LMFDB - Embedded newform 804.2.o.d.365.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(365,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

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

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

chi := DirichletCharacter("804.365");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.o (of order $6$, degree $2$, 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:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			365.11
Character	$\chi$	$=$	804.365
Dual form			804.2.o.d.641.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.536215 + 1.64696i) q^{3} -1.65208 q^{5} +(-3.18562 - 1.83922i) q^{7} +(-2.42495 + 1.76625i) q^{9} +O(q^{10})$	\(q+(0.536215 + 1.64696i) q^{3} -1.65208 q^{5} +(-3.18562 - 1.83922i) q^{7} +(-2.42495 + 1.76625i) q^{9} +(-0.861717 + 1.49254i) q^{11} +(0.239916 - 0.138516i) q^{13} +(-0.885872 - 2.72092i) q^{15} +(6.56403 - 3.78975i) q^{17} +(-3.19312 - 5.53065i) q^{19} +(1.32094 - 6.23280i) q^{21} +(7.82260 - 4.51638i) q^{23} -2.27062 q^{25} +(-4.20923 - 3.04670i) q^{27} +(-3.47854 - 2.00833i) q^{29} +(-4.07196 - 2.35094i) q^{31} +(-2.92021 - 0.618892i) q^{33} +(5.26291 + 3.03854i) q^{35} +(-1.36012 - 2.35579i) q^{37} +(0.356776 + 0.320858i) q^{39} +(-4.35530 + 7.54360i) q^{41} -2.92808i q^{43} +(4.00622 - 2.91799i) q^{45} +(-2.08090 - 1.20141i) q^{47} +(3.26545 + 5.65593i) q^{49} +(9.76129 + 8.77857i) q^{51} -9.51065 q^{53} +(1.42363 - 2.46580i) q^{55} +(7.39655 - 8.22455i) q^{57} -6.73478i q^{59} +(2.73992 - 1.58189i) q^{61} +(10.9735 - 1.16658i) q^{63} +(-0.396361 + 0.228839i) q^{65} +(-8.08790 - 1.25932i) q^{67} +(11.6329 + 10.4618i) q^{69} +(6.76492 + 3.90573i) q^{71} +(7.08579 + 12.2730i) q^{73} +(-1.21754 - 3.73961i) q^{75} +(5.49020 - 3.16977i) q^{77} +(-11.0312 - 6.36886i) q^{79} +(2.76074 - 8.56611i) q^{81} +(-7.52188 + 4.34276i) q^{83} +(-10.8443 + 6.26098i) q^{85} +(1.44240 - 6.80591i) q^{87} +12.4314i q^{89} -1.01904 q^{91} +(1.68847 - 7.96696i) q^{93} +(5.27531 + 9.13710i) q^{95} +(-13.0777 + 7.55041i) q^{97} +(-0.546571 - 5.14133i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 4 q^{9}+O(q^{10}) $ 36 * q + 4 * q^9	$ 36 q + 4 q^{9} - 36 q^{13} + 18 q^{15} + 16 q^{21} + 76 q^{25} + 6 q^{31} + 4 q^{33} + 42 q^{37} - 21 q^{39} + 2 q^{49} + 18 q^{51} + 20 q^{55} + 18 q^{57} - 24 q^{61} - 12 q^{63} - 8 q^{67} + 3 q^{69} + 14 q^{73} + 72 q^{79} - 12 q^{81} - 18 q^{85} - 21 q^{87} - 68 q^{91} + 9 q^{93} - 48 q^{97} + 15 q^{99}+O(q^{100}) $ 36 * q + 4 * q^9 - 36 * q^13 + 18 * q^15 + 16 * q^21 + 76 * q^25 + 6 * q^31 + 4 * q^33 + 42 * q^37 - 21 * q^39 + 2 * q^49 + 18 * q^51 + 20 * q^55 + 18 * q^57 - 24 * q^61 - 12 * q^63 - 8 * q^67 + 3 * q^69 + 14 * q^73 + 72 * q^79 - 12 * q^81 - 18 * q^85 - 21 * q^87 - 68 * q^91 + 9 * q^93 - 48 * q^97 + 15 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$269$	$337$	$403$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

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
$3$	0.536215	+	1.64696i	0.309584	+	0.950872i
$3$	0.536215	+	1.64696i	0.309584	+	0.950872i
$4$		0			0
$5$	−1.65208			−0.738835			−0.369417	−	0.929264i	$-0.620443\pi$
$5$	−1.65208			−0.738835			−0.369417	+	0.929264i	$0.620443\pi$
$6$		0			0
$7$	−3.18562	−	1.83922i	−1.20405	−	0.695159i	−0.242598	−	0.970127i	$-0.578000\pi$
$7$	−3.18562	−	1.83922i	−1.20405	−	0.695159i	−0.961454	+	0.274968i	$0.911333\pi$
$8$		0			0
$9$	−2.42495	+	1.76625i	−0.808316	+	0.588749i
$10$		0			0
$11$	−0.861717	+	1.49254i	−0.259817	+	0.450017i	−0.966193	−	0.257820i	$-0.916996\pi$
$11$	−0.861717	+	1.49254i	−0.259817	+	0.450017i	0.706375	+	0.707837i	$0.250329\pi$
$12$		0			0
$13$	0.239916	−	0.138516i	0.0665407	−	0.0384173i	−0.466361	−	0.884595i	$-0.654435\pi$
$13$	0.239916	−	0.138516i	0.0665407	−	0.0384173i	0.532901	+	0.846177i	$0.321102\pi$
$14$		0			0
$15$	−0.885872	−	2.72092i	−0.228731	−	0.702537i
$16$		0			0
$17$	6.56403	−	3.78975i	1.59201	−	0.919148i	0.599050	−	0.800712i	$-0.295545\pi$
$17$	6.56403	−	3.78975i	1.59201	−	0.919148i	0.992962	−	0.118437i	$-0.0377882\pi$
$18$		0			0
$19$	−3.19312	−	5.53065i	−0.732552	−	1.26882i	−0.955789	−	0.294053i	$-0.904996\pi$
$19$	−3.19312	−	5.53065i	−0.732552	−	1.26882i	0.223237	−	0.974764i	$-0.428338\pi$
$20$		0			0
$21$	1.32094	−	6.23280i	0.288253	−	1.36011i
$22$		0			0
$23$	7.82260	−	4.51638i	1.63112	−	0.941730i	0.647378	−	0.762169i	$-0.275865\pi$
$23$	7.82260	−	4.51638i	1.63112	−	0.941730i	0.983747	−	0.179561i	$-0.0574679\pi$
$24$		0			0
$25$	−2.27062			−0.454123
$26$		0			0
$27$	−4.20923	−	3.04670i	−0.810066	−	0.586338i
$28$		0			0
$29$	−3.47854	−	2.00833i	−0.645948	−	0.372938i	0.140954	−	0.990016i	$-0.454983\pi$
$29$	−3.47854	−	2.00833i	−0.645948	−	0.372938i	−0.786902	+	0.617078i	$0.788316\pi$
$30$		0			0
$31$	−4.07196	−	2.35094i	−0.731345	−	0.422242i	0.0875691	−	0.996158i	$-0.472090\pi$
$31$	−4.07196	−	2.35094i	−0.731345	−	0.422242i	−0.818914	+	0.573916i	$0.805423\pi$
$32$		0			0
$33$	−2.92021	−	0.618892i	−0.508344	−	0.107735i
$34$		0			0
$35$	5.26291	+	3.03854i	0.889595	+	0.513608i
$36$		0			0
$37$	−1.36012	−	2.35579i	−0.223602	−	0.387290i	0.732297	−	0.680985i	$-0.238448\pi$
$37$	−1.36012	−	2.35579i	−0.223602	−	0.387290i	−0.955899	+	0.293695i	$0.905115\pi$
$38$		0			0
$39$	0.356776	+	0.320858i	0.0571299	+	0.0513783i
$40$		0			0
$41$	−4.35530	+	7.54360i	−0.680183	+	1.17811i	0.294742	+	0.955577i	$0.404766\pi$
$41$	−4.35530	+	7.54360i	−0.680183	+	1.17811i	−0.974925	+	0.222535i	$0.928567\pi$
$42$		0			0
$43$		−	2.92808i		−	0.446529i	−0.974758	−	0.223264i	$-0.928329\pi$
$43$		−	2.92808i		−	0.446529i	0.974758	−	0.223264i	$-0.0716713\pi$
$44$		0			0
$45$	4.00622	−	2.91799i	0.597212	−	0.434988i
$46$		0			0
$47$	−2.08090	−	1.20141i	−0.303530	−	0.175243i	0.340497	−	0.940245i	$-0.389405\pi$
$47$	−2.08090	−	1.20141i	−0.303530	−	0.175243i	−0.644028	+	0.765002i	$0.722738\pi$
$48$		0			0
$49$	3.26545	+	5.65593i	0.466493	+	0.807990i
$50$		0			0
$51$	9.76129	+	8.77857i	1.36685	+	1.22925i
$52$		0			0
$53$	−9.51065			−1.30639			−0.653194	−	0.757190i	$-0.726572\pi$
$53$	−9.51065			−1.30639			−0.653194	+	0.757190i	$0.726572\pi$
$54$		0			0
$55$	1.42363	−	2.46580i	0.191962	−	0.332488i
$56$		0			0
$57$	7.39655	−	8.22455i	0.979697	−	1.08937i
$58$		0			0
$59$		−	6.73478i		−	0.876794i	−0.898782	−	0.438397i	$-0.855546\pi$
$59$		−	6.73478i		−	0.876794i	0.898782	−	0.438397i	$-0.144454\pi$
$60$		0			0
$61$	2.73992	−	1.58189i	0.350810	−	0.202541i	−0.314232	−	0.949346i	$-0.601747\pi$
$61$	2.73992	−	1.58189i	0.350810	−	0.202541i	0.665042	+	0.746806i	$0.268414\pi$
$62$		0			0
$63$	10.9735	−	1.16658i	1.38253	−	0.146976i
$64$		0			0
