LMFDB - Embedded newform 875.2.bb.a.857.4

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,-2] 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			857.4
Character	$\chi$	$=$	875.857
Dual form			875.2.bb.a.243.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.78588 + 0.0935941i) q^{2} +(-0.226450 + 0.279642i) q^{3} +(1.19157 - 0.125239i) q^{4} +(0.378240 - 0.520602i) q^{6} +(-2.62695 + 0.314872i) q^{7} +(1.41635 - 0.224327i) q^{8} +(0.596815 + 2.80779i) q^{9} +(4.12989 + 0.877836i) q^{11} +(-0.234809 + 0.361574i) q^{12} +(-0.527217 + 0.268631i) q^{13} +(4.66195 - 0.808191i) q^{14} +(-4.85234 + 1.03140i) q^{16} +(-0.311447 + 0.811348i) q^{17} +(-1.32863 - 4.95853i) q^{18} +(0.667317 - 6.34910i) q^{19} +(0.506820 - 0.805908i) q^{21} +(-7.45766 - 1.18118i) q^{22} +(-0.0848056 - 1.61819i) q^{23} +(-0.258000 + 0.446869i) q^{24} +(0.916406 - 0.529087i) q^{26} +(-1.88216 - 0.959010i) q^{27} +(-3.09076 + 0.704189i) q^{28} +(0.996818 + 1.37200i) q^{29} +(3.65980 + 8.22005i) q^{31} +(5.79889 - 1.55381i) q^{32} +(-1.18069 + 0.956106i) q^{33} +(0.480271 - 1.47812i) q^{34} +(1.06279 + 3.27094i) q^{36} +(3.65442 + 2.37321i) q^{37} +(-0.597511 + 11.4012i) q^{38} +(0.0442678 - 0.208263i) q^{39} +(-5.70437 - 1.85346i) q^{41} +(-0.829693 + 1.48669i) q^{42} +(-3.73281 + 3.73281i) q^{43} +(5.03100 + 0.528779i) q^{44} +(0.302906 + 2.88195i) q^{46} +(-8.99906 + 3.45442i) q^{47} +(0.810389 - 1.59048i) q^{48} +(6.80171 - 1.65430i) q^{49} +(-0.156360 - 0.270823i) q^{51} +(-0.594574 + 0.386121i) q^{52} +(6.59068 + 5.33703i) q^{53} +(3.45108 + 1.53652i) q^{54} +(-3.65004 + 1.03526i) q^{56} +(1.62436 + 1.62436i) q^{57} +(-1.90861 - 2.35694i) q^{58} +(-4.53398 - 5.03550i) q^{59} +(-0.917861 - 0.826446i) q^{61} +(-7.30532 - 14.3375i) q^{62} +(-2.45190 - 7.18801i) q^{63} +(-0.774814 + 0.251752i) q^{64} +(2.01909 - 1.81800i) q^{66} +(10.7014 + 4.10789i) q^{67} +(-0.269499 + 1.00578i) q^{68} +(0.471717 + 0.342723i) q^{69} +(-11.3299 + 8.23164i) q^{71} +(1.47516 + 3.84293i) q^{72} +(1.89921 + 2.92452i) q^{73} +(-6.74848 - 3.89623i) q^{74} -7.64897i q^{76} +(-11.1254 - 1.00564i) q^{77} +(-0.0595648 + 0.376077i) q^{78} +(-5.74668 + 12.9073i) q^{79} +(-7.17266 + 3.19347i) q^{81} +(10.3608 + 2.77617i) q^{82} +(0.477665 + 3.01586i) q^{83} +(0.502981 - 1.02377i) q^{84} +(6.31698 - 7.01572i) q^{86} +(-0.609399 - 0.0319372i) q^{87} +(6.04629 + 0.316873i) q^{88} +(-11.4094 + 12.6715i) q^{89} +(1.30039 - 0.871684i) q^{91} +(-0.303712 - 1.91756i) q^{92} +(-3.12743 - 0.837993i) q^{93} +(15.7479 - 7.01144i) q^{94} +(-0.878647 + 1.97347i) q^{96} +(-1.83327 + 11.5748i) q^{97} +(-11.9922 + 3.59099i) q^{98} +12.1198i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 2 q^{2} - 6 q^{3} + 10 q^{4} + 10 q^{7} - 64 q^{8} + 10 q^{9} - 6 q^{11} + 6 q^{12} + 20 q^{14} - 30 q^{16} + 12 q^{17} + 14 q^{18} + 30 q^{19} - 12 q^{21} + 8 q^{22} - 30 q^{23} - 48 q^{26} + 58 q^{28}+ \cdots - 62 q^{98}+O(q^{100}) $ 288 * q - 2 * q^2 - 6 * q^3 + 10 * q^4 + 10 * q^7 - 64 * q^8 + 10 * q^9 - 6 * q^11 + 6 * q^12 + 20 * q^14 - 30 * q^16 + 12 * q^17 + 14 * q^18 + 30 * q^19 - 12 * q^21 + 8 * q^22 - 30 * q^23 - 48 * q^26 + 58 * q^28 - 18 * q^31 - 8 * q^32 + 150 * q^33 + 40 * q^36 - 12 * q^38 - 30 * q^39 - 166 * q^42 + 108 * q^43 + 10 * q^44 - 6 * q^46 + 24 * q^47 - 16 * q^51 + 24 * q^52 + 40 * q^53 + 30 * q^54 + 4 * q^56 + 216 * q^57 + 114 * q^58 - 90 * q^59 - 18 * q^61 + 16 * q^63 + 100 * q^64 - 90 * q^66 - 74 * q^67 - 342 * q^68 - 24 * q^71 + 222 * q^72 + 216 * q^73 - 90 * q^77 + 32 * q^78 + 10 * q^79 - 10 * q^81 - 216 * q^82 - 20 * q^84 - 6 * q^86 + 18 * q^87 - 58 * q^88 - 120 * q^89 - 12 * q^91 + 24 * q^92 - 106 * q^93 + 30 * q^94 - 90 * q^96 - 62 * q^98

Character values

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

$n$	$127$	$626$
$\chi(n)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−1.78588	+	0.0935941i	−1.26281	+	0.0661810i	−0.671952	−	0.740595i	$-0.734544\pi$
$2$	−1.78588	+	0.0935941i	−1.26281	+	0.0661810i	−0.590857	+	0.806776i	$0.701210\pi$
$3$	−0.226450	+	0.279642i	−0.130741	+	0.161451i	−0.838312	−	0.545190i	$-0.816457\pi$
$3$	−0.226450	+	0.279642i	−0.130741	+	0.161451i	0.707572	+	0.706642i	$0.249791\pi$
$4$	1.19157	−	0.125239i	0.595785	−	0.0626196i
$5$		0			0
$5$		0			0
$6$	0.378240	−	0.520602i	0.154416	−	0.212535i
$7$	−2.62695	+	0.314872i	−0.992893	+	0.119010i
$7$	−2.62695	+	0.314872i	−0.992893	+	0.119010i
$8$	1.41635	−	0.224327i	0.500755	−	0.0793117i
$9$	0.596815	+	2.80779i	0.198938	+	0.935931i
$10$		0			0
$11$	4.12989	+	0.877836i	1.24521	+	0.264678i	0.782960	−	0.622072i	$-0.213709\pi$
$11$	4.12989	+	0.877836i	1.24521	+	0.264678i	0.462250	+	0.886750i	$0.347042\pi$
$12$	−0.234809	+	0.361574i	−0.0677834	+	0.104377i
$13$	−0.527217	+	0.268631i	−0.146224	+	0.0745047i	−0.525571	−	0.850749i	$-0.676148\pi$
$13$	−0.527217	+	0.268631i	−0.146224	+	0.0745047i	0.379348	+	0.925254i	$0.376148\pi$
$14$	4.66195	−	0.808191i	1.24596	−	0.215998i
$15$		0			0
$16$	−4.85234	+	1.03140i	−1.21308	+	0.257849i
$17$	−0.311447	+	0.811348i	−0.0755371	+	0.196781i	−0.966150	−	0.257982i	$-0.916943\pi$
$17$	−0.311447	+	0.811348i	−0.0755371	+	0.196781i	0.890613	+	0.454763i	$0.150276\pi$
$18$	−1.32863	−	4.95853i	−0.313162	−	1.16874i
$19$	0.667317	−	6.34910i	0.153093	−	1.45658i	−0.600702	−	0.799473i	$-0.705112\pi$
$19$	0.667317	−	6.34910i	0.153093	−	1.45658i	0.753795	−	0.657110i	$-0.228221\pi$
$20$		0			0
$21$	0.506820	−	0.805908i	0.110597	−	0.175863i
$22$	−7.45766	−	1.18118i	−1.58998	−	0.251828i
$23$	−0.0848056	−	1.61819i	−0.0176832	−	0.337415i	−0.993117	−	0.117124i	$-0.962633\pi$
$23$	−0.0848056	−	1.61819i	−0.0176832	−	0.337415i	0.975434	−	0.220291i	$-0.0707008\pi$
$24$	−0.258000	+	0.446869i	−0.0526640	+	0.0912168i
$25$		0			0
$26$	0.916406	−	0.529087i	0.179722	−	0.103762i
$27$	−1.88216	−	0.959010i	−0.362223	−	0.184562i
$28$	−3.09076	+	0.704189i	−0.584099	+	0.133079i
$29$	0.996818	+	1.37200i	0.185104	+	0.254774i	0.891477	−	0.453066i	$-0.149670\pi$
$29$	0.996818	+	1.37200i	0.185104	+	0.254774i	−0.706373	+	0.707840i	$0.749670\pi$
$30$		0			0
$31$	3.65980	+	8.22005i	0.657320	+	1.47636i	0.866853	+	0.498563i	$0.166139\pi$
$31$	3.65980	+	8.22005i	0.657320	+	1.47636i	−0.209534	+	0.977801i	$0.567195\pi$
$32$	5.79889	−	1.55381i	1.02511	−	0.274677i
$33$	−1.18069	+	0.956106i	−0.205532	+	0.166437i
$34$	0.480271	−	1.47812i	0.0823657	−	0.253496i
$35$		0			0
$36$	1.06279	+	3.27094i	0.177132	+	0.545157i
$37$	3.65442	+	2.37321i	0.600782	+	0.390153i	0.808896	−	0.587952i	$-0.200066\pi$
$37$	3.65442	+	2.37321i	0.600782	+	0.390153i	−0.208113	+	0.978105i	$0.566732\pi$
$38$	−0.597511	+	11.4012i	−0.0969291	+	1.84952i
$39$	0.0442678	−	0.208263i	0.00708851	−	0.0333488i
$40$		0			0
$41$	−5.70437	−	1.85346i	−0.890873	−	0.289462i	−0.172408	−	0.985026i	$-0.555155\pi$
$41$	−5.70437	−	1.85346i	−0.890873	−	0.289462i	−0.718465	+	0.695563i	$0.755155\pi$
$42$	−0.829693	+	1.48669i	−0.128024	+	0.229401i
$43$	−3.73281	+	3.73281i	−0.569248	+	0.569248i	−0.931918	−	0.362670i	$-0.881865\pi$
$43$	−3.73281	+	3.73281i	−0.569248	+	0.569248i	0.362670	+	0.931918i	$0.381865\pi$
$44$	5.03100	+	0.528779i	0.758452	+	0.0797165i
$45$		0			0
$46$	0.302906	+	2.88195i	0.0446610	+	0.424921i
$47$	−8.99906	+	3.45442i	−1.31265	+	0.503878i	−0.911185	−	0.411997i	$-0.864831\pi$
$47$	−8.99906	+	3.45442i	−1.31265	+	0.503878i	−0.401463	+	0.915875i	$0.631498\pi$
$48$	0.810389	−	1.59048i	0.116970	−	0.229566i
$49$	6.80171	−	1.65430i	0.971673	−	0.236329i
$50$		0			0
$51$	−0.156360	−	0.270823i	−0.0218948	−	0.0379228i
$52$	−0.594574	+	0.386121i	−0.0824525	+	0.0535453i
$53$	6.59068	+	5.33703i	0.905300	+	0.733098i	0.964203	−	0.265166i	$-0.0854268\pi$
$53$	6.59068	+	5.33703i	0.905300	+	0.733098i	−0.0589026	+	0.998264i	$0.518760\pi$
$54$	3.45108	+	1.53652i	0.469632	+	0.209094i
$55$		0			0
$56$	−3.65004	+	1.03526i	−0.487757	+	0.138343i
$57$	1.62436	+	1.62436i	0.215152	+	0.215152i
$58$	−1.90861	−	2.35694i	−0.250613	−	0.309481i
$59$	−4.53398	−	5.03550i	−0.590274	−	0.655566i	0.371813	−	0.928308i	$-0.378736\pi$
$59$	−4.53398	−	5.03550i	−0.590274	−	0.655566i	−0.962087	+	0.272742i	$0.912070\pi$
$60$		0			0
$61$	−0.917861	−	0.826446i	−0.117520	−	0.105816i	0.608276	−	0.793726i	$-0.291862\pi$
$61$	−0.917861	−	0.826446i	−0.117520	−	0.105816i	−0.725796	+	0.687910i	$0.758528\pi$
$62$	−7.30532	−	14.3375i	−0.927777	−	1.82086i
$63$	−2.45190	−	7.18801i	−0.308910	−	0.905604i
$64$	−0.774814	+	0.251752i	−0.0968517	+	0.0314690i
$65$		0			0
$66$	2.01909	−	1.81800i	0.248533	−	0.223780i
$67$	10.7014	+	4.10789i	1.30739	+	0.501859i	0.909549	−	0.415596i	$-0.136427\pi$
$67$	10.7014	+	4.10789i	1.30739	+	0.501859i	0.397838	+	0.917455i	$0.369760\pi$
$68$	−0.269499	+	1.00578i	−0.0326815	+	0.121969i
