LMFDB - Embedded newform 804.2.ba.b.41.2

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			41.2
Character	$\chi$	$=$	804.41
Dual form			804.2.ba.b.353.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.69899 - 0.336812i) q^{3} +(-0.202812 + 1.41059i) q^{5} +(-0.147283 - 1.54242i) q^{7} +(2.77312 + 1.14448i) q^{9} +O(q^{10})$	\(q+(-1.69899 - 0.336812i) q^{3} +(-0.202812 + 1.41059i) q^{5} +(-0.147283 - 1.54242i) q^{7} +(2.77312 + 1.14448i) q^{9} +(-2.41940 + 0.968583i) q^{11} +(-1.91962 - 2.01323i) q^{13} +(0.819678 - 2.32826i) q^{15} +(3.53951 - 1.22504i) q^{17} +(-0.0830309 - 0.00792849i) q^{19} +(-0.269274 + 2.67016i) q^{21} +(0.357259 - 0.0170183i) q^{23} +(2.84884 + 0.836495i) q^{25} +(-4.32601 - 2.87847i) q^{27} +(2.14642 - 1.23924i) q^{29} +(2.40107 - 2.51817i) q^{31} +(4.43676 - 0.830725i) q^{33} +(2.20559 + 0.105065i) q^{35} +(3.28486 - 5.68954i) q^{37} +(2.58332 + 4.06701i) q^{39} +(1.45686 + 0.280786i) q^{41} +(-6.93510 - 6.00930i) q^{43} +(-2.17681 + 3.67961i) q^{45} +(5.86207 - 11.3708i) q^{47} +(4.51613 - 0.870413i) q^{49} +(-6.42619 + 0.889171i) q^{51} +(1.34621 + 1.55361i) q^{53} +(-0.875587 - 3.60922i) q^{55} +(0.138398 + 0.0414362i) q^{57} +(-0.862133 - 2.93616i) q^{59} +(4.16017 - 10.3916i) q^{61} +(1.35684 - 4.44587i) q^{63} +(3.22916 - 2.29948i) q^{65} +(8.16291 + 0.605750i) q^{67} +(-0.612710 - 0.0914151i) q^{69} +(3.54925 + 1.22841i) q^{71} +(-3.48722 - 1.39607i) q^{73} +(-4.55840 - 2.38072i) q^{75} +(1.85030 + 3.58908i) q^{77} +(-2.37878 + 0.577087i) q^{79} +(6.38033 + 6.34755i) q^{81} +(3.35310 - 4.26381i) q^{83} +(1.01017 + 5.24124i) q^{85} +(-4.06414 + 1.38251i) q^{87} +(-4.10997 + 6.39524i) q^{89} +(-2.82253 + 3.25737i) q^{91} +(-4.92754 + 3.46963i) q^{93} +(0.0280235 - 0.115514i) q^{95} +(1.05636 + 0.609890i) q^{97} +(-7.81780 - 0.0829650i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−1.69899	−	0.336812i	−0.980911	−	0.194459i
$3$	−1.69899	−	0.336812i	−0.980911	−	0.194459i
$4$		0			0
$5$	−0.202812	+	1.41059i	−0.0907002	+	0.630834i	0.892871	+	0.450313i	$0.148688\pi$
$5$	−0.202812	+	1.41059i	−0.0907002	+	0.630834i	−0.983571	+	0.180521i	$0.942222\pi$
$6$		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
$9$	2.77312	+	1.14448i	0.924372	+	0.381493i
$10$		0			0
$11$	−2.41940	+	0.968583i	−0.729477	+	0.292039i	−0.706515	−	0.707698i	$-0.749734\pi$
$11$	−2.41940	+	0.968583i	−0.729477	+	0.292039i	−0.0229619	+	0.999736i	$0.507310\pi$
$12$		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
$15$	0.819678	−	2.32826i	0.211640	−	0.601154i
$16$		0			0
$17$	3.53951	−	1.22504i	0.858458	−	0.297115i	0.137846	−	0.990454i	$-0.455982\pi$
$17$	3.53951	−	1.22504i	0.858458	−	0.297115i	0.720612	+	0.693339i	$0.243861\pi$
$18$		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
$21$	−0.269274	+	2.67016i	−0.0587603	+	0.582677i
$22$		0			0
$23$	0.357259	−	0.0170183i	0.0744936	−	0.00354857i	−0.0103020	−	0.999947i	$-0.503279\pi$
$23$	0.357259	−	0.0170183i	0.0744936	−	0.00354857i	0.0847956	+	0.996398i	$0.472976\pi$
$24$		0			0
$25$	2.84884	+	0.836495i	0.569768	+	0.167299i
$26$		0			0
$27$	−4.32601	−	2.87847i	−0.832541	−	0.553963i
$28$		0			0
$29$	2.14642	−	1.23924i	0.398581	−	0.230121i	−0.287291	−	0.957843i	$-0.592755\pi$
$29$	2.14642	−	1.23924i	0.398581	−	0.230121i	0.685872	+	0.727723i	$0.259421\pi$
$30$		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
$33$	4.43676	−	0.830725i	0.772342	−	0.144611i
$34$		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
$39$	2.58332	+	4.06701i	0.413662	+	0.651243i
$40$		0			0
$41$	1.45686	+	0.280786i	0.227523	+	0.0438514i	0.301738	−	0.953391i	$-0.402433\pi$
$41$	1.45686	+	0.280786i	0.227523	+	0.0438514i	−0.0742156	+	0.997242i	$0.523645\pi$
$42$		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
$45$	−2.17681	+	3.67961i	−0.324500	+	0.548524i
$46$		0			0
$47$	5.86207	−	11.3708i	0.855071	−	1.65861i	0.107716	−	0.994182i	$-0.465646\pi$
$47$	5.86207	−	11.3708i	0.855071	−	1.65861i	0.747355	−	0.664425i	$-0.231323\pi$
$48$		0			0
$49$	4.51613	−	0.870413i	0.645162	−	0.124345i
$50$		0			0
$51$	−6.42619	+	0.889171i	−0.899847	+	0.124509i
$52$		0			0
$53$	1.34621	+	1.55361i	0.184916	+	0.213405i	0.840637	−	0.541598i	$-0.182181\pi$
$53$	1.34621	+	1.55361i	0.184916	+	0.213405i	−0.655721	+	0.755003i	$0.727635\pi$
$54$		0			0
$55$	−0.875587	−	3.60922i	−0.118064	−	0.486667i
$56$		0			0
$57$	0.138398	+	0.0414362i	0.0183313	+	0.00548836i
$58$		0			0
$59$	−0.862133	−	2.93616i	−0.112240	−	0.382255i	0.884144	−	0.467214i	$-0.154742\pi$
$59$	−0.862133	−	2.93616i	−0.112240	−	0.382255i	−0.996384	+	0.0849590i	$0.972924\pi$
$60$		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
$63$	1.35684	−	4.44587i	0.170945	−	0.560127i
