LMFDB - Embedded newform 804.2.s.b.161.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("804.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$200$
Relative dimension:	$20$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			161.13
Character	$\chi$	$=$	804.161
Dual form			804.2.s.b.5.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.429842 + 1.67787i) q^{3} +(-3.03558 - 0.891328i) q^{5} +(-1.25477 + 1.08727i) q^{7} +(-2.63047 + 1.44244i) q^{9} +O(q^{10})$	\(q+(0.429842 + 1.67787i) q^{3} +(-3.03558 - 0.891328i) q^{5} +(-1.25477 + 1.08727i) q^{7} +(-2.63047 + 1.44244i) q^{9} +(1.88696 + 0.554063i) q^{11} +(-0.265744 + 0.413506i) q^{13} +(0.190706 - 5.47644i) q^{15} +(-2.11532 + 0.304138i) q^{17} +(4.38841 - 5.06450i) q^{19} +(-2.36364 - 1.63799i) q^{21} +(-5.82102 - 2.65837i) q^{23} +(4.21404 + 2.70820i) q^{25} +(-3.55090 - 3.79356i) q^{27} -9.06475i q^{29} +(-3.35609 - 5.22218i) q^{31} +(-0.118546 + 3.40423i) q^{33} +(4.77808 - 2.18207i) q^{35} -7.61322 q^{37} +(-0.808036 - 0.268141i) q^{39} +(-0.191141 - 1.32941i) q^{41} +(-3.41972 + 0.491681i) q^{43} +(9.27070 - 2.03402i) q^{45} +(-4.53234 - 2.06985i) q^{47} +(-0.603899 + 4.20021i) q^{49} +(-1.41956 - 3.41850i) q^{51} +(-0.353730 + 2.46024i) q^{53} +(-5.23419 - 3.36381i) q^{55} +(10.3839 + 5.18623i) q^{57} +(1.69949 + 2.64446i) q^{59} +(2.44051 + 8.31163i) q^{61} +(1.73233 - 4.66995i) q^{63} +(1.17526 - 1.01837i) q^{65} +(-8.02999 - 1.58723i) q^{67} +(1.95827 - 10.9096i) q^{69} +(15.3838 + 2.21185i) q^{71} +(5.08429 - 1.49288i) q^{73} +(-2.73262 + 8.23470i) q^{75} +(-2.97012 + 1.35641i) q^{77} +(-1.14758 + 1.78567i) q^{79} +(4.83876 - 7.58857i) q^{81} +(-2.84309 + 9.68269i) q^{83} +(6.69233 + 0.962212i) q^{85} +(15.2094 - 3.89641i) q^{87} +(4.82981 - 2.20570i) q^{89} +(-0.116143 - 0.807790i) q^{91} +(7.31953 - 7.87579i) q^{93} +(-17.8355 + 11.4622i) q^{95} -13.2013i q^{97} +(-5.76280 + 1.26438i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 200 q - 10 q^{9}+O(q^{10}) $ 200 * q - 10 * q^9	$ 200 q - 10 q^{9} + 2 q^{15} + 6 q^{19} - 10 q^{21} - 20 q^{25} - 44 q^{31} - 5 q^{33} + 78 q^{39} - 22 q^{43} - 22 q^{45} - 16 q^{49} + 36 q^{55} + 66 q^{57} + 176 q^{61} + 132 q^{63} + 46 q^{67} - 26 q^{73} - 165 q^{75} - 44 q^{79} + 42 q^{81} - 66 q^{87} - 20 q^{91} + 84 q^{93} - 55 q^{99}+O(q^{100}) $ 200 * q - 10 * q^9 + 2 * q^15 + 6 * q^19 - 10 * q^21 - 20 * q^25 - 44 * q^31 - 5 * q^33 + 78 * q^39 - 22 * q^43 - 22 * q^45 - 16 * q^49 + 36 * q^55 + 66 * q^57 + 176 * q^61 + 132 * q^63 + 46 * q^67 - 26 * q^73 - 165 * q^75 - 44 * q^79 + 42 * q^81 - 66 * q^87 - 20 * q^91 + 84 * q^93 - 55 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$269$	$337$	$403$
$\chi(n)$	$-1$	$e\left(\frac{17}{22}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.429842	+	1.67787i	0.248170	+	0.968717i
$3$	0.429842	+	1.67787i	0.248170	+	0.968717i
$4$		0			0
$5$	−3.03558	−	0.891328i	−1.35755	−	0.398614i	−0.479655	−	0.877457i	$-0.659238\pi$
$5$	−3.03558	−	0.891328i	−1.35755	−	0.398614i	−0.877900	+	0.478843i	$0.841056\pi$
$6$		0			0
$7$	−1.25477	+	1.08727i	−0.474259	+	0.410948i	−0.858920	−	0.512110i	$-0.828864\pi$
$7$	−1.25477	+	1.08727i	−0.474259	+	0.410948i	0.384661	+	0.923058i	$0.374318\pi$
$8$		0			0
$9$	−2.63047	+	1.44244i	−0.876824	+	0.480812i
$10$		0			0
$11$	1.88696	+	0.554063i	0.568941	+	0.167056i	0.553536	−	0.832825i	$-0.313278\pi$
$11$	1.88696	+	0.554063i	0.568941	+	0.167056i	0.0154049	+	0.999881i	$0.495096\pi$
$12$		0			0
$13$	−0.265744	+	0.413506i	−0.0737042	+	0.114686i	−0.876149	−	0.482040i	$-0.839896\pi$
$13$	−0.265744	+	0.413506i	−0.0737042	+	0.114686i	0.802445	+	0.596726i	$0.203532\pi$
$14$		0			0
$15$	0.190706	−	5.47644i	0.0492402	−	1.41401i
$16$		0			0
$17$	−2.11532	+	0.304138i	−0.513042	+	0.0737642i	−0.393973	−	0.919122i	$-0.628900\pi$
$17$	−2.11532	+	0.304138i	−0.513042	+	0.0737642i	−0.119068	+	0.992886i	$0.537991\pi$
$18$		0			0
$19$	4.38841	−	5.06450i	1.00677	−	1.16188i	0.0199928	−	0.999800i	$-0.493636\pi$
$19$	4.38841	−	5.06450i	1.00677	−	1.16188i	0.986778	−	0.162076i	$-0.0518189\pi$
$20$		0			0
$21$	−2.36364	−	1.63799i	−0.515789	−	0.357438i
$22$		0			0
$23$	−5.82102	−	2.65837i	−1.21377	−	0.554309i	−0.297440	−	0.954740i	$-0.596133\pi$
$23$	−5.82102	−	2.65837i	−1.21377	−	0.554309i	−0.916327	+	0.400432i	$0.868860\pi$
$24$		0			0
$25$	4.21404	+	2.70820i	0.842809	+	0.541640i
$26$		0			0
$27$	−3.55090	−	3.79356i	−0.683372	−	0.730071i
$28$		0			0
$29$		−	9.06475i		−	1.68328i	−0.540038	−	0.841641i	$-0.681590\pi$
$29$		−	9.06475i		−	1.68328i	0.540038	−	0.841641i	$-0.318410\pi$
$30$		0			0
$31$	−3.35609	−	5.22218i	−0.602772	−	0.937931i	−0.999797	−	0.0201238i	$-0.993594\pi$
$31$	−3.35609	−	5.22218i	−0.602772	−	0.937931i	0.397026	−	0.917808i	$-0.370042\pi$
$32$		0			0
$33$	−0.118546	+	3.40423i	−0.0206362	+	0.592601i
$34$		0			0
$35$	4.77808	−	2.18207i	0.807642	−	0.368838i
$36$		0			0
$37$	−7.61322			−1.25161			−0.625803	−	0.779981i	$-0.715228\pi$
$37$	−7.61322			−1.25161			−0.625803	+	0.779981i	$0.715228\pi$
$38$		0			0
$39$	−0.808036	−	0.268141i	−0.129389	−	0.0429369i
$40$		0			0
$41$	−0.191141	−	1.32941i	−0.0298512	−	0.207619i	0.969437	−	0.245340i	$-0.0788995\pi$
$41$	−0.191141	−	1.32941i	−0.0298512	−	0.207619i	−0.999288	+	0.0377203i	$0.987990\pi$
$42$		0			0
$43$	−3.41972	+	0.491681i	−0.521502	+	0.0749807i	−0.398039	−	0.917369i	$-0.630309\pi$
$43$	−3.41972	+	0.491681i	−0.521502	+	0.0749807i	−0.123463	+	0.992349i	$0.539400\pi$
$44$		0			0
$45$	9.27070	−	2.03402i	1.38199	−	0.303215i
$46$		0			0
$47$	−4.53234	−	2.06985i	−0.661110	−	0.301919i	0.0564606	−	0.998405i	$-0.482018\pi$
$47$	−4.53234	−	2.06985i	−0.661110	−	0.301919i	−0.717570	+	0.696486i	$0.754746\pi$
$48$		0			0
$49$	−0.603899	+	4.20021i	−0.0862713	+	0.600030i
$50$		0			0
$51$	−1.41956	−	3.41850i	−0.198778	−	0.478686i
$52$		0			0
$53$	−0.353730	+	2.46024i	−0.0485885	+	0.337941i	0.950998	+	0.309196i	$0.100060\pi$
$53$	−0.353730	+	2.46024i	−0.0485885	+	0.337941i	−0.999587	+	0.0287444i	$0.990849\pi$
$54$		0			0
$55$	−5.23419	−	3.36381i	−0.705778	−	0.453576i
$56$		0			0
$57$	10.3839	+	5.18623i	1.37538	+	0.686934i
$58$		0			0
$59$	1.69949	+	2.64446i	0.221255	+	0.344280i	0.934081	−	0.357061i	$-0.116221\pi$
$59$	1.69949	+	2.64446i	0.221255	+	0.344280i	−0.712826	+	0.701341i	$0.752585\pi$
$60$		0			0
$61$	2.44051	+	8.31163i	0.312476	+	1.06419i	0.954673	+	0.297656i	$0.0962047\pi$
$61$	2.44051	+	8.31163i	0.312476	+	1.06419i	−0.642197	+	0.766539i	$0.721977\pi$
$62$		0			0
$63$	1.73233	−	4.66995i	0.218253	−	0.588358i
$64$		0			0
$65$	1.17526	−	1.01837i	0.145773	−	0.126313i
$66$		0			0
$67$	−8.02999	−	1.58723i	−0.981019	−	0.193911i
$67$	−8.02999	−	1.58723i	−0.981019	−	0.193911i
$68$		0			0
$69$	1.95827	−	10.9096i	0.235748	−	1.31336i
$70$		0			0
$71$	15.3838	+	2.21185i	1.82572	+	0.262499i	0.967878	−	0.251419i	$-0.0808971\pi$
$71$	15.3838	+	2.21185i	1.82572	+	0.262499i	0.857840	+	0.513917i	$0.171806\pi$
