LMFDB - Embedded newform 804.2.ba.b.41.14

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			41.14
Character	$\chi$	$=$	804.41
Dual form			804.2.ba.b.353.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.399410 - 1.68537i) q^{3} +(0.202812 - 1.41059i) q^{5} +(-0.147283 - 1.54242i) q^{7} +(-2.68094 - 1.34631i) q^{9} +O(q^{10})$	\(q+(0.399410 - 1.68537i) q^{3} +(0.202812 - 1.41059i) q^{5} +(-0.147283 - 1.54242i) q^{7} +(-2.68094 - 1.34631i) q^{9} +(2.41940 - 0.968583i) q^{11} +(-1.91962 - 2.01323i) q^{13} +(-2.29636 - 0.905215i) q^{15} +(-3.53951 + 1.22504i) q^{17} +(-0.0830309 - 0.00792849i) q^{19} +(-2.65838 - 0.367831i) q^{21} +(-0.357259 + 0.0170183i) q^{23} +(2.84884 + 0.836495i) q^{25} +(-3.33982 + 3.98065i) q^{27} +(-2.14642 + 1.23924i) q^{29} +(2.40107 - 2.51817i) q^{31} +(-0.666088 - 4.46445i) q^{33} +(-2.20559 - 0.105065i) q^{35} +(3.28486 - 5.68954i) q^{37} +(-4.15976 + 2.43116i) q^{39} +(-1.45686 - 0.280786i) q^{41} +(-6.93510 - 6.00930i) q^{43} +(-2.44281 + 3.50866i) q^{45} +(-5.86207 + 11.3708i) q^{47} +(4.51613 - 0.870413i) q^{49} +(0.650925 + 6.45468i) q^{51} +(-1.34621 - 1.55361i) q^{53} +(-0.875587 - 3.60922i) q^{55} +(-0.0465258 + 0.136771i) q^{57} +(0.862133 + 2.93616i) q^{59} +(4.16017 - 10.3916i) q^{61} +(-1.68171 + 4.33343i) q^{63} +(-3.22916 + 2.29948i) q^{65} +(8.16291 + 0.605750i) q^{67} +(-0.114010 + 0.608910i) q^{69} +(-3.54925 - 1.22841i) q^{71} +(-3.48722 - 1.39607i) q^{73} +(2.54766 - 4.46724i) q^{75} +(-1.85030 - 3.58908i) q^{77} +(-2.37878 + 0.577087i) q^{79} +(5.37492 + 7.21874i) q^{81} +(-3.35310 + 4.26381i) q^{83} +(1.01017 + 5.24124i) q^{85} +(1.23127 + 4.11248i) q^{87} +(4.10997 - 6.39524i) q^{89} +(-2.82253 + 3.25737i) q^{91} +(-3.28504 - 5.05248i) q^{93} +(-0.0280235 + 0.115514i) q^{95} +(1.05636 + 0.609890i) q^{97} +(-7.79029 - 0.660540i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	0.399410	−	1.68537i	0.230599	−	0.973049i
$3$	0.399410	−	1.68537i	0.230599	−	0.973049i
$4$		0			0
$5$	0.202812	−	1.41059i	0.0907002	−	0.630834i	−0.892871	−	0.450313i	$-0.851312\pi$
$5$	0.202812	−	1.41059i	0.0907002	−	0.630834i	0.983571	−	0.180521i	$-0.0577784\pi$
$6$		0			0
$7$	−0.147283	−	1.54242i	−0.0556679	−	0.582980i	−0.979673	−	0.200600i	$-0.935711\pi$
$7$	−0.147283	−	1.54242i	−0.0556679	−	0.582980i	0.924005	−	0.382380i	$-0.124895\pi$
$8$		0			0
$9$	−2.68094	−	1.34631i	−0.893648	−	0.448769i
$10$		0			0
$11$	2.41940	−	0.968583i	0.729477	−	0.292039i	0.0229619	−	0.999736i	$-0.492690\pi$
$11$	2.41940	−	0.968583i	0.729477	−	0.292039i	0.706515	+	0.707698i	$0.250266\pi$
$12$		0			0
$13$	−1.91962	−	2.01323i	−0.532405	−	0.558371i	0.401515	−	0.915853i	$-0.368484\pi$
$13$	−1.91962	−	2.01323i	−0.532405	−	0.558371i	−0.933920	+	0.357482i	$0.883635\pi$
$14$		0			0
$15$	−2.29636	−	0.905215i	−0.592917	−	0.233726i
$16$		0			0
$17$	−3.53951	+	1.22504i	−0.858458	+	0.297115i	−0.720612	−	0.693339i	$-0.756139\pi$
$17$	−3.53951	+	1.22504i	−0.858458	+	0.297115i	−0.137846	+	0.990454i	$0.544018\pi$
$18$		0			0
$19$	−0.0830309	−	0.00792849i	−0.0190486	−	0.00181892i	0.0855274	−	0.996336i	$-0.472742\pi$
$19$	−0.0830309	−	0.00792849i	−0.0190486	−	0.00181892i	−0.104576	+	0.994517i	$0.533349\pi$
$20$		0			0
$21$	−2.65838	−	0.367831i	−0.580105	−	0.0802673i
$22$		0			0
$23$	−0.357259	+	0.0170183i	−0.0744936	+	0.00354857i	−0.0847956	−	0.996398i	$-0.527024\pi$
$23$	−0.357259	+	0.0170183i	−0.0744936	+	0.00354857i	0.0103020	+	0.999947i	$0.496721\pi$
$24$		0			0
$25$	2.84884	+	0.836495i	0.569768	+	0.167299i
$26$		0			0
$27$	−3.33982	+	3.98065i	−0.642748	+	0.766077i
$28$		0			0
$29$	−2.14642	+	1.23924i	−0.398581	+	0.230121i	−0.685872	−	0.727723i	$-0.740579\pi$
$29$	−2.14642	+	1.23924i	−0.398581	+	0.230121i	0.287291	+	0.957843i	$0.407245\pi$
$30$		0			0
$31$	2.40107	−	2.51817i	0.431245	−	0.452277i	−0.471875	−	0.881666i	$-0.656422\pi$
$31$	2.40107	−	2.51817i	0.431245	−	0.452277i	0.903120	+	0.429389i	$0.141271\pi$
$32$		0			0
$33$	−0.666088	−	4.46445i	−0.115951	−	0.777161i
$34$		0			0
$35$	−2.20559	−	0.105065i	−0.372813	−	0.0177593i
$36$		0			0
$37$	3.28486	−	5.68954i	0.540027	−	0.935354i	−0.458875	−	0.888501i	$-0.651747\pi$
$37$	3.28486	−	5.68954i	0.540027	−	0.935354i	0.998902	−	0.0468534i	$-0.0149193\pi$
$38$		0			0
$39$	−4.15976	+	2.43116i	−0.666094	+	0.389297i
$40$		0			0
$41$	−1.45686	−	0.280786i	−0.227523	−	0.0438514i	0.0742156	−	0.997242i	$-0.476355\pi$
$41$	−1.45686	−	0.280786i	−0.227523	−	0.0438514i	−0.301738	+	0.953391i	$0.597567\pi$
$42$		0			0
$43$	−6.93510	−	6.00930i	−1.05759	−	0.916409i	−0.0609383	−	0.998142i	$-0.519409\pi$
$43$	−6.93510	−	6.00930i	−1.05759	−	0.916409i	−0.996654	+	0.0817323i	$0.973955\pi$
$44$		0			0
$45$	−2.44281	+	3.50866i	−0.364153	+	0.523040i
$46$		0			0
$47$	−5.86207	+	11.3708i	−0.855071	+	1.65861i	−0.107716	+	0.994182i	$0.534354\pi$
$47$	−5.86207	+	11.3708i	−0.855071	+	1.65861i	−0.747355	+	0.664425i	$0.768677\pi$
$48$		0			0
$49$	4.51613	−	0.870413i	0.645162	−	0.124345i
$50$		0			0
$51$	0.650925	+	6.45468i	0.0911478	+	0.903836i
$52$		0			0
$53$	−1.34621	−	1.55361i	−0.184916	−	0.213405i	0.655721	−	0.755003i	$-0.272365\pi$
$53$	−1.34621	−	1.55361i	−0.184916	−	0.213405i	−0.840637	+	0.541598i	$0.817819\pi$
$54$		0			0
$55$	−0.875587	−	3.60922i	−0.118064	−	0.486667i
$56$		0			0
$57$	−0.0465258	+	0.136771i	−0.00616249	+	0.0181158i
$58$		0			0
$59$	0.862133	+	2.93616i	0.112240	+	0.382255i	0.996384	−	0.0849590i	$-0.0270759\pi$
$59$	0.862133	+	2.93616i	0.112240	+	0.382255i	−0.884144	+	0.467214i	$0.845258\pi$
$60$		0			0
$61$	4.16017	−	10.3916i	0.532655	−	1.33051i	−0.381209	−	0.924489i	$-0.624492\pi$
$61$	4.16017	−	10.3916i	0.532655	−	1.33051i	0.913864	−	0.406020i	$-0.133084\pi$
$62$		0			0
$63$	−1.68171	+	4.33343i	−0.211876	+	0.545961i
$64$		0			0
$65$	−3.22916	+	2.29948i	−0.400529	+	0.285215i
$66$		0			0
$67$	8.16291	+	0.605750i	0.997258	+	0.0740041i
$67$	8.16291	+	0.605750i	0.997258	+	0.0740041i
$68$		0			0
$69$	−0.114010	+	0.608910i	−0.0137252	+	0.0733042i
$70$		0			0
$71$	−3.54925	−	1.22841i	−0.421219	−	0.145785i	0.108232	−	0.994126i	$-0.465481\pi$
$71$	−3.54925	−	1.22841i	−0.421219	−	0.145785i	−0.529451	+	0.848340i	$0.677602\pi$
$72$		0			0
$73$	−3.48722	−	1.39607i	−0.408148	−	0.163398i	0.158498	−	0.987359i	$-0.449335\pi$
$73$	−3.48722	−	1.39607i	−0.408148	−	0.163398i	−0.566646	+	0.823962i	$0.691759\pi$
$74$		0			0
$75$	2.54766	−	4.46724i	0.294178	−	0.515833i
$76$		0			0
$77$	−1.85030	−	3.58908i	−0.210861	−	0.409014i
$78$		0			0
$79$	−2.37878	+	0.577087i	−0.267634	+	0.0649273i	−0.367330	−	0.930091i	$-0.619728\pi$
$79$	−2.37878	+	0.577087i	−0.267634	+	0.0649273i	0.0996961	+	0.995018i	$0.468213\pi$
$80$		0			0
$81$	5.37492	+	7.21874i	0.597213	+	0.802082i
$82$		0			0
$83$	−3.35310	+	4.26381i	−0.368051	+	0.468014i	−0.934439	−	0.356124i	$-0.884098\pi$
$83$	−3.35310	+	4.26381i	−0.368051	+	0.468014i	0.566388	+	0.824139i	$0.308340\pi$
