LMFDB - Embedded newform 850.2.s.d.243.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [850,2,Mod(7,850)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(850, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([4, 11]))

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

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

chi := DirichletCharacter("850.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 850 = 2 \cdot 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	850.s (of order $16$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.78728417181$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$5$ over $\Q(\zeta_{16})$
Twist minimal:	no (minimal twist has level 170)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			243.5
Character	$\chi$	$=$	850.243
Dual form			850.2.s.d.7.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.923880 - 0.382683i) q^{2} +(0.664558 - 3.34096i) q^{3} +(0.707107 + 0.707107i) q^{4} +(-1.89250 + 2.83233i) q^{6} +(-0.923351 - 0.616963i) q^{7} +(-0.382683 - 0.923880i) q^{8} +(-7.94873 - 3.29247i) q^{9} +O(q^{10})$	\(q+(-0.923880 - 0.382683i) q^{2} +(0.664558 - 3.34096i) q^{3} +(0.707107 + 0.707107i) q^{4} +(-1.89250 + 2.83233i) q^{6} +(-0.923351 - 0.616963i) q^{7} +(-0.382683 - 0.923880i) q^{8} +(-7.94873 - 3.29247i) q^{9} +(-0.833476 - 0.556911i) q^{11} +(2.83233 - 1.89250i) q^{12} +4.43010i q^{13} +(0.616963 + 0.923351i) q^{14} +1.00000i q^{16} +(-1.67349 - 3.76821i) q^{17} +(6.08369 + 6.08369i) q^{18} +(-0.506906 + 0.209967i) q^{19} +(-2.67487 + 2.67487i) q^{21} +(0.556911 + 0.833476i) q^{22} +(-3.06456 + 0.609578i) q^{23} +(-3.34096 + 0.664558i) q^{24} +(1.69533 - 4.09288i) q^{26} +(-10.6049 + 15.8713i) q^{27} +(-0.216649 - 1.08917i) q^{28} +(-0.588900 + 2.96060i) q^{29} +(-1.23768 + 0.826988i) q^{31} +(0.382683 - 0.923880i) q^{32} +(-2.41451 + 2.41451i) q^{33} +(0.104069 + 4.12179i) q^{34} +(-3.29247 - 7.94873i) q^{36} +(-5.66357 - 1.12655i) q^{37} +0.548671 q^{38} +(14.8008 + 2.94406i) q^{39} +(-1.75620 - 8.82901i) q^{41} +(3.49488 - 1.44763i) q^{42} +(0.174344 - 0.0722156i) q^{43} +(-0.195561 - 0.983152i) q^{44} +(3.06456 + 0.609578i) q^{46} +6.10055 q^{47} +(3.34096 + 0.664558i) q^{48} +(-2.20685 - 5.32781i) q^{49} +(-13.7016 + 3.08686i) q^{51} +(-3.13255 + 3.13255i) q^{52} +(4.77327 - 11.5237i) q^{53} +(15.8713 - 10.6049i) q^{54} +(-0.216649 + 1.08917i) q^{56} +(0.364624 + 1.83309i) q^{57} +(1.67705 - 2.50988i) q^{58} +(-4.57691 + 11.0496i) q^{59} +(1.88405 - 0.374760i) q^{61} +(1.45994 - 0.290400i) q^{62} +(5.30813 + 7.94418i) q^{63} +(-0.707107 + 0.707107i) q^{64} +(3.15471 - 1.30672i) q^{66} +(0.568902 + 0.568902i) q^{67} +(1.48119 - 3.84786i) q^{68} +10.6437i q^{69} +(-2.52638 - 3.78099i) q^{71} +8.60364i q^{72} +(-1.51695 + 1.01360i) q^{73} +(4.80134 + 3.20816i) q^{74} +(-0.506906 - 0.209967i) q^{76} +(0.425997 + 1.02845i) q^{77} +(-12.5475 - 8.38397i) q^{78} +(2.90998 - 4.35510i) q^{79} +(27.7269 + 27.7269i) q^{81} +(-1.75620 + 8.82901i) q^{82} +(11.1278 + 4.60927i) q^{83} -3.78284 q^{84} -0.188708 q^{86} +(9.49989 + 3.93498i) q^{87} +(-0.195561 + 0.983152i) q^{88} +(-4.95294 - 4.95294i) q^{89} +(2.73321 - 4.09054i) q^{91} +(-2.59800 - 1.73593i) q^{92} +(1.94043 + 4.68460i) q^{93} +(-5.63618 - 2.33458i) q^{94} +(-2.83233 - 1.89250i) q^{96} +(-5.62719 + 3.75997i) q^{97} +5.76678i q^{98} +(4.79146 + 7.17093i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q+O(q^{10}) $ 40 * q	$ 40 q + 16 q^{18} - 8 q^{26} - 24 q^{27} - 8 q^{28} - 8 q^{29} - 16 q^{31} - 32 q^{33} - 8 q^{34} - 16 q^{37} + 32 q^{39} - 56 q^{41} + 8 q^{42} + 48 q^{43} - 16 q^{44} + 96 q^{47} - 16 q^{49} - 32 q^{51} + 16 q^{52} + 40 q^{53} + 24 q^{54} - 8 q^{56} + 8 q^{57} - 16 q^{58} + 24 q^{61} + 24 q^{62} + 24 q^{63} + 16 q^{67} - 24 q^{68} + 24 q^{71} - 16 q^{73} - 32 q^{74} - 40 q^{77} - 16 q^{78} + 104 q^{79} + 48 q^{81} - 56 q^{82} - 16 q^{83} + 96 q^{86} + 8 q^{87} - 16 q^{88} + 16 q^{89} + 48 q^{91} - 8 q^{92} - 136 q^{93} + 8 q^{94} - 144 q^{97} - 160 q^{99}+O(q^{100}) $ 40 * q + 16 * q^18 - 8 * q^26 - 24 * q^27 - 8 * q^28 - 8 * q^29 - 16 * q^31 - 32 * q^33 - 8 * q^34 - 16 * q^37 + 32 * q^39 - 56 * q^41 + 8 * q^42 + 48 * q^43 - 16 * q^44 + 96 * q^47 - 16 * q^49 - 32 * q^51 + 16 * q^52 + 40 * q^53 + 24 * q^54 - 8 * q^56 + 8 * q^57 - 16 * q^58 + 24 * q^61 + 24 * q^62 + 24 * q^63 + 16 * q^67 - 24 * q^68 + 24 * q^71 - 16 * q^73 - 32 * q^74 - 40 * q^77 - 16 * q^78 + 104 * q^79 + 48 * q^81 - 56 * q^82 - 16 * q^83 + 96 * q^86 + 8 * q^87 - 16 * q^88 + 16 * q^89 + 48 * q^91 - 8 * q^92 - 136 * q^93 + 8 * q^94 - 144 * q^97 - 160 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/850\mathbb{Z}\right)^\times$.

$n$	$477$	$751$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{16}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.923880	−	0.382683i	−0.653281	−	0.270598i
$2$	−0.923880	−	0.382683i	−0.653281	−	0.270598i
$3$	0.664558	−	3.34096i	0.383683	−	1.92890i	0.0135921	−	0.999908i	$-0.495673\pi$
$3$	0.664558	−	3.34096i	0.383683	−	1.92890i	0.370091	−	0.928996i	$-0.379327\pi$
$4$	0.707107	+	0.707107i	0.353553	+	0.353553i
$5$		0			0
$5$		0			0
$6$	−1.89250	+	2.83233i	−0.772610	+	1.15629i
$7$	−0.923351	−	0.616963i	−0.348994	−	0.233190i	0.368701	−	0.929548i	$-0.379803\pi$
$7$	−0.923351	−	0.616963i	−0.348994	−	0.233190i	−0.717695	+	0.696358i	$0.754803\pi$
$8$	−0.382683	−	0.923880i	−0.135299	−	0.326641i
$9$	−7.94873	−	3.29247i	−2.64958	−	1.09749i
$10$		0			0
$11$	−0.833476	−	0.556911i	−0.251302	−	0.167915i	0.423539	−	0.905878i	$-0.360788\pi$
$11$	−0.833476	−	0.556911i	−0.251302	−	0.167915i	−0.674841	+	0.737963i	$0.735788\pi$
$12$	2.83233	−	1.89250i	0.817623	−	0.546318i
$13$			4.43010i			1.22869i	0.789038	+	0.614344i	$0.210579\pi$
$13$			4.43010i			1.22869i	−0.789038	+	0.614344i	$0.789421\pi$
$14$	0.616963	+	0.923351i	0.164890	+	0.246776i
$15$		0			0
$16$			1.00000i			0.250000i
$17$	−1.67349	−	3.76821i	−0.405881	−	0.913926i
$17$	−1.67349	−	3.76821i	−0.405881	−	0.913926i
$18$	6.08369	+	6.08369i	1.43394	+	1.43394i
$19$	−0.506906	+	0.209967i	−0.116292	+	0.0481698i	−0.440071	−	0.897963i	$-0.645047\pi$
$19$	−0.506906	+	0.209967i	−0.116292	+	0.0481698i	0.323779	+	0.946133i	$0.395047\pi$
$20$		0			0
$21$	−2.67487	+	2.67487i	−0.583704	+	0.583704i
$22$	0.556911	+	0.833476i	0.118734	+	0.177698i
$23$	−3.06456	+	0.609578i	−0.639004	+	0.127106i	−0.503950	−	0.863733i	$-0.668121\pi$
$23$	−3.06456	+	0.609578i	−0.639004	+	0.127106i	−0.135053	+	0.990838i	$0.543121\pi$
$24$	−3.34096	+	0.664558i	−0.681970	+	0.135652i
$25$		0			0
$26$	1.69533	−	4.09288i	0.332481	−	0.802680i
$27$	−10.6049	+	15.8713i	−2.04091	+	3.05444i
$28$	−0.216649	−	1.08917i	−0.0409428	−	0.205833i
$29$	−0.588900	+	2.96060i	−0.109356	+	0.549770i	0.886799	+	0.462156i	$0.152924\pi$
$29$	−0.588900	+	2.96060i	−0.109356	+	0.549770i	−0.996155	+	0.0876136i	$0.972076\pi$
$30$		0			0
$31$	−1.23768	+	0.826988i	−0.222293	+	0.148531i	−0.661731	−	0.749742i	$-0.730178\pi$
$31$	−1.23768	+	0.826988i	−0.222293	+	0.148531i	0.439438	+	0.898273i	$0.355178\pi$
$32$	0.382683	−	0.923880i	0.0676495	−	0.163320i
$33$	−2.41451	+	2.41451i	−0.420312	+	0.420312i
$34$	0.104069	+	4.12179i	0.0178477	+	0.706882i
$35$		0			0
$36$	−3.29247	−	7.94873i	−0.548745	−	1.32479i
$37$	−5.66357	−	1.12655i	−0.931086	−	0.185204i	−0.293831	−	0.955857i	$-0.594930\pi$
$37$	−5.66357	−	1.12655i	−0.931086	−	0.185204i	−0.637255	+	0.770653i	$0.719930\pi$
$38$	0.548671			0.0890063
$39$	14.8008	+	2.94406i	2.37002	+	0.471427i
$40$		0			0
$41$	−1.75620	−	8.82901i	−0.274272	−	1.37886i	−0.834722	−	0.550672i	$-0.814372\pi$
$41$	−1.75620	−	8.82901i	−0.274272	−	1.37886i	0.560449	−	0.828189i	$-0.310628\pi$
$42$	3.49488	−	1.44763i	0.539272	−	0.223374i
$43$	0.174344	−	0.0722156i	0.0265872	−	0.0110128i	−0.369350	−	0.929290i	$-0.620420\pi$
$43$	0.174344	−	0.0722156i	0.0265872	−	0.0110128i	0.395937	+	0.918278i	$0.370420\pi$
$44$	−0.195561	−	0.983152i	−0.0294819	−	0.148216i
$45$		0			0
$46$	3.06456	+	0.609578i	0.451844	+	0.0898774i
$47$	6.10055			0.889857			0.444929	−	0.895566i	$-0.353229\pi$
$47$	6.10055			0.889857			0.444929	+	0.895566i	$0.353229\pi$
$48$	3.34096	+	0.664558i	0.482226	+	0.0959207i
$49$	−2.20685	−	5.32781i	−0.315264	−	0.761116i
$50$		0			0
$51$	−13.7016	+	3.08686i	−1.91860	+	0.432247i
$52$	−3.13255	+	3.13255i	−0.434407	+	0.434407i
$53$	4.77327	−	11.5237i	0.655658	−	1.58290i	−0.148784	−	0.988870i	$-0.547536\pi$
$53$	4.77327	−	11.5237i	0.655658	−	1.58290i	0.804443	−	0.594030i	$-0.202464\pi$
$54$	15.8713	−	10.6049i	2.15982	−	1.44314i
$55$		0			0