$72$		0			0
$73$	5.08429	−	1.49288i	0.595071	−	0.174729i	0.0296911	−	0.999559i	$-0.490548\pi$
$73$	5.08429	−	1.49288i	0.595071	−	0.174729i	0.565380	+	0.824830i	$0.308729\pi$
$74$		0			0
$75$	−2.73262	+	8.23470i	−0.315536	+	0.950861i
$76$		0			0
$77$	−2.97012	+	1.35641i	−0.338477	+	0.154577i
$78$		0			0
$79$	−1.14758	+	1.78567i	−0.129113	+	0.200904i	−0.899791	−	0.436321i	$-0.856281\pi$
$79$	−1.14758	+	1.78567i	−0.129113	+	0.200904i	0.770678	+	0.637225i	$0.219918\pi$
$80$		0			0
$81$	4.83876	−	7.58857i	0.537639	−	0.843175i
$82$		0			0
$83$	−2.84309	+	9.68269i	−0.312070	+	1.06281i	0.642860	+	0.765984i	$0.277748\pi$
$83$	−2.84309	+	9.68269i	−0.312070	+	1.06281i	−0.954930	+	0.296830i	$0.904071\pi$
$84$		0			0
$85$	6.69233	+	0.962212i	0.725886	+	0.104367i
$86$		0			0
$87$	15.2094	−	3.89641i	1.63062	−	0.417739i
$88$		0			0
$89$	4.82981	−	2.20570i	0.511959	−	0.233804i	−0.142647	−	0.989774i	$-0.545562\pi$
$89$	4.82981	−	2.20570i	0.511959	−	0.233804i	0.654607	+	0.755970i	$0.272834\pi$
$90$		0			0
$91$	−0.116143	−	0.807790i	−0.0121751	−	0.0846794i
$92$		0			0
$93$	7.31953	−	7.87579i	0.759000	−	0.816681i
$94$		0			0
$95$	−17.8355	+	11.4622i	−1.82989	+	1.17600i
$96$		0			0
$97$		−	13.2013i		−	1.34039i	−0.742186	−	0.670194i	$-0.766211\pi$
$97$		−	13.2013i		−	1.34039i	0.742186	−	0.670194i	$-0.233789\pi$
$98$		0			0
$99$	−5.76280	+	1.26438i	−0.579184	+	0.127075i
$100$		0			0
$101$	−7.61191	+	8.78461i	−0.757413	+	0.874102i	−0.995265	−	0.0971999i	$-0.969011\pi$
$101$	−7.61191	+	8.78461i	−0.757413	+	0.874102i	0.237852	+	0.971302i	$0.423557\pi$
$102$		0			0
$103$	−11.4173	+	7.33743i	−1.12498	+	0.722978i	−0.964506	−	0.264062i	$-0.914938\pi$
$103$	−11.4173	+	7.33743i	−1.12498	+	0.722978i	−0.160471	+	0.987041i	$0.551301\pi$
$104$		0			0
$105$	5.71505	+	7.07903i	0.557732	+	0.690842i
$106$		0			0
$107$	−0.0498318	−	0.169712i	−0.00481742	−	0.0164066i	0.957049	−	0.289926i	$-0.0936306\pi$
$107$	−0.0498318	−	0.169712i	−0.00481742	−	0.0164066i	−0.961867	+	0.273519i	$0.911812\pi$
$108$		0			0
$109$	−8.55064	+	13.3050i	−0.819002	+	1.27439i	0.139761	+	0.990185i	$0.455367\pi$
$109$	−8.55064	+	13.3050i	−0.819002	+	1.27439i	−0.958763	+	0.284207i	$0.908270\pi$
$110$		0			0
$111$	−3.27248	−	12.7740i	−0.310610	−	1.21245i
$112$		0			0
$113$	−2.48008	+	0.728216i	−0.233306	+	0.0685048i	−0.396296	−	0.918123i	$-0.629704\pi$
$113$	−2.48008	+	0.728216i	−0.233306	+	0.0685048i	0.162990	+	0.986628i	$0.447886\pi$
$114$		0			0
$115$	15.3007	+	13.2582i	1.42680	+	1.23633i
$116$		0			0
$117$	0.102576	−	1.47103i	0.00948318	−	0.135997i
$118$		0			0
$119$	2.32357	−	2.68154i	0.213001	−	0.245817i
$120$		0			0
$121$	−6.00014	−	3.85606i	−0.545467	−	0.350551i
$122$		0			0
$123$	2.14842	−	0.892147i	0.193716	−	0.0804422i
$124$		0			0
$125$	−0.0191479	−	0.0220978i	−0.00171264	−	0.00197649i
$126$		0			0
$127$	−8.82859	−	10.1887i	−0.783411	−	0.904104i	0.213940	−	0.976847i	$-0.431370\pi$
$127$	−8.82859	−	10.1887i	−0.783411	−	0.904104i	−0.997351	+	0.0727426i	$0.976825\pi$
$128$		0			0
$129$	−2.29491	−	5.52648i	−0.202056	−	0.486580i
$130$		0			0
$131$	−6.01060	−	2.74495i	−0.525149	−	0.239827i	0.135157	−	0.990824i	$-0.456846\pi$
$131$	−6.01060	−	2.74495i	−0.525149	−	0.239827i	−0.660306	+	0.750997i	$0.729573\pi$
$132$		0			0
$133$			11.1262i			0.964761i
$134$		0			0
$135$	7.39776	+	14.6807i	0.636698	+	1.26351i
$136$		0			0
$137$	4.98287	−	10.9110i	0.425716	−	0.932187i	−0.568287	−	0.822830i	$-0.692394\pi$
$137$	4.98287	−	10.9110i	0.425716	−	0.932187i	0.994003	−	0.109357i	$-0.0348791\pi$
$138$		0			0
$139$	−1.49570	+	5.09389i	−0.126864	+	0.432058i	−0.998289	−	0.0584699i	$-0.981378\pi$
$139$	−1.49570	+	5.09389i	−0.126864	+	0.432058i	0.871426	+	0.490528i	$0.163196\pi$
$140$		0			0
$141$	1.52474	−	8.49437i	0.128406	−	0.715355i
$142$		0			0
$143$	−0.730558	+	0.633032i	−0.0610923	+	0.0529368i
$144$		0			0
$145$	−8.07966	+	27.5168i	−0.670980	+	2.28515i
$146$		0			0
$147$	−7.30697	+	0.792167i	−0.602669	+	0.0653368i
$148$		0			0
$149$	−6.69588	−	5.80202i	−0.548548	−	0.475320i	0.335939	−	0.941884i	$-0.390946\pi$
$149$	−6.69588	−	5.80202i	−0.548548	−	0.475320i	−0.884487	+	0.466564i	$0.845492\pi$
$150$		0			0
$151$	0.234723	+	1.63254i	0.0191015	+	0.132854i	0.997141	−	0.0755670i	$-0.0240767\pi$
$151$	0.234723	+	1.63254i	0.0191015	+	0.132854i	−0.978039	+	0.208421i	$0.933168\pi$
$152$		0			0
$153$	5.12560	−	3.85125i	0.414380	−	0.311355i
$154$		0			0
$155$	5.53302	+	18.8438i	0.444423	+	1.51357i
$156$		0			0
$157$	3.06444	−	6.71020i	0.244569	−	0.535532i	−0.747044	−	0.664775i	$-0.768527\pi$
$157$	3.06444	−	6.71020i	0.244569	−	0.535532i	0.991613	+	0.129243i	$0.0412547\pi$
$158$		0			0
$159$	−4.28001	+	0.464006i	−0.339427	+	0.0367981i
$160$		0			0
$161$	10.1944	−	2.99335i	0.803432	−	0.235909i
$162$		0			0
$163$	−18.5314			−1.45149			−0.725745	−	0.687963i	$-0.758505\pi$
$163$	−18.5314			−1.45149			−0.725745	+	0.687963i	$0.758505\pi$
$164$		0			0
$165$	3.39414	−	10.2282i	0.264234	−	0.796262i
$166$		0			0
$167$	−0.789841	−	0.684402i	−0.0611198	−	0.0529606i	0.623765	−	0.781612i	$-0.285602\pi$
$167$	−0.789841	−	0.684402i	−0.0611198	−	0.0529606i	−0.684885	+	0.728651i	$0.740148\pi$
$168$		0			0
$169$	5.30003	+	11.6054i	0.407694	+	0.892726i
$170$		0			0
$171$	−4.23838	+	19.6520i	−0.324117	+	1.50283i
$172$		0			0
$173$	5.09001	+	7.92020i	0.386986	+	0.602162i	0.979023	−	0.203749i	$-0.0653125\pi$
$173$	5.09001	+	7.92020i	0.386986	+	0.602162i	−0.592037	+	0.805911i	$0.701676\pi$
$174$		0			0
$175$	−8.23219	+	1.18361i	−0.622295	+	0.0894726i
$176$		0			0
$177$	−3.70654	+	3.98823i	−0.278601	+	0.299773i
$178$		0			0
$179$	−1.21859	−	2.66834i	−0.0910818	−	0.199441i	0.858609	−	0.512632i	$-0.171329\pi$
$179$	−1.21859	−	2.66834i	−0.0910818	−	0.199441i	−0.949690	+	0.313191i	$0.898602\pi$
$180$		0			0
$181$	3.89978	−	8.53932i	0.289868	−	0.634723i	−0.707540	−	0.706673i	$-0.750195\pi$
$181$	3.89978	−	8.53932i	0.289868	−	0.634723i	0.997408	+	0.0719506i	$0.0229224\pi$
$182$		0			0
$183$	−12.8968	+	7.66755i	−0.953356	+	0.566801i
$184$		0			0
$185$	23.1106	+	6.78587i	1.69912	+	0.498907i
$186$		0			0
$187$	−4.16005	−	0.598125i	−0.304213	−	0.0437392i
$188$		0			0
$189$	8.58018	+	0.899274i	0.624116	+	0.0654126i
$190$		0			0
$191$	−0.522401	−	1.14390i	−0.0377996	−	0.0827696i	0.889790	−	0.456370i	$-0.150851\pi$
$191$	−0.522401	−	1.14390i	−0.0377996	−	0.0827696i	−0.927590	+	0.373600i	$0.878123\pi$
$192$		0			0
$193$	−2.79049	+	1.79334i	−0.200864	+	0.129087i	−0.637206	−	0.770693i	$-0.719910\pi$
$193$	−2.79049	+	1.79334i	−0.200864	+	0.129087i	0.436342	+	0.899781i	$0.356274\pi$
$194$		0			0
$195$	2.21386	+	1.53419i	0.158538	+	0.109866i
$196$		0			0
$197$	2.73971	−	19.0551i	0.195197	−	1.35762i	−0.622792	−	0.782388i	$-0.714002\pi$
$197$	2.73971	−	19.0551i	0.195197	−	1.35762i	0.817989	−	0.575235i	$-0.195089\pi$
$198$		0			0
$199$	−15.6841	−	18.1004i	−1.11181	−	1.28310i	−0.955369	−	0.295414i	$-0.904542\pi$