$65$	−0.396361	+	0.228839i	−0.0491626	+	0.0283840i
$66$		0			0
$67$	−8.08790	−	1.25932i	−0.988094	−	0.153850i
$67$	−8.08790	−	1.25932i	−0.988094	−	0.153850i
$68$		0			0
$69$	11.6329	+	10.4618i	1.40043	+	1.25945i
$70$		0			0
$71$	6.76492	+	3.90573i	0.802848	+	0.463525i	0.844466	−	0.535609i	$-0.179918\pi$
$71$	6.76492	+	3.90573i	0.802848	+	0.463525i	−0.0416178	+	0.999134i	$0.513251\pi$
$72$		0			0
$73$	7.08579	+	12.2730i	0.829329	+	1.43644i	0.898565	+	0.438840i	$0.144611\pi$
$73$	7.08579	+	12.2730i	0.829329	+	1.43644i	−0.0692359	+	0.997600i	$0.522056\pi$
$74$		0			0
$75$	−1.21754	−	3.73961i	−0.140589	−	0.431813i
$76$		0			0
$77$	5.49020	−	3.16977i	0.625667	−	0.361229i
$78$		0			0
$79$	−11.0312	−	6.36886i	−1.24111	−	0.716553i	−0.271787	−	0.962358i	$-0.587614\pi$
$79$	−11.0312	−	6.36886i	−1.24111	−	0.716553i	−0.969319	+	0.245805i	$0.920948\pi$
$80$		0			0
$81$	2.76074	−	8.56611i	0.306749	−	0.951790i
$82$		0			0
$83$	−7.52188	+	4.34276i	−0.825634	+	0.476680i	−0.852355	−	0.522963i	$-0.824827\pi$
$83$	−7.52188	+	4.34276i	−0.825634	+	0.476680i	0.0267216	+	0.999643i	$0.491493\pi$
$84$		0			0
$85$	−10.8443	+	6.26098i	−1.17623	+	0.679099i
$86$		0			0
$87$	1.44240	−	6.80591i	0.154642	−	0.729670i
$88$		0			0
$89$			12.4314i			1.31773i	0.752262	+	0.658865i	$0.228963\pi$
$89$			12.4314i			1.31773i	−0.752262	+	0.658865i	$0.771037\pi$
$90$		0			0
$91$	−1.01904			−0.106825
$92$		0			0
$93$	1.68847	−	7.96696i	0.175086	−	0.826135i
$94$		0			0
$95$	5.27531	+	9.13710i	0.541235	+	0.937446i
$96$		0			0
$97$	−13.0777	+	7.55041i	−1.32784	+	0.766628i	−0.984965	−	0.172753i	$-0.944734\pi$
$97$	−13.0777	+	7.55041i	−1.32784	+	0.766628i	−0.342874	+	0.939381i	$0.611400\pi$
$98$		0			0
$99$	−0.546571	−	5.14133i	−0.0549325	−	0.516723i
$100$		0			0
$101$	4.04923	−	7.01348i	0.402914	−	0.697867i	−0.591162	−	0.806553i	$-0.701331\pi$
$101$	4.04923	−	7.01348i	0.402914	−	0.697867i	0.994076	+	0.108685i	$0.0346641\pi$
$102$		0			0
$103$	1.80829	−	3.13204i	0.178176	−	0.308609i	−0.763080	−	0.646304i	$-0.776314\pi$
$103$	1.80829	−	3.13204i	0.178176	−	0.308609i	0.941256	+	0.337695i	$0.109647\pi$
$104$		0			0
$105$	−2.18231	+	10.2971i	−0.212971	+	1.00490i
$106$		0			0
$107$		−	9.58691i		−	0.926802i	−0.886149	−	0.463401i	$-0.846629\pi$
$107$		−	9.58691i		−	0.926802i	0.886149	−	0.463401i	$-0.153371\pi$
$108$		0			0
$109$		−	10.6942i		−	1.02431i	−0.858892	−	0.512157i	$-0.828846\pi$
$109$		−	10.6942i		−	1.02431i	0.858892	−	0.512157i	$-0.171154\pi$
$110$		0			0
$111$	3.15058	−	3.50327i	0.299040	−	0.332515i
$112$		0			0
$113$	−1.65725	+	2.87043i	−0.155901	+	0.270028i	−0.933387	−	0.358873i	$-0.883161\pi$
$113$	−1.65725	+	2.87043i	−0.155901	+	0.270028i	0.777486	+	0.628900i	$0.216495\pi$
$114$		0			0
$115$	−12.9236	+	7.46144i	−1.20513	+	0.695783i
$116$		0			0
$117$	−0.337131	+	0.759644i	−0.0311678	+	0.0702291i
$118$		0			0
$119$	−27.8807			−2.55582
$120$		0			0
$121$	4.01489	+	6.95399i	0.364990	+	0.632181i
$122$		0			0
$123$	−14.7594	−	3.12801i	−1.33081	−	0.282043i
$124$		0			0
$125$	12.0117			1.07436
$126$		0			0
$127$	2.04424	−	3.54073i	0.181397	−	0.314189i	−0.760959	−	0.648799i	$-0.775271\pi$
$127$	2.04424	−	3.54073i	0.181397	−	0.314189i	0.942357	+	0.334611i	$0.108605\pi$
$128$		0			0
$129$	4.82243	−	1.57008i	0.424592	−	0.138238i
$130$		0			0
$131$		−	3.10676i		−	0.271439i	−0.990747	−	0.135719i	$-0.956665\pi$
$131$		−	3.10676i		−	0.271439i	0.990747	−	0.135719i	$-0.0433345\pi$
$132$		0			0
$133$			23.4914i			2.03696i
$134$		0			0
$135$	6.95400	+	5.03341i	0.598505	+	0.433207i
$136$		0			0
$137$	7.20766			0.615792			0.307896	−	0.951420i	$-0.400375\pi$
$137$	7.20766			0.615792			0.307896	+	0.951420i	$0.400375\pi$
$138$		0			0
$139$			9.29471i			0.788367i	0.919032	+	0.394184i	$0.128973\pi$
$139$			9.29471i			0.788367i	−0.919032	+	0.394184i	$0.871027\pi$
$140$		0			0
$141$	0.862861	−	4.07137i	0.0726660	−	0.342871i
$142$		0			0
$143$			0.477445i			0.0399259i
$144$		0			0
$145$	5.74684	+	3.31794i	0.477249	+	0.275540i
$146$		0			0
$147$	−7.56410	+	8.41086i	−0.623876	+	0.693716i
$148$		0			0
$149$		−	19.5086i		−	1.59820i	−0.601196	−	0.799102i	$-0.705309\pi$
$149$		−	19.5086i		−	1.59820i	0.601196	−	0.799102i	$-0.294691\pi$
$150$		0			0
$151$	5.02761	+	8.70807i	0.409141	+	0.708653i	0.994794	−	0.101909i	$-0.0324952\pi$
$151$	5.02761	+	8.70807i	0.409141	+	0.708653i	−0.585653	+	0.810562i	$0.699162\pi$
$152$		0			0
$153$	−9.22381	+	20.7836i	−0.745701	+	1.68026i
$154$		0			0
$155$	6.72722	+	3.88396i	0.540343	+	0.311967i
$156$		0			0
$157$	−5.14840	−	8.91729i	−0.410887	−	0.711677i	0.584100	−	0.811682i	$-0.301448\pi$
$157$	−5.14840	−	8.91729i	−0.410887	−	0.711677i	−0.994987	+	0.100005i	$0.968114\pi$
$158$		0			0
$159$	−5.09975	−	15.6637i	−0.404437	−	1.24221i
$160$		0			0
$161$	−33.2264			−2.61861
$162$		0			0
$163$	−0.884907	+	1.53270i	−0.0693112	+	0.120051i	−0.898598	−	0.438772i	$-0.855413\pi$
$163$	−0.884907	+	1.53270i	−0.0693112	+	0.120051i	0.829287	+	0.558823i	$0.188747\pi$
$164$		0			0
$165$	4.82444	+	1.02246i	0.375582	+	0.0795985i
$166$		0			0
$167$	−5.66482	−	3.27058i	−0.438357	−	0.253085i	0.264544	−	0.964374i	$-0.414779\pi$
$167$	−5.66482	−	3.27058i	−0.438357	−	0.253085i	−0.702900	+	0.711288i	$0.748112\pi$
$168$		0			0
$169$	−6.46163	+	11.1919i	−0.497048	+	0.860913i
$170$		0			0
$171$	17.5116	+	7.77169i	1.33915	+	0.594316i
$172$		0			0
$173$	18.2937	−	10.5618i	1.39084	−	0.803002i	0.397433	−	0.917631i	$-0.369901\pi$
$173$	18.2937	−	10.5618i	1.39084	−	0.803002i	0.993408	+	0.114629i	$0.0365679\pi$
$174$		0			0
$175$	7.23332	+	4.17616i	0.546788	+	0.315688i
$176$		0			0
$177$	11.0919	−	3.61129i	0.833719	−	0.271441i
$178$		0			0
$179$	−14.1593			−1.05832			−0.529159	−	0.848523i	$-0.677492\pi$
$179$	−14.1593			−1.05832			−0.529159	+	0.848523i	$0.677492\pi$
$180$		0			0
$181$	7.72125	−	13.3736i	0.573916	−	0.994052i	−0.422243	−	0.906483i	$-0.638757\pi$
$181$	7.72125	−	13.3736i	0.573916	−	0.994052i	0.996158	−	0.0875686i	$-0.0279097\pi$
$182$		0			0
$183$	4.07450	+	3.66430i	0.301195	+	0.270873i
$184$		0			0
$185$	2.24703	+	3.89197i	0.165205	+	0.286143i
$186$		0			0
$187$			13.0627i			0.955243i
$188$		0			0
$189$	7.80545	+	17.4473i	0.567763	+	1.26911i
$190$		0			0
$191$	4.05178	+	7.01788i	0.293176	+	0.507796i	0.974559	−	0.224131i	$-0.0719544\pi$
$191$	4.05178	+	7.01788i	0.293176	+	0.507796i	−0.681383	+	0.731927i	$0.738621\pi$
$192$		0			0
$193$	20.1187			1.44817			0.724087	−	0.689708i	$-0.242261\pi$
$193$	20.1187			1.44817			0.724087	+	0.689708i	$0.242261\pi$
$194$		0			0
$195$	−0.589424	−	0.530084i	−0.0422095	−	0.0379601i
$196$		0			0
$197$	−13.4713	+	23.3330i	−0.959791	+	1.66241i	−0.236790	+	0.971561i	$0.576095\pi$
