LMFDB - Embedded newform 750.2.l.c.143.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [750,2,Mod(107,750)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(750, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 13]))

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

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

chi := DirichletCharacter("750.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 750 = 2 \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	750.l (of order $20$, degree $8$, 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:	$5.98878015160$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 150)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			143.10
Character	$\chi$	$=$	750.143
Dual form			750.2.l.c.257.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.453990 - 0.891007i) q^{2} +(1.51894 + 0.832356i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(1.43122 - 0.975505i) q^{6} +(0.0556476 - 0.0556476i) q^{7} +(-0.987688 + 0.156434i) q^{8} +(1.61437 + 2.52860i) q^{9} +O(q^{10})$	\(q+(0.453990 - 0.891007i) q^{2} +(1.51894 + 0.832356i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(1.43122 - 0.975505i) q^{6} +(0.0556476 - 0.0556476i) q^{7} +(-0.987688 + 0.156434i) q^{8} +(1.61437 + 2.52860i) q^{9} +(1.04749 - 0.340351i) q^{11} +(-0.219422 - 1.71810i) q^{12} +(4.54086 - 2.31368i) q^{13} +(-0.0243189 - 0.0748459i) q^{14} +(-0.309017 + 0.951057i) q^{16} +(0.491350 + 3.10226i) q^{17} +(2.98591 - 0.290452i) q^{18} +(0.824223 - 1.13445i) q^{19} +(0.130844 - 0.0382069i) q^{21} +(0.172297 - 1.08784i) q^{22} +(-2.22575 - 1.13408i) q^{23} +(-1.63045 - 0.584493i) q^{24} -5.09632i q^{26} +(0.347436 + 5.18452i) q^{27} +(-0.0777287 - 0.0123110i) q^{28} +(5.66803 - 4.11807i) q^{29} +(7.72991 + 5.61611i) q^{31} +(0.707107 + 0.707107i) q^{32} +(1.87437 + 0.354913i) q^{33} +(2.98720 + 0.970601i) q^{34} +(1.09678 - 2.79232i) q^{36} +(-4.70325 - 9.23065i) q^{37} +(-0.636609 - 1.24942i) q^{38} +(8.82310 + 0.265260i) q^{39} +(-3.55210 - 1.15415i) q^{41} +(0.0253594 - 0.133928i) q^{42} +(-1.00563 - 1.00563i) q^{43} +(-0.891050 - 0.647386i) q^{44} +(-2.02094 + 1.46830i) q^{46} +(-12.5515 - 1.98797i) q^{47} +(-1.26100 + 1.18739i) q^{48} +6.99381i q^{49} +(-1.83585 + 5.12113i) q^{51} +(-4.54086 - 2.31368i) q^{52} +(-1.06206 + 6.70559i) q^{53} +(4.77718 + 2.04416i) q^{54} +(-0.0462573 + 0.0636677i) q^{56} +(2.19621 - 1.03711i) q^{57} +(-1.09599 - 6.91981i) q^{58} +(2.03647 - 6.26761i) q^{59} +(1.23324 + 3.79553i) q^{61} +(8.51329 - 4.33774i) q^{62} +(0.230546 + 0.0508748i) q^{63} +(0.951057 - 0.309017i) q^{64} +(1.16718 - 1.50895i) q^{66} +(-6.57696 + 1.04169i) q^{67} +(2.22097 - 2.22097i) q^{68} +(-2.43683 - 3.57522i) q^{69} +(7.51096 + 10.3379i) q^{71} +(-1.99005 - 2.24493i) q^{72} +(-0.602914 + 1.18329i) q^{73} -10.3598 q^{74} -1.40225 q^{76} +(0.0393507 - 0.0772302i) q^{77} +(4.24195 - 7.74102i) q^{78} +(-5.85354 - 8.05671i) q^{79} +(-3.78763 + 8.16418i) q^{81} +(-2.64098 + 2.64098i) q^{82} +(-0.871279 + 0.137997i) q^{83} +(-0.107818 - 0.0833977i) q^{84} +(-1.35257 + 0.439477i) q^{86} +(12.0371 - 1.53728i) q^{87} +(-0.981353 + 0.500025i) q^{88} +(1.01326 + 3.11850i) q^{89} +(0.123937 - 0.381439i) q^{91} +(0.390777 + 2.46727i) q^{92} +(7.06668 + 14.9646i) q^{93} +(-7.46957 + 10.2810i) q^{94} +(0.485490 + 1.66262i) q^{96} +(-1.62393 + 10.2531i) q^{97} +(6.23153 + 3.17512i) q^{98} +(2.55165 + 2.09924i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 4 q^{3} + 4 q^{7}+O(q^{10}) $ 80 * q + 4 * q^3 + 4 * q^7	$ 80 q + 4 q^{3} + 4 q^{7} + 16 q^{12} + 20 q^{16} - 8 q^{18} + 40 q^{19} + 4 q^{22} - 56 q^{27} + 4 q^{28} - 96 q^{33} + 40 q^{34} - 64 q^{37} + 40 q^{39} - 4 q^{42} - 24 q^{43} + 16 q^{48} - 64 q^{57} + 20 q^{58} + 4 q^{63} - 104 q^{67} - 140 q^{69} + 8 q^{72} - 60 q^{73} - 60 q^{78} - 80 q^{79} - 40 q^{81} + 96 q^{82} - 60 q^{84} + 80 q^{87} + 24 q^{88} + 12 q^{93} - 12 q^{97}+O(q^{100}) $ 80 * q + 4 * q^3 + 4 * q^7 + 16 * q^12 + 20 * q^16 - 8 * q^18 + 40 * q^19 + 4 * q^22 - 56 * q^27 + 4 * q^28 - 96 * q^33 + 40 * q^34 - 64 * q^37 + 40 * q^39 - 4 * q^42 - 24 * q^43 + 16 * q^48 - 64 * q^57 + 20 * q^58 + 4 * q^63 - 104 * q^67 - 140 * q^69 + 8 * q^72 - 60 * q^73 - 60 * q^78 - 80 * q^79 - 40 * q^81 + 96 * q^82 - 60 * q^84 + 80 * q^87 + 24 * q^88 + 12 * q^93 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/750\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{3}{20}\right)$	$-1$

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 $

$2$	0.453990	−	0.891007i	0.321020	−	0.630037i
$2$	0.453990	−	0.891007i	0.321020	−	0.630037i
$3$	1.51894	+	0.832356i	0.876961	+	0.480561i
$3$	1.51894	+	0.832356i	0.876961	+	0.480561i
$4$	−0.587785	−	0.809017i	−0.293893	−	0.404508i
$5$		0			0
$5$		0			0
$6$	1.43122	−	0.975505i	0.584293	−	0.398248i
$7$	0.0556476	−	0.0556476i	0.0210328	−	0.0210328i	−0.696512	−	0.717545i	$-0.745266\pi$
$7$	0.0556476	−	0.0556476i	0.0210328	−	0.0210328i	0.717545	+	0.696512i	$0.245266\pi$
$8$	−0.987688	+	0.156434i	−0.349201	+	0.0553079i
$9$	1.61437	+	2.52860i	0.538123	+	0.842867i
$10$		0			0
$11$	1.04749	−	0.340351i	0.315831	−	0.102620i	−0.146812	−	0.989164i	$-0.546901\pi$
$11$	1.04749	−	0.340351i	0.315831	−	0.102620i	0.462643	+	0.886545i	$0.346901\pi$
$12$	−0.219422	−	1.71810i	−0.0633416	−	0.495972i
$13$	4.54086	−	2.31368i	1.25941	−	0.641700i	0.308514	−	0.951220i	$-0.400168\pi$
$13$	4.54086	−	2.31368i	1.25941	−	0.641700i	0.950893	+	0.309520i	$0.100168\pi$
$14$	−0.0243189	−	0.0748459i	−0.00649950	−	0.0200034i
$15$		0			0
$16$	−0.309017	+	0.951057i	−0.0772542	+	0.237764i
$17$	0.491350	+	3.10226i	0.119170	+	0.752408i	0.972820	+	0.231562i	$0.0743836\pi$
$17$	0.491350	+	3.10226i	0.119170	+	0.752408i	−0.853650	+	0.520846i	$0.825616\pi$
$18$	2.98591	−	0.290452i	0.703785	−	0.0684602i
$19$	0.824223	−	1.13445i	0.189090	−	0.260260i	−0.703938	−	0.710262i	$-0.748577\pi$
$19$	0.824223	−	1.13445i	0.189090	−	0.260260i	0.893028	+	0.450002i	$0.148577\pi$
$20$		0			0
$21$	0.130844	−	0.0382069i	0.0285525	−	0.00833742i
$22$	0.172297	−	1.08784i	0.0367338	−	0.231928i
$23$	−2.22575	−	1.13408i	−0.464102	−	0.236472i	0.206273	−	0.978495i	$-0.433867\pi$
$23$	−2.22575	−	1.13408i	−0.464102	−	0.236472i	−0.670375	+	0.742023i	$0.733867\pi$
$24$	−1.63045	−	0.584493i	−0.332814	−	0.119309i
$25$		0			0
$26$		−	5.09632i		−	0.999471i
$27$	0.347436	+	5.18452i	0.0668641	+	0.997762i
$28$	−0.0777287	−	0.0123110i	−0.0146893	−	0.00232656i
$29$	5.66803	−	4.11807i	1.05253	−	0.764705i	0.0798355	−	0.996808i	$-0.474560\pi$
$29$	5.66803	−	4.11807i	1.05253	−	0.764705i	0.972691	+	0.232103i	$0.0745605\pi$
$30$		0			0
$31$	7.72991	+	5.61611i	1.38833	+	1.00868i	0.996046	+	0.0888399i	$0.0283160\pi$
$31$	7.72991	+	5.61611i	1.38833	+	1.00868i	0.392287	+	0.919843i	$0.371684\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	1.87437	+	0.354913i	0.326286	+	0.0617824i
$34$	2.98720	+	0.970601i	0.512301	+	0.166457i
$35$		0			0
$36$	1.09678	−	2.79232i	0.182796	−	0.465387i
$37$	−4.70325	−	9.23065i	−0.773210	−	1.51751i	−0.853706	−	0.520755i	$-0.825650\pi$
$37$	−4.70325	−	9.23065i	−0.773210	−	1.51751i	0.0804961	−	0.996755i	$-0.474350\pi$
$38$	−0.636609	−	1.24942i	−0.103272	−	0.202682i
$39$	8.82310	+	0.265260i	1.41283	+	0.0424756i
$40$		0			0
$41$	−3.55210	−	1.15415i	−0.554745	−	0.180248i	0.0182101	−	0.999834i	$-0.494203\pi$
$41$	−3.55210	−	1.15415i	−0.554745	−	0.180248i	−0.572956	+	0.819586i	$0.694203\pi$
$42$	0.0253594	−	0.133928i	0.00391304	−	0.0206656i
$43$	−1.00563	−	1.00563i	−0.153357	−	0.153357i	0.626258	−	0.779616i	$-0.284586\pi$
$43$	−1.00563	−	1.00563i	−0.153357	−	0.153357i	−0.779616	+	0.626258i	$0.784586\pi$
$44$	−0.891050	−	0.647386i	−0.134331	−	0.0975971i
$45$		0			0
$46$	−2.02094	+	1.46830i	−0.297972	+	0.216489i
$47$	−12.5515	−	1.98797i	−1.83083	−	0.289975i	−0.856674	−	0.515858i	$-0.827473\pi$
$47$	−12.5515	−	1.98797i	−1.83083	−	0.289975i	−0.974154	+	0.225883i	$0.927473\pi$
$48$	−1.26100	+	1.18739i	−0.182009	+	0.171385i
$49$			6.99381i			0.999115i
$50$		0			0
$51$	−1.83585	+	5.12113i	−0.257071	+	0.717101i
$52$	−4.54086	−	2.31368i	−0.629704	−	0.320850i
$53$	−1.06206	+	6.70559i	−0.145885	+	0.921083i	0.800802	+	0.598929i	$0.204407\pi$
$53$	−1.06206	+	6.70559i	−0.145885	+	0.921083i	−0.946687	+	0.322154i	$0.895593\pi$
$54$	4.77718	+	2.04416i	0.650091	+	0.278175i
$55$		0			0
$56$	−0.0462573	+	0.0636677i	−0.00618139	+	0.00850795i
$57$	2.19621	−	1.03711i	0.290895	−	0.137369i
$58$	−1.09599	−	6.91981i	−0.143911	−	0.908616i
$59$	2.03647	−	6.26761i	0.265126	−	0.815974i	−0.726538	−	0.687126i	$-0.758872\pi$
$59$	2.03647	−	6.26761i	0.265126	−	0.815974i	0.991664	−	0.128848i	$-0.0411279\pi$
$60$		0			0
$61$	1.23324	+	3.79553i	0.157901	+	0.485968i	0.998443	−	0.0557774i	$-0.0177637\pi$
