LMFDB - Embedded newform 650.2.w.f.457.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [650,2,Mod(193,650)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("650.193"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(650, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([9, 7])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 650 = 2 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	650.w (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,-8,0,-8,0,0,-12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$5.19027613138$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 28x^{14} + 294x^{12} + 1516x^{10} + 4147x^{8} + 6012x^{6} + 4338x^{4} + 1296x^{2} + 81 $ x^16 + 28x^14 + 294x^12 + 1516x^10 + 4147x^8 + 6012x^6 + 4338x^4 + 1296*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			457.4
Root			$-1.28827i$ of defining polynomial
Character	$\chi$	$=$	650.457
Dual form			650.2.w.f.293.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 - 0.866025i) q^{2} +(1.24438 + 0.333429i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.333429 - 1.24438i) q^{6} +(-2.21606 - 1.27944i) q^{7} +1.00000 q^{8} +(-1.16078 - 0.670177i) q^{9} +(0.0237140 - 0.0885018i) q^{11} +(-0.910946 + 0.910946i) q^{12} +(0.871354 - 3.49868i) q^{13} +2.55889i q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.28353 - 4.79019i) q^{17} +1.34035i q^{18} +(-0.520214 + 0.139391i) q^{19} +(-2.33101 - 2.33101i) q^{21} +(-0.0885018 + 0.0237140i) q^{22} +(0.906863 - 3.38446i) q^{23} +(1.24438 + 0.333429i) q^{24} +(-3.46562 + 0.994724i) q^{26} +(-3.95383 - 3.95383i) q^{27} +(2.21606 - 1.27944i) q^{28} +(2.89539 - 1.67166i) q^{29} +(-4.23707 + 4.23707i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.0590182 - 0.102223i) q^{33} +(-3.50666 + 3.50666i) q^{34} +(1.16078 - 0.670177i) q^{36} +(5.43423 - 3.13745i) q^{37} +(0.380823 + 0.380823i) q^{38} +(2.25085 - 4.06313i) q^{39} +(-1.36687 - 0.366251i) q^{41} +(-0.853209 + 3.18422i) q^{42} +(9.47787 - 2.53959i) q^{43} +(0.0647878 + 0.0647878i) q^{44} +(-3.38446 + 0.906863i) q^{46} -4.62826i q^{47} +(-0.333429 - 1.24438i) q^{48} +(-0.226046 - 0.391523i) q^{49} -6.38876i q^{51} +(2.59427 + 2.50395i) q^{52} +(-3.73885 + 3.73885i) q^{53} +(-1.44720 + 5.40103i) q^{54} +(-2.21606 - 1.27944i) q^{56} -0.693818 q^{57} +(-2.89539 - 1.67166i) q^{58} +(1.50751 + 5.62609i) q^{59} +(-1.29095 + 2.23599i) q^{61} +(5.78794 + 1.55087i) q^{62} +(1.71491 + 2.97031i) q^{63} +1.00000 q^{64} -0.118036 q^{66} +(-2.90153 - 5.02560i) q^{67} +(4.79019 + 1.28353i) q^{68} +(2.25696 - 3.90916i) q^{69} +(2.52494 + 9.42322i) q^{71} +(-1.16078 - 0.670177i) q^{72} -16.8672 q^{73} +(-5.43423 - 3.13745i) q^{74} +(0.139391 - 0.520214i) q^{76} +(-0.165785 + 0.165785i) q^{77} +(-4.64420 + 0.0822710i) q^{78} -8.94406i q^{79} +(-1.59120 - 2.75603i) q^{81} +(0.366251 + 1.36687i) q^{82} +13.1459i q^{83} +(3.18422 - 0.853209i) q^{84} +(-6.93828 - 6.93828i) q^{86} +(4.16034 - 1.11476i) q^{87} +(0.0237140 - 0.0885018i) q^{88} +(7.50341 + 2.01053i) q^{89} +(-6.40734 + 6.63844i) q^{91} +(2.47760 + 2.47760i) q^{92} +(-6.68526 + 3.85974i) q^{93} +(-4.00819 + 2.31413i) q^{94} +(-0.910946 + 0.910946i) q^{96} +(-7.07053 + 12.2465i) q^{97} +(-0.226046 + 0.391523i) q^{98} +(-0.0868386 + 0.0868386i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{2} - 8 q^{4} - 12 q^{7} + 16 q^{8} - 24 q^{9} - 4 q^{11} - 8 q^{13} - 8 q^{16} + 8 q^{17} + 16 q^{19} - 4 q^{21} - 4 q^{22} + 4 q^{23} + 4 q^{26} - 36 q^{27} + 12 q^{28} + 36 q^{29} - 8 q^{31}+ \cdots - 36 q^{99}+O(q^{100}) $ 16 * q - 8 * q^2 - 8 * q^4 - 12 * q^7 + 16 * q^8 - 24 * q^9 - 4 * q^11 - 8 * q^13 - 8 * q^16 + 8 * q^17 + 16 * q^19 - 4 * q^21 - 4 * q^22 + 4 * q^23 + 4 * q^26 - 36 * q^27 + 12 * q^28 + 36 * q^29 - 8 * q^31 - 8 * q^32 - 16 * q^34 + 24 * q^36 + 36 * q^37 + 4 * q^38 + 32 * q^41 + 8 * q^42 + 36 * q^43 + 8 * q^44 + 4 * q^46 + 16 * q^49 + 4 * q^52 - 44 * q^53 + 36 * q^54 - 12 * q^56 + 48 * q^57 - 36 * q^58 - 24 * q^59 - 20 * q^61 - 8 * q^62 + 36 * q^63 + 16 * q^64 + 12 * q^67 + 8 * q^68 + 24 * q^69 + 16 * q^71 - 24 * q^72 - 36 * q^74 - 20 * q^76 - 16 * q^77 - 60 * q^78 + 16 * q^81 - 16 * q^82 - 4 * q^84 - 36 * q^86 - 12 * q^87 - 4 * q^88 - 28 * q^89 - 44 * q^91 - 8 * q^92 + 24 * q^93 + 24 * q^94 + 8 * q^97 + 16 * q^98 - 36 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/650\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{12}\right)$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	1.24438	+	0.333429i	0.718441	+	0.192506i	0.599476	−	0.800393i	$-0.295376\pi$
$3$	1.24438	+	0.333429i	0.718441	+	0.192506i	0.118965	+	0.992898i	$0.462042\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	−0.333429	−	1.24438i	−0.136122	−	0.508014i
$7$	−2.21606	−	1.27944i	−0.837593	−	0.483584i	0.0188525	−	0.999822i	$-0.493999\pi$
$7$	−2.21606	−	1.27944i	−0.837593	−	0.483584i	−0.856445	+	0.516238i	$0.827332\pi$
$8$	1.00000			0.353553
$9$	−1.16078	−	0.670177i	−0.386927	−	0.223392i
$10$		0			0
$11$	0.0237140	−	0.0885018i	0.00715003	−	0.0266843i	−0.962259	−	0.272136i	$-0.912270\pi$
$11$	0.0237140	−	0.0885018i	0.00715003	−	0.0266843i	0.969409	+	0.245452i	$0.0789364\pi$
$12$	−0.910946	+	0.910946i	−0.262968	+	0.262968i
$13$	0.871354	−	3.49868i	0.241670	−	0.970359i
$13$	0.871354	−	3.49868i	0.241670	−	0.970359i
$14$			2.55889i			0.683892i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.28353	−	4.79019i	−0.311301	−	1.16179i	−0.927384	−	0.374110i	$-0.877948\pi$
$17$	−1.28353	−	4.79019i	−0.311301	−	1.16179i	0.616083	−	0.787681i	$-0.288719\pi$
$18$			1.34035i			0.315924i
$19$	−0.520214	+	0.139391i	−0.119345	+	0.0319784i	−0.317997	−	0.948092i	$-0.603010\pi$
$19$	−0.520214	+	0.139391i	−0.119345	+	0.0319784i	0.198652	+	0.980070i	$0.436344\pi$
$20$		0			0
$21$	−2.33101	−	2.33101i	−0.508668	−	0.508668i
$22$	−0.0885018	+	0.0237140i	−0.0188686	+	0.00505584i
$23$	0.906863	−	3.38446i	0.189094	−	0.705709i	−0.804623	−	0.593786i	$-0.797633\pi$
$23$	0.906863	−	3.38446i	0.189094	−	0.705709i	0.993717	−	0.111922i	$-0.0357008\pi$
$24$	1.24438	+	0.333429i	0.254007	+	0.0680610i
$25$		0			0
$26$	−3.46562	+	0.994724i	−0.679664	+	0.195082i
$27$	−3.95383	−	3.95383i	−0.760915	−	0.760915i
$28$	2.21606	−	1.27944i	0.418796	−	0.241792i
$29$	2.89539	−	1.67166i	0.537661	−	0.310419i	−0.206470	−	0.978453i	$-0.566197\pi$
$29$	2.89539	−	1.67166i	0.537661	−	0.310419i	0.744130	+	0.668034i	$0.232864\pi$
$30$		0			0
$31$	−4.23707	+	4.23707i	−0.760999	+	0.760999i	−0.976503	−	0.215504i	$-0.930861\pi$
$31$	−4.23707	+	4.23707i	−0.760999	+	0.760999i	0.215504	+	0.976503i	$0.430861\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	0.0590182	−	0.102223i	0.0102737	−	0.0177947i
$34$	−3.50666	+	3.50666i	−0.601387	+	0.601387i
$35$		0			0
$36$	1.16078	−	0.670177i	0.193463	−	0.111696i
$37$	5.43423	−	3.13745i	0.893382	−	0.515794i	0.0183349	−	0.999832i	$-0.494164\pi$
$37$	5.43423	−	3.13745i	0.893382	−	0.515794i	0.875047	+	0.484038i	$0.160830\pi$
$38$	0.380823	+	0.380823i	0.0617776	+	0.0617776i
$39$	2.25085	−	4.06313i	0.360425	−	0.650622i
$40$		0			0
$41$	−1.36687	−	0.366251i	−0.213469	−	0.0571987i	0.150500	−	0.988610i	$-0.451912\pi$
$41$	−1.36687	−	0.366251i	−0.213469	−	0.0571987i	−0.363968	+	0.931411i	$0.618578\pi$
$42$	−0.853209	+	3.18422i	−0.131653	+	0.491336i
$43$	9.47787	−	2.53959i	1.44536	−	0.387284i	0.550954	−	0.834536i	$-0.314264\pi$
$43$	9.47787	−	2.53959i	1.44536	−	0.387284i	0.894408	+	0.447252i	$0.147597\pi$
$44$	0.0647878	+	0.0647878i	0.00976713	+	0.00976713i
$45$		0			0
$46$	−3.38446	+	0.906863i	−0.499011	+	0.133710i
$47$		−	4.62826i		−	0.675101i	−0.941307	−	0.337551i	$-0.890402\pi$
$47$		−	4.62826i		−	0.675101i	0.941307	−	0.337551i	$-0.109598\pi$
$48$	−0.333429	−	1.24438i	−0.0481264	−	0.179610i
$49$	−0.226046	−	0.391523i	−0.0322923	−	0.0559318i
$50$		0			0
$51$		−	6.38876i		−	0.894605i
$52$	2.59427	+	2.50395i	0.359760	+	0.347236i
$53$	−3.73885	+	3.73885i	−0.513570	+	0.513570i	−0.915618	−	0.402049i	$-0.868298\pi$
$53$	−3.73885	+	3.73885i	−0.513570	+	0.513570i	0.402049	+	0.915618i	$0.368298\pi$
$54$	−1.44720	+	5.40103i	−0.196939	+	0.734987i
$55$		0			0
$56$	−2.21606	−	1.27944i	−0.296134	−	0.170973i
$57$	−0.693818			−0.0918985
$58$	−2.89539	−	1.67166i	−0.380184	−	0.219499i
$59$	1.50751	+	5.62609i	0.196261	+	0.732455i	0.991937	+	0.126733i	$0.0404490\pi$
$59$	1.50751	+	5.62609i	0.196261	+	0.732455i	−0.795676	+	0.605722i	$0.792884\pi$
