LMFDB - Embedded newform 804.2.y.b.793.6

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			793.6
Character	$\chi$	$=$	804.793
Dual form			804.2.y.b.73.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.415415 - 0.909632i) q^{3} +(3.42078 - 1.00443i) q^{5} +(-0.977853 - 0.188466i) q^{7} +(-0.654861 + 0.755750i) q^{9} +O(q^{10})$	\(q+(-0.415415 - 0.909632i) q^{3} +(3.42078 - 1.00443i) q^{5} +(-0.977853 - 0.188466i) q^{7} +(-0.654861 + 0.755750i) q^{9} +(-4.40572 - 4.20084i) q^{11} +(-0.140835 - 2.95649i) q^{13} +(-2.33471 - 2.69440i) q^{15} +(-0.551007 - 0.433317i) q^{17} +(1.63529 - 0.315176i) q^{19} +(0.234780 + 0.967778i) q^{21} +(-3.43676 - 0.328170i) q^{23} +(6.48659 - 4.16868i) q^{25} +(0.959493 + 0.281733i) q^{27} +(1.50438 + 2.60567i) q^{29} +(0.0616368 - 1.29392i) q^{31} +(-1.99102 + 5.75267i) q^{33} +(-3.53432 + 0.337487i) q^{35} +(0.278348 - 0.482112i) q^{37} +(-2.63081 + 1.35628i) q^{39} +(6.54034 - 2.61836i) q^{41} +(-0.813520 + 5.65815i) q^{43} +(-1.48104 + 3.24302i) q^{45} +(7.03506 - 9.87937i) q^{47} +(-5.57790 - 2.23305i) q^{49} +(-0.165262 + 0.681220i) q^{51} +(0.324604 + 2.25767i) q^{53} +(-19.2904 - 9.94491i) q^{55} +(-0.966018 - 1.35658i) q^{57} +(-2.23296 - 1.43503i) q^{59} +(-3.49530 + 3.33276i) q^{61} +(0.782790 - 0.615593i) q^{63} +(-3.45136 - 9.97204i) q^{65} +(7.01267 + 4.22167i) q^{67} +(1.12917 + 3.26251i) q^{69} +(-2.29320 + 1.80339i) q^{71} +(1.73724 - 1.65645i) q^{73} +(-6.48659 - 4.16868i) q^{75} +(3.51643 + 4.93813i) q^{77} +(-3.94110 - 2.03178i) q^{79} +(-0.142315 - 0.989821i) q^{81} +(3.45986 - 14.2617i) q^{83} +(-2.32011 - 0.928833i) q^{85} +(1.74526 - 2.45087i) q^{87} +(6.77689 - 14.8393i) q^{89} +(-0.419481 + 2.91755i) q^{91} +(-1.20259 + 0.481445i) q^{93} +(5.27739 - 2.72068i) q^{95} +(-0.358421 + 0.620803i) q^{97} +(6.05991 - 0.578652i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$e\left(\frac{13}{33}\right)$	$1$

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
$3$	−0.415415	−	0.909632i	−0.239840	−	0.525176i
$3$	−0.415415	−	0.909632i	−0.239840	−	0.525176i
$4$		0			0
$5$	3.42078	−	1.00443i	1.52982	−	0.449196i	0.594824	−	0.803856i	$-0.297222\pi$
$5$	3.42078	−	1.00443i	1.52982	−	0.449196i	0.934995	+	0.354660i	$0.115403\pi$
$6$		0			0
$7$	−0.977853	−	0.188466i	−0.369594	−	0.0712333i	0.00107274	−	0.999999i	$-0.499659\pi$
$7$	−0.977853	−	0.188466i	−0.369594	−	0.0712333i	−0.370666	+	0.928766i	$0.620871\pi$
$8$		0			0
$9$	−0.654861	+	0.755750i	−0.218287	+	0.251917i
$10$		0			0
$11$	−4.40572	−	4.20084i	−1.32837	−	1.26660i	−0.938302	−	0.345816i	$-0.887602\pi$
$11$	−4.40572	−	4.20084i	−1.32837	−	1.26660i	−0.390071	−	0.920785i	$-0.627550\pi$
$12$		0			0
$13$	−0.140835	−	2.95649i	−0.0390606	−	0.819982i	−0.930378	−	0.366602i	$-0.880521\pi$
$13$	−0.140835	−	2.95649i	−0.0390606	−	0.819982i	0.891317	−	0.453380i	$-0.149782\pi$
$14$		0			0
$15$	−2.33471	−	2.69440i	−0.602819	−	0.695690i
$16$		0			0
$17$	−0.551007	−	0.433317i	−0.133639	−	0.105095i	0.549102	−	0.835755i	$-0.314970\pi$
$17$	−0.551007	−	0.433317i	−0.133639	−	0.105095i	−0.682741	+	0.730661i	$0.739212\pi$
$18$		0			0
$19$	1.63529	−	0.315176i	0.375161	−	0.0723063i	0.00181451	−	0.999998i	$-0.499422\pi$
$19$	1.63529	−	0.315176i	0.375161	−	0.0723063i	0.373346	+	0.927692i	$0.378210\pi$
$20$		0			0
$21$	0.234780	+	0.967778i	0.0512333	+	0.211186i
$22$		0			0
$23$	−3.43676	−	0.328170i	−0.716613	−	0.0684282i	−0.269621	−	0.962966i	$-0.586899\pi$
$23$	−3.43676	−	0.328170i	−0.716613	−	0.0684282i	−0.446992	+	0.894538i	$0.647505\pi$
$24$		0			0
$25$	6.48659	−	4.16868i	1.29732	−	0.833735i
$26$		0			0
$27$	0.959493	+	0.281733i	0.184655	+	0.0542195i
$28$		0			0
$29$	1.50438	+	2.60567i	0.279357	+	0.483861i	0.971225	−	0.238163i	$-0.0765453\pi$
$29$	1.50438	+	2.60567i	0.279357	+	0.483861i	−0.691868	+	0.722024i	$0.743212\pi$
$30$		0			0
$31$	0.0616368	−	1.29392i	0.0110703	−	0.232394i	−0.986551	−	0.163456i	$-0.947736\pi$
$31$	0.0616368	−	1.29392i	0.0110703	−	0.232394i	0.997621	−	0.0689382i	$-0.0219611\pi$
$32$		0			0
$33$	−1.99102	+	5.75267i	−0.346592	+	1.00141i
$34$		0			0
$35$	−3.53432	+	0.337487i	−0.597409	+	0.0570457i
$36$		0			0
$37$	0.278348	−	0.482112i	0.0457601	−	0.0792588i	−0.842238	−	0.539106i	$-0.818762\pi$
$37$	0.278348	−	0.482112i	0.0457601	−	0.0792588i	0.887998	+	0.459847i	$0.152096\pi$
$38$		0			0
$39$	−2.63081	+	1.35628i	−0.421267	+	0.217178i
$40$		0			0
$41$	6.54034	−	2.61836i	1.02143	−	0.408919i	0.200345	−	0.979725i	$-0.435794\pi$
$41$	6.54034	−	2.61836i	1.02143	−	0.408919i	0.821085	+	0.570806i	$0.193369\pi$
$42$		0			0
$43$	−0.813520	+	5.65815i	−0.124061	+	0.862861i	0.828820	+	0.559515i	$0.189013\pi$
$43$	−0.813520	+	5.65815i	−0.124061	+	0.862861i	−0.952881	+	0.303345i	$0.901896\pi$
$44$		0			0
$45$	−1.48104	+	3.24302i	−0.220780	+	0.483440i
$46$		0			0
$47$	7.03506	−	9.87937i	1.02617	−	1.44105i	0.133118	−	0.991100i	$-0.457501\pi$
$47$	7.03506	−	9.87937i	1.02617	−	1.44105i	0.893052	−	0.449953i	$-0.148559\pi$
$48$		0			0
$49$	−5.57790	−	2.23305i	−0.796843	−	0.319008i
$50$		0			0
$51$	−0.165262	+	0.681220i	−0.0231413	+	0.0953899i
$52$		0			0
$53$	0.324604	+	2.25767i	0.0445878	+	0.310115i	0.999895	+	0.0144996i	$0.00461554\pi$
$53$	0.324604	+	2.25767i	0.0445878	+	0.310115i	−0.955307	+	0.295615i	$0.904475\pi$
$54$		0			0
$55$	−19.2904	−	9.94491i	−2.60112	−	1.34097i
$56$		0			0
$57$	−0.966018	−	1.35658i	−0.127952	−	0.179684i
$58$		0			0
$59$	−2.23296	−	1.43503i	−0.290706	−	0.186826i	0.387157	−	0.922014i	$-0.373457\pi$
$59$	−2.23296	−	1.43503i	−0.290706	−	0.186826i	−0.677863	+	0.735188i	$0.737094\pi$
$60$		0			0
$61$	−3.49530	+	3.33276i	−0.447527	+	0.426716i	−0.880031	−	0.474916i	$-0.842479\pi$
$61$	−3.49530	+	3.33276i	−0.447527	+	0.426716i	0.432504	+	0.901632i	$0.357630\pi$
$62$		0			0
$63$	0.782790	−	0.615593i	0.0986223	−	0.0775574i
$64$		0			0
$65$	−3.45136	−	9.97204i	−0.428088	−	1.23688i
$66$		0			0
$67$	7.01267	+	4.22167i	0.856734	+	0.515759i
$67$	7.01267	+	4.22167i	0.856734	+	0.515759i
$68$		0			0
$69$	1.12917	+	3.26251i	0.135936	+	0.392760i
$70$		0			0
$71$	−2.29320	+	1.80339i	−0.272153	+	0.214023i	−0.744902	−	0.667174i	$-0.767504\pi$
$71$	−2.29320	+	1.80339i	−0.272153	+	0.214023i	0.472750	+	0.881197i	$0.343262\pi$
$72$		0			0
$73$	1.73724	−	1.65645i	0.203328	−	0.193873i	−0.581573	−	0.813495i	$-0.697562\pi$
$73$	1.73724	−	1.65645i	0.203328	−	0.193873i	0.784901	+	0.619621i	$0.212714\pi$
$74$		0			0
$75$	−6.48659	−	4.16868i	−0.749007	−	0.481357i
$76$		0			0
$77$	3.51643	+	4.93813i	0.400734	+	0.562752i
$78$		0			0
$79$	−3.94110	−	2.03178i	−0.443408	−	0.228593i	0.222039	−	0.975038i	$-0.428729\pi$
$79$	−3.94110	−	2.03178i	−0.443408	−	0.228593i	−0.665447	+	0.746445i	$0.731759\pi$
$80$		0			0
$81$	−0.142315	−	0.989821i	−0.0158128	−	0.109980i
$82$		0			0
$83$	3.45986	−	14.2617i	0.379769	−	1.56543i	−0.386115	−	0.922451i	$-0.626183\pi$
