LMFDB - Embedded newform 1183.2.e.j.170.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1183,2,Mod(170,1183)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1183, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("1183.170");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1183 = 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1183.e (of order $3$, degree $2$, 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:	$9.44630255912$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			170.5
Character	$\chi$	$=$	1183.170
Dual form			1183.2.e.j.508.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.249993 + 0.433001i) q^{2} +(-0.424801 - 0.735776i) q^{3} +(0.875007 + 1.51556i) q^{4} +(0.521238 - 0.902810i) q^{5} +0.424789 q^{6} +(-2.40155 + 1.11021i) q^{7} -1.87496 q^{8} +(1.13909 - 1.97296i) q^{9} +O(q^{10})$	\(q+(-0.249993 + 0.433001i) q^{2} +(-0.424801 - 0.735776i) q^{3} +(0.875007 + 1.51556i) q^{4} +(0.521238 - 0.902810i) q^{5} +0.424789 q^{6} +(-2.40155 + 1.11021i) q^{7} -1.87496 q^{8} +(1.13909 - 1.97296i) q^{9} +(0.260612 + 0.451393i) q^{10} +(-1.98365 - 3.43579i) q^{11} +(0.743407 - 1.28762i) q^{12} +(0.119647 - 1.31742i) q^{14} -0.885688 q^{15} +(-1.28129 + 2.21925i) q^{16} +(0.0710177 + 0.123006i) q^{17} +(0.569529 + 0.986453i) q^{18} +(-2.75488 + 4.77160i) q^{19} +1.82435 q^{20} +(1.83705 + 1.29538i) q^{21} +1.98360 q^{22} +(-2.19549 + 3.80270i) q^{23} +(0.796483 + 1.37955i) q^{24} +(1.95662 + 3.38897i) q^{25} -4.48435 q^{27} +(-3.78396 - 2.66823i) q^{28} -8.39759 q^{29} +(0.221416 - 0.383504i) q^{30} +(1.42326 + 2.46516i) q^{31} +(-2.51558 - 4.35712i) q^{32} +(-1.68531 + 2.91905i) q^{33} -0.0710158 q^{34} +(-0.249465 + 2.74683i) q^{35} +3.98684 q^{36} +(-0.421593 + 0.730221i) q^{37} +(-1.37740 - 2.38574i) q^{38} +(-0.977298 + 1.69273i) q^{40} -12.0974 q^{41} +(-1.02015 + 0.471607i) q^{42} +4.82323 q^{43} +(3.47142 - 6.01267i) q^{44} +(-1.18747 - 2.05676i) q^{45} +(-1.09772 - 1.90130i) q^{46} +(-2.27824 + 3.94602i) q^{47} +2.17717 q^{48} +(4.53485 - 5.33246i) q^{49} -1.95657 q^{50} +(0.0603367 - 0.104506i) q^{51} +(0.139800 + 0.242141i) q^{53} +(1.12106 - 1.94173i) q^{54} -4.13582 q^{55} +(4.50280 - 2.08160i) q^{56} +4.68111 q^{57} +(2.09934 - 3.63617i) q^{58} +(-5.39075 - 9.33705i) q^{59} +(-0.774983 - 1.34231i) q^{60} +(2.93177 - 5.07797i) q^{61} -1.42322 q^{62} +(-0.545169 + 6.00279i) q^{63} -2.60963 q^{64} +(-0.842634 - 1.45949i) q^{66} +(2.57223 + 4.45524i) q^{67} +(-0.124282 + 0.215263i) q^{68} +3.73058 q^{69} +(-1.12701 - 0.794706i) q^{70} -3.69880 q^{71} +(-2.13574 + 3.69921i) q^{72} +(-3.30640 - 5.72686i) q^{73} +(-0.210791 - 0.365101i) q^{74} +(1.66235 - 2.87927i) q^{75} -9.64216 q^{76} +(8.57829 + 6.04892i) q^{77} +(-5.96135 + 10.3254i) q^{79} +(1.33571 + 2.31352i) q^{80} +(-1.51231 - 2.61940i) q^{81} +(3.02426 - 5.23818i) q^{82} -2.87321 q^{83} +(-0.355795 + 3.91762i) q^{84} +0.148068 q^{85} +(-1.20578 + 2.08846i) q^{86} +(3.56730 + 6.17875i) q^{87} +(3.71926 + 6.44195i) q^{88} +(0.873824 - 1.51351i) q^{89} +1.18744 q^{90} -7.68427 q^{92} +(1.20921 - 2.09440i) q^{93} +(-1.13909 - 1.97296i) q^{94} +(2.87190 + 4.97427i) q^{95} +(-2.13724 + 3.70181i) q^{96} +2.70291 q^{97} +(1.17528 + 3.29668i) q^{98} -9.03822 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 6 q^{3} - 8 q^{4} - 2 q^{9}+O(q^{10}) $ 24 * q - 6 * q^3 - 8 * q^4 - 2 * q^9	$ 24 q - 6 q^{3} - 8 q^{4} - 2 q^{9} - 24 q^{10} + 2 q^{12} + 8 q^{14} - 16 q^{16} - 34 q^{17} + 60 q^{22} - 6 q^{23} + 10 q^{25} + 24 q^{27} + 4 q^{29} - 22 q^{30} - 24 q^{35} - 52 q^{36} - 38 q^{38} - 2 q^{40} + 32 q^{42} + 44 q^{43} - 76 q^{48} + 12 q^{49} - 8 q^{51} - 16 q^{53} + 60 q^{55} + 54 q^{56} + 10 q^{61} + 164 q^{62} - 4 q^{64} - 68 q^{66} - 22 q^{68} + 28 q^{69} - 66 q^{74} - 2 q^{75} + 38 q^{77} - 70 q^{79} + 28 q^{81} - 10 q^{82} + 20 q^{87} + 28 q^{88} - 132 q^{92} + 2 q^{94} - 4 q^{95}+O(q^{100}) $ 24 * q - 6 * q^3 - 8 * q^4 - 2 * q^9 - 24 * q^10 + 2 * q^12 + 8 * q^14 - 16 * q^16 - 34 * q^17 + 60 * q^22 - 6 * q^23 + 10 * q^25 + 24 * q^27 + 4 * q^29 - 22 * q^30 - 24 * q^35 - 52 * q^36 - 38 * q^38 - 2 * q^40 + 32 * q^42 + 44 * q^43 - 76 * q^48 + 12 * q^49 - 8 * q^51 - 16 * q^53 + 60 * q^55 + 54 * q^56 + 10 * q^61 + 164 * q^62 - 4 * q^64 - 68 * q^66 - 22 * q^68 + 28 * q^69 - 66 * q^74 - 2 * q^75 + 38 * q^77 - 70 * q^79 + 28 * q^81 - 10 * q^82 + 20 * q^87 + 28 * q^88 - 132 * q^92 + 2 * q^94 - 4 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times$.

$n$	$339$	$1016$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.249993	+	0.433001i	−0.176772	+	0.306178i	−0.940773	−	0.339037i	$-0.889899\pi$
$2$	−0.249993	+	0.433001i	−0.176772	+	0.306178i	0.764001	+	0.645215i	$0.223232\pi$
$3$	−0.424801	−	0.735776i	−0.245259	−	0.424801i	0.716946	−	0.697129i	$-0.245540\pi$
$3$	−0.424801	−	0.735776i	−0.245259	−	0.424801i	−0.962204	+	0.272328i	$0.912206\pi$
$4$	0.875007	+	1.51556i	0.437503	+	0.757778i
$5$	0.521238	−	0.902810i	0.233105	−	0.403749i	−0.725616	−	0.688100i	$-0.758445\pi$
$5$	0.521238	−	0.902810i	0.233105	−	0.403749i	0.958720	+	0.284351i	$0.0917782\pi$
$6$	0.424789			0.173420
$7$	−2.40155	+	1.11021i	−0.907699	+	0.419621i
$7$	−2.40155	+	1.11021i	−0.907699	+	0.419621i
$8$	−1.87496			−0.662897
$9$	1.13909	−	1.97296i	0.379696	−	0.657653i
$10$	0.260612	+	0.451393i	0.0824127	+	0.142743i
$11$	−1.98365	−	3.43579i	−0.598094	−	1.03593i	−0.993102	−	0.117251i	$-0.962592\pi$
$11$	−1.98365	−	3.43579i	−0.598094	−	1.03593i	0.395009	−	0.918677i	$-0.370742\pi$
$12$	0.743407	−	1.28762i	0.214603	−	0.371703i
$13$		0			0
$13$		0			0
$14$	0.119647	−	1.31742i	0.0319770	−	0.352095i
$15$	−0.885688			−0.228684
$16$	−1.28129	+	2.21925i	−0.320322	+	0.554813i
$17$	0.0710177	+	0.123006i	0.0172243	+	0.0298334i	0.874509	−	0.485009i	$-0.161184\pi$
$17$	0.0710177	+	0.123006i	0.0172243	+	0.0298334i	−0.857285	+	0.514843i	$0.827850\pi$
$18$	0.569529	+	0.986453i	0.134239	+	0.232509i
$19$	−2.75488	+	4.77160i	−0.632014	+	1.09468i	0.355126	+	0.934818i	$0.384438\pi$
$19$	−2.75488	+	4.77160i	−0.632014	+	1.09468i	−0.987140	+	0.159861i	$0.948895\pi$
$20$	1.82435			0.407936
$21$	1.83705	+	1.29538i	0.400877	+	0.282676i
$22$	1.98360			0.422905
$23$	−2.19549	+	3.80270i	−0.457791	+	0.792917i	−0.998844	−	0.0480711i	$-0.984693\pi$
$23$	−2.19549	+	3.80270i	−0.457791	+	0.792917i	0.541053	+	0.840989i	$0.318026\pi$
$24$	0.796483	+	1.37955i	0.162581	+	0.281599i
$25$	1.95662	+	3.38897i	0.391325	+	0.677794i
$26$		0			0
$27$	−4.48435			−0.863013
$28$	−3.78396	−	2.66823i	−0.715101	−	0.504249i
$29$	−8.39759			−1.55939			−0.779697	−	0.626157i	$-0.784627\pi$
$29$	−8.39759			−1.55939			−0.779697	+	0.626157i	$0.784627\pi$
$30$	0.221416	−	0.383504i	0.0404249	−	0.0700179i
$31$	1.42326	+	2.46516i	0.255625	+	0.442756i	0.965065	−	0.262010i	$-0.0843853\pi$
$31$	1.42326	+	2.46516i	0.255625	+	0.442756i	−0.709440	+	0.704766i	$0.751052\pi$
$32$	−2.51558	−	4.35712i	−0.444696	−	0.770237i
$33$	−1.68531	+	2.91905i	−0.293376	+	0.508141i
$34$	−0.0710158			−0.0121791
$35$	−0.249465	+	2.74683i	−0.0421672	+	0.464298i
$36$	3.98684			0.664473
$37$	−0.421593	+	0.730221i	−0.0693095	+	0.120048i	−0.898598	−	0.438774i	$-0.855413\pi$
$37$	−0.421593	+	0.730221i	−0.0693095	+	0.120048i	0.829288	+	0.558821i	$0.188746\pi$
$38$	−1.37740	−	2.38574i	−0.223445	−	0.387017i
$39$		0			0
$40$	−0.977298	+	1.69273i	−0.154524	+	0.267644i
$41$	−12.0974			−1.88929			−0.944647	−	0.328089i	$-0.893595\pi$
$41$	−12.0974			−1.88929			−0.944647	+	0.328089i	$0.893595\pi$
$42$	−1.02015	+	0.471607i	−0.157413	+	0.0727705i
$43$	4.82323			0.735536			0.367768	−	0.929918i	$-0.380122\pi$
$43$	4.82323			0.735536			0.367768	+	0.929918i	$0.380122\pi$
$44$	3.47142	−	6.01267i	0.523336	−	0.906444i
$45$	−1.18747	−	2.05676i	−0.177018	−	0.306604i
$46$	−1.09772	−	1.90130i	−0.161849	−	0.280331i
$47$	−2.27824	+	3.94602i	−0.332315	+	0.575587i	−0.982965	−	0.183791i	$-0.941163\pi$
$47$	−2.27824	+	3.94602i	−0.332315	+	0.575587i	0.650650	+	0.759378i	$0.274496\pi$
$48$	2.17717			0.314247
$49$	4.53485	−	5.33246i	0.647836	−	0.761780i
$50$	−1.95657			−0.276701
$51$	0.0603367	−	0.104506i	0.00844883	−	0.0146338i
$52$		0			0
$53$	0.139800	+	0.242141i	0.0192030	+	0.0332606i	0.875467	−	0.483278i	$-0.160554\pi$
$53$	0.139800	+	0.242141i	0.0192030	+	0.0332606i	−0.856264	+	0.516538i	$0.827220\pi$
$54$	1.12106	−	1.94173i	0.152557	−	0.264236i
$55$	−4.13582			−0.557673
$56$	4.50280	−	2.08160i	0.601711	−	0.278166i
$57$	4.68111			0.620028
$58$	2.09934	−	3.63617i	0.275657	−	0.477452i
$59$	−5.39075	−	9.33705i	−0.701815	−	1.21558i	−0.967829	−	0.251611i	$-0.919040\pi$
$59$	−5.39075	−	9.33705i	−0.701815	−	1.21558i	0.266013	−	0.963969i	$-0.414294\pi$
$60$	−0.774983	−	1.34231i	−0.100050	−	0.173292i
