LMFDB - Embedded newform 804.2.ba.b.41.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(41,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 33, 53]))

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

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

chi := DirichletCharacter("804.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.ba (of order $66$, degree $20$, 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:	$440$
Relative dimension:	$22$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			41.9
Character	$\chi$	$=$	804.41
Dual form			804.2.ba.b.353.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.709719 - 1.57997i) q^{3} +(0.569745 - 3.96266i) q^{5} +(0.363865 + 3.81057i) q^{7} +(-1.99260 + 2.24267i) q^{9} +O(q^{10})$	\(q+(-0.709719 - 1.57997i) q^{3} +(0.569745 - 3.96266i) q^{5} +(0.363865 + 3.81057i) q^{7} +(-1.99260 + 2.24267i) q^{9} +(-4.23450 + 1.69524i) q^{11} +(-3.77004 - 3.95391i) q^{13} +(-6.66524 + 1.91220i) q^{15} +(6.20169 - 2.14643i) q^{17} +(-6.82859 - 0.652051i) q^{19} +(5.76233 - 3.27933i) q^{21} +(0.473873 - 0.0225734i) q^{23} +(-10.5806 - 3.10675i) q^{25} +(4.95752 + 1.55658i) q^{27} +(-7.56004 + 4.36479i) q^{29} +(-0.649047 + 0.680701i) q^{31} +(5.68373 + 5.48724i) q^{33} +(15.3073 + 0.729177i) q^{35} +(-0.455768 + 0.789413i) q^{37} +(-3.57138 + 8.76271i) q^{39} +(0.877682 + 0.169159i) q^{41} +(0.287793 + 0.249374i) q^{43} +(7.75166 + 9.17375i) q^{45} +(1.32173 - 2.56380i) q^{47} +(-7.51452 + 1.44831i) q^{49} +(-7.79274 - 8.27512i) q^{51} +(2.31995 + 2.67736i) q^{53} +(4.30508 + 17.7458i) q^{55} +(3.81616 + 11.2517i) q^{57} +(-2.25065 - 7.66500i) q^{59} +(0.666695 - 1.66532i) q^{61} +(-9.27086 - 6.77690i) q^{63} +(-17.8160 + 12.6867i) q^{65} +(-2.35801 + 7.83835i) q^{67} +(-0.371982 - 0.732684i) q^{69} +(-0.304090 - 0.105247i) q^{71} +(-3.59390 - 1.43878i) q^{73} +(2.60070 + 18.9220i) q^{75} +(-8.00061 - 15.5190i) q^{77} +(1.01436 - 0.246082i) q^{79} +(-1.05910 - 8.93747i) q^{81} +(7.37794 - 9.38182i) q^{83} +(-4.97218 - 25.7981i) q^{85} +(12.2617 + 8.84685i) q^{87} +(1.27636 - 1.98605i) q^{89} +(13.6948 - 15.8047i) q^{91} +(1.53613 + 0.542368i) q^{93} +(-6.47442 + 26.6879i) q^{95} +(-13.0824 - 7.55312i) q^{97} +(4.63581 - 12.8745i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 440 q - 12 q^{7} + 4 q^{9}+O(q^{10}) $ 440 * q - 12 * q^7 + 4 * q^9	$ 440 q - 12 q^{7} + 4 q^{9} - 2 q^{15} - 10 q^{19} + 22 q^{21} - 68 q^{25} + 50 q^{31} + 11 q^{33} - 22 q^{37} - 45 q^{39} + 22 q^{43} + 22 q^{45} - 18 q^{49} - 6 q^{51} + 126 q^{55} - 183 q^{57} - 56 q^{61} - 141 q^{63} - 12 q^{67} + 33 q^{69} + 356 q^{73} + 165 q^{75} + 228 q^{79} + 24 q^{81} - 6 q^{85} + 75 q^{87} - 4 q^{91} - 75 q^{93} + 12 q^{97} + 88 q^{99}+O(q^{100}) $ 440 * q - 12 * q^7 + 4 * q^9 - 2 * q^15 - 10 * q^19 + 22 * q^21 - 68 * q^25 + 50 * q^31 + 11 * q^33 - 22 * q^37 - 45 * q^39 + 22 * q^43 + 22 * q^45 - 18 * q^49 - 6 * q^51 + 126 * q^55 - 183 * q^57 - 56 * q^61 - 141 * q^63 - 12 * q^67 + 33 * q^69 + 356 * q^73 + 165 * q^75 + 228 * q^79 + 24 * q^81 - 6 * q^85 + 75 * q^87 - 4 * q^91 - 75 * q^93 + 12 * q^97 + 88 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$269$	$337$	$403$
$\chi(n)$	$-1$	$e\left(\frac{53}{66}\right)$	$1$

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
$3$	−0.709719	−	1.57997i	−0.409756	−	0.912195i
$3$	−0.709719	−	1.57997i	−0.409756	−	0.912195i
$4$		0			0
$5$	0.569745	−	3.96266i	0.254798	−	1.77216i	−0.313749	−	0.949506i	$-0.601585\pi$
$5$	0.569745	−	3.96266i	0.254798	−	1.77216i	0.568547	−	0.822651i	$-0.307506\pi$
$6$		0			0
$7$	0.363865	+	3.81057i	0.137528	+	1.44026i	0.756062	+	0.654501i	$0.227121\pi$
$7$	0.363865	+	3.81057i	0.137528	+	1.44026i	−0.618533	+	0.785758i	$0.712273\pi$
$8$		0			0
$9$	−1.99260	+	2.24267i	−0.664200	+	0.747555i
$10$		0			0
$11$	−4.23450	+	1.69524i	−1.27675	+	0.511134i	−0.908224	−	0.418484i	$-0.862562\pi$
$11$	−4.23450	+	1.69524i	−1.27675	+	0.511134i	−0.368526	+	0.929617i	$0.620137\pi$
$12$		0			0
$13$	−3.77004	−	3.95391i	−1.04562	−	1.09662i	−0.995197	−	0.0978884i	$-0.968791\pi$
$13$	−3.77004	−	3.95391i	−1.04562	−	1.09662i	−0.0504242	−	0.998728i	$-0.516057\pi$
$14$		0			0
$15$	−6.66524	+	1.91220i	−1.72096	+	0.493727i
$16$		0			0
$17$	6.20169	−	2.14643i	1.50413	−	0.520585i	0.554022	−	0.832502i	$-0.313092\pi$
$17$	6.20169	−	2.14643i	1.50413	−	0.520585i	0.950109	+	0.311917i	$0.100971\pi$
$18$		0			0
$19$	−6.82859	−	0.652051i	−1.56659	−	0.149591i	−0.724630	−	0.689138i	$-0.757990\pi$
$19$	−6.82859	−	0.652051i	−1.56659	−	0.149591i	−0.841956	+	0.539547i	$0.818596\pi$
$20$		0			0
$21$	5.76233	−	3.27933i	1.25744	−	0.715607i
$22$		0			0
$23$	0.473873	−	0.0225734i	0.0988094	−	0.00470687i	0.00188104	−	0.999998i	$-0.499401\pi$
$23$	0.473873	−	0.0225734i	0.0988094	−	0.00470687i	0.0969284	+	0.995291i	$0.469098\pi$
$24$		0			0
$25$	−10.5806	−	3.10675i	−2.11613	−	0.621351i
$26$		0			0
$27$	4.95752	+	1.55658i	0.954076	+	0.299564i
$28$		0			0
$29$	−7.56004	+	4.36479i	−1.40386	+	0.810521i	−0.994787	−	0.101978i	$-0.967483\pi$
$29$	−7.56004	+	4.36479i	−1.40386	+	0.810521i	−0.409077	+	0.912500i	$0.634149\pi$
$30$		0			0
$31$	−0.649047	+	0.680701i	−0.116572	+	0.122258i	−0.779434	−	0.626484i	$-0.784493\pi$
$31$	−0.649047	+	0.680701i	−0.116572	+	0.122258i	0.662862	+	0.748742i	$0.269342\pi$
$32$		0			0
$33$	5.68373	+	5.48724i	0.989410	+	0.955205i
$34$		0			0
$35$	15.3073	+	0.729177i	2.58741	+	0.123253i
$36$		0			0
$37$	−0.455768	+	0.789413i	−0.0749278	+	0.129779i	−0.901055	−	0.433705i	$-0.857206\pi$
$37$	−0.455768	+	0.789413i	−0.0749278	+	0.129779i	0.826127	+	0.563484i	$0.190539\pi$
$38$		0			0
$39$	−3.57138	+	8.76271i	−0.571878	+	1.40316i
$40$		0			0
$41$	0.877682	+	0.169159i	0.137071	+	0.0264182i	0.257325	−	0.966325i	$-0.417159\pi$
$41$	0.877682	+	0.169159i	0.137071	+	0.0264182i	−0.120254	+	0.992743i	$0.538371\pi$
$42$		0			0
$43$	0.287793	+	0.249374i	0.0438880	+	0.0380292i	0.676529	−	0.736416i	$-0.263483\pi$
$43$	0.287793	+	0.249374i	0.0438880	+	0.0380292i	−0.632641	+	0.774446i	$0.718029\pi$
$44$		0			0
$45$	7.75166	+	9.17375i	1.15555	+	1.36754i
$46$		0			0
$47$	1.32173	−	2.56380i	0.192794	−	0.373969i	−0.772548	−	0.634957i	$-0.781018\pi$
$47$	1.32173	−	2.56380i	0.192794	−	0.373969i	0.965342	+	0.260988i	$0.0840483\pi$
$48$		0			0
$49$	−7.51452	+	1.44831i	−1.07350	+	0.206901i
$50$		0			0
$51$	−7.79274	−	8.27512i	−1.09120	−	1.15875i
$52$		0			0
$53$	2.31995	+	2.67736i	0.318669	+	0.367764i	0.892373	−	0.451299i	$-0.149039\pi$
$53$	2.31995	+	2.67736i	0.318669	+	0.367764i	−0.573703	+	0.819063i	$0.694494\pi$
$54$		0			0
$55$	4.30508	+	17.7458i	0.580496	+	2.39284i
$56$		0			0
$57$	3.81616	+	11.2517i	0.505462	+	1.49033i
$58$		0			0
$59$	−2.25065	−	7.66500i	−0.293009	−	0.997898i	−0.966063	−	0.258305i	$-0.916836\pi$
$59$	−2.25065	−	7.66500i	−0.293009	−	0.997898i	0.673054	−	0.739593i	$-0.264982\pi$
$60$		0			0
$61$	0.666695	−	1.66532i	0.0853616	−	0.213223i	−0.879545	−	0.475815i	$-0.842153\pi$
$61$	0.666695	−	1.66532i	0.0853616	−	0.213223i	0.964907	+	0.262592i	$0.0845774\pi$
$62$		0			0
