LMFDB - Embedded newform 765.2.be.b.451.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [765,2,Mod(406,765)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(765, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 0, 3]))

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

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

chi := DirichletCharacter("765.406");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 765 = 3^{2} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	765.be (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:	$6.10855575463$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 85)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			451.4
Character	$\chi$	$=$	765.451
Dual form			765.2.be.b.631.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.09994 - 1.09994i) q^{2} -0.419729i q^{4} +(-0.382683 + 0.923880i) q^{5} +(-1.32205 - 3.19170i) q^{7} +(1.73820 + 1.73820i) q^{8} +O(q^{10})$	\(q+(1.09994 - 1.09994i) q^{2} -0.419729i q^{4} +(-0.382683 + 0.923880i) q^{5} +(-1.32205 - 3.19170i) q^{7} +(1.73820 + 1.73820i) q^{8} +(0.595282 + 1.43714i) q^{10} +(3.92026 - 1.62382i) q^{11} -0.127392i q^{13} +(-4.96485 - 2.05651i) q^{14} +4.66329 q^{16} +(4.11857 - 0.193278i) q^{17} +(1.81966 - 1.81966i) q^{19} +(0.387779 + 0.160623i) q^{20} +(2.52594 - 6.09815i) q^{22} +(-3.00465 + 1.24457i) q^{23} +(-0.707107 - 0.707107i) q^{25} +(-0.140123 - 0.140123i) q^{26} +(-1.33965 + 0.554901i) q^{28} +(1.87644 - 4.53013i) q^{29} +(4.95543 + 2.05261i) q^{31} +(1.65293 - 1.65293i) q^{32} +(4.31758 - 4.74277i) q^{34} +3.45467 q^{35} +(-1.63681 - 0.677990i) q^{37} -4.00302i q^{38} +(-2.27107 + 0.940707i) q^{40} +(-3.85069 - 9.29639i) q^{41} +(1.79227 + 1.79227i) q^{43} +(-0.681566 - 1.64545i) q^{44} +(-1.93598 + 4.67388i) q^{46} +4.59479i q^{47} +(-3.48941 + 3.48941i) q^{49} -1.55555 q^{50} -0.0534701 q^{52} +(-1.15866 + 1.15866i) q^{53} +4.24326i q^{55} +(3.24984 - 7.84580i) q^{56} +(-2.91889 - 7.04683i) q^{58} +(4.34287 + 4.34287i) q^{59} +(-1.54679 - 3.73428i) q^{61} +(7.70840 - 3.19293i) q^{62} +5.69034i q^{64} +(0.117695 + 0.0487508i) q^{65} -6.88856 q^{67} +(-0.0811242 - 1.72868i) q^{68} +(3.79993 - 3.79993i) q^{70} +(6.66802 + 2.76198i) q^{71} +(-5.59682 + 13.5119i) q^{73} +(-2.54614 + 1.05465i) q^{74} +(-0.763763 - 0.763763i) q^{76} +(-10.3655 - 10.3655i) q^{77} +(-4.75854 + 1.97105i) q^{79} +(-1.78456 + 4.30831i) q^{80} +(-14.4610 - 5.98994i) q^{82} +(-10.2150 + 10.2150i) q^{83} +(-1.39754 + 3.87903i) q^{85} +3.94276 q^{86} +(9.63673 + 3.99166i) q^{88} -0.600876i q^{89} +(-0.406598 + 0.168418i) q^{91} +(0.522381 + 1.26114i) q^{92} +(5.05398 + 5.05398i) q^{94} +(0.984791 + 2.37750i) q^{95} +(-2.93763 + 7.09206i) q^{97} +7.67628i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q+O(q^{10}) $ 24 * q	$ 24 q + 8 q^{11} - 24 q^{16} + 8 q^{17} - 8 q^{19} - 32 q^{22} + 16 q^{23} - 16 q^{26} + 48 q^{28} + 8 q^{29} + 16 q^{34} + 32 q^{35} + 24 q^{37} + 16 q^{40} - 16 q^{41} + 8 q^{43} - 16 q^{44} + 8 q^{46} - 8 q^{50} - 48 q^{52} - 24 q^{53} - 64 q^{56} - 64 q^{58} - 32 q^{59} + 32 q^{61} + 32 q^{62} - 8 q^{65} + 16 q^{67} + 40 q^{68} + 24 q^{71} + 64 q^{74} - 8 q^{76} - 24 q^{77} + 32 q^{80} - 80 q^{82} + 96 q^{83} + 16 q^{86} - 8 q^{88} - 24 q^{91} - 80 q^{92} + 56 q^{94} + 16 q^{95} - 40 q^{97}+O(q^{100}) $ 24 * q + 8 * q^11 - 24 * q^16 + 8 * q^17 - 8 * q^19 - 32 * q^22 + 16 * q^23 - 16 * q^26 + 48 * q^28 + 8 * q^29 + 16 * q^34 + 32 * q^35 + 24 * q^37 + 16 * q^40 - 16 * q^41 + 8 * q^43 - 16 * q^44 + 8 * q^46 - 8 * q^50 - 48 * q^52 - 24 * q^53 - 64 * q^56 - 64 * q^58 - 32 * q^59 + 32 * q^61 + 32 * q^62 - 8 * q^65 + 16 * q^67 + 40 * q^68 + 24 * q^71 + 64 * q^74 - 8 * q^76 - 24 * q^77 + 32 * q^80 - 80 * q^82 + 96 * q^83 + 16 * q^86 - 8 * q^88 - 24 * q^91 - 80 * q^92 + 56 * q^94 + 16 * q^95 - 40 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/765\mathbb{Z}\right)^\times$.

$n$	$307$	$496$	$596$
$\chi(n)$	$1$	$e\left(\frac{1}{8}\right)$	$1$

Coefficient data

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

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

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

$2$	1.09994	−	1.09994i	0.777774	−	0.777774i	−0.201678	−	0.979452i	$-0.564639\pi$
$2$	1.09994	−	1.09994i	0.777774	−	0.777774i	0.979452	+	0.201678i	$0.0646394\pi$
$3$		0			0
$3$		0			0
$4$		−	0.419729i		−	0.209865i
$5$	−0.382683	+	0.923880i	−0.171141	+	0.413171i
$5$	−0.382683	+	0.923880i	−0.171141	+	0.413171i
$6$		0			0
$7$	−1.32205	−	3.19170i	−0.499687	−	1.20635i	−0.949653	−	0.313305i	$-0.898564\pi$
$7$	−1.32205	−	3.19170i	−0.499687	−	1.20635i	0.449966	−	0.893046i	$-0.351436\pi$
$8$	1.73820	+	1.73820i	0.614547	+	0.614547i
$9$		0			0
$10$	0.595282	+	1.43714i	0.188245	+	0.454463i
$11$	3.92026	−	1.62382i	1.18200	−	0.489601i	0.296860	−	0.954921i	$-0.404061\pi$
$11$	3.92026	−	1.62382i	1.18200	−	0.489601i	0.885143	+	0.465320i	$0.154061\pi$
$12$		0			0
$13$		−	0.127392i		−	0.0353322i	−0.999844	−	0.0176661i	$-0.994376\pi$
$13$		−	0.127392i		−	0.0353322i	0.999844	−	0.0176661i	$-0.00562359\pi$
$14$	−4.96485	−	2.05651i	−1.32691	−	0.549625i
$15$		0			0
$16$	4.66329			1.16582
$17$	4.11857	−	0.193278i	0.998901	−	0.0468767i
$17$	4.11857	−	0.193278i	0.998901	−	0.0468767i
$18$		0			0
$19$	1.81966	−	1.81966i	0.417458	−	0.417458i	−0.466869	−	0.884327i	$-0.654618\pi$
$19$	1.81966	−	1.81966i	0.417458	−	0.417458i	0.884327	+	0.466869i	$0.154618\pi$
$20$	0.387779	+	0.160623i	0.0867100	+	0.0359165i
$21$		0			0
$22$	2.52594	−	6.09815i	0.538531	−	1.30013i
$23$	−3.00465	+	1.24457i	−0.626513	+	0.259510i	−0.673271	−	0.739396i	$-0.735111\pi$
$23$	−3.00465	+	1.24457i	−0.626513	+	0.259510i	0.0467576	+	0.998906i	$0.485111\pi$
$24$		0			0
$25$	−0.707107	−	0.707107i	−0.141421	−	0.141421i
$26$	−0.140123	−	0.140123i	−0.0274805	−	0.0274805i
$27$		0			0
$28$	−1.33965	+	0.554901i	−0.253170	+	0.104866i
$29$	1.87644	−	4.53013i	0.348446	−	0.841224i	−0.648358	−	0.761336i	$-0.724544\pi$
$29$	1.87644	−	4.53013i	0.348446	−	0.841224i	0.996804	−	0.0798877i	$-0.0254562\pi$
$30$		0			0
$31$	4.95543	+	2.05261i	0.890021	+	0.368659i	0.780375	−	0.625312i	$-0.215028\pi$
$31$	4.95543	+	2.05261i	0.890021	+	0.368659i	0.109646	+	0.993971i	$0.465028\pi$
$32$	1.65293	−	1.65293i	0.292199	−	0.292199i
$33$		0			0
$34$	4.31758	−	4.74277i	0.740459	−	0.813378i
$35$	3.45467			0.583947
$36$		0			0
$37$	−1.63681	−	0.677990i	−0.269090	−	0.111461i	0.244059	−	0.969761i	$-0.421521\pi$
$37$	−1.63681	−	0.677990i	−0.269090	−	0.111461i	−0.513149	+	0.858300i	$0.671521\pi$
$38$		−	4.00302i		−	0.649376i
$39$		0			0
$40$	−2.27107	+	0.940707i	−0.359087	+	0.148739i
$41$	−3.85069	−	9.29639i	−0.601377	−	1.45185i	−0.872164	−	0.489214i	$-0.837284\pi$
$41$	−3.85069	−	9.29639i	−0.601377	−	1.45185i	0.270787	−	0.962639i	$-0.412716\pi$
$42$		0			0
$43$	1.79227	+	1.79227i	0.273318	+	0.273318i	0.830434	−	0.557116i	$-0.188092\pi$
$43$	1.79227	+	1.79227i	0.273318	+	0.273318i	−0.557116	+	0.830434i	$0.688092\pi$
$44$	−0.681566	−	1.64545i	−0.102750	−	0.248060i
$45$		0			0
$46$	−1.93598	+	4.67388i	−0.285445	+	0.689126i
$47$			4.59479i			0.670219i	0.942179	+	0.335109i	$0.108773\pi$
$47$			4.59479i			0.670219i	−0.942179	+	0.335109i	$0.891227\pi$
$48$		0			0
$49$	−3.48941	+	3.48941i	−0.498487	+	0.498487i
$50$	−1.55555			−0.219988
$51$		0			0
$52$	−0.0534701			−0.00741498
$53$	−1.15866	+	1.15866i	−0.159155	+	0.159155i	−0.782192	−	0.623037i	$-0.785898\pi$
$53$	−1.15866	+	1.15866i	−0.159155	+	0.159155i	0.623037	+	0.782192i	$0.285898\pi$
$54$		0			0
$55$			4.24326i			0.572161i
$56$	3.24984	−	7.84580i	0.434278	−	1.04844i
$57$		0			0
$58$	−2.91889	−	7.04683i	−0.383269	−	0.925294i