$64$		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
$69$	−0.612710	−	0.0914151i	−0.0737616	−	0.0110051i
$70$		0			0
$71$	3.54925	+	1.22841i	0.421219	+	0.145785i	0.529451	−	0.848340i	$-0.322398\pi$
$71$	3.54925	+	1.22841i	0.421219	+	0.145785i	−0.108232	+	0.994126i	$0.534519\pi$
$72$		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
$75$	−4.55840	−	2.38072i	−0.526359	−	0.274902i
$76$		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
$81$	6.38033	+	6.34755i	0.708926	+	0.705283i
$82$		0			0
$83$	3.35310	−	4.26381i	0.368051	−	0.468014i	−0.566388	−	0.824139i	$-0.691660\pi$
$83$	3.35310	−	4.26381i	0.368051	−	0.468014i	0.934439	+	0.356124i	$0.115902\pi$
$84$		0			0
$85$	1.01017	+	5.24124i	0.109568	+	0.568493i
$86$		0			0
$87$	−4.06414	+	1.38251i	−0.435721	+	0.148221i
$88$		0			0
$89$	−4.10997	+	6.39524i	−0.435656	+	0.677894i	−0.987778	−	0.155870i	$-0.950182\pi$
$89$	−4.10997	+	6.39524i	−0.435656	+	0.677894i	0.552122	+	0.833763i	$0.313818\pi$
$90$		0			0
$91$	−2.82253	+	3.25737i	−0.295881	+	0.341465i
$92$		0			0
$93$	−4.92754	+	3.46963i	−0.510962	+	0.359784i
$94$		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
$99$	−7.81780	−	0.0829650i	−0.785719	−	0.00833829i
$100$		0			0
$101$	−6.68674	+	9.39021i	−0.665355	+	0.934360i	−0.999968	−	0.00799517i	$-0.997455\pi$
$101$	−6.68674	+	9.39021i	−0.665355	+	0.934360i	0.334613	+	0.942356i	$0.391394\pi$
$102$		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
$105$	−3.71188	−	0.921374i	−0.362243	−	0.0899169i
$106$		0			0
$107$	−6.25579	+	0.899446i	−0.604770	+	0.0869527i	−0.437896	−	0.899026i	$-0.644276\pi$
$107$	−6.25579	+	0.899446i	−0.604770	+	0.0869527i	−0.166874	+	0.985978i	$0.553367\pi$
$108$		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
$111$	−7.49724	+	8.56007i	−0.711606	+	0.812486i
$112$		0			0
$113$	−6.30125	+	4.95536i	−0.592772	+	0.466161i	−0.868919	−	0.494954i	$-0.835185\pi$
$113$	−6.30125	+	4.95536i	−0.592772	+	0.466161i	0.276147	+	0.961115i	$0.410942\pi$
$114$		0			0
$115$	−0.0484505	+	0.507396i	−0.00451803	+	0.0473149i
$116$		0			0
$117$	−3.01921	−	7.77989i	−0.279126	−	0.719251i
$118$		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
$123$	−2.38061	−	0.967738i	−0.214652	−	0.0872580i
$124$		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
$129$	9.75864	+	12.5455i	0.859200	+	1.10457i
$130$		0			0
$131$	−3.67671	−	5.72108i	−0.321236	−	0.499853i	0.642653	−	0.766157i	$-0.277834\pi$
$131$	−3.67671	−	5.72108i	−0.321236	−	0.499853i	−0.963889	+	0.266305i	$0.914197\pi$
$132$		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	−0.490788	−	0.871279i	$-0.663291\pi$
$137$	1.14559	−	0.736228i	0.0978746	−	0.0629002i	0.588663	+	0.808379i	$0.299655\pi$
$138$		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
$141$	−13.7894	+	17.3445i	−1.16128	+	1.46067i
$142$		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
$147$	−7.96602	−	0.0422677i	−0.657026	−	0.00348618i
$148$		0			0
$149$	−15.7872	+	7.20977i	−1.29334	+	0.590648i	−0.938822	−	0.344403i	$-0.888081\pi$
$149$	−15.7872	+	7.20977i	−1.29334	+	0.590648i	−0.354516	+	0.935050i	$0.615354\pi$
$150$		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
$153$	11.2175	+	0.653730i	0.906881	+	0.0528509i
$154$		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
$159$	−1.76392	−	3.09299i	−0.139888	−	0.245290i
$160$		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
$165$	0.271982	+	6.42693i	0.0211738	+	0.500336i
$166$		0			0
$167$	−2.39412	−	1.70485i	−0.185263	−	0.131925i	0.483663	−	0.875254i	$-0.339306\pi$
$167$	−2.39412	−	1.70485i	−0.185263	−	0.131925i	−0.668925	+	0.743329i	$0.733245\pi$
$168$		0			0
$169$	0.250374	−	5.25600i	0.0192596	−	0.404308i
$170$		0			0
$171$	−0.221180	−	0.117014i	−0.0169141	−	0.00894827i
$172$		0			0
$173$	5.89177	+	1.42933i	0.447943	+	0.108670i	0.453384	−	0.891315i	$-0.350217\pi$
$173$	5.89177	+	1.42933i	0.447943	+	0.108670i	−0.00544065	+	0.999985i	$0.501732\pi$
$174$		0			0
$175$	0.870640	−	4.51731i	0.0658142	−	0.341477i
$176$		0			0
$177$	0.475820	+	5.27887i	0.0357648	+	0.396784i
$178$		0			0
$179$	−4.82757	−	3.10249i	−0.360829	−	0.231891i	0.347647	−	0.937626i	$-0.386981\pi$
$179$	−4.82757	−	3.10249i	−0.360829	−	0.231891i	−0.708476	+	0.705735i	$0.750617\pi$
$180$		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
$183$	−10.5681	+	16.2540i	−0.781216	+	1.20153i
$184$		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
$189$	−3.80267	+	7.09648i	−0.276604	+	0.516193i
$190$		0			0
$191$	−24.0016	+	12.3737i	−1.73669	+	0.895328i	−0.770527	+	0.637407i	$0.780007\pi$
$191$	−24.0016	+	12.3737i	−1.73669	+	0.895328i	−0.966166	+	0.257921i	$0.916963\pi$
$192$		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
$195$	−6.26080	+	2.81916i	−0.448345	+	0.201884i
