LMFDB - Embedded newform 845.2.l.e.699.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(654,845)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(845, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("845.654");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.l (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:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.89539436150784.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2x^{11} + 2x^{10} - 8x^{9} + 4x^{8} + 16x^{7} - 8x^{6} + 20x^{5} + 20x^{4} - 24x^{3} + 8x^{2} - 8x + 4 $ x^12 - 2x^11 + 2x^10 - 8x^9 + 4x^8 + 16x^7 - 8x^6 + 20x^5 + 20x^4 - 24x^3 + 8x^2 - 8*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			699.1
Root			$-0.531325 + 1.98293i$ of defining polynomial
Character	$\chi$	$=$	845.699
Dual form			845.2.l.e.654.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.607160 - 1.05163i) q^{2} +(-1.13545 + 0.655554i) q^{3} +(0.262714 - 0.455034i) q^{4} +(-0.311108 - 2.21432i) q^{5} +(1.37880 + 0.796052i) q^{6} +(-1.45161 + 2.51426i) q^{7} -3.06668 q^{8} +(-0.640498 + 1.10938i) q^{9} +(-2.13976 + 1.67162i) q^{10} +(-0.185606 + 0.107160i) q^{11} +0.688892i q^{12} +3.52543 q^{14} +(1.80485 + 2.31031i) q^{15} +(1.33654 + 2.31495i) q^{16} +(5.56737 + 3.21432i) q^{17} +1.55554 q^{18} +(1.91766 + 1.10716i) q^{19} +(-1.08932 - 0.440168i) q^{20} -3.80642i q^{21} +(0.225385 + 0.130126i) q^{22} +(4.06070 - 2.34445i) q^{23} +(3.48207 - 2.01037i) q^{24} +(-4.80642 + 1.37778i) q^{25} -5.61285i q^{27} +(0.762714 + 1.32106i) q^{28} +(4.35482 + 7.54277i) q^{29} +(1.33376 - 3.30077i) q^{30} -5.59210i q^{31} +(-1.44370 + 2.50055i) q^{32} +(0.140498 - 0.243350i) q^{33} -7.80642i q^{34} +(6.01897 + 2.43212i) q^{35} +(0.336535 + 0.582896i) q^{36} +(-1.14050 - 1.97540i) q^{37} -2.68889i q^{38} +(0.954067 + 6.79060i) q^{40} +(2.64212 - 1.52543i) q^{41} +(-4.00296 + 2.31111i) q^{42} +(-5.50962 - 3.18098i) q^{43} +0.112610i q^{44} +(2.65578 + 1.07313i) q^{45} +(-4.93099 - 2.84691i) q^{46} +1.09679 q^{47} +(-3.03515 - 1.75234i) q^{48} +(-0.714320 - 1.23724i) q^{49} +(4.36719 + 4.21805i) q^{50} -8.42864 q^{51} +6.23506i q^{53} +(-5.90265 + 3.40790i) q^{54} +(0.295030 + 0.377654i) q^{55} +(4.45161 - 7.71041i) q^{56} -2.90321 q^{57} +(5.28814 - 9.15933i) q^{58} +(8.02388 + 4.63259i) q^{59} +(1.52543 - 0.214320i) q^{60} +(0.140498 - 0.243350i) q^{61} +(-5.88083 + 3.39530i) q^{62} +(-1.85950 - 3.22075i) q^{63} +8.85236 q^{64} -0.341219 q^{66} +(-3.88025 - 6.72078i) q^{67} +(2.92525 - 1.68889i) q^{68} +(-3.07382 + 5.32402i) q^{69} +(-1.09679 - 7.80642i) q^{70} +(5.26627 + 3.04048i) q^{71} +(1.96420 - 3.40210i) q^{72} +10.2810 q^{73} +(-1.38493 + 2.39877i) q^{74} +(4.55425 - 4.71528i) q^{75} +(1.00759 - 0.581732i) q^{76} -0.622216i q^{77} +14.2351 q^{79} +(4.71023 - 3.67971i) q^{80} +(1.75803 + 3.04500i) q^{81} +(-3.20838 - 1.85236i) q^{82} +9.52543 q^{83} +(-1.73205 - 1.00000i) q^{84} +(5.38548 - 13.3279i) q^{85} +7.72546i q^{86} +(-9.88938 - 5.70964i) q^{87} +(0.569195 - 0.328625i) q^{88} +(-4.86087 + 2.80642i) q^{89} +(-0.483940 - 3.44446i) q^{90} -2.46367i q^{92} +(3.66593 + 6.34957i) q^{93} +(-0.665926 - 1.15342i) q^{94} +(1.85501 - 4.59075i) q^{95} -3.78568i q^{96} +(-9.02074 + 15.6244i) q^{97} +(-0.867413 + 1.50240i) q^{98} -0.274543i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{2} - 10 q^{4} - 4 q^{5} - 4 q^{7} - 36 q^{8} + 6 q^{9} + 2 q^{10} + 16 q^{14} + 4 q^{15} - 10 q^{16} + 20 q^{18} - 14 q^{20} - 4 q^{25} - 4 q^{28} + 12 q^{29} + 8 q^{30} + 22 q^{32} - 12 q^{33}+ \cdots - 50 q^{98}+O(q^{100}) $ 12 * q + 6 * q^2 - 10 * q^4 - 4 * q^5 - 4 * q^7 - 36 * q^8 + 6 * q^9 + 2 * q^10 + 16 * q^14 + 4 * q^15 - 10 * q^16 + 20 * q^18 - 14 * q^20 - 4 * q^25 - 4 * q^28 + 12 * q^29 + 8 * q^30 + 22 * q^32 - 12 * q^33 - 8 * q^35 - 22 * q^36 - 68 * q^40 - 38 * q^45 + 40 * q^47 + 18 * q^49 + 22 * q^50 - 48 * q^51 + 16 * q^55 + 40 * q^56 - 8 * q^57 + 24 * q^58 - 8 * q^60 - 12 * q^61 - 36 * q^63 + 132 * q^64 - 32 * q^66 + 20 * q^67 - 24 * q^69 - 40 * q^70 + 90 * q^72 + 96 * q^73 - 4 * q^74 + 16 * q^75 + 64 * q^79 - 58 * q^80 - 46 * q^81 + 88 * q^83 + 32 * q^85 - 140 * q^90 + 4 * q^93 + 32 * q^94 + 16 * q^95 - 28 * q^97 - 50 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	−0.607160	−	1.05163i	−0.429327	−	0.743616i	0.567487	−	0.823383i	$-0.307916\pi$
$2$	−0.607160	−	1.05163i	−0.429327	−	0.743616i	−0.996814	+	0.0797666i	$0.974582\pi$
$3$	−1.13545	+	0.655554i	−0.655554	+	0.378484i	−0.790581	−	0.612358i	$-0.790221\pi$
$3$	−1.13545	+	0.655554i	−0.655554	+	0.378484i	0.135027	+	0.990842i	$0.456888\pi$
$4$	0.262714	−	0.455034i	0.131357	−	0.227517i
$5$	−0.311108	−	2.21432i	−0.139132	−	0.990274i
$5$	−0.311108	−	2.21432i	−0.139132	−	0.990274i
$6$	1.37880	+	0.796052i	0.562894	+	0.324987i
$7$	−1.45161	+	2.51426i	−0.548655	+	0.950299i	0.449712	+	0.893174i	$0.351527\pi$
$7$	−1.45161	+	2.51426i	−0.548655	+	0.950299i	−0.998367	+	0.0571253i	$0.981807\pi$
$8$	−3.06668			−1.08423
$9$	−0.640498	+	1.10938i	−0.213499	+	0.369792i
$10$	−2.13976	+	1.67162i	−0.676650	+	0.528612i
$11$	−0.185606	+	0.107160i	−0.0559624	+	0.0323099i	−0.527720	−	0.849418i	$-0.676953\pi$
$11$	−0.185606	+	0.107160i	−0.0559624	+	0.0323099i	0.471758	+	0.881728i	$0.343620\pi$
$12$			0.688892i			0.198866i
$13$		0			0
$13$		0			0
$14$	3.52543			0.942210
$15$	1.80485	+	2.31031i	0.466011	+	0.596519i
$16$	1.33654	+	2.31495i	0.334134	+	0.578737i
$17$	5.56737	+	3.21432i	1.35028	+	0.779587i	0.988289	−	0.152593i	$-0.0487623\pi$
$17$	5.56737	+	3.21432i	1.35028	+	0.779587i	0.361995	+	0.932180i	$0.382096\pi$
$18$	1.55554			0.366644
$19$	1.91766	+	1.10716i	0.439941	+	0.254000i	0.703572	−	0.710624i	$-0.251587\pi$
$19$	1.91766	+	1.10716i	0.439941	+	0.254000i	−0.263632	+	0.964623i	$0.584920\pi$
$20$	−1.08932	−	0.440168i	−0.243580	−	0.0984245i
$21$		−	3.80642i		−	0.830630i
$22$	0.225385	+	0.130126i	0.0480523	+	0.0277430i
$23$	4.06070	−	2.34445i	0.846714	−	0.488851i	−0.0128265	−	0.999918i	$-0.504083\pi$
$23$	4.06070	−	2.34445i	0.846714	−	0.488851i	0.859541	+	0.511067i	$0.170750\pi$
$24$	3.48207	−	2.01037i	0.710774	−	0.410365i
$25$	−4.80642	+	1.37778i	−0.961285	+	0.275557i
$26$		0			0
$27$		−	5.61285i		−	1.08019i
$28$	0.762714	+	1.32106i	0.144139	+	0.249657i
$29$	4.35482	+	7.54277i	0.808669	+	1.40066i	0.913786	+	0.406197i	$0.133145\pi$
$29$	4.35482	+	7.54277i	0.808669	+	1.40066i	−0.105116	+	0.994460i	$0.533522\pi$
$30$	1.33376	−	3.30077i	0.243510	−	0.602635i
$31$		−	5.59210i		−	1.00437i	−0.864760	−	0.502186i	$-0.832529\pi$
$31$		−	5.59210i		−	1.00437i	0.864760	−	0.502186i	$-0.167471\pi$
$32$	−1.44370	+	2.50055i	−0.255212	+	0.442040i
$33$	0.140498	−	0.243350i	0.0244576	−	0.0423618i
$34$		−	7.80642i		−	1.33879i
$35$	6.01897	+	2.43212i	1.01739	+	0.411103i
$36$	0.336535	+	0.582896i	0.0560892	+	0.0971494i
$37$	−1.14050	−	1.97540i	−0.187497	−	0.324754i	0.756918	−	0.653510i	$-0.226704\pi$
$37$	−1.14050	−	1.97540i	−0.187497	−	0.324754i	−0.944415	+	0.328756i	$0.893371\pi$
$38$		−	2.68889i		−	0.436196i
$39$		0			0
$40$	0.954067	+	6.79060i	0.150851	+	1.07369i
$41$	2.64212	−	1.52543i	0.412630	−	0.238232i	−0.279289	−	0.960207i	$-0.590099\pi$
$41$	2.64212	−	1.52543i	0.412630	−	0.238232i	0.691919	+	0.721975i	$0.256766\pi$
$42$	−4.00296	+	2.31111i	−0.617670	+	0.356612i
$43$	−5.50962	−	3.18098i	−0.840209	−	0.485095i	0.0171260	−	0.999853i	$-0.494548\pi$
$43$	−5.50962	−	3.18098i	−0.840209	−	0.485095i	−0.857335	+	0.514758i	$0.827882\pi$
$44$			0.112610i			0.0169765i
$45$	2.65578	+	1.07313i	0.395900	+	0.159973i
$46$	−4.93099	−	2.84691i	−0.727034	−	0.419754i
$47$	1.09679			0.159983			0.0799915	−	0.996796i	$-0.474511\pi$
$47$	1.09679			0.159983			0.0799915	+	0.996796i	$0.474511\pi$
$48$	−3.03515	−	1.75234i	−0.438085	−	0.252929i
$49$	−0.714320	−	1.23724i	−0.102046	−	0.176748i
$50$	4.36719	+	4.21805i	0.617614	+	0.596523i
$51$	−8.42864			−1.18025
$52$		0			0
$53$			6.23506i			0.856452i	0.903672	+	0.428226i	$0.140861\pi$
$53$			6.23506i			0.856452i	−0.903672	+	0.428226i	$0.859139\pi$
$54$	−5.90265	+	3.40790i	−0.803249	+	0.463756i
$55$	0.295030	+	0.377654i	0.0397818	+	0.0509228i
$56$	4.45161	−	7.71041i	0.594871	−	1.03035i
$57$	−2.90321			−0.384540
$58$	5.28814	−	9.15933i	0.694367	−	1.20268i
$59$	8.02388	+	4.63259i	1.04462	+	0.603112i	0.921138	−	0.389235i	$-0.127261\pi$
$59$	8.02388	+	4.63259i	1.04462	+	0.603112i	0.123481	+	0.992347i	$0.460594\pi$
$60$	1.52543	−	0.214320i	0.196932	−	0.0276686i
$61$	0.140498	−	0.243350i	0.0179889	−	0.0311578i	−0.856891	−	0.515498i	$-0.827607\pi$
$61$	0.140498	−	0.243350i	0.0179889	−	0.0311578i	0.874880	+	0.484340i	$0.160940\pi$
$62$	−5.88083	+	3.39530i	−0.746867	+	0.431204i
$63$	−1.85950	−	3.22075i	−0.234275	−	0.405777i
$64$	8.85236			1.10654
$65$		0			0
$66$	−0.341219			−0.0420012