$60$		0			0
$61$	−1.29095	+	2.23599i	−0.165289	+	0.286289i	−0.936758	−	0.349978i	$-0.886189\pi$
$61$	−1.29095	+	2.23599i	−0.165289	+	0.286289i	0.771469	+	0.636267i	$0.219522\pi$
$62$	5.78794	+	1.55087i	0.735069	+	0.196961i
$63$	1.71491	+	2.97031i	0.216058	+	0.374223i
$64$	1.00000			0.125000
$65$		0			0
$66$	−0.118036			−0.0145293
$67$	−2.90153	−	5.02560i	−0.354478	−	0.613974i	0.632550	−	0.774519i	$-0.282008\pi$
$67$	−2.90153	−	5.02560i	−0.354478	−	0.613974i	−0.987029	+	0.160545i	$0.948675\pi$
$68$	4.79019	+	1.28353i	0.580896	+	0.155651i
$69$	2.25696	−	3.90916i	0.271706	−	0.470608i
$70$		0			0
$71$	2.52494	+	9.42322i	0.299656	+	1.11833i	0.937449	+	0.348123i	$0.113181\pi$
$71$	2.52494	+	9.42322i	0.299656	+	1.11833i	−0.637793	+	0.770208i	$0.720153\pi$
$72$	−1.16078	−	0.670177i	−0.136799	−	0.0789811i
$73$	−16.8672			−1.97416			−0.987078	−	0.160238i	$-0.948774\pi$
$73$	−16.8672			−1.97416			−0.987078	+	0.160238i	$0.948774\pi$
$74$	−5.43423	−	3.13745i	−0.631717	−	0.364722i
$75$		0			0
$76$	0.139391	−	0.520214i	0.0159892	−	0.0596726i
$77$	−0.165785	+	0.165785i	−0.0188929	+	0.0188929i
$78$	−4.64420	+	0.0822710i	−0.525853	+	0.00931535i
$79$		−	8.94406i		−	1.00629i	−0.864203	−	0.503143i	$-0.832177\pi$
$79$		−	8.94406i		−	1.00629i	0.864203	−	0.503143i	$-0.167823\pi$
$80$		0			0
$81$	−1.59120	−	2.75603i	−0.176800	−	0.306226i
$82$	0.366251	+	1.36687i	0.0404456	+	0.150945i
$83$			13.1459i			1.44295i	0.692442	+	0.721473i	$0.256535\pi$
$83$			13.1459i			1.44295i	−0.692442	+	0.721473i	$0.743465\pi$
$84$	3.18422	−	0.853209i	0.347427	−	0.0930927i
$85$		0			0
$86$	−6.93828	−	6.93828i	−0.748174	−	0.748174i
$87$	4.16034	−	1.11476i	0.446035	−	0.119515i
$88$	0.0237140	−	0.0885018i	0.00252792	−	0.00943432i
$89$	7.50341	+	2.01053i	0.795360	+	0.213116i	0.633546	−	0.773705i	$-0.281599\pi$
$89$	7.50341	+	2.01053i	0.795360	+	0.213116i	0.161814	+	0.986821i	$0.448265\pi$
$90$		0			0
$91$	−6.40734	+	6.63844i	−0.671671	+	0.695897i
$92$	2.47760	+	2.47760i	0.258307	+	0.258307i
$93$	−6.68526	+	3.85974i	−0.693230	+	0.400236i
$94$	−4.00819	+	2.31413i	−0.413413	+	0.238684i
$95$		0			0
$96$	−0.910946	+	0.910946i	−0.0929731	+	0.0929731i
$97$	−7.07053	+	12.2465i	−0.717904	+	1.24345i	0.243925	+	0.969794i	$0.421565\pi$
$97$	−7.07053	+	12.2465i	−0.717904	+	1.24345i	−0.961829	+	0.273652i	$0.911768\pi$
$98$	−0.226046	+	0.391523i	−0.0228341	+	0.0395498i
$99$	−0.0868386	+	0.0868386i	−0.00872760	+	0.00872760i
$100$		0			0
$101$	12.9174	−	7.45784i	1.28532	−	0.742083i	0.307508	−	0.951545i	$-0.400505\pi$
$101$	12.9174	−	7.45784i	1.28532	−	0.742083i	0.977817	+	0.209463i	$0.0671716\pi$
$102$	−5.53283	+	3.19438i	−0.547832	+	0.316291i
$103$	−1.13328	−	1.13328i	−0.111666	−	0.111666i	0.649066	−	0.760732i	$-0.275160\pi$
$103$	−1.13328	−	1.13328i	−0.111666	−	0.111666i	−0.760732	+	0.649066i	$0.775160\pi$
$104$	0.871354	−	3.49868i	0.0854432	−	0.343074i
$105$		0			0
$106$	5.10736	+	1.36851i	0.496070	+	0.132922i
$107$	−1.78582	+	6.66478i	−0.172642	+	0.644309i	0.824299	+	0.566154i	$0.191569\pi$
$107$	−1.78582	+	6.66478i	−0.172642	+	0.644309i	−0.996941	+	0.0781543i	$0.975097\pi$
$108$	5.40103	−	1.44720i	0.519714	−	0.139257i
$109$	−10.9863	−	10.9863i	−1.05230	−	1.05230i	−0.998555	−	0.0537443i	$-0.982884\pi$
$109$	−10.9863	−	10.9863i	−1.05230	−	1.05230i	−0.0537443	−	0.998555i	$-0.517116\pi$
$110$		0			0
$111$	7.80835	−	2.09224i	0.741135	−	0.198587i
$112$			2.55889i			0.241792i
$113$	−0.423544	−	1.58069i	−0.0398436	−	0.148698i	0.943138	−	0.332400i	$-0.107859\pi$
$113$	−0.423544	−	1.58069i	−0.0398436	−	0.148698i	−0.982982	+	0.183702i	$0.941192\pi$
$114$	0.346909	+	0.600864i	0.0324910	+	0.0562761i
$115$		0			0
$116$			3.34331i			0.310419i
$117$	−3.35618	+	3.47723i	−0.310279	+	0.321470i
$118$	4.11859	−	4.11859i	0.379146	−	0.379146i
$119$	−3.28440	+	12.2576i	−0.301081	+	1.12365i
$120$		0			0
$121$	9.51901	+	5.49580i	0.865364	+	0.499618i
$122$	2.58190			0.233754
$123$	−1.57878	−	0.911507i	−0.142353	−	0.0821878i
$124$	−1.55087	−	5.78794i	−0.139273	−	0.519772i
$125$		0			0
$126$	1.71491	−	2.97031i	0.152776	−	0.264616i
$127$	3.06238	+	0.820562i	0.271742	+	0.0728131i	0.392117	−	0.919915i	$-0.371743\pi$
$127$	3.06238	+	0.820562i	0.271742	+	0.0728131i	−0.120375	+	0.992729i	$0.538410\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	12.6408			1.11296
$130$		0			0
$131$	16.7339			1.46204			0.731022	−	0.682353i	$-0.239043\pi$
$131$	16.7339			1.46204			0.731022	+	0.682353i	$0.239043\pi$
$132$	0.0590182	+	0.102223i	0.00513687	+	0.00889733i
$133$	1.33117	+	0.356685i	0.115427	+	0.0309285i
$134$	−2.90153	+	5.02560i	−0.250654	+	0.434145i
$135$		0			0
$136$	−1.28353	−	4.79019i	−0.110062	−	0.410755i
$137$	1.35907	+	0.784662i	0.116114	+	0.0670382i	0.556932	−	0.830558i	$-0.311978\pi$
$137$	1.35907	+	0.784662i	0.116114	+	0.0670382i	−0.440818	+	0.897596i	$0.645312\pi$
$138$	−4.51391			−0.384250
$139$	−14.3956	−	8.31130i	−1.22102	−	0.704955i	−0.255884	−	0.966708i	$-0.582366\pi$
$139$	−14.3956	−	8.31130i	−1.22102	−	0.704955i	−0.965135	+	0.261752i	$0.915700\pi$
$140$		0			0
$141$	1.54320	−	5.75929i	0.129961	−	0.485020i
$142$	6.89827	−	6.89827i	0.578890	−	0.578890i
$143$	−0.288976	−	0.160084i	−0.0241654	−	0.0133869i
$144$			1.34035i			0.111696i
$145$		0			0
$146$	8.43360	+	14.6074i	0.697970	+	1.20892i
$147$	−0.150741	−	0.562572i	−0.0124329	−	0.0464002i
$148$			6.27491i			0.515794i
$149$	15.5103	−	4.15599i	1.27066	−	0.340472i	0.440375	−	0.897814i	$-0.354846\pi$
$149$	15.5103	−	4.15599i	1.27066	−	0.340472i	0.830283	+	0.557342i	$0.188179\pi$
$150$		0			0
$151$	7.93116	+	7.93116i	0.645428	+	0.645428i	0.951885	−	0.306456i	$-0.0991434\pi$
$151$	7.93116	+	7.93116i	0.645428	+	0.645428i	−0.306456	+	0.951885i	$0.599143\pi$
$152$	−0.520214	+	0.139391i	−0.0421949	+	0.0113061i
$153$	−1.72038	+	6.42055i	−0.139084	+	0.519070i
$154$	0.226466	+	0.0606814i	0.0182492	+	0.00488985i
$155$		0			0
$156$	2.39335	+	3.98086i	0.191621	+	0.318724i
$157$	11.2457	+	11.2457i	0.897507	+	0.897507i	0.995215	−	0.0977078i	$-0.0311511\pi$
$157$	11.2457	+	11.2457i	0.897507	+	0.897507i	−0.0977078	+	0.995215i	$0.531151\pi$
$158$	−7.74578	+	4.47203i	−0.616221	+	0.355776i
$159$	−5.89917	+	3.40589i	−0.467835	+	0.270104i
$160$		0			0
$161$	−6.33989	+	6.33989i	−0.499653	+	0.499653i
$162$	−1.59120	+	2.75603i	−0.125016	+	0.216534i
$163$	8.48209	−	14.6914i	0.664369	−	1.15072i	−0.315088	−	0.949063i	$-0.602034\pi$
$163$	8.48209	−	14.6914i	0.664369	−	1.15072i	0.979456	−	0.201657i	$-0.0646328\pi$
$164$	1.00062	−	1.00062i	0.0781349	−	0.0781349i
$165$		0			0
$166$	11.3847	−	6.57293i	0.883621	−	0.510159i
$167$	14.8524	−	8.57502i	1.14931	−	0.663555i	0.200592	−	0.979675i	$-0.435714\pi$
$167$	14.8524	−	8.57502i	1.14931	−	0.663555i	0.948719	+	0.316120i	$0.102380\pi$
$168$	−2.33101	−	2.33101i	−0.179841	−	0.179841i
$169$	−11.4815	−	6.09717i	−0.883191	−	0.469013i
$170$		0			0
$171$	0.697270	+	0.186833i	0.0533216	+	0.0142875i
$172$	−2.53959	+	9.47787i	−0.193642	+	0.722681i
$173$	17.0027	−	4.55586i	1.29269	−	0.346375i	0.454009	−	0.890997i	$-0.349993\pi$
$173$	17.0027	−	4.55586i	1.29269	−	0.346375i	0.838682	+	0.544622i	$0.183327\pi$
$174$	−3.04558	−	3.04558i	−0.230885	−	0.230885i
$175$		0			0
$176$	−0.0885018	+	0.0237140i	−0.00667107	+	0.00178751i
$177$			7.50362i			0.564007i
$178$	−2.01053	−	7.50341i	−0.150696	−	0.562405i
$179$	10.5213	+	18.2234i	0.786398	+	1.36208i	0.928160	+	0.372181i	$0.121390\pi$
$179$	10.5213	+	18.2234i	0.786398	+	1.36208i	−0.141762	+	0.989901i	$0.545277\pi$
$180$		0			0
$181$		−	25.6164i		−	1.90406i	−0.306012	−	0.952028i	$-0.598995\pi$
$181$		−	25.6164i		−	1.90406i	0.306012	−	0.952028i	$-0.401005\pi$
$182$	8.95272	+	2.22970i	0.663620	+	0.165276i
$183$	−2.35197	+	2.35197i	−0.173863	+	0.173863i
$184$	0.906863	−	3.38446i	0.0668548	−	0.249506i
$185$		0			0
$186$	6.68526	+	3.85974i	0.490187	+	0.283010i
$187$	−0.454378			−0.0332274
$188$	4.00819	+	2.31413i	0.292327	+	0.168775i
$189$	3.70323	+	13.8206i	0.269370	+	1.00530i
$190$		0			0
$191$	−8.21501	+	14.2288i	−0.594417	+	1.02956i	0.399211	+	0.916859i	$0.369284\pi$
$191$	−8.21501	+	14.2288i	−0.594417	+	1.02956i	−0.993629	+	0.112702i	$0.964049\pi$
$192$	1.24438	+	0.333429i	0.0898051	+	0.0240632i
$193$	−5.36350	−	9.28986i	−0.386073	−	0.668699i	0.605844	−	0.795583i	$-0.292835\pi$
$193$	−5.36350	−	9.28986i	−0.386073	−	0.668699i	−0.991917	+	0.126885i	$0.959502\pi$
$194$	14.1411			1.01527
