LMFDB - Embedded newform 1323.2.o.c.881.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(440,1323)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1323, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1323.440");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.o (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$10.5642081874$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{6})$
Coefficient field:	10.0.288778218147.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 7x^{8} - 4x^{7} + 34x^{6} - 19x^{5} + 64x^{4} - x^{3} + 64x^{2} - 21x + 9 $ x^10 - x^9 + 7x^8 - 4x^7 + 34x^6 - 19x^5 + 64x^4 - x^3 + 64x^2 - 21*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			881.4
Root			$-1.04536 + 1.81062i$ of defining polynomial
Character	$\chi$	$=$	1323.881
Dual form			1323.2.o.c.440.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.30778 - 0.755047i) q^{2} +(0.140193 - 0.242822i) q^{4} +(0.387938 - 0.671929i) q^{5} +2.59678i q^{8} +O(q^{10})$	\(q+(1.30778 - 0.755047i) q^{2} +(0.140193 - 0.242822i) q^{4} +(0.387938 - 0.671929i) q^{5} +2.59678i q^{8} -1.17165i q^{10} +(-3.32830 + 1.92159i) q^{11} +(2.54198 + 1.46761i) q^{13} +(2.24108 + 3.88166i) q^{16} +5.39802 q^{17} +0.434804i q^{19} +(-0.108773 - 0.188400i) q^{20} +(-2.90179 + 5.02605i) q^{22} +(-0.0482537 - 0.0278593i) q^{23} +(2.19901 + 3.80879i) q^{25} +4.43247 q^{26} +(0.187994 - 0.108538i) q^{29} +(5.67806 + 3.27823i) q^{31} +(1.36392 + 0.787461i) q^{32} +(7.05942 - 4.07576i) q^{34} -6.29396 q^{37} +(0.328298 + 0.568628i) q^{38} +(1.74485 + 1.00739i) q^{40} +(3.78757 - 6.56026i) q^{41} +(6.42703 + 11.1319i) q^{43} +1.07758i q^{44} -0.0841403 q^{46} +(0.482772 + 0.836186i) q^{47} +(5.75164 + 3.32071i) q^{50} +(0.712737 - 0.411499i) q^{52} -7.46442i q^{53} +2.98184i q^{55} +(0.163903 - 0.283889i) q^{58} +(-1.56219 + 2.70580i) q^{59} +(-3.01744 + 1.74212i) q^{61} +9.90087 q^{62} -6.58603 q^{64} +(1.97226 - 1.13869i) q^{65} +(2.10088 - 3.63884i) q^{67} +(0.756765 - 1.31076i) q^{68} +3.50812i q^{71} -8.15152i q^{73} +(-8.23112 + 4.75224i) q^{74} +(0.105580 + 0.0609566i) q^{76} +(2.48110 + 4.29739i) q^{79} +3.47760 q^{80} -11.4392i q^{82} +(-4.31033 - 7.46571i) q^{83} +(2.09410 - 3.62708i) q^{85} +(16.8103 + 9.70542i) q^{86} +(-4.98996 - 8.64286i) q^{88} -15.6408 q^{89} +(-0.0135297 + 0.00781136i) q^{92} +(1.26272 + 0.729031i) q^{94} +(0.292157 + 0.168677i) q^{95} +(-1.24162 + 0.716849i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 4 q^{4}+O(q^{10}) $ 10 * q + 4 * q^4	$ 10 q + 4 q^{4} - 12 q^{11} - 6 q^{13} - 6 q^{16} + 24 q^{17} - 3 q^{20} + 5 q^{22} - 15 q^{23} + 7 q^{25} - 6 q^{26} + 15 q^{29} - 9 q^{31} + 48 q^{32} - 3 q^{34} - 12 q^{37} - 18 q^{38} - 15 q^{40} - 9 q^{41} + 3 q^{43} + 26 q^{46} + 15 q^{47} - 3 q^{50} + 12 q^{52} + 8 q^{58} - 18 q^{59} + 12 q^{61} + 12 q^{62} + 6 q^{64} - 3 q^{65} - 10 q^{67} + 27 q^{68} - 30 q^{74} - 9 q^{76} + 20 q^{79} + 60 q^{80} - 15 q^{83} + 18 q^{85} + 54 q^{86} - 8 q^{88} - 48 q^{89} - 39 q^{92} - 3 q^{94} - 6 q^{97}+O(q^{100}) $ 10 * q + 4 * q^4 - 12 * q^11 - 6 * q^13 - 6 * q^16 + 24 * q^17 - 3 * q^20 + 5 * q^22 - 15 * q^23 + 7 * q^25 - 6 * q^26 + 15 * q^29 - 9 * q^31 + 48 * q^32 - 3 * q^34 - 12 * q^37 - 18 * q^38 - 15 * q^40 - 9 * q^41 + 3 * q^43 + 26 * q^46 + 15 * q^47 - 3 * q^50 + 12 * q^52 + 8 * q^58 - 18 * q^59 + 12 * q^61 + 12 * q^62 + 6 * q^64 - 3 * q^65 - 10 * q^67 + 27 * q^68 - 30 * q^74 - 9 * q^76 + 20 * q^79 + 60 * q^80 - 15 * q^83 + 18 * q^85 + 54 * q^86 - 8 * q^88 - 48 * q^89 - 39 * q^92 - 3 * q^94 - 6 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	1.30778	−	0.755047i	0.924740	−	0.533899i	0.0395961	−	0.999216i	$-0.487393\pi$
$2$	1.30778	−	0.755047i	0.924740	−	0.533899i	0.885144	+	0.465317i	$0.154060\pi$
$3$		0			0
$3$		0			0
$4$	0.140193	−	0.242822i	0.0700966	−	0.121411i
$5$	0.387938	−	0.671929i	0.173491	−	0.300496i	−0.766147	−	0.642666i	$-0.777829\pi$
$5$	0.387938	−	0.671929i	0.173491	−	0.300496i	0.939638	+	0.342170i	$0.111162\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$			2.59678i			0.918100i
$9$		0			0
$10$		−	1.17165i		−	0.370507i
$11$	−3.32830	+	1.92159i	−1.00352	+	0.579382i	−0.909288	−	0.416168i	$-0.863373\pi$
$11$	−3.32830	+	1.92159i	−1.00352	+	0.579382i	−0.0942318	+	0.995550i	$0.530039\pi$
$12$		0			0
$13$	2.54198	+	1.46761i	0.705019	+	0.407043i	0.809214	−	0.587514i	$-0.199893\pi$
$13$	2.54198	+	1.46761i	0.705019	+	0.407043i	−0.104195	+	0.994557i	$0.533227\pi$
$14$		0			0
$15$		0			0
$16$	2.24108	+	3.88166i	0.560270	+	0.970415i
$17$	5.39802			1.30921			0.654606	−	0.755971i	$-0.272835\pi$
$17$	5.39802			1.30921			0.654606	+	0.755971i	$0.272835\pi$
$18$		0			0
$19$			0.434804i			0.0997509i	0.998755	+	0.0498755i	$0.0158824\pi$
$19$			0.434804i			0.0997509i	−0.998755	+	0.0498755i	$0.984118\pi$
$20$	−0.108773	−	0.188400i	−0.0243223	−	0.0421274i
$21$		0			0
$22$	−2.90179	+	5.02605i	−0.618663	+	1.07156i
$23$	−0.0482537	−	0.0278593i	−0.0100616	−	0.00580906i	0.494961	−	0.868915i	$-0.335182\pi$
$23$	−0.0482537	−	0.0278593i	−0.0100616	−	0.00580906i	−0.505022	+	0.863106i	$0.668516\pi$
$24$		0			0
$25$	2.19901	+	3.80879i	0.439802	+	0.761759i
$26$	4.43247			0.869279
$27$		0			0
$28$		0			0
$29$	0.187994	−	0.108538i	0.0349096	−	0.0201551i	−0.482444	−	0.875927i	$-0.660251\pi$
$29$	0.187994	−	0.108538i	0.0349096	−	0.0201551i	0.517353	+	0.855772i	$0.326917\pi$
$30$		0			0
$31$	5.67806	+	3.27823i	1.01981	+	0.588787i	0.914049	−	0.405604i	$-0.132939\pi$
$31$	5.67806	+	3.27823i	1.01981	+	0.588787i	0.105761	+	0.994392i	$0.466272\pi$
$32$	1.36392	+	0.787461i	0.241110	+	0.139205i
$33$		0			0
$34$	7.05942	−	4.07576i	1.21068	−	0.698987i
$35$		0			0
$36$		0			0
$37$	−6.29396			−1.03472			−0.517361	−	0.855768i	$-0.673085\pi$
$37$	−6.29396			−1.03472			−0.517361	+	0.855768i	$0.673085\pi$
$38$	0.328298	+	0.568628i	0.0532569	+	0.0922437i
$39$		0			0
$40$	1.74485	+	1.00739i	0.275885	+	0.159282i
$41$	3.78757	−	6.56026i	0.591519	−	1.02454i	−0.402509	−	0.915416i	$-0.631862\pi$
$41$	3.78757	−	6.56026i	0.591519	−	1.02454i	0.994028	−	0.109125i	$-0.0348049\pi$
$42$		0			0
$43$	6.42703	+	11.1319i	0.980112	+	1.69760i	0.661914	+	0.749580i	$0.269745\pi$
$43$	6.42703	+	11.1319i	0.980112	+	1.69760i	0.318198	+	0.948024i	$0.396922\pi$
$44$			1.07758i			0.162451i
$45$		0			0
$46$	−0.0841403			−0.0124058
$47$	0.482772	+	0.836186i	0.0704195	+	0.121970i	0.899085	−	0.437774i	$-0.144233\pi$
$47$	0.482772	+	0.836186i	0.0704195	+	0.121970i	−0.828666	+	0.559744i	$0.810900\pi$
$48$		0			0
$49$		0			0
$50$	5.75164	+	3.32071i	0.813405	+	0.469619i
$51$		0			0
$52$	0.712737	−	0.411499i	0.0988388	−	0.0570646i
$53$		−	7.46442i		−	1.02532i	−0.858593	−	0.512658i	$-0.828661\pi$
$53$		−	7.46442i		−	1.02532i	0.858593	−	0.512658i	$-0.171339\pi$
$54$		0			0
$55$			2.98184i			0.402071i
$56$		0			0
$57$		0			0
$58$	0.163903	−	0.283889i	0.0215215	−	0.0372764i
$59$	−1.56219	+	2.70580i	−0.203380	+	0.352265i	−0.949615	−	0.313418i	$-0.898526\pi$
$59$	−1.56219	+	2.70580i	−0.203380	+	0.352265i	0.746235	+	0.665682i	$0.231859\pi$
$60$		0			0
$61$	−3.01744	+	1.74212i	−0.386343	+	0.223055i	−0.680575	−	0.732679i	$-0.738270\pi$
$61$	−3.01744	+	1.74212i	−0.386343	+	0.223055i	0.294231	+	0.955734i	$0.404936\pi$
