	$-0.233176\pi$
$492$	8.56878	+	6.93886i	0.386311	+	0.312828i
$493$	−2.75521	−	0.738256i	−0.124088	−	0.0332494i
$494$	19.4163	−	43.6098i	0.873583	−	1.96210i
$495$		0			0
$496$	18.6720	−	25.6998i	0.838396	−	1.15395i
$497$	−5.16221	+	1.74034i	−0.231557	+	0.0780648i
$498$	−5.73541	+	2.92234i	−0.257010	+	0.130953i
$499$	4.60639	+	2.65950i	0.206210	+	0.119056i	0.599549	−	0.800338i	$-0.295347\pi$
$499$	4.60639	+	2.65950i	0.206210	+	0.119056i	−0.393339	+	0.919394i	$0.628680\pi$
$500$		0			0
$501$	4.35478	+	7.54270i	0.194557	+	0.336983i
$502$	−1.68664	+	32.1830i	−0.0752784	+	1.43640i
$503$	26.0759	−	4.13001i	1.16267	−	0.184148i	0.454865	−	0.890560i	$-0.349687\pi$
$503$	26.0759	−	4.13001i	1.16267	−	0.184148i	0.707801	+	0.706412i	$0.249687\pi$
$504$	−2.63073	−	3.95500i	−0.117182	−	0.176170i
$505$		0			0
$506$	1.42866	+	13.5928i	0.0635119	+	0.604275i
$507$	−1.71834	+	6.41294i	−0.0763143	+	0.284809i
$508$	−11.0425	−	28.7668i	−0.489933	−	1.27632i
$509$	4.37813	+	0.930600i	0.194057	+	0.0412481i	0.303915	−	0.952699i	$-0.401706\pi$
$509$	4.37813	+	0.930600i	0.194057	+	0.0412481i	−0.109858	+	0.993947i	$0.535040\pi$
$510$		0			0
$511$	−1.26408	−	3.18773i	−0.0559195	−	0.141017i
$512$	26.7543	+	13.6320i	1.18238	+	0.602454i
$513$	−11.9707	−	18.4332i	−0.528519	−	0.813847i
$514$	−62.5192	+	13.2889i	−2.75760	+	0.586147i
$515$		0			0
$516$	2.78545	−	13.1045i	0.122623	−	0.576894i
$517$	−0.324701	−	0.0514276i	−0.0142803	−	0.00226178i
$518$	−3.25411	+	34.6217i	−0.142977	+	1.52119i
$519$	6.70259	+	9.22532i	0.294211	+	0.404947i
$520$		0			0
$521$	−25.5618	−	2.68665i	−1.11988	−	0.117704i	−0.473554	−	0.880765i	$-0.657029\pi$
$521$	−25.5618	−	2.68665i	−1.11988	−	0.117704i	−0.646327	+	0.763060i	$0.723696\pi$
$522$	3.84402	+	4.74697i	0.168248	+	0.207769i
$523$	21.9690	+	1.15135i	0.960639	+	0.0503450i	0.526204	−	0.850358i	$-0.323615\pi$
$523$	21.9690	+	1.15135i	0.960639	+	0.0503450i	0.434435	+	0.900703i	$0.356948\pi$
$524$	8.40229			0.367056
$525$		0			0
$526$	0.852467			0.0371693
$527$	−22.9446	−	1.20248i	−0.999483	−	0.0523807i
$528$	−1.71211	−	2.11428i	−0.0745102	−	0.0920124i
$529$	−15.6506	−	1.64494i	−0.680460	−	0.0715192i
$530$		0			0
$531$	−9.33596	−	12.8499i	−0.405146	−	0.557636i
$532$	−25.4974	−	18.0996i	−1.10545	−	0.784717i
$533$	25.3273	+	4.01144i	1.09705	+	0.173755i
$534$	3.82940	−	18.0159i	0.165714	−	0.779624i
$535$		0			0
$536$	−9.33770	+	1.98479i	−0.403327	+	0.0857299i
$537$	0.728191	+	1.12132i	0.0314238	+	0.0483883i
$538$	35.6828	+	18.1813i	1.53840	+	0.783852i
$539$	−3.81524	−	6.28458i	−0.164334	−	0.270696i
$540$		0			0
$541$	−7.92633	−	1.68479i	−0.340780	−	0.0724349i	0.0343432	−	0.999410i	$-0.489066\pi$
$541$	−7.92633	−	1.68479i	−0.340780	−	0.0724349i	−0.375123	+	0.926975i	$0.622399\pi$
$542$	−14.4663	−	37.6860i	−0.621381	−	1.61875i
$543$	0.747801	−	2.79083i	0.0320912	−	0.119766i
$544$	−1.90367	−	18.1122i	−0.0816190	−	0.776553i
$545$		0			0
$546$	18.8631	+	9.35118i	0.807265	+	0.400194i
$547$	−19.0836	+	3.02255i	−0.815958	+	0.129235i	−0.550444	−	0.834872i	$-0.685542\pi$
$547$	−19.0836	+	3.02255i	−0.815958	+	0.129235i	−0.265514	+	0.964107i	$0.585542\pi$
$548$	0.940206	−	17.9402i	0.0401636	−	0.766368i
$549$	6.12533	+	10.6094i	0.261423	+	0.452797i
$550$		0			0
$551$	5.45756	+	3.15092i	0.232500	+	0.134234i
$552$	−3.58011	+	1.82416i	−0.152379	+	0.0776412i
$553$	28.1064	+	5.65167i	1.19521	+	0.240333i
$554$	9.39867	−	12.9362i	0.399311	−	0.549605i
$555$		0			0
$556$	−8.52918	+	19.1568i	−0.361718	+	0.812431i
$557$	17.9964	+	4.82211i	0.762531	+	0.204320i	0.619069	−	0.785336i	$-0.287510\pi$
$557$	17.9964	+	4.82211i	0.762531	+	0.204320i	0.143462	+	0.989656i	$0.454177\pi$
$558$	38.2368	+	30.9636i	1.61869	+	1.31079i
$559$	−9.62832	−	29.6329i	−0.407235	−	1.25334i
$560$		0			0
$561$	−0.608062	+	1.87142i	−0.0256724	+	0.0790116i
$562$	32.8229	−	21.3154i	1.38455	−	0.899137i
$563$	1.13153	+	21.5909i	0.0476883	+	0.909947i	0.912810	+	0.408385i	$0.133908\pi$
$563$	1.13153	+	21.5909i	0.0476883	+	0.909947i	−0.865122	+	0.501562i	$0.832759\pi$
$564$	−0.128209	−	0.603174i	−0.00539855	−	0.0253982i
$565$		0			0
$566$	−5.66670	+	1.84122i	−0.238189	+	0.0773923i
$567$	−7.43581	+	4.40287i	−0.312275	+	0.184903i
$568$	−1.13157	−	1.13157i	−0.0474795	−	0.0474795i
$569$	39.9222	−	4.19599i	1.67362	−	0.175905i	0.780327	−	0.625371i	$-0.215053\pi$
