LMFDB - Embedded newform 189.4.o.a.62.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,4,Mod(62,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 3]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("189.62");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	189.o (of order $6$, degree $2$, not 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:	$11.1513609911$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			62.14
Character	$\chi$	$=$	189.62
Dual form			189.4.o.a.125.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.10556 + 0.638294i) q^{2} +(-3.18516 - 5.51686i) q^{4} +(1.59510 + 2.76280i) q^{5} +(-4.68134 + 17.9188i) q^{7} -18.3450i q^{8} +O(q^{10})$	\(q+(1.10556 + 0.638294i) q^{2} +(-3.18516 - 5.51686i) q^{4} +(1.59510 + 2.76280i) q^{5} +(-4.68134 + 17.9188i) q^{7} -18.3450i q^{8} +4.07258i q^{10} +(38.0908 + 21.9917i) q^{11} +(65.6143 - 37.8824i) q^{13} +(-16.6130 + 16.8223i) q^{14} +(-13.7718 + 23.8534i) q^{16} +104.977 q^{17} -74.7068i q^{19} +(10.1613 - 17.5999i) q^{20} +(28.0744 + 48.6262i) q^{22} +(-46.6533 + 26.9353i) q^{23} +(57.4113 - 99.4393i) q^{25} +96.7206 q^{26} +(113.767 - 31.2481i) q^{28} +(26.3321 + 15.2028i) q^{29} +(111.231 - 64.2193i) q^{31} +(-157.549 + 90.9609i) q^{32} +(116.058 + 67.0062i) q^{34} +(-56.9734 + 15.6488i) q^{35} +46.1138 q^{37} +(47.6849 - 82.5928i) q^{38} +(50.6835 - 29.2621i) q^{40} +(213.104 + 369.107i) q^{41} +(-166.003 + 287.526i) q^{43} -280.188i q^{44} -68.7706 q^{46} +(-170.147 + 294.704i) q^{47} +(-299.170 - 167.768i) q^{49} +(126.943 - 73.2906i) q^{50} +(-417.984 - 241.323i) q^{52} +235.233i q^{53} +140.316i q^{55} +(328.721 + 85.8791i) q^{56} +(19.4078 + 33.6152i) q^{58} +(-272.093 - 471.279i) q^{59} +(321.478 + 185.606i) q^{61} +163.963 q^{62} -11.8909 q^{64} +(209.323 + 120.853i) q^{65} +(-53.3481 - 92.4017i) q^{67} +(-334.368 - 579.143i) q^{68} +(-72.9759 - 19.0651i) q^{70} -974.682i q^{71} -576.299i q^{73} +(50.9815 + 29.4342i) q^{74} +(-412.147 + 237.953i) q^{76} +(-572.382 + 579.592i) q^{77} +(-10.6691 + 18.4794i) q^{79} -87.8696 q^{80} +544.093i q^{82} +(-168.669 + 292.143i) q^{83} +(167.449 + 290.030i) q^{85} +(-367.053 + 211.918i) q^{86} +(403.438 - 698.775i) q^{88} -1024.06 q^{89} +(371.647 + 1353.07i) q^{91} +(297.197 + 171.586i) q^{92} +(-376.216 + 217.208i) q^{94} +(206.400 - 119.165i) q^{95} +(-63.5527 - 36.6922i) q^{97} +(-223.664 - 376.436i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 6 q^{2} + 78 q^{4} + 5 q^{7}+O(q^{10}) $ 44 * q + 6 * q^2 + 78 * q^4 + 5 * q^7	$ 44 q + 6 q^{2} + 78 q^{4} + 5 q^{7} + 18 q^{11} - 204 q^{14} - 242 q^{16} - 34 q^{22} + 102 q^{23} - 352 q^{25} + 300 q^{28} - 246 q^{29} - 1068 q^{32} + 328 q^{37} - 170 q^{43} + 968 q^{46} - 79 q^{49} - 288 q^{50} - 1212 q^{56} - 538 q^{58} - 808 q^{64} - 4350 q^{65} - 590 q^{67} + 384 q^{70} + 5304 q^{74} + 2787 q^{77} - 302 q^{79} - 612 q^{85} + 13692 q^{86} + 1294 q^{88} + 210 q^{91} + 10194 q^{92} - 6336 q^{95}+O(q^{100}) $ 44 * q + 6 * q^2 + 78 * q^4 + 5 * q^7 + 18 * q^11 - 204 * q^14 - 242 * q^16 - 34 * q^22 + 102 * q^23 - 352 * q^25 + 300 * q^28 - 246 * q^29 - 1068 * q^32 + 328 * q^37 - 170 * q^43 + 968 * q^46 - 79 * q^49 - 288 * q^50 - 1212 * q^56 - 538 * q^58 - 808 * q^64 - 4350 * q^65 - 590 * q^67 + 384 * q^70 + 5304 * q^74 + 2787 * q^77 - 302 * q^79 - 612 * q^85 + 13692 * q^86 + 1294 * q^88 + 210 * q^91 + 10194 * q^92 - 6336 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	1.10556	+	0.638294i	0.390874	+	0.225671i	0.682539	−	0.730849i	$-0.260876\pi$
$2$	1.10556	+	0.638294i	0.390874	+	0.225671i	−0.291665	+	0.956521i	$0.594209\pi$
$3$		0			0
$3$		0			0
$4$	−3.18516	−	5.51686i	−0.398145	−	0.689607i
$5$	1.59510	+	2.76280i	0.142670	+	0.247112i	0.928501	−	0.371329i	$-0.121098\pi$
$5$	1.59510	+	2.76280i	0.142670	+	0.247112i	−0.785831	+	0.618441i	$0.787764\pi$
$6$		0			0
$7$	−4.68134	+	17.9188i	−0.252769	+	0.967527i
$7$	−4.68134	+	17.9188i	−0.252769	+	0.967527i
$8$		−	18.3450i		−	0.810742i
$9$		0			0
$10$			4.07258i			0.128786i
$11$	38.0908	+	21.9917i	1.04407	+	0.602795i	0.920984	−	0.389600i	$-0.127387\pi$
$11$	38.0908	+	21.9917i	1.04407	+	0.602795i	0.123088	+	0.992396i	$0.460720\pi$
$12$		0			0
$13$	65.6143	−	37.8824i	1.39986	−	0.808208i	0.405480	−	0.914104i	$-0.367105\pi$
$13$	65.6143	−	37.8824i	1.39986	−	0.808208i	0.994377	+	0.105896i	$0.0337712\pi$
$14$	−16.6130	+	16.8223i	−0.317144	+	0.321138i
$15$		0			0
$16$	−13.7718	+	23.8534i	−0.215184	+	0.372710i
$17$	104.977			1.49769			0.748843	−	0.662748i	$-0.230610\pi$
$17$	104.977			1.49769			0.748843	+	0.662748i	$0.230610\pi$
$18$		0			0
$19$		−	74.7068i		−	0.902048i	−0.892512	−	0.451024i	$-0.851059\pi$
$19$		−	74.7068i		−	0.902048i	0.892512	−	0.451024i	$-0.148941\pi$
$20$	10.1613	−	17.5999i	0.113607	−	0.196773i
$21$		0			0
$22$	28.0744	+	48.6262i	0.272067	+	0.471234i
$23$	−46.6533	+	26.9353i	−0.422952	+	0.244191i	−0.696339	−	0.717713i	$-0.745189\pi$
$23$	−46.6533	+	26.9353i	−0.422952	+	0.244191i	0.273388	+	0.961904i	$0.411856\pi$
$24$		0			0
$25$	57.4113	−	99.4393i	0.459290	−	0.795514i
$26$	96.7206			0.729557
$27$		0			0
$28$	113.767	−	31.2481i	0.767852	−	0.210905i
$29$	26.3321	+	15.2028i	0.168612	+	0.0973481i	0.581931	−	0.813238i	$-0.302297\pi$
$29$	26.3321	+	15.2028i	0.168612	+	0.0973481i	−0.413319	+	0.910586i	$0.635631\pi$
$30$		0			0
$31$	111.231	−	64.2193i	0.644441	−	0.372068i	−0.141882	−	0.989884i	$-0.545315\pi$
$31$	111.231	−	64.2193i	0.644441	−	0.372068i	0.786323	+	0.617815i	$0.211982\pi$
$32$	−157.549	+	90.9609i	−0.870343	+	0.502493i
$33$		0			0
$34$	116.058	+	67.0062i	0.585406	+	0.337984i
$35$	−56.9734	+	15.6488i	−0.275150	+	0.0755751i
$36$		0			0
$37$	46.1138			0.204894			0.102447	−	0.994738i	$-0.467333\pi$
$37$	46.1138			0.204894			0.102447	+	0.994738i	$0.467333\pi$
$38$	47.6849	−	82.5928i	0.203566	−	0.352587i
$39$		0			0
$40$	50.6835	−	29.2621i	0.200344	−	0.115669i
$41$	213.104	+	369.107i	0.811738	+	1.40597i	0.911647	+	0.410975i	$0.134812\pi$
$41$	213.104	+	369.107i	0.811738	+	1.40597i	−0.0999082	+	0.994997i	$0.531855\pi$
$42$		0			0
$43$	−166.003	+	287.526i	−0.588728	+	1.01971i	0.405672	+	0.914019i	$0.367038\pi$
$43$	−166.003	+	287.526i	−0.588728	+	1.01971i	−0.994399	+	0.105687i	$0.966296\pi$
$44$		−	280.188i		−	0.960000i
$45$		0			0
$46$	−68.7706			−0.220428
$47$	−170.147	+	294.704i	−0.528054	+	0.914616i	0.471411	+	0.881913i	$0.343745\pi$
$47$	−170.147	+	294.704i	−0.528054	+	0.914616i	−0.999465	+	0.0327026i	$0.989589\pi$
$48$		0			0
$49$	−299.170	−	167.768i	−0.872216	−	0.489121i
$50$	126.943	−	73.2906i	0.359049	−	0.207297i
$51$		0			0
$52$	−417.984	−	241.323i	−1.11469	−	0.643568i
$53$			235.233i			0.609654i	0.952408	+	0.304827i	$0.0985987\pi$
$53$			235.233i			0.609654i	−0.952408	+	0.304827i	$0.901401\pi$
$54$		0			0
$55$			140.316i			0.344004i
$56$	328.721	+	85.8791i	0.784414	+	0.204930i
$57$		0			0
$58$	19.4078	+	33.6152i	0.0439373	+	0.0761017i
$59$	−272.093	−	471.279i	−0.600398	−	1.03992i	−0.992761	−	0.120109i	$-0.961676\pi$
$59$	−272.093	−	471.279i	−0.600398	−	1.03992i	0.392363	−	0.919811i	$-0.371658\pi$
$60$		0			0
$61$	321.478	+	185.606i	0.674772	+	0.389580i	0.797882	−	0.602813i	$-0.205954\pi$
$61$	321.478	+	185.606i	0.674772	+	0.389580i	−0.123110	+	0.992393i	$0.539287\pi$
$62$	163.963			0.335861
$63$		0			0
$64$	−11.8909			−0.0232244
$65$	209.323	+	120.853i	0.399436	+	0.230614i
$66$		0			0