$61$	2.93177	−	5.07797i	0.375374	−	0.650168i	−0.615009	−	0.788520i	$-0.710847\pi$
$61$	2.93177	−	5.07797i	0.375374	−	0.650168i	0.990383	+	0.138353i	$0.0441808\pi$
$62$	−1.42322			−0.180750
$63$	−0.545169	+	6.00279i	−0.0686848	+	0.756280i
$64$	−2.60963			−0.326204
$65$		0			0
$66$	−0.842634	−	1.45949i	−0.103721	−	0.179650i
$67$	2.57223	+	4.45524i	0.314248	+	0.544294i	0.979277	−	0.202523i	$-0.0649142\pi$
$67$	2.57223	+	4.45524i	0.314248	+	0.544294i	−0.665029	+	0.746818i	$0.731581\pi$
$68$	−0.124282	+	0.215263i	−0.0150714	+	0.0261044i
$69$	3.73058			0.449109
$70$	−1.12701	−	0.794706i	−0.134704	−	0.0949856i
$71$	−3.69880			−0.438967			−0.219484	−	0.975616i	$-0.570437\pi$
$71$	−3.69880			−0.438967			−0.219484	+	0.975616i	$0.570437\pi$
$72$	−2.13574	+	3.69921i	−0.251700	+	0.435956i
$73$	−3.30640	−	5.72686i	−0.386985	−	0.670278i	0.605057	−	0.796182i	$-0.293150\pi$
$73$	−3.30640	−	5.72686i	−0.386985	−	0.670278i	−0.992042	+	0.125904i	$0.959817\pi$
$74$	−0.210791	−	0.365101i	−0.0245040	−	0.0424421i
$75$	1.66235	−	2.87927i	0.191952	−	0.332470i
$76$	−9.64216			−1.10603
$77$	8.57829	+	6.04892i	0.977587	+	0.689339i
$78$		0			0
$79$	−5.96135	+	10.3254i	−0.670705	+	1.16169i	0.307000	+	0.951710i	$0.400675\pi$
$79$	−5.96135	+	10.3254i	−0.670705	+	1.16169i	−0.977705	+	0.209985i	$0.932658\pi$
$80$	1.33571	+	2.31352i	0.149337	+	0.258659i
$81$	−1.51231	−	2.61940i	−0.168035	−	0.291045i
$82$	3.02426	−	5.23818i	0.333974	−	0.578460i
$83$	−2.87321			−0.315376			−0.157688	−	0.987489i	$-0.550404\pi$
$83$	−2.87321			−0.315376			−0.157688	+	0.987489i	$0.550404\pi$
$84$	−0.355795	+	3.91762i	−0.0388204	+	0.427447i
$85$	0.148068			0.0160603
$86$	−1.20578	+	2.08846i	−0.130022	+	0.225205i
$87$	3.56730	+	6.17875i	0.382455	+	0.662432i
$88$	3.71926	+	6.44195i	0.396475	+	0.686714i
$89$	0.873824	−	1.51351i	0.0926252	−	0.160432i	−0.815990	−	0.578066i	$-0.803807\pi$
$89$	0.873824	−	1.51351i	0.0926252	−	0.160432i	0.908615	+	0.417635i	$0.137141\pi$
$90$	1.18744			0.125167
$91$		0			0
$92$	−7.68427			−0.801141
$93$	1.20921	−	2.09440i	0.125389	−	0.217180i
$94$	−1.13909	−	1.97296i	−0.117488	−	0.203495i
$95$	2.87190	+	4.97427i	0.294650	+	0.510350i
$96$	−2.13724	+	3.70181i	−0.218131	+	0.377815i
$97$	2.70291			0.274438			0.137219	−	0.990541i	$-0.456184\pi$
$97$	2.70291			0.274438			0.137219	+	0.990541i	$0.456184\pi$
$98$	1.17528	+	3.29668i	0.118721	+	0.333014i
$99$	−9.03822			−0.908376
$100$	−3.42412	+	5.93074i	−0.342412	+	0.593074i
$101$	−5.73612	−	9.93524i	−0.570765	−	0.988594i	−0.996488	−	0.0837401i	$-0.973313\pi$
$101$	−5.73612	−	9.93524i	−0.570765	−	0.988594i	0.425723	−	0.904854i	$-0.360020\pi$
$102$	0.0301676	+	0.0522517i	0.00298703	+	0.00517369i
$103$	−2.08475	+	3.61090i	−0.205417	+	0.355792i	−0.950265	−	0.311441i	$-0.899188\pi$
$103$	−2.08475	+	3.61090i	−0.205417	+	0.355792i	0.744849	+	0.667233i	$0.232522\pi$
$104$		0			0
$105$	2.12702	−	0.983303i	0.207576	−	0.0959606i
$106$	−0.139796			−0.0135782
$107$	−4.24371	+	7.35032i	−0.410255	+	0.710583i	−0.994917	−	0.100694i	$-0.967894\pi$
$107$	−4.24371	+	7.35032i	−0.410255	+	0.710583i	0.584662	+	0.811277i	$0.301227\pi$
$108$	−3.92383	−	6.79628i	−0.377571	−	0.653972i
$109$	3.21518	+	5.56886i	0.307958	+	0.533400i	0.977916	−	0.209000i	$-0.0670209\pi$
$109$	3.21518	+	5.56886i	0.307958	+	0.533400i	−0.669957	+	0.742400i	$0.733688\pi$
$110$	1.03393	−	1.79081i	0.0985810	−	0.170747i
$111$	0.716373			0.0679951
$112$	0.613225	−	6.75214i	0.0579443	−	0.638018i
$113$	10.9633			1.03134			0.515670	−	0.856788i	$-0.327543\pi$
$113$	10.9633			1.03134			0.515670	+	0.856788i	$0.327543\pi$
$114$	−1.17025	+	2.02692i	−0.109603	+	0.189839i
$115$	2.28874	+	3.96422i	0.213426	+	0.369665i
$116$	−7.34795	−	12.7270i	−0.682240	−	1.18167i
$117$		0			0
$118$	5.39060			0.496245
$119$	−0.307115	−	0.216560i	−0.0281532	−	0.0198521i
$120$	1.66063			0.151594
$121$	−2.36975	+	4.10453i	−0.215432	+	0.373139i
$122$	1.46584	+	2.53892i	0.132711	+	0.229863i
$123$	5.13898	+	8.90097i	0.463366	+	0.802573i
$124$	−2.49073	+	4.31406i	−0.223674	+	0.387414i
$125$	9.29184			0.831087
$126$	−2.46292	−	1.73671i	−0.219415	−	0.154719i
$127$	−2.00787			−0.178170			−0.0890849	−	0.996024i	$-0.528394\pi$
$127$	−2.00787			−0.178170			−0.0890849	+	0.996024i	$0.528394\pi$
$128$	5.68356	−	9.84421i	0.502360	−	0.870113i
$129$	−2.04891	−	3.54882i	−0.180397	−	0.312456i
$130$		0			0
$131$	6.22511	−	10.7822i	0.543890	−	0.942046i	−0.454785	−	0.890601i	$-0.650284\pi$
$131$	6.22511	−	10.7822i	0.543890	−	0.942046i	0.998676	−	0.0514449i	$-0.0163826\pi$
$132$	−5.89864			−0.513411
$133$	1.31849	−	14.5177i	0.114328	−	1.25885i
$134$	−2.57217			−0.222201
$135$	−2.33741	+	4.04851i	−0.201172	+	0.348441i
$136$	−0.133155	−	0.230631i	−0.0114180	−	0.0197765i
$137$	−2.62259	−	4.54246i	−0.224063	−	0.388088i	0.731975	−	0.681332i	$-0.238599\pi$
$137$	−2.62259	−	4.54246i	−0.224063	−	0.388088i	−0.956038	+	0.293243i	$0.905265\pi$
$138$	−0.932620	+	1.61535i	−0.0793899	+	0.137507i
$139$	−20.7385			−1.75902			−0.879510	−	0.475881i	$-0.842129\pi$
$139$	−20.7385			−1.75902			−0.879510	+	0.475881i	$0.842129\pi$
$140$	−4.38125	+	2.02541i	−0.370283	+	0.171179i
$141$	3.87119			0.326013
$142$	0.924676	−	1.60159i	0.0775971	−	0.134402i
$143$		0			0
$144$	2.91900	+	5.05585i	0.243250	+	0.421321i
$145$	−4.37714	+	7.58143i	−0.363502	+	0.629604i
$146$	3.30631			0.273633
$147$	−5.84991	−	1.07141i	−0.482492	−	0.0883681i
$148$	−1.47559			−0.121293
$149$	0.00568799	−	0.00985188i	0.000465978	−	0.000807098i	−0.865792	−	0.500403i	$-0.833185\pi$
$149$	0.00568799	−	0.00985188i	0.000465978	−	0.000807098i	0.866258	+	0.499596i	$0.166518\pi$
$150$	0.831153	+	1.43960i	0.0678633	+	0.117543i
$151$	9.45271	+	16.3726i	0.769251	+	1.33238i	0.937970	+	0.346717i	$0.112704\pi$
$151$	9.45271	+	16.3726i	0.769251	+	1.33238i	−0.168719	+	0.985664i	$0.553963\pi$
$152$	5.16529	−	8.94654i	0.418960	−	0.725660i
$153$	0.323582			0.0261600
$154$	−4.76371	+	2.20222i	−0.383870	+	0.177460i
$155$	2.96743			0.238350
$156$		0			0
$157$	−9.89687	−	17.1419i	−0.789856	−	1.36807i	−0.926054	−	0.377390i	$-0.876822\pi$
$157$	−9.89687	−	17.1419i	−0.789856	−	1.36807i	0.136198	−	0.990682i	$-0.456512\pi$
$158$	−2.98060	−	5.16255i	−0.237124	−	0.410710i
$159$	0.118774	−	0.205723i	0.00941942	−	0.0163149i
$160$	−5.24486			−0.414643
$161$	1.05076	−	11.5698i	0.0828117	−	0.911830i
$162$	1.51227			0.118815
$163$	−4.46627	+	7.73581i	−0.349825	+	0.605915i	−0.986218	−	0.165450i	$-0.947092\pi$
$163$	−4.46627	+	7.73581i	−0.349825	+	0.605915i	0.636393	+	0.771365i	$0.280426\pi$
$164$	−10.5853	−	18.3343i	−0.826572	−	1.43167i
$165$	1.75690	+	3.04304i	0.136774	+	0.236900i
$166$	0.718284	−	1.24410i	0.0557496	−	0.0965612i
$167$	6.13469			0.474716			0.237358	−	0.971422i	$-0.423719\pi$
$167$	6.13469			0.474716			0.237358	+	0.971422i	$0.423719\pi$
$168$	−3.44438	−	2.42879i	−0.265740	−	0.187385i
$169$		0			0
$170$	−0.0370161	+	0.0641138i	−0.00283900	+	0.00491730i
$171$	6.27611	+	10.8705i	0.479946	+	0.831291i
$172$	4.22036	+	7.30987i	0.321799	+	0.557373i
$173$	−12.1314	+	21.0122i	−0.922332	+	1.59753i	−0.126535	+	0.991962i	$0.540386\pi$
$173$	−12.1314	+	21.0122i	−0.922332	+	1.59753i	−0.795797	+	0.605563i	$0.792948\pi$
$174$	−3.56721			−0.270429
$175$	−8.46140	−	5.96650i	−0.639622	−	0.451025i
$176$	10.1665			0.766330
$177$	−4.57999	+	7.93277i	−0.344253	+	0.596263i
$178$	0.436901	+	0.756734i	0.0327471	+	0.0567196i
$179$	2.06838	+	3.58253i	0.154598	+	0.267771i	0.932912	−	0.360103i	$-0.117259\pi$
$179$	2.06838	+	3.58253i	0.154598	+	0.267771i	−0.778315	+	0.627874i	$0.783925\pi$
$180$	2.07809	−	3.59936i	0.154892	−	0.268280i
$181$	7.86568			0.584651			0.292326	−	0.956319i	$-0.405571\pi$
$181$	7.86568			0.584651			0.292326	+	0.956319i	$0.405571\pi$
$182$		0			0
$183$	−4.98167			−0.368256
$184$	4.11645	−	7.12989i	0.303468	−	0.525623i
$185$	0.439501	+	0.761237i	0.0323127	+	0.0559673i
$186$	0.604586	+	1.04717i	0.0443304	+	0.0767825i
$187$	0.281749	−	0.488003i	0.0206035	−	0.0356863i
$188$	−7.97389			−0.581556
$189$	10.7694	−	4.97858i	0.783356	−	0.362139i
$190$	−2.87182			−0.208344
$191$	3.23933	−	5.61069i	0.234390	−	0.405975i	−0.724705	−	0.689059i	$-0.758024\pi$
$191$	3.23933	−	5.61069i	0.234390	−	0.405975i	0.959095	+	0.283084i	$0.0913574\pi$
$192$	1.10857	+	1.92011i	0.0800044	+	0.138572i
$193$	2.41464	+	4.18228i	0.173810	+	0.301047i	0.939749	−	0.341866i	$-0.111059\pi$
$193$	2.41464	+	4.18228i	0.173810	+	0.301047i	−0.765939	+	0.642913i	$0.777726\pi$
$194$	−0.675708	+	1.17036i	−0.0485130	+	0.0840270i
$195$		0			0
$196$	12.0497	+	2.20689i	0.860690	+	0.157635i
$197$	25.8362			1.84075			0.920377	−	0.391032i	$-0.127882\pi$
$197$	25.8362			1.84075			0.920377	+	0.391032i	$0.127882\pi$
$198$	2.25950	−	3.91356i	0.160575	−	0.278125i
