LMFDB - Embedded newform 804.2.q.b.25.3

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			25.3
Character	$\chi$	$=$	804.25
Dual form			804.2.q.b.193.3

$q$-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 $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$e\left(\frac{5}{11}\right)$	$1$

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	−0.646539	−	0.762881i	$-0.723784\pi$
$5$	−0.494572	+	0.317842i	−0.221179	+	0.142143i	0.425359	+	0.905025i	$0.360148\pi$
$6$		0			0
$7$	0.597152	+	4.15328i	0.225702	+	1.56979i	0.715913	+	0.698190i	$0.246011\pi$
$7$	0.597152	+	4.15328i	0.225702	+	1.56979i	−0.490211	+	0.871604i	$0.663080\pi$
$8$		0			0
$9$	−0.142315	−	0.989821i	−0.0474383	−	0.329940i
$10$		0			0
$11$	−3.69287	+	2.37326i	−1.11344	+	0.715566i	−0.962041	−	0.272906i	$-0.912015\pi$
$11$	−3.69287	+	2.37326i	−1.11344	+	0.715566i	−0.151402	+	0.988472i	$0.548379\pi$
$12$		0			0
$13$	0.305369	−	0.668664i	0.0846940	−	0.185454i	−0.862546	−	0.505978i	$-0.831132\pi$
$13$	0.305369	−	0.668664i	0.0846940	−	0.185454i	0.947240	+	0.320524i	$0.103859\pi$
$14$		0			0
$15$	−0.0836667	+	0.581915i	−0.0216027	+	0.150250i
$16$		0			0
$17$	1.69671	+	0.498199i	0.411513	+	0.120831i	0.480935	−	0.876756i	$-0.340297\pi$
$17$	1.69671	+	0.498199i	0.411513	+	0.120831i	−0.0694221	+	0.997587i	$0.522116\pi$
$18$		0			0
$19$	−0.290555	+	2.02085i	−0.0666578	+	0.463615i	0.928966	+	0.370165i	$0.120699\pi$
$19$	−0.290555	+	2.02085i	−0.0666578	+	0.463615i	−0.995624	+	0.0934506i	$0.970210\pi$
$20$		0			0
$21$	3.52989	+	2.26853i	0.770286	+	0.495033i
$22$		0			0
$23$	−4.46336	+	5.15100i	−0.930676	+	1.07406i	0.0664118	+	0.997792i	$0.478845\pi$
$23$	−4.46336	+	5.15100i	−0.930676	+	1.07406i	−0.997088	+	0.0762648i	$0.975701\pi$
$24$		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	0.796613	−	0.604490i	$-0.206623\pi$
$31$	−1.01278	−	2.21768i	−0.181901	−	0.398307i	−0.978513	+	0.206183i	$0.933896\pi$
$32$		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	−0.0283082	−	0.999599i	$-0.509012\pi$
$41$	−3.79415	−	1.11406i	−0.592547	−	0.173987i	−0.564239	+	0.825612i	$0.690830\pi$
$42$		0			0
$43$	9.78801	+	2.87402i	1.49266	+	0.438284i	0.923388	−	0.383867i	$-0.125408\pi$
$43$	9.78801	+	2.87402i	1.49266	+	0.438284i	0.569269	+	0.822151i	$0.307226\pi$
$44$		0			0
$45$	0.384992	+	0.444304i	0.0573912	+	0.0662330i
$46$		0			0
$47$	4.93013	−	5.68967i	0.719133	−	0.829923i	−0.272070	−	0.962278i	$-0.587708\pi$
$47$	4.93013	−	5.68967i	0.719133	−	0.829923i	0.991203	+	0.132354i	$0.0422536\pi$
$48$		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	0.256432	−	0.966562i	$-0.417453\pi$
$53$	7.24167	−	2.12635i	0.994719	−	0.292076i	0.738287	+	0.674486i	$0.235635\pi$
$54$		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	0.877548	+	0.479488i	$0.159178\pi$
$59$	5.10988	+	11.1891i	0.665250	+	1.45669i	−0.212299	+	0.977205i	$0.568095\pi$
$60$		0			0
$61$	8.08332	+	5.19484i	1.03496	+	0.665131i	0.943736	−	0.330700i	$-0.107285\pi$
$61$	8.08332	+	5.19484i	1.03496	+	0.665131i	0.0912273	+	0.995830i	$0.470921\pi$
$62$		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	−0.223002	−	0.974818i	$-0.571586\pi$
$71$	0.981003	−	0.288048i	0.116424	−	0.0341851i	0.339425	+	0.940633i	$0.389767\pi$
$72$		0			0
$73$	−8.46705	−	5.44144i	−0.990994	−	0.636873i	−0.0585864	−	0.998282i	$-0.518659\pi$
$73$	−8.46705	−	5.44144i	−0.990994	−	0.636873i	−0.932407	+	0.361409i	$0.882296\pi$
$74$		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	−0.730281	−	0.683147i	$-0.760611\pi$
$79$	2.34861	−	5.14274i	0.264240	−	0.578604i	0.994520	+	0.104543i	$0.0333380\pi$
$80$		0			0
$81$	−0.959493	+	0.281733i	−0.106610	+	0.0313036i
$82$		0			0
$83$	3.95887	−	2.54421i	0.434543	−	0.279264i	−0.305027	−	0.952344i	$-0.598665\pi$
