LMFDB - Embedded newform 575.2.r.b.57.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [575,2,Mod(7,575)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(575, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([11, 38]))

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

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

chi := DirichletCharacter("575.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 575 = 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	575.r (of order $44$, degree $20$, 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:	$4.59139811622$
Analytic rank:	$0$
Dimension:	$200$
Relative dimension:	$10$ over $\Q(\zeta_{44})$
Twist minimal:	no (minimal twist has level 115)
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			57.10
Character	$\chi$	$=$	575.57
Dual form			575.2.r.b.343.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.66353 + 0.579415i) q^{2} +(-1.52955 - 2.04324i) q^{3} +(4.93941 + 2.25575i) q^{4} +(-2.89012 - 6.32847i) q^{6} +(1.87829 + 0.134338i) q^{7} +(7.48497 + 5.60318i) q^{8} +(-0.990105 + 3.37199i) q^{9} +(-0.338516 + 0.526741i) q^{11} +(-2.94603 - 13.5427i) q^{12} +(-0.187613 - 2.62317i) q^{13} +(4.92504 + 1.44612i) q^{14} +(9.57793 + 11.0535i) q^{16} +(-0.657846 - 0.245364i) q^{17} +(-4.59096 + 8.40771i) q^{18} +(0.374105 - 0.819175i) q^{19} +(-2.59845 - 4.04326i) q^{21} +(-1.20685 + 1.20685i) q^{22} +(-3.44274 - 3.33880i) q^{23} -23.8639i q^{24} +(1.02019 - 7.09560i) q^{26} +(1.23000 - 0.458767i) q^{27} +(8.97459 + 4.90050i) q^{28} +(0.285445 - 0.130359i) q^{29} +(0.816998 + 5.68235i) q^{31} +(10.1447 + 18.5786i) q^{32} +(1.59403 - 0.114008i) q^{33} +(-1.61002 - 1.03470i) q^{34} +(-12.4969 + 14.4222i) q^{36} +(0.233984 - 0.127765i) q^{37} +(1.47108 - 1.96514i) q^{38} +(-5.07280 + 4.39561i) q^{39} +(6.57092 - 1.92940i) q^{41} +(-4.57831 - 12.2749i) q^{42} +(-9.32877 + 6.98343i) q^{43} +(-2.86026 + 1.83818i) q^{44} +(-7.23528 - 10.8878i) q^{46} +(-3.96485 - 3.96485i) q^{47} +(7.93507 - 36.4769i) q^{48} +(-3.41883 - 0.491554i) q^{49} +(0.504871 + 1.71943i) q^{51} +(4.99052 - 13.3801i) q^{52} +(-0.472144 + 6.60144i) q^{53} +(3.54196 - 0.509257i) q^{54} +(13.3062 + 11.5299i) q^{56} +(-2.24598 + 0.488583i) q^{57} +(0.835824 - 0.181822i) q^{58} +(2.23622 + 1.93770i) q^{59} +(-9.02346 + 1.29738i) q^{61} +(-1.11634 + 15.6085i) q^{62} +(-2.31269 + 6.20055i) q^{63} +(8.01475 + 27.2957i) q^{64} +(4.31181 + 0.619945i) q^{66} +(-2.99845 + 13.7837i) q^{67} +(-2.69589 - 2.69589i) q^{68} +(-1.55612 + 12.1412i) q^{69} +(5.95122 - 3.82461i) q^{71} +(-26.3048 + 19.6915i) q^{72} +(-2.49870 - 6.69927i) q^{73} +(0.697253 - 0.204732i) q^{74} +(3.69571 - 3.20235i) q^{76} +(-0.706591 + 0.943895i) q^{77} +(-16.0584 + 8.76857i) q^{78} +(-6.21028 + 7.16705i) q^{79} +(6.05065 + 3.88851i) q^{81} +(18.6198 - 1.33171i) q^{82} +(-0.0212502 - 0.0389168i) q^{83} +(-3.71419 - 25.8328i) q^{84} +(-28.8938 + 13.1953i) q^{86} +(-0.702956 - 0.383843i) q^{87} +(-5.48520 + 2.04587i) q^{88} +(0.678818 - 4.72128i) q^{89} -4.95227i q^{91} +(-9.47358 - 24.2576i) q^{92} +(10.3608 - 10.3608i) q^{93} +(-8.26321 - 12.8578i) q^{94} +(22.4437 - 49.1449i) q^{96} +(4.99601 - 9.14950i) q^{97} +(-8.82136 - 3.29020i) q^{98} +(-1.44100 - 1.66300i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 200 q + 18 q^{2} + 14 q^{3} - 36 q^{6} + 22 q^{7} + 26 q^{8} - 44 q^{11} + 6 q^{12} + 26 q^{13} - 52 q^{16} + 22 q^{17} - 58 q^{18} - 44 q^{21} - 22 q^{23} - 28 q^{26} + 26 q^{27} - 66 q^{28} - 40 q^{31}+ \cdots + 50 q^{98}+O(q^{100}) $ 200 * q + 18 * q^2 + 14 * q^3 - 36 * q^6 + 22 * q^7 + 26 * q^8 - 44 * q^11 + 6 * q^12 + 26 * q^13 - 52 * q^16 + 22 * q^17 - 58 * q^18 - 44 * q^21 - 22 * q^23 - 28 * q^26 + 26 * q^27 - 66 * q^28 - 40 * q^31 + 46 * q^32 - 12 * q^36 - 66 * q^37 + 22 * q^38 - 8 * q^41 - 198 * q^42 + 22 * q^43 - 76 * q^46 - 52 * q^47 - 18 * q^48 - 44 * q^51 - 158 * q^52 + 22 * q^53 + 88 * q^56 - 66 * q^57 + 58 * q^58 + 44 * q^61 - 38 * q^62 + 22 * q^63 + 132 * q^66 + 22 * q^67 + 132 * q^71 + 28 * q^72 - 34 * q^73 + 132 * q^76 + 10 * q^77 - 22 * q^78 - 48 * q^81 + 50 * q^82 + 22 * q^83 + 46 * q^87 + 110 * q^88 - 50 * q^92 + 36 * q^93 + 148 * q^96 + 88 * q^97 + 50 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/575\mathbb{Z}\right)^\times$.

$n$	$51$	$277$
$\chi(n)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	2.66353	+	0.579415i	1.88340	+	0.409709i	0.998434	−	0.0559464i	$-0.0178176\pi$
$2$	2.66353	+	0.579415i	1.88340	+	0.409709i	0.884966	+	0.465655i	$0.154181\pi$
$3$	−1.52955	−	2.04324i	−0.883086	−	1.17966i	−0.982805	−	0.184649i	$-0.940885\pi$
$3$	−1.52955	−	2.04324i	−0.883086	−	1.17966i	0.0997190	−	0.995016i	$-0.468206\pi$
$4$	4.93941	+	2.25575i	2.46970	+	1.12788i
$5$		0			0
$5$		0			0
$6$	−2.89012	−	6.32847i	−1.17988	−	2.58359i
$7$	1.87829	+	0.134338i	0.709926	+	0.0507749i	0.421632	−	0.906767i	$-0.361457\pi$
$7$	1.87829	+	0.134338i	0.709926	+	0.0507749i	0.288294	+	0.957542i	$0.406912\pi$
$8$	7.48497	+	5.60318i	2.64634	+	1.98102i
$9$	−0.990105	+	3.37199i	−0.330035	+	1.12400i
$10$		0			0
$11$	−0.338516	+	0.526741i	−0.102066	+	0.158818i	−0.888530	−	0.458818i	$-0.848273\pi$
$11$	−0.338516	+	0.526741i	−0.102066	+	0.158818i	0.786464	+	0.617636i	$0.211909\pi$
$12$	−2.94603	−	13.5427i	−0.850445	−	3.90943i
$13$	−0.187613	−	2.62317i	−0.0520345	−	0.727537i	−0.954771	−	0.297343i	$-0.903900\pi$
$13$	−0.187613	−	2.62317i	−0.0520345	−	0.727537i	0.902736	−	0.430194i	$-0.141555\pi$
$14$	4.92504	+	1.44612i	1.31627	+	0.386492i
$15$		0			0
$16$	9.57793	+	11.0535i	2.39448	+	2.76338i
$17$	−0.657846	−	0.245364i	−0.159551	−	0.0595094i	0.268420	−	0.963302i	$-0.413499\pi$
$17$	−0.657846	−	0.245364i	−0.159551	−	0.0595094i	−0.427971	+	0.903793i	$0.640771\pi$
$18$	−4.59096	+	8.40771i	−1.08210	+	1.98172i
$19$	0.374105	−	0.819175i	0.0858255	−	0.187932i	−0.861853	−	0.507158i	$-0.830696\pi$
$19$	0.374105	−	0.819175i	0.0858255	−	0.187932i	0.947678	+	0.319227i	$0.103423\pi$
$20$		0			0
$21$	−2.59845	−	4.04326i	−0.567028	−	0.882313i
$22$	−1.20685	+	1.20685i	−0.257301	+	0.257301i
$23$	−3.44274	−	3.33880i	−0.717860	−	0.696187i
$23$	−3.44274	−	3.33880i	−0.717860	−	0.696187i
$24$		−	23.8639i		−	4.87120i
$25$		0			0
$26$	1.02019	−	7.09560i	0.200076	−	1.39156i
$27$	1.23000	−	0.458767i	0.236714	−	0.0882897i
$28$	8.97459	+	4.90050i	1.69604	+	0.926107i
$29$	0.285445	−	0.130359i	0.0530059	−	0.0242070i	−0.388736	−	0.921349i	$-0.627088\pi$
$29$	0.285445	−	0.130359i	0.0530059	−	0.0242070i	0.441742	+	0.897142i	$0.354361\pi$
$30$		0			0
$31$	0.816998	+	5.68235i	0.146737	+	1.02058i	0.921514	+	0.388345i	$0.126953\pi$
$31$	0.816998	+	5.68235i	0.146737	+	1.02058i	−0.774777	+	0.632235i	$0.782138\pi$
$32$	10.1447	+	18.5786i	1.79334	+	3.28426i
$33$	1.59403	−	0.114008i	0.277486	−	0.0198462i
$34$	−1.61002	−	1.03470i	−0.276117	−	0.177449i
$35$		0			0
$36$	−12.4969	+	14.4222i	−2.08282	+	2.40370i
$37$	0.233984	−	0.127765i	0.0384668	−	0.0210044i	−0.459901	−	0.887970i	$-0.652115\pi$
$37$	0.233984	−	0.127765i	0.0384668	−	0.0210044i	0.498367	+	0.866966i	$0.333933\pi$
$38$	1.47108	−	1.96514i	0.238641	−	0.318787i
$39$	−5.07280	+	4.39561i	−0.812298	+	0.703860i
$40$		0			0
$41$	6.57092	−	1.92940i	1.02621	−	0.301321i	0.275039	−	0.961433i	$-0.411309\pi$
$41$	6.57092	−	1.92940i	1.02621	−	0.301321i	0.751167	+	0.660112i	$0.229491\pi$
$42$	−4.57831	−	12.2749i	−0.706449	−	1.89406i
$43$	−9.32877	+	6.98343i	−1.42262	+	1.06496i	−0.436362	+	0.899771i	$0.643733\pi$
$43$	−9.32877	+	6.98343i	−1.42262	+	1.06496i	−0.986261	+	0.165192i	$0.947176\pi$
$44$	−2.86026	+	1.83818i	−0.431201	+	0.277116i
$45$		0			0
$46$	−7.23528	−	10.8878i	−1.06678	−	1.60531i
$47$	−3.96485	−	3.96485i	−0.578333	−	0.578333i	0.356111	−	0.934444i	$-0.384103\pi$
$47$	−3.96485	−	3.96485i	−0.578333	−	0.578333i	−0.934444	+	0.356111i	$0.884103\pi$
$48$	7.93507	−	36.4769i	1.14533	−	5.26499i
$49$	−3.41883	−	0.491554i	−0.488405	−	0.0702220i
$50$		0			0
$51$	0.504871	+	1.71943i	0.0706960	+	0.240769i
$52$	4.99052	−	13.3801i	0.692061	−	1.85549i
$53$	−0.472144	+	6.60144i	−0.0648540	+	0.906777i	0.856026	+	0.516932i	$0.172926\pi$
$53$	−0.472144	+	6.60144i	−0.0648540	+	0.906777i	−0.920880	+	0.389845i	$0.872528\pi$
$54$	3.54196	−	0.509257i	0.482000	−	0.0693011i
$55$		0			0
$56$	13.3062	+	11.5299i	1.77812	+	1.54075i
$57$	−2.24598	+	0.488583i	−0.297488	+	0.0647145i
$58$	0.835824	−	0.181822i	0.109749	−	0.0238745i
$59$	2.23622	+	1.93770i	0.291132	+	0.252267i	0.788164	−	0.615465i	$-0.211032\pi$
$59$	2.23622	+	1.93770i	0.291132	+	0.252267i	−0.497033	+	0.867732i	$0.665577\pi$
$60$		0			0
