LMFDB - Embedded newform 804.2.q.b.193.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(25,804)]

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, 0, 10]))

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

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

chi := DirichletCharacter("804.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.q (of order $11$, 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:	$60$
Relative dimension:	$6$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			193.3
Character	$\chi$	$=$	804.193
Dual form			804.2.q.b.25.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.654861 + 0.755750i) q^{3} +(-0.494572 - 0.317842i) q^{5} +(0.597152 - 4.15328i) q^{7} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})$	\(q+(0.654861 + 0.755750i) q^{3} +(-0.494572 - 0.317842i) q^{5} +(0.597152 - 4.15328i) q^{7} +(-0.142315 + 0.989821i) q^{9} +(-3.69287 - 2.37326i) q^{11} +(0.305369 + 0.668664i) q^{13} +(-0.0836667 - 0.581915i) q^{15} +(1.69671 - 0.498199i) q^{17} +(-0.290555 - 2.02085i) q^{19} +(3.52989 - 2.26853i) q^{21} +(-4.46336 - 5.15100i) q^{23} +(-1.93350 - 4.23377i) q^{25} +(-0.841254 + 0.540641i) q^{27} -4.58239 q^{29} +(-1.01278 + 2.21768i) q^{31} +(-0.624723 - 4.34504i) q^{33} +(-1.61542 + 1.86430i) q^{35} +5.57561 q^{37} +(-0.305369 + 0.668664i) q^{39} +(-3.79415 + 1.11406i) q^{41} +(9.78801 - 2.87402i) q^{43} +(0.384992 - 0.444304i) q^{45} +(4.93013 + 5.68967i) q^{47} +(-10.1767 - 2.98816i) q^{49} +(1.48762 + 0.956037i) q^{51} +(7.24167 + 2.12635i) q^{53} +(1.07207 + 2.34750i) q^{55} +(1.33699 - 1.54296i) q^{57} +(5.10988 - 11.1891i) q^{59} +(8.08332 - 5.19484i) q^{61} +(4.02603 + 1.18215i) q^{63} +(0.0615028 - 0.427761i) q^{65} +(-1.33908 - 8.07508i) q^{67} +(0.969982 - 6.74637i) q^{69} +(0.981003 + 0.288048i) q^{71} +(-8.46705 + 5.44144i) q^{73} +(1.93350 - 4.23377i) q^{75} +(-12.0620 + 13.9203i) q^{77} +(2.34861 + 5.14274i) q^{79} +(-0.959493 - 0.281733i) q^{81} +(3.95887 + 2.54421i) q^{83} +(-0.997494 - 0.292891i) q^{85} +(-3.00083 - 3.46314i) q^{87} +(-2.92583 + 3.37658i) q^{89} +(2.95950 - 0.868988i) q^{91} +(-2.33924 + 0.686863i) q^{93} +(-0.498612 + 1.09181i) q^{95} +8.38224 q^{97} +(2.87466 - 3.31753i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 6 q^{3} + 2 q^{5} + 2 q^{7} - 6 q^{9}+O(q^{10}) $ 60 * q + 6 * q^3 + 2 * q^5 + 2 * q^7 - 6 * q^9	$ 60 q + 6 q^{3} + 2 q^{5} + 2 q^{7} - 6 q^{9} - 11 q^{11} - 2 q^{13} + 9 q^{15} + 21 q^{17} + 10 q^{19} - 2 q^{21} - 10 q^{23} - 36 q^{25} + 6 q^{27} + 4 q^{29} - 24 q^{31} - 32 q^{35} + 2 q^{37} + 2 q^{39} + 10 q^{41} + 23 q^{43} + 2 q^{45} + 66 q^{47} + 34 q^{49} + 23 q^{51} - 13 q^{53} + 27 q^{55} + q^{57} + 35 q^{59} + 56 q^{61} - 9 q^{63} + 48 q^{65} + 13 q^{67} + 10 q^{69} + 76 q^{71} - q^{73} + 36 q^{75} - 38 q^{77} - 46 q^{79} - 6 q^{81} - 26 q^{83} + 42 q^{85} + 7 q^{87} + 58 q^{89} - 40 q^{91} - 9 q^{93} - 29 q^{95} - 46 q^{97}+O(q^{100}) $ 60 * q + 6 * q^3 + 2 * q^5 + 2 * q^7 - 6 * q^9 - 11 * q^11 - 2 * q^13 + 9 * q^15 + 21 * q^17 + 10 * q^19 - 2 * q^21 - 10 * q^23 - 36 * q^25 + 6 * q^27 + 4 * q^29 - 24 * q^31 - 32 * q^35 + 2 * q^37 + 2 * q^39 + 10 * q^41 + 23 * q^43 + 2 * q^45 + 66 * q^47 + 34 * q^49 + 23 * q^51 - 13 * q^53 + 27 * q^55 + q^57 + 35 * q^59 + 56 * q^61 - 9 * q^63 + 48 * q^65 + 13 * q^67 + 10 * q^69 + 76 * q^71 - q^73 + 36 * q^75 - 38 * q^77 - 46 * q^79 - 6 * q^81 - 26 * q^83 + 42 * q^85 + 7 * q^87 + 58 * q^89 - 40 * q^91 - 9 * q^93 - 29 * q^95 - 46 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$e\left(\frac{6}{11}\right)$	$1$

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
$3$	0.654861	+	0.755750i	0.378084	+	0.436332i
$3$	0.654861	+	0.755750i	0.378084	+	0.436332i
$4$		0			0
$5$	−0.494572	−	0.317842i	−0.221179	−	0.142143i	0.425359	−	0.905025i	$-0.360148\pi$
$5$	−0.494572	−	0.317842i	−0.221179	−	0.142143i	−0.646539	+	0.762881i	$0.723784\pi$
$6$		0			0
$7$	0.597152	−	4.15328i	0.225702	−	1.56979i	−0.490211	−	0.871604i	$-0.663080\pi$
$7$	0.597152	−	4.15328i	0.225702	−	1.56979i	0.715913	−	0.698190i	$-0.246011\pi$
$8$		0			0
$9$	−0.142315	+	0.989821i	−0.0474383	+	0.329940i
$10$		0			0
$11$	−3.69287	−	2.37326i	−1.11344	−	0.715566i	−0.151402	−	0.988472i	$-0.548379\pi$
$11$	−3.69287	−	2.37326i	−1.11344	−	0.715566i	−0.962041	+	0.272906i	$0.912015\pi$
$12$		0			0
$13$	0.305369	+	0.668664i	0.0846940	+	0.185454i	0.947240	−	0.320524i	$-0.103859\pi$
$13$	0.305369	+	0.668664i	0.0846940	+	0.185454i	−0.862546	+	0.505978i	$0.831132\pi$
$14$		0			0
$15$	−0.0836667	−	0.581915i	−0.0216027	−	0.150250i
$16$		0			0
$17$	1.69671	−	0.498199i	0.411513	−	0.120831i	−0.0694221	−	0.997587i	$-0.522116\pi$
$17$	1.69671	−	0.498199i	0.411513	−	0.120831i	0.480935	+	0.876756i	$0.340297\pi$
$18$		0			0
$19$	−0.290555	−	2.02085i	−0.0666578	−	0.463615i	−0.995624	−	0.0934506i	$-0.970210\pi$
$19$	−0.290555	−	2.02085i	−0.0666578	−	0.463615i	0.928966	−	0.370165i	$-0.120699\pi$
$20$		0			0
$21$	3.52989	−	2.26853i	0.770286	−	0.495033i
$22$		0			0
$23$	−4.46336	−	5.15100i	−0.930676	−	1.07406i	−0.997088	−	0.0762648i	$-0.975701\pi$
$23$	−4.46336	−	5.15100i	−0.930676	−	1.07406i	0.0664118	−	0.997792i	$-0.478845\pi$
$24$		0			0
$25$	−1.93350	−	4.23377i	−0.386699	−	0.846754i
$26$		0			0
$27$	−0.841254	+	0.540641i	−0.161899	+	0.104046i
$28$		0			0
$29$	−4.58239			−0.850928			−0.425464	−	0.904975i	$-0.639889\pi$
$29$	−4.58239			−0.850928			−0.425464	+	0.904975i	$0.639889\pi$
$30$		0			0
$31$	−1.01278	+	2.21768i	−0.181901	+	0.398307i	−0.978513	−	0.206183i	$-0.933896\pi$
$31$	−1.01278	+	2.21768i	−0.181901	+	0.398307i	0.796613	+	0.604490i	$0.206623\pi$
$32$		0			0
$33$	−0.624723	−	4.34504i	−0.108750	−	0.756375i
$34$		0			0
$35$	−1.61542	+	1.86430i	−0.273056	+	0.315124i
$36$		0			0
$37$	5.57561			0.916624			0.458312	−	0.888791i	$-0.348454\pi$
$37$	5.57561			0.916624			0.458312	+	0.888791i	$0.348454\pi$
$38$		0			0
$39$	−0.305369	+	0.668664i	−0.0488981	+	0.107072i
$40$		0			0
$41$	−3.79415	+	1.11406i	−0.592547	+	0.173987i	−0.564239	−	0.825612i	$-0.690830\pi$
$41$	−3.79415	+	1.11406i	−0.592547	+	0.173987i	−0.0283082	+	0.999599i	$0.509012\pi$
$42$		0			0
$43$	9.78801	−	2.87402i	1.49266	−	0.438284i	0.569269	−	0.822151i	$-0.307226\pi$
$43$	9.78801	−	2.87402i	1.49266	−	0.438284i	0.923388	+	0.383867i	$0.125408\pi$
$44$		0			0
$45$	0.384992	−	0.444304i	0.0573912	−	0.0662330i
$46$		0			0
$47$	4.93013	+	5.68967i	0.719133	+	0.829923i	0.991203	−	0.132354i	$-0.0422536\pi$
$47$	4.93013	+	5.68967i	0.719133	+	0.829923i	−0.272070	+	0.962278i	$0.587708\pi$
$48$		0			0
$49$	−10.1767	−	2.98816i	−1.45382	−	0.426879i
$50$		0			0
$51$	1.48762	+	0.956037i	0.208309	+	0.133872i
$52$		0			0
$53$	7.24167	+	2.12635i	0.994719	+	0.292076i	0.738287	−	0.674486i	$-0.235635\pi$
$53$	7.24167	+	2.12635i	0.994719	+	0.292076i	0.256432	+	0.966562i	$0.417453\pi$
$54$		0			0
$55$	1.07207	+	2.34750i	0.144558	+	0.316537i
$56$		0			0
$57$	1.33699	−	1.54296i	0.177088	−	0.204371i
$58$		0			0
$59$	5.10988	−	11.1891i	0.665250	−	1.45669i	−0.212299	−	0.977205i	$-0.568095\pi$