$67$	−53.3481	−	92.4017i	−0.0972763	−	0.168487i	0.813280	−	0.581872i	$-0.197680\pi$
$67$	−53.3481	−	92.4017i	−0.0972763	−	0.168487i	−0.910556	+	0.413385i	$0.864346\pi$
$68$	−334.368	−	579.143i	−0.596296	−	1.03282i
$69$		0			0
$70$	−72.9759	−	19.0651i	−0.124604	−	0.0325531i
$71$		−	974.682i		−	1.62920i	−0.580020	−	0.814602i	$-0.696955\pi$
$71$		−	974.682i		−	1.62920i	0.580020	−	0.814602i	$-0.303045\pi$
$72$		0			0
$73$		−	576.299i		−	0.923982i	−0.886885	−	0.461991i	$-0.847135\pi$
$73$		−	576.299i		−	0.923982i	0.886885	−	0.461991i	$-0.152865\pi$
$74$	50.9815	+	29.4342i	0.0800876	+	0.0462386i
$75$		0			0
$76$	−412.147	+	237.953i	−0.622059	+	0.359146i
$77$	−572.382	+	579.592i	−0.847129	+	0.857800i
$78$		0			0
$79$	−10.6691	+	18.4794i	−0.0151945	+	0.0263176i	−0.873523	−	0.486783i	$-0.838170\pi$
$79$	−10.6691	+	18.4794i	−0.0151945	+	0.0263176i	0.858328	+	0.513101i	$0.171503\pi$
$80$	−87.8696			−0.122801
$81$		0			0
$82$			544.093i			0.732744i
$83$	−168.669	+	292.143i	−0.223058	+	0.386348i	−0.955735	−	0.294229i	$-0.904937\pi$
$83$	−168.669	+	292.143i	−0.223058	+	0.386348i	0.732677	+	0.680576i	$0.238271\pi$
$84$		0			0
$85$	167.449	+	290.030i	0.213675	+	0.370096i
$86$	−367.053	+	211.918i	−0.460237	+	0.265718i
$87$		0			0
$88$	403.438	−	698.775i	0.488711	−	0.846473i
$89$	−1024.06			−1.21967			−0.609834	−	0.792529i	$-0.708764\pi$
$89$	−1024.06			−1.21967			−0.609834	+	0.792529i	$0.708764\pi$
$90$		0			0
$91$	371.647	+	1353.07i	0.428123	+	1.55869i
$92$	297.197	+	171.586i	0.336792	+	0.194447i
$93$		0			0
$94$	−376.216	+	217.208i	−0.412805	+	0.238333i
$95$	206.400	−	119.165i	0.222907	−	0.128695i
$96$		0			0
$97$	−63.5527	−	36.6922i	−0.0665237	−	0.0384075i	0.466369	−	0.884590i	$-0.345562\pi$
$97$	−63.5527	−	36.6922i	−0.0665237	−	0.0384075i	−0.532893	+	0.846183i	$0.678895\pi$
$98$	−223.664	−	376.436i	−0.230546	−	0.388019i
$99$		0			0
$100$	−731.457			−0.731457
$101$	442.380	−	766.224i	0.435826	−	0.754873i	−0.561537	−	0.827452i	$-0.689790\pi$
$101$	442.380	−	766.224i	0.435826	−	0.754873i	0.997363	+	0.0725790i	$0.0231229\pi$
$102$		0			0
$103$	38.7086	−	22.3484i	0.0370299	−	0.0213792i	−0.481371	−	0.876517i	$-0.659861\pi$
$103$	38.7086	−	22.3484i	0.0370299	−	0.0213792i	0.518401	+	0.855138i	$0.326528\pi$
$104$	−694.953	−	1203.69i	−0.655248	−	1.13492i
$105$		0			0
$106$	−150.148	+	260.063i	−0.137581	+	0.238298i
$107$		−	517.187i		−	0.467274i	−0.972324	−	0.233637i	$-0.924937\pi$
$107$		−	517.187i		−	0.467274i	0.972324	−	0.233637i	$-0.0750628\pi$
$108$		0			0
$109$	−39.6511			−0.0348430			−0.0174215	−	0.999848i	$-0.505546\pi$
$109$	−39.6511			−0.0348430			−0.0174215	+	0.999848i	$0.505546\pi$
$110$	−89.5630	+	155.128i	−0.0776318	+	0.134462i
$111$		0			0
$112$	−362.955	−	358.440i	−0.306215	−	0.302406i
$113$	−627.942	+	362.542i	−0.522759	+	0.301815i	−0.738063	−	0.674732i	$-0.764259\pi$
$113$	−627.942	+	362.542i	−0.522759	+	0.301815i	0.215304	+	0.976547i	$0.430926\pi$
$114$		0			0
$115$	−148.834	−	85.9291i	−0.120685	−	0.0696777i
$116$		−	193.694i		−	0.155035i
$117$		0			0
$118$		−	694.701i		−	0.541970i
$119$	−491.433	+	1881.07i	−0.378568	+	1.44905i
$120$		0			0
$121$	301.771	+	522.682i	0.226725	+	0.392699i
$122$	236.942	+	410.396i	0.175834	+	0.304553i
$123$		0			0
$124$	−708.577	−	409.097i	−0.513162	−	0.296274i
$125$	765.083			0.547449
$126$		0			0
$127$	−567.501			−0.396516			−0.198258	−	0.980150i	$-0.563528\pi$
$127$	−567.501			−0.396516			−0.198258	+	0.980150i	$0.563528\pi$
$128$	1247.24	+	720.097i	0.861265	+	0.497251i
$129$		0			0
$130$	154.279	+	267.220i	0.104086	+	0.180282i
$131$	603.074	+	1044.55i	0.402220	+	0.696665i	0.993994	−	0.109439i	$-0.0349055\pi$
$131$	603.074	+	1044.55i	0.402220	+	0.696665i	−0.591774	+	0.806104i	$0.701572\pi$
$132$		0			0
$133$	1338.66	+	349.728i	0.872756	+	0.228009i
$134$		−	136.207i		−	0.0878098i
$135$		0			0
$136$		−	1925.80i		−	1.21424i
$137$	−522.414	−	301.616i	−0.325787	−	0.188093i	0.328182	−	0.944615i	$-0.393564\pi$
$137$	−522.414	−	301.616i	−0.325787	−	0.188093i	−0.653969	+	0.756521i	$0.726897\pi$
$138$		0			0
$139$	−298.587	+	172.389i	−0.182200	+	0.105193i	−0.588326	−	0.808624i	$-0.700213\pi$
$139$	−298.587	+	172.389i	−0.182200	+	0.105193i	0.406126	+	0.913817i	$0.366879\pi$
$140$	267.802	+	264.470i	0.161667	+	0.159656i
$141$		0			0
$142$	622.134	−	1077.57i	0.367665	−	0.636814i
$143$	3332.40			1.94874
$144$		0			0
$145$			97.0003i			0.0555547i
$146$	367.848	−	637.132i	0.208516	−	0.361160i
$147$		0			0
$148$	−146.880	−	254.403i	−0.0815774	−	0.141296i
$149$	−197.969	+	114.298i	−0.108847	+	0.0628431i	−0.553435	−	0.832892i	$-0.686683\pi$
$149$	−197.969	+	114.298i	−0.108847	+	0.0628431i	0.444588	+	0.895735i	$0.353350\pi$
$150$		0			0
$151$	−1697.35	+	2939.90i	−0.914758	+	1.58441i	−0.107502	+	0.994205i	$0.534285\pi$
$151$	−1697.35	+	2939.90i	−0.914758	+	1.58441i	−0.807256	+	0.590202i	$0.799048\pi$
$152$	−1370.50			−0.731328
$153$		0			0
$154$	−1002.75	+	275.425i	−0.524702	+	0.144119i
$155$	354.850	+	204.873i	0.183885	+	0.106166i
$156$		0			0
$157$	2829.60	−	1633.67i	1.43838	−	0.830452i	0.440647	−	0.897680i	$-0.354749\pi$
$157$	2829.60	−	1633.67i	1.43838	−	0.830452i	0.997738	+	0.0672287i	$0.0214157\pi$
$158$	−23.5905	+	13.6200i	−0.0118782	+	0.00685791i
$159$		0			0
$160$	−502.613	−	290.184i	−0.248344	−	0.143382i
$161$	−264.250	−	962.067i	−0.129353	−	0.470941i
$162$		0			0
$163$	689.462			0.331306			0.165653	−	0.986184i	$-0.447027\pi$
$163$	689.462			0.331306			0.165653	+	0.986184i	$0.447027\pi$
$164$	1357.54	−	2351.33i	0.646379	−	1.11956i
$165$		0			0
$166$	−372.946	+	215.321i	−0.174375	+	0.100675i
$167$	683.829	+	1184.43i	0.316864	+	0.548824i	0.979832	−	0.199823i	$-0.0640368\pi$
$167$	683.829	+	1184.43i	0.316864	+	0.548824i	−0.662968	+	0.748648i	$0.730703\pi$
$168$		0			0
$169$	1771.66	−	3068.60i	0.806399	−	1.39672i
$170$			427.527i			0.192881i
$171$		0			0
$172$	2114.99			0.937596
$173$	−613.500	+	1062.61i	−0.269616	+	0.466988i	−0.968763	−	0.247990i	$-0.920230\pi$
$173$	−613.500	+	1062.61i	−0.269616	+	0.466988i	0.699147	+	0.714978i	$0.253563\pi$
$174$		0			0
$175$	1513.08	+	1494.25i	0.653587	+	0.645457i
$176$	−1049.15	+	605.730i	−0.449335	+	0.259424i
$177$		0			0
$178$	−1132.16	−	653.654i	−0.476737	−	0.275244i
$179$			1597.37i			0.667002i	0.942750	+	0.333501i	$0.108230\pi$
$179$			1597.37i			0.667002i	−0.942750	+	0.333501i	$0.891770\pi$
$180$		0			0
$181$		−	549.998i		−	0.225862i	−0.993603	−	0.112931i	$-0.963976\pi$
$181$		−	549.998i		−	0.225862i	0.993603	−	0.112931i	$-0.0360239\pi$
$182$	−452.782	+	1733.12i	−0.184409	+	0.705866i
$183$		0			0
$184$	494.128	+	855.855i	0.197976	+	0.342905i
$185$	73.5562	+	127.403i	0.0292322	+	0.0506317i
$186$		0			0
$187$	3998.65	+	2308.62i	1.56369	+	0.902798i
$188$	2167.79			0.840968
$189$		0			0
$190$	304.249			0.116171
$191$	−3253.62	−	1878.48i	−1.23258	−	0.711633i	−0.265017	−	0.964244i	$-0.585378\pi$
$191$	−3253.62	−	1878.48i	−1.23258	−	0.711633i	−0.967568	+	0.252611i	$0.918711\pi$
$192$		0			0
$193$	−1311.43	−	2271.46i	−0.489111	−	0.847165i	0.510810	−	0.859693i	$-0.329345\pi$
$193$	−1311.43	−	2271.46i	−0.489111	−	0.847165i	−0.999922	+	0.0125280i	$0.996012\pi$
$194$	−46.8408	−	81.1307i	−0.0173349	−	0.0300250i
$195$		0			0
$196$	27.3504	+	2184.85i	0.00996734	+	0.796228i
$197$			4603.93i			1.66506i	0.553982	+	0.832528i	$0.313107\pi$
$197$			4603.93i			1.66506i	−0.553982	+	0.832528i	$0.686893\pi$
$198$		0			0
