LMFDB - Embedded newform 750.2.l.c.257.5

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			257.5
Character	$\chi$	$=$	750.257
Dual form			750.2.l.c.143.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.453990 - 0.891007i) q^{2} +(1.70181 + 0.322239i) q^{3} +(-0.587785 + 0.809017i) q^{4} +(-0.485490 - 1.66262i) q^{6} +(0.0556476 + 0.0556476i) q^{7} +(0.987688 + 0.156434i) q^{8} +(2.79232 + 1.09678i) q^{9} +O(q^{10})$	\(q+(-0.453990 - 0.891007i) q^{2} +(1.70181 + 0.322239i) q^{3} +(-0.587785 + 0.809017i) q^{4} +(-0.485490 - 1.66262i) q^{6} +(0.0556476 + 0.0556476i) q^{7} +(0.987688 + 0.156434i) q^{8} +(2.79232 + 1.09678i) q^{9} +(-1.04749 - 0.340351i) q^{11} +(-1.26100 + 1.18739i) 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} +(-0.290452 - 2.98591i) q^{18} +(0.824223 + 1.13445i) q^{19} +(0.0767699 + 0.112634i) q^{21} +(0.172297 + 1.08784i) q^{22} +(2.22575 - 1.13408i) q^{23} +(1.63045 + 0.584493i) q^{24} -5.09632i q^{26} +(4.39859 + 2.76630i) 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} +(-1.67296 - 0.916756i) q^{33} +(2.98720 - 0.970601i) q^{34} +(-2.52860 + 1.61437i) q^{36} +(-4.70325 + 9.23065i) q^{37} +(0.636609 - 1.24942i) q^{38} +(6.98213 + 5.40069i) q^{39} +(3.55210 - 1.15415i) q^{41} +(0.0655044 - 0.119537i) 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} +(-0.219422 - 1.71810i) q^{48} -6.99381i q^{49} +(-1.83585 + 5.12113i) q^{51} +(-4.54086 + 2.31368i) q^{52} +(1.06206 + 6.70559i) q^{53} +(0.467880 - 5.17504i) q^{54} +(0.0462573 + 0.0636677i) q^{56} +(1.03711 + 2.19621i) 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} +(0.0943531 + 0.216419i) q^{63} +(0.951057 + 0.309017i) q^{64} +(-0.0573270 + 1.90682i) q^{66} +(-6.57696 - 1.04169i) q^{67} +(-2.22097 - 2.22097i) q^{68} +(4.15326 - 1.21276i) q^{69} +(-7.51096 + 10.3379i) q^{71} +(2.58637 + 1.52009i) q^{72} +(-0.602914 - 1.18329i) q^{73} +10.3598 q^{74} -1.40225 q^{76} +(-0.0393507 - 0.0772302i) q^{77} +(1.64223 - 8.67298i) q^{78} +(-5.85354 + 8.05671i) q^{79} +(6.59415 + 6.12512i) q^{81} +(-2.64098 - 2.64098i) q^{82} +(0.871279 + 0.137997i) q^{83} +(-0.136247 - 0.00409615i) q^{84} +(1.35257 + 0.439477i) q^{86} +(-8.31892 - 8.83463i) 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} +(14.9646 - 7.06668i) q^{93} +(-7.46957 - 10.2810i) q^{94} +(-1.43122 + 0.975505i) 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 $\left(\mathbb{Z}/750\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{17}{20}\right)$	$-1$

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
$3$	1.70181	+	0.322239i	0.982541	+	0.186045i
$3$	1.70181	+	0.322239i	0.982541	+	0.186045i
$4$	−0.587785	+	0.809017i	−0.293893	+	0.404508i
$5$		0			0
$5$		0			0
$6$	−0.485490	−	1.66262i	−0.198200	−	0.678761i
$7$	0.0556476	+	0.0556476i	0.0210328	+	0.0210328i	0.717545	−	0.696512i	$-0.245266\pi$
$7$	0.0556476	+	0.0556476i	0.0210328	+	0.0210328i	−0.696512	+	0.717545i	$0.745266\pi$
$8$	0.987688	+	0.156434i	0.349201	+	0.0553079i
$9$	2.79232	+	1.09678i	0.930775	+	0.365593i
$10$		0			0
$11$	−1.04749	−	0.340351i	−0.315831	−	0.102620i	0.146812	−	0.989164i	$-0.453099\pi$
$11$	−1.04749	−	0.340351i	−0.315831	−	0.102620i	−0.462643	+	0.886545i	$0.653099\pi$
$12$	−1.26100	+	1.18739i	−0.364018	+	0.342769i
$13$	4.54086	+	2.31368i	1.25941	+	0.641700i	0.950893	−	0.309520i	$-0.100168\pi$
$13$	4.54086	+	2.31368i	1.25941	+	0.641700i	0.308514	+	0.951220i	$0.400168\pi$
$14$	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	0.853650	+	0.520846i	$0.174384\pi$
$17$	−0.491350	+	3.10226i	−0.119170	+	0.752408i	−0.972820	+	0.231562i	$0.925616\pi$
$18$	−0.290452	−	2.98591i	−0.0684602	−	0.703785i
$19$	0.824223	+	1.13445i	0.189090	+	0.260260i	0.893028	−	0.450002i	$-0.148577\pi$
$19$	0.824223	+	1.13445i	0.189090	+	0.260260i	−0.703938	+	0.710262i	$0.748577\pi$
$20$		0			0
$21$	0.0767699	+	0.112634i	0.0167526	+	0.0245787i
$22$	0.172297	+	1.08784i	0.0367338	+	0.231928i
$23$	2.22575	−	1.13408i	0.464102	−	0.236472i	−0.206273	−	0.978495i	$-0.566133\pi$
$23$	2.22575	−	1.13408i	0.464102	−	0.236472i	0.670375	+	0.742023i	$0.266133\pi$
$24$	1.63045	+	0.584493i	0.332814	+	0.119309i
$25$		0			0
$26$		−	5.09632i		−	0.999471i
$27$	4.39859	+	2.76630i	0.846508	+	0.532376i
$28$	−0.0777287	+	0.0123110i	−0.0146893	+	0.00232656i
$29$	−5.66803	−	4.11807i	−1.05253	−	0.764705i	−0.0798355	−	0.996808i	$-0.525440\pi$
$29$	−5.66803	−	4.11807i	−1.05253	−	0.764705i	−0.972691	+	0.232103i	$0.925440\pi$
$30$		0			0
$31$	7.72991	−	5.61611i	1.38833	−	1.00868i	0.392287	−	0.919843i	$-0.371684\pi$
$31$	7.72991	−	5.61611i	1.38833	−	1.00868i	0.996046	−	0.0888399i	$-0.0283160\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	−1.67296	−	0.916756i	−0.291225	−	0.159587i
$34$	2.98720	−	0.970601i	0.512301	−	0.166457i
$35$		0			0
$36$	−2.52860	+	1.61437i	−0.421433	+	0.269061i
$37$	−4.70325	+	9.23065i	−0.773210	+	1.51751i	0.0804961	+	0.996755i	$0.474350\pi$
$37$	−4.70325	+	9.23065i	−0.773210	+	1.51751i	−0.853706	+	0.520755i	$0.825650\pi$
$38$	0.636609	−	1.24942i	0.103272	−	0.202682i
$39$	6.98213	+	5.40069i	1.11803	+	0.864803i
$40$		0			0
$41$	3.55210	−	1.15415i	0.554745	−	0.180248i	−0.0182101	−	0.999834i	$-0.505797\pi$
$41$	3.55210	−	1.15415i	0.554745	−	0.180248i	0.572956	+	0.819586i	$0.305797\pi$
$42$	0.0655044	−	0.119537i	0.0101075	−	0.0184450i
$43$	−1.00563	+	1.00563i	−0.153357	+	0.153357i	−0.779616	−	0.626258i	$-0.784586\pi$
$43$	−1.00563	+	1.00563i	−0.153357	+	0.153357i	0.626258	+	0.779616i	$0.284586\pi$
$44$	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	$-0.172527\pi$
$47$	12.5515	−	1.98797i	1.83083	−	0.289975i	0.974154	+	0.225883i	$0.0725268\pi$
$48$	−0.219422	−	1.71810i	−0.0316708	−	0.247986i
$49$		−	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	0.946687	+	0.322154i	$0.104407\pi$
$53$	1.06206	+	6.70559i	0.145885	+	0.921083i	−0.800802	+	0.598929i	$0.795593\pi$
$54$	0.467880	−	5.17504i	0.0636704	−	0.704234i
$55$		0			0
$56$	0.0462573	+	0.0636677i	0.00618139	+	0.00850795i
$57$	1.03711	+	2.19621i	0.137369	+	0.290895i
$58$	−1.09599	+	6.91981i	−0.143911	+	0.908616i
$59$	−2.03647	−	6.26761i	−0.265126	−	0.815974i	−0.991664	−	0.128848i	$-0.958872\pi$
$59$	−2.03647	−	6.26761i	−0.265126	−	0.815974i	0.726538	−	0.687126i	$-0.241128\pi$
$60$		0			0
$61$	1.23324	−	3.79553i	0.157901	−	0.485968i	−0.840543	−	0.541745i	$-0.817764\pi$
$61$	1.23324	−	3.79553i	0.157901	−	0.485968i	0.998443	+	0.0557774i	$0.0177637\pi$
$62$	−8.51329	−	4.33774i	−1.08119	−	0.550894i
$63$	0.0943531	+	0.216419i	0.0118874	+	0.0272663i
$64$	0.951057	+	0.309017i	0.118882	+	0.0386271i
$65$		0			0
$66$	−0.0573270	+	1.90682i	−0.00705647	+	0.234713i
$67$	−6.57696	−	1.04169i	−0.803504	−	0.127263i	−0.258844	−	0.965919i	$-0.583341\pi$
$67$	−6.57696	−	1.04169i	−0.803504	−	0.127263i	−0.544660	+	0.838657i	$0.683341\pi$
$68$	−2.22097	−	2.22097i	−0.269332	−	0.269332i
$69$	4.15326	−	1.21276i	0.499993	−	0.146000i
$70$		0			0
$71$	−7.51096	+	10.3379i	−0.891387	+	1.22689i	0.0817481	+	0.996653i	$0.473950\pi$
$71$	−7.51096	+	10.3379i	−0.891387	+	1.22689i	−0.973135	+	0.230236i	$0.926050\pi$
$72$	2.58637	+	1.52009i	0.304807	+	0.179144i
$73$	−0.602914	−	1.18329i	−0.0705658	−	0.138493i	0.853029	−	0.521864i	$-0.174763\pi$
