LMFDB - Embedded newform 625.2.g.a.26.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [625,2,Mod(26,625)]

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([14]))

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

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

chi := DirichletCharacter("625.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 625 = 5^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	625.g (of order $25$, 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:	$220$
Relative dimension:	$11$ over $\Q(\zeta_{25})$
Twist minimal:	no (minimal twist has level 125)
Sato-Tate group:	$\mathrm{SU}(2)[C_{25}]$

Embedding invariants

Embedding label			26.10
Character	$\chi$	$=$	625.26
Dual form			625.2.g.a.601.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.32504 + 1.60169i) q^{2} +(2.43590 - 0.307726i) q^{3} +(-0.434938 + 2.28002i) q^{4} +(3.72054 + 3.49382i) q^{6} +(-0.629574 + 0.457412i) q^{7} +(-0.584987 + 0.321599i) q^{8} +(2.93319 - 0.753115i) q^{9} +O(q^{10})$	\(q+(1.32504 + 1.60169i) q^{2} +(2.43590 - 0.307726i) q^{3} +(-0.434938 + 2.28002i) q^{4} +(3.72054 + 3.49382i) q^{6} +(-0.629574 + 0.457412i) q^{7} +(-0.584987 + 0.321599i) q^{8} +(2.93319 - 0.753115i) q^{9} +(2.06052 + 2.49074i) q^{11} +(-0.357844 + 5.68776i) q^{12} +(-3.07406 + 0.789285i) q^{13} +(-1.56684 - 0.402296i) q^{14} +(3.02605 + 1.19810i) q^{16} +(-1.16451 - 6.10458i) q^{17} +(5.09284 + 3.70016i) q^{18} +(-4.38516 - 0.553975i) q^{19} +(-1.39282 + 1.30795i) q^{21} +(-1.25914 + 6.60063i) q^{22} +(2.87542 - 4.53094i) q^{23} +(-1.32601 + 0.963402i) q^{24} +(-5.33743 - 3.87787i) q^{26} +(0.0646699 - 0.0256046i) q^{27} +(-0.769085 - 1.63439i) q^{28} +(2.56070 + 5.44177i) q^{29} +(0.00238475 + 0.0125013i) q^{31} +(2.50321 + 7.70409i) q^{32} +(5.78569 + 5.43313i) q^{33} +(8.23465 - 9.95398i) q^{34} +(0.441365 + 7.01530i) q^{36} +(-6.84347 - 2.70952i) q^{37} +(-4.92320 - 7.75772i) q^{38} +(-7.24524 + 2.86859i) q^{39} +(-6.20373 - 9.77552i) q^{41} +(-3.94047 - 0.497797i) q^{42} +(-1.76593 + 5.43498i) q^{43} +(-6.57514 + 3.61471i) q^{44} +(11.0672 - 1.39811i) q^{46} +(5.86131 + 3.22228i) q^{47} +(7.73985 + 1.98725i) q^{48} +(-1.97598 + 6.08145i) q^{49} +(-4.71518 - 14.5118i) q^{51} +(-0.462563 - 7.35223i) q^{52} +(-1.75608 + 1.64907i) q^{53} +(0.126701 + 0.0696543i) q^{54} +(0.221189 - 0.470051i) q^{56} -10.8523 q^{57} +(-5.32302 + 11.3120i) q^{58} +(0.0986283 - 1.56765i) q^{59} +(7.16121 - 11.2843i) q^{61} +(-0.0168634 + 0.0203843i) q^{62} +(-1.50217 + 1.81582i) q^{63} +(-5.53494 + 8.72167i) q^{64} +(-1.03595 + 16.4660i) q^{66} +(3.96761 - 8.43161i) q^{67} +14.4251 q^{68} +(5.60996 - 11.9218i) q^{69} +(4.47304 + 2.45907i) q^{71} +(-1.47368 + 1.38387i) q^{72} +(-0.634423 - 10.0839i) q^{73} +(-4.72802 - 14.5513i) q^{74} +(3.17035 - 9.75733i) q^{76} +(-2.43654 - 0.625598i) q^{77} +(-14.1948 - 7.80366i) q^{78} +(1.81498 - 0.229286i) q^{79} +(-7.81158 + 4.29445i) q^{81} +(7.43721 - 22.8894i) q^{82} +(-3.86348 - 0.488071i) q^{83} +(-2.37636 - 3.74455i) q^{84} +(-11.0451 + 4.37306i) q^{86} +(7.91220 + 12.4676i) q^{87} +(-2.00640 - 0.794389i) q^{88} +(0.254721 + 4.04868i) q^{89} +(1.57432 - 1.90303i) q^{91} +(9.08002 + 8.52670i) q^{92} +(0.00965601 + 0.0297182i) q^{93} +(2.60534 + 13.6576i) q^{94} +(8.46833 + 17.9961i) q^{96} +(0.777570 + 1.65242i) q^{97} +(-12.3589 + 4.89322i) q^{98} +(7.91970 + 5.75400i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 220 q + 20 q^{2} + 20 q^{3} - 20 q^{4} - 20 q^{6} + 15 q^{7} + 5 q^{8} - 20 q^{9}+O(q^{10}) $ 220 * q + 20 * q^2 + 20 * q^3 - 20 * q^4 - 20 * q^6 + 15 * q^7 + 5 * q^8 - 20 * q^9	$ 220 q + 20 q^{2} + 20 q^{3} - 20 q^{4} - 20 q^{6} + 15 q^{7} + 5 q^{8} - 20 q^{9} - 15 q^{11} + 100 q^{12} + 20 q^{13} - 10 q^{14} + 15 q^{17} - 10 q^{18} - 10 q^{19} - 5 q^{21} - 25 q^{22} + 90 q^{23} + 15 q^{24} + 15 q^{26} - 10 q^{27} - 30 q^{28} - 10 q^{29} - 10 q^{31} - 20 q^{32} - 15 q^{33} + 5 q^{34} - 210 q^{36} - 20 q^{37} - 30 q^{38} - 5 q^{41} - 70 q^{42} - 25 q^{43} + 15 q^{44} + 100 q^{47} - 105 q^{48} - 20 q^{49} + 25 q^{51} - 85 q^{52} - 20 q^{53} + 60 q^{54} - 105 q^{56} - 40 q^{57} + 225 q^{58} + 5 q^{59} - 65 q^{62} - 85 q^{63} + 45 q^{64} + 55 q^{66} + 105 q^{67} - 80 q^{68} + 40 q^{69} - 85 q^{71} - 160 q^{72} - 40 q^{73} + 35 q^{74} + 35 q^{76} - 75 q^{77} + 10 q^{78} + 55 q^{81} + 95 q^{82} - 50 q^{83} + 115 q^{84} + 40 q^{86} - 95 q^{87} - 165 q^{88} + 55 q^{89} - 105 q^{91} - 155 q^{92} + 185 q^{93} + 60 q^{94} + 135 q^{96} - 65 q^{97} - 135 q^{98} + 45 q^{99}+O(q^{100}) $ 220 * q + 20 * q^2 + 20 * q^3 - 20 * q^4 - 20 * q^6 + 15 * q^7 + 5 * q^8 - 20 * q^9 - 15 * q^11 + 100 * q^12 + 20 * q^13 - 10 * q^14 + 15 * q^17 - 10 * q^18 - 10 * q^19 - 5 * q^21 - 25 * q^22 + 90 * q^23 + 15 * q^24 + 15 * q^26 - 10 * q^27 - 30 * q^28 - 10 * q^29 - 10 * q^31 - 20 * q^32 - 15 * q^33 + 5 * q^34 - 210 * q^36 - 20 * q^37 - 30 * q^38 - 5 * q^41 - 70 * q^42 - 25 * q^43 + 15 * q^44 + 100 * q^47 - 105 * q^48 - 20 * q^49 + 25 * q^51 - 85 * q^52 - 20 * q^53 + 60 * q^54 - 105 * q^56 - 40 * q^57 + 225 * q^58 + 5 * q^59 - 65 * q^62 - 85 * q^63 + 45 * q^64 + 55 * q^66 + 105 * q^67 - 80 * q^68 + 40 * q^69 - 85 * q^71 - 160 * q^72 - 40 * q^73 + 35 * q^74 + 35 * q^76 - 75 * q^77 + 10 * q^78 + 55 * q^81 + 95 * q^82 - 50 * q^83 + 115 * q^84 + 40 * q^86 - 95 * q^87 - 165 * q^88 + 55 * q^89 - 105 * q^91 - 155 * q^92 + 185 * q^93 + 60 * q^94 + 135 * q^96 - 65 * q^97 - 135 * q^98 + 45 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{25}\right)$

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 $

$2$	1.32504	+	1.60169i	0.936941	+	1.13257i	0.990977	+	0.134029i	$0.0427914\pi$
$2$	1.32504	+	1.60169i	0.936941	+	1.13257i	−0.0540360	+	0.998539i	$0.517209\pi$
$3$	2.43590	−	0.307726i	1.40637	−	0.177666i	0.614771	−	0.788706i	$-0.289249\pi$
$3$	2.43590	−	0.307726i	1.40637	−	0.177666i	0.791600	+	0.611040i	$0.209249\pi$
$4$	−0.434938	+	2.28002i	−0.217469	+	1.14001i
$5$		0			0
$5$		0			0
$6$	3.72054	+	3.49382i	1.51891	+	1.42635i
$7$	−0.629574	+	0.457412i	−0.237956	+	0.172885i	−0.700372	−	0.713778i	$-0.746983\pi$
$7$	−0.629574	+	0.457412i	−0.237956	+	0.172885i	0.462416	+	0.886663i	$0.346983\pi$
$8$	−0.584987	+	0.321599i	−0.206824	+	0.113703i
$9$	2.93319	−	0.753115i	0.977729	−	0.251038i
$10$		0			0
$11$	2.06052	+	2.49074i	0.621270	+	0.750986i	0.983461	−	0.181118i	$-0.0579715\pi$
$11$	2.06052	+	2.49074i	0.621270	+	0.750986i	−0.362192	+	0.932104i	$0.617971\pi$
$12$	−0.357844	+	5.68776i	−0.103301	+	1.64192i
$13$	−3.07406	+	0.789285i	−0.852592	+	0.218908i	−0.649604	−	0.760273i	$-0.725065\pi$
$13$	−3.07406	+	0.789285i	−0.852592	+	0.218908i	−0.202988	+	0.979181i	$0.565065\pi$
$14$	−1.56684	−	0.402296i	−0.418756	−	0.107518i
$15$		0			0
$16$	3.02605	+	1.19810i	0.756512	+	0.299524i
$17$	−1.16451	−	6.10458i	−0.282436	−	1.48058i	−0.786864	−	0.617126i	$-0.788297\pi$
$17$	−1.16451	−	6.10458i	−0.282436	−	1.48058i	0.504429	−	0.863453i	$-0.331703\pi$
$18$	5.09284	+	3.70016i	1.20039	+	0.872137i
$19$	−4.38516	−	0.553975i	−1.00603	−	0.127091i	−0.394983	−	0.918688i	$-0.629250\pi$
$19$	−4.38516	−	0.553975i	−1.00603	−	0.127091i	−0.611042	+	0.791598i	$0.709250\pi$
$20$		0			0
$21$	−1.39282	+	1.30795i	−0.303939	+	0.285418i
$22$	−1.25914	+	6.60063i	−0.268449	+	1.40726i
$23$	2.87542	−	4.53094i	0.599567	−	0.944766i	−0.400034	−	0.916500i	$-0.631002\pi$
$23$	2.87542	−	4.53094i	0.599567	−	0.944766i	0.999600	−	0.0282655i	$-0.00899838\pi$
$24$	−1.32601	+	0.963402i	−0.270670	+	0.196654i
$25$		0			0
$26$	−5.33743	−	3.87787i	−1.04676	−	0.760513i
$27$	0.0646699	−	0.0256046i	0.0124457	−	0.00492761i
$28$	−0.769085	−	1.63439i	−0.145343	−	0.308870i
$29$	2.56070	+	5.44177i	0.475510	+	1.01051i	0.988374	+	0.152041i	$0.0485845\pi$