$62$	9.90087			1.25741
$63$		0			0
$64$	−6.58603			−0.823254
$65$	1.97226	−	1.13869i	0.244629	−	0.141237i
$66$		0			0
$67$	2.10088	−	3.63884i	0.256664	−	0.444555i	−0.708682	−	0.705528i	$-0.750710\pi$
$67$	2.10088	−	3.63884i	0.256664	−	0.444555i	0.965346	+	0.260973i	$0.0840433\pi$
$68$	0.756765	−	1.31076i	0.0917712	−	0.158952i
$69$		0			0
$70$		0			0
$71$			3.50812i			0.416337i	0.978093	+	0.208169i	$0.0667503\pi$
$71$			3.50812i			0.416337i	−0.978093	+	0.208169i	$0.933250\pi$
$72$		0			0
$73$		−	8.15152i		−	0.954063i	−0.878886	−	0.477031i	$-0.841713\pi$
$73$		−	8.15152i		−	0.954063i	0.878886	−	0.477031i	$-0.158287\pi$
$74$	−8.23112	+	4.75224i	−0.956848	+	0.552437i
$75$		0			0
$76$	0.105580	+	0.0609566i	0.0121108	+	0.00699220i
$77$		0			0
$78$		0			0
$79$	2.48110	+	4.29739i	0.279145	+	0.483494i	0.971173	−	0.238377i	$-0.0766155\pi$
$79$	2.48110	+	4.29739i	0.279145	+	0.483494i	−0.692027	+	0.721871i	$0.743282\pi$
$80$	3.47760			0.388807
$81$		0			0
$82$		−	11.4392i		−	1.26325i
$83$	−4.31033	−	7.46571i	−0.473120	−	0.819469i	0.526406	−	0.850233i	$-0.323539\pi$
$83$	−4.31033	−	7.46571i	−0.473120	−	0.819469i	−0.999527	+	0.0307645i	$0.990206\pi$
$84$		0			0
$85$	2.09410	−	3.62708i	0.227137	−	0.393412i
$86$	16.8103	+	9.70542i	1.81270	+	1.04656i
$87$		0			0
$88$	−4.98996	−	8.64286i	−0.531931	−	0.921332i
$89$	−15.6408			−1.65792			−0.828962	−	0.559305i	$-0.811068\pi$
$89$	−15.6408			−1.65792			−0.828962	+	0.559305i	$0.811068\pi$
$90$		0			0
$91$		0			0
$92$	−0.0135297	+	0.00781136i	−0.00141057	+	0.000814391i
$93$		0			0
$94$	1.26272	+	0.729031i	0.130240	+	0.0751938i
$95$	0.292157	+	0.168677i	0.0299747	+	0.0173059i
$96$		0			0
$97$	−1.24162	+	0.716849i	−0.126067	+	0.0727850i	−0.561708	−	0.827336i	$-0.689855\pi$
$97$	−1.24162	+	0.716849i	−0.126067	+	0.0727850i	0.435640	+	0.900121i	$0.356522\pi$
$98$		0			0
$99$		0			0
$100$	1.23314			0.123314
$101$	−8.01096	−	13.8754i	−0.797120	−	1.38065i	−0.921484	−	0.388416i	$-0.873023\pi$
$101$	−8.01096	−	13.8754i	−0.797120	−	1.38065i	0.124364	−	0.992237i	$-0.460311\pi$
$102$		0			0
$103$	14.6064	+	8.43299i	1.43921	+	0.830928i	0.997795	−	0.0663758i	$-0.0211436\pi$
$103$	14.6064	+	8.43299i	1.43921	+	0.830928i	0.441414	+	0.897303i	$0.354477\pi$
$104$	−3.81107	+	6.60097i	−0.373706	+	0.647278i
$105$		0			0
$106$	−5.63599	−	9.76182i	−0.547416	−	0.948152i
$107$			3.88492i			0.375569i	0.982210	+	0.187785i	$0.0601307\pi$
$107$			3.88492i			0.375569i	−0.982210	+	0.187785i	$0.939869\pi$
$108$		0			0
$109$	−2.56509			−0.245691			−0.122845	−	0.992426i	$-0.539202\pi$
$109$	−2.56509			−0.245691			−0.122845	+	0.992426i	$0.539202\pi$
$110$	2.25143	+	3.89959i	0.214665	+	0.371811i
$111$		0			0
$112$		0			0
$113$	9.79043	+	5.65251i	0.921006	+	0.531743i	0.883956	−	0.467570i	$-0.154871\pi$
$113$	9.79043	+	5.65251i	0.921006	+	0.531743i	0.0370501	+	0.999313i	$0.488204\pi$
$114$		0			0
$115$	−0.0374389	+	0.0216154i	−0.00349120	+	0.00201564i
$116$		−	0.0608653i		−	0.00565120i
$117$		0			0
$118$			4.71812i			0.434338i
$119$		0			0
$120$		0			0
$121$	1.88504	−	3.26499i	0.171368	−	0.296817i
$122$	−2.63076	+	4.55662i	−0.238178	+	0.412537i
$123$		0			0
$124$	1.59205	−	0.919171i	0.142970	−	0.0825440i
$125$	7.29170			0.652189
$126$		0			0
$127$	2.65660			0.235735			0.117867	−	0.993029i	$-0.462394\pi$
$127$	2.65660			0.235735			0.117867	+	0.993029i	$0.462394\pi$
$128$	−11.3409	+	6.54769i	−1.00241	+	0.578739i
$129$		0			0
$130$	1.71953	−	2.97830i	0.150812	−	0.261215i
$131$	4.11811	−	7.13278i	0.359801	−	0.623194i	−0.628126	−	0.778111i	$-0.716178\pi$
$131$	4.11811	−	7.13278i	0.359801	−	0.623194i	0.987927	+	0.154918i	$0.0495112\pi$
$132$		0			0
$133$		0			0
$134$		−	6.34507i		−	0.548131i
$135$		0			0
$136$			14.0175i			1.20199i
$137$	15.0058	−	8.66359i	1.28203	−	0.740180i	0.304811	−	0.952413i	$-0.401407\pi$
$137$	15.0058	−	8.66359i	1.28203	−	0.740180i	0.977219	+	0.212233i	$0.0680735\pi$
$138$		0			0
$139$	5.47677	+	3.16201i	0.464533	+	0.268198i	0.713949	−	0.700198i	$-0.246905\pi$
$139$	5.47677	+	3.16201i	0.464533	+	0.268198i	−0.249415	+	0.968397i	$0.580238\pi$
$140$		0			0
$141$		0			0
$142$	2.64880	+	4.58785i	0.222282	+	0.385004i
$143$	−11.2806			−0.943334
$144$		0			0
$145$		−	0.168425i		−	0.0139869i
$146$	−6.15478	−	10.6604i	−0.509373	−	0.882260i
$147$		0			0
$148$	−0.882370	+	1.52831i	−0.0725304	+	0.125626i
$149$	−11.1061	−	6.41211i	−0.909847	−	0.525300i	−0.0294650	−	0.999566i	$-0.509380\pi$
$149$	−11.1061	−	6.41211i	−0.909847	−	0.525300i	−0.880382	+	0.474265i	$0.842714\pi$
$150$		0			0
$151$	−2.62759	−	4.55111i	−0.213830	−	0.370364i	0.739080	−	0.673618i	$-0.235260\pi$
$151$	−2.62759	−	4.55111i	−0.213830	−	0.370364i	−0.952910	+	0.303253i	$0.901927\pi$
$152$	−1.12909			−0.0915813
$153$		0			0
$154$		0			0
$155$	4.40547	−	2.54350i	0.353856	−	0.204299i
$156$		0			0
$157$	−6.91794	−	3.99407i	−0.552111	−	0.318762i	0.197862	−	0.980230i	$-0.436600\pi$
$157$	−6.91794	−	3.99407i	−0.552111	−	0.318762i	−0.749973	+	0.661468i	$0.769934\pi$
$158$	6.48946	+	3.74669i	0.516274	+	0.298071i
$159$		0			0
$160$	1.05823	−	0.610972i	0.0836608	−	0.0483016i
$161$		0			0
$162$		0			0
$163$	−11.5046			−0.901111			−0.450556	−	0.892748i	$-0.648774\pi$
$163$	−11.5046			−0.901111			−0.450556	+	0.892748i	$0.648774\pi$
$164$	−1.06198	−	1.83941i	−0.0829269	−	0.143634i
$165$		0			0
$166$	−11.2739	−	6.50901i	−0.875027	−	0.505197i
$167$	−8.38240	+	14.5187i	−0.648650	+	1.12349i	0.334796	+	0.942291i	$0.391333\pi$
$167$	−8.38240	+	14.5187i	−0.648650	+	1.12349i	−0.983446	+	0.181204i	$0.942001\pi$
$168$		0			0
$169$	−2.19222	−	3.79704i	−0.168632	−	0.292080i
$170$		−	6.32457i		−	0.485072i
$171$		0			0
$172$	3.60410			0.274810
$173$	0.856396	+	1.48332i	0.0651106	+	0.112775i	0.896743	−	0.442552i	$-0.145927\pi$
$173$	0.856396	+	1.48332i	0.0651106	+	0.112775i	−0.831632	+	0.555326i	$0.812593\pi$
$174$		0			0
$175$		0			0
$176$	−14.9180	−	8.61288i	−1.12448	−	0.649220i
$177$		0			0
$178$	−20.4548	+	11.8096i	−1.53315	+	0.885164i
$179$		−	14.3346i		−	1.07142i	−0.844402	−	0.535710i	$-0.820044\pi$
$179$		−	14.3346i		−	1.07142i	0.844402	−	0.535710i	$-0.179956\pi$
$180$		0			0
$181$		−	4.83147i		−	0.359121i	−0.983747	−	0.179560i	$-0.942532\pi$
$181$		−	4.83147i		−	0.359121i	0.983747	−	0.179560i	$-0.0574675\pi$
$182$		0			0
$183$		0			0
$184$	0.0723444	−	0.125304i	0.00533330	−	0.00923755i
$185$	−2.44167	+	4.22909i	−0.179515	+	0.310929i
$186$		0			0
$187$	−17.9662	+	10.3728i	−1.31382	+	0.758534i
$188$	0.270725			0.0197447
$189$		0			0
$190$	0.509437			0.0369584
$191$	−2.72114	+	1.57105i	−0.196895	+	0.113677i	−0.595206	−	0.803573i	$-0.702930\pi$
$191$	−2.72114	+	1.57105i	−0.196895	+	0.113677i	0.398311	+	0.917250i	$0.369596\pi$
$192$		0			0
$193$	−3.00508	+	5.20496i	−0.216311	+	0.374661i	−0.953677	−	0.300832i	$-0.902736\pi$
$193$	−3.00508	+	5.20496i	−0.216311	+	0.374661i	0.737367	+	0.675493i	$0.236069\pi$
$194$	−1.08251	+	1.87496i	−0.0777197	+	0.134615i
$195$		0			0
$196$		0			0
$197$		−	14.0902i		−	1.00388i	−0.864901	−	0.501942i	$-0.832619\pi$
$197$		−	14.0902i		−	1.00388i	0.864901	−	0.501942i	$-0.167381\pi$
$198$		0			0
$199$		−	7.90086i		−	0.560077i	−0.959989	−	0.280038i	$-0.909653\pi$
