LMFDB - Embedded newform 324.3.o.a.65.6

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			65.6
Character	$\chi$	$=$	324.65
Dual form			324.3.o.a.5.6

$q$-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 $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$1$	$e\left(\frac{31}{54}\right)$

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	0.314561	−	0.949237i	$-0.398143\pi$
$5$	−2.52291	−	1.87823i	−0.504581	−	0.375647i	−0.819142	+	0.573591i	$0.805550\pi$
$6$		0			0
$7$	−4.60759	−	3.03046i	−0.658227	−	0.432922i	0.175966	−	0.984396i	$-0.443695\pi$
$7$	−4.60759	−	3.03046i	−0.658227	−	0.432922i	−0.834192	+	0.551474i	$0.814066\pi$
$8$		0			0
$9$	−3.93956	+	8.09196i	−0.437729	+	0.899107i
$10$		0			0
$11$	0.644815	+	5.51675i	0.0586196	+	0.501523i	0.990372	+	0.138429i	$0.0442053\pi$
$11$	0.644815	+	5.51675i	0.0586196	+	0.501523i	−0.931753	+	0.363093i	$0.881721\pi$
$12$		0			0
$13$	3.12574	−	10.4407i	0.240441	−	0.803130i	−0.749543	−	0.661955i	$-0.769727\pi$
$13$	3.12574	−	10.4407i	0.240441	−	0.803130i	0.989985	−	0.141175i	$-0.0450879\pi$
$14$		0			0
$15$	−0.764332	+	9.40485i	−0.0509554	+	0.626990i
$16$		0			0
$17$	−9.72857	+	1.71541i	−0.572269	+	0.100906i	−0.452291	−	0.891870i	$-0.649393\pi$
$17$	−9.72857	+	1.71541i	−0.572269	+	0.100906i	−0.119977	+	0.992777i	$0.538282\pi$
$18$		0			0
$19$	−5.56429	+	31.5567i	−0.292857	+	1.66088i	0.382928	+	0.923778i	$0.374916\pi$
$19$	−5.56429	+	31.5567i	−0.292857	+	1.66088i	−0.675785	+	0.737098i	$0.736195\pi$
$20$		0			0
$21$	−0.379070	+	16.5402i	−0.0180510	+	0.787628i
$22$		0			0
$23$	11.1738	+	16.9889i	0.485817	+	0.738648i	0.992334	−	0.123581i	$-0.0394380\pi$
$23$	11.1738	+	16.9889i	0.485817	+	0.738648i	−0.506518	+	0.862229i	$0.669068\pi$
$24$		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	0.938823	−	0.344401i	$-0.111918\pi$
$29$	18.8382	+	17.7729i	0.649593	+	0.612859i	−0.289230	+	0.957260i	$0.593399\pi$
$30$		0			0
$31$	1.17260	+	20.1327i	0.0378258	+	0.649443i	0.962934	+	0.269739i	$0.0869373\pi$
$31$	1.17260	+	20.1327i	0.0378258	+	0.649443i	−0.925108	+	0.379705i	$0.876026\pi$
$32$		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	−0.468242	−	0.883601i	$-0.655112\pi$
$37$	−51.6114	−	18.7850i	−1.39490	−	0.507703i	−0.926661	+	0.375897i	$0.877335\pi$
$38$		0			0
$39$	−31.5287	+	8.65710i	−0.808428	+	0.221977i
$40$		0			0
$41$	14.2410	+	60.0876i	0.347342	+	1.46555i	0.813872	+	0.581045i	$0.197356\pi$
$41$	14.2410	+	60.0876i	0.347342	+	1.46555i	−0.466530	+	0.884506i	$0.654496\pi$
$42$		0			0
$43$	−8.52424	+	19.7614i	−0.198238	+	0.459568i	−0.988119	−	0.153693i	$-0.950883\pi$
$43$	−8.52424	+	19.7614i	−0.198238	+	0.459568i	0.789880	+	0.613261i	$0.210143\pi$
$44$		0			0
$45$	25.1377	−	13.0158i	0.558616	−	0.289241i
$46$		0			0
$47$	−52.0796	−	3.03329i	−1.10808	−	0.0645381i	−0.505669	−	0.862727i	$-0.668754\pi$
$47$	−52.0796	−	3.03329i	−1.10808	−	0.0645381i	−0.602407	+	0.798189i	$0.705791\pi$
$48$		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	−0.578546	−	0.815650i	$-0.696380\pi$
$53$	−8.55662	+	4.94017i	−0.161446	+	0.0932107i	0.417100	+	0.908860i	$0.363046\pi$
$54$		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	0.669639	+	0.742686i	$0.266449\pi$
$59$	−9.04028	+	77.3445i	−0.153225	+	1.31092i	−0.822865	+	0.568238i	$0.807625\pi$
$60$		0			0
$61$	19.5983	−	9.84264i	0.321284	−	0.161355i	−0.280846	−	0.959753i	$-0.590615\pi$
$61$	19.5983	−	9.84264i	0.321284	−	0.161355i	0.602130	+	0.798398i	$0.294319\pi$
$62$		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	0.329624	−	0.944112i	$-0.393078\pi$
$67$	−42.3478	−	44.8861i	−0.632057	−	0.669941i	−0.961681	+	0.274171i	$0.911597\pi$
$68$		0			0
$69$	25.4388	−	55.4450i	0.368679	−	0.803551i
$70$		0			0
$71$	−61.2446	−	72.9885i	−0.862600	−	1.02801i	−0.999301	−	0.0373940i	$-0.988094\pi$
$71$	−61.2446	−	72.9885i	−0.862600	−	1.02801i	0.136701	−	0.990612i	$-0.456350\pi$
$72$		0			0
$73$	−46.6879	−	39.1758i	−0.639560	−	0.536655i	0.264323	−	0.964434i	$-0.414852\pi$
$73$	−46.6879	−	39.1758i	−0.639560	−	0.536655i	−0.903883	+	0.427779i	$0.859296\pi$