$195$		0			0
$196$	0.452092			0.0322923
$197$	5.94533	+	10.2976i	0.423587	+	0.733675i	0.996287	−	0.0860902i	$-0.0274373\pi$
$197$	5.94533	+	10.2976i	0.423587	+	0.733675i	−0.572700	+	0.819765i	$0.694104\pi$
$198$	0.118624	+	0.0317851i	0.00843022	+	0.00225887i
$199$	−1.80229	+	3.12166i	−0.127761	+	0.221288i	−0.922809	−	0.385258i	$-0.874112\pi$
$199$	−1.80229	+	3.12166i	−0.127761	+	0.221288i	0.795048	+	0.606547i	$0.207446\pi$
$200$		0			0
$201$	−1.93491	−	7.22119i	−0.136478	−	0.509343i
$202$	−12.9174	−	7.45784i	−0.908862	−	0.524732i
$203$	−8.55516			−0.600455
$204$	5.53283	+	3.19438i	0.387375	+	0.223651i
$205$		0			0
$206$	−0.414810	+	1.54809i	−0.0289012	+	0.107861i
$207$	−3.32086	+	3.32086i	−0.230815	+	0.230815i
$208$	−3.46562	+	0.994724i	−0.240298	+	0.0689717i
$209$			0.0493453i			0.00341329i
$210$		0			0
$211$	5.78313	+	10.0167i	0.398127	+	0.689576i	0.993495	−	0.113877i	$-0.0363270\pi$
$211$	5.78313	+	10.0167i	0.398127	+	0.689576i	−0.595368	+	0.803453i	$0.702994\pi$
$212$	−1.36851	−	5.10736i	−0.0939898	−	0.350775i
$213$			12.5679i			0.861139i
$214$	6.66478	−	1.78582i	0.455595	−	0.122076i
$215$		0			0
$216$	−3.95383	−	3.95383i	−0.269024	−	0.269024i
$217$	14.8107	−	3.96851i	1.00541	−	0.269400i
$218$	−4.02127	+	15.0076i	−0.272355	+	1.01644i
$219$	−20.9891	−	5.62402i	−1.41831	−	0.380036i
$220$		0			0
$221$	−17.8777	+	0.316700i	−1.20259	+	0.0213035i
$222$	−5.71611	−	5.71611i	−0.383640	−	0.383640i
$223$	4.28077	−	2.47150i	0.286662	−	0.165504i	−0.349774	−	0.936834i	$-0.613742\pi$
$223$	4.28077	−	2.47150i	0.286662	−	0.165504i	0.636435	+	0.771330i	$0.280408\pi$
$224$	2.21606	−	1.27944i	0.148067	−	0.0854865i
$225$		0			0
$226$	−1.15714	+	1.15714i	−0.0769720	+	0.0769720i
$227$	−8.36313	+	14.4854i	−0.555081	+	0.961428i	0.442817	+	0.896612i	$0.353979\pi$
$227$	−8.36313	+	14.4854i	−0.555081	+	0.961428i	−0.997897	+	0.0648158i	$0.979354\pi$
$228$	0.346909	−	0.600864i	0.0229746	−	0.0397932i
$229$	11.9068	−	11.9068i	0.786822	−	0.786822i	−0.194150	−	0.980972i	$-0.562195\pi$
$229$	11.9068	−	11.9068i	0.786822	−	0.786822i	0.980972	+	0.194150i	$0.0621948\pi$
$230$		0			0
$231$	−0.261576	+	0.151021i	−0.0172104	+	0.00993645i
$232$	2.89539	−	1.67166i	0.190092	−	0.109750i
$233$	−18.4012	−	18.4012i	−1.20550	−	1.20550i	−0.972468	−	0.233034i	$-0.925135\pi$
$233$	−18.4012	−	18.4012i	−1.20550	−	1.20550i	−0.233034	−	0.972468i	$-0.574865\pi$
$234$	4.68946	+	1.16792i	0.306560	+	0.0763494i
$235$		0			0
$236$	−5.62609	−	1.50751i	−0.366227	−	0.0981303i
$237$	2.98221	−	11.1298i	0.193716	−	0.722956i
$238$	12.2576	−	3.28440i	0.794539	−	0.212896i
$239$	10.3185	+	10.3185i	0.667446	+	0.667446i	0.957124	−	0.289678i	$-0.0935483\pi$
$239$	10.3185	+	10.3185i	0.667446	+	0.667446i	−0.289678	+	0.957124i	$0.593548\pi$
$240$		0			0
$241$	−2.20767	+	0.591542i	−0.142208	+	0.0381046i	−0.329221	−	0.944253i	$-0.606786\pi$
$241$	−2.20767	+	0.591542i	−0.142208	+	0.0381046i	0.187013	+	0.982357i	$0.440119\pi$
$242$		−	10.9916i		−	0.706567i
$243$	3.28050	+	12.2430i	0.210444	+	0.785389i
$244$	−1.29095	−	2.23599i	−0.0826446	−	0.143145i
$245$		0			0
$246$			1.82301i			0.116231i
$247$	0.0343935	+	1.94152i	0.00218841	+	0.123536i
$248$	−4.23707	+	4.23707i	−0.269054	+	0.269054i
$249$	−4.38322	+	16.3584i	−0.277775	+	1.03667i
$250$		0			0
$251$	8.32501	+	4.80645i	0.525470	+	0.303380i	0.739170	−	0.673519i	$-0.235218\pi$
$251$	8.32501	+	4.80645i	0.525470	+	0.303380i	−0.213700	+	0.976899i	$0.568551\pi$
$252$	−3.42982			−0.216058
$253$	−0.278025	−	0.160518i	−0.0174793	−	0.0100917i
$254$	−0.820562	−	3.06238i	−0.0514866	−	0.192151i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−26.9330	−	7.21668i	−1.68003	−	0.450164i	−0.712247	−	0.701929i	$-0.752322\pi$
$257$	−26.9330	−	7.21668i	−1.68003	−	0.450164i	−0.967788	+	0.251765i	$0.918989\pi$
$258$	−6.32040	−	10.9473i	−0.393491	−	0.681547i
$259$	−16.0568			−0.997720
$260$		0			0
$261$	−4.48122			−0.277381
$262$	−8.36693	−	14.4920i	−0.516911	−	0.895316i
$263$	26.4833	+	7.09618i	1.63303	+	0.437569i	0.954792	−	0.297274i	$-0.0960775\pi$
$263$	26.4833	+	7.09618i	1.63303	+	0.437569i	0.678237	+	0.734843i	$0.262744\pi$
$264$	0.0590182	−	0.102223i	0.00363232	−	0.00629136i
$265$		0			0
$266$	−0.356685	−	1.33117i	−0.0218698	−	0.0816192i
$267$	8.66669	+	5.00372i	0.530393	+	0.306223i
$268$	5.80306			0.354478
$269$	−1.58851	−	0.917129i	−0.0968534	−	0.0559183i	0.450791	−	0.892630i	$-0.351142\pi$
$269$	−1.58851	−	0.917129i	−0.0968534	−	0.0559183i	−0.547644	+	0.836711i	$0.684475\pi$
$270$		0			0
$271$	−1.52198	+	5.68011i	−0.0924537	+	0.345042i	−0.996621	−	0.0821364i	$-0.973826\pi$
$271$	−1.52198	+	5.68011i	−0.0924537	+	0.345042i	0.904167	+	0.427178i	$0.140492\pi$
$272$	−3.50666	+	3.50666i	−0.212623	+	0.212623i
$273$	−10.1866	+	6.12432i	−0.616520	+	0.370661i
$274$		−	1.56932i		−	0.0948063i
$275$		0			0
$276$	2.25696	+	3.90916i	0.135853	+	0.235304i
$277$	−1.48750	−	5.55142i	−0.0893750	−	0.333552i	0.906732	−	0.421708i	$-0.138569\pi$
$277$	−1.48750	−	5.55142i	−0.0893750	−	0.333552i	−0.996107	+	0.0881559i	$0.971903\pi$
$278$			16.6226i			0.996958i
$279$	7.75788	−	2.07872i	0.464452	−	0.124450i
$280$		0			0
$281$	−16.7234	−	16.7234i	−0.997631	−	0.997631i	0.00236572	−	0.999997i	$-0.499247\pi$
$281$	−16.7234	−	16.7234i	−0.997631	−	0.997631i	−0.999997	+	0.00236572i	$0.999247\pi$
$282$	−5.75929	+	1.54320i	−0.342961	+	0.0918961i
$283$	3.02196	−	11.2781i	0.179637	−	0.670413i	−0.816079	−	0.577941i	$-0.803856\pi$
$283$	3.02196	−	11.2781i	0.179637	−	0.670413i	0.995715	−	0.0924722i	$-0.0294769\pi$
$284$	−9.42322	−	2.52494i	−0.559165	−	0.149828i
$285$		0			0
$286$	0.00585123	+	0.330302i	0.000345990	+	0.0195312i
$287$	2.56046	+	2.56046i	0.151139	+	0.151139i
$288$	1.16078	−	0.670177i	0.0683996	−	0.0394905i
$289$	−6.57603	+	3.79667i	−0.386825	+	0.223334i
$290$		0			0
$291$	−12.8817	+	12.8817i	−0.755142	+	0.755142i
$292$	8.43360	−	14.6074i	0.493539	−	0.854835i
$293$	6.50872	−	11.2734i	0.380243	−	0.658601i	−0.610854	−	0.791744i	$-0.709174\pi$
$293$	6.50872	−	11.2734i	0.380243	−	0.658601i	0.991097	+	0.133143i	$0.0425069\pi$
$294$	−0.411831	+	0.411831i	−0.0240185	+	0.0240185i
$295$		0			0
$296$	5.43423	−	3.13745i	0.315858	−	0.182361i
$297$	−0.443682	+	0.256160i	−0.0257450	+	0.0148639i
$298$	−11.3544	−	11.3544i	−0.657741	−	0.657741i
$299$	−11.0509	−	6.12188i	−0.639092	−	0.354038i
$300$		0			0
$301$	−24.2528	−	6.49852i	−1.39791	−	0.374569i
$302$	2.90300	−	10.8342i	0.167049	−	0.623436i
$303$	18.5607	−	4.97333i	1.06628	−	0.285710i
$304$	0.380823	+	0.380823i	0.0218417	+	0.0218417i
$305$		0			0
$306$	6.42055	−	1.72038i	0.367038	−	0.0983476i
$307$			16.2090i			0.925099i	0.886593	+	0.462549i	$0.153065\pi$
$307$			16.2090i			0.925099i	−0.886593	+	0.462549i	$0.846935\pi$
$308$	−0.0606814	−	0.226466i	−0.00345764	−	0.0129041i
$309$	−1.03236	−	1.78810i	−0.0587289	−	0.101721i
$310$		0			0
$311$		−	29.1452i		−	1.65267i	−0.563178	−	0.826335i	$-0.690422\pi$
$311$		−	29.1452i		−	1.65267i	0.563178	−	0.826335i	$-0.309578\pi$
$312$	2.25085	−	4.06313i	0.127429	−	0.230030i
$313$	−5.10788	+	5.10788i	−0.288714	+	0.288714i	−0.836572	−	0.547857i	$-0.815444\pi$
$313$	−5.10788	+	5.10788i	−0.288714	+	0.288714i	0.547857	+	0.836572i	$0.315444\pi$
$314$	4.11622	−	15.3620i	0.232292	−	0.866926i
$315$		0			0
$316$	7.74578	+	4.47203i	0.435734	+	0.251571i
$317$	−14.4669			−0.812541			−0.406271	−	0.913753i	$-0.633171\pi$
$317$	−14.4669			−0.812541			−0.406271	+	0.913753i	$0.633171\pi$
$318$	5.89917	+	3.40589i	0.330809	+	0.190993i
$319$	−0.0792832	−	0.295889i	−0.00443901	−	0.0165666i
$320$		0			0
$321$	−4.44447	+	7.69805i	−0.248066	+	0.429663i
$322$	8.66045	+	2.32056i	0.482628	+	0.129320i
$323$	1.33542	+	2.31301i	0.0743046	+	0.128699i
$324$	3.18239			0.176800
$325$		0			0
$326$	−16.9642			−0.939559
$327$	−10.0080	−	17.3343i	−0.553441	−	0.958588i
$328$	−1.36687	−	0.366251i	−0.0754725	−	0.0202228i
$329$	−5.92160	+	10.2565i	−0.326468	+	0.565460i
$330$		0			0
$331$	−7.64722	−	28.5398i	−0.420329	−	1.56869i	−0.773916	−	0.633289i	$-0.781705\pi$
$331$	−7.64722	−	28.5398i	−0.420329	−	1.56869i	0.353586	−	0.935402i	$-0.384962\pi$
$332$	−11.3847	−	6.57293i	−0.624814	−	0.360737i
$333$	−8.41060			−0.460898
$334$	−14.8524	−	8.57502i	−0.812685	−	0.469204i
$335$		0			0
$336$	−0.853209	+	3.18422i	−0.0465464	+	0.173713i
$337$	7.42010	−	7.42010i	0.404198	−	0.404198i	−0.475511	−	0.879710i	$-0.657737\pi$