$59$	4.34287	+	4.34287i	0.565393	+	0.565393i	0.930834	−	0.365441i	$-0.119082\pi$
$59$	4.34287	+	4.34287i	0.565393	+	0.565393i	−0.365441	+	0.930834i	$0.619082\pi$
$60$		0			0
$61$	−1.54679	−	3.73428i	−0.198046	−	0.478125i	0.793391	−	0.608713i	$-0.208314\pi$
$61$	−1.54679	−	3.73428i	−0.198046	−	0.478125i	−0.991437	+	0.130587i	$0.958314\pi$
$62$	7.70840	−	3.19293i	0.978968	−	0.405502i
$63$		0			0
$64$			5.69034i			0.711292i
$65$	0.117695	+	0.0487508i	0.0145983	+	0.00604680i
$66$		0			0
$67$	−6.88856			−0.841571			−0.420786	−	0.907160i	$-0.638246\pi$
$67$	−6.88856			−0.841571			−0.420786	+	0.907160i	$0.638246\pi$
$68$	−0.0811242	−	1.72868i	−0.00983776	−	0.209634i
$69$		0			0
$70$	3.79993	−	3.79993i	0.454178	−	0.454178i
$71$	6.66802	+	2.76198i	0.791348	+	0.327787i	0.741485	−	0.670969i	$-0.234122\pi$
$71$	6.66802	+	2.76198i	0.791348	+	0.327787i	0.0498626	+	0.998756i	$0.484122\pi$
$72$		0			0
$73$	−5.59682	+	13.5119i	−0.655058	+	1.58145i	0.150287	+	0.988642i	$0.451980\pi$
$73$	−5.59682	+	13.5119i	−0.655058	+	1.58145i	−0.805345	+	0.592807i	$0.798020\pi$
$74$	−2.54614	+	1.05465i	−0.295983	+	0.122600i
$75$		0			0
$76$	−0.763763	−	0.763763i	−0.0876096	−	0.0876096i
$77$	−10.3655	−	10.3655i	−1.18126	−	1.18126i
$78$		0			0
$79$	−4.75854	+	1.97105i	−0.535378	+	0.221761i	−0.633957	−	0.773369i	$-0.718570\pi$
$79$	−4.75854	+	1.97105i	−0.535378	+	0.221761i	0.0985790	+	0.995129i	$0.468570\pi$
$80$	−1.78456	+	4.30831i	−0.199520	+	0.481684i
$81$		0			0
$82$	−14.4610	−	5.98994i	−1.59695	−	0.661478i
$83$	−10.2150	+	10.2150i	−1.12124	+	1.12124i	−0.129685	+	0.991555i	$0.541397\pi$
$83$	−10.2150	+	10.2150i	−1.12124	+	1.12124i	−0.991555	+	0.129685i	$0.958603\pi$
$84$		0			0
$85$	−1.39754	+	3.87903i	−0.151585	+	0.420740i
$86$	3.94276			0.425159
$87$		0			0
$88$	9.63673	+	3.99166i	1.02728	+	0.425513i
$89$		−	0.600876i		−	0.0636927i	−0.999493	−	0.0318463i	$-0.989861\pi$
$89$		−	0.600876i		−	0.0636927i	0.999493	−	0.0318463i	$-0.0101387\pi$
$90$		0			0
$91$	−0.406598	+	0.168418i	−0.0426230	+	0.0176550i
$92$	0.522381	+	1.26114i	0.0544620	+	0.131483i
$93$		0			0
$94$	5.05398	+	5.05398i	0.521279	+	0.521279i
$95$	0.984791	+	2.37750i	0.101037	+	0.243926i
$96$		0			0
$97$	−2.93763	+	7.09206i	−0.298271	+	0.720090i	0.701700	+	0.712473i	$0.252425\pi$
$97$	−2.93763	+	7.09206i	−0.298271	+	0.720090i	−0.999971	+	0.00761730i	$0.997575\pi$
$98$			7.67628i			0.775421i
$99$		0			0
$100$	−0.296793	+	0.296793i	−0.0296793	+	0.0296793i
$101$	−16.8485			−1.67649			−0.838243	−	0.545297i	$-0.816417\pi$
$101$	−16.8485			−1.67649			−0.838243	+	0.545297i	$0.816417\pi$
$102$		0			0
$103$	4.32255			0.425914			0.212957	−	0.977062i	$-0.431691\pi$
$103$	4.32255			0.425914			0.212957	+	0.977062i	$0.431691\pi$
$104$	0.221433	−	0.221433i	0.0217133	−	0.0217133i
$105$		0			0
$106$			2.54891i			0.247572i
$107$	−1.80647	+	4.36120i	−0.174638	+	0.421613i	−0.986827	−	0.161782i	$-0.948276\pi$
$107$	−1.80647	+	4.36120i	−0.174638	+	0.421613i	0.812189	+	0.583395i	$0.198276\pi$
$108$		0			0
$109$	−5.86580	−	14.1613i	−0.561842	−	1.35641i	−0.908292	−	0.418338i	$-0.862613\pi$
$109$	−5.86580	−	14.1613i	−0.561842	−	1.35641i	0.346450	−	0.938068i	$-0.387387\pi$
$110$	4.66732	+	4.66732i	0.445012	+	0.445012i
$111$		0			0
$112$	−6.16508	−	14.8838i	−0.582545	−	1.40639i
$113$	6.81048	−	2.82099i	0.640676	−	0.265377i	−0.0386052	−	0.999255i	$-0.512291\pi$
$113$	6.81048	−	2.82099i	0.640676	−	0.265377i	0.679282	+	0.733878i	$0.262291\pi$
$114$		0			0
$115$		−	3.25221i		−	0.303270i
$116$	−1.90143	−	0.787596i	−0.176543	−	0.0731265i
$117$		0			0
$118$	9.55378			0.879496
$119$	−6.06183	−	12.8897i	−0.555687	−	1.18160i
$120$		0			0
$121$	4.95345	−	4.95345i	0.450313	−	0.450313i
$122$	−5.80885	−	2.40610i	−0.525909	−	0.217838i
$123$		0			0
$124$	0.861538	−	2.07994i	0.0773684	−	0.186784i
$125$	0.923880	−	0.382683i	0.0826343	−	0.0342282i
$126$		0			0
$127$	−5.67103	−	5.67103i	−0.503223	−	0.503223i	0.409215	−	0.912438i	$-0.365803\pi$
$127$	−5.67103	−	5.67103i	−0.503223	−	0.503223i	−0.912438	+	0.409215i	$0.865803\pi$
$128$	9.56487	+	9.56487i	0.845423	+	0.845423i
$129$		0			0
$130$	0.183080	−	0.0758343i	0.0160572	−	0.00665110i
$131$	−5.43762	+	13.1276i	−0.475087	+	1.14696i	0.486799	+	0.873514i	$0.338164\pi$
$131$	−5.43762	+	13.1276i	−0.475087	+	1.14696i	−0.961887	+	0.273448i	$0.911836\pi$
$132$		0			0
$133$	−8.21348	−	3.40213i	−0.712199	−	0.295002i
$134$	−7.57699	+	7.57699i	−0.654552	+	0.654552i
$135$		0			0
$136$	7.49486	+	6.82295i	0.642679	+	0.585063i
$137$	−8.53083			−0.728838			−0.364419	−	0.931235i	$-0.618732\pi$
$137$	−8.53083			−0.728838			−0.364419	+	0.931235i	$0.618732\pi$
$138$		0			0
$139$	6.31676	+	2.61649i	0.535781	+	0.221928i	0.634133	−	0.773224i	$-0.281357\pi$
$139$	6.31676	+	2.61649i	0.535781	+	0.221928i	−0.0983522	+	0.995152i	$0.531357\pi$
$140$		−	1.45003i		−	0.122550i
$141$		0			0
$142$	10.3724	−	4.29640i	0.870434	−	0.360546i
$143$	−0.206862	−	0.499410i	−0.0172987	−	0.0417627i
$144$		0			0
$145$	3.46721	+	3.46721i	0.287936	+	0.287936i
$146$	8.70612	+	21.0184i	0.720523	+	1.73950i
$147$		0			0
$148$	−0.284572	+	0.687018i	−0.0233917	+	0.0564725i
$149$		−	7.04072i		−	0.576798i	−0.957510	−	0.288399i	$-0.906877\pi$
$149$		−	7.04072i		−	0.576798i	0.957510	−	0.288399i	$-0.0931229\pi$
$150$		0			0
$151$	4.49500	−	4.49500i	0.365798	−	0.365798i	−0.500144	−	0.865942i	$-0.666720\pi$
$151$	4.49500	−	4.49500i	0.365798	−	0.365798i	0.865942	+	0.500144i	$0.166720\pi$
$152$	6.32586			0.513095
$153$		0			0
$154$	−22.8029			−1.83751
$155$	−3.79272	+	3.79272i	−0.304639	+	0.304639i
$156$		0			0
$157$			16.7739i			1.33870i	0.742947	+	0.669351i	$0.233428\pi$
$157$			16.7739i			1.33870i	−0.742947	+	0.669351i	$0.766572\pi$
$158$	−3.06607	+	7.40214i	−0.243923	+	0.588882i
$159$		0			0
$160$	0.894557	+	2.15965i	0.0707209	+	0.170735i
$161$	7.94458	+	7.94458i	0.626121	+	0.626121i
$162$		0			0
$163$	−1.75820	−	4.24468i	−0.137713	−	0.332469i	0.839945	−	0.542672i	$-0.182587\pi$
$163$	−1.75820	−	4.24468i	−0.137713	−	0.332469i	−0.977658	+	0.210203i	$0.932587\pi$
$164$	−3.90197	+	1.61625i	−0.304692	+	0.126208i
$165$		0			0
$166$			22.4717i			1.74414i
$167$	−19.4260	−	8.04650i	−1.50323	−	0.622657i	−0.529079	−	0.848572i	$-0.677463\pi$
$167$	−19.4260	−	8.04650i	−1.50323	−	0.622657i	−0.974147	+	0.225916i	$0.927463\pi$
$168$		0			0
$169$	12.9838			0.998752
$170$	2.72948	+	5.80391i	0.209342	+	0.445139i
$171$		0			0
$172$	0.752266	−	0.752266i	0.0573597	−	0.0573597i
$173$	11.5969	+	4.80360i	0.881698	+	0.365211i	0.777155	−	0.629309i	$-0.216662\pi$
$173$	11.5969	+	4.80360i	0.881698	+	0.365211i	0.104543	+	0.994520i	$0.466662\pi$
$174$		0			0
$175$	−1.32205	+	3.19170i	−0.0999373	+	0.241270i
$176$	18.2813	−	7.57236i	1.37800	−	0.570788i
$177$		0			0
$178$	−0.660926	−	0.660926i	−0.0495385	−	0.0495385i
$179$	8.59390	+	8.59390i	0.642338	+	0.642338i	0.951130	−	0.308791i	$-0.0999245\pi$
$179$	8.59390	+	8.59390i	0.642338	+	0.642338i	−0.308791	+	0.951130i	$0.599925\pi$
$180$		0			0
$181$	−14.1007	+	5.84068i	−1.04809	+	0.434135i	−0.839211	−	0.543806i	$-0.816983\pi$
$181$	−14.1007	+	5.84068i	−1.04809	+	0.434135i	−0.208883	+	0.977941i	$0.566983\pi$
$182$	−0.261983	+	0.632482i	−0.0194194	+	0.0468827i
$183$		0			0
$184$	−7.38600	−	3.05938i	−0.544503	−	0.225540i
$185$	1.25276	−	1.25276i	0.0921049	−	0.0921049i
$186$		0			0
$187$	15.8320	−	7.44554i	1.15775	−	0.544472i
$188$	1.92857			0.140655
$189$		0			0
$190$	3.69831	+	1.53189i	0.268304	+	0.111135i
$191$			8.89972i			0.643961i	0.946746	+	0.321981i	$0.104349\pi$
$191$			8.89972i			0.643961i	−0.946746	+	0.321981i	$0.895651\pi$
$192$		0			0
$193$	16.9844	−	7.03519i	1.22257	−	0.506404i	0.324342	−	0.945940i	$-0.394857\pi$
