LMFDB - Embedded newform 804.2.y.b.361.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(49,804)]

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, 0, 46]))

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

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

chi := DirichletCharacter("804.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.y (of order $33$, 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:	$120$
Relative dimension:	$6$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			361.3
Character	$\chi$	$=$	804.361
Dual form			804.2.y.b.49.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.841254 + 0.540641i) q^{3} +(-0.166640 + 1.15901i) q^{5} +(-3.32963 + 0.317941i) q^{7} +(0.415415 - 0.909632i) q^{9} +O(q^{10})$	\(q+(-0.841254 + 0.540641i) q^{3} +(-0.166640 + 1.15901i) q^{5} +(-3.32963 + 0.317941i) q^{7} +(0.415415 - 0.909632i) q^{9} +(0.135033 - 0.0540592i) q^{11} +(0.954845 - 0.910443i) q^{13} +(-0.486420 - 1.06511i) q^{15} +(0.000287460 + 0.000830562i) q^{17} +(-4.79439 - 0.457809i) q^{19} +(2.62917 - 2.06760i) q^{21} +(-0.346097 - 7.26546i) q^{23} +(3.48194 + 1.02239i) q^{25} +(0.142315 + 0.989821i) q^{27} +(-3.06768 - 5.31337i) q^{29} +(-2.23622 - 2.13224i) q^{31} +(-0.0843707 + 0.118482i) q^{33} +(0.186354 - 3.91204i) q^{35} +(1.40568 - 2.43471i) q^{37} +(-0.311044 + 1.28214i) q^{39} +(-2.34812 - 0.452564i) q^{41} +(5.01284 - 5.78512i) q^{43} +(0.985044 + 0.633050i) q^{45} +(-0.146019 - 0.0752781i) q^{47} +(4.11186 - 0.792495i) q^{49} +(-0.000690862 - 0.000543300i) q^{51} +(-6.16018 - 7.10923i) q^{53} +(0.0401530 + 0.165513i) q^{55} +(4.28081 - 2.20691i) q^{57} +(-6.09362 + 1.78925i) q^{59} +(3.83552 + 1.53551i) q^{61} +(-1.09397 + 3.16082i) q^{63} +(0.896094 + 1.25839i) q^{65} +(-7.35865 + 3.58472i) q^{67} +(4.21916 + 5.92498i) q^{69} +(1.52879 - 4.41715i) q^{71} +(5.95457 + 2.38385i) q^{73} +(-3.48194 + 1.02239i) q^{75} +(-0.432424 + 0.222930i) q^{77} +(1.07456 + 4.42940i) q^{79} +(-0.654861 - 0.755750i) q^{81} +(-11.0604 - 8.69800i) q^{83} +(-0.00101053 + 0.000194763i) q^{85} +(5.45332 + 2.81138i) q^{87} +(-8.69824 - 5.59002i) q^{89} +(-2.88981 + 3.33502i) q^{91} +(3.03401 + 0.584757i) q^{93} +(1.32954 - 5.48044i) q^{95} +(1.06715 - 1.84837i) q^{97} +(0.00692091 - 0.145288i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 12 q^{3} - 2 q^{5} + q^{7} - 12 q^{9}+O(q^{10}) $ 120 * q + 12 * q^3 - 2 * q^5 + q^7 - 12 * q^9	$ 120 q + 12 q^{3} - 2 q^{5} + q^{7} - 12 q^{9} + 11 q^{11} + 2 q^{13} - 9 q^{15} + 48 q^{17} - 4 q^{19} - q^{21} + 22 q^{23} - 42 q^{25} + 12 q^{27} - q^{29} + 27 q^{31} + 17 q^{35} - 8 q^{37} - 2 q^{39} - 58 q^{41} - 17 q^{43} - 2 q^{45} - 84 q^{47} + 101 q^{49} - 26 q^{51} + 28 q^{53} - 9 q^{55} + 26 q^{57} + 34 q^{59} + 16 q^{61} + 12 q^{63} + 144 q^{65} + 23 q^{67} + 11 q^{69} + 173 q^{71} - 2 q^{73} + 42 q^{75} + 128 q^{77} + 31 q^{79} - 12 q^{81} + 47 q^{83} - 75 q^{85} - 10 q^{87} - 67 q^{89} + 16 q^{91} + 6 q^{93} - 79 q^{95} + 10 q^{97}+O(q^{100}) $ 120 * q + 12 * q^3 - 2 * q^5 + q^7 - 12 * q^9 + 11 * q^11 + 2 * q^13 - 9 * q^15 + 48 * q^17 - 4 * q^19 - q^21 + 22 * q^23 - 42 * q^25 + 12 * q^27 - q^29 + 27 * q^31 + 17 * q^35 - 8 * q^37 - 2 * q^39 - 58 * q^41 - 17 * q^43 - 2 * q^45 - 84 * q^47 + 101 * q^49 - 26 * q^51 + 28 * q^53 - 9 * q^55 + 26 * q^57 + 34 * q^59 + 16 * q^61 + 12 * q^63 + 144 * q^65 + 23 * q^67 + 11 * q^69 + 173 * q^71 - 2 * q^73 + 42 * q^75 + 128 * q^77 + 31 * q^79 - 12 * q^81 + 47 * q^83 - 75 * q^85 - 10 * q^87 - 67 * q^89 + 16 * q^91 + 6 * q^93 - 79 * q^95 + 10 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$e\left(\frac{10}{33}\right)$	$1$

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
$3$	−0.841254	+	0.540641i	−0.485698	+	0.312139i
$3$	−0.841254	+	0.540641i	−0.485698	+	0.312139i
$4$		0			0
$5$	−0.166640	+	1.15901i	−0.0745236	+	0.518323i	0.918030	+	0.396512i	$0.129779\pi$
$5$	−0.166640	+	1.15901i	−0.0745236	+	0.518323i	−0.992553	+	0.121811i	$0.961130\pi$
$6$		0			0
$7$	−3.32963	+	0.317941i	−1.25848	+	0.120170i	−0.702899	−	0.711290i	$-0.748111\pi$
$7$	−3.32963	+	0.317941i	−1.25848	+	0.120170i	−0.555584	+	0.831461i	$0.687505\pi$
$8$		0			0
$9$	0.415415	−	0.909632i	0.138472	−	0.303211i
$10$		0			0
$11$	0.135033	−	0.0540592i	0.0407141	−	0.0162995i	−0.351216	−	0.936294i	$-0.614232\pi$
$11$	0.135033	−	0.0540592i	0.0407141	−	0.0162995i	0.391930	+	0.919995i	$0.371807\pi$
$12$		0			0
$13$	0.954845	−	0.910443i	0.264826	−	0.252511i	−0.546018	−	0.837774i	$-0.683857\pi$
$13$	0.954845	−	0.910443i	0.264826	−	0.252511i	0.810844	+	0.585262i	$0.199008\pi$
$14$		0			0
$15$	−0.486420	−	1.06511i	−0.125593	−	0.275010i
$16$		0			0
$17$	0.000287460	0	0.000830562i	6.97193e−5	0	0.000201441i	0.945036	−	0.326967i	$-0.106027\pi$
$17$	0.000287460	0	0.000830562i	6.97193e−5	0	0.000201441i	−0.944966	+	0.327169i	$0.893905\pi$
$18$		0			0
$19$	−4.79439	−	0.457809i	−1.09991	−	0.105029i	−0.470722	−	0.882282i	$-0.656006\pi$
$19$	−4.79439	−	0.457809i	−1.09991	−	0.105029i	−0.629188	+	0.777253i	$0.716612\pi$
$20$		0			0
$21$	2.62917	−	2.06760i	0.573732	−	0.451188i
$22$		0			0
$23$	−0.346097	−	7.26546i	−0.0721661	−	1.51495i	−0.687209	−	0.726460i	$-0.741164\pi$
$23$	−0.346097	−	7.26546i	−0.0721661	−	1.51495i	0.615043	−	0.788494i	$-0.289139\pi$
$24$		0			0
$25$	3.48194	+	1.02239i	0.696388	+	0.204478i
$26$		0			0
$27$	0.142315	+	0.989821i	0.0273885	+	0.190491i
$28$		0			0
$29$	−3.06768	−	5.31337i	−0.569653	−	0.986669i	−0.996600	−	0.0823918i	$-0.973744\pi$
$29$	−3.06768	−	5.31337i	−0.569653	−	0.986669i	0.426947	−	0.904277i	$-0.359589\pi$
$30$		0			0
$31$	−2.23622	−	2.13224i	−0.401638	−	0.382961i	0.462162	−	0.886795i	$-0.347074\pi$
$31$	−2.23622	−	2.13224i	−0.401638	−	0.382961i	−0.863800	+	0.503834i	$0.831922\pi$
$32$		0			0
$33$	−0.0843707	+	0.118482i	−0.0146871	+	0.0206251i
$34$		0			0
$35$	0.186354	−	3.91204i	0.0314995	−	0.661256i
$36$		0			0
$37$	1.40568	−	2.43471i	0.231093	−	0.400264i	−0.727037	−	0.686598i	$-0.759103\pi$
$37$	1.40568	−	2.43471i	0.231093	−	0.400264i	0.958130	+	0.286334i	$0.0924366\pi$
$38$		0			0
$39$	−0.311044	+	1.28214i	−0.0498069	+	0.205307i
$40$		0			0
$41$	−2.34812	−	0.452564i	−0.366715	−	0.0706786i	0.00256473	−	0.999997i	$-0.499184\pi$
$41$	−2.34812	−	0.452564i	−0.366715	−	0.0706786i	−0.369280	+	0.929318i	$0.620396\pi$
$42$		0			0
$43$	5.01284	−	5.78512i	0.764450	−	0.882223i	−0.231435	−	0.972850i	$-0.574342\pi$
$43$	5.01284	−	5.78512i	0.764450	−	0.882223i	0.995885	+	0.0906279i	$0.0288874\pi$
$44$		0			0
$45$	0.985044	+	0.633050i	0.146842	+	0.0943695i
$46$		0			0
$47$	−0.146019	−	0.0752781i	−0.0212991	−	0.0109804i	0.447544	−	0.894262i	$-0.352299\pi$
$47$	−0.146019	−	0.0752781i	−0.0212991	−	0.0109804i	−0.468843	+	0.883281i	$0.655329\pi$
$48$		0			0
$49$	4.11186	−	0.792495i	0.587408	−	0.113214i
$50$		0			0
$51$	−0.000690862	0	0.000543300i	−9.67401e−5	0	7.60772e-5i
$52$		0			0
$53$	−6.16018	−	7.10923i	−0.846166	−	0.976528i	0.153767	−	0.988107i	$-0.450860\pi$
$53$	−6.16018	−	7.10923i	−0.846166	−	0.976528i	−0.999933	+	0.0115791i	$0.996314\pi$
$54$		0			0
$55$	0.0401530	+	0.165513i	0.00541423	+	0.0223178i
$56$		0			0
$57$	4.28081	−	2.20691i	0.567007	−	0.292313i
$58$		0			0
$59$	−6.09362	+	1.78925i	−0.793322	+	0.232940i	−0.653192	−	0.757193i	$-0.726570\pi$