$67$	−3.88025	−	6.72078i	−0.474047	−	0.821074i	0.525511	−	0.850787i	$-0.323874\pi$
$67$	−3.88025	−	6.72078i	−0.474047	−	0.821074i	−0.999558	+	0.0297125i	$0.990541\pi$
$68$	2.92525	−	1.68889i	0.354738	−	0.204808i
$69$	−3.07382	+	5.32402i	−0.370045	+	0.640936i
$70$	−1.09679	−	7.80642i	−0.131091	−	0.933046i
$71$	5.26627	+	3.04048i	0.624991	+	0.360839i	0.778810	−	0.627260i	$-0.215824\pi$
$71$	5.26627	+	3.04048i	0.624991	+	0.360839i	−0.153818	+	0.988099i	$0.549157\pi$
$72$	1.96420	−	3.40210i	0.231483	−	0.400941i
$73$	10.2810			1.20330			0.601650	−	0.798760i	$-0.294510\pi$
$73$	10.2810			1.20330			0.601650	+	0.798760i	$0.294510\pi$
$74$	−1.38493	+	2.39877i	−0.160995	+	0.278851i
$75$	4.55425	−	4.71528i	0.525880	−	0.544474i
$76$	1.00759	−	0.581732i	0.115578	−	0.0667293i
$77$		−	0.622216i		−	0.0709081i
$78$		0			0
$79$	14.2351			1.60157			0.800785	−	0.598952i	$-0.204416\pi$
$79$	14.2351			1.60157			0.800785	+	0.598952i	$0.204416\pi$
$80$	4.71023	−	3.67971i	0.526619	−	0.411405i
$81$	1.75803	+	3.04500i	0.195337	+	0.338333i
$82$	−3.20838	−	1.85236i	−0.354306	−	0.204559i
$83$	9.52543			1.04555			0.522776	−	0.852470i	$-0.324897\pi$
$83$	9.52543			1.04555			0.522776	+	0.852470i	$0.324897\pi$
$84$	−1.73205	−	1.00000i	−0.188982	−	0.109109i
$85$	5.38548	−	13.3279i	0.584137	−	1.44562i
$86$			7.72546i			0.833057i
$87$	−9.88938	−	5.70964i	−1.06025	−	0.612137i
$88$	0.569195	−	0.328625i	0.0606764	−	0.0350315i
$89$	−4.86087	+	2.80642i	−0.515251	+	0.297480i	−0.734989	−	0.678078i	$-0.762813\pi$
$89$	−4.86087	+	2.80642i	−0.515251	+	0.297480i	0.219738	+	0.975559i	$0.429480\pi$
$90$	−0.483940	−	3.44446i	−0.0510118	−	0.363078i
$91$		0			0
$92$		−	2.46367i		−	0.256856i
$93$	3.66593	+	6.34957i	0.380139	+	0.658420i
$94$	−0.665926	−	1.15342i	−0.0686850	−	0.118966i
$95$	1.85501	−	4.59075i	0.190320	−	0.471001i
$96$		−	3.78568i		−	0.386374i
$97$	−9.02074	+	15.6244i	−0.915918	+	1.58642i	−0.110366	+	0.993891i	$0.535202\pi$
$97$	−9.02074	+	15.6244i	−0.915918	+	1.58642i	−0.805552	+	0.592525i	$0.798131\pi$
$98$	−0.867413	+	1.50240i	−0.0876219	+	0.151766i
$99$		−	0.274543i		−	0.0275926i
$100$	−0.635776	+	2.54905i	−0.0635776	+	0.254905i
$101$	1.96989	+	3.41195i	0.196011	+	0.339501i	0.947232	−	0.320550i	$-0.103868\pi$
$101$	1.96989	+	3.41195i	0.196011	+	0.339501i	−0.751220	+	0.660052i	$0.770534\pi$
$102$	5.11753	+	8.86382i	0.506711	+	0.877649i
$103$			2.82225i			0.278084i	0.990286	+	0.139042i	$0.0444023\pi$
$103$			2.82225i			0.278084i	−0.990286	+	0.139042i	$0.955598\pi$
$104$		0			0
$105$	−8.42864	+	1.18421i	−0.822551	+	0.115567i
$106$	6.55699	−	3.78568i	0.636871	−	0.367698i
$107$	14.8242	−	8.55877i	1.43311	−	0.827407i	0.435754	−	0.900066i	$-0.356482\pi$
$107$	14.8242	−	8.55877i	1.43311	−	0.827407i	0.997357	+	0.0726585i	$0.0231483\pi$
$108$	−2.55403	−	1.47457i	−0.245762	−	0.141891i
$109$			16.7239i			1.60186i	0.598757	+	0.800931i	$0.295662\pi$
$109$			16.7239i			1.60186i	−0.598757	+	0.800931i	$0.704338\pi$
$110$	0.218022	−	0.539559i	0.0207876	−	0.0514449i
$111$	2.58996	+	1.49532i	0.245828	+	0.141929i
$112$	−7.76049			−0.733297
$113$	1.02555	+	0.592104i	0.0964760	+	0.0557005i	0.547462	−	0.836831i	$-0.315594\pi$
$113$	1.02555	+	0.592104i	0.0964760	+	0.0557005i	−0.450986	+	0.892531i	$0.648927\pi$
$114$	1.76271	+	3.05311i	0.165093	+	0.285950i
$115$	−6.45467	−	8.26231i	−0.601901	−	0.770465i
$116$	4.57628			0.424897
$117$		0			0
$118$		−	11.2509i		−	1.03573i
$119$	−16.1632	+	9.33185i	−1.48168	+	0.855449i
$120$	−5.53490	−	7.08497i	−0.505265	−	0.646766i
$121$	−5.47703	+	9.48650i	−0.497912	+	0.862409i
$122$	−0.341219			−0.0308925
$123$	−2.00000	+	3.46410i	−0.180334	+	0.312348i
$124$	−2.54460	−	1.46912i	−0.228511	−	0.131931i
$125$	4.54617	+	10.2143i	0.406622	+	0.913597i
$126$	−2.25803	+	3.91102i	−0.201161	+	0.348422i
$127$	−1.99337	+	1.15087i	−0.176883	+	0.102123i	−0.585827	−	0.810436i	$-0.699230\pi$
$127$	−1.99337	+	1.15087i	−0.176883	+	0.102123i	0.408945	+	0.912559i	$0.365897\pi$
$128$	−2.48741	−	4.30831i	−0.219858	−	0.380805i
$129$	8.34122			0.734403
$130$		0			0
$131$	−13.4193			−1.17245			−0.586224	−	0.810149i	$-0.699386\pi$
$131$	−13.4193			−1.17245			−0.586224	+	0.810149i	$0.699386\pi$
$132$	−0.0738216	−	0.127863i	−0.00642535	−	0.0111290i
$133$	−5.56737	+	3.21432i	−0.482752	+	0.278717i
$134$	−4.71186	+	8.16118i	−0.407043	+	0.705018i
$135$	−12.4286	+	1.74620i	−1.06969	+	0.150289i
$136$	−17.0733	−	9.85728i	−1.46402	−	0.845255i
$137$	−9.57628	+	16.5866i	−0.818157	+	1.41709i	0.0888816	+	0.996042i	$0.471671\pi$
$137$	−9.57628	+	16.5866i	−0.818157	+	1.41709i	−0.907039	+	0.421047i	$0.861663\pi$
$138$	7.46520			0.635480
$139$	9.54617	−	16.5345i	0.809696	−	1.40243i	−0.103379	−	0.994642i	$-0.532966\pi$
$139$	9.54617	−	16.5345i	0.809696	−	1.40243i	0.913075	−	0.407792i	$-0.133701\pi$
$140$	2.68796	−	2.09988i	0.227174	−	0.177473i
$141$	−1.24535	+	0.719004i	−0.104877	+	0.0605510i
$142$		−	7.38424i		−	0.619671i
$143$		0			0
$144$	−3.42419			−0.285349
$145$	15.3473	−	11.9896i	1.27452	−	0.995680i
$146$	−6.24221	−	10.8118i	−0.516609	−	0.894793i
$147$	1.62215	+	0.936550i	0.133793	+	0.0772454i
$148$	−1.19850			−0.0985160
$149$	−3.09289	−	1.78568i	−0.253379	−	0.146289i	0.367931	−	0.929853i	$-0.380066\pi$
$149$	−3.09289	−	1.78568i	−0.253379	−	0.146289i	−0.621311	+	0.783564i	$0.713399\pi$
$150$	−7.72390	−	1.92647i	−0.630654	−	0.157296i
$151$			1.26517i			0.102958i	0.998674	+	0.0514792i	$0.0163936\pi$
$151$			1.26517i			0.102958i	−0.998674	+	0.0514792i	$0.983606\pi$
$152$	−5.88083	−	3.39530i	−0.476999	−	0.275395i
$153$	−7.13177	+	4.11753i	−0.576570	+	0.332883i
$154$	−0.654342	+	0.377784i	−0.0527284	+	0.0304427i
$155$	−12.3827	+	1.73975i	−0.994603	+	0.139740i
$156$		0			0
$157$		−	5.61285i		−	0.447954i	−0.974594	−	0.223977i	$-0.928096\pi$
$157$		−	5.61285i		−	0.447954i	0.974594	−	0.223977i	$-0.0719041\pi$
$158$	−8.64296	−	14.9700i	−0.687597	−	1.19095i
$159$	−4.08742	−	7.07962i	−0.324154	−	0.561450i
$160$	5.98617	+	2.41886i	0.473248	+	0.191228i
$161$			13.6128i			1.07284i
$162$	2.13481	−	3.69760i	0.167727	−	0.290511i
$163$	1.85950	−	3.22075i	0.145647	−	0.252269i	−0.783967	−	0.620803i	$-0.786807\pi$
$163$	1.85950	−	3.22075i	0.145647	−	0.252269i	0.929614	+	0.368534i	$0.120140\pi$
$164$		−	1.60300i		−	0.125174i
$165$	−0.582565	−	0.235400i	−0.0453526	−	0.0183258i
$166$	−5.78346	−	10.0172i	−0.448883	−	0.777489i
$167$	3.51828	+	6.09384i	0.272253	+	0.471556i	0.969438	−	0.245335i	$-0.0788979\pi$
$167$	3.51828	+	6.09384i	0.272253	+	0.471556i	−0.697185	+	0.716891i	$0.745565\pi$
$168$			11.6731i			0.900597i
$169$		0			0
$170$	−17.2859	+	2.42864i	−1.32577	+	0.186268i
$171$	−2.45651	+	1.41827i	−0.187854	+	0.108458i
$172$	−2.89491	+	1.67138i	−0.220735	+	0.127441i
$173$	−0.626938	−	0.361963i	−0.0476652	−	0.0275195i	0.475978	−	0.879457i	$-0.342094\pi$
$173$	−0.626938	−	0.361963i	−0.0476652	−	0.0275195i	−0.523643	+	0.851938i	$0.675428\pi$
$174$			13.8666i			1.05123i
$175$	3.51293	−	14.0846i	0.265553	−	1.06469i
$176$	−0.496139	−	0.286446i	−0.0373979	−	0.0215917i
$177$	−12.1476			−0.913073
$178$	5.90265	+	3.40790i	0.442422	+	0.255433i
$179$	2.02074	+	3.50003i	0.151037	+	0.261605i	0.931609	−	0.363462i	$-0.118405\pi$
$179$	2.02074	+	3.50003i	0.151037	+	0.261605i	−0.780572	+	0.625066i	$0.785072\pi$
$180$	1.18602	−	0.926541i	0.0884007	−	0.0690603i
$181$	−2.34122			−0.174021			−0.0870107	−	0.996207i	$-0.527731\pi$
$181$	−2.34122			−0.174021			−0.0870107	+	0.996207i	$0.527731\pi$
$182$		0			0
$183$			0.368416i			0.0272341i
$184$	−12.4529	+	7.18966i	−0.918036	+	0.530029i
$185$	−4.01935	+	3.13999i	−0.295509	+	0.230857i
$186$	4.45161	−	7.71041i	0.326408	−	0.565355i
$187$	−1.37778			−0.100754
$188$	0.288141	−	0.499075i	0.0210149	−	0.0363988i
$189$	14.1121	+	8.14764i	1.02651	+	0.592654i
$190$	−5.95407	+	0.836535i	−0.431953	+	0.0606887i
$191$	1.05086	−	1.82013i	0.0760372	−	0.131700i	−0.825500	−	0.564403i	$-0.809107\pi$
$191$	1.05086	−	1.82013i	0.0760372	−	0.131700i	0.901537	+	0.432702i	$0.142440\pi$
$192$	−10.0514	+	5.80320i	−0.725400	+	0.418810i
$193$	6.76049	+	11.7095i	0.486631	+	0.842869i	0.999882	−	0.0153692i	$-0.00489238\pi$
$193$	6.76049	+	11.7095i	0.486631	+	0.842869i	−0.513251	+	0.858238i	$0.671559\pi$
$194$	21.9081			1.57291
$195$		0			0
$196$	−0.750647			−0.0536176
$197$	1.00000	+	1.73205i	0.0712470	+	0.123404i	0.899448	−	0.437028i	$-0.143969\pi$
$197$	1.00000	+	1.73205i	0.0712470	+	0.123404i	−0.828201	+	0.560431i	$0.810635\pi$
$198$	−0.288718	+	0.166691i	−0.0205183	+	0.0118462i
$199$	−11.0716	+	19.1766i	−0.784845	+	1.35939i	0.144247	+	0.989542i	$0.453924\pi$
$199$	−11.0716	+	19.1766i	−0.784845	+	1.35939i	−0.929092	+	0.369849i	$0.879409\pi$
$200$	14.7397	−	4.22522i	1.04226	−	0.298768i
$201$	8.81167	+	5.08742i	0.621527	+	0.358839i
$202$	2.39207	−	4.14319i	0.168306	−	0.291514i