$193$	16.9844	−	7.03519i	1.22257	−	0.506404i	0.898225	+	0.439536i	$0.144857\pi$
$194$	4.56962	+	11.0320i	0.328080	+	0.792054i
$195$		0			0
$196$	1.46461	+	1.46461i	0.104615	+	0.104615i
$197$	−4.09074	−	9.87591i	−0.291453	−	0.703629i	0.708545	−	0.705666i	$-0.249352\pi$
$197$	−4.09074	−	9.87591i	−0.291453	−	0.703629i	−0.999998	+	0.00203619i	$0.999352\pi$
$198$		0			0
$199$	5.93889	−	14.3377i	0.420996	−	1.01638i	−0.561058	−	0.827777i	$-0.689605\pi$
$199$	5.93889	−	14.3377i	0.420996	−	1.01638i	0.982054	−	0.188599i	$-0.0603945\pi$
$200$		−	2.45819i		−	0.173820i
$201$		0			0
$202$	−18.5323	+	18.5323i	−1.30393	+	1.30393i
$203$	−16.9396			−1.18892
$204$		0			0
$205$	10.0623			0.702785
$206$	4.75454	−	4.75454i	0.331264	−	0.331264i
$207$		0			0
$208$		−	0.594066i		−	0.0411910i
$209$	4.17872	−	10.0883i	0.289048	−	0.697824i
$210$		0			0
$211$	3.34996	+	8.08752i	0.230621	+	0.556768i	0.996251	−	0.0865134i	$-0.0275726\pi$
$211$	3.34996	+	8.08752i	0.230621	+	0.556768i	−0.765630	+	0.643281i	$0.777573\pi$
$212$	0.486324	+	0.486324i	0.0334009	+	0.0334009i
$213$		0			0
$214$	2.81005	+	6.78406i	0.192091	+	0.463748i
$215$	−2.34171	+	0.969967i	−0.159703	+	0.0661512i
$216$		0			0
$217$		−	18.5299i		−	1.25789i
$218$	−22.0286	−	9.12453i	−1.49196	−	0.617991i
$219$		0			0
$220$	1.78102			0.120076
$221$	−0.0246220	−	0.524674i	−0.00165626	−	0.0352934i
$222$		0			0
$223$	−14.9621	+	14.9621i	−1.00193	+	1.00193i	−0.00193640	+	0.999998i	$0.500616\pi$
$223$	−14.9621	+	14.9621i	−1.00193	+	1.00193i	−0.999998	+	0.00193640i	$0.999384\pi$
$224$	−7.46089	−	3.09040i	−0.498502	−	0.206486i
$225$		0			0
$226$	4.38819	−	10.5940i	0.291898	−	0.704705i
$227$	23.6821	−	9.80944i	1.57183	−	0.651075i	0.584741	−	0.811220i	$-0.301196\pi$
$227$	23.6821	−	9.80944i	1.57183	−	0.651075i	0.987094	+	0.160145i	$0.0511961\pi$
$228$		0			0
$229$	−5.02072	−	5.02072i	−0.331779	−	0.331779i	0.521483	−	0.853262i	$-0.325379\pi$
$229$	−5.02072	−	5.02072i	−0.331779	−	0.331779i	−0.853262	+	0.521483i	$0.825379\pi$
$230$	−3.57723	−	3.57723i	−0.235876	−	0.235876i
$231$		0			0
$232$	11.1359	−	4.61264i	0.731108	−	0.302835i
$233$	9.07503	−	21.9091i	0.594525	−	1.43531i	−0.284566	−	0.958657i	$-0.591849\pi$
$233$	9.07503	−	21.9091i	0.594525	−	1.43531i	0.879091	−	0.476654i	$-0.158151\pi$
$234$		0			0
$235$	−4.24503	−	1.75835i	−0.276915	−	0.114702i
$236$	1.82283	−	1.82283i	0.118656	−	0.118656i
$237$		0			0
$238$	−20.8456	−	7.51028i	−1.35122	−	0.486819i
$239$	−0.109315			−0.00707103			−0.00353551	−	0.999994i	$-0.501125\pi$
$239$	−0.109315			−0.00707103			−0.00353551	+	0.999994i	$0.501125\pi$
$240$		0			0
$241$	16.1558	+	6.69194i	1.04069	+	0.431066i	0.836558	−	0.547878i	$-0.184564\pi$
$241$	16.1558	+	6.69194i	1.04069	+	0.431066i	0.204127	+	0.978944i	$0.434564\pi$
$242$		−	10.8970i		−	0.700484i
$243$		0			0
$244$	−1.56739	+	0.649232i	−0.100342	+	0.0415628i
$245$	−1.88846	−	4.55914i	−0.120649	−	0.291273i
$246$		0			0
$247$	−0.231810	−	0.231810i	−0.0147497	−	0.0147497i
$248$	5.04569	+	12.1814i	0.320401	+	0.773518i
$249$		0			0
$250$	0.595282	−	1.43714i	0.0376490	−	0.0908926i
$251$			3.28782i			0.207525i	0.994602	+	0.103763i	$0.0330882\pi$
$251$			3.28782i			0.207525i	−0.994602	+	0.103763i	$0.966912\pi$
$252$		0			0
$253$	−9.75805	+	9.75805i	−0.613484	+	0.613484i
$254$	−12.4756			−0.782787
$255$		0			0
$256$	9.66087			0.603804
$257$	−15.1307	+	15.1307i	−0.943829	+	0.943829i	−0.998504	−	0.0546752i	$-0.982588\pi$
$257$	−15.1307	+	15.1307i	−0.943829	+	0.943829i	0.0546752	+	0.998504i	$0.482588\pi$
$258$		0			0
$259$			6.12055i			0.380313i
$260$	0.0204621	−	0.0494000i	0.00126901	−	0.00306366i
$261$		0			0
$262$	8.45848	+	20.4206i	0.522567	+	1.26159i
$263$	−7.16800	−	7.16800i	−0.441998	−	0.441998i	0.450685	−	0.892683i	$-0.351180\pi$
$263$	−7.16800	−	7.16800i	−0.441998	−	0.441998i	−0.892683	+	0.450685i	$0.851180\pi$
$264$		0			0
$265$	−0.627064	−	1.51387i	−0.0385202	−	0.0929960i
$266$	−12.7765	+	5.29218i	−0.783375	+	0.324484i
$267$		0			0
$268$			2.89133i			0.176616i
$269$	13.9299	+	5.76996i	0.849321	+	0.351800i	0.764522	−	0.644598i	$-0.222975\pi$
$269$	13.9299	+	5.76996i	0.849321	+	0.351800i	0.0847993	+	0.996398i	$0.472975\pi$
$270$		0			0
$271$	−6.80304			−0.413255			−0.206628	−	0.978420i	$-0.566249\pi$
$271$	−6.80304			−0.413255			−0.206628	+	0.978420i	$0.566249\pi$
$272$	19.2061	−	0.901309i	1.16454	−	0.0546499i
$273$		0			0
$274$	−9.38338	+	9.38338i	−0.566871	+	0.566871i
$275$	−3.92026	−	1.62382i	−0.236400	−	0.0979203i
$276$		0			0
$277$	6.62876	−	16.0032i	0.398284	−	0.961542i	−0.589790	−	0.807557i	$-0.700789\pi$
$277$	6.62876	−	16.0032i	0.398284	−	0.961542i	0.988073	−	0.153985i	$-0.0492107\pi$
$278$	9.82602	−	4.07007i	0.589326	−	0.244107i
$279$		0			0
$280$	6.00492	+	6.00492i	0.358862	+	0.358862i
$281$	−12.7436	−	12.7436i	−0.760218	−	0.760218i	0.216143	−	0.976362i	$-0.430652\pi$
$281$	−12.7436	−	12.7436i	−0.760218	−	0.760218i	−0.976362	+	0.216143i	$0.930652\pi$
$282$		0			0
$283$	−17.4625	+	7.23322i	−1.03804	+	0.429970i	−0.835608	−	0.549326i	$-0.814885\pi$
$283$	−17.4625	+	7.23322i	−1.03804	+	0.429970i	−0.202432	+	0.979296i	$0.564885\pi$
$284$	1.15928	−	2.79876i	0.0687909	−	0.166076i
$285$		0			0
$286$	−0.776856	−	0.321784i	−0.0459365	−	0.0190275i
$287$	−24.5805	+	24.5805i	−1.45094	+	1.45094i
$288$		0			0
$289$	16.9253	−	1.59206i	0.995605	−	0.0936504i
$290$	7.62743			0.447898
$291$		0			0
$292$	5.67134	+	2.34915i	0.331890	+	0.137473i
$293$			7.53184i			0.440015i	0.975498	+	0.220007i	$0.0706081\pi$
$293$			7.53184i			0.440015i	−0.975498	+	0.220007i	$0.929392\pi$
$294$		0			0
$295$	−5.67423	+	2.35034i	−0.330367	+	0.136842i
$296$	−1.66663	−	4.02359i	−0.0968707	−	0.233866i
$297$		0			0
$298$	−7.74435	−	7.74435i	−0.448618	−	0.448618i
$299$	0.158548	+	0.382769i	0.00916907	+	0.0221361i
$300$		0			0
$301$	3.35092	−	8.08984i	0.193144	−	0.466290i
$302$		−	9.88844i		−	0.569016i
$303$		0			0
$304$	8.48558	−	8.48558i	0.486681	−	0.486681i
$305$	4.04195			0.231442
$306$		0			0
$307$	−7.77074			−0.443499			−0.221750	−	0.975104i	$-0.571177\pi$
$307$	−7.77074			−0.443499			−0.221750	+	0.975104i	$0.571177\pi$
$308$	−4.35071	+	4.35071i	−0.247905	+	0.247905i
$309$		0			0
$310$			8.34352i			0.473880i
$311$	−3.30824	+	7.98679i	−0.187593	+	0.452889i	−0.989495	−	0.144566i	$-0.953821\pi$
$311$	−3.30824	+	7.98679i	−0.187593	+	0.452889i	0.801902	+	0.597455i	$0.203821\pi$
$312$		0			0
$313$	−4.72153	−	11.3988i	−0.266877	−	0.644298i	0.732456	−	0.680814i	$-0.238374\pi$
$313$	−4.72153	−	11.3988i	−0.266877	−	0.644298i	−0.999333	+	0.0365165i	$0.988374\pi$
$314$	18.4502	+	18.4502i	1.04121	+	1.04121i
$315$		0			0
$316$	0.827308	+	1.99730i	0.0465397	+	0.112357i
$317$	7.55046	−	3.12750i	0.424076	−	0.175658i	−0.160430	−	0.987047i	$-0.551288\pi$
$317$	7.55046	−	3.12750i	0.424076	−	0.175658i	0.584506	+	0.811389i	$0.301288\pi$
$318$		0			0
$319$		−	20.8063i		−	1.16493i
$320$	−5.25719	−	2.17760i	−0.293886	−	0.121731i
$321$		0			0
$322$	17.4771			0.973960
$323$	7.14269	−	7.84609i	0.397430	−	0.436568i
$324$		0			0
$325$	−0.0900798	+	0.0900798i	−0.00499673	+	0.00499673i
$326$	−6.60280	−	2.73497i	−0.365695	−	0.151476i
$327$		0			0
$328$	9.46572	−	22.8523i	0.522657	−	1.26181i
$329$	14.6652	−	6.07452i	0.808519	−	0.334899i
$330$		0			0
$331$	16.5933	+	16.5933i	0.912049	+	0.912049i	0.996433	−	0.0843846i	$-0.0268924\pi$
$331$	16.5933	+	16.5933i	0.912049	+	0.912049i	−0.0843846	+	0.996433i	$0.526892\pi$
$332$	4.28753	+	4.28753i	0.235309	+	0.235309i
$333$		0			0
$334$	−30.2180	+	12.5167i	−1.65346	+	0.684884i
$335$	2.63614	−	6.36420i	0.144028	−	0.347713i
$336$		0			0
$337$	−21.9127	−	9.07655i	−1.19366	−	0.494431i	−0.304716	−	0.952443i	$-0.598562\pi$
$337$	−21.9127	−	9.07655i	−1.19366	−	0.494431i	−0.888946	+	0.458012i	$0.848562\pi$