$74$		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	0.295423	−	0.955366i	$-0.404539\pi$
$79$	10.3218	+	2.44630i	0.130655	+	0.0309659i	−0.164768	+	0.986332i	$0.552688\pi$
$80$		0			0
$81$	−49.9597	−	63.7576i	−0.616786	−	0.787131i
$82$		0			0
$83$	−18.8178	+	79.3985i	−0.226720	+	0.956609i	0.734013	+	0.679136i	$0.237645\pi$
$83$	−18.8178	+	79.3985i	−0.226720	+	0.956609i	−0.960733	+	0.277473i	$0.910503\pi$
$84$		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	−0.671996	−	0.740554i	$-0.734563\pi$
$89$	15.4859	−	18.4553i	0.173998	−	0.207363i	0.845995	+	0.533191i	$0.179007\pi$
$90$		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	−0.963863	−	0.266397i	$-0.914167\pi$
$97$	−91.4351	−	122.819i	−0.942630	−	1.26617i	0.0212336	−	0.999775i	$-0.493241\pi$
$98$		0			0
$99$	−47.1816	−	16.5158i	−0.476582	−	0.166826i
$100$		0			0
$101$	11.9263	+	23.7472i	0.118082	+	0.235121i	0.944907	−	0.327338i	$-0.106152\pi$
$101$	11.9263	+	23.7472i	0.118082	+	0.235121i	−0.826825	+	0.562459i	$0.809855\pi$
$102$		0			0
$103$	17.8257	+	2.08353i	0.173065	+	0.0202284i	0.202184	−	0.979348i	$-0.435196\pi$
$103$	17.8257	+	2.08353i	0.173065	+	0.0202284i	−0.0291189	+	0.999576i	$0.509270\pi$
$104$		0			0
$105$	32.0227	−	41.0174i	0.304978	−	0.390641i
$106$		0			0
$107$	25.0065	+	14.4375i	0.233706	+	0.134930i	0.612281	−	0.790641i	$-0.290252\pi$
$107$	25.0065	+	14.4375i	0.233706	+	0.134930i	−0.378575	+	0.925571i	$0.623586\pi$
$108$		0			0
$109$	−66.5698	−	115.302i	−0.610732	−	1.05782i	−0.991117	−	0.132991i	$-0.957542\pi$
$109$	−66.5698	−	115.302i	−0.610732	−	1.05782i	0.380385	−	0.924828i	$-0.375792\pi$
$110$		0			0
$111$	34.3154	+	161.158i	0.309147	+	1.45188i
$112$		0			0
$113$	102.979	−	44.4207i	0.911316	−	0.393104i	0.111788	−	0.993732i	$-0.464342\pi$
$113$	102.979	−	44.4207i	0.911316	−	0.393104i	0.799528	+	0.600629i	$0.205083\pi$
$114$		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	−0.336677	−	0.941620i	$-0.609303\pi$
$127$	1.35575	−	0.493453i	0.0106752	−	0.00388546i	0.347352	+	0.937735i	$0.387081\pi$
$128$		0			0
$129$	63.8239	−	9.75174i	0.494759	−	0.0755949i
$130$		0			0
$131$	−197.277	+	11.4901i	−1.50593	+	0.0877106i	−0.791144	−	0.611630i	$-0.790514\pi$
$131$	−197.277	+	11.4901i	−1.50593	+	0.0877106i	−0.714789	+	0.699340i	$0.753477\pi$
$132$		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	−0.565855	−	0.824505i	$-0.691454\pi$
$137$	−80.2198	+	24.0162i	−0.585546	+	0.175301i	−0.0196916	+	0.999806i	$0.506268\pi$
$138$		0			0
$139$	−100.560	+	66.1390i	−0.723450	+	0.475820i	−0.857062	−	0.515213i	$-0.827713\pi$
$139$	−100.560	+	66.1390i	−0.723450	+	0.475820i	0.133612	+	0.991034i	$0.457342\pi$
$140$		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	0.272403	−	0.962183i	$-0.412182\pi$
$149$	−4.28158	−	1.28182i	−0.0287354	−	0.00860282i	−0.301139	+	0.953580i	$0.597367\pi$
$150$		0			0
$151$	7.05223	−	0.824288i	0.0467035	−	0.00545886i	−0.0927091	−	0.995693i	$-0.529553\pi$
$151$	7.05223	−	0.824288i	0.0467035	−	0.00545886i	0.139413	+	0.990234i	$0.455479\pi$
$152$		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	−0.927446	−	0.373958i	$-0.878001\pi$
$157$	−47.6030	+	63.9420i	−0.303204	+	0.407274i	0.624242	+	0.781231i	$0.285408\pi$
$158$		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	0.987819	+	0.155608i	$0.0497337\pi$
$167$	237.173	+	176.569i	1.42020	+	1.05730i	0.432381	+	0.901691i	$0.357674\pi$
$168$		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	0.767800	+	0.640689i	$0.221351\pi$
$173$	29.1417	+	249.323i	0.168449	+	1.44118i	−0.599351	+	0.800486i	$0.704575\pi$
$174$		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	−0.160140	−	0.987094i	$-0.551194\pi$
$179$	4.83021	−	0.851697i	0.0269844	−	0.00475808i	0.187124	+	0.982336i	$0.440083\pi$
$180$		0			0
$181$	−30.3013	+	171.847i	−0.167411	+	0.949434i	0.779133	+	0.626859i	$0.215660\pi$
$181$	−30.3013	+	171.847i	−0.167411	+	0.949434i	−0.946544	+	0.322575i	$0.895452\pi$
$182$		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	0.308218	−	0.951316i	$-0.400267\pi$