$63$	−9.27086	−	6.77690i	−1.16802	−	0.853810i
$64$		0			0
$65$	−17.8160	+	12.6867i	−2.20980	+	1.57359i
$66$		0			0
$67$	−2.35801	+	7.83835i	−0.288077	+	0.957607i
$67$	−2.35801	+	7.83835i	−0.288077	+	0.957607i
$68$		0			0
$69$	−0.371982	−	0.732684i	−0.0447814	−	0.0882048i
$70$		0			0
$71$	−0.304090	−	0.105247i	−0.0360889	−	0.0124905i	0.308964	−	0.951074i	$-0.400018\pi$
$71$	−0.304090	−	0.105247i	−0.0360889	−	0.0124905i	−0.345053	+	0.938583i	$0.612139\pi$
$72$		0			0
$73$	−3.59390	−	1.43878i	−0.420634	−	0.168396i	0.151683	−	0.988429i	$-0.451531\pi$
$73$	−3.59390	−	1.43878i	−0.420634	−	0.168396i	−0.572316	+	0.820033i	$0.693955\pi$
$74$		0			0
$75$	2.60070	+	18.9220i	0.300303	+	2.18492i
$76$		0			0
$77$	−8.00061	−	15.5190i	−0.911754	−	1.76856i
$78$		0			0
$79$	1.01436	−	0.246082i	0.114125	−	0.0276864i	−0.178290	−	0.983978i	$-0.557056\pi$
$79$	1.01436	−	0.246082i	0.114125	−	0.0276864i	0.292415	+	0.956292i	$0.405541\pi$
$80$		0			0
$81$	−1.05910	−	8.93747i	−0.117678	−	0.993052i
$82$		0			0
$83$	7.37794	−	9.38182i	0.809835	−	1.02979i	−0.189022	−	0.981973i	$-0.560532\pi$
$83$	7.37794	−	9.38182i	0.809835	−	1.02979i	0.998856	−	0.0478154i	$-0.0152259\pi$
$84$		0			0
$85$	−4.97218	−	25.7981i	−0.539309	−	2.79820i
$86$		0			0
$87$	12.2617	+	8.84685i	1.31460	+	0.948482i
$88$		0			0
$89$	1.27636	−	1.98605i	0.135294	−	0.210521i	−0.766995	−	0.641653i	$-0.778249\pi$
$89$	1.27636	−	1.98605i	0.135294	−	0.210521i	0.902289	+	0.431131i	$0.141885\pi$
$90$		0			0
$91$	13.6948	−	15.8047i	1.43561	−	1.65678i
$92$		0			0
$93$	1.53613	+	0.542368i	0.159289	+	0.0562409i
$94$		0			0
$95$	−6.47442	+	26.6879i	−0.664261	+	2.73812i
$96$		0			0
$97$	−13.0824	−	7.55312i	−1.32831	−	0.766903i	−0.343275	−	0.939235i	$-0.611536\pi$
$97$	−13.0824	−	7.55312i	−1.32831	−	0.766903i	−0.985039	+	0.172332i	$0.944870\pi$
$98$		0			0
$99$	4.63581	−	12.8745i	0.465917	−	1.29394i
$100$		0			0
$101$	8.64998	−	12.1472i	0.860705	−	1.20869i	−0.115816	−	0.993271i	$-0.536948\pi$
$101$	8.64998	−	12.1472i	0.860705	−	1.20869i	0.976521	−	0.215421i	$-0.0691123\pi$
$102$		0			0
$103$	−2.77344	−	2.64447i	−0.273275	−	0.260568i	0.541031	−	0.841002i	$-0.318034\pi$
$103$	−2.77344	−	2.64447i	−0.273275	−	0.260568i	−0.814307	+	0.580435i	$0.802883\pi$
$104$		0			0
$105$	−9.71180	−	24.7026i	−0.947775	−	2.41072i
$106$		0			0
$107$	−9.27796	+	1.33397i	−0.896935	+	0.128960i	−0.575337	−	0.817917i	$-0.695129\pi$
$107$	−9.27796	+	1.33397i	−0.896935	+	0.128960i	−0.321598	+	0.946876i	$0.604220\pi$
$108$		0			0
$109$	−1.85530	+	6.31856i	−0.177705	+	0.605208i	0.821673	+	0.569959i	$0.193041\pi$
$109$	−1.85530	+	6.31856i	−0.177705	+	0.605208i	−0.999379	+	0.0352495i	$0.988777\pi$
$110$		0			0
$111$	1.57071	+	0.159838i	0.149086	+	0.0151711i
$112$		0			0
$113$	−1.89021	+	1.48648i	−0.177816	+	0.139836i	−0.703100	−	0.711091i	$-0.748201\pi$
$113$	−1.89021	+	1.48648i	−0.177816	+	0.139836i	0.525284	+	0.850927i	$0.323959\pi$
$114$		0			0
$115$	0.180536	−	1.89066i	0.0168351	−	0.176305i
$116$		0			0
$117$	16.3795	−	0.576394i	1.51428	−	0.0532876i
$118$		0			0
$119$	10.4357	+	22.8510i	0.956637	+	2.09474i
$120$		0			0
$121$	7.09610	−	6.76612i	0.645100	−	0.615102i
$122$		0			0
$123$	−0.355641	−	1.50676i	−0.0320670	−	0.135860i
$124$		0			0
$125$	−10.0239	+	21.9493i	−0.896564	+	1.96320i
$126$		0			0
$127$	−9.16081	+	0.874751i	−0.812890	+	0.0776216i	−0.493217	−	0.869906i	$-0.664179\pi$
$127$	−9.16081	+	0.874751i	−0.812890	+	0.0776216i	−0.319673	+	0.947528i	$0.603573\pi$
$128$		0			0
$129$	0.189751	−	0.631689i	0.0167067	−	0.0556171i
$130$		0			0
$131$	−6.10471	−	9.49911i	−0.533371	−	0.829941i	0.465098	−	0.885259i	$-0.346019\pi$
$131$	−6.10471	−	9.49911i	−0.533371	−	0.829941i	−0.998469	+	0.0553182i	$0.982383\pi$
$132$		0			0
$133$		−	26.2581i		−	2.27686i
$134$		0			0
$135$	8.99273	−	18.7581i	0.773971	−	1.61444i
$136$		0			0
$137$	6.28180	−	4.03707i	0.536690	−	0.344910i	−0.244053	−	0.969762i	$-0.578477\pi$
$137$	6.28180	−	4.03707i	0.536690	−	0.344910i	0.780743	+	0.624852i	$0.214841\pi$
$138$		0			0
$139$	17.1347	+	2.46360i	1.45335	+	0.208960i	0.823305	−	0.567600i	$-0.192128\pi$
$139$	17.1347	+	2.46360i	1.45335	+	0.208960i	0.630044	+	0.776560i	$0.283037\pi$
$140$		0			0
$141$	−4.98878	−	0.268716i	−0.420131	−	0.0226300i
$142$		0			0
$143$	22.6671	+	10.3517i	1.89552	+	0.865653i
$144$		0			0
$145$	12.9889	+	32.4447i	1.07867	+	2.69439i
$146$		0			0
$147$	7.62147	+	10.8448i	0.628608	+	0.894465i
$148$		0			0
$149$	6.30772	−	2.88064i	0.516749	−	0.235991i	−0.139930	−	0.990161i	$-0.544688\pi$
$149$	6.30772	−	2.88064i	0.516749	−	0.235991i	0.656679	+	0.754170i	$0.271961\pi$
$150$		0			0
$151$	−3.12993	−	9.04333i	−0.254710	−	0.735936i	−0.997772	−	0.0667138i	$-0.978749\pi$
$151$	−3.12993	−	9.04333i	−0.254710	−	0.735936i	0.743062	−	0.669222i	$-0.233373\pi$
$152$		0			0
$153$	−7.54377	+	18.1853i	−0.609878	+	1.47019i
$154$		0			0
$155$	2.32760	+	2.95978i	0.186957	+	0.237735i
$156$		0			0
$157$	0.0258516	+	0.542692i	0.00206318	+	0.0433116i	0.999664	−	0.0259150i	$-0.00824991\pi$
$157$	0.0258516	+	0.542692i	0.00206318	+	0.0433116i	−0.997601	+	0.0692265i	$0.977947\pi$
$158$		0			0
$159$	2.58364	−	5.56562i	0.204896	−	0.441382i
$160$		0			0
$161$	0.258443	+	1.79751i	0.0203682	+	0.141664i
$162$		0			0
$163$	1.36123	+	2.35772i	0.106620	+	0.184671i	0.914399	−	0.404815i	$-0.132664\pi$
$163$	1.36123	+	2.35772i	0.106620	+	0.184671i	−0.807779	+	0.589485i	$0.799331\pi$
$164$		0			0
$165$	24.9823	−	19.3964i	1.94487	−	1.51001i
$166$		0			0
$167$	−13.3168	−	9.48282i	−1.03048	−	0.733803i	−0.0659645	−	0.997822i	$-0.521012\pi$
$167$	−13.3168	−	9.48282i	−1.03048	−	0.733803i	−0.964517	+	0.264019i	$0.914952\pi$
$168$		0			0
$169$	−0.801593	+	16.8275i	−0.0616610	+	1.29442i
$170$		0			0
$171$	15.0690	−	14.0150i	1.15235	−	1.07175i
$172$		0			0
$173$	−13.3200	−	3.23140i	−1.01270	−	0.245679i	−0.305123	−	0.952313i	$-0.598698\pi$
$173$	−13.3200	−	3.23140i	−1.01270	−	0.245679i	−0.707579	+	0.706634i	$0.750213\pi$
$174$		0			0
$175$	7.98857	−	41.4486i	0.603879	−	3.13322i
$176$		0			0
$177$	−10.5131	+	8.99594i	−0.790215	+	0.676176i
$178$		0			0
$179$	3.78598	+	2.43310i	0.282977	+	0.181858i	0.674428	−	0.738341i	$-0.264390\pi$
$179$	3.78598	+	2.43310i	0.282977	+	0.181858i	−0.391451	+	0.920199i	$0.628027\pi$
$180$		0			0
$181$	2.98907	+	1.54097i	0.222176	+	0.114540i	0.565722	−	0.824596i	$-0.308598\pi$
$181$	2.98907	+	1.54097i	0.222176	+	0.114540i	−0.343546	+	0.939136i	$0.611628\pi$
$182$		0			0
$183$	−3.10432	+	0.128554i	−0.229478	+	0.00950300i
$184$		0			0
$185$	2.86851	+	2.25582i	0.210897	+	0.165851i
$186$		0			0
$187$	−22.6224	+	19.6024i	−1.65431	+	1.43347i
$188$		0			0
$189$	−4.12759	+	19.4574i	−0.300238	+	1.41532i
$190$		0			0
$191$	−7.89943	+	4.07244i	−0.571583	+	0.294671i	−0.719685	−	0.694301i	$-0.755714\pi$
$191$	−7.89943	+	4.07244i	−0.571583	+	0.294671i	0.148102	+	0.988972i	$0.452683\pi$
$192$		0			0
$193$	2.52896	−	0.742570i	0.182039	−	0.0534514i	−0.189443	−	0.981892i	$-0.560668\pi$
$193$	2.52896	−	0.742570i	0.182039	−	0.0534514i	0.371481	+	0.928440i	$0.378850\pi$
$194$		0			0
$195$	32.6889	+	19.1447i	2.34090	+	1.37098i