$83$	3.45986	−	14.2617i	0.379769	−	1.56543i	0.765884	−	0.642979i	$-0.222302\pi$
$84$		0			0
$85$	−2.32011	−	0.928833i	−0.251651	−	0.100746i
$86$		0			0
$87$	1.74526	−	2.45087i	0.187111	−	0.262761i
$88$		0			0
$89$	6.77689	−	14.8393i	0.718349	−	1.57296i	−0.0978548	−	0.995201i	$-0.531198\pi$
$89$	6.77689	−	14.8393i	0.718349	−	1.57296i	0.816204	−	0.577764i	$-0.196075\pi$
$90$		0			0
$91$	−0.419481	+	2.91755i	−0.0439735	+	0.305843i
$92$		0			0
$93$	−1.20259	+	0.481445i	−0.124703	+	0.0499235i
$94$		0			0
$95$	5.27739	−	2.72068i	0.541449	−	0.279136i
$96$		0			0
$97$	−0.358421	+	0.620803i	−0.0363921	+	0.0630330i	−0.883648	−	0.468152i	$-0.844920\pi$
$97$	−0.358421	+	0.620803i	−0.0363921	+	0.0630330i	0.847256	+	0.531185i	$0.178253\pi$
$98$		0			0
$99$	6.05991	−	0.578652i	0.609044	−	0.0581567i
$100$		0			0
$101$	1.52188	−	4.39718i	0.151433	−	0.437536i	−0.843613	−	0.536951i	$-0.819576\pi$
$101$	1.52188	−	4.39718i	0.151433	−	0.437536i	0.995046	+	0.0994151i	$0.0316972\pi$
$102$		0			0
$103$	−0.819338	+	17.2000i	−0.0807318	+	1.69477i	0.488477	+	0.872577i	$0.337553\pi$
$103$	−0.819338	+	17.2000i	−0.0807318	+	1.69477i	−0.569209	+	0.822193i	$0.692751\pi$
$104$		0			0
$105$	1.77520	+	3.07473i	0.173242	+	0.300063i
$106$		0			0
$107$	16.9460	+	4.97580i	1.63823	+	0.481029i	0.965834	−	0.259160i	$-0.0834459\pi$
$107$	16.9460	+	4.97580i	1.63823	+	0.481029i	0.672399	+	0.740189i	$0.265264\pi$
$108$		0			0
$109$	−0.0961584	+	0.0617972i	−0.00921030	+	0.00591910i	−0.545238	−	0.838281i	$-0.683561\pi$
$109$	−0.0961584	+	0.0617972i	−0.00921030	+	0.00591910i	0.536028	+	0.844200i	$0.319924\pi$
$110$		0			0
$111$	−0.554175	−	0.0529173i	−0.0525999	−	0.00502269i
$112$		0			0
$113$	1.99456	+	8.22171i	0.187633	+	0.773433i	0.985370	+	0.170428i	$0.0545150\pi$
$113$	1.99456	+	8.22171i	0.187633	+	0.773433i	−0.797737	+	0.603005i	$0.793970\pi$
$114$		0			0
$115$	−12.0860	+	2.32939i	−1.12703	+	0.217216i
$116$		0			0
$117$	2.32659	+	1.82965i	0.215094	+	0.169151i
$118$		0			0
$119$	0.457139	+	0.527566i	0.0419058	+	0.0483619i
$120$		0			0
$121$	1.23986	+	26.0279i	0.112715	+	2.36617i
$122$		0			0
$123$	−5.09870	−	4.86160i	−0.459734	−	0.438356i
$124$		0			0
$125$	6.32851	−	7.30349i	0.566039	−	0.653244i
$126$		0			0
$127$	−9.74210	−	1.87764i	−0.864471	−	0.166613i	−0.262306	−	0.964985i	$-0.584483\pi$
$127$	−9.74210	−	1.87764i	−0.864471	−	0.166613i	−0.602165	+	0.798372i	$0.705695\pi$
$128$		0			0
$129$	5.48479	−	1.61048i	0.482909	−	0.141795i
$130$		0			0
$131$	7.64449	+	16.7391i	0.667903	+	1.46250i	0.874971	+	0.484176i	$0.160881\pi$
$131$	7.64449	+	16.7391i	0.667903	+	1.46250i	−0.207068	+	0.978327i	$0.566392\pi$
$132$		0			0
$133$	−1.65847			−0.143808
$134$		0			0
$135$	3.56520			0.306843
$136$		0			0
$137$	−3.99872	−	8.75597i	−0.341633	−	0.748073i	0.658356	−	0.752707i	$-0.271252\pi$
$137$	−3.99872	−	8.75597i	−0.341633	−	0.748073i	−0.999989	+	0.00463413i	$0.998525\pi$
$138$		0			0
$139$	−0.320422	+	0.0940843i	−0.0271778	+	0.00798013i	−0.295293	−	0.955407i	$-0.595417\pi$
$139$	−0.320422	+	0.0940843i	−0.0271778	+	0.00798013i	0.268115	+	0.963387i	$0.413599\pi$
$140$		0			0
$141$	−11.9091	−	2.29528i	−1.00292	−	0.193298i
$142$		0			0
$143$	−11.7993	+	13.6171i	−0.986704	+	1.13872i
$144$		0			0
$145$	7.76339	+	7.40237i	0.644714	+	0.614734i
$146$		0			0
$147$	0.285886	+	6.00148i	0.0235795	+	0.494994i
$148$		0			0
$149$	12.8007	+	14.7728i	1.04867	+	1.21023i	0.977096	+	0.212800i	$0.0682582\pi$
$149$	12.8007	+	14.7728i	1.04867	+	1.21023i	0.0715786	+	0.997435i	$0.477196\pi$
$150$		0			0
$151$	9.91058	+	7.79377i	0.806512	+	0.634248i	0.933871	−	0.357609i	$-0.116408\pi$
$151$	9.91058	+	7.79377i	0.806512	+	0.634248i	−0.127360	+	0.991857i	$0.540650\pi$
$152$		0			0
$153$	0.688312	−	0.132661i	0.0556467	−	0.0107250i
$154$		0			0
$155$	−1.08880	−	4.48811i	−0.0874549	−	0.360494i
$156$		0			0
$157$	−4.45408	−	0.425313i	−0.355474	−	0.0339437i	−0.0842086	−	0.996448i	$-0.526836\pi$
$157$	−4.45408	−	0.425313i	−0.355474	−	0.0339437i	−0.271266	+	0.962504i	$0.587442\pi$
$158$		0			0
$159$	1.91880	−	1.23314i	0.152171	−	0.0977944i
$160$		0			0
$161$	3.29879	+	0.968613i	0.259981	+	0.0763374i
$162$		0			0
$163$	6.20504	+	10.7474i	0.486016	+	0.841805i	0.999871	−	0.0160726i	$-0.00511629\pi$
$163$	6.20504	+	10.7474i	0.486016	+	0.841805i	−0.513855	+	0.857877i	$0.671783\pi$
$164$		0			0
$165$	−1.03267	+	21.6785i	−0.0803935	+	1.68767i
$166$		0			0
$167$	7.03400	−	20.3234i	0.544307	−	1.57267i	−0.251966	−	0.967736i	$-0.581077\pi$
$167$	7.03400	−	20.3234i	0.544307	−	1.57267i	0.796274	−	0.604937i	$-0.206802\pi$
$168$		0			0
$169$	4.22015	−	0.402975i	0.324627	−	0.0309981i
$170$		0			0
$171$	−0.832692	+	1.44226i	−0.0636776	+	0.110293i
$172$		0			0
$173$	12.1009	−	6.23844i	0.920013	−	0.474300i	0.0679207	−	0.997691i	$-0.478364\pi$
$173$	12.1009	−	6.23844i	0.920013	−	0.474300i	0.852093	+	0.523391i	$0.175333\pi$
$174$		0			0
$175$	−7.12858	+	2.85385i	−0.538870	+	0.215731i
$176$		0			0
$177$	−0.377749	+	2.62730i	−0.0283934	+	0.197480i
$178$		0			0
$179$	−8.91766	+	19.5270i	−0.666537	+	1.45951i	0.209765	+	0.977752i	$0.432730\pi$
$179$	−8.91766	+	19.5270i	−0.666537	+	1.45951i	−0.876303	+	0.481761i	$0.839997\pi$
$180$		0			0
$181$	−0.337106	+	0.473399i	−0.0250569	+	0.0351875i	−0.826914	−	0.562328i	$-0.809906\pi$
$181$	−0.337106	+	0.473399i	−0.0250569	+	0.0351875i	0.801857	+	0.597515i	$0.203845\pi$
$182$		0			0
$183$	4.48358	+	1.79496i	0.331436	+	0.132687i
$184$		0			0
$185$	0.467918	−	1.92878i	0.0344020	−	0.141807i
$186$		0			0
$187$	0.607286	+	4.22376i	0.0444091	+	0.308872i
$188$		0			0
$189$	−0.885146	−	0.456324i	−0.0643849	−	0.0331927i
$190$		0			0
$191$	0.413610	+	0.580835i	0.0299278	+	0.0420277i	0.829269	−	0.558850i	$-0.188757\pi$
$191$	0.413610	+	0.580835i	0.0299278	+	0.0420277i	−0.799341	+	0.600878i	$0.794818\pi$
$192$		0			0
$193$	19.3684	+	12.4473i	1.39417	+	0.895979i	0.999737	−	0.0229451i	$-0.00730428\pi$
$193$	19.3684	+	12.4473i	1.39417	+	0.895979i	0.394434	+	0.918924i	$0.370941\pi$
$194$		0			0
$195$	−7.63714	+	7.28200i	−0.546907	+	0.521475i
$196$		0			0
$197$	−15.0701	+	11.8512i	−1.07370	+	0.844366i	−0.988382	−	0.151988i	$-0.951432\pi$
$197$	−15.0701	+	11.8512i	−1.07370	+	0.844366i	−0.0853159	+	0.996354i	$0.527190\pi$
$198$		0			0
$199$	−1.46068	−	4.22036i	−0.103545	−	0.299174i	0.881314	−	0.472531i	$-0.156660\pi$
$199$	−1.46068	−	4.22036i	−0.103545	−	0.299174i	−0.984859	+	0.173358i	$0.944538\pi$
$200$		0			0
$201$	0.926998	−	8.13269i	0.0653854	−	0.573636i
$202$		0			0
$203$	−0.979987	−	2.83149i	−0.0687816	−	0.198731i
$204$		0			0
$205$	19.7431	−	15.5262i	1.37892	−	1.08439i
$206$		0			0
$207$	2.49861	−	2.38242i	0.173665	−	0.165590i
$208$		0			0
$209$	−8.52862	−	5.48101i	−0.589937	−	0.379129i
$210$		0			0
$211$	−13.3928	−	18.8076i	−0.922000	−	1.29477i	−0.955397	−	0.295326i	$-0.904572\pi$