$56$	−0.216649	+	1.08917i	−0.0289509	+	0.145546i
$57$	0.364624	+	1.83309i	0.0482956	+	0.242799i
$58$	1.67705	−	2.50988i	0.220207	−	0.329563i
$59$	−4.57691	+	11.0496i	−0.595862	+	1.43854i	0.281900	+	0.959444i	$0.409035\pi$
$59$	−4.57691	+	11.0496i	−0.595862	+	1.43854i	−0.877763	+	0.479095i	$0.840965\pi$
$60$		0			0
$61$	1.88405	−	0.374760i	0.241227	−	0.0479831i	−0.0729959	−	0.997332i	$-0.523256\pi$
$61$	1.88405	−	0.374760i	0.241227	−	0.0479831i	0.314223	+	0.949349i	$0.398256\pi$
$62$	1.45994	−	0.290400i	0.185412	−	0.0368808i
$63$	5.30813	+	7.94418i	0.668762	+	1.00087i
$64$	−0.707107	+	0.707107i	−0.0883883	+	0.0883883i
$65$		0			0
$66$	3.15471	−	1.30672i	0.388318	−	0.160846i
$67$	0.568902	+	0.568902i	0.0695024	+	0.0695024i	0.741004	−	0.671501i	$-0.234350\pi$
$67$	0.568902	+	0.568902i	0.0695024	+	0.0695024i	−0.671501	+	0.741004i	$0.734350\pi$
$68$	1.48119	−	3.84786i	0.179621	−	0.466622i
$69$			10.6437i			1.28134i
$70$		0			0
$71$	−2.52638	−	3.78099i	−0.299826	−	0.448721i	0.650714	−	0.759323i	$-0.274470\pi$
$71$	−2.52638	−	3.78099i	−0.299826	−	0.448721i	−0.950540	+	0.310601i	$0.899470\pi$
$72$			8.60364i			1.01395i
$73$	−1.51695	+	1.01360i	−0.177546	+	0.118632i	−0.641168	−	0.767401i	$-0.721550\pi$
$73$	−1.51695	+	1.01360i	−0.177546	+	0.118632i	0.463622	+	0.886033i	$0.346550\pi$
$74$	4.80134	+	3.20816i	0.558145	+	0.372941i
$75$		0			0
$76$	−0.506906	−	0.209967i	−0.0581461	−	0.0240849i
$77$	0.425997	+	1.02845i	0.0485469	+	0.117203i
$78$	−12.5475	−	8.38397i	−1.42072	−	0.949298i
$79$	2.90998	−	4.35510i	0.327399	−	0.489987i	−0.630857	−	0.775899i	$-0.717297\pi$
$79$	2.90998	−	4.35510i	0.327399	−	0.489987i	0.958256	+	0.285912i	$0.0922966\pi$
$80$		0			0
$81$	27.7269	+	27.7269i	3.08076	+	3.08076i
$82$	−1.75620	+	8.82901i	−0.193940	+	0.975002i
$83$	11.1278	+	4.60927i	1.22143	+	0.505933i	0.897864	−	0.440273i	$-0.145118\pi$
$83$	11.1278	+	4.60927i	1.22143	+	0.505933i	0.323566	+	0.946206i	$0.395118\pi$
$84$	−3.78284			−0.412741
$85$		0			0
$86$	−0.188708			−0.0203490
$87$	9.49989	+	3.93498i	1.01849	+	0.421874i
$88$	−0.195561	+	0.983152i	−0.0208469	+	0.104804i
$89$	−4.95294	−	4.95294i	−0.525011	−	0.525011i	0.394070	−	0.919081i	$-0.371067\pi$
$89$	−4.95294	−	4.95294i	−0.525011	−	0.525011i	−0.919081	+	0.394070i	$0.871067\pi$
$90$		0			0
$91$	2.73321	−	4.09054i	0.286518	−	0.428805i
$92$	−2.59800	−	1.73593i	−0.270861	−	0.180983i
$93$	1.94043	+	4.68460i	0.201213	+	0.485771i
$94$	−5.63618	−	2.33458i	−0.581327	−	0.240794i
$95$		0			0
$96$	−2.83233	−	1.89250i	−0.289073	−	0.193153i
$97$	−5.62719	+	3.75997i	−0.571354	+	0.381767i	−0.807426	−	0.589969i	$-0.799140\pi$
$97$	−5.62719	+	3.75997i	−0.571354	+	0.381767i	0.236072	+	0.971736i	$0.424140\pi$
$98$			5.76678i			0.582533i
$99$	4.79146	+	7.17093i	0.481560	+	0.720705i
$100$		0			0
$101$			0.342654i			0.0340954i	0.999855	+	0.0170477i	$0.00542671\pi$
$101$			0.342654i			0.0340954i	−0.999855	+	0.0170477i	$0.994573\pi$
$102$	13.8399	+	2.39148i	1.37035	+	0.236792i
$103$	7.67310	+	7.67310i	0.756053	+	0.756053i	0.975602	−	0.219548i	$-0.0704583\pi$
$103$	7.67310	+	7.67310i	0.756053	+	0.756053i	−0.219548	+	0.975602i	$0.570458\pi$
$104$	4.09288	−	1.69533i	0.401340	−	0.166240i
$105$		0			0
$106$	−8.81985	+	8.81985i	−0.856659	+	0.856659i
$107$	−6.51964	−	9.75732i	−0.630277	−	0.943276i	−0.999901	−	0.0140946i	$-0.995513\pi$
$107$	−6.51964	−	9.75732i	−0.630277	−	0.943276i	0.369624	−	0.929182i	$-0.379487\pi$
$108$	−18.7215	+	3.72394i	−1.80148	+	0.358337i
$109$	−9.42080	+	1.87391i	−0.902349	+	0.179488i	−0.624398	−	0.781107i	$-0.714656\pi$
$109$	−9.42080	+	1.87391i	−0.902349	+	0.179488i	−0.277952	+	0.960595i	$0.589656\pi$
$110$		0			0
$111$	−7.52754	+	18.1731i	−0.714483	+	1.72491i
$112$	0.616963	−	0.923351i	0.0582975	−	0.0872484i
$113$	−1.10458	−	5.55310i	−0.103910	−	0.522392i	−0.997321	−	0.0731509i	$-0.976695\pi$
$113$	−1.10458	−	5.55310i	−0.103910	−	0.522392i	0.893411	−	0.449241i	$-0.148305\pi$
$114$	0.364624	−	1.83309i	0.0341502	−	0.171684i
$115$		0			0
$116$	−2.50988	+	1.67705i	−0.233036	+	0.155710i
$117$	14.5860	−	35.2137i	1.34847	−	3.25550i
$118$	8.45702	−	8.45702i	0.778532	−	0.778532i
$119$	−0.779632	+	4.51186i	−0.0714688	+	0.413602i
$120$		0			0
$121$	−3.82499	−	9.23433i	−0.347726	−	0.839485i
$122$	−1.88405	−	0.374760i	−0.170573	−	0.0339292i
$123$	−30.6645			−2.76492
$124$	−1.45994	−	0.290400i	−0.131106	−	0.0260787i
$125$		0			0
$126$	−1.86397	−	9.37080i	−0.166055	−	0.834817i
$127$	−9.33030	+	3.86473i	−0.827930	+	0.342940i	−0.756083	−	0.654476i	$-0.772889\pi$
$127$	−9.33030	+	3.86473i	−0.827930	+	0.342940i	−0.0718470	+	0.997416i	$0.522889\pi$
$128$	0.923880	−	0.382683i	0.0816602	−	0.0338248i
$129$	−0.125408	−	0.630467i	−0.0110415	−	0.0555095i
$130$		0			0
$131$	−3.08463	−	0.613572i	−0.269506	−	0.0536080i	0.0584873	−	0.998288i	$-0.481372\pi$
$131$	−3.08463	−	0.613572i	−0.269506	−	0.0536080i	−0.327993	+	0.944680i	$0.606372\pi$
$132$	−3.41463			−0.297205
$133$	0.597595	+	0.118869i	0.0518180	+	0.0103072i
$134$	−0.307887	−	0.743306i	−0.0265974	−	0.0642118i
$135$		0			0
$136$	−2.84096	+	2.98813i	−0.243610	+	0.256230i
$137$	2.59083	−	2.59083i	0.221350	−	0.221350i	−0.587717	−	0.809067i	$-0.699973\pi$
$137$	2.59083	−	2.59083i	0.221350	−	0.221350i	0.809067	+	0.587717i	$0.199973\pi$
$138$	4.07315	−	9.83345i	0.346729	−	0.837079i
$139$	−9.79226	+	6.54298i	−0.830569	+	0.554968i	−0.896596	−	0.442849i	$-0.853968\pi$
$139$	−9.79226	+	6.54298i	−0.830569	+	0.554968i	0.0660271	+	0.997818i	$0.478968\pi$
$140$		0			0
$141$	4.05417	−	20.3817i	0.341423	−	1.71645i
$142$	0.887146	+	4.45998i	0.0744476	+	0.374274i
$143$	2.46717	−	3.69238i	0.206315	−	0.308772i
$144$	3.29247	−	7.94873i	0.274373	−	0.662394i
$145$		0			0
$146$	1.78937	−	0.355928i	0.148089	−	0.0294568i
$147$	−19.2666	+	3.83236i	−1.58908	+	0.316088i
$148$	−3.20816	−	4.80134i	−0.263709	−	0.394668i
$149$	11.9930	−	11.9930i	0.982508	−	0.982508i	−0.0173417	−	0.999850i	$-0.505520\pi$
$149$	11.9930	−	11.9930i	0.982508	−	0.982508i	0.999850	+	0.0173417i	$0.00552032\pi$
$150$		0			0
$151$	10.3652	−	4.29340i	0.843507	−	0.349392i	0.0812715	−	0.996692i	$-0.474102\pi$
$151$	10.3652	−	4.29340i	0.843507	−	0.349392i	0.762235	+	0.647300i	$0.224102\pi$
$152$	0.387969	+	0.387969i	0.0314685	+	0.0314685i
$153$	0.895372	+	35.4624i	0.0723866	+	2.86697i
$154$		−	1.11318i		−	0.0897029i
$155$		0			0
$156$	8.38397	+	12.5475i	0.671255	+	1.00460i
$157$		−	7.42419i		−	0.592515i	−0.955108	−	0.296257i	$-0.904261\pi$
$157$		−	7.42419i		−	0.592515i	0.955108	−	0.296257i	$-0.0957386\pi$
$158$	−4.35510	+	2.90998i	−0.346473	+	0.231506i
$159$	−35.3280	−	23.6054i	−2.80170	−	1.87203i
$160$		0			0
$161$	3.20575	+	1.32786i	0.252648	+	0.104650i
$162$	−15.0057	−	36.2269i	−1.17896	−	2.84625i
$163$	−13.1019	−	8.75441i	−1.02622	−	0.685698i	−0.0759457	−	0.997112i	$-0.524198\pi$
$163$	−13.1019	−	8.75441i	−1.02622	−	0.685698i	−0.950274	+	0.311414i	$0.899198\pi$
$164$	5.00124	−	7.48488i	0.390531	−	0.584471i
$165$		0			0
$166$	−8.51681	−	8.51681i	−0.661033	−	0.661033i
$167$	3.53881	−	17.7908i	0.273841	−	1.37669i	−0.561734	−	0.827318i	$-0.689866\pi$
$167$	3.53881	−	17.7908i	0.273841	−	1.37669i	0.835575	−	0.549376i	$-0.185134\pi$
$168$	3.49488	+	1.44763i	0.269636	+	0.111687i
$169$	−6.62579			−0.509676
$170$		0			0
$171$	4.72057			0.360991
$172$	0.174344	+	0.0722156i	0.0132936	+	0.00550639i
$173$	4.02708	−	20.2455i	0.306173	−	1.53924i	−0.454883	−	0.890551i	$-0.650319\pi$
$173$	4.02708	−	20.2455i	0.306173	−	1.53924i	0.761056	−	0.648686i	$-0.224681\pi$
$174$	−7.27090	−	7.27090i	−0.551205	−	0.551205i
$175$		0			0
$176$	0.556911	−	0.833476i	0.0419787	−	0.0628256i
$177$	33.8747	+	22.6344i	2.54618	+	1.70130i
$178$	2.68051	+	6.47133i	0.200913	+	0.485047i
$179$	6.30681	+	2.61237i	0.471393	+	0.195257i	0.605717	−	0.795680i	$-0.292886\pi$
$179$	6.30681	+	2.61237i	0.471393	+	0.195257i	−0.134324	+	0.990937i	$0.542886\pi$
$180$		0			0
$181$	3.95885	+	2.64522i	0.294259	+	0.196618i	0.693933	−	0.720040i	$-0.255876\pi$
$181$	3.95885	+	2.64522i	0.294259	+	0.196618i	−0.399674	+	0.916658i	$0.630876\pi$
$182$	−4.09054	+	2.73321i	−0.303211	+	0.202599i
$183$		−	6.54357i		−	0.483714i
$184$	1.73593	+	2.59800i	0.127975	+	0.191527i
$185$		0			0
$186$		−	5.07058i		−	0.371793i
$187$	−0.703746	+	4.07270i	−0.0514630	+	0.297825i
$188$	4.31374	+	4.31374i	0.314612	+	0.314612i
$189$	19.5841	−	8.11199i	1.42453	−	0.590060i
$190$		0			0
$191$	−7.17897	+	7.17897i	−0.519452	+	0.519452i	−0.917406	−	0.397954i	$-0.869720\pi$
$191$	−7.17897	+	7.17897i	−0.519452	+	0.519452i	0.397954	+	0.917406i	$0.369720\pi$