$59$	5.10988	−	11.1891i	0.665250	−	1.45669i	0.877548	−	0.479488i	$-0.159178\pi$
$60$		0			0
$61$	8.08332	−	5.19484i	1.03496	−	0.665131i	0.0912273	−	0.995830i	$-0.470921\pi$
$61$	8.08332	−	5.19484i	1.03496	−	0.665131i	0.943736	+	0.330700i	$0.107285\pi$
$62$		0			0
$63$	4.02603	+	1.18215i	0.507232	+	0.148937i
$64$		0			0
$65$	0.0615028	−	0.427761i	0.00762848	−	0.0530573i
$66$		0			0
$67$	−1.33908	−	8.07508i	−0.163595	−	0.986528i
$67$	−1.33908	−	8.07508i	−0.163595	−	0.986528i
$68$		0			0
$69$	0.969982	−	6.74637i	0.116772	−	0.812168i
$70$		0			0
$71$	0.981003	+	0.288048i	0.116424	+	0.0341851i	0.339425	−	0.940633i	$-0.389767\pi$
$71$	0.981003	+	0.288048i	0.116424	+	0.0341851i	−0.223002	+	0.974818i	$0.571586\pi$
$72$		0			0
$73$	−8.46705	+	5.44144i	−0.990994	+	0.636873i	−0.932407	−	0.361409i	$-0.882296\pi$
$73$	−8.46705	+	5.44144i	−0.990994	+	0.636873i	−0.0585864	+	0.998282i	$0.518659\pi$
$74$		0			0
$75$	1.93350	−	4.23377i	0.223261	−	0.488873i
$76$		0			0
$77$	−12.0620	+	13.9203i	−1.37460	+	1.58637i
$78$		0			0
$79$	2.34861	+	5.14274i	0.264240	+	0.578604i	0.994520	−	0.104543i	$-0.0333380\pi$
$79$	2.34861	+	5.14274i	0.264240	+	0.578604i	−0.730281	+	0.683147i	$0.760611\pi$
$80$		0			0
$81$	−0.959493	−	0.281733i	−0.106610	−	0.0313036i
$82$		0			0
$83$	3.95887	+	2.54421i	0.434543	+	0.279264i	0.739570	−	0.673080i	$-0.235029\pi$
$83$	3.95887	+	2.54421i	0.434543	+	0.279264i	−0.305027	+	0.952344i	$0.598665\pi$
$84$		0			0
$85$	−0.997494	−	0.292891i	−0.108193	−	0.0317685i
$86$		0			0
$87$	−3.00083	−	3.46314i	−0.321722	−	0.371287i
$88$		0			0
$89$	−2.92583	+	3.37658i	−0.310137	+	0.357917i	−0.889324	−	0.457277i	$-0.848825\pi$
$89$	−2.92583	+	3.37658i	−0.310137	+	0.357917i	0.579187	+	0.815195i	$0.303370\pi$
$90$		0			0
$91$	2.95950	−	0.868988i	0.310240	−	0.0910947i
$92$		0			0
$93$	−2.33924	+	0.686863i	−0.242568	+	0.0712244i
$94$		0			0
$95$	−0.498612	+	1.09181i	−0.0511565	+	0.112017i
$96$		0			0
$97$	8.38224			0.851087			0.425544	−	0.904938i	$-0.360083\pi$
$97$	8.38224			0.851087			0.425544	+	0.904938i	$0.360083\pi$
$98$		0			0
$99$	2.87466	−	3.31753i	0.288914	−	0.333425i
$100$		0			0
$101$	2.23446	+	15.5410i	0.222337	+	1.54639i	0.729165	+	0.684338i	$0.239909\pi$
$101$	2.23446	+	15.5410i	0.222337	+	1.54639i	−0.506828	+	0.862047i	$0.669182\pi$
$102$		0			0
$103$	0.353899	−	0.774930i	0.0348707	−	0.0763561i	−0.891395	−	0.453227i	$-0.850273\pi$
$103$	0.353899	−	0.774930i	0.0348707	−	0.0763561i	0.926266	+	0.376871i	$0.123000\pi$
$104$		0			0
$105$	−2.46682			−0.240737
$106$		0			0
$107$	−10.2879	+	6.61164i	−0.994570	+	0.639171i	−0.933355	−	0.358954i	$-0.883134\pi$
$107$	−10.2879	+	6.61164i	−0.994570	+	0.639171i	−0.0612142	+	0.998125i	$0.519497\pi$
$108$		0			0
$109$	−5.80264	−	12.7060i	−0.555792	−	1.21701i	−0.954024	−	0.299730i	$-0.903104\pi$
$109$	−5.80264	−	12.7060i	−0.555792	−	1.21701i	0.398232	−	0.917285i	$-0.369624\pi$
$110$		0			0
$111$	3.65124	+	4.21376i	0.346561	+	0.399953i
$112$		0			0
$113$	−12.6785	+	8.14800i	−1.19270	+	0.766500i	−0.977678	−	0.210110i	$-0.932618\pi$
$113$	−12.6785	+	8.14800i	−1.19270	+	0.766500i	−0.215019	+	0.976610i	$0.568981\pi$
$114$		0			0
$115$	0.570251	+	3.96618i	0.0531762	+	0.369849i
$116$		0			0
$117$	−0.705316	+	0.207100i	−0.0652065	+	0.0191464i
$118$		0			0
$119$	−1.05597	−	7.34442i	−0.0968005	−	0.673262i
$120$		0			0
$121$	3.43535	+	7.52238i	0.312305	+	0.683852i
$122$		0			0
$123$	−3.32659	−	2.13787i	−0.299949	−	0.192765i
$124$		0			0
$125$	−0.807750	+	5.61802i	−0.0722474	+	0.502491i
$126$		0			0
$127$	0.183221	−	1.27433i	0.0162583	−	0.113079i	−0.980076	−	0.198622i	$-0.936353\pi$
$127$	0.183221	−	1.27433i	0.0162583	−	0.113079i	0.996334	+	0.0855431i	$0.0272625\pi$
$128$		0			0
$129$	8.58182	+	5.51520i	0.755587	+	0.485587i
$130$		0			0
$131$	2.96329	+	3.41982i	0.258904	+	0.298791i	0.870288	−	0.492543i	$-0.163932\pi$
$131$	2.96329	+	3.41982i	0.258904	+	0.298791i	−0.611384	+	0.791334i	$0.709387\pi$
$132$		0			0
$133$	−8.56668			−0.742825
$134$		0			0
$135$	0.587899			0.0505983
$136$		0			0
$137$	−7.31498	−	8.44193i	−0.624961	−	0.721243i	0.351680	−	0.936120i	$-0.385610\pi$
$137$	−7.31498	−	8.44193i	−0.624961	−	0.721243i	−0.976641	+	0.214877i	$0.931065\pi$
$138$		0			0
$139$	−12.4567	−	8.00543i	−1.05656	−	0.679011i	−0.107534	−	0.994201i	$-0.534295\pi$
$139$	−12.4567	−	8.00543i	−1.05656	−	0.679011i	−0.949029	+	0.315190i	$0.897932\pi$
$140$		0			0
$141$	−1.07142	+	7.45188i	−0.0902297	+	0.627562i
$142$		0			0
$143$	0.459229	−	3.19401i	0.0384027	−	0.267097i
$144$		0			0
$145$	2.26632	+	1.45648i	0.188208	+	0.120954i
$146$		0			0
$147$	−4.40604	−	9.64788i	−0.363404	−	0.795744i
$148$		0			0
$149$	−0.395047	−	2.74762i	−0.0323635	−	0.225093i	0.967220	−	0.253939i	$-0.0817261\pi$
$149$	−0.395047	−	2.74762i	−0.0323635	−	0.225093i	−0.999584	+	0.0288452i	$0.990817\pi$
$150$		0			0
$151$	3.04434	−	0.893899i	0.247745	−	0.0727445i	−0.155502	−	0.987836i	$-0.549700\pi$
$151$	3.04434	−	0.893899i	0.247745	−	0.0727445i	0.403247	+	0.915091i	$0.367881\pi$
$152$		0			0
$153$	0.251661	+	1.75034i	0.0203456	+	0.141507i
$154$		0			0
$155$	1.20576	−	0.774898i	0.0968493	−	0.0622413i
$156$		0			0
$157$	15.8766	+	18.3225i	1.26709	+	1.46230i	0.824801	+	0.565423i	$0.191287\pi$
$157$	15.8766	+	18.3225i	1.26709	+	1.46230i	0.442287	+	0.896874i	$0.354167\pi$
$158$		0			0
$159$	3.13530	+	6.86535i	0.248645	+	0.544457i
$160$		0			0
$161$	−24.0589	+	15.4617i	−1.89610	+	1.21855i
$162$		0			0
$163$	20.2473			1.58589			0.792945	−	0.609293i	$-0.208547\pi$
$163$	20.2473			1.58589			0.792945	+	0.609293i	$0.208547\pi$
$164$		0			0
$165$	−1.07207	+	2.34750i	−0.0834603	+	0.182753i
$166$		0			0
$167$	−1.82959	−	12.7251i	−0.141578	−	0.984698i	−0.929473	−	0.368889i	$-0.879738\pi$
$167$	−1.82959	−	12.7251i	−0.141578	−	0.984698i	0.787895	−	0.615809i	$-0.211171\pi$
$168$		0			0
$169$	8.15933	−	9.41637i	0.627641	−	0.724336i
$170$		0			0
$171$	2.04163			0.156128
$172$		0			0
$173$	−2.41690	+	5.29228i	−0.183754	+	0.402364i	−0.978982	−	0.203945i	$-0.934624\pi$
$173$	−2.41690	+	5.29228i	−0.183754	+	0.402364i	0.795229	+	0.606310i	$0.207351\pi$
$174$		0			0
$175$	−18.7386	+	5.50216i	−1.41651	+	0.415924i
$176$		0			0
$177$	11.8024	−	3.46550i	0.887122	−	0.260483i
$178$		0			0
$179$	12.2800	−	14.1718i	0.917847	−	1.05925i	−0.0801993	−	0.996779i	$-0.525556\pi$
$179$	12.2800	−	14.1718i	0.917847	−	1.05925i	0.998047	−	0.0624734i	$-0.0198989\pi$
$180$		0			0
$181$	14.4598	+	16.6875i	1.07479	+	1.24038i	0.969281	+	0.245957i	$0.0791023\pi$
$181$	14.4598	+	16.6875i	1.07479	+	1.24038i	0.105511	+	0.994418i	$0.466352\pi$
$182$		0			0
$183$	9.21945	+	2.70707i	0.681521	+	0.200113i
$184$		0			0
$185$	−2.75754	−	1.77216i	−0.202738	−	0.130292i
$186$		0			0
$187$	−7.44810	−	2.18696i	−0.544659	−	0.159926i
$188$		0			0
$189$	1.74308	+	3.81681i	0.126790	+	0.277632i
$190$		0			0
$191$	−9.81541	+	11.3276i	−0.710218	+	0.819636i	−0.990095	−	0.140400i	$-0.955161\pi$
$191$	−9.81541	+	11.3276i	−0.710218	+	0.819636i	0.279876	+	0.960036i	$0.409707\pi$
$192$		0			0
$193$	1.17496	−	2.57281i	0.0845757	−	0.185195i	−0.862619	−	0.505854i	$-0.831177\pi$
