LMFDB - Embedded newform 891.2.n.g.136.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [891,2,Mod(136,891)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(891, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 6]))

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

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

chi := DirichletCharacter("891.136");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$891 = 3^{4} \cdot 11$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	891.n (of order $15$ , degree $8$ , not 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:	$7.11467082010$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 297)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			136.2
Character	$\chi$	$=$	891.136
Dual form			891.2.n.g.190.2

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.974523 + 0.433886i) q^{2} +(-0.576823 + 0.640627i) q^{4} +(-1.12149 - 0.499319i) q^{5} +(1.49928 + 0.318682i) q^{7} +(0.943455 - 2.90366i) q^{8} +1.30957 q^{10} +(-2.72022 + 1.89748i) q^{11} +(-0.244819 + 2.32930i) q^{13} +(-1.59935 + 0.339953i) q^{14} +(0.160219 + 1.52438i) q^{16} +(2.87322 - 2.08752i) q^{17} +(-0.884422 + 2.72197i) q^{19} +(0.966779 - 0.430438i) q^{20} +(1.82763 - 3.02940i) q^{22} +(-1.14719 - 1.98698i) q^{23} +(-2.33723 - 2.59576i) q^{25} +(-0.772068 - 2.37618i) q^{26} +(-1.06898 + 0.776656i) q^{28} +(-8.11142 - 1.72414i) q^{29} +(-0.505332 + 4.80791i) q^{31} +(2.23554 + 3.87207i) q^{32} +(-1.89428 + 3.28098i) q^{34} +(-1.52230 - 1.10602i) q^{35} +(1.24401 + 3.82868i) q^{37} +(-0.319134 - 3.03636i) q^{38} +(-2.50793 + 2.78534i) q^{40} +(-4.73479 + 1.00641i) q^{41} +(3.76241 - 6.51669i) q^{43} +(0.353510 - 2.83715i) q^{44} +(1.98008 + 1.43861i) q^{46} +(-6.12307 - 6.80035i) q^{47} +(-4.24853 - 1.89157i) q^{49} +(3.40395 + 1.51554i) q^{50} +(-1.35100 - 1.50043i) q^{52} +(-5.00934 - 3.63950i) q^{53} +(3.99814 - 0.769743i) q^{55} +(2.33985 - 4.05273i) q^{56} +(8.65285 - 1.83922i) q^{58} +(7.28368 - 8.08935i) q^{59} +(0.0640888 + 0.609764i) q^{61} +(-1.59363 - 4.90467i) q^{62} +(-6.33871 - 4.60534i) q^{64} +(1.43763 - 2.49004i) q^{65} +(-4.32982 - 7.49947i) q^{67} +(-0.320020 + 3.04479i) q^{68} +(1.96341 + 0.417335i) q^{70} +(-12.6352 + 9.18000i) q^{71} +(-4.68358 - 14.4146i) q^{73} +(-2.87353 - 3.19138i) q^{74} +(-1.23361 - 2.13668i) q^{76} +(-4.68306 + 1.97797i) q^{77} +(-1.77447 + 0.790044i) q^{79} +(0.581468 - 1.78958i) q^{80} +(4.17749 - 3.03513i) q^{82} +(0.557528 + 5.30452i) q^{83} +(-4.26463 + 0.906474i) q^{85} +(-0.839060 + 7.98312i) q^{86} +(2.94322 + 9.68876i) q^{88} +5.84063 q^{89} +(-1.10936 + 3.41426i) q^{91} +(1.93464 + 0.411220i) q^{92} +(8.91764 + 3.97039i) q^{94} +(2.35100 - 2.61105i) q^{95} +(-7.77043 + 3.45962i) q^{97} +4.96102 q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$32 q - 2 q^{4} - 8 q^{7} - 24 q^{10} - 8 q^{13} + 2 q^{16} + 20 q^{19} + 24 q^{22} + 16 q^{25} - 60 q^{28} + 6 q^{31} - 32 q^{34} + 24 q^{37} + 40 q^{40} + 80 q^{43} - 24 q^{46} - 40 q^{49} - 12 q^{52}+ \cdots + 46 q^{94}+O(q^{100})$ 32 * q - 2 * q^4 - 8 * q^7 - 24 * q^10 - 8 * q^13 + 2 * q^16 + 20 * q^19 + 24 * q^22 + 16 * q^25 - 60 * q^28 + 6 * q^31 - 32 * q^34 + 24 * q^37 + 40 * q^40 + 80 * q^43 - 24 * q^46 - 40 * q^49 - 12 * q^52 + 112 * q^55 + 50 * q^58 + 6 * q^61 + 12 * q^64 - 64 * q^67 - 74 * q^70 - 64 * q^73 - 52 * q^76 + 4 * q^79 + 8 * q^82 - 70 * q^85 - 56 * q^88 - 188 * q^91 + 46 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/891\mathbb{Z}\right)^\times$ .

$n$	$244$	$650$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{3}\right)$

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

)

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

$2$	−0.974523	+	0.433886i	−0.689092	+	0.306803i	−0.721245	−	0.692680i	$-0.756430\pi$
$2$	−0.974523	+	0.433886i	−0.689092	+	0.306803i	0.0321538	+	0.999483i	$0.489763\pi$
$3$		0			0
$3$		0			0
$4$	−0.576823	+	0.640627i	−0.288412	+	0.320313i
$5$	−1.12149	−	0.499319i	−0.501546	−	0.223302i	0.140339	−	0.990103i	$-0.455181\pi$
$5$	−1.12149	−	0.499319i	−0.501546	−	0.223302i	−0.641885	+	0.766801i	$0.721847\pi$
$6$		0			0
$7$	1.49928	+	0.318682i	0.566675	+	0.120450i	0.482335	−	0.875987i	$-0.339789\pi$
$7$	1.49928	+	0.318682i	0.566675	+	0.120450i	0.0843394	+	0.996437i	$0.473122\pi$
$8$	0.943455	−	2.90366i	0.333562	−	1.02660i
$9$		0			0
$10$	1.30957			0.414121
$11$	−2.72022	+	1.89748i	−0.820176	+	0.572111i
$11$	−2.72022	+	1.89748i	−0.820176	+	0.572111i
$12$		0			0
$13$	−0.244819	+	2.32930i	−0.0679007	+	0.646032i	0.906653	+	0.421877i	$0.138629\pi$
$13$	−0.244819	+	2.32930i	−0.0679007	+	0.646032i	−0.974554	+	0.224154i	$0.928038\pi$
$14$	−1.59935	+	0.339953i	−0.427445	+	0.0908563i
$15$		0			0
$16$	0.160219	+	1.52438i	0.0400547	+	0.381095i
$17$	2.87322	−	2.08752i	0.696858	−	0.506297i	−0.182049	−	0.983289i	$-0.558273\pi$
$17$	2.87322	−	2.08752i	0.696858	−	0.506297i	0.878908	+	0.476992i	$0.158273\pi$
$18$		0			0
$19$	−0.884422	+	2.72197i	−0.202900	+	0.624463i	0.796893	+	0.604121i	$0.206476\pi$
$19$	−0.884422	+	2.72197i	−0.202900	+	0.624463i	−0.999793	+	0.0203420i	$0.993524\pi$
$20$	0.966779	−	0.430438i	0.216178	−	0.0962488i
$21$		0			0
$22$	1.82763	−	3.02940i	0.389651	−	0.645870i
$23$	−1.14719	−	1.98698i	−0.239205	−	0.414315i	0.721282	−	0.692642i	$-0.243553\pi$
$23$	−1.14719	−	1.98698i	−0.239205	−	0.414315i	−0.960486	+	0.278327i	$0.910220\pi$
$24$		0			0
$25$	−2.33723	−	2.59576i	−0.467447	−	0.519152i
$26$	−0.772068	−	2.37618i	−0.151415	−	0.466007i
$27$		0			0
$28$	−1.06898	+	0.776656i	−0.202017	+	0.146774i
$29$	−8.11142	−	1.72414i	−1.50625	−	0.320164i	−0.620458	−	0.784240i	$-0.713053\pi$
$29$	−8.11142	−	1.72414i	−1.50625	−	0.320164i	−0.885796	+	0.464076i	$0.846387\pi$
$30$		0			0
$31$	−0.505332	+	4.80791i	−0.0907603	+	0.863526i	0.850530	+	0.525927i	$0.176282\pi$
$31$	−0.505332	+	4.80791i	−0.0907603	+	0.863526i	−0.941290	+	0.337599i	$0.890385\pi$
$32$	2.23554	+	3.87207i	0.395192	+	0.684492i
$33$		0			0
$34$	−1.89428	+	3.28098i	−0.324866	+	0.562684i
$35$	−1.52230	−	1.10602i	−0.257316	−	0.186951i
$36$		0			0
$37$	1.24401	+	3.82868i	0.204515	+	0.629432i	0.999733	+	0.0231083i	$0.00735626\pi$
$37$	1.24401	+	3.82868i	0.204515	+	0.629432i	−0.795218	+	0.606323i	$0.792644\pi$
$38$	−0.319134	−	3.03636i	−0.0517704	−	0.492563i
$39$		0			0
$40$	−2.50793	+	2.78534i	−0.396538	+	0.440400i
$41$	−4.73479	+	1.00641i	−0.739450	+	0.157175i	−0.562212	−	0.826993i	$-0.690050\pi$
$41$	−4.73479	+	1.00641i	−0.739450	+	0.157175i	−0.177238	+	0.984168i	$0.556716\pi$
$42$		0			0
$43$	3.76241	−	6.51669i	0.573763	−	0.993786i	−0.422412	−	0.906404i	$-0.638816\pi$
$43$	3.76241	−	6.51669i	0.573763	−	0.993786i	0.996175	−	0.0873824i	$-0.0278502\pi$
$44$	0.353510	−	2.83715i	0.0532936	−	0.427717i
$45$		0			0
$46$	1.98008	+	1.43861i	0.291947	+	0.212112i
$47$	−6.12307	−	6.80035i	−0.893141	−	0.991933i	0.106856	−	0.994274i	$-0.465921\pi$
$47$	−6.12307	−	6.80035i	−0.893141	−	0.991933i	−0.999997	+	0.00234105i	$0.999255\pi$
$48$		0			0
$49$	−4.24853	−	1.89157i	−0.606933	−	0.270224i
$50$	3.40395	+	1.51554i	0.481391	+	0.214329i
$51$		0			0
$52$	−1.35100	−	1.50043i	−0.187349	−	0.208073i
$53$	−5.00934	−	3.63950i	−0.688085	−	0.499923i	0.187945	−	0.982180i	$-0.439817\pi$
$53$	−5.00934	−	3.63950i	−0.688085	−	0.499923i	−0.876030	+	0.482256i	$0.839817\pi$
$54$		0			0
$55$	3.99814	−	0.769743i	0.539110	−	0.103792i
$56$	2.33985	−	4.05273i	0.312675	−	0.541569i
$57$		0			0
$58$	8.65285	−	1.83922i	1.13617	−	0.241501i
$59$	7.28368	−	8.08935i	0.948254	−	1.05314i	−0.0502645	−	0.998736i	$-0.516006\pi$