$211$	−13.3928	−	18.8076i	−0.922000	−	1.29477i	0.0333967	−	0.999442i	$-0.489368\pi$
$212$		0			0
$213$	2.59305	+	1.33681i	0.177673	+	0.0915968i
$214$		0			0
$215$	2.90036	+	20.1724i	0.197803	+	1.37575i
$216$		0			0
$217$	−0.304130	+	1.25364i	−0.0206457	+	0.0851028i
$218$		0			0
$219$	−2.22844	−	0.892132i	−0.150584	−	0.0602847i
$220$		0			0
$221$	−1.20350	+	1.69007i	−0.0809558	+	0.113687i
$222$		0			0
$223$	8.17921	−	17.9100i	0.547720	−	1.19934i	−0.410118	−	0.912032i	$-0.634512\pi$
$223$	8.17921	−	17.9100i	0.547720	−	1.19934i	0.957838	−	0.287308i	$-0.0927602\pi$
$224$		0			0
$225$	−1.09734	+	7.63214i	−0.0731557	+	0.508809i
$226$		0			0
$227$	8.38429	−	3.35656i	0.556485	−	0.222783i	−0.0763346	−	0.997082i	$-0.524322\pi$
$227$	8.38429	−	3.35656i	0.556485	−	0.222783i	0.632820	+	0.774299i	$0.281897\pi$
$228$		0			0
$229$	−12.7300	+	6.56279i	−0.841224	+	0.433681i	−0.824285	−	0.566175i	$-0.808422\pi$
$229$	−12.7300	+	6.56279i	−0.841224	+	0.433681i	−0.0169392	+	0.999857i	$0.505392\pi$
$230$		0			0
$231$	3.03110	−	5.25003i	0.199432	−	0.345426i
$232$		0			0
$233$	−0.259237	+	0.0247542i	−0.0169832	+	0.00162170i	−0.103544	−	0.994625i	$-0.533018\pi$
$233$	−0.259237	+	0.0247542i	−0.0169832	+	0.00162170i	0.0865610	+	0.996247i	$0.472412\pi$
$234$		0			0
$235$	14.1423	−	40.8614i	0.922539	−	2.66550i
$236$		0			0
$237$	−0.210978	+	4.42898i	−0.0137045	+	0.287693i
$238$		0			0
$239$	12.7373	+	22.0617i	0.823909	+	1.42705i	0.902750	+	0.430166i	$0.141545\pi$
$239$	12.7373	+	22.0617i	0.823909	+	1.42705i	−0.0788405	+	0.996887i	$0.525122\pi$
$240$		0			0
$241$	−8.21683	−	2.41268i	−0.529293	−	0.155414i	0.00615776	−	0.999981i	$-0.498040\pi$
$241$	−8.21683	−	2.41268i	−0.529293	−	0.155414i	−0.535450	+	0.844567i	$0.679858\pi$
$242$		0			0
$243$	−0.841254	+	0.540641i	−0.0539664	+	0.0346821i
$244$		0			0
$245$	−21.3237	−	2.03617i	−1.36232	−	0.130086i
$246$		0			0
$247$	−1.16212	−	4.79032i	−0.0739439	−	0.304801i
$248$		0			0
$249$	−14.4102	+	2.77734i	−0.913210	+	0.176007i
$250$		0			0
$251$	−10.5376	−	8.28684i	−0.665126	−	0.523061i	0.227546	−	0.973767i	$-0.426930\pi$
$251$	−10.5376	−	8.28684i	−0.665126	−	0.523061i	−0.892672	+	0.450707i	$0.851172\pi$
$252$		0			0
$253$	13.7628	+	15.8831i	0.865258	+	0.998561i
$254$		0			0
$255$	0.118913	+	2.49630i	0.00744664	+	0.156324i
$256$		0			0
$257$	−6.73956	−	6.42616i	−0.420402	−	0.400853i	0.450131	−	0.892963i	$-0.351377\pi$
$257$	−6.73956	−	6.42616i	−0.420402	−	0.400853i	−0.870533	+	0.492110i	$0.836226\pi$
$258$		0			0
$259$	−0.363045	+	0.418976i	−0.0225585	+	0.0260339i
$260$		0			0
$261$	−2.95440	−	0.569413i	−0.182873	−	0.0352458i
$262$		0			0
$263$	9.36499	−	2.74981i	0.577470	−	0.169560i	0.0200613	−	0.999799i	$-0.493614\pi$
$263$	9.36499	−	2.74981i	0.577470	−	0.169560i	0.557409	+	0.830238i	$0.311796\pi$
$264$		0			0
$265$	3.37808	+	7.39695i	0.207514	+	0.454391i
$266$		0			0
$267$	−16.3135			−0.998373
$268$		0			0
$269$	23.9821			1.46222			0.731108	−	0.682262i	$-0.239004\pi$
$269$	23.9821			1.46222			0.731108	+	0.682262i	$0.239004\pi$
$270$		0			0
$271$	0.379180	+	0.830288i	0.0230335	+	0.0504364i	0.920799	−	0.390037i	$-0.127538\pi$
$271$	0.379180	+	0.830288i	0.0230335	+	0.0504364i	−0.897766	+	0.440474i	$0.854811\pi$
$272$		0			0
$273$	2.82816	−	0.830422i	0.171168	−	0.0502594i
$274$		0			0
$275$	−46.0900	−	8.88312i	−2.77933	−	0.535672i
$276$		0			0
$277$	−7.58298	+	8.75123i	−0.455617	+	0.525810i	−0.936355	−	0.351054i	$-0.885823\pi$
$277$	−7.58298	+	8.75123i	−0.455617	+	0.525810i	0.480738	+	0.876864i	$0.340369\pi$
$278$		0			0
$279$	0.937513	+	0.893917i	0.0561274	+	0.0535174i
$280$		0			0
$281$	−1.05250	−	22.0947i	−0.0627870	−	1.31806i	−0.782003	−	0.623274i	$-0.785802\pi$
$281$	−1.05250	−	22.0947i	−0.0627870	−	1.31806i	0.719216	−	0.694786i	$-0.244501\pi$
$282$		0			0
$283$	9.55858	+	11.0312i	0.568199	+	0.655736i	0.965025	−	0.262157i	$-0.0844340\pi$
$283$	9.55858	+	11.0312i	0.568199	+	0.655736i	−0.396826	+	0.917894i	$0.629889\pi$
$284$		0			0
$285$	−4.66713	−	3.67027i	−0.276457	−	0.217408i
$286$		0			0
$287$	−6.88896	+	1.32774i	−0.406643	+	0.0783739i
$288$		0			0
$289$	−3.89206	−	16.0433i	−0.228944	−	0.943722i
$290$		0			0
$291$	0.713596	+	0.0681401i	0.0418317	+	0.00399445i
$292$		0			0
$293$	14.1046	−	9.06449i	0.824000	−	0.529553i	−0.0593658	−	0.998236i	$-0.518908\pi$
$293$	14.1046	−	9.06449i	0.824000	−	0.529553i	0.883366	+	0.468683i	$0.155271\pi$
$294$		0			0
$295$	−9.07985	−	2.66608i	−0.528649	−	0.155225i
$296$		0			0
$297$	−3.04374	−	5.27191i	−0.176616	−	0.305907i
$298$		0			0
$299$	−0.486217	+	10.2069i	−0.0281186	+	0.590283i
$300$		0			0
$301$	1.86187	−	5.37952i	0.107316	−	0.310070i
$302$		0			0
$303$	−4.63203	+	0.442305i	−0.266103	+	0.0254098i
$304$		0			0
$305$	−8.60911	+	14.9114i	−0.492956	+	0.853826i
$306$		0			0
$307$	8.41826	−	4.33992i	0.480456	−	0.247692i	−0.200945	−	0.979602i	$-0.564401\pi$
$307$	8.41826	−	4.33992i	0.480456	−	0.247692i	0.681401	+	0.731910i	$0.261371\pi$
$308$		0			0
$309$	15.9861	−	6.39985i	0.909415	−	0.364075i
$310$		0			0
$311$	0.881308	−	6.12963i	0.0499744	−	0.347579i	−0.949458	−	0.313894i	$-0.898366\pi$
$311$	0.881308	−	6.12963i	0.0499744	−	0.347579i	0.999432	−	0.0336856i	$-0.0107245\pi$
$312$		0			0
$313$	−13.4435	+	29.4372i	−0.759872	+	1.66389i	−0.0121049	+	0.999927i	$0.503853\pi$
$313$	−13.4435	+	29.4372i	−0.759872	+	1.66389i	−0.747767	+	0.663961i	$0.768874\pi$
$314$		0			0
$315$	2.05943	−	2.89207i	0.116036	−	0.162950i
$316$		0			0
$317$	12.6397	+	5.06016i	0.709914	+	0.284207i	0.698381	−	0.715727i	$-0.253904\pi$
$317$	12.6397	+	5.06016i	0.709914	+	0.284207i	0.0115339	+	0.999933i	$0.496329\pi$
$318$		0			0
$319$	4.31812	−	17.7995i	0.241768	−	0.996582i
$320$		0			0
$321$	−2.51348	−	17.4817i	−0.140289	−	0.975731i
$322$		0			0
$323$	−1.03763	−	0.534934i	−0.0577351	−	0.0297645i
$324$		0			0
$325$	−13.2382	−	18.5904i	−0.734322	−	1.03121i
$326$		0			0
$327$	0.0961584	+	0.0617972i	0.00531757	+	0.00341739i
$328$		0			0
$329$	−8.74118	+	8.33470i	−0.481917	+	0.459507i
$330$		0			0
$331$	−7.40487	+	5.82325i	−0.407008	+	0.320075i	−0.800588	−	0.599216i	$-0.795479\pi$
$331$	−7.40487	+	5.82325i	−0.407008	+	0.320075i	0.393579	+	0.919291i	$0.371237\pi$
$332$		0			0
$333$	0.182077	+	0.526078i	0.00997777	+	0.0288289i
$334$		0			0
$335$	28.2292	+	7.39766i	1.54232	+	0.404177i
$336$		0			0
$337$	10.0728	+	29.1035i	0.548702	+	1.58537i	0.788818	+	0.614627i	$0.210693\pi$
$337$	10.0728	+	29.1035i	0.548702	+	1.58537i	−0.240116	+	0.970744i	$0.577185\pi$
$338$		0			0
$339$	6.65016	−	5.22974i	0.361187	−	0.284041i
$340$		0			0
$341$	−5.70709	+	5.44170i	−0.309056	+	0.294684i
$342$		0			0
$343$	10.8978	+	7.00362i	0.588428	+	0.378160i
$344$		0			0
$345$	7.13959	+	10.0262i	0.384383	+	0.539790i
$346$		0			0
$347$	−25.1251	−	12.9529i	−1.34878	−	0.695347i	−0.375905	−	0.926658i	$-0.622668\pi$