$199$	−8.55731	−	14.8217i	−0.606612	−	1.05068i	−0.991795	−	0.127842i	$-0.959195\pi$
$199$	−8.55731	−	14.8217i	−0.606612	−	1.05068i	0.385183	−	0.922840i	$-0.374138\pi$
$200$	−3.66858	−	6.35417i	−0.259408	−	0.449308i
$201$	2.18537	−	3.78518i	0.154144	−	0.266986i
$202$	5.73596			0.403581
$203$	20.1672	−	9.32312i	1.41546	−	0.654355i
$204$	0.211180			0.0147856
$205$	−6.30561	+	10.9216i	−0.440403	+	0.762800i
$206$	−1.04235	−	1.80540i	−0.0726238	−	0.125788i
$207$	5.00171	+	8.66322i	0.347643	+	0.602136i
$208$		0			0
$209$	21.8589			1.51201
$210$	−0.105970	+	1.16682i	−0.00731262	+	0.0805184i
$211$	18.2911			1.25921			0.629607	−	0.776914i	$-0.283216\pi$
$211$	18.2911			1.25921			0.629607	+	0.776914i	$0.283216\pi$
$212$	−0.244652	+	0.423750i	−0.0168028	+	0.0291032i
$213$	1.57125	+	2.72149i	0.107661	+	0.186474i
$214$	−2.12180	−	3.67506i	−0.145043	−	0.251222i
$215$	2.51405	−	4.35446i	0.171457	−	0.296972i
$216$	8.40796			0.572089
$217$	−6.15488	−	4.34008i	−0.417821	−	0.294624i
$218$	−3.21509			−0.217754
$219$	−2.80912	+	4.86555i	−0.189823	+	0.328783i
$220$	−3.61887	−	6.26806i	−0.243984	−	0.422593i
$221$		0			0
$222$	−0.179088	+	0.310190i	−0.0120196	+	0.0208186i
$223$	11.5087			0.770679			0.385340	−	0.922775i	$-0.374084\pi$
$223$	11.5087			0.770679			0.385340	+	0.922775i	$0.374084\pi$
$224$	10.8786	+	7.67099i	0.726858	+	0.512539i
$225$	8.91507			0.594338
$226$	−2.74075	+	4.74711i	−0.182312	+	0.315773i
$227$	8.95223	+	15.5057i	0.594181	+	1.02915i	0.993662	+	0.112410i	$0.0358569\pi$
$227$	8.95223	+	15.5057i	0.594181	+	1.02915i	−0.399481	+	0.916741i	$0.630810\pi$
$228$	4.09600	+	7.09448i	0.271264	+	0.469843i
$229$	−1.93175	+	3.34589i	−0.127654	+	0.221103i	−0.922767	−	0.385358i	$-0.874078\pi$
$229$	−1.93175	+	3.34589i	−0.127654	+	0.221103i	0.795113	+	0.606461i	$0.207411\pi$
$230$	−2.28868			−0.150911
$231$	0.806593	−	8.88129i	0.0530699	−	0.584346i
$232$	15.7451			1.03372
$233$	−12.5321	+	21.7062i	−0.821004	+	1.42202i	0.0839312	+	0.996472i	$0.473252\pi$
$233$	−12.5321	+	21.7062i	−0.821004	+	1.42202i	−0.904935	+	0.425549i	$0.860081\pi$
$234$		0			0
$235$	2.37501	+	4.11363i	0.154928	+	0.268344i
$236$	9.43388	−	16.3400i	0.614093	−	1.06364i
$237$	10.1295			0.657985
$238$	0.170548	−	0.0788427i	0.0110550	−	0.00511061i
$239$	−7.80462			−0.504839			−0.252419	−	0.967618i	$-0.581226\pi$
$239$	−7.80462			−0.504839			−0.252419	+	0.967618i	$0.581226\pi$
$240$	1.13482	−	1.96557i	0.0732524	−	0.126877i
$241$	−10.8826	−	18.8493i	−0.701012	−	1.21419i	−0.968112	−	0.250519i	$-0.919399\pi$
$241$	−10.8826	−	18.8493i	−0.701012	−	1.21419i	0.267100	−	0.963669i	$-0.413935\pi$
$242$	−1.18484	−	2.05221i	−0.0761647	−	0.131921i
$243$	−8.01138	+	13.8761i	−0.513930	+	0.890154i
$244$	10.2613			0.656910
$245$	−2.45046	−	6.87359i	−0.156554	−	0.439137i
$246$	−5.13884			−0.327640
$247$		0			0
$248$	−2.66855	−	4.62207i	−0.169453	−	0.293502i
$249$	1.22054	+	2.11404i	0.0773488	+	0.133972i
$250$	−2.32290	+	4.02338i	−0.146913	+	0.254461i
$251$	7.67980			0.484745			0.242372	−	0.970183i	$-0.422074\pi$
$251$	7.67980			0.484745			0.242372	+	0.970183i	$0.422074\pi$
$252$	−9.57458	+	4.42624i	−0.603142	+	0.278827i
$253$	17.4203			1.09521
$254$	0.501955	−	0.869411i	0.0314954	−	0.0545517i
$255$	−0.0628995	−	0.108945i	−0.00393892	−	0.00682241i
$256$	0.232070	+	0.401958i	0.0145044	+	0.0251224i
$257$	−6.81187	+	11.7985i	−0.424913	+	0.735971i	−0.996412	−	0.0846316i	$-0.973029\pi$
$257$	−6.81187	+	11.7985i	−0.424913	+	0.735971i	0.571499	+	0.820603i	$0.306362\pi$
$258$	2.04886			0.127556
$259$	0.201775	−	2.22172i	0.0125377	−	0.138051i
$260$		0			0
$261$	−9.56560	+	16.5681i	−0.592096	+	1.02554i
$262$	3.11247	+	5.39096i	0.192289	+	0.333055i
$263$	5.86158	+	10.1525i	0.361440	+	0.626033i	0.988198	−	0.153181i	$-0.0489518\pi$
$263$	5.86158	+	10.1525i	0.361440	+	0.626033i	−0.626758	+	0.779214i	$0.715618\pi$
$264$	3.15989	−	5.47309i	0.194478	−	0.336845i
$265$	0.291476			0.0179052
$266$	5.95658	+	4.20024i	0.365221	+	0.257533i
$267$	−1.48481			−0.0908686
$268$	−4.50144	+	7.79673i	−0.274970	+	0.476261i
$269$	−4.59938	−	7.96636i	−0.280429	−	0.485717i	0.691061	−	0.722796i	$-0.257143\pi$
$269$	−4.59938	−	7.96636i	−0.280429	−	0.485717i	−0.971490	+	0.237079i	$0.923810\pi$
$270$	−1.16867	−	2.02420i	−0.0711232	−	0.123189i
$271$	1.28184	−	2.22022i	0.0778665	−	0.134869i	−0.824463	−	0.565916i	$-0.808523\pi$
$271$	1.28184	−	2.22022i	0.0778665	−	0.134869i	0.902329	+	0.431048i	$0.141856\pi$
$272$	−0.363976			−0.0220693
$273$		0			0
$274$	2.62252			0.158432
$275$	7.76252	−	13.4451i	0.468097	−	0.810769i
$276$	3.26428	+	5.65391i	0.196487	+	0.340325i
$277$	0.466941	+	0.808765i	0.0280558	+	0.0485940i	0.879712	−	0.475506i	$-0.157735\pi$
$277$	0.466941	+	0.808765i	0.0280558	+	0.0485940i	−0.851657	+	0.524100i	$0.824402\pi$
$278$	5.18450	−	8.97981i	0.310945	−	0.538573i
$279$	6.48488			0.388240
$280$	0.467736	−	5.15018i	0.0279525	−	0.307782i
$281$	6.45288			0.384947			0.192473	−	0.981302i	$-0.438349\pi$
$281$	6.45288			0.384947			0.192473	+	0.981302i	$0.438349\pi$
$282$	−0.967771	+	1.67623i	−0.0576299	+	0.0998180i
$283$	−11.0873	−	19.2037i	−0.659071	−	1.14154i	−0.980857	−	0.194731i	$-0.937616\pi$
$283$	−11.0873	−	19.2037i	−0.659071	−	1.14154i	0.321786	−	0.946812i	$-0.395717\pi$
$284$	−3.23648	−	5.60575i	−0.192050	−	0.332640i
$285$	2.43997	−	4.22615i	0.144531	−	0.250335i
$286$		0			0
$287$	29.0524	−	13.4307i	1.71491	−	0.792788i
$288$	−11.4619			−0.675398
$289$	8.48991	−	14.7050i	0.499407	−	0.864998i
$290$	−2.18851	−	3.79061i	−0.128514	−	0.222593i
$291$	−1.14820	−	1.98873i	−0.0673085	−	0.116582i
$292$	5.78625	−	10.0221i	0.338615	−	0.586498i
$293$	24.2026			1.41393			0.706964	−	0.707249i	$-0.250064\pi$
$293$	24.2026			1.41393			0.706964	+	0.707249i	$0.250064\pi$
$294$	1.92636	−	2.26517i	0.112347	−	0.132107i
$295$	−11.2394			−0.654385
$296$	0.790469	−	1.36913i	0.0459451	−	0.0795792i
$297$	8.89539	+	15.4073i	0.516163	+	0.894020i
$298$	0.00284392	+	0.00492581i	0.000164744	+	0.000285345i
$299$		0			0
$300$	5.81827			0.335918
$301$	−11.5832	+	5.35481i	−0.667645	+	0.308646i
$302$	−9.45246			−0.543928
$303$	−4.87341	+	8.44100i	−0.279970	+	0.484923i
$304$	−7.05959	−	12.2276i	−0.404895	−	0.701299i
$305$	−3.05630	−	5.29366i	−0.175003	−	0.303114i
$306$	−0.0808933	+	0.140111i	−0.00462436	+	0.00800963i
$307$	24.2924			1.38644			0.693220	−	0.720726i	$-0.256191\pi$
$307$	24.2924			1.38644			0.693220	+	0.720726i	$0.256191\pi$
$308$	−1.66142	+	18.2937i	−0.0946684	+	1.04238i
$309$	3.54242			0.201521
$310$	−0.741837	+	1.28490i	−0.0421335	+	0.0729774i
$311$	−1.99355	−	3.45294i	−0.113044	−	0.195798i	0.803952	−	0.594694i	$-0.202727\pi$
$311$	−1.99355	−	3.45294i	−0.113044	−	0.195798i	−0.916996	+	0.398896i	$0.869393\pi$
$312$		0			0
$313$	−14.2377	+	24.6604i	−0.804763	+	1.39389i	0.111688	+	0.993743i	$0.464374\pi$
$313$	−14.2377	+	24.6604i	−0.804763	+	1.39389i	−0.916451	+	0.400147i	$0.868959\pi$
$314$	9.89661			0.558498
$315$	5.13521	+	3.62106i	0.289336	+	0.204024i
$316$	−20.8649			−1.17374
$317$	8.40806	−	14.5632i	0.472244	−	0.817950i	−0.527252	−	0.849709i	$-0.676778\pi$
$317$	8.40806	−	14.5632i	0.472244	−	0.817950i	0.999496	+	0.0317591i	$0.0101109\pi$
$318$	0.0593856	+	0.102859i	0.00333018	+	0.00576804i
$319$	16.6579	+	28.8523i	0.932664	+	1.61542i
$320$	−1.36024	+	2.35600i	−0.0760396	+	0.131704i
$321$	7.21093			0.402475
$322$	4.74706	+	3.34736i	0.264543	+	0.186541i
$323$	−0.782582			−0.0435440
$324$	2.64657	−	4.58399i	0.147031	−	0.254666i
$325$		0			0
$326$	−2.23308	−	3.86780i	−0.123679	−	0.214218i
$327$	2.73162	−	4.73131i	0.151059	−	0.261642i
$328$	22.6821			1.25241
$329$	1.09037	−	12.0059i	0.0601139	−	0.661906i
$330$	−1.75685			−0.0967115
$331$	3.10459	−	5.37730i	0.170644	−	0.295563i	−0.768002	−	0.640448i	$-0.778749\pi$
$331$	3.10459	−	5.37730i	0.170644	−	0.295563i	0.938645	+	0.344885i	$0.112082\pi$
$332$	−2.51408	−	4.35451i	−0.137978	−	0.238985i
$333$	0.960464	+	1.66357i	0.0526331	+	0.0911632i
$334$	−1.53363	+	2.65633i	−0.0839165	+	0.145348i
$335$	5.36298			0.293011
$336$	−5.22857	+	2.41712i	−0.285242	+	0.131865i
$337$	−7.69650			−0.419255			−0.209628	−	0.977781i	$-0.567225\pi$
$337$	−7.69650			−0.419255			−0.209628	+	0.977781i	$0.567225\pi$
$338$		0			0
$339$	−4.65721	−	8.06653i	−0.252945	−	0.438114i
$340$	0.129561	+	0.224406i	0.00702642	+	0.0121701i
$341$	5.64651	−	9.78005i	0.305776	−	0.529619i
$342$	−6.27594			−0.339364
$343$	−4.97049	+	17.8408i	−0.268381	+	0.963313i
$344$	−9.04335			−0.487585
$345$	1.94452	−	3.36801i	0.104689	−	0.181327i
$346$	−6.06553	−	10.5058i	−0.326085	−	0.564795i
$347$	−15.2047	−	26.3353i	−0.816231	−	1.41375i	−0.908440	−	0.418015i	$-0.862726\pi$
$347$	−15.2047	−	26.3353i	−0.816231	−	1.41375i	0.0922088	−	0.995740i	$-0.470607\pi$