$69$	0.471717	+	0.342723i	0.0567881	+	0.0412590i
$70$		0			0
$71$	−11.3299	+	8.23164i	−1.34461	+	0.976915i	−0.345348	+	0.938475i	$0.612239\pi$
$71$	−11.3299	+	8.23164i	−1.34461	+	0.976915i	−0.999261	+	0.0384406i	$0.987761\pi$
$72$	1.47516	+	3.84293i	0.173850	+	0.452894i
$73$	1.89921	+	2.92452i	0.222285	+	0.342289i	0.932165	−	0.362033i	$-0.117917\pi$
$73$	1.89921	+	2.92452i	0.222285	+	0.342289i	−0.709880	+	0.704323i	$0.751251\pi$
$74$	−6.74848	−	3.89623i	−0.784494	−	0.452928i
$75$		0			0
$76$		−	7.64897i		−	0.877397i
$77$	−11.1254	−	1.00564i	−1.26786	−	0.114604i
$78$	−0.0595648	+	0.376077i	−0.00674438	+	0.0425823i
$79$	−5.74668	+	12.9073i	−0.646552	+	1.45218i	0.231123	+	0.972924i	$0.425760\pi$
$79$	−5.74668	+	12.9073i	−0.646552	+	1.45218i	−0.877675	+	0.479255i	$0.840907\pi$
$80$		0			0
$81$	−7.17266	+	3.19347i	−0.796962	+	0.354830i
$82$	10.3608	+	2.77617i	1.14416	+	0.306577i
$83$	0.477665	+	3.01586i	0.0524305	+	0.331033i	0.999936	+	0.0112944i	$0.00359520\pi$
$83$	0.477665	+	3.01586i	0.0524305	+	0.331033i	−0.947506	+	0.319739i	$0.896405\pi$
$84$	0.502981	−	1.02377i	0.0548797	−	0.111702i
$85$		0			0
$86$	6.31698	−	7.01572i	0.681178	−	0.756525i
$87$	−0.609399	−	0.0319372i	−0.0653344	−	0.00342403i
$88$	6.04629	+	0.316873i	0.644537	+	0.0337787i
$89$	−11.4094	+	12.6715i	−1.20940	+	1.34317i	−0.286523	+	0.958073i	$0.592500\pi$
$89$	−11.4094	+	12.6715i	−1.20940	+	1.34317i	−0.922875	+	0.385100i	$0.874167\pi$
$90$		0			0
$91$	1.30039	−	0.871684i	0.136318	−	0.0913774i
$92$	−0.303712	−	1.91756i	−0.0316642	−	0.199920i
$93$	−3.12743	−	0.837993i	−0.324300	−	0.0868958i
$94$	15.7479	−	7.01144i	1.62428	−	0.723174i
$95$		0			0
$96$	−0.878647	+	1.97347i	−0.0896765	+	0.201417i
$97$	−1.83327	+	11.5748i	−0.186140	+	1.17524i	0.700800	+	0.713358i	$0.252826\pi$
$97$	−1.83327	+	11.5748i	−0.186140	+	1.17524i	−0.886940	+	0.461884i	$0.847174\pi$
$98$	−11.9922	+	3.59099i	−1.21140	+	0.362745i
$99$			12.1198i			1.21809i
$100$		0			0
$101$	3.84878	+	2.22209i	0.382967	+	0.221106i	0.679109	−	0.734038i	$-0.262367\pi$
$101$	3.84878	+	2.22209i	0.382967	+	0.221106i	−0.296141	+	0.955144i	$0.595700\pi$
$102$	0.304588	+	0.469024i	0.0301587	+	0.0464403i
$103$	−0.751133	−	1.95677i	−0.0740114	−	0.192806i	0.891584	−	0.452855i	$-0.149595\pi$
$103$	−0.751133	−	1.95677i	−0.0740114	−	0.192806i	−0.965595	+	0.260049i	$0.916261\pi$
$104$	−0.686462	+	0.498744i	−0.0673131	+	0.0489058i
$105$		0			0
$106$	−12.2697	−	8.91446i	−1.19174	−	0.865849i
$107$	1.06590	−	3.97800i	0.103045	−	0.384568i	−0.895071	−	0.445923i	$-0.852876\pi$
$107$	1.06590	−	3.97800i	0.103045	−	0.384568i	0.998116	+	0.0613552i	$0.0195422\pi$
$108$	−2.36284	−	0.907008i	−0.227364	−	0.0872769i
$109$	−8.87403	+	7.99021i	−0.849977	+	0.765323i	−0.973902	−	0.226968i	$-0.927119\pi$
$109$	−8.87403	+	7.99021i	−0.849977	+	0.765323i	0.123925	+	0.992292i	$0.460452\pi$
$110$		0			0
$111$	−1.49119	+	0.484517i	−0.141537	+	0.0459883i
$112$	12.4221	−	4.23729i	1.17378	−	0.400386i
$113$	−1.62124	−	3.18186i	−0.152513	−	0.299324i	0.802091	−	0.597202i	$-0.203721\pi$
$113$	−1.62124	−	3.18186i	−0.152513	−	0.299324i	−0.954604	+	0.297878i	$0.903721\pi$
$114$	−3.05295	−	2.74889i	−0.285935	−	0.257457i
$115$		0			0
$116$	1.35961	+	1.51000i	0.126236	+	0.140200i
$117$	−1.06891	−	1.31999i	−0.0988208	−	0.122034i
$118$	8.56845	+	8.56845i	0.788789	+	0.788789i
$119$	0.562685	−	2.22943i	0.0515813	−	0.204372i
$120$		0			0
$121$	6.23643	+	2.77664i	0.566948	+	0.252421i
$122$	1.71654	+	1.39003i	0.155408	+	0.125847i
$123$	1.81006	−	1.17547i	0.163207	−	0.105988i
$124$	5.39038	+	9.33642i	0.484071	+	0.838435i
$125$		0			0
$126$	5.05155	+	12.6074i	0.450028	+	1.12316i
$127$	−1.49373	+	2.93160i	−0.132547	+	0.260138i	−0.947735	−	0.319058i	$-0.896633\pi$
$127$	−1.49373	+	2.93160i	−0.132547	+	0.260138i	0.815188	+	0.579196i	$0.196633\pi$
$128$	−9.84925	+	3.78077i	−0.870559	+	0.334176i
$129$	−0.198557	−	1.88914i	−0.0174820	−	0.166330i
$130$		0			0
$131$	−3.66772	−	0.385493i	−0.320450	−	0.0336806i	−0.0570620	−	0.998371i	$-0.518173\pi$
$131$	−3.66772	−	0.385493i	−0.320450	−	0.0336806i	−0.263388	+	0.964690i	$0.584840\pi$
$132$	−1.28714	+	1.28714i	−0.112031	+	0.112031i
$133$	0.246144	+	16.8889i	0.0213434	+	1.46445i
$134$	−19.4960	−	6.33462i	−1.68419	−	0.547228i
$135$		0			0
$136$	−0.259110	+	1.21902i	−0.0222185	+	0.104530i
$137$	−0.0527989	+	1.00746i	−0.00451092	+	0.0860734i	−0.999957	−	0.00925064i	$-0.997055\pi$
$137$	−0.0527989	+	1.00746i	−0.00451092	+	0.0860734i	0.995446	+	0.0953240i	$0.0303887\pi$
$138$	−0.874508	−	0.567912i	−0.0744431	−	0.0483439i
$139$	−3.10037	−	9.54195i	−0.262970	−	0.809337i	−0.992154	−	0.125020i	$-0.960100\pi$
$139$	−3.10037	−	9.54195i	−0.262970	−	0.809337i	0.729185	−	0.684317i	$-0.239900\pi$
$140$		0			0
$141$	1.07183	−	3.29877i	0.0902647	−	0.277806i
$142$	19.4634	−	15.7611i	1.63333	−	1.32265i
$143$	−2.41316	+	0.646606i	−0.201799	+	0.0540719i
$144$	−5.79190	−	13.0088i	−0.482658	−	1.08407i
$145$		0			0
$146$	−3.66548	−	5.04510i	−0.303357	−	0.417535i
$147$	−1.07763	+	2.27666i	−0.0888816	+	0.187776i
$148$	4.65171	+	2.37017i	0.382369	+	0.194827i
$149$	−6.19698	+	3.57783i	−0.507676	+	0.293107i	−0.731878	−	0.681436i	$-0.761356\pi$
$149$	−6.19698	+	3.57783i	−0.507676	+	0.293107i	0.224202	+	0.974543i	$0.428023\pi$
$150$		0			0
$151$	12.2345	−	21.1907i	0.995627	−	1.72448i	0.416908	−	0.908949i	$-0.363114\pi$
$151$	12.2345	−	21.1907i	0.995627	−	1.72448i	0.578718	−	0.815527i	$-0.303553\pi$
$152$	−0.479124	−	9.14223i	−0.0388621	−	0.741532i
$153$	−2.46397	−	0.390255i	−0.199200	−	0.0315502i
$154$	19.9628	+	0.754685i	1.60865	+	0.0608142i
$155$		0			0
$156$	0.0266654	−	0.253705i	0.00213494	−	0.0203126i
$157$	5.19791	+	19.3989i	0.414838	+	1.54820i	0.785159	+	0.619294i	$0.212581\pi$
$157$	5.19791	+	19.3989i	0.414838	+	1.54820i	−0.370321	+	0.928904i	$0.620752\pi$
$158$	9.05485	−	23.5887i	0.720365	−	1.87662i
$159$	−2.98492	+	0.634464i	−0.236719	+	0.0503162i
$160$		0			0
$161$	0.732301	+	4.22419i	0.0577134	+	0.332913i
$162$	12.5106	−	6.37449i	0.982928	−	0.500827i
$163$	8.78818	−	13.5326i	0.688343	−	1.05996i	−0.305822	−	0.952089i	$-0.598931\pi$
$163$	8.78818	−	13.5326i	0.688343	−	1.05996i	0.994165	−	0.107867i	$-0.0344020\pi$
$164$	−7.02929	−	1.49412i	−0.548895	−	0.116671i
$165$		0			0
$166$	−1.13532	−	5.34126i	−0.0881179	−	0.414562i
$167$	10.0363	−	1.58959i	0.776630	−	0.123006i	0.244478	−	0.969655i	$-0.421383\pi$
$167$	10.0363	−	1.58959i	0.776630	−	0.123006i	0.532152	+	0.846649i	$0.321383\pi$
$168$	0.537046	−	1.25514i	0.0414340	−	0.0968361i
$169$	−7.43541	+	10.2340i	−0.571955	+	0.787228i
$170$		0			0
$171$	18.2252	−	1.91555i	1.39372	−	0.146486i
$172$	−3.98041	+	4.91540i	−0.303503	+	0.374795i
$173$	3.35004	−	0.175568i	0.254699	−	0.0133482i	0.0754409	−	0.997150i	$-0.475964\pi$
$173$	3.35004	−	0.175568i	0.254699	−	0.0133482i	0.179258	+	0.983802i	$0.442630\pi$
$174$	1.09130			0.0827315
$175$		0			0
$176$	−20.9450			−1.57879
$177$	2.43485	−	0.127605i	0.183015	−	0.00959140i
$178$	19.1899	−	23.6976i	1.43835	−	1.77621i
$179$	2.88851	−	0.303595i	0.215897	−	0.0226917i	0.00403785	−	0.999992i	$-0.498715\pi$
$179$	2.88851	−	0.303595i	0.215897	−	0.0226917i	0.211860	+	0.977300i	$0.432048\pi$
$180$		0			0
$181$	4.64922	−	6.39910i	0.345574	−	0.475641i	−0.600485	−	0.799636i	$-0.705026\pi$
$181$	4.64922	−	6.39910i	0.345574	−	0.475641i	0.946059	+	0.323994i	$0.105026\pi$
$182$	−2.24076	+	1.67843i	−0.166096	+	0.124414i
$183$	0.438958	−	0.0695242i	0.0324487	−	0.00513937i
$184$	−0.483118	−	2.27289i	−0.0356159	−	0.167560i
$185$		0			0
$186$	5.66366	+	1.20385i	0.415279	+	0.0882704i
$187$	−1.99847	+	3.07738i	−0.146143	+	0.225040i
$188$	−10.2904	+	5.24321i	−0.750504	+	0.382401i
$189$	5.24631	+	1.92663i	0.381613	+	0.140142i
$190$		0			0
$191$	14.2348	−	3.02570i	1.03000	−	0.218932i	0.338237	−	0.941061i	$-0.390170\pi$
$191$	14.2348	−	3.02570i	1.03000	−	0.218932i	0.691758	+	0.722129i	$0.256836\pi$
$192$	0.105056	−	0.273680i	0.00758175	−	0.0197511i
$193$	0.160877	+	0.600403i	0.0115802	+	0.0432179i	0.971474	−	0.237145i	$-0.0762117\pi$
$193$	0.160877	+	0.600403i	0.0115802	+	0.0432179i	−0.959894	+	0.280363i	$0.909545\pi$
$194$	2.19067	−	20.8428i	0.157281	−	1.49643i
$195$		0			0
$196$	7.89754	−	2.82306i	0.564110	−	0.201647i
$197$	−24.1044	−	3.81776i	−1.71736	−	0.272004i	−0.781383	−	0.624052i	$-0.785485\pi$
$197$	−24.1044	−	3.81776i	−1.71736	−	0.272004i	−0.935982	+	0.352048i	$0.885485\pi$
$198$	−1.13434	−	21.6445i	−0.0806141	−	1.53821i
$199$	4.29215	−	7.43422i	0.304262	−	0.526998i	−0.672835	−	0.739793i	$-0.734923\pi$
$199$	4.29215	−	7.43422i	0.304262	−	0.526998i	0.977097	+	0.212795i	$0.0682568\pi$
$200$		0			0
$201$	−3.57207	+	2.06234i	−0.251955	+	0.145466i
$202$	−7.08143	−	3.60817i	−0.498248	−	0.253870i
