LMFDB - Embedded newform 625.2.h.b.24.19

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			24.19
Character	$\chi$	$=$	625.24
Dual form			625.2.h.b.599.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.60169 + 1.32504i) q^{2} +(0.307726 - 2.43590i) q^{3} +(0.434938 + 2.28002i) q^{4} +(3.72054 - 3.49382i) q^{6} +(0.457412 - 0.629574i) q^{7} +(-0.321599 + 0.584987i) q^{8} +(-2.93319 - 0.753115i) q^{9} +O(q^{10})$	\(q+(1.60169 + 1.32504i) q^{2} +(0.307726 - 2.43590i) q^{3} +(0.434938 + 2.28002i) q^{4} +(3.72054 - 3.49382i) q^{6} +(0.457412 - 0.629574i) q^{7} +(-0.321599 + 0.584987i) q^{8} +(-2.93319 - 0.753115i) q^{9} +(2.06052 - 2.49074i) q^{11} +(5.68776 - 0.357844i) q^{12} +(-0.789285 + 3.07406i) q^{13} +(1.56684 - 0.402296i) q^{14} +(3.02605 - 1.19810i) q^{16} +(-6.10458 - 1.16451i) q^{17} +(-3.70016 - 5.09284i) q^{18} +(4.38516 - 0.553975i) q^{19} +(-1.39282 - 1.30795i) q^{21} +(6.60063 - 1.25914i) q^{22} +(4.53094 - 2.87542i) q^{23} +(1.32601 + 0.963402i) q^{24} +(-5.33743 + 3.87787i) q^{26} +(-0.0256046 + 0.0646699i) q^{27} +(1.63439 + 0.769085i) q^{28} +(-2.56070 + 5.44177i) q^{29} +(0.00238475 - 0.0125013i) q^{31} +(7.70409 + 2.50321i) q^{32} +(-5.43313 - 5.78569i) q^{33} +(-8.23465 - 9.95398i) q^{34} +(0.441365 - 7.01530i) q^{36} +(-2.70952 - 6.84347i) q^{37} +(7.75772 + 4.92320i) q^{38} +(7.24524 + 2.86859i) q^{39} +(-6.20373 + 9.77552i) q^{41} +(-0.497797 - 3.94047i) q^{42} +(-5.43498 + 1.76593i) q^{43} +(6.57514 + 3.61471i) q^{44} +(11.0672 + 1.39811i) q^{46} +(3.22228 + 5.86131i) q^{47} +(-1.98725 - 7.73985i) q^{48} +(1.97598 + 6.08145i) q^{49} +(-4.71518 + 14.5118i) q^{51} +(-7.35223 - 0.462563i) q^{52} +(-1.64907 + 1.75608i) q^{53} +(-0.126701 + 0.0696543i) q^{54} +(0.221189 + 0.470051i) q^{56} -10.8523i q^{57} +(-11.3120 + 5.32302i) q^{58} +(-0.0986283 - 1.56765i) q^{59} +(7.16121 + 11.2843i) q^{61} +(0.0203843 - 0.0168634i) q^{62} +(-1.81582 + 1.50217i) q^{63} +(5.53494 + 8.72167i) q^{64} +(-1.03595 - 16.4660i) q^{66} +(-8.43161 + 3.96761i) q^{67} -14.4251i q^{68} +(-5.60996 - 11.9218i) q^{69} +(4.47304 - 2.45907i) q^{71} +(1.38387 - 1.47368i) q^{72} +(10.0839 + 0.634423i) q^{73} +(4.72802 - 14.5513i) q^{74} +(3.17035 + 9.75733i) q^{76} +(-0.625598 - 2.43654i) q^{77} +(7.80366 + 14.1948i) q^{78} +(-1.81498 - 0.229286i) q^{79} +(-7.81158 - 4.29445i) q^{81} +(-22.8894 + 7.43721i) q^{82} +(0.488071 + 3.86348i) q^{83} +(2.37636 - 3.74455i) q^{84} +(-11.0451 - 4.37306i) q^{86} +(12.4676 + 7.91220i) q^{87} +(0.794389 + 2.00640i) q^{88} +(-0.254721 + 4.04868i) q^{89} +(1.57432 + 1.90303i) q^{91} +(8.52670 + 9.08002i) q^{92} +(-0.0297182 - 0.00965601i) q^{93} +(-2.60534 + 13.6576i) q^{94} +(8.46833 - 17.9961i) q^{96} +(1.65242 + 0.777570i) q^{97} +(-4.89322 + 12.3589i) q^{98} +(-7.91970 + 5.75400i) 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 $\left(\mathbb{Z}/625\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{11}{50}\right)$

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 $

$2$	1.60169	+	1.32504i	1.13257	+	0.936941i	0.998539	−	0.0540360i	$-0.0172086\pi$
$2$	1.60169	+	1.32504i	1.13257	+	0.936941i	0.134029	+	0.990977i	$0.457209\pi$
$3$	0.307726	−	2.43590i	0.177666	−	1.40637i	−0.611040	−	0.791600i	$-0.709249\pi$
$3$	0.307726	−	2.43590i	0.177666	−	1.40637i	0.788706	−	0.614771i	$-0.210751\pi$
$4$	0.434938	+	2.28002i	0.217469	+	1.14001i
$5$		0			0
$5$		0			0
$6$	3.72054	−	3.49382i	1.51891	−	1.42635i
$7$	0.457412	−	0.629574i	0.172885	−	0.237956i	−0.713778	−	0.700372i	$-0.753017\pi$
$7$	0.457412	−	0.629574i	0.172885	−	0.237956i	0.886663	+	0.462416i	$0.153017\pi$
$8$	−0.321599	+	0.584987i	−0.113703	+	0.206824i
$9$	−2.93319	−	0.753115i	−0.977729	−	0.251038i
$10$		0			0
$11$	2.06052	−	2.49074i	0.621270	−	0.750986i	−0.362192	−	0.932104i	$-0.617971\pi$
$11$	2.06052	−	2.49074i	0.621270	−	0.750986i	0.983461	+	0.181118i	$0.0579715\pi$
$12$	5.68776	−	0.357844i	1.64192	−	0.103301i
$13$	−0.789285	+	3.07406i	−0.218908	+	0.852592i	0.760273	+	0.649604i	$0.225065\pi$
$13$	−0.789285	+	3.07406i	−0.218908	+	0.852592i	−0.979181	+	0.202988i	$0.934935\pi$
$14$	1.56684	−	0.402296i	0.418756	−	0.107518i
$15$		0			0
$16$	3.02605	−	1.19810i	0.756512	−	0.299524i
$17$	−6.10458	−	1.16451i	−1.48058	−	0.282436i	−0.617126	−	0.786864i	$-0.711703\pi$
$17$	−6.10458	−	1.16451i	−1.48058	−	0.282436i	−0.863453	+	0.504429i	$0.831703\pi$
$18$	−3.70016	−	5.09284i	−0.872137	−	1.20039i
$19$	4.38516	−	0.553975i	1.00603	−	0.127091i	0.394983	−	0.918688i	$-0.370750\pi$
$19$	4.38516	−	0.553975i	1.00603	−	0.127091i	0.611042	+	0.791598i	$0.290750\pi$
$20$		0			0
$21$	−1.39282	−	1.30795i	−0.303939	−	0.285418i
$22$	6.60063	−	1.25914i	1.40726	−	0.268449i
$23$	4.53094	−	2.87542i	0.944766	−	0.599567i	0.0282655	−	0.999600i	$-0.491002\pi$
$23$	4.53094	−	2.87542i	0.944766	−	0.599567i	0.916500	+	0.400034i	$0.131002\pi$
$24$	1.32601	+	0.963402i	0.270670	+	0.196654i
$25$		0			0
$26$	−5.33743	+	3.87787i	−1.04676	+	0.760513i
$27$	−0.0256046	+	0.0646699i	−0.00492761	+	0.0124457i
$28$	1.63439	+	0.769085i	0.308870	+	0.145343i
$29$	−2.56070	+	5.44177i	−0.475510	+	1.01051i	0.512864	+	0.858470i	$0.328584\pi$
$29$	−2.56070	+	5.44177i	−0.475510	+	1.01051i	−0.988374	+	0.152041i	$0.951416\pi$
$30$		0			0
$31$	0.00238475	−	0.0125013i	0.000428314	−	0.00224530i	−0.982072	−	0.188504i	$-0.939636\pi$
$31$	0.00238475	−	0.0125013i	0.000428314	−	0.00224530i	0.982501	+	0.186259i	$0.0596362\pi$
$32$	7.70409	+	2.50321i	1.36190	+	0.442509i
$33$	−5.43313	−	5.78569i	−0.945786	−	1.00716i
$34$	−8.23465	−	9.95398i	−1.41223	−	1.70709i
$35$		0			0
$36$	0.441365	−	7.01530i	0.0735608	−	1.16922i
$37$	−2.70952	−	6.84347i	−0.445443	−	1.12506i	−0.963022	−	0.269424i	$-0.913167\pi$
$37$	−2.70952	−	6.84347i	−0.445443	−	1.12506i	0.517579	−	0.855635i	$-0.326833\pi$
$38$	7.75772	+	4.92320i	1.25847	+	0.798648i
$39$	7.24524	+	2.86859i	1.16017	+	0.459343i
$40$		0			0
$41$	−6.20373	+	9.77552i	−0.968861	+	1.52668i	−0.123596	+	0.992333i	$0.539443\pi$
$41$	−6.20373	+	9.77552i	−0.968861	+	1.52668i	−0.845265	+	0.534347i	$0.820557\pi$
$42$	−0.497797	−	3.94047i	−0.0768118	−	0.608028i
$43$	−5.43498	+	1.76593i	−0.828827	+	0.269302i	−0.692551	−	0.721369i	$-0.743513\pi$
$43$	−5.43498	+	1.76593i	−0.828827	+	0.269302i	−0.136276	+	0.990671i	$0.543513\pi$
$44$	6.57514	+	3.61471i	0.991240	+	0.544939i
$45$		0			0
$46$	11.0672	+	1.39811i	1.63177	+	0.206141i
$47$	3.22228	+	5.86131i	0.470018	+	0.854959i	0.999976	+	0.00693559i	$0.00220769\pi$
$47$	3.22228	+	5.86131i	0.470018	+	0.854959i	−0.529958	+	0.848024i	$0.677792\pi$
$48$	−1.98725	−	7.73985i	−0.286836	−	1.11715i
$49$	1.97598	+	6.08145i	0.282283	+	0.868778i
$50$		0			0
$51$	−4.71518	+	14.5118i	−0.660258	+	2.03206i
$52$	−7.35223	−	0.462563i	−1.01957	−	0.0641459i
$53$	−1.64907	+	1.75608i	−0.226518	+	0.241217i	−0.832181	−	0.554504i	$-0.812908\pi$
$53$	−1.64907	+	1.75608i	−0.226518	+	0.241217i	0.605663	+	0.795721i	$0.292908\pi$
$54$	−0.126701	+	0.0696543i	−0.0172418	+	0.00947875i
$55$		0			0
$56$	0.221189	+	0.470051i	0.0295576	+	0.0628132i
$57$		−	10.8523i		−	1.43742i
$58$	−11.3120	+	5.32302i	−1.48534	+	0.698946i
$59$	−0.0986283	−	1.56765i	−0.0128403	−	0.204091i	−0.999216	−	0.0395840i	$-0.987397\pi$
$59$	−0.0986283	−	1.56765i	−0.0128403	−	0.204091i	0.986376	−	0.164507i	$-0.0526033\pi$
$60$		0			0
$61$	7.16121	+	11.2843i	0.916899	+	1.44480i	0.895516	+	0.445030i	$0.146807\pi$
$61$	7.16121	+	11.2843i	0.916899	+	1.44480i	0.0213827	+	0.999771i	$0.493193\pi$
$62$	0.0203843	−	0.0168634i	0.00258881	−	0.00214165i
$63$	−1.81582	+	1.50217i	−0.228771	+	0.189256i
$64$	5.53494	+	8.72167i	0.691868	+	1.09021i
$65$		0			0
$66$	−1.03595	−	16.4660i	−0.127517	−	2.02682i
$67$	−8.43161	+	3.96761i	−1.03009	+	0.484721i	−0.865113	−	0.501577i	$-0.832753\pi$
$67$	−8.43161	+	3.96761i	−1.03009	+	0.484721i	−0.164972	+	0.986298i	$0.552753\pi$
$68$		−	14.4251i		−	1.74930i
$69$	−5.60996	−	11.9218i	−0.675360	−	1.43521i
$70$		0			0
$71$	4.47304	−	2.45907i	0.530852	−	0.291838i	−0.193697	−	0.981061i	$-0.562048\pi$
$71$	4.47304	−	2.45907i	0.530852	−	0.291838i	0.724549	+	0.689223i	$0.242048\pi$
$72$	1.38387	−	1.47368i	0.163091	−	0.173674i
$73$	10.0839	+	0.634423i	1.18023	+	0.0742536i	0.640752	−	0.767748i	$-0.278623\pi$
$73$	10.0839	+	0.634423i	1.18023	+	0.0742536i	0.539476	+	0.842001i	$0.318623\pi$
$74$	4.72802	−	14.5513i	0.549621	−	1.69156i
$75$		0			0
$76$	3.17035	+	9.75733i	0.363664	+	1.11924i