$197$	−13.4713	+	23.3330i	−0.959791	+	1.66241i	−0.723001	+	0.690847i	$0.757238\pi$
$198$		0			0
$199$	−10.8780	−	18.8413i	−0.771124	−	1.33563i	−0.936947	−	0.349470i	$-0.886362\pi$
$199$	−10.8780	−	18.8413i	−0.771124	−	1.33563i	0.165824	−	0.986155i	$-0.446972\pi$
$200$		0			0
$201$	−2.26281	−	13.9957i	−0.159606	−	0.987181i
$202$		0			0
$203$	7.38753	+	12.7956i	0.518503	+	0.898074i
$204$		0			0
$205$	7.19532	−	12.4627i	0.502543	−	0.870430i
$206$		0			0
$207$	−10.9924	+	24.7686i	−0.764021	+	1.72154i
$208$		0			0
$209$	11.0063			0.761319
$210$		0			0
$211$	−1.94863	−	3.37513i	−0.134149	−	0.232354i	0.791123	−	0.611657i	$-0.209497\pi$
$211$	−1.94863	−	3.37513i	−0.134149	−	0.232354i	−0.925272	+	0.379304i	$0.876164\pi$
$212$		0			0
$213$	−2.80513	+	13.2359i	−0.192204	+	0.906906i
$214$		0			0
$215$			4.83744i			0.329911i
$216$		0			0
$217$	8.64780	+	14.9784i	0.587051	+	1.01680i
$218$		0			0
$219$	−16.4135	+	18.2509i	−1.10912	+	1.23328i
$220$		0			0
$221$	1.04988	−	1.81844i	0.0706224	−	0.122322i
$222$		0			0
$223$	−11.5147			−0.771083			−0.385541	−	0.922691i	$-0.625985\pi$
$223$	−11.5147			−0.771083			−0.385541	+	0.922691i	$0.625985\pi$
$224$		0			0
$225$	5.50613	−	4.01047i	0.367075	−	0.267365i
$226$		0			0
$227$	−11.4318	−	6.60014i	−0.758754	−	0.438067i	0.0700941	−	0.997540i	$-0.477670\pi$
$227$	−11.4318	−	6.60014i	−0.758754	−	0.438067i	−0.828848	+	0.559473i	$0.811003\pi$
$228$		0			0
$229$	−0.555963	+	0.320985i	−0.0367391	+	0.0212113i	−0.518257	−	0.855225i	$-0.673419\pi$
$229$	−0.555963	+	0.320985i	−0.0367391	+	0.0212113i	0.481518	+	0.876436i	$0.340086\pi$
$230$		0			0
$231$	8.16441	+	7.34246i	0.537179	+	0.483099i
$232$		0			0
$233$	5.24469	−	9.08408i	0.343591	−	0.595118i	−0.641506	−	0.767118i	$-0.721690\pi$
$233$	5.24469	−	9.08408i	0.343591	−	0.595118i	0.985097	+	0.172001i	$0.0550232\pi$
$234$		0			0
$235$	3.43782	+	1.98483i	0.224259	+	0.129476i
$236$		0			0
$237$	4.57417	−	21.5830i	0.297124	−	1.40197i
$238$		0			0
$239$	10.6004	−	18.3604i	0.685682	−	1.18764i	−0.287540	−	0.957769i	$-0.592837\pi$
$239$	10.6004	−	18.3604i	0.685682	−	1.18764i	0.973222	−	0.229868i	$-0.0738293\pi$
$240$		0			0
$241$	−5.87856			−0.378671			−0.189336	−	0.981912i	$-0.560633\pi$
$241$	−5.87856			−0.378671			−0.189336	+	0.981912i	$0.560633\pi$
$242$		0			0
$243$	15.5884	−	0.0464460i	0.999996	−	0.00297951i
$244$		0			0
$245$	−5.39480	−	9.34407i	−0.344661	−	0.596971i
$246$		0			0
$247$	−1.53216	−	0.884594i	−0.0974891	−	0.0562853i
$248$		0			0
$249$	−11.1857	−	10.0596i	−0.708864	−	0.637500i
$250$		0			0
$251$	−6.05644	−	10.4901i	−0.382279	−	0.662127i	0.609108	−	0.793087i	$-0.291527\pi$
$251$	−6.05644	−	10.4901i	−0.382279	−	0.662127i	−0.991388	+	0.130960i	$0.958194\pi$
$252$		0			0
$253$			15.5674i			0.978712i
$254$		0			0
$255$	−16.1265	−	14.5029i	−1.00988	−	0.908210i
$256$		0			0
$257$	19.0378	+	10.9915i	1.18754	+	0.685629i	0.957748	−	0.287609i	$-0.0928604\pi$
$257$	19.0378	+	10.9915i	1.18754	+	0.685629i	0.229797	+	0.973239i	$0.426194\pi$
$258$		0			0
$259$			10.0062i			0.621756i
$260$		0			0
$261$	11.9825	−	1.27385i	0.741697	−	0.0788494i
$262$		0			0
$263$			23.1508i			1.42754i	0.700380	+	0.713770i	$0.253014\pi$
$263$			23.1508i			1.42754i	−0.700380	+	0.713770i	$0.746986\pi$
$264$		0			0
$265$	15.7124			0.965205
$266$		0			0
$267$	−20.4741	+	6.66592i	−1.25299	+	0.407947i
$268$		0			0
$269$			9.05672i			0.552198i	0.961129	+	0.276099i	$0.0890418\pi$
$269$			9.05672i			0.552198i	−0.961129	+	0.276099i	$0.910958\pi$
$270$		0			0
$271$		−	0.626122i		−	0.0380342i	−0.999819	−	0.0190171i	$-0.993946\pi$
$271$		−	0.626122i		−	0.0380342i	0.999819	−	0.0190171i	$-0.00605370\pi$
$272$		0			0
$273$	−0.546425	−	1.67832i	−0.0330711	−	0.101577i
$274$		0			0
$275$	1.95663	−	3.38898i	0.117989	−	0.204363i
$276$		0			0
$277$	−12.9933			−0.780690			−0.390345	−	0.920669i	$-0.627644\pi$
$277$	−12.9933			−0.780690			−0.390345	+	0.920669i	$0.627644\pi$
$278$		0			0
$279$	14.0266	−	1.49116i	0.839752	−	0.0892735i
$280$		0			0
$281$	6.57008	+	11.3797i	0.391938	+	0.678857i	0.992705	−	0.120567i	$-0.0384713\pi$
$281$	6.57008	+	11.3797i	0.391938	+	0.678857i	−0.600767	+	0.799424i	$0.705138\pi$
$282$		0			0
$283$	−14.0197			−0.833382			−0.416691	−	0.909048i	$-0.636810\pi$
$283$	−14.0197			−0.833382			−0.416691	+	0.909048i	$0.636810\pi$
$284$		0			0
$285$	−12.2197	+	13.5877i	−0.723834	+	0.804863i
$286$		0			0
$287$	27.7486	−	16.0207i	1.63795	−	0.945671i
$288$		0			0
$289$	20.2243	−	35.0296i	1.18967	−	2.06056i
$290$		0			0
$291$	−19.4477	−	17.4898i	−1.14004	−	1.02527i
$292$		0			0
$293$			27.8026i			1.62424i	0.583488	+	0.812122i	$0.301688\pi$
$293$			27.8026i			1.62424i	−0.583488	+	0.812122i	$0.698312\pi$
$294$		0			0
$295$			11.1264i			0.647806i
$296$		0			0
$297$	8.17448	−	3.65704i	0.474331	−	0.212203i
$298$		0			0
$299$	1.25118	−	2.16710i	0.0723575	−	0.125327i
$300$		0			0
$301$	−5.38539	+	9.32776i	−0.310409	+	0.537643i
$302$		0			0
$303$	13.7222	+	2.90819i	0.788318	+	0.167071i
$304$		0			0
$305$	−4.52657	+	2.61342i	−0.259191	+	0.149644i
$306$		0			0
$307$	3.41808	+	5.92028i	0.195080	+	0.337888i	0.946927	−	0.321449i	$-0.104170\pi$
$307$	3.41808	+	5.92028i	0.195080	+	0.337888i	−0.751847	+	0.659338i	$0.770837\pi$
$308$		0			0
$309$	6.12798	+	1.29873i	0.348608	+	0.0738819i
$310$		0			0
$311$	4.48268			0.254190			0.127095	−	0.991891i	$-0.459435\pi$
$311$	4.48268			0.254190			0.127095	+	0.991891i	$0.459435\pi$
$312$		0			0
$313$		−	11.8875i		−	0.671920i	−0.941876	−	0.335960i	$-0.890939\pi$
$313$		−	11.8875i		−	0.671920i	0.941876	−	0.335960i	$-0.109061\pi$
$314$		0			0
$315$	−18.1291	+	1.92729i	−1.02146	+	0.108591i
$316$		0			0
$317$	−4.55822	+	2.63169i	−0.256015	+	0.147811i	−0.622516	−	0.782607i	$-0.713889\pi$
$317$	−4.55822	+	2.63169i	−0.256015	+	0.147811i	0.366500	+	0.930418i	$0.380556\pi$
$318$		0			0
$319$	5.99503	−	3.46123i	0.335657	−	0.193792i
$320$		0			0
$321$	15.7892	−	5.14064i	0.881270	−	0.286923i
$322$		0			0
$323$	−41.9195	−	24.2022i	−2.33246	−	1.34665i
$324$		0			0
$325$	−0.544757	+	0.314516i	−0.0302177	+	0.0174462i
$326$		0			0
$327$	17.6128	−	5.73437i	0.973993	−	0.317111i
$328$		0			0
$329$	4.41930	+	7.65446i	0.243644	+	0.422004i
$330$		0			0
$331$	8.77361	+	5.06544i	0.482241	+	0.278422i	0.721350	−	0.692571i	$-0.243522\pi$
$331$	8.77361	+	5.06544i	0.482241	+	0.278422i	−0.239109	+	0.970993i	$0.576855\pi$
$332$		0			0
$333$	7.45912	+	3.31037i	0.408757	+	0.181407i
$334$		0			0
$335$	13.3619	+	2.08050i	0.730038	+	0.113670i
$336$		0			0
$337$	13.5429	−	7.81900i	0.737729	−	0.425928i	−0.0835142	−	0.996507i	$-0.526614\pi$
$337$	13.5429	−	7.81900i	0.737729	−	0.425928i	0.821243	+	0.570579i	$0.193281\pi$