$199$		−	3145.00i		−	1.12032i	−0.828385	−	0.560158i	$-0.810740\pi$
$199$		−	3145.00i		−	1.12032i	0.828385	−	0.560158i	$-0.189260\pi$
$200$	−1824.21	−	1053.21i	−0.644957	−	0.372366i
$201$		0			0
$202$	978.154	−	564.737i	0.340706	−	0.196707i
$203$	−395.687	+	400.671i	−0.136807	+	0.138530i
$204$		0			0
$205$	−679.846	+	1177.53i	−0.231622	+	0.401181i
$206$	57.0596			0.0192987
$207$		0			0
$208$			2086.83i			0.695653i
$209$	1642.93	−	2845.64i	0.543751	−	0.941804i
$210$		0			0
$211$	341.927	+	592.236i	0.111560	+	0.193228i	0.916400	−	0.400265i	$-0.131082\pi$
$211$	341.927	+	592.236i	0.111560	+	0.193228i	−0.804839	+	0.593493i	$0.797748\pi$
$212$	1297.74	−	749.253i	0.420422	−	0.242731i
$213$		0			0
$214$	330.118	−	571.780i	0.105450	−	0.182645i
$215$	−1059.17			−0.335976
$216$		0			0
$217$	630.025	+	2293.76i	0.197092	+	0.717562i
$218$	−43.8366	−	25.3091i	−0.0136192	−	0.00786307i
$219$		0			0
$220$	774.104	−	446.929i	0.237228	−	0.136963i
$221$	6887.99	−	3976.78i	2.09655	−	1.21044i
$222$		0			0
$223$	−2030.24	−	1172.16i	−0.609664	−	0.351990i	0.163170	−	0.986598i	$-0.447828\pi$
$223$	−2030.24	−	1172.16i	−0.609664	−	0.351990i	−0.772834	+	0.634608i	$0.781161\pi$
$224$	−892.374	−	3248.91i	−0.266180	−	0.969094i
$225$		0			0
$226$	−925.635			−0.272444
$227$	1536.15	−	2660.69i	0.449154	−	0.777958i	−0.549177	−	0.835706i	$-0.685059\pi$
$227$	1536.15	−	2660.69i	0.449154	−	0.777958i	0.998331	+	0.0577480i	$0.0183920\pi$
$228$		0			0
$229$	−1213.76	+	700.766i	−0.350252	+	0.202218i	−0.664796	−	0.747025i	$-0.731482\pi$
$229$	−1213.76	+	700.766i	−0.350252	+	0.202218i	0.314544	+	0.949243i	$0.398148\pi$
$230$	−109.696	−	189.999i	−0.0314485	−	0.0544704i
$231$		0			0
$232$	278.896	−	483.062i	0.0789242	−	0.136701i
$233$			5201.59i			1.46252i	0.682098	+	0.731261i	$0.261068\pi$
$233$			5201.59i			1.46252i	−0.682098	+	0.731261i	$0.738932\pi$
$234$		0			0
$235$	−1085.61			−0.301350
$236$	−1733.32	+	3002.20i	−0.478091	+	0.828078i
$237$		0			0
$238$	−1743.98	+	1765.95i	−0.474981	+	0.480964i
$239$	1811.86	−	1046.08i	0.490373	−	0.283117i	−0.234356	−	0.972151i	$-0.575298\pi$
$239$	1811.86	−	1046.08i	0.490373	−	0.283117i	0.724729	+	0.689034i	$0.241965\pi$
$240$		0			0
$241$	−6077.25	−	3508.70i	−1.62436	−	0.937823i	−0.985735	−	0.168303i	$-0.946171\pi$
$241$	−6077.25	−	3508.70i	−1.62436	−	0.937823i	−0.638622	−	0.769520i	$-0.720495\pi$
$242$			770.474i			0.204661i
$243$		0			0
$244$		−	2364.73i		−	0.620437i
$245$	−13.6968	−	1094.15i	−0.00357167	−	0.285318i
$246$		0			0
$247$	−2830.08	−	4901.84i	−0.729042	−	1.26274i
$248$	−1178.10	−	2040.53i	−0.301651	−	0.522476i
$249$		0			0
$250$	845.844	+	488.348i	0.213984	+	0.123543i
$251$	−7255.60			−1.82458			−0.912290	−	0.409545i	$-0.865687\pi$
$251$	−7255.60			−1.82458			−0.912290	+	0.409545i	$0.865687\pi$
$252$		0			0
$253$	−2369.41			−0.588789
$254$	−627.406	−	362.233i	−0.154988	−	0.0894823i
$255$		0			0
$256$	966.831	+	1674.60i	0.236043	+	0.408838i
$257$	505.462	+	875.487i	0.122684	+	0.212496i	0.920825	−	0.389975i	$-0.127516\pi$
$257$	505.462	+	875.487i	0.122684	+	0.212496i	−0.798141	+	0.602471i	$0.794183\pi$
$258$		0			0
$259$	−215.874	+	826.306i	−0.0517907	+	0.198240i
$260$		−	1539.74i		−	0.367272i
$261$		0			0
$262$			1539.75i			0.363078i
$263$	−2754.95	−	1590.57i	−0.645921	−	0.372923i	0.140971	−	0.990014i	$-0.454978\pi$
$263$	−2754.95	−	1590.57i	−0.645921	−	0.372923i	−0.786892	+	0.617091i	$0.788311\pi$
$264$		0			0
$265$	−649.900	+	375.220i	−0.150653	+	0.0869795i
$266$	1256.74	+	1241.10i	0.289682	+	0.286079i
$267$		0			0
$268$	−339.845	+	588.628i	−0.0774601	+	0.134165i
$269$	1227.12			0.278137			0.139069	−	0.990283i	$-0.455589\pi$
$269$	1227.12			0.278137			0.139069	+	0.990283i	$0.455589\pi$
$270$		0			0
$271$			7222.65i			1.61898i	0.587131	+	0.809492i	$0.300257\pi$
$271$			7222.65i			1.61898i	−0.587131	+	0.809492i	$0.699743\pi$
$272$	−1445.72	+	2504.06i	−0.322278	+	0.558202i
$273$		0			0
$274$	−385.039	−	666.908i	−0.0848945	−	0.147042i
$275$	4373.68	−	2525.15i	0.959065	−	0.553716i
$276$		0			0
$277$	−1132.04	+	1960.75i	−0.245551	+	0.425306i	−0.962286	−	0.272039i	$-0.912302\pi$
$277$	−1132.04	+	1960.75i	−0.245551	+	0.425306i	0.716736	+	0.697345i	$0.245635\pi$
$278$	−440.141			−0.0949564
$279$		0			0
$280$	287.077	+	1045.18i	0.0612719	+	0.223076i
$281$	−859.806	−	496.409i	−0.182533	−	0.105385i	0.405949	−	0.913896i	$-0.366941\pi$
$281$	−859.806	−	496.409i	−0.182533	−	0.105385i	−0.588482	+	0.808510i	$0.700274\pi$
$282$		0			0
$283$	−4936.03	+	2849.82i	−1.03681	+	0.598601i	−0.918927	−	0.394427i	$-0.870943\pi$
$283$	−4936.03	+	2849.82i	−1.03681	+	0.598601i	−0.117880	+	0.993028i	$0.537610\pi$
$284$	−5377.19	+	3104.52i	−1.12351	+	0.648660i
$285$		0			0
$286$	3684.16	+	2127.05i	0.761710	+	0.439773i
$287$	−7611.59	+	2090.66i	−1.56550	+	0.429993i
$288$		0			0
$289$	6107.16			1.24306
$290$	−61.9147	+	107.239i	−0.0125371	+	0.0217149i
$291$		0			0
$292$	−3179.36	+	1835.60i	−0.637185	+	0.367879i
$293$	−1110.55	−	1923.52i	−0.221429	−	0.383527i	0.733813	−	0.679352i	$-0.237739\pi$
$293$	−1110.55	−	1923.52i	−0.221429	−	0.383527i	−0.955242	+	0.295825i	$0.904406\pi$
$294$		0			0
$295$	868.032	−	1503.48i	0.171318	−	0.296731i
$296$		−	845.958i		−	0.166116i
$297$		0			0
$298$	−291.822			−0.0567275
$299$	−2040.75	+	3534.68i	−0.394714	+	0.683665i
$300$		0			0
$301$	−4375.02	−	4320.60i	−0.837781	−	0.827359i
$302$	−3753.04	+	2166.82i	−0.715110	+	0.412869i
$303$		0			0
$304$	1782.01	+	1028.85i	0.336202	+	0.194106i
$305$			1184.24i			0.222326i
$306$		0			0
$307$			3006.91i			0.559002i	0.960145	+	0.279501i	$0.0901690\pi$
$307$			3006.91i			0.559002i	−0.960145	+	0.279501i	$0.909831\pi$
$308$	5020.65	+	1311.66i	0.928826	+	0.242658i
$309$		0			0
$310$	261.538	+	452.997i	0.0479173	+	0.0829952i
$311$	−1269.29	−	2198.47i	−0.231430	−	0.400848i	0.726799	−	0.686850i	$-0.241007\pi$
$311$	−1269.29	−	2198.47i	−0.231430	−	0.400848i	−0.958229	+	0.286002i	$0.907674\pi$
$312$		0			0
$313$	−4916.75	−	2838.69i	−0.887895	−	0.512627i	−0.0146418	−	0.999893i	$-0.504661\pi$
$313$	−4916.75	−	2838.69i	−0.887895	−	0.512627i	−0.873253	+	0.487266i	$0.837994\pi$
$314$	4171.05			0.749636
$315$		0			0
$316$	135.931			0.0241984
$317$	−6662.61	−	3846.66i	−1.18047	−	0.681545i	−0.224347	−	0.974509i	$-0.572025\pi$
$317$	−6662.61	−	3846.66i	−1.18047	−	0.681545i	−0.956123	+	0.292964i	$0.905358\pi$
$318$		0			0
$319$	668.672	+	1158.17i	0.117362	+	0.203277i
$320$	−18.9672	−	32.8521i	−0.00331343	−	0.00573903i
$321$		0			0
$322$	321.938	−	1232.29i	0.0557172	−	0.213270i
$323$		−	7842.50i		−	1.35098i
$324$		0			0
$325$		−	8699.52i		−	1.48481i
$326$	762.240	+	440.080i	0.129499	+	0.0747661i
$327$		0			0
$328$	6771.27	−	3909.39i	1.13988	−	0.658110i
$329$	−4484.23	−	4428.45i	−0.751440	−	0.742092i
$330$		0			0
$331$	852.222	−	1476.09i	0.141518	−	0.245116i	−0.786551	−	0.617526i	$-0.788135\pi$
$331$	852.222	−	1476.09i	0.141518	−	0.245116i	0.928068	+	0.372410i	$0.121468\pi$
$332$	2148.95			0.355238
$333$		0			0
$334$			1745.94i			0.286028i
$335$	170.191	−	294.780i	0.0277569	−	0.0480763i
$336$		0			0
$337$	3770.46	+	6530.62i	0.609466	+	1.05563i	0.991329	+	0.131407i	$0.0419493\pi$
$337$	3770.46	+	6530.62i	0.609466	+	1.05563i	−0.381863	+	0.924219i	$0.624717\pi$
$338$	3917.35	−	2261.68i	0.630401	−	0.363962i
$339$		0			0
$340$	1066.70	−	1847.59i	0.170147	−	0.294704i
$341$	5649.17			0.897125
$342$		0			0