$191$	−119.101	−	112.366i	−0.623567	−	0.588305i	−0.931785	+	0.363011i	$0.881749\pi$
$192$		0			0
$193$	11.8548	+	203.540i	0.0614241	+	1.05461i	0.878396	+	0.477933i	$0.158614\pi$
$193$	11.8548	+	203.540i	0.0614241	+	1.05461i	−0.816972	+	0.576677i	$0.804349\pi$
$194$		0			0
$195$	95.8040	+	37.3772i	0.491302	+	0.191678i
$196$		0			0
$197$	−74.6460	−	205.088i	−0.378914	−	1.04106i	−0.971807	−	0.235776i	$-0.924237\pi$
$197$	−74.6460	−	205.088i	−0.378914	−	1.04106i	0.592894	−	0.805281i	$-0.297985\pi$
$198$		0			0
$199$	−23.0111	−	8.37537i	−0.115634	−	0.0420873i	0.283555	−	0.958956i	$-0.408486\pi$
$199$	−23.0111	−	8.37537i	−0.115634	−	0.0420873i	−0.399189	+	0.916869i	$0.630708\pi$
$200$		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	0.998806	+	0.0488624i	$0.0155596\pi$
$211$	73.6231	+	170.678i	0.348925	+	0.808899i	−0.649881	+	0.760036i	$0.725181\pi$
$212$		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	−0.284891	−	0.958560i	$-0.591957\pi$
$223$	69.9923	−	35.1515i	0.313867	−	0.157630i	0.598758	+	0.800930i	$0.295661\pi$
$224$		0			0
$225$	134.180	+	21.9547i	0.596357	+	0.0975764i
$226$		0			0
$227$	−270.895	+	201.674i	−1.19337	+	0.888430i	−0.995772	−	0.0918540i	$-0.970721\pi$
$227$	−270.895	+	201.674i	−1.19337	+	0.888430i	−0.197596	+	0.980284i	$0.563313\pi$
$228$		0			0
$229$	154.888	+	164.172i	0.676367	+	0.716907i	0.971100	−	0.238673i	$-0.0767123\pi$
$229$	154.888	+	164.172i	0.676367	+	0.716907i	−0.294733	+	0.955579i	$0.595231\pi$
$230$		0			0
$231$	−91.4925	+	8.57413i	−0.396071	+	0.0371175i
$232$		0			0
$233$	−176.360	−	210.177i	−0.756909	−	0.902049i	0.240740	−	0.970590i	$-0.422610\pi$
$233$	−176.360	−	210.177i	−0.756909	−	0.902049i	−0.997648	+	0.0685410i	$0.978166\pi$
$234$		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	−0.371314	−	0.928508i	$-0.621093\pi$
$239$	142.252	−	283.247i	0.595197	−	1.18513i	0.966511	−	0.256627i	$-0.0826112\pi$
$240$		0			0
$241$	−304.379	−	72.1391i	−1.26298	−	0.299332i	−0.456038	−	0.889960i	$-0.650732\pi$
$241$	−304.379	−	72.1391i	−1.26298	−	0.299332i	−0.806944	+	0.590628i	$0.798880\pi$
$242$		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	−0.650002	−	0.759933i	$-0.725232\pi$
$251$	53.0256	−	63.1935i	0.211257	−	0.251767i	0.861259	+	0.508166i	$0.169676\pi$
$252$		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	−0.656581	−	0.754256i	$-0.727998\pi$
$257$	14.9632	−	14.1170i	0.0582225	−	0.0549301i	0.714803	+	0.699326i	$0.246516\pi$
$258$		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	0.997191	+	0.0749012i	$0.0238641\pi$
$263$	121.451	+	241.828i	0.461790	+	0.919499i	−0.535401	+	0.844598i	$0.679840\pi$
$264$		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	0.565858	−	0.824502i	$-0.308545\pi$
$269$	36.2471	+	20.9273i	0.134748	+	0.0777966i	−0.431111	+	0.902299i	$0.641878\pi$
$270$		0			0
$271$	159.519	+	276.295i	0.588631	+	1.01954i	0.994412	+	0.105569i	$0.0336664\pi$
$271$	159.519	+	276.295i	0.588631	+	1.01954i	−0.405781	+	0.913971i	$0.633000\pi$
$272$		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	0.894095	+	0.447877i	$0.147820\pi$
$277$	−12.7281	+	218.533i	−0.0459498	+	0.788928i	−0.940045	+	0.341051i	$0.889217\pi$
$278$		0			0
$279$	−167.533	−	69.8256i	−0.600476	−	0.250271i
$280$		0			0
$281$	−380.850	−	164.283i	−1.35534	−	0.584636i	−0.410407	−	0.911902i	$-0.634613\pi$
$281$	−380.850	−	164.283i	−1.35534	−	0.584636i	−0.944932	+	0.327266i	$0.893873\pi$
$282$		0			0
$283$	174.395	−	41.3323i	0.616236	−	0.146051i	0.0893695	−	0.995999i	$-0.471515\pi$
$283$	174.395	−	41.3323i	0.616236	−	0.146051i	0.526867	+	0.849948i	$0.323367\pi$
$284$		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	0.397942	−	0.917411i	$-0.369725\pi$
$293$	263.611	−	15.3536i	0.899698	−	0.0524014i	0.501756	+	0.865009i	$0.332688\pi$
$294$		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	0.991676	−	0.128755i	$-0.0410980\pi$
$307$	4.84099	+	27.4546i	0.0157687	+	0.0894287i	−0.975908	+	0.218183i	$0.929987\pi$
$308$		0			0
$309$	−23.0552	−	48.6553i	−0.0746121	−	0.157460i
$310$		0			0
$311$	363.335	+	108.775i	1.16828	+	0.349760i	0.811458	−	0.584411i	$-0.198675\pi$
