LMFDB - Embedded newform 324.3.o.a.5.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,3,Mod(5,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([0, 23]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("324.5");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	324.o (of order $54$, degree $18$, 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:	$8.82836056527$
Analytic rank:	$0$
Dimension:	$324$
Relative dimension:	$18$ over $\Q(\zeta_{54})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{54}]$

Embedding invariants

Embedding label			5.7
Character	$\chi$	$=$	324.5
Dual form			324.3.o.a.65.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40095 - 2.65280i) q^{3} +(1.05662 - 0.786622i) q^{5} +(-3.63828 + 2.39294i) q^{7} +(-5.07467 + 7.43288i) q^{9} +O(q^{10})$	\(q+(-1.40095 - 2.65280i) q^{3} +(1.05662 - 0.786622i) q^{5} +(-3.63828 + 2.39294i) q^{7} +(-5.07467 + 7.43288i) q^{9} +(0.102829 - 0.879762i) q^{11} +(-5.05132 - 16.8726i) q^{13} +(-3.56702 - 1.70097i) q^{15} +(-25.3507 - 4.47002i) q^{17} +(1.99904 + 11.3371i) q^{19} +(11.4450 + 6.29924i) q^{21} +(-22.2073 + 33.7646i) q^{23} +(-6.67242 + 22.2874i) q^{25} +(26.8273 + 3.04895i) q^{27} +(26.3326 - 24.8435i) q^{29} +(-2.94284 + 50.5267i) q^{31} +(-2.47789 + 0.959719i) q^{33} +(-1.96194 + 5.39037i) q^{35} +(-52.9367 + 19.2674i) q^{37} +(-37.6829 + 37.0378i) q^{39} +(10.9812 - 46.3332i) q^{41} +(-16.1115 - 37.3508i) q^{43} +(0.484891 + 11.8456i) q^{45} +(-11.3117 + 0.658832i) q^{47} +(-11.8969 + 27.5802i) q^{49} +(23.6571 + 73.5126i) q^{51} +(-19.9552 - 11.5211i) q^{53} +(-0.583389 - 1.01046i) q^{55} +(27.2745 - 21.1858i) q^{57} +(-1.62732 - 13.9226i) q^{59} +(-41.2423 - 20.7127i) q^{61} +(0.676659 - 39.1863i) q^{63} +(-18.6097 - 13.8544i) q^{65} +(-42.5466 + 45.0968i) q^{67} +(120.682 + 11.6089i) q^{69} +(80.7693 - 96.2571i) q^{71} +(59.5008 - 49.9271i) q^{73} +(68.4717 - 13.5230i) q^{75} +(1.73109 + 3.44689i) q^{77} +(-35.6596 + 8.45149i) q^{79} +(-29.4955 - 75.4388i) q^{81} +(-1.52870 - 6.45010i) q^{83} +(-30.3022 + 15.2184i) q^{85} +(-102.795 - 35.0504i) q^{87} +(-73.1252 - 87.1472i) q^{89} +(58.7531 + 49.2997i) q^{91} +(138.160 - 62.9787i) q^{93} +(11.0302 + 10.4065i) q^{95} +(-59.2463 + 79.5816i) q^{97} +(6.01734 + 5.22882i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 324 q+O(q^{10}) $ 324 * q	$ 324 q - 135 q^{21} - 81 q^{23} + 27 q^{27} + 81 q^{29} + 189 q^{33} + 243 q^{35} + 216 q^{41} + 432 q^{45} + 324 q^{47} + 126 q^{51} - 216 q^{57} - 378 q^{59} - 540 q^{63} - 108 q^{65} - 351 q^{67} + 504 q^{69} + 648 q^{71} + 450 q^{75} + 432 q^{77} - 54 q^{79} - 72 q^{81} - 216 q^{83} + 270 q^{85} - 1008 q^{87} - 648 q^{89} - 684 q^{93} - 432 q^{95} + 459 q^{97} - 252 q^{99}+O(q^{100}) $ 324 * q - 135 * q^21 - 81 * q^23 + 27 * q^27 + 81 * q^29 + 189 * q^33 + 243 * q^35 + 216 * q^41 + 432 * q^45 + 324 * q^47 + 126 * q^51 - 216 * q^57 - 378 * q^59 - 540 * q^63 - 108 * q^65 - 351 * q^67 + 504 * q^69 + 648 * q^71 + 450 * q^75 + 432 * q^77 - 54 * q^79 - 72 * q^81 - 216 * q^83 + 270 * q^85 - 1008 * q^87 - 648 * q^89 - 684 * q^93 - 432 * q^95 + 459 * q^97 - 252 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$1$	$e\left(\frac{23}{54}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−1.40095	−	2.65280i	−0.466984	−	0.884266i
$3$	−1.40095	−	2.65280i	−0.466984	−	0.884266i
$4$		0			0
$5$	1.05662	−	0.786622i	0.211323	−	0.157324i	−0.486293	−	0.873796i	$-0.661651\pi$
$5$	1.05662	−	0.786622i	0.211323	−	0.157324i	0.697617	+	0.716471i	$0.254244\pi$
$6$		0			0
$7$	−3.63828	+	2.39294i	−0.519755	+	0.341848i	−0.782127	−	0.623119i	$-0.785865\pi$
$7$	−3.63828	+	2.39294i	−0.519755	+	0.341848i	0.262373	+	0.964967i	$0.415495\pi$
$8$		0			0
$9$	−5.07467	+	7.43288i	−0.563852	+	0.825876i
$10$		0			0
$11$	0.102829	−	0.879762i	0.00934813	−	0.0799784i	−0.987759	−	0.155988i	$-0.950144\pi$
$11$	0.102829	−	0.879762i	0.00934813	−	0.0799784i	0.997107	+	0.0760096i	$0.0242180\pi$
$12$		0			0
$13$	−5.05132	−	16.8726i	−0.388563	−	1.29789i	−0.898990	−	0.437970i	$-0.855698\pi$
$13$	−5.05132	−	16.8726i	−0.388563	−	1.29789i	0.510427	−	0.859921i	$-0.329487\pi$
$14$		0			0
$15$	−3.56702	−	1.70097i	−0.237801	−	0.113398i
$16$		0			0
$17$	−25.3507	−	4.47002i	−1.49122	−	0.262942i	−0.632168	−	0.774831i	$-0.717835\pi$
$17$	−25.3507	−	4.47002i	−1.49122	−	0.262942i	−0.859052	+	0.511889i	$0.828946\pi$
$18$		0			0
$19$	1.99904	+	11.3371i	0.105212	+	0.596689i	0.991135	+	0.132857i	$0.0424150\pi$
$19$	1.99904	+	11.3371i	0.105212	+	0.596689i	−0.885923	+	0.463833i	$0.846474\pi$
$20$		0			0
$21$	11.4450	+	6.29924i	0.545002	+	0.299964i
$22$		0			0
$23$	−22.2073	+	33.7646i	−0.965535	+	1.46802i	−0.0836858	+	0.996492i	$0.526669\pi$
$23$	−22.2073	+	33.7646i	−0.965535	+	1.46802i	−0.881849	+	0.471532i	$0.843701\pi$
$24$		0			0
$25$	−6.67242	+	22.2874i	−0.266897	+	0.891497i
$26$		0			0
$27$	26.8273	+	3.04895i	0.993604	+	0.112924i
$28$		0			0
$29$	26.3326	−	24.8435i	0.908019	−	0.856672i	−0.0821393	−	0.996621i	$-0.526175\pi$
$29$	26.3326	−	24.8435i	0.908019	−	0.856672i	0.990159	+	0.139949i	$0.0446938\pi$
$30$		0			0
$31$	−2.94284	+	50.5267i	−0.0949305	+	1.62989i	0.529147	+	0.848530i	$0.322512\pi$
$31$	−2.94284	+	50.5267i	−0.0949305	+	1.62989i	−0.624077	+	0.781363i	$0.714525\pi$
$32$		0			0
$33$	−2.47789	+	0.959719i	−0.0750876	+	0.0290824i
$34$		0			0
$35$	−1.96194	+	5.39037i	−0.0560553	+	0.154011i
$36$		0			0
$37$	−52.9367	+	19.2674i	−1.43072	+	0.520740i	−0.937138	−	0.348958i	$-0.886536\pi$
$37$	−52.9367	+	19.2674i	−1.43072	+	0.520740i	−0.493584	+	0.869698i	$0.664313\pi$
$38$		0			0
$39$	−37.6829	+	37.0378i	−0.966228	+	0.949687i
$40$		0			0
$41$	10.9812	−	46.3332i	0.267833	−	1.13008i	−0.658262	−	0.752789i	$-0.728708\pi$
$41$	10.9812	−	46.3332i	0.267833	−	1.13008i	0.926096	−	0.377289i	$-0.123144\pi$
$42$		0			0
$43$	−16.1115	−	37.3508i	−0.374687	−	0.868622i	−0.996352	−	0.0853389i	$-0.972803\pi$
$43$	−16.1115	−	37.3508i	−0.374687	−	0.868622i	0.621665	−	0.783283i	$-0.286457\pi$
$44$		0			0
$45$	0.484891	+	11.8456i	0.0107754	+	0.263235i
$46$		0			0
$47$	−11.3117	+	0.658832i	−0.240674	+	0.0140177i	−0.178058	−	0.984020i	$-0.556982\pi$
$47$	−11.3117	+	0.658832i	−0.240674	+	0.0140177i	−0.0626164	+	0.998038i	$0.519944\pi$
$48$		0			0
$49$	−11.8969	+	27.5802i	−0.242795	+	0.562862i
$50$		0			0
$51$	23.6571	+	73.5126i	0.463865	+	1.44142i
$52$		0			0
$53$	−19.9552	−	11.5211i	−0.376513	−	0.217380i	0.299787	−	0.954006i	$-0.403084\pi$
$53$	−19.9552	−	11.5211i	−0.376513	−	0.217380i	−0.676300	+	0.736626i	$0.736418\pi$
$54$		0			0
$55$	−0.583389	−	1.01046i	−0.0106071	−	0.0183720i
$56$		0			0
$57$	27.2745	−	21.1858i	0.478500	−	0.371680i
$58$		0			0
$59$	−1.62732	−	13.9226i	−0.0275817	−	0.235976i	−0.999996	−	0.00271729i	$-0.999135\pi$
$59$	−1.62732	−	13.9226i	−0.0275817	−	0.235976i	0.972415	−	0.233259i	$-0.0749390\pi$
$60$		0			0
$61$	−41.2423	−	20.7127i	−0.676103	−	0.339552i	0.0773963	−	0.997000i	$-0.475339\pi$
$61$	−41.2423	−	20.7127i	−0.676103	−	0.339552i	−0.753499	+	0.657449i	$0.771636\pi$
$62$		0			0
$63$	0.676659	−	39.1863i	0.0107406	−	0.622005i
