LMFDB - Embedded newform 324.3.o.a.5.6

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			5.6
Character	$\chi$	$=$	324.5
Dual form			324.3.o.a.65.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.59067 + 2.54358i) q^{3} +(-2.52291 + 1.87823i) q^{5} +(-4.60759 + 3.03046i) q^{7} +(-3.93956 - 8.09196i) q^{9} +O(q^{10})$	\(q+(-1.59067 + 2.54358i) q^{3} +(-2.52291 + 1.87823i) q^{5} +(-4.60759 + 3.03046i) q^{7} +(-3.93956 - 8.09196i) q^{9} +(0.644815 - 5.51675i) q^{11} +(3.12574 + 10.4407i) q^{13} +(-0.764332 - 9.40485i) q^{15} +(-9.72857 - 1.71541i) q^{17} +(-5.56429 - 31.5567i) q^{19} +(-0.379070 - 16.5402i) q^{21} +(11.1738 - 16.9889i) q^{23} +(-4.33279 + 14.4725i) q^{25} +(26.8491 + 2.85102i) q^{27} +(18.8382 - 17.7729i) q^{29} +(1.17260 - 20.1327i) q^{31} +(13.0066 + 10.4154i) q^{33} +(5.93260 - 16.2997i) q^{35} +(-51.6114 + 18.7850i) q^{37} +(-31.5287 - 8.65710i) q^{39} +(14.2410 - 60.0876i) q^{41} +(-8.52424 - 19.7614i) q^{43} +(25.1377 + 13.0158i) q^{45} +(-52.0796 + 3.03329i) q^{47} +(-7.36173 + 17.0664i) q^{49} +(19.8382 - 22.0167i) q^{51} +(-8.55662 - 4.94017i) q^{53} +(8.73493 + 15.1293i) q^{55} +(89.1177 + 36.0429i) q^{57} +(-9.04028 - 77.3445i) q^{59} +(19.5983 + 9.84264i) q^{61} +(42.6742 + 25.3457i) q^{63} +(-27.4960 - 20.4700i) q^{65} +(-42.3478 + 44.8861i) q^{67} +(25.4388 + 55.4450i) q^{69} +(-61.2446 + 72.9885i) q^{71} +(-46.6879 + 39.1758i) q^{73} +(-29.9200 - 34.0417i) q^{75} +(13.7472 + 27.3730i) q^{77} +(10.3218 - 2.44630i) q^{79} +(-49.9597 + 63.7576i) q^{81} +(-18.8178 - 79.3985i) q^{83} +(27.7662 - 13.9447i) q^{85} +(15.2415 + 76.1871i) q^{87} +(15.4859 + 18.4553i) q^{89} +(-46.0422 - 38.6340i) q^{91} +(49.3440 + 35.0071i) q^{93} +(73.3089 + 69.1634i) q^{95} +(-91.4351 + 122.819i) q^{97} +(-47.1816 + 16.5158i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−1.59067	+	2.54358i	−0.530222	+	0.847859i
$3$	−1.59067	+	2.54358i	−0.530222	+	0.847859i
$4$		0			0
$5$	−2.52291	+	1.87823i	−0.504581	+	0.375647i	−0.819142	−	0.573591i	$-0.805550\pi$
$5$	−2.52291	+	1.87823i	−0.504581	+	0.375647i	0.314561	+	0.949237i	$0.398143\pi$
$6$		0			0
$7$	−4.60759	+	3.03046i	−0.658227	+	0.432922i	−0.834192	−	0.551474i	$-0.814066\pi$
$7$	−4.60759	+	3.03046i	−0.658227	+	0.432922i	0.175966	+	0.984396i	$0.443695\pi$
$8$		0			0
$9$	−3.93956	−	8.09196i	−0.437729	−	0.899107i
$10$		0			0
$11$	0.644815	−	5.51675i	0.0586196	−	0.501523i	−0.931753	−	0.363093i	$-0.881721\pi$
$11$	0.644815	−	5.51675i	0.0586196	−	0.501523i	0.990372	−	0.138429i	$-0.0442053\pi$
$12$		0			0
$13$	3.12574	+	10.4407i	0.240441	+	0.803130i	0.989985	+	0.141175i	$0.0450879\pi$
$13$	3.12574	+	10.4407i	0.240441	+	0.803130i	−0.749543	+	0.661955i	$0.769727\pi$
$14$		0			0
$15$	−0.764332	−	9.40485i	−0.0509554	−	0.626990i
$16$		0			0
$17$	−9.72857	−	1.71541i	−0.572269	−	0.100906i	−0.119977	−	0.992777i	$-0.538282\pi$
$17$	−9.72857	−	1.71541i	−0.572269	−	0.100906i	−0.452291	+	0.891870i	$0.649393\pi$
$18$		0			0
$19$	−5.56429	−	31.5567i	−0.292857	−	1.66088i	−0.675785	−	0.737098i	$-0.736195\pi$
$19$	−5.56429	−	31.5567i	−0.292857	−	1.66088i	0.382928	−	0.923778i	$-0.374916\pi$
$20$		0			0
$21$	−0.379070	−	16.5402i	−0.0180510	−	0.787628i
$22$		0			0
$23$	11.1738	−	16.9889i	0.485817	−	0.738648i	−0.506518	−	0.862229i	$-0.669068\pi$
$23$	11.1738	−	16.9889i	0.485817	−	0.738648i	0.992334	+	0.123581i	$0.0394380\pi$
$24$		0			0
$25$	−4.33279	+	14.4725i	−0.173312	+	0.578901i
$26$		0			0
$27$	26.8491	+	2.85102i	0.994409	+	0.105593i
$28$		0			0
$29$	18.8382	−	17.7729i	0.649593	−	0.612859i	−0.289230	−	0.957260i	$-0.593399\pi$
$29$	18.8382	−	17.7729i	0.649593	−	0.612859i	0.938823	+	0.344401i	$0.111918\pi$
$30$		0			0
$31$	1.17260	−	20.1327i	0.0378258	−	0.649443i	−0.925108	−	0.379705i	$-0.876026\pi$
$31$	1.17260	−	20.1327i	0.0378258	−	0.649443i	0.962934	−	0.269739i	$-0.0869373\pi$
$32$		0			0
$33$	13.0066	+	10.4154i	0.394139	+	0.315619i
$34$		0			0
$35$	5.93260	−	16.2997i	0.169503	−	0.465705i
$36$		0			0
$37$	−51.6114	+	18.7850i	−1.39490	+	0.507703i	−0.926661	−	0.375897i	$-0.877335\pi$
$37$	−51.6114	+	18.7850i	−1.39490	+	0.507703i	−0.468242	+	0.883601i	$0.655112\pi$
$38$		0			0
$39$	−31.5287	−	8.65710i	−0.808428	−	0.221977i
$40$		0			0
$41$	14.2410	−	60.0876i	0.347342	−	1.46555i	−0.466530	−	0.884506i	$-0.654496\pi$
$41$	14.2410	−	60.0876i	0.347342	−	1.46555i	0.813872	−	0.581045i	$-0.197356\pi$
$42$		0			0
$43$	−8.52424	−	19.7614i	−0.198238	−	0.459568i	0.789880	−	0.613261i	$-0.210143\pi$
$43$	−8.52424	−	19.7614i	−0.198238	−	0.459568i	−0.988119	+	0.153693i	$0.950883\pi$
$44$		0			0
$45$	25.1377	+	13.0158i	0.558616	+	0.289241i
$46$		0			0
$47$	−52.0796	+	3.03329i	−1.10808	+	0.0645381i	−0.602407	−	0.798189i	$-0.705791\pi$
$47$	−52.0796	+	3.03329i	−1.10808	+	0.0645381i	−0.505669	+	0.862727i	$0.668754\pi$
$48$		0			0
$49$	−7.36173	+	17.0664i	−0.150239	+	0.348294i
$50$		0			0
$51$	19.8382	−	22.0167i	0.388984	−	0.431700i
$52$		0			0
$53$	−8.55662	−	4.94017i	−0.161446	−	0.0932107i	0.417100	−	0.908860i	$-0.363046\pi$
$53$	−8.55662	−	4.94017i	−0.161446	−	0.0932107i	−0.578546	+	0.815650i	$0.696380\pi$
$54$		0			0
$55$	8.73493	+	15.1293i	0.158817	+	0.275079i
$56$		0			0
$57$	89.1177	+	36.0429i	1.56347	+	0.632331i
$58$		0			0
$59$	−9.04028	−	77.3445i	−0.153225	−	1.31092i	−0.822865	−	0.568238i	$-0.807625\pi$
$59$	−9.04028	−	77.3445i	−0.153225	−	1.31092i	0.669639	−	0.742686i	$-0.266449\pi$
$60$		0			0
$61$	19.5983	+	9.84264i	0.321284	+	0.161355i	0.602130	−	0.798398i	$-0.294319\pi$
$61$	19.5983	+	9.84264i	0.321284	+	0.161355i	−0.280846	+	0.959753i	$0.590615\pi$
$62$		0			0
$63$	42.6742	+	25.3457i	0.677369	+	0.402313i
$64$		0			0
$65$	−27.4960	−	20.4700i	−0.423015	−	0.314923i
$66$		0			0
$67$	−42.3478	+	44.8861i	−0.632057	+	0.669941i	−0.961681	−	0.274171i	$-0.911597\pi$
$67$	−42.3478	+	44.8861i	−0.632057	+	0.669941i	0.329624	+	0.944112i	$0.393078\pi$
$68$		0			0
$69$	25.4388	+	55.4450i	0.368679	+	0.803551i
$70$		0			0
$71$	−61.2446	+	72.9885i	−0.862600	+	1.02801i	0.136701	+	0.990612i	$0.456350\pi$
$71$	−61.2446	+	72.9885i	−0.862600	+	1.02801i	−0.999301	+	0.0373940i	$0.988094\pi$
$72$		0			0
$73$	−46.6879	+	39.1758i	−0.639560	+	0.536655i	−0.903883	−	0.427779i	$-0.859296\pi$
$73$	−46.6879	+	39.1758i	−0.639560	+	0.536655i	0.264323	+	0.964434i	$0.414852\pi$
$74$		0			0
$75$	−29.9200	−	34.0417i	−0.398933	−	0.453890i
$76$		0			0
$77$	13.7472	+	27.3730i	0.178535	+	0.355493i
$78$		0			0
$79$	10.3218	−	2.44630i	0.130655	−	0.0309659i	−0.164768	−	0.986332i	$-0.552688\pi$
$79$	10.3218	−	2.44630i	0.130655	−	0.0309659i	0.295423	+	0.955366i	$0.404539\pi$
$80$		0			0
$81$	−49.9597	+	63.7576i	−0.616786	+	0.787131i
$82$		0			0
$83$	−18.8178	−	79.3985i	−0.226720	−	0.956609i	−0.960733	−	0.277473i	$-0.910503\pi$