$199$		−	7.90086i		−	0.560077i	0.959989	−	0.280038i	$-0.0903472\pi$
$200$	−9.89060	+	5.71034i	−0.699371	+	0.403782i
$201$		0			0
$202$	−20.9531	−	12.0973i	−1.47426	−	0.851163i
$203$		0			0
$204$		0			0
$205$	−2.93869	−	5.08995i	−0.205247	−	0.355498i
$206$	25.4692			1.77453
$207$		0			0
$208$			13.1561i			0.912215i
$209$	−0.835517	−	1.44716i	−0.0577939	−	0.100102i
$210$		0			0
$211$	2.57821	−	4.46559i	0.177491	−	0.307424i	−0.763529	−	0.645773i	$-0.776535\pi$
$211$	2.57821	−	4.46559i	0.177491	−	0.307424i	0.941021	+	0.338349i	$0.109868\pi$
$212$	−1.81252	−	1.04646i	−0.124485	−	0.0718712i
$213$		0			0
$214$	2.93330	+	5.08062i	0.200516	+	0.347304i
$215$	9.97315			0.680164
$216$		0			0
$217$		0			0
$218$	−3.35457	+	1.93676i	−0.227200	+	0.131174i
$219$		0			0
$220$	0.724055	+	0.418033i	0.0488158	+	0.0281838i
$221$	13.7217	+	7.92220i	0.923019	+	0.532905i
$222$		0			0
$223$	−3.79823	+	2.19291i	−0.254348	+	0.146848i	−0.621754	−	0.783213i	$-0.713580\pi$
$223$	−3.79823	+	2.19291i	−0.254348	+	0.146848i	0.367405	+	0.930061i	$0.380246\pi$
$224$		0			0
$225$		0			0
$226$	17.0716			1.13559
$227$	−4.83697	−	8.37788i	−0.321041	−	0.556059i	0.659662	−	0.751562i	$-0.270699\pi$
$227$	−4.83697	−	8.37788i	−0.321041	−	0.556059i	−0.980703	+	0.195503i	$0.937366\pi$
$228$		0			0
$229$	−7.66705	−	4.42657i	−0.506653	−	0.292516i	0.224804	−	0.974404i	$-0.427826\pi$
$229$	−7.66705	−	4.42657i	−0.506653	−	0.292516i	−0.731457	+	0.681888i	$0.761159\pi$
$230$	−0.0326412	+	0.0565363i	−0.00215230	+	0.00372789i
$231$		0			0
$232$	0.281850	+	0.488179i	0.0185044	+	0.0320505i
$233$		−	12.8878i		−	0.844310i	−0.906524	−	0.422155i	$-0.861274\pi$
$233$		−	12.8878i		−	0.844310i	0.906524	−	0.422155i	$-0.138726\pi$
$234$		0			0
$235$	0.749143			0.0488687
$236$	0.438017	+	0.758668i	0.0285125	+	0.0493851i
$237$		0			0
$238$		0			0
$239$	−4.18421	−	2.41575i	−0.270654	−	0.156262i	0.358531	−	0.933518i	$-0.383278\pi$
$239$	−4.18421	−	2.41575i	−0.270654	−	0.156262i	−0.629185	+	0.777256i	$0.716611\pi$
$240$		0			0
$241$	8.68938	−	5.01681i	0.559732	−	0.323161i	−0.193306	−	0.981139i	$-0.561921\pi$
$241$	8.68938	−	5.01681i	0.559732	−	0.323161i	0.753038	+	0.657977i	$0.228588\pi$
$242$		−	5.69319i		−	0.365972i
$243$		0			0
$244$			0.976932i			0.0625417i
$245$		0			0
$246$		0			0
$247$	−0.638125	+	1.10526i	−0.0406029	+	0.0703263i
$248$	−8.51284	+	14.7447i	−0.540566	+	0.936288i
$249$		0			0
$250$	9.53594	−	5.50558i	0.603106	−	0.348203i
$251$	−7.98203			−0.503821			−0.251911	−	0.967751i	$-0.581059\pi$
$251$	−7.98203			−0.503821			−0.251911	+	0.967751i	$0.581059\pi$
$252$		0			0
$253$	0.214137			0.0134627
$254$	3.47424	−	2.00586i	0.217993	−	0.125859i
$255$		0			0
$256$	−3.30160	+	5.71853i	−0.206350	+	0.357408i
$257$	1.34115	−	2.32294i	0.0836585	−	0.144901i	−0.821160	−	0.570698i	$-0.806673\pi$
$257$	1.34115	−	2.32294i	0.0836585	−	0.144901i	0.904819	+	0.425797i	$0.140006\pi$
$258$		0			0
$259$		0			0
$260$		−	0.638544i		−	0.0396008i
$261$		0			0
$262$		−	12.4375i		−	0.768390i
$263$	−20.2961	+	11.7179i	−1.25151	+	0.722560i	−0.971409	−	0.237411i	$-0.923701\pi$
$263$	−20.2961	+	11.7179i	−1.25151	+	0.722560i	−0.280101	+	0.959971i	$0.590368\pi$
$264$		0			0
$265$	−5.01556	−	2.89573i	−0.308103	−	0.177883i
$266$		0			0
$267$		0			0
$268$	−0.589059	−	1.02028i	−0.0359825	−	0.0623236i
$269$	3.97910			0.242610			0.121305	−	0.992615i	$-0.461292\pi$
$269$	3.97910			0.242610			0.121305	+	0.992615i	$0.461292\pi$
$270$		0			0
$271$		−	12.5058i		−	0.759671i	−0.925054	−	0.379836i	$-0.875981\pi$
$271$		−	12.5058i		−	0.759671i	0.925054	−	0.379836i	$-0.124019\pi$
$272$	12.0974	+	20.9533i	0.733511	+	1.27048i
$273$		0			0
$274$	13.0828	−	22.6601i	0.790363	−	1.36895i
$275$	−14.6379	−	8.45120i	−0.882699	−	0.509626i
$276$		0			0
$277$	9.84547	+	17.0529i	0.591557	+	1.02461i	0.994023	+	0.109172i	$0.0348199\pi$
$277$	9.84547	+	17.0529i	0.591557	+	1.02461i	−0.402466	+	0.915435i	$0.631847\pi$
$278$	9.54988			0.572764
$279$		0			0
$280$		0			0
$281$	−7.03456	+	4.06141i	−0.419647	+	0.242283i	−0.694926	−	0.719081i	$-0.744563\pi$
$281$	−7.03456	+	4.06141i	−0.419647	+	0.242283i	0.275279	+	0.961364i	$0.411230\pi$
$282$		0			0
$283$	1.16390	+	0.671978i	0.0691867	+	0.0399450i	0.534194	−	0.845362i	$-0.320615\pi$
$283$	1.16390	+	0.671978i	0.0691867	+	0.0399450i	−0.465008	+	0.885307i	$0.653948\pi$
$284$	0.851847	+	0.491814i	0.0505478	+	0.0291838i
$285$		0			0
$286$	−14.7526	+	8.51741i	−0.872339	+	0.503645i
$287$		0			0
$288$		0			0
$289$	12.1386			0.714034
$290$	−0.127169	−	0.220262i	−0.00746760	−	0.0129343i
$291$		0			0
$292$	−1.97936	−	1.14279i	−0.115834	−	0.0668765i
$293$	−10.6300	+	18.4117i	−0.621012	+	1.07562i	0.368285	+	0.929713i	$0.379945\pi$
$293$	−10.6300	+	18.4117i	−0.621012	+	1.07562i	−0.989298	+	0.145912i	$0.953388\pi$
$294$		0			0
$295$	1.21207	+	2.09936i	0.0705693	+	0.122230i
$296$		−	16.3440i		−	0.949978i
$297$		0			0
$298$	−19.3658			−1.12183
$299$	−0.0817733	−	0.141636i	−0.00472907	−	0.00819100i
$300$		0			0
$301$		0			0
$302$	−6.87261	−	3.96790i	−0.395474	−	0.228327i
$303$		0			0
$304$	−1.68776	+	0.974430i	−0.0967998	+	0.0558874i
$305$			2.70334i			0.154793i
$306$		0			0
$307$		−	13.2098i		−	0.753925i	−0.926229	−	0.376962i	$-0.876969\pi$
$307$		−	13.2098i		−	0.753925i	0.926229	−	0.376962i	$-0.123031\pi$
$308$		0			0
$309$		0			0
$310$	3.84093	−	6.65268i	0.218150	−	0.377847i
$311$	10.2687	−	17.7859i	0.582283	−	1.00854i	−0.412925	−	0.910765i	$-0.635493\pi$
$311$	10.2687	−	17.7859i	0.582283	−	1.00854i	0.995208	−	0.0977785i	$-0.0311737\pi$
$312$		0			0
$313$	14.2976	−	8.25471i	0.808147	−	0.466584i	−0.0381649	−	0.999271i	$-0.512151\pi$
$313$	14.2976	−	8.25471i	0.808147	−	0.466584i	0.846312	+	0.532688i	$0.178818\pi$
$314$	−12.0629			−0.680746
$315$		0			0
$316$	1.39133			0.0782685
$317$	8.11112	−	4.68296i	0.455566	−	0.263021i	−0.254612	−	0.967043i	$-0.581948\pi$
$317$	8.11112	−	4.68296i	0.455566	−	0.263021i	0.710178	+	0.704022i	$0.248614\pi$
$318$		0			0
$319$	−0.417133	+	0.722496i	−0.0233550	+	0.0404520i
$320$	−2.55497	+	4.42534i	−0.142827	+	0.247384i
$321$		0			0
$322$		0			0
$323$			2.34708i			0.130595i
$324$		0			0
$325$			12.9092i			0.716072i
$326$	−15.0455	+	8.68653i	−0.833294	+	0.481102i
$327$		0			0
$328$	17.0356	+	9.83548i	0.940631	+	0.543074i
$329$		0			0
$330$		0			0
$331$	−14.4220	−	24.9796i	−0.792702	−	1.37300i	−0.924288	−	0.381696i	$-0.875340\pi$
$331$	−14.4220	−	24.9796i	−0.792702	−	1.37300i	0.131586	−	0.991305i	$-0.457993\pi$
$332$	−2.41712			−0.132656
$333$		0			0
$334$			25.3164i			1.38525i
$335$	−1.63003	−	2.82329i	−0.0890579	−	0.154253i
$336$		0			0
$337$	−6.26205	+	10.8462i	−0.341116	+	0.590829i	−0.984640	−	0.174596i	$-0.944138\pi$
$337$	−6.26205	+	10.8462i	−0.341116	+	0.590829i	0.643525	+	0.765425i	$0.277471\pi$
$338$	−5.73388	−	3.31046i	−0.311882	−	0.180065i
$339$		0			0
$340$	−0.587156	−	1.01698i	−0.0318430	−	0.0551537i
$341$	−25.1977			−1.36453
$342$		0			0
$343$		0			0
$344$	−28.9072	+	16.6896i	−1.55857	+	0.899841i
$345$		0			0
$346$	2.23996	+	1.29324i	0.120421	+	0.0695250i
$347$	24.8740	+	14.3610i	1.33531	+	0.770939i	0.986107	−	0.166109i	$-0.0531204\pi$
$347$	24.8740	+	14.3610i	1.33531	+	0.770939i	0.349199	+	0.937049i	$0.386454\pi$
$348$		0			0
