LMFDB - Embedded newform 945.2.u.a.584.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [945,2,Mod(89,945)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(945, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 3, 5]))

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

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

chi := DirichletCharacter("945.89");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 945 = 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	945.u (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:	$7.54586299101$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$44$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 315)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			584.13
Character	$\chi$	$=$	945.584
Dual form			945.2.u.a.89.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.665500 + 1.15268i) q^{2} +(0.114220 + 0.197834i) q^{4} +(1.38997 + 1.75157i) q^{5} +(-1.25852 - 2.32726i) q^{7} -2.96605 q^{8} +O(q^{10})$	\(q+(-0.665500 + 1.15268i) q^{2} +(0.114220 + 0.197834i) q^{4} +(1.38997 + 1.75157i) q^{5} +(-1.25852 - 2.32726i) q^{7} -2.96605 q^{8} +(-2.94402 + 0.436517i) q^{10} +1.52676i q^{11} +(-0.272143 + 0.471366i) q^{13} +(3.52013 + 0.0981180i) q^{14} +(1.74547 - 3.02324i) q^{16} +(-4.41967 - 2.55170i) q^{17} +(-5.57286 + 3.21749i) q^{19} +(-0.187759 + 0.475046i) q^{20} +(-1.75986 - 1.01606i) q^{22} -1.59765 q^{23} +(-1.13599 + 4.86924i) q^{25} +(-0.362222 - 0.627388i) q^{26} +(0.316663 - 0.514797i) q^{28} +(-0.841685 + 0.485947i) q^{29} +(-3.25769 + 1.88083i) q^{31} +(-0.642834 - 1.11342i) q^{32} +(5.88258 - 3.39631i) q^{34} +(2.32705 - 5.43919i) q^{35} +(-6.59583 + 3.80810i) q^{37} -8.56496i q^{38} +(-4.12271 - 5.19525i) q^{40} +(1.77448 - 3.07349i) q^{41} +(-1.37551 + 0.794149i) q^{43} +(-0.302045 + 0.174386i) q^{44} +(1.06324 - 1.84158i) q^{46} +(11.0266 + 6.36621i) q^{47} +(-3.83225 + 5.85780i) q^{49} +(-4.85668 - 4.54991i) q^{50} -0.124336 q^{52} +(-4.29946 + 7.44689i) q^{53} +(-2.67422 + 2.12214i) q^{55} +(3.73284 + 6.90277i) q^{56} -1.29359i q^{58} +(1.49496 + 2.58934i) q^{59} +(-4.30634 - 2.48626i) q^{61} -5.00676i q^{62} +8.69310 q^{64} +(-1.20390 + 0.178505i) q^{65} +(13.0006 - 7.50588i) q^{67} -1.16582i q^{68} +(4.72100 + 6.30213i) q^{70} -15.7373i q^{71} +(-4.54256 + 7.86795i) q^{73} -10.1372i q^{74} +(-1.27306 - 0.735001i) q^{76} +(3.55316 - 1.92146i) q^{77} +(0.794017 - 1.37528i) q^{79} +(7.72156 - 1.14489i) q^{80} +(2.36184 + 4.09082i) q^{82} +(-8.77611 + 5.06689i) q^{83} +(-1.67372 - 11.2881i) q^{85} -2.11402i q^{86} -4.52844i q^{88} +(-0.784525 - 1.35884i) q^{89} +(1.43949 + 0.0401234i) q^{91} +(-0.182483 - 0.316070i) q^{92} +(-14.6764 + 8.47343i) q^{94} +(-13.3817 - 5.28904i) q^{95} +(-4.53143 - 7.84866i) q^{97} +(-4.20181 - 8.31573i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 38 q^{4} + 6 q^{5}+O(q^{10}) $ 88 * q - 38 * q^4 + 6 * q^5	$ 88 q - 38 q^{4} + 6 q^{5} - 6 q^{10} + 12 q^{14} - 26 q^{16} - 12 q^{19} - 6 q^{20} - 2 q^{25} - 12 q^{26} - 6 q^{29} - 6 q^{31} + 12 q^{34} + 6 q^{41} - 84 q^{44} - 18 q^{46} + 10 q^{49} - 30 q^{50} + 90 q^{56} + 6 q^{59} + 12 q^{61} - 8 q^{64} - 54 q^{65} - 30 q^{70} + 48 q^{76} + 8 q^{79} - 69 q^{80} - 7 q^{85} + 72 q^{89} + 20 q^{91} - 6 q^{94} + 93 q^{95}+O(q^{100}) $ 88 * q - 38 * q^4 + 6 * q^5 - 6 * q^10 + 12 * q^14 - 26 * q^16 - 12 * q^19 - 6 * q^20 - 2 * q^25 - 12 * q^26 - 6 * q^29 - 6 * q^31 + 12 * q^34 + 6 * q^41 - 84 * q^44 - 18 * q^46 + 10 * q^49 - 30 * q^50 + 90 * q^56 + 6 * q^59 + 12 * q^61 - 8 * q^64 - 54 * q^65 - 30 * q^70 + 48 * q^76 + 8 * q^79 - 69 * q^80 - 7 * q^85 + 72 * q^89 + 20 * q^91 - 6 * q^94 + 93 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/945\mathbb{Z}\right)^\times$.

$n$	$136$	$596$	$757$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	−0.665500	+	1.15268i	−0.470580	+	0.815068i	−0.999434	−	0.0336450i	$-0.989288\pi$
$2$	−0.665500	+	1.15268i	−0.470580	+	0.815068i	0.528854	+	0.848713i	$0.322622\pi$
$3$		0			0
$3$		0			0
$4$	0.114220	+	0.197834i	0.0571098	+	0.0989171i
$5$	1.38997	+	1.75157i	0.621612	+	0.783325i
$5$	1.38997	+	1.75157i	0.621612	+	0.783325i
$6$		0			0
$7$	−1.25852	−	2.32726i	−0.475676	−	0.879620i
$7$	−1.25852	−	2.32726i	−0.475676	−	0.879620i
$8$	−2.96605			−1.04866
$9$		0			0
$10$	−2.94402	+	0.436517i	−0.930981	+	0.138039i
$11$			1.52676i			0.460335i	0.973151	+	0.230167i	$0.0739274\pi$
$11$			1.52676i			0.460335i	−0.973151	+	0.230167i	$0.926073\pi$
$12$		0			0
$13$	−0.272143	+	0.471366i	−0.0754789	+	0.130733i	−0.901294	−	0.433207i	$-0.857382\pi$
$13$	−0.272143	+	0.471366i	−0.0754789	+	0.130733i	0.825816	+	0.563940i	$0.190715\pi$
$14$	3.52013	+	0.0981180i	0.940794	+	0.0262231i
$15$		0			0
$16$	1.74547	−	3.02324i	0.436367	−	0.755810i
$17$	−4.41967	−	2.55170i	−1.07193	−	0.618877i	−0.143219	−	0.989691i	$-0.545745\pi$
$17$	−4.41967	−	2.55170i	−1.07193	−	0.618877i	−0.928707	+	0.370814i	$0.879079\pi$
$18$		0			0
$19$	−5.57286	+	3.21749i	−1.27850	+	0.738143i	−0.976573	−	0.215188i	$-0.930964\pi$
$19$	−5.57286	+	3.21749i	−1.27850	+	0.738143i	−0.301928	+	0.953331i	$0.597630\pi$
$20$	−0.187759	+	0.475046i	−0.0419841	+	0.106224i
$21$		0			0
$22$	−1.75986	−	1.01606i	−0.375204	−	0.216624i
$23$	−1.59765			−0.333133			−0.166567	−	0.986030i	$-0.553268\pi$
$23$	−1.59765			−0.333133			−0.166567	+	0.986030i	$0.553268\pi$
$24$		0			0
$25$	−1.13599	+	4.86924i	−0.227197	+	0.973849i
$26$	−0.362222	−	0.627388i	−0.0710377	−	0.123041i
$27$		0			0
$28$	0.316663	−	0.514797i	0.0598437	−	0.0972875i
$29$	−0.841685	+	0.485947i	−0.156297	+	0.0902381i	−0.576109	−	0.817373i	$-0.695429\pi$
$29$	−0.841685	+	0.485947i	−0.156297	+	0.0902381i	0.419812	+	0.907611i	$0.362096\pi$
$30$		0			0
$31$	−3.25769	+	1.88083i	−0.585098	+	0.337807i	−0.763157	−	0.646213i	$-0.776352\pi$
$31$	−3.25769	+	1.88083i	−0.585098	+	0.337807i	0.178059	+	0.984020i	$0.443018\pi$
$32$	−0.642834	−	1.11342i	−0.113638	−	0.196827i
$33$		0			0
$34$	5.88258	−	3.39631i	1.00885	−	0.582462i
$35$	2.32705	−	5.43919i	0.393343	−	0.919392i
$36$		0			0
$37$	−6.59583	+	3.80810i	−1.08435	+	0.626048i	−0.932066	−	0.362289i	$-0.881995\pi$
$37$	−6.59583	+	3.80810i	−1.08435	+	0.626048i	−0.152282	+	0.988337i	$0.548662\pi$
$38$		−	8.56496i		−	1.38942i
$39$		0			0
$40$	−4.12271	−	5.19525i	−0.651858	−	0.821440i
$41$	1.77448	−	3.07349i	0.277128	−	0.479999i	−0.693542	−	0.720416i	$-0.743951\pi$
$41$	1.77448	−	3.07349i	0.277128	−	0.479999i	0.970670	+	0.240417i	$0.0772842\pi$
$42$		0			0
$43$	−1.37551	+	0.794149i	−0.209763	+	0.121107i	−0.601201	−	0.799098i	$-0.705311\pi$
$43$	−1.37551	+	0.794149i	−0.209763	+	0.121107i	0.391438	+	0.920204i	$0.371978\pi$
$44$	−0.302045	+	0.174386i	−0.0455350	+	0.0262896i
$45$		0			0
$46$	1.06324	−	1.84158i	0.156766	−	0.271526i
$47$	11.0266	+	6.36621i	1.60839	+	0.928607i	0.989730	+	0.142953i	$0.0456597\pi$
$47$	11.0266	+	6.36621i	1.60839	+	0.928607i	0.618665	+	0.785655i	$0.287674\pi$
$48$		0			0
$49$	−3.83225	+	5.85780i	−0.547464	+	0.836829i
$50$	−4.85668	−	4.54991i	−0.686838	−	0.643455i
$51$		0			0
$52$	−0.124336			−0.0172423
$53$	−4.29946	+	7.44689i	−0.590577	+	1.02291i	0.403578	+	0.914945i	$0.367766\pi$
$53$	−4.29946	+	7.44689i	−0.590577	+	1.02291i	−0.994155	+	0.107964i	$0.965567\pi$
$54$		0			0
$55$	−2.67422	+	2.12214i	−0.360592	+	0.286149i
$56$	3.73284	+	6.90277i	0.498822	+	0.922421i
$57$		0			0
$58$		−	1.29359i		−	0.169857i
$59$	1.49496	+	2.58934i	0.194627	+	0.337104i	0.946778	−	0.321887i	$-0.104317\pi$
$59$	1.49496	+	2.58934i	0.194627	+	0.337104i	−0.752151	+	0.658991i	$0.770984\pi$
$60$		0			0