$311$	363.335	+	108.775i	1.16828	+	0.349760i	0.356824	+	0.934172i	$0.383860\pi$
$312$		0			0
$313$	518.083	−	60.5552i	1.65522	−	0.193467i	0.763419	−	0.645903i	$-0.223519\pi$
$313$	518.083	−	60.5552i	1.65522	−	0.193467i	0.891797	+	0.452436i	$0.149445\pi$
$314$		0			0
$315$	−155.268	−	16.2073i	−0.492915	−	0.0514517i
$316$		0			0
$317$	20.6710	−	31.4288i	0.0652083	−	0.0991444i	−0.801412	−	0.598113i	$-0.795917\pi$
$317$	20.6710	−	31.4288i	0.0652083	−	0.0991444i	0.866620	+	0.498969i	$0.166288\pi$
$318$		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	0.462013	−	0.886873i	$-0.347127\pi$
$331$	−56.0498	−	36.8645i	−0.169335	−	0.111373i	−0.631347	+	0.775500i	$0.717498\pi$
$332$		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	−0.522924	−	0.852379i	$-0.675159\pi$
$337$	128.856	−	430.410i	0.382363	−	1.27718i	0.905287	−	0.424801i	$-0.139656\pi$
$338$		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	−0.999828	−	0.0185713i	$-0.994088\pi$
$347$	−215.441	−	327.563i	−0.620869	−	0.943985i	0.378959	−	0.925413i	$-0.376282\pi$
$348$		0			0
$349$	−154.625	−	516.485i	−0.443053	−	1.47990i	−0.829982	−	0.557790i	$-0.811649\pi$
$349$	−154.625	−	516.485i	−0.443053	−	1.47990i	0.386929	−	0.922110i	$-0.373536\pi$
$350$		0			0
$351$	54.1565	−	289.234i	0.154292	−	0.824029i
$352$		0			0
$353$	−409.040	−	385.909i	−1.15875	−	1.09323i	−0.994276	−	0.106847i	$-0.965925\pi$
$353$	−409.040	−	385.909i	−1.15875	−	1.09323i	−0.164478	−	0.986381i	$-0.552594\pi$
$354$		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	−0.827639	−	0.561260i	$-0.810317\pi$
$359$	−199.030	−	546.831i	−0.554402	−	1.52321i	0.273238	−	0.961947i	$-0.411905\pi$
$360$		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	−0.794276	−	0.607558i	$-0.792149\pi$
$367$	70.7248	−	163.959i	0.192711	−	0.446754i	0.986986	+	0.160804i	$0.0514087\pi$
$368$		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	0.997959	−	0.0638573i	$-0.0203403\pi$
$373$	99.4679	+	230.592i	0.266670	+	0.618210i	−0.731289	+	0.682068i	$0.761081\pi$
$374$		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	−0.249918	−	0.968267i	$-0.580404\pi$
$379$	270.449	−	468.431i	0.713585	−	1.23597i	0.963503	−	0.267698i	$-0.0862631\pi$
$380$		0			0
$381$	−3.41168	−	2.66354i	−0.00895455	−	0.00699092i
$382$		0			0
$383$	58.5939	−	501.303i	0.152987	−	1.30888i	−0.670653	−	0.741771i	$-0.733986\pi$
$383$	58.5939	−	501.303i	0.152987	−	1.30888i	0.823640	−	0.567113i	$-0.191940\pi$
$384$		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	−0.168619	−	0.985681i	$-0.553931\pi$
$389$	282.917	−	210.624i	0.727293	−	0.541449i	0.895912	+	0.444232i	$0.146523\pi$
$390$		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	0.374109	−	0.927385i	$-0.377949\pi$
$397$	−188.267	−	157.975i	−0.474224	−	0.397921i	−0.848333	+	0.529464i	$0.822393\pi$
$398$		0			0
$399$	−519.844	−	103.997i	−1.30287	−	0.260643i
$400$		0			0
$401$	−288.518	+	574.486i	−0.719495	+	1.43263i	0.174546	+	0.984649i	$0.444154\pi$
$401$	−288.518	+	574.486i	−0.719495	+	1.43263i	−0.894042	+	0.447984i	$0.852142\pi$
$402$		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	0.878439	−	0.477854i	$-0.158585\pi$
$409$	417.061	+	209.456i	1.01971	+	0.512117i	0.141270	+	0.989971i	$0.454881\pi$
$410$		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	0.199559	−	0.979886i	$-0.436049\pi$
$419$	498.355	−	470.173i	1.18939	−	1.12213i	0.989831	−	0.142247i	$-0.0454326\pi$
$420$		0			0
$421$	108.550	+	145.807i	0.257838	+	0.346336i	0.912127	−	0.409909i	$-0.134439\pi$
$421$	108.550	+	145.807i	0.257838	+	0.346336i	−0.654289	+	0.756245i	$0.727032\pi$
$422$		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	0.733008	−	0.680220i	$-0.238116\pi$
$431$	219.993	+	127.013i	0.510425	+	0.294694i	−0.222583	+	0.974914i	$0.571449\pi$
$432$		0			0
$433$	115.287	+	199.683i	0.266252	+	0.461161i	0.967891	−	0.251371i	$-0.0808814\pi$
$433$	115.287	+	199.683i	0.266252	+	0.461161i	−0.701639	+	0.712532i	$0.747548\pi$
$434$		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	0.910156	+	0.414267i	$0.135962\pi$