$61$	1.23324	+	3.79553i	0.157901	+	0.485968i	−0.840543	+	0.541745i	$0.817764\pi$
$62$	8.51329	−	4.33774i	1.08119	−	0.550894i
$63$	0.230546	+	0.0508748i	0.0290461	+	0.00640962i
$64$	0.951057	−	0.309017i	0.118882	−	0.0386271i
$65$		0			0
$66$	1.16718	−	1.50895i	0.143670	−	0.185739i
$67$	−6.57696	+	1.04169i	−0.803504	+	0.127263i	−0.544660	−	0.838657i	$-0.683341\pi$
$67$	−6.57696	+	1.04169i	−0.803504	+	0.127263i	−0.258844	+	0.965919i	$0.583341\pi$
$68$	2.22097	−	2.22097i	0.269332	−	0.269332i
$69$	−2.43683	−	3.57522i	−0.293360	−	0.430406i
$70$		0			0
$71$	7.51096	+	10.3379i	0.891387	+	1.22689i	0.973135	+	0.230236i	$0.0739497\pi$
$71$	7.51096	+	10.3379i	0.891387	+	1.22689i	−0.0817481	+	0.996653i	$0.526050\pi$
$72$	−1.99005	−	2.24493i	−0.234530	−	0.264567i
$73$	−0.602914	+	1.18329i	−0.0705658	+	0.138493i	−0.923595	−	0.383371i	$-0.874763\pi$
$73$	−0.602914	+	1.18329i	−0.0705658	+	0.138493i	0.853029	+	0.521864i	$0.174763\pi$
$74$	−10.3598			−1.20430
$75$		0			0
$76$	−1.40225			−0.160849
$77$	0.0393507	−	0.0772302i	0.00448443	−	0.00880119i
$78$	4.24195	−	7.74102i	0.480307	−	0.876498i
$79$	−5.85354	−	8.05671i	−0.658575	−	0.906451i	0.340858	−	0.940115i	$-0.389282\pi$
$79$	−5.85354	−	8.05671i	−0.658575	−	0.906451i	−0.999433	+	0.0336639i	$0.989282\pi$
$80$		0			0
$81$	−3.78763	+	8.16418i	−0.420848	+	0.907131i
$82$	−2.64098	+	2.64098i	−0.291647	+	0.291647i
$83$	−0.871279	+	0.137997i	−0.0956353	+	0.0151471i	−0.204069	−	0.978957i	$-0.565417\pi$
$83$	−0.871279	+	0.137997i	−0.0956353	+	0.0151471i	0.108433	+	0.994104i	$0.465417\pi$
$84$	−0.107818	−	0.0833977i	−0.0117639	−	0.00909943i
$85$		0			0
$86$	−1.35257	+	0.439477i	−0.145851	+	0.0473900i
$87$	12.0371	−	1.53728i	1.29051	−	0.164814i
$88$	−0.981353	+	0.500025i	−0.104613	+	0.0533028i
$89$	1.01326	+	3.11850i	0.107406	+	0.330560i	0.990288	−	0.139035i	$-0.0444000\pi$
$89$	1.01326	+	3.11850i	0.107406	+	0.330560i	−0.882882	+	0.469595i	$0.844400\pi$
$90$		0			0
$91$	0.123937	−	0.381439i	0.0129921	−	0.0399856i
$92$	0.390777	+	2.46727i	0.0407413	+	0.257230i
$93$	7.06668	+	14.9646i	0.732781	+	1.55175i
$94$	−7.46957	+	10.2810i	−0.770427	+	1.06040i
$95$		0			0
$96$	0.485490	+	1.66262i	0.0495501	+	0.169690i
$97$	−1.62393	+	10.2531i	−0.164885	+	1.04104i	0.756953	+	0.653469i	$0.226687\pi$
$97$	−1.62393	+	10.2531i	−0.164885	+	1.04104i	−0.921838	+	0.387575i	$0.873313\pi$
$98$	6.23153	+	3.17512i	0.629479	+	0.320736i
$99$	2.55165	+	2.09924i	0.256450	+	0.210981i
$100$		0			0
$101$		−	14.0377i		−	1.39680i	−0.715708	−	0.698399i	$-0.753896\pi$
$101$		−	14.0377i		−	1.39680i	0.715708	−	0.698399i	$-0.246104\pi$
$102$	3.72950	+	3.96070i	0.369276	+	0.392168i
$103$	−13.0416	−	2.06559i	−1.28503	−	0.203529i	−0.523705	−	0.851900i	$-0.675451\pi$
$103$	−13.0416	−	2.06559i	−1.28503	−	0.203529i	−0.761324	+	0.648371i	$0.775451\pi$
$104$	−4.12301	+	2.99554i	−0.404295	+	0.293737i
$105$		0			0
$106$	5.49256	+	3.99058i	0.533484	+	0.387599i
$107$	−13.7619	−	13.7619i	−1.33041	−	1.33041i	−0.904999	−	0.425413i	$-0.860129\pi$
$107$	−13.7619	−	13.7619i	−1.33041	−	1.33041i	−0.425413	−	0.904999i	$-0.639871\pi$
$108$	3.99015	−	3.32847i	0.383952	−	0.320282i
$109$	−11.7044	−	3.80299i	−1.12108	−	0.364260i	−0.310898	−	0.950443i	$-0.600630\pi$
$109$	−11.7044	−	3.80299i	−1.12108	−	0.364260i	−0.810178	+	0.586183i	$0.800630\pi$
$110$		0			0
$111$	0.539221	−	17.9356i	0.0511805	−	1.70237i
$112$	0.0357280	+	0.0701201i	0.00337598	+	0.00662572i
$113$	−3.46581	−	6.80204i	−0.326036	−	0.639882i	0.668565	−	0.743654i	$-0.266909\pi$
$113$	−3.46581	−	6.80204i	−0.326036	−	0.639882i	−0.994601	+	0.103771i	$0.966909\pi$
$114$	0.0729862	−	2.42768i	0.00683579	−	0.227373i
$115$		0			0
$116$	−6.66317	−	2.16499i	−0.618660	−	0.201015i
$117$	13.1810	+	7.74688i	1.21858	+	0.716199i
$118$	−4.65995	−	4.65995i	−0.428983	−	0.428983i
$119$	0.199976	+	0.145291i	0.0183317	+	0.0133188i
$120$		0			0
$121$	−7.91779	+	5.75261i	−0.719799	+	0.522964i
$122$	3.94172	+	0.624308i	0.356867	+	0.0565222i
$123$	−4.43478	−	4.70970i	−0.399870	−	0.424659i
$124$		−	9.55469i		−	0.858037i
$125$		0			0
$126$	0.149996	−	0.182322i	0.0133627	−	0.0162425i
$127$	2.87091	+	1.46280i	0.254752	+	0.129803i	0.576703	−	0.816954i	$-0.304339\pi$
$127$	2.87091	+	1.46280i	0.254752	+	0.129803i	−0.321952	+	0.946756i	$0.604339\pi$
$128$	0.156434	−	0.987688i	0.0138270	−	0.0873001i
$129$	−0.690452	−	2.36454i	−0.0607909	−	0.208186i
$130$		0			0
$131$	−3.12598	+	4.30255i	−0.273118	+	0.375915i	−0.923439	−	0.383744i	$-0.874634\pi$
$131$	−3.12598	+	4.30255i	−0.273118	+	0.375915i	0.650321	+	0.759660i	$0.274634\pi$
$132$	−0.814598	−	1.72501i	−0.0709017	−	0.150143i
$133$	−0.0172632	−	0.108995i	−0.00149690	−	0.00945109i
$134$	−2.05773	+	6.33303i	−0.177761	+	0.547091i
$135$		0			0
$136$	−0.970601	−	2.98720i	−0.0832283	−	0.256150i
$137$	10.2341	−	5.21451i	0.874354	−	0.445506i	0.0415907	−	0.999135i	$-0.486757\pi$
$137$	10.2341	−	5.21451i	0.874354	−	0.445506i	0.832763	+	0.553629i	$0.186757\pi$
$138$	−4.29184	+	0.548120i	−0.365346	+	0.0466591i
$139$	−10.3684	+	3.36891i	−0.879440	+	0.285747i	−0.713725	−	0.700426i	$-0.752993\pi$
$139$	−10.3684	+	3.36891i	−0.879440	+	0.285747i	−0.165715	+	0.986174i	$0.552993\pi$
$140$		0			0
$141$	−17.4103	−	13.4669i	−1.46622	−	1.13412i
$142$	12.6211	−	1.99898i	1.05914	−	0.167751i
$143$	3.96905	−	3.96905i	0.331909	−	0.331909i
$144$	−2.90371	+	0.753975i	−0.241976	+	0.0628312i
$145$		0			0
$146$	0.780598	+	1.07440i	0.0646028	+	0.0889181i
$147$	−5.82134	+	10.6232i	−0.480136	+	0.876186i
$148$	−4.70325	+	9.23065i	−0.386605	+	0.758755i
$149$	14.3679			1.17707			0.588534	−	0.808472i	$-0.299705\pi$
$149$	14.3679			1.17707			0.588534	+	0.808472i	$0.299705\pi$
$150$		0			0
$151$	−0.326435			−0.0265649			−0.0132824	−	0.999912i	$-0.504228\pi$
$151$	−0.326435			−0.0265649			−0.0132824	+	0.999912i	$0.504228\pi$
$152$	−0.636609	+	1.24942i	−0.0516358	+	0.101341i
$153$	−7.05115	+	6.25061i	−0.570052	+	0.505332i
$154$	−0.0509477	−	0.0701235i	−0.00410548	−	0.00565071i
$155$		0			0
$156$	−4.97149	−	7.29396i	−0.398038	−	0.583984i
$157$	−3.47556	+	3.47556i	−0.277380	+	0.277380i	−0.832062	−	0.554682i	$-0.812840\pi$
$157$	−3.47556	+	3.47556i	−0.277380	+	0.277380i	0.554682	+	0.832062i	$0.312840\pi$
$158$	−9.83604	+	1.55788i	−0.782513	+	0.123938i
$159$	−7.19464	+	9.30139i	−0.570572	+	0.737648i
$160$		0			0
$161$	−0.186967	+	0.0607491i	−0.0147350	+	0.00478770i
$162$	5.55479	+	7.08127i	0.436425	+	0.556357i
$163$	1.36590	−	0.695961i	0.106986	−	0.0545119i	−0.399679	−	0.916655i	$-0.630878\pi$
$163$	1.36590	−	0.695961i	0.106986	−	0.0545119i	0.506664	+	0.862143i	$0.330878\pi$
$164$	1.15415	+	3.55210i	0.0901239	+	0.277373i
$165$		0			0
$166$	−0.272596	+	0.838964i	−0.0211576	+	0.0651163i
$167$	3.50144	+	22.1072i	0.270949	+	1.71071i	0.629336	+	0.777133i	$0.283327\pi$
$167$	3.50144	+	22.1072i	0.270949	+	1.71071i	−0.358387	+	0.933573i	$0.616673\pi$
$168$	−0.123256	+	0.0582050i	−0.00950943	+	0.00449061i
$169$	7.62505	−	10.4950i	0.586542	−	0.807306i
$170$		0			0
$171$	4.19916	+	0.252718i	0.321118	+	0.0193258i
$172$	−0.222477	+	1.40467i	−0.0169637	+	0.107105i
$173$	12.6292	+	6.43491i	0.960182	+	0.489237i	0.862542	−	0.505985i	$-0.168871\pi$
$173$	12.6292	+	6.43491i	0.960182	+	0.489237i	0.0976395	+	0.995222i	$0.468871\pi$
$174$	4.09500	−	11.4230i	0.310441	−	0.865979i
$175$		0			0
$176$			1.10140i			0.0830211i
$177$	8.31016	−	7.82507i	0.624630	−	0.588168i
$178$	3.23861	+	0.512946i	0.242744	+	0.0384469i
$179$	−12.2896	+	8.92889i	−0.918565	+	0.667377i	−0.943167	−	0.332320i	$-0.892168\pi$
$179$	−12.2896	+	8.92889i	−0.918565	+	0.667377i	0.0246011	+	0.999697i	$0.492168\pi$
$180$		0			0
$181$	−8.30933	−	6.03708i	−0.617627	−	0.448733i	0.234465	−	0.972125i	$-0.424666\pi$
$181$	−8.30933	−	6.03708i	−0.617627	−	0.448733i	−0.852092	+	0.523392i	$0.824666\pi$
$182$	−0.283598	−	0.283598i	−0.0210217	−	0.0210217i
$183$	−1.28601	+	6.79169i	−0.0950645	+	0.502056i
$184$	2.37576	+	0.771931i	0.175143	+	0.0569075i
$185$		0			0
$186$	16.5417	+	0.497315i	1.21290	+	0.0364649i
$187$	1.57054	+	3.08236i	0.114849	+	0.225405i
$188$	5.76930	+	11.3229i	0.420770	+	0.825807i
$189$	0.307840	+	0.269172i	0.0223921	+	0.0195794i
$190$		0			0
$191$	10.3303	+	3.35652i	0.747475	+	0.242869i	0.657894	−	0.753110i	$-0.271447\pi$
$191$	10.3303	+	3.35652i	0.747475	+	0.242869i	0.0895805	+	0.995980i	$0.471447\pi$
$192$	1.70181	+	0.322239i	0.122818	+	0.0232556i
$193$	−13.7241	−	13.7241i	−0.987880	−	0.987880i	0.0120476	−	0.999927i	$-0.496165\pi$
$193$	−13.7241	−	13.7241i	−0.987880	−	0.987880i	−0.999927	+	0.0120476i	$0.996165\pi$
$194$	8.39833	+	6.10174i	0.602965	+	0.438080i
$195$		0			0
$196$	5.65811	−	4.11086i	0.404151	−	0.293633i
$197$	12.0795	+	1.91320i	0.860625	+	0.136310i	0.571120	−	0.820867i	$-0.306509\pi$
