LMFDB - Embedded newform 1386.2.ba.b.1187.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1386,2,Mod(989,1386)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1386, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2, 3]))

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

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

chi := DirichletCharacter("1386.989");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1386.ba (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$11.0672657201$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1187.12
Character	$\chi$	$=$	1386.1187
Dual form			1386.2.ba.b.989.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.78334 - 1.02961i) q^{5} +(0.289722 + 2.62984i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.78334 - 1.02961i) q^{5} +(0.289722 + 2.62984i) q^{7} -1.00000 q^{8} +(1.78334 + 1.02961i) q^{10} +(-1.29385 - 3.05384i) q^{11} -6.97891i q^{13} +(-2.13265 + 1.56583i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.66515 - 4.61618i) q^{17} +(7.36851 - 4.25421i) q^{19} +2.05923i q^{20} +(1.99778 - 2.64743i) q^{22} +(1.35506 - 0.782344i) q^{23} +(-0.379791 + 0.657818i) q^{25} +(6.04391 - 3.48945i) q^{26} +(-2.42237 - 1.06401i) q^{28} -2.87708 q^{29} +(-4.39314 + 7.60915i) q^{31} +(0.500000 - 0.866025i) q^{32} +5.33030 q^{34} +(3.22439 + 4.39161i) q^{35} +(-1.82231 - 3.15633i) q^{37} +(7.36851 + 4.25421i) q^{38} +(-1.78334 + 1.02961i) q^{40} +2.42621 q^{41} +7.55213i q^{43} +(3.29163 + 0.406418i) q^{44} +(1.35506 + 0.782344i) q^{46} +(10.2450 - 5.91497i) q^{47} +(-6.83212 + 1.52384i) q^{49} -0.759582 q^{50} +(6.04391 + 3.48945i) q^{52} +(9.93207 + 5.73428i) q^{53} +(-5.45165 - 4.11389i) q^{55} +(-0.289722 - 2.62984i) q^{56} +(-1.43854 - 2.49162i) q^{58} +(-3.49197 - 2.01609i) q^{59} +(-4.39206 + 2.53576i) q^{61} -8.78629 q^{62} +1.00000 q^{64} +(-7.18558 - 12.4458i) q^{65} +(-4.75461 + 8.23523i) q^{67} +(2.66515 + 4.61618i) q^{68} +(-2.19105 + 4.98821i) q^{70} -3.30443i q^{71} +(-0.828178 - 0.478149i) q^{73} +(1.82231 - 3.15633i) q^{74} +8.50842i q^{76} +(7.65627 - 4.28737i) q^{77} +(7.75287 - 4.47612i) q^{79} +(-1.78334 - 1.02961i) q^{80} +(1.21310 + 2.10116i) q^{82} +7.50706 q^{83} -10.9763i q^{85} +(-6.54033 + 3.77606i) q^{86} +(1.29385 + 3.05384i) q^{88} +(-2.99174 + 1.72728i) q^{89} +(18.3534 - 2.02194i) q^{91} +1.56469i q^{92} +(10.2450 + 5.91497i) q^{94} +(8.76039 - 15.1734i) q^{95} -5.95332 q^{97} +(-4.73575 - 5.15487i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{2} - 16 q^{4} - 32 q^{8}+O(q^{10}) $ 32 * q + 16 * q^2 - 16 * q^4 - 32 * q^8	$ 32 q + 16 q^{2} - 16 q^{4} - 32 q^{8} + 2 q^{11} - 16 q^{16} + 4 q^{17} + 4 q^{22} + 4 q^{25} + 16 q^{29} + 4 q^{31} + 16 q^{32} + 8 q^{34} + 16 q^{35} + 4 q^{37} - 32 q^{41} + 2 q^{44} + 20 q^{49} + 8 q^{50} - 12 q^{55} + 8 q^{58} + 8 q^{62} + 32 q^{64} - 8 q^{67} + 4 q^{68} - 4 q^{70} - 4 q^{74} + 14 q^{77} - 16 q^{82} + 88 q^{83} - 2 q^{88} - 24 q^{95} - 32 q^{97} - 8 q^{98}+O(q^{100}) $ 32 * q + 16 * q^2 - 16 * q^4 - 32 * q^8 + 2 * q^11 - 16 * q^16 + 4 * q^17 + 4 * q^22 + 4 * q^25 + 16 * q^29 + 4 * q^31 + 16 * q^32 + 8 * q^34 + 16 * q^35 + 4 * q^37 - 32 * q^41 + 2 * q^44 + 20 * q^49 + 8 * q^50 - 12 * q^55 + 8 * q^58 + 8 * q^62 + 32 * q^64 - 8 * q^67 + 4 * q^68 - 4 * q^70 - 4 * q^74 + 14 * q^77 - 16 * q^82 + 88 * q^83 - 2 * q^88 - 24 * q^95 - 32 * q^97 - 8 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$1135$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	1.78334	−	1.02961i	0.797535	−	0.460457i	−0.0450733	−	0.998984i	$-0.514352\pi$
$5$	1.78334	−	1.02961i	0.797535	−	0.460457i	0.842609	+	0.538526i	$0.181019\pi$
$6$		0			0
$7$	0.289722	+	2.62984i	0.109504	+	0.993986i
$7$	0.289722	+	2.62984i	0.109504	+	0.993986i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	1.78334	+	1.02961i	0.563943	+	0.325592i
$11$	−1.29385	−	3.05384i	−0.390109	−	0.920768i
$11$	−1.29385	−	3.05384i	−0.390109	−	0.920768i
$12$		0			0
$13$		−	6.97891i		−	1.93560i	−0.251719	−	0.967800i	$-0.580996\pi$
$13$		−	6.97891i		−	1.93560i	0.251719	−	0.967800i	$-0.419004\pi$
$14$	−2.13265	+	1.56583i	−0.569974	+	0.418485i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.66515	−	4.61618i	0.646394	−	1.11959i	−0.337584	−	0.941295i	$-0.609610\pi$
$17$	2.66515	−	4.61618i	0.646394	−	1.11959i	0.983978	−	0.178292i	$-0.0570570\pi$
$18$		0			0
$19$	7.36851	−	4.25421i	1.69045	−	0.975983i	0.736303	−	0.676652i	$-0.236570\pi$
$19$	7.36851	−	4.25421i	1.69045	−	0.975983i	0.954149	−	0.299331i	$-0.0967636\pi$
$20$			2.05923i			0.460457i
$21$		0			0
$22$	1.99778	−	2.64743i	0.425929	−	0.564433i
$23$	1.35506	−	0.782344i	0.282549	−	0.163130i	−0.352028	−	0.935990i	$-0.614508\pi$
$23$	1.35506	−	0.782344i	0.282549	−	0.163130i	0.634577	+	0.772860i	$0.281174\pi$
$24$		0			0
$25$	−0.379791	+	0.657818i	−0.0759582	+	0.131564i
$26$	6.04391	−	3.48945i	1.18531	−	0.684338i
$27$		0			0
$28$	−2.42237	−	1.06401i	−0.457785	−	0.201080i
$29$	−2.87708			−0.534260			−0.267130	−	0.963660i	$-0.586075\pi$
$29$	−2.87708			−0.534260			−0.267130	+	0.963660i	$0.586075\pi$
$30$		0			0
$31$	−4.39314	+	7.60915i	−0.789032	+	1.36664i	0.137529	+	0.990498i	$0.456084\pi$
$31$	−4.39314	+	7.60915i	−0.789032	+	1.36664i	−0.926561	+	0.376145i	$0.877249\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$		0			0
$34$	5.33030			0.914139
$35$	3.22439	+	4.39161i	0.545022	+	0.742317i
$36$		0			0
$37$	−1.82231	−	3.15633i	−0.299585	−	0.518897i	0.676456	−	0.736483i	$-0.263515\pi$
$37$	−1.82231	−	3.15633i	−0.299585	−	0.518897i	−0.976041	+	0.217586i	$0.930182\pi$
$38$	7.36851	+	4.25421i	1.19533	+	0.690124i
$39$		0			0
$40$	−1.78334	+	1.02961i	−0.281971	+	0.162796i
$41$	2.42621			0.378910			0.189455	−	0.981889i	$-0.439328\pi$
$41$	2.42621			0.378910			0.189455	+	0.981889i	$0.439328\pi$
$42$		0			0
$43$			7.55213i			1.15169i	0.817559	+	0.575844i	$0.195327\pi$
$43$			7.55213i			1.15169i	−0.817559	+	0.575844i	$0.804673\pi$
$44$	3.29163	+	0.406418i	0.496232	+	0.0612698i
$45$		0			0
$46$	1.35506	+	0.782344i	0.199793	+	0.115350i
$47$	10.2450	−	5.91497i	1.49439	−	0.862787i	0.494412	−	0.869228i	$-0.335384\pi$
$47$	10.2450	−	5.91497i	1.49439	−	0.862787i	0.999979	+	0.00644106i	$0.00205027\pi$
$48$		0			0
$49$	−6.83212	+	1.52384i	−0.976018	+	0.217692i
$50$	−0.759582			−0.107421
$51$		0			0
$52$	6.04391	+	3.48945i	0.838140	+	0.483900i
$53$	9.93207	+	5.73428i	1.36427	+	0.787664i	0.990190	−	0.139730i	$-0.0446236\pi$
$53$	9.93207	+	5.73428i	1.36427	+	0.787664i	0.374085	+	0.927395i	$0.377957\pi$
$54$		0			0
$55$	−5.45165	−	4.11389i	−0.735101	−	0.554717i
$56$	−0.289722	−	2.62984i	−0.0387157	−	0.351427i
$57$		0			0
$58$	−1.43854	−	2.49162i	−0.188890	−	0.327166i
$59$	−3.49197	−	2.01609i	−0.454616	−	0.262473i	0.255162	−	0.966898i	$-0.417871\pi$
$59$	−3.49197	−	2.01609i	−0.454616	−	0.262473i	−0.709778	+	0.704426i	$0.751205\pi$
$60$		0			0
$61$	−4.39206	+	2.53576i	−0.562346	+	0.324670i	−0.754086	−	0.656775i	$-0.771920\pi$
$61$	−4.39206	+	2.53576i	−0.562346	+	0.324670i	0.191741	+	0.981446i	$0.438587\pi$
$62$	−8.78629			−1.11586
$63$		0			0
$64$	1.00000			0.125000
$65$	−7.18558	−	12.4458i	−0.891261	−	1.54371i
$66$		0			0
$67$	−4.75461	+	8.23523i	−0.580868	+	1.00609i	0.414508	+	0.910045i	$0.363954\pi$
$67$	−4.75461	+	8.23523i	−0.580868	+	1.00609i	−0.995377	+	0.0960479i	$0.969380\pi$