$439$	−18.4113	+	316.111i	−0.0419393	+	0.720069i	−0.952095	+	0.305803i	$0.901075\pi$
$440$		0			0
$441$	167.103	+	7.66339i	0.378918	+	0.0173773i
$442$		0			0
$443$	224.222	+	96.7200i	0.506145	+	0.218330i	0.633812	−	0.773487i	$-0.281489\pi$
$443$	224.222	+	96.7200i	0.506145	+	0.218330i	−0.127667	+	0.991817i	$0.540749\pi$
$444$		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	0.416237	+	0.909256i	$0.363349\pi$
$449$	−218.698	+	600.868i	−0.487078	+	1.33824i	−0.903315	+	0.428979i	$0.858873\pi$
$450$		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	−0.485379	−	0.874304i	$-0.661318\pi$
$457$	189.960	−	201.346i	0.415668	−	0.440582i	0.901047	+	0.433722i	$0.142800\pi$
$458$		0			0
$459$	−256.312	+	73.7935i	−0.558415	+	0.160770i
$460$		0			0
$461$	−571.275	+	171.028i	−1.23921	+	0.370994i	−0.838343	−	0.545143i	$-0.816475\pi$
$461$	−571.275	+	171.028i	−1.23921	+	0.370994i	−0.400865	+	0.916137i	$0.631290\pi$
$462$		0			0
$463$	491.968	−	323.572i	1.06257	−	0.698860i	0.107185	−	0.994239i	$-0.465816\pi$
$463$	491.968	−	323.572i	1.06257	−	0.698860i	0.955380	+	0.295379i	$0.0954458\pi$
$464$		0			0
$465$	−190.242	−	4.35998i	−0.409122	−	0.00937631i
$466$		0			0
$467$	−701.939	−	123.771i	−1.50308	−	0.265034i	−0.639323	−	0.768939i	$-0.720785\pi$
$467$	−701.939	−	123.771i	−1.50308	−	0.265034i	−0.863759	+	0.503905i	$0.831896\pi$
$468$		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	0.120149	−	0.992756i	$-0.461663\pi$
$479$	471.396	−	716.722i	0.984125	−	1.49629i	0.863976	−	0.503533i	$-0.167967\pi$
$480$		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	0.886940	−	0.461885i	$-0.152827\pi$
$491$	343.128	+	255.449i	0.698835	+	0.520264i	−0.188104	+	0.982149i	$0.560234\pi$
$492$		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	0.802803	+	0.596245i	$0.203341\pi$
$499$	−97.5900	+	325.973i	−0.195571	+	0.653253i	−0.998374	+	0.0570082i	$0.981844\pi$
$500$		0			0
$501$	71.8533	−	884.131i	0.143420	−	1.76473i
$502$		0			0
$503$	−599.268	+	105.667i	−1.19139	+	0.210074i	−0.733972	−	0.679180i	$-0.762336\pi$
$503$	−599.268	+	105.667i	−1.19139	+	0.210074i	−0.457415	+	0.889253i	$0.651225\pi$
$504$		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	0.661245	−	0.750170i	$-0.270028\pi$
$509$	−147.345	−	224.027i	−0.289479	−	0.440131i	−0.950724	+	0.310039i	$0.899658\pi$
$510$		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	−0.996967	−	0.0778211i	$-0.975204\pi$
$521$	−147.583	−	405.481i	−0.283268	−	0.778274i	0.713699	−	0.700453i	$-0.247019\pi$
$522$		0			0
$523$	−619.082	−	225.327i	−1.18371	−	0.430836i	−0.326201	−	0.945300i	$-0.605769\pi$
$523$	−619.082	−	225.327i	−1.18371	−	0.430836i	−0.857512	+	0.514464i	$0.827991\pi$
$524$		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	−0.950952	−	0.309338i	$-0.899892\pi$
$541$	−112.301	+	194.512i	−0.207581	+	0.359541i	0.743371	+	0.668880i	$0.233226\pi$
$542$		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	−0.793160	−	0.609013i	$-0.791566\pi$
$547$	−425.730	+	213.810i	−0.778300	+	0.390877i	0.0148606	+	0.999890i	$0.495270\pi$
$548$		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	0.989566	−	0.144083i	$-0.0460233\pi$
$557$	376.440	+	448.624i	0.675835	+	0.805429i	−0.313730	+	0.949512i	$0.601579\pi$
$558$		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	−0.999992	−	0.00400743i	$-0.998724\pi$
$563$	−224.988	+	447.988i	−0.399624	+	0.795716i	0.600368	+	0.799724i	$0.295021\pi$
$564$		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	0.817712	+	0.575627i	$0.195242\pi$
$569$	−97.5056	+	411.409i	−0.171363	+	0.723038i	−0.989075	+	0.147411i	$0.952906\pi$
$570$		0			0
$571$	−529.303	−	265.826i	−0.926976	−	0.465545i	−0.0797722	−	0.996813i	$-0.525419\pi$
$571$	−529.303	−	265.826i	−0.926976	−	0.465545i	−0.847204	+	0.531268i	$0.821716\pi$
$572$		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	−0.897512	−	0.440990i	$-0.854627\pi$
$577$	−357.205	+	299.730i	−0.619073	+	0.519464i	0.278439	+	0.960454i	$0.410183\pi$
$578$		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	0.989170	+	0.146771i	$0.0468881\pi$