$84$		0			0
$85$	1.01017	+	5.24124i	0.109568	+	0.568493i
$86$		0			0
$87$	1.23127	+	4.11248i	0.132006	+	0.440904i
$88$		0			0
$89$	4.10997	−	6.39524i	0.435656	−	0.677894i	−0.552122	−	0.833763i	$-0.686182\pi$
$89$	4.10997	−	6.39524i	0.435656	−	0.677894i	0.987778	+	0.155870i	$0.0498180\pi$
$90$		0			0
$91$	−2.82253	+	3.25737i	−0.295881	+	0.341465i
$92$		0			0
$93$	−3.28504	−	5.05248i	−0.340643	−	0.523917i
$94$		0			0
$95$	−0.0280235	+	0.115514i	−0.00287515	+	0.0118515i
$96$		0			0
$97$	1.05636	+	0.609890i	0.107257	+	0.0619250i	0.552669	−	0.833401i	$-0.313609\pi$
$97$	1.05636	+	0.609890i	0.107257	+	0.0619250i	−0.445412	+	0.895326i	$0.646943\pi$
$98$		0			0
$99$	−7.79029	−	0.660540i	−0.782954	−	0.0663868i
$100$		0			0
$101$	6.68674	−	9.39021i	0.665355	−	0.934360i	−0.334613	−	0.942356i	$-0.608606\pi$
$101$	6.68674	−	9.39021i	0.665355	−	0.934360i	0.999968	+	0.00799517i	$0.00254497\pi$
$102$		0			0
$103$	0.528083	+	0.503526i	0.0520335	+	0.0496139i	0.715650	−	0.698459i	$-0.246131\pi$
$103$	0.528083	+	0.503526i	0.0520335	+	0.0496139i	−0.663616	+	0.748073i	$0.730979\pi$
$104$		0			0
$105$	−1.05801	+	3.67527i	−0.103251	+	0.358670i
$106$		0			0
$107$	6.25579	−	0.899446i	0.604770	−	0.0869527i	0.166874	−	0.985978i	$-0.446633\pi$
$107$	6.25579	−	0.899446i	0.604770	−	0.0869527i	0.437896	+	0.899026i	$0.355724\pi$
$108$		0			0
$109$	3.35712	−	11.4333i	0.321554	−	1.09511i	−0.627138	−	0.778908i	$-0.715774\pi$
$109$	3.35712	−	11.4333i	0.321554	−	1.09511i	0.948692	−	0.316203i	$-0.102408\pi$
$110$		0			0
$111$	−8.27697	−	7.80865i	−0.785616	−	0.741165i
$112$		0			0
$113$	6.30125	−	4.95536i	0.592772	−	0.466161i	−0.276147	−	0.961115i	$-0.589058\pi$
$113$	6.30125	−	4.95536i	0.592772	−	0.466161i	0.868919	+	0.494954i	$0.164815\pi$
$114$		0			0
$115$	−0.0484505	+	0.507396i	−0.00451803	+	0.0473149i
$116$		0			0
$117$	2.43595	+	7.98176i	0.225204	+	0.737914i
$118$		0			0
$119$	2.41083	+	5.27899i	0.221001	+	0.483924i
$120$		0			0
$121$	−3.04572	+	2.90409i	−0.276883	+	0.264008i
$122$		0			0
$123$	−1.05511	+	2.34319i	−0.0951361	+	0.211278i
$124$		0			0
$125$	4.71775	−	10.3304i	0.421969	−	0.923983i
$126$		0			0
$127$	11.8766	−	1.13408i	1.05388	−	0.100633i	0.446292	−	0.894887i	$-0.352744\pi$
$127$	11.8766	−	1.13408i	1.05388	−	0.100633i	0.607586	+	0.794254i	$0.292138\pi$
$128$		0			0
$129$	−12.8978	+	9.28804i	−1.13559	+	0.817766i
$130$		0			0
$131$	3.67671	+	5.72108i	0.321236	+	0.499853i	0.963889	−	0.266305i	$-0.0858027\pi$
$131$	3.67671	+	5.72108i	0.321236	+	0.499853i	−0.642653	+	0.766157i	$0.722166\pi$
$132$		0			0
$133$			0.129236i			0.0112062i
$134$		0			0
$135$	4.93771	+	5.51843i	0.424970	+	0.474951i
$136$		0			0
$137$	−1.14559	+	0.736228i	−0.0978746	+	0.0629002i	−0.588663	−	0.808379i	$-0.700345\pi$
$137$	−1.14559	+	0.736228i	−0.0978746	+	0.0629002i	0.490788	+	0.871279i	$0.336709\pi$
$138$		0			0
$139$	10.8784	+	1.56408i	0.922694	+	0.132663i	0.587258	−	0.809400i	$-0.300207\pi$
$139$	10.8784	+	1.56408i	0.922694	+	0.132663i	0.335436	+	0.942063i	$0.391116\pi$
$140$		0			0
$141$	16.8227	+	14.4214i	1.41673	+	1.21450i
$142$		0			0
$143$	−6.59431	−	3.01152i	−0.551444	−	0.251836i
$144$		0			0
$145$	1.31273	+	3.27905i	0.109017	+	0.272310i
$146$		0			0
$147$	0.336818	−	7.95900i	0.0277803	−	0.656448i
$148$		0			0
$149$	15.7872	−	7.20977i	1.29334	−	0.590648i	0.354516	−	0.935050i	$-0.384646\pi$
$149$	15.7872	−	7.20977i	1.29334	−	0.590648i	0.938822	+	0.344403i	$0.111919\pi$
$150$		0			0
$151$	0.992148	+	2.86662i	0.0807399	+	0.233283i	0.978145	−	0.207926i	$-0.0666712\pi$
$151$	0.992148	+	2.86662i	0.0807399	+	0.233283i	−0.897405	+	0.441208i	$0.854550\pi$
$152$		0			0
$153$	11.1385	+	1.48101i	0.900495	+	0.119733i
$154$		0			0
$155$	−3.06514	−	3.89764i	−0.246198	−	0.313066i
$156$		0			0
$157$	0.328555	+	6.89723i	0.0262216	+	0.550459i	0.973311	+	0.229489i	$0.0737056\pi$
$157$	0.328555	+	6.89723i	0.0262216	+	0.550459i	−0.947090	+	0.320969i	$0.895991\pi$
$158$		0			0
$159$	−3.15610	+	1.64834i	−0.250295	+	0.130722i
$160$		0			0
$161$	0.0788676	+	0.548536i	0.00621564	+	0.0432307i
$162$		0			0
$163$	3.61487	+	6.26113i	0.283138	+	0.490410i	0.972156	−	0.234335i	$-0.0752912\pi$
$163$	3.61487	+	6.26113i	0.283138	+	0.490410i	−0.689018	+	0.724744i	$0.741958\pi$
$164$		0			0
$165$	−6.43259	+	0.0341313i	−0.500776	+	0.00265712i
$166$		0			0
$167$	2.39412	+	1.70485i	0.185263	+	0.131925i	0.668925	−	0.743329i	$-0.266755\pi$
$167$	2.39412	+	1.70485i	0.185263	+	0.131925i	−0.483663	+	0.875254i	$0.660694\pi$
$168$		0			0
$169$	0.250374	−	5.25600i	0.0192596	−	0.404308i
$170$		0			0
$171$	0.211927	+	0.133041i	0.0162065	+	0.0101739i
$172$		0			0
$173$	−5.89177	−	1.42933i	−0.447943	−	0.108670i	0.00544065	−	0.999985i	$-0.498268\pi$
$173$	−5.89177	−	1.42933i	−0.447943	−	0.108670i	−0.453384	+	0.891315i	$0.649783\pi$
$174$		0			0
$175$	0.870640	−	4.51731i	0.0658142	−	0.341477i
$176$		0			0
$177$	5.29285	−	0.280284i	0.397835	−	0.0210675i
$178$		0			0
$179$	4.82757	+	3.10249i	0.360829	+	0.231891i	0.708476	−	0.705735i	$-0.249383\pi$
$179$	4.82757	+	3.10249i	0.360829	+	0.231891i	−0.347647	+	0.937626i	$0.613019\pi$
$180$		0			0
$181$	20.1033	+	10.3640i	1.49427	+	0.770348i	0.995352	−	0.0963033i	$-0.0307019\pi$
$181$	20.1033	+	10.3640i	1.49427	+	0.770348i	0.498915	+	0.866651i	$0.333732\pi$
$182$		0			0
$183$	−15.8521	−	11.1619i	−1.17182	−	0.825114i
$184$		0			0
$185$	−7.35939	−	5.78748i	−0.541073	−	0.425504i
$186$		0			0
$187$	−7.37695	+	6.39217i	−0.539456	+	0.467442i
$188$		0			0
$189$	6.63174	+	4.56512i	0.482388	+	0.332064i
$190$		0			0
$191$	24.0016	−	12.3737i	1.73669	−	0.895328i	0.770527	−	0.637407i	$-0.219993\pi$
$191$	24.0016	−	12.3737i	1.73669	−	0.895328i	0.966166	−	0.257921i	$-0.0830374\pi$
$192$		0			0
$193$	2.62247	−	0.770026i	0.188769	−	0.0554277i	−0.185981	−	0.982553i	$-0.559546\pi$
$193$	2.62247	−	0.770026i	0.188769	−	0.0554277i	0.374751	+	0.927126i	$0.377728\pi$
$194$		0			0
$195$	2.58571	+	6.36077i	0.185167	+	0.455504i
$196$		0			0
$197$	−0.305616	+	0.883020i	−0.0217743	+	0.0629126i	−0.955364	−	0.295430i	$-0.904537\pi$
$197$	−0.305616	+	0.883020i	−0.0217743	+	0.0629126i	0.933590	+	0.358343i	$0.116658\pi$
$198$		0			0
$199$	0.0656217	+	0.0921528i	0.00465180	+	0.00653254i	0.816895	−	0.576786i	$-0.195693\pi$
$199$	0.0656217	+	0.0921528i	0.00465180	+	0.00653254i	−0.812244	+	0.583319i	$0.801754\pi$
$200$		0			0
$201$	4.28126	−	13.5156i	0.301977	−	0.953315i
$202$		0			0
$203$	2.22756	+	3.12817i	0.156344	+	0.219555i
$204$		0			0
$205$	−0.691541	+	1.99808i	−0.0482993	+	0.139552i
$206$		0			0
$207$	0.980702	+	0.435354i	0.0681635	+	0.0302592i
$208$		0			0
$209$	−0.208565	+	0.0612401i	−0.0144267	+	0.00423607i
$210$		0			0
$211$	−18.2747	+	9.42126i	−1.25808	+	0.648587i	−0.952778	−	0.303668i	$-0.901789\pi$
$211$	−18.2747	+	9.42126i	−1.25808	+	0.648587i	−0.305305	+	0.952255i	$0.598758\pi$
