LMFDB - Embedded newform 625.2.h.b.274.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [625,2,Mod(24,625)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(625, base_ring=CyclotomicField(50))

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

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

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

chi := DirichletCharacter("625.24");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 625 = 5^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	625.h (of order $50$, degree $20$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.99065012633$
Analytic rank:	$0$
Dimension:	$440$
Relative dimension:	$22$ over $\Q(\zeta_{50})$
Twist minimal:	no (minimal twist has level 125)
Sato-Tate group:	$\mathrm{SU}(2)[C_{50}]$

Embedding invariants

Embedding label			274.13
Character	$\chi$	$=$	625.274
Dual form			625.2.h.b.349.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.201300 + 0.784012i) q^{2} +(-2.56313 + 0.488943i) q^{3} +(1.17846 - 0.647864i) q^{4} +(-0.899294 - 1.91110i) q^{6} +(0.380304 - 0.523443i) q^{7} +(1.85336 + 1.97363i) q^{8} +(3.54123 - 1.40207i) q^{9} +O(q^{10})$	\(q+(0.201300 + 0.784012i) q^{2} +(-2.56313 + 0.488943i) q^{3} +(1.17846 - 0.647864i) q^{4} +(-0.899294 - 1.91110i) q^{6} +(0.380304 - 0.523443i) q^{7} +(1.85336 + 1.97363i) q^{8} +(3.54123 - 1.40207i) q^{9} +(-0.370305 + 0.0950783i) q^{11} +(-2.70378 + 2.23676i) q^{12} +(-2.38088 - 6.01342i) q^{13} +(0.486940 + 0.192793i) q^{14} +(0.266898 - 0.420564i) q^{16} +(-1.75924 + 3.20004i) q^{17} +(1.81209 + 2.49413i) q^{18} +(1.14413 - 5.99774i) q^{19} +(-0.718833 + 1.52760i) q^{21} +(-0.149085 - 0.271185i) q^{22} +(6.01178 + 0.378229i) q^{23} +(-5.71539 - 4.15247i) q^{24} +(4.23532 - 3.07714i) q^{26} +(-1.78165 + 1.13067i) q^{27} +(0.109053 - 0.863242i) q^{28} +(3.96750 + 0.501211i) q^{29} +(0.629836 + 0.346255i) q^{31} +(5.53328 + 1.79787i) q^{32} +(0.902652 - 0.424756i) q^{33} +(-2.86300 - 0.735094i) q^{34} +(3.26485 - 3.94652i) q^{36} +(-2.57349 - 1.63319i) q^{37} +(4.93261 - 0.310334i) q^{38} +(9.04272 + 14.2491i) q^{39} +(-0.0888833 - 1.41276i) q^{41} +(-1.34236 - 0.256068i) q^{42} +(9.37601 - 3.04645i) q^{43} +(-0.374793 + 0.351954i) q^{44} +(0.913635 + 4.78944i) q^{46} +(8.91355 - 9.49196i) q^{47} +(-0.478462 + 1.20846i) q^{48} +(2.03376 + 6.25926i) q^{49} +(2.94451 - 9.06227i) q^{51} +(-6.70166 - 5.54409i) q^{52} +(-2.37085 - 1.11564i) q^{53} +(-1.24511 - 1.16923i) q^{54} +(1.73792 - 0.219550i) q^{56} +15.9324i q^{57} +(0.405701 + 3.21146i) q^{58} +(-1.48994 - 1.80103i) q^{59} +(-0.689122 + 10.9533i) q^{61} +(-0.144682 + 0.563500i) q^{62} +(0.612837 - 2.38684i) q^{63} +(-0.233151 + 3.70582i) q^{64} +(0.514718 + 0.622187i) q^{66} +(-0.0669046 - 0.529604i) q^{67} +4.91087i q^{68} +(-15.5939 + 1.96997i) q^{69} +(-5.36705 - 5.04000i) q^{71} +(9.33033 + 4.39052i) q^{72} +(2.27552 + 1.88247i) q^{73} +(0.762395 - 2.34641i) q^{74} +(-2.53741 - 7.80934i) q^{76} +(-0.0910604 + 0.229992i) q^{77} +(-9.35112 + 9.95794i) q^{78} +(-0.744146 - 3.90095i) q^{79} +(-4.31547 + 4.05249i) q^{81} +(1.08973 - 0.354074i) q^{82} +(-8.40773 - 1.60386i) q^{83} +(0.142560 + 2.26592i) q^{84} +(4.27585 + 6.73765i) q^{86} +(-10.4143 + 0.655210i) q^{87} +(-0.873958 - 0.554631i) q^{88} +(5.03780 - 6.08965i) q^{89} +(-4.05314 - 1.04067i) q^{91} +(7.32969 - 3.44909i) q^{92} +(-1.78365 - 0.579543i) q^{93} +(9.23611 + 5.07759i) q^{94} +(-15.0616 - 1.90272i) q^{96} +(-0.470603 + 3.72521i) q^{97} +(-4.49794 + 2.85448i) q^{98} +(-1.17803 + 0.855889i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 440 q + 40 q^{4} - 40 q^{6} + 40 q^{9}+O(q^{10}) $ 440 * q + 40 * q^4 - 40 * q^6 + 40 * q^9	$ 440 q + 40 q^{4} - 40 q^{6} + 40 q^{9} - 30 q^{11} + 20 q^{14} + 20 q^{19} - 10 q^{21} - 30 q^{24} + 30 q^{26} + 20 q^{29} - 20 q^{31} - 10 q^{34} - 420 q^{36} - 10 q^{41} - 30 q^{44} + 40 q^{49} + 50 q^{51} - 120 q^{54} - 210 q^{56} - 10 q^{59} - 90 q^{64} + 110 q^{66} - 80 q^{69} - 170 q^{71} - 70 q^{74} + 70 q^{76} + 110 q^{81} - 230 q^{84} + 80 q^{86} - 110 q^{89} - 210 q^{91} - 120 q^{94} + 270 q^{96} - 90 q^{99}+O(q^{100}) $ 440 * q + 40 * q^4 - 40 * q^6 + 40 * q^9 - 30 * q^11 + 20 * q^14 + 20 * q^19 - 10 * q^21 - 30 * q^24 + 30 * q^26 + 20 * q^29 - 20 * q^31 - 10 * q^34 - 420 * q^36 - 10 * q^41 - 30 * q^44 + 40 * q^49 + 50 * q^51 - 120 * q^54 - 210 * q^56 - 10 * q^59 - 90 * q^64 + 110 * q^66 - 80 * q^69 - 170 * q^71 - 70 * q^74 + 70 * q^76 + 110 * q^81 - 230 * q^84 + 80 * q^86 - 110 * q^89 - 210 * q^91 - 120 * q^94 + 270 * q^96 - 90 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/625\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{21}{50}\right)$

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 $

$2$	0.201300	+	0.784012i	0.142341	+	0.554380i	0.999243	+	0.0389014i	$0.0123858\pi$
$2$	0.201300	+	0.784012i	0.142341	+	0.554380i	−0.856902	+	0.515479i	$0.827614\pi$
$3$	−2.56313	+	0.488943i	−1.47982	+	0.282291i	−0.863158	−	0.504935i	$-0.831517\pi$
$3$	−2.56313	+	0.488943i	−1.47982	+	0.282291i	−0.616665	+	0.787226i	$0.711517\pi$
$4$	1.17846	−	0.647864i	0.589230	−	0.323932i
$5$		0			0
$5$		0			0
$6$	−0.899294	−	1.91110i	−0.367135	−	0.780202i
$7$	0.380304	−	0.523443i	0.143741	−	0.197843i	−0.731076	−	0.682296i	$-0.760981\pi$
$7$	0.380304	−	0.523443i	0.143741	−	0.197843i	0.874817	+	0.484453i	$0.160981\pi$
$8$	1.85336	+	1.97363i	0.655261	+	0.697783i
$9$	3.54123	−	1.40207i	1.18041	−	0.467357i
$10$		0			0
$11$	−0.370305	+	0.0950783i	−0.111651	+	0.0286672i	−0.304102	−	0.952639i	$-0.598356\pi$
$11$	−0.370305	+	0.0950783i	−0.111651	+	0.0286672i	0.192451	+	0.981307i	$0.438356\pi$
$12$	−2.70378	+	2.23676i	−0.780513	+	0.645697i
$13$	−2.38088	−	6.01342i	−0.660338	−	1.66782i	−0.741357	−	0.671111i	$-0.765817\pi$
$13$	−2.38088	−	6.01342i	−0.660338	−	1.66782i	0.0810190	−	0.996713i	$-0.474183\pi$
$14$	0.486940	+	0.192793i	0.130140	+	0.0515262i
$15$		0			0
$16$	0.266898	−	0.420564i	0.0667246	−	0.105141i
$17$	−1.75924	+	3.20004i	−0.426678	+	0.776124i	−0.999037	−	0.0438794i	$-0.986028\pi$
$17$	−1.75924	+	3.20004i	−0.426678	+	0.776124i	0.572359	+	0.820003i	$0.306028\pi$
$18$	1.81209	+	2.49413i	0.427114	+	0.587871i
$19$	1.14413	−	5.99774i	0.262482	−	1.37598i	−0.569873	−	0.821733i	$-0.693008\pi$
$19$	1.14413	−	5.99774i	0.262482	−	1.37598i	0.832355	−	0.554244i	$-0.186992\pi$
$20$		0			0
$21$	−0.718833	+	1.52760i	−0.156862	+	0.333349i
$22$	−0.149085	−	0.271185i	−0.0317850	−	0.0578167i
$23$	6.01178	+	0.378229i	1.25354	+	0.0788662i	0.675635	−	0.737236i	$-0.263869\pi$
$23$	6.01178	+	0.378229i	1.25354	+	0.0788662i	0.577908	+	0.816102i	$0.303869\pi$
$24$	−5.71539	−	4.15247i	−1.16665	−	0.847620i
$25$		0			0
$26$	4.23532	−	3.07714i	0.830615	−	0.603477i
$27$	−1.78165	+	1.13067i	−0.342879	+	0.217598i
$28$	0.109053	−	0.863242i	0.0206090	−	0.163137i
$29$	3.96750	+	0.501211i	0.736746	+	0.0930726i	0.484746	−	0.874655i	$-0.338912\pi$
$29$	3.96750	+	0.501211i	0.736746	+	0.0930726i	0.251999	+	0.967727i	$0.418912\pi$
$30$		0			0
$31$	0.629836	+	0.346255i	0.113122	+	0.0621893i	0.537310	−	0.843385i	$-0.319440\pi$
$31$	0.629836	+	0.346255i	0.113122	+	0.0621893i	−0.424188	+	0.905574i	$0.639440\pi$
$32$	5.53328	+	1.79787i	0.978155	+	0.317822i
$33$	0.902652	−	0.424756i	0.157132	−	0.0739405i
$34$	−2.86300	−	0.735094i	−0.491001	−	0.126068i
$35$		0			0
$36$	3.26485	−	3.94652i	0.544141	−	0.657753i
$37$	−2.57349	−	1.63319i	−0.423080	−	0.268495i	0.307197	−	0.951646i	$-0.400609\pi$
$37$	−2.57349	−	1.63319i	−0.423080	−	0.268495i	−0.730277	+	0.683151i	$0.760609\pi$
$38$	4.93261	−	0.310334i	0.800175	−	0.0503428i
$39$	9.04272	+	14.2491i	1.44799	+	2.28167i
$40$		0			0
$41$	−0.0888833	−	1.41276i	−0.0138812	−	0.220636i	−0.998852	−	0.0479122i	$-0.984743\pi$
$41$	−0.0888833	−	1.41276i	−0.0138812	−	0.220636i	0.984970	−	0.172724i	$-0.0552568\pi$
$42$	−1.34236	−	0.256068i	−0.207130	−	0.0395121i
$43$	9.37601	−	3.04645i	1.42983	−	0.464579i	0.511118	−	0.859511i	$-0.329232\pi$
$43$	9.37601	−	3.04645i	1.42983	−	0.464579i	0.918711	+	0.394931i	$0.129232\pi$
$44$	−0.374793	+	0.351954i	−0.0565021	+	0.0530590i
$45$		0			0
$46$	0.913635	+	4.78944i	0.134708	+	0.706165i
$47$	8.91355	−	9.49196i	1.30017	−	1.38455i	0.421715	−	0.906729i	$-0.361428\pi$
$47$	8.91355	−	9.49196i	1.30017	−	1.38455i	0.878460	−	0.477817i	$-0.158572\pi$
$48$	−0.478462	+	1.20846i	−0.0690601	+	0.174426i
$49$	2.03376	+	6.25926i	0.290537	+	0.894180i
$50$		0			0
$51$	2.94451	−	9.06227i	0.412314	−	1.26897i
$52$	−6.70166	−	5.54409i	−0.929353	−	0.768827i
$53$	−2.37085	−	1.11564i	−0.325661	−	0.153245i	0.255998	−	0.966677i	$-0.417596\pi$
$53$	−2.37085	−	1.11564i	−0.325661	−	0.153245i	−0.581659	+	0.813433i	$0.697596\pi$
$54$	−1.24511	−	1.16923i	−0.169438	−	0.159113i
$55$		0			0