$61$	−9.02346	+	1.29738i	−1.15534	+	0.166112i	−0.693232	−	0.720714i	$-0.743814\pi$
$61$	−9.02346	+	1.29738i	−1.15534	+	0.166112i	−0.462103	+	0.886826i	$0.652905\pi$
$62$	−1.11634	+	15.6085i	−0.141775	+	1.98228i
$63$	−2.31269	+	6.20055i	−0.291371	+	0.781196i
$64$	8.01475	+	27.2957i	1.00184	+	3.41197i
$65$		0			0
$66$	4.31181	+	0.619945i	0.530748	+	0.0763100i
$67$	−2.99845	+	13.7837i	−0.366319	+	1.68394i	0.312723	+	0.949844i	$0.398759\pi$
$67$	−2.99845	+	13.7837i	−0.366319	+	1.68394i	−0.679042	+	0.734099i	$0.737605\pi$
$68$	−2.69589	−	2.69589i	−0.326924	−	0.326924i
$69$	−1.55612	+	12.1412i	−0.187335	+	1.46163i
$70$		0			0
$71$	5.95122	−	3.82461i	0.706279	−	0.453898i	−0.137560	−	0.990493i	$-0.543926\pi$
$71$	5.95122	−	3.82461i	0.706279	−	0.453898i	0.843840	+	0.536595i	$0.180290\pi$
$72$	−26.3048	+	19.6915i	−3.10005	+	2.32067i
$73$	−2.49870	−	6.69927i	−0.292451	−	0.784091i	−0.997210	−	0.0746444i	$-0.976218\pi$
$73$	−2.49870	−	6.69927i	−0.292451	−	0.784091i	0.704759	−	0.709446i	$-0.251055\pi$
$74$	0.697253	−	0.204732i	0.0810540	−	0.0237996i
$75$		0			0
$76$	3.69571	−	3.20235i	0.423927	−	0.367335i
$77$	−0.706591	+	0.943895i	−0.0805235	+	0.107567i
$78$	−16.0584	+	8.76857i	−1.81826	+	0.992845i
$79$	−6.21028	+	7.16705i	−0.698712	+	0.806356i	−0.988578	−	0.150711i	$-0.951844\pi$
$79$	−6.21028	+	7.16705i	−0.698712	+	0.806356i	0.289866	+	0.957067i	$0.406389\pi$
$80$		0			0
$81$	6.05065	+	3.88851i	0.672294	+	0.432057i
$82$	18.6198	−	1.33171i	2.05621	−	0.147063i
$83$	−0.0212502	−	0.0389168i	−0.00233251	−	0.00427168i	0.876510	−	0.481383i	$-0.159866\pi$
$83$	−0.0212502	−	0.0389168i	−0.00233251	−	0.00427168i	−0.878843	+	0.477112i	$0.841684\pi$
$84$	−3.71419	−	25.8328i	−0.405252	−	2.81859i
$85$		0			0
$86$	−28.8938	+	13.1953i	−3.11569	+	1.42289i
$87$	−0.702956	−	0.383843i	−0.0753648	−	0.0411523i
$88$	−5.48520	+	2.04587i	−0.584725	+	0.218091i
$89$	0.678818	−	4.72128i	0.0719545	−	0.500455i	−0.921693	−	0.387920i	$-0.873194\pi$
$89$	0.678818	−	4.72128i	0.0719545	−	0.500455i	0.993648	−	0.112535i	$-0.0358971\pi$
$90$		0			0
$91$		−	4.95227i		−	0.519139i
$92$	−9.47358	−	24.2576i	−0.987689	−	2.52903i
$93$	10.3608	−	10.3608i	1.07436	−	1.07436i
$94$	−8.26321	−	12.8578i	−0.852285	−	1.32618i
$95$		0			0
$96$	22.4437	−	49.1449i	2.29065	−	5.01583i
$97$	4.99601	−	9.14950i	0.507267	−	0.928991i	−0.491057	−	0.871127i	$-0.663389\pi$
$97$	4.99601	−	9.14950i	0.507267	−	0.928991i	0.998325	−	0.0578636i	$-0.0184288\pi$
$98$	−8.82136	−	3.29020i	−0.891091	−	0.332360i
$99$	−1.44100	−	1.66300i	−0.144826	−	0.167138i
$100$		0			0
$101$	−1.17854	−	0.346050i	−0.117269	−	0.0344332i	0.222572	−	0.974916i	$-0.428555\pi$
$101$	−1.17854	−	0.346050i	−0.117269	−	0.0344332i	−0.339840	+	0.940483i	$0.610373\pi$
$102$	0.348473	+	4.87229i	0.0345039	+	0.482428i
$103$	0.585505	+	2.69152i	0.0576916	+	0.265204i	0.996954	−	0.0779971i	$-0.0248525\pi$
$103$	0.585505	+	2.69152i	0.0576916	+	0.265204i	−0.939262	+	0.343201i	$0.888489\pi$
$104$	13.2938	−	20.6856i	1.30357	−	2.02839i
$105$		0			0
$106$	−5.08255	+	17.3096i	−0.493661	+	1.68125i
$107$	−12.2682	−	9.18388i	−1.18601	−	0.887839i	−0.190429	−	0.981701i	$-0.560988\pi$
$107$	−12.2682	−	9.18388i	−1.18601	−	0.887839i	−0.995585	+	0.0938620i	$0.970079\pi$
$108$	7.11034	+	0.508541i	0.684193	+	0.0489344i
$109$	−2.70126	−	5.91493i	−0.258734	−	0.566548i	0.735032	−	0.678032i	$-0.237167\pi$
$109$	−2.70126	−	5.91493i	−0.258734	−	0.566548i	−0.993766	+	0.111484i	$0.964440\pi$
$110$		0			0
$111$	−0.618945	−	0.282663i	−0.0587476	−	0.0268291i
$112$	16.5052	+	22.0484i	1.55960	+	2.08338i
$113$	18.8419	+	4.09881i	1.77250	+	0.385584i	0.975778	−	0.218761i	$-0.0702017\pi$
$113$	18.8419	+	4.09881i	1.77250	+	0.385584i	0.796722	+	0.604345i	$0.206565\pi$
$114$	−6.26533			−0.586802
$115$		0			0
$116$	1.70399			0.158211
$117$	9.03106	+	1.96459i	0.834922	+	0.181626i
$118$	4.83352	+	6.45682i	0.444961	+	0.594399i
$119$	−1.20266	−	0.549237i	−0.110248	−	0.0503485i
$120$		0			0
$121$	4.40670	+	9.64933i	0.400609	+	0.877212i
$122$	−24.7860	−	1.77273i	−2.24402	−	0.160495i
$123$	−13.9928	−	10.4749i	−1.26169	−	0.944486i
$124$	−8.78247	+	29.9104i	−0.788689	+	2.68603i
$125$		0			0
$126$	−9.75261	+	15.1754i	−0.868831	+	1.35193i
$127$	−0.541705	−	2.49018i	−0.0480685	−	0.220967i	0.946846	−	0.321686i	$-0.104250\pi$
$127$	−0.541705	−	2.49018i	−0.0480685	−	0.220967i	−0.994915	+	0.100718i	$0.967886\pi$
$128$	2.51176	+	35.1190i	0.222010	+	3.10411i
$129$	28.5376	+	8.37940i	2.51260	+	0.737765i
$130$		0			0
$131$	−7.52420	−	8.68339i	−0.657392	−	0.758671i	0.324957	−	0.945729i	$-0.394650\pi$
$131$	−7.52420	−	8.68339i	−0.657392	−	0.758671i	−0.982349	+	0.187058i	$0.940105\pi$
$132$	8.13075	+	3.03261i	0.707691	+	0.263955i
$133$	0.812722	−	1.48839i	0.0704720	−	0.129060i
$134$	−15.9729	+	34.9759i	−1.37985	+	3.02145i
$135$		0			0
$136$	−3.54914	−	5.52257i	−0.304336	−	0.473556i
$137$	5.48458	−	5.48458i	0.468579	−	0.468579i	−0.432875	−	0.901454i	$-0.642501\pi$
$137$	5.48458	−	5.48458i	0.468579	−	0.468579i	0.901454	+	0.432875i	$0.142501\pi$
$138$	−11.1796	+	31.4368i	−0.951668	+	2.67608i
$139$		−	6.48562i		−	0.550103i	−0.961429	−	0.275052i	$-0.911305\pi$
$139$		−	6.48562i		−	0.550103i	0.961429	−	0.275052i	$-0.0886949\pi$
$140$		0			0
$141$	−2.03670	+	14.1656i	−0.171521	+	1.19296i
$142$	18.0673	−	6.73875i	1.51617	−	0.565503i
$143$	1.44524	+	0.789162i	0.120857	+	0.0659930i
$144$	−46.7555	+	21.3525i	−3.89629	+	1.77938i
$145$		0			0
$146$	−2.77370	−	19.2915i	−0.229553	−	1.59658i
$147$	4.22491	+	7.73735i	0.348465	+	0.638166i
$148$	1.44395	−	0.103273i	0.118692	−	0.00848901i
$149$	−9.69019	−	6.22751i	−0.793852	−	0.510177i	0.0797526	−	0.996815i	$-0.474587\pi$
$149$	−9.69019	−	6.22751i	−0.793852	−	0.510177i	−0.873604	+	0.486637i	$0.838223\pi$
$150$		0			0
$151$	12.3540	−	14.2573i	1.00536	−	1.16024i	0.0183059	−	0.999832i	$-0.494173\pi$
$151$	12.3540	−	14.2573i	1.00536	−	1.16024i	0.987050	−	0.160411i	$-0.0512818\pi$
$152$	7.39015	−	4.03533i	0.599420	−	0.327308i
$153$	1.47870	−	1.97531i	0.119546	−	0.159695i
$154$	−2.42893	+	2.10468i	−0.195729	+	0.169600i
$155$		0			0
$156$	−34.9720	+	10.2687i	−2.80000	+	0.822155i
$157$	5.79824	+	15.5457i	0.462750	+	1.24068i	0.933552	+	0.358442i	$0.116692\pi$
$157$	5.79824	+	15.5457i	0.462750	+	1.24068i	−0.470802	+	0.882239i	$0.656035\pi$
$158$	−20.6940	+	15.4913i	−1.64632	+	1.23242i
$159$	14.2105	−	9.13252i	1.12696	−	0.724256i
$160$		0			0
$161$	−6.01792	−	6.73371i	−0.474279	−	0.530690i
$162$	13.8630	+	13.8630i	1.08918	+	1.08918i
$163$	−1.50944	+	6.93880i	−0.118229	+	0.543489i	0.879486	+	0.475924i	$0.157886\pi$
$163$	−1.50944	+	6.93880i	−0.118229	+	0.543489i	−0.997715	+	0.0675644i	$0.978477\pi$
$164$	36.8087	+	5.29229i	2.87428	+	0.413259i
$165$		0			0
$166$	−0.0340515	−	0.115969i	−0.00264291	−	0.00900093i
$167$	1.68576	−	4.51969i	0.130448	−	0.349744i	−0.855262	−	0.518196i	$-0.826604\pi$
$167$	1.68576	−	4.51969i	0.130448	−	0.349744i	0.985710	+	0.168452i	$0.0538767\pi$
$168$	3.20582	−	44.8233i	0.247335	−	3.45819i
$169$	6.02185	−	0.865811i	0.463219	−	0.0666009i
$170$		0			0
$171$	2.39185	+	2.07255i	0.182909	+	0.158492i
$172$	−61.8314	+	13.4506i	−4.71460	+	1.02560i
$173$	15.7707	−	3.43070i	1.19902	−	0.260831i	0.431654	−	0.902039i	$-0.357930\pi$
$173$	15.7707	−	3.43070i	1.19902	−	0.260831i	0.767367	+	0.641208i	$0.221566\pi$
$174$	−1.64994	−	1.42968i	−0.125082	−	0.108384i
$175$		0			0
$176$	−9.06463	+	1.30330i	−0.683272	+	0.0982397i
$177$	0.538767	−	7.53295i	0.0404962	−	0.566211i
$178$	4.54363	−	12.1820i	0.340560	−	0.913076i
$179$	−2.20385	−	7.50562i	−0.164723	−	0.560996i	−0.999939	−	0.0110732i	$-0.996475\pi$
$179$	−2.20385	−	7.50562i	−0.164723	−	0.560996i	0.835215	−	0.549923i	$-0.185343\pi$
$180$		0			0
$181$	−0.718152	−	0.103255i	−0.0533798	−	0.00767486i	0.115573	−	0.993299i	$-0.463130\pi$
$181$	−0.718152	−	0.103255i	−0.0533798	−	0.00767486i	−0.168953	+	0.985624i	$0.554039\pi$
$182$	2.86942	−	13.1905i	0.212696	−	0.977747i
$183$	16.4527	+	16.4527i	1.21622	+	1.21622i
$184$	−7.06091	−	44.2811i	−0.520537	−	3.26444i
$185$		0			0
$186$	33.5993	−	21.5930i	2.46362	−	1.58327i
$187$	0.351934	−	0.263455i	0.0257360	−	0.0192657i
$188$	−10.6403	−	28.5277i	−0.776023	−	2.08060i
$189$	2.37193	−	0.696460i	0.172532	−	0.0506600i
$190$		0			0
$191$	−0.881798	+	0.764082i	−0.0638046	+	0.0552870i	−0.686179	−	0.727432i	$-0.740713\pi$
$191$	−0.881798	+	0.764082i	−0.0638046	+	0.0552870i	0.622375	+	0.782719i	$0.286168\pi$
$192$	43.5127	−	58.1262i	3.14026	−	4.19490i
$193$	17.3023	−	9.44775i	1.24544	−	0.680064i	0.284998	−	0.958528i	$-0.408007\pi$
$193$	17.3023	−	9.44775i	1.24544	−	0.680064i	0.960447	+	0.278464i	$0.0898253\pi$