$343$	4406.73	−	4575.40i	0.693706	−	0.720258i
$344$	5274.67	+	3045.33i	0.826718	+	0.477306i
$345$		0			0
$346$	−1356.52	+	783.188i	−0.210772	+	0.121689i
$347$	1623.73	−	937.459i	0.251199	−	0.145030i	−0.369114	−	0.929384i	$-0.620339\pi$
$347$	1623.73	−	937.459i	0.251199	−	0.145030i	0.620313	+	0.784354i	$0.287005\pi$
$348$		0			0
$349$	−1501.48	−	866.879i	−0.230293	−	0.132960i	0.380414	−	0.924816i	$-0.375781\pi$
$349$	−1501.48	−	866.879i	−0.230293	−	0.132960i	−0.610707	+	0.791856i	$0.709115\pi$
$350$	719.020	+	2617.77i	0.109809	+	0.399788i
$351$		0			0
$352$	−8001.54			−1.21160
$353$	4678.78	−	8103.88i	0.705457	−	1.22189i	−0.261070	−	0.965320i	$-0.584075\pi$
$353$	4678.78	−	8103.88i	0.705457	−	1.22189i	0.966526	−	0.256567i	$-0.0825914\pi$
$354$		0			0
$355$	2692.85	−	1554.72i	0.402596	−	0.232439i
$356$	3261.81	+	5649.61i	0.485605	+	0.841092i
$357$		0			0
$358$	−1019.60	+	1765.99i	−0.150523	+	0.260714i
$359$			11558.3i			1.69923i	0.527401	+	0.849616i	$0.323167\pi$
$359$			11558.3i			1.69923i	−0.527401	+	0.849616i	$0.676833\pi$
$360$		0			0
$361$	1277.89			0.186309
$362$	351.061	−	608.055i	0.0509706	−	0.0882836i
$363$		0			0
$364$	6280.96	−	6360.08i	0.904428	−	0.915821i
$365$	1592.20	−	919.255i	0.228327	−	0.131825i
$366$		0			0
$367$	7156.41	+	4131.76i	1.01788	+	0.587673i	0.913489	−	0.406864i	$-0.133378\pi$
$367$	7156.41	+	4131.76i	1.01788	+	0.587673i	0.104390	+	0.994536i	$0.466711\pi$
$368$		−	1483.79i		−	0.210184i
$369$		0			0
$370$			187.802i			0.0263875i
$371$	−4215.10	−	1101.20i	−0.589857	−	0.154101i
$372$		0			0
$373$	4591.28	+	7952.33i	0.637339	+	1.10390i	0.986014	+	0.166660i	$0.0532981\pi$
$373$	4591.28	+	7952.33i	0.637339	+	1.10390i	−0.348676	+	0.937243i	$0.613369\pi$
$374$	2947.16	+	5104.64i	0.407471	+	0.705761i
$375$		0			0
$376$	5406.34	+	3121.35i	0.741517	+	0.428115i
$377$	2303.68			0.314710
$378$		0			0
$379$	−9297.03			−1.26004			−0.630022	−	0.776577i	$-0.716954\pi$
$379$	−9297.03			−1.26004			−0.630022	+	0.776577i	$0.716954\pi$
$380$	−1314.83	−	759.119i	−0.177499	−	0.102479i
$381$		0			0
$382$	−2398.05	−	4153.54i	−0.321190	−	0.556318i
$383$	3674.74	+	6364.84i	0.490262	+	0.849159i	0.999937	−	0.0112079i	$-0.00356767\pi$
$383$	3674.74	+	6364.84i	0.490262	+	0.849159i	−0.509675	+	0.860367i	$0.670234\pi$
$384$		0			0
$385$	−2514.30	−	656.867i	−0.332833	−	0.0869534i
$386$		−	3348.30i		−	0.441513i
$387$		0			0
$388$			467.482i			0.0611670i
$389$	4531.66	+	2616.35i	0.590653	+	0.341014i	0.765356	−	0.643607i	$-0.222563\pi$
$389$	4531.66	+	2616.35i	0.590653	+	0.341014i	−0.174702	+	0.984621i	$0.555896\pi$
$390$		0			0
$391$	−4897.52	+	2827.59i	−0.633448	+	0.365722i
$392$	−3077.71	+	5488.27i	−0.396551	+	0.707142i
$393$		0			0
$394$	−2938.66	+	5089.91i	−0.375755	+	0.650827i
$395$	−68.0730			−0.00867120
$396$		0			0
$397$		−	10045.1i		−	1.26990i	−0.772554	−	0.634949i	$-0.781021\pi$
$397$		−	10045.1i		−	1.26990i	0.772554	−	0.634949i	$-0.218979\pi$
$398$	2007.44	−	3476.98i	0.252823	−	0.437903i
$399$		0			0
$400$	1581.31	+	2738.91i	0.197664	+	0.342364i
$401$	6480.01	−	3741.24i	0.806974	−	0.465906i	−0.0389302	−	0.999242i	$-0.512395\pi$
$401$	6480.01	−	3741.24i	0.806974	−	0.465906i	0.845904	+	0.533335i	$0.179062\pi$
$402$		0			0
$403$	4865.57	−	8427.41i	0.601417	−	1.04169i
$404$	−5636.20			−0.694088
$405$		0			0
$406$	−693.201	+	190.400i	−0.0847364	+	0.0232744i
$407$	1756.51	+	1014.12i	0.213924	+	0.123509i
$408$		0			0
$409$	9878.34	−	5703.26i	1.19426	−	0.689506i	0.234990	−	0.971998i	$-0.424494\pi$
$409$	9878.34	−	5703.26i	1.19426	−	0.689506i	0.959270	+	0.282491i	$0.0911609\pi$
$410$	−1503.22	+	867.883i	−0.181070	+	0.104541i
$411$		0			0
$412$	−246.587	−	142.367i	−0.0294865	−	0.0170240i
$413$	9718.53	−	2669.38i	1.15791	−	0.318042i
$414$		0			0
$415$	−1076.18			−0.127295
$416$	−6891.64	+	11936.7i	−0.812237	+	1.40684i
$417$		0			0
$418$	3632.71	−	2097.35i	0.425076	−	0.245418i
$419$	−3027.27	−	5243.38i	−0.352964	−	0.611351i	0.633804	−	0.773494i	$-0.281493\pi$
$419$	−3027.27	−	5243.38i	−0.352964	−	0.611351i	−0.986767	+	0.162143i	$0.948159\pi$
$420$		0			0
$421$	−3434.60	+	5948.91i	−0.397606	+	0.688674i	−0.993430	−	0.114441i	$-0.963492\pi$
$421$	−3434.60	+	5948.91i	−0.397606	+	0.688674i	0.595824	+	0.803115i	$0.296826\pi$
$422$			873.002i			0.100704i
$423$		0			0
$424$	4315.34			0.494272
$425$	6026.86	−	10438.8i	0.687873	−	1.19143i
$426$		0			0
$427$	−4830.79	+	4891.64i	−0.547490	+	0.554386i
$428$	−2853.25	+	1647.32i	−0.322236	+	0.186043i
$429$		0			0
$430$	−1170.97	−	676.062i	−0.131324	−	0.0758200i
$431$			7761.64i			0.867436i	0.901049	+	0.433718i	$0.142799\pi$
$431$			7761.64i			0.867436i	−0.901049	+	0.433718i	$0.857201\pi$
$432$		0			0
$433$		−	7474.70i		−	0.829586i	−0.909916	−	0.414793i	$-0.863854\pi$
$433$		−	7474.70i		−	0.829586i	0.909916	−	0.414793i	$-0.136146\pi$
$434$	−767.567	+	2938.03i	−0.0848950	+	0.324954i
$435$		0			0
$436$	126.295	+	218.750i	0.0138726	+	0.0240280i
$437$	2012.25	+	3485.32i	0.220272	+	0.381523i
$438$		0			0
$439$	−804.050	−	464.219i	−0.0874151	−	0.0504691i	0.455655	−	0.890156i	$-0.349405\pi$
$439$	−804.050	−	464.219i	−0.0874151	−	0.0504691i	−0.543070	+	0.839687i	$0.682738\pi$
$440$	2574.10			0.278898
$441$		0			0
$442$	10153.4			1.09265
$443$	−4799.04	−	2770.72i	−0.514693	−	0.297158i	0.220068	−	0.975485i	$-0.429372\pi$
$443$	−4799.04	−	2770.72i	−0.514693	−	0.297158i	−0.734761	+	0.678326i	$0.762706\pi$
$444$		0			0
$445$	−1633.49	−	2829.28i	−0.174010	−	0.301395i
$446$	−1496.37	−	2591.78i	−0.158868	−	0.275167i
$447$		0			0
$448$	55.6653	−	213.071i	0.00587039	−	0.0224702i
$449$		−	13088.2i		−	1.37566i	−0.725873	−	0.687829i	$-0.758564\pi$
$449$		−	13088.2i		−	1.37566i	0.725873	−	0.687829i	$-0.241436\pi$
$450$		0			0
$451$			18746.1i			1.95725i
$452$	4000.19	+	2309.51i	0.416268	+	0.240332i
$453$		0			0
$454$	3396.61	−	1961.04i	0.351126	−	0.202722i
$455$	−3145.45	+	3185.08i	−0.324090	+	0.328173i
$456$		0			0
$457$	5771.25	−	9996.10i	0.590739	−	1.02319i	−0.403394	−	0.915026i	$-0.632170\pi$
$457$	5771.25	−	9996.10i	0.590739	−	1.02319i	0.994133	−	0.108164i	$-0.0344971\pi$
$458$	−1789.18			−0.182539
$459$		0			0
$460$			1094.79i			0.110967i
$461$	−4557.29	+	7893.46i	−0.460421	+	0.797473i	−0.998982	−	0.0451139i	$-0.985635\pi$
$461$	−4557.29	+	7893.46i	−0.460421	+	0.797473i	0.538561	+	0.842587i	$0.318968\pi$
$462$		0			0
$463$	−1592.53	−	2758.34i	−0.159851	−	0.276871i	0.774964	−	0.632006i	$-0.217768\pi$
$463$	−1592.53	−	2758.34i	−0.159851	−	0.276871i	−0.934815	+	0.355135i	$0.884435\pi$
$464$	−725.279	+	418.740i	−0.0725651	+	0.0418955i
$465$		0			0
$466$	−3320.15	+	5750.66i	−0.330049	+	0.571662i
$467$	995.144			0.0986077			0.0493038	−	0.998784i	$-0.484300\pi$
$467$	995.144			0.0986077			0.0493038	+	0.998784i	$0.484300\pi$
$468$		0			0
$469$	1905.47	−	523.373i	0.187605	−	0.0515291i
$470$	−1200.20	−	692.938i	−0.117790	−	0.0680061i
$471$		0			0
$472$	−8645.60	+	4991.54i	−0.843106	+	0.486768i
$473$	−12646.4	+	7301.40i	−1.22935	+	0.709765i
$474$		0			0
$475$	−7428.79	−	4289.02i	−0.717592	−	0.414302i
$476$	11942.9	−	3280.33i	1.15000	−	0.315869i
$477$		0			0
$478$	2670.82			0.255565
$479$	−6951.30	+	12040.0i	−0.663075	+	1.14848i	0.316728	+	0.948516i	$0.397416\pi$
$479$	−6951.30	+	12040.0i	−0.663075	+	1.14848i	−0.979803	+	0.199964i	$0.935917\pi$
$480$		0			0
$481$	3025.73	−	1746.90i	0.286822	−	0.165597i
$482$	−4479.17	−	7758.15i	−0.423279	−	0.733141i
$483$		0			0
