LMFDB - Embedded newform 804.2.s.b.5.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(5,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 5]))

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

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

chi := DirichletCharacter("804.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.s (of order $22$, degree $10$, 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:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$200$
Relative dimension:	$20$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			5.10
Character	$\chi$	$=$	804.5
Dual form			804.2.s.b.161.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.393301 + 1.68681i) q^{3} +(3.45254 - 1.01376i) q^{5} +(-0.403229 - 0.349400i) q^{7} +(-2.69063 - 1.32685i) q^{9} +O(q^{10})$	\(q+(-0.393301 + 1.68681i) q^{3} +(3.45254 - 1.01376i) q^{5} +(-0.403229 - 0.349400i) q^{7} +(-2.69063 - 1.32685i) q^{9} +(-0.843418 + 0.247650i) q^{11} +(2.49538 + 3.88288i) q^{13} +(0.352124 + 6.22247i) q^{15} +(6.49699 + 0.934126i) q^{17} +(-1.01843 - 1.17533i) q^{19} +(0.747960 - 0.542749i) q^{21} +(-1.87132 + 0.854604i) q^{23} +(6.68605 - 4.29687i) q^{25} +(3.29636 - 4.01672i) q^{27} +3.54360i q^{29} +(2.94854 - 4.58802i) q^{31} +(-0.0860200 - 1.52008i) q^{33} +(-1.74637 - 0.797540i) q^{35} +6.30938 q^{37} +(-7.53110 + 2.68207i) q^{39} +(-1.58851 + 11.0483i) q^{41} +(4.21011 + 0.605322i) q^{43} +(-10.6346 - 1.85334i) q^{45} +(-8.24517 + 3.76544i) q^{47} +(-0.955691 - 6.64697i) q^{49} +(-4.13096 + 10.5918i) q^{51} +(-0.880650 - 6.12505i) q^{53} +(-2.66088 + 1.71004i) q^{55} +(2.38311 - 1.25564i) q^{57} +(0.431424 - 0.671308i) q^{59} +(-1.65734 + 5.64439i) q^{61} +(0.621339 + 1.47513i) q^{63} +(12.5517 + 10.8761i) q^{65} +(4.80367 + 6.62757i) q^{67} +(-0.705558 - 3.49267i) q^{69} +(-3.24010 + 0.465856i) q^{71} +(-4.50675 - 1.32330i) q^{73} +(4.61835 + 12.9680i) q^{75} +(0.426619 + 0.194830i) q^{77} +(-1.15200 - 1.79255i) q^{79} +(5.47896 + 7.14010i) q^{81} +(-0.393211 - 1.33915i) q^{83} +(23.3781 - 3.36126i) q^{85} +(-5.97736 - 1.39370i) q^{87} +(0.163010 + 0.0744440i) q^{89} +(0.350470 - 2.43757i) q^{91} +(6.57944 + 6.77810i) q^{93} +(-4.70767 - 3.02544i) q^{95} -3.07848i q^{97} +(2.59792 + 0.452751i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 200 q - 10 q^{9}+O(q^{10}) $ 200 * q - 10 * q^9	$ 200 q - 10 q^{9} + 2 q^{15} + 6 q^{19} - 10 q^{21} - 20 q^{25} - 44 q^{31} - 5 q^{33} + 78 q^{39} - 22 q^{43} - 22 q^{45} - 16 q^{49} + 36 q^{55} + 66 q^{57} + 176 q^{61} + 132 q^{63} + 46 q^{67} - 26 q^{73} - 165 q^{75} - 44 q^{79} + 42 q^{81} - 66 q^{87} - 20 q^{91} + 84 q^{93} - 55 q^{99}+O(q^{100}) $ 200 * q - 10 * q^9 + 2 * q^15 + 6 * q^19 - 10 * q^21 - 20 * q^25 - 44 * q^31 - 5 * q^33 + 78 * q^39 - 22 * q^43 - 22 * q^45 - 16 * q^49 + 36 * q^55 + 66 * q^57 + 176 * q^61 + 132 * q^63 + 46 * q^67 - 26 * q^73 - 165 * q^75 - 44 * q^79 + 42 * q^81 - 66 * q^87 - 20 * q^91 + 84 * q^93 - 55 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$-1$	$e\left(\frac{5}{22}\right)$	$1$

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			0
$2$		0			0
$3$	−0.393301	+	1.68681i	−0.227073	+	0.973878i
$3$	−0.393301	+	1.68681i	−0.227073	+	0.973878i
$4$		0			0
$5$	3.45254	−	1.01376i	1.54402	−	0.453366i	0.604715	−	0.796442i	$-0.293287\pi$
$5$	3.45254	−	1.01376i	1.54402	−	0.453366i	0.939308	+	0.343076i	$0.111469\pi$
$6$		0			0
$7$	−0.403229	−	0.349400i	−0.152406	−	0.132061i	0.575320	−	0.817928i	$-0.304877\pi$
$7$	−0.403229	−	0.349400i	−0.152406	−	0.132061i	−0.727726	+	0.685868i	$0.759423\pi$
$8$		0			0
$9$	−2.69063	−	1.32685i	−0.896876	−	0.442282i
$10$		0			0
$11$	−0.843418	+	0.247650i	−0.254300	+	0.0746692i	−0.406398	−	0.913696i	$-0.633215\pi$
$11$	−0.843418	+	0.247650i	−0.254300	+	0.0746692i	0.152098	+	0.988365i	$0.451397\pi$
$12$		0			0
$13$	2.49538	+	3.88288i	0.692093	+	1.07692i	0.992397	+	0.123074i	$0.0392753\pi$
$13$	2.49538	+	3.88288i	0.692093	+	1.07692i	−0.300305	+	0.953843i	$0.597088\pi$
$14$		0			0
$15$	0.352124	+	6.22247i	0.0909179	+	1.60664i
$16$		0			0
$17$	6.49699	+	0.934126i	1.57575	+	0.226559i	0.874023	−	0.485885i	$-0.161503\pi$
$17$	6.49699	+	0.934126i	1.57575	+	0.226559i	0.701729	+	0.712444i	$0.252412\pi$
$18$		0			0
$19$	−1.01843	−	1.17533i	−0.233644	−	0.269640i	0.626805	−	0.779176i	$-0.284362\pi$
$19$	−1.01843	−	1.17533i	−0.233644	−	0.269640i	−0.860449	+	0.509537i	$0.829817\pi$
$20$		0			0
$21$	0.747960	−	0.542749i	0.163218	−	0.118438i
$22$		0			0
$23$	−1.87132	+	0.854604i	−0.390198	+	0.178197i	−0.600846	−	0.799365i	$-0.705170\pi$
$23$	−1.87132	+	0.854604i	−0.390198	+	0.178197i	0.210649	+	0.977562i	$0.432442\pi$
$24$		0			0
$25$	6.68605	−	4.29687i	1.33721	−	0.859373i
$26$		0			0
$27$	3.29636	−	4.01672i	0.634384	−	0.773018i
$28$		0			0
$29$			3.54360i			0.658030i	0.944325	+	0.329015i	$0.106717\pi$
$29$			3.54360i			0.658030i	−0.944325	+	0.329015i	$0.893283\pi$
$30$		0			0
$31$	2.94854	−	4.58802i	0.529574	−	0.824033i	−0.468664	−	0.883377i	$-0.655264\pi$
$31$	2.94854	−	4.58802i	0.529574	−	0.824033i	0.998238	+	0.0593434i	$0.0189007\pi$
$32$		0			0
$33$	−0.0860200	−	1.52008i	−0.0149742	−	0.264613i
$34$		0			0
$35$	−1.74637	−	0.797540i	−0.295190	−	0.134809i
$36$		0			0
$37$	6.30938			1.03726			0.518628	−	0.855000i	$-0.326443\pi$
$37$	6.30938			1.03726			0.518628	+	0.855000i	$0.326443\pi$
$38$		0			0
$39$	−7.53110	+	2.68207i	−1.20594	+	0.429475i
$40$		0			0
$41$	−1.58851	+	11.0483i	−0.248084	+	1.72546i	0.361182	+	0.932495i	$0.382373\pi$
$41$	−1.58851	+	11.0483i	−0.248084	+	1.72546i	−0.609266	+	0.792966i	$0.708536\pi$
$42$		0			0
$43$	4.21011	+	0.605322i	0.642035	+	0.0923107i	0.455640	−	0.890164i	$-0.349410\pi$
$43$	4.21011	+	0.605322i	0.642035	+	0.0923107i	0.186395	+	0.982475i	$0.440320\pi$
$44$		0			0
$45$	−10.6346	−	1.85334i	−1.58531	−	0.276280i
$46$		0			0
$47$	−8.24517	+	3.76544i	−1.20268	+	0.549246i	−0.913032	−	0.407887i	$-0.866266\pi$
$47$	−8.24517	+	3.76544i	−1.20268	+	0.549246i	−0.289649	+	0.957133i	$0.593538\pi$
$48$		0			0
$49$	−0.955691	−	6.64697i	−0.136527	−	0.949568i
$50$		0			0
$51$	−4.13096	+	10.5918i	−0.578451	+	1.48314i
$52$		0			0
$53$	−0.880650	−	6.12505i	−0.120967	−	0.841341i	−0.956465	−	0.291848i	$-0.905730\pi$
$53$	−0.880650	−	6.12505i	−0.120967	−	0.841341i	0.835498	−	0.549493i	$-0.185179\pi$
$54$		0			0
$55$	−2.66088	+	1.71004i	−0.358792	+	0.230582i
$56$		0			0
$57$	2.38311	−	1.25564i	0.315650	−	0.166313i
$58$		0			0
$59$	0.431424	−	0.671308i	0.0561666	−	0.0873969i	−0.812035	−	0.583609i	$-0.801640\pi$
$59$	0.431424	−	0.671308i	0.0561666	−	0.0873969i	0.868201	+	0.496212i	$0.165276\pi$
$60$		0			0
$61$	−1.65734	+	5.64439i	−0.212201	+	0.722689i	0.782751	+	0.622335i	$0.213816\pi$
$61$	−1.65734	+	5.64439i	−0.212201	+	0.722689i	−0.994952	+	0.100354i	$0.968002\pi$
$62$		0			0
$63$	0.621339	+	1.47513i	0.0782814	+	0.185849i
$64$		0			0
$65$	12.5517	+	10.8761i	1.55684	+	1.34901i
$66$		0			0
$67$	4.80367	+	6.62757i	0.586862	+	0.809687i