$203$	−25.2859			−1.77472
$204$	−2.21432	+	3.83531i	−0.155033	+	0.268526i
$205$	−4.19977	−	5.37592i	−0.293325	−	0.375471i
$206$	2.96796	−	1.71355i	0.206788	−	0.119389i
$207$			6.00645i			0.417477i
$208$		0			0
$209$	−0.474572			−0.0328269
$210$	6.36288	+	8.14482i	0.439081	+	0.562046i
$211$	−9.82717	−	17.0212i	−0.676530	−	1.17178i	−0.976019	−	0.217685i	$-0.930150\pi$
$211$	−9.82717	−	17.0212i	−0.676530	−	1.17178i	0.299489	−	0.954100i	$-0.403184\pi$
$212$	2.83716	+	1.63804i	0.194857	+	0.112501i
$213$	−7.97280			−0.546287
$214$	−18.0013	−	10.3931i	−1.23055	−	0.710456i
$215$	−5.32962	+	13.1897i	−0.363477	+	0.899530i
$216$			17.2128i			1.17118i
$217$	14.0600	+	8.11753i	0.954453	+	0.551054i
$218$	17.5874	−	10.1541i	1.19117	−	0.687722i
$219$	−11.6736	+	6.73975i	−0.788828	+	0.455430i
$220$	0.249353	−	0.0350337i	0.0168114	−	0.00236197i
$221$		0			0
$222$		−	3.63158i		−	0.243736i
$223$	9.83431	+	17.0335i	0.658554	+	1.14065i	0.980990	+	0.194058i	$0.0621650\pi$
$223$	9.83431	+	17.0335i	0.658554	+	1.14065i	−0.322436	+	0.946591i	$0.604502\pi$
$224$	−4.19135	−	7.25964i	−0.280047	−	0.485055i
$225$	1.55003	−	6.21460i	0.103335	−	0.414306i
$226$		−	1.43801i		−	0.0956548i
$227$	6.63581	−	11.4936i	0.440434	−	0.762855i	−0.557287	−	0.830320i	$-0.688158\pi$
$227$	6.63581	−	11.4936i	0.440434	−	0.762855i	0.997722	+	0.0674650i	$0.0214911\pi$
$228$	−0.762714	+	1.32106i	−0.0505120	+	0.0874893i
$229$		−	2.42864i		−	0.160489i	−0.996775	−	0.0802445i	$-0.974430\pi$
$229$		−	2.42864i		−	0.160489i	0.996775	−	0.0802445i	$-0.0255701\pi$
$230$	−4.76989	+	11.8045i	−0.314517	+	0.778364i
$231$	0.407896	+	0.706496i	0.0268376	+	0.0464841i
$232$	−13.3548	−	23.1312i	−0.876787	−	1.51864i
$233$		−	16.1748i		−	1.05965i	−0.848107	−	0.529825i	$-0.822258\pi$
$233$		−	16.1748i		−	1.05965i	0.848107	−	0.529825i	$-0.177742\pi$
$234$		0			0
$235$	−0.341219	−	2.42864i	−0.0222587	−	0.158427i
$236$	4.21597	−	2.43409i	0.274436	−	0.158446i
$237$	−16.1632	+	9.33185i	−1.04992	+	0.606169i
$238$	19.6273	+	11.3319i	1.27225	+	0.734535i
$239$			12.7763i			0.826431i	0.910633	+	0.413215i	$0.135594\pi$
$239$			12.7763i			0.826431i	−0.910633	+	0.413215i	$0.864406\pi$
$240$	−2.93599	+	7.26595i	−0.189517	+	0.469015i
$241$	−5.10807	−	2.94914i	−0.329040	−	0.189971i	0.326375	−	0.945240i	$-0.394173\pi$
$241$	−5.10807	−	2.94914i	−0.329040	−	0.189971i	−0.655415	+	0.755269i	$0.727506\pi$
$242$	13.3017			0.855068
$243$	10.5903	+	6.11430i	0.679367	+	0.392233i
$244$	−0.0738216	−	0.127863i	−0.00472594	−	0.00818557i
$245$	−2.51741	+	1.96665i	−0.160831	+	0.125644i
$246$	4.85728			0.309689
$247$		0			0
$248$			17.1492i			1.08897i
$249$	−10.8157	+	6.24443i	−0.685415	+	0.395725i
$250$	7.98145	−	10.9826i	0.504791	−	0.694602i
$251$	−1.03657	+	1.79538i	−0.0654274	+	0.113324i	−0.896884	−	0.442267i	$-0.854174\pi$
$251$	−1.03657	+	1.79538i	−0.0654274	+	0.113324i	0.831456	+	0.555590i	$0.187508\pi$
$252$	−1.95407			−0.123095
$253$	−0.502461	+	0.870288i	−0.0315895	+	0.0547145i
$254$	2.42058	+	1.39752i	0.151881	+	0.0876885i
$255$	2.62222	+	18.6637i	0.164210	+	1.16877i
$256$	5.83185	−	10.1011i	0.364491	−	0.631316i
$257$	15.9323	−	9.19850i	0.993827	−	0.573787i	0.0874113	−	0.996172i	$-0.472141\pi$
$257$	15.9323	−	9.19850i	0.993827	−	0.573787i	0.906416	+	0.422386i	$0.138807\pi$
$258$	−5.06445	−	8.77189i	−0.315299	−	0.546114i
$259$	6.62222			0.411484
$260$		0			0
$261$	−11.1570			−0.690602
$262$	8.14764	+	14.1121i	0.503363	+	0.871850i
$263$	9.54851	−	5.51283i	0.588786	−	0.339936i	−0.175831	−	0.984420i	$-0.556261\pi$
$263$	9.54851	−	5.51283i	0.588786	−	0.339936i	0.764617	+	0.644484i	$0.222928\pi$
$264$	−0.430862	+	0.746276i	−0.0265177	+	0.0459301i
$265$	13.8064	−	1.93978i	0.848122	−	0.119160i
$266$	6.76056	+	3.90321i	0.414517	+	0.239321i
$267$	3.67952	−	6.37312i	0.225183	−	0.390029i
$268$	−4.07758			−0.249078
$269$	−8.07160	+	13.9804i	−0.492134	+	0.852401i	−0.999959	−	0.00905911i	$-0.997116\pi$
$269$	−8.07160	+	13.9804i	−0.492134	+	0.852401i	0.507825	+	0.861460i	$0.330450\pi$
$270$	9.38253	+	12.0101i	0.571003	+	0.730913i
$271$	−11.2682	+	6.50569i	−0.684493	+	0.395192i	−0.801546	−	0.597933i	$-0.795989\pi$
$271$	−11.2682	+	6.50569i	−0.684493	+	0.395192i	0.117053	+	0.993126i	$0.462655\pi$
$272$			17.1842i			1.04195i
$273$		0			0
$274$	23.2573			1.40503
$275$	0.744460	−	0.770781i	0.0448926	−	0.0464799i
$276$	1.61507	+	2.79738i	0.0972158	+	0.168383i
$277$	−6.55699	−	3.78568i	−0.393971	−	0.227459i	0.289908	−	0.957054i	$-0.406375\pi$
$277$	−6.55699	−	3.78568i	−0.393971	−	0.227459i	−0.683879	+	0.729595i	$0.739709\pi$
$278$	−23.1842			−1.39050
$279$	6.20374	+	3.58173i	0.371408	+	0.214433i
$280$	−18.4582	−	7.45851i	−1.10309	−	0.445731i
$281$		−	6.75557i		−	0.403003i	−0.979488	−	0.201502i	$-0.935418\pi$
$281$		−	6.75557i		−	0.403003i	0.979488	−	0.201502i	$-0.0645822\pi$
$282$	1.51225	+	0.873100i	0.0900534	+	0.0519924i
$283$	−16.5289	+	9.54294i	−0.982539	+	0.567269i	−0.903036	−	0.429565i	$-0.858667\pi$
$283$	−16.5289	+	9.54294i	−0.982539	+	0.567269i	−0.0795033	+	0.996835i	$0.525333\pi$
$284$	2.76704	−	1.59755i	0.164194	−	0.0947974i
$285$	0.903212	+	6.42864i	0.0535017	+	0.380800i
$286$		0			0
$287$			8.85728i			0.522829i
$288$	−1.84937	−	3.20320i	−0.108975	−	0.188750i
$289$	12.1637	+	21.0682i	0.715512	+	1.23930i
$290$	−21.9269	−	8.86010i	−1.28759	−	0.520283i
$291$		−	23.6543i		−	1.38664i
$292$	2.70096	−	4.67820i	0.158062	−	0.273771i
$293$	4.04371	−	7.00391i	0.236236	−	0.409173i	−0.723395	−	0.690434i	$-0.757419\pi$
$293$	4.04371	−	7.00391i	0.236236	−	0.409173i	0.959631	+	0.281261i	$0.0907528\pi$
$294$		−	2.27454i		−	0.132654i
$295$	7.76174	−	19.2087i	0.451906	−	1.11837i
$296$	3.49754	+	6.05792i	0.203290	+	0.352109i
$297$	0.601472	+	1.04178i	0.0349009	+	0.0604502i
$298$			4.33677i			0.251223i
$299$		0			0
$300$	−0.949145	−	3.31111i	−0.0547989	−	0.191167i
$301$	15.9956	−	9.23506i	0.921971	−	0.532300i
$302$	1.33050	−	0.768163i	0.0765616	−	0.0442028i
$303$	−4.47343	−	2.58274i	−0.256992	−	0.148374i
$304$			5.91903i			0.339480i
$305$	−0.582565	−	0.235400i	−0.0333576	−	0.0134790i
$306$	8.66025	+	5.00000i	0.495074	+	0.285831i
$307$	13.4336			0.766694			0.383347	−	0.923604i	$-0.374771\pi$
$307$	13.4336			0.766694			0.383347	+	0.923604i	$0.374771\pi$
$308$	−0.283129	−	0.163465i	−0.0161328	−	0.00931426i
$309$	−1.85013	−	3.20453i	−0.105250	−	0.182299i
$310$	9.34786	+	11.9657i	0.530923	+	0.679609i
$311$	−20.2034			−1.14563			−0.572815	−	0.819684i	$-0.694149\pi$
$311$	−20.2034			−1.14563			−0.572815	+	0.819684i	$0.694149\pi$
$312$		0			0
$313$			15.1111i			0.854129i	0.904221	+	0.427064i	$0.140452\pi$
$313$			15.1111i			0.854129i	−0.904221	+	0.427064i	$0.859548\pi$
$314$	−5.90265	+	3.40790i	−0.333106	+	0.192319i
$315$	−6.55327	+	5.11953i	−0.369235	+	0.288453i
$316$	3.73975	−	6.47743i	0.210377	−	0.364384i
$317$	22.2810			1.25143			0.625713	−	0.780054i	$-0.284808\pi$
$317$	22.2810			1.25143			0.625713	+	0.780054i	$0.284808\pi$
$318$	−4.96343	+	8.59692i	−0.278336	+	0.482091i
$319$	−1.61656	−	0.933323i	−0.0905102	−	0.0522561i
$320$	−2.75404	−	19.6019i	−0.153955	−	1.09578i
$321$	−11.2215	+	19.4361i	−0.626321	+	1.08482i
$322$	14.3157	−	8.26517i	0.797783	−	0.460600i
$323$	7.11753	+	12.3279i	0.396030	+	0.685944i
$324$	1.84743			0.102635
$325$		0			0
$326$	−4.51606			−0.250121
$327$	−10.9634	−	18.9892i	−0.606279	−	1.05011i
$328$	−8.10252	+	4.67799i	−0.447387	+	0.258299i
$329$	−1.59210	+	2.75761i	−0.0877755	+	0.152032i
$330$	0.106156	+	0.755569i	0.00584370	+	0.0415927i
$331$	−7.14974	−	4.12790i	−0.392985	−	0.226890i	0.290468	−	0.956885i	$-0.406189\pi$
$331$	−7.14974	−	4.12790i	−0.392985	−	0.226890i	−0.683453	+	0.729995i	$0.739522\pi$
$332$	2.50246	−	4.33439i	0.137340	−	0.237881i
$333$	2.92195			0.160122
$334$	4.27232	−	7.39988i	0.233771	−	0.404903i
$335$	−13.6748	+	10.6830i	−0.747133	+	0.583674i
$336$	8.81167	−	5.08742i	0.480716	−	0.277542i
$337$		−	13.7462i		−	0.748803i	−0.927267	−	0.374402i	$-0.877848\pi$
$337$		−	13.7462i		−	0.748803i	0.927267	−	0.374402i	$-0.122152\pi$
$338$		0			0
$339$	−1.55262			−0.0843270
$340$	−4.64981	−	5.95200i	−0.252172	−	0.322793i
$341$	0.599249	+	1.03793i	0.0324512	+	0.0562071i
$342$	2.98299	+	1.72223i	0.161302	+	0.0931276i
$343$	−16.1748			−0.873359
$344$	16.8962	+	9.75504i	0.910984	+	0.525957i
$345$	12.7454	+	5.15008i	0.686187	+	0.277271i
$346$			0.879077i			0.0472595i
$347$	1.05589	+	0.609621i	0.0566834	+	0.0327262i	0.528074	−	0.849198i	$-0.322914\pi$
$347$	1.05589	+	0.609621i	0.0566834	+	0.0327262i	−0.471390	+	0.881925i	$0.656248\pi$
$348$	−5.19615	+	3.00000i	−0.278543	+	0.160817i
$349$	19.4956	−	11.2558i	1.04358	−	0.602510i	0.122733	−	0.992440i	$-0.460834\pi$
$349$	19.4956	−	11.2558i	1.04358	−	0.602510i	0.920844	+	0.389930i	$0.127501\pi$
$350$	−16.9447	+	4.85728i	−0.905732	+	0.259632i
