LMFDB - Embedded newform 315.2.ce.a.53.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(53,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 8]))

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

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

chi := DirichletCharacter("315.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.ce (of order $12$, 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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			53.3
Character	$\chi$	$=$	315.53
Dual form			315.2.ce.a.107.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.543545 + 2.02854i) q^{2} +(-2.08747 - 1.20520i) q^{4} +(-1.61611 - 1.54538i) q^{5} +(1.07923 - 2.41563i) q^{7} +(0.609443 - 0.609443i) q^{8} +O(q^{10})$	\(q+(-0.543545 + 2.02854i) q^{2} +(-2.08747 - 1.20520i) q^{4} +(-1.61611 - 1.54538i) q^{5} +(1.07923 - 2.41563i) q^{7} +(0.609443 - 0.609443i) q^{8} +(4.01329 - 2.43835i) q^{10} +(-4.56441 - 2.63527i) q^{11} +(-3.08333 - 3.08333i) q^{13} +(4.31359 + 3.50225i) q^{14} +(-1.50538 - 2.60740i) q^{16} +(5.92744 - 1.58825i) q^{17} +(0.715930 - 0.413342i) q^{19} +(1.51108 + 5.17367i) q^{20} +(7.82670 - 7.82670i) q^{22} +(1.33984 + 0.359008i) q^{23} +(0.223603 + 4.99500i) q^{25} +(7.93057 - 4.57872i) q^{26} +(-5.16417 + 3.74187i) q^{28} -7.45552 q^{29} +(-2.97481 + 5.15253i) q^{31} +(7.77248 - 2.08263i) q^{32} +12.8873i q^{34} +(-5.47721 + 2.23611i) q^{35} +(2.12029 + 0.568131i) q^{37} +(0.449340 + 1.67696i) q^{38} +(-1.92674 + 0.0431042i) q^{40} +2.00950i q^{41} +(-1.73260 - 1.73260i) q^{43} +(6.35205 + 11.0021i) q^{44} +(-1.45652 + 2.52277i) q^{46} +(1.11993 - 4.17964i) q^{47} +(-4.67055 - 5.21402i) q^{49} +(-10.2541 - 2.26142i) q^{50} +(2.72032 + 10.1524i) q^{52} +(-1.78346 - 6.65598i) q^{53} +(3.30410 + 11.3126i) q^{55} +(-0.814463 - 2.12991i) q^{56} +(4.05241 - 15.1238i) q^{58} +(4.07871 - 7.06453i) q^{59} +(1.12332 + 1.94566i) q^{61} +(-8.83515 - 8.83515i) q^{62} +10.8772i q^{64} +(0.218075 + 9.74790i) q^{65} +(-1.25282 - 4.67558i) q^{67} +(-14.2875 - 3.82832i) q^{68} +(-1.55891 - 12.3261i) q^{70} -9.40254i q^{71} +(10.4696 - 2.80532i) q^{73} +(-2.30495 + 3.99229i) q^{74} -1.99264 q^{76} +(-11.2919 + 8.18190i) q^{77} +(-7.72665 + 4.46099i) q^{79} +(-1.59656 + 6.54023i) q^{80} +(-4.07634 - 1.09225i) q^{82} +(-2.36096 + 2.36096i) q^{83} +(-12.0338 - 6.59336i) q^{85} +(4.45639 - 2.57290i) q^{86} +(-4.38779 + 1.17571i) q^{88} +(4.69600 + 8.13371i) q^{89} +(-10.7758 + 4.12058i) q^{91} +(-2.36419 - 2.36419i) q^{92} +(7.86983 + 4.54365i) q^{94} +(-1.79579 - 0.438378i) q^{95} +(5.63773 - 5.63773i) q^{97} +(13.1155 - 6.64032i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 8 q^{7}+O(q^{10}) $ 64 * q + 8 * q^7	$ 64 q + 8 q^{7} + 8 q^{10} + 32 q^{16} - 48 q^{22} - 16 q^{25} + 88 q^{28} + 32 q^{31} - 16 q^{37} - 40 q^{40} - 16 q^{43} - 80 q^{52} - 32 q^{55} - 88 q^{58} + 48 q^{61} - 32 q^{67} - 112 q^{70} - 88 q^{73} - 320 q^{76} - 56 q^{82} + 16 q^{85} + 120 q^{88} - 128 q^{91} + 208 q^{97}+O(q^{100}) $ 64 * q + 8 * q^7 + 8 * q^10 + 32 * q^16 - 48 * q^22 - 16 * q^25 + 88 * q^28 + 32 * q^31 - 16 * q^37 - 40 * q^40 - 16 * q^43 - 80 * q^52 - 32 * q^55 - 88 * q^58 + 48 * q^61 - 32 * q^67 - 112 * q^70 - 88 * q^73 - 320 * q^76 - 56 * q^82 + 16 * q^85 + 120 * q^88 - 128 * q^91 + 208 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.543545	+	2.02854i	−0.384344	+	1.43439i	0.454854	+	0.890566i	$0.349691\pi$
$2$	−0.543545	+	2.02854i	−0.384344	+	1.43439i	−0.839198	+	0.543826i	$0.816975\pi$
$3$		0			0
$3$		0			0
$4$	−2.08747	−	1.20520i	−1.04373	−	0.602600i
$5$	−1.61611	−	1.54538i	−0.722745	−	0.691115i
$5$	−1.61611	−	1.54538i	−0.722745	−	0.691115i
$6$		0			0
$7$	1.07923	−	2.41563i	0.407909	−	0.913023i
$7$	1.07923	−	2.41563i	0.407909	−	0.913023i
$8$	0.609443	−	0.609443i	0.215471	−	0.215471i
$9$		0			0
$10$	4.01329	−	2.43835i	1.26911	−	0.771074i
$11$	−4.56441	−	2.63527i	−1.37622	−	0.794563i	−0.384520	−	0.923117i	$-0.625633\pi$
$11$	−4.56441	−	2.63527i	−1.37622	−	0.794563i	−0.991703	+	0.128554i	$0.958966\pi$
$12$		0			0
$13$	−3.08333	−	3.08333i	−0.855161	−	0.855161i	0.135602	−	0.990763i	$-0.456703\pi$
$13$	−3.08333	−	3.08333i	−0.855161	−	0.855161i	−0.990763	+	0.135602i	$0.956703\pi$
$14$	4.31359	+	3.50225i	1.15286	+	0.936016i
$15$		0			0
$16$	−1.50538	−	2.60740i	−0.376346	−	0.651850i
$17$	5.92744	−	1.58825i	1.43761	−	0.385208i	0.545917	−	0.837839i	$-0.316181\pi$
$17$	5.92744	−	1.58825i	1.43761	−	0.385208i	0.891698	+	0.452632i	$0.149515\pi$
$18$		0			0
$19$	0.715930	−	0.413342i	0.164245	−	0.0948272i	−0.415624	−	0.909536i	$-0.636437\pi$
$19$	0.715930	−	0.413342i	0.164245	−	0.0948272i	0.579870	+	0.814709i	$0.303103\pi$
$20$	1.51108	+	5.17367i	0.337888	+	1.15687i
$21$		0			0
$22$	7.82670	−	7.82670i	1.66866	−	1.66866i
$23$	1.33984	+	0.359008i	0.279375	+	0.0748583i	0.395786	−	0.918343i	$-0.370472\pi$
$23$	1.33984	+	0.359008i	0.279375	+	0.0748583i	−0.116411	+	0.993201i	$0.537139\pi$
$24$		0			0
$25$	0.223603	+	4.99500i	0.0447206	+	0.999000i
$26$	7.93057	−	4.57872i	1.55531	−	0.897960i
$27$		0			0
$28$	−5.16417	+	3.74187i	−0.975936	+	0.707147i
$29$	−7.45552			−1.38445			−0.692227	−	0.721680i	$-0.743370\pi$
$29$	−7.45552			−1.38445			−0.692227	+	0.721680i	$0.743370\pi$
$30$		0			0
$31$	−2.97481	+	5.15253i	−0.534292	+	0.925421i	0.464905	+	0.885361i	$0.346088\pi$
$31$	−2.97481	+	5.15253i	−0.534292	+	0.925421i	−0.999197	+	0.0400607i	$0.987245\pi$
$32$	7.77248	−	2.08263i	1.37399	−	0.368160i
$33$		0			0
$34$			12.8873i			2.21016i
$35$	−5.47721	+	2.23611i	−0.925818	+	0.377971i
$36$		0			0
$37$	2.12029	+	0.568131i	0.348574	+	0.0934002i	0.428858	−	0.903372i	$-0.358916\pi$
$37$	2.12029	+	0.568131i	0.348574	+	0.0934002i	−0.0802838	+	0.996772i	$0.525583\pi$
$38$	0.449340	+	1.67696i	0.0728925	+	0.272039i
$39$		0			0
$40$	−1.92674	+	0.0431042i	−0.304645	+	0.00681537i
$41$			2.00950i			0.313831i	0.987612	+	0.156915i	$0.0501550\pi$
$41$			2.00950i			0.313831i	−0.987612	+	0.156915i	$0.949845\pi$
$42$		0			0
$43$	−1.73260	−	1.73260i	−0.264219	−	0.264219i	0.562546	−	0.826766i	$-0.309822\pi$
$43$	−1.73260	−	1.73260i	−0.264219	−	0.264219i	−0.826766	+	0.562546i	$0.809822\pi$
$44$	6.35205	+	11.0021i	0.957607	+	1.65862i
$45$		0			0
$46$	−1.45652	+	2.52277i	−0.214752	+	0.371962i
$47$	1.11993	−	4.17964i	0.163359	−	0.609664i	−0.834885	−	0.550425i	$-0.814466\pi$
$47$	1.11993	−	4.17964i	0.163359	−	0.609664i	0.998244	−	0.0592391i	$-0.0188675\pi$
$48$		0			0
$49$	−4.67055	−	5.21402i	−0.667221	−	0.744860i
$50$	−10.2541	−	2.26142i	−1.45014	−	0.319813i
$51$		0			0
$52$	2.72032	+	10.1524i	0.377241	+	1.40788i
$53$	−1.78346	−	6.65598i	−0.244978	−	0.914269i	−0.973395	−	0.229135i	$-0.926410\pi$
$53$	−1.78346	−	6.65598i	−0.244978	−	0.914269i	0.728417	−	0.685134i	$-0.240256\pi$
$54$		0			0
$55$	3.30410	+	11.3126i	0.445524	+	1.52539i
$56$	−0.814463	−	2.12991i	−0.108837	−	0.284622i
$57$		0			0
$58$	4.05241	−	15.1238i	0.532107	−	1.98585i
$59$	4.07871	−	7.06453i	0.531003	−	0.919724i	−0.468343	−	0.883547i	$-0.655149\pi$
$59$	4.07871	−	7.06453i	0.531003	−	0.919724i	0.999345	−	0.0361768i	$-0.0115179\pi$
$60$		0			0
$61$	1.12332	+	1.94566i	0.143827	+	0.249116i	0.928935	−	0.370244i	$-0.120726\pi$
$61$	1.12332	+	1.94566i	0.143827	+	0.249116i	−0.785108	+	0.619359i	$0.787392\pi$
$62$	−8.83515	−	8.83515i	−1.12206	−	1.12206i
$63$		0			0
$64$			10.8772i			1.35965i
$65$	0.218075	+	9.74790i	0.0270489	+	1.20908i
$66$		0			0
$67$	−1.25282	−	4.67558i	−0.153056	−	0.571213i	−0.999264	−	0.0383603i	$-0.987787\pi$
$67$	−1.25282	−	4.67558i	−0.153056	−	0.571213i	0.846208	−	0.532853i	$-0.178880\pi$
$68$	−14.2875	−	3.82832i	−1.73261	−	0.464253i
$69$		0			0