$192$	1.89250	+	2.83233i	0.136579	+	0.204406i
$193$	−7.54568	+	1.50093i	−0.543150	+	0.108039i	−0.459037	−	0.888417i	$-0.651806\pi$
$193$	−7.54568	+	1.50093i	−0.543150	+	0.108039i	−0.0841126	+	0.996456i	$0.526806\pi$
$194$	6.63772	−	1.32032i	0.476561	−	0.0947938i
$195$		0			0
$196$	2.20685	−	5.32781i	0.157632	−	0.380558i
$197$	−2.64933	+	3.96501i	−0.188757	+	0.282495i	−0.913763	−	0.406248i	$-0.866837\pi$
$197$	−2.64933	+	3.96501i	−0.188757	+	0.282495i	0.725006	+	0.688743i	$0.241837\pi$
$198$	−1.68254	−	8.45868i	−0.119573	−	0.601132i
$199$	−2.16119	+	10.8650i	−0.153203	+	0.770201i	0.825417	+	0.564523i	$0.190940\pi$
$199$	−2.16119	+	10.8650i	−0.153203	+	0.770201i	−0.978620	+	0.205678i	$0.934060\pi$
$200$		0			0
$201$	2.27874	−	1.52261i	0.160730	−	0.107397i
$202$	0.131128	−	0.316571i	0.00922614	−	0.0222739i
$203$	2.37034	−	2.37034i	0.166365	−	0.166365i
$204$	−11.8712	−	7.50574i	−0.831151	−	0.525507i
$205$		0			0
$206$	−4.15265	−	10.0254i	−0.289329	−	0.698502i
$207$	26.3663	+	5.24459i	1.83259	+	0.364524i
$208$	−4.43010			−0.307172
$209$	0.539427	+	0.107299i	0.0373130	+	0.00742201i
$210$		0			0
$211$	1.63864	+	8.23800i	0.112809	+	0.567127i	0.995303	+	0.0968050i	$0.0308623\pi$
$211$	1.63864	+	8.23800i	0.112809	+	0.567127i	−0.882495	+	0.470322i	$0.844138\pi$
$212$	11.5237	−	4.77327i	0.791450	−	0.327829i
$213$	−14.3111	+	5.92784i	−0.980578	+	0.406169i
$214$	2.28939	+	11.5095i	0.156500	+	0.786777i
$215$		0			0
$216$	18.7215	+	3.72394i	1.27384	+	0.253382i
$217$	1.65303			0.112215
$218$	9.42080	+	1.87391i	0.638057	+	0.126918i
$219$	2.37828	+	5.74167i	0.160709	+	0.387986i
$220$		0			0
$221$	16.6936	−	7.41372i	1.12293	−	0.498701i
$222$	13.9091	−	13.9091i	0.933517	−	0.933517i
$223$	−7.56256	+	18.2576i	−0.506426	+	1.22262i	0.439501	+	0.898242i	$0.355155\pi$
$223$	−7.56256	+	18.2576i	−0.506426	+	1.22262i	−0.945927	+	0.324379i	$0.894845\pi$
$224$	−0.923351	+	0.616963i	−0.0616940	+	0.0412226i
$225$		0			0
$226$	−1.10458	+	5.55310i	−0.0734756	+	0.369387i
$227$	−1.07198	−	5.38919i	−0.0711496	−	0.357693i	0.928766	−	0.370666i	$-0.120871\pi$
$227$	−1.07198	−	5.38919i	−0.0711496	−	0.357693i	−0.999916	+	0.0129727i	$0.995871\pi$
$228$	−1.03836	+	1.55402i	−0.0687672	+	0.102917i
$229$	1.33019	−	3.21137i	0.0879016	−	0.212213i	−0.873815	−	0.486258i	$-0.838362\pi$
$229$	1.33019	−	3.21137i	0.0879016	−	0.212213i	0.961717	+	0.274045i	$0.0883616\pi$
$230$		0			0
$231$	3.71910	−	0.739775i	0.244699	−	0.0486736i
$232$	2.96060	−	0.588900i	0.194373	−	0.0386632i
$233$	−6.72649	−	10.0669i	−0.440667	−	0.659505i	0.542952	−	0.839764i	$-0.317306\pi$
$233$	−6.72649	−	10.0669i	−0.440667	−	0.659505i	−0.983619	+	0.180259i	$0.942306\pi$
$234$	−26.9514	+	26.9514i	−1.76187	+	1.76187i
$235$		0			0
$236$	−11.0496	+	4.57691i	−0.719270	+	0.297931i
$237$	−12.6163	−	12.6163i	−0.819519	−	0.819519i
$238$	2.44690	−	3.87007i	0.158609	−	0.250859i
$239$			14.2194i			0.919776i	0.887977	+	0.459888i	$0.152110\pi$
$239$			14.2194i			0.919776i	−0.887977	+	0.459888i	$0.847890\pi$
$240$		0			0
$241$	−2.87172	−	4.29783i	−0.184984	−	0.276848i	0.727374	−	0.686241i	$-0.240740\pi$
$241$	−2.87172	−	4.29783i	−0.184984	−	0.276848i	−0.912358	+	0.409393i	$0.865740\pi$
$242$			9.99517i			0.642514i
$243$	63.4464	−	42.3935i	4.07009	−	2.71955i
$244$	1.59722	+	1.06723i	0.102251	+	0.0683221i
$245$		0			0
$246$	28.3303	+	11.7348i	1.80627	+	0.748183i
$247$	−0.930177	−	2.24565i	−0.0591857	−	0.142887i
$248$	1.23768	+	0.826988i	0.0785925	+	0.0525138i
$249$	22.7944	−	34.1142i	1.44454	−	2.16190i
$250$		0			0
$251$	−18.4621	−	18.4621i	−1.16531	−	1.16531i	−0.983295	−	0.182020i	$-0.941736\pi$
$251$	−18.4621	−	18.4621i	−1.16531	−	1.16531i	−0.182020	−	0.983295i	$-0.558264\pi$
$252$	−1.86397	+	9.37080i	−0.117419	+	0.590305i
$253$	2.89371	+	1.19862i	0.181926	+	0.0753563i
$254$	10.0990			0.633670
$255$		0			0
$256$	−1.00000			−0.0625000
$257$	−17.2444	−	7.14288i	−1.07568	−	0.445561i	−0.226688	−	0.973967i	$-0.572790\pi$
$257$	−17.2444	−	7.14288i	−1.07568	−	0.445561i	−0.848991	+	0.528407i	$0.822790\pi$
$258$	−0.125408	+	0.630467i	−0.00780754	+	0.0392512i
$259$	4.53442	+	4.53442i	0.281755	+	0.281755i
$260$		0			0
$261$	14.4287	−	21.5941i	0.893114	−	1.33664i
$262$	2.61503	+	1.74731i	0.161557	+	0.107949i
$263$	−9.00268	−	21.7344i	−0.555129	−	1.34020i	−0.913583	−	0.406652i	$-0.866696\pi$
$263$	−9.00268	−	21.7344i	−0.555129	−	1.34020i	0.358454	−	0.933547i	$-0.383304\pi$
$264$	3.15471	+	1.30672i	0.194159	+	0.0804232i
$265$		0			0
$266$	−0.506616	−	0.338510i	−0.0310626	−	0.0207554i
$267$	−19.8391	+	13.2561i	−1.21413	+	0.811258i
$268$			0.804548i			0.0491456i
$269$	−0.188978	−	0.282826i	−0.0115222	−	0.0172442i	0.825664	−	0.564162i	$-0.190801\pi$
$269$	−0.188978	−	0.282826i	−0.0115222	−	0.0172442i	−0.837186	+	0.546918i	$0.815801\pi$
$270$		0			0
$271$		−	2.26776i		−	0.137757i	−0.997625	−	0.0688783i	$-0.978058\pi$
$271$		−	2.26776i		−	0.137757i	0.997625	−	0.0688783i	$-0.0219420\pi$
$272$	3.76821	−	1.67349i	0.228482	−	0.101470i
$273$	−11.8499	−	11.8499i	−0.717191	−	0.717191i
$274$	−3.38509	+	1.40215i	−0.204500	+	0.0847069i
$275$		0			0
$276$	−7.52620	+	7.52620i	−0.453024	+	0.453024i
$277$	4.60443	+	6.89102i	0.276654	+	0.414041i	0.943612	−	0.331054i	$-0.107404\pi$
$277$	4.60443	+	6.89102i	0.276654	+	0.414041i	−0.666958	+	0.745095i	$0.732404\pi$
$278$	11.5508	−	2.29759i	0.692769	−	0.137800i
$279$	12.5608	−	2.49849i	0.751994	−	0.149581i
$280$		0			0
$281$	−0.165173	+	0.398764i	−0.00985342	+	0.0237883i	−0.928730	−	0.370758i	$-0.879098\pi$
$281$	−0.165173	+	0.398764i	−0.00985342	+	0.0237883i	0.918876	+	0.394546i	$0.129098\pi$
$282$	−11.5453	+	17.2788i	−0.687513	+	1.02894i
$283$	−5.19719	−	26.1280i	−0.308941	−	1.55315i	−0.753529	−	0.657415i	$-0.771650\pi$
$283$	−5.19719	−	26.1280i	−0.308941	−	1.55315i	0.444588	−	0.895735i	$-0.353350\pi$
$284$	0.887146	−	4.45998i	0.0526424	−	0.264651i
$285$		0			0
$286$	−3.69238	+	2.46717i	−0.218335	+	0.145887i
$287$	−3.82559	+	9.23579i	−0.225817	+	0.545171i
$288$	−6.08369	+	6.08369i	−0.358485	+	0.358485i
$289$	−11.3989	+	12.6121i	−0.670522	+	0.741890i
$290$		0			0
$291$	8.82230	+	21.2989i	0.517172	+	1.24856i
$292$	−1.78937	−	0.355928i	−0.104715	−	0.0208291i
$293$	7.34635			0.429178			0.214589	−	0.976704i	$-0.431159\pi$
$293$	7.34635			0.429178			0.214589	+	0.976704i	$0.431159\pi$
$294$	19.2666	+	3.83236i	1.12365	+	0.223508i
$295$		0			0
$296$	1.12655	+	5.66357i	0.0654797	+	0.329188i
$297$	17.6778	−	7.32240i	1.02577	−	0.424889i
$298$	−15.6697	+	6.49059i	−0.907719	+	0.375989i
$299$	−2.70049	−	13.5763i	−0.156173	−	0.785137i
$300$		0			0
$301$	−0.205535	−	0.0408834i	−0.0118468	−	0.00235648i
$302$	−11.2192			−0.645592
$303$	1.14479	+	0.227714i	0.0657667	+	0.0130818i
$304$	−0.209967	−	0.506906i	−0.0120425	−	0.0290731i
$305$		0			0
$306$	12.7437	−	33.1056i	0.728507	−	1.89252i
$307$	10.1701	−	10.1701i	0.580438	−	0.580438i	−0.354586	−	0.935024i	$-0.615378\pi$
$307$	10.1701	−	10.1701i	0.580438	−	0.580438i	0.935024	+	0.354586i	$0.115378\pi$
$308$	−0.425997	+	1.02845i	−0.0242734	+	0.0586013i
$309$	30.7347	−	20.5363i	1.74844	−	1.16827i
$310$		0			0
$311$	5.14414	−	25.8613i	0.291697	−	1.46646i	−0.505544	−	0.862801i	$-0.668708\pi$
$311$	5.14414	−	25.8613i	0.291697	−	1.46646i	0.797242	−	0.603660i	$-0.206292\pi$
$312$	−2.94406	−	14.8008i	−0.166674	−	0.837929i
$313$	−12.7980	+	19.1536i	−0.723386	+	1.08262i	0.269435	+	0.963019i	$0.413163\pi$
$313$	−12.7980	+	19.1536i	−0.723386	+	1.08262i	−0.992821	+	0.119606i	$0.961837\pi$
$314$	−2.84111	+	6.85905i	−0.160333	+	0.387079i
$315$		0			0
$316$	5.13719	−	1.02185i	0.288989	−	0.0574835i
$317$	−19.1629	+	3.81173i	−1.07629	+	0.214088i	−0.701247	−	0.712918i	$-0.747373\pi$
$317$	−19.1629	+	3.81173i	−1.07629	+	0.214088i	−0.375046	+	0.927006i	$0.622373\pi$
$318$	23.6054	+	35.3280i	1.32373	+	1.98110i
$319$	2.13962	−	2.13962i	0.119796	−	0.119796i
$320$		0			0
$321$	−36.9315	+	15.2975i	−2.06131	+	0.853824i
$322$	−2.45357	−	2.45357i	−0.136732	−	0.136732i
$323$	1.63950	+	1.55875i	0.0912245	+	0.0867313i
$324$			39.2117i			2.17843i
$325$		0			0
$326$	8.75441	+	13.1019i	0.484862	+	0.725647i
$327$			32.7198i			1.80941i
$328$	−7.48488	+	5.00124i	−0.413283	+	0.276147i
$329$	−5.63295	−	3.76382i	−0.310555	−	0.207506i
$330$		0			0
$331$	14.3226	+	5.93263i	0.787243	+	0.326087i	0.739835	−	0.672789i	$-0.234904\pi$
$331$	14.3226	+	5.93263i	0.787243	+	0.326087i	0.0474085	+	0.998876i	$0.484904\pi$
$332$	4.60927	+	11.1278i	0.252966	+	0.610715i
$333$	41.3090	+	27.6018i	2.26372	+	1.51257i
$334$	−10.0777	+	15.0823i	−0.551426	+	0.825268i
$335$		0			0
$336$	−2.67487	−	2.67487i	−0.145926	−	0.145926i