$199$	−15.6841	−	18.1004i	−1.11181	−	1.28310i	−0.156444	−	0.987687i	$-0.550003\pi$
$200$		0			0
$201$	−0.788472	−	14.1555i	−0.0556145	−	0.998452i
$202$		0			0
$203$	9.85579	+	11.3742i	0.691741	+	0.798311i
$204$		0			0
$205$	−0.604719	+	4.20592i	−0.0422354	+	0.293754i
$206$		0			0
$207$	19.1466	−	1.40368i	1.33078	−	0.0975627i
$208$		0			0
$209$	11.0868	−	7.12507i	0.766892	−	0.492851i
$210$		0			0
$211$	5.24189	+	11.4781i	0.360867	+	0.790188i	0.999781	+	0.0209101i	$0.00665639\pi$
$211$	5.24189	+	11.4781i	0.360867	+	0.790188i	−0.638915	+	0.769278i	$0.720616\pi$
$212$		0			0
$213$	2.90141	+	26.7627i	0.198801	+	1.83375i
$214$		0			0
$215$	10.8191	+	1.55555i	0.737856	+	0.106088i
$216$		0			0
$217$	9.88903	+	2.90368i	0.671311	+	0.197115i
$218$		0			0
$219$	4.69030	+	7.88906i	0.316941	+	0.533093i
$220$		0			0
$221$	0.436372	−	0.955522i	0.0293536	−	0.0642754i
$222$		0			0
$223$	−8.49959	−	18.6115i	−0.569175	−	1.24632i	−0.947236	−	0.320538i	$-0.896136\pi$
$223$	−8.49959	−	18.6115i	−0.569175	−	1.24632i	0.378061	−	0.925781i	$-0.376591\pi$
$224$		0			0
$225$	−14.9913	−	1.04536i	−0.999422	−	0.0696904i
$226$		0			0
$227$	−0.499215	+	0.0717763i	−0.0331341	+	0.00476396i	−0.158862	−	0.987301i	$-0.550782\pi$
$227$	−0.499215	+	0.0717763i	−0.0331341	+	0.00476396i	0.125728	+	0.992065i	$0.459873\pi$
$228$		0			0
$229$	9.32943	+	14.5169i	0.616506	+	0.959302i	0.999370	+	0.0354972i	$0.0113015\pi$
$229$	9.32943	+	14.5169i	0.616506	+	0.959302i	−0.382864	+	0.923805i	$0.625062\pi$
$230$		0			0
$231$	−3.55256	−	4.40042i	−0.233741	−	0.289527i
$232$		0			0
$233$	3.47909	+	7.61814i	0.227923	+	0.499081i	0.988696	−	0.149937i	$-0.0479072\pi$
$233$	3.47909	+	7.61814i	0.227923	+	0.499081i	−0.760773	+	0.649018i	$0.775180\pi$
$234$		0			0
$235$	11.9134	+	10.3230i	0.777144	+	0.673399i
$236$		0			0
$237$	−3.48940	−	1.15793i	−0.226661	−	0.0752157i
$238$		0			0
$239$	−22.3180			−1.44363			−0.721814	−	0.692087i	$-0.756692\pi$
$239$	−22.3180			−1.44363			−0.721814	+	0.692087i	$0.756692\pi$
$240$		0			0
$241$	6.56454	−	1.92752i	0.422859	−	0.124163i	−0.0633779	−	0.997990i	$-0.520187\pi$
$241$	6.56454	−	1.92752i	0.422859	−	0.124163i	0.486237	+	0.873827i	$0.338369\pi$
$242$		0			0
$243$	14.8125	+	4.85689i	0.950223	+	0.311570i
$244$		0			0
$245$	5.57695	−	12.2118i	0.356298	−	0.780185i
$246$		0			0
$247$	0.928005	+	3.16050i	0.0590476	+	0.201098i
$248$		0			0
$249$	−17.4683	−	0.608302i	−1.10701	−	0.0385495i
$250$		0			0
$251$	1.72705	+	12.0119i	0.109010	+	0.758183i	0.968855	+	0.247628i	$0.0796509\pi$
$251$	1.72705	+	12.0119i	0.109010	+	0.758183i	−0.859845	+	0.510555i	$0.829440\pi$
$252$		0			0
$253$	−9.51115	−	8.24146i	−0.597961	−	0.518136i
$254$		0			0
$255$	1.26219	+	11.6424i	0.0790411	+	0.729078i
$256$		0			0
$257$	4.41723	−	15.0437i	0.275539	−	0.938400i	−0.699176	−	0.714950i	$-0.746450\pi$
$257$	4.41723	−	15.0437i	0.275539	−	0.938400i	0.974715	−	0.223451i	$-0.0717322\pi$
$258$		0			0
$259$	9.55285	−	8.27759i	0.593585	−	0.514344i
$260$		0			0
$261$	13.0753	+	23.8446i	0.809342	+	1.47594i
$262$		0			0
$263$	5.74550	−	19.5674i	0.354282	−	1.20658i	−0.568963	−	0.822363i	$-0.692655\pi$
$263$	5.74550	−	19.5674i	0.354282	−	1.20658i	0.923245	−	0.384212i	$-0.125527\pi$
$264$		0			0
$265$	3.26666	−	7.15299i	0.200669	−	0.439405i
$266$		0			0
$267$	5.77693	+	7.15568i	0.353543	+	0.437920i
$268$		0			0
$269$			13.4572i			0.820497i	0.911974	+	0.410249i	$0.134558\pi$
$269$			13.4572i			0.820497i	−0.911974	+	0.410249i	$0.865442\pi$
$270$		0			0
$271$	29.4231	+	13.4371i	1.78733	+	0.816245i	0.971160	+	0.238430i	$0.0766326\pi$
$271$	29.4231	+	13.4371i	1.78733	+	0.816245i	0.816168	+	0.577815i	$0.196095\pi$
$272$		0			0
$273$	1.30544	−	0.542094i	0.0790089	−	0.0328090i
$274$		0			0
$275$	6.45123	+	7.44512i	0.389024	+	0.448958i
$276$		0			0
$277$	11.6975	+	13.4996i	0.702834	+	0.811114i	0.989133	−	0.147026i	$-0.0469702\pi$
$277$	11.6975	+	13.4996i	0.702834	+	0.811114i	−0.286298	+	0.958141i	$0.592425\pi$
$278$		0			0
$279$	16.3608	+	8.89585i	0.979493	+	0.532580i
$280$		0			0
$281$	19.2147	+	12.3486i	1.14626	+	0.736654i	0.968890	−	0.247491i	$-0.0796061\pi$
$281$	19.2147	+	12.3486i	1.14626	+	0.736654i	0.177366	+	0.984145i	$0.443242\pi$
$282$		0			0
$283$	−2.67257	+	3.08431i	−0.158868	+	0.183343i	−0.829603	−	0.558354i	$-0.811433\pi$
$283$	−2.67257	+	3.08431i	−0.158868	+	0.183343i	0.670735	+	0.741697i	$0.265979\pi$
$284$		0			0
$285$	−26.8985	−	24.9987i	−1.59333	−	1.48080i
$286$		0			0
$287$	1.68526	+	1.46029i	0.0994779	+	0.0861981i
$288$		0			0
$289$	−11.9293	+	3.50275i	−0.701722	+	0.206044i
$290$		0			0
$291$	22.1500	−	5.67448i	1.29846	−	0.332644i
$292$		0			0
$293$	−5.44028	+	8.46524i	−0.317825	+	0.494545i	−0.963004	−	0.269486i	$-0.913146\pi$
$293$	−5.44028	+	8.46524i	−0.317825	+	0.494545i	0.645180	+	0.764031i	$0.276782\pi$
$294$		0			0
$295$	−2.80187	−	9.54230i	−0.163131	−	0.555574i
$296$		0			0
$297$	−4.59856	−	9.12573i	−0.266835	−	0.529529i
$298$		0			0
$299$	2.64615	−	1.70058i	0.153031	−	0.0983471i
$300$		0			0
$301$	3.75638	−	4.33509i	0.216514	−	0.249870i
$302$		0			0
$303$	−18.0113	−	8.99577i	−1.03472	−	0.516793i
$304$		0			0
$305$		−	27.4060i		−	1.56926i
$306$		0			0
$307$	−11.2516	+	7.23094i	−0.642161	+	0.412692i	−0.820794	−	0.571224i	$-0.806469\pi$
$307$	−11.2516	+	7.23094i	−0.642161	+	0.412692i	0.178633	+	0.983916i	$0.442832\pi$
$308$		0			0
$309$	−17.2189	−	16.0027i	−0.979546	−	0.910362i
$310$		0			0
$311$	−3.74884	−	26.0738i	−0.212577	−	1.47851i	−0.764506	−	0.644617i	$-0.777017\pi$
$311$	−3.74884	−	26.0738i	−0.212577	−	1.47851i	0.551928	−	0.833892i	$-0.313892\pi$
$312$		0			0
$313$	8.46340	−	3.86511i	0.478380	−	0.218469i	−0.161606	−	0.986855i	$-0.551667\pi$
$313$	8.46340	−	3.86511i	0.478380	−	0.218469i	0.639986	+	0.768387i	$0.278940\pi$
$314$		0			0
$315$	−9.42109	+	12.6320i	−0.530818	+	0.711730i
$316$		0			0
$317$	−29.9478	−	4.30584i	−1.68203	−	0.241840i	−0.765971	−	0.642875i	$-0.777741\pi$
$317$	−29.9478	−	4.30584i	−1.68203	−	0.241840i	−0.916063	+	0.401035i	$0.868651\pi$
$318$		0			0
$319$	5.02244	−	17.1048i	0.281202	−	0.957688i
$320$		0			0
$321$	0.263334	−	0.156560i	0.0146978	−	0.00873835i
$322$		0			0
$323$	−7.74261	+	12.0477i	−0.430811	+	0.670354i
$324$		0			0
$325$	−2.23971	+	1.02284i	−0.124237	+	0.0567371i
$326$		0			0
$327$	−25.9995	−	8.62775i	−1.43778	−	0.477116i
$328$		0			0
$329$	7.93753	−	2.33067i	0.437610	−	0.128494i
$330$		0			0
$331$	−24.4599	−	3.51681i	−1.34444	−	0.193301i	−0.567758	−	0.823195i	$-0.692189\pi$
$331$	−24.4599	−	3.51681i	−1.34444	−	0.193301i	−0.776681	+	0.629894i	$0.783098\pi$
$332$		0			0
$333$	20.0263	−	10.9816i	1.09744	−	0.601787i
$334$		0			0
$335$	22.9610	+	11.9755i	1.25449	+	0.654293i
$336$		0			0
$337$	−6.09098	+	5.27786i	−0.331797	+	0.287503i	−0.804786	−	0.593565i	$-0.797720\pi$
$337$	−6.09098	+	5.27786i	−0.331797	+	0.287503i	0.472990	+	0.881068i	$0.343175\pi$
$338$		0			0
$339$	−2.28789	−	3.84822i	−0.124261	−	0.209007i