$569$	39.9222	−	4.19599i	1.67362	−	0.175905i	0.893297	+	0.449466i	$0.148386\pi$
$570$		0			0
$571$	−3.48054	+	33.1151i	−0.145656	+	1.38582i	0.640577	+	0.767894i	$0.278695\pi$
$571$	−3.48054	+	33.1151i	−0.145656	+	1.38582i	−0.786233	+	0.617930i	$0.787971\pi$
$572$	10.6551	+	4.09009i	0.445510	+	0.171015i
$573$	1.11800	+	2.19419i	0.0467050	+	0.0916638i
$574$	10.7765	−	29.0245i	0.449803	−	1.21146i
$575$		0			0
$576$	−12.2962	+	21.2976i	−0.512342	+	0.887402i
$577$	−4.80800	−	3.12235i	−0.200160	−	0.129985i	0.440667	−	0.897670i	$-0.354742\pi$
$577$	−4.80800	−	3.12235i	−0.200160	−	0.129985i	−0.640827	+	0.767685i	$0.721408\pi$
$578$	19.3573	−	15.6752i	0.805156	−	0.652002i
$579$	−12.9359	+	5.75944i	−0.537598	+	0.239354i
$580$		0			0
$581$	7.00969	+	6.85708i	0.290811	+	0.284480i
$582$	6.08774	−	6.08774i	0.252345	−	0.252345i
$583$	0.185146	−	0.228636i	0.00766797	−	0.00946915i
$584$	0.674046	−	0.748604i	0.0278922	−	0.0309775i
$585$		0			0
$586$	−1.28538	+	1.15736i	−0.0530985	+	0.0478101i
$587$	−5.48135	+	10.7577i	−0.226239	+	0.444020i	−0.976024	−	0.217662i	$-0.930157\pi$
$587$	−5.48135	+	10.7577i	−0.226239	+	0.444020i	0.749785	+	0.661682i	$0.230157\pi$
$588$	8.44069	−	10.9056i	0.348088	−	0.449741i
$589$	48.2769	+	15.6861i	1.98922	+	0.646335i
$590$		0			0
$591$	−11.9480	−	10.7580i	−0.491475	−	0.442526i
$592$	18.3007	−	7.02499i	0.752155	−	0.288725i
$593$	−11.2370	−	41.9372i	−0.461449	−	1.72215i	−0.668401	−	0.743802i	$-0.733021\pi$
$593$	−11.2370	−	41.9372i	−0.461449	−	1.72215i	0.206951	−	0.978351i	$-0.433646\pi$
$594$	7.83623	−	5.69336i	0.321525	−	0.233601i
$595$		0			0
$596$	−3.37823	−	2.45442i	−0.138377	−	0.100537i
$597$	0.0571202	−	0.148803i	0.00233778	−	0.00609011i
$598$	−32.4736	+	50.0050i	−1.32794	+	2.04485i
$599$	−0.677665	+	0.391250i	−0.0276887	+	0.0159860i	−0.513780	−	0.857922i	$-0.671755\pi$
$599$	−0.677665	+	0.391250i	−0.0276887	+	0.0159860i	0.486092	+	0.873908i	$0.338422\pi$
$600$		0			0
$601$			7.23002i			0.294919i	0.989068	+	0.147459i	$0.0471095\pi$
$601$			7.23002i			0.294919i	−0.989068	+	0.147459i	$0.952890\pi$
$602$	−37.3675	+	4.34375i	−1.52299	+	0.177038i
$603$	4.43864	+	28.0244i	0.180755	+	1.14124i
$604$	−6.04803	−	13.5841i	−0.246091	−	0.552729i
$605$		0			0
$606$	24.1170	+	10.7376i	0.979686	+	0.436184i
$607$	1.71540	−	0.459640i	0.0696260	−	0.0186562i	−0.223838	−	0.974626i	$-0.571859\pi$
$607$	1.71540	−	0.459640i	0.0696260	−	0.0186562i	0.293464	+	0.955970i	$0.405192\pi$
$608$	−6.29427	+	39.7405i	−0.255267	+	1.61169i
$609$	−1.48800	+	2.34747i	−0.0602968	+	0.0951245i
$610$		0			0
$611$	−0.959623	−	1.06577i	−0.0388222	−	0.0431164i
$612$	12.3401	−	0.646717i	0.498819	−	0.0261420i
$613$	1.09418	−	0.0573433i	0.0441934	−	0.00231608i	−0.0302265	−	0.999543i	$-0.509623\pi$
$613$	1.09418	−	0.0573433i	0.0441934	−	0.00231608i	0.0744198	+	0.997227i	$0.476290\pi$
$614$	20.5783	+	22.8545i	0.830473	+	0.922334i
$615$		0			0
$616$	1.15624	−	1.82410i	0.0465864	−	0.0734950i
$617$	−5.03752	+	31.8056i	−0.202803	+	1.28045i	0.650691	+	0.759343i	$0.274479\pi$
$617$	−5.03752	+	31.8056i	−0.202803	+	1.28045i	−0.853494	+	0.521103i	$0.825521\pi$
$618$	−11.3897	+	3.05185i	−0.458160	+	0.122764i
$619$	−16.9052	−	7.52667i	−0.679476	−	0.302522i	0.0378261	−	0.999284i	$-0.487957\pi$
$619$	−16.9052	−	7.52667i	−0.679476	−	0.302522i	−0.717302	+	0.696762i	$0.754623\pi$
$620$		0			0
$621$	11.1658	+	25.0789i	0.448069	+	1.00638i
$622$	−3.88654	−	24.5386i	−0.155836	−	0.983910i
$623$	−27.8702	+	3.23974i	−1.11660	+	0.129797i
$624$		−	11.8683i		−	0.475111i
$625$		0			0
$626$	18.2402	−	10.5310i	0.729023	−	0.420902i
$627$	2.36773	−	3.64598i	0.0945578	−	0.145606i
$628$	−9.18549	+	23.9290i	−0.366541	+	0.954871i
$629$	−11.4704	−	8.33374i	−0.457355	−	0.332288i
$630$		0			0
$631$	20.5730	−	14.9472i	0.818998	−	0.595037i	−0.0974273	−	0.995243i	$-0.531061\pi$
$631$	20.5730	−	14.9472i	0.818998	−	0.595037i	0.916425	+	0.400206i	$0.131061\pi$
$632$	2.17968	+	8.13469i	0.0867031	+	0.323580i
$633$	4.93515	−	1.89443i	0.196155	−	0.0752968i
$634$	−29.3763	−	26.4506i	−1.16668	−	1.05049i
$635$		0			0
$636$	0.524836	+	0.170530i	0.0208111	+	0.00676194i
$637$	4.31887	−	31.7803i	0.171120	−	1.25918i
$638$	−1.26082	+	2.47450i	−0.0499165	+	0.0979666i
$639$	−3.53468	+	3.18264i	−0.139830	+	0.125903i
$640$		0			0
$641$	25.0351	−	27.8043i	0.988828	−	1.09820i	−0.00633676	−	0.999980i	$-0.502017\pi$