$83$	3.95887	−	2.54421i	0.434543	−	0.279264i	0.739570	+	0.673080i	$0.235029\pi$
$84$		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	0.579187	−	0.815195i	$-0.303370\pi$
$89$	−2.92583	−	3.37658i	−0.310137	−	0.357917i	−0.889324	+	0.457277i	$0.848825\pi$
$90$		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	−0.506828	−	0.862047i	$-0.669182\pi$
$101$	2.23446	−	15.5410i	0.222337	−	1.54639i	0.729165	−	0.684338i	$-0.239909\pi$
$102$		0			0
$103$	0.353899	+	0.774930i	0.0348707	+	0.0763561i	0.926266	−	0.376871i	$-0.123000\pi$
$103$	0.353899	+	0.774930i	0.0348707	+	0.0763561i	−0.891395	+	0.453227i	$0.850273\pi$
$104$		0			0
$105$	−2.46682			−0.240737
$106$		0			0
$107$	−10.2879	−	6.61164i	−0.994570	−	0.639171i	−0.0612142	−	0.998125i	$-0.519497\pi$
$107$	−10.2879	−	6.61164i	−0.994570	−	0.639171i	−0.933355	+	0.358954i	$0.883134\pi$
$108$		0			0
$109$	−5.80264	+	12.7060i	−0.555792	+	1.21701i	0.398232	+	0.917285i	$0.369624\pi$
$109$	−5.80264	+	12.7060i	−0.555792	+	1.21701i	−0.954024	+	0.299730i	$0.903104\pi$
$110$		0			0
$111$	3.65124	−	4.21376i	0.346561	−	0.399953i
$112$		0			0
$113$	−12.6785	−	8.14800i	−1.19270	−	0.766500i	−0.215019	−	0.976610i	$-0.568981\pi$
$113$	−12.6785	−	8.14800i	−1.19270	−	0.766500i	−0.977678	+	0.210110i	$0.932618\pi$
$114$		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	0.996334	−	0.0855431i	$-0.0272625\pi$
$127$	0.183221	+	1.27433i	0.0162583	+	0.113079i	−0.980076	+	0.198622i	$0.936353\pi$
$128$		0			0
$129$	8.58182	−	5.51520i	0.755587	−	0.485587i
$130$		0			0
$131$	2.96329	−	3.41982i	0.258904	−	0.298791i	−0.611384	−	0.791334i	$-0.709387\pi$
$131$	2.96329	−	3.41982i	0.258904	−	0.298791i	0.870288	+	0.492543i	$0.163932\pi$
$132$		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	−0.976641	−	0.214877i	$-0.931065\pi$
$137$	−7.31498	+	8.44193i	−0.624961	+	0.721243i	0.351680	+	0.936120i	$0.385610\pi$
$138$		0			0
$139$	−12.4567	+	8.00543i	−1.05656	+	0.679011i	−0.949029	−	0.315190i	$-0.897932\pi$
$139$	−12.4567	+	8.00543i	−1.05656	+	0.679011i	−0.107534	+	0.994201i	$0.534295\pi$
$140$		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	−0.999584	−	0.0288452i	$-0.990817\pi$
$149$	−0.395047	+	2.74762i	−0.0323635	+	0.225093i	0.967220	+	0.253939i	$0.0817261\pi$
$150$		0			0
$151$	3.04434	+	0.893899i	0.247745	+	0.0727445i	0.403247	−	0.915091i	$-0.367881\pi$
$151$	3.04434	+	0.893899i	0.247745	+	0.0727445i	−0.155502	+	0.987836i	$0.549700\pi$
$152$		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	0.442287	−	0.896874i	$-0.354167\pi$
$157$	15.8766	−	18.3225i	1.26709	−	1.46230i	0.824801	−	0.565423i	$-0.191287\pi$
$158$		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	0.787895	+	0.615809i	$0.211171\pi$
$167$	−1.82959	+	12.7251i	−0.141578	+	0.984698i	−0.929473	+	0.368889i	$0.879738\pi$
$168$		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	0.795229	−	0.606310i	$-0.207351\pi$
$173$	−2.41690	−	5.29228i	−0.183754	−	0.402364i	−0.978982	+	0.203945i	$0.934624\pi$
$174$		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	0.998047	+	0.0624734i	$0.0198989\pi$
$179$	12.2800	+	14.1718i	0.917847	+	1.05925i	−0.0801993	+	0.996779i	$0.525556\pi$
$180$		0			0
$181$	14.4598	−	16.6875i	1.07479	−	1.24038i	0.105511	−	0.994418i	$-0.466352\pi$
$181$	14.4598	−	16.6875i	1.07479	−	1.24038i	0.969281	−	0.245957i	$-0.0791023\pi$
$182$		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	0.279876	−	0.960036i	$-0.409707\pi$
$191$	−9.81541	−	11.3276i	−0.710218	−	0.819636i	−0.990095	+	0.140400i	$0.955161\pi$
$192$		0			0
$193$	1.17496	+	2.57281i	0.0845757	+	0.185195i	0.947195	−	0.320660i	$-0.103905\pi$
$193$	1.17496	+	2.57281i	0.0845757	+	0.185195i	−0.862619	+	0.505854i	$0.831177\pi$
$194$		0			0
$195$	0.363556	+	0.233643i	0.0260348	+	0.0167316i