$61$	−4.30634	−	2.48626i	−0.551370	−	0.318334i	0.198304	−	0.980140i	$-0.436457\pi$
$61$	−4.30634	−	2.48626i	−0.551370	−	0.318334i	−0.749674	+	0.661807i	$0.769790\pi$
$62$		−	5.00676i		−	0.635859i
$63$		0			0
$64$	8.69310			1.08664
$65$	−1.20390	+	0.178505i	−0.149325	+	0.0221408i
$66$		0			0
$67$	13.0006	−	7.50588i	1.58827	−	0.916990i	0.594681	−	0.803962i	$-0.297278\pi$
$67$	13.0006	−	7.50588i	1.58827	−	0.916990i	0.993592	−	0.113028i	$-0.0360549\pi$
$68$		−	1.16582i		−	0.141376i
$69$		0			0
$70$	4.72100	+	6.30213i	0.564267	+	0.753248i
$71$		−	15.7373i		−	1.86768i	−0.357693	−	0.933839i	$-0.616437\pi$
$71$		−	15.7373i		−	1.86768i	0.357693	−	0.933839i	$-0.383563\pi$
$72$		0			0
$73$	−4.54256	+	7.86795i	−0.531666	+	0.920873i	0.467650	+	0.883914i	$0.345101\pi$
$73$	−4.54256	+	7.86795i	−0.531666	+	0.920873i	−0.999317	+	0.0369598i	$0.988233\pi$
$74$		−	10.1372i		−	1.17842i
$75$		0			0
$76$	−1.27306	−	0.735001i	−0.146030	−	0.0843104i
$77$	3.55316	−	1.92146i	0.404920	−	0.218970i
$78$		0			0
$79$	0.794017	−	1.37528i	0.0893339	−	0.154731i	−0.817896	−	0.575366i	$-0.804859\pi$
$79$	0.794017	−	1.37528i	0.0893339	−	0.154731i	0.907230	+	0.420635i	$0.138193\pi$
$80$	7.72156	−	1.14489i	0.863296	−	0.128003i
$81$		0			0
$82$	2.36184	+	4.09082i	0.260821	+	0.451755i
$83$	−8.77611	+	5.06689i	−0.963303	+	0.556164i	−0.897188	−	0.441648i	$-0.854394\pi$
$83$	−8.77611	+	5.06689i	−0.963303	+	0.556164i	−0.0661153	+	0.997812i	$0.521061\pi$
$84$		0			0
$85$	−1.67372	−	11.2881i	−0.181540	−	1.22437i
$86$		−	2.11402i		−	0.227961i
$87$		0			0
$88$		−	4.52844i		−	0.482734i
$89$	−0.784525	−	1.35884i	−0.0831595	−	0.144036i	0.821446	−	0.570286i	$-0.193168\pi$
$89$	−0.784525	−	1.35884i	−0.0831595	−	0.144036i	−0.904605	+	0.426250i	$0.859834\pi$
$90$		0			0
$91$	1.43949	+	0.0401234i	0.150899	+	0.00420608i
$92$	−0.182483	−	0.316070i	−0.0190252	−	0.0329526i
$93$		0			0
$94$	−14.6764	+	8.47343i	−1.51376	+	0.873967i
$95$	−13.3817	−	5.28904i	−1.37294	−	0.542644i
$96$		0			0
$97$	−4.53143	−	7.84866i	−0.460097	−	0.796911i	0.538869	−	0.842390i	$-0.318852\pi$
$97$	−4.53143	−	7.84866i	−0.460097	−	0.796911i	−0.998965	+	0.0454790i	$0.985519\pi$
$98$	−4.20181	−	8.31573i	−0.424447	−	0.840015i
$99$		0			0
$100$	−1.09305	+	0.331426i	−0.109305	+	0.0331426i
$101$	−7.30520			−0.726895			−0.363447	−	0.931615i	$-0.618400\pi$
$101$	−7.30520			−0.726895			−0.363447	+	0.931615i	$0.618400\pi$
$102$		0			0
$103$	14.9249			1.47060			0.735298	−	0.677744i	$-0.237042\pi$
$103$	14.9249			1.47060			0.735298	+	0.677744i	$0.237042\pi$
$104$	0.807191	−	1.39810i	0.0791516	−	0.137095i
$105$		0			0
$106$	−5.72258	−	9.91181i	−0.555827	−	0.962720i
$107$	−0.0479458	−	0.0830445i	−0.00463509	−	0.00802822i	0.863699	−	0.504009i	$-0.168142\pi$
$107$	−0.0479458	−	0.0830445i	−0.00463509	−	0.00802822i	−0.868334	+	0.495981i	$0.834809\pi$
$108$		0			0
$109$	−2.94991	+	5.10939i	−0.282550	+	0.489391i	−0.972012	−	0.234931i	$-0.924514\pi$
$109$	−2.94991	+	5.10939i	−0.282550	+	0.489391i	0.689462	+	0.724322i	$0.257847\pi$
$110$	−0.666456	−	4.49481i	−0.0635440	−	0.428563i
$111$		0			0
$112$	−9.23257	−	0.257343i	−0.872395	−	0.0243166i
$113$	−1.52166	+	2.63560i	−0.143146	+	0.247936i	−0.928680	−	0.370883i	$-0.879055\pi$
$113$	−1.52166	+	2.63560i	−0.143146	+	0.247936i	0.785534	+	0.618819i	$0.212389\pi$
$114$		0			0
$115$	−2.22068	−	2.79839i	−0.207079	−	0.260952i
$116$	−0.192274	−	0.111009i	−0.0178522	−	0.0103070i
$117$		0			0
$118$	−3.97958			−0.366350
$119$	−0.376209	+	13.4971i	−0.0344871	+	1.23727i
$120$		0			0
$121$	8.66901			0.788092
$122$	5.73173	−	3.30922i	0.518927	−	0.299603i
$123$		0			0
$124$	−0.744184	−	0.429655i	−0.0668297	−	0.0385841i
$125$	−10.1078	+	4.77832i	−0.904069	+	0.427386i
$126$		0			0
$127$		−	12.7646i		−	1.13267i	−0.824174	−	0.566337i	$-0.808360\pi$
$127$		−	12.7646i		−	1.13267i	0.824174	−	0.566337i	$-0.191640\pi$
$128$	−4.49959	+	7.79352i	−0.397711	+	0.688856i
$129$		0			0
$130$	0.595436	−	1.50651i	0.0522232	−	0.132129i
$131$	−0.809819			−0.0707542			−0.0353771	−	0.999374i	$-0.511263\pi$
$131$	−0.809819			−0.0707542			−0.0353771	+	0.999374i	$0.511263\pi$
$132$		0			0
$133$	14.5015	+	8.92019i	1.25744	+	0.773479i
$134$			19.9807i			1.72607i
$135$		0			0
$136$	13.1090	+	7.56846i	1.12408	+	0.648990i
$137$	10.0795			0.861150			0.430575	−	0.902555i	$-0.358311\pi$
$137$	10.0795			0.861150			0.430575	+	0.902555i	$0.358311\pi$
$138$		0			0
$139$	−15.5010	−	8.94953i	−1.31478	−	0.759089i	−0.331897	−	0.943316i	$-0.607689\pi$
$139$	−15.5010	−	8.94953i	−1.31478	−	0.759089i	−0.982884	+	0.184227i	$0.941022\pi$
$140$	1.34185	−	0.160893i	0.113407	−	0.0135979i
$141$		0			0
$142$	18.1401	+	10.4732i	1.52228	+	0.878891i
$143$	−0.719661	−	0.415496i	−0.0601811	−	0.0347456i
$144$		0			0
$145$	−2.02108	−	0.798819i	−0.167842	−	0.0663383i
$146$	−6.04615	−	10.4722i	−0.500383	−	0.866688i
$147$		0			0
$148$	−1.50675	−	0.869920i	−0.123854	−	0.0715070i
$149$			22.0219i			1.80410i	0.431630	+	0.902051i	$0.357939\pi$
$149$			22.0219i			1.80410i	−0.431630	+	0.902051i	$0.642061\pi$
$150$		0			0
$151$	2.52613			0.205574			0.102787	−	0.994703i	$-0.467224\pi$
$151$	2.52613			0.205574			0.102787	+	0.994703i	$0.467224\pi$
$152$	16.5294	−	9.54325i	1.34071	−	0.774059i
$153$		0			0
$154$	−0.149802	+	5.37438i	−0.0120714	+	0.433080i
$155$	−7.82248	−	3.09178i	−0.628316	−	0.248338i
$156$		0			0
$157$	2.42583	+	4.20166i	0.193602	+	0.335329i	0.946441	−	0.322876i	$-0.104650\pi$
$157$	2.42583	+	4.20166i	0.193602	+	0.335329i	−0.752839	+	0.658204i	$0.771316\pi$
$158$	1.05684	+	1.83050i	0.0840774	+	0.145626i
$159$		0			0
$160$	1.05672	−	2.67359i	0.0835408	−	0.211366i
$161$	2.01068	+	3.71814i	0.158463	+	0.293031i
$162$		0			0
$163$	5.91592	−	3.41556i	0.463370	−	0.267527i	−0.250090	−	0.968223i	$-0.580460\pi$
$163$	5.91592	−	3.41556i	0.463370	−	0.267527i	0.713460	+	0.700696i	$0.247127\pi$
$164$	0.810723			0.0633068
$165$		0			0
$166$		−	13.4881i		−	1.04688i
$167$	16.5339	+	9.54584i	1.27943	+	0.738679i	0.976743	−	0.214411i	$-0.0687832\pi$
$167$	16.5339	+	9.54584i	1.27943	+	0.738679i	0.302686	+	0.953090i	$0.402117\pi$
$168$		0			0
$169$	6.35188	+	11.0018i	0.488606	+	0.846290i
$170$	14.1254	+	5.58299i	1.08337	+	0.428195i
$171$		0			0
$172$	−0.314220	−	0.181415i	−0.0239590	−	0.0138327i
$173$	2.61388	+	1.50912i	0.198730	+	0.114737i	0.596063	−	0.802938i	$-0.296731\pi$
$173$	2.61388	+	1.50912i	0.198730	+	0.114737i	−0.397333	+	0.917674i	$0.630064\pi$
$174$		0			0
$175$	12.7616	−	3.48431i	0.964690	−	0.263389i
$176$	4.61575	+	2.66491i	0.347926	+	0.200875i
$177$		0			0
$178$	2.08841			0.156533
$179$	11.5375	+	6.66115i	0.862350	+	0.497878i	0.864798	−	0.502119i	$-0.167446\pi$
$179$	11.5375	+	6.66115i	0.862350	+	0.497878i	−0.00244873	+	0.999997i	$0.500779\pi$
$180$		0			0
$181$			9.41089i			0.699506i	0.936842	+	0.349753i	$0.113734\pi$
$181$			9.41089i			0.699506i	−0.936842	+	0.349753i	$0.886266\pi$
$182$	−1.00423	+	1.63256i	−0.0744383	+	0.121014i
$183$		0			0
$184$	4.73871			0.349343
$185$	−15.8381	−	6.25991i	−1.16444	−	0.460238i
$186$		0			0
$187$	3.89582	−	6.74776i	0.284891	−	0.493445i
$188$			2.90858i			0.212130i
$189$		0			0
$190$	15.0021	−	11.9050i	1.08837	−	0.863680i
$191$	4.34453	+	2.50831i	0.314359	+	0.181495i	0.648875	−	0.760895i	$-0.275240\pi$
$191$	4.34453	+	2.50831i	0.314359	+	0.181495i	−0.334516	+	0.942390i	$0.608573\pi$
$192$		0			0
$193$	−5.83264	+	3.36748i	−0.419843	+	0.242396i	−0.695010	−	0.719000i	$-0.744600\pi$
$193$	−5.83264	+	3.36748i	−0.419843	+	0.242396i	0.275167	+	0.961396i	$0.411267\pi$
$194$	12.0627			0.866048
$195$		0			0
$196$	−1.59659	−	0.0890742i	−0.114042	−	0.00636244i