$587$	303.014	+	603.350i	0.516207	+	1.02785i	−0.472963	+	0.881082i	$0.656816\pi$
$588$		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	0.818840	−	0.574022i	$-0.194617\pi$
$593$	433.568	+	250.320i	0.731143	+	0.422126i	−0.0876972	+	0.996147i	$0.527951\pi$
$594$		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	−0.719115	−	0.694892i	$-0.755452\pi$
$599$	−423.586	+	182.717i	−0.707155	+	0.305037i	0.0119594	+	0.999928i	$0.496193\pi$
$600$		0			0
$601$	18.6918	−	320.925i	0.0311011	−	0.533986i	−0.946392	−	0.323020i	$-0.895302\pi$
$601$	18.6918	−	320.925i	0.0311011	−	0.533986i	0.977493	−	0.210966i	$-0.0676610\pi$
$602$		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	−0.740231	−	0.672353i	$-0.765284\pi$
$607$	−667.684	+	158.244i	−1.09997	+	0.260699i	−0.359743	+	0.933052i	$0.617136\pi$
$608$		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	0.387680	−	0.921794i	$-0.373277\pi$
$613$	782.910	−	284.956i	1.27718	−	0.464855i	0.889498	+	0.456940i	$0.151054\pi$
$614$		0			0
$615$	−575.999	+	88.0077i	−0.936584	+	0.143102i
$616$		0			0
$617$	−818.763	+	47.6875i	−1.32701	+	0.0772893i	−0.706947	−	0.707266i	$-0.749928\pi$
$617$	−818.763	+	47.6875i	−1.32701	+	0.0772893i	−0.620059	+	0.784555i	$0.712891\pi$
$618$		0			0
$619$	−692.819	+	734.346i	−1.11926	+	1.18634i	−0.138652	+	0.990341i	$0.544277\pi$
$619$	−692.819	+	734.346i	−1.11926	+	1.18634i	−0.980604	+	0.196001i	$0.937205\pi$
$620$		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	−0.760324	−	0.649543i	$-0.774960\pi$
$631$	−169.114	−	959.095i	−0.268010	−	1.51996i	0.492314	−	0.870417i	$-0.336151\pi$
$632$		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	−0.898525	−	0.438923i	$-0.855360\pi$
$641$	−89.4910	+	136.064i	−0.139612	+	0.212269i	0.758913	+	0.651192i	$0.225731\pi$
$642$		0			0
$643$	142.884	−	191.926i	0.222214	−	0.298486i	−0.677010	−	0.735974i	$-0.736725\pi$
$643$	142.884	−	191.926i	0.222214	−	0.298486i	0.899224	+	0.437488i	$0.144132\pi$
$644$		0			0
$645$	−179.338	−	95.2734i	−0.278043	−	0.147711i
$646$		0			0
$647$			848.415i			1.31131i	0.755062	+	0.655653i	$0.227607\pi$
$647$			848.415i			1.31131i	−0.755062	+	0.655653i	$0.772393\pi$
$648$		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	0.958580	−	0.284824i	$-0.0919352\pi$
$653$	627.301	+	467.008i	0.960645	+	0.715174i	0.00206526	+	0.999998i	$0.499343\pi$
$654$		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	0.997715	−	0.0675667i	$-0.0215235\pi$
$659$	7.45433	+	63.7759i	0.0113116	+	0.0967768i	−0.986403	+	0.164343i	$0.947449\pi$
$660$		0			0
$661$	281.575	−	940.527i	0.425984	−	1.42289i	−0.428564	−	0.903512i	$-0.640980\pi$
$661$	281.575	−	940.527i	0.425984	−	1.42289i	0.854547	−	0.519373i	$-0.173835\pi$
$662$		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	−0.743805	−	0.668396i	$-0.766981\pi$
$673$	−329.538	−	1100.73i	−0.489655	−	1.63556i	0.254150	−	0.967165i	$-0.418204\pi$
$674$		0			0
$675$	−157.593	−	376.221i	−0.233471	−	0.557364i
$676$		0			0
$677$	−637.451	−	601.404i	−0.941582	−	0.888337i	0.0523167	−	0.998631i	$-0.483339\pi$
$677$	−637.451	−	601.404i	−0.941582	−	0.888337i	−0.993899	+	0.110293i	$0.964821\pi$
$678$		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	0.974850	+	0.222864i	$0.0715406\pi$
$683$	253.615	+	696.803i	0.371326	+	1.02021i	−0.603524	+	0.797345i	$0.706237\pi$
$684$		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	−0.877400	−	0.479759i	$-0.840724\pi$
$691$	50.9074	−	118.017i	0.0736721	−	0.170791i	0.951073	+	0.308968i	$0.0999835\pi$
$692$		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	0.0944999	−	0.995525i	$-0.469875\pi$
$701$	703.734	−	406.301i	1.00390	−	0.579602i	0.909400	+	0.415923i	$0.136541\pi$
$702$		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	−0.632382	+	0.774657i	$0.717923\pi$
$709$	−1156.65	+	580.892i	−1.63138	+	0.819312i	−0.999002	+	0.0446555i	$0.985781\pi$
$710$		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	0.983353	−	0.181705i	$-0.0581615\pi$
$719$	455.595	+	542.957i	0.633651	+	0.755156i	−0.349702	+	0.936861i	$0.613717\pi$