$348$	−6.24283	+	10.8129i	−0.334651	+	0.579632i
$349$	−16.1581			−0.864924			−0.432462	−	0.901652i	$-0.642355\pi$
$349$	−16.1581			−0.864924			−0.432462	+	0.901652i	$0.642355\pi$
$350$	4.69880	−	2.17221i	0.251161	−	0.116110i
$351$		0			0
$352$	−9.98008	+	17.2860i	−0.531940	+	0.921347i
$353$	5.92119	+	10.2558i	0.315153	+	0.545861i	0.979470	−	0.201590i	$-0.0646108\pi$
$353$	5.92119	+	10.2558i	0.315153	+	0.545861i	−0.664317	+	0.747451i	$0.731277\pi$
$354$	−2.28993	−	3.96628i	−0.121709	−	0.210805i
$355$	−1.92796	+	3.33932i	−0.102325	+	0.177233i
$356$	3.05841			0.162095
$357$	−0.0288772	+	0.317963i	−0.00152834	+	0.0168284i
$358$	−2.06832			−0.109314
$359$	−15.6826	+	27.1631i	−0.827698	+	1.43362i	0.0721417	+	0.997394i	$0.477017\pi$
$359$	−15.6826	+	27.1631i	−0.827698	+	1.43362i	−0.899840	+	0.436221i	$0.856317\pi$
$360$	2.22646	+	3.85634i	0.117345	+	0.203247i
$361$	−5.67876	−	9.83591i	−0.298882	−	0.517679i
$362$	−1.96637	+	3.40585i	−0.103350	+	0.179007i
$363$	4.02669			0.211346
$364$		0			0
$365$	−6.89369			−0.360832
$366$	1.24538	−	2.15707i	0.0650973	−	0.112752i
$367$	−12.0387	−	20.8517i	−0.628415	−	1.08845i	−0.987870	−	0.155285i	$-0.950370\pi$
$367$	−12.0387	−	20.8517i	−0.628415	−	1.08845i	0.359454	−	0.933163i	$-0.382963\pi$
$368$	−5.62610	−	9.74470i	−0.293281	−	0.507977i
$369$	−13.7800	+	23.8676i	−0.717358	+	1.24250i
$370$	−0.439489			−0.0228479
$371$	−0.604564	−	0.426305i	−0.0313874	−	0.0221326i
$372$	4.23225			0.219432
$373$	9.19612	−	15.9281i	0.476157	−	0.824728i	−0.523470	−	0.852044i	$-0.675363\pi$
$373$	9.19612	−	15.9281i	0.476157	−	0.824728i	0.999627	+	0.0273160i	$0.00869604\pi$
$374$	0.140871	+	0.243995i	0.00728425	+	0.0126167i
$375$	−3.94718	−	6.83672i	−0.203831	−	0.353046i
$376$	4.27160	−	7.39862i	0.220291	−	0.381555i
$377$		0			0
$378$	−0.536539	+	5.90776i	−0.0275966	+	0.303862i
$379$	8.13740			0.417990			0.208995	−	0.977917i	$-0.432981\pi$
$379$	8.13740			0.417990			0.208995	+	0.977917i	$0.432981\pi$
$380$	−5.02586	+	8.70504i	−0.257821	+	0.446559i
$381$	0.852946	+	1.47735i	0.0436977	+	0.0756867i
$382$	1.61962	+	2.80527i	0.0828671	+	0.143530i
$383$	−11.1856	+	19.3739i	−0.571555	+	0.989962i	0.424852	+	0.905263i	$0.360326\pi$
$383$	−11.1856	+	19.3739i	−0.571555	+	0.989962i	−0.996407	+	0.0846992i	$0.973007\pi$
$384$	−9.65752			−0.492833
$385$	9.93236	−	4.59164i	0.506200	−	0.234012i
$386$	−2.41458			−0.122899
$387$	5.49409	−	9.51604i	0.279280	−	0.483727i
$388$	2.36506	+	4.09641i	0.120068	+	0.207963i
$389$	10.6973	+	18.5283i	0.542374	+	0.939420i	0.998767	+	0.0496415i	$0.0158079\pi$
$389$	10.6973	+	18.5283i	0.542374	+	0.939420i	−0.456393	+	0.889778i	$0.650859\pi$
$390$		0			0
$391$	−0.623674			−0.0315406
$392$	−8.50265	+	9.99813i	−0.429449	+	0.504982i
$393$	−10.5777			−0.533576
$394$	−6.45888	+	11.1871i	−0.325394	+	0.563599i
$395$	6.21456	+	10.7639i	0.312689	+	0.541592i
$396$	−7.90851	−	13.6979i	−0.397417	−	0.688347i
$397$	−0.598365	+	1.03640i	−0.0300311	+	0.0520154i	−0.880650	−	0.473767i	$-0.842894\pi$
$397$	−0.598365	+	1.03640i	−0.0300311	+	0.0520154i	0.850619	+	0.525782i	$0.176227\pi$
$398$	8.55708			0.428928
$399$	−11.2419	+	5.19703i	−0.562799	+	0.260177i
$400$	−10.0280			−0.501399
$401$	18.1375	−	31.4150i	0.905741	−	1.56879i	0.0858220	−	0.996310i	$-0.472648\pi$
$401$	18.1375	−	31.4150i	0.905741	−	1.56879i	0.819919	−	0.572479i	$-0.194018\pi$
$402$	1.09266	+	1.89254i	0.0544968	+	0.0943913i
$403$		0			0
$404$	10.0383	−	17.3868i	0.499423	−	0.865026i
$405$	−3.15309			−0.156679
$406$	−1.00475	+	11.0631i	−0.0498647	+	0.549055i
$407$	3.34518			0.165814
$408$	−0.113129	+	0.195945i	−0.00560071	+	0.00970071i
$409$	−7.33616	−	12.7066i	−0.362750	−	0.628301i	0.625662	−	0.780094i	$-0.284829\pi$
$409$	−7.33616	−	12.7066i	−0.362750	−	0.628301i	−0.988412	+	0.151793i	$0.951495\pi$
$410$	−3.15272	−	5.46067i	−0.155702	−	0.269683i
$411$	−2.22816	+	3.85928i	−0.109907	+	0.190364i
$412$	−7.29669			−0.359482
$413$	23.3122	+	16.4385i	1.14712	+	0.808884i
$414$	−5.00158			−0.245814
$415$	−1.49763	+	2.59397i	−0.0735156	+	0.127333i
$416$		0			0
$417$	8.80975	+	15.2589i	0.431415	+	0.747233i
$418$	−5.46458	+	9.46494i	−0.267282	+	0.462945i
$419$	−5.93348			−0.289870			−0.144935	−	0.989441i	$-0.546297\pi$
$419$	−5.93348			−0.289870			−0.144935	+	0.989441i	$0.546297\pi$
$420$	3.35141	+	2.36322i	0.163532	+	0.115314i
$421$	2.63174			0.128263			0.0641317	−	0.997941i	$-0.479572\pi$
$421$	2.63174			0.128263			0.0641317	+	0.997941i	$0.479572\pi$
$422$	−4.57266	+	7.92008i	−0.222594	+	0.385544i
$423$	5.19023	+	8.98974i	0.252358	+	0.437096i
$424$	−0.262119	−	0.454004i	−0.0127296	−	0.0220484i
$425$	−0.277910	+	0.481354i	−0.0134806	+	0.0233491i
$426$	−1.57121			−0.0761255
$427$	−1.40315	+	15.4499i	−0.0679030	+	0.747672i
$428$	−14.8531			−0.717952
$429$		0			0
$430$	1.25699	+	2.17717i	0.0606175	+	0.104993i
$431$	−9.41883	−	16.3139i	−0.453689	−	0.785812i	0.544923	−	0.838486i	$-0.316559\pi$
$431$	−9.41883	−	16.3139i	−0.453689	−	0.785812i	−0.998612	+	0.0526738i	$0.983226\pi$
$432$	5.74573	−	9.95190i	0.276442	−	0.478811i
$433$	19.1355			0.919591			0.459796	−	0.888025i	$-0.347923\pi$
$433$	19.1355			0.919591			0.459796	+	0.888025i	$0.347923\pi$
$434$	3.41794	−	1.58008i	0.164066	−	0.0758463i
$435$	7.43765			0.356608
$436$	−5.62661	+	9.74557i	−0.269466	+	0.466728i
$437$	−12.0966	−	20.9520i	−0.578660	−	1.00227i
$438$	−1.40452	−	2.43271i	−0.0671108	−	0.116239i
$439$	0.632554	−	1.09561i	0.0301901	−	0.0522908i	−0.850536	−	0.525918i	$-0.823722\pi$
$439$	0.632554	−	1.09561i	0.0301901	−	0.0522908i	0.880726	+	0.473627i	$0.157055\pi$
$440$	7.75448			0.369680
$441$	−5.35512	−	15.0212i	−0.255006	−	0.715296i
$442$		0			0
$443$	10.4696	−	18.1339i	0.497426	−	0.861568i	−0.502569	−	0.864537i	$-0.667612\pi$
$443$	10.4696	−	18.1339i	0.497426	−	0.861568i	0.999996	+	0.00296930i	$0.000945159\pi$
$444$	0.626831	+	1.08570i	0.0297481	+	0.0515252i
$445$	−0.910940	−	1.57779i	−0.0431827	−	0.0747946i
$446$	−2.87710	+	4.98328i	−0.136234	+	0.235965i
$447$	−0.00966505			−0.000457141
$448$	6.26715	−	2.89725i	0.296095	−	0.136882i
$449$	−17.8632			−0.843018			−0.421509	−	0.906824i	$-0.638499\pi$
$449$	−17.8632			−0.843018			−0.421509	+	0.906824i	$0.638499\pi$
$450$	−2.22871	+	3.86023i	−0.105062	+	0.181973i
$451$	23.9970	+	41.5640i	1.12997	+	1.95717i
$452$	9.59295	+	16.6155i	0.451214	+	0.781526i
$453$	8.03104	−	13.9102i	0.377331	−	0.653557i
$454$	−8.95199			−0.420138
$455$		0			0
$456$	−8.77687			−0.411015
$457$	3.28298	−	5.68629i	0.153571	−	0.265994i	−0.778966	−	0.627066i	$-0.784256\pi$
$457$	3.28298	−	5.68629i	0.153571	−	0.265994i	0.932538	+	0.361072i	$0.117589\pi$
$458$	−0.965850	−	1.67290i	−0.0451312	−	0.0781695i
$459$	−0.318468	−	0.551603i	−0.0148648	−	0.0257466i
$460$	−4.00533	+	6.93744i	−0.186749	+	0.323460i
$461$	−5.11364			−0.238166			−0.119083	−	0.992884i	$-0.537995\pi$
$461$	−5.11364			−0.238166			−0.119083	+	0.992884i	$0.537995\pi$
$462$	3.64397	+	2.56952i	0.169533	+	0.119545i
$463$	−33.3239			−1.54869			−0.774347	−	0.632761i	$-0.781921\pi$
$463$	−33.3239			−1.54869			−0.774347	+	0.632761i	$0.781921\pi$
$464$	10.7597	−	18.6364i	0.499508	−	0.865173i
$465$	−1.26057	−	2.18336i	−0.0584574	−	0.101251i
$466$	−6.26587	−	10.8528i	−0.290261	−	0.502747i
$467$	6.47472	−	11.2145i	0.299614	−	0.518947i	−0.676433	−	0.736504i	$-0.736475\pi$
$467$	6.47472	−	11.2145i	0.299614	−	0.518947i	0.976048	+	0.217557i	$0.0698087\pi$
$468$		0			0
$469$	−11.1236	−	7.84374i	−0.513641	−	0.362190i
$470$	−2.37494			−0.109548
$471$	−8.40840	+	14.5638i	−0.387439	+	0.671063i
$472$	10.1074	+	17.5066i	0.465231	+	0.805805i
$473$	−9.56761	−	16.5716i	−0.439919	−	0.761962i
$474$	−2.53232	+	4.38611i	−0.116313	+	0.201461i
$475$	−21.5611			−0.989290
$476$	0.0594814	−	0.654942i	0.00272633	−	0.0300192i
$477$	0.636979			0.0291652
$478$	1.95110	−	3.37941i	0.0892414	−	0.154571i
$479$	13.5060	+	23.3930i	0.617104	+	1.06885i	0.990012	+	0.140987i	$0.0450274\pi$
$479$	13.5060	+	23.3930i	0.617104	+	1.06885i	−0.372908	+	0.927868i	$0.621639\pi$
$480$	2.22802	+	3.85905i	0.101695	+	0.176141i
$481$		0			0
$482$	10.8823			0.495677
$483$	−8.95917	+	4.14174i	−0.407656	+	0.188456i
$484$	−8.29420			−0.377009
$485$	1.40886	−	2.44021i	0.0639729	−	0.110804i
$486$	−4.00558	−	6.93788i	−0.181697	−	0.314708i
$487$	16.0419	+	27.7854i	0.726928	+	1.25908i	0.958175	+	0.286182i	$0.0923862\pi$
$487$	16.0419	+	27.7854i	0.726928	+	1.25908i	−0.231247	+	0.972895i	$0.574280\pi$
$488$	−5.49694	+	9.52097i	−0.248835	+	0.430994i
$489$	7.58910			0.343191
$490$	3.58887	+	0.657299i	0.162129	+	0.0296937i
$491$	−28.6040			−1.29088			−0.645440	−	0.763811i	$-0.723326\pi$
$491$	−28.6040			−1.29088			−0.645440	+	0.763811i	$0.723326\pi$