$73$	−0.602914	−	1.18329i	−0.0705658	−	0.138493i	−0.923595	+	0.383371i	$0.874763\pi$
$74$	10.3598			1.20430
$75$		0			0
$76$	−1.40225			−0.160849
$77$	−0.0393507	−	0.0772302i	−0.00448443	−	0.00880119i
$78$	1.64223	−	8.67298i	0.185946	−	0.982022i
$79$	−5.85354	+	8.05671i	−0.658575	+	0.906451i	−0.999433	−	0.0336639i	$-0.989282\pi$
$79$	−5.85354	+	8.05671i	−0.658575	+	0.906451i	0.340858	+	0.940115i	$0.389282\pi$
$80$		0			0
$81$	6.59415	+	6.12512i	0.732684	+	0.680569i
$82$	−2.64098	−	2.64098i	−0.291647	−	0.291647i
$83$	0.871279	+	0.137997i	0.0956353	+	0.0151471i	0.204069	−	0.978957i	$-0.434583\pi$
$83$	0.871279	+	0.137997i	0.0956353	+	0.0151471i	−0.108433	+	0.994104i	$0.534583\pi$
$84$	−0.136247	−	0.00409615i	−0.0148657	−	0.000446927i
$85$		0			0
$86$	1.35257	+	0.439477i	0.145851	+	0.0473900i
$87$	−8.31892	−	8.83463i	−0.891882	−	0.947172i
$88$	−0.981353	−	0.500025i	−0.104613	−	0.0533028i
$89$	−1.01326	+	3.11850i	−0.107406	+	0.330560i	−0.990288	−	0.139035i	$-0.955600\pi$
$89$	−1.01326	+	3.11850i	−0.107406	+	0.330560i	0.882882	+	0.469595i	$0.155600\pi$
$90$		0			0
$91$	0.123937	+	0.381439i	0.0129921	+	0.0399856i
$92$	−0.390777	+	2.46727i	−0.0407413	+	0.257230i
$93$	14.9646	−	7.06668i	1.55175	−	0.732781i
$94$	−7.46957	−	10.2810i	−0.770427	−	1.06040i
$95$		0			0
$96$	−1.43122	+	0.975505i	−0.146073	+	0.0995621i
$97$	−1.62393	−	10.2531i	−0.164885	−	1.04104i	−0.921838	−	0.387575i	$-0.873313\pi$
$97$	−1.62393	−	10.2531i	−0.164885	−	1.04104i	0.756953	−	0.653469i	$-0.226687\pi$
$98$	−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	$-0.246104\pi$
$102$	5.39642	−	0.689188i	0.534325	−	0.0682398i
$103$	−13.0416	+	2.06559i	−1.28503	+	0.203529i	−0.761324	−	0.648371i	$-0.775451\pi$
$103$	−13.0416	+	2.06559i	−1.28503	+	0.203529i	−0.523705	+	0.851900i	$0.675451\pi$
$104$	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	0.425413	−	0.904999i	$-0.360129\pi$
$107$	13.7619	−	13.7619i	1.33041	−	1.33041i	0.904999	−	0.425413i	$-0.139871\pi$
$108$	−4.82341	+	1.93254i	−0.464133	+	0.185958i
$109$	−11.7044	+	3.80299i	−1.12108	+	0.364260i	−0.810178	−	0.586183i	$-0.800630\pi$
$109$	−11.7044	+	3.80299i	−1.12108	+	0.364260i	−0.310898	+	0.950443i	$0.600630\pi$
$110$		0			0
$111$	−10.9785	+	14.1933i	−1.04204	+	1.34716i
$112$	0.0357280	−	0.0701201i	0.00337598	−	0.00662572i
$113$	3.46581	−	6.80204i	0.326036	−	0.639882i	−0.668565	−	0.743654i	$-0.733091\pi$
$113$	3.46581	−	6.80204i	0.326036	−	0.639882i	0.994601	+	0.103771i	$0.0330911\pi$
$114$	1.48600	−	1.92113i	0.139177	−	0.179930i
$115$		0			0
$116$	6.66317	−	2.16499i	0.618660	−	0.201015i
$117$	10.1420	+	11.4409i	0.937624	+	1.05771i
$118$	−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
$123$	6.41692	−	0.819518i	0.578594	−	0.0738935i
$124$			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	−0.321952	−	0.946756i	$-0.604339\pi$
$127$	2.87091	−	1.46280i	0.254752	−	0.129803i	0.576703	+	0.816954i	$0.304339\pi$
$128$	−0.156434	−	0.987688i	−0.0138270	−	0.0873001i
$129$	−2.03545	+	1.38734i	−0.179211	+	0.122149i
$130$		0			0
$131$	3.12598	+	4.30255i	0.273118	+	0.375915i	0.923439	−	0.383744i	$-0.125366\pi$
$131$	3.12598	+	4.30255i	0.273118	+	0.375915i	−0.650321	+	0.759660i	$0.725366\pi$
$132$	1.72501	−	0.814598i	0.150143	−	0.0709017i
$133$	−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	$-0.513243\pi$
$137$	−10.2341	−	5.21451i	−0.874354	−	0.445506i	−0.832763	+	0.553629i	$0.813243\pi$
$138$	−2.96612	−	3.15000i	−0.252493	−	0.268146i
$139$	−10.3684	−	3.36891i	−0.879440	−	0.285747i	−0.165715	−	0.986174i	$-0.552993\pi$
$139$	−10.3684	−	3.36891i	−0.879440	−	0.285747i	−0.713725	+	0.700426i	$0.752993\pi$
$140$		0			0
$141$	22.0009	+	0.661442i	1.85281	+	0.0557034i
$142$	12.6211	+	1.99898i	1.05914	+	0.167751i
$143$	−3.96905	−	3.96905i	−0.331909	−	0.331909i
$144$	0.180223	−	2.99458i	0.0150186	−	0.249548i
$145$		0			0
$146$	−0.780598	+	1.07440i	−0.0646028	+	0.0889181i
$147$	2.25367	−	11.9021i	0.185880	−	0.981672i
$148$	−4.70325	−	9.23065i	−0.386605	−	0.758755i
$149$	−14.3679			−1.17707			−0.588534	−	0.808472i	$-0.700295\pi$
$149$	−14.3679			−1.17707			−0.588534	+	0.808472i	$0.700295\pi$
$150$		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
$153$	−4.77450	+	8.12361i	−0.385995	+	0.656755i
$154$	−0.0509477	+	0.0701235i	−0.00410548	+	0.00565071i
$155$		0			0
$156$	−8.47324	+	2.47421i	−0.678402	+	0.198096i
$157$	−3.47556	−	3.47556i	−0.277380	−	0.277380i	0.554682	−	0.832062i	$-0.312840\pi$
$157$	−3.47556	−	3.47556i	−0.277380	−	0.277380i	−0.832062	+	0.554682i	$0.812840\pi$
$158$	9.83604	+	1.55788i	0.782513	+	0.123938i
$159$	−0.353372	+	11.7539i	−0.0280242	+	0.932144i
$160$		0			0
$161$	0.186967	+	0.0607491i	0.0147350	+	0.00478770i
$162$	2.46384	−	8.65618i	0.193578	−	0.680094i
$163$	1.36590	+	0.695961i	0.106986	+	0.0545119i	0.506664	−	0.862143i	$-0.330878\pi$
$163$	1.36590	+	0.695961i	0.106986	+	0.0545119i	−0.399679	+	0.916655i	$0.630878\pi$
$164$	−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	0.358387	+	0.933573i	$0.383327\pi$
$167$	−3.50144	+	22.1072i	−0.270949	+	1.71071i	−0.629336	+	0.777133i	$0.716673\pi$
$168$	0.0582050	+	0.123256i	0.00449061	+	0.00950943i
$169$	7.62505	+	10.4950i	0.586542	+	0.807306i
$170$		0			0
$171$	1.05726	+	4.07173i	0.0808509	+	0.311373i
$172$	−0.222477	−	1.40467i	−0.0169637	−	0.107105i
$173$	−12.6292	+	6.43491i	−0.960182	+	0.489237i	−0.862542	−	0.505985i	$-0.831129\pi$
$173$	−12.6292	+	6.43491i	−0.960182	+	0.489237i	−0.0976395	+	0.995222i	$0.531129\pi$
$174$	−4.09500	+	11.4230i	−0.310441	+	0.865979i
$175$		0			0
$176$			1.10140i			0.0830211i
$177$	−1.44602	−	11.3225i	−0.108690	−	0.851053i
$178$	3.23861	−	0.512946i	0.242744	−	0.0384469i
$179$	12.2896	+	8.92889i	0.918565	+	0.667377i	0.943167	−	0.332320i	$-0.107832\pi$
$179$	12.2896	+	8.92889i	0.918565	+	0.667377i	−0.0246011	+	0.999697i	$0.507832\pi$
$180$		0			0
$181$	−8.30933	+	6.03708i	−0.617627	+	0.448733i	−0.852092	−	0.523392i	$-0.824666\pi$
$181$	−8.30933	+	6.03708i	−0.617627	+	0.448733i	0.234465	+	0.972125i	$0.424666\pi$
$182$	0.283598	−	0.283598i	0.0210217	−	0.0210217i
$183$	3.32181	−	6.06188i	0.245556	−	0.448107i
$184$	2.37576	−	0.771931i	0.175143	−	0.0569075i
$185$		0			0
$186$	−13.0902	−	10.1253i	−0.959823	−	0.742425i
$187$	1.57054	−	3.08236i	0.114849	−	0.225405i
$188$	−5.76930	+	11.3229i	−0.420770	+	0.825807i
$189$	0.0908325	+	0.398709i	0.00660709	+	0.0290018i
$190$		0			0
$191$	−10.3303	+	3.35652i	−0.747475	+	0.242869i	−0.657894	−	0.753110i	$-0.728553\pi$
$191$	−10.3303	+	3.35652i	−0.747475	+	0.242869i	−0.0895805	+	0.995980i	$0.528553\pi$
$192$	1.51894	+	0.832356i	0.109620	+	0.0600701i
$193$	−13.7241	+	13.7241i	−0.987880	+	0.987880i	−0.999927	−	0.0120476i	$-0.996165\pi$
$193$	−13.7241	+	13.7241i	−0.987880	+	0.987880i	0.0120476	+	0.999927i	$0.496165\pi$
$194$	−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	$-0.693491\pi$
$197$	−12.0795	+	1.91320i	−0.860625	+	0.136310i	−0.289506	+	0.957176i	$0.593491\pi$
$198$	−0.712010	+	3.22657i	−0.0506003	+	0.229302i
$199$		−	15.9356i		−	1.12965i	−0.825212	−	0.564823i	$-0.808944\pi$
$199$		−	15.9356i		−	1.12965i	0.825212	−	0.564823i	$-0.191056\pi$
$200$		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
$204$	−3.06399	−	4.49536i	−0.214522	−	0.314738i