$349$	−11.0854	+	6.40017i	−0.593389	+	0.342593i	−0.766436	−	0.642320i	$-0.777972\pi$
$349$	−11.0854	+	6.40017i	−0.593389	+	0.342593i	0.173048	+	0.984913i	$0.444639\pi$
$350$		0			0
$351$		0			0
$352$	−6.05272			−0.322611
$353$	13.4991	+	23.3811i	0.718485	+	1.24445i	0.961600	+	0.274455i	$0.0884975\pi$
$353$	13.4991	+	23.3811i	0.718485	+	1.24445i	−0.243115	+	0.969998i	$0.578169\pi$
$354$		0			0
$355$	2.35721	+	1.36093i	0.125108	+	0.0722309i
$356$	−2.19274	+	3.79793i	−0.116215	+	0.201290i
$357$		0			0
$358$	−10.8233	−	18.7465i	−0.572030	−	0.990785i
$359$			28.0210i			1.47889i	0.673217	+	0.739445i	$0.264912\pi$
$359$			28.0210i			1.47889i	−0.673217	+	0.739445i	$0.735088\pi$
$360$		0			0
$361$	18.8109			0.990050
$362$	−3.64799	−	6.31851i	−0.191734	−	0.332093i
$363$		0			0
$364$		0			0
$365$	−5.47724	−	3.16228i	−0.286692	−	0.165522i
$366$		0			0
$367$	28.9584	−	16.7191i	1.51161	−	0.872731i	0.511706	−	0.859160i	$-0.329014\pi$
$367$	28.9584	−	16.7191i	1.51161	−	0.872731i	0.999908	−	0.0135705i	$-0.00431975\pi$
$368$		−	0.249739i		−	0.0130186i
$369$		0			0
$370$			7.37430i			0.383372i
$371$		0			0
$372$		0			0
$373$	3.98403	−	6.90053i	0.206285	−	0.357296i	−0.744256	−	0.667894i	$-0.767196\pi$
$373$	3.98403	−	6.90053i	0.206285	−	0.357296i	0.950541	+	0.310598i	$0.100529\pi$
$374$	−15.6639	+	27.1307i	−0.809961	+	1.40289i
$375$		0			0
$376$	−2.17139	+	1.25365i	−0.111981	+	0.0646522i
$377$	0.637169			0.0328159
$378$		0			0
$379$	3.88714			0.199669			0.0998345	−	0.995004i	$-0.468169\pi$
$379$	3.88714			0.199669			0.0998345	+	0.995004i	$0.468169\pi$
$380$	0.0819169	−	0.0472948i	0.00420225	−	0.00242617i
$381$		0			0
$382$	−2.37244	+	4.10918i	−0.121384	+	0.210244i
$383$	−6.34150	+	10.9838i	−0.324036	+	0.561246i	−0.981317	−	0.192399i	$-0.938373\pi$
$383$	−6.34150	+	10.9838i	−0.324036	+	0.561246i	0.657281	+	0.753646i	$0.271706\pi$
$384$		0			0
$385$		0			0
$386$			9.07592i			0.461952i
$387$		0			0
$388$			0.401989i			0.0204079i
$389$	17.8067	−	10.2807i	0.902835	−	0.521252i	0.0247163	−	0.999695i	$-0.492132\pi$
$389$	17.8067	−	10.2807i	0.902835	−	0.521252i	0.878119	+	0.478442i	$0.158798\pi$
$390$		0			0
$391$	−0.260474	−	0.150385i	−0.0131727	−	0.00760529i
$392$		0			0
$393$		0			0
$394$	−10.6388	−	18.4269i	−0.535973	−	0.928332i
$395$	3.85005			0.193717
$396$		0			0
$397$		−	14.9703i		−	0.751336i	−0.926754	−	0.375668i	$-0.877413\pi$
$397$		−	14.9703i		−	0.751336i	0.926754	−	0.375668i	$-0.122587\pi$
$398$	−5.96552	−	10.3326i	−0.299025	−	0.517926i
$399$		0			0
$400$	−9.85630	+	17.0716i	−0.492815	+	0.853580i
$401$	8.93429	+	5.15821i	0.446157	+	0.257589i	0.706206	−	0.708007i	$-0.250405\pi$
$401$	8.93429	+	5.15821i	0.446157	+	0.257589i	−0.260049	+	0.965595i	$0.583739\pi$
$402$		0			0
$403$	9.62235	+	16.6664i	0.479323	+	0.830212i
$404$	−4.49232			−0.223502
$405$		0			0
$406$		0			0
$407$	20.9482	−	12.0944i	1.03836	−	0.599499i
$408$		0			0
$409$	−16.0387	−	9.25995i	−0.793063	−	0.457875i	0.0479769	−	0.998848i	$-0.484723\pi$
$409$	−16.0387	−	9.25995i	−0.793063	−	0.457875i	−0.841040	+	0.540973i	$0.818056\pi$
$410$	−7.68631	−	4.43769i	−0.379600	−	0.219162i
$411$		0			0
$412$	4.09543	−	2.36450i	0.201767	−	0.116490i
$413$		0			0
$414$		0			0
$415$	−6.68857			−0.328329
$416$	2.31138	+	4.00342i	0.113325	+	0.196284i
$417$		0			0
$418$	−2.18535	−	1.26171i	−0.106889	−	0.0617122i
$419$	6.37677	−	11.0449i	0.311526	−	0.539578i	−0.667167	−	0.744908i	$-0.732493\pi$
$419$	6.37677	−	11.0449i	0.311526	−	0.539578i	0.978693	+	0.205330i	$0.0658267\pi$
$420$		0			0
$421$	6.78793	+	11.7570i	0.330824	+	0.573003i	0.982674	−	0.185345i	$-0.0593402\pi$
$421$	6.78793	+	11.7570i	0.330824	+	0.573003i	−0.651850	+	0.758348i	$0.726007\pi$
$422$		−	7.78668i		−	0.379050i
$423$		0			0
$424$	19.3835			0.941344
$425$	11.8703	+	20.5599i	0.575793	+	0.997303i
$426$		0			0
$427$		0			0
$428$	0.943342	+	0.544639i	0.0455982	+	0.0263261i
$429$		0			0
$430$	13.0427	−	7.53020i	0.628975	−	0.363139i
$431$			36.1500i			1.74129i	0.491915	+	0.870643i	$0.336297\pi$
$431$			36.1500i			1.74129i	−0.491915	+	0.870643i	$0.663703\pi$
$432$		0			0
$433$		−	33.0085i		−	1.58629i	−0.609034	−	0.793144i	$-0.708443\pi$
$433$		−	33.0085i		−	1.58629i	0.609034	−	0.793144i	$-0.291557\pi$
$434$		0			0
$435$		0			0
$436$	−0.359608	+	0.622859i	−0.0172221	+	0.0298295i
$437$	0.0121133	−	0.0209809i	0.000579459	−	0.00100365i
$438$		0			0
$439$	26.4673	−	15.2809i	1.26321	−	0.729317i	0.289519	−	0.957172i	$-0.406505\pi$
$439$	26.4673	−	15.2809i	1.26321	−	0.729317i	0.973695	+	0.227856i	$0.0731714\pi$
$440$	−7.74318			−0.369141
$441$		0			0
$442$	23.9266			1.13807
$443$	−17.9290	+	10.3513i	−0.851833	+	0.491806i	−0.861269	−	0.508150i	$-0.830330\pi$
$443$	−17.9290	+	10.3513i	−0.851833	+	0.491806i	0.00943615	+	0.999955i	$0.496996\pi$
$444$		0			0
$445$	−6.06767	+	10.5095i	−0.287635	+	0.498199i
$446$	−3.31150	+	5.73569i	−0.156804	+	0.271593i
$447$		0			0
$448$		0			0
$449$			6.40243i			0.302150i	0.988522	+	0.151075i	$0.0482734\pi$
$449$			6.40243i			0.302150i	−0.988522	+	0.151075i	$0.951727\pi$
$450$		0			0
$451$			29.1127i			1.37086i
$452$	2.74510	−	1.58489i	0.129119	−	0.0745467i
$453$		0			0
$454$	−12.6514	−	7.30428i	−0.593759	−	0.342807i
$455$		0			0
$456$		0			0
$457$	1.57340	+	2.72521i	0.0736007	+	0.127480i	0.900477	−	0.434904i	$-0.143218\pi$
$457$	1.57340	+	2.72521i	0.0736007	+	0.127480i	−0.826876	+	0.562384i	$0.809884\pi$
$458$	−13.3691			−0.624696
$459$		0			0
$460$			0.0121213i			0.000565159i
$461$	7.44225	+	12.8904i	0.346620	+	0.600364i	0.985647	−	0.168821i	$-0.0539959\pi$
$461$	7.44225	+	12.8904i	0.346620	+	0.600364i	−0.639026	+	0.769185i	$0.720663\pi$
$462$		0			0
$463$	13.3616	−	23.1429i	0.620964	−	1.07554i	−0.368342	−	0.929690i	$-0.620075\pi$
$463$	13.3616	−	23.1429i	0.620964	−	1.07554i	0.989307	−	0.145851i	$-0.0465921\pi$
$464$	0.842618	+	0.486486i	0.0391175	+	0.0225845i
$465$		0			0
$466$	−9.73092	−	16.8544i	−0.450776	−	0.780767i
$467$	24.7934			1.14730			0.573650	−	0.819100i	$-0.305527\pi$
$467$	24.7934			1.14730			0.573650	+	0.819100i	$0.305527\pi$
$468$		0			0
$469$		0			0
$470$	0.979714	−	0.565638i	0.0451908	−	0.0260909i
$471$		0			0
$472$	−7.02636	−	4.05667i	−0.323414	−	0.186723i
$473$	−42.7821	−	24.7003i	−1.96712	−	1.13572i
$474$		0			0
$475$	−1.65608	+	0.956138i	−0.0759861	+	0.0438706i
$476$		0			0
$477$		0			0
$478$	−7.29603			−0.333713
$479$	−6.26354	−	10.8488i	−0.286189	−	0.495693i	0.686708	−	0.726933i	$-0.259055\pi$
$479$	−6.26354	−	10.8488i	−0.286189	−	0.495693i	−0.972897	+	0.231240i	$0.925722\pi$
$480$		0			0
$481$	−15.9991	−	9.23711i	−0.729498	−	0.421176i
$482$	7.57587	−	13.1218i	0.345071	−	0.597681i
$483$		0			0
$484$	−0.528540	−	0.915459i	−0.0240246	−	0.0416118i
$485$			1.11237i			0.0505103i
$486$		0			0
$487$	−3.39496			−0.153840			−0.0769202	−	0.997037i	$-0.524509\pi$
$487$	−3.39496			−0.153840			−0.0769202	+	0.997037i	$0.524509\pi$
$488$	−4.52390	−	7.83562i	−0.204787	−	0.354702i
$489$		0			0
$490$		0			0
$491$	−0.780171	−	0.450432i	−0.0352086	−	0.0203277i	0.482292	−	0.876010i	$-0.339804\pi$
$491$	−0.780171	−	0.450432i	−0.0352086	−	0.0203277i	−0.517501	+	0.855683i	$0.673138\pi$
$492$		0			0
$493$	1.01479	−	0.585891i	0.0457040	−	0.0263872i
$494$			1.92726i			0.0867114i