$83$	−18.8178	−	79.3985i	−0.226720	−	0.956609i	0.734013	−	0.679136i	$-0.237645\pi$
$84$		0			0
$85$	27.7662	−	13.9447i	0.326661	−	0.164055i
$86$		0			0
$87$	15.2415	+	76.1871i	0.175190	+	0.875714i
$88$		0			0
$89$	15.4859	+	18.4553i	0.173998	+	0.207363i	0.845995	−	0.533191i	$-0.179007\pi$
$89$	15.4859	+	18.4553i	0.173998	+	0.207363i	−0.671996	+	0.740554i	$0.734563\pi$
$90$		0			0
$91$	−46.0422	−	38.6340i	−0.505958	−	0.424549i
$92$		0			0
$93$	49.3440	+	35.0071i	0.530580	+	0.376420i
$94$		0			0
$95$	73.3089	+	69.1634i	0.771673	+	0.728036i
$96$		0			0
$97$	−91.4351	+	122.819i	−0.942630	+	1.26617i	0.0212336	+	0.999775i	$0.493241\pi$
$97$	−91.4351	+	122.819i	−0.942630	+	1.26617i	−0.963863	+	0.266397i	$0.914167\pi$
$98$		0			0
$99$	−47.1816	+	16.5158i	−0.476582	+	0.166826i
$100$		0			0
$101$	11.9263	−	23.7472i	0.118082	−	0.235121i	−0.826825	−	0.562459i	$-0.809855\pi$
$101$	11.9263	−	23.7472i	0.118082	−	0.235121i	0.944907	+	0.327338i	$0.106152\pi$
$102$		0			0
$103$	17.8257	−	2.08353i	0.173065	−	0.0202284i	−0.0291189	−	0.999576i	$-0.509270\pi$
$103$	17.8257	−	2.08353i	0.173065	−	0.0202284i	0.202184	+	0.979348i	$0.435196\pi$
$104$		0			0
$105$	32.0227	+	41.0174i	0.304978	+	0.390641i
$106$		0			0
$107$	25.0065	−	14.4375i	0.233706	−	0.134930i	−0.378575	−	0.925571i	$-0.623586\pi$
$107$	25.0065	−	14.4375i	0.233706	−	0.134930i	0.612281	+	0.790641i	$0.290252\pi$
$108$		0			0
$109$	−66.5698	+	115.302i	−0.610732	+	1.05782i	0.380385	+	0.924828i	$0.375792\pi$
$109$	−66.5698	+	115.302i	−0.610732	+	1.05782i	−0.991117	+	0.132991i	$0.957542\pi$
$110$		0			0
$111$	34.3154	−	161.158i	0.309147	−	1.45188i
$112$		0			0
$113$	102.979	+	44.4207i	0.911316	+	0.393104i	0.799528	−	0.600629i	$-0.205083\pi$
$113$	102.979	+	44.4207i	0.911316	+	0.393104i	0.111788	+	0.993732i	$0.464342\pi$
$114$		0			0
$115$	3.71874	+	63.8484i	0.0323369	+	0.555203i
$116$		0			0
$117$	72.1716	−	66.4251i	0.616851	−	0.567736i
$118$		0			0
$119$	50.0237	−	21.5781i	0.420367	−	0.181329i
$120$		0			0
$121$	87.7197	+	20.7900i	0.724956	+	0.171818i
$122$		0			0
$123$	130.185	+	131.802i	1.05841	+	1.07156i
$124$		0			0
$125$	−43.1453	−	118.541i	−0.345163	−	0.948327i
$126$		0			0
$127$	1.35575	+	0.493453i	0.0106752	+	0.00388546i	0.347352	−	0.937735i	$-0.387081\pi$
$127$	1.35575	+	0.493453i	0.0106752	+	0.00388546i	−0.336677	+	0.941620i	$0.609303\pi$
$128$		0			0
$129$	63.8239	+	9.75174i	0.494759	+	0.0755949i
$130$		0			0
$131$	−197.277	−	11.4901i	−1.50593	−	0.0877106i	−0.714789	−	0.699340i	$-0.753477\pi$
$131$	−197.277	−	11.4901i	−1.50593	−	0.0877106i	−0.791144	+	0.611630i	$0.790514\pi$
$132$		0			0
$133$	121.269	+	128.538i	0.911797	+	0.966448i
$134$		0			0
$135$	−73.0925	+	43.2359i	−0.541426	+	0.320266i
$136$		0			0
$137$	−80.2198	−	24.0162i	−0.585546	−	0.175301i	−0.0196916	−	0.999806i	$-0.506268\pi$
$137$	−80.2198	−	24.0162i	−0.585546	−	0.175301i	−0.565855	+	0.824505i	$0.691454\pi$
$138$		0			0
$139$	−100.560	−	66.1390i	−0.723450	−	0.475820i	0.133612	−	0.991034i	$-0.457342\pi$
$139$	−100.560	−	66.1390i	−0.723450	−	0.475820i	−0.857062	+	0.515213i	$0.827713\pi$
$140$		0			0
$141$	75.1258	−	137.293i	0.532807	−	0.973712i
$142$		0			0
$143$	59.6142	−	10.5116i	0.416882	−	0.0735076i
$144$		0			0
$145$	−14.1453	+	80.2219i	−0.0975537	+	0.553254i
$146$		0			0
$147$	−31.6997	−	45.8721i	−0.215644	−	0.312055i
$148$		0			0
$149$	−4.28158	+	1.28182i	−0.0287354	+	0.00860282i	−0.301139	−	0.953580i	$-0.597367\pi$
$149$	−4.28158	+	1.28182i	−0.0287354	+	0.00860282i	0.272403	+	0.962183i	$0.412182\pi$
$150$		0			0
$151$	7.05223	+	0.824288i	0.0467035	+	0.00545886i	0.139413	−	0.990234i	$-0.455479\pi$
$151$	7.05223	+	0.824288i	0.0467035	+	0.00545886i	−0.0927091	+	0.995693i	$0.529553\pi$
$152$		0			0
$153$	24.4453	+	85.4812i	0.159773	+	0.558701i
$154$		0			0
$155$	34.8556	+	52.9954i	0.224875	+	0.341906i
$156$		0			0
$157$	−47.6030	−	63.9420i	−0.303204	−	0.407274i	0.624242	−	0.781231i	$-0.285408\pi$
$157$	−47.6030	−	63.9420i	−0.303204	−	0.407274i	−0.927446	+	0.373958i	$0.878001\pi$
$158$		0			0
$159$	26.1764	−	13.9063i	0.164631	−	0.0874608i
$160$		0			0
$161$			112.140i			0.696519i
$162$		0			0
$163$	−220.718			−1.35410			−0.677050	−	0.735937i	$-0.736742\pi$
$163$	−220.718			−1.35410			−0.677050	+	0.735937i	$0.736742\pi$
$164$		0			0
$165$	−52.3770	−	1.84776i	−0.317436	−	0.0111986i
$166$		0			0
$167$	237.173	−	176.569i	1.42020	−	1.05730i	0.432381	−	0.901691i	$-0.357674\pi$
$167$	237.173	−	176.569i	1.42020	−	1.05730i	0.987819	−	0.155608i	$-0.0497337\pi$
$168$		0			0
$169$	41.9597	−	27.5973i	0.248282	−	0.163298i
$170$		0			0
$171$	−233.434	+	169.346i	−1.36511	+	0.990325i
$172$		0			0
$173$	29.1417	−	249.323i	0.168449	−	1.44118i	−0.599351	−	0.800486i	$-0.704575\pi$
$173$	29.1417	−	249.323i	0.168449	−	1.44118i	0.767800	−	0.640689i	$-0.221351\pi$
$174$		0			0
$175$	−23.8947	−	79.8137i	−0.136541	−	0.456079i
$176$		0			0
$177$	211.112	+	100.035i	1.19272	+	0.565167i
$178$		0			0
$179$	4.83021	+	0.851697i	0.0269844	+	0.00475808i	0.187124	−	0.982336i	$-0.440083\pi$
$179$	4.83021	+	0.851697i	0.0269844	+	0.00475808i	−0.160140	+	0.987094i	$0.551194\pi$
$180$		0			0
$181$	−30.3013	−	171.847i	−0.167411	−	0.949434i	−0.946544	−	0.322575i	$-0.895452\pi$
$181$	−30.3013	−	171.847i	−0.167411	−	0.949434i	0.779133	−	0.626859i	$-0.215660\pi$
$182$		0			0
$183$	−56.2099	+	34.1934i	−0.307158	+	0.186849i
$184$		0			0
$185$	94.9280	−	144.331i	0.513125	−	0.780168i
$186$		0			0
$187$	−15.7366	+	52.5639i	−0.0841530	+	0.281091i
$188$		0			0
$189$	−132.349	+	68.2286i	−0.700260	+	0.360998i
$190$		0			0
$191$	−119.101	+	112.366i	−0.623567	+	0.588305i	−0.931785	−	0.363011i	$-0.881749\pi$
$191$	−119.101	+	112.366i	−0.623567	+	0.588305i	0.308218	+	0.951316i	$0.400267\pi$
$192$		0			0
$193$	11.8548	−	203.540i	0.0614241	−	1.05461i	−0.816972	−	0.576677i	$-0.804349\pi$
$193$	11.8548	−	203.540i	0.0614241	−	1.05461i	0.878396	−	0.477933i	$-0.158614\pi$
$194$		0			0
$195$	95.8040	−	37.3772i	0.491302	−	0.191678i
$196$		0			0
$197$	−74.6460	+	205.088i	−0.378914	+	1.04106i	0.592894	+	0.805281i	$0.297985\pi$
$197$	−74.6460	+	205.088i	−0.378914	+	1.04106i	−0.971807	+	0.235776i	$0.924237\pi$
$198$		0			0
$199$	−23.0111	+	8.37537i	−0.115634	+	0.0420873i	−0.399189	−	0.916869i	$-0.630708\pi$
$199$	−23.0111	+	8.37537i	−0.115634	+	0.0420873i	0.283555	+	0.958956i	$0.408486\pi$
$200$		0			0
$201$	−46.8099	−	179.114i	−0.232885	−	0.891112i
$202$		0			0
$203$	−32.9385	+	138.979i	−0.162259	+	0.684623i
$204$		0			0
$205$	76.9297	+	178.343i	0.375267	+	0.869967i
$206$		0			0
$207$	−181.493	−	23.4889i	−0.876780	−	0.113473i
$208$		0			0
$209$	−177.678	+	10.3486i	−0.850134	+	0.0495147i
$210$		0			0
$211$	73.6231	−	170.678i	0.348925	−	0.808899i	−0.649881	−	0.760036i	$-0.725181\pi$