$196$		0			0
$197$	4.11304	−	11.8839i	0.293042	−	0.846690i	−0.698349	−	0.715757i	$-0.746082\pi$
$197$	4.11304	−	11.8839i	0.293042	−	0.846690i	0.991391	−	0.130933i	$-0.0417971\pi$
$198$		0			0
$199$	−5.40198	−	7.58602i	−0.382936	−	0.537759i	0.577452	−	0.816425i	$-0.304047\pi$
$199$	−5.40198	−	7.58602i	−0.382936	−	0.537759i	−0.960388	+	0.278666i	$0.910108\pi$
$200$		0			0
$201$	14.0579	−	1.83745i	0.991566	−	0.129604i
$202$		0			0
$203$	−19.3832	−	27.2198i	−1.36043	−	1.91046i
$204$		0			0
$205$	1.17038	−	3.38158i	0.0817426	−	0.236180i
$206$		0			0
$207$	−0.893615	+	1.10772i	−0.0621105	+	0.0769918i
$208$		0			0
$209$	30.0211	−	8.81498i	2.07660	−	0.609745i
$210$		0			0
$211$	−8.13656	+	4.19469i	−0.560144	+	0.288774i	−0.714956	−	0.699170i	$-0.753553\pi$
$211$	−8.13656	+	4.19469i	−0.560144	+	0.288774i	0.154812	+	0.987944i	$0.450523\pi$
$212$		0			0
$213$	0.0495321	+	0.555148i	0.00339388	+	0.0380381i
$214$		0			0
$215$	1.15215	−	0.998347i	0.0785763	−	0.0680867i
$216$		0			0
$217$	−2.83002	−	2.22555i	−0.192114	−	0.151080i
$218$		0			0
$219$	0.277430	+	6.69937i	0.0187470	+	0.452702i
$220$		0			0
$221$	−31.8674	−	16.4288i	−2.14363	−	1.10512i
$222$		0			0
$223$	20.3495	+	13.0778i	1.36270	+	0.875755i	0.998456	−	0.0555480i	$-0.0176906\pi$
$223$	20.3495	+	13.0778i	1.36270	+	0.875755i	0.364245	+	0.931303i	$0.381327\pi$
$224$		0			0
$225$	28.0504	−	17.5383i	1.87002	−	1.16922i
$226$		0			0
$227$	3.78530	−	19.6400i	0.251239	−	1.30355i	−0.608799	−	0.793324i	$-0.708348\pi$
$227$	3.78530	−	19.6400i	0.251239	−	1.30355i	0.860038	−	0.510229i	$-0.170439\pi$
$228$		0			0
$229$	−6.67849	−	1.62018i	−0.441327	−	0.107065i	0.00893740	−	0.999960i	$-0.497155\pi$
$229$	−6.67849	−	1.62018i	−0.441327	−	0.107065i	−0.450264	+	0.892895i	$0.648670\pi$
$230$		0			0
$231$	−18.8414	+	23.6548i	−1.23967	+	1.55637i
$232$		0			0
$233$	1.02952	−	21.6122i	0.0674458	−	1.41586i	−0.670954	−	0.741499i	$-0.734115\pi$
$233$	1.02952	−	21.6122i	0.0674458	−	1.41586i	0.738400	−	0.674363i	$-0.235582\pi$
$234$		0			0
$235$	−9.40643	−	6.69829i	−0.613608	−	0.436948i
$236$		0			0
$237$	−1.10872	−	1.42802i	−0.0720188	−	0.0927595i
$238$		0			0
$239$	−13.4972	−	23.3778i	−0.873059	−	1.51218i	−0.858816	−	0.512284i	$-0.828800\pi$
$239$	−13.4972	−	23.3778i	−0.873059	−	1.51218i	−0.0142427	−	0.999899i	$-0.504534\pi$
$240$		0			0
$241$	0.119122	+	0.828514i	0.00767334	+	0.0533692i	0.993298	−	0.115578i	$-0.0368722\pi$
$241$	0.119122	+	0.828514i	0.00767334	+	0.0533692i	−0.985625	+	0.168948i	$0.945963\pi$
$242$		0			0
$243$	−13.3693	+	8.01643i	−0.857638	+	0.514254i
$244$		0			0
$245$	1.45779	+	30.6027i	0.0931345	+	1.95513i
$246$		0			0
$247$	23.1659	+	29.4579i	1.47401	+	1.87436i
$248$		0			0
$249$	−20.0592	−	4.99847i	−1.27120	−	0.316765i
$250$		0			0
$251$	2.83602	+	8.19414i	0.179008	+	0.517210i	0.998432	−	0.0559781i	$-0.0178277\pi$
$251$	2.83602	+	8.19414i	0.179008	+	0.517210i	−0.819424	+	0.573188i	$0.805706\pi$
$252$		0			0
$253$	−1.96835	+	0.898916i	−0.123749	+	0.0565143i
$254$		0			0
$255$	−37.2314	+	26.1653i	−2.33152	+	1.63854i
$256$		0			0
$257$	3.09708	+	7.73614i	0.193191	+	0.482567i	0.993060	−	0.117607i	$-0.0375223\pi$
$257$	3.09708	+	7.73614i	0.193191	+	0.482567i	−0.799870	+	0.600174i	$0.795098\pi$
$258$		0			0
$259$	−3.17395	−	1.44949i	−0.197220	−	0.0900672i
$260$		0			0
$261$	5.27536	−	25.6519i	0.326537	−	1.58781i
$262$		0			0
$263$	2.25468	+	0.324173i	0.139029	+	0.0199894i	0.211478	−	0.977383i	$-0.432172\pi$
$263$	2.25468	+	0.324173i	0.139029	+	0.0199894i	−0.0724488	+	0.997372i	$0.523081\pi$
$264$		0			0
$265$	11.9313	−	7.66776i	0.732932	−	0.471027i
$266$		0			0
$267$	−4.04376	−	0.607067i	−0.247474	−	0.0371519i
$268$		0			0
$269$			18.6624i			1.13787i	0.822383	+	0.568934i	$0.192644\pi$
$269$			18.6624i			1.13787i	−0.822383	+	0.568934i	$0.807356\pi$
$270$		0			0
$271$	−7.96322	−	12.3910i	−0.483731	−	0.752700i	0.510509	−	0.859872i	$-0.329457\pi$
$271$	−7.96322	−	12.3910i	−0.483731	−	0.752700i	−0.994240	+	0.107172i	$0.965820\pi$
$272$		0			0
$273$	−34.6904	−	10.4205i	−2.09956	−	0.630679i
$274$		0			0
$275$	50.0704	−	4.78114i	3.01936	−	0.288314i
$276$		0			0
$277$	3.23729	−	7.08868i	0.194510	−	0.425918i	−0.787097	−	0.616829i	$-0.788417\pi$
$277$	3.23729	−	7.08868i	0.194510	−	0.425918i	0.981607	+	0.190911i	$0.0611443\pi$
$278$		0			0
$279$	−0.233294	−	2.81196i	−0.0139670	−	0.168348i
$280$		0			0
$281$	19.8167	−	18.8951i	1.18216	−	1.12719i	0.192873	−	0.981224i	$-0.438220\pi$
$281$	19.8167	−	18.8951i	1.18216	−	1.12719i	0.989290	−	0.145966i	$-0.0466289\pi$
$282$		0			0
$283$	6.67726	+	14.6212i	0.396922	+	0.869138i	0.997573	+	0.0696269i	$0.0221809\pi$
$283$	6.67726	+	14.6212i	0.396922	+	0.869138i	−0.600651	+	0.799511i	$0.705092\pi$
$284$		0			0
$285$	46.7611	−	8.71153i	2.76989	−	0.516027i
$286$		0			0
$287$	−0.325235	+	3.40602i	−0.0191980	+	0.201051i
$288$		0			0
$289$	20.4909	−	16.1143i	1.20535	−	0.947898i
$290$		0			0
$291$	−2.64887	+	26.0303i	−0.155280	+	1.52592i
$292$		0			0
$293$	−0.694325	+	2.36465i	−0.0405629	+	0.138145i	−0.977285	−	0.211929i	$-0.932025\pi$
$293$	−0.694325	+	2.36465i	−0.0405629	+	0.138145i	0.936722	+	0.350074i	$0.113844\pi$
$294$		0			0
$295$	−31.6561	+	4.55146i	−1.84309	+	0.264996i
$296$		0			0
$297$	−23.6314	+	1.81284i	−1.37123	+	0.105192i
$298$		0			0
$299$	−1.87578	−	1.78855i	−0.108479	−	0.103434i
$300$		0			0
$301$	−0.845539	+	1.18739i	−0.0487361	+	0.0684402i
$302$		0			0
$303$	−25.3312	−	5.04560i	−1.45524	−	0.289862i
$304$		0			0
$305$	−6.21927	−	3.59070i	−0.356114	−	0.205603i
$306$		0			0
$307$	5.41852	−	22.3354i	0.309251	−	1.27475i	−0.578975	−	0.815345i	$-0.696547\pi$
$307$	5.41852	−	22.3354i	0.309251	−	1.27475i	0.888227	−	0.459406i	$-0.151938\pi$
$308$		0			0
$309$	−2.20982	+	6.25878i	−0.125712	+	0.356050i
$310$		0			0
$311$	−9.33597	+	10.7743i	−0.529394	+	0.610953i	−0.955958	−	0.293504i	$-0.905179\pi$
$311$	−9.33597	+	10.7743i	−0.529394	+	0.610953i	0.426564	+	0.904458i	$0.359724\pi$
$312$		0			0
$313$	−7.74371	+	12.0494i	−0.437700	+	0.681075i	−0.988098	−	0.153828i	$-0.950840\pi$
$313$	−7.74371	+	12.0494i	−0.437700	+	0.681075i	0.550398	+	0.834903i	$0.314476\pi$
$314$		0			0
$315$	−32.1366	+	32.8762i	−1.81069	+	1.85236i
$316$		0			0
$317$	−0.497571	−	2.58165i	−0.0279464	−	0.145000i	0.965275	−	0.261235i	$-0.0841296\pi$
$317$	−0.497571	−	2.58165i	−0.0279464	−	0.145000i	−0.993222	+	0.116235i	$0.962917\pi$
$318$		0			0
$319$	24.6136	−	31.2988i	1.37810	−	1.75240i
$320$		0			0
$321$	8.69237	+	13.7121i	0.485161	+	0.765337i
$322$		0			0
$323$	−43.7484	+	10.6132i	−2.43423	+	0.590537i
$324$		0			0
$325$	27.6056	+	53.5474i	1.53128	+	2.97028i
$326$		0			0
$327$	11.2999	−	1.55309i	0.624884	−	0.0858860i
$328$		0			0
$329$	10.2505	+	4.10367i	0.565127	+	0.226243i
$330$		0			0
$331$	12.2573	+	4.24230i	0.673723	+	0.233178i	0.642444	−	0.766333i	$-0.277921\pi$
$331$	12.2573	+	4.24230i	0.673723	+	0.233178i	0.0312795	+	0.999511i	$0.490042\pi$
$332$		0			0
$333$	−0.862227	−	2.59512i	−0.0472498	−	0.142212i
$334$		0			0
$335$	29.7173	+	13.8099i	1.62363	+	0.754513i
$336$		0			0