$641$	25.0351	−	27.8043i	0.988828	−	1.09820i	0.995164	−	0.0982243i	$-0.0313163\pi$
$642$	21.4978	−	26.5475i	0.848449	−	1.04775i
$643$	−14.7951	+	14.7951i	−0.583460	+	0.583460i	−0.935852	−	0.352392i	$-0.885368\pi$
$643$	−14.7951	+	14.7951i	−0.583460	+	0.583460i	0.352392	+	0.935852i	$0.385368\pi$
$644$	27.9180	+	27.3102i	1.10012	+	1.07617i
$645$		0			0
$646$	21.4678	−	9.55808i	0.844639	−	0.376058i
$647$	20.0874	−	16.2665i	0.789719	−	0.639502i	−0.147177	−	0.989110i	$-0.547019\pi$
$647$	20.0874	−	16.2665i	0.789719	−	0.639502i	0.936896	+	0.349608i	$0.113685\pi$
$648$	−2.12896	−	1.38256i	−0.0836334	−	0.0543122i
$649$	3.61080	−	6.25410i	0.141736	−	0.245495i
$650$		0			0
$651$	−7.79252	+	20.9877i	−0.305413	+	0.822572i
$652$	6.00718	+	11.7898i	0.235259	+	0.461723i
$653$	24.5514	+	9.42440i	0.960770	+	0.368805i	0.787669	−	0.616099i	$-0.211288\pi$
$653$	24.5514	+	9.42440i	0.960770	+	0.368805i	0.173101	+	0.984904i	$0.444621\pi$
$654$	−3.47089	+	33.0234i	−0.135723	+	1.29132i
$655$		0			0
$656$	−17.3573	+	1.82432i	−0.677687	+	0.0712278i
$657$	−2.11712	−	2.11712i	−0.0825967	−	0.0825967i
$658$	−1.48993	+	0.882215i	−0.0580836	+	0.0343923i
$659$	−5.69893	+	1.85169i	−0.221999	+	0.0721317i	−0.417904	−	0.908491i	$-0.637235\pi$
$659$	−5.69893	+	1.85169i	−0.221999	+	0.0721317i	0.195906	+	0.980623i	$0.437235\pi$
$660$		0			0
$661$	9.56586	+	45.0038i	0.372069	+	1.75045i	0.622792	+	0.782387i	$0.285998\pi$
$661$	9.56586	+	45.0038i	0.372069	+	1.75045i	−0.250723	+	0.968059i	$0.580668\pi$
$662$	−3.40478	−	64.9671i	−0.132331	−	2.52502i
$663$	−7.19918	+	4.67520i	−0.279593	+	0.181570i
$664$	−0.890129	+	2.73954i	−0.0345437	+	0.106315i
$665$		0			0
$666$	9.38224	+	28.8756i	0.363555	+	1.11891i
$667$	−6.11699	−	4.95344i	−0.236851	−	0.191798i
$668$	24.0205	+	6.43627i	0.929381	+	0.249027i
$669$	−4.50498	+	10.1184i	−0.174173	+	0.391198i
$670$		0			0
$671$	−3.27395	+	4.50620i	−0.126389	+	0.173960i
$672$	−17.3973	−	3.49826i	−0.671114	−	0.134948i
$673$	15.5853	−	7.94108i	0.600767	−	0.306106i	−0.127030	−	0.991899i	$-0.540544\pi$
$673$	15.5853	−	7.94108i	0.600767	−	0.306106i	0.727797	+	0.685793i	$0.240544\pi$
$674$	63.0398	+	36.3960i	2.42820	+	1.40192i
$675$		0			0
$676$	9.47819	+	16.4167i	0.364546	+	0.631412i
$677$	1.82763	−	34.8733i	0.0702417	−	1.34029i	−0.705262	−	0.708947i	$-0.749170\pi$
$677$	1.82763	−	34.8733i	0.0702417	−	1.34029i	0.775503	−	0.631344i	$-0.217496\pi$
$678$	−14.9717	+	2.37128i	−0.574984	+	0.0910685i
$679$	−11.7505	−	5.82520i	−0.450943	−	0.223551i
$680$		0			0
$681$	0.421309	+	4.00849i	0.0161446	+	0.153606i
$682$	−5.78987	+	21.6081i	−0.221706	+	0.827417i
$683$	−14.5817	−	37.9867i	−0.557954	−	1.45352i	−0.864974	−	0.501817i	$-0.832665\pi$
$683$	−14.5817	−	37.9867i	−0.557954	−	1.45352i	0.307020	−	0.951703i	$-0.400668\pi$
$684$	−26.7039	−	5.67610i	−1.02105	−	0.217031i
$685$		0			0
$686$	−36.5897	−	12.6763i	−1.39700	−	0.483985i
$687$	−4.94891	−	2.52160i	−0.188813	−	0.0962049i
$688$	11.5498	+	17.7852i	0.440333	+	0.678053i
$689$	1.25537	−	0.266838i	0.0478260	−	0.0101657i
$690$		0			0
$691$	−3.69969	+	17.4057i	−0.140743	+	0.662144i	0.850044	+	0.526712i	$0.176575\pi$
$691$	−3.69969	+	17.4057i	−0.140743	+	0.662144i	−0.990787	+	0.135432i	$0.956758\pi$
$692$	32.1577	+	5.09328i	1.22245	+	0.193618i
$693$	−5.23434	−	3.71565i	−0.198836	−	0.141146i
$694$	33.1078	+	45.5689i	1.25675	+	1.72977i
$695$		0			0
$696$	−0.811972	−	0.0853417i	−0.0307777	−	0.00323487i
$697$	7.94408	+	9.81012i	0.300903	+	0.371585i
$698$	60.4013	+	3.16550i	2.28622	+	0.119816i
$699$	7.17212			0.271275
$700$		0			0
$701$	−20.8675			−0.788156			−0.394078	−	0.919077i	$-0.628936\pi$
$701$	−20.8675			−0.788156			−0.394078	+	0.919077i	$0.628936\pi$
$702$	42.1969	+	2.21144i	1.59262	+	0.0834656i
$703$	19.7129	+	24.3434i	0.743485	+	0.918128i
$704$	−11.1201	−	1.16877i	−0.419105	−	0.0440497i
$705$		0			0
$706$	14.3393	+	19.7364i	0.539667	+	0.742788i
$707$	3.76330	−	40.0393i	0.141533	−	1.50583i
$708$	13.3791	+	2.11905i	0.502819	+	0.0796387i
$709$	0.161305	−	0.758882i	0.00605795	−	0.0285004i	−0.975015	−	0.222140i	$-0.928696\pi$
$709$	0.161305	−	0.758882i	0.00605795	−	0.0285004i	0.981073	+	0.193639i	$0.0620292\pi$
$710$		0			0
$711$	24.4840	−	5.20424i	0.918223	−	0.195174i
$712$	−4.48897	−	6.91241i	−0.168231	−	0.259054i
$713$	−56.4913	−	28.7838i	−2.11562	−	1.07796i