$59$	7.28368	−	8.08935i	0.948254	−	1.05314i	0.998519	−	0.0544072i	$-0.0173269\pi$
$60$		0			0
$61$	0.0640888	+	0.609764i	0.00820573	+	0.0780723i	0.997858	−	0.0654118i	$-0.0208361\pi$
$61$	0.0640888	+	0.609764i	0.00820573	+	0.0780723i	−0.989653	+	0.143484i	$0.954169\pi$
$62$	−1.59363	−	4.90467i	−0.202391	−	0.622894i
$63$		0			0
$64$	−6.33871	−	4.60534i	−0.792338	−	0.575667i
$65$	1.43763	−	2.49004i	0.178316	−	0.308852i
$66$		0			0
$67$	−4.32982	−	7.49947i	−0.528972	−	0.916206i	−0.999429	−	0.0337834i	$-0.989244\pi$
$67$	−4.32982	−	7.49947i	−0.528972	−	0.916206i	0.470457	−	0.882423i	$-0.344089\pi$
$68$	−0.320020	+	3.04479i	−0.0388082	+	0.369235i
$69$		0			0
$70$	1.96341	+	0.417335i	0.234672	+	0.0498810i
$71$	−12.6352	+	9.18000i	−1.49952	+	1.08947i	−0.528950	+	0.848653i	$0.677414\pi$
$71$	−12.6352	+	9.18000i	−1.49952	+	1.08947i	−0.970572	+	0.240813i	$0.922586\pi$
$72$		0			0
$73$	−4.68358	−	14.4146i	−0.548172	−	1.68710i	−0.713326	−	0.700832i	$-0.752812\pi$
$73$	−4.68358	−	14.4146i	−0.548172	−	1.68710i	0.165154	−	0.986268i	$-0.447188\pi$
$74$	−2.87353	−	3.19138i	−0.334041	−	0.370990i
$75$		0			0
$76$	−1.23361	−	2.13668i	−0.141505	−	0.245094i
$77$	−4.68306	+	1.97797i	−0.533684	+	0.225410i
$78$		0			0
$79$	−1.77447	+	0.790044i	−0.199643	+	0.0888869i	−0.504123	−	0.863632i	$-0.668184\pi$
$79$	−1.77447	+	0.790044i	−0.199643	+	0.0888869i	0.304480	+	0.952519i	$0.401517\pi$
$80$	0.581468	−	1.78958i	0.0650101	−	0.200081i
$81$		0			0
$82$	4.17749	−	3.03513i	0.461327	−	0.335174i
$83$	0.557528	+	5.30452i	0.0611966	+	0.582247i	0.981556	+	0.191174i	$0.0612294\pi$
$83$	0.557528	+	5.30452i	0.0611966	+	0.582247i	−0.920360	+	0.391073i	$0.872104\pi$
$84$		0			0
$85$	−4.26463	+	0.906474i	−0.462564	+	0.0983209i
$86$	−0.839060	+	7.98312i	−0.0904782	+	0.860842i
$87$		0			0
$88$	2.94322	+	9.68876i	0.313748	+	1.03283i
$89$	5.84063			0.619105			0.309553	−	0.950882i	$-0.399821\pi$
$89$	5.84063			0.619105			0.309553	+	0.950882i	$0.399821\pi$
$90$		0			0
$91$	−1.10936	+	3.41426i	−0.116292	+	0.357911i
$92$	1.93464	+	0.411220i	0.201700	+	0.0428727i
$93$		0			0
$94$	8.91764	+	3.97039i	0.919785	+	0.409514i
$95$	2.35100	−	2.61105i	0.241208	−	0.267888i
$96$		0			0
$97$	−7.77043	+	3.45962i	−0.788968	+	0.351271i	−0.761345	−	0.648347i	$-0.775461\pi$
$97$	−7.77043	+	3.45962i	−0.788968	+	0.351271i	−0.0276232	+	0.999618i	$0.508794\pi$
$98$	4.96102			0.501139
$99$		0			0
$100$	3.01108			0.301108
$101$	−0.685375	+	0.305149i	−0.0681973	+	0.0303634i	−0.440552	−	0.897727i	$-0.645217\pi$
$101$	−0.685375	+	0.305149i	−0.0681973	+	0.0303634i	0.372355	+	0.928091i	$0.378551\pi$
$102$		0			0
$103$	7.23084	−	8.03066i	0.712476	−	0.791285i	−0.272834	−	0.962061i	$-0.587961\pi$
$103$	7.23084	−	8.03066i	0.712476	−	0.791285i	0.985310	+	0.170777i	$0.0546276\pi$
$104$	6.53251	+	2.90846i	0.640566	+	0.285198i
$105$		0			0
$106$	6.46084	+	1.37329i	0.627532	+	0.133386i
$107$	−1.23326	+	3.79558i	−0.119224	+	0.366932i	−0.992804	−	0.119747i	$-0.961792\pi$
$107$	−1.23326	+	3.79558i	−0.119224	+	0.366932i	0.873581	+	0.486679i	$0.161792\pi$
$108$		0			0
$109$	−13.1110			−1.25580			−0.627902	−	0.778293i	$-0.716086\pi$
$109$	−13.1110			−1.25580			−0.627902	+	0.778293i	$0.716086\pi$
$110$	−3.56230	+	2.48487i	−0.339652	+	0.236923i
$111$		0			0
$112$	−0.245579	+	2.33653i	−0.0232051	+	0.220781i
$113$	−2.23469	+	0.474998i	−0.210222	+	0.0446841i	−0.311819	−	0.950142i	$-0.600938\pi$
$113$	−2.23469	+	0.474998i	−0.210222	+	0.0446841i	0.101597	+	0.994826i	$0.467605\pi$
$114$		0			0
$115$	0.294417	+	2.80120i	0.0274546	+	0.261213i
$116$	5.78338	−	4.20187i	0.536974	−	0.390134i
$117$		0			0
$118$	−3.58826	+	11.0435i	−0.330326	+	1.01664i
$119$	4.97302	−	2.21413i	0.455876	−	0.202969i
$120$		0			0
$121$	3.79917	−	10.3231i	0.345379	−	0.938463i
$122$	−0.327024	−	0.566422i	−0.0296073	−	0.0512814i
$123$		0			0
$124$	−2.78859	−	3.09704i	−0.250423	−	0.278123i
$125$	3.22185	+	9.91584i	0.288171	+	0.886900i
$126$		0			0
$127$	−1.28021	+	0.930131i	−0.113601	+	0.0825357i	−0.643135	−	0.765753i	$-0.722367\pi$
$127$	−1.28021	+	0.930131i	−0.113601	+	0.0825357i	0.529534	+	0.848288i	$0.322367\pi$
$128$	−0.571357	−	0.121446i	−0.0505013	−	0.0107344i
$129$		0			0
$130$	−0.320607	+	3.05037i	−0.0281191	+	0.267535i
$131$	−2.82125	−	4.88655i	−0.246494	−	0.426940i	0.716057	−	0.698042i	$-0.245945\pi$
$131$	−2.82125	−	4.88655i	−0.246494	−	0.426940i	−0.962551	+	0.271102i	$0.912612\pi$
$132$		0			0
$133$	−2.19344	+	3.79915i	−0.190195	+	0.329428i
$134$	7.47342	+	5.42976i	0.645605	+	0.469060i
$135$		0			0
$136$	−3.35068	−	10.3123i	−0.287318	−	0.884274i
$137$	2.26293	+	21.5304i	0.193335	+	1.83946i	0.475043	+	0.879963i	$0.342433\pi$
$137$	2.26293	+	21.5304i	0.193335	+	1.83946i	−0.281707	+	0.959500i	$0.590901\pi$
$138$		0			0
$139$	−14.0920	+	15.6507i	−1.19527	+	1.32748i	−0.263397	+	0.964687i	$0.584843\pi$
$139$	−14.0920	+	15.6507i	−1.19527	+	1.32748i	−0.931870	+	0.362792i	$0.881824\pi$
$140$	1.58665	−	0.337252i	0.134096	−	0.0285030i
$141$		0			0
$142$	8.33021	−	14.4283i	0.699056	−	1.21080i
$143$	−3.75383	−	6.80074i	−0.313911	−	0.568707i
$144$		0			0
$145$	8.23599	+	5.98379i	0.683961	+	0.496927i
$146$	10.8185	+	12.0152i	0.895349	+	0.994386i
$147$		0			0
$148$	−3.17033	−	1.41152i	−0.260600	−	0.116027i
$149$	−12.7865	−	5.69292i	−1.04751	−	0.466383i	−0.190505	−	0.981686i	$-0.561012\pi$
$149$	−12.7865	−	5.69292i	−1.04751	−	0.466383i	−0.857008	+	0.515304i	$0.827679\pi$
$150$		0			0
$151$	−14.0296	−	15.5814i	−1.14171	−	1.26800i	−0.958553	−	0.284913i	$-0.908035\pi$
$151$	−14.0296	−	15.5814i	−1.14171	−	1.26800i	−0.183156	−	0.983084i	$-0.558631\pi$
$152$	7.06925	+	5.13611i	0.573392	+	0.416594i
$153$		0			0
$154$	3.70554	−	3.95948i	0.298601	−	0.319064i
$155$	2.96741	−	5.13970i	0.238348	−	0.412831i
$156$		0			0
$157$	17.1274	−	3.64054i	1.36691	−	0.290547i	0.534720	−	0.845029i	$-0.320417\pi$
$157$	17.1274	−	3.64054i	1.36691	−	0.290547i	0.832195	+	0.554483i	$0.187084\pi$
$158$	1.38647	−	1.53983i	0.110302	−	0.122502i
$159$		0			0
$160$	−0.573737	−	5.45874i	−0.0453579	−	0.431551i
$161$	−1.08674	−	3.34463i	−0.0856469	−	0.263594i
$162$		0			0
$163$	−0.154783	−	0.112456i	−0.0121235	−	0.00880824i	0.581707	−	0.813398i	$-0.302385\pi$
$163$	−0.154783	−	0.112456i	−0.0121235	−	0.00880824i	−0.593831	+	0.804590i	$0.702385\pi$
$164$	2.08640	−	3.61376i	0.162921	−	0.282187i
$165$		0			0
$166$	−2.84488	−	4.92747i	−0.220805	−	0.382446i
$167$	−0.100227	+	0.953592i	−0.00775576	+	0.0737912i	−0.997715	−	0.0675609i	$-0.978478\pi$
$167$	−0.100227	+	0.953592i	−0.00775576	+	0.0737912i	0.989959	+	0.141352i	$0.0451450\pi$
$168$		0			0
$169$	7.35021	+	1.56234i	0.565401	+	0.120180i
$170$	3.76267	−	2.73374i	0.288584	−	0.209668i
$171$		0			0
$172$	2.00452	+	6.16928i	0.152843	+	0.470403i
$173$	14.4789	+	16.0805i	1.10081	+	1.22258i	0.973007	+	0.230777i	$0.0741267\pi$
$173$	14.4789	+	16.0805i	1.10081	+	1.22258i	0.127805	+	0.991799i	$0.459207\pi$
$174$		0			0
$175$	−2.67695	−	4.63661i	−0.202358	−	0.350495i
$176$	−3.32830	−	3.84263i	−0.250880	−	0.289649i
$177$		0			0
$178$	−5.69183	+	2.53416i	−0.426620	+	0.189944i
$179$	−6.33539	+	19.4983i	−0.473529	+	1.45737i	0.374402	+	0.927266i	$0.377848\pi$
$179$	−6.33539	+	19.4983i	−0.473529	+	1.45737i	−0.847931	+	0.530106i	$0.822152\pi$
$180$		0			0
$181$	8.43682	−	6.12971i	0.627104	−	0.455618i	−0.228292	−	0.973593i	$-0.573314\pi$
$181$	8.43682	−	6.12971i	0.627104	−	0.455618i	0.855396	+	0.517975i	$0.173314\pi$
$182$	−0.400300	−	3.80860i	−0.0296722	−	0.282313i
$183$		0			0
$184$	−6.85184	+	1.45640i	−0.505124	+	0.107367i
$185$	0.516586	−	4.91499i	0.0379802	−	0.361357i
$186$		0			0
$187$	−3.85477	+	11.1304i	−0.281889	+	0.813933i