$196$		0			0
$197$	5.65570	−	1.66066i	0.402952	−	0.118317i	−0.0739753	−	0.997260i	$-0.523569\pi$
$197$	5.65570	−	1.66066i	0.402952	−	0.118317i	0.476928	+	0.878943i	$0.341750\pi$
$198$		0			0
$199$	−0.873858	−	6.07781i	−0.0619461	−	0.430845i	−0.997068	−	0.0765189i	$-0.975619\pi$
$199$	−0.873858	−	6.07781i	−0.0619461	−	0.430845i	0.935122	−	0.354326i	$-0.115290\pi$
$200$		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	0.664538	−	0.747254i	$-0.268628\pi$
$211$	−2.46479	−	2.84452i	−0.169683	−	0.195825i	−0.834222	+	0.551429i	$0.814083\pi$
$212$		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	−0.999729	−	0.0232915i	$-0.992585\pi$
$223$	−13.1488	−	15.1745i	−0.880507	−	1.01616i	0.119222	−	0.992868i	$-0.461960\pi$
$224$		0			0
$225$	4.46584	+	1.31129i	0.297723	+	0.0874193i
$226$		0			0
$227$	17.4762	+	5.13147i	1.15993	+	0.340587i	0.804407	−	0.594079i	$-0.202483\pi$
$227$	17.4762	+	5.13147i	1.15993	+	0.340587i	0.355527	+	0.934666i	$0.384301\pi$
$228$		0			0
$229$	−11.4945	−	25.1694i	−0.759577	−	1.66324i	−0.748349	−	0.663305i	$-0.769153\pi$
$229$	−11.4945	−	25.1694i	−0.759577	−	1.66324i	−0.0112286	−	0.999937i	$-0.503574\pi$
$230$		0			0
$231$	−18.4193			−1.21190
$232$		0			0
$233$	3.94989	+	4.55842i	0.258766	+	0.298632i	0.870235	−	0.492636i	$-0.163967\pi$
$233$	3.94989	+	4.55842i	0.258766	+	0.298632i	−0.611469	+	0.791268i	$0.709421\pi$
$234$		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	0.596113	−	0.802901i	$-0.296711\pi$
$241$	1.76048	+	1.13139i	0.113403	+	0.0728794i	−0.482710	+	0.875780i	$0.660348\pi$
$242$		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	0.642395	−	0.766374i	$-0.277941\pi$
$251$	12.1750	+	3.57490i	0.768480	+	0.225646i	0.126084	+	0.992020i	$0.459759\pi$
$252$		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	−0.547007	−	0.837128i	$-0.684233\pi$
$257$	−0.204620	+	0.131501i	−0.0127638	+	0.00820282i	0.534243	+	0.845331i	$0.320597\pi$
$258$		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	−0.889789	−	0.456372i	$-0.849148\pi$
$263$	−13.6921	+	8.79936i	−0.844290	+	0.542592i	0.0454993	+	0.998964i	$0.485512\pi$
$264$		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	−0.796192	−	0.605044i	$-0.793156\pi$
$271$	−1.38277	+	1.59580i	−0.0839971	+	0.0969378i	0.712195	+	0.701982i	$0.247701\pi$
$272$		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	0.935697	+	0.352804i	$0.114772\pi$
$277$	2.28511	+	15.8933i	0.137299	+	0.954934i	−0.798398	+	0.602129i	$0.794319\pi$
$278$		0			0
$279$	−2.05097	+	1.31808i	−0.122789	+	0.0789114i
$280$		0			0
$281$	−0.171736	+	0.376050i	−0.0102449	+	0.0224333i	−0.914685	−	0.404167i	$-0.867562\pi$
$281$	−0.171736	+	0.376050i	−0.0102449	+	0.0224333i	0.904440	+	0.426600i	$0.140289\pi$
$282$		0			0
$283$	−3.10270	+	21.5798i	−0.184436	+	1.28278i	0.661681	+	0.749786i	$0.269843\pi$
$283$	−3.10270	+	21.5798i	−0.184436	+	1.28278i	−0.846117	+	0.532997i	$0.821066\pi$
$284$		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	−0.901147	−	0.433514i	$-0.857273\pi$
$293$	0.284265	−	0.622453i	0.0166069	−	0.0363641i	0.917754	+	0.397150i	$0.130001\pi$
$294$		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	0.999273	+	0.0381338i	$0.0121413\pi$
$307$	6.54789	+	14.3379i	0.373708	+	0.818306i	−0.625565	+	0.780172i	$0.715131\pi$
$308$		0			0
$309$	0.817408	+	0.240013i	0.0465007	+	0.0136538i
$310$		0			0
$311$	23.0760	+	6.77573i	1.30852	+	0.384216i	0.860337	−	0.509725i	$-0.170253\pi$
$311$	23.0760	+	6.77573i	1.30852	+	0.384216i	0.448183	+	0.893942i	$0.352071\pi$
$312$		0			0
$313$	10.0254	+	11.5700i	0.566671	+	0.653974i	0.964685	−	0.263406i	$-0.0848458\pi$
$313$	10.0254	+	11.5700i	0.566671	+	0.653974i	−0.398014	+	0.917379i	$0.630300\pi$
$314$		0			0
$315$	−1.61542	+	1.86430i	−0.0910188	+	0.105041i