$714$	3.82042	+	9.63428i	0.142976	+	0.360554i
$715$		0			0
$716$	3.73407	+	0.793701i	0.139549	+	0.0296620i
$717$	−5.71101	−	14.8777i	−0.213282	−	0.555618i
$718$	2.40915	−	8.99106i	0.0899086	−	0.335543i
$719$	−3.85474	−	36.6754i	−0.143757	−	1.36776i	−0.793946	−	0.607988i	$-0.791977\pi$
$719$	−3.85474	−	36.6754i	−0.143757	−	1.36776i	0.650189	−	0.759773i	$-0.274690\pi$
$720$		0			0
$721$	9.94835	+	14.9562i	0.370496	+	0.556997i
$722$	−12.0411	+	1.90712i	−0.448122	+	0.0709755i
$723$	−1.12822	+	21.5278i	−0.0419591	+	0.800628i
$724$	−4.12478	−	7.14434i	−0.153296	−	0.265517i
$725$		0			0
$726$	−14.8859	−	8.59439i	−0.552468	−	0.318968i
$727$	−17.7421	+	9.04006i	−0.658019	+	0.335277i	−0.750915	−	0.660398i	$-0.770387\pi$
$727$	−17.7421	+	9.04006i	−0.658019	+	0.335277i	0.0928967	+	0.995676i	$0.470387\pi$
$728$	8.92772	−	3.00980i	0.330883	−	0.111551i
$729$	2.02583	−	2.78831i	0.0750307	−	0.103271i
$730$		0			0
$731$	6.23857	−	14.0121i	0.230742	−	0.518254i
$732$	−10.0919	−	2.70410i	−0.373006	−	0.0999466i
$733$	0.0311408	+	0.0252173i	0.00115021	+	0.000931422i	0.629895	−	0.776680i	$-0.283098\pi$
$733$	0.0311408	+	0.0252173i	0.00115021	+	0.000931422i	−0.628745	+	0.777611i	$0.716431\pi$
$734$	−16.5940	−	51.0711i	−0.612496	−	1.88507i
$735$		0			0
$736$	15.5297	−	47.7955i	0.572432	−	1.76177i
$737$	−10.8194	+	7.02618i	−0.398537	+	0.258813i
$738$	−1.41473	−	26.9947i	−0.0520771	−	0.993689i
$739$	−4.01685	−	18.8978i	−0.147762	−	0.695167i	−0.988189	−	0.153241i	$-0.951029\pi$
$739$	−4.01685	−	18.8978i	−0.147762	−	0.695167i	0.840427	−	0.541925i	$-0.182304\pi$
$740$		0			0
$741$	18.0366	−	5.86045i	0.662592	−	0.215289i
$742$	−0.0170523	−	1.54947i	−0.000626011	−	0.0568829i
$743$	−16.7789	−	16.7789i	−0.615557	−	0.615557i	0.328831	−	0.944389i	$-0.393345\pi$
$743$	−16.7789	−	16.7789i	−0.615557	−	0.615557i	−0.944389	+	0.328831i	$0.893345\pi$
$744$	−6.54044	+	0.687427i	−0.239784	+	0.0252023i
$745$		0			0
$746$	7.82715	−	74.4703i	0.286572	−	2.72655i
$747$	7.99289	+	3.06818i	0.292445	+	0.112259i
$748$	2.55067	+	5.00597i	0.0932617	+	0.183036i
$749$	−48.7843	−	18.1132i	−1.78254	−	0.661840i
$750$		0			0
$751$	−6.63402	+	11.4905i	−0.242079	+	0.419293i	−0.961306	−	0.275482i	$-0.911163\pi$
$751$	−6.63402	+	11.4905i	−0.242079	+	0.419293i	0.719227	+	0.694775i	$0.244496\pi$
$752$	0.818615	+	0.531615i	0.0298518	+	0.0193860i
$753$	−9.94991	+	8.05728i	−0.362595	+	0.293623i
$754$	−11.0679	+	4.92773i	−0.403068	+	0.179457i
$755$		0			0
$756$	6.86883	−	26.8116i	0.249817	−	0.975130i
$757$	−1.13591	+	1.13591i	−0.0412853	+	0.0412853i	−0.727448	−	0.686163i	$-0.759294\pi$
$757$	−1.13591	+	1.13591i	−0.0412853	+	0.0412853i	0.686163	+	0.727448i	$0.259294\pi$
$758$	−29.8712	+	36.8879i	−1.08497	+	1.33983i
$759$	−3.63330	+	4.03519i	−0.131880	+	0.146468i
$760$		0			0
$761$	−23.6079	+	21.2567i	−0.855787	+	0.770554i	−0.974974	−	0.222318i	$-0.928638\pi$
$761$	−23.6079	+	21.2567i	−0.855787	+	0.770554i	0.119187	+	0.992872i	$0.461971\pi$
$762$	10.2440	−	20.1050i	0.371102	−	0.728328i
$763$	49.3595	−	11.0608i	1.78693	−	0.400427i
$764$	6.68717	+	2.17279i	0.241933	+	0.0786089i
$765$		0			0
$766$	−33.7996	−	30.4333i	−1.22123	−	1.09960i
$767$	29.4111	−	11.2899i	1.06197	−	0.407654i
$768$	1.83093	+	6.83311i	0.0660679	+	0.246569i
$769$	−11.1412	+	8.09458i	−0.401763	+	0.291898i	−0.770259	−	0.637731i	$-0.779873\pi$
$769$	−11.1412	+	8.09458i	−0.401763	+	0.291898i	0.368495	+	0.929630i	$0.379873\pi$
$770$		0			0
$771$	−20.5429	−	14.9253i	−0.739834	−	0.537521i
$772$	−14.4890	+	37.7451i	−0.521470	+	1.35848i
$773$	−5.46989	+	8.42289i	−0.196738	+	0.302950i	−0.923247	−	0.384207i	$-0.874475\pi$
$773$	−5.46989	+	8.42289i	−0.196738	+	0.302950i	0.726509	+	0.687157i	$0.241142\pi$
$774$	−28.4449	+	16.4227i	−1.02243	+	0.590302i
$775$		0			0
$776$		−	3.85263i		−	0.138301i
$777$	−11.0866	+	8.24280i	−0.397729	+	0.295709i
$778$	4.25155	+	26.8433i	0.152426	+	0.962377i
$779$	−11.3434	−	25.4776i	−0.406418	−	0.912830i
$780$		0			0
$781$	−1.97561	−	0.879597i	−0.0706928	−	0.0314745i
$782$	−28.3510	+	7.59663i	−1.01383	+	0.271655i
$783$	−0.872614	+	5.50947i	−0.0311847	+	0.196892i
$784$	2.75896	+	21.6538i	0.0985341	+	0.773349i
$785$		0			0
$786$	4.11711	+	4.57252i	0.146853	+	0.163096i
$787$	−21.4984	+	1.12669i	−0.766337	+	0.0401620i	−0.431499	−	0.902114i	$-0.642015\pi$