$196$		0			0
$197$	0.305616	−	0.883020i	0.0217743	−	0.0629126i	−0.933590	−	0.358343i	$-0.883342\pi$
$197$	0.305616	−	0.883020i	0.0217743	−	0.0629126i	0.955364	+	0.295430i	$0.0954630\pi$
$198$		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
$201$	−13.6647	−	3.77853i	−0.963830	−	0.266517i
$202$		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
$207$	1.01020	+	0.361681i	0.0702135	+	0.0251386i
$208$		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
$213$	−5.61639	−	3.28248i	−0.384829	−	0.224912i
$214$		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
$219$	5.45452	+	3.54644i	0.368583	+	0.239646i
$220$		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
$225$	6.94281	+	5.58013i	0.462854	+	0.372009i
$226$		0			0
$227$	4.20062	−	21.7949i	0.278805	−	1.44658i	−0.524704	−	0.851285i	$-0.675824\pi$
$227$	4.20062	−	21.7949i	0.278805	−	1.44658i	0.803509	−	0.595292i	$-0.202964\pi$
$228$		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
$231$	−1.93479	−	6.72101i	−0.127300	−	0.442210i
$232$		0			0
$233$	0.859288	−	18.0387i	0.0562938	−	1.18175i	−0.777211	−	0.629240i	$-0.783366\pi$
$233$	0.859288	−	18.0387i	0.0562938	−	1.18175i	0.833505	−	0.552512i	$-0.186331\pi$
$234$		0			0
$235$	14.8507	+	10.5751i	0.968750	+	0.689844i
$236$		0			0
$237$	4.23589	−	0.179259i	0.275151	−	0.0116442i
$238$		0			0
$239$	11.4331	+	19.8027i	0.739545	+	1.28093i	0.952700	+	0.303911i	$0.0982925\pi$
$239$	11.4331	+	19.8027i	0.739545	+	1.28093i	−0.213156	+	0.977018i	$0.568374\pi$
$240$		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
$243$	−8.70218	−	12.9334i	−0.558245	−	0.829676i
$244$		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
$249$	−7.13298	+	6.11480i	−0.452034	+	0.387510i
$250$		0			0
$251$	−2.54986	−	7.36734i	−0.160946	−	0.465022i	0.835477	−	0.549525i	$-0.185191\pi$
$251$	−2.54986	−	7.36734i	−0.160946	−	0.465022i	−0.996423	+	0.0845023i	$0.973070\pi$
$252$		0			0
$253$	−0.847869	+	0.387209i	−0.0533050	+	0.0243436i
$254$		0			0
$255$	0.0490542	−	9.24504i	0.00307190	−	0.578947i
$256$		0			0
$257$	−10.2940	−	25.7132i	−0.642122	−	1.60394i	−0.788724	−	0.614748i	$-0.789258\pi$
$257$	−10.2940	−	25.7132i	−0.642122	−	1.60394i	0.146602	−	0.989196i	$-0.453166\pi$
$258$		0			0
$259$	−9.25947	−	4.22866i	−0.575355	−	0.262756i
$260$		0			0
$261$	7.37057	−	0.980013i	0.456227	−	0.0606613i
$262$		0			0
$263$	6.22844	+	0.895514i	0.384062	+	0.0552198i	0.331642	−	0.943405i	$-0.392397\pi$
$263$	6.22844	+	0.895514i	0.384062	+	0.0552198i	0.0524201	+	0.998625i	$0.483307\pi$
$264$		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	$-0.869447\pi$
$269$		−	13.0797i		−	0.797486i	0.917063	−	0.398743i	$-0.130553\pi$
$270$		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
$273$	5.89256	−	4.58357i	0.356634	−	0.277410i
$274$		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
$279$	9.54044	−	4.23520i	0.571171	−	0.253555i
$280$		0			0
$281$	−14.5570	+	13.8800i	−0.868396	+	0.828013i	−0.986291	−	0.165012i	$-0.947234\pi$
$281$	−14.5570	+	13.8800i	−0.868396	+	0.828013i	0.117896	+	0.993026i	$0.462385\pi$
$282$		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
$285$	−0.0865182	+	0.186819i	−0.00512490	+	0.0110662i
$286$		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
$291$	−1.58932	−	1.39199i	−0.0931679	−	0.0815999i
$292$		0			0
$293$	0.126387	−	0.430435i	0.00738362	−	0.0251463i	−0.955719	−	0.294282i	$-0.904920\pi$
$293$	0.126387	−	0.430435i	0.00738362	−	0.0251463i	0.963102	+	0.269135i	$0.0867379\pi$
$294$		0			0
$295$	4.31656	−	0.620627i	0.251320	−	0.0361343i
$296$		0			0
$297$	13.2544	+	2.77409i	0.769099	+	0.160969i
$298$		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
$303$	14.5234	−	13.7017i	0.834348	−	0.787140i
$304$		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
$309$	−0.727612	−	1.03335i	−0.0413924	−	0.0587852i
$310$		0			0
$311$	4.38634	−	5.06210i	0.248726	−	0.287045i	−0.617633	−	0.786466i	$-0.711908\pi$
$311$	4.38634	−	5.06210i	0.248726	−	0.287045i	0.866360	+	0.499421i	$0.166454\pi$
$312$		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
$315$	5.99611	+	2.81561i	0.337843	+	0.158642i
$316$		0			0
$317$	1.11635	+	5.79218i	0.0627005	+	0.325321i	0.999713	−	0.0239760i	$-0.00763251\pi$
$317$	1.11635	+	5.79218i	0.0627005	+	0.325321i	−0.937012	+	0.349297i	$0.886420\pi$
$318$		0			0
$319$	−3.99276	+	5.07721i	−0.223552	+	0.284269i
$320$		0			0
$321$	10.9314	+	0.578878i	0.610134	+	0.0323098i
$322$		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
$327$	−9.55458	+	18.2943i	−0.528369	+	1.01168i
$328$		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
$333$	15.6208	−	12.0183i	0.856017	−	0.658598i
$334$		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