$68$	2.66515	+	4.61618i	0.323197	+	0.559794i
$69$		0			0
$70$	−2.19105	+	4.98821i	−0.261880	+	0.596205i
$71$		−	3.30443i		−	0.392163i	−0.980588	−	0.196082i	$-0.937178\pi$
$71$		−	3.30443i		−	0.392163i	0.980588	−	0.196082i	$-0.0628217\pi$
$72$		0			0
$73$	−0.828178	−	0.478149i	−0.0969309	−	0.0559631i	0.450751	−	0.892650i	$-0.351156\pi$
$73$	−0.828178	−	0.478149i	−0.0969309	−	0.0559631i	−0.547682	+	0.836687i	$0.684490\pi$
$74$	1.82231	−	3.15633i	0.211839	−	0.366915i
$75$		0			0
$76$			8.50842i			0.975983i
$77$	7.65627	−	4.28737i	0.872513	−	0.488592i
$78$		0			0
$79$	7.75287	−	4.47612i	0.872266	−	0.503603i	0.00416551	−	0.999991i	$-0.498674\pi$
$79$	7.75287	−	4.47612i	0.872266	−	0.503603i	0.868101	+	0.496388i	$0.165341\pi$
$80$	−1.78334	−	1.02961i	−0.199384	−	0.115114i
$81$		0			0
$82$	1.21310	+	2.10116i	0.133965	+	0.232034i
$83$	7.50706			0.824007			0.412003	−	0.911182i	$-0.364829\pi$
$83$	7.50706			0.824007			0.412003	+	0.911182i	$0.364829\pi$
$84$		0			0
$85$		−	10.9763i		−	1.19055i
$86$	−6.54033	+	3.77606i	−0.705262	+	0.407183i
$87$		0			0
$88$	1.29385	+	3.05384i	0.137925	+	0.325541i
$89$	−2.99174	+	1.72728i	−0.317124	+	0.183092i	−0.650110	−	0.759840i	$-0.725277\pi$
$89$	−2.99174	+	1.72728i	−0.317124	+	0.183092i	0.332986	+	0.942932i	$0.391944\pi$
$90$		0			0
$91$	18.3534	−	2.02194i	1.92396	−	0.211957i
$92$			1.56469i			0.163130i
$93$		0			0
$94$	10.2450	+	5.91497i	1.05669	+	0.610082i
$95$	8.76039	−	15.1734i	0.898797	−	1.55676i
$96$		0			0
$97$	−5.95332			−0.604468			−0.302234	−	0.953234i	$-0.597732\pi$
$97$	−5.95332			−0.604468			−0.302234	+	0.953234i	$0.597732\pi$
$98$	−4.73575	−	5.15487i	−0.478383	−	0.520721i
$99$		0			0
$100$	−0.379791	−	0.657818i	−0.0379791	−	0.0657818i
$101$	1.95460	−	3.38547i	0.194490	−	0.336867i	−0.752243	−	0.658886i	$-0.771028\pi$
$101$	1.95460	−	3.38547i	0.194490	−	0.336867i	0.946733	+	0.322019i	$0.104361\pi$
$102$		0			0
$103$	1.72042	+	2.97985i	0.169518	+	0.293614i	0.938250	−	0.345957i	$-0.112446\pi$
$103$	1.72042	+	2.97985i	0.169518	+	0.293614i	−0.768733	+	0.639570i	$0.779112\pi$
$104$			6.97891i			0.684338i
$105$		0			0
$106$			11.4686i			1.11393i
$107$	1.00997	+	1.74932i	0.0976377	+	0.169114i	0.910706	−	0.413054i	$-0.135538\pi$
$107$	1.00997	+	1.74932i	0.0976377	+	0.169114i	−0.813069	+	0.582168i	$0.802205\pi$
$108$		0			0
$109$	−3.05488	−	1.76373i	−0.292604	−	0.168935i	0.346512	−	0.938046i	$-0.387366\pi$
$109$	−3.05488	−	1.76373i	−0.292604	−	0.168935i	−0.639116	+	0.769111i	$0.720699\pi$
$110$	0.836906	−	6.77821i	0.0797959	−	0.646277i
$111$		0			0
$112$	2.13265	−	1.56583i	0.201516	−	0.147957i
$113$		−	7.60125i		−	0.715065i	−0.933901	−	0.357533i	$-0.883618\pi$
$113$		−	7.60125i		−	0.715065i	0.933901	−	0.357533i	$-0.116382\pi$
$114$		0			0
$115$	1.61102	−	2.79038i	0.150229	−	0.260204i
$116$	1.43854	−	2.49162i	0.133565	−	0.231342i
$117$		0			0
$118$		−	4.03218i		−	0.371193i
$119$	12.9120	+	5.67151i	1.18364	+	0.519907i
$120$		0			0
$121$	−7.65192	+	7.90241i	−0.695629	+	0.718401i
$122$	−4.39206	−	2.53576i	−0.397638	−	0.229577i
$123$		0			0
$124$	−4.39314	−	7.60915i	−0.394516	−	0.683322i
$125$			11.8603i			1.06082i
$126$		0			0
$127$			6.33932i			0.562523i	0.959631	+	0.281262i	$0.0907529\pi$
$127$			6.33932i			0.562523i	−0.959631	+	0.281262i	$0.909247\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$		0			0
$130$	7.18558	−	12.4458i	0.630217	−	1.09157i
$131$	6.50013	+	11.2586i	0.567919	+	0.983664i	0.996772	+	0.0802898i	$0.0255846\pi$
$131$	6.50013	+	11.2586i	0.567919	+	0.983664i	−0.428853	+	0.903374i	$0.641082\pi$
$132$		0			0
$133$	13.3227	+	18.1455i	1.15523	+	1.57341i
$134$	−9.50922			−0.821472
$135$		0			0
$136$	−2.66515	+	4.61618i	−0.228535	+	0.395834i
$137$	−7.97258	−	4.60297i	−0.681144	−	0.393258i	0.119142	−	0.992877i	$-0.461986\pi$
$137$	−7.97258	−	4.60297i	−0.681144	−	0.393258i	−0.800286	+	0.599619i	$0.795319\pi$
$138$		0			0
$139$		−	18.5202i		−	1.57087i	−0.618946	−	0.785433i	$-0.712440\pi$
$139$		−	18.5202i		−	1.57087i	0.618946	−	0.785433i	$-0.287560\pi$
$140$	−5.41544	+	0.596603i	−0.457688	+	0.0504221i
$141$		0			0
$142$	2.86172	−	1.65221i	0.240150	−	0.138651i
$143$	−21.3125	+	9.02964i	−1.78224	+	0.755096i
$144$		0			0
$145$	−5.13082	+	2.96228i	−0.426092	+	0.246004i
$146$		−	0.956297i		−	0.0791437i
$147$		0			0
$148$	3.64461			0.299585
$149$	−6.04969	−	10.4784i	−0.495610	−	0.858422i	0.504377	−	0.863483i	$-0.331722\pi$
$149$	−6.04969	−	10.4784i	−0.495610	−	0.858422i	−0.999987	+	0.00506166i	$0.998389\pi$
$150$		0			0
$151$	−4.47659	−	2.58456i	−0.364300	−	0.210329i	0.306665	−	0.951817i	$-0.400787\pi$
$151$	−4.47659	−	2.58456i	−0.364300	−	0.210329i	−0.670965	+	0.741489i	$0.734120\pi$
$152$	−7.36851	+	4.25421i	−0.597665	+	0.345062i
$153$		0			0
$154$	7.54111	+	4.48683i	0.607680	+	0.361559i
$155$			18.0930i			1.45326i
$156$		0			0
$157$	0.478738	−	0.829198i	0.0382074	−	0.0661772i	−0.846289	−	0.532724i	$-0.821169\pi$
$157$	0.478738	−	0.829198i	0.0382074	−	0.0661772i	0.884497	+	0.466546i	$0.154502\pi$
$158$	7.75287	+	4.47612i	0.616785	+	0.356101i
$159$		0			0
$160$		−	2.05923i		−	0.162796i
$161$	2.45003	+	3.33693i	0.193089	+	0.262987i
$162$		0			0
$163$	8.54401	+	14.7987i	0.669219	+	1.15912i	0.978123	+	0.208027i	$0.0667043\pi$
$163$	8.54401	+	14.7987i	0.669219	+	1.15912i	−0.308904	+	0.951093i	$0.599962\pi$
$164$	−1.21310	+	2.10116i	−0.0947274	+	0.164073i
$165$		0			0
$166$	3.75353	+	6.50130i	0.291330	+	0.504599i
$167$	−17.6200			−1.36348			−0.681738	−	0.731596i	$-0.738776\pi$
$167$	−17.6200			−1.36348			−0.681738	+	0.731596i	$0.738776\pi$
$168$		0			0
$169$	−35.7051			−2.74655
$170$	9.50576	−	5.48815i	0.729058	−	0.420922i
$171$		0			0
$172$	−6.54033	−	3.77606i	−0.498696	−	0.287922i
$173$	8.05455	+	13.9509i	0.612376	+	1.06067i	0.990839	+	0.135050i	$0.0431196\pi$
$173$	8.05455	+	13.9509i	0.612376	+	1.06067i	−0.378462	+	0.925617i	$0.623547\pi$
$174$		0			0
$175$	−1.83999	−	0.808206i	−0.139090	−	0.0610947i
$176$	−1.99778	+	2.64743i	−0.150589	+	0.199557i
$177$		0			0
$178$	−2.99174	−	1.72728i	−0.224241	−	0.129465i
$179$	−7.99155	−	4.61392i	−0.597316	−	0.344861i	0.170669	−	0.985328i	$-0.445407\pi$
$179$	−7.99155	−	4.61392i	−0.597316	−	0.344861i	−0.767985	+	0.640468i	$0.778741\pi$
$180$		0			0
$181$	5.46346			0.406096			0.203048	−	0.979169i	$-0.434915\pi$
$181$	5.46346			0.406096			0.203048	+	0.979169i	$0.434915\pi$
$182$	10.9278	+	14.8836i	0.810019	+	1.10324i
$183$		0			0
$184$	−1.35506	+	0.782344i	−0.0998963	+	0.0576752i
$185$	−6.49959	−	3.75254i	−0.477859	−	0.275892i
$186$		0			0
$187$	−17.5454	−	2.16633i	−1.28304	−	0.158418i
$188$			11.8299i			0.862787i
$189$		0			0
$190$	17.5208			1.27109
$191$	17.8512	−	10.3064i	1.29167	−	0.745746i	0.312720	−	0.949845i	$-0.398760\pi$
$191$	17.8512	−	10.3064i	1.29167	−	0.745746i	0.978950	+	0.204099i	$0.0654265\pi$
$192$		0			0
$193$	11.2631	+	6.50274i	0.810734	+	0.468077i	0.847211	−	0.531257i	$-0.178280\pi$
$193$	11.2631	+	6.50274i	0.810734	+	0.468077i	−0.0364770	+	0.999334i	$0.511614\pi$
$194$	−2.97666	−	5.15573i	−0.213712	−	0.370160i
$195$		0			0
$196$	2.09637	−	6.67871i	0.149741	−	0.477051i
$197$	18.4806			1.31669			0.658345	−	0.752716i	$-0.271257\pi$
$197$	18.4806			1.31669			0.658345	+	0.752716i	$0.271257\pi$
$198$		0			0
$199$	5.65478	−	9.79436i	0.400856	−	0.694304i	−0.592973	−	0.805222i	$-0.702046\pi$
$199$	5.65478	−	9.79436i	0.400856	−	0.694304i	0.993829	+	0.110919i	$0.0353793\pi$