$203$	−3.05059	−	3.29031i	−0.214110	−	0.230934i
$204$	−0.220231	−	0.303123i	−0.0154193	−	0.0212228i
$205$		0			0
$206$	1.52458	+	3.42426i	0.106222	+	0.238579i
$207$	4.49292	−	1.20387i	0.312280	−	0.0836751i
$208$	2.28117	−	1.84726i	0.158171	−	0.128084i
$209$	8.32941	−	25.6353i	0.576158	−	1.77323i
$210$		0			0
$211$	1.28435	+	3.95282i	0.0884183	+	0.272123i	0.985483	−	0.169777i	$-0.0543046\pi$
$211$	1.28435	+	3.95282i	0.0884183	+	0.272123i	−0.897064	+	0.441900i	$0.854305\pi$
$212$	8.52167	+	5.53404i	0.585271	+	0.380079i
$213$	0.263735	−	5.03236i	0.0180708	−	0.344812i
$214$	−1.53126	+	7.20400i	−0.104675	+	0.492455i
$215$		0			0
$216$	−2.88093	−	0.936071i	−0.196023	−	0.0636916i
$217$	−12.2024	−	20.4413i	−0.828351	−	1.38764i
$218$	15.1001	−	15.1001i	1.02271	−	1.02271i
$219$	−1.24789	−	0.131159i	−0.0843249	−	0.00886290i
$220$		0			0
$221$	−0.0537525	−	0.511421i	−0.00361578	−	0.0344019i
$222$	2.61774	−	1.00486i	0.175691	−	0.0674416i
$223$	−5.77436	+	11.3328i	−0.386680	+	0.758902i	−0.999510	−	0.0313132i	$-0.990031\pi$
$223$	−5.77436	+	11.3328i	−0.386680	+	0.758902i	0.612830	+	0.790215i	$0.290031\pi$
$224$	−14.7441	+	5.90768i	−0.985134	+	0.394723i
$225$		0			0
$226$	3.19314	+	5.53069i	0.212405	+	0.367896i
$227$	5.87260	−	3.81371i	0.389778	−	0.253125i	−0.334841	−	0.942275i	$-0.608682\pi$
$227$	5.87260	−	3.81371i	0.389778	−	0.253125i	0.724619	+	0.689150i	$0.242016\pi$
$228$	2.13897	+	1.73211i	0.141657	+	0.114712i
$229$	13.5136	+	6.01664i	0.893003	+	0.397591i	0.801347	−	0.598200i	$-0.204117\pi$
$229$	13.5136	+	6.01664i	0.893003	+	0.397591i	0.0916563	+	0.995791i	$0.470784\pi$
$230$		0			0
$231$	2.80057	−	2.88341i	0.184264	−	0.189714i
$232$	1.71962	+	1.71962i	0.112899	+	0.112899i
$233$	1.60547	+	1.98260i	0.105178	+	0.129884i	0.827017	−	0.562177i	$-0.190036\pi$
$233$	1.60547	+	1.98260i	0.105178	+	0.129884i	−0.721839	+	0.692061i	$0.756703\pi$
$234$	2.03249	+	2.25731i	0.132868	+	0.147565i
$235$		0			0
$236$	−6.03320	−	5.43232i	−0.392728	−	0.353614i
$237$	−2.30808	−	4.52986i	−0.149926	−	0.294246i
$238$	−0.796227	+	4.03417i	−0.0516118	+	0.261496i
$239$	0.945911	−	0.307345i	0.0611859	−	0.0198805i	−0.278264	−	0.960505i	$-0.589759\pi$
$239$	0.945911	−	0.307345i	0.0611859	−	0.0198805i	0.339450	+	0.940624i	$0.389759\pi$
$240$		0			0
$241$	−3.98537	+	3.58844i	−0.256720	+	0.231152i	−0.787434	−	0.616399i	$-0.788591\pi$
$241$	−3.98537	+	3.58844i	−0.256720	+	0.231152i	0.530713	+	0.847551i	$0.321924\pi$
$242$	−11.3974	−	4.37505i	−0.732653	−	0.281239i
$243$	2.37141	−	8.85021i	0.152126	−	0.567741i
$244$	−1.19720	−	0.869816i	−0.0766428	−	0.0556843i
$245$		0			0
$246$	−3.12253	+	2.26865i	−0.199086	+	0.144644i
$247$	1.35374	+	3.52661i	0.0861364	+	0.224393i
$248$	7.02754	+	10.8215i	0.446249	+	0.687163i
$249$	−0.951527	−	0.549365i	−0.0603006	−	0.0348146i
$250$		0			0
$251$		−	15.5071i		−	0.978800i	−0.872059	−	0.489400i	$-0.837216\pi$
$251$		−	15.5071i		−	0.978800i	0.872059	−	0.489400i	$-0.162784\pi$
$252$	−3.82183	−	8.25794i	−0.240753	−	0.520202i
$253$	1.07026	−	6.75739i	0.0672870	−	0.424833i
$254$	2.39324	−	5.37530i	0.150165	−	0.337277i
$255$		0			0
$256$	18.7242	−	8.33657i	1.17027	−	0.521036i
$257$	−15.0766	−	4.03975i	−0.940449	−	0.251993i	−0.244145	−	0.969739i	$-0.578507\pi$
$257$	−15.0766	−	4.03975i	−0.940449	−	0.251993i	−0.696305	+	0.717746i	$0.745174\pi$
$258$	0.531412	+	3.35520i	0.0330842	+	0.208886i
$259$	−10.3472	−	5.08362i	−0.642945	−	0.315881i
$260$		0			0
$261$	−3.25738	+	3.61769i	−0.201627	+	0.223929i
$262$	6.58619	+	0.345168i	0.406896	+	0.0213245i
$263$	4.10463	+	0.215114i	0.253102	+	0.0132645i	0.178465	−	0.983946i	$-0.442887\pi$
$263$	4.10463	+	0.215114i	0.253102	+	0.0132645i	0.0746370	+	0.997211i	$0.476220\pi$
$264$	−1.45779	+	1.61904i	−0.0897208	+	0.0996451i
$265$		0			0
$266$	−2.02028	−	30.1385i	−0.123872	−	1.84791i
$267$	−0.959811	−	6.06001i	−0.0587395	−	0.370866i
$268$	13.2660	+	3.55461i	0.810349	+	0.217132i
$269$	10.7761	−	4.79784i	0.657032	−	0.292529i	−0.0510119	−	0.998698i	$-0.516245\pi$
$269$	10.7761	−	4.79784i	0.657032	−	0.292529i	0.708044	+	0.706169i	$0.249578\pi$
$270$		0			0
$271$	−2.73943	+	6.15287i	−0.166409	+	0.373760i	−0.977431	−	0.211255i	$-0.932245\pi$
$271$	−2.73943	+	6.15287i	−0.166409	+	0.373760i	0.811022	+	0.585015i	$0.198912\pi$
$272$	0.674426	−	4.25816i	0.0408931	−	0.258189i
$273$	−0.0507128	+	0.561036i	−0.00306928	+	0.0339554i
$274$		−	1.80415i		−	0.108993i
$275$		0			0
$276$	0.605007	+	0.349301i	0.0364171	+	0.0210254i
$277$	16.5873	+	25.5422i	0.996635	+	1.53468i	0.836778	+	0.547543i	$0.184437\pi$
$277$	16.5873	+	25.5422i	0.996635	+	1.53468i	0.159857	+	0.987140i	$0.448897\pi$
$278$	6.42996	+	16.7506i	0.385643	+	1.00464i
$279$	−20.8960	+	15.1818i	−1.25101	+	0.908911i
$280$		0			0
$281$	3.78178	+	2.74762i	0.225602	+	0.163909i	0.694845	−	0.719160i	$-0.255473\pi$
$281$	3.78178	+	2.74762i	0.225602	+	0.163909i	−0.469243	+	0.883069i	$0.655473\pi$
$282$	−1.60542	+	5.99152i	−0.0956016	+	0.356790i
$283$	−5.22881	−	2.00715i	−0.310821	−	0.119313i	0.197957	−	0.980211i	$-0.436569\pi$
$283$	−5.22881	−	2.00715i	−0.310821	−	0.119313i	−0.508778	+	0.860898i	$0.669903\pi$
$284$	−12.4694	+	11.2275i	−0.739924	+	0.666231i
$285$		0			0
$286$	4.24911	−	1.38062i	0.251255	−	0.0816377i
$287$	15.5687	+	3.07280i	0.918991	+	0.181382i
$288$	7.82364	+	15.3547i	0.461012	+	0.904787i
$289$	12.0722	+	10.8698i	0.710128	+	0.639402i
$290$		0			0
$291$	−2.82166	−	3.13377i	−0.165408	−	0.183705i
$292$	2.62930	+	3.24692i	0.153868	+	0.190012i
$293$	−7.38400	−	7.38400i	−0.431378	−	0.431378i	0.457719	−	0.889097i	$-0.348667\pi$
$293$	−7.38400	−	7.38400i	−0.431378	−	0.431378i	−0.889097	+	0.457719i	$0.848667\pi$
$294$	1.71144	−	4.16671i	0.0998133	−	0.243007i
$295$		0			0
$296$	5.70830	+	2.54150i	0.331788	+	0.147722i
$297$	−6.93128	−	5.61284i	−0.402194	−	0.325690i
$298$	10.7322	−	6.96958i	0.621700	−	0.403737i
$299$	0.479406	+	0.830355i	0.0277247	+	0.0480207i
$300$		0			0
$301$	8.63053	−	10.9812i	0.497456	−	0.632948i
$302$	−19.8660	+	38.9892i	−1.14316	+	2.24358i
$303$	−1.49294	+	0.573087i	−0.0857674	+	0.0329230i
$304$	3.31039	+	31.4962i	0.189864	+	1.80643i
$305$		0			0
$306$	4.43689	+	0.466336i	0.253640	+	0.0266587i
$307$	19.4310	−	19.4310i	1.10899	−	1.10899i	0.115702	−	0.993284i	$-0.463088\pi$
$307$	19.4310	−	19.4310i	1.10899	−	1.10899i	0.993284	−	0.115702i	$-0.0369117\pi$
$308$	−13.3827	+	0.195044i	−0.762549	+	0.0111137i
$309$	0.717289	+	0.233061i	0.0408051	+	0.0132584i
$310$		0			0
$311$	3.11924	−	14.6749i	0.176876	−	0.832135i	−0.796808	−	0.604232i	$-0.793480\pi$
$311$	3.11924	−	14.6749i	0.176876	−	0.832135i	0.973684	−	0.227902i	$-0.0731867\pi$
$312$	0.0159793	−	0.304904i	0.000904652	−	0.0172618i
$313$	−25.5775	−	16.6103i	−1.44573	−	0.938867i	−0.999023	−	0.0441858i	$-0.985931\pi$
$313$	−25.5775	−	16.6103i	−1.44573	−	0.938867i	−0.446705	−	0.894681i	$-0.647403\pi$
$314$	−11.0985	−	34.1576i	−0.626323	−	1.92762i
$315$		0			0
$316$	−5.23108	+	16.0996i	−0.294271	+	0.905674i
$317$	−19.6529	+	15.9146i	−1.10382	+	0.893852i	−0.994967	−	0.100206i	$-0.968050\pi$
$317$	−19.6529	+	15.9146i	−1.10382	+	0.893852i	−0.108849	+	0.994058i	$0.534717\pi$
$318$	5.27133	−	1.41245i	0.295601	−	0.0792061i
$319$	2.91236	+	6.54127i	0.163061	+	0.366241i
$320$		0			0
$321$	0.871043	+	1.19889i	0.0486169	+	0.0669154i
$322$	−1.70316	−	7.47537i	−0.0949136	−	0.416586i
$323$	4.94349	+	2.51883i	0.275063	+	0.140152i
$324$	−8.14678	+	4.70355i	−0.452599	+	0.261308i
$325$		0			0
$326$	−14.4281	+	24.9902i	−0.799097	+	1.38408i
$327$	−0.224878	−	4.29093i	−0.0124358	−	0.237289i
$328$	−8.49516	−	1.34550i	−0.469066	−	0.0742928i
$329$	22.5524	−	11.9081i	1.24335	−	0.656516i
$330$		0			0
$331$	0.691950	−	6.58346i	0.0380330	−	0.361860i	−0.958909	−	0.283714i	$-0.908433\pi$
$331$	0.691950	−	6.58346i	0.0380330	−	0.361860i	0.996942	−	0.0781459i	$-0.0249000\pi$
$332$	0.946875	+	3.53378i	0.0519665	+	0.193942i
$333$	−4.48246	+	11.6772i	−0.245637	+	0.639907i
$334$	−17.7748	+	3.77815i	−0.972595	+	0.206731i
$335$		0			0
$336$	−1.62805	+	4.43327i	−0.0888175	+	0.241855i
$337$	4.40088	−	2.24236i	0.239731	−	0.122149i	−0.329998	−	0.943982i	$-0.607048\pi$
$337$	4.40088	−	2.24236i	0.239731	−	0.122149i	0.569729	+	0.821833i	$0.307048\pi$
$338$	12.3209	−	18.9726i	0.670170	−	1.03197i
$339$	1.25691	+	0.267165i	0.0682660	+	0.0145104i
$340$		0			0
$341$	7.89874	+	37.1606i	0.427741	+	2.01236i
$342$	−32.3688	+	5.12671i	−1.75030	+	0.277221i
$343$	−17.3468	+	6.48744i	−0.936642	+	0.350289i
$344$	−4.44958	+	6.12432i	−0.239905	+	0.330201i
$345$		0			0
$346$	−5.96635	+	0.627089i	−0.320753	+	0.0337125i
$347$	16.2036	−	20.0098i	0.869857	−	1.07418i	−0.126755	−	0.991934i	$-0.540456\pi$
$347$	16.2036	−	20.0098i	0.869857	−	1.07418i	0.996612	−	0.0822499i	$-0.0262106\pi$