$316$		0			0
$317$	−0.910124	+	0.267237i	−0.0511177	+	0.0150095i	−0.307191	−	0.951648i	$-0.599389\pi$
$317$	−0.910124	+	0.267237i	−0.0511177	+	0.0150095i	0.256074	+	0.966657i	$0.417571\pi$
$318$		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	−0.296141	−	0.955144i	$-0.595700\pi$
$331$	−0.525438	+	0.154283i	−0.0288807	+	0.00848013i	0.267260	+	0.963624i	$0.413882\pi$
$332$		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	0.948133	+	0.317875i	$0.102969\pi$
$337$	2.34907	+	16.3381i	0.127962	+	0.889994i	−0.820171	+	0.572119i	$0.806122\pi$
$338$		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	−0.141021	−	0.990007i	$-0.545038\pi$
$347$	13.0307	−	28.5333i	0.699525	−	1.53175i	0.840546	−	0.541740i	$-0.182234\pi$
$348$		0			0
$349$	−7.02621	+	2.06308i	−0.376104	+	0.110434i	−0.464321	−	0.885667i	$-0.653701\pi$
$349$	−7.02621	+	2.06308i	−0.376104	+	0.110434i	0.0882164	+	0.996101i	$0.471883\pi$
$350$		0			0
$351$	−0.618399	+	0.397421i	−0.0330077	+	0.0212128i
$352$		0			0
$353$	6.78260	−	1.99155i	0.361001	−	0.106000i	−0.0962018	−	0.995362i	$-0.530669\pi$
$353$	6.78260	−	1.99155i	0.361001	−	0.106000i	0.457203	+	0.889362i	$0.348851\pi$
$354$		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	0.922839	−	0.385186i	$-0.125863\pi$
$359$	28.2491	+	8.29470i	1.49093	+	0.437777i	0.568094	+	0.822964i	$0.307681\pi$
$360$		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	0.531355	−	0.847150i	$-0.321683\pi$
$367$	−7.33324	−	8.46301i	−0.382792	−	0.441765i	−0.914146	+	0.405384i	$0.867138\pi$
$368$		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	−0.573616	−	0.819124i	$-0.694460\pi$
$379$	6.20647	−	7.16265i	0.318805	−	0.367921i	0.892421	+	0.451204i	$0.149005\pi$
$380$		0			0
$381$	1.08306	+	0.696040i	0.0554869	+	0.0356592i
$382$		0			0
$383$	−4.70141	+	32.6990i	−0.240231	+	1.67084i	0.410752	+	0.911747i	$0.365266\pi$
$383$	−4.70141	+	32.6990i	−0.240231	+	1.67084i	−0.650982	+	0.759093i	$0.725643\pi$
$384$		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	−0.946856	−	0.321657i	$-0.895760\pi$
$389$	−1.65092	+	3.61500i	−0.0837047	+	0.183288i	0.863151	+	0.504945i	$0.168487\pi$
$390$		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	−0.570095	−	0.821579i	$-0.693094\pi$
$397$	−1.18727	+	0.763009i	−0.0595872	+	0.0382943i	0.510508	+	0.859873i	$0.329457\pi$
$398$		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	0.991023	−	0.133690i	$-0.0426827\pi$
$409$	0.0501255	+	0.348631i	0.00247855	+	0.0172387i	−0.988545	+	0.150929i	$0.951774\pi$
$410$		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	0.722939	−	0.690912i	$-0.242791\pi$
$419$	19.6011	+	5.75542i	0.957579	+	0.281170i	0.234640	+	0.972082i	$0.424609\pi$
$420$		0			0
$421$	0.554770	−	3.85851i	0.0270378	−	0.188052i	−0.971826	−	0.235697i	$-0.924263\pi$
$421$	0.554770	−	3.85851i	0.0270378	−	0.188052i	0.998864	+	0.0476452i	$0.0151717\pi$
$422$		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	−0.998861	−	0.0477139i	$-0.984806\pi$
$433$	−7.92406	−	17.3513i	−0.380806	−	0.833849i	0.618055	−	0.786135i	$-0.287921\pi$
$434$		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	−0.0725515	−	0.997365i	$-0.523114\pi$
$443$	−14.1608	−	4.15800i	−0.672802	−	0.197552i	−0.600250	+	0.799812i	$0.704932\pi$
$444$		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	−0.601318	−	0.799010i	$-0.705357\pi$
$449$	5.83003	−	6.72822i	0.275136	−	0.317524i	0.876454	+	0.481486i	$0.159903\pi$
$450$		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	−0.529702	−	0.848184i	$-0.677696\pi$
$457$	9.79507	−	21.4482i	0.458194	−	1.00330i	0.987896	−	0.155121i	$-0.0495767\pi$
$458$		0			0
$459$	−1.15802	−	1.33642i	−0.0540516	−	0.0623789i
$460$		0			0
$461$	14.3405	+	31.4014i	0.667905	+	1.46251i	0.874968	+	0.484180i	$0.160882\pi$