$64$		0			0
$65$	−18.6097	−	13.8544i	−0.286302	−	0.213144i
$66$		0			0
$67$	−42.5466	+	45.0968i	−0.635024	+	0.673086i	−0.962346	−	0.271827i	$-0.912372\pi$
$67$	−42.5466	+	45.0968i	−0.635024	+	0.673086i	0.327322	+	0.944913i	$0.393854\pi$
$68$		0			0
$69$	120.682	+	11.6089i	1.74901	+	0.168246i
$70$		0			0
$71$	80.7693	−	96.2571i	1.13760	−	1.35573i	0.211978	−	0.977274i	$-0.432009\pi$
$71$	80.7693	−	96.2571i	1.13760	−	1.35573i	0.925618	−	0.378460i	$-0.123546\pi$
$72$		0			0
$73$	59.5008	−	49.9271i	0.815080	−	0.683933i	−0.136735	−	0.990608i	$-0.543661\pi$
$73$	59.5008	−	49.9271i	0.815080	−	0.683933i	0.951814	+	0.306675i	$0.0992164\pi$
$74$		0			0
$75$	68.4717	−	13.5230i	0.912957	−	0.180307i
$76$		0			0
$77$	1.73109	+	3.44689i	0.0224817	+	0.0447648i
$78$		0			0
$79$	−35.6596	+	8.45149i	−0.451388	+	0.106981i	−0.450021	−	0.893018i	$-0.648583\pi$
$79$	−35.6596	+	8.45149i	−0.451388	+	0.106981i	−0.00136724	+	0.999999i	$0.500435\pi$
$80$		0			0
$81$	−29.4955	−	75.4388i	−0.364142	−	0.931343i
$82$		0			0
$83$	−1.52870	−	6.45010i	−0.0184181	−	0.0777121i	0.963060	−	0.269288i	$-0.0867883\pi$
$83$	−1.52870	−	6.45010i	−0.0184181	−	0.0777121i	−0.981478	+	0.191576i	$0.938640\pi$
$84$		0			0
$85$	−30.3022	+	15.2184i	−0.356497	+	0.179039i
$86$		0			0
$87$	−102.795	−	35.0504i	−1.18156	−	0.402878i
$88$		0			0
$89$	−73.1252	−	87.1472i	−0.821631	−	0.979182i	0.178357	−	0.983966i	$-0.442922\pi$
$89$	−73.1252	−	87.1472i	−0.821631	−	0.979182i	−0.999989	+	0.00478390i	$0.998477\pi$
$90$		0			0
$91$	58.7531	+	49.2997i	0.645639	+	0.541755i
$92$		0			0
$93$	138.160	−	62.9787i	1.48559	−	0.677190i
$94$		0			0
$95$	11.0302	+	10.4065i	0.116108	+	0.109542i
$96$		0			0
$97$	−59.2463	+	79.5816i	−0.610786	+	0.820429i	−0.994687	−	0.102946i	$-0.967173\pi$
$97$	−59.2463	+	79.5816i	−0.610786	+	0.820429i	0.383900	+	0.923374i	$0.374581\pi$
$98$		0			0
$99$	6.01734	+	5.22882i	0.0607813	+	0.0528164i
$100$		0			0
$101$	67.2080	−	133.822i	0.665426	−	1.32497i	−0.267030	−	0.963688i	$-0.586042\pi$
$101$	67.2080	−	133.822i	0.665426	−	1.32497i	0.932456	−	0.361284i	$-0.117662\pi$
$102$		0			0
$103$	85.7742	−	10.0256i	0.832759	−	0.0973356i	0.310980	−	0.950416i	$-0.399343\pi$
$103$	85.7742	−	10.0256i	0.832759	−	0.0973356i	0.521779	+	0.853081i	$0.325269\pi$
$104$		0			0
$105$	17.0481	−	2.34704i	0.162363	−	0.0223527i
$106$		0			0
$107$	−54.0083	+	31.1817i	−0.504751	+	0.291418i	−0.730673	−	0.682727i	$-0.760794\pi$
$107$	−54.0083	+	31.1817i	−0.504751	+	0.291418i	0.225923	+	0.974145i	$0.427460\pi$
$108$		0			0
$109$	33.2197	−	57.5383i	0.304768	−	0.527874i	−0.672442	−	0.740150i	$-0.734754\pi$
$109$	33.2197	−	57.5383i	0.304768	−	0.527874i	0.977210	+	0.212276i	$0.0680877\pi$
$110$		0			0
$111$	125.274	+	113.438i	1.12860	+	1.02196i
$112$		0			0
$113$	−93.8943	−	40.5021i	−0.830923	−	0.358425i	−0.0622450	−	0.998061i	$-0.519826\pi$
$113$	−93.8943	−	40.5021i	−0.830923	−	0.358425i	−0.768678	+	0.639636i	$0.779085\pi$
$114$		0			0
$115$	3.09534	+	53.1450i	0.0269160	+	0.462130i
$116$		0			0
$117$	151.046	+	48.0769i	1.29099	+	0.410913i
$118$		0			0
$119$	102.930	−	44.3995i	0.864955	−	0.373105i
$120$		0			0
$121$	116.975	+	27.7236i	0.966736	+	0.229121i
$122$		0			0
$123$	−138.297	+	35.7798i	−1.12436	+	0.290892i
$124$		0			0
$125$	21.7450	+	59.7438i	0.173960	+	0.477950i
$126$		0			0
$127$	−201.479	−	73.3322i	−1.58645	−	0.577419i	−0.609853	−	0.792515i	$-0.708771\pi$
$127$	−201.479	−	73.3322i	−1.58645	−	0.577419i	−0.976593	+	0.215096i	$0.930994\pi$
$128$		0			0
$129$	−76.5125	+	95.0673i	−0.593120	+	0.736956i
$130$		0			0
$131$	68.9240	+	4.01437i	0.526137	+	0.0306440i	0.319158	−	0.947701i	$-0.396600\pi$
$131$	68.9240	+	4.01437i	0.526137	+	0.0306440i	0.206979	+	0.978345i	$0.433637\pi$
$132$		0			0
$133$	−34.4020	−	36.4640i	−0.258662	−	0.274166i
$134$		0			0
$135$	30.7446	−	17.8814i	0.227737	−	0.132455i
$136$		0			0
$137$	73.1173	+	21.8899i	0.533703	+	0.159780i	0.542303	−	0.840183i	$-0.317552\pi$
$137$	73.1173	+	21.8899i	0.533703	+	0.159780i	−0.00860018	+	0.999963i	$0.502738\pi$
$138$		0			0
$139$	−83.1785	−	54.7074i	−0.598407	−	0.393578i	0.213860	−	0.976864i	$-0.431396\pi$
$139$	−83.1785	−	54.7074i	−0.598407	−	0.393578i	−0.812267	+	0.583286i	$0.801767\pi$
$140$		0			0
$141$	17.5949	+	29.0847i	0.124786	+	0.206274i
$142$		0			0
$143$	−15.3633	+	2.70896i	−0.107436	+	0.0189438i
$144$		0			0
$145$	8.28099	−	46.9638i	0.0571103	−	0.323889i
$146$		0			0
$147$	89.8318	−	7.07838i	0.611101	−	0.0481522i
$148$		0			0
$149$	34.6895	−	10.3854i	0.232816	−	0.0697004i	−0.168270	−	0.985741i	$-0.553818\pi$
$149$	34.6895	−	10.3854i	0.232816	−	0.0697004i	0.401086	+	0.916041i	$0.368633\pi$
$150$		0			0
$151$	−79.1363	−	9.24970i	−0.524081	−	0.0612563i	−0.150061	−	0.988677i	$-0.547947\pi$
$151$	−79.1363	−	9.24970i	−0.524081	−	0.0612563i	−0.374020	+	0.927420i	$0.622021\pi$
$152$		0			0
$153$	161.872	−	165.745i	1.05798	−	1.08330i
$154$		0			0
$155$	36.6360	+	55.7023i	0.236361	+	0.359369i
$156$		0			0
$157$	130.675	+	175.528i	0.832328	+	1.11801i	0.991416	+	0.130746i	$0.0417373\pi$
$157$	130.675	+	175.528i	0.832328	+	1.11801i	−0.159088	+	0.987264i	$0.550855\pi$
$158$		0			0
$159$	−2.60697	+	69.0776i	−0.0163960	+	0.434450i
$160$		0			0
$161$		−	175.986i		−	1.09308i
$162$		0			0
$163$	22.9884			0.141033			0.0705166	−	0.997511i	$-0.477535\pi$
$163$	22.9884			0.141033			0.0705166	+	0.997511i	$0.477535\pi$
$164$		0			0
$165$	−1.86324	+	2.96322i	−0.0112924	+	0.0179589i
$166$		0			0
$167$	−108.837	+	81.0259i	−0.651716	+	0.485185i	−0.871520	−	0.490359i	$-0.836866\pi$
$167$	−108.837	+	81.0259i	−0.651716	+	0.485185i	0.219804	+	0.975544i	$0.429458\pi$
$168$		0			0
$169$	−117.971	+	77.5905i	−0.698051	+	0.459116i
$170$		0			0
$171$	−94.4118	−	42.6734i	−0.552116	−	0.249552i
$172$		0			0
$173$	8.78992	−	75.2026i	0.0508088	−	0.434697i	−0.943761	−	0.330628i	$-0.892740\pi$
$173$	8.78992	−	75.2026i	0.0508088	−	0.434697i	0.994570	−	0.104069i	$-0.0331864\pi$
$174$		0			0
$175$	−29.0562	−	97.0546i	−0.166036	−	0.554598i
$176$		0			0
$177$	−34.6541	+	23.8218i	−0.195786	+	0.134587i
$178$		0			0
$179$	−285.704	−	50.3772i	−1.59611	−	0.281437i	−0.696310	−	0.717741i	$-0.745176\pi$
$179$	−285.704	−	50.3772i	−1.59611	−	0.281437i	−0.899799	+	0.436304i	$0.856287\pi$
$180$		0			0
$181$	4.79250	+	27.1796i	0.0264779	+	0.150163i	0.995180	−	0.0980610i	$-0.0312640\pi$
$181$	4.79250	+	27.1796i	0.0264779	+	0.150163i	−0.968703	+	0.248225i	$0.920153\pi$
$182$		0			0
$183$	2.83199	+	138.425i	0.0154753	+	0.756420i
$184$		0			0
$185$	−40.7777	+	61.9995i	−0.220420	+	0.335132i
$186$		0			0
$187$	−6.53936	+	21.8430i	−0.0349698	+	0.116807i
$188$		0			0
$189$	−104.901	+	53.1031i	−0.555033	+	0.280969i
$190$		0			0
$191$	−74.4869	+	70.2748i	−0.389984	+	0.367931i	−0.856115	−	0.516785i	$-0.827129\pi$
$191$	−74.4869	+	70.2748i	−0.389984	+	0.367931i	0.466132	+	0.884715i	$0.345647\pi$
$192$		0			0
$193$	−5.02042	+	86.1973i	−0.0260125	+	0.446618i	0.960006	+	0.279980i	$0.0903280\pi$
$193$	−5.02042	+	86.1973i	−0.0260125	+	0.446618i	−0.986018	+	0.166637i	$0.946709\pi$
$194$		0			0