$200$	0.379791	−	0.657818i	0.0268553	−	0.0465147i
$201$		0			0
$202$	3.90921			0.275051
$203$	−0.833552	−	7.56626i	−0.0585039	−	0.531048i
$204$		0			0
$205$	4.32676	−	2.49806i	0.302194	−	0.174472i
$206$	−1.72042	+	2.97985i	−0.119867	+	0.207616i
$207$		0			0
$208$	−6.04391	+	3.48945i	−0.419070	+	0.241950i
$209$	−22.5254	−	16.9980i	−1.55812	−	1.17578i
$210$		0			0
$211$			21.8547i			1.50454i	0.658854	+	0.752271i	$0.271041\pi$
$211$			21.8547i			1.50454i	−0.658854	+	0.752271i	$0.728959\pi$
$212$	−9.93207	+	5.73428i	−0.682137	+	0.393832i
$213$		0			0
$214$	−1.00997	+	1.74932i	−0.0690403	+	0.119581i
$215$	7.77577	+	13.4680i	0.530303	+	0.918512i
$216$		0			0
$217$	−21.2836	−	9.34873i	−1.44483	−	0.634633i
$218$		−	3.52747i		−	0.238910i
$219$		0			0
$220$	6.28856	−	2.66432i	0.423975	−	0.179629i
$221$	−32.2159	−	18.5998i	−2.16707	−	1.25116i
$222$		0			0
$223$	−18.3441			−1.22841			−0.614207	−	0.789145i	$-0.710524\pi$
$223$	−18.3441			−1.22841			−0.614207	+	0.789145i	$0.710524\pi$
$224$	2.42237	+	1.06401i	0.161851	+	0.0710924i
$225$		0			0
$226$	6.58287	−	3.80062i	0.437886	−	0.252814i
$227$	0.871542	−	1.50956i	0.0578463	−	0.100193i	−0.835652	−	0.549259i	$-0.814910\pi$
$227$	0.871542	−	1.50956i	0.0578463	−	0.100193i	0.893498	+	0.449066i	$0.148243\pi$
$228$		0			0
$229$	14.1778	+	24.5567i	0.936895	+	1.62275i	0.771219	+	0.636570i	$0.219647\pi$
$229$	14.1778	+	24.5567i	0.936895	+	1.62275i	0.165676	+	0.986180i	$0.447019\pi$
$230$	3.22205			0.212456
$231$		0			0
$232$	2.87708			0.188890
$233$	−10.4076	−	18.0264i	−0.681823	−	1.18095i	−0.974424	−	0.224717i	$-0.927854\pi$
$233$	−10.4076	−	18.0264i	−0.681823	−	1.18095i	0.292601	−	0.956235i	$-0.405479\pi$
$234$		0			0
$235$	12.1803	−	21.0968i	0.794553	−	1.37621i
$236$	3.49197	−	2.01609i	0.227308	−	0.131236i
$237$		0			0
$238$	1.54430	+	14.0178i	0.100102	+	0.908642i
$239$	−7.45803			−0.482420			−0.241210	−	0.970473i	$-0.577544\pi$
$239$	−7.45803			−0.482420			−0.241210	+	0.970473i	$0.577544\pi$
$240$		0			0
$241$	5.76722	+	3.32971i	0.371500	+	0.214485i	0.674113	−	0.738628i	$-0.264526\pi$
$241$	5.76722	+	3.32971i	0.371500	+	0.214485i	−0.302614	+	0.953113i	$0.597859\pi$
$242$	−10.6696	−	2.67555i	−0.685871	−	0.171991i
$243$		0			0
$244$		−	5.07151i		−	0.324670i
$245$	−10.6151	+	9.75198i	−0.678171	+	0.623031i
$246$		0			0
$247$	−29.6897	−	51.4242i	−1.88911	−	3.27204i
$248$	4.39314	−	7.60915i	0.278965	−	0.483181i
$249$		0			0
$250$	−10.2713	+	5.93015i	−0.649615	+	0.375055i
$251$			19.8684i			1.25408i	0.778986	+	0.627042i	$0.215734\pi$
$251$			19.8684i			1.25408i	−0.778986	+	0.627042i	$0.784266\pi$
$252$		0			0
$253$	−4.14240	−	3.12591i	−0.260430	−	0.196524i
$254$	−5.49001	+	3.16966i	−0.344474	+	0.198882i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−19.1251	+	11.0419i	−1.19299	+	0.688773i	−0.958983	−	0.283463i	$-0.908517\pi$
$257$	−19.1251	+	11.0419i	−1.19299	+	0.688773i	−0.234006	+	0.972235i	$0.575183\pi$
$258$		0			0
$259$	7.77267	−	5.70683i	0.482970	−	0.354605i
$260$	14.3712			0.891261
$261$		0			0
$262$	−6.50013	+	11.2586i	−0.401579	+	0.695556i
$263$	5.60069	−	9.70067i	0.345353	−	0.598169i	−0.640065	−	0.768321i	$-0.721093\pi$
$263$	5.60069	−	9.70067i	0.345353	−	0.598169i	0.985418	+	0.170152i	$0.0544258\pi$
$264$		0			0
$265$	23.6164			1.45074
$266$	−9.05308	+	20.6105i	−0.555080	+	1.26371i
$267$		0			0
$268$	−4.75461	−	8.23523i	−0.290434	−	0.503047i
$269$	−3.35811	−	1.93880i	−0.204747	−	0.118211i	0.394121	−	0.919059i	$-0.371049\pi$
$269$	−3.35811	−	1.93880i	−0.204747	−	0.118211i	−0.598868	+	0.800848i	$0.704383\pi$
$270$		0			0
$271$	2.49796	−	1.44220i	0.151740	−	0.0876073i	−0.422207	−	0.906499i	$-0.638745\pi$
$271$	2.49796	−	1.44220i	0.151740	−	0.0876073i	0.573948	+	0.818892i	$0.305411\pi$
$272$	−5.33030			−0.323197
$273$		0			0
$274$		−	9.20594i		−	0.556151i
$275$	2.50026	+	0.308708i	0.150772	+	0.0186158i
$276$		0			0
$277$	−18.4381	−	10.6453i	−1.10784	−	0.639612i	−0.169571	−	0.985518i	$-0.554238\pi$
$277$	−18.4381	−	10.6453i	−1.10784	−	0.639612i	−0.938269	+	0.345906i	$0.887572\pi$
$278$	16.0390	−	9.26012i	0.961955	−	0.555385i
$279$		0			0
$280$	−3.22439	−	4.39161i	−0.192694	−	0.262449i
$281$	14.7696			0.881078			0.440539	−	0.897733i	$-0.354787\pi$
$281$	14.7696			0.881078			0.440539	+	0.897733i	$0.354787\pi$
$282$		0			0
$283$	−0.509546	−	0.294187i	−0.0302894	−	0.0174876i	0.484779	−	0.874637i	$-0.338900\pi$
$283$	−0.509546	−	0.294187i	−0.0302894	−	0.0174876i	−0.515068	+	0.857149i	$0.672233\pi$
$284$	2.86172	+	1.65221i	0.169812	+	0.0980408i
$285$		0			0
$286$	−18.4761	−	13.9423i	−1.09252	−	0.824428i
$287$	0.702924	+	6.38054i	0.0414923	+	0.376631i
$288$		0			0
$289$	−5.70605	−	9.88317i	−0.335650	−	0.581363i
$290$	−5.13082	−	2.96228i	−0.301292	−	0.173951i
$291$		0			0
$292$	0.828178	−	0.478149i	0.0484654	−	0.0279815i
$293$	−1.57886			−0.0922380			−0.0461190	−	0.998936i	$-0.514685\pi$
$293$	−1.57886			−0.0922380			−0.0461190	+	0.998936i	$0.514685\pi$
$294$		0			0
$295$	−8.30318			−0.483430
$296$	1.82231	+	3.15633i	0.105919	+	0.183458i
$297$		0			0
$298$	6.04969	−	10.4784i	0.350449	−	0.606996i
$299$	−5.45991	−	9.45683i	−0.315754	−	0.546903i
$300$		0			0
$301$	−19.8609	+	2.18801i	−1.14476	+	0.126115i
$302$		−	5.16913i		−	0.297450i
$303$		0			0
$304$	−7.36851	−	4.25421i	−0.422613	−	0.243996i
$305$	−5.22170	+	9.04425i	−0.298994	+	0.517872i
$306$		0			0
$307$		−	14.9956i		−	0.855842i	−0.903816	−	0.427921i	$-0.859246\pi$
$307$		−	14.9956i		−	0.855842i	0.903816	−	0.427921i	$-0.140754\pi$
$308$	−0.115158	+	8.77421i	−0.00656171	+	0.499957i
$309$		0			0
$310$	−15.6690	+	9.04648i	−0.889937	+	0.513806i
$311$	9.46660	+	5.46555i	0.536802	+	0.309923i	0.743782	−	0.668422i	$-0.233030\pi$
$311$	9.46660	+	5.46555i	0.536802	+	0.309923i	−0.206980	+	0.978345i	$0.566363\pi$
$312$		0			0
$313$	6.10928	+	10.5816i	0.345317	+	0.598107i	0.985411	−	0.170190i	$-0.0544380\pi$
$313$	6.10928	+	10.5816i	0.345317	+	0.598107i	−0.640094	+	0.768296i	$0.721105\pi$
$314$	0.957476			0.0540335
$315$		0			0
$316$			8.95224i			0.503603i
$317$	−19.9526	+	11.5197i	−1.12065	+	0.647008i	−0.941567	−	0.336826i	$-0.890647\pi$
$317$	−19.9526	+	11.5197i	−1.12065	+	0.647008i	−0.179084	+	0.983834i	$0.557313\pi$
$318$		0			0
$319$	3.72250	+	8.78615i	0.208420	+	0.491930i
$320$	1.78334	−	1.02961i	0.0996919	−	0.0575572i
$321$		0			0
$322$	−1.66485	+	3.79025i	−0.0927785	+	0.211222i
$323$		−	45.3525i		−	2.52348i
$324$		0			0
$325$	4.59085	+	2.65053i	0.254654	+	0.147025i
$326$	−8.54401	+	14.7987i	−0.473209	+	0.819622i
$327$		0			0
$328$	−2.42621			−0.133965
$329$	18.5236	+	25.2291i	1.02124	+	1.39092i
$330$		0			0
$331$	−0.855231	−	1.48130i	−0.0470077	−	0.0814198i	0.841564	−	0.540157i	$-0.181635\pi$
$331$	−0.855231	−	1.48130i	−0.0470077	−	0.0814198i	−0.888572	+	0.458737i	$0.848302\pi$
$332$	−3.75353	+	6.50130i	−0.206002	+	0.356805i
$333$		0			0
$334$	−8.81000	−	15.2594i	−0.482062	−	0.834956i
$335$			19.5817i			1.06986i
$336$		0			0
$337$		−	4.45772i		−	0.242828i	−0.992602	−	0.121414i	$-0.961257\pi$
$337$		−	4.45772i		−	0.242828i	0.992602	−	0.121414i	$-0.0387428\pi$
$338$	−17.8526	−	30.9216i	−0.971052	−	1.68191i
$339$		0			0
$340$	9.50576	+	5.48815i	0.515522	+	0.297637i
$341$	28.9212	+	3.57090i	1.56617	+	0.193375i
$342$		0			0
$343$	−5.98688	−	17.5259i	−0.323261	−	0.946310i
$344$		−	7.55213i		−	0.407183i