$347$	−25.1251	−	12.9529i	−1.34878	−	0.695347i	−0.972880	+	0.231311i	$0.925698\pi$
$348$		0			0
$349$	−1.89710	−	13.1946i	−0.101549	−	0.706290i	−0.975456	−	0.220196i	$-0.929330\pi$
$349$	−1.89710	−	13.1946i	−0.101549	−	0.706290i	0.873906	−	0.486094i	$-0.161579\pi$
$350$		0			0
$351$	0.697809	−	2.87641i	0.0372463	−	0.153531i
$352$		0			0
$353$	9.31018	+	3.72724i	0.495531	+	0.198381i	0.605947	−	0.795505i	$-0.292794\pi$
$353$	9.31018	+	3.72724i	0.495531	+	0.198381i	−0.110416	+	0.993885i	$0.535218\pi$
$354$		0			0
$355$	−6.03315	+	8.47237i	−0.320206	+	0.449667i
$356$		0			0
$357$	0.289989	−	0.634987i	0.0153478	−	0.0336071i
$358$		0			0
$359$	−0.341539	+	2.37545i	−0.0180257	+	0.125372i	−0.996847	−	0.0793433i	$-0.974718\pi$
$359$	−0.341539	+	2.37545i	−0.0180257	+	0.125372i	0.978822	+	0.204715i	$0.0656267\pi$
$360$		0			0
$361$	−15.0642	+	6.03078i	−0.792850	+	0.317409i
$362$		0			0
$363$	23.1607	−	11.9402i	1.21562	−	0.626697i
$364$		0			0
$365$	4.27892	−	7.41130i	0.223969	−	0.387925i
$366$		0			0
$367$	28.3777	−	2.70975i	1.48131	−	0.141448i	0.677141	−	0.735853i	$-0.263219\pi$
$367$	28.3777	−	2.70975i	1.48131	−	0.141448i	0.804165	+	0.594406i	$0.202613\pi$
$368$		0			0
$369$	−2.30419	+	6.65752i	−0.119951	+	0.346577i
$370$		0			0
$371$	0.108078	−	2.26885i	0.00561115	−	0.117793i
$372$		0			0
$373$	11.1311	+	19.2796i	0.576344	+	0.998258i	0.995894	+	0.0905253i	$0.0288546\pi$
$373$	11.1311	+	19.2796i	0.576344	+	0.998258i	−0.419550	+	0.907732i	$0.637812\pi$
$374$		0			0
$375$	−9.27244	−	2.72263i	−0.478827	−	0.140596i
$376$		0			0
$377$	7.49176	−	4.81466i	0.385845	−	0.247968i
$378$		0			0
$379$	−17.1609	−	1.63867i	−0.881497	−	0.0841728i	−0.355517	−	0.934670i	$-0.615695\pi$
$379$	−17.1609	−	1.63867i	−0.881497	−	0.0841728i	−0.525980	+	0.850497i	$0.676301\pi$
$380$		0			0
$381$	2.33906	+	9.64172i	0.119833	+	0.493960i
$382$		0			0
$383$	0.260914	−	0.0502870i	0.0133321	−	0.00256954i	−0.182581	−	0.983191i	$-0.558445\pi$
$383$	0.260914	−	0.0502870i	0.0133321	−	0.00256954i	0.195913	+	0.980621i	$0.437233\pi$
$384$		0			0
$385$	16.9889	+	13.3602i	0.865836	+	0.680901i
$386$		0			0
$387$	−3.74341	−	4.32012i	−0.190288	−	0.219604i
$388$		0			0
$389$	0.246827	+	5.18155i	0.0125147	+	0.262715i	0.996450	+	0.0841887i	$0.0268299\pi$
$389$	0.246827	+	5.18155i	0.0125147	+	0.262715i	−0.983935	+	0.178526i	$0.942867\pi$
$390$		0			0
$391$	1.75147	+	1.67003i	0.0885759	+	0.0844569i
$392$		0			0
$393$	12.0508	−	13.9074i	0.607882	−	0.701533i
$394$		0			0
$395$	−15.5224	−	2.99170i	−0.781017	−	0.150529i
$396$		0			0
$397$	15.6967	−	4.60897i	0.787795	−	0.231318i	0.137000	−	0.990571i	$-0.456254\pi$
$397$	15.6967	−	4.60897i	0.787795	−	0.231318i	0.650795	+	0.759254i	$0.274436\pi$
$398$		0			0
$399$	0.688954	+	1.50860i	0.0344908	+	0.0755244i
$400$		0			0
$401$	−16.3535			−0.816653			−0.408326	−	0.912836i	$-0.633887\pi$
$401$	−16.3535			−0.816653			−0.408326	+	0.912836i	$0.633887\pi$
$402$		0			0
$403$	−3.83413			−0.190992
$404$		0			0
$405$	−1.48104	−	3.24302i	−0.0735933	−	0.161147i
$406$		0			0
$407$	−3.25160	+	0.954756i	−0.161176	+	0.0473255i
$408$		0			0
$409$	9.70363	+	1.87022i	0.479813	+	0.0924765i	0.423423	−	0.905932i	$-0.360829\pi$
$409$	9.70363	+	1.87022i	0.479813	+	0.0924765i	0.0563909	+	0.998409i	$0.482041\pi$
$410$		0			0
$411$	−6.30358	+	7.27472i	−0.310933	+	0.358835i
$412$		0			0
$413$	1.91305	+	1.82409i	0.0941350	+	0.0897575i
$414$		0			0
$415$	−2.48952	−	52.2615i	−0.122206	−	2.56542i
$416$		0			0
$417$	0.218690	+	0.252382i	0.0107093	+	0.0123592i
$418$		0			0
$419$	−31.1583	−	24.5032i	−1.52218	−	1.19706i	−0.915634	−	0.402014i	$-0.868310\pi$
$419$	−31.1583	−	24.5032i	−1.52218	−	1.19706i	−0.606551	−	0.795045i	$-0.707447\pi$
$420$		0			0
$421$	−38.9298	+	7.50310i	−1.89732	+	0.365679i	−0.997505	−	0.0705900i	$-0.977512\pi$
$421$	−38.9298	+	7.50310i	−1.89732	+	0.365679i	−0.899816	+	0.436269i	$0.856300\pi$
$422$		0			0
$423$	2.85934	+	11.7864i	0.139026	+	0.573072i
$424$		0			0
$425$	−5.38051	−	0.513777i	−0.260993	−	0.0249218i
$426$		0			0
$427$	4.04600	−	2.60020i	0.195799	−	0.125833i
$428$		0			0
$429$	17.2881	+	5.07625i	0.834678	+	0.245084i
$430$		0			0
$431$	2.04057	+	3.53437i	0.0982908	+	0.170245i	0.910977	−	0.412457i	$-0.135329\pi$
$431$	2.04057	+	3.53437i	0.0982908	+	0.170245i	−0.812686	+	0.582701i	$0.801996\pi$
$432$		0			0
$433$	1.13320	−	23.7887i	0.0544579	−	1.14321i	−0.791919	−	0.610627i	$-0.790918\pi$
$433$	1.13320	−	23.7887i	0.0544579	−	1.14321i	0.846377	−	0.532585i	$-0.178779\pi$
$434$		0			0
$435$	3.50841	−	10.1369i	0.168215	−	0.486026i
$436$		0			0
$437$	−5.72352	+	0.546530i	−0.273793	+	0.0261441i
$438$		0			0
$439$	2.47183	−	4.28133i	0.117974	−	0.204337i	−0.800991	−	0.598677i	$-0.795693\pi$
$439$	2.47183	−	4.28133i	0.117974	−	0.204337i	0.918965	+	0.394340i	$0.129027\pi$
$440$		0			0
$441$	5.34038	−	2.75316i	0.254304	−	0.131103i
$442$		0			0
$443$	−12.7828	+	5.11748i	−0.607331	+	0.243139i	−0.654883	−	0.755730i	$-0.727282\pi$
$443$	−12.7828	+	5.11748i	−0.607331	+	0.243139i	0.0475522	+	0.998869i	$0.484858\pi$
$444$		0			0
$445$	8.27717	−	57.5690i	0.392375	−	2.72903i
$446$		0			0
$447$	8.12021	−	17.7808i	0.384073	−	0.841002i
$448$		0			0
$449$	19.4935	−	27.3748i	0.919956	−	1.29190i	−0.0362918	−	0.999341i	$-0.511555\pi$
$449$	19.4935	−	27.3748i	0.919956	−	1.29190i	0.956248	−	0.292557i	$-0.0945060\pi$
$450$		0			0
$451$	−39.8142	−	15.9392i	−1.87478	−	0.750548i
$452$		0			0
$453$	2.97246	−	12.2526i	0.139658	−	0.575679i
$454$		0			0
$455$	1.49553	+	10.4016i	0.0701116	+	0.487637i
$456$		0			0
$457$	−29.8631	−	15.3955i	−1.39694	−	0.720172i	−0.415080	−	0.909785i	$-0.636246\pi$
$457$	−29.8631	−	15.3955i	−1.39694	−	0.720172i	−0.981859	+	0.189613i	$0.939277\pi$
$458$		0			0
$459$	−0.406608	−	0.571001i	−0.0189788	−	0.0266520i
$460$		0			0
$461$	−15.4882	−	9.95367i	−0.721358	−	0.463588i	0.127751	−	0.991806i	$-0.459224\pi$
$461$	−15.4882	−	9.95367i	−0.721358	−	0.463588i	−0.849109	+	0.528218i	$0.822860\pi$
$462$		0			0
$463$	−3.62976	+	3.46097i	−0.168689	+	0.160845i	−0.769721	−	0.638380i	$-0.779605\pi$
$463$	−3.62976	+	3.46097i	−0.168689	+	0.160845i	0.601032	+	0.799225i	$0.294756\pi$
$464$		0			0
$465$	−3.63022	+	2.85484i	−0.168348	+	0.132390i
$466$		0			0
$467$	7.24686	+	20.9384i	0.335345	+	0.968915i	0.979046	+	0.203638i	$0.0652766\pi$
$467$	7.24686	+	20.9384i	0.335345	+	0.968915i	−0.643701	+	0.765277i	$0.722602\pi$
$468$		0			0
$469$	−6.06172	−	5.44982i	−0.279904	−	0.251649i
$470$		0			0
$471$	1.46341	+	4.22826i	0.0674306	+	0.194828i
$472$		0			0
$473$	27.3531	−	21.5108i	1.25770	−	0.989065i
$474$		0			0
$475$	9.29358	−	8.86141i	0.426418	−	0.406589i
$476$		0			0
$477$	−1.91880	−	1.23314i	−0.0878560	−	0.0564616i
$478$		0			0
$479$	5.46495	+	7.67445i	0.249700	+	0.350655i	0.920334	−	0.391134i	$-0.127917\pi$