$787$	−21.4984	+	1.12669i	−0.766337	+	0.0401620i	−0.334838	+	0.942276i	$0.608682\pi$
$788$	−45.8425	+	2.40250i	−1.63307	+	0.0855856i
$789$	0.226612	+	0.251678i	0.00806760	+	0.00895998i
$790$		0			0
$791$	10.7091	+	20.4581i	0.380773	+	0.727407i
$792$	0.294977	−	1.86241i	0.0104815	−	0.0661779i
$793$	−23.4705	+	6.28891i	−0.833463	+	0.223326i
$794$	9.12721	+	4.06369i	0.323912	+	0.144215i
$795$		0			0
$796$	−0.185104	−	0.415750i	−0.00656084	−	0.0147359i
$797$	0.825084	+	5.20937i	0.0292260	+	0.184526i	0.997983	−	0.0634877i	$-0.0202224\pi$
$797$	0.825084	+	5.20937i	0.0292260	+	0.184526i	−0.968757	+	0.248013i	$0.920222\pi$
$798$	−2.64390	−	22.7444i	−0.0935931	−	0.805144i
$799$		−	0.705981i		−	0.0249758i
$800$		0			0
$801$	−21.2154	+	12.2487i	−0.749608	+	0.432786i
$802$	17.2717	−	26.5961i	0.609885	−	0.939140i
$803$	0.487846	−	1.27088i	0.0172157	−	0.0448485i
$804$	−19.5768	−	14.2234i	−0.690422	−	0.501621i
$805$		0			0
$806$	−78.9508	+	57.3611i	−2.78092	+	2.02046i
$807$	4.11784	+	15.3680i	0.144955	+	0.540979i
$808$	11.0289	−	4.23359i	0.387995	−	0.148937i
$809$	−6.16004	−	5.54653i	−0.216575	−	0.195005i	0.553701	−	0.832716i	$-0.313215\pi$
$809$	−6.16004	−	5.54653i	−0.216575	−	0.195005i	−0.770276	+	0.637710i	$0.779882\pi$
$810$		0			0
$811$	−22.9445	−	7.45511i	−0.805689	−	0.261784i	−0.122918	−	0.992417i	$-0.539225\pi$
$811$	−22.9445	−	7.45511i	−0.805689	−	0.261784i	−0.682771	+	0.730632i	$0.739225\pi$
$812$	1.73524	+	7.74365i	0.0608951	+	0.271749i
$813$	7.28065	−	14.2891i	0.255343	−	0.501140i
$814$	−10.2587	+	9.23695i	−0.359566	+	0.323755i
$815$		0			0
$816$	3.90932	−	4.34174i	0.136854	−	0.151991i
$817$	−21.3255	+	26.3349i	−0.746087	+	0.921340i
$818$	15.1952	−	15.1952i	0.531288	−	0.531288i
$819$	−7.54481	−	26.9670i	−0.263637	−	0.942303i
$820$		0			0
$821$	10.2681	−	4.57166i	0.358359	−	0.159552i	−0.219657	−	0.975577i	$-0.570494\pi$
$821$	10.2681	−	4.57166i	0.358359	−	0.159552i	0.578016	+	0.816025i	$0.303827\pi$
$822$	10.2237	−	8.27902i	0.356594	−	0.288764i
$823$	−14.3955	−	9.34851i	−0.501794	−	0.325869i	0.268799	−	0.963196i	$-0.413373\pi$
$823$	−14.3955	−	9.34851i	−0.501794	−	0.325869i	−0.770593	+	0.637327i	$0.780040\pi$
$824$	−2.63830	+	4.56967i	−0.0919096	+	0.159192i
$825$		0			0
$826$	−6.36329	−	37.5005i	−0.221407	−	1.30481i
$827$	−10.5674	−	20.7397i	−0.367465	−	0.721190i	0.631046	−	0.775745i	$-0.282626\pi$
$827$	−10.5674	−	20.7397i	−0.367465	−	0.721190i	−0.998511	+	0.0545555i	$0.982626\pi$
$828$	31.8339	+	12.2199i	1.10630	+	0.424671i
$829$	−2.64740	+	25.1883i	−0.0919480	+	0.874827i	0.847191	+	0.531289i	$0.178292\pi$
$829$	−2.64740	+	25.1883i	−0.0919480	+	0.874827i	−0.939139	+	0.343538i	$0.888375\pi$
$830$		0			0
$831$	6.31767	−	0.664014i	0.219157	−	0.0230344i
$832$	−34.4910	−	34.4910i	−1.19576	−	1.19576i
$833$	12.0482	−	10.2035i	0.417445	−	0.353531i
$834$	−14.6044	+	4.74526i	−0.505710	+	0.164315i
$835$		0			0
$836$	−2.58073	−	12.1414i	−0.0892565	−	0.419919i
$837$	2.35155	+	44.8703i	0.0812816	+	1.55095i
$838$	−31.3967	+	20.3893i	−1.08458	+	0.704335i
$839$	−17.1783	+	52.8695i	−0.593062	+	1.82526i	−0.0289189	+	0.999582i	$0.509206\pi$
$839$	−17.1783	+	52.8695i	−0.593062	+	1.82526i	−0.564144	+	0.825677i	$0.690794\pi$
$840$		0			0
$841$	8.46726	+	26.0596i	0.291975	+	0.898605i
$842$	27.2885	+	22.0978i	0.940424	+	0.761540i
$843$	15.0184	+	4.02417i	0.517261	+	0.138600i
$844$	6.13909	−	13.7886i	0.211316	−	0.474624i
$845$		0			0
$846$	−0.888617	+	1.22308i	−0.0305513	+	0.0420502i
$847$	−5.16193	+	25.6709i	−0.177366	+	0.882062i
$848$	−0.778302	+	0.396565i	−0.0267270	+	0.0136181i
$849$	−2.04998	−	1.18355i	−0.0703550	−	0.0406195i
$850$		0			0
$851$	−19.5621	−	33.8826i	−0.670581	−	1.16148i
$852$	0.212298	−	4.05088i	0.00727319	−	0.138781i
$853$	−41.8419	+	6.62710i	−1.43264	+	0.226908i	−0.824023	−	0.566557i	$-0.808275\pi$
$853$	−41.8419	+	6.62710i	−1.43264	+	0.226908i	−0.608616	+	0.793465i	$0.708275\pi$
$854$	1.85770	+	29.2784i	0.0635693	+	1.00189i
$855$		0			0
$856$	−1.59787	−	15.2028i	−0.0546142	−	0.519620i
$857$	9.84983	−	36.7601i	0.336464	−	1.25570i	−0.565810	−	0.824536i	$-0.691436\pi$
$857$	9.84983	−	36.7601i	0.336464	−	1.25570i	0.902274	−	0.431164i	$-0.141897\pi$
$858$	2.99514	+	7.80261i	0.102252	+	0.266377i
$859$	50.1863	+	10.6674i	1.71233	+	0.363968i	0.956711	−	0.291040i	$-0.0940012\pi$
$859$	50.1863	+	10.6674i	1.71233	+	0.363968i	0.755622	+	0.655008i	$0.227335\pi$