$29$	2.56070	+	5.44177i	0.475510	+	1.01051i	−0.512864	+	0.858470i	$0.671416\pi$
$30$		0			0
$31$	0.00238475	+	0.0125013i	0.000428314	+	0.00224530i	0.982501	−	0.186259i	$-0.0596362\pi$
$31$	0.00238475	+	0.0125013i	0.000428314	+	0.00224530i	−0.982072	+	0.188504i	$0.939636\pi$
$32$	2.50321	+	7.70409i	0.442509	+	1.36190i
$33$	5.78569	+	5.43313i	1.00716	+	0.945786i
$34$	8.23465	−	9.95398i	1.41223	−	1.70709i
$35$		0			0
$36$	0.441365	+	7.01530i	0.0735608	+	1.16922i
$37$	−6.84347	−	2.70952i	−1.12506	−	0.445443i	−0.269424	−	0.963022i	$-0.586833\pi$
$37$	−6.84347	−	2.70952i	−1.12506	−	0.445443i	−0.855635	+	0.517579i	$0.826833\pi$
$38$	−4.92320	−	7.75772i	−0.798648	−	1.25847i
$39$	−7.24524	+	2.86859i	−1.16017	+	0.459343i
$40$		0			0
$41$	−6.20373	−	9.77552i	−0.968861	−	1.52668i	−0.845265	−	0.534347i	$-0.820557\pi$
$41$	−6.20373	−	9.77552i	−0.968861	−	1.52668i	−0.123596	−	0.992333i	$-0.539443\pi$
$42$	−3.94047	−	0.497797i	−0.608028	−	0.0768118i
$43$	−1.76593	+	5.43498i	−0.269302	+	0.828827i	0.721369	+	0.692551i	$0.243513\pi$
$43$	−1.76593	+	5.43498i	−0.269302	+	0.828827i	−0.990671	+	0.136276i	$0.956487\pi$
$44$	−6.57514	+	3.61471i	−0.991240	+	0.544939i
$45$		0			0
$46$	11.0672	−	1.39811i	1.63177	−	0.206141i
$47$	5.86131	+	3.22228i	0.854959	+	0.470018i	0.848024	−	0.529958i	$-0.177792\pi$
$47$	5.86131	+	3.22228i	0.854959	+	0.470018i	0.00693559	+	0.999976i	$0.497792\pi$
$48$	7.73985	+	1.98725i	1.11715	+	0.286836i
$49$	−1.97598	+	6.08145i	−0.282283	+	0.868778i
$50$		0			0
$51$	−4.71518	−	14.5118i	−0.660258	−	2.03206i
$52$	−0.462563	−	7.35223i	−0.0641459	−	1.01957i
$53$	−1.75608	+	1.64907i	−0.241217	+	0.226518i	−0.795721	−	0.605663i	$-0.792908\pi$
$53$	−1.75608	+	1.64907i	−0.241217	+	0.226518i	0.554504	+	0.832181i	$0.312908\pi$
$54$	0.126701	+	0.0696543i	0.0172418	+	0.00947875i
$55$		0			0
$56$	0.221189	−	0.470051i	0.0295576	−	0.0628132i
$57$	−10.8523			−1.43742
$58$	−5.32302	+	11.3120i	−0.698946	+	1.48534i
$59$	0.0986283	−	1.56765i	0.0128403	−	0.204091i	−0.986376	−	0.164507i	$-0.947397\pi$
$59$	0.0986283	−	1.56765i	0.0128403	−	0.204091i	0.999216	−	0.0395840i	$-0.0126033\pi$
$60$		0			0
$61$	7.16121	−	11.2843i	0.916899	−	1.44480i	0.0213827	−	0.999771i	$-0.493193\pi$
$61$	7.16121	−	11.2843i	0.916899	−	1.44480i	0.895516	−	0.445030i	$-0.146807\pi$
$62$	−0.0168634	+	0.0203843i	−0.00214165	+	0.00258881i
$63$	−1.50217	+	1.81582i	−0.189256	+	0.228771i
$64$	−5.53494	+	8.72167i	−0.691868	+	1.09021i
$65$		0			0
$66$	−1.03595	+	16.4660i	−0.127517	+	2.02682i
$67$	3.96761	−	8.43161i	0.484721	−	1.03009i	−0.501577	−	0.865113i	$-0.667247\pi$
$67$	3.96761	−	8.43161i	0.484721	−	1.03009i	0.986298	−	0.164972i	$-0.0527534\pi$
$68$	14.4251			1.74930
$69$	5.60996	−	11.9218i	0.675360	−	1.43521i
$70$		0			0
$71$	4.47304	+	2.45907i	0.530852	+	0.291838i	0.724549	−	0.689223i	$-0.242048\pi$
$71$	4.47304	+	2.45907i	0.530852	+	0.291838i	−0.193697	+	0.981061i	$0.562048\pi$
$72$	−1.47368	+	1.38387i	−0.173674	+	0.163091i
$73$	−0.634423	−	10.0839i	−0.0742536	−	1.18023i	−0.842001	−	0.539476i	$-0.818623\pi$
$73$	−0.634423	−	10.0839i	−0.0742536	−	1.18023i	0.767748	−	0.640752i	$-0.221377\pi$
$74$	−4.72802	−	14.5513i	−0.549621	−	1.69156i
$75$		0			0
$76$	3.17035	−	9.75733i	0.363664	−	1.11924i
$77$	−2.43654	−	0.625598i	−0.277670	−	0.0712935i
$78$	−14.1948	−	7.80366i	−1.60725	−	0.883591i
$79$	1.81498	−	0.229286i	0.204201	−	0.0257966i	−0.0225670	−	0.999745i	$-0.507184\pi$
$79$	1.81498	−	0.229286i	0.204201	−	0.0257966i	0.226769	+	0.973949i	$0.427184\pi$
$80$		0			0
$81$	−7.81158	+	4.29445i	−0.867954	+	0.477162i
$82$	7.43721	−	22.8894i	0.821303	−	2.52771i
$83$	−3.86348	−	0.488071i	−0.424072	−	0.0535727i	−0.0895985	−	0.995978i	$-0.528558\pi$
$83$	−3.86348	−	0.488071i	−0.424072	−	0.0535727i	−0.334473	+	0.942405i	$0.608558\pi$
$84$	−2.37636	−	3.74455i	−0.259282	−	0.408564i
$85$		0			0
$86$	−11.0451	+	4.37306i	−1.19102	+	0.471560i
$87$	7.91220	+	12.4676i	0.848277	+	1.33667i
$88$	−2.00640	−	0.794389i	−0.213883	−	0.0846821i
$89$	0.254721	+	4.04868i	0.0270004	+	0.429159i	0.988186	+	0.153257i	$0.0489764\pi$
$89$	0.254721	+	4.04868i	0.0270004	+	0.429159i	−0.961186	+	0.275902i	$0.911024\pi$
$90$		0			0
$91$	1.57432	−	1.90303i	0.165034	−	0.199491i
$92$	9.08002	+	8.52670i	0.946657	+	0.888970i
$93$	0.00965601	+	0.0297182i	0.00100128	+	0.00308163i
$94$	2.60534	+	13.6576i	0.268720	+	1.40868i
$95$		0			0
$96$	8.46833	+	17.9961i	0.864296	+	1.83672i
$97$	0.777570	+	1.65242i	0.0789502	+	0.167778i	0.940405	−	0.340057i	$-0.110446\pi$
$97$	0.777570	+	1.65242i	0.0789502	+	0.167778i	−0.861455	+	0.507834i	$0.830446\pi$
$98$	−12.3589	+	4.89322i	−1.24843	+	0.494289i
$99$	7.91970	+	5.75400i	0.795960	+	0.578299i
$100$		0			0
$101$	−0.242135	+	0.175921i	−0.0240933	+	0.0175048i	−0.599767	−	0.800175i	$-0.704740\pi$
$101$	−0.242135	+	0.175921i	−0.0240933	+	0.0175048i	0.575673	+	0.817680i	$0.304740\pi$
$102$	16.9957	−	26.7810i	1.68283	−	2.65171i
$103$	−2.99809	+	15.7165i	−0.295411	+	1.54860i	0.456737	+	0.889602i	$0.349018\pi$
$103$	−2.99809	+	15.7165i	−0.295411	+	1.54860i	−0.752148	+	0.658995i	$0.770982\pi$
$104$	1.54445	−	1.45034i	0.151446	−	0.142217i
$105$		0			0
$106$	−4.96818	−	0.627627i	−0.482552	−	0.0609605i
$107$	−15.0619	−	10.9431i	−1.45609	−	1.05791i	−0.984361	−	0.176163i	$-0.943631\pi$
$107$	−15.0619	−	10.9431i	−1.45609	−	1.05791i	−0.471726	−	0.881745i	$-0.656369\pi$
$108$	0.0302518	+	0.158585i	0.00291098	+	0.0152599i
$109$	−4.84439	−	1.91803i	−0.464008	−	0.183714i	0.124476	−	0.992223i	$-0.460275\pi$
$109$	−4.84439	−	1.91803i	−0.464008	−	0.183714i	−0.588484	+	0.808509i	$0.700275\pi$
$110$		0			0
$111$	−17.5038	−	4.49422i	−1.66139	−	0.426573i
$112$	−2.45314	+	0.629860i	−0.231800	+	0.0595162i
$113$	−0.619002	+	9.83875i	−0.0582308	+	0.925552i	0.855133	+	0.518408i	$0.173475\pi$
$113$	−0.619002	+	9.83875i	−0.0582308	+	0.925552i	−0.913364	+	0.407144i	$0.866525\pi$
$114$	−14.3797	−	17.3821i	−1.34678	−	1.62798i
$115$		0			0
$116$	−13.5211	+	3.47163i	−1.25540	+	0.322333i
$117$	−8.42238	+	4.63024i	−0.778649	+	0.428066i
$118$	2.64158	−	1.91922i	0.243177	−	0.176679i
$119$	3.52546	+	3.31062i	0.323178	+	0.303484i
$120$		0			0
$121$	0.103150	−	0.540733i	0.00937731	−	0.0491576i
$122$	27.5628	−	3.48199i	2.49542	−	0.315244i
$123$	−18.1199	−	21.9032i	−1.63382	−	1.97494i
$124$	−0.0295405			−0.00265282
$125$		0			0
$126$	−4.89881			−0.436421
$127$	4.40137	+	5.32035i	0.390559	+	0.472104i	0.928744	−	0.370722i	$-0.120890\pi$
$127$	4.40137	+	5.32035i	0.390559	+	0.472104i	−0.538185	+	0.842827i	$0.680890\pi$
$128$	−5.23007	+	0.660711i	−0.462277	+	0.0583992i
$129$	−2.62916	+	13.7825i	−0.231484	+	1.21348i
$130$		0			0
$131$	−4.45323	−	4.18186i	−0.389080	−	0.365371i	0.465180	−	0.885216i	$-0.345990\pi$
$131$	−4.45323	−	4.18186i	−0.389080	−	0.365371i	−0.854260	+	0.519845i	$0.825990\pi$
$132$	−14.9041	+	10.8284i	−1.29723	+	0.942495i
$133$	3.01418	−	1.65706i	0.261362	−	0.143685i
$134$	18.7621	−	4.81728i	1.62080	−	0.416150i
$135$		0			0
$136$	2.64446	+	3.19660i	0.226760	+	0.274106i
$137$	−0.846660	+	13.4573i	−0.0723351	+	1.14973i	0.779667	+	0.626195i	$0.215388\pi$
$137$	−0.846660	+	13.4573i	−0.0723351	+	1.14973i	−0.852002	+	0.523539i	$0.824612\pi$
$138$	26.5284	−	6.81134i	2.25825	−	0.579820i
$139$	5.66146	+	1.45362i	0.480199	+	0.123294i	0.481027	−	0.876706i	$-0.340264\pi$
$139$	5.66146	+	1.45362i	0.480199	+	0.123294i	−0.000828731		1.00000i	$0.500264\pi$
$140$		0			0
$141$	15.2692	+	6.04549i	1.28590	+	0.509122i
$142$	1.98825	+	10.4228i	0.166850	+	0.874661i
$143$	−8.30007	−	6.03035i	−0.694086	−	0.504283i
$144$	9.77827	+	1.23528i	0.814856	+	0.102940i
$145$		0			0
$146$	15.3106	−	14.3776i	1.26712	−	1.18990i
$147$	−2.94188	+	15.4219i	−0.242642	+	1.27198i