$212$		0			0
$213$	−3.48793	+	5.49117i	−0.238989	+	0.376248i
$214$		0			0
$215$	−9.88316	+	8.56381i	−0.674026	+	0.584047i
$216$		0			0
$217$	−4.23772	−	3.33258i	−0.287675	−	0.226230i
$218$		0			0
$219$	−3.74572	+	5.31965i	−0.253113	+	0.359468i
$220$		0			0
$221$	9.26079	+	4.77427i	0.622948	+	0.321152i
$222$		0			0
$223$	−5.19600	−	3.33927i	−0.347950	−	0.223614i	0.354979	−	0.934874i	$-0.384488\pi$
$223$	−5.19600	−	3.33927i	−0.347950	−	0.223614i	−0.702928	+	0.711261i	$0.748125\pi$
$224$		0			0
$225$	−6.51140	−	6.07801i	−0.434093	−	0.405200i
$226$		0			0
$227$	−4.20062	+	21.7949i	−0.278805	+	1.44658i	0.524704	+	0.851285i	$0.324176\pi$
$227$	−4.20062	+	21.7949i	−0.278805	+	1.44658i	−0.803509	+	0.595292i	$0.797036\pi$
$228$		0			0
$229$	4.93842	+	1.19805i	0.326340	+	0.0791693i	0.395582	−	0.918431i	$-0.370543\pi$
$229$	4.93842	+	1.19805i	0.326340	+	0.0791693i	−0.0692419	+	0.997600i	$0.522058\pi$
$230$		0			0
$231$	−6.78796	+	1.68493i	−0.446615	+	0.110860i
$232$		0			0
$233$	−0.859288	+	18.0387i	−0.0562938	+	1.18175i	0.777211	+	0.629240i	$0.216634\pi$
$233$	−0.859288	+	18.0387i	−0.0562938	+	1.18175i	−0.833505	+	0.552512i	$0.813669\pi$
$234$		0			0
$235$	14.8507	+	10.5751i	0.968750	+	0.689844i
$236$		0			0
$237$	0.0224955	+	4.23962i	0.00146124	+	0.275393i
$238$		0			0
$239$	−11.4331	−	19.8027i	−0.739545	−	1.28093i	−0.952700	−	0.303911i	$-0.901707\pi$
$239$	−11.4331	−	19.8027i	−0.739545	−	1.28093i	0.213156	−	0.977018i	$-0.431626\pi$
$240$		0			0
$241$	−2.88317	−	20.0529i	−0.185722	−	1.29172i	−0.842934	−	0.538017i	$-0.819174\pi$
$241$	−2.88317	−	20.0529i	−0.185722	−	1.29172i	0.657213	−	0.753705i	$-0.271735\pi$
$242$		0			0
$243$	14.3130	−	6.17549i	0.918182	−	0.396158i
$244$		0			0
$245$	−0.311869	−	6.54693i	−0.0199246	−	0.418268i
$246$		0			0
$247$	0.143425	+	0.182380i	0.00912595	+	0.0116046i
$248$		0			0
$249$	5.84684	+	7.35422i	0.370529	+	0.466055i
$250$		0			0
$251$	2.54986	+	7.36734i	0.160946	+	0.465022i	0.996423	−	0.0845023i	$-0.0269300\pi$
$251$	2.54986	+	7.36734i	0.160946	+	0.465022i	−0.835477	+	0.549525i	$0.814809\pi$
$252$		0			0
$253$	−0.847869	+	0.387209i	−0.0533050	+	0.0243436i
$254$		0			0
$255$	9.23690	+	0.390898i	0.578437	+	0.0244790i
$256$		0			0
$257$	10.2940	+	25.7132i	0.642122	+	1.60394i	0.788724	+	0.614748i	$0.210742\pi$
$257$	10.2940	+	25.7132i	0.642122	+	1.60394i	−0.146602	+	0.989196i	$0.546834\pi$
$258$		0			0
$259$	−9.25947	−	4.22866i	−0.575355	−	0.262756i
$260$		0			0
$261$	7.42284	−	0.432586i	0.459462	−	0.0267764i
$262$		0			0
$263$	−6.22844	−	0.895514i	−0.384062	−	0.0552198i	−0.0524201	−	0.998625i	$-0.516693\pi$
$263$	−6.22844	−	0.895514i	−0.384062	−	0.0552198i	−0.331642	+	0.943405i	$0.607603\pi$
$264$		0			0
$265$	−2.46453	+	1.58386i	−0.151395	+	0.0972957i
$266$		0			0
$267$	−9.13678	−	9.48114i	−0.559162	−	0.580236i
$268$		0			0
$269$			13.0797i			0.797486i	0.917063	+	0.398743i	$0.130553\pi$
$269$			13.0797i			0.797486i	−0.917063	+	0.398743i	$0.869447\pi$
$270$		0			0
$271$	4.10696	+	6.39055i	0.249480	+	0.388199i	0.943295	−	0.331954i	$-0.107708\pi$
$271$	4.10696	+	6.39055i	0.249480	+	0.388199i	−0.693815	+	0.720153i	$0.744072\pi$
$272$		0			0
$273$	4.36253	+	6.05803i	0.264032	+	0.366649i
$274$		0			0
$275$	7.70270	−	0.735519i	0.464491	−	0.0443535i
$276$		0			0
$277$	6.98148	−	15.2873i	0.419477	−	0.918526i	−0.575442	−	0.817843i	$-0.695170\pi$
$277$	6.98148	−	15.2873i	0.419477	−	0.918526i	0.994919	−	0.100683i	$-0.0321028\pi$
$278$		0			0
$279$	−9.82737	+	3.51850i	−0.588349	+	0.210647i
$280$		0			0
$281$	14.5570	−	13.8800i	0.868396	−	0.828013i	−0.117896	−	0.993026i	$-0.537615\pi$
$281$	14.5570	−	13.8800i	0.868396	−	0.828013i	0.986291	+	0.165012i	$0.0527664\pi$
$282$		0			0
$283$	0.488456	+	1.06957i	0.0290357	+	0.0635793i	0.923594	−	0.383372i	$-0.125237\pi$
$283$	0.488456	+	1.06957i	0.0290357	+	0.0635793i	−0.894558	+	0.446951i	$0.852510\pi$
$284$		0			0
$285$	0.183492	+	0.0933675i	0.0108691	+	0.00553061i
$286$		0			0
$287$	−0.218519	+	2.28844i	−0.0128988	+	0.135082i
$288$		0			0
$289$	−2.33548	+	1.83664i	−0.137381	+	0.108038i
$290$		0			0
$291$	1.44981	−	1.53676i	0.0849894	−	0.0900866i
$292$		0			0
$293$	−0.126387	+	0.430435i	−0.00738362	+	0.0251463i	−0.963102	−	0.269135i	$-0.913262\pi$
$293$	−0.126387	+	0.430435i	−0.00738362	+	0.0251463i	0.955719	+	0.294282i	$0.0950803\pi$
$294$		0			0
$295$	4.31656	−	0.620627i	0.251320	−	0.0361343i
$296$		0			0
$297$	−4.22477	+	12.8657i	−0.245146	+	0.746543i
$298$		0			0
$299$	0.720061	+	0.686577i	0.0416422	+	0.0397058i
$300$		0			0
$301$	−8.24744	+	11.5819i	−0.475375	+	0.667570i
$302$		0			0
$303$	−13.1552	−	15.0202i	−0.755748	−	0.862886i
$304$		0			0
$305$	−13.8145	−	7.97583i	−0.791018	−	0.456694i
$306$		0			0
$307$	−7.26725	+	29.9560i	−0.414764	+	1.70968i	0.254859	+	0.966978i	$0.417971\pi$
$307$	−7.26725	+	29.9560i	−0.414764	+	1.70968i	−0.669623	+	0.742701i	$0.733544\pi$
$308$		0			0
$309$	1.05955	−	0.688902i	0.0602756	−	0.0391903i
$310$		0			0
$311$	−4.38634	+	5.06210i	−0.248726	+	0.287045i	−0.866360	−	0.499421i	$-0.833546\pi$
$311$	−4.38634	+	5.06210i	−0.248726	+	0.287045i	0.617633	+	0.786466i	$0.288092\pi$
$312$		0			0
$313$	10.4654	−	16.2844i	0.591538	−	0.920450i	−0.408433	−	0.912788i	$-0.633925\pi$
$313$	10.4654	−	16.2844i	0.591538	−	0.920450i	0.999971	−	0.00766215i	$-0.00243896\pi$
$314$		0			0
$315$	5.77161	+	3.25107i	0.325194	+	0.183177i
$316$		0			0
$317$	−1.11635	−	5.79218i	−0.0627005	−	0.325321i	0.937012	−	0.349297i	$-0.113580\pi$
$317$	−1.11635	−	5.79218i	−0.0627005	−	0.325321i	−0.999713	+	0.0239760i	$0.992367\pi$
$318$		0			0
$319$	−3.99276	+	5.07721i	−0.223552	+	0.284269i
$320$		0			0
$321$	0.982721	−	10.9026i	0.0548502	−	0.608522i
$322$		0			0
$323$	0.303602	−	0.0736529i	0.0168928	−	0.00409816i
$324$		0			0
$325$	−3.78462	−	7.34113i	−0.209933	−	0.407213i
$326$		0			0
$327$	−17.9285	−	10.2246i	−0.991447	−	0.565419i
$328$		0			0
$329$	18.4020	+	7.36705i	1.01453	+	0.406158i
$330$		0			0
$331$	−0.801830	−	0.277516i	−0.0440726	−	0.0152537i	0.304943	−	0.952371i	$-0.401363\pi$
$331$	−0.801830	−	0.277516i	−0.0440726	−	0.0152537i	−0.349015	+	0.937117i	$0.613484\pi$
$332$		0			0
$333$	−16.4664	+	10.8309i	−0.902352	+	0.593530i
$334$		0			0
$335$	2.51000	−	11.3916i	0.137136	−	0.622392i
$336$		0			0
$337$	−3.49556	+	2.48918i	−0.190415	+	0.135594i	−0.671289	−	0.741196i	$-0.734259\pi$
$337$	−3.49556	+	2.48918i	−0.190415	+	0.135594i	0.480874	+	0.876790i	$0.340320\pi$
$338$		0			0
$339$	−5.83484	−	12.5992i	−0.316905	−	0.684293i
$340$		0			0
$341$	3.37010	−	8.41811i	0.182501	−	0.455866i
$342$		0			0
$343$	−5.06338	−	17.2443i	−0.273397	−	0.931104i
$344$		0			0
$345$	0.835799	+	0.284316i	0.0449979	+	0.0153070i
$346$		0			0
$347$	−5.13930	−	21.1845i	−0.275892	−	1.13724i	−0.926037	−	0.377433i	$-0.876807\pi$
$347$	−5.13930	−	21.1845i	−0.275892	−	1.13724i	0.650145	−	0.759810i	$-0.274708\pi$