$211$	73.6231	−	170.678i	0.348925	−	0.808899i	0.998806	−	0.0488624i	$-0.0155596\pi$
$212$		0			0
$213$	−88.2321	−	271.881i	−0.414235	−	1.27643i
$214$		0			0
$215$	58.6224	+	33.8457i	0.272662	+	0.157422i
$216$		0			0
$217$	55.6086	+	96.3168i	0.256261	+	0.443856i
$218$		0			0
$219$	−25.3818	−	181.070i	−0.115899	−	0.826803i
$220$		0			0
$221$	−12.4989	−	106.935i	−0.0565561	−	0.483868i
$222$		0			0
$223$	69.9923	+	35.1515i	0.313867	+	0.157630i	0.598758	−	0.800930i	$-0.295661\pi$
$223$	69.9923	+	35.1515i	0.313867	+	0.157630i	−0.284891	+	0.958560i	$0.591957\pi$
$224$		0			0
$225$	134.180	−	21.9547i	0.596357	−	0.0975764i
$226$		0			0
$227$	−270.895	−	201.674i	−1.19337	−	0.888430i	−0.197596	−	0.980284i	$-0.563313\pi$
$227$	−270.895	−	201.674i	−1.19337	−	0.888430i	−0.995772	+	0.0918540i	$0.970721\pi$
$228$		0			0
$229$	154.888	−	164.172i	0.676367	−	0.716907i	−0.294733	−	0.955579i	$-0.595231\pi$
$229$	154.888	−	164.172i	0.676367	−	0.716907i	0.971100	+	0.238673i	$0.0767123\pi$
$230$		0			0
$231$	−91.4925	−	8.57413i	−0.396071	−	0.0371175i
$232$		0			0
$233$	−176.360	+	210.177i	−0.756909	+	0.902049i	−0.997648	−	0.0685410i	$-0.978166\pi$
$233$	−176.360	+	210.177i	−0.756909	+	0.902049i	0.240740	+	0.970590i	$0.422610\pi$
$234$		0			0
$235$	125.695	−	105.470i	0.534871	−	0.448810i
$236$		0			0
$237$	−10.1961	+	30.1455i	−0.0430216	+	0.127196i
$238$		0			0
$239$	142.252	+	283.247i	0.595197	+	1.18513i	0.966511	+	0.256627i	$0.0826112\pi$
$239$	142.252	+	283.247i	0.595197	+	1.18513i	−0.371314	+	0.928508i	$0.621093\pi$
$240$		0			0
$241$	−304.379	+	72.1391i	−1.26298	+	0.299332i	−0.806944	−	0.590628i	$-0.798880\pi$
$241$	−304.379	+	72.1391i	−1.26298	+	0.299332i	−0.456038	+	0.889960i	$0.650732\pi$
$242$		0			0
$243$	−82.7033	−	228.493i	−0.340343	−	0.940302i
$244$		0			0
$245$	−13.4818	−	56.8840i	−0.0550276	−	0.232180i
$246$		0			0
$247$	312.081	−	156.733i	1.26348	−	0.634546i
$248$		0			0
$249$	231.889	+	78.4320i	0.931282	+	0.314988i
$250$		0			0
$251$	53.0256	+	63.1935i	0.211257	+	0.251767i	0.861259	−	0.508166i	$-0.169676\pi$
$251$	53.0256	+	63.1935i	0.211257	+	0.251767i	−0.650002	+	0.759933i	$0.725232\pi$
$252$		0			0
$253$	−86.5185	−	72.5976i	−0.341970	−	0.286947i
$254$		0			0
$255$	−8.69731	+	92.8068i	−0.0341071	+	0.363948i
$256$		0			0
$257$	14.9632	+	14.1170i	0.0582225	+	0.0549301i	0.714803	−	0.699326i	$-0.246516\pi$
$257$	14.9632	+	14.1170i	0.0582225	+	0.0549301i	−0.656581	+	0.754256i	$0.727998\pi$
$258$		0			0
$259$	180.877	−	242.960i	0.698366	−	0.938068i
$260$		0			0
$261$	−218.032	−	82.4203i	−0.835371	−	0.315787i
$262$		0			0
$263$	121.451	−	241.828i	0.461790	−	0.919499i	−0.535401	−	0.844598i	$-0.679840\pi$
$263$	121.451	−	241.828i	0.461790	−	0.919499i	0.997191	−	0.0749012i	$-0.0238641\pi$
$264$		0			0
$265$	30.8663	−	3.60776i	0.116477	−	0.0136142i
$266$		0			0
$267$	−71.5754	+	10.0332i	−0.268073	+	0.0375776i
$268$		0			0
$269$	36.2471	−	20.9273i	0.134748	−	0.0777966i	−0.431111	−	0.902299i	$-0.641878\pi$
$269$	36.2471	−	20.9273i	0.134748	−	0.0777966i	0.565858	+	0.824502i	$0.308545\pi$
$270$		0			0
$271$	159.519	−	276.295i	0.588631	−	1.01954i	−0.405781	−	0.913971i	$-0.633000\pi$
$271$	159.519	−	276.295i	0.588631	−	1.01954i	0.994412	−	0.105569i	$-0.0336664\pi$
$272$		0			0
$273$	171.506	−	55.6581i	0.628228	−	0.203876i
$274$		0			0
$275$	77.0474	+	33.2350i	0.280172	+	0.120855i
$276$		0			0
$277$	−12.7281	−	218.533i	−0.0459498	−	0.788928i	−0.940045	−	0.341051i	$-0.889217\pi$
$277$	−12.7281	−	218.533i	−0.0459498	−	0.788928i	0.894095	−	0.447877i	$-0.147820\pi$
$278$		0			0
$279$	−167.533	+	69.8256i	−0.600476	+	0.250271i
$280$		0			0
$281$	−380.850	+	164.283i	−1.35534	+	0.584636i	−0.944932	−	0.327266i	$-0.893873\pi$
$281$	−380.850	+	164.283i	−1.35534	+	0.584636i	−0.410407	+	0.911902i	$0.634613\pi$
$282$		0			0
$283$	174.395	+	41.3323i	0.616236	+	0.146051i	0.526867	−	0.849948i	$-0.323367\pi$
$283$	174.395	+	41.3323i	0.616236	+	0.146051i	0.0893695	+	0.995999i	$0.471515\pi$
$284$		0			0
$285$	−292.532	+	76.4510i	−1.02643	+	0.268249i
$286$		0			0
$287$	116.476	+	320.015i	0.405840	+	1.11504i
$288$		0			0
$289$	−179.869	−	65.4669i	−0.622383	−	0.226529i
$290$		0			0
$291$	−166.956	−	427.936i	−0.573732	−	1.47057i
$292$		0			0
$293$	263.611	+	15.3536i	0.899698	+	0.0524014i	0.501756	−	0.865009i	$-0.332688\pi$
$293$	263.611	+	15.3536i	0.899698	+	0.0524014i	0.397942	+	0.917411i	$0.369725\pi$
$294$		0			0
$295$	168.079	+	178.153i	0.569759	+	0.603909i
$296$		0			0
$297$	33.0410	−	146.281i	0.111249	−	0.492529i
$298$		0			0
$299$	212.302	+	63.5591i	0.710041	+	0.212572i
$300$		0			0
$301$	99.1623	+	65.2201i	0.329443	+	0.216678i
$302$		0			0
$303$	41.4321	+	68.1094i	0.136740	+	0.224784i
$304$		0			0
$305$	−67.9314	+	11.9781i	−0.222726	+	0.0392726i
$306$		0			0
$307$	4.84099	−	27.4546i	0.0157687	−	0.0894287i	−0.975908	−	0.218183i	$-0.929987\pi$
$307$	4.84099	−	27.4546i	0.0157687	−	0.0894287i	0.991676	+	0.128755i	$0.0410980\pi$
$308$		0			0
$309$	−23.0552	+	48.6553i	−0.0746121	+	0.157460i
$310$		0			0
$311$	363.335	−	108.775i	1.16828	−	0.349760i	0.356824	−	0.934172i	$-0.383860\pi$
$311$	363.335	−	108.775i	1.16828	−	0.349760i	0.811458	+	0.584411i	$0.198675\pi$
$312$		0			0
$313$	518.083	+	60.5552i	1.65522	+	0.193467i	0.891797	−	0.452436i	$-0.149445\pi$
$313$	518.083	+	60.5552i	1.65522	+	0.193467i	0.763419	+	0.645903i	$0.223519\pi$
$314$		0			0
$315$	−155.268	+	16.2073i	−0.492915	+	0.0514517i
$316$		0			0
$317$	20.6710	+	31.4288i	0.0652083	+	0.0991444i	0.866620	−	0.498969i	$-0.166288\pi$
$317$	20.6710	+	31.4288i	0.0652083	+	0.0991444i	−0.801412	+	0.598113i	$0.795917\pi$
$318$		0			0
$319$	−85.9015	−	115.386i	−0.269284	−	0.361711i
$320$		0			0
$321$	−3.05408	+	86.5713i	−0.00951425	+	0.269693i
$322$		0			0
$323$			316.546i			0.980019i
$324$		0			0
$325$	−164.646			−0.506604
$326$		0			0
$327$	−187.390	−	352.733i	−0.573058	−	1.07869i
$328$		0			0
$329$	230.769	−	171.801i	0.701425	−	0.522192i
$330$		0			0
$331$	−56.0498	+	36.8645i	−0.169335	+	0.111373i	−0.631347	−	0.775500i	$-0.717498\pi$
$331$	−56.0498	+	36.8645i	−0.169335	+	0.111373i	0.462013	+	0.886873i	$0.347127\pi$
$332$		0			0
$333$	355.334	+	343.633i	1.06707	+	1.03193i
$334$		0			0
$335$	22.5330	−	192.782i	0.0672628	−	0.575470i
$336$		0			0
$337$	128.856	+	430.410i	0.382363	+	1.27718i	0.905287	+	0.424801i	$0.139656\pi$
$337$	128.856	+	430.410i	0.382363	+	1.27718i	−0.522924	+	0.852379i	$0.675159\pi$
$338$		0			0
$339$	−276.792	+	191.276i	−0.816496	+	0.564236i
$340$		0			0
$341$	−110.311	−	19.4508i	−0.323493	−	0.0570406i
$342$		0			0
$343$	−64.7237	−	367.066i	−0.188699	−	1.07016i
$344$		0			0
$345$	−168.319	−	92.1025i	−0.487880	−	0.266964i
$346$		0			0
$347$	−215.441	+	327.563i	−0.620869	+	0.943985i	0.378959	+	0.925413i	$0.376282\pi$