$338$	14.2813	−	14.2813i	0.776803	−	0.776803i
$339$		0			0
$340$	1.62814	+	0.586590i	0.0882984	+	0.0318123i
$341$	22.7596			1.23250
$342$		0			0
$343$	−6.59159	−	2.73032i	−0.355912	−	0.147424i
$344$			6.23063i			0.335933i
$345$		0			0
$346$	18.0396	−	7.47223i	0.969813	−	0.401710i
$347$	−2.68599	−	6.48456i	−0.144192	−	0.348109i	0.835240	−	0.549885i	$-0.185329\pi$
$347$	−2.68599	−	6.48456i	−0.144192	−	0.348109i	−0.979432	+	0.201776i	$0.935329\pi$
$348$		0			0
$349$	−20.7773	−	20.7773i	−1.11219	−	1.11219i	−0.992855	−	0.119331i	$-0.961925\pi$
$349$	−20.7773	−	20.7773i	−1.11219	−	1.11219i	−0.119331	−	0.992855i	$-0.538075\pi$
$350$	2.05651	+	4.96485i	0.109925	+	0.265382i
$351$		0			0
$352$	3.79583	−	9.16396i	0.202319	−	0.488440i
$353$		−	9.09110i		−	0.483870i	−0.970292	−	0.241935i	$-0.922218\pi$
$353$		−	9.09110i		−	0.483870i	0.970292	−	0.241935i	$-0.0777821\pi$
$354$		0			0
$355$	−5.10348	+	5.10348i	−0.270865	+	0.270865i
$356$	−0.252205			−0.0133668
$357$		0			0
$358$	18.9055			0.999188
$359$	−3.70529	+	3.70529i	−0.195558	+	0.195558i	−0.798093	−	0.602535i	$-0.794157\pi$
$359$	−3.70529	+	3.70529i	−0.195558	+	0.195558i	0.602535	+	0.798093i	$0.294157\pi$
$360$		0			0
$361$			12.3777i			0.651458i
$362$	−9.08546	+	21.9342i	−0.477521	+	1.15284i
$363$		0			0
$364$	0.0706900	+	0.170661i	0.00370516	+	0.00894506i
$365$	−10.3416	−	10.3416i	−0.541302	−	0.541302i
$366$		0			0
$367$	−6.97736	−	16.8448i	−0.364215	−	0.879293i	−0.994674	−	0.103071i	$-0.967133\pi$
$367$	−6.97736	−	16.8448i	−0.364215	−	0.879293i	0.630459	−	0.776223i	$-0.282867\pi$
$368$	−14.0115	+	5.80377i	−0.730402	+	0.302543i
$369$		0			0
$370$		−	2.75592i		−	0.143274i
$371$	5.22991	+	2.16630i	0.271524	+	0.112469i
$372$		0			0
$373$	18.5489			0.960428			0.480214	−	0.877151i	$-0.340559\pi$
$373$	18.5489			0.960428			0.480214	+	0.877151i	$0.340559\pi$
$374$	9.22462	−	25.6039i	0.476994	−	1.32395i
$375$		0			0
$376$	−7.98666	+	7.98666i	−0.411881	+	0.411881i
$377$	−0.577102	−	0.239044i	−0.0297223	−	0.0123114i
$378$		0			0
$379$	−7.67735	+	18.5348i	−0.394359	+	0.952067i	0.594619	+	0.804007i	$0.297303\pi$
$379$	−7.67735	+	18.5348i	−0.394359	+	0.952067i	−0.988978	+	0.148060i	$0.952697\pi$
$380$	0.997904	−	0.413346i	0.0511914	−	0.0212042i
$381$		0			0
$382$	9.78914	+	9.78914i	0.500856	+	0.500856i
$383$	7.72751	+	7.72751i	0.394857	+	0.394857i	0.876415	−	0.481557i	$-0.159929\pi$
$383$	7.72751	+	7.72751i	0.394857	+	0.394857i	−0.481557	+	0.876415i	$0.659929\pi$
$384$		0			0
$385$	13.5432	−	5.60978i	0.690226	−	0.285901i
$386$	10.9436	−	26.4201i	0.557013	−	1.34475i
$387$		0			0
$388$	2.97674	+	1.23301i	0.151121	+	0.0625965i
$389$	−16.7947	+	16.7947i	−0.851526	+	0.851526i	−0.990321	−	0.138795i	$-0.955677\pi$
$389$	−16.7947	+	16.7947i	−0.851526	+	0.851526i	0.138795	+	0.990321i	$0.455677\pi$
$390$		0			0
$391$	−12.1343	+	5.70657i	−0.613659	+	0.288594i
$392$	−12.1306			−0.612688
$393$		0			0
$394$	−15.3624	−	6.36333i	−0.773949	−	0.320580i
$395$		−	5.15061i		−	0.259155i
$396$		0			0
$397$	−26.2259	+	10.8631i	−1.31624	+	0.545205i	−0.926699	−	0.375804i	$-0.877367\pi$
$397$	−26.2259	+	10.8631i	−1.31624	+	0.545205i	−0.389542	+	0.921009i	$0.627367\pi$
$398$	−9.23822	−	22.3030i	−0.463070	−	1.11795i
$399$		0			0
$400$	−3.29744	−	3.29744i	−0.164872	−	0.164872i
$401$	3.33935	+	8.06191i	0.166759	+	0.402592i	0.985063	−	0.172193i	$-0.0550854\pi$
$401$	3.33935	+	8.06191i	0.166759	+	0.402592i	−0.818304	+	0.574786i	$0.805085\pi$
$402$		0			0
$403$	0.261486	−	0.631282i	0.0130255	−	0.0314464i
$404$			7.07179i			0.351835i
$405$		0			0
$406$	−18.6325	+	18.6325i	−0.924714	+	0.924714i
$407$	−7.51766			−0.372637
$408$		0			0
$409$	10.5572			0.522020			0.261010	−	0.965336i	$-0.415944\pi$
$409$	10.5572			0.522020			0.261010	+	0.965336i	$0.415944\pi$
$410$	11.0680	−	11.0680i	0.546608	−	0.546608i
$411$		0			0
$412$		−	1.81430i		−	0.0893841i
$413$	8.11967	−	19.6026i	0.399543	−	0.964582i
$414$		0			0
$415$	−5.52831	−	13.3465i	−0.271374	−	0.655155i
$416$	−0.210570	−	0.210570i	−0.0103240	−	0.0103240i
$417$		0			0
$418$	−6.50020	−	15.6929i	−0.317935	−	0.767564i
$419$	−13.2011	+	5.46806i	−0.644915	+	0.267132i	−0.681075	−	0.732214i	$-0.738487\pi$
$419$	−13.2011	+	5.46806i	−0.644915	+	0.267132i	0.0361604	+	0.999346i	$0.488487\pi$
$420$		0			0
$421$			18.2694i			0.890398i	0.895432	+	0.445199i	$0.146867\pi$
$421$			18.2694i			0.890398i	−0.895432	+	0.445199i	$0.853133\pi$
$422$	12.5805	+	5.21102i	0.612410	+	0.253669i
$423$		0			0
$424$	−4.02798			−0.195616
$425$	−3.04894	−	2.77560i	−0.147895	−	0.134637i
$426$		0			0
$427$	−9.87378	+	9.87378i	−0.477826	+	0.477826i
$428$	1.83052	+	0.758227i	0.0884816	+	0.0366503i
$429$		0			0
$430$	−1.50883	+	3.64264i	−0.0727622	+	0.175664i
$431$	−19.4407	+	8.05261i	−0.936427	+	0.387881i	−0.798113	−	0.602508i	$-0.794168\pi$
$431$	−19.4407	+	8.05261i	−0.936427	+	0.387881i	−0.138314	+	0.990388i	$0.544168\pi$
$432$		0			0
$433$	2.52902	+	2.52902i	0.121537	+	0.121537i	0.765259	−	0.643722i	$-0.222611\pi$
$433$	2.52902	+	2.52902i	0.121537	+	0.121537i	−0.643722	+	0.765259i	$0.722611\pi$
$434$	−20.3817	−	20.3817i	−0.978355	−	0.978355i
$435$		0			0
$436$	−5.94391	+	2.46205i	−0.284661	+	0.117911i
$437$	−3.20275	+	7.73212i	−0.153208	+	0.369878i
$438$		0			0
$439$	3.03763	+	1.25823i	0.144978	+	0.0600520i	0.453993	−	0.891005i	$-0.349999\pi$
$439$	3.03763	+	1.25823i	0.144978	+	0.0600520i	−0.309014	+	0.951057i	$0.599999\pi$
$440$	−7.37563	+	7.37563i	−0.351619	+	0.351619i
$441$		0			0
$442$	−0.604191	−	0.550026i	−0.0287384	−	0.0261621i
$443$	24.9391			1.18489			0.592447	−	0.805609i	$-0.298162\pi$
$443$	24.9391			1.18489			0.592447	+	0.805609i	$0.298162\pi$
$444$		0			0
$445$	0.555137	+	0.229945i	0.0263160	+	0.0109004i
$446$			32.9147i			1.55856i
$447$		0			0
$448$	18.1619	−	7.52289i	0.858068	−	0.355423i
$449$	−3.69533	−	8.92132i	−0.174394	−	0.421023i	0.812380	−	0.583128i	$-0.198172\pi$
$449$	−3.69533	−	8.92132i	−0.174394	−	0.421023i	−0.986773	+	0.162105i	$0.948172\pi$
$450$		0			0
$451$	−30.1914	−	30.1914i	−1.42166	−	1.42166i
$452$	−1.18405	−	2.85856i	−0.0556932	−	0.134455i
$453$		0			0
$454$	15.2590	−	36.8386i	0.716143	−	1.72892i
$455$		−	0.440098i		−	0.0206321i
$456$		0			0
$457$	14.4798	−	14.4798i	0.677338	−	0.677338i	−0.282059	−	0.959397i	$-0.591018\pi$
$457$	14.4798	−	14.4798i	0.677338	−	0.677338i	0.959397	+	0.282059i	$0.0910175\pi$
$458$	−11.0450			−0.516098
$459$		0			0
$460$	−1.36505			−0.0636457
$461$	13.3288	−	13.3288i	0.620785	−	0.620785i	−0.324947	−	0.945732i	$-0.605346\pi$
$461$	13.3288	−	13.3288i	0.620785	−	0.620785i	0.945732	+	0.324947i	$0.105346\pi$
$462$		0			0
$463$		−	2.13430i		−	0.0991892i	−0.998769	−	0.0495946i	$-0.984207\pi$
$463$		−	2.13430i		−	0.0991892i	0.998769	−	0.0495946i	$-0.0157929\pi$
$464$	8.75038	−	21.1253i	0.406226	−	0.980716i
$465$		0			0
$466$	−14.1166	−	34.0806i	−0.653941	−	1.57875i
$467$	−16.4498	−	16.4498i	−0.761208	−	0.761208i	0.215333	−	0.976541i	$-0.430916\pi$
$467$	−16.4498	−	16.4498i	−0.761208	−	0.761208i	−0.976541	+	0.215333i	$0.930916\pi$
$468$		0			0
$469$	9.10700	+	21.9862i	0.420522	+	1.01523i
$470$	−6.60335	+	2.73520i	−0.304590	+	0.126165i
$471$		0			0
$472$			15.0976i			0.694921i
$473$	9.93647	+	4.11582i	0.456879	+	0.189246i
$474$		0			0
$475$	−2.57338			−0.118075
$476$	−5.41020	+	2.54433i	−0.247976	+	0.116619i
$477$		0			0
$478$	−0.120240	+	0.120240i	−0.00549966	+	0.00549966i
$479$	28.8369	+	11.9446i	1.31759	+	0.545763i	0.927090	−	0.374839i	$-0.122302\pi$
$479$	28.8369	+	11.9446i	1.31759	+	0.545763i	0.390500	+	0.920603i	$0.372302\pi$
$480$		0			0
$481$	−0.0863705	+	0.208517i	−0.00393816	+	0.00950755i
$482$	25.1311	−	10.4096i	1.14469	−	0.474146i