$56$	1.73792	−	0.219550i	0.232239	−	0.0293387i
$57$			15.9324i			2.11030i
$58$	0.405701	+	3.21146i	0.0532712	+	0.421685i
$59$	−1.48994	−	1.80103i	−0.193974	−	0.234474i	0.664555	−	0.747239i	$-0.268621\pi$
$59$	−1.48994	−	1.80103i	−0.193974	−	0.234474i	−0.858529	+	0.512765i	$0.828621\pi$
$60$		0			0
$61$	−0.689122	+	10.9533i	−0.0882330	+	1.40242i	0.666066	+	0.745893i	$0.267977\pi$
$61$	−0.689122	+	10.9533i	−0.0882330	+	1.40242i	−0.754299	+	0.656531i	$0.772023\pi$
$62$	−0.144682	+	0.563500i	−0.0183747	+	0.0715646i
$63$	0.612837	−	2.38684i	0.0772102	−	0.300714i
$64$	−0.233151	+	3.70582i	−0.0291438	+	0.463228i
$65$		0			0
$66$	0.514718	+	0.622187i	0.0633573	+	0.0765859i
$67$	−0.0669046	−	0.529604i	−0.00817369	−	0.0647015i	0.987500	−	0.157617i	$-0.0503812\pi$
$67$	−0.0669046	−	0.529604i	−0.00817369	−	0.0647015i	−0.995674	+	0.0929159i	$0.970381\pi$
$68$			4.91087i			0.595530i
$69$	−15.5939	+	1.96997i	−1.87728	+	0.237156i
$70$		0			0
$71$	−5.36705	−	5.04000i	−0.636952	−	0.598138i	0.297286	−	0.954789i	$-0.403919\pi$
$71$	−5.36705	−	5.04000i	−0.636952	−	0.598138i	−0.934238	+	0.356651i	$0.883919\pi$
$72$	9.33033	+	4.39052i	1.09959	+	0.517428i
$73$	2.27552	+	1.88247i	0.266329	+	0.220327i	0.760997	−	0.648756i	$-0.224710\pi$
$73$	2.27552	+	1.88247i	0.266329	+	0.220327i	−0.494668	+	0.869082i	$0.664710\pi$
$74$	0.762395	−	2.34641i	0.0886266	−	0.272765i
$75$		0			0
$76$	−2.53741	−	7.80934i	−0.291061	−	0.895793i
$77$	−0.0910604	+	0.229992i	−0.0103773	+	0.0262101i
$78$	−9.35112	+	9.95794i	−1.05881	+	1.12751i
$79$	−0.744146	−	3.90095i	−0.0837230	−	0.438891i	−0.999323	−	0.0368002i	$-0.988283\pi$
$79$	−0.744146	−	3.90095i	−0.0837230	−	0.438891i	0.915600	−	0.402091i	$-0.131717\pi$
$80$		0			0
$81$	−4.31547	+	4.05249i	−0.479496	+	0.450277i
$82$	1.08973	−	0.354074i	0.120340	−	0.0391009i
$83$	−8.40773	−	1.60386i	−0.922868	−	0.176046i	−0.296014	−	0.955184i	$-0.595658\pi$
$83$	−8.40773	−	1.60386i	−0.922868	−	0.176046i	−0.626854	+	0.779137i	$0.715658\pi$
$84$	0.142560	+	2.26592i	0.0155545	+	0.247232i
$85$		0			0
$86$	4.27585	+	6.73765i	0.461076	+	0.726540i
$87$	−10.4143	+	0.655210i	−1.11653	+	0.0702459i
$88$	−0.873958	−	0.554631i	−0.0931643	−	0.0591238i
$89$	5.03780	−	6.08965i	0.534006	−	0.645502i	−0.432656	−	0.901559i	$-0.642424\pi$
$89$	5.03780	−	6.08965i	0.534006	−	0.645502i	0.966662	+	0.256057i	$0.0824236\pi$
$90$		0			0
$91$	−4.05314	−	1.04067i	−0.424885	−	0.109092i
$92$	7.32969	−	3.44909i	0.764173	−	0.359592i
$93$	−1.78365	−	0.579543i	−0.184956	−	0.0600958i
$94$	9.23611	+	5.07759i	0.952632	+	0.523714i
$95$		0			0
$96$	−15.0616	−	1.90272i	−1.53721	−	0.194195i
$97$	−0.470603	+	3.72521i	−0.0477825	+	0.378237i	0.950032	+	0.312154i	$0.101050\pi$
$97$	−0.470603	+	3.72521i	−0.0477825	+	0.378237i	−0.997814	+	0.0660837i	$0.978950\pi$
$98$	−4.49794	+	2.85448i	−0.454360	+	0.288346i
$99$	−1.17803	+	0.855889i	−0.118396	+	0.0860200i
$100$		0			0
$101$	2.40915	+	1.75035i	0.239719	+	0.174166i	0.701158	−	0.713006i	$-0.252667\pi$
$101$	2.40915	+	1.75035i	0.239719	+	0.174166i	−0.461439	+	0.887172i	$0.652667\pi$
$102$	7.69766	+	0.484296i	0.762182	+	0.0479524i
$103$	−8.22563	−	14.9624i	−0.810496	−	1.47429i	−0.879097	−	0.476642i	$-0.841854\pi$
$103$	−8.22563	−	14.9624i	−0.810496	−	1.47429i	0.0686017	−	0.997644i	$-0.478146\pi$
$104$	7.45562	−	15.8440i	0.731084	−	1.55363i
$105$		0			0
$106$	0.397420	−	2.08335i	0.0386009	−	0.202353i
$107$	−1.79950	−	2.47680i	−0.173964	−	0.239441i	0.713128	−	0.701034i	$-0.247278\pi$
$107$	−1.79950	−	2.47680i	−0.173964	−	0.239441i	−0.887092	+	0.461593i	$0.847278\pi$
$108$	−1.36709	+	2.48672i	−0.131548	+	0.239285i
$109$	6.34317	−	9.99524i	0.607566	−	0.957371i	−0.391738	−	0.920077i	$-0.628126\pi$
$109$	6.34317	−	9.99524i	0.607566	−	0.957371i	0.999304	−	0.0372940i	$-0.0118738\pi$
$110$		0			0
$111$	7.39473	+	2.92778i	0.701877	+	0.277893i
$112$	−0.118639	−	0.299648i	−0.0112103	−	0.0283141i
$113$	−2.97404	+	2.46034i	−0.279774	+	0.231449i	−0.766718	−	0.641984i	$-0.778112\pi$
$113$	−2.97404	+	2.46034i	−0.279774	+	0.231449i	0.486944	+	0.873433i	$0.338112\pi$
$114$	−12.4912	+	3.20719i	−1.16991	+	0.300381i
$115$		0			0
$116$	5.00025	−	1.97974i	0.464262	−	0.183814i
$117$	−16.8625	−	17.9567i	−1.55894	−	1.66010i
$118$	1.11210	−	1.53068i	0.102377	−	0.140910i
$119$	1.00599	+	2.13785i	0.0922193	+	0.195976i
$120$		0			0
$121$	−9.51129	+	5.22887i	−0.864662	+	0.475352i
$122$	−8.72622	+	1.66462i	−0.790035	+	0.150707i
$123$	0.918577	+	3.57762i	0.0828253	+	0.322583i
$124$	0.966564			0.0868000
$125$		0			0
$126$	1.99468			0.177700
$127$	3.68105	+	14.3367i	0.326640	+	1.27218i	0.893761	+	0.448544i	$0.148057\pi$
$127$	3.68105	+	14.3367i	0.326640	+	1.27218i	−0.567121	+	0.823635i	$0.691943\pi$
$128$	8.47762	−	1.61719i	0.749323	−	0.142941i
$129$	−22.5424	+	12.3928i	−1.98475	+	1.09112i
$130$		0			0
$131$	−0.428267	−	0.910113i	−0.0374178	−	0.0795169i	0.885244	−	0.465127i	$-0.153991\pi$
$131$	−0.428267	−	0.910113i	−0.0374178	−	0.0795169i	−0.922662	+	0.385610i	$0.873991\pi$
$132$	0.788556	−	1.08535i	0.0686350	−	0.0944680i
$133$	−2.70436	−	2.87985i	−0.234498	−	0.249715i
$134$	0.401748	−	0.159063i	0.0347057	−	0.0137410i
$135$		0			0
$136$	−9.57618	+	2.45875i	−0.821151	+	0.210836i
$137$	1.28210	−	1.06064i	0.109537	−	0.0906169i	−0.581043	−	0.813873i	$-0.697355\pi$
$137$	1.28210	−	1.06064i	0.109537	−	0.0906169i	0.690580	+	0.723256i	$0.257355\pi$
$138$	−4.68353	−	11.8292i	−0.398688	−	1.00697i
$139$	0.0583355	+	0.0230967i	0.00494796	+	0.00195903i	0.370597	−	0.928794i	$-0.379153\pi$
$139$	0.0583355	+	0.0230967i	0.00494796	+	0.00195903i	−0.365649	+	0.930753i	$0.619153\pi$
$140$		0			0
$141$	−18.2055	+	28.6873i	−1.53318	+	2.41591i
$142$	2.87103	−	5.22238i	0.240931	−	0.438253i
$143$	1.45340	+	2.00043i	0.121539	+	0.167285i
$144$	0.355486	−	1.86353i	0.0296239	−	0.155294i
$145$		0			0
$146$	−1.01782	+	2.16297i	−0.0842352	+	0.179009i
$147$	−8.27320	−	15.0489i	−0.682362	−	1.24121i
$148$	−4.09085	−	0.257374i	−0.336266	−	0.0211560i
$149$	−14.1000	−	10.2443i	−1.15512	−	0.839243i	−0.165965	−	0.986132i	$-0.553074\pi$
$149$	−14.1000	−	10.2443i	−1.15512	−	0.839243i	−0.989153	+	0.146889i	$0.953074\pi$
$150$		0			0
$151$	−6.26136	+	4.54915i	−0.509543	+	0.370204i	−0.812650	−	0.582752i	$-0.801976\pi$
$151$	−6.26136	+	4.54915i	−0.509543	+	0.370204i	0.303107	+	0.952956i	$0.401976\pi$
$152$	13.9578	−	8.85788i	1.13213	−	0.718469i
$153$	−1.74317	+	13.7986i	−0.140927	+	1.11555i
$154$	−0.198647	−	0.0250950i	−0.0160074	−	0.00202221i
$155$		0			0
$156$	19.8879	+	10.9335i	1.59231	+	0.875380i
$157$	−13.9060	−	4.51835i	−1.10982	−	0.360603i	−0.303948	−	0.952689i	$-0.598305\pi$
$157$	−13.9060	−	4.51835i	−1.10982	−	0.360603i	−0.805875	+	0.592085i	$0.798305\pi$
$158$	2.90859	−	1.36868i	0.231395	−	0.108886i
$159$	6.62227	+	1.70031i	0.525180	+	0.134843i
$160$		0			0
$161$	2.48428	−	3.00298i	0.195789	−	0.236668i
$162$	−4.04591	−	2.56761i	−0.317876	−	0.201731i
$163$	−12.0225	+	0.756394i	−0.941677	+	0.0592453i	−0.526202	−	0.850359i	$-0.676385\pi$
$163$	−12.0225	+	0.756394i	−0.941677	+	0.0592453i	−0.415475	+	0.909605i	$0.636385\pi$
$164$	−1.02002	−	1.60730i	−0.0796503	−	0.125509i
$165$		0			0
$166$	−0.435031	−	6.91461i	−0.0337649	−	0.536678i
$167$	2.40117	+	0.458047i	0.185808	+	0.0354448i	0.279445	−	0.960162i	$-0.409849\pi$
$167$	2.40117	+	0.458047i	0.185808	+	0.0354448i	−0.0936373	+	0.995606i	$0.529849\pi$
$168$	−4.34716	+	1.41248i	−0.335391	+	0.108975i
$169$	−21.0161	+	19.7354i	−1.61662	+	1.51811i
$170$		0			0
$171$	−4.35763	−	22.8435i	−0.333237	−	1.74689i
$172$	9.07558	−	9.66451i	0.692006	−	0.736912i
$173$	−9.31508	+	23.5272i	−0.708212	+	1.78874i	−0.0999666	+	0.994991i	$0.531874\pi$
$173$	−9.31508	+	23.5272i	−0.708212	+	1.78874i	−0.608246	+	0.793749i	$0.708126\pi$
$174$	−2.61008	−	8.03301i	−0.197870	−	0.608981i
$175$		0			0
$176$	−0.0588474	+	0.181114i	−0.00443579	+	0.0136519i
$177$	4.69951	+	3.88777i	0.353237	+	0.292223i
$178$	5.78847	+	2.72385i	0.433864	+	0.204161i
$179$	13.2681	+	12.4596i	0.991705	+	0.931273i	0.997637	−	0.0687098i	$-0.0218882\pi$
$179$	13.2681	+	12.4596i	0.991705	+	0.931273i	−0.00593206	+	0.999982i	$0.501888\pi$
$180$		0			0
$181$	17.0174	−	2.14980i	1.26489	−	0.159793i	0.535881	−	0.844293i	$-0.319979\pi$
$181$	17.0174	−	2.14980i	1.26489	−	0.159793i	0.729013	+	0.684500i	$0.239979\pi$
$182$		−	3.38720i		−	0.251076i
$183$	−3.58922	−	28.4116i	−0.265323	−	2.10025i
$184$	10.3955	+	12.5660i	0.766367	+	0.926378i
$185$		0			0
$186$	0.0953198	−	1.51506i	0.00698918	−	0.111090i
$187$	0.347201	−	1.35226i	0.0253898	−	0.0988868i
$188$	4.35476	−	16.9607i	0.317604	−	1.23698i
$189$	−0.0857271	+	1.36259i	−0.00623573	+	0.0991140i
$190$		0			0
$191$	11.1953	+	13.5328i	0.810064	+	0.979199i	0.999997	−	0.00259790i	$-0.000826938\pi$
$191$	11.1953	+	13.5328i	0.810064	+	0.979199i	−0.189933	+	0.981797i	$0.560827\pi$