$194$	18.6084	−	21.4752i	1.33600	−	1.54183i
$195$		0			0
$196$	−15.7782	−	10.1400i	−1.12701	−	0.724288i
$197$	5.65515	−	0.404464i	0.402912	−	0.0288169i	0.131587	−	0.991305i	$-0.457993\pi$
$197$	5.65515	−	0.404464i	0.402912	−	0.0288169i	0.271325	+	0.962488i	$0.412538\pi$
$198$	−2.87457	−	5.26439i	−0.204287	−	0.374124i
$199$	1.95540	+	13.6001i	0.138614	+	0.964085i	0.933820	+	0.357744i	$0.116454\pi$
$199$	1.95540	+	13.6001i	0.138614	+	0.964085i	−0.795205	+	0.606341i	$0.792637\pi$
$200$		0			0
$201$	32.7496	−	14.9562i	2.30998	−	1.05493i
$202$	−2.93856	−	1.60458i	−0.206757	−	0.112898i
$203$	0.553661	−	0.206505i	0.0388593	−	0.0144938i
$204$	−1.38485	+	9.63183i	−0.0969588	+	0.674363i
$205$		0			0
$206$			7.50821i			0.523122i
$207$	14.6671	−	8.30311i	1.01943	−	0.577106i
$208$	27.1983	−	27.1983i	1.88587	−	1.88587i
$209$	0.304853	+	0.474360i	0.0210871	+	0.0328122i
$210$		0			0
$211$	6.80328	−	14.8971i	0.468357	−	1.02556i	−0.517146	−	0.855897i	$-0.673005\pi$
$211$	6.80328	−	14.8971i	0.468357	−	1.02556i	0.985502	−	0.169661i	$-0.0542673\pi$
$212$	−17.2233	+	31.5421i	−1.18290	+	2.16632i
$213$	−16.9173	−	6.30982i	−1.15915	−	0.432342i
$214$	−27.3555	−	31.5699i	−1.86998	−	2.15808i
$215$		0			0
$216$	11.7771	+	3.45806i	0.801328	+	0.235291i
$217$	0.771203	+	10.7828i	0.0523527	+	0.731986i
$218$	−3.76768	−	17.3198i	−0.255180	−	1.17304i
$219$	−9.86633	+	15.3523i	−0.666705	+	1.03741i
$220$		0			0
$221$	−0.520211	+	1.77167i	−0.0349932	+	0.119176i
$222$	−1.48480	−	1.11151i	−0.0996532	−	0.0745994i
$223$	−18.8420	−	1.34761i	−1.26176	−	0.0902426i	−0.575621	−	0.817717i	$-0.695240\pi$
$223$	−18.8420	−	1.34761i	−1.26176	−	0.0902426i	−0.686135	+	0.727474i	$0.740694\pi$
$224$	16.5588	+	36.2588i	1.10638	+	2.42264i
$225$		0			0
$226$	47.8112	+	21.8346i	3.18035	+	1.45242i
$227$	−8.23865	−	11.0056i	−0.546819	−	0.730464i	0.438961	−	0.898506i	$-0.355347\pi$
$227$	−8.23865	−	11.0056i	−0.546819	−	0.730464i	−0.985780	+	0.168042i	$0.946256\pi$
$228$	−12.1959	−	2.65306i	−0.807696	−	0.175703i
$229$	8.81270			0.582360			0.291180	−	0.956668i	$-0.405952\pi$
$229$	8.81270			0.582360			0.291180	+	0.956668i	$0.405952\pi$
$230$		0			0
$231$	3.00937			0.198002
$232$	2.86697	+	0.623672i	0.188226	+	0.0409461i
$233$	3.32554	+	4.44241i	0.217864	+	0.291032i	0.896137	−	0.443778i	$-0.146362\pi$
$233$	3.32554	+	4.44241i	0.217864	+	0.291032i	−0.678273	+	0.734810i	$0.737271\pi$
$234$	22.9162	+	10.4655i	1.49808	+	0.684149i
$235$		0			0
$236$	6.67465	+	14.6154i	0.434483	+	0.951385i
$237$	24.1429	+	1.72674i	1.56825	+	0.112164i
$238$	−2.88509	−	2.15975i	−0.187012	−	0.139996i
$239$	1.21124	−	4.12509i	0.0783483	−	0.266830i	−0.910998	−	0.412411i	$-0.864687\pi$
$239$	1.21124	−	4.12509i	0.0783483	−	0.266830i	0.989346	+	0.145581i	$0.0465051\pi$
$240$		0			0
$241$	0.0866550	−	0.134838i	0.00558194	−	0.00868567i	−0.838451	−	0.544976i	$-0.816539\pi$
$241$	0.0866550	−	0.134838i	0.00558194	−	0.00868567i	0.844033	+	0.536291i	$0.180175\pi$
$242$	6.14641	+	28.2546i	0.395106	+	1.81627i
$243$	−1.59056	−	22.2389i	−0.102034	−	1.42662i
$244$	−47.4971	−	13.9464i	−3.04069	−	0.892827i
$245$		0			0
$246$	−31.2009	−	36.0077i	−1.98929	−	2.29577i
$247$	−2.21902	−	0.827653i	−0.141193	−	0.0526623i
$248$	−25.7240	+	47.1100i	−1.63348	+	2.99149i
$249$	−0.0470132	+	0.102944i	−0.00297934	+	0.00652384i
$250$		0			0
$251$	7.73871	+	12.0417i	0.488463	+	0.760063i	0.994754	−	0.102300i	$-0.0326201\pi$
$251$	7.73871	+	12.0417i	0.488463	+	0.760063i	−0.506291	+	0.862363i	$0.668984\pi$
$252$	−25.4102	+	25.4102i	−1.60069	+	1.60069i
$253$	2.92410	−	0.683195i	0.183837	−	0.0429521i
$254$		−	6.94653i		−	0.435864i
$255$		0			0
$256$	−5.56117	+	38.6788i	−0.347573	+	2.41742i
$257$	−20.4056	+	7.61089i	−1.27287	+	0.474754i	−0.892904	−	0.450248i	$-0.851336\pi$
$257$	−20.4056	+	7.61089i	−1.27287	+	0.474754i	−0.379962	+	0.925002i	$0.624063\pi$
$258$	71.1556	+	38.8539i	4.42996	+	2.41894i
$259$	0.456653	−	0.208547i	0.0283750	−	0.0129584i
$260$		0			0
$261$	0.156947	+	1.09159i	0.00971475	+	0.0675676i
$262$	−15.0096	−	27.4881i	−0.927299	−	1.69822i
$263$	23.6124	−	1.68880i	1.45601	−	0.104136i	0.679236	−	0.733920i	$-0.262311\pi$
$263$	23.6124	−	1.68880i	1.45601	−	0.104136i	0.776770	+	0.629784i	$0.216857\pi$
$264$	12.5701	+	8.07831i	0.773636	+	0.497186i
$265$		0			0
$266$	3.02711	−	3.49347i	0.185604	−	0.214198i
$267$	−10.6850	+	5.83444i	−0.653911	+	0.357062i
$268$	−45.9031	+	61.3194i	−2.80398	+	3.74568i
$269$	12.9397	−	11.2123i	0.788945	−	0.683624i	−0.164104	−	0.986443i	$-0.552473\pi$
$269$	12.9397	−	11.2123i	0.788945	−	0.683624i	0.953048	+	0.302819i	$0.0979277\pi$
$270$		0			0
$271$	−15.5892	+	4.57742i	−0.946979	+	0.278058i	−0.718529	−	0.695497i	$-0.755184\pi$
$271$	−15.5892	+	4.57742i	−0.946979	+	0.278058i	−0.228451	+	0.973556i	$0.573366\pi$
$272$	−3.58867	−	9.62159i	−0.217595	−	0.583395i
$273$	−10.1187	+	7.57474i	−0.612410	+	0.458444i
$274$	17.7862	−	11.4305i	1.07450	−	0.690541i
$275$		0			0
$276$	−35.0738	+	56.4600i	−2.11119	+	3.39849i
$277$	−2.00389	−	2.00389i	−0.120402	−	0.120402i	0.644338	−	0.764741i	$-0.277133\pi$
$277$	−2.00389	−	2.00389i	−0.120402	−	0.120402i	−0.764741	+	0.644338i	$0.777133\pi$
$278$	3.75787	−	17.2746i	0.225382	−	1.03606i
$279$	−19.9697	−	2.87121i	−1.19556	−	0.171895i
$280$		0			0
$281$	−0.703529	−	2.39600i	−0.0419690	−	0.142933i	0.935843	−	0.352417i	$-0.114640\pi$
$281$	−0.703529	−	2.39600i	−0.0419690	−	0.142933i	−0.977812	+	0.209483i	$0.932822\pi$
$282$	−13.6326	+	36.5503i	−0.811808	+	2.17654i
$283$	2.34060	−	32.7258i	0.139134	−	1.94535i	−0.151373	−	0.988477i	$-0.548369\pi$
$283$	2.34060	−	32.7258i	0.139134	−	1.94535i	0.290507	−	0.956873i	$-0.406176\pi$
$284$	38.0228	−	5.46686i	2.25624	−	0.324398i
$285$		0			0
$286$	3.39219	+	2.93935i	0.200584	+	0.173807i
$287$	12.6013	−	2.74124i	0.743829	−	0.161810i
$288$	−72.6911	+	15.8130i	−4.28337	+	0.931789i
$289$	−12.4752	−	10.8098i	−0.733834	−	0.635871i
$290$		0			0
$291$	−26.3362	+	3.78658i	−1.54386	+	0.221973i
$292$	2.76980	−	38.7269i	0.162090	−	2.26632i
$293$	−6.80768	+	18.2521i	−0.397709	+	1.06630i	0.571618	+	0.820520i	$0.306316\pi$
$293$	−6.80768	+	18.2521i	−0.397709	+	1.06630i	−0.969326	+	0.245778i	$0.920957\pi$
$294$	6.77004	+	23.0566i	0.394837	+	1.34469i
$295$		0			0
$296$	2.46725	+	0.354738i	0.143406	+	0.0206187i
$297$	−0.174724	+	0.803192i	−0.0101385	+	0.0466059i
$298$	−22.2018	−	22.2018i	−1.28612	−	1.28612i
$299$	−8.11233	+	9.65729i	−0.469148	+	0.558496i
$300$		0			0
$301$	−18.4602	+	11.8637i	−1.06403	+	0.683811i
$302$	41.1662	−	30.8166i	2.36885	−	1.77330i
$303$	1.09557	+	2.93733i	0.0629388	+	0.168745i
$304$	12.6379	−	3.71083i	0.724835	−	0.212831i
$305$		0			0
$306$	5.08309	−	4.40452i	0.290581	−	0.251790i
$307$	−17.2631	+	23.0608i	−0.985257	+	1.31615i	−0.0367733	+	0.999324i	$0.511708\pi$
$307$	−17.2631	+	23.0608i	−0.985257	+	1.31615i	−0.948484	+	0.316826i	$0.897383\pi$
$308$	−5.61933	+	3.06839i	−0.320191	+	0.174838i
$309$	4.60387	−	5.31315i	0.261905	−	0.302254i
$310$		0			0
$311$	−5.35705	−	3.44277i	−0.303771	−	0.195222i	0.379871	−	0.925040i	$-0.375968\pi$
$311$	−5.35705	−	3.44277i	−0.303771	−	0.195222i	−0.683642	+	0.729818i	$0.739605\pi$
$312$	−62.5991	+	4.47718i	−3.54398	+	0.253470i
$313$	15.9366	+	29.1856i	0.900788	+	1.64967i	0.750340	+	0.661053i	$0.229890\pi$
$313$	15.9366	+	29.1856i	0.900788	+	1.64967i	0.150449	+	0.988618i	$0.451928\pi$
$314$	6.43638	+	44.7660i	0.363226	+	2.52629i
$315$		0			0
$316$	−46.8422	+	21.3921i	−2.63508	+	1.20340i
$317$	19.1230	+	10.4419i	1.07405	+	0.586477i	0.916092	−	0.400968i	$-0.131326\pi$
$317$	19.1230	+	10.4419i	1.07405	+	0.586477i	0.157961	+	0.987445i	$0.449508\pi$
$318$	43.1416	−	16.0910i	2.41926	−	0.902337i
$319$	−0.0279626	+	0.194484i	−0.00156561	+	0.0108890i
$320$		0			0
$321$			39.1141i			2.18314i
$322$	−12.1273	−	21.4223i	−0.675828	−	1.19382i
$323$	−0.447099	+	0.447099i	−0.0248773	+	0.0248773i
$324$	21.1151	+	32.8557i	1.17306	+	1.82532i
$325$		0			0
$326$	−8.04090	+	17.6071i	−0.445344	+	0.975168i
$327$	−7.95391	+	14.5665i	−0.439852	+	0.805529i
$328$	59.9939	+	22.3766i	3.31261	+	1.23554i
$329$	−6.91450	−	7.97976i	−0.381209	−	0.439938i
$330$		0			0
$331$	8.25389	+	2.42356i	0.453675	+	0.133211i	0.500584	−	0.865688i	$-0.333119\pi$
$331$	8.25389	+	2.42356i	0.453675	+	0.133211i	−0.0469087	+	0.998899i	$0.514937\pi$
$332$	−0.0171767	−	0.240161i	−0.000942692	−	0.0131806i
$333$	0.199153	+	0.915493i	0.0109135	+	0.0501687i
$334$	7.10884	−	11.0616i	0.388978	−	0.605262i
$335$		0			0
$336$	19.8046	−	67.4481i	1.08043	−	3.67960i
$337$	−5.29945	−	3.96712i	−0.288680	−	0.216103i	0.445116	−	0.895473i	$-0.353162\pi$
$337$	−5.29945	−	3.96712i	−0.288680	−	0.216103i	−0.733796	+	0.679370i	$0.762253\pi$