$340$		0			0
$341$	−3.43941	−	11.7135i	−0.186254	−	0.634324i
$342$		0			0
$343$	−10.0924	−	15.7040i	−0.544937	−	0.847938i
$344$		0			0
$345$	−15.6685	+	31.3715i	−0.843564	+	1.68898i
$346$		0			0
$347$	−18.3774	−	11.8104i	−0.986551	−	0.634018i	−0.0553285	−	0.998468i	$-0.517621\pi$
$347$	−18.3774	−	11.8104i	−0.986551	−	0.634018i	−0.931223	+	0.364450i	$0.881257\pi$
$348$		0			0
$349$	3.30080	−	22.9575i	0.176688	−	1.22889i	−0.687674	−	0.726019i	$-0.741368\pi$
$349$	3.30080	−	22.9575i	0.176688	−	1.22889i	0.864362	−	0.502870i	$-0.167723\pi$
$350$		0			0
$351$	2.51229	−	0.460204i	0.134096	−	0.0245639i
$352$		0			0
$353$	−4.36249	+	30.3418i	−0.232192	+	1.61493i	0.456397	+	0.889776i	$0.349140\pi$
$353$	−4.36249	+	30.3418i	−0.232192	+	1.61493i	−0.688588	+	0.725152i	$0.741769\pi$
$354$		0			0
$355$	−44.7273	−	20.4263i	−2.37388	−	1.08411i
$356$		0			0
$357$	5.49804	+	2.74600i	0.290987	+	0.145334i
$358$		0			0
$359$	−32.0809	+	4.61254i	−1.69317	+	0.243441i	−0.920324	−	0.391156i	$-0.872075\pi$
$359$	−32.0809	+	4.61254i	−1.69317	+	0.243441i	−0.772843	+	0.634597i	$0.781166\pi$
$360$		0			0
$361$	−3.68700	−	25.6436i	−0.194052	−	1.34966i
$362$		0			0
$363$	3.89083	−	11.7249i	0.204216	−	0.615399i
$364$		0			0
$365$	−16.7644			−0.877491
$366$		0			0
$367$	20.5231	−	9.37259i	1.07130	−	0.489245i	0.199897	−	0.979817i	$-0.435939\pi$
$367$	20.5231	−	9.37259i	1.07130	−	0.489245i	0.871401	+	0.490571i	$0.163212\pi$
$368$		0			0
$369$	2.42038	+	3.22127i	0.126000	+	0.167693i
$370$		0			0
$371$	−2.23109	−	3.47164i	−0.115832	−	0.180239i
$372$		0			0
$373$			27.4560i			1.42162i	0.703386	+	0.710808i	$0.251670\pi$
$373$			27.4560i			1.42162i	−0.703386	+	0.710808i	$0.748330\pi$
$374$		0			0
$375$	0.0288466	−	0.0416262i	0.00148963	−	0.00214957i
$376$		0			0
$377$	3.74833	+	2.40890i	0.193049	+	0.124065i
$378$		0			0
$379$	24.4741	+	11.1769i	1.25715	+	0.574121i	0.928851	−	0.370454i	$-0.120798\pi$
$379$	24.4741	+	11.1769i	1.25715	+	0.574121i	0.328298	+	0.944574i	$0.393525\pi$
$380$		0			0
$381$	13.3004	−	19.1927i	0.681402	−	0.983274i
$382$		0			0
$383$	−1.40639	+	1.62306i	−0.0718631	+	0.0829344i	−0.790543	−	0.612407i	$-0.790201\pi$
$383$	−1.40639	+	1.62306i	−0.0718631	+	0.0829344i	0.718680	+	0.695341i	$0.244747\pi$
$384$		0			0
$385$	10.2251	−	1.47014i	0.521117	−	0.0749254i
$386$		0			0
$387$	8.28625	−	6.22608i	0.421214	−	0.316489i
$388$		0			0
$389$	13.8927	−	21.6175i	0.704388	−	1.09605i	−0.286066	−	0.958210i	$-0.592348\pi$
$389$	13.8927	−	21.6175i	0.704388	−	1.09605i	0.990455	−	0.137839i	$-0.0440158\pi$
$390$		0			0
$391$	13.1219	+	3.85293i	0.663601	+	0.194851i
$392$		0			0
$393$	2.02205	−	11.2649i	0.101999	−	0.568238i
$394$		0			0
$395$	5.07520	−	4.39769i	0.255361	−	0.221272i
$396$		0			0
$397$	−18.8203	−	5.52612i	−0.944561	−	0.277348i	−0.227041	−	0.973885i	$-0.572905\pi$
$397$	−18.8203	−	5.52612i	−0.944561	−	0.277348i	−0.717521	+	0.696537i	$0.754723\pi$
$398$		0			0
$399$	−18.6682	+	4.78250i	−0.934580	+	0.239424i
$400$		0			0
$401$	−35.2908			−1.76234			−0.881169	−	0.472801i	$-0.843243\pi$
$401$	−35.2908			−1.76234			−0.881169	+	0.472801i	$0.843243\pi$
$402$		0			0
$403$	3.05126			0.151994
$404$		0			0
$405$	−21.4524	+	18.7228i	−1.06598	+	0.930345i
$406$		0			0
$407$	−14.3659	−	4.21820i	−0.712089	−	0.209088i
$408$		0			0
$409$	17.4769	−	15.1438i	0.864178	−	0.748815i	−0.105183	−	0.994453i	$-0.533543\pi$
$409$	17.4769	−	15.1438i	0.864178	−	0.748815i	0.969362	+	0.245638i	$0.0789975\pi$
$410$		0			0
$411$	20.4490	+	3.67060i	1.00867	+	0.181057i
$412$		0			0
$413$	−5.00771	−	1.47040i	−0.246413	−	0.0723535i
$414$		0			0
$415$	17.2609	−	26.8585i	0.847305	−	1.31843i
$416$		0			0
$417$	−9.18978	−	0.320016i	−0.450025	−	0.0156713i
$418$		0			0
$419$	−3.08530	+	0.443600i	−0.150727	+	0.0216713i	−0.217265	−	0.976113i	$-0.569714\pi$
$419$	−3.08530	+	0.443600i	−0.150727	+	0.0216713i	0.0665382	+	0.997784i	$0.478805\pi$
$420$		0			0
$421$	5.87434	−	6.77935i	0.286298	−	0.330406i	−0.594323	−	0.804226i	$-0.702580\pi$
$421$	5.87434	−	6.77935i	0.286298	−	0.330406i	0.880621	+	0.473821i	$0.157126\pi$
$422$		0			0
$423$	14.9078	−	1.09293i	0.724843	−	0.0531401i
$424$		0			0
$425$	−9.73773	−	4.44707i	−0.472350	−	0.215715i
$426$		0			0
$427$	−12.0992	−	7.77571i	−0.585523	−	0.376293i
$428$		0			0
$429$	−1.37617	−	0.953674i	−0.0664420	−	0.0460438i
$430$		0			0
$431$			9.40488i			0.453017i	0.974009	+	0.226508i	$0.0727311\pi$
$431$			9.40488i			0.453017i	−0.974009	+	0.226508i	$0.927269\pi$
$432$		0			0
$433$	8.59786	+	13.3785i	0.413187	+	0.642931i	0.984004	−	0.178146i	$-0.0570100\pi$
$433$	8.59786	+	13.3785i	0.413187	+	0.642931i	−0.570817	+	0.821077i	$0.693374\pi$
$434$		0			0
$435$	−49.6425	−	1.72870i	−2.38018	−	0.0828851i
$436$		0			0
$437$	−39.0084	+	17.8145i	−1.86602	+	0.852184i
$438$		0			0
$439$	33.0069			1.57533			0.787667	−	0.616101i	$-0.211289\pi$
$439$	33.0069			1.57533			0.787667	+	0.616101i	$0.211289\pi$
$440$		0			0
$441$	−4.47000	−	11.9196i	−0.212857	−	0.567601i
$442$		0			0
$443$	−4.12806	−	28.7113i	−0.196130	−	1.36411i	−0.815382	−	0.578923i	$-0.803473\pi$
$443$	−4.12806	−	28.7113i	−0.196130	−	1.36411i	0.619252	−	0.785192i	$-0.287436\pi$
$444$		0			0
$445$	−16.6273	+	2.39065i	−0.788210	+	0.113328i
$446$		0			0
$447$	6.85683	−	13.7287i	0.324317	−	0.649348i
$448$		0			0
$449$	−5.06841	−	2.31467i	−0.239193	−	0.109236i	0.292212	−	0.956353i	$-0.405609\pi$
$449$	−5.06841	−	2.31467i	−0.239193	−	0.109236i	−0.531405	+	0.847118i	$0.678336\pi$
$450$		0			0
$451$	0.375902	−	2.61446i	0.0177005	−	0.123110i
$452$		0			0
$453$	−2.63829	+	1.09557i	−0.123957	+	0.0514743i
$454$		0			0
$455$	−0.367445	+	2.55564i	−0.0172261	+	0.119810i
$456$		0			0
$457$	27.5754	+	17.7216i	1.28992	+	0.828982i	0.992077	−	0.125633i	$-0.0400961\pi$
$457$	27.5754	+	17.7216i	1.28992	+	0.828982i	0.297844	+	0.954615i	$0.403732\pi$
$458$		0			0
$459$	8.66508	+	6.94464i	0.404451	+	0.324148i
$460$		0			0
$461$	10.4093	+	16.1972i	0.484810	+	0.754379i	0.994360	−	0.106062i	$-0.0338242\pi$
$461$	10.4093	+	16.1972i	0.484810	+	0.754379i	−0.509549	+	0.860441i	$0.670188\pi$
$462$		0			0
$463$	3.57771	+	12.1846i	0.166270	+	0.566265i	0.999903	+	0.0139452i	$0.00443904\pi$
$463$	3.57771	+	12.1846i	0.166270	+	0.566265i	−0.833632	+	0.552320i	$0.813743\pi$
$464$		0			0
$465$	−29.2390	+	17.3835i	−1.35592	+	0.806141i
$466$		0			0
$467$	−9.15972	+	7.93694i	−0.423861	+	0.367278i	−0.840516	−	0.541787i	$-0.817748\pi$
$467$	−9.15972	+	7.93694i	−0.423861	+	0.367278i	0.416654	+	0.909065i	$0.363203\pi$
$468$		0			0
$469$	11.8015	−	6.73912i	0.544944	−	0.311184i
$470$		0			0
$471$	12.5760	+	2.25740i	0.579473	+	0.104016i
$472$		0			0
$473$	−6.72530	−	0.966953i	−0.309230	−	0.0444605i
$474$		0			0
$475$	32.2086	−	9.45731i	1.47783	−	0.433931i
$476$		0			0
$477$	−2.61827	−	6.98184i	−0.119882	−	0.319676i
$478$		0			0
$479$	−10.5795	+	4.83151i	−0.483391	+	0.220757i	−0.642178	−	0.766556i	$-0.721969\pi$