$197$	−9.71422			−0.692109			−0.346055	−	0.938214i	$-0.612479\pi$
$197$	−9.71422			−0.692109			−0.346055	+	0.938214i	$0.612479\pi$
$198$		0			0
$199$	−12.7246	−	7.34656i	−0.902024	−	0.520784i	−0.0241678	−	0.999708i	$-0.507694\pi$
$199$	−12.7246	−	7.34656i	−0.902024	−	0.520784i	−0.877856	+	0.478924i	$0.841027\pi$
$200$	3.36940	−	14.4424i	0.238252	−	1.02123i
$201$		0			0
$202$	4.86161	−	8.42056i	0.342062	−	0.592468i
$203$	2.19020	+	1.34724i	0.153722	+	0.0945579i
$204$		0			0
$205$	7.84991	−	1.16392i	0.548261	−	0.0812920i
$206$	−9.93253	+	17.2036i	−0.692032	+	1.19863i
$207$		0			0
$208$	0.950034	+	1.64551i	0.0658730	+	0.114095i
$209$	−4.91233	−	8.50840i	−0.339793	−	0.588538i
$210$		0			0
$211$	−11.0384	+	19.1191i	−0.759916	+	1.31621i	0.182977	+	0.983117i	$0.441427\pi$
$211$	−11.0384	+	19.1191i	−0.759916	+	1.31621i	−0.942893	+	0.333096i	$0.891907\pi$
$212$	−1.96433			−0.134911
$213$		0			0
$214$	0.127632			0.00872472
$215$	−3.30291	−	1.30545i	−0.225257	−	0.0890312i
$216$		0			0
$217$	8.47704	+	5.21442i	0.575459	+	0.353978i
$218$	−3.92633	−	6.80060i	−0.265924	−	0.460595i
$219$		0			0
$220$	−0.725281	−	0.286662i	−0.0488984	−	0.0193268i
$221$	2.40556	−	1.38885i	0.161816	−	0.0934243i
$222$		0			0
$223$	0.469387	+	0.813003i	0.0314325	+	0.0544427i	0.881314	−	0.472532i	$-0.156660\pi$
$223$	0.469387	+	0.813003i	0.0314325	+	0.0544427i	−0.849881	+	0.526974i	$0.823326\pi$
$224$	−1.78220	+	2.89730i	−0.119078	+	0.193584i
$225$		0			0
$226$	−2.02534	−	3.50798i	−0.134723	−	0.233348i
$227$			8.48570i			0.563216i	0.959530	+	0.281608i	$0.0908677\pi$
$227$			8.48570i			0.563216i	−0.959530	+	0.281608i	$0.909132\pi$
$228$		0			0
$229$			16.1752i			1.06888i	0.845205	+	0.534442i	$0.179478\pi$
$229$			16.1752i			1.06888i	−0.845205	+	0.534442i	$0.820522\pi$
$230$	4.70351	−	0.697401i	0.310141	−	0.0459853i
$231$		0			0
$232$	2.49648	−	1.44134i	0.163902	−	0.0946289i
$233$	10.8182	+	18.7377i	0.708726	+	1.22755i	0.965330	+	0.261033i	$0.0840632\pi$
$233$	10.8182	+	18.7377i	0.708726	+	1.22755i	−0.256604	+	0.966517i	$0.582604\pi$
$234$		0			0
$235$	4.17575	+	28.1627i	0.272396	+	1.83713i
$236$	−0.341507	+	0.591508i	−0.0222302	+	0.0385039i
$237$		0			0
$238$	−15.3074	−	9.41594i	−0.992233	−	0.610345i
$239$	14.5181	+	8.38203i	0.939098	+	0.542189i	0.889677	−	0.456590i	$-0.150929\pi$
$239$	14.5181	+	8.38203i	0.939098	+	0.542189i	0.0494206	+	0.998778i	$0.484263\pi$
$240$		0			0
$241$			8.34316i			0.537430i	0.963220	+	0.268715i	$0.0865990\pi$
$241$			8.34316i			0.537430i	−0.963220	+	0.268715i	$0.913401\pi$
$242$	−5.76923	+	9.99259i	−0.370860	+	0.642348i
$243$		0			0
$244$		−	1.13592i		−	0.0727199i
$245$	−15.5870	+	1.42970i	−0.995820	+	0.0913400i
$246$		0			0
$247$		−	3.50247i		−	0.222857i
$248$	9.66248	−	5.57863i	0.613568	−	0.354244i
$249$		0			0
$250$	1.21886	−	14.8310i	0.0770876	−	0.937997i
$251$	−14.3398			−0.905120			−0.452560	−	0.891734i	$-0.649489\pi$
$251$	−14.3398			−0.905120			−0.452560	+	0.891734i	$0.649489\pi$
$252$		0			0
$253$		−	2.43922i		−	0.153353i
$254$	14.7135	+	8.49483i	0.923205	+	0.533013i
$255$		0			0
$256$	2.70415	+	4.68372i	0.169009	+	0.292732i
$257$			3.98730i			0.248721i	0.992237	+	0.124361i	$0.0396880\pi$
$257$			3.98730i			0.248721i	−0.992237	+	0.124361i	$0.960312\pi$
$258$		0			0
$259$	17.1634	+	10.5576i	1.06648	+	0.656018i
$260$	−0.172823	−	0.217784i	−0.0107180	−	0.0135064i
$261$		0			0
$262$	0.538935	−	0.933462i	0.0332955	−	0.0576695i
$263$	14.2252			0.877162			0.438581	−	0.898692i	$-0.355481\pi$
$263$	14.2252			0.877162			0.438581	+	0.898692i	$0.355481\pi$
$264$		0			0
$265$	−19.0198	+	2.82012i	−1.16838	+	0.173238i
$266$	−19.9329	+	10.7792i	−1.22216	+	0.660914i
$267$		0			0
$268$	2.96984	+	1.71464i	0.181412	+	0.104738i
$269$	−12.2036	+	21.1372i	−0.744064	+	1.28876i	0.206566	+	0.978433i	$0.433771\pi$
$269$	−12.2036	+	21.1372i	−0.744064	+	1.28876i	−0.950631	+	0.310325i	$0.899562\pi$
$270$		0			0
$271$	22.0669	−	12.7404i	1.34047	−	0.773922i	0.353595	−	0.935399i	$-0.384959\pi$
$271$	22.0669	−	12.7404i	1.34047	−	0.773922i	0.986876	+	0.161477i	$0.0516257\pi$
$272$	−15.4288	+	8.90781i	−0.935507	+	0.540115i
$273$		0			0
$274$	−6.70791	+	11.6184i	−0.405240	+	0.701896i
$275$	−7.43415	−	1.73438i	−0.448296	−	0.104587i
$276$		0			0
$277$			5.50056i			0.330497i	0.986252	+	0.165248i	$0.0528425\pi$
$277$			5.50056i			0.330497i	−0.986252	+	0.165248i	$0.947157\pi$
$278$	20.6319	−	11.9118i	1.23742	−	0.714423i
$279$		0			0
$280$	−6.90215	+	16.1329i	−0.412482	+	0.964127i
$281$	2.21797	−	1.28055i	0.132313	−	0.0763909i	−0.432382	−	0.901690i	$-0.642327\pi$
$281$	2.21797	−	1.28055i	0.132313	−	0.0763909i	0.564695	+	0.825299i	$0.308994\pi$
$282$		0			0
$283$	−16.1592	−	27.9886i	−0.960566	−	1.66375i	−0.721083	−	0.692849i	$-0.756355\pi$
$283$	−16.1592	−	27.9886i	−0.960566	−	1.66375i	−0.239484	−	0.970900i	$-0.576978\pi$
$284$	3.11338	−	1.79751i	0.184745	−	0.106663i
$285$		0			0
$286$	0.957869	−	0.553026i	0.0566400	−	0.0327011i
$287$	−9.38603	−	0.261621i	−0.554040	−	0.0154430i
$288$		0			0
$289$	4.52230	+	7.83286i	0.266018	+	0.460757i
$290$	2.26581	−	1.79805i	0.133053	−	0.105585i
$291$		0			0
$292$	−2.07540			−0.121454
$293$	−10.3895	−	5.99837i	−0.606960	−	0.350429i	0.164815	−	0.986325i	$-0.447297\pi$
$293$	−10.3895	−	5.99837i	−0.606960	−	0.350429i	−0.771775	+	0.635896i	$0.780631\pi$
$294$		0			0
$295$	−2.45747	+	6.21762i	−0.143080	+	0.362004i
$296$	19.5636	−	11.2950i	1.13711	−	0.656510i
$297$		0			0
$298$	−25.3842	−	14.6556i	−1.47046	−	0.848973i
$299$	0.434789	−	0.753077i	0.0251445	−	0.0435516i
$300$		0			0
$301$	3.57929	+	2.20170i	0.206307	+	0.126904i
$302$	−1.68114	+	2.91182i	−0.0967388	+	0.167557i
$303$		0			0
$304$			22.4641i			1.28841i
$305$	−1.63080	−	10.9987i	−0.0933793	−	0.629782i
$306$		0			0
$307$	−18.0306			−1.02906			−0.514531	−	0.857472i	$-0.672034\pi$
$307$	−18.0306			−1.02906			−0.514531	+	0.857472i	$0.672034\pi$
$308$	0.785970	+	0.483468i	0.0447848	+	0.0275481i
$309$		0			0
$310$	8.76969	−	6.95923i	0.498085	−	0.395258i
$311$	−13.9288	−	24.1255i	−0.789832	−	1.36803i	−0.926069	−	0.377353i	$-0.876834\pi$
$311$	−13.9288	−	24.1255i	−0.789832	−	1.36803i	0.136237	−	0.990676i	$-0.456499\pi$
$312$		0			0
$313$	−7.38582	+	12.7926i	−0.417471	+	0.723082i	−0.995684	−	0.0928043i	$-0.970417\pi$
$313$	−7.38582	+	12.7926i	−0.417471	+	0.723082i	0.578213	+	0.815886i	$0.303750\pi$
$314$	−6.45755			−0.364421
$315$		0			0
$316$	0.362769			0.0204074
$317$	−6.37024	+	11.0336i	−0.357788	+	0.619708i	−0.987591	−	0.157048i	$-0.949802\pi$
$317$	−6.37024	+	11.0336i	−0.357788	+	0.619708i	0.629803	+	0.776755i	$0.283136\pi$
$318$		0			0
$319$	−0.741924	−	1.28505i	−0.0415397	−	0.0719489i
$320$	12.0831	+	15.2266i	0.675467	+	0.851191i
$321$		0			0
$322$	−5.62393	−	0.156758i	−0.313409	−	0.00873580i
$323$	32.8402			1.82728
$324$		0			0
$325$	−1.98604	−	1.86060i	−0.110166	−	0.103207i
$326$			9.09221i			0.503571i
$327$		0			0
$328$	−5.26321	+	9.11614i	−0.290612	+	0.503355i
$329$	0.938603	−	33.6737i	0.0517468	−	1.85649i
$330$		0			0
$331$	8.96821	−	15.5334i	0.492937	−	0.853793i	−0.507030	−	0.861929i	$-0.669257\pi$
$331$	8.96821	−	15.5334i	0.492937	−	0.853793i	0.999967	+	0.00813612i	$0.00258983\pi$
$332$	−2.00481	−	1.15748i	−0.110028	−	0.0635248i
$333$		0			0
$334$	−22.0066	+	12.7055i	−1.20415	+	0.695215i
$335$	31.2174	+	12.3385i	1.70559	+	0.674123i
$336$		0			0
$337$	10.5362	+	6.08308i	0.573944	+	0.331366i	0.758723	−	0.651414i	$-0.225824\pi$
$337$	10.5362	+	6.08308i	0.573944	+	0.331366i	−0.184779	+	0.982780i	$0.559157\pi$
$338$	−16.9087			−0.919712
$339$		0			0
$340$	2.04201	−	1.62044i	0.110743	−	0.0878809i