$348$	−0.730141	+	0.0382651i	−0.0391397	+	0.00205122i
$349$	23.8148			1.27478			0.637389	−	0.770543i	$-0.280015\pi$
$349$	23.8148			1.27478			0.637389	+	0.770543i	$0.280015\pi$
$350$		0			0
$351$	1.24993			0.0667163
$352$	25.3128	−	1.32659i	1.34918	−	0.0707073i
$353$	−19.9280	+	24.6090i	−1.06066	+	1.30980i	−0.111929	+	0.993716i	$0.535703\pi$
$353$	−19.9280	+	24.6090i	−1.06066	+	1.30980i	−0.948730	+	0.316089i	$0.897630\pi$
$354$	−4.33642	+	0.455776i	−0.230478	+	0.0242242i
$355$		0			0
$356$	−12.0082	+	16.5279i	−0.636433	+	0.875975i
$357$	0.496024	+	0.662205i	0.0262524	+	0.0350476i
$358$	−5.13013	+	0.812532i	−0.271136	+	0.0429437i
$359$	2.63745	+	12.4082i	0.139199	+	0.654881i	0.991313	+	0.131524i	$0.0419871\pi$
$359$	2.63745	+	12.4082i	0.139199	+	0.654881i	−0.852114	+	0.523357i	$0.824680\pi$
$360$		0			0
$361$	−21.2809	−	4.52340i	−1.12005	−	0.238073i
$362$	−7.70404	+	11.8632i	−0.404915	+	0.623515i
$363$	−2.18870	+	1.11520i	−0.114877	+	0.0585328i
$364$	1.44034	−	1.20153i	0.0754941	−	0.0629775i
$365$		0			0
$366$	−0.777421	+	0.165246i	−0.0406364	+	0.00863754i
$367$	−2.81310	+	7.32836i	−0.146842	+	0.382538i	−0.987198	−	0.159497i	$-0.949013\pi$
$367$	−2.81310	+	7.32836i	−0.146842	+	0.382538i	0.840356	+	0.542035i	$0.182346\pi$
$368$	2.08050	+	7.76452i	0.108453	+	0.404754i
$369$	1.79969	−	17.1229i	0.0936879	−	0.891381i
$370$		0			0
$371$	−18.9939	−	11.9449i	−0.986112	−	0.620147i
$372$	−3.83151	−	0.606851i	−0.198654	−	0.0314638i
$373$	0.190823	+	3.64111i	0.00988042	+	0.188530i	0.999111	+	0.0421626i	$0.0134248\pi$
$373$	0.190823	+	3.64111i	0.00988042	+	0.188530i	−0.989230	+	0.146367i	$0.953242\pi$
$374$	3.28101	−	5.68288i	0.169657	−	0.293855i
$375$		0			0
$376$	−11.9709	+	6.91139i	−0.617351	+	0.356428i
$377$	−0.894102	−	0.455567i	−0.0460486	−	0.0234629i
$378$	−9.54961	−	2.94971i	−0.491179	−	0.151717i
$379$	−12.1944	−	16.7841i	−0.626384	−	0.862143i	0.371414	−	0.928467i	$-0.378873\pi$
$379$	−12.1944	−	16.7841i	−0.626384	−	0.862143i	−0.997798	+	0.0663239i	$0.978873\pi$
$380$		0			0
$381$	−0.481546	−	1.08157i	−0.0246703	−	0.0554105i
$382$	−25.1385	+	6.73584i	−1.28620	+	0.344636i
$383$	15.0992	−	12.2271i	0.771533	−	0.624775i	−0.160546	−	0.987028i	$-0.551326\pi$
$383$	15.0992	−	12.2271i	0.771533	−	0.624775i	0.932080	+	0.362253i	$0.117992\pi$
$384$	1.17310	−	3.61042i	0.0598643	−	0.184243i
$385$		0			0
$386$	−0.343502	−	1.05719i	−0.0174838	−	0.0538096i
$387$	−12.7087	−	8.25315i	−0.646022	−	0.419531i
$388$	−0.734850	+	14.0218i	−0.0373064	+	0.711848i
$389$	−3.18105	+	14.9656i	−0.161285	+	0.758788i	0.820930	+	0.571029i	$0.193456\pi$
$389$	−3.18105	+	14.9656i	−0.161285	+	0.758788i	−0.982215	+	0.187759i	$0.939878\pi$
$390$		0			0
$391$	1.33933	+	0.435173i	0.0677326	+	0.0220077i
$392$	9.26248	−	3.86888i	0.467826	−	0.195408i
$393$	0.938353	−	0.938353i	0.0473337	−	0.0473337i
$394$	43.4049	+	4.56204i	2.18671	+	0.229832i
$395$		0			0
$396$	1.51787	+	14.4416i	0.0762760	+	0.725717i
$397$	27.2933	−	10.4769i	1.36981	−	0.525822i	0.441379	−	0.897321i	$-0.354489\pi$
$397$	27.2933	−	10.4769i	1.36981	−	0.525822i	0.928434	+	0.371499i	$0.121156\pi$
$398$	−6.96947	+	13.6784i	−0.349348	+	0.685634i
$399$	−4.77858	−	3.75565i	−0.239228	−	0.188017i
$400$		0			0
$401$	10.9327	+	18.9359i	0.545952	+	0.945616i	0.998546	+	0.0538996i	$0.0171651\pi$
$401$	10.9327	+	18.9359i	0.545952	+	0.945616i	−0.452595	+	0.891716i	$0.649502\pi$
$402$	6.18628	−	4.01742i	0.308544	−	0.200371i
$403$	−4.13767	−	3.35062i	−0.206112	−	0.166906i
$404$	4.86438	+	2.16576i	0.242012	+	0.107751i
$405$		0			0
$406$	5.75595	+	5.59059i	0.285663	+	0.277456i
$407$	13.0091	+	13.0091i	0.644836	+	0.644836i
$408$	−0.282213	−	0.348504i	−0.0139716	−	0.0172535i
$409$	−20.5599	−	22.8341i	−1.01662	−	1.12907i	−0.991594	−	0.129385i	$-0.958700\pi$
$409$	−20.5599	−	22.8341i	−1.01662	−	1.12907i	−0.0250261	−	0.999687i	$-0.507967\pi$
$410$		0			0
$411$	−0.269773	−	0.242904i	−0.0133069	−	0.0119816i
$412$	−1.14009	−	2.23756i	−0.0561683	−	0.110237i
$413$	13.4961	+	11.8004i	0.664098	+	0.580658i
$414$	−7.91115	+	2.57049i	−0.388812	+	0.126333i
$415$		0			0
$416$	−2.63987	+	2.37695i	−0.129431	+	0.116540i
$417$	3.37041	+	1.29378i	0.165049	+	0.0633566i
$418$	−12.4760	+	46.5612i	−0.610223	+	2.27738i
$419$	8.60424	+	6.25134i	0.420345	+	0.305398i	0.777776	−	0.628541i	$-0.216348\pi$
$419$	8.60424	+	6.25134i	0.420345	+	0.305398i	−0.357432	+	0.933939i	$0.616348\pi$
$420$		0			0
$421$	17.2687	−	12.5464i	0.841623	−	0.611475i	−0.0812007	−	0.996698i	$-0.525875\pi$
$421$	17.2687	−	12.5464i	0.841623	−	0.611475i	0.922824	+	0.385223i	$0.125875\pi$
$422$	−2.66366	−	6.93906i	−0.129665	−	0.337788i
$423$	−15.0701	−	23.2059i	−0.732731	−	1.12831i
$424$	10.5319	+	6.08062i	0.511476	+	0.295301i
$425$		0			0
$426$			9.01188i			0.436627i
$427$	2.67140	+	1.88202i	0.129278	+	0.0910774i
$428$	0.771896	−	4.87356i	0.0373110	−	0.235572i
$429$	0.365642	−	0.821246i	0.0176534	−	0.0396501i
$430$		0			0
$431$	−7.00187	+	3.11743i	−0.337268	+	0.150161i	−0.568381	−	0.822765i	$-0.692430\pi$
$431$	−7.00187	+	3.11743i	−0.337268	+	0.150161i	0.231113	+	0.972927i	$0.425763\pi$
$432$	10.1220	+	2.71219i	0.486996	+	0.130490i
$433$	3.21139	+	20.2759i	0.154330	+	0.974399i	0.936330	+	0.351121i	$0.114199\pi$
$433$	3.21139	+	20.2759i	0.154330	+	0.974399i	−0.782000	+	0.623278i	$0.785801\pi$
$434$	23.7052	+	35.3636i	1.13788	+	1.69751i
$435$		0			0
$436$	−9.57334	+	10.6323i	−0.458480	+	0.509194i
$437$	−10.3306	−	0.541405i	−0.494180	−	0.0258989i
$438$	2.24087	+	0.117439i	0.107073	+	0.00561145i
$439$	−8.37290	+	9.29905i	−0.399617	+	0.443820i	−0.909048	−	0.416692i	$-0.863189\pi$
$439$	−8.37290	+	9.29905i	−0.399617	+	0.443820i	0.509431	+	0.860512i	$0.329856\pi$
$440$		0			0
$441$	8.70430	+	18.1105i	0.414491	+	0.862404i
$442$	0.143862	+	0.908306i	0.00684280	+	0.0432037i
$443$	−33.8090	−	9.05910i	−1.60632	−	0.430411i	−0.659373	−	0.751816i	$-0.729178\pi$
$443$	−33.8090	−	9.05910i	−1.60632	−	0.430411i	−0.946942	+	0.321405i	$0.895845\pi$
$444$	−1.71618	+	0.764091i	−0.0814462	+	0.0362622i
$445$		0			0
$446$	9.25164	−	20.7795i	0.438078	−	0.983939i
$447$	0.402793	−	2.54313i	0.0190514	−	0.120286i
$448$	1.95613	−	0.905307i	0.0924182	−	0.0427717i
$449$		−	4.28525i		−	0.202233i	−0.994875	−	0.101117i	$-0.967758\pi$
$449$		−	4.28525i		−	0.202233i	0.994875	−	0.101117i	$-0.0322416\pi$
$450$		0			0
$451$	−21.9314	−	12.6621i	−1.03271	−	0.596235i
$452$	−2.33031	−	3.58837i	−0.109609	−	0.168783i
$453$	3.15532	+	8.21990i	0.148250	+	0.386205i
$454$	−10.1308	+	7.36048i	−0.475464	+	0.345445i
$455$		0			0
$456$	2.66505	+	1.93627i	0.124802	+	0.0906742i
$457$	4.57736	−	17.0829i	0.214120	−	0.799107i	−0.772355	−	0.635192i	$-0.780921\pi$
$457$	4.57736	−	17.0829i	0.214120	−	0.799107i	0.986474	−	0.163915i	$-0.0524122\pi$
$458$	−24.6968	−	9.48021i	−1.15401	−	0.442981i
$459$	1.36429	−	1.22841i	0.0636794	−	0.0573372i
$460$		0			0
$461$	−23.7965	+	7.73195i	−1.10831	+	0.360113i	−0.805297	−	0.592872i	$-0.797994\pi$
$461$	−23.7965	+	7.73195i	−1.10831	+	0.360113i	−0.303017	+	0.952985i	$0.597994\pi$
$462$	−4.73161	+	5.41154i	−0.220135	+	0.251768i
$463$	12.3939	+	24.3244i	0.575994	+	1.13045i	0.976773	+	0.214277i	$0.0687396\pi$
$463$	12.3939	+	24.3244i	0.575994	+	1.13045i	−0.400779	+	0.916175i	$0.631260\pi$
$464$	−6.25198	−	5.62931i	−0.290241	−	0.261334i
$465$		0			0
$466$	−3.05275	−	3.39042i	−0.141416	−	0.157058i
$467$	4.45476	+	5.50117i	0.206142	+	0.254564i	0.869723	−	0.493541i	$-0.164298\pi$
$467$	4.45476	+	5.50117i	0.206142	+	0.254564i	−0.663581	+	0.748104i	$0.730964\pi$
$468$	−1.43900	−	1.43900i	−0.0665177	−	0.0665177i
$469$	−29.4056	−	7.42165i	−1.35782	−	0.342700i
$470$		0			0
$471$	−6.60180	−	2.93931i	−0.304195	−	0.135436i
$472$	−7.55129	−	6.11492i	−0.347576	−	0.281462i
$473$	−18.6929	+	12.1393i	−0.859500	+	0.558166i
$474$	4.54592	+	7.87377i	0.208801	+	0.361654i
$475$		0			0
$476$	0.391267	−	2.72700i	0.0179337	−	0.124992i
$477$	−11.0519	+	21.6905i	−0.506030	+	0.993140i
$478$	−1.66052	+	0.637414i	−0.0759504	+	0.0291546i
$479$	3.94813	+	37.5639i	0.180394	+	1.71634i	0.592809	+	0.805343i	$0.298019\pi$
$479$	3.94813	+	37.5639i	0.180394	+	1.71634i	−0.412415	+	0.910996i	$0.635315\pi$
$480$		0			0
$481$	−2.56419	−	0.269507i	−0.116917	−	0.0122885i
$482$	6.78154	−	6.78154i	0.308891	−	0.308891i
$483$	−1.34709	−	0.751784i	−0.0612947	−	0.0342074i
$484$	7.77889	+	2.52751i	0.353586	+	0.114887i
$485$		0			0
$486$	−3.40672	+	16.0274i	−0.154532	+	0.727017i
$487$	−0.687869	+	13.1253i	−0.0311703	+	0.594765i	0.937738	+	0.347344i	$0.112916\pi$
$487$	−0.687869	+	13.1253i	−0.0311703	+	0.594765i	−0.968908	+	0.247421i	$0.920417\pi$
$488$	−1.48540	−	0.964633i	−0.0672411	−	0.0436669i
$489$	1.79421	+	5.52200i	0.0811368	+	0.249713i