$348$		0			0
$349$	−11.2600	−	12.9947i	−0.602732	−	0.695590i	0.369600	−	0.929191i	$-0.379495\pi$
$349$	−11.2600	−	12.9947i	−0.602732	−	0.695590i	−0.972333	+	0.233601i	$0.924949\pi$
$350$		0			0
$351$	14.4252	−	0.917488i	0.769958	−	0.0489719i
$352$		0			0
$353$	−33.7883	+	6.51216i	−1.79837	+	0.346607i	−0.975224	−	0.221221i	$-0.928996\pi$
$353$	−33.7883	+	6.51216i	−1.79837	+	0.346607i	−0.823147	+	0.567829i	$0.807784\pi$
$354$		0			0
$355$	−2.45261	+	4.75740i	−0.130171	+	0.252496i
$356$		0			0
$357$	9.85996	−	1.95467i	0.521844	−	0.103452i
$358$		0			0
$359$	−9.21787	−	7.98733i	−0.486501	−	0.421555i	0.376762	−	0.926310i	$-0.377037\pi$
$359$	−9.21787	−	7.98733i	−0.486501	−	0.421555i	−0.863263	+	0.504755i	$0.831583\pi$
$360$		0			0
$361$	−18.6498	−	3.59446i	−0.981569	−	0.189182i
$362$		0			0
$363$	3.67797	+	6.29308i	0.193043	+	0.330301i
$364$		0			0
$365$	−2.67653	+	4.63589i	−0.140096	+	0.242653i
$366$		0			0
$367$	−12.5256	−	0.596669i	−0.653832	−	0.0311459i	−0.281955	−	0.959428i	$-0.590983\pi$
$367$	−12.5256	−	0.596669i	−0.653832	−	0.0311459i	−0.371877	+	0.928282i	$0.621286\pi$
$368$		0			0
$369$	3.52772	+	2.71414i	0.183646	+	0.141293i
$370$		0			0
$371$	−2.19805	+	2.30525i	−0.114117	+	0.119682i
$372$		0			0
$373$	17.8677	−	10.3159i	0.925152	−	0.534137i	0.0398769	−	0.999205i	$-0.487303\pi$
$373$	17.8677	−	10.3159i	0.925152	−	0.534137i	0.885275	+	0.465068i	$0.153970\pi$
$374$		0			0
$375$	−15.5263	−	12.0772i	−0.801774	−	0.623666i
$376$		0			0
$377$	6.61519	+	1.94239i	0.340700	+	0.100038i
$378$		0			0
$379$	3.61034	−	0.171982i	0.185451	−	0.00883410i	0.0453489	−	0.998971i	$-0.485560\pi$
$379$	3.61034	−	0.171982i	0.185451	−	0.00883410i	0.140102	+	0.990137i	$0.455257\pi$
$380$		0			0
$381$	2.83229	−	20.4694i	0.145103	−	1.04868i
$382$		0			0
$383$	−33.6647	−	3.21459i	−1.72019	−	0.164258i	−0.812234	−	0.583332i	$-0.801749\pi$
$383$	−33.6647	−	3.21459i	−1.72019	−	0.164258i	−0.907952	+	0.419075i	$0.862355\pi$
$384$		0			0
$385$	−5.43798	+	1.88210i	−0.277145	+	0.0959208i
$386$		0			0
$387$	10.5023	+	25.4474i	0.533860	+	1.29356i
$388$		0			0
$389$	−5.78914	−	6.07148i	−0.293521	−	0.307836i	0.560417	−	0.828211i	$-0.310641\pi$
$389$	−5.78914	−	6.07148i	−0.293521	−	0.307836i	−0.853938	+	0.520374i	$0.825792\pi$
$390$		0			0
$391$	1.24367	−	0.497891i	0.0628952	−	0.0251795i
$392$		0			0
$393$	11.1106	−	3.91157i	0.560458	−	0.197312i
$394$		0			0
$395$	0.331586	+	3.47252i	0.0166839	+	0.174722i
$396$		0			0
$397$	−0.615406	+	4.28024i	−0.0308864	+	0.214819i	−0.999420	−	0.0340648i	$-0.989155\pi$
$397$	−0.615406	+	4.28024i	−0.0308864	+	0.214819i	0.968533	+	0.248884i	$0.0800638\pi$
$398$		0			0
$399$	0.217811	+	0.0516182i	0.0109042	+	0.00258414i
$400$		0			0
$401$	−8.18648			−0.408813			−0.204407	−	0.978886i	$-0.565526\pi$
$401$	−8.18648			−0.408813			−0.204407	+	0.978886i	$0.565526\pi$
$402$		0			0
$403$	−9.67881			−0.482136
$404$		0			0
$405$	11.2728	−	6.11775i	0.560148	−	0.303993i
$406$		0			0
$407$	2.43660	−	16.9469i	0.120778	−	0.840029i
$408$		0			0
$409$	0.349654	+	3.66174i	0.0172893	+	0.181062i	0.999991	−	0.00413133i	$-0.00131505\pi$
$409$	0.349654	+	3.66174i	0.0172893	+	0.181062i	−0.982702	+	0.185193i	$0.940709\pi$
$410$		0			0
$411$	0.783255	+	2.22480i	0.0386351	+	0.109741i
$412$		0			0
$413$	4.40181	−	1.76222i	0.216599	−	0.0867131i
$414$		0			0
$415$	5.33444	+	5.59460i	0.261857	+	0.274628i
$416$		0			0
$417$	6.98099	−	17.7094i	0.341860	−	0.867234i
$418$		0			0
$419$	19.7012	−	6.81865i	0.962466	−	0.333113i	0.199750	−	0.979847i	$-0.435987\pi$
$419$	19.7012	−	6.81865i	0.962466	−	0.333113i	0.762716	+	0.646734i	$0.223866\pi$
$420$		0			0
$421$	−2.93353	−	0.280118i	−0.142972	−	0.0136521i	0.0233249	−	0.999728i	$-0.492575\pi$
$421$	−2.93353	−	0.280118i	−0.142972	−	0.0136521i	−0.166296	+	0.986076i	$0.553181\pi$
$422$		0			0
$423$	31.0245	−	22.5924i	1.50846	−	1.09848i
$424$		0			0
$425$	−11.1082	+	0.529151i	−0.538829	+	0.0256676i
$426$		0			0
$427$	−16.6409	−	4.88622i	−0.805312	−	0.236461i
$428$		0			0
$429$	−7.70935	+	9.91102i	−0.372211	+	0.478508i
$430$		0			0
$431$	0.139674	−	0.0806411i	0.00672788	−	0.00388434i	−0.496632	−	0.867961i	$-0.665430\pi$
$431$	0.139674	−	0.0806411i	0.00672788	−	0.00388434i	0.503360	+	0.864077i	$0.332097\pi$
$432$		0			0
$433$	−9.23625	+	9.68670i	−0.443866	+	0.465513i	−0.907218	−	0.420661i	$-0.861798\pi$
$433$	−9.23625	+	9.68670i	−0.443866	+	0.465513i	0.463352	+	0.886174i	$0.346647\pi$
$434$		0			0
$435$	6.05074	−	0.902758i	0.290111	−	0.0432840i
$436$		0			0
$437$	0.0297984	+	0.00141947i	0.00142545	+	6.79027e-5i
$438$		0			0
$439$	10.2184	−	17.6988i	0.487699	−	0.844719i	−0.512201	−	0.858865i	$-0.671170\pi$
$439$	10.2184	−	17.6988i	0.487699	−	0.844719i	0.999900	+	0.0141468i	$0.00450321\pi$
$440$		0			0
$441$	−13.2793	−	3.74657i	−0.632349	−	0.178408i
$442$		0			0
$443$	−2.47875	−	0.477739i	−0.117769	−	0.0226981i	0.130026	−	0.991511i	$-0.458494\pi$
$443$	−2.47875	−	0.477739i	−0.117769	−	0.0226981i	−0.247795	+	0.968812i	$0.579706\pi$
$444$		0			0
$445$	−8.18749	−	7.09450i	−0.388124	−	0.336312i
$446$		0			0
$447$	−5.84557	−	29.4869i	−0.276486	−	1.39468i
$448$		0			0
$449$	−15.3573	+	29.7891i	−0.724757	+	1.40583i	0.181623	+	0.983368i	$0.441865\pi$
$449$	−15.3573	+	29.7891i	−0.724757	+	1.40583i	−0.906380	+	0.422464i	$0.861165\pi$
$450$		0			0
$451$	−3.79668	+	0.731751i	−0.178779	+	0.0344568i
$452$		0			0
$453$	5.22760	−	0.527180i	0.245614	−	0.0247691i
$454$		0			0
$455$	4.02236	+	4.64206i	0.188571	+	0.217623i
$456$		0			0
$457$	1.47064	+	6.06204i	0.0687935	+	0.283571i	0.995810	−	0.0914510i	$-0.0291505\pi$
$457$	1.47064	+	6.06204i	0.0687935	+	0.283571i	−0.927016	+	0.375021i	$0.877635\pi$
$458$		0			0
$459$	6.94488	−	18.1810i	0.324159	−	0.848615i
$460$		0			0
$461$	0.207098	+	0.705312i	0.00964552	+	0.0328496i	0.964175	−	0.265266i	$-0.0854599\pi$
$461$	0.207098	+	0.705312i	0.00964552	+	0.0328496i	−0.954530	+	0.298116i	$0.903642\pi$
$462$		0			0
$463$	2.50929	−	6.26790i	0.116616	−	0.291294i	−0.858564	−	0.512707i	$-0.828643\pi$
$463$	2.50929	−	6.26790i	0.116616	−	0.291294i	0.975180	+	0.221413i	$0.0710670\pi$
$464$		0			0
$465$	−7.79321	+	3.60913i	−0.361401	+	0.167370i
$466$		0			0
$467$	−16.6138	+	11.8307i	−0.768796	+	0.547457i	−0.895807	−	0.444444i	$-0.853401\pi$
$467$	−16.6138	+	11.8307i	−0.768796	+	0.547457i	0.127010	+	0.991901i	$0.459462\pi$
$468$		0			0
$469$	−0.267940	−	12.6799i	−0.0123723	−	0.585501i
$470$		0			0
$471$	11.7556	+	2.20108i	0.541670	+	0.101420i
$472$		0			0
$473$	−22.5993	−	7.82169i	−1.03912	−	0.359642i
$474$		0			0
$475$	−0.229910	−	0.0920419i	−0.0105490	−	0.00422317i
$476$		0			0
$477$	1.51748	+	5.97756i	0.0694807	+	0.273694i
$478$		0			0
$479$	9.11674	+	17.6840i	0.416554	+	0.808003i	0.999991	−	0.00415563i	$-0.00132278\pi$
$479$	9.11674	+	17.6840i	0.416554	+	0.808003i	−0.583437	+	0.812158i	$0.698292\pi$
