LMFDB - Embedded newform 864.2.w.b.107.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(107,864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 5, 4]))

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

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

chi := DirichletCharacter("864.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.w (of order $8$, degree $4$, 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:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			107.7
Character	$\chi$	$=$	864.107
Dual form			864.2.w.b.323.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.23132 + 0.695593i) q^{2} +(1.03230 - 1.71300i) q^{4} +(2.52121 + 1.04432i) q^{5} +(-2.75999 + 2.75999i) q^{7} +(-0.0795431 + 2.82731i) q^{8} +O(q^{10})$	\(q+(-1.23132 + 0.695593i) q^{2} +(1.03230 - 1.71300i) q^{4} +(2.52121 + 1.04432i) q^{5} +(-2.75999 + 2.75999i) q^{7} +(-0.0795431 + 2.82731i) q^{8} +(-3.83084 + 0.467845i) q^{10} +(3.15673 + 1.30756i) q^{11} +(1.32814 + 3.20642i) q^{13} +(1.47860 - 5.31826i) q^{14} +(-1.86871 - 3.53665i) q^{16} -0.590942 q^{17} +(-7.23425 + 2.99653i) q^{19} +(4.39156 - 3.24077i) q^{20} +(-4.79648 + 0.585775i) q^{22} +(-0.159561 + 0.159561i) q^{23} +(1.73037 + 1.73037i) q^{25} +(-3.86573 - 3.02428i) q^{26} +(1.87871 + 7.57698i) q^{28} +(-2.09659 - 5.06161i) q^{29} -10.3283i q^{31} +(4.76106 + 3.05489i) q^{32} +(0.727639 - 0.411055i) q^{34} +(-9.84082 + 4.07620i) q^{35} +(-2.97558 + 7.18370i) q^{37} +(6.82332 - 8.72178i) q^{38} +(-3.15316 + 7.04517i) q^{40} +(7.49577 + 7.49577i) q^{41} +(-2.83493 + 6.84412i) q^{43} +(5.49855 - 4.05768i) q^{44} +(0.0854814 - 0.307461i) q^{46} +1.79382i q^{47} -8.23506i q^{49} +(-3.33426 - 0.927004i) q^{50} +(6.86363 + 1.03488i) q^{52} +(1.90176 - 4.59125i) q^{53} +(6.59328 + 6.59328i) q^{55} +(-7.58380 - 8.02287i) q^{56} +(6.10239 + 4.77409i) q^{58} +(-4.80007 + 11.5884i) q^{59} +(9.75001 - 4.03859i) q^{61} +(7.18429 + 12.7174i) q^{62} +(-7.98735 - 0.449786i) q^{64} +9.47106i q^{65} +(-0.992689 - 2.39656i) q^{67} +(-0.610029 + 1.01228i) q^{68} +(9.28182 - 11.8643i) q^{70} +(0.925964 + 0.925964i) q^{71} +(2.09420 - 2.09420i) q^{73} +(-1.33303 - 10.9152i) q^{74} +(-2.33488 + 15.4856i) q^{76} +(-12.3214 + 5.10369i) q^{77} -9.57332 q^{79} +(-1.01803 - 10.8682i) q^{80} +(-14.4437 - 4.01569i) q^{82} +(0.839042 + 2.02563i) q^{83} +(-1.48989 - 0.617132i) q^{85} +(-1.27002 - 10.3993i) q^{86} +(-3.94798 + 8.82105i) q^{88} +(-9.00492 + 9.00492i) q^{89} +(-12.5153 - 5.18402i) q^{91} +(0.108613 + 0.438044i) q^{92} +(-1.24777 - 2.20877i) q^{94} -21.3684 q^{95} -2.36775 q^{97} +(5.72825 + 10.1400i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q+O(q^{10}) $ 128 * q	$ 128 q + 8 q^{10} + 32 q^{16} - 32 q^{22} + 64 q^{40} + 64 q^{46} + 40 q^{52} + 64 q^{55} + 64 q^{58} + 32 q^{61} + 96 q^{64} - 64 q^{67} - 48 q^{70} - 32 q^{76} - 32 q^{79} + 40 q^{82} + 40 q^{88} - 48 q^{91} + 72 q^{94}+O(q^{100}) $ 128 * q + 8 * q^10 + 32 * q^16 - 32 * q^22 + 64 * q^40 + 64 * q^46 + 40 * q^52 + 64 * q^55 + 64 * q^58 + 32 * q^61 + 96 * q^64 - 64 * q^67 - 48 * q^70 - 32 * q^76 - 32 * q^79 + 40 * q^82 + 40 * q^88 - 48 * q^91 + 72 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.23132	+	0.695593i	−0.870675	+	0.491859i
$2$	−1.23132	+	0.695593i	−0.870675	+	0.491859i
$3$		0			0
$3$		0			0
$4$	1.03230	−	1.71300i	0.516150	−	0.856498i
$5$	2.52121	+	1.04432i	1.12752	+	0.467034i	0.866937	−	0.498418i	$-0.166085\pi$
$5$	2.52121	+	1.04432i	1.12752	+	0.467034i	0.260583	+	0.965452i	$0.416085\pi$
$6$		0			0
$7$	−2.75999	+	2.75999i	−1.04318	+	1.04318i	−0.0441523	+	0.999025i	$0.514059\pi$
$7$	−2.75999	+	2.75999i	−1.04318	+	1.04318i	−0.999025	+	0.0441523i	$0.985941\pi$
$8$	−0.0795431	+	2.82731i	−0.0281227	+	0.999604i
$9$		0			0
$10$	−3.83084	+	0.467845i	−1.21142	+	0.147946i
$11$	3.15673	+	1.30756i	0.951791	+	0.394245i	0.803904	−	0.594759i	$-0.202753\pi$
$11$	3.15673	+	1.30756i	0.951791	+	0.394245i	0.147887	+	0.989004i	$0.452753\pi$
$12$		0			0
$13$	1.32814	+	3.20642i	0.368360	+	0.889301i	0.994019	+	0.109204i	$0.0348302\pi$
$13$	1.32814	+	3.20642i	0.368360	+	0.889301i	−0.625659	+	0.780097i	$0.715170\pi$
$14$	1.47860	−	5.31826i	0.395172	−	1.42136i
$15$		0			0
$16$	−1.86871	−	3.53665i	−0.467178	−	0.884163i
$17$	−0.590942			−0.143324			−0.0716622	−	0.997429i	$-0.522830\pi$
$17$	−0.590942			−0.143324			−0.0716622	+	0.997429i	$0.522830\pi$
$18$		0			0
$19$	−7.23425	+	2.99653i	−1.65965	+	0.687450i	−0.998051	−	0.0624058i	$-0.980123\pi$
$19$	−7.23425	+	2.99653i	−1.65965	+	0.687450i	−0.661601	+	0.749856i	$0.730123\pi$
$20$	4.39156	−	3.24077i	0.981983	−	0.724659i
$21$		0			0
$22$	−4.79648	+	0.585775i	−1.02261	+	0.124888i
$23$	−0.159561	+	0.159561i	−0.0332709	+	0.0332709i	−0.723547	−	0.690276i	$-0.757489\pi$
$23$	−0.159561	+	0.159561i	−0.0332709	+	0.0332709i	0.690276	+	0.723547i	$0.257489\pi$
$24$		0			0
$25$	1.73037	+	1.73037i	0.346073	+	0.346073i
$26$	−3.86573	−	3.02428i	−0.758133	−	0.593111i
$27$		0			0
$28$	1.87871	+	7.57698i	0.355044	+	1.43192i
$29$	−2.09659	−	5.06161i	−0.389326	−	0.939917i	−0.990083	−	0.140485i	$-0.955134\pi$
$29$	−2.09659	−	5.06161i	−0.389326	−	0.939917i	0.600756	−	0.799432i	$-0.294866\pi$
$30$		0			0
$31$		−	10.3283i		−	1.85501i	−0.373805	−	0.927507i	$-0.621947\pi$
$31$		−	10.3283i		−	1.85501i	0.373805	−	0.927507i	$-0.378053\pi$
$32$	4.76106	+	3.05489i	0.841644	+	0.540033i
$33$		0			0
$34$	0.727639	−	0.411055i	0.124789	−	0.0704954i
$35$	−9.84082	+	4.07620i	−1.66340	+	0.689004i
$36$		0			0
$37$	−2.97558	+	7.18370i	−0.489183	+	1.18099i	0.465949	+	0.884812i	$0.345713\pi$
$37$	−2.97558	+	7.18370i	−0.489183	+	1.18099i	−0.955132	+	0.296181i	$0.904287\pi$
$38$	6.82332	−	8.72178i	1.10689	−	1.41486i
$39$		0			0
$40$	−3.15316	+	7.04517i	−0.498558	+	1.11394i
$41$	7.49577	+	7.49577i	1.17064	+	1.17064i	0.982057	+	0.188586i	$0.0603903\pi$
$41$	7.49577	+	7.49577i	1.17064	+	1.17064i	0.188586	+	0.982057i	$0.439610\pi$
$42$		0			0
$43$	−2.83493	+	6.84412i	−0.432322	+	1.04372i	0.546214	+	0.837645i	$0.316068\pi$
$43$	−2.83493	+	6.84412i	−0.432322	+	1.04372i	−0.978537	+	0.206073i	$0.933932\pi$
$44$	5.49855	−	4.05768i	0.828937	−	0.611718i
$45$		0			0
$46$	0.0854814	−	0.307461i	0.0126035	−	0.0453327i
$47$			1.79382i			0.261656i	0.991405	+	0.130828i	$0.0417635\pi$
$47$			1.79382i			0.261656i	−0.991405	+	0.130828i	$0.958236\pi$
$48$		0			0
$49$		−	8.23506i		−	1.17644i
$50$	−3.33426	−	0.927004i	−0.471536	−	0.131098i
$51$		0			0
$52$	6.86363	+	1.03488i	0.951814	+	0.143513i
$53$	1.90176	−	4.59125i	0.261226	−	0.630656i	−0.737789	−	0.675032i	$-0.764130\pi$
$53$	1.90176	−	4.59125i	0.261226	−	0.630656i	0.999015	+	0.0443757i	$0.0141299\pi$
$54$		0			0
$55$	6.59328	+	6.59328i	0.889038	+	0.889038i
$56$	−7.58380	−	8.02287i	−1.01343	−	1.07210i
$57$		0			0
$58$	6.10239	+	4.77409i	0.801283	+	0.626869i
$59$	−4.80007	+	11.5884i	−0.624916	+	1.50868i	0.220950	+	0.975285i	$0.429084\pi$
$59$	−4.80007	+	11.5884i	−0.624916	+	1.50868i	−0.845866	+	0.533395i	$0.820916\pi$
$60$		0			0
$61$	9.75001	−	4.03859i	1.24836	−	0.517088i	0.342043	−	0.939684i	$-0.388881\pi$
$61$	9.75001	−	4.03859i	1.24836	−	0.517088i	0.906318	+	0.422597i	$0.138881\pi$
$62$	7.18429	+	12.7174i	0.912405	+	1.61512i
$63$		0			0
$64$	−7.98735	−	0.449786i	−0.998418	−	0.0562232i
$65$			9.47106i			1.17474i
$66$		0			0
$67$	−0.992689	−	2.39656i	−0.121276	−	0.292787i	0.851569	−	0.524242i	$-0.175651\pi$
$67$	−0.992689	−	2.39656i	−0.121276	−	0.292787i	−0.972846	+	0.231455i	$0.925651\pi$
$68$	−0.610029	+	1.01228i	−0.0739769	+	0.122757i