$338$	16.5410	+	1.18304i	0.899714	+	0.0643488i
$339$	−20.4448	−	44.7679i	−1.11041	−	2.43146i
$340$		0			0
$341$	−3.26969	−	1.49322i	−0.177064	−	0.0808623i
$342$	5.16989	+	6.90616i	0.279556	+	0.373443i
$343$	−19.2359	−	4.18451i	−1.03864	−	0.225942i
$344$	−108.955			−5.87446
$345$		0			0
$346$	43.9934			2.36510
$347$	9.35860	+	2.03584i	0.502396	+	0.109289i	0.456619	−	0.889662i	$-0.349060\pi$
$347$	9.35860	+	2.03584i	0.502396	+	0.109289i	0.0457765	+	0.998952i	$0.485424\pi$
$348$	−2.60633	−	3.48165i	−0.139714	−	0.186636i
$349$	15.9385	+	7.27885i	0.853167	+	0.389628i	0.793485	−	0.608589i	$-0.208264\pi$
$349$	15.9385	+	7.27885i	0.853167	+	0.389628i	0.0596813	+	0.998217i	$0.480992\pi$
$350$		0			0
$351$	−1.43419	−	3.14043i	−0.0765513	−	0.167624i
$352$	−13.2202	−	0.945531i	−0.704641	−	0.0503970i
$353$	−1.78605	−	1.33702i	−0.0950616	−	0.0711622i	0.550690	−	0.834710i	$-0.314365\pi$
$353$	−1.78605	−	1.33702i	−0.0950616	−	0.0711622i	−0.645751	+	0.763548i	$0.723456\pi$
$354$	5.79973	−	19.7521i	0.308252	−	1.04981i
$355$		0			0
$356$	14.0030	−	21.7891i	0.742157	−	1.15482i
$357$	0.717307	+	3.29741i	0.0379639	+	0.174517i
$358$	−1.52114	−	21.2684i	−0.0803950	−	1.12407i
$359$	4.20106	+	1.23354i	0.221723	+	0.0651038i	0.390707	−	0.920515i	$-0.372230\pi$
$359$	4.20106	+	1.23354i	0.221723	+	0.0651038i	−0.168984	+	0.985619i	$0.554049\pi$
$360$		0			0
$361$	11.9113	+	13.7463i	0.626908	+	0.723491i
$362$	−1.85299	−	0.691131i	−0.0973912	−	0.0363250i
$363$	12.9756	−	23.7631i	0.681043	−	1.24724i
$364$	11.1711	−	24.4613i	0.585524	−	1.28212i
$365$		0			0
$366$	34.2892	+	53.3551i	1.79233	+	2.78892i
$367$	−14.2775	+	14.2775i	−0.745280	+	0.745280i	−0.973589	−	0.228309i	$-0.926680\pi$
$367$	−14.2775	+	14.2775i	−0.745280	+	0.745280i	0.228309	+	0.973589i	$0.426680\pi$
$368$	3.93116	−	70.0332i	0.204926	−	3.65073i
$369$			24.0674i			1.25290i
$370$		0			0
$371$	−1.77364	+	12.3360i	−0.0920830	+	0.640452i
$372$	74.5472	−	27.8047i	3.86509	−	1.44161i
$373$	−14.4002	−	7.86310i	−0.745614	−	0.407136i	0.0610591	−	0.998134i	$-0.480552\pi$
$373$	−14.4002	−	7.86310i	−0.745614	−	0.407136i	−0.806673	+	0.590998i	$0.798734\pi$
$374$	1.09004	−	0.497803i	0.0563645	−	0.0257408i
$375$		0			0
$376$	−7.46102	−	51.8926i	−0.384773	−	2.67615i
$377$	−0.395506	−	0.724315i	−0.0203696	−	0.0373041i
$378$	6.72123	−	0.480712i	0.345703	−	0.0247252i
$379$	4.03462	+	2.59289i	0.207244	+	0.133188i	0.640146	−	0.768253i	$-0.278874\pi$
$379$	4.03462	+	2.59289i	0.207244	+	0.133188i	−0.432902	+	0.901441i	$0.642510\pi$
$380$		0			0
$381$	−4.25946	+	4.91568i	−0.218219	+	0.251838i
$382$	−2.79142	+	1.52423i	−0.142821	+	0.0779863i
$383$	−7.93517	+	10.6001i	−0.405468	+	0.541642i	−0.956075	−	0.293123i	$-0.905306\pi$
$383$	−7.93517	+	10.6001i	−0.405468	+	0.541642i	0.550607	+	0.834765i	$0.314396\pi$
$384$	67.9146	−	58.8484i	3.46575	−	3.00309i
$385$		0			0
$386$	51.5593	−	15.1392i	2.62430	−	0.770564i
$387$	−14.3116	−	38.3708i	−0.727498	−	1.95050i
$388$	45.3163	−	33.9233i	2.30059	−	1.72220i
$389$	11.1062	−	7.13754i	0.563108	−	0.361888i	−0.227908	−	0.973683i	$-0.573189\pi$
$389$	11.1062	−	7.13754i	0.563108	−	0.361888i	0.791016	+	0.611795i	$0.209552\pi$
$390$		0			0
$391$	1.44557	+	3.04114i	0.0731056	+	0.153797i
$392$	−22.8356	−	22.8356i	−1.15337	−	1.15337i
$393$	−6.23360	+	28.6554i	−0.314444	+	1.44547i
$394$	15.2970	+	2.19938i	0.770652	+	0.110803i
$395$		0			0
$396$	−3.36636	−	11.4648i	−0.169166	−	0.576126i
$397$	5.07488	−	13.6063i	0.254701	−	0.682879i	−0.745171	−	0.666873i	$-0.767632\pi$
$397$	5.07488	−	13.6063i	0.254701	−	0.682879i	0.999872	−	0.0160058i	$-0.00509501\pi$
$398$	−2.67184	+	37.3572i	−0.133927	+	1.87255i
$399$	−4.28423	+	0.615980i	−0.214480	+	0.0308376i
$400$		0			0
$401$	−12.3145	−	10.6706i	−0.614955	−	0.532862i	0.290734	−	0.956804i	$-0.406101\pi$
$401$	−12.3145	−	10.6706i	−0.614955	−	0.532862i	−0.905689	+	0.423942i	$0.860646\pi$
$402$	95.8954	−	20.8608i	4.78283	−	1.04044i
$403$	14.7525	−	3.20921i	0.734874	−	0.159862i
$404$	−5.04067	−	4.36777i	−0.250783	−	0.217305i
$405$		0			0
$406$	1.59434	−	0.229232i	0.0791259	−	0.0113766i
$407$	−0.0119083	+	0.166500i	−0.000590272	+	0.00825308i
$408$	−5.85534	+	15.6988i	−0.289882	+	0.777205i
$409$	−1.62410	−	5.53116i	−0.0803064	−	0.273498i	0.909545	−	0.415606i	$-0.136430\pi$
$409$	−1.62410	−	5.53116i	−0.0803064	−	0.273498i	−0.989851	+	0.142107i	$0.954612\pi$
$410$		0			0
$411$	−19.5952	−	2.81737i	−0.966562	−	0.138971i
$412$	−3.17936	+	14.6153i	−0.156636	+	0.720043i
$413$	3.93997	+	3.93997i	0.193873	+	0.193873i
$414$	43.8771	−	13.6173i	2.15644	−	0.669252i
$415$		0			0
$416$	46.8316	−	30.0968i	2.29611	−	1.47562i
$417$	−13.2517	+	9.92008i	−0.648937	+	0.485788i
$418$	0.537133	+	1.44011i	0.0262720	+	0.0704380i
$419$	−29.0927	+	8.54240i	−1.42127	+	0.417324i	−0.899934	−	0.436026i	$-0.856386\pi$
$419$	−29.0927	+	8.54240i	−1.42127	+	0.417324i	−0.521339	+	0.853349i	$0.674567\pi$
$420$		0			0
$421$	12.6074	−	10.9244i	0.614448	−	0.532422i	−0.291085	−	0.956697i	$-0.594016\pi$
$421$	12.6074	−	10.9244i	0.614448	−	0.532422i	0.905533	+	0.424275i	$0.139471\pi$
$422$	26.7523	−	35.7369i	1.30228	−	1.73965i
$423$	17.2951	−	9.44382i	0.840914	−	0.459174i
$424$	−40.5230	+	46.7661i	−1.96797	+	2.27116i
$425$		0			0
$426$	−41.4037	−	26.6085i	−2.00601	−	1.28919i
$427$	−17.1229	+	1.22466i	−0.828636	+	0.0592652i
$428$	−39.8812	−	73.0370i	−1.92773	−	3.53037i
$429$	−0.598123	−	4.16003i	−0.0288776	−	0.200848i
$430$		0			0
$431$	20.1413	−	9.19824i	0.970174	−	0.443063i	0.133671	−	0.991026i	$-0.457324\pi$
$431$	20.1413	−	9.19824i	0.970174	−	0.443063i	0.836503	+	0.547962i	$0.184596\pi$
$432$	16.8519	+	9.20181i	0.810786	+	0.442722i
$433$	−21.2074	+	7.90994i	−1.01916	+	0.380128i	−0.802840	−	0.596195i	$-0.796679\pi$
$433$	−21.2074	+	7.90994i	−1.01916	+	0.380128i	−0.216321	+	0.976322i	$0.569406\pi$
$434$	−4.19362	+	29.1672i	−0.201300	+	1.40007i
$435$		0			0
$436$		−	35.3096i		−	1.69102i
$437$	−4.02300	+	1.57115i	−0.192446	+	0.0751581i
$438$	−35.1746	+	35.1746i	−1.68071	+	1.68071i
$439$	14.4740	+	22.5219i	0.690805	+	1.07491i	0.992587	+	0.121536i	$0.0387821\pi$
$439$	14.4740	+	22.5219i	0.690805	+	1.07491i	−0.301782	+	0.953377i	$0.597582\pi$
$440$		0			0
$441$	5.04252	−	11.0416i	0.240120	−	0.525790i
$442$	−2.41213	+	4.41749i	−0.114733	+	0.210119i
$443$	15.3418	+	5.72218i	0.728909	+	0.271869i	0.686397	−	0.727227i	$-0.259191\pi$
$443$	15.3418	+	5.72218i	0.728909	+	0.271869i	0.0425117	+	0.999096i	$0.486464\pi$
$444$	−2.41960	−	2.79237i	−0.114829	−	0.132520i
$445$		0			0
$446$	−49.4055	−	14.5068i	−2.33942	−	0.686915i
$447$	2.09734	+	29.3247i	0.0992008	+	1.38701i
$448$	11.3872	+	52.3459i	0.537993	+	2.47311i
$449$	7.17802	−	11.1692i	0.338752	−	0.527108i	−0.629527	−	0.776978i	$-0.716751\pi$
$449$	7.17802	−	11.1692i	0.338752	−	0.527108i	0.968279	+	0.249870i	$0.0803879\pi$
$450$		0			0
$451$	−1.20807	+	4.11431i	−0.0568857	+	0.193735i
$452$	83.8221	+	62.7484i	3.94266	+	2.95144i
$453$	−48.0272	−	3.43497i	−2.25651	−	0.161389i
$454$	−15.5671	−	34.0872i	−0.730601	−	1.59979i
$455$		0			0
$456$	−19.5487	−	8.92760i	−0.915453	−	0.418073i
$457$	−3.42418	−	4.57417i	−0.160176	−	0.213970i	0.713272	−	0.700887i	$-0.247212\pi$
$457$	−3.42418	−	4.57417i	−0.160176	−	0.213970i	−0.873448	+	0.486917i	$0.838121\pi$
$458$	23.4729	+	5.10622i	1.09682	+	0.238598i
$459$	−0.921716			−0.0430220
$460$		0			0
$461$	−40.1698			−1.87090			−0.935448	−	0.353465i	$-0.885003\pi$
$461$	−40.1698			−1.87090			−0.935448	+	0.353465i	$0.885003\pi$
$462$	8.01554	+	1.74367i	0.372917	+	0.0811231i
$463$	10.7973	+	14.4235i	0.501793	+	0.670318i	0.977901	−	0.209070i	$-0.0670435\pi$
$463$	10.7973	+	14.4235i	0.501793	+	0.670318i	−0.476107	+	0.879387i	$0.657953\pi$
$464$	4.17490	+	1.90661i	0.193815	+	0.0885123i
$465$		0			0
$466$	6.28369	+	13.7594i	0.291086	+	0.637390i
$467$	−23.0029	−	1.64520i	−1.06445	−	0.0761306i	−0.471888	−	0.881659i	$-0.656427\pi$
$467$	−23.0029	−	1.64520i	−1.06445	−	0.0761306i	−0.592558	+	0.805528i	$0.701882\pi$
$468$	40.1764	+	30.0757i	1.85716	+	1.39025i
$469$	−7.48362	+	25.4869i	−0.345562	+	1.17687i
$470$		0			0
$471$	22.8949	−	35.6251i	1.05494	−	1.64152i
$472$	5.88080	+	27.0336i	0.270686	+	1.24432i
$473$	−0.520522	−	7.27784i	−0.0239336	−	0.334636i
$474$	63.3049	+	18.5880i	2.90769	+	0.853775i
$475$		0			0
$476$	−4.70149	−	5.42581i	−0.215492	−	0.248691i
$477$	−21.7925	−	8.12818i	−0.997810	−	0.372164i
$478$	5.61630	−	10.2855i	0.256884	−	0.470447i
$479$	13.1399	−	28.7724i	0.600378	−	1.31464i	−0.328586	−	0.944474i	$-0.606572\pi$
$479$	13.1399	−	28.7724i	0.600378	−	1.31464i	0.928964	−	0.370170i	$-0.120700\pi$