$480$		0			0
$481$	−17.7600	+	4.30854i	−0.809788	+	0.196452i
$482$		0			0
$483$	0.955987	+	0.0861696i	0.0434989	+	0.00392085i
$484$		0			0
$485$	1.07455	−	1.36640i	0.0487926	−	0.0620449i
$486$		0			0
$487$	−1.09713	−	5.69243i	−0.0497155	−	0.257949i	0.948564	−	0.316586i	$-0.102537\pi$
$487$	−1.09713	−	5.69243i	−0.0497155	−	0.257949i	−0.998279	+	0.0586373i	$0.981324\pi$
$488$		0			0
$489$	11.9961	−	3.59163i	0.542484	−	0.162419i
$490$		0			0
$491$	18.9279	−	29.4524i	0.854204	−	1.32917i	−0.0886844	−	0.996060i	$-0.528266\pi$
$491$	18.9279	−	29.4524i	0.854204	−	1.32917i	0.942889	−	0.333108i	$-0.108097\pi$
$492$		0			0
$493$	6.07918	−	7.01575i	0.273793	−	0.315973i
$494$		0			0
$495$	−2.51171	+	10.8549i	−0.112893	+	0.487893i
$496$		0			0
$497$	−1.37198	+	5.65536i	−0.0615416	+	0.253678i
$498$		0			0
$499$	29.2314	+	16.8767i	1.30858	+	0.755507i	0.981859	−	0.189615i	$-0.0607240\pi$
$499$	29.2314	+	16.8767i	1.30858	+	0.755507i	0.326718	+	0.945122i	$0.394057\pi$
$500$		0			0
$501$	3.82953	−	3.35405i	0.171091	−	0.149848i
$502$		0			0
$503$	9.88721	−	13.8846i	0.440849	−	0.619086i	−0.533046	−	0.846086i	$-0.678953\pi$
$503$	9.88721	−	13.8846i	0.440849	−	0.619086i	0.973895	+	0.227001i	$0.0728920\pi$
$504$		0			0
$505$	−11.8896	−	11.3367i	−0.529079	−	0.504475i
$506$		0			0
$507$	−8.75831	−	2.52127i	−0.388970	−	0.111974i
$508$		0			0
$509$	−27.9399	+	4.01716i	−1.23842	+	0.178057i	−0.730237	−	0.683194i	$-0.760590\pi$
$509$	−27.9399	+	4.01716i	−1.23842	+	0.178057i	−0.508179	+	0.861251i	$0.669681\pi$
$510$		0			0
$511$	−1.63972	+	5.58437i	−0.0725369	+	0.247038i
$512$		0			0
$513$	0.308869	−	0.304038i	0.0136369	−	0.0134236i
$514$		0			0
$515$	0.817369	−	0.642786i	0.0360176	−	0.0283245i
$516$		0			0
$517$	−3.16912	+	33.1885i	−0.139378	+	1.45963i
$518$		0			0
$519$	−4.76218	+	9.35893i	−0.209036	+	0.410811i
$520$		0			0
$521$	5.69828	+	12.4775i	0.249646	+	0.546649i	0.992420	−	0.122894i	$-0.0392174\pi$
$521$	5.69828	+	12.4775i	0.249646	+	0.546649i	−0.742774	+	0.669543i	$0.766490\pi$
$522$		0			0
$523$	0.277148	−	0.264260i	0.0121188	−	0.0115553i	−0.683995	−	0.729486i	$-0.739759\pi$
$523$	0.277148	−	0.264260i	0.0121188	−	0.0115553i	0.696114	+	0.717931i	$0.254911\pi$
$524$		0			0
$525$	−7.26560	−	3.27161i	−0.317097	−	0.142785i
$526$		0			0
$527$	−5.41377	+	11.8545i	−0.235827	+	0.516390i
$528$		0			0
$529$	−22.7685	+	2.17413i	−0.989935	+	0.0945274i
$530$		0			0
$531$	1.64163	−	9.03236i	0.0712408	−	0.391971i
$532$		0			0
$533$	2.23131	+	3.47199i	0.0966489	+	0.150389i
$534$		0			0
$535$		−	9.00675i		−	0.389396i
$536$		0			0
$537$	7.15702	−	6.89708i	0.308848	−	0.297631i
$538$		0			0
$539$	10.0833	−	6.48013i	0.434317	−	0.279119i
$540$		0			0
$541$	−16.3582	−	2.35195i	−0.703294	−	0.101118i	−0.218616	−	0.975811i	$-0.570154\pi$
$541$	−16.3582	−	2.35195i	−0.703294	−	0.101118i	−0.484678	+	0.874693i	$0.661063\pi$
$542$		0			0
$543$	25.4966	−	29.7420i	1.09416	−	1.27635i
$544$		0			0
$545$	−15.4468	−	7.05432i	−0.661669	−	0.302174i
$546$		0			0
$547$	1.10381	+	2.75718i	0.0471955	+	0.117889i	0.950093	−	0.311968i	$-0.100988\pi$
$547$	1.10381	+	2.75718i	0.0471955	+	0.117889i	−0.902897	+	0.429857i	$0.858564\pi$
$548$		0			0
$549$	−25.1435	+	22.2584i	−1.07310	+	0.949967i
$550$		0			0
$551$	0.188045	−	0.0858772i	0.00801098	−	0.00365849i
$552$		0			0
$553$	1.24047	+	3.58409i	0.0527500	+	0.152411i
$554$		0			0
$555$	−12.6935	+	10.0917i	−0.538807	+	0.428369i
$556$		0			0
$557$	−24.7197	−	31.4337i	−1.04741	−	1.33189i	−0.941314	−	0.337531i	$-0.890408\pi$
$557$	−24.7197	−	31.4337i	−1.04741	−	1.33189i	−0.106094	−	0.994356i	$-0.533834\pi$
$558$		0			0
$559$	1.21460	+	25.4975i	0.0513720	+	1.07843i
$560$		0			0
$561$	7.82674	+	14.9860i	0.330445	+	0.632709i
$562$		0			0
$563$	3.39797	+	23.6334i	0.143208	+	0.996030i	0.927014	+	0.375026i	$0.122366\pi$
$563$	3.39797	+	23.6334i	0.143208	+	0.996030i	−0.783807	+	0.621005i	$0.786725\pi$
$564$		0			0
$565$	−5.71200	−	9.89348i	−0.240306	−	0.416222i
$566$		0			0
$567$	10.3427	−	9.35359i	0.434353	−	0.392814i
$568$		0			0
$569$	−0.941694	−	0.670577i	−0.0394778	−	0.0281120i	0.560148	−	0.828393i	$-0.310744\pi$
$569$	−0.941694	−	0.670577i	−0.0394778	−	0.0281120i	−0.599626	+	0.800281i	$0.704684\pi$
$570$		0			0
$571$	−2.14806	+	45.0934i	−0.0898936	+	1.88710i	0.282848	+	0.959165i	$0.408721\pi$
$571$	−2.14806	+	45.0934i	−0.0898936	+	1.88710i	−0.372742	+	0.927935i	$0.621582\pi$
$572$		0			0
$573$	−11.2678	−	45.3937i	−0.470717	−	1.89635i
$574$		0			0
$575$	−1.03201	−	0.250362i	−0.0430377	−	0.0104408i
$576$		0			0
$577$	−5.19434	+	26.9508i	−0.216243	+	1.12198i	0.697779	+	0.716313i	$0.254172\pi$
$577$	−5.19434	+	26.9508i	−0.216243	+	1.12198i	−0.914022	+	0.405664i	$0.867040\pi$
$578$		0			0
$579$	−0.250340	−	4.72739i	−0.0104038	−	0.196463i
$580$		0			0
$581$	7.07045	+	4.54390i	0.293332	+	0.188513i
$582$		0			0
$583$	−4.76183	−	2.45489i	−0.197215	−	0.101671i
$584$		0			0
$585$	11.7530	−	1.81733i	0.485927	−	0.0751372i
$586$		0			0
$587$	−2.28824	−	1.79949i	−0.0944459	−	0.0742730i	0.569820	−	0.821770i	$-0.307013\pi$
$587$	−2.28824	−	1.79949i	−0.0944459	−	0.0742730i	−0.664265	+	0.747497i	$0.731256\pi$
$588$		0			0
$589$	−0.219328	+	0.190049i	−0.00903727	+	0.00783084i
$590$		0			0
$591$	1.36615	+	0.867763i	0.0561959	+	0.0356950i
$592$		0			0
$593$	8.77838	−	4.52557i	0.360485	−	0.185843i	−0.268464	−	0.963290i	$-0.586516\pi$
$593$	8.77838	−	4.52557i	0.360485	−	0.185843i	0.628948	+	0.777447i	$0.283486\pi$
$594$		0			0
$595$	7.93542	−	2.33005i	0.325321	−	0.0955227i
$596$		0			0
$597$	0.181522	−	0.0737902i	0.00742918	−	0.00302003i
$598$		0			0
$599$	−12.1844	+	35.2044i	−0.497839	+	1.43841i	0.364080	+	0.931368i	$0.381383\pi$
$599$	−12.1844	+	35.2044i	−0.497839	+	1.43841i	−0.861920	+	0.507045i	$0.830738\pi$
$600$		0			0
$601$	−7.04162	−	9.88857i	−0.287234	−	0.403363i	0.645597	−	0.763678i	$-0.276609\pi$
$601$	−7.04162	−	9.88857i	−0.287234	−	0.403363i	−0.932831	+	0.360315i	$0.882669\pi$
$602$		0			0
$603$	−21.0688	−	12.6138i	−0.857987	−	0.513672i
$604$		0			0
$605$	3.47876	+	4.88524i	0.141432	+	0.198613i
$606$		0			0
$607$	3.42463	−	9.89481i	0.139001	−	0.401618i	−0.853918	−	0.520407i	$-0.825780\pi$
$607$	3.42463	−	9.89481i	0.139001	−	0.401618i	0.992919	+	0.118789i	$0.0379014\pi$
$608$		0			0
$609$	6.16183	−	2.50484i	0.249690	−	0.101501i
$610$		0			0
$611$	34.1451	−	10.0259i	1.38136	−	0.405604i
$612$		0			0
$613$	−27.7057	+	14.2833i	−1.11902	+	0.576896i	−0.915558	−	0.402187i	$-0.868250\pi$
$613$	−27.7057	+	14.2833i	−1.11902	+	0.576896i	−0.203464	+	0.979082i	$0.565220\pi$
$614$		0			0
$615$	3.09129	+	1.96355i	0.124653	+	0.0791781i
$616$		0			0
$617$	29.9576	−	25.9584i	1.20605	−	1.04505i	0.208292	−	0.978067i	$-0.433209\pi$
$617$	29.9576	−	25.9584i	1.20605	−	1.04505i	0.997754	−	0.0669789i	$-0.0213360\pi$
$618$		0			0