$341$	−2.87157	−	4.97370i	−0.155504	−	0.269341i
$342$		0			0
$343$	18.4556	+	1.54647i	0.996508	+	0.0835013i
$344$	4.07982	−	2.35549i	0.219969	−	0.126999i
$345$		0			0
$346$	−3.47907	+	2.00864i	−0.187036	+	0.107985i
$347$	−8.41501	−	14.5752i	−0.451741	−	0.782439i	0.546753	−	0.837294i	$-0.315864\pi$
$347$	−8.41501	−	14.5752i	−0.451741	−	0.782439i	−0.998494	+	0.0548552i	$0.982530\pi$
$348$		0			0
$349$	−13.0578	+	7.53890i	−0.698966	+	0.403548i	−0.806962	−	0.590603i	$-0.798890\pi$
$349$	−13.0578	+	7.53890i	−0.698966	+	0.403548i	0.107996	+	0.994151i	$0.465557\pi$
$350$	−4.47658	+	17.0289i	−0.239283	+	0.910233i
$351$		0			0
$352$	1.69992	−	0.981452i	0.0906063	−	0.0523115i
$353$		−	25.8941i		−	1.37820i	−0.724664	−	0.689102i	$-0.758005\pi$
$353$		−	25.8941i		−	1.37820i	0.724664	−	0.689102i	$-0.241995\pi$
$354$		0			0
$355$	27.5650	−	21.8744i	1.46300	−	1.16097i
$356$	0.179216	−	0.310412i	0.00949845	−	0.0164518i
$357$		0			0
$358$	−15.3563	+	8.86599i	−0.811608	+	0.468582i
$359$	−6.00976	+	3.46974i	−0.317183	+	0.183126i	−0.650136	−	0.759818i	$-0.725288\pi$
$359$	−6.00976	+	3.46974i	−0.317183	+	0.183126i	0.332953	+	0.942943i	$0.391955\pi$
$360$		0			0
$361$	11.2045	−	19.4068i	0.589710	−	1.02141i
$362$	−10.8477	−	6.26294i	−0.570144	−	0.329173i
$363$		0			0
$364$	0.156480	+	0.289363i	0.00820177	+	0.0151667i
$365$	−20.0953	+	2.97957i	−1.05183	+	0.155958i
$366$		0			0
$367$	−20.6123			−1.07596			−0.537978	−	0.842959i	$-0.680812\pi$
$367$	−20.6123			−1.07596			−0.537978	+	0.842959i	$0.680812\pi$
$368$	−2.78865	+	4.83008i	−0.145368	+	0.251785i
$369$		0			0
$370$	17.7560	−	14.0903i	0.923088	−	0.732521i
$371$	22.7418	+	0.633891i	1.18069	+	0.0329100i
$372$		0			0
$373$			27.5339i			1.42565i	0.701341	+	0.712826i	$0.252585\pi$
$373$			27.5339i			1.42565i	−0.701341	+	0.712826i	$0.747415\pi$
$374$	5.18534	+	8.98127i	0.268127	+	0.464410i
$375$		0			0
$376$	−32.7055	−	18.8825i	−1.68666	−	0.973791i
$377$		−	0.528989i		−	0.0272443i
$378$		0			0
$379$	−7.90435			−0.406019			−0.203010	−	0.979177i	$-0.565072\pi$
$379$	−7.90435			−0.406019			−0.203010	+	0.979177i	$0.565072\pi$
$380$	−0.482104	−	3.25148i	−0.0247314	−	0.166797i
$381$		0			0
$382$	−5.78257	+	3.33857i	−0.295862	+	0.170816i
$383$			17.7849i			0.908764i	0.890807	+	0.454382i	$0.150140\pi$
$383$			17.7849i			0.908764i	−0.890807	+	0.454382i	$0.849860\pi$
$384$		0			0
$385$	8.30433	+	3.55284i	0.423228	+	0.181069i
$386$		−	8.96423i		−	0.456267i
$387$		0			0
$388$	1.03516	−	1.79294i	0.0525521	−	0.0910229i
$389$		−	15.5097i		−	0.786372i	−0.919459	−	0.393186i	$-0.871373\pi$
$389$		−	15.5097i		−	0.786372i	0.919459	−	0.393186i	$-0.128627\pi$
$390$		0			0
$391$	7.06108	+	4.07672i	0.357094	+	0.206168i
$392$	11.3667	−	17.3746i	0.574103	−	0.877547i
$393$		0			0
$394$	6.46481	−	11.1974i	0.325692	−	0.564116i
$395$	3.51255	−	0.520815i	0.176736	−	0.0262050i
$396$		0			0
$397$	0.143317	+	0.248232i	0.00719287	+	0.0124584i	0.869599	−	0.493758i	$-0.164377\pi$
$397$	0.143317	+	0.248232i	0.00719287	+	0.0124584i	−0.862407	+	0.506216i	$0.831044\pi$
$398$	16.9365	−	9.77827i	0.848948	−	0.490140i
$399$		0			0
$400$	12.7381	+	11.9335i	0.636903	+	0.596674i
$401$		−	7.39051i		−	0.369064i	−0.982826	−	0.184532i	$-0.940923\pi$
$401$		−	7.39051i		−	0.369064i	0.982826	−	0.184532i	$-0.0590770\pi$
$402$		0			0
$403$		−	2.04742i		−	0.101989i
$404$	−0.834397	−	1.44522i	−0.0415128	−	0.0719023i
$405$		0			0
$406$	−3.01052	+	1.62801i	−0.149410	+	0.0807969i
$407$	−5.81405	−	10.0702i	−0.288192	−	0.499163i
$408$		0			0
$409$	24.2568	−	14.0047i	1.19942	−	0.692486i	0.238995	−	0.971021i	$-0.423182\pi$
$409$	24.2568	−	14.0047i	1.19942	−	0.692486i	0.960426	+	0.278535i	$0.0898488\pi$
$410$	−3.88248	+	9.82302i	−0.191742	+	0.485124i
$411$		0			0
$412$	1.70472	+	2.95266i	0.0839855	+	0.145467i
$413$	4.14463	−	6.73789i	0.203944	−	0.331550i
$414$		0			0
$415$	−21.0735	−	8.32916i	−1.03446	−	0.408862i
$416$	0.699771			0.0343091
$417$		0			0
$418$	13.0766			0.639598
$419$	−9.55120	+	16.5432i	−0.466607	+	0.808187i	−0.999272	−	0.0381390i	$-0.987857\pi$
$419$	−9.55120	+	16.5432i	−0.466607	+	0.808187i	0.532666	+	0.846326i	$0.321190\pi$
$420$		0			0
$421$	−7.21927	−	12.5041i	−0.351846	−	0.609415i	0.634727	−	0.772736i	$-0.281113\pi$
$421$	−7.21927	−	12.5041i	−0.351846	−	0.609415i	−0.986573	+	0.163322i	$0.947779\pi$
$422$	−14.6921	−	25.4475i	−0.715202	−	1.23877i
$423$		0			0
$424$	12.7524	−	22.0879i	0.619313	−	1.07268i
$425$	17.4455	−	18.6217i	0.846232	−	0.903287i
$426$		0			0
$427$	−0.366563	+	13.1510i	−0.0177392	+	0.636420i
$428$	0.0109527	−	0.0189706i	0.000529419	−	0.000916980i
$429$		0			0
$430$	3.70286	−	2.93842i	0.178568	−	0.141703i
$431$	21.1884	+	12.2331i	1.02061	+	0.589248i	0.914280	−	0.405083i	$-0.132757\pi$
$431$	21.1884	+	12.2331i	1.02061	+	0.589248i	0.106328	+	0.994331i	$0.466091\pi$
$432$		0			0
$433$	33.1673			1.59392			0.796959	−	0.604033i	$-0.206441\pi$
$433$	33.1673			1.59392			0.796959	+	0.604033i	$0.206441\pi$
$434$	−11.6520	+	6.30111i	−0.559315	+	0.302463i
$435$		0			0
$436$	−1.34775			−0.0645455
$437$	8.90348	−	5.14042i	0.425911	−	0.245900i
$438$		0			0
$439$	1.00257	+	0.578834i	0.0478501	+	0.0276263i	0.523734	−	0.851882i	$-0.324539\pi$
$439$	1.00257	+	0.578834i	0.0478501	+	0.0276263i	−0.475884	+	0.879508i	$0.657872\pi$
$440$	7.93188	−	6.29438i	0.378138	−	0.300073i
$441$		0			0
$442$			3.69713i			0.175854i
$443$	−2.21976	+	3.84473i	−0.105464	+	0.182669i	−0.913928	−	0.405877i	$-0.866966\pi$
$443$	−2.21976	+	3.84473i	−0.105464	+	0.182669i	0.808464	+	0.588546i	$0.200299\pi$
$444$		0			0
$445$	1.28963	−	3.26289i	0.0611345	−	0.154676i
$446$	−1.24951			−0.0591660
$447$		0			0
$448$	−10.9404	−	20.2311i	−0.516887	−	0.955828i
$449$		−	22.9654i		−	1.08381i	−0.840441	−	0.541903i	$-0.817704\pi$
$449$		−	22.9654i		−	1.08381i	0.840441	−	0.541903i	$-0.182296\pi$
$450$		0			0
$451$	4.69248	+	2.70920i	0.220960	+	0.127571i
$452$	−0.695216			−0.0327002
$453$		0			0
$454$	−9.78129	−	5.64723i	−0.459059	−	0.265038i
$455$	1.93056	+	2.57713i	0.0905060	+	0.120818i
$456$		0			0
$457$	6.86888	+	3.96575i	0.321313	+	0.185510i	0.651977	−	0.758238i	$-0.273940\pi$
$457$	6.86888	+	3.96575i	0.321313	+	0.185510i	−0.330665	+	0.943748i	$0.607273\pi$
$458$	−18.6448	−	10.7646i	−0.871213	−	0.502995i
$459$		0			0
$460$	0.299973	−	0.758958i	0.0139863	−	0.0353866i
$461$	−18.3483	−	31.7802i	−0.854566	−	1.48015i	−0.877047	−	0.480404i	$-0.840490\pi$
$461$	−18.3483	−	31.7802i	−0.854566	−	1.48015i	0.0224816	−	0.999747i	$-0.492843\pi$
$462$		0			0
$463$	18.3716	+	10.6068i	0.853799	+	0.492941i	0.861931	−	0.507026i	$-0.169255\pi$
$463$	18.3716	+	10.6068i	0.853799	+	0.492941i	−0.00813177	+	0.999967i	$0.502588\pi$
$464$			3.39282i			0.157508i
$465$		0			0
$466$	−28.7981			−1.33405
$467$	−30.8411	+	17.8061i	−1.42716	+	0.823970i	−0.996896	−	0.0787347i	$-0.974912\pi$
$467$	−30.8411	+	17.8061i	−1.42716	+	0.823970i	−0.430262	+	0.902704i	$0.641579\pi$
$468$		0			0
$469$	−33.8296	−	20.8094i	−1.56211	−	0.960887i
$470$	−35.2415	−	13.9290i	−1.62557	−	0.642495i
$471$		0			0
$472$	−4.43412	−	7.68013i	−0.204097	−	0.353507i
$473$	−1.21247	−	2.10006i	−0.0557495	−	0.0965610i
$474$		0			0
$475$	−9.33605	−	30.7906i	−0.428367	−	1.41277i
$476$	−2.71315	+	1.46720i	−0.124357	+	0.0672491i
$477$		0			0
$478$	−19.3236	+	11.1565i	−0.883841	+	0.510286i
$479$	−14.1300			−0.645617			−0.322809	−	0.946464i	$-0.604627\pi$
$479$	−14.1300			−0.645617			−0.322809	+	0.946464i	$0.604627\pi$
$480$		0			0
$481$		−	4.14540i		−	0.189014i
$482$	−9.61699	−	5.55237i	−0.438042	−	0.252904i
$483$		0			0
$484$	0.990171	+	1.71503i	0.0450078	+	0.0779558i