$67$	4.80367	+	6.62757i	0.586862	+	0.809687i
$68$		0			0
$69$	−0.705558	−	3.49267i	−0.0849392	−	0.420468i
$70$		0			0
$71$	−3.24010	+	0.465856i	−0.384529	+	0.0552869i	−0.331869	−	0.943326i	$-0.607679\pi$
$71$	−3.24010	+	0.465856i	−0.384529	+	0.0552869i	−0.0526601	+	0.998612i	$0.516770\pi$
$72$		0			0
$73$	−4.50675	−	1.32330i	−0.527475	−	0.154881i	0.00714274	−	0.999974i	$-0.497726\pi$
$73$	−4.50675	−	1.32330i	−0.527475	−	0.154881i	−0.534618	+	0.845094i	$0.679545\pi$
$74$		0			0
$75$	4.61835	+	12.9680i	0.533281	+	1.49742i
$76$		0			0
$77$	0.426619	+	0.194830i	0.0486178	+	0.0222030i
$78$		0			0
$79$	−1.15200	−	1.79255i	−0.129610	−	0.201678i	0.770383	−	0.637582i	$-0.220065\pi$
$79$	−1.15200	−	1.79255i	−0.129610	−	0.201678i	−0.899993	+	0.435904i	$0.856429\pi$
$80$		0			0
$81$	5.47896	+	7.14010i	0.608774	+	0.793344i
$82$		0			0
$83$	−0.393211	−	1.33915i	−0.0431605	−	0.146991i	0.935094	−	0.354400i	$-0.115315\pi$
$83$	−0.393211	−	1.33915i	−0.0431605	−	0.146991i	−0.978254	+	0.207409i	$0.933497\pi$
$84$		0			0
$85$	23.3781	−	3.36126i	2.53571	−	0.364580i
$86$		0			0
$87$	−5.97736	−	1.39370i	−0.640841	−	0.149420i
$88$		0			0
$89$	0.163010	+	0.0744440i	0.0172790	+	0.00789105i	0.424036	−	0.905645i	$-0.360613\pi$
$89$	0.163010	+	0.0744440i	0.0172790	+	0.00789105i	−0.406757	+	0.913536i	$0.633340\pi$
$90$		0			0
$91$	0.350470	−	2.43757i	0.0367392	−	0.255527i
$92$		0			0
$93$	6.57944	+	6.77810i	0.682256	+	0.702856i
$94$		0			0
$95$	−4.70767	−	3.02544i	−0.482997	−	0.310403i
$96$		0			0
$97$		−	3.07848i		−	0.312572i	−0.987712	−	0.156286i	$-0.950048\pi$
$97$		−	3.07848i		−	0.312572i	0.987712	−	0.156286i	$-0.0499522\pi$
$98$		0			0
$99$	2.59792	+	0.452751i	0.261100	+	0.0455032i
$100$		0			0
$101$	2.92667	+	3.37755i	0.291214	+	0.336079i	0.882438	−	0.470428i	$-0.155901\pi$
$101$	2.92667	+	3.37755i	0.291214	+	0.336079i	−0.591224	+	0.806507i	$0.701355\pi$
$102$		0			0
$103$	1.49986	+	0.963903i	0.147786	+	0.0949762i	0.612444	−	0.790514i	$-0.290186\pi$
$103$	1.49986	+	0.963903i	0.147786	+	0.0949762i	−0.464658	+	0.885490i	$0.653823\pi$
$104$		0			0
$105$	2.03214	−	2.63211i	0.198317	−	0.256868i
$106$		0			0
$107$	1.95591	−	6.66122i	0.189085	−	0.643965i	−0.809313	−	0.587378i	$-0.800160\pi$
$107$	1.95591	−	6.66122i	0.189085	−	0.643965i	0.998398	−	0.0565865i	$-0.0180217\pi$
$108$		0			0
$109$	−10.3159	−	16.0519i	−0.988088	−	1.53750i	−0.835709	−	0.549173i	$-0.814943\pi$
$109$	−10.3159	−	16.0519i	−0.988088	−	1.53750i	−0.152380	−	0.988322i	$-0.548694\pi$
$110$		0			0
$111$	−2.48149	+	10.6427i	−0.235532	+	1.01016i
$112$		0			0
$113$	−14.7239	−	4.32334i	−1.38511	−	0.406705i	−0.497566	−	0.867426i	$-0.665773\pi$
$113$	−14.7239	−	4.32334i	−1.38511	−	0.406705i	−0.887545	+	0.460721i	$0.847591\pi$
$114$		0			0
$115$	−5.59445	+	4.84762i	−0.521685	+	0.452043i
$116$		0			0
$117$	−1.56215	−	13.7584i	−0.144421	−	1.27196i
$118$		0			0
$119$	−2.29339	−	2.64671i	−0.210235	−	0.242624i
$120$		0			0
$121$	−8.60377	+	5.52930i	−0.782161	+	0.502664i
$122$		0			0
$123$	−18.0116	−	7.02484i	−1.62406	−	0.633408i
$124$		0			0
$125$	6.94597	−	8.01608i	0.621266	−	0.716980i
$126$		0			0
$127$	12.7273	−	14.6881i	1.12937	−	1.30336i	0.181971	−	0.983304i	$-0.441752\pi$
$127$	12.7273	−	14.6881i	1.12937	−	1.30336i	0.947398	−	0.320058i	$-0.103702\pi$
$128$		0			0
$129$	−2.67690	+	6.86356i	−0.235688	+	0.604303i
$130$		0			0
$131$	−11.7755	+	5.37767i	−1.02883	+	0.469849i	−0.857021	−	0.515281i	$-0.827687\pi$
$131$	−11.7755	+	5.37767i	−1.02883	+	0.469849i	−0.171806	+	0.985131i	$0.554960\pi$
$132$		0			0
$133$			0.829767i			0.0719500i
$134$		0			0
$135$	7.30883	−	17.2096i	0.629044	−	1.48116i
$136$		0			0
$137$	−7.14425	−	15.6437i	−0.610374	−	1.33653i	−0.922318	−	0.386432i	$-0.873707\pi$
$137$	−7.14425	−	15.6437i	−0.610374	−	1.33653i	0.311944	−	0.950101i	$-0.399020\pi$
$138$		0			0
$139$	5.06115	+	17.2367i	0.429281	+	1.46200i	0.836145	+	0.548509i	$0.184804\pi$
$139$	5.06115	+	17.2367i	0.429281	+	1.46200i	−0.406864	+	0.913489i	$0.633378\pi$
$140$		0			0
$141$	−3.10874	−	15.3889i	−0.261803	−	1.29598i
$142$		0			0
$143$	−3.06624	−	2.65691i	−0.256412	−	0.222182i
$144$		0			0
$145$	3.59235	+	12.2344i	0.298328	+	1.01601i
$146$		0			0
$147$	11.5880	+	1.00220i	0.955765	+	0.0826599i
$148$		0			0
$149$	−5.57355	+	4.82951i	−0.456603	+	0.395649i	−0.852568	−	0.522617i	$-0.824956\pi$
$149$	−5.57355	+	4.82951i	−0.456603	+	0.395649i	0.395965	+	0.918266i	$0.370410\pi$
$150$		0			0
$151$	2.82914	−	19.6771i	0.230232	−	1.60130i	−0.466869	−	0.884327i	$-0.654618\pi$
$151$	2.82914	−	19.6771i	0.230232	−	1.60130i	0.697101	−	0.716973i	$-0.254473\pi$
$152$		0			0
$153$	−16.2415	−	11.1339i	−1.31305	−	0.900122i
$154$		0			0
$155$	5.52882	−	18.8294i	0.444086	−	1.51242i
$156$		0			0
$157$	−5.31680	−	11.6422i	−0.424327	−	0.929146i	−0.994213	−	0.107423i	$-0.965740\pi$
$157$	−5.31680	−	11.6422i	−0.424327	−	0.929146i	0.569886	−	0.821723i	$-0.306987\pi$
$158$		0			0
$159$	10.6781	+	0.923505i	0.846831	+	0.0732387i
$160$		0			0
$161$	1.05317	+	0.309238i	0.0830014	+	0.0243714i
$162$		0			0
$163$	13.1841			1.03266			0.516328	−	0.856391i	$-0.327299\pi$
$163$	13.1841			1.03266			0.516328	+	0.856391i	$0.327299\pi$
$164$		0			0
$165$	−1.83798	−	5.16094i	−0.143087	−	0.401779i
$166$		0			0
$167$	−16.9979	+	14.7288i	−1.31534	+	1.13975i	−0.335042	+	0.942203i	$0.608750\pi$
$167$	−16.9979	+	14.7288i	−1.31534	+	1.13975i	−0.980294	+	0.197542i	$0.936704\pi$
$168$		0			0
$169$	−3.44947	+	7.55328i	−0.265344	+	0.581022i
$170$		0			0
$171$	1.18074	+	4.51368i	0.0902931	+	0.345170i
$172$		0			0
$173$	3.64796	−	5.67634i	0.277349	−	0.431564i	−0.674434	−	0.738335i	$-0.735612\pi$
$173$	3.64796	−	5.67634i	0.277349	−	0.431564i	0.951783	+	0.306771i	$0.0992487\pi$
$174$		0			0
$175$	−4.19733	−	0.603485i	−0.317289	−	0.0456192i
$176$		0			0
$177$	0.962688	+	0.991754i	0.0723600	+	0.0745448i
$178$		0			0
$179$	7.58099	−	16.6001i	0.566630	−	1.24075i	−0.381942	−	0.924186i	$-0.624745\pi$
$179$	7.58099	−	16.6001i	0.566630	−	1.24075i	0.948572	−	0.316560i	$-0.102528\pi$
$180$		0			0
$181$	−7.25678	−	15.8901i	−0.539392	−	1.18110i	−0.961562	−	0.274587i	$-0.911459\pi$
$181$	−7.25678	−	15.8901i	−0.539392	−	1.18110i	0.422170	−	0.906517i	$-0.361269\pi$
$182$		0			0
$183$	−8.86915	−	5.01556i	−0.655626	−	0.370761i
$184$		0			0
$185$	21.7834	−	6.39618i	1.60155	−	0.470256i
$186$		0			0
$187$	−5.71101	+	0.821120i	−0.417631	+	0.0600462i
$188$		0			0
$189$	−2.73263	+	0.467910i	−0.198769	+	0.0340354i
$190$		0			0
$191$	4.54526	−	9.95273i	0.328883	−	0.720154i	−0.670887	−	0.741559i	$-0.734087\pi$
$191$	4.54526	−	9.95273i	0.328883	−	0.720154i	0.999771	+	0.0214049i	$0.00681392\pi$
$192$		0			0
$193$	−10.0851	−	6.48129i	−0.725941	−	0.466534i	0.124758	−	0.992187i	$-0.460185\pi$
$193$	−10.0851	−	6.48129i	−0.725941	−	0.466534i	−0.850699	+	0.525653i	$0.823821\pi$
$194$		0			0
$195$	−23.2824	+	16.8947i	−1.66729	+	1.20985i
$196$		0			0
$197$	−1.10270	−	7.66945i	−0.0785642	−	0.546426i	−0.990650	−	0.136427i	$-0.956438\pi$