$337$	1.49770	−	7.52942i	0.0815847	−	0.410154i	−0.918313	−	0.395855i	$-0.870448\pi$
$337$	1.49770	−	7.52942i	0.0815847	−	0.410154i	0.999898	−	0.0142990i	$-0.00455166\pi$
$338$	6.12143	+	2.53558i	0.332962	+	0.137917i
$339$	−19.2867			−1.04751
$340$		0			0
$341$	1.49213			0.0808034
$342$	−4.36124	−	1.80648i	−0.235829	−	0.0976835i
$343$	−2.76591	+	13.9051i	−0.149345	+	0.750807i
$344$	−0.133437	−	0.133437i	−0.00719444	−	0.00719444i
$345$		0			0
$346$	−11.4682	+	17.1633i	−0.616532	+	0.922705i
$347$	13.5756	+	9.07091i	0.728775	+	0.486952i	0.863765	−	0.503895i	$-0.168100\pi$
$347$	13.5756	+	9.07091i	0.728775	+	0.486952i	−0.134990	+	0.990847i	$0.543100\pi$
$348$	3.93498	+	9.49989i	0.210937	+	0.509247i
$349$	1.69599	+	0.702502i	0.0907842	+	0.0376041i	0.427613	−	0.903962i	$-0.359354\pi$
$349$	1.69599	+	0.702502i	0.0907842	+	0.0376041i	−0.336829	+	0.941566i	$0.609354\pi$
$350$		0			0
$351$	−70.3117	−	46.9808i	−3.75296	−	2.50765i
$352$	−0.833476	+	0.556911i	−0.0444244	+	0.0296834i
$353$			19.2067i			1.02227i	0.859501	+	0.511134i	$0.170775\pi$
$353$			19.2067i			1.02227i	−0.859501	+	0.511134i	$0.829225\pi$
$354$	−22.6344	−	33.8747i	−1.20300	−	1.80042i
$355$		0			0
$356$		−	7.00452i		−	0.371239i
$357$	14.5558	+	5.60311i	0.770377	+	0.296548i
$358$	−4.82702	−	4.82702i	−0.255116	−	0.255116i
$359$	14.0392	−	5.81524i	0.740962	−	0.306916i	0.0199139	−	0.999802i	$-0.493661\pi$
$359$	14.0392	−	5.81524i	0.740962	−	0.306916i	0.721048	+	0.692885i	$0.243661\pi$
$360$		0			0
$361$	−13.2222	+	13.2222i	−0.695903	+	0.695903i
$362$	−2.64522	−	3.95885i	−0.139030	−	0.208073i
$363$	−33.3934	+	6.64237i	−1.75270	+	0.348634i
$364$	4.82512	−	0.959775i	0.252905	−	0.0503059i
$365$		0			0
$366$	−2.50411	+	6.04547i	−0.130892	+	0.316002i
$367$	8.17305	−	12.2318i	0.426630	−	0.638496i	−0.554424	−	0.832235i	$-0.687061\pi$
$367$	8.17305	−	12.2318i	0.426630	−	0.638496i	0.981053	+	0.193738i	$0.0620613\pi$
$368$	−0.609578	−	3.06456i	−0.0317764	−	0.159751i
$369$	−15.1097	+	75.9617i	−0.786580	+	3.95441i
$370$		0			0
$371$	−11.5171	+	7.69547i	−0.597937	+	0.399529i
$372$	−1.94043	+	4.68460i	−0.100606	+	0.242885i
$373$	1.82717	−	1.82717i	0.0946071	−	0.0946071i	−0.658219	−	0.752826i	$-0.728690\pi$
$373$	1.82717	−	1.82717i	0.0946071	−	0.0946071i	0.752826	+	0.658219i	$0.228690\pi$
$374$	2.20873	−	3.49337i	0.114211	−	0.180638i
$375$		0			0
$376$	−2.33458	−	5.63618i	−0.120397	−	0.290664i
$377$	−13.1158	−	2.60889i	−0.675496	−	0.134364i
$378$	−21.1977			−1.09029
$379$	−1.77933	−	0.353931i	−0.0913981	−	0.0181802i	0.149179	−	0.988810i	$-0.452337\pi$
$379$	−1.77933	−	0.353931i	−0.0913981	−	0.0181802i	−0.240577	+	0.970630i	$0.577337\pi$
$380$		0			0
$381$	6.71140	+	33.7405i	0.343835	+	1.72858i
$382$	9.37977	−	3.88523i	0.479911	−	0.198786i
$383$	−19.0782	+	7.90246i	−0.974852	+	0.403797i	−0.812516	−	0.582939i	$-0.801903\pi$
$383$	−19.0782	+	7.90246i	−0.974852	+	0.403797i	−0.162336	+	0.986736i	$0.551903\pi$
$384$	−0.664558	−	3.34096i	−0.0339131	−	0.170493i
$385$		0			0
$386$	7.54568	+	1.50093i	0.384065	+	0.0763953i
$387$	−1.62358			−0.0825312
$388$	−6.63772	−	1.32032i	−0.336979	−	0.0670293i
$389$	−0.669963	−	1.61743i	−0.0339685	−	0.0820071i	0.905985	−	0.423310i	$-0.139132\pi$
$389$	−0.669963	−	1.61743i	−0.0339685	−	0.0820071i	−0.939953	+	0.341303i	$0.889132\pi$
$390$		0			0
$391$	7.42552	+	10.5278i	0.375525	+	0.532413i
$392$	−4.07773	+	4.07773i	−0.205956	+	0.205956i
$393$	−4.09984	+	9.89788i	−0.206809	+	0.499282i
$394$	3.96501	−	2.64933i	0.199754	−	0.133472i
$395$		0			0
$396$	−1.68254	+	8.45868i	−0.0845507	+	0.425065i
$397$	−0.326653	−	1.64219i	−0.0163942	−	0.0824193i	0.971722	−	0.236128i	$-0.0758784\pi$
$397$	−0.326653	−	1.64219i	−0.0163942	−	0.0824193i	−0.988116	+	0.153708i	$0.950878\pi$
$398$	6.15454	−	9.21092i	0.308499	−	0.461702i
$399$	0.794272	−	1.91754i	0.0397634	−	0.0959972i
$400$		0			0
$401$	20.5762	−	4.09286i	1.02753	−	0.204388i	0.347581	−	0.937650i	$-0.387003\pi$
$401$	20.5762	−	4.09286i	1.02753	−	0.204388i	0.679946	+	0.733262i	$0.262003\pi$
$402$	−2.68796	+	0.534669i	−0.134063	+	0.0266669i
$403$	−3.66364	−	5.48303i	−0.182499	−	0.273129i
$404$	−0.242293	+	0.242293i	−0.0120545	+	0.0120545i
$405$		0			0
$406$	−3.09700	+	1.28282i	−0.153702	+	0.0636653i
$407$	4.09306	+	4.09306i	0.202885	+	0.202885i
$408$	8.09525	+	11.4773i	0.400775	+	0.568212i
$409$		−	38.0662i		−	1.88225i	−0.338057	−	0.941126i	$-0.609770\pi$
$409$		−	38.0662i		−	1.88225i	0.338057	−	0.941126i	$-0.390230\pi$
$410$		0			0
$411$	−6.93410	−	10.3776i	−0.342034	−	0.511890i
$412$			10.8514i			0.534611i
$413$	11.0433	−	7.37890i	0.543406	−	0.363092i
$414$	−22.3523	−	14.9353i	−1.09856	−	0.734031i
$415$		0			0
$416$	4.09288	+	1.69533i	0.200670	+	0.0831202i
$417$	15.3523	+	37.0637i	0.751805	+	1.81502i
$418$	−0.457304	−	0.305561i	−0.0223675	−	0.0149455i
$419$	7.41531	−	11.0978i	0.362262	−	0.542163i	−0.604908	−	0.796296i	$-0.706790\pi$
$419$	7.41531	−	11.0978i	0.362262	−	0.542163i	0.967169	+	0.254133i	$0.0817900\pi$
$420$		0			0
$421$	14.3935	+	14.3935i	0.701496	+	0.701496i	0.964732	−	0.263236i	$-0.0847897\pi$
$421$	14.3935	+	14.3935i	0.701496	+	0.701496i	−0.263236	+	0.964732i	$0.584790\pi$
$422$	1.63864	−	8.23800i	0.0797677	−	0.401019i
$423$	−48.4916	−	20.0859i	−2.35774	−	0.976610i
$424$	−12.4731			−0.605749
$425$		0			0
$426$	15.4902			0.750502
$427$	−1.97085	−	0.816352i	−0.0953760	−	0.0395060i
$428$	2.28939	−	11.5095i	0.110662	−	0.556335i
$429$	−10.6965	−	10.6965i	−0.516433	−	0.516433i
$430$		0			0
$431$	−11.5624	+	17.3044i	−0.556943	+	0.833524i	−0.997951	−	0.0639791i	$-0.979621\pi$
$431$	−11.5624	+	17.3044i	−0.556943	+	0.833524i	0.441008	+	0.897503i	$0.354621\pi$
$432$	−15.8713	−	10.6049i	−0.763611	−	0.510228i
$433$	2.48560	+	6.00076i	0.119450	+	0.288378i	0.972284	−	0.233805i	$-0.0751177\pi$
$433$	2.48560	+	6.00076i	0.119450	+	0.288378i	−0.852833	+	0.522183i	$0.825118\pi$
$434$	−1.52720	−	0.632587i	−0.0733080	−	0.0303652i
$435$		0			0
$436$	−7.98657	−	5.33646i	−0.382487	−	0.255570i
$437$	1.42545	−	0.952456i	0.0681886	−	0.0455621i
$438$		−	6.21474i		−	0.296952i
$439$	−10.0507	−	15.0419i	−0.479692	−	0.717910i	0.510149	−	0.860086i	$-0.329590\pi$
$439$	−10.0507	−	15.0419i	−0.479692	−	0.717910i	−0.989841	+	0.142176i	$0.954590\pi$
$440$		0			0
$441$			49.6153i			2.36263i
$442$	−18.2600	+	0.461036i	−0.868537	+	0.0219293i
$443$	26.2032	+	26.2032i	1.24495	+	1.24495i	0.957922	+	0.287029i	$0.0926676\pi$
$443$	26.2032	+	26.2032i	1.24495	+	1.24495i	0.287029	+	0.957922i	$0.407332\pi$
$444$	−18.1731	+	7.52754i	−0.862457	+	0.357241i
$445$		0			0
$446$	13.9738	−	13.9738i	0.661678	−	0.661678i
$447$	−32.0982	−	48.0383i	−1.51819	−	2.27213i
$448$	1.08917	−	0.216649i	0.0514583	−	0.0102357i
$449$	31.4989	−	6.26553i	1.48653	−	0.295689i	0.615975	−	0.787765i	$-0.288762\pi$
$449$	31.4989	−	6.26553i	1.48653	−	0.295689i	0.870552	+	0.492077i	$0.163762\pi$
$450$		0			0
$451$	−3.45322	+	8.33682i	−0.162606	+	0.392565i
$452$	3.14558	−	4.70769i	0.147956	−	0.221431i
$453$	−7.45581	−	37.4829i	−0.350304	−	1.76110i
$454$	−1.07198	+	5.38919i	−0.0503104	+	0.252927i
$455$		0			0
$456$	1.55402	−	1.03836i	0.0727735	−	0.0486257i
$457$	9.51343	−	22.9675i	0.445020	−	1.07437i	−0.529145	−	0.848532i	$-0.677487\pi$
$457$	9.51343	−	22.9675i	0.445020	−	1.07437i	0.974164	−	0.225841i	$-0.0725129\pi$
$458$	−2.45788	+	2.45788i	−0.114849	+	0.114849i
$459$	77.5538	+	13.4010i	3.61990	+	0.625505i
$460$		0			0
$461$	4.92471	+	11.8893i	0.229367	+	0.553740i	0.996101	−	0.0882249i	$-0.0281194\pi$
$461$	4.92471	+	11.8893i	0.229367	+	0.553740i	−0.766734	+	0.641965i	$0.778119\pi$
$462$	−3.71910	−	0.739775i	−0.173028	−	0.0344175i
$463$	26.9358			1.25181			0.625907	−	0.779898i	$-0.284729\pi$
$463$	26.9358			1.25181			0.625907	+	0.779898i	$0.284729\pi$
$464$	−2.96060	−	0.588900i	−0.137442	−	0.0273390i
$465$		0			0
$466$	2.36203	+	11.8747i	0.109419	+	0.550086i
$467$	11.0508	−	4.57740i	0.511371	−	0.211817i	−0.112051	−	0.993702i	$-0.535742\pi$
$467$	11.0508	−	4.57740i	0.511371	−	0.211817i	0.623422	+	0.781886i	$0.285742\pi$
$468$	35.2137	−	14.5860i	1.62775	−	0.674237i
$469$	−0.174304	−	0.876287i	−0.00804863	−	0.0404632i
$470$		0			0
$471$	−24.8039	−	4.93380i	−1.14290	−	0.227338i
$472$	11.9600			0.550505
$473$	−0.185529	−	0.0369040i	−0.00853063	−	0.00169685i
$474$	6.82791	+	16.4840i	0.313617	+	0.757137i
$475$		0			0
$476$	−3.74165	+	2.63909i	−0.171498	+	0.120962i
$477$	−75.8828	+	75.8828i	−3.47443	+	3.47443i
$478$	5.44152	−	13.1370i	0.248890	−	0.600872i
$479$	−23.8498	+	15.9359i	−1.08972	+	0.728131i	−0.964523	−	0.264000i	$-0.914958\pi$