$485$	7.44894	−	18.8465i	0.338239	−	0.855775i
$486$		0			0
$487$	4.47207	+	2.58195i	0.202649	+	0.116999i	0.597890	−	0.801578i	$-0.296006\pi$
$487$	4.47207	+	2.58195i	0.202649	+	0.116999i	−0.395242	+	0.918577i	$0.629339\pi$
$488$	12.7728	+	7.37439i	0.578198	+	0.333823i
$489$		0			0
$490$	8.72519	−	18.9183i	0.394164	−	0.854643i
$491$	18.9696	+	10.9521i	0.856086	+	0.494261i	0.862700	−	0.505717i	$-0.168772\pi$
$491$	18.9696	+	10.9521i	0.856086	+	0.494261i	−0.00661389	+	0.999978i	$0.502105\pi$
$492$		0			0
$493$	4.95996			0.223385
$494$	4.03723	+	2.33089i	0.181643	+	0.104872i
$495$		0			0
$496$			13.1317i			0.589631i
$497$	−36.6248	+	19.8058i	−1.64285	+	0.888410i
$498$		0			0
$499$	40.5345			1.81457			0.907286	−	0.420514i	$-0.138150\pi$
$499$	40.5345			1.81457			0.907286	+	0.420514i	$0.138150\pi$
$500$	−2.09983	−	1.45389i	−0.0939070	−	0.0650199i
$501$		0			0
$502$	9.54314	−	16.5292i	0.425931	−	0.737734i
$503$		−	12.2595i		−	0.546624i	−0.961926	−	0.273312i	$-0.911881\pi$
$503$		−	12.2595i		−	0.546624i	0.961926	−	0.273312i	$-0.0881191\pi$
$504$		0			0
$505$	−10.1540	−	12.7956i	−0.451846	−	0.569395i
$506$	2.81164	+	1.62330i	0.124993	+	0.0721646i
$507$		0			0
$508$	2.52527	−	1.45797i	0.112041	−	0.0646868i
$509$	−23.5887			−1.04555			−0.522776	−	0.852470i	$-0.675104\pi$
$509$	−23.5887			−1.04555			−0.522776	+	0.852470i	$0.675104\pi$
$510$		0			0
$511$	24.0276	+	0.669733i	1.06292	+	0.0296272i
$512$	−25.1968			−1.11355
$513$		0			0
$514$	−4.59608	−	2.65355i	−0.202725	−	0.117043i
$515$	20.7451	+	26.1420i	0.914140	+	1.15196i
$516$		0			0
$517$	−9.71966	+	16.8349i	−0.427470	+	0.740400i
$518$	−23.5918	+	12.7578i	−1.03656	+	0.560547i
$519$		0			0
$520$	3.57083	−	0.529455i	0.156591	−	0.0232181i
$521$	−4.41092	+	7.63994i	−0.193246	+	0.334712i	−0.946324	−	0.323219i	$-0.895235\pi$
$521$	−4.41092	+	7.63994i	−0.193246	+	0.334712i	0.753078	+	0.657931i	$0.228568\pi$
$522$		0			0
$523$	−6.43951	−	11.1536i	−0.281580	−	0.487711i	0.690194	−	0.723624i	$-0.257525\pi$
$523$	−6.43951	−	11.1536i	−0.281580	−	0.487711i	−0.971774	+	0.235914i	$0.924192\pi$
$524$	−0.0924972	−	0.160210i	−0.00404076	−	0.00699880i
$525$		0			0
$526$	−9.46685	+	16.3971i	−0.412774	+	0.714946i
$527$	19.1972			0.836243
$528$		0			0
$529$	−20.4475			−0.889022
$530$	9.40701	−	23.8006i	0.408615	−	1.03383i
$531$		0			0
$532$	−0.108365	+	3.88775i	−0.00469822	+	0.168555i
$533$	0.965826	+	1.67286i	0.0418346	+	0.0724596i
$534$		0			0
$535$	0.0788152	−	0.199409i	0.00340748	−	0.00862122i
$536$	−38.5604	+	22.2628i	−1.66555	+	0.961608i
$537$		0			0
$538$	−16.2429	−	28.1336i	−0.700283	−	1.21293i
$539$	−8.94344	−	5.85092i	−0.385221	−	0.252017i
$540$		0			0
$541$	−8.28729	−	14.3540i	−0.356298	−	0.617127i	0.631041	−	0.775750i	$-0.282628\pi$
$541$	−8.28729	−	14.3540i	−0.356298	−	0.617127i	−0.987339	+	0.158623i	$0.949295\pi$
$542$			33.9148i			1.45677i
$543$		0			0
$544$			6.56127i			0.281312i
$545$	−13.0497	+	1.93491i	−0.558989	+	0.0828826i
$546$		0			0
$547$	−34.7814	+	20.0811i	−1.48715	+	0.858605i	−0.999893	−	0.0146554i	$-0.995335\pi$
$547$	−34.7814	+	20.0811i	−1.48715	+	0.858605i	−0.487254	+	0.873260i	$0.662002\pi$
$548$	1.15128	+	1.99407i	0.0491801	+	0.0851825i
$549$		0			0
$550$	6.94661	−	7.41497i	0.296204	−	0.316175i
$551$	3.12706	−	5.41623i	0.133217	−	0.230739i
$552$		0			0
$553$	−4.19991	−	0.117066i	−0.178599	−	0.00497815i
$554$	−6.34038	−	3.66062i	−0.269377	−	0.155525i
$555$		0			0
$556$		−	4.08885i		−	0.173406i
$557$	11.6686	−	20.2106i	0.494414	−	0.856349i	−0.505566	−	0.862788i	$-0.668716\pi$
$557$	11.6686	−	20.2106i	0.494414	−	0.856349i	0.999979	+	0.00643874i	$0.00204953\pi$
$558$		0			0
$559$		−	0.864488i		−	0.0365640i
$560$	−12.3822	−	16.5292i	−0.523243	−	0.698485i
$561$		0			0
$562$			3.40881i			0.143792i
$563$	−4.91494	+	2.83764i	−0.207140	+	0.119592i	−0.599982	−	0.800014i	$-0.704825\pi$
$563$	−4.91494	+	2.83764i	−0.207140	+	0.119592i	0.392841	+	0.919606i	$0.371492\pi$
$564$		0			0
$565$	−6.73150	+	0.998096i	−0.283196	+	0.0419902i
$566$	43.0159			1.80809
$567$		0			0
$568$			46.6778i			1.95856i
$569$	26.3804	+	15.2307i	1.10592	+	0.638505i	0.937770	−	0.347256i	$-0.112887\pi$
$569$	26.3804	+	15.2307i	1.10592	+	0.638505i	0.168152	+	0.985761i	$0.446220\pi$
$570$		0			0
$571$	2.83753	+	4.91474i	0.118747	+	0.205675i	0.919271	−	0.393625i	$-0.128779\pi$
$571$	2.83753	+	4.91474i	0.118747	+	0.205675i	−0.800525	+	0.599300i	$0.795446\pi$
$572$		−	0.189831i		−	0.00793725i
$573$		0			0
$574$	6.54797	−	10.6450i	0.273307	−	0.444313i
$575$	1.81491	−	7.77935i	0.0756870	−	0.324421i
$576$		0			0
$577$	−4.68851	+	8.12073i	−0.195185	+	0.338071i	−0.946961	−	0.321348i	$-0.895864\pi$
$577$	−4.68851	+	8.12073i	−0.195185	+	0.338071i	0.751776	+	0.659418i	$0.229197\pi$
$578$	−12.0384			−0.500730
$579$		0			0
$580$	−0.0728137	−	0.491080i	−0.00302342	−	0.0203910i
$581$	22.8369	+	14.0475i	0.947433	+	0.582788i
$582$		0			0
$583$	−11.3696	−	6.56424i	−0.470880	−	0.271863i
$584$	13.4735	−	23.3367i	0.557536	−	0.965681i
$585$		0			0
$586$	13.8284	−	7.98383i	0.571246	−	0.329809i
$587$	27.1045	−	15.6488i	1.11872	−	0.645896i	0.177649	−	0.984094i	$-0.443151\pi$
$587$	27.1045	−	15.6488i	1.11872	−	0.645896i	0.941075	+	0.338198i	$0.109817\pi$
$588$		0			0
$589$	12.1031	−	20.9632i	0.498699	−	0.863772i
$590$	−5.53148	−	6.97050i	−0.227727	−	0.286971i
$591$		0			0
$592$			26.5877i			1.09275i
$593$	−12.9800	+	7.49399i	−0.533024	+	0.307741i	−0.742247	−	0.670127i	$-0.766240\pi$
$593$	−12.9800	+	7.49399i	−0.533024	+	0.307741i	0.209223	+	0.977868i	$0.432906\pi$
$594$		0			0
$595$	−24.1640	+	18.1015i	−0.990626	+	0.742089i
$596$	−4.35668	+	2.51533i	−0.178457	+	0.103032i
$597$		0			0
$598$	0.578705	+	1.00235i	0.0236650	+	0.0409890i
$599$	25.0583	−	14.4674i	1.02385	−	0.591122i	0.108635	−	0.994082i	$-0.465352\pi$
$599$	25.0583	−	14.4674i	1.02385	−	0.591122i	0.915218	+	0.402960i	$0.132019\pi$
$600$		0			0
$601$	−11.7947	+	6.80966i	−0.481115	+	0.277772i	−0.720881	−	0.693059i	$-0.756263\pi$
$601$	−11.7947	+	6.80966i	−0.481115	+	0.277772i	0.239766	+	0.970831i	$0.422929\pi$
$602$	−4.91988	+	2.66054i	−0.200519	+	0.108436i
$603$		0			0
$604$	0.288534	+	0.499756i	0.0117403	+	0.0203348i
$605$	12.0496	+	15.1844i	0.489887	+	0.617332i
$606$		0			0
$607$	−31.5358			−1.28000			−0.640000	−	0.768375i	$-0.721066\pi$
$607$	−31.5358			−1.28000			−0.640000	+	0.768375i	$0.721066\pi$
$608$	7.16485	+	4.13663i	0.290573	+	0.167762i
$609$		0			0
$610$	13.7632	+	5.43983i	0.557257	+	0.220252i
$611$	−6.00163	+	3.46504i	−0.242800	+	0.140181i
$612$		0			0
$613$	−34.0310	−	19.6478i	−1.37450	−	0.793567i	−0.383008	−	0.923745i	$-0.625112\pi$
$613$	−34.0310	−	19.6478i	−1.37450	−	0.793567i	−0.991491	+	0.130177i	$0.958445\pi$
$614$	11.9994	−	20.7835i	0.484255	−	0.838755i
$615$		0			0
$616$	−10.5388	+	5.69914i	−0.424622	+	0.229625i
$617$	16.0543	−	27.8069i	0.646324	−	1.11947i	−0.337670	−	0.941264i	$-0.609639\pi$
$617$	16.0543	−	27.8069i	0.646324	−	1.11947i	0.983994	−	0.178201i	$-0.0570278\pi$
$618$		0			0
$619$			19.4825i			0.783069i	0.920163	+	0.391535i	$0.128056\pi$
$619$			19.4825i			0.783069i	−0.920163	+	0.391535i	$0.871944\pi$
$620$	−0.281821	−	1.90070i	−0.0113182	−	0.0763338i
$621$		0			0
$622$	37.0786			1.48672
$623$	−2.17502	+	3.53592i	−0.0871404	+	0.141663i
$624$		0			0
$625$	−22.4191	−	11.0628i	−0.896763	−	0.442512i
$626$	−9.83053	−	17.0270i	−0.392907	−	0.680535i
$627$		0			0
$628$	−0.554154	+	0.959824i	−0.0221132	+	0.0383011i
$629$	38.8685			1.54979
$630$		0			0
$631$	−21.9672			−0.874501			−0.437250	−	0.899340i	$-0.644048\pi$
$631$	−21.9672			−0.874501			−0.437250	+	0.899340i	$0.644048\pi$