$337$	−17.1383	+	12.2041i	−0.933581	+	0.664800i	−0.942160	−	0.335163i	$-0.891209\pi$
$337$	−17.1383	+	12.2041i	−0.933581	+	0.664800i	0.00857916	+	0.999963i	$0.497269\pi$
$338$		0			0
$339$	3.69010	+	1.93149i	0.200419	+	0.104904i
$340$		0			0
$341$	1.59444	−	3.98272i	0.0863438	−	0.215676i
$342$		0			0
$343$	−0.704029	−	2.39770i	−0.0380140	−	0.129464i
$344$		0			0
$345$	−3.11532	+	1.05660i	−0.167723	+	0.0568852i
$346$		0			0
$347$	5.98733	+	24.6801i	0.321417	+	1.32490i	0.871749	+	0.489952i	$0.162986\pi$
$347$	5.98733	+	24.6801i	0.321417	+	1.32490i	−0.550332	+	0.834946i	$0.685499\pi$
$348$		0			0
$349$	−16.2936	−	18.8039i	−0.872179	−	1.00655i	−0.999891	−	0.0147371i	$-0.995309\pi$
$349$	−16.2936	−	18.8039i	−0.872179	−	1.00655i	0.127712	−	0.991811i	$-0.459237\pi$
$350$		0			0
$351$	−12.5355	−	25.4700i	−0.669095	−	1.35949i
$352$		0			0
$353$	−18.3506	+	3.53680i	−0.976706	+	0.188245i	−0.652539	−	0.757755i	$-0.726296\pi$
$353$	−18.3506	+	3.53680i	−0.976706	+	0.188245i	−0.324167	+	0.946000i	$0.605084\pi$
$354$		0			0
$355$	−0.590311	+	1.14504i	−0.0313304	+	0.0607726i
$356$		0			0
$357$	28.6974	−	32.7058i	1.51883	−	1.73097i
$358$		0			0
$359$	−15.0463	−	13.0377i	−0.794113	−	0.688103i	0.160143	−	0.987094i	$-0.448805\pi$
$359$	−15.0463	−	13.0377i	−0.794113	−	0.688103i	−0.954256	+	0.298991i	$0.903350\pi$
$360$		0			0
$361$	27.5478	+	5.30941i	1.44989	+	0.279443i
$362$		0			0
$363$	−15.7265	−	6.40957i	−0.825426	−	0.336415i
$364$		0			0
$365$	−7.74900	+	13.4217i	−0.405601	+	0.702522i
$366$		0			0
$367$	−19.1788	−	0.913599i	−1.00113	−	0.0476895i	−0.459387	−	0.888236i	$-0.651931\pi$
$367$	−19.1788	−	0.913599i	−1.00113	−	0.0476895i	−0.541739	+	0.840547i	$0.682234\pi$
$368$		0			0
$369$	−2.12824	+	1.63128i	−0.110792	+	0.0849210i
$370$		0			0
$371$	−9.35813	+	9.81452i	−0.485850	+	0.509544i
$372$		0			0
$373$	−21.7588	+	12.5624i	−1.12663	+	0.650458i	−0.943084	−	0.332554i	$-0.892090\pi$
$373$	−21.7588	+	12.5624i	−1.12663	+	0.650458i	−0.183542	+	0.983012i	$0.558756\pi$
$374$		0			0
$375$	41.7933	+	0.259631i	2.15820	+	0.0134073i
$376$		0			0
$377$	45.7596	+	13.4362i	2.35674	+	0.692002i
$378$		0			0
$379$	12.2492	−	0.583500i	0.629198	−	0.0299724i	0.269439	−	0.963018i	$-0.413162\pi$
$379$	12.2492	−	0.583500i	0.629198	−	0.0299724i	0.359759	+	0.933045i	$0.382859\pi$
$380$		0			0
$381$	7.88367	+	13.8530i	0.403893	+	0.709708i
$382$		0			0
$383$	−1.23833	−	0.118247i	−0.0632759	−	0.00604212i	0.0633701	−	0.997990i	$-0.479815\pi$
$383$	−1.23833	−	0.118247i	−0.0632759	−	0.00604212i	−0.126646	+	0.991948i	$0.540421\pi$
$384$		0			0
$385$	−66.0549	+	22.8618i	−3.36647	+	1.16515i
$386$		0			0
$387$	−1.13272	+	0.148521i	−0.0575793	+	0.00754975i
$388$		0			0
$389$	23.8600	+	25.0237i	1.20975	+	1.26875i	0.953241	+	0.302210i	$0.0977243\pi$
$389$	23.8600	+	25.0237i	1.20975	+	1.26875i	0.256510	+	0.966541i	$0.417427\pi$
$390$		0			0
$391$	2.89037	−	1.15713i	0.146172	−	0.0585185i
$392$		0			0
$393$	−10.6757	+	16.3869i	−0.538516	+	0.826612i
$394$		0			0
$395$	−0.397212	−	4.15979i	−0.0199859	−	0.209302i
$396$		0			0
$397$	2.89713	−	20.1500i	0.145403	−	1.01130i	−0.778219	−	0.627993i	$-0.783877\pi$
$397$	2.89713	−	20.1500i	0.145403	−	1.01130i	0.923622	−	0.383306i	$-0.125214\pi$
$398$		0			0
$399$	−41.4869	+	18.6358i	−2.07694	+	0.932959i
$400$		0			0
$401$	33.0777			1.65182			0.825912	−	0.563799i	$-0.190661\pi$
$401$	33.0777			1.65182			0.825912	+	0.563799i	$0.190661\pi$
$402$		0			0
$403$	5.13836			0.255960
$404$		0			0
$405$	−36.0196	−	0.895227i	−1.78983	−	0.0444842i
$406$		0			0
$407$	0.591706	−	4.11541i	0.0293298	−	0.203993i
$408$		0			0
$409$	3.30888	+	34.6522i	0.163614	+	1.71344i	0.588753	+	0.808313i	$0.299619\pi$
$409$	3.30888	+	34.6522i	0.163614	+	1.71344i	−0.425139	+	0.905128i	$0.639775\pi$
$410$		0			0
$411$	−10.8367	−	7.05986i	−0.534537	−	0.348237i
$412$		0			0
$413$	28.3891	−	11.3653i	1.39693	−	0.559248i
$414$		0			0
$415$	−32.9734	−	34.5816i	−1.61860	−	1.69754i
$416$		0			0
$417$	−8.26842	−	28.8208i	−0.404906	−	1.41136i
$418$		0			0
$419$	−19.5218	+	6.75657i	−0.953703	+	0.330080i	−0.759226	−	0.650827i	$-0.774422\pi$
$419$	−19.5218	+	6.75657i	−0.953703	+	0.330080i	−0.194477	+	0.980907i	$0.562301\pi$
$420$		0			0
$421$	17.7061	+	1.69072i	0.862941	+	0.0824009i	0.517134	−	0.855905i	$-0.326999\pi$
$421$	17.7061	+	1.69072i	0.862941	+	0.0824009i	0.345807	+	0.938306i	$0.387605\pi$
$422$		0			0
$423$	3.11607	+	8.07283i	0.151508	+	0.392514i
$424$		0			0
$425$	−72.2862	+	3.44342i	−3.50640	+	0.167030i
$426$		0			0
$427$	6.58841	+	1.93453i	0.318836	+	0.0936186i
$428$		0			0
$429$	0.268122	−	43.1600i	0.0129451	−	2.08379i
$430$		0			0
$431$	−13.2824	+	7.66862i	−0.639793	+	0.369384i	−0.784535	−	0.620085i	$-0.787098\pi$
$431$	−13.2824	+	7.66862i	−0.639793	+	0.369384i	0.144742	+	0.989469i	$0.453765\pi$
$432$		0			0
$433$	27.6278	−	28.9752i	1.32771	−	1.39246i	0.466230	−	0.884664i	$-0.345612\pi$
$433$	27.6278	−	28.9752i	1.32771	−	1.39246i	0.861478	−	0.507796i	$-0.169539\pi$
$434$		0			0
$435$	42.0431	−	43.5487i	2.01581	−	2.08800i
$436$		0			0
$437$	−3.25061	−	0.154845i	−0.155498	−	0.00740726i
$438$		0			0
$439$	0.819748	−	1.41985i	0.0391245	−	0.0677655i	−0.845800	−	0.533500i	$-0.820876\pi$
$439$	0.819748	−	1.41985i	0.0391245	−	0.0677655i	0.884925	+	0.465734i	$0.154210\pi$
$440$		0			0
$441$	11.7254	−	19.7385i	0.558351	−	0.939926i
$442$		0			0
$443$	16.7254	+	3.22355i	0.794646	+	0.153155i	0.570389	−	0.821375i	$-0.306792\pi$
$443$	16.7254	+	3.22355i	0.794646	+	0.153155i	0.224257	+	0.974530i	$0.428005\pi$
$444$		0			0
$445$	−7.14286	−	6.18932i	−0.338604	−	0.293402i
$446$		0			0
$447$	−9.02803	−	7.92156i	−0.427011	−	0.374677i
$448$		0			0
$449$	−0.467197	+	0.906237i	−0.0220484	+	0.0427679i	−0.899602	−	0.436710i	$-0.856144\pi$
$449$	−0.467197	+	0.906237i	−0.0220484	+	0.0427679i	0.877554	+	0.479478i	$0.159174\pi$
$450$		0			0
$451$	−4.00331	+	0.771575i	−0.188509	+	0.0363320i
$452$		0			0
$453$	−12.0668	+	11.3634i	−0.566948	+	0.533900i
$454$		0			0
$455$	−54.8261	−	63.2727i	−2.57029	−	2.96627i
$456$		0			0
$457$	1.17246	+	4.83294i	0.0548453	+	0.226075i	0.992638	−	0.121121i	$-0.0386489\pi$
$457$	1.17246	+	4.83294i	0.0548453	+	0.226075i	−0.937792	+	0.347196i	$0.887134\pi$
$458$		0			0
$459$	34.0861	−	0.987523i	1.59100	−	0.0460936i
$460$		0			0
$461$	−11.2355	−	38.2645i	−0.523288	−	1.78215i	−0.617464	−	0.786599i	$-0.711840\pi$
$461$	−11.2355	−	38.2645i	−0.523288	−	1.78215i	0.0941766	−	0.995556i	$-0.469978\pi$
$462$		0			0
$463$	−10.8258	+	27.0415i	−0.503118	+	1.25673i	0.431834	+	0.901953i	$0.357866\pi$
$463$	−10.8258	+	27.0415i	−0.503118	+	1.25673i	−0.934952	+	0.354774i	$0.884558\pi$
$464$		0			0
$465$	3.02442	−	5.77814i	0.140254	−	0.267955i
$466$		0			0
$467$	−23.3011	+	16.5926i	−1.07825	+	0.767815i	−0.973957	−	0.226732i	$-0.927196\pi$
$467$	−23.3011	+	16.5926i	−1.07825	+	0.767815i	−0.104288	+	0.994547i	$0.533256\pi$
$468$		0			0
$469$	−30.7266	−	6.13325i	−1.41882	−	0.283207i
$470$		0			0
$471$	0.839089	−	0.426004i	0.0386632	−	0.0196292i
$472$		0			0
$473$	−1.64141	−	0.568097i	−0.0754721	−	0.0261211i
$474$		0			0
$475$	70.2250	+	28.1139i	3.22214	+	1.28995i