$351$		0			0
$352$		−	0.618825i		−	0.0329835i
$353$	−7.14050	−	12.3677i	−0.380050	−	0.658267i	0.611019	−	0.791616i	$-0.290760\pi$
$353$	−7.14050	−	12.3677i	−0.380050	−	0.658267i	−0.991069	+	0.133350i	$0.957427\pi$
$354$	7.37556	+	12.7748i	0.392007	+	0.678975i
$355$	5.09422	−	12.6071i	0.270373	−	0.669117i
$356$			2.94914i			0.156304i
$357$	12.2351	−	21.1918i	0.647548	−	1.12159i
$358$	2.45383	−	4.25016i	0.129689	−	0.224628i
$359$		−	12.1541i		−	0.641469i	−0.947169	−	0.320734i	$-0.896070\pi$
$359$		−	12.1541i		−	0.641469i	0.947169	−	0.320734i	$-0.103930\pi$
$360$	−8.14440	−	3.29095i	−0.429248	−	0.173448i
$361$	−7.04839	−	12.2082i	−0.370968	−	0.642536i
$362$	1.42149	+	2.46210i	0.0747121	+	0.129405i
$363$		−	14.3620i		−	0.753808i
$364$		0			0
$365$	−3.19850	−	22.7654i	−0.167417	−	1.19160i
$366$	0.387438	−	0.223688i	0.0202517	−	0.0116923i
$367$	4.03330	−	2.32862i	0.210536	−	0.121553i	−0.391024	−	0.920380i	$-0.627879\pi$
$367$	4.03330	−	2.32862i	0.210536	−	0.121553i	0.601561	+	0.798827i	$0.294546\pi$
$368$	10.8545	+	6.26687i	0.565832	+	0.326683i
$369$			3.90813i			0.203449i
$370$	5.74250	+	2.32040i	0.298538	+	0.120632i
$371$	−15.6765	−	9.05086i	−0.813885	−	0.469897i
$372$	3.85236			0.199735
$373$	−30.2591	−	17.4701i	−1.56676	−	0.904569i	−0.996543	−	0.0830740i	$-0.973526\pi$
$373$	−30.2591	−	17.4701i	−1.56676	−	0.904569i	−0.570216	−	0.821495i	$-0.693140\pi$
$374$	0.836535	+	1.44892i	0.0432562	+	0.0749220i
$375$	−11.8580	−	8.61762i	−0.612344	−	0.445012i
$376$	−3.36349			−0.173459
$377$		0			0
$378$		−	19.7877i		−	1.01777i
$379$	15.1309	−	8.73583i	0.777222	−	0.448729i	−0.0582228	−	0.998304i	$-0.518543\pi$
$379$	15.1309	−	8.73583i	0.777222	−	0.448729i	0.835445	+	0.549574i	$0.185210\pi$
$380$	−1.60161	−	2.05014i	−0.0821609	−	0.105170i
$381$	1.50891	−	2.61352i	0.0773040	−	0.133895i
$382$	−2.55215			−0.130579
$383$	−9.33900	+	16.1756i	−0.477200	+	0.826535i	−0.999659	−	0.0261296i	$-0.991682\pi$
$383$	−9.33900	+	16.1756i	−0.477200	+	0.826535i	0.522458	+	0.852665i	$0.325015\pi$
$384$	5.64866	+	3.26126i	0.288257	+	0.166425i
$385$	−1.37778	+	0.193576i	−0.0702184	+	0.00986555i
$386$	8.20940	−	14.2191i	0.417847	−	0.723733i
$387$	7.05780	−	4.07483i	0.358768	−	0.207135i
$388$	4.73975	+	8.20948i	0.240624	+	0.416773i
$389$	1.61285			0.0817746			0.0408873	−	0.999164i	$-0.486982\pi$
$389$	1.61285			0.0817746			0.0408873	+	0.999164i	$0.486982\pi$
$390$		0			0
$391$	30.1432			1.52441
$392$	2.19059	+	3.79421i	0.110641	+	0.191636i
$393$	15.2369	−	8.79706i	0.768602	−	0.443753i
$394$	1.21432	−	2.10326i	0.0611765	−	0.105961i
$395$	−4.42864	−	31.5210i	−0.222829	−	1.58599i
$396$	−0.124926	−	0.0721262i	−0.00627778	−	0.00362448i
$397$	3.28814	−	5.69523i	0.165027	−	0.285835i	−0.771638	−	0.636062i	$-0.780562\pi$
$397$	3.28814	−	5.69523i	0.165027	−	0.285835i	0.936665	+	0.350227i	$0.113896\pi$
$398$	26.8889			1.34782
$399$	4.21432	−	7.29942i	0.210980	−	0.365428i
$400$	−9.61345	−	9.28516i	−0.480673	−	0.464258i
$401$	18.9730	−	10.9541i	0.947466	−	0.547020i	0.0551735	−	0.998477i	$-0.482429\pi$
$401$	18.9730	−	10.9541i	0.947466	−	0.547020i	0.892293	+	0.451457i	$0.149095\pi$
$402$		−	12.3555i		−	0.616237i
$403$		0			0
$404$	2.07007			0.102990
$405$	6.19566	−	4.84016i	0.307865	−	0.240510i
$406$	15.3526	+	26.5915i	0.761936	+	1.31971i
$407$	0.423367	+	0.244431i	0.0209855	+	0.0121160i
$408$	25.8479			1.27966
$409$	−8.82790	−	5.09679i	−0.436511	−	0.252020i	0.265605	−	0.964082i	$-0.414428\pi$
$409$	−8.82790	−	5.09679i	−0.436511	−	0.252020i	−0.702117	+	0.712062i	$0.747762\pi$
$410$	−3.10356	+	7.68065i	−0.153274	+	0.379320i
$411$		−	25.1111i		−	1.23864i
$412$	1.28422	+	0.741443i	0.0632688	+	0.0365283i
$413$	−23.2950	+	13.4494i	−1.14627	+	0.661801i
$414$	6.31658	−	3.64688i	0.310443	−	0.179234i
$415$	−2.96343	−	21.0923i	−0.145469	−	1.03538i
$416$		0			0
$417$			25.0321i			1.22583i
$418$	0.288141	+	0.499075i	0.0140935	+	0.0244106i
$419$	3.65878	+	6.33719i	0.178743	+	0.309592i	0.941450	−	0.337152i	$-0.109464\pi$
$419$	3.65878	+	6.33719i	0.178743	+	0.309592i	−0.762707	+	0.646744i	$0.776130\pi$
$420$	−1.67547	+	4.14642i	−0.0817543	+	0.202325i
$421$		−	7.86665i		−	0.383397i	−0.981454	−	0.191698i	$-0.938600\pi$
$421$		−	7.86665i		−	0.383397i	0.981454	−	0.191698i	$-0.0613996\pi$
$422$	−11.9333	+	20.6691i	−0.580905	+	1.00616i
$423$	−0.702491	+	1.21675i	−0.0341563	+	0.0591604i
$424$		−	19.1209i		−	0.928594i
$425$	−31.1878	−	7.77875i	−1.51283	−	0.377325i
$426$	4.84077	+	8.38445i	0.234536	+	0.406228i
$427$	0.407896	+	0.706496i	0.0197395	+	0.0341898i
$428$		−	8.99402i		−	0.434743i
$429$		0			0
$430$	17.1066	−	2.40345i	0.824955	−	0.115905i
$431$	−33.7053	+	19.4598i	−1.62353	+	0.937343i	−0.637560	+	0.770401i	$0.720056\pi$
$431$	−33.7053	+	19.4598i	−1.62353	+	0.937343i	−0.985967	+	0.166943i	$0.946611\pi$
$432$	12.9934	−	7.50177i	0.625147	−	0.360929i
$433$	−17.4967	−	10.1017i	−0.840837	−	0.485457i	0.0167119	−	0.999860i	$-0.494680\pi$
$433$	−17.4967	−	10.1017i	−0.840837	−	0.485457i	−0.857548	+	0.514403i	$0.828014\pi$
$434$		−	19.7146i		−	0.946329i
$435$	−9.56630	+	23.6746i	−0.458669	+	1.13511i
$436$	7.60995	+	4.39361i	0.364450	+	0.210416i
$437$	10.3827			0.496672
$438$	14.1755	+	8.18421i	0.677330	+	0.391057i
$439$	−5.44446	−	9.43008i	−0.259850	−	0.450073i	0.706352	−	0.707861i	$-0.250340\pi$
$439$	−5.44446	−	9.43008i	−0.259850	−	0.450073i	−0.966202	+	0.257788i	$0.917006\pi$
$440$	−0.904761	−	1.15814i	−0.0431328	−	0.0552122i
$441$	1.83008			0.0871468
$442$		0			0
$443$		−	28.6287i		−	1.36019i	−0.733124	−	0.680095i	$-0.761939\pi$
$443$		−	28.6287i		−	1.36019i	0.733124	−	0.680095i	$-0.238061\pi$
$444$	1.36084	−	0.785680i	0.0645825	−	0.0372867i
$445$	7.72657	+	9.89042i	0.366275	+	0.468851i
$446$	11.9420	−	20.6842i	0.565470	−	0.979423i
$447$	4.68244			0.221472
$448$	−12.8501	+	22.2571i	−0.607112	+	1.05155i
$449$	9.46601	+	5.46520i	0.446729	+	0.257919i	0.706448	−	0.707765i	$-0.250297\pi$
$449$	9.46601	+	5.46520i	0.446729	+	0.257919i	−0.259719	+	0.965684i	$0.583630\pi$
$450$	−7.47658	+	2.14320i	−0.352449	+	0.101031i
$451$	−0.326929	+	0.566258i	−0.0153945	+	0.0266641i
$452$	0.538855	−	0.311108i	0.0253456	−	0.0146333i
$453$	−0.829390	−	1.43655i	−0.0389682	−	0.0674948i
$454$	−16.1160			−0.756361
$455$		0			0
$456$	8.90321			0.416931
$457$	5.70318	+	9.87820i	0.266784	+	0.462083i	0.968029	−	0.250837i	$-0.0807058\pi$
$457$	5.70318	+	9.87820i	0.266784	+	0.462083i	−0.701246	+	0.712920i	$0.747372\pi$
$458$	−2.55403	+	1.47457i	−0.119342	+	0.0689022i
$459$	18.0415	−	31.2488i	0.842105	−	1.45857i
$460$	−5.45536	+	0.766468i	−0.254357	+	0.0357368i
$461$	22.6321	+	13.0667i	1.05408	+	0.608576i	0.923790	−	0.382900i	$-0.125074\pi$
$461$	22.6321	+	13.0667i	1.05408	+	0.608576i	0.130294	+	0.991475i	$0.458408\pi$
$462$	0.495316	−	0.857913i	0.0230442	−	0.0399137i
$463$	−7.92242			−0.368186			−0.184093	−	0.982909i	$-0.558935\pi$
$463$	−7.92242			−0.368186			−0.184093	+	0.982909i	$0.558935\pi$
$464$	−11.6407	+	20.1623i	−0.540408	+	0.936013i
$465$	12.9195	−	10.0929i	0.599126	−	0.468049i
$466$	−17.0100	+	9.82071i	−0.787972	+	0.454936i
$467$			10.8923i			0.504036i	0.967723	+	0.252018i	$0.0810942\pi$
$467$			10.8923i			0.504036i	−0.967723	+	0.252018i	$0.918906\pi$
$468$		0			0
$469$	22.5303			1.04035
$470$	−2.34686	+	1.83341i	−0.108253	+	0.0845689i
$471$	3.67952	+	6.37312i	0.169544	+	0.293658i
$472$	−24.6066	−	14.2066i	−1.13261	−	0.653914i
$473$	1.36349			0.0626935
$474$	19.6273	+	11.3319i	0.901514	+	0.520489i
$475$	−10.7425	−	2.67936i	−0.492900	−	0.122938i
$476$			9.80642i			0.449477i
$477$	−6.91703	−	3.99355i	−0.316709	−	0.182852i
$478$	13.4360	−	7.75726i	0.614547	−	0.354809i
$479$	−7.90839	+	4.56591i	−0.361344	+	0.208622i	−0.669670	−	0.742659i	$-0.733564\pi$
$479$	−7.90839	+	4.56591i	−0.361344	+	0.208622i	0.308326	+	0.951281i	$0.400231\pi$
$480$	−8.38271	+	1.17775i	−0.382616	+	0.0537569i
$481$		0			0
$482$			7.16241i			0.326239i
$483$	−8.92396	−	15.4567i	−0.406054	−	0.703306i
$484$	2.87778	+	4.98447i	0.130808	+	0.226567i
$485$	37.4038	+	15.1139i	1.69842	+	0.686289i
$486$		−	14.8494i		−	0.673584i
$487$	8.09457	−	14.0202i	0.366800	−	0.635316i	−0.622263	−	0.782808i	$-0.713787\pi$
$487$	8.09457	−	14.0202i	0.366800	−	0.635316i	0.989063	+	0.147492i	$0.0471201\pi$
$488$	−0.430862	+	0.746276i	−0.0195042	+	0.0337823i
$489$			4.87601i			0.220501i
$490$	3.59666	+	1.45332i	0.162480	+	0.0656543i
$491$	13.1318	+	22.7450i	0.592631	+	1.02647i	0.993877	+	0.110496i	$0.0352440\pi$
$491$	13.1318	+	22.7450i	0.592631	+	1.02647i	−0.401246	+	0.915970i	$0.631423\pi$
$492$	1.05086	+	1.82013i	0.0473762	+	0.0820580i
$493$			55.9911i			2.52171i
$494$		0			0
$495$	−0.607926	+	0.0854124i	−0.0273242	+	0.00383900i
$496$	12.9454	−	7.47404i	0.581267	−	0.335595i
$497$	−15.2891	+	8.82717i	−0.685810	+	0.395953i