$632$	−2.35510	+	4.07915i	−0.0936807	+	0.162260i
$633$		0			0
$634$	−8.47879	−	14.6857i	−0.336736	−	0.583243i
$635$	22.3580	−	17.7423i	0.887252	−	0.704083i
$636$		0			0
$637$	−1.71825	−	3.40055i	−0.0680794	−	0.134735i
$638$	1.97500			0.0781910
$639$		0			0
$640$	−19.9052	+	2.95139i	−0.786820	+	0.116664i
$641$		−	17.6720i		−	0.698002i	−0.937122	−	0.349001i	$-0.886521\pi$
$641$		−	17.6720i		−	0.698002i	0.937122	−	0.349001i	$-0.113479\pi$
$642$		0			0
$643$	−1.54367	+	2.67371i	−0.0608762	+	0.105441i	−0.894857	−	0.446352i	$-0.852723\pi$
$643$	−1.54367	+	2.67371i	−0.0608762	+	0.105441i	0.833981	+	0.551793i	$0.186056\pi$
$644$	−0.505917	+	0.822465i	−0.0199359	+	0.0324097i
$645$		0			0
$646$	−21.8552	+	37.8543i	−0.859880	+	1.48936i
$647$	−28.8964	−	16.6834i	−1.13604	−	0.655891i	−0.190591	−	0.981670i	$-0.561040\pi$
$647$	−28.8964	−	16.6834i	−1.13604	−	0.655891i	−0.945446	+	0.325779i	$0.894374\pi$
$648$		0			0
$649$	−3.95330	+	2.28244i	−0.155181	+	0.0895935i
$650$	3.46638	−	1.05104i	0.135963	−	0.0412254i
$651$		0			0
$652$	1.35143	+	0.780247i	0.0529260	+	0.0305568i
$653$	14.4076			0.563812			0.281906	−	0.959442i	$-0.409033\pi$
$653$	14.4076			0.563812			0.281906	+	0.959442i	$0.409033\pi$
$654$		0			0
$655$	−1.12562	−	1.41845i	−0.0439817	−	0.0554236i
$656$	−6.19461	−	10.7294i	−0.241859	−	0.418912i
$657$		0			0
$658$	38.1904	+	23.4918i	1.48882	+	0.915805i
$659$	−28.6839	+	16.5606i	−1.11736	+	0.645111i	−0.940727	−	0.339165i	$-0.889856\pi$
$659$	−28.6839	+	16.5606i	−1.11736	+	0.645111i	−0.176638	+	0.984276i	$0.556522\pi$
$660$		0			0
$661$	21.8890	−	12.6376i	0.851382	−	0.491546i	−0.00973497	−	0.999953i	$-0.503099\pi$
$661$	21.8890	−	12.6376i	0.851382	−	0.491546i	0.861117	+	0.508407i	$0.169765\pi$
$662$	11.9367	+	20.6749i	0.463932	+	0.803555i
$663$		0			0
$664$	26.0304	−	15.0287i	1.01018	−	0.583225i
$665$	4.53224	+	37.7991i	0.175753	+	1.46579i
$666$		0			0
$667$	1.34472	−	0.776374i	0.0520677	−	0.0300613i
$668$			4.36129i			0.168743i
$669$		0			0
$670$	−34.9975	+	27.7724i	−1.35207	+	1.07294i
$671$	3.79592	−	6.57473i	0.146540	−	0.253815i
$672$		0			0
$673$	1.35817	−	0.784142i	0.0523538	−	0.0302265i	−0.473595	−	0.880743i	$-0.657044\pi$
$673$	1.35817	−	0.784142i	0.0523538	−	0.0302265i	0.525948	+	0.850516i	$0.323710\pi$
$674$	−14.0237	+	8.09658i	−0.540172	+	0.311869i
$675$		0			0
$676$	−1.45102	+	2.51324i	−0.0558084	+	0.0966630i
$677$	−2.14687	−	1.23950i	−0.0825111	−	0.0476378i	0.458177	−	0.888861i	$-0.348503\pi$
$677$	−2.14687	−	1.23950i	−0.0825111	−	0.0476378i	−0.540688	+	0.841223i	$0.681836\pi$
$678$		0			0
$679$	−12.5630	+	20.4235i	−0.482122	+	0.783782i
$680$	4.96433	+	33.4812i	0.190373	+	1.28394i
$681$		0			0
$682$	7.64411			0.292708
$683$	−11.8521	+	20.5284i	−0.453508	+	0.785499i	−0.998601	−	0.0528765i	$-0.983161\pi$
$683$	−11.8521	+	20.5284i	−0.453508	+	0.785499i	0.545093	+	0.838376i	$0.316494\pi$
$684$		0			0
$685$	14.0102	+	17.6549i	0.535301	+	0.674561i
$686$	−14.0648	+	20.2442i	−0.536995	+	0.772927i
$687$		0			0
$688$			5.54465i			0.211388i
$689$	−2.34014	−	4.05324i	−0.0891522	−	0.154416i
$690$		0			0
$691$	30.9176	+	17.8503i	1.17616	+	0.679056i	0.955123	−	0.296209i	$-0.0957226\pi$
$691$	30.9176	+	17.8503i	1.17616	+	0.679056i	0.221037	+	0.975266i	$0.429056\pi$
$692$			0.689486i			0.0262103i
$693$		0			0
$694$	22.4007			0.850321
$695$	−5.87020	−	39.5907i	−0.222669	−	1.50176i
$696$		0			0
$697$	−15.6852	+	9.05588i	−0.594121	+	0.343016i
$698$		−	20.0686i		−	0.759606i
$699$		0			0
$700$	2.14695	+	2.12671i	0.0811469	+	0.0803822i
$701$			4.20953i			0.158992i	0.996835	+	0.0794958i	$0.0253310\pi$
$701$			4.20953i			0.158992i	−0.996835	+	0.0794958i	$0.974669\pi$
$702$		0			0
$703$	24.5051	−	42.4440i	0.924226	−	1.60081i
$704$			13.2723i			0.500217i
$705$		0			0
$706$	29.8476	+	17.2325i	1.12333	+	0.648555i
$707$	9.19375	+	17.0011i	0.345766	+	0.639391i
$708$		0			0
$709$	−18.4340	+	31.9287i	−0.692305	+	1.19911i	0.278775	+	0.960356i	$0.410071\pi$
$709$	−18.4340	+	31.9287i	−0.692305	+	1.19911i	−0.971081	+	0.238752i	$0.923262\pi$
$710$	6.86962	+	46.3310i	0.257812	+	1.73877i
$711$		0			0
$712$	2.32694	+	4.03038i	0.0872059	+	0.151045i
$713$	5.20465	−	3.00490i	0.194916	−	0.112535i
$714$		0			0
$715$	−0.272534	−	1.83806i	−0.0101922	−	0.0687396i
$716$			3.04334i			0.113735i
$717$		0			0
$718$		−	9.23644i		−	0.344701i
$719$	−11.7121	−	20.2859i	−0.436787	−	0.756537i	0.560653	−	0.828051i	$-0.310550\pi$
$719$	−11.7121	−	20.2859i	−0.436787	−	0.756537i	−0.997440	+	0.0715142i	$0.977217\pi$
$720$		0			0
$721$	−18.7833	−	34.7341i	−0.699527	−	1.29357i
$722$	14.9132	+	25.8304i	0.555011	+	0.961307i
$723$		0			0
$724$	−1.86180	+	1.07491i	−0.0691931	+	0.0399486i
$725$	−1.41005	−	4.65040i	−0.0523680	−	0.172712i
$726$		0			0
$727$	6.11544	+	10.5922i	0.226809	+	0.392845i	0.956861	−	0.290547i	$-0.0938373\pi$
$727$	6.11544	+	10.5922i	0.226809	+	0.392845i	−0.730052	+	0.683392i	$0.760504\pi$
$728$	−4.26959	−	0.119008i	−0.158242	−	0.00441074i
$729$		0			0
$730$	9.93890	−	25.1463i	0.367855	−	0.930706i
$731$	8.10570			0.299800
$732$		0			0
$733$	10.5549			0.389854			0.194927	−	0.980818i	$-0.437553\pi$
$733$	10.5549			0.389854			0.194927	+	0.980818i	$0.437553\pi$
$734$	13.7175	−	23.7594i	0.506323	−	0.876977i
$735$		0			0
$736$	1.02702	+	1.77886i	0.0378566	+	0.0655696i
$737$	11.4597	+	19.8487i	0.422122	+	0.731137i
$738$		0			0
$739$	19.5197	−	33.8092i	0.718046	−	1.24369i	−0.243728	−	0.969844i	$-0.578370\pi$
$739$	19.5197	−	33.8092i	0.718046	−	1.24369i	0.961773	−	0.273848i	$-0.0882964\pi$
$740$	−0.570601	−	3.84833i	−0.0209757	−	0.141467i
$741$		0			0
$742$	−15.8653	+	25.7921i	−0.582435	+	0.946859i
$743$	−9.41956	+	16.3152i	−0.345570	+	0.598545i	−0.985457	−	0.169924i	$-0.945648\pi$
$743$	−9.41956	+	16.3152i	−0.345570	+	0.598545i	0.639887	+	0.768469i	$0.278981\pi$
$744$		0			0
$745$	−38.5728	+	30.6097i	−1.41320	+	1.12145i
$746$	−31.7378	−	18.3238i	−1.16200	−	0.670882i
$747$		0			0
$748$	1.77992			0.0650802
$749$	−0.132925	+	0.216095i	−0.00485698	+	0.00789595i
$750$		0			0
$751$	15.7892			0.576154			0.288077	−	0.957607i	$-0.406984\pi$
$751$	15.7892			0.576154			0.288077	+	0.957607i	$0.406984\pi$
$752$	38.4932	−	22.2240i	1.40370	−	0.810427i
$753$		0			0
$754$	0.609755	+	0.352042i	0.0222060	+	0.0128206i
$755$	3.51124	+	4.42470i	0.127787	+	0.161031i
$756$		0			0
$757$		−	35.5774i		−	1.29308i	−0.762879	−	0.646541i	$-0.776215\pi$
$757$		−	35.5774i		−	1.29308i	0.762879	−	0.646541i	$-0.223785\pi$
$758$	5.26034	−	9.11118i	0.191064	−	0.330933i
$759$		0			0
$760$	39.6909	+	15.6876i	1.43974	+	0.569048i
$761$	32.6102			1.18212			0.591060	−	0.806628i	$-0.298710\pi$
$761$	32.6102			1.18212			0.591060	+	0.806628i	$0.298710\pi$
$762$		0			0
$763$	15.6034	+	0.434920i	0.564880	+	0.0157452i
$764$			1.14599i			0.0414606i
$765$		0			0
$766$	−20.5002	−	11.8358i	−0.740704	−	0.427646i
$767$	−1.62737			−0.0587609
$768$		0			0
$769$	−9.54526	−	5.51096i	−0.344211	−	0.198730i	0.317922	−	0.948117i	$-0.397015\pi$
$769$	−9.54526	−	5.51096i	−0.344211	−	0.198730i	−0.662133	+	0.749387i	$0.730348\pi$
$770$	−9.62182	+	7.20782i	−0.346746	+	0.259752i
$771$		0			0
$772$	−1.33240	−	0.769264i	−0.0479543	−	0.0276864i
$773$	−26.1710	−	15.1099i	−0.941306	−	0.543464i	−0.0509369	−	0.998702i	$-0.516221\pi$
$773$	−26.1710	−	15.1099i	−0.941306	−	0.543464i	−0.890370	+	0.455238i	$0.849554\pi$
$774$		0			0
$775$	−5.45751	−	17.9991i	−0.196040	−	0.646546i
$776$	13.4404	+	23.2795i	0.482484	+	0.835687i
$777$		0			0
$778$	17.8777	+	10.3217i	0.640947	+	0.370051i
$779$			22.8375i			0.818239i
$780$		0			0
$781$	24.0271			0.859757