$70$	−1.55891	−	12.3261i	−0.186326	−	1.47326i
$71$		−	9.40254i		−	1.11588i	−0.829883	−	0.557938i	$-0.811593\pi$
$71$		−	9.40254i		−	1.11588i	0.829883	−	0.557938i	$-0.188407\pi$
$72$		0			0
$73$	10.4696	−	2.80532i	1.22537	−	0.328337i	0.412596	−	0.910914i	$-0.364622\pi$
$73$	10.4696	−	2.80532i	1.22537	−	0.328337i	0.812776	+	0.582576i	$0.197955\pi$
$74$	−2.30495	+	3.99229i	−0.267945	+	0.464094i
$75$		0			0
$76$	−1.99264			−0.228572
$77$	−11.2919	+	8.18190i	−1.28683	+	0.932414i
$78$		0			0
$79$	−7.72665	+	4.46099i	−0.869316	+	0.501900i	−0.867121	−	0.498098i	$-0.834032\pi$
$79$	−7.72665	+	4.46099i	−0.869316	+	0.501900i	−0.00219536	+	0.999998i	$0.500699\pi$
$80$	−1.59656	+	6.54023i	−0.178501	+	0.731220i
$81$		0			0
$82$	−4.07634	−	1.09225i	−0.450156	−	0.120619i
$83$	−2.36096	+	2.36096i	−0.259149	+	0.259149i	−0.824708	−	0.565559i	$-0.808660\pi$
$83$	−2.36096	+	2.36096i	−0.259149	+	0.259149i	0.565559	+	0.824708i	$0.308660\pi$
$84$		0			0
$85$	−12.0338	−	6.59336i	−1.30525	−	0.715150i
$86$	4.45639	−	2.57290i	0.480545	−	0.277443i
$87$		0			0
$88$	−4.38779	+	1.17571i	−0.467740	+	0.125331i
$89$	4.69600	+	8.13371i	0.497775	+	0.862171i	0.999997	−	0.00256755i	$-0.000817278\pi$
$89$	4.69600	+	8.13371i	0.497775	+	0.862171i	−0.502222	+	0.864739i	$0.667484\pi$
$90$		0			0
$91$	−10.7758	+	4.12058i	−1.12961	+	0.431954i
$92$	−2.36419	−	2.36419i	−0.246484	−	0.246484i
$93$		0			0
$94$	7.86983	+	4.54365i	0.811711	+	0.468641i
$95$	−1.79579	−	0.438378i	−0.184244	−	0.0449766i
$96$		0			0
$97$	5.63773	−	5.63773i	0.572425	−	0.572425i	−0.360381	−	0.932805i	$-0.617353\pi$
$97$	5.63773	−	5.63773i	0.572425	−	0.572425i	0.932805	+	0.360381i	$0.117353\pi$
$98$	13.1155	−	6.64032i	1.32486	−	0.670774i
$99$		0			0
$100$	5.55321	−	10.6964i	0.555321	−	1.06964i
$101$	−2.48432	−	1.43432i	−0.247199	−	0.142721i	0.371282	−	0.928520i	$-0.378918\pi$
$101$	−2.48432	−	1.43432i	−0.247199	−	0.142721i	−0.618481	+	0.785800i	$0.712252\pi$
$102$		0			0
$103$	−3.42790	+	12.7931i	−0.337761	+	1.26054i	0.563085	+	0.826399i	$0.309615\pi$
$103$	−3.42790	+	12.7931i	−0.337761	+	1.26054i	−0.900845	+	0.434141i	$0.857052\pi$
$104$	−3.75822			−0.368524
$105$		0			0
$106$	14.4713			1.40558
$107$	0.582948	−	2.17559i	0.0563557	−	0.210322i	−0.932006	−	0.362442i	$-0.881943\pi$
$107$	0.582948	−	2.17559i	0.0563557	−	0.210322i	0.988362	+	0.152119i	$0.0486098\pi$
$108$		0			0
$109$	−5.93541	−	3.42681i	−0.568509	−	0.328229i	0.188045	−	0.982160i	$-0.439785\pi$
$109$	−5.93541	−	3.42681i	−0.568509	−	0.328229i	−0.756554	+	0.653932i	$0.773118\pi$
$110$	−24.7440	+	0.553560i	−2.35925	+	0.0527799i
$111$		0			0
$112$	−7.92317	+	0.822479i	−0.748669	+	0.0777170i
$113$	−7.93099	+	7.93099i	−0.746085	+	0.746085i	−0.973741	−	0.227657i	$-0.926894\pi$
$113$	−7.93099	+	7.93099i	−0.746085	+	0.746085i	0.227657	+	0.973741i	$0.426894\pi$
$114$		0			0
$115$	−1.61051	−	2.65075i	−0.150181	−	0.247184i
$116$	15.5632	+	8.98539i	1.44500	+	0.834273i
$117$		0			0
$118$	12.1137	+	12.1137i	1.11516	+	1.11516i
$119$	2.56041	−	16.0326i	0.234712	−	1.46970i
$120$		0			0
$121$	8.38925	+	14.5306i	0.762659	+	1.32096i
$122$	−4.55741	+	1.22115i	−0.412608	+	0.110558i
$123$		0			0
$124$	12.4197	−	7.17049i	1.11532	−	0.643929i
$125$	7.35780	−	8.41800i	0.658102	−	0.752929i
$126$		0			0
$127$	−9.99049	+	9.99049i	−0.886512	+	0.886512i	−0.994186	−	0.107674i	$-0.965660\pi$
$127$	−9.99049	+	9.99049i	−0.886512	+	0.886512i	0.107674	+	0.994186i	$0.465660\pi$
$128$	−6.51989	−	1.74700i	−0.576283	−	0.154414i
$129$		0			0
$130$	−19.8925	−	4.85604i	−1.74469	−	0.425903i
$131$	8.53252	−	4.92625i	0.745490	−	0.430409i	−0.0785723	−	0.996908i	$-0.525036\pi$
$131$	8.53252	−	4.92625i	0.745490	−	0.430409i	0.824062	+	0.566500i	$0.191703\pi$
$132$		0			0
$133$	−0.225833	−	2.17551i	−0.0195822	−	0.188641i
$134$	10.1656			0.878170
$135$		0			0
$136$	2.64448	−	4.58038i	0.226763	−	0.392764i
$137$	16.5993	−	4.44777i	1.41818	−	0.379999i	0.533339	−	0.845901i	$-0.320937\pi$
$137$	16.5993	−	4.44777i	1.41818	−	0.379999i	0.884836	+	0.465902i	$0.154270\pi$
$138$		0			0
$139$		−	0.162309i		−	0.0137669i	−0.999976	−	0.00688344i	$-0.997809\pi$
$139$		−	0.162309i		−	0.0137669i	0.999976	−	0.00688344i	$-0.00219108\pi$
$140$	14.1285	+	1.93334i	1.19407	+	0.163397i
$141$		0			0
$142$	19.0734	+	5.11070i	1.60060	+	0.428880i
$143$	5.94820	+	22.1990i	0.497413	+	1.85637i
$144$		0			0
$145$	12.0489	+	11.5216i	1.00061	+	0.956817i
$146$			22.7628i			1.88386i
$147$		0			0
$148$	−3.74134	−	3.74134i	−0.307536	−	0.307536i
$149$	7.41605	+	12.8450i	0.607546	+	1.05230i	0.991644	+	0.129008i	$0.0411794\pi$
$149$	7.41605	+	12.8450i	0.607546	+	1.05230i	−0.384097	+	0.923293i	$0.625487\pi$
$150$		0			0
$151$	11.0748	−	19.1821i	0.901255	−	1.56102i	0.0753877	−	0.997154i	$-0.475981\pi$
$151$	11.0748	−	19.1821i	0.901255	−	1.56102i	0.825867	−	0.563865i	$-0.190686\pi$
$152$	0.184410	−	0.688226i	0.0149576	−	0.0558225i
$153$		0			0
$154$	−10.4596	−	27.3532i	−0.842862	−	2.20418i
$155$	12.7702	−	3.72982i	1.02573	−	0.299586i
$156$		0			0
$157$	2.22682	+	8.31062i	0.177720	+	0.663259i	0.996072	+	0.0885428i	$0.0282210\pi$
$157$	2.22682	+	8.31062i	0.177720	+	0.663259i	−0.818353	+	0.574717i	$0.805112\pi$
$158$	−4.84949	−	18.0985i	−0.385805	−	1.43984i
$159$		0			0
$160$	−15.7796	−	8.64568i	−1.24749	−	0.683501i
$161$	2.31321	−	2.84910i	0.182307	−	0.224540i
$162$		0			0
$163$	4.03843	−	15.0716i	0.316314	−	1.18050i	−0.606446	−	0.795125i	$-0.707405\pi$
$163$	4.03843	−	15.0716i	0.316314	−	1.18050i	0.922760	−	0.385376i	$-0.125928\pi$
$164$	2.42185	−	4.19476i	0.189115	−	0.327556i
$165$		0			0
$166$	−3.50600	−	6.07257i	−0.272119	−	0.471323i
$167$	−6.66498	−	6.66498i	−0.515752	−	0.515752i	0.400531	−	0.916283i	$-0.368826\pi$
$167$	−6.66498	−	6.66498i	−0.515752	−	0.515752i	−0.916283	+	0.400531i	$0.868826\pi$
$168$		0			0
$169$			6.01381i			0.462601i
$170$	19.9158	−	20.8273i	1.52747	−	1.59738i
$171$		0			0
$172$	1.52862	+	5.70488i	0.116556	+	0.434993i
$173$	17.2341	+	4.61787i	1.31029	+	0.351090i	0.845330	−	0.534244i	$-0.179404\pi$
$173$	17.2341	+	4.61787i	1.31029	+	0.351090i	0.464956	+	0.885334i	$0.346070\pi$
$174$		0			0
$175$	12.3074	+	4.85058i	0.930351	+	0.366670i
$176$			15.8683i			1.19612i
$177$		0			0
$178$	−19.0520	+	5.10497i	−1.42801	+	0.382634i
$179$	−1.05273	+	1.82337i	−0.0786844	+	0.136285i	−0.902683	−	0.430307i	$-0.858405\pi$
$179$	−1.05273	+	1.82337i	−0.0786844	+	0.136285i	0.823998	+	0.566592i	$0.191739\pi$
$180$		0			0
$181$	17.3824			1.29202			0.646012	−	0.763327i	$-0.276436\pi$
$181$	17.3824			1.29202			0.646012	+	0.763327i	$0.276436\pi$
$182$	−2.50162	−	24.0988i	−0.185432	−	1.78632i
$183$		0			0
$184$	1.03535	−	0.597758i	0.0763268	−	0.0440673i
$185$	−2.54864	−	4.19482i	−0.187380	−	0.308409i
$186$		0			0
$187$	−31.2407	−	8.37093i	−2.28455	−	0.612143i
$188$	−7.37513	+	7.37513i	−0.537887	+	0.537887i
$189$		0			0
$190$	1.86536	−	3.40455i	0.135327	−	0.246992i
$191$	−5.64933	+	3.26164i	−0.408771	+	0.236004i	−0.690262	−	0.723560i	$-0.742505\pi$
$191$	−5.64933	+	3.26164i	−0.408771	+	0.236004i	0.281491	+	0.959564i	$0.409171\pi$
$192$		0			0
$193$	12.9008	−	3.45675i	0.928617	−	0.248822i	0.237352	−	0.971424i	$-0.423720\pi$
$193$	12.9008	−	3.45675i	0.928617	−	0.248822i	0.691265	+	0.722601i	$0.257054\pi$
$194$	8.37198	+	14.5007i	0.601073	+	1.04109i
$195$		0			0
$196$	3.46568	+	16.5130i	0.247549	+	1.17950i
$197$	17.6076	+	17.6076i	1.25449	+	1.25449i	0.953686	+	0.300803i	$0.0972545\pi$
$197$	17.6076	+	17.6076i	1.25449	+	1.25449i	0.300803	+	0.953686i	$0.402745\pi$
$198$		0			0
$199$	−23.5601	−	13.6024i	−1.67013	−	0.964250i	−0.967562	−	0.252633i	$-0.918704\pi$
$199$	−23.5601	−	13.6024i	−1.67013	−	0.964250i	−0.702568	−	0.711617i	$-0.747963\pi$