$77$	−0.625598	−	2.43654i	−0.0712935	−	0.277670i
$78$	7.80366	+	14.1948i	0.883591	+	1.60725i
$79$	−1.81498	−	0.229286i	−0.204201	−	0.0257966i	0.0225670	−	0.999745i	$-0.492816\pi$
$79$	−1.81498	−	0.229286i	−0.204201	−	0.0257966i	−0.226769	+	0.973949i	$0.572816\pi$
$80$		0			0
$81$	−7.81158	−	4.29445i	−0.867954	−	0.477162i
$82$	−22.8894	+	7.43721i	−2.52771	+	0.821303i
$83$	0.488071	+	3.86348i	0.0535727	+	0.424072i	0.995978	+	0.0895985i	$0.0285584\pi$
$83$	0.488071	+	3.86348i	0.0535727	+	0.424072i	−0.942405	+	0.334473i	$0.891442\pi$
$84$	2.37636	−	3.74455i	0.259282	−	0.408564i
$85$		0			0
$86$	−11.0451	−	4.37306i	−1.19102	−	0.471560i
$87$	12.4676	+	7.91220i	1.33667	+	0.848277i
$88$	0.794389	+	2.00640i	0.0846821	+	0.213883i
$89$	−0.254721	+	4.04868i	−0.0270004	+	0.429159i	0.961186	+	0.275902i	$0.0889764\pi$
$89$	−0.254721	+	4.04868i	−0.0270004	+	0.429159i	−0.988186	+	0.153257i	$0.951024\pi$
$90$		0			0
$91$	1.57432	+	1.90303i	0.165034	+	0.199491i
$92$	8.52670	+	9.08002i	0.888970	+	0.946657i
$93$	−0.0297182	−	0.00965601i	−0.00308163	−	0.00100128i
$94$	−2.60534	+	13.6576i	−0.268720	+	1.40868i
$95$		0			0
$96$	8.46833	−	17.9961i	0.864296	−	1.83672i
$97$	1.65242	+	0.777570i	0.167778	+	0.0789502i	0.507834	−	0.861455i	$-0.330446\pi$
$97$	1.65242	+	0.777570i	0.167778	+	0.0789502i	−0.340057	+	0.940405i	$0.610446\pi$
$98$	−4.89322	+	12.3589i	−0.494289	+	1.24843i
$99$	−7.91970	+	5.75400i	−0.795960	+	0.578299i
$100$		0			0
$101$	−0.242135	−	0.175921i	−0.0240933	−	0.0175048i	0.575673	−	0.817680i	$-0.304740\pi$
$101$	−0.242135	−	0.175921i	−0.0240933	−	0.0175048i	−0.599767	+	0.800175i	$0.704740\pi$
$102$	−26.7810	+	16.9957i	−2.65171	+	1.68283i
$103$	−15.7165	+	2.99809i	−1.54860	+	0.295411i	−0.889602	−	0.456737i	$-0.849018\pi$
$103$	−15.7165	+	2.99809i	−1.54860	+	0.295411i	−0.658995	+	0.752148i	$0.729018\pi$
$104$	−1.54445	−	1.45034i	−0.151446	−	0.142217i
$105$		0			0
$106$	−4.96818	+	0.627627i	−0.482552	+	0.0609605i
$107$	−10.9431	−	15.0619i	−1.05791	−	1.45609i	−0.881745	−	0.471726i	$-0.843631\pi$
$107$	−10.9431	−	15.0619i	−1.05791	−	1.45609i	−0.176163	−	0.984361i	$-0.556369\pi$
$108$	−0.158585	−	0.0302518i	−0.0152599	−	0.00291098i
$109$	4.84439	−	1.91803i	0.464008	−	0.183714i	−0.124476	−	0.992223i	$-0.539725\pi$
$109$	4.84439	−	1.91803i	0.464008	−	0.183714i	0.588484	+	0.808509i	$0.299725\pi$
$110$		0			0
$111$	−17.5038	+	4.49422i	−1.66139	+	0.426573i
$112$	0.629860	−	2.45314i	0.0595162	−	0.231800i
$113$	−9.83875	+	0.619002i	−0.925552	+	0.0582308i	−0.518408	−	0.855133i	$-0.673475\pi$
$113$	−9.83875	+	0.619002i	−0.925552	+	0.0582308i	−0.407144	+	0.913364i	$0.633475\pi$
$114$	14.3797	−	17.3821i	1.34678	−	1.62798i
$115$		0			0
$116$	−13.5211	−	3.47163i	−1.25540	−	0.322333i
$117$	4.63024	−	8.42238i	0.428066	−	0.778649i
$118$	1.91922	−	2.64158i	0.176679	−	0.243177i
$119$	−3.52546	+	3.31062i	−0.323178	+	0.303484i
$120$		0			0
$121$	0.103150	+	0.540733i	0.00937731	+	0.0491576i
$122$	−3.48199	+	27.5628i	−0.315244	+	2.49542i
$123$	21.9032	+	18.1199i	1.97494	+	1.63382i
$124$	0.0295405			0.00265282
$125$		0			0
$126$	−4.89881			−0.436421
$127$	5.32035	+	4.40137i	0.472104	+	0.390559i	0.842827	−	0.538185i	$-0.180890\pi$
$127$	5.32035	+	4.40137i	0.472104	+	0.390559i	−0.370722	+	0.928744i	$0.620890\pi$
$128$	−0.660711	+	5.23007i	−0.0583992	+	0.462277i
$129$	2.62916	+	13.7825i	0.231484	+	1.21348i
$130$		0			0
$131$	−4.45323	+	4.18186i	−0.389080	+	0.365371i	−0.854260	−	0.519845i	$-0.825990\pi$
$131$	−4.45323	+	4.18186i	−0.389080	+	0.365371i	0.465180	+	0.885216i	$0.345990\pi$
$132$	10.8284	−	14.9041i	0.942495	−	1.29723i
$133$	1.65706	−	3.01418i	0.143685	−	0.261362i
$134$	−18.7621	−	4.81728i	−1.62080	−	0.416150i
$135$		0			0
$136$	2.64446	−	3.19660i	0.226760	−	0.274106i
$137$	13.4573	−	0.846660i	1.14973	−	0.0723351i	0.523539	−	0.852002i	$-0.324612\pi$
$137$	13.4573	−	0.846660i	1.14973	−	0.0723351i	0.626195	+	0.779667i	$0.284612\pi$
$138$	6.81134	−	26.5284i	0.579820	−	2.25825i
$139$	−5.66146	+	1.45362i	−0.480199	+	0.123294i	−0.481027	−	0.876706i	$-0.659736\pi$
$139$	−5.66146	+	1.45362i	−0.480199	+	0.123294i	0.000828731		1.00000i	$0.499736\pi$
$140$		0			0
$141$	15.2692	−	6.04549i	1.28590	−	0.509122i
$142$	10.4228	+	1.98825i	0.874661	+	0.166850i
$143$	6.03035	+	8.30007i	0.504283	+	0.694086i
$144$	−9.77827	+	1.23528i	−0.814856	+	0.102940i
$145$		0			0
$146$	15.3106	+	14.3776i	1.26712	+	1.18990i
$147$	15.4219	−	2.94188i	1.27198	−	0.242642i
$148$	14.4248	−	9.15426i	1.18571	−	0.752475i
$149$	−14.9590	−	10.8683i	−1.22549	−	0.890370i	−0.228945	−	0.973439i	$-0.573528\pi$
$149$	−14.9590	−	10.8683i	−1.22549	−	0.890370i	−0.996544	+	0.0830697i	$0.973528\pi$
$150$		0			0
$151$	16.0977	−	11.6956i	1.31001	−	0.951778i	0.310010	−	0.950733i	$-0.399668\pi$
$151$	16.0977	−	11.6956i	1.31001	−	0.951778i	0.999999	−	0.00104421i	$-0.000332383\pi$
$152$	−1.08620	+	2.74342i	−0.0881023	+	0.222521i
$153$	17.0289	+	8.01318i	1.37670	+	0.647828i
$154$	2.22649	−	4.73153i	0.179416	−	0.381278i
$155$		0			0
$156$	−3.38923	+	17.7670i	−0.271356	+	1.42250i
$157$	1.28248	+	0.416703i	0.102353	+	0.0332566i	0.359746	−	0.933050i	$-0.382863\pi$
$157$	1.28248	+	0.416703i	0.102353	+	0.0332566i	−0.257393	+	0.966307i	$0.582863\pi$
$158$	−2.60323	−	2.77216i	−0.207102	−	0.220541i
$159$	3.77019	+	4.55738i	0.298996	+	0.361424i
$160$		0			0
$161$	0.262216	−	4.16781i	0.0206656	−	0.328470i
$162$	−6.82145	−	17.2290i	−0.535944	−	1.35364i
$163$	−3.70060	−	2.34847i	−0.289854	−	0.183947i	0.382947	−	0.923770i	$-0.374909\pi$
$163$	−3.70060	−	2.34847i	−0.289854	−	0.183947i	−0.672801	+	0.739823i	$0.734909\pi$
$164$	−24.9867	−	9.89292i	−1.95113	−	0.772507i
$165$		0			0
$166$	−4.33750	+	6.83481i	−0.336656	+	0.530484i
$167$	0.700234	+	5.54292i	0.0541857	+	0.428924i	0.995750	+	0.0920922i	$0.0293554\pi$
$167$	0.700234	+	5.54292i	0.0541857	+	0.428924i	−0.941565	+	0.336832i	$0.890645\pi$
$168$	1.21306	−	0.394149i	0.0935900	−	0.0304092i
$169$	2.56510	+	1.41017i	0.197315	+	0.108475i
$170$		0			0
$171$	−13.2797	−	1.67762i	−1.01553	−	0.128291i
$172$	−6.39025	−	11.6238i	−0.487252	−	0.886308i
$173$	−3.58908	−	13.9786i	−0.272873	−	1.06277i	−0.946241	−	0.323463i	$-0.895153\pi$
$173$	−3.58908	−	13.9786i	−0.272873	−	1.06277i	0.673368	−	0.739308i	$-0.264847\pi$
$174$	9.48537	+	29.1930i	0.719084	+	2.21311i
$175$		0			0
$176$	3.25108	−	10.0058i	0.245059	−	0.754215i
$177$	−3.84900	−	0.242159i	−0.289309	−	0.0182018i
$178$	−5.77263	+	6.14722i	−0.432677	+	0.460754i
$179$	1.34083	−	0.737128i	0.100218	−	0.0550956i	−0.430856	−	0.902421i	$-0.641788\pi$
$179$	1.34083	−	0.737128i	0.100218	−	0.0550956i	0.531075	+	0.847325i	$0.321788\pi$
$180$		0			0
$181$	−1.67103	−	3.55112i	−0.124207	−	0.263952i	0.833047	−	0.553202i	$-0.186594\pi$
$181$	−1.67103	−	3.55112i	−0.124207	−	0.263952i	−0.957254	+	0.289250i	$0.906594\pi$
$182$			5.13409i			0.380564i
$183$	29.6911	−	13.9716i	2.19483	−	1.03281i
$184$	0.224937	+	3.57527i	0.0165826	+	0.263573i
$185$		0			0
$186$	−0.0348048	−	0.0548436i	−0.00255201	−	0.00402133i
$187$	−15.4791	+	12.8054i	−1.13194	+	0.936426i
$188$	−11.9624	+	9.89618i	−0.872450	+	0.721753i
$189$	0.0290026	+	0.0457008i	0.00210963	+	0.00332424i
$190$		0			0
$191$	−1.05847	−	16.8239i	−0.0765880	−	1.21733i	−0.829232	−	0.558904i	$-0.811222\pi$
$191$	−1.05847	−	16.8239i	−0.0765880	−	1.21733i	0.752644	−	0.658428i	$-0.228778\pi$
$192$	22.9484	−	10.7987i	1.65616	−	0.779329i
$193$		−	6.29614i		−	0.453206i	−0.973987	−	0.226603i	$-0.927238\pi$
$193$		−	6.29614i		−	0.453206i	0.973987	−	0.226603i	$-0.0727620\pi$
$194$	1.61636	+	3.43494i	0.116048	+	0.246614i
$195$		0			0
$196$	−13.0064	+	7.15034i	−0.929030	+	0.510738i
$197$	7.19757	−	7.66463i	0.512805	−	0.546082i	−0.419499	−	0.907756i	$-0.637794\pi$
$197$	7.19757	−	7.66463i	0.512805	−	0.546082i	0.932305	+	0.361673i	$0.117794\pi$
$198$	−20.3092	−	1.27775i	−1.44331	−	0.0908054i
$199$	−2.95165	+	9.08423i	−0.209237	+	0.643964i	0.790276	+	0.612751i	$0.209937\pi$
$199$	−2.95165	+	9.08423i	−0.209237	+	0.643964i	−0.999513	+	0.0312133i	$0.990063\pi$
$200$		0			0
$201$	7.07010	+	21.7595i	0.498687	+	1.53480i
$202$	−0.154724	−	0.602610i	−0.0108863	−	0.0423995i
$203$	2.25470	+	4.10128i	0.158249	+	0.287853i
$204$	−35.1381	−	4.43898i	−2.46016	−	0.310791i
$205$		0			0
$206$	−29.1456	−	16.0229i	−2.03067	−	1.11637i
$207$	−15.4556	+	5.02183i	−1.07424	+	0.349042i
$208$	1.29461	+	10.2479i	0.0897651	+	0.710564i