$197$	12.0795	+	1.91320i	0.860625	+	0.136310i	0.289506	+	0.957176i	$0.406509\pi$
$198$	3.02886	−	1.32050i	0.215252	−	0.0938440i
$199$			15.9356i			1.12965i	0.825212	+	0.564823i	$0.191056\pi$
$199$			15.9356i			1.12965i	−0.825212	+	0.564823i	$0.808944\pi$
$200$		0			0
$201$	−10.8571	−	3.89211i	−0.765799	−	0.274528i
$202$	−12.5076	−	6.37296i	−0.880034	−	0.448400i
$203$	0.0862519	−	0.544573i	0.00605369	−	0.0382215i
$204$	5.22217	−	1.52489i	0.365625	−	0.106764i
$205$		0			0
$206$	−7.76123	+	10.6824i	−0.540750	+	0.744279i
$207$	−0.725556	−	7.45886i	−0.0504296	−	0.518427i
$208$	0.797241	+	5.03358i	0.0552787	+	0.349016i
$209$	0.477258	−	1.46885i	0.0330126	−	0.101602i
$210$		0			0
$211$	−3.41758	−	10.5182i	−0.235276	−	0.724104i	−0.997085	−	0.0763026i	$-0.975689\pi$
$211$	−3.41758	−	10.5182i	−0.235276	−	0.724104i	0.761809	−	0.647802i	$-0.224311\pi$
$212$	6.04920	−	3.08222i	0.415461	−	0.211688i
$213$	2.80386	+	21.9545i	0.192117	+	1.50430i
$214$	−18.5097	+	6.01417i	−1.26530	+	0.411120i
$215$		0			0
$216$	−1.15420	−	5.06634i	−0.0785331	−	0.344721i
$217$	0.742674	−	0.117628i	0.0504160	−	0.00798511i
$218$	−8.70216	+	8.70216i	−0.589385	+	0.589385i
$219$	−1.90071	+	1.29550i	−0.128438	+	0.0875420i
$220$		0			0
$221$	9.40879	+	12.9501i	0.632904	+	0.871117i
$222$	−15.7359	−	8.62304i	−1.05613	−	0.578741i
$223$	−2.49393	+	4.89460i	−0.167006	+	0.327767i	−0.959308	−	0.282362i	$-0.908882\pi$
$223$	−2.49393	+	4.89460i	−0.167006	+	0.327767i	0.792302	+	0.610129i	$0.208882\pi$
$224$	0.0786976			0.00525820
$225$		0			0
$226$	−7.63411			−0.507814
$227$	−3.07043	+	6.02606i	−0.203792	+	0.399964i	−0.970170	−	0.242426i	$-0.922057\pi$
$227$	−3.07043	+	6.02606i	−0.203792	+	0.399964i	0.766378	+	0.642390i	$0.222057\pi$
$228$	−2.12994	−	1.16717i	−0.141059	−	0.0772979i
$229$	1.78525	+	2.45719i	0.117973	+	0.162376i	0.863919	−	0.503630i	$-0.168003\pi$
$229$	1.78525	+	2.45719i	0.117973	+	0.162376i	−0.745947	+	0.666006i	$0.768003\pi$
$230$		0			0
$231$	0.124054	−	0.0845543i	0.00816218	−	0.00556326i
$232$	−4.95404	+	4.95404i	−0.325249	+	0.325249i
$233$	−1.36565	+	0.216297i	−0.0894666	+	0.0141701i	−0.201007	−	0.979590i	$-0.564421\pi$
$233$	−1.36565	+	0.216297i	−0.0894666	+	0.0141701i	0.111541	+	0.993760i	$0.464421\pi$
$234$	12.8866	−	8.22734i	0.842421	−	0.537838i
$235$		0			0
$236$	−6.26761	+	2.03647i	−0.407987	+	0.132563i
$237$	−2.18514	−	17.1099i	−0.141940	−	1.11141i
$238$	0.220242	−	0.112219i	0.0142762	−	0.00727408i
$239$	−3.51376	−	10.8143i	−0.227287	−	0.699516i	−0.998051	−	0.0623963i	$-0.980126\pi$
$239$	−3.51376	−	10.8143i	−0.227287	−	0.699516i	0.770765	−	0.637120i	$-0.219874\pi$
$240$		0			0
$241$	−2.72661	+	8.39163i	−0.175636	+	0.540552i	−0.999662	−	0.0259998i	$-0.991723\pi$
$241$	−2.72661	+	8.39163i	−0.175636	+	0.540552i	0.824026	+	0.566552i	$0.191723\pi$
$242$	1.53101	+	9.66643i	0.0984172	+	0.621382i
$243$	−12.5487	+	9.24826i	−0.804999	+	0.593276i
$244$	2.34577	−	3.22867i	0.150172	−	0.206695i
$245$		0			0
$246$	−6.20972	+	1.81326i	−0.395917	+	0.115609i
$247$	1.11793	−	7.05835i	0.0711323	−	0.449112i
$248$	−8.51329	−	4.33774i	−0.540595	−	0.275447i
$249$	−1.43828	−	0.515604i	−0.0911475	−	0.0326751i
$250$		0			0
$251$		−	14.6104i		−	0.922197i	−0.887349	−	0.461099i	$-0.847455\pi$
$251$		−	14.6104i		−	0.922197i	0.887349	−	0.461099i	$-0.152545\pi$
$252$	−0.0943531	−	0.216419i	−0.00594369	−	0.0136331i
$253$	−2.71745	−	0.430401i	−0.170844	−	0.0270591i
$254$	2.60673	−	1.89390i	0.163561	−	0.118834i
$255$		0			0
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−1.57229	−	1.57229i	−0.0980767	−	0.0980767i	0.656366	−	0.754443i	$-0.272093\pi$
$257$	−1.57229	−	1.57229i	−0.0980767	−	0.0980767i	−0.754443	+	0.656366i	$0.772093\pi$
$258$	−2.42028	−	0.458280i	−0.150680	−	0.0285313i
$259$	−0.775389	−	0.251939i	−0.0481803	−	0.0156547i
$260$		0			0
$261$	19.5632	+	7.68411i	1.21093	+	0.475634i
$262$	2.41443	+	4.73859i	0.149164	+	0.292751i
$263$	−8.79695	−	17.2650i	−0.542443	−	1.06460i	−0.985747	−	0.168233i	$-0.946194\pi$
$263$	−8.79695	−	17.2650i	−0.542443	−	1.06460i	0.443304	−	0.896371i	$-0.353806\pi$
$264$	−1.90682	−	0.0573270i	−0.117356	−	0.00352823i
$265$		0			0
$266$	−0.104953	−	0.0341012i	−0.00643507	−	0.00209088i
$267$	−1.05661	+	5.58021i	−0.0646638	+	0.341503i
$268$	4.70859	+	4.70859i	0.287623	+	0.287623i
$269$	4.44596	+	3.23018i	0.271075	+	0.196948i	0.715015	−	0.699109i	$-0.246420\pi$
$269$	4.44596	+	3.23018i	0.271075	+	0.196948i	−0.443940	+	0.896056i	$0.646420\pi$
$270$		0			0
$271$	6.02194	−	4.37520i	0.365807	−	0.265774i	−0.389663	−	0.920957i	$-0.627409\pi$
$271$	6.02194	−	4.37520i	0.365807	−	0.265774i	0.755470	+	0.655183i	$0.227409\pi$
$272$	−3.10226	−	0.491350i	−0.188102	−	0.0297924i
$273$	0.505746	−	0.476224i	0.0306091	−	0.0288224i
$274$		−	11.4859i		−	0.693891i
$275$		0			0
$276$	−1.46008	+	4.07290i	−0.0878863	+	0.245160i
$277$	17.0144	+	8.66928i	1.02230	+	0.520886i	0.883004	−	0.469365i	$-0.155517\pi$
$277$	17.0144	+	8.66928i	1.02230	+	0.520886i	0.139293	+	0.990251i	$0.455517\pi$
$278$	−1.70545	+	10.7678i	−0.102286	+	0.645810i
$279$	−1.72197	+	28.6123i	−0.103092	+	1.71297i
$280$		0			0
$281$	−0.827936	+	1.13956i	−0.0493905	+	0.0679802i	−0.832998	−	0.553276i	$-0.813377\pi$
$281$	−0.827936	+	1.13956i	−0.0493905	+	0.0679802i	0.783607	+	0.621256i	$0.213377\pi$
$282$	−19.9033	+	9.39887i	−1.18522	+	0.559694i
$283$	1.49164	+	9.41786i	0.0886689	+	0.559834i	0.991528	+	0.129896i	$0.0414644\pi$
$283$	1.49164	+	9.41786i	0.0886689	+	0.559834i	−0.902859	+	0.429937i	$0.858536\pi$
$284$	3.94874	−	12.1530i	0.234315	−	0.721147i
$285$		0			0
$286$	−1.73454	−	5.33836i	−0.102565	−	0.315664i
$287$	−0.261892	+	0.133440i	−0.0154590	+	0.00787674i
$288$	−0.646460	+	2.92952i	−0.0380930	+	0.172624i
$289$	6.78537	−	2.20470i	0.399139	−	0.129688i
$290$		0			0
$291$	−11.0009	+	14.2222i	−0.644883	+	0.833718i
$292$	1.31168	−	0.207750i	0.0767604	−	0.0121577i
$293$	22.0266	−	22.0266i	1.28681	−	1.28681i	0.350091	−	0.936716i	$-0.386151\pi$
$293$	22.0266	−	22.0266i	1.28681	−	1.28681i	0.936716	−	0.350091i	$-0.113849\pi$
$294$	6.82250	+	10.0097i	0.397896	+	0.583776i
$295$		0			0
$296$	6.08934	+	8.38126i	0.353936	+	0.487151i
$297$	2.12849	+	5.31250i	0.123508	+	0.308262i
$298$	6.52291	−	12.8019i	0.377862	−	0.741596i
$299$	−12.7307			−0.736237
$300$		0			0
$301$	−0.111922			−0.00645107
$302$	−0.148198	+	0.290856i	−0.00852785	+	0.0167369i
$303$	11.6843	−	21.3224i	0.671247	−	1.22494i
$304$	0.824223	+	1.13445i	0.0472724	+	0.0650649i
$305$		0			0
$306$	2.36818	+	9.12034i	0.135380	+	0.521375i
$307$	1.56450	−	1.56450i	0.0892910	−	0.0892910i	−0.661050	−	0.750341i	$-0.729889\pi$
$307$	1.56450	−	1.56450i	0.0892910	−	0.0892910i	0.750341	+	0.661050i	$0.229889\pi$
$308$	−0.0856103	+	0.0135593i	−0.00487810	+	0.000772615i
$309$	−18.0902	−	13.9928i	−1.02911	−	0.796022i
$310$		0			0
$311$	−12.9644	+	4.21240i	−0.735145	+	0.238863i	−0.652577	−	0.757722i	$-0.726312\pi$
$311$	−12.9644	+	4.21240i	−0.735145	+	0.238863i	−0.0825681	+	0.996585i	$0.526312\pi$
$312$	−8.75597	+	1.11824i	−0.495709	+	0.0633081i
$313$	17.0167	−	8.67043i	0.961839	−	0.490082i	0.0987386	−	0.995113i	$-0.468519\pi$
$313$	17.0167	−	8.67043i	0.961839	−	0.490082i	0.863101	+	0.505032i	$0.168519\pi$
$314$	1.51888	+	4.67462i	0.0857152	+	0.263804i
$315$		0			0
$316$	−3.07739	+	9.47123i	−0.173117	+	0.532798i
$317$	1.42135	+	8.97408i	0.0798312	+	0.504034i	0.994911	+	0.100761i	$0.0321277\pi$
$317$	1.42135	+	8.97408i	0.0798312	+	0.504034i	−0.915079	+	0.403274i	$0.867872\pi$
$318$	5.02130	+	10.6332i	0.281580	+	0.596281i
$319$	4.53563	−	6.24276i	0.253947	−	0.349528i
$320$		0			0
$321$	−9.44872	−	32.3583i	−0.527376	−	1.80606i
$322$	−0.0307532	+	0.194168i	−0.00171381	+	0.0108206i
$323$	3.92433	+	1.99954i	0.218355	+	0.111258i
$324$	8.83128	−	1.73453i	0.490626	−	0.0963625i
$325$		0			0
$326$		−	1.53299i		−	0.0849043i
$327$	−14.6128	−	15.5187i	−0.808092	−	0.858187i
$328$	3.68892	+	0.584268i	0.203687	+	0.0322608i
$329$	−0.809088	+	0.587837i	−0.0446065	+	0.0324085i
$330$		0			0
$331$	8.94485	+	6.49882i	0.491654	+	0.357207i	0.805820	−	0.592161i	$-0.201725\pi$
$331$	8.94485	+	6.49882i	0.491654	+	0.357207i	−0.314166	+	0.949368i	$0.601725\pi$
$332$	0.623767	+	0.623767i	0.0342336	+	0.0342336i
$333$	15.7478	−	26.7943i	0.862977	−	1.46832i
$334$	21.2873	+	6.91666i	1.16479	+	0.378463i
$335$		0			0
$336$	−0.00409615	+	0.136247i	−0.000223464	+	0.00743287i
$337$	−7.85531	−	15.4169i	−0.427906	−	0.839813i	−0.999810	−	0.0194923i	$-0.993795\pi$
$337$	−7.85531	−	15.4169i	−0.427906	−	0.839813i	0.571904	−	0.820321i	$-0.306205\pi$
$338$	−5.88940	−	11.5586i	−0.320341	−	0.628705i
$339$	0.397350	−	13.2167i	0.0215811	−	0.717833i
$340$		0			0
$341$	10.0085	+	3.25195i	0.541989	+	0.176103i