$69$		0			0
$70$	9.28182	−	11.8643i	1.10939	−	1.41806i
$71$	0.925964	+	0.925964i	0.109892	+	0.109892i	0.759915	−	0.650023i	$-0.225241\pi$
$71$	0.925964	+	0.925964i	0.109892	+	0.109892i	−0.650023	+	0.759915i	$0.725241\pi$
$72$		0			0
$73$	2.09420	−	2.09420i	0.245108	−	0.245108i	−0.573851	−	0.818959i	$-0.694551\pi$
$73$	2.09420	−	2.09420i	0.245108	−	0.245108i	0.818959	+	0.573851i	$0.194551\pi$
$74$	−1.33303	−	10.9152i	−0.154962	−	1.26887i
$75$		0			0
$76$	−2.33488	+	15.4856i	−0.267829	+	1.77632i
$77$	−12.3214	+	5.10369i	−1.40415	+	0.581620i
$78$		0			0
$79$	−9.57332			−1.07708			−0.538541	−	0.842599i	$-0.681024\pi$
$79$	−9.57332			−1.07708			−0.538541	+	0.842599i	$0.681024\pi$
$80$	−1.01803	−	10.8682i	−0.113819	−	1.21510i
$81$		0			0
$82$	−14.4437	−	4.01569i	−1.59504	−	0.443458i
$83$	0.839042	+	2.02563i	0.0920969	+	0.222341i	0.963215	−	0.268732i	$-0.0866046\pi$
$83$	0.839042	+	2.02563i	0.0920969	+	0.222341i	−0.871118	+	0.491074i	$0.836605\pi$
$84$		0			0
$85$	−1.48989	−	0.617132i	−0.161601	−	0.0669374i
$86$	−1.27002	−	10.3993i	−0.136950	−	1.12138i
$87$		0			0
$88$	−3.94798	+	8.82105i	−0.420856	+	0.940328i
$89$	−9.00492	+	9.00492i	−0.954520	+	0.954520i	−0.999010	−	0.0444899i	$-0.985834\pi$
$89$	−9.00492	+	9.00492i	−0.954520	+	0.954520i	0.0444899	+	0.999010i	$0.485834\pi$
$90$		0			0
$91$	−12.5153	−	5.18402i	−1.31196	−	0.543433i
$92$	0.108613	+	0.438044i	0.0113237	+	0.0456692i
$93$		0			0
$94$	−1.24777	−	2.20877i	−0.128698	−	0.227817i
$95$	−21.3684			−2.19235
$96$		0			0
$97$	−2.36775			−0.240409			−0.120205	−	0.992749i	$-0.538355\pi$
$97$	−2.36775			−0.240409			−0.120205	+	0.992749i	$0.538355\pi$
$98$	5.72825	+	10.1400i	0.578641	+	1.02429i
$99$		0			0
$100$	4.75037	−	1.17785i	0.475037	−	0.117785i
$101$	−2.47915	−	1.02690i	−0.246685	−	0.102180i	0.255915	−	0.966699i	$-0.417623\pi$
$101$	−2.47915	−	1.02690i	−0.246685	−	0.102180i	−0.502600	+	0.864519i	$0.667623\pi$
$102$		0			0
$103$	−3.24401	+	3.24401i	−0.319641	+	0.319641i	−0.848629	−	0.528988i	$-0.822572\pi$
$103$	−3.24401	+	3.24401i	−0.319641	+	0.319641i	0.528988	+	0.848629i	$0.322572\pi$
$104$	−9.17118	+	3.50002i	−0.899308	+	0.343205i
$105$		0			0
$106$	0.851969	+	6.97614i	0.0827505	+	0.677583i
$107$	14.1677	+	5.86846i	1.36964	+	0.567325i	0.941692	−	0.336477i	$-0.109235\pi$
$107$	14.1677	+	5.86846i	1.36964	+	0.567325i	0.427952	+	0.903802i	$0.359235\pi$
$108$		0			0
$109$	3.77718	+	9.11892i	0.361788	+	0.873434i	0.995039	+	0.0994874i	$0.0317203\pi$
$109$	3.77718	+	9.11892i	0.361788	+	0.873434i	−0.633250	+	0.773947i	$0.718280\pi$
$110$	−12.7047	−	3.53220i	−1.21134	−	0.336782i
$111$		0			0
$112$	14.9187	+	4.60349i	1.40969	+	0.434989i
$113$	2.67342			0.251494			0.125747	−	0.992062i	$-0.459867\pi$
$113$	2.67342			0.251494			0.125747	+	0.992062i	$0.459867\pi$
$114$		0			0
$115$	−0.568921	+	0.235655i	−0.0530522	+	0.0219749i
$116$	−10.8348	−	1.63365i	−1.00599	−	0.151681i
$117$		0			0
$118$	−2.15038	−	17.6079i	−0.197959	−	1.62094i
$119$	1.63099	−	1.63099i	0.149513	−	0.149513i
$120$		0			0
$121$	0.477079	+	0.477079i	0.0433708	+	0.0433708i
$122$	−9.19617	+	11.7548i	−0.832582	+	1.06423i
$123$		0			0
$124$	−17.6923	−	10.6619i	−1.58882	−	0.957466i
$125$	−2.66604	−	6.43638i	−0.238458	−	0.575688i
$126$		0			0
$127$			1.71540i			0.152217i	0.997100	+	0.0761086i	$0.0242496\pi$
$127$			1.71540i			0.152217i	−0.997100	+	0.0761086i	$0.975750\pi$
$128$	10.1479	−	5.00211i	0.896952	−	0.442129i
$129$		0			0
$130$	−6.58801	−	11.6619i	−0.577807	−	1.02282i
$131$	18.1991	−	7.53833i	1.59007	−	0.658627i	0.600098	−	0.799926i	$-0.295128\pi$
$131$	18.1991	−	7.53833i	1.59007	−	0.658627i	0.989967	+	0.141300i	$0.0451281\pi$
$132$		0			0
$133$	11.6961	−	28.2368i	1.01418	−	2.44844i
$134$	2.88935	+	2.26043i	0.249602	+	0.195271i
$135$		0			0
$136$	0.0470054	−	1.67078i	0.00403068	−	0.143268i
$137$	3.91910	+	3.91910i	0.334831	+	0.334831i	0.854418	−	0.519587i	$-0.173914\pi$
$137$	3.91910	+	3.91910i	0.334831	+	0.334831i	−0.519587	+	0.854418i	$0.673914\pi$
$138$		0			0
$139$	1.68121	−	4.05881i	0.142599	−	0.344264i	−0.836403	−	0.548114i	$-0.815346\pi$
$139$	1.68121	−	4.05881i	0.142599	−	0.344264i	0.979002	+	0.203851i	$0.0653458\pi$
$140$	−3.17616	+	21.0651i	−0.268434	+	1.78033i
$141$		0			0
$142$	−1.78425	−	0.496064i	−0.149731	−	0.0416288i
$143$			11.8584i			0.991653i
$144$		0			0
$145$		−	14.9509i		−	1.24160i
$146$	−1.12192	+	4.03535i	−0.0928509	+	0.333968i
$147$		0			0
$148$	9.23395	+	12.5129i	0.759026	+	1.02855i
$149$	−0.668420	+	1.61371i	−0.0547591	+	0.132200i	−0.948891	−	0.315603i	$-0.897793\pi$
$149$	−0.668420	+	1.61371i	−0.0547591	+	0.132200i	0.894132	+	0.447803i	$0.147793\pi$
$150$		0			0
$151$	11.5617	+	11.5617i	0.940874	+	0.940874i	0.998347	−	0.0574728i	$-0.0183042\pi$
$151$	11.5617	+	11.5617i	0.940874	+	0.940874i	−0.0574728	+	0.998347i	$0.518304\pi$
$152$	−7.89667	−	20.6918i	−0.640504	−	1.67833i
$153$		0			0
$154$	11.6215	−	14.8550i	0.936487	−	1.19705i
$155$	10.7860	−	26.0398i	0.866355	−	2.09157i
$156$		0			0
$157$	−1.08925	+	0.451183i	−0.0869317	+	0.0360083i	−0.425726	−	0.904852i	$-0.639981\pi$
$157$	−1.08925	+	0.451183i	−0.0869317	+	0.0360083i	0.338794	+	0.940861i	$0.389981\pi$
$158$	11.7878	−	6.65913i	0.937789	−	0.529772i
$159$		0			0
$160$	8.81335	+	12.6741i	0.696756	+	1.00197i
$161$		−	0.880775i		−	0.0694148i
$162$		0			0
$163$	4.66290	+	11.2572i	0.365227	+	0.881735i	0.994518	+	0.104566i	$0.0333452\pi$
$163$	4.66290	+	11.2572i	0.365227	+	0.881735i	−0.629291	+	0.777169i	$0.716655\pi$
$164$	20.5781	−	5.10234i	1.60688	−	0.398426i
$165$		0			0
$166$	−2.44214	−	1.91056i	−0.189547	−	0.148289i
$167$	−5.24577	−	5.24577i	−0.405930	−	0.405930i	0.474387	−	0.880316i	$-0.342670\pi$
$167$	−5.24577	−	5.24577i	−0.405930	−	0.405930i	−0.880316	+	0.474387i	$0.842670\pi$
$168$		0			0
$169$	0.675224	−	0.675224i	0.0519403	−	0.0519403i
$170$	2.26380	−	0.276469i	0.173626	−	0.0212042i
$171$		0			0
$172$	8.79746	+	11.9214i	0.670800	+	0.908998i
$173$	1.03300	−	0.427881i	0.0785373	−	0.0325312i	−0.343069	−	0.939310i	$-0.611466\pi$
$173$	1.03300	−	0.427881i	0.0785373	−	0.0325312i	0.421606	+	0.906779i	$0.361466\pi$
$174$		0			0
$175$	−9.55157			−0.722031
$176$	−1.27464	−	13.6077i	−0.0960796	−	1.02572i
$177$		0			0
$178$	4.82418	−	17.3517i	0.361588	−	1.30057i
$179$	−5.08357	−	12.2728i	−0.379964	−	0.917314i	−0.991971	−	0.126462i	$-0.959638\pi$
$179$	−5.08357	−	12.2728i	−0.379964	−	0.917314i	0.612008	−	0.790852i	$-0.290362\pi$
$180$		0			0
$181$	2.51534	+	1.04189i	0.186964	+	0.0774429i	0.474201	−	0.880416i	$-0.342737\pi$
$181$	2.51534	+	1.04189i	0.186964	+	0.0774429i	−0.287237	+	0.957859i	$0.592737\pi$
$182$	19.0164	−	2.32239i	1.40959	−	0.172147i
$183$		0			0
$184$	−0.438438	−	0.463822i	−0.0323220	−	0.0341934i
$185$	−15.0042	+	15.0042i	−1.10313	+	1.10313i
$186$		0			0
$187$	−1.86545	−	0.772693i	−0.136415	−	0.0565049i
$188$	3.07281	+	1.85176i	0.224108	+	0.135054i
$189$		0			0
$190$	26.3114	−	14.8637i	1.90883	−	1.07833i
$191$	8.74031			0.632426			0.316213	−	0.948688i	$-0.397589\pi$
$191$	8.74031			0.632426			0.316213	+	0.948688i	$0.397589\pi$
$192$		0			0
$193$	14.0025			1.00792			0.503962	−	0.863726i	$-0.331875\pi$
$193$	14.0025			1.00792			0.503962	+	0.863726i	$0.331875\pi$
$194$	2.91546	−	1.64699i	0.209318	−	0.118247i
$195$		0			0
$196$	−14.1066	−	8.50105i	−1.00762	−	0.607218i
$197$	20.0422	+	8.30177i	1.42795	+	0.591477i	0.956845	−	0.290600i	$-0.0938548\pi$
$197$	20.0422	+	8.30177i	1.42795	+	0.591477i	0.471106	+	0.882076i	$0.343855\pi$
$198$		0			0
$199$	3.93311	−	3.93311i	0.278811	−	0.278811i	−0.553824	−	0.832634i	$-0.686832\pi$