$209$	7.65590	−	12.0638i	0.529570	−	0.834468i
$210$		0			0
$211$	6.24127	+	2.47110i	0.429667	+	0.170117i	0.572996	−	0.819558i	$-0.305781\pi$
$211$	6.24127	+	2.47110i	0.429667	+	0.170117i	−0.143329	+	0.989675i	$0.545781\pi$
$212$	−4.72116	−	2.99614i	−0.324250	−	0.205776i
$213$	−4.61360	−	11.6526i	−0.316118	−	0.798424i
$214$	2.43005	−	38.6245i	0.166115	−	2.64032i
$215$		0			0
$216$	−0.0295966	−	0.0357762i	−0.00201380	−	0.00243426i
$217$	−0.00677968	−	0.00721963i	−0.000460235	−	0.000490100i
$218$	10.3007	+	3.34689i	0.697650	+	0.226680i
$219$	4.64847	−	24.3681i	0.314114	−	1.64665i
$220$		0			0
$221$	8.39804	−	17.8467i	0.564913	−	1.20050i
$222$	−33.9908	−	15.9948i	−2.28131	−	1.07350i
$223$	2.02160	−	5.10599i	0.135377	−	0.341922i	−0.846235	−	0.532809i	$-0.821136\pi$
$223$	2.02160	−	5.10599i	0.135377	−	0.341922i	0.981612	+	0.190887i	$0.0611364\pi$
$224$	5.09990	−	3.70529i	0.340751	−	0.247570i
$225$		0			0
$226$	−16.5789	−	12.0452i	−1.10281	−	0.801238i
$227$	15.2306	−	9.66561i	1.01089	−	0.641529i	0.0762352	−	0.997090i	$-0.475710\pi$
$227$	15.2306	−	9.66561i	1.01089	−	0.641529i	0.934653	+	0.355561i	$0.115710\pi$
$228$	24.7435	−	4.72008i	1.63868	−	0.312595i
$229$	−11.3947	−	10.7003i	−0.752984	−	0.707099i	0.209688	−	0.977768i	$-0.432755\pi$
$229$	−11.3947	−	10.7003i	−0.752984	−	0.707099i	−0.962672	+	0.270669i	$0.912755\pi$
$230$		0			0
$231$	−6.12770	+	0.774108i	−0.403173	+	0.0509326i
$232$	−2.35984	−	3.24805i	−0.154931	−	0.213245i
$233$	−18.5079	−	3.53056i	−1.21249	−	0.231295i	−0.458809	−	0.888535i	$-0.651724\pi$
$233$	−18.5079	−	3.53056i	−1.21249	−	0.231295i	−0.753681	+	0.657240i	$0.771724\pi$
$234$	18.5762	−	7.35483i	1.21436	−	0.480800i
$235$		0			0
$236$	3.53139	−	0.906706i	0.229874	−	0.0590215i
$237$	−1.11704	+	4.35057i	−0.0725593	+	0.282600i
$238$	−10.0334	+	0.631247i	−0.650368	+	0.0409177i
$239$	4.44545	−	5.37363i	0.287552	−	0.347591i	−0.606881	−	0.794793i	$-0.707579\pi$
$239$	4.44545	−	5.37363i	0.287552	−	0.347591i	0.894433	+	0.447202i	$0.147579\pi$
$240$		0			0
$241$	18.6366	+	4.78508i	1.20049	+	0.308234i	0.795424	−	0.606053i	$-0.207248\pi$
$241$	18.6366	+	4.78508i	1.20049	+	0.308234i	0.405068	+	0.914287i	$0.367248\pi$
$242$	−0.551275	+	1.00277i	−0.0354373	+	0.0644603i
$243$	−12.9874	+	17.8756i	−0.833140	+	1.14672i
$244$	−22.6137	+	21.2357i	−1.44769	+	1.35947i
$245$		0			0
$246$	11.0727	+	58.0450i	0.705968	+	3.70081i
$247$	−1.75819	+	13.9175i	−0.111871	+	0.885550i
$248$	0.00654617	+	0.00541547i	0.000415682	+	0.000343882i
$249$	9.56126			0.605920
$250$		0			0
$251$	−9.68217			−0.611133			−0.305567	−	0.952171i	$-0.598846\pi$
$251$	−9.68217			−0.611133			−0.305567	+	0.952171i	$0.598846\pi$
$252$	−4.21476	−	3.48675i	−0.265505	−	0.219645i
$253$	2.17416	−	17.2102i	0.136688	−	1.08200i
$254$	2.68958	+	14.0993i	0.168760	+	0.884668i
$255$		0			0
$256$	7.07181	−	6.64087i	0.441988	−	0.415054i
$257$	−0.725549	+	0.998633i	−0.0452585	+	0.0622930i	−0.831046	−	0.556203i	$-0.812258\pi$
$257$	−0.725549	+	0.998633i	−0.0452585	+	0.0622930i	0.785788	+	0.618496i	$0.212258\pi$
$258$	−14.0512	+	25.5591i	−0.874792	+	1.59124i
$259$	−5.54784	−	1.42444i	−0.344726	−	0.0885105i
$260$		0			0
$261$	11.6093	−	14.0332i	0.718597	−	0.868634i
$262$	−12.6738	+	0.797368i	−0.782990	+	0.0492616i
$263$	−2.53228	+	9.86257i	−0.156147	+	0.608152i	0.841541	+	0.540193i	$0.181649\pi$
$263$	−2.53228	+	9.86257i	−0.156147	+	0.608152i	−0.997688	+	0.0679590i	$0.978351\pi$
$264$	5.13185	−	1.31763i	0.315843	−	0.0810948i
$265$		0			0
$266$	6.64799	−	2.63213i	0.407614	−	0.161386i
$267$	9.78381	+	1.86636i	0.598759	+	0.114219i
$268$	−12.7135	−	17.4986i	−0.776599	−	1.06890i
$269$	31.8523	−	4.02388i	1.94207	−	0.245340i	0.945335	−	0.326101i	$-0.105735\pi$
$269$	31.8523	−	4.02388i	1.94207	−	0.245340i	0.996734	+	0.0807606i	$0.0257349\pi$
$270$		0			0
$271$	−5.44124	−	5.10966i	−0.330532	−	0.310390i	0.501457	−	0.865183i	$-0.332798\pi$
$271$	−5.44124	−	5.10966i	−0.330532	−	0.310390i	−0.831989	+	0.554793i	$0.812798\pi$
$272$	−19.8680	+	3.79001i	−1.20467	+	0.229803i
$273$	5.12005	−	3.24928i	0.309880	−	0.196656i
$274$	22.6763	+	16.4753i	1.36992	+	0.995308i
$275$		0			0
$276$	24.7420	−	17.9761i	1.48929	−	1.08203i
$277$	0.387243	−	0.978065i	0.0232672	−	0.0587662i	−0.917678	−	0.397324i	$-0.869939\pi$
$277$	0.387243	−	0.978065i	0.0232672	−	0.0587662i	0.940946	+	0.338558i	$0.109939\pi$
$278$	−10.9940	−	5.17339i	−0.659377	−	0.310279i
$279$	−0.0164098	+	0.0348727i	−0.000982432	+	0.00208777i
$280$		0			0
$281$	0.975796	−	5.11530i	0.0582111	−	0.305153i	−0.941260	−	0.337684i	$-0.890357\pi$
$281$	0.975796	−	5.11530i	0.0582111	−	0.305153i	0.999471	+	0.0325303i	$0.0103566\pi$
$282$	32.4670	+	10.5492i	1.93338	+	0.628194i
$283$	21.5628	+	22.9620i	1.28177	+	1.36495i	0.897058	+	0.441914i	$0.145700\pi$
$283$	21.5628	+	22.9620i	1.28177	+	1.36495i	0.384715	+	0.923035i	$0.374300\pi$
$284$	7.55224	+	9.12908i	0.448143	+	0.541712i
$285$		0			0
$286$	−1.33911	+	21.2846i	−0.0791834	+	1.25858i
$287$	3.31675	+	8.37715i	0.195781	+	0.494487i
$288$	−20.7123	−	13.1445i	−1.22049	−	0.774544i
$289$	20.1037	+	7.95960i	1.18257	+	0.468212i
$290$		0			0
$291$	2.40258	−	3.78586i	0.140842	−	0.221931i
$292$	2.93936	+	23.2674i	0.172013	+	1.36162i
$293$	2.15446	−	0.700027i	0.125865	−	0.0408960i	−0.245407	−	0.969420i	$-0.578922\pi$
$293$	2.15446	−	0.700027i	0.125865	−	0.0408960i	0.371272	+	0.928524i	$0.378922\pi$
$294$	28.5992	+	15.7226i	1.66794	+	0.916958i
$295$		0			0
$296$	4.87472	+	0.615821i	0.283338	+	0.0357939i
$297$	0.108317	+	0.197028i	0.00628519	+	0.0114327i
$298$	−9.55877	−	37.2289i	−0.553725	−	2.15662i
$299$	5.26302	+	16.1979i	0.304368	+	0.936750i
$300$		0			0
$301$	−1.37424	+	4.22948i	−0.0792100	+	0.243783i
$302$	41.2806	+	2.59716i	2.37543	+	0.149450i
$303$	−0.503039	+	0.535682i	−0.0288988	+	0.0307741i
$304$	12.6060	−	6.93020i	0.723003	−	0.397474i
$305$		0			0
$306$	16.6573	+	35.3985i	0.952234	+	2.02360i
$307$			18.9044i			1.07893i	0.842008	+	0.539466i	$0.181374\pi$
$307$			18.9044i			1.07893i	−0.842008	+	0.539466i	$0.818626\pi$
$308$	5.28328	−	2.48612i	0.301043	−	0.141660i
$309$	2.46667	+	39.2066i	0.140324	+	2.23038i
$310$		0			0
$311$	−7.84921	−	12.3684i	−0.445088	−	0.701346i	0.545517	−	0.838100i	$-0.316333\pi$
$311$	−7.84921	−	12.3684i	−0.445088	−	0.701346i	−0.990605	+	0.136753i	$0.956333\pi$
$312$	−4.00816	+	3.31584i	−0.226917	+	0.187722i
$313$	−6.58773	+	5.44984i	−0.372360	+	0.308043i	−0.804716	−	0.593660i	$-0.797682\pi$
$313$	−6.58773	+	5.44984i	−0.372360	+	0.308043i	0.432356	+	0.901703i	$0.357682\pi$
$314$	1.50199	+	2.36676i	0.0847624	+	0.133564i
$315$		0			0
$316$	−0.266628	−	4.23793i	−0.0149990	−	0.238402i
$317$	5.59830	−	2.63436i	0.314432	−	0.147960i	−0.262087	−	0.965044i	$-0.584411\pi$
$317$	5.59830	−	2.63436i	0.314432	−	0.147960i	0.576519	+	0.817084i	$0.304411\pi$
$318$			12.2952i			0.689478i
$319$	8.27765	+	17.5909i	0.463459	+	0.984901i
$320$		0			0
$321$	−40.0568	+	22.0214i	−2.23575	+	1.22911i
$322$	5.94249	−	6.32811i	0.331162	−	0.352652i
$323$	−27.4147	−	1.72479i	−1.52540	−	0.0959697i
$324$	6.39391	−	19.6784i	0.355217	−	1.09325i
$325$		0			0
$326$	−2.81542	−	8.66496i	−0.155932	−	0.479908i
$327$	−3.18139	−	12.3907i	−0.175931	−	0.685207i
$328$	−3.72344	−	6.77291i	−0.205592	−	0.373971i
$329$	5.16403	+	0.652369i	0.284702	+	0.0359663i
$330$		0			0
$331$	16.2091	+	8.91105i	0.890935	+	0.489796i	0.860331	−	0.509736i	$-0.170257\pi$
$331$	16.2091	+	8.91105i	0.890935	+	0.489796i	0.0306039	+	0.999532i	$0.490257\pi$
$332$	−8.59654	+	2.79319i	−0.471796	+	0.153296i
$333$	2.79362	+	22.1138i	0.153089	+	1.21183i
$334$	−6.22301	+	9.80589i	−0.340508	+	0.536555i
$335$		0			0
$336$	−5.78180	−	2.28918i	−0.315423	−	0.124885i
$337$	−11.0306	−	7.00020i	−0.600873	−	0.381325i	0.200321	−	0.979730i	$-0.435801\pi$
$337$	−11.0306	−	7.00020i	−0.600873	−	0.381325i	−0.801194	+	0.598405i	$0.795801\pi$
$338$	2.23997	+	5.65751i	0.121838	+	0.307728i
$339$	−1.51981	+	24.1568i	−0.0825450	+	1.31201i
$340$		0			0
$341$	−0.0262237	−	0.0316990i	−0.00142009	−	0.00171660i
$342$	−19.0471	−	20.2831i	−1.02995	−	1.09679i
$343$	9.91331	+	3.22103i	0.535269	+	0.173919i
$344$	0.714840	−	3.74732i	0.0385416	−	0.202042i
$345$		0			0
$346$	12.7735	−	27.1450i	0.686706	−	1.45933i
$347$	1.42516	+	0.670629i	0.0765066	+	0.0360013i	0.463652	−	0.886017i	$-0.346539\pi$
$347$	1.42516	+	0.670629i	0.0765066	+	0.0360013i	−0.387145	+	0.922019i	$0.626539\pi$