$347$	−215.441	+	327.563i	−0.620869	+	0.943985i	−0.999828	+	0.0185713i	$0.994088\pi$
$348$		0			0
$349$	−154.625	+	516.485i	−0.443053	+	1.47990i	0.386929	+	0.922110i	$0.373536\pi$
$349$	−154.625	+	516.485i	−0.443053	+	1.47990i	−0.829982	+	0.557790i	$0.811649\pi$
$350$		0			0
$351$	54.1565	+	289.234i	0.154292	+	0.824029i
$352$		0			0
$353$	−409.040	+	385.909i	−1.15875	+	1.09323i	−0.164478	+	0.986381i	$0.552594\pi$
$353$	−409.040	+	385.909i	−1.15875	+	1.09323i	−0.994276	+	0.106847i	$0.965925\pi$
$354$		0			0
$355$	17.4249	−	299.175i	0.0490843	−	0.842745i
$356$		0			0
$357$	−24.6854	+	161.563i	−0.0691467	+	0.452557i
$358$		0			0
$359$	−199.030	+	546.831i	−0.554402	+	1.52321i	0.273238	+	0.961947i	$0.411905\pi$
$359$	−199.030	+	546.831i	−0.554402	+	1.52321i	−0.827639	+	0.561260i	$0.810317\pi$
$360$		0			0
$361$	−625.632	+	227.711i	−1.73305	+	0.630780i
$362$		0			0
$363$	−192.414	+	190.052i	−0.530065	+	0.523559i
$364$		0			0
$365$	44.2079	−	186.528i	0.121117	−	0.511035i
$366$		0			0
$367$	70.7248	+	163.959i	0.192711	+	0.446754i	0.986986	−	0.160804i	$-0.0514087\pi$
$367$	70.7248	+	163.959i	0.192711	+	0.446754i	−0.794276	+	0.607558i	$0.792149\pi$
$368$		0			0
$369$	−542.330	+	121.481i	−1.46973	+	0.329217i
$370$		0			0
$371$	54.3963	−	3.16822i	0.146621	−	0.00853969i
$372$		0			0
$373$	99.4679	−	230.592i	0.266670	−	0.618210i	−0.731289	−	0.682068i	$-0.761081\pi$
$373$	99.4679	−	230.592i	0.266670	−	0.618210i	0.997959	+	0.0638573i	$0.0203403\pi$
$374$		0			0
$375$	370.147	+	78.8154i	0.987060	+	0.210174i
$376$		0			0
$377$	244.445	+	141.130i	0.648394	+	0.374351i
$378$		0			0
$379$	270.449	+	468.431i	0.713585	+	1.23597i	0.963503	+	0.267698i	$0.0862631\pi$
$379$	270.449	+	468.431i	0.713585	+	1.23597i	−0.249918	+	0.968267i	$0.580404\pi$
$380$		0			0
$381$	−3.41168	+	2.66354i	−0.00895455	+	0.00699092i
$382$		0			0
$383$	58.5939	+	501.303i	0.152987	+	1.30888i	0.823640	+	0.567113i	$0.191940\pi$
$383$	58.5939	+	501.303i	0.152987	+	1.30888i	−0.670653	+	0.741771i	$0.733986\pi$
$384$		0			0
$385$	−86.0958	−	43.2389i	−0.223625	−	0.112309i
$386$		0			0
$387$	−126.327	+	146.829i	−0.326426	+	0.379404i
$388$		0			0
$389$	282.917	+	210.624i	0.727293	+	0.541449i	0.895912	−	0.444232i	$-0.146523\pi$
$389$	282.917	+	210.624i	0.727293	+	0.541449i	−0.168619	+	0.985681i	$0.553931\pi$
$390$		0			0
$391$	−137.848	+	146.110i	−0.352552	+	0.373683i
$392$		0			0
$393$	343.028	−	483.513i	0.872845	−	1.23031i
$394$		0			0
$395$	−21.4461	+	25.5585i	−0.0542940	+	0.0647050i
$396$		0			0
$397$	−188.267	+	157.975i	−0.474224	+	0.397921i	−0.848333	−	0.529464i	$-0.822393\pi$
$397$	−188.267	+	157.975i	−0.474224	+	0.397921i	0.374109	+	0.927385i	$0.377949\pi$
$398$		0			0
$399$	−519.844	+	103.997i	−1.30287	+	0.260643i
$400$		0			0
$401$	−288.518	−	574.486i	−0.719495	−	1.43263i	−0.894042	−	0.447984i	$-0.852142\pi$
$401$	−288.518	−	574.486i	−0.719495	−	1.43263i	0.174546	−	0.984649i	$-0.444154\pi$
$402$		0			0
$403$	213.865	−	50.6869i	0.530682	−	0.125774i
$404$		0			0
$405$	6.29182	−	254.690i	0.0155353	−	0.628865i
$406$		0			0
$407$	70.3524	+	296.840i	0.172856	+	0.729337i
$408$		0			0
$409$	417.061	−	209.456i	1.01971	−	0.512117i	0.141270	−	0.989971i	$-0.454881\pi$
$409$	417.061	−	209.456i	1.01971	−	0.512117i	0.878439	+	0.477854i	$0.158585\pi$
$410$		0			0
$411$	188.690	−	165.843i	0.459100	−	0.403512i
$412$		0			0
$413$	276.043	+	328.975i	0.668385	+	0.796550i
$414$		0			0
$415$	196.605	+	164.971i	0.473746	+	0.397520i
$416$		0			0
$417$	328.186	−	150.576i	0.787017	−	0.361093i
$418$		0			0
$419$	498.355	+	470.173i	1.18939	+	1.12213i	0.989831	+	0.142247i	$0.0454326\pi$
$419$	498.355	+	470.173i	1.18939	+	1.12213i	0.199559	+	0.979886i	$0.436049\pi$
$420$		0			0
$421$	108.550	−	145.807i	0.257838	−	0.346336i	−0.654289	−	0.756245i	$-0.727032\pi$
$421$	108.550	−	145.807i	0.257838	−	0.346336i	0.912127	+	0.409909i	$0.134439\pi$
$422$		0			0
$423$	229.716	+	409.476i	0.543064	+	0.968029i
$424$		0			0
$425$	66.9782	−	133.364i	0.157596	−	0.313799i
$426$		0			0
$427$	−120.129	+	14.0410i	−0.281331	+	0.0328829i
$428$		0			0
$429$	−68.0892	+	168.354i	−0.158716	+	0.392433i
$430$		0			0
$431$	219.993	−	127.013i	0.510425	−	0.294694i	−0.222583	−	0.974914i	$-0.571449\pi$
$431$	219.993	−	127.013i	0.510425	−	0.294694i	0.733008	+	0.680220i	$0.238116\pi$
$432$		0			0
$433$	115.287	−	199.683i	0.266252	−	0.461161i	−0.701639	−	0.712532i	$-0.747548\pi$
$433$	115.287	−	199.683i	0.266252	−	0.461161i	0.967891	+	0.251371i	$0.0808814\pi$
$434$		0			0
$435$	−181.550	−	163.586i	−0.417357	−	0.376059i
$436$		0			0
$437$	−598.287	−	258.076i	−1.36908	−	0.590563i
$438$		0			0
$439$	−18.4113	−	316.111i	−0.0419393	−	0.720069i	−0.952095	−	0.305803i	$-0.901075\pi$
$439$	−18.4113	−	316.111i	−0.0419393	−	0.720069i	0.910156	−	0.414267i	$-0.135962\pi$
$440$		0			0
$441$	167.103	−	7.66339i	0.378918	−	0.0173773i
$442$		0			0
$443$	224.222	−	96.7200i	0.506145	−	0.218330i	−0.127667	−	0.991817i	$-0.540749\pi$
$443$	224.222	−	96.7200i	0.506145	−	0.218330i	0.633812	+	0.773487i	$0.281489\pi$
$444$		0			0
$445$	−73.7328	−	17.4750i	−0.165692	−	0.0392696i
$446$		0			0
$447$	3.55015	−	12.9295i	0.00794217	−	0.0289250i
$448$		0			0
$449$	−218.698	−	600.868i	−0.487078	−	1.33824i	−0.903315	−	0.428979i	$-0.858873\pi$
$449$	−218.698	−	600.868i	−0.487078	−	1.33824i	0.416237	−	0.909256i	$-0.363349\pi$
$450$		0			0
$451$	−322.305	−	117.309i	−0.714645	−	0.260110i
$452$		0			0
$453$	−13.3144	+	16.6267i	−0.0293916	+	0.0367036i
$454$		0			0
$455$	188.724	+	10.9919i	0.414777	+	0.0241580i
$456$		0			0
$457$	189.960	+	201.346i	0.415668	+	0.440582i	0.901047	−	0.433722i	$-0.142800\pi$
$457$	189.960	+	201.346i	0.415668	+	0.440582i	−0.485379	+	0.874304i	$0.661318\pi$
$458$		0			0
$459$	−256.312	−	73.7935i	−0.558415	−	0.160770i
$460$		0			0
$461$	−571.275	−	171.028i	−1.23921	−	0.370994i	−0.400865	−	0.916137i	$-0.631290\pi$
$461$	−571.275	−	171.028i	−1.23921	−	0.370994i	−0.838343	+	0.545143i	$0.816475\pi$
$462$		0			0
$463$	491.968	+	323.572i	1.06257	+	0.698860i	0.955380	−	0.295379i	$-0.0954458\pi$
$463$	491.968	+	323.572i	1.06257	+	0.698860i	0.107185	+	0.994239i	$0.465816\pi$
$464$		0			0
$465$	−190.242	+	4.35998i	−0.409122	+	0.00937631i
$466$		0			0
$467$	−701.939	+	123.771i	−1.50308	+	0.265034i	−0.863759	−	0.503905i	$-0.831896\pi$
$467$	−701.939	+	123.771i	−1.50308	+	0.265034i	−0.639323	+	0.768939i	$0.720785\pi$
$468$		0			0
$469$	59.0959	−	335.150i	0.126004	−	0.714605i
$470$		0			0
$471$	238.362	−	19.3717i	0.506076	−	0.0411288i
$472$		0			0
$473$	−114.515	+	34.2836i	−0.242104	+	0.0724812i
$474$		0			0
$475$	480.813	+	56.1990i	1.01224	+	0.118314i
$476$		0			0
$477$	−6.26627	+	88.7019i	−0.0131368	+	0.185958i
$478$		0			0
$479$	471.396	+	716.722i	0.984125	+	1.49629i	0.863976	+	0.503533i	$0.167967\pi$