$199$	3.93311	−	3.93311i	0.278811	−	0.278811i	0.832634	+	0.553824i	$0.186832\pi$
$200$	−5.02991	+	4.75464i	−0.355669	+	0.336204i
$201$		0			0
$202$	3.76694	−	0.460041i	0.265041	−	0.0323684i
$203$	19.7565	+	8.18342i	1.38664	+	0.574364i
$204$		0			0
$205$	11.0704	+	26.7264i	0.773193	+	1.86665i
$206$	1.73790	−	6.25092i	0.121085	−	0.435522i
$207$		0			0
$208$	8.85807	−	10.6891i	0.614197	−	0.741153i
$209$	−26.7548			−1.85067
$210$		0			0
$211$	0.0143948	−	0.00596253i	0.000990981	−	0.000410478i	−0.382188	−	0.924085i	$-0.624829\pi$
$211$	0.0143948	−	0.00596253i	0.000990981	−	0.000410478i	0.383179	+	0.923674i	$0.374829\pi$
$212$	−5.90161	−	7.99725i	−0.405324	−	0.549253i
$213$		0			0
$214$	−21.5270	+	2.62901i	−1.47156	+	0.179716i
$215$	−14.2949	+	14.2949i	−0.974904	+	0.974904i
$216$		0			0
$217$	28.5059	+	28.5059i	1.93511	+	1.93511i
$218$	−10.9940	−	8.60093i	−0.744606	−	0.582529i
$219$		0			0
$220$	18.1005	−	4.48802i	1.22034	−	0.302582i
$221$	−0.784855	−	1.89481i	−0.0527951	−	0.127459i
$222$		0			0
$223$		−	4.89819i		−	0.328007i	−0.986460	−	0.164003i	$-0.947559\pi$
$223$		−	4.89819i		−	0.328007i	0.986460	−	0.164003i	$-0.0524408\pi$
$224$	−21.5719	+	4.70901i	−1.44133	+	0.314634i
$225$		0			0
$226$	−3.29184	+	1.85961i	−0.218970	+	0.123700i
$227$	14.3690	−	5.95182i	0.953702	−	0.395036i	0.149081	−	0.988825i	$-0.452369\pi$
$227$	14.3690	−	5.95182i	0.953702	−	0.395036i	0.804621	+	0.593789i	$0.202369\pi$
$228$		0			0
$229$	10.8779	−	26.2615i	0.718831	−	1.73541i	0.0421779	−	0.999110i	$-0.486570\pi$
$229$	10.8779	−	26.2615i	0.718831	−	1.73541i	0.676653	−	0.736302i	$-0.263430\pi$
$230$	0.536604	−	0.685905i	0.0353826	−	0.0452272i
$231$		0			0
$232$	14.4775	−	5.52508i	0.950494	−	0.362739i
$233$	5.60795	+	5.60795i	0.367389	+	0.367389i	0.866524	−	0.499135i	$-0.166349\pi$
$233$	5.60795	+	5.60795i	0.367389	+	0.367389i	−0.499135	+	0.866524i	$0.666349\pi$
$234$		0			0
$235$	−1.87332	+	4.52260i	−0.122202	+	0.295022i
$236$	14.8958	+	20.1852i	0.969632	+	1.31394i
$237$		0			0
$238$	−0.873767	+	3.14278i	−0.0566379	+	0.203716i
$239$			5.98860i			0.387370i	0.981064	+	0.193685i	$0.0620440\pi$
$239$			5.98860i			0.387370i	−0.981064	+	0.193685i	$0.937956\pi$
$240$		0			0
$241$			10.8688i			0.700119i	0.936727	+	0.350060i	$0.113839\pi$
$241$			10.8688i			0.700119i	−0.936727	+	0.350060i	$0.886161\pi$
$242$	−0.919289	−	0.255584i	−0.0590942	−	0.0164296i
$243$		0			0
$244$	3.14685	−	20.8708i	0.201456	−	1.33611i
$245$	8.60003	−	20.7623i	0.549436	−	1.32646i
$246$		0			0
$247$	−19.2162	−	19.2162i	−1.22270	−	1.22270i
$248$	29.2012	+	0.821544i	1.85428	+	0.0521681i
$249$		0			0
$250$	7.75985	+	6.07077i	0.490776	+	0.383949i
$251$	−6.65686	+	16.0711i	−0.420177	+	1.01440i	0.562118	+	0.827057i	$0.309987\pi$
$251$	−6.65686	+	16.0711i	−0.420177	+	1.01440i	−0.982295	+	0.187340i	$0.940013\pi$
$252$		0			0
$253$	−0.712330	+	0.295057i	−0.0447838	+	0.0185501i
$254$	−1.19322	−	2.11221i	−0.0748693	−	0.132532i
$255$		0			0
$256$	−9.01582	+	13.2180i	−0.563489	+	0.826124i
$257$		−	21.7746i		−	1.35826i	−0.734016	−	0.679132i	$-0.762356\pi$
$257$		−	21.7746i		−	1.35826i	0.734016	−	0.679132i	$-0.237644\pi$
$258$		0			0
$259$	−11.6143	−	28.0395i	−0.721680	−	1.74229i
$260$	16.2239	+	9.77698i	1.00616	+	0.606342i
$261$		0			0
$262$	−17.1653	+	21.9413i	−1.06048	+	1.35554i
$263$	−21.2274	−	21.2274i	−1.30894	−	1.30894i	−0.922181	−	0.386759i	$-0.873594\pi$
$263$	−21.2274	−	21.2274i	−1.30894	−	1.30894i	−0.386759	−	0.922181i	$-0.626406\pi$
$264$		0			0
$265$	9.58946	−	9.58946i	0.589076	−	0.589076i
$266$	5.23973	+	42.9043i	0.321268	+	2.63063i
$267$		0			0
$268$	−5.13005	−	0.773499i	−0.313368	−	0.0472490i
$269$	23.8820	−	9.89224i	1.45611	−	0.603140i	0.492466	−	0.870332i	$-0.336096\pi$
$269$	23.8820	−	9.89224i	1.45611	−	0.603140i	0.963644	+	0.267191i	$0.0860956\pi$
$270$		0			0
$271$	−23.4044			−1.42172			−0.710858	−	0.703336i	$-0.751693\pi$
$271$	−23.4044			−1.42172			−0.710858	+	0.703336i	$0.751693\pi$
$272$	1.10430	+	2.08996i	0.0669581	+	0.126722i
$273$		0			0
$274$	−7.55177	−	2.09957i	−0.456219	−	0.126840i
$275$	3.19974	+	7.72486i	0.192952	+	0.465827i
$276$		0			0
$277$	9.75927	+	4.04242i	0.586377	+	0.242885i	0.656091	−	0.754682i	$-0.272209\pi$
$277$	9.75927	+	4.04242i	0.586377	+	0.242885i	−0.0697138	+	0.997567i	$0.522209\pi$
$278$	0.753167	+	6.16713i	0.0451720	+	0.369880i
$279$		0			0
$280$	−10.7419	−	28.1473i	−0.641952	−	1.68212i
$281$	3.80315	−	3.80315i	0.226877	−	0.226877i	−0.584510	−	0.811387i	$-0.698713\pi$
$281$	3.80315	−	3.80315i	0.226877	−	0.226877i	0.811387	+	0.584510i	$0.198713\pi$
$282$		0			0
$283$	−1.23164	−	0.510161i	−0.0732133	−	0.0303259i	0.345776	−	0.938317i	$-0.387616\pi$
$283$	−1.23164	−	0.510161i	−0.0732133	−	0.0303259i	−0.418990	+	0.907991i	$0.637616\pi$
$284$	2.54205	−	0.630300i	0.150843	−	0.0374014i
$285$		0			0
$286$	−8.24865	−	14.6015i	−0.487753	−	0.863407i
$287$	−41.3765			−2.44237
$288$		0			0
$289$	−16.6508			−0.979458
$290$	10.3997	+	18.4093i	0.610693	+	1.08103i
$291$		0			0
$292$	−1.42552	−	5.74921i	−0.0834220	−	0.336447i
$293$	−18.8646	−	7.81398i	−1.10208	−	0.456497i	−0.243878	−	0.969806i	$-0.578420\pi$
$293$	−18.8646	−	7.81398i	−1.10208	−	0.456497i	−0.858204	+	0.513308i	$0.828420\pi$
$294$		0			0
$295$	−24.2040	+	24.2040i	−1.40921	+	1.40921i
$296$	−20.0738	−	8.98431i	−1.16677	−	0.522202i
$297$		0			0
$298$	−0.299446	−	2.45194i	−0.0173464	−	0.142037i
$299$	−0.723542	−	0.299701i	−0.0418435	−	0.0173321i
$300$		0			0
$301$	−11.0653	−	26.7140i	−0.637794	−	1.53977i
$302$	−22.2783	−	6.19389i	−1.28197	−	0.356419i
$303$		0			0
$304$	24.1164	+	19.9854i	1.38317	+	1.14624i
$305$	28.7994			1.64905
$306$		0			0
$307$	27.7787	−	11.5063i	1.58541	−	0.656700i	0.596155	−	0.802869i	$-0.296694\pi$
$307$	27.7787	−	11.5063i	1.58541	−	0.656700i	0.989260	+	0.146169i	$0.0466944\pi$
$308$	−3.97678	+	26.3751i	−0.226598	+	1.50286i
$309$		0			0
$310$	4.83204	+	39.5660i	0.274441	+	2.24720i
$311$	22.6894	−	22.6894i	1.28660	−	1.28660i	0.349759	−	0.936840i	$-0.386264\pi$
$311$	22.6894	−	22.6894i	1.28660	−	1.28660i	0.936840	−	0.349759i	$-0.113736\pi$
$312$		0			0
$313$	3.91668	+	3.91668i	0.221384	+	0.221384i	0.809081	−	0.587697i	$-0.199965\pi$
$313$	3.91668	+	3.91668i	0.221384	+	0.221384i	−0.587697	+	0.809081i	$0.699965\pi$
$314$	1.02738	−	1.31323i	0.0579783	−	0.0741097i
$315$		0			0
$316$	−9.88253	+	16.3991i	−0.555936	+	0.922519i
$317$	4.65965	+	11.2494i	0.261712	+	0.631828i	0.999045	−	0.0437013i	$-0.0139150\pi$
$317$	4.65965	+	11.2494i	0.261712	+	0.631828i	−0.737333	+	0.675530i	$0.763915\pi$
$318$		0			0
$319$		−	18.7196i		−	1.04809i
$320$	−19.6681	−	9.47535i	−1.09948	−	0.529688i
$321$		0			0
$322$	0.612661	+	1.08452i	0.0341423	+	0.0604378i
$323$	4.27502	−	1.77077i	0.237869	−	0.0985285i
$324$		0			0
$325$	−3.25011	+	7.84645i	−0.180283	+	0.435243i
$326$	−13.5720	−	10.6178i	−0.751683	−	0.588065i
$327$		0			0
$328$	−21.7891	+	20.5966i	−1.20310	+	1.13726i
$329$	−4.95093	−	4.95093i	−0.272953	−	0.272953i
$330$		0			0
$331$	−7.70040	+	18.5904i	−0.423252	+	1.02182i	0.558130	+	0.829754i	$0.311519\pi$
$331$	−7.70040	+	18.5904i	−0.423252	+	1.02182i	−0.981382	+	0.192067i	$0.938481\pi$
$332$	4.33604	+	0.653778i	0.237971	+	0.0358808i
$333$		0			0
$334$	10.1081	+	2.81030i	0.553093	+	0.153773i
$335$		−	7.07892i		−	0.386763i
$336$		0			0
$337$			2.60397i			0.141847i	0.997482	+	0.0709237i	$0.0225947\pi$
$337$			2.60397i			0.141847i	−0.997482	+	0.0709237i	$0.977405\pi$
$338$	−0.361736	+	1.30110i	−0.0196758	+	0.0707704i
$339$		0			0