$492$	−8.99328	+	15.5768i	−0.405448	+	0.702257i
$493$	−0.596378	−	1.03296i	−0.0268595	−	0.0465220i
$494$		0			0
$495$	−4.71106	+	8.15980i	−0.211746	+	0.366756i
$496$	−7.29442			−0.327529
$497$	8.88285	−	4.10646i	0.398450	−	0.184200i
$498$	−1.22051			−0.0546924
$499$	−0.899082	+	1.55726i	−0.0402484	+	0.0697123i	−0.885448	−	0.464739i	$-0.846148\pi$
$499$	−0.899082	+	1.55726i	−0.0402484	+	0.0697123i	0.845199	+	0.534451i	$0.179482\pi$
$500$	8.13042	+	14.0823i	0.363603	+	0.629780i
$501$	−2.60602	−	4.51376i	−0.116428	−	0.201660i
$502$	−1.91990	+	3.32536i	−0.0856893	+	0.148418i
$503$	29.0772			1.29649			0.648245	−	0.761432i	$-0.275503\pi$
$503$	29.0772			1.29649			0.648245	+	0.761432i	$0.275503\pi$
$504$	1.02217	−	11.2550i	0.0455310	−	0.501336i
$505$	−11.9595			−0.532191
$506$	−4.35497	+	7.54303i	−0.193602	+	0.335329i
$507$		0			0
$508$	−1.75690	−	3.04304i	−0.0779499	−	0.135013i
$509$	−11.5957	+	20.0843i	−0.513969	+	0.890220i	0.485900	+	0.874014i	$0.338492\pi$
$509$	−11.5957	+	20.0843i	−0.513969	+	0.890220i	−0.999869	+	0.0162054i	$0.994841\pi$
$510$	0.0628979			0.00278516
$511$	14.2985	+	10.0825i	0.632529	+	0.446024i
$512$	22.5022			0.994464
$513$	12.3539	−	21.3975i	0.545436	−	0.944723i
$514$	−3.40585	−	5.89910i	−0.150225	−	0.260198i
$515$	2.17330	+	3.76427i	0.0957671	+	0.165874i
$516$	3.58562	−	6.21048i	0.157848	−	0.273401i
$517$	18.0769			0.795022
$518$	0.911564	+	0.642783i	0.0400518	+	0.0282423i
$519$	20.6137			0.904840
$520$		0			0
$521$	−16.6255	−	28.7962i	−0.728376	−	1.26158i	−0.957569	−	0.288203i	$-0.906942\pi$
$521$	−16.6255	−	28.7962i	−0.728376	−	1.26158i	0.229193	−	0.973381i	$-0.426391\pi$
$522$	−4.78267	−	8.28383i	−0.209332	−	0.362574i
$523$	−19.3560	+	33.5256i	−0.846380	+	1.46597i	0.0380367	+	0.999276i	$0.487890\pi$
$523$	−19.3560	+	33.5256i	−0.846380	+	1.46597i	−0.884417	+	0.466697i	$0.845444\pi$
$524$	21.7881			0.951816
$525$	−0.795602	+	8.76027i	−0.0347229	+	0.382330i
$526$	−5.86142			−0.255570
$527$	−0.202153	+	0.350140i	−0.00880594	+	0.0152523i
$528$	−4.31874	−	7.48028i	−0.187949	−	0.325537i
$529$	1.85966	+	3.22102i	0.0808546	+	0.140044i
$530$	−0.0728671	+	0.126210i	−0.00316514	+	0.00548219i
$531$	−24.5622			−1.06591
$532$	23.1561	−	10.7049i	1.00394	−	0.464115i
$533$		0			0
$534$	0.371191	−	0.642922i	0.0160630	−	0.0278220i
$535$	4.42396	+	7.66253i	0.191265	+	0.331280i
$536$	−4.82283	−	8.35338i	−0.208314	−	0.360811i
$537$	1.75730	−	3.04372i	0.0758329	−	0.131346i
$538$	4.59926			0.198288
$539$	−27.3168	−	5.00304i	−1.17662	−	0.215496i
$540$	−8.18100			−0.352054
$541$	−11.3337	+	19.6306i	−0.487275	+	0.843986i	−0.999893	−	0.0146313i	$-0.995343\pi$
$541$	−11.3337	+	19.6306i	−0.487275	+	0.843986i	0.512618	+	0.858617i	$0.328676\pi$
$542$	0.640905	+	1.11008i	0.0275292	+	0.0476820i
$543$	−3.34135	−	5.78738i	−0.143391	−	0.248360i
$544$	0.357302	−	0.618865i	0.0153192	−	0.0265336i
$545$	6.70349			0.287146
$546$		0			0
$547$	−9.21134			−0.393848			−0.196924	−	0.980419i	$-0.563095\pi$
$547$	−9.21134			−0.393848			−0.196924	+	0.980419i	$0.563095\pi$
$548$	4.58957	−	7.94936i	0.196057	−	0.339580i
$549$	−6.67909	−	11.5685i	−0.285056	−	0.493732i
$550$	3.88116	+	6.72236i	0.165493	+	0.286642i
$551$	23.1344	−	40.0699i	0.985558	−	1.70704i
$552$	−6.99468			−0.297713
$553$	2.85311	−	31.4152i	0.121327	−	1.33591i
$554$	−0.466928			−0.0198379
$555$	0.373400	−	0.646748i	0.0158500	−	0.0274529i
$556$	−18.1464	−	31.4304i	−0.769577	−	1.33295i
$557$	5.66403	+	9.81039i	0.239993	+	0.415680i	0.960712	−	0.277547i	$-0.0895216\pi$
$557$	5.66403	+	9.81039i	0.239993	+	0.415680i	−0.720719	+	0.693227i	$0.756188\pi$
$558$	−1.62118	+	2.80796i	−0.0686299	+	0.118871i
$559$		0			0
$560$	−5.77627	−	4.07310i	−0.244092	−	0.172120i
$561$	−0.478748			−0.0202128
$562$	−1.61318	+	2.79411i	−0.0680478	+	0.117862i
$563$	−16.3193	−	28.2659i	−0.687777	−	1.19127i	−0.972555	−	0.232672i	$-0.925253\pi$
$563$	−16.3193	−	28.2659i	−0.687777	−	1.19127i	0.284778	−	0.958594i	$-0.408080\pi$
$564$	3.38732	+	5.86700i	0.142632	+	0.247045i
$565$	5.71448	−	9.89776i	0.240410	−	0.416402i
$566$	11.0870			0.466021
$567$	6.53998	+	4.61162i	0.274653	+	0.193670i
$568$	6.93510			0.290990
$569$	−17.5045	+	30.3188i	−0.733829	+	1.27103i	0.221407	+	0.975182i	$0.428935\pi$
$569$	−17.5045	+	30.3188i	−0.733829	+	1.27103i	−0.955235	+	0.295847i	$0.904398\pi$
$570$	1.21995	+	2.11302i	0.0510981	+	0.0885046i
$571$	−13.1273	−	22.7371i	−0.549360	−	0.951519i	−0.998319	−	0.0579663i	$-0.981538\pi$
$571$	−13.1273	−	22.7371i	−0.549360	−	0.951519i	0.448959	−	0.893552i	$-0.351795\pi$
$572$		0			0
$573$	−5.50428			−0.229945
$574$	−1.44742	+	15.9373i	−0.0604140	+	0.665211i
$575$	−17.1830			−0.716580
$576$	−2.97260	+	5.14870i	−0.123858	+	0.214529i
$577$	12.2863	+	21.2806i	0.511487	+	0.885922i	0.999911	+	0.0133154i	$0.00423855\pi$
$577$	12.2863	+	21.2806i	0.511487	+	0.885922i	−0.488424	+	0.872606i	$0.662428\pi$
$578$	4.24484	+	7.35228i	0.176562	+	0.305815i
$579$	2.05148	−	3.55327i	0.0852567	−	0.147669i
$580$	−15.3201			−0.636133
$581$	6.90015	−	3.18988i	0.286267	−	0.132338i
$582$	1.14817			0.0475930
$583$	0.554629	−	0.960646i	0.0229704	−	0.0397859i
$584$	6.19936	+	10.7376i	0.256531	+	0.444325i
$585$		0			0
$586$	−6.05048	+	10.4797i	−0.249943	+	0.432914i
$587$	−20.5279			−0.847279			−0.423639	−	0.905831i	$-0.639248\pi$
$587$	−20.5279			−0.847279			−0.423639	+	0.905831i	$0.639248\pi$
$588$	−3.49493	−	9.80335i	−0.144129	−	0.404283i
$589$	−15.6837			−0.646235
$590$	2.80978	−	4.86669i	0.115677	−	0.200358i
$591$	−10.9752	−	19.0097i	−0.451461	−	0.781954i
$592$	−1.08036	−	1.87124i	−0.0444027	−	0.0769077i
$593$	19.1417	−	33.1545i	0.786057	−	1.36149i	−0.142308	−	0.989822i	$-0.545452\pi$
$593$	19.1417	−	33.1545i	0.786057	−	1.36149i	0.928365	−	0.371669i	$-0.121214\pi$
$594$	−8.89515			−0.364972
$595$	−0.355593	+	0.164387i	−0.0145779	+	0.00673923i
$596$	0.0199081			0.000815468
$597$	−7.27030	+	12.5925i	−0.297554	+	0.515378i
$598$		0			0
$599$	−7.03567	−	12.1861i	−0.287470	−	0.497912i	0.685735	−	0.727851i	$-0.259481\pi$
$599$	−7.03567	−	12.1861i	−0.287470	−	0.497912i	−0.973205	+	0.229939i	$0.926147\pi$
$600$	−3.11683	+	5.39851i	−0.127244	+	0.220393i
$601$	−20.2342			−0.825369			−0.412685	−	0.910874i	$-0.635409\pi$
$601$	−20.2342			−0.825369			−0.412685	+	0.910874i	$0.635409\pi$
$602$	0.577085	−	6.35421i	0.0235202	−	0.258978i
$603$	11.7200			0.477276
$604$	−16.5424	+	28.6522i	−0.673099	+	1.16584i
$605$	2.47041	+	4.27887i	0.100436	+	0.173961i
$606$	−2.43664	−	4.22039i	−0.0989818	−	0.171441i
$607$	−3.27563	+	5.67356i	−0.132954	+	0.230283i	−0.924814	−	0.380420i	$-0.875780\pi$
$607$	−3.27563	+	5.67356i	−0.132954	+	0.230283i	0.791860	+	0.610703i	$0.209113\pi$
$608$	27.7205			1.12422
$609$	−15.4268	−	10.8781i	−0.625125	−	0.440803i
$610$	3.05621			0.123742
$611$		0			0
$612$	0.283136	+	0.490406i	0.0114451	+	0.0198235i
$613$	−16.6622	−	28.8598i	−0.672980	−	1.16564i	−0.977055	−	0.212988i	$-0.931681\pi$
$613$	−16.6622	−	28.8598i	−0.672980	−	1.16564i	0.304075	−	0.952648i	$-0.401653\pi$
$614$	−6.07294	+	10.5186i	−0.245084	+	0.424498i
$615$	10.7145			0.432051
$616$	−16.0839	−	11.3415i	−0.648040	−	0.456961i
$617$	6.76038			0.272162			0.136081	−	0.990698i	$-0.456549\pi$
$617$	6.76038			0.272162			0.136081	+	0.990698i	$0.456549\pi$
$618$	−0.885581	+	1.53387i	−0.0356233	+	0.0617013i
$619$	−8.80931	−	15.2582i	−0.354076	−	0.613278i	0.632883	−	0.774247i	$-0.281871\pi$
$619$	−8.80931	−	15.2582i	−0.354076	−	0.613278i	−0.986959	+	0.160970i	$0.948538\pi$
$620$	2.59652	+	4.49731i	0.104279	+	0.180616i
$621$	9.84534	−	17.0526i	0.395080	−	0.684298i
$622$	1.99350			0.0799321
$623$	−0.418213	+	4.60489i	−0.0167554	+	0.184491i
$624$		0			0
$625$	−4.93986	+	8.55609i	−0.197594	+	0.342244i
$626$	−7.11866	−	12.3299i	−0.284519	−	0.492801i
$627$	−9.28569	−	16.0833i	−0.370835	−	0.642304i
$628$	17.3197	−	29.9985i	0.691130	−	1.19707i
$629$	−0.119762			−0.00477524
$630$	−2.85169	+	1.31831i	−0.113614	+	0.0525228i
$631$	−15.7519			−0.627074			−0.313537	−	0.949576i	$-0.601514\pi$
$631$	−15.7519			−0.627074			−0.313537	+	0.949576i	$0.601514\pi$
$632$	11.1773	−	19.3596i	0.444608	−	0.770084i
$633$	−7.77009	−	13.4582i	−0.308833	−	0.534915i
$634$	4.20392	+	7.28140i	0.166959	+	0.289181i
$635$	−1.04658	+	1.81273i	−0.0415322	+	0.0719359i
$636$	0.415713			0.0164841
$637$		0			0
$638$	−16.6575			−0.659475
$639$	−4.21327	+	7.29759i	−0.166674	+	0.288688i
$640$	−5.92497	−	10.2623i	−0.234205	−	0.405655i
$641$	10.4702	+	18.1350i	0.413550	+	0.716289i	0.995275	−	0.0970962i	$-0.0309554\pi$
$641$	10.4702	+	18.1350i	0.413550	+	0.716289i	−0.581725	+	0.813385i	$0.697622\pi$
$642$	−1.80268	+	3.12234i	−0.0711463	+	0.123229i
$643$	−18.9315			−0.746586			−0.373293	−	0.927713i	$-0.621771\pi$