$197$	−1.10270	−	7.66945i	−0.0785642	−	0.546426i	0.912086	−	0.409999i	$-0.134471\pi$
$198$		0			0
$199$	0.317248	−	0.366124i	0.0224891	−	0.0259538i	−0.744394	−	0.667741i	$-0.767261\pi$
$199$	0.317248	−	0.366124i	0.0224891	−	0.0259538i	0.766883	+	0.641787i	$0.221807\pi$
$200$		0			0
$201$	−13.0687	+	5.49623i	−0.921797	+	0.387674i
$202$		0			0
$203$	1.23813	−	1.42888i	0.0868999	−	0.100288i
$204$		0			0
$205$	5.71593	+	39.7552i	0.399218	+	2.77662i
$206$		0			0
$207$	6.16896	+	0.183533i	0.428772	+	0.0127564i
$208$		0			0
$209$	1.15003	+	0.739082i	0.0795495	+	0.0511234i
$210$		0			0
$211$	4.84812	−	10.6159i	0.333758	−	0.730828i	−0.666129	−	0.745836i	$-0.732050\pi$
$211$	4.84812	−	10.6159i	0.333758	−	0.730828i	0.999887	+	0.0150079i	$0.00477734\pi$
$212$		0			0
$213$	0.488526	−	5.64864i	0.0334732	−	0.387038i
$214$		0			0
$215$	15.1492	−	2.17813i	1.03317	−	0.148547i
$216$		0			0
$217$	−2.79199	+	0.819803i	−0.189533	+	0.0556518i
$218$		0			0
$219$	4.00466	−	7.08156i	0.270610	−	0.478527i
$220$		0			0
$221$	12.5853	+	27.5580i	0.846581	+	1.85375i
$222$		0			0
$223$	−11.2385	+	24.6088i	−0.752584	+	1.64793i	0.00908061	+	0.999959i	$0.497110\pi$
$223$	−11.2385	+	24.6088i	−0.752584	+	1.64793i	−0.761665	+	0.647971i	$0.775618\pi$
$224$		0			0
$225$	−23.6910	+	2.68991i	−1.57940	+	0.179327i
$226$		0			0
$227$	10.3756	+	1.49178i	0.688652	+	0.0990132i	0.477752	−	0.878495i	$-0.341452\pi$
$227$	10.3756	+	1.49178i	0.688652	+	0.0990132i	0.210899	+	0.977508i	$0.432361\pi$
$228$		0			0
$229$	3.49616	−	5.44013i	0.231033	−	0.359494i	−0.706310	−	0.707903i	$-0.749641\pi$
$229$	3.49616	−	5.44013i	0.231033	−	0.359494i	0.937343	+	0.348409i	$0.113278\pi$
$230$		0			0
$231$	−0.496431	+	0.642997i	−0.0326628	+	0.0423061i
$232$		0			0
$233$	−2.37287	+	5.19586i	−0.155452	+	0.340392i	−0.971294	−	0.237883i	$-0.923547\pi$
$233$	−2.37287	+	5.19586i	−0.155452	+	0.340392i	0.815842	+	0.578275i	$0.196274\pi$
$234$		0			0
$235$	−24.6495	+	21.3589i	−1.60796	+	1.39330i
$236$		0			0
$237$	3.47677	−	1.23819i	0.225840	−	0.0804292i
$238$		0			0
$239$	3.72434			0.240907			0.120454	−	0.992719i	$-0.461565\pi$
$239$	3.72434			0.240907			0.120454	+	0.992719i	$0.461565\pi$
$240$		0			0
$241$	1.00745	+	0.295814i	0.0648955	+	0.0190550i	0.314019	−	0.949417i	$-0.398324\pi$
$241$	1.00745	+	0.295814i	0.0648955	+	0.0190550i	−0.249124	+	0.968472i	$0.580143\pi$
$242$		0			0
$243$	−14.1988	+	6.43374i	−0.910856	+	0.412724i
$244$		0			0
$245$	−10.0380	−	21.9801i	−0.641303	−	1.40426i
$246$		0			0
$247$	2.02231	−	6.88734i	0.128676	−	0.438231i
$248$		0			0
$249$	2.41354	−	0.136580i	0.152952	−	0.00865541i
$250$		0			0
$251$	−1.48784	+	10.3481i	−0.0939115	+	0.653169i	0.887437	+	0.460930i	$0.152484\pi$
$251$	−1.48784	+	10.3481i	−0.0939115	+	0.653169i	−0.981348	+	0.192239i	$0.938425\pi$
$252$		0			0
$253$	1.36666	−	1.18422i	0.0859214	−	0.0744513i
$254$		0			0
$255$	−3.52483	+	40.7563i	−0.220734	+	2.55226i
$256$		0			0
$257$	4.05802	+	13.8203i	0.253132	+	0.862089i	0.983787	+	0.179342i	$0.0573968\pi$
$257$	4.05802	+	13.8203i	0.253132	+	0.862089i	−0.730655	+	0.682747i	$0.760785\pi$
$258$		0			0
$259$	−2.54412	−	2.20450i	−0.158084	−	0.136981i
$260$		0			0
$261$	4.70181	−	9.53451i	0.291035	−	0.590171i
$262$		0			0
$263$	6.35551	+	21.6449i	0.391898	+	1.33468i	0.885357	+	0.464912i	$0.153914\pi$
$263$	6.35551	+	21.6449i	0.391898	+	1.33468i	−0.493460	+	0.869769i	$0.664268\pi$
$264$		0			0
$265$	−9.24979	−	20.2542i	−0.568210	−	1.24421i
$266$		0			0
$267$	−0.189684	+	0.245687i	−0.0116085	+	0.0150358i
$268$		0			0
$269$		−	23.7751i		−	1.44960i	−0.688962	−	0.724798i	$-0.741933\pi$
$269$		−	23.7751i		−	1.44960i	0.688962	−	0.724798i	$-0.258067\pi$
$270$		0			0
$271$	27.9570	−	12.7676i	1.69827	−	0.775574i	0.700168	−	0.713978i	$-0.253108\pi$
$271$	27.9570	−	12.7676i	1.69827	−	0.775574i	0.998101	−	0.0615959i	$-0.0196190\pi$
$272$		0			0
$273$	3.97387	+	1.54988i	0.240510	+	0.0938027i
$274$		0			0
$275$	−4.57502	+	5.27985i	−0.275884	+	0.318387i
$276$		0			0
$277$	3.85148	−	4.44485i	0.231413	−	0.267065i	−0.628153	−	0.778090i	$-0.716189\pi$
$277$	3.85148	−	4.44485i	0.231413	−	0.267065i	0.859566	+	0.511025i	$0.170734\pi$
$278$		0			0
$279$	−14.0210	+	8.43240i	−0.839417	+	0.504835i
$280$		0			0
$281$	4.93616	−	3.17228i	0.294467	−	0.189242i	−0.385063	−	0.922890i	$-0.625820\pi$
$281$	4.93616	−	3.17228i	0.294467	−	0.189242i	0.679530	+	0.733648i	$0.262184\pi$
$282$		0			0
$283$	−17.6010	−	20.3126i	−1.04627	−	1.20746i	−0.977742	−	0.209813i	$-0.932715\pi$
$283$	−17.6010	−	20.3126i	−1.04627	−	1.20746i	−0.0685298	−	0.997649i	$-0.521831\pi$
$284$		0			0
$285$	6.95486	−	6.75102i	0.411970	−	0.399896i
$286$		0			0
$287$	4.50082	−	3.89998i	0.265675	−	0.230209i
$288$		0			0
$289$	25.0269	+	7.34856i	1.47217	+	0.432268i
$290$		0			0
$291$	5.19279	+	1.21077i	0.304407	+	0.0709765i
$292$		0			0
$293$	−3.40318	−	5.29545i	−0.198816	−	0.309364i	0.727503	−	0.686105i	$-0.240681\pi$
$293$	−3.40318	−	5.29545i	−0.198816	−	0.309364i	−0.926319	+	0.376741i	$0.877045\pi$
$294$		0			0
$295$	0.808964	−	2.75508i	0.0470997	−	0.160407i
$296$		0			0
$297$	−1.78547	+	4.20411i	−0.103603	+	0.243947i
$298$		0			0
$299$	−7.98798	−	5.13356i	−0.461957	−	0.296881i
$300$		0			0
$301$	−1.48614	−	1.71509i	−0.0856595	−	0.0988563i
$302$		0			0
$303$	−6.84834	+	3.60832i	−0.393427	+	0.207293i
$304$		0			0
$305$			21.1676i			1.21205i
$306$		0			0
$307$	−25.9210	−	16.6584i	−1.47939	−	0.950747i	−0.997208	−	0.0746775i	$-0.976207\pi$
$307$	−25.9210	−	16.6584i	−1.47939	−	0.950747i	−0.482184	−	0.876070i	$-0.660156\pi$
$308$		0			0
$309$	−2.21581	+	2.15087i	−0.126053	+	0.122359i
$310$		0			0
$311$	−3.85323	+	26.7998i	−0.218497	+	1.51968i	0.525094	+	0.851044i	$0.324030\pi$
$311$	−3.85323	+	26.7998i	−0.218497	+	1.51968i	−0.743591	+	0.668635i	$0.766879\pi$
$312$		0			0
$313$	0.0443396	+	0.0202492i	0.00250622	+	0.00114455i	0.416668	−	0.909059i	$-0.363198\pi$
$313$	0.0443396	+	0.0202492i	0.00250622	+	0.00114455i	−0.414162	+	0.910203i	$0.635925\pi$
$314$		0			0
$315$	3.64062	+	4.46305i	0.205126	+	0.251464i
$316$		0			0
$317$	−24.3438	+	3.50011i	−1.36728	+	0.196586i	−0.786560	−	0.617514i	$-0.788140\pi$
$317$	−24.3438	+	3.50011i	−1.36728	+	0.196586i	−0.580725	+	0.814100i	$0.697231\pi$
$318$		0			0
$319$	−0.877571	−	2.98873i	−0.0491346	−	0.167337i
$320$		0			0
$321$	10.4669	+	5.91911i	0.584207	+	0.330372i
$322$		0			0
$323$	−5.51883	−	8.58747i	−0.307076	−	0.477819i
$324$		0			0
$325$	33.3684	+	15.2389i	1.85095	+	0.845299i
$326$		0			0
$327$	31.1337	−	11.0878i	1.72170	−	0.613154i
$328$		0			0
$329$	4.64033	+	1.36252i	0.255830	+	0.0751184i
$330$		0			0
$331$	−28.6734	+	4.12262i	−1.57603	+	0.226600i	−0.874137	−	0.485679i	$-0.838572\pi$
$331$	−28.6734	+	4.12262i	−1.57603	+	0.226600i	−0.701897	+	0.712278i	$0.747663\pi$
$332$		0			0
$333$	−16.9762	−	8.37157i	−0.930290	−	0.458759i
$334$		0			0
$335$	23.3036	+	18.0122i	1.27321	+	0.984112i
$336$		0			0
$337$	18.6056	+	16.1218i	1.01351	+	0.878213i	0.992583	−	0.121568i	$-0.0387924\pi$