$348$	−12.6174	+	31.8678i	−0.676361	+	1.70829i
$349$	−7.85282	+	5.70541i	−0.420352	+	0.305404i	−0.777779	−	0.628537i	$-0.783654\pi$
$349$	−7.85282	+	5.70541i	−0.420352	+	0.305404i	0.357427	+	0.933941i	$0.383654\pi$
$350$		0			0
$351$	−0.178590	−	0.129753i	−0.00953243	−	0.00692572i
$352$	22.1093	−	14.0310i	1.17843	−	0.747853i
$353$	−31.3011	+	5.97101i	−1.66599	+	0.317805i	−0.932302	−	0.361681i	$-0.882203\pi$
$353$	−31.3011	+	5.97101i	−1.66599	+	0.317805i	−0.733689	+	0.679486i	$0.762203\pi$
$354$	−5.84405	−	5.48792i	−0.310608	−	0.291680i
$355$		0			0
$356$	−9.34187	+	1.18015i	−0.495118	+	0.0625480i
$357$	6.97949	+	9.60644i	0.369394	+	0.508427i
$358$	3.12432	+	0.595996i	0.165126	+	0.0314994i
$359$	−14.9378	+	5.91429i	−0.788386	+	0.312144i	−0.727596	−	0.686006i	$-0.759362\pi$
$359$	−14.9378	+	5.91429i	−0.788386	+	0.312144i	−0.0607906	+	0.998151i	$0.519362\pi$
$360$		0			0
$361$	0.519683	−	0.133432i	0.0273517	−	0.00702273i
$362$	2.02888	−	7.90197i	0.106636	−	0.415318i
$363$	1.34892	−	0.0848667i	0.0707998	−	0.00445434i
$364$	−3.65421	+	4.41719i	−0.191533	+	0.231523i
$365$		0			0
$366$	66.0688	+	16.9636i	3.45347	+	0.886700i
$367$	2.93587	−	5.34033i	0.153251	−	0.278763i	−0.788525	−	0.615002i	$-0.789155\pi$
$367$	2.93587	−	5.34033i	0.153251	−	0.278763i	0.941777	+	0.336239i	$0.109155\pi$
$368$	10.2658	−	14.1297i	0.535142	−	0.736559i
$369$	25.5588	−	24.0013i	1.33054	−	1.24946i
$370$		0			0
$371$	0.351279	+	1.84147i	0.0182375	+	0.0956042i
$372$	0.00909039	−	0.0719579i	0.000471315	−	0.00373084i
$373$	18.4846	+	15.2917i	0.957094	+	0.791777i	0.978128	−	0.208002i	$-0.0666960\pi$
$373$	18.4846	+	15.2917i	0.957094	+	0.791777i	−0.0210347	+	0.999779i	$0.506696\pi$
$374$	−41.7604			−2.15938
$375$		0			0
$376$	−4.46507			−0.230269
$377$	−14.7072	−	12.1669i	−0.757460	−	0.626625i
$378$	−0.0141019	+	0.111628i	−0.000725324	+	0.00574153i
$379$	−5.07836	−	26.6217i	−0.260858	−	1.36746i	−0.835694	−	0.549196i	$-0.814934\pi$
$379$	−5.07836	−	26.6217i	−0.260858	−	1.36746i	0.574836	−	0.818269i	$-0.305066\pi$
$380$		0			0
$381$	12.3585	−	11.6054i	0.633147	−	0.594565i
$382$	20.5969	−	28.3492i	1.05383	−	1.45047i
$383$	9.60131	−	17.4647i	0.490604	−	0.892405i	−0.508897	−	0.860827i	$-0.669947\pi$
$383$	9.60131	−	17.4647i	0.490604	−	0.892405i	0.999501	−	0.0315779i	$-0.0100532\pi$
$384$	12.5366	+	3.21886i	0.639757	+	0.164262i
$385$		0			0
$386$	8.34261	−	10.0845i	0.424628	−	0.513287i
$387$	17.2718	−	1.08665i	0.877974	−	0.0552374i
$388$	−1.05418	+	4.10575i	−0.0535178	+	0.208438i
$389$	−28.8080	+	7.39663i	−1.46062	+	0.375024i	−0.893669	−	0.448726i	$-0.851878\pi$
$389$	−28.8080	+	7.39663i	−1.46062	+	0.375024i	−0.566953	+	0.823750i	$0.691878\pi$
$390$		0			0
$391$	−31.0080	+	12.2769i	−1.56814	+	0.620870i
$392$	−4.19304	−	0.799866i	−0.211781	−	0.0403993i
$393$	8.81623	+	12.1345i	0.444720	+	0.612105i
$394$	21.6842	−	2.73935i	1.09243	−	0.138007i
$395$		0			0
$396$	−16.5638	−	15.5545i	−0.832364	−	0.781642i
$397$	13.4257	−	2.56108i	0.673815	−	0.128537i	0.160892	−	0.986972i	$-0.448563\pi$
$397$	13.4257	−	2.56108i	0.673815	−	0.128537i	0.512922	+	0.858435i	$0.328563\pi$
$398$	−16.7646	+	10.6391i	−0.840331	+	0.533291i
$399$	−6.83233	−	4.96398i	−0.342044	−	0.248510i
$400$		0			0
$401$	10.6129	−	7.71074i	0.529984	−	0.385056i	−0.290368	−	0.956915i	$-0.593778\pi$
$401$	10.6129	−	7.71074i	0.529984	−	0.385056i	0.820352	+	0.571859i	$0.193778\pi$
$402$	−17.5080	+	44.2202i	−0.873221	+	2.20550i
$403$	0.0365476	+	0.0171980i	0.00182056	+	0.000856692i
$404$	0.295791	−	0.628589i	0.0147162	−	0.0312735i
$405$		0			0
$406$	−1.82301	+	9.55654i	−0.0904743	+	0.474283i
$407$	−22.6283	−	7.35239i	−1.12164	−	0.364444i
$408$	−6.97284	−	7.42532i	−0.345207	−	0.367608i
$409$	−7.71814	−	9.32962i	−0.381637	−	0.461320i	0.544359	−	0.838852i	$-0.316773\pi$
$409$	−7.71814	−	9.32962i	−0.381637	−	0.461320i	−0.925997	+	0.377532i	$0.876773\pi$
$410$		0			0
$411$	2.07878	−	33.0412i	0.102538	−	1.62980i
$412$	−13.6714	−	34.5301i	−0.673543	−	1.70118i
$413$	−1.03207	−	0.654969i	−0.0507846	−	0.0322289i
$414$	−31.4093	−	12.4358i	−1.54368	−	0.611186i
$415$		0			0
$416$	−13.7758	+	21.7071i	−0.675412	+	1.06428i
$417$	1.79869	+	14.2381i	0.0880822	+	0.697242i
$418$	28.2473	−	9.17811i	1.38162	−	0.448916i
$419$	−9.95753	−	5.47420i	−0.486457	−	0.267432i	0.219596	−	0.975591i	$-0.429526\pi$
$419$	−9.95753	−	5.47420i	−0.486457	−	0.267432i	−0.706053	+	0.708159i	$0.749526\pi$
$420$		0			0
$421$	−23.6601	−	2.98896i	−1.15312	−	0.145673i	−0.474564	−	0.880221i	$-0.657394\pi$
$421$	−23.6601	−	2.98896i	−1.15312	−	0.145673i	−0.678557	+	0.734548i	$0.737394\pi$
$422$	6.72231	+	12.2278i	0.327237	+	0.595242i
$423$	−5.03732	−	19.6191i	−0.244923	−	0.953911i
$424$	−0.496946	−	1.52944i	−0.0241338	−	0.0742763i
$425$		0			0
$426$	8.05056	−	24.7771i	0.390051	−	1.20045i
$427$	10.3799	+	0.653047i	0.502318	+	0.0316032i
$428$	29.5819	−	31.5015i	1.42989	−	1.52268i
$429$	22.0739	−	12.1352i	1.06574	−	0.585894i
$430$		0			0
$431$	9.96374	+	21.1740i	0.479937	+	1.01992i	0.987400	+	0.158244i	$0.0505833\pi$
$431$	9.96374	+	21.1740i	0.479937	+	1.01992i	−0.507463	+	0.861673i	$0.669417\pi$
$432$			0.226371i			0.0108913i
$433$	−23.4818	+	11.0497i	−1.12846	+	0.531014i	−0.897088	−	0.441851i	$-0.854322\pi$
$433$	−23.4818	+	11.0497i	−1.12846	+	0.531014i	−0.231373	+	0.972865i	$0.574322\pi$
$434$	−0.00129270	−	0.0205469i	−6.20518e−5	−	0.000986285i
$435$		0			0
$436$	6.48016	+	10.2111i	0.310343	+	0.489023i
$437$	18.2760	−	15.1192i	0.874259	−	0.723250i
$438$	39.7340	−	32.8709i	1.89857	−	1.57063i
$439$	−2.11965	−	3.34003i	−0.101165	−	0.159411i	0.789975	−	0.613139i	$-0.210094\pi$
$439$	−2.11965	−	3.34003i	−0.101165	−	0.159411i	−0.891140	+	0.453728i	$0.850094\pi$
$440$		0			0
$441$	−1.21590	−	19.3262i	−0.0579000	−	0.920294i
$442$	37.0986	−	17.4573i	1.76460	−	0.830359i
$443$			11.5842i			0.550383i	0.961389	+	0.275191i	$0.0887412\pi$
$443$			11.5842i			0.550383i	−0.961389	+	0.275191i	$0.911259\pi$
$444$	−17.8600	−	37.9545i	−0.847599	−	1.80124i
$445$		0			0
$446$	10.0036	−	5.49953i	0.473684	−	0.260410i
$447$	−31.0775	+	33.0942i	−1.46992	+	1.56530i
$448$	8.02269	+	0.504745i	0.379036	+	0.0238469i
$449$	7.65420	−	23.5572i	0.361224	−	1.11173i	−0.591088	−	0.806607i	$-0.701302\pi$
$449$	7.65420	−	23.5572i	0.361224	−	1.11173i	0.952312	−	0.305126i	$-0.0986985\pi$
$450$		0			0
$451$	11.5654	+	35.5945i	0.544592	+	1.67608i
$452$	−5.69059	−	22.1634i	−0.267663	−	1.04248i
$453$	−23.5358	−	42.8114i	−1.10581	−	2.01146i
$454$	37.2020	+	4.69970i	1.74597	+	0.220568i
$455$		0			0
$456$	6.34846	+	3.49010i	0.297294	+	0.163439i
$457$	−14.7875	+	4.80474i	−0.691729	+	0.224756i	−0.633723	−	0.773560i	$-0.718474\pi$
$457$	−14.7875	+	4.80474i	−0.691729	+	0.224756i	−0.0580056	+	0.998316i	$0.518474\pi$
$458$	−4.07249	−	32.2371i	−0.190295	−	1.50634i
$459$	0.231615	−	0.364966i	0.0108108	−	0.0170352i
$460$		0			0
$461$	−17.1720	−	6.79886i	−0.799778	−	0.316654i	−0.0675514	−	0.997716i	$-0.521519\pi$
$461$	−17.1720	−	6.79886i	−0.799778	−	0.316654i	−0.732226	+	0.681061i	$0.761519\pi$
$462$	−10.8404	−	6.87953i	−0.504341	−	0.320065i
$463$	−3.20396	−	8.09227i	−0.148900	−	0.376080i	0.836113	−	0.548557i	$-0.184823\pi$
$463$	−3.20396	−	8.09227i	−0.148900	−	0.376080i	−0.985013	+	0.172478i	$0.944823\pi$
$464$	−1.22904	+	19.5350i	−0.0570567	+	0.906890i
$465$		0			0
$466$	−24.9658	−	30.1784i	−1.15652	−	1.39799i
$467$	−26.5114	−	28.2318i	−1.22680	−	1.30641i	−0.937002	−	0.349325i	$-0.886411\pi$
$467$	−26.5114	−	28.2318i	−1.22680	−	1.30641i	−0.289801	−	0.957087i	$-0.593589\pi$
$468$	21.2171	+	6.89385i	0.980761	+	0.318668i
$469$	−1.35881	+	7.12315i	−0.0627442	+	0.328917i
$470$		0			0
$471$	1.40970	−	2.99577i	0.0649557	−	0.138038i
$472$	0.948775	+	0.446460i	0.0436709	+	0.0205500i
$473$	−6.80041	+	17.1759i	−0.312683	+	0.789747i
$474$	−7.55380	+	5.48816i	−0.346958	+	0.252080i
$475$		0			0
$476$	−9.08166	−	6.59821i	−0.416257	−	0.302428i
$477$	6.15957	−	3.90898i	0.282028	−	0.178980i
$478$	14.2405	−	2.71652i	0.651345	−	0.124251i
$479$	−16.1778	−	15.1920i	−0.739184	−	0.694140i	0.220448	−	0.975399i	$-0.429248\pi$
$479$	−16.1778	−	15.1920i	−0.739184	−	0.694140i	−0.959632	+	0.281259i	$0.909248\pi$
$480$		0			0
$481$	23.1758	−	2.92779i	1.05673	−	0.133496i
$482$	23.5098	+	32.3584i	1.07084	+	1.47389i
$483$	−10.0717	−	1.92128i	−0.458278	−	0.0874213i
$484$	−1.18802	+	0.470371i	−0.0540009	+	0.0213805i
$485$		0			0