$490$		0			0
$491$	−7.21929	+	22.2187i	−0.325802	+	1.00272i	0.645275	+	0.763950i	$0.276743\pi$
$491$	−7.21929	+	22.2187i	−0.325802	+	1.00272i	−0.971077	+	0.238765i	$0.923257\pi$
$492$	2.00960	−	1.62734i	0.0905997	−	0.0733662i
$493$	−1.42363	+	0.381460i	−0.0641170	+	0.0171801i
$494$	−2.74769	−	6.17142i	−0.123624	−	0.277665i
$495$		0			0
$496$	−26.2367	−	36.1118i	−1.17806	−	1.62147i
$497$	27.1711	−	25.1915i	1.21879	−	1.12999i
$498$	1.75073	+	0.892043i	0.0784522	+	0.0399734i
$499$	7.78986	−	4.49748i	0.348722	−	0.201335i	−0.315400	−	0.948959i	$-0.602139\pi$
$499$	7.78986	−	4.49748i	0.348722	−	0.201335i	0.664122	+	0.747624i	$0.268805\pi$
$500$		0			0
$501$	−1.82819	+	3.16652i	−0.0816777	+	0.141470i
$502$	1.45137	+	27.6939i	0.0647780	+	1.23604i
$503$	35.5693	+	5.63363i	1.58596	+	0.251191i	0.886239	−	0.463228i	$-0.153309\pi$
$503$	35.5693	+	5.63363i	1.58596	+	0.251191i	0.699718	+	0.714419i	$0.253309\pi$
$504$	−5.08521	−	9.63069i	−0.226513	−	0.428985i
$505$		0			0
$506$	−1.27892	+	12.1681i	−0.0568547	+	0.540937i
$507$	−1.17810	−	4.39673i	−0.0523213	−	0.195266i
$508$	−1.41273	+	3.68029i	−0.0626797	+	0.163286i
$509$	8.98152	−	1.90908i	0.398099	−	0.0846185i	−0.00451185	−	0.999990i	$-0.501436\pi$
$509$	8.98152	−	1.90908i	0.398099	−	0.0846185i	0.402611	+	0.915371i	$0.368103\pi$
$510$		0			0
$511$	−5.90997	−	7.08456i	−0.261442	−	0.313403i
$512$	−13.8588	+	7.06144i	−0.612480	+	0.312074i
$513$	−7.34485	+	11.3101i	−0.324283	+	0.499352i
$514$	27.3030	+	5.80344i	1.20429	+	0.255979i
$515$		0			0
$516$	−0.473189	−	2.22618i	−0.0208310	−	0.0980021i
$517$	−40.1976	+	6.36667i	−1.76789	+	0.280006i
$518$	18.9547	+	8.11030i	0.832822	+	0.356346i
$519$	−0.709520	+	0.976571i	−0.0311445	+	0.0428667i
$520$		0			0
$521$	−12.1370	+	1.27565i	−0.531732	+	0.0558872i	−0.366590	−	0.930383i	$-0.619475\pi$
$521$	−12.1370	+	1.27565i	−0.531732	+	0.0558872i	−0.165142	+	0.986270i	$0.552808\pi$
$522$	5.47871	−	6.76564i	0.239796	−	0.296124i
$523$	20.3847	−	1.06831i	0.891359	−	0.0467141i	0.398845	−	0.917019i	$-0.369411\pi$
$523$	20.3847	−	1.06831i	0.891359	−	0.0467141i	0.492514	+	0.870304i	$0.336078\pi$
$524$	−4.41862			−0.193028
$525$		0			0
$526$	−7.35051			−0.320498
$527$	−7.80915	+	0.409260i	−0.340172	+	0.0178277i
$528$	4.74300	−	5.85711i	0.206412	−	0.254898i
$529$	20.2627	−	2.12969i	0.880985	−	0.0925953i
$530$		0			0
$531$	11.4327	−	15.7357i	0.496136	−	0.682873i
$532$	2.40845	+	20.0934i	0.104419	+	0.871162i
$533$	3.50534	−	0.555191i	0.151833	−	0.0240480i
$534$	2.28129	+	10.7326i	0.0987211	+	0.464446i
$535$		0			0
$536$	16.0785	+	3.41758i	0.694484	+	0.147617i
$537$	−0.569204	+	0.876498i	−0.0245630	+	0.0378237i
$538$	−18.7958	+	9.57695i	−0.810346	+	0.412892i
$539$	29.5426	−	0.861311i	1.27249	−	0.0370993i
$540$		0			0
$541$	17.2586	−	3.66843i	0.742006	−	0.157718i	0.178627	−	0.983917i	$-0.442835\pi$
$541$	17.2586	−	3.66843i	0.742006	−	0.157718i	0.563379	+	0.826199i	$0.309501\pi$
$542$	4.31643	−	11.2447i	0.185407	−	0.483001i
$543$	0.736644	+	2.74919i	0.0316124	+	0.117979i
$544$	−0.545370	+	5.18885i	−0.0233825	+	0.222470i
$545$		0			0
$546$	0.0380575	−	1.00669i	0.00162871	−	0.0430824i
$547$	−2.95974	−	0.468776i	−0.126549	−	0.0200434i	0.0928385	−	0.995681i	$-0.470406\pi$
$547$	−2.95974	−	0.468776i	−0.126549	−	0.0200434i	−0.219388	+	0.975638i	$0.570406\pi$
$548$	0.0632602	+	1.20708i	0.00270234	+	0.0515637i
$549$	1.77270	−	3.07040i	0.0756568	−	0.131041i
$550$		0			0
$551$	9.37617	−	5.41333i	0.399438	−	0.230616i
$552$	0.744998	+	0.379595i	0.0317092	+	0.0161567i
$553$	11.0321	−	35.7162i	0.469133	−	1.51881i
$554$	−32.0136	−	44.0629i	−1.36013	−	1.87205i
$555$		0			0
$556$	−4.88933	−	10.9816i	−0.207354	−	0.465724i
$557$	−30.2559	+	8.10705i	−1.28198	+	0.343507i	−0.834610	−	0.550841i	$-0.814307\pi$
$557$	−30.2559	+	8.10705i	−1.28198	+	0.343507i	−0.447373	+	0.894347i	$0.647641\pi$
$558$	35.8968	−	29.0687i	1.51963	−	1.23057i
$559$	0.965254	−	2.97075i	0.0408259	−	0.125649i
$560$		0			0
$561$	−0.408011	−	1.25573i	−0.0172262	−	0.0530169i
$562$	−7.01097	−	4.55298i	−0.295740	−	0.192056i
$563$	0.973818	−	18.5816i	0.0410415	−	0.783119i	−0.898142	−	0.439705i	$-0.855083\pi$
$563$	0.973818	−	18.5816i	0.0410415	−	0.783119i	0.939184	−	0.343414i	$-0.111584\pi$
$564$	0.864032	−	4.06495i	0.0363823	−	0.171165i
$565$		0			0
$566$	9.52590	+	3.09515i	0.400404	+	0.130099i
$567$	17.8367	−	10.6476i	0.749070	−	0.447155i
$568$	−14.2005	+	14.2005i	−0.595838	+	0.595838i
$569$	1.55796	+	0.163748i	0.0653132	+	0.00686469i	0.137129	−	0.990553i	$-0.456213\pi$
$569$	1.55796	+	0.163748i	0.0653132	+	0.00686469i	−0.0718155	+	0.997418i	$0.522879\pi$
$570$		0			0
$571$	1.38221	+	13.1509i	0.0578437	+	0.550346i	0.984617	+	0.174725i	$0.0559038\pi$
$571$	1.38221	+	13.1509i	0.0578437	+	0.550346i	−0.926773	+	0.375621i	$0.877430\pi$
$572$	−2.79448	+	1.07270i	−0.116843	+	0.0448518i
$573$	−2.37736	+	4.66582i	−0.0993154	+	0.194918i
$574$	−28.0914	−	4.03053i	−1.17251	−	0.168231i
$575$		0			0
$576$	−1.16929	−	2.02527i	−0.0487204	−	0.0843861i
$577$	7.78982	−	5.05877i	0.324294	−	0.210599i	−0.372216	−	0.928146i	$-0.621402\pi$
$577$	7.78982	−	5.05877i	0.324294	−	0.210599i	0.696510	+	0.717547i	$0.254735\pi$
$578$	−22.5768	−	18.2824i	−0.939073	−	0.760446i
$579$	−0.204328	−	0.0909729i	−0.00849160	−	0.00378070i
$580$		0			0
$581$	−2.20441	−	7.77210i	−0.0914543	−	0.322441i
$582$	5.33245	+	5.33245i	0.221037	+	0.221037i
$583$	22.5338	+	27.8269i	0.933254	+	1.15247i
$584$	3.34599	+	3.71610i	0.138458	+	0.153773i
$585$		0			0
$586$	13.8781	+	12.4959i	0.573297	+	0.516199i
$587$	−6.05467	−	11.8830i	−0.249903	−	0.490462i	0.731643	−	0.681688i	$-0.238754\pi$
$587$	−6.05467	−	11.8830i	−0.249903	−	0.490462i	−0.981546	+	0.191226i	$0.938754\pi$
$588$	−0.998948	+	2.84776i	−0.0411959	+	0.117440i
$589$	54.6321	−	17.7511i	2.25108	−	0.731419i
$590$		0			0
$591$	6.52603	−	5.87606i	0.268445	−	0.241709i
$592$	−20.1802	−	7.74645i	−0.829400	−	0.318377i
$593$	9.45404	−	35.2829i	0.388231	−	1.44890i	−0.444780	−	0.895640i	$-0.646718\pi$
$593$	9.45404	−	35.2829i	0.388231	−	1.44890i	0.833011	−	0.553257i	$-0.186615\pi$
$594$	12.9038	+	9.37515i	0.529449	+	0.384667i
$595$		0			0
$596$	−6.93605	+	5.03934i	−0.284112	+	0.206419i
$597$	1.10696	+	2.88374i	0.0453050	+	0.118024i
$598$	−0.933878	−	1.43805i	−0.0381891	−	0.0588061i
$599$	−0.214739	−	0.123980i	−0.00877399	−	0.00506567i	0.495607	−	0.868547i	$-0.334946\pi$
$599$	−0.214739	−	0.123980i	−0.00877399	−	0.00506567i	−0.504381	+	0.863481i	$0.668279\pi$
$600$		0			0
$601$			19.3484i			0.789237i	0.918845	+	0.394618i	$0.129123\pi$
$601$			19.3484i			0.789237i	−0.918845	+	0.394618i	$0.870877\pi$
$602$	−14.3853	+	20.4190i	−0.586302	+	0.832215i
$603$	−5.14734	+	32.4991i	−0.209616	+	1.32346i
$604$	11.9243	−	26.7825i	0.485194	−	1.08976i
$605$		0			0
$606$	2.61258	−	1.16320i	0.106129	−	0.0472517i
$607$	−34.8976	−	9.35079i	−1.41645	−	0.379537i	−0.532227	−	0.846601i	$-0.678645\pi$
$607$	−34.8976	−	9.35079i	−1.41645	−	0.379537i	−0.884223	+	0.467065i	$0.845312\pi$
$608$	−5.99558	−	37.8546i	−0.243153	−	1.53521i
$609$	1.61091	−	0.107985i	0.0652776	−	0.00437577i
$610$		0			0
$611$	3.81650	−	4.23865i	0.154399	−	0.171477i
$612$	−2.98487	−	0.156431i	−0.120656	−	0.00632333i
$613$	−15.5902	−	0.817047i	−0.629681	−	0.0330002i	−0.265174	−	0.964201i	$-0.585429\pi$
$613$	−15.5902	−	0.817047i	−0.629681	−	0.0330002i	−0.364508	+	0.931200i	$0.618763\pi$
$614$	−32.8828	+	36.5201i	−1.32704	+	1.47383i
$615$		0			0
$616$	−15.9831	+	1.07140i	−0.643976	+	0.0431679i
$617$	−4.34934	−	27.4606i	−0.175098	−	1.10552i	−0.906074	−	0.423120i	$-0.860935\pi$
$617$	−4.34934	−	27.4606i	−0.175098	−	1.10552i	0.730976	−	0.682403i	$-0.239065\pi$
$618$	−1.30281	−	0.349086i	−0.0524065	−	0.0140423i
$619$	−32.8458	+	14.6239i	−1.32018	+	0.587784i	−0.941272	−	0.337648i	$-0.890369\pi$
$619$	−32.8458	+	14.6239i	−1.32018	+	0.587784i	−0.378913	+	0.925432i	$0.623702\pi$
$620$		0			0
$621$	−1.39224	+	3.12702i	−0.0558687	+	0.125483i
$622$	−4.19711	+	26.4995i	−0.168289	+	1.06253i
$623$	25.9821	−	36.8798i	1.04095	−	1.47756i
$624$			1.05622i			0.0422827i
$625$		0			0
$626$	47.2331	+	27.2700i	1.88781	+	1.08993i
$627$	5.28251	+	8.13436i	0.210963	+	0.324855i
$628$	8.62317	+	22.4641i	0.344102	+	0.896416i
$629$	−3.06365	+	2.22587i	−0.122156	+	0.0887514i
$630$		0			0
$631$	23.2118	+	16.8644i	0.924048	+	0.671360i	0.944528	−	0.328430i	$-0.106520\pi$
$631$	23.2118	+	16.8644i	0.924048	+	0.671360i	−0.0204802	+	0.999790i	$0.506520\pi$
$632$	−5.24385	+	19.5703i	−0.208589	+	0.778465i
$633$	−1.39622	−	0.535957i	−0.0554946	−	0.0213024i
$634$	33.6082	−	30.2610i	1.33475	−	1.20182i
$635$		0			0
$636$	−3.47728	+	1.12984i	−0.137883	+	0.0448009i
$637$	−3.14158	+	2.69933i	−0.124474	+	0.106951i