$337$	18.6056	+	16.1218i	1.01351	+	0.878213i	0.0209282	+	0.999781i	$0.493338\pi$
$338$		0			0
$339$	13.0836	−	23.1360i	0.710602	−	1.25658i
$340$		0			0
$341$	−1.35063	+	4.59983i	−0.0731408	+	0.249095i
$342$		0			0
$343$	−3.95629	+	6.15611i	−0.213620	+	0.332399i
$344$		0			0
$345$	−5.97669	−	11.3433i	−0.321774	−	0.610704i
$346$		0			0
$347$	−10.9803	+	7.05658i	−0.589451	+	0.378817i	−0.801102	−	0.598528i	$-0.795752\pi$
$347$	−10.9803	+	7.05658i	−0.589451	+	0.378817i	0.211651	+	0.977345i	$0.432116\pi$
$348$		0			0
$349$	3.55366	+	24.7162i	0.190223	+	1.32303i	0.831417	+	0.555650i	$0.187530\pi$
$349$	3.55366	+	24.7162i	0.190223	+	1.32303i	−0.641194	+	0.767379i	$0.721561\pi$
$350$		0			0
$351$	23.8221	+	2.77614i	1.27153	+	0.148180i
$352$		0			0
$353$	−5.20707	−	36.2159i	−0.277144	−	1.92758i	−0.364084	−	0.931366i	$-0.618618\pi$
$353$	−5.20707	−	36.2159i	−0.277144	−	1.92758i	0.0869396	−	0.996214i	$-0.472291\pi$
$354$		0			0
$355$	−10.7143	+	4.89305i	−0.568656	+	0.259696i
$356$		0			0
$357$	5.36648	−	2.82755i	0.284024	−	0.149650i
$358$		0			0
$359$	12.3469	+	1.77521i	0.651643	+	0.0936921i	0.460205	−	0.887813i	$-0.347776\pi$
$359$	12.3469	+	1.77521i	0.651643	+	0.0936921i	0.191438	+	0.981505i	$0.438685\pi$
$360$		0			0
$361$	2.35978	−	16.4126i	0.124199	−	0.863822i
$362$		0			0
$363$	−5.94299	−	16.6876i	−0.311926	−	0.875870i
$364$		0			0
$365$	−16.9012			−0.884651
$366$		0			0
$367$	29.9811	+	13.6919i	1.56500	+	0.714712i	0.994317	−	0.106459i	$-0.0339512\pi$
$367$	29.9811	+	13.6919i	1.56500	+	0.714712i	0.570683	+	0.821170i	$0.306678\pi$
$368$		0			0
$369$	18.9335	−	27.6193i	0.985641	−	1.43780i
$370$		0			0
$371$	−1.78499	+	2.77750i	−0.0926720	+	0.144200i
$372$		0			0
$373$		−	34.5460i		−	1.78872i	−0.447344	−	0.894362i	$-0.647630\pi$
$373$		−	34.5460i		−	1.78872i	0.447344	−	0.894362i	$-0.352370\pi$
$374$		0			0
$375$	10.7897	+	14.8692i	0.557178	+	0.767844i
$376$		0			0
$377$	−13.7594	+	8.84261i	−0.708644	+	0.455418i
$378$		0			0
$379$	−6.63231	+	3.02887i	−0.340679	+	0.155583i	−0.578406	−	0.815749i	$-0.696325\pi$
$379$	−6.63231	+	3.02887i	−0.340679	+	0.155583i	0.237727	+	0.971332i	$0.423598\pi$
$380$		0			0
$381$	19.7704	+	27.2454i	1.01287	+	1.39583i
$382$		0			0
$383$	−7.80832	−	9.01128i	−0.398986	−	0.460455i	0.520335	−	0.853962i	$-0.325807\pi$
$383$	−7.80832	−	9.01128i	−0.398986	−	0.460455i	−0.919321	+	0.393507i	$0.871262\pi$
$384$		0			0
$385$	1.67043	+	0.240172i	0.0851330	+	0.0122403i
$386$		0			0
$387$	−10.5247	−	7.21486i	−0.534999	−	0.366752i
$388$		0			0
$389$	−4.09382	−	6.37010i	−0.207565	−	0.322977i	0.721826	−	0.692075i	$-0.243303\pi$
$389$	−4.09382	−	6.37010i	−0.207565	−	0.322977i	−0.929391	+	0.369098i	$0.879667\pi$
$390$		0			0
$391$	−12.9563	+	3.80430i	−0.655227	+	0.192392i
$392$		0			0
$393$	−4.43979	−	21.9780i	−0.223958	−	1.10864i
$394$		0			0
$395$	−5.79454	−	5.02100i	−0.291555	−	0.252634i
$396$		0			0
$397$	−19.8773	+	5.83650i	−0.997612	+	0.292925i	−0.739476	−	0.673183i	$-0.764927\pi$
$397$	−19.8773	+	5.83650i	−0.997612	+	0.292925i	−0.258136	+	0.966108i	$0.583108\pi$
$398$		0			0
$399$	−1.39966	−	0.326349i	−0.0700705	−	0.0163379i
$400$		0			0
$401$	32.6440			1.63016			0.815082	−	0.579346i	$-0.196692\pi$
$401$	32.6440			1.63016			0.815082	+	0.579346i	$0.196692\pi$
$402$		0			0
$403$	25.1725			1.25393
$404$		0			0
$405$	26.1547	+	19.0971i	1.29964	+	0.948944i
$406$		0			0
$407$	−5.32144	+	1.56252i	−0.263774	+	0.0774511i
$408$		0			0
$409$	−1.77856	−	1.54113i	−0.0879442	−	0.0762041i	0.609779	−	0.792571i	$-0.291258\pi$
$409$	−1.77856	−	1.54113i	−0.0879442	−	0.0762041i	−0.697723	+	0.716367i	$0.745804\pi$
$410$		0			0
$411$	29.1978	−	5.89826i	1.44022	−	0.290940i
$412$		0			0
$413$	−0.408517	+	0.119952i	−0.0201018	+	0.00590243i
$414$		0			0
$415$	−2.71515	−	4.22486i	−0.133282	−	0.207390i
$416$		0			0
$417$	−31.0655	+	1.75797i	−1.52128	+	0.0860880i
$418$		0			0
$419$	−26.2060	−	3.76786i	−1.28025	−	0.184072i	−0.531575	−	0.847011i	$-0.678400\pi$
$419$	−26.2060	−	3.76786i	−1.28025	−	0.184072i	−0.748673	+	0.662939i	$0.769309\pi$
$420$		0			0
$421$	12.7519	+	14.7165i	0.621490	+	0.717238i	0.975989	−	0.217818i	$-0.0698940\pi$
$421$	12.7519	+	14.7165i	0.621490	+	0.717238i	−0.354499	+	0.935056i	$0.615349\pi$
$422$		0			0
$423$	27.1808	+	0.808658i	1.32158	+	0.0393183i
$424$		0			0
$425$	47.4530	−	21.6711i	2.30181	−	1.05120i
$426$		0			0
$427$	2.64043	−	1.69690i	0.127780	−	0.0821189i
$428$		0			0
$429$	5.68765	−	4.12718i	0.274602	−	0.199262i
$430$		0			0
$431$			26.5469i			1.27872i	0.768908	+	0.639360i	$0.220801\pi$
$431$			26.5469i			1.27872i	−0.768908	+	0.639360i	$0.779199\pi$
$432$		0			0
$433$	−13.6277	+	21.2051i	−0.654904	+	1.01905i	0.341944	+	0.939720i	$0.388915\pi$
$433$	−13.6277	+	21.2051i	−0.654904	+	1.01905i	−0.996848	+	0.0793307i	$0.974722\pi$
$434$		0			0
$435$	−22.0500	+	1.24778i	−1.05721	+	0.0598267i
$436$		0			0
$437$	2.91026	+	1.32907i	0.139216	+	0.0635780i
$438$		0			0
$439$	−9.69798			−0.462859			−0.231430	−	0.972852i	$-0.574340\pi$
$439$	−9.69798			−0.462859			−0.231430	+	0.972852i	$0.574340\pi$
$440$		0			0
$441$	−6.24810	+	19.1526i	−0.297529	+	0.912028i
$442$		0			0
$443$	−3.46305	+	24.0860i	−0.164534	+	1.14436i	0.725418	+	0.688309i	$0.241647\pi$
$443$	−3.46305	+	24.0860i	−0.164534	+	1.14436i	−0.889952	+	0.456054i	$0.849263\pi$
$444$		0			0
$445$	0.638265	+	0.0917687i	0.0302567	+	0.00435025i
$446$		0			0
$447$	−5.95436	−	11.3009i	−0.281632	−	0.534516i
$448$		0			0
$449$	−18.5737	+	8.48232i	−0.876547	+	0.400306i	−0.802291	−	0.596934i	$-0.796386\pi$
$449$	−18.5737	+	8.48232i	−0.876547	+	0.400306i	−0.0742564	+	0.997239i	$0.523658\pi$
$450$		0			0
$451$	−1.39634	−	9.71176i	−0.0657511	−	0.457309i
$452$		0			0
$453$	32.0787	+	12.5112i	1.50719	+	0.587829i
$454$		0			0
$455$	−1.26109	−	8.77111i	−0.0591210	−	0.411196i
$456$		0			0
$457$	−11.6428	+	7.48240i	−0.544629	+	0.350012i	−0.783847	−	0.620954i	$-0.786745\pi$
$457$	−11.6428	+	7.48240i	−0.544629	+	0.350012i	0.239218	+	0.970966i	$0.423109\pi$
$458$		0			0
$459$	25.1685	−	23.0174i	1.17477	−	1.07436i
$460$		0			0
$461$	−9.65928	+	15.0301i	−0.449877	+	0.700023i	−0.989922	−	0.141613i	$-0.954771\pi$
$461$	−9.65928	+	15.0301i	−0.449877	+	0.700023i	0.540045	+	0.841636i	$0.318407\pi$
$462$		0			0
$463$	−4.26786	+	14.5350i	−0.198344	+	0.675498i	0.798911	+	0.601450i	$0.205410\pi$
$463$	−4.26786	+	14.5350i	−0.198344	+	0.675498i	−0.997255	+	0.0740482i	$0.976408\pi$
$464$		0			0
$465$	29.5871	+	16.7317i	1.37207	+	0.775913i
$466$		0			0
$467$	12.3289	+	10.6831i	0.570516	+	0.494355i	0.891678	−	0.452669i	$-0.149528\pi$
$467$	12.3289	+	10.6831i	0.570516	+	0.494355i	−0.321163	+	0.947024i	$0.604074\pi$
$468$		0			0
$469$	0.378694	−	4.35083i	0.0174865	−	0.200903i
$470$		0			0
$471$	21.7292	−	4.38953i	1.00123	−	0.202259i
$472$		0			0
$473$	−3.70079	+	0.532093i	−0.170162	+	0.0244657i
$474$		0			0
$475$	−11.8595	−	3.48227i	−0.544153	−	0.159778i
$476$		0			0
$477$	−5.75750	+	17.6487i	−0.263618	+	0.808080i