$188$	7.88841			0.575322
$189$		0			0
$190$	−1.15821	+	3.56460i	−0.0840252	+	0.258603i
$191$	20.1925	+	4.29206i	1.46108	+	0.310562i	0.868798	−	0.495167i	$-0.164893\pi$
$191$	20.1925	+	4.29206i	1.46108	+	0.310562i	0.592284	+	0.805730i	$0.298227\pi$
$192$		0			0
$193$	−5.47401	−	2.43719i	−0.394028	−	0.175433i	0.200152	−	0.979765i	$-0.435857\pi$
$193$	−5.47401	−	2.43719i	−0.394028	−	0.175433i	−0.594180	+	0.804332i	$0.702523\pi$
$194$	6.07139	−	6.74296i	0.435900	−	0.484116i
$195$		0			0
$196$	3.66244	−	1.63062i	0.261603	−	0.116473i
$197$	1.41800			0.101028			0.0505141	−	0.998723i	$-0.483914\pi$
$197$	1.41800			0.101028			0.0505141	+	0.998723i	$0.483914\pi$
$198$		0			0
$199$	6.07350			0.430539			0.215269	−	0.976555i	$-0.430937\pi$
$199$	6.07350			0.430539			0.215269	+	0.976555i	$0.430937\pi$
$200$	−9.74227	+	4.33754i	−0.688883	+	0.306710i
$201$		0			0
$202$	0.535514	−	0.594748i	0.0376786	−	0.0418464i
$203$	−11.6118	−	5.16993i	−0.814992	−	0.362858i
$204$		0			0
$205$	5.81254	+	1.23549i	0.405965	+	0.0862906i
$206$	−3.56223	+	10.9634i	−0.248192	+	0.763858i
$207$		0			0
$208$	−3.58996			−0.248919
$209$	−2.75905	−	9.08252i	−0.190848	−	0.628251i
$210$		0			0
$211$	−1.66663	+	15.8569i	−0.114736	+	1.09164i	0.773990	+	0.633197i	$0.218258\pi$
$211$	−1.66663	+	15.8569i	−0.114736	+	1.09164i	−0.888726	+	0.458439i	$0.848409\pi$
$212$	5.22106	−	1.10977i	0.358584	−	0.0762193i
$213$		0			0
$214$	−0.445008	−	4.23397i	−0.0304201	−	0.289428i
$215$	−7.47342	+	5.42976i	−0.509683	+	0.370306i
$216$		0			0
$217$	−2.28983	+	7.04737i	−0.155444	+	0.478406i
$218$	12.7769	−	5.68866i	0.865364	−	0.385285i
$219$		0			0
$220$	−1.81310	+	3.00532i	−0.122239	+	0.202619i
$221$	4.15903	+	7.20366i	0.279767	+	0.484571i
$222$		0			0
$223$	17.6034	+	19.5506i	1.17881	+	1.30920i	0.941203	+	0.337842i	$0.109697\pi$
$223$	17.6034	+	19.5506i	1.17881	+	1.30920i	0.237609	+	0.971361i	$0.423636\pi$
$224$	2.11775	+	6.51775i	0.141498	+	0.435485i
$225$		0			0
$226$	1.97166	−	1.43250i	0.131153	−	0.0952883i
$227$	−2.72150	−	0.578474i	−0.180633	−	0.0383946i	0.116707	−	0.993166i	$-0.462766\pi$
$227$	−2.72150	−	0.578474i	−0.180633	−	0.0383946i	−0.297340	+	0.954772i	$0.596099\pi$
$228$		0			0
$229$	−2.19722	+	20.9052i	−0.145197	+	1.38145i	0.642923	+	0.765931i	$0.277721\pi$
$229$	−2.19722	+	20.9052i	−0.145197	+	1.38145i	−0.788120	+	0.615522i	$0.788945\pi$
$230$	−1.50231	−	2.60209i	−0.0990597	−	0.171576i
$231$		0			0
$232$	−12.6591	+	21.9261i	−0.831108	+	1.43952i
$233$	−11.0308	−	8.01437i	−0.722654	−	0.525039i	0.164577	−	0.986364i	$-0.447374\pi$
$233$	−11.0308	−	8.01437i	−0.722654	−	0.525039i	−0.887231	+	0.461326i	$0.847374\pi$
$234$		0			0
$235$	3.47141	+	10.6839i	0.226450	+	0.696940i
$236$	0.980858	+	9.33224i	0.0638484	+	0.607477i
$237$		0			0
$238$	−3.88564	+	4.31544i	−0.251869	+	0.279728i
$239$	19.8335	−	4.21575i	1.28292	−	0.272694i	0.484501	−	0.874791i	$-0.339001\pi$
$239$	19.8335	−	4.21575i	1.28292	−	0.272694i	0.798423	+	0.602097i	$0.205668\pi$
$240$		0			0
$241$	13.1966	−	22.8571i	0.850066	−	1.47236i	−0.0310821	−	0.999517i	$-0.509895\pi$
$241$	13.1966	−	22.8571i	0.850066	−	1.47236i	0.881148	−	0.472841i	$-0.156771\pi$
$242$	0.776668	+	11.7085i	0.0499261	+	0.752651i
$243$		0			0
$244$	−0.427599	−	0.310669i	−0.0273742	−	0.0198885i
$245$	3.82019	+	4.24275i	0.244063	+	0.271059i
$246$		0			0
$247$	−6.12376	−	2.72647i	−0.389646	−	0.173481i
$248$	13.4838	+	6.00336i	0.856220	+	0.381214i
$249$		0			0
$250$	−7.44211	−	8.26530i	−0.470680	−	0.522743i
$251$	4.51620	+	3.28121i	0.285060	+	0.207108i	0.721121	−	0.692809i	$-0.243627\pi$
$251$	4.51620	+	3.28121i	0.285060	+	0.207108i	−0.436062	+	0.899917i	$0.643627\pi$
$252$		0			0
$253$	6.89085	+	3.22827i	0.433224	+	0.202960i
$254$	0.844029	−	1.46190i	0.0529591	−	0.0917278i
$255$		0			0
$256$	15.9372	−	3.38756i	0.996075	−	0.211722i
$257$	−18.4755	+	20.5191i	−1.15247	+	1.27995i	−0.198482	+	0.980105i	$0.563601\pi$
$257$	−18.4755	+	20.5191i	−1.15247	+	1.27995i	−0.953988	+	0.299843i	$0.903066\pi$
$258$		0			0
$259$	0.644995	+	6.13671i	0.0400780	+	0.381317i
$260$	0.765932	+	2.35730i	0.0475011	+	0.146193i
$261$		0			0
$262$	4.86957	+	3.53795i	0.300843	+	0.218575i
$263$	14.7278	−	25.5093i	0.908156	−	1.57297i	0.0915315	−	0.995802i	$-0.470824\pi$
$263$	14.7278	−	25.5093i	0.908156	−	1.57297i	0.816624	−	0.577170i	$-0.195843\pi$
$264$		0			0
$265$	3.80065	+	6.58292i	0.233472	+	0.404385i
$266$	0.489161	−	4.65406i	0.0299924	−	0.285359i
$267$		0			0
$268$	7.30190	+	1.55207i	0.446035	+	0.0948076i
$269$	−14.7566	+	10.7213i	−0.899723	+	0.653687i	−0.938395	−	0.345565i	$-0.887687\pi$
$269$	−14.7566	+	10.7213i	−0.899723	+	0.653687i	0.0386718	+	0.999252i	$0.487687\pi$
$270$		0			0
$271$	−2.16675	−	6.66858i	−0.131621	−	0.405087i	0.863428	−	0.504472i	$-0.168313\pi$
$271$	−2.16675	−	6.66858i	−0.131621	−	0.405087i	−0.995049	+	0.0993842i	$0.968313\pi$
$272$	3.64251	+	4.04542i	0.220860	+	0.245289i
$273$		0			0
$274$	−11.5470	−	20.0000i	−0.697579	−	1.20824i
$275$	11.2832	+	2.62619i	0.680401	+	0.158365i
$276$		0			0
$277$	−10.5132	+	4.68079i	−0.631678	+	0.281241i	−0.697494	−	0.716590i	$-0.745702\pi$
$277$	−10.5132	+	4.68079i	−0.631678	+	0.281241i	0.0658158	+	0.997832i	$0.479035\pi$
$278$	6.94234	−	21.3663i	0.416374	−	1.28147i
$279$		0			0
$280$	−4.64772	+	3.37677i	−0.277755	+	0.201801i
$281$	−1.18477	−	11.2724i	−0.0706776	−	0.672453i	−0.971301	−	0.237853i	$-0.923556\pi$
$281$	−1.18477	−	11.2724i	−0.0706776	−	0.672453i	0.900624	−	0.434600i	$-0.143110\pi$
$282$		0			0
$283$	−4.47815	+	0.951861i	−0.266199	+	0.0565823i	−0.339077	−	0.940759i	$-0.610115\pi$
$283$	−4.47815	+	0.951861i	−0.266199	+	0.0565823i	0.0728785	+	0.997341i	$0.476781\pi$
$284$	1.40731	−	13.3897i	0.0835086	−	0.794531i
$285$		0			0
$286$	6.60894	+	4.99875i	0.390795	+	0.295582i
$287$	−7.41950			−0.437959
$288$		0			0
$289$	−1.35562	+	4.17217i	−0.0797423	+	0.245422i
$290$	−10.6224	−	2.25787i	−0.623771	−	0.132587i
$291$		0			0
$292$	11.9360	+	5.31424i	0.698500	+	0.310992i
$293$	−17.6011	+	19.5480i	−1.02827	+	1.14200i	−0.0385063	+	0.999258i	$0.512260\pi$
$293$	−17.6011	+	19.5480i	−1.02827	+	1.14200i	−0.989759	+	0.142746i	$0.954407\pi$
$294$		0			0
$295$	−12.2077	+	5.43524i	−0.710762	+	0.316452i
$296$	12.2909			0.714391
$297$		0			0
$298$	14.9308			0.864920
$299$	4.90914	−	2.18569i	0.283903	−	0.126402i
$300$		0			0
$301$	7.71767	−	8.57134i	0.444839	−	0.494044i
$302$	20.4327	+	9.09721i	1.17577	+	0.523486i
$303$		0			0
$304$	−4.29101	−	0.912083i	−0.246107	−	0.0523116i
$305$	0.232592	−	0.715845i	0.0133182	−	0.0409892i
$306$		0			0
$307$	−14.7093			−0.839504			−0.419752	−	0.907639i	$-0.637883\pi$
$307$	−14.7093			−0.839504			−0.419752	+	0.907639i	$0.637883\pi$
$308$	1.43416	−	4.14103i	0.0817188	−	0.235957i
$309$		0			0
$310$	−0.661765	+	6.29627i	−0.0375857	+	0.357604i
$311$	7.61753	−	1.61916i	0.431950	−	0.0918139i	0.0131950	−	0.999913i	$-0.495800\pi$
$311$	7.61753	−	1.61916i	0.431950	−	0.0918139i	0.418755	+	0.908099i	$0.362466\pi$
$312$		0			0
$313$	−1.89613	−	18.0405i	−0.107176	−	1.01971i	−0.907475	−	0.420106i	$-0.861993\pi$
$313$	−1.89613	−	18.0405i	−0.107176	−	1.01971i	0.800299	−	0.599601i	$-0.204674\pi$
$314$	−15.1115	+	10.9791i	−0.852789	+	0.619588i
$315$		0			0
$316$	0.517430	−	1.59249i	0.0291077	−	0.0895844i
$317$	−17.7696	+	7.91152i	−0.998039	+	0.444356i	−0.839712	−	0.543031i	$-0.817276\pi$
$317$	−17.7696	+	7.91152i	−0.998039	+	0.444356i	−0.158326	+	0.987387i	$0.550610\pi$
$318$		0			0
$319$	25.3363	−	10.7012i	1.41856	−	0.599153i
$320$	4.80926	+	8.32988i	0.268846	+	0.465655i
$321$		0			0
$322$	2.51024	+	2.78790i	0.139890	+	0.155364i