$59$	−6.09362	+	1.78925i	−0.793322	+	0.232940i	−0.140131	+	0.990133i	$0.544752\pi$
$60$		0			0
$61$	3.83552	+	1.53551i	0.491088	+	0.196602i	0.603971	−	0.797006i	$-0.293584\pi$
$61$	3.83552	+	1.53551i	0.491088	+	0.196602i	−0.112883	+	0.993608i	$0.536009\pi$
$62$		0			0
$63$	−1.09397	+	3.16082i	−0.137827	+	0.398225i
$64$		0			0
$65$	0.896094	+	1.25839i	0.111147	+	0.156084i
$66$		0			0
$67$	−7.35865	+	3.58472i	−0.899002	+	0.437944i
$67$	−7.35865	+	3.58472i	−0.899002	+	0.437944i
$68$		0			0
$69$	4.21916	+	5.92498i	0.507927	+	0.713284i
$70$		0			0
$71$	1.52879	−	4.41715i	0.181434	−	0.524219i	−0.817207	−	0.576345i	$-0.804479\pi$
$71$	1.52879	−	4.41715i	0.181434	−	0.524219i	0.998641	+	0.0521260i	$0.0165998\pi$
$72$		0			0
$73$	5.95457	+	2.38385i	0.696930	+	0.279008i	0.692952	−	0.720984i	$-0.256310\pi$
$73$	5.95457	+	2.38385i	0.696930	+	0.279008i	0.00397740	+	0.999992i	$0.498734\pi$
$74$		0			0
$75$	−3.48194	+	1.02239i	−0.402060	+	0.118055i
$76$		0			0
$77$	−0.432424	+	0.222930i	−0.0492793	+	0.0254052i
$78$		0			0
$79$	1.07456	+	4.42940i	0.120898	+	0.498346i	0.999773	+	0.0212956i	$0.00677910\pi$
$79$	1.07456	+	4.42940i	0.120898	+	0.498346i	−0.878876	+	0.477051i	$0.841706\pi$
$80$		0			0
$81$	−0.654861	−	0.755750i	−0.0727623	−	0.0839722i
$82$		0			0
$83$	−11.0604	−	8.69800i	−1.21404	−	0.954730i	−0.214281	−	0.976772i	$-0.568741\pi$
$83$	−11.0604	−	8.69800i	−1.21404	−	0.954730i	−0.999757	+	0.0220421i	$0.992983\pi$
$84$		0			0
$85$	−0.00101053		0.000194763i	−0.000109607		2.11251e-5i
$86$		0			0
$87$	5.45332	+	2.81138i	0.584657	+	0.301412i
$88$		0			0
$89$	−8.69824	−	5.59002i	−0.922012	−	0.592541i	−0.00877101	−	0.999962i	$-0.502792\pi$
$89$	−8.69824	−	5.59002i	−0.922012	−	0.592541i	−0.913241	+	0.407421i	$0.866428\pi$
$90$		0			0
$91$	−2.88981	+	3.33502i	−0.302935	+	0.349605i
$92$		0			0
$93$	3.03401	+	0.584757i	0.314612	+	0.0606364i
$94$		0			0
$95$	1.32954	−	5.48044i	0.136408	−	0.562282i
$96$		0			0
$97$	1.06715	−	1.84837i	0.108353	−	0.187673i	−0.806750	−	0.590893i	$-0.798776\pi$
$97$	1.06715	−	1.84837i	0.108353	−	0.187673i	0.915103	+	0.403220i	$0.132109\pi$
$98$		0			0
$99$	0.00692091	−	0.145288i	0.000695577	−	0.0146020i
$100$		0			0
$101$	1.11527	−	1.56618i	0.110973	−	0.155840i	−0.755354	−	0.655317i	$-0.772535\pi$
$101$	1.11527	−	1.56618i	0.110973	−	0.155840i	0.866327	+	0.499477i	$0.166474\pi$
$102$		0			0
$103$	−4.44633	−	4.23956i	−0.438110	−	0.417737i	0.438656	−	0.898655i	$-0.355455\pi$
$103$	−4.44633	−	4.23956i	−0.438110	−	0.417737i	−0.876765	+	0.480919i	$0.840303\pi$
$104$		0			0
$105$	1.95824	+	3.39177i	0.191105	+	0.331003i
$106$		0			0
$107$	0.140607	+	0.977941i	0.0135930	+	0.0945411i	0.995489	−	0.0948819i	$-0.0302474\pi$
$107$	0.140607	+	0.977941i	0.0135930	+	0.0945411i	−0.981896	+	0.189423i	$0.939338\pi$
$108$		0			0
$109$	2.57299	+	0.755499i	0.246448	+	0.0723636i	0.402624	−	0.915366i	$-0.368098\pi$
$109$	2.57299	+	0.755499i	0.246448	+	0.0723636i	−0.156176	+	0.987729i	$0.549917\pi$
$110$		0			0
$111$	0.133770	+	2.80818i	0.0126969	+	0.266540i
$112$		0			0
$113$	3.00763	−	2.36523i	0.282934	−	0.222502i	−0.466598	−	0.884469i	$-0.654521\pi$
$113$	3.00763	−	2.36523i	0.282934	−	0.222502i	0.749533	+	0.661967i	$0.230278\pi$
$114$		0			0
$115$	8.47839	+	0.809588i	0.790614	+	0.0754944i
$116$		0			0
$117$	−0.431511	−	1.24677i	−0.0398932	−	0.115264i
$118$		0			0
$119$	−0.00122121	−	0.00267407i	−0.000111948	−	0.000245131i
$120$		0			0
$121$	−7.94576	+	7.57627i	−0.722342	+	0.688752i
$122$		0			0
$123$	2.22004	−	0.888771i	0.200175	−	0.0801378i
$124$		0			0
$125$	−4.19728	+	9.19077i	−0.375416	+	0.822047i
$126$		0			0
$127$	11.2684	−	1.07601i	0.999913	−	0.0954801i	0.417758	−	0.908558i	$-0.362816\pi$
$127$	11.2684	−	1.07601i	0.999913	−	0.0954801i	0.582155	+	0.813078i	$0.302210\pi$
$128$		0			0
$129$	−1.08939	+	7.57690i	−0.0959157	+	0.667108i
$130$		0			0
$131$	−13.0073	+	8.35932i	−1.13646	+	0.730357i	−0.966898	−	0.255163i	$-0.917871\pi$
$131$	−13.0073	+	8.35932i	−1.13646	+	0.730357i	−0.169559	+	0.985520i	$0.554234\pi$
$132$		0			0
$133$	16.1091			1.39684
$134$		0			0
$135$	−1.17092			−0.100777
$136$		0			0
$137$	−3.57702	+	2.29881i	−0.305605	+	0.196401i	−0.684450	−	0.729059i	$-0.739958\pi$
$137$	−3.57702	+	2.29881i	−0.305605	+	0.196401i	0.378845	+	0.925460i	$0.376321\pi$
$138$		0			0
$139$	−3.02873	+	21.0653i	−0.256894	+	1.78673i	0.297747	+	0.954645i	$0.403765\pi$
$139$	−3.02873	+	21.0653i	−0.256894	+	1.78673i	−0.554641	+	0.832090i	$0.687144\pi$
$140$		0			0
$141$	0.163537	−	0.0156159i	0.0137723	−	0.00131510i
$142$		0			0
$143$	0.0797181	−	0.174558i	0.00666636	−	0.0145973i
$144$		0			0
$145$	6.66943	−	2.67004i	0.553866	−	0.221734i
$146$		0			0
$147$	−3.03066	+	2.88973i	−0.249965	+	0.238341i
$148$		0			0
$149$	1.22998	+	2.69328i	0.100764	+	0.220642i	0.953299	−	0.302027i	$-0.0976634\pi$
$149$	1.22998	+	2.69328i	0.100764	+	0.220642i	−0.852535	+	0.522670i	$0.824936\pi$
$150$		0			0
$151$	0.605102	+	1.74833i	0.0492425	+	0.142277i	0.966941	−	0.255001i	$-0.0820759\pi$
$151$	0.605102	+	1.74833i	0.0492425	+	0.142277i	−0.917698	+	0.397278i	$0.869955\pi$
$152$		0			0
$153$	0.000874921	0	8.35448e-5i	7.07332e−5	0	6.75420e-6i
$154$		0			0
$155$	2.84392	−	2.23648i	0.228429	−	0.179639i
$156$		0			0
$157$	0.206296	+	4.33068i	0.0164642	+	0.345626i	0.992037	+	0.125949i	$0.0401975\pi$
$157$	0.206296	+	4.33068i	0.0164642	+	0.345626i	−0.975573	+	0.219678i	$0.929499\pi$
$158$		0			0
$159$	9.02582	+	2.65022i	0.715794	+	0.210176i
$160$		0			0
$161$	3.46236	+	24.0813i	0.272872	+	1.89787i
$162$		0			0
$163$	−8.32642	−	14.4218i	−0.652176	−	1.12960i	−0.982594	−	0.185767i	$-0.940523\pi$
$163$	−8.32642	−	14.4218i	−0.652176	−	1.12960i	0.330418	−	0.943835i	$-0.392810\pi$
$164$		0			0
$165$	−0.123262	−	0.117530i	−0.00959593	−	0.00914970i
$166$		0			0
$167$	4.78393	−	6.71809i	0.370192	−	0.519861i	−0.586895	−	0.809663i	$-0.699650\pi$
$167$	4.78393	−	6.71809i	0.370192	−	0.519861i	0.957087	+	0.289802i	$0.0935893\pi$
$168$		0			0
$169$	−0.535742	+	11.2466i	−0.0412109	+	0.865124i
$170$		0			0
$171$	−2.40810	+	4.17095i	−0.184152	+	0.318961i
$172$		0			0
$173$	−0.0556620	+	0.229442i	−0.00423190	+	0.0174441i	−0.973888	−	0.227027i	$-0.927099\pi$
$173$	−0.0556620	+	0.229442i	−0.00423190	+	0.0174441i	0.969656	+	0.244472i	$0.0786145\pi$
$174$		0			0
$175$	−11.9186	−	2.29713i	−0.900964	−	0.173647i
$176$		0			0
$177$	4.15894	−	4.79967i	0.312605	−	0.360766i
$178$		0			0
$179$	16.5006	+	10.6043i	1.23331	+	0.792603i	0.984404	−	0.175924i	$-0.0562912\pi$
$179$	16.5006	+	10.6043i	1.23331	+	0.792603i	0.248910	+	0.968527i	$0.419928\pi$
$180$		0			0
$181$	15.7742	+	8.13217i	1.17249	+	0.604459i	0.930669	−	0.365862i	$-0.119226\pi$
$181$	15.7742	+	8.13217i	1.17249	+	0.604459i	0.241818	+	0.970322i	$0.422256\pi$
$182$		0			0
$183$	−4.05680	+	0.781884i	−0.299887	+	0.0577985i
$184$		0			0
$185$	2.58760	+	2.03491i	0.190244	+	0.149610i
$186$		0			0
$187$	8.37162e−5	0	9.66137e-5i	6.12194e−6	0	7.06509e-6i
$188$		0			0
$189$	−0.788561	−	3.25049i	−0.0573594	−	0.236439i
$190$		0			0
$191$	−3.95415	+	2.03851i	−0.286112	+	0.147501i	−0.595309	−	0.803497i	$-0.702970\pi$
$191$	−3.95415	+	2.03851i	−0.286112	+	0.147501i	0.309196	+	0.950998i	$0.399940\pi$
$192$		0			0