$195$	−10.6816	+	68.7770i	−0.0547775	+	0.352702i
$196$		0			0
$197$	123.605	−	339.602i	0.627437	−	1.72387i	−0.0605704	−	0.998164i	$-0.519292\pi$
$197$	123.605	−	339.602i	0.627437	−	1.72387i	0.688007	−	0.725704i	$-0.258486\pi$
$198$		0			0
$199$	325.194	−	118.361i	1.63414	−	0.594778i	0.648138	−	0.761523i	$-0.275548\pi$
$199$	325.194	−	118.361i	1.63414	−	0.594778i	0.986000	+	0.166745i	$0.0533257\pi$
$200$		0			0
$201$	179.238	+	49.6891i	0.891733	+	0.247210i
$202$		0			0
$203$	−36.3564	+	153.400i	−0.179096	+	0.755664i
$204$		0			0
$205$	−24.8438	−	57.5945i	−0.121189	−	0.280949i
$206$		0			0
$207$	−138.273	−	336.408i	−0.667987	−	1.62516i
$208$		0			0
$209$	10.1795	−	0.592889i	0.0487058	−	0.00283679i
$210$		0			0
$211$	−126.593	+	293.475i	−0.599966	+	1.39088i	0.299588	+	0.954069i	$0.403151\pi$
$211$	−126.593	+	293.475i	−0.599966	+	1.39088i	−0.899554	+	0.436810i	$0.856108\pi$
$212$		0			0
$213$	−368.505	−	79.4130i	−1.73007	−	0.372831i
$214$		0			0
$215$	−46.4047	−	26.7917i	−0.215836	−	0.124613i
$216$		0			0
$217$	−110.200	−	190.872i	−0.507835	−	0.879596i
$218$		0			0
$219$	−215.804	−	87.8981i	−0.985408	−	0.401361i
$220$		0			0
$221$	52.6339	+	450.312i	0.238162	+	2.03761i
$222$		0			0
$223$	−33.4852	−	16.8169i	−0.150158	−	0.0754121i	0.372133	−	0.928179i	$-0.378626\pi$
$223$	−33.4852	−	16.8169i	−0.150158	−	0.0754121i	−0.522291	+	0.852767i	$0.674923\pi$
$224$		0			0
$225$	−131.800	−	162.697i	−0.585776	−	0.723096i
$226$		0			0
$227$	115.242	+	85.7943i	0.507673	+	0.377948i	0.820305	−	0.571926i	$-0.193803\pi$
$227$	115.242	+	85.7943i	0.507673	+	0.377948i	−0.312633	+	0.949874i	$0.601211\pi$
$228$		0			0
$229$	−99.4039	+	105.362i	−0.434078	+	0.460096i	−0.907076	−	0.420968i	$-0.861691\pi$
$229$	−99.4039	+	105.362i	−0.434078	+	0.460096i	0.472997	+	0.881064i	$0.343172\pi$
$230$		0			0
$231$	6.71872	−	9.42116i	0.0290854	−	0.0407843i
$232$		0			0
$233$	−109.199	+	130.139i	−0.468666	+	0.558535i	−0.947659	−	0.319284i	$-0.896558\pi$
$233$	−109.199	+	130.139i	−0.468666	+	0.558535i	0.478993	+	0.877819i	$0.341002\pi$
$234$		0			0
$235$	−11.4339	+	9.59417i	−0.0486548	+	0.0408262i
$236$		0			0
$237$	72.3775	+	82.7577i	0.305390	+	0.349188i
$238$		0			0
$239$	138.792	+	276.358i	0.580720	+	1.15631i	0.971768	+	0.235938i	$0.0758162\pi$
$239$	138.792	+	276.358i	0.580720	+	1.15631i	−0.391048	+	0.920370i	$0.627887\pi$
$240$		0			0
$241$	−209.721	+	49.7048i	−0.870211	+	0.206244i	−0.641381	−	0.767222i	$-0.721638\pi$
$241$	−209.721	+	49.7048i	−0.870211	+	0.206244i	−0.228830	+	0.973466i	$0.573490\pi$
$242$		0			0
$243$	−158.802	+	183.932i	−0.653507	+	0.756921i
$244$		0			0
$245$	9.12470	+	38.5001i	0.0372437	+	0.157143i
$246$		0			0
$247$	181.188	−	90.9962i	0.733556	−	0.368406i
$248$		0			0
$249$	−14.9692	+	13.0916i	−0.0601172	+	0.0525768i
$250$		0			0
$251$	164.515	+	196.062i	0.655440	+	0.781123i	0.986724	−	0.162408i	$-0.0519262\pi$
$251$	164.515	+	196.062i	0.655440	+	0.781123i	−0.331284	+	0.943531i	$0.607482\pi$
$252$		0			0
$253$	27.4212	+	23.0091i	0.108384	+	0.0909452i
$254$		0			0
$255$	82.8232	+	59.0655i	0.324797	+	0.231629i
$256$		0			0
$257$	−91.5983	−	86.4186i	−0.356414	−	0.336259i	0.487120	−	0.873335i	$-0.338047\pi$
$257$	−91.5983	−	86.4186i	−0.356414	−	0.336259i	−0.843534	+	0.537076i	$0.819529\pi$
$258$		0			0
$259$	146.493	−	196.774i	0.565611	−	0.759747i
$260$		0			0
$261$	51.0298	+	321.799i	0.195516	+	1.23295i
$262$		0			0
$263$	53.9252	−	107.374i	0.205039	−	0.408266i	−0.767486	−	0.641066i	$-0.778493\pi$
$263$	53.9252	−	107.374i	0.205039	−	0.408266i	0.972525	+	0.232800i	$0.0747888\pi$
$264$		0			0
$265$	−30.1477	+	3.52377i	−0.113765	+	0.0132972i
$266$		0			0
$267$	−128.739	+	316.075i	−0.482168	+	1.18380i
$268$		0			0
$269$	−400.114	+	231.006i	−1.48741	+	0.858757i	−0.999897	−	0.0143575i	$-0.995430\pi$
$269$	−400.114	+	231.006i	−1.48741	+	0.858757i	−0.487514	+	0.873115i	$0.662096\pi$
$270$		0			0
$271$	231.413	−	400.819i	0.853923	−	1.47904i	−0.0237184	−	0.999719i	$-0.507551\pi$
$271$	231.413	−	400.819i	0.853923	−	1.47904i	0.877641	−	0.479319i	$-0.159116\pi$
$272$		0			0
$273$	48.4719	−	224.927i	0.177553	−	0.823907i
$274$		0			0
$275$	18.9215	+	8.16194i	0.0688055	+	0.0296798i
$276$		0			0
$277$	−3.49796	−	60.0577i	−0.0126280	−	0.216815i	−0.998719	−	0.0506064i	$-0.983885\pi$
$277$	−3.49796	−	60.0577i	−0.0126280	−	0.216815i	0.986091	−	0.166208i	$-0.0531524\pi$
$278$		0			0
$279$	−360.625	−	278.280i	−1.29256	−	0.997419i
$280$		0			0
$281$	−163.242	+	70.4158i	−0.580933	+	0.250590i	−0.666206	−	0.745767i	$-0.732083\pi$
$281$	−163.242	+	70.4158i	−0.580933	+	0.250590i	0.0852730	+	0.996358i	$0.472824\pi$
$282$		0			0
$283$	328.753	+	77.9159i	1.16167	+	0.275321i	0.765858	−	0.643010i	$-0.222314\pi$
$283$	328.753	+	77.9159i	1.16167	+	0.275321i	0.395814	+	0.918331i	$0.370463\pi$
$284$		0			0
$285$	12.1535	−	43.8400i	0.0426438	−	0.153824i
$286$		0			0
$287$	70.9198	+	194.850i	0.247107	+	0.678922i
$288$		0			0
$289$	351.108	+	127.793i	1.21491	+	0.442189i
$290$		0			0
$291$	294.115	+	45.6784i	1.01070	+	0.156971i
$292$		0			0
$293$	−104.095	−	6.06285i	−0.355274	−	0.0206923i	−0.120420	−	0.992723i	$-0.538424\pi$
$293$	−104.095	−	6.06285i	−0.355274	−	0.0206923i	−0.234854	+	0.972031i	$0.575461\pi$
$294$		0			0
$295$	−12.6713	−	13.4308i	−0.0429535	−	0.0455281i
$296$		0			0
$297$	5.44099	−	23.2881i	0.0183198	−	0.0784112i
$298$		0			0
$299$	681.871	+	204.139i	2.28051	+	0.682739i
$300$		0			0
$301$	147.996	+	97.3387i	0.491682	+	0.323384i
$302$		0			0
$303$	−449.158	+	9.18918i	−1.48237	+	0.0303273i
$304$		0			0
$305$	−59.8703	+	10.5568i	−0.196296	+	0.0346123i
$306$		0			0
$307$	−18.8221	+	106.746i	−0.0613099	+	0.347706i	0.938686	+	0.344774i	$0.112044\pi$
$307$	−18.8221	+	106.746i	−0.0613099	+	0.347706i	−0.999996	+	0.00293187i	$0.999067\pi$
$308$		0			0
$309$	−146.761	−	213.496i	−0.474956	−	0.690926i
$310$		0			0
$311$	−93.2358	+	27.9130i	−0.299793	+	0.0897523i	−0.433167	−	0.901314i	$-0.642604\pi$
$311$	−93.2358	+	27.9130i	−0.299793	+	0.0897523i	0.133374	+	0.991066i	$0.457419\pi$
$312$		0			0
$313$	−440.061	−	51.4357i	−1.40595	−	0.164331i	−0.620958	−	0.783844i	$-0.713256\pi$
$313$	−440.061	−	51.4357i	−1.40595	−	0.164331i	−0.784987	+	0.619512i	$0.787330\pi$
$314$		0			0
$315$	−30.1098	−	41.9372i	−0.0955868	−	0.133134i
$316$		0			0
$317$	−20.9355	−	31.8308i	−0.0660425	−	0.100413i	0.800957	−	0.598722i	$-0.204325\pi$
$317$	−20.9355	−	31.8308i	−0.0660425	−	0.100413i	−0.866999	+	0.498310i	$0.833954\pi$
$318$		0			0
$319$	−19.1486	−	25.7210i	−0.0600270	−	0.0806302i
$320$		0			0
$321$	158.382	+	99.5890i	0.493401	+	0.310246i
$322$		0			0
$323$		−	296.340i		−	0.917460i
$324$		0			0
$325$	409.751			1.26077
$326$		0			0
$327$	−199.177	−	7.51687i	−0.609103	−	0.0229874i
$328$		0			0
$329$	39.5786	−	29.4652i	0.120300	−	0.0895599i
$330$		0			0
$331$	−97.9061	+	64.3938i	−0.295789	+	0.194543i	−0.688726	−	0.725022i	$-0.741829\pi$
$331$	−97.9061	+	64.3938i	−0.295789	+	0.194543i	0.392937	+	0.919565i	$0.371459\pi$
$332$		0			0
$333$	125.424	−	491.248i	0.376649	−	1.47522i
$334$		0			0
$335$	−9.48135	+	81.1181i	−0.0283025	+	0.242144i