$484$	1922.38	−	3329.65i	0.180539	−	0.312702i
$485$		−	234.111i		−	0.0219184i
$486$		0			0
$487$	−7608.36			−0.707942			−0.353971	−	0.935256i	$-0.615169\pi$
$487$	−7608.36			−0.707942			−0.353971	+	0.935256i	$0.615169\pi$
$488$	3404.93	−	5897.52i	0.315849	−	0.547066i
$489$		0			0
$490$	683.250	−	1218.39i	0.0629920	−	0.112329i
$491$	−14278.7	+	8243.83i	−1.31240	+	0.757717i	−0.982494	−	0.186296i	$-0.940352\pi$
$491$	−14278.7	+	8243.83i	−1.31240	+	0.757717i	−0.329910	+	0.944012i	$0.607018\pi$
$492$		0			0
$493$	2764.26	+	1595.95i	0.252528	+	0.145797i
$494$		−	7225.69i		−	0.658095i
$495$		0			0
$496$			3537.65i			0.320253i
$497$	17465.2	+	4562.82i	1.57630	+	0.411812i
$498$		0			0
$499$	1546.08	+	2677.88i	0.138701	+	0.240237i	0.927005	−	0.375049i	$-0.122374\pi$
$499$	1546.08	+	2677.88i	0.138701	+	0.240237i	−0.788304	+	0.615286i	$0.789041\pi$
$500$	−2436.91	−	4220.86i	−0.217964	−	0.377525i
$501$		0			0
$502$	−8021.49	−	4631.21i	−0.713181	−	0.411755i
$503$	−5624.21			−0.498551			−0.249275	−	0.968433i	$-0.580192\pi$
$503$	−5624.21			−0.498551			−0.249275	+	0.968433i	$0.580192\pi$
$504$		0			0
$505$	2822.56			0.248718
$506$	−2619.52	−	1512.38i	−0.230142	−	0.132873i
$507$		0			0
$508$	1807.58	+	3130.82i	0.157871	+	0.273441i
$509$	−2174.06	−	3765.58i	−0.189319	−	0.327910i	0.755704	−	0.654913i	$-0.227295\pi$
$509$	−2174.06	−	3765.58i	−0.189319	−	0.327910i	−0.945023	+	0.327003i	$0.893961\pi$
$510$		0			0
$511$	10326.6	+	2697.85i	0.893977	+	0.233553i
$512$		−	9053.06i		−	0.781431i
$513$		0			0
$514$			1290.54i			0.110745i
$515$	123.489	+	71.2961i	0.0105661	+	0.00610035i
$516$		0			0
$517$	−12962.1	+	7483.66i	−1.10265	+	0.636617i
$518$	−766.088	+	775.739i	−0.0649807	+	0.0657992i
$519$		0			0
$520$	2217.04	−	3840.03i	0.186969	−	0.323839i
$521$	−16584.8			−1.39461			−0.697305	−	0.716774i	$-0.745618\pi$
$521$	−16584.8			−1.39461			−0.697305	+	0.716774i	$0.745618\pi$
$522$		0			0
$523$		−	15080.9i		−	1.26088i	−0.776237	−	0.630441i	$-0.782874\pi$
$523$		−	15080.9i		−	1.26088i	0.776237	−	0.630441i	$-0.217126\pi$
$524$	3841.77	−	6654.14i	0.320284	−	0.554747i
$525$		0			0
$526$	−2030.50	−	3516.93i	−0.168316	−	0.291532i
$527$	11676.7	−	6741.54i	0.965171	−	0.557242i
$528$		0			0
$529$	−4632.48	+	8023.69i	−0.380741	+	0.659463i
$530$	−958.003			−0.0785151
$531$		0			0
$532$	−2334.45	−	8499.14i	−0.190246	−	0.692640i
$533$	27965.4	+	16145.8i	2.27263	+	1.31211i
$534$		0			0
$535$	1428.88	−	824.966i	0.115469	−	0.0666662i
$536$	−1695.11	+	978.671i	−0.136600	+	0.0788660i
$537$		0			0
$538$	1356.65	+	783.264i	0.108717	+	0.0627675i
$539$	−7706.10	−	12969.7i	−0.615817	−	1.03645i
$540$		0			0
$541$	−17064.6			−1.35613			−0.678064	−	0.735003i	$-0.737181\pi$
$541$	−17064.6			−1.35613			−0.678064	+	0.735003i	$0.737181\pi$
$542$	−4610.18	+	7985.06i	−0.365358	+	0.632819i
$543$		0			0
$544$	−16539.0	+	9548.80i	−1.30350	+	0.752576i
$545$	−63.2476	−	109.548i	−0.00497106	−	0.00861013i
$546$		0			0
$547$	226.704	−	392.663i	0.0177206	−	0.0306929i	−0.857029	−	0.515268i	$-0.827692\pi$
$547$	226.704	−	392.663i	0.0177206	−	0.0306929i	0.874750	+	0.484575i	$0.161026\pi$
$548$			3842.78i			0.299554i
$549$		0			0
$550$	6447.15			0.499831
$551$	1135.76	−	1967.19i	0.0878127	−	0.152096i
$552$		0			0
$553$	−281.183	−	277.685i	−0.0216223	−	0.0213533i
$554$	−2503.07	+	1445.15i	−0.191959	+	0.110827i
$555$		0			0
$556$	1902.10	+	1098.18i	0.145084	+	0.0837644i
$557$		−	19320.2i		−	1.46970i	−0.678229	−	0.734850i	$-0.737252\pi$
$557$		−	19320.2i		−	1.46970i	0.678229	−	0.734850i	$-0.262748\pi$
$558$		0			0
$559$			25154.5i			1.90326i
$560$	411.347	−	1574.52i	0.0310403	−	0.118814i
$561$		0			0
$562$	−633.710	−	1097.62i	−0.0475649	−	0.0823848i
$563$	1038.78	+	1799.22i	0.0777608	+	0.134686i	0.902283	−	0.431143i	$-0.141890\pi$
$563$	1038.78	+	1799.22i	0.0777608	+	0.134686i	−0.824523	+	0.565829i	$0.808556\pi$
$564$		0			0
$565$	−2003.26	−	1156.58i	−0.149164	−	0.0861201i
$566$	−7276.09			−0.540348
$567$		0			0
$568$	−17880.5			−1.32086
$569$	−16935.0	−	9777.42i	−1.24772	−	0.720370i	−0.277064	−	0.960851i	$-0.589361\pi$
$569$	−16935.0	−	9777.42i	−1.24772	−	0.720370i	−0.970654	+	0.240481i	$0.922695\pi$
$570$		0			0
$571$	−3001.96	−	5199.54i	−0.220014	−	0.381075i	0.734798	−	0.678286i	$-0.237277\pi$
$571$	−3001.96	−	5199.54i	−0.220014	−	0.381075i	−0.954812	+	0.297211i	$0.903944\pi$
$572$	−10614.2	−	18384.4i	−0.775879	−	1.34386i
$573$		0			0
$574$	−9749.51	−	2547.08i	−0.708949	−	0.185215i
$575$			6185.56i			0.448619i
$576$		0			0
$577$			18306.7i			1.32083i	0.750901	+	0.660415i	$0.229619\pi$
$577$			18306.7i			1.32083i	−0.750901	+	0.660415i	$0.770381\pi$
$578$	6751.83	+	3898.17i	0.485881	+	0.280523i
$579$		0			0
$580$	535.137	−	308.961i	0.0383109	−	0.0221188i
$581$	−4445.27	−	4389.97i	−0.317420	−	0.313471i
$582$		0			0
$583$	−5173.17	+	8960.18i	−0.367497	+	0.636523i
$584$	−10572.2			−0.749111
$585$		0			0
$586$		−	2835.42i		−	0.199881i
$587$	−10160.7	+	17598.8i	−0.714440	+	1.23745i	0.248735	+	0.968572i	$0.419985\pi$
$587$	−10160.7	+	17598.8i	−0.714440	+	1.23745i	−0.963175	+	0.268875i	$0.913348\pi$
$588$		0			0
$589$	−4797.62	−	8309.72i	−0.335624	−	0.581317i
$590$	1919.32	−	1108.12i	0.133927	−	0.0773230i
$591$		0			0
$592$	−635.069	+	1099.97i	−0.0440898	+	0.0763658i
$593$	27525.8			1.90616			0.953078	−	0.302725i	$-0.0978965\pi$
$593$	27525.8			1.90616			0.953078	+	0.302725i	$0.0978965\pi$
$594$		0			0
$595$	−5980.89	+	1642.76i	−0.412088	+	0.113188i
$596$	1261.13	+	728.112i	0.0866741	+	0.0500413i
$597$		0			0
$598$	−4512.34	+	2605.20i	−0.308567	+	0.178151i
$599$	17841.0	−	10300.5i	1.21697	−	0.702616i	0.252699	−	0.967545i	$-0.418682\pi$
$599$	17841.0	−	10300.5i	1.21697	−	0.702616i	0.964268	+	0.264929i	$0.0853484\pi$
$600$		0			0
$601$	13383.7	+	7727.08i	0.908374	+	0.524450i	0.879907	−	0.475145i	$-0.157604\pi$
$601$	13383.7	+	7727.08i	0.908374	+	0.524450i	0.0284661	+	0.999595i	$0.490938\pi$
$602$	−2079.03	−	7569.23i	−0.140756	−	0.512456i
$603$		0			0
$604$	21625.3			1.45682
$605$	−962.710	+	1667.46i	−0.0646938	+	0.112053i
$606$		0			0
$607$	21073.4	−	12166.7i	1.40913	−	0.813562i	0.413827	−	0.910356i	$-0.364192\pi$
$607$	21073.4	−	12166.7i	1.40913	−	0.813562i	0.995305	+	0.0967932i	$0.0308585\pi$
$608$	6795.40	+	11770.0i	0.453273	+	0.785091i
$609$		0			0
$610$	−755.894	+	1309.25i	−0.0501725	+	0.0869014i
$611$			25782.4i			1.70711i
$612$		0			0
$613$	16221.1			1.06879			0.534393	−	0.845236i	$-0.320540\pi$
$613$	16221.1			1.06879			0.534393	+	0.845236i	$0.320540\pi$
$614$	−1919.30	+	3324.32i	−0.126151	+	0.218499i
$615$		0			0
$616$	10632.6	+	10500.3i	0.695455	+	0.686803i
$617$	−17506.0	+	10107.1i	−1.14224	+	0.659475i	−0.946986	−	0.321276i	$-0.895888\pi$
$617$	−17506.0	+	10107.1i	−1.14224	+	0.659475i	−0.195259	+	0.980752i	$0.562555\pi$
$618$		0			0
$619$	14613.8	+	8437.29i	0.948915	+	0.547857i	0.892744	−	0.450565i	$-0.148777\pi$
$619$	14613.8	+	8437.29i	0.948915	+	0.547857i	0.0561715	+	0.998421i	$0.482111\pi$
$620$		−	2610.21i		−	0.169078i
$621$		0			0
$622$		−	3240.71i		−	0.208908i
$623$	4793.99	−	18350.0i	0.308294	−	1.18006i
$624$		0			0
$625$	−5956.03	−	10316.1i	−0.381186	−	0.660233i
$626$	−3623.84	−	6276.67i	−0.231370	−	0.400745i
$627$		0			0
$628$	−18025.4	−	10407.0i	−1.14537	−	0.661280i
$629$	4840.89			0.306866
$630$		0			0
$631$	30726.8			1.93853			0.969266	−	0.246014i	$-0.0791209\pi$
$631$	30726.8			1.93853			0.969266	+	0.246014i	$0.0791209\pi$