$323$	3.14102	+	9.66706i	0.174771	+	0.537890i
$324$		0			0
$325$	6.61851	−	4.80863i	0.367129	−	0.266735i
$326$	0.199632	+	0.0424331i	0.0110566	+	0.00235015i
$327$		0			0
$328$	−1.54479	+	14.6977i	−0.0852968	+	0.811545i
$329$	−7.01304	−	12.1469i	−0.386642	−	0.669683i
$330$		0			0
$331$	10.3118	−	17.8606i	0.566788	−	0.981706i	−0.430092	−	0.902785i	$-0.641519\pi$
$331$	10.3118	−	17.8606i	0.566788	−	0.981706i	0.996881	−	0.0789215i	$-0.0251476\pi$
$332$	−3.71981	−	2.70260i	−0.204151	−	0.148325i
$333$		0			0
$334$	−0.316077	−	0.972784i	−0.0172949	−	0.0532284i
$335$	1.11122	+	10.5725i	0.0607124	+	0.577640i
$336$		0			0
$337$	−2.20600	+	2.45001i	−0.120168	+	0.133460i	−0.800227	−	0.599697i	$-0.795288\pi$
$337$	−2.20600	+	2.45001i	−0.120168	+	0.133460i	0.680059	+	0.733158i	$0.261954\pi$
$338$	−7.84083	+	1.66662i	−0.426485	+	0.0906521i
$339$		0			0
$340$	1.87922	−	3.25491i	0.101915	−	0.176522i
$341$	−7.74828	−	14.0374i	−0.419593	−	0.760169i
$342$		0			0
$343$	−14.4472	−	10.4965i	−0.780077	−	0.566759i
$344$	−15.3726	−	17.0730i	−0.828833	−	0.920513i
$345$		0			0
$346$	−21.0871	−	9.38859i	−1.13365	−	0.504734i
$347$	7.34341	+	3.26950i	0.394215	+	0.175516i	0.594264	−	0.804270i	$-0.297443\pi$
$347$	7.34341	+	3.26950i	0.394215	+	0.175516i	−0.200049	+	0.979786i	$0.564110\pi$
$348$		0			0
$349$	2.00281	+	2.22434i	0.107208	+	0.119066i	0.794360	−	0.607447i	$-0.207806\pi$
$349$	2.00281	+	2.22434i	0.107208	+	0.119066i	−0.687152	+	0.726513i	$0.741140\pi$
$350$	4.62050	+	3.35699i	0.246976	+	0.179439i
$351$		0			0
$352$	−13.4283	−	6.29099i	−0.715732	−	0.335311i
$353$	−4.95736	+	8.58641i	−0.263854	+	0.457008i	−0.967263	−	0.253777i	$-0.918327\pi$
$353$	−4.95736	+	8.58641i	−0.263854	+	0.457008i	0.703409	+	0.710786i	$0.251660\pi$
$354$		0			0
$355$	18.7540	−	3.98628i	0.995359	−	0.211570i
$356$	−3.36901	+	3.74166i	−0.178557	+	0.198308i
$357$		0			0
$358$	−2.28606	−	21.7504i	−0.120822	−	1.14954i
$359$	−4.69829	−	14.4598i	−0.247966	−	0.763161i	−0.995134	−	0.0985263i	$-0.968587\pi$
$359$	−4.69829	−	14.4598i	−0.247966	−	0.763161i	0.747168	−	0.664635i	$-0.231413\pi$
$360$		0			0
$361$	8.74440	+	6.35318i	0.460232	+	0.334378i
$362$	−5.56228	+	9.63416i	−0.292347	+	0.506360i
$363$		0			0
$364$	−1.54736	−	2.68011i	−0.0811037	−	0.140476i
$365$	−1.94489	+	18.5044i	−0.101800	+	0.968566i
$366$		0			0
$367$	1.35764	+	0.288576i	0.0708684	+	0.0150635i	0.243209	−	0.969974i	$-0.421800\pi$
$367$	1.35764	+	0.288576i	0.0708684	+	0.0150635i	−0.172341	+	0.985037i	$0.555133\pi$
$368$	2.84512	−	2.06710i	0.148312	−	0.107755i
$369$		0			0
$370$	1.62912	+	5.01391i	0.0846938	+	0.260661i
$371$	−6.35056	−	7.05301i	−0.329705	−	0.366174i
$372$		0			0
$373$	−9.56704	−	16.5706i	−0.495362	−	0.857993i	0.504623	−	0.863340i	$-0.331631\pi$
$373$	−9.56704	−	16.5706i	−0.495362	−	0.857993i	−0.999986	+	0.00534681i	$0.998298\pi$
$374$	−1.07274	−	12.5193i	−0.0554702	−	0.647359i
$375$		0			0
$376$	−25.5227	+	11.3634i	−1.31623	+	0.586025i
$377$	6.00187	−	18.4718i	0.309112	−	0.951348i
$378$		0			0
$379$	0.383874	−	0.278900i	0.0197183	−	0.0143262i	−0.577882	−	0.816120i	$-0.696121\pi$
$379$	0.383874	−	0.278900i	0.0197183	−	0.0143262i	0.597601	+	0.801794i	$0.296121\pi$
$380$	0.316598	+	3.01223i	0.0162411	+	0.154524i
$381$		0			0
$382$	−21.5404	+	4.57854i	−1.10210	+	0.234259i
$383$	2.17877	−	20.7296i	0.111330	−	1.05923i	−0.786107	−	0.618090i	$-0.787907\pi$
$383$	2.17877	−	20.7296i	0.111330	−	1.05923i	0.897437	−	0.441143i	$-0.145427\pi$
$384$		0			0
$385$	6.23964	+	0.120075i	0.318002	+	0.00611960i
$386$	6.39201			0.325345
$387$		0			0
$388$	2.26584	−	6.97354i	0.115031	−	0.354028i
$389$	−2.60760	−	0.554263i	−0.132211	−	0.0281022i	0.141331	−	0.989962i	$-0.454862\pi$
$389$	−2.60760	−	0.554263i	−0.132211	−	0.0281022i	−0.273542	+	0.961860i	$0.588195\pi$
$390$		0			0
$391$	−7.44398	−	3.31427i	−0.376458	−	0.167610i
$392$	−9.50077	+	10.5517i	−0.479861	+	0.532940i
$393$		0			0
$394$	−1.38187	+	0.615250i	−0.0696178	+	0.0309958i
$395$	2.38453			0.119979
$396$		0			0
$397$	−15.5756			−0.781716			−0.390858	−	0.920451i	$-0.627822\pi$
$397$	−15.5756			−0.781716			−0.390858	+	0.920451i	$0.627822\pi$
$398$	−5.91876	+	2.63520i	−0.296681	+	0.132091i
$399$		0			0
$400$	3.58245	−	3.97872i	0.179123	−	0.198936i
$401$	−7.53398	−	3.35435i	−0.376229	−	0.167508i	0.209905	−	0.977722i	$-0.432684\pi$
$401$	−7.53398	−	3.35435i	−0.376229	−	0.167508i	−0.586135	+	0.810214i	$0.699351\pi$
$402$		0			0
$403$	−11.0754	−	2.35414i	−0.551703	−	0.117268i
$404$	0.199854	−	0.615086i	0.00994309	−	0.0306017i
$405$		0			0
$406$	13.5592			0.672930
$407$	−10.6488	−	8.05436i	−0.527843	−	0.399240i
$408$		0			0
$409$	−0.420562	+	4.00138i	−0.0207955	+	0.197856i	−0.999987	−	0.00508227i	$-0.998382\pi$
$409$	−0.420562	+	4.00138i	−0.0207955	+	0.197856i	0.979192	+	0.202938i	$0.0650489\pi$
$410$	−6.20052	+	1.31796i	−0.306222	+	0.0650894i
$411$		0			0
$412$	0.973742	+	9.26454i	0.0479728	+	0.456431i
$413$	13.4982	−	9.80702i	0.664203	−	0.482572i
$414$		0			0
$415$	2.02339	−	6.22735i	0.0993243	−	0.305689i
$416$	−9.56653	+	4.25929i	−0.469037	+	0.208829i
$417$		0			0
$418$	6.62954	+	7.65401i	0.324261	+	0.374370i
$419$	−16.0205	−	27.7484i	−0.782654	−	1.35560i	−0.930390	−	0.366570i	$-0.880532\pi$
$419$	−16.0205	−	27.7484i	−0.782654	−	1.35560i	0.147736	−	0.989027i	$-0.452801\pi$
$420$		0			0
$421$	17.0533	+	18.9396i	0.831128	+	0.923061i	0.998019	−	0.0629147i	$-0.0200396\pi$
$421$	17.0533	+	18.9396i	0.831128	+	0.923061i	−0.166891	+	0.985975i	$0.553373\pi$
$422$	−5.25592	−	16.1761i	−0.255854	−	0.787439i
$423$		0			0
$424$	−15.2939	+	11.1117i	−0.742739	+	0.539631i
$425$	−12.1341	−	2.57918i	−0.588589	−	0.125109i
$426$		0			0
$427$	−0.0982337	+	0.934631i	−0.00475386	+	0.0452300i
$428$	−1.72018	−	2.97943i	−0.0831479	−	0.144016i
$429$		0			0
$430$	4.92713	−	8.53403i	0.237607	−	0.411548i
$431$	−16.7429	−	12.1644i	−0.806477	−	0.585940i	0.106330	−	0.994331i	$-0.466090\pi$
$431$	−16.7429	−	12.1644i	−0.806477	−	0.585940i	−0.912807	+	0.408391i	$0.866090\pi$
$432$		0			0
$433$	−4.45957	−	13.7251i	−0.214313	−	0.659588i	−0.999202	−	0.0399509i	$-0.987280\pi$
$433$	−4.45957	−	13.7251i	−0.214313	−	0.659588i	0.784889	−	0.619637i	$-0.212720\pi$
$434$	−0.826260	−	7.86134i	−0.0396618	−	0.377357i
$435$		0			0
$436$	7.56271	−	8.39924i	0.362188	−	0.402251i
$437$	6.42311	−	1.36527i	0.307259	−	0.0653099i
$438$		0			0
$439$	−4.47700	+	7.75438i	−0.213675	+	0.370097i	−0.952862	−	0.303404i	$-0.901877\pi$
$439$	−4.47700	+	7.75438i	−0.213675	+	0.370097i	0.739187	+	0.673501i	$0.235210\pi$
$440$	1.53700	−	12.3355i	0.0732736	−	0.588070i
$441$		0			0
$442$	−7.17864	−	5.21559i	−0.341453	−	0.248080i
$443$	6.86391	+	7.62314i	0.326114	+	0.362186i	0.883799	−	0.467866i	$-0.154977\pi$
$443$	6.86391	+	7.62314i	0.326114	+	0.362186i	−0.557685	+	0.830053i	$0.688310\pi$
$444$		0			0
$445$	−6.55021	−	2.91634i	−0.310510	−	0.138248i
$446$	−25.6376	−	11.4146i	−1.21398	−	0.540497i
$447$		0			0
$448$	−8.03586	−	8.92473i	−0.379659	−	0.421654i
$449$	16.5355	+	12.0137i	0.780359	+	0.566964i	0.905087	−	0.425227i	$-0.139806\pi$
$449$	16.5355	+	12.0137i	0.780359	+	0.566964i	−0.124728	+	0.992191i	$0.539806\pi$
$450$		0			0
$451$	10.9700	−	11.7218i	0.516558	−	0.551958i
$452$	0.984725	−	1.70559i	0.0463176	−	0.0802244i
$453$		0			0
$454$	2.90316	−	0.617086i	0.136252	−	0.0289613i
$455$	2.94894	−	3.27513i	0.138248	−	0.153540i
$456$		0			0
$457$	4.02296	+	38.2759i	0.188186	+	1.79047i	0.527254	+	0.849708i	$0.323222\pi$
$457$	4.02296	+	38.2759i	0.188186	+	1.79047i	−0.339068	+	0.940762i	$0.610112\pi$
$458$	−6.92921	−	21.3259i	−0.323781	−	0.996494i