$193$	1.17496	−	2.57281i	0.0845757	−	0.185195i	0.947195	+	0.320660i	$0.103905\pi$
$194$		0			0
$195$	0.363556	−	0.233643i	0.0260348	−	0.0167316i
$196$		0			0
$197$	5.65570	+	1.66066i	0.402952	+	0.118317i	0.476928	−	0.878943i	$-0.341750\pi$
$197$	5.65570	+	1.66066i	0.402952	+	0.118317i	−0.0739753	+	0.997260i	$0.523569\pi$
$198$		0			0
$199$	−0.873858	+	6.07781i	−0.0619461	+	0.430845i	0.935122	+	0.354326i	$0.115290\pi$
$199$	−0.873858	+	6.07781i	−0.0619461	+	0.430845i	−0.997068	+	0.0765189i	$0.975619\pi$
$200$		0			0
$201$	5.22582	−	6.30006i	0.368601	−	0.444372i
$202$		0			0
$203$	−2.73638	+	19.0320i	−0.192056	+	1.33578i
$204$		0			0
$205$	2.23058	+	0.654956i	0.155790	+	0.0457441i
$206$		0			0
$207$	5.73377	−	3.68487i	0.398525	−	0.256116i
$208$		0			0
$209$	−3.72304	+	8.15231i	−0.257528	+	0.563907i
$210$		0			0
$211$	−2.46479	+	2.84452i	−0.169683	+	0.195825i	−0.834222	−	0.551429i	$-0.814083\pi$
$211$	−2.46479	+	2.84452i	−0.169683	+	0.195825i	0.664538	+	0.747254i	$0.268628\pi$
$212$		0			0
$213$	0.424728	+	0.930024i	0.0291019	+	0.0637242i
$214$		0			0
$215$	−5.75436	−	1.68963i	−0.392444	−	0.115232i
$216$		0			0
$217$	8.60587	+	5.53065i	0.584204	+	0.375445i
$218$		0			0
$219$	−9.65711	−	2.83558i	−0.652567	−	0.191611i
$220$		0			0
$221$	0.851250	+	0.982395i	0.0572613	+	0.0660830i
$222$		0			0
$223$	−13.1488	+	15.1745i	−0.880507	+	1.01616i	0.119222	+	0.992868i	$0.461960\pi$
$223$	−13.1488	+	15.1745i	−0.880507	+	1.01616i	−0.999729	+	0.0232915i	$0.992585\pi$
$224$		0			0
$225$	4.46584	−	1.31129i	0.297723	−	0.0874193i
$226$		0			0
$227$	17.4762	−	5.13147i	1.15993	−	0.340587i	0.355527	−	0.934666i	$-0.384301\pi$
$227$	17.4762	−	5.13147i	1.15993	−	0.340587i	0.804407	+	0.594079i	$0.202483\pi$
$228$		0			0
$229$	−11.4945	+	25.1694i	−0.759577	+	1.66324i	−0.0112286	+	0.999937i	$0.503574\pi$
$229$	−11.4945	+	25.1694i	−0.759577	+	1.66324i	−0.748349	+	0.663305i	$0.769153\pi$
$230$		0			0
$231$	−18.4193			−1.21190
$232$		0			0
$233$	3.94989	−	4.55842i	0.258766	−	0.298632i	−0.611469	−	0.791268i	$-0.709421\pi$
$233$	3.94989	−	4.55842i	0.258766	−	0.298632i	0.870235	+	0.492636i	$0.163967\pi$
$234$		0			0
$235$	−0.629886	−	4.38095i	−0.0410892	−	0.285782i
$236$		0			0
$237$	−2.34861	+	5.14274i	−0.152559	+	0.334057i
$238$		0			0
$239$	3.83055			0.247778			0.123889	−	0.992296i	$-0.460463\pi$
$239$	3.83055			0.247778			0.123889	+	0.992296i	$0.460463\pi$
$240$		0			0
$241$	1.76048	−	1.13139i	0.113403	−	0.0728794i	−0.482710	−	0.875780i	$-0.660348\pi$
$241$	1.76048	−	1.13139i	0.113403	−	0.0728794i	0.596113	+	0.802901i	$0.296711\pi$
$242$		0			0
$243$	−0.415415	−	0.909632i	−0.0266489	−	0.0583529i
$244$		0			0
$245$	4.08336	+	4.71245i	0.260876	+	0.301067i
$246$		0			0
$247$	1.26255	−	0.811388i	0.0803338	−	0.0516274i
$248$		0			0
$249$	0.669722	+	4.65802i	0.0424419	+	0.295190i
$250$		0			0
$251$	12.1750	−	3.57490i	0.768480	−	0.225646i	0.126084	−	0.992020i	$-0.459759\pi$
$251$	12.1750	−	3.57490i	0.768480	−	0.225646i	0.642395	+	0.766374i	$0.277941\pi$
$252$		0			0
$253$	4.25795	+	29.6147i	0.267695	+	1.86186i
$254$		0			0
$255$	−0.431868	−	0.945659i	−0.0270446	−	0.0592194i
$256$		0			0
$257$	−0.204620	−	0.131501i	−0.0127638	−	0.00820282i	0.534243	−	0.845331i	$-0.320597\pi$
$257$	−0.204620	−	0.131501i	−0.0127638	−	0.00820282i	−0.547007	+	0.837128i	$0.684233\pi$
$258$		0			0
$259$	3.32948	−	23.1571i	0.206884	−	1.43891i
$260$		0			0
$261$	0.652142	−	4.53575i	0.0403666	−	0.280756i
$262$		0			0
$263$	−13.6921	−	8.79936i	−0.844290	−	0.542592i	0.0454993	−	0.998964i	$-0.485512\pi$
$263$	−13.6921	−	8.79936i	−0.844290	−	0.542592i	−0.889789	+	0.456372i	$0.849148\pi$
$264$		0			0
$265$	−2.90568	−	3.35334i	−0.178495	−	0.205994i
$266$		0			0
$267$	−4.46786			−0.273429
$268$		0			0
$269$	−15.3389			−0.935226			−0.467613	−	0.883933i	$-0.654886\pi$
$269$	−15.3389			−0.935226			−0.467613	+	0.883933i	$0.654886\pi$
$270$		0			0
$271$	−1.38277	−	1.59580i	−0.0839971	−	0.0969378i	0.712195	−	0.701982i	$-0.247701\pi$
$271$	−1.38277	−	1.59580i	−0.0839971	−	0.0969378i	−0.796192	+	0.605044i	$0.793156\pi$
$272$		0			0
$273$	2.59480	+	1.66758i	0.157044	+	0.100926i
$274$		0			0
$275$	−2.90770	+	20.2235i	−0.175341	+	1.21952i
$276$		0			0
$277$	2.28511	−	15.8933i	0.137299	−	0.954934i	−0.798398	−	0.602129i	$-0.794319\pi$
$277$	2.28511	−	15.8933i	0.137299	−	0.954934i	0.935697	−	0.352804i	$-0.114772\pi$
$278$		0			0
$279$	−2.05097	−	1.31808i	−0.122789	−	0.0789114i
$280$		0			0
$281$	−0.171736	−	0.376050i	−0.0102449	−	0.0224333i	0.904440	−	0.426600i	$-0.140289\pi$
$281$	−0.171736	−	0.376050i	−0.0102449	−	0.0224333i	−0.914685	+	0.404167i	$0.867562\pi$
$282$		0			0
$283$	−3.10270	−	21.5798i	−0.184436	−	1.28278i	−0.846117	−	0.532997i	$-0.821066\pi$
$283$	−3.10270	−	21.5798i	−0.184436	−	1.28278i	0.661681	−	0.749786i	$-0.269843\pi$
$284$		0			0
$285$	−1.15165	+	0.338156i	−0.0682181	+	0.0200306i
$286$		0			0
$287$	2.36134	+	16.4234i	0.139385	+	0.969446i
$288$		0			0
$289$	−11.6707	+	7.50029i	−0.686511	+	0.441194i
$290$		0			0
$291$	5.48920	+	6.33487i	0.321782	+	0.371357i
$292$		0			0
$293$	0.284265	+	0.622453i	0.0166069	+	0.0363641i	0.917754	−	0.397150i	$-0.130001\pi$
$293$	0.284265	+	0.622453i	0.0166069	+	0.0363641i	−0.901147	+	0.433514i	$0.857273\pi$
$294$		0			0
$295$	−6.08356	+	3.90967i	−0.354199	+	0.227630i
$296$		0			0
$297$	4.38973			0.254718
$298$		0			0
$299$	2.08131	−	4.55744i	0.120366	−	0.263564i
$300$		0			0
$301$	−6.09169	−	42.3686i	−0.351119	−	2.44209i
$302$		0			0
$303$	−10.2818	+	11.8659i	−0.590676	+	0.681676i
$304$		0			0
$305$	−5.64892			−0.323456
$306$		0			0
$307$	6.54789	−	14.3379i	0.373708	−	0.818306i	−0.625565	−	0.780172i	$-0.715131\pi$
$307$	6.54789	−	14.3379i	0.373708	−	0.818306i	0.999273	−	0.0381338i	$-0.0121413\pi$
$308$		0			0
$309$	0.817408	−	0.240013i	0.0465007	−	0.0136538i
$310$		0			0
$311$	23.0760	−	6.77573i	1.30852	−	0.384216i	0.448183	−	0.893942i	$-0.352071\pi$
$311$	23.0760	−	6.77573i	1.30852	−	0.384216i	0.860337	+	0.509725i	$0.170253\pi$
$312$		0			0
$313$	10.0254	−	11.5700i	0.566671	−	0.653974i	−0.398014	−	0.917379i	$-0.630300\pi$
$313$	10.0254	−	11.5700i	0.566671	−	0.653974i	0.964685	+	0.263406i	$0.0848458\pi$
$314$		0			0
$315$	−1.61542	−	1.86430i	−0.0910188	−	0.105041i
$316$		0			0
$317$	−0.910124	−	0.267237i	−0.0511177	−	0.0150095i	0.256074	−	0.966657i	$-0.417571\pi$
$317$	−0.910124	−	0.267237i	−0.0511177	−	0.0150095i	−0.307191	+	0.951648i	$0.599389\pi$
$318$		0			0
$319$	16.9222	+	10.8752i	0.947460	+	0.608895i
$320$		0			0
$321$	−11.7339	−	3.44538i	−0.654922	−	0.192302i
$322$		0			0
$323$	−1.49977	−	3.28405i	−0.0834497	−	0.182729i
$324$		0			0
$325$	2.24054	−	2.58572i	0.124283	−	0.143430i
$326$		0			0
$327$	5.80264	−	12.7060i	0.320887	−	0.702644i
$328$		0			0
$329$	26.5748	−	17.0786i	1.46512	−	0.941575i
$330$		0			0
$331$	−0.525438	−	0.154283i	−0.0288807	−	0.00848013i	0.267260	−	0.963624i	$-0.413882\pi$
$331$	−0.525438	−	0.154283i	−0.0288807	−	0.00848013i	−0.296141	+	0.955144i	$0.595700\pi$
$332$		0			0