$480$		0			0
$481$	−0.379048	−	0.589810i	−0.0172831	−	0.0268930i
$482$	0.308935	−	0.308935i	0.0140716	−	0.0140716i
$483$	−4.55386	+	22.5956i	−0.207208	+	1.02813i
$484$			57.6024i			2.61829i
$485$		0			0
$486$	8.64905	−	60.1555i	0.392329	−	2.72871i
$487$	12.2027	−	4.55136i	0.552955	−	0.206242i	−0.0574256	−	0.998350i	$-0.518289\pi$
$487$	12.2027	−	4.55136i	0.552955	−	0.206242i	0.610381	+	0.792108i	$0.291016\pi$
$488$	−74.8097	−	40.8492i	−3.38648	−	1.84916i
$489$	16.4864	−	7.52908i	0.745541	−	0.340477i
$490$		0			0
$491$	1.56156	+	10.8609i	0.0704723	+	0.490145i	0.994239	+	0.107189i	$0.0341850\pi$
$491$	1.56156	+	10.8609i	0.0704723	+	0.490145i	−0.923766	+	0.382956i	$0.874906\pi$
$492$	−45.4873	−	83.3038i	−2.05073	−	3.75562i
$493$	−0.219764	+	0.0157179i	−0.00989769	+	0.000707896i
$494$	−5.43088	−	3.49022i	−0.244347	−	0.157032i
$495$		0			0
$496$	−54.9848	+	63.4559i	−2.46889	+	2.84925i
$497$	11.6919	−	6.38425i	0.524452	−	0.286373i
$498$	−0.184869	+	0.246956i	−0.00828416	+	0.0110663i
$499$	−26.0855	+	22.6032i	−1.16775	+	1.01186i	−0.168086	+	0.985772i	$0.553759\pi$
$499$	−26.0855	+	22.6032i	−1.16775	+	1.01186i	−0.999660	+	0.0260851i	$0.991696\pi$
$500$		0			0
$501$	−11.8132	+	3.46868i	−0.527777	+	0.154969i
$502$	13.6352	+	36.5573i	0.608567	+	1.63163i
$503$	−11.0415	+	8.26553i	−0.492314	+	0.368542i	−0.816401	−	0.577486i	$-0.804034\pi$
$503$	−11.0415	+	8.26553i	−0.492314	+	0.368542i	0.324087	+	0.946027i	$0.394943\pi$
$504$	−52.0532	+	33.4526i	−2.31863	+	1.49010i
$505$		0			0
$506$	8.18429	−	0.125441i	0.363836	−	0.00557654i
$507$	−10.9798	−	10.9798i	−0.487629	−	0.487629i
$508$	2.94152	−	13.5219i	0.130509	−	0.599939i
$509$	22.1258	+	3.18121i	0.980709	+	0.141005i	0.613979	−	0.789323i	$-0.289568\pi$
$509$	22.1258	+	3.18121i	0.980709	+	0.141005i	0.366730	+	0.930327i	$0.380477\pi$
$510$		0			0
$511$	−3.79331	−	12.9188i	−0.167806	−	0.571495i
$512$	−12.6151	+	33.8223i	−0.557513	+	1.49475i
$513$	0.0843390	−	1.17921i	0.00372366	−	0.0520635i
$514$	−58.7608	+	8.44852i	−2.59183	+	0.372648i
$515$		0			0
$516$	122.057	+	105.763i	5.37326	+	4.65596i
$517$	3.43061	−	0.746285i	0.150878	−	0.0328216i
$518$	1.33714	−	0.290878i	0.0587508	−	0.0127804i
$519$	−31.1317	−	26.9758i	−1.36653	−	1.18411i
$520$		0			0
$521$	26.3748	−	3.79213i	1.15550	−	0.166136i	0.462195	−	0.886779i	$-0.347062\pi$
$521$	26.3748	−	3.79213i	1.15550	−	0.166136i	0.693307	+	0.720643i	$0.256153\pi$
$522$	−0.214451	+	2.99841i	−0.00938625	+	0.131237i
$523$	−3.91444	+	10.4950i	−0.171166	+	0.458915i	−0.994002	−	0.109365i	$-0.965118\pi$
$523$	−3.91444	+	10.4950i	−0.171166	+	0.458915i	0.822835	+	0.568280i	$0.192391\pi$
$524$	−17.5775	−	59.8635i	−0.767877	−	2.61515i
$525$		0			0
$526$	63.8710	+	9.18326i	2.78491	+	0.400409i
$527$	0.856783	−	3.93857i	0.0373221	−	0.171567i
$528$	16.5277	+	16.5277i	0.719277	+	0.719277i
$529$	0.704880	+	22.9892i	0.0306470	+	0.999530i
$530$		0			0
$531$	−8.74800	+	5.62200i	−0.379631	+	0.243974i
$532$	7.37180	−	5.51846i	0.319608	−	0.239256i
$533$	−6.29393	−	16.8747i	−0.272620	−	0.730923i
$534$	−31.8404	+	9.34917i	−1.37787	+	0.404578i
$535$		0			0
$536$	−99.6757	+	86.3695i	−4.30533	+	3.73059i
$537$	−11.9649	+	15.9832i	−0.516322	+	0.689726i
$538$	40.9617	−	22.3668i	1.76598	−	0.964301i
$539$	1.41625	−	1.63444i	0.0610023	−	0.0704004i
$540$		0			0
$541$	−19.0798	−	12.2618i	−0.820305	−	0.527178i	0.0618788	−	0.998084i	$-0.480291\pi$
$541$	−19.0798	−	12.2618i	−0.820305	−	0.527178i	−0.882183	+	0.470906i	$0.843927\pi$
$542$	−44.1747	+	3.15943i	−1.89746	+	0.135709i
$543$	0.887475	+	1.62529i	0.0380852	+	0.0697479i
$544$	−2.11512	−	14.7110i	−0.0906851	−	0.630728i
$545$		0			0
$546$	−31.3403	+	14.3126i	−1.34124	+	0.612524i
$547$	11.4414	+	6.24748i	0.489199	+	0.267123i	0.704861	−	0.709345i	$-0.251009\pi$
$547$	11.4414	+	6.24748i	0.489199	+	0.267123i	−0.215662	+	0.976468i	$0.569191\pi$
$548$	39.4624	−	14.7187i	1.68575	−	0.628753i
$549$	4.55943	−	31.7115i	0.194592	−	1.35342i
$550$		0			0
$551$		−	0.282598i		−	0.0120391i
$552$	−79.6767	+	82.1572i	−3.39127	+	3.49684i
$553$	−12.6275	+	12.6275i	−0.536976	+	0.536976i
$554$	−4.17634	−	6.49851i	−0.177436	−	0.276095i
$555$		0			0
$556$	14.6299	−	32.0351i	0.620448	−	1.35859i
$557$	21.5196	−	39.4102i	0.911814	−	1.66986i	0.185332	−	0.982676i	$-0.440664\pi$
$557$	21.5196	−	39.4102i	0.911814	−	1.66986i	0.726482	−	0.687186i	$-0.241154\pi$
$558$	−51.5263	−	19.2183i	−2.18128	−	0.813577i
$559$	20.0689	+	23.1608i	0.848825	+	0.979596i
$560$		0			0
$561$	−1.07660	−	0.316119i	−0.0454541	−	0.0133465i
$562$	−0.485591	−	6.78945i	−0.0204834	−	0.286396i
$563$	1.12605	+	5.17637i	0.0474573	+	0.218158i	0.994768	−	0.102158i	$-0.0325747\pi$
$563$	1.12605	+	5.17637i	0.0474573	+	0.218158i	−0.947311	+	0.320316i	$0.896211\pi$
$564$	−42.0141	+	65.3752i	−1.76911	+	2.75279i
$565$		0			0
$566$	25.1961	−	85.8101i	1.05907	−	3.60687i
$567$	10.8425	+	8.11658i	0.455341	+	0.340864i
$568$	65.9747	+	4.71860i	2.76823	+	0.197988i
$569$	12.6740	+	27.7522i	0.531321	+	1.16343i	0.964973	+	0.262350i	$0.0844977\pi$
$569$	12.6740	+	27.7522i	0.531321	+	1.16343i	−0.433651	+	0.901081i	$0.642775\pi$
$570$		0			0
$571$	1.89474	+	0.865299i	0.0792924	+	0.0362116i	0.454666	−	0.890662i	$-0.349758\pi$
$571$	1.89474	+	0.865299i	0.0792924	+	0.0362116i	−0.375374	+	0.926873i	$0.622486\pi$
$572$	5.35848	+	7.15809i	0.224049	+	0.299295i
$573$	2.90995	+	0.633022i	0.121565	+	0.0264449i
$574$	35.1522			1.46722
$575$		0			0
$576$	−99.9764			−4.16568
$577$	−0.132742	−	0.0288762i	−0.00552612	−	0.00120213i	0.209801	−	0.977744i	$-0.432718\pi$
$577$	−0.132742	−	0.0288762i	−0.00552612	−	0.00120213i	−0.215327	+	0.976542i	$0.569082\pi$
$578$	−26.9647	−	36.0206i	−1.12158	−	1.49826i
$579$	−45.7687	−	20.9019i	−1.90208	−	0.868652i
$580$		0			0
$581$	−0.0346860	−	0.0759517i	−0.00143902	−	0.00315101i
$582$	−72.3414	−	5.17396i	−2.99865	−	0.214467i
$583$	−3.31742	−	2.48339i	−0.137393	−	0.102851i
$584$	18.8345	−	64.1445i	0.779378	−	2.65432i
$585$		0			0
$586$	−28.7080	+	44.6705i	−1.18592	+	1.84532i
$587$	−4.15144	−	19.0839i	−0.171348	−	0.787676i	−0.979938	−	0.199303i	$-0.936132\pi$
$587$	−4.15144	−	19.0839i	−0.171348	−	0.787676i	0.808590	−	0.588373i	$-0.200231\pi$
$588$	3.41502	+	47.7483i	0.140833	+	1.96911i
$589$	4.96048	+	1.45653i	0.204393	+	0.0600152i
$590$		0			0
$591$	−9.47624	−	10.9362i	−0.389800	−	0.449854i
$592$	3.65334	+	1.36263i	0.150151	+	0.0560036i
$593$	8.80591	−	16.1268i	0.361616	−	0.662249i	−0.632012	−	0.774958i	$-0.717771\pi$
$593$	8.80591	−	16.1268i	0.361616	−	0.662249i	0.993628	+	0.112709i	$0.0359527\pi$
$594$	−0.930763	+	2.03809i	−0.0381897	+	0.0836237i
$595$		0			0
$596$	−33.8161	−	52.6189i	−1.38516	−	2.15535i
$597$	24.7974	−	24.7974i	1.01489	−	1.01489i
$598$	−27.2030	+	21.0221i	−1.11241	+	0.859656i
$599$		−	30.0593i		−	1.22819i	−0.789232	−	0.614095i	$-0.789521\pi$
$599$		−	30.0593i		−	1.22819i	0.789232	−	0.614095i	$-0.210479\pi$
$600$		0			0
$601$	−1.70361	+	11.8489i	−0.0694919	+	0.483327i	0.925121	+	0.379671i	$0.123963\pi$
$601$	−1.70361	+	11.8489i	−0.0694919	+	0.483327i	−0.994613	+	0.103655i	$0.966946\pi$
$602$	−56.0434	+	20.9031i	−2.28416	+	0.851947i
$603$	−43.5096	−	23.7580i	−1.77185	−	0.967502i
$604$	93.1825	−	42.5550i	3.79154	−	1.73154i
$605$		0			0
$606$	1.21614	+	8.45846i	0.0494025	+	0.343602i
$607$	16.8553	+	30.8683i	0.684137	+	1.25290i	0.956787	+	0.290791i	$0.0939183\pi$
$607$	16.8553	+	30.8683i	0.684137	+	1.25290i	−0.272649	+	0.962113i	$0.587900\pi$
$608$	19.0143	−	1.35993i	0.771132	−	0.0551524i
$609$	−1.26879	−	0.815401i	−0.0514139	−	0.0330417i
$610$		0			0
$611$	−9.65663	+	11.1443i	−0.390665	+	0.450852i
$612$	11.7597	−	6.42129i	0.475358	−	0.259565i
$613$	−1.65805	+	2.21490i	−0.0669680	+	0.0894588i	−0.832775	−	0.553612i	$-0.813249\pi$
$613$	−1.65805	+	2.21490i	−0.0669680	+	0.0894588i	0.765807	+	0.643071i	$0.222340\pi$
$614$	−59.3426	+	51.4206i	−2.39487	+	2.07517i
$615$		0			0
$616$	−10.5776	+	3.10587i	−0.426185	+	0.125139i
$617$	−13.3328	−	35.7466i	−0.536758	−	1.43910i	−0.868479	−	0.495727i	$-0.834902\pi$
$617$	−13.3328	−	35.7466i	−0.536758	−	1.43910i	0.331720	−	0.943378i	$-0.392371\pi$
$618$	15.3411	−	11.4842i	0.617108	−	0.461961i
$619$	18.7737	−	12.0651i	0.754577	−	0.484937i	−0.105931	−	0.994373i	$-0.533782\pi$
$619$	18.7737	−	12.0651i	0.754577	−	0.484937i	0.860508	+	0.509436i	$0.170146\pi$
$620$		0			0
$621$	−5.76630	−	2.52731i	−0.231394	−	0.101417i
$622$	−12.2739	−	12.2739i	−0.492138	−	0.492138i
$623$	1.90926	−	8.77673i	0.0764929	−	0.351632i
$624$	−97.1739	−	13.9715i	−3.89007	−	0.559308i
$625$		0			0
$626$	25.5369	+	86.9707i	1.02066	+	3.47605i
$627$	0.502944	−	1.34844i	0.0200856	−	0.0538517i