$339$	12.3748	−	6.29676i	0.672106	−	0.341993i
$340$		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
$345$	0.253214	−	0.845741i	0.0136326	−	0.0455332i
$346$		0			0
$347$	5.13930	+	21.1845i	0.275892	+	1.13724i	0.926037	+	0.377433i	$0.123193\pi$
$347$	5.13930	+	21.1845i	0.275892	+	1.13724i	−0.650145	+	0.759810i	$0.725292\pi$
$348$		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
$351$	2.50923	+	14.2348i	0.133933	+	0.759800i
$352$		0			0
$353$	33.7883	−	6.51216i	1.79837	−	0.346607i	0.823147	−	0.567829i	$-0.192216\pi$
$353$	33.7883	−	6.51216i	1.79837	−	0.346607i	0.975224	+	0.221221i	$0.0710044\pi$
$354$		0			0
$355$	−2.45261	+	4.75740i	−0.130171	+	0.252496i
$356$		0			0
$357$	2.31795	+	9.78093i	0.122679	+	0.517662i
$358$		0			0
$359$	9.21787	+	7.98733i	0.486501	+	0.421555i	0.863263	−	0.504755i	$-0.168417\pi$
$359$	9.21787	+	7.98733i	0.486501	+	0.421555i	−0.376762	+	0.926310i	$0.622963\pi$
$360$		0			0
$361$	−18.6498	−	3.59446i	−0.981569	−	0.189182i
$362$		0			0
$363$	6.15277	−	3.90817i	0.322937	−	0.205126i
$364$		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
$369$	3.71867	+	2.44599i	0.193586	+	0.127333i
$370$		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
$375$	11.4948	−	15.9623i	0.593590	−	0.824289i
$376$		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
$381$	−20.5602	−	2.07340i	−1.05333	−	0.106224i
$382$		0			0
$383$	33.6647	+	3.21459i	1.72019	+	0.164258i	0.907952	−	0.419075i	$-0.137645\pi$
$383$	33.6647	+	3.21459i	1.72019	+	0.164258i	0.812234	+	0.583332i	$0.198251\pi$
$384$		0			0
$385$	−5.43798	+	1.88210i	−0.277145	+	0.0959208i
$386$		0			0
$387$	−12.3543	−	24.6016i	−0.628005	−	1.25057i
$388$		0			0
$389$	5.78914	+	6.07148i	0.293521	+	0.307836i	0.853938	−	0.520374i	$-0.174208\pi$
$389$	5.78914	+	6.07148i	0.293521	+	0.307836i	−0.560417	+	0.828211i	$0.689359\pi$
$390$		0			0
$391$	1.24367	−	0.497891i	0.0628952	−	0.0251795i
$392$		0			0
$393$	4.31976	+	10.9584i	0.217903	+	0.552778i
$394$		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
$399$	0.0435284	−	0.219571i	0.00217914	−	0.0109923i
$400$		0			0
$401$	8.18648			0.408813			0.204407	−	0.978886i	$-0.434474\pi$
$401$	8.18648			0.408813			0.204407	+	0.978886i	$0.434474\pi$
$402$		0			0
$403$	−9.67881			−0.482136
$404$		0			0
$405$	−10.2478	+	7.71266i	−0.509216	+	0.383245i
$406$		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
$411$	−2.19432	+	0.864992i	−0.108238	+	0.0426669i
$412$		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
$417$	−17.9555	−	6.32133i	−0.879283	−	0.309557i
$418$		0			0
$419$	−19.7012	+	6.81865i	−0.962466	+	0.333113i	−0.762716	−	0.646734i	$-0.776134\pi$
$419$	−19.7012	+	6.81865i	−0.962466	+	0.333113i	−0.199750	+	0.979847i	$0.564013\pi$
$420$		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
$423$	29.2699	−	24.8236i	1.42315	−	1.20697i
$424$		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
$429$	−10.1893	−	7.33757i	−0.491945	−	0.354261i
$430$		0			0
$431$	−0.139674	+	0.0806411i	−0.00672788	+	0.00388434i	−0.503360	−	0.864077i	$-0.667903\pi$
$431$	−0.139674	+	0.0806411i	−0.00672788	+	0.00388434i	0.496632	+	0.867961i	$0.334570\pi$
$432$		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
$435$	−1.12589	−	6.01321i	−0.0539825	−	0.288312i
$436$		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
$441$	13.5199	+	2.75486i	0.643806	+	0.131184i
$442$		0			0
$443$	2.47875	+	0.477739i	0.117769	+	0.0226981i	0.247795	−	0.968812i	$-0.420294\pi$
$443$	2.47875	+	0.477739i	0.117769	+	0.0226981i	−0.130026	+	0.991511i	$0.541506\pi$
$444$		0			0
$445$	−8.18749	−	7.09450i	−0.388124	−	0.336312i
$446$		0			0
$447$	29.2506	−	6.93199i	1.38351	−	0.327872i
$448$		0			0
$449$	15.3573	−	29.7891i	0.724757	−	1.40583i	−0.181623	−	0.983368i	$-0.558135\pi$
$449$	15.3573	−	29.7891i	0.724757	−	1.40583i	0.906380	−	0.422464i	$-0.138835\pi$
$450$		0			0
$451$	−3.79668	+	0.731751i	−0.178779	+	0.0344568i
$452$		0			0
$453$	−0.720133	−	5.20452i	−0.0338348	−	0.244530i
$454$		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
$459$	−18.8382	−	4.88887i	−0.879292	−	0.228193i
$460$		0			0
$461$	−0.207098	−	0.705312i	−0.00964552	−	0.0328496i	0.954530	−	0.298116i	$-0.0963583\pi$
$461$	−0.207098	−	0.705312i	−0.00964552	−	0.0328496i	−0.964175	+	0.265266i	$0.914540\pi$
$462$		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
$465$	−3.89486	−	7.65441i	−0.180620	−	0.354965i
$466$		0			0
$467$	16.6138	−	11.8307i	0.768796	−	0.547457i	−0.127010	−	0.991901i	$-0.540538\pi$
$467$	16.6138	−	11.8307i	0.768796	−	0.547457i	0.895807	+	0.444444i	$0.146599\pi$
$468$		0			0
$469$	−0.267940	−	12.6799i	−0.0123723	−	0.585501i
$470$		0			0
$471$	1.76486	−	11.8290i	0.0813204	−	0.545050i
$472$		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