$148$	9.15426	−	14.4248i	0.752475	−	1.18571i
$149$	14.9590	−	10.8683i	1.22549	−	0.890370i	0.228945	−	0.973439i	$-0.426472\pi$
$149$	14.9590	−	10.8683i	1.22549	−	0.890370i	0.996544	+	0.0830697i	$0.0264724\pi$
$150$		0			0
$151$	16.0977	+	11.6956i	1.31001	+	0.951778i	0.999999	+	0.00104421i	$0.000332383\pi$
$151$	16.0977	+	11.6956i	1.31001	+	0.951778i	0.310010	+	0.950733i	$0.399668\pi$
$152$	2.74342	−	1.08620i	0.222521	−	0.0881023i
$153$	−8.01318	−	17.0289i	−0.647828	−	1.37670i
$154$	−2.22649	−	4.73153i	−0.179416	−	0.381278i
$155$		0			0
$156$	−3.38923	−	17.7670i	−0.271356	−	1.42250i
$157$	0.416703	+	1.28248i	0.0332566	+	0.102353i	0.966307	−	0.257393i	$-0.0828634\pi$
$157$	0.416703	+	1.28248i	0.0332566	+	0.102353i	−0.933050	+	0.359746i	$0.882863\pi$
$158$	2.77216	+	2.60323i	0.220541	+	0.207102i
$159$	−3.77019	+	4.55738i	−0.298996	+	0.361424i
$160$		0			0
$161$	0.262216	+	4.16781i	0.0206656	+	0.328470i
$162$	−17.2290	−	6.82145i	−1.35364	−	0.535944i
$163$	2.34847	+	3.70060i	0.183947	+	0.289854i	0.923770	−	0.382947i	$-0.125091\pi$
$163$	2.34847	+	3.70060i	0.183947	+	0.289854i	−0.739823	+	0.672801i	$0.765091\pi$
$164$	24.9867	−	9.89292i	1.95113	−	0.772507i
$165$		0			0
$166$	−4.33750	−	6.83481i	−0.336656	−	0.530484i
$167$	5.54292	+	0.700234i	0.428924	+	0.0541857i	0.336832	−	0.941565i	$-0.390645\pi$
$167$	5.54292	+	0.700234i	0.428924	+	0.0541857i	0.0920922	+	0.995750i	$0.470645\pi$
$168$	0.394149	−	1.21306i	0.0304092	−	0.0935900i
$169$	−2.56510	+	1.41017i	−0.197315	+	0.108475i
$170$		0			0
$171$	−13.2797	+	1.67762i	−1.01553	+	0.128291i
$172$	−11.6238	−	6.39025i	−0.886308	−	0.487252i
$173$	13.9786	+	3.58908i	1.06277	+	0.272873i	0.739308	−	0.673368i	$-0.235153\pi$
$173$	13.9786	+	3.58908i	1.06277	+	0.272873i	0.323463	+	0.946241i	$0.395153\pi$
$174$	−9.48537	+	29.1930i	−0.719084	+	2.21311i
$175$		0			0
$176$	3.25108	+	10.0058i	0.245059	+	0.754215i
$177$	−0.242159	−	3.84900i	−0.0182018	−	0.289309i
$178$	−6.14722	+	5.77263i	−0.460754	+	0.432677i
$179$	−1.34083	−	0.737128i	−0.100218	−	0.0550956i	0.430856	−	0.902421i	$-0.358212\pi$
$179$	−1.34083	−	0.737128i	−0.100218	−	0.0550956i	−0.531075	+	0.847325i	$0.678212\pi$
$180$		0			0
$181$	−1.67103	+	3.55112i	−0.124207	+	0.263952i	−0.957254	−	0.289250i	$-0.906594\pi$
$181$	−1.67103	+	3.55112i	−0.124207	+	0.263952i	0.833047	+	0.553202i	$0.186594\pi$
$182$	5.13409			0.380564
$183$	13.9716	−	29.6911i	1.03281	−	2.19483i
$184$	−0.224937	+	3.57527i	−0.0165826	+	0.263573i
$185$		0			0
$186$	−0.0348048	+	0.0548436i	−0.00255201	+	0.00402133i
$187$	12.8054	−	15.4791i	0.936426	−	1.13194i
$188$	−9.89618	+	11.9624i	−0.721753	+	0.872450i
$189$	−0.0290026	+	0.0457008i	−0.00210963	+	0.00332424i
$190$		0			0
$191$	−1.05847	+	16.8239i	−0.0765880	+	1.21733i	0.752644	+	0.658428i	$0.228778\pi$
$191$	−1.05847	+	16.8239i	−0.0765880	+	1.21733i	−0.829232	+	0.558904i	$0.811222\pi$
$192$	−10.7987	+	22.9484i	−0.779329	+	1.65616i
$193$	6.29614			0.453206			0.226603	−	0.973987i	$-0.427238\pi$
$193$	6.29614			0.453206			0.226603	+	0.973987i	$0.427238\pi$
$194$	−1.61636	+	3.43494i	−0.116048	+	0.246614i
$195$		0			0
$196$	−13.0064	−	7.15034i	−0.929030	−	0.510738i
$197$	−7.66463	+	7.19757i	−0.546082	+	0.512805i	−0.907756	−	0.419499i	$-0.862206\pi$
$197$	−7.66463	+	7.19757i	−0.546082	+	0.512805i	0.361673	+	0.932305i	$0.382206\pi$
$198$	1.27775	+	20.3092i	0.0908054	+	1.44331i
$199$	2.95165	+	9.08423i	0.209237	+	0.643964i	0.999513	+	0.0312133i	$0.00993711\pi$
$199$	2.95165	+	9.08423i	0.209237	+	0.643964i	−0.790276	+	0.612751i	$0.790063\pi$
$200$		0			0
$201$	7.07010	−	21.7595i	0.498687	−	1.53480i
$202$	−0.602610	−	0.154724i	−0.0423995	−	0.0108863i
$203$	−4.10128	−	2.25470i	−0.287853	−	0.158249i
$204$	35.1381	−	4.43898i	2.46016	−	0.310791i
$205$		0			0
$206$	−29.1456	+	16.0229i	−2.03067	+	1.11637i
$207$	5.02183	−	15.4556i	0.349042	−	1.07424i
$208$	−10.2479	−	1.29461i	−0.710564	−	0.0897651i
$209$	−7.65590	−	12.0638i	−0.529570	−	0.834468i
$210$		0			0
$211$	6.24127	−	2.47110i	0.429667	−	0.170117i	−0.143329	−	0.989675i	$-0.545781\pi$
$211$	6.24127	−	2.47110i	0.429667	−	0.170117i	0.572996	+	0.819558i	$0.305781\pi$
$212$	−2.99614	−	4.72116i	−0.205776	−	0.324250i
$213$	11.6526	+	4.61360i	0.798424	+	0.316118i
$214$	−2.43005	−	38.6245i	−0.166115	−	2.64032i
$215$		0			0
$216$	−0.0295966	+	0.0357762i	−0.00201380	+	0.00243426i
$217$	−0.00721963	−	0.00677968i	−0.000490100	−	0.000460235i
$218$	−3.34689	−	10.3007i	−0.226680	−	0.697650i
$219$	−4.64847	−	24.3681i	−0.314114	−	1.64665i
$220$		0			0
$221$	8.39804	+	17.8467i	0.564913	+	1.20050i
$222$	−15.9948	−	33.9908i	−1.07350	−	2.28131i
$223$	5.10599	−	2.02160i	0.341922	−	0.135377i	−0.190887	−	0.981612i	$-0.561136\pi$
$223$	5.10599	−	2.02160i	0.341922	−	0.135377i	0.532809	+	0.846235i	$0.321136\pi$
$224$	−5.09990	−	3.70529i	−0.340751	−	0.247570i
$225$		0			0
$226$	−16.5789	+	12.0452i	−1.10281	+	0.801238i
$227$	−9.66561	+	15.2306i	−0.641529	+	1.01089i	0.355561	+	0.934653i	$0.384290\pi$
$227$	−9.66561	+	15.2306i	−0.641529	+	1.01089i	−0.997090	+	0.0762352i	$0.975710\pi$
$228$	4.72008	−	24.7435i	0.312595	−	1.63868i
$229$	11.3947	−	10.7003i	0.752984	−	0.707099i	−0.209688	−	0.977768i	$-0.567245\pi$
$229$	11.3947	−	10.7003i	0.752984	−	0.707099i	0.962672	+	0.270669i	$0.0872450\pi$
$230$		0			0
$231$	−6.12770	−	0.774108i	−0.403173	−	0.0509326i
$232$	−3.24805	−	2.35984i	−0.213245	−	0.154931i
$233$	3.53056	+	18.5079i	0.231295	+	1.21249i	0.888535	+	0.458809i	$0.151724\pi$
$233$	3.53056	+	18.5079i	0.231295	+	1.21249i	−0.657240	+	0.753681i	$0.728276\pi$
$234$	−18.5762	−	7.35483i	−1.21436	−	0.480800i
$235$		0			0
$236$	3.53139	+	0.906706i	0.229874	+	0.0590215i
$237$	4.35057	−	1.11704i	0.282600	−	0.0725593i
$238$	−0.631247	+	10.0334i	−0.0409177	+	0.650368i
$239$	−4.44545	−	5.37363i	−0.287552	−	0.347591i	0.606881	−	0.794793i	$-0.292421\pi$
$239$	−4.44545	−	5.37363i	−0.287552	−	0.347591i	−0.894433	+	0.447202i	$0.852421\pi$
$240$		0			0
$241$	18.6366	−	4.78508i	1.20049	−	0.308234i	0.405068	−	0.914287i	$-0.367248\pi$
$241$	18.6366	−	4.78508i	1.20049	−	0.308234i	0.795424	+	0.606053i	$0.207248\pi$
$242$	1.00277	−	0.551275i	0.0644603	−	0.0354373i
$243$	−17.8756	+	12.9874i	−1.14672	+	0.833140i
$244$	22.6137	+	21.2357i	1.44769	+	1.35947i
$245$		0			0
$246$	11.0727	−	58.0450i	0.705968	−	3.70081i
$247$	13.9175	−	1.75819i	0.885550	−	0.111871i
$248$	−0.00541547	−	0.00654617i	−0.000343882	−	0.000415682i
$249$	−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	$0.598846\pi$
$252$	−3.48675	−	4.21476i	−0.219645	−	0.265505i
$253$	17.2102	−	2.17416i	1.08200	−	0.136688i
$254$	−2.68958	+	14.0993i	−0.168760	+	0.884668i
$255$		0			0
$256$	7.07181	+	6.64087i	0.441988	+	0.415054i
$257$	0.998633	−	0.725549i	0.0622930	−	0.0452585i	−0.556203	−	0.831046i	$-0.687742\pi$
$257$	0.998633	−	0.725549i	0.0622930	−	0.0452585i	0.618496	+	0.785788i	$0.287742\pi$
$258$	−25.5591	+	14.0512i	−1.59124	+	0.874792i
$259$	5.54784	−	1.42444i	0.344726	−	0.0885105i
$260$		0			0
$261$	11.6093	+	14.0332i	0.718597	+	0.868634i
$262$	0.797368	−	12.6738i	0.0492616	−	0.782990i
$263$	−9.86257	+	2.53228i	−0.608152	+	0.156147i	−0.540193	−	0.841541i	$-0.681649\pi$
$263$	−9.86257	+	2.53228i	−0.608152	+	0.156147i	−0.0679590	+	0.997688i	$0.521649\pi$
$264$	−5.13185	−	1.31763i	−0.315843	−	0.0810948i
$265$		0			0
$266$	6.64799	+	2.63213i	0.407614	+	0.161386i
$267$	1.86636	+	9.78381i	0.114219	+	0.598759i
$268$	17.4986	+	12.7135i	1.06890	+	0.776599i
$269$	−31.8523	−	4.02388i	−1.94207	−	0.245340i	−0.945335	−	0.326101i	$-0.894265\pi$
$269$	−31.8523	−	4.02388i	−1.94207	−	0.245340i	−0.996734	+	0.0807606i	$0.974265\pi$
$270$		0			0
$271$	−5.44124	+	5.10966i	−0.330532	+	0.310390i	−0.831989	−	0.554793i	$-0.812798\pi$