$483$		0			0
$484$	−2.07911	−	2.07911i	−0.0945048	−	0.0945048i
$485$	−5.42803	−	5.42803i	−0.246474	−	0.246474i
$486$		0			0
$487$	13.5374	−	5.60737i	0.613438	−	0.254094i	−0.0542599	−	0.998527i	$-0.517280\pi$
$487$	13.5374	−	5.60737i	0.613438	−	0.254094i	0.667698	+	0.744433i	$0.267280\pi$
$488$	3.80230	−	9.17956i	0.172122	−	0.415539i
$489$		0			0
$490$	−7.09196	−	2.93758i	−0.320382	−	0.132707i
$491$	−9.80148	+	9.80148i	−0.442334	+	0.442334i	−0.892796	−	0.450461i	$-0.851259\pi$
$491$	−9.80148	+	9.80148i	−0.442334	+	0.442334i	0.450461	+	0.892796i	$0.351259\pi$
$492$		0			0
$493$	6.85268	−	19.0203i	0.308629	−	0.856633i
$494$	−0.509953			−0.0229439
$495$		0			0
$496$	23.1086	+	9.57188i	1.03761	+	0.429790i
$497$		−	24.9338i		−	1.11843i
$498$		0			0
$499$	36.9847	−	15.3196i	1.65566	−	0.685798i	0.657929	−	0.753080i	$-0.271433\pi$
$499$	36.9847	−	15.3196i	1.65566	−	0.685798i	0.997734	+	0.0672815i	$0.0214326\pi$
$500$	−0.160623	−	0.387779i	−0.00718329	−	0.0173420i
$501$		0			0
$502$	3.61639	+	3.61639i	0.161408	+	0.161408i
$503$	−15.0174	−	36.2551i	−0.669591	−	1.61654i	−0.782296	−	0.622907i	$-0.785951\pi$
$503$	−15.0174	−	36.2551i	−0.669591	−	1.61654i	0.112704	−	0.993629i	$-0.464049\pi$
$504$		0			0
$505$	6.44763	−	15.5660i	0.286916	−	0.692676i
$506$			21.4665i			0.954303i
$507$		0			0
$508$	−2.38030	+	2.38030i	−0.105609	+	0.105609i
$509$	26.7005			1.18348			0.591740	−	0.806129i	$-0.298441\pi$
$509$	26.7005			1.18348			0.591740	+	0.806129i	$0.298441\pi$
$510$		0			0
$511$	50.5253			2.23511
$512$	−8.50339	+	8.50339i	−0.375800	+	0.375800i
$513$		0			0
$514$			33.2857i			1.46817i
$515$	−1.65417	+	3.99352i	−0.0728914	+	0.175975i
$516$		0			0
$517$	7.46113	+	18.0128i	0.328140	+	0.792200i
$518$	6.73223	+	6.73223i	0.295797	+	0.295797i
$519$		0			0
$520$	0.119839	+	0.289316i	0.00525527	+	0.0126874i
$521$	−4.28773	+	1.77604i	−0.187849	+	0.0778096i	−0.474625	−	0.880188i	$-0.657416\pi$
$521$	−4.28773	+	1.77604i	−0.187849	+	0.0778096i	0.286776	+	0.957998i	$0.407416\pi$
$522$		0			0
$523$			9.21401i			0.402900i	0.979499	+	0.201450i	$0.0645654\pi$
$523$			9.21401i			0.402900i	−0.979499	+	0.201450i	$0.935435\pi$
$524$	5.51003	+	2.28233i	0.240707	+	0.0997040i
$525$		0			0
$526$	−15.7687			−0.687549
$527$	20.8060	+	7.49603i	0.906324	+	0.326532i
$528$		0			0
$529$	−8.78447	+	8.78447i	−0.381934	+	0.381934i
$530$	−2.35489	−	0.975427i	−0.102290	−	0.0423699i
$531$		0			0
$532$	−1.42797	+	3.44743i	−0.0619105	+	0.149465i
$533$	−1.18429	+	0.490548i	−0.0512972	+	0.0212480i
$534$		0			0
$535$	−3.33792	−	3.33792i	−0.144311	−	0.144311i
$536$	−11.9737	−	11.9737i	−0.517185	−	0.517185i
$537$		0			0
$538$	21.6686	−	8.97544i	0.934201	−	0.386959i
$539$	−8.01321	+	19.3456i	−0.345153	+	0.833274i
$540$		0			0
$541$	−29.5380	−	12.2350i	−1.26994	−	0.526025i	−0.356991	−	0.934108i	$-0.616197\pi$
$541$	−29.5380	−	12.2350i	−1.26994	−	0.526025i	−0.912945	+	0.408083i	$0.866197\pi$
$542$	−7.48292	+	7.48292i	−0.321419	+	0.321419i
$543$		0			0
$544$	6.48822	−	7.12717i	0.278180	−	0.305575i
$545$	15.3281			0.656583
$546$		0			0
$547$	7.76844	+	3.21779i	0.332155	+	0.137583i	0.542527	−	0.840038i	$-0.317468\pi$
$547$	7.76844	+	3.21779i	0.332155	+	0.137583i	−0.210372	+	0.977621i	$0.567468\pi$
$548$			3.58064i			0.152957i
$549$		0			0
$550$	−6.09815	+	2.52594i	−0.260026	+	0.107706i
$551$	−4.82880	−	11.6578i	−0.205714	−	0.496637i
$552$		0			0
$553$	12.5820	+	12.5820i	0.535042	+	0.535042i
$554$	−10.3114	−	24.8938i	−0.438087	−	1.05764i
$555$		0			0
$556$	1.09822	−	2.65133i	0.0465747	−	0.112441i
$557$		−	1.01642i		−	0.0430670i	−0.999768	−	0.0215335i	$-0.993145\pi$
$557$		−	1.01642i		−	0.0430670i	0.999768	−	0.0215335i	$-0.00685486\pi$
$558$		0			0
$559$	0.228320	−	0.228320i	0.00965692	−	0.00965692i
$560$	16.1101			0.680777
$561$		0			0
$562$	−28.0343			−1.18256
$563$	−7.34466	+	7.34466i	−0.309541	+	0.309541i	−0.844731	−	0.535191i	$-0.820240\pi$
$563$	−7.34466	+	7.34466i	−0.309541	+	0.309541i	0.535191	+	0.844731i	$0.320240\pi$
$564$		0			0
$565$			7.37161i			0.310126i
$566$	−11.2516	+	27.1638i	−0.472941	+	1.14178i
$567$		0			0
$568$	6.78947	+	16.3912i	0.284880	+	0.687761i
$569$	16.9517	+	16.9517i	0.710651	+	0.710651i	0.966671	−	0.256020i	$-0.0824113\pi$
$569$	16.9517	+	16.9517i	0.710651	+	0.710651i	−0.256020	+	0.966671i	$0.582411\pi$
$570$		0			0
$571$	−4.53513	−	10.9488i	−0.189789	−	0.458192i	0.800129	−	0.599827i	$-0.204764\pi$
$571$	−4.53513	−	10.9488i	−0.189789	−	0.458192i	−0.989919	+	0.141635i	$0.954764\pi$
$572$	−0.209617	+	0.0868261i	−0.00876452	+	0.00363038i
$573$		0			0
$574$			54.0741i			2.25701i
$575$	3.00465	+	1.24457i	0.125303	+	0.0519021i
$576$		0			0
$577$	22.5581			0.939107			0.469553	−	0.882904i	$-0.344415\pi$
$577$	22.5581			0.939107			0.469553	+	0.882904i	$0.344415\pi$
$578$	16.8656	−	20.3679i	0.701517	−	0.847195i
$579$		0			0
$580$	1.45529	−	1.45529i	0.0604276	−	0.0604276i
$581$	46.1079	+	19.0985i	1.91288	+	0.792340i
$582$		0			0
$583$	−2.66079	+	6.42372i	−0.110199	+	0.266043i
$584$	−33.2148	+	13.7580i	−1.37444	+	0.569311i
$585$		0			0
$586$	8.28456	+	8.28456i	0.342232	+	0.342232i
$587$	29.8211	+	29.8211i	1.23085	+	1.23085i	0.963638	+	0.267210i	$0.0861019\pi$
$587$	29.8211	+	29.8211i	1.23085	+	1.23085i	0.267210	+	0.963638i	$0.413898\pi$
$588$		0			0
$589$	12.7522	−	5.28214i	0.525446	−	0.217647i
$590$	−3.65607	+	8.82654i	−0.150518	+	0.363383i
$591$		0			0
$592$	−7.63292	−	3.16166i	−0.313711	−	0.129943i
$593$	6.00168	−	6.00168i	0.246460	−	0.246460i	−0.573056	−	0.819516i	$-0.694242\pi$
$593$	6.00168	−	6.00168i	0.246460	−	0.246460i	0.819516	+	0.573056i	$0.194242\pi$
$594$		0			0
$595$	14.2283	−	0.667711i	0.583305	−	0.0273735i
$596$	−2.95519			−0.121049
$597$		0			0
$598$	0.595415	+	0.246629i	0.0243483	+	0.0100854i
$599$		−	17.0226i		−	0.695523i	−0.937583	−	0.347762i	$-0.886942\pi$
$599$		−	17.0226i		−	0.695523i	0.937583	−	0.347762i	$-0.113058\pi$
$600$		0			0
$601$	−18.7530	+	7.76773i	−0.764949	+	0.316852i	−0.730825	−	0.682565i	$-0.760864\pi$
$601$	−18.7530	+	7.76773i	−0.764949	+	0.316852i	−0.0341247	+	0.999418i	$0.510864\pi$
$602$	−5.21252	−	12.5841i	−0.212446	−	0.512891i
$603$		0			0
$604$	−1.88668	−	1.88668i	−0.0767679	−	0.0767679i
$605$	2.68079	+	6.47199i	0.108989	+	0.263124i
$606$		0			0
$607$	−18.6877	+	45.1162i	−0.758512	+	1.83121i	−0.255879	+	0.966709i	$0.582365\pi$
$607$	−18.6877	+	45.1162i	−0.758512	+	1.83121i	−0.502633	+	0.864500i	$0.667635\pi$
$608$		−	6.01552i		−	0.243961i
$609$		0			0
$610$	4.44590	−	4.44590i	0.180009	−	0.180009i
$611$	0.585340			0.0236803
$612$		0			0
$613$	−21.5320			−0.869669			−0.434834	−	0.900510i	$-0.643193\pi$
$613$	−21.5320			−0.869669			−0.434834	+	0.900510i	$0.643193\pi$
$614$	−8.54733	+	8.54733i	−0.344942	+	0.344942i
$615$		0			0
$616$		−	36.0347i		−	1.45188i
$617$	1.77029	−	4.27386i	0.0712692	−	0.172059i	−0.884231	−	0.467050i	$-0.845317\pi$
$617$	1.77029	−	4.27386i	0.0712692	−	0.172059i	0.955500	+	0.294991i	$0.0953167\pi$
$618$		0			0
$619$	17.8427	+	43.0760i	0.717158	+	1.73137i	0.681288	+	0.732016i	$0.261420\pi$
$619$	17.8427	+	43.0760i	0.717158	+	1.73137i	0.0358698	+	0.999356i	$0.488580\pi$
$620$	1.59191	+	1.59191i	0.0639328	+	0.0639328i
$621$		0			0
$622$	5.14612	+	12.4238i	0.206341	+	0.498150i
$623$	−1.91782	+	0.794386i	−0.0768357	+	0.0318264i
$624$		0			0
$625$			1.00000i			0.0400000i
$626$	−17.7314	−	7.34457i	−0.708688	−	0.293548i
$627$		0			0
$628$	7.04048			0.280946
$629$	−6.87237	−	2.47599i	−0.274019	−	0.0987243i
$630$		0			0
$631$	18.5948	−	18.5948i	0.740246	−	0.740246i	−0.232380	−	0.972625i	$-0.574651\pi$
$631$	18.5948	−	18.5948i	0.740246	−	0.740246i	0.972625	+	0.232380i	$0.0746511\pi$
$632$	−11.6974	−	4.84522i	−0.465297	−	0.192732i