$720$		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	−0.240793	−	0.970577i	$-0.577407\pi$
$727$	−648.169	−	153.619i	−0.891567	−	0.211305i	−0.650774	+	0.759271i	$0.725556\pi$
$728$		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	0.975161	−	0.221498i	$-0.0710947\pi$
$733$	1011.41	+	507.947i	1.37982	+	0.692970i	0.404657	+	0.914469i	$0.367391\pi$
$734$		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	−0.913675	−	0.406446i	$-0.866768\pi$
$739$	−496.654	+	416.742i	−0.672062	+	0.563927i	0.241613	+	0.970373i	$0.422324\pi$
$740$		0			0
$741$	−97.7542	−	1043.11i	−0.131922	−	1.40771i
$742$		0			0
$743$	403.392	−	380.581i	0.542923	−	0.512222i	−0.365198	−	0.930930i	$-0.618999\pi$
$743$	403.392	−	380.581i	0.542923	−	0.512222i	0.908121	+	0.418709i	$0.137517\pi$
$744$		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	−0.853260	−	0.521486i	$-0.825378\pi$
$751$	−1354.64	−	158.335i	−1.80378	−	0.210832i	−0.950523	+	0.310654i	$0.899452\pi$
$752$		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	0.996934	+	0.0782493i	$0.0249330\pi$
$757$	428.638	+	742.423i	0.566233	+	0.980744i	−0.430701	+	0.902495i	$0.641734\pi$
$758$		0			0
$759$	322.280	+	104.588i	0.424611	+	0.137797i
$760$		0			0
$761$	−380.819	+	164.269i	−0.500419	+	0.215860i	−0.631300	−	0.775538i	$-0.717478\pi$
$761$	−380.819	+	164.269i	−0.500419	+	0.215860i	0.130882	+	0.991398i	$0.458219\pi$
$762$		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	0.676043	−	0.736862i	$-0.263693\pi$
$769$	1238.77	−	293.593i	1.61088	−	0.381786i	0.934837	+	0.355076i	$0.115545\pi$
$770$		0			0
$771$	−59.7092	−	15.6045i	−0.0774438	−	0.0202393i
$772$		0			0
$773$	232.607	−	639.083i	0.300915	−	0.826757i	−0.693427	−	0.720527i	$-0.743900\pi$
$773$	232.607	−	639.083i	0.300915	−	0.826757i	0.994342	−	0.106230i	$-0.0338779\pi$
$774$		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	−0.650552	−	0.759462i	$-0.725462\pi$
$787$	−165.957	+	109.152i	−0.210873	+	0.138693i	0.439679	+	0.898155i	$0.355092\pi$
$788$		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	−0.235465	−	0.971883i	$-0.575661\pi$
$797$	−770.102	−	230.554i	−0.966251	−	0.289277i	−0.730786	+	0.682606i	$0.760846\pi$
$798$		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	$0.191619\pi$
$809$			916.244i			1.13256i	−0.824212	+	0.566282i	$0.808381\pi$
$810$		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	−0.973523	−	0.228588i	$-0.926589\pi$
$821$	−64.8241	−	554.605i	−0.0789575	−	0.675524i	0.894566	−	0.446936i	$-0.147485\pi$
$822$		0			0
$823$	421.484	−	1407.85i	0.512131	−	1.71064i	−0.175414	−	0.984495i	$-0.556126\pi$
$823$	421.484	−	1407.85i	0.512131	−	1.71064i	0.687545	−	0.726142i	$-0.258688\pi$
$824$		0			0
$825$	−207.093	−	143.110i	−0.251021	−	0.173467i
$826$		0			0
$827$	−74.8901	+	13.2051i	−0.0905564	+	0.0159675i	−0.218743	−	0.975783i	$-0.570196\pi$
$827$	−74.8901	+	13.2051i	−0.0905564	+	0.0159675i	0.128186	+	0.991750i	$0.459084\pi$
$828$		0			0
$829$	−176.628	+	1001.71i	−0.213062	+	1.20833i	0.671177	+	0.741298i	$0.265789\pi$
$829$	−176.628	+	1001.71i	−0.213062	+	1.20833i	−0.884238	+	0.467036i	$0.845322\pi$
$830$		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	0.844663	−	0.535298i	$-0.179801\pi$
$839$	301.523	+	284.472i	0.359384	+	0.339061i	−0.485280	+	0.874359i	$0.661282\pi$
$840$		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	−0.932825	−	0.360329i	$-0.882664\pi$
$853$	−26.0914	+	60.4867i	−0.0305878	+	0.0709106i	0.902237	+	0.431240i	$0.141924\pi$
$854$		0			0
$855$	270.862	+	865.687i	0.316798	+	1.01250i
$856$		0			0
$857$	379.994	+	22.1321i	0.443400	+	0.0258251i	0.278393	−	0.960467i	$-0.410198\pi$
$857$	379.994	+	22.1321i	0.443400	+	0.0258251i	0.165007	+	0.986292i	$0.447235\pi$
$858$		0			0
$859$	−628.309	−	1456.58i	−0.731442	−	1.69567i	−0.718274	−	0.695760i	$-0.755068\pi$
$859$	−628.309	−	1456.58i	−0.731442	−	1.69567i	−0.0131678	−	0.999913i	$-0.504192\pi$
$860$		0			0
$861$	−999.258	+	212.772i	−1.16058	+	0.247122i
$862$		0			0
$863$	−1401.65	+	809.244i	−1.62416	+	0.937711i	−0.638373	+	0.769727i	$0.720392\pi$