$192$	−1.21434	−	9.61249i	−0.0876375	−	0.693722i
$193$		−	10.0389i		−	0.722617i	−0.932446	−	0.361309i	$-0.882330\pi$
$193$		−	10.0389i		−	0.722617i	0.932446	−	0.361309i	$-0.117670\pi$
$194$	−3.01534	+	0.380926i	−0.216489	+	0.0273489i
$195$		0			0
$196$	6.45185	+	6.05869i	0.460847	+	0.432764i
$197$	16.6569	+	7.83814i	1.18676	+	0.558445i	0.914816	−	0.403870i	$-0.132335\pi$
$197$	16.6569	+	7.83814i	1.18676	+	0.558445i	0.271939	+	0.962315i	$0.412335\pi$
$198$	−0.908164	−	0.751299i	−0.0645404	−	0.0533925i
$199$	−5.34423	+	16.4478i	−0.378842	+	1.16596i	0.562008	+	0.827132i	$0.310029\pi$
$199$	−5.34423	+	16.4478i	−0.378842	+	1.16596i	−0.940850	+	0.338824i	$0.889971\pi$
$200$		0			0
$201$	0.430431	+	1.32473i	0.0303603	+	0.0934393i
$202$	−0.887333	+	2.24115i	−0.0624325	+	0.157687i
$203$	1.77121	−	1.88615i	0.124314	−	0.132381i
$204$	−2.40113	−	12.5872i	−0.168113	−	0.881279i
$205$		0			0
$206$	10.0749	−	9.46092i	0.701948	−	0.659173i
$207$	21.8194	−	7.08955i	1.51655	−	0.492758i
$208$	−3.16449	−	0.603658i	−0.219418	−	0.0418561i
$209$	0.146577	+	2.32978i	0.0101390	+	0.161154i
$210$		0			0
$211$	−7.11331	−	11.2088i	−0.489700	−	0.771644i	0.506170	−	0.862434i	$-0.331061\pi$
$211$	−7.11331	−	11.2088i	−0.489700	−	0.771644i	−0.995870	+	0.0907895i	$0.971061\pi$
$212$	−3.51673	+	0.221254i	−0.241530	+	0.0151958i
$213$	16.2207	+	10.2940i	1.11142	+	0.705332i
$214$	1.57960	−	1.90941i	0.107979	−	0.130524i
$215$		0			0
$216$	−5.53357	−	1.42078i	−0.376512	−	0.0966718i
$217$	0.420774	−	0.198001i	0.0285640	−	0.0134412i
$218$	9.11327	+	2.96108i	0.617228	+	0.200550i
$219$	−6.75286	−	3.71242i	−0.456316	−	0.250862i
$220$		0			0
$221$	23.4317	+	2.96012i	1.57619	+	0.199119i
$222$	−0.806855	+	6.38692i	−0.0541526	+	0.428662i
$223$	2.20281	−	1.39794i	0.147511	−	0.0936133i	−0.460023	−	0.887907i	$-0.652159\pi$
$223$	2.20281	−	1.39794i	0.147511	−	0.0936133i	0.607534	+	0.794294i	$0.292159\pi$
$224$	3.04541	−	2.21262i	0.203480	−	0.147837i
$225$		0			0
$226$	−2.52761	−	1.83641i	−0.168134	−	0.122156i
$227$	20.7123	+	1.30311i	1.37472	+	0.0864902i	0.732886	−	0.680351i	$-0.238173\pi$
$227$	20.7123	+	1.30311i	1.37472	+	0.0864902i	0.641837	+	0.766841i	$0.278173\pi$
$228$	10.3220	+	18.7757i	0.683593	+	1.24345i
$229$	9.56403	−	20.3246i	0.632009	−	1.34309i	−0.290412	−	0.956902i	$-0.593792\pi$
$229$	9.56403	−	20.3246i	0.632009	−	1.34309i	0.922421	−	0.386186i	$-0.126208\pi$
$230$		0			0
$231$	0.120946	−	0.634023i	0.00795769	−	0.0417157i
$232$	6.36399	+	8.75928i	0.417817	+	0.575075i
$233$	−7.43965	+	13.5327i	−0.487388	+	0.886555i	0.512228	+	0.858849i	$0.328820\pi$
$233$	−7.43965	+	13.5327i	−0.487388	+	0.886555i	−0.999616	+	0.0277059i	$0.991180\pi$
$234$	10.6839	−	16.8351i	0.698426	−	1.10054i
$235$		0			0
$236$	−2.92266	−	1.15716i	−0.190249	−	0.0753249i
$237$	3.81468	+	9.63479i	0.247790	+	0.625847i
$238$	−1.47359	+	1.21906i	−0.0955186	+	0.0790199i
$239$	−4.80175	+	1.23288i	−0.310599	+	0.0797483i	−0.400772	−	0.916178i	$-0.631258\pi$
$239$	−4.80175	+	1.23288i	−0.310599	+	0.0797483i	0.0901728	+	0.995926i	$0.471258\pi$
$240$		0			0
$241$	−5.25502	+	2.08061i	−0.338506	+	0.134024i	−0.531227	−	0.847230i	$-0.678269\pi$
$241$	−5.25502	+	2.08061i	−0.338506	+	0.134024i	0.192721	+	0.981254i	$0.438269\pi$
$242$	−6.01412	−	6.40439i	−0.386602	−	0.411690i
$243$	12.8006	−	17.6185i	0.821158	−	1.13023i
$244$	6.28414	+	13.3545i	0.402301	+	0.854932i
$245$		0			0
$246$	−2.61999	+	1.44035i	−0.167044	+	0.0918334i
$247$	−38.7910	+	7.39978i	−2.46821	+	0.470837i
$248$	0.483934	+	1.88480i	0.0307298	+	0.119685i
$249$	22.3343			1.41538
$250$		0			0
$251$	−23.0280			−1.45351			−0.726756	−	0.686896i	$-0.758973\pi$
$251$	−23.0280			−1.45351			−0.726756	+	0.686896i	$0.758973\pi$
$252$	−0.824146	−	3.20984i	−0.0519163	−	0.202201i
$253$	−2.26216	+	0.431529i	−0.142221	+	0.0271300i
$254$	−10.4992	+	5.77197i	−0.658776	+	0.362165i
$255$		0			0
$256$	6.13641	+	13.0405i	0.383526	+	0.815033i
$257$	−7.35467	+	10.1228i	−0.458772	+	0.631445i	−0.974253	−	0.225455i	$-0.927613\pi$
$257$	−7.35467	+	10.1228i	−0.458772	+	0.631445i	0.515482	+	0.856901i	$0.327613\pi$
$258$	−14.2539	−	15.1788i	−0.887407	−	0.944992i
$259$	−1.83359	+	0.725970i	−0.113934	+	0.0451096i
$260$		0			0
$261$	14.7525	−	3.78781i	0.913159	−	0.234459i
$262$	0.627329	−	0.518972i	0.0387565	−	0.0320622i
$263$	5.62364	+	14.2037i	0.346769	+	0.875837i	0.993574	+	0.113182i	$0.0361045\pi$
$263$	5.62364	+	14.2037i	0.346769	+	0.875837i	−0.646806	+	0.762655i	$0.723896\pi$
$264$	2.51125	+	0.994274i	0.154557	+	0.0611933i
$265$		0			0
$266$	1.71345	−	2.69996i	0.105058	−	0.165545i
$267$	−9.93503	+	18.0717i	−0.608014	+	1.10597i
$268$	−0.421956	−	0.580773i	−0.0257751	−	0.0354763i
$269$	0.0509368	−	0.267020i	0.00310567	−	0.0162805i	−0.980701	−	0.195515i	$-0.937362\pi$
$269$	0.0509368	−	0.267020i	0.00310567	−	0.0162805i	0.983806	+	0.179235i	$0.0573621\pi$
$270$		0			0
$271$	10.4917	−	22.2959i	0.637323	−	1.35438i	−0.281443	−	0.959578i	$-0.590813\pi$
$271$	10.4917	−	22.2959i	0.637323	−	1.35438i	0.918766	−	0.394802i	$-0.129187\pi$
$272$	0.876286	+	1.59396i	0.0531326	+	0.0966479i
$273$	10.8975	+	0.685615i	0.659549	+	0.0414953i
$274$	1.08964	+	0.791672i	0.0658277	+	0.0478266i
$275$		0			0
$276$	−17.1005	+	12.4243i	−1.02933	+	0.747852i
$277$	6.53736	−	4.14874i	0.392792	−	0.249274i	−0.324733	−	0.945806i	$-0.605275\pi$
$277$	6.53736	−	4.14874i	0.392792	−	0.249274i	0.717526	+	0.696532i	$0.245275\pi$
$278$	−0.00636512	+	0.0503851i	−0.000381754	+	0.00302190i
$279$	2.71587	+	0.343094i	0.162595	+	0.0205405i
$280$		0			0
$281$	−17.8871	−	9.83349i	−1.06705	−	0.586617i	−0.151352	−	0.988480i	$-0.548363\pi$
$281$	−17.8871	−	9.83349i	−1.06705	−	0.586617i	−0.915700	+	0.401863i	$0.868363\pi$
$282$	−26.1560	−	8.49859i	−1.55757	−	0.506084i
$283$	2.88144	−	1.35590i	0.171284	−	0.0806001i	−0.338226	−	0.941065i	$-0.609827\pi$
$283$	2.88144	−	1.35590i	0.171284	−	0.0806001i	0.509510	+	0.860465i	$0.329827\pi$
$284$	−9.59010	−	2.46232i	−0.569067	−	0.146112i
$285$		0			0
$286$	−1.27579	+	1.54217i	−0.0754393	+	0.0911904i
$287$	−0.773301	−	0.490752i	−0.0456465	−	0.0289682i
$288$	22.1154	−	1.39138i	1.30316	−	0.0819879i
$289$	1.96372	+	3.09432i	0.115513	+	0.182019i
$290$		0			0
$291$	−0.615197	−	9.77828i	−0.0360635	−	0.573213i
$292$	3.90119	+	0.744193i	0.228300	+	0.0435506i
$293$	−3.89735	+	1.26632i	−0.227685	+	0.0739795i	−0.420638	−	0.907229i	$-0.638194\pi$
$293$	−3.89735	+	1.26632i	−0.227685	+	0.0739795i	0.192952	+	0.981208i	$0.438194\pi$
$294$	10.1331	−	9.51563i	0.590975	−	0.554963i
$295$		0			0
$296$	−1.54630	−	8.10601i	−0.0898771	−	0.471152i
$297$	0.552254	−	0.588091i	0.0320450	−	0.0341245i
$298$	5.19329	−	13.1167i	0.300839	−	0.759833i
$299$	−12.0389	−	37.0519i	−0.696227	−	2.14277i
$300$		0			0
$301$	1.97109	−	6.06638i	0.113612	−	0.349661i
$302$	−4.82700	−	3.99324i	−0.277763	−	0.229785i
$303$	−7.03078	−	3.30843i	−0.403908	−	0.190065i
$304$	−2.21707	−	2.08197i	−0.127158	−	0.119409i
$305$		0			0
$306$	−11.1692	+	1.41100i	−0.638501	+	0.0806614i
$307$			14.1579i			0.808032i	0.914752	+	0.404016i	$0.132386\pi$
$307$			14.1579i			0.808032i	−0.914752	+	0.404016i	$0.867614\pi$
$308$	0.0416927	+	0.330032i	0.00237566	+	0.0188053i
$309$	28.3991	+	34.3286i	1.61557	+	1.95289i
$310$		0			0
$311$	−1.02064	+	16.2226i	−0.0578752	+	0.919901i	0.856784	+	0.515675i	$0.172459\pi$
$311$	−1.02064	+	16.2226i	−0.0578752	+	0.919901i	−0.914659	+	0.404225i	$0.867541\pi$
$312$	−11.3629	+	44.2556i	−0.643298	+	2.50548i
$313$	−7.50771	+	29.2406i	−0.424361	+	1.65278i	0.293027	+	0.956104i	$0.405337\pi$
$313$	−7.50771	+	29.2406i	−0.424361	+	1.65278i	−0.717389	+	0.696673i	$0.754663\pi$
$314$	0.743151	−	11.8120i	0.0419384	−	0.666592i
$315$		0			0
$316$	−3.40423	−	4.11501i	−0.191503	−	0.231488i
$317$	0.585293	+	4.63307i	0.0328733	+	0.260219i	0.999983	+	0.00585885i	$0.00186494\pi$
$317$	0.585293	+	4.63307i	0.0328733	+	0.260219i	−0.967110	+	0.254360i	$0.918135\pi$
$318$			5.53421i			0.310343i
$319$	−1.51684	+	0.191621i	−0.0849267	+	0.0107287i
$320$		0			0
$321$	5.82335	+	5.46849i	0.325028	+	0.305221i
$322$	2.85446	+	1.34321i	0.159073	+	0.0748540i
$323$	17.1802	+	14.2127i	0.955933	+	0.790816i
$324$	−2.46014	+	7.57154i	−0.136675	+	0.420641i
$325$		0			0
$326$	−3.01316	−	9.27354i	−0.166883	−	0.513614i
$327$	−11.3713	+	28.7205i	−0.628832	+	1.58825i
$328$	2.62353	−	2.79377i	0.144860	−	0.154260i
$329$	−1.57865	−	8.27556i	−0.0870337	−	0.456246i
$330$		0			0
$331$	4.84397	−	4.54879i	0.266249	−	0.250024i	−0.539911	−	0.841722i	$-0.681542\pi$
$331$	4.84397	−	4.54879i	0.266249	−	0.250024i	0.806160	+	0.591698i	$0.201542\pi$
$332$	−10.9473	+	3.55698i	−0.600809	+	0.195215i
$333$	−11.4032	−	2.17527i	−0.624890	−	0.119204i
$334$	0.124241	+	1.97475i	0.00679815	+	0.108053i
$335$		0			0
$336$	0.450598	+	0.710029i	0.0245821	+	0.0387352i