$643$	−18.9315			−0.746586			−0.373293	+	0.927713i	$0.621771\pi$
$644$	18.4541	−	8.53118i	0.727195	−	0.336176i
$645$	−4.27188			−0.168205
$646$	0.195640	−	0.338859i	0.00769736	−	0.0133322i
$647$	18.8384	+	32.6291i	0.740614	+	1.28278i	0.952216	+	0.305426i	$0.0987988\pi$
$647$	18.8384	+	32.6291i	0.740614	+	1.28278i	−0.211601	+	0.977356i	$0.567868\pi$
$648$	2.83552	+	4.91126i	0.111390	+	0.192933i
$649$	−21.3867	+	37.0429i	−0.839503	+	1.45406i
$650$		0			0
$651$	−0.578727	+	6.37229i	−0.0226821	+	0.249750i
$652$	−15.6321			−0.612199
$653$	−14.5163	+	25.1430i	−0.568066	+	0.983920i	0.428691	+	0.903451i	$0.358975\pi$
$653$	−14.5163	+	25.1430i	−0.568066	+	0.983920i	−0.996757	+	0.0804686i	$0.974358\pi$
$654$	1.36577	+	2.36559i	0.0534060	+	0.0925019i
$655$	−6.48952	−	11.2402i	−0.253567	−	0.439190i
$656$	15.5002	−	26.8472i	0.605182	−	1.04821i
$657$	−15.0651			−0.587747
$658$	4.92598	+	3.47352i	0.192035	+	0.135412i
$659$	−1.41830			−0.0552493			−0.0276247	−	0.999618i	$-0.508794\pi$
$659$	−1.41830			−0.0552493			−0.0276247	+	0.999618i	$0.508794\pi$
$660$	−3.07459	+	5.32535i	−0.119678	+	0.207289i
$661$	−2.29649	−	3.97764i	−0.0893231	−	0.154712i	0.817902	−	0.575357i	$-0.195137\pi$
$661$	−2.29649	−	3.97764i	−0.0893231	−	0.154712i	−0.907225	+	0.420645i	$0.861804\pi$
$662$	1.55225	+	2.68858i	0.0603300	+	0.104495i
$663$		0			0
$664$	5.38715			0.209062
$665$	−12.4195	−	8.75753i	−0.481607	−	0.339602i
$666$	−0.960439			−0.0372162
$667$	18.4368	−	31.9335i	0.713877	−	1.23647i
$668$	5.36789	+	9.29746i	0.207690	+	0.359730i
$669$	−4.88890	−	8.46782i	−0.189016	−	0.327385i
$670$	−1.34071	+	2.32218i	−0.0517961	+	0.0897135i
$671$	−23.2624			−0.898036
$672$	1.02289	−	11.2629i	0.0394587	−	0.434475i
$673$	−4.20223			−0.161984			−0.0809920	−	0.996715i	$-0.525809\pi$
$673$	−4.20223			−0.161984			−0.0809920	+	0.996715i	$0.525809\pi$
$674$	1.92407	−	3.33259i	0.0741126	−	0.128367i
$675$	−8.77418	−	15.1973i	−0.337718	−	0.584945i
$676$		0			0
$677$	−4.04354	+	7.00361i	−0.155406	+	0.269171i	−0.933207	−	0.359340i	$-0.883002\pi$
$677$	−4.04354	+	7.00361i	−0.155406	+	0.269171i	0.777801	+	0.628511i	$0.216335\pi$
$678$	4.65709			0.178854
$679$	−6.49115	+	3.00080i	−0.249108	+	0.115160i
$680$	−0.277622			−0.0106463
$681$	7.60583	−	13.1737i	0.291456	−	0.504817i
$682$	2.82318	+	4.88989i	0.108105	+	0.187244i
$683$	−12.3433	−	21.3792i	−0.472302	−	0.818051i	0.527196	−	0.849744i	$-0.323243\pi$
$683$	−12.3433	−	21.3792i	−0.472302	−	0.818051i	−0.999498	+	0.0316929i	$0.989910\pi$
$684$	−10.9833	+	19.0236i	−0.419956	+	0.727386i
$685$	−5.46797			−0.208920
$686$	−6.48250	−	6.61231i	−0.247503	−	0.252459i
$687$	3.28244			0.125233
$688$	−6.17994	+	10.7040i	−0.235608	+	0.408085i
$689$		0			0
$690$	0.972234	+	1.68396i	0.0370123	+	0.0641072i
$691$	5.62835	−	9.74859i	0.214113	−	0.370854i	−0.738885	−	0.673831i	$-0.764647\pi$
$691$	5.62835	−	9.74859i	0.214113	−	0.370854i	0.952998	+	0.302978i	$0.0979807\pi$
$692$	−42.4602			−1.61409
$693$	21.7057	−	10.0344i	0.824532	−	0.381174i
$694$	15.2043			0.577147
$695$	−10.8097	+	18.7230i	−0.410035	+	0.710202i
$696$	−6.68854	−	11.5849i	−0.253528	−	0.439124i
$697$	−0.859128	−	1.48805i	−0.0325418	−	0.0563640i
$698$	4.03942	−	6.99648i	0.152894	−	0.264821i
$699$	21.2946			0.805434
$700$	1.63878	−	18.0445i	0.0619402	−	0.682016i
$701$	−22.2305			−0.839635			−0.419818	−	0.907608i	$-0.637906\pi$
$701$	−22.2305			−0.839635			−0.419818	+	0.907608i	$0.637906\pi$
$702$		0			0
$703$	−2.32288	−	4.02335i	−0.0876091	−	0.151743i
$704$	5.17660	+	8.96614i	0.195101	+	0.337924i
$705$	2.01781	−	3.49495i	0.0759951	−	0.131627i
$706$	−5.92103			−0.222841
$707$	24.8058	+	17.4916i	0.932918	+	0.657841i
$708$	−16.0301			−0.602447
$709$	−11.8870	+	20.5889i	−0.446427	+	0.773234i	−0.998150	−	0.0607929i	$-0.980637\pi$
$709$	−11.8870	+	20.5889i	−0.446427	+	0.773234i	0.551723	+	0.834027i	$0.313970\pi$
$710$	−0.963952	−	1.66961i	−0.0361765	−	0.0626595i
$711$	13.5810	+	23.5230i	0.509328	+	0.882182i
$712$	−1.63838	+	2.83776i	−0.0614010	+	0.106350i
$713$	−12.4990			−0.468092
$714$	−0.130459	−	0.0919926i	−0.00488232	−	0.00344274i
$715$		0			0
$716$	−3.61969	+	6.26948i	−0.135274	+	0.234301i
$717$	3.31541	+	5.74246i	0.123816	+	0.214456i
$718$	−7.84111	−	13.5812i	−0.292628	−	0.506846i
$719$	−10.3904	+	17.9967i	−0.387496	+	0.671163i	−0.992112	−	0.125354i	$-0.959993\pi$
$719$	−10.3904	+	17.9967i	−0.387496	+	0.671163i	0.604616	+	0.796517i	$0.293327\pi$
$720$	6.08597			0.226811
$721$	0.997764	−	10.9863i	0.0371587	−	0.409150i
$722$	5.67861			0.211336
$723$	−9.24589	+	16.0144i	−0.343859	+	0.595580i
$724$	6.88252	+	11.9209i	0.255787	+	0.443036i
$725$	−16.4309	−	28.4592i	−0.610229	−	1.05695i
$726$	−1.00665	+	1.74356i	−0.0373601	+	0.0647097i
$727$	26.7719			0.992915			0.496457	−	0.868061i	$-0.334634\pi$
$727$	26.7719			0.992915			0.496457	+	0.868061i	$0.334634\pi$
$728$		0			0
$729$	4.53910			0.168115
$730$	1.72338	−	2.98497i	0.0637850	−	0.110479i
$731$	0.342535	+	0.593287i	0.0126691	+	0.0219435i
$732$	−4.35899	−	7.55000i	−0.161113	−	0.279056i
$733$	−2.62824	+	4.55224i	−0.0970761	+	0.168141i	−0.910473	−	0.413568i	$-0.864282\pi$
$733$	−2.62824	+	4.55224i	−0.0970761	+	0.168141i	0.813397	+	0.581709i	$0.197616\pi$
$734$	12.0384			0.444345
$735$	−4.01647	+	4.72290i	−0.148150	+	0.174207i
$736$	22.0917			0.814312
$737$	10.2048	−	17.6753i	0.375900	−	0.651078i
$738$	−6.88981	−	11.9335i	−0.253617	−	0.439278i
$739$	3.57501	+	6.19209i	0.131509	+	0.227780i	0.924258	−	0.381768i	$-0.124685\pi$
$739$	3.57501	+	6.19209i	0.131509	+	0.227780i	−0.792750	+	0.609547i	$0.791351\pi$
$740$	−0.769132	+	1.33218i	−0.0282738	+	0.0489717i
$741$		0			0
$742$	0.335727	−	0.155204i	0.0123249	−	0.00569771i
$743$	0.713641			0.0261810			0.0130905	−	0.999914i	$-0.495833\pi$
$743$	0.713641			0.0261810			0.0130905	+	0.999914i	$0.495833\pi$
$744$	−2.26721	+	3.92692i	−0.0831198	+	0.143968i
$745$	−0.00592959	−	0.0102703i	−0.000217243	−	0.000376276i
$746$	4.59794	+	7.96386i	0.168342	+	0.291578i
$747$	−3.27284	+	5.66873i	−0.119747	+	0.207408i
$748$	0.986128			0.0360564
$749$	2.03104	−	22.3636i	0.0742127	−	0.817147i
$750$	3.94707			0.144127
$751$	12.8507	−	22.2580i	0.468927	−	0.812205i	−0.530442	−	0.847721i	$-0.677974\pi$
$751$	12.8507	−	22.2580i	0.468927	−	0.812205i	0.999369	+	0.0355158i	$0.0113074\pi$
$752$	−5.83815	−	10.1120i	−0.212896	−	0.368746i
$753$	−3.26238	−	5.65062i	−0.118888	−	0.205920i
$754$		0			0
$755$	19.7084			0.717263
$756$	16.9686	+	11.9653i	0.617142	+	0.435173i
$757$	16.3885			0.595650			0.297825	−	0.954621i	$-0.403739\pi$
$757$	16.3885			0.595650			0.297825	+	0.954621i	$0.403739\pi$
$758$	−2.03430	+	3.52350i	−0.0738889	+	0.127979i
$759$	−7.40018	−	12.8175i	−0.268609	−	0.465245i
$760$	−5.38468	−	9.32654i	−0.195323	−	0.338309i
$761$	−4.15999	+	7.20531i	−0.150800	+	0.261192i	−0.931522	−	0.363686i	$-0.881518\pi$
$761$	−4.15999	+	7.20531i	−0.150800	+	0.261192i	0.780722	+	0.624878i	$0.214851\pi$
$762$	−0.852923			−0.0308981
$763$	−13.9040	−	9.80433i	−0.503359	−	0.354941i
$764$	11.3378			0.410185
$765$	0.168663	−	0.292133i	0.00609802	−	0.0105621i
$766$	−5.59263	−	9.68671i	−0.202070	−	0.349995i
$767$		0			0
$768$	0.197167	−	0.341504i	0.00711466	−	0.0123230i
$769$	−25.5588			−0.921675			−0.460838	−	0.887485i	$-0.652451\pi$
$769$	−25.5588			−0.921675			−0.460838	+	0.887485i	$0.652451\pi$
$770$	−0.494838	+	5.44860i	−0.0178327	+	0.196354i
$771$	11.5748			0.416855
$772$	−4.22565	+	7.31905i	−0.152085	+	0.263418i
$773$	4.20038	+	7.27528i	0.151077	+	0.261674i	0.931624	−	0.363424i	$-0.118392\pi$
$773$	4.20038	+	7.27528i	0.151077	+	0.261674i	−0.780546	+	0.625098i	$0.785059\pi$
$774$	2.74697	+	4.75789i	0.0987378	+	0.171019i
$775$	−5.56957	+	9.64678i	−0.200065	+	0.346523i
$776$	−5.06783			−0.181925
$777$	−1.72040	+	0.795326i	−0.0617191	+	0.0285322i
$778$	−10.6970			−0.383506
$779$	33.3269	−	57.7238i	1.19406	−	2.06817i
$780$		0			0
$781$	7.33714	+	12.7083i	0.262544	+	0.454739i
$782$	0.155914	−	0.270052i	0.00557549	−	0.00965703i
$783$	37.6577			1.34578
$784$	6.02363	+	16.8964i	0.215130	+	0.603443i
$785$	−20.6345			−0.736476
$786$	2.64436	−	4.58017i	0.0943212	−	0.163369i
$787$	17.5322	+	30.3667i	0.624956	+	1.08246i	0.988549	+	0.150898i	$0.0482164\pi$
$787$	17.5322	+	30.3667i	0.624956	+	1.08246i	−0.363593	+	0.931558i	$0.618450\pi$
$788$	22.6069	+	39.1562i	0.805336	+	1.39488i
$789$	4.98000	−	8.62562i	0.177293	−	0.307080i
$790$	−6.21440			−0.221098
$791$	−26.3288	+	12.1716i	−0.936146	+	0.432772i
$792$	16.9463			0.602160
$793$		0			0
$794$	−0.299175	−	0.518186i	−0.0106173	−	0.0183897i
$795$	−0.123819	−	0.214461i	−0.00439142	−	0.00760616i
$796$	14.9754	−	25.9382i	0.530789	−	0.919354i
$797$	−24.5752			−0.870500			−0.435250	−	0.900310i	$-0.643340\pi$