$619$	20.8262	+	16.3779i	0.837075	+	0.658283i	0.941783	−	0.336220i	$-0.109149\pi$
$619$	20.8262	+	16.3779i	0.837075	+	0.658283i	−0.104709	+	0.994503i	$0.533391\pi$
$620$		0			0
$621$	1.12543	−	1.47896i	0.0451621	−	0.0593487i
$622$		0			0
$623$	−10.4695	−	5.39739i	−0.419451	−	0.216242i
$624$		0			0
$625$	−1.12631	−	0.723833i	−0.0450522	−	0.0289533i
$626$		0			0
$627$	0.0199095	+	0.375968i	0.000795109	+	0.0150147i
$628$		0			0
$629$	−4.65689	+	24.1623i	−0.185682	+	0.963412i
$630$		0			0
$631$	28.0316	+	6.80039i	1.11592	+	0.270719i	0.750989	−	0.660315i	$-0.229577\pi$
$631$	28.0316	+	6.80039i	1.11592	+	0.270719i	0.364931	+	0.931034i	$0.381092\pi$
$632$		0			0
$633$	8.57922	+	34.5626i	0.340994	+	1.37374i
$634$		0			0
$635$	0.809000	−	16.9830i	0.0321042	−	0.673950i
$636$		0			0
$637$	−10.4216	−	7.42117i	−0.412918	−	0.294038i
$638$		0			0
$639$	7.86153	+	8.07167i	0.310997	+	0.319310i
$640$		0			0
$641$	−4.54237	−	7.86762i	−0.179413	−	0.310752i	0.762267	−	0.647263i	$-0.224087\pi$
$641$	−4.54237	−	7.86762i	−0.179413	−	0.310752i	−0.941680	+	0.336511i	$0.890753\pi$
$642$		0			0
$643$	4.62181	+	32.1454i	0.182267	+	1.26769i	0.851387	+	0.524538i	$0.175762\pi$
$643$	4.62181	+	32.1454i	0.182267	+	1.26769i	−0.669120	+	0.743154i	$0.733329\pi$
$644$		0			0
$645$	10.4858	+	20.0773i	0.412876	+	0.790541i
$646$		0			0
$647$	2.07032	+	43.4613i	0.0813926	+	1.70864i	0.558260	+	0.829666i	$0.311469\pi$
$647$	2.07032	+	43.4613i	0.0813926	+	1.70864i	−0.476867	+	0.878975i	$0.658228\pi$
$648$		0			0
$649$	4.92976	+	6.26870i	0.193510	+	0.246068i
$650$		0			0
$651$	−7.30921	+	5.81106i	−0.286471	+	0.227753i
$652$		0			0
$653$	13.5176	+	39.0564i	0.528983	+	1.52840i	0.820394	+	0.571798i	$0.193754\pi$
$653$	13.5176	+	39.0564i	0.528983	+	1.52840i	−0.291411	+	0.956598i	$0.594125\pi$
$654$		0			0
$655$	8.81576	−	4.02602i	0.344460	−	0.157310i
$656$		0			0
$657$	7.46949	+	8.43765i	0.291413	+	0.329184i
$658$		0			0
$659$	15.5343	+	38.8029i	0.605132	+	1.51155i	0.841708	+	0.539933i	$0.181551\pi$
$659$	15.5343	+	38.8029i	0.605132	+	1.51155i	−0.236576	+	0.971613i	$0.576025\pi$
$660$		0			0
$661$	27.5555	+	12.5842i	1.07178	+	0.489468i	0.871563	−	0.490283i	$-0.163107\pi$
$661$	27.5555	+	12.5842i	1.07178	+	0.489468i	0.200222	+	0.979751i	$0.435834\pi$
$662$		0			0
$663$	11.7453	−	13.7010i	0.456148	−	0.532101i
$664$		0			0
$665$	0.182299	+	0.0262107i	0.00706926	+	0.00101641i
$666$		0			0
$667$	0.745739	−	0.479257i	0.0288751	−	0.0185569i
$668$		0			0
$669$	−7.70323	+	7.42344i	−0.297824	+	0.287007i
$670$		0			0
$671$		−	29.1709i		−	1.12613i
$672$		0			0
$673$	−25.0388	−	38.9611i	−0.965174	−	1.50184i	−0.861832	−	0.507195i	$-0.830683\pi$
$673$	−25.0388	−	38.9611i	−0.965174	−	1.50184i	−0.103343	−	0.994646i	$-0.532954\pi$
$674$		0			0
$675$	−12.8444	+	8.54651i	−0.494381	+	0.328955i
$676$		0			0
$677$	21.2689	−	2.03094i	0.817432	−	0.0780553i	0.322041	−	0.946726i	$-0.395631\pi$
$677$	21.2689	−	2.03094i	0.817432	−	0.0780553i	0.495391	+	0.868670i	$0.335025\pi$
$678$		0			0
$679$	0.785123	−	1.71918i	0.0301302	−	0.0659760i
$680$		0			0
$681$	35.0547	+	15.7847i	1.34330	+	0.604870i
$682$		0			0
$683$	5.96693	−	5.68946i	0.228318	−	0.217701i	−0.567281	−	0.823524i	$-0.692005\pi$
$683$	5.96693	−	5.68946i	0.228318	−	0.217701i	0.795599	+	0.605823i	$0.207156\pi$
$684$		0			0
$685$	0.806174	+	1.76527i	0.0308023	+	0.0674477i
$686$		0			0
$687$	3.99161	−	7.84456i	0.152289	−	0.299288i
$688$		0			0
$689$	−0.543575	+	5.69257i	−0.0207086	+	0.216870i
$690$		0			0
$691$	−11.6624	+	9.17143i	−0.443659	+	0.348898i	−0.814863	−	0.579654i	$-0.803188\pi$
$691$	−11.6624	+	9.17143i	−0.443659	+	0.348898i	0.371203	+	0.928552i	$0.378945\pi$
$692$		0			0
$693$	0.128549	+	12.1132i	0.00488317	+	0.460142i
$694$		0			0
$695$	4.41254	−	15.0277i	0.167377	−	0.570034i
$696$		0			0
$697$	5.50053	−	0.790857i	0.208347	−	0.0299558i
$698$		0			0
$699$	30.0586	+	8.65303i	1.13692	+	0.327288i
$700$		0			0
$701$	2.13427	+	2.03502i	0.0806103	+	0.0768618i	0.729313	−	0.684180i	$-0.239840\pi$
$701$	2.13427	+	2.03502i	0.0806103	+	0.0768618i	−0.648703	+	0.761042i	$0.724688\pi$
$702$		0			0
$703$	−0.317854	+	0.446364i	−0.0119881	+	0.0168349i
$704$		0			0
$705$	23.7545	−	20.8051i	0.894645	−	0.783564i
$706$		0			0
$707$	−15.4685	−	8.93074i	−0.581753	−	0.335875i
$708$		0			0
$709$	1.26490	−	5.21399i	0.0475043	−	0.195815i	−0.943115	−	0.332467i	$-0.892119\pi$
$709$	1.26490	−	5.21399i	0.0475043	−	0.195815i	0.990619	+	0.136652i	$0.0436341\pi$
$710$		0			0
$711$	7.15432	+	1.65543i	0.268308	+	0.0620836i
$712$		0			0
$713$	−0.814948	+	0.940501i	−0.0305201	+	0.0352220i
$714$		0			0
$715$	−5.58542	+	8.69108i	−0.208883	+	0.325028i
$716$		0			0
$717$	−37.9413	+	11.3596i	−1.41695	+	0.424232i
$718$		0			0
$719$	−6.71790	−	34.8558i	−0.250535	−	1.29990i	−0.861303	−	0.508092i	$-0.830351\pi$
$719$	−6.71790	−	34.8558i	−0.250535	−	1.29990i	0.610768	−	0.791810i	$-0.290861\pi$
$720$		0			0
$721$	0.698871	−	0.888687i	0.0260273	−	0.0330964i
$722$		0			0
$723$	−34.9481	−	3.15011i	−1.29974	−	0.117154i
$724$		0			0
$725$	−7.15144	+	1.73492i	−0.265598	+	0.0644333i
$726$		0			0
$727$	4.27368	+	8.28979i	0.158502	+	0.307451i	0.954692	−	0.297596i	$-0.0961847\pi$
$727$	4.27368	+	8.28979i	0.158502	+	0.307451i	−0.796190	+	0.605047i	$0.793154\pi$
$728$		0			0
$729$	−4.69123	−	26.5893i	−0.173749	−	0.984790i
$730$		0			0
$731$	31.9085	+	12.7742i	1.18018	+	0.472472i
$732$		0			0
$733$	−37.0304	−	12.8163i	−1.36775	−	0.473382i	−0.458151	−	0.888874i	$-0.651488\pi$
$733$	−37.0304	−	12.8163i	−1.36775	−	0.473382i	−0.909597	+	0.415493i	$0.863609\pi$
$734$		0			0
$735$	−11.1586	−	2.08929i	−0.411590	−	0.0770647i
$736$		0			0
$737$	20.3361	−	6.44090i	0.749089	−	0.237254i
$738$		0			0
$739$	−4.98582	+	3.55039i	−0.183406	+	0.130603i	−0.668073	−	0.744096i	$-0.732880\pi$
$739$	−4.98582	+	3.55039i	−0.183406	+	0.130603i	0.484666	+	0.874699i	$0.338941\pi$
$740$		0			0
$741$	0.364664	−	0.168881i	0.0133963	−	0.00620398i
$742$		0			0
$743$	16.6185	−	41.5110i	0.609674	−	1.52289i	−0.226263	−	0.974066i	$-0.572651\pi$
$743$	16.6185	−	41.5110i	0.609674	−	1.52289i	0.835937	−	0.548825i	$-0.184925\pi$
$744$		0			0
$745$	−6.96818	−	23.7315i	−0.255295	−	0.869453i
$746$		0			0
$747$	14.7299	−	6.91675i	0.538938	−	0.253071i
$748$		0			0
$749$	−2.30870	−	9.51658i	−0.0843580	−	0.347728i
$750$		0			0
$751$	25.8809	+	29.8682i	0.944408	+	1.08990i	0.995830	+	0.0912277i	$0.0290791\pi$
$751$	25.8809	+	29.8682i	0.944408	+	1.08990i	−0.0514223	+	0.998677i	$0.516375\pi$
$752$		0			0
$753$	13.4351	−	1.35487i	0.489603	−	0.0493743i
$754$		0			0
$755$	4.24484	−	0.818127i	0.154486	−	0.0297747i
$756$		0			0
$757$	−12.3112	+	23.8803i	−0.447457	+	0.867946i	0.551962	+	0.833869i	$0.313879\pi$
$757$	−12.3112	+	23.8803i	−0.447457	+	0.867946i	−0.999419	+	0.0340765i	$0.989151\pi$
$758$		0			0
$759$	0.313943	+	1.58363i	0.0113954	+	0.0574820i
$760$		0			0