$333$	−0.793491	+	5.51885i	−0.0434831	+	0.302431i
$334$		0			0
$335$	−1.90433	+	4.41932i	−0.104045	+	0.241453i
$336$		0			0
$337$	2.34907	−	16.3381i	0.127962	−	0.889994i	−0.820171	−	0.572119i	$-0.806122\pi$
$337$	2.34907	−	16.3381i	0.127962	−	0.889994i	0.948133	−	0.317875i	$-0.102969\pi$
$338$		0			0
$339$	−14.4605	−	4.24599i	−0.785388	−	0.230611i
$340$		0			0
$341$	9.00321	−	5.78601i	0.487551	−	0.313330i
$342$		0			0
$343$	−6.28616	+	13.7648i	−0.339421	+	0.743228i
$344$		0			0
$345$	−2.62401	+	3.02827i	−0.141272	+	0.163036i
$346$		0			0
$347$	13.0307	+	28.5333i	0.699525	+	1.53175i	0.840546	+	0.541740i	$0.182234\pi$
$347$	13.0307	+	28.5333i	0.699525	+	1.53175i	−0.141021	+	0.990007i	$0.545038\pi$
$348$		0			0
$349$	−7.02621	−	2.06308i	−0.376104	−	0.110434i	0.0882164	−	0.996101i	$-0.471883\pi$
$349$	−7.02621	−	2.06308i	−0.376104	−	0.110434i	−0.464321	+	0.885667i	$0.653701\pi$
$350$		0			0
$351$	−0.618399	−	0.397421i	−0.0330077	−	0.0212128i
$352$		0			0
$353$	6.78260	+	1.99155i	0.361001	+	0.106000i	0.457203	−	0.889362i	$-0.348851\pi$
$353$	6.78260	+	1.99155i	0.361001	+	0.106000i	−0.0962018	+	0.995362i	$0.530669\pi$
$354$		0			0
$355$	−0.393622	−	0.454265i	−0.0208913	−	0.0241099i
$356$		0			0
$357$	4.85903	−	5.60762i	0.257167	−	0.296787i
$358$		0			0
$359$	28.2491	−	8.29470i	1.49093	−	0.437777i	0.568094	−	0.822964i	$-0.307681\pi$
$359$	28.2491	−	8.29470i	1.49093	−	0.437777i	0.922839	+	0.385186i	$0.125863\pi$
$360$		0			0
$361$	14.2309	−	4.17858i	0.748997	−	0.219925i
$362$		0			0
$363$	−3.43535	+	7.52238i	−0.180309	+	0.394822i
$364$		0			0
$365$	5.91709			0.309715
$366$		0			0
$367$	−7.33324	+	8.46301i	−0.382792	+	0.441765i	−0.914146	−	0.405384i	$-0.867138\pi$
$367$	−7.33324	+	8.46301i	−0.382792	+	0.441765i	0.531355	+	0.847150i	$0.321683\pi$
$368$		0			0
$369$	−0.562760	−	3.91408i	−0.0292961	−	0.203759i
$370$		0			0
$371$	13.1557	−	28.8069i	0.683009	−	1.49558i
$372$		0			0
$373$	−29.7927			−1.54261			−0.771303	−	0.636468i	$-0.780395\pi$
$373$	−29.7927			−1.54261			−0.771303	+	0.636468i	$0.780395\pi$
$374$		0			0
$375$	−4.77478	+	3.06857i	−0.246569	+	0.158460i
$376$		0			0
$377$	−1.39932	−	3.06408i	−0.0720685	−	0.157808i
$378$		0			0
$379$	6.20647	+	7.16265i	0.318805	+	0.367921i	0.892421	−	0.451204i	$-0.149005\pi$
$379$	6.20647	+	7.16265i	0.318805	+	0.367921i	−0.573616	+	0.819124i	$0.694460\pi$
$380$		0			0
$381$	1.08306	−	0.696040i	0.0554869	−	0.0356592i
$382$		0			0
$383$	−4.70141	−	32.6990i	−0.240231	−	1.67084i	−0.650982	−	0.759093i	$-0.725643\pi$
$383$	−4.70141	−	32.6990i	−0.240231	−	1.67084i	0.410752	−	0.911747i	$-0.365266\pi$
$384$		0			0
$385$	10.3900	−	3.05079i	0.529525	−	0.155482i
$386$		0			0
$387$	1.45179	+	10.0974i	0.0737985	+	0.513280i
$388$		0			0
$389$	−1.65092	−	3.61500i	−0.0837047	−	0.183288i	0.863151	−	0.504945i	$-0.168487\pi$
$389$	−1.65092	−	3.61500i	−0.0837047	−	0.183288i	−0.946856	+	0.321657i	$0.895760\pi$
$390$		0			0
$391$	−10.1393	−	6.51611i	−0.512765	−	0.329534i
$392$		0			0
$393$	−0.643985	+	4.47902i	−0.0324848	+	0.225937i
$394$		0			0
$395$	0.473023	−	3.28995i	0.0238004	−	0.165535i
$396$		0			0
$397$	−1.18727	−	0.763009i	−0.0595872	−	0.0382943i	0.510508	−	0.859873i	$-0.329457\pi$
$397$	−1.18727	−	0.763009i	−0.0595872	−	0.0382943i	−0.570095	+	0.821579i	$0.693094\pi$
$398$		0			0
$399$	−5.60998	−	6.47426i	−0.280850	−	0.324119i
$400$		0			0
$401$	−9.44230			−0.471526			−0.235763	−	0.971811i	$-0.575759\pi$
$401$	−9.44230			−0.471526			−0.235763	+	0.971811i	$0.575759\pi$
$402$		0			0
$403$	−1.79215			−0.0892735
$404$		0			0
$405$	0.384992	+	0.444304i	0.0191304	+	0.0220777i
$406$		0			0
$407$	−20.5900	−	13.2324i	−1.02061	−	0.655905i
$408$		0			0
$409$	0.0501255	−	0.348631i	0.00247855	−	0.0172387i	−0.988545	−	0.150929i	$-0.951774\pi$
$409$	0.0501255	−	0.348631i	0.00247855	−	0.0172387i	0.991023	+	0.133690i	$0.0426827\pi$
$410$		0			0
$411$	1.58970	−	11.0566i	0.0784139	−	0.545381i
$412$		0			0
$413$	−43.4200	−	27.9044i	−2.13656	−	1.37308i
$414$		0			0
$415$	−1.14929	−	2.51659i	−0.0564164	−	0.123535i
$416$		0			0
$417$	−2.10730	−	14.6566i	−0.103195	−	0.717736i
$418$		0			0
$419$	19.6011	−	5.75542i	0.957579	−	0.281170i	0.234640	−	0.972082i	$-0.424609\pi$
$419$	19.6011	−	5.75542i	0.957579	−	0.281170i	0.722939	+	0.690912i	$0.242791\pi$
$420$		0			0
$421$	0.554770	+	3.85851i	0.0270378	+	0.188052i	0.998864	−	0.0476452i	$-0.0151717\pi$
$421$	0.554770	+	3.85851i	0.0270378	+	0.188052i	−0.971826	+	0.235697i	$0.924263\pi$
$422$		0			0
$423$	−6.33339	+	4.07022i	−0.307940	+	0.197901i
$424$		0			0
$425$	−5.38985	−	6.22021i	−0.261446	−	0.301725i
$426$		0			0
$427$	−16.7487	−	36.6744i	−0.810524	−	1.77480i
$428$		0			0
$429$	2.71460	−	1.74457i	0.131062	−	0.0842286i
$430$		0			0
$431$	34.3078			1.65255			0.826275	−	0.563267i	$-0.190456\pi$
$431$	34.3078			1.65255			0.826275	+	0.563267i	$0.190456\pi$
$432$		0			0
$433$	−7.92406	+	17.3513i	−0.380806	+	0.833849i	0.618055	+	0.786135i	$0.287921\pi$
$433$	−7.92406	+	17.3513i	−0.380806	+	0.833849i	−0.998861	+	0.0477139i	$0.984806\pi$
$434$		0			0
$435$	0.383393	+	2.66656i	0.0183823	+	0.127852i
$436$		0			0
$437$	−9.11255	+	10.5164i	−0.435913	+	0.503070i
$438$		0			0
$439$	−25.2960			−1.20731			−0.603657	−	0.797244i	$-0.706290\pi$
$439$	−25.2960			−1.20731			−0.603657	+	0.797244i	$0.706290\pi$
$440$		0			0
$441$	4.40604	−	9.64788i	0.209811	−	0.459423i
$442$		0			0
$443$	−14.1608	+	4.15800i	−0.672802	+	0.197552i	−0.600250	−	0.799812i	$-0.704932\pi$
$443$	−14.1608	+	4.15800i	−0.672802	+	0.197552i	−0.0725515	+	0.997365i	$0.523114\pi$
$444$		0			0
$445$	2.52025	−	0.740013i	0.119471	−	0.0350800i
$446$		0			0
$447$	1.81781	−	2.09786i	0.0859794	−	0.0992255i
$448$		0			0
$449$	5.83003	+	6.72822i	0.275136	+	0.317524i	0.876454	−	0.481486i	$-0.159903\pi$
$449$	5.83003	+	6.72822i	0.275136	+	0.317524i	−0.601318	+	0.799010i	$0.705357\pi$
$450$		0			0
$451$	16.6553	+	4.89043i	0.784267	+	0.230281i
$452$		0			0
$453$	2.66918	+	1.71538i	0.125409	+	0.0805956i
$454$		0			0
$455$	−1.73989	−	0.510877i	−0.0815672	−	0.0239503i
$456$		0			0
$457$	9.79507	+	21.4482i	0.458194	+	1.00330i	0.987896	+	0.155121i	$0.0495767\pi$
$457$	9.79507	+	21.4482i	0.458194	+	1.00330i	−0.529702	+	0.848184i	$0.677696\pi$
$458$		0			0
$459$	−1.15802	+	1.33642i	−0.0540516	+	0.0623789i
$460$		0			0
$461$	14.3405	−	31.4014i	0.667905	−	1.46251i	−0.207063	−	0.978328i	$-0.566391\pi$
$461$	14.3405	−	31.4014i	0.667905	−	1.46251i	0.874968	−	0.484180i	$-0.160882\pi$
$462$		0			0
$463$	−8.47795	+	5.44845i	−0.394004	+	0.253211i	−0.722610	−	0.691256i	$-0.757058\pi$
$463$	−8.47795	+	5.44845i	−0.394004	+	0.253211i	0.328606	+	0.944467i	$0.393421\pi$
$464$		0			0
$465$	1.37524	+	0.403806i	0.0637751	+	0.0187260i
$466$		0			0
$467$	2.92132	−	20.3182i	0.135183	−	0.940216i	−0.803468	−	0.595347i	$-0.797014\pi$
$467$	2.92132	−	20.3182i	0.135183	−	0.940216i	0.938651	−	0.344869i	$-0.112076\pi$
$468$		0			0
$469$	−34.3377	+	0.739537i	−1.58557	+	0.0341487i
$470$		0			0
$471$	−3.45031	+	23.9974i	−0.158982	+	1.10574i
$472$		0			0
$473$	−42.9667	−	12.6162i	−1.97561	−	0.580092i