$479$	5.46495	+	7.67445i	0.249700	+	0.350655i	−0.670634	+	0.741789i	$0.733978\pi$
$480$		0			0
$481$	−1.46456	−	0.755034i	−0.0667782	−	0.0344266i
$482$		0			0
$483$	−0.489287	−	3.40306i	−0.0222633	−	0.154845i
$484$		0			0
$485$	−0.602525	+	2.48364i	−0.0273592	+	0.112776i
$486$		0			0
$487$	24.3275	+	9.73928i	1.10239	+	0.441329i	0.850259	−	0.526365i	$-0.176445\pi$
$487$	24.3275	+	9.73928i	1.10239	+	0.441329i	0.252128	+	0.967694i	$0.418870\pi$
$488$		0			0
$489$	7.19855	−	10.1090i	0.325530	−	0.457143i
$490$		0			0
$491$	−7.92338	+	17.3498i	−0.357577	+	0.782985i	0.642286	+	0.766465i	$0.277986\pi$
$491$	−7.92338	+	17.3498i	−0.357577	+	0.782985i	−0.999864	+	0.0165200i	$0.994741\pi$
$492$		0			0
$493$	0.300154	−	2.08762i	0.0135183	−	0.0940216i
$494$		0			0
$495$	20.1484	−	8.06621i	0.905604	−	0.362549i
$496$		0			0
$497$	2.58229	−	1.33126i	0.115831	−	0.0597153i
$498$		0			0
$499$	−0.136988	+	0.237270i	−0.00613243	+	0.0106217i	−0.869075	−	0.494680i	$-0.835285\pi$
$499$	−0.136988	+	0.237270i	−0.00613243	+	0.0106217i	0.862943	+	0.505301i	$0.168619\pi$
$500$		0			0
$501$	−21.4089	+	2.04430i	−0.956477	+	0.0913325i
$502$		0			0
$503$	2.69163	−	7.77697i	0.120014	−	0.346758i	−0.868953	−	0.494895i	$-0.835207\pi$
$503$	2.69163	−	7.77697i	0.120014	−	0.346758i	0.988967	+	0.148137i	$0.0473277\pi$
$504$		0			0
$505$	0.789346	−	16.5704i	0.0351255	−	0.737374i
$506$		0			0
$507$	−2.11967	−	3.67138i	−0.0941379	−	0.163052i
$508$		0			0
$509$	−31.8549	−	9.35343i	−1.41194	−	0.414584i	−0.515175	−	0.857085i	$-0.672273\pi$
$509$	−31.8549	−	9.35343i	−1.41194	−	0.414584i	−0.896768	+	0.442502i	$0.854091\pi$
$510$		0			0
$511$	−2.01095	+	1.29236i	−0.0889591	+	0.0571705i
$512$		0			0
$513$	1.65784	+	0.158305i	0.0731956	+	0.00698933i
$514$		0			0
$515$	14.4735	+	59.6605i	0.637778	+	2.62896i
$516$		0			0
$517$	−72.4961	+	13.9725i	−3.18838	+	0.614509i
$518$		0			0
$519$	−10.7016	−	8.41581i	−0.469747	−	0.369413i
$520$		0			0
$521$	−28.2385	−	32.5889i	−1.23715	−	1.42775i	−0.866651	−	0.498915i	$-0.833732\pi$
$521$	−28.2385	−	32.5889i	−1.23715	−	1.42775i	−0.370500	−	0.928833i	$-0.620814\pi$
$522$		0			0
$523$	1.72801	+	36.2753i	0.0755605	+	1.58621i	0.645004	+	0.764179i	$0.276856\pi$
$523$	1.72801	+	36.2753i	0.0755605	+	1.58621i	−0.569443	+	0.822031i	$0.692841\pi$
$524$		0			0
$525$	5.55728	+	5.29885i	0.242539	+	0.231261i
$526$		0			0
$527$	−0.594638	+	0.686249i	−0.0259028	+	0.0298935i
$528$		0			0
$529$	−10.8808	−	2.09710i	−0.473077	−	0.0911781i
$530$		0			0
$531$	2.54680	−	0.747809i	0.110522	−	0.0324521i
$532$		0			0
$533$	−8.66226	−	18.9677i	−0.375204	−	0.821582i
$534$		0			0
$535$	62.9664			2.72228
$536$		0			0
$537$	21.4669			0.926364
$538$		0			0
$539$	15.1939	+	33.2701i	0.654449	+	1.43304i
$540$		0			0
$541$	40.3725	−	11.8544i	1.73575	−	0.509662i	0.747733	−	0.664000i	$-0.231143\pi$
$541$	40.3725	−	11.8544i	1.73575	−	0.509662i	0.988018	+	0.154338i	$0.0493243\pi$
$542$		0			0
$543$	0.570658	+	0.109985i	0.0244893	+	0.00471992i
$544$		0			0
$545$	−0.266866	+	0.307979i	−0.0114313	+	0.0131924i
$546$		0			0
$547$	−20.9127	−	19.9402i	−0.894163	−	0.852583i	0.0955830	−	0.995421i	$-0.469528\pi$
$547$	−20.9127	−	19.9402i	−0.894163	−	0.852583i	−0.989746	+	0.142839i	$0.954377\pi$
$548$		0			0
$549$	−0.229798	−	4.82406i	−0.00980756	−	0.205886i
$550$		0			0
$551$	3.28135	+	3.78688i	0.139790	+	0.161326i
$552$		0			0
$553$	3.47089	+	2.72954i	0.147597	+	0.116072i
$554$		0			0
$555$	−1.94886	+	0.375612i	−0.0827246	+	0.0159439i
$556$		0			0
$557$	−7.25372	−	29.9002i	−0.307350	−	1.26691i	−0.890662	−	0.454665i	$-0.849759\pi$
$557$	−7.25372	−	29.9002i	−0.307350	−	1.26691i	0.583313	−	0.812248i	$-0.301756\pi$
$558$		0			0
$559$	16.8428	+	1.60830i	0.712376	+	0.0680237i
$560$		0			0
$561$	3.58980	−	2.30702i	0.151561	−	0.0974025i
$562$		0			0
$563$	29.6648	+	8.71036i	1.25022	+	0.367098i	0.838846	−	0.544368i	$-0.183231\pi$
$563$	29.6648	+	8.71036i	1.25022	+	0.367098i	0.411375	+	0.911466i	$0.365049\pi$
$564$		0			0
$565$	15.0811	+	26.1213i	0.634467	+	1.09893i
$566$		0			0
$567$	−0.0473844	+	0.994721i	−0.00198996	+	0.0417744i
$568$		0			0
$569$	−5.30220	+	15.3197i	−0.222280	+	0.642235i	0.777629	+	0.628723i	$0.216422\pi$
$569$	−5.30220	+	15.3197i	−0.222280	+	0.642235i	−0.999909	+	0.0135117i	$0.995699\pi$
$570$		0			0
$571$	−16.3789	+	1.56399i	−0.685434	+	0.0654510i	−0.431962	−	0.901892i	$-0.642179\pi$
$571$	−16.3789	+	1.56399i	−0.685434	+	0.0654510i	−0.253472	+	0.967343i	$0.581573\pi$
$572$		0			0
$573$	0.356526	−	0.617521i	0.0148941	−	0.0257973i
$574$		0			0
$575$	−23.6609	+	12.1980i	−0.986726	+	0.508692i
$576$		0			0
$577$	−5.47711	+	2.19271i	−0.228015	+	0.0912835i	−0.482857	−	0.875699i	$-0.660401\pi$
$577$	−5.47711	+	2.19271i	−0.228015	+	0.0912835i	0.254842	+	0.966983i	$0.417977\pi$
$578$		0			0
$579$	3.27656	−	22.7890i	0.136169	−	0.947077i
$580$		0			0
$581$	−6.07108	+	13.2938i	−0.251871	+	0.551521i
$582$		0			0
$583$	8.05400	−	11.3103i	0.333563	−	0.468423i
$584$		0			0
$585$	9.79652	+	3.92194i	0.405036	+	0.162152i
$586$		0			0
$587$	−4.99559	+	20.5921i	−0.206190	+	0.849927i	0.770875	+	0.636986i	$0.219819\pi$
$587$	−4.99559	+	20.5921i	−0.206190	+	0.849927i	−0.977065	+	0.212941i	$0.931696\pi$
$588$		0			0
$589$	−0.307017	−	2.13535i	−0.0126504	−	0.0879857i
$590$		0			0
$591$	17.0406	+	8.78504i	0.700957	+	0.361368i
$592$		0			0
$593$	−5.98436	−	8.40385i	−0.245748	−	0.345105i	0.673216	−	0.739446i	$-0.264912\pi$
$593$	−5.98436	−	8.40385i	−0.245748	−	0.345105i	−0.918964	+	0.394341i	$0.870973\pi$
$594$		0			0
$595$	2.09367	+	1.34552i	0.0858323	+	0.0551611i
$596$		0			0
$597$	−3.23219	+	3.08189i	−0.132285	+	0.126133i
$598$		0			0
$599$	−21.9505	+	17.2621i	−0.896874	+	0.705309i	−0.956133	−	0.292933i	$-0.905369\pi$
$599$	−21.9505	+	17.2621i	−0.896874	+	0.705309i	0.0592590	+	0.998243i	$0.481126\pi$
$600$		0			0
$601$	−2.46864	−	7.13268i	−0.100698	−	0.290948i	0.883387	−	0.468643i	$-0.155257\pi$
$601$	−2.46864	−	7.13268i	−0.100698	−	0.290948i	−0.984086	+	0.177695i	$0.943136\pi$
$602$		0			0
$603$	−7.78285	+	2.53521i	−0.316942	+	0.103242i
$604$		0			0
$605$	30.3845	+	87.7903i	1.23531	+	3.56918i
$606$		0			0
$607$	5.37156	−	4.22424i	0.218025	−	0.171457i	−0.503173	−	0.864186i	$-0.667834\pi$
$607$	5.37156	−	4.22424i	0.218025	−	0.171457i	0.721198	+	0.692729i	$0.243592\pi$
$608$		0			0
$609$	−2.16851	+	2.06767i	−0.0878724	+	0.0837862i
$610$		0			0
$611$	−30.1990	−	19.4077i	−1.22172	−	0.785153i
$612$		0			0
$613$	−13.5952	−	19.0918i	−0.549104	−	0.771109i	0.443001	−	0.896521i	$-0.353914\pi$
$613$	−13.5952	−	19.0918i	−0.549104	−	0.771109i	−0.992105	+	0.125413i	$0.959975\pi$
$614$		0			0
$615$	−22.3247	−	11.5092i	−0.900218	−	0.464095i
$616$		0			0
$617$	−0.200811	−	1.39667i	−0.00808434	−	0.0562279i	0.985380	−	0.170371i	$-0.0544967\pi$
$617$	−0.200811	−	1.39667i	−0.00808434	−	0.0562279i	−0.993464	+	0.114143i	$0.963588\pi$