$459$		0			0
$460$	−1.96435	−	1.42718i	−0.0915882	−	0.0665427i
$461$	−9.77045	+	16.9229i	−0.455055	+	0.788178i	−0.998691	−	0.0511424i	$-0.983714\pi$
$461$	−9.77045	+	16.9229i	−0.455055	+	0.788178i	0.543636	+	0.839321i	$0.317047\pi$
$462$		0			0
$463$	8.26314	+	14.3122i	0.384021	+	0.665144i	0.991633	−	0.129090i	$-0.0412057\pi$
$463$	8.26314	+	14.3122i	0.384021	+	0.665144i	−0.607612	+	0.794234i	$0.707872\pi$
$464$	1.32864	−	12.6411i	0.0616803	−	0.586849i
$465$		0			0
$466$	14.2271	+	3.02407i	0.659058	+	0.140087i
$467$	23.7147	−	17.2297i	1.09739	−	0.797297i	0.116754	−	0.993161i	$-0.462751\pi$
$467$	23.7147	−	17.2297i	1.09739	−	0.797297i	0.980631	+	0.195864i	$0.0627510\pi$
$468$		0			0
$469$	−4.10167	−	12.6236i	−0.189398	−	0.582906i
$470$	−8.01855	−	8.90550i	−0.369868	−	0.410780i
$471$		0			0
$472$	−16.6169	−	28.7812i	−0.764853	−	1.32476i
$473$	2.13069	+	24.8659i	0.0979690	+	1.14334i
$474$		0			0
$475$	9.13268	−	4.06613i	0.419036	−	0.186567i
$476$	−1.45012	+	4.46301i	−0.0664661	+	0.204562i
$477$		0			0
$478$	−17.4991	+	12.7138i	−0.800389	+	0.581517i
$479$	−1.61899	−	15.4037i	−0.0739737	−	0.703813i	−0.967167	−	0.254140i	$-0.918207\pi$
$479$	−1.61899	−	15.4037i	−0.0739737	−	0.703813i	0.893194	−	0.449672i	$-0.148459\pi$
$480$		0			0
$481$	−9.22271	+	1.96035i	−0.420519	+	0.0893842i
$482$	−2.94298	+	28.0006i	−0.134049	+	1.27539i
$483$		0			0
$484$	4.42181	+	8.38845i	0.200991	+	0.381293i
$485$	10.4419			0.474143
$486$		0			0
$487$	−1.19788	+	3.68670i	−0.0542811	+	0.167060i	−0.974522	−	0.224293i	$-0.927993\pi$
$487$	−1.19788	+	3.68670i	−0.0542811	+	0.167060i	0.920241	+	0.391353i	$0.127993\pi$
$488$	1.83101	+	0.389193i	0.0828859	+	0.0176179i
$489$		0			0
$490$	−5.56373	−	2.47713i	−0.251344	−	0.111905i
$491$	4.85611	−	5.39326i	0.219153	−	0.243395i	−0.623536	−	0.781795i	$-0.714304\pi$
$491$	4.85611	−	5.39326i	0.219153	−	0.243395i	0.842689	+	0.538400i	$0.180971\pi$
$492$		0			0
$493$	−26.9051	+	11.9789i	−1.21174	+	0.539503i
$494$	7.15072			0.321726
$495$		0			0
$496$	−7.41004			−0.332721
$497$	−21.8692	+	9.73679i	−0.980967	+	0.436755i
$498$		0			0
$499$	24.0197	−	26.6766i	1.07527	−	1.19421i	0.0952207	−	0.995456i	$-0.469644\pi$
$499$	24.0197	−	26.6766i	1.07527	−	1.19421i	0.980050	−	0.198753i	$-0.0636890\pi$
$500$	−8.21079	−	3.65568i	−0.367198	−	0.163487i
$501$		0			0
$502$	−5.82481	−	1.23810i	−0.259974	−	0.0552592i
$503$	4.52869	−	13.9379i	0.201924	−	0.621459i	−0.797901	−	0.602788i	$-0.794056\pi$
$503$	4.52869	−	13.9379i	0.201924	−	0.621459i	0.999826	−	0.0186711i	$-0.00594354\pi$
$504$		0			0
$505$	0.921008			0.0409843
$506$	−8.11599	−	0.156184i	−0.360800	−	0.00694321i
$507$		0			0
$508$	0.142591	−	1.35666i	0.00632644	−	0.0601921i
$509$	0.394683	−	0.0838925i	0.0174940	−	0.00371847i	−0.199156	−	0.979968i	$-0.563820\pi$
$509$	0.394683	−	0.0838925i	0.0174940	−	0.00371847i	0.216650	+	0.976249i	$0.430487\pi$
$510$		0			0
$511$	−2.42834	−	23.1041i	−0.107423	−	1.02206i
$512$	−13.1162	+	9.52950i	−0.579661	+	0.421148i
$513$		0			0
$514$	9.10185	−	28.0126i	0.401465	−	1.23558i
$515$	−12.1192	+	5.39581i	−0.534035	+	0.237768i
$516$		0			0
$517$	29.5596	+	6.88007i	1.30003	+	0.302585i
$518$	−3.29119	−	5.70051i	−0.144607	−	0.250466i
$519$		0			0
$520$	−5.87389	−	6.52362i	−0.257587	−	0.286080i
$521$	−3.50114	−	10.7754i	−0.153388	−	0.472079i	0.844606	−	0.535388i	$-0.179835\pi$
$521$	−3.50114	−	10.7754i	−0.153388	−	0.472079i	−0.997994	+	0.0633089i	$0.979835\pi$
$522$		0			0
$523$	11.6876	−	8.49154i	0.511063	−	0.371309i	−0.302164	−	0.953256i	$-0.597709\pi$
$523$	11.6876	−	8.49154i	0.511063	−	0.371309i	0.813227	+	0.581947i	$0.197709\pi$
$524$	4.75781	+	1.01130i	0.207846	+	0.0441791i
$525$		0			0
$526$	−3.28447	+	31.2496i	−0.143209	+	1.36255i
$527$	8.58466	+	14.8691i	0.373954	+	0.647707i
$528$		0			0
$529$	8.86793	−	15.3597i	0.385562	−	0.667813i
$530$	−6.56005	−	4.76616i	−0.284950	−	0.207029i
$531$		0			0
$532$	−1.16861	−	3.59661i	−0.0506657	−	0.155933i
$533$	−1.18506	−	11.2751i	−0.0513309	−	0.488380i
$534$		0			0
$535$	3.27829	−	3.64091i	0.141733	−	0.157410i
$536$	−25.8609	+	5.49690i	−1.11702	+	0.237430i
$537$		0			0
$538$	9.72880	−	16.8508i	0.419438	−	0.726488i
$539$	15.1461	−	2.91601i	0.652391	−	0.125602i
$540$		0			0
$541$	18.9044	+	13.7349i	0.812765	+	0.590509i	0.914631	−	0.404290i	$-0.132481\pi$
$541$	18.9044	+	13.7349i	0.812765	+	0.590509i	−0.101866	+	0.994798i	$0.532481\pi$
$542$	5.00495	+	5.55856i	0.214981	+	0.238761i
$543$		0			0
$544$	14.5062	+	6.45859i	0.621949	+	0.276910i
$545$	14.7038	+	6.54657i	0.629843	+	0.280424i
$546$		0			0
$547$	2.45284	+	2.72416i	0.104876	+	0.116476i	0.793297	−	0.608834i	$-0.208363\pi$
$547$	2.45284	+	2.72416i	0.104876	+	0.116476i	−0.688421	+	0.725311i	$0.741696\pi$
$548$	−15.0982	−	10.9695i	−0.644965	−	0.468594i
$549$		0			0
$550$	−12.1352	+	2.33633i	−0.517446	+	0.0996213i
$551$	11.8670	−	20.5542i	0.505550	−	0.875638i
$552$		0			0
$553$	−2.91220	+	0.619006i	−0.123839	+	0.0263228i
$554$	8.21445	−	9.12307i	0.348999	−	0.387602i
$555$		0			0
$556$	−1.89770	−	18.0554i	−0.0804805	−	0.765721i
$557$	10.6998	+	32.9306i	0.453365	+	1.39531i	0.873044	+	0.487641i	$0.162142\pi$
$557$	10.6998	+	32.9306i	0.453365	+	1.39531i	−0.419680	+	0.907672i	$0.637858\pi$
$558$		0			0
$559$	14.2582	+	10.3592i	0.603059	+	0.438148i
$560$	1.44209	−	2.49777i	0.0609394	−	0.105550i
$561$		0			0
$562$	6.04550	+	10.4711i	0.255014	+	0.441698i
$563$	4.02554	−	38.3005i	0.169656	−	1.61417i	−0.496280	−	0.868163i	$-0.665301\pi$
$563$	4.02554	−	38.3005i	0.169656	−	1.61417i	0.665936	−	0.746009i	$-0.268032\pi$
$564$		0			0
$565$	2.74336	+	0.583119i	0.115414	+	0.0245320i
$566$	3.95107	−	2.87062i	0.166076	−	0.120661i
$567$		0			0
$568$	14.7348	+	45.3492i	0.618260	+	1.90281i
$569$	−17.1727	−	19.0722i	−0.719915	−	0.799547i	0.266497	−	0.963836i	$-0.414134\pi$
$569$	−17.1727	−	19.0722i	−0.719915	−	0.799547i	−0.986412	+	0.164289i	$0.947467\pi$
$570$		0			0
$571$	−11.2142	−	19.4236i	−0.469300	−	0.812852i	0.530084	−	0.847945i	$-0.322160\pi$
$571$	−11.2142	−	19.4236i	−0.469300	−	0.812852i	−0.999384	+	0.0350935i	$0.988827\pi$
$572$	6.52204	+	1.51802i	0.272700	+	0.0634716i
$573$		0			0
$574$	7.23048	−	3.21922i	0.301794	−	0.134367i
$575$	−2.47649	+	7.62187i	−0.103277	+	0.317854i
$576$		0			0
$577$	−16.4972	+	11.9859i	−0.686786	+	0.498979i	−0.875602	−	0.483033i	$-0.839535\pi$
$577$	−16.4972	+	11.9859i	−0.686786	+	0.498979i	0.188816	+	0.982013i	$0.439535\pi$
$578$	−0.489161	−	4.65406i	−0.0203464	−	0.193583i
$579$		0			0
$580$	−8.58409	+	1.82460i	−0.356435	+	0.0757625i
$581$	−0.854565	+	8.13064i	−0.0354533	+	0.337316i
$582$		0			0
$583$	20.5323	+	0.395123i	0.850363	+	0.0163643i
$584$	−46.2738			−1.91482
$585$		0			0
$586$	8.67107	−	26.6868i	0.358198	−	1.10242i
$587$	6.56503	+	1.39544i	0.270968	+	0.0575960i	0.341391	−	0.939921i	$-0.389102\pi$
$587$	6.56503	+	1.39544i	0.270968	+	0.0575960i	−0.0704238	+	0.997517i	$0.522435\pi$
$588$		0			0
$589$	−12.6401	−	5.62772i	−0.520825	−	0.231886i
$590$	9.53845	−	10.5935i	0.392692	−	0.436129i
$591$		0			0
$592$	−5.63705	+	2.50978i	−0.231681	+	0.103151i
$593$	−12.4707			−0.512110			−0.256055	−	0.966662i	$-0.582423\pi$
$593$	−12.4707			−0.512110			−0.256055	+	0.966662i	$0.582423\pi$
$594$		0			0
$595$	−6.68275			−0.273966
$596$	11.0226	−	4.90758i	0.451503	−	0.201022i
$597$		0			0
$598$	−3.83573	+	4.26001i	−0.156855	+	0.174205i
$599$	4.92101	+	2.19097i	0.201067	+	0.0895207i	0.504800	−	0.863237i	$-0.331566\pi$
$599$	4.92101	+	2.19097i	0.201067	+	0.0895207i	−0.303733	+	0.952757i	$0.598233\pi$
$600$		0			0
$601$	−39.7356	−	8.44606i	−1.62085	−	0.344522i	−0.694005	−	0.719970i	$-0.744155\pi$