$633$		0			0
$634$	4.86498	−	11.7451i	0.193213	−	0.466457i
$635$	7.40956	−	3.06914i	0.294039	−	0.121795i
$636$		0			0
$637$	0.444523	+	0.444523i	0.0176127	+	0.0176127i
$638$	−22.8856	−	22.8856i	−0.906051	−	0.906051i
$639$		0			0
$640$	−12.4971	+	5.17647i	−0.493992	+	0.204618i
$641$	−2.51210	+	6.06476i	−0.0992222	+	0.239544i	−0.965694	−	0.259682i	$-0.916382\pi$
$641$	−2.51210	+	6.06476i	−0.0992222	+	0.239544i	0.866472	+	0.499226i	$0.166382\pi$
$642$		0			0
$643$	−5.91935	−	2.45187i	−0.233436	−	0.0966925i	0.262899	−	0.964823i	$-0.415321\pi$
$643$	−5.91935	−	2.45187i	−0.233436	−	0.0966925i	−0.496335	+	0.868131i	$0.665321\pi$
$644$	3.33457	−	3.33457i	0.131400	−	0.131400i
$645$		0			0
$646$	−0.773695	−	16.4867i	−0.0304406	−	0.648662i
$647$	8.03230			0.315782			0.157891	−	0.987457i	$-0.449530\pi$
$647$	8.03230			0.315782			0.157891	+	0.987457i	$0.449530\pi$
$648$		0			0
$649$	24.0772	+	9.97311i	0.945114	+	0.391479i
$650$			0.198164i			0.00777265i
$651$		0			0
$652$	−1.78161	+	0.737969i	−0.0697734	+	0.0289011i
$653$	17.6821	+	42.6883i	0.691953	+	1.67052i	0.740808	+	0.671717i	$0.234443\pi$
$653$	17.6821	+	42.6883i	0.691953	+	1.67052i	−0.0488551	+	0.998806i	$0.515557\pi$
$654$		0			0
$655$	−10.0474	−	10.0474i	−0.392585	−	0.392585i
$656$	−17.9569	−	43.3517i	−0.701098	−	1.69260i
$657$		0			0
$658$	9.44921	−	22.8124i	0.368369	−	0.889321i
$659$		−	47.9496i		−	1.86785i	−0.357465	−	0.933926i	$-0.616359\pi$
$659$		−	47.9496i		−	1.86785i	0.357465	−	0.933926i	$-0.383641\pi$
$660$		0			0
$661$	−26.7821	+	26.7821i	−1.04170	+	1.04170i	−0.0426129	+	0.999092i	$0.513568\pi$
$661$	−26.7821	+	26.7821i	−1.04170	+	1.04170i	−0.999092	+	0.0426129i	$0.986432\pi$
$662$	36.5032			1.41874
$663$		0			0
$664$	−35.5114			−1.37811
$665$	6.28632	−	6.28632i	0.243773	−	0.243773i
$666$		0			0
$667$			15.9468i			0.617463i
$668$	−3.37735	+	8.15364i	−0.130674	+	0.315474i
$669$		0			0
$670$	−4.10064	−	9.89981i	−0.158421	−	0.382463i
$671$	−12.1276	−	12.1276i	−0.468182	−	0.468182i
$672$		0			0
$673$	1.55425	+	3.75229i	0.0599119	+	0.144640i	0.951001	−	0.309189i	$-0.100058\pi$
$673$	1.55425	+	3.75229i	0.0599119	+	0.144640i	−0.891089	+	0.453829i	$0.850058\pi$
$674$	−34.0863	+	14.1190i	−1.31295	+	0.543844i
$675$		0			0
$676$		−	5.44967i		−	0.209603i
$677$	−3.22013	−	1.33382i	−0.123760	−	0.0512629i	0.319944	−	0.947436i	$-0.396336\pi$
$677$	−3.22013	−	1.33382i	−0.123760	−	0.0512629i	−0.443704	+	0.896173i	$0.646336\pi$
$678$		0			0
$679$	26.5194			1.01772
$680$	−9.17174	+	4.31332i	−0.351720	+	0.165408i
$681$		0			0
$682$	25.0342	−	25.0342i	0.958609	−	0.958609i
$683$	13.0097	+	5.38880i	0.497803	+	0.206197i	0.617436	−	0.786621i	$-0.288172\pi$
$683$	13.0097	+	5.38880i	0.497803	+	0.206197i	−0.119632	+	0.992818i	$0.538172\pi$
$684$		0			0
$685$	3.26461	−	7.88145i	0.124734	−	0.301135i
$686$	−10.2535	+	4.24715i	−0.391482	+	0.162157i
$687$		0			0
$688$	8.35784	+	8.35784i	0.318640	+	0.318640i
$689$	0.147604	+	0.147604i	0.00562328	+	0.00562328i
$690$		0			0
$691$	−41.2601	+	17.0905i	−1.56961	+	0.650153i	−0.986724	−	0.162403i	$-0.948075\pi$
$691$	−41.2601	+	17.0905i	−1.56961	+	0.650153i	−0.582883	+	0.812556i	$0.698075\pi$
$692$	2.01621	−	4.86756i	0.0766448	−	0.185037i
$693$		0			0
$694$	−10.0870	−	4.17819i	−0.382899	−	0.158602i
$695$	−4.83464	+	4.83464i	−0.183388	+	0.183388i
$696$		0			0
$697$	−17.6561	−	37.5436i	−0.668774	−	1.42207i
$698$	−45.7076			−1.73006
$699$		0			0
$700$	1.33965	+	0.554901i	0.0506340	+	0.0209733i
$701$			1.84833i			0.0698103i	0.999391	+	0.0349052i	$0.0111129\pi$
$701$			1.84833i			0.0698103i	−0.999391	+	0.0349052i	$0.988887\pi$
$702$		0			0
$703$	−4.21215	+	1.74473i	−0.158864	+	0.0658037i
$704$	9.24011	+	22.3076i	0.348250	+	0.840749i
$705$		0			0
$706$	−9.99965	−	9.99965i	−0.376342	−	0.376342i
$707$	22.2745	+	53.7753i	0.837717	+	2.02243i
$708$		0			0
$709$	11.4834	−	27.7233i	0.431267	−	1.04117i	−0.547613	−	0.836732i	$-0.684463\pi$
$709$	11.4834	−	27.7233i	0.431267	−	1.04117i	0.978879	−	0.204438i	$-0.0655367\pi$
$710$			11.2270i			0.421343i
$711$		0			0
$712$	1.04444	−	1.04444i	0.0391421	−	0.0391421i
$713$	−17.4439			−0.653281
$714$		0			0
$715$	0.540557			0.0202157
$716$	3.60711	−	3.60711i	0.134804	−	0.134804i
$717$		0			0
$718$			8.15119i			0.304200i
$719$	−14.6916	+	35.4687i	−0.547904	+	1.32276i	0.371130	+	0.928581i	$0.378970\pi$
$719$	−14.6916	+	35.4687i	−0.547904	+	1.32276i	−0.919034	+	0.394177i	$0.871030\pi$
$720$		0			0
$721$	−5.71461	−	13.7963i	−0.212823	−	0.513801i
$722$	13.6147	+	13.6147i	0.506687	+	0.506687i
$723$		0			0
$724$	2.45150	+	5.91846i	0.0911094	+	0.219958i
$725$	−4.53013	+	1.87644i	−0.168245	+	0.0696892i
$726$		0			0
$727$			0.0992434i			0.00368073i	0.999998	+	0.00184037i	$0.000585807\pi$
$727$			0.0992434i			0.00368073i	−0.999998	+	0.00184037i	$0.999414\pi$
$728$	−0.999493	−	0.414004i	−0.0370437	−	0.0153440i
$729$		0			0
$730$	−22.7502			−0.842022
$731$	7.72798	+	7.03517i	0.285830	+	0.260205i
$732$		0			0
$733$	10.2168	−	10.2168i	0.377365	−	0.377365i	−0.492786	−	0.870151i	$-0.664021\pi$
$733$	10.2168	−	10.2168i	0.377365	−	0.377365i	0.870151	+	0.492786i	$0.164021\pi$
$734$	−26.2030	−	10.8536i	−0.967169	−	0.400614i
$735$		0			0
$736$	−2.90929	+	7.02364i	−0.107238	+	0.258895i
$737$	−27.0049	+	11.1858i	−0.994739	+	0.412035i
$738$		0			0
$739$	−3.22478	−	3.22478i	−0.118625	−	0.118625i	0.645302	−	0.763928i	$-0.276732\pi$
$739$	−3.22478	−	3.22478i	−0.118625	−	0.118625i	−0.763928	+	0.645302i	$0.776732\pi$
$740$	−0.525821	−	0.525821i	−0.0193295	−	0.0193295i
$741$		0			0
$742$	8.13538	−	3.36978i	0.298659	−	0.123709i
$743$	−12.7331	+	30.7404i	−0.467131	+	1.12776i	0.498278	+	0.867017i	$0.333966\pi$
$743$	−12.7331	+	30.7404i	−0.467131	+	1.12776i	−0.965410	+	0.260738i	$0.916034\pi$
$744$		0			0
$745$	6.50477	+	2.69437i	0.238316	+	0.0987139i
$746$	20.4027	−	20.4027i	0.746996	−	0.746996i
$747$		0			0
$748$	−3.12511	−	6.64516i	−0.114265	−	0.242971i
$749$	16.3079			0.595877
$750$		0			0
$751$	−24.4052	−	10.1090i	−0.890558	−	0.368881i	−0.109976	−	0.993934i	$-0.535077\pi$
$751$	−24.4052	−	10.1090i	−0.890558	−	0.368881i	−0.780582	+	0.625053i	$0.785077\pi$
$752$			21.4268i			0.781355i
$753$		0			0
$754$	−0.897710	+	0.371844i	−0.0326927	+	0.0135418i
$755$	2.43267	+	5.87300i	0.0885341	+	0.213740i
$756$		0			0
$757$	15.6840	+	15.6840i	0.570043	+	0.570043i	0.932140	−	0.362097i	$-0.117939\pi$
$757$	15.6840	+	15.6840i	0.570043	+	0.570043i	−0.362097	+	0.932140i	$0.617939\pi$
$758$	11.9425	+	28.8317i	0.433771	+	1.04722i
$759$		0			0
$760$	−2.42080	+	5.84433i	−0.0878117	+	0.211996i
$761$			23.1817i			0.840337i	0.907446	+	0.420168i	$0.138029\pi$
$761$			23.1817i			0.840337i	−0.907446	+	0.420168i	$0.861971\pi$
$762$		0			0
$763$	−37.4438	+	37.4438i	−1.35556	+	1.35556i
$764$	3.73547			0.135145
$765$		0			0
$766$	16.9996			0.614219
$767$	0.553247	−	0.553247i	0.0199766	−	0.0199766i
$768$		0			0
$769$		−	16.7701i		−	0.604747i	−0.953190	−	0.302373i	$-0.902221\pi$
$769$		−	16.7701i		−	0.604747i	0.953190	−	0.302373i	$-0.0977789\pi$
$770$	8.72629	−	21.0671i	0.314474	−	0.759206i
$771$		0			0
$772$	−2.95287	−	7.12886i	−0.106276	−	0.256573i
$773$	−9.68077	−	9.68077i	−0.348193	−	0.348193i	0.511243	−	0.859436i	$-0.329185\pi$
$773$	−9.68077	−	9.68077i	−0.348193	−	0.348193i	−0.859436	+	0.511243i	$0.829185\pi$
$774$		0			0
$775$	−2.05261	−	4.95543i	−0.0737318	−	0.178004i
$776$	−17.4336	+	7.22124i	−0.625830	+	0.259227i
$777$		0			0
$778$			36.9463i			1.32459i
$779$	−23.9232	−	9.90931i	−0.857137	−	0.355038i
$780$		0			0
$781$	30.6253			1.09586
$782$	−7.07014	+	19.6239i	−0.252828	+	0.701749i
$783$		0			0
$784$	−16.2721	+	16.2721i	−0.581147	+	0.581147i