$200$	3.18044	+	2.90789i	0.224891	+	0.205619i
$201$		0			0
$202$	4.25992	−	4.25992i	0.299727	−	0.299727i
$203$	−8.04618	+	18.0098i	−0.564731	+	1.26404i
$204$		0			0
$205$	3.10544	−	3.24756i	0.216893	−	0.226820i
$206$	−24.0880	−	13.9072i	−1.67829	−	0.968962i
$207$		0			0
$208$	−3.39788	+	12.6811i	−0.235601	+	0.879273i
$209$	−4.35707			−0.301384
$210$		0			0
$211$	5.10256			0.351275			0.175637	−	0.984455i	$-0.443801\pi$
$211$	5.10256			0.351275			0.175637	+	0.984455i	$0.443801\pi$
$212$	−4.29887	+	16.0436i	−0.295247	+	1.10188i
$213$		0			0
$214$	4.09641	+	2.36506i	0.280025	+	0.161672i
$215$	0.122542	+	5.47760i	0.00835730	+	0.373569i
$216$		0			0
$217$	9.23611	+	12.7468i	0.626988	+	0.865308i
$218$	10.1776	−	10.1776i	0.689312	−	0.689312i
$219$		0			0
$220$	6.73679	−	27.5968i	0.454194	−	1.86058i
$221$	−23.1733	−	13.3791i	−1.55881	−	0.899977i
$222$		0			0
$223$	1.94192	+	1.94192i	0.130041	+	0.130041i	0.769131	−	0.639091i	$-0.220689\pi$
$223$	1.94192	+	1.94192i	0.130041	+	0.130041i	−0.639091	+	0.769131i	$0.720689\pi$
$224$	3.35739	−	21.0231i	0.224325	−	1.40466i
$225$		0			0
$226$	−11.7775	−	20.3992i	−0.783425	−	1.35693i
$227$	−8.96498	+	2.40216i	−0.595027	+	0.159437i	−0.543750	−	0.839248i	$-0.682996\pi$
$227$	−8.96498	+	2.40216i	−0.595027	+	0.159437i	−0.0512771	+	0.998684i	$0.516329\pi$
$228$		0			0
$229$	4.81889	−	2.78219i	0.318441	−	0.183852i	−0.332256	−	0.943189i	$-0.607810\pi$
$229$	4.81889	−	2.78219i	0.318441	−	0.183852i	0.650698	+	0.759337i	$0.274477\pi$
$230$	6.25253	−	1.82618i	0.412279	−	0.120415i
$231$		0			0
$232$	−4.54371	+	4.54371i	−0.298309	+	0.298309i
$233$	−12.3939	−	3.32094i	−0.811952	−	0.217562i	−0.171127	−	0.985249i	$-0.554741\pi$
$233$	−12.3939	−	3.32094i	−0.811952	−	0.217562i	−0.640825	+	0.767687i	$0.721408\pi$
$234$		0			0
$235$	−8.26907	+	5.02403i	−0.539414	+	0.327732i
$236$	−17.0284	+	9.83133i	−1.10845	+	0.639965i
$237$		0			0
$238$	31.1310	+	13.9083i	2.01792	+	0.901542i
$239$	−16.4305			−1.06280			−0.531399	−	0.847122i	$-0.678333\pi$
$239$	−16.4305			−1.06280			−0.531399	+	0.847122i	$0.678333\pi$
$240$		0			0
$241$	10.3424	−	17.9136i	0.666213	−	1.15392i	−0.312741	−	0.949838i	$-0.601247\pi$
$241$	10.3424	−	17.9136i	0.666213	−	1.15392i	0.978955	−	0.204077i	$-0.0654193\pi$
$242$	−34.0358	+	9.11987i	−2.18790	+	0.586247i
$243$		0			0
$244$		−	5.41533i		−	0.346681i
$245$	−0.509537	+	15.6442i	−0.0325531	+	0.999470i
$246$		0			0
$247$	−3.48191	−	0.932976i	−0.221549	−	0.0593638i
$248$	1.32719	+	4.95315i	0.0842768	+	0.314525i
$249$		0			0
$250$	13.0769	+	19.5011i	0.827058	+	1.23336i
$251$		−	1.12355i		−	0.0709181i	−0.999371	−	0.0354590i	$-0.988711\pi$
$251$		−	1.12355i		−	0.0709181i	0.999371	−	0.0354590i	$-0.0112893\pi$
$252$		0			0
$253$	−5.16948	−	5.16948i	−0.325003	−	0.325003i
$254$	−14.8358	−	25.6963i	−0.930880	−	1.61233i
$255$		0			0
$256$	−3.78952	+	6.56364i	−0.236845	+	0.410228i
$257$	3.90136	−	14.5601i	0.243360	−	0.908233i	−0.730840	−	0.682549i	$-0.760872\pi$
$257$	3.90136	−	14.5601i	0.243360	−	0.908233i	0.974200	−	0.225684i	$-0.0724618\pi$
$258$		0			0
$259$	3.66067	−	4.50871i	0.227463	−	0.280158i
$260$	11.2929	−	20.6113i	0.700359	−	1.27826i
$261$		0			0
$262$	5.35528	+	19.9862i	0.330850	+	1.23475i
$263$	−0.0389751	−	0.145457i	−0.00240331	−	0.00896926i	0.964714	−	0.263301i	$-0.0848112\pi$
$263$	−0.0389751	−	0.145457i	−0.00240331	−	0.00896926i	−0.967117	+	0.254332i	$0.918145\pi$
$264$		0			0
$265$	−7.40375	+	13.5129i	−0.454809	+	0.830091i
$266$	4.53585	+	0.724377i	0.278111	+	0.0444144i
$267$		0			0
$268$	−3.01980	+	11.2700i	−0.184463	+	0.688427i
$269$	−4.98972	+	8.64245i	−0.304229	+	0.526939i	−0.977089	−	0.212830i	$-0.931732\pi$
$269$	−4.98972	+	8.64245i	−0.304229	+	0.526939i	0.672861	+	0.739769i	$0.265065\pi$
$270$		0			0
$271$	−11.8458	−	20.5176i	−0.719583	−	1.24635i	−0.961165	−	0.275974i	$-0.911000\pi$
$271$	−11.8458	−	20.5176i	−0.719583	−	1.24635i	0.241582	−	0.970380i	$-0.422334\pi$
$272$	−13.0643	−	13.0643i	−0.792138	−	0.792138i
$273$		0			0
$274$			36.0899i			2.18027i
$275$	12.1425	−	23.3885i	0.732222	−	1.41038i
$276$		0			0
$277$	−2.61292	−	9.75155i	−0.156995	−	0.585914i	−0.998926	−	0.0463289i	$-0.985248\pi$
$277$	−2.61292	−	9.75155i	−0.156995	−	0.585914i	0.841931	−	0.539585i	$-0.181419\pi$
$278$	0.329250	+	0.0882223i	0.0197471	+	0.00529122i
$279$		0			0
$280$	−1.97527	+	4.70082i	−0.118045	+	0.280928i
$281$			6.74970i			0.402653i	0.979524	+	0.201327i	$0.0645252\pi$
$281$			6.74970i			0.402653i	−0.979524	+	0.201327i	$0.935475\pi$
$282$		0			0
$283$	6.51193	−	1.74487i	0.387094	−	0.103722i	−0.0600229	−	0.998197i	$-0.519117\pi$
$283$	6.51193	−	1.74487i	0.387094	−	0.103722i	0.447117	+	0.894475i	$0.352451\pi$
$284$	−11.3319	+	19.6275i	−0.672427	+	1.16468i
$285$		0			0
$286$	−48.2645			−2.85394
$287$	4.85420	+	2.16870i	0.286535	+	0.128014i
$288$		0			0
$289$	17.8895	−	10.3285i	1.05233	−	0.607560i
$290$	−29.9211	+	18.1791i	−1.75703	+	1.06752i
$291$		0			0
$292$	−25.2359	−	6.76194i	−1.47682	−	0.395713i
$293$	9.44875	−	9.44875i	0.552002	−	0.552002i	−0.375016	−	0.927018i	$-0.622363\pi$
$293$	9.44875	−	9.44875i	0.552002	−	0.552002i	0.927018	+	0.375016i	$0.122363\pi$
$294$		0			0
$295$	−17.5090	+	5.11388i	−1.01941	+	0.297742i
$296$	1.63844	−	0.945955i	0.0952325	−	0.0549825i
$297$		0			0
$298$	−30.0874	+	8.06191i	−1.74292	+	0.467014i
$299$	−3.02421	−	5.23809i	−0.174895	−	0.302926i
$300$		0			0
$301$	−6.05519	+	2.31546i	−0.349016	+	0.133461i
$302$	32.8920	+	32.8920i	1.89272	+	1.89272i
$303$		0			0
$304$	−2.15550	−	1.24448i	−0.123626	−	0.0713757i
$305$	1.19136	−	4.88035i	0.0682173	−	0.279448i
$306$		0			0
$307$	3.77862	−	3.77862i	0.215657	−	0.215657i	−0.591008	−	0.806665i	$-0.701270\pi$
$307$	3.77862	−	3.77862i	0.215657	−	0.215657i	0.806665	+	0.591008i	$0.201270\pi$
$308$	33.4322	−	3.47049i	1.90498	−	0.197750i
$309$		0			0
$310$	0.624885	+	27.9322i	0.0354911	+	1.58644i
$311$	11.9360	+	6.89126i	0.676829	+	0.390767i	0.798659	−	0.601784i	$-0.205543\pi$
$311$	11.9360	+	6.89126i	0.676829	+	0.390767i	−0.121830	+	0.992551i	$0.538876\pi$
$312$		0			0
$313$	5.67554	−	21.1814i	0.320800	−	1.19724i	−0.597666	−	0.801745i	$-0.703905\pi$
$313$	5.67554	−	21.1814i	0.320800	−	1.19724i	0.918467	−	0.395498i	$-0.129428\pi$
$314$	−18.0688			−1.01968
$315$		0			0
$316$	21.5055			1.20978
$317$	0.263008	−	0.981559i	0.0147720	−	0.0551298i	−0.958146	−	0.286279i	$-0.907582\pi$
$317$	0.263008	−	0.981559i	0.0147720	−	0.0551298i	0.972918	+	0.231149i	$0.0742484\pi$
$318$		0			0
$319$	34.0301	+	19.6473i	1.90532	+	1.10004i
$320$	16.8094	−	17.5788i	0.939677	−	0.982683i
$321$		0			0
$322$	4.52216	+	6.24105i	0.252010	+	0.347800i
$323$	3.58714	−	3.58714i	0.199594	−	0.199594i
$324$		0			0
$325$	14.7118	−	16.0907i	0.816062	−	0.892549i
$326$	28.3783	+	16.3842i	1.57173	+	0.907437i
$327$		0			0
$328$	1.22467	+	1.22467i	0.0676213	+	0.0676213i
$329$	−8.88782	−	7.21612i	−0.490001	−	0.397838i
$330$		0			0
$331$	15.3711	+	26.6236i	0.844873	+	1.46336i	0.885732	+	0.464198i	$0.153657\pi$
$331$	15.3711	+	26.6236i	0.844873	+	1.46336i	−0.0408587	+	0.999165i	$0.513009\pi$
$332$	7.77385	−	2.08300i	0.426646	−	0.114319i
$333$		0			0
$334$	17.1429	−	9.89744i	0.938016	−	0.541564i
$335$	−5.20086	+	9.49232i	−0.284153	+	0.518621i
$336$		0			0
$337$	4.31112	−	4.31112i	0.234842	−	0.234842i	−0.579869	−	0.814710i	$-0.696896\pi$
$337$	4.31112	−	4.31112i	0.234842	−	0.234842i	0.814710	+	0.579869i	$0.196896\pi$
$338$	−12.1992	−	3.26877i	−0.663551	−	0.177798i
$339$		0			0
$340$	17.1739	+	28.2666i	0.931386	+	1.53297i
$341$	27.1566	−	15.6788i	1.47061	−	0.849057i
$342$		0			0
$343$	−17.6357	+	5.65522i	−0.952239	+	0.305353i
$344$	−2.11184			−0.113863