$479$	−10.5795	+	4.83151i	−0.483391	+	0.220757i	0.158787	+	0.987313i	$0.449242\pi$
$480$		0			0
$481$	2.02317	−	3.14811i	0.0922485	−	0.143541i
$482$		0			0
$483$	9.40443	+	15.8182i	0.427916	+	0.719752i
$484$		0			0
$485$	−11.7667	+	40.0736i	−0.534298	+	1.81965i
$486$		0			0
$487$	19.4795	+	2.80073i	0.882702	+	0.126913i	0.568735	−	0.822521i	$-0.307433\pi$
$487$	19.4795	+	2.80073i	0.882702	+	0.126913i	0.313967	+	0.949434i	$0.398342\pi$
$488$		0			0
$489$	−7.96558	−	31.0932i	−0.360216	−	1.40608i
$490$		0			0
$491$	13.2953	−	6.07174i	0.600006	−	0.274014i	−0.0921686	−	0.995743i	$-0.529380\pi$
$491$	13.2953	−	6.07174i	0.600006	−	0.274014i	0.692175	+	0.721730i	$0.256653\pi$
$492$		0			0
$493$	2.75693	+	19.1749i	0.124166	+	0.863593i
$494$		0			0
$495$	18.6205	+	1.29842i	0.836927	+	0.0583595i
$496$		0			0
$497$	−21.7080	+	13.9509i	−0.973737	+	0.625783i
$498$		0			0
$499$		−	28.0049i		−	1.25367i	−0.779152	−	0.626835i	$-0.784350\pi$
$499$		−	28.0049i		−	1.25367i	0.779152	−	0.626835i	$-0.215650\pi$
$500$		0			0
$501$	0.808827	−	1.61943i	0.0361357	−	0.0723509i
$502$		0			0
$503$	19.7335	−	22.7737i	0.879874	−	1.01543i	−0.119870	−	0.992790i	$-0.538248\pi$
$503$	19.7335	−	22.7737i	0.879874	−	1.01543i	0.999744	−	0.0226388i	$-0.00720677\pi$
$504$		0			0
$505$	30.9366	−	19.8817i	1.37666	−	0.884725i
$506$		0			0
$507$	−17.1942	+	13.8812i	−0.763621	+	0.616488i
$508$		0			0
$509$	9.53776	+	32.4826i	0.422754	+	1.43977i	0.845723	+	0.533622i	$0.179170\pi$
$509$	9.53776	+	32.4826i	0.422754	+	1.43977i	−0.422969	+	0.906144i	$0.639012\pi$
$510$		0			0
$511$	−4.75646	+	7.40120i	−0.210414	+	0.327410i
$512$		0			0
$513$	−34.7953	+	1.33584i	−1.53625	+	0.0589789i
$514$		0			0
$515$	41.1981	−	12.0969i	1.81541	−	0.533051i
$516$		0			0
$517$	−7.40553	−	6.41693i	−0.325695	−	0.282216i
$518$		0			0
$519$	−11.1011	+	11.9448i	−0.487286	+	0.524318i
$520$		0			0
$521$	1.50801	−	1.74034i	0.0660672	−	0.0762457i	−0.721754	−	0.692150i	$-0.756664\pi$
$521$	1.50801	−	1.74034i	0.0660672	−	0.0762457i	0.787821	+	0.615904i	$0.211209\pi$
$522$		0			0
$523$	−17.2890	−	11.1110i	−0.755994	−	0.485848i	0.104994	−	0.994473i	$-0.466518\pi$
$523$	−17.2890	−	11.1110i	−0.755994	−	0.485848i	−0.860988	+	0.508625i	$0.830154\pi$
$524$		0			0
$525$	−5.52449	−	13.3038i	−0.241108	−	0.580624i
$526$		0			0
$527$	8.68749	+	10.0259i	0.378433	+	0.436735i
$528$		0			0
$529$	11.7555	+	13.5666i	0.511111	+	0.589853i
$530$		0			0
$531$	−8.28494	−	4.50477i	−0.359536	−	0.195491i
$532$		0			0
$533$	0.600515	+	0.274246i	0.0260112	+	0.0118789i
$534$		0			0
$535$			0.559590i			0.0241932i
$536$		0			0
$537$	3.95332	−	3.19160i	0.170598	−	0.137728i
$538$		0			0
$539$	−3.46671	+	7.59105i	−0.149322	+	0.326969i
$540$		0			0
$541$	4.57439	−	15.5790i	0.196669	−	0.669792i	−0.800816	−	0.598910i	$-0.795601\pi$
$541$	4.57439	−	15.5790i	0.196669	−	0.669792i	0.997485	−	0.0708815i	$-0.0225812\pi$
$542$		0			0
$543$	16.0041	+	2.87274i	0.686803	+	0.123281i
$544$		0			0
$545$	37.8153	−	32.7672i	1.61983	−	1.40359i
$546$		0			0
$547$	−0.529705	+	1.80401i	−0.0226485	+	0.0771338i	−0.970042	−	0.242938i	$-0.921889\pi$
$547$	−0.529705	+	1.80401i	−0.0226485	+	0.0771338i	0.947393	+	0.320072i	$0.103707\pi$
$548$		0			0
$549$	−18.4087	−	18.3432i	−0.785664	−	0.782869i
$550$		0			0
$551$	−45.9084	−	39.7799i	−1.95576	−	1.69468i
$552$		0			0
$553$	−0.501547	−	3.48834i	−0.0213280	−	0.148339i
$554$		0			0
$555$	−1.45189	+	41.6933i	−0.0616293	+	1.76978i
$556$		0			0
$557$	6.93447	+	23.6166i	0.293823	+	1.00067i	0.965625	+	0.259939i	$0.0837024\pi$
$557$	6.93447	+	23.6166i	0.293823	+	1.00067i	−0.671802	+	0.740731i	$0.734479\pi$
$558$		0			0
$559$	0.705457	−	1.54473i	0.0298376	−	0.0653353i
$560$		0			0
$561$	−0.784593	−	7.23711i	−0.0331255	−	0.305551i
$562$		0			0
$563$	33.1018	−	9.71955i	1.39507	−	0.409630i	0.504083	−	0.863655i	$-0.331830\pi$
$563$	33.1018	−	9.71955i	1.39507	−	0.409630i	0.890989	+	0.454025i	$0.150012\pi$
$564$		0			0
$565$	8.17756			0.344033
$566$		0			0
$567$	2.17926	+	14.7829i	0.0915204	+	0.620825i
$568$		0			0
$569$	24.9932	+	21.6567i	1.04777	+	0.907897i	0.995873	−	0.0907554i	$-0.0289282\pi$
$569$	24.9932	+	21.6567i	1.04777	+	0.907897i	0.0518959	+	0.998653i	$0.483474\pi$
$570$		0			0
$571$	−14.8373	−	32.4892i	−0.620922	−	1.35963i	−0.914847	−	0.403800i	$-0.867689\pi$
$571$	−14.8373	−	32.4892i	−0.620922	−	1.35963i	0.293925	−	0.955828i	$-0.405038\pi$
$572$		0			0
$573$	1.69476	−	1.36821i	0.0707995	−	0.0571580i
$574$		0			0
$575$	−17.3306	−	26.9670i	−0.722737	−	1.12460i
$576$		0			0
$577$	9.17105	−	1.31860i	0.381796	−	0.0548940i	0.0512549	−	0.998686i	$-0.483678\pi$
$577$	9.17105	−	1.31860i	0.381796	−	0.0548940i	0.330541	+	0.943792i	$0.392769\pi$
$578$		0			0
$579$	−4.20846	−	3.91122i	−0.174898	−	0.162545i
$580$		0			0
$581$	−6.96022	−	15.2408i	−0.288759	−	0.632294i
$582$		0			0
$583$	−2.03060	+	4.44640i	−0.0840991	+	0.184151i
$584$		0			0
$585$	−1.62255	+	4.37402i	−0.0670843	+	0.180843i
$586$		0			0
$587$	−16.8520	−	4.94820i	−0.695557	−	0.204234i	−0.0852039	−	0.996364i	$-0.527154\pi$
$587$	−16.8520	−	4.94820i	−0.695557	−	0.204234i	−0.610353	+	0.792130i	$0.708972\pi$
$588$		0			0
$589$	−41.1756	−	5.92016i	−1.69661	−	0.243936i
$590$		0			0
$591$	33.1496	−	3.59383i	1.36359	−	0.147830i
$592$		0			0
$593$	1.40647	+	3.07974i	0.0577569	+	0.126470i	0.936310	−	0.351175i	$-0.114218\pi$
$593$	1.40647	+	3.07974i	0.0577569	+	0.126470i	−0.878553	+	0.477645i	$0.841491\pi$
$594$		0			0
$595$	−9.44353	+	6.06899i	−0.387147	+	0.248804i
$596$		0			0
$597$	23.6283	−	34.0961i	0.967043	−	1.39546i
$598$		0			0
$599$	1.19705	−	8.32568i	0.0489102	−	0.340178i	−0.950643	−	0.310287i	$-0.899575\pi$
$599$	1.19705	−	8.32568i	0.0489102	−	0.340178i	0.999553	−	0.0298910i	$-0.00951603\pi$
$600$		0			0
$601$	6.82435	+	7.87571i	0.278371	+	0.321257i	0.877668	−	0.479270i	$-0.159098\pi$
$601$	6.82435	+	7.87571i	0.278371	+	0.321257i	−0.599297	+	0.800527i	$0.704553\pi$
$602$		0			0
$603$	23.4121	−	7.40759i	0.953415	−	0.301660i
$604$		0			0
$605$	14.7769	+	17.0535i	0.600768	+	0.693323i
$606$		0			0
$607$	3.16796	−	22.0337i	0.128584	−	0.894319i	−0.818768	−	0.574124i	$-0.805343\pi$
$607$	3.16796	−	22.0337i	0.128584	−	0.894319i	0.947352	−	0.320194i	$-0.103748\pi$
$608$		0			0
$609$	−14.8479	+	21.4258i	−0.601668	+	0.868217i
$610$		0			0
$611$	2.06034	−	1.32410i	0.0833523	−	0.0535673i
$612$		0			0
$613$	−4.49055	−	9.83293i	−0.181372	−	0.397148i	0.797007	−	0.603970i	$-0.206415\pi$
$613$	−4.49055	−	9.83293i	−0.181372	−	0.397148i	−0.978379	+	0.206822i	$0.933688\pi$
$614$		0			0
$615$	−7.31690	+	0.793243i	−0.295046	+	0.0319866i
$616$		0			0
$617$	26.6415	+	3.83047i	1.07255	+	0.154209i	0.655891	−	0.754856i	$-0.272293\pi$
$617$	26.6415	+	3.83047i	1.07255	+	0.154209i	0.416655	+	0.909065i	$0.363202\pi$
$618$		0			0
$619$	10.5222	+	3.08959i	0.422922	+	0.124181i	0.486266	−	0.873811i	$-0.338358\pi$