$345$		0			0
$346$	−8.05455	+	13.9509i	−0.433016	+	0.750005i
$347$	9.27272	−	16.0608i	0.497786	−	0.862190i	−0.502211	−	0.864745i	$-0.667480\pi$
$347$	9.27272	−	16.0608i	0.497786	−	0.862190i	0.999997	+	0.00255476i	$0.000813206\pi$
$348$		0			0
$349$			16.0494i			0.859104i	0.903042	+	0.429552i	$0.141329\pi$
$349$			16.0494i			0.859104i	−0.903042	+	0.429552i	$0.858671\pi$
$350$	−0.220067	−	1.99758i	−0.0117631	−	0.106775i
$351$		0			0
$352$	−3.29163	−	0.406418i	−0.175444	−	0.0216621i
$353$	−5.81710	−	3.35850i	−0.309613	−	0.178755i	0.337140	−	0.941454i	$-0.390540\pi$
$353$	−5.81710	−	3.35850i	−0.309613	−	0.178755i	−0.646753	+	0.762699i	$0.723874\pi$
$354$		0			0
$355$	−3.40228	−	5.89292i	−0.180574	−	0.312764i
$356$		−	3.45457i		−	0.183092i
$357$		0			0
$358$		−	9.22784i		−	0.487707i
$359$	17.4909	+	30.2952i	0.923136	+	1.59892i	0.794531	+	0.607223i	$0.207717\pi$
$359$	17.4909	+	30.2952i	0.923136	+	1.59892i	0.128605	+	0.991696i	$0.458950\pi$
$360$		0			0
$361$	26.6966	−	46.2399i	1.40509	−	2.43368i
$362$	2.73173	+	4.73150i	0.143577	+	0.248682i
$363$		0			0
$364$	−7.42565	+	16.9055i	−0.389210	+	0.886089i
$365$	−1.96923			−0.103074
$366$		0			0
$367$	1.89294	−	3.27867i	0.0988107	−	0.171145i	−0.812382	−	0.583126i	$-0.801830\pi$
$367$	1.89294	−	3.27867i	0.0988107	−	0.171145i	0.911193	+	0.411981i	$0.135163\pi$
$368$	−1.35506	−	0.782344i	−0.0706374	−	0.0407825i
$369$		0			0
$370$		−	7.50508i		−	0.390171i
$371$	−12.2027	+	27.7811i	−0.633533	+	1.44232i
$372$		0			0
$373$	−16.3482	+	9.43867i	−0.846480	+	0.488716i	−0.859462	−	0.511200i	$-0.829201\pi$
$373$	−16.3482	+	9.43867i	−0.846480	+	0.488716i	0.0129814	+	0.999916i	$0.495868\pi$
$374$	−6.89659	−	16.2779i	−0.356614	−	0.841710i
$375$		0			0
$376$	−10.2450	+	5.91497i	−0.528347	+	0.305041i
$377$			20.0789i			1.03411i
$378$		0			0
$379$	14.1679			0.727755			0.363878	−	0.931447i	$-0.381453\pi$
$379$	14.1679			0.727755			0.363878	+	0.931447i	$0.381453\pi$
$380$	8.76039	+	15.1734i	0.449399	+	0.778381i
$381$		0			0
$382$	17.8512	+	10.3064i	0.913349	+	0.527322i
$383$	−23.0987	+	13.3360i	−1.18029	+	0.681439i	−0.956081	−	0.293103i	$-0.905312\pi$
$383$	−23.0987	+	13.3360i	−1.18029	+	0.681439i	−0.224206	+	0.974542i	$0.571979\pi$
$384$		0			0
$385$	9.23941	−	15.5289i	0.470884	−	0.791424i
$386$			13.0055i			0.661961i
$387$		0			0
$388$	2.97666	−	5.15573i	0.151117	−	0.261742i
$389$	−2.99247	−	1.72771i	−0.151724	−	0.0875981i	0.422216	−	0.906495i	$-0.361252\pi$
$389$	−2.99247	−	1.72771i	−0.151724	−	0.0875981i	−0.573940	+	0.818897i	$0.694586\pi$
$390$		0			0
$391$		−	8.34026i		−	0.421785i
$392$	6.83212	−	1.52384i	0.345074	−	0.0769657i
$393$		0			0
$394$	9.24031	+	16.0047i	0.465520	+	0.806305i
$395$	9.21735	−	15.9649i	0.463775	−	0.803283i
$396$		0			0
$397$	11.1910	+	19.3833i	0.561659	+	0.972822i	0.997352	+	0.0727269i	$0.0231701\pi$
$397$	11.1910	+	19.3833i	0.561659	+	0.972822i	−0.435693	+	0.900096i	$0.643497\pi$
$398$	11.3096			0.566897
$399$		0			0
$400$	0.759582			0.0379791
$401$	5.81710	−	3.35850i	0.290492	−	0.167716i	−0.347672	−	0.937616i	$-0.613028\pi$
$401$	5.81710	−	3.35850i	0.290492	−	0.167716i	0.638164	+	0.769901i	$0.279694\pi$
$402$		0			0
$403$	53.1035	+	30.6593i	2.64528	+	1.52725i
$404$	1.95460	+	3.38547i	0.0972451	+	0.168434i
$405$		0			0
$406$	6.13580	−	4.50501i	0.304515	−	0.223580i
$407$	−7.28114	+	9.64884i	−0.360913	+	0.478275i
$408$		0			0
$409$	1.30162	+	0.751492i	0.0643611	+	0.0371589i	0.531835	−	0.846848i	$-0.321503\pi$
$409$	1.30162	+	0.751492i	0.0643611	+	0.0371589i	−0.467474	+	0.884007i	$0.654836\pi$
$410$	4.32676	+	2.49806i	0.213683	+	0.123370i
$411$		0			0
$412$	−3.44084			−0.169518
$413$	4.29030	−	9.76744i	0.211112	−	0.480624i
$414$		0			0
$415$	13.3877	−	7.72937i	0.657175	−	0.379420i
$416$	−6.04391	−	3.48945i	−0.296327	−	0.171085i
$417$		0			0
$418$	3.45797	−	28.0066i	0.169135	−	1.36985i
$419$			15.6194i			0.763058i	0.924357	+	0.381529i	$0.124602\pi$
$419$			15.6194i			0.763058i	−0.924357	+	0.381529i	$0.875398\pi$
$420$		0			0
$421$	9.70442			0.472965			0.236482	−	0.971636i	$-0.424005\pi$
$421$	9.70442			0.472965			0.236482	+	0.971636i	$0.424005\pi$
$422$	−18.9267	+	10.9274i	−0.921339	+	0.531936i
$423$		0			0
$424$	−9.93207	−	5.73428i	−0.482344	−	0.278481i
$425$	2.02440	+	3.50637i	0.0981979	+	0.170084i
$426$		0			0
$427$	−7.94111	−	10.8158i	−0.384297	−	0.523411i
$428$	−2.01995			−0.0976377
$429$		0			0
$430$	−7.77577	+	13.4680i	−0.374981	+	0.649486i
$431$	−11.7521	+	20.3553i	−0.566081	+	0.980480i	0.430868	+	0.902415i	$0.358208\pi$
$431$	−11.7521	+	20.3553i	−0.566081	+	0.980480i	−0.996948	+	0.0780652i	$0.975126\pi$
$432$		0			0
$433$	−18.3720			−0.882902			−0.441451	−	0.897285i	$-0.645536\pi$
$433$	−18.3720			−0.882902			−0.441451	+	0.897285i	$0.645536\pi$
$434$	−2.54558	−	23.1065i	−0.122192	−	1.10915i
$435$		0			0
$436$	3.05488	−	1.76373i	0.146302	−	0.0844675i
$437$	6.65651	−	11.5294i	0.318424	−	0.551527i
$438$		0			0
$439$	11.8078	−	6.81724i	0.563556	−	0.325369i	−0.191016	−	0.981587i	$-0.561178\pi$
$439$	11.8078	−	6.81724i	0.563556	−	0.325369i	0.754571	+	0.656218i	$0.227845\pi$
$440$	5.45165	+	4.11389i	0.259897	+	0.196122i
$441$		0			0
$442$		−	37.1997i		−	1.76941i
$443$	−18.9667	+	10.9504i	−0.901133	+	0.520270i	−0.877568	−	0.479453i	$-0.840835\pi$
$443$	−18.9667	+	10.9504i	−0.901133	+	0.520270i	−0.0235656	+	0.999722i	$0.507502\pi$
$444$		0			0
$445$	−3.55687	+	6.16068i	−0.168612	+	0.292044i
$446$	−9.17207	−	15.8865i	−0.434310	−	0.752247i
$447$		0			0
$448$	0.289722	+	2.62984i	0.0136881	+	0.124248i
$449$		−	34.6012i		−	1.63293i	−0.577395	−	0.816465i	$-0.695931\pi$
$449$		−	34.6012i		−	1.63293i	0.577395	−	0.816465i	$-0.304069\pi$
$450$		0			0
$451$	−3.13914	−	7.40926i	−0.147816	−	0.348888i
$452$	6.58287	+	3.80062i	0.309632	+	0.178766i
$453$		0			0
$454$	1.74308			0.0818070
$455$	30.6486	−	22.5027i	1.43683	−	1.05494i
$456$		0			0
$457$	−22.7285	+	13.1223i	−1.06319	+	0.613835i	−0.926314	−	0.376753i	$-0.877041\pi$
$457$	−22.7285	+	13.1223i	−1.06319	+	0.613835i	−0.136879	+	0.990588i	$0.543707\pi$
$458$	−14.1778	+	24.5567i	−0.662485	+	1.14746i
$459$		0			0
$460$	1.61102	+	2.79038i	0.0751144	+	0.130102i
$461$	−42.1747			−1.96427			−0.982136	−	0.188175i	$-0.939743\pi$
$461$	−42.1747			−1.96427			−0.982136	+	0.188175i	$0.939743\pi$
$462$		0			0
$463$	26.1308			1.21440			0.607200	−	0.794549i	$-0.292293\pi$
$463$	26.1308			1.21440			0.607200	+	0.794549i	$0.292293\pi$
$464$	1.43854	+	2.49162i	0.0667826	+	0.115671i
$465$		0			0
$466$	10.4076	−	18.0264i	0.482121	−	0.835059i
$467$	4.98050	−	2.87549i	0.230470	−	0.133062i	−0.380319	−	0.924855i	$-0.624186\pi$
$467$	4.98050	−	2.87549i	0.230470	−	0.133062i	0.610789	+	0.791794i	$0.290852\pi$
$468$		0			0
$469$	−23.0349	−	10.1179i	−1.06365	−	0.467203i
$470$	24.3605			1.12367
$471$		0			0
$472$	3.49197	+	2.01609i	0.160731	+	0.0927981i
$473$	23.0630	−	9.77129i	1.06044	−	0.449285i
$474$		0			0
$475$			6.46285i			0.296536i
$476$	−11.3677	+	8.34633i	−0.521036	+	0.382553i
$477$		0			0
$478$	−3.72902	−	6.45884i	−0.170561	−	0.295421i
$479$	−6.97303	+	12.0776i	−0.318606	+	0.551842i	−0.980197	−	0.198023i	$-0.936548\pi$
$479$	−6.97303	+	12.0776i	−0.318606	+	0.551842i	0.661591	+	0.749865i	$0.269881\pi$
$480$		0			0
$481$	−22.0277	+	12.7177i	−1.00438	+	0.579877i
$482$			6.65942i			0.303328i
$483$		0			0
$484$	−3.01773	−	10.5780i	−0.137169	−	0.480817i