$193$	−11.8283	+	3.47309i	−0.851416	+	0.249998i	−0.678193	−	0.734884i	$-0.737237\pi$
$193$	−11.8283	+	3.47309i	−0.851416	+	0.249998i	−0.173224	+	0.984883i	$0.555418\pi$
$194$		0			0
$195$	−1.43418	−	0.574158i	−0.102704	−	0.0411163i
$196$		0			0
$197$	0.833637	−	2.40864i	0.0593942	−	0.171608i	−0.911400	−	0.411521i	$-0.864998\pi$
$197$	0.833637	−	2.40864i	0.0593942	−	0.171608i	0.970794	+	0.239913i	$0.0771189\pi$
$198$		0			0
$199$	7.88437	+	11.0721i	0.558908	+	0.784877i	0.993265	−	0.115864i	$-0.0369636\pi$
$199$	7.88437	+	11.0721i	0.558908	+	0.784877i	−0.434357	+	0.900741i	$0.643024\pi$
$200$		0			0
$201$	4.25244	−	6.99405i	0.299944	−	0.493322i
$202$		0			0
$203$	11.9036	+	16.7162i	0.835467	+	1.17325i
$204$		0			0
$205$	0.915816	−	2.64608i	0.0639633	−	0.184810i
$206$		0			0
$207$	−6.75267	−	2.70336i	−0.469343	−	0.187897i
$208$		0			0
$209$	−0.672152	+	0.197362i	−0.0464937	+	0.0136518i
$210$		0			0
$211$	−16.5467	+	8.53041i	−1.13912	+	0.587257i	−0.921347	−	0.388742i	$-0.872910\pi$
$211$	−16.5467	+	8.53041i	−1.13912	+	0.587257i	−0.217774	+	0.975999i	$0.569879\pi$
$212$		0			0
$213$	1.10199	+	4.54247i	0.0755071	+	0.311245i
$214$		0			0
$215$	5.86965	+	6.77394i	0.400307	+	0.461979i
$216$		0			0
$217$	8.12373	+	6.38857i	0.551475	+	0.433684i
$218$		0			0
$219$	−6.29811	+	1.21386i	−0.425587	+	0.0820251i
$220$		0			0
$221$	0.00103066		0.000531342i	6.93296e−5		3.57419e-5i
$222$		0			0
$223$	−5.65846	−	3.63647i	−0.378919	−	0.243516i	0.337292	−	0.941400i	$-0.390489\pi$
$223$	−5.65846	−	3.63647i	−0.378919	−	0.243516i	−0.716211	+	0.697884i	$0.754125\pi$
$224$		0			0
$225$	2.37645	−	2.74257i	0.158430	−	0.182838i
$226$		0			0
$227$	−19.5805	−	3.77383i	−1.29960	−	0.250478i	−0.507918	−	0.861406i	$-0.669585\pi$
$227$	−19.5805	−	3.77383i	−1.29960	−	0.250478i	−0.791687	+	0.610927i	$0.790797\pi$
$228$		0			0
$229$	0.107523	−	0.443217i	0.00710533	−	0.0292886i	−0.968149	−	0.250376i	$-0.919446\pi$
$229$	0.107523	−	0.443217i	0.00710533	−	0.0292886i	0.975254	+	0.221088i	$0.0709608\pi$
$230$		0			0
$231$	0.243253	−	0.421326i	0.0160049	−	0.0277212i
$232$		0			0
$233$	0.342513	−	7.19024i	0.0224388	−	0.471048i	−0.959484	−	0.281764i	$-0.909080\pi$
$233$	0.342513	−	7.19024i	0.0224388	−	0.471048i	0.981922	−	0.189284i	$-0.0606167\pi$
$234$		0			0
$235$	0.111580	−	0.156693i	0.00727870	−	0.0102215i
$236$		0			0
$237$	−3.29869	−	3.14530i	−0.214273	−	0.204309i
$238$		0			0
$239$	−12.0771	−	20.9181i	−0.781199	−	1.35308i	−0.931243	−	0.364398i	$-0.881275\pi$
$239$	−12.0771	−	20.9181i	−0.781199	−	1.35308i	0.150044	−	0.988679i	$-0.452058\pi$
$240$		0			0
$241$	−3.25859	−	22.6640i	−0.209904	−	1.45992i	−0.773463	−	0.633841i	$-0.781477\pi$
$241$	−3.25859	−	22.6640i	−0.209904	−	1.45992i	0.563559	−	0.826076i	$-0.309432\pi$
$242$		0			0
$243$	0.959493	+	0.281733i	0.0615515	+	0.0180732i
$244$		0			0
$245$	0.233308	+	4.89773i	0.0149055	+	0.312904i
$246$		0			0
$247$	−4.99471	+	3.92789i	−0.317806	+	0.249925i
$248$		0			0
$249$	14.0071	+	1.33752i	0.887664	+	0.0847617i
$250$		0			0
$251$	−0.103287	−	0.298428i	−0.00651942	−	0.0188366i	0.941694	−	0.336470i	$-0.109233\pi$
$251$	−0.103287	−	0.298428i	−0.00651942	−	0.0188366i	−0.948214	+	0.317633i	$0.897112\pi$
$252$		0			0
$253$	−0.439500	−	0.962370i	−0.0276311	−	0.0605037i
$254$		0			0
$255$	0.000744814	0	0.000710178i	4.66420e−5	0	4.44731e-5i
$256$		0			0
$257$	23.7797	−	9.51997i	1.48334	−	0.593839i	0.518126	−	0.855304i	$-0.326630\pi$
$257$	23.7797	−	9.51997i	1.48334	−	0.593839i	0.965213	+	0.261465i	$0.0842057\pi$
$258$		0			0
$259$	−3.90631	+	8.55362i	−0.242726	+	0.531496i
$260$		0			0
$261$	−6.10757	+	0.583203i	−0.378049	+	0.0360993i
$262$		0			0
$263$	3.05352	−	21.2377i	0.188288	−	1.30957i	−0.648150	−	0.761513i	$-0.724457\pi$
$263$	3.05352	−	21.2377i	0.188288	−	1.30957i	0.836438	−	0.548061i	$-0.184634\pi$
$264$		0			0
$265$	9.26618	−	5.95501i	0.569217	−	0.365813i
$266$		0			0
$267$	10.3396			0.632774
$268$		0			0
$269$	−13.4055			−0.817350			−0.408675	−	0.912680i	$-0.634009\pi$
$269$	−13.4055			−0.817350			−0.408675	+	0.912680i	$0.634009\pi$
$270$		0			0
$271$	6.54992	−	4.20938i	0.397880	−	0.255702i	−0.326367	−	0.945243i	$-0.605824\pi$
$271$	6.54992	−	4.20938i	0.397880	−	0.255702i	0.724246	+	0.689542i	$0.242188\pi$
$272$		0			0
$273$	0.628017	−	4.36795i	0.0380093	−	0.264360i
$274$		0			0
$275$	0.525447	−	0.0501741i	0.0316857	−	0.00302562i
$276$		0			0
$277$	−2.45278	+	5.37084i	−0.147373	+	0.322702i	−0.968894	−	0.247476i	$-0.920399\pi$
$277$	−2.45278	+	5.37084i	−0.147373	+	0.322702i	0.821521	+	0.570179i	$0.193126\pi$
$278$		0			0
$279$	−2.86851	+	1.14838i	−0.171733	+	0.0687516i
$280$		0			0
$281$	3.73654	−	3.56279i	0.222903	−	0.212538i	−0.570396	−	0.821370i	$-0.693210\pi$
$281$	3.73654	−	3.56279i	0.222903	−	0.212538i	0.793299	+	0.608832i	$0.208362\pi$
$282$		0			0
$283$	6.30989	+	13.8167i	0.375084	+	0.821320i	0.999200	+	0.0399880i	$0.0127320\pi$
$283$	6.30989	+	13.8167i	0.375084	+	0.821320i	−0.624116	+	0.781332i	$0.714541\pi$
$284$		0			0
$285$	1.84447	+	5.32925i	0.109257	+	0.315677i
$286$		0			0
$287$	7.96228	+	0.760305i	0.469998	+	0.0448794i
$288$		0			0
$289$	13.3629	−	10.5087i	0.786053	−	0.618159i
$290$		0			0
$291$	0.101554	+	2.13189i	0.00595323	+	0.124974i
$292$		0			0
$293$	−28.3209	−	8.31576i	−1.65452	−	0.485812i	−0.684539	−	0.728977i	$-0.739996\pi$
$293$	−28.3209	−	8.31576i	−1.65452	−	0.485812i	−0.969985	+	0.243165i	$0.921815\pi$
$294$		0			0
$295$	−1.05831	−	7.36071i	−0.0616172	−	0.428557i
$296$		0			0
$297$	0.0727262	+	0.125965i	0.00422000	+	0.00730926i
$298$		0			0
$299$	−6.94525	−	6.62229i	−0.401654	−	0.382977i
$300$		0			0
$301$	−14.8516	+	20.8561i	−0.856030	+	1.20213i
$302$		0			0
$303$	−0.0914852	+	1.92051i	−0.00525569	+	0.110330i
$304$		0			0
$305$	−2.41881	+	4.18951i	−0.138501	+	0.239891i
$306$		0			0
$307$	6.09522	−	25.1248i	0.347873	−	1.43395i	−0.482086	−	0.876124i	$-0.660121\pi$
$307$	6.09522	−	25.1248i	0.347873	−	1.43395i	0.829958	−	0.557826i	$-0.188364\pi$
$308$		0			0
$309$	6.03257	+	1.16268i	0.343181	+	0.0661427i
$310$		0			0
$311$	−2.89473	+	3.34070i	−0.164145	+	0.189434i	−0.831863	−	0.554981i	$-0.812726\pi$
$311$	−2.89473	+	3.34070i	−0.164145	+	0.189434i	0.667718	+	0.744414i	$0.267271\pi$
$312$		0			0
$313$	7.14223	+	4.59003i	0.403703	+	0.259444i	0.726699	−	0.686956i	$-0.241054\pi$
$313$	7.14223	+	4.59003i	0.403703	+	0.259444i	−0.322996	+	0.946400i	$0.604690\pi$
$314$		0			0
$315$	−3.48111	−	1.79464i	−0.196138	−	0.101116i
$316$		0			0
$317$	6.58581	−	1.26931i	0.369896	−	0.0712916i	−0.000916009	−	1.00000i	$-0.500292\pi$
$317$	6.58581	−	1.26931i	0.369896	−	0.0712916i	0.370812	+	0.928708i	$0.379079\pi$
$318$		0			0
$319$	−0.701476	−	0.551646i	−0.0392751	−	0.0308863i
$320$		0			0
$321$	−0.647000	−	0.746678i	−0.0361120	−	0.0416755i
$322$		0			0
$323$	−0.000997959	−	0.00411364i	−5.55279e−5	−	0.000228889i
$324$		0			0
$325$	4.25554	−	2.19388i	0.236055	−	0.121695i
$326$		0			0
$327$	−2.57299	+	0.755499i	−0.142287	+	0.0417792i
$328$		0			0
$329$	0.510124	+	0.204223i	0.0281240	+	0.0112592i
$330$		0			0
$331$	−8.97060	+	25.9188i	−0.493069	+	1.42463i	0.374461	+	0.927243i	$0.377828\pi$
$331$	−8.97060	+	25.9188i	−0.493069	+	1.42463i	−0.867530	+	0.497386i	$0.834293\pi$
$332$		0			0