$205$		0			0
$206$	7.76123	+	10.6824i	0.540750	+	0.744279i
$207$	7.45886	−	0.725556i	0.518427	−	0.0504296i
$208$	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	0.761809	+	0.647802i	$0.224311\pi$
$211$	−3.41758	+	10.5182i	−0.235276	+	0.724104i	−0.997085	+	0.0763026i	$0.975689\pi$
$212$	−6.04920	−	3.08222i	−0.415461	−	0.211688i
$213$	−16.1135	+	15.1729i	−1.10408	+	1.03963i
$214$	−18.5097	−	6.01417i	−1.26530	−	0.411120i
$215$		0			0
$216$	3.91169	+	3.42034i	0.266157	+	0.232724i
$217$	0.742674	+	0.117628i	0.0504160	+	0.00798511i
$218$	8.70216	+	8.70216i	0.589385	+	0.589385i
$219$	−0.644746	−	2.20801i	−0.0435679	−	0.149204i
$220$		0			0
$221$	−9.40879	+	12.9501i	−0.632904	+	0.871117i
$222$	17.6304	+	3.33833i	1.18328	+	0.224054i
$223$	−2.49393	−	4.89460i	−0.167006	−	0.327767i	0.792302	−	0.610129i	$-0.208882\pi$
$223$	−2.49393	−	4.89460i	−0.167006	−	0.327767i	−0.959308	+	0.282362i	$0.908882\pi$
$224$	−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	$-0.0779432\pi$
$227$	3.07043	+	6.02606i	0.203792	+	0.399964i	−0.766378	+	0.642390i	$0.777943\pi$
$228$	−2.38637	−	0.451860i	−0.158041	−	0.0299251i
$229$	1.78525	−	2.45719i	0.117973	−	0.162376i	−0.745947	−	0.666006i	$-0.768003\pi$
$229$	1.78525	−	2.45719i	0.117973	−	0.162376i	0.863919	+	0.503630i	$0.168003\pi$
$230$		0			0
$231$	−0.0420810	−	0.144111i	−0.00276873	−	0.00948184i
$232$	−4.95404	−	4.95404i	−0.325249	−	0.325249i
$233$	1.36565	+	0.216297i	0.0894666	+	0.0141701i	0.201007	−	0.979590i	$-0.435579\pi$
$233$	1.36565	+	0.216297i	0.0894666	+	0.0141701i	−0.111541	+	0.993760i	$0.535579\pi$
$234$	5.58954	−	14.2306i	0.365400	−	0.930283i
$235$		0			0
$236$	6.26761	+	2.03647i	0.407987	+	0.132563i
$237$	−12.5578	+	11.8248i	−0.815717	+	0.768101i
$238$	0.220242	+	0.112219i	0.0142762	+	0.00727408i
$239$	3.51376	−	10.8143i	0.227287	−	0.699516i	−0.770765	−	0.637120i	$-0.780126\pi$
$239$	3.51376	−	10.8143i	0.227287	−	0.699516i	0.998051	−	0.0623963i	$-0.0198743\pi$
$240$		0			0
$241$	−2.72661	−	8.39163i	−0.175636	−	0.540552i	0.824026	−	0.566552i	$-0.191723\pi$
$241$	−2.72661	−	8.39163i	−0.175636	−	0.540552i	−0.999662	+	0.0259998i	$0.991723\pi$
$242$	−1.53101	+	9.66643i	−0.0984172	+	0.621382i
$243$	9.24826	+	12.5487i	0.593276	+	0.804999i
$244$	2.34577	+	3.22867i	0.150172	+	0.206695i
$245$		0			0
$246$	−3.64342	−	5.34547i	−0.232296	−	0.340814i
$247$	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	$-0.152545\pi$
$252$	−0.230546	−	0.0508748i	−0.0145230	−	0.00320481i
$253$	−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	$-0.727907\pi$
$257$	1.57229	−	1.57229i	0.0980767	−	0.0980767i	0.754443	+	0.656366i	$0.227907\pi$
$258$	2.16020	+	1.18376i	0.134488	+	0.0736975i
$259$	−0.775389	+	0.251939i	−0.0481803	+	0.0156547i
$260$		0			0
$261$	−11.3104	−	17.7155i	−0.700095	−	1.09656i
$262$	2.41443	−	4.73859i	0.149164	−	0.292751i
$263$	8.79695	−	17.2650i	0.542443	−	1.06460i	−0.443304	−	0.896371i	$-0.646194\pi$
$263$	8.79695	−	17.2650i	0.542443	−	1.06460i	0.985747	−	0.168233i	$-0.0538061\pi$
$264$	−1.50895	−	1.16718i	−0.0928695	−	0.0718348i
$265$		0			0
$266$	0.104953	−	0.0341012i	0.00643507	−	0.00209088i
$267$	−2.72928	+	4.98058i	−0.167029	+	0.304807i
$268$	4.70859	−	4.70859i	0.287623	−	0.287623i
$269$	−4.44596	+	3.23018i	−0.271075	+	0.196948i	−0.715015	−	0.699109i	$-0.753580\pi$
$269$	−4.44596	+	3.23018i	−0.271075	+	0.196948i	0.443940	+	0.896056i	$0.353580\pi$
$270$		0			0
$271$	6.02194	+	4.37520i	0.365807	+	0.265774i	0.755470	−	0.655183i	$-0.227409\pi$
$271$	6.02194	+	4.37520i	0.365807	+	0.265774i	−0.389663	+	0.920957i	$0.627409\pi$
$272$	3.10226	−	0.491350i	0.188102	−	0.0297924i
$273$	0.0880031	+	0.689074i	0.00532619	+	0.0417047i
$274$			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	0.139293	−	0.990251i	$-0.455517\pi$
$277$	17.0144	−	8.66928i	1.02230	−	0.520886i	0.883004	+	0.469365i	$0.155517\pi$
$278$	1.70545	+	10.7678i	0.102286	+	0.645810i
$279$	27.7440	−	7.20400i	1.66099	−	0.431292i
$280$		0			0
$281$	0.827936	+	1.13956i	0.0493905	+	0.0679802i	0.832998	−	0.553276i	$-0.186623\pi$
$281$	0.827936	+	1.13956i	0.0493905	+	0.0679802i	−0.783607	+	0.621256i	$0.786623\pi$
$282$	−9.39887	−	19.9033i	−0.559694	−	1.18522i
$283$	1.49164	−	9.41786i	0.0886689	−	0.559834i	−0.902859	−	0.429937i	$-0.858536\pi$
$283$	1.49164	−	9.41786i	0.0886689	−	0.559834i	0.991528	−	0.129896i	$-0.0414644\pi$
$284$	−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
$288$	−2.75001	+	1.19893i	−0.162046	+	0.0706478i
$289$	6.78537	+	2.20470i	0.399139	+	0.129688i
$290$		0			0
$291$	0.540319	−	17.9721i	0.0316740	−	1.05355i
$292$	1.31168	+	0.207750i	0.0767604	+	0.0121577i
$293$	−22.0266	−	22.0266i	−1.28681	−	1.28681i	−0.936716	−	0.350091i	$-0.886151\pi$
$293$	−22.0266	−	22.0266i	−1.28681	−	1.28681i	−0.350091	−	0.936716i	$-0.613849\pi$
$294$	−11.6280	+	3.39542i	−0.678161	+	0.198025i
$295$		0			0
$296$	−6.08934	+	8.38126i	−0.353936	+	0.487151i
$297$	−3.66597	−	4.39475i	−0.212721	−	0.255009i
$298$	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
$303$	4.52347	−	23.8894i	0.259867	−	1.37241i
$304$	0.824223	−	1.13445i	0.0472724	−	0.0650649i
$305$		0			0
$306$	9.40577	+	0.566067i	0.537692	+	0.0323599i
$307$	1.56450	+	1.56450i	0.0892910	+	0.0892910i	0.750341	−	0.661050i	$-0.229889\pi$
$307$	1.56450	+	1.56450i	0.0892910	+	0.0892910i	−0.661050	+	0.750341i	$0.729889\pi$
$308$	0.0856103	+	0.0135593i	0.00487810	+	0.000772615i
$309$	−22.8600	−	0.687269i	−1.30046	−	0.0390974i
$310$		0			0
$311$	12.9644	+	4.21240i	0.735145	+	0.238863i	0.652577	−	0.757722i	$-0.273688\pi$
$311$	12.9644	+	4.21240i	0.735145	+	0.238863i	0.0825681	+	0.996585i	$0.473688\pi$
$312$	6.05131	+	6.42644i	0.342588	+	0.363826i
$313$	17.0167	+	8.67043i	0.961839	+	0.490082i	0.863101	−	0.505032i	$-0.168519\pi$
$313$	17.0167	+	8.67043i	0.961839	+	0.490082i	0.0987386	+	0.995113i	$0.468519\pi$
$314$	−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	0.915079	+	0.403274i	$0.132128\pi$
$317$	−1.42135	+	8.97408i	−0.0798312	+	0.504034i	−0.994911	+	0.100761i	$0.967872\pi$
$318$	10.6332	−	5.02130i	0.596281	−	0.281580i
$319$	4.53563	+	6.24276i	0.253947	+	0.349528i
$320$		0			0
$321$	27.8548	−	18.9855i	1.55470	−	1.05967i
$322$	−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
$327$	−21.1441	+	2.70036i	−1.16927	+	0.149330i
$328$	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	−0.314166	−	0.949368i	$-0.601725\pi$
$331$	8.94485	−	6.49882i	0.491654	−	0.357207i	0.805820	+	0.592161i	$0.201725\pi$
$332$	−0.623767	+	0.623767i	−0.0342336	+	0.0342336i
$333$	−23.2570	+	20.6166i	−1.27448	+	1.12978i
$334$	21.2873	−	6.91666i	1.16479	−	0.378463i
$335$		0			0
$336$	0.0833977	−	0.107818i	0.00454971	−	0.00588197i
$337$	−7.85531	+	15.4169i	−0.427906	+	0.839813i	0.571904	+	0.820321i	$0.306205\pi$
$337$	−7.85531	+	15.4169i	−0.427906	+	0.839813i	−0.999810	+	0.0194923i	$0.993795\pi$
$338$	5.88940	−	11.5586i	0.320341	−	0.628705i
$339$	8.09004	−	10.4590i	0.439391	−	0.568054i
$340$		0			0
$341$	−10.0085	+	3.25195i	−0.541989	+	0.176103i
$342$	3.14795	−	2.79056i	0.170222	−	0.150896i
$343$	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	$-0.418534\pi$
$347$	14.7693	−	2.33923i	0.792857	−	0.125576i	0.539709	+	0.841851i	$0.318534\pi$