$485$	−10.6168	+	6.12962i	−0.482085	+	0.278332i
$486$		0			0
$487$	−7.77700	+	13.4702i	−0.352410	+	0.610391i	−0.986671	−	0.162727i	$-0.947971\pi$
$487$	−7.77700	+	13.4702i	−0.352410	+	0.610391i	0.634261	+	0.773119i	$0.281304\pi$
$488$	4.39206	−	2.53576i	0.198819	−	0.114788i
$489$		0			0
$490$	−13.7530	−	4.31691i	−0.621297	−	0.195018i
$491$	−14.7267			−0.664609			−0.332304	−	0.943172i	$-0.607826\pi$
$491$	−14.7267			−0.664609			−0.332304	+	0.943172i	$0.607826\pi$
$492$		0			0
$493$	−7.66785	+	13.2811i	−0.345343	+	0.598151i
$494$	29.6897	−	51.4242i	1.33580	−	2.31368i
$495$		0			0
$496$	8.78629			0.394516
$497$	8.69011	−	0.957363i	0.389805	−	0.0429436i
$498$		0			0
$499$	3.51020	+	6.07984i	0.157138	+	0.272171i	0.933835	−	0.357703i	$-0.116440\pi$
$499$	3.51020	+	6.07984i	0.157138	+	0.272171i	−0.776697	+	0.629874i	$0.783107\pi$
$500$	−10.2713	−	5.93015i	−0.459347	−	0.265204i
$501$		0			0
$502$	−17.2066	+	9.93421i	−0.767966	+	0.443385i
$503$	−20.7055			−0.923213			−0.461607	−	0.887085i	$-0.652727\pi$
$503$	−20.7055			−0.923213			−0.461607	+	0.887085i	$0.652727\pi$
$504$		0			0
$505$		−	8.04994i		−	0.358218i
$506$	0.635917	−	5.15037i	0.0282699	−	0.228962i
$507$		0			0
$508$	−5.49001	−	3.16966i	−0.243580	−	0.140631i
$509$	19.4116	−	11.2073i	0.860403	−	0.496754i	−0.00374431	−	0.999993i	$-0.501192\pi$
$509$	19.4116	−	11.2073i	0.860403	−	0.496754i	0.864147	+	0.503239i	$0.167859\pi$
$510$		0			0
$511$	1.01751	−	2.31651i	0.0450122	−	0.102476i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−19.1251	−	11.0419i	−0.843571	−	0.487036i
$515$	6.13620	+	3.54273i	0.270393	+	0.156112i
$516$		0			0
$517$	−31.3189	−	23.6336i	−1.37740	−	1.03941i
$518$	8.82859	+	3.87792i	0.387906	+	0.170386i
$519$		0			0
$520$	7.18558	+	12.4458i	0.315108	+	0.545784i
$521$	20.0520	+	11.5770i	0.878494	+	0.507199i	0.870161	−	0.492767i	$-0.164014\pi$
$521$	20.0520	+	11.5770i	0.878494	+	0.507199i	0.00833225	+	0.999965i	$0.497348\pi$
$522$		0			0
$523$	−18.0181	+	10.4027i	−0.787875	+	0.454880i	−0.839214	−	0.543801i	$-0.816985\pi$
$523$	−18.0181	+	10.4027i	−0.787875	+	0.454880i	0.0513386	+	0.998681i	$0.483651\pi$
$524$	−13.0003			−0.567919
$525$		0			0
$526$	11.2014			0.488403
$527$	23.4168	+	40.5590i	1.02005	+	1.76678i
$528$		0			0
$529$	−10.2759	+	17.7983i	−0.446777	+	0.773841i
$530$	11.8082	+	20.4524i	0.512915	+	0.888395i
$531$		0			0
$532$	−22.3758	+	2.46507i	−0.970114	+	0.106875i
$533$		−	16.9323i		−	0.733418i
$534$		0			0
$535$	3.60226	+	2.07976i	0.155739	+	0.0899160i
$536$	4.75461	−	8.23523i	0.205368	−	0.355708i
$537$		0			0
$538$		−	3.87761i		−	0.167175i
$539$	13.4933	+	18.8926i	0.581197	+	0.813763i
$540$		0			0
$541$	16.4366	−	9.48967i	0.706664	−	0.407993i	−0.103160	−	0.994665i	$-0.532896\pi$
$541$	16.4366	−	9.48967i	0.706664	−	0.407993i	0.809825	+	0.586672i	$0.199562\pi$
$542$	2.49796	+	1.44220i	0.107297	+	0.0619477i
$543$		0			0
$544$	−2.66515	−	4.61618i	−0.114267	−	0.197917i
$545$	−7.26386			−0.311149
$546$		0			0
$547$			27.3881i			1.17103i	0.810661	+	0.585515i	$0.199108\pi$
$547$			27.3881i			1.17103i	−0.810661	+	0.585515i	$0.800892\pi$
$548$	7.97258	−	4.60297i	0.340572	−	0.196629i
$549$		0			0
$550$	0.982783	+	2.31965i	0.0419060	+	0.0989100i
$551$	−21.1998	+	12.2397i	−0.903142	+	0.521429i
$552$		0			0
$553$	14.0177	+	19.0920i	0.596092	+	0.811874i
$554$		−	21.2905i		−	0.904548i
$555$		0			0
$556$	16.0390	+	9.26012i	0.680205	+	0.392717i
$557$	5.98411	−	10.3648i	0.253555	−	0.439170i	−0.710947	−	0.703245i	$-0.751734\pi$
$557$	5.98411	−	10.3648i	0.253555	−	0.439170i	0.964502	+	0.264076i	$0.0850669\pi$
$558$		0			0
$559$	52.7056			2.22921
$560$	2.19105	−	4.98821i	0.0925886	−	0.210790i
$561$		0			0
$562$	7.38478	+	12.7908i	0.311508	+	0.539548i
$563$	−3.34982	+	5.80206i	−0.141178	+	0.244527i	−0.927940	−	0.372728i	$-0.878422\pi$
$563$	−3.34982	+	5.80206i	−0.141178	+	0.244527i	0.786762	+	0.617256i	$0.211756\pi$
$564$		0			0
$565$	−7.82635	−	13.5556i	−0.329257	−	0.570290i
$566$		−	0.588373i		−	0.0247312i
$567$		0			0
$568$			3.30443i			0.138651i
$569$	−7.52076	−	13.0263i	−0.315287	−	0.546092i	0.664212	−	0.747544i	$-0.268767\pi$
$569$	−7.52076	−	13.0263i	−0.315287	−	0.546092i	−0.979498	+	0.201452i	$0.935434\pi$
$570$		0			0
$571$	24.3794	+	14.0755i	1.02025	+	0.589040i	0.914176	−	0.405318i	$-0.132839\pi$
$571$	24.3794	+	14.0755i	1.02025	+	0.589040i	0.106072	+	0.994358i	$0.466173\pi$
$572$	2.83635	−	22.9720i	0.118594	−	0.960507i
$573$		0			0
$574$	−5.17424	+	3.79902i	−0.215969	+	0.158568i
$575$			1.18851i			0.0495643i
$576$		0			0
$577$	−11.3717	+	19.6964i	−0.473410	+	0.819970i	−0.999537	−	0.0304358i	$-0.990310\pi$
$577$	−11.3717	+	19.6964i	−0.473410	+	0.819970i	0.526127	+	0.850406i	$0.323644\pi$
$578$	5.70605	−	9.88317i	0.237340	−	0.411086i
$579$		0			0
$580$		−	5.92456i		−	0.246004i
$581$	2.17496	+	19.7424i	0.0902324	+	0.819051i
$582$		0			0
$583$	4.66103	−	37.7503i	0.193040	−	1.56346i
$584$	0.828178	+	0.478149i	0.0342702	+	0.0197859i
$585$		0			0
$586$	−0.789430	−	1.36733i	−0.0326110	−	0.0564840i
$587$		−	18.9106i		−	0.780523i	−0.920704	−	0.390261i	$-0.872385\pi$
$587$		−	18.9106i		−	0.780523i	0.920704	−	0.390261i	$-0.127615\pi$
$588$		0			0
$589$			74.7574i			3.08033i
$590$	−4.15159	−	7.19077i	−0.170918	−	0.296039i
$591$		0			0
$592$	−1.82231	+	3.15633i	−0.0748963	+	0.129724i
$593$	−16.7412	−	28.9966i	−0.687479	−	1.19075i	−0.972651	−	0.232273i	$-0.925384\pi$
$593$	−16.7412	−	28.9966i	−0.687479	−	1.19075i	0.285171	−	0.958477i	$-0.407949\pi$
$594$		0			0
$595$	28.8659	−	3.18007i	1.18339	−	0.130370i
$596$	12.0994			0.495610
$597$		0			0
$598$	5.45991	−	9.45683i	0.223272	−	0.386719i
$599$	−7.22458	−	4.17111i	−0.295188	−	0.170427i	0.345091	−	0.938569i	$-0.387848\pi$
$599$	−7.22458	−	4.17111i	−0.295188	−	0.170427i	−0.640279	+	0.768142i	$0.721181\pi$
$600$		0			0
$601$			18.8871i			0.770420i	0.922829	+	0.385210i	$0.125871\pi$
$601$			18.8871i			0.770420i	−0.922829	+	0.385210i	$0.874129\pi$
$602$	−11.8253	−	16.1060i	−0.481964	−	0.656433i
$603$		0			0
$604$	4.47659	−	2.58456i	0.182150	−	0.105164i
$605$	−5.50957	+	21.9712i	−0.223996	+	0.893258i
$606$		0			0
$607$	34.0729	−	19.6720i	1.38298	−	0.798461i	0.390464	−	0.920618i	$-0.372314\pi$
$607$	34.0729	−	19.6720i	1.38298	−	0.798461i	0.992511	+	0.122157i	$0.0389812\pi$
$608$		−	8.50842i		−	0.345062i
$609$		0			0
$610$	−10.4434			−0.422841
$611$	−41.2800	−	71.4991i	−1.67001	−	2.89254i
$612$		0			0
$613$	−8.07950	−	4.66470i	−0.326328	−	0.188405i	0.327882	−	0.944719i	$-0.393665\pi$
$613$	−8.07950	−	4.66470i	−0.326328	−	0.188405i	−0.654210	+	0.756313i	$0.726999\pi$
$614$	12.9865	−	7.49778i	0.524094	−	0.302586i
$615$		0			0
$616$	−7.65627	+	4.28737i	−0.308480	+	0.172743i
$617$			46.3271i			1.86506i	0.361093	+	0.932530i	$0.382404\pi$
$617$			46.3271i			1.86506i	−0.361093	+	0.932530i	$0.617596\pi$
$618$		0			0
$619$	12.3541	−	21.3979i	0.496552	−	0.860053i	−0.503440	−	0.864030i	$-0.667933\pi$
$619$	12.3541	−	21.3979i	0.496552	−	0.860053i	0.999992	+	0.00397706i	$0.00126594\pi$
$620$	−15.6690	−	9.04648i	−0.629281	−	0.363315i
$621$		0			0
$622$			10.9311i			0.438297i
$623$	−5.40925	−	7.36737i	−0.216717	−	0.295168i
$624$		0			0
$625$	10.3126	+	17.8619i	0.412502	+	0.714475i
$626$	−6.10928	+	10.5816i	−0.244176	+	0.422925i
$627$		0			0
$628$	0.478738	+	0.829198i	0.0191037	+	0.0330886i
$629$	−19.4269			−0.774600