$342$	2.13155	−	3.62675i	0.115261	−	0.196112i
$343$	0.778722	+	0.778722i	0.0420470	+	0.0420470i
$344$	1.15057	+	0.835934i	0.0620343	+	0.0450706i
$345$		0			0
$346$	11.4671	−	8.33133i	0.616475	−	0.447895i
$347$	−14.7693	−	2.33923i	−0.792857	−	0.125576i	−0.253148	−	0.967428i	$-0.581466\pi$
$347$	−14.7693	−	2.33923i	−0.792857	−	0.125576i	−0.539709	+	0.841851i	$0.681466\pi$
$348$	−8.31892	−	8.83463i	−0.445941	−	0.473586i
$349$			0.345103i			0.0184729i	0.999957	+	0.00923647i	$0.00294010\pi$
$349$			0.345103i			0.0184729i	−0.999957	+	0.00923647i	$0.997060\pi$
$350$		0			0
$351$	13.5730	+	22.7383i	0.724473	+	1.21368i
$352$	0.981353	+	0.500025i	0.0523063	+	0.0266514i
$353$	3.13409	−	19.7879i	0.166811	−	1.05320i	−0.752190	−	0.658947i	$-0.771002\pi$
$353$	3.13409	−	19.7879i	0.166811	−	1.05320i	0.919001	−	0.394256i	$-0.128998\pi$
$354$	−3.19945	−	10.9569i	−0.170049	−	0.582354i
$355$		0			0
$356$	1.92734	−	2.65275i	0.102149	−	0.140596i
$357$	0.182818	+	0.387139i	0.00967574	+	0.0204896i
$358$	2.37636	+	15.0037i	0.125594	+	0.792971i
$359$	−5.66877	+	17.4467i	−0.299186	+	0.920800i	0.682597	+	0.730795i	$0.260850\pi$
$359$	−5.66877	+	17.4467i	−0.299186	+	0.920800i	−0.981783	+	0.190005i	$0.939150\pi$
$360$		0			0
$361$	5.26370	+	16.2000i	0.277037	+	0.852632i
$362$	−9.15143	+	4.66289i	−0.480989	+	0.245076i
$363$	−16.8149	+	2.14746i	−0.882552	+	0.112713i
$364$	−0.381439	+	0.123937i	−0.0199928	+	0.00649606i
$365$		0			0
$366$	5.46760	+	4.22920i	0.285796	+	0.221064i
$367$	0.0192492	−	0.00304877i	0.00100480	−	0.000159144i	−0.155932	−	0.987768i	$-0.549838\pi$
$367$	0.0192492	−	0.00304877i	0.00100480	−	0.000159144i	0.156937	+	0.987609i	$0.449838\pi$
$368$	1.76637	−	1.76637i	0.0920783	−	0.0920783i
$369$	−2.81602	−	10.8451i	−0.146596	−	0.564572i
$370$		0			0
$371$	0.314049	+	0.432251i	0.0163046	+	0.0224414i
$372$	7.95290	−	14.5130i	0.412339	−	0.752465i
$373$	3.17602	−	6.23329i	0.164448	−	0.322748i	−0.794047	−	0.607856i	$-0.792030\pi$
$373$	3.17602	−	6.23329i	0.164448	−	0.322748i	0.958495	+	0.285109i	$0.0920297\pi$
$374$	3.45942			0.178882
$375$		0			0
$376$	12.7080			0.655364
$377$	16.2098	−	31.8136i	0.834848	−	1.63848i
$378$	0.379591	−	0.152086i	0.0195241	−	0.00782246i
$379$	7.15293	+	9.84516i	0.367421	+	0.505712i	0.952198	−	0.305483i	$-0.0988178\pi$
$379$	7.15293	+	9.84516i	0.367421	+	0.505712i	−0.584776	+	0.811194i	$0.698818\pi$
$380$		0			0
$381$	3.14317	+	4.61152i	0.161030	+	0.236256i
$382$	7.68054	−	7.68054i	0.392971	−	0.392971i
$383$	−0.936062	+	0.148258i	−0.0478305	+	0.00757561i	−0.180304	−	0.983611i	$-0.557708\pi$
$383$	−0.936062	+	0.148258i	−0.0478305	+	0.00757561i	0.132473	+	0.991187i	$0.457708\pi$
$384$	1.05972	−	1.37003i	0.0540788	−	0.0699141i
$385$		0			0
$386$	−18.4588	+	5.99764i	−0.939530	+	0.305272i
$387$	0.919380	−	4.16630i	0.0467347	−	0.211785i
$388$	9.24945	−	4.71283i	0.469570	−	0.239258i
$389$	−6.14102	−	18.9001i	−0.311362	−	0.958273i	−0.977226	−	0.212200i	$-0.931937\pi$
$389$	−6.14102	−	18.9001i	−0.311362	−	0.958273i	0.665864	−	0.746073i	$-0.268063\pi$
$390$		0			0
$391$	2.42458	−	7.46210i	0.122616	−	0.377374i
$392$	−1.09407	−	6.90770i	−0.0552590	−	0.348892i
$393$	−8.32944	+	3.93339i	−0.420164	+	0.198413i
$394$	7.18863	−	9.89430i	0.362158	−	0.498468i
$395$		0			0
$396$	0.198497	−	3.29823i	0.00997485	−	0.165742i
$397$	4.21926	−	26.6394i	0.211759	−	1.33699i	−0.621198	−	0.783654i	$-0.713354\pi$
$397$	4.21926	−	26.6394i	0.211759	−	1.33699i	0.832957	−	0.553338i	$-0.186646\pi$
$398$	14.1987	+	7.23462i	0.711719	+	0.362639i
$399$	0.0645011	−	0.179927i	0.00322909	−	0.00900759i
$400$		0			0
$401$		−	33.9394i		−	1.69485i	−0.530912	−	0.847427i	$-0.678151\pi$
$401$		−	33.9394i		−	1.69485i	0.530912	−	0.847427i	$-0.321849\pi$
$402$	−8.39690	+	7.90675i	−0.418800	+	0.394353i
$403$	48.0943	+	7.61739i	2.39575	+	0.379449i
$404$	−11.3567	+	8.25112i	−0.565017	+	0.410509i
$405$		0			0
$406$	−0.446060	−	0.324082i	−0.0221376	−	0.0160839i
$407$	−8.06828	−	8.06828i	−0.399930	−	0.399930i
$408$	1.01213	−	5.34527i	0.0501078	−	0.264630i
$409$	15.1218	+	4.91338i	0.747726	+	0.242951i	0.658002	−	0.753016i	$-0.271402\pi$
$409$	15.1218	+	4.91338i	0.747726	+	0.242951i	0.0897236	+	0.995967i	$0.471402\pi$
$410$		0			0
$411$	19.8853	+	0.597835i	0.980867	+	0.0294890i
$412$	5.99458	+	11.7650i	0.295332	+	0.579621i
$413$	−0.235453	−	0.462102i	−0.0115859	−	0.0227386i
$414$	−6.97529	−	2.73978i	−0.342817	−	0.134653i
$415$		0			0
$416$	4.84689	+	1.57485i	0.237638	+	0.0772134i
$417$	−18.5532	−	3.51305i	−0.908554	−	0.172035i
$418$	−1.09208	−	1.09208i	−0.0534155	−	0.0534155i
$419$	−22.2455	−	16.1623i	−1.08677	−	0.789582i	−0.107916	−	0.994160i	$-0.534418\pi$
$419$	−22.2455	−	16.1623i	−1.08677	−	0.789582i	−0.978850	+	0.204578i	$0.934418\pi$
$420$		0			0
$421$	25.8507	−	18.7816i	1.25988	−	0.915359i	0.261132	−	0.965303i	$-0.415904\pi$
$421$	25.8507	−	18.7816i	1.25988	−	0.915359i	0.998752	+	0.0499438i	$0.0159042\pi$
$422$	−10.9234	−	1.73009i	−0.531741	−	0.0842194i
$423$	−15.2360	−	34.9471i	−0.740800	−	1.69919i
$424$		−	6.78917i		−	0.329711i
$425$		0			0
$426$	20.8346	+	7.46889i	1.00944	+	0.361869i
$427$	0.279839	+	0.142585i	0.0135424	+	0.00690018i
$428$	−3.04457	+	19.2226i	−0.147165	+	0.929162i
$429$	9.33242	−	2.72509i	0.450573	−	0.131569i
$430$		0			0
$431$	5.09101	−	7.00718i	0.245225	−	0.337524i	−0.668607	−	0.743616i	$-0.733109\pi$
$431$	5.09101	−	7.00718i	0.245225	−	0.337524i	0.913832	+	0.406093i	$0.133109\pi$
$432$	−5.03814	−	1.27167i	−0.242398	−	0.0611835i
$433$	1.68664	+	10.6490i	0.0810548	+	0.511760i	0.994495	+	0.104786i	$0.0334159\pi$
$433$	1.68664	+	10.6490i	0.0810548	+	0.511760i	−0.913440	+	0.406974i	$0.866584\pi$
$434$	0.232360	−	0.715129i	0.0111536	−	0.0343273i
$435$		0			0
$436$	3.80299	+	11.7044i	0.182130	+	0.560538i
$437$	−3.12107	+	1.59026i	−0.149301	+	0.0760726i
$438$	0.291399	+	2.28169i	0.0139236	+	0.109023i
$439$	32.6251	−	10.6006i	1.55711	−	0.505937i	0.601078	−	0.799190i	$-0.294738\pi$
$439$	32.6251	−	10.6006i	1.55711	−	0.505937i	0.956035	+	0.293253i	$0.0947379\pi$
$440$		0			0
$441$	−17.6845	+	11.2906i	−0.842121	+	0.537646i
$442$	15.8101	−	2.50408i	0.752011	−	0.119107i
$443$	−4.58214	+	4.58214i	−0.217704	+	0.217704i	−0.807530	−	0.589826i	$-0.799196\pi$
$443$	−4.58214	+	4.58214i	−0.217704	+	0.217704i	0.589826	+	0.807530i	$0.299196\pi$
$444$	−14.8272	+	10.1060i	−0.703666	+	0.479612i
$445$		0			0
$446$	3.22891	+	4.44421i	0.152893	+	0.210439i
$447$	21.8241	+	11.9592i	1.03224	+	0.565653i
$448$	0.0357280	−	0.0701201i	0.00168799	−	0.00331286i
$449$	22.7460			1.07345			0.536726	−	0.843756i	$-0.319661\pi$
$449$	22.7460			1.07345			0.536726	+	0.843756i	$0.319661\pi$
$450$		0			0
$451$	−4.11362			−0.193703
$452$	−3.46581	+	6.80204i	−0.163018	+	0.319941i
$453$	−0.495835	−	0.271710i	−0.0232964	−	0.0127660i
$454$	3.97531	+	5.47155i	0.186571	+	0.256792i
$455$		0			0
$456$	−2.00693	+	1.36790i	−0.0939831	+	0.0640580i
$457$	−6.28077	+	6.28077i	−0.293802	+	0.293802i	−0.838580	−	0.544778i	$-0.816614\pi$
$457$	−6.28077	+	6.28077i	−0.293802	+	0.293802i	0.544778	+	0.838580i	$0.316614\pi$
$458$	2.99986	−	0.475131i	0.140174	−	0.0222014i
$459$	−15.9130	+	3.62525i	−0.742756	+	0.169212i
$460$		0			0
$461$	21.3397	−	6.93369i	0.993889	−	0.322934i	0.233468	−	0.972364i	$-0.424993\pi$
$461$	21.3397	−	6.93369i	0.993889	−	0.322934i	0.760421	+	0.649430i	$0.224993\pi$
$462$	−0.0190189	−	0.148920i	−0.000884839	−	0.00692839i
$463$	−21.5722	+	10.9916i	−1.00255	+	0.510823i	−0.876603	−	0.481214i	$-0.840196\pi$
$463$	−21.5722	+	10.9916i	−1.00255	+	0.510823i	−0.125944	+	0.992037i	$0.540196\pi$
$464$	2.16499	+	6.66317i	0.100507	+	0.309330i
$465$		0			0
$466$	−0.427269	+	1.31500i	−0.0197929	+	0.0609161i
$467$	−2.10730	−	13.3049i	−0.0975140	−	0.615679i	−0.987247	−	0.159197i	$-0.949109\pi$
$467$	−2.10730	−	13.3049i	−0.0975140	−	0.615679i	0.889733	−	0.456482i	$-0.150891\pi$
$468$	−1.48024	−	15.2171i	−0.0684240	−	0.703413i
$469$	−0.308025	+	0.423960i	−0.0142233	+	0.0195766i
$470$		0			0
$471$	−8.17208	+	2.38627i	−0.376550	+	0.109954i
$472$	−1.03093	+	6.50902i	−0.0474523	+	0.299602i
$473$	−1.39566	−	0.711123i	−0.0641724	−	0.0326975i
$474$	−16.2371	−	5.82076i	−0.745793	−	0.267356i
$475$		0			0
$476$		−	0.247184i		−	0.0113296i
$477$	−18.6703	+	8.13976i	−0.854855	+	0.372694i
$478$	−11.2308	−	1.77878i	−0.513684	−	0.0813596i
$479$	13.9808	−	10.1576i	0.638797	−	0.464113i	−0.220639	−	0.975355i	$-0.570814\pi$
$479$	13.9808	−	10.1576i	0.638797	−	0.464113i	0.859437	+	0.511242i	$0.170814\pi$
$480$		0			0
$481$	−42.7136	−	31.0332i	−1.94757	−	1.41499i
$482$	6.23914	+	6.23914i	0.284185	+	0.284185i
$483$	−0.334556	−	0.0633484i	−0.0152228	−	0.00288245i
$484$	9.30791	+	3.02432i	0.423087	+	0.137469i
$485$		0			0
$486$	2.54327	+	15.3796i	0.115365	+	0.697632i