$476$		0			0
$477$	−10.6272	−	0.132043i	−0.486584	−	0.00604582i
$478$		0			0
$479$	5.00608	+	9.71045i	0.228734	+	0.443682i	0.975073	−	0.221884i	$-0.0712206\pi$
$479$	5.00608	+	9.71045i	0.228734	+	0.443682i	−0.746339	+	0.665566i	$0.768190\pi$
$480$		0			0
$481$	4.83953	−	1.17406i	0.220664	−	0.0535324i
$482$		0			0
$483$	2.65659	−	1.68406i	0.120879	−	0.0766274i
$484$		0			0
$485$	−37.3841	+	47.5377i	−1.69752	+	2.15858i
$486$		0			0
$487$	2.04050	+	10.5871i	0.0924641	+	0.479749i	0.998411	+	0.0563572i	$0.0179486\pi$
$487$	2.04050	+	10.5871i	0.0924641	+	0.479749i	−0.905947	+	0.423392i	$0.860839\pi$
$488$		0			0
$489$	2.75903	−	3.82402i	0.124768	−	0.172928i
$490$		0			0
$491$	18.0872	−	28.1443i	0.816265	−	1.27013i	−0.143591	−	0.989637i	$-0.545865\pi$
$491$	18.0872	−	28.1443i	0.816265	−	1.27013i	0.959855	−	0.280495i	$-0.0904987\pi$
$492$		0			0
$493$	−37.5163	+	43.2962i	−1.68965	+	1.94996i
$494$		0			0
$495$	−48.3761	−	25.7053i	−2.17434	−	1.15537i
$496$		0			0
$497$	0.290402	−	1.19705i	0.0130263	−	0.0536951i
$498$		0			0
$499$	15.0922	+	8.71346i	0.675618	+	0.390068i	0.798202	−	0.602390i	$-0.205785\pi$
$499$	15.0922	+	8.71346i	0.675618	+	0.390068i	−0.122584	+	0.992458i	$0.539118\pi$
$500$		0			0
$501$	−5.53141	+	27.7702i	−0.247125	+	1.24068i
$502$		0			0
$503$	8.60875	−	12.0893i	0.383845	−	0.539035i	−0.576774	−	0.816904i	$-0.695689\pi$
$503$	8.60875	−	12.0893i	0.383845	−	0.539035i	0.960619	+	0.277869i	$0.0896280\pi$
$504$		0			0
$505$	−43.2070	−	41.1978i	−1.92269	−	1.83328i
$506$		0			0
$507$	27.1558	−	10.6763i	1.20603	−	0.474151i
$508$		0			0
$509$	−30.5372	+	4.39058i	−1.35354	+	0.194609i	−0.780621	−	0.625005i	$-0.785097\pi$
$509$	−30.5372	+	4.39058i	−1.35354	+	0.194609i	−0.572916	+	0.819614i	$0.694188\pi$
$510$		0			0
$511$	4.17487	−	14.2183i	0.184685	−	0.628981i
$512$		0			0
$513$	−32.8379	−	13.8618i	−1.44983	−	0.612014i
$514$		0			0
$515$	−12.0593	+	9.48354i	−0.531397	+	0.417895i
$516$		0			0
$517$	−1.25062	+	13.0971i	−0.0550021	+	0.576009i
$518$		0			0
$519$	4.34796	+	23.3386i	0.190854	+	1.02445i
$520$		0			0
$521$	0.431533	+	0.944926i	0.0189058	+	0.0413980i	0.918849	−	0.394608i	$-0.129120\pi$
$521$	0.431533	+	0.944926i	0.0189058	+	0.0413980i	−0.899944	+	0.436006i	$0.856392\pi$
$522$		0			0
$523$	−17.2682	+	16.4652i	−0.755086	+	0.719973i	−0.966286	−	0.257470i	$-0.917111\pi$
$523$	−17.2682	+	16.4652i	−0.755086	+	0.719973i	0.211200	+	0.977443i	$0.432263\pi$
$524$		0			0
$525$	−71.1572	+	16.7952i	−3.10555	+	0.733002i
$526$		0			0
$527$	−2.56412	+	5.61463i	−0.111695	+	0.244577i
$528$		0			0
$529$	−22.6718	+	2.16490i	−0.985731	+	0.0941259i
$530$		0			0
$531$	21.6747	+	10.2258i	0.940600	+	0.443763i
$532$		0			0
$533$	−2.64006	−	4.10801i	−0.114354	−	0.177938i
$534$		0			0
$535$			37.5255i			1.62237i
$536$		0			0
$537$	1.15724	−	7.70854i	0.0499387	−	0.332648i
$538$		0			0
$539$	29.3650	−	18.8718i	1.26484	−	0.812864i
$540$		0			0
$541$	44.8532	+	6.44892i	1.92839	+	0.277261i	0.996369	−	0.0851428i	$-0.0271346\pi$
$541$	44.8532	+	6.44892i	1.92839	+	0.277261i	0.932021	+	0.362403i	$0.118044\pi$
$542$		0			0
$543$	0.313289	−	5.81629i	0.0134445	−	0.249601i
$544$		0			0
$545$	23.9813	+	10.9519i	1.02724	+	0.469127i
$546$		0			0
$547$	13.0376	+	32.5664i	0.557448	+	1.39244i	0.892847	+	0.450361i	$0.148705\pi$
$547$	13.0376	+	32.5664i	0.557448	+	1.39244i	−0.335399	+	0.942076i	$0.608871\pi$
$548$		0			0
$549$	2.40631	+	4.81350i	0.102699	+	0.205435i
$550$		0			0
$551$	54.4705	−	24.8758i	2.32052	−	1.05975i
$552$		0			0
$553$	1.30680	+	3.77576i	0.0555710	+	0.160562i
$554$		0			0
$555$	1.52829	−	6.13315i	0.0648723	−	0.260338i
$556$		0			0
$557$	12.5450	+	15.9522i	0.531547	+	0.675917i	0.975466	−	0.220150i	$-0.0706547\pi$
$557$	12.5450	+	15.9522i	0.531547	+	0.675917i	−0.443919	+	0.896067i	$0.646412\pi$
$558$		0			0
$559$	−0.0989901	−	2.07806i	−0.00418683	−	0.0878925i
$560$		0			0
$561$	47.0267	+	21.8304i	1.98547	+	0.921682i
$562$		0			0
$563$	5.67121	+	39.4441i	0.239013	+	1.66237i	0.656979	+	0.753909i	$0.271834\pi$
$563$	5.67121	+	39.4441i	0.239013	+	1.66237i	−0.417966	+	0.908463i	$0.637257\pi$
$564$		0			0
$565$	4.81347	+	8.33718i	0.202504	+	0.350748i
$566$		0			0
$567$	33.6714	−	7.28780i	1.41407	−	0.306059i
$568$		0			0
$569$	15.4182	+	10.9793i	0.646366	+	0.460275i	0.855633	−	0.517583i	$-0.173168\pi$
$569$	15.4182	+	10.9793i	0.646366	+	0.460275i	−0.209267	+	0.977859i	$0.567108\pi$
$570$		0			0
$571$	−0.213972	+	4.49182i	−0.00895444	+	0.187977i	0.989958	+	0.141359i	$0.0451473\pi$
$571$	−0.213972	+	4.49182i	−0.00895444	+	0.187977i	−0.998913	+	0.0466176i	$0.985156\pi$
$572$		0			0
$573$	12.0407	+	9.59056i	0.503007	+	0.400651i
$574$		0			0
$575$	−5.08401	−	1.23337i	−0.212018	−	0.0514350i
$576$		0			0
$577$	−1.10764	+	5.74698i	−0.0461116	+	0.239250i	−0.997671	−	0.0682166i	$-0.978269\pi$
$577$	−1.10764	+	5.74698i	−0.0461116	+	0.239250i	0.951559	+	0.307467i	$0.0994812\pi$
$578$		0			0
$579$	−2.96809	−	3.46866i	−0.123350	−	0.144153i
$580$		0			0
$581$	38.4346	+	24.7004i	1.59454	+	1.02475i
$582$		0			0
$583$	−14.3626	−	7.40443i	−0.594838	−	0.306660i
$584$		0			0
$585$	7.04807	−	65.2347i	0.291402	−	2.69712i
$586$		0			0
$587$	7.45216	+	5.86044i	0.307584	+	0.241886i	0.760004	−	0.649918i	$-0.225197\pi$
$587$	7.45216	+	5.86044i	0.307584	+	0.241886i	−0.452420	+	0.891805i	$0.649439\pi$
$588$		0			0
$589$	4.87593	−	4.22502i	0.200909	−	0.174089i
$590$		0			0
$591$	−21.6952	+	1.93572i	−0.892422	+	0.0796248i
$592$		0			0
$593$	24.9153	−	12.8447i	1.02315	−	0.527470i	0.136854	−	0.990591i	$-0.456301\pi$
$593$	24.9153	−	12.8447i	1.02315	−	0.527470i	0.886295	+	0.463121i	$0.153271\pi$
$594$		0			0
$595$	96.4963	−	28.3339i	3.95596	−	1.16158i
$596$		0			0
$597$	−8.15179	+	13.9189i	−0.333630	+	0.569663i
$598$		0			0
$599$	−5.73363	+	16.5662i	−0.234270	+	0.676879i	0.765183	+	0.643813i	$0.222648\pi$
$599$	−5.73363	+	16.5662i	−0.234270	+	0.676879i	−0.999453	+	0.0330660i	$0.989473\pi$
$600$		0			0
$601$	12.0619	+	16.9386i	0.492016	+	0.690939i	0.983697	−	0.179836i	$-0.0575567\pi$
$601$	12.0619	+	16.9386i	0.492016	+	0.690939i	−0.491681	+	0.870775i	$0.663617\pi$
$602$		0			0
$603$	−12.8802	−	20.9069i	−0.524524	−	0.851396i
$604$		0			0
$605$	−22.7689	−	31.9744i	−0.925687	−	1.29994i
$606$		0			0
$607$	10.1742	−	29.3965i	0.412959	−	1.19317i	−0.526402	−	0.850236i	$-0.676459\pi$
$607$	10.1742	−	29.3965i	0.412959	−	1.19317i	0.939361	−	0.342931i	$-0.111420\pi$
$608$		0			0
$609$	−29.2499	+	49.9432i	−1.18527	+	2.02380i
$610$		0			0
$611$	−15.1200	+	4.43964i	−0.611690	+	0.179608i
$612$		0			0
$613$	−42.3253	+	21.8202i	−1.70950	+	0.881309i	−0.729072	+	0.684437i	$0.760048\pi$
$613$	−42.3253	+	21.8202i	−1.70950	+	0.881309i	−0.980429	+	0.196873i	$0.936921\pi$
$614$		0			0
$615$	−6.17343	+	0.550813i	−0.248937	+	0.0222109i
$616$		0			0
$617$	15.9181	−	13.7931i	0.640839	−	0.555290i	−0.272671	−	0.962107i	$-0.587907\pi$
$617$	15.9181	−	13.7931i	0.640839	−	0.555290i	0.913509	+	0.406818i	$0.133362\pi$
$618$		0			0
$619$	0.0630314	+	0.0495684i	0.00253345	+	0.00199232i	0.619425	−	0.785056i	$-0.287366\pi$