$345$		0			0
$346$	−18.7350	+	32.4500i	−1.00720	+	1.74452i
$347$	−2.43863	+	0.653428i	−0.130912	+	0.0350779i	−0.323680	−	0.946167i	$-0.604920\pi$
$347$	−2.43863	+	0.653428i	−0.130912	+	0.0350779i	0.192768	+	0.981244i	$0.438254\pi$
$348$		0			0
$349$		−	28.4720i		−	1.52407i	−0.647535	−	0.762036i	$-0.724200\pi$
$349$		−	28.4720i		−	1.52407i	0.647535	−	0.762036i	$-0.275800\pi$
$350$	−16.5292	+	22.3295i	−0.883523	+	1.19356i
$351$		0			0
$352$	−40.9651	−	10.9766i	−2.18345	−	0.585053i
$353$	6.87029	+	25.6403i	0.365668	+	1.36469i	0.866512	+	0.499156i	$0.166356\pi$
$353$	6.87029	+	25.6403i	0.365668	+	1.36469i	−0.500844	+	0.865538i	$0.666977\pi$
$354$		0			0
$355$	−14.5305	+	15.1955i	−0.771198	+	0.806494i
$356$		−	22.6385i		−	1.19984i
$357$		0			0
$358$	−3.12658	−	3.12658i	−0.165245	−	0.165245i
$359$	−10.8363	−	18.7690i	−0.571917	−	0.990589i	−0.996369	−	0.0851385i	$-0.972867\pi$
$359$	−10.8363	−	18.7690i	−0.571917	−	0.990589i	0.424452	−	0.905450i	$-0.360467\pi$
$360$		0			0
$361$	−9.15830	+	15.8626i	−0.482016	+	0.834876i
$362$	−9.44811	+	35.2608i	−0.496582	+	1.85327i
$363$		0			0
$364$	27.4602	+	4.38541i	1.43931	+	0.229858i
$365$	−21.2552	−	11.6458i	−1.11255	−	0.609569i
$366$		0			0
$367$	−2.45780	−	9.17264i	−0.128296	−	0.478808i	0.871640	−	0.490147i	$-0.163057\pi$
$367$	−2.45780	−	9.17264i	−0.128296	−	0.478808i	−0.999936	+	0.0113397i	$0.996390\pi$
$368$	−1.08089	−	4.03393i	−0.0563452	−	0.210283i
$369$		0			0
$370$	9.89465	−	2.88995i	0.514398	−	0.150241i
$371$	−18.0032	−	2.87511i	−0.934677	−	0.149268i
$372$		0			0
$373$	−1.47912	+	5.52014i	−0.0765858	+	0.285822i	−0.993588	−	0.113060i	$-0.963935\pi$
$373$	−1.47912	+	5.52014i	−0.0765858	+	0.285822i	0.917002	+	0.398882i	$0.130602\pi$
$374$	33.9615	−	58.8230i	1.75611	−	3.04167i
$375$		0			0
$376$	−1.86472	−	3.22979i	−0.0961655	−	0.166564i
$377$	22.9878	+	22.9878i	1.18393	+	1.18393i
$378$		0			0
$379$			13.5439i			0.695704i	0.937549	+	0.347852i	$0.113089\pi$
$379$			13.5439i			0.695704i	−0.937549	+	0.347852i	$0.886911\pi$
$380$	3.22032	+	3.07939i	0.165199	+	0.157969i
$381$		0			0
$382$	−3.54570	−	13.2327i	−0.181414	−	0.677045i
$383$	−31.0945	−	8.33174i	−1.58885	−	0.425732i	−0.647201	−	0.762319i	$-0.724061\pi$
$383$	−31.0945	−	8.33174i	−1.58885	−	0.425732i	−0.941652	+	0.336587i	$0.890727\pi$
$384$		0			0
$385$	30.8930	+	4.22739i	1.57445	+	0.215448i
$386$			28.0486i			1.42763i
$387$		0			0
$388$	−18.5632	+	4.97399i	−0.942403	+	0.252516i
$389$	−4.23368	+	7.33294i	−0.214656	+	0.371795i	−0.953166	−	0.302447i	$-0.902196\pi$
$389$	−4.23368	+	7.33294i	−0.214656	+	0.371795i	0.738510	+	0.674242i	$0.235530\pi$
$390$		0			0
$391$	8.51198			0.430469
$392$	−6.02408	−	0.331215i	−0.304262	−	0.0167289i
$393$		0			0
$394$	−45.2882	+	26.1471i	−2.28158	+	1.31727i
$395$	19.3810	+	4.73118i	0.975165	+	0.238052i
$396$		0			0
$397$	22.9205	+	6.14153i	1.15035	+	0.308234i	0.783104	−	0.621891i	$-0.213635\pi$
$397$	22.9205	+	6.14153i	1.15035	+	0.308234i	0.367242	+	0.930125i	$0.380302\pi$
$398$	40.3990	−	40.3990i	2.02502	−	2.02502i
$399$		0			0
$400$	12.6874	−	8.10241i	0.634368	−	0.405121i
$401$	0.802149	−	0.463121i	0.0400574	−	0.0231272i	−0.479838	−	0.877357i	$-0.659304\pi$
$401$	0.802149	−	0.463121i	0.0400574	−	0.0231272i	0.519895	+	0.854230i	$0.325971\pi$
$402$		0			0
$403$	25.0592	−	6.71460i	1.24829	−	0.334478i
$404$	3.45730	+	5.98821i	0.172007	+	0.297925i
$405$		0			0
$406$	−32.1600	−	26.1111i	−1.59608	−	1.29587i
$407$	−8.18073	−	8.18073i	−0.405504	−	0.405504i
$408$		0			0
$409$	−1.56516	−	0.903646i	−0.0773922	−	0.0446824i	0.460805	−	0.887502i	$-0.347561\pi$
$409$	−1.56516	−	0.903646i	−0.0773922	−	0.0446824i	−0.538197	+	0.842819i	$0.680894\pi$
$410$	4.89986	+	8.06469i	0.241987	+	0.398287i
$411$		0			0
$412$	22.5739	−	22.5739i	1.11213	−	1.11213i
$413$	−12.6635	−	17.4769i	−0.623128	−	0.859981i
$414$		0			0
$415$	7.46413	−	0.166984i	0.366400	−	0.00819692i
$416$	−30.3865	−	17.5437i	−1.48982	−	0.860149i
$417$		0			0
$418$	2.36826	−	8.83847i	0.115835	−	0.432303i
$419$	−10.6027			−0.517977			−0.258988	−	0.965880i	$-0.583389\pi$
$419$	−10.6027			−0.517977			−0.258988	+	0.965880i	$0.583389\pi$
$420$		0			0
$421$	−37.3135			−1.81855			−0.909273	−	0.416199i	$-0.863362\pi$
$421$	−37.3135			−1.81855			−0.909273	+	0.416199i	$0.863362\pi$
$422$	−2.77347	+	10.3507i	−0.135010	+	0.503866i
$423$		0			0
$424$	−5.14336	−	2.96952i	−0.249784	−	0.144213i
$425$	9.25871	+	29.2524i	0.449113	+	1.41895i
$426$		0			0
$427$	5.91230	−	0.613738i	0.286116	−	0.0297008i
$428$	−3.83891	+	3.83891i	−0.185561	+	0.185561i
$429$		0			0
$430$	−11.1781	−	2.72874i	−0.539056	−	0.131591i
$431$	−6.55967	−	3.78723i	−0.315968	−	0.182424i	0.333626	−	0.942706i	$-0.391728\pi$
$431$	−6.55967	−	3.78723i	−0.315968	−	0.182424i	−0.649594	+	0.760281i	$0.725061\pi$
$432$		0			0
$433$	−1.92607	−	1.92607i	−0.0925610	−	0.0925610i	0.659310	−	0.751871i	$-0.270848\pi$
$433$	−1.92607	−	1.92607i	−0.0925610	−	0.0925610i	−0.751871	+	0.659310i	$0.770848\pi$
$434$	−30.8776	+	11.8073i	−1.48217	+	0.566771i
$435$		0			0
$436$	8.25998	+	14.3067i	0.395581	+	0.685167i
$437$	1.10762	−	0.296786i	0.0529847	−	0.0141972i
$438$		0			0
$439$	12.1550	−	7.01771i	0.580128	−	0.334937i	−0.181057	−	0.983473i	$-0.557952\pi$
$439$	12.1550	−	7.01771i	0.580128	−	0.334937i	0.761184	+	0.648536i	$0.224618\pi$
$440$	8.90805	+	4.88074i	0.424675	+	0.232680i
$441$		0			0
$442$	39.7358	−	39.7358i	1.89004	−	1.89004i
$443$	6.68912	+	1.79234i	0.317809	+	0.0851568i	0.414197	−	0.910187i	$-0.364062\pi$
$443$	6.68912	+	1.79234i	0.317809	+	0.0851568i	−0.0963880	+	0.995344i	$0.530729\pi$
$444$		0			0
$445$	4.98043	−	20.4020i	0.236095	−	0.967149i
$446$	−4.99478	+	2.88373i	−0.236509	+	0.136549i
$447$		0			0
$448$	26.2754	+	11.7390i	1.24139	+	0.554615i
$449$	−10.2092			−0.481802			−0.240901	−	0.970550i	$-0.577443\pi$
$449$	−10.2092			−0.481802			−0.240901	+	0.970550i	$0.577443\pi$
$450$		0			0
$451$	5.29556	−	9.17218i	0.249358	−	0.431901i
$452$	26.1141	−	6.99726i	1.22831	−	0.329123i
$453$		0			0
$454$		−	19.4915i		−	0.914780i
$455$	23.7827	+	9.99339i	1.11495	+	0.468497i
$456$		0			0
$457$	1.21714	+	0.326133i	0.0569356	+	0.0152558i	0.287174	−	0.957878i	$-0.407284\pi$
$457$	1.21714	+	0.326133i	0.0569356	+	0.0152558i	−0.230239	+	0.973134i	$0.573951\pi$
$458$	3.02449	+	11.2875i	0.141325	+	0.527432i
$459$		0			0
$460$	0.167212	+	7.47435i	0.00779632	+	0.348493i
$461$			11.0727i			0.515707i	0.966184	+	0.257853i	$0.0830152\pi$
$461$			11.0727i			0.515707i	−0.966184	+	0.257853i	$0.916985\pi$
$462$		0			0
$463$	−26.2387	−	26.2387i	−1.21941	−	1.21941i	−0.967837	−	0.251578i	$-0.919051\pi$
$463$	−26.2387	−	26.2387i	−1.21941	−	1.21941i	−0.251578	−	0.967837i	$-0.580949\pi$
$464$	11.2234	+	19.4395i	0.521034	+	0.902457i
$465$		0			0
$466$	13.4733	−	23.3364i	0.624138	−	1.08104i
$467$	−1.47399	+	5.50099i	−0.0682080	+	0.254556i	−0.991608	−	0.129284i	$-0.958732\pi$
$467$	−1.47399	+	5.50099i	−0.0682080	+	0.254556i	0.923400	+	0.383840i	$0.125399\pi$
$468$		0			0
$469$	−12.6466	−	2.01966i	−0.583964	−	0.0932592i
$470$	−5.69682	−	19.5049i	−0.262775	−	0.899693i
$471$		0			0
$472$	−1.81969	−	6.79117i	−0.0837579	−	0.312589i
$473$	3.34245	+	12.4742i	0.153686	+	0.573563i
$474$		0			0
$475$	2.22473	+	3.48364i	0.102077	+	0.159840i
$476$	−24.6673	+	30.3817i	−1.13062	+	1.39254i
$477$		0			0
$478$	8.93069	−	33.3298i	0.408480	−	1.52447i
$479$	17.4877	−	30.2897i	0.799036	−	1.38397i	−0.121209	−	0.992627i	$-0.538677\pi$
$479$	17.4877	−	30.2897i	0.799036	−	1.38397i	0.920245	−	0.391343i	$-0.127989\pi$
$480$		0			0
$481$	−4.78583	−	8.28930i	−0.218215	−	0.377959i
$482$	30.7168	+	30.7168i	1.39911	+	1.39911i
$483$		0			0