$336$		0			0
$337$	103.067	+	344.268i	0.305837	+	1.02157i	0.963378	+	0.268147i	$0.0864114\pi$
$337$	103.067	+	344.268i	0.305837	+	1.02157i	−0.657541	+	0.753419i	$0.728403\pi$
$338$		0			0
$339$	24.0977	+	305.824i	0.0710846	+	0.902136i
$340$		0			0
$341$	44.1489	+	7.78463i	0.129469	+	0.0228288i
$342$		0			0
$343$	−59.7662	−	338.951i	−0.174246	−	0.988195i
$344$		0			0
$345$	136.646	−	82.6649i	0.396077	−	0.239608i
$346$		0			0
$347$	−180.008	+	273.688i	−0.518754	+	0.788727i	−0.995935	−	0.0900779i	$-0.971288\pi$
$347$	−180.008	+	273.688i	−0.518754	+	0.788727i	0.477181	+	0.878805i	$0.341659\pi$
$348$		0			0
$349$	99.7425	−	333.163i	0.285795	−	0.954623i	−0.687715	−	0.725980i	$-0.741386\pi$
$349$	99.7425	−	333.163i	0.285795	−	0.954623i	0.973511	−	0.228642i	$-0.0734285\pi$
$350$		0			0
$351$	−84.0696	−	468.047i	−0.239514	−	1.33347i
$352$		0			0
$353$	384.472	−	362.731i	1.08916	−	1.02757i	0.0896547	−	0.995973i	$-0.471424\pi$
$353$	384.472	−	362.731i	1.08916	−	1.02757i	0.999501	−	0.0315924i	$-0.0100578\pi$
$354$		0			0
$355$	9.62424	−	165.242i	0.0271105	−	0.465470i
$356$		0			0
$357$	−261.982	−	210.850i	−0.733844	−	0.590616i
$358$		0			0
$359$	9.34524	−	25.6758i	0.0260313	−	0.0715204i	−0.925996	−	0.377533i	$-0.876773\pi$
$359$	9.34524	−	25.6758i	0.0260313	−	0.0715204i	0.952028	+	0.306012i	$0.0989948\pi$
$360$		0			0
$361$	214.695	−	78.1427i	0.594724	−	0.216462i
$362$		0			0
$363$	−90.3313	−	349.150i	−0.248847	−	0.961847i
$364$		0			0
$365$	23.5958	−	99.5585i	0.0646460	−	0.272763i
$366$		0			0
$367$	−105.196	−	243.873i	−0.286639	−	0.664503i	0.712677	−	0.701492i	$-0.247483\pi$
$367$	−105.196	−	243.873i	−0.286639	−	0.664503i	−0.999316	+	0.0369892i	$0.988223\pi$
$368$		0			0
$369$	288.663	+	316.747i	0.782286	+	0.858394i
$370$		0			0
$371$	100.172	−	5.83435i	0.270005	−	0.0157260i
$372$		0			0
$373$	45.3015	−	105.021i	0.121452	−	0.281557i	−0.846634	−	0.532175i	$-0.821375\pi$
$373$	45.3015	−	105.021i	0.121452	−	0.281557i	0.968086	+	0.250619i	$0.0806340\pi$
$374$		0			0
$375$	128.025	−	141.383i	0.341399	−	0.377022i
$376$		0			0
$377$	−552.188	−	318.806i	−1.46469	−	0.845639i
$378$		0			0
$379$	−295.427	−	511.695i	−0.779491	−	1.35012i	−0.932236	−	0.361852i	$-0.882145\pi$
$379$	−295.427	−	511.695i	−0.779491	−	1.35012i	0.152745	−	0.988266i	$-0.451189\pi$
$380$		0			0
$381$	87.7263	+	637.217i	0.230253	+	1.67248i
$382$		0			0
$383$	−2.46582	−	21.0964i	−0.00643817	−	0.0550821i	0.989637	−	0.143589i	$-0.0458644\pi$
$383$	−2.46582	−	21.0964i	−0.00643817	−	0.0550821i	−0.996076	+	0.0885072i	$0.971790\pi$
$384$		0			0
$385$	4.54050	+	2.28033i	0.0117935	+	0.00592292i
$386$		0			0
$387$	359.385	+	69.7874i	0.928642	+	0.180329i
$388$		0			0
$389$	249.617	+	185.833i	0.641689	+	0.477720i	0.868151	−	0.496300i	$-0.165308\pi$
$389$	249.617	+	185.833i	0.641689	+	0.477720i	−0.226462	+	0.974020i	$0.572716\pi$
$390$		0			0
$391$	713.900	−	756.689i	1.82583	−	1.93527i
$392$		0			0
$393$	−85.9099	−	188.465i	−0.218600	−	0.479556i
$394$		0			0
$395$	−31.0305	+	36.9807i	−0.0785581	+	0.0936219i
$396$		0			0
$397$	−103.559	+	86.8961i	−0.260853	+	0.218882i	−0.763829	−	0.645419i	$-0.776683\pi$
$397$	−103.559	+	86.8961i	−0.260853	+	0.218882i	0.502976	+	0.864301i	$0.332239\pi$
$398$		0			0
$399$	−48.5361	+	142.346i	−0.121644	+	0.356757i
$400$		0			0
$401$	312.153	+	621.547i	0.778435	+	1.54999i	0.834145	+	0.551545i	$0.185962\pi$
$401$	312.153	+	621.547i	0.778435	+	1.54999i	−0.0557095	+	0.998447i	$0.517742\pi$
$402$		0			0
$403$	867.381	−	205.573i	2.15231	−	0.510107i
$404$		0			0
$405$	−90.5073	−	56.5081i	−0.223475	−	0.139526i
$406$		0			0
$407$	11.5073	+	48.5530i	0.0282734	+	0.119295i
$408$		0			0
$409$	−608.719	+	305.710i	−1.48831	+	0.747457i	−0.992646	−	0.121057i	$-0.961372\pi$
$409$	−608.719	+	305.710i	−1.48831	+	0.747457i	−0.495665	+	0.868514i	$0.665075\pi$
$410$		0			0
$411$	−44.3644	−	224.632i	−0.107943	−	0.546550i
$412$		0			0
$413$	39.2366	+	46.7603i	0.0950038	+	0.113221i
$414$		0			0
$415$	−6.68905	−	5.61278i	−0.0161182	−	0.0135248i
$416$		0			0
$417$	−28.5985	+	297.298i	−0.0685815	+	0.712945i
$418$		0			0
$419$	445.414	+	420.227i	1.06304	+	1.00293i	0.999988	+	0.00491779i	$0.00156539\pi$
$419$	445.414	+	420.227i	1.06304	+	1.00293i	0.0630536	+	0.998010i	$0.479916\pi$
$420$		0			0
$421$	−17.1951	+	23.0970i	−0.0408435	+	0.0548623i	−0.822076	−	0.569378i	$-0.807184\pi$
$421$	−17.1951	+	23.0970i	−0.0408435	+	0.0548623i	0.781232	+	0.624240i	$0.214591\pi$
$422$		0			0
$423$	52.5061	−	87.4219i	0.124128	−	0.206671i
$424$		0			0
$425$	268.776	−	535.177i	0.632414	−	1.25924i
$426$		0			0
$427$	199.615	−	23.3317i	0.467483	−	0.0546409i
$428$		0			0
$429$	28.7095	+	36.9606i	0.0669220	+	0.0861551i
$430$		0			0
$431$	476.994	−	275.393i	1.10671	−	0.638962i	0.168738	−	0.985661i	$-0.446031\pi$
$431$	476.994	−	275.393i	1.10671	−	0.638962i	0.937976	+	0.346699i	$0.112698\pi$
$432$		0			0
$433$	−201.537	+	349.073i	−0.465444	+	0.806173i	−0.999221	−	0.0394524i	$-0.987439\pi$
$433$	−201.537	+	349.073i	−0.465444	+	0.806173i	0.533778	+	0.845625i	$0.320772\pi$
$434$		0			0
$435$	−136.187	+	43.8263i	−0.313073	+	0.100750i
$436$		0			0
$437$	−427.185	−	184.270i	−0.977541	−	0.421670i
$438$		0			0
$439$	14.6584	+	251.674i	0.0333903	+	0.573290i	0.972966	+	0.230949i	$0.0741829\pi$
$439$	14.6584	+	251.674i	0.0333903	+	0.573290i	−0.939576	+	0.342342i	$0.888780\pi$
$440$		0			0
$441$	−144.628	−	228.389i	−0.327954	−	0.517889i
$442$		0			0
$443$	−633.762	+	273.378i	−1.43061	+	0.617107i	−0.963650	−	0.267169i	$-0.913912\pi$
$443$	−633.762	+	273.378i	−1.43061	+	0.617107i	−0.466965	+	0.884276i	$0.654653\pi$
$444$		0			0
$445$	−145.817	−	34.5593i	−0.327679	−	0.0776614i
$446$		0			0
$447$	−76.1486	−	77.4749i	−0.170355	−	0.173322i
$448$		0			0
$449$	−41.8244	−	114.912i	−0.0931502	−	0.255928i	0.884364	−	0.466798i	$-0.154593\pi$
$449$	−41.8244	−	114.912i	−0.0931502	−	0.255928i	−0.977514	+	0.210870i	$0.932370\pi$
$450$		0			0
$451$	−39.6330	−	14.4252i	−0.0878781	−	0.0319850i
$452$		0			0
$453$	86.3285	+	222.891i	0.190571	+	0.492033i
$454$		0			0
$455$	100.860	+	5.87442i	0.221670	+	0.0129108i
$456$		0			0
$457$	495.145	+	524.823i	1.08347	+	1.14841i	0.988233	+	0.152954i	$0.0488785\pi$
$457$	495.145	+	524.823i	1.08347	+	1.14841i	0.0952342	+	0.995455i	$0.469640\pi$
$458$		0			0
$459$	−666.463	−	197.212i	−1.45199	−	0.429655i
$460$		0			0
$461$	−36.0803	−	10.8017i	−0.0782652	−	0.0234311i	0.247431	−	0.968905i	$-0.420414\pi$
$461$	−36.0803	−	10.8017i	−0.0782652	−	0.0234311i	−0.325696	+	0.945474i	$0.605599\pi$
$462$		0			0
$463$	−165.199	−	108.653i	−0.356800	−	0.234671i	0.358435	−	0.933555i	$-0.383310\pi$
$463$	−165.199	−	108.653i	−0.356800	−	0.234671i	−0.715236	+	0.698883i	$0.753681\pi$
$464$		0			0
$465$	96.4416	−	175.224i	0.207401	−	0.376826i
$466$		0			0
$467$	225.643	−	39.7870i	0.483176	−	0.0851969i	0.0732458	−	0.997314i	$-0.476664\pi$
$467$	225.643	−	39.7870i	0.483176	−	0.0851969i	0.409930	+	0.912117i	$0.365553\pi$
$468$		0			0
$469$	46.8829	−	265.886i	0.0999635	−	0.566921i
$470$		0			0
$471$	282.569	−	592.561i	0.599935	−	1.25809i