$863$	−1401.65	+	809.244i	−1.62416	+	0.937711i	−0.985790	+	0.167984i	$0.946274\pi$
$864$		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	0.0627887	−	0.998027i	$-0.480001\pi$
$877$	−821.925	−	871.189i	−0.937201	−	0.993375i	−0.999989	+	0.00465234i	$0.998519\pi$
$878$		0			0
$879$	−458.371	−	646.093i	−0.521468	−	0.735032i
$880$		0			0
$881$	−507.356	−	604.643i	−0.575886	−	0.686314i	0.396942	−	0.917844i	$-0.370071\pi$
$881$	−507.356	−	604.643i	−0.575886	−	0.686314i	−0.972828	+	0.231529i	$0.925627\pi$
$882$		0			0
$883$	995.205	+	835.076i	1.12707	+	0.945726i	0.998940	−	0.0460310i	$-0.0146573\pi$
$883$	995.205	+	835.076i	1.12707	+	0.945726i	0.128132	+	0.991757i	$0.459102\pi$
$884$		0			0
$885$	−720.503	−	144.139i	−0.814128	−	0.162869i
$886$		0			0
$887$	338.717	−	674.441i	0.381868	−	0.760362i	−0.617794	−	0.786340i	$-0.711974\pi$
$887$	338.717	−	674.441i	0.381868	−	0.760362i	0.999663	+	0.0259774i	$0.00826981\pi$
$888$		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	0.972066	+	0.234709i	$0.0754137\pi$
$907$	832.737	+	1118.56i	0.918123	+	1.23325i	−0.0539428	+	0.998544i	$0.517179\pi$
$908$		0			0
$909$	−239.146	+	2.95346i	−0.263087	+	0.00324913i
$910$		0			0
$911$	−193.636	−	385.560i	−0.212553	−	0.423227i	0.761940	−	0.647648i	$-0.224247\pi$
$911$	−193.636	−	385.560i	−0.212553	−	0.423227i	−0.974492	+	0.224421i	$0.927951\pi$
$912$		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	0.546083	−	0.837731i	$-0.316118\pi$
$919$	−415.806	−	720.197i	−0.452455	−	0.783675i	−0.998538	+	0.0540560i	$0.982785\pi$
$920$		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	0.484154	−	0.874983i	$-0.339127\pi$
$929$	167.184	+	72.1160i	0.179961	+	0.0776276i	−0.304193	+	0.952610i	$0.598387\pi$
$930$		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	−0.198236	−	0.980154i	$-0.563521\pi$
$937$	262.302	−	95.4700i	0.279938	−	0.101889i	0.478174	+	0.878265i	$0.341299\pi$
$938$		0			0
$939$	−978.123	−	1221.46i	−1.04166	−	1.30081i
$940$		0			0
$941$	−1303.49	+	75.9199i	−1.38522	+	0.0806800i	−0.734486	−	0.678624i	$-0.762577\pi$
$941$	−1303.49	+	75.9199i	−1.38522	+	0.0806800i	−0.650737	+	0.759304i	$0.725540\pi$
$942$		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	−0.493294	−	0.869863i	$-0.664207\pi$
$947$	−404.784	+	121.184i	−0.427438	+	0.127967i	0.0658561	+	0.997829i	$0.479022\pi$
$948$		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	0.862041	−	0.506839i	$-0.169186\pi$
$953$	1428.30	+	251.849i	1.49875	+	0.264269i	0.636705	+	0.771108i	$0.280297\pi$
$954$		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	−0.997304	−	0.0733820i	$-0.976621\pi$
$967$	−619.823	+	832.566i	−0.640975	+	0.860978i	0.356329	+	0.934360i	$0.384028\pi$
$968$		0			0
$969$	−805.160	+	503.519i	−0.830918	+	0.519628i
$970$		0			0
$971$		−	47.9636i		−	0.0493961i	−0.999695	−	0.0246981i	$-0.992138\pi$
$971$		−	47.9636i		−	0.0493961i	0.999695	−	0.0246981i	$-0.00786244\pi$
$972$		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	0.800389	−	0.599481i	$-0.204626\pi$
$977$	445.166	+	331.414i	0.455646	+	0.339216i	−0.344743	+	0.938697i	$0.612034\pi$
$978$		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	0.865775	+	0.500434i	$0.166826\pi$
$983$	136.386	+	1166.86i	0.138745	+	1.18704i	−0.727030	+	0.686606i	$0.759100\pi$
$984$		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	−0.991443	−	0.130543i	$-0.958328\pi$
$991$	−15.0065	+	85.1062i	−0.0151428	+	0.0858791i	0.976300	+	0.216423i	$0.0694389\pi$
$992$		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	0.900244	+	0.435385i	$0.143388\pi$
$997$	386.187	+	1289.95i	0.387349	+	1.29384i	−0.512895	+	0.858451i	$0.671427\pi$
$998$		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.65.6	yes	324
81.5	odd	54	inner	324.3.o.a.5.6	✓	324

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
324.3.o.a.5.6	✓	324	81.5	odd	54	inner
324.3.o.a.65.6	yes	324	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
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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