$632$	339.004	+	195.724i	0.0213368	+	0.0123188i
$633$		0			0
$634$	−4910.60	−	8505.41i	−0.307610	−	0.532797i
$635$	−905.222	−	1567.89i	−0.0565711	−	0.0979840i
$636$		0			0
$637$	−25985.3	+	325.289i	−1.61629	+	0.0202330i
$638$			1707.24i			0.105941i
$639$		0			0
$640$			4594.51i			0.283772i
$641$	−13756.1	−	7942.11i	−0.847636	−	0.489383i	0.0122166	−	0.999925i	$-0.496111\pi$
$641$	−13756.1	−	7942.11i	−0.847636	−	0.489383i	−0.859852	+	0.510543i	$0.829445\pi$
$642$		0			0
$643$	−1909.66	+	1102.54i	−0.117122	+	0.0676206i	−0.557417	−	0.830233i	$-0.688207\pi$
$643$	−1909.66	+	1102.54i	−0.117122	+	0.0676206i	0.440294	+	0.897853i	$0.354874\pi$
$644$	−4465.91	+	4522.16i	−0.273263	+	0.276705i
$645$		0			0
$646$	5005.82	−	8670.34i	0.304878	−	0.528065i
$647$	−3584.90			−0.217831			−0.108916	−	0.994051i	$-0.534738\pi$
$647$	−3584.90			−0.217831			−0.108916	+	0.994051i	$0.534738\pi$
$648$		0			0
$649$		−	23935.1i		−	1.44767i
$650$	5552.86	−	9617.83i	0.335078	−	0.580373i
$651$		0			0
$652$	−2196.05	−	3803.66i	−0.131908	−	0.228471i
$653$	394.355	−	227.681i	0.0236329	−	0.0136445i	−0.488137	−	0.872767i	$-0.662323\pi$
$653$	394.355	−	227.681i	0.0236329	−	0.0136445i	0.511770	+	0.859123i	$0.328990\pi$
$654$		0			0
$655$	−1923.93	+	3332.34i	−0.114770	+	0.198787i
$656$	−11739.3			−0.698692
$657$		0			0
$658$	−2130.93	−	7758.17i	−0.126250	−	0.459643i
$659$	−8929.73	−	5155.58i	−0.527850	−	0.304754i	0.212291	−	0.977207i	$-0.431908\pi$
$659$	−8929.73	−	5155.58i	−0.527850	−	0.304754i	−0.740140	+	0.672452i	$0.765241\pi$
$660$		0			0
$661$	−7083.52	+	4089.67i	−0.416818	+	0.240650i	−0.693715	−	0.720250i	$-0.744027\pi$
$661$	−7083.52	+	4089.67i	−0.416818	+	0.240650i	0.276897	+	0.960900i	$0.410694\pi$
$662$	1884.36	−	1087.94i	0.110631	−	0.0638730i
$663$		0			0
$664$	5359.36	+	3094.23i	0.313228	+	0.180842i
$665$	1169.07	+	4256.30i	0.0681724	+	0.248199i
$666$		0			0
$667$	−1637.97			−0.0950862
$668$	4356.21	−	7545.18i	0.252316	−	0.437023i
$669$		0			0
$670$	376.313	−	217.265i	0.0216989	−	0.0125279i
$671$	8163.57	+	14139.7i	0.469674	+	0.813499i
$672$		0			0
$673$	11433.9	−	19804.0i	0.654893	−	1.13431i	−0.327028	−	0.945015i	$-0.606047\pi$
$673$	11433.9	−	19804.0i	0.654893	−	1.13431i	0.981921	−	0.189293i	$-0.0606195\pi$
$674$			9626.65i			0.550155i
$675$		0			0
$676$	−22572.1			−1.28426
$677$	2461.68	−	4263.75i	0.139749	−	0.242052i	−0.787653	−	0.616120i	$-0.788704\pi$
$677$	2461.68	−	4263.75i	0.139749	−	0.242052i	0.927401	+	0.374067i	$0.122037\pi$
$678$		0			0
$679$	954.993	−	967.023i	0.0539754	−	0.0546553i
$680$	5320.60	−	3071.85i	0.300053	−	0.173235i
$681$		0			0
$682$	6245.48	+	3605.83i	0.350663	+	0.202455i
$683$			15195.6i			0.851310i	0.904885	+	0.425655i	$0.139956\pi$
$683$			15195.6i			0.851310i	−0.904885	+	0.425655i	$0.860044\pi$
$684$		0			0
$685$		−	1924.43i		−	0.107341i
$686$	7792.36	−	2245.58i	0.433693	−	0.124981i
$687$		0			0
$688$	−4572.32	−	7919.50i	−0.253370	−	0.438849i
$689$	8911.18	+	15434.6i	0.492727	+	0.853428i
$690$		0			0
$691$	4745.60	+	2739.88i	0.261261	+	0.150839i	0.624910	−	0.780697i	$-0.285136\pi$
$691$	4745.60	+	2739.88i	0.261261	+	0.150839i	−0.363649	+	0.931536i	$0.618469\pi$
$692$	7816.39			0.429385
$693$		0			0
$694$	2393.50			0.130916
$695$	−952.554	−	549.957i	−0.0519891	−	0.0300159i
$696$		0			0
$697$	22371.0	+	38747.7i	1.21573	+	2.10570i
$698$	−1106.65	−	1916.77i	−0.0600104	−	0.103941i
$699$		0			0
$700$	3424.20	−	13106.9i	0.184889	−	0.707704i
$701$		−	5356.09i		−	0.288583i	−0.989535	−	0.144292i	$-0.953910\pi$
$701$		−	5356.09i		−	0.288583i	0.989535	−	0.144292i	$-0.0460903\pi$
$702$		0			0
$703$		−	3445.02i		−	0.184824i
$704$	−452.933	−	261.501i	−0.0242479	−	0.0139996i
$705$		0			0
$706$	10345.3	−	5972.88i	0.551489	−	0.318402i
$707$	11658.9	+	11513.9i	0.620197	+	0.612482i
$708$		0			0
$709$	−6540.71	+	11328.8i	−0.346462	+	0.600090i	−0.985618	−	0.168987i	$-0.945950\pi$
$709$	−6540.71	+	11328.8i	−0.346462	+	0.600090i	0.639156	+	0.769077i	$0.279284\pi$
$710$	3969.47			0.209819
$711$		0			0
$712$			18786.4i			0.988836i
$713$	−3459.53	+	5992.08i	−0.181712	+	0.314734i
$714$		0			0
$715$	5315.52	+	9206.75i	0.278027	+	0.481556i
$716$	8812.49	−	5087.89i	0.459970	−	0.265564i
$717$		0			0
$718$	−7377.61	+	12778.4i	−0.383468	+	0.664186i
$719$	11546.9			0.598925			0.299463	−	0.954108i	$-0.403193\pi$
$719$	11546.9			0.598925			0.299463	+	0.954108i	$0.403193\pi$
$720$		0			0
$721$	219.250	+	798.235i	0.0113250	+	0.0412314i
$722$	1412.78	+	815.671i	0.0728232	+	0.0420445i
$723$		0			0
$724$	−3034.26	+	1751.83i	−0.155756	+	0.0899259i
$725$	3023.52	−	1745.63i	0.154884	−	0.0894221i
$726$		0			0
$727$	8018.50	+	4629.49i	0.409064	+	0.236173i	0.690388	−	0.723440i	$-0.257440\pi$
$727$	8018.50	+	4629.49i	0.409064	+	0.236173i	−0.281323	+	0.959613i	$0.590773\pi$
$728$	24822.1	−	6817.86i	1.26369	−	0.347097i
$729$		0			0
$730$	2347.02			0.118996
$731$	−17426.5	+	30183.7i	−0.881729	+	1.52720i
$732$		0			0
$733$	30748.8	−	17752.8i	1.54943	−	0.894564i	0.551246	−	0.834343i	$-0.314153\pi$
$733$	30748.8	−	17752.8i	1.54943	−	0.894564i	0.998185	−	0.0602216i	$-0.0191808\pi$
$734$	5274.55	+	9135.79i	0.265242	+	0.459412i
$735$		0			0
$736$	4900.12	−	8487.25i	0.245409	−	0.425060i
$737$		−	4692.87i		−	0.234551i
$738$		0			0
$739$	−17773.8			−0.884734			−0.442367	−	0.896834i	$-0.645861\pi$
$739$	−17773.8			−0.884734			−0.442367	+	0.896834i	$0.645861\pi$
$740$	468.577	−	811.599i	0.0232773	−	0.0403175i
$741$		0			0
$742$	−3957.14	−	3907.92i	−0.195783	−	0.193348i
$743$	−9171.95	+	5295.43i	−0.452875	+	0.261468i	−0.709044	−	0.705164i	$-0.750873\pi$
$743$	−9171.95	+	5295.43i	−0.452875	+	0.261468i	0.256168	+	0.966632i	$0.417540\pi$
$744$		0			0
$745$	−631.562	−	364.633i	−0.0310586	−	0.0179317i
$746$			11722.3i			0.575316i
$747$		0			0
$748$		−	29413.3i		−	1.43778i
$749$	9267.39	+	2421.13i	0.452100	+	0.118112i
$750$		0			0
$751$	−2521.66	−	4367.64i	−0.122525	−	0.212220i	0.798238	−	0.602343i	$-0.205766\pi$
$751$	−2521.66	−	4367.64i	−0.122525	−	0.212220i	−0.920763	+	0.390123i	$0.872433\pi$
$752$	−4686.46	−	8117.19i	−0.227257	−	0.393621i
$753$		0			0
$754$	2546.85	+	1470.43i	0.123012	+	0.0710210i
$755$	−10829.8			−0.522035
$756$		0			0
$757$	−36576.1			−1.75612			−0.878060	−	0.478551i	$-0.841162\pi$
$757$	−36576.1			−1.75612			−0.878060	+	0.478551i	$0.841162\pi$
$758$	−10278.4	−	5934.25i	−0.492518	−	0.284356i
$759$		0			0
$760$	−2186.08	−	3786.40i	−0.104339	−	0.180720i
$761$	9686.08	+	16776.8i	0.461393	+	0.799157i	0.999031	−	0.0440195i	$-0.0140164\pi$
$761$	9686.08	+	16776.8i	0.461393	+	0.799157i	−0.537637	+	0.843176i	$0.680683\pi$
$762$		0			0
$763$	185.620	−	710.502i	0.00880722	−	0.0337116i
$764$			23933.0i			1.13333i
$765$		0			0
$766$			9382.26i			0.442552i
$767$	−35706.4	−	20615.1i	−1.68094	−	0.970492i
$768$		0			0
$769$	983.118	−	567.603i	0.0461016	−	0.0266168i	−0.476772	−	0.879027i	$-0.658193\pi$
$769$	983.118	−	567.603i	0.0461016	−	0.0266168i	0.522874	+	0.852410i	$0.324860\pi$
$770$	−2360.43	−	2331.07i	−0.110473	−	0.109099i
$771$		0			0
$772$	−8354.20	+	14469.9i	−0.389474	+	0.674589i
$773$	4858.97			0.226087			0.113043	−	0.993590i	$-0.463940\pi$
$773$	4858.97			0.226087			0.113043	+	0.993590i	$0.463940\pi$
$774$		0			0
$775$		−	14747.6i		−	0.683550i
$776$	−673.118	+	1165.87i	−0.0311385	+	0.0539335i
$777$		0			0
$778$	3340.01	+	5785.06i	0.153914	+	0.266587i