$478$		0			0
$479$	5.69939	+	2.60282i	0.260412	+	0.118926i	0.541343	−	0.840802i	$-0.317916\pi$
$479$	5.69939	+	2.60282i	0.260412	+	0.118926i	−0.280931	+	0.959728i	$0.590643\pi$
$480$		0			0
$481$	15.7443	+	24.4986i	0.717877	+	1.11704i
$482$		0			0
$483$	−0.935838	+	1.65487i	−0.0425821	+	0.0752991i
$484$		0			0
$485$	−3.12083	−	10.6286i	−0.141709	−	0.482618i
$486$		0			0
$487$	−5.71344	+	0.821468i	−0.258901	+	0.0372243i	−0.270543	−	0.962708i	$-0.587203\pi$
$487$	−5.71344	+	0.821468i	−0.258901	+	0.0372243i	0.0116422	+	0.999932i	$0.496294\pi$
$488$		0			0
$489$	−5.18531	+	22.2389i	−0.234488	+	1.00568i
$490$		0			0
$491$	18.9804	+	8.66806i	0.856574	+	0.391184i	0.794775	−	0.606904i	$-0.207589\pi$
$491$	18.9804	+	8.66806i	0.856574	+	0.391184i	0.0617992	+	0.998089i	$0.480316\pi$
$492$		0			0
$493$	−3.31017	+	23.0227i	−0.149082	+	1.03689i
$494$		0			0
$495$	9.42839	−	1.07051i	0.423775	−	0.0481160i
$496$		0			0
$497$	1.46927	+	0.944243i	0.0659058	+	0.0423551i
$498$		0			0
$499$		−	8.03703i		−	0.359787i	−0.983686	−	0.179893i	$-0.942425\pi$
$499$		−	8.03703i		−	0.359787i	0.983686	−	0.179893i	$-0.0575753\pi$
$500$		0			0
$501$	−18.1593	−	34.4650i	−0.811296	−	1.53978i
$502$		0			0
$503$	0.626975	+	0.723568i	0.0279554	+	0.0322623i	0.769555	−	0.638580i	$-0.220478\pi$
$503$	0.626975	+	0.723568i	0.0279554	+	0.0322623i	−0.741600	+	0.670843i	$0.765933\pi$
$504$		0			0
$505$	13.5284	+	8.69420i	0.602008	+	0.386887i
$506$		0			0
$507$	−11.3842	−	8.78930i	−0.505592	−	0.390346i
$508$		0			0
$509$	−7.88963	+	26.8696i	−0.349702	+	1.19097i	0.577493	+	0.816396i	$0.304031\pi$
$509$	−7.88963	+	26.8696i	−0.349702	+	1.19097i	−0.927195	+	0.374579i	$0.877787\pi$
$510$		0			0
$511$	1.35489	+	2.10825i	0.0599368	+	0.0932635i
$512$		0			0
$513$	−8.07809	+	0.216435i	−0.356657	+	0.00955584i
$514$		0			0
$515$	6.15550	+	1.80742i	0.271244	+	0.0796443i
$516$		0			0
$517$	6.02161	−	5.21775i	0.264830	−	0.229477i
$518$		0			0
$519$	8.14013	+	8.38591i	0.357312	+	0.368101i
$520$		0			0
$521$	21.7553	+	25.1070i	0.953119	+	1.09996i	0.994904	+	0.100831i	$0.0321502\pi$
$521$	21.7553	+	25.1070i	0.953119	+	1.09996i	−0.0417847	+	0.999127i	$0.513304\pi$
$522$		0			0
$523$	−3.23105	+	2.07647i	−0.141284	+	0.0907977i	−0.609373	−	0.792883i	$-0.708579\pi$
$523$	−3.23105	+	2.07647i	−0.141284	+	0.0907977i	0.468089	+	0.883681i	$0.344943\pi$
$524$		0			0
$525$	2.66878	−	6.84273i	0.116475	−	0.298641i
$526$		0			0
$527$	23.4425	−	27.0540i	1.02117	−	1.17849i
$528$		0			0
$529$	−12.2903	+	14.1838i	−0.534361	+	0.616685i
$530$		0			0
$531$	−2.05152	+	1.23381i	−0.0890285	+	0.0535427i
$532$		0			0
$533$	−46.8633	+	21.4018i	−2.02988	+	0.927013i
$534$		0			0
$535$		−	24.9809i		−	1.08002i
$536$		0			0
$537$	25.0195	+	19.3165i	1.07967	+	0.833568i
$538$		0			0
$539$	2.45217	+	5.36950i	0.105622	+	0.231281i
$540$		0			0
$541$	4.61900	+	15.7309i	0.198586	+	0.676323i	0.997221	+	0.0745062i	$0.0237381\pi$
$541$	4.61900	+	15.7309i	0.198586	+	0.676323i	−0.798634	+	0.601817i	$0.794444\pi$
$542$		0			0
$543$	29.6577	−	5.99117i	1.27273	−	0.257106i
$544$		0			0
$545$	−51.8889	−	44.9620i	−2.22268	−	1.92596i
$546$		0			0
$547$	−8.24133	−	28.0674i	−0.352374	−	1.20007i	−0.924907	−	0.380193i	$-0.875858\pi$
$547$	−8.24133	−	28.0674i	−0.352374	−	1.20007i	0.572533	−	0.819881i	$-0.305961\pi$
$548$		0			0
$549$	11.9485	−	12.9879i	0.509950	−	0.554310i
$550$		0			0
$551$	4.16491	−	3.60891i	0.177431	−	0.153745i
$552$		0			0
$553$	−0.161796	+	1.12532i	−0.00688027	+	0.0478534i
$554$		0			0
$555$	2.22168	+	39.2600i	0.0943051	+	1.66649i
$556$		0			0
$557$	−6.62330	+	22.5569i	−0.280638	+	0.955765i	0.691700	+	0.722185i	$0.256862\pi$
$557$	−6.62330	+	22.5569i	−0.280638	+	0.955765i	−0.972338	+	0.233580i	$0.924956\pi$
$558$		0			0
$559$	8.15541	+	17.8578i	0.344937	+	0.755306i
$560$		0			0
$561$	0.861079	−	9.95632i	0.0363548	−	0.420356i
$562$		0			0
$563$	−26.7894	−	7.86607i	−1.12904	−	0.331515i	−0.336708	−	0.941609i	$-0.609314\pi$
$563$	−26.7894	−	7.86607i	−1.12904	−	0.331515i	−0.792329	+	0.610094i	$0.791132\pi$
$564$		0			0
$565$	−55.2178			−2.32303
$566$		0			0
$567$	0.285472	−	4.79344i	0.0119887	−	0.201306i
$568$		0			0
$569$	−27.6340	+	23.9450i	−1.15848	+	1.00382i	−0.158612	+	0.987341i	$0.550702\pi$
$569$	−27.6340	+	23.9450i	−1.15848	+	1.00382i	−0.999864	+	0.0164839i	$0.994753\pi$
$570$		0			0
$571$	14.5299	−	31.8160i	0.608057	−	1.33146i	−0.315838	−	0.948813i	$-0.602285\pi$
$571$	14.5299	−	31.8160i	0.608057	−	1.33146i	0.923895	−	0.382646i	$-0.124987\pi$
$572$		0			0
$573$	15.0007	+	11.5814i	0.626662	+	0.483820i
$574$		0			0
$575$	−8.83964	+	13.7547i	−0.368638	+	0.573612i
$576$		0			0
$577$	−11.5894	−	1.66631i	−0.482475	−	0.0693694i	−0.103214	−	0.994659i	$-0.532913\pi$
$577$	−11.5894	−	1.66631i	−0.482475	−	0.0693694i	−0.379261	+	0.925290i	$0.623822\pi$
$578$		0			0
$579$	14.8992	−	14.4625i	0.619188	−	0.601041i
$580$		0			0
$581$	−0.309346	+	0.677374i	−0.0128338	+	0.0281022i
$582$		0			0
$583$	2.25962	+	4.94789i	0.0935840	+	0.204920i
$584$		0			0
$585$	−19.3410	−	45.9177i	−0.799652	−	1.89846i
$586$		0			0
$587$	12.3037	−	3.61268i	0.507826	−	0.149111i	−0.0177754	−	0.999842i	$-0.505658\pi$
$587$	12.3037	−	3.61268i	0.507826	−	0.149111i	0.525602	+	0.850731i	$0.323840\pi$
$588$		0			0
$589$	−8.39534	+	1.20707i	−0.345924	+	0.0497364i
$590$		0			0
$591$	13.3706	+	1.15636i	0.549992	+	0.0475664i
$592$		0			0
$593$	11.9991	−	26.2744i	0.492744	−	1.07896i	−0.486016	−	0.873950i	$-0.661550\pi$
$593$	11.9991	−	26.2744i	0.492744	−	1.07896i	0.978760	−	0.205009i	$-0.0657223\pi$
$594$		0			0
$595$	−10.6011	−	6.81294i	−0.434604	−	0.279303i
$596$		0			0
$597$	0.492806	+	0.679133i	0.0201692	+	0.0277951i
$598$		0			0
$599$	4.51941	+	31.4332i	0.184658	+	1.28432i	0.845571	+	0.533862i	$0.179260\pi$
$599$	4.51941	+	31.4332i	0.184658	+	1.28432i	−0.660913	+	0.750462i	$0.729831\pi$
$600$		0			0
$601$	−16.0531	+	18.5263i	−0.654820	+	0.755703i	−0.981922	−	0.189287i	$-0.939382\pi$
$601$	−16.0531	+	18.5263i	−0.654820	+	0.755703i	0.327102	+	0.944989i	$0.393928\pi$
$602$		0			0
$603$	−4.13113	−	24.2061i	−0.168232	−	0.985747i
$604$		0			0
$605$	−24.0995	+	27.8123i	−0.979783	+	1.13073i
$606$		0			0
$607$	−4.93516	−	34.3248i	−0.200312	−	1.39320i	−0.803360	−	0.595494i	$-0.796956\pi$
$607$	−4.93516	−	34.3248i	−0.200312	−	1.39320i	0.603048	−	0.797705i	$-0.293953\pi$
$608$		0			0
$609$	1.92329	+	2.65047i	0.0779355	+	0.107402i
$610$		0			0
$611$	−35.1956	−	22.6188i	−1.42386	−	0.915059i
$612$		0			0
$613$	−1.27604	+	2.79414i	−0.0515388	+	0.112854i	−0.933650	−	0.358188i	$-0.883395\pi$
$613$	−1.27604	+	2.79414i	−0.0515388	+	0.112854i	0.882111	+	0.471042i	$0.156122\pi$
$614$		0			0
$615$	−69.3074	−	5.99409i	−2.79474	−	0.241705i
$616$		0			0
$617$	39.1417	−	5.62773i	1.57578	−	0.226564i	0.701749	−	0.712424i	$-0.252403\pi$
$617$	39.1417	−	5.62773i	1.57578	−	0.226564i	0.874036	+	0.485861i	$0.161494\pi$
$618$		0			0
$619$	6.65459	−	1.95396i	0.267471	−	0.0785364i	−0.145247	−	0.989395i	$-0.546398\pi$