$477$	1.95512	+	5.84905i	0.0895190	+	0.267810i
$478$		0			0
$479$	−9.11674	−	17.6840i	−0.416554	−	0.808003i	0.583437	−	0.812158i	$-0.301708\pi$
$479$	−9.11674	−	17.6840i	−0.416554	−	0.808003i	−0.999991	+	0.00415563i	$0.998677\pi$
$480$		0			0
$481$	−17.7600	+	4.30854i	−0.809788	+	0.196452i
$482$		0			0
$483$	−0.0507587	+	0.958520i	−0.00230960	+	0.0436142i
$484$		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
$489$	−4.03278	−	11.8551i	−0.182369	−	0.536107i
$490$		0			0
$491$	−18.9279	+	29.4524i	−0.854204	+	1.32917i	0.0886844	+	0.996060i	$0.471734\pi$
$491$	−18.9279	+	29.4524i	−0.854204	+	1.32917i	−0.942889	+	0.333108i	$0.891903\pi$
$492$		0			0
$493$	6.07918	−	7.01575i	0.273793	−	0.315973i
$494$		0			0
$495$	1.70257	−	11.0109i	0.0765250	−	0.494902i
$496$		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
$501$	3.49337	+	3.70288i	0.156072	+	0.165432i
$502$		0			0
$503$	−9.88721	+	13.8846i	−0.440849	+	0.619086i	−0.973895	−	0.227001i	$-0.927108\pi$
$503$	−9.88721	+	13.8846i	−0.440849	+	0.619086i	0.533046	+	0.846086i	$0.321047\pi$
$504$		0			0
$505$	−11.8896	−	11.3367i	−0.529079	−	0.504475i
$506$		0			0
$507$	−2.19567	+	8.84555i	−0.0975131	+	0.392845i
$508$		0			0
$509$	27.9399	−	4.01716i	1.23842	−	0.178057i	0.508179	−	0.861251i	$-0.330319\pi$
$509$	27.9399	−	4.01716i	1.23842	−	0.178057i	0.730237	+	0.683194i	$0.239410\pi$
$510$		0			0
$511$	−1.63972	+	5.58437i	−0.0725369	+	0.247038i
$512$		0			0
$513$	0.336371	+	0.273301i	0.0148511	+	0.0120665i
$514$		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
$519$	−9.52863	−	4.41283i	−0.418261	−	0.193702i
$520$		0			0
$521$	−5.69828	−	12.4775i	−0.249646	−	0.546649i	0.742774	−	0.669543i	$-0.233510\pi$
$521$	−5.69828	−	12.4775i	−0.249646	−	0.546649i	−0.992420	+	0.122894i	$0.960783\pi$
$522$		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
$525$	−3.00069	+	7.38161i	−0.130961	+	0.322160i
$526$		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
$531$	0.969575	−	9.12899i	0.0420760	−	0.396165i
$532$		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
$543$	−30.6645	−	24.3793i	−1.31594	−	1.04622i
$544$		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
$549$	23.4296	−	24.0559i	0.999951	−	1.02668i
$550$		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
$555$	−10.5542	−	12.3116i	−0.448001	−	0.522598i
$556$		0			0
$557$	24.7197	+	31.4337i	1.04741	+	1.33189i	0.941314	+	0.337531i	$0.109592\pi$
$557$	24.7197	+	31.4337i	1.04741	+	1.33189i	0.106094	+	0.994356i	$0.466166\pi$
$558$		0			0
$559$	1.21460	+	25.4975i	0.0513720	+	1.07843i
$560$		0			0
$561$	14.6863	−	8.37556i	0.620056	−	0.353616i
$562$		0			0
$563$	−3.39797	−	23.6334i	−0.143208	−	0.996030i	−0.927014	−	0.375026i	$-0.877634\pi$
$563$	−3.39797	−	23.6334i	−0.143208	−	0.996030i	0.783807	−	0.621005i	$-0.213275\pi$
$564$		0			0
$565$	−5.71200	−	9.89348i	−0.240306	−	0.416222i
$566$		0			0
$567$	8.85087	−	10.7760i	0.371702	−	0.452551i
$568$		0			0
$569$	0.941694	+	0.670577i	0.0394778	+	0.0281120i	0.599626	−	0.800281i	$-0.295316\pi$
$569$	0.941694	+	0.670577i	0.0394778	+	0.0281120i	−0.560148	+	0.828393i	$0.689256\pi$
$570$		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
$573$	44.9460	−	12.9387i	1.87765	−	0.540522i
$574$		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
$579$	−4.71490	+	0.424985i	−0.195944	+	0.0176618i
$580$		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
$585$	11.5866	−	2.68100i	0.479045	−	0.110846i
$586$		0			0
$587$	2.28824	+	1.79949i	0.0944459	+	0.0742730i	0.664265	−	0.747497i	$-0.268744\pi$
$587$	2.28824	+	1.79949i	0.0944459	+	0.0742730i	−0.569820	+	0.821770i	$0.692987\pi$
$588$		0			0
$589$	−0.219328	+	0.190049i	−0.00903727	+	0.00783084i
$590$		0			0
$591$	−0.816650	+	1.39731i	−0.0335925	+	0.0574774i
$592$		0			0
$593$	−8.77838	+	4.52557i	−0.360485	+	0.185843i	−0.628948	−	0.777447i	$-0.716514\pi$
$593$	−8.77838	+	4.52557i	−0.360485	+	0.185843i	0.268464	+	0.963290i	$0.413484\pi$
$594$		0			0
$595$	7.93542	−	2.33005i	0.325321	−	0.0955227i
$596$		0			0
$597$	−0.0804523	−	0.178669i	−0.00329269	−	0.00731242i
$598$		0			0
$599$	12.1844	−	35.2044i	0.497839	−	1.43841i	−0.364080	−	0.931368i	$-0.618617\pi$
$599$	12.1844	−	35.2044i	0.497839	−	1.43841i	0.861920	−	0.507045i	$-0.169262\pi$
$600$		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
$603$	21.9434	+	11.0221i	0.893605	+	0.448854i
$604$		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
$609$	2.73099	+	6.06499i	0.110665	+	0.245766i
$610$		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
$615$	1.84790	−	3.16179i	0.0745143	−	0.127496i
$616$		0			0
$617$	−29.9576	+	25.9584i	−1.20605	+	1.04505i	−0.208292	+	0.978067i	$0.566791\pi$