$779$	27574.8	−	15920.3i	1.26825	−	0.732227i
$780$		0			0
$781$	21434.9	−	37126.4i	0.982077	−	1.70101i
$782$	−7219.33			−0.330131
$783$		0			0
$784$	8121.95	−	4825.76i	0.369987	−	0.219832i
$785$	9026.99	+	5211.74i	0.410429	+	0.236962i
$786$		0			0
$787$	6311.59	−	3644.00i	0.285875	−	0.165050i	−0.350205	−	0.936673i	$-0.613888\pi$
$787$	6311.59	−	3644.00i	0.285875	−	0.165050i	0.636080	+	0.771623i	$0.280555\pi$
$788$	25399.2	−	14664.2i	1.14824	−	0.662934i
$789$		0			0
$790$	−75.2586	−	43.4506i	−0.00338934	−	0.00195684i
$791$	−3556.73	−	12949.2i	−0.159877	−	0.582073i
$792$		0			0
$793$	28124.8			1.25945
$794$	6411.74	−	11105.5i	0.286580	−	0.496370i
$795$		0			0
$796$	−17350.5	+	10017.3i	−0.772579	+	0.446049i
$797$	−4956.07	−	8584.16i	−0.220267	−	0.381514i	0.734622	−	0.678477i	$-0.237360\pi$
$797$	−4956.07	−	8584.16i	−0.220267	−	0.381514i	−0.954889	+	0.296963i	$0.904026\pi$
$798$		0			0
$799$	−17861.5	+	30937.1i	−0.790859	+	1.36981i
$800$			20888.7i			0.923160i
$801$		0			0
$802$	9552.05			0.420567
$803$	12673.8	−	21951.7i	0.556972	−	0.964704i
$804$		0			0
$805$	2236.49	−	2264.66i	0.0979204	−	0.0991539i
$806$	10758.3	−	6211.33i	0.470157	−	0.271445i
$807$		0			0
$808$	−14056.4	−	8115.45i	−0.612007	−	0.353342i
$809$			39890.5i			1.73359i	0.498664	+	0.866795i	$0.333824\pi$
$809$			39890.5i			1.73359i	−0.498664	+	0.866795i	$0.666176\pi$
$810$		0			0
$811$			17543.5i			0.759601i	0.925069	+	0.379800i	$0.124007\pi$
$811$			17543.5i			0.759601i	−0.925069	+	0.379800i	$0.875993\pi$
$812$	3470.77	+	906.746i	0.150000	+	0.0391879i
$813$		0			0
$814$	1294.62	+	2242.34i	0.0557448	+	0.0965529i
$815$	1099.76	+	1904.84i	0.0472675	+	0.0818697i
$816$		0			0
$817$	21480.2	+	12401.6i	0.919824	+	0.531061i
$818$	14561.4			0.622407
$819$		0			0
$820$	8661.67			0.368876
$821$	869.844	+	502.205i	0.0369766	+	0.0213484i	0.518374	−	0.855154i	$-0.326537\pi$
$821$	869.844	+	502.205i	0.0369766	+	0.0213484i	−0.481398	+	0.876502i	$0.659871\pi$
$822$		0			0
$823$	404.664	+	700.898i	0.0171394	+	0.0296862i	0.874468	−	0.485083i	$-0.161211\pi$
$823$	404.664	+	700.898i	0.0171394	+	0.0296862i	−0.857329	+	0.514770i	$0.827877\pi$
$824$	−409.982	−	710.110i	−0.0173330	−	0.0300217i
$825$		0			0
$826$	12448.2	+	3252.13i	0.524370	+	0.136993i
$827$		−	27558.4i		−	1.15877i	−0.815056	−	0.579383i	$-0.803294\pi$
$827$		−	27558.4i		−	1.15877i	0.815056	−	0.579383i	$-0.196706\pi$
$828$		0			0
$829$		−	11232.4i		−	0.470588i	−0.971924	−	0.235294i	$-0.924395\pi$
$829$		−	11232.4i		−	0.470588i	0.971924	−	0.235294i	$-0.0756053\pi$
$830$	−1189.78	−	686.917i	−0.0497563	−	0.0287268i
$831$		0			0
$832$	−780.212	+	450.456i	−0.0325108	+	0.0187701i
$833$	−31406.0	−	17611.8i	−1.30631	−	0.732549i
$834$		0			0
$835$	−2181.55	+	3778.56i	−0.0904141	+	0.156602i
$836$	−20932.0			−0.865967
$837$		0			0
$838$		−	7729.16i		−	0.318615i
$839$	10338.7	−	17907.2i	0.425425	−	0.736859i	−0.571035	−	0.820926i	$-0.693458\pi$
$839$	10338.7	−	17907.2i	0.425425	−	0.736859i	0.996460	+	0.0840675i	$0.0267911\pi$
$840$		0			0
$841$	−11732.2	−	20320.8i	−0.481047	−	0.833197i
$842$	−7594.31	+	4384.58i	−0.310828	+	0.179457i
$843$		0			0
$844$	2178.19	−	3772.73i	0.0888345	−	0.153866i
$845$	11303.9			0.460197
$846$		0			0
$847$	−10778.6	+	2960.53i	−0.437256	+	0.120100i
$848$	−5611.10	−	3239.57i	−0.227224	−	0.131188i
$849$		0			0
$850$	13326.1	−	7693.83i	0.537743	−	0.310466i
$851$	−2151.36	+	1242.09i	−0.0866601	+	0.0500332i
$852$		0			0
$853$	−12678.1	−	7319.71i	−0.508899	−	0.293813i	0.223482	−	0.974708i	$-0.428258\pi$
$853$	−12678.1	−	7319.71i	−0.508899	−	0.293813i	−0.732381	+	0.680895i	$0.761591\pi$
$854$	−8463.02	+	2324.53i	−0.339109	+	0.0931425i
$855$		0			0
$856$	−9487.79			−0.378839
$857$	5363.52	−	9289.90i	0.213786	−	0.370288i	−0.739110	−	0.673584i	$-0.764754\pi$
$857$	5363.52	−	9289.90i	0.213786	−	0.370288i	0.952896	+	0.303296i	$0.0980872\pi$
$858$		0			0
$859$	−37326.6	+	21550.5i	−1.48262	+	0.855988i	−0.999805	−	0.0197364i	$-0.993717\pi$
$859$	−37326.6	+	21550.5i	−1.48262	+	0.855988i	−0.482810	+	0.875725i	$0.660384\pi$
$860$	3373.63	+	5843.29i	0.133767	+	0.231691i
$861$		0			0
$862$	−4954.21	+	8580.94i	−0.195755	+	0.339058i
$863$		−	2755.10i		−	0.108673i	−0.998523	−	0.0543363i	$-0.982696\pi$
$863$		−	2755.10i		−	0.108673i	0.998523	−	0.0543363i	$-0.0173043\pi$
$864$		0			0
$865$	−3914.38			−0.153865
$866$	4771.06	−	8263.71i	0.187214	−	0.324264i
$867$		0			0
$868$	10647.6	−	10781.8i	0.416365	−	0.421609i
$869$	−812.785	+	469.262i	−0.0317283	+	0.0183183i
$870$		0			0
$871$	−7000.80	−	4041.92i	−0.272346	−	0.157239i
$872$			727.400i			0.0282487i
$873$		0			0
$874$			5137.63i			0.198836i
$875$	−3581.61	+	13709.4i	−0.138378	+	0.529671i
$876$		0			0
$877$	14479.0	+	25078.4i	0.557494	+	0.965609i	0.997705	+	0.0677140i	$0.0215705\pi$
$877$	14479.0	+	25078.4i	0.557494	+	0.965609i	−0.440210	+	0.897895i	$0.645096\pi$
$878$	−592.617	−	1026.44i	−0.0227789	−	0.0394541i
$879$		0			0
$880$	−3347.02	−	1932.40i	−0.128214	−	0.0740242i
$881$	−41511.7			−1.58747			−0.793737	−	0.608261i	$-0.791867\pi$
$881$	−41511.7			−1.58747			−0.793737	+	0.608261i	$0.791867\pi$
$882$		0			0
$883$	34478.4			1.31403			0.657016	−	0.753877i	$-0.271818\pi$
$883$	34478.4			1.31403			0.657016	+	0.753877i	$0.271818\pi$
$884$	−43878.7	−	25333.4i	−1.66946	−	0.963862i
$885$		0			0
$886$	−3537.08	−	6126.40i	−0.134120	−	0.232303i
$887$	19033.5	+	32967.0i	0.720499	+	1.24794i	0.960800	+	0.277242i	$0.0894203\pi$
$887$	19033.5	+	32967.0i	0.720499	+	1.24794i	−0.240302	+	0.970698i	$0.577246\pi$
$888$		0			0
$889$	2656.67	−	10169.0i	0.100227	−	0.383640i
$890$		−	4170.58i		−	0.157077i
$891$		0			0
$892$			14934.1i			0.560572i
$893$	22016.4	+	12711.2i	0.825028	+	0.476330i
$894$		0			0
$895$	−4413.22	+	2547.98i	−0.164824	+	0.0951614i
$896$	−18742.1	+	18978.2i	−0.698805	+	0.707607i
$897$		0			0
$898$	8354.13	−	14469.8i	0.310446	−	0.537709i
$899$	3905.26			0.144881
$900$		0			0
$901$			24694.0i			0.913070i
$902$	−11965.5	+	20724.9i	−0.441695	+	0.765037i
$903$		0			0
$904$	6650.84	+	11519.6i	0.244694	+	0.423823i
$905$	1519.53	−	877.303i	0.0558133	−	0.0322238i
$906$		0			0
$907$	13062.6	−	22625.2i	0.478212	−	0.828287i	−0.521476	−	0.853266i	$-0.674619\pi$
$907$	13062.6	−	22625.2i	0.478212	−	0.828287i	0.999688	+	0.0249790i	$0.00795188\pi$
$908$	−19571.6			−0.715314
$909$		0			0
$910$	−5510.50	+	1513.56i	−0.200738	+	0.0551364i
$911$	−13990.6	−	8077.47i	−0.508813	−	0.293763i	0.223532	−	0.974696i	$-0.428241\pi$
$911$	−13990.6	−	8077.47i	−0.508813	−	0.293763i	−0.732346	+	0.680933i	$0.761574\pi$
$912$		0			0
$913$	−12849.4	+	7418.63i	−0.465777	+	0.268917i
$914$	12760.9	−	7367.52i	0.461809	−	0.266626i
$915$		0			0
$916$	7732.06	+	4464.11i	0.278902	+	0.161024i
$917$	−21540.4	+	5916.47i	−0.775710	+	0.213063i
$918$		0			0
$919$	−26587.5			−0.954344			−0.477172	−	0.878810i	$-0.658338\pi$
$919$	−26587.5			−0.954344			−0.477172	+	0.878810i	$0.658338\pi$
$920$	−1576.37	+	2730.35i	−0.0564906	+	0.0978446i
$921$		0			0
$922$	−10076.7	+	5817.79i	−0.359933	+	0.207808i
$923$	−36923.4	−	63953.1i	−1.31674	−	2.28065i
$924$		0			0
$925$	2647.45	−	4585.52i	0.0941057	−	0.162996i
$926$		−	4066.01i		−	0.144295i
$927$		0			0
$928$	−5531.45			−0.195667
$929$	−14089.6	+	24403.9i	−0.497594	+	0.861857i	−0.999996	−	0.00277655i	$-0.999116\pi$
$929$	−14089.6	+	24403.9i	−0.497594	+	0.861857i	0.502403	+	0.864634i	$0.332450\pi$
$930$		0			0