$638$	−5.81335	−	11.4094i	−0.230153	−	0.451701i
$639$	−29.8746	−	26.8992i	−1.18182	−	1.06412i
$640$		0			0
$641$	12.0398	+	13.3716i	0.475545	+	0.528146i	0.932416	−	0.361387i	$-0.117697\pi$
$641$	12.0398	+	13.3716i	0.475545	+	0.528146i	−0.456871	+	0.889533i	$0.651030\pi$
$642$	−1.66779	−	2.05955i	−0.0658223	−	0.0812838i
$643$	−9.47610	−	9.47610i	−0.373701	−	0.373701i	0.495122	−	0.868823i	$-0.335123\pi$
$643$	−9.47610	−	9.47610i	−0.373701	−	0.373701i	−0.868823	+	0.495122i	$0.835123\pi$
$644$	1.40162	+	4.94171i	0.0552317	+	0.194731i
$645$		0			0
$646$	−9.06424	−	4.03566i	−0.356628	−	0.158781i
$647$	10.7662	+	8.71831i	0.423264	+	0.342752i	0.817168	−	0.576399i	$-0.195543\pi$
$647$	10.7662	+	8.71831i	0.423264	+	0.342752i	−0.393905	+	0.919151i	$0.628876\pi$
$648$	−9.44260	+	6.13209i	−0.370940	+	0.240891i
$649$	−14.3045	−	24.7762i	−0.561502	−	0.972549i
$650$		0			0
$651$	8.47946	+	1.21662i	0.332336	+	0.0476832i
$652$	8.77692	−	17.2257i	0.343731	−	0.674610i
$653$	−34.2673	+	13.1540i	−1.34098	+	0.514754i	−0.919859	−	0.392249i	$-0.871697\pi$
$653$	−34.2673	+	13.1540i	−1.34098	+	0.514754i	−0.421122	+	0.907004i	$0.638364\pi$
$654$	0.803212	+	7.64205i	0.0314081	+	0.298828i
$655$		0			0
$656$	29.5912	+	3.11016i	1.15534	+	0.121431i
$657$	−7.07798	+	7.07798i	−0.276138	+	0.276138i
$658$	−39.1613	+	23.3773i	−1.52667	+	0.911341i
$659$	17.1826	+	5.58297i	0.669340	+	0.217482i	0.623922	−	0.781486i	$-0.285538\pi$
$659$	17.1826	+	5.58297i	0.669340	+	0.217482i	0.0454175	+	0.998968i	$0.485538\pi$
$660$		0			0
$661$	5.47564	−	25.7609i	0.212978	−	1.00198i	−0.733619	−	0.679561i	$-0.762170\pi$
$661$	5.47564	−	25.7609i	0.212978	−	1.00198i	0.946596	−	0.322421i	$-0.104497\pi$
$662$	−0.619568	+	11.8221i	−0.0240802	+	0.459477i
$663$	0.155187	+	0.100780i	0.00602696	+	0.00391396i
$664$	1.35308	+	4.16435i	0.0525097	+	0.161608i
$665$		0			0
$666$	6.91223	−	21.2737i	0.267843	−	0.824337i
$667$	2.13562	−	1.72939i	0.0826916	−	0.0669623i
$668$	11.7598	−	3.15104i	0.455002	−	0.121917i
$669$	−1.86153	−	4.18107i	−0.0719709	−	0.161649i
$670$		0			0
$671$	−3.06518	−	4.21886i	−0.118330	−	0.162867i
$672$	1.68677	−	5.46087i	0.0650685	−	0.210658i
$673$	45.5727	+	23.2205i	1.75670	+	0.895083i	0.954598	+	0.297896i	$0.0962850\pi$
$673$	45.5727	+	23.2205i	1.75670	+	0.895083i	0.802102	+	0.597187i	$0.203715\pi$
$674$	−7.64957	+	4.41648i	−0.294651	+	0.170117i
$675$		0			0
$676$	−7.57813	+	13.1257i	−0.291466	+	0.504835i
$677$	−2.06961	−	39.4906i	−0.0795417	−	1.51775i	−0.688903	−	0.724854i	$-0.741907\pi$
$677$	−2.06961	−	39.4906i	−0.0795417	−	1.51775i	0.609361	−	0.792893i	$-0.291426\pi$
$678$	−2.26970	−	0.359485i	−0.0871673	−	0.0138059i
$679$	1.17132	−	30.9836i	0.0449512	−	1.18904i
$680$		0			0
$681$	−0.263374	+	2.50584i	−0.0100925	+	0.0960240i
$682$	−17.5842	−	65.6252i	−0.673335	−	2.51292i
$683$	−3.90584	+	10.1751i	−0.149453	+	0.389338i	−0.987785	−	0.155822i	$-0.950198\pi$
$683$	−3.90584	+	10.1751i	−0.149453	+	0.389338i	0.838332	+	0.545159i	$0.183531\pi$
$684$	21.4767	−	4.56502i	0.821183	−	0.174548i
$685$		0			0
$686$	30.3722	−	13.2094i	1.15962	−	0.504336i
$687$	−4.74265	+	2.41650i	−0.180943	+	0.0921953i
$688$	14.2628	−	21.9628i	0.543766	−	0.837326i
$689$	−4.90841	−	1.04332i	−0.186996	−	0.0397471i
$690$		0			0
$691$	−7.18035	−	33.7809i	−0.273153	−	1.28509i	−0.874080	−	0.485782i	$-0.838535\pi$
$691$	−7.18035	−	33.7809i	−0.273153	−	1.28509i	0.600927	−	0.799304i	$-0.294798\pi$
$692$	3.96983	−	0.628759i	0.150910	−	0.0239018i
$693$	−3.81618	−	31.8381i	−0.144965	−	1.20943i
$694$	−27.0650	+	37.2518i	−1.02737	+	1.41406i
$695$		0			0
$696$	−0.870285	+	0.0914706i	−0.0329881	+	0.00346719i
$697$	3.28041	−	4.05097i	0.124255	−	0.153442i
$698$	−42.5304	+	2.22893i	−1.60980	+	0.0843661i
$699$	−0.917976			−0.0347211
$700$		0			0
$701$	16.6461			0.628716			0.314358	−	0.949305i	$-0.398211\pi$
$701$	16.6461			0.628716			0.314358	+	0.949305i	$0.398211\pi$
$702$	−2.23223	+	0.116986i	−0.0842499	+	0.00441535i
$703$	17.5064	−	21.6186i	0.660265	−	0.815360i
$704$	−3.42090	+	0.359551i	−0.128930	+	0.0135511i
$705$		0			0
$706$	33.2858	−	45.8139i	1.25273	−	1.72423i
$707$	−10.8102	−	4.62545i	−0.406560	−	0.173958i
$708$	2.88532	−	0.456990i	0.108437	−	0.0171747i
$709$	3.91289	+	18.4087i	0.146952	+	0.691353i	0.988506	+	0.151181i	$0.0483075\pi$
$709$	3.91289	+	18.4087i	0.146952	+	0.691353i	−0.841555	+	0.540172i	$0.818359\pi$
$710$		0			0
$711$	−39.6706	−	8.43225i	−1.48776	−	0.316234i
$712$	−13.3172	+	20.5067i	−0.499082	+	0.768519i
$713$	12.9912	−	6.61935i	0.486525	−	0.247897i
$714$	−0.947818	−	1.13620i	−0.0354712	−	0.0425210i
$715$		0			0
$716$	3.40384	−	0.723509i	0.127208	−	0.0270388i
$717$	−0.128255	+	0.334115i	−0.00478976	+	0.0124777i
$718$	−5.87151	−	21.9128i	−0.219123	−	0.817777i
$719$	4.33832	−	41.2764i	0.161792	−	1.53935i	−0.548926	−	0.835871i	$-0.684963\pi$
$719$	4.33832	−	41.2764i	0.161792	−	1.53935i	0.710718	−	0.703477i	$-0.248370\pi$
$720$		0			0
$721$	2.58932	+	4.90382i	0.0964313	+	0.182628i
$722$	38.4285	+	6.08648i	1.43016	+	0.226515i
$723$	−0.100994	−	1.92708i	−0.00375601	−	0.0716688i
$724$	4.73846	−	8.20725i	0.176103	−	0.305020i
$725$		0			0
$726$	3.80439	−	2.19646i	0.141194	−	0.0815184i
$727$	17.6929	+	9.01500i	0.656195	+	0.334348i	0.750188	−	0.661225i	$-0.229963\pi$
$727$	17.6929	+	9.01500i	0.656195	+	0.334348i	−0.0939929	+	0.995573i	$0.529963\pi$
$728$	1.64626	−	1.52632i	0.0610144	−	0.0565692i
$729$	−11.9070	−	16.3886i	−0.441001	−	0.606985i
$730$		0			0
$731$	−1.86603	−	4.19118i	−0.0690177	−	0.155016i
$732$	0.514343	−	0.137818i	0.0190107	−	0.00509389i
$733$	7.70405	−	6.23862i	0.284556	−	0.230429i	−0.476406	−	0.879225i	$-0.658061\pi$
$733$	7.70405	−	6.23862i	0.284556	−	0.230429i	0.760962	+	0.648797i	$0.224727\pi$
$734$	4.33796	−	13.3509i	0.160117	−	0.492790i
$735$		0			0
$736$	−3.00613	−	9.25192i	−0.110807	−	0.341030i
$737$	40.5897	+	26.3593i	1.49514	+	0.970956i
$738$	−1.61143	+	30.7479i	−0.0593174	+	1.13184i
$739$	−1.91774	+	9.02225i	−0.0705451	+	0.331889i	−0.999241	−	0.0389534i	$-0.987598\pi$
$739$	−1.91774	+	9.02225i	−0.0705451	+	0.331889i	0.928696	+	0.370842i	$0.120931\pi$
$740$		0			0
$741$	−1.29274	−	0.420038i	−0.0474901	−	0.0154305i
$742$	35.0388	+	19.5544i	1.28631	+	0.717866i
$743$	31.8855	−	31.8855i	1.16976	−	1.16976i	0.187500	−	0.982265i	$-0.439962\pi$
$743$	31.8855	−	31.8855i	1.16976	−	1.16976i	0.982265	−	0.187500i	$-0.0600383\pi$
$744$	−4.61752	−	0.485321i	−0.169286	−	0.0177927i
$745$		0			0
$746$	−0.681574	−	6.48474i	−0.0249542	−	0.237423i
$747$	−8.18282	+	3.14109i	−0.299394	+	0.114927i
$748$	−1.99592	+	3.91720i	−0.0729779	+	0.143227i
$749$	−1.54751	+	10.7856i	−0.0565447	+	0.394098i
$750$		0			0
$751$	−4.83420	−	8.37308i	−0.176403	−	0.305538i	0.764243	−	0.644928i	$-0.223113\pi$
$751$	−4.83420	−	8.37308i	−0.176403	−	0.305538i	−0.940646	+	0.339390i	$0.889779\pi$
$752$	40.1036	−	26.0436i	1.46243	−	0.949712i
$753$	4.33644	+	3.51158i	0.158029	+	0.127969i
$754$	1.63940	+	0.729907i	0.0597034	+	0.0265816i
$755$		0			0
$756$	6.49264	+	1.63867i	0.236135	+	0.0595979i
$757$	29.1640	+	29.1640i	1.05998	+	1.05998i	0.998082	+	0.0619022i	$0.0197167\pi$
$757$	29.1640	+	29.1640i	1.05998	+	1.05998i	0.0619022	+	0.998082i	$0.480283\pi$
$758$	23.3486	+	28.8332i	0.848061	+	1.04727i
$759$	1.64729	+	1.82950i	0.0597928	+	0.0664066i
$760$		0			0
$761$	−2.78122	−	2.50423i	−0.100819	−	0.0907781i	0.617180	−	0.786822i	$-0.288275\pi$
$761$	−2.78122	−	2.50423i	−0.100819	−	0.0907781i	−0.717999	+	0.696044i	$0.754942\pi$
$762$	0.961213	+	1.88649i	0.0348211	+	0.0683402i
$763$	20.7957	−	23.7840i	0.752855	−	0.861040i
$764$	16.5829	−	5.38810i	0.599947	−	0.194934i
$765$		0			0
$766$	−25.8210	+	23.2493i	−0.932951	+	0.840033i
$767$	3.74308	+	1.43683i	0.135155	+	0.0518811i
$768$	−1.90884	+	7.12390i	−0.0688795	+	0.257062i
$769$	16.8695	+	12.2564i	0.608330	+	0.441977i	0.848826	−	0.528673i	$-0.177310\pi$
$769$	16.8695	+	12.2564i	0.608330	+	0.441977i	−0.240496	+	0.970650i	$0.577310\pi$
$770$		0			0
$771$	4.54376	−	3.30124i	0.163640	−	0.118891i
$772$	0.266891	+	0.695274i	0.00960561	+	0.0250235i
$773$	−10.3343	−	15.9134i	−0.371698	−	0.572365i	0.602483	−	0.798132i	$-0.294178\pi$
$773$	−10.3343	−	15.9134i	−0.371698	−	0.572365i	−0.974181	+	0.225766i	$0.927511\pi$
$774$	23.4688	+	13.5497i	0.843567	+	0.487034i
$775$		0			0
$776$			16.8052i			0.603271i
$777$	3.76472	−	1.74233i	0.135058	−	0.0625059i
$778$	4.28028	−	27.0246i	0.153455	−	0.968879i
$779$	−15.5744	+	34.9807i	−0.558012	+	1.25332i
$780$		0			0
$781$	−54.0172	+	24.0500i	−1.93289	+	0.860577i
$782$	−2.43261	−	0.651815i	−0.0869898	−	0.0233089i
$783$	−0.560410	−	3.53829i	−0.0200274	−	0.126448i
$784$	−31.2980	+	15.0425i	−1.11778	+	0.537232i
$785$		0			0
$786$	−1.58796	+	1.76361i	−0.0566408	+	0.0629060i