$461$	14.3405	+	31.4014i	0.667905	+	1.46251i	−0.207063	+	0.978328i	$0.566391\pi$
$462$		0			0
$463$	−8.47795	−	5.44845i	−0.394004	−	0.253211i	0.328606	−	0.944467i	$-0.393421\pi$
$463$	−8.47795	−	5.44845i	−0.394004	−	0.253211i	−0.722610	+	0.691256i	$0.757058\pi$
$464$		0			0
$465$	1.37524	−	0.403806i	0.0637751	−	0.0187260i
$466$		0			0
$467$	2.92132	+	20.3182i	0.135183	+	0.940216i	0.938651	+	0.344869i	$0.112076\pi$
$467$	2.92132	+	20.3182i	0.135183	+	0.940216i	−0.803468	+	0.595347i	$0.797014\pi$
$468$		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	0.885257	−	0.465103i	$-0.153983\pi$
$479$	6.54181	+	7.54966i	0.298903	+	0.344953i	−0.586354	+	0.810055i	$0.699437\pi$
$480$		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	−0.489460	−	0.872026i	$-0.662806\pi$
$487$	−9.48412	+	2.78479i	−0.429767	+	0.126191i	0.0596931	+	0.998217i	$0.480988\pi$
$488$		0			0
$489$	13.2592	−	15.3019i	0.599600	−	0.691975i
$490$		0			0
$491$	24.2434	+	27.9784i	1.09409	+	1.26265i	0.962482	+	0.271347i	$0.0874692\pi$
$491$	24.2434	+	27.9784i	1.09409	+	1.26265i	0.131610	+	0.991302i	$0.457985\pi$
$492$		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	−0.958479	−	0.285162i	$-0.907953\pi$
$503$	0.931065	−	6.47570i	0.0415142	−	0.288737i	0.999994	−	0.00357569i	$-0.00113818\pi$
$504$		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	0.999995	−	0.00327348i	$-0.00104198\pi$
$509$	31.8659	+	20.4789i	1.41243	+	0.907713i	0.412435	+	0.910987i	$0.364678\pi$
$510$		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	0.586378	+	0.810038i	$0.300554\pi$
$521$	−4.66692	+	32.4592i	−0.204462	+	1.42206i	−0.790839	+	0.612024i	$0.790356\pi$
$522$		0			0
$523$	17.8650	−	39.1189i	0.781181	−	1.71055i	0.0808539	−	0.996726i	$-0.474235\pi$
$523$	17.8650	−	39.1189i	0.781181	−	1.71055i	0.700327	−	0.713822i	$-0.253037\pi$
$524$		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	−0.373195	−	0.927753i	$-0.621738\pi$
$541$	7.34270	−	4.71887i	0.315687	−	0.202880i	0.688883	+	0.724873i	$0.258102\pi$
$542$		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	−0.956328	−	0.292295i	$-0.905581\pi$
$547$	−25.4396	+	16.3491i	−1.08772	+	0.699036i	−0.131393	+	0.991330i	$0.541945\pi$
$548$		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	0.996013	−	0.0892137i	$-0.0284354\pi$
$557$	31.3565	+	20.1516i	1.32862	+	0.853852i	0.332607	+	0.943066i	$0.392072\pi$
$558$		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	0.334798	−	0.942290i	$-0.391332\pi$
$563$	−9.09383	−	5.84425i	−0.383259	−	0.246306i	−0.718057	+	0.695984i	$0.754968\pi$
$564$		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	−0.537239	−	0.843430i	$-0.680533\pi$
$569$	5.14906	−	35.8125i	0.215860	−	1.50134i	0.753099	−	0.657907i	$-0.228558\pi$
$570$		0			0
$571$	3.30313	+	3.81202i	0.138232	+	0.159528i	0.820644	−	0.571439i	$-0.193615\pi$
$571$	3.30313	+	3.81202i	0.138232	+	0.159528i	−0.682413	+	0.730967i	$0.739069\pi$
$572$		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	0.976239	−	0.216697i	$-0.0695282\pi$
$577$	40.3634	+	11.8518i	1.68035	+	0.493395i	0.704110	+	0.710091i	$0.251346\pi$
$578$		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	−0.966055	−	0.258336i	$-0.916826\pi$
$587$	−27.4354	+	17.6316i	−1.13238	+	0.727735i	−0.166323	+	0.986071i	$0.553190\pi$
$588$		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	0.900901	−	0.434024i	$-0.142907\pi$
$593$	8.35464	+	9.64177i	0.343084	+	0.395940i	−0.557818	+	0.829964i	$0.688361\pi$
$594$		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	−0.0757449	−	0.997127i	$-0.524133\pi$
$599$	9.78054	−	2.87183i	0.399622	−	0.117340i	0.475367	+	0.879788i	$0.342315\pi$
$600$		0			0
$601$	0.785168	+	5.46097i	0.0320277	+	0.222757i	0.999549	−	0.0300323i	$-0.00956101\pi$