$619$	6.65459	−	1.95396i	0.267471	−	0.0785364i	0.412718	+	0.910859i	$0.364580\pi$
$620$		0			0
$621$	−2.73584	+	10.3337i	−0.109786	+	0.414675i
$622$		0			0
$623$	−0.0397195	−	0.0869735i	−0.00159133	−	0.00348452i
$624$		0			0
$625$	−0.653146	+	1.43019i	−0.0261259	+	0.0572076i
$626$		0			0
$627$	−1.69900	+	1.64920i	−0.0678514	+	0.0658628i
$628$		0			0
$629$	40.9920	+	5.89376i	1.63446	+	0.234999i
$630$		0			0
$631$	2.95415	−	4.59675i	0.117603	−	0.182994i	−0.777462	−	0.628931i	$-0.783493\pi$
$631$	2.95415	−	4.59675i	0.117603	−	0.182994i	0.895065	+	0.445937i	$0.147129\pi$
$632$		0			0
$633$	16.0002	+	12.3531i	0.635950	+	0.490991i
$634$		0			0
$635$	29.0515	−	63.6138i	1.15287	−	2.52444i
$636$		0			0
$637$	23.4246	−	20.2975i	0.928116	−	0.804218i
$638$		0			0
$639$	9.33601	+	3.04566i	0.369327	+	0.120485i
$640$		0			0
$641$	−1.86830			−0.0737935			−0.0368968	−	0.999319i	$-0.511747\pi$
$641$	−1.86830			−0.0737935			−0.0368968	+	0.999319i	$0.511747\pi$
$642$		0			0
$643$	−21.5122	−	6.31654i	−0.848357	−	0.249100i	−0.171472	−	0.985189i	$-0.554852\pi$
$643$	−21.5122	−	6.31654i	−0.848357	−	0.249100i	−0.676885	+	0.736089i	$0.736671\pi$
$644$		0			0
$645$	−2.28412	+	26.4104i	−0.0899372	+	1.03991i
$646$		0			0
$647$	−7.18251	−	15.7275i	−0.282374	−	0.618312i	0.714297	−	0.699842i	$-0.246746\pi$
$647$	−7.18251	−	15.7275i	−0.282374	−	0.618312i	−0.996671	+	0.0815305i	$0.974019\pi$
$648$		0			0
$649$	−0.197621	+	0.673035i	−0.00775730	+	0.0264190i
$650$		0			0
$651$	−0.284755	−	5.03198i	−0.0111604	−	0.197219i
$652$		0			0
$653$	1.42691	−	9.92438i	0.0558393	−	0.388371i	−0.942667	−	0.333735i	$-0.891691\pi$
$653$	1.42691	−	9.92438i	0.0558393	−	0.388371i	0.998506	−	0.0546361i	$-0.0173999\pi$
$654$		0			0
$655$	−35.2036	+	30.5041i	−1.37552	+	1.19189i
$656$		0			0
$657$	10.3702	+	9.54028i	0.404579	+	0.372202i
$658$		0			0
$659$	−4.69024	−	15.9735i	−0.182706	−	0.622239i	−0.999005	−	0.0446089i	$-0.985796\pi$
$659$	−4.69024	−	15.9735i	−0.182706	−	0.622239i	0.816299	−	0.577630i	$-0.196022\pi$
$660$		0			0
$661$	5.32675	+	4.61565i	0.207187	+	0.179528i	0.752273	−	0.658852i	$-0.228958\pi$
$661$	5.32675	+	4.61565i	0.207187	+	0.179528i	−0.545086	+	0.838380i	$0.683503\pi$
$662$		0			0
$663$	−51.4349	+	10.3904i	−1.99757	+	0.403530i
$664$		0			0
$665$	0.841182	+	2.86480i	0.0326197	+	0.111092i
$666$		0			0
$667$	−3.02837	−	6.63121i	−0.117259	−	0.256762i
$668$		0			0
$669$	−37.0902	−	28.6358i	−1.43399	−	1.10712i
$670$		0			0
$671$		−	5.17102i		−	0.199625i
$672$		0			0
$673$	−11.4992	+	5.25151i	−0.443262	+	0.202431i	−0.624527	−	0.781003i	$-0.714708\pi$
$673$	−11.4992	+	5.25151i	−0.443262	+	0.202431i	0.181265	+	0.983434i	$0.441981\pi$
$674$		0			0
$675$	4.78033	−	41.0200i	0.183995	−	1.57886i
$676$		0			0
$677$	19.7763	−	22.8231i	0.760065	−	0.877162i	−0.235438	−	0.971889i	$-0.575652\pi$
$677$	19.7763	−	22.8231i	0.760065	−	0.877162i	0.995503	+	0.0947271i	$0.0301979\pi$
$678$		0			0
$679$	−1.07562	+	1.24133i	−0.0412785	+	0.0476379i
$680$		0			0
$681$	−6.59708	+	16.9149i	−0.252801	+	0.648179i
$682$		0			0
$683$	−7.04095	+	4.52494i	−0.269415	+	0.173142i	−0.668372	−	0.743827i	$-0.733009\pi$
$683$	−7.04095	+	4.52494i	−0.269415	+	0.173142i	0.398957	+	0.916969i	$0.369372\pi$
$684$		0			0
$685$	−40.5247	−	46.7680i	−1.54837	−	1.78691i
$686$		0			0
$687$	7.80140	+	8.03696i	0.297642	+	0.306629i
$688$		0			0
$689$	21.5853	−	18.7038i	0.822334	−	0.712557i
$690$		0			0
$691$	15.4212	+	4.52806i	0.586648	+	0.172255i	0.561569	−	0.827430i	$-0.310198\pi$
$691$	15.4212	+	4.52806i	0.586648	+	0.172255i	0.0250794	+	0.999685i	$0.492016\pi$
$692$		0			0
$693$	−0.889364	−	1.09027i	−0.0337841	−	0.0414161i
$694$		0			0
$695$	34.9476	+	54.3796i	1.32564	+	2.06274i
$696$		0			0
$697$	−20.6411	+	70.2971i	−0.781837	+	2.66269i
$698$		0			0
$699$	−7.83115	−	6.04611i	−0.296201	−	0.228685i
$700$		0			0
$701$	−27.0674	−	17.3951i	−1.02232	−	0.657005i	−0.0817670	−	0.996651i	$-0.526056\pi$
$701$	−27.0674	−	17.3951i	−1.02232	−	0.657005i	−0.940553	+	0.339646i	$0.889693\pi$
$702$		0			0
$703$	−6.42567	−	7.41562i	−0.242349	−	0.279685i
$704$		0			0
$705$	−26.3337	−	49.9794i	−0.991784	−	1.88233i
$706$		0			0
$707$		−	2.38450i		−	0.0896785i
$708$		0			0
$709$	15.4091	+	9.90282i	0.578700	+	0.371908i	0.797005	−	0.603973i	$-0.206416\pi$
$709$	15.4091	+	9.90282i	0.578700	+	0.371908i	−0.218305	+	0.975881i	$0.570053\pi$
$710$		0			0
$711$	0.721172	+	6.35162i	0.0270461	+	0.238204i
$712$		0			0
$713$	−1.59673	+	11.1055i	−0.0597980	+	0.415904i
$714$		0			0
$715$	−13.2798	−	6.06467i	−0.496635	−	0.226806i
$716$		0			0
$717$	−1.46479	+	6.28223i	−0.0547034	+	0.234614i
$718$		0			0
$719$	−13.1317	+	1.88805i	−0.489729	+	0.0704125i	−0.382756	−	0.923849i	$-0.625025\pi$
$719$	−13.1317	+	1.88805i	−0.489729	+	0.0704125i	−0.106973	+	0.994262i	$0.534116\pi$
$720$		0			0
$721$	−0.268000	−	0.912725i	−0.00998085	−	0.0339917i
$722$		0			0
$723$	−0.895211	+	1.58303i	−0.0332933	+	0.0588734i
$724$		0			0
$725$	15.2264	+	23.6927i	0.565493	+	0.879924i
$726$		0			0
$727$	27.4715	+	12.5458i	1.01886	+	0.465298i	0.853587	−	0.520950i	$-0.174422\pi$
$727$	27.4715	+	12.5458i	1.01886	+	0.465298i	0.165274	+	0.986248i	$0.447149\pi$
$728$		0			0
$729$	−5.26805	−	26.4811i	−0.195113	−	0.980781i
$730$		0			0
$731$	26.7876	+	7.86554i	0.990774	+	0.290918i
$732$		0			0
$733$	21.1843	−	3.04584i	0.782460	−	0.112501i	0.260504	−	0.965473i	$-0.416111\pi$
$733$	21.1843	−	3.04584i	0.782460	−	0.112501i	0.521957	+	0.852972i	$0.325202\pi$
$734$		0			0
$735$	41.0241	−	8.28732i	1.51320	−	0.305682i
$736$		0			0
$737$	−5.69282	−	4.40019i	−0.209698	−	0.162083i
$738$		0			0
$739$	28.5238	+	24.7160i	1.04927	+	0.909194i	0.995997	−	0.0893860i	$-0.0284905\pi$
$739$	28.5238	+	24.7160i	1.04927	+	0.909194i	0.0532690	+	0.998580i	$0.483036\pi$
$740$		0			0
$741$	10.8222	+	6.12004i	0.397565	+	0.224825i
$742$		0			0
$743$	14.6368	−	49.8485i	0.536973	−	1.82876i	−0.0222593	−	0.999752i	$-0.507086\pi$
$743$	14.6368	−	49.8485i	0.536973	−	1.82876i	0.559233	−	0.829011i	$-0.311096\pi$
$744$		0			0
$745$	−14.3469	+	22.3243i	−0.525632	+	0.817899i
$746$		0			0
$747$	−0.718866	+	4.12490i	−0.0263019	+	0.150922i
$748$		0			0
$749$	−3.11611	+	2.00260i	−0.113860	+	0.0731735i
$750$		0			0
$751$	−5.71140	−	39.7236i	−0.208412	−	1.44954i	−0.778341	−	0.627842i	$-0.783938\pi$
$751$	−5.71140	−	39.7236i	−0.208412	−	1.44954i	0.569929	−	0.821694i	$-0.306971\pi$
$752$		0			0
$753$	−16.8701	−	6.57963i	−0.614782	−	0.239775i
$754$		0			0
$755$	−10.1801	−	70.8040i	−0.370491	−	2.57682i
$756$		0			0
$757$	−5.39167	+	2.46229i	−0.195964	+	0.0894936i	−0.510980	−	0.859593i	$-0.670717\pi$
$757$	−5.39167	+	2.46229i	−0.195964	+	0.0894936i	0.315016	+	0.949086i	$0.397990\pi$
$758$		0			0
$759$	1.46004	+	2.77105i	0.0529961	+	0.100583i
$760$		0			0
$761$	14.3473	+	2.06283i	0.520090	+	0.0747777i	0.397361	−	0.917663i	$-0.369926\pi$
$761$	14.3473	+	2.06283i	0.520090	+	0.0747777i	0.122729	+	0.992440i	$0.460835\pi$
$762$		0			0
$763$	−1.44885	+	10.0770i	−0.0524520	+	0.364811i