$479$	471.396	+	716.722i	0.984125	+	1.49629i	0.120149	+	0.992756i	$0.461663\pi$
$480$		0			0
$481$	−357.452	−	480.142i	−0.743144	−	0.998216i
$482$		0			0
$483$	−285.235	−	178.376i	−0.590550	−	0.369309i
$484$		0			0
$485$		−	481.596i		−	0.992982i
$486$		0			0
$487$	627.663			1.28884			0.644418	−	0.764674i	$-0.277100\pi$
$487$	627.663			1.28884			0.644418	+	0.764674i	$0.277100\pi$
$488$		0			0
$489$	351.089	−	561.414i	0.717974	−	1.14809i
$490$		0			0
$491$	343.128	−	255.449i	0.698835	−	0.520264i	−0.188104	−	0.982149i	$-0.560234\pi$
$491$	343.128	−	255.449i	0.698835	−	0.520264i	0.886940	+	0.461885i	$0.152827\pi$
$492$		0			0
$493$	−213.756	+	140.590i	−0.433583	+	0.285172i
$494$		0			0
$495$	88.0142	−	130.286i	0.177807	−	0.263204i
$496$		0			0
$497$	61.0013	−	521.900i	0.122739	−	1.05010i
$498$		0			0
$499$	−97.5900	−	325.973i	−0.195571	−	0.653253i	−0.998374	−	0.0570082i	$-0.981844\pi$
$499$	−97.5900	−	325.973i	−0.195571	−	0.653253i	0.802803	−	0.596245i	$-0.203341\pi$
$500$		0			0
$501$	71.8533	+	884.131i	0.143420	+	1.76473i
$502$		0			0
$503$	−599.268	−	105.667i	−1.19139	−	0.210074i	−0.457415	−	0.889253i	$-0.651225\pi$
$503$	−599.268	−	105.667i	−1.19139	−	0.210074i	−0.733972	+	0.679180i	$0.762336\pi$
$504$		0			0
$505$	14.5139	+	82.3124i	0.0287404	+	0.162995i
$506$		0			0
$507$	3.45206	+	150.626i	0.00680880	+	0.297092i
$508$		0			0
$509$	−147.345	+	224.027i	−0.289479	+	0.440131i	−0.950724	−	0.310039i	$-0.899658\pi$
$509$	−147.345	+	224.027i	−0.289479	+	0.440131i	0.661245	+	0.750170i	$0.270028\pi$
$510$		0			0
$511$	96.3979	−	321.991i	0.188646	−	0.630120i
$512$		0			0
$513$	−59.4273	−	863.130i	−0.115843	−	1.68252i
$514$		0			0
$515$	−41.0593	+	38.7374i	−0.0797267	+	0.0752183i
$516$		0			0
$517$	−16.8478	+	289.266i	−0.0325877	+	0.559508i
$518$		0			0
$519$	587.818	+	470.714i	1.13260	+	0.906964i
$520$		0			0
$521$	−147.583	+	405.481i	−0.283268	+	0.778274i	0.713699	+	0.700453i	$0.247019\pi$
$521$	−147.583	+	405.481i	−0.283268	+	0.778274i	−0.996967	+	0.0778211i	$0.975204\pi$
$522$		0			0
$523$	−619.082	+	225.327i	−1.18371	+	0.430836i	−0.857512	−	0.514464i	$-0.827991\pi$
$523$	−619.082	+	225.327i	−1.18371	+	0.430836i	−0.326201	+	0.945300i	$0.605769\pi$
$524$		0			0
$525$	241.021	+	66.1791i	0.459087	+	0.126055i
$526$		0			0
$527$	−45.9436	+	193.851i	−0.0871795	+	0.367839i
$528$		0			0
$529$	45.7566	+	106.076i	0.0864964	+	0.200521i
$530$		0			0
$531$	−590.254	+	377.857i	−1.11159	+	0.711596i
$532$		0			0
$533$	671.869	−	39.1319i	1.26054	−	0.0734183i
$534$		0			0
$535$	−35.9721	+	83.3926i	−0.0672375	+	0.155874i
$536$		0			0
$537$	−9.84961	+	10.9312i	−0.0183419	+	0.0203561i
$538$		0			0
$539$	89.4041	+	51.6175i	0.165870	+	0.0957653i
$540$		0			0
$541$	−112.301	−	194.512i	−0.207581	−	0.359541i	0.743371	−	0.668880i	$-0.233226\pi$
$541$	−112.301	−	194.512i	−0.207581	−	0.359541i	−0.950952	+	0.309338i	$0.899892\pi$
$542$		0			0
$543$	485.307	+	196.278i	0.893751	+	0.361470i
$544$		0			0
$545$	−48.6153	−	415.931i	−0.0892024	−	0.763175i
$546$		0			0
$547$	−425.730	−	213.810i	−0.778300	−	0.390877i	0.0148606	−	0.999890i	$-0.495270\pi$
$547$	−425.730	−	213.810i	−0.778300	−	0.390877i	−0.793160	+	0.609013i	$0.791566\pi$
$548$		0			0
$549$	2.43745	−	197.364i	0.00443980	−	0.359498i
$550$		0			0
$551$	−665.675	−	495.577i	−1.20812	−	0.899413i
$552$		0			0
$553$	−40.1450	+	42.5512i	−0.0725950	+	0.0769462i
$554$		0			0
$555$	216.118	+	471.039i	0.389403	+	0.848719i
$556$		0			0
$557$	376.440	−	448.624i	0.675835	−	0.805429i	−0.313730	−	0.949512i	$-0.601579\pi$
$557$	376.440	−	448.624i	0.675835	−	0.805429i	0.989566	+	0.144083i	$0.0460233\pi$
$558$		0			0
$559$	179.678	−	150.768i	0.321428	−	0.269710i
$560$		0			0
$561$	−108.669	−	123.639i	−0.193705	−	0.220390i
$562$		0			0
$563$	−224.988	−	447.988i	−0.399624	−	0.795716i	0.600368	−	0.799724i	$-0.295021\pi$
$563$	−224.988	−	447.988i	−0.399624	−	0.795716i	−0.999992	+	0.00400743i	$0.998724\pi$
$564$		0			0
$565$	−343.238	+	81.3489i	−0.607501	+	0.143980i
$566$		0			0
$567$	36.9787	−	445.169i	0.0652182	−	0.785131i
$568$		0			0
$569$	−97.5056	−	411.409i	−0.171363	−	0.723038i	−0.989075	−	0.147411i	$-0.952906\pi$
$569$	−97.5056	−	411.409i	−0.171363	−	0.723038i	0.817712	−	0.575627i	$-0.195242\pi$
$570$		0			0
$571$	−529.303	+	265.826i	−0.926976	+	0.465545i	−0.847204	−	0.531268i	$-0.821716\pi$
$571$	−529.303	+	265.826i	−0.926976	+	0.465545i	−0.0797722	+	0.996813i	$0.525419\pi$
$572$		0			0
$573$	−96.3619	−	481.681i	−0.168171	−	0.840629i
$574$		0			0
$575$	197.459	+	235.322i	0.343407	+	0.409256i
$576$		0			0
$577$	−357.205	−	299.730i	−0.619073	−	0.519464i	0.278439	−	0.960454i	$-0.410183\pi$
$577$	−357.205	−	299.730i	−0.619073	−	0.519464i	−0.897512	+	0.440990i	$0.854627\pi$
$578$		0			0
$579$	498.862	+	353.917i	0.861592	+	0.611256i
$580$		0			0
$581$	327.318	+	308.809i	0.563371	+	0.531513i
$582$		0			0
$583$	−32.7711	+	44.0192i	−0.0562111	+	0.0755046i
$584$		0			0
$585$	−57.3203	+	303.139i	−0.0979833	+	0.518187i
$586$		0			0
$587$	303.014	−	603.350i	0.516207	−	1.02785i	−0.472963	−	0.881082i	$-0.656816\pi$
$587$	303.014	−	603.350i	0.516207	−	1.02785i	0.989170	−	0.146771i	$-0.0468881\pi$
$588$		0			0
$589$	−641.847	+	75.0211i	−1.08972	+	0.127370i
$590$		0			0
$591$	−402.921	−	516.095i	−0.681761	−	0.873257i
$592$		0			0
$593$	433.568	−	250.320i	0.731143	−	0.422126i	−0.0876972	−	0.996147i	$-0.527951\pi$
$593$	433.568	−	250.320i	0.731143	−	0.422126i	0.818840	+	0.574022i	$0.194617\pi$
$594$		0			0
$595$	−85.6763	+	148.396i	−0.143994	+	0.249405i
$596$		0			0
$597$	15.2996	−	71.8530i	0.0256275	−	0.120357i
$598$		0			0
$599$	−423.586	−	182.717i	−0.707155	−	0.305037i	0.0119594	−	0.999928i	$-0.496193\pi$
$599$	−423.586	−	182.717i	−0.707155	−	0.305037i	−0.719115	+	0.694892i	$0.755452\pi$
$600$		0			0
$601$	18.6918	+	320.925i	0.0311011	+	0.533986i	0.977493	+	0.210966i	$0.0676610\pi$
$601$	18.6918	+	320.925i	0.0311011	+	0.533986i	−0.946392	+	0.323020i	$0.895302\pi$
$602$		0			0
$603$	530.048	+	165.845i	0.879018	+	0.275034i
$604$		0			0
$605$	−260.357	+	112.307i	−0.430342	+	0.185631i
$606$		0			0
$607$	−667.684	−	158.244i	−1.09997	−	0.260699i	−0.359743	−	0.933052i	$-0.617136\pi$
$607$	−667.684	−	158.244i	−1.09997	−	0.260699i	−0.740231	+	0.672353i	$0.765284\pi$
$608$		0			0
$609$	−301.108	−	304.850i	−0.494431	−	0.500575i
$610$		0			0
$611$	−194.457	−	534.266i	−0.318260	−	0.874412i
$612$		0			0
$613$	782.910	+	284.956i	1.27718	+	0.464855i	0.889498	−	0.456940i	$-0.151054\pi$
$613$	782.910	+	284.956i	1.27718	+	0.464855i	0.387680	+	0.921794i	$0.373277\pi$
$614$		0			0
$615$	−575.999	−	88.0077i	−0.936584	−	0.143102i
$616$		0			0
$617$	−818.763	−	47.6875i	−1.32701	−	0.0772893i	−0.620059	−	0.784555i	$-0.712891\pi$