$338$		0			0
$339$	−5.61612	−	1.19025i	−0.305026	−	0.0646453i
$340$		0			0
$341$	7.01774	−	4.05170i	0.380032	−	0.219412i
$342$		0			0
$343$			1.72554i			0.0931703i
$344$		0			0
$345$	−19.2185	−	17.2837i	−1.03469	−	0.930523i
$346$		0			0
$347$	−2.66586	+	4.61741i	−0.143111	+	0.247876i	−0.928667	−	0.370916i	$-0.879044\pi$
$347$	−2.66586	+	4.61741i	−0.143111	+	0.247876i	0.785556	+	0.618791i	$0.212377\pi$
$348$		0			0
$349$	−15.5378			−0.831721			−0.415861	−	0.909428i	$-0.636520\pi$
$349$	−15.5378			−0.831721			−0.415861	+	0.909428i	$0.636520\pi$
$350$		0			0
$351$	−1.43188	−	0.147909i	−0.0764279	−	0.00789478i
$352$		0			0
$353$	−11.9775	−	20.7457i	−0.637500	−	1.10418i	−0.985980	−	0.166866i	$-0.946635\pi$
$353$	−11.9775	−	20.7457i	−0.637500	−	1.10418i	0.348479	−	0.937316i	$-0.386698\pi$
$354$		0			0
$355$	−11.1762	−	6.45259i	−0.593172	−	0.342468i
$356$		0			0
$357$	−14.9500	−	45.9183i	−0.791240	−	2.43026i
$358$		0			0
$359$		−	21.9468i		−	1.15831i	−0.815219	−	0.579153i	$-0.803384\pi$
$359$		−	21.9468i		−	1.15831i	0.815219	−	0.579153i	$-0.196616\pi$
$360$		0			0
$361$	−10.8920	+	18.8656i	−0.573266	+	0.992925i
$362$		0			0
$363$	−9.30010	+	10.3412i	−0.488128	+	0.542772i
$364$		0			0
$365$	−11.7063	−	20.2760i	−0.612737	−	1.06129i
$366$		0			0
$367$	−27.9925	−	16.1615i	−1.46119	−	0.843621i	−0.462127	−	0.886814i	$-0.652914\pi$
$367$	−27.9925	−	16.1615i	−1.46119	−	0.843621i	−0.999067	+	0.0431927i	$0.986247\pi$
$368$		0			0
$369$	−2.76249	−	25.9854i	−0.143809	−	1.35274i
$370$		0			0
$371$	30.2973	+	17.4922i	1.57296	+	0.908148i
$372$		0			0
$373$	16.7648	+	9.67916i	0.868048	+	0.501168i	0.866699	−	0.498831i	$-0.166237\pi$
$373$	16.7648	+	9.67916i	0.868048	+	0.501168i	0.00134882	+	0.999999i	$0.499571\pi$
$374$		0			0
$375$	6.44084	+	19.7827i	0.332603	+	1.02158i
$376$		0			0
$377$	−1.11274			−0.0573091
$378$		0			0
$379$	28.2818	−	16.3285i	1.45274	−	0.838739i	0.454103	−	0.890949i	$-0.349960\pi$
$379$	28.2818	−	16.3285i	1.45274	−	0.838739i	0.998636	+	0.0522096i	$0.0166264\pi$
$380$		0			0
$381$	6.92759	+	1.46819i	0.354911	+	0.0752176i
$382$		0			0
$383$	−9.03393	−	15.6472i	−0.461612	−	0.799536i	0.537429	−	0.843309i	$-0.319396\pi$
$383$	−9.03393	−	15.6472i	−0.461612	−	0.799536i	−0.999042	+	0.0437729i	$0.986062\pi$
$384$		0			0
$385$	−9.07028	+	5.23673i	−0.462264	+	0.266888i
$386$		0			0
$387$	5.17172	+	7.10045i	0.262893	+	0.360936i
$388$		0			0
$389$	6.14905	−	3.55015i	0.311769	−	0.180000i	−0.335949	−	0.941880i	$-0.609057\pi$
$389$	6.14905	−	3.55015i	0.311769	−	0.180000i	0.647718	+	0.761880i	$0.275724\pi$
$390$		0			0
$391$	34.2319	−	59.2913i	1.73118	−	2.99849i
$392$		0			0
$393$	5.11670	−	1.66589i	0.258103	−	0.0840329i
$394$		0			0
$395$	18.2245	+	10.5219i	0.916972	+	0.529414i
$396$		0			0
$397$	−29.7060			−1.49090			−0.745451	−	0.666561i	$-0.767766\pi$
$397$	−29.7060			−1.49090			−0.745451	+	0.666561i	$0.767766\pi$
$398$		0			0
$399$	−38.6894	+	12.5964i	−1.93689	+	0.630610i
$400$		0			0
$401$	0.619450			0.0309339			0.0154669	−	0.999880i	$-0.495077\pi$
$401$	0.619450			0.0309339			0.0154669	+	0.999880i	$0.495077\pi$
$402$		0			0
$403$	−1.30257			−0.0648856
$404$		0			0
$405$	−4.56098	+	14.1519i	−0.226637	+	0.703216i
$406$		0			0
$407$	4.68814			0.232383
$408$		0			0
$409$	−9.15497	−	5.28563i	−0.452684	−	0.261357i	0.256279	−	0.966603i	$-0.417503\pi$
$409$	−9.15497	−	5.28563i	−0.452684	−	0.261357i	−0.708963	+	0.705245i	$0.750837\pi$
$410$		0			0
$411$	3.86485	+	11.8707i	0.190639	+	0.585540i
$412$		0			0
$413$	−12.3867	+	21.4545i	−0.609511	+	1.05570i
$414$		0			0
$415$	12.4268	−	7.17461i	0.610007	−	0.352188i
$416$		0			0
$417$	−15.3080	+	4.98396i	−0.749636	+	0.244066i
$418$		0			0
$419$	7.00038	−	4.04167i	0.341991	−	0.197449i	−0.319161	−	0.947700i	$-0.603401\pi$
$419$	7.00038	−	4.04167i	0.341991	−	0.197449i	0.661152	+	0.750252i	$0.270068\pi$
$420$		0			0
$421$	−6.75824	−	11.7056i	−0.329377	−	0.570497i	0.653012	−	0.757348i	$-0.273505\pi$
$421$	−6.75824	−	11.7056i	−0.329377	−	0.570497i	−0.982388	+	0.186851i	$0.940172\pi$
$422$		0			0
$423$	7.16806	−	0.762031i	0.348523	−	0.0370512i
$424$		0			0
$425$	−14.9044	+	8.60506i	−0.722970	+	0.417407i
$426$		0			0
$427$	−11.6378			−0.563192
$428$		0			0
$429$	−0.786332	+	0.256013i	−0.0379644	+	0.0123604i
$430$		0			0
$431$	12.5172	+	7.22680i	0.602931	+	0.348103i	0.770194	−	0.637810i	$-0.220159\pi$
$431$	12.5172	+	7.22680i	0.602931	+	0.348103i	−0.167263	+	0.985912i	$0.553493\pi$
$432$		0			0
$433$	−26.7826	−	15.4630i	−1.28709	−	0.743102i	−0.308956	−	0.951076i	$-0.599980\pi$
$433$	−26.7826	−	15.4630i	−1.28709	−	0.743102i	−0.978134	+	0.207974i	$0.933313\pi$
$434$		0			0
$435$	−2.38297	+	11.2439i	−0.114255	+	0.539105i
$436$		0			0
$437$	−49.9570	−	28.8427i	−2.38977	−	1.37973i
$438$		0			0
$439$	12.8295	+	22.2213i	0.612317	+	1.06056i	0.990849	+	0.134976i	$0.0430958\pi$
$439$	12.8295	+	22.2213i	0.612317	+	1.06056i	−0.378532	+	0.925588i	$0.623571\pi$
$440$		0			0
$441$	−17.9083	−	7.94774i	−0.852777	−	0.378464i
$442$		0			0
$443$	−6.77359	+	11.7322i	−0.321823	+	0.557414i	−0.980864	−	0.194693i	$-0.937629\pi$
$443$	−6.77359	+	11.7322i	−0.321823	+	0.557414i	0.659041	+	0.752107i	$0.270962\pi$
$444$		0			0
$445$		−	20.5378i		−	0.973584i
$446$		0			0
$447$	32.1298	−	10.4608i	1.51969	−	0.494778i
$448$		0			0
$449$	3.69861	+	2.13540i	0.174548	+	0.100776i	0.584729	−	0.811229i	$-0.301201\pi$
$449$	3.69861	+	2.13540i	0.174548	+	0.100776i	−0.410180	+	0.912004i	$0.634534\pi$
$450$		0			0
$451$	−7.50606	−	13.0009i	−0.353447	−	0.612188i
$452$		0			0
$453$	−11.6460	+	12.9497i	−0.547175	+	0.608428i
$454$		0			0
$455$	1.68354			0.0789257
$456$		0			0
$457$	−6.53507	+	11.3191i	−0.305698	+	0.529484i	−0.977416	−	0.211322i	$-0.932223\pi$
$457$	−6.53507	+	11.3191i	−0.305698	+	0.529484i	0.671719	+	0.740806i	$0.265556\pi$
$458$		0			0
$459$	−39.1757	−	4.04674i	−1.82857	−	0.188886i
$460$		0			0
$461$			3.45300i			0.160822i	0.996762	+	0.0804111i	$0.0256233\pi$
$461$			3.45300i			0.160822i	−0.996762	+	0.0804111i	$0.974377\pi$
$462$		0			0
$463$	26.1920	−	15.1220i	1.21725	−	0.702778i	0.252919	−	0.967487i	$-0.418609\pi$
$463$	26.1920	−	15.1220i	1.21725	−	0.702778i	0.964328	+	0.264709i	$0.0852760\pi$
$464$		0			0
$465$	−2.78949	+	13.1621i	−0.129360	+	0.610377i
$466$		0			0
$467$	16.5116	−	9.53295i	0.764064	−	0.441132i	−0.0666893	−	0.997774i	$-0.521244\pi$
$467$	16.5116	−	9.53295i	0.764064	−	0.441132i	0.830753	+	0.556641i	$0.187910\pi$
$468$		0			0
$469$	23.4488	+	18.8871i	1.08277	+	0.872126i
$470$		0			0
$471$	11.9258	−	13.2608i	0.549510	−	0.611024i
$472$		0			0
$473$	4.37027	+	2.52318i	0.200945	+	0.116016i