$785$	−15.4970	−	6.41908i	−0.553113	−	0.229107i
$786$		0			0
$787$	−11.1862	+	27.0058i	−0.398743	+	0.962651i	0.589221	+	0.807972i	$0.299435\pi$
$787$	−11.1862	+	27.0058i	−0.398743	+	0.962651i	−0.987965	+	0.154680i	$0.950565\pi$
$788$	−4.14521	+	1.71700i	−0.147667	+	0.0611656i
$789$		0			0
$790$	−5.66535	−	5.66535i	−0.201564	−	0.201564i
$791$	−18.0076	−	18.0076i	−0.640275	−	0.640275i
$792$		0			0
$793$	−0.475718	+	0.197049i	−0.0168932	+	0.00699740i
$794$	−16.8981	+	40.7957i	−0.599692	+	1.44778i
$795$		0			0
$796$	−6.01797	−	2.49272i	−0.213301	−	0.0883522i
$797$	−10.0043	+	10.0043i	−0.354369	+	0.354369i	−0.861732	−	0.507363i	$-0.830620\pi$
$797$	−10.0043	+	10.0043i	−0.354369	+	0.354369i	0.507363	+	0.861732i	$0.330620\pi$
$798$		0			0
$799$	0.888070	+	18.9240i	0.0314176	+	0.669482i
$800$	−2.33759			−0.0826463
$801$		0			0
$802$	12.5407	+	5.19452i	0.442827	+	0.183425i
$803$			62.0584i			2.18999i
$804$		0			0
$805$	−10.3801	+	4.29958i	−0.365850	+	0.151540i
$806$	−0.406753	−	0.981990i	−0.0143273	−	0.0345891i
$807$		0			0
$808$	−29.2860	−	29.2860i	−1.03028	−	1.03028i
$809$	−6.56799	−	15.8565i	−0.230918	−	0.557486i	0.765368	−	0.643593i	$-0.222557\pi$
$809$	−6.56799	−	15.8565i	−0.230918	−	0.557486i	−0.996286	+	0.0861076i	$0.972557\pi$
$810$		0			0
$811$	17.3259	−	41.8285i	0.608396	−	1.46880i	−0.256348	−	0.966585i	$-0.582519\pi$
$811$	17.3259	−	41.8285i	0.608396	−	1.46880i	0.864744	−	0.502214i	$-0.167481\pi$
$812$			7.11003i			0.249513i
$813$		0			0
$814$	−8.26897	+	8.26897i	−0.289827	+	0.289827i
$815$	4.59441			0.160935
$816$		0			0
$817$	6.52262			0.228197
$818$	11.6123	−	11.6123i	0.406013	−	0.406013i
$819$		0			0
$820$		−	4.22346i		−	0.147490i
$821$	9.18115	−	22.1652i	0.320424	−	0.773572i	−0.678805	−	0.734319i	$-0.737502\pi$
$821$	9.18115	−	22.1652i	0.320424	−	0.773572i	0.999229	−	0.0392539i	$-0.0124981\pi$
$822$		0			0
$823$	16.5962	+	40.0669i	0.578509	+	1.39664i	0.894151	+	0.447766i	$0.147780\pi$
$823$	16.5962	+	40.0669i	0.578509	+	1.39664i	−0.315642	+	0.948878i	$0.602220\pi$
$824$	7.51346	+	7.51346i	0.261744	+	0.261744i
$825$		0			0
$826$	−12.6305	−	30.4928i	−0.439473	−	1.06098i
$827$	35.5628	−	14.7306i	1.23664	−	0.512233i	0.333978	−	0.942581i	$-0.391609\pi$
$827$	35.5628	−	14.7306i	1.23664	−	0.512233i	0.902663	+	0.430347i	$0.141609\pi$
$828$		0			0
$829$		−	54.4489i		−	1.89109i	−0.325492	−	0.945545i	$-0.605530\pi$
$829$		−	54.4489i		−	1.89109i	0.325492	−	0.945545i	$-0.394470\pi$
$830$	−20.7612	−	8.59955i	−0.720630	−	0.298495i
$831$		0			0
$832$	0.724904			0.0251315
$833$	−13.6970	+	15.0458i	−0.474572	+	0.521307i
$834$		0			0
$835$	14.8680	−	14.8680i	0.514528	−	0.514528i
$836$	−4.23437	−	1.75393i	−0.146449	−	0.0606610i
$837$		0			0
$838$	−8.50583	+	20.5349i	−0.293829	+	0.709366i
$839$	10.9808	−	4.54840i	0.379100	−	0.157028i	−0.184993	−	0.982740i	$-0.559226\pi$
$839$	10.9808	−	4.54840i	0.379100	−	0.157028i	0.564093	+	0.825712i	$0.309226\pi$
$840$		0			0
$841$	3.50507	+	3.50507i	0.120864	+	0.120864i
$842$	20.0953	+	20.0953i	0.692529	+	0.692529i
$843$		0			0
$844$	3.39457	−	1.40608i	0.116846	−	0.0483991i
$845$	−4.96867	+	11.9954i	−0.170928	+	0.412656i
$846$		0			0
$847$	−22.3586	−	9.26124i	−0.768251	−	0.318220i
$848$	−5.40317	+	5.40317i	−0.185546	+	0.185546i
$849$		0			0
$850$	−6.40664	+	0.300653i	−0.219746	+	0.0103123i
$851$	5.76186			0.197514
$852$		0			0
$853$	−31.7617	−	13.1561i	−1.08750	−	0.450457i	−0.234365	−	0.972149i	$-0.575301\pi$
$853$	−31.7617	−	13.1561i	−1.08750	−	0.450457i	−0.853134	+	0.521692i	$0.825301\pi$
$854$			21.7211i			0.743281i
$855$		0			0
$856$	−10.7206	+	4.44064i	−0.366424	+	0.151778i
$857$	−7.05760	−	17.0386i	−0.241083	−	0.582026i	0.756308	−	0.654216i	$-0.227001\pi$
$857$	−7.05760	−	17.0386i	−0.241083	−	0.582026i	−0.997391	+	0.0721899i	$0.977001\pi$
$858$		0			0
$859$	17.2644	+	17.2644i	0.589054	+	0.589054i	0.937375	−	0.348321i	$-0.113248\pi$
$859$	17.2644	+	17.2644i	0.589054	+	0.589054i	−0.348321	+	0.937375i	$0.613248\pi$
$860$	0.407123	+	0.982883i	0.0138828	+	0.0335160i
$861$		0			0
$862$	−12.5262	+	30.2410i	−0.426645	+	1.03001i
$863$			22.5253i			0.766770i	0.923589	+	0.383385i	$0.125242\pi$
$863$			22.5253i			0.766770i	−0.923589	+	0.383385i	$0.874758\pi$
$864$		0			0
$865$	−8.87590	+	8.87590i	−0.301790	+	0.301790i
$866$	5.56353			0.189056
$867$		0			0
$868$	−7.77753			−0.263987
$869$	−15.4541	+	15.4541i	−0.524243	+	0.524243i
$870$		0			0
$871$			0.877548i			0.0297346i
$872$	14.4192	−	34.8111i	0.488297	−	1.17885i
$873$		0			0
$874$	4.98203	+	12.0277i	0.168520	+	0.406843i
$875$	−2.44282	−	2.44282i	−0.0825825	−	0.0825825i
$876$		0			0
$877$	21.6461	+	52.2583i	0.730937	+	1.76464i	0.639451	+	0.768832i	$0.279162\pi$
$877$	21.6461	+	52.2583i	0.730937	+	1.76464i	0.0914856	+	0.995806i	$0.470838\pi$
$878$	4.72519	−	1.95724i	0.159467	−	0.0660535i
$879$		0			0
$880$			19.7875i			0.667037i
$881$	−30.6744	−	12.7058i	−1.03345	−	0.428068i	−0.199492	−	0.979899i	$-0.563929\pi$
$881$	−30.6744	−	12.7058i	−1.03345	−	0.428068i	−0.833956	+	0.551831i	$0.813929\pi$
$882$		0			0
$883$	−11.2453			−0.378433			−0.189217	−	0.981935i	$-0.560595\pi$
$883$	−11.2453			−0.378433			−0.189217	+	0.981935i	$0.560595\pi$
$884$	−0.220221	+	0.0103346i	−0.00740682	+	0.000347590i
$885$		0			0
$886$	27.4315	−	27.4315i	0.921580	−	0.921580i
$887$	0.934751	+	0.387187i	0.0313859	+	0.0130005i	0.398321	−	0.917246i	$-0.369593\pi$
$887$	0.934751	+	0.387187i	0.0313859	+	0.0130005i	−0.366935	+	0.930246i	$0.619593\pi$
$888$		0			0
$889$	−10.6029	+	25.5976i	−0.355609	+	0.858516i
$890$	0.863542	−	0.357691i	0.0289460	−	0.0119898i
$891$		0			0
$892$	6.28002	+	6.28002i	0.210271	+	0.210271i
$893$	8.36094	+	8.36094i	0.279788	+	0.279788i
$894$		0			0
$895$	−11.2285	+	4.65099i	−0.375326	+	0.155465i
$896$	17.8830	−	43.1734i	0.597430	−	1.44232i
$897$		0			0
$898$	−13.8775	−	5.74827i	−0.463100	−	0.191822i
$899$	18.5971	−	18.5971i	0.620249	−	0.620249i
$900$		0			0
$901$	−4.54809	+	4.99598i	−0.151519	+	0.166440i
$902$	−66.4174			−2.21146
$903$		0			0
$904$	16.7414	+	6.93453i	0.556812	+	0.230639i
$905$		−	15.2624i		−	0.507341i
$906$		0			0
$907$	16.9354	−	7.01488i	0.562331	−	0.232925i	−0.0833657	−	0.996519i	$-0.526567\pi$
$907$	16.9354	−	7.01488i	0.562331	−	0.232925i	0.645697	+	0.763594i	$0.276567\pi$
$908$	−4.11731	−	9.94006i	−0.136638	−	0.329872i
$909$		0			0
$910$	−0.484081	−	0.484081i	−0.0160471	−	0.0160471i
$911$	−10.6365	−	25.6787i	−0.352402	−	0.850772i	−0.996323	−	0.0856806i	$-0.972694\pi$
$911$	−10.6365	−	25.6787i	−0.352402	−	0.850772i	0.643921	−	0.765092i	$-0.277306\pi$
$912$		0			0
$913$	−23.4580	+	56.6327i	−0.776348	+	1.87427i
$914$		−	31.8538i		−	1.05363i
$915$		0			0
$916$	−2.10734	+	2.10734i	−0.0696286	+	0.0696286i
$917$	49.0881			1.62103
$918$		0			0
$919$	−13.6372			−0.449850			−0.224925	−	0.974376i	$-0.572214\pi$
$919$	−13.6372			−0.449850			−0.224925	+	0.974376i	$0.572214\pi$
$920$	5.65300	−	5.65300i	0.186374	−	0.186374i
$921$		0			0
$922$		−	29.3218i		−	0.965661i
$923$	0.351855	−	0.849453i	0.0115814	−	0.0279601i
$924$		0			0
$925$	0.677990	+	1.63681i	0.0222922	+	0.0538181i
$926$	−2.34760	−	2.34760i	−0.0771468	−	0.0771468i
$927$		0			0
$928$	−4.38635	−	10.5896i	−0.143989	−	0.347620i
$929$	48.4225	−	20.0573i	1.58869	−	0.658057i	0.598931	−	0.800800i	$-0.295592\pi$
$929$	48.4225	−	20.0573i	1.58869	−	0.658057i	0.989760	+	0.142743i	$0.0455922\pi$
$930$		0			0
$931$			12.6991i			0.416195i
$932$	−9.19587	−	3.80905i	−0.301221	−	0.124770i
$933$		0			0
$934$	−36.1876			−1.18409
$935$	0.820127	+	17.4762i	0.0268210	+	0.571532i
$936$		0			0
$937$	22.9966	−	22.9966i	0.751266	−	0.751266i	−0.223450	−	0.974715i	$-0.571732\pi$
$937$	22.9966	−	22.9966i	0.751266	−	0.751266i	0.974715	+	0.223450i	$0.0717318\pi$