$761$	25.0471	+	21.7035i	0.907958	+	0.786750i	0.977523	−	0.210827i	$-0.0676157\pi$
$761$	25.0471	+	21.7035i	0.907958	+	0.786750i	−0.0695652	+	0.997577i	$0.522161\pi$
$762$		0			0
$763$	−18.1294	−	3.49416i	−0.656329	−	0.126497i
$764$		0			0
$765$	4.34812	−	15.4115i	0.157206	−	0.557203i
$766$		0			0
$767$	4.25621	−	7.37197i	0.153683	−	0.266186i
$768$		0			0
$769$	3.40997	+	0.162437i	0.122966	+	0.00585762i	0.108975	−	0.994044i	$-0.465243\pi$
$769$	3.40997	+	0.162437i	0.122966	+	0.00585762i	0.0139916	+	0.999902i	$0.495546\pi$
$770$		0			0
$771$	47.4477	−	7.07911i	1.70879	−	0.254948i
$772$		0			0
$773$	−11.5079	+	12.0691i	−0.413910	+	0.434096i	−0.897376	−	0.441267i	$-0.854529\pi$
$773$	−11.5079	+	12.0691i	−0.413910	+	0.434096i	0.483466	+	0.875363i	$0.339378\pi$
$774$		0			0
$775$	8.94671	−	5.16538i	0.321375	−	0.185546i
$776$		0			0
$777$	−10.8252	+	13.9167i	−0.388351	+	0.499257i
$778$		0			0
$779$	0.118738	+	0.0348646i	0.00425422	+	0.00124915i
$780$		0			0
$781$	−9.77688	+	0.465730i	−0.349844	+	0.0166651i
$782$		0			0
$783$	2.23569	−	12.6830i	0.0798969	−	0.453254i
$784$		0			0
$785$	9.79578	+	0.935384i	0.349626	+	0.0333853i
$786$		0			0
$787$	−19.8262	+	6.86191i	−0.706727	+	0.244601i	−0.656705	−	0.754147i	$-0.728050\pi$
$787$	−19.8262	+	6.86191i	−0.706727	+	0.244601i	−0.0500221	+	0.998748i	$0.515929\pi$
$788$		0			0
$789$	−3.99697	+	10.1395i	−0.142296	+	0.360977i
$790$		0			0
$791$	−8.57132	−	8.98934i	−0.304761	−	0.319624i
$792$		0			0
$793$	−28.9067	+	11.5725i	−1.02651	+	0.410951i
$794$		0			0
$795$	1.68503	+	4.78626i	0.0597619	+	0.169751i
$796$		0			0
$797$	−0.315915	−	3.30841i	−0.0111903	−	0.117190i	0.988151	−	0.153486i	$-0.0490501\pi$
$797$	−0.315915	−	3.30841i	−0.0111903	−	0.117190i	−0.999341	+	0.0362963i	$0.988444\pi$
$798$		0			0
$799$	6.81918	−	47.4284i	0.241245	−	1.67790i
$800$		0			0
$801$	−19.6285	+	11.6120i	−0.693540	+	0.410290i
$802$		0			0
$803$	−9.78919			−0.345453
$804$		0			0
$805$	0.789754			0.0278352
$806$		0			0
$807$	22.0442	+	5.22418i	0.775993	+	0.183900i
$808$		0			0
$809$	7.37705	−	51.3085i	0.259363	−	1.80391i	−0.278022	−	0.960575i	$-0.589679\pi$
$809$	7.37705	−	51.3085i	0.259363	−	1.80391i	0.537386	−	0.843337i	$-0.319412\pi$
$810$		0			0
$811$	4.74317	+	49.6727i	0.166555	+	1.74424i	0.563244	+	0.826291i	$0.309553\pi$
$811$	4.74317	+	49.6727i	0.166555	+	1.74424i	−0.396688	+	0.917953i	$0.629841\pi$
$812$		0			0
$813$	12.4108	−	4.36930i	0.435266	−	0.153238i
$814$		0			0
$815$	9.56501	−	3.82925i	0.335048	−	0.134133i
$816$		0			0
$817$	0.528183	+	0.553942i	0.0184788	+	0.0193800i
$818$		0			0
$819$	11.9525	−	4.93284i	0.417653	−	0.172367i
$820$		0			0
$821$	35.8686	−	12.4142i	1.25182	−	0.433260i	0.380871	−	0.924628i	$-0.375624\pi$
$821$	35.8686	−	12.4142i	1.25182	−	0.433260i	0.870952	+	0.491368i	$0.163503\pi$
$822$		0			0
$823$	40.2095	+	3.83954i	1.40161	+	0.133838i	0.768317	−	0.640070i	$-0.221095\pi$
$823$	40.2095	+	3.83954i	1.40161	+	0.133838i	0.633298	+	0.773908i	$0.281701\pi$
$824$		0			0
$825$	1.83691	−	13.2757i	0.0639531	−	0.462200i
$826$		0			0
$827$	38.4021	−	1.82932i	1.33537	−	0.0636115i	0.632296	−	0.774727i	$-0.282113\pi$
$827$	38.4021	−	1.82932i	1.33537	−	0.0636115i	0.703075	+	0.711116i	$0.251810\pi$
$828$		0			0
$829$	−10.8813	−	3.19504i	−0.377924	−	0.110968i	0.0872531	−	0.996186i	$-0.472191\pi$
$829$	−10.8813	−	3.19504i	−0.377924	−	0.110968i	−0.465177	+	0.885218i	$0.654009\pi$
$830$		0			0
$831$	−22.9763	−	17.8723i	−0.797039	−	0.619982i
$832$		0			0
$833$	−14.9186	+	8.61326i	−0.516899	+	0.298432i
$834$		0			0
$835$	2.89039	−	3.03135i	0.100026	−	0.104904i
$836$		0			0
$837$	2.00483	+	17.9681i	0.0692970	+	0.621068i
$838$		0			0
$839$	17.8042	+	0.848117i	0.614668	+	0.0292803i	0.352608	−	0.935771i	$-0.385295\pi$
$839$	17.8042	+	0.848117i	0.614668	+	0.0292803i	0.262060	+	0.965051i	$0.415598\pi$
$840$		0			0
$841$	−11.4286	+	19.7949i	−0.394089	+	0.682582i
$842$		0			0
$843$	−17.5788	−	30.0777i	−0.605446	−	1.03593i
$844$		0			0
$845$	−7.36328	−	1.41916i	−0.253304	−	0.0488204i
$846$		0			0
$847$	4.92791	+	4.27006i	0.169325	+	0.146721i
$848$		0			0
$849$	1.99771	−	0.396033i	0.0685614	−	0.0135918i
$850$		0			0
$851$	−1.07672	+	2.08854i	−0.0369094	+	0.0715942i
$852$		0			0
$853$	38.8301	−	7.48389i	1.32952	−	0.256244i	0.525472	−	0.850811i	$-0.323889\pi$
$853$	38.8301	−	7.48389i	1.32952	−	0.256244i	0.804046	+	0.594567i	$0.202677\pi$
$854$		0			0
$855$	0.230647	−	0.271959i	0.00788796	−	0.00930082i
$856$		0			0
$857$	10.3061	+	11.8939i	0.352050	+	0.406287i	0.903960	−	0.427616i	$-0.140646\pi$
$857$	10.3061	+	11.8939i	0.352050	+	0.406287i	−0.551911	+	0.833903i	$0.686101\pi$
$858$		0			0
$859$	−0.141362	−	0.582702i	−0.00482321	−	0.0198815i	0.969349	−	0.245687i	$-0.0790137\pi$
$859$	−0.141362	−	0.582702i	−0.00482321	−	0.0198815i	−0.974172	+	0.225806i	$0.927499\pi$
$860$		0			0
$861$	3.76959	+	1.28231i	0.128467	+	0.0437010i
$862$		0			0
$863$	−15.1957	−	51.7517i	−0.517267	−	1.76165i	−0.639126	−	0.769102i	$-0.720704\pi$
$863$	−15.1957	−	51.7517i	−0.517267	−	1.76165i	0.121859	−	0.992547i	$-0.461114\pi$
$864$		0			0
$865$	−3.21112	+	8.02098i	−0.109181	+	0.272721i
$866$		0			0
$867$	2.16260	+	4.66971i	0.0734459	+	0.158592i
$868$		0			0
$869$	−5.19628	+	3.70025i	−0.176272	+	0.125522i
$870$		0			0
$871$	−14.4501	−	17.5967i	−0.489624	−	0.596240i
$872$		0			0
$873$	−2.01094	−	3.05727i	−0.0680602	−	0.103473i
$874$		0			0
$875$	−16.6287	−	5.75526i	−0.562154	−	0.194563i
$876$		0			0
$877$	49.3682	+	19.7641i	1.66705	+	0.667385i	0.997176	−	0.0750936i	$-0.0239255\pi$
$877$	49.3682	+	19.7641i	1.66705	+	0.667385i	0.669870	+	0.742478i	$0.266350\pi$
$878$		0			0
$879$	0.674962	+	0.384929i	0.0227659	+	0.0129833i
$880$		0			0
$881$	19.0945	+	37.0381i	0.643310	+	1.24785i	0.954702	+	0.297565i	$0.0961745\pi$
$881$	19.0945	+	37.0381i	0.643310	+	1.24785i	−0.311392	+	0.950282i	$0.600795\pi$
$882$		0			0
$883$	44.2066	−	10.7244i	1.48767	−	0.360905i	0.592114	−	0.805854i	$-0.298293\pi$
$883$	44.2066	−	10.7244i	1.48767	−	0.360905i	0.895556	+	0.444949i	$0.146778\pi$
$884$		0			0
$885$	0.678088	−	7.52288i	0.0227937	−	0.252879i
$886$		0			0
$887$	−17.0181	+	21.6403i	−0.571411	+	0.726609i	−0.982763	−	0.184868i	$-0.940814\pi$
$887$	−17.0181	+	21.6403i	−0.571411	+	0.726609i	0.411352	+	0.911477i	$0.365057\pi$
$888$		0			0
$889$	−3.49845	−	18.1517i	−0.117334	−	0.608788i
$890$		0			0
$891$	19.9960	+	12.2590i	0.669893	+	0.410692i
$892$		0			0
$893$	0.576887	−	0.897653i	0.0193048	−	0.0300388i
$894$		0			0
$895$	5.35542	−	6.18049i	0.179012	−	0.206591i
$896$		0			0
$897$	1.44473	−	0.939344i	0.0482383	−	0.0313638i
$898$		0			0
$899$	−2.03310	+	8.38057i	−0.0678078	+	0.279508i
$900$		0			0
$901$	6.66816	+	3.84986i	0.222149	+	0.128258i
$902$		0			0
$903$	16.2257	+	18.5259i	0.539957	+	0.616504i
$904$		0			0
$905$	18.6965	−	26.2555i	0.621492	−	0.872763i
$906$		0			0