$479$	−23.8498	+	15.9359i	−1.08972	+	0.728131i	−0.125202	+	0.992131i	$0.539958\pi$
$480$		0			0
$481$	4.99075	−	25.0902i	0.227559	−	1.14401i
$482$	1.00841	+	5.06964i	0.0459320	+	0.230916i
$483$	6.56674	−	9.82782i	0.298797	−	0.447181i
$484$	3.82499	−	9.23433i	0.173863	−	0.419742i
$485$		0			0
$486$	−74.8401	+	14.8866i	−3.39482	+	0.675271i
$487$	33.0161	−	6.56730i	1.49610	−	0.297593i	0.621876	−	0.783116i	$-0.286371\pi$
$487$	33.0161	−	6.56730i	1.49610	−	0.297593i	0.874224	+	0.485523i	$0.161371\pi$
$488$	−1.06723	−	1.59722i	−0.0483110	−	0.0723026i
$489$	−37.9551	+	37.9551i	−1.71639	+	1.71639i
$490$		0			0
$491$	11.5798	−	4.79652i	0.522590	−	0.216464i	−0.105764	−	0.994391i	$-0.533729\pi$
$491$	11.5798	−	4.79652i	0.522590	−	0.216464i	0.628354	+	0.777927i	$0.283729\pi$
$492$	−21.6831	−	21.6831i	−0.977548	−	0.977548i
$493$	12.1417	−	2.73543i	0.546834	−	0.123198i
$494$			2.43067i			0.109361i
$495$		0			0
$496$	−0.826988	−	1.23768i	−0.0371329	−	0.0555733i
$497$			5.04986i			0.226517i
$498$	−34.1142	+	22.7944i	−1.52870	+	1.02144i
$499$	5.43966	+	3.63466i	0.243512	+	0.162710i	0.671338	−	0.741152i	$-0.265720\pi$
$499$	5.43966	+	3.63466i	0.243512	+	0.162710i	−0.427825	+	0.903862i	$0.640720\pi$
$500$		0			0
$501$	−57.0866	−	23.6460i	−2.55044	−	1.05643i
$502$	9.99159	+	24.1218i	0.445947	+	1.07661i
$503$	8.19153	+	5.47341i	0.365242	+	0.244047i	0.724625	−	0.689143i	$-0.242013\pi$
$503$	8.19153	+	5.47341i	0.365242	+	0.244047i	−0.359383	+	0.933190i	$0.617013\pi$
$504$	5.30813	−	7.94418i	0.236443	−	0.353862i
$505$		0			0
$506$	−2.21475	−	2.21475i	−0.0984577	−	0.0984577i
$507$	−4.40322	+	22.1365i	−0.195554	+	0.983116i
$508$	−9.33030	−	3.86473i	−0.413965	−	0.171470i
$509$	32.3534			1.43404			0.717020	−	0.697052i	$-0.245506\pi$
$509$	32.3534			1.43404			0.717020	+	0.697052i	$0.245506\pi$
$510$		0			0
$511$	2.02603			0.0896264
$512$	0.923880	+	0.382683i	0.0408301	+	0.0169124i
$513$	2.04322	−	10.2720i	0.0902104	−	0.453519i
$514$	13.1983	+	13.1983i	0.582153	+	0.582153i
$515$		0			0
$516$	0.357131	−	0.534484i	0.0157218	−	0.0235294i
$517$	−5.08466	−	3.39746i	−0.223623	−	0.149420i
$518$	−2.45401	−	5.92451i	−0.107823	−	0.260308i
$519$	−64.9632	−	26.9086i	−2.85157	−	1.18116i
$520$		0			0
$521$	6.37903	+	4.26233i	0.279471	+	0.186736i	0.687404	−	0.726276i	$-0.258750\pi$
$521$	6.37903	+	4.26233i	0.279471	+	0.186736i	−0.407933	+	0.913012i	$0.633750\pi$
$522$	−21.5941	+	14.4287i	−0.945147	+	0.631527i
$523$			21.2279i			0.928230i	0.885775	+	0.464115i	$0.153628\pi$
$523$			21.2279i			0.928230i	−0.885775	+	0.464115i	$0.846372\pi$
$524$	−1.74731	−	2.61503i	−0.0763314	−	0.114238i
$525$		0			0
$526$			23.5251i			1.02574i
$527$	5.18750	+	3.27987i	0.225971	+	0.142873i
$528$	−2.41451	−	2.41451i	−0.105078	−	0.105078i
$529$	−12.2293	+	5.06555i	−0.531709	+	0.220241i
$530$		0			0
$531$	72.7612	−	72.7612i	3.15757	−	3.15757i
$532$	0.338510	+	0.506616i	0.0146763	+	0.0219646i
$533$	39.1134	−	7.78014i	1.69419	−	0.336995i
$534$	23.4018	−	4.65491i	1.01270	−	0.201438i
$535$		0			0
$536$	0.307887	−	0.743306i	0.0132987	−	0.0321059i
$537$	12.9190	−	19.3347i	0.557498	−	0.834355i
$538$	0.0663603	+	0.333616i	0.00286099	+	0.0143832i
$539$	−1.12776	+	5.66962i	−0.0485759	+	0.244208i
$540$		0			0
$541$	−22.8895	+	15.2943i	−0.984095	+	0.657551i	−0.939892	−	0.341471i	$-0.889075\pi$
$541$	−22.8895	+	15.2943i	−0.984095	+	0.657551i	−0.0442028	+	0.999023i	$0.514075\pi$
$542$	−0.867834	+	2.09514i	−0.0372766	+	0.0899938i
$543$	11.4685	−	11.4685i	0.492159	−	0.492159i
$544$	−4.12179	+	0.104069i	−0.176720	+	0.00446192i
$545$		0			0
$546$	6.41314	+	15.4827i	0.274457	+	0.662598i
$547$	5.52336	+	1.09867i	0.236162	+	0.0469755i	0.311752	−	0.950163i	$-0.399084\pi$
$547$	5.52336	+	1.09867i	0.236162	+	0.0469755i	−0.0755903	+	0.997139i	$0.524084\pi$
$548$	3.66399			0.156518
$549$	−16.2096	−	3.22430i	−0.691811	−	0.137610i
$550$		0			0
$551$	−0.323113	−	1.62440i	−0.0137651	−	0.0692016i
$552$	9.83345	−	4.07315i	0.418539	−	0.173365i
$553$	−5.37387	+	2.22593i	−0.228520	+	0.0946561i
$554$	−1.61686	−	8.12851i	−0.0686939	−	0.345347i
$555$		0			0
$556$	−11.5508	−	2.29759i	−0.489861	−	0.0974395i
$557$	−27.2007			−1.15253			−0.576266	−	0.817262i	$-0.695491\pi$
$557$	−27.2007			−1.15253			−0.576266	+	0.817262i	$0.695491\pi$
$558$	−12.5608	−	2.49849i	−0.531740	−	0.105770i
$559$	0.319922	+	0.772361i	0.0135313	+	0.0326674i
$560$		0			0
$561$	13.1390	+	5.05773i	0.554731	+	0.213538i
$562$	0.305201	−	0.305201i	0.0128741	−	0.0128741i
$563$	−15.2574	+	36.8345i	−0.643021	+	1.55239i	0.179562	+	0.983747i	$0.442532\pi$
$563$	−15.2574	+	36.8345i	−0.643021	+	1.55239i	−0.822583	+	0.568644i	$0.807468\pi$
$564$	17.2788	−	11.5453i	0.727567	−	0.486145i
$565$		0			0
$566$	−5.19719	+	26.1280i	−0.218454	+	1.09824i
$567$	−8.49517	−	42.7081i	−0.356763	−	1.79357i
$568$	−2.52638	+	3.78099i	−0.106004	+	0.158647i
$569$	−4.40995	+	10.6465i	−0.184875	+	0.446327i	−0.988959	−	0.148188i	$-0.952656\pi$
$569$	−4.40995	+	10.6465i	−0.184875	+	0.446327i	0.804085	+	0.594515i	$0.202656\pi$
$570$		0			0
$571$	21.2192	−	4.22076i	0.887996	−	0.176633i	0.270043	−	0.962848i	$-0.412962\pi$
$571$	21.2192	−	4.22076i	0.887996	−	0.176633i	0.617953	+	0.786215i	$0.287962\pi$
$572$	4.35546	−	0.866355i	0.182111	−	0.0362241i
$573$	19.2138	+	28.7555i	0.802668	+	1.20128i
$574$	7.06877	−	7.06877i	0.295045	−	0.295045i
$575$		0			0
$576$	7.94873	−	3.29247i	0.331197	−	0.137186i
$577$	30.0318	+	30.0318i	1.25024	+	1.25024i	0.955612	+	0.294630i	$0.0951962\pi$
$577$	30.0318	+	30.0318i	1.25024	+	1.25024i	0.294630	+	0.955612i	$0.404804\pi$
$578$	15.3576	−	7.28993i	0.638793	−	0.303221i
$579$			26.2073i			1.08914i
$580$		0			0
$581$	−7.43107	−	11.1214i	−0.308293	−	0.461393i
$582$		−	23.0538i		−	0.955610i
$583$	−10.3961	+	6.94643i	−0.430561	+	0.287692i
$584$	1.51695	+	1.01360i	0.0627720	+	0.0419429i
$585$		0			0
$586$	−6.78714	−	2.81133i	−0.280374	−	0.116135i
$587$	−0.383934	−	0.926898i	−0.0158466	−	0.0382572i	0.915758	−	0.401730i	$-0.131591\pi$
$587$	−0.383934	−	0.926898i	−0.0158466	−	0.0382572i	−0.931605	+	0.363473i	$0.881591\pi$
$588$	−16.3334	−	10.9136i	−0.673578	−	0.450071i
$589$	0.453745	−	0.679077i	0.0186962	−	0.0279809i
$590$		0			0
$591$	11.4863	+	11.4863i	0.472483	+	0.472483i
$592$	1.12655	−	5.66357i	0.0463011	−	0.232771i
$593$	8.21255	+	3.40175i	0.337249	+	0.139693i	0.544880	−	0.838514i	$-0.316575\pi$
$593$	8.21255	+	3.40175i	0.337249	+	0.139693i	−0.207631	+	0.978207i	$0.566575\pi$
$594$	−19.1344			−0.785092
$595$		0			0
$596$	16.9607			0.694738
$597$	34.8634	+	14.4409i	1.42686	+	0.591026i
$598$	−2.70049	+	13.5763i	−0.110431	+	0.555176i
$599$	−6.14617	−	6.14617i	−0.251126	−	0.251126i	0.570306	−	0.821432i	$-0.306824\pi$
$599$	−6.14617	−	6.14617i	−0.251126	−	0.251126i	−0.821432	+	0.570306i	$0.806824\pi$
$600$		0			0
$601$	10.2301	−	15.3104i	0.417294	−	0.624525i	−0.561959	−	0.827165i	$-0.689952\pi$
$601$	10.2301	−	15.3104i	0.417294	−	0.624525i	0.979253	+	0.202640i	$0.0649522\pi$
$602$	0.174244	+	0.116426i	0.00710166	+	0.00474518i
$603$	−2.64895	−	6.39514i	−0.107874	−	0.260430i
$604$	10.3652	+	4.29340i	0.421753	+	0.174696i
$605$		0			0
$606$	−0.970509	−	0.648474i	−0.0394243	−	0.0263424i
$607$	−34.7226	+	23.2009i	−1.40935	+	0.941696i	−0.409783	+	0.912183i	$0.634396\pi$
$607$	−34.7226	+	23.2009i	−1.40935	+	0.941696i	−0.999564	+	0.0295133i	$0.990604\pi$
$608$			0.548671i			0.0222516i
$609$	−6.34399	−	9.49445i	−0.257071	−	0.384734i
$610$		0			0
$611$			27.0261i			1.09336i
$612$	−24.4426	+	25.7088i	−0.988033	+	1.03922i
$613$	14.8737	+	14.8737i	0.600741	+	0.600741i	0.940509	−	0.339768i	$-0.110349\pi$
$613$	14.8737	+	14.8737i	0.600741	+	0.600741i	−0.339768	+	0.940509i	$0.610349\pi$
$614$	−13.2879	+	5.50402i	−0.536255	+	0.222124i
$615$		0			0
$616$	0.787140	−	0.787140i	0.0317148	−	0.0317148i
$617$	15.8137	+	23.6669i	0.636635	+	0.952792i	0.999778	+	0.0210586i	$0.00670366\pi$
$617$	15.8137	+	23.6669i	0.636635	+	0.952792i	−0.363143	+	0.931733i	$0.618296\pi$
$618$	−36.2541	+	7.21139i	−1.45835	+	0.290085i
$619$	15.5083	−	3.08480i	0.623332	−	0.123988i	0.126688	−	0.991943i	$-0.459565\pi$
$619$	15.5083	−	3.08480i	0.623332	−	0.123988i	0.496644	+	0.867954i	$0.334565\pi$
$620$		0			0
$621$	22.8245	−	55.1031i	0.915914	−	2.21121i
$622$	−14.6493	+	21.9242i	−0.587382	+	0.879079i
$623$	1.51752	+	7.62909i	0.0607982	+	0.305653i
$624$	−2.94406	+	14.8008i	−0.117857	+	0.592505i
$625$		0			0
$626$	19.1536	−	12.7980i	0.765531	−	0.511511i
$627$	0.716961	−	1.73090i	0.0286327	−	0.0691254i
$628$	5.24969	−	5.24969i	0.209486	−	0.209486i
$629$	5.23283	+	23.2268i	0.208646	+	0.926114i