$498$	13.1337	+	7.58274i	0.588534	+	0.339791i
$499$		−	30.0306i		−	1.34435i	−0.740391	−	0.672177i	$-0.765359\pi$
$499$		−	30.0306i		−	1.34435i	0.740391	−	0.672177i	$-0.234641\pi$
$500$	5.84220	+	0.614782i	0.261271	+	0.0274939i
$501$	−7.98969	−	4.61285i	−0.356953	−	0.206087i
$502$	2.51744			0.112359
$503$	14.4889	+	8.36519i	0.646030	+	0.372985i	0.786933	−	0.617038i	$-0.211667\pi$
$503$	14.4889	+	8.36519i	0.646030	+	0.372985i	−0.140904	+	0.990023i	$0.545001\pi$
$504$	5.70249	+	9.87700i	0.254009	+	0.439957i
$505$	6.94229	−	5.42345i	0.308928	−	0.241340i
$506$	1.22030			0.0542488
$507$		0			0
$508$			1.20940i			0.0536583i
$509$	10.3649	−	5.98418i	0.459416	−	0.265244i	−0.252383	−	0.967628i	$-0.581214\pi$
$509$	10.3649	−	5.98418i	0.459416	−	0.265244i	0.711799	+	0.702383i	$0.247881\pi$
$510$	18.0352	−	14.0895i	0.798614	−	0.623892i
$511$	−14.9240	+	25.8490i	−0.660197	+	1.14349i
$512$	−24.1131			−1.06566
$513$	6.21432	−	10.7635i	0.274369	−	0.475221i
$514$	−19.3469	−	11.1699i	−0.853354	−	0.492684i
$515$	6.24935	−	0.878023i	0.275379	−	0.0386903i
$516$	2.19135	−	3.79554i	0.0964689	−	0.167089i
$517$	−0.203571	+	0.117532i	−0.00895303	+	0.00516904i
$518$	−4.02074	−	6.96413i	−0.176661	−	0.305986i
$519$	0.949145			0.0416628
$520$		0			0
$521$	5.75065			0.251940			0.125970	−	0.992034i	$-0.459796\pi$
$521$	5.75065			0.251940			0.125970	+	0.992034i	$0.459796\pi$
$522$	6.77409	+	11.7331i	0.296494	+	0.513542i
$523$	−18.0164	+	10.4018i	−0.787801	+	0.454837i	−0.839188	−	0.543842i	$-0.816969\pi$
$523$	−18.0164	+	10.4018i	−0.787801	+	0.454837i	0.0513870	+	0.998679i	$0.483636\pi$
$524$	−3.52543	+	6.10622i	−0.154009	+	0.266751i
$525$	5.24443	+	18.2953i	0.228886	+	0.798472i
$526$	−11.5949	−	6.69434i	−0.505563	−	0.291887i
$527$	17.9748	−	31.1333i	0.782995	−	1.35619i
$528$	0.751123			0.0326884
$529$	−0.507145	+	0.878401i	−0.0220498	+	0.0381913i
$530$	−10.4226	−	13.3415i	−0.452730	−	0.579519i
$531$	−10.2786	+	5.93433i	−0.446051	+	0.257528i
$532$			3.37778i			0.146446i
$533$		0			0
$534$	−8.93624			−0.386709
$535$	−23.5638	−	30.1629i	−1.01875	−	1.30405i
$536$	11.8995	+	20.6105i	0.513978	+	0.890237i
$537$	−4.58892	−	2.64941i	−0.198026	−	0.114331i
$538$	19.6030			0.845145
$539$	0.265165	+	0.153093i	0.0114214	+	0.00659417i
$540$	−2.47059	+	6.11420i	−0.106317	+	0.263113i
$541$		−	16.6222i		−	0.714645i	−0.933981	−	0.357322i	$-0.883690\pi$
$541$		−	16.6222i		−	0.714645i	0.933981	−	0.357322i	$-0.116310\pi$
$542$	13.6832	+	7.89999i	0.587743	+	0.339333i
$543$	2.65834	−	1.53480i	0.114080	−	0.0658644i
$544$	−16.0752	+	9.28100i	−0.689217	+	0.397919i
$545$	37.0321	−	5.20294i	1.58628	−	0.222870i
$546$		0			0
$547$			29.9748i			1.28163i	0.767695	+	0.640815i	$0.221404\pi$
$547$			29.9748i			1.28163i	−0.767695	+	0.640815i	$0.778596\pi$
$548$	5.03164	+	8.71506i	0.214941	+	0.372289i
$549$	0.179978	+	0.311730i	0.00768126	+	0.0133043i
$550$	−1.26258	−	0.314910i	−0.0538368	−	0.0134278i
$551$			19.2859i			0.821608i
$552$	9.42642	−	16.3270i	0.401215	−	0.694925i
$553$	−20.6637	+	35.7906i	−0.878710	+	1.52197i
$554$			9.19405i			0.390618i
$555$	2.50535	−	6.20021i	0.106346	−	0.263184i
$556$	−5.01582	−	8.68766i	−0.212718	−	0.368439i
$557$	−2.51828	−	4.36179i	−0.106703	−	0.184815i	0.807730	−	0.589553i	$-0.200696\pi$
$557$	−2.51828	−	4.36179i	−0.106703	−	0.184815i	−0.914433	+	0.404738i	$0.867363\pi$
$558$		−	8.69874i		−	0.368247i
$559$		0			0
$560$	2.41435	+	17.1842i	0.102025	+	0.726165i
$561$	1.56441	−	0.903212i	0.0660494	−	0.0381336i
$562$	−7.10437	+	4.10171i	−0.299680	+	0.173020i
$563$	2.49629	+	1.44123i	0.105206	+	0.0607408i	0.551680	−	0.834056i	$-0.313987\pi$
$563$	2.49629	+	1.44123i	0.105206	+	0.0607408i	−0.446474	+	0.894797i	$0.647320\pi$
$564$			0.755569i			0.0318152i
$565$	0.992050	−	2.45511i	0.0417358	−	0.103287i
$566$	20.0713	+	11.5882i	0.843661	+	0.487088i
$567$	−10.2079			−0.428690
$568$	−16.1500	−	9.32418i	−0.677637	−	0.391234i
$569$	2.18643	+	3.78701i	0.0916600	+	0.158760i	0.908210	−	0.418515i	$-0.137449\pi$
$569$	2.18643	+	3.78701i	0.0916600	+	0.158760i	−0.816550	+	0.577275i	$0.804116\pi$
$570$	6.21217	−	4.85306i	0.260199	−	0.203272i
$571$	1.58120			0.0661714			0.0330857	−	0.999453i	$-0.489467\pi$
$571$	1.58120			0.0661714			0.0330857	+	0.999453i	$0.489467\pi$
$572$		0			0
$573$			2.75557i			0.115116i
$574$	9.31460	−	5.37778i	0.388784	−	0.224464i
$575$	−16.2873	+	16.8632i	−0.679227	+	0.703243i
$576$	−5.66992	+	9.82059i	−0.236247	+	0.409191i
$577$	−7.61729			−0.317112			−0.158556	−	0.987350i	$-0.550684\pi$
$577$	−7.61729			−0.317112			−0.158556	+	0.987350i	$0.550684\pi$
$578$	14.7706	−	25.5835i	0.614377	−	1.06413i
$579$	−15.3524	−	8.86373i	−0.638025	−	0.368364i
$580$	−1.42372	−	10.1334i	−0.0591166	−	0.420765i
$581$	−13.8272	+	23.9494i	−0.573648	+	0.993587i
$582$	−24.8756	+	14.3620i	−1.03113	+	0.595323i
$583$	−0.668149	−	1.15727i	−0.0276719	−	0.0479291i
$584$	−31.5285			−1.30466
$585$		0			0
$586$	−9.82071			−0.405690
$587$	23.4121	+	40.5510i	0.966322	+	1.67372i	0.706021	+	0.708191i	$0.250488\pi$
$587$	23.4121	+	40.5510i	0.966322	+	1.67372i	0.260301	+	0.965528i	$0.416178\pi$
$588$	0.852324	−	0.492089i	0.0351492	−	0.0202934i
$589$	6.19135	−	10.7237i	0.255110	−	0.441864i
$590$	−24.9131	+	3.50024i	−1.02565	+	0.144103i
$591$	−2.27091	−	1.31111i	−0.0934126	−	0.0539318i
$592$	3.04863	−	5.28039i	0.125298	−	0.217023i
$593$	−15.9398			−0.654568			−0.327284	−	0.944926i	$-0.606133\pi$
$593$	−15.9398			−0.654568			−0.327284	+	0.944926i	$0.606133\pi$
$594$	0.730379	−	1.26505i	0.0299678	−	0.0519058i
$595$	25.6922	+	32.8874i	1.05328	+	1.34825i
$596$	−1.62509	+	0.938246i	−0.0665662	+	0.0384320i
$597$		−	29.0321i		−	1.18821i
$598$		0			0
$599$	−18.4889			−0.755434			−0.377717	−	0.925921i	$-0.623291\pi$
$599$	−18.4889			−0.755434			−0.377717	+	0.925921i	$0.623291\pi$
$600$	−13.9664	+	14.4602i	−0.570177	+	0.590337i
$601$	−10.3778	−	17.9748i	−0.423319	−	0.733209i	0.572943	−	0.819595i	$-0.305802\pi$
$601$	−10.3778	−	17.9748i	−0.423319	−	0.733209i	−0.996262	+	0.0863857i	$0.972468\pi$
$602$	−19.4238	−	11.2143i	−0.791654	−	0.457062i
$603$	9.94116			0.404835
$604$	0.575697	+	0.332379i	0.0234248	+	0.0135243i
$605$	22.7101	+	9.17658i	0.923297	+	0.373081i
$606$			6.27254i			0.254804i
$607$	31.2432	+	18.0383i	1.26812	+	0.732150i	0.974632	−	0.223812i	$-0.0718501\pi$
$607$	31.2432	+	18.0383i	1.26812	+	0.732150i	0.293489	+	0.955962i	$0.405183\pi$
$608$	−5.53703	+	3.19680i	−0.224556	+	0.129647i
$609$	28.7110	−	16.5763i	1.16343	−	0.671705i
$610$	0.106156	+	0.755569i	0.00429813	+	0.0305921i
$611$		0			0
$612$			4.32693i			0.174906i
$613$	4.97481	+	8.61662i	0.200931	+	0.348022i	0.948829	−	0.315792i	$-0.102270\pi$
$613$	4.97481	+	8.61662i	0.200931	+	0.348022i	−0.747898	+	0.663814i	$0.768937\pi$
$614$	−8.15632	−	14.1272i	−0.329162	−	0.570126i
$615$	8.29284	+	3.35093i	0.334400	+	0.135123i
$616$			1.90813i			0.0768809i
$617$	−1.04593	+	1.81161i	−0.0421077	+	0.0729326i	−0.886311	−	0.463090i	$-0.846741\pi$
$617$	−1.04593	+	1.81161i	−0.0421077	+	0.0729326i	0.844203	+	0.536023i	$0.180074\pi$
$618$	−2.24665	+	3.89132i	−0.0903737	+	0.156532i
$619$			18.4681i			0.742296i	0.928574	+	0.371148i	$0.121036\pi$
$619$			18.4681i			0.742296i	−0.928574	+	0.371148i	$0.878964\pi$
$620$	−2.46146	+	6.09160i	−0.0988548	+	0.244645i
$621$	−13.1590	−	22.7921i	−0.528053	−	0.914615i
$622$	12.2667	+	21.2466i	0.491850	+	0.851909i
$623$		−	16.2953i		−	0.652857i
$624$		0			0
$625$	21.2034	−	13.2444i	0.848137	−	0.529777i
$626$	15.8913	−	9.17484i	0.635144	−	0.366700i
$627$	0.538855	−	0.311108i	0.0215198	−	0.0124244i
$628$	−2.55403	−	1.47457i	−0.101917	−	0.0588418i
$629$		−	14.6637i		−	0.584680i
$630$	9.36274	+	3.78325i	0.373021	+	0.150728i
$631$	−33.4855	−	19.3329i	−1.33304	−	0.769629i	−0.347272	−	0.937764i	$-0.612892\pi$
$631$	−33.4855	−	19.3329i	−1.33304	−	0.769629i	−0.985764	+	0.168136i	$0.946225\pi$
$632$	−43.6543			−1.73648
$633$	22.3166	+	12.8845i	0.887004	+	0.512112i
$634$	−13.5281	−	23.4314i	−0.537271	−	0.930580i
$635$	3.16855	+	4.05590i	0.125740	+	0.160954i
$636$	−4.29529			−0.170319
$637$		0			0
$638$			2.26671i			0.0897398i
$639$	−6.74607	+	3.89485i	−0.266871	+	0.154078i
$640$	−8.76613	+	6.84826i	−0.346512	+	0.270701i
$641$	12.2859	−	21.2798i	0.485265	−	0.840503i	−0.514592	−	0.857435i	$-0.672057\pi$
$641$	12.2859	−	21.2798i	0.485265	−	0.840503i	0.999857	+	0.0169322i	$0.00538994\pi$
$642$	27.2529			1.07559
$643$	13.7469	−	23.8103i	0.542125	−	0.938987i	−0.456657	−	0.889643i	$-0.650953\pi$
$643$	13.7469	−	23.8103i	0.542125	−	0.938987i	0.998782	−	0.0493445i	$-0.0157132\pi$
$644$	6.19430	+	3.57628i	0.244090	+	0.140925i
$645$	−2.59502	−	18.4701i	−0.102179	−	0.727261i
$646$	8.64296	−	14.9700i	0.340053	−	0.588989i
$647$	11.9349	−	6.89062i	0.469209	−	0.270898i	−0.246699	−	0.969092i	$-0.579346\pi$