$337$	7.42010	−	7.42010i	0.404198	−	0.404198i	0.879710	+	0.475511i	$0.157737\pi$
$338$	0.460439	+	12.9918i	0.0250446	+	0.706663i
$339$		−	2.10819i		−	0.114501i
$340$		0			0
$341$	0.274510	+	0.475465i	0.0148656	+	0.0257479i
$342$	−0.186833	−	0.697270i	−0.0101028	−	0.0377040i
$343$			19.0691i			1.02963i
$344$	9.47787	−	2.53959i	0.511013	−	0.136925i
$345$		0			0
$346$	−12.4468	−	12.4468i	−0.669146	−	0.669146i
$347$	3.44872	−	0.924081i	0.185137	−	0.0496073i	−0.165059	−	0.986284i	$-0.552782\pi$
$347$	3.44872	−	0.924081i	0.185137	−	0.0496073i	0.350196	+	0.936676i	$0.386115\pi$
$348$	−1.11476	+	4.16034i	−0.0597573	+	0.223017i
$349$	−2.89921	−	0.776840i	−0.155191	−	0.0415833i	0.180387	−	0.983596i	$-0.442265\pi$
$349$	−2.89921	−	0.776840i	−0.155191	−	0.0415833i	−0.335578	+	0.942012i	$0.608932\pi$
$350$		0			0
$351$	−17.2784	+	10.3880i	−0.922250	+	0.554470i
$352$	0.0647878	+	0.0647878i	0.00345320	+	0.00345320i
$353$	−9.92204	+	5.72849i	−0.528097	+	0.304897i	−0.740241	−	0.672342i	$-0.765289\pi$
$353$	−9.92204	+	5.72849i	−0.528097	+	0.304897i	0.212144	+	0.977238i	$0.431955\pi$
$354$	6.49833	−	3.75181i	0.345382	−	0.199406i
$355$		0			0
$356$	−5.49288	+	5.49288i	−0.291122	+	0.291122i
$357$	−8.17406	+	14.1579i	−0.432617	+	0.749315i
$358$	10.5213	−	18.2234i	0.556068	−	0.963137i
$359$	5.20578	−	5.20578i	0.274751	−	0.274751i	−0.556259	−	0.831009i	$-0.687764\pi$
$359$	5.20578	−	5.20578i	0.274751	−	0.274751i	0.831009	+	0.556259i	$0.187764\pi$
$360$		0			0
$361$	−16.2033	+	9.35497i	−0.852805	+	0.492367i
$362$	−22.1845	+	12.8082i	−1.16599	+	0.673185i
$363$	10.0128	+	10.0128i	0.525534	+	0.525534i
$364$	−2.54539	−	8.86813i	−0.133415	−	0.464817i
$365$		0			0
$366$	3.21286	+	0.860882i	0.167939	+	0.0449990i
$367$	4.62496	−	17.2606i	0.241421	−	0.900995i	−0.733728	−	0.679443i	$-0.762221\pi$
$367$	4.62496	−	17.2606i	0.241421	−	0.900995i	0.975149	−	0.221551i	$-0.0711120\pi$
$368$	−3.38446	+	0.906863i	−0.176427	+	0.0472735i
$369$	1.34118	+	1.34118i	0.0698190	+	0.0698190i
$370$		0			0
$371$	13.0692	−	3.50187i	0.678517	−	0.181808i
$372$		−	7.71948i		−	0.400236i
$373$	−8.24794	−	30.7817i	−0.427062	−	1.59382i	−0.759379	−	0.650649i	$-0.774497\pi$
$373$	−8.24794	−	30.7817i	−0.427062	−	1.59382i	0.332317	−	0.943168i	$-0.392170\pi$
$374$	0.227189	+	0.393503i	0.0117477	+	0.0203475i
$375$		0			0
$376$		−	4.62826i		−	0.238684i
$377$	−3.32567	−	11.5866i	−0.171281	−	0.596743i
$378$	10.1174	−	10.1174i	0.520383	−	0.520383i
$379$	1.40831	−	5.25589i	0.0723401	−	0.269977i	−0.920277	−	0.391268i	$-0.872037\pi$
$379$	1.40831	−	5.25589i	0.0723401	−	0.269977i	0.992617	+	0.121291i	$0.0387034\pi$
$380$		0			0
$381$	3.53715	+	2.04217i	0.181214	+	0.104624i
$382$	16.4300			0.840633
$383$	−14.2766	−	8.24259i	−0.729499	−	0.421177i	0.0887398	−	0.996055i	$-0.471716\pi$
$383$	−14.2766	−	8.24259i	−0.729499	−	0.421177i	−0.818239	+	0.574878i	$0.805049\pi$
$384$	−0.333429	−	1.24438i	−0.0170153	−	0.0635018i
$385$		0			0
$386$	−5.36350	+	9.28986i	−0.272995	+	0.472841i
$387$	−12.7037	−	3.40395i	−0.645765	−	0.173032i
$388$	−7.07053	−	12.2465i	−0.358952	−	0.621723i
$389$	3.84183			0.194789			0.0973943	−	0.995246i	$-0.468949\pi$
$389$	3.84183			0.194789			0.0973943	+	0.995246i	$0.468949\pi$
$390$		0			0
$391$	−17.3762			−0.878751
$392$	−0.226046	−	0.391523i	−0.0114170	−	0.0197749i
$393$	20.8232	+	5.57956i	1.05039	+	0.281452i
$394$	5.94533	−	10.2976i	0.299522	−	0.518786i
$395$		0			0
$396$	−0.0317851	−	0.118624i	−0.00159726	−	0.00596106i
$397$	−0.589034	−	0.340079i	−0.0295627	−	0.0170681i	0.485146	−	0.874433i	$-0.338767\pi$
$397$	−0.589034	−	0.340079i	−0.0295627	−	0.0170681i	−0.514709	+	0.857365i	$0.672100\pi$
$398$	3.60458			0.180681
$399$	1.53754	+	0.887701i	0.0769735	+	0.0444407i
$400$		0			0
$401$	9.00357	−	33.6018i	0.449617	−	1.67799i	−0.253834	−	0.967248i	$-0.581692\pi$
$401$	9.00357	−	33.6018i	0.449617	−	1.67799i	0.703451	−	0.710744i	$-0.251642\pi$
$402$	−5.28628	+	5.28628i	−0.263655	+	0.263655i
$403$	11.1321	+	18.5161i	0.554532	+	0.922353i
$404$			14.9157i			0.742083i
$405$		0			0
$406$	4.27758	+	7.40899i	0.212293	+	0.367702i
$407$	−0.148803	−	0.555341i	−0.00737589	−	0.0275272i
$408$		−	6.38876i		−	0.316291i
$409$	−2.29556	+	0.615094i	−0.113508	+	0.0304145i	−0.315126	−	0.949050i	$-0.602047\pi$
$409$	−2.29556	+	0.615094i	−0.113508	+	0.0304145i	0.201618	+	0.979464i	$0.435380\pi$
$410$		0			0
$411$	1.42957	+	1.42957i	0.0705155	+	0.0705155i
$412$	1.54809	−	0.414810i	0.0762691	−	0.0204362i
$413$	3.85754	−	14.3965i	0.189817	−	0.708407i
$414$	4.53637	+	1.21552i	0.222951	+	0.0597394i
$415$		0			0
$416$	2.59427	+	2.50395i	0.127194	+	0.122766i
$417$	−15.1423	−	15.1423i	−0.741522	−	0.741522i
$418$	0.0427343	−	0.0246727i	0.00209020	−	0.00120678i
$419$	−17.8272	+	10.2925i	−0.870916	+	0.502824i	−0.867653	−	0.497171i	$-0.834372\pi$
$419$	−17.8272	+	10.2925i	−0.870916	+	0.502824i	−0.00326359	+	0.999995i	$0.501039\pi$
$420$		0			0
$421$	−26.8726	+	26.8726i	−1.30969	+	1.30969i	−0.388056	+	0.921636i	$0.626853\pi$
$421$	−26.8726	+	26.8726i	−1.30969	+	1.30969i	−0.921636	+	0.388056i	$0.873147\pi$
$422$	5.78313	−	10.0167i	0.281518	−	0.487604i
$423$	−3.10175	+	5.37239i	−0.150812	+	0.261215i
$424$	−3.73885	+	3.73885i	−0.181574	+	0.181574i
$425$		0			0
$426$	10.8841	−	6.28396i	0.527338	−	0.304459i
$427$	5.72165	−	3.30340i	0.276890	−	0.159863i
$428$	−4.87896	−	4.87896i	−0.235833	−	0.235833i
$429$	−0.306218	−	0.295558i	−0.0147843	−	0.0142697i
$430$		0			0
$431$	37.0974	+	9.94023i	1.78692	+	0.478804i	0.991817	−	0.127670i	$-0.0407499\pi$
$431$	37.0974	+	9.94023i	1.78692	+	0.478804i	0.795103	+	0.606474i	$0.207417\pi$
$432$	−1.44720	+	5.40103i	−0.0696285	+	0.259857i
$433$	17.1108	−	4.58483i	0.822293	−	0.220333i	0.176944	−	0.984221i	$-0.443379\pi$
$433$	17.1108	−	4.58483i	0.822293	−	0.220333i	0.645349	+	0.763888i	$0.276712\pi$
$434$	−10.8422	−	10.8422i	−0.520441	−	0.520441i
$435$		0			0
$436$	15.0076	−	4.02127i	0.718734	−	0.192584i
$437$			1.88705i			0.0902698i
$438$	5.62402	+	20.9891i	0.268726	+	1.00290i
$439$	16.1431	+	27.9606i	0.770467	+	1.33449i	0.937307	+	0.348504i	$0.113310\pi$
$439$	16.1431	+	27.9606i	0.770467	+	1.33449i	−0.166841	+	0.985984i	$0.553357\pi$
$440$		0			0
$441$			0.605963i			0.0288554i
$442$	9.21313	+	15.3242i	0.438224	+	0.728899i
$443$	20.3365	−	20.3365i	0.966217	−	0.966217i	−0.0332305	−	0.999448i	$-0.510580\pi$
$443$	20.3365	−	20.3365i	0.966217	−	0.966217i	0.999448	+	0.0332305i	$0.0105795\pi$
$444$	−2.09224	+	7.80835i	−0.0992933	+	0.370568i
$445$		0			0
$446$	−4.28077	−	2.47150i	−0.202700	−	0.117029i
$447$	20.6864			0.978435
$448$	−2.21606	−	1.27944i	−0.104699	−	0.0604480i
$449$	3.54277	+	13.2218i	0.167194	+	0.623976i	0.997750	+	0.0670412i	$0.0213559\pi$
$449$	3.54277	+	13.2218i	0.167194	+	0.623976i	−0.830556	+	0.556934i	$0.811977\pi$
$450$		0			0
$451$	−0.0648277	+	0.112285i	−0.00305262	+	0.00528728i
$452$	1.58069	+	0.423544i	0.0743492	+	0.0199218i
$453$	7.22486	+	12.5138i	0.339453	+	0.587951i
$454$	16.7263			0.785003
$455$		0			0
$456$	−0.693818			−0.0324910
$457$	4.84323	+	8.38872i	0.226557	+	0.392408i	0.956785	−	0.290795i	$-0.0939198\pi$
$457$	4.84323	+	8.38872i	0.226557	+	0.392408i	−0.730229	+	0.683203i	$0.760586\pi$
$458$	−16.2650	−	4.35818i	−0.760012	−	0.203644i
$459$	−13.8647	+	24.0144i	−0.647151	+	1.12090i
$460$		0			0
$461$	1.45272	+	5.42163i	0.0676600	+	0.252511i	0.991469	−	0.130343i	$-0.0416079\pi$
$461$	1.45272	+	5.42163i	0.0676600	+	0.252511i	−0.923809	+	0.382854i	$0.874941\pi$
$462$	0.261576	+	0.151021i	0.0121696	+	0.00702613i
$463$	−24.9809			−1.16096			−0.580480	−	0.814274i	$-0.697135\pi$
$463$	−24.9809			−1.16096			−0.580480	+	0.814274i	$0.697135\pi$
$464$	−2.89539	−	1.67166i	−0.134415	−	0.0776047i
$465$		0			0
$466$	−6.73531	+	25.1365i	−0.312007	+	1.16443i
$467$	−25.0346	+	25.0346i	−1.15846	+	1.15846i	−0.173657	+	0.984806i	$0.555558\pi$
$467$	−25.0346	+	25.0346i	−1.15846	+	1.15846i	−0.984806	+	0.173657i	$0.944442\pi$
$468$	−1.33328	−	4.64516i	−0.0616310	−	0.214722i
$469$			14.8494i			0.685681i
$470$		0			0
$471$	10.2443	+	17.7436i	0.472031	+	0.817581i
$472$	1.50751	+	5.62609i	0.0693886	+	0.258962i
$473$		−	0.899032i		−	0.0413375i
$474$	−11.1298	+	2.98221i	−0.511207	+	0.136978i
$475$		0			0
$476$	−8.97315	−	8.97315i	−0.411284	−	0.411284i
$477$	6.84567	−	1.83429i	0.313441	−	0.0839864i
$478$	3.77682	−	14.0953i	0.172748	−	0.644703i
$479$	30.2380	+	8.10224i	1.38161	+	0.370201i	0.871705	−	0.490031i	$-0.163014\pi$