$271$	−5.44124	+	5.10966i	−0.330532	+	0.310390i	0.501457	+	0.865183i	$0.332798\pi$
$272$	3.79001	−	19.8680i	0.229803	−	1.20467i
$273$	3.24928	−	5.12005i	0.196656	−	0.309880i
$274$	−22.6763	+	16.4753i	−1.36992	+	0.995308i
$275$		0			0
$276$	24.7420	+	17.9761i	1.48929	+	1.08203i
$277$	−0.978065	+	0.387243i	−0.0587662	+	0.0232672i	−0.397324	−	0.917678i	$-0.630061\pi$
$277$	−0.978065	+	0.387243i	−0.0587662	+	0.0232672i	0.338558	+	0.940946i	$0.390061\pi$
$278$	5.17339	+	10.9940i	0.310279	+	0.659377i
$279$	0.0164098	+	0.0348727i	0.000982432	+	0.00208777i
$280$		0			0
$281$	0.975796	+	5.11530i	0.0582111	+	0.305153i	0.999471	−	0.0325303i	$-0.0103566\pi$
$281$	0.975796	+	5.11530i	0.0582111	+	0.305153i	−0.941260	+	0.337684i	$0.890357\pi$
$282$	10.5492	+	32.4670i	0.628194	+	1.93338i
$283$	−22.9620	−	21.5628i	−1.36495	−	1.28177i	−0.923035	−	0.384715i	$-0.874300\pi$
$283$	−22.9620	−	21.5628i	−1.36495	−	1.28177i	−0.441914	−	0.897058i	$-0.645700\pi$
$284$	−7.55224	+	9.12908i	−0.448143	+	0.541712i
$285$		0			0
$286$	−1.33911	−	21.2846i	−0.0791834	−	1.25858i
$287$	8.37715	+	3.31675i	0.494487	+	0.195781i
$288$	13.1445	+	20.7123i	0.774544	+	1.22049i
$289$	−20.1037	+	7.95960i	−1.18257	+	0.468212i
$290$		0			0
$291$	2.40258	+	3.78586i	0.140842	+	0.221931i
$292$	23.2674	+	2.93936i	1.36162	+	0.172013i
$293$	0.700027	−	2.15446i	0.0408960	−	0.125865i	−0.928524	−	0.371272i	$-0.878922\pi$
$293$	0.700027	−	2.15446i	0.0408960	−	0.125865i	0.969420	+	0.245407i	$0.0789217\pi$
$294$	−28.5992	+	15.7226i	−1.66794	+	0.916958i
$295$		0			0
$296$	4.87472	−	0.615821i	0.283338	−	0.0357939i
$297$	0.197028	+	0.108317i	0.0114327	+	0.00628519i
$298$	37.2289	+	9.55877i	2.15662	+	0.553725i
$299$	−5.26302	+	16.1979i	−0.304368	+	0.936750i
$300$		0			0
$301$	−1.37424	−	4.22948i	−0.0792100	−	0.243783i
$302$	2.59716	+	41.2806i	0.149450	+	2.37543i
$303$	−0.535682	+	0.503039i	−0.0307741	+	0.0288988i
$304$	−12.6060	−	6.93020i	−0.723003	−	0.397474i
$305$		0			0
$306$	16.6573	−	35.3985i	0.952234	−	2.02360i
$307$	18.9044			1.07893			0.539466	−	0.842008i	$-0.318626\pi$
$307$	18.9044			1.07893			0.539466	+	0.842008i	$0.318626\pi$
$308$	2.48612	−	5.28328i	0.141660	−	0.301043i
$309$	−2.46667	+	39.2066i	−0.140324	+	2.23038i
$310$		0			0
$311$	−7.84921	+	12.3684i	−0.445088	+	0.701346i	−0.990605	−	0.136753i	$-0.956333\pi$
$311$	−7.84921	+	12.3684i	−0.445088	+	0.701346i	0.545517	+	0.838100i	$0.316333\pi$
$312$	3.31584	−	4.00816i	0.187722	−	0.226917i
$313$	−5.44984	+	6.58773i	−0.308043	+	0.372360i	−0.901703	−	0.432356i	$-0.857682\pi$
$313$	−5.44984	+	6.58773i	−0.308043	+	0.372360i	0.593660	+	0.804716i	$0.297682\pi$
$314$	−1.50199	+	2.36676i	−0.0847624	+	0.133564i
$315$		0			0
$316$	−0.266628	+	4.23793i	−0.0149990	+	0.238402i
$317$	−2.63436	+	5.59830i	−0.147960	+	0.314432i	−0.965044	−	0.262087i	$-0.915589\pi$
$317$	−2.63436	+	5.59830i	−0.147960	+	0.314432i	0.817084	+	0.576519i	$0.195589\pi$
$318$	−12.2952			−0.689478
$319$	−8.27765	+	17.5909i	−0.463459	+	0.984901i
$320$		0			0
$321$	−40.0568	−	22.0214i	−2.23575	−	1.22911i
$322$	−6.32811	+	5.94249i	−0.352652	+	0.331162i
$323$	1.72479	+	27.4147i	0.0959697	+	1.52540i
$324$	−6.39391	−	19.6784i	−0.355217	−	1.09325i
$325$		0			0
$326$	−2.81542	+	8.66496i	−0.155932	+	0.479908i
$327$	−12.3907	−	3.18139i	−0.685207	−	0.175931i
$328$	6.77291	+	3.72344i	0.373971	+	0.205592i
$329$	−5.16403	+	0.652369i	−0.284702	+	0.0359663i
$330$		0			0
$331$	16.2091	−	8.91105i	0.890935	−	0.489796i	0.0306039	−	0.999532i	$-0.490257\pi$
$331$	16.2091	−	8.91105i	0.890935	−	0.489796i	0.860331	+	0.509736i	$0.170257\pi$
$332$	2.79319	−	8.59654i	0.153296	−	0.471796i
$333$	−22.1138	−	2.79362i	−1.21183	−	0.153089i
$334$	6.22301	+	9.80589i	0.340508	+	0.536555i
$335$		0			0
$336$	−5.78180	+	2.28918i	−0.315423	+	0.124885i
$337$	−7.00020	−	11.0306i	−0.381325	−	0.600873i	0.598405	−	0.801194i	$-0.295801\pi$
$337$	−7.00020	−	11.0306i	−0.381325	−	0.600873i	−0.979730	+	0.200321i	$0.935801\pi$
$338$	−5.65751	−	2.23997i	−0.307728	−	0.121838i
$339$	1.51981	+	24.1568i	0.0825450	+	1.31201i
$340$		0			0
$341$	−0.0262237	+	0.0316990i	−0.00142009	+	0.00171660i
$342$	−20.2831	−	19.0471i	−1.09679	−	1.02995i
$343$	−3.22103	−	9.91331i	−0.173919	−	0.535269i
$344$	−0.714840	−	3.74732i	−0.0385416	−	0.202042i
$345$		0			0
$346$	12.7735	+	27.1450i	0.686706	+	1.45933i
$347$	0.670629	+	1.42516i	0.0360013	+	0.0765066i	0.922019	−	0.387145i	$-0.126539\pi$
$347$	0.670629	+	1.42516i	0.0360013	+	0.0765066i	−0.886017	+	0.463652i	$0.846539\pi$
$348$	−31.8678	+	12.6174i	−1.70829	+	0.676361i
$349$	7.85282	+	5.70541i	0.420352	+	0.305404i	0.777779	−	0.628537i	$-0.216346\pi$
$349$	7.85282	+	5.70541i	0.420352	+	0.305404i	−0.357427	+	0.933941i	$0.616346\pi$
$350$		0			0
$351$	−0.178590	+	0.129753i	−0.00953243	+	0.00692572i
$352$	−14.0310	+	22.1093i	−0.747853	+	1.17843i
$353$	−5.97101	+	31.3011i	−0.317805	+	1.66599i	0.361681	+	0.932302i	$0.382203\pi$
$353$	−5.97101	+	31.3011i	−0.317805	+	1.66599i	−0.679486	+	0.733689i	$0.737797\pi$
$354$	5.84405	−	5.48792i	0.310608	−	0.291680i
$355$		0			0
$356$	−9.34187	−	1.18015i	−0.495118	−	0.0625480i
$357$	9.60644	+	6.97949i	0.508427	+	0.369394i
$358$	−0.595996	−	3.12432i	−0.0314994	−	0.165126i
$359$	14.9378	+	5.91429i	0.788386	+	0.312144i	0.727596	−	0.686006i	$-0.240638\pi$
$359$	14.9378	+	5.91429i	0.788386	+	0.312144i	0.0607906	+	0.998151i	$0.480638\pi$
$360$		0			0
$361$	0.519683	+	0.133432i	0.0273517	+	0.00702273i
$362$	−7.90197	+	2.02888i	−0.415318	+	0.106636i
$363$	0.0848667	−	1.34892i	0.00445434	−	0.0707998i
$364$	3.65421	+	4.41719i	0.191533	+	0.231523i
$365$		0			0
$366$	66.0688	−	16.9636i	3.45347	−	0.886700i
$367$	−5.34033	+	2.93587i	−0.278763	+	0.153251i	−0.615002	−	0.788525i	$-0.710845\pi$
$367$	−5.34033	+	2.93587i	−0.278763	+	0.153251i	0.336239	+	0.941777i	$0.390845\pi$
$368$	14.1297	−	10.2658i	0.736559	−	0.535142i
$369$	−25.5588	−	24.0013i	−1.33054	−	1.24946i
$370$		0			0
$371$	0.351279	−	1.84147i	0.0182375	−	0.0956042i
$372$	−0.0719579	+	0.00909039i	−0.00373084	+	0.000471315i
$373$	−15.2917	−	18.4846i	−0.791777	−	0.957094i	0.208002	−	0.978128i	$-0.433304\pi$
$373$	−15.2917	−	18.4846i	−0.791777	−	0.957094i	−0.999779	+	0.0210347i	$0.993304\pi$
$374$	41.7604			2.15938
$375$		0			0
$376$	−4.46507			−0.230269
$377$	−12.1669	−	14.7072i	−0.626625	−	0.757460i
$378$	−0.111628	+	0.0141019i	−0.00574153	+	0.000725324i
$379$	5.07836	−	26.6217i	0.260858	−	1.36746i	−0.574836	−	0.818269i	$-0.694934\pi$
$379$	5.07836	−	26.6217i	0.260858	−	1.36746i	0.835694	−	0.549196i	$-0.185066\pi$
$380$		0			0
$381$	12.3585	+	11.6054i	0.633147	+	0.594565i
$382$	−28.3492	+	20.5969i	−1.45047	+	1.05383i
$383$	17.4647	−	9.60131i	0.892405	−	0.490604i	0.0315779	−	0.999501i	$-0.489947\pi$
$383$	17.4647	−	9.60131i	0.892405	−	0.490604i	0.860827	+	0.508897i	$0.169947\pi$
$384$	−12.5366	+	3.21886i	−0.639757	+	0.164262i
$385$		0			0
$386$	8.34261	+	10.0845i	0.424628	+	0.513287i
$387$	−1.08665	+	17.2718i	−0.0552374	+	0.877974i
$388$	−4.10575	+	1.05418i	−0.208438	+	0.0535178i
$389$	28.8080	+	7.39663i	1.46062	+	0.375024i	0.893669	−	0.448726i	$-0.148122\pi$
$389$	28.8080	+	7.39663i	1.46062	+	0.375024i	0.566953	+	0.823750i	$0.308122\pi$
$390$		0			0
$391$	−31.0080	−	12.2769i	−1.56814	−	0.620870i
$392$	−0.799866	−	4.19304i	−0.0403993	−	0.211781i
$393$	−12.1345	−	8.81623i	−0.612105	−	0.444720i
$394$	−21.6842	−	2.73935i	−1.09243	−	0.138007i
$395$		0			0
$396$	−16.5638	+	15.5545i	−0.832364	+	0.781642i
$397$	−2.56108	+	13.4257i	−0.128537	+	0.673815i	0.858435	+	0.512922i	$0.171437\pi$
$397$	−2.56108	+	13.4257i	−0.128537	+	0.673815i	−0.986972	+	0.160892i	$0.948563\pi$
$398$	−10.6391	+	16.7646i	−0.533291	+	0.840331i
$399$	6.83233	−	4.96398i	0.342044	−	0.248510i
$400$		0			0