$647$	11.9349	−	6.89062i	0.469209	−	0.270898i	0.715909	+	0.698194i	$0.246013\pi$
$648$	−5.39131	−	9.33802i	−0.211791	−	0.366832i
$649$	−1.98571			−0.0779459
$650$		0			0
$651$	−21.2859			−0.834261
$652$	−0.977034	−	1.69227i	−0.0382636	−	0.0662745i
$653$	−1.83636	+	1.06022i	−0.0718623	+	0.0414897i	−0.535501	−	0.844535i	$-0.679877\pi$
$653$	−1.83636	+	1.06022i	−0.0718623	+	0.0414897i	0.463638	+	0.886025i	$0.346544\pi$
$654$	−13.3131	+	23.0590i	−0.520584	+	0.901678i
$655$	4.17484	+	29.7146i	0.163125	+	1.16104i
$656$	7.06257	+	4.07758i	0.275747	+	0.159203i
$657$	−6.58496	+	11.4055i	−0.256904	+	0.444970i
$658$	3.86665			0.150738
$659$	16.9447	−	29.3491i	0.660072	−	1.14328i	−0.320525	−	0.947240i	$-0.603859\pi$
$659$	16.9447	−	29.3491i	0.660072	−	1.14328i	0.980596	−	0.196038i	$-0.0628075\pi$
$660$	−0.260163	+	0.203244i	−0.0101268	+	0.00791125i
$661$	32.3624	−	18.6844i	1.25875	−	0.726741i	0.285920	−	0.958253i	$-0.407701\pi$
$661$	32.3624	−	18.6844i	1.25875	−	0.726741i	0.972832	+	0.231513i	$0.0743675\pi$
$662$			10.0252i			0.389640i
$663$		0			0
$664$	−29.2114			−1.13362
$665$	8.84958	+	11.3279i	0.343172	+	0.439278i
$666$	−1.77409	−	3.07281i	−0.0687446	−	0.119069i
$667$	35.3672	+	20.4193i	1.36942	+	0.790637i
$668$	3.69721			0.143049
$669$	−22.3328	−	12.8938i	−0.863436	−	0.498505i
$670$	19.5374	+	7.89456i	0.754794	+	0.304993i
$671$			0.0602231i			0.00232489i
$672$	9.51817	+	5.49532i	0.367171	+	0.211986i
$673$	30.7099	−	17.7304i	1.18378	−	0.683456i	0.226894	−	0.973919i	$-0.427143\pi$
$673$	30.7099	−	17.7304i	1.18378	−	0.683456i	0.956886	+	0.290463i	$0.0938095\pi$
$674$	−14.4559	+	8.34614i	−0.556822	+	0.321481i
$675$	7.73329	+	26.9777i	0.297655	+	1.03837i
$676$		0			0
$677$		−	15.3047i		−	0.588206i	−0.955774	−	0.294103i	$-0.904979\pi$
$677$		−	15.3047i		−	0.588206i	0.955774	−	0.294103i	$-0.0950208\pi$
$678$	0.942691	+	1.63279i	0.0362038	+	0.0627069i
$679$	−26.1891	−	45.3609i	−1.00505	−	1.74079i
$680$	−16.5155	+	40.8724i	−0.633342	+	1.56739i
$681$			17.4005i			0.666790i
$682$	0.727680	−	1.26038i	0.0278643	−	0.0482624i
$683$	6.54839	−	11.3422i	0.250567	−	0.433995i	−0.713115	−	0.701047i	$-0.752716\pi$
$683$	6.54839	−	11.3422i	0.250567	−	0.433995i	0.963682	+	0.267052i	$0.0860495\pi$
$684$			1.49039i			0.0569866i
$685$	39.7073	+	16.0447i	1.51714	+	0.613038i
$686$	9.82071	+	17.0100i	0.374957	+	0.649444i
$687$	1.59210	+	2.75761i	0.0607426	+	0.105209i
$688$		−	17.0060i		−	0.648347i
$689$		0			0
$690$	−2.32248	−	16.5303i	−0.0884154	−	0.629300i
$691$	−15.9417	+	9.20395i	−0.606451	+	0.350135i	−0.771575	−	0.636138i	$-0.780531\pi$
$691$	−15.9417	+	9.20395i	−0.606451	+	0.350135i	0.165124	+	0.986273i	$0.447198\pi$
$692$	−0.329411	+	0.190185i	−0.0125223	+	0.00722976i
$693$	0.690271	+	0.398528i	0.0262212	+	0.0151388i
$694$		−	1.48055i		−	0.0562009i
$695$	−39.5825	−	15.9943i	−1.50145	−	0.606698i
$696$	30.3275	+	17.5096i	1.14956	+	0.663700i
$697$	19.6128			0.742890
$698$	−23.6739	−	13.6681i	−0.896071	−	0.517347i
$699$	10.6035	+	18.3658i	0.401060	+	0.694657i
$700$	−5.48606	−	5.29871i	−0.207354	−	0.200273i
$701$	31.3689			1.18479			0.592393	−	0.805649i	$-0.298183\pi$
$701$	31.3689			1.18479			0.592393	+	0.805649i	$0.298183\pi$
$702$		0			0
$703$		−	5.05086i		−	0.190497i
$704$	−1.64305	+	0.948617i	−0.0619249	+	0.0357524i
$705$	1.97954	+	2.53392i	0.0745539	+	0.0954329i
$706$	−8.67085	+	15.0183i	−0.326332	+	0.565223i
$707$	−11.4380			−0.430171
$708$	−3.19135	+	5.52759i	−0.119938	+	0.207739i
$709$	−8.20948	−	4.73975i	−0.308314	−	0.178005i	0.337858	−	0.941197i	$-0.390298\pi$
$709$	−8.20948	−	4.73975i	−0.308314	−	0.178005i	−0.646172	+	0.763192i	$0.723631\pi$
$710$	−16.3511	+	2.29729i	−0.613644	+	0.0862159i
$711$	−9.11753	+	15.7920i	−0.341934	+	0.592247i
$712$	14.9067	−	8.60639i	0.558653	−	0.322538i
$713$	−13.1104	−	22.7079i	−0.490988	−	0.850416i
$714$	−29.7146			−1.11204
$715$		0			0
$716$	2.12351			0.0793592
$717$	−8.37556	−	14.5069i	−0.312791	−	0.541770i
$718$	−12.7816	+	7.37948i	−0.477006	+	0.275400i
$719$	14.8113	−	25.6540i	0.552370	−	0.956733i	−0.445733	−	0.895166i	$-0.647057\pi$
$719$	14.8113	−	25.6540i	0.552370	−	0.956733i	0.998103	−	0.0615669i	$-0.0196098\pi$
$720$	1.06529	+	7.58226i	0.0397011	+	0.282574i
$721$	−7.09585	−	4.09679i	−0.264263	−	0.152572i
$722$	−8.55900	+	14.8246i	−0.318533	+	0.551716i
$723$	7.73329			0.287604
$724$	−0.615071	+	1.06533i	−0.0228589	+	0.0395928i
$725$	−31.3234	−	30.2537i	−1.16332	−	1.12360i
$726$	−15.1035	+	8.72001i	−0.560543	+	0.323630i
$727$			42.6702i			1.58255i	0.611461	+	0.791274i	$0.290582\pi$
$727$			42.6702i			1.58255i	−0.611461	+	0.791274i	$0.709418\pi$
$728$		0			0
$729$	−26.5812			−0.984489
$730$	−21.9988	+	17.1859i	−0.814213	+	0.636078i
$731$	−20.4494	−	35.4194i	−0.756348	−	1.31003i
$732$	0.167642	+	0.0967881i	0.00619622	+	0.00357739i
$733$	−26.0830			−0.963397			−0.481698	−	0.876337i	$-0.659980\pi$
$733$	−26.0830			−0.963397			−0.481698	+	0.876337i	$0.659980\pi$
$734$	−4.89771	−	2.82769i	−0.180778	−	0.104372i
$735$	1.56916	−	3.88333i	0.0578792	−	0.143239i
$736$			13.5387i			0.499042i
$737$	1.44040	+	0.831613i	0.0530577	+	0.0306329i
$738$	4.10992	−	2.37286i	0.151288	−	0.0873463i
$739$	−24.4814	+	14.1344i	−0.900564	+	0.519941i	−0.877383	−	0.479791i	$-0.840713\pi$
$739$	−24.4814	+	14.1344i	−0.900564	+	0.519941i	−0.0231807	+	0.999731i	$0.507379\pi$
$740$	0.372862	+	2.65386i	0.0137067	+	0.0975578i
$741$		0			0
$742$			21.9813i			0.806958i
$743$	10.3341	+	17.8991i	0.379120	+	0.656656i	0.990935	−	0.134346i	$-0.0428933\pi$
$743$	10.3341	+	17.8991i	0.379120	+	0.656656i	−0.611814	+	0.791002i	$0.709560\pi$
$744$	−11.2422	−	19.4721i	−0.412159	−	0.713881i
$745$	−2.99185	+	7.40418i	−0.109613	+	0.271268i
$746$			42.4286i			1.55342i
$747$	−6.10102	+	10.5673i	−0.223225	+	0.386636i
$748$	−0.361963	+	0.626938i	−0.0132347	+	0.0229231i
$749$			49.6958i			1.81585i
$750$	−1.86286	+	17.7025i	−0.0680219	+	0.646405i
$751$	1.23014	+	2.13067i	0.0448885	+	0.0777491i	0.887597	−	0.460621i	$-0.152373\pi$
$751$	1.23014	+	2.13067i	0.0448885	+	0.0777491i	−0.842708	+	0.538371i	$0.819040\pi$
$752$	1.46590	+	2.53901i	0.0534557	+	0.0925880i
$753$		−	2.71810i		−	0.0990530i
$754$		0			0
$755$	2.80150	−	0.393606i	0.101957	−	0.0143248i
$756$	7.41490	−	4.28100i	0.269677	−	0.155698i
$757$	42.0918	−	24.3017i	1.52985	−	0.883262i	0.530487	−	0.847693i	$-0.322009\pi$
$757$	42.0918	−	24.3017i	1.52985	−	0.883262i	0.999367	−	0.0355687i	$-0.0113243\pi$
$758$	−18.3738	−	10.6081i	−0.667365	−	0.385303i
$759$		−	1.31756i		−	0.0478244i
$760$	−5.68871	+	14.0784i	−0.206351	+	0.510676i
$761$	−11.9729	−	6.91258i	−0.434019	−	0.250581i	0.267038	−	0.963686i	$-0.413955\pi$
$761$	−11.9729	−	6.91258i	−0.434019	−	0.250581i	−0.701057	+	0.713105i	$0.747288\pi$
$762$	−3.66461			−0.132755
$763$	−42.0482	−	24.2766i	−1.52225	−	0.878870i
$764$	−0.552148	−	0.956349i	−0.0199760	−	0.0345995i
$765$	11.3363	+	14.5110i	0.409864	+	0.524647i
$766$	22.6811			0.819500
$767$		0			0
$768$			15.2924i			0.551816i
$769$	33.7480	−	19.4844i	1.21698	−	0.702626i	0.252712	−	0.967541i	$-0.418677\pi$
$769$	33.7480	−	19.4844i	1.21698	−	0.702626i	0.964272	+	0.264915i	$0.0853440\pi$
$770$	1.04011	+	1.33139i	0.0374828	+	0.0479800i
$771$	−12.0602	+	20.8889i	−0.434338	+	0.752296i
$772$	7.10430			0.255689
$773$	−0.222996	+	0.386241i	−0.00802061	+	0.0138921i	−0.870008	−	0.493038i	$-0.835886\pi$
$773$	−0.222996	+	0.386241i	−0.00802061	+	0.0138921i	0.861987	+	0.506930i	$0.169220\pi$
$774$	−8.57043	−	4.94814i	−0.308058	−	0.177857i
$775$	7.70471	+	26.8780i	0.276761	+	0.965487i
$776$	27.6637	−	47.9149i	0.993069	−	1.72005i
$777$	−7.51921	+	4.34122i	−0.269750	+	0.155740i
$778$	−0.979256	−	1.69612i	−0.0351080	−	0.0608089i
$779$	6.75557			0.242043
$780$		0			0
$781$	−1.30327			−0.0466347
$782$	−18.3017	−	31.6995i	−0.654469	−	1.13357i
$783$	42.3364	−	24.4429i	1.51298	−	0.873519i
$784$	1.90943	−	3.30722i	0.0681938	−	0.118115i
$785$	−12.4286	+	1.74620i	−0.443597	+	0.0623246i
$786$	−18.5025	−	10.6824i	−0.659963	−	0.381030i
$787$	−16.9518	+	29.3615i	−0.604268	+	1.04662i	0.387899	+	0.921702i	$0.373201\pi$
$787$	−16.9518	+	29.3615i	−0.604268	+	1.04662i	−0.992167	+	0.124921i	$0.960132\pi$
$788$	1.05086			0.0374352
$789$	−7.22792	+	12.5191i	−0.257321	+	0.445693i
$790$	−30.4596	+	23.7956i	−1.08370	+	0.846608i
$791$	−2.97740	+	1.71900i	−0.105864	+	0.0611207i
$792$			0.841934i			0.0299168i
$793$		0			0
$794$	−7.98571			−0.283402
$795$	−14.4049	+	11.2534i	−0.510890	+	0.399116i
$796$	5.81732	+	10.0759i	0.206190	+	0.357131i
$797$	−8.91598	−	5.14764i	−0.315820	−	0.182339i	0.333708	−	0.942677i	$-0.391700\pi$
$797$	−8.91598	−	5.14764i	−0.315820	−	0.182339i	−0.649528	+	0.760338i	$0.725033\pi$
$798$	−10.2351			−0.362317
$799$	6.10622	+	3.52543i	0.216023	+	0.124721i
$800$	3.49379	−	14.0078i	0.123524	−	0.495251i