$601$	0.785168	+	5.46097i	0.0320277	+	0.222757i	−0.967521	+	0.252790i	$0.918652\pi$
$602$		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	−0.170994	−	0.985272i	$-0.554698\pi$
$607$	5.36688	−	1.57586i	0.217835	−	0.0639621i	0.388829	+	0.921310i	$0.372880\pi$
$608$		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	0.866076	−	0.499912i	$-0.166634\pi$
$613$	6.14011	+	7.08607i	0.247997	+	0.286204i	−0.618079	+	0.786116i	$0.712089\pi$
$614$		0			0
$615$	0.965734	−	2.11466i	0.0389422	−	0.0852714i
$616$		0			0
$617$	38.0311	−	11.1669i	1.53108	−	0.449564i	0.595696	−	0.803210i	$-0.296876\pi$
$617$	38.0311	−	11.1669i	1.53108	−	0.449564i	0.935380	+	0.353645i	$0.115058\pi$
$618$		0			0
$619$	9.63379	−	6.19126i	0.387215	−	0.248848i	−0.332521	−	0.943096i	$-0.607899\pi$
$619$	9.63379	−	6.19126i	0.387215	−	0.248848i	0.719736	+	0.694248i	$0.244263\pi$
$620$		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	−0.668500	−	0.743712i	$-0.733063\pi$
$631$	−19.9145	−	43.6068i	−0.792786	−	1.73596i	−0.124286	−	0.992246i	$-0.539664\pi$
$632$		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	0.406153	−	0.913805i	$-0.366870\pi$
$643$	−6.50043	−	4.17757i	−0.256352	−	0.164747i	−0.662505	+	0.749058i	$0.730506\pi$
$644$		0			0
$645$	−2.49137	+	5.45533i	−0.0980974	+	0.214803i
$646$		0			0
$647$	2.28881	−	2.64143i	0.0899825	−	0.103845i	−0.708973	−	0.705236i	$-0.750841\pi$
$647$	2.28881	−	2.64143i	0.0899825	−	0.103845i	0.798955	+	0.601391i	$0.205386\pi$
$648$		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	0.388377	−	0.921501i	$-0.373036\pi$
$653$	5.54261	+	1.62746i	0.216899	+	0.0636873i	−0.171478	+	0.985188i	$0.554854\pi$
$654$		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	−0.849026	−	0.528351i	$-0.822811\pi$
$659$	−18.5119	+	11.8969i	−0.721120	+	0.463436i	0.127906	+	0.991786i	$0.459174\pi$
$660$		0			0
$661$	5.35099	+	37.2169i	0.208129	+	1.44757i	0.779254	+	0.626708i	$0.215598\pi$
$661$	5.35099	+	37.2169i	0.208129	+	1.44757i	−0.571125	+	0.820863i	$0.693493\pi$
$662$		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	−0.991512	−	0.130017i	$-0.958497\pi$
$673$	−18.7228	+	21.6073i	−0.721712	+	0.832900i	0.269800	+	0.962916i	$0.413042\pi$
$674$		0			0
$675$	3.91551	−	2.51635i	0.150708	−	0.0968542i
$676$		0			0
$677$	−1.50688	−	10.4806i	−0.0579141	−	0.402801i	−0.998072	−	0.0620629i	$-0.980232\pi$
$677$	−1.50688	−	10.4806i	−0.0579141	−	0.402801i	0.940158	−	0.340738i	$-0.110677\pi$
$678$		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	0.372519	+	0.928025i	$0.378494\pi$
$683$	−14.9693	+	32.7781i	−0.572783	+	1.25422i	−0.945302	+	0.326196i	$0.894233\pi$
$684$		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	0.0821437	−	0.996620i	$-0.473823\pi$
$691$	−20.7743	−	13.3508i	−0.790291	−	0.507889i	−0.872434	+	0.488732i	$0.837460\pi$
$692$		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	0.783152	−	0.621830i	$-0.213611\pi$
$701$	−5.28605	−	11.5748i	−0.199651	−	0.437175i	−0.982803	+	0.184655i	$0.940883\pi$
$702$		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	0.969772	−	0.244013i	$-0.0784639\pi$
$709$	4.00188	+	8.76290i	0.150294	+	0.329098i	−0.819478	+	0.573110i	$0.805737\pi$
$710$		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	−0.486585	−	0.873633i	$-0.661758\pi$
$719$	−11.3586	+	3.33519i	−0.423605	+	0.124382i	0.0629802	+	0.998015i	$0.479939\pi$
$720$		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	−0.966009	−	0.258509i	$-0.916769\pi$
$727$	−29.2389	−	33.7434i	−1.08441	−	1.25148i	−0.118401	−	0.992966i	$-0.537777\pi$
$728$		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	−0.152969	−	0.988231i	$-0.548884\pi$
$733$	6.83950	−	2.00826i	0.252623	−	0.0741768i	0.405592	+	0.914054i	$0.367065\pi$