$782$	−9.39830	+	5.42611i	−0.336082	+	0.194037i
$783$		0			0
$784$	11.0205	+	21.8104i	0.393588	+	0.778944i
$785$	−3.98767	+	10.0892i	−0.142326	+	0.360098i
$786$		0			0
$787$	−3.98198	−	6.89700i	−0.141942	−	0.245851i	0.786286	−	0.617863i	$-0.212001\pi$
$787$	−3.98198	−	6.89700i	−0.141942	−	0.245851i	−0.928228	+	0.372012i	$0.878668\pi$
$788$	−1.10955	−	1.92180i	−0.0395262	−	0.0684615i
$789$		0			0
$790$	−1.73727	+	4.39545i	−0.0618093	+	0.156383i
$791$	8.04877	+	0.224347i	0.286181	+	0.00797685i
$792$		0			0
$793$	2.34388	−	1.35324i	0.0832336	−	0.0480549i
$794$	−0.381510			−0.0135393
$795$		0			0
$796$		−	3.35649i		−	0.118967i
$797$	−33.7323	−	19.4753i	−1.19486	−	0.689852i	−0.235454	−	0.971886i	$-0.575658\pi$
$797$	−33.7323	−	19.4753i	−1.19486	−	0.689852i	−0.959404	+	0.282034i	$0.908991\pi$
$798$		0			0
$799$	−32.4893	−	56.2731i	−1.14939	−	1.99080i
$800$	6.15177	−	1.86528i	0.217498	−	0.0659477i
$801$		0			0
$802$	8.51889	+	4.91838i	0.300812	+	0.173674i
$803$	−12.0124	−	6.93539i	−0.423910	−	0.244745i
$804$		0			0
$805$	−3.71781	+	8.68993i	−0.131036	+	0.306280i
$806$	2.36002	+	1.36256i	0.0831280	+	0.0479940i
$807$		0			0
$808$	21.6676			0.762264
$809$	3.39460	+	1.95987i	0.119348	+	0.0689054i	0.558485	−	0.829514i	$-0.311383\pi$
$809$	3.39460	+	1.95987i	0.119348	+	0.0689054i	−0.439138	+	0.898420i	$0.644716\pi$
$810$		0			0
$811$			43.8832i			1.54095i	0.637472	+	0.770474i	$0.279980\pi$
$811$			43.8832i			1.54095i	−0.637472	+	0.770474i	$0.720020\pi$
$812$	−0.0163667	+	0.587179i	−0.000574358	+	0.0206059i
$813$		0			0
$814$	15.4770			0.542469
$815$	14.2055	+	5.61463i	0.497597	+	0.196672i
$816$		0			0
$817$	5.11033	−	8.85136i	0.178788	−	0.309670i
$818$			37.2804i			1.30348i
$819$		0			0
$820$	1.12688	+	1.42004i	0.0393523	+	0.0495898i
$821$	−16.3785	−	9.45611i	−0.571612	−	0.330020i	0.186181	−	0.982516i	$-0.440389\pi$
$821$	−16.3785	−	9.45611i	−0.571612	−	0.330020i	−0.757793	+	0.652495i	$0.773722\pi$
$822$		0			0
$823$	5.97209	−	3.44799i	0.208174	−	0.120189i	−0.392289	−	0.919842i	$-0.628317\pi$
$823$	5.97209	−	3.44799i	0.208174	−	0.120189i	0.600462	+	0.799653i	$0.294983\pi$
$824$	−44.2681			−1.54215
$825$		0			0
$826$	5.00838	+	9.26150i	0.174264	+	0.322249i
$827$	25.2231			0.877092			0.438546	−	0.898709i	$-0.355494\pi$
$827$	25.2231			0.877092			0.438546	+	0.898709i	$0.355494\pi$
$828$		0			0
$829$	32.6101	+	18.8275i	1.13260	+	0.653905i	0.944587	−	0.328262i	$-0.106463\pi$
$829$	32.6101	+	18.8275i	1.13260	+	0.653905i	0.188010	+	0.982167i	$0.439796\pi$
$830$	23.6253	−	18.7480i	0.820045	−	0.650751i
$831$		0			0
$832$	−2.36577	+	4.09763i	−0.0820182	+	0.142060i
$833$	31.8846	−	16.1108i	1.10474	−	0.558206i
$834$		0			0
$835$	6.26134	+	42.2286i	0.216683	+	1.46138i
$836$	1.12217	−	1.94365i	0.0388110	−	0.0672226i
$837$		0			0
$838$	−12.7127	−	22.0190i	−0.439151	−	0.760632i
$839$	5.38545	+	9.32787i	0.185926	+	0.322034i	0.943888	−	0.330265i	$-0.107138\pi$
$839$	5.38545	+	9.32787i	0.185926	+	0.322034i	−0.757962	+	0.652299i	$0.773805\pi$
$840$		0			0
$841$	−14.0277	+	24.2967i	−0.483714	+	0.837817i
$842$	19.2177			0.662286
$843$		0			0
$844$	−5.04322			−0.173595
$845$	−10.4415	+	26.4178i	−0.359197	+	0.908801i
$846$		0			0
$847$	−10.9101	−	20.1750i	−0.374877	−	0.693222i
$848$	15.0092	+	25.9966i	0.515416	+	0.892727i
$849$		0			0
$850$	9.85491	+	32.5019i	0.338021	+	1.11480i
$851$	10.5378	−	6.08402i	0.361232	−	0.208557i
$852$		0			0
$853$	−3.27573	−	5.67372i	−0.112159	−	0.194265i	0.804482	−	0.593977i	$-0.202443\pi$
$853$	−3.27573	−	5.67372i	−0.112159	−	0.194265i	−0.916640	+	0.399713i	$0.869110\pi$
$854$	−14.9149	−	9.17450i	−0.510378	−	0.313945i
$855$		0			0
$856$	0.142210	+	0.246314i	0.00486063	+	0.00841885i
$857$			22.1358i			0.756146i	0.925776	+	0.378073i	$0.123413\pi$
$857$			22.1358i			0.756146i	−0.925776	+	0.378073i	$0.876587\pi$
$858$		0			0
$859$		−	12.4292i		−	0.424079i	−0.977261	−	0.212039i	$-0.931990\pi$
$859$		−	12.4292i		−	0.424079i	0.977261	−	0.212039i	$-0.0680105\pi$
$860$	−0.118994	−	0.802538i	−0.00405767	−	0.0273663i
$861$		0			0
$862$	−28.2017	+	16.2823i	−0.960555	+	0.554576i
$863$	0.359565	+	0.622785i	0.0122397	+	0.0211999i	0.872080	−	0.489363i	$-0.162771\pi$
$863$	0.359565	+	0.622785i	0.0122397	+	0.0211999i	−0.859841	+	0.510562i	$0.829437\pi$
$864$		0			0
$865$	0.989870	+	6.67602i	0.0336566	+	0.226992i
$866$	−22.0728	+	38.2313i	−0.750065	+	1.29915i
$867$		0			0
$868$	−0.0633462	+	2.27264i	−0.00215011	+	0.0771383i
$869$	2.09972	+	1.21227i	0.0712280	+	0.0411235i
$870$		0			0
$871$			8.17070i			0.276853i
$872$	8.74958	−	15.1547i	0.296298	−	0.513204i
$873$		0			0
$874$			13.6838i			0.462862i
$875$	23.8413	+	17.5098i	0.805982	+	0.591940i
$876$		0			0
$877$		−	36.2413i		−	1.22378i	−0.790942	−	0.611892i	$-0.790409\pi$
$877$		−	36.2413i		−	1.22378i	0.790942	−	0.611892i	$-0.209591\pi$
$878$	−1.33442	+	0.770428i	−0.0450345	+	0.0260007i
$879$		0			0
$880$	1.74797	+	11.7889i	0.0589242	+	0.397405i
$881$	−55.7865			−1.87950			−0.939748	−	0.341869i	$-0.888940\pi$
$881$	−55.7865			−1.87950			−0.939748	+	0.341869i	$0.888940\pi$
$882$		0			0
$883$		−	23.7897i		−	0.800586i	−0.916387	−	0.400293i	$-0.868908\pi$
$883$		−	23.7897i		−	0.800586i	0.916387	−	0.400293i	$-0.131092\pi$
$884$	0.549525	+	0.317269i	0.0184825	+	0.0106709i
$885$		0			0
$886$	−2.95450	−	5.11734i	−0.0992583	−	0.171920i
$887$		−	13.5631i		−	0.455403i	−0.973731	−	0.227702i	$-0.926879\pi$
$887$		−	13.5631i		−	0.455403i	0.973731	−	0.227702i	$-0.0731211\pi$
$888$		0			0
$889$	−29.7065	+	16.0645i	−0.996323	+	0.538786i
$890$	2.90281	+	3.65799i	0.0973025	+	0.122616i
$891$		0			0
$892$	−0.107227	+	0.185722i	−0.00359021	+	0.00621842i
$893$	−81.9329			−2.74178
$894$		0			0
$895$	4.36921	+	29.4674i	0.146046	+	0.984987i
$896$	23.8003	+	0.663397i	0.795114	+	0.0221625i
$897$		0			0
$898$	26.4718	+	15.2835i	0.883374	+	0.510016i
$899$	1.82797	−	3.16613i	0.0609661	−	0.105596i
$900$		0			0
$901$	38.0044	−	21.9418i	1.26611	−	0.730989i
$902$	−6.24569	+	3.60595i	−0.207959	+	0.120065i
$903$		0			0
$904$	4.51334	−	7.81733i	0.150111	−	0.260001i
$905$	−16.4838	+	13.0808i	−0.547941	+	0.434821i
$906$		0			0
$907$		−	26.2698i		−	0.872276i	−0.899880	−	0.436138i	$-0.856346\pi$
$907$		−	26.2698i		−	0.872276i	0.899880	−	0.436138i	$-0.143654\pi$
$908$	−1.67876	+	0.969233i	−0.0557117	+	0.0321651i
$909$		0			0
$910$	−4.25539	+	0.510236i	−0.141065	+	0.0169142i
$911$	10.8162	−	6.24472i	0.358356	−	0.206897i	−0.310004	−	0.950735i	$-0.600330\pi$
$911$	10.8162	−	6.24472i	0.358356	−	0.206897i	0.668359	+	0.743839i	$0.266997\pi$
$912$		0			0
$913$	−7.73591	−	13.3990i	−0.256021	−	0.443442i
$914$	−9.14248	+	5.27841i	−0.302406	+	0.174594i
$915$		0			0
$916$	−3.20000	+	1.84752i	−0.105731	+	0.0610438i
$917$	1.01917	+	1.88466i	0.0336561	+	0.0622369i
$918$		0			0
$919$	−5.65826	−	9.80040i	−0.186649	−	0.323285i	0.757482	−	0.652856i	$-0.226429\pi$
$919$	−5.65826	−	9.80040i	−0.186649	−	0.323285i	−0.944131	+	0.329571i	$0.893096\pi$
$920$	6.58665	+	8.30018i	0.217155	+	0.273649i
$921$		0			0
$922$	48.8432			1.60856
$923$	7.41804	+	4.28281i	0.244168	+	0.140970i
$924$		0			0
$925$	−11.0498	−	36.4426i	−0.363315	−	1.19823i
$926$	−24.4526	+	14.1177i	−0.803561	+	0.463936i
$927$		0			0
$928$	1.08213	+	0.624767i	0.0355226	+	0.0205090i
$929$	−13.6964	+	23.7228i	−0.449363	+	0.778319i	−0.998345	−	0.0575149i	$-0.981682\pi$
$929$	−13.6964	+	23.7228i	−0.449363	+	0.778319i	0.548982	+	0.835834i	$0.315016\pi$
$930$		0			0
$931$	2.50916	−	44.9749i	0.0822344	−	1.47399i
$932$	−2.47131	+	4.28043i	−0.0809504	+	0.140210i
$933$		0			0
$934$		−	47.3999i		−	1.55097i