$618$		0			0
$619$	−4.01310	+	16.5422i	−0.161300	+	0.664889i	0.832530	+	0.553980i	$0.186891\pi$
$619$	−4.01310	+	16.5422i	−0.161300	+	0.664889i	−0.993831	+	0.110909i	$0.964624\pi$
$620$		0			0
$621$	−3.20509	−	1.28312i	−0.128616	−	0.0514899i
$622$		0			0
$623$	−9.42350	+	13.2335i	−0.377545	+	0.530187i
$624$		0			0
$625$	−1.70296	+	3.72896i	−0.0681184	+	0.149158i
$626$		0			0
$627$	−1.44279	+	10.0348i	−0.0576193	+	0.400751i
$628$		0			0
$629$	−0.362279	+	0.145035i	−0.0144450	+	0.00578291i
$630$		0			0
$631$	14.9004	−	7.68170i	0.593176	−	0.305804i	−0.135376	−	0.990794i	$-0.543224\pi$
$631$	14.9004	−	7.68170i	0.593176	−	0.305804i	0.728552	+	0.684991i	$0.240194\pi$
$632$		0			0
$633$	−11.5444	+	19.9955i	−0.458849	+	0.794750i
$634$		0			0
$635$	−35.2115	+	3.36229i	−1.39733	+	0.133429i
$636$		0			0
$637$	−5.81644	+	16.8055i	−0.230456	+	0.665858i
$638$		0			0
$639$	0.138814	−	2.91406i	0.00549138	−	0.115278i
$640$		0			0
$641$	−23.0181	−	39.8685i	−0.909160	−	1.57471i	−0.815234	−	0.579131i	$-0.803392\pi$
$641$	−23.0181	−	39.8685i	−0.909160	−	1.57471i	−0.0939253	−	0.995579i	$-0.529941\pi$
$642$		0			0
$643$	37.5845	+	11.0358i	1.48219	+	0.435209i	0.920039	−	0.391828i	$-0.128157\pi$
$643$	37.5845	+	11.0358i	1.48219	+	0.435209i	0.562148	+	0.827037i	$0.309975\pi$
$644$		0			0
$645$	17.1446	−	11.0182i	0.675069	−	0.433841i
$646$		0			0
$647$	29.4079	+	2.80811i	1.15614	+	0.110398i	0.655459	−	0.755231i	$-0.272475\pi$
$647$	29.4079	+	2.80811i	1.15614	+	0.110398i	0.500685	+	0.865630i	$0.333081\pi$
$648$		0			0
$649$	3.80942	+	15.7026i	0.149533	+	0.616383i
$650$		0			0
$651$	1.26669	−	0.244135i	0.0496457	−	0.00956841i
$652$		0			0
$653$	−5.38208	−	4.23252i	−0.210617	−	0.165631i	0.507278	−	0.861783i	$-0.330652\pi$
$653$	−5.38208	−	4.23252i	−0.210617	−	0.165631i	−0.717895	+	0.696151i	$0.754894\pi$
$654$		0			0
$655$	42.9634	+	49.5824i	1.67872	+	1.93735i
$656$		0			0
$657$	0.114215	+	2.39766i	0.00445594	+	0.0935417i
$658$		0			0
$659$	7.24743	+	6.91041i	0.282320	+	0.269191i	0.817986	−	0.575239i	$-0.195091\pi$
$659$	7.24743	+	6.91041i	0.282320	+	0.269191i	−0.535666	+	0.844430i	$0.679939\pi$
$660$		0			0
$661$	−32.4527	+	37.4524i	−1.26226	+	1.45673i	−0.429536	+	0.903050i	$0.641323\pi$
$661$	−32.4527	+	37.4524i	−1.26226	+	1.45673i	−0.832728	+	0.553682i	$0.813222\pi$
$662$		0			0
$663$	2.03729	+	0.392656i	0.0791219	+	0.0152495i
$664$		0			0
$665$	−5.67327	+	1.66582i	−0.220000	+	0.0645978i
$666$		0			0
$667$	−4.31510	−	9.44874i	−0.167081	−	0.365857i
$668$		0			0
$669$	−19.6892			−0.761230
$670$		0			0
$671$	29.3997			1.13496
$672$		0			0
$673$	16.4875	+	36.1026i	0.635546	+	1.39165i	0.903654	+	0.428263i	$0.140874\pi$
$673$	16.4875	+	36.1026i	0.635546	+	1.39165i	−0.268108	+	0.963389i	$0.586398\pi$
$674$		0			0
$675$	7.39829	−	2.17233i	0.284760	−	0.0836131i
$676$		0			0
$677$	−34.7196	−	6.69166i	−1.33438	−	0.257181i	−0.528338	−	0.849034i	$-0.677185\pi$
$677$	−34.7196	−	6.69166i	−1.33438	−	0.257181i	−0.806046	+	0.591853i	$0.798397\pi$
$678$		0			0
$679$	0.467483	−	0.539504i	0.0179404	−	0.0207043i
$680$		0			0
$681$	−6.53620	−	6.23225i	−0.250468	−	0.238820i
$682$		0			0
$683$	0.509399	+	10.6936i	0.0194916	+	0.409180i	0.987436	+	0.158017i	$0.0505100\pi$
$683$	0.509399	+	10.6936i	0.0194916	+	0.409180i	−0.967945	+	0.251163i	$0.919187\pi$
$684$		0			0
$685$	−22.4735	−	25.9358i	−0.858668	−	0.990956i
$686$		0			0
$687$	11.2580	+	8.85336i	0.429518	+	0.337777i
$688$		0			0
$689$	6.62906	−	1.27765i	0.252547	−	0.0486745i
$690$		0			0
$691$	−9.94105	−	40.9776i	−0.378175	−	1.55886i	−0.769524	−	0.638618i	$-0.779506\pi$
$691$	−9.94105	−	40.9776i	−0.378175	−	1.55886i	0.391349	−	0.920243i	$-0.372009\pi$
$692$		0			0
$693$	−6.03476	−	0.576250i	−0.229242	−	0.0218899i
$694$		0			0
$695$	−1.00159	+	0.643683i	−0.0379925	+	0.0244163i
$696$		0			0
$697$	−4.73835	−	1.39131i	−0.179478	−	0.0526995i
$698$		0			0
$699$	0.130208	+	0.225527i	0.00492493	+	0.00853022i
$700$		0			0
$701$	−0.855114	+	17.9511i	−0.0322972	+	0.678002i	0.923433	+	0.383759i	$0.125371\pi$
$701$	−0.855114	+	17.9511i	−0.0322972	+	0.678002i	−0.955731	+	0.294243i	$0.904932\pi$
$702$		0			0
$703$	0.303229	−	0.876121i	0.0114365	−	0.0330435i
$704$		0			0
$705$	−43.0437	+	4.11018i	−1.62112	+	0.154798i
$706$		0			0
$707$	−2.31689	+	4.01298i	−0.0871357	+	0.150923i
$708$		0			0
$709$	40.6240	−	20.9431i	1.52567	−	0.786536i	0.527649	−	0.849462i	$-0.323074\pi$
$709$	40.6240	−	20.9431i	1.52567	−	0.786536i	0.998018	+	0.0629263i	$0.0200433\pi$
$710$		0			0
$711$	4.11638	−	1.64795i	0.154376	−	0.0618030i
$712$		0			0
$713$	−0.636455	+	4.42664i	−0.0238354	+	0.165779i
$714$		0			0
$715$	−26.6853	+	58.4326i	−0.997972	+	2.18525i
$716$		0			0
$717$	14.7768	−	20.7510i	0.551848	−	0.774962i
$718$		0			0
$719$	11.2972	+	4.52273i	0.421316	+	0.168669i	0.572626	−	0.819817i	$-0.305925\pi$
$719$	11.2972	+	4.52273i	0.421316	+	0.168669i	−0.151310	+	0.988486i	$0.548349\pi$
$720$		0			0
$721$	4.04281	−	16.6647i	0.150562	−	0.620625i
$722$		0			0
$723$	1.21874	+	8.47655i	0.0453256	+	0.315246i
$724$		0			0
$725$	20.6205	+	10.6306i	0.765827	+	0.394811i
$726$		0			0
$727$	12.5925	+	17.6837i	0.467029	+	0.655851i	0.979168	−	0.203052i	$-0.0650861\pi$
$727$	12.5925	+	17.6837i	0.467029	+	0.655851i	−0.512139	+	0.858903i	$0.671147\pi$
$728$		0			0
$729$	0.841254	+	0.540641i	0.0311575	+	0.0200237i
$730$		0			0
$731$	2.90003	−	2.76517i	0.107261	−	0.102274i
$732$		0			0
$733$	32.5868	−	25.6265i	1.20362	−	0.946538i	0.204146	−	0.978940i	$-0.434558\pi$
$733$	32.5868	−	25.6265i	1.20362	−	0.946538i	0.999475	+	0.0324027i	$0.0103159\pi$
$734$		0			0
$735$	7.00603	+	20.2426i	0.258421	+	0.746659i
$736$		0			0
$737$	−13.1613	−	48.0586i	−0.484801	−	1.77026i
$738$		0			0
$739$	−9.50958	−	27.4761i	−0.349815	−	1.01073i	−0.973428	−	0.228992i	$-0.926457\pi$
$739$	−9.50958	−	27.4761i	−0.349815	−	1.01073i	0.623613	−	0.781733i	$-0.285664\pi$
$740$		0			0
$741$	−3.87467	+	3.04707i	−0.142340	+	0.111937i
$742$		0			0
$743$	23.5591	−	22.4635i	0.864298	−	0.824107i	−0.121404	−	0.992603i	$-0.538740\pi$
$743$	23.5591	−	22.4635i	0.864298	−	0.824107i	0.985702	+	0.168497i	$0.0538912\pi$
$744$		0			0
$745$	58.6267	+	37.6771i	2.14791	+	1.38038i
$746$		0			0
$747$	8.51258	+	11.9542i	0.311459	+	0.437383i
$748$		0			0
$749$	−15.6329	−	8.05934i	−0.571215	−	0.294482i
$750$		0			0
$751$	5.51189	+	38.3360i	0.201132	+	1.39890i	0.800934	+	0.598753i	$0.204337\pi$
$751$	5.51189	+	38.3360i	0.201132	+	1.39890i	−0.599802	+	0.800149i	$0.704754\pi$
$752$		0			0
$753$	−3.16051	+	13.0278i	−0.115175	+	0.474759i
$754$		0			0
$755$	41.7302	+	16.7063i	1.51872	+	0.608003i
$756$		0			0
$757$	18.2155	−	25.5800i	0.662052	−	0.929722i	−0.337882	−	0.941188i	$-0.609711\pi$
$757$	18.2155	−	25.5800i	0.662052	−	0.929722i	0.999934	+	0.0114664i	$0.00364996\pi$