$479$	30.2380	+	8.10224i	1.38161	+	0.370201i	0.509904	+	0.860232i	$0.329681\pi$
$480$		0			0
$481$	−6.24181	−	21.7465i	−0.284602	−	0.991553i
$482$	1.61612	+	1.61612i	0.0736124	+	0.0736124i
$483$	−10.0031	+	5.77530i	−0.455158	+	0.262785i
$484$	−9.51901	+	5.49580i	−0.432682	+	0.249809i
$485$		0			0
$486$	8.96250	−	8.96250i	0.406547	−	0.406547i
$487$	8.94924	−	15.5005i	0.405529	−	0.702396i	−0.588854	−	0.808239i	$-0.700421\pi$
$487$	8.94924	−	15.5005i	0.405529	−	0.702396i	0.994383	+	0.105843i	$0.0337541\pi$
$488$	−1.29095	+	2.23599i	−0.0584386	+	0.101219i
$489$	15.4535	−	15.4535i	0.698829	−	0.698829i
$490$		0			0
$491$	−6.94640	+	4.01050i	−0.313487	+	0.180992i	−0.648486	−	0.761227i	$-0.724597\pi$
$491$	−6.94640	+	4.01050i	−0.313487	+	0.180992i	0.334999	+	0.942218i	$0.391264\pi$
$492$	1.57878	−	0.911507i	0.0711767	−	0.0410939i
$493$	−11.7239	−	11.7239i	−0.528016	−	0.528016i
$494$	1.66421	−	1.00054i	0.0748762	−	0.0450166i
$495$		0			0
$496$	5.78794	+	1.55087i	0.259886	+	0.0696363i
$497$	6.46105	−	24.1130i	0.289818	−	1.08161i
$498$	16.3584	−	4.38322i	0.733037	−	0.196417i
$499$	−15.6970	−	15.6970i	−0.702693	−	0.702693i	0.262295	−	0.964988i	$-0.415521\pi$
$499$	−15.6970	−	15.6970i	−0.702693	−	0.702693i	−0.964988	+	0.262295i	$0.915521\pi$
$500$		0			0
$501$	21.3411	−	5.71833i	0.953450	−	0.255476i
$502$		−	9.61289i		−	0.429044i
$503$	4.55322	+	16.9929i	0.203018	+	0.757674i	0.990045	+	0.140755i	$0.0449529\pi$
$503$	4.55322	+	16.9929i	0.203018	+	0.757674i	−0.787026	+	0.616919i	$0.788380\pi$
$504$	1.71491	+	2.97031i	0.0763881	+	0.132308i
$505$		0			0
$506$			0.321036i			0.0142718i
$507$	−12.2543	−	11.4154i	−0.544233	−	0.506977i
$508$	−2.24182	+	2.24182i	−0.0994645	+	0.0994645i
$509$	3.66823	−	13.6900i	0.162591	−	0.606799i	−0.835744	−	0.549120i	$-0.814963\pi$
$509$	3.66823	−	13.6900i	0.162591	−	0.606799i	0.998335	−	0.0576796i	$-0.0183702\pi$
$510$		0			0
$511$	37.3788	+	21.5806i	1.65354	+	0.954671i
$512$	1.00000			0.0441942
$513$	2.60796	+	1.50571i	0.115144	+	0.0664786i
$514$	7.21668	+	26.9330i	0.318314	+	1.18796i
$515$		0			0
$516$	−6.32040	+	10.9473i	−0.278240	+	0.481926i
$517$	−0.409609	−	0.109754i	−0.0180146	−	0.00482699i
$518$	8.02840	+	13.9056i	0.352747	+	0.610977i
$519$	22.6768			0.995401
$520$		0			0
$521$	22.6688			0.993140			0.496570	−	0.867997i	$-0.334593\pi$
$521$	22.6688			0.993140			0.496570	+	0.867997i	$0.334593\pi$
$522$	2.24061	+	3.88085i	0.0980688	+	0.169860i
$523$	3.54564	+	0.950050i	0.155040	+	0.0415428i	0.335504	−	0.942039i	$-0.391093\pi$
$523$	3.54564	+	0.950050i	0.155040	+	0.0415428i	−0.180464	+	0.983582i	$0.557760\pi$
$524$	−8.36693	+	14.4920i	−0.365511	+	0.633084i
$525$		0			0
$526$	−7.09618	−	26.4833i	−0.309408	−	1.15473i
$527$	25.7347	+	14.8580i	1.12102	+	0.647223i
$528$	−0.118036			−0.00513687
$529$	9.28642	+	5.36152i	0.403757	+	0.233109i
$530$		0			0
$531$	2.02059	−	7.54095i	0.0876862	−	0.327249i
$532$	−0.974483	+	0.974483i	−0.0422492	+	0.0422492i
$533$	−2.47242	+	4.46309i	−0.107092	+	0.193318i
$534$		−	10.0074i		−	0.433064i
$535$		0			0
$536$	−2.90153	−	5.02560i	−0.125327	−	0.217073i
$537$	7.01622	+	26.1849i	0.302772	+	1.12996i
$538$			1.83426i			0.0790804i
$539$	−0.0400109	+	0.0107209i	−0.00172339	+	0.000461782i
$540$		0			0
$541$	20.8478	+	20.8478i	0.896315	+	0.896315i	0.995108	−	0.0987932i	$-0.0314982\pi$
$541$	20.8478	+	20.8478i	0.896315	+	0.896315i	−0.0987932	+	0.995108i	$0.531498\pi$
$542$	5.68011	−	1.52198i	0.243982	−	0.0653747i
$543$	8.54128	−	31.8765i	0.366541	−	1.36795i
$544$	4.79019	+	1.28353i	0.205378	+	0.0550308i
$545$		0			0
$546$	10.3971	+	5.75968i	0.444955	+	0.246492i
$547$	19.6566	+	19.6566i	0.840453	+	0.840453i	0.988918	−	0.148464i	$-0.0474330\pi$
$547$	19.6566	+	19.6566i	0.840453	+	0.840453i	−0.148464	+	0.988918i	$0.547433\pi$
$548$	−1.35907	+	0.784662i	−0.0580568	+	0.0335191i
$549$	2.99702	−	1.73033i	0.127910	−	0.0738487i
$550$		0			0
$551$	−1.27321	+	1.27321i	−0.0542405	+	0.0542405i
$552$	2.25696	−	3.90916i	0.0960625	−	0.166385i
$553$	−11.4434	+	19.8206i	−0.486624	+	0.842857i
$554$	−4.06392	+	4.06392i	−0.172659	+	0.172659i
$555$		0			0
$556$	14.3956	−	8.31130i	0.610509	−	0.352478i
$557$	−16.1172	+	9.30526i	−0.682907	+	0.394276i	−0.800949	−	0.598732i	$-0.795671\pi$
$557$	−16.1172	+	9.30526i	−0.682907	+	0.394276i	0.118043	+	0.993009i	$0.462338\pi$
$558$	−5.67917	−	5.67917i	−0.240418	−	0.240418i
$559$	−0.626622	−	35.3729i	−0.0265033	−	1.49611i
$560$		0			0
$561$	−0.565417	−	0.151503i	−0.0238719	−	0.00639646i
$562$	−6.12117	+	22.8445i	−0.258206	+	0.963638i
$563$	−15.0868	+	4.04249i	−0.635832	+	0.170371i	−0.562315	−	0.826923i	$-0.690089\pi$
$563$	−15.0868	+	4.04249i	−0.635832	+	0.170371i	−0.0735174	+	0.997294i	$0.523422\pi$
$564$	4.21610	+	4.21610i	0.177530	+	0.177530i
$565$		0			0
$566$	−11.2781	+	3.02196i	−0.474054	+	0.127022i
$567$			8.14338i			0.341990i
$568$	2.52494	+	9.42322i	0.105944	+	0.395389i
$569$	−14.9708	−	25.9302i	−0.627610	−	1.08705i	−0.988030	−	0.154262i	$-0.950700\pi$
$569$	−14.9708	−	25.9302i	−0.627610	−	1.08705i	0.360420	−	0.932790i	$-0.382633\pi$
$570$		0			0
$571$		−	14.1166i		−	0.590760i	−0.955380	−	0.295380i	$-0.904554\pi$
$571$		−	14.1166i		−	0.590760i	0.955380	−	0.295380i	$-0.0954463\pi$
$572$	0.283125	−	0.170219i	0.0118380	−	0.00711719i
$573$	−14.9669	+	14.9669i	−0.625250	+	0.625250i
$574$	0.937194	−	3.49766i	0.0391177	−	0.145989i
$575$		0			0
$576$	−1.16078	−	0.670177i	−0.0483658	−	0.0279240i
$577$	12.5961			0.524383			0.262191	−	0.965016i	$-0.415555\pi$
$577$	12.5961			0.524383			0.262191	+	0.965016i	$0.415555\pi$
$578$	6.57603	+	3.79667i	0.273527	+	0.157921i
$579$	−3.57670	−	13.3484i	−0.148643	−	0.554742i
$580$		0			0
$581$	16.8194	−	29.1321i	0.697786	−	1.20860i
$582$	17.5968	+	4.71505i	0.729411	+	0.195445i
$583$	0.242232	+	0.419557i	0.0100322	+	0.0173763i
$584$	−16.8672			−0.697970
$585$		0			0
$586$	−13.0174			−0.537745
$587$	4.62345	+	8.00804i	0.190830	+	0.330527i	0.945526	−	0.325548i	$-0.105549\pi$
$587$	4.62345	+	8.00804i	0.190830	+	0.330527i	−0.754696	+	0.656075i	$0.772215\pi$
$588$	0.562572	+	0.150741i	0.0232001	+	0.00621644i
$589$	1.61357	−	2.79479i	0.0664860	−	0.115157i
$590$		0			0
$591$	3.96470	+	14.7965i	0.163086	+	0.608645i
$592$	−5.43423	−	3.13745i	−0.223346	−	0.128949i
$593$	−37.5185			−1.54070			−0.770351	−	0.637620i	$-0.779919\pi$
$593$	−37.5185			−1.54070			−0.770351	+	0.637620i	$0.779919\pi$
$594$	0.443682	+	0.256160i	0.0182045	+	0.0105104i
$595$		0			0
$596$	−4.15599	+	15.5103i	−0.170236	+	0.635329i
$597$	−3.28358	+	3.28358i	−0.134388	+	0.134388i
$598$	0.223761	+	12.6313i	0.00915027	+	0.516534i
$599$		−	15.1335i		−	0.618339i	−0.951007	−	0.309169i	$-0.899949\pi$
$599$		−	15.1335i		−	0.618339i	0.951007	−	0.309169i	$-0.100051\pi$
$600$		0			0
$601$	5.22436	+	9.04885i	0.213106	+	0.369110i	0.952685	−	0.303959i	$-0.0983087\pi$
$601$	5.22436	+	9.04885i	0.213106	+	0.369110i	−0.739579	+	0.673070i	$0.764975\pi$
$602$	6.49852	+	24.2528i	0.264860	+	0.988471i
$603$			7.77815i			0.316751i
$604$	−10.8342	+	2.90300i	−0.440836	+	0.118122i
$605$		0			0
$606$	−13.5874	−	13.5874i	−0.551950	−	0.551950i
$607$	−17.7255	+	4.74954i	−0.719457	+	0.192778i	−0.599929	−	0.800053i	$-0.704805\pi$
$607$	−17.7255	+	4.74954i	−0.719457	+	0.192778i	−0.119527	+	0.992831i	$0.538138\pi$
$608$	0.139391	−	0.520214i	0.00565304	−	0.0210974i
$609$	−10.6458	−	2.85254i	−0.431391	−	0.115591i
$610$		0			0
$611$	−16.1928	−	4.03285i	−0.655090	−	0.163152i
$612$	−4.70017	−	4.70017i	−0.189993	−	0.189993i
$613$	11.7455	−	6.78127i	0.474396	−	0.273893i	−0.243682	−	0.969855i	$-0.578355\pi$
$613$	11.7455	−	6.78127i	0.474396	−	0.273893i	0.718078	+	0.695962i	$0.245022\pi$
$614$	14.0374	−	8.10452i	0.566505	−	0.327072i
$615$		0			0
$616$	−0.165785	+	0.165785i	−0.00667966	+	0.00667966i
$617$	8.39942	−	14.5482i	0.338148	−	0.585689i	−0.645937	−	0.763391i	$-0.723533\pi$
$617$	8.39942	−	14.5482i	0.338148	−	0.585689i	0.984084	+	0.177702i	$0.0568663\pi$
$618$	−1.03236	+	1.78810i	−0.0415276	+	0.0719279i
$619$	−6.17048	+	6.17048i	−0.248012	+	0.248012i	−0.820155	−	0.572142i	$-0.806113\pi$
$619$	−6.17048	+	6.17048i	−0.248012	+	0.248012i	0.572142	+	0.820155i	$0.306113\pi$
$620$		0			0
$621$	−16.9672	+	9.79599i	−0.680869	+	0.393100i
$622$	−25.2405	+	14.5726i	−1.01205	+	0.584307i
$623$	−14.0557	−	14.0557i	−0.563128	−	0.563128i
$624$	−4.64420	+	0.0822710i	−0.185917	+	0.00329347i