$474$		0			0
$475$	−7.99404	+	5.13745i	−0.366792	+	0.235723i
$476$		0			0
$477$	−3.13530	+	6.86535i	−0.143555	+	0.314343i
$478$		0			0
$479$	6.54181	−	7.54966i	0.298903	−	0.344953i	−0.586354	−	0.810055i	$-0.699437\pi$
$479$	6.54181	−	7.54966i	0.298903	−	0.344953i	0.885257	+	0.465103i	$0.153983\pi$
$480$		0			0
$481$	1.70261	+	3.72821i	0.0776325	+	0.169992i
$482$		0			0
$483$	−27.4404	−	8.05722i	−1.24858	−	0.366616i
$484$		0			0
$485$	−4.14562	−	2.66423i	−0.188243	−	0.120976i
$486$		0			0
$487$	−9.48412	−	2.78479i	−0.429767	−	0.126191i	0.0596931	−	0.998217i	$-0.480988\pi$
$487$	−9.48412	−	2.78479i	−0.429767	−	0.126191i	−0.489460	+	0.872026i	$0.662806\pi$
$488$		0			0
$489$	13.2592	+	15.3019i	0.599600	+	0.691975i
$490$		0			0
$491$	24.2434	−	27.9784i	1.09409	−	1.26265i	0.131610	−	0.991302i	$-0.457985\pi$
$491$	24.2434	−	27.9784i	1.09409	−	1.26265i	0.962482	−	0.271347i	$-0.0874692\pi$
$492$		0			0
$493$	−7.77499	+	2.28294i	−0.350168	+	0.102819i
$494$		0			0
$495$	−2.47618	+	0.727071i	−0.111296	+	0.0326794i
$496$		0			0
$497$	1.78215	−	3.90237i	0.0799405	−	0.175045i
$498$		0			0
$499$	20.3365			0.910386			0.455193	−	0.890393i	$-0.349570\pi$
$499$	20.3365			0.910386			0.455193	+	0.890393i	$0.349570\pi$
$500$		0			0
$501$	8.41886	−	9.71589i	0.376127	−	0.434074i
$502$		0			0
$503$	0.931065	+	6.47570i	0.0415142	+	0.288737i	0.999994	+	0.00357569i	$0.00113818\pi$
$503$	0.931065	+	6.47570i	0.0415142	+	0.288737i	−0.958479	+	0.285162i	$0.907953\pi$
$504$		0			0
$505$	3.83448	−	8.39634i	0.170632	−	0.373632i
$506$		0			0
$507$	12.4596			0.553352
$508$		0			0
$509$	31.8659	−	20.4789i	1.41243	−	0.907713i	0.412435	−	0.910987i	$-0.364678\pi$
$509$	31.8659	−	20.4789i	1.41243	−	0.907713i	0.999995	+	0.00327348i	$0.00104198\pi$
$510$		0			0
$511$	17.5437	+	38.4154i	0.776090	+	1.69940i
$512$		0			0
$513$	1.33699	+	1.54296i	0.0590294	+	0.0681235i
$514$		0			0
$515$	−0.421334	+	0.270775i	−0.0185662	+	0.0119318i
$516$		0			0
$517$	−4.70323	−	32.7117i	−0.206848	−	1.43866i
$518$		0			0
$519$	−5.58237	+	1.63913i	−0.245039	+	0.0719499i
$520$		0			0
$521$	−4.66692	−	32.4592i	−0.204462	−	1.42206i	−0.790839	−	0.612024i	$-0.790356\pi$
$521$	−4.66692	−	32.4592i	−0.204462	−	1.42206i	0.586378	−	0.810038i	$-0.300554\pi$
$522$		0			0
$523$	17.8650	+	39.1189i	0.781181	+	1.71055i	0.700327	+	0.713822i	$0.253037\pi$
$523$	17.8650	+	39.1189i	0.781181	+	1.71055i	0.0808539	+	0.996726i	$0.474235\pi$
$524$		0			0
$525$	−16.4294	−	10.5586i	−0.717040	−	0.460814i
$526$		0			0
$527$	−0.613549	+	4.26733i	−0.0267266	+	0.185888i
$528$		0			0
$529$	−3.33791	+	23.2157i	−0.145126	+	1.00938i
$530$		0			0
$531$	10.3480	+	6.65024i	0.449064	+	0.288596i
$532$		0			0
$533$	−1.90355	−	2.19681i	−0.0824518	−	0.0951545i
$534$		0			0
$535$	7.18957			0.310832
$536$		0			0
$537$	18.7520			0.809209
$538$		0			0
$539$	30.4897	+	35.1869i	1.31328	+	1.51561i
$540$		0			0
$541$	7.34270	+	4.71887i	0.315687	+	0.202880i	0.688883	−	0.724873i	$-0.258102\pi$
$541$	7.34270	+	4.71887i	0.315687	+	0.202880i	−0.373195	+	0.927753i	$0.621738\pi$
$542$		0			0
$543$	−3.14242	+	21.8560i	−0.134854	+	0.937932i
$544$		0			0
$545$	−1.16868	+	8.12835i	−0.0500608	+	0.348180i
$546$		0			0
$547$	−25.4396	−	16.3491i	−1.08772	−	0.699036i	−0.131393	−	0.991330i	$-0.541945\pi$
$547$	−25.4396	−	16.3491i	−1.08772	−	0.699036i	−0.956328	+	0.292295i	$0.905581\pi$
$548$		0			0
$549$	3.99158	+	8.74035i	0.170357	+	0.373029i
$550$		0			0
$551$	1.33143	+	9.26033i	0.0567210	+	0.394503i
$552$		0			0
$553$	22.7618	−	6.68345i	0.967928	−	0.284209i
$554$		0			0
$555$	−0.466493	−	3.24453i	−0.0198015	−	0.137723i
$556$		0			0
$557$	31.3565	−	20.1516i	1.32862	−	0.853852i	0.332607	−	0.943066i	$-0.392072\pi$
$557$	31.3565	−	20.1516i	1.32862	−	0.853852i	0.996013	+	0.0892137i	$0.0284354\pi$
$558$		0			0
$559$	4.91070	+	5.66725i	0.207701	+	0.239699i
$560$		0			0
$561$	−3.22467	−	7.06105i	−0.136146	−	0.298118i
$562$		0			0
$563$	−9.09383	+	5.84425i	−0.383259	+	0.246306i	−0.718057	−	0.695984i	$-0.754968\pi$
$563$	−9.09383	+	5.84425i	−0.383259	+	0.246306i	0.334798	+	0.942290i	$0.391332\pi$
$564$		0			0
$565$	8.86023			0.372753
$566$		0			0
$567$	−1.74308	+	3.81681i	−0.0732024	+	0.160291i
$568$		0			0
$569$	5.14906	+	35.8125i	0.215860	+	1.50134i	0.753099	+	0.657907i	$0.228558\pi$
$569$	5.14906	+	35.8125i	0.215860	+	1.50134i	−0.537239	+	0.843430i	$0.680533\pi$
$570$		0			0
$571$	3.30313	−	3.81202i	0.138232	−	0.159528i	−0.682413	−	0.730967i	$-0.739069\pi$
$571$	3.30313	−	3.81202i	0.138232	−	0.159528i	0.820644	+	0.571439i	$0.193615\pi$
$572$		0			0
$573$	−14.9886			−0.626156
$574$		0			0
$575$	−13.1782	+	28.8563i	−0.549570	+	1.20339i
$576$		0			0
$577$	40.3634	−	11.8518i	1.68035	−	0.493395i	0.704110	−	0.710091i	$-0.251346\pi$
$577$	40.3634	−	11.8518i	1.68035	−	0.493395i	0.976239	+	0.216697i	$0.0695282\pi$
$578$		0			0
$579$	2.71384	−	0.796855i	0.112783	−	0.0331161i
$580$		0			0
$581$	12.9309	−	14.9230i	0.536463	−	0.619112i
$582$		0			0
$583$	−21.6962	−	25.0387i	−0.898563	−	1.03700i
$584$		0			0
$585$	0.414655	+	0.121754i	0.0171439	+	0.00503389i
$586$		0			0
$587$	−27.4354	−	17.6316i	−1.13238	−	0.727735i	−0.166323	−	0.986071i	$-0.553190\pi$
$587$	−27.4354	−	17.6316i	−1.13238	−	0.727735i	−0.966055	+	0.258336i	$0.916826\pi$
$588$		0			0
$589$	4.77587	+	1.40232i	0.196786	+	0.0577817i
$590$		0			0
$591$	2.44865	+	5.36180i	0.100724	+	0.220555i
$592$		0			0
$593$	8.35464	−	9.64177i	0.343084	−	0.395940i	−0.557818	−	0.829964i	$-0.688361\pi$
$593$	8.35464	−	9.64177i	0.343084	−	0.395940i	0.900901	+	0.434024i	$0.142907\pi$
$594$		0			0
$595$	−1.81211	+	3.96798i	−0.0742894	+	0.162671i
$596$		0			0
$597$	−5.16556	+	3.31970i	−0.211412	+	0.135866i
$598$		0			0
$599$	9.78054	+	2.87183i	0.399622	+	0.117340i	0.475367	−	0.879788i	$-0.342315\pi$
$599$	9.78054	+	2.87183i	0.399622	+	0.117340i	−0.0757449	+	0.997127i	$0.524133\pi$
$600$		0			0
$601$	0.785168	−	5.46097i	0.0320277	−	0.222757i	−0.967521	−	0.252790i	$-0.918652\pi$
$601$	0.785168	−	5.46097i	0.0320277	−	0.222757i	0.999549	+	0.0300323i	$0.00956101\pi$
$602$		0			0
$603$	8.18346	−	0.176248i	0.333256	−	0.00717739i
$604$		0			0
$605$	0.691898	−	4.81226i	0.0281297	−	0.195646i
$606$		0			0
$607$	5.36688	+	1.57586i	0.217835	+	0.0639621i	0.388829	−	0.921310i	$-0.372880\pi$
$607$	5.36688	+	1.57586i	0.217835	+	0.0639621i	−0.170994	+	0.985272i	$0.554698\pi$
$608$		0			0
$609$	−16.1753	+	10.3953i	−0.655458	+	0.421237i
$610$		0			0
$611$	−2.29897	+	5.03404i	−0.0930064	+	0.203656i
$612$		0			0
$613$	6.14011	−	7.08607i	0.247997	−	0.286204i	−0.618079	−	0.786116i	$-0.712089\pi$
$613$	6.14011	−	7.08607i	0.247997	−	0.286204i	0.866076	+	0.499912i	$0.166634\pi$
$614$		0			0
$615$	0.965734	+	2.11466i	0.0389422	+	0.0852714i
$616$		0			0
$617$	38.0311	+	11.1669i	1.53108	+	0.449564i	0.935380	−	0.353645i	$-0.115058\pi$
$617$	38.0311	+	11.1669i	1.53108	+	0.449564i	0.595696	+	0.803210i	$0.296876\pi$
$618$		0			0
$619$	9.63379	+	6.19126i	0.387215	+	0.248848i	0.719736	−	0.694248i	$-0.244263\pi$
$619$	9.63379	+	6.19126i	0.387215	+	0.248848i	−0.332521	+	0.943096i	$0.607899\pi$