$340$	−2.59516	+	1.91511i	−0.140742	+	0.103861i
$341$	13.5049	−	32.6037i	0.731330	−	1.76559i
$342$		0			0
$343$	3.40875	+	3.40875i	0.184055	+	0.184055i
$344$	−19.1249	−	8.55962i	−1.03115	−	0.461504i
$345$		0			0
$346$	−0.974318	+	1.24540i	−0.0523797	+	0.0669533i
$347$	5.55043	−	13.3999i	0.297962	−	0.719345i	−0.702012	−	0.712165i	$-0.747715\pi$
$347$	5.55043	−	13.3999i	0.297962	−	0.719345i	0.999974	−	0.00717963i	$-0.00228537\pi$
$348$		0			0
$349$	−26.6749	+	11.0491i	−1.42788	+	0.591445i	−0.956826	−	0.290662i	$-0.906125\pi$
$349$	−26.6749	+	11.0491i	−1.42788	+	0.591445i	−0.471049	+	0.882107i	$0.656125\pi$
$350$	11.7610	−	6.64401i	0.628654	−	0.355137i
$351$		0			0
$352$	11.0349	+	15.8688i	0.588164	+	0.845812i
$353$			26.3575i			1.40287i	0.712733	+	0.701435i	$0.247457\pi$
$353$			26.3575i			1.40287i	−0.712733	+	0.701435i	$0.752543\pi$
$354$		0			0
$355$	1.36755	+	3.30155i	0.0725819	+	0.175228i
$356$	6.12962	+	24.7212i	0.324869	+	1.31022i
$357$		0			0
$358$	14.7964	+	11.5757i	0.782014	+	0.611794i
$359$	8.24427	+	8.24427i	0.435116	+	0.435116i	0.890364	−	0.455248i	$-0.150450\pi$
$359$	8.24427	+	8.24427i	0.435116	+	0.435116i	−0.455248	+	0.890364i	$0.650450\pi$
$360$		0			0
$361$	29.9202	−	29.9202i	1.57475	−	1.57475i
$362$	−3.82192	+	0.466756i	−0.200876	+	0.0245321i
$363$		0			0
$364$	−21.7998	+	16.0873i	−1.14262	+	0.843201i
$365$	7.46694	−	3.09291i	0.390838	−	0.161890i
$366$		0			0
$367$	11.1861			0.583911			0.291955	−	0.956432i	$-0.405694\pi$
$367$	11.1861			0.583911			0.291955	+	0.956432i	$0.405694\pi$
$368$	0.862488	+	0.266139i	0.0449603	+	0.0138734i
$369$		0			0
$370$	8.03813	−	28.9117i	0.417883	−	1.50305i
$371$	7.42296	+	17.9206i	0.385381	+	0.930391i
$372$		0			0
$373$	−3.24489	−	1.34408i	−0.168014	−	0.0695937i	0.297091	−	0.954849i	$-0.403984\pi$
$373$	−3.24489	−	1.34408i	−0.168014	−	0.0695937i	−0.465105	+	0.885255i	$0.653984\pi$
$374$	2.83444	−	0.346159i	0.146566	−	0.0178995i
$375$		0			0
$376$	−5.07169	−	0.142686i	−0.261552	−	0.00735848i
$377$	13.4451	−	13.4451i	0.692456	−	0.692456i
$378$		0			0
$379$	−8.58745	−	3.55704i	−0.441108	−	0.182713i	0.151065	−	0.988524i	$-0.451730\pi$
$379$	−8.58745	−	3.55704i	−0.441108	−	0.182713i	−0.592173	+	0.805811i	$0.701730\pi$
$380$	−22.0586	+	36.6040i	−1.13158	+	1.87775i
$381$		0			0
$382$	−10.7621	+	6.07970i	−0.550638	+	0.311064i
$383$	5.36313			0.274043			0.137021	−	0.990568i	$-0.456247\pi$
$383$	5.36313			0.274043			0.137021	+	0.990568i	$0.456247\pi$
$384$		0			0
$385$	−36.3947			−1.85485
$386$	−17.2416	+	9.74007i	−0.877575	+	0.495756i
$387$		0			0
$388$	−2.44423	+	4.05595i	−0.124087	+	0.205910i
$389$	−26.8411	−	11.1180i	−1.36090	−	0.563703i	−0.421593	−	0.906785i	$-0.638529\pi$
$389$	−26.8411	−	11.1180i	−1.36090	−	0.563703i	−0.939305	+	0.343082i	$0.888529\pi$
$390$		0			0
$391$	0.0942916	−	0.0942916i	0.00476853	−	0.00476853i
$392$	23.2831	+	0.655043i	1.17597	+	0.0330846i
$393$		0			0
$394$	−30.4531	+	3.71911i	−1.53420	+	0.187366i
$395$	−24.1363	−	9.99760i	−1.21443	−	0.503034i
$396$		0			0
$397$	−8.95757	−	21.6255i	−0.449568	−	1.08535i	−0.972484	−	0.232969i	$-0.925156\pi$
$397$	−8.95757	−	21.6255i	−0.449568	−	1.08535i	0.522916	−	0.852384i	$-0.324844\pi$
$398$	−2.10707	+	7.57876i	−0.105618	+	0.379889i
$399$		0			0
$400$	2.88614	−	9.35326i	0.144307	−	0.467663i
$401$	23.1692			1.15702			0.578508	−	0.815677i	$-0.303635\pi$
$401$	23.1692			1.15702			0.578508	+	0.815677i	$0.303635\pi$
$402$		0			0
$403$	33.1168	−	13.7174i	1.64967	−	0.683314i
$404$	−4.31830	+	3.18671i	−0.214844	+	0.158545i
$405$		0			0
$406$	−30.0189	+	3.66609i	−1.48982	+	0.181945i
$407$	−18.7863	+	18.7863i	−0.931200	+	0.931200i
$408$		0			0
$409$	9.55511	+	9.55511i	0.472470	+	0.472470i	0.902713	−	0.430243i	$-0.141572\pi$
$409$	9.55511	+	9.55511i	0.472470	+	0.472470i	−0.430243	+	0.902713i	$0.641572\pi$
$410$	−32.2219	−	25.2082i	−1.59133	−	1.24495i
$411$		0			0
$412$	2.20818	+	8.90576i	0.108789	+	0.438755i
$413$	−18.7357	−	45.2319i	−0.921923	−	2.22572i
$414$		0			0
$415$			5.98326i			0.293707i
$416$	−3.47189	+	19.3233i	−0.170223	+	0.947401i
$417$		0			0
$418$	32.9437	−	18.6104i	1.61133	−	0.910266i
$419$	23.0106	−	9.53132i	1.12414	−	0.465635i	0.258357	−	0.966049i	$-0.416819\pi$
$419$	23.0106	−	9.53132i	1.12414	−	0.465635i	0.865786	+	0.500414i	$0.166819\pi$
$420$		0			0
$421$	3.24536	−	7.83499i	0.158169	−	0.381854i	−0.824851	−	0.565350i	$-0.808741\pi$
$421$	3.24536	−	7.83499i	0.158169	−	0.381854i	0.983021	+	0.183496i	$0.0587413\pi$
$422$	−0.0135771	+	0.0173547i	−0.000660925	+	0.000844815i
$423$		0			0
$424$	12.8296	+	5.74205i	0.623060	+	0.278859i
$425$	−1.02255	−	1.02255i	−0.0496007	−	0.0496007i
$426$		0			0
$427$	−15.7635	+	38.0563i	−0.762847	+	1.84168i
$428$	24.6780	−	18.2112i	1.19285	−	0.880273i
$429$		0			0
$430$	7.65816	−	27.5450i	0.369309	−	1.32834i
$431$		−	30.0761i		−	1.44871i	−0.689425	−	0.724357i	$-0.742137\pi$
$431$		−	30.0761i		−	1.44871i	0.689425	−	0.724357i	$-0.257863\pi$
$432$		0			0
$433$			21.9066i			1.05277i	0.850248	+	0.526383i	$0.176452\pi$
$433$			21.9066i			1.05277i	−0.850248	+	0.526383i	$0.823548\pi$
$434$	−54.9285	−	15.2714i	−2.63665	−	0.733051i
$435$		0			0
$436$	19.5199	+	2.94316i	0.934832	+	0.140952i
$437$	0.676178	−	1.63244i	0.0323460	−	0.0780901i
$438$		0			0
$439$	13.0681	+	13.0681i	0.623704	+	0.623704i	0.946477	−	0.322772i	$-0.104615\pi$
$439$	13.0681	+	13.0681i	0.623704	+	0.623704i	−0.322772	+	0.946477i	$0.604615\pi$
$440$	−19.1657	+	18.1168i	−0.913688	+	0.863684i
$441$		0			0
$442$	2.28442	+	1.78718i	0.108659	+	0.0850073i
$443$	−0.842262	+	2.03340i	−0.0400171	+	0.0966097i	−0.942624	−	0.333855i	$-0.891650\pi$
$443$	−0.842262	+	2.03340i	−0.0400171	+	0.0966097i	0.902607	+	0.430465i	$0.141650\pi$
$444$		0			0
$445$	−32.1073	+	13.2993i	−1.52203	+	0.630447i
$446$	3.40715	+	6.03124i	0.161333	+	0.285587i
$447$		0			0
$448$	23.2864	−	20.8036i	1.10018	−	0.982876i
$449$			19.3731i			0.914273i	0.889397	+	0.457136i	$0.151125\pi$
$449$			19.3731i			0.914273i	−0.889397	+	0.457136i	$0.848875\pi$
$450$		0			0
$451$	13.8610	+	33.4633i	0.652687	+	1.57573i
$452$	2.75977	−	4.57956i	0.129809	−	0.215404i
$453$		0			0
$454$	−13.5528	+	17.3236i	−0.636062	+	0.813035i
$455$	−26.1400	−	26.1400i	−1.22546	−	1.22546i
$456$		0			0
$457$	−21.9729	+	21.9729i	−1.02785	+	1.02785i	−0.0282457	+	0.999601i	$0.508992\pi$
$457$	−21.9729	+	21.9729i	−1.02785	+	1.02785i	−0.999601	+	0.0282457i	$0.991008\pi$
$458$	4.87319	+	39.9030i	0.227709	+	1.86454i
$459$		0			0
$460$	−0.183621	+	1.21783i	−0.00856139	+	0.0567815i
$461$	14.2919	−	5.91990i	0.665640	−	0.275717i	−0.0241695	−	0.999708i	$-0.507694\pi$
$461$	14.2919	−	5.91990i	0.665640	−	0.275717i	0.689810	+	0.723991i	$0.257694\pi$
$462$		0			0
$463$	11.7181			0.544588			0.272294	−	0.962214i	$-0.412218\pi$
$463$	11.7181			0.544588			0.272294	+	0.962214i	$0.412218\pi$
$464$	−13.9832	+	16.8736i	−0.649155	+	0.783337i
$465$		0			0
$466$	−10.8060	−	3.00433i	−0.500580	−	0.139173i
$467$	2.20567	+	5.32497i	0.102066	+	0.246410i	0.966661	−	0.256060i	$-0.0824246\pi$
$467$	2.20567	+	5.32497i	0.102066	+	0.246410i	−0.864594	+	0.502470i	$0.832425\pi$
$468$		0			0
$469$	9.35429	+	3.87467i	0.431941	+	0.178916i
$470$	−0.839231	−	6.87184i	−0.0387108	−	0.316974i
$471$		0			0
$472$	−32.3821	−	14.4931i	−1.49051	−	0.667097i
$473$	−17.8982	+	17.8982i	−0.822961	+	0.822961i
$474$		0			0
$475$	−17.7030	−	7.33282i	−0.812269	−	0.336453i
$476$	−1.11021	−	4.47756i	−0.0508864	−	0.205229i
$477$		0			0
$478$	−4.16563	−	7.37388i	−0.190531	−	0.337274i
$479$	26.8644			1.22747			0.613734	−	0.789513i	$-0.289667\pi$