$601$	−39.7356	−	8.44606i	−1.62085	−	0.344522i	−0.926843	+	0.375448i	$0.877489\pi$
$602$	−3.80206	+	11.7015i	−0.154961	+	0.476919i
$603$		0			0
$604$	18.0744			0.735439
$605$	−9.41525	+	9.68025i	−0.382784	+	0.393558i
$606$		0			0
$607$	−3.89942	+	37.1005i	−0.158273	+	1.50586i	0.570609	+	0.821222i	$0.306707\pi$
$607$	−3.89942	+	37.1005i	−0.158273	+	1.50586i	−0.728881	+	0.684640i	$0.759959\pi$
$608$	−12.5168	+	2.66053i	−0.507624	+	0.107899i
$609$		0			0
$610$	0.0839284	+	0.798526i	0.00339816	+	0.0323314i
$611$	17.3391	−	12.5976i	0.701465	−	0.509644i
$612$		0			0
$613$	−2.35013	+	7.23295i	−0.0949208	+	0.292136i	−0.987233	−	0.159283i	$-0.949082\pi$
$613$	−2.35013	+	7.23295i	−0.0949208	+	0.292136i	0.892312	+	0.451419i	$0.149082\pi$
$614$	14.3345	−	6.38215i	0.578495	−	0.257563i
$615$		0			0
$616$	1.32507	+	15.4641i	0.0533887	+	0.623067i
$617$	19.1321	+	33.1378i	0.770229	+	1.33408i	0.937437	+	0.348154i	$0.113191\pi$
$617$	19.1321	+	33.1378i	0.770229	+	1.33408i	−0.167208	+	0.985922i	$0.553475\pi$
$618$		0			0
$619$	20.6758	+	22.9628i	0.831030	+	0.922952i	0.998013	−	0.0630078i	$-0.0200693\pi$
$619$	20.6758	+	22.9628i	0.831030	+	0.922952i	−0.166983	+	0.985960i	$0.553403\pi$
$620$	1.58096	+	4.86570i	0.0634929	+	0.195411i
$621$		0			0
$622$	−6.72093	+	4.88304i	−0.269485	+	0.195792i
$623$	8.75674	+	1.86130i	0.350831	+	0.0745715i
$624$		0			0
$625$	−0.487660	+	4.63978i	−0.0195064	+	0.185591i
$626$	9.67531	+	16.7581i	0.386703	+	0.669790i
$627$		0			0
$628$	−7.54725	+	13.0722i	−0.301168	+	0.521638i
$629$	11.5668	+	8.40375i	0.461197	+	0.335079i
$630$		0			0
$631$	1.73983	+	5.35465i	0.0692616	+	0.213165i	0.979696	−	0.200488i	$-0.0642527\pi$
$631$	1.73983	+	5.35465i	0.0692616	+	0.213165i	−0.910435	+	0.413653i	$0.864253\pi$
$632$	0.619885	+	5.89781i	0.0246577	+	0.234602i
$633$		0			0
$634$	13.8842	−	15.4199i	0.551410	−	0.612403i
$635$	1.90018	−	0.403896i	0.0754064	−	0.0160281i
$636$		0			0
$637$	5.44616	−	9.43302i	0.215785	−	0.373750i
$638$	−20.0477	+	21.4216i	−0.793698	+	0.848091i
$639$		0			0
$640$	0.580131	+	0.421490i	0.0229317	+	0.0166609i
$641$	−28.2970	−	31.4271i	−1.11767	−	1.24129i	−0.967565	−	0.252623i	$-0.918707\pi$
$641$	−28.2970	−	31.4271i	−1.11767	−	1.24129i	−0.150101	−	0.988671i	$-0.547960\pi$
$642$		0			0
$643$	−11.0663	−	4.92704i	−0.436413	−	0.194304i	0.176757	−	0.984254i	$-0.443439\pi$
$643$	−11.0663	−	4.92704i	−0.436413	−	0.194304i	−0.613170	+	0.789951i	$0.710106\pi$
$644$	2.76952	+	1.23307i	0.109134	+	0.0485897i
$645$		0			0
$646$	−7.25540	−	8.05793i	−0.285460	−	0.317035i
$647$	−33.3540	−	24.2331i	−1.31128	−	0.952703i	−0.999997	−	0.00238648i	$-0.999240\pi$
$647$	−33.3540	−	24.2331i	−1.31128	−	0.952703i	−0.311286	−	0.950316i	$-0.600760\pi$
$648$		0			0
$649$	−4.46385	+	35.8254i	−0.175221	+	1.40627i
$650$	−4.36349	+	7.55779i	−0.171150	+	0.296441i
$651$		0			0
$652$	0.161325	−	0.0342906i	0.00631796	−	0.00134292i
$653$	9.22275	−	10.2429i	0.360914	−	0.400836i	−0.535152	−	0.844756i	$-0.679746\pi$
$653$	9.22275	−	10.2429i	0.360914	−	0.400836i	0.896067	+	0.443920i	$0.146412\pi$
$654$		0			0
$655$	0.724054	+	6.88892i	0.0282911	+	0.269172i
$656$	−2.29275	−	7.05637i	−0.0895170	−	0.275505i
$657$		0			0
$658$	12.1048	+	8.79462i	0.471892	+	0.342850i
$659$	−3.71441	+	6.43354i	−0.144693	+	0.250615i	−0.929258	−	0.369431i	$-0.879553\pi$
$659$	−3.71441	+	6.43354i	−0.144693	+	0.250615i	0.784566	+	0.620046i	$0.212886\pi$
$660$		0			0
$661$	5.34746	+	9.26208i	0.207992	+	0.360253i	0.951082	−	0.308939i	$-0.0999738\pi$
$661$	5.34746	+	9.26208i	0.207992	+	0.360253i	−0.743090	+	0.669192i	$0.766640\pi$
$662$	−2.29965	+	21.8797i	−0.0893784	+	0.850378i
$663$		0			0
$664$	15.9285	+	3.38571i	0.618146	+	0.131391i
$665$	4.35691	−	3.16548i	0.168954	−	0.122752i
$666$		0			0
$667$	5.87948	+	18.0952i	0.227654	+	0.700648i
$668$	−0.553084	−	0.614262i	−0.0213994	−	0.0237665i
$669$		0			0
$670$	−5.67018	−	9.82105i	−0.219058	−	0.379420i
$671$	−1.33135	−	1.53708i	−0.0513961	−	0.0593385i
$672$		0			0
$673$	−17.7402	+	7.89843i	−0.683833	+	0.304462i	−0.719091	−	0.694916i	$-0.755441\pi$
$673$	−17.7402	+	7.89843i	−0.683833	+	0.304462i	0.0352578	+	0.999378i	$0.488775\pi$
$674$	1.08677	−	3.34474i	0.0418609	−	0.128834i
$675$		0			0
$676$	−5.24065	+	3.80755i	−0.201563	+	0.146444i
$677$	3.39166	+	32.2695i	0.130352	+	1.24022i	0.842697	+	0.538388i	$0.180967\pi$
$677$	3.39166	+	32.2695i	0.130352	+	1.24022i	−0.712345	+	0.701830i	$0.752367\pi$
$678$		0			0
$679$	−12.7526	+	2.71064i	−0.489399	+	0.104025i
$680$	−1.39139	+	13.2382i	−0.0533575	+	0.507663i
$681$		0			0
$682$	13.6415	+	10.3179i	0.522361	+	0.395093i
$683$	20.5244			0.785344			0.392672	−	0.919679i	$-0.371551\pi$
$683$	20.5244			0.785344			0.392672	+	0.919679i	$0.371551\pi$
$684$		0			0
$685$	8.21267	−	25.2760i	0.313790	−	0.965747i
$686$	18.6334	+	3.96066i	0.711428	+	0.151219i
$687$		0			0
$688$	10.5367	+	4.69125i	0.401709	+	0.178852i
$689$	9.70386	−	10.7772i	0.369688	−	0.410580i
$690$		0			0
$691$	−26.9949	+	12.0189i	−1.02694	+	0.457221i	−0.849878	−	0.526979i	$-0.823325\pi$
$691$	−26.9949	+	12.0189i	−1.02694	+	0.457221i	−0.177058	+	0.984200i	$0.556658\pi$
$692$	−18.6534			−0.709094
$693$		0			0
$694$	−8.57491			−0.325499
$695$	23.6188	−	10.5157i	0.895910	−	0.398885i
$696$		0			0
$697$	−11.5032	+	12.7756i	−0.435715	+	0.483910i
$698$	−2.91689	−	1.29868i	−0.110406	−	0.0491559i
$699$		0			0
$700$	4.51446	+	0.959578i	0.170631	+	0.0362686i
$701$	−6.24195	+	19.2108i	−0.235755	+	0.725580i	0.761265	+	0.648441i	$0.224579\pi$
$701$	−6.24195	+	19.2108i	−0.235755	+	0.725580i	−0.997020	+	0.0771395i	$0.975421\pi$
$702$		0			0
$703$	−11.5218			−0.434553
$704$	25.9812	+	0.499980i	0.979203	+	0.0188437i
$705$		0			0
$706$	1.10555	−	10.5186i	0.0416078	−	0.395872i
$707$	−1.12481	+	0.239087i	−0.0423030	+	0.00899178i
$708$		0			0
$709$	−1.09128	−	10.3828i	−0.0409837	−	0.389934i	−0.995716	−	0.0924669i	$-0.970525\pi$
$709$	−1.09128	−	10.3828i	−0.0409837	−	0.389934i	0.954732	−	0.297467i	$-0.0961419\pi$
$710$	−16.5466	+	12.0218i	−0.620983	+	0.451171i
$711$		0			0
$712$	5.51037	−	16.9592i	0.206510	−	0.635572i
$713$	10.1330	−	4.51148i	0.379482	−	0.168956i
$714$		0			0
$715$	0.814140	+	9.50133i	0.0304471	+	0.355329i
$716$	−8.83675	−	15.3057i	−0.330245	−	0.572001i
$717$		0			0
$718$	10.8525	+	12.0529i	0.405012	+	0.449811i
$719$	5.23808	+	16.1212i	0.195348	+	0.601218i	0.999972	+	0.00743448i	$0.00236649\pi$
$719$	5.23808	+	16.1212i	0.195348	+	0.601218i	−0.804625	+	0.593784i	$0.797634\pi$
$720$		0			0
$721$	13.4003	−	9.73588i	0.499053	−	0.362583i
$722$	−11.2782	−	2.39725i	−0.419730	−	0.0892164i
$723$		0			0
$724$	−0.939696	+	8.94061i	−0.0349235	+	0.332275i
$725$	14.4828	+	25.0850i	0.537879	+	0.931634i
$726$		0			0
$727$	13.1039	−	22.6966i	0.485996	−	0.841769i	−0.513875	−	0.857865i	$-0.671790\pi$
$727$	13.1039	−	22.6966i	0.485996	−	0.841769i	0.999870	+	0.0160961i	$0.00512378\pi$
$728$	8.86719	+	6.44239i	0.328640	+	0.238771i
$729$		0			0
$730$	−6.13346	−	18.8768i	−0.227010	−	0.698663i
$731$	−2.79346	−	26.5780i	−0.103320	−	0.983023i
$732$		0			0
$733$	−11.2286	+	12.4707i	−0.414739	+	0.460614i	−0.913926	−	0.405880i	$-0.866965\pi$
$733$	−11.2286	+	12.4707i	−0.414739	+	0.460614i	0.499188	+	0.866494i	$0.333632\pi$
$734$	−1.44826	+	0.307838i	−0.0534564	+	0.0113625i
$735$		0			0
$736$	5.12916	−	8.88397i	0.189064	−	0.327468i
$737$	26.0081	+	12.1845i	0.958022	+	0.448820i
$738$		0			0
$739$	−7.71218	−	5.60322i	−0.283697	−	0.206118i	0.436831	−	0.899543i	$-0.356101\pi$
$739$	−7.71218	−	5.60322i	−0.283697	−	0.206118i	−0.720528	+	0.693425i	$0.756101\pi$