$935$	17.2342	−	2.55536i	0.563619	−	0.0835692i
$936$		0			0
$937$	19.0277			0.621609			0.310804	−	0.950474i	$-0.399402\pi$
$937$	19.0277			0.621609			0.310804	+	0.950474i	$0.399402\pi$
$938$	46.5001	−	25.1461i	1.51828	−	0.821049i
$939$		0			0
$940$	−5.09459	+	4.04284i	−0.166167	+	0.131863i
$941$	12.7729	+	22.1233i	0.416384	+	0.721198i	0.995573	−	0.0939955i	$-0.0299639\pi$
$941$	12.7729	+	22.1233i	0.416384	+	0.721198i	−0.579189	+	0.815193i	$0.696631\pi$
$942$		0			0
$943$	−2.83500	+	4.91037i	−0.0923203	+	0.159904i
$944$	10.4376			0.339715
$945$		0			0
$946$	3.22760			0.104938
$947$	−13.7203	+	23.7643i	−0.445851	+	0.772237i	−0.998111	−	0.0614349i	$-0.980432\pi$
$947$	−13.7203	+	23.7643i	−0.445851	+	0.772237i	0.552260	+	0.833672i	$0.313766\pi$
$948$		0			0
$949$	−2.47245	−	4.28241i	−0.0802592	−	0.139013i
$950$	41.7049	+	9.72969i	1.35308	+	0.315673i
$951$		0			0
$952$	1.11586	−	40.0330i	0.0361651	−	1.29748i
$953$	49.3870			1.59980			0.799901	−	0.600132i	$-0.204885\pi$
$953$	49.3870			1.59980			0.799901	+	0.600132i	$0.204885\pi$
$954$		0			0
$955$	1.64526	+	11.0962i	0.0532394	+	0.359065i
$956$			3.82957i			0.123857i
$957$		0			0
$958$	9.40353	−	16.2874i	0.303814	−	0.526222i
$959$	−12.6853	−	23.4576i	−0.409629	−	0.757485i
$960$		0			0
$961$	−8.42498	+	14.5925i	−0.271773	+	0.470725i
$962$	4.77831	+	2.75876i	0.154059	+	0.0889460i
$963$		0			0
$964$	−1.65056	+	0.952953i	−0.0531610	+	0.0306925i
$965$	−14.0056	−	5.53560i	−0.450855	−	0.178197i
$966$		0			0
$967$	41.2438	+	23.8121i	1.32631	+	0.765747i	0.984727	−	0.174104i	$-0.0557028\pi$
$967$	41.2438	+	23.8121i	1.32631	+	0.765747i	0.341585	+	0.939851i	$0.389036\pi$
$968$	−25.7127			−0.826439
$969$		0			0
$970$	16.7667	+	21.1286i	0.538346	+	0.678398i
$971$	20.5995	+	35.6794i	0.661070	+	1.14501i	0.980335	+	0.197341i	$0.0632307\pi$
$971$	20.5995	+	35.6794i	0.661070	+	1.14501i	−0.319265	+	0.947665i	$0.603436\pi$
$972$		0			0
$973$	−1.31947	+	47.3381i	−0.0423004	+	1.51759i
$974$	−5.95232	+	3.43658i	−0.190725	+	0.110115i
$975$		0			0
$976$	−15.0332	+	8.67939i	−0.481199	+	0.277821i
$977$	−3.73492	−	6.46907i	−0.119491	−	0.206964i	0.800075	−	0.599900i	$-0.204793\pi$
$977$	−3.73492	−	6.46907i	−0.119491	−	0.206964i	−0.919566	+	0.392936i	$0.871459\pi$
$978$		0			0
$979$	2.07461	−	1.19778i	0.0663050	−	0.0382812i
$980$	−2.06319	−	2.92035i	−0.0659062	−	0.0932872i
$981$		0			0
$982$	−25.2485	+	14.5772i	−0.805713	+	0.465178i
$983$		−	23.6415i		−	0.754046i	−0.926204	−	0.377023i	$-0.876948\pi$
$983$		−	23.6415i		−	0.754046i	0.926204	−	0.377023i	$-0.123052\pi$
$984$		0			0
$985$	−13.5024	−	17.0151i	−0.430223	−	0.542147i
$986$	−3.30085	+	5.71724i	−0.105121	+	0.182074i
$987$		0			0
$988$	0.692909	−	0.400051i	0.0220444	−	0.0127273i
$989$	2.19758	−	1.26877i	0.0698789	−	0.0403446i
$990$		0			0
$991$	−20.6478	+	35.7631i	−0.655899	+	1.13605i	0.325768	+	0.945450i	$0.394377\pi$
$991$	−20.6478	+	35.7631i	−0.655899	+	1.13605i	−0.981668	+	0.190601i	$0.938956\pi$
$992$	4.18831	+	2.41812i	0.132979	+	0.0767754i
$993$		0			0
$994$	1.54412	−	55.3974i	0.0489764	−	1.75710i
$995$	−4.81878	−	32.4995i	−0.152766	−	1.03030i
$996$		0			0
$997$	39.9598			1.26554			0.632769	−	0.774341i	$-0.281918\pi$
$997$	39.9598			1.26554			0.632769	+	0.774341i	$0.281918\pi$
$998$	−26.9757	+	46.7233i	−0.853900	+	1.47900i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	945.2.u.a.584.13		88
3.2	odd	2		315.2.u.a.59.32	yes	88
5.4	even	2	inner	945.2.u.a.584.32		88
7.5	odd	6		945.2.bq.a.719.32		88
9.2	odd	6		945.2.bq.a.899.13		88
9.7	even	3		315.2.bq.a.164.32	yes	88
15.14	odd	2		315.2.u.a.59.13	✓	88
21.5	even	6		315.2.bq.a.194.13	yes	88
35.19	odd	6		945.2.bq.a.719.13		88
45.29	odd	6		945.2.bq.a.899.32		88
45.34	even	6		315.2.bq.a.164.13	yes	88
63.47	even	6	inner	945.2.u.a.89.32		88
63.61	odd	6		315.2.u.a.299.13	yes	88
105.89	even	6		315.2.bq.a.194.32	yes	88
315.124	odd	6		315.2.u.a.299.32	yes	88
315.299	even	6	inner	945.2.u.a.89.13		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.u.a.59.13	✓	88	15.14	odd	2
315.2.u.a.59.32	yes	88	3.2	odd	2
315.2.u.a.299.13	yes	88	63.61	odd	6
315.2.u.a.299.32	yes	88	315.124	odd	6
315.2.bq.a.164.13	yes	88	45.34	even	6
315.2.bq.a.164.32	yes	88	9.7	even	3
315.2.bq.a.194.13	yes	88	21.5	even	6
315.2.bq.a.194.32	yes	88	105.89	even	6
945.2.u.a.89.13		88	315.299	even	6	inner
945.2.u.a.89.32		88	63.47	even	6	inner
945.2.u.a.584.13		88	1.1	even	1	trivial
945.2.u.a.584.32		88	5.4	even	2	inner
945.2.bq.a.719.13		88	35.19	odd	6
945.2.bq.a.719.32		88	7.5	odd	6
945.2.bq.a.899.13		88	9.2	odd	6
945.2.bq.a.899.32		88	45.29	odd	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:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.u (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.665500 + 1.15268i) q^{2} +(0.114220 + 0.197834i) q^{4} +(1.38997 + 1.75157i) q^{5} +(-1.25852 - 2.32726i) q^{7} -2.96605 q^{8} +O(q^{10})\)	\(q+(-0.665500 + 1.15268i) q^{2} +(0.114220 + 0.197834i) q^{4} +(1.38997 + 1.75157i) q^{5} +(-1.25852 - 2.32726i) q^{7} -2.96605 q^{8} +(-2.94402 + 0.436517i) q^{10} +1.52676i q^{11} +(-0.272143 + 0.471366i) q^{13} +(3.52013 + 0.0981180i) q^{14} +(1.74547 - 3.02324i) q^{16} +(-4.41967 - 2.55170i) q^{17} +(-5.57286 + 3.21749i) q^{19} +(-0.187759 + 0.475046i) q^{20} +(-1.75986 - 1.01606i) q^{22} -1.59765 q^{23} +(-1.13599 + 4.86924i) q^{25} +(-0.362222 - 0.627388i) q^{26} +(0.316663 - 0.514797i) q^{28} +(-0.841685 + 0.485947i) q^{29} +(-3.25769 + 1.88083i) q^{31} +(-0.642834 - 1.11342i) q^{32} +(5.88258 - 3.39631i) q^{34} +(2.32705 - 5.43919i) q^{35} +(-6.59583 + 3.80810i) q^{37} -8.56496i q^{38} +(-4.12271 - 5.19525i) q^{40} +(1.77448 - 3.07349i) q^{41} +(-1.37551 + 0.794149i) q^{43} +(-0.302045 + 0.174386i) q^{44} +(1.06324 - 1.84158i) q^{46} +(11.0266 + 6.36621i) q^{47} +(-3.83225 + 5.85780i) q^{49} +(-4.85668 - 4.54991i) q^{50} -0.124336 q^{52} +(-4.29946 + 7.44689i) q^{53} +(-2.67422 + 2.12214i) q^{55} +(3.73284 + 6.90277i) q^{56} -1.29359i q^{58} +(1.49496 + 2.58934i) q^{59} +(-4.30634 - 2.48626i) q^{61} -5.00676i q^{62} +8.69310 q^{64} +(-1.20390 + 0.178505i) q^{65} +(13.0006 - 7.50588i) q^{67} -1.16582i q^{68} +(4.72100 + 6.30213i) q^{70} -15.7373i q^{71} +(-4.54256 + 7.86795i) q^{73} -10.1372i q^{74} +(-1.27306 - 0.735001i) q^{76} +(3.55316 - 1.92146i) q^{77} +(0.794017 - 1.37528i) q^{79} +(7.72156 - 1.14489i) q^{80} +(2.36184 + 4.09082i) q^{82} +(-8.77611 + 5.06689i) q^{83} +(-1.67372 - 11.2881i) q^{85} -2.11402i q^{86} -4.52844i q^{88} +(-0.784525 - 1.35884i) q^{89} +(1.43949 + 0.0401234i) q^{91} +(-0.182483 - 0.316070i) q^{92} +(-14.6764 + 8.47343i) q^{94} +(-13.3817 - 5.28904i) q^{95} +(-4.53143 - 7.84866i) q^{97} +(-4.20181 - 8.31573i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 38 q^{4} + 6 q^{5}+O(q^{10}) \) 88 * q - 38 * q^4 + 6 * q^5	\( 88 q - 38 q^{4} + 6 q^{5} - 6 q^{10} + 12 q^{14} - 26 q^{16} - 12 q^{19} - 6 q^{20} - 2 q^{25} - 12 q^{26} - 6 q^{29} - 6 q^{31} + 12 q^{34} + 6 q^{41} - 84 q^{44} - 18 q^{46} + 10 q^{49} - 30 q^{50} + 90 q^{56} + 6 q^{59} + 12 q^{61} - 8 q^{64} - 54 q^{65} - 30 q^{70} + 48 q^{76} + 8 q^{79} - 69 q^{80} - 7 q^{85} + 72 q^{89} + 20 q^{91} - 6 q^{94} + 93 q^{95}+O(q^{100}) \) 88 * q - 38 * q^4 + 6 * q^5 - 6 * q^10 + 12 * q^14 - 26 * q^16 - 12 * q^19 - 6 * q^20 - 2 * q^25 - 12 * q^26 - 6 * q^29 - 6 * q^31 + 12 * q^34 + 6 * q^41 - 84 * q^44 - 18 * q^46 + 10 * q^49 - 30 * q^50 + 90 * q^56 + 6 * q^59 + 12 * q^61 - 8 * q^64 - 54 * q^65 - 30 * q^70 + 48 * q^76 + 8 * q^79 - 69 * q^80 - 7 * q^85 + 72 * q^89 + 20 * q^91 - 6 * q^94 + 93 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more