$487$	−1.64469	−	3.22789i	−0.0745281	−	0.146270i	0.850736	−	0.525593i	$-0.176157\pi$
$487$	−1.64469	−	3.22789i	−0.0745281	−	0.146270i	−0.925264	+	0.379324i	$0.876157\pi$
$488$	−1.81181	−	3.55588i	−0.0820169	−	0.160967i
$489$	2.65401	+	0.0797909i	0.120019	+	0.00360827i
$490$		0			0
$491$	5.48953	+	1.78366i	0.247739	+	0.0804953i	0.430254	−	0.902708i	$-0.358424\pi$
$491$	5.48953	+	1.78366i	0.247739	+	0.0804953i	−0.182515	+	0.983203i	$0.558424\pi$
$492$	−1.20353	+	6.35610i	−0.0542593	+	0.286555i
$493$	15.5603	+	15.5603i	0.700800	+	0.700800i
$494$	−5.78150	−	4.20051i	−0.260122	−	0.188990i
$495$		0			0
$496$	−7.72991	+	5.61611i	−0.347083	+	0.252171i
$497$	0.993249	+	0.157315i	0.0445533	+	0.00705655i
$498$	−1.11237	+	1.04744i	−0.0498467	+	0.0469370i
$499$			28.5582i			1.27844i	0.769024	+	0.639220i	$0.220743\pi$
$499$			28.5582i			1.27844i	−0.769024	+	0.639220i	$0.779257\pi$
$500$		0			0
$501$	−13.0826	+	36.4940i	−0.584486	+	1.63043i
$502$	−13.0179	−	6.63296i	−0.581018	−	0.296044i
$503$	−3.76856	+	23.7938i	−0.168032	+	1.06091i	0.749138	+	0.662414i	$0.230468\pi$
$503$	−3.76856	+	23.7938i	−0.168032	+	1.06091i	−0.917170	+	0.398497i	$0.869532\pi$
$504$	−0.235666	−	0.0141831i	−0.0104974	−	0.000631765i
$505$		0			0
$506$	−1.61718	+	2.22586i	−0.0718926	+	0.0989517i
$507$	20.3176	−	9.59451i	0.902335	−	0.426107i
$508$	−0.504047	−	3.18243i	−0.0223635	−	0.141197i
$509$	−1.35722	+	4.17708i	−0.0601576	+	0.185146i	−0.976619	−	0.214977i	$-0.931032\pi$
$509$	−1.35722	+	4.17708i	−0.0601576	+	0.185146i	0.916462	+	0.400123i	$0.131032\pi$
$510$		0			0
$511$	0.0322963	+	0.0993978i	0.00142870	+	0.00439710i
$512$	−0.891007	+	0.453990i	−0.0393773	+	0.0200637i
$513$	6.16793	+	3.87906i	0.272321	+	0.171265i
$514$	−2.11472	+	0.687116i	−0.0932765	+	0.0303074i
$515$		0			0
$516$	−1.50711	+	1.94843i	−0.0663470	+	0.0857747i
$517$	−13.8242	+	2.18954i	−0.607989	+	0.0962960i
$518$	−0.576498	+	0.576498i	−0.0253299	+	0.0253299i
$519$	13.8269	+	20.2863i	0.606934	+	0.890468i
$520$		0			0
$521$	−3.85216	−	5.30205i	−0.168766	−	0.232287i	0.716254	−	0.697840i	$-0.245855\pi$
$521$	−3.85216	−	5.30205i	−0.168766	−	0.232287i	−0.885020	+	0.465553i	$0.845855\pi$
$522$	15.7281	−	13.9424i	0.688401	−	0.610244i
$523$	−4.06078	+	7.96973i	−0.177566	+	0.348492i	−0.962585	−	0.270979i	$-0.912653\pi$
$523$	−4.06078	+	7.96973i	−0.177566	+	0.348492i	0.785020	+	0.619471i	$0.212653\pi$
$524$	5.31824			0.232328
$525$		0			0
$526$	−19.3769			−0.844875
$527$	−13.6245	+	26.7397i	−0.593494	+	1.16480i
$528$	−0.916756	+	1.67296i	−0.0398967	+	0.0728063i
$529$	−9.85121	−	13.5590i	−0.428314	−	0.589523i
$530$		0			0
$531$	19.1359	−	4.96881i	0.830427	−	0.215628i
$532$	−0.0780320	+	0.0780320i	−0.00338312	+	0.00338312i
$533$	−18.7999	+	2.97762i	−0.814315	+	0.128975i
$534$	4.49231	+	3.47481i	0.194401	+	0.150370i
$535$		0			0
$536$	6.33303	−	2.05773i	0.273545	−	0.0888803i
$537$	−26.0992	+	3.33318i	−1.12626	+	0.143837i
$538$	4.89653	−	2.49491i	0.211105	−	0.107563i
$539$	2.38035	+	7.32596i	0.102529	+	0.315551i
$540$		0			0
$541$	4.98127	−	15.3308i	0.214161	−	0.659121i	−0.785051	−	0.619432i	$-0.787363\pi$
$541$	4.98127	−	15.3308i	0.214161	−	0.659121i	0.999212	−	0.0396896i	$-0.0126369\pi$
$542$	−1.16442	−	7.35189i	−0.0500163	−	0.315791i
$543$	−7.59639	−	16.0863i	−0.325992	−	0.690329i
$544$	−1.84619	+	2.54107i	−0.0791548	+	0.108947i
$545$		0			0
$546$	−0.194715	−	0.666824i	−0.00833301	−	0.0285374i
$547$	−3.70025	+	23.3625i	−0.158211	+	0.998907i	0.772994	+	0.634413i	$0.218758\pi$
$547$	−3.70025	+	23.3625i	−0.158211	+	0.998907i	−0.931206	+	0.364494i	$0.881242\pi$
$548$	−10.2341	−	5.21451i	−0.437177	−	0.222753i
$549$	−7.60647	+	9.24576i	−0.324636	+	0.394599i
$550$		0			0
$551$		−	9.82428i		−	0.418528i
$552$	2.96612	+	3.15000i	0.126246	+	0.134073i
$553$	−0.774072	−	0.122601i	−0.0329169	−	0.00521353i
$554$	15.4488	−	11.2242i	0.656355	−	0.476870i
$555$		0			0
$556$	8.81992	+	6.40805i	0.374048	+	0.271762i
$557$	27.5142	+	27.5142i	1.16581	+	1.16581i	0.983181	+	0.182634i	$0.0584623\pi$
$557$	27.5142	+	27.5142i	1.16581	+	1.16581i	0.182634	+	0.983181i	$0.441538\pi$
$558$	24.7120	+	14.5240i	1.04614	+	0.614850i
$559$	−6.89314	−	2.23972i	−0.291549	−	0.0947299i
$560$		0			0
$561$	−0.180060	+	5.98918i	−0.00760215	+	0.252863i
$562$	0.639477	+	1.25504i	0.0269747	+	0.0529408i
$563$	11.3007	+	22.1789i	0.476267	+	0.934728i	0.996727	+	0.0808412i	$0.0257607\pi$
$563$	11.3007	+	22.1789i	0.476267	+	0.934728i	−0.520460	+	0.853886i	$0.674239\pi$
$564$	−0.661442	+	22.0009i	−0.0278517	+	0.926406i
$565$		0			0
$566$	9.06857	+	2.94656i	0.381180	+	0.123853i
$567$	0.243544	+	0.665090i	0.0102279	+	0.0279311i
$568$	−9.03570	−	9.03570i	−0.379129	−	0.379129i
$569$	25.9540	+	18.8567i	1.08805	+	0.790515i	0.979069	−	0.203529i	$-0.0652412\pi$
$569$	25.9540	+	18.8567i	1.08805	+	0.790515i	0.108981	+	0.994044i	$0.465241\pi$
$570$		0			0
$571$	−34.1170	+	24.7874i	−1.42775	+	1.03732i	−0.437322	+	0.899305i	$0.644073\pi$
$571$	−34.1170	+	24.7874i	−1.42775	+	1.03732i	−0.990430	+	0.138017i	$0.955927\pi$
$572$	−5.54398	−	0.878080i	−0.231805	−	0.0367144i
$573$	12.8973	+	13.6968i	0.538793	+	0.572194i
$574$			0.293928i			0.0122683i
$575$		0			0
$576$	2.31674	+	1.90597i	0.0965306	+	0.0794156i
$577$	19.6556	+	10.0150i	0.818274	+	0.416931i	0.812435	−	0.583052i	$-0.198141\pi$
$577$	19.6556	+	10.0150i	0.818274	+	0.416931i	0.00583873	+	0.999983i	$0.498141\pi$
$578$	1.11609	−	7.04672i	0.0464233	−	0.293105i
$579$	−9.42275	−	32.2694i	−0.391596	−	1.34107i
$580$		0			0
$581$	−0.0408054	+	0.0561638i	−0.00169289	+	0.00233007i
$582$	7.67775	+	16.2586i	0.318253	+	0.673940i
$583$	1.16975	+	7.38553i	0.0484462	+	0.305877i
$584$	0.410385	−	1.26303i	0.0169818	−	0.0522647i
$585$		0			0
$586$	−9.62597	−	29.6257i	−0.397645	−	1.22383i
$587$	−11.4960	+	5.85750i	−0.474490	+	0.241765i	−0.674846	−	0.737958i	$-0.735790\pi$
$587$	−11.4960	+	5.85750i	−0.474490	+	0.241765i	0.200356	+	0.979723i	$0.435790\pi$
$588$	12.0160	−	1.53459i	0.495533	−	0.0632855i
$589$	12.7423	−	4.14024i	0.525039	−	0.170596i
$590$		0			0
$591$	16.7555	+	12.9604i	0.689230	+	0.533121i
$592$	10.2323	−	1.62063i	0.420543	−	0.0666075i
$593$	−3.75033	+	3.75033i	−0.154007	+	0.154007i	−0.779905	−	0.625898i	$-0.784733\pi$
$593$	−3.75033	+	3.75033i	−0.154007	+	0.154007i	0.625898	+	0.779905i	$0.284733\pi$
$594$	5.69979	+	0.515322i	0.233865	+	0.0211439i
$595$		0			0
$596$	−8.44527	−	11.6239i	−0.345932	−	0.476134i
$597$	−13.2641	+	24.2053i	−0.542864	+	0.990656i
$598$	−5.77963	+	11.3432i	−0.236347	+	0.463856i
$599$	−29.8620			−1.22013			−0.610065	−	0.792352i	$-0.708857\pi$
$599$	−29.8620			−1.22013			−0.610065	+	0.792352i	$0.708857\pi$
$600$		0			0
$601$	19.0008			0.775058			0.387529	−	0.921858i	$-0.373329\pi$
$601$	19.0008			0.775058			0.387529	+	0.921858i	$0.373329\pi$
$602$	−0.0508115	+	0.0997231i	−0.00207092	+	0.00406441i
$603$	−13.2517	−	14.9488i	−0.539649	−	0.608764i
$604$	0.191874	+	0.264091i	0.00780722	+	0.0107457i
$605$		0			0
$606$	−13.6938	−	20.0910i	−0.556273	−	0.816139i
$607$	29.8007	−	29.8007i	1.20957	−	1.20957i	0.238406	−	0.971165i	$-0.423375\pi$
$607$	29.8007	−	29.8007i	1.20957	−	1.20957i	0.971165	−	0.238406i	$-0.0766250\pi$
$608$	1.38499	−	0.219361i	0.0561687	−	0.00889625i
$609$	0.584290	−	0.755382i	0.0236766	−	0.0306096i
$610$		0			0
$611$	−61.5942	+	20.0132i	−2.49184	+	0.809646i
$612$	9.20142	+	2.03048i	0.371945	+	0.0820775i
$613$	−1.17929	+	0.600877i	−0.0476310	+	0.0242692i	−0.477644	−	0.878554i	$-0.658509\pi$
$613$	−1.17929	+	0.600877i	−0.0476310	+	0.0242692i	0.430013	+	0.902823i	$0.358509\pi$
$614$	−0.683714	−	2.10425i	−0.0275924	−	0.0849208i
$615$		0			0
$616$	−0.0267848	+	0.0824351i	−0.00107919	+	0.00332141i
$617$	−6.57400	−	41.5066i	−0.264659	−	1.67099i	−0.659087	−	0.752067i	$-0.729057\pi$
$617$	−6.57400	−	41.5066i	−0.264659	−	1.67099i	0.394428	−	0.918927i	$-0.370943\pi$
$618$	−20.6804	+	9.76586i	−0.831889	+	0.392841i
$619$	9.51877	−	13.1015i	0.382592	−	0.526592i	−0.573677	−	0.819082i	$-0.694484\pi$
$619$	9.51877	−	13.1015i	0.382592	−	0.526592i	0.956269	+	0.292489i	$0.0944836\pi$
$620$		0			0
$621$	5.10635	−	11.9335i	0.204911	−	0.478875i
$622$	−2.13245	+	13.4638i	−0.0855036	+	0.539848i
$623$	0.229923	+	0.117151i	0.00921165	+	0.00469357i
$624$	−2.97877	+	8.30930i	−0.119246	+	0.332638i
$625$		0			0
$626$		−	19.0983i		−	0.763320i
$627$	1.94753	−	1.83385i	0.0777769	−	0.0732368i
$628$	4.85468	+	0.768905i	0.193723	+	0.0306827i
$629$	26.3249	−	19.1262i	1.04964	−	0.762611i
$630$		0			0
$631$	−9.33690	−	6.78365i	−0.371696	−	0.270053i	0.386218	−	0.922408i	$-0.373781\pi$
$631$	−9.33690	−	6.78365i	−0.371696	−	0.270053i	−0.757914	+	0.652355i	$0.773781\pi$
$632$	7.04182	+	7.04182i	0.280109	+	0.280109i
$633$	3.56380	−	18.8212i	0.141648	−	0.748076i