$630$		0			0
$631$	−15.6824			−0.624306			−0.312153	−	0.950032i	$-0.601050\pi$
$631$	−15.6824			−0.624306			−0.312153	+	0.950032i	$0.601050\pi$
$632$	−7.75287	+	4.47612i	−0.308393	+	0.178051i
$633$		0			0
$634$	−19.9526	−	11.5197i	−0.792420	−	0.457504i
$635$	6.52705	+	11.3052i	0.259018	+	0.448632i
$636$		0			0
$637$	10.6348	+	47.6807i	0.421364	+	1.88918i
$638$	−5.74778	+	7.61686i	−0.227557	+	0.301554i
$639$		0			0
$640$	1.78334	+	1.02961i	0.0704928	+	0.0406991i
$641$	−21.5853	−	12.4623i	−0.852568	−	0.492231i	0.00894816	−	0.999960i	$-0.497152\pi$
$641$	−21.5853	−	12.4623i	−0.852568	−	0.492231i	−0.861517	+	0.507729i	$0.830485\pi$
$642$		0			0
$643$	−22.4327			−0.884658			−0.442329	−	0.896853i	$-0.645848\pi$
$643$	−22.4327			−0.884658			−0.442329	+	0.896853i	$0.645848\pi$
$644$	−4.11488	+	0.453324i	−0.162149	+	0.0178635i
$645$		0			0
$646$	39.2764	−	22.6762i	1.54531	−	0.892184i
$647$	−23.0631	−	13.3155i	−0.906705	−	0.523486i	−0.0273356	−	0.999626i	$-0.508702\pi$
$647$	−23.0631	−	13.3155i	−0.906705	−	0.523486i	−0.879370	+	0.476140i	$0.842036\pi$
$648$		0			0
$649$	−1.63875	+	13.2725i	−0.0643266	+	0.520989i
$650$			5.30106i			0.207924i
$651$		0			0
$652$	−17.0880			−0.669219
$653$	5.78961	−	3.34263i	0.226565	−	0.130807i	−0.382421	−	0.923988i	$-0.624910\pi$
$653$	5.78961	−	3.34263i	0.226565	−	0.130807i	0.608986	+	0.793181i	$0.291576\pi$
$654$		0			0
$655$	23.1839	+	13.3852i	0.905871	+	0.523005i
$656$	−1.21310	−	2.10116i	−0.0473637	−	0.0820364i
$657$		0			0
$658$	−12.5872	+	28.6565i	−0.490701	+	1.11715i
$659$	−1.73849			−0.0677218			−0.0338609	−	0.999427i	$-0.510780\pi$
$659$	−1.73849			−0.0677218			−0.0338609	+	0.999427i	$0.510780\pi$
$660$		0			0
$661$	13.9433	−	24.1506i	0.542333	−	0.939349i	−0.456436	−	0.889756i	$-0.650874\pi$
$661$	13.9433	−	24.1506i	0.542333	−	0.939349i	0.998770	−	0.0495927i	$-0.0157923\pi$
$662$	0.855231	−	1.48130i	0.0332395	−	0.0575725i
$663$		0			0
$664$	−7.50706			−0.291330
$665$	42.4418	+	18.6424i	1.64582	+	0.722920i
$666$		0			0
$667$	−3.89861	+	2.25087i	−0.150955	+	0.0871539i
$668$	8.81000	−	15.2594i	0.340869	−	0.590403i
$669$		0			0
$670$	−16.9582	+	9.79083i	−0.655153	+	0.378253i
$671$	13.4265	+	10.1318i	0.518323	+	0.391133i
$672$		0			0
$673$		−	3.61388i		−	0.139305i	−0.997571	−	0.0696525i	$-0.977811\pi$
$673$		−	3.61388i		−	0.139305i	0.997571	−	0.0696525i	$-0.0221890\pi$
$674$	3.86050	−	2.22886i	0.148701	−	0.0858526i
$675$		0			0
$676$	17.8526	−	30.9216i	0.686637	−	1.18929i
$677$	7.73709	+	13.4010i	0.297361	+	0.515044i	0.975531	−	0.219861i	$-0.0705603\pi$
$677$	7.73709	+	13.4010i	0.297361	+	0.515044i	−0.678171	+	0.734904i	$0.737227\pi$
$678$		0			0
$679$	−1.72480	−	15.6563i	−0.0661919	−	0.600833i
$680$			10.9763i			0.420922i
$681$		0			0
$682$	11.3681	+	26.8319i	0.435307	+	1.02745i
$683$	22.4201	+	12.9442i	0.857879	+	0.495297i	0.863302	−	0.504688i	$-0.168393\pi$
$683$	22.4201	+	12.9442i	0.857879	+	0.495297i	−0.00542219	+	0.999985i	$0.501726\pi$
$684$		0			0
$685$	−18.9571			−0.724315
$686$	12.1844	−	13.9477i	0.465204	−	0.532527i
$687$		0			0
$688$	6.54033	−	3.77606i	0.249348	−	0.143961i
$689$	40.0190	−	69.3150i	1.52460	−	2.64069i
$690$		0			0
$691$	22.4617	+	38.9047i	0.854481	+	1.48001i	0.877125	+	0.480262i	$0.159458\pi$
$691$	22.4617	+	38.9047i	0.854481	+	1.48001i	−0.0226438	+	0.999744i	$0.507208\pi$
$692$	−16.1091			−0.612376
$693$		0			0
$694$	18.5454			0.703976
$695$	−19.0687	−	33.0279i	−0.723317	−	1.25282i
$696$		0			0
$697$	6.46621	−	11.1998i	0.244925	−	0.424223i
$698$	−13.8992	+	8.02470i	−0.526092	+	0.303739i
$699$		0			0
$700$	1.61992	−	1.18937i	0.0612273	−	0.0449541i
$701$	10.0235			0.378583			0.189292	−	0.981921i	$-0.439381\pi$
$701$	10.0235			0.378583			0.189292	+	0.981921i	$0.439381\pi$
$702$		0			0
$703$	−26.8554	−	15.5049i	−1.01287	−	0.584780i
$704$	−1.29385	−	3.05384i	−0.0487637	−	0.115096i
$705$		0			0
$706$		−	6.71701i		−	0.252798i
$707$	9.46954	+	4.15945i	0.356139	+	0.156432i
$708$		0			0
$709$	9.17467	+	15.8910i	0.344562	+	0.596799i	0.985274	−	0.170982i	$-0.0546941\pi$
$709$	9.17467	+	15.8910i	0.344562	+	0.596799i	−0.640712	+	0.767781i	$0.721361\pi$
$710$	3.40228	−	5.89292i	0.127685	−	0.221158i
$711$		0			0
$712$	2.99174	−	1.72728i	0.112120	−	0.0647327i
$713$			13.7478i			0.514859i
$714$		0			0
$715$	−28.7104	+	38.0466i	−1.07371	+	1.42286i
$716$	7.99155	−	4.61392i	0.298658	−	0.172430i
$717$		0			0
$718$	−17.4909	+	30.2952i	−0.652756	+	1.13061i
$719$	40.5198	−	23.3941i	1.51113	−	0.872454i	0.511219	−	0.859450i	$-0.329194\pi$
$719$	40.5198	−	23.3941i	1.51113	−	0.872454i	0.999915	−	0.0130036i	$-0.00413929\pi$
$720$		0			0
$721$	−7.33810	+	5.38776i	−0.273285	+	0.200651i
$722$	53.3933			1.98709
$723$		0			0
$724$	−2.73173	+	4.73150i	−0.101524	+	0.175845i
$725$	1.09269	−	1.89259i	0.0405815	−	0.0702892i
$726$		0			0
$727$	−6.15090			−0.228124			−0.114062	−	0.993474i	$-0.536386\pi$
$727$	−6.15090			−0.228124			−0.114062	+	0.993474i	$0.536386\pi$
$728$	−18.3534	+	2.02194i	−0.680223	+	0.0749381i
$729$		0			0
$730$	−0.984617	−	1.70541i	−0.0364423	−	0.0631199i
$731$	34.8619	+	20.1276i	1.28942	+	0.744444i
$732$		0			0
$733$	18.6845	−	10.7875i	0.690128	−	0.398446i	−0.113532	−	0.993534i	$-0.536216\pi$
$733$	18.6845	−	10.7875i	0.690128	−	0.398446i	0.803660	+	0.595089i	$0.202883\pi$
$734$	3.78588			0.139739
$735$		0			0
$736$		−	1.56469i		−	0.0576752i
$737$	31.3008	+	3.86472i	1.15298	+	0.142359i
$738$		0			0
$739$	21.3942	+	12.3520i	0.787000	+	0.454375i	0.838905	−	0.544277i	$-0.183196\pi$
$739$	21.3942	+	12.3520i	0.787000	+	0.454375i	−0.0519053	+	0.998652i	$0.516529\pi$
$740$	6.49959	−	3.75254i	0.238930	−	0.137946i
$741$		0			0
$742$	−30.1605	+	3.32269i	−1.10723	+	0.121980i
$743$	10.6465			0.390583			0.195292	−	0.980745i	$-0.437435\pi$
$743$	10.6465			0.390583			0.195292	+	0.980745i	$0.437435\pi$
$744$		0			0
$745$	−21.5774	−	12.4577i	−0.790533	−	0.456414i
$746$	−16.3482	−	9.43867i	−0.598552	−	0.345574i
$747$		0			0
$748$	10.6488	−	14.1116i	0.389358	−	0.515970i
$749$	−4.30783	+	3.16288i	−0.157405	+	0.115569i
$750$		0			0
$751$	15.2351	+	26.3879i	0.555935	+	0.962908i	0.997830	+	0.0658410i	$0.0209730\pi$
$751$	15.2351	+	26.3879i	0.555935	+	0.962908i	−0.441895	+	0.897067i	$0.645694\pi$
$752$	−10.2450	−	5.91497i	−0.373598	−	0.215697i
$753$		0			0
$754$	−17.3888	+	10.0394i	−0.633263	+	0.365615i
$755$	−10.6444			−0.387390
$756$		0			0
$757$	43.9876			1.59876			0.799379	−	0.600827i	$-0.205162\pi$
$757$	43.9876			1.59876			0.799379	+	0.600827i	$0.205162\pi$
$758$	7.08394	+	12.2697i	0.257300	+	0.445657i
$759$		0			0
$760$	−8.76039	+	15.1734i	−0.317773	+	0.550399i
$761$	2.85261	+	4.94087i	0.103407	+	0.179106i	0.913086	−	0.407766i	$-0.133692\pi$
$761$	2.85261	+	4.94087i	0.103407	+	0.179106i	−0.809679	+	0.586873i	$0.800359\pi$
$762$		0			0
$763$	3.75327	−	8.54483i	0.135878	−	0.309344i
$764$			20.6128i			0.745746i
$765$		0			0
$766$	−23.0987	−	13.3360i	−0.834589	−	0.481850i
$767$	−14.0701	+	24.3702i	−0.508042	+	0.879955i
$768$		0			0
$769$			4.02217i			0.145043i	0.997367	+	0.0725215i	$0.0231046\pi$
$769$			4.02217i			0.145043i	−0.997367	+	0.0725215i	$0.976895\pi$
$770$	18.0681	+	0.237136i	0.651129	+	0.00854578i
$771$		0			0
$772$	−11.2631	+	6.50274i	−0.405367	+	0.234039i
$773$	13.6864	+	7.90184i	0.492265	+	0.284210i	0.725514	−	0.688208i	$-0.241602\pi$