$472$		0			0
$473$	−34.5165	+	10.3336i	−0.0729736	+	0.0218469i
$474$		0			0
$475$	−266.013	−	31.0925i	−0.560028	−	0.0654578i
$476$		0			0
$477$	186.901	−	89.8586i	0.391826	−	0.188383i
$478$		0			0
$479$	−38.2991	−	58.2309i	−0.0799564	−	0.121568i	0.793296	−	0.608837i	$-0.208364\pi$
$479$	−38.2991	−	58.2309i	−0.0799564	−	0.121568i	−0.873252	+	0.487269i	$0.837993\pi$
$480$		0			0
$481$	592.491	+	795.853i	1.23179	+	1.65458i
$482$		0			0
$483$	−466.854	+	246.547i	−0.966572	+	0.510450i
$484$		0			0
$485$			130.692i			0.269467i
$486$		0			0
$487$	67.9011			0.139427			0.0697137	−	0.997567i	$-0.477791\pi$
$487$	67.9011			0.139427			0.0697137	+	0.997567i	$0.477791\pi$
$488$		0			0
$489$	−32.2057	−	60.9836i	−0.0658603	−	0.124711i
$490$		0			0
$491$	−618.995	+	460.825i	−1.26068	+	0.938544i	−0.999641	−	0.0267840i	$-0.991473\pi$
$491$	−618.995	+	460.825i	−1.26068	+	0.938544i	−0.261042	+	0.965328i	$0.584066\pi$
$492$		0			0
$493$	−778.601	+	512.094i	−1.57931	+	1.03873i
$494$		0			0
$495$	10.4711	+	0.791483i	0.0211538	+	0.00159896i
$496$		0			0
$497$	−63.5245	+	543.487i	−0.127816	+	1.09353i
$498$		0			0
$499$	79.2466	+	264.702i	0.158811	+	0.530465i	0.999946	−	0.0103593i	$-0.00329754\pi$
$499$	79.2466	+	264.702i	0.158811	+	0.530465i	−0.841136	+	0.540824i	$0.818112\pi$
$500$		0			0
$501$	367.420	+	175.208i	0.733374	+	0.349717i
$502$		0			0
$503$	367.059	+	64.7224i	0.729739	+	0.128673i	0.526160	−	0.850386i	$-0.323631\pi$
$503$	367.059	+	64.7224i	0.729739	+	0.128673i	0.203579	+	0.979058i	$0.434742\pi$
$504$		0			0
$505$	−34.2544	−	194.266i	−0.0678304	−	0.384685i
$506$		0			0
$507$	371.103	+	204.252i	0.731959	+	0.402863i
$508$		0			0
$509$	261.971	−	398.307i	0.514677	−	0.782529i	−0.480870	−	0.876792i	$-0.659679\pi$
$509$	261.971	−	398.307i	0.514677	−	0.782529i	0.995547	+	0.0942631i	$0.0300495\pi$
$510$		0			0
$511$	−97.0084	+	324.031i	−0.189840	+	0.634111i
$512$		0			0
$513$	19.0625	+	310.239i	0.0371588	+	0.604754i
$514$		0			0
$515$	82.7442	−	78.0651i	0.160668	−	0.151583i
$516$		0			0
$517$	−0.583561	+	10.0194i	−0.00112874	+	0.0193798i
$518$		0			0
$519$	−211.811	+	82.0373i	−0.408115	+	0.158068i
$520$		0			0
$521$	−169.007	+	464.342i	−0.324389	+	0.891251i	0.665115	+	0.746741i	$0.268383\pi$
$521$	−169.007	+	464.342i	−0.324389	+	0.891251i	−0.989503	+	0.144510i	$0.953840\pi$
$522$		0			0
$523$	82.6741	−	30.0909i	0.158077	−	0.0575352i	−0.261770	−	0.965130i	$-0.584306\pi$
$523$	82.6741	−	30.0909i	0.158077	−	0.0575352i	0.419846	+	0.907595i	$0.362084\pi$
$524$		0			0
$525$	−216.760	+	213.049i	−0.412876	+	0.405808i
$526$		0			0
$527$	300.458	−	1267.73i	0.570130	−	2.40557i
$528$		0			0
$529$	−437.355	−	1013.90i	−0.826758	−	1.91664i
$530$		0			0
$531$	111.743	+	58.5569i	0.210439	+	0.110277i
$532$		0			0
$533$	−837.230	+	48.7631i	−1.57079	+	0.0914880i
$534$		0			0
$535$	−32.5379	+	75.4313i	−0.0608185	+	0.140993i
$536$		0			0
$537$	266.616	+	828.490i	0.496492	+	1.54281i
$538$		0			0
$539$	23.0407	+	13.3025i	0.0427471	+	0.0246800i
$540$		0			0
$541$	138.642	+	240.135i	0.256270	+	0.443873i	0.965240	−	0.261366i	$-0.0841730\pi$
$541$	138.642	+	240.135i	0.256270	+	0.443873i	−0.708970	+	0.705239i	$0.750840\pi$
$542$		0			0
$543$	65.3879	−	50.7908i	0.120420	−	0.0935374i
$544$		0			0
$545$	−10.1603	−	86.9273i	−0.0186428	−	0.159500i
$546$		0			0
$547$	−410.687	−	206.255i	−0.750799	−	0.377065i	0.0318795	−	0.999492i	$-0.489851\pi$
$547$	−410.687	−	206.255i	−0.750799	−	0.377065i	−0.782678	+	0.622426i	$0.786147\pi$
$548$		0			0
$549$	363.246	−	201.439i	0.661650	−	0.366920i
$550$		0			0
$551$	334.293	+	248.872i	0.606702	+	0.451673i
$552$		0			0
$553$	109.516	−	116.080i	0.198040	−	0.209910i
$554$		0			0
$555$	221.600	+	21.3167i	0.399278	+	0.0384084i
$556$		0			0
$557$	−608.359	+	725.014i	−1.09221	+	1.30164i	−0.142052	+	0.989859i	$0.545370\pi$
$557$	−608.359	+	725.014i	−1.09221	+	1.30164i	−0.950154	+	0.311781i	$0.899074\pi$
$558$		0			0
$559$	−548.819	+	460.514i	−0.981787	+	0.823817i
$560$		0			0
$561$	67.1063	−	13.2534i	0.119619	−	0.0236245i
$562$		0			0
$563$	−165.897	−	330.328i	−0.294666	−	0.586728i	0.696774	−	0.717290i	$-0.254618\pi$
$563$	−165.897	−	330.328i	−0.294666	−	0.586728i	−0.991440	+	0.130563i	$0.958322\pi$
$564$		0			0
$565$	−131.070	+	31.0642i	−0.231983	+	0.0549809i
$566$		0			0
$567$	287.833	+	203.887i	0.507643	+	0.359589i
$568$		0			0
$569$	−97.9687	−	413.363i	−0.172177	−	0.726472i	−0.988793	−	0.149291i	$-0.952301\pi$
$569$	−97.9687	−	413.363i	−0.172177	−	0.726472i	0.816616	−	0.577181i	$-0.195847\pi$
$570$		0			0
$571$	−183.309	+	92.0614i	−0.321032	+	0.161228i	−0.602016	−	0.798484i	$-0.705636\pi$
$571$	−183.309	+	92.0614i	−0.321032	+	0.161228i	0.280984	+	0.959713i	$0.409339\pi$
$572$		0			0
$573$	290.777	+	99.1471i	0.507465	+	0.173032i
$574$		0			0
$575$	−604.349	−	720.235i	−1.05104	−	1.25258i
$576$		0			0
$577$	355.484	+	298.287i	0.616091	+	0.516962i	0.896572	−	0.442898i	$-0.146050\pi$
$577$	355.484	+	298.287i	0.616091	+	0.516962i	−0.280481	+	0.959860i	$0.590494\pi$
$578$		0			0
$579$	235.697	−	107.440i	0.407076	−	0.185561i
$580$		0			0
$581$	20.9965	+	19.8092i	0.0361386	+	0.0340950i
$582$		0			0
$583$	−12.1878	+	16.3711i	−0.0209054	+	0.0280808i
$584$		0			0
$585$	197.416	−	68.0171i	0.337463	−	0.116268i
$586$		0			0
$587$	64.0060	−	127.446i	0.109039	−	0.217115i	−0.832495	−	0.554033i	$-0.813088\pi$
$587$	64.0060	−	127.446i	0.109039	−	0.217115i	0.941534	+	0.336918i	$0.109384\pi$
$588$		0			0
$589$	−578.709	+	67.6414i	−0.982528	+	0.114841i
$590$		0			0
$591$	−1074.06	+	147.867i	−1.81736	+	0.250198i
$592$		0			0
$593$	−73.1016	+	42.2053i	−0.123274	+	0.0711724i	−0.560369	−	0.828243i	$-0.689341\pi$
$593$	−73.1016	+	42.2053i	−0.123274	+	0.0711724i	0.437095	+	0.899415i	$0.356007\pi$
$594$		0			0
$595$	73.8316	−	127.880i	0.124087	−	0.214924i
$596$		0			0
$597$	−769.568	−	696.855i	−1.28906	−	1.16726i
$598$		0			0
$599$	−912.280	−	393.519i	−1.52301	−	0.656960i	−0.540188	−	0.841544i	$-0.681647\pi$
$599$	−912.280	−	393.519i	−1.52301	−	0.656960i	−0.982817	+	0.184584i	$0.940906\pi$
$600$		0			0
$601$	64.4266	+	1106.16i	0.107199	+	1.84054i	0.440543	+	0.897732i	$0.354786\pi$
$601$	64.4266	+	1106.16i	0.107199	+	1.84054i	−0.333344	+	0.942805i	$0.608177\pi$
$602$		0			0
$603$	−119.289	−	545.095i	−0.197826	−	0.903972i
$604$		0			0
$605$	145.406	−	62.7219i	0.240340	−	0.103673i
$606$		0			0
$607$	−686.367	−	162.672i	−1.13075	−	0.267993i	−0.377684	−	0.925935i	$-0.623279\pi$
$607$	−686.367	−	162.672i	−1.13075	−	0.267993i	−0.753069	+	0.657941i	$0.771427\pi$
$608$		0			0
$609$	457.872	−	118.460i	0.751843	−	0.194515i
$610$		0			0
$611$	68.2552	+	187.530i	0.111711	+	0.306922i
$612$		0			0
$613$	−1102.34	−	401.218i	−1.79827	−	0.654516i	−0.998532	−	0.0541655i	$-0.982750\pi$
$613$	−1102.34	−	401.218i	−1.79827	−	0.654516i	−0.799737	−	0.600351i	$-0.795028\pi$
$614$		0			0
$615$	−117.981	+	146.593i	−0.191840	+	0.238362i
$616$		0			0
$617$	200.561	+	11.6813i	0.325058	+	0.0189324i	0.219898	−	0.975523i	$-0.429428\pi$
$617$	200.561	+	11.6813i	0.325058	+	0.0189324i	0.105160	+	0.994455i	$0.466465\pi$