$634$	8.64124	+	2.80771i	0.343188	+	0.111508i
$635$		0			0
$636$	11.7539	+	0.353372i	0.466072	+	0.0140121i
$637$	16.1814	+	31.7579i	0.641132	+	1.25829i
$638$	−3.50321	−	6.87543i	−0.138693	−	0.272201i
$639$	−14.0151	+	35.6815i	−0.554428	+	1.41154i
$640$		0			0
$641$	15.5088	+	5.03912i	0.612561	+	0.199033i	0.598835	−	0.800873i	$-0.295631\pi$
$641$	15.5088	+	5.03912i	0.612561	+	0.199033i	0.0137264	+	0.999906i	$0.495631\pi$
$642$	−33.1211	−	6.27149i	−1.30719	−	0.247516i
$643$	−12.8296	−	12.8296i	−0.505952	−	0.505952i	0.407330	−	0.913281i	$-0.366460\pi$
$643$	−12.8296	−	12.8296i	−0.505952	−	0.505952i	−0.913281	+	0.407330i	$0.866460\pi$
$644$	0.159043	+	0.115552i	0.00626719	+	0.00455338i
$645$		0			0
$646$	3.56321	−	2.58883i	0.140193	−	0.101856i
$647$	25.1179	+	3.97829i	0.987488	+	0.156403i	0.629229	−	0.777220i	$-0.283371\pi$
$647$	25.1179	+	3.97829i	0.987488	+	0.156403i	0.358259	+	0.933622i	$0.383371\pi$
$648$	2.46384	−	8.65618i	0.0967889	−	0.340047i
$649$		−	7.25839i		−	0.284917i
$650$		0			0
$651$	1.22599	+	0.439499i	0.0480502	+	0.0172253i
$652$	−1.36590	−	0.695961i	−0.0534928	−	0.0272559i
$653$	−4.76127	+	30.0615i	−0.186323	+	1.17640i	0.700281	+	0.713867i	$0.253058\pi$
$653$	−4.76127	+	30.0615i	−0.186323	+	1.17640i	−0.886604	+	0.462529i	$0.846942\pi$
$654$	−20.4614	+	5.97478i	−0.800103	+	0.233633i
$655$		0			0
$656$	2.19532	−	3.02160i	0.0857129	−	0.117974i
$657$	−3.96538	+	0.385730i	−0.154704	+	0.0150488i
$658$	0.156448	+	0.987775i	0.00609899	+	0.0385075i
$659$	3.19473	−	9.83236i	0.124449	−	0.383014i	−0.869351	−	0.494195i	$-0.835463\pi$
$659$	3.19473	−	9.83236i	0.124449	−	0.383014i	0.993800	+	0.111180i	$0.0354631\pi$
$660$		0			0
$661$	3.97825	+	12.2438i	0.154736	+	0.476229i	0.998134	−	0.0610606i	$-0.0194483\pi$
$661$	3.97825	+	12.2438i	0.154736	+	0.476229i	−0.843398	+	0.537289i	$0.819448\pi$
$662$	9.85137	−	5.01952i	0.382884	−	0.195089i
$663$	3.51232	+	27.5019i	0.136407	+	1.06809i
$664$	0.838964	−	0.272596i	0.0325581	−	0.0105788i
$665$		0			0
$666$	−16.7245	−	26.1958i	−0.648063	−	1.01507i
$667$	−17.2859	+	2.73781i	−0.669311	+	0.106008i
$668$	15.8270	−	15.8270i	0.612365	−	0.612365i
$669$	−7.86218	+	5.35879i	−0.303969	+	0.207183i
$670$		0			0
$671$	2.58363	+	3.55605i	0.0997397	+	0.137280i
$672$	0.119537	+	0.0655044i	0.00461124	+	0.00252689i
$673$	−15.3006	+	30.0291i	−0.589794	+	1.15754i	0.382540	+	0.923939i	$0.375049\pi$
$673$	−15.3006	+	30.0291i	−0.589794	+	1.15754i	−0.972334	+	0.233596i	$0.924951\pi$
$674$	−17.3028			−0.666479
$675$		0			0
$676$	−12.9725			−0.498943
$677$	−7.07682	+	13.8891i	−0.271984	+	0.533800i	−0.986085	−	0.166244i	$-0.946836\pi$
$677$	−7.07682	+	13.8891i	−0.271984	+	0.533800i	0.714100	+	0.700044i	$0.246836\pi$
$678$	−11.5958	−	6.35430i	−0.445333	−	0.244035i
$679$	0.480192	+	0.660928i	0.0184281	+	0.0253641i
$680$		0			0
$681$	−9.67963	+	6.59754i	−0.370924	+	0.252818i
$682$	7.44126	−	7.44126i	0.284940	−	0.284940i
$683$	−26.5524	+	4.20549i	−1.01600	+	0.160919i	−0.642157	−	0.766573i	$-0.721960\pi$
$683$	−26.5524	+	4.20549i	−1.01600	+	0.160919i	−0.373844	+	0.927492i	$0.621960\pi$
$684$	−2.26375	−	3.54573i	−0.0865567	−	0.135575i
$685$		0			0
$686$	1.04738	−	0.340314i	0.0399891	−	0.0129932i
$687$	0.666439	+	5.21829i	0.0254262	+	0.199090i
$688$	1.26717	−	0.645655i	0.0483104	−	0.0246154i
$689$	10.6919	+	32.9064i	0.407330	+	1.25363i
$690$		0			0
$691$	7.00128	−	21.5477i	0.266341	−	0.819714i	−0.725040	−	0.688707i	$-0.758179\pi$
$691$	7.00128	−	21.5477i	0.266341	−	0.819714i	0.991381	−	0.131007i	$-0.0418212\pi$
$692$	−2.21732	−	13.9996i	−0.0842898	−	0.532185i
$693$	0.258811	−	0.0251756i	0.00983141	−	0.000956343i
$694$	−8.78938	+	12.0975i	−0.333640	+	0.459217i
$695$		0			0
$696$	−11.6484	+	3.40137i	−0.441532	+	0.128929i
$697$	1.83514	−	11.5866i	0.0695110	−	0.438875i
$698$	0.307489	+	0.156673i	0.0116386	+	0.00593018i
$699$	−2.25438	−	0.808162i	−0.0852684	−	0.0305675i
$700$		0			0
$701$			37.8133i			1.42819i	0.700049	+	0.714095i	$0.253161\pi$
$701$			37.8133i			1.42819i	−0.700049	+	0.714095i	$0.746839\pi$
$702$	26.4220	−	1.77065i	0.997235	−	0.0668288i
$703$	−14.3482	−	2.27253i	−0.541153	−	0.0857102i
$704$	0.891050	−	0.647386i	0.0335827	−	0.0243993i
$705$		0			0
$706$	−16.2083	−	11.7760i	−0.610007	−	0.443196i
$707$	−0.781162	−	0.781162i	−0.0293786	−	0.0293786i
$708$	−11.2152	−	2.12360i	−0.421493	−	0.0798099i
$709$	−37.7779	−	12.2748i	−1.41878	−	0.460989i	−0.503565	−	0.863958i	$-0.667978\pi$
$709$	−37.7779	−	12.2748i	−1.41878	−	0.460989i	−0.915214	+	0.402968i	$0.867978\pi$
$710$		0			0
$711$	10.9224	−	27.8078i	0.409623	−	1.04287i
$712$	−1.48863	−	2.92160i	−0.0557887	−	0.109491i
$713$	−10.8358	−	21.2664i	−0.405803	−	0.796433i
$714$	0.427941	+	0.0128657i	0.0160153	+	0.000481488i
$715$		0			0
$716$	14.4473	+	4.69420i	0.539919	+	0.175430i
$717$	3.66410	−	19.3509i	0.136838	−	0.722673i
$718$	12.9715	+	12.9715i	0.484093	+	0.484093i
$719$	−25.6075	−	18.6049i	−0.954998	−	0.693847i	−0.00301445	−	0.999995i	$-0.500960\pi$
$719$	−25.6075	−	18.6049i	−0.954998	−	0.693847i	−0.951984	+	0.306149i	$0.900960\pi$
$720$		0			0
$721$	−0.840680	+	0.610790i	−0.0313086	+	0.0227470i
$722$	16.8240	+	2.66466i	0.626124	+	0.0991682i
$723$	−11.1264	+	10.4769i	−0.413794	+	0.389640i
$724$			10.2709i			0.381715i
$725$		0			0
$726$	−5.72039	+	15.9571i	−0.212304	+	0.592223i
$727$	45.9671	+	23.4214i	1.70483	+	0.868652i	0.984580	+	0.174934i	$0.0559711\pi$
$727$	45.9671	+	23.4214i	1.70483	+	0.868652i	0.720246	+	0.693719i	$0.244029\pi$
$728$	−0.0627409	+	0.396131i	−0.00232533	+	0.0146816i
$729$	−26.7586	+	3.60258i	−0.991058	+	0.133429i
$730$		0			0
$731$	2.62561	−	3.61384i	0.0971117	−	0.133663i
$732$	6.25049	−	2.95165i	0.231025	−	0.109096i
$733$	−3.31036	−	20.9008i	−0.122271	−	0.771988i	−0.970276	−	0.242000i	$-0.922197\pi$
$733$	−3.31036	−	20.9008i	−0.122271	−	0.771988i	0.848005	−	0.529988i	$-0.177803\pi$
$734$	0.00602247	−	0.0185352i	0.000222293	−	0.000684148i
$735$		0			0
$736$	−0.771931	−	2.37576i	−0.0284538	−	0.0875717i
$737$	−6.53478	+	3.32964i	−0.240712	+	0.122649i
$738$	−10.9415	−	2.41446i	−0.402761	−	0.0888776i
$739$	−11.8537	+	3.85150i	−0.436046	+	0.141680i	−0.518811	−	0.854889i	$-0.673625\pi$
$739$	−11.8537	+	3.85150i	−0.436046	+	0.141680i	0.0827648	+	0.996569i	$0.473625\pi$
$740$		0			0
$741$	7.57313	−	9.79070i	0.278206	−	0.359670i
$742$	0.527714	−	0.0835816i	0.0193730	−	0.00306838i
$743$	−2.30237	+	2.30237i	−0.0844658	+	0.0844658i	−0.748077	−	0.663612i	$-0.769023\pi$
$743$	−2.30237	+	2.30237i	−0.0844658	+	0.0844658i	0.663612	+	0.748077i	$0.269023\pi$
$744$	−9.32066	−	13.6749i	−0.341712	−	0.501345i
$745$		0			0
$746$	−4.11202	−	5.65971i	−0.150552	−	0.207217i
$747$	−1.75550	−	1.98034i	−0.0642305	−	0.0724567i
$748$	1.57054	−	3.08236i	0.0574247	−	0.112702i
$749$	−1.53163			−0.0559646
$750$		0			0
$751$	18.7652			0.684751			0.342375	−	0.939563i	$-0.388769\pi$
$751$	18.7652			0.684751			0.342375	+	0.939563i	$0.388769\pi$
$752$	5.76930	−	11.3229i	0.210385	−	0.412904i
$753$	12.1610	−	22.1923i	0.443172	−	0.808731i
$754$	−20.9870	−	28.8861i	−0.764301	−	1.05197i
$755$		0			0
$756$	0.0368210	−	0.407264i	0.00133917	−	0.0148120i
$757$	−7.02667	+	7.02667i	−0.255389	+	0.255389i	−0.823176	−	0.567787i	$-0.807800\pi$
$757$	−7.02667	+	7.02667i	−0.255389	+	0.255389i	0.567787	+	0.823176i	$0.307800\pi$
$758$	12.0195	−	1.90370i	0.436567	−	0.0691453i
$759$	−3.76939	−	2.91564i	−0.136820	−	0.105831i
$760$		0			0
$761$	−48.1462	+	15.6436i	−1.74530	+	0.567081i	−0.995515	−	0.0946038i	$-0.969842\pi$
$761$	−48.1462	+	15.6436i	−1.74530	+	0.567081i	−0.749782	+	0.661685i	$0.769842\pi$
$762$	5.53587	−	0.706997i	0.200543	−	0.0256118i
$763$	−0.862948	+	0.439694i	−0.0312408	+	0.0159180i
$764$	−3.35652	−	10.3303i	−0.121435	−	0.373737i
$765$		0			0
$766$	−0.292865	+	0.901344i	−0.0105816	+	0.0325669i
$767$	−5.25394	−	33.1721i	−0.189709	−	1.19777i
$768$	−0.739603	−	1.56620i	−0.0266881	−	0.0565154i
$769$	−21.2813	+	29.2912i	−0.767422	+	1.05627i	0.229138	+	0.973394i	$0.426409\pi$
$769$	−21.2813	+	29.2912i	−0.767422	+	1.05627i	−0.996560	+	0.0828721i	$0.973591\pi$
$770$		0			0
$771$	−1.07951	−	3.69692i	−0.0388777	−	0.133141i
$772$	−3.03620	+	19.1698i	−0.109275	+	0.689936i
$773$	20.9544	+	10.6768i	0.753679	+	0.384019i	0.788227	−	0.615384i	$-0.210999\pi$
$773$	20.9544	+	10.6768i	0.753679	+	0.384019i	−0.0345481	+	0.999403i	$0.510999\pi$
$774$	−3.29481	−	2.71063i	−0.118429	−	0.0974317i
$775$		0			0
$776$		−	10.3809i		−	0.372653i
$777$	−0.968067	−	1.02808i	−0.0347292	−	0.0368822i
$778$	−19.6281	−	3.10878i	−0.703701	−	0.111455i
$779$	−4.23704	+	3.07839i	−0.151808	+	0.110295i
$780$		0			0
$781$	11.3862	+	8.27256i	0.407430	+	0.296015i
$782$	−5.54804	−	5.54804i	−0.198397	−	0.198397i
$783$	23.3195	+	27.9553i	0.833370	+	0.999040i