$764$		0			0
$765$	−67.3616	−	21.9752i	−2.43546	−	0.794515i
$766$		0			0
$767$	3.68318			0.132992
$768$		0			0
$769$	0.524680	+	0.239613i	0.0189204	+	0.00864067i	0.424853	−	0.905262i	$-0.360326\pi$
$769$	0.524680	+	0.239613i	0.0189204	+	0.00864067i	−0.405932	+	0.913903i	$0.633053\pi$
$770$		0			0
$771$	−24.9083	+	1.40953i	−0.897049	+	0.0507631i
$772$		0			0
$773$	22.0997	−	34.3878i	0.794872	−	1.23684i	−0.172881	−	0.984943i	$-0.555308\pi$
$773$	22.0997	−	34.3878i	0.794872	−	1.23684i	0.967753	−	0.251902i	$-0.0810561\pi$
$774$		0			0
$775$		−	43.3453i		−	1.55701i
$776$		0			0
$777$	4.71916	−	3.42441i	0.169299	−	0.122850i
$778$		0			0
$779$	14.6033	−	9.38495i	0.523216	−	0.336251i
$780$		0			0
$781$	2.61739	−	1.19532i	0.0936574	−	0.0427719i
$782$		0			0
$783$	14.2336	+	11.6810i	0.508669	+	0.417444i
$784$		0			0
$785$	−30.1588	−	34.8051i	−1.07641	−	1.24225i
$786$		0			0
$787$	−4.25085	−	0.611180i	−0.151526	−	0.0217862i	0.0661341	−	0.997811i	$-0.478933\pi$
$787$	−4.25085	−	0.611180i	−0.151526	−	0.0217862i	−0.217661	+	0.976025i	$0.569843\pi$
$788$		0			0
$789$	−39.0103	+	2.20756i	−1.38880	+	0.0785911i
$790$		0			0
$791$	4.42654	+	6.88783i	0.157390	+	0.244903i
$792$		0			0
$793$	−26.0522	+	7.64961i	−0.925140	+	0.271645i
$794$		0			0
$795$	37.8029	−	7.63659i	1.34073	−	0.270842i
$796$		0			0
$797$	9.82992	+	8.51768i	0.348194	+	0.301712i	0.811345	−	0.584568i	$-0.198736\pi$
$797$	9.82992	+	8.51768i	0.348194	+	0.301712i	−0.463151	+	0.886279i	$0.653281\pi$
$798$		0			0
$799$	−57.0862	+	16.7620i	−2.01956	+	0.592997i
$800$		0			0
$801$	−0.339823	−	0.416590i	−0.0120070	−	0.0147195i
$802$		0			0
$803$	4.12879			0.145702
$804$		0			0
$805$	3.94960			0.139205
$806$		0			0
$807$	40.1040	+	9.35079i	1.41173	+	0.329163i
$808$		0			0
$809$	−8.03454	+	2.35915i	−0.282479	+	0.0829434i	−0.419903	−	0.907569i	$-0.637936\pi$
$809$	−8.03454	+	2.35915i	−0.282479	+	0.0829434i	0.137424	+	0.990512i	$0.456118\pi$
$810$		0			0
$811$	37.1314	+	32.1745i	1.30386	+	1.12980i	0.983185	+	0.182612i	$0.0584552\pi$
$811$	37.1314	+	32.1745i	1.30386	+	1.12980i	0.320675	+	0.947189i	$0.396090\pi$
$812$		0			0
$813$	10.5408	+	52.1796i	0.369684	+	1.83002i
$814$		0			0
$815$	45.5185	−	13.3654i	1.59444	−	0.468171i
$816$		0			0
$817$	−3.57625	−	5.56475i	−0.125117	−	0.194686i
$818$		0			0
$819$	−4.17727	+	6.09358i	−0.145966	+	0.212927i
$820$		0			0
$821$	10.7141	+	1.54046i	0.373925	+	0.0537623i	0.326715	−	0.945123i	$-0.394058\pi$
$821$	10.7141	+	1.54046i	0.373925	+	0.0537623i	0.0472093	+	0.998885i	$0.484967\pi$
$822$		0			0
$823$	18.2802	+	21.0965i	0.637207	+	0.735376i	0.978878	−	0.204443i	$-0.0655383\pi$
$823$	18.2802	+	21.0965i	0.637207	+	0.735376i	−0.341671	+	0.939820i	$0.610993\pi$
$824$		0			0
$825$	−7.10673	−	9.79374i	−0.247424	−	0.340974i
$826$		0			0
$827$	29.3769	−	13.4160i	1.02154	−	0.466520i	0.167025	−	0.985953i	$-0.446584\pi$
$827$	29.3769	−	13.4160i	1.02154	−	0.466520i	0.854511	+	0.519433i	$0.173857\pi$
$828$		0			0
$829$	−0.390341	+	0.250857i	−0.0135571	+	0.00871263i	−0.547402	−	0.836870i	$-0.684383\pi$
$829$	−0.390341	+	0.250857i	−0.0135571	+	0.00871263i	0.533845	+	0.845583i	$0.320747\pi$
$830$		0			0
$831$	5.98281	+	8.24487i	0.207541	+	0.286011i
$832$		0			0
$833$		−	44.0781i		−	1.52721i
$834$		0			0
$835$	−43.7545	+	68.0833i	−1.51419	+	2.35612i
$836$		0			0
$837$	−8.70934	−	26.9672i	−0.301039	−	0.932124i
$838$		0			0
$839$	1.12718	+	0.514765i	0.0389145	+	0.0177717i	0.434777	−	0.900538i	$-0.356827\pi$
$839$	1.12718	+	0.514765i	0.0389145	+	0.0177717i	−0.395863	+	0.918310i	$0.629554\pi$
$840$		0			0
$841$	16.4429			0.566997
$842$		0			0
$843$	3.40962	+	9.57401i	0.117434	+	0.329747i
$844$		0			0
$845$	−4.25223	+	29.5749i	−0.146281	+	1.01741i
$846$		0			0
$847$	5.40122	+	0.776579i	0.185588	+	0.0266836i
$848$		0			0
$849$	41.1860	−	21.7005i	1.41350	−	0.744759i
$850$		0			0
$851$	−11.8069	+	5.39202i	−0.404735	+	0.184836i
$852$		0			0
$853$	1.20455	+	8.37782i	0.0412430	+	0.286851i	0.999997	+	0.00261263i	$0.000831626\pi$
$853$	1.20455	+	8.37782i	0.0412430	+	0.286851i	−0.958754	+	0.284238i	$0.908259\pi$
$854$		0			0
$855$	8.65231	+	14.3867i	0.295903	+	0.492014i
$856$		0			0
$857$	−0.752111	−	5.23105i	−0.0256916	−	0.178689i	0.972935	−	0.231079i	$-0.0742254\pi$
$857$	−0.752111	−	5.23105i	−0.0256916	−	0.178689i	−0.998627	+	0.0523893i	$0.983316\pi$
$858$		0			0
$859$	−14.0470	+	9.02749i	−0.479279	+	0.308014i	−0.757881	−	0.652393i	$-0.773765\pi$
$859$	−14.0470	+	9.02749i	−0.479279	+	0.308014i	0.278602	+	0.960407i	$0.410129\pi$
$860$		0			0
$861$	4.80834	+	9.12588i	0.163868	+	0.311009i
$862$		0			0
$863$	−27.6128	+	42.9663i	−0.939950	+	1.46259i	−0.0541456	+	0.998533i	$0.517244\pi$
$863$	−27.6128	+	42.9663i	−0.939950	+	1.46259i	−0.885805	+	0.464058i	$0.846393\pi$
$864$		0			0
$865$	6.84030	−	23.2959i	0.232577	−	0.792085i
$866$		0			0
$867$	−22.2387	+	39.3253i	−0.755266	+	1.33556i
$868$		0			0
$869$	1.41554	+	1.22658i	0.0480190	+	0.0416087i
$870$		0			0
$871$	−13.7471	+	35.1904i	−0.465803	+	1.19238i
$872$		0			0
$873$	−4.08466	+	8.28304i	−0.138245	+	0.280338i
$874$		0			0
$875$	−5.60163	+	0.805393i	−0.189370	+	0.0272272i
$876$		0			0
$877$	50.6601	+	14.8751i	1.71067	+	0.502298i	0.982996	−	0.183626i	$-0.0587835\pi$
$877$	50.6601	+	14.8751i	1.71067	+	0.502298i	0.727673	+	0.685924i	$0.240602\pi$
$878$		0			0
$879$	10.2709	−	3.65780i	0.346428	−	0.123374i
$880$		0			0
$881$	−11.6521	−	5.32133i	−0.392569	−	0.179280i	0.209344	−	0.977842i	$-0.432867\pi$
$881$	−11.6521	−	5.32133i	−0.392569	−	0.179280i	−0.601913	+	0.798562i	$0.705594\pi$
$882$		0			0
$883$	−30.1429	−	46.9032i	−1.01439	−	1.57842i	−0.798494	−	0.602003i	$-0.794370\pi$
$883$	−30.1429	−	46.9032i	−1.01439	−	1.57842i	−0.215895	−	0.976417i	$-0.569267\pi$
$884$		0			0
$885$	4.32911	+	2.44814i	0.145522	+	0.0822933i
$886$		0			0
$887$	3.69021	+	12.5677i	0.123905	+	0.421982i	0.997960	−	0.0638455i	$-0.0203365\pi$
$887$	3.69021	+	12.5677i	0.123905	+	0.421982i	−0.874055	+	0.485828i	$0.838518\pi$
$888$		0			0
$889$	−10.2641	+	1.47575i	−0.344246	+	0.0494951i
$890$		0			0
$891$	−6.38930	−	4.66522i	−0.214050	−	0.156291i
$892$		0			0
$893$	12.8228	+	5.85597i	0.429098	+	0.195962i
$894$		0			0
$895$	9.34525	−	64.9976i	0.312377	−	2.17263i
$896$		0			0
$897$	11.8010	−	11.4551i	0.394024	−	0.382476i
$898$		0			0
$899$	16.2581	+	10.4485i	0.542238	+	0.348475i
$900$		0			0
$901$		−	40.6170i		−	1.35315i
$902$		0			0
$903$	3.47753	−	1.83228i	0.115725	−	0.0609743i
$904$		0			0
$905$	−41.1630	−	47.5047i	−1.36831	−	1.57911i
$906$		0			0
$907$	−35.3424	−	22.7132i	−1.17353	−	0.754180i	−0.199341	−	0.979930i	$-0.563880\pi$
$907$	−35.3424	−	22.7132i	−1.17353	−	0.754180i	−0.974185	+	0.225751i	$0.927517\pi$
$908$		0			0
$909$	−3.39308	−	12.9710i	−0.112541	−	0.430220i
$910$		0			0
$911$	5.42432	−	18.4735i	0.179716	−	0.612055i	−0.819523	−	0.573046i	$-0.805762\pi$
$911$	5.42432	−	18.4735i	0.179716	−	0.612055i	0.999239	−	0.0390092i	$-0.0124202\pi$
$912$		0			0