$773$	13.6864	+	7.90184i	0.492265	+	0.284210i	−0.233248	+	0.972417i	$0.574936\pi$
$774$		0			0
$775$	−3.33695	−	5.77977i	−0.119867	−	0.207616i
$776$	5.95332			0.213712
$777$		0			0
$778$		−	3.45541i		−	0.123882i
$779$	17.8775	−	10.3216i	0.640529	−	0.369810i
$780$		0			0
$781$	−10.0912	+	4.27542i	−0.361091	+	0.152987i
$782$	7.22287	−	4.17013i	0.258289	−	0.149123i
$783$		0			0
$784$	4.73575	+	5.15487i	0.169134	+	0.184103i
$785$		−	1.97166i		−	0.0703716i
$786$		0			0
$787$	9.40102	+	5.42768i	0.335110	+	0.193476i	0.658108	−	0.752924i	$-0.271357\pi$
$787$	9.40102	+	5.42768i	0.335110	+	0.193476i	−0.322997	+	0.946400i	$0.604691\pi$
$788$	−9.24031	+	16.0047i	−0.329172	+	0.570143i
$789$		0			0
$790$	18.4347			0.655877
$791$	19.9901	−	2.20225i	0.710765	−	0.0783028i
$792$		0			0
$793$	17.6968	+	30.6518i	0.628432	+	1.08848i
$794$	−11.1910	+	19.3833i	−0.397153	+	0.687889i
$795$		0			0
$796$	5.65478	+	9.79436i	0.200428	+	0.347152i
$797$		−	53.5614i		−	1.89724i	−0.316414	−	0.948621i	$-0.602479\pi$
$797$		−	53.5614i		−	1.89724i	0.316414	−	0.948621i	$-0.397521\pi$
$798$		0			0
$799$		−	63.0571i		−	2.23080i
$800$	0.379791	+	0.657818i	0.0134276	+	0.0232574i
$801$		0			0
$802$	5.81710	+	3.35850i	0.205409	+	0.118593i
$803$	−0.388656	+	3.14778i	−0.0137154	+	0.111083i
$804$		0			0
$805$	7.80499	+	3.42830i	0.275090	+	0.120832i
$806$			61.3187i			2.15986i
$807$		0			0
$808$	−1.95460	+	3.38547i	−0.0687627	+	0.119100i
$809$	−11.3084	+	19.5867i	−0.397582	+	0.688632i	−0.993427	−	0.114468i	$-0.963484\pi$
$809$	−11.3084	+	19.5867i	−0.397582	+	0.688632i	0.595845	+	0.803099i	$0.296817\pi$
$810$		0			0
$811$			4.51083i			0.158396i	0.996859	+	0.0791982i	$0.0252360\pi$
$811$			4.51083i			0.158396i	−0.996859	+	0.0791982i	$0.974764\pi$
$812$	6.96935	+	3.06125i	0.244576	+	0.107429i
$813$		0			0
$814$	−11.9967	−	1.48123i	−0.420484	−	0.0519172i
$815$	30.4738	+	17.5941i	1.06745	+	0.616293i
$816$		0			0
$817$	32.1283	+	55.6479i	1.12403	+	1.94687i
$818$			1.50298i			0.0525506i
$819$		0			0
$820$			4.99611i			0.174472i
$821$	−14.1814	−	24.5629i	−0.494935	−	0.857253i	0.505048	−	0.863091i	$-0.331475\pi$
$821$	−14.1814	−	24.5629i	−0.494935	−	0.857253i	−0.999983	+	0.00583875i	$0.998141\pi$
$822$		0			0
$823$	−1.18222	+	2.04767i	−0.0412097	+	0.0713772i	−0.885895	−	0.463887i	$-0.846454\pi$
$823$	−1.18222	+	2.04767i	−0.0412097	+	0.0713772i	0.844685	+	0.535264i	$0.179788\pi$
$824$	−1.72042	−	2.97985i	−0.0599336	−	0.103808i
$825$		0			0
$826$	10.6040	−	1.16821i	0.368960	−	0.0406472i
$827$	31.0362			1.07923			0.539617	−	0.841911i	$-0.318569\pi$
$827$	31.0362			1.07923			0.539617	+	0.841911i	$0.318569\pi$
$828$		0			0
$829$	11.1654	−	19.3391i	0.387791	−	0.671674i	−0.604361	−	0.796711i	$-0.706572\pi$
$829$	11.1654	−	19.3391i	0.387791	−	0.671674i	0.992152	+	0.125037i	$0.0399049\pi$
$830$	13.3877	+	7.72937i	0.464693	+	0.268290i
$831$		0			0
$832$		−	6.97891i		−	0.241950i
$833$	−11.1743	+	35.5996i	−0.387167	+	1.23345i
$834$		0			0
$835$	−31.4225	+	18.1418i	−1.08742	+	0.627823i
$836$	25.9834	−	11.0086i	0.898655	−	0.380740i
$837$		0			0
$838$	−13.5268	+	7.80971i	−0.467276	+	0.269782i
$839$			39.0283i			1.34741i	0.739003	+	0.673703i	$0.235297\pi$
$839$			39.0283i			1.34741i	−0.739003	+	0.673703i	$0.764703\pi$
$840$		0			0
$841$	−20.7224			−0.714566
$842$	4.85221	+	8.40428i	0.167218	+	0.289631i
$843$		0			0
$844$	−18.9267	−	10.9274i	−0.651485	−	0.376135i
$845$	−63.6745	+	36.7625i	−2.19047	+	1.26467i
$846$		0			0
$847$	−22.9990	−	17.8338i	−0.790255	−	0.612778i
$848$		−	11.4686i		−	0.393832i
$849$		0			0
$850$	−2.02440	+	3.50637i	−0.0694364	+	0.120267i
$851$	−4.93866	−	2.85134i	−0.169295	−	0.0977426i
$852$		0			0
$853$		−	38.6365i		−	1.32289i	−0.749995	−	0.661444i	$-0.769944\pi$
$853$		−	38.6365i		−	1.32289i	0.749995	−	0.661444i	$-0.230056\pi$
$854$	5.39616	−	12.2851i	0.184653	−	0.420387i
$855$		0			0
$856$	−1.00997	−	1.74932i	−0.0345202	−	0.0597907i
$857$	−6.30291	+	10.9170i	−0.215303	+	0.372916i	−0.953366	−	0.301815i	$-0.902407\pi$
$857$	−6.30291	+	10.9170i	−0.215303	+	0.372916i	0.738063	+	0.674732i	$0.235741\pi$
$858$		0			0
$859$	14.7546	+	25.5558i	0.503421	+	0.871951i	0.999992	+	0.00395510i	$0.00125895\pi$
$859$	14.7546	+	25.5558i	0.503421	+	0.871951i	−0.496571	+	0.867996i	$0.665408\pi$
$860$	−15.5515			−0.530303
$861$		0			0
$862$	−23.5043			−0.800559
$863$	−1.60259	+	0.925254i	−0.0545527	+	0.0314960i	−0.527028	−	0.849848i	$-0.676694\pi$
$863$	−1.60259	+	0.925254i	−0.0545527	+	0.0314960i	0.472476	+	0.881344i	$0.343360\pi$
$864$		0			0
$865$	28.7281	+	16.5862i	0.976784	+	0.563946i
$866$	−9.18600	−	15.9106i	−0.312153	−	0.540665i
$867$		0			0
$868$	18.7381	−	13.7578i	0.636011	−	0.466970i
$869$	−23.7004	−	17.8846i	−0.803981	−	0.606695i
$870$		0			0
$871$	57.4729	+	33.1820i	1.94739	+	1.12433i
$872$	3.05488	+	1.76373i	0.103451	+	0.0597275i
$873$		0			0
$874$	13.3130			0.450320
$875$	−31.1907	+	3.43618i	−1.05444	+	0.116164i
$876$		0			0
$877$	14.0961	−	8.13840i	0.475992	−	0.274814i	−0.242753	−	0.970088i	$-0.578050\pi$
$877$	14.0961	−	8.13840i	0.475992	−	0.274814i	0.718745	+	0.695274i	$0.244717\pi$
$878$	11.8078	+	6.81724i	0.398494	+	0.230071i
$879$		0			0
$880$	−0.836906	+	6.77821i	−0.0282121	+	0.228494i
$881$			30.0489i			1.01237i	0.862424	+	0.506187i	$0.168945\pi$
$881$			30.0489i			1.01237i	−0.862424	+	0.506187i	$0.831055\pi$
$882$		0			0
$883$	−30.4464			−1.02460			−0.512302	−	0.858805i	$-0.671207\pi$
$883$	−30.4464			−1.02460			−0.512302	+	0.858805i	$0.671207\pi$
$884$	32.2159	−	18.5998i	1.08354	−	0.625580i
$885$		0			0
$886$	−18.9667	−	10.9504i	−0.637197	−	0.367886i
$887$	−1.84407	−	3.19402i	−0.0619178	−	0.107245i	0.833405	−	0.552663i	$-0.186388\pi$
$887$	−1.84407	−	3.19402i	−0.0619178	−	0.107245i	−0.895323	+	0.445418i	$0.853055\pi$
$888$		0			0
$889$	−16.6714	+	1.83664i	−0.559141	+	0.0615988i
$890$	−7.11374			−0.238453
$891$		0			0
$892$	9.17207	−	15.8865i	0.307104	−	0.531919i
$893$	50.3271	−	87.1690i	1.68413	−	2.91700i
$894$		0			0
$895$	−19.0022			−0.635174
$896$	−2.13265	+	1.56583i	−0.0712468	+	0.0523106i
$897$		0			0
$898$	29.9655	−	17.3006i	0.999961	−	0.577328i
$899$	12.6394	−	21.8921i	0.421548	−	0.730143i
$900$		0			0
$901$	52.9409	−	30.5654i	1.76372	−	1.01828i
$902$	4.84703	−	6.42320i	0.161389	−	0.213869i
$903$		0			0
$904$			7.60125i			0.252814i
$905$	9.74323	−	5.62526i	0.323876	−	0.186990i
$906$		0			0
$907$	−10.3787	+	17.9765i	−0.344620	+	0.596899i	−0.985285	−	0.170922i	$-0.945325\pi$
$907$	−10.3787	+	17.9765i	−0.344620	+	0.596899i	0.640665	+	0.767820i	$0.278659\pi$
$908$	0.871542	+	1.50956i	0.0289231	+	0.0500964i
$909$		0			0
$910$	34.8123	+	15.2911i	1.15401	+	0.506895i
$911$		−	30.1614i		−	0.999290i	−0.866230	−	0.499645i	$-0.833464\pi$
$911$		−	30.1614i		−	0.999290i	0.866230	−	0.499645i	$-0.166536\pi$
$912$		0			0
$913$	−9.71298	−	22.9254i	−0.321453	−	0.758719i
$914$	−22.7285	−	13.1223i	−0.751791	−	0.434047i
$915$		0			0
$916$	−28.3556			−0.936895
$917$	−27.7250	+	20.3561i	−0.915559	+	0.672219i
$918$		0			0
$919$	42.7967	−	24.7087i	1.41173	−	0.815065i	0.416182	−	0.909281i	$-0.363368\pi$
$919$	42.7967	−	24.7087i	1.41173	−	0.815065i	0.995552	+	0.0942164i	$0.0300346\pi$
$920$	−1.61102	+	2.79038i	−0.0531139	+	0.0919960i
$921$		0			0
$922$	−21.0873	−	36.5244i	−0.694475	−	1.20287i
$923$	−23.0613			−0.759071
$924$		0			0
$925$	2.76838			0.0910238
$926$	13.0654	+	22.6299i	0.429356	+	0.743666i