$486$	−44.4875	+	11.4225i	−2.01799	+	0.518133i
$487$	−3.05307	+	11.8909i	−0.138348	+	0.538830i	0.861186	+	0.508291i	$0.169722\pi$
$487$	−3.05307	+	11.8909i	−0.138348	+	0.538830i	−0.999534	+	0.0305390i	$0.990278\pi$
$488$	−8.90419	+	0.560204i	−0.403074	+	0.0253592i
$489$	−6.85943	+	8.29163i	−0.310194	+	0.374960i
$490$		0			0
$491$	−1.41728	−	0.363896i	−0.0639611	−	0.0164224i	0.216574	−	0.976266i	$-0.430512\pi$
$491$	−1.41728	−	0.363896i	−0.0639611	−	0.0164224i	−0.280535	+	0.959844i	$0.590512\pi$
$492$	−31.7873	+	57.8208i	−1.43308	+	2.60676i
$493$	21.9690	−	30.2378i	0.989435	−	1.36184i
$494$	−21.2573	+	19.9619i	−0.956410	+	0.898129i
$495$		0			0
$496$	−0.00776140	−	0.0406867i	−0.000348497	−	0.00182689i
$497$	0.497853	−	3.94091i	0.0223318	−	0.176774i
$498$	15.3142	+	12.6690i	0.686245	+	0.567712i
$499$	−11.5060			−0.515081			−0.257540	−	0.966268i	$-0.582912\pi$
$499$	−11.5060			−0.515081			−0.257540	+	0.966268i	$0.582912\pi$
$500$		0			0
$501$	13.7175			0.612853
$502$	−15.5079	−	12.8292i	−0.692150	−	0.572596i
$503$	−0.885262	+	7.00757i	−0.0394719	+	0.312452i	0.960001	+	0.279996i	$0.0903331\pi$
$503$	−0.885262	+	7.00757i	−0.0394719	+	0.312452i	−0.999473	+	0.0324565i	$0.989667\pi$
$504$	−0.294787	−	1.54533i	−0.0131309	−	0.0688344i
$505$		0			0
$506$	26.2865	−	24.6847i	1.16858	−	1.09737i
$507$	4.22440	−	5.81438i	0.187612	−	0.258226i
$508$	−7.72122	+	14.0448i	−0.342574	+	0.623139i
$509$	10.1123	+	2.59639i	0.448219	+	0.115083i	0.466051	−	0.884758i	$-0.345676\pi$
$509$	10.1123	+	2.59639i	0.448219	+	0.115083i	−0.0178318	+	0.999841i	$0.505676\pi$
$510$		0			0
$511$	5.01190	−	6.05835i	0.221713	−	0.268005i
$512$	30.6487	−	1.92825i	1.35449	−	0.0852176i
$513$	−0.0764550	+	0.297772i	−0.00337557	+	0.0131470i
$514$	−2.48533	+	0.638125i	−0.109623	+	0.0281465i
$515$		0			0
$516$	−30.2810	+	11.9891i	−1.33305	+	0.527790i
$517$	21.2386	+	4.05147i	0.934071	+	0.178183i
$518$	−6.99849	−	9.63260i	−0.307496	−	0.423232i
$519$	−35.1549	+	4.44110i	−1.54313	+	0.194943i
$520$		0			0
$521$	−4.42096	−	4.15155i	−0.193686	−	0.181883i	0.581637	−	0.813449i	$-0.302413\pi$
$521$	−4.42096	−	4.15155i	−0.193686	−	0.181883i	−0.775322	+	0.631566i	$0.782413\pi$
$522$	37.1890	−	7.09419i	1.62772	−	0.310504i
$523$	22.3024	−	14.1536i	0.975217	−	0.618892i	0.0501689	−	0.998741i	$-0.484024\pi$
$523$	22.3024	−	14.1536i	0.975217	−	0.618892i	0.925049	+	0.379849i	$0.124024\pi$
$524$	−11.4716	−	8.33461i	−0.501140	−	0.364099i
$525$		0			0
$526$	−17.1242	+	12.4414i	−0.746650	+	0.542473i
$527$	−0.0291158	+	0.0735382i	−0.00126831	+	0.00320338i
$528$	−23.3727	−	10.9984i	−1.01717	−	0.478642i
$529$	2.46843	−	5.24568i	0.107323	−	0.228073i
$530$		0			0
$531$	−0.891326	+	4.67249i	−0.0386803	+	0.202769i
$532$	7.59311	+	2.46715i	0.329203	+	0.106965i
$533$	−25.1541	−	26.7863i	−1.08954	−	1.16025i
$534$	13.1977	+	15.9532i	0.571119	+	0.690364i
$535$		0			0
$536$	0.390597	−	6.20837i	0.0168712	−	0.268161i
$537$	−1.38297	−	3.49297i	−0.0596794	−	0.150733i
$538$	56.3494	+	35.7604i	2.42939	+	1.54174i
$539$	19.2188	+	7.60928i	0.827814	+	0.327755i
$540$		0			0
$541$	17.3707	−	27.3719i	0.746826	−	1.17681i	−0.232120	−	0.972687i	$-0.574566\pi$
$541$	17.3707	−	27.3719i	0.746826	−	1.17681i	0.978946	−	0.204122i	$-0.0654338\pi$
$542$	−1.94471	−	15.3939i	−0.0835323	−	0.661226i
$543$	−9.16440	+	2.97769i	−0.393282	+	0.127785i
$544$	−44.1153	−	24.2526i	−1.89143	−	1.03982i
$545$		0			0
$546$	12.5062	+	1.57990i	0.535214	+	0.0676133i
$547$	−9.57786	−	17.4221i	−0.409520	−	0.744913i	0.588455	−	0.808530i	$-0.299736\pi$
$547$	−9.57786	−	17.4221i	−0.409520	−	0.744913i	−0.997974	+	0.0636167i	$0.979736\pi$
$548$	7.78349	+	30.3147i	0.332494	+	1.29498i
$549$	−12.5068	−	38.4921i	−0.533778	−	1.64280i
$550$		0			0
$551$	−8.21449	+	25.2816i	−0.349949	+	1.07703i
$552$	8.77825	+	0.552281i	0.373627	+	0.0235066i
$553$	−0.974547	+	1.03779i	−0.0414420	+	0.0441312i
$554$	1.91622	−	1.05345i	0.0814122	−	0.0447567i
$555$		0			0
$556$	−5.77666	−	12.2760i	−0.244985	−	0.520619i
$557$			40.9886i			1.73674i	0.495913	+	0.868372i	$0.334833\pi$
$557$			40.9886i			1.73674i	−0.495913	+	0.868372i	$0.665167\pi$
$558$	−0.0724911	+	0.0341117i	−0.00306879	+	0.00144406i
$559$	−1.13884	−	18.1013i	−0.0481677	−	0.765604i
$560$		0			0
$561$	26.4295	+	41.6462i	1.11585	+	1.75830i
$562$	8.34088	−	6.90018i	0.351839	−	0.291067i
$563$	6.77876	−	5.60788i	0.285691	−	0.236344i	−0.483529	−	0.875328i	$-0.660645\pi$
$563$	6.77876	−	5.60788i	0.285691	−	0.236344i	0.769220	+	0.638984i	$0.220645\pi$
$564$	20.4250	+	32.1847i	0.860048	+	1.35522i
$565$		0			0
$566$	4.11144	+	65.3495i	0.172817	+	2.74684i
$567$	−6.27679	+	2.95363i	−0.263600	+	0.124041i
$568$			3.40751i			0.142976i
$569$	3.85270	+	8.18740i	0.161513	+	0.343234i	0.969160	−	0.246434i	$-0.0792588\pi$
$569$	3.85270	+	8.18740i	0.161513	+	0.343234i	−0.807646	+	0.589667i	$0.799259\pi$
$570$		0			0
$571$	−13.3539	+	7.34135i	−0.558842	+	0.307226i	−0.736028	−	0.676951i	$-0.763301\pi$
$571$	−13.3539	+	7.34135i	−0.558842	+	0.307226i	0.177186	+	0.984177i	$0.443301\pi$
$572$	−16.3015	+	17.3594i	−0.681601	+	0.725831i
$573$	−41.3071	−	2.59882i	−1.72563	−	0.108567i
$574$	−5.78761	+	17.8124i	−0.241570	+	0.743476i
$575$		0			0
$576$	−9.66661	−	29.7508i	−0.402775	−	1.23961i
$577$	−0.0478187	−	0.186241i	−0.00199072	−	0.00775333i	0.967580	−	0.252565i	$-0.0812740\pi$
$577$	−0.0478187	−	0.186241i	−0.00199072	−	0.00775333i	−0.969571	+	0.244811i	$0.921274\pi$
$578$	21.6531	+	39.3869i	0.900652	+	1.63828i
$579$	−15.3368	−	1.93749i	−0.637376	−	0.0805193i
$580$		0			0
$581$	2.65559	+	1.45992i	0.110173	+	0.0605679i
$582$	8.86459	−	2.88028i	0.367449	−	0.119391i
$583$	0.976002	+	7.72585i	0.0404219	+	0.319972i
$584$	−3.61410	+	5.69491i	−0.149552	+	0.235657i
$585$		0			0
$586$	4.37835	+	1.73351i	0.180868	+	0.0716107i
$587$	−12.8733	−	8.16964i	−0.531338	−	0.337197i	0.242942	−	0.970041i	$-0.421888\pi$
$587$	−12.8733	−	8.16964i	−0.531338	−	0.337197i	−0.774280	+	0.632844i	$0.781888\pi$
$588$	13.4151	+	33.8827i	0.553230	+	1.39730i
$589$	0.00353212	−	0.0561414i	0.000145538	−	0.00231327i
$590$		0			0
$591$	−16.4554	−	19.8912i	−0.676886	−	0.818215i
$592$	−16.3983	−	17.4624i	−0.673965	−	0.717700i
$593$	−43.3208	−	14.0758i	−1.77897	−	0.578023i	−0.780108	−	0.625645i	$-0.784836\pi$
$593$	−43.3208	−	14.0758i	−1.77897	−	0.578023i	−0.998865	+	0.0476219i	$0.984836\pi$
$594$	−0.0875784	+	0.459102i	−0.00359339	+	0.0188372i
$595$		0			0
$596$	18.2739	−	38.8339i	0.748526	−	1.59070i
$597$	21.2200	+	9.98539i	0.868478	+	0.408675i
$598$	−13.0331	+	32.9178i	−0.532962	+	1.34611i
$599$	16.4139	−	11.9254i	0.670653	−	0.487258i	−0.199590	−	0.979879i	$-0.563961\pi$
$599$	16.4139	−	11.9254i	0.670653	−	0.487258i	0.870244	+	0.492621i	$0.163961\pi$
$600$		0			0
$601$	−5.83295	−	4.23788i	−0.237931	−	0.172867i	0.462430	−	0.886656i	$-0.346978\pi$
$601$	−5.83295	−	4.23788i	−0.237931	−	0.172867i	−0.700361	+	0.713789i	$0.746978\pi$
$602$	−7.80533	+	4.95341i	−0.318121	+	0.201886i
$603$	27.7196	−	5.28779i	1.12883	−	0.215335i
$604$	33.6678	+	31.6162i	1.36992	+	1.28644i
$605$		0			0
$606$	−1.51551	+	0.191454i	−0.0615635	+	0.00777728i
$607$	−1.77657	−	2.44524i	−0.0721087	−	0.0992490i	0.771439	−	0.636303i	$-0.219537\pi$
$607$	−1.77657	−	2.44524i	−0.0721087	−	0.0992490i	−0.843548	+	0.537054i	$0.819537\pi$
$608$	35.1704	+	6.70911i	1.42635	+	0.272090i
$609$	10.6842	−	4.23016i	0.432944	−	0.171415i
$610$		0			0
$611$	−20.5613	+	5.27925i	−0.831822	+	0.213576i
$612$	−10.8637	+	42.3115i	−0.439141	+	1.71034i
$613$	24.1150	−	1.51718i	0.973994	−	0.0612785i	0.432189	−	0.901783i	$-0.357741\pi$
$613$	24.1150	−	1.51718i	0.973994	−	0.0612785i	0.541805	+	0.840504i	$0.317741\pi$
$614$	−25.0490	+	30.2790i	−1.01090	+	1.22196i
$615$		0			0
$616$	1.62654	+	0.417624i	0.0655351	+	0.0168265i
$617$	−16.0590	+	29.2112i	−0.646511	+	1.17600i	0.326491	+	0.945200i	$0.394134\pi$
$617$	−16.0590	+	29.2112i	−0.646511	+	1.17600i	−0.973002	+	0.230798i	$0.925866\pi$
$618$	−47.9993	+	66.0653i	−1.93081	+	2.65754i
$619$	8.36904	−	7.85905i	0.336380	−	0.315882i	−0.497888	−	0.867242i	$-0.665891\pi$
$619$	8.36904	−	7.85905i	0.336380	−	0.315882i	0.834268	+	0.551360i	$0.185891\pi$
$620$		0			0
$621$	0.0699402	+	0.366639i	0.00280660	+	0.0147127i
$622$	3.81651	−	30.2108i	0.153028	−	1.21134i
$623$	2.43243	+	2.01228i	0.0974532	+	0.0806203i
$624$	25.3613			1.01526
$625$		0			0
$626$	−17.7727			−0.710342
$627$	−27.0303	−	22.3614i	−1.07949	−	0.893028i