$619$	0.0630314	+	0.0495684i	0.00253345	+	0.00199232i	−0.616891	+	0.787048i	$0.711608\pi$
$620$		0			0
$621$	2.38438	+	0.625715i	0.0956817	+	0.0251091i
$622$		0			0
$623$	8.03241	+	4.14100i	0.321812	+	0.165905i
$624$		0			0
$625$	34.8826	+	22.4177i	1.39531	+	0.896708i
$626$		0			0
$627$	−35.2339	−	41.1762i	−1.40711	−	1.64442i
$628$		0			0
$629$	−1.13212	+	5.87397i	−0.0451404	+	0.234211i
$630$		0			0
$631$	−26.7125	−	6.48038i	−1.06341	−	0.257980i	−0.334362	−	0.942445i	$-0.608521\pi$
$631$	−26.7125	−	6.48038i	−1.06341	−	0.257980i	−0.729046	+	0.684465i	$0.760036\pi$
$632$		0			0
$633$	12.4021	+	9.87846i	0.492941	+	0.392633i
$634$		0			0
$635$	−1.75298	+	36.7996i	−0.0695649	+	1.46035i
$636$		0			0
$637$	34.0565	+	24.2515i	1.34937	+	0.960881i
$638$		0			0
$639$	0.841963	−	0.472258i	0.0333075	−	0.0186822i
$640$		0			0
$641$	18.5552	+	32.1386i	0.732888	+	1.26940i	0.955644	+	0.294525i	$0.0951613\pi$
$641$	18.5552	+	32.1386i	0.732888	+	1.26940i	−0.222756	+	0.974874i	$0.571505\pi$
$642$		0			0
$643$	−5.39724	−	37.5386i	−0.212846	−	1.48038i	−0.763589	−	0.645703i	$-0.776565\pi$
$643$	−5.39724	−	37.5386i	−0.212846	−	1.48038i	0.550743	−	0.834675i	$-0.314345\pi$
$644$		0			0
$645$	−2.39506	−	1.11182i	−0.0943055	−	0.0437779i
$646$		0			0
$647$	−1.07522	−	22.5717i	−0.0422714	−	0.887385i	−0.916051	−	0.401063i	$-0.868641\pi$
$647$	−1.07522	−	22.5717i	−0.0422714	−	0.887385i	0.873779	−	0.486323i	$-0.161662\pi$
$648$		0			0
$649$	22.5244	+	28.6421i	0.884159	+	1.12430i
$650$		0			0
$651$	−1.50779	+	6.05086i	−0.0590948	+	0.237152i
$652$		0			0
$653$	13.9877	+	40.4147i	0.547380	+	1.58155i	0.791088	+	0.611702i	$0.209515\pi$
$653$	13.9877	+	40.4147i	0.547380	+	1.58155i	−0.243708	+	0.969849i	$0.578364\pi$
$654$		0			0
$655$	−41.1199	+	18.7788i	−1.60669	+	0.733750i
$656$		0			0
$657$	10.3879	−	5.19300i	0.405270	−	0.202598i
$658$		0			0
$659$	−0.755882	−	1.88810i	−0.0294450	−	0.0735500i	0.912917	−	0.408146i	$-0.133824\pi$
$659$	−0.755882	−	1.88810i	−0.0294450	−	0.0735500i	−0.942362	+	0.334596i	$0.891400\pi$
$660$		0			0
$661$	14.3871	+	6.57039i	0.559595	+	0.255558i	0.675072	−	0.737752i	$-0.264112\pi$
$661$	14.3871	+	6.57039i	0.559595	+	0.255558i	−0.115477	+	0.993310i	$0.536840\pi$
$662$		0			0
$663$	−3.34008	+	62.0093i	−0.129718	+	2.40824i
$664$		0			0
$665$	−104.052	−	14.9604i	−4.03496	−	0.580139i
$666$		0			0
$667$	−3.48397	+	2.23901i	−0.134900	+	0.0866950i
$668$		0			0
$669$	6.22013	−	41.4331i	0.240484	−	1.60190i
$670$		0			0
$671$			8.18202i			0.315864i
$672$		0			0
$673$	24.7710	+	38.5444i	0.954850	+	1.48578i	0.872172	+	0.489200i	$0.162711\pi$
$673$	24.7710	+	38.5444i	0.954850	+	1.48578i	0.0826789	+	0.996576i	$0.473652\pi$
$674$		0			0
$675$	−47.6178	−	31.8714i	−1.83281	−	1.22673i
$676$		0			0
$677$	−45.8487	+	4.37802i	−1.76211	+	0.168261i	−0.925301	−	0.379234i	$-0.876188\pi$
$677$	−45.8487	+	4.37802i	−1.76211	+	0.168261i	−0.836809	+	0.547495i	$0.815582\pi$
$678$		0			0
$679$	24.0214	−	52.5996i	0.921858	−	2.01859i
$680$		0			0
$681$	−33.7171	+	7.95823i	−1.29204	+	0.304960i
$682$		0			0
$683$	11.3455	−	10.8179i	0.434122	−	0.413934i	−0.441250	−	0.897384i	$-0.645465\pi$
$683$	11.3455	−	10.8179i	0.434122	−	0.413934i	0.875372	+	0.483450i	$0.160616\pi$
$684$		0			0
$685$	−12.4185	−	27.1928i	−0.474487	−	1.03898i
$686$		0			0
$687$	2.18001	+	11.7017i	0.0831725	+	0.446447i
$688$		0			0
$689$	1.83974	−	19.2666i	0.0700885	−	0.734000i
$690$		0			0
$691$	12.4877	−	9.82041i	0.475053	−	0.373586i	−0.351735	−	0.936100i	$-0.614408\pi$
$691$	12.4877	−	9.82041i	0.475053	−	0.373586i	0.826788	+	0.562514i	$0.190166\pi$
$692$		0			0
$693$	50.7460	+	12.9805i	1.92768	+	0.493088i
$694$		0			0
$695$	19.5249	−	66.4955i	0.740620	−	2.52232i
$696$		0			0
$697$	5.80620	−	0.834806i	0.219926	−	0.0316205i
$698$		0			0
$699$	−34.8772	+	13.7120i	−1.31918	+	0.518634i
$700$		0			0
$701$	−11.8887	−	11.3358i	−0.449030	−	0.428149i	0.431520	−	0.902104i	$-0.357978\pi$
$701$	−11.8887	−	11.3358i	−0.449030	−	0.428149i	−0.880549	+	0.473955i	$0.842826\pi$
$702$		0			0
$703$	3.62699	−	5.09339i	0.136795	−	0.192101i
$704$		0			0
$705$	−3.90716	+	19.6158i	−0.147152	+	0.738772i
$706$		0			0
$707$	49.4351	+	28.5414i	1.85920	+	1.07341i
$708$		0			0
$709$	7.93887	−	32.7245i	0.298151	−	1.22899i	−0.603793	−	0.797141i	$-0.706345\pi$
$709$	7.93887	−	32.7245i	0.298151	−	1.22899i	0.901944	−	0.431853i	$-0.142140\pi$
$710$		0			0
$711$	−1.46934	+	2.76522i	−0.0551046	+	0.103704i
$712$		0			0
$713$	−0.292200	+	0.337217i	−0.0109430	+	0.0126289i
$714$		0			0
$715$	53.9348	−	83.9241i	2.01705	−	3.13858i
$716$		0			0
$717$	−27.3569	+	37.9167i	−1.02166	+	1.41603i
$718$		0			0
$719$	−9.26034	−	48.0472i	−0.345353	−	1.79186i	−0.574539	−	0.818477i	$-0.694819\pi$
$719$	−9.26034	−	48.0472i	−0.345353	−	1.79186i	0.229187	−	0.973382i	$-0.426393\pi$
$720$		0			0
$721$	9.06778	−	11.5306i	0.337702	−	0.429423i
$722$		0			0
$723$	1.22448	−	0.776221i	0.0455390	−	0.0288680i
$724$		0			0
$725$	93.5503	−	22.6951i	3.47437	−	0.842873i
$726$		0			0
$727$	2.88289	+	5.59202i	0.106920	+	0.207397i	0.936226	−	0.351399i	$-0.114294\pi$
$727$	2.88289	+	5.59202i	0.106920	+	0.207397i	−0.829305	+	0.558796i	$0.811264\pi$
$728$		0			0
$729$	22.1541	+	15.4336i	0.820522	+	0.571614i
$730$		0			0
$731$	2.32007	+	0.928815i	0.0858108	+	0.0343535i
$732$		0			0
$733$	−3.72505	−	1.28925i	−0.137588	−	0.0476196i	0.257406	−	0.966303i	$-0.417132\pi$
$733$	−3.72505	−	1.28925i	−0.137588	−	0.0476196i	−0.394994	+	0.918684i	$0.629253\pi$
$734$		0			0
$735$	47.3167	−	24.0226i	1.74530	−	0.886085i
$736$		0			0
$737$	−3.30289	−	37.1889i	−0.121664	−	1.36987i
$738$		0			0
$739$	−9.69527	+	6.90397i	−0.356646	+	0.253967i	−0.744310	−	0.667834i	$-0.767222\pi$
$739$	−9.69527	+	6.90397i	−0.356646	+	0.253967i	0.387664	+	0.921801i	$0.373282\pi$
$740$		0			0
$741$	30.1012	−	57.5082i	1.10580	−	2.11262i
$742$		0			0
$743$	12.4358	−	31.0630i	0.456224	−	1.13959i	−0.504827	−	0.863220i	$-0.668444\pi$
$743$	12.4358	−	31.0630i	0.456224	−	1.13959i	0.961051	−	0.276371i	$-0.0891320\pi$
$744$		0			0
$745$	−7.82122	−	26.6366i	−0.286547	−	0.975890i
$746$		0			0
$747$	6.33900	+	35.2405i	0.231932	+	1.28938i
$748$		0			0
$749$	−8.45911	−	34.8689i	−0.309089	−	1.27408i
$750$		0			0
$751$	12.8772	+	14.8611i	0.469897	+	0.542290i	0.940383	−	0.340118i	$-0.110467\pi$
$751$	12.8772	+	14.8611i	0.469897	+	0.542290i	−0.470486	+	0.882407i	$0.655921\pi$
$752$		0			0
$753$	10.9337	−	10.2964i	0.398447	−	0.375220i
$754$		0			0
$755$	−37.6190	+	7.25046i	−1.36909	+	0.263871i
$756$		0			0
$757$	4.60302	−	8.92862i	0.167300	−	0.324516i	−0.790250	−	0.612785i	$-0.790049\pi$
$757$	4.60302	−	8.92862i	0.167300	−	0.324516i	0.957550	+	0.288269i	$0.0930796\pi$
$758$		0			0
$759$	2.81723	+	2.47195i	0.102259	+	0.0897263i
$760$		0			0
$761$	−29.0122	−	25.1392i	−1.05169	−	0.911295i	−0.0554962	−	0.998459i	$-0.517674\pi$
$761$	−29.0122	−	25.1392i	−1.05169	−	0.911295i	−0.996194	+	0.0871642i	$0.972220\pi$
$762$		0			0
$763$	−24.7524	−	4.77063i	−0.896096	−	0.172708i
$764$		0			0
$765$	67.7642	+	40.2544i	2.45002	+	1.45540i
$766$		0			0
$767$	−21.8217	+	37.7962i	−0.787934	+	1.36474i