$617$	−29.9576	+	25.9584i	−1.20605	+	1.04505i	−0.997754	+	0.0669789i	$0.978664\pi$
$618$		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
$621$	−1.59449	−	0.954738i	−0.0639848	−	0.0383123i
$622$		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
$627$	−0.374975	+	0.0337990i	−0.0149751	+	0.00134980i
$628$		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
$633$	34.2217	−	9.85146i	1.36019	−	0.391561i
$634$		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
$639$	8.43660	+	7.46856i	0.333747	+	0.295452i
$640$		0			0
$641$	4.54237	+	7.86762i	0.179413	+	0.310752i	0.941680	−	0.336511i	$-0.109247\pi$
$641$	4.54237	+	7.86762i	0.179413	+	0.310752i	−0.762267	+	0.647263i	$0.775913\pi$
$642$		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
$645$	−19.6758	+	11.2210i	−0.774732	+	0.441828i
$646$		0			0
$647$	−2.07032	−	43.4613i	−0.0813926	−	1.70864i	−0.558260	−	0.829666i	$-0.688531\pi$
$647$	−2.07032	−	43.4613i	−0.0813926	−	1.70864i	0.476867	−	0.878975i	$-0.341772\pi$
$648$		0			0
$649$	4.92976	+	6.26870i	0.193510	+	0.246068i
$650$		0			0
$651$	6.07738	+	7.08932i	0.238191	+	0.277853i
$652$		0			0
$653$	−13.5176	−	39.0564i	−0.528983	−	1.52840i	−0.820394	−	0.571798i	$-0.806246\pi$
$653$	−13.5176	−	39.0564i	−0.528983	−	1.52840i	0.291411	−	0.956598i	$-0.405875\pi$
$654$		0			0
$655$	8.81576	−	4.02602i	0.344460	−	0.157310i
$656$		0			0
$657$	−8.07268	−	7.86251i	−0.314945	−	0.306746i
$658$		0			0
$659$	−15.5343	−	38.8029i	−0.605132	−	1.51155i	−0.841708	−	0.539933i	$-0.818449\pi$
$659$	−15.5343	−	38.8029i	−0.605132	−	1.51155i	0.236576	−	0.971613i	$-0.423975\pi$
$660$		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
$663$	14.1259	+	11.2306i	0.548606	+	0.436159i
$664$		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
$675$	−9.91629	−	11.8190i	−0.381678	−	0.454914i
$676$		0			0
$677$	−21.2689	+	2.03094i	−0.817432	+	0.0780553i	−0.495391	−	0.868670i	$-0.664975\pi$
$677$	−21.2689	+	2.03094i	−0.817432	+	0.0780553i	−0.322041	+	0.946726i	$0.604369\pi$
$678$		0			0
$679$	0.785123	−	1.71918i	0.0301302	−	0.0659760i
$680$		0			0
$681$	−14.4776	+	35.6144i	−0.554782	+	1.36475i
$682$		0			0
$683$	−5.96693	+	5.68946i	−0.228318	+	0.217701i	−0.795599	−	0.605823i	$-0.792844\pi$
$683$	−5.96693	+	5.68946i	−0.228318	+	0.217701i	0.567281	+	0.823524i	$0.307995\pi$
$684$		0			0
$685$	0.806174	+	1.76527i	0.0308023	+	0.0674477i
$686$		0			0
$687$	−7.98680	−	3.69879i	−0.304715	−	0.141118i
$688$		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
$693$	1.02347	+	12.0706i	0.0388782	+	0.458523i
$694$		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
$699$	−7.53556	+	30.3580i	−0.285021	+	1.14825i
$700$		0			0
$701$	−2.13427	−	2.03502i	−0.0806103	−	0.0768618i	0.648703	−	0.761042i	$-0.275312\pi$
$701$	−2.13427	−	2.03502i	−0.0806103	−	0.0768618i	−0.729313	+	0.684180i	$0.760160\pi$
$702$		0			0
$703$	−0.317854	+	0.446364i	−0.0119881	+	0.0168349i
$704$		0			0
$705$	−21.6693	−	22.9689i	−0.816111	−	0.865057i
$706$		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
$711$	−7.25710	−	1.12214i	−0.272163	−	0.0420836i
$712$		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
$717$	−12.7549	−	37.4953i	−0.476340	−	1.40029i
$718$		0			0
$719$	6.71790	+	34.8558i	0.250535	+	1.29990i	0.861303	+	0.508092i	$0.169649\pi$
$719$	6.71790	+	34.8558i	0.250535	+	1.29990i	−0.610768	+	0.791810i	$0.709139\pi$
$720$		0			0
$721$	0.698871	−	0.888687i	0.0260273	−	0.0330964i
$722$		0			0
$723$	−1.85559	+	35.0407i	−0.0690102	+	1.30318i
$724$		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
$729$	10.4288	+	24.9046i	0.386251	+	0.922394i
$730$		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
$735$	1.67523	−	11.2282i	0.0617916	−	0.414158i
$736$		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
$741$	−0.182250	−	0.358169i	−0.00669513	−	0.0131577i
$742$		0			0
$743$	−16.6185	+	41.5110i	−0.609674	+	1.52289i	0.226263	+	0.974066i	$0.427349\pi$
$743$	−16.6185	+	41.5110i	−0.609674	+	1.52289i	−0.835937	+	0.548825i	$0.815075\pi$
$744$		0			0
$745$	−6.96818	−	23.7315i	−0.255295	−	0.869453i
$746$		0			0
$747$	14.1784	−	7.98649i	0.518760	−	0.292211i
$748$		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
$753$	1.85077	+	13.3758i	0.0674459	+	0.487443i
$754$		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
$759$	1.57093	−	0.372290i	0.0570213	−	0.0135133i
$760$		0			0
$761$	−25.0471	−	21.7035i	−0.907958	−	0.786750i	0.0695652	−	0.997577i	$-0.477839\pi$
$761$	−25.0471	−	21.7035i	−0.907958	−	0.786750i	−0.977523	+	0.210827i	$0.932384\pi$
$762$		0			0
$763$	−18.1294	−	3.49416i	−0.656329	−	0.126497i
$764$		0			0
$765$	−3.19719	+	15.6907i	−0.115594	+	0.567298i
$766$		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
$771$	8.82886	+	47.1535i	0.317964	+	1.69819i