$333$	−1.63075	−	2.29007i	−0.0893646	−	0.125495i
$334$		0			0
$335$	−2.92847	−	9.12608i	−0.159999	−	0.498611i
$336$		0			0
$337$	−11.7908	−	16.5579i	−0.642287	−	0.901966i	0.357199	−	0.934028i	$-0.383732\pi$
$337$	−11.7908	−	16.5579i	−0.642287	−	0.901966i	−0.999486	+	0.0320622i	$0.989793\pi$
$338$		0			0
$339$	−1.25144	+	3.61581i	−0.0679690	+	0.196384i
$340$		0			0
$341$	−0.417232	−	0.167034i	−0.0225944	−	0.00904542i
$342$		0			0
$343$	9.02603	−	2.65028i	0.487360	−	0.143102i
$344$		0			0
$345$	−7.57017	+	3.90269i	−0.407564	+	0.210114i
$346$		0			0
$347$	8.36165	+	34.4672i	0.448877	+	1.85030i	0.521959	+	0.852970i	$0.325201\pi$
$347$	8.36165	+	34.4672i	0.448877	+	1.85030i	−0.0730821	+	0.997326i	$0.523284\pi$
$348$		0			0
$349$	−11.7696	−	13.5828i	−0.630010	−	0.727071i	0.347565	−	0.937656i	$-0.387009\pi$
$349$	−11.7696	−	13.5828i	−0.630010	−	0.727071i	−0.977576	+	0.210585i	$0.932463\pi$
$350$		0			0
$351$	1.03706	+	0.815556i	0.0553544	+	0.0435312i
$352$		0			0
$353$	3.58337	−	0.690638i	0.190724	−	0.0367590i	−0.0929948	−	0.995667i	$-0.529644\pi$
$353$	3.58337	−	0.690638i	0.190724	−	0.0367590i	0.283718	+	0.958908i	$0.408432\pi$
$354$		0			0
$355$	4.86474	+	2.50795i	0.258194	+	0.133108i
$356$		0			0
$357$	0.00247305	+	0.00158934i	0.000130888	+	8.41166e-5i
$358$		0			0
$359$	10.3305	−	11.9220i	0.545221	−	0.629219i	−0.414542	−	0.910030i	$-0.636058\pi$
$359$	10.3305	−	11.9220i	0.545221	−	0.629219i	0.959763	+	0.280811i	$0.0906036\pi$
$360$		0			0
$361$	4.11998	+	0.794062i	0.216841	+	0.0417927i
$362$		0			0
$363$	2.58836	−	10.6694i	0.135854	−	0.559997i
$364$		0			0
$365$	−3.75517	+	6.50414i	−0.196554	+	0.340442i
$366$		0			0
$367$	0.225953	−	4.74334i	0.0117947	−	0.247600i	−0.985268	−	0.171015i	$-0.945295\pi$
$367$	0.225953	−	4.74334i	0.0117947	−	0.247600i	0.997063	−	0.0765851i	$-0.0244017\pi$
$368$		0			0
$369$	−1.38711	+	1.94793i	−0.0722102	+	0.101405i
$370$		0			0
$371$	22.7715	+	21.7125i	1.18224	+	1.12726i
$372$		0			0
$373$	−17.5031	−	30.3162i	−0.906274	−	1.56971i	−0.819197	−	0.573512i	$-0.805581\pi$
$373$	−17.5031	−	30.3162i	−0.906274	−	1.56971i	−0.0870771	−	0.996202i	$-0.527753\pi$
$374$		0			0
$375$	−1.43793	−	10.0010i	−0.0742541	−	0.516449i
$376$		0			0
$377$	−7.76668	−	2.28050i	−0.400004	−	0.117452i
$378$		0			0
$379$	−0.650668	−	13.6592i	−0.0334226	−	0.701626i	−0.951947	−	0.306262i	$-0.900922\pi$
$379$	−0.650668	−	13.6592i	−0.0334226	−	0.701626i	0.918525	−	0.395364i	$-0.129381\pi$
$380$		0			0
$381$	−8.89789	+	6.99737i	−0.455853	+	0.358486i
$382$		0			0
$383$	14.4979	+	1.38438i	0.740810	+	0.0707388i	0.458636	−	0.888624i	$-0.348338\pi$
$383$	14.4979	+	1.38438i	0.740810	+	0.0707388i	0.282174	+	0.959363i	$0.408944\pi$
$384$		0			0
$385$	−0.186318	−	0.538331i	−0.00949565	−	0.0274359i
$386$		0			0
$387$	−3.17992	−	6.96306i	−0.161645	−	0.353952i
$388$		0			0
$389$	6.19917	−	5.91090i	0.314310	−	0.299694i	−0.516458	−	0.856312i	$-0.672750\pi$
$389$	6.19917	−	5.91090i	0.314310	−	0.299694i	0.830768	+	0.556618i	$0.187901\pi$
$390$		0			0
$391$	0.00593492	−	0.00237598i	0.000300142	−	0.000120159i
$392$		0			0
$393$	6.42309	−	14.0646i	0.324002	−	0.709466i
$394$		0			0
$395$	−5.31277	+	0.507308i	−0.267314	+	0.0255254i
$396$		0			0
$397$	−3.51897	+	24.4750i	−0.176612	+	1.22836i	0.687920	+	0.725787i	$0.258524\pi$
$397$	−3.51897	+	24.4750i	−0.176612	+	1.22836i	−0.864532	+	0.502578i	$0.832385\pi$
$398$		0			0
$399$	−13.5519	+	8.70925i	−0.678441	+	0.436008i
$400$		0			0
$401$	−0.247632			−0.0123662			−0.00618308	−	0.999981i	$-0.501968\pi$
$401$	−0.247632			−0.0123662			−0.00618308	+	0.999981i	$0.501968\pi$
$402$		0			0
$403$	−4.07653			−0.203066
$404$		0			0
$405$	0.985044	−	0.633050i	0.0489472	−	0.0314565i
$406$		0			0
$407$	0.0581953	−	0.404757i	0.00288463	−	0.0200631i
$408$		0			0
$409$	−2.54179	+	0.242712i	−0.125684	+	0.0120013i	−0.157708	−	0.987486i	$-0.550411\pi$
$409$	−2.54179	+	0.242712i	−0.125684	+	0.0120013i	0.0320247	+	0.999487i	$0.489804\pi$
$410$		0			0
$411$	1.76635	−	3.86777i	0.0871276	−	0.190783i
$412$		0			0
$413$	19.7206	−	7.89495i	0.970389	−	0.388485i
$414$		0			0
$415$	11.9241	−	11.3696i	0.585333	−	0.558114i
$416$		0			0
$417$	−8.84082	−	19.3587i	−0.432937	−	0.948000i
$418$		0			0
$419$	−8.84835	−	25.5656i	−0.432270	−	1.24896i	−0.925395	−	0.379004i	$-0.876267\pi$
$419$	−8.84835	−	25.5656i	−0.432270	−	1.24896i	0.493125	−	0.869958i	$-0.335855\pi$
$420$		0			0
$421$	−8.94091	−	0.853753i	−0.435753	−	0.0416094i	−0.125125	−	0.992141i	$-0.539933\pi$
$421$	−8.94091	−	0.853753i	−0.435753	−	0.0416094i	−0.310628	+	0.950532i	$0.600539\pi$
$422$		0			0
$423$	−0.129134	+	0.101552i	−0.00627870	+	0.00493763i
$424$		0			0
$425$	0.000151761		0.00318586i	7.36150e−6		0.000154537i
$426$		0			0
$427$	−13.2591	−	3.89321i	−0.641651	−	0.188406i
$428$		0			0
$429$	0.0273102	+	0.189947i	0.00131855	+	0.00917071i
$430$		0			0
$431$	−8.59009	−	14.8785i	−0.413770	−	0.716671i	0.581529	−	0.813526i	$-0.302455\pi$
$431$	−8.59009	−	14.8785i	−0.413770	−	0.716671i	−0.995298	+	0.0968555i	$0.969122\pi$
$432$		0			0
$433$	−22.0091	−	20.9856i	−1.05769	−	1.00850i	−0.999948	−	0.0101717i	$-0.996762\pi$
$433$	−22.0091	−	20.9856i	−1.05769	−	1.00850i	−0.0577396	−	0.998332i	$-0.518389\pi$
$434$		0			0
$435$	−4.16715	+	5.85194i	−0.199800	+	0.280579i
$436$		0			0
$437$	−1.66687	+	34.9919i	−0.0797372	+	1.67389i
$438$		0			0
$439$	−7.68776	+	13.3156i	−0.366917	+	0.635518i	−0.989082	−	0.147368i	$-0.952920\pi$
$439$	−7.68776	+	13.3156i	−0.366917	+	0.635518i	0.622165	+	0.782886i	$0.286253\pi$
$440$		0			0
$441$	0.987248	−	4.06949i	0.0470118	−	0.193785i
$442$		0			0
$443$	19.7499	+	3.80648i	0.938345	+	0.180851i	0.635423	−	0.772164i	$-0.280826\pi$
$443$	19.7499	+	3.80648i	0.938345	+	0.180851i	0.302922	+	0.953015i	$0.402038\pi$
$444$		0			0
$445$	7.92834	−	9.14979i	0.375839	−	0.433742i
$446$		0			0
$447$	−2.49082	−	1.60075i	−0.117812	−	0.0757131i
$448$		0			0
$449$	−16.5943	−	8.55494i	−0.783132	−	0.403732i	0.0197997	−	0.999804i	$-0.493697\pi$
$449$	−16.5943	−	8.55494i	−0.783132	−	0.403732i	−0.802931	+	0.596072i	$0.796727\pi$
$450$		0			0
$451$	−0.341540	+	0.0658265i	−0.0160825	+	0.00309965i
$452$		0			0
$453$	−1.45426	−	1.14364i	−0.0683272	−	0.0537331i
$454$		0			0
$455$	−3.38375	−	3.90506i	−0.158633	−	0.183072i
$456$		0			0
$457$	−7.01628	−	28.9215i	−0.328208	−	1.35289i	−0.861842	−	0.507176i	$-0.830689\pi$
$457$	−7.01628	−	28.9215i	−0.328208	−	1.35289i	0.533634	−	0.845715i	$-0.320826\pi$
$458$		0			0
$459$	−0.000781198	0	0.000402736i	−3.64632e−5	0	1.87981e-5i
$460$		0			0
$461$	−26.6394	+	7.82203i	−1.24072	+	0.364308i	−0.835286	−	0.549816i	$-0.814698\pi$
$461$	−26.6394	+	7.82203i	−1.24072	+	0.364308i	−0.405435	+	0.914124i	$0.632880\pi$
$462$		0			0
$463$	−1.01921	−	0.408029i	−0.0473666	−	0.0189627i	0.347858	−	0.937547i	$-0.386909\pi$
$463$	−1.01921	−	0.408029i	−0.0473666	−	0.0189627i	−0.395225	+	0.918584i	$0.629333\pi$
$464$		0			0
$465$	−1.18332	+	3.41899i	−0.0548753	+	0.158552i
$466$		0			0
$467$	14.5999	+	20.5027i	0.675604	+	0.948753i	0.999996	+	0.00283004i	$0.000900832\pi$
$467$	14.5999	+	20.5027i	0.675604	+	0.948753i	−0.324392	+	0.945923i	$0.605160\pi$
$468$		0			0
$469$	23.3619	−	14.2754i	1.07875	−	0.659178i
$470$		0			0
$471$	−2.51489	−	3.53167i	−0.115880	−	0.162731i
$472$		0			0