$630$		0			0
$631$	−12.6072	−	30.4365i	−0.501885	−	1.21166i	−0.948456	−	0.316910i	$-0.897355\pi$
$631$	−12.6072	−	30.4365i	−0.501885	−	1.21166i	0.446570	−	0.894749i	$-0.352645\pi$
$632$	−5.13719	−	1.02185i	−0.204346	−	0.0406470i
$633$	28.6118			1.13722
$634$	19.1629	+	3.81173i	0.761054	+	0.151383i
$635$		0			0
$636$	−8.28913	−	41.6723i	−0.328685	−	1.65241i
$637$	23.6027	−	9.77657i	0.935174	−	0.387362i
$638$	−2.79555	+	1.15796i	−0.110677	+	0.0458439i
$639$	7.63269	+	38.3721i	0.301944	+	1.51798i
$640$		0			0
$641$	13.3488	+	2.65524i	0.527246	+	0.104876i	0.451534	−	0.892254i	$-0.350877\pi$
$641$	13.3488	+	2.65524i	0.527246	+	0.104876i	0.0757122	+	0.997130i	$0.475877\pi$
$642$	39.9744			1.57766
$643$	−2.41613	−	0.480598i	−0.0952828	−	0.0189529i	0.147219	−	0.989104i	$-0.452968\pi$
$643$	−2.41613	−	0.480598i	−0.0952828	−	0.0189529i	−0.242501	+	0.970151i	$0.577968\pi$
$644$	1.32786	+	3.20575i	0.0523252	+	0.126324i
$645$		0			0
$646$	−0.918195	−	2.06751i	−0.0361259	−	0.0813451i
$647$	21.2530	−	21.2530i	0.835542	−	0.835542i	−0.152727	−	0.988268i	$-0.548805\pi$
$647$	21.2530	−	21.2530i	0.835542	−	0.835542i	0.988268	+	0.152727i	$0.0488055\pi$
$648$	15.0057	−	36.2269i	0.589478	−	1.42313i
$649$	9.96840	−	6.66067i	0.391294	−	0.261454i
$650$		0			0
$651$	1.09853	−	5.52270i	0.0430549	−	0.216452i
$652$	−3.07414	−	15.4547i	−0.120393	−	0.605255i
$653$	−2.90787	+	4.35193i	−0.113794	+	0.170304i	−0.883995	−	0.467497i	$-0.845156\pi$
$653$	−2.90787	+	4.35193i	−0.113794	+	0.170304i	0.770201	+	0.637801i	$0.220156\pi$
$654$	12.5213	−	30.2292i	0.489623	−	1.18205i
$655$		0			0
$656$	8.82901	−	1.75620i	0.344715	−	0.0685681i
$657$	15.3951	−	3.06227i	0.600620	−	0.119471i
$658$	3.76382	+	5.63295i	0.146729	+	0.219595i
$659$	5.87271	−	5.87271i	0.228768	−	0.228768i	−0.583410	−	0.812178i	$-0.698282\pi$
$659$	5.87271	−	5.87271i	0.228768	−	0.228768i	0.812178	+	0.583410i	$0.198282\pi$
$660$		0			0
$661$	29.9673	−	12.4128i	1.16559	−	0.482804i	0.285858	−	0.958272i	$-0.407721\pi$
$661$	29.9673	−	12.4128i	1.16559	−	0.482804i	0.879733	+	0.475468i	$0.157721\pi$
$662$	−10.9621	−	10.9621i	−0.426053	−	0.426053i
$663$	−13.6751	−	60.6994i	−0.531097	−	2.35737i
$664$		−	12.0446i		−	0.467421i
$665$		0			0
$666$	−27.6018	−	41.3090i	−1.06955	−	1.60069i
$667$		−	9.43190i		−	0.365205i
$668$	15.0823	−	10.0777i	0.583552	−	0.389917i
$669$	55.9722	+	37.3994i	2.16401	+	1.44595i
$670$		0			0
$671$	−1.77901	−	0.736892i	−0.0686781	−	0.0284474i
$672$	1.44763	+	3.49488i	0.0558435	+	0.134818i
$673$	1.99854	+	1.33538i	0.0770379	+	0.0514751i	0.593493	−	0.804839i	$-0.297749\pi$
$673$	1.99854	+	1.33538i	0.0770379	+	0.0514751i	−0.516455	+	0.856314i	$0.672749\pi$
$674$	−4.26508	+	6.38314i	−0.164285	+	0.245869i
$675$		0			0
$676$	−4.68514	−	4.68514i	−0.180198	−	0.180198i
$677$	8.15809	−	41.0135i	0.313541	−	1.57628i	−0.426992	−	0.904256i	$-0.640427\pi$
$677$	8.15809	−	41.0135i	0.313541	−	1.57628i	0.740532	−	0.672021i	$-0.234573\pi$
$678$	17.8186	+	7.38071i	0.684320	+	0.283455i
$679$	7.51563			0.288423
$680$		0			0
$681$	−18.7175			−0.717255
$682$	−1.37855	−	0.571014i	−0.0527874	−	0.0218652i
$683$	−4.68103	+	23.5331i	−0.179115	+	0.900470i	0.781780	+	0.623555i	$0.214312\pi$
$683$	−4.68103	+	23.5331i	−0.179115	+	0.900470i	−0.960894	+	0.276916i	$0.910688\pi$
$684$	3.33795	+	3.33795i	0.127630	+	0.127630i
$685$		0			0
$686$	7.87663	−	11.7882i	0.300731	−	0.450076i
$687$	−9.84506	−	6.57826i	−0.375612	−	0.250976i
$688$	0.0722156	+	0.174344i	0.00275319	+	0.00664680i
$689$	51.0511	+	21.1460i	1.94489	+	0.805600i
$690$		0			0
$691$	37.4684	+	25.0356i	1.42536	+	0.952398i	0.998851	+	0.0479168i	$0.0152582\pi$
$691$	37.4684	+	25.0356i	1.42536	+	0.952398i	0.426513	+	0.904481i	$0.359742\pi$
$692$	17.1633	−	11.4682i	0.652451	−	0.435954i
$693$		−	9.57743i		−	0.363817i
$694$	−9.07091	−	13.5756i	−0.344327	−	0.515322i
$695$		0			0
$696$		−	10.2826i		−	0.389761i
$697$	−30.3306	+	21.3930i	−1.14885	+	0.810317i
$698$	−1.29805	−	1.29805i	−0.0491321	−	0.0491321i
$699$	−38.1032	+	15.7829i	−1.44120	+	0.596963i
$700$		0			0
$701$	−28.9028	+	28.9028i	−1.09164	+	1.09164i	−0.0962904	+	0.995353i	$0.530698\pi$
$701$	−28.9028	+	28.9028i	−1.09164	+	1.09164i	−0.995353	+	0.0962904i	$0.969302\pi$
$702$	46.9808	+	70.3117i	1.77317	+	2.65374i
$703$	3.10744	−	0.618108i	0.117199	−	0.0233124i
$704$	0.983152	−	0.195561i	0.0370539	−	0.00737048i
$705$		0			0
$706$	7.35008	−	17.7447i	0.276624	−	0.667829i
$707$	0.211405	−	0.316390i	0.00795071	−	0.0118991i
$708$	7.94813	+	39.9580i	0.298709	+	1.50171i
$709$	8.57537	−	43.1113i	0.322055	−	1.61908i	−0.392675	−	0.919677i	$-0.628450\pi$
$709$	8.57537	−	43.1113i	0.322055	−	1.61908i	0.714729	−	0.699401i	$-0.246550\pi$
$710$		0			0
$711$	−37.4697	+	25.0364i	−1.40522	+	0.938940i
$712$	−2.68051	+	6.47133i	−0.100457	+	0.242523i
$713$	3.28881	−	3.28881i	0.123167	−	0.123167i
$714$	−11.3036	−	10.7469i	−0.423027	−	0.402192i
$715$		0			0
$716$	2.61237	+	6.30681i	0.0976287	+	0.235697i
$717$	47.5064	+	9.44961i	1.77416	+	0.352902i
$718$	−15.1959			−0.567108
$719$	2.24438	+	0.446435i	0.0837012	+	0.0166492i	0.236763	−	0.971567i	$-0.423913\pi$
$719$	2.24438	+	0.446435i	0.0837012	+	0.0166492i	−0.153062	+	0.988217i	$0.548913\pi$
$720$		0			0
$721$	−2.35094	−	11.8190i	−0.0875537	−	0.440162i
$722$	17.2756	−	7.15578i	0.642931	−	0.266311i
$723$	−16.2673	+	6.73814i	−0.604988	+	0.250594i
$724$	0.928878	+	4.66979i	0.0345215	+	0.173551i
$725$		0			0
$726$	33.3934	+	6.64237i	1.23935	+	0.246521i
$727$	3.30429			0.122549			0.0612747	−	0.998121i	$-0.480483\pi$
$727$	3.30429			0.122549			0.0612747	+	0.998121i	$0.480483\pi$
$728$	−4.82512	−	0.959775i	−0.178831	−	0.0355716i
$729$	−54.4542	−	131.464i	−2.01682	−	4.86904i
$730$		0			0
$731$	−0.563886	−	0.536113i	−0.0208561	−	0.0198289i
$732$	4.62700	−	4.62700i	0.171019	−	0.171019i
$733$	13.0877	−	31.5964i	0.483404	−	1.16704i	−0.474579	−	0.880213i	$-0.657400\pi$
$733$	13.0877	−	31.5964i	0.483404	−	1.16704i	0.957982	−	0.286827i	$-0.0926004\pi$
$734$	−12.2318	+	8.17305i	−0.451485	+	0.301673i
$735$		0			0
$736$	−0.609578	+	3.06456i	−0.0224693	+	0.112961i
$737$	−0.157338	−	0.790993i	−0.00579563	−	0.0291366i
$738$	43.0288	−	64.3972i	1.58391	−	2.37049i
$739$	15.4004	−	37.1799i	0.566514	−	1.36769i	−0.337961	−	0.941160i	$-0.609737\pi$
$739$	15.4004	−	37.1799i	0.566514	−	1.36769i	0.904475	−	0.426526i	$-0.140263\pi$
$740$		0			0
$741$	−8.12077	+	1.61532i	−0.298324	+	0.0593403i
$742$	13.5853	−	2.70229i	0.498733	−	0.0992042i
$743$	−20.9647	−	31.3758i	−0.769119	−	1.15107i	−0.984645	−	0.174569i	$-0.944147\pi$
$743$	−20.9647	−	31.3758i	−0.769119	−	1.15107i	0.215526	−	0.976498i	$-0.430853\pi$
$744$	3.58544	−	3.58544i	0.131449	−	0.131449i
$745$		0			0
$746$	−2.38731	+	0.988856i	−0.0874056	+	0.0362046i
$747$	−73.2756	−	73.2756i	−2.68101	−	2.68101i
$748$	−3.37746	+	2.38221i	−0.123492	+	0.0871022i
$749$			13.0318i			0.476172i
$750$		0			0
$751$	11.8751	+	17.7723i	0.433328	+	0.648521i	0.982299	−	0.187321i	$-0.0599803\pi$
$751$	11.8751	+	17.7723i	0.433328	+	0.648521i	−0.548971	+	0.835841i	$0.684980\pi$
$752$			6.10055i			0.222464i
$753$	−73.9501	+	49.4119i	−2.69489	+	1.80067i
$754$	11.1190	+	7.42948i	0.404930	+	0.270566i
$755$		0			0
$756$	19.5841	+	8.11199i	0.712266	+	0.295030i
$757$	−12.9486	−	31.2607i	−0.470625	−	1.13619i	−0.963888	−	0.266309i	$-0.914196\pi$
$757$	−12.9486	−	31.2607i	−0.470625	−	1.13619i	0.493263	−	0.869880i	$-0.335804\pi$
$758$	1.50844	+	1.00791i	0.0547891	+	0.0366089i
$759$	5.92756	−	8.87122i	0.215157	−	0.322005i
$760$		0			0
$761$	−24.4932	−	24.4932i	−0.887877	−	0.887877i	0.106442	−	0.994319i	$-0.466054\pi$
$761$	−24.4932	−	24.4932i	−0.887877	−	0.887877i	−0.994319	+	0.106442i	$0.966054\pi$
$762$	6.71140	−	33.7405i	0.243128	−	1.22229i
$763$	9.85484	+	4.08201i	0.356769	+	0.147779i
$764$	−10.1526			−0.367308
$765$		0			0
$766$	20.6501			0.746119
$767$	−48.9510	−	20.2762i	−1.76752	−	0.732129i
$768$	−0.664558	+	3.34096i	−0.0239802	+	0.120556i
$769$	27.9366	+	27.9366i	1.00742	+	1.00742i	0.999972	+	0.00744621i	$0.00237022\pi$
$769$	27.9366	+	27.9366i	1.00742	+	1.00742i	0.00744621	+	0.999972i	$0.497630\pi$
$770$		0			0
$771$	−35.3240	+	52.8661i	−1.27216	+	1.90393i
$772$	−6.39692	−	4.27428i	−0.230230	−	0.153835i
$773$	−18.0733	−	43.6329i	−0.650053	−	1.56937i	−0.812700	−	0.582683i	$-0.802003\pi$
$773$	−18.0733	−	43.6329i	−0.650053	−	1.56937i	0.162647	−	0.986684i	$-0.447997\pi$
$774$	1.49999	+	0.621317i	0.0539161	+	0.0223328i
$775$		0			0
$776$	5.62719	+	3.75997i	0.202004	+	0.134975i
$777$	18.1627	−	12.1359i	0.651583	−	0.435374i