$484$		−	40.4429i		−	1.83831i
$485$	−17.8236	+	0.398741i	−0.809328	+	0.0181059i
$486$		0			0
$487$	−3.77358	−	14.0832i	−0.170997	−	0.638170i	−0.997199	−	0.0747954i	$-0.976170\pi$
$487$	−3.77358	−	14.0832i	−0.170997	−	0.638170i	0.826202	−	0.563374i	$-0.190497\pi$
$488$	1.87037	+	0.501163i	0.0846675	+	0.0226866i
$489$		0			0
$490$	−31.4578	−	9.53693i	−1.42112	−	0.430834i
$491$		−	31.7534i		−	1.43301i	−0.697581	−	0.716506i	$-0.745740\pi$
$491$		−	31.7534i		−	1.43301i	0.697581	−	0.716506i	$-0.254260\pi$
$492$		0			0
$493$	−44.1921	+	11.8412i	−1.99031	+	0.533303i
$494$	3.78515	−	6.55607i	0.170302	−	0.294972i
$495$		0			0
$496$	17.9129			0.804315
$497$	−22.7131	−	10.1475i	−1.01882	−	0.455175i
$498$		0			0
$499$	−21.5305	+	12.4307i	−0.963838	+	0.556472i	−0.897352	−	0.441315i	$-0.854512\pi$
$499$	−21.5305	+	12.4307i	−0.963838	+	0.556472i	−0.0664862	+	0.997787i	$0.521179\pi$
$500$	−25.5046	+	8.70469i	−1.14060	+	0.389286i
$501$		0			0
$502$	2.27917	+	0.610702i	0.101724	+	0.0272570i
$503$	24.5634	−	24.5634i	1.09523	−	1.09523i	0.100269	−	0.994960i	$-0.468030\pi$
$503$	24.5634	−	24.5634i	1.09523	−	1.09523i	0.994960	−	0.100269i	$-0.0319703\pi$
$504$		0			0
$505$	1.79836	+	6.15724i	0.0800258	+	0.273994i
$506$	13.2963	−	7.67664i	0.591094	−	0.341268i
$507$		0			0
$508$	32.8954	−	8.81429i	1.45950	−	0.391071i
$509$	7.24256	+	12.5445i	0.321021	+	0.556024i	0.980699	−	0.195524i	$-0.0626407\pi$
$509$	7.24256	+	12.5445i	0.321021	+	0.556024i	−0.659678	+	0.751548i	$0.729307\pi$
$510$		0			0
$511$	4.52243	−	28.3182i	0.200060	−	1.25272i
$512$	−20.8006	−	20.8006i	−0.919265	−	0.919265i
$513$		0			0
$514$	27.4151	+	15.8281i	1.20923	+	0.698148i
$515$	25.3100	−	15.3776i	1.11529	−	0.677617i
$516$		0			0
$517$	−16.1263	+	16.1263i	−0.709234	+	0.709234i
$518$	7.15634	+	9.87649i	0.314432	+	0.433948i
$519$		0			0
$520$	6.07369	+	5.80788i	0.266349	+	0.254692i
$521$	−11.7217	−	6.76754i	−0.513538	−	0.296491i	0.220749	−	0.975331i	$-0.429150\pi$
$521$	−11.7217	−	6.76754i	−0.513538	−	0.296491i	−0.734287	+	0.678839i	$0.762483\pi$
$522$		0			0
$523$	−8.70690	+	32.4946i	−0.380726	+	1.42089i	0.464069	+	0.885799i	$0.346389\pi$
$523$	−8.70690	+	32.4946i	−0.380726	+	1.42089i	−0.844795	+	0.535090i	$0.820278\pi$
$524$	−23.7485			−1.03746
$525$		0			0
$526$	0.316249			0.0137891
$527$	−9.44951	+	35.2660i	−0.411627	+	1.53621i
$528$		0			0
$529$	−18.2523	−	10.5380i	−0.793579	−	0.458173i
$530$	−23.3872	−	22.3636i	−1.01587	−	0.971415i
$531$		0			0
$532$	−2.15051	+	4.81348i	−0.0932363	+	0.208691i
$533$	6.19594	−	6.19594i	0.268376	−	0.268376i
$534$		0			0
$535$	−4.30422	+	2.61511i	−0.186088	+	0.113061i
$536$	−3.61302	−	2.08598i	−0.156059	−	0.0901005i
$537$		0			0
$538$	−14.8194	−	14.8194i	−0.638909	−	0.638909i
$539$	7.57798	+	36.1071i	0.326407	+	1.55524i
$540$		0			0
$541$	−4.22782	−	7.32280i	−0.181768	−	0.314832i	0.760714	−	0.649087i	$-0.224849\pi$
$541$	−4.22782	−	7.32280i	−0.181768	−	0.314832i	−0.942483	+	0.334255i	$0.891515\pi$
$542$	48.0594	−	12.8775i	2.06433	−	0.553135i
$543$		0			0
$544$	42.7632	−	24.6893i	1.83345	−	1.05855i
$545$	4.29653	+	14.7105i	0.184043	+	0.630130i
$546$		0			0
$547$	1.77542	−	1.77542i	0.0759115	−	0.0759115i	−0.668132	−	0.744043i	$-0.732906\pi$
$547$	1.77542	−	1.77542i	0.0759115	−	0.0759115i	0.744043	+	0.668132i	$0.232906\pi$
$548$	−40.0110	−	10.7209i	−1.70919	−	0.457975i
$549$		0			0
$550$	40.8444	+	37.3443i	1.74161	+	1.59236i
$551$	−5.33762	+	3.08168i	−0.227390	+	0.131284i
$552$		0			0
$553$	2.43730	+	23.4791i	0.103644	+	0.998435i
$554$	21.2016			0.900770
$555$		0			0
$556$	−0.195615	+	0.338815i	−0.00829593	+	0.0143690i
$557$	4.58174	−	1.22767i	0.194135	−	0.0520182i	−0.160442	−	0.987045i	$-0.551292\pi$
$557$	4.58174	−	1.22767i	0.194135	−	0.0520182i	0.354576	+	0.935027i	$0.384625\pi$
$558$		0			0
$559$			10.6844i			0.451900i
$560$	14.0757	+	10.9151i	0.594808	+	0.461247i
$561$		0			0
$562$	−13.6920	−	3.66876i	−0.577562	−	0.154757i
$563$	−1.43628	−	5.36027i	−0.0605320	−	0.225909i	0.929033	−	0.369998i	$-0.120641\pi$
$563$	−1.43628	−	5.36027i	−0.0605320	−	0.225909i	−0.989565	+	0.144089i	$0.953975\pi$
$564$		0			0
$565$	25.0737	−	0.560937i	1.05486	−	0.0235988i
$566$			14.1581i			0.595110i
$567$		0			0
$568$	−5.73031	−	5.73031i	−0.240438	−	0.240438i
$569$	4.89338	+	8.47559i	0.205141	+	0.355315i	0.950178	−	0.311709i	$-0.100901\pi$
$569$	4.89338	+	8.47559i	0.205141	+	0.355315i	−0.745036	+	0.667024i	$0.767568\pi$
$570$		0			0
$571$	−8.38542	+	14.5240i	−0.350919	+	0.607809i	−0.986411	−	0.164298i	$-0.947464\pi$
$571$	−8.38542	+	14.5240i	−0.350919	+	0.607809i	0.635492	+	0.772108i	$0.280797\pi$
$572$	14.3375	−	53.5084i	0.599483	−	2.23730i
$573$		0			0
$574$	−7.03776	+	8.66815i	−0.293751	+	0.361801i
$575$	−1.49365	+	6.77275i	−0.0622896	+	0.282443i
$576$		0			0
$577$	0.857337	+	3.19963i	0.0356914	+	0.133202i	0.981473	−	0.191602i	$-0.0613683\pi$
$577$	0.857337	+	3.19963i	0.0356914	+	0.133202i	−0.945781	+	0.324804i	$0.894702\pi$
$578$	11.2280	+	41.9036i	0.467025	+	1.74296i
$579$		0			0
$580$	−11.2659	−	38.5723i	−0.467790	−	1.60163i
$581$	3.15520	+	8.25121i	0.130900	+	0.342318i
$582$		0			0
$583$	−9.39981	+	35.0806i	−0.389300	+	1.45289i
$584$	4.67093	−	8.09029i	0.193285	−	0.334779i
$585$		0			0
$586$	14.0313	+	24.3030i	0.579629	+	1.00395i
$587$	3.26504	+	3.26504i	0.134763	+	0.134763i	0.771270	−	0.636508i	$-0.219622\pi$
$587$	3.26504	+	3.26504i	0.134763	+	0.134763i	−0.636508	+	0.771270i	$0.719622\pi$
$588$		0			0
$589$			4.91846i			0.202662i
$590$	−0.856768	−	38.2973i	−0.0352726	−	1.57667i
$591$		0			0
$592$	−1.71051	−	6.38372i	−0.0703016	−	0.262369i
$593$	−30.9988	−	8.30609i	−1.27297	−	0.341090i	−0.441800	−	0.897114i	$-0.645660\pi$
$593$	−30.9988	−	8.30609i	−1.27297	−	0.341090i	−0.831167	+	0.556023i	$0.812327\pi$
$594$		0			0
$595$	−28.9143	+	21.9536i	−1.18537	+	0.900008i
$596$		−	35.7513i		−	1.46443i
$597$		0			0
$598$	12.2694	−	3.28759i	0.501735	−	0.134439i
$599$	−13.0304	+	22.5692i	−0.532406	+	0.922154i	0.466878	+	0.884322i	$0.345379\pi$
$599$	−13.0304	+	22.5692i	−0.532406	+	0.922154i	−0.999284	+	0.0378326i	$0.987955\pi$
$600$		0			0
$601$	35.9572			1.46673			0.733363	−	0.679838i	$-0.237950\pi$
$601$	35.9572			1.46673			0.733363	+	0.679838i	$0.237950\pi$
$602$	−1.40572	−	13.5417i	−0.0572931	−	0.551920i
$603$		0			0
$604$	−46.2366	+	26.6947i	−1.88134	+	1.08619i
$605$	8.89738	−	36.4476i	0.361730	−	1.48181i
$606$		0			0
$607$	41.8512	+	11.2140i	1.69869	+	0.455162i	0.972608	−	0.232450i	$-0.0746741\pi$
$607$	41.8512	+	11.2140i	1.69869	+	0.455162i	0.726079	+	0.687612i	$0.241341\pi$
$608$	4.70371	−	4.70371i	0.190761	−	0.190761i
$609$		0			0
$610$	9.25241	+	5.06941i	0.374619	+	0.205255i
$611$	−16.3403	+	9.43409i	−0.661059	+	0.381662i
$612$		0			0
$613$	−25.4400	+	6.81664i	−1.02751	+	0.275321i	−0.732930	−	0.680304i	$-0.761848\pi$
$613$	−25.4400	+	6.81664i	−1.02751	+	0.275321i	−0.294583	+	0.955626i	$0.595181\pi$
$614$	5.61121	+	9.71891i	0.226450	+	0.392223i
$615$		0			0
$616$	−1.89535	+	11.8681i	−0.0763656	+	0.478181i
$617$	−15.3840	−	15.3840i	−0.619337	−	0.619337i	0.326025	−	0.945361i	$-0.394291\pi$
$617$	−15.3840	−	15.3840i	−0.619337	−	0.619337i	−0.945361	+	0.326025i	$0.894291\pi$
$618$		0			0
$619$	33.2752	+	19.2115i	1.33744	+	0.772174i	0.986428	−	0.164196i	$-0.0525028\pi$
$619$	33.2752	+	19.2115i	1.33744	+	0.772174i	0.351016	+	0.936369i	$0.385836\pi$
$620$	−31.1526	−	7.60480i	−1.25112	−	0.305416i
$621$		0			0
$622$	−20.4669	+	20.4669i	−0.820649	+	0.820649i
$623$	24.7161	−	2.56570i	0.990229	−	0.102793i
$624$		0			0
$625$	−24.9000	+	2.23379i	−0.996000	+	0.0893518i
$626$	39.8823	+	23.0261i	1.59402	+	0.920307i
$627$		0			0
$628$	5.36754	−	20.0319i	0.214188	−	0.799361i