$772$		0			0
$773$	11.5079	−	12.0691i	0.413910	−	0.434096i	−0.483466	−	0.875363i	$-0.660622\pi$
$773$	11.5079	−	12.0691i	0.413910	−	0.434096i	0.897376	+	0.441267i	$0.145471\pi$
$774$		0			0
$775$	8.94671	−	5.16538i	0.321375	−	0.185546i
$776$		0			0
$777$	14.3075	+	10.3031i	0.513277	+	0.369623i
$778$		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
$783$	−12.8526	−	0.817466i	−0.459314	−	0.0292139i
$784$		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
$789$	−10.2804	−	3.61928i	−0.365993	−	0.128850i
$790$		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
$795$	4.72067	−	1.86087i	0.167425	−	0.0659983i
$796$		0			0
$797$	0.315915	+	3.30841i	0.0111903	+	0.117190i	0.999341	−	0.0362963i	$-0.0115560\pi$
$797$	0.315915	+	3.30841i	0.0111903	+	0.117190i	−0.988151	+	0.153486i	$0.950950\pi$
$798$		0			0
$799$	6.81918	−	47.4284i	0.241245	−	1.67790i
$800$		0			0
$801$	−18.7166	+	13.0309i	−0.661320	+	0.460426i
$802$		0			0
$803$	9.78919			0.345453
$804$		0			0
$805$	0.789754			0.0278352
$806$		0			0
$807$	−4.40542	+	22.2223i	−0.155078	+	0.782263i
$808$		0			0
$809$	−7.37705	+	51.3085i	−0.259363	+	1.80391i	0.278022	+	0.960575i	$0.410321\pi$
$809$	−7.37705	+	51.3085i	−0.259363	+	1.80391i	−0.537386	+	0.843337i	$0.680588\pi$
$810$		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
$813$	−4.82526	−	12.2407i	−0.169229	−	0.429302i
$814$		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
$819$	−11.5552	+	5.80274i	−0.403771	+	0.202764i
$820$		0			0
$821$	−35.8686	+	12.4142i	−1.25182	+	0.433260i	−0.870952	−	0.491368i	$-0.836497\pi$
$821$	−35.8686	+	12.4142i	−1.25182	+	0.433260i	−0.380871	+	0.924628i	$0.624376\pi$
$822$		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
$825$	13.3345	+	1.34473i	0.464249	+	0.0468174i
$826$		0			0
$827$	−38.4021	+	1.82932i	−1.33537	+	0.0636115i	−0.703075	−	0.711116i	$-0.748190\pi$
$827$	−38.4021	+	1.82932i	−1.33537	+	0.0636115i	−0.632296	+	0.774727i	$0.717887\pi$
$828$		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
$831$	−17.0104	+	23.6215i	−0.590084	+	0.819421i
$832$		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
$837$	−17.6356	+	3.98222i	−0.609574	+	0.137646i
$838$		0			0
$839$	−17.8042	−	0.848117i	−0.614668	−	0.0292803i	−0.262060	−	0.965051i	$-0.584402\pi$
$839$	−17.8042	−	0.848117i	−0.614668	−	0.0292803i	−0.352608	+	0.935771i	$0.614705\pi$
$840$		0			0
$841$	−11.4286	+	19.7949i	−0.394089	+	0.682582i
$842$		0			0
$843$	29.4071	−	18.6790i	1.01283	−	0.643340i
$844$		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
$849$	−0.469636	−	1.98170i	−0.0161179	−	0.0680119i
$850$		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
$855$	0.209916	−	0.288262i	0.00717898	−	0.00985837i
$856$		0			0
$857$	−10.3061	−	11.8939i	−0.352050	−	0.406287i	0.551911	−	0.833903i	$-0.313899\pi$
$857$	−10.3061	−	11.8939i	−0.352050	−	0.406287i	−0.903960	+	0.427616i	$0.859354\pi$
$858$		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
$861$	−1.14204	+	3.81443i	−0.0389205	+	0.129995i
$862$		0			0
$863$	15.1957	+	51.7517i	0.517267	+	1.76165i	0.639126	+	0.769102i	$0.279296\pi$
$863$	15.1957	+	51.7517i	0.517267	+	1.76165i	−0.121859	+	0.992547i	$0.538886\pi$
$864$		0			0
$865$	−3.21112	+	8.02098i	−0.109181	+	0.272721i
$866$		0			0
$867$	4.58655	−	2.33381i	0.155767	−	0.0792603i
$868$		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
$873$	2.23140	+	2.90028i	0.0755215	+	0.0981595i
$874$		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
$879$	−0.359706	+	0.688735i	−0.0121326	+	0.0232305i
$880$		0			0
$881$	−19.0945	−	37.0381i	−0.643310	−	1.24785i	−0.954702	−	0.297565i	$-0.903825\pi$
$881$	−19.0945	−	37.0381i	−0.643310	−	1.24785i	0.311392	−	0.950282i	$-0.399205\pi$
$882$		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
$885$	−7.54281	−	0.399431i	−0.253549	−	0.0134267i
$886$		0			0
$887$	17.0181	−	21.6403i	0.571411	−	0.726609i	−0.411352	−	0.911477i	$-0.634943\pi$
$887$	17.0181	−	21.6403i	0.571411	−	0.726609i	0.982763	+	0.184868i	$0.0591858\pi$
$888$		0			0
$889$	−3.49845	−	18.1517i	−0.117334	−	0.608788i
$890$		0			0
$891$	−21.5847	−	9.17739i	−0.723115	−	0.307454i
$892$		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
$897$	0.992127	+	1.40901i	0.0331261	+	0.0470455i
$898$		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
$903$	17.9132	−	16.8997i	0.596115	−	0.562386i
$904$		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
$909$	−29.2900	+	18.3873i	−0.971487	+	0.609868i
$910$		0			0
$911$	46.1549	−	6.63607i	1.52918	−	0.219863i	0.674209	−	0.738540i	$-0.264485\pi$
$911$	46.1549	−	6.63607i	1.52918	−	0.219863i	0.854970	+	0.518677i	$0.173575\pi$
$912$		0			0
$913$	−3.98264	+	13.5636i	−0.131806	+	0.448891i
$914$		0			0