$619$	10.5222	+	3.08959i	0.422922	+	0.124181i	−0.0633442	+	0.997992i	$0.520177\pi$
$620$		0			0
$621$	10.5852	+	31.5220i	0.424769	+	1.26493i
$622$		0			0
$623$	−3.66213	+	8.01894i	−0.146720	+	0.321272i
$624$		0			0
$625$	−10.3661	−	22.6987i	−0.414646	−	0.907948i
$626$		0			0
$627$	16.7205	+	15.5396i	0.667753	+	0.620590i
$628$		0			0
$629$	16.1044	−	2.31547i	0.642126	−	0.0923237i
$630$		0			0
$631$	3.61806	+	5.62981i	0.144033	+	0.224119i	0.905773	−	0.423763i	$-0.139291\pi$
$631$	3.61806	+	5.62981i	0.144033	+	0.224119i	−0.761740	+	0.647882i	$0.775655\pi$
$632$		0			0
$633$	−17.0056	+	13.7290i	−0.675912	+	0.545678i
$634$		0			0
$635$	17.7184	+	38.7979i	0.703134	+	1.53965i
$636$		0			0
$637$	−1.57633	−	1.36590i	−0.0624564	−	0.0541188i
$638$		0			0
$639$	−43.6570	+	16.3719i	−1.72705	+	0.647662i
$640$		0			0
$641$	−38.4911			−1.52031			−0.760153	−	0.649744i	$-0.774876\pi$
$641$	−38.4911			−1.52031			−0.760153	+	0.649744i	$0.774876\pi$
$642$		0			0
$643$	−17.8153	+	5.23103i	−0.702565	+	0.206292i	−0.613455	−	0.789730i	$-0.710221\pi$
$643$	−17.8153	+	5.23103i	−0.702565	+	0.206292i	−0.0891106	+	0.996022i	$0.528402\pi$
$644$		0			0
$645$	2.04050	+	18.8216i	0.0803445	+	0.741101i
$646$		0			0
$647$	6.81847	−	14.9304i	0.268062	−	0.586973i	−0.726955	−	0.686685i	$-0.759065\pi$
$647$	6.81847	−	14.9304i	0.268062	−	0.586973i	0.995016	+	0.0997123i	$0.0317923\pi$
$648$		0			0
$649$	1.74168	+	5.93163i	0.0683671	+	0.232837i
$650$		0			0
$651$	−0.621264	+	17.8406i	−0.0243493	+	0.699228i
$652$		0			0
$653$	2.92846	+	20.3679i	0.114599	+	0.797056i	0.963347	+	0.268258i	$0.0864480\pi$
$653$	2.92846	+	20.3679i	0.114599	+	0.797056i	−0.848748	+	0.528798i	$0.822643\pi$
$654$		0			0
$655$	15.7990	+	13.6899i	0.617320	+	0.534911i
$656$		0			0
$657$	−11.2207	+	11.2608i	−0.437761	+	0.439324i
$658$		0			0
$659$	7.65218	−	26.0609i	0.298087	−	1.01519i	−0.665189	−	0.746675i	$-0.731649\pi$
$659$	7.65218	−	26.0609i	0.298087	−	1.01519i	0.963276	−	0.268515i	$-0.0865328\pi$
$660$		0			0
$661$	−0.502433	+	0.435361i	−0.0195424	+	0.0169336i	−0.664577	−	0.747220i	$-0.731388\pi$
$661$	−0.502433	+	0.435361i	−0.0195424	+	0.0169336i	0.645035	+	0.764153i	$0.276843\pi$
$662$		0			0
$663$	1.79081	+	0.321451i	0.0695493	+	0.0124841i
$664$		0			0
$665$	9.91706	−	33.7744i	0.384567	−	1.30972i
$666$		0			0
$667$	−24.0975	+	52.7661i	−0.933057	+	2.04311i
$668$		0			0
$669$	27.5741	−	22.2612i	1.06608	−	0.860667i
$670$		0			0
$671$			17.0359i			0.657665i
$672$		0			0
$673$	−25.8441	−	11.8026i	−0.996218	−	0.454958i	−0.150513	−	0.988608i	$-0.548093\pi$
$673$	−25.8441	−	11.8026i	−0.996218	−	0.454958i	−0.845705	+	0.533650i	$0.820820\pi$
$674$		0			0
$675$	−4.68994	−	25.6028i	−0.180516	−	0.985451i
$676$		0			0
$677$	16.5731	+	19.1264i	0.636956	+	0.735086i	0.978834	−	0.204658i	$-0.0656083\pi$
$677$	16.5731	+	19.1264i	0.636956	+	0.735086i	−0.341878	+	0.939744i	$0.611063\pi$
$678$		0			0
$679$	14.3533	+	16.5646i	0.550830	+	0.635691i
$680$		0			0
$681$	−0.335015	−	0.806763i	−0.0128378	−	0.0309152i
$682$		0			0
$683$	8.34714	+	5.36438i	0.319395	+	0.205262i	0.690507	−	0.723325i	$-0.257387\pi$
$683$	8.34714	+	5.36438i	0.319395	+	0.205262i	−0.371113	+	0.928588i	$0.621024\pi$
$684$		0			0
$685$	−24.8512	+	28.6798i	−0.949515	+	1.09580i
$686$		0			0
$687$	−20.3472	+	21.8935i	−0.776294	+	0.835289i
$688$		0			0
$689$	−0.923324	−	0.800065i	−0.0351758	−	0.0304800i
$690$		0			0
$691$	34.4370	−	10.1116i	1.31005	−	0.384664i	0.449156	−	0.893454i	$-0.351725\pi$
$691$	34.4370	−	10.1116i	1.31005	−	0.384664i	0.860891	+	0.508789i	$0.169907\pi$
$692$		0			0
$693$	5.85629	−	7.85221i	0.222462	−	0.298281i
$694$		0			0
$695$	9.08065	−	14.1298i	0.344449	−	0.535973i
$696$		0			0
$697$	0.808649	+	2.75401i	0.0306298	+	0.104315i
$698$		0			0
$699$	−11.2868	+	9.11204i	−0.426904	+	0.344649i
$700$		0			0
$701$	16.4770	−	10.5891i	0.622329	−	0.399946i	−0.191134	−	0.981564i	$-0.561216\pi$
$701$	16.4770	−	10.5891i	0.622329	−	0.399946i	0.813462	+	0.581618i	$0.197580\pi$
$702$		0			0
$703$	−33.4099	+	38.5571i	−1.26008	+	1.45421i
$704$		0			0
$705$	−12.1997	+	24.4263i	−0.459469	+	0.919949i
$706$		0			0
$707$		−	19.2989i		−	0.725808i
$708$		0			0
$709$	−1.83525	+	1.17944i	−0.0689242	+	0.0442949i	−0.574649	−	0.818400i	$-0.694861\pi$
$709$	−1.83525	+	1.17944i	−0.0689242	+	0.0442949i	0.505725	+	0.862695i	$0.331225\pi$
$710$		0			0
$711$	0.442963	−	6.35247i	0.0166124	−	0.238236i
$712$		0			0
$713$	5.65338	+	39.3202i	0.211721	+	1.47255i
$714$		0			0
$715$	2.78191	−	1.27046i	0.104037	−	0.0475123i
$716$		0			0
$717$	−9.59320	−	37.4465i	−0.358265	−	1.39847i
$718$		0			0
$719$	−38.6622	−	5.55878i	−1.44186	−	0.207308i	−0.623412	−	0.781893i	$-0.714254\pi$
$719$	−38.6622	−	5.55878i	−1.44186	−	0.207308i	−0.818444	+	0.574586i	$0.805163\pi$
$720$		0			0
$721$	6.34832	−	21.6204i	0.236424	−	0.805186i
$722$		0			0
$723$	6.05584	+	10.1859i	0.225219	+	0.378817i
$724$		0			0
$725$	24.5492	−	38.1992i	0.911733	−	1.41868i
$726$		0			0
$727$	32.1464	−	14.6808i	1.19224	−	0.544480i	0.282346	−	0.959313i	$-0.408887\pi$
$727$	32.1464	−	14.6808i	1.19224	−	0.544480i	0.909898	+	0.414833i	$0.136160\pi$
$728$		0			0
$729$	−1.78217	+	26.9411i	−0.0660064	+	0.997819i
$730$		0			0
$731$	7.08427	−	2.08013i	0.262021	−	0.0769364i
$732$		0			0
$733$	38.3382	+	5.51219i	1.41605	+	0.203598i	0.807477	−	0.589899i	$-0.200832\pi$
$733$	38.3382	+	5.51219i	1.41605	+	0.203598i	0.608575	+	0.793496i	$0.291742\pi$
$734$		0			0
$735$	22.8870	+	4.10822i	0.844200	+	0.151534i
$736$		0			0
$737$	−14.2729	−	7.44416i	−0.525748	−	0.274209i
$738$		0			0
$739$	−29.6209	+	25.6666i	−1.08962	+	0.944162i	−0.998663	−	0.0516923i	$-0.983538\pi$
$739$	−29.6209	+	25.6666i	−1.08962	+	0.944162i	−0.0909584	+	0.995855i	$0.528993\pi$
$740$		0			0
$741$	−4.90399	+	2.91558i	−0.180153	+	0.107107i
$742$		0			0
$743$	1.52119	+	5.18069i	0.0558070	+	0.190061i	0.982679	−	0.185317i	$-0.0593311\pi$
$743$	1.52119	+	5.18069i	0.0558070	+	0.190061i	−0.926872	+	0.375378i	$0.877513\pi$
$744$		0			0
$745$	15.1544	+	23.5807i	0.555215	+	0.863931i
$746$		0			0
$747$	−6.48799	−	29.5710i	−0.237383	−	1.08195i
$748$		0			0
$749$	0.247049	+	0.158769i	0.00902698	+	0.00580129i
$750$		0			0
$751$	1.94020	−	13.4944i	0.0707988	−	0.492416i	−0.923312	−	0.384050i	$-0.874529\pi$
$751$	1.94020	−	13.4944i	0.0707988	−	0.492416i	0.994111	−	0.108366i	$-0.0345619\pi$
$752$		0			0
$753$	−19.4120	+	8.06096i	−0.707411	+	0.293758i
$754$		0			0
$755$	0.742604	−	5.16492i	0.0270261	−	0.187971i
$756$		0			0
$757$	−25.7166	−	11.7444i	−0.934685	−	0.426857i	−0.110947	−	0.993826i	$-0.535388\pi$
$757$	−25.7166	−	11.7444i	−0.934685	−	0.426857i	−0.823739	+	0.566970i	$0.808116\pi$
$758$		0			0
$759$	9.73977	−	19.5010i	0.353531	−	0.707840i
$760$		0			0
$761$	23.0095	−	3.30826i	0.834093	−	0.119924i	0.287980	−	0.957636i	$-0.407016\pi$
$761$	23.0095	−	3.30826i	0.834093	−	0.119924i	0.546113	+	0.837712i	$0.316107\pi$
$762$		0			0
$763$	−3.73703	−	25.9916i	−0.135290	−	0.940959i