$628$	−0.392294	+	3.10533i	−0.0156542	+	0.123916i
$629$	8.57120	+	44.9318i	0.341756	+	1.79155i
$630$		0			0
$631$	14.7988	−	13.8970i	0.589130	−	0.553230i	−0.331605	−	0.943418i	$-0.607590\pi$
$631$	14.7988	−	13.8970i	0.589130	−	0.553230i	0.920735	+	0.390188i	$0.127590\pi$
$632$	0.717827	−	0.988004i	0.0285536	−	0.0393007i
$633$	7.93996	−	14.4427i	0.315585	−	0.574047i
$634$	12.4574	+	3.19851i	0.494745	+	0.127029i
$635$		0			0
$636$	−8.75113	+	10.5783i	−0.347005	+	0.419457i
$637$	−20.2544	+	1.27430i	−0.802507	+	0.0504895i
$638$	−10.0503	+	39.1434i	−0.397896	+	1.54970i
$639$	−14.9722	+	3.84421i	−0.592292	+	0.152075i
$640$		0			0
$641$	−16.1026	+	6.37546i	−0.636014	+	0.251816i	−0.663930	−	0.747795i	$-0.731113\pi$
$641$	−16.1026	+	6.37546i	−0.636014	+	0.251816i	0.0279163	+	0.999610i	$0.491113\pi$
$642$	−93.3378	−	17.8051i	−3.68375	−	0.702713i
$643$	20.2453	+	27.8652i	0.798395	+	1.09890i	0.993012	+	0.118018i	$0.0376539\pi$
$643$	20.2453	+	27.8652i	0.798395	+	1.09890i	−0.194616	+	0.980879i	$0.562346\pi$
$644$	9.61676	−	1.21488i	0.378953	−	0.0478729i
$645$		0			0
$646$	−41.6245	−	39.0880i	−1.63770	−	1.53790i
$647$	−40.0637	+	7.64256i	−1.57507	+	0.300460i	−0.899528	−	0.436864i	$-0.856089\pi$
$647$	−40.0637	+	7.64256i	−1.57507	+	0.300460i	−0.675539	+	0.737324i	$0.736089\pi$
$648$	5.02440	−	3.18858i	0.197377	−	0.125259i
$649$	−4.10784	−	2.98452i	−0.161247	−	0.117153i
$650$		0			0
$651$	−0.0196726	+	0.0142930i	−0.000771030	+	0.000560186i
$652$	3.74505	−	9.45890i	0.146667	−	0.370439i
$653$	38.8863	+	18.2985i	1.52174	+	0.716075i	0.991297	−	0.131646i	$-0.0420263\pi$
$653$	38.8863	+	18.2985i	1.52174	+	0.716075i	0.530441	+	0.847722i	$0.322026\pi$
$654$	11.3225	−	24.0615i	0.442745	−	0.940880i
$655$		0			0
$656$	−7.06077	+	37.0139i	−0.275677	+	1.44515i
$657$	−29.1001	−	9.45519i	−1.13530	−	0.368882i
$658$	7.40678	+	7.88742i	0.288746	+	0.307484i
$659$	−22.5002	−	27.1981i	−0.876485	−	1.05949i	−0.997762	−	0.0668697i	$-0.978699\pi$
$659$	−22.5002	−	27.1981i	−0.876485	−	1.05949i	0.121277	−	0.992619i	$-0.461301\pi$
$660$		0			0
$661$	−0.409348	+	6.50640i	−0.0159218	+	0.253070i	0.982012	+	0.188819i	$0.0604658\pi$
$661$	−0.409348	+	6.50640i	−0.0159218	+	0.253070i	−0.997934	+	0.0642510i	$0.979534\pi$
$662$	14.1546	+	35.7504i	0.550134	+	1.38948i
$663$	−40.8887	−	25.9487i	−1.58798	−	1.00777i
$664$	−2.41705	−	0.956977i	−0.0937997	−	0.0371379i
$665$		0			0
$666$	−24.8270	+	39.1211i	−0.962027	+	1.51591i
$667$	4.04499	+	32.0194i	0.156623	+	1.23980i
$668$	−12.3334	+	4.00738i	−0.477195	+	0.155050i
$669$	−11.8156	−	6.49568i	−0.456818	−	0.251138i
$670$		0			0
$671$	42.8619	+	5.41472i	1.65467	+	0.209033i
$672$	−7.45637	−	13.5631i	−0.287636	−	0.523207i
$673$	6.31015	+	24.5764i	0.243238	+	0.947351i	0.966477	+	0.256753i	$0.0826526\pi$
$673$	6.31015	+	24.5764i	0.243238	+	0.947351i	−0.723239	+	0.690598i	$0.757347\pi$
$674$	−8.39204	−	25.8280i	−0.323249	−	0.994859i
$675$		0			0
$676$	−2.09957	+	6.46182i	−0.0807528	+	0.248532i
$677$	30.7824	+	1.93666i	1.18306	+	0.0744320i	0.642105	−	0.766617i	$-0.278061\pi$
$677$	30.7824	+	1.93666i	1.18306	+	0.0744320i	0.540959	+	0.841049i	$0.318061\pi$
$678$	−34.4428	+	36.6779i	−1.32277	+	1.40861i
$679$	1.24537	−	0.684650i	0.0477931	−	0.0262745i
$680$		0			0
$681$	−18.8577	−	40.0746i	−0.722627	−	1.53566i
$682$		−	0.0855193i		−	0.00327470i
$683$	−0.565314	+	0.266017i	−0.0216312	+	0.0101788i	−0.436564	−	0.899673i	$-0.643805\pi$
$683$	−0.565314	+	0.266017i	−0.0216312	+	0.0101788i	0.414933	+	0.909852i	$0.363805\pi$
$684$	−1.95084	−	31.0077i	−0.0745923	−	1.18561i
$685$		0			0
$686$	11.6101	+	18.2946i	0.443276	+	0.698491i
$687$	−29.5715	+	24.4637i	−1.12822	+	0.933347i
$688$	−14.3308	+	11.8554i	−0.546355	+	0.451984i
$689$	−4.09672	−	6.45540i	−0.156073	−	0.245931i
$690$		0			0
$691$	2.07242	+	32.9402i	0.0788386	+	1.25310i	0.816266	+	0.577676i	$0.196040\pi$
$691$	2.07242	+	32.9402i	0.0788386	+	1.25310i	−0.737427	+	0.675427i	$0.763960\pi$
$692$	30.3104	−	14.2630i	1.15223	−	0.542198i
$693$			7.61798i			0.289383i
$694$	1.39406	+	2.96253i	0.0529178	+	0.112456i
$695$		0			0
$696$	−8.63812	+	4.74885i	−0.327427	+	0.180005i
$697$	49.2549	−	52.4512i	1.86566	−	1.98673i
$698$	−20.1377	−	1.26696i	−0.762222	−	0.0479550i
$699$	−14.2955	+	43.9969i	−0.540705	+	1.66412i
$700$		0			0
$701$	−7.08536	−	21.8065i	−0.267610	−	0.823620i	−0.991081	−	0.133264i	$-0.957454\pi$
$701$	−7.08536	−	21.8065i	−0.267610	−	0.823620i	0.723470	−	0.690356i	$-0.242546\pi$
$702$	−0.114119	−	0.444463i	−0.00430713	−	0.0167752i
$703$	−15.6728	−	28.5087i	−0.591111	−	1.07523i
$704$	33.1283	+	4.18507i	1.24857	+	0.157731i
$705$		0			0
$706$	−58.0466	−	31.9114i	−2.18461	−	1.20100i
$707$	−0.221511	+	0.0719733i	−0.00833078	+	0.00270683i
$708$	−1.12195	−	8.88114i	−0.0421654	−	0.333774i
$709$	3.41258	−	5.37737i	0.128162	−	0.201951i	−0.774187	−	0.632957i	$-0.781841\pi$
$709$	3.41258	−	5.37737i	0.128162	−	0.201951i	0.902349	+	0.431005i	$0.141841\pi$
$710$		0			0
$711$	5.15101	+	2.03943i	0.193178	+	0.0764845i
$712$	−2.28651	−	1.45106i	−0.0856905	−	0.0543808i
$713$	−0.0251414	−	0.0634998i	−0.000941551	−	0.00237809i
$714$	−1.54988	+	24.6346i	−0.0580028	+	0.921928i
$715$		0			0
$716$	2.26385	+	2.73652i	0.0846040	+	0.102269i
$717$	−11.7217	−	12.4823i	−0.437753	−	0.466160i
$718$	−31.7624	−	10.3202i	−1.18536	−	0.385147i
$719$	2.48139	−	13.0079i	0.0925403	−	0.485113i	−0.905599	−	0.424135i	$-0.860578\pi$
$719$	2.48139	−	13.0079i	0.0925403	−	0.485113i	0.998139	−	0.0609778i	$-0.0194219\pi$
$720$		0			0
$721$	−5.30141	+	11.2661i	−0.197435	+	0.419571i
$722$	1.00917	+	0.474881i	0.0375576	+	0.0176732i
$723$	17.3910	−	43.9246i	0.646778	−	1.63357i
$724$	7.36984	−	5.35450i	0.273898	−	0.198998i
$725$		0			0
$726$	2.27300	+	1.65143i	0.0843590	+	0.0612904i
$727$	−23.7258	+	15.0569i	−0.879943	+	0.558429i	−0.897300	−	0.441421i	$-0.854475\pi$
$727$	−23.7258	+	15.0569i	−0.879943	+	0.558429i	0.0173574	+	0.999849i	$0.494475\pi$
$728$	−1.61955	+	0.308945i	−0.0600244	+	0.0114503i
$729$	20.0521	+	18.8302i	0.742670	+	0.697414i
$730$		0			0
$731$	35.2348	−	4.45119i	1.30321	−	0.164633i
$732$	44.7693	+	61.6196i	1.65472	+	2.27753i
$733$	15.5934	+	2.97459i	0.575954	+	0.109869i	0.467125	−	0.884191i	$-0.345290\pi$
$733$	15.5934	+	2.97459i	0.575954	+	0.109869i	0.108829	+	0.994060i	$0.465290\pi$
$734$	11.7785	−	4.66343i	0.434752	−	0.172130i
$735$		0			0
$736$	42.1045	−	10.8106i	1.55199	−	0.398484i
$737$	−7.49120	+	29.1763i	−0.275942	+	1.07472i
$738$	72.7400	−	4.57641i	2.67759	−	0.168460i
$739$	32.8772	−	39.7417i	1.20941	−	1.46192i	0.361009	−	0.932562i	$-0.382432\pi$
$739$	32.8772	−	39.7417i	1.20941	−	1.46192i	0.848398	−	0.529360i	$-0.177568\pi$
$740$		0			0
$741$	33.3607	+	8.56557i	1.22554	+	0.314664i
$742$	−1.87737	+	3.41492i	−0.0689204	+	0.125366i
$743$	13.2830	−	18.2825i	0.487307	−	0.670720i	−0.492582	−	0.870266i	$-0.663947\pi$
$743$	13.2830	−	18.2825i	0.487307	−	0.670720i	0.979888	+	0.199546i	$0.0639467\pi$
$744$	0.0152060	−	0.0142794i	0.000557479	−	0.000523507i
$745$		0			0
$746$	9.34446	+	48.9854i	0.342125	+	1.79348i
$747$	1.47804	−	11.6999i	0.0540786	−	0.428076i
$748$	−35.9291	−	29.7232i	−1.31370	−	1.08679i
$749$	−14.4881			−0.529382
$750$		0			0
$751$	−44.1937			−1.61265			−0.806326	−	0.591471i	$-0.798547\pi$
$751$	−44.1937			−1.61265			−0.806326	+	0.591471i	$0.798547\pi$
$752$	16.7732	+	13.8760i	0.611655	+	0.506005i
$753$	−2.97946	+	23.5849i	−0.108578	+	0.859480i
$754$	−7.43490	−	38.9751i	−0.270763	−	1.41939i
$755$		0			0
$756$	−0.0915846	+	0.0860037i	−0.00333090	+	0.00312792i
$757$	3.03106	−	4.17190i	0.110166	−	0.151630i	−0.750374	−	0.661014i	$-0.770126\pi$
$757$	3.03106	−	4.17190i	0.110166	−	0.151630i	0.860540	+	0.509383i	$0.170126\pi$
$758$	27.1407	−	49.3688i	0.985795	−	1.79315i
$759$	−41.2535	−	10.5921i	−1.49741	−	0.384468i
$760$		0			0
$761$	10.8259	−	13.0862i	0.392437	−	0.474375i	−0.536879	−	0.843659i	$-0.680397\pi$
$761$	10.8259	−	13.0862i	0.392437	−	0.474375i	0.929317	+	0.369284i	$0.120397\pi$
$762$	35.1722	−	2.21285i	1.27415	−	0.0801630i
$763$	1.00834	−	3.92723i	0.0365044	−	0.142175i
$764$	37.8984	−	9.73067i	1.37112	−	0.352043i
$765$		0			0
$766$	38.5197	−	15.2510i	1.39177	−	0.551042i
$767$	4.89690	+	0.934134i	0.176817	+	0.0337296i
$768$	−14.0004	−	19.2698i	−0.505194	−	0.695340i
$769$	−15.4047	+	1.94606i	−0.555507	+	0.0701768i	−0.398075	−	0.917353i	$-0.630321\pi$