$938$	34.2006	+	14.1664i	1.11669	+	0.462548i
$939$		0			0
$940$	−0.738030	+	1.78176i	−0.0240719	+	0.0581147i
$941$	−16.0374	+	6.64290i	−0.522804	+	0.216552i	−0.628448	−	0.777852i	$-0.716310\pi$
$941$	−16.0374	+	6.64290i	−0.522804	+	0.216552i	0.105644	+	0.994404i	$0.466310\pi$
$942$		0			0
$943$	23.1400	+	23.1400i	0.753541	+	0.753541i
$944$	20.2520	+	20.2520i	0.659148	+	0.659148i
$945$		0			0
$946$	15.4566	−	6.40235i	0.502539	−	0.208158i
$947$	−5.46073	+	13.1834i	−0.177450	+	0.428402i	−0.987430	−	0.158055i	$-0.949478\pi$
$947$	−5.46073	+	13.1834i	−0.177450	+	0.428402i	0.809980	+	0.586457i	$0.199478\pi$
$948$		0			0
$949$	1.72131	+	0.712990i	0.0558761	+	0.0231446i
$950$	−2.83056	+	2.83056i	−0.0918356	+	0.0918356i
$951$		0			0
$952$	11.8683	−	32.9416i	0.384653	−	1.06764i
$953$	−30.1090			−0.975326			−0.487663	−	0.873032i	$-0.662150\pi$
$953$	−30.1090			−0.975326			−0.487663	+	0.873032i	$0.662150\pi$
$954$		0			0
$955$	−8.22227	−	3.40577i	−0.266066	−	0.110208i
$956$			0.0458829i			0.00148396i
$957$		0			0
$958$	44.8571	−	18.5804i	1.44927	−	0.600306i
$959$	11.2781	+	27.2279i	0.364190	+	0.879233i
$960$		0			0
$961$	−1.57724	−	1.57724i	−0.0508787	−	0.0508787i
$962$	0.134354	+	0.324358i	0.00433173	+	0.0104577i
$963$		0			0
$964$	2.80880	−	6.78105i	0.0904654	−	0.218403i
$965$			18.3838i			0.591796i
$966$		0			0
$967$	−12.3882	+	12.3882i	−0.398378	+	0.398378i	−0.877661	−	0.479282i	$-0.840897\pi$
$967$	−12.3882	+	12.3882i	−0.398378	+	0.398378i	0.479282	+	0.877661i	$0.340897\pi$
$968$	17.2202			0.553477
$969$		0			0
$970$	−11.9410			−0.383402
$971$	8.22783	−	8.22783i	0.264044	−	0.264044i	−0.562651	−	0.826695i	$-0.690218\pi$
$971$	8.22783	−	8.22783i	0.264044	−	0.264044i	0.826695	+	0.562651i	$0.190218\pi$
$972$		0			0
$973$		−	23.6203i		−	0.757234i
$974$	8.72253	−	21.0581i	0.279488	−	0.674744i
$975$		0			0
$976$	−7.21312	−	17.4140i	−0.230886	−	0.557409i
$977$	−30.6475	−	30.6475i	−0.980501	−	0.980501i	0.0193125	−	0.999813i	$-0.493852\pi$
$977$	−30.6475	−	30.6475i	−0.980501	−	0.980501i	−0.999813	+	0.0193125i	$0.993852\pi$
$978$		0			0
$979$	−0.975716	−	2.35559i	−0.0311840	−	0.0752849i
$980$	−1.91360	+	0.792640i	−0.0611278	+	0.0253200i
$981$		0			0
$982$			21.5620i			0.688072i
$983$	−41.0128	−	16.9881i	−1.30811	−	0.541835i	−0.383774	−	0.923427i	$-0.625376\pi$
$983$	−41.0128	−	16.9881i	−1.30811	−	0.541835i	−0.924331	+	0.381592i	$0.875376\pi$
$984$		0			0
$985$	10.6896			0.340599
$986$	−13.3837	−	28.4587i	−0.426223	−	0.906310i
$987$		0			0
$988$	−0.0972974	+	0.0972974i	−0.00309544	+	0.00309544i
$989$	−7.61573	−	3.15454i	−0.242166	−	0.100308i
$990$		0			0
$991$	−22.0859	+	53.3201i	−0.701583	+	1.69377i	0.0184501	+	0.999830i	$0.494127\pi$
$991$	−22.0859	+	53.3201i	−0.701583	+	1.69377i	−0.720033	+	0.693940i	$0.755873\pi$
$992$	11.5838	−	4.79815i	0.367785	−	0.152341i
$993$		0			0
$994$	−27.4256	−	27.4256i	−0.869889	−	0.869889i
$995$	10.9736	+	10.9736i	0.347887	+	0.347887i
$996$		0			0
$997$	10.7781	−	4.46444i	0.341346	−	0.141390i	−0.205424	−	0.978673i	$-0.565857\pi$
$997$	10.7781	−	4.46444i	0.341346	−	0.141390i	0.546770	+	0.837283i	$0.315857\pi$
$998$	23.8303	−	57.5315i	0.754336	−	1.82113i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	765.2.be.b.451.4		24
3.2	odd	2		85.2.l.a.26.3	✓	24
15.2	even	4		425.2.n.f.349.3		24
15.8	even	4		425.2.n.c.349.4		24
15.14	odd	2		425.2.m.b.26.4		24
17.2	even	8	inner	765.2.be.b.631.4		24
51.2	odd	8		85.2.l.a.36.3	yes	24
51.11	even	16		1445.2.a.p.1.4		12
51.23	even	16		1445.2.a.q.1.4		12
51.41	even	16		1445.2.d.j.866.17		24
51.44	even	16		1445.2.d.j.866.18		24
255.2	even	8		425.2.n.c.274.4		24
255.53	even	8		425.2.n.f.274.3		24
255.74	even	16		7225.2.a.bq.1.9		12
255.104	odd	8		425.2.m.b.376.4		24
255.164	even	16		7225.2.a.bs.1.9		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.l.a.26.3	✓	24	3.2	odd	2
85.2.l.a.36.3	yes	24	51.2	odd	8
425.2.m.b.26.4		24	15.14	odd	2
425.2.m.b.376.4		24	255.104	odd	8
425.2.n.c.274.4		24	255.2	even	8
425.2.n.c.349.4		24	15.8	even	4
425.2.n.f.274.3		24	255.53	even	8
425.2.n.f.349.3		24	15.2	even	4
765.2.be.b.451.4		24	1.1	even	1	trivial
765.2.be.b.631.4		24	17.2	even	8	inner
1445.2.a.p.1.4		12	51.11	even	16
1445.2.a.q.1.4		12	51.23	even	16
1445.2.d.j.866.17		24	51.41	even	16
1445.2.d.j.866.18		24	51.44	even	16
7225.2.a.bq.1.9		12	255.74	even	16
7225.2.a.bs.1.9		12	255.164	even	16

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:	\( N \)	\(=\)	\( 765 = 3^{2} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	765.be (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.09994 - 1.09994i) q^{2} -0.419729i q^{4} +(-0.382683 + 0.923880i) q^{5} +(-1.32205 - 3.19170i) q^{7} +(1.73820 + 1.73820i) q^{8} +O(q^{10})\)	\(q+(1.09994 - 1.09994i) q^{2} -0.419729i q^{4} +(-0.382683 + 0.923880i) q^{5} +(-1.32205 - 3.19170i) q^{7} +(1.73820 + 1.73820i) q^{8} +(0.595282 + 1.43714i) q^{10} +(3.92026 - 1.62382i) q^{11} -0.127392i q^{13} +(-4.96485 - 2.05651i) q^{14} +4.66329 q^{16} +(4.11857 - 0.193278i) q^{17} +(1.81966 - 1.81966i) q^{19} +(0.387779 + 0.160623i) q^{20} +(2.52594 - 6.09815i) q^{22} +(-3.00465 + 1.24457i) q^{23} +(-0.707107 - 0.707107i) q^{25} +(-0.140123 - 0.140123i) q^{26} +(-1.33965 + 0.554901i) q^{28} +(1.87644 - 4.53013i) q^{29} +(4.95543 + 2.05261i) q^{31} +(1.65293 - 1.65293i) q^{32} +(4.31758 - 4.74277i) q^{34} +3.45467 q^{35} +(-1.63681 - 0.677990i) q^{37} -4.00302i q^{38} +(-2.27107 + 0.940707i) q^{40} +(-3.85069 - 9.29639i) q^{41} +(1.79227 + 1.79227i) q^{43} +(-0.681566 - 1.64545i) q^{44} +(-1.93598 + 4.67388i) q^{46} +4.59479i q^{47} +(-3.48941 + 3.48941i) q^{49} -1.55555 q^{50} -0.0534701 q^{52} +(-1.15866 + 1.15866i) q^{53} +4.24326i q^{55} +(3.24984 - 7.84580i) q^{56} +(-2.91889 - 7.04683i) q^{58} +(4.34287 + 4.34287i) q^{59} +(-1.54679 - 3.73428i) q^{61} +(7.70840 - 3.19293i) q^{62} +5.69034i q^{64} +(0.117695 + 0.0487508i) q^{65} -6.88856 q^{67} +(-0.0811242 - 1.72868i) q^{68} +(3.79993 - 3.79993i) q^{70} +(6.66802 + 2.76198i) q^{71} +(-5.59682 + 13.5119i) q^{73} +(-2.54614 + 1.05465i) q^{74} +(-0.763763 - 0.763763i) q^{76} +(-10.3655 - 10.3655i) q^{77} +(-4.75854 + 1.97105i) q^{79} +(-1.78456 + 4.30831i) q^{80} +(-14.4610 - 5.98994i) q^{82} +(-10.2150 + 10.2150i) q^{83} +(-1.39754 + 3.87903i) q^{85} +3.94276 q^{86} +(9.63673 + 3.99166i) q^{88} -0.600876i q^{89} +(-0.406598 + 0.168418i) q^{91} +(0.522381 + 1.26114i) q^{92} +(5.05398 + 5.05398i) q^{94} +(0.984791 + 2.37750i) q^{95} +(-2.93763 + 7.09206i) q^{97} +7.67628i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q+O(q^{10}) \) 24 * q	\( 24 q + 8 q^{11} - 24 q^{16} + 8 q^{17} - 8 q^{19} - 32 q^{22} + 16 q^{23} - 16 q^{26} + 48 q^{28} + 8 q^{29} + 16 q^{34} + 32 q^{35} + 24 q^{37} + 16 q^{40} - 16 q^{41} + 8 q^{43} - 16 q^{44} + 8 q^{46} - 8 q^{50} - 48 q^{52} - 24 q^{53} - 64 q^{56} - 64 q^{58} - 32 q^{59} + 32 q^{61} + 32 q^{62} - 8 q^{65} + 16 q^{67} + 40 q^{68} + 24 q^{71} + 64 q^{74} - 8 q^{76} - 24 q^{77} + 32 q^{80} - 80 q^{82} + 96 q^{83} + 16 q^{86} - 8 q^{88} - 24 q^{91} - 80 q^{92} + 56 q^{94} + 16 q^{95} - 40 q^{97}+O(q^{100}) \) 24 * q + 8 * q^11 - 24 * q^16 + 8 * q^17 - 8 * q^19 - 32 * q^22 + 16 * q^23 - 16 * q^26 + 48 * q^28 + 8 * q^29 + 16 * q^34 + 32 * q^35 + 24 * q^37 + 16 * q^40 - 16 * q^41 + 8 * q^43 - 16 * q^44 + 8 * q^46 - 8 * q^50 - 48 * q^52 - 24 * q^53 - 64 * q^56 - 64 * q^58 - 32 * q^59 + 32 * q^61 + 32 * q^62 - 8 * q^65 + 16 * q^67 + 40 * q^68 + 24 * q^71 + 64 * q^74 - 8 * q^76 - 24 * q^77 + 32 * q^80 - 80 * q^82 + 96 * q^83 + 16 * q^86 - 8 * q^88 - 24 * q^91 - 80 * q^92 + 56 * q^94 + 16 * q^95 - 40 * q^97

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