$784$	−6.65151	−	2.16121i	−0.237554	−	0.0771859i
$785$		0			0
$786$	−0.276811	+	9.20730i	−0.00987351	+	0.328414i
$787$	14.2872	+	28.0403i	0.509285	+	0.999529i	0.992293	+	0.123913i	$0.0395443\pi$
$787$	14.2872	+	28.0403i	0.509285	+	0.999529i	−0.483008	+	0.875616i	$0.660456\pi$
$788$	−5.55232	−	10.8970i	−0.197793	−	0.388191i
$789$	1.00856	−	33.5467i	0.0359056	−	1.19429i
$790$		0			0
$791$	−0.571382	−	0.185653i	−0.0203160	−	0.00660107i
$792$	−2.84863	−	1.67423i	−0.101222	−	0.0594910i
$793$	14.3816	+	14.3816i	0.510707	+	0.510707i
$794$	−21.8203	−	15.8534i	−0.774375	−	0.562616i
$795$		0			0
$796$	12.8922	−	9.36672i	0.456952	−	0.331995i
$797$	6.24831	+	0.989635i	0.221326	+	0.0350547i	0.266113	−	0.963942i	$-0.414261\pi$
$797$	6.24831	+	0.989635i	0.221326	+	0.0350547i	−0.0447862	+	0.998997i	$0.514261\pi$
$798$	−0.131033	−	0.139156i	−0.00463851	−	0.00492606i
$799$		−	39.9149i		−	1.41209i
$800$		0			0
$801$	−6.24966	+	7.59654i	−0.220821	+	0.268410i
$802$	−30.2402	−	15.4082i	−1.06782	−	0.544081i
$803$	−0.228816	+	1.44469i	−0.00807473	+	0.0509818i
$804$	3.23285	+	11.0713i	0.114014	+	0.390454i
$805$		0			0
$806$	28.6215	−	39.3941i	1.00815	−	1.38760i
$807$	4.06450	+	8.60707i	0.143077	+	0.302983i
$808$	2.19597	+	13.8648i	0.0772540	+	0.487763i
$809$	−10.4456	+	32.1483i	−0.367249	+	1.13028i	0.581312	+	0.813681i	$0.302539\pi$
$809$	−10.4456	+	32.1483i	−0.367249	+	1.13028i	−0.948561	+	0.316595i	$0.897461\pi$
$810$		0			0
$811$	−11.3720	−	34.9993i	−0.399324	−	1.22899i	−0.925543	−	0.378643i	$-0.876391\pi$
$811$	−11.3720	−	34.9993i	−0.399324	−	1.22899i	0.526219	−	0.850349i	$-0.323609\pi$
$812$	−0.491266	+	0.250313i	−0.0172401	+	0.00878425i
$813$	12.7887	−	1.63327i	0.448519	−	0.0572813i
$814$	−10.8518	+	3.52597i	−0.380356	+	0.123585i
$815$		0			0
$816$	−4.30317	−	3.32851i	−0.150641	−	0.116521i
$817$	−1.96970	+	0.311969i	−0.0689110	+	0.0109144i
$818$	11.2430	−	11.2430i	0.393103	−	0.393103i
$819$	1.16459	−	0.302395i	0.0406939	−	0.0105666i
$820$		0			0
$821$	1.94467	+	2.67661i	0.0678695	+	0.0934144i	0.841602	−	0.540098i	$-0.181613\pi$
$821$	1.94467	+	2.67661i	0.0678695	+	0.0934144i	−0.773733	+	0.633512i	$0.781613\pi$
$822$	9.56039	−	17.4465i	0.333457	−	0.608516i
$823$	16.1380	−	31.6727i	0.562537	−	1.10404i	−0.418136	−	0.908385i	$-0.637316\pi$
$823$	16.1380	−	31.6727i	0.562537	−	1.10404i	0.980673	−	0.195656i	$-0.0626837\pi$
$824$	13.2042			0.459990
$825$		0			0
$826$	−0.518630			−0.0180454
$827$	4.05871	−	7.96567i	0.141135	−	0.276993i	−0.809609	−	0.586969i	$-0.800321\pi$
$827$	4.05871	−	7.96567i	0.141135	−	0.276993i	0.950744	+	0.309976i	$0.100321\pi$
$828$	−5.60787	+	4.97120i	−0.194887	+	0.172761i
$829$	6.82593	+	9.39508i	0.237074	+	0.326305i	0.910932	−	0.412556i	$-0.135364\pi$
$829$	6.82593	+	9.39508i	0.237074	+	0.326305i	−0.673858	+	0.738861i	$0.735364\pi$
$830$		0			0
$831$	18.6280	+	27.3302i	0.646198	+	0.948073i
$832$	3.60364	−	3.60364i	0.124934	−	0.124934i
$833$	−21.6966	+	3.43640i	−0.751743	+	0.119064i
$834$	−11.5531	+	14.9361i	−0.400052	+	0.517195i
$835$		0			0
$836$	−1.46885	+	0.477258i	−0.0508012	+	0.0165063i
$837$	−26.4312	+	42.0271i	−0.913596	+	1.45267i
$838$	−24.5000	+	12.4834i	−0.846339	+	0.431231i
$839$	−1.99464	−	6.13888i	−0.0688628	−	0.211938i	0.910703	−	0.413062i	$-0.135541\pi$
$839$	−1.99464	−	6.13888i	−0.0688628	−	0.211938i	−0.979566	+	0.201124i	$0.935541\pi$
$840$		0			0
$841$	6.20662	−	19.1020i	0.214021	−	0.658690i
$842$	−4.99858	−	31.5598i	−0.172262	−	1.08762i
$843$	−2.20610	+	1.04178i	−0.0759822	+	0.0358809i
$844$	−6.50062	+	8.94734i	−0.223761	+	0.307980i
$845$		0			0
$846$	−38.0551	−	2.29027i	−1.30836	−	0.0787410i
$847$	−0.120487	+	0.760725i	−0.00413998	+	0.0261388i
$848$	−6.04920	−	3.08222i	−0.207730	−	0.105844i
$849$	−5.57329	+	15.5468i	−0.191275	+	0.533563i
$850$		0			0
$851$			25.8790i			0.887121i
$852$	16.1135	−	15.1729i	0.552040	−	0.519816i
$853$	−26.0890	−	4.13209i	−0.893271	−	0.141480i	−0.307109	−	0.951674i	$-0.599362\pi$
$853$	−26.0890	−	4.13209i	−0.893271	−	0.141480i	−0.586162	+	0.810194i	$0.699362\pi$
$854$	0.254089	−	0.184606i	0.00869474	−	0.00631710i
$855$		0			0
$856$	15.7453	+	11.4396i	0.538163	+	0.390998i
$857$	21.7170	+	21.7170i	0.741840	+	0.741840i	0.972932	−	0.231092i	$-0.0742298\pi$
$857$	21.7170	+	21.7170i	0.741840	+	0.741840i	−0.231092	+	0.972932i	$0.574230\pi$
$858$	1.80875	−	9.55241i	0.0617498	−	0.326114i
$859$	2.16755	+	0.704281i	0.0739560	+	0.0240298i	0.345761	−	0.938322i	$-0.387621\pi$
$859$	2.16755	+	0.704281i	0.0739560	+	0.0240298i	−0.271805	+	0.962352i	$0.587621\pi$
$860$		0			0
$861$	−0.508868	−	0.0152987i	−0.0173422	−	0.000521380i
$862$	−3.93217	−	7.71732i	−0.133930	−	0.262853i
$863$	−0.924026	−	1.81350i	−0.0314542	−	0.0617324i	0.874745	−	0.484584i	$-0.161029\pi$
$863$	−0.924026	−	1.81350i	−0.0314542	−	0.0617324i	−0.906199	+	0.422852i	$0.861029\pi$
$864$	−3.42034	+	3.91169i	−0.116362	+	0.133078i
$865$		0			0
$866$	10.2541	+	3.33175i	0.348448	+	0.113218i
$867$	12.1417	+	2.29903i	0.412353	+	0.0780792i
$868$	−0.531696	−	0.531696i	−0.0180469	−	0.0180469i
$869$	−8.87365	−	6.44709i	−0.301018	−	0.218702i
$870$		0			0
$871$	−27.4549	+	19.9472i	−0.930274	+	0.675884i
$872$	12.1552	+	1.92520i	0.411627	+	0.0651953i
$873$	−28.5476	+	12.4460i	−0.966190	+	0.421233i
$874$			3.50286i			0.118486i
$875$		0			0
$876$	2.16529	+	0.776226i	0.0731584	+	0.0262263i
$877$	5.66858	+	2.88829i	0.191414	+	0.0975305i	0.547071	−	0.837086i	$-0.315743\pi$
$877$	5.66858	+	2.88829i	0.191414	+	0.0975305i	−0.355657	+	0.934617i	$0.615743\pi$
$878$	5.36634	−	33.8818i	0.181105	−	1.14345i
$879$	51.7911	−	15.1231i	1.74687	−	0.510091i
$880$		0			0
$881$	3.61099	−	4.97010i	0.121657	−	0.167447i	−0.743844	−	0.668353i	$-0.767000\pi$
$881$	3.61099	−	4.97010i	0.121657	−	0.167447i	0.865502	+	0.500906i	$0.167000\pi$
$882$	2.03137	+	20.8829i	0.0683996	+	0.703162i
$883$	−6.19390	−	39.1067i	−0.208441	−	1.31605i	−0.840789	−	0.541362i	$-0.817909\pi$
$883$	−6.19390	−	39.1067i	−0.208441	−	1.31605i	0.632348	−	0.774684i	$-0.282091\pi$
$884$	4.94649	−	15.2237i	0.166369	−	0.512030i
$885$		0			0
$886$	2.00247	+	6.16296i	0.0672742	+	0.207049i
$887$	−43.0525	+	21.9363i	−1.44556	+	0.736550i	−0.988263	−	0.152763i	$-0.951183\pi$
$887$	−43.0525	+	21.9363i	−1.44556	+	0.736550i	−0.457299	+	0.889313i	$0.651183\pi$
$888$	2.27316	+	17.7991i	0.0762824	+	0.597300i
$889$	0.241160	−	0.0783578i	0.00808826	−	0.00262804i
$890$		0			0
$891$	−1.18883	+	9.84104i	−0.0398273	+	0.329687i
$892$	5.42571	−	0.859348i	0.181666	−	0.0287731i
$893$	−12.6005	+	12.6005i	−0.421660	+	0.421660i
$894$	20.5637	−	14.0160i	0.687753	−	0.468766i
$895$		0			0
$896$	−0.0462573	−	0.0636677i	−0.00154535	−	0.00212699i
$897$	−19.3372	−	10.5965i	−0.645652	−	0.353807i
$898$	10.3265	−	20.2669i	0.344599	−	0.676314i
$899$	66.9409			2.23260
$900$		0			0
$901$	−21.3243			−0.710416
$902$	−1.86754	+	3.66526i	−0.0621824	+	0.122040i
$903$	−0.170003	−	0.0931588i	−0.00565734	−	0.00310013i
$904$	4.48722	+	6.17613i	0.149243	+	0.205415i
$905$		0			0
$906$	−0.467200	+	0.318439i	−0.0155217	+	0.0105794i
$907$	−24.7561	+	24.7561i	−0.822014	+	0.822014i	−0.986397	−	0.164383i	$-0.947437\pi$
$907$	−24.7561	+	24.7561i	−0.822014	+	0.822014i	0.164383	+	0.986397i	$0.447437\pi$
$908$	6.67994	−	1.05800i	0.221682	−	0.0351109i
$909$	35.4956	−	22.6619i	1.17731	−	0.751649i
$910$		0			0
$911$	−48.5335	+	15.7695i	−1.60799	+	0.522466i	−0.969065	−	0.246806i	$-0.920619\pi$
$911$	−48.5335	+	15.7695i	−1.60799	+	0.522466i	−0.638921	+	0.769272i	$0.720619\pi$
$912$	0.307684	+	2.40920i	0.0101884	+	0.0797767i
$913$	−0.865690	+	0.441091i	−0.0286502	+	0.0145980i
$914$	2.74480	+	8.44762i	0.0907898	+	0.279422i
$915$		0			0
$916$	0.938563	−	2.88860i	0.0310110	−	0.0954420i
$917$	0.0654729	+	0.413380i	0.00216211	+	0.0136510i
$918$	−3.99424	+	15.8244i	−0.131830	+	0.522284i
$919$	−6.34757	+	8.73668i	−0.209387	+	0.288196i	−0.900774	−	0.434288i	$-0.857000\pi$
$919$	−6.34757	+	8.73668i	−0.209387	+	0.288196i	0.691387	+	0.722485i	$0.257000\pi$
$920$		0			0
$921$	3.67862	−	1.07417i	0.121215	−	0.0353950i
$922$	3.51006	−	22.1617i	0.115598	−	0.729855i
$923$	58.0249	+	29.5652i	1.90991	+	0.973150i
$924$	−0.141323	−	0.0506624i	−0.00464919	−	0.00166667i
$925$		0			0
$926$			24.2111i			0.795626i
$927$	−15.8309	−	36.3117i	−0.519956	−	1.19263i
$928$	6.91981	+	1.09599i	0.227154	+	0.0359777i
$929$	−38.0194	+	27.6227i	−1.24738	+	0.906272i	−0.998067	−	0.0621513i	$-0.980204\pi$
$929$	−38.0194	+	27.6227i	−1.24738	+	0.906272i	−0.249310	+	0.968424i	$0.580204\pi$
$930$		0			0
$931$	7.93409	+	5.76446i	0.260029	+	0.188922i
$932$	0.977696	+	0.977696i	0.0320255	+	0.0320255i
$933$	−23.1984	−	4.39263i	−0.759482	−	0.143808i
$934$	−12.8115	−	4.16270i	−0.419204	−	0.136208i
$935$		0			0