$337$	17.9575	−	1.12979i	0.978205	−	0.0615434i	0.434369	−	0.900735i	$-0.356971\pi$
$337$	17.9575	−	1.12979i	0.978205	−	0.0615434i	0.543836	+	0.839192i	$0.316971\pi$
$338$	−19.7033	−	12.5041i	−1.07172	−	0.680134i
$339$	6.41987	−	7.76029i	0.348680	−	0.421481i
$340$		0			0
$341$	−0.266153	−	0.0683365i	−0.0144130	−	0.00370063i
$342$	17.0324	−	8.01484i	0.921007	−	0.433393i
$343$	8.35722	+	2.71543i	0.451247	+	0.146619i
$344$	23.3897	+	12.8586i	1.26109	+	0.693289i
$345$		0			0
$346$	−20.3207	−	2.56710i	−1.09245	−	0.138008i
$347$	1.17595	−	9.30862i	0.0631284	−	0.499713i	−0.928573	−	0.371150i	$-0.878964\pi$
$347$	1.17595	−	9.30862i	0.0631284	−	0.499713i	0.991701	−	0.128563i	$-0.0410364\pi$
$348$	−11.8483	+	7.51917i	−0.635136	+	0.403070i
$349$	8.33548	−	6.05608i	0.446188	−	0.324175i	−0.341901	−	0.939736i	$-0.611071\pi$
$349$	8.33548	−	6.05608i	0.446188	−	0.324175i	0.788089	+	0.615561i	$0.211071\pi$
$350$		0			0
$351$	11.0411	+	8.02184i	0.589331	+	0.428174i
$352$	−2.21994	−	0.139667i	−0.118323	−	0.00744427i
$353$	1.91214	+	3.47818i	0.101773	+	0.185125i	0.922291	−	0.386496i	$-0.126315\pi$
$353$	1.91214	+	3.47818i	0.101773	+	0.185125i	−0.820518	+	0.571621i	$0.806315\pi$
$354$	−2.10205	+	4.46708i	−0.111723	+	0.237423i
$355$		0			0
$356$	1.99158	−	10.4402i	0.105553	−	0.553331i
$357$	−3.62378	−	4.98770i	−0.191791	−	0.263977i
$358$	−7.09759	+	12.9105i	−0.375119	+	0.682339i
$359$	3.66038	−	5.76784i	0.193188	−	0.304415i	−0.733902	−	0.679256i	$-0.762303\pi$
$359$	3.66038	−	5.76784i	0.193188	−	0.304415i	0.927089	+	0.374841i	$0.122303\pi$
$360$		0			0
$361$	−16.9981	−	6.73003i	−0.894638	−	0.354212i
$362$	5.11107	+	12.9091i	0.268632	+	0.678487i
$363$	21.8220	−	18.0527i	1.14536	−	0.947523i
$364$	−5.45068	+	1.39950i	−0.285693	+	0.0733536i
$365$		0			0
$366$	21.5525	−	8.53324i	1.12657	−	0.446040i
$367$	5.64577	+	6.01214i	0.294707	+	0.313831i	0.859233	−	0.511584i	$-0.170941\pi$
$367$	5.64577	+	6.01214i	0.294707	+	0.313831i	−0.564526	+	0.825415i	$0.690941\pi$
$368$	1.76360	−	2.42739i	0.0919342	−	0.126537i
$369$	−2.29554	−	4.87828i	−0.119501	−	0.253953i
$370$		0			0
$371$	−1.48561	+	0.816723i	−0.0771293	+	0.0424022i
$372$	−2.47743	+	0.472594i	−0.128449	+	0.0245029i
$373$	−6.12253	−	23.8457i	−0.317012	−	1.23468i	−0.904860	−	0.425710i	$-0.860024\pi$
$373$	−6.12253	−	23.8457i	−0.317012	−	1.23468i	0.587847	−	0.808972i	$-0.299976\pi$
$374$	1.13008			0.0584349
$375$		0			0
$376$	35.2536			1.81807
$377$	−6.43215	−	25.0516i	−0.331272	−	1.29022i
$378$	−1.08555	+	0.207079i	−0.0558344	+	0.0106510i
$379$	10.1742	−	5.59331i	0.522613	−	0.287309i	−0.198530	−	0.980095i	$-0.563617\pi$
$379$	10.1742	−	5.59331i	0.522613	−	0.287309i	0.721144	+	0.692786i	$0.243617\pi$
$380$		0			0
$381$	−16.4448	−	34.9470i	−0.842494	−	1.79039i
$382$	−8.35626	+	11.5014i	−0.427543	+	0.588463i
$383$	12.7876	+	13.6174i	0.653413	+	0.695815i	0.967297	−	0.253647i	$-0.0816301\pi$
$383$	12.7876	+	13.6174i	0.653413	+	0.695815i	−0.313883	+	0.949462i	$0.601630\pi$
$384$	−20.9385	+	8.29014i	−1.06851	+	0.423055i
$385$		0			0
$386$	7.87063	−	2.02083i	0.400605	−	0.102858i
$387$	28.9313	−	23.9340i	1.47066	−	1.21663i
$388$	1.85884	+	4.69490i	0.0943684	+	0.238347i
$389$	−13.7322	−	5.43697i	−0.696250	−	0.275665i	−0.00677810	−	0.999977i	$-0.502158\pi$
$389$	−13.7322	−	5.43697i	−0.696250	−	0.275665i	−0.689472	+	0.724312i	$0.742158\pi$
$390$		0			0
$391$	−11.7865	+	18.5725i	−0.596069	+	0.939254i
$392$	−8.58417	+	15.6145i	−0.433566	+	0.788653i
$393$	1.54269	+	2.12334i	0.0778186	+	0.107108i
$394$	−2.79216	+	14.6370i	−0.140667	+	0.737403i
$395$		0			0
$396$	−0.833762	+	1.77183i	−0.0418981	+	0.0890380i
$397$	−10.2275	−	18.6038i	−0.513305	−	0.933699i	−0.998249	−	0.0591533i	$-0.981160\pi$
$397$	−10.2275	−	18.6038i	−0.513305	−	0.933699i	0.484944	−	0.874545i	$-0.338840\pi$
$398$	−13.9711	−	0.878986i	−0.700307	−	0.0440596i
$399$	8.33970	+	6.05914i	0.417507	+	0.303337i
$400$		0			0
$401$	17.7613	−	12.9043i	0.886958	−	0.644412i	−0.0481253	−	0.998841i	$-0.515325\pi$
$401$	17.7613	−	12.9043i	0.886958	−	0.644412i	0.935083	+	0.354429i	$0.115325\pi$
$402$	−0.951959	+	0.604131i	−0.0474794	+	0.0301313i
$403$	0.582614	−	4.61186i	0.0290221	−	0.229733i
$404$	3.97308	+	0.501916i	0.197668	+	0.0249713i
$405$		0			0
$406$	1.83530	+	1.00897i	0.0910846	+	0.0500742i
$407$	1.10826	+	0.360096i	0.0549344	+	0.0178493i
$408$	23.3428	−	10.9843i	1.15564	−	0.543803i
$409$	−19.5982	−	5.03197i	−0.969070	−	0.248815i	−0.269199	−	0.963085i	$-0.586759\pi$
$409$	−19.5982	−	5.03197i	−0.969070	−	0.248815i	−0.699871	+	0.714270i	$0.746759\pi$
$410$		0			0
$411$	−2.76759	+	3.34544i	−0.136515	+	0.165018i
$412$	−19.3872	−	12.3035i	−0.955137	−	0.606149i
$413$	−1.50937	+	0.0949613i	−0.0742711	+	0.00467274i
$414$	9.95053	+	15.6795i	0.489042	+	0.770607i
$415$		0			0
$416$	−2.36273	−	37.5545i	−0.115842	−	1.84126i
$417$	−0.160814	−	0.0306770i	−0.00787511	−	0.00150226i
$418$	−1.79707	+	0.583903i	−0.0878975	+	0.0285596i
$419$	13.5564	−	12.7303i	0.662274	−	0.621917i	−0.278707	−	0.960376i	$-0.589906\pi$
$419$	13.5564	−	12.7303i	0.662274	−	0.621917i	0.940981	+	0.338459i	$0.109906\pi$
$420$		0			0
$421$	3.44497	+	18.0591i	0.167897	+	0.880149i	0.962142	+	0.272550i	$0.0878671\pi$
$421$	3.44497	+	18.0591i	0.167897	+	0.880149i	−0.794244	+	0.607599i	$0.792133\pi$
$422$	7.35591	−	7.83325i	0.358080	−	0.381316i
$423$	18.2565	−	46.1106i	0.887661	−	2.24198i
$424$	−2.19218	−	6.74685i	−0.106462	−	0.327656i
$425$		0			0
$426$	−4.80537	+	14.7894i	−0.232821	+	0.716549i
$427$	5.47134	+	4.52629i	0.264777	+	0.219042i
$428$	−3.72526	−	1.75298i	−0.180067	−	0.0847333i
$429$	−4.70335	−	4.41674i	−0.227080	−	0.213242i
$430$		0			0
$431$	14.9116	−	1.88377i	0.718265	−	0.0907380i	0.242299	−	0.970202i	$-0.422098\pi$
$431$	14.9116	−	1.88377i	0.718265	−	0.0907380i	0.475966	+	0.879464i	$0.342098\pi$
$432$			1.05107i			0.0505699i
$433$	0.133828	+	1.05936i	0.00643135	+	0.0509094i	0.995004	−	0.0998373i	$-0.0318322\pi$
$433$	0.133828	+	1.05936i	0.00643135	+	0.0509094i	−0.988572	+	0.150747i	$0.951832\pi$
$434$	0.239937	+	0.290034i	0.0115173	+	0.0139221i
$435$		0			0
$436$	0.999621	−	15.8885i	0.0478731	−	0.760922i
$437$	9.14678	−	35.6244i	0.437550	−	1.70414i
$438$	1.55123	−	6.04163i	0.0741205	−	0.288680i
$439$	1.49275	−	23.7266i	0.0712450	−	1.13241i	−0.786248	−	0.617911i	$-0.787979\pi$
$439$	1.49275	−	23.7266i	0.0712450	−	1.13241i	0.857493	−	0.514496i	$-0.172021\pi$
$440$		0			0
$441$	15.9779	+	19.3140i	0.760854	+	0.919714i
$442$	2.39604	+	18.9666i	0.113968	+	0.902150i
$443$			16.0523i			0.762669i	0.924437	+	0.381335i	$0.124535\pi$
$443$			16.0523i			0.762669i	−0.924437	+	0.381335i	$0.875465\pi$
$444$	10.6112	−	1.34051i	0.503586	−	0.0636176i
$445$		0			0
$446$	1.53943	+	1.44562i	0.0728941	+	0.0684522i
$447$	41.1490	+	19.3632i	1.94628	+	0.915850i
$448$	1.85112	+	1.53138i	0.0874571	+	0.0723508i
$449$	−12.4842	+	38.4225i	−0.589167	+	1.81327i	−0.00731540	+	0.999973i	$0.502329\pi$
$449$	−12.4842	+	38.4225i	−0.589167	+	1.81327i	−0.581851	+	0.813295i	$0.697671\pi$
$450$		0			0
$451$	0.167237	+	0.514701i	0.00787487	+	0.0242363i
$452$	−1.91082	+	4.82618i	−0.0898774	+	0.227005i
$453$	13.8244	−	14.7215i	0.649527	−	0.691676i
$454$	3.14773	+	16.5010i	0.147730	+	0.774430i
$455$		0			0
$456$	−31.4446	+	29.5284i	−1.47253	+	1.38280i
$457$	1.72959	−	0.561976i	0.0809066	−	0.0262881i	−0.268284	−	0.963340i	$-0.586457\pi$
$457$	1.72959	−	0.561976i	0.0809066	−	0.0262881i	0.349191	+	0.937052i	$0.386457\pi$
$458$	17.8600	+	3.40697i	0.834542	+	0.159197i
$459$	−0.483844	−	7.69048i	−0.0225839	−	0.358961i
$460$		0			0
$461$	16.6138	+	26.1792i	0.773784	+	1.21929i	0.971035	+	0.238936i	$0.0767985\pi$
$461$	16.6138	+	26.1792i	0.773784	+	1.21929i	−0.197251	+	0.980353i	$0.563202\pi$
$462$	0.521428	−	0.0328055i	0.0242590	−	0.00152625i
$463$	10.5487	+	6.69442i	0.490241	+	0.311116i	0.757870	−	0.652406i	$-0.226240\pi$
$463$	10.5487	+	6.69442i	0.490241	+	0.311116i	−0.267629	+	0.963522i	$0.586240\pi$
$464$	1.26971	−	1.53482i	0.0589448	−	0.0712520i
$465$		0			0
$466$	−12.1074	−	3.10865i	−0.560864	−	0.144005i
$467$	−3.29390	+	1.54999i	−0.152424	+	0.0717251i	−0.500478	−	0.865749i	$-0.666842\pi$
$467$	−3.29390	+	1.54999i	−0.152424	+	0.0717251i	0.348054	+	0.937474i	$0.386842\pi$
$468$	−31.5053	−	10.2367i	−1.45633	−	0.473191i
$469$	−0.302662	−	0.166390i	−0.0139756	−	0.00768316i
$470$		0			0
$471$	37.8522	+	4.78184i	1.74414	+	0.220336i
$472$	0.793165	−	6.27855i	0.0365084	−	0.288993i
$473$	−3.18234	+	2.01957i	−0.146324	+	0.0928601i
$474$	−6.78589	+	4.93024i	−0.311686	+	0.226453i
$475$		0			0
$476$	2.57056	+	1.86762i	0.117821	+	0.0856022i
$477$	−9.95992	−	0.626625i	−0.456033	−	0.0286912i
$478$	−1.93318	−	3.51645i	−0.0884217	−	0.160839i
$479$	−10.6916	+	22.7207i	−0.488510	+	1.03814i	0.496880	+	0.867820i	$0.334479\pi$