$618$		0			0
$619$	−256.698	−	272.084i	−0.414698	−	0.439554i	0.486027	−	0.873944i	$-0.338446\pi$
$619$	−256.698	−	272.084i	−0.414698	−	0.439554i	−0.900725	+	0.434390i	$0.856964\pi$
$620$		0			0
$621$	−698.708	+	838.103i	−1.12513	+	1.34960i
$622$		0			0
$623$	474.588	+	142.082i	0.761778	+	0.228061i
$624$		0			0
$625$	−415.964	−	273.584i	−0.665543	−	0.437734i
$626$		0			0
$627$	−15.8338	−	26.1736i	−0.0252533	−	0.0417441i
$628$		0			0
$629$	1428.11	−	251.814i	2.27045	−	0.400341i
$630$		0			0
$631$	−122.780	+	696.320i	−0.194580	+	1.10352i	0.718435	+	0.695594i	$0.244859\pi$
$631$	−122.780	+	696.320i	−0.194580	+	1.10352i	−0.913015	+	0.407925i	$0.866252\pi$
$632$		0			0
$633$	955.881	−	75.3195i	1.51008	−	0.118988i
$634$		0			0
$635$	−270.570	+	81.0035i	−0.426095	+	0.127565i
$636$		0			0
$637$	525.445	+	61.4157i	0.824874	+	0.0964140i
$638$		0			0
$639$	305.591	+	1088.82i	0.478232	+	1.70395i
$640$		0			0
$641$	−591.063	−	898.668i	−0.922096	−	1.40198i	−0.915640	−	0.401999i	$-0.868315\pi$
$641$	−591.063	−	898.668i	−0.922096	−	1.40198i	−0.00645568	−	0.999979i	$-0.502055\pi$
$642$		0			0
$643$	−102.096	−	137.138i	−0.158780	−	0.213279i	0.715613	−	0.698497i	$-0.246147\pi$
$643$	−102.096	−	137.138i	−0.158780	−	0.213279i	−0.874393	+	0.485218i	$0.838740\pi$
$644$		0			0
$645$	−6.06236	+	160.636i	−0.00939901	+	0.249048i
$646$		0			0
$647$			56.2609i			0.0869565i	0.999054	+	0.0434783i	$0.0138439\pi$
$647$			56.2609i			0.0869565i	−0.999054	+	0.0434783i	$0.986156\pi$
$648$		0			0
$649$	−12.4159			−0.0191308
$650$		0			0
$651$	−351.961	+	559.742i	−0.540646	+	0.859819i
$652$		0			0
$653$	980.248	−	729.767i	1.50115	−	1.11756i	0.539948	−	0.841698i	$-0.318444\pi$
$653$	980.248	−	729.767i	1.50115	−	1.11756i	0.961197	−	0.275863i	$-0.0889636\pi$
$654$		0			0
$655$	75.9841	−	49.9755i	0.116006	−	0.0762985i
$656$		0			0
$657$	69.1556	+	695.626i	0.105260	+	1.05879i
$658$		0			0
$659$	−37.2683	+	318.851i	−0.0565528	+	0.483840i	0.935050	+	0.354517i	$0.115355\pi$
$659$	−37.2683	+	318.851i	−0.0565528	+	0.483840i	−0.991602	+	0.129323i	$0.958720\pi$
$660$		0			0
$661$	−190.640	−	636.781i	−0.288411	−	0.963360i	−0.972293	−	0.233767i	$-0.924895\pi$
$661$	−190.640	−	636.781i	−0.288411	−	0.963360i	0.683881	−	0.729593i	$-0.260291\pi$
$662$		0			0
$663$	1120.85	−	770.492i	1.69057	−	1.16213i
$664$		0			0
$665$	−65.0332	−	11.4671i	−0.0977942	−	0.0172438i
$666$		0			0
$667$	254.054	+	1440.81i	0.380891	+	2.16014i
$668$		0			0
$669$	2.29933	+	112.389i	0.00343697	+	0.167996i
$670$		0			0
$671$	−22.4631	+	34.1535i	−0.0334771	+	0.0508995i
$672$		0			0
$673$	145.600	−	486.339i	0.216345	−	0.722643i	−0.779065	−	0.626943i	$-0.784306\pi$
$673$	145.600	−	486.339i	0.216345	−	0.722643i	0.995410	−	0.0957002i	$-0.0305090\pi$
$674$		0			0
$675$	−246.956	+	577.567i	−0.365861	+	0.855655i
$676$		0			0
$677$	−149.815	+	141.343i	−0.221292	+	0.208778i	−0.788902	−	0.614520i	$-0.789350\pi$
$677$	−149.815	+	141.343i	−0.221292	+	0.208778i	0.567609	+	0.823298i	$0.307868\pi$
$678$		0			0
$679$	25.1211	−	431.313i	0.0369972	−	0.635218i
$680$		0			0
$681$	66.1467	−	425.907i	0.0971317	−	0.625413i
$682$		0			0
$683$	400.942	−	1101.58i	0.587030	−	1.61285i	−0.188873	−	0.982001i	$-0.560484\pi$
$683$	400.942	−	1101.58i	0.587030	−	1.61285i	0.775904	−	0.630851i	$-0.217294\pi$
$684$		0			0
$685$	94.4761	−	34.3865i	0.137921	−	0.0501992i
$686$		0			0
$687$	418.764	+	116.091i	0.609555	+	0.168983i
$688$		0			0
$689$	−93.5911	+	394.892i	−0.135836	+	0.573138i
$690$		0			0
$691$	400.083	+	927.497i	0.578991	+	1.34225i	0.916162	+	0.400809i	$0.131271\pi$
$691$	400.083	+	927.497i	0.578991	+	1.34225i	−0.337170	+	0.941444i	$0.609470\pi$
$692$		0			0
$693$	−34.4050	−	4.62480i	−0.0496465	−	0.00667360i
$694$		0			0
$695$	−130.922	+	7.62533i	−0.188377	+	0.0109717i
$696$		0			0
$697$	−485.491	+	1125.49i	−0.696544	+	1.61477i
$698$		0			0
$699$	498.214	+	107.366i	0.712753	+	0.153599i
$700$		0			0
$701$	−827.278	−	477.629i	−1.18014	−	0.681354i	−0.224093	−	0.974568i	$-0.571942\pi$
$701$	−827.278	−	477.629i	−1.18014	−	0.681354i	−0.956047	+	0.293214i	$0.905275\pi$
$702$		0			0
$703$	−324.259	−	561.633i	−0.461250	−	0.798908i
$704$		0			0
$705$	41.4697	+	16.8908i	0.0588223	+	0.0239586i
$706$		0			0
$707$	75.7062	+	647.708i	0.107081	+	0.916135i
$708$		0			0
$709$	105.679	+	53.0742i	0.149054	+	0.0748578i	0.521763	−	0.853091i	$-0.325275\pi$
$709$	105.679	+	53.0742i	0.149054	+	0.0748578i	−0.372709	+	0.927948i	$0.621571\pi$
$710$		0			0
$711$	118.142	−	307.942i	0.166163	−	0.433112i
$712$		0			0
$713$	−1640.66	−	1221.42i	−2.30106	−	1.71308i
$714$		0			0
$715$	−14.1022	+	14.9474i	−0.0197233	+	0.0209055i
$716$		0			0
$717$	538.680	−	755.351i	0.751297	−	1.05349i
$718$		0			0
$719$	−217.523	+	259.234i	−0.302536	+	0.360548i	−0.895798	−	0.444461i	$-0.853395\pi$
$719$	−217.523	+	259.234i	−0.302536	+	0.360548i	0.593262	+	0.805009i	$0.297840\pi$
$720$		0			0
$721$	−288.080	+	241.728i	−0.399557	+	0.335268i
$722$		0			0
$723$	425.666	+	486.713i	0.588749	+	0.673186i
$724$		0			0
$725$	377.996	+	752.651i	0.521373	+	1.03814i
$726$		0			0
$727$	640.773	−	151.866i	0.881393	−	0.208894i	0.235089	−	0.971974i	$-0.424462\pi$
$727$	640.773	−	151.866i	0.881393	−	0.208894i	0.646304	+	0.763080i	$0.276314\pi$
$728$		0			0
$729$	710.408	+	163.590i	0.974496	+	0.224404i
$730$		0			0
$731$	241.481	+	1018.89i	0.330343	+	1.39383i
$732$		0			0
$733$	−464.043	+	233.051i	−0.633074	+	0.317942i	−0.736238	−	0.676723i	$-0.763400\pi$
$733$	−464.043	+	233.051i	−0.633074	+	0.317942i	0.103164	+	0.994664i	$0.467103\pi$
$734$		0			0
$735$	89.3498	−	78.1428i	0.121564	−	0.106317i
$736$		0			0
$737$	35.2994	+	42.0682i	0.0478960	+	0.0570803i
$738$		0			0
$739$	614.828	+	515.902i	0.831973	+	0.698108i	0.955743	−	0.294203i	$-0.0950540\pi$
$739$	614.828	+	515.902i	0.831973	+	0.698108i	−0.123770	+	0.992311i	$0.539498\pi$
$740$		0			0
$741$	−495.231	−	353.175i	−0.668327	−	0.476619i
$742$		0			0
$743$	−771.921	−	728.270i	−1.03892	−	0.980175i	−0.0391061	−	0.999235i	$-0.512451\pi$
$743$	−771.921	−	728.270i	−1.03892	−	0.980175i	−0.999818	+	0.0190604i	$0.993933\pi$
$744$		0			0
$745$	28.4842	−	38.2609i	0.0382338	−	0.0513569i
$746$		0			0
$747$	55.7005	+	21.3695i	0.0745656	+	0.0286070i
$748$		0			0
$749$	121.882	−	242.686i	0.162726	−	0.324014i
$750$		0			0
$751$	22.6115	−	2.64290i	0.0301085	−	0.00351918i	−0.101025	−	0.994884i	$-0.532212\pi$
$751$	22.6115	−	2.64290i	0.0301085	−	0.00351918i	0.131134	+	0.991365i	$0.458138\pi$
$752$		0			0
$753$	289.634	−	711.099i	0.384640	−	0.944355i
$754$		0			0
$755$	−90.8928	+	52.4770i	−0.120388	+	0.0695059i
$756$		0			0
$757$	687.048	−	1190.00i	0.907593	−	1.57200i	0.0901938	−	0.995924i	$-0.471251\pi$
$757$	687.048	−	1190.00i	0.907593	−	1.57200i	0.817399	−	0.576072i	$-0.195415\pi$
$758$		0			0
$759$	22.6228	−	104.978i	0.0298060	−	0.138310i
$760$		0			0
$761$	−554.457	−	239.169i	−0.728590	−	0.314283i	−0.000721465	−	1.00000i	$-0.500230\pi$
$761$	−554.457	−	239.169i	−0.728590	−	0.314283i	−0.727869	+	0.685717i	$0.759489\pi$
$762$		0			0
$763$	16.8226	+	288.833i	0.0220480	+	0.378549i