$474$		0			0
$475$	7.25036	+	12.5580i	0.332669	+	0.576200i
$476$		0			0
$477$	23.0628	−	16.7982i	1.05597	−	0.769135i
$478$		0			0
$479$	−6.54319	+	3.77771i	−0.298966	+	0.172608i	−0.641978	−	0.766723i	$-0.721886\pi$
$479$	−6.54319	+	3.77771i	−0.298966	+	0.172608i	0.343012	+	0.939331i	$0.388553\pi$
$480$		0			0
$481$	−0.652628	−	0.376795i	−0.0297573	−	0.0171804i
$482$		0			0
$483$	−17.8165	−	54.7226i	−0.810679	−	2.48996i
$484$		0			0
$485$	21.6055	−	12.4739i	0.981053	−	0.566411i
$486$		0			0
$487$	2.20825	−	1.27493i	0.100065	−	0.0577727i	−0.449132	−	0.893465i	$-0.648267\pi$
$487$	2.20825	−	1.27493i	0.100065	−	0.0577727i	0.549198	+	0.835693i	$0.314933\pi$
$488$		0			0
$489$	−2.99880	−	0.635547i	−0.135610	−	0.0287404i
$490$		0			0
$491$		−	5.12983i		−	0.231506i	−0.993278	−	0.115753i	$-0.963072\pi$
$491$		−	5.12983i		−	0.231506i	0.993278	−	0.115753i	$-0.0369281\pi$
$492$		0			0
$493$	−30.4443			−1.37114
$494$		0			0
$495$	0.902982	+	8.49391i	0.0405860	+	0.381773i
$496$		0			0
$497$	−14.3670	−	24.8843i	−0.644447	−	1.11622i
$498$		0			0
$499$	37.1348	−	21.4398i	1.66238	−	0.959777i	0.690809	−	0.723037i	$-0.257255\pi$
$499$	37.1348	−	21.4398i	1.66238	−	0.959777i	0.971573	−	0.236739i	$-0.0760788\pi$
$500$		0			0
$501$	2.34896	−	11.0835i	0.104944	−	0.495172i
$502$		0			0
$503$	−9.21628	+	15.9631i	−0.410934	+	0.711758i	−0.994992	−	0.0999536i	$-0.968131\pi$
$503$	−9.21628	+	15.9631i	−0.410934	+	0.711758i	0.584058	+	0.811712i	$0.301464\pi$
$504$		0			0
$505$	−6.68968	+	11.5869i	−0.297687	+	0.515609i
$506$		0			0
$507$	−21.8974	−	4.64079i	−0.972496	−	0.206105i
$508$		0			0
$509$			10.5894i			0.469366i	0.972072	+	0.234683i	$0.0754053\pi$
$509$			10.5894i			0.469366i	−0.972072	+	0.234683i	$0.924595\pi$
$510$		0			0
$511$		−	52.1293i		−	2.30606i
$512$		0			0
$513$	−3.40966	+	33.0083i	−0.150540	+	1.45735i
$514$		0			0
$515$	−2.98744	+	5.17440i	−0.131642	+	0.228011i
$516$		0			0
$517$	3.58629	−	2.07055i	0.157725	−	0.0910625i
$518$		0			0
$519$	27.2043	+	24.4655i	1.19413	+	1.07392i
$520$		0			0
$521$	19.6656			0.861567			0.430784	−	0.902455i	$-0.358237\pi$
$521$	19.6656			0.861567			0.430784	+	0.902455i	$0.358237\pi$
$522$		0			0
$523$	4.35379	+	7.54099i	0.190378	+	0.329745i	0.945376	−	0.325983i	$-0.105695\pi$
$523$	4.35379	+	7.54099i	0.190378	+	0.329745i	−0.754997	+	0.655728i	$0.772362\pi$
$524$		0			0
$525$	−2.99935	+	14.1523i	−0.130902	+	0.617657i
$526$		0			0
$527$	−35.6379			−1.55241
$528$		0			0
$529$	29.2954	−	50.7411i	1.27371	−	2.20613i
$530$		0			0
$531$	11.8953	+	16.3315i	0.516211	+	0.708726i
$532$		0			0
$533$			2.41311i			0.104523i
$534$		0			0
$535$			15.8384i			0.684753i
$536$		0			0
$537$	−7.59244	−	23.3198i	−0.327638	−	1.00632i
$538$		0			0
$539$	−11.2556			−0.484812
$540$		0			0
$541$		−	8.93248i		−	0.384037i	−0.981391	−	0.192019i	$-0.938497\pi$
$541$		−	8.93248i		−	0.384037i	0.981391	−	0.192019i	$-0.0615034\pi$
$542$		0			0
$543$	26.1660	+	5.54546i	1.12289	+	0.237979i
$544$		0			0
$545$			17.6677i			0.756799i
$546$		0			0
$547$	14.9433	+	8.62754i	0.638931	+	0.368887i	0.784203	−	0.620505i	$-0.213072\pi$
$547$	14.9433	+	8.62754i	0.638931	+	0.368887i	−0.145271	+	0.989392i	$0.546406\pi$
$548$		0			0
$549$	−3.85014	+	8.67538i	−0.164320	+	0.370256i
$550$		0			0
$551$			25.6514i			1.09279i
$552$		0			0
$553$	23.4275	+	40.5775i	0.996237	+	1.72553i
$554$		0			0
$555$	−5.20502	+	5.78769i	−0.220941	+	0.245674i
$556$		0			0
$557$	38.0246	+	21.9535i	1.61115	+	0.930200i	0.989103	+	0.147224i	$0.0470337\pi$
$557$	38.0246	+	21.9535i	1.61115	+	0.930200i	0.622051	+	0.782977i	$0.286300\pi$
$558$		0			0
$559$	−0.405585	−	0.702494i	−0.0171544	−	0.0297123i
$560$		0			0
$561$	−21.5138	+	7.00444i	−0.908314	+	0.295728i
$562$		0			0
$563$	18.8144			0.792933			0.396466	−	0.918049i	$-0.370236\pi$
$563$	18.8144			0.792933			0.396466	+	0.918049i	$0.370236\pi$
$564$		0			0
$565$	2.73791	−	4.74220i	0.115185	−	0.199506i
$566$		0			0
$567$	−24.5496	+	22.2108i	−1.03099	+	0.932765i
$568$		0			0
$569$	21.5083	+	12.4178i	0.901676	+	0.520583i	0.877744	−	0.479131i	$-0.159048\pi$
$569$	21.5083	+	12.4178i	0.901676	+	0.520583i	0.0239324	+	0.999714i	$0.492381\pi$
$570$		0			0
$571$	5.10033	−	8.83403i	0.213442	−	0.369693i	−0.739347	−	0.673324i	$-0.764866\pi$
$571$	5.10033	−	8.83403i	0.213442	−	0.369693i	0.952790	+	0.303631i	$0.0981991\pi$
$572$		0			0
$573$	−9.38554	+	10.4362i	−0.392087	+	0.435978i
$574$		0			0
$575$	−17.7621	+	10.2550i	−0.740732	+	0.427662i
$576$		0			0
$577$	22.5804	+	13.0368i	0.940035	+	0.542729i	0.889971	−	0.456017i	$-0.150724\pi$
$577$	22.5804	+	13.0368i	0.940035	+	0.542729i	0.0500635	+	0.998746i	$0.484058\pi$
$578$		0			0
$579$	10.7879	+	33.1346i	0.448331	+	1.37703i
$580$		0			0
$581$	31.9491			1.32547
$582$		0			0
$583$	8.19549	−	14.1950i	0.339422	−	0.587897i
$584$		0			0
$585$	0.556969	−	1.25500i	0.0230278	−	0.0518877i
$586$		0			0
$587$	−13.3544	−	23.1304i	−0.551194	−	0.954696i	−0.998189	−	0.0601593i	$-0.980839\pi$
$587$	−13.3544	−	23.1304i	−0.551194	−	0.954696i	0.446995	−	0.894537i	$-0.352494\pi$
$588$		0			0
$589$			30.0274i			1.23726i
$590$		0			0
$591$	−45.6520	−	9.67520i	−1.87787	−	0.397985i
$592$		0			0
$593$	−9.71985	−	16.8353i	−0.399147	−	0.691342i	0.594474	−	0.804115i	$-0.297360\pi$
$593$	−9.71985	−	16.8353i	−0.399147	−	0.691342i	−0.993621	+	0.112773i	$0.964027\pi$
$594$		0			0
$595$	46.0612			1.88833
$596$		0			0
$597$	25.1979	−	28.0187i	1.03128	−	1.14673i
$598$		0			0
$599$	−13.9455	+	24.1543i	−0.569797	+	0.986918i	0.426788	+	0.904352i	$0.359645\pi$
$599$	−13.9455	+	24.1543i	−0.569797	+	0.986918i	−0.996586	+	0.0825663i	$0.973688\pi$
$600$		0			0
$601$	−13.0041	−	22.5237i	−0.530447	−	0.918761i	−0.999369	−	0.0355217i	$-0.988691\pi$
$601$	−13.0041	−	22.5237i	−0.530447	−	0.918761i	0.468922	−	0.883240i	$-0.344643\pi$
$602$		0			0
$603$	21.8370	−	11.2315i	0.889271	−	0.457380i
$604$		0			0
$605$	−6.63294	−	11.4886i	−0.269667	−	0.467077i
$606$		0			0
$607$	11.2787	−	19.5354i	0.457790	−	0.792916i	−0.541054	−	0.840988i	$-0.681974\pi$
$607$	11.2787	−	19.5354i	0.457790	−	0.792916i	0.998844	+	0.0480722i	$0.0153078\pi$
$608$		0			0
$609$	−17.1125	+	19.0281i	−0.693433	+	0.771059i
$610$		0			0
$611$	−0.665655			−0.0269295
$612$		0			0
$613$	15.7477	+	27.2758i	0.636042	+	1.10166i	0.986293	+	0.165002i	$0.0527630\pi$
$613$	15.7477	+	27.2758i	0.636042	+	1.10166i	−0.350251	+	0.936656i	$0.613904\pi$
$614$		0			0
$615$	24.3837	+	5.16773i	0.983246	+	0.208383i
$616$		0			0
$617$			7.14407i			0.287610i	0.989606	+	0.143805i	$0.0459337\pi$
$617$			7.14407i			0.287610i	−0.989606	+	0.143805i	$0.954066\pi$
$618$		0			0