$628$	−6.42733	+	89.8658i	−0.256478	+	3.58604i
$629$	−0.185274	+	0.0266384i	−0.00738737	+	0.00106214i
$630$		0			0
$631$	6.26642	+	5.42988i	0.249462	+	0.216160i	0.770611	−	0.637305i	$-0.219951\pi$
$631$	6.26642	+	5.42988i	0.249462	+	0.216160i	−0.521149	+	0.853466i	$0.674496\pi$
$632$	−86.6420	+	18.8478i	−3.44644	+	0.749726i
$633$	−40.8443	+	8.88513i	−1.62341	+	0.353152i
$634$	44.8844	+	38.8925i	1.78259	+	1.54462i
$635$		0			0
$636$	90.7920	−	13.0539i	3.60014	−	0.517622i
$637$	−0.648013	+	9.06041i	−0.0256752	+	0.358987i
$638$	−0.187166	+	0.501813i	−0.00740999	+	0.0198669i
$639$	7.00423	+	23.8542i	0.277083	+	0.943658i
$640$		0			0
$641$	−35.5107	−	5.10566i	−1.40259	−	0.201662i	−0.600861	−	0.799353i	$-0.705176\pi$
$641$	−35.5107	−	5.10566i	−1.40259	−	0.201662i	−0.801726	+	0.597692i	$0.796085\pi$
$642$	−22.6633	+	104.182i	−0.894450	+	4.11172i
$643$	23.2345	+	23.2345i	0.916279	+	0.916279i	0.996756	−	0.0804779i	$-0.0256446\pi$
$643$	23.2345	+	23.2345i	0.916279	+	0.916279i	−0.0804779	+	0.996756i	$0.525645\pi$
$644$	−14.5354	−	46.8354i	−0.572775	−	1.84557i
$645$		0			0
$646$	−1.44992	+	0.931806i	−0.0570463	+	0.0366614i
$647$	21.6292	−	16.1914i	0.850333	−	0.636551i	−0.0826075	−	0.996582i	$-0.526325\pi$
$647$	21.6292	−	16.1914i	0.850333	−	0.636551i	0.932940	+	0.360031i	$0.117234\pi$
$648$	23.5009	+	63.0083i	0.923201	+	2.47520i
$649$	−1.77766	+	0.521969i	−0.0697794	+	0.0204891i
$650$		0			0
$651$	20.8523	−	18.0686i	0.817266	−	0.708165i
$652$	−23.1080	+	30.8686i	−0.904978	+	1.20891i
$653$	−20.4573	+	11.1705i	−0.800555	+	0.437136i	−0.826784	−	0.562520i	$-0.809832\pi$
$653$	−20.4573	+	11.1705i	−0.800555	+	0.437136i	0.0262286	+	0.999656i	$0.491650\pi$
$654$	−29.6255	+	34.1897i	−1.15845	+	1.33692i
$655$		0			0
$656$	84.2625	+	54.1522i	3.28990	+	2.11429i
$657$	25.0639	−	1.79260i	0.977834	−	0.0699361i
$658$	−13.7934	−	25.2607i	−0.537722	−	0.984764i
$659$	3.25005	+	22.6046i	0.126604	+	0.880550i	0.949814	+	0.312814i	$0.101272\pi$
$659$	3.25005	+	22.6046i	0.126604	+	0.880550i	−0.823211	+	0.567736i	$0.807819\pi$
$660$		0			0
$661$	−8.22561	+	3.75651i	−0.319939	+	0.146111i	−0.568910	−	0.822400i	$-0.692635\pi$
$661$	−8.22561	+	3.75651i	−0.319939	+	0.146111i	0.248971	+	0.968511i	$0.419908\pi$
$662$	20.5802	+	11.2377i	0.799874	+	0.436764i
$663$	4.41564	−	1.64695i	0.171489	−	0.0639622i
$664$	0.0590009	−	0.410360i	0.00228968	−	0.0159251i
$665$		0			0
$666$			2.55384i			0.0989591i
$667$	−1.41795	−	0.504254i	−0.0549034	−	0.0195248i
$668$	18.5219	−	18.5219i	0.716635	−	0.716635i
$669$	26.0663	+	40.5600i	1.00778	+	1.56814i
$670$		0			0
$671$	2.37120	−	5.19221i	0.0915392	−	0.200443i
$672$	48.7578	−	89.2932i	1.88087	−	3.44456i
$673$	−14.7227	−	5.49127i	−0.567517	−	0.211673i	0.0492939	−	0.998784i	$-0.484303\pi$
$673$	−14.7227	−	5.49127i	−0.567517	−	0.211673i	−0.616811	+	0.787111i	$0.711576\pi$
$674$	−11.8166	−	13.6371i	−0.455160	−	0.525283i
$675$		0			0
$676$	31.6974	+	9.30720i	1.21913	+	0.357969i
$677$	0.478597	+	6.69166i	0.0183940	+	0.257181i	0.998325	+	0.0578469i	$0.0184235\pi$
$677$	0.478597	+	6.69166i	0.0183940	+	0.257181i	−0.979931	+	0.199335i	$0.936122\pi$
$678$	−28.5162	−	131.087i	−1.09516	−	5.03436i
$679$	10.6131	−	16.5142i	0.407292	−	0.633758i
$680$		0			0
$681$	−9.88554	+	33.6671i	−0.378815	+	1.29013i
$682$	−7.84373	−	5.87174i	−0.300352	−	0.224841i
$683$	4.97112	+	0.355542i	0.190215	+	0.0136044i	0.166122	−	0.986105i	$-0.446876\pi$
$683$	4.97112	+	0.355542i	0.190215	+	0.0136044i	0.0240933	+	0.999710i	$0.492330\pi$
$684$	7.13915	+	15.6326i	0.272972	+	0.597726i
$685$		0			0
$686$	−48.8108	−	22.2911i	−1.86360	−	0.851079i
$687$	−13.4795	−	18.0064i	−0.514273	−	0.686989i
$688$	−166.542	−	36.2290i	−6.34935	−	1.38122i
$689$	17.4053			0.663089
$690$		0			0
$691$	−24.3053			−0.924617			−0.462308	−	0.886719i	$-0.652979\pi$
$691$	−24.3053			−0.924617			−0.462308	+	0.886719i	$0.652979\pi$
$692$	85.6365	+	18.6291i	3.25541	+	0.708171i
$693$	−2.48320	−	3.31717i	−0.0943291	−	0.126009i
$694$	23.7473	+	10.8450i	0.901435	+	0.411672i
$695$		0			0
$696$	−3.11087	−	6.81185i	−0.117917	−	0.258202i
$697$	−4.79606	−	0.343021i	−0.181664	−	0.0129928i
$698$	38.2351	+	28.6224i	1.44722	+	1.08338i
$699$	3.99031	−	13.5898i	0.150928	−	0.514012i
$700$		0			0
$701$	11.0877	−	17.2529i	0.418778	−	0.651632i	−0.566208	−	0.824262i	$-0.691590\pi$
$701$	11.0877	−	17.2529i	0.418778	−	0.651632i	0.984987	+	0.172630i	$0.0552266\pi$
$702$	−2.00039	−	9.19563i	−0.0754997	−	0.347067i
$703$	−0.0171273	−	0.239472i	−0.000645970	−	0.00903184i
$704$	−17.0909	−	5.01834i	−0.644138	−	0.189136i
$705$		0			0
$706$	−3.98250	−	4.59605i	−0.149883	−	0.172975i
$707$	−2.16714	−	0.808303i	−0.0815038	−	0.0303994i
$708$	19.6536	−	35.9930i	0.738629	−	1.35270i
$709$	−4.12217	+	9.02630i	−0.154811	+	0.338990i	−0.971107	−	0.238645i	$-0.923297\pi$
$709$	−4.12217	+	9.02630i	−0.154811	+	0.338990i	0.816295	+	0.577635i	$0.196024\pi$
$710$		0			0
$711$	−18.0184	−	28.0371i	−0.675742	−	1.05147i
$712$	31.5351	−	31.5351i	1.18183	−	1.18183i
$713$	16.1595	−	22.2906i	0.605178	−	0.834790i
$714$			9.19836i			0.344240i
$715$		0			0
$716$	6.04510	−	42.0446i	0.225916	−	1.57128i
$717$	−10.2812	+	3.83468i	−0.383958	+	0.143209i
$718$	10.4749	+	5.71973i	0.390920	+	0.213459i
$719$	−9.55228	+	4.36238i	−0.356240	+	0.162689i	−0.585493	−	0.810678i	$-0.699099\pi$
$719$	−9.55228	+	4.36238i	−0.356240	+	0.162689i	0.229253	+	0.973367i	$0.426372\pi$
$720$		0			0
$721$	0.738174	+	5.13411i	0.0274910	+	0.191204i
$722$	23.7612	+	43.5153i	0.884299	+	1.61947i
$723$	−0.408049	+	0.0291842i	−0.0151755	+	0.00108537i
$724$	−3.31433	−	2.12999i	−0.123176	−	0.0791605i
$725$		0			0
$726$	48.3296	−	55.7754i	1.79368	−	2.07002i
$727$	20.0762	−	10.9624i	0.744586	−	0.406575i	−0.0617047	−	0.998094i	$-0.519654\pi$
$727$	20.0762	−	10.9624i	0.744586	−	0.406575i	0.806290	+	0.591520i	$0.201472\pi$
$728$	27.7485	−	37.0676i	1.02843	−	1.37382i
$729$	−26.6995	+	23.1352i	−0.988870	+	0.856860i
$730$		0			0
$731$	7.85037	−	2.30508i	0.290356	−	0.0852563i
$732$	44.1533	+	118.380i	1.63195	+	4.37543i
$733$	5.37537	−	4.02395i	0.198544	−	0.148628i	−0.495380	−	0.868676i	$-0.664971\pi$
$733$	5.37537	−	4.02395i	0.198544	−	0.148628i	0.693924	+	0.720048i	$0.255880\pi$
$734$	−46.3012	+	29.7560i	−1.70901	+	1.09831i
$735$		0			0
$736$	27.1047	−	97.8323i	0.999092	−	3.60615i
$737$	−6.24540	−	6.24540i	−0.230052	−	0.230052i
$738$	−13.9450	+	64.1042i	−0.513323	+	2.35971i
$739$	3.53564	+	0.508349i	0.130061	+	0.0186999i	0.207038	−	0.978333i	$-0.433618\pi$
$739$	3.53564	+	0.508349i	0.130061	+	0.0186999i	−0.0769770	+	0.997033i	$0.524527\pi$
$740$		0			0
$741$	1.70301	+	5.79993i	0.0625618	+	0.213066i
$742$	−11.8718	+	31.8295i	−0.435828	+	1.16850i
$743$	1.53174	−	21.4165i	0.0561941	−	0.785696i	−0.888735	−	0.458421i	$-0.848415\pi$
$743$	1.53174	−	21.4165i	0.0561941	−	0.785696i	0.944929	−	0.327275i	$-0.106130\pi$
$744$	135.603	−	19.4968i	4.97145	−	0.714786i
$745$		0			0
$746$	−33.7993	−	29.2873i	−1.23748	−	1.07228i
$747$	0.152267	−	0.0331237i	0.00557116	−	0.00121193i
$748$	2.33263	−	0.507433i	0.0852895	−	0.0185536i
$749$	−21.8095	−	18.8980i	−0.796902	−	0.690520i
$750$		0			0
$751$	−34.8402	+	5.00927i	−1.27134	+	0.182791i	−0.744758	−	0.667334i	$-0.767435\pi$
$751$	−34.8402	+	5.00927i	−1.27134	+	0.182791i	−0.526580	+	0.850125i	$0.676526\pi$
$752$	5.85050	−	81.8007i	0.213346	−	2.98296i
$753$	12.7673	−	34.2303i	0.465265	−	1.24742i
$754$	−0.633763	−	2.15840i	−0.0230803	−	0.0786042i
$755$		0			0
$756$	13.2869	+	1.91037i	0.483241	+	0.0694796i
$757$	10.0712	−	46.2968i	0.366046	−	1.68268i	−0.313927	−	0.949447i	$-0.601645\pi$
$757$	10.0712	−	46.2968i	0.366046	−	1.68268i	0.679973	−	0.733237i	$-0.261992\pi$
$758$	9.24397	+	9.24397i	0.335756	+	0.335756i
$759$	−5.86849	−	4.92966i	−0.213013	−	0.178935i
$760$		0			0
$761$	−21.3031	+	13.6907i	−0.772237	+	0.496286i	−0.866449	−	0.499266i	$-0.833603\pi$
$761$	−21.3031	+	13.6907i	−0.772237	+	0.496286i	0.0942122	+	0.995552i	$0.469967\pi$
$762$	−14.1934	+	10.6251i	−0.514174	+	0.384905i
$763$	−4.27914	−	11.4728i	−0.154915	−	0.415344i
$764$	−6.07913	+	1.78500i	−0.219935	+	0.0645789i
$765$		0			0
$766$	−27.2775	+	23.6360i	−0.985574	+	0.854005i
$767$	4.66337	−	6.22954i	0.168385	−	0.224936i
$768$	87.5361	−	47.7983i	3.15869	−	1.72477i
$769$	−22.6888	+	26.1843i	−0.818179	+	0.944228i	−0.999230	−	0.0392453i	$-0.987505\pi$
$769$	−22.6888	+	26.1843i	−0.818179	+	0.944228i	0.181051	+	0.983474i	$0.442050\pi$
$770$		0			0
$771$	46.7622	+	30.0523i	1.68410	+	1.08231i
$772$	106.775	−	7.63668i	3.84291	−	0.274850i
$773$	16.3948	+	30.0247i	0.589678	+	1.07992i	0.986768	+	0.162136i	$0.0518382\pi$