$764$		0			0
$765$	−18.9919	+	7.12219i	−0.686654	+	0.257503i
$766$		0			0
$767$	−1.54513			−0.0557915
$768$		0			0
$769$	27.0155	−	12.3376i	0.974203	−	0.444904i	0.136267	−	0.990672i	$-0.456490\pi$
$769$	27.0155	−	12.3376i	0.974203	−	0.444904i	0.837936	+	0.545769i	$0.183762\pi$
$770$		0			0
$771$	27.1400	+	0.945100i	0.977424	+	0.0340369i
$772$		0			0
$773$	20.4015	+	31.7453i	0.733791	+	1.14180i	0.984779	+	0.173811i	$0.0556080\pi$
$773$	20.4015	+	31.7453i	0.733791	+	1.14180i	−0.250988	+	0.967990i	$0.580756\pi$
$774$		0			0
$775$		−	31.0955i		−	1.11698i
$776$		0			0
$777$	17.9949	+	12.4703i	0.645564	+	0.447371i
$778$		0			0
$779$	−7.57162	−	4.86598i	−0.271281	−	0.174342i
$780$		0			0
$781$	27.8031	+	12.6973i	0.994874	+	0.454344i
$782$		0			0
$783$	−34.3876	+	32.1880i	−1.22891	+	1.15031i
$784$		0			0
$785$	−15.2834	+	17.6379i	−0.545487	+	0.629525i
$786$		0			0
$787$	20.4159	−	2.93537i	0.727750	−	0.104635i	0.231525	−	0.972829i	$-0.425628\pi$
$787$	20.4159	−	2.93537i	0.727750	−	0.104635i	0.496224	+	0.868194i	$0.334719\pi$
$788$		0			0
$789$	35.3011	+	1.22929i	1.25675	+	0.0437640i
$790$		0			0
$791$	2.32017	−	3.61025i	0.0824956	−	0.128366i
$792$		0			0
$793$	−4.08546	−	1.19960i	−0.145079	−	0.0425990i
$794$		0			0
$795$	13.4059	+	2.40636i	0.475459	+	0.0853449i
$796$		0			0
$797$	−4.80838	+	4.16648i	−0.170321	+	0.147584i	−0.735851	−	0.677144i	$-0.763217\pi$
$797$	−4.80838	+	4.16648i	−0.170321	+	0.147584i	0.565529	+	0.824728i	$0.308672\pi$
$798$		0			0
$799$	10.2169	+	2.99995i	0.361448	+	0.106131i
$800$		0			0
$801$	−9.52310	+	12.7687i	−0.336482	+	0.451161i
$802$		0			0
$803$	10.4210			0.367750
$804$		0			0
$805$	−33.6140			−1.18474
$806$		0			0
$807$	−22.5793	+	5.78445i	−0.794829	+	0.203622i
$808$		0			0
$809$	−35.2824	−	10.3599i	−1.24046	−	0.364233i	−0.405275	−	0.914195i	$-0.632824\pi$
$809$	−35.2824	−	10.3599i	−1.24046	−	0.364233i	−0.835190	+	0.549962i	$0.814642\pi$
$810$		0			0
$811$	−23.6978	+	20.5343i	−0.832142	+	0.721055i	−0.962754	−	0.270378i	$-0.912851\pi$
$811$	−23.6978	+	20.5343i	−0.832142	+	0.721055i	0.130612	+	0.991434i	$0.458306\pi$
$812$		0			0
$813$	−9.89833	+	55.1439i	−0.347150	+	1.93398i
$814$		0			0
$815$	56.2536	+	16.5176i	1.97048	+	0.578585i
$816$		0			0
$817$	−12.5170	+	19.4769i	−0.437915	+	0.681409i
$818$		0			0
$819$	1.47070	+	1.95734i	0.0513903	+	0.0683950i
$820$		0			0
$821$	−38.5856	+	5.54777i	−1.34665	+	0.193618i	−0.777637	−	0.628713i	$-0.783582\pi$
$821$	−38.5856	+	5.54777i	−1.34665	+	0.193618i	−0.569008	+	0.822332i	$0.692673\pi$
$822$		0			0
$823$	−20.3803	+	23.5201i	−0.710412	+	0.819860i	−0.990120	−	0.140226i	$-0.955217\pi$
$823$	−20.3803	+	23.5201i	−0.710412	+	0.819860i	0.279707	+	0.960085i	$0.409763\pi$
$824$		0			0
$825$	−9.71890	+	14.0245i	−0.338369	+	0.488272i
$826$		0			0
$827$	23.5792	+	10.7682i	0.819928	+	0.374449i	0.780796	−	0.624785i	$-0.214814\pi$
$827$	23.5792	+	10.7682i	0.819928	+	0.374449i	0.0391316	+	0.999234i	$0.487541\pi$
$828$		0			0
$829$	42.3710	+	27.2302i	1.47161	+	0.945744i	0.997881	+	0.0650718i	$0.0207276\pi$
$829$	42.3710	+	27.2302i	1.47161	+	0.945744i	0.473726	+	0.880672i	$0.342909\pi$
$830$		0			0
$831$	−17.6225	+	25.4295i	−0.611318	+	0.882141i
$832$		0			0
$833$		−	9.06848i		−	0.314204i
$834$		0			0
$835$	1.78760	+	2.78157i	0.0618626	+	0.0962601i
$836$		0			0
$837$	−7.89349	+	31.2750i	−0.272839	+	1.08102i
$838$		0			0
$839$	5.17316	−	2.36250i	0.178597	−	0.0815626i	−0.324110	−	0.946019i	$-0.605065\pi$
$839$	5.17316	−	2.36250i	0.178597	−	0.0815626i	0.502707	+	0.864457i	$0.332337\pi$
$840$		0			0
$841$	−53.1696			−1.83343
$842$		0			0
$843$	−12.4599	+	37.5477i	−0.429143	+	1.29321i
$844$		0			0
$845$	−5.74443	−	39.9534i	−0.197614	−	1.37444i
$846$		0			0
$847$	11.7214	−	1.68528i	0.402751	−	0.0579068i
$848$		0			0
$849$	−6.32384	−	3.15845i	−0.217034	−	0.108398i
$850$		0			0
$851$	44.3167	+	20.2388i	1.51916	+	0.693776i
$852$		0			0
$853$	−5.34641	+	37.1851i	−0.183058	+	1.27319i	0.666423	+	0.745574i	$0.267825\pi$
$853$	−5.34641	+	37.1851i	−0.183058	+	1.27319i	−0.849481	+	0.527620i	$0.823085\pi$
$854$		0			0
$855$	30.3824	−	55.8776i	1.03905	−	1.91097i
$856$		0			0
$857$	1.31686	−	9.15896i	0.0449831	−	0.312864i	−0.954890	−	0.296958i	$-0.904028\pi$
$857$	1.31686	−	9.15896i	0.0449831	−	0.312864i	0.999873	−	0.0159057i	$-0.00506315\pi$
$858$		0			0
$859$	−11.3383	−	7.28670i	−0.386858	−	0.248619i	0.332726	−	0.943023i	$-0.392031\pi$
$859$	−11.3383	−	7.28670i	−0.386858	−	0.248619i	−0.719585	+	0.694405i	$0.755668\pi$
$860$		0			0
$861$	−1.72577	+	3.45534i	−0.0588142	+	0.117758i
$862$		0			0
$863$	18.7742	+	29.2133i	0.639082	+	0.994431i	0.998131	+	0.0611122i	$0.0194647\pi$
$863$	18.7742	+	29.2133i	0.639082	+	0.994431i	−0.359049	+	0.933319i	$0.616899\pi$
$864$		0			0
$865$	−8.39164	−	28.5793i	−0.285324	−	0.971726i
$866$		0			0
$867$	−11.0049	−	18.5101i	−0.373745	−	0.628636i
$868$		0			0
$869$	−3.15482	+	2.73367i	−0.107020	+	0.0927333i
$870$		0			0
$871$	2.79025	−	2.89865i	0.0945440	−	0.0982170i
$872$		0			0
$873$	19.0420	+	34.7256i	0.644475	+	1.17528i
$874$		0			0
$875$	0.0480524	+	0.00690890i	0.00162447	+	0.000233563i
$876$		0			0
$877$	−15.7737	+	4.63157i	−0.532639	+	0.156397i	−0.536982	−	0.843594i	$-0.680436\pi$
$877$	−15.7737	+	4.63157i	−0.532639	+	0.156397i	0.00434291	+	0.999991i	$0.498618\pi$
$878$		0			0
$879$	−16.5420	−	5.48934i	−0.557948	−	0.185151i
$880$		0			0
$881$	−47.5745	+	21.7265i	−1.60282	+	0.731986i	−0.997929	−	0.0643192i	$-0.979512\pi$
$881$	−47.5745	+	21.7265i	−1.60282	+	0.731986i	−0.604896	+	0.796305i	$0.706785\pi$
$882$		0			0
$883$	3.53273	−	5.49704i	0.118886	−	0.184990i	−0.776710	−	0.629858i	$-0.783113\pi$
$883$	3.53273	−	5.49704i	0.118886	−	0.184990i	0.895596	+	0.444868i	$0.146749\pi$
$884$		0			0
$885$	14.8063	−	8.80285i	0.497710	−	0.295905i
$886$		0			0
$887$	3.77935	−	12.8713i	0.126898	−	0.432176i	−0.871395	−	0.490583i	$-0.836784\pi$
$887$	3.77935	−	12.8713i	0.126898	−	0.432176i	0.998293	+	0.0584071i	$0.0186022\pi$
$888$		0			0
$889$	22.1557	+	3.18551i	0.743079	+	0.106839i
$890$		0			0
$891$	13.3351	−	11.6384i	0.446743	−	0.389901i
$892$		0			0
$893$	−30.3725	+	13.8707i	−1.01638	+	0.464164i
$894$		0			0
$895$	1.32077	+	9.18614i	0.0441484	+	0.307059i
$896$		0			0
$897$	3.99078	+	3.70891i	0.133248	+	0.123837i
$898$		0			0
$899$	−47.3377	+	30.4221i	−1.57880	+	1.01463i
$900$		0			0
$901$		−	5.31180i		−	0.176962i
$902$		0			0
$903$	8.88835	+	4.43929i	0.295786	+	0.147730i
$904$		0			0
$905$	−19.4494	+	22.4459i	−0.646521	+	0.746125i
$906$		0			0
$907$	12.5379	−	8.05759i	0.416313	−	0.267548i	−0.315673	−	0.948868i	$-0.602230\pi$
$907$	12.5379	−	8.05759i	0.416313	−	0.267548i	0.731985	+	0.681320i	$0.238594\pi$
$908$		0			0
$909$	7.35167	−	34.0874i	0.243839	−	1.13061i
$910$		0			0
$911$	−5.82720	−	19.8456i	−0.193064	−	0.657515i	−0.997945	−	0.0640789i	$-0.979589\pi$
$911$	−5.82720	−	19.8456i	−0.193064	−	0.657515i	0.804881	−	0.593436i	$-0.202229\pi$