$479$	−10.6916	+	22.7207i	−0.488510	+	1.03814i	−0.985389	+	0.170317i	$0.945521\pi$
$480$		0			0
$481$	−3.69387	+	19.3639i	−0.168426	+	0.882920i
$482$	−2.68906	−	3.70117i	−0.122483	−	0.168584i
$483$	−4.89925	+	8.91170i	−0.222923	+	0.405496i
$484$	−7.82108	+	12.3240i	−0.355504	+	0.560184i
$485$		0			0
$486$	16.3899	+	6.48921i	0.743460	+	0.294357i
$487$	−2.07827	−	5.24912i	−0.0941755	−	0.237860i	0.875051	−	0.484031i	$-0.160828\pi$
$487$	−2.07827	−	5.24912i	−0.0941755	−	0.237860i	−0.969227	+	0.246171i	$0.920828\pi$
$488$	−22.8949	+	18.9403i	−1.03640	+	0.857387i
$489$	30.4454	−	7.81706i	1.37679	−	0.353500i
$490$		0			0
$491$	18.3466	−	7.26393i	0.827970	−	0.327817i	0.0843646	−	0.996435i	$-0.473114\pi$
$491$	18.3466	−	7.26393i	0.827970	−	0.327817i	0.743606	+	0.668618i	$0.233114\pi$
$492$	3.40032	+	3.62097i	0.153298	+	0.163246i
$493$	−8.58366	+	11.8144i	−0.386589	+	0.532094i
$494$	−13.6101	−	28.9230i	−0.612349	−	1.30131i
$495$		0			0
$496$	0.313725	−	0.172472i	0.0140867	−	0.00774421i
$497$	−4.67926	+	0.892617i	−0.209894	+	0.0400393i
$498$	4.49589	+	17.5103i	0.201466	+	0.784657i
$499$	−22.3477			−1.00042			−0.500210	−	0.865904i	$-0.666744\pi$
$499$	−22.3477			−1.00042			−0.500210	+	0.865904i	$0.666744\pi$
$500$		0			0
$501$	−6.37846			−0.284969
$502$	−4.63553	−	18.0542i	−0.206894	−	0.805798i
$503$	−14.2812	+	2.72429i	−0.636768	+	0.121470i	−0.495649	−	0.868523i	$-0.665070\pi$
$503$	−14.2812	+	2.72429i	−0.636768	+	0.121470i	−0.141119	+	0.989993i	$0.545070\pi$
$504$	5.84655	−	3.21417i	0.260426	−	0.143170i
$505$		0			0
$506$	−0.793696	−	1.68669i	−0.0352841	−	0.0749825i
$507$	44.2174	−	60.8600i	1.96376	−	2.70289i
$508$	13.6262	+	14.5104i	0.604566	+	0.643797i
$509$	−8.68523	+	3.43873i	−0.384966	+	0.152419i	−0.552633	−	0.833425i	$-0.686377\pi$
$509$	−8.68523	+	3.43873i	−0.384966	+	0.152419i	0.167667	+	0.985844i	$0.446377\pi$
$510$		0			0
$511$	1.85075	−	0.475193i	0.0818725	−	0.0210213i
$512$	4.31115	−	3.56649i	0.190528	−	0.157618i
$513$	4.74303	+	11.9795i	0.209410	+	0.528909i
$514$	−9.41692	−	3.72842i	−0.415362	−	0.164454i
$515$		0			0
$516$	−18.5365	+	29.2088i	−0.816023	+	1.28585i
$517$	−2.39826	+	4.36241i	−0.105475	+	0.191859i
$518$	−0.938271	−	1.29142i	−0.0412252	−	0.0567417i
$519$	12.3723	−	64.8577i	0.543083	−	2.84694i
$520$		0			0
$521$	−8.28676	+	17.6103i	−0.363049	+	0.771519i	0.636950	+	0.770905i	$0.280196\pi$
$521$	−8.28676	+	17.6103i	−0.363049	+	0.771519i	−1.00000		0.000614502i	$0.999804\pi$
$522$	5.93937	+	10.8037i	0.259959	+	0.472864i
$523$	3.45358	+	0.217281i	0.151015	+	0.00950104i	0.138118	−	0.990416i	$-0.455895\pi$
$523$	3.45358	+	0.217281i	0.151015	+	0.00950104i	0.0128968	+	0.999917i	$0.495895\pi$
$524$	−1.09432	−	0.795073i	−0.0478058	−	0.0347329i
$525$		0			0
$526$	−10.0038	+	7.26820i	−0.436187	+	0.316909i
$527$	−2.21606	+	1.40636i	−0.0965332	+	0.0612618i
$528$	0.0622791	−	0.492990i	0.00271035	−	0.0214546i
$529$	13.1798	+	1.66500i	0.573035	+	0.0723912i
$530$		0			0
$531$	−7.80140	−	4.28885i	−0.338552	−	0.186120i
$532$	−5.05273	−	1.64173i	−0.219064	−	0.0711781i
$533$	−8.28390	+	3.89811i	−0.358815	+	0.168846i
$534$	−16.1684	−	4.15134i	−0.699674	−	0.179646i
$535$		0			0
$536$	0.921243	−	1.11359i	0.0397916	−	0.0480998i
$537$	−40.0999	−	25.4481i	−1.73044	−	1.09817i
$538$	0.219600	−	0.0138161i	0.00946764	−	0.000595653i
$539$	−1.34823	−	2.12447i	−0.0580724	−	0.0915075i
$540$		0			0
$541$	−1.76979	−	28.1301i	−0.0760894	−	1.20941i	−0.832016	−	0.554751i	$-0.812814\pi$
$541$	−1.76979	−	28.1301i	−0.0760894	−	1.20941i	0.755927	−	0.654656i	$-0.227186\pi$
$542$	19.5922	+	3.73742i	0.841558	+	0.160536i
$543$	−42.5667	+	13.8307i	−1.82671	+	0.593534i
$544$	−15.4876	+	14.5438i	−0.664026	+	0.623562i
$545$		0			0
$546$	1.65615	+	8.68182i	0.0708765	+	0.371548i
$547$	−24.4784	+	26.0668i	−1.04662	+	1.11454i	−0.0533673	+	0.998575i	$0.516995\pi$
$547$	−24.4784	+	26.0668i	−1.04662	+	1.11454i	−0.993254	+	0.115963i	$0.963005\pi$
$548$	0.823749	−	2.08055i	0.0351888	−	0.0888767i
$549$	12.9169	+	39.7543i	0.551282	+	1.69667i
$550$		0			0
$551$	7.54547	−	23.2226i	0.321448	−	0.989314i
$552$	−32.7891	−	27.1255i	−1.39560	−	1.15454i
$553$	−2.32493	−	1.09403i	−0.0988659	−	0.0465228i
$554$	4.56863	+	4.29023i	0.194103	+	0.182274i
$555$		0			0
$556$	0.0837096	−	0.0105750i	0.00355008	−	0.000448479i
$557$			22.1092i			0.936797i	0.883517	+	0.468398i	$0.155169\pi$
$557$			22.1092i			0.936797i	−0.883517	+	0.468398i	$0.844831\pi$
$558$	0.277715	+	2.19834i	0.0117566	+	0.0930630i
$559$	−40.6428	−	49.1287i	−1.71901	−	2.07792i
$560$		0			0
$561$	−0.228743	+	3.63577i	−0.00965755	+	0.153502i
$562$	4.10891	−	16.0031i	0.173324	−	0.675052i
$563$	5.55833	−	21.6483i	0.234256	−	0.912366i	−0.737302	−	0.675563i	$-0.763901\pi$
$563$	5.55833	−	21.6483i	0.234256	−	0.912366i	0.971558	−	0.236803i	$-0.0760995\pi$
$564$	−2.86901	+	45.6016i	−0.120807	+	1.92017i
$565$		0			0
$566$	1.64308	+	1.98614i	0.0690637	+	0.0834837i
$567$	0.480062	+	3.80008i	0.0201607	+	0.159588i
$568$		−	19.9335i		−	0.836391i
$569$	13.8899	−	1.75470i	0.582295	−	0.0735610i	0.171333	−	0.985213i	$-0.445193\pi$
$569$	13.8899	−	1.75470i	0.582295	−	0.0735610i	0.410963	+	0.911652i	$0.365193\pi$
$570$		0			0
$571$	24.8898	+	23.3730i	1.04160	+	0.978131i	0.999780	−	0.0209937i	$-0.00668298\pi$
$571$	24.8898	+	23.3730i	1.04160	+	0.978131i	0.0418244	+	0.999125i	$0.486683\pi$
$572$	3.00878	+	1.41583i	0.125804	+	0.0591987i
$573$	−35.3118	−	29.2124i	−1.47517	−	1.22037i
$574$	0.229090	−	0.705066i	0.00956202	−	0.0294289i
$575$		0			0
$576$	4.37019	+	13.4501i	0.182091	+	0.560419i
$577$	−13.5135	+	34.1312i	−0.562574	+	1.42090i	0.318502	+	0.947922i	$0.396820\pi$
$577$	−13.5135	+	34.1312i	−0.562574	+	1.42090i	−0.881075	+	0.472976i	$0.843180\pi$
$578$	−2.03069	+	2.16246i	−0.0844655	+	0.0899467i
$579$	4.90846	+	25.7310i	0.203988	+	1.06935i
$580$		0			0
$581$	−4.03702	+	3.79101i	−0.167484	+	0.157278i
$582$	7.54245	−	2.45069i	0.312644	−	0.101584i
$583$	0.984011	+	0.187710i	0.0407536	+	0.00777416i
$584$	0.502054	+	7.97992i	0.0207751	+	0.330211i
$585$		0			0
$586$	−1.77735	−	2.80065i	−0.0734216	−	0.115694i
$587$	−4.49081	+	0.282538i	−0.185355	+	0.0116616i	−0.155197	−	0.987884i	$-0.549601\pi$
$587$	−4.49081	+	0.282538i	−0.185355	+	0.0116616i	−0.0301585	+	0.999545i	$0.509601\pi$
$588$	−19.4993	−	12.3746i	−0.804137	−	0.510321i
$589$	2.79737	−	3.38143i	0.115263	−	0.139330i
$590$		0			0
$591$	−46.5262	−	11.9459i	−1.91383	−	0.491388i
$592$	−1.37372	+	0.646425i	−0.0564597	+	0.0265679i
$593$	−15.9040	−	5.16751i	−0.653097	−	0.212204i	−0.0363178	−	0.999340i	$-0.511563\pi$
$593$	−15.9040	−	5.16751i	−0.653097	−	0.212204i	−0.616779	+	0.787136i	$0.711563\pi$
$594$	0.572239	+	0.314591i	0.0234792	+	0.0129078i
$595$		0			0
$596$	−23.2532	−	2.93756i	−0.952489	−	0.120327i
$597$	5.65588	−	44.7709i	0.231480	−	1.83235i
$598$	26.6257	−	16.8972i	1.08881	−	0.690977i
$599$	−3.79459	+	2.75693i	−0.155043	+	0.112645i	−0.662602	−	0.748972i	$-0.730548\pi$
$599$	−3.79459	+	2.75693i	−0.155043	+	0.112645i	0.507559	+	0.861617i	$0.330548\pi$
$600$		0			0
$601$	2.83842	+	2.06223i	0.115781	+	0.0841201i	0.644169	−	0.764883i	$-0.277203\pi$
$601$	2.83842	+	2.06223i	0.115781	+	0.0841201i	−0.528388	+	0.849003i	$0.677203\pi$
$602$	5.15290	+	0.324193i	0.210016	+	0.0132131i
$603$	−0.979467	−	1.78164i	−0.0398870	−	0.0725542i
$604$	−4.43154	+	9.41751i	−0.180317	+	0.383193i
$605$		0			0
$606$	1.17855	−	6.17820i	0.0478755	−	0.250972i
$607$	9.02610	+	12.4234i	0.366358	+	0.504249i	0.951906	−	0.306389i	$-0.0991208\pi$
$607$	9.02610	+	12.4234i	0.366358	+	0.504249i	−0.585548	+	0.810637i	$0.699121\pi$
$608$	17.1140	−	31.1302i	0.694063	−	1.26250i
$609$	−3.61762	+	5.70045i	−0.146593	+	0.230994i
$610$		0			0
$611$	−78.3013	−	31.0017i	−3.16773	−	1.25419i
$612$	6.88539	+	17.3905i	0.278325	+	0.702969i
$613$	−6.38651	+	5.28338i	−0.257949	+	0.213394i	−0.757405	−	0.652945i	$-0.773533\pi$
$613$	−6.38651	+	5.28338i	−0.257949	+	0.213394i	0.499456	+	0.866339i	$0.333533\pi$
$614$	−11.0999	+	2.84998i	−0.447957	+	0.115016i
$615$		0			0
$616$	−0.622687	+	0.246539i	−0.0250888	+	0.00993335i
$617$	−14.1267	−	15.0434i	−0.568721	−	0.605626i	0.378738	−	0.925504i	$-0.376358\pi$
$617$	−14.1267	−	15.0434i	−0.568721	−	0.605626i	−0.947459	+	0.319878i	$0.896358\pi$
$618$	−21.1973	+	29.1756i	−0.852680	+	1.17361i
$619$	2.08971	+	4.44085i	0.0839923	+	0.178493i	0.942411	−	0.334457i	$-0.108553\pi$
$619$	2.08971	+	4.44085i	0.0839923	+	0.178493i	−0.858419	+	0.512950i	$0.828553\pi$
$620$		0			0
$621$	−11.1386	+	6.12348i	−0.446975	+	0.245727i
$622$	−12.9242	+	2.46542i	−0.518212	+	0.0988543i
$623$	−1.27169	−	4.95292i	−0.0509493	−	0.198434i
$624$	8.40613			0.336515
$625$		0			0
$626$	−24.4363			−0.976670
$627$	−1.51482	−	5.89985i	−0.0604963	−	0.235617i