$740$	2.85070	+	3.16602i	0.104794	+	0.116385i
$741$		0			0
$742$	9.24896	+	4.11790i	0.339540	+	0.151173i
$743$	2.51547	+	1.11996i	0.0922837	+	0.0410874i	0.452359	−	0.891836i	$-0.350582\pi$
$743$	2.51547	+	1.11996i	0.0922837	+	0.0410874i	−0.360076	+	0.932923i	$0.617249\pi$
$744$		0			0
$745$	11.4974	+	12.7691i	0.421231	+	0.467824i
$746$	16.5130	+	11.9974i	0.604585	+	0.439257i
$747$		0			0
$748$	−4.90689	−	8.88972i	−0.179414	−	0.325040i
$749$	−3.05858	+	5.29762i	−0.111758	+	0.193571i
$750$		0			0
$751$	−33.8877	+	7.20306i	−1.23658	+	0.262843i	−0.779398	−	0.626530i	$-0.784475\pi$
$751$	−33.8877	+	7.20306i	−1.23658	+	0.262843i	−0.457183	+	0.889373i	$0.651141\pi$
$752$	9.38528	−	10.4234i	0.342246	−	0.380103i
$753$		0			0
$754$	2.16571	+	20.6054i	0.0788705	+	0.750403i
$755$	7.95391	+	24.4796i	0.289472	+	0.890905i
$756$		0			0
$757$	−3.15478	−	2.29208i	−0.114663	−	0.0833072i	0.528976	−	0.848637i	$-0.322576\pi$
$757$	−3.15478	−	2.29208i	−0.114663	−	0.0833072i	−0.643639	+	0.765329i	$0.722576\pi$
$758$	−0.253083	+	0.438352i	−0.00919238	+	0.0159217i
$759$		0			0
$760$	−5.36353	−	9.28991i	−0.194556	−	0.336981i
$761$	0.229726	−	2.18570i	0.00832756	−	0.0792315i	−0.989569	−	0.144061i	$-0.953984\pi$
$761$	0.229726	−	2.18570i	0.00832756	−	0.0792315i	0.997896	+	0.0648298i	$0.0206504\pi$
$762$		0			0
$763$	−19.6570	−	4.17823i	−0.711632	−	0.151262i
$764$	−14.3971	+	10.4601i	−0.520870	+	0.378434i
$765$		0			0
$766$	6.87102	+	21.1468i	0.248260	+	0.764065i
$767$	17.0593	+	18.9463i	0.615977	+	0.684112i
$768$		0			0
$769$	−19.8299	−	34.3464i	−0.715085	−	1.23856i	−0.962927	−	0.269763i	$-0.913055\pi$
$769$	−19.8299	−	34.3464i	−0.715085	−	1.23856i	0.247842	−	0.968801i	$-0.420279\pi$
$770$	−6.13277	+	2.59027i	−0.221010	+	0.0933470i
$771$		0			0
$772$	4.71887	−	2.10097i	0.169836	−	0.0756157i
$773$	−4.55217	+	14.0102i	−0.163730	+	0.503910i	−0.998940	−	0.0460208i	$-0.985346\pi$
$773$	−4.55217	+	14.0102i	−0.163730	+	0.503910i	0.835210	+	0.549931i	$0.185346\pi$
$774$		0			0
$775$	13.6613	−	9.92549i	0.490727	−	0.356534i
$776$	2.71449	+	25.8267i	0.0974446	+	0.927123i
$777$		0			0
$778$	2.78165	−	0.591259i	0.0997271	−	0.0211977i
$779$	1.44813	−	13.7780i	0.0518847	−	0.493650i
$780$		0			0
$781$	16.9516	−	48.9466i	0.606577	−	1.75145i
$782$	8.69234			0.310838
$783$		0			0
$784$	2.20277	−	6.77944i	0.0786705	−	0.242123i
$785$	−21.0260	−	4.46921i	−0.750450	−	0.159513i
$786$		0			0
$787$	−0.481320	−	0.214297i	−0.0171572	−	0.00763887i	0.398140	−	0.917325i	$-0.369656\pi$
$787$	−0.481320	−	0.214297i	−0.0171572	−	0.00763887i	−0.415297	+	0.909686i	$0.636322\pi$
$788$	−0.817935	+	0.908409i	−0.0291377	+	0.0323607i
$789$		0			0
$790$	−2.32378	+	1.03461i	−0.0826764	+	0.0368099i
$791$	−3.50180			−0.124510
$792$		0			0
$793$	−1.43601			−0.0509943
$794$	15.1788	−	6.75802i	0.538674	−	0.239833i
$795$		0			0
$796$	−3.50333	+	3.89085i	−0.124172	+	0.137907i
$797$	5.14617	+	2.29122i	0.182287	+	0.0811593i	0.495851	−	0.868408i	$-0.334856\pi$
$797$	5.14617	+	2.29122i	0.182287	+	0.0811593i	−0.313564	+	0.949567i	$0.601523\pi$
$798$		0			0
$799$	−31.7888	−	6.75691i	−1.12461	−	0.239042i
$800$	4.82599	−	14.8529i	0.170625	−	0.525128i
$801$		0			0
$802$	8.79744			0.310649
$803$	40.0917	+	30.3238i	1.41481	+	1.07010i
$804$		0			0
$805$	−0.451276	+	4.29360i	−0.0159054	+	0.151330i
$806$	11.8146	−	2.51127i	0.416152	−	0.0884558i
$807$		0			0
$808$	0.239426	+	2.27799i	0.00842298	+	0.0801393i
$809$	19.1292	−	13.8982i	0.672549	−	0.488635i	−0.198329	−	0.980136i	$-0.563551\pi$
$809$	19.1292	−	13.8982i	0.672549	−	0.488635i	0.870877	+	0.491500i	$0.163551\pi$
$810$		0			0
$811$	−4.98249	+	15.3345i	−0.174959	+	0.538468i	−0.999632	−	0.0271423i	$-0.991359\pi$
$811$	−4.98249	+	15.3345i	−0.174959	+	0.538468i	0.824673	+	0.565610i	$0.191359\pi$
$812$	10.0100	−	4.45673i	0.351281	−	0.156401i
$813$		0			0
$814$	13.8722	+	3.22879i	0.486220	+	0.113169i
$815$	0.117436	+	0.203404i	0.00411359	+	0.00712494i
$816$		0			0
$817$	14.4107	+	16.0047i	0.504166	+	0.559933i
$818$	−1.32629	−	4.08191i	−0.0463728	−	0.142721i
$819$		0			0
$820$	−4.14430	+	3.01101i	−0.144725	+	0.105149i
$821$	20.2751	+	4.30961i	0.707607	+	0.150407i	0.547638	−	0.836715i	$-0.315527\pi$
$821$	20.2751	+	4.30961i	0.707607	+	0.150407i	0.159969	+	0.987122i	$0.448861\pi$
$822$		0			0
$823$	2.76458	−	26.3032i	0.0963673	−	0.916873i	−0.834375	−	0.551197i	$-0.814171\pi$
$823$	2.76458	−	26.3032i	0.0963673	−	0.916873i	0.930742	−	0.365676i	$-0.119162\pi$
$824$	−16.4963	−	28.5724i	−0.574676	−	0.995368i
$825$		0			0
$826$	−8.89919	+	15.4138i	−0.309642	+	0.536316i
$827$	42.3796	+	30.7905i	1.47368	+	1.07069i	0.979526	+	0.201319i	$0.0645227\pi$
$827$	42.3796	+	30.7905i	1.47368	+	1.07069i	0.494156	+	0.869373i	$0.335477\pi$
$828$		0			0
$829$	8.69589	+	26.7632i	0.302021	+	0.929525i	0.980772	+	0.195156i	$0.0625215\pi$
$829$	8.69589	+	26.7632i	0.302021	+	0.929525i	−0.678751	+	0.734368i	$0.737479\pi$
$830$	0.730119	+	6.94662i	0.0253428	+	0.241121i
$831$		0			0
$832$	12.2791	−	13.6373i	0.425700	−	0.472787i
$833$	−16.1557	+	3.43399i	−0.559760	+	0.118981i
$834$		0			0
$835$	0.588550	−	1.01940i	0.0203676	−	0.0352777i
$836$	7.40999	+	3.47148i	0.256280	+	0.120064i
$837$		0			0
$838$	27.6520	+	20.0904i	0.955223	+	0.694010i
$839$	29.2738	+	32.5119i	1.01064	+	1.12243i	0.992456	+	0.122600i	$0.0391232\pi$
$839$	29.2738	+	32.5119i	1.01064	+	1.12243i	0.0181884	+	0.999835i	$0.494210\pi$
$840$		0			0
$841$	36.3297	+	16.1750i	1.25275	+	0.557760i
$842$	−24.8365	−	11.0579i	−0.855921	−	0.381081i
$843$		0			0
$844$	−9.19702	−	10.2143i	−0.316575	−	0.351592i
$845$	−7.46309	−	5.42225i	−0.256738	−	0.186531i
$846$		0			0
$847$	8.98580	−	14.2665i	0.308756	−	0.490202i
$848$	4.74538	−	8.21924i	0.162957	−	0.282250i
$849$		0			0
$850$	12.9440	−	2.75133i	0.443976	−	0.0943700i
$851$	6.18042	−	6.86405i	0.211862	−	0.235297i
$852$		0			0
$853$	2.20199	+	20.9505i	0.0753946	+	0.717332i	0.965292	+	0.261172i	$0.0841089\pi$
$853$	2.20199	+	20.9505i	0.0753946	+	0.717332i	−0.889898	+	0.456160i	$0.849224\pi$
$854$	−0.309792	−	0.953442i	−0.0106009	−	0.0326261i
$855$		0			0
$856$	9.85753	+	7.16191i	0.336923	+	0.244789i
$857$	−9.44141	+	16.3530i	−0.322512	+	0.558608i	−0.981006	−	0.193979i	$-0.937861\pi$
$857$	−9.44141	+	16.3530i	−0.322512	+	0.558608i	0.658493	+	0.752587i	$0.271194\pi$
$858$		0			0
$859$	21.5417	+	37.3113i	0.734992	+	1.27304i	0.954727	+	0.297485i	$0.0961477\pi$
$859$	21.5417	+	37.3113i	0.734992	+	1.27304i	−0.219734	+	0.975560i	$0.570519\pi$
$860$	0.832392	−	7.91968i	0.0283843	−	0.270059i
$861$		0			0
$862$	21.5943	+	4.59001i	0.735505	+	0.156336i
$863$	−12.9855	+	9.43449i	−0.442030	+	0.321154i	−0.786441	−	0.617665i	$-0.788079\pi$
$863$	−12.9855	+	9.43449i	−0.442030	+	0.321154i	0.344411	+	0.938819i	$0.388079\pi$
$864$		0			0
$865$	−8.20867	−	25.2637i	−0.279103	−	0.858992i
$866$	10.3011	+	11.4405i	0.350045	+	0.388764i
$867$		0			0
$868$	−3.19391	−	5.53201i	−0.108408	−	0.187769i
$869$	3.32785	−	5.51610i	0.112889	−	0.187121i
$870$		0			0
$871$	18.5285	−	8.24944i	0.627816	−	0.279522i
$872$	−12.3696	+	38.0698i	−0.418888	+	1.28920i
$873$		0			0
$874$	−5.66709	+	4.11738i	−0.191692	+	0.139273i
$875$	1.67046	+	15.8934i	0.0564719	+	0.537294i
$876$		0			0
$877$	−15.0582	+	3.20073i	−0.508481	+	0.108081i	−0.455006	−	0.890488i	$-0.650363\pi$
$877$	−15.0582	+	3.20073i	−0.508481	+	0.108081i	−0.0534747	+	0.998569i	$0.517030\pi$
$878$	0.998420	−	9.49933i	0.0336950	−	0.320587i
$879$		0			0
$880$	1.81396	+	5.97136i	0.0611485	+	0.201294i
$881$	−3.84430			−0.129518			−0.0647589	−	0.997901i	$-0.520628\pi$
$881$	−3.84430			−0.129518			−0.0647589	+	0.997901i	$0.520628\pi$