$734$		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	−0.591872	−	0.806032i	$-0.701611\pi$
$739$	−6.82496	−	47.4687i	−0.251060	−	1.74616i	0.340812	−	0.940131i	$-0.389298\pi$
$740$		0			0
$741$	1.44000	−	0.422821i	0.0528996	−	0.0155327i
$742$		0			0
$743$	−36.8061	−	23.6539i	−1.35029	−	0.867776i	−0.352600	−	0.935774i	$-0.614703\pi$
$743$	−36.8061	−	23.6539i	−1.35029	−	0.867776i	−0.997685	+	0.0679979i	$0.978339\pi$
$744$		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	−0.0432267	−	0.999065i	$-0.513764\pi$
$751$	12.6209	−	3.70584i	0.460544	−	0.135228i	0.503771	+	0.863837i	$0.331946\pi$
$752$		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	−0.712141	−	0.702037i	$-0.752274\pi$
$757$	2.31387	−	2.67034i	0.0840989	−	0.0970553i	0.796239	+	0.604982i	$0.206820\pi$
$758$		0			0
$759$	−19.5929	−	22.6115i	−0.711179	−	0.820744i
$760$		0			0
$761$	−2.33044	−	0.684279i	−0.0844784	−	0.0248051i	0.239220	−	0.970965i	$-0.423108\pi$
$761$	−2.33044	−	0.684279i	−0.0844784	−	0.0248051i	−0.323699	+	0.946160i	$0.604926\pi$
$762$		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	0.986103	+	0.166138i	$0.0531296\pi$
$769$	28.0140	+	32.3299i	1.01021	+	1.16585i	0.0241097	+	0.999709i	$0.492325\pi$
$770$		0			0
$771$	−0.0346155	+	0.240756i	−0.00124665	+	0.00867063i
$772$		0			0
$773$	−3.73649	−	8.18178i	−0.134392	−	0.294278i	0.830457	−	0.557083i	$-0.188080\pi$
$773$	−3.73649	−	8.18178i	−0.134392	−	0.294278i	−0.964849	+	0.262805i	$0.915352\pi$
$774$		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	0.0393883	−	0.999224i	$-0.487459\pi$
$787$	−13.1206	−	3.85254i	−0.467698	−	0.137328i	−0.507086	+	0.861896i	$0.669277\pi$
$788$		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	−0.795973	−	0.605332i	$-0.793040\pi$
$797$	−5.72484	−	39.8171i	−0.202784	−	1.41040i	0.593189	−	0.805063i	$-0.297869\pi$
$798$		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	−0.463991	−	0.885840i	$-0.653583\pi$
$809$	4.23939	−	2.72449i	0.149049	−	0.0957880i	0.613040	+	0.790052i	$0.289947\pi$
$810$		0			0
$811$	−0.0642199	−	0.446659i	−0.00225506	−	0.0156843i	0.988663	−	0.150153i	$-0.0479765\pi$
$811$	−0.0642199	−	0.446659i	−0.00225506	−	0.0156843i	−0.990918	+	0.134468i	$0.957067\pi$
$812$		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	0.784475	−	0.620160i	$-0.212932\pi$
$821$	31.7801	+	9.33149i	1.10913	+	0.325671i	0.324659	+	0.945831i	$0.394751\pi$
$822$		0			0
$823$	−3.76838	+	26.2097i	−0.131358	+	0.913612i	0.812430	+	0.583059i	$0.198144\pi$
$823$	−3.76838	+	26.2097i	−0.131358	+	0.913612i	−0.943787	+	0.330553i	$0.892765\pi$
$824$		0			0
$825$	−17.1880	−	11.0461i	−0.598410	−	0.384575i
$826$		0			0
$827$	−24.6863	+	28.4895i	−0.858425	+	0.990675i	0.141575	+	0.989928i	$0.454783\pi$
$827$	−24.6863	+	28.4895i	−0.858425	+	0.990675i	−1.00000		0.000747747i	$0.999762\pi$
$828$		0			0
$829$	8.29080	−	18.1543i	0.287951	−	0.630525i	−0.709277	−	0.704930i	$-0.750978\pi$
$829$	8.29080	−	18.1543i	0.287951	−	0.630525i	0.997228	+	0.0744046i	$0.0237056\pi$
$830$		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	0.926971	+	0.375134i	$0.122403\pi$
$839$	33.7843	+	38.9892i	1.16636	+	1.34606i	0.239394	+	0.970922i	$0.423051\pi$
$840$		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	0.298353	−	0.954456i	$-0.403563\pi$
$853$	31.1151	−	9.13622i	1.06536	−	0.312818i	0.767008	+	0.641638i	$0.221745\pi$
$854$		0			0
$855$	−1.00973	+	0.648917i	−0.0345322	+	0.0221925i
$856$		0			0
$857$	−24.7558	+	7.26897i	−0.845643	+	0.248303i	−0.675724	−	0.737155i	$-0.736169\pi$
$857$	−24.7558	+	7.26897i	−0.845643	+	0.248303i	−0.169919	+	0.985458i	$0.554351\pi$
$858$		0			0
$859$	−6.80871	+	14.9090i	−0.232310	+	0.508689i	−0.989505	−	0.144501i	$-0.953842\pi$
$859$	−6.80871	+	14.9090i	−0.232310	+	0.508689i	0.757194	+	0.653190i	$0.226570\pi$