$787$	−17.3752	−	0.910595i	−0.619359	−	0.0324592i	−0.259923	−	0.965629i	$-0.583697\pi$
$787$	−17.3752	−	0.910595i	−0.619359	−	0.0324592i	−0.359435	+	0.933170i	$0.617031\pi$
$788$	−29.2002	−	1.53032i	−1.04021	−	0.0545153i
$789$	−0.989646	+	1.09911i	−0.0352323	+	0.0391295i
$790$		0			0
$791$	5.26079	+	7.84810i	0.187052	+	0.279046i
$792$	2.71880	+	17.1658i	0.0966084	+	0.609962i
$793$	0.705921	+	0.189151i	0.0250680	+	0.00671694i
$794$	−47.7621	+	21.2651i	−1.69501	+	0.754668i
$795$		0			0
$796$	4.18334	−	9.39594i	0.148275	−	0.333030i
$797$	−0.210477	+	1.32890i	−0.00745547	+	0.0470720i	−0.991136	−	0.132854i	$-0.957586\pi$
$797$	−0.210477	+	1.32890i	−0.00745547	+	0.0470720i	0.983680	+	0.179926i	$0.0575858\pi$
$798$	8.88548	+	6.25989i	0.314543	+	0.221598i
$799$		−	8.37724i		−	0.296365i
$800$		0			0
$801$	−42.3882	−	24.4728i	−1.49771	−	0.864705i
$802$	−21.2968	−	32.7941i	−0.752015	−	1.15800i
$803$	5.27627	+	13.7452i	0.186196	+	0.485056i
$804$	−3.99809	+	2.90479i	−0.141002	+	0.102444i
$805$		0			0
$806$	7.70298	+	5.59655i	0.271326	+	0.197130i
$807$	−1.09857	+	4.09993i	−0.0386716	+	0.144324i
$808$	5.94968	+	2.28387i	0.209309	+	0.0803462i
$809$	10.7064	−	9.64006i	0.376416	−	0.338927i	−0.459108	−	0.888380i	$-0.651831\pi$
$809$	10.7064	−	9.64006i	0.376416	−	0.338927i	0.835524	+	0.549454i	$0.185164\pi$
$810$		0			0
$811$	6.31358	−	2.05141i	0.221700	−	0.0720346i	−0.196061	−	0.980592i	$-0.562815\pi$
$811$	6.31358	−	2.05141i	0.221700	−	0.0720346i	0.417761	+	0.908557i	$0.362815\pi$
$812$	−4.04707	−	3.53858i	−0.142024	−	0.124180i
$813$	−1.10026	−	2.15938i	−0.0385877	−	0.0757326i
$814$	−24.4502	−	22.0151i	−0.856980	−	0.771628i
$815$		0			0
$816$	1.03804	+	1.15286i	0.0363386	+	0.0403581i
$817$	21.2090	+	26.1909i	0.742008	+	0.916304i
$818$	38.8546	+	38.8546i	1.35852	+	1.35852i
$819$	3.22360	+	3.13099i	0.112642	+	0.109406i
$820$		0			0
$821$	18.0995	+	8.05844i	0.631678	+	0.281241i	0.697494	−	0.716590i	$-0.254298\pi$
$821$	18.0995	+	8.05844i	0.631678	+	0.281241i	−0.0658157	+	0.997832i	$0.520965\pi$
$822$	0.504517	+	0.408550i	0.0175970	+	0.0142498i
$823$	19.3281	−	12.5518i	0.673734	−	0.437528i	−0.161905	−	0.986806i	$-0.551764\pi$
$823$	19.3281	−	12.5518i	0.673734	−	0.437528i	0.835640	+	0.549278i	$0.185097\pi$
$824$	−1.50282	−	2.60297i	−0.0523533	−	0.0906786i
$825$		0			0
$826$	−25.2068	−	19.8109i	−0.877058	−	0.689309i
$827$	18.3211	−	35.9571i	0.637086	−	1.25035i	−0.316317	−	0.948653i	$-0.602446\pi$
$827$	18.3211	−	35.9571i	0.637086	−	1.25035i	0.953403	−	0.301698i	$-0.0975536\pi$
$828$	5.20286	−	1.99719i	0.180812	−	0.0694072i
$829$	−1.29555	−	12.3263i	−0.0449962	−	0.428110i	−0.993711	−	0.111976i	$-0.964282\pi$
$829$	−1.29555	−	12.3263i	−0.0449962	−	0.428110i	0.948715	−	0.316133i	$-0.102385\pi$
$830$		0			0
$831$	−10.8989	−	1.14552i	−0.378078	−	0.0397376i
$832$	0.340867	−	0.340867i	0.0118174	−	0.0118174i
$833$	−0.776159	+	6.03378i	−0.0268923	+	0.209058i
$834$	−6.14024	−	1.99508i	−0.212619	−	0.0690841i
$835$		0			0
$836$	6.71454	−	31.5894i	0.232227	−	1.09254i
$837$	0.994766	−	18.9813i	0.0343841	−	0.656089i
$838$	−15.9512	−	10.3589i	−0.551027	−	0.357841i
$839$	−8.58250	−	26.4142i	−0.296301	−	0.911920i	−0.982781	−	0.184772i	$-0.940845\pi$
$839$	−8.58250	−	26.4142i	−0.296301	−	0.911920i	0.686481	−	0.727148i	$-0.259155\pi$
$840$		0			0
$841$	8.07275	−	24.8454i	0.278371	−	0.856737i
$842$	−29.6655	+	24.0227i	−1.02234	+	0.827875i
$843$	−1.62473	+	0.435346i	−0.0559588	+	0.0149941i
$844$	2.02544	+	4.54921i	0.0697185	+	0.156590i
$845$		0			0
$846$	29.0853	+	40.0324i	0.999972	+	1.37634i
$847$	−17.2571	−	5.33040i	−0.592959	−	0.183155i
$848$	−37.4848	−	19.0995i	−1.28723	−	0.655879i
$849$	1.74535	−	1.00768i	0.0599002	−	0.0345834i
$850$		0			0
$851$	3.53038	−	6.11479i	0.121020	−	0.209612i
$852$	−0.315990	−	6.02944i	−0.0108256	−	0.206565i
$853$	27.2295	+	4.31272i	0.932319	+	0.147665i	0.604074	−	0.796928i	$-0.293543\pi$
$853$	27.2295	+	4.31272i	0.932319	+	0.147665i	0.328245	+	0.944593i	$0.393543\pi$
$854$	−4.94695	−	3.11104i	−0.169281	−	0.106458i
$855$		0			0
$856$	0.617313	−	5.87334i	0.0210993	−	0.200747i
$857$	−1.80489	−	6.73593i	−0.0616538	−	0.230095i	0.928223	−	0.372024i	$-0.121336\pi$
$857$	−1.80489	−	6.73593i	−0.0616538	−	0.230095i	−0.989877	+	0.141929i	$0.954669\pi$
$858$	−0.576130	+	1.50087i	−0.0196688	+	0.0512389i
$859$	−7.73489	+	1.64410i	−0.263911	+	0.0560961i	−0.337967	−	0.941158i	$-0.609739\pi$
$859$	−7.73489	+	1.64410i	−0.263911	+	0.0560961i	0.0740555	+	0.997254i	$0.476406\pi$
$860$		0			0
$861$	−4.38481	+	3.65782i	−0.149434	+	0.124658i
$862$	12.2127	−	6.22270i	0.415968	−	0.211946i
$863$	8.12671	−	12.5140i	0.276637	−	0.425983i	−0.672856	−	0.739774i	$-0.734932\pi$
$863$	8.12671	−	12.5140i	0.276637	−	0.425983i	0.949492	+	0.313791i	$0.101599\pi$
$864$	−12.4046	−	2.63667i	−0.422012	−	0.0897015i
$865$		0			0
$866$	−7.63288	−	35.9099i	−0.259376	−	1.22027i
$867$	−5.77340	+	0.914417i	−0.196075	+	0.0310552i
$868$	−17.1000	−	22.8290i	−0.580413	−	0.774867i
$869$	−35.0636	+	48.2610i	−1.18945	+	1.63714i
$870$		0			0
$871$	−6.74548	+	0.708979i	−0.228562	+	0.0240228i
$872$	−10.7763	+	13.3076i	−0.364931	+	0.450652i
$873$	−33.5937	+	1.76057i	−1.13698	+	0.0595864i
$874$	18.4999			0.625770
$875$		0			0
$876$	−1.50338			−0.0507945
$877$	−28.8481	+	1.51186i	−0.974131	+	0.0510520i	−0.532754	−	0.846270i	$-0.678843\pi$
$877$	−28.8481	+	1.51186i	−0.974131	+	0.0510520i	−0.441376	+	0.897322i	$0.645510\pi$
$878$	14.0827	−	17.3907i	0.475268	−	0.586907i
$879$	3.73698	−	0.392773i	0.126045	−	0.0132479i
$880$		0			0
$881$	−26.6392	+	36.6657i	−0.897498	+	1.23530i	0.0737612	+	0.997276i	$0.476500\pi$
$881$	−26.6392	+	36.6657i	−0.897498	+	1.23530i	−0.971259	+	0.238024i	$0.923500\pi$
$882$	−17.2399	−	31.5285i	−0.580497	−	1.06162i
$883$	2.28067	−	0.361222i	0.0767506	−	0.0121561i	−0.117941	−	0.993021i	$-0.537629\pi$
$883$	2.28067	−	0.361222i	0.0767506	−	0.0121561i	0.194692	+	0.980865i	$0.437629\pi$
$884$	−0.128100	−	0.602662i	−0.00430846	−	0.0202697i
$885$		0			0
$886$	61.2268	+	13.0142i	2.05695	+	0.437219i
$887$	20.7799	−	31.9982i	0.697720	−	1.07440i	−0.295180	−	0.955442i	$-0.595379\pi$
$887$	20.7799	−	31.9982i	0.697720	−	1.07440i	0.992900	−	0.118953i	$-0.0379539\pi$
$888$	−2.00335	+	1.02076i	−0.0672281	+	0.0342544i
$889$	3.00086	−	8.17150i	0.100646	−	0.274063i
$890$		0			0
$891$	−32.4257	+	6.89229i	−1.08630	+	0.230900i
$892$	−5.46125	+	14.2270i	−0.182856	+	0.476356i
$893$	15.9272	+	59.4411i	0.532983	+	1.98912i
$894$	−0.481318	+	4.57944i	−0.0160977	+	0.153159i
$895$		0			0
$896$	24.6830	−	13.0331i	0.824601	−	0.435407i
$897$	−0.340763	−	0.0539716i	−0.0113778	−	0.00180206i
$898$	0.401074	+	7.65295i	0.0133840	+	0.255382i
$899$	−7.62977	+	13.2152i	−0.254467	+	0.440750i
$900$		0			0
$901$	−6.38284	+	3.68513i	−0.212643	+	0.122770i
$902$	40.3520	+	20.5604i	1.34357	+	0.684586i
$903$	1.11644	+	4.90016i	0.0371527	+	0.163067i
$904$	−3.01002	−	4.14293i	−0.100112	−	0.137792i
$905$		0			0
$906$	−6.40437	−	14.3845i	−0.212771	−	0.477891i
$907$	33.3004	−	8.92281i	1.10572	−	0.296277i	0.340629	−	0.940198i	$-0.389360\pi$
$907$	33.3004	−	8.92281i	1.10572	−	0.296277i	0.765092	+	0.643921i	$0.222693\pi$
$908$	6.52000	−	5.27979i	0.216374	−	0.175216i
$909$	−3.94217	+	12.1327i	−0.130753	+	0.402418i
$910$		0			0
$911$	5.06918	+	15.6013i	0.167949	+	0.516895i	0.999242	−	0.0389409i	$-0.0123984\pi$
$911$	5.06918	+	15.6013i	0.167949	+	0.516895i	−0.831292	+	0.555836i	$0.812398\pi$
$912$	−9.55731	−	6.20659i	−0.316474	−	0.205521i
$913$	−0.674723	+	12.8745i	−0.0223301	+	0.426083i
$914$	−6.57576	+	30.9365i	−0.217507	+	1.02329i
$915$		0			0
$916$	16.8559	+	5.47682i	0.556935	+	0.180959i
$917$	9.75628	−	0.142192i	0.322181	−	0.00469558i
$918$	−2.32148	+	2.32148i	−0.0766203	+	0.0766203i
$919$	0.795668	+	0.0836281i	0.0262467	+	0.00275864i	0.117643	−	0.993056i	$-0.462466\pi$
$919$	0.795668	+	0.0836281i	0.0262467	+	0.00275864i	−0.0913960	+	0.995815i	$0.529133\pi$
$920$		0			0
$921$	1.03358	+	9.83387i	0.0340577	+	0.324037i
$922$	41.7741	−	16.0356i	1.37576	−	0.528103i
$923$	3.76204	−	7.38341i	0.123829	−	0.243028i
$924$	2.97596	−	3.78653i	0.0979019	−	0.124568i
$925$		0			0
$926$	−24.4107	−	42.2806i	−0.802185	−	1.38943i
$927$	5.04592	−	3.27686i	0.165730	−	0.107626i
$928$	7.91227	+	6.40723i	0.259733	+	0.210328i
$929$	−28.9365	−	12.8834i	−0.949377	−	0.422690i	−0.127172	−	0.991881i	$-0.540590\pi$
$929$	−28.9365	−	12.8834i	−0.949377	−	0.422690i	−0.822205	+	0.569191i	$0.807257\pi$
$930$		0			0
$931$	−5.96444	−	44.2887i	−0.195476	−	1.45150i
$932$	2.16134	+	2.16134i	0.0707969	+	0.0707969i
$933$	3.39736	+	4.19538i	0.111224	+	0.137351i
$934$	−8.47055	−	9.40750i	−0.277165	−	0.307823i
$935$		0			0
$936$	−1.81006	−	1.62979i	−0.0591637	−	0.0532712i