$629$	13.4702			0.537094
$630$		0			0
$631$	18.7435			0.746166			0.373083	−	0.927798i	$-0.378301\pi$
$631$	18.7435			0.746166			0.373083	+	0.927798i	$0.378301\pi$
$632$	−1.99024	+	7.42767i	−0.0791674	+	0.295457i
$633$		0			0
$634$	1.84817	+	1.06704i	0.0734002	+	0.0423777i
$635$	31.5848	−	0.706599i	1.25340	−	0.0280405i
$636$		0			0
$637$	−1.67570	+	30.4773i	−0.0663938	+	1.20756i
$638$	−58.3521	+	58.3521i	−2.31018	+	2.31018i
$639$		0			0
$640$	7.83707	+	12.8991i	0.309787	+	0.509880i
$641$	40.9445	+	23.6393i	1.61721	+	0.933696i	0.987638	+	0.156753i	$0.0501028\pi$
$641$	40.9445	+	23.6393i	1.61721	+	0.933696i	0.629571	+	0.776943i	$0.283231\pi$
$642$		0			0
$643$	−13.3512	−	13.3512i	−0.526519	−	0.526519i	0.393014	−	0.919533i	$-0.371432\pi$
$643$	−13.3512	−	13.3512i	−0.526519	−	0.526519i	−0.919533	+	0.393014i	$0.871432\pi$
$644$	−8.26250	+	3.15951i	−0.325588	+	0.124502i
$645$		0			0
$646$	5.32687	+	9.22640i	0.209583	+	0.363008i
$647$	22.6340	−	6.06475i	0.889833	−	0.238430i	0.215188	−	0.976573i	$-0.430964\pi$
$647$	22.6340	−	6.06475i	0.889833	−	0.238430i	0.674645	+	0.738143i	$0.264297\pi$
$648$		0			0
$649$	−37.2338	+	21.4970i	−1.46156	+	0.843830i
$650$	24.6440	+	38.5893i	0.966616	+	1.51360i
$651$		0			0
$652$	−26.5944	+	26.5944i	−1.04152	+	1.04152i
$653$	1.30016	+	0.348376i	0.0508790	+	0.0136330i	0.284169	−	0.958774i	$-0.408282\pi$
$653$	1.30016	+	0.348376i	0.0508790	+	0.0136330i	−0.233290	+	0.972407i	$0.574949\pi$
$654$		0			0
$655$	−21.4024	−	5.22463i	−0.836261	−	0.204143i
$656$	5.23957	−	3.02507i	0.204571	−	0.118109i
$657$		0			0
$658$	19.4691	−	14.1070i	0.758984	−	0.549947i
$659$	−3.98138			−0.155093			−0.0775463	−	0.996989i	$-0.524709\pi$
$659$	−3.98138			−0.155093			−0.0775463	+	0.996989i	$0.524709\pi$
$660$		0			0
$661$	−9.25451	+	16.0293i	−0.359959	+	0.623467i	−0.987954	−	0.154751i	$-0.950543\pi$
$661$	−9.25451	+	16.0293i	−0.359959	+	0.623467i	0.627995	+	0.778218i	$0.283876\pi$
$662$	−62.3617	+	16.7098i	−2.42376	+	0.649444i
$663$		0			0
$664$			2.87774i			0.111678i
$665$	−2.99702	+	3.86486i	−0.116219	+	0.149873i
$666$		0			0
$667$	−9.98916	−	2.67659i	−0.386782	−	0.103638i
$668$	5.88030	+	21.9456i	0.227516	+	0.849100i
$669$		0			0
$670$	−16.4286	−	15.7096i	−0.634693	−	0.606916i
$671$		−	11.8410i		−	0.457118i
$672$		0			0
$673$	33.8364	+	33.8364i	1.30430	+	1.30430i	0.925466	+	0.378831i	$0.123674\pi$
$673$	33.8364	+	33.8364i	1.30430	+	1.30430i	0.378831	+	0.925466i	$0.376326\pi$
$674$	6.40197	+	11.0885i	0.246595	+	0.427115i
$675$		0			0
$676$	7.24785	−	12.5536i	0.278763	−	0.482832i
$677$	6.30342	−	23.5247i	0.242260	−	0.904127i	−0.732481	−	0.680788i	$-0.761637\pi$
$677$	6.30342	−	23.5247i	0.242260	−	0.904127i	0.974741	−	0.223339i	$-0.0716958\pi$
$678$		0			0
$679$	−7.53429	−	19.7031i	−0.289140	−	0.756134i
$680$	−11.3522	+	3.31565i	−0.435337	+	0.127150i
$681$		0			0
$682$	17.0443	+	63.6102i	0.652660	+	2.43576i
$683$	0.556248	+	2.07594i	0.0212842	+	0.0794338i	0.975751	−	0.218883i	$-0.0702414\pi$
$683$	0.556248	+	2.07594i	0.0212842	+	0.0794338i	−0.954467	+	0.298317i	$0.903575\pi$
$684$		0			0
$685$	−33.6998	−	18.4642i	−1.28760	−	0.705480i
$686$	−1.88601	−	38.8486i	−0.0720083	−	1.48324i
$687$		0			0
$688$	−1.90936	+	7.12582i	−0.0727936	+	0.271669i
$689$	−15.0236	+	26.0216i	−0.572352	+	0.991343i
$690$		0			0
$691$	−19.9595	−	34.5709i	−0.759297	−	1.31514i	−0.943210	−	0.332198i	$-0.892210\pi$
$691$	−19.9595	−	34.5709i	−0.759297	−	1.31514i	0.183913	−	0.982942i	$-0.441123\pi$
$692$	−30.4102	−	30.4102i	−1.15602	−	1.15602i
$693$		0			0
$694$		−	5.30201i		−	0.201262i
$695$	−0.250829	+	0.262309i	−0.00951450	+	0.00994995i
$696$		0			0
$697$	3.19159	+	11.9112i	0.120890	+	0.451168i
$698$	57.7565	+	15.4758i	2.18612	+	0.585768i
$699$		0			0
$700$	−19.8454	−	24.9583i	−0.750084	−	0.943336i
$701$		−	22.3078i		−	0.842554i	−0.906932	−	0.421277i	$-0.861582\pi$
$701$		−	22.3078i		−	0.842554i	0.906932	−	0.421277i	$-0.138418\pi$
$702$		0			0
$703$	1.75281	−	0.469665i	0.0661086	−	0.0177138i
$704$	28.6644	−	49.6482i	1.08033	−	1.87119i
$705$		0			0
$706$	−55.7465			−2.09805
$707$	−6.14594	+	4.45325i	−0.231142	+	0.167482i
$708$		0			0
$709$	21.6102	−	12.4766i	0.811587	−	0.468570i	−0.0359194	−	0.999355i	$-0.511436\pi$
$709$	21.6102	−	12.4766i	0.811587	−	0.468570i	0.847507	+	0.530784i	$0.178103\pi$
$710$	−22.9267	−	37.7351i	−0.860422	−	1.41617i
$711$		0			0
$712$	7.81897	+	2.09509i	0.293028	+	0.0785167i
$713$	−5.83556	+	5.83556i	−0.218543	+	0.218543i
$714$		0			0
$715$	24.6929	−	45.0681i	0.923463	−	1.68545i
$716$	4.39506	−	2.53749i	0.164251	−	0.0948305i
$717$		0			0
$718$	43.9636	−	11.7800i	1.64071	−	0.439626i
$719$	−7.26610	−	12.5853i	−0.270980	−	0.469351i	0.698133	−	0.715968i	$-0.254014\pi$
$719$	−7.26610	−	12.5853i	−0.270980	−	0.469351i	−0.969113	+	0.246617i	$0.920681\pi$
$720$		0			0
$721$	27.2039	+	22.0871i	1.01313	+	0.822568i
$722$	−27.2000	−	27.2000i	−1.01228	−	1.01228i
$723$		0			0
$724$	−36.2852	−	20.9493i	−1.34853	−	0.778574i
$725$	−1.66708	−	37.2403i	−0.0619137	−	1.38307i
$726$		0			0
$727$	−31.0485	+	31.0485i	−1.15153	+	1.15153i	−0.165280	+	0.986247i	$0.552853\pi$
$727$	−31.0485	+	31.0485i	−1.15153	+	1.15153i	−0.986247	+	0.165280i	$0.947147\pi$
$728$	−4.05597	+	9.07848i	−0.150324	+	0.336471i
$729$		0			0
$730$	35.1771	−	36.7870i	1.30196	−	1.36155i
$731$	−13.0217	−	7.51808i	−0.481625	−	0.278066i
$732$		0			0
$733$	7.11907	−	26.5687i	0.262949	−	0.981339i	−0.700545	−	0.713608i	$-0.747060\pi$
$733$	7.11907	−	26.5687i	0.262949	−	0.981339i	0.963494	−	0.267731i	$-0.0862737\pi$
$734$	19.9430			0.736108
$735$		0			0
$736$	11.1615			0.411419
$737$	−6.60302	+	24.6428i	−0.243225	+	0.907729i
$738$		0			0
$739$	31.7514	+	18.3317i	1.16800	+	0.674343i	0.953207	−	0.302318i	$-0.0977605\pi$
$739$	31.7514	+	18.3317i	1.16800	+	0.674343i	0.214788	+	0.976661i	$0.431094\pi$
$740$	0.264614	+	11.8282i	0.00972742	+	0.434813i
$741$		0			0
$742$	15.6178	−	34.9573i	0.573347	−	1.28332i
$743$	8.72347	−	8.72347i	0.320033	−	0.320033i	−0.528747	−	0.848780i	$-0.677338\pi$
$743$	8.72347	−	8.72347i	0.320033	−	0.320033i	0.848780	+	0.528747i	$0.177338\pi$
$744$		0			0
$745$	7.86523	−	32.2194i	0.288160	−	1.18043i
$746$	−10.3938	−	6.00089i	−0.380546	−	0.219708i
$747$		0			0
$748$	55.1254	+	55.1254i	2.01559	+	2.01559i
$749$	−4.62629	−	3.75614i	−0.169041	−	0.137246i
$750$		0			0
$751$	−0.601042	−	1.04103i	−0.0219323	−	0.0379879i	0.854851	−	0.518874i	$-0.173649\pi$
$751$	−0.601042	−	1.04103i	−0.0219323	−	0.0379879i	−0.876783	+	0.480886i	$0.840315\pi$
$752$	−12.5839	+	3.37186i	−0.458889	+	0.122959i
$753$		0			0
$754$	−59.1265	+	34.1367i	−2.15326	+	1.24318i
$755$	−47.5417	+	13.8856i	−1.73022	+	0.505348i
$756$		0			0
$757$	−30.7530	+	30.7530i	−1.11774	+	1.11774i	−0.125664	+	0.992073i	$0.540106\pi$
$757$	−30.7530	+	30.7530i	−1.11774	+	1.11774i	−0.992073	+	0.125664i	$0.959894\pi$
$758$	−27.4743	−	7.36172i	−0.997912	−	0.267390i
$759$		0			0
$760$	−1.36160	+	0.827264i	−0.0493903	+	0.0300080i
$761$	−15.6243	+	9.02069i	−0.566380	+	0.327000i	−0.755702	−	0.654915i	$-0.772704\pi$
$761$	−15.6243	+	9.02069i	−0.566380	+	0.327000i	0.189322	+	0.981915i	$0.439371\pi$
$762$		0			0
$763$	−14.6835	+	10.6395i	−0.531580	+	0.385174i
$764$	15.7237			0.568864
$765$		0			0
$766$	33.8025	−	58.5476i	1.22133	−	2.11541i
$767$	−34.3583	+	9.20627i	−1.24060	+	0.332419i
$768$		0			0
$769$		−	12.9379i		−	0.466554i	−0.972410	−	0.233277i	$-0.925055\pi$
$769$		−	12.9379i		−	0.466554i	0.972410	−	0.233277i	$-0.0749448\pi$
$770$	−25.3671	+	60.3698i	−0.914168	+	2.17558i
$771$		0			0
$772$	−31.0960	−	8.33215i	−1.11917	−	0.299881i
$773$	−4.04629	−	15.1010i	−0.145535	−	0.543144i	−0.999731	−	0.0231927i	$-0.992617\pi$