$882$		0			0
$883$	6.15742	−	18.9506i	0.207214	−	0.637738i	−0.792402	−	0.610000i	$-0.791170\pi$
$883$	6.15742	−	18.9506i	0.207214	−	0.637738i	0.999615	−	0.0277382i	$-0.00883048\pi$
$884$	−7.01388	−	1.49085i	−0.235902	−	0.0501426i
$885$		0			0
$886$	−9.99661	−	4.45078i	−0.335843	−	0.149527i
$887$	−7.77782	+	8.63814i	−0.261154	+	0.290040i	−0.859434	−	0.511246i	$-0.829184\pi$
$887$	−7.77782	+	8.63814i	−0.261154	+	0.290040i	0.598281	+	0.801287i	$0.295851\pi$
$888$		0			0
$889$	−2.21582	+	0.986545i	−0.0743161	+	0.0330877i
$890$	7.64868			0.256384
$891$		0			0
$892$	−22.6787			−0.759338
$893$	23.9257	−	10.6524i	0.800644	−	0.356470i
$894$		0			0
$895$	16.8410	−	18.7038i	0.562931	−	0.625198i
$896$	−0.817922	−	0.364162i	−0.0273249	−	0.0121658i
$897$		0			0
$898$	−21.3268	−	4.53316i	−0.711685	−	0.151273i
$899$	12.3885	−	38.1277i	0.413178	−	1.27163i
$900$		0			0
$901$	−21.9904			−0.732608
$902$	−5.60461	+	16.1829i	−0.186613	+	0.538832i
$903$		0			0
$904$	−0.729099	+	6.93692i	−0.0242495	+	0.230718i
$905$	−12.5225	+	2.66174i	−0.416262	+	0.0884792i
$906$		0			0
$907$	−3.15142	−	29.9838i	−0.104641	−	0.995596i	−0.913292	−	0.407306i	$-0.866468\pi$
$907$	−3.15142	−	29.9838i	−0.104641	−	0.995596i	0.808650	−	0.588290i	$-0.200198\pi$
$908$	1.94041	−	1.40979i	0.0643948	−	0.0467856i
$909$		0			0
$910$	−1.45278	+	4.47119i	−0.0481591	+	0.148218i
$911$	21.2477	−	9.46009i	0.703968	−	0.313427i	−0.0233502	−	0.999727i	$-0.507433\pi$
$911$	21.2477	−	9.46009i	0.703968	−	0.313427i	0.727318	+	0.686301i	$0.240767\pi$
$912$		0			0
$913$	−11.5818	−	13.3716i	−0.383302	−	0.442534i
$914$	−20.5278	−	35.5552i	−0.679000	−	1.17606i
$915$		0			0
$916$	−12.1250	−	13.4662i	−0.400621	−	0.444935i
$917$	−2.67259	−	8.22539i	−0.0882567	−	0.271626i
$918$		0			0
$919$	−19.1223	+	13.8932i	−0.630787	+	0.458294i	−0.856673	−	0.515860i	$-0.827472\pi$
$919$	−19.1223	+	13.8932i	−0.630787	+	0.458294i	0.225886	+	0.974154i	$0.427472\pi$
$920$	8.41148	+	1.78791i	0.277318	+	0.0589458i
$921$		0			0
$922$	2.17892	−	20.7310i	0.0717588	−	0.682740i
$923$	−18.2896	−	31.6786i	−0.602011	−	1.04271i
$924$		0			0
$925$	7.03079	−	12.1777i	0.231171	−	0.400400i
$926$	−14.2625	−	10.3623i	−0.468694	−	0.340526i
$927$		0			0
$928$	−11.4574	−	35.2624i	−0.376109	−	1.15755i
$929$	−5.68883	−	54.1256i	−0.186645	−	1.77580i	−0.541322	−	0.840815i	$-0.682076\pi$
$929$	−5.68883	−	54.1256i	−0.186645	−	1.77580i	0.354677	−	0.934989i	$-0.384591\pi$
$930$		0			0
$931$	8.90629	−	9.89144i	0.291892	−	0.324179i
$932$	11.4971	−	2.44377i	0.376599	−	0.0800485i
$933$		0			0
$934$	−15.6348	+	27.0802i	−0.511586	+	0.886092i
$935$	9.88070	−	10.5578i	0.323133	−	0.345278i
$936$		0			0
$937$	−21.9192	−	15.9253i	−0.716070	−	0.520255i	0.169056	−	0.985606i	$-0.445928\pi$
$937$	−21.9192	−	15.9253i	−0.716070	−	0.520255i	−0.885126	+	0.465351i	$0.845928\pi$
$938$	9.47439	+	10.5224i	0.309350	+	0.343568i
$939$		0			0
$940$	−8.84678	−	3.93884i	−0.288550	−	0.128471i
$941$	33.6137	+	14.9658i	1.09577	+	0.487870i	0.873357	−	0.487081i	$-0.161938\pi$
$941$	33.6137	+	14.9658i	1.09577	+	0.487870i	0.222418	+	0.974951i	$0.428605\pi$
$942$		0			0
$943$	7.43141	+	8.25341i	0.242000	+	0.268768i
$944$	13.4982	+	9.80702i	0.439329	+	0.319191i
$945$		0			0
$946$	−12.8654	−	23.3079i	−0.418289	−	0.757806i
$947$	−29.5145	+	51.1206i	−0.959093	+	1.66120i	−0.234381	+	0.972145i	$0.575306\pi$
$947$	−29.5145	+	51.1206i	−0.959093	+	1.66120i	−0.724712	+	0.689052i	$0.758027\pi$
$948$		0			0
$949$	34.7225	−	7.38051i	1.12714	−	0.239581i
$950$	−7.13577	+	7.92508i	−0.231515	+	0.257123i
$951$		0			0
$952$	−1.73725	−	16.5289i	−0.0563047	−	0.535704i
$953$	12.3238	+	37.9287i	0.399206	+	1.22863i	0.925637	+	0.378413i	$0.123530\pi$
$953$	12.3238	+	37.9287i	0.399206	+	1.22863i	−0.526431	+	0.850218i	$0.676470\pi$
$954$		0			0
$955$	−20.5026	−	14.8960i	−0.663449	−	0.482024i
$956$	−8.73972	+	15.1376i	−0.282663	+	0.489586i
$957$		0			0
$958$	8.26118	+	14.3088i	0.266907	+	0.462296i
$959$	−3.46857	+	33.0012i	−0.112006	+	1.06566i
$960$		0			0
$961$	7.46193	+	1.58608i	0.240707	+	0.0511640i
$962$	8.13718	−	5.91201i	0.262353	−	0.190611i
$963$		0			0
$964$	7.03081	+	21.6386i	0.226447	+	0.696932i
$965$	4.92212	+	5.46656i	0.158449	+	0.175975i
$966$		0			0
$967$	11.1643	+	19.3371i	0.359019	+	0.621838i	0.987797	−	0.155746i	$-0.0497781\pi$
$967$	11.1643	+	19.3371i	0.359019	+	0.621838i	−0.628779	+	0.777584i	$0.716445\pi$
$968$	−26.3904	−	20.7709i	−0.848219	−	0.667600i
$969$		0			0
$970$	−10.1759	+	4.53060i	−0.326728	+	0.145469i
$971$	5.35373	−	16.4771i	0.171809	−	0.528775i	−0.827664	−	0.561224i	$-0.810331\pi$
$971$	5.35373	−	16.4771i	0.171809	−	0.528775i	0.999473	+	0.0324490i	$0.0103307\pi$
$972$		0			0
$973$	−26.1155	+	18.9740i	−0.837223	+	0.608278i
$974$	−0.432242	−	4.11251i	−0.0138499	−	0.131773i
$975$		0			0
$976$	−0.919243	+	0.195391i	−0.0294243	+	0.00625432i
$977$	−2.10562	+	20.0337i	−0.0673648	+	0.640934i	0.907792	+	0.419420i	$0.137766\pi$
$977$	−2.10562	+	20.0337i	−0.0673648	+	0.640934i	−0.975157	+	0.221514i	$0.928900\pi$
$978$		0			0
$979$	−15.8878	+	11.0825i	−0.507776	+	0.354197i
$980$	−4.92160			−0.157215
$981$		0			0
$982$	−2.39234	+	7.36286i	−0.0763425	+	0.234958i
$983$	−24.4304	−	5.19284i	−0.779208	−	0.165626i	−0.198897	−	0.980020i	$-0.563736\pi$
$983$	−24.4304	−	5.19284i	−0.779208	−	0.165626i	−0.580311	+	0.814395i	$0.697069\pi$
$984$		0			0
$985$	−1.59027	−	0.708035i	−0.0506703	−	0.0225599i
$986$	21.0221	−	23.3474i	0.669481	−	0.743534i
$987$		0			0
$988$	5.27898	−	2.35035i	0.167947	−	0.0747747i
$989$	−17.2648			−0.548987
$990$		0			0
$991$	−3.49555			−0.111040			−0.0555199	−	0.998458i	$-0.517682\pi$
$991$	−3.49555			−0.111040			−0.0555199	+	0.998458i	$0.517682\pi$
$992$	−19.7463	+	8.79161i	−0.626945	+	0.279134i
$993$		0			0
$994$	17.0874	−	18.9775i	0.541979	−	0.601928i
$995$	−6.81137	−	3.03262i	−0.215935	−	0.0961404i
$996$		0			0
$997$	−7.20387	−	1.53123i	−0.228149	−	0.0484946i	0.0924185	−	0.995720i	$-0.470540\pi$
$997$	−7.20387	−	1.53123i	−0.228149	−	0.0484946i	−0.320567	+	0.947226i	$0.603874\pi$
$998$	−11.8332	+	36.4188i	−0.374573	+	1.15282i
$999$		0			0

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	891.2.n.g.136.2		32
3.2	odd	2	inner	891.2.n.g.136.3		32
9.2	odd	6		297.2.f.c.136.2	✓	16
9.4	even	3	inner	891.2.n.g.433.3		32
9.5	odd	6	inner	891.2.n.g.433.2		32
9.7	even	3		297.2.f.c.136.3	yes	16
11.3	even	5	inner	891.2.n.g.784.3		32
33.14	odd	10	inner	891.2.n.g.784.2		32
99.14	odd	30	inner	891.2.n.g.190.3		32
99.16	even	15		3267.2.a.bg.1.3		8
99.25	even	15		297.2.f.c.190.3	yes	16
99.38	odd	30		3267.2.a.bg.1.6		8
99.47	odd	30		297.2.f.c.190.2	yes	16
99.58	even	15	inner	891.2.n.g.190.2		32
99.61	odd	30		3267.2.a.bh.1.6		8
99.83	even	30		3267.2.a.bh.1.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
297.2.f.c.136.2	✓	16	9.2	odd	6
297.2.f.c.136.3	yes	16	9.7	even	3
297.2.f.c.190.2	yes	16	99.47	odd	30
297.2.f.c.190.3	yes	16	99.25	even	15
891.2.n.g.136.2		32	1.1	even	1	trivial
891.2.n.g.136.3		32	3.2	odd	2	inner
891.2.n.g.190.2		32	99.58	even	15	inner
891.2.n.g.190.3		32	99.14	odd	30	inner
891.2.n.g.433.2		32	9.5	odd	6	inner
891.2.n.g.433.3		32	9.4	even	3	inner
891.2.n.g.784.2		32	33.14	odd	10	inner
891.2.n.g.784.3		32	11.3	even	5	inner
3267.2.a.bg.1.3		8	99.16	even	15
3267.2.a.bg.1.6		8	99.38	odd	30
3267.2.a.bh.1.3		8	99.83	even	30
3267.2.a.bh.1.6		8	99.61	odd	30

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

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	891.2.n.g.136.2

Level	$891$
Weight	$2$
Character	891.136
Analytic conductor	$7.115$
Analytic rank	$0$
Dimension	$32$
Inner twists	$8$