$768$		0			0
$769$	15.2605	+	0.726948i	0.550308	+	0.0262144i	0.320895	−	0.947115i	$-0.396016\pi$
$769$	15.2605	+	0.726948i	0.550308	+	0.0262144i	0.229413	+	0.973329i	$0.426319\pi$
$770$		0			0
$771$	10.0248	−	10.3838i	0.361034	−	0.373962i
$772$		0			0
$773$	7.80493	−	8.18557i	0.280724	−	0.294415i	−0.568243	−	0.822861i	$-0.692377\pi$
$773$	7.80493	−	8.18557i	0.280724	−	0.294415i	0.848967	+	0.528446i	$0.177225\pi$
$774$		0			0
$775$	8.98210	−	5.18582i	0.322646	−	0.186280i
$776$		0			0
$777$	−0.0375437	+	6.04347i	−0.00134687	+	0.216808i
$778$		0			0
$779$	−5.88303	−	1.72741i	−0.210781	−	0.0618910i
$780$		0			0
$781$	1.46609	−	0.0698384i	0.0524608	−	0.00249901i
$782$		0			0
$783$	−44.2732	+	9.87074i	−1.58220	+	0.352751i
$784$		0			0
$785$	2.16524	+	0.206755i	0.0772806	+	0.00737940i
$786$		0			0
$787$	−11.7965	+	4.08281i	−0.420500	+	0.145537i	−0.529120	−	0.848547i	$-0.677478\pi$
$787$	−11.7965	+	4.08281i	−0.420500	+	0.145537i	0.108620	+	0.994083i	$0.465357\pi$
$788$		0			0
$789$	−1.08800	−	3.79239i	−0.0387339	−	0.135013i
$790$		0			0
$791$	−6.35210	−	6.66189i	−0.225855	−	0.236870i
$792$		0			0
$793$	−9.09800	+	3.64229i	−0.323080	+	0.129342i
$794$		0			0
$795$	−20.5827	−	13.4091i	−0.729992	−	0.475571i
$796$		0			0
$797$	−1.06895	−	11.1945i	−0.0378641	−	0.396530i	−0.994460	−	0.105114i	$-0.966479\pi$
$797$	−1.06895	−	11.1945i	−0.0378641	−	0.396530i	0.956596	−	0.291417i	$-0.0941267\pi$
$798$		0			0
$799$	2.69396	−	18.7369i	0.0953055	−	0.662864i
$800$		0			0
$801$	1.91078	+	6.81985i	0.0675141	+	0.240968i
$802$		0			0
$803$	17.6574			0.623117
$804$		0			0
$805$	7.27018			0.256240
$806$		0			0
$807$	29.4860	−	13.2451i	1.03796	−	0.466248i
$808$		0			0
$809$	3.00066	−	20.8700i	0.105498	−	0.733752i	−0.866571	−	0.499054i	$-0.833681\pi$
$809$	3.00066	−	20.8700i	0.105498	−	0.733752i	0.972068	−	0.234698i	$-0.0754100\pi$
$810$		0			0
$811$	−2.10189	−	22.0120i	−0.0738074	−	0.772946i	−0.954293	−	0.298873i	$-0.903389\pi$
$811$	−2.10189	−	22.0120i	−0.0738074	−	0.772946i	0.880485	−	0.474073i	$-0.157217\pi$
$812$		0			0
$813$	−13.9258	+	21.3758i	−0.488398	+	0.749681i
$814$		0			0
$815$	10.1184	−	4.05080i	0.354432	−	0.141893i
$816$		0			0
$817$	−1.80262	−	1.89053i	−0.0630656	−	0.0661413i
$818$		0			0
$819$	8.15630	+	62.2053i	0.285004	+	2.17363i
$820$		0			0
$821$	−39.6846	+	13.7350i	−1.38500	+	0.479354i	−0.915051	−	0.403339i	$-0.867849\pi$
$821$	−39.6846	+	13.7350i	−1.38500	+	0.479354i	−0.469951	+	0.882693i	$0.655728\pi$
$822$		0			0
$823$	−0.452658	−	0.0432236i	−0.0157787	−	0.00150668i	0.0871637	−	0.996194i	$-0.472220\pi$
$823$	−0.452658	−	0.0432236i	−0.0157787	−	0.00150668i	−0.102942	+	0.994687i	$0.532826\pi$
$824$		0			0
$825$	−43.0899	−	75.7164i	−1.50020	−	2.63611i
$826$		0			0
$827$	−31.0398	+	1.47861i	−1.07936	+	0.0514162i	−0.579718	−	0.814817i	$-0.696837\pi$
$827$	−31.0398	+	1.47861i	−1.07936	+	0.0514162i	−0.499640	+	0.866233i	$0.666534\pi$
$828$		0			0
$829$	−39.0372	−	11.4623i	−1.35582	−	0.398104i	−0.478530	−	0.878071i	$-0.658830\pi$
$829$	−39.0372	−	11.4623i	−1.35582	−	0.398104i	−0.877286	+	0.479967i	$0.840648\pi$
$830$		0			0
$831$	−13.4975	−	0.0838499i	−0.468222	−	0.00290872i
$832$		0			0
$833$	−43.4941	+	25.1113i	−1.50698	+	0.870056i
$834$		0			0
$835$	−45.1644	+	47.3671i	−1.56298	+	1.63920i
$836$		0			0
$837$	−4.27723	+	2.36430i	−0.147843	+	0.0817221i
$838$		0			0
$839$	−0.820105	−	0.0390664i	−0.0283132	−	0.00134872i	0.0334205	−	0.999441i	$-0.489360\pi$
$839$	−0.820105	−	0.0390664i	−0.0283132	−	0.00134872i	−0.0617337	+	0.998093i	$0.519663\pi$
$840$		0			0
$841$	23.6028	−	40.8812i	0.813889	−	1.40970i
$842$		0			0
$843$	−43.9180	−	17.8994i	−1.51261	−	0.616490i
$844$		0			0
$845$	66.2251	+	12.7638i	2.27821	+	0.439089i
$846$		0			0
$847$	28.3648	+	24.5782i	0.974625	+	0.844517i
$848$		0			0
$849$	18.3620	−	20.9268i	0.630182	−	0.718205i
$850$		0			0
$851$	−0.198157	+	0.384370i	−0.00679272	+	0.0131760i
$852$		0			0
$853$	24.2582	−	4.67538i	0.830583	−	0.160082i	0.243800	−	0.969826i	$-0.421606\pi$
$853$	24.2582	−	4.67538i	0.830583	−	0.160082i	0.586784	+	0.809744i	$0.300394\pi$
$854$		0			0
$855$	−46.9511	−	67.6982i	−1.60569	−	2.31523i
$856$		0			0
$857$	22.0215	+	25.4141i	0.752239	+	0.868130i	0.994783	−	0.102010i	$-0.0325274\pi$
$857$	22.0215	+	25.4141i	0.752239	+	0.868130i	−0.242544	+	0.970140i	$0.577982\pi$
$858$		0			0
$859$	−9.03079	−	37.2254i	−0.308126	−	1.27011i	−0.889672	−	0.456600i	$-0.849067\pi$
$859$	−9.03079	−	37.2254i	−0.308126	−	1.27011i	0.581545	−	0.813514i	$-0.302448\pi$
$860$		0			0
$861$	5.61222	−	1.90345i	0.191264	−	0.0648695i
$862$		0			0
$863$	12.8860	+	43.8857i	0.438645	+	1.49389i	0.821570	+	0.570108i	$0.193098\pi$
$863$	12.8860	+	43.8857i	0.438645	+	1.49389i	−0.382925	+	0.923779i	$0.625083\pi$
$864$		0			0
$865$	−20.3940	+	50.9417i	−0.693416	+	1.73207i
$866$		0			0
$867$	−40.0028	−	20.9385i	−1.35857	−	0.711107i
$868$		0			0
$869$	−3.87816	+	2.76163i	−0.131558	+	0.0936818i
$870$		0			0
$871$	39.8819	−	20.2276i	1.35135	−	0.685385i
$872$		0			0
$873$	43.0070	−	14.2891i	1.45557	−	0.483612i
$874$		0			0
$875$	−87.2865	−	30.2101i	−2.95082	−	1.02129i
$876$		0			0
$877$	5.25632	+	2.10432i	0.177493	+	0.0710577i	0.458707	−	0.888588i	$-0.348313\pi$
$877$	5.25632	+	2.10432i	0.177493	+	0.0710577i	−0.281214	+	0.959645i	$0.590737\pi$
$878$		0			0
$879$	4.22885	−	0.581227i	0.142636	−	0.0196043i
$880$		0			0
$881$	−20.9178	−	40.5748i	−0.704737	−	1.36700i	−0.920573	−	0.390570i	$-0.872278\pi$
$881$	−20.9178	−	40.5748i	−0.704737	−	1.36700i	0.215836	−	0.976430i	$-0.430752\pi$
$882$		0			0
$883$	18.6994	−	4.53643i	0.629285	−	0.152663i	0.0915826	−	0.995797i	$-0.470807\pi$
$883$	18.6994	−	4.53643i	0.629285	−	0.152663i	0.537703	+	0.843135i	$0.319292\pi$
$884$		0			0
$885$	29.6581	+	46.7854i	0.996946	+	1.57267i
$886$		0			0
$887$	−6.10443	+	7.76242i	−0.204967	+	0.260636i	−0.877659	−	0.479286i	$-0.840896\pi$
$887$	−6.10443	+	7.76242i	−0.204967	+	0.260636i	0.672692	+	0.739923i	$0.265138\pi$
$888$		0			0
$889$	−6.66659	−	34.5896i	−0.223590	−	1.16010i
$890$		0			0
$891$	19.6359	+	36.0503i	0.657827	+	1.20773i
$892$		0			0
$893$	−10.6973	+	16.6453i	−0.357971	+	0.557014i
$894$		0			0
$895$	11.7986	−	13.6163i	0.394384	−	0.455143i
$896$		0			0
$897$	−1.49458	+	4.23303i	−0.0499025	+	0.141337i
$898$		0			0
$899$	1.93570	−	7.97908i	0.0645594	−	0.266117i
$900$		0			0
$901$	20.1344	+	11.6246i	0.670773	+	0.387271i
$902$		0			0
$903$	2.47614	+	0.493210i	0.0824007	+	0.0164130i
$904$		0			0
$905$	7.80937	−	10.9667i	0.259592	−	0.364546i
$906$		0			0
$907$	9.04429	+	8.62371i	0.300311	+	0.286346i	0.825219	−	0.564813i	$-0.191052\pi$
$907$	9.04429	+	8.62371i	0.300311	+	0.286346i	−0.524908	+	0.851159i	$0.675900\pi$
$908$		0			0
$909$	10.0062	+	43.6035i	0.331883	+	1.44624i
$910$		0			0
$911$	−5.12557	+	0.736945i	−0.169818	+	0.0244161i	−0.226699	−	0.973965i	$-0.572793\pi$
$911$	−5.12557	+	0.736945i	−0.169818	+	0.0244161i	0.0568814	+	0.998381i	$0.481884\pi$
$912$		0			0
$913$	−15.3375	+	52.2347i	−0.507597	+	1.72872i
$914$		0			0
$915$	−1.25926	+	12.3746i	−0.0416297	+	0.409093i
$916$		0			0