$495$		0			0
$496$			29.3871i			1.31952i
$497$		0			0
$498$		0			0
$499$	−10.9344	+	18.9390i	−0.489492	+	0.847825i	−0.999927	−	0.0120916i	$-0.996151\pi$
$499$	−10.9344	+	18.9390i	−0.489492	+	0.847825i	0.510435	+	0.859916i	$0.329484\pi$
$500$	1.02225	−	1.77058i	0.0457162	−	0.0791829i
$501$		0			0
$502$	−10.4387	+	6.02681i	−0.465904	+	0.268990i
$503$	42.9876			1.91672			0.958362	−	0.285557i	$-0.0921785\pi$
$503$	42.9876			1.91672			0.958362	+	0.285557i	$0.0921785\pi$
$504$		0			0
$505$	−12.4310			−0.553173
$506$	0.280044	−	0.161684i	0.0124495	−	0.00718771i
$507$		0			0
$508$	0.372436	−	0.645079i	0.0165242	−	0.0286207i
$509$	15.0416	−	26.0528i	0.666708	−	1.15477i	−0.312111	−	0.950046i	$-0.601036\pi$
$509$	15.0416	−	26.0528i	0.666708	−	1.15477i	0.978819	−	0.204727i	$-0.0656305\pi$
$510$		0			0
$511$		0			0
$512$		−	16.2193i		−	0.716799i
$513$		0			0
$514$		−	4.05052i		−	0.178661i
$515$	11.3327	−	6.54296i	0.499380	−	0.288317i
$516$		0			0
$517$	−3.21362	−	1.85538i	−0.141335	−	0.0815997i
$518$		0			0
$519$		0			0
$520$	2.95692	+	5.12153i	0.129669	+	0.224594i
$521$	−12.0167			−0.526463			−0.263231	−	0.964733i	$-0.584788\pi$
$521$	−12.0167			−0.526463			−0.263231	+	0.964733i	$0.584788\pi$
$522$		0			0
$523$			18.6120i			0.813847i	0.913462	+	0.406924i	$0.133399\pi$
$523$			18.6120i			0.813847i	−0.913462	+	0.406924i	$0.866601\pi$
$524$	−1.15466	−	1.99993i	−0.0504417	−	0.0873675i
$525$		0			0
$526$	−17.6952	+	30.6490i	−0.771548	+	1.33636i
$527$	30.6503	+	17.6959i	1.33515	+	0.770847i
$528$		0			0
$529$	−11.4984	−	19.9159i	−0.499933	−	0.865909i
$530$	−8.74566			−0.379887
$531$		0			0
$532$		0			0
$533$	19.2559	−	11.1174i	0.834064	−	0.481547i
$534$		0			0
$535$	2.61039	+	1.50711i	0.112857	+	0.0651580i
$536$	9.44926	+	5.45554i	0.408146	+	0.235643i
$537$		0			0
$538$	5.20379	−	3.00441i	0.224351	−	0.129529i
$539$		0			0
$540$		0			0
$541$	42.2484			1.81640			0.908201	−	0.418534i	$-0.137456\pi$
$541$	42.2484			1.81640			0.908201	+	0.418534i	$0.137456\pi$
$542$	−9.44245	−	16.3548i	−0.405588	−	0.702499i
$543$		0			0
$544$	7.36247	+	4.25072i	0.315663	+	0.182248i
$545$	−0.995095	+	1.72356i	−0.0426252	+	0.0738290i
$546$		0			0
$547$	−6.92349	−	11.9918i	−0.296027	−	0.512734i	0.679196	−	0.733957i	$-0.262329\pi$
$547$	−6.92349	−	11.9918i	−0.296027	−	0.512734i	−0.975223	+	0.221223i	$0.928995\pi$
$548$		−	4.85830i		−	0.207536i
$549$		0			0
$550$	−25.5242			−1.08836
$551$	0.0471929	+	0.0817405i	0.00201049	+	0.00348226i
$552$		0			0
$553$		0			0
$554$	25.7514	+	14.8676i	1.09407	+	0.631664i
$555$		0			0
$556$	1.53561	−	0.886585i	0.0651244	−	0.0375996i
$557$		−	31.4431i		−	1.33229i	−0.745824	−	0.666143i	$-0.767944\pi$
$557$		−	31.4431i		−	1.33229i	0.745824	−	0.666143i	$-0.232056\pi$
$558$		0			0
$559$			37.7296i			1.59579i
$560$		0			0
$561$		0			0
$562$	−6.13311	+	10.6229i	−0.258710	+	0.448098i
$563$	17.0829	−	29.5884i	0.719956	−	1.24700i	−0.241060	−	0.970510i	$-0.577495\pi$
$563$	17.0829	−	29.5884i	0.719956	−	1.24700i	0.961017	−	0.276491i	$-0.0891716\pi$
$564$		0			0
$565$	7.59616	−	4.38565i	0.319573	−	0.184506i
$566$	2.02950			0.0853063
$567$		0			0
$568$	−9.10981			−0.382239
$569$	19.6652	−	11.3537i	0.824407	−	0.475972i	−0.0275266	−	0.999621i	$-0.508763\pi$
$569$	19.6652	−	11.3537i	0.824407	−	0.475972i	0.851934	+	0.523649i	$0.175430\pi$
$570$		0			0
$571$	5.29931	−	9.17867i	0.221769	−	0.384116i	−0.733576	−	0.679607i	$-0.762150\pi$
$571$	5.29931	−	9.17867i	0.221769	−	0.384116i	0.955345	+	0.295492i	$0.0954835\pi$
$572$	−1.58147	+	2.73918i	−0.0661245	+	0.114531i
$573$		0			0
$574$		0			0
$575$		−	0.245051i		−	0.0102193i
$576$		0			0
$577$		−	14.5749i		−	0.606761i	−0.952869	−	0.303381i	$-0.901885\pi$
$577$		−	14.5749i		−	0.606761i	0.952869	−	0.303381i	$-0.0981153\pi$
$578$	15.8746	−	9.16520i	0.660296	−	0.381222i
$579$		0			0
$580$	−0.0408971	−	0.0236120i	−0.00169816	−	0.000980434i
$581$		0			0
$582$		0			0
$583$	14.3436	+	24.8438i	0.594050	+	1.02893i
$584$	21.1677			0.875925
$585$		0			0
$586$			32.1047i			1.32623i
$587$	−15.0927	−	26.1414i	−0.622944	−	1.07897i	−0.988935	−	0.148352i	$-0.952603\pi$
$587$	−15.0927	−	26.1414i	−0.622944	−	1.07897i	0.365991	−	0.930619i	$-0.380730\pi$
$588$		0			0
$589$	−1.42539	+	2.46884i	−0.0587321	+	0.101727i
$590$	3.17024	+	1.83034i	0.130517	+	0.0753538i
$591$		0			0
$592$	−14.1053	−	24.4310i	−0.579723	−	1.00411i
$593$	−30.5822			−1.25586			−0.627930	−	0.778270i	$-0.716098\pi$
$593$	−30.5822			−1.25586			−0.627930	+	0.778270i	$0.716098\pi$
$594$		0			0
$595$		0			0
$596$	−3.11400	+	1.79787i	−0.127554	+	0.0736435i
$597$		0			0
$598$	−0.213883	−	0.123485i	−0.00874633	−	0.00504970i
$599$	2.33872	+	1.35026i	0.0955573	+	0.0551701i	0.547017	−	0.837121i	$-0.315763\pi$
$599$	2.33872	+	1.35026i	0.0955573	+	0.0551701i	−0.451460	+	0.892291i	$0.649097\pi$
$600$		0			0
$601$	21.0197	−	12.1357i	0.857411	−	0.495026i	−0.00573343	−	0.999984i	$-0.501825\pi$
$601$	21.0197	−	12.1357i	0.857411	−	0.495026i	0.863144	+	0.504957i	$0.168492\pi$
$602$		0			0
$603$		0			0
$604$	−1.47348			−0.0599550
$605$	−1.46256	−	2.53323i	−0.0594616	−	0.102990i
$606$		0			0
$607$	−18.5486	−	10.7090i	−0.752865	−	0.434667i	0.0738631	−	0.997268i	$-0.476467\pi$
$607$	−18.5486	−	10.7090i	−0.752865	−	0.434667i	−0.826728	+	0.562601i	$0.809801\pi$
$608$	−0.342391	+	0.593039i	−0.0138858	+	0.0240509i
$609$		0			0
$610$	2.04115	+	3.53537i	0.0826437	+	0.143143i
$611$			2.83409i			0.114655i
$612$		0			0
$613$	5.90612			0.238546			0.119273	−	0.992862i	$-0.461944\pi$
$613$	5.90612			0.238546			0.119273	+	0.992862i	$0.461944\pi$
$614$	−9.97404	−	17.2756i	−0.402520	−	0.697185i
$615$		0			0
$616$		0			0
$617$	1.19246	+	0.688465i	0.0480065	+	0.0277166i	0.523811	−	0.851834i	$-0.324510\pi$
$617$	1.19246	+	0.688465i	0.0480065	+	0.0277166i	−0.475805	+	0.879551i	$0.657843\pi$
$618$		0			0
$619$	−29.2918	+	16.9116i	−1.17734	+	0.679736i	−0.955397	−	0.295324i	$-0.904572\pi$
$619$	−29.2918	+	16.9116i	−1.17734	+	0.679736i	−0.221941	+	0.975060i	$0.571239\pi$
$620$		−	1.42633i		−	0.0572826i
$621$		0			0
$622$		−	31.0133i		−	1.24352i
$623$		0			0
$624$		0			0
$625$	−8.16631	+	14.1445i	−0.326652	+	0.565779i
$626$	12.4654	−	21.5907i	0.498218	−	0.862938i
$627$		0			0
$628$	−1.93969	+	1.11988i	−0.0774022	+	0.0446882i
$629$	−33.9749			−1.35467
$630$		0			0
$631$	−25.0205			−0.996049			−0.498024	−	0.867163i	$-0.665941\pi$
$631$	−25.0205			−0.996049			−0.498024	+	0.867163i	$0.665941\pi$
$632$	−11.1594	+	6.44287i	−0.443896	+	0.256283i
$633$		0			0
$634$	7.07171	−	12.2486i	0.280853	−	0.486452i
$635$	1.03059	−	1.78504i	0.0408979	−	0.0708373i
$636$		0			0
$637$		0			0
$638$			1.25982i			0.0498768i
$639$		0			0
$640$			10.1604i			0.401625i
$641$	9.25173	−	5.34149i	0.365421	−	0.210976i	−0.306035	−	0.952020i	$-0.599002\pi$
$641$	9.25173	−	5.34149i	0.365421	−	0.210976i	0.671456	+	0.741044i	$0.265669\pi$
$642$		0			0
$643$	38.1128	+	22.0044i	1.50302	+	0.867771i	0.999994	+	0.00350106i	$0.00111442\pi$
$643$	38.1128	+	22.0044i	1.50302	+	0.867771i	0.503029	+	0.864270i	$0.332219\pi$
$644$		0			0
$645$		0			0
$646$	1.77216	+	3.06946i	0.0697246	+	0.120766i
$647$	−47.0086			−1.84810			−0.924050	−	0.382272i	$-0.875142\pi$