$479$	26.8644			1.22747			0.613734	+	0.789513i	$0.289667\pi$
$480$		0			0
$481$	−26.9859			−1.23045
$482$	−7.56025	−	13.3829i	−0.344360	−	0.609576i
$483$		0			0
$484$	1.30972	−	0.324746i	0.0595328	−	0.0147612i
$485$	−5.96961	−	2.47269i	−0.271066	−	0.112279i
$486$		0			0
$487$	2.18372	−	2.18372i	0.0989540	−	0.0989540i	−0.655897	−	0.754851i	$-0.727709\pi$
$487$	2.18372	−	2.18372i	0.0989540	−	0.0989540i	0.754851	+	0.655897i	$0.227709\pi$
$488$	10.6428	+	27.8875i	0.481776	+	1.26241i
$489$		0			0
$490$	3.85273	+	31.5472i	0.174049	+	1.42516i
$491$	−5.76037	−	2.38602i	−0.259962	−	0.107680i	0.248896	−	0.968530i	$-0.419932\pi$
$491$	−5.76037	−	2.38602i	−0.259962	−	0.107680i	−0.508858	+	0.860850i	$0.669932\pi$
$492$		0			0
$493$	1.23896	+	2.99112i	0.0558000	+	0.134713i
$494$	37.0280	+	10.2947i	1.66597	+	0.463179i
$495$		0			0
$496$	−36.5276	+	19.3006i	−1.64014	+	0.866623i
$497$	−5.11130			−0.229273
$498$		0			0
$499$	36.2360	−	15.0094i	1.62215	−	0.671915i	0.627827	−	0.778353i	$-0.283945\pi$
$499$	36.2360	−	15.0094i	1.62215	−	0.671915i	0.994319	+	0.106438i	$0.0339446\pi$
$500$	−13.7777	−	2.07737i	−0.616155	−	0.0929026i
$501$		0			0
$502$	−2.98221	−	24.4191i	−0.133102	−	1.08988i
$503$	−19.0408	+	19.0408i	−0.848989	+	0.848989i	−0.990007	−	0.141018i	$-0.954962\pi$
$503$	−19.0408	+	19.0408i	−0.848989	+	0.848989i	0.141018	+	0.990007i	$0.454962\pi$
$504$		0			0
$505$	−5.17806	−	5.17806i	−0.230421	−	0.230421i
$506$	0.671867	−	0.858801i	0.0298681	−	0.0381784i
$507$		0			0
$508$	2.93847	+	1.77081i	0.130374	+	0.0785669i
$509$	−7.93740	−	19.1626i	−0.351819	−	0.849366i	−0.996396	−	0.0848265i	$-0.972966\pi$
$509$	−7.93740	−	19.1626i	−0.351819	−	0.849366i	0.644577	−	0.764540i	$-0.277034\pi$
$510$		0			0
$511$			11.5599i			0.511382i
$512$	1.90702	−	22.5469i	0.0842793	−	0.996442i
$513$		0			0
$514$	15.1463	+	26.8116i	0.668074	+	1.18261i
$515$	−11.5666	+	4.79104i	−0.509685	+	0.211119i
$516$		0			0
$517$	−2.34553	+	5.66262i	−0.103156	+	0.249042i
$518$	33.8051	+	26.4467i	1.48531	+	1.16200i
$519$		0			0
$520$	−26.7776	−	0.753358i	−1.17428	−	0.0330369i
$521$	12.3022	+	12.3022i	0.538968	+	0.538968i	0.923226	−	0.384258i	$-0.125543\pi$
$521$	12.3022	+	12.3022i	0.538968	+	0.538968i	−0.384258	+	0.923226i	$0.625543\pi$
$522$		0			0
$523$	−8.52879	+	20.5903i	−0.372938	+	0.900352i	0.620312	+	0.784355i	$0.287006\pi$
$523$	−8.52879	+	20.5903i	−0.372938	+	0.900352i	−0.993250	+	0.115997i	$0.962994\pi$
$524$	5.87383	−	38.9569i	0.256600	−	1.70184i
$525$		0			0
$526$	40.9034	+	11.3721i	1.78348	+	0.495848i
$527$			6.10342i			0.265869i
$528$		0			0
$529$			22.9491i			0.997786i
$530$	−5.13733	+	18.4781i	−0.223151	+	0.802635i
$531$		0			0
$532$	−36.2957	−	49.1842i	−1.57362	−	2.13241i
$533$	−14.0791	+	33.9900i	−0.609835	+	1.47227i
$534$		0			0
$535$	29.5912	+	29.5912i	1.27934	+	1.27934i
$536$	6.85478	−	2.61601i	0.296081	−	0.112994i
$537$		0			0
$538$	−22.5254	+	28.7927i	−0.971138	+	1.24134i
$539$	10.7679	−	25.9959i	0.463804	−	1.11972i
$540$		0			0
$541$	−19.2526	+	7.97468i	−0.827733	+	0.342858i	−0.756005	−	0.654566i	$-0.772851\pi$
$541$	−19.2526	+	7.97468i	−0.827733	+	0.342858i	−0.0717281	+	0.997424i	$0.522851\pi$
$542$	28.8183	−	16.2799i	1.23785	−	0.699283i
$543$		0			0
$544$	−2.81351	−	1.80526i	−0.120628	−	0.0773999i
$545$			26.9353i			1.15378i
$546$		0			0
$547$	−8.48430	−	20.4829i	−0.362762	−	0.875786i	−0.994894	−	0.100925i	$-0.967820\pi$
$547$	−8.48430	−	20.4829i	−0.362762	−	0.875786i	0.632132	−	0.774861i	$-0.282180\pi$
$548$	10.7591	−	2.66772i	0.459606	−	0.113959i
$549$		0			0
$550$	−9.31327	−	7.28606i	−0.397119	−	0.310679i
$551$	30.3345	+	30.3345i	1.29229	+	1.29229i
$552$		0			0
$553$	26.4222	−	26.4222i	1.12359	−	1.12359i
$554$	−14.8287	+	1.81097i	−0.630010	+	0.0769405i
$555$		0			0
$556$	−5.21721	−	7.06982i	−0.221259	−	0.299827i
$557$	−10.1488	+	4.20379i	−0.430020	+	0.178120i	−0.587186	−	0.809452i	$-0.699764\pi$
$557$	−10.1488	+	4.20379i	−0.430020	+	0.178120i	0.157166	+	0.987572i	$0.449764\pi$
$558$		0			0
$559$	−25.7103			−1.08743
$560$	32.8058	+	27.1863i	1.38630	+	1.14883i
$561$		0			0
$562$	−2.03745	+	7.32833i	−0.0859446	+	0.309127i
$563$	−1.74171	−	4.20487i	−0.0734045	−	0.177214i	0.882918	−	0.469526i	$-0.155575\pi$
$563$	−1.74171	−	4.20487i	−0.0734045	−	0.177214i	−0.956323	+	0.292312i	$0.905575\pi$
$564$		0			0
$565$	6.74025	+	2.79190i	0.283565	+	0.117456i
$566$	1.87141	−	0.228547i	0.0786610	−	0.00960656i
$567$		0			0
$568$	−2.69164	+	2.54433i	−0.112939	+	0.106758i
$569$	−0.631696	+	0.631696i	−0.0264821	+	0.0264821i	−0.720224	−	0.693742i	$-0.755961\pi$
$569$	−0.631696	+	0.631696i	−0.0264821	+	0.0264821i	0.693742	+	0.720224i	$0.255961\pi$
$570$		0			0
$571$	−25.4015	−	10.5217i	−1.06302	−	0.440318i	−0.218498	−	0.975837i	$-0.570116\pi$
$571$	−25.4015	−	10.5217i	−1.06302	−	0.440318i	−0.844523	+	0.535519i	$0.820116\pi$
$572$	20.3135	+	12.2415i	0.849349	+	0.511842i
$573$		0			0
$574$	50.9477	−	28.7812i	2.12651	−	1.20130i
$575$	−0.552199			−0.0230283
$576$		0			0
$577$	−43.7938			−1.82316			−0.911579	−	0.411125i	$-0.865136\pi$
$577$	−43.7938			−1.82316			−0.911579	+	0.411125i	$0.865136\pi$
$578$	20.5025	−	11.5822i	0.852790	−	0.481755i
$579$		0			0
$580$	−25.6108	−	15.4338i	−1.06343	−	0.640854i
$581$	−7.90645	−	3.27496i	−0.328015	−	0.135868i
$582$		0			0
$583$	12.0067	−	12.0067i	0.497266	−	0.497266i
$584$	5.75438	+	6.08754i	0.238118	+	0.251904i
$585$		0			0
$586$	28.6637	−	3.50059i	1.18409	−	0.144608i
$587$	19.8031	+	8.20270i	0.817361	+	0.338562i	0.751887	−	0.659292i	$-0.229144\pi$
$587$	19.8031	+	8.20270i	0.817361	+	0.338562i	0.0654740	+	0.997854i	$0.479144\pi$
$588$		0			0
$589$	30.9490	+	74.7174i	1.27523	+	3.07868i
$590$	12.9667	−	46.6390i	0.533832	−	1.92010i
$591$		0			0
$592$	30.9668	−	2.90066i	1.27273	−	0.119217i
$593$	−42.0009			−1.72477			−0.862385	−	0.506254i	$-0.831030\pi$
$593$	−42.0009			−1.72477			−0.862385	+	0.506254i	$0.831030\pi$
$594$		0			0
$595$	5.81535	−	2.40880i	0.238406	−	0.0987511i
$596$	2.07427	+	2.81083i	0.0849653	+	0.115136i
$597$		0			0
$598$	1.09938	−	0.134263i	0.0449570	−	0.00549042i
$599$	−6.18006	+	6.18006i	−0.252510	+	0.252510i	−0.821999	−	0.569489i	$-0.807141\pi$
$599$	−6.18006	+	6.18006i	−0.252510	+	0.252510i	0.569489	+	0.821999i	$0.307141\pi$
$600$		0			0
$601$	−20.0432	−	20.0432i	−0.817580	−	0.817580i	0.168177	−	0.985757i	$-0.446212\pi$
$601$	−20.0432	−	20.0432i	−0.817580	−	0.817580i	−0.985757	+	0.168177i	$0.946212\pi$
$602$	32.2071	+	25.1966i	1.31266	+	1.02694i
$603$		0			0
$604$	31.7402	−	7.86998i	1.29149	−	0.320225i
$605$	0.704593	+	1.70104i	0.0286458	+	0.0691570i
$606$		0			0
$607$		−	24.2670i		−	0.984968i	−0.870321	−	0.492484i	$-0.836089\pi$
$607$		−	24.2670i		−	0.984968i	0.870321	−	0.492484i	$-0.163911\pi$
$608$	−43.5967	−	7.83320i	−1.76808	−	0.317678i
$609$		0			0
$610$	−35.4613	+	20.0327i	−1.43579	+	0.811099i
$611$	−5.75174	+	2.38245i	−0.232691	+	0.0963836i
$612$		0			0
$613$	8.04176	−	19.4145i	0.324804	−	0.784145i	−0.674158	−	0.738587i	$-0.735493\pi$
$613$	8.04176	−	19.4145i	0.324804	−	0.784145i	0.998962	−	0.0455583i	$-0.0145067\pi$
$614$	−26.2008	+	33.4906i	−1.05738	+	1.35157i
$615$		0			0
$616$	−13.4496	−	35.2424i	−0.541901	−	1.41996i
$617$	−11.8374	−	11.8374i	−0.476557	−	0.476557i	0.427472	−	0.904029i	$-0.359404\pi$
$617$	−11.8374	−	11.8374i	−0.476557	−	0.476557i	−0.904029	+	0.427472i	$0.859404\pi$
$618$		0			0
$619$	15.4059	−	37.1932i	0.619216	−	1.49492i	−0.233400	−	0.972381i	$-0.574985\pi$
$619$	15.4059	−	37.1932i	0.619216	−	1.49492i	0.852616	−	0.522538i	$-0.175015\pi$