$628$	−19.3150	+	3.68453i	−0.770753	+	0.147029i
$629$	9.75366	−	5.36212i	0.388904	−	0.213802i
$630$		0			0
$631$	−2.28055	−	4.84641i	−0.0907872	−	0.192933i	0.854276	−	0.519819i	$-0.174001\pi$
$631$	−2.28055	−	4.84641i	−0.0907872	−	0.192933i	−0.945064	+	0.326886i	$0.894001\pi$
$632$	6.31985	−	8.69853i	0.251390	−	0.346009i
$633$	23.7128	+	25.2515i	0.942498	+	1.00366i
$634$	−3.51456	+	1.39151i	−0.139581	+	0.0552641i
$635$		0			0
$636$	8.90566	−	2.28658i	0.353132	−	0.0906689i
$637$	32.7974	−	27.1324i	1.29948	−	1.07503i
$638$	−0.455573	−	1.15065i	−0.0180363	−	0.0455545i
$639$	−26.0724	−	10.3228i	−1.03141	−	0.408363i
$640$		0			0
$641$	19.2339	−	30.3077i	0.759692	−	1.19708i	−0.215669	−	0.976466i	$-0.569193\pi$
$641$	19.2339	−	30.3077i	0.759692	−	1.19708i	0.975361	−	0.220616i	$-0.0708067\pi$
$642$	−3.11512	+	5.66638i	−0.122944	+	0.223634i
$643$	20.5073	+	28.2259i	0.808729	+	1.11312i	0.991518	+	0.129968i	$0.0414873\pi$
$643$	20.5073	+	28.2259i	0.808729	+	1.11312i	−0.182790	+	0.983152i	$0.558513\pi$
$644$	0.982105	−	5.14837i	0.0387004	−	0.202874i
$645$		0			0
$646$	−7.68455	+	16.3305i	−0.302345	+	0.642515i
$647$	13.3540	+	24.2908i	0.524999	+	0.954970i	0.997293	+	0.0735290i	$0.0234261\pi$
$647$	13.3540	+	24.2908i	0.524999	+	0.954970i	−0.472294	+	0.881441i	$0.656574\pi$
$648$	−15.9962	−	1.00640i	−0.628391	−	0.0395350i
$649$	0.722972	+	0.525270i	0.0283791	+	0.0206187i
$650$		0			0
$651$	−0.981686	+	0.713236i	−0.0384753	+	0.0279539i
$652$	−13.6780	+	8.68035i	−0.535673	+	0.339949i
$653$	3.37957	−	26.7520i	0.132253	−	1.04689i	−0.776666	−	0.629913i	$-0.783091\pi$
$653$	3.37957	−	26.7520i	0.132253	−	1.04689i	0.908918	−	0.416974i	$-0.136909\pi$
$654$	−24.8063	−	3.13376i	−0.970002	−	0.122540i
$655$		0			0
$656$	−0.617879	−	0.339682i	−0.0241241	−	0.0132623i
$657$	10.6975	+	3.47582i	0.417349	+	0.135605i
$658$	6.17035	−	2.90355i	0.240545	−	0.113192i
$659$	17.9921	+	4.61958i	0.700871	+	0.179953i	0.582278	−	0.812990i	$-0.302162\pi$
$659$	17.9921	+	4.61958i	0.700871	+	0.179953i	0.118593	+	0.992943i	$0.462162\pi$
$660$		0			0
$661$	6.91570	−	8.35965i	0.268990	−	0.325153i	−0.618672	−	0.785650i	$-0.712329\pi$
$661$	6.91570	−	8.35965i	0.268990	−	0.325153i	0.887661	+	0.460497i	$0.152329\pi$
$662$	4.54140	+	2.88206i	0.176506	+	0.112014i
$663$	−61.5058	+	3.86962i	−2.38869	+	0.150284i
$664$	−12.4171	−	19.5662i	−0.481878	−	0.759318i
$665$		0			0
$666$	−0.590021	−	9.37811i	−0.0228628	−	0.363394i
$667$	23.6621	+	4.51379i	0.916202	+	0.174775i
$668$	3.12644	−	1.01584i	0.120965	−	0.0393041i
$669$	−4.96256	+	4.66016i	−0.191864	+	0.180172i
$670$		0			0
$671$	−0.786234	−	4.12158i	−0.0303522	−	0.159112i
$672$	−6.72393	+	7.16026i	−0.259381	+	0.276213i
$673$	−10.2884	+	25.9856i	−0.396590	+	1.00167i	0.585061	+	0.810989i	$0.301070\pi$
$673$	−10.2884	+	25.9856i	−0.396590	+	1.00167i	−0.981652	+	0.190684i	$0.938930\pi$
$674$	4.50060	+	13.8514i	0.173357	+	0.533537i
$675$		0			0
$676$	−11.9807	+	36.8729i	−0.460798	+	1.41819i
$677$	−22.8114	−	18.8713i	−0.876714	−	0.725281i	0.0858577	−	0.996307i	$-0.472637\pi$
$677$	−22.8114	−	18.8713i	−0.876714	−	0.725281i	−0.962572	+	0.271026i	$0.912637\pi$
$678$	7.37648	+	3.47111i	0.283292	+	0.133307i
$679$	1.77096	+	1.66304i	0.0679632	+	0.0638217i
$680$		0			0
$681$	−53.7254	+	6.78709i	−2.05876	+	0.260082i
$682$		−	0.222423i		−	0.00851703i
$683$	3.61704	+	28.6318i	0.138402	+	1.09557i	0.896380	+	0.443287i	$0.146188\pi$
$683$	3.61704	+	28.6318i	0.138402	+	1.09557i	−0.757978	+	0.652281i	$0.773812\pi$
$684$	−19.9348	−	24.0970i	−0.762226	−	0.921373i
$685$		0			0
$686$	−0.446617	+	7.09877i	−0.0170519	+	0.271032i
$687$	−14.5763	+	56.7708i	−0.556119	+	2.16594i
$688$	1.22121	−	4.75631i	0.0465583	−	0.181333i
$689$	−1.06408	+	16.9131i	−0.0405383	+	0.644338i
$690$		0			0
$691$	8.59487	+	10.3894i	0.326964	+	0.395232i	0.908223	−	0.418487i	$-0.137439\pi$
$691$	8.59487	+	10.3894i	0.326964	+	0.395232i	−0.581258	+	0.813719i	$0.697439\pi$
$692$	4.26498	+	33.7608i	0.162130	+	1.28339i
$693$			0.942129i			0.0357885i
$694$	7.53479	−	0.951865i	0.286017	−	0.0361323i
$695$		0			0
$696$	−20.5945	−	19.3395i	−0.780633	−	0.733063i
$697$	4.67725	+	2.20095i	0.177164	+	0.0833668i
$698$	6.42597	+	5.31603i	0.243227	+	0.201215i
$699$	12.4521	−	38.3235i	0.470981	−	1.44953i
$700$		0			0
$701$	9.54262	+	29.3692i	0.360420	+	1.10926i	0.952800	+	0.303600i	$0.0981885\pi$
$701$	9.54262	+	29.3692i	0.360420	+	1.10926i	−0.592380	+	0.805659i	$0.701812\pi$
$702$	−4.06664	+	10.2712i	−0.153485	+	0.387660i
$703$	−12.7399	+	13.5666i	−0.480493	+	0.511673i
$704$	−0.266006	−	1.39445i	−0.0100255	−	0.0525555i
$705$		0			0
$706$	−2.34202	+	2.19930i	−0.0881429	+	0.0827717i
$707$	1.83242	−	0.595388i	0.0689151	−	0.0223919i
$708$	8.05694	+	1.53694i	0.302798	+	0.0577619i
$709$	−0.0367345	−	0.583878i	−0.00137959	−	0.0219280i	0.997277	−	0.0737507i	$-0.0234969\pi$
$709$	−0.0367345	−	0.583878i	−0.00137959	−	0.0219280i	−0.998656	+	0.0518227i	$0.983497\pi$
$710$		0			0
$711$	−8.10460	−	12.7708i	−0.303946	−	0.478943i
$712$	21.3556	−	1.34358i	0.800333	−	0.0503527i
$713$	3.65547	+	2.31983i	0.136899	+	0.0868785i
$714$	3.18095	−	3.84511i	0.119044	−	0.143899i
$715$		0			0
$716$	23.7081	+	6.08719i	0.886012	+	0.227489i
$717$	11.7047	−	5.50780i	0.437119	−	0.205693i
$718$	5.25889	+	1.70872i	0.196260	+	0.0637687i
$719$	9.66359	+	5.31260i	0.360391	+	0.198127i	0.651654	−	0.758516i	$-0.274075\pi$
$719$	9.66359	+	5.31260i	0.360391	+	0.198127i	−0.291263	+	0.956643i	$0.594075\pi$
$720$		0			0
$721$	−10.9602	−	1.38459i	−0.408179	−	0.0515649i
$722$	1.85470	−	14.6815i	0.0690249	−	0.546388i
$723$	12.4520	−	7.90228i	0.463095	−	0.293889i
$724$	18.6616	−	13.5584i	0.693552	−	0.503895i
$725$		0			0
$726$	18.5463	+	13.4747i	0.688319	+	0.500093i
$727$	−0.716047	−	0.0450499i	−0.0265567	−	0.00167081i	0.0495066	−	0.998774i	$-0.484235\pi$
$727$	−0.716047	−	0.0450499i	−0.0265567	−	0.00167081i	−0.0760633	+	0.997103i	$0.524235\pi$
$728$	−5.45803	−	9.92813i	−0.202288	−	0.367961i
$729$	−16.6333	+	35.3476i	−0.616049	+	1.30917i
$730$		0			0
$731$	−6.74586	+	35.3630i	−0.249505	+	1.30795i
$732$	−22.6366	−	31.1566i	−0.836673	−	1.15158i
$733$	−8.85941	+	16.1152i	−0.327230	+	0.595228i	−0.987835	−	0.155505i	$-0.950300\pi$
$733$	−8.85941	+	16.1152i	−0.327230	+	0.595228i	0.660606	+	0.750733i	$0.270300\pi$
$734$	−3.57709	+	5.63660i	−0.132033	+	0.208051i
$735$		0			0
$736$	32.5849	+	12.9013i	1.20109	+	0.475547i
$737$	0.0751290	+	0.189754i	0.00276741	+	0.00698969i
$738$	3.36254	−	2.78173i	0.123777	−	0.102397i
$739$	−12.0460	+	3.09289i	−0.443119	+	0.113774i	−0.463656	−	0.886015i	$-0.653463\pi$
$739$	−12.0460	+	3.09289i	−0.443119	+	0.113774i	0.0205364	+	0.999789i	$0.493463\pi$
$740$		0			0
$741$	95.8082	−	37.9331i	3.51960	−	1.39351i
$742$	−0.939375	−	1.00033i	−0.0344855	−	0.0367234i
$743$	−10.8728	+	14.9651i	−0.398885	+	0.549018i	−0.960464	−	0.278405i	$-0.910194\pi$
$743$	−10.8728	+	14.9651i	−0.398885	+	0.549018i	0.561579	+	0.827423i	$0.310194\pi$
$744$	−2.16194	−	4.59436i	−0.0792606	−	0.168437i
$745$		0			0
$746$	17.4628	−	9.60027i	0.639359	−	0.351491i
$747$	−32.0224	+	6.10860i	−1.17164	+	0.223502i
$748$	−0.466917	−	1.81852i	−0.0170722	−	0.0664917i
$749$	−1.98082			−0.0723775
$750$		0			0
$751$	4.10129			0.149658			0.0748291	−	0.997196i	$-0.476159\pi$
$751$	4.10129			0.149658			0.0748291	+	0.997196i	$0.476159\pi$
$752$	−1.61297	−	6.28211i	−0.0588190	−	0.229085i
$753$	59.0236	−	11.2593i	2.15094	−	0.410314i
$754$	18.3459	−	10.0858i	0.668119	−	0.367302i
$755$		0			0
$756$	0.781749	+	1.66130i	0.0284319	+	0.0604209i
$757$	19.0981	−	26.2863i	0.694133	−	0.955392i	−0.305861	−	0.952076i	$-0.598944\pi$
$757$	19.0981	−	26.2863i	0.694133	−	0.955392i	0.999995	−	0.00331614i	$-0.00105556\pi$
$758$	6.43329	+	6.85076i	0.233668	+	0.248831i
$759$	5.58720	−	2.21213i	0.202803	−	0.0802952i
$760$		0			0
$761$	5.36021	−	1.37627i	0.194307	−	0.0498896i	−0.150282	−	0.988643i	$-0.548018\pi$
$761$	5.36021	−	1.37627i	0.194307	−	0.0498896i	0.344589	+	0.938754i	$0.388018\pi$
$762$	24.0885	−	19.9278i	0.872636	−	0.721907i
$763$	−2.81961	−	7.12152i	−0.102077	−	0.257816i
$764$	21.9606	+	8.69484i	0.794508	+	0.314568i
$765$		0			0
$766$	−8.10204	+	12.7668i	−0.292738	+	0.461282i
$767$	−7.28298	+	13.2477i	−0.262973	+	0.478346i
$768$	−22.1045	−	30.4242i	−0.797626	−	1.09784i
$769$	−7.56667	+	39.6659i	−0.272861	+	1.43039i	0.536909	+	0.843640i	$0.319592\pi$
$769$	−7.56667	+	39.6659i	−0.272861	+	1.43039i	−0.809770	+	0.586747i	$0.800408\pi$
$770$		0			0
$771$	13.9015	−	29.5421i	0.500649	−	1.06393i
$772$	−6.50386	−	11.8305i	−0.234079	−	0.425788i
$773$	21.0356	+	1.32345i	0.756597	+	0.0476011i	0.436404	−	0.899751i	$-0.356252\pi$
$773$	21.0356	+	1.32345i	0.756597	+	0.0476011i	0.320194	+	0.947352i	$0.396252\pi$
$774$	24.5884	+	17.8645i	0.883812	+	0.642127i
$775$		0			0