$348$	12.0371	−	1.53728i	0.645256	−	0.0824070i
$349$		−	0.345103i		−	0.0184729i	−0.999957	−	0.00923647i	$-0.997060\pi$
$349$		−	0.345103i		−	0.0184729i	0.999957	−	0.00923647i	$-0.00294010\pi$
$350$		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	−0.919001	−	0.394256i	$-0.871002\pi$
$353$	−3.13409	−	19.7879i	−0.166811	−	1.05320i	0.752190	−	0.658947i	$-0.228998\pi$
$354$	−9.43196	+	6.42874i	−0.501303	+	0.341683i
$355$		0			0
$356$	−1.92734	−	2.65275i	−0.102149	−	0.140596i
$357$	−0.387139	+	0.182818i	−0.0204896	+	0.00967574i
$358$	2.37636	−	15.0037i	0.125594	−	0.792971i
$359$	5.66877	+	17.4467i	0.299186	+	0.920800i	0.981783	+	0.190005i	$0.0608505\pi$
$359$	5.66877	+	17.4467i	0.299186	+	0.920800i	−0.682597	+	0.730795i	$0.739150\pi$
$360$		0			0
$361$	5.26370	−	16.2000i	0.277037	−	0.852632i
$362$	9.15143	+	4.66289i	0.480989	+	0.245076i
$363$	−11.6209	−	12.3413i	−0.609937	−	0.647749i
$364$	−0.381439	−	0.123937i	−0.0199928	−	0.00649606i
$365$		0			0
$366$	−6.90925	−	0.207721i	−0.361152	−	0.0108578i
$367$	0.0192492	+	0.00304877i	0.00100480	+	0.000159144i	0.156937	−	0.987609i	$-0.449838\pi$
$367$	0.0192492	+	0.00304877i	0.00100480	+	0.000159144i	−0.155932	+	0.987768i	$0.549838\pi$
$368$	−1.76637	−	1.76637i	−0.0920783	−	0.0920783i
$369$	11.1845	+	0.673114i	0.582240	+	0.0350409i
$370$		0			0
$371$	−0.314049	+	0.432251i	−0.0163046	+	0.0224414i
$372$	−3.07889	+	16.2603i	−0.159633	+	0.843057i
$373$	3.17602	+	6.23329i	0.164448	+	0.322748i	0.958495	−	0.285109i	$-0.0920297\pi$
$373$	3.17602	+	6.23329i	0.164448	+	0.322748i	−0.794047	+	0.607856i	$0.792030\pi$
$374$	−3.45942			−0.178882
$375$		0			0
$376$	12.7080			0.655364
$377$	−16.2098	−	31.8136i	−0.834848	−	1.63848i
$378$	0.314015	−	0.261942i	0.0161512	−	0.0134729i
$379$	7.15293	−	9.84516i	0.367421	−	0.505712i	−0.584776	−	0.811194i	$-0.698818\pi$
$379$	7.15293	−	9.84516i	0.367421	−	0.505712i	0.952198	+	0.305483i	$0.0988178\pi$
$380$		0			0
$381$	5.35711	−	1.56429i	0.274453	−	0.0801412i
$382$	7.68054	+	7.68054i	0.392971	+	0.392971i
$383$	0.936062	+	0.148258i	0.0478305	+	0.00757561i	0.180304	−	0.983611i	$-0.442292\pi$
$383$	0.936062	+	0.148258i	0.0478305	+	0.00757561i	−0.132473	+	0.991187i	$0.542292\pi$
$384$	0.0520493	−	1.73127i	0.00265613	−	0.0883484i
$385$		0			0
$386$	18.4588	+	5.99764i	0.939530	+	0.305272i
$387$	−3.91100	+	1.70509i	−0.198807	+	0.0866748i
$388$	9.24945	+	4.71283i	0.469570	+	0.239258i
$389$	6.14102	−	18.9001i	0.311362	−	0.958273i	−0.665864	−	0.746073i	$-0.731937\pi$
$389$	6.14102	−	18.9001i	0.311362	−	0.958273i	0.977226	−	0.212200i	$-0.0680630\pi$
$390$		0			0
$391$	2.42458	+	7.46210i	0.122616	+	0.377374i
$392$	1.09407	−	6.90770i	0.0552590	−	0.348892i
$393$	3.93339	+	8.32944i	0.198413	+	0.420164i
$394$	7.18863	+	9.89430i	0.362158	+	0.498468i
$395$		0			0
$396$	3.19814	−	0.830427i	0.160713	−	0.0417305i
$397$	4.21926	+	26.6394i	0.211759	+	1.33699i	0.832957	+	0.553338i	$0.186646\pi$
$397$	4.21926	+	26.6394i	0.211759	+	1.33699i	−0.621198	+	0.783654i	$0.713354\pi$
$398$	−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	$-0.321849\pi$
$402$	1.46112	+	11.4407i	0.0728739	+	0.570611i
$403$	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
$408$	−2.61437	+	4.77089i	−0.129431	+	0.236194i
$409$	15.1218	−	4.91338i	0.747726	−	0.242951i	0.0897236	−	0.995967i	$-0.471402\pi$
$409$	15.1218	−	4.91338i	0.747726	−	0.242951i	0.658002	+	0.753016i	$0.271402\pi$
$410$		0			0
$411$	−15.7361	−	12.1719i	−0.776205	−	0.600396i
$412$	5.99458	−	11.7650i	0.295332	−	0.579621i
$413$	0.235453	−	0.462102i	0.0115859	−	0.0227386i
$414$	−4.03273	−	6.31650i	−0.198198	−	0.310439i
$415$		0			0
$416$	−4.84689	+	1.57485i	−0.237638	+	0.0772134i
$417$	−16.5595	−	9.07436i	−0.810924	−	0.444373i
$418$	−1.09208	+	1.09208i	−0.0534155	+	0.0534155i
$419$	22.2455	−	16.1623i	1.08677	−	0.789582i	0.107916	−	0.994160i	$-0.465582\pi$
$419$	22.2455	−	16.1623i	1.08677	−	0.789582i	0.978850	+	0.204578i	$0.0655823\pi$
$420$		0			0
$421$	25.8507	+	18.7816i	1.25988	+	0.915359i	0.998752	−	0.0499438i	$-0.0159042\pi$
$421$	25.8507	+	18.7816i	1.25988	+	0.915359i	0.261132	+	0.965303i	$0.415904\pi$
$422$	10.9234	−	1.73009i	0.531741	−	0.0842194i
$423$	37.2283	+	8.21520i	1.81010	+	0.399437i
$424$			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
$429$	−5.47559	−	8.03356i	−0.264364	−	0.387864i
$430$		0			0
$431$	−5.09101	−	7.00718i	−0.245225	−	0.337524i	0.668607	−	0.743616i	$-0.266891\pi$
$431$	−5.09101	−	7.00718i	−0.245225	−	0.337524i	−0.913832	+	0.406093i	$0.866891\pi$
$432$	1.27167	−	5.03814i	0.0611835	−	0.242398i
$433$	1.68664	−	10.6490i	0.0810548	−	0.511760i	−0.913440	−	0.406974i	$-0.866584\pi$
$433$	1.68664	−	10.6490i	0.0810548	−	0.511760i	0.994495	−	0.104786i	$-0.0334159\pi$
$434$	−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
$438$	−1.67464	+	1.57689i	−0.0800176	+	0.0753467i
$439$	32.6251	+	10.6006i	1.55711	+	0.505937i	0.956035	−	0.293253i	$-0.0947379\pi$
$439$	32.6251	+	10.6006i	1.55711	+	0.505937i	0.601078	+	0.799190i	$0.294738\pi$
$440$		0			0
$441$	7.67066	−	19.5290i	0.365269	−	0.929951i
$442$	15.8101	+	2.50408i	0.752011	+	0.119107i
$443$	4.58214	+	4.58214i	0.217704	+	0.217704i	0.807530	−	0.589826i	$-0.200804\pi$
$443$	4.58214	+	4.58214i	0.217704	+	0.217704i	−0.589826	+	0.807530i	$0.700804\pi$
$444$	−5.02958	−	17.2244i	−0.238693	−	0.817434i
$445$		0			0
$446$	−3.22891	+	4.44421i	−0.152893	+	0.210439i
$447$	−24.4515	−	4.62991i	−1.15652	−	0.218987i
$448$	0.0357280	+	0.0701201i	0.00168799	+	0.00331286i
$449$	−22.7460			−1.07345			−0.536726	−	0.843756i	$-0.680339\pi$
$449$	−22.7460			−1.07345			−0.536726	+	0.843756i	$0.680339\pi$
$450$		0			0
$451$	−4.11362			−0.193703
$452$	3.46581	+	6.80204i	0.163018	+	0.319941i
$453$	−0.555530	−	0.105190i	−0.0261011	−	0.00494225i
$454$	3.97531	−	5.47155i	0.186571	−	0.256792i
$455$		0			0
$456$	0.680779	+	2.33141i	0.0318804	+	0.109178i
$457$	−6.28077	−	6.28077i	−0.293802	−	0.293802i	0.544778	−	0.838580i	$-0.316614\pi$
$457$	−6.28077	−	6.28077i	−0.293802	−	0.293802i	−0.838580	+	0.544778i	$0.816614\pi$
$458$	−2.99986	−	0.475131i	−0.140174	−	0.0222014i
$459$	−10.7430	+	12.2863i	−0.501442	+	0.573477i
$460$		0			0
$461$	−21.3397	−	6.93369i	−0.993889	−	0.322934i	−0.233468	−	0.972364i	$-0.575007\pi$
$461$	−21.3397	−	6.93369i	−0.993889	−	0.322934i	−0.760421	+	0.649430i	$0.775007\pi$
$462$	−0.109300	+	0.102920i	−0.00508509	+	0.00478826i
$463$	−21.5722	−	10.9916i	−1.00255	−	0.510823i	−0.125944	−	0.992037i	$-0.540196\pi$
$463$	−21.5722	−	10.9916i	−1.00255	−	0.510823i	−0.876603	+	0.481214i	$0.840196\pi$
$464$	−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	−0.889733	−	0.456482i	$-0.849109\pi$
$467$	2.10730	−	13.3049i	0.0975140	−	0.615679i	0.987247	−	0.159197i	$-0.0508906\pi$
$468$	−15.2171	+	1.48024i	−0.703413	+	0.0684240i
$469$	−0.308025	−	0.423960i	−0.0142233	−	0.0195766i
$470$		0			0
$471$	−4.79479	−	7.03472i	−0.220932	−	0.324143i
$472$	−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
$477$	−4.38893	+	19.8890i	−0.200955	+	0.910656i
$478$	−11.2308	+	1.77878i	−0.513684	+	0.0813596i
$479$	−13.9808	−	10.1576i	−0.638797	−	0.464113i	0.220639	−	0.975355i	$-0.429186\pi$
$479$	−13.9808	−	10.1576i	−0.638797	−	0.464113i	−0.859437	+	0.511242i	$0.829186\pi$