$801$		−	7.19004i		−	0.254047i
$802$	−23.0393	−	13.3017i	−0.813546	−	0.469701i
$803$	−1.90822	+	1.10171i	−0.0673396	+	0.0388785i
$804$	4.62989	−	2.67307i	0.163284	−	0.0942719i
$805$	30.1432	−	4.23506i	1.06241	−	0.149266i
$806$		0			0
$807$		−	21.1655i		−	0.745060i
$808$	−6.04101	−	10.4633i	−0.212522	−	0.368099i
$809$	3.97211	+	6.87990i	0.139652	+	0.241884i	0.927365	−	0.374158i	$-0.122068\pi$
$809$	3.97211	+	6.87990i	0.139652	+	0.241884i	−0.787713	+	0.616043i	$0.788735\pi$
$810$	−8.85182	−	3.57680i	−0.311021	−	0.125676i
$811$		−	8.12245i		−	0.285218i	−0.989779	−	0.142609i	$-0.954451\pi$
$811$		−	8.12245i		−	0.285218i	0.989779	−	0.142609i	$-0.0455491\pi$
$812$	−6.64296	+	11.5059i	−0.233122	+	0.403779i
$813$	8.52966	−	14.7738i	0.299148	−	0.518140i
$814$		−	0.593635i		−	0.0208069i
$815$	−7.71028	−	3.11553i	−0.270079	−	0.109132i
$816$	−11.2652	−	19.5119i	−0.394360	−	0.683052i
$817$	−7.04371	−	12.2001i	−0.246428	−	0.426826i
$818$			12.3783i			0.432796i
$819$		0			0
$820$	−3.54956	+	0.498707i	−0.123956	+	0.0174156i
$821$	−19.2314	+	11.1032i	−0.671180	+	0.387506i	−0.796524	−	0.604608i	$-0.793330\pi$
$821$	−19.2314	+	11.1032i	−0.671180	+	0.387506i	0.125344	+	0.992113i	$0.459997\pi$
$822$	−26.4076	+	15.2464i	−0.921071	+	0.531781i
$823$	−9.62806	−	5.55877i	−0.335613	−	0.193766i	0.322717	−	0.946495i	$-0.395404\pi$
$823$	−9.62806	−	5.55877i	−0.335613	−	0.193766i	−0.658330	+	0.752729i	$0.728737\pi$
$824$		−	8.65491i		−	0.301508i
$825$	−0.340010	+	1.36322i	−0.0118376	+	0.0474612i
$826$	28.2876	+	16.3319i	0.984251	+	0.568258i
$827$	23.1570			0.805248			0.402624	−	0.915365i	$-0.368098\pi$
$827$	23.1570			0.805248			0.402624	+	0.915365i	$0.368098\pi$
$828$	2.73314	+	1.57798i	0.0949831	+	0.0548385i
$829$	13.5598	+	23.4862i	0.470950	+	0.815710i	0.999448	−	0.0332250i	$-0.0105778\pi$
$829$	13.5598	+	23.4862i	0.470950	+	0.815710i	−0.528498	+	0.848935i	$0.677244\pi$
$830$	−20.3821	+	15.9229i	−0.707473	+	0.552691i
$831$	9.92687			0.344359
$832$		0			0
$833$		−	9.18421i		−	0.318214i
$834$	26.3246	−	15.1985i	0.911545	−	0.526281i
$835$	12.3992	−	9.68644i	0.429090	−	0.335213i
$836$	−0.124677	+	0.215946i	−0.00431203	+	0.00746866i
$837$	−31.3876			−1.08492
$838$	4.44293	−	7.69538i	0.153478	−	0.265832i
$839$	−21.9931	−	12.6977i	−0.759287	−	0.438374i	0.0697528	−	0.997564i	$-0.477779\pi$
$839$	−21.9931	−	12.6977i	−0.759287	−	0.438374i	−0.829040	+	0.559190i	$0.811112\pi$
$840$	25.8479	−	3.63158i	0.891838	−	0.125302i
$841$	−23.4289	+	40.5800i	−0.807892	+	1.39931i
$842$	−8.27282	+	4.77631i	−0.285100	+	0.164603i
$843$	4.42864	+	7.67063i	0.152530	+	0.264190i
$844$	−10.3269			−0.355468
$845$		0			0
$846$	1.70610			0.0586568
$847$	−15.9010	−	27.5413i	−0.546364	−	0.946331i
$848$	−14.4338	+	8.33338i	−0.495660	+	0.286170i
$849$	12.5118	−	21.6711i	0.429405	−	0.743751i
$850$	10.7556	+	37.5210i	0.368913	+	1.28696i
$851$	−9.26244	−	5.34767i	−0.317512	−	0.183316i
$852$	−2.09457	+	3.62789i	−0.0717586	+	0.124290i
$853$	−25.0651			−0.858214			−0.429107	−	0.903254i	$-0.641172\pi$
$853$	−25.0651			−0.858214			−0.429107	+	0.903254i	$0.641172\pi$
$854$	0.495316	−	0.857913i	0.0169494	−	0.0293572i
$855$	3.90474	+	4.99827i	0.133539	+	0.170937i
$856$	−45.4611	+	26.2470i	−1.55383	+	0.897103i
$857$		−	7.61285i		−	0.260050i	−0.991511	−	0.130025i	$-0.958494\pi$
$857$		−	7.61285i		−	0.260050i	0.991511	−	0.130025i	$-0.0415057\pi$
$858$		0			0
$859$	−42.1432			−1.43791			−0.718954	−	0.695058i	$-0.755379\pi$
$859$	−42.1432			−1.43791			−0.718954	+	0.695058i	$0.755379\pi$
$860$	4.60159	+	5.89027i	0.156913	+	0.200857i
$861$	−5.80642	−	10.0570i	−0.197882	−	0.342742i
$862$	40.9290	+	23.6304i	1.39405	+	0.804853i
$863$	51.5768			1.75569			0.877847	−	0.478942i	$-0.158980\pi$
$863$	51.5768			1.75569			0.877847	+	0.478942i	$0.158980\pi$
$864$	14.0352	+	8.10324i	0.477488	+	0.275678i
$865$	−0.606456	+	1.50085i	−0.0206201	+	0.0510305i
$866$			24.5334i			0.833679i
$867$	−27.6226	−	15.9479i	−0.938113	−	0.541620i
$868$	7.38750	−	4.26517i	0.250748	−	0.144769i
$869$	−2.64212	+	1.52543i	−0.0896277	+	0.0517466i
$870$	30.7052	−	4.31402i	1.04100	−	0.146259i
$871$		0			0
$872$		−	51.2869i		−	1.73679i
$873$	−11.5555	−	20.0148i	−0.391096	−	0.677398i
$874$	−6.30396	−	10.9188i	−0.213235	−	0.369333i
$875$	−32.2807	−	3.39693i	−1.09129	−	0.114837i
$876$			7.08250i			0.239295i
$877$	−17.0350	+	29.5055i	−0.575232	+	0.996331i	0.420784	+	0.907161i	$0.361755\pi$
$877$	−17.0350	+	29.5055i	−0.575232	+	0.996331i	−0.996016	+	0.0891706i	$0.971578\pi$
$878$	−6.61132	+	11.4511i	−0.223121	+	0.386457i
$879$			10.6035i			0.357646i
$880$	−0.479930	+	1.18773i	−0.0161784	+	0.0400382i
$881$	1.85950	+	3.22075i	0.0626482	+	0.108510i	0.895648	−	0.444763i	$-0.146712\pi$
$881$	1.85950	+	3.22075i	0.0626482	+	0.108510i	−0.833000	+	0.553273i	$0.813379\pi$
$882$	−1.11115	−	1.92457i	−0.0374144	−	0.0648037i
$883$		−	42.0163i		−	1.41396i	−0.707233	−	0.706981i	$-0.750057\pi$
$883$		−	42.0163i		−	1.41396i	0.707233	−	0.706981i	$-0.249943\pi$
$884$		0			0
$885$	3.77923	+	26.8988i	0.127037	+	0.904192i
$886$	−30.1068	+	17.3822i	−1.01146	+	0.583966i
$887$	−34.9109	+	20.1558i	−1.17219	+	0.676765i	−0.954195	−	0.299184i	$-0.903285\pi$
$887$	−34.9109	+	20.1558i	−1.17219	+	0.676765i	−0.217996	+	0.975950i	$0.569952\pi$
$888$	−7.94258	−	4.58565i	−0.266536	−	0.153884i
$889$		−	6.68244i		−	0.224122i
$890$	5.70981	−	14.1306i	0.191393	−	0.473658i
$891$	−0.652603	−	0.376780i	−0.0218630	−	0.0126226i
$892$	10.3344			0.346023
$893$	2.10326	+	1.21432i	0.0703830	+	0.0406357i
$894$	−2.84299	−	4.92420i	−0.0950838	−	0.164690i
$895$	7.12152	−	5.56346i	0.238046	−	0.185966i
$896$	14.4429			0.482504
$897$		0			0
$898$		−	13.2730i		−	0.442926i
$899$	42.1799	−	24.3526i	1.40678	−	0.812205i
$900$	−2.42064	−	2.33797i	−0.0806879	−	0.0779325i
$901$	−20.0415	+	34.7129i	−0.667679	+	1.15645i
$902$	0.793993			0.0264371
$903$	−12.1082	+	20.9720i	−0.402934	+	0.697903i
$904$	−3.14504	−	1.81579i	−0.104603	−	0.0603923i
$905$	0.728372	+	5.18421i	0.0242119	+	0.172329i
$906$	−1.00715	+	1.74443i	−0.0334602	+	0.0579547i
$907$	−30.1740	+	17.4210i	−1.00191	+	0.578454i	−0.908813	−	0.417203i	$-0.863010\pi$
$907$	−30.1740	+	17.4210i	−1.00191	+	0.578454i	−0.0930980	+	0.995657i	$0.529677\pi$
$908$	−3.48664	−	6.03904i	−0.115708	−	0.200412i
$909$	−5.04684			−0.167393
$910$		0			0
$911$	23.2672			0.770876			0.385438	−	0.922734i	$-0.374050\pi$
$911$	23.2672			0.770876			0.385438	+	0.922734i	$0.374050\pi$
$912$	−3.88025	−	6.72078i	−0.128488	−	0.222547i
$913$	−1.76798	+	1.02074i	−0.0585116	+	0.0337817i
$914$	6.92549	−	11.9953i	0.229075	−	0.396769i
$915$	0.815792	−	0.114617i	0.0269692	−	0.00378913i
$916$	−1.10511	−	0.638037i	−0.0365139	−	0.0210813i
$917$	19.4795	−	33.7395i	0.643270	−	1.11418i
$918$	−43.8163			−1.44615
$919$	−1.61285	+	2.79353i	−0.0532029	+	0.0921502i	−0.891400	−	0.453217i	$-0.850276\pi$
$919$	−1.61285	+	2.79353i	−0.0532029	+	0.0921502i	0.838197	+	0.545367i	$0.183610\pi$
$920$	19.7944	+	25.3378i	0.652601	+	0.835364i
$921$	−15.2532	+	8.80642i	−0.502609	+	0.290182i
$922$		−	31.7342i		−	1.04511i
$923$		0			0
$924$	0.428639			0.0141012
$925$	8.20339	+	7.92325i	0.269726	+	0.260515i
$926$	4.81018	+	8.33147i	0.158072	+	0.273789i
$927$	−3.13093	−	1.80764i	−0.102833	−	0.0593708i
$928$	−25.1481			−0.825527
$929$	−34.0748	−	19.6731i	−1.11796	−	0.645453i	−0.177078	−	0.984197i	$-0.556665\pi$
$929$	−34.0748	−	19.6731i	−1.11796	−	0.645453i	−0.940878	+	0.338744i	$0.889998\pi$
$930$	−18.4582	−	7.45851i	−0.605269	−	0.244574i
$931$		−	3.16346i		−	0.103678i
$932$	−7.36010	−	4.24935i	−0.241088	−	0.139192i
$933$	22.9400	−	13.2444i	0.751023	−	0.433603i
$934$	11.4547	−	6.61338i	0.374809	−	0.216396i
$935$	0.428639	+	3.05086i	0.0140180	+	0.0997736i
$936$		0			0
$937$		−	51.6040i		−	1.68583i	−0.538048	−	0.842914i	$-0.680838\pi$
$937$		−	51.6040i		−	1.68583i	0.538048	−	0.842914i	$-0.319162\pi$
$938$	−13.6795	−	23.6936i	−0.446652	−	0.773624i
$939$	−9.90613	−	17.1579i	−0.323274	−	0.559927i
$940$	−1.19476	−	0.482771i	−0.0389686	−	0.0157462i
$941$			37.5081i			1.22273i	0.791349	+	0.611364i	$0.209379\pi$
$941$			37.5081i			1.22273i	−0.791349	+	0.611364i	$0.790621\pi$
$942$	4.46812	−	7.73901i	0.145579	−	0.252151i
$943$	7.15257	−	12.3886i	0.232920	−	0.403429i
$944$			24.7665i			0.806080i
$945$	13.6511	−	33.7836i	0.444070	−	1.09898i
$946$	−0.827859	−	1.43389i	−0.0269160	−	0.0466199i
$947$	−19.0580	−	33.0094i	−0.619302	−	1.07266i	−0.989613	−	0.143755i	$-0.954082\pi$
$947$	−19.0580	−	33.0094i	−0.619302	−	1.07266i	0.370312	−	0.928908i	$-0.379251\pi$
$948$			9.80642i			0.318498i
$949$		0			0
$950$	3.70471	+	12.9240i	0.120197	+	0.419308i
$951$	−25.2990	+	14.6064i	−0.820377	+	0.473645i
$952$	49.5674	−	28.6178i	1.60649	−	0.927507i
$953$	−24.8868	−	14.3684i	−0.806163	−	0.465439i	0.0394584	−	0.999221i	$-0.487437\pi$