$860$		0			0
$861$	11.4338	−	4.53401i	0.389663	−	0.154519i
$862$	−16.6643	−	8.49088i	−0.567588	−	0.289200i
$863$	11.9023	+	18.3280i	0.405161	+	0.623893i	0.981077	−	0.193616i	$-0.0620215\pi$
$863$	11.9023	+	18.3280i	0.405161	+	0.623893i	−0.575917	+	0.817508i	$0.695355\pi$
$864$	−34.8369	+	7.40481i	−1.18517	+	0.251917i
$865$		0			0
$866$	7.66009	−	36.0379i	0.260300	−	1.22462i
$867$	9.77363	+	1.54799i	0.331930	+	0.0525725i
$868$	26.6404	+	58.1060i	0.904236	+	1.97224i
$869$	6.68946	+	9.20725i	0.226924	+	0.312334i
$870$		0			0
$871$	−55.9695	−	5.88263i	−1.89645	−	0.199325i
$872$	9.35116	+	11.5477i	0.316670	+	0.391055i
$873$	−11.4352	−	0.599293i	−0.387023	−	0.0202830i
$874$	64.8458			2.19344
$875$		0			0
$876$	2.55345			0.0862732
$877$	1.41416	+	0.0741129i	0.0477527	+	0.00250261i	0.0761974	−	0.997093i	$-0.475722\pi$
$877$	1.41416	+	0.0741129i	0.0477527	+	0.00250261i	−0.0284446	+	0.999595i	$0.509055\pi$
$878$	−36.0580	−	44.5280i	−1.21690	−	1.50275i
$879$	−0.683387	−	0.0718269i	−0.0230501	−	0.00242266i
$880$		0			0
$881$	5.05676	+	6.96003i	0.170367	+	0.234489i	0.885659	−	0.464335i	$-0.153707\pi$
$881$	5.05676	+	6.96003i	0.170367	+	0.234489i	−0.715293	+	0.698825i	$0.753707\pi$
$882$	−33.7160	+	2.51208i	−1.13528	+	0.0845860i
$883$	−40.2254	−	6.37108i	−1.35369	−	0.214404i	−0.562919	−	0.826512i	$-0.690322\pi$
$883$	−40.2254	−	6.37108i	−1.35369	−	0.214404i	−0.790774	+	0.612108i	$0.790322\pi$
$884$	−5.09580	+	23.9739i	−0.171390	+	0.806328i
$885$		0			0
$886$	22.6684	−	4.81832i	0.761561	−	0.161875i
$887$	−13.5120	−	20.8067i	−0.453689	−	0.698619i	0.535619	−	0.844459i	$-0.320078\pi$
$887$	−13.5120	−	20.8067i	−0.453689	−	0.698619i	−0.989308	+	0.145840i	$0.953411\pi$
$888$	−3.61591	−	1.84240i	−0.121342	−	0.0618269i
$889$	−34.0076	−	5.00330i	−1.14058	−	0.167805i
$890$		0			0
$891$	−3.35549	−	0.713231i	−0.112413	−	0.0238941i
$892$	11.3331	+	29.5239i	0.379462	+	0.988532i
$893$	−0.403688	+	1.50658i	−0.0135089	+	0.0504159i
$894$	−0.319632	−	3.04109i	−0.0106901	−	0.101709i
$895$		0			0
$896$	−13.4603	+	8.95336i	−0.449678	+	0.299111i
$897$	−23.3957	+	3.70552i	−0.781160	+	0.123724i
$898$	4.38972	−	83.7609i	0.146487	−	2.79514i
$899$	−6.44144	−	11.1569i	−0.214834	−	0.372103i
$900$		0			0
$901$	0.547146	+	0.315895i	0.0182281	+	0.0105240i
$902$	10.9509	−	5.57975i	0.364624	−	0.185785i
$903$	−11.2159	−	9.87750i	−0.373241	−	0.328703i
$904$	−3.98709	+	5.48776i	−0.132609	+	0.182520i
$905$		0			0
$906$	4.42892	−	9.94752i	0.147141	−	0.330484i
$907$	−30.1426	−	8.07670i	−1.00087	−	0.268182i	−0.279060	−	0.960274i	$-0.590023\pi$
$907$	−30.1426	−	8.07670i	−1.00087	−	0.268182i	−0.721810	+	0.692091i	$0.756690\pi$
$908$	8.94357	+	7.24236i	0.296803	+	0.240346i
$909$	−10.8504	−	33.3940i	−0.359883	−	1.10761i
$910$		0			0
$911$	−11.4702	+	35.3017i	−0.380025	+	1.16960i	0.560000	+	0.828492i	$0.310801\pi$
$911$	−11.4702	+	35.3017i	−0.380025	+	1.16960i	−0.940025	+	0.341105i	$0.889199\pi$
$912$	−10.8253	+	7.03001i	−0.358460	+	0.232787i
$913$	0.203726	+	3.88732i	0.00674234	+	0.128651i
$914$	14.7720	+	69.4967i	0.488614	+	2.29875i
$915$		0			0
$916$	−15.0826	+	4.90064i	−0.498344	+	0.161922i
$917$	4.59695	−	8.16845i	0.151805	−	0.269746i
$918$	14.7084	+	14.7084i	0.485448	+	0.485448i
$919$	−42.2670	+	4.44244i	−1.39426	+	0.146543i	−0.771678	−	0.636013i	$-0.780583\pi$
$919$	−42.2670	+	4.44244i	−1.39426	+	0.146543i	−0.622581	+	0.782555i	$0.713916\pi$
$920$		0			0
$921$	−1.27711	+	12.1509i	−0.0420822	+	0.400385i
$922$	61.6771	+	23.6756i	2.03123	+	0.779715i
$923$	−4.28295	−	8.40577i	−0.140975	−	0.276679i
$924$	5.39729	−	0.915841i	0.177558	−	0.0301290i
$925$		0			0
$926$	19.9093	−	34.4838i	0.654259	−	1.13321i
$927$	13.1531	+	8.54171i	0.432004	+	0.280546i
$928$	7.93588	−	6.42635i	0.260508	−	0.210955i
$929$	13.8640	−	6.17267i	0.454864	−	0.202519i	−0.166498	−	0.986042i	$-0.553246\pi$
$929$	13.8640	−	6.17267i	0.454864	−	0.202519i	0.621363	+	0.783523i	$0.286579\pi$
$930$		0			0
$931$	−31.5457	+	14.8853i	−1.03387	+	0.487848i
$932$	14.4802	−	14.4802i	0.474315	−	0.474315i
$933$	6.21151	−	7.67057i	0.203356	−	0.251123i
$934$	−8.33650	+	9.25862i	−0.272778	+	0.302951i
$935$		0			0
$936$	6.11301	−	5.50418i	0.199810	−	0.179910i
$937$	−11.3453	+	22.2665i	−0.370636	+	0.727415i	−0.998712	−	0.0507375i	$-0.983843\pi$