$647$	−47.0086			−1.84810			−0.924050	+	0.382272i	$0.875142\pi$
$648$		0			0
$649$		−	12.0076i		−	0.471339i
$650$	9.74704	+	16.8824i	0.382310	+	0.662181i
$651$		0			0
$652$	−1.61287	+	2.79357i	−0.0631648	+	0.109405i
$653$	−29.3918	−	16.9694i	−1.15019	−	0.664063i	−0.201257	−	0.979538i	$-0.564503\pi$
$653$	−29.3918	−	16.9694i	−1.15019	−	0.664063i	−0.948934	+	0.315475i	$0.897836\pi$
$654$		0			0
$655$	−3.19515	−	5.53416i	−0.124845	−	0.216237i
$656$	33.9530			1.32564
$657$		0			0
$658$		0			0
$659$	1.36652	−	0.788962i	0.0532322	−	0.0307336i	−0.473148	−	0.880983i	$-0.656882\pi$
$659$	1.36652	−	0.788962i	0.0532322	−	0.0307336i	0.526380	+	0.850249i	$0.323549\pi$
$660$		0			0
$661$	2.08470	+	1.20360i	0.0810854	+	0.0468147i	0.539994	−	0.841669i	$-0.318426\pi$
$661$	2.08470	+	1.20360i	0.0810854	+	0.0468147i	−0.458909	+	0.888483i	$0.651760\pi$
$662$	−37.7215	−	21.7785i	−1.46609	−	0.846446i
$663$		0			0
$664$	19.3868	−	11.1930i	0.752354	−	0.434372i
$665$		0			0
$666$		0			0
$667$	−0.0120952			−0.000468328
$668$	2.35031	+	4.07086i	0.0909363	+	0.157506i
$669$		0			0
$670$	−4.26344	−	2.46150i	−0.164711	−	0.0950959i
$671$	6.69529	−	11.5966i	0.258469	−	0.447681i
$672$		0			0
$673$	12.1767	+	21.0906i	0.469377	+	0.812984i	0.999387	−	0.0350069i	$-0.0111453\pi$
$673$	12.1767	+	21.0906i	0.469377	+	0.812984i	−0.530010	+	0.847991i	$0.677812\pi$
$674$			18.9126i			0.728485i
$675$		0			0
$676$	−1.22934			−0.0472822
$677$	−4.83847	−	8.38048i	−0.185958	−	0.322088i	0.757941	−	0.652323i	$-0.226205\pi$
$677$	−4.83847	−	8.38048i	−0.185958	−	0.322088i	−0.943899	+	0.330235i	$0.892872\pi$
$678$		0			0
$679$		0			0
$680$	9.41873	+	5.43791i	0.361192	+	0.208534i
$681$		0			0
$682$	−32.9531	+	19.0255i	−1.26184	+	0.728522i
$683$			21.5167i			0.823315i	0.911339	+	0.411658i	$0.135050\pi$
$683$			21.5167i			0.823315i	−0.911339	+	0.411658i	$0.864950\pi$
$684$		0			0
$685$		−	13.4437i		−	0.513659i
$686$		0			0
$687$		0			0
$688$	−28.8069	+	49.8951i	−1.09825	+	1.90223i
$689$	10.9549	−	18.9744i	0.417348	−	0.722868i
$690$		0			0
$691$	−25.4980	+	14.7213i	−0.969989	+	0.560023i	−0.899233	−	0.437470i	$-0.855874\pi$
$691$	−25.4980	+	14.7213i	−0.969989	+	0.560023i	−0.0707559	+	0.997494i	$0.522541\pi$
$692$	0.480244			0.0182561
$693$		0			0
$694$	43.3730			1.64642
$695$	4.24929	−	2.45333i	0.161185	−	0.0930602i
$696$		0			0
$697$	20.4454	−	35.4124i	0.774423	−	1.34134i
$698$	−9.66486	+	16.7400i	−0.365820	+	0.633619i
$699$		0			0
$700$		0			0
$701$			40.4325i			1.52712i	0.645740	+	0.763558i	$0.276549\pi$
$701$			40.4325i			1.52712i	−0.645740	+	0.763558i	$0.723451\pi$
$702$		0			0
$703$		−	2.73664i		−	0.103214i
$704$	21.9203	−	12.6557i	0.826151	−	0.476979i
$705$		0			0
$706$	35.3077	+	20.3849i	1.32882	+	0.767197i
$707$		0			0
$708$		0			0
$709$	7.95114	+	13.7718i	0.298611	+	0.517210i	0.975818	−	0.218582i	$-0.0701433\pi$
$709$	7.95114	+	13.7718i	0.298611	+	0.517210i	−0.677207	+	0.735792i	$0.736810\pi$
$710$	4.11028			0.154256
$711$		0			0
$712$		−	40.6158i		−	1.52214i
$713$	−0.182658	−	0.316373i	−0.00684061	−	0.0118483i
$714$		0			0
$715$	−4.37619	+	7.57978i	−0.163660	+	0.283468i
$716$	−3.48076	−	2.00962i	−0.130082	−	0.0751028i
$717$		0			0
$718$	21.1572	+	36.6453i	0.789578	+	1.36759i
$719$	26.0976			0.973277			0.486638	−	0.873603i	$-0.338223\pi$
$719$	26.0976			0.973277			0.486638	+	0.873603i	$0.338223\pi$
$720$		0			0
$721$		0			0
$722$	24.6006	−	14.2032i	0.915539	−	0.528587i
$723$		0			0
$724$	−1.17319	−	0.677340i	−0.0436011	−	0.0251731i
$725$	0.826800	+	0.477353i	0.0307066	+	0.0177285i
$726$		0			0
$727$	−3.74533	+	2.16237i	−0.138907	+	0.0801977i	−0.567843	−	0.823137i	$-0.692222\pi$
$727$	−3.74533	+	2.16237i	−0.138907	+	0.0801977i	0.428936	+	0.903335i	$0.358889\pi$
$728$		0			0
$729$		0			0
$730$	−9.55070			−0.353487
$731$	34.6932	+	60.0904i	1.28317	+	2.22252i
$732$		0			0
$733$	36.6480	+	21.1587i	1.35362	+	0.781515i	0.988755	−	0.149544i	$-0.0477805\pi$
$733$	36.6480	+	21.1587i	1.35362	+	0.781515i	0.364869	+	0.931059i	$0.381114\pi$
$734$	25.2475	−	43.7299i	0.931901	−	1.61410i
$735$		0			0
$736$	−0.0438762	−	0.0759958i	−0.00161730	−	0.00280124i
$737$			16.1482i			0.594826i
$738$		0			0
$739$	−3.24241			−0.119274			−0.0596369	−	0.998220i	$-0.518994\pi$
$739$	−3.24241			−0.119274			−0.0596369	+	0.998220i	$0.518994\pi$
$740$	0.684610	+	1.18578i	0.0251668	+	0.0435901i
$741$		0			0
$742$		0			0
$743$	−5.41770	−	3.12791i	−0.198756	−	0.114752i	0.397319	−	0.917681i	$-0.369941\pi$
$743$	−5.41770	−	3.12791i	−0.198756	−	0.114752i	−0.596075	+	0.802929i	$0.703274\pi$
$744$		0			0
$745$	−8.61696	+	4.97500i	−0.315701	+	0.182270i
$746$		−	12.0325i		−	0.440542i
$747$		0			0
$748$			5.81678i			0.212682i
$749$		0			0
$750$		0			0
$751$	9.45315	−	16.3733i	0.344950	−	0.597471i	−0.640395	−	0.768046i	$-0.721229\pi$
$751$	9.45315	−	16.3733i	0.344950	−	0.597471i	0.985345	+	0.170575i	$0.0545625\pi$
$752$	−2.16386	+	3.74791i	−0.0789078	+	0.136672i
$753$		0			0
$754$	0.833277	−	0.481093i	0.0303462	−	0.0175204i
$755$	−4.07736			−0.148390
$756$		0			0
$757$	−40.7873			−1.48244			−0.741220	−	0.671262i	$-0.765752\pi$
$757$	−40.7873			−1.48244			−0.741220	+	0.671262i	$0.765752\pi$
$758$	5.08353	−	2.93498i	0.184642	−	0.106603i
$759$		0			0
$760$	−0.438017	+	0.758668i	−0.0158886	+	0.0275198i
$761$	21.3106	−	36.9110i	0.772508	−	1.33802i	−0.163676	−	0.986514i	$-0.552335\pi$
$761$	21.3106	−	36.9110i	0.772508	−	1.33802i	0.936184	−	0.351509i	$-0.114331\pi$
$762$		0			0
$763$		0			0
$764$			0.881003i			0.0318736i
$765$		0			0
$766$			19.1525i			0.692009i
$767$	−7.94213	+	4.58539i	−0.286774	+	0.165569i
$768$		0			0
$769$	0.932209	+	0.538211i	0.0336163	+	0.0194084i	0.516714	−	0.856158i	$-0.327155\pi$
$769$	0.932209	+	0.538211i	0.0336163	+	0.0194084i	−0.483098	+	0.875566i	$0.660488\pi$
$770$		0			0
$771$		0			0
$772$	0.842584	+	1.45940i	0.0303253	+	0.0525249i
$773$	−5.93711			−0.213543			−0.106771	−	0.994284i	$-0.534051\pi$
$773$	−5.93711			−0.213543			−0.106771	+	0.994284i	$0.534051\pi$
$774$		0			0
$775$			28.8354i			1.03580i
$776$	−1.86150	−	3.22421i	−0.0668240	−	0.115742i
$777$		0			0
$778$	15.5248	−	26.8898i	0.556592	−	0.964046i
$779$	2.85243	+	1.64685i	0.102199	+	0.0590046i
$780$		0			0
$781$	−6.74118	−	11.6761i	−0.241218	−	0.417802i
$782$	−0.454191			−0.0162418
$783$		0			0
$784$		0			0
$785$	−5.36746	+	3.09891i	−0.191573	+	0.110605i
$786$		0			0
$787$	−7.65434	−	4.41923i	−0.272848	−	0.157529i	0.357333	−	0.933977i	$-0.383686\pi$
$787$	−7.65434	−	4.41923i	−0.272848	−	0.157529i	−0.630181	+	0.776448i	$0.717019\pi$
$788$	−3.42140	−	1.97535i	−0.121882	−	0.0703688i
$789$		0			0
$790$	5.03502	−	2.90697i	0.179138	−	0.103425i
$791$		0			0
$792$		0			0
$793$	−10.2270			−0.363172
$794$	−11.3033	−	19.5778i	−0.401138	−	0.694791i
$795$		0			0
$796$	−1.91850	−	1.10765i	−0.0679994	−	0.0392595i
$797$	19.0123	−	32.9303i	0.673450	−	1.16645i	−0.303469	−	0.952841i	$-0.598145\pi$
$797$	19.0123	−	32.9303i	0.673450	−	1.16645i	0.976919	−	0.213609i	$-0.0685218\pi$
$798$		0			0
$799$	2.60601	+	4.51374i	0.0921940	+	0.159685i
$800$			6.92653i			0.244890i
$801$		0			0
$802$	15.5788			0.550106
$803$	15.6639	+	27.1307i	0.552767	+	0.957421i
$804$		0			0
$805$		0			0
$806$	25.1678	+	14.5307i	0.886499	+	0.511821i