$773$	−4.04629	−	15.1010i	−0.145535	−	0.543144i	0.854196	−	0.519951i	$-0.174050\pi$
$774$		0			0
$775$	−26.4020	−	13.7071i	−0.948389	−	0.492372i
$776$		−	6.87175i		−	0.246681i
$777$		0			0
$778$	−12.5739	−	12.5739i	−0.450798	−	0.450798i
$779$	0.830610	+	1.43866i	0.0297597	+	0.0515453i
$780$		0			0
$781$	−24.7782	+	42.9171i	−0.886633	+	1.53569i
$782$	−4.62664	+	17.2669i	−0.165448	+	0.617462i
$783$		0			0
$784$	−6.56408	+	20.0271i	−0.234431	+	0.715253i
$785$	9.24427	−	16.8721i	0.329942	−	0.602192i
$786$		0			0
$787$	−9.00519	−	33.6078i	−0.321000	−	1.19799i	−0.918272	−	0.395950i	$-0.870415\pi$
$787$	−9.00519	−	33.6078i	−0.321000	−	1.19799i	0.597272	−	0.802039i	$-0.296251\pi$
$788$	−15.5346	−	57.9760i	−0.553398	−	2.06531i
$789$		0			0
$790$	−20.1318	+	36.7435i	−0.716258	+	1.30727i
$791$	10.5990	+	27.7177i	0.376858	+	0.985527i
$792$		0			0
$793$	2.53551	−	9.46267i	0.0900387	−	0.336029i
$794$	−24.9166	+	43.1569i	−0.884258	+	1.53158i
$795$		0			0
$796$	32.7873	+	56.7893i	1.16211	+	2.01284i
$797$	−32.8278	−	32.8278i	−1.16282	−	1.16282i	−0.983855	−	0.178965i	$-0.942725\pi$
$797$	−32.8278	−	32.8278i	−1.16282	−	1.16282i	−0.178965	−	0.983855i	$-0.557275\pi$
$798$		0			0
$799$		−	26.5533i		−	0.939388i
$800$	12.1407	+	38.3578i	0.429238	+	1.35615i
$801$		0			0
$802$	0.503454	+	1.87892i	0.0177776	+	0.0663468i
$803$	−55.1803	−	14.7855i	−1.94727	−	0.521769i
$804$		0			0
$805$	−8.14134	+	1.02965i	−0.286944	+	0.0362905i
$806$			54.4833i			1.91909i
$807$		0			0
$808$	−2.38819	+	0.639914i	−0.0840163	+	0.0225121i
$809$	−3.20070	+	5.54377i	−0.112531	+	0.194909i	−0.916790	−	0.399370i	$-0.869229\pi$
$809$	−3.20070	+	5.54377i	−0.112531	+	0.194909i	0.804259	+	0.594278i	$0.202562\pi$
$810$		0			0
$811$	49.8024			1.74880			0.874399	−	0.485207i	$-0.161256\pi$
$811$	49.8024			1.74880			0.874399	+	0.485207i	$0.161256\pi$
$812$	38.5015	−	27.8976i	1.35114	−	0.979013i
$813$		0			0
$814$	21.0415	−	12.1483i	0.737504	−	0.425798i
$815$	−29.8179	+	18.1164i	−1.04448	+	0.634592i
$816$		0			0
$817$	−1.95658	−	0.524263i	−0.0684520	−	0.0183417i
$818$	2.68381	−	2.68381i	0.0938373	−	0.0938373i
$819$		0			0
$820$	−10.3965	+	3.03651i	−0.363060	+	0.106040i
$821$	23.6228	−	13.6386i	0.824442	−	0.475992i	−0.0275041	−	0.999622i	$-0.508756\pi$
$821$	23.6228	−	13.6386i	0.824442	−	0.475992i	0.851946	+	0.523630i	$0.175423\pi$
$822$		0			0
$823$	−7.51122	+	2.01263i	−0.261825	+	0.0701557i	−0.387343	−	0.921936i	$-0.626607\pi$
$823$	−7.51122	+	2.01263i	−0.261825	+	0.0701557i	0.125519	+	0.992091i	$0.459941\pi$
$824$	5.70754	+	9.88576i	0.198832	+	0.344387i
$825$		0			0
$826$	42.3356	−	16.1888i	1.47305	−	0.563281i
$827$	18.1337	+	18.1337i	0.630569	+	0.630569i	0.948211	−	0.317641i	$-0.102891\pi$
$827$	18.1337	+	18.1337i	0.630569	+	0.630569i	−0.317641	+	0.948211i	$0.602891\pi$
$828$		0			0
$829$	17.7444	+	10.2448i	0.616290	+	0.355815i	0.775423	−	0.631442i	$-0.217537\pi$
$829$	17.7444	+	10.2448i	0.616290	+	0.355815i	−0.159133	+	0.987257i	$0.550870\pi$
$830$	−3.71836	+	15.2320i	−0.129066	+	0.528712i
$831$		0			0
$832$	33.5381	−	33.5381i	1.16272	−	1.16272i
$833$	−35.9655	−	23.4878i	−1.24613	−	0.813803i
$834$		0			0
$835$	0.471395	+	21.0712i	0.0163133	+	0.729201i
$836$	9.09524	+	5.25114i	0.314565	+	0.181614i
$837$		0			0
$838$	5.76305	−	21.5080i	0.199081	−	0.742982i
$839$	50.2790			1.73582			0.867911	−	0.496719i	$-0.165462\pi$
$839$	50.2790			1.73582			0.867911	+	0.496719i	$0.165462\pi$
$840$		0			0
$841$	26.5847			0.916714
$842$	20.2815	−	75.6917i	0.698948	−	2.60851i
$843$		0			0
$844$	−10.6514	−	6.14961i	−0.366637	−	0.211678i
$845$	9.29362	−	9.71896i	0.319710	−	0.334342i
$846$		0			0
$847$	44.1545	−	4.58354i	1.51717	−	0.157492i
$848$	−14.6700	+	14.6700i	−0.503770	+	0.503770i
$849$		0			0
$850$	−64.3721	+	2.88164i	−2.20794	+	0.0988395i
$851$	2.63688	+	1.52240i	0.0903911	+	0.0521874i
$852$		0			0
$853$	−10.9628	−	10.9628i	−0.375358	−	0.375358i	0.494066	−	0.869424i	$-0.335510\pi$
$853$	−10.9628	−	10.9628i	−0.375358	−	0.375358i	−0.869424	+	0.494066i	$0.835510\pi$
$854$	−1.96861	+	12.3269i	−0.0673645	+	0.421819i
$855$		0			0
$856$	−0.970625	−	1.68117i	−0.0331753	−	0.0574613i
$857$	−6.91224	+	1.85213i	−0.236118	+	0.0632676i	−0.374937	−	0.927050i	$-0.622336\pi$
$857$	−6.91224	+	1.85213i	−0.236118	+	0.0632676i	0.138820	+	0.990318i	$0.455669\pi$
$858$		0			0
$859$	−8.82744	+	5.09652i	−0.301188	+	0.173891i	−0.642977	−	0.765886i	$-0.722301\pi$
$859$	−8.82744	+	5.09652i	−0.301188	+	0.173891i	0.341788	+	0.939777i	$0.388967\pi$
$860$	6.34580	−	11.5820i	0.216390	−	0.394943i
$861$		0			0
$862$	11.2480	−	11.2480i	0.383109	−	0.383109i
$863$	6.21581	+	1.66552i	0.211589	+	0.0566950i	0.363056	−	0.931767i	$-0.381733\pi$
$863$	6.21581	+	1.66552i	0.211589	+	0.0566950i	−0.151468	+	0.988462i	$0.548400\pi$
$864$		0			0
$865$	−20.7158	−	34.0962i	−0.704359	−	1.15931i
$866$	4.95401	−	2.86020i	0.168344	−	0.0971934i
$867$		0			0
$868$	−3.91766	−	37.7399i	−0.132974	−	1.28098i
$869$	47.0235			1.59516
$870$		0			0
$871$	−10.5535	+	18.2792i	−0.357592	+	0.619367i
$872$	−5.70573	+	1.52885i	−0.193220	+	0.0517733i
$873$		0			0
$874$			2.40816i			0.0814574i
$875$	−12.3941	−	26.8587i	−0.418996	−	0.907988i
$876$		0			0
$877$	1.87668	+	0.502855i	0.0633709	+	0.0169802i	0.290365	−	0.956916i	$-0.406223\pi$
$877$	1.87668	+	0.502855i	0.0633709	+	0.0169802i	−0.226994	+	0.973896i	$0.572890\pi$
$878$	7.62887	+	28.4713i	0.257462	+	0.960861i
$879$		0			0
$880$	24.5226	−	25.6449i	0.826657	−	0.864491i
$881$			22.1815i			0.747314i	0.927567	+	0.373657i	$0.121896\pi$
$881$			22.1815i			0.747314i	−0.927567	+	0.373657i	$0.878104\pi$
$882$		0			0
$883$	−12.0170	−	12.0170i	−0.404404	−	0.404404i	0.475378	−	0.879782i	$-0.342311\pi$
$883$	−12.0170	−	12.0170i	−0.404404	−	0.404404i	−0.879782	+	0.475378i	$0.842311\pi$
$884$	32.2491	+	55.8570i	1.08465	+	1.87867i
$885$		0			0
$886$	−7.27167	+	12.5949i	−0.244296	+	0.423134i
$887$	3.78840	−	14.1385i	0.127202	−	0.474725i	−0.872706	−	0.488245i	$-0.837637\pi$
$887$	3.78840	−	14.1385i	0.127202	−	0.474725i	0.999909	+	0.0135205i	$0.00430384\pi$
$888$		0			0
$889$	13.3513	+	34.9153i	0.447790	+	1.17102i
$890$	38.6792	+	21.1924i	1.29653	+	0.710371i
$891$		0			0
$892$	−1.71329	−	6.39410i	−0.0573653	−	0.214090i
$893$	−0.925830	−	3.45525i	−0.0309817	−	0.115625i
$894$		0			0
$895$	4.51912	−	1.31991i	0.151058	−	0.0441196i
$896$	−11.2565	+	13.8643i	−0.376055	+	0.463172i
$897$		0			0
$898$	5.54916	−	20.7097i	0.185178	−	0.691093i
$899$	22.1788	−	38.4147i	0.739703	−	1.28120i
$900$		0			0
$901$	−21.1428	−	36.6203i	−0.704367	−	1.22000i
$902$	15.7277	+	15.7277i	0.523676	+	0.523676i
$903$		0			0
$904$			9.66697i			0.321519i
$905$	−28.0918	−	26.8624i	−0.933804	−	0.892937i
$906$		0			0
$907$	10.4032	+	38.8255i	0.345434	+	1.28918i	0.892104	+	0.451830i	$0.149229\pi$
$907$	10.4032	+	38.8255i	0.345434	+	1.28918i	−0.546670	+	0.837348i	$0.684105\pi$
$908$	21.6092	+	5.79017i	0.717127	+	0.192153i
$909$		0			0
$910$	−33.1989	+	42.8122i	−1.10053	+	1.41921i
$911$		−	17.4943i		−	0.579613i	−0.957085	−	0.289807i	$-0.906409\pi$
$911$		−	17.4943i		−	0.579613i	0.957085	−	0.289807i	$-0.0935910\pi$
$912$		0			0
$913$	16.9981	−	4.55464i	0.562556	−	0.150736i
$914$	−1.32314	+	2.29175i	−0.0437657	+	0.0758045i
$915$		0			0
$916$	−13.4124			−0.443157
$917$	−2.69150	−	25.9280i	−0.0888811	−	0.856216i
$918$		0			0
$919$	28.8885	−	16.6788i	0.952943	−	0.550182i	0.0589490	−	0.998261i	$-0.481225\pi$
$919$	28.8885	−	16.6788i	0.952943	−	0.550182i	0.893994	+	0.448079i	$0.147892\pi$
$920$	−2.59700	−	0.633964i	−0.0856204	−	0.0209012i
$921$		0			0
$922$	−22.4614	−	6.01851i	−0.739726	−	0.198209i
$923$	−28.9911	+	28.9911i	−0.954253	+	0.954253i