$953$	−24.8868	−	14.3684i	−0.806163	−	0.465439i	−0.845622	+	0.533783i	$0.820770\pi$
$954$			9.69888i			0.314013i
$955$	−4.35729	−	1.76067i	−0.140999	−	0.0569740i
$956$	5.81365	+	3.35651i	0.188027	+	0.108557i
$957$	2.44738			0.0791124
$958$	9.60331	+	5.54448i	0.310269	+	0.179134i
$959$	−27.8020	−	48.1544i	−0.897773	−	1.55499i
$960$	15.9772	+	20.4517i	0.515662	+	0.660075i
$961$	−0.271628			−0.00876221
$962$		0			0
$963$			21.9275i			0.706604i
$964$	−2.68392	+	1.54956i	−0.0864432	+	0.0499080i
$965$	23.8254	−	18.6128i	0.766966	−	0.599168i
$966$	−10.8365	+	18.7694i	−0.348660	+	0.603897i
$967$	29.0593			0.934485			0.467242	−	0.884129i	$-0.345248\pi$
$967$	29.0593			0.934485			0.467242	+	0.884129i	$0.345248\pi$
$968$	16.7963	−	29.0920i	0.539853	−	0.935053i
$969$	−16.1632	−	9.33185i	−0.519238	−	0.299782i
$970$	−6.81579	−	48.5116i	−0.218842	−	1.55761i
$971$	19.9289	−	34.5178i	0.639548	−	1.10773i	−0.345984	−	0.938240i	$-0.612455\pi$
$971$	19.9289	−	34.5178i	0.639548	−	1.10773i	0.985532	−	0.169489i	$-0.0542118\pi$
$972$	5.56443	−	3.21262i	0.178479	−	0.103045i
$973$	27.7146	+	48.0030i	0.888488	+	1.53891i
$974$	−19.6588			−0.629908
$975$		0			0
$976$	0.751123			0.0240429
$977$	6.43086	+	11.1386i	0.205742	+	0.356355i	0.950369	−	0.311126i	$-0.100706\pi$
$977$	6.43086	+	11.1386i	0.205742	+	0.356355i	−0.744627	+	0.667481i	$0.767373\pi$
$978$	5.12777	−	2.96052i	0.163968	−	0.0946670i
$979$	0.601472	−	1.04178i	0.0192231	−	0.0332954i
$980$	0.233532	+	1.66217i	0.00745991	+	0.0530961i
$981$	−18.5531	−	10.7116i	−0.592355	−	0.341996i
$982$	15.9462	−	27.6197i	0.508865	−	0.881379i
$983$	45.4880			1.45084			0.725420	−	0.688306i	$-0.241645\pi$
$983$	45.4880			1.45084			0.725420	+	0.688306i	$0.241645\pi$
$984$	6.13335	−	10.6233i	0.195524	−	0.338658i
$985$	3.52421	−	2.75317i	0.112291	−	0.0877234i
$986$	58.8820	−	33.9956i	1.87519	−	1.08264i
$987$		−	4.17484i		−	0.132887i
$988$		0			0
$989$	−29.8306			−0.948557
$990$	0.458930	+	0.587455i	0.0145858	+	0.0186705i
$991$	−4.03503	−	6.98888i	−0.128177	−	0.222009i	0.794793	−	0.606880i	$-0.207579\pi$
$991$	−4.03503	−	6.98888i	−0.128177	−	0.222009i	−0.922970	+	0.384871i	$0.874246\pi$
$992$	13.9834	+	8.07329i	0.443972	+	0.256327i
$993$	10.8243			0.343497
$994$	18.5659	+	10.7190i	0.588873	+	0.339986i
$995$	45.9075	+	18.5501i	1.45537	+	0.588077i
$996$			6.56199i			0.207925i
$997$	−28.4193	−	16.4079i	−0.900049	−	0.519643i	−0.0228326	−	0.999739i	$-0.507268\pi$
$997$	−28.4193	−	16.4079i	−0.900049	−	0.519643i	−0.877216	+	0.480096i	$0.840602\pi$
$998$	−31.5811	+	18.2334i	−0.999683	+	0.577167i
$999$	−11.0876	+	6.40144i	−0.350797	+	0.202533i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.l.e.699.1		12
5.4	even	2		845.2.l.d.699.6		12
13.2	odd	12		65.2.b.a.14.3	✓	6
13.3	even	3		845.2.d.a.844.5		6
13.4	even	6		845.2.l.d.654.6		12
13.5	odd	4		845.2.n.f.484.3		12
13.6	odd	12		845.2.n.f.529.4		12
13.7	odd	12		845.2.n.g.529.3		12
13.8	odd	4		845.2.n.g.484.4		12
13.9	even	3	inner	845.2.l.e.654.2		12
13.10	even	6		845.2.d.b.844.1		6
13.11	odd	12		845.2.b.c.339.4		6
13.12	even	2		845.2.l.d.699.5		12
39.2	even	12		585.2.c.b.469.4		6
52.15	even	12		1040.2.d.c.209.5		6
65.2	even	12		325.2.a.j.1.3		3
65.4	even	6	inner	845.2.l.e.654.1		12
65.9	even	6		845.2.l.d.654.5		12
65.19	odd	12		845.2.n.f.529.3		12
65.24	odd	12		845.2.b.c.339.3		6
65.28	even	12		325.2.a.k.1.1		3
65.29	even	6		845.2.d.b.844.2		6
65.34	odd	4		845.2.n.g.484.3		12
65.37	even	12		4225.2.a.bh.1.1		3
65.44	odd	4		845.2.n.f.484.4		12
65.49	even	6		845.2.d.a.844.6		6
65.54	odd	12		65.2.b.a.14.4	yes	6
65.59	odd	12		845.2.n.g.529.4		12
65.63	even	12		4225.2.a.ba.1.3		3
65.64	even	2	inner	845.2.l.e.699.2		12
195.2	odd	12		2925.2.a.bj.1.1		3
195.119	even	12		585.2.c.b.469.3		6
195.158	odd	12		2925.2.a.bf.1.3		3
260.67	odd	12		5200.2.a.cj.1.2		3
260.119	even	12		1040.2.d.c.209.2		6
260.223	odd	12		5200.2.a.cb.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.b.a.14.3	✓	6	13.2	odd	12
65.2.b.a.14.4	yes	6	65.54	odd	12
325.2.a.j.1.3		3	65.2	even	12
325.2.a.k.1.1		3	65.28	even	12
585.2.c.b.469.3		6	195.119	even	12
585.2.c.b.469.4		6	39.2	even	12
845.2.b.c.339.3		6	65.24	odd	12
845.2.b.c.339.4		6	13.11	odd	12
845.2.d.a.844.5		6	13.3	even	3
845.2.d.a.844.6		6	65.49	even	6
845.2.d.b.844.1		6	13.10	even	6
845.2.d.b.844.2		6	65.29	even	6
845.2.l.d.654.5		12	65.9	even	6
845.2.l.d.654.6		12	13.4	even	6
845.2.l.d.699.5		12	13.12	even	2
845.2.l.d.699.6		12	5.4	even	2
845.2.l.e.654.1		12	65.4	even	6	inner
845.2.l.e.654.2		12	13.9	even	3	inner
845.2.l.e.699.1		12	1.1	even	1	trivial
845.2.l.e.699.2		12	65.64	even	2	inner
845.2.n.f.484.3		12	13.5	odd	4
845.2.n.f.484.4		12	65.44	odd	4
845.2.n.f.529.3		12	65.19	odd	12
845.2.n.f.529.4		12	13.6	odd	12
845.2.n.g.484.3		12	65.34	odd	4
845.2.n.g.484.4		12	13.8	odd	4
845.2.n.g.529.3		12	13.7	odd	12
845.2.n.g.529.4		12	65.59	odd	12
1040.2.d.c.209.2		6	260.119	even	12
1040.2.d.c.209.5		6	52.15	even	12
2925.2.a.bf.1.3		3	195.158	odd	12
2925.2.a.bj.1.1		3	195.2	odd	12
4225.2.a.ba.1.3		3	65.63	even	12
4225.2.a.bh.1.1		3	65.37	even	12
5200.2.a.cb.1.2		3	260.223	odd	12
5200.2.a.cj.1.2		3	260.67	odd	12

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:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.l (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.607160 - 1.05163i) q^{2} +(-1.13545 + 0.655554i) q^{3} +(0.262714 - 0.455034i) q^{4} +(-0.311108 - 2.21432i) q^{5} +(1.37880 + 0.796052i) q^{6} +(-1.45161 + 2.51426i) q^{7} -3.06668 q^{8} +(-0.640498 + 1.10938i) q^{9} +(-2.13976 + 1.67162i) q^{10} +(-0.185606 + 0.107160i) q^{11} +0.688892i q^{12} +3.52543 q^{14} +(1.80485 + 2.31031i) q^{15} +(1.33654 + 2.31495i) q^{16} +(5.56737 + 3.21432i) q^{17} +1.55554 q^{18} +(1.91766 + 1.10716i) q^{19} +(-1.08932 - 0.440168i) q^{20} -3.80642i q^{21} +(0.225385 + 0.130126i) q^{22} +(4.06070 - 2.34445i) q^{23} +(3.48207 - 2.01037i) q^{24} +(-4.80642 + 1.37778i) q^{25} -5.61285i q^{27} +(0.762714 + 1.32106i) q^{28} +(4.35482 + 7.54277i) q^{29} +(1.33376 - 3.30077i) q^{30} -5.59210i q^{31} +(-1.44370 + 2.50055i) q^{32} +(0.140498 - 0.243350i) q^{33} -7.80642i q^{34} +(6.01897 + 2.43212i) q^{35} +(0.336535 + 0.582896i) q^{36} +(-1.14050 - 1.97540i) q^{37} -2.68889i q^{38} +(0.954067 + 6.79060i) q^{40} +(2.64212 - 1.52543i) q^{41} +(-4.00296 + 2.31111i) q^{42} +(-5.50962 - 3.18098i) q^{43} +0.112610i q^{44} +(2.65578 + 1.07313i) q^{45} +(-4.93099 - 2.84691i) q^{46} +1.09679 q^{47} +(-3.03515 - 1.75234i) q^{48} +(-0.714320 - 1.23724i) q^{49} +(4.36719 + 4.21805i) q^{50} -8.42864 q^{51} +6.23506i q^{53} +(-5.90265 + 3.40790i) q^{54} +(0.295030 + 0.377654i) q^{55} +(4.45161 - 7.71041i) q^{56} -2.90321 q^{57} +(5.28814 - 9.15933i) q^{58} +(8.02388 + 4.63259i) q^{59} +(1.52543 - 0.214320i) q^{60} +(0.140498 - 0.243350i) q^{61} +(-5.88083 + 3.39530i) q^{62} +(-1.85950 - 3.22075i) q^{63} +8.85236 q^{64} -0.341219 q^{66} +(-3.88025 - 6.72078i) q^{67} +(2.92525 - 1.68889i) q^{68} +(-3.07382 + 5.32402i) q^{69} +(-1.09679 - 7.80642i) q^{70} +(5.26627 + 3.04048i) q^{71} +(1.96420 - 3.40210i) q^{72} +10.2810 q^{73} +(-1.38493 + 2.39877i) q^{74} +(4.55425 - 4.71528i) q^{75} +(1.00759 - 0.581732i) q^{76} -0.622216i q^{77} +14.2351 q^{79} +(4.71023 - 3.67971i) q^{80} +(1.75803 + 3.04500i) q^{81} +(-3.20838 - 1.85236i) q^{82} +9.52543 q^{83} +(-1.73205 - 1.00000i) q^{84} +(5.38548 - 13.3279i) q^{85} +7.72546i q^{86} +(-9.88938 - 5.70964i) q^{87} +(0.569195 - 0.328625i) q^{88} +(-4.86087 + 2.80642i) q^{89} +(-0.483940 - 3.44446i) q^{90} -2.46367i q^{92} +(3.66593 + 6.34957i) q^{93} +(-0.665926 - 1.15342i) q^{94} +(1.85501 - 4.59075i) q^{95} -3.78568i q^{96} +(-9.02074 + 15.6244i) q^{97} +(-0.867413 + 1.50240i) q^{98} -0.274543i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{2} - 10 q^{4} - 4 q^{5} - 4 q^{7} - 36 q^{8} + 6 q^{9} + 2 q^{10} + 16 q^{14} + 4 q^{15} - 10 q^{16} + 20 q^{18} - 14 q^{20} - 4 q^{25} - 4 q^{28} + 12 q^{29} + 8 q^{30} + 22 q^{32} - 12 q^{33}+ \cdots - 50 q^{98}+O(q^{100}) \) 12 * q + 6 * q^2 - 10 * q^4 - 4 * q^5 - 4 * q^7 - 36 * q^8 + 6 * q^9 + 2 * q^10 + 16 * q^14 + 4 * q^15 - 10 * q^16 + 20 * q^18 - 14 * q^20 - 4 * q^25 - 4 * q^28 + 12 * q^29 + 8 * q^30 + 22 * q^32 - 12 * q^33 - 8 * q^35 - 22 * q^36 - 68 * q^40 - 38 * q^45 + 40 * q^47 + 18 * q^49 + 22 * q^50 - 48 * q^51 + 16 * q^55 + 40 * q^56 - 8 * q^57 + 24 * q^58 - 8 * q^60 - 12 * q^61 - 36 * q^63 + 132 * q^64 - 32 * q^66 + 20 * q^67 - 24 * q^69 - 40 * q^70 + 90 * q^72 + 96 * q^73 - 4 * q^74 + 16 * q^75 + 64 * q^79 - 58 * q^80 - 46 * q^81 + 88 * q^83 + 32 * q^85 - 140 * q^90 + 4 * q^93 + 32 * q^94 + 16 * q^95 - 28 * q^97 - 50 * q^98

Introduction

L-functions

Modular forms

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