$937$	8.75168	+	17.1761i	0.285905	+	0.561120i	0.988635	−	0.150337i	$-0.0480357\pi$
$937$	8.75168	+	17.1761i	0.285905	+	0.561120i	−0.702730	+	0.711457i	$0.748036\pi$
$938$	53.2095	+	10.5020i	1.73735	+	0.342902i
$939$	10.4370	−	3.39117i	0.340597	−	0.110667i
$940$		0			0
$941$	38.3796	−	34.5572i	1.25114	−	1.12653i	0.264368	−	0.964422i	$-0.414837\pi$
$941$	38.3796	−	34.5572i	1.25114	−	1.12653i	0.986773	−	0.162110i	$-0.0518299\pi$
$942$	12.0651	+	4.63137i	0.393103	+	0.150898i
$943$	−2.51549	+	9.38792i	−0.0819155	+	0.305713i
$944$	27.1940	+	19.7576i	0.885089	+	0.643055i
$945$		0			0
$946$	32.2471	−	23.4289i	1.04844	−	0.761739i
$947$	17.1035	+	44.5560i	0.555788	+	1.44788i	0.867373	+	0.497659i	$0.165807\pi$
$947$	17.1035	+	44.5560i	0.555788	+	1.44788i	−0.311585	+	0.950218i	$0.600860\pi$
$948$	−3.31755	−	5.10858i	−0.107749	−	0.165919i
$949$	−1.78691	−	1.03167i	−0.0580056	−	0.0334895i
$950$		0			0
$951$		−	9.09962i		−	0.295076i
$952$	0.296835	−	3.28388i	0.00962046	−	0.106431i
$953$	−0.224666	+	1.41848i	−0.00727764	+	0.0459492i	−0.991060	−	0.133418i	$-0.957405\pi$
$953$	−0.224666	+	1.41848i	−0.00727764	+	0.0459492i	0.983782	+	0.179367i	$0.0574049\pi$
$954$	17.7072	−	39.7711i	0.573292	−	1.28764i
$955$		0			0
$956$	1.08863	−	0.484689i	0.0352088	−	0.0156760i
$957$	−2.48872	−	0.666849i	−0.0804488	−	0.0215562i
$958$	−10.5666	−	66.7152i	−0.341393	−	2.15547i
$959$	−0.178522	−	2.66318i	−0.00576477	−	0.0859985i
$960$		0			0
$961$	−33.4320	+	37.1300i	−1.07845	+	1.19774i
$962$	4.60456	+	0.241315i	0.148457	+	0.00778030i
$963$	11.8055	+	0.618702i	0.380428	+	0.0199374i
$964$	−4.29944	+	4.77501i	−0.138476	+	0.153793i
$965$		0			0
$966$	2.47611	+	1.21652i	0.0796675	+	0.0391408i
$967$	−1.15537	−	7.29472i	−0.0371542	−	0.234582i	0.962122	−	0.272619i	$-0.0878897\pi$
$967$	−1.15537	−	7.29472i	−0.0371542	−	0.234582i	−0.999276	+	0.0380364i	$0.987890\pi$
$968$	9.45583	+	2.53368i	0.303922	+	0.0814356i
$969$	−1.82382	+	0.812019i	−0.0585897	+	0.0260858i
$970$		0			0
$971$	−12.4406	+	27.9420i	−0.399237	+	0.896701i	0.596338	+	0.802733i	$0.296622\pi$
$971$	−12.4406	+	27.9420i	−0.399237	+	0.896701i	−0.995575	+	0.0939680i	$0.970045\pi$
$972$	1.71731	−	10.8426i	0.0550826	−	0.347778i
$973$	11.1490	+	24.0900i	0.357420	+	0.772289i
$974$		−	23.5047i		−	0.753138i
$975$		0			0
$976$	5.30617	+	3.06352i	0.169846	+	0.0980608i
$977$	−21.0894	−	32.4748i	−0.674708	−	1.03896i	−0.995768	−	0.0919010i	$-0.970706\pi$
$977$	−21.0894	−	32.4748i	−0.674708	−	1.03896i	0.321060	−	0.947059i	$-0.395961\pi$
$978$	−3.72107	−	9.69371i	−0.118987	−	0.309971i
$979$	−58.2432	+	42.3162i	−1.86146	+	1.35243i
$980$		0			0
$981$	−27.7310	−	20.1478i	−0.885383	−	0.643268i
$982$	10.8133	−	40.3556i	0.345065	−	1.28780i
$983$	−49.8274	−	19.1270i	−1.58925	−	0.610055i	−0.606514	−	0.795073i	$-0.707432\pi$
$983$	−49.8274	−	19.1270i	−1.58925	−	0.610055i	−0.982735	+	0.185018i	$0.940766\pi$
$984$	2.29998	−	2.07091i	0.0733208	−	0.0660183i
$985$		0			0
$986$	2.50673	−	0.814485i	0.0798305	−	0.0259385i
$987$	−1.77696	+	9.00318i	−0.0565614	+	0.286574i
$988$	2.05475	+	4.03267i	0.0653702	+	0.128296i
$989$	6.35694	+	5.72382i	0.202139	+	0.182007i
$990$		0			0
$991$	12.2468	+	13.6014i	0.389032	+	0.432063i	0.905568	−	0.424202i	$-0.139445\pi$
$991$	12.2468	+	13.6014i	0.389032	+	0.432063i	−0.516536	+	0.856266i	$0.672779\pi$
$992$	33.9952	+	41.9805i	1.07935	+	1.33288i
$993$	1.68432	+	1.68432i	0.0534503	+	0.0534503i
$994$	−46.1666	+	47.5322i	−1.46431	+	1.50763i
$995$		0			0
$996$	−1.20261	−	0.535438i	−0.0381063	−	0.0169660i
$997$	33.7256	+	27.3105i	1.06810	+	0.864931i	0.991235	−	0.132110i	$-0.0421753\pi$
$997$	33.7256	+	27.3105i	1.06810	+	0.864931i	0.0768658	+	0.997041i	$0.475509\pi$
$998$	−13.4908	+	8.76105i	−0.427045	+	0.277326i
$999$	−4.60228	−	7.97139i	−0.145610	−	0.252203i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	875.2.bb.a.857.4		288
5.2	odd	4		175.2.x.a.108.4	yes	288
5.3	odd	4		875.2.bb.c.143.15		288
5.4	even	2		875.2.bb.b.857.15		288
7.5	odd	6	inner	875.2.bb.a.607.15		288
25.3	odd	20	inner	875.2.bb.a.493.15		288
25.4	even	10		175.2.x.a.122.4	yes	288
25.21	even	5		875.2.bb.c.507.15		288
25.22	odd	20		875.2.bb.b.493.4		288
35.12	even	12		175.2.x.a.33.4	✓	288
35.19	odd	6		875.2.bb.b.607.4		288
35.33	even	12		875.2.bb.c.768.15		288
175.47	even	60		875.2.bb.b.243.15		288
175.54	odd	30		175.2.x.a.47.4	yes	288
175.96	odd	30		875.2.bb.c.257.15		288
175.103	even	60	inner	875.2.bb.a.243.4		288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.33.4	✓	288	35.12	even	12
175.2.x.a.47.4	yes	288	175.54	odd	30
175.2.x.a.108.4	yes	288	5.2	odd	4
175.2.x.a.122.4	yes	288	25.4	even	10
875.2.bb.a.243.4		288	175.103	even	60	inner
875.2.bb.a.493.15		288	25.3	odd	20	inner
875.2.bb.a.607.15		288	7.5	odd	6	inner
875.2.bb.a.857.4		288	1.1	even	1	trivial
875.2.bb.b.243.15		288	175.47	even	60
875.2.bb.b.493.4		288	25.22	odd	20
875.2.bb.b.607.4		288	35.19	odd	6
875.2.bb.b.857.15		288	5.4	even	2
875.2.bb.c.143.15		288	5.3	odd	4
875.2.bb.c.257.15		288	175.96	odd	30
875.2.bb.c.507.15		288	25.21	even	5
875.2.bb.c.768.15		288	35.33	even	12

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+(-1.78588 + 0.0935941i) q^{2} +(-0.226450 + 0.279642i) q^{3} +(1.19157 - 0.125239i) q^{4} +(0.378240 - 0.520602i) q^{6} +(-2.62695 + 0.314872i) q^{7} +(1.41635 - 0.224327i) q^{8} +(0.596815 + 2.80779i) q^{9} +(4.12989 + 0.877836i) q^{11} +(-0.234809 + 0.361574i) q^{12} +(-0.527217 + 0.268631i) q^{13} +(4.66195 - 0.808191i) q^{14} +(-4.85234 + 1.03140i) q^{16} +(-0.311447 + 0.811348i) q^{17} +(-1.32863 - 4.95853i) q^{18} +(0.667317 - 6.34910i) q^{19} +(0.506820 - 0.805908i) q^{21} +(-7.45766 - 1.18118i) q^{22} +(-0.0848056 - 1.61819i) q^{23} +(-0.258000 + 0.446869i) q^{24} +(0.916406 - 0.529087i) q^{26} +(-1.88216 - 0.959010i) q^{27} +(-3.09076 + 0.704189i) q^{28} +(0.996818 + 1.37200i) q^{29} +(3.65980 + 8.22005i) q^{31} +(5.79889 - 1.55381i) q^{32} +(-1.18069 + 0.956106i) q^{33} +(0.480271 - 1.47812i) q^{34} +(1.06279 + 3.27094i) q^{36} +(3.65442 + 2.37321i) q^{37} +(-0.597511 + 11.4012i) q^{38} +(0.0442678 - 0.208263i) q^{39} +(-5.70437 - 1.85346i) q^{41} +(-0.829693 + 1.48669i) q^{42} +(-3.73281 + 3.73281i) q^{43} +(5.03100 + 0.528779i) q^{44} +(0.302906 + 2.88195i) q^{46} +(-8.99906 + 3.45442i) q^{47} +(0.810389 - 1.59048i) q^{48} +(6.80171 - 1.65430i) q^{49} +(-0.156360 - 0.270823i) q^{51} +(-0.594574 + 0.386121i) q^{52} +(6.59068 + 5.33703i) q^{53} +(3.45108 + 1.53652i) q^{54} +(-3.65004 + 1.03526i) q^{56} +(1.62436 + 1.62436i) q^{57} +(-1.90861 - 2.35694i) q^{58} +(-4.53398 - 5.03550i) q^{59} +(-0.917861 - 0.826446i) q^{61} +(-7.30532 - 14.3375i) q^{62} +(-2.45190 - 7.18801i) q^{63} +(-0.774814 + 0.251752i) q^{64} +(2.01909 - 1.81800i) q^{66} +(10.7014 + 4.10789i) q^{67} +(-0.269499 + 1.00578i) q^{68} +(0.471717 + 0.342723i) q^{69} +(-11.3299 + 8.23164i) q^{71} +(1.47516 + 3.84293i) q^{72} +(1.89921 + 2.92452i) q^{73} +(-6.74848 - 3.89623i) q^{74} -7.64897i q^{76} +(-11.1254 - 1.00564i) q^{77} +(-0.0595648 + 0.376077i) q^{78} +(-5.74668 + 12.9073i) q^{79} +(-7.17266 + 3.19347i) q^{81} +(10.3608 + 2.77617i) q^{82} +(0.477665 + 3.01586i) q^{83} +(0.502981 - 1.02377i) q^{84} +(6.31698 - 7.01572i) q^{86} +(-0.609399 - 0.0319372i) q^{87} +(6.04629 + 0.316873i) q^{88} +(-11.4094 + 12.6715i) q^{89} +(1.30039 - 0.871684i) q^{91} +(-0.303712 - 1.91756i) q^{92} +(-3.12743 - 0.837993i) q^{93} +(15.7479 - 7.01144i) q^{94} +(-0.878647 + 1.97347i) q^{96} +(-1.83327 + 11.5748i) q^{97} +(-11.9922 + 3.59099i) q^{98} +12.1198i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 2 q^{2} - 6 q^{3} + 10 q^{4} + 10 q^{7} - 64 q^{8} + 10 q^{9} - 6 q^{11} + 6 q^{12} + 20 q^{14} - 30 q^{16} + 12 q^{17} + 14 q^{18} + 30 q^{19} - 12 q^{21} + 8 q^{22} - 30 q^{23} - 48 q^{26} + 58 q^{28}+ \cdots - 62 q^{98}+O(q^{100}) \) 288 * q - 2 * q^2 - 6 * q^3 + 10 * q^4 + 10 * q^7 - 64 * q^8 + 10 * q^9 - 6 * q^11 + 6 * q^12 + 20 * q^14 - 30 * q^16 + 12 * q^17 + 14 * q^18 + 30 * q^19 - 12 * q^21 + 8 * q^22 - 30 * q^23 - 48 * q^26 + 58 * q^28 - 18 * q^31 - 8 * q^32 + 150 * q^33 + 40 * q^36 - 12 * q^38 - 30 * q^39 - 166 * q^42 + 108 * q^43 + 10 * q^44 - 6 * q^46 + 24 * q^47 - 16 * q^51 + 24 * q^52 + 40 * q^53 + 30 * q^54 + 4 * q^56 + 216 * q^57 + 114 * q^58 - 90 * q^59 - 18 * q^61 + 16 * q^63 + 100 * q^64 - 90 * q^66 - 74 * q^67 - 342 * q^68 - 24 * q^71 + 222 * q^72 + 216 * q^73 - 90 * q^77 + 32 * q^78 + 10 * q^79 - 10 * q^81 - 216 * q^82 - 20 * q^84 - 6 * q^86 + 18 * q^87 - 58 * q^88 - 120 * q^89 - 12 * q^91 + 24 * q^92 - 106 * q^93 + 30 * q^94 - 90 * q^96 - 62 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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