$620$	−33.4716	−	45.3573i	−1.34425	−	1.82159i
$621$		0			0
$622$	−12.1553	+	43.7205i	−0.487384	+	1.75303i
$623$		−	49.7069i		−	1.99147i
$624$		0			0
$625$		−	31.2472i		−	1.24989i
$626$	−7.54711	−	2.09827i	−0.301643	−	0.0838639i
$627$		0			0
$628$	−0.351560	+	2.33164i	−0.0140288	+	0.0930426i
$629$	1.75840	−	4.24515i	0.0701119	−	0.169265i
$630$		0			0
$631$	6.05602	+	6.05602i	0.241086	+	0.241086i	0.817299	−	0.576213i	$-0.195470\pi$
$631$	6.05602	+	6.05602i	0.241086	+	0.241086i	−0.576213	+	0.817299i	$0.695470\pi$
$632$	0.761492	−	27.0667i	0.0302905	−	1.07666i
$633$		0			0
$634$	−13.5625	−	10.6104i	−0.538636	−	0.421392i
$635$	−1.79143	+	4.32489i	−0.0710906	+	0.171628i
$636$		0			0
$637$	26.4051	−	10.9373i	1.04621	−	0.433353i
$638$	13.0212	+	23.0498i	0.515514	+	0.912550i
$639$		0			0
$640$	30.8087	−	2.01378i	1.21782	−	0.0796017i
$641$			36.3868i			1.43719i	0.695428	+	0.718596i	$0.255215\pi$
$641$			36.3868i			1.43719i	−0.695428	+	0.718596i	$0.744785\pi$
$642$		0			0
$643$	−4.88236	−	11.7871i	−0.192541	−	0.464836i	0.797897	−	0.602794i	$-0.205946\pi$
$643$	−4.88236	−	11.7871i	−0.192541	−	0.464836i	−0.990438	+	0.137958i	$0.955946\pi$
$644$	−1.50877	−	0.909224i	−0.0594537	−	0.0358285i
$645$		0			0
$646$	−4.03219	+	5.15407i	−0.158644	+	0.202784i
$647$	−9.93527	−	9.93527i	−0.390596	−	0.390596i	0.484304	−	0.874900i	$-0.339073\pi$
$647$	−9.93527	−	9.93527i	−0.390596	−	0.390596i	−0.874900	+	0.484304i	$0.839073\pi$
$648$		0			0
$649$	−30.3051	+	30.3051i	−1.18958	+	1.18958i
$650$	−1.45602	−	11.9222i	−0.0571096	−	0.467629i
$651$		0			0
$652$	24.0971	+	3.63331i	0.943716	+	0.142292i
$653$	39.3974	−	16.3189i	1.54174	−	0.638609i	0.559940	−	0.828533i	$-0.310824\pi$
$653$	39.3974	−	16.3189i	1.54174	−	0.638609i	0.981799	+	0.189924i	$0.0608240\pi$
$654$		0			0
$655$	53.7563			2.10043
$656$	12.5025	−	40.5174i	0.488140	−	1.58194i
$657$		0			0
$658$	9.54001	+	2.65234i	0.371908	+	0.103399i
$659$	−0.324511	−	0.783439i	−0.0126412	−	0.0305184i	0.917433	−	0.397890i	$-0.130258\pi$
$659$	−0.324511	−	0.783439i	−0.0126412	−	0.0305184i	−0.930074	+	0.367372i	$0.880258\pi$
$660$		0			0
$661$	−34.0918	−	14.1213i	−1.32602	−	0.549254i	−0.396499	−	0.918035i	$-0.629775\pi$
$661$	−34.0918	−	14.1213i	−1.32602	−	0.549254i	−0.929516	+	0.368781i	$0.879775\pi$
$662$	−3.44970	−	28.2471i	−0.134077	−	1.09785i
$663$		0			0
$664$	−5.79381	+	2.21111i	−0.224844	+	0.0858076i
$665$	58.9765	−	58.9765i	2.28701	−	2.28701i
$666$		0			0
$667$	1.14217	+	0.473103i	0.0442251	+	0.0183186i
$668$	−14.4012	+	3.57077i	−0.557198	+	0.138157i
$669$		0			0
$670$	4.92405	+	8.71642i	0.190233	+	0.336745i
$671$	36.0589			1.39204
$672$		0			0
$673$	6.89911			0.265941			0.132971	−	0.991120i	$-0.457548\pi$
$673$	6.89911			0.265941			0.132971	+	0.991120i	$0.457548\pi$
$674$	−1.81130	−	3.20632i	−0.0697688	−	0.123503i
$675$		0			0
$676$	−0.459623	−	1.85369i	−0.0176778	−	0.0712958i
$677$	4.31555	+	1.78756i	0.165860	+	0.0687016i	0.464069	−	0.885799i	$-0.346389\pi$
$677$	4.31555	+	1.78756i	0.165860	+	0.0687016i	−0.298208	+	0.954501i	$0.596389\pi$
$678$		0			0
$679$	6.53497	−	6.53497i	0.250789	−	0.250789i
$680$	1.86333	−	4.16329i	0.0714556	−	0.159655i
$681$		0			0
$682$	6.05005	+	49.5394i	0.231669	+	1.89696i
$683$	41.0393	+	16.9990i	1.57032	+	0.650450i	0.986844	−	0.161677i	$-0.0516902\pi$
$683$	41.0393	+	16.9990i	1.57032	+	0.650450i	0.583481	+	0.812127i	$0.301690\pi$
$684$		0			0
$685$	5.78808	+	13.9737i	0.221151	+	0.533906i
$686$	−6.56837	−	1.82616i	−0.250781	−	0.0697231i
$687$		0			0
$688$	29.5029	−	2.76355i	1.12479	−	0.105359i
$689$	17.2473			0.657068
$690$		0			0
$691$	12.8229	−	5.31141i	0.487805	−	0.202056i	−0.125204	−	0.992131i	$-0.539959\pi$
$691$	12.8229	−	5.31141i	0.487805	−	0.202056i	0.613010	+	0.790075i	$0.289959\pi$
$692$	0.333403	−	2.21122i	0.0126741	−	0.0840580i
$693$		0			0
$694$	2.48654	+	20.3604i	0.0943877	+	0.772871i
$695$	8.47738	−	8.47738i	0.321565	−	0.321565i
$696$		0			0
$697$	−4.42956	−	4.42956i	−0.167782	−	0.167782i
$698$	25.1597	−	32.1599i	0.952308	−	1.21727i
$699$		0			0
$700$	−9.86009	+	16.3618i	−0.372676	+	0.618418i
$701$	8.19089	+	19.7746i	0.309366	+	0.746875i	0.999726	+	0.0234092i	$0.00745207\pi$
$701$	8.19089	+	19.7746i	0.309366	+	0.746875i	−0.690360	+	0.723466i	$0.742548\pi$
$702$		0			0
$703$		−	60.8851i		−	2.29633i
$704$	−24.6258	−	11.8638i	−0.928120	−	0.447134i
$705$		0			0
$706$	−18.3341	−	32.4546i	−0.690014	−	1.22144i
$707$	9.67666	−	4.00820i	0.363928	−	0.150744i
$708$		0			0
$709$	9.96351	−	24.0540i	0.374187	−	0.903368i	−0.618843	−	0.785514i	$-0.712398\pi$
$709$	9.96351	−	24.0540i	0.374187	−	0.903368i	0.993031	−	0.117854i	$-0.0376015\pi$
$710$	−3.98043	−	3.11401i	−0.149383	−	0.116867i
$711$		0			0
$712$	−24.7434	−	26.1760i	−0.927299	−	0.980986i
$713$	1.64800	+	1.64800i	0.0617180	+	0.0617180i
$714$		0			0
$715$	−12.3840	+	29.8976i	−0.463136	+	1.11811i
$716$	−26.2711	−	3.96110i	−0.981796	−	0.148033i
$717$		0			0
$718$	−15.8860	−	4.41668i	−0.592860	−	0.164829i
$719$		−	5.76004i		−	0.214813i	−0.994215	−	0.107407i	$-0.965745\pi$
$719$		−	5.76004i		−	0.214813i	0.994215	−	0.107407i	$-0.0342547\pi$
$720$		0			0
$721$		−	17.9068i		−	0.666885i
$722$	−16.0291	+	57.6537i	−0.596541	+	2.14565i
$723$		0			0
$724$	4.38134	−	3.23323i	0.162831	−	0.120162i
$725$	5.13057	−	12.3863i	0.190545	−	0.460015i
$726$		0			0
$727$	21.5257	+	21.5257i	0.798345	+	0.798345i	0.982834	−	0.184490i	$-0.0590633\pi$
$727$	21.5257	+	21.5257i	0.798345	+	0.798345i	−0.184490	+	0.982834i	$0.559063\pi$
$728$	15.6523	−	34.9724i	0.580114	−	1.29616i
$729$		0			0
$730$	−7.04279	+	9.00232i	−0.260665	+	0.333191i
$731$	1.67528	−	4.04448i	0.0619624	−	0.149590i
$732$		0			0
$733$	−44.7210	+	18.5240i	−1.65181	+	0.684201i	−0.997408	−	0.0719482i	$-0.977078\pi$
$733$	−44.7210	+	18.5240i	−1.65181	+	0.684201i	−0.654399	+	0.756149i	$0.727078\pi$
$734$	−13.7737	+	7.78099i	−0.508396	+	0.287202i
$735$		0			0
$736$	−1.24712	+	0.272239i	−0.0459696	+	0.0100349i
$737$		−	8.86331i		−	0.326484i
$738$		0			0
$739$	3.66287	+	8.84296i	0.134741	+	0.325293i	0.976821	−	0.214060i	$-0.0686688\pi$
$739$	3.66287	+	8.84296i	0.134741	+	0.325293i	−0.842080	+	0.539353i	$0.818669\pi$
$740$	10.2133	+	41.1908i	0.375447	+	1.51421i
$741$		0			0
$742$	−21.6055	−	16.9026i	−0.793163	−	0.620516i
$743$	16.4056	+	16.4056i	0.601862	+	0.601862i	0.940807	−	0.338944i	$-0.110070\pi$
$743$	16.4056	+	16.4056i	0.601862	+	0.601862i	−0.338944	+	0.940807i	$0.610070\pi$
$744$		0			0
$745$	−3.37046	+	3.37046i	−0.123484	+	0.123484i
$746$	4.93043	−	0.602134i	0.180516	−	0.0220457i
$747$		0			0
$748$	−3.24932	+	2.39785i	−0.118807	+	0.0876742i
$749$	−55.2995	+	22.9058i	−2.02060	+	0.836961i
$750$		0			0
$751$	−9.92382			−0.362125			−0.181063	−	0.983472i	$-0.557954\pi$
$751$	−9.92382			−0.362125			−0.181063	+	0.983472i	$0.557954\pi$
$752$	6.34412	−	3.35214i	0.231346	−	0.122240i
$753$		0			0
$754$	−7.20289	+	25.9075i	−0.262314	+	0.943495i
$755$	17.0753	+	41.2234i	0.621434	+	1.50027i
$756$		0			0
$757$	−29.5310	−	12.2321i	−1.07332	−	0.444584i	−0.225160	−	0.974322i	$-0.572290\pi$
$757$	−29.5310	−	12.2321i	−1.07332	−	0.444584i	−0.848162	+	0.529738i	$0.822290\pi$
$758$	13.0482	−	1.59352i	0.473930	−	0.0578792i
$759$		0			0
$760$	1.69971	−	60.4151i	0.0616550	−	2.19149i
$761$	−20.8932	+	20.8932i	−0.757380	+	0.757380i	−0.975845	−	0.218465i	$-0.929895\pi$
$761$	−20.8932	+	20.8932i	−0.757380	+	0.757380i	0.218465	+	0.975845i	$0.429895\pi$
$762$		0			0
$763$	−35.5931	−	14.7431i	−1.28856	−	0.533737i
$764$	9.02262	−	14.9721i	0.326427	−	0.541672i
$765$		0			0