$619$	−0.850071	−	1.47237i	−0.0341672	−	0.0591794i	0.848436	−	0.529298i	$-0.177545\pi$
$619$	−0.850071	−	1.47237i	−0.0341672	−	0.0591794i	−0.882603	+	0.470118i	$0.844211\pi$
$620$		0			0
$621$	−46.6872	−	4.82265i	−1.87349	−	0.193526i
$622$		0			0
$623$	22.8641	−	39.6018i	0.916032	−	1.58661i
$624$		0			0
$625$	−8.49121			−0.339649
$626$		0			0
$627$	5.90172	+	18.1269i	0.235692	+	0.723917i
$628$		0			0
$629$	−17.8557	−	10.3090i	−0.711954	−	0.411047i
$630$		0			0
$631$	9.37041	−	5.41001i	0.373030	−	0.215369i	−0.301751	−	0.953387i	$-0.597571\pi$
$631$	9.37041	−	5.41001i	0.373030	−	0.215369i	0.674781	+	0.738018i	$0.264238\pi$
$632$		0			0
$633$	4.51382	−	5.01911i	0.179408	−	0.199492i
$634$		0			0
$635$	−3.37726	+	5.84958i	−0.134022	+	0.232134i
$636$		0			0
$637$	1.56687	+	0.904632i	0.0620816	+	0.0358428i
$638$		0			0
$639$	−23.3031	+	2.47733i	−0.921855	+	0.0980018i
$640$		0			0
$641$	22.8666	−	39.6061i	0.903175	−	1.56435i	0.0798268	−	0.996809i	$-0.474563\pi$
$641$	22.8666	−	39.6061i	0.903175	−	1.56435i	0.823348	−	0.567536i	$-0.192103\pi$
$642$		0			0
$643$	−21.0011			−0.828201			−0.414101	−	0.910231i	$-0.635904\pi$
$643$	−21.0011			−0.828201			−0.414101	+	0.910231i	$0.635904\pi$
$644$		0			0
$645$	−7.96707	+	2.59391i	−0.313703	+	0.102135i
$646$		0			0
$647$	19.2291	+	33.3058i	0.755975	+	1.30939i	0.944888	+	0.327393i	$0.106170\pi$
$647$	19.2291	+	33.3058i	0.755975	+	1.30939i	−0.188914	+	0.981994i	$0.560497\pi$
$648$		0			0
$649$	10.0519	+	5.80347i	0.394572	+	0.227806i
$650$		0			0
$651$	−20.0318	+	22.2742i	−0.785108	+	0.872996i
$652$		0			0
$653$	−5.64033	−	9.76933i	−0.220723	−	0.382303i	0.734305	−	0.678820i	$-0.237508\pi$
$653$	−5.64033	−	9.76933i	−0.220723	−	0.382303i	−0.955028	+	0.296517i	$0.904175\pi$
$654$		0			0
$655$			5.13262i			0.200548i
$656$		0			0
$657$	−38.8597	−	17.2460i	−1.51606	−	0.672831i
$658$		0			0
$659$	28.2943	+	16.3357i	1.10219	+	0.636350i	0.936795	−	0.349878i	$-0.113777\pi$
$659$	28.2943	+	16.3357i	1.10219	+	0.636350i	0.165395	+	0.986227i	$0.447110\pi$
$660$		0			0
$661$		−	23.3462i		−	0.908062i	−0.890986	−	0.454031i	$-0.849986\pi$
$661$		−	23.3462i		−	0.908062i	0.890986	−	0.454031i	$-0.150014\pi$
$662$		0			0
$663$	3.55786	+	0.754030i	0.138176	+	0.0292841i
$664$		0			0
$665$		−	38.8098i		−	1.50498i
$666$		0			0
$667$	−36.2816			−1.40483
$668$		0			0
$669$	−6.17436	−	18.9643i	−0.238715	−	0.733201i
$670$		0			0
$671$			5.45257i			0.210494i
$672$		0			0
$673$			24.0490i			0.927019i	0.886092	+	0.463510i	$0.153410\pi$
$673$			24.0490i			0.927019i	−0.886092	+	0.463510i	$0.846590\pi$
$674$		0			0
$675$	9.55755	+	6.91789i	0.367870	+	0.266270i
$676$		0			0
$677$	−11.8839	+	20.5836i	−0.456736	+	0.791090i	−0.998786	−	0.0492559i	$-0.984315\pi$
$677$	−11.8839	+	20.5836i	−0.456736	+	0.791090i	0.542050	+	0.840346i	$0.317648\pi$
$678$		0			0
$679$	55.5474			2.13172
$680$		0			0
$681$	4.74028	−	22.3668i	0.181648	−	0.857097i
$682$		0			0
$683$	−1.57948	−	2.73573i	−0.0604370	−	0.104680i	0.834224	−	0.551426i	$-0.185916\pi$
$683$	−1.57948	−	2.73573i	−0.0604370	−	0.104680i	−0.894661	+	0.446746i	$0.852583\pi$
$684$		0			0
$685$	−11.9077			−0.454968
$686$		0			0
$687$	−0.826765	−	0.743531i	−0.0315431	−	0.0283675i
$688$		0			0
$689$	−2.28176	+	1.31737i	−0.0869280	+	0.0501879i
$690$		0			0
$691$	8.22190	−	14.2407i	0.312776	−	0.541744i	−0.666186	−	0.745785i	$-0.732074\pi$
$691$	8.22190	−	14.2407i	0.312776	−	0.541744i	0.978962	+	0.204042i	$0.0654078\pi$
$692$		0			0
$693$	−7.71486	+	17.3836i	−0.293063	+	0.660348i
$694$		0			0
$695$		−	15.3556i		−	0.582473i
$696$		0			0
$697$			66.0219i			2.50076i
$698$		0			0
$699$	17.7734	+	3.76678i	0.672251	+	0.142473i
$700$		0			0
$701$	−10.0559	+	17.4173i	−0.379806	+	0.657842i	−0.991034	−	0.133612i	$-0.957342\pi$
$701$	−10.0559	+	17.4173i	−0.379806	+	0.657842i	0.611228	+	0.791454i	$0.290676\pi$
$702$		0			0
$703$	−8.68604	+	15.0447i	−0.327600	+	0.567420i
$704$		0			0
$705$	−1.42552	+	6.72625i	−0.0536881	+	0.253325i
$706$		0			0
$707$	−25.7986	+	14.8949i	−0.970258	+	0.560179i
$708$		0			0
$709$	−5.02164	−	8.69774i	−0.188592	−	0.326650i	0.756189	−	0.654353i	$-0.227059\pi$
$709$	−5.02164	−	8.69774i	−0.188592	−	0.326650i	−0.944781	+	0.327703i	$0.893726\pi$
$710$		0			0
$711$	37.9990	−	4.03965i	1.42508	−	0.151499i
$712$		0			0
$713$	−42.4710			−1.59055
$714$		0			0
$715$		−	0.788779i		−	0.0294986i
$716$		0			0
$717$	35.9229	+	7.61328i	1.34157	+	0.284323i
$718$		0			0
$719$	−39.7547	+	22.9524i	−1.48260	+	0.855979i	−0.999805	−	0.0197555i	$-0.993711\pi$
$719$	−39.7547	+	22.9524i	−1.48260	+	0.855979i	−0.482794	+	0.875734i	$0.660378\pi$
$720$		0			0
$721$	−11.5210	+	6.65167i	−0.429066	+	0.247721i
$722$		0			0
$723$	−3.15217	−	9.68175i	−0.117230	−	0.360068i
$724$		0			0
$725$	7.89843	+	4.56016i	0.293340	+	0.169360i
$726$		0			0
$727$	−14.0644	+	8.12010i	−0.521621	+	0.301158i	−0.737598	−	0.675241i	$-0.764040\pi$
$727$	−14.0644	+	8.12010i	−0.521621	+	0.301158i	0.215977	+	0.976399i	$0.430706\pi$
$728$		0			0
$729$	8.43522	+	25.6485i	0.312415	+	0.949946i
$730$		0			0
$731$	−11.0967	−	19.2200i	−0.410426	−	0.710879i
$732$		0			0
$733$	−3.38613	−	1.95498i	−0.125070	−	0.0722089i	0.436160	−	0.899869i	$-0.356338\pi$
$733$	−3.38613	−	1.95498i	−0.125070	−	0.0722089i	−0.561230	+	0.827660i	$0.689672\pi$
$734$		0			0
$735$	12.4965	−	13.8954i	0.460942	−	0.512541i
$736$		0			0
$737$	8.84905	−	10.9863i	0.325959	−	0.404686i
$738$		0			0
$739$	−36.9210	+	21.3164i	−1.35816	+	0.784135i	−0.989376	−	0.145380i	$-0.953560\pi$
$739$	−36.9210	+	21.3164i	−1.35816	+	0.784135i	−0.368785	+	0.929515i	$0.620226\pi$
$740$		0			0
$741$	0.635322	−	2.99774i	0.0233391	−	0.110125i
$742$		0			0
$743$	12.7987	−	7.38935i	0.469540	−	0.271089i	−0.246507	−	0.969141i	$-0.579283\pi$
$743$	12.7987	−	7.38935i	0.469540	−	0.271089i	0.716047	+	0.698052i	$0.245950\pi$
$744$		0			0
$745$			32.2298i			1.18081i
$746$		0			0
$747$	10.5698	−	23.8165i	0.386728	−	0.871399i
$748$		0			0
$749$	−17.6324	+	30.5403i	−0.644275	+	1.11592i
$750$		0			0
$751$	−23.5775			−0.860355			−0.430178	−	0.902744i	$-0.641549\pi$
$751$	−23.5775			−0.860355			−0.430178	+	0.902744i	$0.641549\pi$
$752$		0			0
$753$	14.0292	−	15.5996i	0.511251	−	0.568483i
$754$		0			0
$755$	−8.30603	−	14.3865i	−0.302287	−	0.523577i
$756$		0			0
$757$	−1.11311	−	0.642652i	−0.0404565	−	0.0233576i	0.479635	−	0.877468i	$-0.340769\pi$
$757$	−1.11311	−	0.642652i	−0.0404565	−	0.0233576i	−0.520092	+	0.854110i	$0.674102\pi$
$758$		0			0
$759$	−25.6388	+	8.34745i	−0.930630	+	0.302993i
$760$		0			0
$761$		−	9.09669i		−	0.329755i	−0.986314	−	0.164877i	$-0.947277\pi$
$761$		−	9.09669i		−	0.329755i	0.986314	−	0.164877i	$-0.0527228\pi$
$762$		0			0