$907$	−31.5127	−	30.0473i	−1.04636	−	0.997705i	−0.0463636	−	0.998925i	$-0.514763\pi$
$907$	−31.5127	−	30.0473i	−1.04636	−	0.997705i	−0.999999	+	0.00121963i	$0.999612\pi$
$908$		0			0
$909$	−30.5689	+	16.1722i	−1.01390	+	0.536399i
$910$		0			0
$911$	−46.1549	+	6.63607i	−1.52918	+	0.219863i	−0.854970	−	0.518677i	$-0.826425\pi$
$911$	−46.1549	+	6.63607i	−1.52918	+	0.219863i	−0.674209	+	0.738540i	$0.735515\pi$
$912$		0			0
$913$	−3.98264	+	13.5636i	−0.131806	+	0.448891i
$914$		0			0
$915$	−18.9599	+	20.0970i	−0.626794	+	0.664386i
$916$		0			0
$917$	8.28279	−	6.51366i	0.273522	−	0.215100i
$918$		0			0
$919$	−1.69859	+	17.7885i	−0.0560315	+	0.586788i	0.923238	+	0.384228i	$0.125532\pi$
$919$	−1.69859	+	17.7885i	−0.0560315	+	0.586788i	−0.979270	+	0.202560i	$0.935074\pi$
$920$		0			0
$921$	47.5843	+	24.2127i	1.56796	+	0.797836i
$922$		0			0
$923$	4.34013	+	9.50355i	0.142857	+	0.312813i
$924$		0			0
$925$	14.1173	−	13.4608i	0.464174	−	0.442589i
$926$		0			0
$927$	−0.737860	−	2.06089i	−0.0242345	−	0.0676884i
$928$		0			0
$929$	−6.72664	+	14.7293i	−0.220694	+	0.483252i	−0.987300	−	0.158865i	$-0.949216\pi$
$929$	−6.72664	+	14.7293i	−0.220694	+	0.483252i	0.766606	+	0.642117i	$0.221944\pi$
$930$		0			0
$931$	−0.381880	+	0.0364651i	−0.0125156	+	0.00119509i
$932$		0			0
$933$	6.77957	+	9.41445i	0.221953	+	0.308215i
$934$		0			0
$935$	7.52058	+	11.7022i	0.245949	+	0.382704i
$936$		0			0
$937$			36.9927i			1.20850i	0.796795	+	0.604250i	$0.206527\pi$
$937$			36.9927i			1.20850i	−0.796795	+	0.604250i	$0.793473\pi$
$938$		0			0
$939$	−23.2653	−	24.1422i	−0.759235	−	0.787850i
$940$		0			0
$941$	−30.1623	+	19.3842i	−0.983264	+	0.631905i	−0.930342	−	0.366693i	$-0.880490\pi$
$941$	−30.1623	+	19.3842i	−0.983264	+	0.631905i	−0.0529219	+	0.998599i	$0.516853\pi$
$942$		0			0
$943$	0.525253	+	0.0755199i	0.0171046	+	0.00245927i
$944$		0			0
$945$	7.78450	−	8.42880i	0.253230	−	0.274189i
$946$		0			0
$947$	5.10967	+	2.33351i	0.166042	+	0.0758289i	0.496702	−	0.867921i	$-0.334544\pi$
$947$	5.10967	+	2.33351i	0.166042	+	0.0758289i	−0.330660	+	0.943750i	$0.607271\pi$
$948$		0			0
$949$	3.88350	+	9.70051i	0.126064	+	0.314892i
$950$		0			0
$951$	−10.2078	−	0.431988i	−0.331012	−	0.0140082i
$952$		0			0
$953$	6.34797	−	2.89902i	0.205631	−	0.0939084i	−0.309937	−	0.950757i	$-0.600308\pi$
$953$	6.34797	−	2.89902i	0.205631	−	0.0939084i	0.515568	+	0.856849i	$0.327581\pi$
$954$		0			0
$955$	−12.5863	−	36.3659i	−0.407285	−	1.17677i
$956$		0			0
$957$	6.96223	+	8.75716i	0.225057	+	0.283079i
$958$		0			0
$959$	1.30430	+	1.65855i	0.0421180	+	0.0535574i
$960$		0			0
$961$	0.898997	+	18.8723i	0.0289999	+	0.608783i
$962$		0			0
$963$	−17.9823	−	6.01084i	−0.579473	−	0.193697i
$964$		0			0
$965$	−0.554322	−	3.85539i	−0.0178443	−	0.124109i
$966$		0			0
$967$	13.9889	+	24.2294i	0.449852	+	0.779166i	0.998376	−	0.0569685i	$-0.0181435\pi$
$967$	13.9889	+	24.2294i	0.449852	+	0.779166i	−0.548524	+	0.836135i	$0.684810\pi$
$968$		0			0
$969$	−0.00287107	−	0.541099i	−9.22321e−5	−	0.0173826i
$970$		0			0
$971$	−28.3879	−	20.2149i	−0.911010	−	0.648728i	0.0253837	−	0.999678i	$-0.491919\pi$
$971$	−28.3879	−	20.2149i	−0.911010	−	0.648728i	−0.936394	+	0.350950i	$0.885859\pi$
$972$		0			0
$973$	0.810259	−	17.0094i	0.0259757	−	0.545297i
$974$		0			0
$975$	−13.8841	+	3.44636i	−0.444648	+	0.110372i
$976$		0			0
$977$	20.0489	+	4.86380i	0.641420	+	0.155607i	0.543261	−	0.839564i	$-0.317189\pi$
$977$	20.0489	+	4.86380i	0.641420	+	0.155607i	0.0981593	+	0.995171i	$0.468705\pi$
$978$		0			0
$979$	3.74935	−	19.4535i	0.119830	−	0.621736i
$980$		0			0
$981$	−24.3930	+	26.1323i	−0.778808	+	0.834341i
$982$		0			0
$983$	−23.1987	−	14.9089i	−0.739923	−	0.475520i	0.115592	−	0.993297i	$-0.463123\pi$
$983$	−23.1987	−	14.9089i	−0.739923	−	0.475520i	−0.855516	+	0.517777i	$0.826760\pi$
$984$		0			0
$985$	1.18360	+	0.610186i	0.0377125	+	0.0194421i
$986$		0			0
$987$	19.7661	−	28.0717i	0.629163	−	0.893532i
$988$		0			0
$989$	2.57989	+	2.02885i	0.0820358	+	0.0645137i
$990$		0			0
$991$	−16.2720	+	14.0997i	−0.516896	+	0.447893i	−0.873826	−	0.486238i	$-0.838369\pi$
$991$	−16.2720	+	14.0997i	−0.516896	+	0.447893i	0.356930	+	0.934131i	$0.383823\pi$
$992$		0			0
$993$	−0.787976	+	1.24054i	−0.0250057	+	0.0393673i
$994$		0			0
$995$	0.143299	−	0.0738755i	0.00454287	−	0.00234201i
$996$		0			0
$997$	12.1773	−	3.57558i	0.385659	−	0.113240i	−0.0831548	−	0.996537i	$-0.526500\pi$
$997$	12.1773	−	3.57558i	0.385659	−	0.113240i	0.468814	+	0.883297i	$0.344681\pi$
$998$		0			0
$999$	11.6773	+	32.0779i	0.369452	+	1.01490i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.ba.b.41.14	yes	440
3.2	odd	2	inner	804.2.ba.b.41.2	✓	440
67.18	odd	66	inner	804.2.ba.b.353.2	yes	440
201.152	even	66	inner	804.2.ba.b.353.14	yes	440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.ba.b.41.2	✓	440	3.2	odd	2	inner
804.2.ba.b.41.14	yes	440	1.1	even	1	trivial
804.2.ba.b.353.2	yes	440	67.18	odd	66	inner
804.2.ba.b.353.14	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)

\(f(q)\)	\(=\)	\(q+(0.399410 - 1.68537i) q^{3} +(0.202812 - 1.41059i) q^{5} +(-0.147283 - 1.54242i) q^{7} +(-2.68094 - 1.34631i) q^{9} +O(q^{10})\)	\(q+(0.399410 - 1.68537i) q^{3} +(0.202812 - 1.41059i) q^{5} +(-0.147283 - 1.54242i) q^{7} +(-2.68094 - 1.34631i) q^{9} +(2.41940 - 0.968583i) q^{11} +(-1.91962 - 2.01323i) q^{13} +(-2.29636 - 0.905215i) q^{15} +(-3.53951 + 1.22504i) q^{17} +(-0.0830309 - 0.00792849i) q^{19} +(-2.65838 - 0.367831i) q^{21} +(-0.357259 + 0.0170183i) q^{23} +(2.84884 + 0.836495i) q^{25} +(-3.33982 + 3.98065i) q^{27} +(-2.14642 + 1.23924i) q^{29} +(2.40107 - 2.51817i) q^{31} +(-0.666088 - 4.46445i) q^{33} +(-2.20559 - 0.105065i) q^{35} +(3.28486 - 5.68954i) q^{37} +(-4.15976 + 2.43116i) q^{39} +(-1.45686 - 0.280786i) q^{41} +(-6.93510 - 6.00930i) q^{43} +(-2.44281 + 3.50866i) q^{45} +(-5.86207 + 11.3708i) q^{47} +(4.51613 - 0.870413i) q^{49} +(0.650925 + 6.45468i) q^{51} +(-1.34621 - 1.55361i) q^{53} +(-0.875587 - 3.60922i) q^{55} +(-0.0465258 + 0.136771i) q^{57} +(0.862133 + 2.93616i) q^{59} +(4.16017 - 10.3916i) q^{61} +(-1.68171 + 4.33343i) q^{63} +(-3.22916 + 2.29948i) q^{65} +(8.16291 + 0.605750i) q^{67} +(-0.114010 + 0.608910i) q^{69} +(-3.54925 - 1.22841i) q^{71} +(-3.48722 - 1.39607i) q^{73} +(2.54766 - 4.46724i) q^{75} +(-1.85030 - 3.58908i) q^{77} +(-2.37878 + 0.577087i) q^{79} +(5.37492 + 7.21874i) q^{81} +(-3.35310 + 4.26381i) q^{83} +(1.01017 + 5.24124i) q^{85} +(1.23127 + 4.11248i) q^{87} +(4.10997 - 6.39524i) q^{89} +(-2.82253 + 3.25737i) q^{91} +(-3.28504 - 5.05248i) q^{93} +(-0.0280235 + 0.115514i) q^{95} +(1.05636 + 0.609890i) q^{97} +(-7.79029 - 0.660540i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 440 q - 12 q^{7} + 4 q^{9}+O(q^{10}) \) 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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