$766$	−6.60373	+	3.73056i	−0.238602	+	0.134790i
$767$	−43.5324			−1.57186
$768$		0			0
$769$	29.8737			1.07727			0.538636	−	0.842538i	$-0.318940\pi$
$769$	29.8737			1.07727			0.538636	+	0.842538i	$0.318940\pi$
$770$	44.8136	−	25.3159i	1.61497	−	0.912323i
$771$		0			0
$772$	14.4548	−	23.9863i	0.520240	−	0.863286i
$773$	17.3188	+	7.17370i	0.622916	+	0.258020i	0.671740	−	0.740787i	$-0.265547\pi$
$773$	17.3188	+	7.17370i	0.622916	+	0.258020i	−0.0488241	+	0.998807i	$0.515547\pi$
$774$		0			0
$775$	17.8717	−	17.8717i	0.641971	−	0.641971i
$776$	0.188339	−	6.69437i	0.00676096	−	0.240314i
$777$		0			0
$778$	40.7836	−	4.98074i	1.46216	−	0.178568i
$779$	−76.6876	−	31.7650i	−2.74762	−	1.13810i
$780$		0			0
$781$	1.71227	+	4.13378i	0.0612697	+	0.147918i
$782$	−0.0505146	+	0.181692i	−0.00180640	+	0.00649728i
$783$		0			0
$784$	−29.1245	+	15.3890i	−1.04016	+	0.549606i
$785$	−3.21741			−0.114834
$786$		0			0
$787$	8.61517	−	3.56852i	0.307098	−	0.127204i	−0.223812	−	0.974632i	$-0.571850\pi$
$787$	8.61517	−	3.56852i	0.307098	−	0.127204i	0.530910	+	0.847428i	$0.321850\pi$
$788$	34.9105	−	25.7624i	1.24364	−	0.917747i
$789$		0			0
$790$	36.6738	−	4.47883i	1.30480	−	0.159350i
$791$	−7.37860	+	7.37860i	−0.262353	+	0.262353i
$792$		0			0
$793$	25.8988	+	25.8988i	0.919693	+	0.919693i
$794$	26.0722	+	20.3971i	0.925268	+	0.723866i
$795$		0			0
$796$	−2.67725	−	10.7975i	−0.0948927	−	0.382709i
$797$	20.2314	+	48.8429i	0.716632	+	1.73010i	0.682723	+	0.730678i	$0.260796\pi$
$797$	20.2314	+	48.8429i	0.716632	+	1.73010i	0.0339094	+	0.999425i	$0.489204\pi$
$798$		0			0
$799$		−	1.06004i		−	0.0375017i
$800$	2.95230	+	13.5244i	0.104379	+	0.478161i
$801$		0			0
$802$	−28.5287	+	16.1164i	−1.00738	+	0.569088i
$803$	9.34914	−	3.87254i	0.329924	−	0.136659i
$804$		0			0
$805$	0.919811	−	2.22062i	0.0324191	−	0.0782666i
$806$	−31.2357	+	39.9264i	−1.10023	+	1.40635i
$807$		0			0
$808$	3.10056	−	6.92765i	0.109077	−	0.243714i
$809$	−10.6030	−	10.6030i	−0.372780	−	0.372780i	0.495709	−	0.868489i	$-0.334908\pi$
$809$	−10.6030	−	10.6030i	−0.372780	−	0.372780i	−0.868489	+	0.495709i	$0.834908\pi$
$810$		0			0
$811$	2.22239	−	5.36533i	0.0780388	−	0.188402i	−0.880045	−	0.474890i	$-0.842488\pi$
$811$	2.22239	−	5.36533i	0.0780388	−	0.188402i	0.958084	+	0.286488i	$0.0924878\pi$
$812$	34.4128	−	25.3951i	1.20765	−	0.891194i
$813$		0			0
$814$	10.0643	−	36.1995i	0.352754	−	1.26879i
$815$			33.2514i			1.16475i
$816$		0			0
$817$		−	58.0070i		−	2.02941i
$818$	−18.4119	−	5.11893i	−0.643756	−	0.178979i
$819$		0			0
$820$	57.2102	+	8.62604i	1.99787	+	0.301234i
$821$	−5.60014	+	13.5199i	−0.195446	+	0.471849i	−0.990972	−	0.134071i	$-0.957195\pi$
$821$	−5.60014	+	13.5199i	−0.195446	+	0.471849i	0.795526	+	0.605920i	$0.207195\pi$
$822$		0			0
$823$	10.6818	+	10.6818i	0.372344	+	0.372344i	0.868330	−	0.495986i	$-0.165193\pi$
$823$	10.6818	+	10.6818i	0.372344	+	0.372344i	−0.495986	+	0.868330i	$0.665193\pi$
$824$	−8.91377	−	9.42984i	−0.310526	−	0.328504i
$825$		0			0
$826$	54.5327	+	42.6626i	1.89743	+	1.48442i
$827$	−13.1159	+	31.6645i	−0.456084	+	1.10108i	0.513886	+	0.857858i	$0.328205\pi$
$827$	−13.1159	+	31.6645i	−0.456084	+	1.10108i	−0.969970	+	0.243225i	$0.921795\pi$
$828$		0			0
$829$	10.7022	−	4.43299i	0.371703	−	0.153964i	−0.189009	−	0.981975i	$-0.560528\pi$
$829$	10.7022	−	4.43299i	0.371703	−	0.153964i	0.560712	+	0.828011i	$0.310528\pi$
$830$	−4.16192	−	7.36731i	−0.144462	−	0.255723i
$831$		0			0
$832$	−9.16613	−	26.2082i	−0.317778	−	0.908605i
$833$			4.86644i			0.168612i
$834$		0			0
$835$	−7.74742	−	18.7039i	−0.268111	−	0.647276i
$836$	−27.6189	+	45.8308i	−0.955221	+	1.58509i
$837$		0			0
$838$	−21.7036	+	27.7422i	−0.749737	+	0.958337i
$839$	7.53551	+	7.53551i	0.260155	+	0.260155i	0.825117	−	0.564962i	$-0.191109\pi$
$839$	7.53551	+	7.53551i	0.260155	+	0.260155i	−0.564962	+	0.825117i	$0.691109\pi$
$840$		0			0
$841$	−0.718101	+	0.718101i	−0.0247621	+	0.0247621i
$842$	1.45389	+	11.9048i	0.0501043	+	0.410268i
$843$		0			0
$844$	0.00464598	−	0.0308134i	0.000159921	−	0.00106064i
$845$	2.40753	−	0.997232i	0.0828216	−	0.0343058i
$846$		0			0
$847$	−2.63346			−0.0904868
$848$	−19.7915	+	1.85387i	−0.679642	+	0.0636623i
$849$		0			0
$850$	1.97036	+	0.547805i	0.0675827	+	0.0187896i
$851$	−0.671453	−	1.62103i	−0.0230171	−	0.0555682i
$852$		0			0
$853$	42.9049	+	17.7718i	1.46904	+	0.608495i	0.966639	−	0.256142i	$-0.0824514\pi$
$853$	42.9049	+	17.7718i	1.46904	+	0.608495i	0.502398	+	0.864637i	$0.332451\pi$
$854$	−7.06187	−	57.8245i	−0.241652	−	1.97871i
$855$		0			0
$856$	−17.7189	+	39.5897i	−0.605619	+	1.35315i
$857$	−34.8090	+	34.8090i	−1.18905	+	1.18905i	−0.211722	+	0.977330i	$0.567907\pi$
$857$	−34.8090	+	34.8090i	−1.18905	+	1.18905i	−0.977330	+	0.211722i	$0.932093\pi$
$858$		0			0
$859$	46.1865	+	19.1311i	1.57586	+	0.652744i	0.987752	−	0.156034i	$-0.0498711\pi$
$859$	46.1865	+	19.1311i	1.57586	+	0.652744i	0.588113	+	0.808779i	$0.299871\pi$
$860$	9.73049	+	39.2437i	0.331807	+	1.33820i
$861$		0			0
$862$	20.9207	+	37.0333i	0.712563	+	1.26136i
$863$	22.7029			0.772817			0.386408	−	0.922328i	$-0.373716\pi$
$863$	22.7029			0.772817			0.386408	+	0.922328i	$0.373716\pi$
$864$		0			0
$865$	3.05125			0.103745
$866$	−15.2381	−	26.9741i	−0.517812	−	0.916616i
$867$		0			0
$868$	78.2572	−	19.4039i	2.65622	−	0.658611i
$869$	−30.2204	−	12.5177i	−1.02516	−	0.424634i
$870$		0			0
$871$	6.36595	−	6.36595i	0.215702	−	0.215702i
$872$	−26.0825	+	9.95391i	−0.883263	+	0.337082i
$873$		0			0
$874$	0.302921	+	2.48040i	0.0102465	+	0.0839008i
$875$	25.1226	+	10.4061i	0.849298	+	0.351791i
$876$		0			0
$877$	−1.27679	−	3.08245i	−0.0431143	−	0.104087i	0.900855	−	0.434119i	$-0.142940\pi$
$877$	−1.27679	−	3.08245i	−0.0431143	−	0.104087i	−0.943970	+	0.330032i	$0.892940\pi$
$878$	−25.1810	−	7.00091i	−0.849818	−	0.236269i
$879$		0			0
$880$	10.9972	−	35.6391i	0.370715	−	1.20139i
$881$	−11.2063			−0.377551			−0.188776	−	0.982020i	$-0.560452\pi$
$881$	−11.2063			−0.377551			−0.188776	+	0.982020i	$0.560452\pi$
$882$		0			0
$883$	30.3540	−	12.5730i	1.02149	−	0.423117i	0.191859	−	0.981423i	$-0.438548\pi$
$883$	30.3540	−	12.5730i	1.02149	−	0.423117i	0.829635	+	0.558306i	$0.188548\pi$
$884$	−4.05601	−	0.611556i	−0.136418	−	0.0205689i
$885$		0			0
$886$	−0.377325	−	3.08964i	−0.0126765	−	0.103798i
$887$	−0.515994	+	0.515994i	−0.0173254	+	0.0173254i	−0.715716	−	0.698391i	$-0.753900\pi$
$887$	−0.515994	+	0.515994i	−0.0173254	+	0.0173254i	0.698391	+	0.715716i	$0.253900\pi$
$888$		0			0
$889$	−4.73448	−	4.73448i	−0.158789	−	0.158789i
$890$	30.2835	−	38.7093i	1.01511	−	1.29754i
$891$		0			0
$892$	−8.39058	−	5.05640i	−0.280937	−	0.169301i
$893$	−5.37523	−	12.9770i	−0.179875	−	0.434257i
$894$		0			0
$895$		−	36.2512i		−	1.21175i
$896$	−14.2022	+	41.8137i	−0.474461	+	1.39690i
$897$		0			0
$898$	−13.4758	−	23.8545i	−0.449693	−	0.796034i
$899$	−52.2777	+	21.6541i	−1.74356	+	0.722206i
$900$		0			0
$901$	−1.12383	+	2.71316i	−0.0374401	+	0.0903885i
$902$	−40.3442	−	31.5625i	−1.34331	−	1.05092i
$903$		0			0
$904$	−0.212652	+	7.55858i	−0.00707271	+	0.251395i
$905$	5.25364	+	5.25364i	0.174637	+	0.174637i
$906$		0			0
$907$	9.86989	−	23.8280i	0.327724	−	0.791196i	−0.671036	−	0.741424i	$-0.734151\pi$
$907$	9.86989	−	23.8280i	0.327724	−	0.791196i	0.998761	−	0.0497718i	$-0.0158494\pi$
$908$	4.63764	−	30.7581i	0.153905	−	1.02074i
$909$		0			0
$910$	50.3696	+	14.0039i	1.66973	+	0.464225i
$911$			12.7084i			0.421049i	0.977589	+	0.210524i	$0.0675171\pi$
$911$			12.7084i			0.421049i	−0.977589	+	0.210524i	$0.932483\pi$
$912$		0			0