$480$		0			0
$481$	−42.7136	+	31.0332i	−1.94757	+	1.41499i
$482$	−6.23914	+	6.23914i	−0.284185	+	0.284185i
$483$	0.298606	+	0.163631i	0.0135871	+	0.00744549i
$484$	9.30791	−	3.02432i	0.423087	−	0.137469i
$485$		0			0
$486$	6.98235	−	13.9372i	0.316726	−	0.632206i
$487$	−1.64469	+	3.22789i	−0.0745281	+	0.146270i	−0.925264	−	0.379324i	$-0.876157\pi$
$487$	−1.64469	+	3.22789i	−0.0745281	+	0.146270i	0.850736	+	0.525593i	$0.176157\pi$
$488$	1.81181	−	3.55588i	0.0820169	−	0.160967i
$489$	2.10024	+	1.62454i	0.0949761	+	0.0734643i
$490$		0			0
$491$	−5.48953	+	1.78366i	−0.247739	+	0.0804953i	−0.430254	−	0.902708i	$-0.641576\pi$
$491$	−5.48953	+	1.78366i	−0.247739	+	0.0804953i	0.182515	+	0.983203i	$0.441576\pi$
$492$	−3.10877	+	5.67310i	−0.140154	+	0.255763i
$493$	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
$498$	−0.193560	−	1.51560i	−0.00867365	−	0.0679157i
$499$		−	28.5582i		−	1.27844i	−0.769024	−	0.639220i	$-0.779257\pi$
$499$		−	28.5582i		−	1.27844i	0.769024	−	0.639220i	$-0.220743\pi$
$500$		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	0.917170	+	0.398497i	$0.130468\pi$
$503$	3.76856	+	23.7938i	0.168032	+	1.06091i	−0.749138	+	0.662414i	$0.769532\pi$
$504$	0.0593360	+	0.228515i	0.00264304	+	0.0101789i
$505$		0			0
$506$	1.61718	+	2.22586i	0.0718926	+	0.0989517i
$507$	9.59451	+	20.3176i	0.426107	+	0.902335i
$508$	−0.504047	+	3.18243i	−0.0223635	+	0.141197i
$509$	1.35722	+	4.17708i	0.0601576	+	0.185146i	0.976619	−	0.214977i	$-0.0689675\pi$
$509$	1.35722	+	4.17708i	0.0601576	+	0.185146i	−0.916462	+	0.400123i	$0.868968\pi$
$510$		0			0
$511$	0.0322963	−	0.0993978i	0.00142870	−	0.00439710i
$512$	0.891007	+	0.453990i	0.0393773	+	0.0200637i
$513$	0.487193	+	7.27001i	0.0215101	+	0.320979i
$514$	−2.11472	−	0.687116i	−0.0932765	−	0.0303074i
$515$		0			0
$516$	0.0740233	−	2.46217i	0.00325869	−	0.108391i
$517$	−13.8242	−	2.18954i	−0.607989	−	0.0962960i
$518$	0.576498	+	0.576498i	0.0253299	+	0.0253299i
$519$	−23.5661	+	6.88138i	−1.03444	+	0.302059i
$520$		0			0
$521$	3.85216	−	5.30205i	0.168766	−	0.232287i	−0.716254	−	0.697840i	$-0.754145\pi$
$521$	3.85216	−	5.30205i	0.168766	−	0.232287i	0.885020	+	0.465553i	$0.154145\pi$
$522$	−10.6499	+	18.1203i	−0.466132	+	0.793104i
$523$	−4.06078	−	7.96973i	−0.177566	−	0.348492i	0.785020	−	0.619471i	$-0.212653\pi$
$523$	−4.06078	−	7.96973i	−0.177566	−	0.348492i	−0.962585	+	0.270979i	$0.912653\pi$
$524$	−5.31824			−0.232328
$525$		0			0
$526$	−19.3769			−0.844875
$527$	13.6245	+	26.7397i	0.593494	+	1.16480i
$528$	−0.354913	+	1.87437i	−0.0154456	+	0.0815716i
$529$	−9.85121	+	13.5590i	−0.428314	+	0.589523i
$530$		0			0
$531$	1.18770	−	19.7348i	0.0515416	−	0.856416i
$532$	−0.0780320	−	0.0780320i	−0.00338312	−	0.00338312i
$533$	18.7999	+	2.97762i	0.814315	+	0.128975i
$534$	5.67680	+	0.170669i	0.245659	+	0.00738556i
$535$		0			0
$536$	−6.33303	−	2.05773i	−0.273545	−	0.0888803i
$537$	18.0373	+	19.1555i	0.778367	+	0.826619i
$538$	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	0.999212	+	0.0396896i	$0.0126369\pi$
$541$	4.98127	+	15.3308i	0.214161	+	0.659121i	−0.785051	+	0.619432i	$0.787363\pi$
$542$	1.16442	−	7.35189i	0.0500163	−	0.315791i
$543$	−16.0863	+	7.59639i	−0.690329	+	0.325992i
$544$	−1.84619	−	2.54107i	−0.0791548	−	0.108947i
$545$		0			0
$546$	0.574017	−	0.391244i	0.0245657	−	0.0167437i
$547$	−3.70025	−	23.3625i	−0.158211	−	0.998907i	−0.931206	−	0.364494i	$-0.881242\pi$
$547$	−3.70025	−	23.3625i	−0.158211	−	0.998907i	0.772994	−	0.634413i	$-0.218758\pi$
$548$	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
$552$	4.29184	−	0.548120i	0.182673	−	0.0233295i
$553$	−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	−0.182634	+	0.983181i	$0.558462\pi$
$557$	−27.5142	+	27.5142i	−1.16581	+	1.16581i	−0.983181	+	0.182634i	$0.941538\pi$
$558$	−19.0143	−	21.4496i	−0.804941	−	0.908033i
$559$	−6.89314	+	2.23972i	−0.291549	+	0.0947299i
$560$		0			0
$561$	3.66602	−	4.73951i	0.154780	−	0.200102i
$562$	0.639477	−	1.25504i	0.0269747	−	0.0529408i
$563$	−11.3007	+	22.1789i	−0.476267	+	0.934728i	0.520460	+	0.853886i	$0.325761\pi$
$563$	−11.3007	+	22.1789i	−0.476267	+	0.934728i	−0.996727	+	0.0808412i	$0.974239\pi$
$564$	−13.4669	+	17.4103i	−0.567061	+	0.733108i
$565$		0			0
$566$	−9.06857	+	2.94656i	−0.381180	+	0.123853i
$567$	0.0261004	+	0.707797i	0.00109611	+	0.0297247i
$568$	−9.03570	+	9.03570i	−0.379129	+	0.379129i
$569$	−25.9540	+	18.8567i	−1.08805	+	0.790515i	−0.979069	−	0.203529i	$-0.934759\pi$
$569$	−25.9540	+	18.8567i	−1.08805	+	0.790515i	−0.108981	+	0.994044i	$0.534759\pi$
$570$		0			0
$571$	−34.1170	−	24.7874i	−1.42775	−	1.03732i	−0.990430	−	0.138017i	$-0.955927\pi$
$571$	−34.1170	−	24.7874i	−1.42775	−	1.03732i	−0.437322	−	0.899305i	$-0.644073\pi$
$572$	5.54398	−	0.878080i	0.231805	−	0.0367144i
$573$	−18.6618	+	2.38334i	−0.779609	+	0.0995655i
$574$		−	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	0.00583873	−	0.999983i	$-0.498141\pi$
$577$	19.6556	−	10.0150i	0.818274	−	0.416931i	0.812435	+	0.583052i	$0.198141\pi$
$578$	−1.11609	−	7.04672i	−0.0464233	−	0.293105i
$579$	−27.7782	+	18.9333i	−1.15442	+	0.786843i
$580$		0			0
$581$	0.0408054	+	0.0561638i	0.00169289	+	0.00233007i
$582$	−16.2586	+	7.67775i	−0.673940	+	0.318253i
$583$	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	$-0.264210\pi$
$587$	11.4960	+	5.85750i	0.474490	+	0.241765i	−0.200356	+	0.979723i	$0.564210\pi$
$588$	8.30436	+	8.81916i	0.342466	+	0.363696i
$589$	12.7423	+	4.14024i	0.525039	+	0.170596i
$590$		0			0
$591$	−21.1735	−	0.636564i	−0.870960	−	0.0261848i
$592$	10.2323	+	1.62063i	0.420543	+	0.0666075i
$593$	3.75033	+	3.75033i	0.154007	+	0.154007i	0.779905	−	0.625898i	$-0.215267\pi$
$593$	3.75033	+	3.75033i	0.154007	+	0.154007i	−0.625898	+	0.779905i	$0.715267\pi$
$594$	−2.25143	+	5.26158i	−0.0923774	+	0.215885i
$595$		0			0
$596$	8.44527	−	11.6239i	0.345932	−	0.476134i
$597$	5.13507	−	27.1194i	0.210165	−	1.10992i
$598$	−5.77963	−	11.3432i	−0.236347	−	0.463856i
$599$	29.8620			1.22013			0.610065	−	0.792352i	$-0.291143\pi$
$599$	29.8620			1.22013			0.610065	+	0.792352i	$0.291143\pi$
$600$		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
$603$	−17.2225	−	10.1222i	−0.701355	−	0.412208i
$604$	0.191874	−	0.264091i	0.00780722	−	0.0107457i
$605$		0			0
$606$	−23.3393	+	6.81513i	−0.948092	+	0.276846i
$607$	29.8007	+	29.8007i	1.20957	+	1.20957i	0.971165	+	0.238406i	$0.0766250\pi$
$607$	29.8007	+	29.8007i	1.20957	+	1.20957i	0.238406	+	0.971165i	$0.423375\pi$
$608$	−1.38499	−	0.219361i	−0.0561687	−	0.00889625i
$609$	0.0286980	−	0.954554i	0.00116290	−	0.0386805i
$610$		0			0
$611$	61.5942	+	20.0132i	2.49184	+	0.809646i
$612$	−3.76576	−	8.63759i	−0.152222	−	0.349154i
$613$	−1.17929	−	0.600877i	−0.0476310	−	0.0242692i	0.430013	−	0.902823i	$-0.358509\pi$
$613$	−1.17929	−	0.600877i	−0.0476310	−	0.0242692i	−0.477644	+	0.878554i	$0.658509\pi$
$614$	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	−0.394428	−	0.918927i	$-0.629057\pi$
$617$	6.57400	−	41.5066i	0.264659	−	1.67099i	0.659087	−	0.752067i	$-0.270943\pi$
$618$	9.76586	+	20.6804i	0.392841	+	0.831889i
$619$	9.51877	+	13.1015i	0.382592	+	0.526592i	0.956269	−	0.292489i	$-0.0944836\pi$