$937$	−11.3453	+	22.2665i	−0.370636	+	0.727415i	0.628076	+	0.778152i	$0.283843\pi$
$938$	−20.2847	+	64.8497i	−0.662319	+	2.11742i
$939$	7.95790	+	2.58568i	0.259696	+	0.0843805i
$940$		0			0
$941$	12.3945	+	11.1600i	0.404049	+	0.363807i	0.845955	−	0.533254i	$-0.179031\pi$
$941$	12.3945	+	11.1600i	0.404049	+	0.363807i	−0.441906	+	0.897061i	$0.645698\pi$
$942$	−17.5230	+	6.72646i	−0.570931	+	0.219160i
$943$	9.01555	+	33.6465i	0.293587	+	1.09568i
$944$	−17.3467	+	12.6031i	−0.564586	+	0.410196i
$945$		0			0
$946$	−12.0816	−	8.77782i	−0.392808	−	0.285392i
$947$	−8.57180	+	22.3303i	−0.278546	+	0.725637i	0.720922	+	0.693017i	$0.243719\pi$
$947$	−8.57180	+	22.3303i	−0.278546	+	0.725637i	−0.999468	+	0.0326209i	$0.989615\pi$
$948$	−11.6267	+	17.9035i	−0.377617	+	0.581478i
$949$	5.14293	−	2.96927i	0.166947	−	0.0963866i
$950$		0			0
$951$		−	15.7043i		−	0.509247i
$952$	4.25742	+	1.83966i	0.137984	+	0.0596236i
$953$	−8.33470	−	52.6232i	−0.269987	−	1.70463i	−0.634077	−	0.773270i	$-0.718620\pi$
$953$	−8.33470	−	52.6232i	−0.269987	−	1.70463i	0.364090	−	0.931364i	$-0.381380\pi$
$954$	−0.550286	−	1.23596i	−0.0178162	−	0.0400158i
$955$		0			0
$956$	−41.5677	−	18.5071i	−1.34440	−	0.598563i
$957$	−1.06573	+	0.285561i	−0.0344500	+	0.00923086i
$958$	6.81999	−	43.0597i	0.220344	−	1.39120i
$959$	−16.9265	−	10.7293i	−0.546586	−	0.346466i
$960$		0			0
$961$	−48.6936	−	54.0798i	−1.57076	−	1.74451i
$962$	−60.1379	+	3.15169i	−1.93892	+	0.101615i
$963$	−45.3726	+	2.37788i	−1.46211	+	0.0766261i
$964$	41.1858	+	45.7415i	1.32651	+	1.47323i
$965$		0			0
$966$	−1.18239	+	28.5749i	−0.0380429	+	0.919384i
$967$	4.98535	−	31.4763i	0.160318	−	1.01221i	−0.768008	−	0.640441i	$-0.778752\pi$
$967$	4.98535	−	31.4763i	0.160318	−	1.01221i	0.928326	−	0.371768i	$-0.121248\pi$
$968$	−7.42978	+	1.99080i	−0.238802	+	0.0639868i
$969$	8.52869	+	3.79722i	0.273981	+	0.121984i
$970$		0			0
$971$	−15.7478	−	35.3701i	−0.505370	−	1.13508i	−0.968551	−	0.248816i	$-0.919958\pi$
$971$	−15.7478	−	35.3701i	−0.505370	−	1.13508i	0.463180	−	0.886264i	$-0.346708\pi$
$972$	−5.91604	−	37.3524i	−0.189757	−	1.19808i
$973$	13.9573	+	18.7727i	0.447451	+	0.601824i
$974$		−	61.3676i		−	1.96634i
$975$		0			0
$976$	14.3221	−	8.26889i	0.458441	−	0.264681i
$977$	−15.7448	+	24.2449i	−0.503721	+	0.775663i	−0.995470	−	0.0950743i	$-0.969691\pi$
$977$	−15.7448	+	24.2449i	−0.503721	+	0.775663i	0.491749	+	0.870737i	$0.336358\pi$
$978$	−3.47246	+	9.04607i	−0.111037	+	0.289261i
$979$	−9.01096	−	6.54684i	−0.287991	−	0.209238i
$980$		0			0
$981$	35.7300	−	25.9594i	1.14077	−	0.828818i
$982$	−9.74367	−	36.3639i	−0.310933	−	1.16042i
$983$	−9.13410	+	3.50625i	−0.291332	+	0.111832i	−0.499645	−	0.866230i	$-0.666536\pi$
$983$	−9.13410	+	3.50625i	−0.291332	+	0.111832i	0.208313	+	0.978062i	$0.433203\pi$
$984$	2.68510	+	2.41768i	0.0855979	+	0.0770727i
$985$		0			0
$986$	−5.67209	−	1.84297i	−0.180636	−	0.0586922i
$987$	−0.656531	−	0.205360i	−0.0208976	−	0.00653669i
$988$	24.5831	−	48.2471i	0.782093	−	1.53494i
$989$	31.4535	−	28.3209i	1.00016	−	0.900552i
$990$		0			0
$991$	−16.3474	+	18.1556i	−0.519291	+	0.576732i	−0.944561	−	0.328335i	$-0.893513\pi$
$991$	−16.3474	+	18.1556i	−0.519291	+	0.576732i	0.425270	+	0.905067i	$0.360179\pi$
$992$	51.7642	−	63.9235i	1.64352	−	2.02957i
$993$	18.2755	−	18.2755i	0.579955	−	0.579955i
$994$	−10.9691	+	3.06894i	−0.347920	+	0.0973408i
$995$		0			0
$996$	−6.67037	+	2.96984i	−0.211359	+	0.0941030i
$997$	−16.9735	+	13.7449i	−0.537556	+	0.435305i	−0.859262	−	0.511535i	$-0.829077\pi$
$997$	−16.9735	+	13.7449i	−0.537556	+	0.435305i	0.321706	+	0.946840i	$0.395744\pi$
$998$	9.32712	+	6.05710i	0.295245	+	0.191734i
$999$	−13.8634	+	24.0121i	−0.438619	+	0.759710i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	875.2.bb.c.243.16		288
5.2	odd	4		875.2.bb.a.257.3		288
5.3	odd	4		875.2.bb.b.257.16		288
5.4	even	2		175.2.x.a.103.3	yes	288
7.3	odd	6	inner	875.2.bb.c.493.3		288
25.6	even	5		875.2.bb.a.768.3		288
25.8	odd	20		175.2.x.a.117.16	yes	288
25.17	odd	20	inner	875.2.bb.c.607.3		288
25.19	even	10		875.2.bb.b.768.16		288
35.3	even	12		875.2.bb.b.507.16		288
35.17	even	12		875.2.bb.a.507.3		288
35.24	odd	6		175.2.x.a.3.16	✓	288
175.17	even	60	inner	875.2.bb.c.857.16		288
175.31	odd	30		875.2.bb.a.143.3		288
175.94	odd	30		875.2.bb.b.143.16		288
175.108	even	60		175.2.x.a.17.3	yes	288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.3.16	✓	288	35.24	odd	6