$625$		0			0
$626$	6.97749	+	1.86961i	0.278877	+	0.0747248i
$627$	−0.0164532	+	0.0614041i	−0.000657077	+	0.00245224i
$628$	−15.3620	+	4.11622i	−0.613009	+	0.164255i
$629$	−22.0040	−	22.0040i	−0.877356	−	0.877356i
$630$		0			0
$631$	6.07256	−	1.62714i	0.241745	−	0.0647753i	−0.135912	−	0.990721i	$-0.543397\pi$
$631$	6.07256	−	1.62714i	0.241745	−	0.0647753i	0.377657	+	0.925946i	$0.376730\pi$
$632$		−	8.94406i		−	0.355776i
$633$	3.85653	+	14.3928i	0.153283	+	0.572061i
$634$	7.23344	+	12.5287i	0.287277	+	0.497578i
$635$		0			0
$636$		−	6.81177i		−	0.270104i
$637$	−1.56678	+	0.449707i	−0.0620780	+	0.0178180i
$638$	−0.216606	+	0.216606i	−0.00857550	+	0.00857550i
$639$	3.38432	−	12.6304i	0.133882	−	0.499653i
$640$		0			0
$641$	38.2476	+	22.0822i	1.51069	+	0.872196i	0.999922	+	0.0124761i	$0.00397137\pi$
$641$	38.2476	+	22.0822i	1.51069	+	0.872196i	0.510766	+	0.859720i	$0.329362\pi$
$642$	8.88894			0.350818
$643$	−27.2150	−	15.7126i	−1.07325	−	0.619644i	−0.144185	−	0.989551i	$-0.546056\pi$
$643$	−27.2150	−	15.7126i	−1.07325	−	0.619644i	−0.929069	+	0.369907i	$0.879390\pi$
$644$	−2.32056	−	8.66045i	−0.0914429	−	0.341270i
$645$		0			0
$646$	1.33542	−	2.31301i	0.0525413	−	0.0910041i
$647$	−13.4595	−	3.60647i	−0.529149	−	0.141785i	−0.0156538	−	0.999877i	$-0.504983\pi$
$647$	−13.4595	−	3.60647i	−0.529149	−	0.141785i	−0.513495	+	0.858092i	$0.671650\pi$
$648$	−1.59120	−	2.75603i	−0.0625081	−	0.108267i
$649$	0.533668			0.0209483
$650$		0			0
$651$	19.7533			0.774192
$652$	8.48209	+	14.6914i	0.332184	+	0.575360i
$653$	32.2071	+	8.62986i	1.26036	+	0.337712i	0.826330	−	0.563186i	$-0.190425\pi$
$653$	32.2071	+	8.62986i	1.26036	+	0.337712i	0.434030	+	0.900899i	$0.357091\pi$
$654$	−10.0080	+	17.3343i	−0.391342	+	0.677824i
$655$		0			0
$656$	0.366251	+	1.36687i	0.0142997	+	0.0533672i
$657$	19.5791	+	11.3040i	0.763854	+	0.441011i
$658$	11.8432			0.461696
$659$	−10.3567	−	5.97945i	−0.403440	−	0.232926i	0.284527	−	0.958668i	$-0.408163\pi$
$659$	−10.3567	−	5.97945i	−0.403440	−	0.232926i	−0.687967	+	0.725742i	$0.741497\pi$
$660$		0			0
$661$	2.86356	−	10.6870i	0.111380	−	0.415675i	−0.887611	−	0.460594i	$-0.847636\pi$
$661$	2.86356	−	10.6870i	0.111380	−	0.415675i	0.998991	+	0.0449194i	$0.0143031\pi$
$662$	−20.8926	+	20.8926i	−0.812014	+	0.812014i
$663$	−22.3522	−	5.56687i	−0.868088	−	0.216199i
$664$			13.1459i			0.510159i
$665$		0			0
$666$	4.20530	+	7.28379i	0.162952	+	0.282241i
$667$	−3.03193	−	11.3153i	−0.117397	−	0.438130i
$668$			17.1500i			0.663555i
$669$	6.15096	−	1.64814i	0.237810	−	0.0637209i
$670$		0			0
$671$	0.167276	+	0.167276i	0.00645761	+	0.00645761i
$672$	3.18422	−	0.853209i	0.122834	−	0.0329132i
$673$	7.50840	−	28.0217i	0.289428	−	1.08016i	−0.656115	−	0.754661i	$-0.727801\pi$
$673$	7.50840	−	28.0217i	0.289428	−	1.08016i	0.945543	−	0.325498i	$-0.105532\pi$
$674$	−10.1360	−	2.71594i	−0.390426	−	0.104614i
$675$		0			0
$676$	11.0210	−	6.89467i	0.423886	−	0.265180i
$677$	−8.60647	−	8.60647i	−0.330774	−	0.330774i	0.522107	−	0.852880i	$-0.325146\pi$
$677$	−8.60647	−	8.60647i	−0.330774	−	0.330774i	−0.852880	+	0.522107i	$0.825146\pi$
$678$	−1.82575	+	1.05409i	−0.0701173	+	0.0404823i
$679$	31.3375	−	18.0927i	1.20262	−	0.694334i
$680$		0			0
$681$	−15.2367	+	15.2367i	−0.583873	+	0.583873i
$682$	0.274510	−	0.475465i	0.0105115	−	0.0182065i
$683$	−6.63734	+	11.4962i	−0.253971	+	0.439890i	−0.964615	−	0.263661i	$-0.915070\pi$
$683$	−6.63734	+	11.4962i	−0.253971	+	0.439890i	0.710645	+	0.703551i	$0.248403\pi$
$684$	−0.510437	+	0.510437i	−0.0195171	+	0.0195171i
$685$		0			0
$686$	16.5143	−	9.53453i	0.630519	−	0.364030i
$687$	18.7866	−	10.8464i	0.716753	−	0.413817i
$688$	−6.93828	−	6.93828i	−0.264520	−	0.264520i
$689$	9.82316	+	16.3389i	0.374232	+	0.622461i
$690$		0			0
$691$	16.6558	+	4.46290i	0.633616	+	0.169777i	0.561310	−	0.827606i	$-0.310298\pi$
$691$	16.6558	+	4.46290i	0.633616	+	0.169777i	0.0723059	+	0.997383i	$0.476964\pi$
$692$	−4.55586	+	17.0027i	−0.173188	+	0.646345i
$693$	0.303545	−	0.0813346i	0.0115307	−	0.00308964i
$694$	−2.52464	−	2.52464i	−0.0958339	−	0.0958339i
$695$		0			0
$696$	4.16034	−	1.11476i	0.157697	−	0.0422548i
$697$			7.01764i			0.265812i
$698$	0.776840	+	2.89921i	0.0294038	+	0.109737i
$699$	−16.7625	−	29.0335i	−0.634016	−	1.09815i
$700$		0			0
$701$			25.4441i			0.961010i	0.876992	+	0.480505i	$0.159547\pi$
$701$			25.4441i			0.961010i	−0.876992	+	0.480505i	$0.840453\pi$
$702$	17.6354	+	9.76950i	0.665607	+	0.368726i
$703$	−2.38963	+	2.38963i	−0.0901265	+	0.0901265i
$704$	0.0237140	−	0.0885018i	0.000893754	−	0.00333554i
$705$		0			0
$706$	9.92204	+	5.72849i	0.373421	+	0.215595i
$707$	−38.1675			−1.43544
$708$	−6.49833	−	3.75181i	−0.244222	−	0.141002i
$709$	−9.53579	−	35.5881i	−0.358124	−	1.33654i	−0.876507	−	0.481389i	$-0.840132\pi$
$709$	−9.53579	−	35.5881i	−0.358124	−	1.33654i	0.518383	−	0.855149i	$-0.326534\pi$
$710$		0			0
$711$	−5.99410	+	10.3821i	−0.224796	+	0.389359i
$712$	7.50341	+	2.01053i	0.281202	+	0.0753479i
$713$	10.4977	+	18.1826i	0.393143	+	0.680944i
$714$	16.3481			0.611813
$715$		0			0
$716$	−21.0426			−0.786398
$717$	9.39957	+	16.2805i	0.351033	+	0.608007i
$718$	−7.11123	−	1.90545i	−0.265389	−	0.0711107i
$719$	−4.28637	+	7.42421i	−0.159855	+	0.276876i	−0.934816	−	0.355132i	$-0.884436\pi$
$719$	−4.28637	+	7.42421i	−0.159855	+	0.276876i	0.774961	+	0.632008i	$0.217769\pi$
$720$		0			0
$721$	1.06145	+	3.96140i	0.0395306	+	0.147530i
$722$	16.2033	+	9.35497i	0.603024	+	0.348156i
$723$	−2.94440			−0.109504
$724$	22.1845	+	12.8082i	0.824480	+	0.476014i
$725$		0			0
$726$	3.66493	−	13.6777i	0.136018	−	0.507627i
$727$	18.8997	−	18.8997i	0.700952	−	0.700952i	−0.263663	−	0.964615i	$-0.584931\pi$
$727$	18.8997	−	18.8997i	0.700952	−	0.700952i	0.964615	+	0.263663i	$0.0849307\pi$
$728$	−6.40734	+	6.63844i	−0.237472	+	0.246037i
$729$			25.8759i			0.958366i
$730$		0			0
$731$	−24.3302	−	42.1412i	−0.899885	−	1.55865i
$732$	−0.860882	−	3.21286i	−0.0318191	−	0.118751i
$733$			19.8330i			0.732549i	0.930507	+	0.366274i	$0.119367\pi$
$733$			19.8330i			0.732549i	−0.930507	+	0.366274i	$0.880633\pi$
$734$	−17.2606	+	4.62496i	−0.637099	+	0.170710i
$735$		0			0
$736$	2.47760	+	2.47760i	0.0913254	+	0.0913254i
$737$	−0.513581	+	0.137614i	−0.0189180	+	0.00506906i
$738$	0.490905	−	1.83208i	0.0180705	−	0.0674399i
$739$	10.5108	+	2.81635i	0.386645	+	0.103601i	0.446905	−	0.894582i	$-0.352526\pi$
$739$	10.5108	+	2.81635i	0.386645	+	0.103601i	−0.0602599	+	0.998183i	$0.519193\pi$
$740$		0			0
$741$	−0.604561	+	2.42745i	−0.0222091	+	0.0891744i
$742$	−9.56729	−	9.56729i	−0.351226	−	0.351226i
$743$	21.7084	−	12.5334i	0.796406	−	0.459805i	−0.0458071	−	0.998950i	$-0.514586\pi$
$743$	21.7084	−	12.5334i	0.796406	−	0.459805i	0.842213	+	0.539145i	$0.181253\pi$
$744$	−6.68526	+	3.85974i	−0.245094	+	0.141505i
$745$		0			0
$746$	−22.5338	+	22.5338i	−0.825020	+	0.825020i
$747$	8.81006	−	15.2595i	0.322343	−	0.558315i
$748$	0.227189	−	0.393503i	0.00830685	−	0.0143879i
$749$	12.4847	−	12.4847i	0.456181	−	0.456181i
$750$		0			0
$751$	−22.2080	+	12.8218i	−0.810380	+	0.467873i	−0.847088	−	0.531453i	$-0.821646\pi$
$751$	−22.2080	+	12.8218i	−0.810380	+	0.467873i	0.0367077	+	0.999326i	$0.488313\pi$
$752$	−4.00819	+	2.31413i	−0.146164	+	0.0843876i
$753$	8.75683	+	8.75683i	0.319117	+	0.319117i
$754$	−8.37149	+	8.67344i	−0.304872	+	0.315868i
$755$		0			0
$756$	−13.8206	−	3.70323i	−0.502652	−	0.134685i
$757$	−0.963145	+	3.59451i	−0.0350061	+	0.130645i	−0.981218	−	0.192904i	$-0.938209\pi$
$757$	−0.963145	+	3.59451i	−0.0350061	+	0.130645i	0.946211	+	0.323549i	$0.104876\pi$
$758$	−5.25589	+	1.40831i	−0.190902	+	0.0511522i
$759$	−0.292447	−	0.292447i	−0.0106151	−	0.0106151i
$760$		0			0
$761$	27.4934	−	7.36683i	0.996634	−	0.267047i	0.276600	−	0.960985i	$-0.410792\pi$
$761$	27.4934	−	7.36683i	0.996634	−	0.267047i	0.720035	+	0.693938i	$0.244126\pi$
$762$		−	4.08435i		−	0.147960i
$763$	10.2900	+	38.4028i	0.372523	+	1.39027i
$764$	−8.21501	−	14.2288i	−0.297209	−	0.514781i
$765$		0			0
$766$			16.4852i			0.595634i
$767$	20.9975	−	0.371965i	0.758174	−	0.0134309i
$768$	−0.910946	+	0.910946i	−0.0328709	+	0.0328709i
$769$	9.79895	−	36.5702i	0.353359	−	1.31875i	−0.529178	−	0.848511i	$-0.677500\pi$
$769$	9.79895	−	36.5702i	0.353359	−	1.31875i	0.882537	−	0.470243i	$-0.155834\pi$
$770$		0			0
$771$	−31.1085	−	17.9605i	−1.12035	−	0.646832i
$772$	10.7270			0.386073