$912$		0			0
$913$	−10.7296	+	16.6956i	−0.355099	+	0.552545i
$914$		0			0
$915$	45.9835	−	11.7802i	1.52017	−	0.389443i
$916$		0			0
$917$	10.5264	−	3.09084i	0.347613	−	0.102068i
$918$		0			0
$919$	−1.75998	−	1.52503i	−0.0580563	−	0.0503060i	0.625349	−	0.780345i	$-0.284956\pi$
$919$	−1.75998	−	1.52503i	−0.0580563	−	0.0503060i	−0.683406	+	0.730039i	$0.739502\pi$
$920$		0			0
$921$	−16.9690	−	15.7705i	−0.559146	−	0.519654i
$922$		0			0
$923$	−5.00276	+	5.77350i	−0.164668	+	0.190037i
$924$		0			0
$925$	−32.0824	−	20.6181i	−1.05486	−	0.677920i
$926$		0			0
$927$	19.4490	−	35.7696i	0.638789	−	1.17483i
$928$		0			0
$929$	11.6187	+	13.4087i	0.381197	+	0.439925i	0.913630	−	0.406548i	$-0.133267\pi$
$929$	11.6187	+	13.4087i	0.381197	+	0.439925i	−0.532433	+	0.846472i	$0.678722\pi$
$930$		0			0
$931$	18.6218	+	21.4907i	0.610305	+	0.704329i
$932$		0			0
$933$	42.1369	−	17.4977i	1.37950	−	0.572848i
$934$		0			0
$935$	12.0951	+	5.52363i	0.395551	+	0.180642i
$936$		0			0
$937$		−	10.8302i		−	0.353808i	−0.984228	−	0.176904i	$-0.943392\pi$
$937$		−	10.8302i		−	0.353808i	0.984228	−	0.176904i	$-0.0566082\pi$
$938$		0			0
$939$	10.1231	+	12.5391i	0.330354	+	0.409197i
$940$		0			0
$941$	21.5369	−	47.1593i	0.702083	−	1.53735i	−0.135344	−	0.990799i	$-0.543214\pi$
$941$	21.5369	−	47.1593i	0.702083	−	1.53735i	0.837427	−	0.546549i	$-0.184059\pi$
$942$		0			0
$943$	−2.42144	+	8.24666i	−0.0788529	+	0.268548i
$944$		0			0
$945$	−25.2443	−	10.3776i	−0.821198	−	0.337583i
$946$		0			0
$947$	19.8133	−	17.1683i	0.643845	−	0.557895i	−0.270556	−	0.962704i	$-0.587207\pi$
$947$	19.8133	−	17.1683i	0.643845	−	0.557895i	0.914401	+	0.404809i	$0.132662\pi$
$948$		0			0
$949$	−0.733805	+	2.49911i	−0.0238203	+	0.0811245i
$950$		0			0
$951$	−5.64820	−	52.0992i	−0.183155	−	1.68943i
$952$		0			0
$953$	−39.9486	−	34.6157i	−1.29406	−	1.12131i	−0.985421	−	0.170132i	$-0.945581\pi$
$953$	−39.9486	−	34.6157i	−1.29406	−	1.12131i	−0.308641	−	0.951179i	$-0.599874\pi$
$954$		0			0
$955$	0.566203	+	3.93803i	0.0183219	+	0.127432i
$956$		0			0
$957$	30.8585	+	1.07459i	0.997514	+	0.0347365i
$958$		0			0
$959$	5.61076	+	19.1085i	0.181181	+	0.617045i
$960$		0			0
$961$	−3.12995	+	6.85364i	−0.100966	+	0.221085i
$962$		0			0
$963$	0.375879	+	0.374542i	0.0121125	+	0.0120695i
$964$		0			0
$965$	10.0692	−	2.95659i	0.324140	−	0.0951761i
$966$		0			0
$967$	−21.5661			−0.693519			−0.346760	−	0.937954i	$-0.612718\pi$
$967$	−21.5661			−0.693519			−0.346760	+	0.937954i	$0.612718\pi$
$968$		0			0
$969$	−23.5426	−	7.81244i	−0.756297	−	0.250972i
$970$		0			0
$971$	−5.62422	−	4.87341i	−0.180490	−	0.156395i	0.559930	−	0.828540i	$-0.310828\pi$
$971$	−5.62422	−	4.87341i	−0.180490	−	0.156395i	−0.740420	+	0.672145i	$0.765373\pi$
$972$		0			0
$973$	−3.66165	−	8.01789i	−0.117387	−	0.257042i
$974$		0			0
$975$	−2.67892	−	3.31828i	−0.0857940	−	0.106270i
$976$		0			0
$977$	−33.2762	−	51.7787i	−1.06460	−	1.65655i	−0.679504	−	0.733672i	$-0.737805\pi$
$977$	−33.2762	−	51.7787i	−1.06460	−	1.65655i	−0.385095	−	0.922877i	$-0.625831\pi$
$978$		0			0
$979$	10.3358	−	1.48606i	0.330333	−	0.0474947i
$980$		0			0
$981$	3.30051	−	47.3323i	0.105377	−	1.51120i
$982$		0			0
$983$	16.6720	+	36.5065i	0.531754	+	1.16438i	0.964795	+	0.263004i	$0.0847132\pi$
$983$	16.6720	+	36.5065i	0.531754	+	1.16438i	−0.433041	+	0.901374i	$0.642560\pi$
$984$		0			0
$985$	−25.3010	+	55.4015i	−0.806157	+	1.76524i
$986$		0			0
$987$	7.32244	+	12.3163i	0.233076	+	0.392032i
$988$		0			0
$989$	21.2133	+	6.22879i	0.674544	+	0.198064i
$990$		0			0
$991$	29.9842	+	4.31108i	0.952481	+	0.136946i	0.601000	−	0.799249i	$-0.294769\pi$
$991$	29.9842	+	4.31108i	0.952481	+	0.136946i	0.351481	+	0.936195i	$0.385678\pi$
$992$		0			0
$993$	−4.61318	−	42.5522i	−0.146395	−	1.35035i
$994$		0			0
$995$	31.4769	+	68.9249i	0.997886	+	2.18506i
$996$		0			0
$997$	31.4100	−	20.1860i	0.994764	−	0.639296i	0.0613569	−	0.998116i	$-0.480457\pi$
$997$	31.4100	−	20.1860i	0.994764	−	0.639296i	0.933407	+	0.358820i	$0.116821\pi$
$998$		0			0
$999$	27.0338	+	28.8812i	0.855311	+	0.913760i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.s.b.161.13	yes	200
3.2	odd	2	inner	804.2.s.b.161.18	yes	200
67.5	odd	22	inner	804.2.s.b.5.18	yes	200
201.5	even	22	inner	804.2.s.b.5.13	✓	200

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.s.b.5.13	✓	200	201.5	even	22	inner
804.2.s.b.5.18	yes	200	67.5	odd	22	inner
804.2.s.b.161.13	yes	200	1.1	even	1	trivial
804.2.s.b.161.18	yes	200	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.429842 + 1.67787i) q^{3} +(-3.03558 - 0.891328i) q^{5} +(-1.25477 + 1.08727i) q^{7} +(-2.63047 + 1.44244i) q^{9} +O(q^{10})\)	\(q+(0.429842 + 1.67787i) q^{3} +(-3.03558 - 0.891328i) q^{5} +(-1.25477 + 1.08727i) q^{7} +(-2.63047 + 1.44244i) q^{9} +(1.88696 + 0.554063i) q^{11} +(-0.265744 + 0.413506i) q^{13} +(0.190706 - 5.47644i) q^{15} +(-2.11532 + 0.304138i) q^{17} +(4.38841 - 5.06450i) q^{19} +(-2.36364 - 1.63799i) q^{21} +(-5.82102 - 2.65837i) q^{23} +(4.21404 + 2.70820i) q^{25} +(-3.55090 - 3.79356i) q^{27} -9.06475i q^{29} +(-3.35609 - 5.22218i) q^{31} +(-0.118546 + 3.40423i) q^{33} +(4.77808 - 2.18207i) q^{35} -7.61322 q^{37} +(-0.808036 - 0.268141i) q^{39} +(-0.191141 - 1.32941i) q^{41} +(-3.41972 + 0.491681i) q^{43} +(9.27070 - 2.03402i) q^{45} +(-4.53234 - 2.06985i) q^{47} +(-0.603899 + 4.20021i) q^{49} +(-1.41956 - 3.41850i) q^{51} +(-0.353730 + 2.46024i) q^{53} +(-5.23419 - 3.36381i) q^{55} +(10.3839 + 5.18623i) q^{57} +(1.69949 + 2.64446i) q^{59} +(2.44051 + 8.31163i) q^{61} +(1.73233 - 4.66995i) q^{63} +(1.17526 - 1.01837i) q^{65} +(-8.02999 - 1.58723i) q^{67} +(1.95827 - 10.9096i) q^{69} +(15.3838 + 2.21185i) q^{71} +(5.08429 - 1.49288i) q^{73} +(-2.73262 + 8.23470i) q^{75} +(-2.97012 + 1.35641i) q^{77} +(-1.14758 + 1.78567i) q^{79} +(4.83876 - 7.58857i) q^{81} +(-2.84309 + 9.68269i) q^{83} +(6.69233 + 0.962212i) q^{85} +(15.2094 - 3.89641i) q^{87} +(4.82981 - 2.20570i) q^{89} +(-0.116143 - 0.807790i) q^{91} +(7.31953 - 7.87579i) q^{93} +(-17.8355 + 11.4622i) q^{95} -13.2013i q^{97} +(-5.76280 + 1.26438i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 200 q - 10 q^{9}+O(q^{10}) \) 200 * q - 10 * q^9	\( 200 q - 10 q^{9} + 2 q^{15} + 6 q^{19} - 10 q^{21} - 20 q^{25} - 44 q^{31} - 5 q^{33} + 78 q^{39} - 22 q^{43} - 22 q^{45} - 16 q^{49} + 36 q^{55} + 66 q^{57} + 176 q^{61} + 132 q^{63} + 46 q^{67} - 26 q^{73} - 165 q^{75} - 44 q^{79} + 42 q^{81} - 66 q^{87} - 20 q^{91} + 84 q^{93} - 55 q^{99}+O(q^{100}) \) 200 * q - 10 * q^9 + 2 * q^15 + 6 * q^19 - 10 * q^21 - 20 * q^25 - 44 * q^31 - 5 * q^33 + 78 * q^39 - 22 * q^43 - 22 * q^45 - 16 * q^49 + 36 * q^55 + 66 * q^57 + 176 * q^61 + 132 * q^63 + 46 * q^67 - 26 * q^73 - 165 * q^75 - 44 * q^79 + 42 * q^81 - 66 * q^87 - 20 * q^91 + 84 * q^93 - 55 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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