$764$		0			0
$765$	40.6575	−	302.461i	0.0531471	−	0.395374i
$766$		0			0
$767$	−226.690	+	97.7846i	−0.295554	+	0.127490i
$768$		0			0
$769$	1320.13	+	312.876i	1.71668	+	0.406861i	0.966967	−	0.254900i	$-0.0820426\pi$
$769$	1320.13	+	312.876i	1.71668	+	0.406861i	0.749715	+	0.661761i	$0.230191\pi$
$770$		0			0
$771$	−100.926	+	364.060i	−0.130903	+	0.472192i
$772$		0			0
$773$	228.966	+	629.080i	0.296205	+	0.813816i	0.995125	+	0.0986170i	$0.0314419\pi$
$773$	228.966	+	629.080i	0.296205	+	0.813816i	−0.698921	+	0.715199i	$0.746336\pi$
$774$		0			0
$775$	−1106.47	−	402.723i	−1.42771	−	0.519643i
$776$		0			0
$777$	−727.233	−	112.945i	−0.935949	−	0.145360i
$778$		0			0
$779$	547.236	+	31.8729i	0.702485	+	0.0409151i
$780$		0			0
$781$	−76.3779	−	80.9559i	−0.0977950	−	0.103657i
$782$		0			0
$783$	782.178	−	586.197i	0.998950	−	0.748655i
$784$		0			0
$785$	276.148	+	82.6733i	0.351781	+	0.105316i
$786$		0			0
$787$	−701.183	−	461.175i	−0.890957	−	0.585991i	0.0194019	−	0.999812i	$-0.493824\pi$
$787$	−701.183	−	461.175i	−0.890957	−	0.585991i	−0.910359	+	0.413820i	$0.864194\pi$
$788$		0			0
$789$	−360.388	+	7.37305i	−0.456765	+	0.00934481i
$790$		0			0
$791$	438.533	−	77.3252i	0.554403	−	0.0977563i
$792$		0			0
$793$	−141.148	+	800.490i	−0.177992	+	1.00945i
$794$		0			0
$795$	51.5834	+	75.0392i	0.0648848	+	0.0943890i
$796$		0			0
$797$	1358.97	−	406.848i	1.70510	−	0.510474i	0.721745	−	0.692159i	$-0.243340\pi$
$797$	1358.97	−	406.848i	1.70510	−	0.510474i	0.983357	+	0.181685i	$0.0581550\pi$
$798$		0			0
$799$	289.705	+	33.8617i	0.362584	+	0.0423800i
$800$		0			0
$801$	1018.84	−	101.288i	1.27196	−	0.126452i
$802$		0			0
$803$	−37.8055	−	57.4805i	−0.0470804	−	0.0715822i
$804$		0			0
$805$	−138.434	−	185.949i	−0.171968	−	0.230993i
$806$		0			0
$807$	1173.35	+	737.793i	1.45397	+	0.914241i
$808$		0			0
$809$		−	679.161i		−	0.839507i	−0.907638	−	0.419753i	$-0.862117\pi$
$809$		−	679.161i		−	0.839507i	0.907638	−	0.419753i	$-0.137883\pi$
$810$		0			0
$811$	−748.216			−0.922584			−0.461292	−	0.887248i	$-0.652614\pi$
$811$	−748.216			−0.922584			−0.461292	+	0.887248i	$0.652614\pi$
$812$		0			0
$813$	−1387.49	−	52.3635i	−1.70663	−	0.0644078i
$814$		0			0
$815$	24.2900	−	18.0832i	0.0298036	−	0.0221880i
$816$		0			0
$817$	391.242	−	257.324i	0.478876	−	0.314962i
$818$		0			0
$819$	−664.592	+	186.525i	−0.811467	+	0.227748i
$820$		0			0
$821$	29.5727	−	253.011i	0.0360204	−	0.308174i	−0.963203	−	0.268774i	$-0.913381\pi$
$821$	29.5727	−	253.011i	0.0360204	−	0.308174i	0.999224	−	0.0393995i	$-0.0125445\pi$
$822$		0			0
$823$	−166.479	−	556.080i	−0.202283	−	0.675674i	−0.997585	−	0.0694595i	$-0.977873\pi$
$823$	−166.479	−	556.080i	−0.202283	−	0.675674i	0.795301	−	0.606214i	$-0.207313\pi$
$824$		0			0
$825$	−4.85615	−	61.6294i	−0.00588624	−	0.0747023i
$826$		0			0
$827$	1248.36	+	220.119i	1.50950	+	0.266166i	0.866297	−	0.499530i	$-0.166494\pi$
$827$	1248.36	+	220.119i	1.50950	+	0.266166i	0.643204	+	0.765695i	$0.277605\pi$
$828$		0			0
$829$	138.488	+	785.407i	0.167055	+	0.947415i	0.946920	+	0.321468i	$0.104176\pi$
$829$	138.488	+	785.407i	0.167055	+	0.947415i	−0.779866	+	0.625947i	$0.784713\pi$
$830$		0			0
$831$	−154.420	+	93.4173i	−0.185825	+	0.112416i
$832$		0			0
$833$	424.881	−	645.999i	0.510061	−	0.775510i
$834$		0			0
$835$	−51.2619	+	171.227i	−0.0613915	+	0.205062i
$836$		0			0
$837$	−233.002	+	1346.52i	−0.278377	+	1.60875i
$838$		0			0
$839$	9.04192	−	8.53061i	0.0107770	−	0.0101676i	−0.680834	−	0.732437i	$-0.738383\pi$
$839$	9.04192	−	8.53061i	0.0107770	−	0.0101676i	0.691611	+	0.722270i	$0.256901\pi$
$840$		0			0
$841$	27.3050	−	468.808i	0.0324673	−	0.557442i
$842$		0			0
$843$	415.494	+	334.399i	0.492875	+	0.396678i
$844$		0			0
$845$	−63.6154	+	174.782i	−0.0752845	+	0.206842i
$846$		0			0
$847$	−491.929	+	179.048i	−0.580790	+	0.211390i
$848$		0			0
$849$	−253.872	−	981.272i	−0.299025	−	1.15580i
$850$		0			0
$851$	525.027	−	2215.26i	0.616953	−	2.60313i
$852$		0			0
$853$	−377.627	−	875.437i	−0.442704	−	1.02630i	−0.982795	−	0.184697i	$-0.940870\pi$
$853$	−377.627	−	875.437i	−0.442704	−	1.02630i	0.540091	−	0.841606i	$-0.318390\pi$
$854$		0			0
$855$	−133.325	+	29.1770i	−0.155936	+	0.0341251i
$856$		0			0
$857$	1182.15	−	68.8521i	1.37940	−	0.0803409i	0.647662	−	0.761928i	$-0.275747\pi$
$857$	1182.15	−	68.8521i	1.37940	−	0.0803409i	0.731737	+	0.681587i	$0.238710\pi$
$858$		0			0
$859$	335.181	−	777.038i	0.390200	−	0.904584i	−0.603995	−	0.796988i	$-0.706425\pi$
$859$	335.181	−	777.038i	0.390200	−	0.904584i	0.994195	−	0.107596i	$-0.0343153\pi$
$860$		0			0
$861$	417.544	−	461.112i	0.484952	−	0.535554i
$862$		0			0
$863$	−710.752	−	410.353i	−0.823582	−	0.475495i	0.0280679	−	0.999606i	$-0.491065\pi$
$863$	−710.752	−	410.353i	−0.823582	−	0.475495i	−0.851650	+	0.524111i	$0.824398\pi$
$864$		0			0
$865$	−49.8684	−	86.3747i	−0.0576514	−	0.0998551i
$866$		0			0
$867$	−152.877	−	1110.45i	−0.176328	−	1.28079i
$868$		0			0
$869$	3.76844	+	32.2411i	0.00433652	+	0.0371013i
$870$		0			0
$871$	975.815	+	490.073i	1.12034	+	0.562655i
$872$		0			0
$873$	−290.865	−	844.221i	−0.333179	−	0.967034i
$874$		0			0
$875$	−222.077	−	165.331i	−0.253803	−	0.188949i
$876$		0			0
$877$	888.471	−	941.724i	1.01308	−	1.07380i	0.0158157	−	0.999875i	$-0.494965\pi$
$877$	888.471	−	941.724i	1.01308	−	1.07380i	0.997264	−	0.0739265i	$-0.0235530\pi$
$878$		0			0
$879$	129.749	+	284.637i	0.147610	+	0.323819i
$880$		0			0
$881$	−376.445	+	448.629i	−0.427292	+	0.509227i	−0.936139	−	0.351630i	$-0.885628\pi$
$881$	−376.445	+	448.629i	−0.427292	+	0.509227i	0.508847	+	0.860857i	$0.330072\pi$
$882$		0			0
$883$	−136.880	+	114.856i	−0.155017	+	0.130074i	−0.716997	−	0.697076i	$-0.754484\pi$
$883$	−136.880	+	114.856i	−0.155017	+	0.130074i	0.561981	+	0.827150i	$0.310040\pi$
$884$		0			0
$885$	−17.8773	+	52.4302i	−0.0202003	+	0.0592432i
$886$		0			0
$887$	435.858	+	867.865i	0.491385	+	0.978428i	0.993522	+	0.113640i	$0.0362509\pi$
$887$	435.858	+	867.865i	0.491385	+	0.978428i	−0.502137	+	0.864788i	$0.667453\pi$
$888$		0			0
$889$	908.516	−	215.322i	1.02195	−	0.242207i
$890$		0			0
$891$	−69.4012	+	18.1917i	−0.0778914	+	0.0204172i
$892$		0			0
$893$	−30.0817	−	126.925i	−0.0336862	−	0.142133i
$894$		0			0
$895$	−341.507	+	171.511i	−0.381572	+	0.191633i
$896$		0			0
$897$	−413.730	−	2094.86i	−0.461237	−	2.33540i
$898$		0			0
$899$	1177.77	+	1403.61i	1.31009	+	1.56130i
$900$		0			0
$901$	454.379	+	381.269i	0.504305	+	0.423162i
$902$		0			0
$903$	50.8841	−	528.971i	0.0563501	−	0.585793i
$904$		0			0
$905$	26.4439	+	24.9485i	0.0292198	+	0.0275674i
$906$		0			0
$907$	1.75887	−	2.36258i	0.00193922	−	0.00260482i	−0.801153	−	0.598460i	$-0.795779\pi$
$907$	1.75887	−	2.36258i	0.00193922	−	0.00260482i	0.803092	+	0.595855i	$0.203187\pi$
$908$		0			0
$909$	653.626	+	1178.65i	0.719061	+	1.29665i
$910$		0			0
$911$	167.127	−	332.776i	0.183454	−	0.365287i	−0.783042	−	0.621969i	$-0.786333\pi$
$911$	167.127	−	332.776i	0.183454	−	0.365287i	0.966496	+	0.256682i	$0.0826293\pi$
$912$		0			0
$913$	−5.83175	+	0.681634i	−0.00638746	+	0.000746587i