$860$		0			0
$861$	−10.8657	−	12.5397i	−0.370301	−	0.427350i
$862$		0			0
$863$	−24.0333	−	52.6256i	−0.818103	−	1.79140i	−0.567657	−	0.823265i	$-0.692150\pi$
$863$	−24.0333	−	52.6256i	−0.818103	−	1.79140i	−0.250445	−	0.968131i	$-0.580577\pi$
$864$		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	0.355133	−	0.934816i	$-0.384436\pi$
$877$	−10.2962	−	6.61698i	−0.347679	−	0.223439i	−0.702811	+	0.711377i	$0.748072\pi$
$878$		0			0
$879$	−0.284265	−	0.622453i	−0.00958801	−	0.0209948i
$880$		0			0
$881$	−24.8359	−	28.6621i	−0.836742	−	0.965652i	0.163038	−	0.986620i	$-0.447871\pi$
$881$	−24.8359	−	28.6621i	−0.836742	−	0.965652i	−0.999780	+	0.0209676i	$0.993325\pi$
$882$		0			0
$883$	−0.763635	+	1.67213i	−0.0256984	+	0.0562716i	−0.922046	−	0.387080i	$-0.873484\pi$
$883$	−0.763635	+	1.67213i	−0.0256984	+	0.0562716i	0.896348	+	0.443352i	$0.146211\pi$
$884$		0			0
$885$	−6.93862	+	2.03736i	−0.233239	+	0.0684851i
$886$		0			0
$887$	−19.8305	+	12.7443i	−0.665843	+	0.427911i	−0.829425	−	0.558618i	$-0.811332\pi$
$887$	−19.8305	+	12.7443i	−0.665843	+	0.427911i	0.163582	+	0.986530i	$0.447695\pi$
$888$		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	−0.745530	−	0.666473i	$-0.767803\pi$
$907$	−22.9185	−	50.1846i	−0.760998	−	1.66635i	−0.0154683	−	0.999880i	$-0.504924\pi$
$908$		0			0
$909$	−15.7008			−0.520762
$910$		0			0
$911$	24.8880	+	15.9946i	0.824577	+	0.529923i	0.883550	−	0.468336i	$-0.155146\pi$
$911$	24.8880	+	15.9946i	0.824577	+	0.529923i	−0.0589736	+	0.998260i	$0.518783\pi$
$912$		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	−0.747233	−	0.664562i	$-0.768618\pi$
$919$	4.75826	−	33.0944i	0.156961	−	1.09168i	0.904194	−	0.427123i	$-0.140473\pi$
$920$		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	−0.308075	−	0.951362i	$-0.599685\pi$
$929$	−8.54977	−	59.4650i	−0.280509	−	1.95098i	0.0275660	−	0.999620i	$-0.491224\pi$
$930$		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	−0.854462	−	0.519514i	$-0.826113\pi$
$941$	−6.70675	+	7.74001i	−0.218634	+	0.252317i	0.635828	+	0.771831i	$0.280659\pi$
$942$		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	−0.984384	−	0.176036i	$-0.943673\pi$
$947$	−2.75328	−	19.1495i	−0.0894695	−	0.622274i	0.894914	−	0.446238i	$-0.147237\pi$
$948$		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	0.227613	+	0.973752i	$0.426908\pi$
$953$	−8.18437	+	56.9235i	−0.265118	+	1.84393i	−0.492730	+	0.870182i	$0.664001\pi$
$954$		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	0.452765	+	0.891630i	$0.350438\pi$
$971$	−7.25615	+	50.4677i	−0.232861	+	1.61958i	−0.685626	+	0.727954i	$0.740471\pi$
$972$		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	0.790717	−	0.612181i	$-0.209708\pi$
$977$	−5.93096	−	12.9870i	−0.189748	−	0.415490i	−0.980466	+	0.196691i	$0.936980\pi$
$978$		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	−0.959346	−	0.282233i	$-0.908925\pi$
$983$	−34.5564	−	39.8802i	−1.10218	−	1.27198i	−0.142831	−	0.989747i	$-0.545621\pi$
$984$		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	−0.608638	−	0.793448i	$-0.708284\pi$
$991$	−21.7744	+	6.39353i	−0.691686	+	0.203097i	−0.0830482	+	0.996546i	$0.526466\pi$
$992$		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	0.999618	−	0.0276355i	$-0.00879778\pi$
$997$	10.2342	+	22.4099i	0.324122	+	0.709728i	−0.675496	+	0.737364i	$0.736071\pi$
$998$		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.25.3	✓	60
67.59	even	11	inner	804.2.q.b.193.3	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.q.b.25.3	✓	60	1.1	even	1	trivial
804.2.q.b.193.3	yes	60	67.59	even	11	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.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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