$619$	9.51877	+	13.1015i	0.382592	+	0.526592i	−0.573677	+	0.819082i	$0.694484\pi$
$620$		0			0
$621$	12.9274	+	1.16877i	0.518758	+	0.0469013i
$622$	−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
$627$	−0.338883	−	2.65349i	−0.0135337	−	0.105970i
$628$	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	−0.757914	−	0.652355i	$-0.773781\pi$
$631$	−9.33690	+	6.78365i	−0.371696	+	0.270053i	0.386218	+	0.922408i	$0.373781\pi$
$632$	−7.04182	+	7.04182i	−0.280109	+	0.280109i
$633$	−9.20545	+	16.7988i	−0.365884	+	0.667691i
$634$	8.64124	−	2.80771i	0.343188	−	0.111508i
$635$		0			0
$636$	−9.30139	−	7.19464i	−0.368824	−	0.285286i
$637$	16.1814	−	31.7579i	0.641132	−	1.25829i
$638$	3.50321	−	6.87543i	0.138693	−	0.272201i
$639$	−32.3115	+	20.6290i	−1.27822	+	0.816073i
$640$		0			0
$641$	−15.5088	+	5.03912i	−0.612561	+	0.199033i	−0.598835	−	0.800873i	$-0.704369\pi$
$641$	−15.5088	+	5.03912i	−0.612561	+	0.199033i	−0.0137264	+	0.999906i	$0.504369\pi$
$642$	−29.5620	−	16.1995i	−1.16672	−	0.639344i
$643$	−12.8296	+	12.8296i	−0.505952	+	0.505952i	−0.913281	−	0.407330i	$-0.866460\pi$
$643$	−12.8296	+	12.8296i	−0.505952	+	0.505952i	0.407330	+	0.913281i	$0.366460\pi$
$644$	−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	$-0.716629\pi$
$647$	−25.1179	+	3.97829i	−0.987488	+	0.156403i	−0.358259	+	0.933622i	$0.616629\pi$
$648$	5.55479	+	7.08127i	0.218213	+	0.278178i
$649$			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	0.886604	+	0.462529i	$0.153058\pi$
$653$	4.76127	+	30.0615i	0.186323	+	1.17640i	−0.700281	+	0.713867i	$0.746942\pi$
$654$	12.0053	+	17.6136i	0.469443	+	0.688747i
$655$		0			0
$656$	−2.19532	−	3.02160i	−0.0857129	−	0.117974i
$657$	−0.385730	−	3.96538i	−0.0150488	−	0.154704i
$658$	0.156448	−	0.987775i	0.00609899	−	0.0385075i
$659$	−3.19473	−	9.83236i	−0.124449	−	0.383014i	0.869351	−	0.494195i	$-0.164537\pi$
$659$	−3.19473	−	9.83236i	−0.124449	−	0.383014i	−0.993800	+	0.111180i	$0.964537\pi$
$660$		0			0
$661$	3.97825	−	12.2438i	0.154736	−	0.476229i	−0.843398	−	0.537289i	$-0.819448\pi$
$661$	3.97825	−	12.2438i	0.154736	−	0.476229i	0.998134	+	0.0610606i	$0.0194483\pi$
$662$	−9.85137	−	5.01952i	−0.382884	−	0.195089i
$663$	−20.1850	+	19.0067i	−0.783921	+	0.738161i
$664$	0.838964	+	0.272596i	0.0325581	+	0.0105788i
$665$		0			0
$666$	28.9279	+	11.3624i	1.12093	+	0.440284i
$667$	−17.2859	−	2.73781i	−0.669311	−	0.106008i
$668$	−15.8270	−	15.8270i	−0.612365	−	0.612365i
$669$	−2.66696	−	9.13333i	−0.103111	−	0.353115i
$670$		0			0
$671$	−2.58363	+	3.55605i	−0.0997397	+	0.137280i
$672$	−0.133928	−	0.0253594i	−0.00516640	−	0.000978260i
$673$	−15.3006	−	30.0291i	−0.589794	−	1.15754i	−0.972334	−	0.233596i	$-0.924951\pi$
$673$	−15.3006	−	30.0291i	−0.589794	−	1.15754i	0.382540	−	0.923939i	$-0.375049\pi$
$674$	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	$-0.0531639\pi$
$677$	7.07682	+	13.8891i	0.271984	+	0.533800i	−0.714100	+	0.700044i	$0.753164\pi$
$678$	−12.9918	−	2.46001i	−0.498948	−	0.0944759i
$679$	0.480192	−	0.660928i	0.0184281	−	0.0253641i
$680$		0			0
$681$	3.28346	+	11.2446i	0.125823	+	0.430895i
$682$	7.44126	+	7.44126i	0.284940	+	0.284940i
$683$	26.5524	+	4.20549i	1.01600	+	0.160919i	0.642157	−	0.766573i	$-0.278040\pi$
$683$	26.5524	+	4.20549i	1.01600	+	0.160919i	0.373844	+	0.927492i	$0.378040\pi$
$684$	−3.91554	−	1.53796i	−0.149715	−	0.0588054i
$685$		0			0
$686$	−1.04738	−	0.340314i	−0.0399891	−	0.0129932i
$687$	3.82996	−	3.60640i	0.146122	−	0.137593i
$688$	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	0.991381	+	0.131007i	$0.0418212\pi$
$691$	7.00128	+	21.5477i	0.266341	+	0.819714i	−0.725040	+	0.688707i	$0.758179\pi$
$692$	2.21732	−	13.9996i	0.0842898	−	0.532185i
$693$	−0.0251756	−	0.258811i	−0.000956343	−	0.00983141i
$694$	−8.78938	−	12.0975i	−0.333640	−	0.459217i
$695$		0			0
$696$	−6.83446	−	10.0272i	−0.259060	−	0.380081i
$697$	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	$0.746839\pi$
$702$	14.0980	−	22.4166i	0.532094	−	0.846061i
$703$	−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
$708$	10.0101	+	5.48536i	0.376201	+	0.206152i
$709$	−37.7779	+	12.2748i	−1.41878	+	0.460989i	−0.915214	−	0.402968i	$-0.867978\pi$
$709$	−37.7779	+	12.2748i	−1.41878	+	0.460989i	−0.503565	+	0.863958i	$0.667978\pi$
$710$		0			0
$711$	−25.1814	+	16.0769i	−0.944377	+	0.602931i
$712$	−1.48863	+	2.92160i	−0.0557887	+	0.109491i
$713$	10.8358	−	21.2664i	0.405803	−	0.796433i
$714$	0.338649	+	0.261946i	0.0126736	+	0.00980309i
$715$		0			0
$716$	−14.4473	+	4.69420i	−0.539919	+	0.175430i
$717$	9.46453	−	17.2716i	0.353459	−	0.645018i
$718$	12.9715	−	12.9715i	0.484093	−	0.484093i
$719$	25.6075	−	18.6049i	0.954998	−	0.693847i	0.00301445	−	0.999995i	$-0.499040\pi$
$719$	25.6075	−	18.6049i	0.954998	−	0.693847i	0.951984	+	0.306149i	$0.0990405\pi$
$720$		0			0
$721$	−0.840680	−	0.610790i	−0.0313086	−	0.0227470i
$722$	−16.8240	+	2.66466i	−0.626124	+	0.0991682i
$723$	−1.93606	−	15.1596i	−0.0720029	−	0.563791i
$724$		−	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	0.720246	−	0.693719i	$-0.244029\pi$
$727$	45.9671	−	23.4214i	1.70483	−	0.868652i	0.984580	−	0.174934i	$-0.0559711\pi$
$728$	0.0627409	+	0.396131i	0.00232533	+	0.0146816i
$729$	11.6951	+	24.3357i	0.433152	+	0.901321i
$730$		0			0
$731$	−2.62561	−	3.61384i	−0.0971117	−	0.133663i
$732$	2.95165	+	6.25049i	0.109096	+	0.231025i
$733$	−3.31036	+	20.9008i	−0.122271	+	0.771988i	0.848005	+	0.529988i	$0.177803\pi$
$733$	−3.31036	+	20.9008i	−0.122271	+	0.771988i	−0.970276	+	0.242000i	$0.922197\pi$
$734$	−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
$738$	−4.47789	−	10.2710i	−0.164834	−	0.378082i
$739$	−11.8537	−	3.85150i	−0.436046	−	0.141680i	0.0827648	−	0.996569i	$-0.473625\pi$
$739$	−11.8537	−	3.85150i	−0.436046	−	0.141680i	−0.518811	+	0.854889i	$0.673625\pi$
$740$		0			0
$741$	−0.371961	+	12.3722i	−0.0136643	+	0.454505i
$742$	0.527714	+	0.0835816i	0.0193730	+	0.00306838i
$743$	2.30237	+	2.30237i	0.0844658	+	0.0844658i	0.748077	−	0.663612i	$-0.230977\pi$
$743$	2.30237	+	2.30237i	0.0844658	+	0.0844658i	−0.663612	+	0.748077i	$0.730977\pi$
$744$	15.8858	−	4.63870i	0.582402	−	0.170063i
$745$		0			0
$746$	4.11202	−	5.65971i	0.150552	−	0.207217i
$747$	2.28154	+	1.34093i	0.0834772	+	0.0490621i
$748$	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
$753$	4.70802	−	24.8641i	0.171570	−	0.906097i
$754$	−20.9870	+	28.8861i	−0.764301	+	1.05197i
$755$		0			0
$756$	−0.375952	−	0.160870i	−0.0136733	−	0.00585079i
$757$	−7.02667	−	7.02667i	−0.255389	−	0.255389i	0.567787	−	0.823176i	$-0.307800\pi$
$757$	−7.02667	−	7.02667i	−0.255389	−	0.255389i	−0.823176	+	0.567787i	$0.807800\pi$
$758$	−12.0195	−	1.90370i	−0.436567	−	0.0691453i
$759$	−4.76327	−	0.143204i	−0.172896	−	0.00519798i
$760$		0			0
$761$	48.1462	+	15.6436i	1.74530	+	0.567081i	0.995515	−	0.0946038i	$-0.0301584\pi$
$761$	48.1462	+	15.6436i	1.74530	+	0.567081i	0.749782	+	0.661685i	$0.230158\pi$
$762$	−3.82587	−	4.06305i	−0.138597	−	0.147189i
$763$	−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
$768$	−1.56620	+	0.739603i	−0.0565154	+	0.0266881i
$769$	−21.2813	−	29.2912i	−0.767422	−	1.05627i	−0.996560	−	0.0828721i	$-0.973591\pi$
$769$	−21.2813	−	29.2912i	−0.767422	−	1.05627i	0.229138	−	0.973394i	$-0.426409\pi$