$758$		0			0
$759$	8.73050	−	19.1171i	0.316897	−	0.693908i
$760$		0			0
$761$	−0.776833	+	5.40299i	−0.0281602	+	0.195858i	−0.999045	−	0.0436875i	$-0.986089\pi$
$761$	−0.776833	+	5.40299i	−0.0281602	+	0.195858i	0.970885	+	0.239546i	$0.0769985\pi$
$762$		0			0
$763$	0.105675	−	0.0423060i	0.00382571	−	0.00153158i
$764$		0			0
$765$	2.22131	−	1.14517i	0.0803118	−	0.0414036i
$766$		0			0
$767$	−3.92818	+	6.80381i	−0.141839	+	0.245671i
$768$		0			0
$769$	8.47834	−	0.809583i	0.305737	−	0.0291943i	0.0589398	−	0.998262i	$-0.481228\pi$
$769$	8.47834	−	0.809583i	0.305737	−	0.0291943i	0.246797	+	0.969067i	$0.420622\pi$
$770$		0			0
$771$	−3.04572	+	8.80004i	−0.109689	+	0.316926i
$772$		0			0
$773$	−1.97559	+	41.4728i	−0.0710571	+	1.49167i	0.628900	+	0.777486i	$0.283506\pi$
$773$	−1.97559	+	41.4728i	−0.0710571	+	1.49167i	−0.699957	+	0.714185i	$0.746797\pi$
$774$		0			0
$775$	−4.99410	−	8.65004i	−0.179394	−	0.310719i
$776$		0			0
$777$	0.531928	+	0.156188i	0.0190828	+	0.00560322i
$778$		0			0
$779$	9.87010	−	6.34313i	0.353633	−	0.227266i
$780$		0			0
$781$	17.6789	+	1.68813i	0.632602	+	0.0604062i
$782$		0			0
$783$	0.709344	+	2.92396i	0.0253499	+	0.104494i
$784$		0			0
$785$	−15.6636	+	3.01892i	−0.559059	+	0.107750i
$786$		0			0
$787$	−14.9377	−	11.7471i	−0.532472	−	0.418740i	0.315387	−	0.948963i	$-0.397866\pi$
$787$	−14.9377	−	11.7471i	−0.532472	−	0.418740i	−0.847858	+	0.530223i	$0.822108\pi$
$788$		0			0
$789$	−6.39167	−	7.37638i	−0.227550	−	0.262606i
$790$		0			0
$791$	−0.400881	−	8.41553i	−0.0142537	−	0.299222i
$792$		0			0
$793$	10.3455	+	9.86444i	0.367380	+	0.350296i
$794$		0			0
$795$	5.32520	−	6.14561i	0.188865	−	0.217962i
$796$		0			0
$797$	−17.4827	−	3.36951i	−0.619268	−	0.119354i	−0.130038	−	0.991509i	$-0.541510\pi$
$797$	−17.4827	−	3.36951i	−0.619268	−	0.119354i	−0.489230	+	0.872155i	$0.662722\pi$
$798$		0			0
$799$	−8.15727	+	2.39519i	−0.288583	+	0.0847357i
$800$		0			0
$801$	6.77689	+	14.8393i	0.239450	+	0.524322i
$802$		0			0
$803$	−14.6123			−0.515656
$804$		0			0
$805$	12.2573			0.432015
$806$		0			0
$807$	−9.96254	−	21.8149i	−0.350698	−	0.767921i
$808$		0			0
$809$	−14.2767	+	4.19203i	−0.501943	+	0.147384i	−0.522896	−	0.852397i	$-0.675148\pi$
$809$	−14.2767	+	4.19203i	−0.501943	+	0.147384i	0.0209525	+	0.999780i	$0.493330\pi$
$810$		0			0
$811$	−22.3891	−	4.31515i	−0.786188	−	0.151525i	−0.219669	−	0.975574i	$-0.570498\pi$
$811$	−22.3891	−	4.31515i	−0.786188	−	0.151525i	−0.566518	+	0.824049i	$0.691710\pi$
$812$		0			0
$813$	0.597739	−	0.689828i	0.0209636	−	0.0241933i
$814$		0			0
$815$	32.0211	+	30.5321i	1.12165	+	1.06949i
$816$		0			0
$817$	0.452975	+	9.50912i	0.0158476	+	0.332682i
$818$		0			0
$819$	−1.93024	−	2.22761i	−0.0674480	−	0.0778391i
$820$		0			0
$821$	5.62612	+	4.42443i	0.196353	+	0.154414i	0.711495	−	0.702691i	$-0.248018\pi$
$821$	5.62612	+	4.42443i	0.196353	+	0.154414i	−0.515142	+	0.857105i	$0.672261\pi$
$822$		0			0
$823$	10.3954	−	2.00356i	0.362363	−	0.0698397i	−0.00482044	−	0.999988i	$-0.501534\pi$
$823$	10.3954	−	2.00356i	0.362363	−	0.0698397i	0.367183	+	0.930149i	$0.380322\pi$
$824$		0			0
$825$	11.0661	+	45.6151i	0.385273	+	1.58811i
$826$		0			0
$827$	8.77296	+	0.837716i	0.305066	+	0.0291302i	0.246466	−	0.969151i	$-0.420731\pi$
$827$	8.77296	+	0.837716i	0.305066	+	0.0291302i	0.0585993	+	0.998282i	$0.481337\pi$
$828$		0			0
$829$	−23.6789	+	15.2175i	−0.822403	+	0.528527i	−0.882856	−	0.469645i	$-0.844382\pi$
$829$	−23.6789	+	15.2175i	−0.822403	+	0.528527i	0.0604522	+	0.998171i	$0.480746\pi$
$830$		0			0
$831$	11.1105	+	3.26233i	0.385418	+	0.113169i
$832$		0			0
$833$	2.10584	+	3.64743i	0.0729631	+	0.126376i
$834$		0			0
$835$	3.64829	−	76.5871i	0.126254	−	2.65041i
$836$		0			0
$837$	0.423678	−	1.22414i	0.0146445	−	0.0423124i
$838$		0			0
$839$	−19.1231	+	1.82603i	−0.660202	+	0.0630417i	−0.419779	−	0.907626i	$-0.637892\pi$
$839$	−19.1231	+	1.82603i	−0.660202	+	0.0630417i	−0.240423	+	0.970668i	$0.577286\pi$
$840$		0			0
$841$	9.97366	−	17.2749i	0.343919	−	0.595685i
$842$		0			0
$843$	−19.6608	+	10.1359i	−0.677155	+	0.349098i
$844$		0			0
$845$	14.0314	−	5.61734i	0.482696	−	0.193242i
$846$		0			0
$847$	3.69296	−	25.6851i	0.126892	−	0.882551i
$848$		0			0
$849$	6.06355	−	13.2773i	0.208100	−	0.455676i
$850$		0			0
$851$	−1.11483	+	1.56556i	−0.0382158	+	0.0536666i
$852$		0			0
$853$	−40.0922	−	16.0505i	−1.37273	−	0.549559i	−0.436107	−	0.899895i	$-0.643643\pi$
$853$	−40.0922	−	16.0505i	−1.37273	−	0.549559i	−0.936624	+	0.350336i	$0.886067\pi$
$854$		0			0
$855$	−1.39980	+	5.77005i	−0.0478721	+	0.197332i
$856$		0			0
$857$	1.56282	+	10.8697i	0.0533850	+	0.371301i	0.998948	+	0.0458612i	$0.0146032\pi$
$857$	1.56282	+	10.8697i	0.0533850	+	0.371301i	−0.945563	+	0.325440i	$0.894488\pi$
$858$		0			0
$859$	39.0664	+	20.1402i	1.33293	+	0.687173i	0.969648	−	0.244506i	$-0.0786258\pi$
$859$	39.0664	+	20.1402i	1.33293	+	0.687173i	0.363282	+	0.931679i	$0.381656\pi$
$860$		0			0
$861$	4.06953	+	5.71486i	0.138689	+	0.194762i
$862$		0			0
$863$	29.6393	+	19.0480i	1.00893	+	0.648401i	0.937117	−	0.349017i	$-0.113484\pi$
$863$	29.6393	+	19.0480i	1.00893	+	0.648401i	0.0718155	+	0.997418i	$0.477121\pi$
$864$		0			0
$865$	35.1284	−	33.4949i	1.19440	−	1.13886i
$866$		0			0
$867$	−12.9767	+	10.2050i	−0.440710	+	0.346578i
$868$		0			0
$869$	8.82818	+	25.5074i	0.299476	+	0.865278i
$870$		0			0
$871$	11.4937	−	21.3274i	0.389449	−	0.722652i
$872$		0			0
$873$	−0.234456	−	0.677416i	−0.00793513	−	0.0229271i
$874$		0			0
$875$	−7.56481	+	5.94903i	−0.255737	+	0.201114i
$876$		0			0
$877$	−0.243793	+	0.232457i	−0.00823232	+	0.00784950i	−0.694184	−	0.719798i	$-0.744235\pi$
$877$	−0.243793	+	0.232457i	−0.00823232	+	0.00784950i	0.685952	+	0.727647i	$0.259386\pi$
$878$		0			0
$879$	−14.1046	−	9.06449i	−0.475737	−	0.305738i
$880$		0			0
$881$	−33.1975	−	46.6194i	−1.11845	−	1.57065i	−0.775563	−	0.631271i	$-0.782534\pi$
$881$	−33.1975	−	46.6194i	−1.11845	−	1.57065i	−0.342889	−	0.939376i	$-0.611406\pi$
$882$		0			0
$883$	−35.5146	−	18.3091i	−1.19516	−	0.616149i	−0.258374	−	0.966045i	$-0.583187\pi$
$883$	−35.5146	−	18.3091i	−1.19516	−	0.616149i	−0.936789	+	0.349896i	$0.886217\pi$
$884$		0			0
$885$	1.34675	+	9.36685i	0.0452705	+	0.314863i
$886$		0			0
$887$	7.69883	−	31.7350i	0.258501	−	1.06556i	−0.683501	−	0.729950i	$-0.739543\pi$
$887$	7.69883	−	31.7350i	0.258501	−	1.06556i	0.942002	−	0.335607i	$-0.108941\pi$
$888$		0			0
$889$	9.17247	+	3.67210i	0.307635	+	0.123158i
$890$		0			0
$891$	−3.53108	+	4.95871i	−0.118296	+	0.166123i
$892$		0			0
$893$	8.39062	−	18.3729i	0.280781	−	0.614825i
$894$		0			0
$895$	−10.8919	+	75.7546i	−0.364075	+	2.53220i
$896$		0			0
$897$	9.48655	−	3.79784i	0.316747	−	0.126806i
$898$		0			0
$899$	3.46424	−	1.78594i	0.115539	−	0.0595645i
$900$		0			0
$901$	0.799427	−	1.38465i	0.0266328	−	0.0461293i