$473$	0.364161	−	1.05217i	0.0167441	−	0.0483790i
$474$		0			0
$475$	−16.2257	−	6.49580i	−0.744487	−	0.298048i
$476$		0			0
$477$	−9.02582	+	2.65022i	−0.413264	+	0.121345i
$478$		0			0
$479$	9.53759	−	4.91697i	0.435784	−	0.224662i	−0.226353	−	0.974045i	$-0.572680\pi$
$479$	9.53759	−	4.91697i	0.435784	−	0.224662i	0.662136	+	0.749383i	$0.269650\pi$
$480$		0			0
$481$	−0.874458	−	3.60456i	−0.0398718	−	0.164354i
$482$		0			0
$483$	−15.9320	−	18.3866i	−0.724933	−	0.836617i
$484$		0			0
$485$	1.96444	+	1.54485i	0.0892004	+	0.0701480i
$486$		0			0
$487$	23.3678	−	4.50377i	1.05889	−	0.204085i	0.370063	−	0.929007i	$-0.379336\pi$
$487$	23.3678	−	4.50377i	1.05889	−	0.204085i	0.688831	+	0.724922i	$0.258124\pi$
$488$		0			0
$489$	14.8016	+	7.63078i	0.669353	+	0.345076i
$490$		0			0
$491$	11.5965	+	7.45263i	0.523343	+	0.336332i	0.775493	−	0.631356i	$-0.217501\pi$
$491$	11.5965	+	7.45263i	0.523343	+	0.336332i	−0.252150	+	0.967688i	$0.581138\pi$
$492$		0			0
$493$	0.00353125	−	0.00407528i	0.000159039	−	0.000183541i
$494$		0			0
$495$	0.167236	+	0.0322321i	0.00751670	+	0.00144873i
$496$		0			0
$497$	−3.68591	+	15.1935i	−0.165336	+	0.681523i
$498$		0			0
$499$	14.2289	−	24.6452i	0.636973	−	1.10327i	−0.349120	−	0.937078i	$-0.613519\pi$
$499$	14.2289	−	24.6452i	0.636973	−	1.10327i	0.986093	−	0.166192i	$-0.0531472\pi$
$500$		0			0
$501$	−0.392425	+	8.23801i	−0.0175322	+	0.368047i
$502$		0			0
$503$	12.6654	−	17.7861i	0.564723	−	0.793043i	−0.429189	−	0.903215i	$-0.641201\pi$
$503$	12.6654	−	17.7861i	0.564723	−	0.793043i	0.993913	+	0.110172i	$0.0351401\pi$
$504$		0			0
$505$	1.62936	+	1.55359i	0.0725055	+	0.0691339i
$506$		0			0
$507$	−5.62968	−	9.75090i	−0.250023	−	0.433053i
$508$		0			0
$509$	−2.41846	−	16.8207i	−0.107196	−	0.745566i	−0.970538	−	0.240947i	$-0.922542\pi$
$509$	−2.41846	−	16.8207i	−0.107196	−	0.745566i	0.863342	−	0.504619i	$-0.168367\pi$
$510$		0			0
$511$	−20.5844	−	6.04414i	−0.910602	−	0.267377i
$512$		0			0
$513$	−0.229164	−	4.81075i	−0.0101178	−	0.212400i
$514$		0			0
$515$	5.65462	−	4.44684i	0.249172	−	0.195951i
$516$		0			0
$517$	−0.0237869	−	0.00227138i	−0.00104615	−	9.98950e-5i
$518$		0			0
$519$	−0.0772198	−	0.223112i	−0.00338957	−	0.00979353i
$520$		0			0
$521$	15.3325	+	33.5734i	0.671727	+	1.47088i	0.871177	+	0.490969i	$0.163357\pi$
$521$	15.3325	+	33.5734i	0.671727	+	1.47088i	−0.199450	+	0.979908i	$0.563916\pi$
$522$		0			0
$523$	0.666250	−	0.635268i	0.0291331	−	0.0277783i	−0.675373	−	0.737477i	$-0.736017\pi$
$523$	0.666250	−	0.635268i	0.0291331	−	0.0277783i	0.704506	+	0.709698i	$0.251169\pi$
$524$		0			0
$525$	11.2685	−	4.51123i	0.491798	−	0.196886i
$526$		0			0
$527$	0.00112813	−	0.00247026i	4.91420e−5	−	0.000107606i
$528$		0			0
$529$	−29.7713	+	2.84281i	−1.29440	+	0.123601i
$530$		0			0
$531$	−0.903824	+	6.28624i	−0.0392226	+	0.272799i
$532$		0			0
$533$	−2.65413	+	1.70570i	−0.114963	+	0.0738823i
$534$		0			0
$535$	−1.15687			−0.0500158
$536$		0			0
$537$	−19.6143			−0.846421
$538$		0			0
$539$	0.512396	−	0.329297i	0.0220705	−	0.0141838i
$540$		0			0
$541$	−0.0920435	+	0.640177i	−0.00395726	+	0.0275233i	−0.991704	−	0.128539i	$-0.958971\pi$
$541$	−0.0920435	+	0.640177i	−0.00395726	+	0.0275233i	0.987747	+	0.156063i	$0.0498802\pi$
$542$		0			0
$543$	−17.6667	+	1.68696i	−0.758150	+	0.0723945i
$544$		0			0
$545$	−1.30439	+	2.85622i	−0.0558740	+	0.122347i
$546$		0			0
$547$	−11.0223	+	4.41266i	−0.471280	+	0.188672i	−0.595131	−	0.803629i	$-0.702900\pi$
$547$	−11.0223	+	4.41266i	−0.471280	+	0.188672i	0.123851	+	0.992301i	$0.460475\pi$
$548$		0			0
$549$	2.99008	−	2.85103i	0.127613	−	0.121679i
$550$		0			0
$551$	12.2751	+	26.8788i	0.522939	+	1.14508i
$552$		0			0
$553$	−4.98618	−	14.4066i	−0.212034	−	0.612632i
$554$		0			0
$555$	−3.27699	−	0.312914i	−0.139100	−	0.0132825i
$556$		0			0
$557$	−8.78243	+	6.90658i	−0.372124	+	0.292641i	−0.786654	−	0.617394i	$-0.788188\pi$
$557$	−8.78243	+	6.90658i	−0.372124	+	0.292641i	0.414530	+	0.910036i	$0.363946\pi$
$558$		0			0
$559$	−0.480541	−	10.0878i	−0.0203247	−	0.426668i
$560$		0			0
$561$	−0.000122660	0	3.60162e-5i	−5.17870e−6	0	1.52060e-6i
$562$		0			0
$563$	0.467395	+	3.25080i	0.0196983	+	0.137005i	0.997297	−	0.0734711i	$-0.0234077\pi$
$563$	0.467395	+	3.25080i	0.0196983	+	0.137005i	−0.977599	+	0.210476i	$0.932499\pi$
$564$		0			0
$565$	2.24012	+	3.88001i	0.0942427	+	0.163233i
$566$		0			0
$567$	2.42073	+	2.30816i	0.101661	+	0.0969336i
$568$		0			0
$569$	−15.0157	+	21.0866i	−0.629490	+	0.883994i	−0.998976	−	0.0452417i	$-0.985594\pi$
$569$	−15.0157	+	21.0866i	−0.629490	+	0.883994i	0.369486	+	0.929236i	$0.379534\pi$
$570$		0			0
$571$	−1.35467	+	28.4380i	−0.0566912	+	1.19009i	0.773935	+	0.633265i	$0.218286\pi$
$571$	−1.35467	+	28.4380i	−0.0566912	+	1.19009i	−0.830626	+	0.556830i	$0.812017\pi$
$572$		0			0
$573$	2.22434	−	3.85267i	0.0929232	−	0.160948i
$574$		0			0
$575$	6.22304	−	25.6517i	0.259519	−	1.06975i
$576$		0			0
$577$	−9.35840	−	1.80368i	−0.389595	−	0.0750884i	−0.00930792	−	0.999957i	$-0.502963\pi$
$577$	−9.35840	−	1.80368i	−0.389595	−	0.0750884i	−0.380288	+	0.924868i	$0.624175\pi$
$578$		0			0
$579$	8.07287	−	9.31659i	0.335497	−	0.387184i
$580$		0			0
$581$	39.5925	+	25.4446i	1.64258	+	1.05562i
$582$		0			0
$583$	−1.21615	−	0.626969i	−0.0503678	−	0.0259664i
$584$		0			0
$585$	1.51692	−	0.292362i	0.0627169	−	0.0120877i
$586$		0			0
$587$	28.9952	+	22.8021i	1.19676	+	0.941143i	0.999233	−	0.0391543i	$-0.0124664\pi$
$587$	28.9952	+	22.8021i	1.19676	+	0.941143i	0.197528	+	0.980297i	$0.436709\pi$
$588$		0			0
$589$	9.74519	+	11.2465i	0.401543	+	0.463406i
$590$		0			0
$591$	0.600907	+	2.47697i	0.0247180	+	0.101889i
$592$		0			0
$593$	−2.09304	+	1.07904i	−0.0859508	+	0.0443107i	−0.500666	−	0.865641i	$-0.666912\pi$
$593$	−2.09304	+	1.07904i	−0.0859508	+	0.0443107i	0.414715	+	0.909951i	$0.363881\pi$
$594$		0			0
$595$	0.00330276		0.000969779i	0.000135400		3.97571e-5i
$596$		0			0
$597$	−12.6188	−	5.05179i	−0.516452	−	0.206756i
$598$		0			0
$599$	14.6010	−	42.1867i	0.596579	−	1.72370i	−0.0893171	−	0.996003i	$-0.528468\pi$
$599$	14.6010	−	42.1867i	0.596579	−	1.72370i	0.685896	−	0.727699i	$-0.259410\pi$
$600$		0			0
$601$	17.9369	+	25.1888i	0.731660	+	1.02747i	0.997976	+	0.0635865i	$0.0202539\pi$
$601$	17.9369	+	25.1888i	0.731660	+	1.02747i	−0.266317	+	0.963886i	$0.585807\pi$
$602$		0			0
$603$	0.203884	+	8.18281i	0.00830278	+	0.333230i
$604$		0			0
$605$	−7.45686	−	10.4717i	−0.303165	−	0.425735i
$606$		0			0
$607$	5.31093	−	15.3449i	0.215564	−	0.622831i	−0.784433	−	0.620214i	$-0.787046\pi$
$607$	5.31093	−	15.3449i	0.215564	−	0.622831i	0.999997	−	0.00261723i	$-0.000833091\pi$
$608$		0			0
$609$	−19.0514	−	7.62703i	−0.772002	−	0.309063i
$610$		0			0
$611$	−0.207962	+	0.0610631i	−0.00841324	+	0.00247035i
$612$		0			0
$613$	−9.00806	+	4.64398i	−0.363832	+	0.187568i	−0.630443	−	0.776236i	$-0.717127\pi$
$613$	−9.00806	+	4.64398i	−0.363832	+	0.187568i	0.266611	+	0.963804i	$0.414096\pi$
$614$		0			0
$615$	0.660143	+	2.72115i	0.0266195	+	0.109727i
$616$		0			0
$617$	18.8954	+	21.8065i	0.760701	+	0.877896i	0.995560	−	0.0941335i	$-0.0300081\pi$
$617$	18.8954	+	21.8065i	0.760701	+	0.877896i	−0.234858	+	0.972030i	$0.575463\pi$
$618$		0			0