$620$		0			0
$621$	6.53966	+	1.92022i	0.262428	+	0.0770557i
$622$		0			0
$623$	12.2768	+	14.1681i	0.491858	+	0.567634i
$624$		0			0
$625$	−13.0547	+	15.0659i	−0.522188	+	0.602637i
$626$		0			0
$627$	−8.59918	+	2.52495i	−0.343418	+	0.100837i
$628$		0			0
$629$	9.46019	−	2.77776i	0.377202	−	0.110757i
$630$		0			0
$631$	−19.9145	+	43.6068i	−0.792786	+	1.73596i	−0.124286	+	0.992246i	$0.539664\pi$
$631$	−19.9145	+	43.6068i	−0.792786	+	1.73596i	−0.668500	+	0.743712i	$0.733063\pi$
$632$		0			0
$633$	−3.76384			−0.149599
$634$		0			0
$635$	−0.495652	+	0.572013i	−0.0196694	+	0.0226997i
$636$		0			0
$637$	−1.10958	−	7.71730i	−0.0439632	−	0.305770i
$638$		0			0
$639$	−0.424728	+	0.930024i	−0.0168020	+	0.0367912i
$640$		0			0
$641$	−33.3452			−1.31706			−0.658529	−	0.752556i	$-0.728821\pi$
$641$	−33.3452			−1.31706			−0.658529	+	0.752556i	$0.728821\pi$
$642$		0			0
$643$	−6.50043	+	4.17757i	−0.256352	+	0.164747i	−0.662505	−	0.749058i	$-0.730506\pi$
$643$	−6.50043	+	4.17757i	−0.256352	+	0.164747i	0.406153	+	0.913805i	$0.366870\pi$
$644$		0			0
$645$	−2.49137	−	5.45533i	−0.0980974	−	0.214803i
$646$		0			0
$647$	2.28881	+	2.64143i	0.0899825	+	0.103845i	0.798955	−	0.601391i	$-0.205386\pi$
$647$	2.28881	+	2.64143i	0.0899825	+	0.103845i	−0.708973	+	0.705236i	$0.750841\pi$
$648$		0			0
$649$	−45.4248	+	29.1927i	−1.78308	+	1.14591i
$650$		0			0
$651$	1.45585	+	10.1257i	0.0570594	+	0.396857i
$652$		0			0
$653$	5.54261	−	1.62746i	0.216899	−	0.0636873i	−0.171478	−	0.985188i	$-0.554854\pi$
$653$	5.54261	−	1.62746i	0.216899	−	0.0636873i	0.388377	+	0.921501i	$0.373036\pi$
$654$		0			0
$655$	−0.378598	−	2.63321i	−0.0147931	−	0.102888i
$656$		0			0
$657$	−4.18107	−	9.15527i	−0.163119	−	0.357181i
$658$		0			0
$659$	−18.5119	−	11.8969i	−0.721120	−	0.463436i	0.127906	−	0.991786i	$-0.459174\pi$
$659$	−18.5119	−	11.8969i	−0.721120	−	0.463436i	−0.849026	+	0.528351i	$0.822811\pi$
$660$		0			0
$661$	5.35099	−	37.2169i	0.208129	−	1.44757i	−0.571125	−	0.820863i	$-0.693493\pi$
$661$	5.35099	−	37.2169i	0.208129	−	1.44757i	0.779254	−	0.626708i	$-0.215598\pi$
$662$		0			0
$663$	−0.184994	+	1.28666i	−0.00718458	+	0.0499699i
$664$		0			0
$665$	4.23684	+	2.72285i	0.164298	+	0.105588i
$666$		0			0
$667$	20.4529	+	23.6039i	0.791938	+	0.913945i
$668$		0			0
$669$	−20.0787			−0.776289
$670$		0			0
$671$	−42.1794			−1.62832
$672$		0			0
$673$	−18.7228	−	21.6073i	−0.721712	−	0.832900i	0.269800	−	0.962916i	$-0.413042\pi$
$673$	−18.7228	−	21.6073i	−0.721712	−	0.832900i	−0.991512	+	0.130017i	$0.958497\pi$
$674$		0			0
$675$	3.91551	+	2.51635i	0.150708	+	0.0968542i
$676$		0			0
$677$	−1.50688	+	10.4806i	−0.0579141	+	0.402801i	0.940158	+	0.340738i	$0.110677\pi$
$677$	−1.50688	+	10.4806i	−0.0579141	+	0.402801i	−0.998072	+	0.0620629i	$0.980232\pi$
$678$		0			0
$679$	5.00547	−	34.8138i	0.192092	−	1.33603i
$680$		0			0
$681$	15.3226	+	9.84721i	0.587162	+	0.377346i
$682$		0			0
$683$	−14.9693	−	32.7781i	−0.572783	−	1.25422i	−0.945302	−	0.326196i	$-0.894233\pi$
$683$	−14.9693	−	32.7781i	−0.572783	−	1.25422i	0.372519	−	0.928025i	$-0.378494\pi$
$684$		0			0
$685$	0.934581	+	6.50015i	0.0357085	+	0.248358i
$686$		0			0
$687$	−26.5491	+	7.79551i	−1.01291	+	0.297417i
$688$		0			0
$689$	0.789567	+	5.49156i	0.0300801	+	0.209212i
$690$		0			0
$691$	−20.7743	+	13.3508i	−0.790291	+	0.507889i	−0.872434	−	0.488732i	$-0.837460\pi$
$691$	−20.7743	+	13.3508i	−0.790291	+	0.507889i	0.0821437	+	0.996620i	$0.473823\pi$
$692$		0			0
$693$	−12.0620	−	13.9203i	−0.458199	−	0.528790i
$694$		0			0
$695$	3.61627	+	7.91852i	0.137173	+	0.300367i
$696$		0			0
$697$	−5.88255	+	3.78049i	−0.222818	+	0.143196i
$698$		0			0
$699$	6.03165			0.228138
$700$		0			0
$701$	−5.28605	+	11.5748i	−0.199651	+	0.437175i	−0.982803	−	0.184655i	$-0.940883\pi$
$701$	−5.28605	+	11.5748i	−0.199651	+	0.437175i	0.783152	+	0.621830i	$0.213611\pi$
$702$		0			0
$703$	−1.62002	−	11.2675i	−0.0611002	−	0.424961i
$704$		0			0
$705$	2.89842	−	3.34495i	0.109161	−	0.125978i
$706$		0			0
$707$	65.8804			2.47769
$708$		0			0
$709$	4.00188	−	8.76290i	0.150294	−	0.329098i	−0.819478	−	0.573110i	$-0.805737\pi$
$709$	4.00188	−	8.76290i	0.150294	−	0.329098i	0.969772	+	0.244013i	$0.0784639\pi$
$710$		0			0
$711$	−5.42464	+	1.59282i	−0.203440	+	0.0597354i
$712$		0			0
$713$	15.9437	−	4.68148i	0.597095	−	0.175323i
$714$		0			0
$715$	−1.24231	+	1.43371i	−0.0464599	+	0.0536176i
$716$		0			0
$717$	2.50848	+	2.89494i	0.0936808	+	0.108113i
$718$		0			0
$719$	−11.3586	−	3.33519i	−0.423605	−	0.124382i	0.0629802	−	0.998015i	$-0.479939\pi$
$719$	−11.3586	−	3.33519i	−0.423605	−	0.124382i	−0.486585	+	0.873633i	$0.661758\pi$
$720$		0			0
$721$	−3.00717	−	1.93259i	−0.111993	−	0.0719735i
$722$		0			0
$723$	2.00792	+	0.589578i	0.0746753	+	0.0219266i
$724$		0			0
$725$	8.86004	+	19.4008i	0.329053	+	0.720527i
$726$		0			0
$727$	−29.2389	+	33.7434i	−1.08441	+	1.25148i	−0.118401	+	0.992966i	$0.537777\pi$
$727$	−29.2389	+	33.7434i	−1.08441	+	1.25148i	−0.966009	+	0.258509i	$0.916769\pi$
$728$		0			0
$729$	0.415415	−	0.909632i	0.0153857	−	0.0336901i
$730$		0			0
$731$	15.1756	−	9.75276i	0.561290	−	0.360719i
$732$		0			0
$733$	6.83950	+	2.00826i	0.252623	+	0.0741768i	0.405592	−	0.914054i	$-0.367065\pi$
$733$	6.83950	+	2.00826i	0.252623	+	0.0741768i	−0.152969	+	0.988231i	$0.548884\pi$
$734$		0			0
$735$	−0.887399	+	6.17200i	−0.0327322	+	0.227658i
$736$		0			0
$737$	−14.2192	+	32.9982i	−0.523772	+	1.21551i
$738$		0			0
$739$	−6.82496	+	47.4687i	−0.251060	+	1.74616i	0.340812	+	0.940131i	$0.389298\pi$
$739$	−6.82496	+	47.4687i	−0.251060	+	1.74616i	−0.591872	+	0.806032i	$0.701611\pi$
$740$		0			0
$741$	1.44000	+	0.422821i	0.0528996	+	0.0155327i
$742$		0			0
$743$	−36.8061	+	23.6539i	−1.35029	+	0.867776i	−0.997685	−	0.0679979i	$-0.978339\pi$
$743$	−36.8061	+	23.6539i	−1.35029	+	0.867776i	−0.352600	+	0.935774i	$0.614703\pi$
$744$		0			0
$745$	−0.677928	+	1.48446i	−0.0248374	+	0.0543863i
$746$		0			0
$747$	−3.08172	+	3.55650i	−0.112754	+	0.130125i
$748$		0			0
$749$	21.3166	+	46.6768i	0.778890	+	1.70553i
$750$		0			0
$751$	12.6209	+	3.70584i	0.460544	+	0.135228i	0.503771	−	0.863837i	$-0.331946\pi$
$751$	12.6209	+	3.70584i	0.460544	+	0.135228i	−0.0432267	+	0.999065i	$0.513764\pi$
$752$		0			0
$753$	10.6747	+	6.86019i	0.389006	+	0.249999i
$754$		0			0
$755$	−1.78976	−	0.525522i	−0.0651362	−	0.0191257i
$756$		0			0
$757$	2.31387	+	2.67034i	0.0840989	+	0.0970553i	0.796239	−	0.604982i	$-0.206820\pi$
$757$	2.31387	+	2.67034i	0.0840989	+	0.0970553i	−0.712141	+	0.702037i	$0.752274\pi$
$758$		0			0
$759$	−19.5929	+	22.6115i	−0.711179	+	0.820744i
$760$		0			0
$761$	−2.33044	+	0.684279i	−0.0844784	+	0.0248051i	−0.323699	−	0.946160i	$-0.604926\pi$
$761$	−2.33044	+	0.684279i	−0.0844784	+	0.0248051i	0.239220	+	0.970965i	$0.423108\pi$
$762$		0			0
$763$	−56.2367	+	16.5126i	−2.03590	+	0.597796i
$764$		0			0
$765$	0.431868	−	0.945659i	0.0156142	−	0.0341904i
$766$		0			0
$767$	9.04213			0.326492
$768$		0			0
$769$	28.0140	−	32.3299i	1.01021	−	1.16585i	0.0241097	−	0.999709i	$-0.492325\pi$