$778$			1.75070i			0.0627656i
$779$	2.74403	+	4.10674i	0.0983153	+	0.147139i
$780$		0			0
$781$			4.55833i			0.163110i
$782$	−2.83148	−	12.5680i	−0.101253	−	0.449431i
$783$	−40.7435	−	40.7435i	−1.45605	−	1.45605i
$784$	5.32781	−	2.20685i	0.190279	−	0.0788161i
$785$		0			0
$786$	7.57551	−	7.57551i	0.270210	−	0.270210i
$787$	17.3249	+	25.9285i	0.617565	+	0.924252i	1.00000		0.000269208i	$8.56916e-5\pi$
$787$	17.3249	+	25.9285i	0.617565	+	0.924252i	−0.382435	+	0.923983i	$0.624914\pi$
$788$	−4.67705	+	0.930323i	−0.166613	+	0.0331414i
$789$	−78.5965	+	15.6338i	−2.79811	+	0.556578i
$790$		0			0
$791$	−2.40614	+	5.80894i	−0.0855526	+	0.206542i
$792$	4.79146	−	7.17093i	0.170257	−	0.254808i
$793$	1.66022	+	8.34651i	0.0589563	+	0.296393i
$794$	−0.326653	+	1.64219i	−0.0115925	+	0.0582793i
$795$		0			0
$796$	−9.21092	+	6.15454i	−0.326473	+	0.218142i
$797$	−8.93522	+	21.5715i	−0.316502	+	0.764103i	0.682933	+	0.730481i	$0.260704\pi$
$797$	−8.93522	+	21.5715i	−0.316502	+	0.764103i	−0.999435	+	0.0336218i	$0.989296\pi$
$798$	−1.46762	+	1.46762i	−0.0519533	+	0.0519533i
$799$	−10.2092	−	22.9882i	−0.361176	−	0.813264i
$800$		0			0
$801$	23.0622	+	55.6770i	0.814862	+	1.96725i
$802$	−20.5762	−	4.09286i	−0.726571	−	0.144524i
$803$	1.82883			0.0645379
$804$	2.68796	+	0.534669i	0.0947971	+	0.0188563i
$805$		0			0
$806$	1.28650	+	6.46767i	0.0453150	+	0.227814i
$807$	−1.07050	+	0.443414i	−0.0376832	+	0.0156089i
$808$	0.316571	−	0.131128i	0.0111369	−	0.00461307i
$809$	0.811177	+	4.07806i	0.0285194	+	0.143377i	0.992422	−	0.122880i	$-0.0392130\pi$
$809$	0.811177	+	4.07806i	0.0285194	+	0.143377i	−0.963902	+	0.266257i	$0.914213\pi$
$810$		0			0
$811$	17.7718	+	3.53503i	0.624053	+	0.124132i	0.496981	−	0.867762i	$-0.334442\pi$
$811$	17.7718	+	3.53503i	0.624053	+	0.124132i	0.127072	+	0.991893i	$0.459442\pi$
$812$	3.35217			0.117638
$813$	−7.57649	−	1.50706i	−0.265719	−	0.0528548i
$814$	−2.21515	−	5.34784i	−0.0776409	−	0.187442i
$815$		0			0
$816$	−3.08686	−	13.7016i	−0.108062	−	0.479651i
$817$	−0.0732131	+	0.0732131i	−0.00256140	+	0.00256140i
$818$	−14.5673	+	35.1686i	−0.509333	+	1.22964i
$819$	−35.1935	+	23.5156i	−1.22976	+	0.821700i
$820$		0			0
$821$	−4.40020	+	22.1213i	−0.153568	+	0.772038i	0.824842	+	0.565364i	$0.191264\pi$
$821$	−4.40020	+	22.1213i	−0.153568	+	0.772038i	−0.978410	+	0.206675i	$0.933736\pi$
$822$	2.43493	+	12.2412i	0.0849281	+	0.426962i
$823$	−24.7335	+	37.0162i	−0.862154	+	1.29031i	0.0934416	+	0.995625i	$0.470213\pi$
$823$	−24.7335	+	37.0162i	−0.862154	+	1.29031i	−0.955596	+	0.294680i	$0.904787\pi$
$824$	4.15265	−	10.0254i	0.144665	−	0.349251i
$825$		0			0
$826$	−13.0265	+	2.59113i	−0.453249	+	0.0901568i
$827$	19.2440	−	3.82787i	0.669180	−	0.133108i	0.151203	−	0.988503i	$-0.451685\pi$
$827$	19.2440	−	3.82787i	0.669180	−	0.133108i	0.517977	+	0.855395i	$0.326685\pi$
$828$	14.9353	+	22.3523i	0.519038	+	0.776796i
$829$	−8.97190	+	8.97190i	−0.311607	+	0.311607i	−0.845532	−	0.533925i	$-0.820716\pi$
$829$	−8.97190	+	8.97190i	−0.311607	+	0.311607i	0.533925	+	0.845532i	$0.320716\pi$
$830$		0			0
$831$	26.0825	−	10.8037i	0.904793	−	0.374777i
$832$	−3.13255	−	3.13255i	−0.108602	−	0.108602i
$833$	−16.3832	+	17.2319i	−0.567644	+	0.597051i
$834$		−	40.1175i		−	1.38916i
$835$		0			0
$836$	0.305561	+	0.457304i	0.0105680	+	0.0158162i
$837$		−	28.4137i		−	0.982121i
$838$	−11.0978	+	7.41531i	−0.383367	+	0.256158i
$839$	−14.2297	−	9.50797i	−0.491263	−	0.328252i	0.285142	−	0.958485i	$-0.407959\pi$
$839$	−14.2297	−	9.50797i	−0.491263	−	0.328252i	−0.776406	+	0.630234i	$0.782959\pi$
$840$		0			0
$841$	18.3742	+	7.61082i	0.633591	+	0.262442i
$842$	−7.78970	−	18.8060i	−0.268451	−	0.648098i
$843$	1.22249	+	0.816840i	0.0421047	+	0.0281335i
$844$	−4.66645	+	6.98384i	−0.160626	+	0.240394i
$845$		0			0
$846$	37.1139	+	37.1139i	1.27600	+	1.27600i
$847$	−2.16544	+	10.8864i	−0.0744054	+	0.374061i
$848$	11.5237	+	4.77327i	0.395725	+	0.163915i
$849$	−90.7465			−3.11441
$850$		0			0
$851$	18.0431			0.618508
$852$	−14.3111	−	5.92784i	−0.490289	−	0.203084i
$853$	8.43242	−	42.3926i	0.288721	−	1.45150i	−0.515359	−	0.856974i	$-0.672341\pi$
$853$	8.43242	−	42.3926i	0.288721	−	1.45150i	0.804079	−	0.594522i	$-0.202659\pi$
$854$	1.50842	+	1.50842i	0.0516171	+	0.0516171i
$855$		0			0
$856$	−6.51964	+	9.75732i	−0.222837	+	0.333498i
$857$	−19.2685	−	12.8748i	−0.658201	−	0.439796i	0.181099	−	0.983465i	$-0.442035\pi$
$857$	−19.2685	−	12.8748i	−0.658201	−	0.439796i	−0.839300	+	0.543669i	$0.817035\pi$
$858$	5.78891	+	13.9757i	0.197630	+	0.477122i
$859$	−38.0926	−	15.7785i	−1.29970	−	0.538354i	−0.377839	−	0.925871i	$-0.623333\pi$
$859$	−38.0926	−	15.7785i	−1.29970	−	0.538354i	−0.921862	+	0.387517i	$0.873333\pi$
$860$		0			0
$861$	28.3141	+	18.9189i	0.964941	+	0.644753i
$862$	17.3044	−	11.5624i	0.589390	−	0.393818i
$863$			13.6290i			0.463935i	0.972724	+	0.231968i	$0.0745163\pi$
$863$			13.6290i			0.463935i	−0.972724	+	0.231968i	$0.925484\pi$
$864$	10.6049	+	15.8713i	0.360786	+	0.539954i
$865$		0			0
$866$		−	6.49518i		−	0.220715i
$867$	34.5614	+	46.4646i	1.17377	+	1.57802i
$868$	1.16887	+	1.16887i	0.0396740	+	0.0396740i
$869$	−4.85080	+	2.00927i	−0.164552	+	0.0681597i
$870$		0			0
$871$	−2.52029	+	2.52029i	−0.0853968	+	0.0853968i
$872$	5.33646	+	7.98657i	0.180715	+	0.270459i
$873$	57.1086	−	11.3596i	1.93283	−	0.384464i
$874$	−1.68143	+	0.334458i	−0.0568753	+	0.0113132i
$875$		0			0
$876$	−2.37828	+	5.74167i	−0.0803546	+	0.193993i
$877$	25.8203	−	38.6429i	0.871891	−	1.30488i	−0.0794822	−	0.996836i	$-0.525327\pi$
$877$	25.8203	−	38.6429i	0.871891	−	1.30488i	0.951373	−	0.308041i	$-0.0996733\pi$
$878$	3.52932	+	17.7431i	0.119109	+	0.598801i
$879$	4.88208	−	24.5439i	0.164668	−	0.827844i
$880$		0			0
$881$	4.84417	−	3.23677i	0.163204	−	0.109050i	−0.471286	−	0.881980i	$-0.656210\pi$
$881$	4.84417	−	3.23677i	0.163204	−	0.109050i	0.634490	+	0.772931i	$0.281210\pi$
$882$	18.9870	−	45.8386i	0.639324	−	1.54346i
$883$	−0.724623	+	0.724623i	−0.0243855	+	0.0243855i	−0.719194	−	0.694809i	$-0.755489\pi$
$883$	−0.724623	+	0.724623i	−0.0243855	+	0.0243855i	0.694809	+	0.719194i	$0.255489\pi$
$884$	17.0464	+	6.56184i	0.573333	+	0.220699i
$885$		0			0
$886$	−14.1811	−	34.2361i	−0.476422	−	1.15018i
$887$	43.8506	+	8.72243i	1.47236	+	0.292871i	0.865087	−	0.501622i	$-0.167263\pi$
$887$	43.8506	+	8.72243i	1.47236	+	0.292871i	0.607273	+	0.794493i	$0.292263\pi$
$888$	19.6704			0.660096
$889$	10.9995	+	2.18794i	0.368913	+	0.0733813i
$890$		0			0
$891$	−7.66828	−	38.5511i	−0.256897	−	1.29151i
$892$	−18.2576	+	7.56256i	−0.611311	+	0.253213i
$893$	−3.09241	+	1.28092i	−0.103484	+	0.0428643i
$894$	11.2714	+	56.6650i	0.376971	+	1.89516i
$895$		0			0
$896$	−1.08917	−	0.216649i	−0.0363865	−	0.00723772i
$897$	−47.1524			−1.57437
$898$	−31.4989	−	6.26553i	−1.05113	−	0.209083i
$899$	−1.71951	−	4.15128i	−0.0573490	−	0.138453i
$900$		0			0
$901$	−51.4117	+	1.29807i	−1.71277	+	0.0432449i
$902$	6.38072	−	6.38072i	0.212455	−	0.212455i
$903$	−0.273180	+	0.659514i	−0.00909085	+	0.0219473i
$904$	−4.70769	+	3.14558i	−0.156575	+	0.104620i
$905$		0			0
$906$	−7.45581	+	37.4829i	−0.247703	+	1.24528i
$907$	6.61375	+	33.2496i	0.219606	+	1.10403i	0.920492	+	0.390761i	$0.127788\pi$
$907$	6.61375	+	33.2496i	0.219606	+	1.10403i	−0.700886	+	0.713273i	$0.747212\pi$
$908$	3.05273	−	4.56874i	0.101309	−	0.151619i
$909$	1.12818	−	2.72367i	0.0374194	−	0.0903383i
$910$		0			0
$911$	−20.1173	+	4.00159i	−0.666517	+	0.132578i	−0.516741	−	0.856142i	$-0.672855\pi$
$911$	−20.1173	+	4.00159i	−0.666517	+	0.132578i	−0.149776	+	0.988720i	$0.547855\pi$
$912$	−1.83309	+	0.364624i	−0.0606996	+	0.0120739i
$913$	−6.70776	−	10.0389i	−0.221995	−	0.332238i
$914$	−17.5785	+	17.5785i	−0.581446	+	0.581446i
$915$		0			0
$916$	3.21137	−	1.33019i	0.106107	−	0.0439508i
$917$	2.46965	+	2.46965i	0.0815550	+	0.0815550i
$918$	−66.5220	−	42.0595i	−2.19555	−	1.38817i
$919$			12.2300i			0.403430i	0.979444	+	0.201715i	$0.0646515\pi$
$919$			12.2300i			0.403430i	−0.979444	+	0.201715i	$0.935348\pi$
$920$		0			0
$921$	−27.2192	−	40.7365i	−0.896905	−	1.34231i
$922$		−	12.8689i		−	0.423814i
$923$	16.7502	−	11.1921i	0.551339	−	0.368393i
$924$	3.15290	+	2.10670i	0.103723	+	0.0693054i
$925$		0			0
$926$	−24.8855	−	10.3079i	−0.817787	−	0.338738i
$927$	−35.7279	−	86.2549i	−1.17346	−	2.83298i
$928$	2.50988	+	1.67705i	0.0823907	+	0.0550517i
$929$	13.7243	−	20.5398i	0.450279	−	0.673890i	−0.534999	−	0.844853i	$-0.679688\pi$
$929$	13.7243	−	20.5398i	0.450279	−	0.673890i	0.985277	+	0.170963i	$0.0546879\pi$
$930$		0			0
$931$	2.23733	+	2.23733i	0.0733256	+	0.0733256i