$619$	17.3281	+	13.6270i	0.696477	+	0.547715i	0.902425	−	0.430848i	$-0.141785\pi$
$619$	17.3281	+	13.6270i	0.696477	+	0.547715i	−0.205948	+	0.978563i	$0.566028\pi$
$620$		0			0
$621$	7.14225	−	1.37656i	0.286609	−	0.0552393i
$622$		0			0
$623$	30.7392	+	15.8472i	1.23154	+	0.634904i
$624$		0			0
$625$	5.31155	+	3.41353i	0.212462	+	0.136541i
$626$		0			0
$627$	0.458749	−	0.529424i	0.0183207	−	0.0211432i
$628$		0			0
$629$	0.00242626		0.000467622i	9.67411e−5		1.86453e-5i
$630$		0			0
$631$	4.42033	−	18.2209i	0.175971	−	0.725361i	−0.813614	−	0.581406i	$-0.802503\pi$
$631$	4.42033	−	18.2209i	0.175971	−	0.725361i	0.989584	−	0.143955i	$-0.0459820\pi$
$632$		0			0
$633$	9.30807	−	16.1220i	0.369962	−	0.640794i
$634$		0			0
$635$	−0.630675	+	13.2395i	−0.0250276	+	0.525394i
$636$		0			0
$637$	3.20466	−	4.50032i	0.126973	−	0.178309i
$638$		0			0
$639$	−3.38290	−	3.22558i	−0.133825	−	0.127602i
$640$		0			0
$641$	5.98473	+	10.3658i	0.236382	+	0.409426i	0.959674	−	0.281117i	$-0.0907048\pi$
$641$	5.98473	+	10.3658i	0.236382	+	0.409426i	−0.723291	+	0.690543i	$0.757372\pi$
$642$		0			0
$643$	−1.05921	−	7.36696i	−0.0417711	−	0.290525i	−0.999990	−	0.00448834i	$-0.998571\pi$
$643$	−1.05921	−	7.36696i	−0.0417711	−	0.290525i	0.958219	−	0.286036i	$-0.0923378\pi$
$644$		0			0
$645$	−8.60013	−	2.52523i	−0.338630	−	0.0994307i
$646$		0			0
$647$	0.239070	+	5.01870i	0.00939881	+	0.197305i	0.998683	+	0.0513034i	$0.0163375\pi$
$647$	0.239070	+	5.01870i	0.00939881	+	0.197305i	−0.989284	+	0.146002i	$0.953359\pi$
$648$		0			0
$649$	−0.726117	+	0.571025i	−0.0285026	+	0.0224147i
$650$		0			0
$651$	−10.2880	−	0.982389i	−0.403220	−	0.0385028i
$652$		0			0
$653$	−11.0551	−	31.9416i	−0.432620	−	1.24997i	−0.925125	−	0.379663i	$-0.876040\pi$
$653$	−11.0551	−	31.9416i	−0.432620	−	1.24997i	0.492505	−	0.870309i	$-0.336081\pi$
$654$		0			0
$655$	−7.52095	−	16.4686i	−0.293868	−	0.643481i
$656$		0			0
$657$	4.64204	−	4.42618i	0.181103	−	0.172682i
$658$		0			0
$659$	20.2461	−	8.10532i	0.788676	−	0.315738i	0.0578708	−	0.998324i	$-0.481569\pi$
$659$	20.2461	−	8.10532i	0.788676	−	0.315738i	0.730806	+	0.682586i	$0.239145\pi$
$660$		0			0
$661$	−2.73585	+	5.99066i	−0.106412	+	0.233010i	−0.955346	−	0.295489i	$-0.904518\pi$
$661$	−2.73585	+	5.99066i	−0.106412	+	0.233010i	0.848934	+	0.528499i	$0.177245\pi$
$662$		0			0
$663$	−0.00115431		0.000110223i	−4.48297e−5		4.28072e-6i
$664$		0			0
$665$	−2.68442	+	18.6706i	−0.104097	+	0.724014i
$666$		0			0
$667$	−37.5424	+	24.1270i	−1.45365	+	0.934202i
$668$		0			0
$669$	6.72623			0.260051
$670$		0			0
$671$	0.600931			0.0231987
$672$		0			0
$673$	11.9949	−	7.70866i	0.462370	−	0.297147i	−0.288641	−	0.957438i	$-0.593203\pi$
$673$	11.9949	−	7.70866i	0.462370	−	0.297147i	0.751010	+	0.660291i	$0.229567\pi$
$674$		0			0
$675$	−0.516451	+	3.59200i	−0.0198782	+	0.138256i
$676$		0			0
$677$	5.92509	−	0.565778i	0.227720	−	0.0217446i	0.0194276	−	0.999811i	$-0.493816\pi$
$677$	5.92509	−	0.565778i	0.227720	−	0.0217446i	0.208292	+	0.978067i	$0.433210\pi$
$678$		0			0
$679$	−2.96556	+	6.49367i	−0.113808	+	0.249204i
$680$		0			0
$681$	18.5125	−	7.41127i	0.709399	−	0.284001i
$682$		0			0
$683$	−8.06649	+	7.69138i	−0.308656	+	0.294303i	−0.828535	−	0.559937i	$-0.810825\pi$
$683$	−8.06649	+	7.69138i	−0.308656	+	0.294303i	0.519879	+	0.854240i	$0.325977\pi$
$684$		0			0
$685$	−2.06826	−	4.52886i	−0.0790242	−	0.173039i
$686$		0			0
$687$	0.149167	+	0.430989i	0.00569107	+	0.0164433i
$688$		0			0
$689$	−12.3546	−	1.17972i	−0.470672	−	0.0449437i
$690$		0			0
$691$	−3.98785	+	3.13608i	−0.151705	+	0.119302i	−0.691127	−	0.722734i	$-0.742885\pi$
$691$	−3.98785	+	3.13608i	−0.151705	+	0.119302i	0.539422	+	0.842036i	$0.318643\pi$
$692$		0			0
$693$	0.0231489	+	0.485955i	0.000879353	+	0.0184599i
$694$		0			0
$695$	−23.9101	−	7.02064i	−0.906961	−	0.266308i
$696$		0			0
$697$	−0.000299110	−	0.00208036i	−1.13296e−5	−	7.87991e-5i
$698$		0			0
$699$	3.59920	+	6.23399i	0.136134	+	0.235791i
$700$		0			0
$701$	−31.9255	−	30.4409i	−1.20581	−	1.14974i	−0.984658	−	0.174497i	$-0.944170\pi$
$701$	−31.9255	−	30.4409i	−1.20581	−	1.14974i	−0.221151	−	0.975240i	$-0.570981\pi$
$702$		0			0
$703$	−7.85402	+	11.0294i	−0.296220	+	0.415983i
$704$		0			0
$705$	−0.00915291	+	0.192143i	−0.000344718	+	0.00723653i
$706$		0			0
$707$	−3.21548	+	5.56938i	−0.120931	+	0.209458i
$708$		0			0
$709$	−1.23585	+	5.09423i	−0.0464132	+	0.191318i	−0.990299	−	0.138955i	$-0.955626\pi$
$709$	−1.23585	+	5.09423i	−0.0464132	+	0.191318i	0.943886	+	0.330273i	$0.107141\pi$
$710$		0			0
$711$	4.47551	+	0.862584i	0.167845	+	0.0323494i
$712$		0			0
$713$	−14.7177	+	16.9852i	−0.551183	+	0.636099i
$714$		0			0
$715$	0.189030	+	0.121482i	0.00706932	+	0.00454318i
$716$		0			0
$717$	21.4690	+	11.0680i	0.801775	+	0.413344i
$718$		0			0
$719$	20.5074	−	3.95248i	0.764797	−	0.147403i	0.208088	−	0.978110i	$-0.433276\pi$
$719$	20.5074	−	3.95248i	0.764797	−	0.147403i	0.556709	+	0.830708i	$0.312064\pi$
$720$		0			0
$721$	16.1526	+	12.7025i	0.601553	+	0.473066i
$722$		0			0
$723$	14.9944	+	17.3044i	0.557647	+	0.643559i
$724$		0			0
$725$	−5.24913	−	21.6372i	−0.194948	−	0.803585i
$726$		0			0
$727$	−3.37723	+	1.74108i	−0.125254	+	0.0645732i	−0.519715	−	0.854340i	$-0.673962\pi$
$727$	−3.37723	+	1.74108i	−0.125254	+	0.0645732i	0.394460	+	0.918913i	$0.370932\pi$
$728$		0			0
$729$	−0.959493	+	0.281733i	−0.0355368	+	0.0104345i
$730$		0			0
$731$	0.00624589	+	0.00250048i	0.000231013	+	9.24835e-5i
$732$		0			0
$733$	−6.26301	+	18.0958i	−0.231330	+	0.668383i	0.768271	+	0.640125i	$0.221117\pi$
$733$	−6.26301	+	18.0958i	−0.231330	+	0.668383i	−0.999601	+	0.0282584i	$0.991004\pi$
$734$		0			0
$735$	−2.84418	−	3.99410i	−0.104909	−	0.147324i
$736$		0			0
$737$	−0.799876	+	0.881860i	−0.0294638	+	0.0324837i
$738$		0			0
$739$	8.62960	+	12.1186i	0.317445	+	0.445789i	0.942210	−	0.335024i	$-0.108744\pi$
$739$	8.62960	+	12.1186i	0.317445	+	0.445789i	−0.624765	+	0.780813i	$0.714805\pi$
$740$		0			0
$741$	2.07824	−	6.00469i	0.0763462	−	0.220588i
$742$		0			0
$743$	24.1592	+	9.67189i	0.886316	+	0.354827i	0.769742	−	0.638355i	$-0.220385\pi$
$743$	24.1592	+	9.67189i	0.886316	+	0.354827i	0.116573	+	0.993182i	$0.462809\pi$
$744$		0			0
$745$	−3.32649	+	0.976746i	−0.121873	+	0.0357852i
$746$		0			0
$747$	−12.5066	+	6.44762i	−0.457594	+	0.235906i
$748$		0			0
$749$	−0.779096	−	3.21148i	−0.0284675	−	0.117345i
$750$		0			0
$751$	12.8350	+	14.8124i	0.468356	+	0.540511i	0.939954	−	0.341302i	$-0.110868\pi$
$751$	12.8350	+	14.8124i	0.468356	+	0.540511i	−0.471598	+	0.881814i	$0.656323\pi$
$752$		0			0
$753$	0.248233	+	0.195213i	0.00904611	+	0.00711394i
$754$		0			0
$755$	−2.12716	+	0.409976i	−0.0774152	+	0.0149206i
$756$		0			0
$757$	33.0051	+	17.0153i	1.19959	+	0.618432i	0.937962	−	0.346737i	$-0.112710\pi$
$757$	33.0051	+	17.0153i	1.19959	+	0.618432i	0.261628	+	0.965169i	$0.415741\pi$
$758$		0			0
$759$	0.890027	+	0.571986i	0.0323059	+	0.0207618i
$760$		0			0
$761$	−27.8808	+	32.1762i	−1.01068	+	1.16639i	−0.0246698	+	0.999696i	$0.507853\pi$
$761$	−27.8808	+	32.1762i	−1.01068	+	1.16639i	−0.986009	+	0.166690i	$0.946692\pi$
$762$		0			0
$763$	−8.80732	−	1.69747i	−0.318846	−	0.0614526i
$764$		0			0
$765$	−0.000242626		0.00100012i	−8.77215e−6		3.61593e-5i
$766$		0			0
$767$	−4.18946	+	7.25635i	−0.151273	+	0.262012i