$776$	−8.22437	+	5.97535i	−0.295238	+	0.214503i
$777$	4.34477	−	2.75727i	0.155868	−	0.0989167i
$778$	1.49835	−	11.8607i	0.0537185	−	0.425226i
$779$	−8.57506	−	1.08328i	−0.307233	−	0.0388126i
$780$		0			0
$781$	2.46664	+	1.35605i	0.0882634	+	0.0485232i
$782$	−16.9337	−	5.50210i	−0.605548	−	0.196755i
$783$	−7.63541	+	3.59295i	−0.272867	+	0.128402i
$784$	3.17523	+	0.815260i	0.113401	+	0.0291164i
$785$		0			0
$786$	−1.35418	+	1.63692i	−0.0483019	+	0.0583869i
$787$	17.6367	+	11.1926i	0.628682	+	0.398974i	0.811649	−	0.584145i	$-0.198570\pi$
$787$	17.6367	+	11.1926i	0.628682	+	0.398974i	−0.182967	+	0.983119i	$0.558570\pi$
$788$	24.7076	−	1.55447i	0.880170	−	0.0553756i
$789$	−21.3589	−	33.6562i	−0.760397	−	1.19819i
$790$		0			0
$791$	0.156809	+	2.49241i	0.00557550	+	0.0886200i
$792$	−3.87252	−	0.738722i	−0.137604	−	0.0262493i
$793$	67.5074	−	21.9345i	2.39726	−	0.778917i
$794$	12.5268	−	11.7635i	0.444560	−	0.417469i
$795$		0			0
$796$	4.35800	+	22.8455i	0.154465	+	0.809736i
$797$	−37.2442	+	39.6611i	−1.31926	+	1.40487i	−0.464738	+	0.885448i	$0.653851\pi$
$797$	−37.2442	+	39.6611i	−1.31926	+	1.40487i	−0.854520	+	0.519419i	$0.826149\pi$
$798$	−3.07166	+	7.75813i	−0.108736	+	0.274635i
$799$	14.6936	+	45.2223i	0.519823	+	1.59985i
$800$		0			0
$801$	9.30186	−	28.6282i	0.328665	−	1.01153i
$802$	13.6925	+	11.3274i	0.483499	+	0.399986i
$803$	−1.02162	−	0.480737i	−0.0360521	−	0.0169649i
$804$	1.36549	+	1.28228i	0.0481572	+	0.0452226i
$805$		0			0
$806$	3.73304	−	0.471592i	0.131491	−	0.0166111i
$807$			0.709311i			0.0249689i
$808$	1.01048	+	7.99879i	0.0355486	+	0.281396i
$809$	11.4513	+	13.8422i	0.402606	+	0.486667i	0.932384	−	0.361469i	$-0.117725\pi$
$809$	11.4513	+	13.8422i	0.402606	+	0.486667i	−0.529778	+	0.848136i	$0.677725\pi$
$810$		0			0
$811$	2.08961	−	33.2135i	0.0733763	−	1.16628i	−0.773252	−	0.634099i	$-0.781371\pi$
$811$	2.08961	−	33.2135i	0.0733763	−	1.16628i	0.846629	−	0.532184i	$-0.178629\pi$
$812$	0.865333	−	3.37025i	0.0303672	−	0.118273i
$813$	−15.9900	+	62.2771i	−0.560795	+	2.18415i
$814$	−0.0592264	+	0.941376i	−0.00207588	+	0.0329952i
$815$		0			0
$816$	−3.02539	−	3.65706i	−0.105910	−	0.128023i
$817$	−7.54445	−	59.7204i	−0.263947	−	2.08935i
$818$		−	16.3782i		−	0.572649i
$819$	−15.8122	+	1.99754i	−0.552523	+	0.0697998i
$820$		0			0
$821$	11.2680	+	10.5814i	0.393257	+	0.369293i	0.855803	−	0.517302i	$-0.173064\pi$
$821$	11.2680	+	10.5814i	0.393257	+	0.369293i	−0.462545	+	0.886596i	$0.653064\pi$
$822$	−3.17998	−	1.49638i	−0.110914	−	0.0521923i
$823$	−21.5867	−	17.8581i	−0.752465	−	0.622493i	0.180036	−	0.983660i	$-0.442378\pi$
$823$	−21.5867	−	17.8581i	−0.752465	−	0.622493i	−0.932501	+	0.361167i	$0.882378\pi$
$824$	14.2851	−	43.9650i	0.497645	−	1.53159i
$825$		0			0
$826$	−0.378286	−	1.16425i	−0.0131623	−	0.0405093i
$827$	9.18432	−	23.1969i	0.319370	−	0.806636i	−0.678061	−	0.735005i	$-0.737180\pi$
$827$	9.18432	−	23.1969i	0.319370	−	0.806636i	0.997431	−	0.0716310i	$-0.0228204\pi$
$828$	21.1202	−	22.4908i	0.733979	−	0.781608i
$829$	−4.36653	−	22.8901i	−0.151656	−	0.795007i	−0.974092	−	0.226150i	$-0.927386\pi$
$829$	−4.36653	−	22.8901i	−0.151656	−	0.795007i	0.822437	−	0.568857i	$-0.192614\pi$
$830$		0			0
$831$	−14.7276	+	13.8301i	−0.510895	+	0.479762i
$832$	22.8398	−	7.42110i	0.791827	−	0.257280i
$833$	−23.6077	−	4.50342i	−0.817960	−	0.156034i
$834$	−0.00832082	−	0.132256i	−0.000288126	−	0.00457964i
$835$		0			0
$836$	1.68212	+	2.65059i	0.0581772	+	0.0916726i
$837$	−1.51365	+	0.0952309i	−0.0523194	+	0.00329166i
$838$	12.7096	+	8.06577i	0.439047	+	0.278628i
$839$	−10.0685	+	12.1708i	−0.347604	+	0.420181i	−0.915120	−	0.403181i	$-0.867904\pi$
$839$	−10.0685	+	12.1708i	−0.347604	+	0.420181i	0.567516	+	0.823362i	$0.307904\pi$
$840$		0			0
$841$	−12.5991	−	3.23490i	−0.434452	−	0.111548i
$842$	−13.4651	+	6.33620i	−0.464038	+	0.218360i
$843$	50.6548	+	16.4587i	1.74464	+	0.566869i
$844$	−15.6445	−	8.60065i	−0.538507	−	0.296047i
$845$		0			0
$846$	39.8263	+	5.03123i	1.36926	+	0.172977i
$847$	−0.880159	+	6.96718i	−0.0302426	+	0.239395i
$848$	−1.10197	+	0.699333i	−0.0378419	+	0.0240152i
$849$	−6.72254	+	4.88421i	−0.230717	+	0.167626i
$850$		0			0
$851$	−14.8536	−	10.7917i	−0.509174	−	0.369936i
$852$	25.7846	+	1.62223i	0.883365	+	0.0555766i
$853$	−3.62971	−	6.60242i	−0.124279	−	0.226063i	0.806847	−	0.590761i	$-0.201172\pi$
$853$	−3.62971	−	6.60242i	−0.124279	−	0.226063i	−0.931126	+	0.364698i	$0.881172\pi$
$854$	−2.44728	+	5.20074i	−0.0837443	+	0.177966i
$855$		0			0
$856$	1.55316	−	8.14193i	0.0530858	−	0.278285i
$857$	−3.76915	−	5.18779i	−0.128752	−	0.177212i	0.739774	−	0.672855i	$-0.234932\pi$
$857$	−3.76915	−	5.18779i	−0.128752	−	0.177212i	−0.868526	+	0.495643i	$0.834932\pi$
$858$	2.51599	−	4.57657i	0.0858945	−	0.156241i
$859$	−18.8986	+	29.7795i	−0.644812	+	1.01606i	0.351978	+	0.936008i	$0.385509\pi$
$859$	−18.8986	+	29.7795i	−0.644812	+	1.01606i	−0.996791	+	0.0800535i	$0.974491\pi$
$860$		0			0
$861$	2.22202	+	0.879760i	0.0757262	+	0.0299821i
$862$	4.47860	+	11.3116i	0.152542	+	0.385276i
$863$	25.1536	−	20.8089i	0.856239	−	0.708343i	−0.101854	−	0.994799i	$-0.532477\pi$
$863$	25.1536	−	20.8089i	0.856239	−	0.708343i	0.958093	+	0.286456i	$0.0924774\pi$
$864$	−11.8912	+	3.05314i	−0.404547	+	0.103870i
$865$		0			0
$866$	−0.803608	+	0.318171i	−0.0273077	+	0.0108119i
$867$	−6.54620	−	6.97100i	−0.222321	−	0.236748i
$868$	0.367588	−	0.505941i	0.0124767	−	0.0171728i
$869$	0.646457	+	1.37379i	0.0219296	+	0.0466027i
$870$		0			0
$871$	−3.02544	+	1.66325i	−0.102513	+	0.0563571i
$872$	31.4831	−	6.00572i	1.06615	−	0.203379i
$873$	3.55649	+	13.8516i	0.120369	+	0.468806i
$874$	29.7712			1.00702
$875$		0			0
$876$	−10.3631			−0.350138
$877$	0.975894	+	3.80086i	0.0329536	+	0.128346i	0.982932	−	0.183971i	$-0.0588951\pi$
$877$	0.975894	+	3.80086i	0.0329536	+	0.128346i	−0.949978	+	0.312316i	$0.898895\pi$
$878$	18.9024	−	3.60582i	0.637925	−	0.121691i
$879$	9.37024	−	5.15133i	0.316050	−	0.173750i
$880$		0			0
$881$	9.80316	+	20.8328i	0.330277	+	0.701874i	0.999138	−	0.0415135i	$-0.0132180\pi$
$881$	9.80316	+	20.8328i	0.330277	+	0.701874i	−0.668861	+	0.743387i	$0.733218\pi$
$882$	−11.9260	+	16.4148i	−0.401571	+	0.552715i
$883$	−3.61276	−	3.84719i	−0.121579	−	0.129468i	0.665299	−	0.746577i	$-0.268304\pi$
$883$	−3.61276	−	3.84719i	−0.121579	−	0.129468i	−0.786878	+	0.617108i	$0.788304\pi$
$884$	29.5311	−	11.6922i	0.993239	−	0.393251i
$885$		0			0
$886$	−12.5852	+	3.23133i	−0.422809	+	0.108559i
$887$	−7.10261	+	5.87579i	−0.238482	+	0.197290i	−0.748986	−	0.662586i	$-0.769459\pi$
$887$	−7.10261	+	5.87579i	−0.238482	+	0.197290i	0.510504	+	0.859876i	$0.329459\pi$
$888$	7.92675	+	20.0207i	0.266004	+	0.671850i
$889$	8.90437	+	3.52549i	0.298643	+	0.118241i
$890$		0			0
$891$	1.21274	−	1.91097i	0.0406282	−	0.0640198i
$892$	1.69024	−	3.07454i	0.0565936	−	0.102943i
$893$	−46.7321	−	64.3212i	−1.56383	−	2.15243i
$894$	−6.89772	+	36.1591i	−0.230694	+	1.20934i
$895$		0			0
$896$	2.37756	−	5.05258i	0.0794288	−	0.168795i
$897$	48.9735	+	89.0824i	1.63518	+	2.97437i
$898$	−32.6367	−	2.05333i	−1.08910	−	0.0685205i
$899$	2.32533	+	1.68945i	0.0775539	+	0.0563462i
$900$		0			0
$901$	7.74097	−	5.62414i	0.257889	−	0.187367i
$902$	−0.369867	+	0.234725i	−0.0123152	+	0.00781548i
$903$	−2.08603	+	16.5127i	−0.0694189	+	0.549507i
$904$	−10.3677	−	1.30975i	−0.344826	−	0.0435617i
$905$		0			0
$906$	14.3247	+	7.87506i	0.475905	+	0.261631i
$907$	3.76051	+	1.22187i	0.124866	+	0.0405714i	0.370783	−	0.928719i	$-0.379089\pi$
$907$	3.76051	+	1.22187i	0.124866	+	0.0405714i	−0.245918	+	0.969291i	$0.579089\pi$
$908$	25.2529	−	11.8831i	0.838045	−	0.394354i
$909$	10.9855	+	2.82059i	0.364365	+	0.0935530i
$910$		0			0
$911$	8.09385	−	9.78378i	0.268161	−	0.324151i	−0.619194	−	0.785238i	$-0.712540\pi$
$911$	8.09385	−	9.78378i	0.268161	−	0.324151i	0.887355	+	0.461087i	$0.152540\pi$
$912$	6.70060	+	4.25233i	0.221879	+	0.140809i
$913$	3.26592	−	0.205474i	0.108086	−	0.00680020i
$914$	0.788762	+	1.24289i	0.0260899	+	0.0411111i
$915$		0			0
$916$	−1.89675	−	30.1479i	−0.0626703	−	0.996116i
$917$	−0.639263	−	0.121946i	−0.0211103	−	0.00402701i
$918$	5.93203	−	1.92743i	0.195786	−	0.0636148i
$919$	36.1633	−	33.9596i	1.19292	−	1.12022i	0.202910	−	0.979197i	$-0.434960\pi$
$919$	36.1633	−	33.9596i	1.19292	−	1.12022i	0.990006	−	0.141025i	$-0.0450398\pi$
$920$		0			0
$921$	−6.92238	−	36.2884i	−0.228100	−	1.19574i
$922$	−17.1805	+	18.2953i	−0.565808	+	0.602525i
$923$	−17.5293	+	44.2740i	−0.576985	+	1.45730i
$924$	−0.268230	−	0.825528i	−0.00882413	−	0.0271579i
$925$		0			0
$926$	−3.12505	+	9.61791i	−0.102695	+	0.316064i
$927$	−50.1072	−	41.4522i	−1.64573	−	1.36147i
$928$	21.0522	+	9.90639i	0.691071	+	0.325193i
$929$	2.28208	+	2.14301i	0.0748725	+	0.0703099i	0.721080	−	0.692852i	$-0.243646\pi$