$769$	−15.4047	+	1.94606i	−0.555507	+	0.0701768i	−0.157432	+	0.987530i	$0.550321\pi$
$770$		0			0
$771$	2.20930	+	2.07468i	0.0795662	+	0.0747176i
$772$	14.3554	−	2.73843i	0.516661	−	0.0985583i
$773$	7.06432	−	4.48315i	0.254086	−	0.161248i	−0.402683	−	0.915339i	$-0.631922\pi$
$773$	7.06432	−	4.48315i	0.254086	−	0.161248i	0.656769	+	0.754091i	$0.271922\pi$
$774$	29.1039	+	21.1452i	1.04612	+	0.760050i
$775$		0			0
$776$	−0.986286	+	0.716579i	−0.0354056	+	0.0257237i
$777$	−5.17702	+	13.0757i	−0.185725	+	0.469087i
$778$	−55.9423	−	26.3245i	−2.00563	−	0.943777i
$779$	−21.7890	+	46.3040i	−0.780672	+	1.65901i
$780$		0			0
$781$	3.09187	−	16.2081i	0.110636	−	0.579972i
$782$	−65.9326	−	21.4228i	−2.35774	−	0.766077i
$783$	−0.286353	−	0.304935i	−0.0102334	−	0.0108975i
$784$	13.2656	+	16.0353i	0.473770	+	0.572690i
$785$		0			0
$786$	−1.95775	+	31.1176i	−0.0698307	+	1.10993i
$787$	18.9661	+	47.9028i	0.676067	+	1.70755i	0.706207	+	0.708006i	$0.250405\pi$
$787$	18.9661	+	47.9028i	0.676067	+	1.70755i	−0.0301394	+	0.999546i	$0.509595\pi$
$788$	20.6060	+	13.0770i	0.734060	+	0.465848i
$789$	23.2450	+	9.20336i	0.827545	+	0.327648i
$790$		0			0
$791$	−4.11066	+	6.47736i	−0.146158	+	0.230308i
$792$	−0.819045	−	6.48341i	−0.0291035	−	0.230378i
$793$	−40.3407	+	13.1075i	−1.43254	+	0.465461i
$794$	24.8973	+	13.6874i	0.883572	+	0.485748i
$795$		0			0
$796$	−21.9961	−	2.77875i	−0.779629	−	0.0984901i
$797$	−7.68325	−	13.9758i	−0.272155	−	0.495047i	0.704545	−	0.709660i	$-0.251151\pi$
$797$	−7.68325	−	13.9758i	−0.272155	−	0.495047i	−0.976699	+	0.214612i	$0.931151\pi$
$798$	−4.36585	−	17.0038i	−0.154549	−	0.601930i
$799$	−12.8451	−	39.5332i	−0.454428	−	1.39859i
$800$		0			0
$801$	3.79626	−	11.6837i	0.134134	−	0.412823i
$802$	27.2156	+	1.71226i	0.961018	+	0.0604621i
$803$	22.3582	−	23.8090i	0.789003	−	0.840203i
$804$	−46.5372	+	25.5840i	−1.64124	+	0.902280i
$805$		0			0
$806$	0.0357500	+	0.0759727i	0.00125924	+	0.00267602i
$807$		−	78.8274i		−	2.77486i
$808$	0.180782	−	0.0850697i	0.00635990	−	0.00299274i
$809$	2.33909	+	37.1787i	0.0822379	+	1.30713i	0.795379	+	0.606113i	$0.207272\pi$
$809$	2.33909	+	37.1787i	0.0822379	+	1.30713i	−0.713141	+	0.701021i	$0.752728\pi$
$810$		0			0
$811$	15.9114	+	25.0723i	0.558723	+	0.880407i	0.999855	−	0.0170354i	$-0.00542281\pi$
$811$	15.9114	+	25.0723i	0.558723	+	0.880407i	−0.441132	+	0.897442i	$0.645423\pi$
$812$	−8.37036	+	6.92456i	−0.293742	+	0.243005i
$813$	−14.1211	+	11.6820i	−0.495247	+	0.409704i
$814$	−26.5014	−	41.7596i	−0.928875	−	1.46367i
$815$		0			0
$816$	3.11822	+	49.5627i	0.109160	+	1.73504i
$817$	−22.8550	+	10.7547i	−0.799595	+	0.376261i
$818$		−	25.1700i		−	0.880048i
$819$	−3.18458	−	6.76758i	−0.111278	−	0.236478i
$820$		0			0
$821$	−22.3092	+	12.2646i	−0.778598	+	0.428038i	−0.820903	−	0.571067i	$-0.806530\pi$
$821$	−22.3092	+	12.2646i	−0.778598	+	0.428038i	0.0423058	+	0.999105i	$0.486530\pi$
$822$	47.1103	−	50.1674i	1.64316	−	1.74979i
$823$	9.65525	+	0.607457i	0.336561	+	0.0211746i	0.230172	−	0.973150i	$-0.426071\pi$
$823$	9.65525	+	0.607457i	0.336561	+	0.0211746i	0.106389	+	0.994325i	$0.466071\pi$
$824$	3.30059	−	10.1582i	0.114981	−	0.353876i
$825$		0			0
$826$	−0.785195	−	2.41658i	−0.0273204	−	0.0840836i
$827$	−10.5485	−	41.0839i	−0.366809	−	1.42863i	−0.837553	−	0.546356i	$-0.816014\pi$
$827$	−10.5485	−	41.0839i	−0.366809	−	1.42863i	0.470744	−	0.882270i	$-0.343986\pi$
$828$	−18.1721	−	33.0550i	−0.631525	−	1.14874i
$829$	−0.209963	−	0.0265245i	−0.00729232	−	0.000921234i	0.121686	−	0.992569i	$-0.461170\pi$
$829$	−0.209963	−	0.0265245i	−0.00729232	−	0.000921234i	−0.128979	+	0.991647i	$0.541170\pi$
$830$		0			0
$831$	−2.26331	−	1.24426i	−0.0785133	−	0.0431630i
$832$	−31.1796	+	10.1309i	−1.08096	+	0.351225i
$833$	−4.98063	−	39.4258i	−0.172569	−	1.36602i
$834$	−15.9850	+	25.1884i	−0.553516	+	0.872202i
$835$		0			0
$836$	30.8355	+	12.2086i	1.06647	+	0.422245i
$837$	0.000747398	0	0.000474313i	2.58339e−5	0	1.63947e-5i
$838$	−8.69540	−	21.9621i	−0.300377	−	0.758667i
$839$	2.96801	−	47.1751i	0.102467	−	1.62867i	−0.525758	−	0.850634i	$-0.676218\pi$
$839$	2.96801	−	47.1751i	0.102467	−	1.62867i	0.628225	−	0.778032i	$-0.283782\pi$
$840$		0			0
$841$	−4.57033	−	5.52458i	−0.157597	−	0.190503i
$842$	−33.9357	−	36.1378i	−1.16950	−	1.24539i
$843$	−12.1601	−	3.95106i	−0.418817	−	0.136082i
$844$	−2.91959	+	15.3050i	−0.100496	+	0.526821i
$845$		0			0
$846$	17.9277	−	38.0983i	0.616368	−	1.30985i
$847$	0.387614	+	0.182397i	0.0133186	+	0.00626724i
$848$	−2.88621	+	7.28974i	−0.0991129	+	0.250331i
$849$	62.5687	−	45.4588i	2.14735	−	1.56014i
$850$		0			0
$851$	−31.9545	−	23.2163i	−1.09539	−	0.795845i
$852$	24.5616	−	15.5873i	0.841467	−	0.534011i
$853$	3.86126	−	0.736574i	0.132207	−	0.0252198i	−0.120853	−	0.992670i	$-0.538563\pi$
$853$	3.86126	−	0.736574i	0.132207	−	0.0252198i	0.253060	+	0.967451i	$0.418563\pi$
$854$	15.7601	+	14.7997i	0.539299	+	0.506435i
$855$		0			0
$856$	12.3303	−	1.55768i	0.421441	−	0.0532404i
$857$	17.5475	+	24.1520i	0.599410	+	0.825017i	0.995654	−	0.0931279i	$-0.0296866\pi$
$857$	17.5475	+	24.1520i	0.599410	+	0.825017i	−0.396244	+	0.918145i	$0.629687\pi$
$858$	51.4351	+	9.81178i	1.75597	+	0.334969i
$859$	−35.8707	+	14.2022i	−1.22389	+	0.484574i	−0.889098	−	0.457717i	$-0.848667\pi$
$859$	−35.8707	+	14.2022i	−1.22389	+	0.484574i	−0.334796	+	0.942291i	$0.608667\pi$
$860$		0			0
$861$	21.4266	−	5.50141i	0.730216	−	0.187488i
$862$	−12.0975	+	47.1166i	−0.412042	+	1.60480i
$863$	−5.85166	+	0.368155i	−0.199193	+	0.0125322i	−0.162074	−	0.986779i	$-0.551818\pi$
$863$	−5.85166	+	0.368155i	−0.199193	+	0.0125322i	−0.0371194	+	0.999311i	$0.511818\pi$
$864$	−0.359143	+	0.434129i	−0.0122183	+	0.0147694i
$865$		0			0
$866$	−52.2518	−	13.4160i	−1.77559	−	0.455893i
$867$	25.5753	−	46.5212i	0.868582	−	1.57994i
$868$	0.0135122	−	0.0185979i	0.000458633	−	0.000631255i
$869$	−4.31090	+	4.04820i	−0.146237	+	0.137326i
$870$		0			0
$871$	−5.54175	−	29.0509i	−0.187775	−	0.984351i
$872$	−0.435930	+	3.45074i	−0.0147625	+	0.116857i
$873$	−4.26126	−	3.52522i	−0.144222	−	0.119311i
$874$	49.3060			1.66780
$875$		0			0
$876$	57.5817			1.94551
$877$	−4.11957	−	3.40800i	−0.139108	−	0.115080i	0.565268	−	0.824908i	$-0.308773\pi$
$877$	−4.11957	−	3.40800i	−0.139108	−	0.115080i	−0.704376	+	0.709828i	$0.748773\pi$
$878$	1.03063	−	8.15831i	0.0347822	−	0.275330i
$879$	−1.04222	−	5.46348i	−0.0351531	−	0.184279i
$880$		0			0
$881$	−10.9723	+	10.3037i	−0.369666	+	0.347139i	−0.847010	−	0.531577i	$-0.821600\pi$
$881$	−10.9723	+	10.3037i	−0.369666	+	0.347139i	0.477344	+	0.878717i	$0.341600\pi$
$882$	23.6604	−	32.5657i	0.796686	−	1.09654i
$883$	19.8232	−	36.0582i	0.667102	−	1.21345i	−0.298743	−	0.954334i	$-0.596567\pi$
$883$	19.8232	−	36.0582i	0.667102	−	1.21345i	0.965845	−	0.259121i	$-0.0834328\pi$
$884$	44.3436	+	11.3855i	1.49144	+	0.382936i
$885$		0			0
$886$	−15.3495	+	18.5544i	−0.515676	+	0.623346i
$887$	−3.68358	+	0.231751i	−0.123683	+	0.00778145i	−0.124511	−	0.992218i	$-0.539736\pi$
$887$	−3.68358	+	0.231751i	−0.123683	+	0.00778145i	0.000828554		1.00000i	$0.499736\pi$
$888$	3.00016	−	11.6849i	0.100679	−	0.392118i
$889$	5.20458	−	1.33631i	0.174556	−	0.0448184i
$890$		0			0
$891$	−26.7923	+	10.6078i	−0.897575	+	0.355375i
$892$	12.5211	+	2.38852i	0.419236	+	0.0799735i
$893$	17.3772	+	23.9177i	0.581507	+	0.800376i
$894$	−93.6277	+	11.8279i	−3.13138	+	0.395585i
$895$		0			0
$896$	2.99049	+	2.80826i	0.0999054	+	0.0938174i
$897$	41.0761	−	7.83569i	1.37149	−	0.261626i
$898$	43.4738	−	27.5893i	1.45074	−	0.920667i
$899$	0.0619226	+	0.0449894i	0.00206523	+	0.00150048i
$900$		0			0
$901$	12.1119	−	8.79980i	0.403505	−	0.293164i
$902$	−28.6398	+	72.3360i	−0.953603	+	2.40853i
$903$	9.87973	+	4.64905i	0.328777	+	0.154711i
$904$	2.80203	−	5.95462i	0.0931941	−	0.198048i
$905$		0			0
$906$	19.0296	−	99.7565i	0.632215	−	3.31419i
$907$	52.5047	+	17.0598i	1.74339	+	0.566462i	0.995274	−	0.0971061i	$-0.0309586\pi$
$907$	52.5047	+	17.0598i	1.74339	+	0.566462i	0.748116	+	0.663568i	$0.230959\pi$
$908$	28.6622	+	30.5221i	0.951188	+	1.01291i
$909$	0.577739	+	0.698366i	0.0191624	+	0.0231633i
$910$		0			0
$911$	−0.324565	+	5.15882i	−0.0107533	+	0.170919i	0.988984	+	0.148020i	$0.0472899\pi$
$911$	−0.324565	+	5.15882i	−0.0107533	+	0.170919i	−0.999738	+	0.0228998i	$0.992710\pi$
$912$	−13.0021	−	32.8396i	−0.430543	−	1.08743i
$913$	10.6286	+	6.74511i	0.351755	+	0.223231i