$913$			7.49147i			0.247931i
$914$	11.7715	−	42.3398i	0.389365	−	1.40048i
$915$		0			0
$916$	−33.7567	−	45.7436i	−1.11535	−	1.51141i
$917$	−29.4237	+	71.0350i	−0.971655	+	2.34578i
$918$		0			0
$919$	0.104711	+	0.104711i	0.00345410	+	0.00345410i	0.708832	−	0.705378i	$-0.249223\pi$
$919$	0.104711	+	0.104711i	0.00345410	+	0.00345410i	−0.705378	+	0.708832i	$0.749223\pi$
$920$	−0.621015	−	1.62726i	−0.0204743	−	0.0536492i
$921$		0			0
$922$	−13.4801	+	17.2306i	−0.443942	+	0.567461i
$923$	−1.73922	+	4.19884i	−0.0572470	+	0.138207i
$924$		0			0
$925$	−17.5793	+	7.28157i	−0.578003	+	0.239417i
$926$	−14.4288	+	8.15106i	−0.474159	+	0.267861i
$927$		0			0
$928$	5.48067	−	30.5034i	0.179912	−	1.00132i
$929$		−	37.4417i		−	1.22842i	−0.789142	−	0.614211i	$-0.789474\pi$
$929$		−	37.4417i		−	1.22842i	0.789142	−	0.614211i	$-0.210526\pi$
$930$		0			0
$931$	24.6766	+	59.5745i	0.808742	+	1.95248i
$932$	15.3955	−	3.81731i	0.504296	−	0.125040i
$933$		0			0
$934$	−6.41990	−	5.02249i	−0.210066	−	0.164341i
$935$	−3.89625	−	3.89625i	−0.127421	−	0.127421i
$936$		0			0
$937$	17.1870	−	17.1870i	0.561473	−	0.561473i	−0.368252	−	0.929726i	$-0.620044\pi$
$937$	17.1870	−	17.1870i	0.561473	−	0.561473i	0.929726	+	0.368252i	$0.120044\pi$
$938$	−14.2133	+	1.73582i	−0.464081	+	0.0566764i
$939$		0			0
$940$	5.81337	+	7.87768i	0.189611	+	0.256942i
$941$	24.0095	−	9.94505i	0.782686	−	0.324199i	0.0446872	−	0.999001i	$-0.485771\pi$
$941$	24.0095	−	9.94505i	0.782686	−	0.324199i	0.737999	+	0.674802i	$0.235771\pi$
$942$		0			0
$943$	−2.39207			−0.0778966
$944$	49.9541	−	4.67921i	1.62587	−	0.152295i
$945$		0			0
$946$	9.58856	−	34.4883i	0.311751	−	1.12131i
$947$	−4.61956	−	11.1526i	−0.150115	−	0.362411i	0.830877	−	0.556456i	$-0.187839\pi$
$947$	−4.61956	−	11.1526i	−0.150115	−	0.362411i	−0.980993	+	0.194045i	$0.937839\pi$
$948$		0			0
$949$	9.49629	+	3.93349i	0.308263	+	0.127687i
$950$	26.8987	−	3.28503i	0.872709	−	0.106580i
$951$		0			0
$952$	4.48158	+	4.74105i	0.145249	+	0.153658i
$953$	−1.06510	+	1.06510i	−0.0345020	+	0.0345020i	−0.724147	−	0.689645i	$-0.757766\pi$
$953$	−1.06510	+	1.06510i	−0.0345020	+	0.0345020i	0.689645	+	0.724147i	$0.257766\pi$
$954$		0			0
$955$	22.0362	+	9.12767i	0.713073	+	0.295365i
$956$	10.2584	+	6.18203i	0.331782	+	0.199941i
$957$		0			0
$958$	−33.0787	+	18.6867i	−1.06873	+	0.603741i
$959$	−21.6333			−0.698577
$960$		0			0
$961$	−75.6735			−2.44108
$962$	33.2284	−	18.7712i	1.07133	−	0.605209i
$963$		0			0
$964$	18.6182	+	11.2198i	0.599651	+	0.361367i
$965$	35.3033	+	14.6231i	1.13645	+	0.470735i
$966$		0			0
$967$	10.1354	−	10.1354i	0.325932	−	0.325932i	−0.525105	−	0.851037i	$-0.675974\pi$
$967$	10.1354	−	10.1354i	0.325932	−	0.325932i	0.851037	+	0.525105i	$0.175974\pi$
$968$	−1.38680	+	1.31090i	−0.0445733	+	0.0421339i
$969$		0			0
$970$	9.07049	−	1.10774i	0.291236	−	0.0355675i
$971$	−26.7422	−	11.0770i	−0.858200	−	0.355478i	−0.0901964	−	0.995924i	$-0.528749\pi$
$971$	−26.7422	−	11.0770i	−0.858200	−	0.355478i	−0.768003	+	0.640446i	$0.778749\pi$
$972$		0			0
$973$	6.56213	+	15.8424i	0.210372	+	0.507883i
$974$	−1.16988	+	4.20785i	−0.0374854	+	0.134828i
$975$		0			0
$976$	−32.5030	−	26.9354i	−1.04040	−	0.862182i
$977$	−32.5184			−1.04036			−0.520178	−	0.854058i	$-0.674134\pi$
$977$	−32.5184			−1.04036			−0.520178	+	0.854058i	$0.674134\pi$
$978$		0			0
$979$	−40.2006	+	16.6517i	−1.28482	+	0.532189i
$980$	−26.6880	−	36.1648i	−0.852516	−	1.15524i
$981$		0			0
$982$	8.75257	−	1.06892i	0.279306	−	0.0341105i
$983$	−31.1438	+	31.1438i	−0.993333	+	0.993333i	−0.999978	−	0.00664485i	$-0.997885\pi$
$983$	−31.1438	+	31.1438i	−0.993333	+	0.993333i	0.00664485	+	0.999978i	$0.497885\pi$
$984$		0			0
$985$	41.8610	+	41.8610i	1.33380	+	1.33380i
$986$	−3.60616	−	2.82121i	−0.114843	−	0.0898456i
$987$		0			0
$988$	−52.7543	+	13.0804i	−1.67834	+	0.416144i
$989$	−0.639713	−	1.54440i	−0.0203417	−	0.0491092i
$990$		0			0
$991$		−	16.8817i		−	0.536265i	−0.963382	−	0.268132i	$-0.913594\pi$
$991$		−	16.8817i		−	0.536265i	0.963382	−	0.268132i	$-0.0864065\pi$
$992$	31.5517	−	49.1736i	1.00177	−	1.56126i
$993$		0			0
$994$	6.29364	−	3.55538i	0.199622	−	0.112770i
$995$	14.0236	−	5.80877i	0.444578	−	0.184150i
$996$		0			0
$997$	−1.51762	+	3.66385i	−0.0480634	+	0.116035i	−0.946088	−	0.323910i	$-0.895002\pi$
$997$	−1.51762	+	3.66385i	−0.0480634	+	0.116035i	0.898024	+	0.439946i	$0.145002\pi$
$998$	−34.1777	+	43.6870i	−1.08187	+	1.38289i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.w.b.107.7	✓	128
3.2	odd	2	inner	864.2.w.b.107.26	yes	128
32.3	odd	8	inner	864.2.w.b.323.26	yes	128
96.35	even	8	inner	864.2.w.b.323.7	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.w.b.107.7	✓	128	1.1	even	1	trivial
864.2.w.b.107.26	yes	128	3.2	odd	2	inner
864.2.w.b.323.7	yes	128	96.35	even	8	inner
864.2.w.b.323.26	yes	128	32.3	odd	8	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.w (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.23132 + 0.695593i) q^{2} +(1.03230 - 1.71300i) q^{4} +(2.52121 + 1.04432i) q^{5} +(-2.75999 + 2.75999i) q^{7} +(-0.0795431 + 2.82731i) q^{8} +O(q^{10})\)	\(q+(-1.23132 + 0.695593i) q^{2} +(1.03230 - 1.71300i) q^{4} +(2.52121 + 1.04432i) q^{5} +(-2.75999 + 2.75999i) q^{7} +(-0.0795431 + 2.82731i) q^{8} +(-3.83084 + 0.467845i) q^{10} +(3.15673 + 1.30756i) q^{11} +(1.32814 + 3.20642i) q^{13} +(1.47860 - 5.31826i) q^{14} +(-1.86871 - 3.53665i) q^{16} -0.590942 q^{17} +(-7.23425 + 2.99653i) q^{19} +(4.39156 - 3.24077i) q^{20} +(-4.79648 + 0.585775i) q^{22} +(-0.159561 + 0.159561i) q^{23} +(1.73037 + 1.73037i) q^{25} +(-3.86573 - 3.02428i) q^{26} +(1.87871 + 7.57698i) q^{28} +(-2.09659 - 5.06161i) q^{29} -10.3283i q^{31} +(4.76106 + 3.05489i) q^{32} +(0.727639 - 0.411055i) q^{34} +(-9.84082 + 4.07620i) q^{35} +(-2.97558 + 7.18370i) q^{37} +(6.82332 - 8.72178i) q^{38} +(-3.15316 + 7.04517i) q^{40} +(7.49577 + 7.49577i) q^{41} +(-2.83493 + 6.84412i) q^{43} +(5.49855 - 4.05768i) q^{44} +(0.0854814 - 0.307461i) q^{46} +1.79382i q^{47} -8.23506i q^{49} +(-3.33426 - 0.927004i) q^{50} +(6.86363 + 1.03488i) q^{52} +(1.90176 - 4.59125i) q^{53} +(6.59328 + 6.59328i) q^{55} +(-7.58380 - 8.02287i) q^{56} +(6.10239 + 4.77409i) q^{58} +(-4.80007 + 11.5884i) q^{59} +(9.75001 - 4.03859i) q^{61} +(7.18429 + 12.7174i) q^{62} +(-7.98735 - 0.449786i) q^{64} +9.47106i q^{65} +(-0.992689 - 2.39656i) q^{67} +(-0.610029 + 1.01228i) q^{68} +(9.28182 - 11.8643i) q^{70} +(0.925964 + 0.925964i) q^{71} +(2.09420 - 2.09420i) q^{73} +(-1.33303 - 10.9152i) q^{74} +(-2.33488 + 15.4856i) q^{76} +(-12.3214 + 5.10369i) q^{77} -9.57332 q^{79} +(-1.01803 - 10.8682i) q^{80} +(-14.4437 - 4.01569i) q^{82} +(0.839042 + 2.02563i) q^{83} +(-1.48989 - 0.617132i) q^{85} +(-1.27002 - 10.3993i) q^{86} +(-3.94798 + 8.82105i) q^{88} +(-9.00492 + 9.00492i) q^{89} +(-12.5153 - 5.18402i) q^{91} +(0.108613 + 0.438044i) q^{92} +(-1.24777 - 2.20877i) q^{94} -21.3684 q^{95} -2.36775 q^{97} +(5.72825 + 10.1400i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q+O(q^{10}) \) 128 * q	\( 128 q + 8 q^{10} + 32 q^{16} - 32 q^{22} + 64 q^{40} + 64 q^{46} + 40 q^{52} + 64 q^{55} + 64 q^{58} + 32 q^{61} + 96 q^{64} - 64 q^{67} - 48 q^{70} - 32 q^{76} - 32 q^{79} + 40 q^{82} + 40 q^{88} - 48 q^{91} + 72 q^{94}+O(q^{100}) \) 128 * q + 8 * q^10 + 32 * q^16 - 32 * q^22 + 64 * q^40 + 64 * q^46 + 40 * q^52 + 64 * q^55 + 64 * q^58 + 32 * q^61 + 96 * q^64 - 64 * q^67 - 48 * q^70 - 32 * q^76 - 32 * q^79 + 40 * q^82 + 40 * q^88 - 48 * q^91 + 72 * q^94

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