$770$		0			0
$771$	3.18239	−	2.16909i	0.114611	−	0.0781178i
$772$	−3.03620	−	19.1698i	−0.109275	−	0.689936i
$773$	−20.9544	+	10.6768i	−0.753679	+	0.384019i	−0.788227	−	0.615384i	$-0.789001\pi$
$773$	−20.9544	+	10.6768i	−0.753679	+	0.384019i	0.0345481	+	0.999403i	$0.489001\pi$
$774$	3.29481	+	2.71063i	0.118429	+	0.0974317i
$775$		0			0
$776$		−	10.3809i		−	0.372653i
$777$	−1.40075	+	0.178893i	−0.0502516	+	0.00641774i
$778$	−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
$783$	−13.5395	−	33.7932i	−0.483862	−	1.20767i
$784$	−6.65151	+	2.16121i	−0.237554	+	0.0771859i
$785$		0			0
$786$	5.63586	−	7.28616i	0.201025	−	0.259889i
$787$	14.2872	−	28.0403i	0.509285	−	0.999529i	−0.483008	−	0.875616i	$-0.660456\pi$
$787$	14.2872	−	28.0403i	0.509285	−	0.999529i	0.992293	−	0.123913i	$-0.0395443\pi$
$788$	5.55232	−	10.8970i	0.197793	−	0.388191i
$789$	20.5342	−	26.5470i	0.731036	−	0.945099i
$790$		0			0
$791$	0.571382	−	0.185653i	0.0203160	−	0.00660107i
$792$	−2.19184	−	2.47256i	−0.0778837	−	0.0878585i
$793$	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	$-0.585739\pi$
$797$	−6.24831	+	0.989635i	−0.221326	+	0.0350547i	0.0447862	+	0.998997i	$0.485739\pi$
$798$	0.189599	−	0.0242140i	0.00671172	−	0.000857167i
$799$			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
$804$	9.53041	−	6.49584i	0.336112	−	0.229091i
$805$		0			0
$806$	−28.6215	−	39.3941i	−1.00815	−	1.38760i
$807$	−8.60707	+	4.06450i	−0.302983	+	0.143077i
$808$	2.19597	−	13.8648i	0.0772540	−	0.487763i
$809$	10.4456	+	32.1483i	0.367249	+	1.13028i	0.948561	+	0.316595i	$0.102539\pi$
$809$	10.4456	+	32.1483i	0.367249	+	1.13028i	−0.581312	+	0.813681i	$0.697461\pi$
$810$		0			0
$811$	−11.3720	+	34.9993i	−0.399324	+	1.22899i	0.526219	+	0.850349i	$0.323609\pi$
$811$	−11.3720	+	34.9993i	−0.399324	+	1.22899i	−0.925543	+	0.378643i	$0.876391\pi$
$812$	0.491266	+	0.250313i	0.0172401	+	0.00878425i
$813$	8.83835	+	9.38626i	0.309975	+	0.329191i
$814$	−10.8518	−	3.52597i	−0.380356	−	0.123585i
$815$		0			0
$816$	5.43779	+	0.163483i	0.190361	+	0.00572306i
$817$	−1.96970	−	0.311969i	−0.0689110	−	0.0109144i
$818$	−11.2430	−	11.2430i	−0.393103	−	0.393103i
$819$	−0.0722816	+	1.20103i	−0.00252572	+	0.0419675i
$820$		0			0
$821$	−1.94467	+	2.67661i	−0.0678695	+	0.0934144i	−0.841602	−	0.540098i	$-0.818387\pi$
$821$	−1.94467	+	2.67661i	−0.0678695	+	0.0934144i	0.773733	+	0.633512i	$0.218387\pi$
$822$	−3.70121	+	19.5469i	−0.129095	+	0.681777i
$823$	16.1380	+	31.6727i	0.562537	+	1.10404i	0.980673	+	0.195656i	$0.0626837\pi$
$823$	16.1380	+	31.6727i	0.562537	+	1.10404i	−0.418136	+	0.908385i	$0.637316\pi$
$824$	−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	$-0.199679\pi$
$827$	−4.05871	−	7.96567i	−0.141135	−	0.276993i	−0.950744	+	0.309976i	$0.899679\pi$
$828$	−3.79722	+	6.46082i	−0.131963	+	0.224529i
$829$	6.82593	−	9.39508i	0.237074	−	0.326305i	−0.673858	−	0.738861i	$-0.735364\pi$
$829$	6.82593	−	9.39508i	0.237074	−	0.326305i	0.910932	+	0.412556i	$0.135364\pi$
$830$		0			0
$831$	31.7489	−	9.27078i	1.10136	−	0.321600i
$832$	3.60364	+	3.60364i	0.124934	+	0.124934i
$833$	21.6966	+	3.43640i	0.751743	+	0.119064i
$834$	−0.567443	+	18.8743i	−0.0196489	+	0.653565i
$835$		0			0
$836$	1.46885	+	0.477258i	0.0508012	+	0.0165063i
$837$	49.5365	−	3.31965i	1.71223	−	0.114744i
$838$	−24.5000	−	12.4834i	−0.846339	−	0.431231i
$839$	1.99464	−	6.13888i	0.0688628	−	0.211938i	−0.910703	−	0.413062i	$-0.864459\pi$
$839$	1.99464	−	6.13888i	0.0688628	−	0.211938i	0.979566	+	0.201124i	$0.0644594\pi$
$840$		0			0
$841$	6.20662	+	19.1020i	0.214021	+	0.658690i
$842$	4.99858	−	31.5598i	0.172262	−	1.08762i
$843$	1.04178	+	2.20610i	0.0358809	+	0.0759822i
$844$	−6.50062	−	8.94734i	−0.223761	−	0.307980i
$845$		0			0
$846$	−9.58150	−	36.9003i	−0.329419	−	1.26866i
$847$	−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
$852$	−2.80386	−	21.9545i	−0.0960586	−	0.752150i
$853$	−26.0890	+	4.13209i	−0.893271	+	0.141480i	−0.586162	−	0.810194i	$-0.699362\pi$
$853$	−26.0890	+	4.13209i	−0.893271	+	0.141480i	−0.307109	+	0.951674i	$0.599362\pi$
$854$	−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	$-0.925770\pi$
$857$	−21.7170	+	21.7170i	−0.741840	+	0.741840i	0.231092	+	0.972932i	$0.425770\pi$
$858$	−4.67208	+	8.52595i	−0.159502	+	0.291071i
$859$	2.16755	−	0.704281i	0.0739560	−	0.0240298i	−0.271805	−	0.962352i	$-0.587621\pi$
$859$	2.16755	−	0.704281i	0.0739560	−	0.0240298i	0.345761	+	0.938322i	$0.387621\pi$
$860$		0			0
$861$	0.402691	+	0.311482i	0.0137237	+	0.0106153i
$862$	−3.93217	+	7.71732i	−0.133930	+	0.262853i
$863$	0.924026	−	1.81350i	0.0314542	−	0.0617324i	−0.874745	−	0.484584i	$-0.838971\pi$
$863$	0.924026	−	1.81350i	0.0314542	−	0.0617324i	0.906199	+	0.422852i	$0.138971\pi$
$864$	−5.06634	+	1.15420i	−0.172360	+	0.0392666i
$865$		0			0
$866$	−10.2541	+	3.33175i	−0.348448	+	0.113218i
$867$	10.8370	+	5.93849i	0.368043	+	0.201682i
$868$	−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
$873$	6.71083	−	30.4111i	0.227127	−	1.02926i
$874$		−	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	−0.355657	−	0.934617i	$-0.615743\pi$
$877$	5.66858	−	2.88829i	0.191414	−	0.0975305i	0.547071	+	0.837086i	$0.315743\pi$
$878$	−5.36634	−	33.8818i	−0.181105	−	1.14345i
$879$	−30.3873	−	44.5829i	−1.02494	−	1.50374i
$880$		0			0
$881$	−3.61099	−	4.97010i	−0.121657	−	0.167447i	0.743844	−	0.668353i	$-0.233000\pi$
$881$	−3.61099	−	4.97010i	−0.121657	−	0.167447i	−0.865502	+	0.500906i	$0.833000\pi$
$882$	−20.8829	+	2.03137i	−0.703162	+	0.0683996i
$883$	−6.19390	+	39.1067i	−0.208441	+	1.31605i	0.632348	+	0.774684i	$0.282091\pi$
$883$	−6.19390	+	39.1067i	−0.208441	+	1.31605i	−0.840789	+	0.541362i	$0.817909\pi$
$884$	−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	$-0.0488170\pi$
$887$	43.0525	+	21.9363i	1.44556	+	0.736550i	0.457299	+	0.889313i	$0.348817\pi$
$888$	−13.0637	+	12.3011i	−0.438388	+	0.412798i
$889$	0.241160	+	0.0783578i	0.00808826	+	0.00262804i
$890$		0			0
$891$	−4.82263	−	8.66035i	−0.161564	−	0.290133i
$892$	5.42571	+	0.859348i	0.181666	+	0.0287731i
$893$	12.6005	+	12.6005i	0.421660	+	0.421660i
$894$	6.97549	+	23.8884i	0.233295	+	0.798948i
$895$		0			0
$896$	0.0462573	−	0.0636677i	0.00154535	−	0.00212699i
$897$	21.6653	+	4.10233i	0.723383	+	0.136973i
$898$	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
$903$	−0.190470	−	0.0360655i	−0.00633844	−	0.00120019i
$904$	4.48722	−	6.17613i	0.149243	−	0.205415i
$905$		0			0
$906$	0.158481	+	0.542736i	0.00526517	+	0.0180312i
$907$	−24.7561	−	24.7561i	−0.822014	−	0.822014i	0.164383	−	0.986397i	$-0.447437\pi$
$907$	−24.7561	−	24.7561i	−0.822014	−	0.822014i	−0.986397	+	0.164383i	$0.947437\pi$
$908$	−6.67994	−	1.05800i	−0.221682	−	0.0351109i
$909$	15.3962	−	39.1977i	0.510660	−	1.30010i
$910$		0			0
$911$	48.5335	+	15.7695i	1.60799	+	0.522466i	0.969065	−	0.246806i	$-0.0793810\pi$
$911$	48.5335	+	15.7695i	1.60799	+	0.522466i	0.638921	+	0.769272i	$0.279381\pi$
$912$	1.76823	−	1.66502i	0.0585521	−	0.0551342i
$913$	−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
$918$	15.8244	+	3.99424i	0.522284	+	0.131830i
$919$	−6.34757	−	8.73668i	−0.209387	−	0.288196i	0.691387	−	0.722485i	$-0.257000\pi$
$919$	−6.34757	−	8.73668i	−0.209387	−	0.288196i	−0.900774	+	0.434288i	$0.857000\pi$