$914$	−30.0514	−	11.8982i	−0.994013	−	0.393558i
$915$		0			0
$916$	19.4411	−	30.6342i	0.642351	−	1.01218i
$917$	0.595828	+	4.71647i	0.0196760	+	0.155751i
$918$	0.854568	−	0.277666i	0.0282050	−	0.00916435i
$919$	−34.5276	−	18.9817i	−1.13896	−	0.626148i	−0.203322	−	0.979112i	$-0.565174\pi$
$919$	−34.5276	−	18.9817i	−1.13896	−	0.626148i	−0.935637	+	0.352964i	$0.885174\pi$
$920$		0			0
$921$	46.0493	+	5.81738i	1.51738	+	0.191689i
$922$	−18.4955	−	33.6431i	−0.609116	−	1.10798i
$923$	4.02884	+	15.6913i	0.132611	+	0.516485i
$924$	−4.43015	−	13.6346i	−0.145741	−	0.448546i
$925$		0			0
$926$	5.59079	−	17.2067i	0.183725	−	0.565447i
$927$	48.3575	+	3.04239i	1.58827	+	0.0999253i
$928$	−33.3498	+	35.5139i	−1.09476	+	1.16580i
$929$	−23.2303	+	12.7709i	−0.762160	+	0.419001i	−0.814896	−	0.579607i	$-0.803206\pi$
$929$	−23.2303	+	12.7709i	−0.762160	+	0.419001i	0.0527356	+	0.998609i	$0.483206\pi$
$930$		0			0
$931$	12.0340	+	25.5735i	0.394397	+	0.838137i
$932$		−	43.7339i		−	1.43255i
$933$	−32.5436	+	15.3139i	−1.06543	+	0.501353i
$934$	−5.05502	−	80.3472i	−0.165405	−	2.62904i
$935$		0			0
$936$	3.43790	+	5.41727i	0.112371	+	0.177069i
$937$	−0.381511	+	0.315613i	−0.0124634	+	0.0103106i	−0.643635	−	0.765333i	$-0.722574\pi$
$937$	−0.381511	+	0.315613i	−0.0124634	+	0.0103106i	0.631171	+	0.775643i	$0.282574\pi$
$938$	−11.6148	+	9.60862i	−0.379238	+	0.313733i
$939$	11.2481	+	17.7241i	0.367067	+	0.578405i
$940$		0			0
$941$	−3.61488	−	57.4569i	−0.117842	−	1.87304i	−0.403863	−	0.914820i	$-0.632333\pi$
$941$	−3.61488	−	57.4569i	−0.117842	−	1.87304i	0.286021	−	0.958223i	$-0.407667\pi$
$942$	6.22742	−	2.93040i	0.202900	−	0.0954776i
$943$			62.1306i			2.02325i
$944$	−2.17665	−	4.62562i	−0.0708440	−	0.150551i
$945$		0			0
$946$	−33.6508	+	18.4997i	−1.09408	+	0.601476i
$947$	−20.7350	+	22.0805i	−0.673796	+	0.717519i	−0.971474	−	0.237147i	$-0.923788\pi$
$947$	−20.7350	+	22.0805i	−0.673796	+	0.717519i	0.297678	+	0.954666i	$0.403788\pi$
$948$	−10.4052	−	0.654642i	−0.337946	−	0.0212618i
$949$	−9.90931	+	30.4977i	−0.321670	+	0.989998i
$950$		0			0
$951$	−4.69430	−	14.4476i	−0.152223	−	0.468495i
$952$	−0.802888	−	3.12704i	−0.0260217	−	0.101348i
$953$	19.1977	+	34.9205i	0.621874	+	1.13118i	0.980279	+	0.197619i	$0.0633208\pi$
$953$	19.1977	+	34.9205i	0.621874	+	1.13118i	−0.358405	+	0.933566i	$0.616679\pi$
$954$	15.0453	+	1.90066i	0.487109	+	0.0615362i
$955$		0			0
$956$	14.1855	+	7.79854i	0.458792	+	0.252223i
$957$	45.3970	−	14.7504i	1.46748	−	0.476812i
$958$	−5.78198	−	45.7691i	−0.186807	−	1.47873i
$959$	5.62249	−	8.85962i	0.181560	−	0.286092i
$960$		0			0
$961$	28.8229	+	11.4118i	0.929772	+	0.368123i
$962$	41.0000	+	26.0194i	1.32189	+	0.838899i
$963$	20.7548	+	52.4207i	0.668815	+	1.68923i
$964$	−2.80431	+	44.5732i	−0.0903207	+	1.43561i
$965$		0			0
$966$	−13.5860	−	16.4227i	−0.437123	−	0.528390i
$967$	34.5659	+	36.8089i	1.11156	+	1.18369i	0.981354	+	0.192208i	$0.0615649\pi$
$967$	34.5659	+	36.8089i	1.11156	+	1.18369i	0.130209	+	0.991487i	$0.458435\pi$
$968$	−0.349495	−	0.113558i	−0.0112332	−	0.00364989i
$969$	−12.6376	+	66.2489i	−0.405980	+	2.12822i
$970$		0			0
$971$	8.63645	−	18.3534i	0.277157	−	0.588988i	−0.716983	−	0.697091i	$-0.754477\pi$
$971$	8.63645	−	18.3534i	0.277157	−	0.588988i	0.994140	+	0.108103i	$0.0344775\pi$
$972$	−46.4054	−	21.8367i	−1.48845	−	0.700414i
$973$	−1.67446	+	4.22921i	−0.0536808	+	0.135582i
$974$	−20.6460	+	15.0002i	−0.661540	+	0.480637i
$975$		0			0
$976$	35.1898	+	25.5669i	1.12640	+	0.818375i
$977$	17.4798	−	11.0930i	0.559228	−	0.354897i	−0.225977	−	0.974133i	$-0.572558\pi$
$977$	17.4798	−	11.0930i	0.559228	−	0.354897i	0.785205	+	0.619236i	$0.212558\pi$
$978$	−21.9734	+	4.19165i	−0.702632	+	0.134034i
$979$	9.55934	+	8.97682i	0.305518	+	0.286900i
$980$		0			0
$981$	−15.6540	+	1.97756i	−0.499793	+	0.0631386i
$982$	−1.78788	−	2.46080i	−0.0570534	−	0.0785273i
$983$	−48.8807	−	9.32449i	−1.55905	−	0.297405i	−0.665511	−	0.746388i	$-0.731786\pi$
$983$	−48.8807	−	9.32449i	−1.55905	−	0.297405i	−0.893540	+	0.448983i	$0.851786\pi$
$984$	−17.6440	+	6.98574i	−0.562469	+	0.222697i
$985$		0			0
$986$	75.2537	−	19.3219i	2.39657	−	0.615333i
$987$	3.17822	−	12.3783i	0.101164	−	0.394007i
$988$	−32.4970	+	2.04454i	−1.03387	+	0.0650453i
$989$	−19.5478	+	23.6292i	−0.621583	+	0.751365i
$990$		0			0
$991$	−50.6629	−	13.0080i	−1.60936	−	0.413214i	−0.666260	−	0.745720i	$-0.732106\pi$
$991$	−50.6629	−	13.0080i	−1.60936	−	0.413214i	−0.943101	+	0.332506i	$0.892106\pi$
$992$	0.0496658	−	0.0903417i	0.00157689	−	0.00286835i
$993$	26.6944	−	36.7418i	0.847123	−	1.16596i
$994$	6.01926	−	5.65246i	0.190919	−	0.179285i
$995$		0			0
$996$	4.15855	+	21.7999i	0.131769	+	0.690756i
$997$	−5.04743	+	39.9545i	−0.159854	+	1.26537i	0.684272	+	0.729226i	$0.260120\pi$
$997$	−5.04743	+	39.9545i	−0.159854	+	1.26537i	−0.844126	+	0.536145i	$0.819880\pi$
$998$	−18.4291	−	15.2459i	−0.583364	−	0.482600i
$999$	0.511943			0.0161972

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	625.2.h.b.24.19		440
5.2	odd	4		125.2.g.a.71.2	✓	220
5.3	odd	4		625.2.g.a.601.10		220
5.4	even	2	inner	625.2.h.b.24.4		440
125.8	odd	100		625.2.g.a.26.10		220
125.44	even	50	inner	625.2.h.b.599.19		440
125.81	even	25	inner	625.2.h.b.599.4		440
125.117	odd	100		125.2.g.a.81.2	yes	220

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
125.2.g.a.71.2	✓	220	5.2	odd	4
125.2.g.a.81.2	yes	220	125.117	odd	100
625.2.g.a.26.10		220	125.8	odd	100
625.2.g.a.601.10		220	5.3	odd	4
625.2.h.b.24.4		440	5.4	even	2	inner
625.2.h.b.24.19		440	1.1	even	1	trivial
625.2.h.b.599.4		440	125.81	even	25	inner
625.2.h.b.599.19		440	125.44	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)

\(f(q)\)	\(=\)	\(q+(1.60169 + 1.32504i) q^{2} +(0.307726 - 2.43590i) q^{3} +(0.434938 + 2.28002i) q^{4} +(3.72054 - 3.49382i) q^{6} +(0.457412 - 0.629574i) q^{7} +(-0.321599 + 0.584987i) q^{8} +(-2.93319 - 0.753115i) q^{9} +O(q^{10})\)	\(q+(1.60169 + 1.32504i) q^{2} +(0.307726 - 2.43590i) q^{3} +(0.434938 + 2.28002i) q^{4} +(3.72054 - 3.49382i) q^{6} +(0.457412 - 0.629574i) q^{7} +(-0.321599 + 0.584987i) q^{8} +(-2.93319 - 0.753115i) q^{9} +(2.06052 - 2.49074i) q^{11} +(5.68776 - 0.357844i) q^{12} +(-0.789285 + 3.07406i) q^{13} +(1.56684 - 0.402296i) q^{14} +(3.02605 - 1.19810i) q^{16} +(-6.10458 - 1.16451i) q^{17} +(-3.70016 - 5.09284i) q^{18} +(4.38516 - 0.553975i) q^{19} +(-1.39282 - 1.30795i) q^{21} +(6.60063 - 1.25914i) q^{22} +(4.53094 - 2.87542i) q^{23} +(1.32601 + 0.963402i) q^{24} +(-5.33743 + 3.87787i) q^{26} +(-0.0256046 + 0.0646699i) q^{27} +(1.63439 + 0.769085i) q^{28} +(-2.56070 + 5.44177i) q^{29} +(0.00238475 - 0.0125013i) q^{31} +(7.70409 + 2.50321i) q^{32} +(-5.43313 - 5.78569i) q^{33} +(-8.23465 - 9.95398i) q^{34} +(0.441365 - 7.01530i) q^{36} +(-2.70952 - 6.84347i) q^{37} +(7.75772 + 4.92320i) q^{38} +(7.24524 + 2.86859i) q^{39} +(-6.20373 + 9.77552i) q^{41} +(-0.497797 - 3.94047i) q^{42} +(-5.43498 + 1.76593i) q^{43} +(6.57514 + 3.61471i) q^{44} +(11.0672 + 1.39811i) q^{46} +(3.22228 + 5.86131i) q^{47} +(-1.98725 - 7.73985i) q^{48} +(1.97598 + 6.08145i) q^{49} +(-4.71518 + 14.5118i) q^{51} +(-7.35223 - 0.462563i) q^{52} +(-1.64907 + 1.75608i) q^{53} +(-0.126701 + 0.0696543i) q^{54} +(0.221189 + 0.470051i) q^{56} -10.8523i q^{57} +(-11.3120 + 5.32302i) q^{58} +(-0.0986283 - 1.56765i) q^{59} +(7.16121 + 11.2843i) q^{61} +(0.0203843 - 0.0168634i) q^{62} +(-1.81582 + 1.50217i) q^{63} +(5.53494 + 8.72167i) q^{64} +(-1.03595 - 16.4660i) q^{66} +(-8.43161 + 3.96761i) q^{67} -14.4251i q^{68} +(-5.60996 - 11.9218i) q^{69} +(4.47304 - 2.45907i) q^{71} +(1.38387 - 1.47368i) q^{72} +(10.0839 + 0.634423i) q^{73} +(4.72802 - 14.5513i) q^{74} +(3.17035 + 9.75733i) q^{76} +(-0.625598 - 2.43654i) q^{77} +(7.80366 + 14.1948i) q^{78} +(-1.81498 - 0.229286i) q^{79} +(-7.81158 - 4.29445i) q^{81} +(-22.8894 + 7.43721i) q^{82} +(0.488071 + 3.86348i) q^{83} +(2.37636 - 3.74455i) q^{84} +(-11.0451 - 4.37306i) q^{86} +(12.4676 + 7.91220i) q^{87} +(0.794389 + 2.00640i) q^{88} +(-0.254721 + 4.04868i) q^{89} +(1.57432 + 1.90303i) q^{91} +(8.52670 + 9.08002i) q^{92} +(-0.0297182 - 0.00965601i) q^{93} +(-2.60534 + 13.6576i) q^{94} +(8.46833 - 17.9961i) q^{96} +(1.65242 + 0.777570i) q^{97} +(-4.89322 + 12.3589i) q^{98} +(-7.91970 + 5.75400i) 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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