$797$	−24.5752			−0.870500			−0.435250	+	0.900310i	$0.643340\pi$
$798$	0.560080	−	6.16697i	0.0198266	−	0.218309i
$799$	−0.647181			−0.0228956
$800$	9.84409	−	17.0505i	0.348041	−	0.602825i
$801$	−1.99073	−	3.44804i	−0.0703389	−	0.121831i
$802$	9.06848	+	15.7071i	0.320219	+	0.554636i
$803$	−13.1175	+	22.7202i	−0.462907	+	0.801778i
$804$	7.64887			0.269755
$805$	−9.89765	−	6.97926i	−0.348846	−	0.245987i
$806$		0			0
$807$	−3.90764	+	6.76823i	−0.137555	+	0.238253i
$808$	10.7550	+	18.6282i	0.378358	+	0.655336i
$809$	15.9006	+	27.5406i	0.559035	+	0.968277i	0.997577	+	0.0695667i	$0.0221617\pi$
$809$	15.9006	+	27.5406i	0.559035	+	0.968277i	−0.438542	+	0.898711i	$0.644505\pi$
$810$	0.788253	−	1.36529i	0.0276964	−	0.0479715i
$811$	−10.3633			−0.363905			−0.181953	−	0.983307i	$-0.558242\pi$
$811$	−10.3633			−0.363905			−0.181953	+	0.983307i	$0.558242\pi$
$812$	31.7762	+	22.4067i	1.11512	+	0.786323i
$813$	−2.17811			−0.0763898
$814$	−0.836272	+	1.44847i	−0.0293113	+	0.0507687i
$815$	4.65598	+	8.06439i	0.163092	+	0.282483i
$816$	0.154617	+	0.267805i	0.00541269	+	0.00937505i
$817$	−13.2874	+	23.0145i	−0.464868	+	0.805176i
$818$	7.33597			0.256496
$819$		0			0
$820$	−22.0698			−0.770711
$821$	−2.02796	+	3.51253i	−0.0707762	+	0.122588i	−0.899242	−	0.437452i	$-0.855881\pi$
$821$	−2.02796	+	3.51253i	−0.0707762	+	0.122588i	0.828465	+	0.560040i	$0.189214\pi$
$822$	−1.11405	−	1.92959i	−0.0388569	−	0.0673021i
$823$	−4.35848	−	7.54912i	−0.151927	−	0.263146i	0.780009	−	0.625769i	$-0.215215\pi$
$823$	−4.35848	−	7.54912i	−0.151927	−	0.263146i	−0.931936	+	0.362623i	$0.881881\pi$
$824$	3.90882	−	6.77027i	0.136170	−	0.235854i
$825$	−13.1901			−0.459220
$826$	−12.9458	+	5.98472i	−0.450441	+	0.208235i
$827$	−23.5788			−0.819915			−0.409957	−	0.912105i	$-0.634456\pi$
$827$	−23.5788			−0.819915			−0.409957	+	0.912105i	$0.634456\pi$
$828$	−8.75307	+	15.1608i	−0.304190	+	0.526873i
$829$	14.5203	+	25.1499i	0.504311	+	0.873492i	0.999988	+	0.00498467i	$0.00158668\pi$
$829$	14.5203	+	25.1499i	0.504311	+	0.873492i	−0.495677	+	0.868507i	$0.665080\pi$
$830$	−0.748793	−	1.29695i	−0.0259910	−	0.0450177i
$831$	0.396714	−	0.687128i	0.0137618	−	0.0238362i
$832$		0			0
$833$	0.977980	+	0.179116i	0.0338850	+	0.00620601i
$834$	−8.80951			−0.305048
$835$	3.19763	−	5.53846i	0.110659	−	0.191666i
$836$	19.1267	+	33.1284i	0.661511	+	1.14577i
$837$	−6.38240	−	11.0546i	−0.220608	−	0.382104i
$838$	1.48333	−	2.56921i	0.0512408	−	0.0887517i
$839$	11.5574			0.399007			0.199503	−	0.979897i	$-0.436067\pi$
$839$	11.5574			0.399007			0.199503	+	0.979897i	$0.436067\pi$
$840$	−3.98807	+	1.84365i	−0.137602	+	0.0636120i
$841$	41.5196			1.43171
$842$	−0.657918	+	1.13955i	−0.0226734	+	0.0392714i
$843$	−2.74119	−	4.74788i	−0.0944116	−	0.163526i
$844$	16.0049	+	27.7212i	0.550910	+	0.954205i
$845$		0			0
$846$	−5.19009			−0.178439
$847$	1.13417	−	12.4882i	0.0389704	−	0.429098i
$848$	−0.716496			−0.0246046
$849$	−9.41977	+	16.3155i	−0.323286	+	0.559947i
$850$	−0.138951	−	0.240670i	−0.00476598	−	0.00825493i
$851$	−1.85121	−	3.20638i	−0.0634586	−	0.109913i
$852$	−2.74972	+	4.76265i	−0.0942038	+	0.163166i
$853$	−1.51845			−0.0519906			−0.0259953	−	0.999662i	$-0.508275\pi$
$853$	−1.51845			−0.0519906			−0.0259953	+	0.999662i	$0.508275\pi$
$854$	−6.33903	−	4.46993i	−0.216917	−	0.152958i
$855$	13.0854			0.447511
$856$	7.95678	−	13.7815i	0.271957	−	0.471043i
$857$	3.00060	+	5.19718i	0.102498	+	0.177532i	0.912713	−	0.408600i	$-0.133983\pi$
$857$	3.00060	+	5.19718i	0.102498	+	0.177532i	−0.810215	+	0.586133i	$0.800650\pi$
$858$		0			0
$859$	−0.838021	+	1.45150i	−0.0285929	+	0.0495244i	−0.879968	−	0.475033i	$-0.842436\pi$
$859$	−0.838021	+	1.45150i	−0.0285929	+	0.0495244i	0.851375	+	0.524558i	$0.175769\pi$
$860$	8.79924			0.300051
$861$	−22.2235	−	15.6707i	−0.757374	−	0.534057i
$862$	9.41858			0.320798
$863$	−21.0252	+	36.4167i	−0.715706	+	1.23964i	0.246980	+	0.969021i	$0.420562\pi$
$863$	−21.0252	+	36.4167i	−0.715706	+	1.23964i	−0.962687	+	0.270619i	$0.912772\pi$
$864$	11.2807	+	19.5388i	0.383779	+	0.664724i
$865$	12.6467	+	21.9047i	0.429999	+	0.744781i
$866$	−4.78374	+	8.28567i	−0.162558	+	0.281559i
$867$	−14.4261			−0.489936
$868$	1.19206	−	13.1257i	0.0404613	−	0.445514i
$869$	47.3010			1.60458
$870$	−1.85936	+	3.22051i	−0.0630383	+	0.109186i
$871$		0			0
$872$	−6.02832	−	10.4414i	−0.204145	−	0.353589i
$873$	3.07885	−	5.33272i	0.104203	−	0.180485i
$874$	12.0963			0.409164
$875$	−22.3148	+	10.3159i	−0.754377	+	0.348742i
$876$	−9.83201			−0.332193
$877$	15.4315	−	26.7281i	0.521084	−	0.902545i	−0.478615	−	0.878025i	$-0.658861\pi$
$877$	15.4315	−	26.7281i	0.521084	−	0.902545i	0.999699	−	0.0245198i	$-0.00780566\pi$
$878$	0.316268	+	0.547793i	0.0106735	+	0.0184871i
$879$	−10.2813	−	17.8077i	−0.346778	−	0.600638i
$880$	5.29917	−	9.17843i	0.178635	−	0.309405i
$881$	−55.7338			−1.87772			−0.938860	−	0.344298i	$-0.888117\pi$
$881$	−55.7338			−1.87772			−0.938860	+	0.344298i	$0.888117\pi$
$882$	7.84295	+	1.43643i	0.264086	+	0.0483671i
$883$	2.92007			0.0982681			0.0491341	−	0.998792i	$-0.484354\pi$
$883$	2.92007			0.0982681			0.0491341	+	0.998792i	$0.484354\pi$
$884$		0			0
$885$	4.77452	+	8.26971i	0.160494	+	0.277983i
$886$	5.23467	+	9.06671i	0.175862	+	0.304602i
$887$	−0.939545	+	1.62734i	−0.0315468	+	0.0546407i	−0.881368	−	0.472431i	$-0.843377\pi$
$887$	−0.939545	+	1.62734i	−0.0315468	+	0.0546407i	0.849821	+	0.527071i	$0.176710\pi$
$888$	−1.34317			−0.0450737
$889$	4.82200	−	2.22917i	0.161725	−	0.0747639i
$890$	0.910916			0.0305340
$891$	−5.99980	+	10.3920i	−0.201001	+	0.348144i
$892$	10.0702	+	17.4421i	0.337175	+	0.584004i
$893$	−12.5526	−	21.7417i	−0.420055	−	0.727557i
$894$	0.00241620	−	0.00418498i	8.08097e−5	−	0.000139967i
$895$	4.31246			0.144150
$896$	−2.72015	+	29.9513i	−0.0908740	+	1.00060i
$897$		0			0
$898$	4.46569	−	7.73480i	0.149022	−	0.258114i
$899$	−11.9520	−	20.7014i	−0.398621	−	0.690431i
$900$	7.80074	+	13.5113i	0.260025	+	0.450376i
$901$	−0.0198566	+	0.0343926i	−0.000661518	+	0.00114578i
$902$	−23.9964			−0.798991
$903$	8.86050	+	6.24793i	0.294859	+	0.207918i
$904$	−20.5557			−0.683672
$905$	4.09989	−	7.10121i	0.136285	−	0.236052i
$906$	4.01541	+	6.95490i	0.133403	+	0.231061i
$907$	17.8082	+	30.8447i	0.591311	+	1.02418i	0.994056	+	0.108868i	$0.0347227\pi$
$907$	17.8082	+	30.8447i	0.591311	+	1.02418i	−0.402745	+	0.915312i	$0.631944\pi$
$908$	−15.6665	+	27.1352i	−0.519912	+	0.900514i
$909$	−26.1358			−0.866869
$910$		0			0
$911$	44.2844			1.46721			0.733604	−	0.679577i	$-0.237837\pi$
$911$	44.2844			1.46721			0.733604	+	0.679577i	$0.237837\pi$
$912$	−5.99784	+	10.3886i	−0.198608	+	0.344000i
$913$	5.69946	+	9.87175i	0.188624	+	0.326707i
$914$	1.64145	+	2.84307i	0.0542943	+	0.0940404i
$915$	−2.59663	+	4.49750i	−0.0858420	+	0.148683i
$916$	−6.76118			−0.223396
$917$	−2.97934	+	32.8052i	−0.0983866	+	1.08332i
$918$	0.318459			0.0105107
$919$	−13.0564	+	22.6144i	−0.430691	+	0.745979i	−0.996933	−	0.0782603i	$-0.975063\pi$
$919$	−13.0564	+	22.6144i	−0.430691	+	0.745979i	0.566242	+	0.824239i	$0.308397\pi$
$920$	−4.29129	−	7.43274i	−0.141480	−	0.245050i
$921$	−10.3194	−	17.8738i	−0.340037	−	0.588961i
$922$	1.27838	−	2.21421i	0.0421010	−	0.0729211i
$923$		0			0
$924$	14.1659	−	6.54875i	0.466023	−	0.215438i
$925$	−3.29960			−0.108490
$926$	8.33076	−	14.4293i	0.273766	−	0.474176i
$927$	4.74944	+	8.22626i	0.155992	+	0.270186i
$928$	21.1248	+	36.5893i	0.693457	+	1.20110i
$929$	−5.01157	+	8.68030i	−0.164424	+	0.284791i	−0.936451	−	0.350799i	$-0.885910\pi$
$929$	−5.01157	+	8.68030i	−0.164424	+	0.284791i	0.772026	+	0.635591i	$0.219243\pi$
$930$	1.26053			0.0413345
$931$	12.9514	+	36.3288i	0.424464	+	1.19063i
$932$	−43.8626			−1.43677
$933$	−1.69373	+	2.93362i	−0.0554501	+	0.0960425i
$934$	3.23727	+	5.60712i	0.105927	+	0.183471i
$935$	−0.293716	−	0.508731i	−0.00960554	−	0.0166373i
$936$		0			0
$937$	−0.916838			−0.0299518			−0.0149759	−	0.999888i	$-0.504767\pi$
$937$	−0.916838			−0.0299518			−0.0149759	+	0.999888i	$0.504767\pi$
$938$	6.17718	−	2.85565i	0.201692	−	0.0932404i
$939$	24.1928			0.789501
$940$	−4.15629	+	7.19891i	−0.135563	+	0.234803i
$941$	−8.54482	−	14.8001i	−0.278553	−	0.482468i	0.692472	−	0.721445i	$-0.256522\pi$
$941$	−8.54482	−	14.8001i	−0.278553	−	0.482468i	−0.971025	+	0.238976i	$0.923188\pi$
$942$	−4.20409	−	7.28169i	−0.136977	−	0.237250i
$943$	26.5597	−	46.0027i	0.864902	−	1.49805i
$944$	27.6284			0.899227
$945$	1.11869	−	12.3177i	0.0363909	−	0.400695i
$946$	9.56735			0.311062
$947$	10.8777	−	18.8408i	0.353479	−	0.612243i	−0.633378	−	0.773843i	$-0.718332\pi$
$947$	10.8777	−	18.8408i	0.353479	−	0.612243i	0.986856	+	0.161600i	$0.0516654\pi$
$948$	8.86342	+	15.3519i	0.287871	+	0.498607i
$949$		0			0