$914$		0			0
$915$	111.880	+	144.034i	0.122274	+	0.157415i
$916$		0			0
$917$	−260.371	+	150.325i	−0.283938	+	0.163932i
$918$		0			0
$919$	−394.926	+	684.032i	−0.429735	+	0.744322i	−0.996849	−	0.0793166i	$-0.974726\pi$
$919$	−394.926	+	684.032i	−0.429735	+	0.744322i	0.567115	+	0.823639i	$0.308060\pi$
$920$		0			0
$921$	309.543	−	99.6142i	0.336095	−	0.108159i
$922$		0			0
$923$	−2032.10	−	876.561i	−2.20162	−	0.949687i
$924$		0			0
$925$	−76.2046	−	1308.38i	−0.0823834	−	1.41447i
$926$		0			0
$927$	−360.757	+	688.426i	−0.389166	+	0.742639i
$928$		0			0
$929$	−970.217	+	418.511i	−1.04437	+	0.450496i	−0.847979	−	0.530030i	$-0.822181\pi$
$929$	−970.217	+	418.511i	−1.04437	+	0.450496i	−0.196388	+	0.980526i	$0.562921\pi$
$930$		0			0
$931$	−336.462	−	79.7430i	−0.361399	−	0.0856531i
$932$		0			0
$933$	204.666	+	208.231i	0.219364	+	0.223184i
$934$		0			0
$935$	10.2726	+	28.2237i	0.0109867	+	0.0301857i
$936$		0			0
$937$	238.245	+	86.7140i	0.254263	+	0.0925443i	0.466007	−	0.884781i	$-0.345692\pi$
$937$	238.245	+	86.7140i	0.254263	+	0.0925443i	−0.211744	+	0.977325i	$0.567914\pi$
$938$		0			0
$939$	480.056	+	1239.45i	0.511241	+	1.31997i
$940$		0			0
$941$	−200.371	−	11.6703i	−0.212935	−	0.0124020i	−0.0486540	−	0.998816i	$-0.515493\pi$
$941$	−200.371	−	11.6703i	−0.212935	−	0.0124020i	−0.164280	+	0.986414i	$0.552530\pi$
$942$		0			0
$943$	1320.56	+	1399.71i	1.40038	+	1.48432i
$944$		0			0
$945$	−69.0684	+	138.627i	−0.0730883	+	0.146696i
$946$		0			0
$947$	−1352.38	−	404.877i	−1.42807	−	0.427536i	−0.522831	−	0.852437i	$-0.675124\pi$
$947$	−1352.38	−	404.877i	−1.42807	−	0.427536i	−0.905240	+	0.424900i	$0.860309\pi$
$948$		0			0
$949$	−1142.96	−	751.734i	−1.20438	−	0.792133i
$950$		0			0
$951$	−55.1112	+	100.131i	−0.0579507	+	0.105290i
$952$		0			0
$953$	−325.122	+	57.3279i	−0.341157	+	0.0601551i	−0.341602	−	0.939845i	$-0.610969\pi$
$953$	−325.122	+	57.3279i	−0.341157	+	0.0601551i	0.000445092		1.00000i	$0.499858\pi$
$954$		0			0
$955$	−23.4244	+	132.847i	−0.0245282	+	0.139106i
$956$		0			0
$957$	−41.4064	+	86.8313i	−0.0432669	+	0.0907328i
$958$		0			0
$959$	−318.403	+	95.3235i	−0.332015	+	0.0993989i
$960$		0			0
$961$	−1589.78	−	185.819i	−1.65430	−	0.193360i
$962$		0			0
$963$	42.3042	−	559.674i	0.0439296	−	0.581178i
$964$		0			0
$965$	62.5000	+	95.0267i	0.0647669	+	0.0984732i
$966$		0			0
$967$	165.594	+	222.431i	0.171245	+	0.230022i	0.879458	−	0.475977i	$-0.157906\pi$
$967$	165.594	+	222.431i	0.171245	+	0.230022i	−0.708212	+	0.705999i	$0.750498\pi$
$968$		0			0
$969$	−786.129	+	415.158i	−0.811278	+	0.428439i
$970$		0			0
$971$			1088.17i			1.12067i	0.828266	+	0.560335i	$0.189328\pi$
$971$			1088.17i			1.12067i	−0.828266	+	0.560335i	$0.810672\pi$
$972$		0			0
$973$	433.538			0.445569
$974$		0			0
$975$	−574.041	−	1086.99i	−0.588760	−	1.11486i
$976$		0			0
$977$	72.1768	−	53.7336i	0.0738759	−	0.0549986i	−0.559587	−	0.828772i	$-0.689040\pi$
$977$	72.1768	−	53.7336i	0.0738759	−	0.0549986i	0.633463	+	0.773773i	$0.281633\pi$
$978$		0			0
$979$	−84.1882	+	55.3715i	−0.0859941	+	0.0565592i
$980$		0			0
$981$	259.096	+	538.906i	0.264114	+	0.549343i
$982$		0			0
$983$	−213.541	+	1826.96i	−0.217234	+	1.85856i	0.242042	+	0.970266i	$0.422183\pi$
$983$	−213.541	+	1826.96i	−0.217234	+	1.85856i	−0.459276	+	0.888294i	$0.651891\pi$
$984$		0			0
$985$	−136.535	−	456.060i	−0.138615	−	0.463005i
$986$		0			0
$987$	−133.613	−	63.7148i	−0.135373	−	0.0645540i
$988$		0			0
$989$	1618.93	+	285.460i	1.63693	+	0.288635i
$990$		0			0
$991$	−93.5646	−	530.631i	−0.0944143	−	0.535450i	−0.994925	−	0.100617i	$-0.967918\pi$
$991$	−93.5646	−	530.631i	−0.0944143	−	0.535450i	0.900511	−	0.434833i	$-0.143193\pi$
$992$		0			0
$993$	307.986	+	169.512i	0.310157	+	0.170707i
$994$		0			0
$995$	250.500	−	380.866i	0.251759	−	0.382780i
$996$		0			0
$997$	−4.53903	+	15.1614i	−0.00455269	+	0.0152070i	−0.960236	−	0.279191i	$-0.909934\pi$
$997$	−4.53903	+	15.1614i	−0.00455269	+	0.0152070i	0.955683	+	0.294398i	$0.0951190\pi$
$998$		0			0
$999$	−1478.89	+	355.491i	−1.48037	+	0.355846i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.3.o.a.5.7	✓	324
81.65	odd	54	inner	324.3.o.a.65.7	yes	324

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
324.3.o.a.5.7	✓	324	1.1	even	1	trivial
324.3.o.a.65.7	yes	324	81.65	odd	54	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:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	324.o (of order \(54\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40095 - 2.65280i) q^{3} +(1.05662 - 0.786622i) q^{5} +(-3.63828 + 2.39294i) q^{7} +(-5.07467 + 7.43288i) q^{9} +O(q^{10})\)	\(q+(-1.40095 - 2.65280i) q^{3} +(1.05662 - 0.786622i) q^{5} +(-3.63828 + 2.39294i) q^{7} +(-5.07467 + 7.43288i) q^{9} +(0.102829 - 0.879762i) q^{11} +(-5.05132 - 16.8726i) q^{13} +(-3.56702 - 1.70097i) q^{15} +(-25.3507 - 4.47002i) q^{17} +(1.99904 + 11.3371i) q^{19} +(11.4450 + 6.29924i) q^{21} +(-22.2073 + 33.7646i) q^{23} +(-6.67242 + 22.2874i) q^{25} +(26.8273 + 3.04895i) q^{27} +(26.3326 - 24.8435i) q^{29} +(-2.94284 + 50.5267i) q^{31} +(-2.47789 + 0.959719i) q^{33} +(-1.96194 + 5.39037i) q^{35} +(-52.9367 + 19.2674i) q^{37} +(-37.6829 + 37.0378i) q^{39} +(10.9812 - 46.3332i) q^{41} +(-16.1115 - 37.3508i) q^{43} +(0.484891 + 11.8456i) q^{45} +(-11.3117 + 0.658832i) q^{47} +(-11.8969 + 27.5802i) q^{49} +(23.6571 + 73.5126i) q^{51} +(-19.9552 - 11.5211i) q^{53} +(-0.583389 - 1.01046i) q^{55} +(27.2745 - 21.1858i) q^{57} +(-1.62732 - 13.9226i) q^{59} +(-41.2423 - 20.7127i) q^{61} +(0.676659 - 39.1863i) q^{63} +(-18.6097 - 13.8544i) q^{65} +(-42.5466 + 45.0968i) q^{67} +(120.682 + 11.6089i) q^{69} +(80.7693 - 96.2571i) q^{71} +(59.5008 - 49.9271i) q^{73} +(68.4717 - 13.5230i) q^{75} +(1.73109 + 3.44689i) q^{77} +(-35.6596 + 8.45149i) q^{79} +(-29.4955 - 75.4388i) q^{81} +(-1.52870 - 6.45010i) q^{83} +(-30.3022 + 15.2184i) q^{85} +(-102.795 - 35.0504i) q^{87} +(-73.1252 - 87.1472i) q^{89} +(58.7531 + 49.2997i) q^{91} +(138.160 - 62.9787i) q^{93} +(11.0302 + 10.4065i) q^{95} +(-59.2463 + 79.5816i) q^{97} +(6.01734 + 5.22882i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 324 q+O(q^{10}) \) 324 * q	\( 324 q - 135 q^{21} - 81 q^{23} + 27 q^{27} + 81 q^{29} + 189 q^{33} + 243 q^{35} + 216 q^{41} + 432 q^{45} + 324 q^{47} + 126 q^{51} - 216 q^{57} - 378 q^{59} - 540 q^{63} - 108 q^{65} - 351 q^{67} + 504 q^{69} + 648 q^{71} + 450 q^{75} + 432 q^{77} - 54 q^{79} - 72 q^{81} - 216 q^{83} + 270 q^{85} - 1008 q^{87} - 648 q^{89} - 684 q^{93} - 432 q^{95} + 459 q^{97} - 252 q^{99}+O(q^{100}) \) 324 * q - 135 * q^21 - 81 * q^23 + 27 * q^27 + 81 * q^29 + 189 * q^33 + 243 * q^35 + 216 * q^41 + 432 * q^45 + 324 * q^47 + 126 * q^51 - 216 * q^57 - 378 * q^59 - 540 * q^63 - 108 * q^65 - 351 * q^67 + 504 * q^69 + 648 * q^71 + 450 * q^75 + 432 * q^77 - 54 * q^79 - 72 * q^81 - 216 * q^83 + 270 * q^85 - 1008 * q^87 - 648 * q^89 - 684 * q^93 - 432 * q^95 + 459 * q^97 - 252 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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