$401$	10.6129	+	7.71074i	0.529984	+	0.385056i	0.820352	−	0.571859i	$-0.193778\pi$
$401$	10.6129	+	7.71074i	0.529984	+	0.385056i	−0.290368	+	0.956915i	$0.593778\pi$
$402$	44.2202	−	17.5080i	2.20550	−	0.873221i
$403$	−0.0171980	−	0.0365476i	−0.000856692	−	0.00182056i
$404$	−0.295791	−	0.628589i	−0.0147162	−	0.0312735i
$405$		0			0
$406$	−1.82301	−	9.55654i	−0.0904743	−	0.474283i
$407$	−7.35239	−	22.6283i	−0.364444	−	1.12164i
$408$	7.42532	+	6.97284i	0.367608	+	0.345207i
$409$	7.71814	−	9.32962i	0.381637	−	0.461320i	−0.544359	−	0.838852i	$-0.683227\pi$
$409$	7.71814	−	9.32962i	0.381637	−	0.461320i	0.925997	+	0.377532i	$0.123227\pi$
$410$		0			0
$411$	2.07878	+	33.0412i	0.102538	+	1.62980i
$412$	−34.5301	−	13.6714i	−1.70118	−	0.673543i
$413$	0.654969	+	1.03207i	0.0322289	+	0.0507846i
$414$	31.4093	−	12.4358i	1.54368	−	0.611186i
$415$		0			0
$416$	−13.7758	−	21.7071i	−0.675412	−	1.06428i
$417$	14.2381	+	1.79869i	0.697242	+	0.0880822i
$418$	9.17811	−	28.2473i	0.448916	−	1.38162i
$419$	9.95753	−	5.47420i	0.486457	−	0.267432i	−0.219596	−	0.975591i	$-0.570474\pi$
$419$	9.95753	−	5.47420i	0.486457	−	0.267432i	0.706053	+	0.708159i	$0.250474\pi$
$420$		0			0
$421$	−23.6601	+	2.98896i	−1.15312	+	0.145673i	−0.678557	−	0.734548i	$-0.737394\pi$
$421$	−23.6601	+	2.98896i	−1.15312	+	0.145673i	−0.474564	+	0.880221i	$0.657394\pi$
$422$	12.2278	+	6.72231i	0.595242	+	0.327237i
$423$	19.6191	+	5.03732i	0.953911	+	0.244923i
$424$	0.496946	−	1.52944i	0.0241338	−	0.0742763i
$425$		0			0
$426$	8.05056	+	24.7771i	0.390051	+	1.20045i
$427$	0.653047	+	10.3799i	0.0316032	+	0.502318i
$428$	31.5015	−	29.5819i	1.52268	−	1.42989i
$429$	−22.0739	−	12.1352i	−1.06574	−	0.585894i
$430$		0			0
$431$	9.96374	−	21.1740i	0.479937	−	1.01992i	−0.507463	−	0.861673i	$-0.669417\pi$
$431$	9.96374	−	21.1740i	0.479937	−	1.01992i	0.987400	−	0.158244i	$-0.0505833\pi$
$432$	0.226371			0.0108913
$433$	−11.0497	+	23.4818i	−0.531014	+	1.12846i	0.441851	+	0.897088i	$0.354322\pi$
$433$	−11.0497	+	23.4818i	−0.531014	+	1.12846i	−0.972865	+	0.231373i	$0.925678\pi$
$434$	0.00129270	−	0.0205469i	6.20518e−5	−	0.000986285i
$435$		0			0
$436$	6.48016	−	10.2111i	0.310343	−	0.489023i
$437$	−15.1192	+	18.2760i	−0.723250	+	0.874259i
$438$	32.8709	−	39.7340i	1.57063	−	1.89857i
$439$	2.11965	−	3.34003i	0.101165	−	0.159411i	−0.789975	−	0.613139i	$-0.789906\pi$
$439$	2.11965	−	3.34003i	0.101165	−	0.159411i	0.891140	+	0.453728i	$0.149906\pi$
$440$		0			0
$441$	−1.21590	+	19.3262i	−0.0579000	+	0.920294i
$442$	−17.4573	+	37.0986i	−0.830359	+	1.76460i
$443$	−11.5842			−0.550383			−0.275191	−	0.961389i	$-0.588741\pi$
$443$	−11.5842			−0.550383			−0.275191	+	0.961389i	$0.588741\pi$
$444$	17.8600	−	37.9545i	0.847599	−	1.80124i
$445$		0			0
$446$	10.0036	+	5.49953i	0.473684	+	0.260410i
$447$	33.0942	−	31.0775i	1.56530	−	1.46992i
$448$	−0.504745	−	8.02269i	−0.0238469	−	0.379036i
$449$	−7.65420	−	23.5572i	−0.361224	−	1.11173i	−0.952312	−	0.305126i	$-0.901302\pi$
$449$	−7.65420	−	23.5572i	−0.361224	−	1.11173i	0.591088	−	0.806607i	$-0.298698\pi$
$450$		0			0
$451$	11.5654	−	35.5945i	0.544592	−	1.67608i
$452$	−22.1634	−	5.69059i	−1.04248	−	0.267663i
$453$	42.8114	+	23.5358i	2.01146	+	1.10581i
$454$	−37.2020	+	4.69970i	−1.74597	+	0.220568i
$455$		0			0
$456$	6.34846	−	3.49010i	0.297294	−	0.163439i
$457$	4.80474	−	14.7875i	0.224756	−	0.691729i	−0.773560	−	0.633723i	$-0.781526\pi$
$457$	4.80474	−	14.7875i	0.224756	−	0.691729i	0.998316	−	0.0580056i	$-0.0184741\pi$
$458$	32.2371	+	4.07249i	1.50634	+	0.190295i
$459$	−0.231615	−	0.364966i	−0.0108108	−	0.0170352i
$460$		0			0
$461$	−17.1720	+	6.79886i	−0.799778	+	0.316654i	−0.732226	−	0.681061i	$-0.761519\pi$
$461$	−17.1720	+	6.79886i	−0.799778	+	0.316654i	−0.0675514	+	0.997716i	$0.521519\pi$
$462$	−6.87953	−	10.8404i	−0.320065	−	0.504341i
$463$	8.09227	+	3.20396i	0.376080	+	0.148900i	0.548557	−	0.836113i	$-0.315177\pi$
$463$	8.09227	+	3.20396i	0.376080	+	0.148900i	−0.172478	+	0.985013i	$0.555177\pi$
$464$	1.22904	+	19.5350i	0.0570567	+	0.906890i
$465$		0			0
$466$	−24.9658	+	30.1784i	−1.15652	+	1.39799i
$467$	−28.2318	−	26.5114i	−1.30641	−	1.22680i	−0.957087	−	0.289801i	$-0.906411\pi$
$467$	−28.2318	−	26.5114i	−1.30641	−	1.22680i	−0.349325	−	0.937002i	$-0.613589\pi$
$468$	−6.89385	−	21.2171i	−0.318668	−	0.980761i
$469$	1.35881	+	7.12315i	0.0627442	+	0.328917i
$470$		0			0
$471$	1.40970	+	2.99577i	0.0649557	+	0.138038i
$472$	0.446460	+	0.948775i	0.0205500	+	0.0436709i
$473$	−17.1759	+	6.80041i	−0.789747	+	0.312683i
$474$	7.55380	+	5.48816i	0.346958	+	0.252080i
$475$		0			0
$476$	−9.08166	+	6.59821i	−0.416257	+	0.302428i
$477$	−3.90898	+	6.15957i	−0.178980	+	0.282028i
$478$	2.71652	−	14.2405i	0.124251	−	0.651345i
$479$	16.1778	−	15.1920i	0.739184	−	0.694140i	−0.220448	−	0.975399i	$-0.570752\pi$
$479$	16.1778	−	15.1920i	0.739184	−	0.694140i	0.959632	+	0.281259i	$0.0907519\pi$
$480$		0			0
$481$	23.1758	+	2.92779i	1.05673	+	0.133496i
$482$	32.3584	+	23.5098i	1.47389	+	1.07084i
$483$	1.92128	+	10.0717i	0.0874213	+	0.458278i
$484$	1.18802	+	0.470371i	0.0540009	+	0.0213805i
$485$		0			0
$486$	−44.4875	−	11.4225i	−2.01799	−	0.518133i
$487$	11.8909	−	3.05307i	0.538830	−	0.138348i	0.0305390	−	0.999534i	$-0.490278\pi$
$487$	11.8909	−	3.05307i	0.538830	−	0.138348i	0.508291	+	0.861186i	$0.330278\pi$
$488$	−0.560204	+	8.90419i	−0.0253592	+	0.403074i
$489$	6.85943	+	8.29163i	0.310194	+	0.374960i
$490$		0			0
$491$	−1.41728	+	0.363896i	−0.0639611	+	0.0164224i	−0.280535	−	0.959844i	$-0.590512\pi$
$491$	−1.41728	+	0.363896i	−0.0639611	+	0.0164224i	0.216574	+	0.976266i	$0.430512\pi$
$492$	57.8208	−	31.7873i	2.60676	−	1.43308i
$493$	30.2378	−	21.9690i	1.36184	−	0.989435i
$494$	21.2573	+	19.9619i	0.956410	+	0.898129i
$495$		0			0
$496$	−0.00776140	+	0.0406867i	−0.000348497	+	0.00182689i
$497$	−3.94091	+	0.497853i	−0.176774	+	0.0223318i
$498$	−12.6690	−	15.3142i	−0.567712	−	0.686245i
$499$	11.5060			0.515081			0.257540	−	0.966268i	$-0.417088\pi$
$499$	11.5060			0.515081			0.257540	+	0.966268i	$0.417088\pi$
$500$		0			0
$501$	13.7175			0.612853
$502$	−12.8292	−	15.5079i	−0.572596	−	0.692150i
$503$	−7.00757	+	0.885262i	−0.312452	+	0.0394719i	−0.279996	−	0.960001i	$-0.590333\pi$
$503$	−7.00757	+	0.885262i	−0.312452	+	0.0394719i	−0.0324565	+	0.999473i	$0.510333\pi$
$504$	0.294787	−	1.54533i	0.0131309	−	0.0688344i
$505$		0			0
$506$	26.2865	+	24.6847i	1.16858	+	1.09737i
$507$	−5.81438	+	4.22440i	−0.258226	+	0.187612i
$508$	−14.0448	+	7.72122i	−0.623139	+	0.342574i
$509$	−10.1123	+	2.59639i	−0.448219	+	0.115083i	−0.466051	−	0.884758i	$-0.654324\pi$
$509$	−10.1123	+	2.59639i	−0.448219	+	0.115083i	0.0178318	+	0.999841i	$0.494324\pi$
$510$		0			0
$511$	5.01190	+	6.05835i	0.221713	+	0.268005i
$512$	−1.92825	+	30.6487i	−0.0852176	+	1.35449i
$513$	−0.297772	+	0.0764550i	−0.0131470	+	0.00337557i
$514$	2.48533	+	0.638125i	0.109623	+	0.0281465i
$515$		0			0
$516$	−30.2810	−	11.9891i	−1.33305	−	0.527790i
$517$	4.05147	+	21.2386i	0.178183	+	0.934071i
$518$	9.63260	+	6.99849i	0.423232	+	0.307496i
$519$	35.1549	+	4.44110i	1.54313	+	0.194943i
$520$		0			0
$521$	−4.42096	+	4.15155i	−0.193686	+	0.181883i	−0.775322	−	0.631566i	$-0.782413\pi$
$521$	−4.42096	+	4.15155i	−0.193686	+	0.181883i	0.581637	+	0.813449i	$0.302413\pi$
$522$	−7.09419	+	37.1890i	−0.310504	+	1.62772i
$523$	14.1536	−	22.3024i	0.618892	−	0.975217i	−0.379849	−	0.925049i	$-0.624024\pi$
$523$	14.1536	−	22.3024i	0.618892	−	0.975217i	0.998741	−	0.0501689i	$-0.0159760\pi$
$524$	11.4716	−	8.33461i	0.501140	−	0.364099i
$525$		0			0
$526$	−17.1242	−	12.4414i	−0.746650	−	0.542473i
$527$	0.0735382	−	0.0291158i	0.00320338	−	0.00126831i
$528$	10.9984	+	23.3727i	0.478642	+	1.01717i