$931$	−12533.4	+	22350.0i	−0.441210	+	0.786781i
$932$	28696.4	−	16567.9i	1.00857	−	0.582296i
$933$		0			0
$934$	1100.19	+	635.195i	0.0385432	+	0.0222529i
$935$			14730.0i			0.515210i
$936$		0			0
$937$			10247.7i			0.357288i	0.983914	+	0.178644i	$0.0571711\pi$
$937$			10247.7i			0.357288i	−0.983914	+	0.178644i	$0.942829\pi$
$938$	2440.68	+	637.632i	0.0849584	+	0.0221956i
$939$		0			0
$940$	3457.84	+	5989.15i	0.119981	+	0.207813i
$941$	−7953.42	−	13775.7i	−0.275530	−	0.477232i	0.694739	−	0.719262i	$-0.255520\pi$
$941$	−7953.42	−	13775.7i	−0.275530	−	0.477232i	−0.970269	+	0.242030i	$0.922187\pi$
$942$		0			0
$943$	−19884.0	−	11480.0i	−0.686652	−	0.396439i
$944$	14988.8			0.516784
$945$		0			0
$946$	−18641.8			−0.640694
$947$	28572.1	+	16496.1i	0.980432	+	0.566053i	0.902401	−	0.430898i	$-0.141803\pi$
$947$	28572.1	+	16496.1i	0.980432	+	0.566053i	0.0780317	+	0.996951i	$0.475136\pi$
$948$		0			0
$949$	−21831.6	−	37813.5i	−0.746769	−	1.29344i
$950$	−5475.31	−	9483.51i	−0.186992	−	0.323880i
$951$		0			0
$952$	34508.1	+	9015.33i	1.17481	+	0.306921i
$953$		−	37129.3i		−	1.26205i	−0.775761	−	0.631027i	$-0.782634\pi$
$953$		−	37129.3i		−	1.26205i	0.775761	−	0.631027i	$-0.217366\pi$
$954$		0			0
$955$		−	11985.5i		−	0.406116i
$956$	−11542.1	−	6663.84i	−0.390479	−	0.225443i
$957$		0			0
$958$	−15370.1	+	8873.96i	−0.518358	+	0.299274i
$959$	7850.20	−	7949.09i	0.264334	−	0.267664i
$960$		0			0
$961$	−6647.27	+	11513.4i	−0.223130	+	0.386473i
$962$	4460.16			0.149482
$963$		0			0
$964$			44703.1i			1.49356i
$965$	4183.71	−	7246.41i	0.139563	−	0.241731i
$966$		0			0
$967$	−31.4682	−	54.5045i	−0.00104648	−	0.00181256i	0.865502	−	0.500906i	$-0.167000\pi$
$967$	−31.4682	−	54.5045i	−0.00104648	−	0.00181256i	−0.866548	+	0.499093i	$0.833666\pi$
$968$	9588.60	−	5535.98i	0.318377	−	0.183815i
$969$		0			0
$970$	149.432	−	258.823i	0.00494636	−	0.00856734i
$971$	−26793.4			−0.885521			−0.442761	−	0.896640i	$-0.646001\pi$
$971$	−26793.4			−0.885521			−0.442761	+	0.896640i	$0.646001\pi$
$972$		0			0
$973$	−1691.23	−	6157.35i	−0.0557229	−	0.202873i
$974$	−8411.49	−	4856.38i	−0.276716	−	0.159762i
$975$		0			0
$976$	−8854.66	+	5112.24i	−0.290400	+	0.167663i
$977$	−22941.3	+	13245.2i	−0.751235	+	0.433726i	−0.826140	−	0.563465i	$-0.809468\pi$
$977$	−22941.3	+	13245.2i	−0.751235	+	0.433726i	0.0749048	+	0.997191i	$0.476135\pi$
$978$		0			0
$979$	−39007.3	−	22520.9i	−1.27342	−	0.735211i
$980$	−5992.67	+	3560.62i	−0.195336	+	0.116061i
$981$		0			0
$982$	−21048.0			−0.683979
$983$	11945.2	−	20689.7i	0.387582	−	0.671313i	−0.604541	−	0.796574i	$-0.706644\pi$
$983$	11945.2	−	20689.7i	0.387582	−	0.671313i	0.992124	+	0.125261i	$0.0399769\pi$
$984$		0			0
$985$	−12719.7	+	7343.73i	−0.411456	+	0.237554i
$986$	2037.37	+	3528.83i	0.0658043	+	0.113976i
$987$		0			0
$988$	−18028.5	+	31226.3i	−0.580529	+	1.00551i
$989$		−	17885.4i		−	0.575048i
$990$		0			0
$991$	377.774			0.0121094			0.00605468	−	0.999982i	$-0.498073\pi$
$991$	377.774			0.0121094			0.00605468	+	0.999982i	$0.498073\pi$
$992$	−11682.9	+	20235.3i	−0.373923	+	0.647654i
$993$		0			0
$994$	16396.4	+	16192.4i	0.523200	+	0.516692i
$995$	8689.00	−	5016.59i	0.276844	−	0.159836i
$996$		0			0
$997$	854.102	+	493.116i	0.0271311	+	0.0156641i	0.513504	−	0.858087i	$-0.328347\pi$
$997$	854.102	+	493.116i	0.0271311	+	0.0156641i	−0.486373	+	0.873751i	$0.661680\pi$
$998$			3947.40i			0.125203i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.4.o.a.62.14		44
3.2	odd	2		63.4.o.a.20.10	yes	44
7.6	odd	2	inner	189.4.o.a.62.13		44
9.2	odd	6		567.4.c.c.566.20		44
9.4	even	3		63.4.o.a.41.9	yes	44
9.5	odd	6	inner	189.4.o.a.125.13		44
9.7	even	3		567.4.c.c.566.25		44
21.20	even	2		63.4.o.a.20.9	✓	44
63.13	odd	6		63.4.o.a.41.10	yes	44
63.20	even	6		567.4.c.c.566.26		44
63.34	odd	6		567.4.c.c.566.19		44
63.41	even	6	inner	189.4.o.a.125.14		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.4.o.a.20.9	✓	44	21.20	even	2
63.4.o.a.20.10	yes	44	3.2	odd	2
63.4.o.a.41.9	yes	44	9.4	even	3
63.4.o.a.41.10	yes	44	63.13	odd	6
189.4.o.a.62.13		44	7.6	odd	2	inner
189.4.o.a.62.14		44	1.1	even	1	trivial
189.4.o.a.125.13		44	9.5	odd	6	inner
189.4.o.a.125.14		44	63.41	even	6	inner
567.4.c.c.566.19		44	63.34	odd	6
567.4.c.c.566.20		44	9.2	odd	6
567.4.c.c.566.25		44	9.7	even	3
567.4.c.c.566.26		44	63.20	even	6

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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	189.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.10556 + 0.638294i) q^{2} +(-3.18516 - 5.51686i) q^{4} +(1.59510 + 2.76280i) q^{5} +(-4.68134 + 17.9188i) q^{7} -18.3450i q^{8} +O(q^{10})\)	\(q+(1.10556 + 0.638294i) q^{2} +(-3.18516 - 5.51686i) q^{4} +(1.59510 + 2.76280i) q^{5} +(-4.68134 + 17.9188i) q^{7} -18.3450i q^{8} +4.07258i q^{10} +(38.0908 + 21.9917i) q^{11} +(65.6143 - 37.8824i) q^{13} +(-16.6130 + 16.8223i) q^{14} +(-13.7718 + 23.8534i) q^{16} +104.977 q^{17} -74.7068i q^{19} +(10.1613 - 17.5999i) q^{20} +(28.0744 + 48.6262i) q^{22} +(-46.6533 + 26.9353i) q^{23} +(57.4113 - 99.4393i) q^{25} +96.7206 q^{26} +(113.767 - 31.2481i) q^{28} +(26.3321 + 15.2028i) q^{29} +(111.231 - 64.2193i) q^{31} +(-157.549 + 90.9609i) q^{32} +(116.058 + 67.0062i) q^{34} +(-56.9734 + 15.6488i) q^{35} +46.1138 q^{37} +(47.6849 - 82.5928i) q^{38} +(50.6835 - 29.2621i) q^{40} +(213.104 + 369.107i) q^{41} +(-166.003 + 287.526i) q^{43} -280.188i q^{44} -68.7706 q^{46} +(-170.147 + 294.704i) q^{47} +(-299.170 - 167.768i) q^{49} +(126.943 - 73.2906i) q^{50} +(-417.984 - 241.323i) q^{52} +235.233i q^{53} +140.316i q^{55} +(328.721 + 85.8791i) q^{56} +(19.4078 + 33.6152i) q^{58} +(-272.093 - 471.279i) q^{59} +(321.478 + 185.606i) q^{61} +163.963 q^{62} -11.8909 q^{64} +(209.323 + 120.853i) q^{65} +(-53.3481 - 92.4017i) q^{67} +(-334.368 - 579.143i) q^{68} +(-72.9759 - 19.0651i) q^{70} -974.682i q^{71} -576.299i q^{73} +(50.9815 + 29.4342i) q^{74} +(-412.147 + 237.953i) q^{76} +(-572.382 + 579.592i) q^{77} +(-10.6691 + 18.4794i) q^{79} -87.8696 q^{80} +544.093i q^{82} +(-168.669 + 292.143i) q^{83} +(167.449 + 290.030i) q^{85} +(-367.053 + 211.918i) q^{86} +(403.438 - 698.775i) q^{88} -1024.06 q^{89} +(371.647 + 1353.07i) q^{91} +(297.197 + 171.586i) q^{92} +(-376.216 + 217.208i) q^{94} +(206.400 - 119.165i) q^{95} +(-63.5527 - 36.6922i) q^{97} +(-223.664 - 376.436i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 6 q^{2} + 78 q^{4} + 5 q^{7}+O(q^{10}) \) 44 * q + 6 * q^2 + 78 * q^4 + 5 * q^7	\( 44 q + 6 q^{2} + 78 q^{4} + 5 q^{7} + 18 q^{11} - 204 q^{14} - 242 q^{16} - 34 q^{22} + 102 q^{23} - 352 q^{25} + 300 q^{28} - 246 q^{29} - 1068 q^{32} + 328 q^{37} - 170 q^{43} + 968 q^{46} - 79 q^{49} - 288 q^{50} - 1212 q^{56} - 538 q^{58} - 808 q^{64} - 4350 q^{65} - 590 q^{67} + 384 q^{70} + 5304 q^{74} + 2787 q^{77} - 302 q^{79} - 612 q^{85} + 13692 q^{86} + 1294 q^{88} + 210 q^{91} + 10194 q^{92} - 6336 q^{95}+O(q^{100}) \) 44 * q + 6 * q^2 + 78 * q^4 + 5 * q^7 + 18 * q^11 - 204 * q^14 - 242 * q^16 - 34 * q^22 + 102 * q^23 - 352 * q^25 + 300 * q^28 - 246 * q^29 - 1068 * q^32 + 328 * q^37 - 170 * q^43 + 968 * q^46 - 79 * q^49 - 288 * q^50 - 1212 * q^56 - 538 * q^58 - 808 * q^64 - 4350 * q^65 - 590 * q^67 + 384 * q^70 + 5304 * q^74 + 2787 * q^77 - 302 * q^79 - 612 * q^85 + 13692 * q^86 + 1294 * q^88 + 210 * q^91 + 10194 * q^92 - 6336 * q^95

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