$927$		0			0
$928$	−1.43854	+	2.49162i	−0.0472224	+	0.0817916i
$929$	6.64222	−	3.83488i	0.217924	−	0.125818i	−0.387065	−	0.922053i	$-0.626511\pi$
$929$	6.64222	−	3.83488i	0.217924	−	0.125818i	0.604989	+	0.796234i	$0.293178\pi$
$930$		0			0
$931$	−43.8598	+	40.2938i	−1.43745	+	1.32057i
$932$	20.8151			0.681823
$933$		0			0
$934$	4.98050	+	2.87549i	0.162967	+	0.0940889i
$935$	−33.5199	+	14.2017i	−1.09622	+	0.464444i
$936$		0			0
$937$		−	1.93121i		−	0.0630899i	−0.999502	−	0.0315449i	$-0.989957\pi$
$937$		−	1.93121i		−	0.0630899i	0.999502	−	0.0315449i	$-0.0100427\pi$
$938$	−2.75503	−	25.0077i	−0.0899548	−	0.816532i
$939$		0			0
$940$	12.1803	+	21.0968i	0.397276	+	0.688103i
$941$	−6.36930	+	11.0319i	−0.207633	+	0.359631i	−0.950968	−	0.309288i	$-0.899909\pi$
$941$	−6.36930	+	11.0319i	−0.207633	+	0.359631i	0.743335	+	0.668919i	$0.233243\pi$
$942$		0			0
$943$	3.28765	−	1.89813i	0.107061	−	0.0618115i
$944$			4.03218i			0.131236i
$945$		0			0
$946$	19.9937	+	15.0875i	0.650051	+	0.490537i
$947$	−41.3900	+	23.8965i	−1.34499	+	0.776532i	−0.987535	−	0.157397i	$-0.949690\pi$
$947$	−41.3900	+	23.8965i	−1.34499	+	0.776532i	−0.357458	+	0.933929i	$0.616357\pi$
$948$		0			0
$949$	−3.33695	+	5.77977i	−0.108322	+	0.187619i
$950$	−5.59699	+	3.23142i	−0.181590	+	0.104841i
$951$		0			0
$952$	−12.9120	−	5.67151i	−0.418479	−	0.183815i
$953$	−44.7647			−1.45007			−0.725036	−	0.688711i	$-0.758177\pi$
$953$	−44.7647			−1.45007			−0.725036	+	0.688711i	$0.758177\pi$
$954$		0			0
$955$	21.2233	−	36.7598i	0.686768	−	1.18952i
$956$	3.72902	−	6.45884i	0.120605	−	0.208894i
$957$		0			0
$958$	−13.9461			−0.450577
$959$	9.79525	−	22.3002i	0.316305	−	0.720111i
$960$		0			0
$961$	−23.0994	−	40.0094i	−0.745142	−	1.29062i
$962$	−22.0277	−	12.7177i	−0.710202	−	0.410035i
$963$		0			0
$964$	−5.76722	+	3.32971i	−0.185750	+	0.107243i
$965$	26.7812			0.862118
$966$		0			0
$967$			3.10584i			0.0998771i	0.998752	+	0.0499386i	$0.0159026\pi$
$967$			3.10584i			0.0998771i	−0.998752	+	0.0499386i	$0.984097\pi$
$968$	7.65192	−	7.90241i	0.245942	−	0.253993i
$969$		0			0
$970$	−10.6168	−	6.12962i	−0.340885	−	0.196810i
$971$	9.39097	−	5.42188i	0.301370	−	0.173996i	−0.341688	−	0.939813i	$-0.610999\pi$
$971$	9.39097	−	5.42188i	0.301370	−	0.173996i	0.643058	+	0.765817i	$0.277665\pi$
$972$		0			0
$973$	48.7053	−	5.36571i	1.56142	−	0.172017i
$974$	−15.5540			−0.498383
$975$		0			0
$976$	4.39206	+	2.53576i	0.140586	+	0.0811676i
$977$	−37.0400	−	21.3850i	−1.18501	−	0.684168i	−0.227844	−	0.973698i	$-0.573168\pi$
$977$	−37.0400	−	21.3850i	−1.18501	−	0.684168i	−0.957169	+	0.289530i	$0.906501\pi$
$978$		0			0
$979$	9.14571	+	6.90147i	0.292298	+	0.220572i
$980$	−3.13794	−	14.0689i	−0.100238	−	0.449414i
$981$		0			0
$982$	−7.36337	−	12.7537i	−0.234975	−	0.406988i
$983$	32.8275	+	18.9529i	1.04703	+	0.604505i	0.921817	−	0.387624i	$-0.126704\pi$
$983$	32.8275	+	18.9529i	1.04703	+	0.604505i	0.125216	+	0.992129i	$0.460038\pi$
$984$		0			0
$985$	32.9573	−	19.0279i	1.05011	−	0.606279i
$986$	−15.3357			−0.488388
$987$		0			0
$988$	59.3795			1.88911
$989$	5.90836	+	10.2336i	0.187875	+	0.325409i
$990$		0			0
$991$	−1.09256	+	1.89236i	−0.0347062	+	0.0601129i	−0.882857	−	0.469642i	$-0.844383\pi$
$991$	−1.09256	+	1.89236i	−0.0347062	+	0.0601129i	0.848151	+	0.529755i	$0.177716\pi$
$992$	4.39314	+	7.60915i	0.139482	+	0.241591i
$993$		0			0
$994$	5.17416	+	7.04718i	0.164114	+	0.223523i
$995$		−	23.2889i		−	0.738309i
$996$		0			0
$997$	−15.6710	−	9.04768i	−0.496307	−	0.286543i	0.230880	−	0.972982i	$-0.425839\pi$
$997$	−15.6710	−	9.04768i	−0.496307	−	0.286543i	−0.727187	+	0.686439i	$0.759173\pi$
$998$	−3.51020	+	6.07984i	−0.111113	+	0.192454i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1386.2.ba.b.1187.12	yes	32
3.2	odd	2		1386.2.ba.a.1187.5	yes	32
7.2	even	3	inner	1386.2.ba.b.989.5	yes	32
11.10	odd	2		1386.2.ba.a.1187.12	yes	32
21.2	odd	6		1386.2.ba.a.989.12	yes	32
33.32	even	2	inner	1386.2.ba.b.1187.5	yes	32
77.65	odd	6		1386.2.ba.a.989.5	✓	32
231.65	even	6	inner	1386.2.ba.b.989.12	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1386.2.ba.a.989.5	✓	32	77.65	odd	6
1386.2.ba.a.989.12	yes	32	21.2	odd	6
1386.2.ba.a.1187.5	yes	32	3.2	odd	2
1386.2.ba.a.1187.12	yes	32	11.10	odd	2
1386.2.ba.b.989.5	yes	32	7.2	even	3	inner
1386.2.ba.b.989.12	yes	32	231.65	even	6	inner
1386.2.ba.b.1187.5	yes	32	33.32	even	2	inner
1386.2.ba.b.1187.12	yes	32	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:	\( N \)	\(=\)	\( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1386.ba (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.78334 - 1.02961i) q^{5} +(0.289722 + 2.62984i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.78334 - 1.02961i) q^{5} +(0.289722 + 2.62984i) q^{7} -1.00000 q^{8} +(1.78334 + 1.02961i) q^{10} +(-1.29385 - 3.05384i) q^{11} -6.97891i q^{13} +(-2.13265 + 1.56583i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.66515 - 4.61618i) q^{17} +(7.36851 - 4.25421i) q^{19} +2.05923i q^{20} +(1.99778 - 2.64743i) q^{22} +(1.35506 - 0.782344i) q^{23} +(-0.379791 + 0.657818i) q^{25} +(6.04391 - 3.48945i) q^{26} +(-2.42237 - 1.06401i) q^{28} -2.87708 q^{29} +(-4.39314 + 7.60915i) q^{31} +(0.500000 - 0.866025i) q^{32} +5.33030 q^{34} +(3.22439 + 4.39161i) q^{35} +(-1.82231 - 3.15633i) q^{37} +(7.36851 + 4.25421i) q^{38} +(-1.78334 + 1.02961i) q^{40} +2.42621 q^{41} +7.55213i q^{43} +(3.29163 + 0.406418i) q^{44} +(1.35506 + 0.782344i) q^{46} +(10.2450 - 5.91497i) q^{47} +(-6.83212 + 1.52384i) q^{49} -0.759582 q^{50} +(6.04391 + 3.48945i) q^{52} +(9.93207 + 5.73428i) q^{53} +(-5.45165 - 4.11389i) q^{55} +(-0.289722 - 2.62984i) q^{56} +(-1.43854 - 2.49162i) q^{58} +(-3.49197 - 2.01609i) q^{59} +(-4.39206 + 2.53576i) q^{61} -8.78629 q^{62} +1.00000 q^{64} +(-7.18558 - 12.4458i) q^{65} +(-4.75461 + 8.23523i) q^{67} +(2.66515 + 4.61618i) q^{68} +(-2.19105 + 4.98821i) q^{70} -3.30443i q^{71} +(-0.828178 - 0.478149i) q^{73} +(1.82231 - 3.15633i) q^{74} +8.50842i q^{76} +(7.65627 - 4.28737i) q^{77} +(7.75287 - 4.47612i) q^{79} +(-1.78334 - 1.02961i) q^{80} +(1.21310 + 2.10116i) q^{82} +7.50706 q^{83} -10.9763i q^{85} +(-6.54033 + 3.77606i) q^{86} +(1.29385 + 3.05384i) q^{88} +(-2.99174 + 1.72728i) q^{89} +(18.3534 - 2.02194i) q^{91} +1.56469i q^{92} +(10.2450 + 5.91497i) q^{94} +(8.76039 - 15.1734i) q^{95} -5.95332 q^{97} +(-4.73575 - 5.15487i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{2} - 16 q^{4} - 32 q^{8}+O(q^{10}) \) 32 * q + 16 * q^2 - 16 * q^4 - 32 * q^8	\( 32 q + 16 q^{2} - 16 q^{4} - 32 q^{8} + 2 q^{11} - 16 q^{16} + 4 q^{17} + 4 q^{22} + 4 q^{25} + 16 q^{29} + 4 q^{31} + 16 q^{32} + 8 q^{34} + 16 q^{35} + 4 q^{37} - 32 q^{41} + 2 q^{44} + 20 q^{49} + 8 q^{50} - 12 q^{55} + 8 q^{58} + 8 q^{62} + 32 q^{64} - 8 q^{67} + 4 q^{68} - 4 q^{70} - 4 q^{74} + 14 q^{77} - 16 q^{82} + 88 q^{83} - 2 q^{88} - 24 q^{95} - 32 q^{97} - 8 q^{98}+O(q^{100}) \) 32 * q + 16 * q^2 - 16 * q^4 - 32 * q^8 + 2 * q^11 - 16 * q^16 + 4 * q^17 + 4 * q^22 + 4 * q^25 + 16 * q^29 + 4 * q^31 + 16 * q^32 + 8 * q^34 + 16 * q^35 + 4 * q^37 - 32 * q^41 + 2 * q^44 + 20 * q^49 + 8 * q^50 - 12 * q^55 + 8 * q^58 + 8 * q^62 + 32 * q^64 - 8 * q^67 + 4 * q^68 - 4 * q^70 - 4 * q^74 + 14 * q^77 - 16 * q^82 + 88 * q^83 - 2 * q^88 - 24 * q^95 - 32 * q^97 - 8 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more