$763$	−19.6689	+	34.0675i	−0.712062	+	1.23333i
$764$		0			0
$765$	15.2385	−	34.3363i	0.550949	−	1.24143i
$766$		0			0
$767$	−0.932872	−	1.61578i	−0.0336840	−	0.0583425i
$768$		0			0
$769$	16.4416	+	9.49253i	0.592898	+	0.342310i	0.766242	−	0.642552i	$-0.222124\pi$
$769$	16.4416	+	9.49253i	0.592898	+	0.342310i	−0.173345	+	0.984861i	$0.555458\pi$
$770$		0			0
$771$	−7.89417	+	37.2483i	−0.284301	+	1.34146i
$772$		0			0
$773$	−7.83845	−	4.52553i	−0.281930	−	0.162772i	0.352367	−	0.935862i	$-0.385377\pi$
$773$	−7.83845	−	4.52553i	−0.281930	−	0.162772i	−0.634297	+	0.773090i	$0.718710\pi$
$774$		0			0
$775$	9.24585	+	5.33810i	0.332121	+	0.191750i
$776$		0			0
$777$	−16.4798	+	5.36548i	−0.591210	+	0.192485i
$778$		0			0
$779$	55.6280			1.99308
$780$		0			0
$781$	−11.6589	+	6.73126i	−0.417188	+	0.240864i
$782$		0			0
$783$	8.52316	+	19.0516i	0.304593	+	0.680849i
$784$		0			0
$785$	8.50559	+	14.7321i	0.303577	+	0.525811i
$786$		0			0
$787$	−4.99732	+	2.88520i	−0.178135	+	0.102846i	−0.586416	−	0.810010i	$-0.699462\pi$
$787$	−4.99732	+	2.88520i	−0.178135	+	0.102846i	0.408281	+	0.912856i	$0.366128\pi$
$788$		0			0
$789$	−38.1285	+	12.4138i	−1.35741	+	0.441943i
$790$		0			0
$791$	10.5587	−	6.09607i	0.375424	−	0.216751i
$792$		0			0
$793$	0.438233	−	0.759042i	0.0155621	−	0.0269544i
$794$		0			0
$795$	8.42522	+	25.8777i	0.298812	+	0.917787i
$796$		0			0
$797$	−14.1652	−	8.17831i	−0.501759	−	0.289691i	0.227681	−	0.973736i	$-0.426886\pi$
$797$	−14.1652	−	8.17831i	−0.501759	−	0.289691i	−0.729440	+	0.684045i	$0.760219\pi$
$798$		0			0
$799$	−18.2121			−0.644299
$800$		0			0
$801$	−21.9570	−	30.1456i	−0.775812	−	1.06514i
$802$		0			0
$803$	−24.4238			−0.861897
$804$		0			0
$805$	54.8929			1.93472
$806$		0			0
$807$	−14.9160	+	4.85635i	−0.525070	+	0.170951i
$808$		0			0
$809$	18.7809			0.660300			0.330150	−	0.943928i	$-0.392901\pi$
$809$	18.7809			0.660300			0.330150	+	0.943928i	$0.392901\pi$
$810$		0			0
$811$	29.7061	+	17.1508i	1.04312	+	0.602247i	0.920716	−	0.390233i	$-0.127606\pi$
$811$	29.7061	+	17.1508i	1.04312	+	0.602247i	0.122406	+	0.992480i	$0.460939\pi$
$812$		0			0
$813$	1.03120	−	0.335736i	0.0361657	−	0.0117748i
$814$		0			0
$815$	1.46194	−	2.53216i	0.0512095	−	0.0886975i
$816$		0			0
$817$	−16.1942	+	9.34973i	−0.566563	+	0.327106i
$818$		0			0
$819$	2.47112	−	1.79988i	0.0863480	−	0.0628929i
$820$		0			0
$821$	−13.6120	+	7.85890i	−0.475062	+	0.274277i	−0.718357	−	0.695675i	$-0.755105\pi$
$821$	−13.6120	+	7.85890i	−0.475062	+	0.274277i	0.243294	+	0.969953i	$0.421772\pi$
$822$		0			0
$823$	2.03886	+	3.53142i	0.0710704	+	0.123097i	0.899371	−	0.437187i	$-0.144025\pi$
$823$	2.03886	+	3.53142i	0.0710704	+	0.123097i	−0.828300	+	0.560284i	$0.810692\pi$
$824$		0			0
$825$	6.63068	+	1.40527i	0.230851	+	0.0489251i
$826$		0			0
$827$	39.0846	−	22.5655i	1.35910	−	0.784679i	0.369601	−	0.929191i	$-0.379494\pi$
$827$	39.0846	−	22.5655i	1.35910	−	0.784679i	0.989503	+	0.144512i	$0.0461611\pi$
$828$		0			0
$829$	−0.978647			−0.0339898			−0.0169949	−	0.999856i	$-0.505410\pi$
$829$	−0.978647			−0.0339898			−0.0169949	+	0.999856i	$0.505410\pi$
$830$		0			0
$831$	−6.96719	−	21.3994i	−0.241689	−	0.742337i
$832$		0			0
$833$	42.8691	+	24.7505i	1.48533	+	0.857553i
$834$		0			0
$835$	9.35875	+	5.40328i	0.323873	+	0.186988i
$836$		0			0
$837$	9.97717	+	22.3017i	0.344861	+	0.770860i
$838$		0			0
$839$	−13.4244	−	7.75059i	−0.463462	−	0.267580i	0.250037	−	0.968236i	$-0.419557\pi$
$839$	−13.4244	−	7.75059i	−0.463462	−	0.267580i	−0.713499	+	0.700656i	$0.752891\pi$
$840$		0			0
$841$	−6.43319	−	11.1426i	−0.221834	−	0.384228i
$842$		0			0
$843$	−15.2190	+	16.9226i	−0.524169	+	0.582846i
$844$		0			0
$845$	10.6752	−	18.4899i	0.367236	−	0.636072i
$846$		0			0
$847$		−	29.5370i		−	1.01490i
$848$		0			0
$849$	−7.51755	−	23.0898i	−0.258002	−	0.792440i
$850$		0			0
$851$	−21.2793	−	12.2856i	−0.729445	−	0.421145i
$852$		0			0
$853$	−1.32248	−	2.29060i	−0.0452807	−	0.0784286i	0.842497	−	0.538701i	$-0.181085\pi$
$853$	−1.32248	−	2.29060i	−0.0452807	−	0.0784286i	−0.887777	+	0.460273i	$0.847752\pi$
$854$		0			0
$855$	−28.9307	−	12.8395i	−0.989409	−	0.439101i
$856$		0			0
$857$	−26.9797			−0.921610			−0.460805	−	0.887501i	$-0.652439\pi$
$857$	−26.9797			−0.921610			−0.460805	+	0.887501i	$0.652439\pi$
$858$		0			0
$859$	−21.9916	+	38.0905i	−0.750342	+	1.29963i	0.197314	+	0.980340i	$0.436778\pi$
$859$	−21.9916	+	38.0905i	−0.750342	+	1.29963i	−0.947657	+	0.319291i	$0.896555\pi$
$860$		0			0
$861$	41.2646	+	37.1104i	1.40630	+	1.26472i
$862$		0			0
$863$			25.9746i			0.884184i	0.896970	+	0.442092i	$0.145764\pi$
$863$			25.9746i			0.884184i	−0.896970	+	0.442092i	$0.854236\pi$
$864$		0			0
$865$	−30.2227	+	17.4491i	−1.02760	+	0.593286i
$866$		0			0
$867$	68.5369	+	14.5253i	2.32763	+	0.493304i
$868$		0			0
$869$	19.0115	−	10.9763i	0.644922	−	0.372346i
$870$		0			0
$871$	−2.11485	+	0.818170i	−0.0716590	+	0.0277226i
$872$		0			0
$873$	18.3768	−	41.4078i	0.621962	−	1.40144i
$874$		0			0
$875$	−38.2646	−	22.0921i	−1.29358	−	0.746849i
$876$		0			0
$877$	−8.38847	−	14.5293i	−0.283259	−	0.490618i	0.688927	−	0.724831i	$-0.258082\pi$
$877$	−8.38847	−	14.5293i	−0.283259	−	0.490618i	−0.972185	+	0.234213i	$0.924749\pi$
$878$		0			0
$879$	−45.7897	+	14.9082i	−1.54445	+	0.502839i
$880$		0			0
$881$	−8.01025	+	4.62472i	−0.269872	+	0.155811i	−0.628830	−	0.777543i	$-0.716466\pi$
$881$	−8.01025	+	4.62472i	−0.269872	+	0.155811i	0.358957	+	0.933354i	$0.383132\pi$
$882$		0			0
$883$	41.9090	+	24.1962i	1.41035	+	0.814267i	0.995421	−	0.0955863i	$-0.0304726\pi$
$883$	41.9090	+	24.1962i	1.41035	+	0.814267i	0.414930	+	0.909853i	$0.363806\pi$
$884$		0			0
$885$	−18.3248	+	5.96615i	−0.615980	+	0.200550i
$886$		0			0
$887$	10.7438	−	6.20293i	0.360741	−	0.208274i	−0.308665	−	0.951171i	$-0.599882\pi$
$887$	10.7438	−	6.20293i	0.360741	−	0.208274i	0.669406	+	0.742897i	$0.266549\pi$
$888$		0			0
$889$	−13.0244	+	7.51961i	−0.436823	+	0.252200i
$890$		0			0
$891$	10.4063	+	11.5021i	0.348623	+	0.385334i
$892$		0			0
$893$			15.3450i			0.513500i
$894$		0			0
$895$	23.3924			0.781922
$896$		0			0
$897$	4.24003	+	0.898606i	0.141570	+	0.0300036i
$898$		0			0
$899$	9.44297	+	16.3557i	0.314941	+	0.545493i
$900$		0			0
$901$	−62.4282	+	36.0430i	−2.07979	+	1.20076i
$902$		0			0
$903$	−18.2502	−	3.86783i	−0.607328	−	0.128713i
$904$		0			0
$905$	−12.7562	+	22.0943i	−0.424029	+	0.734440i
$906$		0			0
$907$	2.42040	−	4.19225i	0.0803679	−	0.139201i	−0.823040	−	0.567983i	$-0.807724\pi$
$907$	2.42040	−	4.19225i	0.0803679	−	0.139201i	0.903408	+	0.428782i	$0.141057\pi$
$908$		0			0
$909$	2.56836	+	24.1593i	0.0851870	+	0.801312i
$910$		0			0