$768$		0			0
$769$	−0.523088	+	10.9810i	−0.0188630	+	0.395984i	0.969617	+	0.244630i	$0.0786664\pi$
$769$	−0.523088	+	10.9810i	−0.0188630	+	0.395984i	−0.988480	+	0.151354i	$0.951637\pi$
$770$		0			0
$771$	−14.8579	+	20.8650i	−0.535094	+	0.751434i
$772$		0			0
$773$	28.1887	+	26.8779i	1.01388	+	0.966731i	0.999450	−	0.0331648i	$-0.0105586\pi$
$773$	28.1887	+	26.8779i	1.01388	+	0.966731i	0.0144285	+	0.999896i	$0.495407\pi$
$774$		0			0
$775$	−5.60642	−	9.71061i	−0.201389	−	0.348815i
$776$		0			0
$777$	−1.33824	−	9.30767i	−0.0480091	−	0.333911i
$778$		0			0
$779$	11.0506	+	3.24476i	0.395931	+	0.116256i
$780$		0			0
$781$	−0.0323499	−	0.679107i	−0.00115757	−	0.0243004i
$782$		0			0
$783$	4.82271	−	3.79262i	0.172350	−	0.135537i
$784$		0			0
$785$	−5.05367	−	0.482567i	−0.180373	−	0.0172235i
$786$		0			0
$787$	17.1553	+	49.5670i	0.611521	+	1.76687i	0.641268	+	0.767317i	$0.278409\pi$
$787$	17.1553	+	49.5670i	0.611521	+	1.76687i	−0.0297473	+	0.999557i	$0.509470\pi$
$788$		0			0
$789$	8.91319	+	19.5172i	0.317318	+	0.694830i
$790$		0			0
$791$	−9.26231	+	8.83159i	−0.329330	+	0.314015i
$792$		0			0
$793$	5.06032	−	2.02585i	0.179697	−	0.0719399i
$794$		0			0
$795$	−4.57568	+	10.0193i	−0.162283	+	0.355350i
$796$		0			0
$797$	−38.0207	+	3.63053i	−1.34676	+	0.128600i	−0.743389	−	0.668859i	$-0.766783\pi$
$797$	−38.0207	+	3.63053i	−1.34676	+	0.128600i	−0.603373	+	0.797459i	$0.706177\pi$
$798$		0			0
$799$	2.05484e−5	0	0.000142917i	7.26950e−7	0	5.05605e-6i
$800$		0			0
$801$	−8.69824	+	5.59002i	−0.307337	+	0.197514i
$802$		0			0
$803$	0.932934			0.0329225
$804$		0			0
$805$	−28.4873			−1.00405
$806$		0			0
$807$	11.2775	−	7.24758i	0.396985	−	0.255127i
$808$		0			0
$809$	−5.91545	+	41.1429i	−0.207976	+	1.44651i	0.571772	+	0.820413i	$0.306256\pi$
$809$	−5.91545	+	41.1429i	−0.207976	+	1.44651i	−0.779748	+	0.626093i	$0.784653\pi$
$810$		0			0
$811$	20.1197	−	1.92120i	0.706498	−	0.0674624i	0.264379	−	0.964419i	$-0.414833\pi$
$811$	20.1197	−	1.92120i	0.706498	−	0.0674624i	0.442119	+	0.896956i	$0.354227\pi$
$812$		0			0
$813$	−3.23438	+	7.08231i	−0.113435	+	0.248388i
$814$		0			0
$815$	18.1025	−	7.24713i	0.634101	−	0.253856i
$816$		0			0
$817$	−26.6820	+	25.4412i	−0.933485	+	0.890076i
$818$		0			0
$819$	1.83317	+	4.01409i	0.0640562	+	0.140264i
$820$		0			0
$821$	−6.65807	−	19.2372i	−0.232368	−	0.671384i	−0.999551	−	0.0299555i	$-0.990463\pi$
$821$	−6.65807	−	19.2372i	−0.232368	−	0.671384i	0.767183	−	0.641428i	$-0.221658\pi$
$822$		0			0
$823$	−13.4106	−	1.28055i	−0.467462	−	0.0446373i	−0.141332	−	0.989962i	$-0.545139\pi$
$823$	−13.4106	−	1.28055i	−0.467462	−	0.0446373i	−0.326130	+	0.945325i	$0.605745\pi$
$824$		0			0
$825$	−0.414908	+	0.326288i	−0.0144453	+	0.0113599i
$826$		0			0
$827$	0.337258	+	7.07991i	0.0117276	+	0.246193i	0.997117	+	0.0758771i	$0.0241757\pi$
$827$	0.337258	+	7.07991i	0.0117276	+	0.246193i	−0.985390	+	0.170316i	$0.945521\pi$
$828$		0			0
$829$	27.4392	+	8.05689i	0.953004	+	0.279827i	0.721037	−	0.692896i	$-0.243666\pi$
$829$	27.4392	+	8.05689i	0.953004	+	0.279827i	0.231967	+	0.972724i	$0.425484\pi$
$830$		0			0
$831$	−0.840285	−	5.84431i	−0.0291491	−	0.202737i
$832$		0			0
$833$	0.00184021	+	0.00318734i	6.37595e−5	+	0.000110435i
$834$		0			0
$835$	6.98911	+	6.66411i	0.241868	+	0.230621i
$836$		0			0
$837$	1.79228	−	2.51691i	0.0619504	−	0.0869972i
$838$		0			0
$839$	−0.191670	+	4.02365i	−0.00661719	+	0.138912i	0.993141	+	0.116923i	$0.0373030\pi$
$839$	−0.191670	+	4.02365i	−0.00661719	+	0.138912i	−0.999758	+	0.0219892i	$0.993000\pi$
$840$		0			0
$841$	−4.32129	+	7.48469i	−0.149010	+	0.258093i
$842$		0			0
$843$	−1.21719	+	5.01733i	−0.0419223	+	0.172806i
$844$		0			0
$845$	−12.9456	−	2.49506i	−0.445343	−	0.0858328i
$846$		0			0
$847$	24.0477	−	27.7525i	0.826287	−	0.953586i
$848$		0			0
$849$	−12.7781	−	8.21199i	−0.438544	−	0.281835i
$850$		0			0
$851$	−18.1758	−	9.37028i	−0.623058	−	0.321209i
$852$		0			0
$853$	−2.34163	+	0.451311i	−0.0801758	+	0.0154526i	−0.229181	−	0.973384i	$-0.573605\pi$
$853$	−2.34163	+	0.451311i	−0.0801758	+	0.0154526i	0.149006	+	0.988836i	$0.452393\pi$
$854$		0			0
$855$	−4.43288	−	3.48605i	−0.151601	−	0.119220i
$856$		0			0
$857$	−9.26506	−	10.6924i	−0.316488	−	0.365247i	0.575108	−	0.818077i	$-0.304960\pi$
$857$	−9.26506	−	10.6924i	−0.316488	−	0.365247i	−0.891597	+	0.452830i	$0.850414\pi$
$858$		0			0
$859$	1.02627	+	4.23033i	0.0350158	+	0.144337i	0.986636	−	0.162939i	$-0.0520975\pi$
$859$	1.02627	+	4.23033i	0.0350158	+	0.144337i	−0.951620	+	0.307277i	$0.900582\pi$
$860$		0			0
$861$	−7.10935	+	3.66512i	−0.242286	+	0.124907i
$862$		0			0
$863$	−9.27592	+	2.72366i	−0.315756	+	0.0927143i	−0.435770	−	0.900058i	$-0.643524\pi$
$863$	−9.27592	+	2.72366i	−0.315756	+	0.0927143i	0.120015	+	0.992772i	$0.461706\pi$
$864$		0			0
$865$	−0.256649	−	0.102747i	−0.00872633	−	0.00349350i
$866$		0			0
$867$	−5.56016	+	16.0650i	−0.188833	+	0.545596i
$868$		0			0
$869$	0.384551	+	0.540027i	0.0130450	+	0.0183192i
$870$		0			0
$871$	−3.76269	+	10.1225i	−0.127494	+	0.342987i
$872$		0			0
$873$	−1.23802	−	1.73856i	−0.0419006	−	0.0588412i
$874$		0			0
$875$	11.0533	−	31.9364i	0.373669	−	1.07965i
$876$		0			0
$877$	−11.6319	−	4.65671i	−0.392781	−	0.157246i	0.166861	−	0.985980i	$-0.446637\pi$
$877$	−11.6319	−	4.65671i	−0.392781	−	0.157246i	−0.559642	+	0.828735i	$0.689061\pi$
$878$		0			0
$879$	28.3209	−	8.31576i	0.955240	−	0.280484i
$880$		0			0
$881$	20.4897	−	10.5632i	0.690316	−	0.355882i	−0.0771081	−	0.997023i	$-0.524569\pi$
$881$	20.4897	−	10.5632i	0.690316	−	0.355882i	0.767424	+	0.641140i	$0.221538\pi$
$882$		0			0
$883$	−2.38728	−	9.84049i	−0.0803383	−	0.331159i	0.917433	−	0.397891i	$-0.130258\pi$
$883$	−2.38728	−	9.84049i	−0.0803383	−	0.331159i	−0.997771	+	0.0667322i	$0.978743\pi$
$884$		0			0
$885$	4.86981	+	5.62006i	0.163697	+	0.188916i
$886$		0			0
$887$	25.9816	+	20.4322i	0.872378	+	0.686046i	0.950442	−	0.310903i	$-0.100631\pi$
$887$	25.9816	+	20.4322i	0.872378	+	0.686046i	−0.0780636	+	0.996948i	$0.524874\pi$
$888$		0			0
$889$	−37.1777	+	7.16541i	−1.24690	+	0.240320i
$890$		0			0
$891$	−0.129283	−	0.0666502i	−0.00433115	−	0.00223286i
$892$		0			0
$893$	0.665610	+	0.427762i	0.0222738	+	0.0143145i
$894$		0			0
$895$	−15.0401	+	17.3572i	−0.502736	+	0.580188i
$896$		0			0
$897$	9.42300	+	1.81613i	0.314625	+	0.0606390i
$898$		0			0
$899$	−4.46935	+	18.4229i	−0.149061	+	0.614438i
$900$		0			0
$901$	0.00413385	−	0.00716003i	0.000137718	−	0.000238535i
$902$		0			0
$903$	1.21827	−	25.5746i	0.0405415	−	0.851070i
$904$		0			0
$905$	−12.0538	+	16.9273i	−0.400683	+	0.562681i
$906$		0			0
$907$	30.3558	+	28.9442i	1.00795	+	0.961075i	0.999244	−	0.0388869i	$-0.0123812\pi$
$907$	30.3558	+	28.9442i	1.00795	+	0.961075i	0.00870306	+	0.999962i	$0.497230\pi$
$908$		0			0
$909$	−0.961344	−	1.66510i	−0.0318858	−	0.0552278i
$910$		0			0
$911$	5.28989	+	36.7920i	0.175262	+	1.21897i	0.867550	+	0.497351i	$0.165694\pi$
$911$	5.28989	+	36.7920i	0.175262	+	1.21897i	−0.692288	+	0.721621i	$0.743397\pi$
$912$		0			0
$913$	−1.96373	−	0.576604i	−0.0649900	−	0.0190828i
$914$		0			0
$915$	−0.230184	−	4.83215i	−0.00760964	−	0.159746i
$916$		0			0
$917$	40.6519	−	31.9690i	1.34244	−	1.05571i
$918$		0			0