$902$		0			0
$903$	−5.66683	+	0.541117i	−0.188580	+	0.0180072i
$904$		0			0
$905$	−0.677669	+	1.95799i	−0.0225265	+	0.0650859i
$906$		0			0
$907$	0.297301	−	6.24111i	0.00987171	−	0.207233i	−0.988543	−	0.150942i	$-0.951769\pi$
$907$	0.297301	−	6.24111i	0.00987171	−	0.207233i	0.998414	−	0.0562912i	$-0.0179275\pi$
$908$		0			0
$909$	2.32655	+	4.02970i	0.0771668	+	0.133657i
$910$		0			0
$911$	−12.1241	−	3.55996i	−0.401689	−	0.117947i	0.0746466	−	0.997210i	$-0.476217\pi$
$911$	−12.1241	−	3.55996i	−0.401689	−	0.117947i	−0.476336	+	0.879263i	$0.658035\pi$
$912$		0			0
$913$	−75.1545	+	48.2988i	−2.48725	+	1.59846i
$914$		0			0
$915$	17.1403	+	1.63670i	0.566640	+	0.0541075i
$916$		0			0
$917$	−4.32044	−	17.8091i	−0.142674	−	0.588109i
$918$		0			0
$919$	22.1780	−	4.27446i	0.731585	−	0.141001i	0.190163	−	0.981753i	$-0.439098\pi$
$919$	22.1780	−	4.27446i	0.731585	−	0.141001i	0.541422	+	0.840751i	$0.317886\pi$
$920$		0			0
$921$	−7.44480	−	5.85465i	−0.245314	−	0.192917i
$922$		0			0
$923$	5.65467	+	6.52584i	0.186126	+	0.214801i
$924$		0			0
$925$	−0.204244	−	4.28761i	−0.00671550	−	0.140976i
$926$		0			0
$927$	−12.4624	−	11.8828i	−0.409318	−	0.390284i
$928$		0			0
$929$	−18.9623	+	21.8837i	−0.622133	+	0.717980i	−0.976111	−	0.217274i	$-0.930284\pi$
$929$	−18.9623	+	21.8837i	−0.622133	+	0.717980i	0.353977	+	0.935254i	$0.384829\pi$
$930$		0			0
$931$	−9.82528	−	1.89367i	−0.322010	−	0.0620624i
$932$		0			0
$933$	−5.94182	+	1.74467i	−0.194526	+	0.0571181i
$934$		0			0
$935$	6.31987	+	13.8386i	0.206682	+	0.452570i
$936$		0			0
$937$	−15.6755			−0.512095			−0.256048	−	0.966664i	$-0.582420\pi$
$937$	−15.6755			−0.512095			−0.256048	+	0.966664i	$0.582420\pi$
$938$		0			0
$939$	32.3616			1.05608
$940$		0			0
$941$	13.9911	+	30.6362i	0.456097	+	0.998712i	0.988360	+	0.152133i	$0.0486143\pi$
$941$	13.9911	+	30.6362i	0.456097	+	0.998712i	−0.532263	+	0.846579i	$0.678658\pi$
$942$		0			0
$943$	−23.3368	+	6.85231i	−0.759952	+	0.223142i
$944$		0			0
$945$	−3.48624	−	0.671917i	−0.113407	−	0.0218575i
$946$		0			0
$947$	3.34357	−	3.85869i	0.108651	−	0.125390i	−0.698819	−	0.715299i	$-0.746291\pi$
$947$	3.34357	−	3.85869i	0.108651	−	0.125390i	0.807470	+	0.589908i	$0.200836\pi$
$948$		0			0
$949$	−5.14195	−	4.90284i	−0.166915	−	0.159153i
$950$		0			0
$951$	−0.647825	−	13.5995i	−0.0210072	−	0.440994i
$952$		0			0
$953$	18.2685	+	21.0830i	0.591775	+	0.682945i	0.970094	−	0.242731i	$-0.0780431\pi$
$953$	18.2685	+	21.0830i	0.591775	+	0.682945i	−0.378319	+	0.925675i	$0.623498\pi$
$954$		0			0
$955$	1.99828	+	1.57146i	0.0646628	+	0.0508514i
$956$		0			0
$957$	−17.9848	+	3.46629i	−0.581367	+	0.112049i
$958$		0			0
$959$	2.25996	+	9.31567i	0.0729778	+	0.300819i
$960$		0			0
$961$	29.1892	+	2.78723i	0.941587	+	0.0899107i
$962$		0			0
$963$	−14.8577	+	9.54849i	−0.478784	+	0.307696i
$964$		0			0
$965$	78.7577	+	23.1253i	2.53530	+	0.744431i
$966$		0			0
$967$	20.2246	+	35.0300i	0.650378	+	1.12649i	0.983031	+	0.183439i	$0.0587228\pi$
$967$	20.2246	+	35.0300i	0.650378	+	1.12649i	−0.332653	+	0.943049i	$0.607944\pi$
$968$		0			0
$969$	−0.0555471	+	1.16608i	−0.00178443	+	0.0374598i
$970$		0			0
$971$	0.279570	−	0.807765i	0.00897183	−	0.0259224i	−0.940426	−	0.339998i	$-0.889573\pi$
$971$	0.279570	−	0.807765i	0.00897183	−	0.0259224i	0.949398	+	0.314076i	$0.101695\pi$
$972$		0			0
$973$	0.331057	−	0.0316121i	0.0106132	−	0.00101344i
$974$		0			0
$975$	−11.4111	+	19.7646i	−0.365448	+	0.632974i
$976$		0			0
$977$	−22.3850	+	11.5403i	−0.716160	+	0.369206i	−0.777476	−	0.628912i	$-0.783500\pi$
$977$	−22.3850	+	11.5403i	−0.716160	+	0.369206i	0.0613163	+	0.998118i	$0.480470\pi$
$978$		0			0
$979$	−92.1947	+	36.9092i	−2.94655	+	1.17962i
$980$		0			0
$981$	0.0162671	−	0.113140i	0.000519369	−	0.00361229i
$982$		0			0
$983$	−2.64352	+	5.78851i	−0.0843153	+	0.184625i	−0.947093	−	0.320958i	$-0.895995\pi$
$983$	−2.64352	+	5.78851i	−0.0843153	+	0.184625i	0.862778	+	0.505583i	$0.168722\pi$
$984$		0			0
$985$	−39.6477	+	55.6773i	−1.26328	+	1.77403i
$986$		0			0
$987$	11.2127	+	4.48890i	0.356905	+	0.142883i
$988$		0			0
$989$	4.65271	−	19.1787i	0.147947	−	0.609848i
$990$		0			0
$991$	−1.95787	−	13.6173i	−0.0621936	−	0.432566i	−0.997000	−	0.0774073i	$-0.975336\pi$
$991$	−1.95787	−	13.6173i	−0.0621936	−	0.432566i	0.934806	−	0.355159i	$-0.115573\pi$
$992$		0			0
$993$	8.37311	+	4.31664i	0.265713	+	0.136984i
$994$		0			0
$995$	−9.23574	−	12.9698i	−0.292793	−	0.411170i
$996$		0			0
$997$	43.5232	+	27.9706i	1.37839	+	0.885839i	0.999220	−	0.0394865i	$-0.0125722\pi$
$997$	43.5232	+	27.9706i	1.37839	+	0.885839i	0.379173	+	0.925326i	$0.376209\pi$
$998$		0			0
$999$	0.402900	−	0.384164i	0.0127472	−	0.0121544i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.y.b.793.6	yes	120
67.6	even	33	inner	804.2.y.b.73.6	✓	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.y.b.73.6	✓	120	67.6	even	33	inner
804.2.y.b.793.6	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)

\(f(q)\)	\(=\)	\(q+(-0.415415 - 0.909632i) q^{3} +(3.42078 - 1.00443i) q^{5} +(-0.977853 - 0.188466i) q^{7} +(-0.654861 + 0.755750i) q^{9} +O(q^{10})\)	\(q+(-0.415415 - 0.909632i) q^{3} +(3.42078 - 1.00443i) q^{5} +(-0.977853 - 0.188466i) q^{7} +(-0.654861 + 0.755750i) q^{9} +(-4.40572 - 4.20084i) q^{11} +(-0.140835 - 2.95649i) q^{13} +(-2.33471 - 2.69440i) q^{15} +(-0.551007 - 0.433317i) q^{17} +(1.63529 - 0.315176i) q^{19} +(0.234780 + 0.967778i) q^{21} +(-3.43676 - 0.328170i) q^{23} +(6.48659 - 4.16868i) q^{25} +(0.959493 + 0.281733i) q^{27} +(1.50438 + 2.60567i) q^{29} +(0.0616368 - 1.29392i) q^{31} +(-1.99102 + 5.75267i) q^{33} +(-3.53432 + 0.337487i) q^{35} +(0.278348 - 0.482112i) q^{37} +(-2.63081 + 1.35628i) q^{39} +(6.54034 - 2.61836i) q^{41} +(-0.813520 + 5.65815i) q^{43} +(-1.48104 + 3.24302i) q^{45} +(7.03506 - 9.87937i) q^{47} +(-5.57790 - 2.23305i) q^{49} +(-0.165262 + 0.681220i) q^{51} +(0.324604 + 2.25767i) q^{53} +(-19.2904 - 9.94491i) q^{55} +(-0.966018 - 1.35658i) q^{57} +(-2.23296 - 1.43503i) q^{59} +(-3.49530 + 3.33276i) q^{61} +(0.782790 - 0.615593i) q^{63} +(-3.45136 - 9.97204i) q^{65} +(7.01267 + 4.22167i) q^{67} +(1.12917 + 3.26251i) q^{69} +(-2.29320 + 1.80339i) q^{71} +(1.73724 - 1.65645i) q^{73} +(-6.48659 - 4.16868i) q^{75} +(3.51643 + 4.93813i) q^{77} +(-3.94110 - 2.03178i) q^{79} +(-0.142315 - 0.989821i) q^{81} +(3.45986 - 14.2617i) q^{83} +(-2.32011 - 0.928833i) q^{85} +(1.74526 - 2.45087i) q^{87} +(6.77689 - 14.8393i) q^{89} +(-0.419481 + 2.91755i) q^{91} +(-1.20259 + 0.481445i) q^{93} +(5.27739 - 2.72068i) q^{95} +(-0.358421 + 0.620803i) q^{97} +(6.05991 - 0.578652i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 12 q^{3} - 2 q^{5} + q^{7} - 12 q^{9}+O(q^{10}) \) 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

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