$924$		0			0
$925$	−2.36371	+	10.7179i	−0.0777183	+	0.352403i
$926$	67.4880	−	38.9642i	2.21779	−	1.28044i
$927$		0			0
$928$	−57.9479	+	15.5271i	−1.90223	+	0.509701i
$929$	8.58559	+	14.8707i	0.281684	+	0.487891i	0.971800	−	0.235808i	$-0.0757737\pi$
$929$	8.58559	+	14.8707i	0.281684	+	0.487891i	−0.690116	+	0.723699i	$0.742440\pi$
$930$		0			0
$931$	−5.49896	−	1.80234i	−0.180221	−	0.0590692i
$932$	21.8695	+	21.8695i	0.716359	+	0.716359i
$933$		0			0
$934$	−10.3578	−	5.98007i	−0.338917	−	0.195674i
$935$	37.5521	+	61.8071i	1.22809	+	2.02131i
$936$		0			0
$937$	20.5617	−	20.5617i	0.671721	−	0.671721i	−0.286391	−	0.958113i	$-0.592456\pi$
$937$	20.5617	−	20.5617i	0.671721	−	0.671721i	0.958113	+	0.286391i	$0.0924558\pi$
$938$	10.9709	−	24.5562i	0.358213	−	0.801789i
$939$		0			0
$940$	23.3164	−	0.521623i	0.760497	−	0.0170135i
$941$	41.7287	+	24.0921i	1.36032	+	0.785379i	0.989666	−	0.143393i	$-0.0458013\pi$
$941$	41.7287	+	24.0921i	1.36032	+	0.785379i	0.370651	+	0.928772i	$0.379135\pi$
$942$		0			0
$943$	−0.721425	+	2.69240i	−0.0234928	+	0.0876764i
$944$	−24.5601			−0.799363
$945$		0			0
$946$	−27.1211			−0.881783
$947$	−1.99645	+	7.45087i	−0.0648760	+	0.242121i	−0.990748	−	0.135718i	$-0.956666\pi$
$947$	−1.99645	+	7.45087i	−0.0648760	+	0.242121i	0.925871	+	0.377839i	$0.123333\pi$
$948$		0			0
$949$	−40.9309	−	23.6314i	−1.32867	−	0.767109i
$950$	−8.27593	+	2.61942i	−0.268507	+	0.0849854i
$951$		0			0
$952$	−8.21052	−	11.3314i	−0.266104	−	0.367252i
$953$	−5.04023	+	5.04023i	−0.163269	+	0.163269i	−0.784013	−	0.620744i	$-0.786831\pi$
$953$	−5.04023	+	5.04023i	−0.163269	+	0.163269i	0.620744	+	0.784013i	$0.286831\pi$
$954$		0			0
$955$	14.1704	+	3.45920i	0.458543	+	0.111937i
$956$	34.2981	+	19.8020i	1.10928	+	0.640442i
$957$		0			0
$958$	51.9383	+	51.9383i	1.67805	+	1.67805i
$959$	7.17022	−	44.8980i	0.231538	−	1.44983i
$960$		0			0
$961$	−2.19903	−	3.80882i	−0.0709363	−	0.122865i
$962$	19.4165	−	5.20262i	0.626012	−	0.167739i
$963$		0			0
$964$	−43.1789	+	24.9294i	−1.39070	+	0.802921i
$965$	−26.1910	−	14.3501i	−0.843118	−	0.461946i
$966$		0			0
$967$	−1.20438	+	1.20438i	−0.0387302	+	0.0387302i	−0.726207	−	0.687476i	$-0.758718\pi$
$967$	−1.20438	+	1.20438i	−0.0387302	+	0.0387302i	0.687476	+	0.726207i	$0.258718\pi$
$968$	13.9683	+	3.74281i	0.448960	+	0.120298i
$969$		0			0
$970$	8.87907	−	36.3726i	0.285090	−	1.16785i
$971$	−33.4168	+	19.2932i	−1.07239	+	0.619147i	−0.928835	−	0.370494i	$-0.879188\pi$
$971$	−33.4168	+	19.2932i	−1.07239	+	0.619147i	−0.143560	+	0.989642i	$0.545855\pi$
$972$		0			0
$973$	−0.392079	−	0.175168i	−0.0125695	−	0.00561563i
$974$	30.6193			0.981107
$975$		0			0
$976$	3.38207	−	5.85792i	0.108257	−	0.187507i
$977$	37.9869	−	10.1786i	1.21531	−	0.325641i	0.406467	−	0.913666i	$-0.366761\pi$
$977$	37.9869	−	10.1786i	1.21531	−	0.325641i	0.808843	+	0.588024i	$0.200094\pi$
$978$		0			0
$979$		−	49.5008i		−	1.58205i
$980$	19.9180	−	32.0426i	0.636258	−	1.02356i
$981$		0			0
$982$	64.4130	+	17.2594i	2.05550	+	0.550770i
$983$	−1.14191	−	4.26167i	−0.0364213	−	0.135926i	0.945321	−	0.326141i	$-0.105748\pi$
$983$	−1.14191	−	4.26167i	−0.0364213	−	0.135926i	−0.981743	+	0.190215i	$0.939082\pi$
$984$		0			0
$985$	−1.24534	−	55.6662i	−0.0396797	−	1.77367i
$986$		−	96.0815i		−	3.05986i
$987$		0			0
$988$	6.14396	+	6.14396i	0.195465	+	0.195465i
$989$	−1.69938	−	2.94342i	−0.0540372	−	0.0935952i
$990$		0			0
$991$	−1.49217	+	2.58451i	−0.0474004	+	0.0820998i	−0.888752	−	0.458388i	$-0.848427\pi$
$991$	−1.49217	+	2.58451i	−0.0474004	+	0.0820998i	0.841352	+	0.540488i	$0.181760\pi$
$992$	−12.3909	+	46.2434i	−0.393411	+	1.46823i
$993$		0			0
$994$	32.9300	−	40.5587i	1.04448	−	1.28644i
$995$	17.0547	+	58.3922i	0.540671	+	1.85116i
$996$		0			0
$997$	−6.74018	−	25.1547i	−0.213464	−	0.796657i	−0.986702	−	0.162541i	$-0.948031\pi$
$997$	−6.74018	−	25.1547i	−0.213464	−	0.796657i	0.773238	−	0.634116i	$-0.218636\pi$
$998$	−13.5132	−	50.4321i	−0.427754	−	1.59640i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.ce.a.53.3	✓	64
3.2	odd	2	inner	315.2.ce.a.53.14	yes	64
5.2	odd	4	inner	315.2.ce.a.242.3	yes	64
7.2	even	3	inner	315.2.ce.a.233.14	yes	64
15.2	even	4	inner	315.2.ce.a.242.14	yes	64
21.2	odd	6	inner	315.2.ce.a.233.3	yes	64
35.2	odd	12	inner	315.2.ce.a.107.14	yes	64
105.2	even	12	inner	315.2.ce.a.107.3	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.ce.a.53.3	✓	64	1.1	even	1	trivial
315.2.ce.a.53.14	yes	64	3.2	odd	2	inner
315.2.ce.a.107.3	yes	64	105.2	even	12	inner
315.2.ce.a.107.14	yes	64	35.2	odd	12	inner
315.2.ce.a.233.3	yes	64	21.2	odd	6	inner
315.2.ce.a.233.14	yes	64	7.2	even	3	inner
315.2.ce.a.242.3	yes	64	5.2	odd	4	inner
315.2.ce.a.242.14	yes	64	15.2	even	4	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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.ce (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.543545 + 2.02854i) q^{2} +(-2.08747 - 1.20520i) q^{4} +(-1.61611 - 1.54538i) q^{5} +(1.07923 - 2.41563i) q^{7} +(0.609443 - 0.609443i) q^{8} +O(q^{10})\)	\(q+(-0.543545 + 2.02854i) q^{2} +(-2.08747 - 1.20520i) q^{4} +(-1.61611 - 1.54538i) q^{5} +(1.07923 - 2.41563i) q^{7} +(0.609443 - 0.609443i) q^{8} +(4.01329 - 2.43835i) q^{10} +(-4.56441 - 2.63527i) q^{11} +(-3.08333 - 3.08333i) q^{13} +(4.31359 + 3.50225i) q^{14} +(-1.50538 - 2.60740i) q^{16} +(5.92744 - 1.58825i) q^{17} +(0.715930 - 0.413342i) q^{19} +(1.51108 + 5.17367i) q^{20} +(7.82670 - 7.82670i) q^{22} +(1.33984 + 0.359008i) q^{23} +(0.223603 + 4.99500i) q^{25} +(7.93057 - 4.57872i) q^{26} +(-5.16417 + 3.74187i) q^{28} -7.45552 q^{29} +(-2.97481 + 5.15253i) q^{31} +(7.77248 - 2.08263i) q^{32} +12.8873i q^{34} +(-5.47721 + 2.23611i) q^{35} +(2.12029 + 0.568131i) q^{37} +(0.449340 + 1.67696i) q^{38} +(-1.92674 + 0.0431042i) q^{40} +2.00950i q^{41} +(-1.73260 - 1.73260i) q^{43} +(6.35205 + 11.0021i) q^{44} +(-1.45652 + 2.52277i) q^{46} +(1.11993 - 4.17964i) q^{47} +(-4.67055 - 5.21402i) q^{49} +(-10.2541 - 2.26142i) q^{50} +(2.72032 + 10.1524i) q^{52} +(-1.78346 - 6.65598i) q^{53} +(3.30410 + 11.3126i) q^{55} +(-0.814463 - 2.12991i) q^{56} +(4.05241 - 15.1238i) q^{58} +(4.07871 - 7.06453i) q^{59} +(1.12332 + 1.94566i) q^{61} +(-8.83515 - 8.83515i) q^{62} +10.8772i q^{64} +(0.218075 + 9.74790i) q^{65} +(-1.25282 - 4.67558i) q^{67} +(-14.2875 - 3.82832i) q^{68} +(-1.55891 - 12.3261i) q^{70} -9.40254i q^{71} +(10.4696 - 2.80532i) q^{73} +(-2.30495 + 3.99229i) q^{74} -1.99264 q^{76} +(-11.2919 + 8.18190i) q^{77} +(-7.72665 + 4.46099i) q^{79} +(-1.59656 + 6.54023i) q^{80} +(-4.07634 - 1.09225i) q^{82} +(-2.36096 + 2.36096i) q^{83} +(-12.0338 - 6.59336i) q^{85} +(4.45639 - 2.57290i) q^{86} +(-4.38779 + 1.17571i) q^{88} +(4.69600 + 8.13371i) q^{89} +(-10.7758 + 4.12058i) q^{91} +(-2.36419 - 2.36419i) q^{92} +(7.86983 + 4.54365i) q^{94} +(-1.79579 - 0.438378i) q^{95} +(5.63773 - 5.63773i) q^{97} +(13.1155 - 6.64032i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 8 q^{7}+O(q^{10}) \) 64 * q + 8 * q^7	\( 64 q + 8 q^{7} + 8 q^{10} + 32 q^{16} - 48 q^{22} - 16 q^{25} + 88 q^{28} + 32 q^{31} - 16 q^{37} - 40 q^{40} - 16 q^{43} - 80 q^{52} - 32 q^{55} - 88 q^{58} + 48 q^{61} - 32 q^{67} - 112 q^{70} - 88 q^{73} - 320 q^{76} - 56 q^{82} + 16 q^{85} + 120 q^{88} - 128 q^{91} + 208 q^{97}+O(q^{100}) \) 64 * q + 8 * q^7 + 8 * q^10 + 32 * q^16 - 48 * q^22 - 16 * q^25 + 88 * q^28 + 32 * q^31 - 16 * q^37 - 40 * q^40 - 16 * q^43 - 80 * q^52 - 32 * q^55 - 88 * q^58 + 48 * q^61 - 32 * q^67 - 112 * q^70 - 88 * q^73 - 320 * q^76 - 56 * q^82 + 16 * q^85 + 120 * q^88 - 128 * q^91 + 208 * q^97

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