$617$	−818.763	−	47.6875i	−1.32701	−	0.0772893i	−0.706947	+	0.707266i	$0.749928\pi$
$618$		0			0
$619$	−692.819	−	734.346i	−1.11926	−	1.18634i	−0.980604	−	0.196001i	$-0.937205\pi$
$619$	−692.819	−	734.346i	−1.11926	−	1.18634i	−0.138652	−	0.990341i	$-0.544277\pi$
$620$		0			0
$621$	348.441	−	424.279i	0.561097	−	0.683220i
$622$		0			0
$623$	−127.280	−	38.1053i	−0.204303	−	0.0611642i
$624$		0			0
$625$	15.9522	+	10.4919i	0.0255234	+	0.0167870i
$626$		0			0
$627$	256.304	−	468.399i	0.408778	−	0.747048i
$628$		0			0
$629$	534.329	−	94.2167i	0.849490	−	0.149788i
$630$		0			0
$631$	−169.114	+	959.095i	−0.268010	+	1.51996i	0.492314	+	0.870417i	$0.336151\pi$
$631$	−169.114	+	959.095i	−0.268010	+	1.51996i	−0.760324	+	0.649543i	$0.774960\pi$
$632$		0			0
$633$	317.022	+	458.757i	0.500824	+	0.724735i
$634$		0			0
$635$	−4.34725	+	1.30148i	−0.00684607	+	0.00204958i
$636$		0			0
$637$	−201.196	−	23.5164i	−0.315849	−	0.0369175i
$638$		0			0
$639$	831.897	+	208.046i	1.30187	+	0.325581i
$640$		0			0
$641$	−89.4910	−	136.064i	−0.139612	−	0.212269i	0.758913	−	0.651192i	$-0.225731\pi$
$641$	−89.4910	−	136.064i	−0.139612	−	0.212269i	−0.898525	+	0.438923i	$0.855360\pi$
$642$		0			0
$643$	142.884	+	191.926i	0.222214	+	0.298486i	0.899224	−	0.437488i	$-0.144132\pi$
$643$	142.884	+	191.926i	0.222214	+	0.298486i	−0.677010	+	0.735974i	$0.736725\pi$
$644$		0			0
$645$	−179.338	+	95.2734i	−0.278043	+	0.147711i
$646$		0			0
$647$		−	848.415i		−	1.31131i	−0.755062	−	0.655653i	$-0.772393\pi$
$647$		−	848.415i		−	1.31131i	0.755062	−	0.655653i	$-0.227607\pi$
$648$		0			0
$649$	−432.519			−0.666440
$650$		0			0
$651$	−333.444	−	11.7633i	−0.512203	−	0.0180696i
$652$		0			0
$653$	627.301	−	467.008i	0.960645	−	0.715174i	0.00206526	−	0.999998i	$-0.499343\pi$
$653$	627.301	−	467.008i	0.960645	−	0.715174i	0.958580	+	0.284824i	$0.0919352\pi$
$654$		0			0
$655$	519.293	−	341.544i	0.792814	−	0.521442i
$656$		0			0
$657$	500.939	+	223.461i	0.762464	+	0.340123i
$658$		0			0
$659$	7.45433	−	63.7759i	0.0113116	−	0.0967768i	−0.986403	−	0.164343i	$-0.947449\pi$
$659$	7.45433	−	63.7759i	0.0113116	−	0.0967768i	0.997715	+	0.0675667i	$0.0215235\pi$
$660$		0			0
$661$	281.575	+	940.527i	0.425984	+	1.42289i	0.854547	+	0.519373i	$0.173835\pi$
$661$	281.575	+	940.527i	0.425984	+	1.42289i	−0.428564	+	0.903512i	$0.640980\pi$
$662$		0			0
$663$	291.879	+	138.306i	0.440239	+	0.208606i
$664$		0			0
$665$	−547.374	−	96.5168i	−0.823119	−	0.145138i
$666$		0			0
$667$	−91.4486	−	518.631i	−0.137104	−	0.777557i
$668$		0			0
$669$	−200.745	+	122.117i	−0.300067	+	0.182536i
$670$		0			0
$671$	66.9366	−	101.772i	0.0997565	−	0.151672i
$672$		0			0
$673$	−329.538	+	1100.73i	−0.489655	+	1.63556i	0.254150	+	0.967165i	$0.418204\pi$
$673$	−329.538	+	1100.73i	−0.489655	+	1.63556i	−0.743805	+	0.668396i	$0.766981\pi$
$674$		0			0
$675$	−157.593	+	376.221i	−0.233471	+	0.557364i
$676$		0			0
$677$	−637.451	+	601.404i	−0.941582	+	0.888337i	−0.993899	−	0.110293i	$-0.964821\pi$
$677$	−637.451	+	601.404i	−0.941582	+	0.888337i	0.0523167	+	0.998631i	$0.483339\pi$
$678$		0			0
$679$	49.0984	−	842.987i	0.0723099	−	1.24151i
$680$		0			0
$681$	943.875	−	368.246i	1.38601	−	0.540743i
$682$		0			0
$683$	253.615	−	696.803i	0.371326	−	1.02021i	−0.603524	−	0.797345i	$-0.706237\pi$
$683$	253.615	−	696.803i	0.371326	−	1.02021i	0.974850	−	0.222864i	$-0.0715406\pi$
$684$		0			0
$685$	247.495	−	90.0809i	0.361307	−	0.131505i
$686$		0			0
$687$	171.208	+	655.112i	0.249211	+	0.953583i
$688$		0			0
$689$	24.8330	−	104.779i	0.0360421	−	0.152074i
$690$		0			0
$691$	50.9074	+	118.017i	0.0736721	+	0.170791i	0.951073	−	0.308968i	$-0.0999835\pi$
$691$	50.9074	+	118.017i	0.0736721	+	0.170791i	−0.877400	+	0.479759i	$0.840724\pi$
$692$		0			0
$693$	167.343	−	219.080i	0.241476	−	0.316132i
$694$		0			0
$695$	377.927	−	22.0117i	0.543779	−	0.0316715i
$696$		0			0
$697$	−241.620	+	560.137i	−0.346656	+	0.803640i
$698$		0			0
$699$	−254.073	−	782.906i	−0.363480	−	1.12004i
$700$		0			0
$701$	703.734	+	406.301i	1.00390	+	0.579602i	0.909400	−	0.415923i	$-0.136541\pi$
$701$	703.734	+	406.301i	1.00390	+	0.579602i	0.0944999	+	0.995525i	$0.469875\pi$
$702$		0			0
$703$	879.973	+	1524.16i	1.25174	+	2.16808i
$704$		0			0
$705$	68.3337	+	487.482i	0.0969272	+	0.691464i
$706$		0			0
$707$	17.0135	+	145.560i	0.0240643	+	0.205883i
$708$		0			0
$709$	−1156.65	−	580.892i	−1.63138	−	0.819312i	−0.999002	−	0.0446555i	$-0.985781\pi$
$709$	−1156.65	−	580.892i	−1.63138	−	0.819312i	−0.632382	−	0.774657i	$-0.717923\pi$
$710$		0			0
$711$	−60.4587	−	73.8860i	−0.0850333	−	0.103918i
$712$		0			0
$713$	−328.931	−	244.880i	−0.461334	−	0.343450i
$714$		0			0
$715$	−130.658	+	138.489i	−0.182738	+	0.193691i
$716$		0			0
$717$	−946.736	−	88.7225i	−1.32041	−	0.123741i
$718$		0			0
$719$	455.595	−	542.957i	0.633651	−	0.755156i	−0.349702	−	0.936861i	$-0.613717\pi$
$719$	455.595	−	542.957i	0.633651	−	0.755156i	0.983353	+	0.181705i	$0.0581615\pi$
$720$		0			0
$721$	−75.8195	+	63.6201i	−0.105159	+	0.0882387i
$722$		0			0
$723$	300.674	−	888.960i	0.415869	−	1.22954i
$724$		0			0
$725$	175.597	+	349.642i	0.242203	+	0.482265i
$726$		0			0
$727$	−648.169	+	153.619i	−0.891567	+	0.211305i	−0.650774	−	0.759271i	$-0.725556\pi$
$727$	−648.169	+	153.619i	−0.891567	+	0.211305i	−0.240793	+	0.970577i	$0.577407\pi$
$728$		0			0
$729$	712.743	+	153.094i	0.977700	+	0.210006i
$730$		0			0
$731$	49.0298	+	206.873i	0.0670722	+	0.283000i
$732$		0			0
$733$	1011.41	−	507.947i	1.37982	−	0.692970i	0.404657	−	0.914469i	$-0.367391\pi$
$733$	1011.41	−	507.947i	1.37982	−	0.692970i	0.975161	+	0.221498i	$0.0710947\pi$
$734$		0			0
$735$	166.134	+	56.1915i	0.226032	+	0.0764511i
$736$		0			0
$737$	220.319	+	262.565i	0.298940	+	0.356262i
$738$		0			0
$739$	−496.654	−	416.742i	−0.672062	−	0.563927i	0.241613	−	0.970373i	$-0.422324\pi$
$739$	−496.654	−	416.742i	−0.672062	−	0.563927i	−0.913675	+	0.406446i	$0.866768\pi$
$740$		0			0
$741$	−97.7542	+	1043.11i	−0.131922	+	1.40771i
$742$		0			0
$743$	403.392	+	380.581i	0.542923	+	0.512222i	0.908121	−	0.418709i	$-0.137517\pi$
$743$	403.392	+	380.581i	0.542923	+	0.512222i	−0.365198	+	0.930930i	$0.618999\pi$
$744$		0			0
$745$	8.39446	−	11.2757i	0.0112677	−	0.0151352i
$746$		0			0
$747$	−568.356	+	465.069i	−0.760851	+	0.622582i
$748$		0			0
$749$	−71.4674	+	142.303i	−0.0954172	+	0.189991i
$750$		0			0
$751$	−1354.64	+	158.335i	−1.80378	+	0.210832i	−0.950523	−	0.310654i	$-0.899452\pi$
$751$	−1354.64	+	158.335i	−1.80378	+	0.210832i	−0.853260	+	0.521486i	$0.825378\pi$
$752$		0			0
$753$	−245.083	+	34.3550i	−0.325476	+	0.0456242i
$754$		0			0
$755$	−19.3403	+	11.1661i	−0.0256163	+	0.0147896i
$756$		0			0
$757$	428.638	−	742.423i	0.566233	−	0.980744i	−0.430701	−	0.902495i	$-0.641734\pi$