$917$	33.9757	−	26.7188i	1.12198	−	0.882332i
$918$		0			0
$919$	3.29318	−	34.4877i	0.108632	−	1.13764i	−0.762633	−	0.646831i	$-0.776094\pi$
$919$	3.29318	−	34.4877i	0.108632	−	1.13764i	0.871265	−	0.490813i	$-0.163300\pi$
$920$		0			0
$921$	−39.1349	+	7.29079i	−1.28954	+	0.240240i
$922$		0			0
$923$	0.730297	+	1.59913i	0.0240380	+	0.0526359i
$924$		0			0
$925$	7.27482	−	6.93653i	0.239195	−	0.228072i
$926$		0			0
$927$	11.4570	−	0.950532i	0.376298	−	0.0312196i
$928$		0			0
$929$	14.9140	−	32.6572i	0.489314	−	1.07145i	−0.490483	−	0.871451i	$-0.663179\pi$
$929$	14.9140	−	32.6572i	0.489314	−	1.07145i	0.979796	−	0.199997i	$-0.0640933\pi$
$930$		0			0
$931$	52.2580	−	4.99003i	1.71269	−	0.163542i
$932$		0			0
$933$	23.6489	+	7.10382i	0.774231	+	0.232569i
$934$		0			0
$935$	64.7887	+	100.813i	2.11882	+	3.29695i
$936$		0			0
$937$		−	23.8759i		−	0.779992i	−0.920817	−	0.389996i	$-0.872476\pi$
$937$		−	23.8759i		−	0.779992i	0.920817	−	0.389996i	$-0.127524\pi$
$938$		0			0
$939$	24.5336	+	3.68310i	0.800623	+	0.120193i
$940$		0			0
$941$	−13.2061	+	8.48706i	−0.430507	+	0.276670i	−0.737897	−	0.674914i	$-0.764181\pi$
$941$	−13.2061	+	8.48706i	−0.430507	+	0.276670i	0.307390	+	0.951584i	$0.400545\pi$
$942$		0			0
$943$	0.419728	+	0.0603478i	0.0136682	+	0.00196520i
$944$		0			0
$945$	74.7513	+	27.4420i	2.43166	+	0.892688i
$946$		0			0
$947$	−28.8626	−	13.1811i	−0.937907	−	0.428328i	−0.112999	−	0.993595i	$-0.536046\pi$
$947$	−28.8626	−	13.1811i	−0.937907	−	0.428328i	−0.824908	+	0.565267i	$0.808773\pi$
$948$		0			0
$949$	7.86034	+	19.6342i	0.255158	+	0.637353i
$950$		0			0
$951$	−3.72578	+	2.61839i	−0.120817	+	0.0849071i
$952$		0			0
$953$	49.6883	−	22.6919i	1.60956	−	0.735062i	0.611156	−	0.791510i	$-0.290705\pi$
$953$	49.6883	−	22.6919i	1.60956	−	0.735062i	0.998406	+	0.0564475i	$0.0179774\pi$
$954$		0			0
$955$	11.6370	+	33.6230i	0.376566	+	1.08802i
$956$		0			0
$957$	−66.9198	−	16.6754i	−2.16321	−	0.539040i
$958$		0			0
$959$	17.6692	+	22.4683i	0.570570	+	0.725538i
$960$		0			0
$961$	1.43295	+	30.0813i	0.0462241	+	0.970364i
$962$		0			0
$963$	15.4956	−	23.4654i	0.499339	−	0.756163i
$964$		0			0
$965$	−1.50169	−	10.4445i	−0.0483412	−	0.336220i
$966$		0			0
$967$	1.67773	+	2.90592i	0.0539522	+	0.0934480i	0.891740	−	0.452548i	$-0.149485\pi$
$967$	1.67773	+	2.90592i	0.0539522	+	0.0934480i	−0.837788	+	0.545996i	$0.816151\pi$
$968$		0			0
$969$	47.8176	+	61.5887i	1.53612	+	1.97851i
$970$		0			0
$971$	22.5390	+	16.0500i	0.723311	+	0.515068i	0.881408	−	0.472356i	$-0.156596\pi$
$971$	22.5390	+	16.0500i	0.723311	+	0.515068i	−0.158097	+	0.987424i	$0.550536\pi$
$972$		0			0
$973$	−3.15299	+	66.1894i	−0.101080	+	2.12194i
$974$		0			0
$975$	65.0110	−	81.6196i	2.08202	−	2.61392i
$976$		0			0
$977$	50.3964	+	12.2260i	1.61233	+	0.391146i	0.937819	−	0.347124i	$-0.112842\pi$
$977$	50.3964	+	12.2260i	1.61233	+	0.391146i	0.674506	+	0.738270i	$0.264357\pi$
$978$		0			0
$979$	−2.03791	+	10.5737i	−0.0651319	+	0.337936i
$980$		0			0
$981$	−10.4736	−	16.7512i	−0.334395	−	0.534823i
$982$		0			0
$983$	−5.20609	−	3.34575i	−0.166049	−	0.106713i	0.454977	−	0.890503i	$-0.349647\pi$
$983$	−5.20609	−	3.34575i	−0.166049	−	0.106713i	−0.621026	+	0.783790i	$0.713284\pi$
$984$		0			0
$985$	−44.7484	−	23.0694i	−1.42580	−	0.735052i
$986$		0			0
$987$	−0.791282	−	19.1079i	−0.0251868	−	0.608210i
$988$		0			0
$989$	0.142007	+	0.111675i	0.00451555	+	0.00355107i
$990$		0			0
$991$	−10.3796	+	8.99399i	−0.329720	+	0.285704i	−0.803950	−	0.594697i	$-0.797272\pi$
$991$	−10.3796	+	8.99399i	−0.329720	+	0.285704i	0.474230	+	0.880401i	$0.342726\pi$
$992$		0			0
$993$	−1.99655	−	22.3770i	−0.0633586	−	0.710113i
$994$		0			0
$995$	−33.1386	+	17.0841i	−1.05056	+	0.541604i
$996$		0			0
$997$	−40.9580	+	12.0263i	−1.29715	+	0.380878i	−0.856196	−	0.516651i	$-0.827179\pi$
$997$	−40.9580	+	12.0263i	−1.29715	+	0.380878i	−0.440956	+	0.897529i	$0.645360\pi$
$998$		0			0
$999$	−3.48827	+	3.20410i	−0.110364	+	0.101373i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.ba.b.41.9	yes	440
3.2	odd	2	inner	804.2.ba.b.41.7	✓	440
67.18	odd	66	inner	804.2.ba.b.353.7	yes	440
201.152	even	66	inner	804.2.ba.b.353.9	yes	440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.ba.b.41.7	✓	440	3.2	odd	2	inner
804.2.ba.b.41.9	yes	440	1.1	even	1	trivial
804.2.ba.b.353.7	yes	440	67.18	odd	66	inner
804.2.ba.b.353.9	yes	440	201.152	even	66	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.ba (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.709719 - 1.57997i) q^{3} +(0.569745 - 3.96266i) q^{5} +(0.363865 + 3.81057i) q^{7} +(-1.99260 + 2.24267i) q^{9} +O(q^{10})\)	\(q+(-0.709719 - 1.57997i) q^{3} +(0.569745 - 3.96266i) q^{5} +(0.363865 + 3.81057i) q^{7} +(-1.99260 + 2.24267i) q^{9} +(-4.23450 + 1.69524i) q^{11} +(-3.77004 - 3.95391i) q^{13} +(-6.66524 + 1.91220i) q^{15} +(6.20169 - 2.14643i) q^{17} +(-6.82859 - 0.652051i) q^{19} +(5.76233 - 3.27933i) q^{21} +(0.473873 - 0.0225734i) q^{23} +(-10.5806 - 3.10675i) q^{25} +(4.95752 + 1.55658i) q^{27} +(-7.56004 + 4.36479i) q^{29} +(-0.649047 + 0.680701i) q^{31} +(5.68373 + 5.48724i) q^{33} +(15.3073 + 0.729177i) q^{35} +(-0.455768 + 0.789413i) q^{37} +(-3.57138 + 8.76271i) q^{39} +(0.877682 + 0.169159i) q^{41} +(0.287793 + 0.249374i) q^{43} +(7.75166 + 9.17375i) q^{45} +(1.32173 - 2.56380i) q^{47} +(-7.51452 + 1.44831i) q^{49} +(-7.79274 - 8.27512i) q^{51} +(2.31995 + 2.67736i) q^{53} +(4.30508 + 17.7458i) q^{55} +(3.81616 + 11.2517i) q^{57} +(-2.25065 - 7.66500i) q^{59} +(0.666695 - 1.66532i) q^{61} +(-9.27086 - 6.77690i) q^{63} +(-17.8160 + 12.6867i) q^{65} +(-2.35801 + 7.83835i) q^{67} +(-0.371982 - 0.732684i) q^{69} +(-0.304090 - 0.105247i) q^{71} +(-3.59390 - 1.43878i) q^{73} +(2.60070 + 18.9220i) q^{75} +(-8.00061 - 15.5190i) q^{77} +(1.01436 - 0.246082i) q^{79} +(-1.05910 - 8.93747i) q^{81} +(7.37794 - 9.38182i) q^{83} +(-4.97218 - 25.7981i) q^{85} +(12.2617 + 8.84685i) q^{87} +(1.27636 - 1.98605i) q^{89} +(13.6948 - 15.8047i) q^{91} +(1.53613 + 0.542368i) q^{93} +(-6.47442 + 26.6879i) q^{95} +(-13.0824 - 7.55312i) q^{97} +(4.63581 - 12.8745i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 440 q - 12 q^{7} + 4 q^{9}+O(q^{10}) \) 440 * q - 12 * q^7 + 4 * q^9	\( 440 q - 12 q^{7} + 4 q^{9} - 2 q^{15} - 10 q^{19} + 22 q^{21} - 68 q^{25} + 50 q^{31} + 11 q^{33} - 22 q^{37} - 45 q^{39} + 22 q^{43} + 22 q^{45} - 18 q^{49} - 6 q^{51} + 126 q^{55} - 183 q^{57} - 56 q^{61} - 141 q^{63} - 12 q^{67} + 33 q^{69} + 356 q^{73} + 165 q^{75} + 228 q^{79} + 24 q^{81} - 6 q^{85} + 75 q^{87} - 4 q^{91} - 75 q^{93} + 12 q^{97} + 88 q^{99}+O(q^{100}) \) 440 * q - 12 * q^7 + 4 * q^9 - 2 * q^15 - 10 * q^19 + 22 * q^21 - 68 * q^25 + 50 * q^31 + 11 * q^33 - 22 * q^37 - 45 * q^39 + 22 * q^43 + 22 * q^45 - 18 * q^49 - 6 * q^51 + 126 * q^55 - 183 * q^57 - 56 * q^61 - 141 * q^63 - 12 * q^67 + 33 * q^69 + 356 * q^73 + 165 * q^75 + 228 * q^79 + 24 * q^81 - 6 * q^85 + 75 * q^87 - 4 * q^91 - 75 * q^93 + 12 * q^97 + 88 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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