175.2.x.a.17.3	yes	288	175.108	even	60
175.2.x.a.103.3	yes	288	5.4	even	2
175.2.x.a.117.16	yes	288	25.8	odd	20
875.2.bb.a.143.3		288	175.31	odd	30
875.2.bb.a.257.3		288	5.2	odd	4
875.2.bb.a.507.3		288	35.17	even	12
875.2.bb.a.768.3		288	25.6	even	5
875.2.bb.b.143.16		288	175.94	odd	30
875.2.bb.b.257.16		288	5.3	odd	4
875.2.bb.b.507.16		288	35.3	even	12
875.2.bb.b.768.16		288	25.19	even	10
875.2.bb.c.243.16		288	1.1	even	1	trivial
875.2.bb.c.493.3		288	7.3	odd	6	inner
875.2.bb.c.607.3		288	25.17	odd	20	inner
875.2.bb.c.857.16		288	175.17	even	60	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 875 = 5^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	875.bb (of order \(60\), degree \(16\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.08800 + 0.109427i) q^{2} +(0.522748 + 0.645540i) q^{3} +(2.35872 + 0.247911i) q^{4} +(1.02086 + 1.40509i) q^{6} +(1.53148 - 2.15744i) q^{7} +(0.767632 + 0.121581i) q^{8} +(0.480279 - 2.25953i) q^{9} +(1.02734 - 0.218367i) q^{11} +(1.07298 + 1.65224i) q^{12} +(4.08239 + 2.08008i) q^{13} +(3.43382 - 4.33715i) q^{14} +(-3.05026 - 0.648353i) q^{16} +(0.808289 + 2.10566i) q^{17} +(1.25008 - 4.66535i) q^{18} +(-0.520869 - 4.95574i) q^{19} +(2.19329 - 0.139164i) q^{21} +(2.16897 - 0.343531i) q^{22} +(-0.325733 + 6.21536i) q^{23} +(0.322792 + 0.559093i) q^{24} +(8.29642 + 4.78994i) q^{26} +(3.93004 - 2.00245i) q^{27} +(4.14720 - 4.70913i) q^{28} +(-0.743348 + 1.02313i) q^{29} +(-4.14336 + 9.30613i) q^{31} +(-7.79943 - 2.08985i) q^{32} +(0.678002 + 0.549035i) q^{33} +(1.45729 + 4.48507i) q^{34} +(1.69301 - 5.21054i) q^{36} +(-5.27200 + 3.42368i) q^{37} +(-0.545281 - 10.4046i) q^{38} +(0.791286 + 3.72271i) q^{39} +(5.32280 - 1.72948i) q^{41} +(4.59482 - 0.0505673i) q^{42} +(-4.80861 - 4.80861i) q^{43} +(2.47733 - 0.260378i) q^{44} +(-1.36026 + 12.9420i) q^{46} +(-0.292218 - 0.112172i) q^{47} +(-1.17598 - 2.30799i) q^{48} +(-2.30911 - 6.60818i) q^{49} +(-0.936759 + 1.62251i) q^{51} +(9.11355 + 5.91841i) q^{52} +(0.217690 - 0.176281i) q^{53} +(8.42504 - 3.75107i) q^{54} +(1.43792 - 1.46992i) q^{56} +(2.92684 - 2.92684i) q^{57} +(-1.66407 + 2.05495i) q^{58} +(4.60084 - 5.10975i) q^{59} +(-3.94111 + 3.54859i) q^{61} +(-9.66967 + 18.9778i) q^{62} +(-4.13927 - 4.49661i) q^{63} +(-10.1249 - 3.28979i) q^{64} +(1.35559 + 1.22058i) q^{66} +(-11.4671 + 4.40181i) q^{67} +(1.38451 + 5.16706i) q^{68} +(-4.18254 + 3.03879i) q^{69} +(-1.66579 - 1.21027i) q^{71} +(0.643393 - 1.67610i) q^{72} +(0.705919 - 1.08702i) q^{73} +(-11.3826 + 6.57173i) q^{74} -11.8183i q^{76} +(1.10223 - 2.55084i) q^{77} +(1.24484 + 7.85959i) q^{78} +(4.40735 + 9.89907i) q^{79} +(-2.98382 - 1.32848i) q^{81} +(11.3033 - 3.02870i) q^{82} +(-0.579789 + 3.66064i) q^{83} +(5.20787 + 0.215495i) q^{84} +(-9.51417 - 10.5666i) q^{86} +(-1.04906 + 0.0549787i) q^{87} +(0.815165 - 0.0427210i) q^{88} +(-7.09604 - 7.88095i) q^{89} +(10.7398 - 5.62191i) q^{91} +(-2.30917 + 14.5795i) q^{92} +(-8.17341 + 2.19006i) q^{93} +(-0.597877 - 0.266192i) q^{94} +(-2.72805 - 6.12730i) q^{96} +(-0.775456 - 4.89604i) q^{97} +(-4.09830 - 14.0505i) q^{98} -2.42618i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q + 8 q^{2} + 24 q^{3} - 10 q^{4} + 10 q^{7} + 36 q^{8} - 10 q^{9} - 6 q^{11} + 36 q^{12} - 20 q^{14} - 30 q^{16} + 42 q^{17} + 14 q^{18} - 30 q^{19} - 12 q^{21} - 32 q^{22} + 40 q^{23} - 48 q^{26}+ \cdots - 222 q^{98}+O(q^{100}) \) 288 * q + 8 * q^2 + 24 * q^3 - 10 * q^4 + 10 * q^7 + 36 * q^8 - 10 * q^9 - 6 * q^11 + 36 * q^12 - 20 * q^14 - 30 * q^16 + 42 * q^17 + 14 * q^18 - 30 * q^19 - 12 * q^21 - 32 * q^22 + 40 * q^23 - 48 * q^26 - 22 * q^28 - 18 * q^31 - 8 * q^32 + 30 * q^33 + 40 * q^36 + 10 * q^37 - 72 * q^38 + 30 * q^39 - 6 * q^42 + 108 * q^43 - 10 * q^44 - 6 * q^46 + 54 * q^47 - 16 * q^51 - 216 * q^52 - 50 * q^53 - 30 * q^54 + 4 * q^56 + 216 * q^57 + 4 * q^58 + 90 * q^59 - 18 * q^61 + 66 * q^63 - 100 * q^64 - 90 * q^66 - 4 * q^67 - 342 * q^68 - 24 * q^71 - 58 * q^72 + 6 * q^73 + 80 * q^77 + 132 * q^78 - 10 * q^79 - 10 * q^81 - 216 * q^82 + 20 * q^84 - 6 * q^86 + 48 * q^87 + 122 * q^88 + 120 * q^89 - 12 * q^91 + 4 * q^92 - 106 * q^93 - 30 * q^94 - 90 * q^96 - 222 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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