$757$	428.638	−	742.423i	0.566233	−	0.980744i	0.996934	−	0.0782493i	$-0.0249330\pi$
$758$		0			0
$759$	322.280	−	104.588i	0.424611	−	0.137797i
$760$		0			0
$761$	−380.819	−	164.269i	−0.500419	−	0.215860i	0.130882	−	0.991398i	$-0.458219\pi$
$761$	−380.819	−	164.269i	−0.500419	−	0.215860i	−0.631300	+	0.775538i	$0.717478\pi$
$762$		0			0
$763$	−42.6925	−	733.002i	−0.0559535	−	0.960684i
$764$		0			0
$765$	−222.227	−	169.747i	−0.290493	−	0.221891i
$766$		0			0
$767$	779.273	−	336.145i	1.01600	−	0.438260i
$768$		0			0
$769$	1238.77	+	293.593i	1.61088	+	0.381786i	0.934837	−	0.355076i	$-0.115545\pi$
$769$	1238.77	+	293.593i	1.61088	+	0.381786i	0.676043	+	0.736862i	$0.263693\pi$
$770$		0			0
$771$	−59.7092	+	15.6045i	−0.0774438	+	0.0202393i
$772$		0			0
$773$	232.607	+	639.083i	0.300915	+	0.826757i	0.994342	+	0.106230i	$0.0338779\pi$
$773$	232.607	+	639.083i	0.300915	+	0.826757i	−0.693427	+	0.720527i	$0.743900\pi$
$774$		0			0
$775$	286.291	+	104.201i	0.369408	+	0.134453i
$776$		0			0
$777$	330.272	+	846.542i	0.425061	+	1.08950i
$778$		0			0
$779$	−1975.40	−	115.054i	−2.53582	−	0.147695i
$780$		0			0
$781$	363.167	+	384.935i	0.465003	+	0.492875i
$782$		0			0
$783$	556.458	−	423.478i	0.710675	−	0.540840i
$784$		0			0
$785$	240.196	+	71.9099i	0.305982	+	0.0916050i
$786$		0			0
$787$	−165.957	−	109.152i	−0.210873	−	0.138693i	0.439679	−	0.898155i	$-0.355092\pi$
$787$	−165.957	−	109.152i	−0.210873	−	0.138693i	−0.650552	+	0.759462i	$0.725462\pi$
$788$		0			0
$789$	421.921	+	693.587i	0.534754	+	0.879071i
$790$		0			0
$791$	−609.098	+	107.400i	−0.770036	+	0.135778i
$792$		0			0
$793$	−41.5048	+	235.385i	−0.0523389	+	0.296829i
$794$		0			0
$795$	−39.9214	+	84.2496i	−0.0502156	+	0.105974i
$796$		0			0
$797$	−770.102	+	230.554i	−0.966251	+	0.289277i	−0.730786	−	0.682606i	$-0.760846\pi$
$797$	−770.102	+	230.554i	−0.966251	+	0.289277i	−0.235465	+	0.971883i	$0.575661\pi$
$798$		0			0
$799$	511.863	+	59.8282i	0.640630	+	0.0748789i
$800$		0			0
$801$	88.3322	−	198.017i	0.110277	−	0.247212i
$802$		0			0
$803$	186.018	+	282.827i	0.231654	+	0.352212i
$804$		0			0
$805$	−210.624	−	282.917i	−0.261645	−	0.351450i
$806$		0			0
$807$	−4.42690	+	125.486i	−0.00548562	+	0.155496i
$808$		0			0
$809$		−	916.244i		−	1.13256i	−0.824212	−	0.566282i	$-0.808381\pi$
$809$		−	916.244i		−	1.13256i	0.824212	−	0.566282i	$-0.191619\pi$
$810$		0			0
$811$	971.453			1.19785			0.598923	−	0.800807i	$-0.295596\pi$
$811$	971.453			1.19785			0.598923	+	0.800807i	$0.295596\pi$
$812$		0			0
$813$	449.037	+	845.242i	0.552320	+	1.03966i
$814$		0			0
$815$	556.852	−	414.561i	0.683254	−	0.508664i
$816$		0			0
$817$	−576.173	+	378.955i	−0.705230	+	0.463837i
$818$		0			0
$819$	−131.238	+	524.772i	−0.160242	+	0.640748i
$820$		0			0
$821$	−64.8241	+	554.605i	−0.0789575	+	0.675524i	0.894566	+	0.446936i	$0.147485\pi$
$821$	−64.8241	+	554.605i	−0.0789575	+	0.675524i	−0.973523	+	0.228588i	$0.926589\pi$
$822$		0			0
$823$	421.484	+	1407.85i	0.512131	+	1.71064i	0.687545	+	0.726142i	$0.258688\pi$
$823$	421.484	+	1407.85i	0.512131	+	1.71064i	−0.175414	+	0.984495i	$0.556126\pi$
$824$		0			0
$825$	−207.093	+	143.110i	−0.251021	+	0.173467i
$826$		0			0
$827$	−74.8901	−	13.2051i	−0.0905564	−	0.0159675i	0.128186	−	0.991750i	$-0.459084\pi$
$827$	−74.8901	−	13.2051i	−0.0905564	−	0.0159675i	−0.218743	+	0.975783i	$0.570196\pi$
$828$		0			0
$829$	−176.628	−	1001.71i	−0.213062	−	1.20833i	−0.884238	−	0.467036i	$-0.845322\pi$
$829$	−176.628	−	1001.71i	−0.213062	−	1.20833i	0.671177	−	0.741298i	$-0.265789\pi$
$830$		0			0
$831$	576.102	+	315.238i	0.693263	+	0.379348i
$832$		0			0
$833$	100.895	−	153.403i	0.121122	−	0.184158i
$834$		0			0
$835$	−266.728	+	890.934i	−0.319435	+	1.06699i
$836$		0			0
$837$	88.8820	−	537.202i	0.106191	−	0.641818i
$838$		0			0
$839$	301.523	−	284.472i	0.359384	−	0.339061i	−0.485280	−	0.874359i	$-0.661282\pi$
$839$	301.523	−	284.472i	0.359384	−	0.339061i	0.844663	+	0.535298i	$0.179801\pi$
$840$		0			0
$841$	−9.89894	+	169.958i	−0.0117704	+	0.202091i
$842$		0			0
$843$	187.940	−	1230.04i	0.222942	−	1.45912i
$844$		0			0
$845$	−54.0261	+	148.435i	−0.0639362	+	0.175663i
$846$		0			0
$847$	−467.179	+	170.039i	−0.551569	+	0.200755i
$848$		0			0
$849$	−382.536	+	377.841i	−0.450572	+	0.445042i
$850$		0			0
$851$	−257.558	+	1086.72i	−0.302653	+	1.27699i
$852$		0			0
$853$	−26.0914	−	60.4867i	−0.0305878	−	0.0709106i	0.902237	−	0.431240i	$-0.141924\pi$
$853$	−26.0914	−	60.4867i	−0.0305878	−	0.0709106i	−0.932825	+	0.360329i	$0.882664\pi$
$854$		0			0
$855$	270.862	−	865.687i	0.316798	−	1.01250i
$856$		0			0
$857$	379.994	−	22.1321i	0.443400	−	0.0258251i	0.165007	−	0.986292i	$-0.447235\pi$
$857$	379.994	−	22.1321i	0.443400	−	0.0258251i	0.278393	+	0.960467i	$0.410198\pi$
$858$		0			0
$859$	−628.309	+	1456.58i	−0.731442	+	1.69567i	−0.0131678	+	0.999913i	$0.504192\pi$
$859$	−628.309	+	1456.58i	−0.731442	+	1.69567i	−0.718274	+	0.695760i	$0.755068\pi$
$860$		0			0
$861$	−999.258	−	212.772i	−1.16058	−	0.247122i
$862$		0			0
$863$	−1401.65	−	809.244i	−1.62416	−	0.937711i	−0.985790	−	0.167984i	$-0.946274\pi$
$863$	−1401.65	−	809.244i	−1.62416	−	0.937711i	−0.638373	−	0.769727i	$-0.720392\pi$
$864$		0			0
$865$	394.766	+	683.754i	0.456377	+	0.790467i
$866$		0			0
$867$	452.631	−	353.374i	0.522066	−	0.407582i
$868$		0			0
$869$	−6.84001	−	58.5200i	−0.00787113	−	0.0673418i
$870$		0			0
$871$	−601.010	−	301.838i	−0.690022	−	0.346542i
$872$		0			0
$873$	1354.06	+	256.037i	1.55104	+	0.293284i
$874$		0			0
$875$	558.029	+	415.437i	0.637747	+	0.474785i
$876$		0			0
$877$	−821.925	+	871.189i	−0.937201	+	0.993375i	−0.999989	−	0.00465234i	$-0.998519\pi$
$877$	−821.925	+	871.189i	−0.937201	+	0.993375i	0.0627887	+	0.998027i	$0.480001\pi$
$878$		0			0
$879$	−458.371	+	646.093i	−0.521468	+	0.735032i
$880$		0			0
$881$	−507.356	+	604.643i	−0.575886	+	0.686314i	−0.972828	−	0.231529i	$-0.925627\pi$
$881$	−507.356	+	604.643i	−0.575886	+	0.686314i	0.396942	+	0.917844i	$0.370071\pi$
$882$		0			0
$883$	995.205	−	835.076i	1.12707	−	0.945726i	0.128132	−	0.991757i	$-0.459102\pi$
$883$	995.205	−	835.076i	1.12707	−	0.945726i	0.998940	+	0.0460310i	$0.0146573\pi$
$884$		0			0
$885$	−720.503	+	144.139i	−0.814128	+	0.162869i
$886$		0			0
$887$	338.717	+	674.441i	0.381868	+	0.760362i	0.999663	−	0.0259774i	$-0.00826981\pi$
$887$	338.717	+	674.441i	0.381868	+	0.760362i	−0.617794	+	0.786340i	$0.711974\pi$
$888$		0			0
$889$	−7.74213	+	1.83492i	−0.00870881	+	0.00206403i
$890$		0			0
$891$	319.520	+	316.727i	0.358608	+	0.355473i
$892$		0			0
$893$	385.506	+	1626.58i	0.431698	+	1.82148i
$894$		0			0
$895$	−13.7859	+	6.92352i	−0.0154032	+	0.00773577i
$896$		0			0
$897$	−499.369	+	438.906i	−0.556711	+	0.489304i
$898$		0			0
$899$	−335.728	−	400.105i	−0.373446	−	0.445055i
$900$		0			0