$769$	28.0140	−	32.3299i	1.01021	−	1.16585i	0.986103	−	0.166138i	$-0.0531296\pi$
$770$		0			0
$771$	−0.0346155	−	0.240756i	−0.00124665	−	0.00867063i
$772$		0			0
$773$	−3.73649	+	8.18178i	−0.134392	+	0.294278i	−0.964849	−	0.262805i	$-0.915352\pi$
$773$	−3.73649	+	8.18178i	−0.134392	+	0.294278i	0.830457	+	0.557083i	$0.188080\pi$
$774$		0			0
$775$	11.3473			0.407609
$776$		0			0
$777$	19.6813	−	12.6484i	0.706063	−	0.453759i
$778$		0			0
$779$	3.35377	+	7.34372i	0.120161	+	0.263116i
$780$		0			0
$781$	−2.93910	−	3.39190i	−0.105169	−	0.121372i
$782$		0			0
$783$	3.85495	−	2.47743i	0.137765	−	0.0885360i
$784$		0			0
$785$	−2.02843	−	14.1080i	−0.0723978	−	0.503538i
$786$		0			0
$787$	−13.1206	+	3.85254i	−0.467698	+	0.137328i	−0.507086	−	0.861896i	$-0.669277\pi$
$787$	−13.1206	+	3.85254i	−0.467698	+	0.137328i	0.0393883	+	0.999224i	$0.487459\pi$
$788$		0			0
$789$	−2.31629	−	16.1101i	−0.0824620	−	0.573536i
$790$		0			0
$791$	26.2699	+	57.5232i	0.934052	+	2.04529i
$792$		0			0
$793$	5.94199	+	3.81869i	0.211006	+	0.135606i
$794$		0			0
$795$	0.631465	−	4.39194i	0.0223958	−	0.155766i
$796$		0			0
$797$	−5.72484	+	39.8171i	−0.202784	+	1.41040i	0.593189	+	0.805063i	$0.297869\pi$
$797$	−5.72484	+	39.8171i	−0.202784	+	1.41040i	−0.795973	+	0.605332i	$0.793040\pi$
$798$		0			0
$799$	11.1996	+	7.19754i	0.396213	+	0.254631i
$800$		0			0
$801$	−2.92583	−	3.37658i	−0.103379	−	0.119306i
$802$		0			0
$803$	44.1817			1.55914
$804$		0			0
$805$	16.8132			0.592588
$806$		0			0
$807$	−10.0448	−	11.5923i	−0.353594	−	0.408069i
$808$		0			0
$809$	4.23939	+	2.72449i	0.149049	+	0.0957880i	0.613040	−	0.790052i	$-0.289947\pi$
$809$	4.23939	+	2.72449i	0.149049	+	0.0957880i	−0.463991	+	0.885840i	$0.653583\pi$
$810$		0			0
$811$	−0.0642199	+	0.446659i	−0.00225506	+	0.0156843i	−0.990918	−	0.134468i	$-0.957067\pi$
$811$	−0.0642199	+	0.446659i	−0.00225506	+	0.0156843i	0.988663	+	0.150153i	$0.0479765\pi$
$812$		0			0
$813$	0.300504	−	2.09005i	0.0105391	−	0.0733013i
$814$		0			0
$815$	−10.0137	−	6.43544i	−0.350766	−	0.225424i
$816$		0			0
$817$	−8.65192	−	18.9451i	−0.302692	−	0.662804i
$818$		0			0
$819$	0.438962	+	3.05305i	0.0153386	+	0.106682i
$820$		0			0
$821$	31.7801	−	9.33149i	1.10913	−	0.325671i	0.324659	−	0.945831i	$-0.394751\pi$
$821$	31.7801	−	9.33149i	1.10913	−	0.325671i	0.784475	+	0.620160i	$0.212932\pi$
$822$		0			0
$823$	−3.76838	−	26.2097i	−0.131358	−	0.913612i	−0.943787	−	0.330553i	$-0.892765\pi$
$823$	−3.76838	−	26.2097i	−0.131358	−	0.913612i	0.812430	−	0.583059i	$-0.198144\pi$
$824$		0			0
$825$	−17.1880	+	11.0461i	−0.598410	+	0.384575i
$826$		0			0
$827$	−24.6863	−	28.4895i	−0.858425	−	0.990675i	−1.00000		0.000747747i	$-0.999762\pi$
$827$	−24.6863	−	28.4895i	−0.858425	−	0.990675i	0.141575	−	0.989928i	$-0.454783\pi$
$828$		0			0
$829$	8.29080	+	18.1543i	0.287951	+	0.630525i	0.997228	−	0.0744046i	$-0.0237056\pi$
$829$	8.29080	+	18.1543i	0.287951	+	0.630525i	−0.709277	+	0.704930i	$0.750978\pi$
$830$		0			0
$831$	13.5078	−	8.68090i	0.468579	−	0.301137i
$832$		0			0
$833$	−18.7557			−0.649845
$834$		0			0
$835$	−3.13971	+	6.87500i	−0.108654	+	0.237919i
$836$		0			0
$837$	−0.346963	−	2.41318i	−0.0119928	−	0.0834117i
$838$		0			0
$839$	33.7843	−	38.9892i	1.16636	−	1.34606i	0.239394	−	0.970922i	$-0.423051\pi$
$839$	33.7843	−	38.9892i	1.16636	−	1.34606i	0.926971	−	0.375134i	$-0.122403\pi$
$840$		0			0
$841$	−8.00172			−0.275921
$842$		0			0
$843$	0.171736	−	0.376050i	0.00591491	−	0.0129519i
$844$		0			0
$845$	−7.02829	+	2.06369i	−0.241781	+	0.0709932i
$846$		0			0
$847$	33.2940	−	9.77600i	1.14400	−	0.335907i
$848$		0			0
$849$	14.2771	−	16.4766i	0.489987	−	0.565475i
$850$		0			0
$851$	−24.8860	−	28.7199i	−0.853080	−	0.984506i
$852$		0			0
$853$	31.1151	+	9.13622i	1.06536	+	0.312818i	0.767008	−	0.641638i	$-0.221745\pi$
$853$	31.1151	+	9.13622i	1.06536	+	0.312818i	0.298353	+	0.954456i	$0.403563\pi$
$854$		0			0
$855$	−1.00973	−	0.648917i	−0.0345322	−	0.0221925i
$856$		0			0
$857$	−24.7558	−	7.26897i	−0.845643	−	0.248303i	−0.169919	−	0.985458i	$-0.554351\pi$
$857$	−24.7558	−	7.26897i	−0.845643	−	0.248303i	−0.675724	+	0.737155i	$0.736169\pi$
$858$		0			0
$859$	−6.80871	−	14.9090i	−0.232310	−	0.508689i	0.757194	−	0.653190i	$-0.226570\pi$
$859$	−6.80871	−	14.9090i	−0.232310	−	0.508689i	−0.989505	+	0.144501i	$0.953842\pi$
$860$		0			0
$861$	−10.8657	+	12.5397i	−0.370301	+	0.427350i
$862$		0			0
$863$	−24.0333	+	52.6256i	−0.818103	+	1.79140i	−0.250445	+	0.968131i	$0.580577\pi$
$863$	−24.0333	+	52.6256i	−0.818103	+	1.79140i	−0.567657	+	0.823265i	$0.692150\pi$
$864$		0			0
$865$	2.87744	−	1.84922i	0.0978359	−	0.0628753i
$866$		0			0
$867$	−13.3110	−	3.90847i	−0.452066	−	0.132739i
$868$		0			0
$869$	3.53197	−	24.5654i	0.119814	−	0.833323i
$870$		0			0
$871$	4.99060	−	3.36127i	0.169100	−	0.113892i
$872$		0			0
$873$	−1.19292	+	8.29692i	−0.0403741	+	0.280808i
$874$		0			0
$875$	22.8509	+	6.70963i	0.772501	+	0.226827i
$876$		0			0
$877$	−10.2962	+	6.61698i	−0.347679	+	0.223439i	−0.702811	−	0.711377i	$-0.748072\pi$
$877$	−10.2962	+	6.61698i	−0.347679	+	0.223439i	0.355133	+	0.934816i	$0.384436\pi$
$878$		0			0
$879$	−0.284265	+	0.622453i	−0.00958801	+	0.0209948i
$880$		0			0
$881$	−24.8359	+	28.6621i	−0.836742	+	0.965652i	−0.999780	−	0.0209676i	$-0.993325\pi$
$881$	−24.8359	+	28.6621i	−0.836742	+	0.965652i	0.163038	+	0.986620i	$0.447871\pi$
$882$		0			0
$883$	−0.763635	−	1.67213i	−0.0256984	−	0.0562716i	0.896348	−	0.443352i	$-0.146211\pi$
$883$	−0.763635	−	1.67213i	−0.0256984	−	0.0562716i	−0.922046	+	0.387080i	$0.873484\pi$
$884$		0			0
$885$	−6.93862	−	2.03736i	−0.233239	−	0.0684851i
$886$		0			0
$887$	−19.8305	−	12.7443i	−0.665843	−	0.427911i	0.163582	−	0.986530i	$-0.447695\pi$
$887$	−19.8305	−	12.7443i	−0.665843	−	0.427911i	−0.829425	+	0.558618i	$0.811332\pi$
$888$		0			0
$889$	−5.18325	−	1.52194i	−0.173841	−	0.0510442i
$890$		0			0
$891$	2.87466	+	3.31753i	0.0963047	+	0.111142i
$892$		0			0
$893$	10.0655	−	11.6162i	0.336829	−	0.388722i
$894$		0			0
$895$	−10.5777	+	3.10590i	−0.353574	+	0.103819i
$896$		0			0
$897$	4.80726	−	1.41154i	0.160510	−	0.0471299i
$898$		0			0
$899$	4.64095	−	10.1623i	0.154784	−	0.338931i
$900$		0			0
$901$	13.3464			0.444632
$902$		0			0
$903$	28.0309	−	32.3493i	0.932808	−	1.07652i
$904$		0			0
$905$	−1.84743	−	12.8491i	−0.0614106	−	0.427120i
$906$		0			0
$907$	−22.9185	+	50.1846i	−0.760998	+	1.66635i	−0.0154683	+	0.999880i	$0.504924\pi$
$907$	−22.9185	+	50.1846i	−0.760998	+	1.66635i	−0.745530	+	0.666473i	$0.767803\pi$
$908$		0			0
$909$	−15.7008			−0.520762
$910$		0			0
$911$	24.8880	−	15.9946i	0.824577	−	0.529923i	−0.0589736	−	0.998260i	$-0.518783\pi$
$911$	24.8880	−	15.9946i	0.824577	−	0.529923i	0.883550	+	0.468336i	$0.155146\pi$
$912$		0			0
$913$	−8.58152	−	18.7909i	−0.284007	−	0.621888i
$914$		0			0
$915$	−3.69926	−	4.26917i	−0.122294	−	0.141134i
$916$		0			0
$917$	15.9730	−	10.2652i	0.527476	−	0.338988i
$918$		0			0
$919$	4.75826	+	33.0944i	0.156961	+	1.09168i	0.904194	+	0.427123i	$0.140473\pi$