$911$		−	15.1071i		−	0.500521i	−0.968178	−	0.250261i	$-0.919484\pi$
$911$		−	15.1071i		−	0.500521i	0.968178	−	0.250261i	$-0.0805163\pi$
$912$		0			0
$913$		−	14.9689i		−	0.495399i
$914$		0			0
$915$	−6.73141	−	6.05373i	−0.222534	−	0.200130i
$916$		0			0
$917$	−5.71400	+	9.89695i	−0.188693	+	0.326826i
$918$		0			0
$919$	33.0521	−	19.0827i	1.09029	−	0.629479i	0.156636	−	0.987656i	$-0.449935\pi$
$919$	33.0521	−	19.0827i	1.09029	−	0.629479i	0.933653	+	0.358178i	$0.116602\pi$
$920$		0			0
$921$	−7.91764	+	8.80398i	−0.260895	+	0.290101i
$922$		0			0
$923$	2.16402			0.0712295
$924$		0			0
$925$	3.08831	+	5.34910i	0.101543	+	0.175877i
$926$		0			0
$927$	1.14696	+	10.7889i	0.0376712	+	0.354355i
$928$		0			0
$929$	43.5820			1.42988			0.714940	−	0.699186i	$-0.246454\pi$
$929$	43.5820			1.42988			0.714940	+	0.699186i	$0.246454\pi$
$930$		0			0
$931$	20.8540	−	36.1201i	0.683461	−	1.18379i
$932$		0			0
$933$	2.40368	+	7.38280i	0.0786930	+	0.241702i
$934$		0			0
$935$		−	21.5808i		−	0.705766i
$936$		0			0
$937$			0.125571i			0.00410223i	0.999998	+	0.00205112i	$0.000652891\pi$
$937$			0.125571i			0.00410223i	−0.999998	+	0.00205112i	$0.999347\pi$
$938$		0			0
$939$	19.5782	−	6.37424i	0.638910	−	0.208016i
$940$		0			0
$941$	12.5545			0.409266			0.204633	−	0.978839i	$-0.434400\pi$
$941$	12.5545			0.409266			0.204633	+	0.978839i	$0.434400\pi$
$942$		0			0
$943$			78.6807i			2.56220i
$944$		0			0
$945$	−12.8953	−	28.8245i	−0.419483	−	0.937660i
$946$		0			0
$947$			36.9117i			1.19947i	0.800199	+	0.599735i	$0.204727\pi$
$947$			36.9117i			1.19947i	−0.800199	+	0.599735i	$0.795273\pi$
$948$		0			0
$949$	3.39999	+	1.96298i	0.110368	+	0.0637212i
$950$		0			0
$951$	−6.77848	−	6.09606i	−0.219807	−	0.197678i
$952$		0			0
$953$		−	33.9883i		−	1.10099i	−0.834839	−	0.550494i	$-0.814439\pi$
$953$		−	33.9883i		−	1.10099i	0.834839	−	0.550494i	$-0.185561\pi$
$954$		0			0
$955$	−6.69388	−	11.5941i	−0.216609	−	0.375177i
$956$		0			0
$957$	8.91512	+	8.01760i	0.288185	+	0.259172i
$958$		0			0
$959$	−22.9609	−	13.2565i	−0.741445	−	0.428074i
$960$		0			0
$961$	−4.44612	−	7.70090i	−0.143423	−	0.248416i
$962$		0			0
$963$	16.9329	+	23.2478i	0.545654	+	0.749149i
$964$		0			0
$965$	−33.2378			−1.06996
$966$		0			0
$967$	28.6692	−	49.6565i	0.921939	−	1.59684i	0.125527	−	0.992090i	$-0.459938\pi$
$967$	28.6692	−	49.6565i	0.921939	−	1.59684i	0.796412	−	0.604754i	$-0.206729\pi$
$968$		0			0
$969$	17.3822	−	82.0173i	0.558398	−	2.63477i
$970$		0			0
$971$	−14.1625	−	8.17671i	−0.454495	−	0.262403i	0.255232	−	0.966880i	$-0.417848\pi$
$971$	−14.1625	−	8.17671i	−0.454495	−	0.262403i	−0.709727	+	0.704477i	$0.751182\pi$
$972$		0			0
$973$	17.0950	−	29.6094i	0.548041	−	0.949234i
$974$		0			0
$975$	−0.810101	−	0.728545i	−0.0259440	−	0.0233321i
$976$		0			0
$977$	−52.6710	+	30.4096i	−1.68509	+	0.972889i	−0.726912	+	0.686731i	$0.759045\pi$
$977$	−52.6710	+	30.4096i	−1.68509	+	0.972889i	−0.958182	+	0.286158i	$0.907622\pi$
$978$		0			0
$979$	−18.5544	−	10.7124i	−0.593000	−	0.342369i
$980$		0			0
$981$	18.8885	+	25.9328i	0.603064	+	0.827970i
$982$		0			0
$983$	17.7110			0.564893			0.282446	−	0.959283i	$-0.408854\pi$
$983$	17.7110			0.564893			0.282446	+	0.959283i	$0.408854\pi$
$984$		0			0
$985$	22.2557	−	38.5481i	0.709127	−	1.22824i
$986$		0			0
$987$	−10.2369	+	11.3828i	−0.325844	+	0.362320i
$988$		0			0
$989$	−13.2243	−	22.9052i	−0.420510	−	0.728344i
$990$		0			0
$991$			17.1592i			0.545079i	0.962145	+	0.272539i	$0.0878635\pi$
$991$			17.1592i			0.545079i	−0.962145	+	0.272539i	$0.912137\pi$
$992$		0			0
$993$	−3.63804	+	17.1659i	−0.115450	+	0.544745i
$994$		0			0
$995$	17.9714	+	31.1274i	0.569733	+	0.986806i
$996$		0			0
$997$	−17.1232			−0.542296			−0.271148	−	0.962538i	$-0.587403\pi$
$997$	−17.1232			−0.542296			−0.271148	+	0.962538i	$0.587403\pi$
$998$		0			0
$999$	−1.45235	+	14.0599i	−0.0459504	+	0.444837i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.o.d.365.11	yes	36
3.2	odd	2	inner	804.2.o.d.365.8	✓	36
67.38	odd	6	inner	804.2.o.d.641.8	yes	36
201.38	even	6	inner	804.2.o.d.641.11	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.o.d.365.8	✓	36	3.2	odd	2	inner
804.2.o.d.365.11	yes	36	1.1	even	1	trivial
804.2.o.d.641.8	yes	36	67.38	odd	6	inner
804.2.o.d.641.11	yes	36	201.38	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.536215 + 1.64696i) q^{3} -1.65208 q^{5} +(-3.18562 - 1.83922i) q^{7} +(-2.42495 + 1.76625i) q^{9} +O(q^{10})\)	\(q+(0.536215 + 1.64696i) q^{3} -1.65208 q^{5} +(-3.18562 - 1.83922i) q^{7} +(-2.42495 + 1.76625i) q^{9} +(-0.861717 + 1.49254i) q^{11} +(0.239916 - 0.138516i) q^{13} +(-0.885872 - 2.72092i) q^{15} +(6.56403 - 3.78975i) q^{17} +(-3.19312 - 5.53065i) q^{19} +(1.32094 - 6.23280i) q^{21} +(7.82260 - 4.51638i) q^{23} -2.27062 q^{25} +(-4.20923 - 3.04670i) q^{27} +(-3.47854 - 2.00833i) q^{29} +(-4.07196 - 2.35094i) q^{31} +(-2.92021 - 0.618892i) q^{33} +(5.26291 + 3.03854i) q^{35} +(-1.36012 - 2.35579i) q^{37} +(0.356776 + 0.320858i) q^{39} +(-4.35530 + 7.54360i) q^{41} -2.92808i q^{43} +(4.00622 - 2.91799i) q^{45} +(-2.08090 - 1.20141i) q^{47} +(3.26545 + 5.65593i) q^{49} +(9.76129 + 8.77857i) q^{51} -9.51065 q^{53} +(1.42363 - 2.46580i) q^{55} +(7.39655 - 8.22455i) q^{57} -6.73478i q^{59} +(2.73992 - 1.58189i) q^{61} +(10.9735 - 1.16658i) q^{63} +(-0.396361 + 0.228839i) q^{65} +(-8.08790 - 1.25932i) q^{67} +(11.6329 + 10.4618i) q^{69} +(6.76492 + 3.90573i) q^{71} +(7.08579 + 12.2730i) q^{73} +(-1.21754 - 3.73961i) q^{75} +(5.49020 - 3.16977i) q^{77} +(-11.0312 - 6.36886i) q^{79} +(2.76074 - 8.56611i) q^{81} +(-7.52188 + 4.34276i) q^{83} +(-10.8443 + 6.26098i) q^{85} +(1.44240 - 6.80591i) q^{87} +12.4314i q^{89} -1.01904 q^{91} +(1.68847 - 7.96696i) q^{93} +(5.27531 + 9.13710i) q^{95} +(-13.0777 + 7.55041i) q^{97} +(-0.546571 - 5.14133i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 4 q^{9}+O(q^{10}) \) 36 * q + 4 * q^9	\( 36 q + 4 q^{9} - 36 q^{13} + 18 q^{15} + 16 q^{21} + 76 q^{25} + 6 q^{31} + 4 q^{33} + 42 q^{37} - 21 q^{39} + 2 q^{49} + 18 q^{51} + 20 q^{55} + 18 q^{57} - 24 q^{61} - 12 q^{63} - 8 q^{67} + 3 q^{69} + 14 q^{73} + 72 q^{79} - 12 q^{81} - 18 q^{85} - 21 q^{87} - 68 q^{91} + 9 q^{93} - 48 q^{97} + 15 q^{99}+O(q^{100}) \) 36 * q + 4 * q^9 - 36 * q^13 + 18 * q^15 + 16 * q^21 + 76 * q^25 + 6 * q^31 + 4 * q^33 + 42 * q^37 - 21 * q^39 + 2 * q^49 + 18 * q^51 + 20 * q^55 + 18 * q^57 - 24 * q^61 - 12 * q^63 - 8 * q^67 + 3 * q^69 + 14 * q^73 + 72 * q^79 - 12 * q^81 - 18 * q^85 - 21 * q^87 - 68 * q^91 + 9 * q^93 - 48 * q^97 + 15 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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