$919$	46.1416	+	4.40598i	1.52207	+	0.145340i	0.822311	−	0.569039i	$-0.192685\pi$
$919$	46.1416	+	4.40598i	1.52207	+	0.145340i	0.699759	+	0.714379i	$0.253291\pi$
$920$		0			0
$921$	8.45589	+	24.4317i	0.278631	+	0.805051i
$922$		0			0
$923$	−2.56180	−	5.60956i	−0.0843227	−	0.184641i
$924$		0			0
$925$	7.38372	−	7.04036i	0.242775	−	0.231486i
$926$		0			0
$927$	−5.70351	+	2.28334i	−0.187328	+	0.0749948i
$928$		0			0
$929$	−19.1697	+	41.9757i	−0.628937	+	1.37718i	0.279901	+	0.960029i	$0.409698\pi$
$929$	−19.1697	+	41.9757i	−0.628937	+	1.37718i	−0.908837	+	0.417151i	$0.863029\pi$
$930$		0			0
$931$	−20.0767	+	1.91709i	−0.657986	+	0.0628301i
$932$		0			0
$933$	0.629085	−	4.37538i	0.0205953	−	0.143244i
$934$		0			0
$935$	−0.000125926	0	8.09279e-5i	−4.11823e−6	0	2.64663e-6i
$936$		0			0
$937$	17.6358			0.576136			0.288068	−	0.957610i	$-0.406987\pi$
$937$	17.6358			0.576136			0.288068	+	0.957610i	$0.406987\pi$
$938$		0			0
$939$	−8.48998			−0.277060
$940$		0			0
$941$	−9.10150	+	5.84918i	−0.296700	+	0.190678i	−0.680518	−	0.732731i	$-0.738245\pi$
$941$	−9.10150	+	5.84918i	−0.296700	+	0.190678i	0.383818	+	0.923409i	$0.374609\pi$
$942$		0			0
$943$	−2.47541	+	17.2168i	−0.0806104	+	0.560657i
$944$		0			0
$945$	3.89875	−	0.372285i	0.126826	−	0.0121104i
$946$		0			0
$947$	14.0641	−	30.7961i	0.457022	−	1.00074i	−0.531134	−	0.847288i	$-0.678234\pi$
$947$	14.0641	−	30.7961i	0.457022	−	1.00074i	0.988156	−	0.153451i	$-0.0490387\pi$
$948$		0			0
$949$	7.85605	−	3.14509i	0.255018	−	0.102094i
$950$		0			0
$951$	−4.85409	+	4.62837i	−0.157405	+	0.150085i
$952$		0			0
$953$	−10.5681	−	23.1410i	−0.342335	−	0.749609i	0.657658	−	0.753317i	$-0.271547\pi$
$953$	−10.5681	−	23.1410i	−0.342335	−	0.749609i	−0.999993	+	0.00370732i	$0.998820\pi$
$954$		0			0
$955$	−1.70372	−	4.92258i	−0.0551311	−	0.159291i
$956$		0			0
$957$	0.888361	+	0.0848282i	0.0287166	+	0.00274211i
$958$		0			0
$959$	11.1793	−	8.79148i	0.360997	−	0.283892i
$960$		0			0
$961$	−1.02077	−	21.4286i	−0.0329280	−	0.691244i
$962$		0			0
$963$	0.947976	+	0.278351i	0.0305481	+	0.00896973i
$964$		0			0
$965$	−2.05427	−	14.2878i	−0.0661294	−	0.459940i
$966$		0			0
$967$	−22.1659	−	38.3925i	−0.712807	−	1.23462i	−0.963799	−	0.266629i	$-0.914090\pi$
$967$	−22.1659	−	38.3925i	−0.712807	−	1.23462i	0.250992	−	0.967989i	$-0.419243\pi$
$968$		0			0
$969$	0.00306354	+	0.00292108i	9.84151e−5	+	9.38386e-5i
$970$		0			0
$971$	23.0031	−	32.3034i	0.738205	−	1.03666i	−0.259281	−	0.965802i	$-0.583486\pi$
$971$	23.0031	−	32.3034i	0.738205	−	1.03666i	0.997486	−	0.0708622i	$-0.0225751\pi$
$972$		0			0
$973$	3.38703	−	71.1026i	0.108583	−	2.27944i
$974$		0			0
$975$	−2.39388	+	4.14633i	−0.0766657	+	0.132789i
$976$		0			0
$977$	2.12553	−	8.76155i	0.0680017	−	0.280307i	−0.927651	−	0.373448i	$-0.878176\pi$
$977$	2.12553	−	8.76155i	0.0680017	−	0.280307i	0.995653	+	0.0931408i	$0.0296907\pi$
$978$		0			0
$979$	−1.47674	−	0.284619i	−0.0471970	−	0.00909647i
$980$		0			0
$981$	1.75609	−	2.02663i	0.0560675	−	0.0647053i
$982$		0			0
$983$	24.9028	+	16.0041i	0.794277	+	0.510451i	0.873744	−	0.486387i	$-0.161685\pi$
$983$	24.9028	+	16.0041i	0.794277	+	0.510451i	−0.0794667	+	0.996838i	$0.525322\pi$
$984$		0			0
$985$	2.65271	+	1.36757i	0.0845223	+	0.0435743i
$986$		0			0
$987$	−0.539554	+	0.103991i	−0.0171742	+	0.00331006i
$988$		0			0
$989$	−43.7665	−	34.4183i	−1.39169	−	1.09444i
$990$		0			0
$991$	33.8136	+	39.0230i	1.07413	+	1.23961i	0.969499	+	0.245095i	$0.0788193\pi$
$991$	33.8136	+	39.0230i	1.07413	+	1.23961i	0.104627	+	0.994512i	$0.466635\pi$
$992$		0			0
$993$	−6.46624	−	26.6542i	−0.205200	−	0.845845i
$994$		0			0
$995$	−14.1464	+	7.29299i	−0.448472	+	0.231203i
$996$		0			0
$997$	−20.0411	+	5.88460i	−0.634708	+	0.186367i	−0.583230	−	0.812307i	$-0.698211\pi$
$997$	−20.0411	+	5.88460i	−0.634708	+	0.186367i	−0.0514782	+	0.998674i	$0.516393\pi$
$998$		0			0
$999$	2.60998	+	1.04488i	0.0825761	+	0.0330585i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.y.b.361.3	yes	120
67.49	even	33	inner	804.2.y.b.49.3	✓	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.y.b.49.3	✓	120	67.49	even	33	inner
804.2.y.b.361.3	yes	120	1.1	even	1	trivial

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.y (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.841254 + 0.540641i) q^{3} +(-0.166640 + 1.15901i) q^{5} +(-3.32963 + 0.317941i) q^{7} +(0.415415 - 0.909632i) q^{9} +O(q^{10})\)	\(q+(-0.841254 + 0.540641i) q^{3} +(-0.166640 + 1.15901i) q^{5} +(-3.32963 + 0.317941i) q^{7} +(0.415415 - 0.909632i) q^{9} +(0.135033 - 0.0540592i) q^{11} +(0.954845 - 0.910443i) q^{13} +(-0.486420 - 1.06511i) q^{15} +(0.000287460 + 0.000830562i) q^{17} +(-4.79439 - 0.457809i) q^{19} +(2.62917 - 2.06760i) q^{21} +(-0.346097 - 7.26546i) q^{23} +(3.48194 + 1.02239i) q^{25} +(0.142315 + 0.989821i) q^{27} +(-3.06768 - 5.31337i) q^{29} +(-2.23622 - 2.13224i) q^{31} +(-0.0843707 + 0.118482i) q^{33} +(0.186354 - 3.91204i) q^{35} +(1.40568 - 2.43471i) q^{37} +(-0.311044 + 1.28214i) q^{39} +(-2.34812 - 0.452564i) q^{41} +(5.01284 - 5.78512i) q^{43} +(0.985044 + 0.633050i) q^{45} +(-0.146019 - 0.0752781i) q^{47} +(4.11186 - 0.792495i) q^{49} +(-0.000690862 - 0.000543300i) q^{51} +(-6.16018 - 7.10923i) q^{53} +(0.0401530 + 0.165513i) q^{55} +(4.28081 - 2.20691i) q^{57} +(-6.09362 + 1.78925i) q^{59} +(3.83552 + 1.53551i) q^{61} +(-1.09397 + 3.16082i) q^{63} +(0.896094 + 1.25839i) q^{65} +(-7.35865 + 3.58472i) q^{67} +(4.21916 + 5.92498i) q^{69} +(1.52879 - 4.41715i) q^{71} +(5.95457 + 2.38385i) q^{73} +(-3.48194 + 1.02239i) q^{75} +(-0.432424 + 0.222930i) q^{77} +(1.07456 + 4.42940i) q^{79} +(-0.654861 - 0.755750i) q^{81} +(-11.0604 - 8.69800i) q^{83} +(-0.00101053 + 0.000194763i) q^{85} +(5.45332 + 2.81138i) q^{87} +(-8.69824 - 5.59002i) q^{89} +(-2.88981 + 3.33502i) q^{91} +(3.03401 + 0.584757i) q^{93} +(1.32954 - 5.48044i) q^{95} +(1.06715 - 1.84837i) q^{97} +(0.00692091 - 0.145288i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 12 q^{3} - 2 q^{5} + q^{7} - 12 q^{9}+O(q^{10}) \) 120 * q + 12 * q^3 - 2 * q^5 + q^7 - 12 * q^9	\( 120 q + 12 q^{3} - 2 q^{5} + q^{7} - 12 q^{9} + 11 q^{11} + 2 q^{13} - 9 q^{15} + 48 q^{17} - 4 q^{19} - q^{21} + 22 q^{23} - 42 q^{25} + 12 q^{27} - q^{29} + 27 q^{31} + 17 q^{35} - 8 q^{37} - 2 q^{39} - 58 q^{41} - 17 q^{43} - 2 q^{45} - 84 q^{47} + 101 q^{49} - 26 q^{51} + 28 q^{53} - 9 q^{55} + 26 q^{57} + 34 q^{59} + 16 q^{61} + 12 q^{63} + 144 q^{65} + 23 q^{67} + 11 q^{69} + 173 q^{71} - 2 q^{73} + 42 q^{75} + 128 q^{77} + 31 q^{79} - 12 q^{81} + 47 q^{83} - 75 q^{85} - 10 q^{87} - 67 q^{89} + 16 q^{91} + 6 q^{93} - 79 q^{95} + 10 q^{97}+O(q^{100}) \) 120 * q + 12 * q^3 - 2 * q^5 + q^7 - 12 * q^9 + 11 * q^11 + 2 * q^13 - 9 * q^15 + 48 * q^17 - 4 * q^19 - q^21 + 22 * q^23 - 42 * q^25 + 12 * q^27 - q^29 + 27 * q^31 + 17 * q^35 - 8 * q^37 - 2 * q^39 - 58 * q^41 - 17 * q^43 - 2 * q^45 - 84 * q^47 + 101 * q^49 - 26 * q^51 + 28 * q^53 - 9 * q^55 + 26 * q^57 + 34 * q^59 + 16 * q^61 + 12 * q^63 + 144 * q^65 + 23 * q^67 + 11 * q^69 + 173 * q^71 - 2 * q^73 + 42 * q^75 + 128 * q^77 + 31 * q^79 - 12 * q^81 + 47 * q^83 - 75 * q^85 - 10 * q^87 - 67 * q^89 + 16 * q^91 + 6 * q^93 - 79 * q^95 + 10 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more