$932$	2.36203	−	11.8747i	0.0773708	−	0.388969i
$933$	−82.9830	−	34.3727i	−2.71674	−	1.12531i
$934$	−11.9613			−0.391386
$935$		0			0
$936$	−38.1150			−1.24583
$937$	−40.7645	−	16.8852i	−1.33172	−	0.551615i	−0.400573	−	0.916265i	$-0.631189\pi$
$937$	−40.7645	−	16.8852i	−1.33172	−	0.551615i	−0.931145	+	0.364650i	$0.881189\pi$
$938$	−0.174304	+	0.876287i	−0.00569124	+	0.0286118i
$939$	55.4863	+	55.4863i	1.81073	+	1.81073i
$940$		0			0
$941$	21.3969	−	32.0227i	0.697518	−	1.04391i	−0.298469	−	0.954419i	$-0.596476\pi$
$941$	21.3969	−	32.0227i	0.697518	−	1.04391i	0.995988	−	0.0894907i	$-0.0285239\pi$
$942$	21.0277	+	14.0503i	0.685120	+	0.457783i
$943$	10.7639	+	25.9865i	0.350522	+	0.846236i
$944$	−11.0496	−	4.57691i	−0.359635	−	0.148966i
$945$		0			0
$946$	0.157284	+	0.105094i	0.00511374	+	0.00341689i
$947$	−5.18781	+	3.46639i	−0.168581	+	0.112642i	−0.636999	−	0.770865i	$-0.719824\pi$
$947$	−5.18781	+	3.46639i	−0.168581	+	0.112642i	0.468417	+	0.883507i	$0.344824\pi$
$948$		−	17.8422i		−	0.579488i
$949$	−4.49033	−	6.72026i	−0.145762	−	0.218149i
$950$		0			0
$951$			66.5554i			2.15821i
$952$	4.46677	−	1.00633i	0.144769	−	0.0326153i
$953$	−36.0165	−	36.0165i	−1.16669	−	1.16669i	−0.982981	−	0.183710i	$-0.941189\pi$
$953$	−36.0165	−	36.0165i	−1.16669	−	1.16669i	−0.183710	−	0.982981i	$-0.558811\pi$
$954$	99.1456	−	41.0675i	3.20996	−	1.32961i
$955$		0			0
$956$	−10.0546	+	10.0546i	−0.325190	+	0.325190i
$957$	−5.72649	−	8.57030i	−0.185111	−	0.277038i
$958$	28.1328	−	5.59595i	0.908928	−	0.180797i
$959$	−3.99070	+	0.793799i	−0.128866	+	0.0256331i
$960$		0			0
$961$	−11.0153	+	26.5932i	−0.355331	+	0.857845i
$962$	−14.2125	+	21.2704i	−0.458228	+	0.685787i
$963$	19.6971	+	99.0240i	0.634730	+	3.19100i
$964$	1.00841	−	5.06964i	0.0324788	−	0.163282i
$965$		0			0
$966$	−9.82782	+	6.56674i	−0.316205	+	0.211281i
$967$	−18.7746	+	45.3258i	−0.603749	+	1.45758i	0.265945	+	0.963988i	$0.414316\pi$
$967$	−18.7746	+	45.3258i	−0.603749	+	1.45758i	−0.869694	+	0.493591i	$0.835684\pi$
$968$	−7.06765	+	7.06765i	−0.227163	+	0.227163i
$969$	6.29728	−	4.44163i	0.202298	−	0.142686i
$970$		0			0
$971$	−14.8579	−	35.8702i	−0.476813	−	1.15113i	−0.961095	−	0.276217i	$-0.910919\pi$
$971$	−14.8579	−	35.8702i	−0.476813	−	1.15113i	0.484282	−	0.874912i	$-0.339081\pi$
$972$	74.8401	+	14.8866i	2.40050	+	0.477489i
$973$	13.0785			0.419277
$974$	−33.0161	−	6.56730i	−1.05790	−	0.210430i
$975$		0			0
$976$	0.374760	+	1.88405i	0.0119958	+	0.0603068i
$977$	−46.2485	+	19.1568i	−1.47962	+	0.612879i	−0.969030	−	0.246944i	$-0.920573\pi$
$977$	−46.2485	+	19.1568i	−1.47962	+	0.612879i	−0.510591	+	0.859824i	$0.670573\pi$
$978$	49.5907	−	20.5412i	1.58574	−	0.656834i
$979$	1.36981	+	6.88651i	0.0437794	+	0.220094i
$980$		0			0
$981$	81.0532	+	16.1225i	2.58783	+	0.514751i
$982$	−12.5339			−0.399973
$983$	−21.4426	−	4.26520i	−0.683913	−	0.136039i	−0.159108	−	0.987261i	$-0.550862\pi$
$983$	−21.4426	−	4.26520i	−0.683913	−	0.136039i	−0.524805	+	0.851222i	$0.675862\pi$
$984$	11.7348	+	28.3303i	0.374091	+	0.903136i
$985$		0			0
$986$	−12.2643	−	2.11922i	−0.390574	−	0.0674896i
$987$	−16.3182	+	16.3182i	−0.519413	+	0.519413i
$988$	0.930177	−	2.24565i	0.0295929	−	0.0714435i
$989$	−0.490265	+	0.327585i	−0.0155895	+	0.0104166i
$990$		0			0
$991$	6.75639	−	33.9667i	0.214624	−	1.07899i	−0.711765	−	0.702418i	$-0.752104\pi$
$991$	6.75639	−	33.9667i	0.214624	−	1.07899i	0.926389	−	0.376569i	$-0.122896\pi$
$992$	0.290400	+	1.45994i	0.00922020	+	0.0463531i
$993$	29.3389	−	43.9087i	0.931041	−	1.39340i
$994$	1.93250	−	4.66547i	0.0612952	−	0.147980i
$995$		0			0
$996$	40.2405	−	8.00433i	1.27507	−	0.253627i
$997$	36.1262	−	7.18595i	1.14413	−	0.227581i	0.413597	−	0.910460i	$-0.364272\pi$
$997$	36.1262	−	7.18595i	1.14413	−	0.227581i	0.730532	+	0.682879i	$0.239272\pi$
$998$	−3.63466	−	5.43966i	−0.115053	−	0.172189i
$999$	77.9415	−	77.9415i	2.46596	−	2.46596i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	850.2.s.d.243.5		40
5.2	odd	4		850.2.v.d.107.1		40
5.3	odd	4		170.2.r.b.107.5	yes	40
5.4	even	2		170.2.o.b.73.1	yes	40
17.7	odd	16		850.2.v.d.143.1		40
85.7	even	16	inner	850.2.s.d.7.5		40
85.24	odd	16		170.2.r.b.143.5	yes	40
85.58	even	16		170.2.o.b.7.1	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.2.o.b.7.1	✓	40	85.58	even	16
170.2.o.b.73.1	yes	40	5.4	even	2
170.2.r.b.107.5	yes	40	5.3	odd	4
170.2.r.b.143.5	yes	40	85.24	odd	16
850.2.s.d.7.5		40	85.7	even	16	inner
850.2.s.d.243.5		40	1.1	even	1	trivial
850.2.v.d.107.1		40	5.2	odd	4
850.2.v.d.143.1		40	17.7	odd	16

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 850 = 2 \cdot 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	850.s (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.923880 - 0.382683i) q^{2} +(0.664558 - 3.34096i) q^{3} +(0.707107 + 0.707107i) q^{4} +(-1.89250 + 2.83233i) q^{6} +(-0.923351 - 0.616963i) q^{7} +(-0.382683 - 0.923880i) q^{8} +(-7.94873 - 3.29247i) q^{9} +O(q^{10})\)	\(q+(-0.923880 - 0.382683i) q^{2} +(0.664558 - 3.34096i) q^{3} +(0.707107 + 0.707107i) q^{4} +(-1.89250 + 2.83233i) q^{6} +(-0.923351 - 0.616963i) q^{7} +(-0.382683 - 0.923880i) q^{8} +(-7.94873 - 3.29247i) q^{9} +(-0.833476 - 0.556911i) q^{11} +(2.83233 - 1.89250i) q^{12} +4.43010i q^{13} +(0.616963 + 0.923351i) q^{14} +1.00000i q^{16} +(-1.67349 - 3.76821i) q^{17} +(6.08369 + 6.08369i) q^{18} +(-0.506906 + 0.209967i) q^{19} +(-2.67487 + 2.67487i) q^{21} +(0.556911 + 0.833476i) q^{22} +(-3.06456 + 0.609578i) q^{23} +(-3.34096 + 0.664558i) q^{24} +(1.69533 - 4.09288i) q^{26} +(-10.6049 + 15.8713i) q^{27} +(-0.216649 - 1.08917i) q^{28} +(-0.588900 + 2.96060i) q^{29} +(-1.23768 + 0.826988i) q^{31} +(0.382683 - 0.923880i) q^{32} +(-2.41451 + 2.41451i) q^{33} +(0.104069 + 4.12179i) q^{34} +(-3.29247 - 7.94873i) q^{36} +(-5.66357 - 1.12655i) q^{37} +0.548671 q^{38} +(14.8008 + 2.94406i) q^{39} +(-1.75620 - 8.82901i) q^{41} +(3.49488 - 1.44763i) q^{42} +(0.174344 - 0.0722156i) q^{43} +(-0.195561 - 0.983152i) q^{44} +(3.06456 + 0.609578i) q^{46} +6.10055 q^{47} +(3.34096 + 0.664558i) q^{48} +(-2.20685 - 5.32781i) q^{49} +(-13.7016 + 3.08686i) q^{51} +(-3.13255 + 3.13255i) q^{52} +(4.77327 - 11.5237i) q^{53} +(15.8713 - 10.6049i) q^{54} +(-0.216649 + 1.08917i) q^{56} +(0.364624 + 1.83309i) q^{57} +(1.67705 - 2.50988i) q^{58} +(-4.57691 + 11.0496i) q^{59} +(1.88405 - 0.374760i) q^{61} +(1.45994 - 0.290400i) q^{62} +(5.30813 + 7.94418i) q^{63} +(-0.707107 + 0.707107i) q^{64} +(3.15471 - 1.30672i) q^{66} +(0.568902 + 0.568902i) q^{67} +(1.48119 - 3.84786i) q^{68} +10.6437i q^{69} +(-2.52638 - 3.78099i) q^{71} +8.60364i q^{72} +(-1.51695 + 1.01360i) q^{73} +(4.80134 + 3.20816i) q^{74} +(-0.506906 - 0.209967i) q^{76} +(0.425997 + 1.02845i) q^{77} +(-12.5475 - 8.38397i) q^{78} +(2.90998 - 4.35510i) q^{79} +(27.7269 + 27.7269i) q^{81} +(-1.75620 + 8.82901i) q^{82} +(11.1278 + 4.60927i) q^{83} -3.78284 q^{84} -0.188708 q^{86} +(9.49989 + 3.93498i) q^{87} +(-0.195561 + 0.983152i) q^{88} +(-4.95294 - 4.95294i) q^{89} +(2.73321 - 4.09054i) q^{91} +(-2.59800 - 1.73593i) q^{92} +(1.94043 + 4.68460i) q^{93} +(-5.63618 - 2.33458i) q^{94} +(-2.83233 - 1.89250i) q^{96} +(-5.62719 + 3.75997i) q^{97} +5.76678i q^{98} +(4.79146 + 7.17093i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q+O(q^{10}) \) 40 * q	\( 40 q + 16 q^{18} - 8 q^{26} - 24 q^{27} - 8 q^{28} - 8 q^{29} - 16 q^{31} - 32 q^{33} - 8 q^{34} - 16 q^{37} + 32 q^{39} - 56 q^{41} + 8 q^{42} + 48 q^{43} - 16 q^{44} + 96 q^{47} - 16 q^{49} - 32 q^{51} + 16 q^{52} + 40 q^{53} + 24 q^{54} - 8 q^{56} + 8 q^{57} - 16 q^{58} + 24 q^{61} + 24 q^{62} + 24 q^{63} + 16 q^{67} - 24 q^{68} + 24 q^{71} - 16 q^{73} - 32 q^{74} - 40 q^{77} - 16 q^{78} + 104 q^{79} + 48 q^{81} - 56 q^{82} - 16 q^{83} + 96 q^{86} + 8 q^{87} - 16 q^{88} + 16 q^{89} + 48 q^{91} - 8 q^{92} - 136 q^{93} + 8 q^{94} - 144 q^{97} - 160 q^{99}+O(q^{100}) \) 40 * q + 16 * q^18 - 8 * q^26 - 24 * q^27 - 8 * q^28 - 8 * q^29 - 16 * q^31 - 32 * q^33 - 8 * q^34 - 16 * q^37 + 32 * q^39 - 56 * q^41 + 8 * q^42 + 48 * q^43 - 16 * q^44 + 96 * q^47 - 16 * q^49 - 32 * q^51 + 16 * q^52 + 40 * q^53 + 24 * q^54 - 8 * q^56 + 8 * q^57 - 16 * q^58 + 24 * q^61 + 24 * q^62 + 24 * q^63 + 16 * q^67 - 24 * q^68 + 24 * q^71 - 16 * q^73 - 32 * q^74 - 40 * q^77 - 16 * q^78 + 104 * q^79 + 48 * q^81 - 56 * q^82 - 16 * q^83 + 96 * q^86 + 8 * q^87 - 16 * q^88 + 16 * q^89 + 48 * q^91 - 8 * q^92 - 136 * q^93 + 8 * q^94 - 144 * q^97 - 160 * q^99

Introduction

L-functions

Modular forms

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