$936$	−14.2306	−	5.58954i	−0.465141	−	0.182700i
$937$	−20.7717	−	40.7667i	−0.678581	−	1.33179i	−0.931301	−	0.364250i	$-0.881325\pi$
$937$	−20.7717	−	40.7667i	−0.678581	−	1.33179i	0.252721	−	0.967539i	$-0.418675\pi$
$938$	0.237911	+	0.466926i	0.00776806	+	0.0152457i
$939$	33.0642	+	0.994051i	1.07901	+	0.0324396i
$940$		0			0
$941$	29.1364	+	9.46699i	0.949820	+	0.308615i	0.742642	−	0.669688i	$-0.233572\pi$
$941$	29.1364	+	9.46699i	0.949820	+	0.308615i	0.207177	+	0.978303i	$0.433572\pi$
$942$	−1.58386	+	8.36473i	−0.0516051	+	0.272537i
$943$	6.59721	+	6.59721i	0.214835	+	0.214835i
$944$	5.33155	+	3.87360i	0.173527	+	0.126075i
$945$		0			0
$946$	−1.26723	+	0.920697i	−0.0412012	+	0.0299344i
$947$	14.2493	+	2.25687i	0.463040	+	0.0733384i	0.383596	−	0.923501i	$-0.374685\pi$
$947$	14.2493	+	2.25687i	0.463040	+	0.0733384i	0.0794442	+	0.996839i	$0.474685\pi$
$948$	−12.5578	+	11.8248i	−0.407859	+	0.384051i
$949$			6.76809i			0.219701i
$950$		0			0
$951$	−5.31067	+	14.8142i	−0.172210	+	0.480382i
$952$	−0.220242	−	0.112219i	−0.00713809	−	0.00363704i
$953$	0.616563	−	3.89283i	0.0199724	−	0.126101i	−0.975688	−	0.219166i	$-0.929666\pi$
$953$	0.616563	−	3.89283i	0.0199724	−	0.126101i	0.995660	+	0.0930649i	$0.0296664\pi$
$954$	−1.22356	+	20.3307i	−0.0396143	+	0.658232i
$955$		0			0
$956$	−6.68358	+	9.19915i	−0.216162	+	0.297522i
$957$	12.0856	−	5.70713i	0.390671	−	0.184485i
$958$	−2.70337	−	17.0684i	−0.0873420	−	0.551455i
$959$	0.279326	−	0.859676i	0.00901989	−	0.0277604i
$960$		0			0
$961$	18.6313	+	57.3413i	0.601010	+	1.84972i
$962$	−47.0424	+	23.9693i	−1.51671	+	0.772801i
$963$	12.5816	−	57.0151i	0.405435	−	1.83729i
$964$	8.39163	−	2.72661i	0.270276	−	0.0878181i
$965$		0			0
$966$	−0.208329	+	0.269332i	−0.00670288	+	0.00866563i
$967$	−51.5598	+	8.16627i	−1.65805	+	0.262610i	−0.914060	−	0.405579i	$-0.867070\pi$
$967$	−51.5598	+	8.16627i	−1.65805	+	0.262610i	−0.743992	+	0.668189i	$0.767070\pi$
$968$	6.92040	−	6.92040i	0.222430	−	0.222430i
$969$	4.29649	+	6.30363i	0.138023	+	0.202502i
$970$		0			0
$971$	−2.69176	−	3.70489i	−0.0863828	−	0.118896i	0.763638	−	0.645644i	$-0.223411\pi$
$971$	−2.69176	−	3.70489i	−0.0863828	−	0.118896i	−0.850021	+	0.526748i	$0.823411\pi$
$972$	14.8579	+	4.71612i	0.476568	+	0.151270i
$973$	−0.389507	+	0.764451i	−0.0124870	+	0.0245072i
$974$	−3.62274			−0.116080
$975$		0			0
$976$	−3.99086			−0.127744
$977$	−1.87651	+	3.68285i	−0.0600348	+	0.117825i	−0.919074	−	0.394085i	$-0.871062\pi$
$977$	−1.87651	+	3.68285i	−0.0600348	+	0.117825i	0.859039	+	0.511910i	$0.171062\pi$
$978$	1.27599	−	2.32852i	0.0408017	−	0.0744578i
$979$	2.12277	+	2.92174i	0.0678439	+	0.0933792i
$980$		0			0
$981$	−9.27896	−	35.7351i	−0.296254	−	1.14093i
$982$	4.08144	−	4.08144i	0.130244	−	0.130244i
$983$	25.6200	−	4.05781i	0.817151	−	0.129424i	0.266153	−	0.963931i	$-0.414247\pi$
$983$	25.6200	−	4.05781i	0.817151	−	0.129424i	0.550998	+	0.834507i	$0.314247\pi$
$984$	5.11694	+	3.95796i	0.163122	+	0.126175i
$985$		0			0
$986$	20.9285	−	6.80010i	0.666501	−	0.216559i
$987$	−1.71825	+	0.219441i	−0.0546924	+	0.00698488i
$988$	−6.36743	+	3.24437i	−0.202575	+	0.103217i
$989$	1.09782	+	3.37875i	0.0349087	+	0.107438i
$990$		0			0
$991$	−7.36863	+	22.6783i	−0.234072	+	0.720400i	0.763171	+	0.646197i	$0.223641\pi$
$991$	−7.36863	+	22.6783i	−0.234072	+	0.720400i	−0.997243	+	0.0742035i	$0.976359\pi$
$992$	1.49468	+	9.43706i	0.0474562	+	0.299627i
$993$	8.17738	+	17.3166i	0.259501	+	0.549526i
$994$	0.591094	−	0.813572i	0.0187484	−	0.0258049i
$995$		0			0
$996$	0.428269	+	1.46666i	0.0135702	+	0.0464729i
$997$	2.45546	−	15.5032i	0.0777652	−	0.490990i	−0.917810	−	0.397020i	$-0.870044\pi$
$997$	2.45546	−	15.5032i	0.0777652	−	0.490990i	0.995575	−	0.0939699i	$-0.0299557\pi$
$998$	25.4455	+	12.9651i	0.805464	+	0.410404i
$999$	46.2225	−	27.5912i	1.46241	−	0.872947i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.2.l.c.143.10		80
3.2	odd	2	inner	750.2.l.c.143.5		80
5.2	odd	4		150.2.l.a.17.9	yes	80
5.3	odd	4		750.2.l.b.107.2		80
5.4	even	2		750.2.l.a.143.1		80
15.2	even	4		150.2.l.a.17.3	✓	80
15.8	even	4		750.2.l.b.107.8		80
15.14	odd	2		750.2.l.a.143.6		80
25.3	odd	20		750.2.l.a.257.6		80
25.4	even	10		750.2.l.b.743.8		80
25.21	even	5		150.2.l.a.53.3	yes	80
25.22	odd	20	inner	750.2.l.c.257.5		80
75.29	odd	10		750.2.l.b.743.2		80
75.47	even	20	inner	750.2.l.c.257.10		80
75.53	even	20		750.2.l.a.257.1		80
75.71	odd	10		150.2.l.a.53.9	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.l.a.17.3	✓	80	15.2	even	4
150.2.l.a.17.9	yes	80	5.2	odd	4
150.2.l.a.53.3	yes	80	25.21	even	5
150.2.l.a.53.9	yes	80	75.71	odd	10
750.2.l.a.143.1		80	5.4	even	2
750.2.l.a.143.6		80	15.14	odd	2
750.2.l.a.257.1		80	75.53	even	20
750.2.l.a.257.6		80	25.3	odd	20
750.2.l.b.107.2		80	5.3	odd	4
750.2.l.b.107.8		80	15.8	even	4
750.2.l.b.743.2		80	75.29	odd	10
750.2.l.b.743.8		80	25.4	even	10
750.2.l.c.143.5		80	3.2	odd	2	inner
750.2.l.c.143.10		80	1.1	even	1	trivial
750.2.l.c.257.5		80	25.22	odd	20	inner
750.2.l.c.257.10		80	75.47	even	20	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	750.l (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.453990 - 0.891007i) q^{2} +(1.51894 + 0.832356i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(1.43122 - 0.975505i) q^{6} +(0.0556476 - 0.0556476i) q^{7} +(-0.987688 + 0.156434i) q^{8} +(1.61437 + 2.52860i) q^{9} +O(q^{10})\)	\(q+(0.453990 - 0.891007i) q^{2} +(1.51894 + 0.832356i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(1.43122 - 0.975505i) q^{6} +(0.0556476 - 0.0556476i) q^{7} +(-0.987688 + 0.156434i) q^{8} +(1.61437 + 2.52860i) q^{9} +(1.04749 - 0.340351i) q^{11} +(-0.219422 - 1.71810i) q^{12} +(4.54086 - 2.31368i) q^{13} +(-0.0243189 - 0.0748459i) q^{14} +(-0.309017 + 0.951057i) q^{16} +(0.491350 + 3.10226i) q^{17} +(2.98591 - 0.290452i) q^{18} +(0.824223 - 1.13445i) q^{19} +(0.130844 - 0.0382069i) q^{21} +(0.172297 - 1.08784i) q^{22} +(-2.22575 - 1.13408i) q^{23} +(-1.63045 - 0.584493i) q^{24} -5.09632i q^{26} +(0.347436 + 5.18452i) q^{27} +(-0.0777287 - 0.0123110i) q^{28} +(5.66803 - 4.11807i) q^{29} +(7.72991 + 5.61611i) q^{31} +(0.707107 + 0.707107i) q^{32} +(1.87437 + 0.354913i) q^{33} +(2.98720 + 0.970601i) q^{34} +(1.09678 - 2.79232i) q^{36} +(-4.70325 - 9.23065i) q^{37} +(-0.636609 - 1.24942i) q^{38} +(8.82310 + 0.265260i) q^{39} +(-3.55210 - 1.15415i) q^{41} +(0.0253594 - 0.133928i) q^{42} +(-1.00563 - 1.00563i) q^{43} +(-0.891050 - 0.647386i) q^{44} +(-2.02094 + 1.46830i) q^{46} +(-12.5515 - 1.98797i) q^{47} +(-1.26100 + 1.18739i) q^{48} +6.99381i q^{49} +(-1.83585 + 5.12113i) q^{51} +(-4.54086 - 2.31368i) q^{52} +(-1.06206 + 6.70559i) q^{53} +(4.77718 + 2.04416i) q^{54} +(-0.0462573 + 0.0636677i) q^{56} +(2.19621 - 1.03711i) q^{57} +(-1.09599 - 6.91981i) q^{58} +(2.03647 - 6.26761i) q^{59} +(1.23324 + 3.79553i) q^{61} +(8.51329 - 4.33774i) q^{62} +(0.230546 + 0.0508748i) q^{63} +(0.951057 - 0.309017i) q^{64} +(1.16718 - 1.50895i) q^{66} +(-6.57696 + 1.04169i) q^{67} +(2.22097 - 2.22097i) q^{68} +(-2.43683 - 3.57522i) q^{69} +(7.51096 + 10.3379i) q^{71} +(-1.99005 - 2.24493i) q^{72} +(-0.602914 + 1.18329i) q^{73} -10.3598 q^{74} -1.40225 q^{76} +(0.0393507 - 0.0772302i) q^{77} +(4.24195 - 7.74102i) q^{78} +(-5.85354 - 8.05671i) q^{79} +(-3.78763 + 8.16418i) q^{81} +(-2.64098 + 2.64098i) q^{82} +(-0.871279 + 0.137997i) q^{83} +(-0.107818 - 0.0833977i) q^{84} +(-1.35257 + 0.439477i) q^{86} +(12.0371 - 1.53728i) q^{87} +(-0.981353 + 0.500025i) q^{88} +(1.01326 + 3.11850i) q^{89} +(0.123937 - 0.381439i) q^{91} +(0.390777 + 2.46727i) q^{92} +(7.06668 + 14.9646i) q^{93} +(-7.46957 + 10.2810i) q^{94} +(0.485490 + 1.66262i) q^{96} +(-1.62393 + 10.2531i) q^{97} +(6.23153 + 3.17512i) q^{98} +(2.55165 + 2.09924i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{3} + 4 q^{7}+O(q^{10}) \) 80 * q + 4 * q^3 + 4 * q^7	\( 80 q + 4 q^{3} + 4 q^{7} + 16 q^{12} + 20 q^{16} - 8 q^{18} + 40 q^{19} + 4 q^{22} - 56 q^{27} + 4 q^{28} - 96 q^{33} + 40 q^{34} - 64 q^{37} + 40 q^{39} - 4 q^{42} - 24 q^{43} + 16 q^{48} - 64 q^{57} + 20 q^{58} + 4 q^{63} - 104 q^{67} - 140 q^{69} + 8 q^{72} - 60 q^{73} - 60 q^{78} - 80 q^{79} - 40 q^{81} + 96 q^{82} - 60 q^{84} + 80 q^{87} + 24 q^{88} + 12 q^{93} - 12 q^{97}+O(q^{100}) \) 80 * q + 4 * q^3 + 4 * q^7 + 16 * q^12 + 20 * q^16 - 8 * q^18 + 40 * q^19 + 4 * q^22 - 56 * q^27 + 4 * q^28 - 96 * q^33 + 40 * q^34 - 64 * q^37 + 40 * q^39 - 4 * q^42 - 24 * q^43 + 16 * q^48 - 64 * q^57 + 20 * q^58 + 4 * q^63 - 104 * q^67 - 140 * q^69 + 8 * q^72 - 60 * q^73 - 60 * q^78 - 80 * q^79 - 40 * q^81 + 96 * q^82 - 60 * q^84 + 80 * q^87 + 24 * q^88 + 12 * q^93 - 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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