$773$	16.3948	+	30.0247i	0.589678	+	1.07992i	−0.397090	+	0.917780i	$0.629980\pi$
$774$	−15.8867	−	110.494i	−0.571034	−	3.97163i
$775$		0			0
$776$	88.6612	−	40.4902i	3.18275	−	1.45351i
$777$	−1.12458	−	0.614069i	−0.0403442	−	0.0220296i
$778$	33.7174	−	12.5759i	1.20883	−	0.450869i
$779$	0.877700	−	6.10453i	0.0314469	−	0.218718i
$780$		0			0
$781$			4.42944i			0.158498i
$782$	2.08824	+	8.93774i	0.0746753	+	0.319613i
$783$	0.291294	−	0.291294i	0.0104100	−	0.0104100i
$784$	−27.3120	−	42.4983i	−0.975427	−	1.51779i
$785$		0			0
$786$	−33.2068	+	72.7127i	−1.18445	+	2.59358i
$787$	12.3341	−	22.5883i	0.439664	−	0.805185i	−0.560065	−	0.828449i	$-0.689224\pi$
$787$	12.3341	−	22.5883i	0.439664	−	0.805185i	0.999729	+	0.0232634i	$0.00740563\pi$
$788$	28.8454	+	10.7588i	1.02758	+	0.383266i
$789$	−39.5670	−	45.6628i	−1.40862	−	1.62564i
$790$		0			0
$791$	34.8399	+	10.2299i	1.23877	+	0.363734i
$792$	−1.46774	−	20.5217i	−0.0521538	−	0.729206i
$793$	5.09616	+	23.4267i	0.180970	+	0.831905i
$794$	21.4008	−	33.3002i	0.759485	−	1.18178i
$795$		0			0
$796$	−21.0199	+	71.5873i	−0.745031	+	2.53734i
$797$	−30.6870	−	22.9720i	−1.08699	−	0.813711i	−0.103492	−	0.994630i	$-0.533002\pi$
$797$	−30.6870	−	22.9720i	−1.08699	−	0.813711i	−0.983498	+	0.180920i	$0.942093\pi$
$798$	−11.7681	−	0.841671i	−0.416586	−	0.0297948i
$799$	1.63543	+	3.58109i	0.0578573	+	0.126690i
$800$		0			0
$801$	15.2480	+	6.96353i	0.538762	+	0.246044i
$802$	−26.6173	−	35.5565i	−0.939889	−	1.25554i
$803$	4.37463	+	0.951643i	0.154377	+	0.0335827i
$804$	195.501			6.89479
$805$		0			0
$806$	41.1532			1.44956
$807$	−42.7012	−	9.28907i	−1.50315	−	0.326991i
$808$	−6.88234	−	9.19373i	−0.242120	−	0.323434i
$809$	22.1760	+	10.1275i	0.779668	+	0.356062i	0.765167	−	0.643832i	$-0.222657\pi$
$809$	22.1760	+	10.1275i	0.779668	+	0.356062i	0.0145015	+	0.999895i	$0.495384\pi$
$810$		0			0
$811$	−1.71142	−	3.74749i	−0.0600961	−	0.131592i	0.877201	−	0.480123i	$-0.159408\pi$
$811$	−1.71142	−	3.74749i	−0.0600961	−	0.131592i	−0.937297	+	0.348531i	$0.886681\pi$
$812$	3.20058	+	0.228910i	0.112318	+	0.00803316i
$813$	33.1973	+	24.8512i	1.16428	+	0.871568i
$814$	−0.128190	+	0.436577i	−0.00449307	+	0.0153020i
$815$		0			0
$816$	−14.1702	+	22.0492i	−0.496055	+	0.771876i
$817$	2.23071	+	10.2544i	0.0780428	+	0.358757i
$818$	−1.12099	−	15.6734i	−0.0391944	−	0.548009i
$819$	16.6990	+	4.90327i	0.583510	+	0.171334i
$820$		0			0
$821$	−30.6809	−	35.4076i	−1.07077	−	1.23573i	−0.970583	−	0.240766i	$-0.922601\pi$
$821$	−30.6809	−	35.4076i	−1.07077	−	1.23573i	−0.100187	−	0.994969i	$-0.531944\pi$
$822$	−50.5601	−	18.8579i	−1.76349	−	0.657746i
$823$	−9.20092	+	16.8502i	−0.320724	+	0.587362i	−0.987448	−	0.157942i	$-0.949514\pi$
$823$	−9.20092	+	16.8502i	−0.320724	+	0.587362i	0.666724	+	0.745304i	$0.267696\pi$
$824$	−10.6986	+	23.4267i	−0.372703	+	0.816107i
$825$		0			0
$826$	8.21134	+	12.7771i	0.285709	+	0.444572i
$827$	−37.9205	+	37.9205i	−1.31862	+	1.31862i	−0.403760	+	0.914865i	$0.632297\pi$
$827$	−37.9205	+	37.9205i	−1.31862	+	1.31862i	−0.914865	+	0.403760i	$0.867703\pi$
$828$	91.1763	−	7.92721i	3.16859	−	0.275490i
$829$		−	43.7742i		−	1.52034i	−0.649723	−	0.760171i	$-0.725115\pi$
$829$		−	43.7742i		−	1.52034i	0.649723	−	0.760171i	$-0.274885\pi$
$830$		0			0
$831$	−1.02938	+	7.15948i	−0.0357087	+	0.248360i
$832$	70.0977	−	26.1451i	2.43020	−	0.906418i
$833$	2.12846	+	1.16222i	0.0737466	+	0.0402687i
$834$	−41.0441	+	18.7442i	−1.42124	+	0.649059i
$835$		0			0
$836$	0.435753	+	3.03073i	0.0150708	+	0.104820i
$837$	3.61178	+	6.61448i	0.124841	+	0.228630i
$838$	−82.4390	+	5.89615i	−2.84781	+	0.203679i
$839$	9.16913	+	5.89264i	0.316553	+	0.203436i	0.689262	−	0.724512i	$-0.257935\pi$
$839$	9.16913	+	5.89264i	0.316553	+	0.203436i	−0.372709	+	0.927948i	$0.621571\pi$
$840$		0			0
$841$	−18.9265	+	21.8423i	−0.652637	+	0.753183i
$842$	39.9100	−	21.7925i	1.37539	−	0.751019i
$843$	−3.81951	+	5.10227i	−0.131551	+	0.175732i
$844$	67.2083	−	58.2363i	2.31340	−	2.00458i
$845$		0			0
$846$	51.5378	−	15.1329i	1.77191	−	0.520278i
$847$	6.98078	+	18.7162i	0.239862	+	0.643096i
$848$	−77.4913	+	58.0093i	−2.66106	+	1.99205i
$849$	−70.4468	+	45.2734i	−2.41773	+	1.55378i
$850$		0			0
$851$	−1.23213	−	0.341364i	−0.0422368	−	0.0117018i
$852$	−69.3279	−	69.3279i	−2.37513	−	2.37513i
$853$	−9.82595	+	45.1692i	−0.336434	+	1.54656i	0.429153	+	0.903232i	$0.358812\pi$
$853$	−9.82595	+	45.1692i	−0.336434	+	1.54656i	−0.765588	+	0.643332i	$0.777552\pi$
$854$	−46.3170	−	6.65938i	−1.58494	−	0.227879i
$855$		0			0
$856$	−40.3684	−	137.482i	−1.37976	−	4.69904i
$857$	−13.2985	+	35.6548i	−0.454269	+	1.21794i	0.484924	+	0.874556i	$0.338847\pi$
$857$	−13.2985	+	35.6548i	−0.454269	+	1.21794i	−0.939194	+	0.343387i	$0.888426\pi$
$858$	0.817271	−	11.4269i	0.0279012	−	0.390109i
$859$	−15.3761	+	2.21075i	−0.524626	+	0.0754298i	−0.399539	−	0.916716i	$-0.630830\pi$
$859$	−15.3761	+	2.21075i	−0.524626	+	0.0754298i	−0.125087	+	0.992146i	$0.539921\pi$
$860$		0			0
$861$	−24.8753	−	21.5545i	−0.847747	−	0.734577i
$862$	58.9766	−	12.8296i	2.00875	−	0.436977i
$863$	−28.8468	+	6.27524i	−0.981957	+	0.213612i	−0.674762	−	0.738035i	$-0.735754\pi$
$863$	−28.8468	+	6.27524i	−0.981957	+	0.213612i	−0.307194	+	0.951647i	$0.599390\pi$
$864$	21.0012	+	18.1977i	0.714476	+	0.619097i
$865$		0			0
$866$	−61.0696	+	8.78048i	−2.07523	+	0.298373i
$867$	−3.00561	+	42.0239i	−0.102076	+	1.42721i
$868$	−20.5141	+	55.0004i	−0.696294	+	1.86684i
$869$	−1.67290	−	5.69737i	−0.0567492	−	0.193270i
$870$		0			0
$871$	36.7195	+	5.27946i	1.24419	+	0.178888i
$872$	12.9236	−	59.4087i	0.437648	−	2.01183i
$873$	25.9054	+	25.9054i	0.876766	+	0.876766i
$874$	−11.6257	+	1.85380i	−0.393246	+	0.0627058i
$875$		0			0
$876$	−83.3648	+	53.5753i	−2.81664	+	1.81014i
$877$	−9.55912	+	7.15587i	−0.322788	+	0.241636i	−0.748367	−	0.663285i	$-0.769162\pi$
$877$	−9.55912	+	7.15587i	−0.322788	+	0.241636i	0.425578	+	0.904922i	$0.360071\pi$
$878$	25.5023	+	68.3743i	0.860660	+	2.30752i
$879$	47.7060	−	14.0078i	1.60908	−	0.472470i
$880$		0			0
$881$	21.0560	−	18.2451i	0.709394	−	0.614693i	−0.223559	−	0.974690i	$-0.571768\pi$
$881$	21.0560	−	18.2451i	0.709394	−	0.614693i	0.932954	+	0.359997i	$0.117222\pi$
$882$	19.8286	−	26.4879i	0.667663	−	0.891893i
$883$	−1.42224	+	0.776599i	−0.0478620	+	0.0261347i	−0.503002	−	0.864285i	$-0.667771\pi$
$883$	−1.42224	+	0.776599i	−0.0478620	+	0.0261347i	0.455140	+	0.890420i	$0.349589\pi$
$884$	−6.56599	+	7.57756i	−0.220838	+	0.254861i
$885$		0			0
$886$	37.5477	+	24.1304i	1.26144	+	0.810678i
$887$	34.3749	−	2.45854i	1.15420	−	0.0825498i	0.518912	−	0.854828i	$-0.326337\pi$
$887$	34.3749	−	2.45854i	1.15420	−	0.0825498i	0.635285	+	0.772278i	$0.280883\pi$
$888$	−3.04897	−	5.58378i	−0.102317	−	0.187379i
$889$	−0.682952	−	4.75004i	−0.0229055	−	0.159311i
$890$		0			0
$891$	−4.09648	+	1.87080i	−0.137237	+	0.0626741i
$892$	−90.0286	−	49.1593i	−3.01438	−	1.64598i
$893$	−4.73118	+	1.76464i	−0.158323	+	0.0590514i
$894$	−11.4048	+	79.3223i	−0.381435	+	2.65294i
$895$		0			0
$896$			66.3010i			2.21496i
$897$	32.1404	+	1.80413i	1.07314	+	0.0602381i
$898$	25.5905	−	25.5905i	0.853966	−	0.853966i
$899$	0.973951	+	1.51550i	0.0324831	+	0.0505447i
$900$		0			0
$901$	1.93035	−	4.22688i	0.0643093	−	0.140818i
$902$	−5.60162	+	10.2586i	−0.186514	+	0.341574i
$903$	52.4762	+	19.5726i	1.74630	+	0.651335i
$904$	118.065	+	136.254i	3.92678	+	4.53175i
$905$		0			0
$906$	−125.932	−	36.9768i	−4.18379	−	1.22847i
$907$	2.18781	+	30.5895i	0.0726449	+	1.01571i	0.894806	+	0.446454i	$0.147313\pi$
$907$	2.18781	+	30.5895i	0.0726449	+	1.01571i	−0.822162	+	0.569254i	$0.807232\pi$
$908$	−15.8683	−	72.9452i	−0.526607	−	2.42077i
$909$	2.33375	−	3.63139i	0.0774057	−	0.120446i
$910$		0			0
$911$	−10.1960	+	34.7242i	−0.337807	+	1.15047i	0.599038	+	0.800721i	$0.295550\pi$
$911$	−10.1960	+	34.7242i	−0.337807	+	1.15047i	−0.936845	+	0.349745i	$0.886268\pi$
$912$	−26.9124	−	20.1464i	−0.891160	−	0.667114i
$913$	0.0276926	+	0.00198062i	0.000916492	+	6.55488e-5i
$914$	−6.47006	−	14.1674i	−0.214010	−	0.468617i
$915$		0			0
$916$	43.5295	+	19.8793i	1.43826	+	0.656829i
$917$	−12.9661	−	17.3207i	−0.428178	−	0.571979i
$918$	−2.45502	−	0.534056i	−0.0810276	−	0.0176265i
$919$	−28.2597			−0.932202			−0.466101	−	0.884732i	$-0.654342\pi$
$919$	−28.2597			−0.932202			−0.466101	+	0.884732i	$0.654342\pi$
$920$		0			0
$921$	73.5235			2.42268
$922$	−106.994	−	23.2750i	−3.52364	−	0.766522i
$923$	−11.1491	−	14.8935i	−0.366978	−	0.490226i
$924$	14.8645	+	6.78839i	0.489006	+	0.223321i
$925$		0			0
$926$	20.4017	+	44.6736i	0.670443	+	1.46807i