$529$	−2.46843	−	5.24568i	−0.107323	−	0.228073i
$530$		0			0
$531$	−0.891326	−	4.67249i	−0.0386803	−	0.202769i
$532$	2.46715	+	7.59311i	0.106965	+	0.329203i
$533$	26.7863	+	25.1541i	1.16025	+	1.08954i
$534$	−13.1977	+	15.9532i	−0.571119	+	0.690364i
$535$		0			0
$536$	0.390597	+	6.20837i	0.0168712	+	0.268161i
$537$	−3.49297	−	1.38297i	−0.150733	−	0.0596794i
$538$	−35.7604	−	56.3494i	−1.54174	−	2.42939i
$539$	−19.2188	+	7.60928i	−0.827814	+	0.327755i
$540$		0			0
$541$	17.3707	+	27.3719i	0.746826	+	1.17681i	0.978946	+	0.204122i	$0.0654338\pi$
$541$	17.3707	+	27.3719i	0.746826	+	1.17681i	−0.232120	+	0.972687i	$0.574566\pi$
$542$	−15.3939	−	1.94471i	−0.661226	−	0.0835323i
$543$	−2.97769	+	9.16440i	−0.127785	+	0.393282i
$544$	44.1153	−	24.2526i	1.89143	−	1.03982i
$545$		0			0
$546$	12.5062	−	1.57990i	0.535214	−	0.0676133i
$547$	−17.4221	−	9.57786i	−0.744913	−	0.409520i	0.0636167	−	0.997974i	$-0.479736\pi$
$547$	−17.4221	−	9.57786i	−0.744913	−	0.409520i	−0.808530	+	0.588455i	$0.799736\pi$
$548$	−30.3147	−	7.78349i	−1.29498	−	0.332494i
$549$	12.5068	−	38.4921i	0.533778	−	1.64280i
$550$		0			0
$551$	−8.21449	−	25.2816i	−0.349949	−	1.07703i
$552$	0.552281	+	8.77825i	0.0235066	+	0.373627i
$553$	−1.03779	+	0.974547i	−0.0441312	+	0.0414420i
$554$	−1.91622	−	1.05345i	−0.0814122	−	0.0447567i
$555$		0			0
$556$	−5.77666	+	12.2760i	−0.244985	+	0.520619i
$557$	40.9886			1.73674			0.868372	−	0.495913i	$-0.165167\pi$
$557$	40.9886			1.73674			0.868372	+	0.495913i	$0.165167\pi$
$558$	−0.0341117	+	0.0724911i	−0.00144406	+	0.00306879i
$559$	1.13884	−	18.1013i	0.0481677	−	0.765604i
$560$		0			0
$561$	26.4295	−	41.6462i	1.11585	−	1.75830i
$562$	−6.90018	+	8.34088i	−0.291067	+	0.351839i
$563$	5.60788	−	6.77876i	0.236344	−	0.285691i	−0.638984	−	0.769220i	$-0.720645\pi$
$563$	5.60788	−	6.77876i	0.236344	−	0.285691i	0.875328	+	0.483529i	$0.160645\pi$
$564$	−20.4250	+	32.1847i	−0.860048	+	1.35522i
$565$		0			0
$566$	4.11144	−	65.3495i	0.172817	−	2.74684i
$567$	2.95363	−	6.27679i	0.124041	−	0.263600i
$568$	−3.40751			−0.142976
$569$	−3.85270	+	8.18740i	−0.161513	+	0.343234i	−0.969160	−	0.246434i	$-0.920741\pi$
$569$	−3.85270	+	8.18740i	−0.161513	+	0.343234i	0.807646	+	0.589667i	$0.200741\pi$
$570$		0			0
$571$	−13.3539	−	7.34135i	−0.558842	−	0.307226i	0.177186	−	0.984177i	$-0.443301\pi$
$571$	−13.3539	−	7.34135i	−0.558842	−	0.307226i	−0.736028	+	0.676951i	$0.763301\pi$
$572$	17.3594	−	16.3015i	0.725831	−	0.681601i
$573$	2.59882	+	41.3071i	0.108567	+	1.72563i
$574$	5.78761	+	17.8124i	0.241570	+	0.743476i
$575$		0			0
$576$	−9.66661	+	29.7508i	−0.402775	+	1.23961i
$577$	−0.186241	−	0.0478187i	−0.00775333	−	0.00199072i	0.244811	−	0.969571i	$-0.421274\pi$
$577$	−0.186241	−	0.0478187i	−0.00775333	−	0.00199072i	−0.252565	+	0.967580i	$0.581274\pi$
$578$	−39.3869	−	21.6531i	−1.63828	−	0.900652i
$579$	15.3368	−	1.93749i	0.637376	−	0.0805193i
$580$		0			0
$581$	2.65559	−	1.45992i	0.110173	−	0.0605679i
$582$	−2.88028	+	8.86459i	−0.119391	+	0.367449i
$583$	−7.72585	−	0.976002i	−0.319972	−	0.0404219i
$584$	3.61410	+	5.69491i	0.149552	+	0.235657i
$585$		0			0
$586$	4.37835	−	1.73351i	0.180868	−	0.0716107i
$587$	−8.16964	−	12.8733i	−0.337197	−	0.531338i	0.632844	−	0.774280i	$-0.281888\pi$
$587$	−8.16964	−	12.8733i	−0.337197	−	0.531338i	−0.970041	+	0.242942i	$0.921888\pi$
$588$	−33.8827	−	13.4151i	−1.39730	−	0.553230i
$589$	−0.00353212	−	0.0561414i	−0.000145538	−	0.00231327i
$590$		0			0
$591$	−16.4554	+	19.8912i	−0.676886	+	0.818215i
$592$	−17.4624	−	16.3983i	−0.717700	−	0.673965i
$593$	14.0758	+	43.3208i	0.578023	+	1.77897i	0.625645	+	0.780108i	$0.284836\pi$
$593$	14.0758	+	43.3208i	0.578023	+	1.77897i	−0.0476219	+	0.998865i	$0.515164\pi$
$594$	0.0875784	+	0.459102i	0.00359339	+	0.0188372i
$595$		0			0
$596$	18.2739	+	38.8339i	0.748526	+	1.59070i
$597$	9.98539	+	21.2200i	0.408675	+	0.868478i
$598$	−32.9178	+	13.0331i	−1.34611	+	0.532962i
$599$	−16.4139	−	11.9254i	−0.670653	−	0.487258i	0.199590	−	0.979879i	$-0.436039\pi$
$599$	−16.4139	−	11.9254i	−0.670653	−	0.487258i	−0.870244	+	0.492621i	$0.836039\pi$
$600$		0			0
$601$	−5.83295	+	4.23788i	−0.237931	+	0.172867i	−0.700361	−	0.713789i	$-0.746978\pi$
$601$	−5.83295	+	4.23788i	−0.237931	+	0.172867i	0.462430	+	0.886656i	$0.346978\pi$
$602$	4.95341	−	7.80533i	0.201886	−	0.318121i
$603$	5.28779	−	27.7196i	0.215335	−	1.12883i
$604$	−33.6678	+	31.6162i	−1.36992	+	1.28644i
$605$		0			0
$606$	−1.51551	−	0.191454i	−0.0615635	−	0.00777728i
$607$	−2.44524	−	1.77657i	−0.0992490	−	0.0721087i	0.537054	−	0.843548i	$-0.319537\pi$
$607$	−2.44524	−	1.77657i	−0.0992490	−	0.0721087i	−0.636303	+	0.771439i	$0.719537\pi$
$608$	−6.70911	−	35.1704i	−0.272090	−	1.42635i
$609$	−10.6842	−	4.23016i	−0.432944	−	0.171415i
$610$		0			0
$611$	−20.5613	−	5.27925i	−0.831822	−	0.213576i
$612$	42.3115	−	10.8637i	1.71034	−	0.439141i
$613$	1.51718	−	24.1150i	0.0612785	−	0.973994i	−0.840504	−	0.541805i	$-0.817741\pi$
$613$	1.51718	−	24.1150i	0.0612785	−	0.973994i	0.901783	−	0.432189i	$-0.142259\pi$
$614$	25.0490	+	30.2790i	1.01090	+	1.22196i
$615$		0			0
$616$	1.62654	−	0.417624i	0.0655351	−	0.0168265i
$617$	29.2112	−	16.0590i	1.17600	−	0.646511i	0.230798	−	0.973002i	$-0.425866\pi$
$617$	29.2112	−	16.0590i	1.17600	−	0.646511i	0.945200	+	0.326491i	$0.105866\pi$
$618$	−66.0653	+	47.9993i	−2.65754	+	1.93081i
$619$	−8.36904	−	7.85905i	−0.336380	−	0.315882i	0.497888	−	0.867242i	$-0.334109\pi$
$619$	−8.36904	−	7.85905i	−0.336380	−	0.315882i	−0.834268	+	0.551360i	$0.814109\pi$
$620$		0			0
$621$	0.0699402	−	0.366639i	0.00280660	−	0.0147127i
$622$	−30.2108	+	3.81651i	−1.21134	+	0.153028i
$623$	−2.01228	−	2.43243i	−0.0806203	−	0.0974532i
$624$	−25.3613			−1.01526
$625$		0			0
$626$	−17.7727			−0.710342
$627$	−22.3614	−	27.0303i	−0.893028	−	1.07949i
$628$	−3.10533	+	0.392294i	−0.123916	+	0.0156542i
$629$	−8.57120	+	44.9318i	−0.341756	+	1.79155i
$630$		0			0
$631$	14.7988	+	13.8970i	0.589130	+	0.553230i	0.920735	−	0.390188i	$-0.127590\pi$
$631$	14.7988	+	13.8970i	0.589130	+	0.553230i	−0.331605	+	0.943418i	$0.607590\pi$
$632$	−0.988004	+	0.717827i	−0.0393007	+	0.0285536i
$633$	14.4427	−	7.93996i	0.574047	−	0.315585i
$634$	−12.4574	+	3.19851i	−0.494745	+	0.127029i
$635$		0			0
$636$	−8.75113	−	10.5783i	−0.347005	−	0.419457i
$637$	1.27430	−	20.2544i	0.0504895	−	0.802507i
$638$	−39.1434	+	10.0503i	−1.54970	+	0.397896i
$639$	14.9722	+	3.84421i	0.592292	+	0.152075i
$640$		0			0
$641$	−16.1026	−	6.37546i	−0.636014	−	0.251816i	0.0279163	−	0.999610i	$-0.491113\pi$
$641$	−16.1026	−	6.37546i	−0.636014	−	0.251816i	−0.663930	+	0.747795i	$0.731113\pi$
$642$	−17.8051	−	93.3378i	−0.702713	−	3.68375i
$643$	−27.8652	−	20.2453i	−1.09890	−	0.798395i	−0.118018	−	0.993012i	$-0.537654\pi$
$643$	−27.8652	−	20.2453i	−1.09890	−	0.798395i	−0.980879	+	0.194616i	$0.937654\pi$
$644$	−9.61676	−	1.21488i	−0.378953	−	0.0478729i
$645$		0			0
$646$	−41.6245	+	39.0880i	−1.63770	+	1.53790i
$647$	7.64256	−	40.0637i	0.300460	−	1.57507i	−0.436864	−	0.899528i	$-0.643911\pi$
$647$	7.64256	−	40.0637i	0.300460	−	1.57507i	0.737324	−	0.675539i	$-0.236089\pi$
$648$	3.18858	−	5.02440i	0.125259	−	0.197377i
$649$	4.10784	−	2.98452i	0.161247	−	0.117153i
$650$		0			0
$651$	−0.0196726	−	0.0142930i	−0.000771030	−	0.000560186i
$652$	−9.45890	+	3.74505i	−0.370439	+	0.146667i
$653$	−18.2985	−	38.8863i	−0.716075	−	1.52174i	−0.847722	−	0.530441i	$-0.822026\pi$
$653$	−18.2985	−	38.8863i	−0.716075	−	1.52174i	0.131646	−	0.991297i	$-0.457974\pi$
$654$	−11.3225	−	24.0615i	−0.442745	−	0.940880i
$655$		0			0
$656$	−7.06077	−	37.0139i	−0.275677	−	1.44515i
$657$	−9.45519	−	29.1001i	−0.368882	−	1.13530i
$658$	−7.88742	−	7.40678i	−0.307484	−	0.288746i
$659$	22.5002	−	27.1981i	0.876485	−	1.05949i	−0.121277	−	0.992619i	$-0.538699\pi$