$807$		0			0
$808$	36.0313	−	20.8027i	1.26758	−	0.731836i
$809$			16.9244i			0.595031i	0.954717	+	0.297516i	$0.0961581\pi$
$809$			16.9244i			0.595031i	−0.954717	+	0.297516i	$0.903842\pi$
$810$		0			0
$811$		−	26.9840i		−	0.947536i	−0.880650	−	0.473768i	$-0.842894\pi$
$811$		−	26.9840i		−	0.947536i	0.880650	−	0.473768i	$-0.157106\pi$
$812$		0			0
$813$		0			0
$814$	18.2637	−	31.6337i	0.640144	−	1.10876i
$815$	−4.46308	+	7.73028i	−0.156335	+	0.270780i
$816$		0			0
$817$	−4.84021	+	2.79450i	−0.169338	+	0.0977671i
$818$	−27.9668			−0.977836
$819$		0			0
$820$	−1.64793			−0.0575484
$821$	27.7572	−	16.0256i	0.968732	−	0.559297i	0.0698823	−	0.997555i	$-0.477738\pi$
$821$	27.7572	−	16.0256i	0.968732	−	0.559297i	0.898849	+	0.438258i	$0.144404\pi$
$822$		0			0
$823$	−10.3974	+	18.0089i	−0.362431	+	0.627749i	−0.988360	−	0.152131i	$-0.951387\pi$
$823$	−10.3974	+	18.0089i	−0.362431	+	0.627749i	0.625929	+	0.779880i	$0.284720\pi$
$824$	−21.8986	+	37.9295i	−0.762875	+	1.32134i
$825$		0			0
$826$		0			0
$827$		−	34.0792i		−	1.18505i	−0.805552	−	0.592525i	$-0.798131\pi$
$827$		−	34.0792i		−	1.18505i	0.805552	−	0.592525i	$-0.201869\pi$
$828$		0			0
$829$		−	33.8591i		−	1.17598i	−0.808869	−	0.587988i	$-0.799920\pi$
$829$		−	33.8591i		−	1.17598i	0.808869	−	0.587988i	$-0.200080\pi$
$830$	−8.74718	+	5.05019i	−0.303619	+	0.175295i
$831$		0			0
$832$	−16.7416	−	9.66575i	−0.580410	−	0.335100i
$833$		0			0
$834$		0			0
$835$	6.50371	+	11.2648i	0.225070	+	0.389833i
$836$	−0.468535			−0.0162046
$837$		0			0
$838$		−	19.2591i		−	0.665293i
$839$	11.7633	+	20.3747i	0.406115	+	0.703412i	0.994451	−	0.105205i	$-0.0335498\pi$
$839$	11.7633	+	20.3747i	0.406115	+	0.703412i	−0.588335	+	0.808617i	$0.700216\pi$
$840$		0			0
$841$	−14.4764	+	25.0739i	−0.499188	+	0.864618i
$842$	17.7542	+	10.2504i	0.611852	+	0.353253i
$843$		0			0
$844$	−0.722895	−	1.25209i	−0.0248831	−	0.0430987i
$845$	−3.40178			−0.117025
$846$		0			0
$847$		0			0
$848$	28.9743	−	16.7283i	0.994983	−	0.574454i
$849$		0			0
$850$	31.0474	+	17.9252i	1.06492	+	0.614831i
$851$	0.303707	+	0.175345i	0.0104109	+	0.00601076i
$852$		0			0
$853$	−39.7270	+	22.9364i	−1.36023	+	0.785328i	−0.989654	−	0.143475i	$-0.954172\pi$
$853$	−39.7270	+	22.9364i	−1.36023	+	0.785328i	−0.370574	+	0.928803i	$0.620839\pi$
$854$		0			0
$855$		0			0
$856$	−10.0883			−0.344810
$857$	−9.12274	−	15.8010i	−0.311627	−	0.539753i	0.667088	−	0.744979i	$-0.267540\pi$
$857$	−9.12274	−	15.8010i	−0.311627	−	0.539753i	−0.978715	+	0.205226i	$0.934207\pi$
$858$		0			0
$859$	5.03737	+	2.90833i	0.171873	+	0.0992309i	0.583469	−	0.812136i	$-0.301695\pi$
$859$	5.03737	+	2.90833i	0.171873	+	0.0992309i	−0.411596	+	0.911367i	$0.635028\pi$
$860$	1.39817	−	2.42170i	0.0476771	−	0.0825792i
$861$		0			0
$862$	27.2950	+	47.2763i	0.929671	+	1.61024i
$863$			31.9921i			1.08903i	0.838753	+	0.544513i	$0.183285\pi$
$863$			31.9921i			1.08903i	−0.838753	+	0.544513i	$0.816715\pi$
$864$		0			0
$865$	1.32892			0.0451845
$866$	−24.9230	−	43.1679i	−0.846918	−	1.46690i
$867$		0			0
$868$		0			0
$869$	−16.5157	−	9.53533i	−0.560256	−	0.323464i
$870$		0			0
$871$	10.6808	−	6.16658i	0.361906	−	0.208946i
$872$		−	6.66097i		−	0.225569i
$873$		0			0
$874$		−	0.0365846i		−	0.00123749i
$875$		0			0
$876$		0			0
$877$	24.1949	−	41.9068i	0.817004	−	1.41509i	−0.0908756	−	0.995862i	$-0.528967\pi$
$877$	24.1949	−	41.9068i	0.817004	−	1.41509i	0.907880	−	0.419231i	$-0.137700\pi$
$878$	23.0756	−	39.9681i	0.778763	−	1.34886i
$879$		0			0
$880$	−11.5745	+	6.68253i	−0.390176	+	0.225268i
$881$	26.6822			0.898946			0.449473	−	0.893294i	$-0.351612\pi$
$881$	26.6822			0.898946			0.449473	+	0.893294i	$0.351612\pi$
$882$		0			0
$883$	35.0484			1.17947			0.589737	−	0.807595i	$-0.299231\pi$
$883$	35.0484			1.17947			0.589737	+	0.807595i	$0.299231\pi$
$884$	3.84736	−	2.22128i	0.129401	−	0.0747096i
$885$		0			0
$886$	−15.6315	+	27.0745i	−0.525149	+	0.909585i
$887$	−6.48380	+	11.2303i	−0.217705	+	0.377076i	−0.954106	−	0.299469i	$-0.903190\pi$
$887$	−6.48380	+	11.2303i	−0.217705	+	0.377076i	0.736401	+	0.676545i	$0.236524\pi$
$888$		0			0
$889$		0			0
$890$			18.3255i			0.614273i
$891$		0			0
$892$			1.22972i			0.0411742i
$893$	−0.363577	+	0.209911i	−0.0121666	+	0.00702441i
$894$		0			0
$895$	−9.63184	−	5.56095i	−0.321957	−	0.185882i
$896$		0			0
$897$		0			0
$898$	4.83414	+	8.37298i	0.161317	+	0.279410i
$899$	1.42325			0.0474682
$900$		0			0
$901$		−	40.2930i		−	1.34236i
$902$	21.9815	+	38.0730i	0.731902	+	1.26769i
$903$		0			0
$904$	−14.6783	+	25.4236i	−0.488193	+	0.845576i
$905$	−3.24641	−	1.87431i	−0.107914	−	0.0623043i
$906$		0			0
$907$	4.56307	+	7.90346i	0.151514	+	0.262430i	0.931784	−	0.363012i	$-0.118252\pi$
$907$	4.56307	+	7.90346i	0.151514	+	0.262430i	−0.780270	+	0.625443i	$0.784918\pi$
$908$	−2.71244			−0.0900155
$909$		0			0
$910$		0			0
$911$	−41.5720	+	24.0016i	−1.37734	+	0.795209i	−0.991839	−	0.127498i	$-0.959305\pi$
$911$	−41.5720	+	24.0016i	−1.37734	+	0.795209i	−0.385503	+	0.922707i	$0.625972\pi$
$912$		0			0
$913$	28.6921	+	16.5654i	0.949571	+	0.548235i
$914$	4.11533	+	2.37599i	0.136123	+	0.0785906i
$915$		0			0
$916$	−2.14973	+	1.24115i	−0.0710292	+	0.0410087i
$917$		0			0
$918$		0			0
$919$	−39.6193			−1.30692			−0.653459	−	0.756962i	$-0.726683\pi$
$919$	−39.6193			−1.30692			−0.653459	+	0.756962i	$0.726683\pi$
$920$	−0.0561303	−	0.0972206i	−0.00185056	−	0.00320527i
$921$		0			0
$922$	19.4657	+	11.2385i	0.641068	+	0.370121i
$923$	−5.14856	+	8.91757i	−0.169467	+	0.293526i
$924$		0			0
$925$	−13.8405	−	23.9724i	−0.455072	−	0.788208i
$926$		−	40.3544i		−	1.32613i
$927$		0			0
$928$	0.341879			0.0112227
$929$	−11.7897	−	20.4204i	−0.386809	−	0.669973i	0.605209	−	0.796066i	$-0.293089\pi$
$929$	−11.7897	−	20.4204i	−0.386809	−	0.669973i	−0.992018	+	0.126093i	$0.959756\pi$
$930$		0			0
$931$		0			0
$932$	−3.12944	−	1.80679i	−0.102508	−	0.0591832i
$933$		0			0
$934$	32.4243	−	18.7202i	1.06096	−	0.612543i
$935$			16.0960i			0.526396i
$936$		0			0
$937$			52.5144i			1.71557i	0.514007	+	0.857786i	$0.328160\pi$
$937$			52.5144i			1.71557i	−0.514007	+	0.857786i	$0.671840\pi$
$938$		0			0
$939$		0			0
$940$	0.105025	−	0.181908i	0.00342553	−	0.00593319i
$941$	−24.5713	+	42.5587i	−0.801000	+	1.38737i	0.117958	+	0.993019i	$0.462365\pi$
$941$	−24.5713	+	42.5587i	−0.801000	+	1.38737i	−0.918958	+	0.394354i	$0.870968\pi$
$942$		0			0
$943$	−0.365528	+	0.211038i	−0.0119032	+	0.00687234i
$944$	−14.0040			−0.455791
$945$		0			0
$946$	−74.5995			−2.42544
$947$	8.04907	−	4.64713i	0.261560	−	0.151012i	−0.363486	−	0.931600i	$-0.618414\pi$
$947$	8.04907	−	4.64713i	0.261560	−	0.151012i	0.625046	+	0.780588i	$0.285080\pi$
$948$		0			0
$949$	11.9633	−	20.7210i	0.388344	−	0.672632i
$950$	−1.44386	+	2.50084i	−0.0468450	+	0.0811379i
$951$		0			0
$952$		0			0
$953$			40.3761i			1.30791i	0.756534	+	0.653955i	$0.226891\pi$
$953$			40.3761i			1.30791i	−0.756534	+	0.653955i	$0.773109\pi$
$954$		0			0
$955$			2.43788i			0.0788881i
$956$	−1.17319	+	0.677344i	−0.0379438	+	0.0219069i
$957$		0			0
$958$	−16.3827	−	9.45854i	−0.529300	−	0.305592i
$959$		0			0
$960$		0			0
$961$	5.99358	+	10.3812i	0.193341	+	0.334877i
$962$	−27.8978			−0.899462
$963$		0			0