$929$	2.28208	+	2.14301i	0.0748725	+	0.0703099i	−0.646208	+	0.763162i	$0.723646\pi$
$930$		0			0
$931$	39.8683	−	5.03654i	1.30663	−	0.165066i
$932$			20.7676i			0.680266i
$933$	−5.31590	−	42.0797i	−0.174035	−	1.37763i
$934$	−1.87827	−	2.27044i	−0.0614590	−	0.0742912i
$935$		0			0
$936$	4.18764	−	66.5606i	0.136877	−	2.17560i
$937$	−5.33639	+	20.7839i	−0.174332	+	0.678979i	0.819972	+	0.572403i	$0.193989\pi$
$937$	−5.33639	+	20.7839i	−0.174332	+	0.678979i	−0.994305	+	0.106576i	$0.966011\pi$
$938$	0.0695256	−	0.270784i	0.00227009	−	0.00884143i
$939$	4.94624	−	78.6183i	0.161415	−	2.56561i
$940$		0			0
$941$	32.1242	+	38.8315i	1.04722	+	1.26587i	0.963022	+	0.269422i	$0.0868326\pi$
$941$	32.1242	+	38.8315i	1.04722	+	1.26587i	0.0841974	+	0.996449i	$0.473167\pi$
$942$	3.87062	+	30.6391i	0.126112	+	0.998277i
$943$		−	8.52681i		−	0.277671i
$944$	−1.15511	+	0.145925i	−0.0375957	+	0.00474944i
$945$		0			0
$946$	−2.22397	−	2.08845i	−0.0723076	−	0.0679014i
$947$	−49.7149	−	23.3940i	−1.61552	−	0.760204i	−0.615898	−	0.787826i	$-0.711207\pi$
$947$	−49.7149	−	23.3940i	−1.61552	−	0.760204i	−0.999618	+	0.0276221i	$0.991207\pi$
$948$	10.7375	+	8.88283i	0.348737	+	0.288501i
$949$	5.90236	−	18.1656i	0.191599	−	0.589680i
$950$		0			0
$951$	−3.76549	−	11.5890i	−0.122104	−	0.375798i
$952$	−2.35484	+	5.94765i	−0.0763209	+	0.192765i
$953$	21.5643	−	22.9637i	0.698537	−	0.743866i	−0.277677	−	0.960674i	$-0.589565\pi$
$953$	21.5643	−	22.9637i	0.698537	−	0.743866i	0.976214	+	0.216808i	$0.0695646\pi$
$954$	−1.51365	−	7.93483i	−0.0490062	−	0.256900i
$955$		0			0
$956$	−4.85993	+	4.56378i	−0.157181	+	0.147603i
$957$	3.79416	−	1.23280i	0.122648	−	0.0398507i
$958$	−19.9655	−	3.80863i	−0.645057	−	0.123051i
$959$	−0.0676000	−	1.07447i	−0.00218292	−	0.0346965i
$960$		0			0
$961$	−16.3338	−	25.7380i	−0.526898	−	0.830258i
$962$	−15.9251	+	1.00192i	−0.513447	+	0.0323033i
$963$	−9.84507	−	6.24787i	−0.317253	−	0.201335i
$964$	−4.84488	+	5.85646i	−0.156043	+	0.188624i
$965$		0			0
$966$	−7.97309	−	2.04714i	−0.256530	−	0.0658657i
$967$	44.8772	−	21.1176i	1.44315	−	0.679097i	0.464682	−	0.885478i	$-0.346169\pi$
$967$	44.8772	−	21.1176i	1.44315	−	0.679097i	0.978472	+	0.206381i	$0.0661686\pi$
$968$	−27.9477	−	9.08075i	−0.898273	−	0.291866i
$969$	−50.9843	−	28.0288i	−1.63785	−	0.900416i
$970$		0			0
$971$	−11.3774	−	1.43730i	−0.365117	−	0.0461250i	−0.0593655	−	0.998236i	$-0.518908\pi$
$971$	−11.3774	−	1.43730i	−0.365117	−	0.0461250i	−0.305752	+	0.952111i	$0.598908\pi$
$972$	3.67060	−	29.0558i	0.117734	−	0.931964i
$973$	0.0342750	−	0.0217516i	0.00109881	−	0.000697323i
$974$	3.69701	−	2.68604i	0.118460	−	0.0860662i
$975$		0			0
$976$	4.42264	+	3.21323i	0.141565	+	0.102853i
$977$	18.1149	+	1.13969i	0.579546	+	0.0364620i	0.349859	−	0.936802i	$-0.386230\pi$
$977$	18.1149	+	1.13969i	0.579546	+	0.0364620i	0.229688	+	0.973264i	$0.426230\pi$
$978$	12.2573	+	22.2960i	0.391946	+	0.712948i
$979$	−1.28653	+	2.73402i	−0.0411177	+	0.0873795i
$980$		0			0
$981$	8.44858	−	44.2890i	0.269742	−	1.41404i
$982$	9.38818	+	12.9217i	0.299589	+	0.412349i
$983$	21.0856	−	38.3546i	0.672527	−	1.22332i	−0.291259	−	0.956644i	$-0.594074\pi$
$983$	21.0856	−	38.3546i	0.672527	−	1.22332i	0.963786	−	0.266678i	$-0.0859260\pi$
$984$	−5.35844	+	8.44355i	−0.170821	+	0.269171i
$985$		0			0
$986$	−10.9905	−	4.35145i	−0.350009	−	0.138578i
$987$	8.09255	+	20.4394i	0.257589	+	0.650595i
$988$	−40.9196	+	33.8516i	−1.30183	+	1.07696i
$989$	57.5188	−	14.7683i	1.82899	−	0.469605i
$990$		0			0
$991$	−29.9351	+	11.8522i	−0.950921	+	0.376496i	−0.791812	−	0.610765i	$-0.790862\pi$
$991$	−29.9351	+	11.8522i	−0.950921	+	0.376496i	−0.159109	+	0.987261i	$0.550862\pi$
$992$	2.86254	+	3.04829i	0.0908857	+	0.0967834i
$993$	−10.1916	+	14.0276i	−0.323421	+	0.445151i
$994$	−1.64176	−	3.48891i	−0.0520734	−	0.110662i
$995$		0			0
$996$	26.3201	−	14.4696i	0.833983	−	0.458486i
$997$	6.30879	−	1.20347i	0.199801	−	0.0381142i	−0.0865090	−	0.996251i	$-0.527571\pi$
$997$	6.30879	−	1.20347i	0.199801	−	0.0381142i	0.286310	+	0.958137i	$0.407571\pi$
$998$	−4.49859	−	17.5209i	−0.142400	−	0.554613i
$999$	6.43168			0.203489

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	625.2.h.b.274.13		440
5.2	odd	4		625.2.g.a.351.4		220
5.3	odd	4		125.2.g.a.21.8	yes	220
5.4	even	2	inner	625.2.h.b.274.10		440
125.6	even	25	inner	625.2.h.b.349.10		440
125.33	odd	100		125.2.g.a.6.8	✓	220
125.92	odd	100		625.2.g.a.276.4		220
125.119	even	50	inner	625.2.h.b.349.13		440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
125.2.g.a.6.8	✓	220	125.33	odd	100
125.2.g.a.21.8	yes	220	5.3	odd	4
625.2.g.a.276.4		220	125.92	odd	100
625.2.g.a.351.4		220	5.2	odd	4
625.2.h.b.274.10		440	5.4	even	2	inner
625.2.h.b.274.13		440	1.1	even	1	trivial
625.2.h.b.349.10		440	125.6	even	25	inner
625.2.h.b.349.13		440	125.119	even	50	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:	\( N \)	\(=\)	\( 625 = 5^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	625.h (of order \(50\), degree \(20\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.201300 + 0.784012i) q^{2} +(-2.56313 + 0.488943i) q^{3} +(1.17846 - 0.647864i) q^{4} +(-0.899294 - 1.91110i) q^{6} +(0.380304 - 0.523443i) q^{7} +(1.85336 + 1.97363i) q^{8} +(3.54123 - 1.40207i) q^{9} +O(q^{10})\)	\(q+(0.201300 + 0.784012i) q^{2} +(-2.56313 + 0.488943i) q^{3} +(1.17846 - 0.647864i) q^{4} +(-0.899294 - 1.91110i) q^{6} +(0.380304 - 0.523443i) q^{7} +(1.85336 + 1.97363i) q^{8} +(3.54123 - 1.40207i) q^{9} +(-0.370305 + 0.0950783i) q^{11} +(-2.70378 + 2.23676i) q^{12} +(-2.38088 - 6.01342i) q^{13} +(0.486940 + 0.192793i) q^{14} +(0.266898 - 0.420564i) q^{16} +(-1.75924 + 3.20004i) q^{17} +(1.81209 + 2.49413i) q^{18} +(1.14413 - 5.99774i) q^{19} +(-0.718833 + 1.52760i) q^{21} +(-0.149085 - 0.271185i) q^{22} +(6.01178 + 0.378229i) q^{23} +(-5.71539 - 4.15247i) q^{24} +(4.23532 - 3.07714i) q^{26} +(-1.78165 + 1.13067i) q^{27} +(0.109053 - 0.863242i) q^{28} +(3.96750 + 0.501211i) q^{29} +(0.629836 + 0.346255i) q^{31} +(5.53328 + 1.79787i) q^{32} +(0.902652 - 0.424756i) q^{33} +(-2.86300 - 0.735094i) q^{34} +(3.26485 - 3.94652i) q^{36} +(-2.57349 - 1.63319i) q^{37} +(4.93261 - 0.310334i) q^{38} +(9.04272 + 14.2491i) q^{39} +(-0.0888833 - 1.41276i) q^{41} +(-1.34236 - 0.256068i) q^{42} +(9.37601 - 3.04645i) q^{43} +(-0.374793 + 0.351954i) q^{44} +(0.913635 + 4.78944i) q^{46} +(8.91355 - 9.49196i) q^{47} +(-0.478462 + 1.20846i) q^{48} +(2.03376 + 6.25926i) q^{49} +(2.94451 - 9.06227i) q^{51} +(-6.70166 - 5.54409i) q^{52} +(-2.37085 - 1.11564i) q^{53} +(-1.24511 - 1.16923i) q^{54} +(1.73792 - 0.219550i) q^{56} +15.9324i q^{57} +(0.405701 + 3.21146i) q^{58} +(-1.48994 - 1.80103i) q^{59} +(-0.689122 + 10.9533i) q^{61} +(-0.144682 + 0.563500i) q^{62} +(0.612837 - 2.38684i) q^{63} +(-0.233151 + 3.70582i) q^{64} +(0.514718 + 0.622187i) q^{66} +(-0.0669046 - 0.529604i) q^{67} +4.91087i q^{68} +(-15.5939 + 1.96997i) q^{69} +(-5.36705 - 5.04000i) q^{71} +(9.33033 + 4.39052i) q^{72} +(2.27552 + 1.88247i) q^{73} +(0.762395 - 2.34641i) q^{74} +(-2.53741 - 7.80934i) q^{76} +(-0.0910604 + 0.229992i) q^{77} +(-9.35112 + 9.95794i) q^{78} +(-0.744146 - 3.90095i) q^{79} +(-4.31547 + 4.05249i) q^{81} +(1.08973 - 0.354074i) q^{82} +(-8.40773 - 1.60386i) q^{83} +(0.142560 + 2.26592i) q^{84} +(4.27585 + 6.73765i) q^{86} +(-10.4143 + 0.655210i) q^{87} +(-0.873958 - 0.554631i) q^{88} +(5.03780 - 6.08965i) q^{89} +(-4.05314 - 1.04067i) q^{91} +(7.32969 - 3.44909i) q^{92} +(-1.78365 - 0.579543i) q^{93} +(9.23611 + 5.07759i) q^{94} +(-15.0616 - 1.90272i) q^{96} +(-0.470603 + 3.72521i) q^{97} +(-4.49794 + 2.85448i) q^{98} +(-1.17803 + 0.855889i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 440 q + 40 q^{4} - 40 q^{6} + 40 q^{9}+O(q^{10}) \) 440 * q + 40 * q^4 - 40 * q^6 + 40 * q^9	\( 440 q + 40 q^{4} - 40 q^{6} + 40 q^{9} - 30 q^{11} + 20 q^{14} + 20 q^{19} - 10 q^{21} - 30 q^{24} + 30 q^{26} + 20 q^{29} - 20 q^{31} - 10 q^{34} - 420 q^{36} - 10 q^{41} - 30 q^{44} + 40 q^{49} + 50 q^{51} - 120 q^{54} - 210 q^{56} - 10 q^{59} - 90 q^{64} + 110 q^{66} - 80 q^{69} - 170 q^{71} - 70 q^{74} + 70 q^{76} + 110 q^{81} - 230 q^{84} + 80 q^{86} - 110 q^{89} - 210 q^{91} - 120 q^{94} + 270 q^{96} - 90 q^{99}+O(q^{100}) \) 440 * q + 40 * q^4 - 40 * q^6 + 40 * q^9 - 30 * q^11 + 20 * q^14 + 20 * q^19 - 10 * q^21 - 30 * q^24 + 30 * q^26 + 20 * q^29 - 20 * q^31 - 10 * q^34 - 420 * q^36 - 10 * q^41 - 30 * q^44 + 40 * q^49 + 50 * q^51 - 120 * q^54 - 210 * q^56 - 10 * q^59 - 90 * q^64 + 110 * q^66 - 80 * q^69 - 170 * q^71 - 70 * q^74 + 70 * q^76 + 110 * q^81 - 230 * q^84 + 80 * q^86 - 110 * q^89 - 210 * q^91 - 120 * q^94 + 270 * q^96 - 90 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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