$913$	0.663283	+	1.03209i	0.0219515	+	0.0341571i
$914$		0			0
$915$	−35.7056	−	8.32524i	−1.18039	−	0.275224i
$916$		0			0
$917$	6.62716	+	1.94591i	0.218848	+	0.0642596i
$918$		0			0
$919$	15.8733	−	13.7543i	0.523611	−	0.453711i	−0.352507	−	0.935809i	$-0.614671\pi$
$919$	15.8733	−	13.7543i	0.523611	−	0.453711i	0.876117	+	0.482098i	$0.160125\pi$
$920$		0			0
$921$	38.2943	−	37.1720i	1.26184	−	1.22486i
$922$		0			0
$923$	−9.89412	−	11.4184i	−0.325669	−	0.375842i
$924$		0			0
$925$	42.1848	−	27.1106i	1.38703	−	0.891389i
$926$		0			0
$927$	−2.75662	−	4.58359i	−0.0905393	−	0.150545i
$928$		0			0
$929$	−37.4359	+	43.2033i	−1.22823	+	1.41746i	−0.351699	+	0.936113i	$0.614396\pi$
$929$	−37.4359	+	43.2033i	−1.22823	+	1.41746i	−0.876533	+	0.481342i	$0.840150\pi$
$930$		0			0
$931$	−6.83910	+	7.89274i	−0.224142	+	0.258674i
$932$		0			0
$933$	−43.6906	−	17.0401i	−1.43037	−	0.557866i
$934$		0			0
$935$	−18.8851	+	8.62453i	−0.617608	+	0.282052i
$936$		0			0
$937$			16.6516i			0.543983i	0.962300	+	0.271991i	$0.0876822\pi$
$937$			16.6516i			0.543983i	−0.962300	+	0.271991i	$0.912318\pi$
$938$		0			0
$939$	−0.0515954	+	0.0668283i	−0.00168375	+	0.00218086i
$940$		0			0
$941$	11.6169	+	25.4375i	0.378700	+	0.829238i	0.998993	+	0.0448672i	$0.0142865\pi$
$941$	11.6169	+	25.4375i	0.378700	+	0.829238i	−0.620293	+	0.784370i	$0.712986\pi$
$942$		0			0
$943$	−6.46934	−	22.0325i	−0.210671	−	0.717478i
$944$		0			0
$945$	−8.96015	+	4.38570i	−0.291474	+	0.142667i
$946$		0			0
$947$	−21.0357	−	18.2275i	−0.683568	−	0.592315i	0.242282	−	0.970206i	$-0.422104\pi$
$947$	−21.0357	−	18.2275i	−0.683568	−	0.592315i	−0.925850	+	0.377891i	$0.876649\pi$
$948$		0			0
$949$	−6.10782	−	20.8013i	−0.198268	−	0.675239i
$950$		0			0
$951$	3.67044	−	42.4399i	0.119022	−	1.37621i
$952$		0			0
$953$	−20.4381	+	17.7097i	−0.662055	+	0.573674i	−0.919727	−	0.392558i	$-0.871590\pi$
$953$	−20.4381	+	17.7097i	−0.662055	+	0.573674i	0.257672	+	0.966233i	$0.417045\pi$
$954$		0			0
$955$	5.60304	−	38.9700i	0.181310	−	1.26104i
$956$		0			0
$957$	5.38656	−	0.304820i	0.174123	−	0.00985344i
$958$		0			0
$959$	−2.58514	+	8.80419i	−0.0834787	+	0.284302i
$960$		0			0
$961$	0.521816	+	1.14262i	0.0168328	+	0.0368586i
$962$		0			0
$963$	−14.1010	+	15.3277i	−0.454400	+	0.493928i
$964$		0			0
$965$	−41.3896	−	12.1531i	−1.33238	−	0.391222i
$966$		0			0
$967$	23.8847			0.768079			0.384040	−	0.923317i	$-0.374533\pi$
$967$	23.8847			0.768079			0.384040	+	0.923317i	$0.374533\pi$
$968$		0			0
$969$	16.6560	−	5.93173i	0.535066	−	0.190555i
$970$		0			0
$971$	−41.4972	+	35.9576i	−1.33171	+	1.15393i	−0.356093	+	0.934450i	$0.615891\pi$
$971$	−41.4972	+	35.9576i	−1.33171	+	1.15393i	−0.975616	+	0.219483i	$0.929563\pi$
$972$		0			0
$973$	3.98170	−	8.71870i	0.127647	−	0.279509i
$974$		0			0
$975$	−38.8288	+	50.2926i	−1.24352	+	1.61065i
$976$		0			0
$977$	−11.9971	+	18.6678i	−0.383820	+	0.597235i	−0.978380	−	0.206816i	$-0.933690\pi$
$977$	−11.9971	+	18.6678i	−0.383820	+	0.597235i	0.594560	+	0.804051i	$0.297326\pi$
$978$		0			0
$979$	−0.155921	−	0.0224181i	−0.00498327	−	0.000716485i
$980$		0			0
$981$	6.45795	+	56.8774i	0.206187	+	1.81596i
$982$		0			0
$983$	13.0673	−	28.6134i	0.416782	−	0.912624i	−0.578508	−	0.815677i	$-0.696365\pi$
$983$	13.0673	−	28.6134i	0.416782	−	0.912624i	0.995289	−	0.0969476i	$-0.0309079\pi$
$984$		0			0
$985$	−11.5821	−	25.3612i	−0.369036	−	0.808075i
$986$		0			0
$987$	−4.12336	+	7.29146i	−0.131248	+	0.232090i
$988$		0			0
$989$	−8.39577	+	2.46522i	−0.266970	+	0.0783895i
$990$		0			0
$991$	20.3238	−	2.92212i	0.645606	−	0.0928241i	0.188269	−	0.982118i	$-0.439712\pi$
$991$	20.3238	−	2.92212i	0.645606	−	0.0928241i	0.457337	+	0.889293i	$0.348803\pi$
$992$		0			0
$993$	4.32324	−	49.9879i	0.137194	−	1.58632i
$994$		0			0
$995$	0.724151	−	1.58567i	0.0229571	−	0.0502691i
$996$		0			0
$997$	28.6238	+	18.3954i	0.906526	+	0.582589i	0.908719	−	0.417409i	$-0.137062\pi$
$997$	28.6238	+	18.3954i	0.906526	+	0.582589i	−0.00219285	+	0.999998i	$0.500698\pi$
$998$		0			0
$999$	20.7980	−	25.3430i	0.658019	−	0.801817i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.s.b.5.10	yes	200
3.2	odd	2	inner	804.2.s.b.5.5	✓	200
67.27	odd	22	inner	804.2.s.b.161.5	yes	200
201.161	even	22	inner	804.2.s.b.161.10	yes	200

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.s.b.5.5	✓	200	3.2	odd	2	inner
804.2.s.b.5.10	yes	200	1.1	even	1	trivial
804.2.s.b.161.5	yes	200	67.27	odd	22	inner
804.2.s.b.161.10	yes	200	201.161	even	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.s (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.393301 + 1.68681i) q^{3} +(3.45254 - 1.01376i) q^{5} +(-0.403229 - 0.349400i) q^{7} +(-2.69063 - 1.32685i) q^{9} +O(q^{10})\)	\(q+(-0.393301 + 1.68681i) q^{3} +(3.45254 - 1.01376i) q^{5} +(-0.403229 - 0.349400i) q^{7} +(-2.69063 - 1.32685i) q^{9} +(-0.843418 + 0.247650i) q^{11} +(2.49538 + 3.88288i) q^{13} +(0.352124 + 6.22247i) q^{15} +(6.49699 + 0.934126i) q^{17} +(-1.01843 - 1.17533i) q^{19} +(0.747960 - 0.542749i) q^{21} +(-1.87132 + 0.854604i) q^{23} +(6.68605 - 4.29687i) q^{25} +(3.29636 - 4.01672i) q^{27} +3.54360i q^{29} +(2.94854 - 4.58802i) q^{31} +(-0.0860200 - 1.52008i) q^{33} +(-1.74637 - 0.797540i) q^{35} +6.30938 q^{37} +(-7.53110 + 2.68207i) q^{39} +(-1.58851 + 11.0483i) q^{41} +(4.21011 + 0.605322i) q^{43} +(-10.6346 - 1.85334i) q^{45} +(-8.24517 + 3.76544i) q^{47} +(-0.955691 - 6.64697i) q^{49} +(-4.13096 + 10.5918i) q^{51} +(-0.880650 - 6.12505i) q^{53} +(-2.66088 + 1.71004i) q^{55} +(2.38311 - 1.25564i) q^{57} +(0.431424 - 0.671308i) q^{59} +(-1.65734 + 5.64439i) q^{61} +(0.621339 + 1.47513i) q^{63} +(12.5517 + 10.8761i) q^{65} +(4.80367 + 6.62757i) q^{67} +(-0.705558 - 3.49267i) q^{69} +(-3.24010 + 0.465856i) q^{71} +(-4.50675 - 1.32330i) q^{73} +(4.61835 + 12.9680i) q^{75} +(0.426619 + 0.194830i) q^{77} +(-1.15200 - 1.79255i) q^{79} +(5.47896 + 7.14010i) q^{81} +(-0.393211 - 1.33915i) q^{83} +(23.3781 - 3.36126i) q^{85} +(-5.97736 - 1.39370i) q^{87} +(0.163010 + 0.0744440i) q^{89} +(0.350470 - 2.43757i) q^{91} +(6.57944 + 6.77810i) q^{93} +(-4.70767 - 3.02544i) q^{95} -3.07848i q^{97} +(2.59792 + 0.452751i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 200 q - 10 q^{9}+O(q^{10}) \) 200 * q - 10 * q^9	\( 200 q - 10 q^{9} + 2 q^{15} + 6 q^{19} - 10 q^{21} - 20 q^{25} - 44 q^{31} - 5 q^{33} + 78 q^{39} - 22 q^{43} - 22 q^{45} - 16 q^{49} + 36 q^{55} + 66 q^{57} + 176 q^{61} + 132 q^{63} + 46 q^{67} - 26 q^{73} - 165 q^{75} - 44 q^{79} + 42 q^{81} - 66 q^{87} - 20 q^{91} + 84 q^{93} - 55 q^{99}+O(q^{100}) \) 200 * q - 10 * q^9 + 2 * q^15 + 6 * q^19 - 10 * q^21 - 20 * q^25 - 44 * q^31 - 5 * q^33 + 78 * q^39 - 22 * q^43 - 22 * q^45 - 16 * q^49 + 36 * q^55 + 66 * q^57 + 176 * q^61 + 132 * q^63 + 46 * q^67 - 26 * q^73 - 165 * q^75 - 44 * q^79 + 42 * q^81 - 66 * q^87 - 20 * q^91 + 84 * q^93 - 55 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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