$901$	74.7693	+	62.7389i	0.0829847	+	0.0696325i
$902$		0			0
$903$	−323.626	+	148.484i	−0.358390	+	0.164434i
$904$		0			0
$905$	399.217	+	376.642i	0.441124	+	0.416179i
$906$		0			0
$907$	832.737	−	1118.56i	0.918123	−	1.23325i	−0.0539428	−	0.998544i	$-0.517179\pi$
$907$	832.737	−	1118.56i	0.918123	−	1.23325i	0.972066	−	0.234709i	$-0.0754137\pi$
$908$		0			0
$909$	−239.146	−	2.95346i	−0.263087	−	0.00324913i
$910$		0			0
$911$	−193.636	+	385.560i	−0.212553	+	0.423227i	−0.974492	−	0.224421i	$-0.927951\pi$
$911$	−193.636	+	385.560i	−0.212553	+	0.423227i	0.761940	+	0.647648i	$0.224247\pi$
$912$		0			0
$913$	−450.156	+	52.6157i	−0.493051	+	0.0576294i
$914$		0			0
$915$	77.5889	−	191.842i	0.0847966	−	0.209663i
$916$		0			0
$917$	943.792	−	544.899i	1.02922	−	0.594219i
$918$		0			0
$919$	−415.806	+	720.197i	−0.452455	+	0.783675i	−0.998538	−	0.0540560i	$-0.982785\pi$
$919$	−415.806	+	720.197i	−0.452455	+	0.783675i	0.546083	+	0.837731i	$0.316118\pi$
$920$		0			0
$921$	62.1325	+	55.9846i	0.0674620	+	0.0607867i
$922$		0			0
$923$	−953.484	−	411.293i	−1.03303	−	0.445605i
$924$		0			0
$925$	−48.2453	−	828.339i	−0.0521570	−	0.895502i
$926$		0			0
$927$	−87.0854	−	136.037i	−0.0939433	−	0.146750i
$928$		0			0
$929$	167.184	−	72.1160i	0.179961	−	0.0776276i	−0.304193	−	0.952610i	$-0.598387\pi$
$929$	167.184	−	72.1160i	0.179961	−	0.0776276i	0.484154	+	0.874983i	$0.339127\pi$
$930$		0			0
$931$	579.522	+	137.349i	0.622472	+	0.147529i
$932$		0			0
$933$	−301.266	+	1097.20i	−0.322901	+	1.17599i
$934$		0			0
$935$	−59.0254	−	162.171i	−0.0631288	−	0.173445i
$936$		0			0
$937$	262.302	+	95.4700i	0.279938	+	0.101889i	0.478174	−	0.878265i	$-0.341299\pi$
$937$	262.302	+	95.4700i	0.279938	+	0.101889i	−0.198236	+	0.980154i	$0.563521\pi$
$938$		0			0
$939$	−978.123	+	1221.46i	−1.04166	+	1.30081i
$940$		0			0
$941$	−1303.49	−	75.9199i	−1.38522	−	0.0806800i	−0.650737	−	0.759304i	$-0.725540\pi$
$941$	−1303.49	−	75.9199i	−1.38522	−	0.0806800i	−0.734486	+	0.678624i	$0.762577\pi$
$942$		0			0
$943$	−861.696	−	913.345i	−0.913782	−	0.968552i
$944$		0			0
$945$	205.755	−	420.717i	0.217731	−	0.445203i
$946$		0			0
$947$	−404.784	−	121.184i	−0.427438	−	0.127967i	0.0658561	−	0.997829i	$-0.479022\pi$
$947$	−404.784	−	121.184i	−0.427438	−	0.127967i	−0.493294	+	0.869863i	$0.664207\pi$
$948$		0			0
$949$	−554.956	−	365.001i	−0.584780	−	0.384616i
$950$		0			0
$951$	−112.822	+	2.58568i	−0.118635	+	0.00271890i
$952$		0			0
$953$	1428.30	−	251.849i	1.49875	−	0.264269i	0.636705	−	0.771108i	$-0.280297\pi$
$953$	1428.30	−	251.849i	1.49875	−	0.264269i	0.862041	+	0.506839i	$0.169186\pi$
$954$		0			0
$955$	89.4312	−	507.190i	0.0936453	−	0.531089i
$956$		0			0
$957$	430.133	−	34.9569i	0.449460	−	0.0365276i
$958$		0			0
$959$	442.400	−	132.446i	0.461314	−	0.138108i
$960$		0			0
$961$	550.550	+	64.3500i	0.572893	+	0.0669615i
$962$		0			0
$963$	−215.343	−	145.474i	−0.223617	−	0.151064i
$964$		0			0
$965$	352.387	+	535.778i	0.365167	+	0.555210i
$966$		0			0
$967$	−619.823	−	832.566i	−0.640975	−	0.860978i	0.356329	−	0.934360i	$-0.384028\pi$
$967$	−619.823	−	832.566i	−0.640975	−	0.860978i	−0.997304	+	0.0733820i	$0.976621\pi$
$968$		0			0
$969$	−805.160	−	503.519i	−0.830918	−	0.519628i
$970$		0			0
$971$			47.9636i			0.0493961i	0.999695	+	0.0246981i	$0.00786244\pi$
$971$			47.9636i			0.0493961i	−0.999695	+	0.0246981i	$0.992138\pi$
$972$		0			0
$973$	663.768			0.682187
$974$		0			0
$975$	261.897	−	418.791i	0.268613	−	0.429529i
$976$		0			0
$977$	445.166	−	331.414i	0.455646	−	0.339216i	−0.344743	−	0.938697i	$-0.612034\pi$
$977$	445.166	−	331.414i	0.455646	−	0.339216i	0.800389	+	0.599481i	$0.204626\pi$
$978$		0			0
$979$	111.799	−	73.5313i	0.114197	−	0.0751086i
$980$		0			0
$981$	1195.28	+	84.4394i	1.21843	+	0.0860749i
$982$		0			0
$983$	136.386	−	1166.86i	0.138745	−	1.18704i	−0.727030	−	0.686606i	$-0.759100\pi$
$983$	136.386	−	1166.86i	0.138745	−	1.18704i	0.865775	−	0.500434i	$-0.166826\pi$
$984$		0			0
$985$	−196.879	−	657.621i	−0.199877	−	0.667635i
$986$		0			0
$987$	69.9130	+	860.256i	0.0708339	+	0.871587i
$988$		0			0
$989$	−430.973	−	75.9921i	−0.435766	−	0.0768373i
$990$		0			0
$991$	−15.0065	−	85.1062i	−0.0151428	−	0.0858791i	0.976300	−	0.216423i	$-0.0694389\pi$
$991$	−15.0065	−	85.1062i	−0.0151428	−	0.0858791i	−0.991443	+	0.130543i	$0.958328\pi$
$992$		0			0
$993$	−4.61127	−	201.206i	−0.00464378	−	0.202625i
$994$		0			0
$995$	42.3240	−	64.3505i	0.0425367	−	0.0646739i
$996$		0			0
$997$	386.187	−	1289.95i	0.387349	−	1.29384i	−0.512895	−	0.858451i	$-0.671427\pi$
$997$	386.187	−	1289.95i	0.387349	−	1.29384i	0.900244	−	0.435385i	$-0.143388\pi$
$998$		0			0
$999$	−1439.27	+	357.215i	−1.44071	+	0.357572i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.3.o.a.5.6	✓	324
81.65	odd	54	inner	324.3.o.a.65.6	yes	324

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
324.3.o.a.5.6	✓	324	1.1	even	1	trivial
324.3.o.a.65.6	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)

\(f(q)\)	\(=\)	\(q+(-1.59067 + 2.54358i) q^{3} +(-2.52291 + 1.87823i) q^{5} +(-4.60759 + 3.03046i) q^{7} +(-3.93956 - 8.09196i) q^{9} +O(q^{10})\)	\(q+(-1.59067 + 2.54358i) q^{3} +(-2.52291 + 1.87823i) q^{5} +(-4.60759 + 3.03046i) q^{7} +(-3.93956 - 8.09196i) q^{9} +(0.644815 - 5.51675i) q^{11} +(3.12574 + 10.4407i) q^{13} +(-0.764332 - 9.40485i) q^{15} +(-9.72857 - 1.71541i) q^{17} +(-5.56429 - 31.5567i) q^{19} +(-0.379070 - 16.5402i) q^{21} +(11.1738 - 16.9889i) q^{23} +(-4.33279 + 14.4725i) q^{25} +(26.8491 + 2.85102i) q^{27} +(18.8382 - 17.7729i) q^{29} +(1.17260 - 20.1327i) q^{31} +(13.0066 + 10.4154i) q^{33} +(5.93260 - 16.2997i) q^{35} +(-51.6114 + 18.7850i) q^{37} +(-31.5287 - 8.65710i) q^{39} +(14.2410 - 60.0876i) q^{41} +(-8.52424 - 19.7614i) q^{43} +(25.1377 + 13.0158i) q^{45} +(-52.0796 + 3.03329i) q^{47} +(-7.36173 + 17.0664i) q^{49} +(19.8382 - 22.0167i) q^{51} +(-8.55662 - 4.94017i) q^{53} +(8.73493 + 15.1293i) q^{55} +(89.1177 + 36.0429i) q^{57} +(-9.04028 - 77.3445i) q^{59} +(19.5983 + 9.84264i) q^{61} +(42.6742 + 25.3457i) q^{63} +(-27.4960 - 20.4700i) q^{65} +(-42.3478 + 44.8861i) q^{67} +(25.4388 + 55.4450i) q^{69} +(-61.2446 + 72.9885i) q^{71} +(-46.6879 + 39.1758i) q^{73} +(-29.9200 - 34.0417i) q^{75} +(13.7472 + 27.3730i) q^{77} +(10.3218 - 2.44630i) q^{79} +(-49.9597 + 63.7576i) q^{81} +(-18.8178 - 79.3985i) q^{83} +(27.7662 - 13.9447i) q^{85} +(15.2415 + 76.1871i) q^{87} +(15.4859 + 18.4553i) q^{89} +(-46.0422 - 38.6340i) q^{91} +(49.3440 + 35.0071i) q^{93} +(73.3089 + 69.1634i) q^{95} +(-91.4351 + 122.819i) q^{97} +(-47.1816 + 16.5158i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 324 q+O(q^{10}) \) 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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