$773$	−6.84714	−	3.95320i	−0.246275	−	0.142187i	0.371783	−	0.928320i	$-0.378747\pi$
$773$	−6.84714	−	3.95320i	−0.246275	−	0.142187i	−0.618057	+	0.786133i	$0.712080\pi$
$774$	3.40395	+	12.7037i	0.122352	+	0.456625i
$775$		0			0
$776$	−7.07053	+	12.2465i	−0.253817	+	0.439624i
$777$	−19.9807	−	5.35381i	−0.716803	−	0.192067i
$778$	−1.92092	−	3.32712i	−0.0688682	−	0.119283i
$779$	0.762114			0.0273056
$780$		0			0
$781$	0.893848			0.0319844
$782$	8.68809	+	15.0482i	0.310686	+	0.538123i
$783$	−18.0573	−	4.83845i	−0.645316	−	0.172912i
$784$	−0.226046	+	0.391523i	−0.00807307	+	0.0139830i
$785$		0			0
$786$	−5.57956	−	20.8232i	−0.199016	−	0.742740i
$787$	−8.20218	−	4.73553i	−0.292376	−	0.168804i	0.346637	−	0.937999i	$-0.387324\pi$
$787$	−8.20218	−	4.73553i	−0.292376	−	0.168804i	−0.639013	+	0.769196i	$0.720657\pi$
$788$	−11.8907			−0.423587
$789$	30.5891	+	17.6606i	1.08900	+	0.628735i
$790$		0			0
$791$	−1.08380	+	4.04480i	−0.0385355	+	0.143817i
$792$	−0.0868386	+	0.0868386i	−0.00308567	+	0.00308567i
$793$	6.69814	+	6.46496i	0.237858	+	0.229577i
$794$			0.680157i			0.0241379i
$795$		0			0
$796$	−1.80229	−	3.12166i	−0.0638805	−	0.110644i
$797$	−4.70044	−	17.5423i	−0.166498	−	0.621380i	−0.997844	−	0.0656247i	$-0.979096\pi$
$797$	−4.70044	−	17.5423i	−0.166498	−	0.621380i	0.831346	−	0.555755i	$-0.187571\pi$
$798$		−	1.77540i		−	0.0628486i
$799$	−22.1702	+	5.94050i	−0.784326	+	0.210160i
$800$		0			0
$801$	−7.36240	−	7.36240i	−0.260138	−	0.260138i
$802$	−33.6018	+	9.00357i	−1.18652	+	0.317927i
$803$	−0.399988	+	1.49278i	−0.0141153	+	0.0526790i
$804$	7.22119	+	1.93491i	0.254672	+	0.0682391i
$805$		0			0
$806$	10.4693	−	18.8988i	0.368767	−	0.665681i
$807$	−1.67091	−	1.67091i	−0.0588188	−	0.0588188i
$808$	12.9174	−	7.45784i	0.454431	−	0.262366i
$809$	−24.4351	+	14.1076i	−0.859092	+	0.495997i	−0.863708	−	0.503992i	$-0.831864\pi$
$809$	−24.4351	+	14.1076i	−0.859092	+	0.495997i	0.00461626	+	0.999989i	$0.498531\pi$
$810$		0			0
$811$	4.21141	−	4.21141i	0.147883	−	0.147883i	−0.629289	−	0.777172i	$-0.716654\pi$
$811$	4.21141	−	4.21141i	0.147883	−	0.147883i	0.777172	+	0.629289i	$0.216654\pi$
$812$	4.27758	−	7.40899i	0.150114	−	0.260004i
$813$	−3.78783	+	6.56072i	−0.132845	+	0.230094i
$814$	−0.406538	+	0.406538i	−0.0142491	+	0.0142491i
$815$		0			0
$816$	−5.53283	+	3.19438i	−0.193688	+	0.111826i
$817$	−4.57652	+	2.64226i	−0.160112	+	0.0924408i
$818$	1.68047	+	1.68047i	0.0587562	+	0.0587562i
$819$	11.8864	−	3.41172i	0.415346	−	0.119215i
$820$		0			0
$821$	7.16102	+	1.91879i	0.249921	+	0.0669662i	0.381605	−	0.924326i	$-0.375372\pi$
$821$	7.16102	+	1.91879i	0.249921	+	0.0669662i	−0.131683	+	0.991292i	$0.542038\pi$
$822$	0.523259	−	1.95283i	0.0182507	−	0.0681127i
$823$	−38.8370	+	10.4063i	−1.35377	+	0.362742i	−0.861526	−	0.507713i	$-0.830491\pi$
$823$	−38.8370	+	10.4063i	−1.35377	+	0.362742i	−0.492247	+	0.870456i	$0.663824\pi$
$824$	−1.13328	−	1.13328i	−0.0394798	−	0.0394798i
$825$		0			0
$826$	−14.3965	+	3.85754i	−0.500920	+	0.134221i
$827$			37.4411i			1.30196i	0.759097	+	0.650978i	$0.225641\pi$
$827$			37.4411i			1.30196i	−0.759097	+	0.650978i	$0.774359\pi$
$828$	−1.21552	−	4.53637i	−0.0422422	−	0.157650i
$829$	24.2487	+	42.0000i	0.842192	+	1.45872i	0.888037	+	0.459771i	$0.152069\pi$
$829$	24.2487	+	42.0000i	0.842192	+	1.45872i	−0.0458449	+	0.998949i	$0.514598\pi$
$830$		0			0
$831$		−	7.40402i		−	0.256843i
$832$	0.871354	−	3.49868i	0.0302087	−	0.121295i
$833$	−1.58533	+	1.58533i	−0.0549285	+	0.0549285i
$834$	−5.54247	+	20.6848i	−0.191920	+	0.716255i
$835$		0			0
$836$	−0.0427343	−	0.0246727i	−0.00147800	−	0.000853322i
$837$	33.5053			1.15811
$838$	17.8272	+	10.2925i	0.615831	+	0.355550i
$839$	8.27108	+	30.8681i	0.285549	+	1.06568i	0.948437	+	0.316966i	$0.102664\pi$
$839$	8.27108	+	30.8681i	0.285549	+	1.06568i	−0.662888	+	0.748719i	$0.730669\pi$
$840$		0			0
$841$	−8.91113	+	15.4345i	−0.307280	+	0.532225i
$842$	36.7087	+	9.83606i	1.26507	+	0.338973i
$843$	−15.2341	−	26.3862i	−0.524689	−	0.908789i
$844$	−11.5663			−0.398127
$845$		0			0
$846$	6.20350			0.213281
$847$	−14.0631	−	24.3581i	−0.483215	−	0.836954i
$848$	5.10736	+	1.36851i	0.175387	+	0.0469949i
$849$	7.52090	−	13.0266i	0.258117	−	0.447071i
$850$		0			0
$851$	−5.69048	−	21.2372i	−0.195067	−	0.728001i
$852$	−10.8841	−	6.28396i	−0.372884	−	0.215285i
$853$	3.51934			0.120500			0.0602500	−	0.998183i	$-0.480810\pi$
$853$	3.51934			0.120500			0.0602500	+	0.998183i	$0.480810\pi$
$854$	−5.72165	−	3.30340i	−0.195791	−	0.113040i
$855$		0			0
$856$	−1.78582	+	6.66478i	−0.0610382	+	0.227798i
$857$	26.3874	−	26.3874i	0.901378	−	0.901378i	−0.0941777	−	0.995555i	$-0.530022\pi$
$857$	26.3874	−	26.3874i	0.901378	−	0.901378i	0.995555	+	0.0941777i	$0.0300222\pi$
$858$	−0.102851	+	0.412971i	−0.00351129	+	0.0140986i
$859$			6.12805i			0.209086i	0.994520	+	0.104543i	$0.0333380\pi$
$859$			6.12805i			0.209086i	−0.994520	+	0.104543i	$0.966662\pi$
$860$		0			0
$861$	2.33244	+	4.03991i	0.0794895	+	0.137680i
$862$	−9.94023	−	37.0974i	−0.338565	−	1.26354i
$863$		−	39.9799i		−	1.36093i	−0.732780	−	0.680466i	$-0.761778\pi$
$863$		−	39.9799i		−	1.36093i	0.732780	−	0.680466i	$-0.238222\pi$
$864$	5.40103	−	1.44720i	0.183747	−	0.0492348i
$865$		0			0
$866$	−12.5260	−	12.5260i	−0.425650	−	0.425650i
$867$	−9.44898	+	2.53185i	−0.320904	+	0.0859860i
$868$	−3.96851	+	14.8107i	−0.134700	+	0.502707i
$869$	−0.791565	−	0.212099i	−0.0268520	−	0.00719497i
$870$		0			0
$871$	−20.1112	+	5.77244i	−0.681442	+	0.195592i
$872$	−10.9863	−	10.9863i	−0.372044	−	0.372044i
$873$	16.4147	−	9.47701i	0.555552	−	0.320748i
$874$	1.63423	−	0.943525i	0.0552788	−	0.0319152i
$875$		0			0
$876$	15.3651	−	15.3651i	0.519139	−	0.519139i
$877$	−8.75805	+	15.1694i	−0.295738	+	0.512234i	−0.975156	−	0.221518i	$-0.928899\pi$
$877$	−8.75805	+	15.1694i	−0.295738	+	0.512234i	0.679418	+	0.733751i	$0.262232\pi$
$878$	16.1431	−	27.9606i	0.544802	−	0.943625i
$879$	11.8582	−	11.8582i	0.399967	−	0.399967i
$880$		0			0
$881$	11.8012	−	6.81345i	0.397594	−	0.229551i	−0.287851	−	0.957675i	$-0.592941\pi$
$881$	11.8012	−	6.81345i	0.397594	−	0.229551i	0.685445	+	0.728124i	$0.259608\pi$
$882$	0.524779	−	0.302981i	0.0176702	−	0.0102019i
$883$	19.1486	+	19.1486i	0.644403	+	0.644403i	0.951635	−	0.307232i	$-0.0994027\pi$
$883$	19.1486	+	19.1486i	0.644403	+	0.644403i	−0.307232	+	0.951635i	$0.599403\pi$
$884$	8.66459	−	15.6409i	0.291422	−	0.526061i
$885$		0			0
$886$	−27.7802	−	7.44368i	−0.933294	−	0.250075i
$887$	14.8713	−	55.5005i	0.499330	−	1.86353i	−0.00495394	−	0.999988i	$-0.501577\pi$
$887$	14.8713	−	55.5005i	0.499330	−	1.86353i	0.504284	−	0.863538i	$-0.331756\pi$
$888$	7.80835	−	2.09224i	0.262031	−	0.0702110i
$889$	−5.73656	−	5.73656i	−0.192398	−	0.192398i
$890$		0			0
$891$	−0.281647	+	0.0754672i	−0.00943554	+	0.00252824i
$892$			4.94301i			0.165504i
$893$	0.645137	+	2.40768i	0.0215887	+	0.0805700i
$894$	−10.3432	−	17.9150i	−0.345929	−	0.599166i
$895$		0			0
$896$			2.55889i			0.0854865i
$897$	−11.7103	−	11.3026i	−0.390995	−	0.377384i
$898$	9.67904	−	9.67904i	0.322994	−	0.322994i
$899$	−5.18505	+	19.3509i	−0.172931	+	0.645388i
$900$		0			0
$901$	22.7087	+	13.1109i	0.756536	+	0.436786i
$902$	0.129655			0.00431705
$903$	−28.0128	−	16.1732i	−0.932208	−	0.538211i
$904$	−0.423544	−	1.58069i	−0.0140869	−	0.0525728i
$905$		0			0
$906$	7.22486	−	12.5138i	0.240030	−	0.415744i
$907$	−50.2248	−	13.4577i	−1.66769	−	0.446855i	−0.703201	−	0.710991i	$-0.748246\pi$
$907$	−50.2248	−	13.4577i	−1.66769	−	0.446855i	−0.964485	+	0.264136i	$0.914913\pi$
$908$	−8.36313	−	14.4854i	−0.277540	−	0.480714i
$909$	−19.9923			−0.663102
$910$		0			0
$911$	−17.0358			−0.564421			−0.282211	−	0.959352i	$-0.591068\pi$
$911$	−17.0358			−0.564421			−0.282211	+	0.959352i	$0.591068\pi$
$912$	0.346909	+	0.600864i	0.0114873	+	0.0198966i
$913$	1.16343	+	0.311741i	0.0385040	+	0.0103171i
$914$	4.84323	−	8.38872i	0.160200	−	0.277474i
$915$		0			0
$916$	4.35818	+	16.2650i	0.143998	+	0.537409i
$917$	−37.0833	−	21.4100i	−1.22460	−	0.707022i
$918$	27.7295			0.915209
$919$	26.2851	+	15.1757i	0.867066	+	0.500601i	0.866372	−	0.499399i	$-0.166446\pi$
$919$	26.2851	+	15.1757i	0.867066	+	0.500601i	0.000693542		1.00000i	$0.499779\pi$
$920$		0			0
$921$	−5.40457	+	20.1701i	−0.178087	+	0.664629i
$922$	3.96891	−	3.96891i	0.130709	−	0.130709i
$923$	35.1689	−	0.623009i	1.15760	−	0.0205066i
$924$		−	0.302042i		−	0.00993645i
$925$		0			0