$950$	5.39012	−	9.33597i	0.174879	−	0.302899i
$951$	−14.2870			−0.463288
$952$	0.575828	+	0.406041i	0.0186627	+	0.0131599i
$953$	−17.8081			−0.576862			−0.288431	−	0.957501i	$-0.593134\pi$
$953$	−17.8081			−0.576862			−0.288431	+	0.957501i	$0.593134\pi$
$954$	−0.159240	+	0.275812i	−0.00515560	+	0.00892976i
$955$	−3.37692	−	5.84900i	−0.109275	−	0.189269i
$956$	−6.82909	−	11.8283i	−0.220869	−	0.382556i
$957$	14.1526	−	24.5130i	0.457488	−	0.792392i
$958$	−13.5056			−0.436347
$959$	11.3414	+	7.99729i	0.366232	+	0.258246i
$960$	2.31132			0.0745975
$961$	11.4487	−	19.8297i	0.369311	−	0.639666i
$962$		0			0
$963$	9.66793	+	16.7453i	0.311545	+	0.539611i
$964$	19.0447	−	32.9865i	0.613390	−	1.06242i
$965$	5.03441			0.162063
$966$	0.446353	−	4.91474i	0.0143612	−	0.158129i
$967$	−35.3813			−1.13779			−0.568893	−	0.822412i	$-0.692628\pi$
$967$	−35.3813			−1.13779			−0.568893	+	0.822412i	$0.692628\pi$
$968$	4.44318	−	7.69582i	0.142809	−	0.247353i
$969$	0.332441	+	0.575805i	0.0106796	+	0.0184975i
$970$	0.704409	+	1.22007i	0.0226172	+	0.0391742i
$971$	−24.8533	+	43.0472i	−0.797582	+	1.38145i	0.123605	+	0.992331i	$0.460554\pi$
$971$	−24.8533	+	43.0472i	−0.797582	+	1.38145i	−0.921187	+	0.389120i	$0.872779\pi$
$972$	−28.0401			−0.899385
$973$	49.8046	−	23.0242i	1.59666	−	0.738122i
$974$	−16.0415			−0.514002
$975$		0			0
$976$	7.51287	+	13.0127i	0.240481	+	0.416526i
$977$	30.6401	+	53.0701i	0.980262	+	1.69786i	0.661346	+	0.750081i	$0.269986\pi$
$977$	30.6401	+	53.0701i	0.980262	+	1.69786i	0.318917	+	0.947783i	$0.396681\pi$
$978$	−1.89723	+	3.28609i	−0.0606666	+	0.105078i
$979$	−6.93346			−0.221594
$980$	8.27314	−	9.72825i	0.264276	−	0.310757i
$981$	14.6495			0.467723
$982$	7.15080	−	12.3856i	0.228191	−	0.395239i
$983$	3.49481	+	6.05318i	0.111467	+	0.193067i	0.916362	−	0.400351i	$-0.131112\pi$
$983$	3.49481	+	6.05318i	0.111467	+	0.193067i	−0.804895	+	0.593417i	$0.797778\pi$
$984$	−9.63536	−	16.6889i	−0.307164	−	0.532024i
$985$	13.4668	−	23.3252i	0.429088	−	0.743203i
$986$	0.596362			0.0189920
$987$	−9.29684	+	4.29785i	−0.295922	+	0.136802i
$988$		0			0
$989$	−10.5893	+	18.3413i	−0.336722	+	0.583219i
$990$	−2.35547	−	4.07979i	−0.0748617	−	0.129664i
$991$	16.3671	+	28.3486i	0.519917	+	0.900522i	0.999732	+	0.0231525i	$0.00737033\pi$
$991$	16.3671	+	28.3486i	0.519917	+	0.900522i	−0.479815	+	0.877370i	$0.659296\pi$
$992$	7.16066	−	12.4026i	0.227351	−	0.393784i
$993$	−5.27532			−0.167407
$994$	−0.442551	+	4.87287i	−0.0140369	+	0.154558i
$995$	−17.8416			−0.565616
$996$	−2.13597	+	3.69960i	−0.0676807	+	0.117226i
$997$	−28.8948	−	50.0473i	−0.915109	−	1.58502i	−0.806742	−	0.590904i	$-0.798771\pi$
$997$	−28.8948	−	50.0473i	−0.915109	−	1.58502i	−0.108367	−	0.994111i	$-0.534562\pi$
$998$	−0.449529	−	0.778607i	−0.0142296	−	0.0246464i
$999$	1.89057	−	3.27456i	0.0598150	−	0.103603i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.e.j.170.5		24
7.2	even	3		8281.2.a.cp.1.8		12
7.4	even	3	inner	1183.2.e.j.508.5		24
7.5	odd	6		8281.2.a.co.1.8		12
13.6	odd	12		91.2.k.b.23.3	yes	12
13.11	odd	12		91.2.u.b.30.4	yes	12
13.12	even	2	inner	1183.2.e.j.170.8		24
39.11	even	12		819.2.do.e.667.3		12
39.32	even	12		819.2.bm.f.478.4		12
91.6	even	12		637.2.k.i.569.3		12
91.11	odd	12		91.2.k.b.4.4	✓	12
91.12	odd	6		8281.2.a.co.1.5		12
91.19	even	12		637.2.q.i.491.3		12
91.24	even	12		637.2.k.i.459.4		12
91.25	even	6	inner	1183.2.e.j.508.8		24
91.32	odd	12		91.2.u.b.88.4	yes	12
91.37	odd	12		637.2.q.g.589.3		12
91.45	even	12		637.2.u.g.361.4		12
91.51	even	6		8281.2.a.cp.1.5		12
91.58	odd	12		637.2.q.g.491.3		12
91.76	even	12		637.2.u.g.30.4		12
91.89	even	12		637.2.q.i.589.3		12
273.11	even	12		819.2.bm.f.550.3		12
273.32	even	12		819.2.do.e.361.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.k.b.4.4	✓	12	91.11	odd	12
91.2.k.b.23.3	yes	12	13.6	odd	12
91.2.u.b.30.4	yes	12	13.11	odd	12
91.2.u.b.88.4	yes	12	91.32	odd	12
637.2.k.i.459.4		12	91.24	even	12
637.2.k.i.569.3		12	91.6	even	12
637.2.q.g.491.3		12	91.58	odd	12
637.2.q.g.589.3		12	91.37	odd	12
637.2.q.i.491.3		12	91.19	even	12
637.2.q.i.589.3		12	91.89	even	12
637.2.u.g.30.4		12	91.76	even	12
637.2.u.g.361.4		12	91.45	even	12
819.2.bm.f.478.4		12	39.32	even	12
819.2.bm.f.550.3		12	273.11	even	12
819.2.do.e.361.3		12	273.32	even	12
819.2.do.e.667.3		12	39.11	even	12
1183.2.e.j.170.5		24	1.1	even	1	trivial
1183.2.e.j.170.8		24	13.12	even	2	inner
1183.2.e.j.508.5		24	7.4	even	3	inner
1183.2.e.j.508.8		24	91.25	even	6	inner
8281.2.a.co.1.5		12	91.12	odd	6
8281.2.a.co.1.8		12	7.5	odd	6
8281.2.a.cp.1.5		12	91.51	even	6
8281.2.a.cp.1.8		12	7.2	even	3

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:	\( N \)	\(=\)	\( 1183 = 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1183.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.249993 + 0.433001i) q^{2} +(-0.424801 - 0.735776i) q^{3} +(0.875007 + 1.51556i) q^{4} +(0.521238 - 0.902810i) q^{5} +0.424789 q^{6} +(-2.40155 + 1.11021i) q^{7} -1.87496 q^{8} +(1.13909 - 1.97296i) q^{9} +O(q^{10})\)	\(q+(-0.249993 + 0.433001i) q^{2} +(-0.424801 - 0.735776i) q^{3} +(0.875007 + 1.51556i) q^{4} +(0.521238 - 0.902810i) q^{5} +0.424789 q^{6} +(-2.40155 + 1.11021i) q^{7} -1.87496 q^{8} +(1.13909 - 1.97296i) q^{9} +(0.260612 + 0.451393i) q^{10} +(-1.98365 - 3.43579i) q^{11} +(0.743407 - 1.28762i) q^{12} +(0.119647 - 1.31742i) q^{14} -0.885688 q^{15} +(-1.28129 + 2.21925i) q^{16} +(0.0710177 + 0.123006i) q^{17} +(0.569529 + 0.986453i) q^{18} +(-2.75488 + 4.77160i) q^{19} +1.82435 q^{20} +(1.83705 + 1.29538i) q^{21} +1.98360 q^{22} +(-2.19549 + 3.80270i) q^{23} +(0.796483 + 1.37955i) q^{24} +(1.95662 + 3.38897i) q^{25} -4.48435 q^{27} +(-3.78396 - 2.66823i) q^{28} -8.39759 q^{29} +(0.221416 - 0.383504i) q^{30} +(1.42326 + 2.46516i) q^{31} +(-2.51558 - 4.35712i) q^{32} +(-1.68531 + 2.91905i) q^{33} -0.0710158 q^{34} +(-0.249465 + 2.74683i) q^{35} +3.98684 q^{36} +(-0.421593 + 0.730221i) q^{37} +(-1.37740 - 2.38574i) q^{38} +(-0.977298 + 1.69273i) q^{40} -12.0974 q^{41} +(-1.02015 + 0.471607i) q^{42} +4.82323 q^{43} +(3.47142 - 6.01267i) q^{44} +(-1.18747 - 2.05676i) q^{45} +(-1.09772 - 1.90130i) q^{46} +(-2.27824 + 3.94602i) q^{47} +2.17717 q^{48} +(4.53485 - 5.33246i) q^{49} -1.95657 q^{50} +(0.0603367 - 0.104506i) q^{51} +(0.139800 + 0.242141i) q^{53} +(1.12106 - 1.94173i) q^{54} -4.13582 q^{55} +(4.50280 - 2.08160i) q^{56} +4.68111 q^{57} +(2.09934 - 3.63617i) q^{58} +(-5.39075 - 9.33705i) q^{59} +(-0.774983 - 1.34231i) q^{60} +(2.93177 - 5.07797i) q^{61} -1.42322 q^{62} +(-0.545169 + 6.00279i) q^{63} -2.60963 q^{64} +(-0.842634 - 1.45949i) q^{66} +(2.57223 + 4.45524i) q^{67} +(-0.124282 + 0.215263i) q^{68} +3.73058 q^{69} +(-1.12701 - 0.794706i) q^{70} -3.69880 q^{71} +(-2.13574 + 3.69921i) q^{72} +(-3.30640 - 5.72686i) q^{73} +(-0.210791 - 0.365101i) q^{74} +(1.66235 - 2.87927i) q^{75} -9.64216 q^{76} +(8.57829 + 6.04892i) q^{77} +(-5.96135 + 10.3254i) q^{79} +(1.33571 + 2.31352i) q^{80} +(-1.51231 - 2.61940i) q^{81} +(3.02426 - 5.23818i) q^{82} -2.87321 q^{83} +(-0.355795 + 3.91762i) q^{84} +0.148068 q^{85} +(-1.20578 + 2.08846i) q^{86} +(3.56730 + 6.17875i) q^{87} +(3.71926 + 6.44195i) q^{88} +(0.873824 - 1.51351i) q^{89} +1.18744 q^{90} -7.68427 q^{92} +(1.20921 - 2.09440i) q^{93} +(-1.13909 - 1.97296i) q^{94} +(2.87190 + 4.97427i) q^{95} +(-2.13724 + 3.70181i) q^{96} +2.70291 q^{97} +(1.17528 + 3.29668i) q^{98} -9.03822 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 6 q^{3} - 8 q^{4} - 2 q^{9}+O(q^{10}) \) 24 * q - 6 * q^3 - 8 * q^4 - 2 * q^9	\( 24 q - 6 q^{3} - 8 q^{4} - 2 q^{9} - 24 q^{10} + 2 q^{12} + 8 q^{14} - 16 q^{16} - 34 q^{17} + 60 q^{22} - 6 q^{23} + 10 q^{25} + 24 q^{27} + 4 q^{29} - 22 q^{30} - 24 q^{35} - 52 q^{36} - 38 q^{38} - 2 q^{40} + 32 q^{42} + 44 q^{43} - 76 q^{48} + 12 q^{49} - 8 q^{51} - 16 q^{53} + 60 q^{55} + 54 q^{56} + 10 q^{61} + 164 q^{62} - 4 q^{64} - 68 q^{66} - 22 q^{68} + 28 q^{69} - 66 q^{74} - 2 q^{75} + 38 q^{77} - 70 q^{79} + 28 q^{81} - 10 q^{82} + 20 q^{87} + 28 q^{88} - 132 q^{92} + 2 q^{94} - 4 q^{95}+O(q^{100}) \) 24 * q - 6 * q^3 - 8 * q^4 - 2 * q^9 - 24 * q^10 + 2 * q^12 + 8 * q^14 - 16 * q^16 - 34 * q^17 + 60 * q^22 - 6 * q^23 + 10 * q^25 + 24 * q^27 + 4 * q^29 - 22 * q^30 - 24 * q^35 - 52 * q^36 - 38 * q^38 - 2 * q^40 + 32 * q^42 + 44 * q^43 - 76 * q^48 + 12 * q^49 - 8 * q^51 - 16 * q^53 + 60 * q^55 + 54 * q^56 + 10 * q^61 + 164 * q^62 - 4 * q^64 - 68 * q^66 - 22 * q^68 + 28 * q^69 - 66 * q^74 - 2 * q^75 + 38 * q^77 - 70 * q^79 + 28 * q^81 - 10 * q^82 + 20 * q^87 + 28 * q^88 - 132 * q^92 + 2 * q^94 - 4 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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