$659$	22.5002	−	27.1981i	0.876485	−	1.05949i	0.997762	−	0.0668697i	$-0.0213012\pi$
$660$		0			0
$661$	−0.409348	−	6.50640i	−0.0159218	−	0.253070i	−0.997934	−	0.0642510i	$-0.979534\pi$
$661$	−0.409348	−	6.50640i	−0.0159218	−	0.253070i	0.982012	−	0.188819i	$-0.0604658\pi$
$662$	35.7504	+	14.1546i	1.38948	+	0.550134i
$663$	25.9487	+	40.8887i	1.00777	+	1.58798i
$664$	2.41705	−	0.956977i	0.0937997	−	0.0371379i
$665$		0			0
$666$	−24.8270	−	39.1211i	−0.962027	−	1.51591i
$667$	32.0194	+	4.04499i	1.23980	+	0.156623i
$668$	−4.00738	+	12.3334i	−0.155050	+	0.477195i
$669$	11.8156	−	6.49568i	0.456818	−	0.251138i
$670$		0			0
$671$	42.8619	−	5.41472i	1.65467	−	0.209033i
$672$	−13.5631	−	7.45637i	−0.523207	−	0.287636i
$673$	−24.5764	−	6.31015i	−0.947351	−	0.243238i	−0.256753	−	0.966477i	$-0.582653\pi$
$673$	−24.5764	−	6.31015i	−0.947351	−	0.243238i	−0.690598	+	0.723239i	$0.742653\pi$
$674$	8.39204	−	25.8280i	0.323249	−	0.994859i
$675$		0			0
$676$	−2.09957	−	6.46182i	−0.0807528	−	0.248532i
$677$	1.93666	+	30.7824i	0.0744320	+	1.18306i	0.841049	+	0.540959i	$0.181939\pi$
$677$	1.93666	+	30.7824i	0.0744320	+	1.18306i	−0.766617	+	0.642105i	$0.778061\pi$
$678$	−36.6779	+	34.4428i	−1.40861	+	1.32277i
$679$	−1.24537	−	0.684650i	−0.0477931	−	0.0262745i
$680$		0			0
$681$	−18.8577	+	40.0746i	−0.722627	+	1.53566i
$682$	−0.0855193			−0.00327470
$683$	−0.266017	+	0.565314i	−0.0101788	+	0.0216312i	−0.909852	−	0.414933i	$-0.863805\pi$
$683$	−0.266017	+	0.565314i	−0.0101788	+	0.0216312i	0.899673	+	0.436564i	$0.143805\pi$
$684$	1.95084	−	31.0077i	0.0745923	−	1.18561i
$685$		0			0
$686$	11.6101	−	18.2946i	0.443276	−	0.698491i
$687$	24.4637	−	29.5715i	0.933347	−	1.12822i
$688$	−11.8554	+	14.3308i	−0.451984	+	0.546355i
$689$	4.09672	−	6.45540i	0.156073	−	0.245931i
$690$		0			0
$691$	2.07242	−	32.9402i	0.0788386	−	1.25310i	−0.737427	−	0.675427i	$-0.763960\pi$
$691$	2.07242	−	32.9402i	0.0788386	−	1.25310i	0.816266	−	0.577676i	$-0.196040\pi$
$692$	−14.2630	+	30.3104i	−0.542198	+	1.15223i
$693$	−7.61798			−0.289383
$694$	−1.39406	+	2.96253i	−0.0529178	+	0.112456i
$695$		0			0
$696$	−8.63812	−	4.74885i	−0.327427	−	0.180005i
$697$	−52.4512	+	49.2549i	−1.98673	+	1.86566i
$698$	1.26696	+	20.1377i	0.0479550	+	0.762222i
$699$	14.2955	+	43.9969i	0.540705	+	1.66412i
$700$		0			0
$701$	−7.08536	+	21.8065i	−0.267610	+	0.823620i	0.723470	+	0.690356i	$0.242546\pi$
$701$	−7.08536	+	21.8065i	−0.267610	+	0.823620i	−0.991081	+	0.133264i	$0.957454\pi$
$702$	−0.444463	−	0.114119i	−0.0167752	−	0.00430713i
$703$	28.5087	+	15.6728i	1.07523	+	0.591111i
$704$	−33.1283	+	4.18507i	−1.24857	+	0.157731i
$705$		0			0
$706$	−58.0466	+	31.9114i	−2.18461	+	1.20100i
$707$	0.0719733	−	0.221511i	0.00270683	−	0.00833078i
$708$	8.88114	+	1.12195i	0.333774	+	0.0421654i
$709$	−3.41258	−	5.37737i	−0.128162	−	0.201951i	0.774187	−	0.632957i	$-0.218159\pi$
$709$	−3.41258	−	5.37737i	−0.128162	−	0.201951i	−0.902349	+	0.431005i	$0.858159\pi$
$710$		0			0
$711$	5.15101	−	2.03943i	0.193178	−	0.0764845i
$712$	−1.45106	−	2.28651i	−0.0543808	−	0.0856905i
$713$	0.0634998	+	0.0251414i	0.00237809	+	0.000941551i
$714$	1.54988	+	24.6346i	0.0580028	+	0.921928i
$715$		0			0
$716$	2.26385	−	2.73652i	0.0846040	−	0.102269i
$717$	−12.4823	−	11.7217i	−0.466160	−	0.437753i
$718$	10.3202	+	31.7624i	0.385147	+	1.18536i
$719$	−2.48139	−	13.0079i	−0.0925403	−	0.485113i	−0.998139	−	0.0609778i	$-0.980578\pi$
$719$	−2.48139	−	13.0079i	−0.0925403	−	0.485113i	0.905599	−	0.424135i	$-0.139422\pi$
$720$		0			0
$721$	−5.30141	−	11.2661i	−0.197435	−	0.419571i
$722$	0.474881	+	1.00917i	0.0176732	+	0.0375576i
$723$	43.9246	−	17.3910i	1.63357	−	0.646778i
$724$	−7.36984	−	5.35450i	−0.273898	−	0.198998i
$725$		0			0
$726$	2.27300	−	1.65143i	0.0843590	−	0.0612904i
$727$	15.0569	−	23.7258i	0.558429	−	0.879943i	−0.441421	−	0.897300i	$-0.645525\pi$
$727$	15.0569	−	23.7258i	0.558429	−	0.879943i	0.999849	+	0.0173574i	$0.00552532\pi$
$728$	−0.308945	+	1.61955i	−0.0114503	+	0.0600244i
$729$	−20.0521	+	18.8302i	−0.742670	+	0.697414i
$730$		0			0
$731$	35.2348	+	4.45119i	1.30321	+	0.164633i
$732$	61.6196	+	44.7693i	2.27753	+	1.65472i
$733$	−2.97459	−	15.5934i	−0.109869	−	0.575954i	−0.994060	−	0.108829i	$-0.965290\pi$
$733$	−2.97459	−	15.5934i	−0.109869	−	0.575954i	0.884191	−	0.467125i	$-0.154710\pi$
$734$	−11.7785	−	4.66343i	−0.434752	−	0.172130i
$735$		0			0
$736$	42.1045	+	10.8106i	1.55199	+	0.398484i
$737$	29.1763	−	7.49120i	1.07472	−	0.275942i
$738$	4.57641	−	72.7400i	0.168460	−	2.67759i
$739$	−32.8772	−	39.7417i	−1.20941	−	1.46192i	−0.848398	−	0.529360i	$-0.822432\pi$
$739$	−32.8772	−	39.7417i	−1.20941	−	1.46192i	−0.361009	−	0.932562i	$-0.617568\pi$
$740$		0			0
$741$	33.3607	−	8.56557i	1.22554	−	0.314664i
$742$	3.41492	−	1.87737i	0.125366	−	0.0689204i
$743$	18.2825	−	13.2830i	0.670720	−	0.487307i	−0.199546	−	0.979888i	$-0.563947\pi$
$743$	18.2825	−	13.2830i	0.670720	−	0.487307i	0.870266	+	0.492582i	$0.163947\pi$
$744$	−0.0152060	−	0.0142794i	−0.000557479	−	0.000523507i
$745$		0			0
$746$	9.34446	−	48.9854i	0.342125	−	1.79348i
$747$	−11.6999	+	1.47804i	−0.428076	+	0.0540786i
$748$	29.7232	+	35.9291i	1.08679	+	1.31370i
$749$	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	$0.798547\pi$
$752$	13.8760	+	16.7732i	0.506005	+	0.611655i
$753$	−23.5849	+	2.97946i	−0.859480	+	0.108578i
$754$	7.43490	−	38.9751i	0.270763	−	1.41939i
$755$		0			0
$756$	−0.0915846	−	0.0860037i	−0.00333090	−	0.00312792i
$757$	−4.17190	+	3.03106i	−0.151630	+	0.110166i	−0.661014	−	0.750374i	$-0.729874\pi$
$757$	−4.17190	+	3.03106i	−0.151630	+	0.110166i	0.509383	+	0.860540i	$0.329874\pi$
$758$	49.3688	−	27.1407i	1.79315	−	0.985795i
$759$	41.2535	−	10.5921i	1.49741	−	0.384468i
$760$		0			0
$761$	10.8259	+	13.0862i	0.392437	+	0.474375i	0.929317	−	0.369284i	$-0.120397\pi$
$761$	10.8259	+	13.0862i	0.392437	+	0.474375i	−0.536879	+	0.843659i	$0.680397\pi$
$762$	−2.21285	+	35.1722i	−0.0801630	+	1.27415i
$763$	3.92723	−	1.00834i	0.142175	−	0.0365044i
$764$	−37.8984	−	9.73067i	−1.37112	−	0.352043i
$765$		0			0
$766$	38.5197	+	15.2510i	1.39177	+	0.551042i
$767$	0.934134	+	4.89690i	0.0337296	+	0.176817i
$768$	19.2698	+	14.0004i	0.695340	+	0.505194i
$769$	15.4047	+	1.94606i	0.555507	+	0.0701768i	0.398075	−	0.917353i	$-0.369679\pi$
$769$	15.4047	+	1.94606i	0.555507	+	0.0701768i	0.157432	+	0.987530i	$0.449679\pi$
$770$		0			0
$771$	2.20930	−	2.07468i	0.0795662	−	0.0747176i
$772$	−2.73843	+	14.3554i	−0.0985583	+	0.516661i
$773$	4.48315	−	7.06432i	0.161248	−	0.254086i	−0.754091	−	0.656769i	$-0.771922\pi$
$773$	4.48315	−	7.06432i	0.161248	−	0.254086i	0.915339	+	0.402683i	$0.131922\pi$
$774$	−29.1039	+	21.1452i	−1.04612	+	0.760050i
$775$		0			0
$776$	−0.986286	−	0.716579i	−0.0354056	−	0.0257237i
$777$	13.0757	−	5.17702i	0.469087	−	0.185725i
$778$	26.3245	+	55.9423i	0.943777	+	2.00563i
$779$	21.7890	+	46.3040i	0.780672	+	1.65901i
$780$		0			0
$781$	3.09187	+	16.2081i	0.110636	+	0.579972i
$782$	−21.4228	−	65.9326i	−0.766077	−	2.35774i
$783$	0.304935	+	0.286353i	0.0108975	+	0.0102334i
$784$	−13.2656	+	16.0353i	−0.473770	+	0.572690i
$785$		0			0
$786$	−1.95775	−	31.1176i	−0.0698307	−	1.10993i
$787$	47.9028	+	18.9661i	1.70755	+	0.676067i	0.999546	−	0.0301394i	$-0.00959512\pi$
$787$	47.9028	+	18.9661i	1.70755	+	0.676067i	0.708006	+	0.706207i	$0.249595\pi$
$788$	−13.0770	−	20.6060i	−0.465848	−	0.734060i
$789$	−23.2450	+	9.20336i	−0.827545	+	0.327648i
$790$		0			0
$791$	−4.11066	−	6.47736i	−0.146158	−	0.230308i
$792$	−6.48341	−	0.819045i	−0.230378	−	0.0291035i
$793$	−13.1075	+	40.3407i	−0.465461	+	1.43254i
$794$	−24.8973	+	13.6874i	−0.883572	+	0.485748i
$795$		0			0
$796$	−21.9961	+	2.77875i	−0.779629	+	0.0984901i