$926$	12.4904	+	21.6341i	0.410462	+	0.710940i
$927$	0.555993	+	2.07499i	0.0182612	+	0.0681517i
$928$			3.34331i			0.109750i
$929$	−0.286693	+	0.0768193i	−0.00940611	+	0.00252036i	−0.263519	−	0.964654i	$-0.584883\pi$
$929$	−0.286693	+	0.0768193i	−0.00940611	+	0.00252036i	0.254113	+	0.967175i	$0.418217\pi$
$930$		0			0
$931$	0.172167	+	0.172167i	0.00564254	+	0.00564254i
$932$	25.1365	−	6.73531i	0.823374	−	0.220622i
$933$	9.71786	−	36.2675i	0.318148	−	1.18735i
$934$	34.1979	+	9.16330i	1.11899	+	0.299832i
$935$		0			0
$936$	−3.35618	+	3.47723i	−0.109700	+	0.113657i
$937$	12.8581	+	12.8581i	0.420056	+	0.420056i	0.885223	−	0.465167i	$-0.154006\pi$
$937$	12.8581	+	12.8581i	0.420056	+	0.420056i	−0.465167	+	0.885223i	$0.654006\pi$
$938$	12.8599	−	7.42469i	0.419892	−	0.242425i
$939$	−8.05924	+	4.65300i	−0.263003	+	0.151845i
$940$		0			0
$941$	−13.5707	+	13.5707i	−0.442393	+	0.442393i	−0.892816	−	0.450423i	$-0.851273\pi$
$941$	−13.5707	+	13.5707i	−0.442393	+	0.442393i	0.450423	+	0.892816i	$0.351273\pi$
$942$	10.2443	−	17.7436i	0.333776	−	0.578117i
$943$	−2.47912	+	4.29396i	−0.0807313	+	0.139831i
$944$	4.11859	−	4.11859i	0.134049	−	0.134049i
$945$		0			0
$946$	−0.778585	+	0.449516i	−0.0253140	+	0.0146150i
$947$	1.17806	−	0.680154i	0.0382819	−	0.0221020i	−0.480737	−	0.876865i	$-0.659631\pi$
$947$	1.17806	−	0.680154i	0.0382819	−	0.0221020i	0.519019	+	0.854763i	$0.326297\pi$
$948$	8.14756	+	8.14756i	0.264620	+	0.264620i
$949$	−14.6973	+	59.0129i	−0.477094	+	1.91564i
$950$		0			0
$951$	−18.0022	−	4.82369i	−0.583763	−	0.156419i
$952$	−3.28440	+	12.2576i	−0.106448	+	0.397270i
$953$	23.3689	−	6.26167i	0.756992	−	0.202835i	0.140375	−	0.990098i	$-0.455169\pi$
$953$	23.3689	−	6.26167i	0.756992	−	0.202835i	0.616617	+	0.787263i	$0.288503\pi$
$954$	−5.01137	−	5.01137i	−0.162249	−	0.162249i
$955$		0			0
$956$	−14.0953	+	3.77682i	−0.455874	+	0.122151i
$957$		−	0.394632i		−	0.0127567i
$958$	−8.10224	−	30.2380i	−0.261772	−	0.976945i
$959$	−2.00786	−	3.47772i	−0.0648372	−	0.112301i
$960$		0			0
$961$		−	4.90544i		−	0.158240i
$962$	−15.7121	+	16.2788i	−0.506578	+	0.524849i
$963$	6.53953	−	6.53953i	0.210733	−	0.210733i
$964$	0.591542	−	2.20767i	0.0190523	−	0.0711041i
$965$		0			0
$966$	10.0031	+	5.77530i	0.321845	+	0.185817i
$967$	−17.5560			−0.564562			−0.282281	−	0.959332i	$-0.591091\pi$
$967$	−17.5560			−0.564562			−0.282281	+	0.959332i	$0.591091\pi$
$968$	9.51901	+	5.49580i	0.305953	+	0.176642i
$969$	0.890534	+	3.32352i	0.0286081	+	0.106767i
$970$		0			0
$971$	3.98217	−	6.89733i	0.127794	−	0.221346i	−0.795028	−	0.606573i	$-0.792544\pi$
$971$	3.98217	−	6.89733i	0.127794	−	0.221346i	0.922822	+	0.385228i	$0.125877\pi$
$972$	−12.2430	−	3.28050i	−0.392694	−	0.105222i
$973$	21.2677	+	36.8367i	0.681811	+	1.18093i
$974$	−17.8985			−0.573504
$975$		0			0
$976$	2.58190			0.0826446
$977$	12.3293	+	21.3550i	0.394450	+	0.683207i	0.993031	−	0.117855i	$-0.0376018\pi$
$977$	12.3293	+	21.3550i	0.394450	+	0.683207i	−0.598581	+	0.801062i	$0.704268\pi$
$978$	−21.1098	−	5.65636i	−0.675017	−	0.180870i
$979$	0.355872	−	0.616388i	0.0113737	−	0.0196998i
$980$		0			0
$981$	5.38993	+	20.1155i	0.172087	+	0.642238i
$982$	6.94640	+	4.01050i	0.221668	+	0.127980i
$983$	55.7916			1.77948			0.889738	−	0.456472i	$-0.150887\pi$
$983$	55.7916			1.77948			0.889738	+	0.456472i	$0.150887\pi$
$984$	−1.57878	−	0.911507i	−0.0503295	−	0.0290578i
$985$		0			0
$986$	−4.29123	+	16.0151i	−0.136661	+	0.510024i
$987$	−10.7885	+	10.7885i	−0.343402	+	0.343402i
$988$	−1.69860	−	0.940973i	−0.0540397	−	0.0299363i
$989$		−	34.3805i		−	1.09324i
$990$		0			0
$991$	−21.9771	−	38.0654i	−0.698125	−	1.20919i	−0.969116	−	0.246606i	$-0.920685\pi$
$991$	−21.9771	−	38.0654i	−0.698125	−	1.20919i	0.270991	−	0.962582i	$-0.412649\pi$
$992$	−1.55087	−	5.78794i	−0.0492403	−	0.183767i
$993$		−	38.0641i		−	1.20793i
$994$	−24.1130	+	6.46105i	−0.764817	+	0.204932i
$995$		0			0
$996$	−11.9752	−	11.9752i	−0.379448	−	0.379448i
$997$	−16.1247	+	4.32061i	−0.510676	+	0.136835i	−0.504950	−	0.863148i	$-0.668489\pi$
$997$	−16.1247	+	4.32061i	−0.510676	+	0.136835i	−0.00572561	+	0.999984i	$0.501823\pi$
$998$	−5.74549	+	21.4425i	−0.181870	+	0.678750i
$999$	−33.8910	−	9.08106i	−1.07226	−	0.287312i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	650.2.w.f.457.4	yes	16
5.2	odd	4		650.2.t.f.93.4	yes	16
5.3	odd	4		650.2.t.h.93.1	yes	16
5.4	even	2		650.2.w.h.457.1	yes	16
13.7	odd	12		650.2.t.h.7.1	yes	16
65.7	even	12		650.2.w.h.293.1	yes	16
65.33	even	12	inner	650.2.w.f.293.4	yes	16
65.59	odd	12		650.2.t.f.7.4	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
650.2.t.f.7.4	✓	16	65.59	odd	12
650.2.t.f.93.4	yes	16	5.2	odd	4
650.2.t.h.7.1	yes	16	13.7	odd	12
650.2.t.h.93.1	yes	16	5.3	odd	4
650.2.w.f.293.4	yes	16	65.33	even	12	inner
650.2.w.f.457.4	yes	16	1.1	even	1	trivial
650.2.w.h.293.1	yes	16	65.7	even	12
650.2.w.h.457.1	yes	16	5.4	even	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	650.w (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(1.24438 + 0.333429i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.333429 - 1.24438i) q^{6} +(-2.21606 - 1.27944i) q^{7} +1.00000 q^{8} +(-1.16078 - 0.670177i) q^{9} +(0.0237140 - 0.0885018i) q^{11} +(-0.910946 + 0.910946i) q^{12} +(0.871354 - 3.49868i) q^{13} +2.55889i q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.28353 - 4.79019i) q^{17} +1.34035i q^{18} +(-0.520214 + 0.139391i) q^{19} +(-2.33101 - 2.33101i) q^{21} +(-0.0885018 + 0.0237140i) q^{22} +(0.906863 - 3.38446i) q^{23} +(1.24438 + 0.333429i) q^{24} +(-3.46562 + 0.994724i) q^{26} +(-3.95383 - 3.95383i) q^{27} +(2.21606 - 1.27944i) q^{28} +(2.89539 - 1.67166i) q^{29} +(-4.23707 + 4.23707i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.0590182 - 0.102223i) q^{33} +(-3.50666 + 3.50666i) q^{34} +(1.16078 - 0.670177i) q^{36} +(5.43423 - 3.13745i) q^{37} +(0.380823 + 0.380823i) q^{38} +(2.25085 - 4.06313i) q^{39} +(-1.36687 - 0.366251i) q^{41} +(-0.853209 + 3.18422i) q^{42} +(9.47787 - 2.53959i) q^{43} +(0.0647878 + 0.0647878i) q^{44} +(-3.38446 + 0.906863i) q^{46} -4.62826i q^{47} +(-0.333429 - 1.24438i) q^{48} +(-0.226046 - 0.391523i) q^{49} -6.38876i q^{51} +(2.59427 + 2.50395i) q^{52} +(-3.73885 + 3.73885i) q^{53} +(-1.44720 + 5.40103i) q^{54} +(-2.21606 - 1.27944i) q^{56} -0.693818 q^{57} +(-2.89539 - 1.67166i) q^{58} +(1.50751 + 5.62609i) q^{59} +(-1.29095 + 2.23599i) q^{61} +(5.78794 + 1.55087i) q^{62} +(1.71491 + 2.97031i) q^{63} +1.00000 q^{64} -0.118036 q^{66} +(-2.90153 - 5.02560i) q^{67} +(4.79019 + 1.28353i) q^{68} +(2.25696 - 3.90916i) q^{69} +(2.52494 + 9.42322i) q^{71} +(-1.16078 - 0.670177i) q^{72} -16.8672 q^{73} +(-5.43423 - 3.13745i) q^{74} +(0.139391 - 0.520214i) q^{76} +(-0.165785 + 0.165785i) q^{77} +(-4.64420 + 0.0822710i) q^{78} -8.94406i q^{79} +(-1.59120 - 2.75603i) q^{81} +(0.366251 + 1.36687i) q^{82} +13.1459i q^{83} +(3.18422 - 0.853209i) q^{84} +(-6.93828 - 6.93828i) q^{86} +(4.16034 - 1.11476i) q^{87} +(0.0237140 - 0.0885018i) q^{88} +(7.50341 + 2.01053i) q^{89} +(-6.40734 + 6.63844i) q^{91} +(2.47760 + 2.47760i) q^{92} +(-6.68526 + 3.85974i) q^{93} +(-4.00819 + 2.31413i) q^{94} +(-0.910946 + 0.910946i) q^{96} +(-7.07053 + 12.2465i) q^{97} +(-0.226046 + 0.391523i) q^{98} +(-0.0868386 + 0.0868386i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{2} - 8 q^{4} - 12 q^{7} + 16 q^{8} - 24 q^{9} - 4 q^{11} - 8 q^{13} - 8 q^{16} + 8 q^{17} + 16 q^{19} - 4 q^{21} - 4 q^{22} + 4 q^{23} + 4 q^{26} - 36 q^{27} + 12 q^{28} + 36 q^{29} - 8 q^{31}+ \cdots - 36 q^{99}+O(q^{100}) \) 16 * q - 8 * q^2 - 8 * q^4 - 12 * q^7 + 16 * q^8 - 24 * q^9 - 4 * q^11 - 8 * q^13 - 8 * q^16 + 8 * q^17 + 16 * q^19 - 4 * q^21 - 4 * q^22 + 4 * q^23 + 4 * q^26 - 36 * q^27 + 12 * q^28 + 36 * q^29 - 8 * q^31 - 8 * q^32 - 16 * q^34 + 24 * q^36 + 36 * q^37 + 4 * q^38 + 32 * q^41 + 8 * q^42 + 36 * q^43 + 8 * q^44 + 4 * q^46 + 16 * q^49 + 4 * q^52 - 44 * q^53 + 36 * q^54 - 12 * q^56 + 48 * q^57 - 36 * q^58 - 24 * q^59 - 20 * q^61 - 8 * q^62 + 36 * q^63 + 16 * q^64 + 12 * q^67 + 8 * q^68 + 24 * q^69 + 16 * q^71 - 24 * q^72 - 36 * q^74 - 20 * q^76 - 16 * q^77 - 60 * q^78 + 16 * q^81 - 16 * q^82 - 4 * q^84 - 36 * q^86 - 12 * q^87 - 4 * q^88 - 28 * q^89 - 44 * q^91 - 8 * q^92 + 24 * q^93 + 24 * q^94 + 8 * q^97 + 16 * q^98 - 36 * q^99

Introduction

L-functions

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