$919$	4.75826	+	33.0944i	0.156961	+	1.09168i	−0.747233	+	0.664562i	$0.768618\pi$
$920$		0			0
$921$	15.1238	−	4.44075i	0.498346	−	0.146328i
$922$		0			0
$923$	0.106960	+	0.743922i	0.00352063	+	0.0244865i
$924$		0			0
$925$	−10.7804	−	23.6058i	−0.354458	−	0.776155i
$926$		0			0
$927$	0.716678	+	0.460581i	0.0235388	+	0.0151275i
$928$		0			0
$929$	−8.54977	+	59.4650i	−0.280509	+	1.95098i	0.0275660	+	0.999620i	$0.491224\pi$
$929$	−8.54977	+	59.4650i	−0.280509	+	1.95098i	−0.308075	+	0.951362i	$0.599685\pi$
$930$		0			0
$931$	−3.08173	+	21.4339i	−0.101000	+	0.702467i
$932$		0			0
$933$	20.2323	+	13.0025i	0.662377	+	0.425684i
$934$		0			0
$935$	2.98851	+	3.44893i	0.0977348	+	0.112792i
$936$		0			0
$937$	−7.20342			−0.235326			−0.117663	−	0.993054i	$-0.537540\pi$
$937$	−7.20342			−0.235326			−0.117663	+	0.993054i	$0.537540\pi$
$938$		0			0
$939$	15.3093			0.499599
$940$		0			0
$941$	−6.70675	−	7.74001i	−0.218634	−	0.252317i	0.635828	−	0.771831i	$-0.280659\pi$
$941$	−6.70675	−	7.74001i	−0.218634	−	0.252317i	−0.854462	+	0.519514i	$0.826113\pi$
$942$		0			0
$943$	22.6732	+	14.5712i	0.738341	+	0.474503i
$944$		0			0
$945$	0.351065	−	2.44171i	0.0114201	−	0.0794289i
$946$		0			0
$947$	−2.75328	+	19.1495i	−0.0894695	+	0.622274i	0.894914	+	0.446238i	$0.147237\pi$
$947$	−2.75328	+	19.1495i	−0.0894695	+	0.622274i	−0.984384	+	0.176036i	$0.943673\pi$
$948$		0			0
$949$	−6.22407	−	3.99997i	−0.202042	−	0.129844i
$950$		0			0
$951$	−0.394041	−	0.862829i	−0.0127776	−	0.0279791i
$952$		0			0
$953$	−8.18437	−	56.9235i	−0.265118	−	1.84393i	−0.492730	−	0.870182i	$-0.664001\pi$
$953$	−8.18437	−	56.9235i	−0.265118	−	1.84393i	0.227613	−	0.973752i	$-0.426908\pi$
$954$		0			0
$955$	8.45481	−	2.48256i	0.273591	−	0.0803337i
$956$		0			0
$957$	2.86272	+	19.9107i	0.0925387	+	0.643621i
$958$		0			0
$959$	−39.4299	+	25.3401i	−1.27326	+	0.818273i
$960$		0			0
$961$	16.4083	+	18.9362i	0.529300	+	0.610845i
$962$		0			0
$963$	−5.08022	−	11.1241i	−0.163708	−	0.358470i
$964$		0			0
$965$	−1.39885	+	0.898987i	−0.0450306	+	0.0289394i
$966$		0			0
$967$	39.4979			1.27017			0.635083	−	0.772444i	$-0.280966\pi$
$967$	39.4979			1.27017			0.635083	+	0.772444i	$0.280966\pi$
$968$		0			0
$969$	1.49977	−	3.28405i	0.0481797	−	0.105499i
$970$		0			0
$971$	−7.25615	−	50.4677i	−0.232861	−	1.61958i	−0.685626	−	0.727954i	$-0.740471\pi$
$971$	−7.25615	−	50.4677i	−0.232861	−	1.61958i	0.452765	−	0.891630i	$-0.350438\pi$
$972$		0			0
$973$	−40.6873	+	46.9557i	−1.30438	+	1.50533i
$974$		0			0
$975$	3.42140			0.109572
$976$		0			0
$977$	−5.93096	+	12.9870i	−0.189748	+	0.415490i	−0.980466	−	0.196691i	$-0.936980\pi$
$977$	−5.93096	+	12.9870i	−0.189748	+	0.415490i	0.790717	+	0.612181i	$0.209708\pi$
$978$		0			0
$979$	18.8182	−	5.52553i	0.601433	−	0.176597i
$980$		0			0
$981$	13.4025	−	3.93532i	0.427908	−	0.125645i
$982$		0			0
$983$	−34.5564	+	39.8802i	−1.10218	+	1.27198i	−0.142831	+	0.989747i	$0.545621\pi$
$983$	−34.5564	+	39.8802i	−1.10218	+	1.27198i	−0.959346	+	0.282233i	$0.908925\pi$
$984$		0			0
$985$	−2.26932	−	2.61894i	−0.0723067	−	0.0834463i
$986$		0			0
$987$	30.3100	+	8.89981i	0.964777	+	0.283284i
$988$		0			0
$989$	−58.4915	−	37.5902i	−1.85992	−	1.19530i
$990$		0			0
$991$	−21.7744	−	6.39353i	−0.691686	−	0.203097i	−0.0830482	−	0.996546i	$-0.526466\pi$
$991$	−21.7744	−	6.39353i	−0.691686	−	0.203097i	−0.608638	+	0.793448i	$0.708284\pi$
$992$		0			0
$993$	−0.227490	−	0.498133i	−0.00721917	−	0.0158078i
$994$		0			0
$995$	2.36397	−	2.72817i	0.0749429	−	0.0864887i
$996$		0			0
$997$	10.2342	−	22.4099i	0.324122	−	0.709728i	−0.675496	−	0.737364i	$-0.736071\pi$
$997$	10.2342	−	22.4099i	0.324122	−	0.709728i	0.999618	+	0.0276355i	$0.00879778\pi$
$998$		0			0
$999$	−4.69050	+	3.01440i	−0.148401	+	0.0953714i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.q.b.193.3	yes	60
67.25	even	11	inner	804.2.q.b.25.3	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.q.b.25.3	✓	60	67.25	even	11	inner
804.2.q.b.193.3	yes	60	1.1	even	1	trivial

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.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.654861 + 0.755750i) q^{3} +(-0.494572 - 0.317842i) q^{5} +(0.597152 - 4.15328i) q^{7} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})\)	\(q+(0.654861 + 0.755750i) q^{3} +(-0.494572 - 0.317842i) q^{5} +(0.597152 - 4.15328i) q^{7} +(-0.142315 + 0.989821i) q^{9} +(-3.69287 - 2.37326i) q^{11} +(0.305369 + 0.668664i) q^{13} +(-0.0836667 - 0.581915i) q^{15} +(1.69671 - 0.498199i) q^{17} +(-0.290555 - 2.02085i) q^{19} +(3.52989 - 2.26853i) q^{21} +(-4.46336 - 5.15100i) q^{23} +(-1.93350 - 4.23377i) q^{25} +(-0.841254 + 0.540641i) q^{27} -4.58239 q^{29} +(-1.01278 + 2.21768i) q^{31} +(-0.624723 - 4.34504i) q^{33} +(-1.61542 + 1.86430i) q^{35} +5.57561 q^{37} +(-0.305369 + 0.668664i) q^{39} +(-3.79415 + 1.11406i) q^{41} +(9.78801 - 2.87402i) q^{43} +(0.384992 - 0.444304i) q^{45} +(4.93013 + 5.68967i) q^{47} +(-10.1767 - 2.98816i) q^{49} +(1.48762 + 0.956037i) q^{51} +(7.24167 + 2.12635i) q^{53} +(1.07207 + 2.34750i) q^{55} +(1.33699 - 1.54296i) q^{57} +(5.10988 - 11.1891i) q^{59} +(8.08332 - 5.19484i) q^{61} +(4.02603 + 1.18215i) q^{63} +(0.0615028 - 0.427761i) q^{65} +(-1.33908 - 8.07508i) q^{67} +(0.969982 - 6.74637i) q^{69} +(0.981003 + 0.288048i) q^{71} +(-8.46705 + 5.44144i) q^{73} +(1.93350 - 4.23377i) q^{75} +(-12.0620 + 13.9203i) q^{77} +(2.34861 + 5.14274i) q^{79} +(-0.959493 - 0.281733i) q^{81} +(3.95887 + 2.54421i) q^{83} +(-0.997494 - 0.292891i) q^{85} +(-3.00083 - 3.46314i) q^{87} +(-2.92583 + 3.37658i) q^{89} +(2.95950 - 0.868988i) q^{91} +(-2.33924 + 0.686863i) q^{93} +(-0.498612 + 1.09181i) q^{95} +8.38224 q^{97} +(2.87466 - 3.31753i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 6 q^{3} + 2 q^{5} + 2 q^{7} - 6 q^{9}+O(q^{10}) \) 60 * q + 6 * q^3 + 2 * q^5 + 2 * q^7 - 6 * q^9	\( 60 q + 6 q^{3} + 2 q^{5} + 2 q^{7} - 6 q^{9} - 11 q^{11} - 2 q^{13} + 9 q^{15} + 21 q^{17} + 10 q^{19} - 2 q^{21} - 10 q^{23} - 36 q^{25} + 6 q^{27} + 4 q^{29} - 24 q^{31} - 32 q^{35} + 2 q^{37} + 2 q^{39} + 10 q^{41} + 23 q^{43} + 2 q^{45} + 66 q^{47} + 34 q^{49} + 23 q^{51} - 13 q^{53} + 27 q^{55} + q^{57} + 35 q^{59} + 56 q^{61} - 9 q^{63} + 48 q^{65} + 13 q^{67} + 10 q^{69} + 76 q^{71} - q^{73} + 36 q^{75} - 38 q^{77} - 46 q^{79} - 6 q^{81} - 26 q^{83} + 42 q^{85} + 7 q^{87} + 58 q^{89} - 40 q^{91} - 9 q^{93} - 29 q^{95} - 46 q^{97}+O(q^{100}) \) 60 * q + 6 * q^3 + 2 * q^5 + 2 * q^7 - 6 * q^9 - 11 * q^11 - 2 * q^13 + 9 * q^15 + 21 * q^17 + 10 * q^19 - 2 * q^21 - 10 * q^23 - 36 * q^25 + 6 * q^27 + 4 * q^29 - 24 * q^31 - 32 * q^35 + 2 * q^37 + 2 * q^39 + 10 * q^41 + 23 * q^43 + 2 * q^45 + 66 * q^47 + 34 * q^49 + 23 * q^51 - 13 * q^53 + 27 * q^55 + q^57 + 35 * q^59 + 56 * q^61 - 9 * q^63 + 48 * q^65 + 13 * q^67 + 10 * q^69 + 76 * q^71 - q^73 + 36 * q^75 - 38 * q^77 - 46 * q^79 - 6 * q^81 - 26 * q^83 + 42 * q^85 + 7 * q^87 + 58 * q^89 - 40 * q^91 - 9 * q^93 - 29 * q^95 - 46 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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