$964$		−	2.81329i		−	0.0906100i
$965$	2.33157	+	4.03840i	0.0750560	+	0.130001i
$966$		0			0
$967$	8.78620	−	15.2181i	0.282545	−	0.489383i	−0.689466	−	0.724318i	$-0.742155\pi$
$967$	8.78620	−	15.2181i	0.282545	−	0.489383i	0.972011	+	0.234936i	$0.0754879\pi$
$968$	8.47846	+	4.89504i	0.272508	+	0.157333i
$969$		0			0
$970$	0.839894	+	1.45474i	0.0269674	+	0.0467089i
$971$	40.2641			1.29214			0.646068	−	0.763280i	$-0.276412\pi$
$971$	40.2641			1.29214			0.646068	+	0.763280i	$0.276412\pi$
$972$		0			0
$973$		0			0
$974$	−4.43986	+	2.56336i	−0.142262	+	0.0821353i
$975$		0			0
$976$	−13.5246	−	7.80845i	−0.432913	−	0.249942i
$977$	−22.9591	−	13.2555i	−0.734527	−	0.424080i	0.0855487	−	0.996334i	$-0.472736\pi$
$977$	−22.9591	−	13.2555i	−0.734527	−	0.424080i	−0.820076	+	0.572254i	$0.806069\pi$
$978$		0			0
$979$	52.0573	−	30.0553i	1.66376	−	0.960572i
$980$		0			0
$981$		0			0
$982$	−1.36039			−0.0434118
$983$	19.1357	+	33.1440i	0.610334	+	1.05713i	0.991184	+	0.132493i	$0.0422982\pi$
$983$	19.1357	+	33.1440i	0.610334	+	1.05713i	−0.380850	+	0.924637i	$0.624368\pi$
$984$		0			0
$985$	−9.46759	−	5.46612i	−0.301663	−	0.174165i
$986$	0.884752	−	1.53243i	0.0281762	−	0.0488027i
$987$		0			0
$988$	0.178921	+	0.309901i	0.00569225	+	0.00985926i
$989$		−	0.716209i		−	0.0227741i
$990$		0			0
$991$	−60.9018			−1.93461			−0.967305	−	0.253615i	$-0.918380\pi$
$991$	−60.9018			−1.93461			−0.967305	+	0.253615i	$0.918380\pi$
$992$	5.16295	+	8.94250i	0.163924	+	0.283925i
$993$		0			0
$994$		0			0
$995$	−5.30881	−	3.06504i	−0.168301	−	0.0971684i
$996$		0			0
$997$	−12.4807	+	7.20573i	−0.395267	+	0.228208i	−0.684440	−	0.729069i	$-0.739953\pi$
$997$	−12.4807	+	7.20573i	−0.395267	+	0.228208i	0.289173	+	0.957277i	$0.406620\pi$
$998$			33.0240i			1.04536i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1323.2.o.c.881.4		10
3.2	odd	2		441.2.o.d.293.2		10
7.2	even	3		1323.2.s.b.962.2		10
7.3	odd	6		1323.2.i.b.1097.4		10
7.4	even	3		189.2.i.b.152.4		10
7.5	odd	6		189.2.s.b.17.2		10
7.6	odd	2		1323.2.o.d.881.4		10
9.2	odd	6		1323.2.o.d.440.4		10
9.7	even	3		441.2.o.c.146.2		10
21.2	odd	6		441.2.s.b.374.4		10
21.5	even	6		63.2.s.b.59.4	yes	10
21.11	odd	6		63.2.i.b.5.2	✓	10
21.17	even	6		441.2.i.b.68.2		10
21.20	even	2		441.2.o.c.293.2		10
28.11	odd	6		3024.2.ca.b.2609.3		10
28.19	even	6		3024.2.df.b.17.3		10
63.2	odd	6		1323.2.i.b.521.2		10
63.4	even	3		567.2.p.c.404.2		10
63.5	even	6		567.2.p.c.80.2		10
63.11	odd	6		189.2.s.b.89.2		10
63.16	even	3		441.2.i.b.227.4		10
63.20	even	6	inner	1323.2.o.c.440.4		10
63.25	even	3		63.2.s.b.47.4	yes	10
63.32	odd	6		567.2.p.d.404.4		10
63.34	odd	6		441.2.o.d.146.2		10
63.38	even	6		1323.2.s.b.656.2		10
63.40	odd	6		567.2.p.d.80.4		10
63.47	even	6		189.2.i.b.143.2		10
63.52	odd	6		441.2.s.b.362.4		10
63.61	odd	6		63.2.i.b.38.4	yes	10
84.11	even	6		1008.2.ca.b.257.2		10
84.47	odd	6		1008.2.df.b.689.4		10
252.11	even	6		3024.2.df.b.1601.3		10
252.47	odd	6		3024.2.ca.b.2033.3		10
252.151	odd	6		1008.2.df.b.929.4		10
252.187	even	6		1008.2.ca.b.353.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.i.b.5.2	✓	10	21.11	odd	6
63.2.i.b.38.4	yes	10	63.61	odd	6
63.2.s.b.47.4	yes	10	63.25	even	3
63.2.s.b.59.4	yes	10	21.5	even	6
189.2.i.b.143.2		10	63.47	even	6
189.2.i.b.152.4		10	7.4	even	3
189.2.s.b.17.2		10	7.5	odd	6
189.2.s.b.89.2		10	63.11	odd	6
441.2.i.b.68.2		10	21.17	even	6
441.2.i.b.227.4		10	63.16	even	3
441.2.o.c.146.2		10	9.7	even	3
441.2.o.c.293.2		10	21.20	even	2
441.2.o.d.146.2		10	63.34	odd	6
441.2.o.d.293.2		10	3.2	odd	2
441.2.s.b.362.4		10	63.52	odd	6
441.2.s.b.374.4		10	21.2	odd	6
567.2.p.c.80.2		10	63.5	even	6
567.2.p.c.404.2		10	63.4	even	3
567.2.p.d.80.4		10	63.40	odd	6
567.2.p.d.404.4		10	63.32	odd	6
1008.2.ca.b.257.2		10	84.11	even	6
1008.2.ca.b.353.2		10	252.187	even	6
1008.2.df.b.689.4		10	84.47	odd	6
1008.2.df.b.929.4		10	252.151	odd	6
1323.2.i.b.521.2		10	63.2	odd	6
1323.2.i.b.1097.4		10	7.3	odd	6
1323.2.o.c.440.4		10	63.20	even	6	inner
1323.2.o.c.881.4		10	1.1	even	1	trivial
1323.2.o.d.440.4		10	9.2	odd	6
1323.2.o.d.881.4		10	7.6	odd	2
1323.2.s.b.656.2		10	63.38	even	6
1323.2.s.b.962.2		10	7.2	even	3
3024.2.ca.b.2033.3		10	252.47	odd	6
3024.2.ca.b.2609.3		10	28.11	odd	6
3024.2.df.b.17.3		10	28.19	even	6
3024.2.df.b.1601.3		10	252.11	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1323 = 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1323.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.30778 - 0.755047i) q^{2} +(0.140193 - 0.242822i) q^{4} +(0.387938 - 0.671929i) q^{5} +2.59678i q^{8} +O(q^{10})\)	\(q+(1.30778 - 0.755047i) q^{2} +(0.140193 - 0.242822i) q^{4} +(0.387938 - 0.671929i) q^{5} +2.59678i q^{8} -1.17165i q^{10} +(-3.32830 + 1.92159i) q^{11} +(2.54198 + 1.46761i) q^{13} +(2.24108 + 3.88166i) q^{16} +5.39802 q^{17} +0.434804i q^{19} +(-0.108773 - 0.188400i) q^{20} +(-2.90179 + 5.02605i) q^{22} +(-0.0482537 - 0.0278593i) q^{23} +(2.19901 + 3.80879i) q^{25} +4.43247 q^{26} +(0.187994 - 0.108538i) q^{29} +(5.67806 + 3.27823i) q^{31} +(1.36392 + 0.787461i) q^{32} +(7.05942 - 4.07576i) q^{34} -6.29396 q^{37} +(0.328298 + 0.568628i) q^{38} +(1.74485 + 1.00739i) q^{40} +(3.78757 - 6.56026i) q^{41} +(6.42703 + 11.1319i) q^{43} +1.07758i q^{44} -0.0841403 q^{46} +(0.482772 + 0.836186i) q^{47} +(5.75164 + 3.32071i) q^{50} +(0.712737 - 0.411499i) q^{52} -7.46442i q^{53} +2.98184i q^{55} +(0.163903 - 0.283889i) q^{58} +(-1.56219 + 2.70580i) q^{59} +(-3.01744 + 1.74212i) q^{61} +9.90087 q^{62} -6.58603 q^{64} +(1.97226 - 1.13869i) q^{65} +(2.10088 - 3.63884i) q^{67} +(0.756765 - 1.31076i) q^{68} +3.50812i q^{71} -8.15152i q^{73} +(-8.23112 + 4.75224i) q^{74} +(0.105580 + 0.0609566i) q^{76} +(2.48110 + 4.29739i) q^{79} +3.47760 q^{80} -11.4392i q^{82} +(-4.31033 - 7.46571i) q^{83} +(2.09410 - 3.62708i) q^{85} +(16.8103 + 9.70542i) q^{86} +(-4.98996 - 8.64286i) q^{88} -15.6408 q^{89} +(-0.0135297 + 0.00781136i) q^{92} +(1.26272 + 0.729031i) q^{94} +(0.292157 + 0.168677i) q^{95} +(-1.24162 + 0.716849i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{4}+O(q^{10}) \) 10 * q + 4 * q^4	\( 10 q + 4 q^{4} - 12 q^{11} - 6 q^{13} - 6 q^{16} + 24 q^{17} - 3 q^{20} + 5 q^{22} - 15 q^{23} + 7 q^{25} - 6 q^{26} + 15 q^{29} - 9 q^{31} + 48 q^{32} - 3 q^{34} - 12 q^{37} - 18 q^{38} - 15 q^{40} - 9 q^{41} + 3 q^{43} + 26 q^{46} + 15 q^{47} - 3 q^{50} + 12 q^{52} + 8 q^{58} - 18 q^{59} + 12 q^{61} + 12 q^{62} + 6 q^{64} - 3 q^{65} - 10 q^{67} + 27 q^{68} - 30 q^{74} - 9 q^{76} + 20 q^{79} + 60 q^{80} - 15 q^{83} + 18 q^{85} + 54 q^{86} - 8 q^{88} - 48 q^{89} - 39 q^{92} - 3 q^{94} - 6 q^{97}+O(q^{100}) \) 10 * q + 4 * q^4 - 12 * q^11 - 6 * q^13 - 6 * q^16 + 24 * q^17 - 3 * q^20 + 5 * q^22 - 15 * q^23 + 7 * q^25 - 6 * q^26 + 15 * q^29 - 9 * q^31 + 48 * q^32 - 3 * q^34 - 12 * q^37 - 18 * q^38 - 15 * q^40 - 9 * q^41 + 3 * q^43 + 26 * q^46 + 15 * q^47 - 3 * q^50 + 12 * q^52 + 8 * q^58 - 18 * q^59 + 12 * q^61 + 12 * q^62 + 6 * q^64 - 3 * q^65 - 10 * q^67 + 27 * q^68 - 30 * q^74 - 9 * q^76 + 20 * q^79 + 60 * q^80 - 15 * q^83 + 18 * q^85 + 54 * q^86 - 8 * q^88 - 48 * q^89 - 39 * q^92 - 3 * q^94 - 6 * q^97

Introduction

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