$920$		0			0
$921$	2.15835	+	3.16664i	0.0711200	+	0.104344i
$922$	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
$927$	−38.6819	−	8.53597i	−1.27048	−	0.280358i
$928$	6.91981	−	1.09599i	0.227154	−	0.0359777i
$929$	38.0194	+	27.6227i	1.24738	+	0.906272i	0.998067	−	0.0621513i	$-0.0197961\pi$
$929$	38.0194	+	27.6227i	1.24738	+	0.906272i	0.249310	+	0.968424i	$0.419796\pi$
$930$		0			0
$931$	7.93409	−	5.76446i	0.260029	−	0.188922i
$932$	−0.977696	+	0.977696i	−0.0320255	+	0.0320255i
$933$	20.7056	+	11.3463i	0.677871	+	0.371463i
$934$	−12.8115	+	4.16270i	−0.419204	+	0.136208i
$935$		0			0
$936$	8.22734	+	12.8866i	0.268919	+	0.421210i
$937$	−20.7717	+	40.7667i	−0.678581	+	1.33179i	0.252721	+	0.967539i	$0.418675\pi$
$937$	−20.7717	+	40.7667i	−0.678581	+	1.33179i	−0.931301	+	0.364250i	$0.881325\pi$
$938$	−0.237911	+	0.466926i	−0.00776806	+	0.0152457i
$939$	26.1652	+	20.2389i	0.853870	+	0.660470i
$940$		0			0
$941$	−29.1364	+	9.46699i	−0.949820	+	0.308615i	−0.742642	−	0.669688i	$-0.766428\pi$
$941$	−29.1364	+	9.46699i	−0.949820	+	0.308615i	−0.207177	+	0.978303i	$0.566428\pi$
$942$	−4.09119	+	7.46589i	−0.133298	+	0.243252i
$943$	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	$-0.625315\pi$
$947$	−14.2493	+	2.25687i	−0.463040	+	0.0733384i	−0.0794442	+	0.996839i	$0.525315\pi$
$948$	−2.18514	−	17.1099i	−0.0709701	−	0.555704i
$949$		−	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	$-0.0703336\pi$
$953$	−0.616563	−	3.89283i	−0.0199724	−	0.126101i	−0.995660	+	0.0930649i	$0.970334\pi$
$954$	19.7138	−	5.11887i	0.638257	−	0.165729i
$955$		0			0
$956$	6.68358	+	9.19915i	0.216162	+	0.297522i
$957$	5.70713	+	12.0856i	0.184485	+	0.390671i
$958$	−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
$963$	53.5214	−	23.3339i	1.72470	−	0.751925i
$964$	8.39163	+	2.72661i	0.270276	+	0.0878181i
$965$		0			0
$966$	0.0102323	−	0.340347i	0.000329218	−	0.0109505i
$967$	−51.5598	−	8.16627i	−1.65805	−	0.262610i	−0.743992	−	0.668189i	$-0.767070\pi$
$967$	−51.5598	−	8.16627i	−1.65805	−	0.262610i	−0.914060	+	0.405579i	$0.867070\pi$
$968$	−6.92040	−	6.92040i	−0.222430	−	0.222430i
$969$	−7.32280	+	2.13828i	−0.235242	+	0.0686914i
$970$		0			0
$971$	2.69176	−	3.70489i	0.0863828	−	0.118896i	−0.763638	−	0.645644i	$-0.776589\pi$
$971$	2.69176	−	3.70489i	0.0863828	−	0.118896i	0.850021	+	0.526748i	$0.176589\pi$
$972$	−15.5881	+	0.106057i	−0.499988	+	0.00340179i
$973$	−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	$-0.128938\pi$
$977$	1.87651	+	3.68285i	0.0600348	+	0.117825i	−0.859039	+	0.511910i	$0.828938\pi$
$978$	0.493987	−	2.60885i	0.0157960	−	0.0834219i
$979$	2.12277	−	2.92174i	0.0678439	−	0.0933792i
$980$		0			0
$981$	−36.8535	−	2.21795i	−1.17664	−	0.0708137i
$982$	4.08144	+	4.08144i	0.130244	+	0.130244i
$983$	−25.6200	−	4.05781i	−0.817151	−	0.129424i	−0.266153	−	0.963931i	$-0.585753\pi$
$983$	−25.6200	−	4.05781i	−0.817151	−	0.129424i	−0.550998	+	0.834507i	$0.685753\pi$
$984$	6.46612	+	0.194399i	0.206132	+	0.00619722i
$985$		0			0
$986$	−20.9285	−	6.80010i	−0.666501	−	0.216559i
$987$	1.18749	+	1.26111i	0.0377983	+	0.0401415i
$988$	−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	−0.997243	−	0.0742035i	$-0.976359\pi$
$991$	−7.36863	−	22.6783i	−0.234072	−	0.720400i	0.763171	−	0.646197i	$-0.223641\pi$
$992$	−1.49468	+	9.43706i	−0.0474562	+	0.299627i
$993$	17.3166	−	8.17738i	0.549526	−	0.259501i
$994$	0.591094	+	0.813572i	0.0187484	+	0.0258049i
$995$		0			0
$996$	−1.26253	+	0.860532i	−0.0400049	+	0.0272670i
$997$	2.45546	+	15.5032i	0.0777652	+	0.490990i	0.995575	+	0.0939699i	$0.0299557\pi$
$997$	2.45546	+	15.5032i	0.0777652	+	0.490990i	−0.917810	+	0.397020i	$0.870044\pi$
$998$	−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.257.5		80
3.2	odd	2	inner	750.2.l.c.257.10		80
5.2	odd	4		750.2.l.b.743.8		80
5.3	odd	4		150.2.l.a.53.3	yes	80
5.4	even	2		750.2.l.a.257.6		80
15.2	even	4		750.2.l.b.743.2		80
15.8	even	4		150.2.l.a.53.9	yes	80
15.14	odd	2		750.2.l.a.257.1		80
25.6	even	5		150.2.l.a.17.9	yes	80
25.8	odd	20	inner	750.2.l.c.143.10		80
25.17	odd	20		750.2.l.a.143.1		80
25.19	even	10		750.2.l.b.107.2		80
75.8	even	20	inner	750.2.l.c.143.5		80
75.17	even	20		750.2.l.a.143.6		80
75.44	odd	10		750.2.l.b.107.8		80
75.56	odd	10		150.2.l.a.17.3	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.l.a.17.3	✓	80	75.56	odd	10
150.2.l.a.17.9	yes	80	25.6	even	5
150.2.l.a.53.3	yes	80	5.3	odd	4
150.2.l.a.53.9	yes	80	15.8	even	4
750.2.l.a.143.1		80	25.17	odd	20
750.2.l.a.143.6		80	75.17	even	20
750.2.l.a.257.1		80	15.14	odd	2
750.2.l.a.257.6		80	5.4	even	2
750.2.l.b.107.2		80	25.19	even	10
750.2.l.b.107.8		80	75.44	odd	10
750.2.l.b.743.2		80	15.2	even	4
750.2.l.b.743.8		80	5.2	odd	4
750.2.l.c.143.5		80	75.8	even	20	inner
750.2.l.c.143.10		80	25.8	odd	20	inner
750.2.l.c.257.5		80	1.1	even	1	trivial
750.2.l.c.257.10		80	3.2	odd	2	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)

\(f(q)\)	\(=\)	\(q+(-0.453990 - 0.891007i) q^{2} +(1.70181 + 0.322239i) q^{3} +(-0.587785 + 0.809017i) q^{4} +(-0.485490 - 1.66262i) q^{6} +(0.0556476 + 0.0556476i) q^{7} +(0.987688 + 0.156434i) q^{8} +(2.79232 + 1.09678i) q^{9} +O(q^{10})\)	\(q+(-0.453990 - 0.891007i) q^{2} +(1.70181 + 0.322239i) q^{3} +(-0.587785 + 0.809017i) q^{4} +(-0.485490 - 1.66262i) q^{6} +(0.0556476 + 0.0556476i) q^{7} +(0.987688 + 0.156434i) q^{8} +(2.79232 + 1.09678i) q^{9} +(-1.04749 - 0.340351i) q^{11} +(-1.26100 + 1.18739i) 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} +(-0.290452 - 2.98591i) q^{18} +(0.824223 + 1.13445i) q^{19} +(0.0767699 + 0.112634i) q^{21} +(0.172297 + 1.08784i) q^{22} +(2.22575 - 1.13408i) q^{23} +(1.63045 + 0.584493i) q^{24} -5.09632i q^{26} +(4.39859 + 2.76630i) 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} +(-1.67296 - 0.916756i) q^{33} +(2.98720 - 0.970601i) q^{34} +(-2.52860 + 1.61437i) q^{36} +(-4.70325 + 9.23065i) q^{37} +(0.636609 - 1.24942i) q^{38} +(6.98213 + 5.40069i) q^{39} +(3.55210 - 1.15415i) q^{41} +(0.0655044 - 0.119537i) 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} +(-0.219422 - 1.71810i) q^{48} -6.99381i q^{49} +(-1.83585 + 5.12113i) q^{51} +(-4.54086 + 2.31368i) q^{52} +(1.06206 + 6.70559i) q^{53} +(0.467880 - 5.17504i) q^{54} +(0.0462573 + 0.0636677i) q^{56} +(1.03711 + 2.19621i) 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} +(0.0943531 + 0.216419i) q^{63} +(0.951057 + 0.309017i) q^{64} +(-0.0573270 + 1.90682i) q^{66} +(-6.57696 - 1.04169i) q^{67} +(-2.22097 - 2.22097i) q^{68} +(4.15326 - 1.21276i) q^{69} +(-7.51096 + 10.3379i) q^{71} +(2.58637 + 1.52009i) q^{72} +(-0.602914 - 1.18329i) q^{73} +10.3598 q^{74} -1.40225 q^{76} +(-0.0393507 - 0.0772302i) q^{77} +(1.64223 - 8.67298i) q^{78} +(-5.85354 + 8.05671i) q^{79} +(6.59415 + 6.12512i) q^{81} +(-2.64098 - 2.64098i) q^{82} +(0.871279 + 0.137997i) q^{83} +(-0.136247 - 0.00409615i) q^{84} +(1.35257 + 0.439477i) q^{86} +(-8.31892 - 8.83463i) 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} +(14.9646 - 7.06668i) q^{93} +(-7.46957 - 10.2810i) q^{94} +(-1.43122 + 0.975505i) 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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