$927$	−9.65550	−	0.690575i	−0.317128	−	0.0226815i
$928$	5.31763	+	3.98073i	0.174560	+	0.130674i
$929$	−3.41489	+	11.6300i	−0.112039	+	0.381570i	−0.996353	−	0.0853222i	$-0.972808\pi$
$929$	−3.41489	+	11.6300i	−0.112039	+	0.381570i	0.884314	+	0.466892i	$0.154626\pi$
$930$		0			0
$931$	−1.68167	+	2.61673i	−0.0551146	+	0.0857599i
$932$	6.40525	+	29.4445i	0.209811	+	0.964485i
$933$	1.15948	+	16.2116i	0.0379596	+	0.530745i
$934$	−60.3156	−	17.7102i	−1.97359	−	0.579497i
$935$		0			0
$936$	56.5893	+	65.3075i	1.84968	+	2.13464i
$937$	5.00361	+	1.86625i	0.163461	+	0.0609677i	0.429862	−	0.902894i	$-0.358562\pi$
$937$	5.00361	+	1.86625i	0.163461	+	0.0609677i	−0.266402	+	0.963862i	$0.585835\pi$
$938$	−34.7004	+	63.5489i	−1.13301	+	2.07495i
$939$	35.2575	−	77.2031i	1.15058	−	2.51943i
$940$		0			0
$941$	−14.6570	−	22.8067i	−0.477803	−	0.743476i	0.515763	−	0.856731i	$-0.327509\pi$
$941$	−14.6570	−	22.8067i	−0.477803	−	0.743476i	−0.993566	+	0.113255i	$0.963872\pi$
$942$	81.6229	−	81.6229i	2.65942	−	2.65942i
$943$	−29.0638	−	15.2966i	−0.946448	−	0.498125i
$944$			43.2773i			1.40856i
$945$		0			0
$946$	2.83047	−	19.6864i	0.0920265	−	0.640059i
$947$	22.1918	−	8.27712i	0.721137	−	0.268970i	0.0380178	−	0.999277i	$-0.487896\pi$
$947$	22.1918	−	8.27712i	0.721137	−	0.268970i	0.683119	+	0.730307i	$0.260623\pi$
$948$	115.357	+	62.9895i	3.74661	+	2.04580i
$949$	−17.1046	+	7.81139i	−0.555237	+	0.253568i
$950$		0			0
$951$	−7.91416	−	55.0442i	−0.256634	−	1.78493i
$952$	−5.92441	−	10.8497i	−0.192011	−	0.351642i
$953$	17.6298	−	1.26091i	0.571085	−	0.0408448i	0.217189	−	0.976130i	$-0.430311\pi$
$953$	17.6298	−	1.26091i	0.571085	−	0.0408448i	0.353896	+	0.935285i	$0.384857\pi$
$954$	−53.3354	−	34.2766i	−1.72680	−	1.10975i
$955$		0			0
$956$	15.2880	−	17.6432i	0.494448	−	0.570623i
$957$	0.440148	−	0.240339i	0.0142280	−	0.00776905i
$958$	51.6697	−	69.0226i	1.66937	−	2.23002i
$959$	11.0384	−	9.56483i	0.356449	−	0.308864i
$960$		0			0
$961$	−1.87729	+	0.551223i	−0.0605579	+	0.0177814i
$962$	−0.667861	−	1.79060i	−0.0215327	−	0.0577314i
$963$	43.1148	−	32.2753i	1.38935	−	1.04006i
$964$	0.732185	−	0.470547i	0.0235821	−	0.0151553i
$965$		0			0
$966$	−25.2216	+	57.5454i	−0.811491	+	1.85149i
$967$	35.9237	+	35.9237i	1.15523	+	1.15523i	0.985489	+	0.169739i	$0.0542924\pi$
$967$	35.9237	+	35.9237i	1.15523	+	1.15523i	0.169739	+	0.985489i	$0.445708\pi$
$968$	−21.0829	+	96.9165i	−0.677630	+	3.11501i
$969$	1.59739	+	0.229670i	0.0513156	+	0.00737806i
$970$		0			0
$971$	1.34882	+	4.59367i	0.0432858	+	0.147418i	0.978300	−	0.207191i	$-0.0664322\pi$
$971$	1.34882	+	4.59367i	0.0432858	+	0.147418i	−0.935015	+	0.354609i	$0.884614\pi$
$972$	42.3090	−	113.435i	1.35706	−	3.63842i
$973$	0.871264	−	12.1819i	0.0279314	−	0.390532i
$974$	35.1393	−	5.05226i	1.12593	−	0.161885i
$975$		0			0
$976$	−100.767	−	87.3148i	−3.22546	−	2.79488i
$977$	−6.81062	+	1.48156i	−0.217891	+	0.0473993i	−0.320186	−	0.947355i	$-0.603745\pi$
$977$	−6.81062	+	1.48156i	−0.217891	+	0.0473993i	0.102294	+	0.994754i	$0.467382\pi$
$978$	48.2745	−	10.5015i	1.54365	−	0.335800i
$979$	2.25710	+	1.95579i	0.0721373	+	0.0625073i
$980$		0			0
$981$	22.6196	−	3.25221i	0.722189	−	0.103835i
$982$	−2.13371	+	29.8331i	−0.0680893	+	0.952013i
$983$	8.34134	−	22.3640i	0.266047	−	0.713301i	−0.733392	−	0.679806i	$-0.762064\pi$
$983$	8.34134	−	22.3640i	0.266047	−	0.713301i	0.999439	−	0.0334941i	$-0.0106635\pi$
$984$	−46.0430	−	156.808i	−1.46780	−	4.99885i
$985$		0			0
$986$	−0.594456	−	0.0854699i	−0.0189313	−	0.00272191i
$987$	−5.72848	+	26.3334i	−0.182340	+	0.838202i
$988$	−9.09368	−	9.09368i	−0.289308	−	0.289308i
$989$	55.4327	+	7.10475i	1.76266	+	0.225918i
$990$		0			0
$991$	11.9433	−	7.67552i	0.379393	−	0.243821i	−0.337020	−	0.941497i	$-0.609419\pi$
$991$	11.9433	−	7.67552i	0.379393	−	0.243821i	0.716413	+	0.697676i	$0.245783\pi$
$992$	−97.2819	+	72.8243i	−3.08870	+	2.31217i
$993$	−7.67282	−	20.5716i	−0.243490	−	0.652821i
$994$	34.8408	−	10.2302i	1.10508	−	0.324482i
$995$		0			0
$996$	−0.464434	+	0.402435i	−0.0147162	+	0.0127516i
$997$	−13.3288	+	17.8053i	−0.422129	+	0.563898i	−0.960311	−	0.278930i	$-0.910020\pi$
$997$	−13.3288	+	17.8053i	−0.422129	+	0.563898i	0.538183	+	0.842828i	$0.319111\pi$
$998$	−82.5760	+	45.0899i	−2.61390	+	1.42730i
$999$	0.229187	−	0.264495i	0.00725114	−	0.00836826i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	575.2.r.b.57.10		200
5.2	odd	4		115.2.l.a.103.1	yes	200
5.3	odd	4	inner	575.2.r.b.218.10		200
5.4	even	2		115.2.l.a.57.1	✓	200
23.21	odd	22	inner	575.2.r.b.182.10		200
115.44	odd	22		115.2.l.a.67.1	yes	200
115.67	even	44		115.2.l.a.113.1	yes	200
115.113	even	44	inner	575.2.r.b.343.10		200

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.2.l.a.57.1	✓	200	5.4	even	2
115.2.l.a.67.1	yes	200	115.44	odd	22
115.2.l.a.103.1	yes	200	5.2	odd	4
115.2.l.a.113.1	yes	200	115.67	even	44
575.2.r.b.57.10		200	1.1	even	1	trivial
575.2.r.b.182.10		200	23.21	odd	22	inner
575.2.r.b.218.10		200	5.3	odd	4	inner
575.2.r.b.343.10		200	115.113	even	44	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 575 = 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	575.r (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(2.66353 + 0.579415i) q^{2} +(-1.52955 - 2.04324i) q^{3} +(4.93941 + 2.25575i) q^{4} +(-2.89012 - 6.32847i) q^{6} +(1.87829 + 0.134338i) q^{7} +(7.48497 + 5.60318i) q^{8} +(-0.990105 + 3.37199i) q^{9} +(-0.338516 + 0.526741i) q^{11} +(-2.94603 - 13.5427i) q^{12} +(-0.187613 - 2.62317i) q^{13} +(4.92504 + 1.44612i) q^{14} +(9.57793 + 11.0535i) q^{16} +(-0.657846 - 0.245364i) q^{17} +(-4.59096 + 8.40771i) q^{18} +(0.374105 - 0.819175i) q^{19} +(-2.59845 - 4.04326i) q^{21} +(-1.20685 + 1.20685i) q^{22} +(-3.44274 - 3.33880i) q^{23} -23.8639i q^{24} +(1.02019 - 7.09560i) q^{26} +(1.23000 - 0.458767i) q^{27} +(8.97459 + 4.90050i) q^{28} +(0.285445 - 0.130359i) q^{29} +(0.816998 + 5.68235i) q^{31} +(10.1447 + 18.5786i) q^{32} +(1.59403 - 0.114008i) q^{33} +(-1.61002 - 1.03470i) q^{34} +(-12.4969 + 14.4222i) q^{36} +(0.233984 - 0.127765i) q^{37} +(1.47108 - 1.96514i) q^{38} +(-5.07280 + 4.39561i) q^{39} +(6.57092 - 1.92940i) q^{41} +(-4.57831 - 12.2749i) q^{42} +(-9.32877 + 6.98343i) q^{43} +(-2.86026 + 1.83818i) q^{44} +(-7.23528 - 10.8878i) q^{46} +(-3.96485 - 3.96485i) q^{47} +(7.93507 - 36.4769i) q^{48} +(-3.41883 - 0.491554i) q^{49} +(0.504871 + 1.71943i) q^{51} +(4.99052 - 13.3801i) q^{52} +(-0.472144 + 6.60144i) q^{53} +(3.54196 - 0.509257i) q^{54} +(13.3062 + 11.5299i) q^{56} +(-2.24598 + 0.488583i) q^{57} +(0.835824 - 0.181822i) q^{58} +(2.23622 + 1.93770i) q^{59} +(-9.02346 + 1.29738i) q^{61} +(-1.11634 + 15.6085i) q^{62} +(-2.31269 + 6.20055i) q^{63} +(8.01475 + 27.2957i) q^{64} +(4.31181 + 0.619945i) q^{66} +(-2.99845 + 13.7837i) q^{67} +(-2.69589 - 2.69589i) q^{68} +(-1.55612 + 12.1412i) q^{69} +(5.95122 - 3.82461i) q^{71} +(-26.3048 + 19.6915i) q^{72} +(-2.49870 - 6.69927i) q^{73} +(0.697253 - 0.204732i) q^{74} +(3.69571 - 3.20235i) q^{76} +(-0.706591 + 0.943895i) q^{77} +(-16.0584 + 8.76857i) q^{78} +(-6.21028 + 7.16705i) q^{79} +(6.05065 + 3.88851i) q^{81} +(18.6198 - 1.33171i) q^{82} +(-0.0212502 - 0.0389168i) q^{83} +(-3.71419 - 25.8328i) q^{84} +(-28.8938 + 13.1953i) q^{86} +(-0.702956 - 0.383843i) q^{87} +(-5.48520 + 2.04587i) q^{88} +(0.678818 - 4.72128i) q^{89} -4.95227i q^{91} +(-9.47358 - 24.2576i) q^{92} +(10.3608 - 10.3608i) q^{93} +(-8.26321 - 12.8578i) q^{94} +(22.4437 - 49.1449i) q^{96} +(4.99601 - 9.14950i) q^{97} +(-8.82136 - 3.29020i) q^{98} +(-1.44100 - 1.66300i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 200 q + 18 q^{2} + 14 q^{3} - 36 q^{6} + 22 q^{7} + 26 q^{8} - 44 q^{11} + 6 q^{12} + 26 q^{13} - 52 q^{16} + 22 q^{17} - 58 q^{18} - 44 q^{21} - 22 q^{23} - 28 q^{26} + 26 q^{27} - 66 q^{28} - 40 q^{31}+ \cdots + 50 q^{98}+O(q^{100}) \) 200 * q + 18 * q^2 + 14 * q^3 - 36 * q^6 + 22 * q^7 + 26 * q^8 - 44 * q^11 + 6 * q^12 + 26 * q^13 - 52 * q^16 + 22 * q^17 - 58 * q^18 - 44 * q^21 - 22 * q^23 - 28 * q^26 + 26 * q^27 - 66 * q^28 - 40 * q^31 + 46 * q^32 - 12 * q^36 - 66 * q^37 + 22 * q^38 - 8 * q^41 - 198 * q^42 + 22 * q^43 - 76 * q^46 - 52 * q^47 - 18 * q^48 - 44 * q^51 - 158 * q^52 + 22 * q^53 + 88 * q^56 - 66 * q^57 + 58 * q^58 + 44 * q^61 - 38 * q^62 + 22 * q^63 + 132 * q^66 + 22 * q^67 + 132 * q^71 + 28 * q^72 - 34 * q^73 + 132 * q^76 + 10 * q^77 - 22 * q^78 - 48 * q^81 + 50 * q^82 + 22 * q^83 + 46 * q^87 + 110 * q^88 - 50 * q^92 + 36 * q^93 + 148 * q^96 + 88 * q^97 + 50 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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