$915$	−20.7844	−	18.2037i	−0.687110	−	0.601797i
$916$		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
$921$	22.4365	−	48.4472i	0.739308	−	1.59639i
$922$		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
$927$	0.888159	+	2.00072i	0.0291710	+	0.0657121i
$928$		0			0
$929$	6.72664	−	14.7293i	0.220694	−	0.483252i	−0.766606	−	0.642117i	$-0.778056\pi$
$929$	6.72664	−	14.7293i	0.220694	−	0.483252i	0.987300	+	0.158865i	$0.0507835\pi$
$930$		0			0
$931$	−0.381880	+	0.0364651i	−0.0125156	+	0.00119509i
$932$		0			0
$933$	−9.15731	+	7.12307i	−0.299797	+	0.233199i
$934$		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	0.0529219	−	0.998599i	$-0.483147\pi$
$941$	30.1623	−	19.3842i	0.983264	−	0.631905i	0.930342	+	0.366693i	$0.119510\pi$
$942$		0			0
$943$	0.525253	+	0.0755199i	0.0171046	+	0.00245927i
$944$		0			0
$945$	−9.23898	−	6.80325i	−0.300544	−	0.221310i
$946$		0			0
$947$	−5.10967	−	2.33351i	−0.166042	−	0.0758289i	0.330660	−	0.943750i	$-0.392729\pi$
$947$	−5.10967	−	2.33351i	−0.166042	−	0.0758289i	−0.496702	+	0.867921i	$0.665456\pi$
$948$		0			0
$949$	3.88350	+	9.70051i	0.126064	+	0.314892i
$950$		0			0
$951$	0.0542106	−	10.2168i	0.00175790	−	0.331304i
$952$		0			0
$953$	−6.34797	+	2.89902i	−0.205631	+	0.0939084i	−0.515568	−	0.856849i	$-0.672419\pi$
$953$	−6.34797	+	2.89902i	−0.205631	+	0.0939084i	0.309937	+	0.950757i	$0.399692\pi$
$954$		0			0
$955$	−12.5863	−	36.3659i	−0.407285	−	1.17677i
$956$		0			0
$957$	8.49371	−	7.28130i	0.274563	−	0.235371i
$958$		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
$963$	−18.3774	−	4.66535i	−0.592204	−	0.150339i
$964$		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
$969$	0.540622	−	0.0228787i	0.0173673	−	0.000734969i
$970$		0			0
$971$	28.3879	+	20.2149i	0.911010	+	0.648728i	0.936394	−	0.350950i	$-0.114141\pi$
$971$	28.3879	+	20.2149i	0.911010	+	0.648728i	−0.0253837	+	0.999678i	$0.508081\pi$
$972$		0			0
$973$	0.810259	−	17.0094i	0.0259757	−	0.545297i
$974$		0			0
$975$	3.95743	+	13.7472i	0.126739	+	0.440262i
$976$		0			0
$977$	−20.0489	−	4.86380i	−0.641420	−	0.155607i	−0.0981593	−	0.995171i	$-0.531295\pi$
$977$	−20.0489	−	4.86380i	−0.641420	−	0.155607i	−0.543261	+	0.839564i	$0.682811\pi$
$978$		0			0
$979$	3.74935	−	19.4535i	0.119830	−	0.621736i
$980$		0			0
$981$	22.3949	−	27.8637i	0.715013	−	0.889619i
$982$		0			0
$983$	23.1987	+	14.9089i	0.739923	+	0.475520i	0.855516	−	0.517777i	$-0.173240\pi$
$983$	23.1987	+	14.9089i	0.739923	+	0.475520i	−0.115592	+	0.993297i	$0.536877\pi$
$984$		0			0
$985$	1.18360	+	0.610186i	0.0377125	+	0.0194421i
$986$		0			0
$987$	28.7834	+	18.7145i	0.916187	+	0.595690i
$988$		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
$993$	1.26883	+	0.741562i	0.0402650	+	0.0235328i
$994$		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
$999$	−30.5875	+	15.1576i	−0.967746	+	0.479566i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-1.69899 - 0.336812i) q^{3} +(-0.202812 + 1.41059i) q^{5} +(-0.147283 - 1.54242i) q^{7} +(2.77312 + 1.14448i) q^{9} +O(q^{10})\)	\(q+(-1.69899 - 0.336812i) q^{3} +(-0.202812 + 1.41059i) q^{5} +(-0.147283 - 1.54242i) q^{7} +(2.77312 + 1.14448i) q^{9} +(-2.41940 + 0.968583i) q^{11} +(-1.91962 - 2.01323i) q^{13} +(0.819678 - 2.32826i) q^{15} +(3.53951 - 1.22504i) q^{17} +(-0.0830309 - 0.00792849i) q^{19} +(-0.269274 + 2.67016i) q^{21} +(0.357259 - 0.0170183i) q^{23} +(2.84884 + 0.836495i) q^{25} +(-4.32601 - 2.87847i) q^{27} +(2.14642 - 1.23924i) q^{29} +(2.40107 - 2.51817i) q^{31} +(4.43676 - 0.830725i) q^{33} +(2.20559 + 0.105065i) q^{35} +(3.28486 - 5.68954i) q^{37} +(2.58332 + 4.06701i) q^{39} +(1.45686 + 0.280786i) q^{41} +(-6.93510 - 6.00930i) q^{43} +(-2.17681 + 3.67961i) q^{45} +(5.86207 - 11.3708i) q^{47} +(4.51613 - 0.870413i) q^{49} +(-6.42619 + 0.889171i) q^{51} +(1.34621 + 1.55361i) q^{53} +(-0.875587 - 3.60922i) q^{55} +(0.138398 + 0.0414362i) q^{57} +(-0.862133 - 2.93616i) q^{59} +(4.16017 - 10.3916i) q^{61} +(1.35684 - 4.44587i) q^{63} +(3.22916 - 2.29948i) q^{65} +(8.16291 + 0.605750i) q^{67} +(-0.612710 - 0.0914151i) q^{69} +(3.54925 + 1.22841i) q^{71} +(-3.48722 - 1.39607i) q^{73} +(-4.55840 - 2.38072i) q^{75} +(1.85030 + 3.58908i) q^{77} +(-2.37878 + 0.577087i) q^{79} +(6.38033 + 6.34755i) q^{81} +(3.35310 - 4.26381i) q^{83} +(1.01017 + 5.24124i) q^{85} +(-4.06414 + 1.38251i) q^{87} +(-4.10997 + 6.39524i) q^{89} +(-2.82253 + 3.25737i) q^{91} +(-4.92754 + 3.46963i) q^{93} +(0.0280235 - 0.115514i) q^{95} +(1.05636 + 0.609890i) q^{97} +(-7.81780 - 0.0829650i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 440 q - 12 q^{7} + 4 q^{9}+O(q^{10}) \) 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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