$797$	−13.9758	−	7.68325i	−0.495047	−	0.272155i	0.214612	−	0.976699i	$-0.431151\pi$
$797$	−13.9758	−	7.68325i	−0.495047	−	0.272155i	−0.709660	+	0.704545i	$0.751151\pi$
$798$	17.0038	+	4.36585i	0.601930	+	0.154549i
$799$	12.8451	−	39.5332i	0.454428	−	1.39859i
$800$		0			0
$801$	3.79626	+	11.6837i	0.134134	+	0.412823i
$802$	1.71226	+	27.2156i	0.0604621	+	0.961018i
$803$	23.8090	−	22.3582i	0.840203	−	0.789003i
$804$	46.5372	+	25.5840i	1.64124	+	0.902280i
$805$		0			0
$806$	0.0357500	−	0.0759727i	0.00125924	−	0.00267602i
$807$	−78.8274			−2.77486
$808$	0.0850697	−	0.180782i	0.00299274	−	0.00635990i
$809$	−2.33909	+	37.1787i	−0.0822379	+	1.30713i	0.713141	+	0.701021i	$0.247272\pi$
$809$	−2.33909	+	37.1787i	−0.0822379	+	1.30713i	−0.795379	+	0.606113i	$0.792728\pi$
$810$		0			0
$811$	15.9114	−	25.0723i	0.558723	−	0.880407i	−0.441132	−	0.897442i	$-0.645423\pi$
$811$	15.9114	−	25.0723i	0.558723	−	0.880407i	0.999855	+	0.0170354i	$0.00542281\pi$
$812$	6.92456	−	8.37036i	0.243005	−	0.293742i
$813$	−11.6820	+	14.1211i	−0.409704	+	0.495247i
$814$	26.5014	−	41.7596i	0.928875	−	1.46367i
$815$		0			0
$816$	3.11822	−	49.5627i	0.109160	−	1.73504i
$817$	10.7547	−	22.8550i	0.376261	−	0.799595i
$818$	25.1700			0.880048
$819$	3.18458	−	6.76758i	0.111278	−	0.236478i
$820$		0			0
$821$	−22.3092	−	12.2646i	−0.778598	−	0.428038i	0.0423058	−	0.999105i	$-0.486530\pi$
$821$	−22.3092	−	12.2646i	−0.778598	−	0.428038i	−0.820903	+	0.571067i	$0.806530\pi$
$822$	−50.1674	+	47.1103i	−1.74979	+	1.64316i
$823$	−0.607457	−	9.65525i	−0.0211746	−	0.336561i	−0.994325	−	0.106389i	$-0.966071\pi$
$823$	−0.607457	−	9.65525i	−0.0211746	−	0.336561i	0.973150	−	0.230172i	$-0.0739289\pi$
$824$	−3.30059	−	10.1582i	−0.114981	−	0.353876i
$825$		0			0
$826$	−0.785195	+	2.41658i	−0.0273204	+	0.0840836i
$827$	−41.0839	−	10.5485i	−1.42863	−	0.366809i	−0.546356	−	0.837553i	$-0.683986\pi$
$827$	−41.0839	−	10.5485i	−1.42863	−	0.366809i	−0.882270	+	0.470744i	$0.843986\pi$
$828$	33.0550	+	18.1721i	1.14874	+	0.631525i
$829$	0.209963	−	0.0265245i	0.00729232	−	0.000921234i	−0.121686	−	0.992569i	$-0.538830\pi$
$829$	0.209963	−	0.0265245i	0.00729232	−	0.000921234i	0.128979	+	0.991647i	$0.458830\pi$
$830$		0			0
$831$	−2.26331	+	1.24426i	−0.0785133	+	0.0431630i
$832$	10.1309	−	31.1796i	0.351225	−	1.08096i
$833$	39.4258	+	4.98063i	1.36602	+	0.172569i
$834$	15.9850	+	25.1884i	0.553516	+	0.872202i
$835$		0			0
$836$	30.8355	−	12.2086i	1.06647	−	0.422245i
$837$	0.000474313	0	0.000747398i	1.63947e−5	0	2.58339e-5i
$838$	21.9621	+	8.69540i	0.758667	+	0.300377i
$839$	−2.96801	−	47.1751i	−0.102467	−	1.62867i	−0.628225	−	0.778032i	$-0.716218\pi$
$839$	−2.96801	−	47.1751i	−0.102467	−	1.62867i	0.525758	−	0.850634i	$-0.323782\pi$
$840$		0			0
$841$	−4.57033	+	5.52458i	−0.157597	+	0.190503i
$842$	−36.1378	−	33.9357i	−1.24539	−	1.16950i
$843$	3.95106	+	12.1601i	0.136082	+	0.418817i
$844$	2.91959	+	15.3050i	0.100496	+	0.526821i
$845$		0			0
$846$	17.9277	+	38.0983i	0.616368	+	1.30985i
$847$	0.182397	+	0.387614i	0.00626724	+	0.0133186i
$848$	−7.28974	+	2.88621i	−0.250331	+	0.0991129i
$849$	−62.5687	−	45.4588i	−2.14735	−	1.56014i
$850$		0			0
$851$	−31.9545	+	23.2163i	−1.09539	+	0.795845i
$852$	−15.5873	+	24.5616i	−0.534011	+	0.841467i
$853$	0.736574	−	3.86126i	0.0252198	−	0.132207i	−0.967451	−	0.253060i	$-0.918563\pi$
$853$	0.736574	−	3.86126i	0.0252198	−	0.132207i	0.992670	+	0.120853i	$0.0385630\pi$
$854$	−15.7601	+	14.7997i	−0.539299	+	0.506435i
$855$		0			0
$856$	12.3303	+	1.55768i	0.421441	+	0.0532404i
$857$	24.1520	+	17.5475i	0.825017	+	0.599410i	0.918145	−	0.396244i	$-0.129687\pi$
$857$	24.1520	+	17.5475i	0.825017	+	0.599410i	−0.0931279	+	0.995654i	$0.529687\pi$
$858$	−9.81178	−	51.4351i	−0.334969	−	1.75597i
$859$	35.8707	+	14.2022i	1.22389	+	0.484574i	0.889098	−	0.457717i	$-0.151333\pi$
$859$	35.8707	+	14.2022i	1.22389	+	0.484574i	0.334796	+	0.942291i	$0.391333\pi$
$860$		0			0
$861$	21.4266	+	5.50141i	0.730216	+	0.187488i
$862$	47.1166	−	12.0975i	1.60480	−	0.412042i
$863$	−0.368155	+	5.85166i	−0.0125322	+	0.199193i	0.986779	+	0.162074i	$0.0518182\pi$
$863$	−0.368155	+	5.85166i	−0.0125322	+	0.199193i	−0.999311	+	0.0371194i	$0.988182\pi$
$864$	0.359143	+	0.434129i	0.0122183	+	0.0147694i
$865$		0			0
$866$	−52.2518	+	13.4160i	−1.77559	+	0.455893i
$867$	−46.5212	+	25.5753i	−1.57994	+	0.868582i
$868$	0.0185979	−	0.0135122i	0.000631255	−	0.000458633i
$869$	4.31090	+	4.04820i	0.146237	+	0.137326i
$870$		0			0
$871$	−5.54175	+	29.0509i	−0.187775	+	0.984351i
$872$	3.45074	−	0.435930i	0.116857	−	0.0147625i
$873$	3.52522	+	4.26126i	0.119311	+	0.144222i
$874$	−49.3060			−1.66780
$875$		0			0
$876$	57.5817			1.94551
$877$	−3.40800	−	4.11957i	−0.115080	−	0.139108i	0.709828	−	0.704376i	$-0.248773\pi$
$877$	−3.40800	−	4.11957i	−0.115080	−	0.139108i	−0.824908	+	0.565268i	$0.808773\pi$
$878$	8.15831	−	1.03063i	0.275330	−	0.0347822i
$879$	1.04222	−	5.46348i	0.0351531	−	0.184279i
$880$		0			0
$881$	−10.9723	−	10.3037i	−0.369666	−	0.347139i	0.477344	−	0.878717i	$-0.341600\pi$
$881$	−10.9723	−	10.3037i	−0.369666	−	0.347139i	−0.847010	+	0.531577i	$0.821600\pi$
$882$	−32.5657	+	23.6604i	−1.09654	+	0.796686i
$883$	36.0582	−	19.8232i	1.21345	−	0.667102i	0.259121	−	0.965845i	$-0.416567\pi$
$883$	36.0582	−	19.8232i	1.21345	−	0.667102i	0.954334	+	0.298743i	$0.0965672\pi$
$884$	−44.3436	+	11.3855i	−1.49144	+	0.382936i
$885$		0			0
$886$	−15.3495	−	18.5544i	−0.515676	−	0.623346i
$887$	0.231751	−	3.68358i	0.00778145	−	0.123683i	−0.992218	−	0.124511i	$-0.960264\pi$
$887$	0.231751	−	3.68358i	0.00778145	−	0.123683i	1.00000		0.000828554i	$0.000263737\pi$
$888$	11.6849	−	3.00016i	0.392118	−	0.100679i
$889$	−5.20458	−	1.33631i	−0.174556	−	0.0448184i
$890$		0			0
$891$	−26.7923	−	10.6078i	−0.897575	−	0.355375i
$892$	2.38852	+	12.5211i	0.0799735	+	0.419236i
$893$	−23.9177	−	17.3772i	−0.800376	−	0.581507i
$894$	93.6277	+	11.8279i	3.13138	+	0.395585i
$895$		0			0
$896$	2.99049	−	2.80826i	0.0999054	−	0.0938174i
$897$	−7.83569	+	41.0761i	−0.261626	+	1.37149i
$898$	27.5893	−	43.4738i	0.920667	−	1.45074i
$899$	−0.0619226	+	0.0449894i	−0.00206523	+	0.00150048i
$900$		0			0
$901$	12.1119	+	8.79980i	0.403505	+	0.293164i
$902$	72.3360	−	28.6398i	2.40853	−	0.953603i
$903$	−4.64905	−	9.87973i	−0.154711	−	0.328777i
$904$	−2.80203	−	5.95462i	−0.0931941	−	0.198048i
$905$		0			0
$906$	19.0296	+	99.7565i	0.632215	+	3.31419i
$907$	17.0598	+	52.5047i	0.566462	+	1.74339i	0.663568	+	0.748116i	$0.269041\pi$
$907$	17.0598	+	52.5047i	0.566462	+	1.74339i	−0.0971061	+	0.995274i	$0.530959\pi$
$908$	−30.5221	−	28.6622i	−1.01291	−	0.951188i
$909$	−0.577739	+	0.698366i	−0.0191624	+	0.0231633i
$910$		0			0
$911$	−0.324565	−	5.15882i	−0.0107533	−	0.170919i	−0.999738	−	0.0228998i	$-0.992710\pi$
$911$	−0.324565	−	5.15882i	−0.0107533	−	0.170919i	0.988984	−	0.148020i	$-0.0472899\pi$
$912$	−32.8396	−	13.0021i	−1.08743	−	0.430543i
$913$	−6.74511	−	10.6286i	−0.223231	−	0.351755i
$914$	30.0514	−	11.8982i	0.994013	−	0.393558i
$915$		0			0
$916$	19.4411	+	30.6342i	0.642351	+	1.01218i
$917$	4.71647	+	0.595828i	0.155751	+	0.0196760i
$918$	0.277666	−	0.854568i	0.00916435	−	0.0282050i
$919$	34.5276	−	18.9817i	1.13896	−	0.626148i	0.203322	−	0.979112i	$-0.434826\pi$
$919$	34.5276	−	18.9817i	1.13896	−	0.626148i	0.935637	+	0.352964i	$0.114826\pi$
$920$		0			0
$921$	46.0493	−	5.81738i	1.51738	−	0.191689i
$922$	−33.6431	−	18.4955i	−1.10798	−	0.609116i
$923$	−15.6913	−	4.02884i	−0.516485	−	0.132611i
$924$	4.43015	−	13.6346i	0.145741	−	0.448546i
$925$		0			0
$926$	5.59079	+	17.2067i	0.183725	+	0.565447i
$927$	3.04239	+	48.3575i	0.0999253	+	1.58827i
$928$	−35.5139	+	33.3498i	−1.16580	+	1.09476i
$929$	23.2303	+	12.7709i	0.762160	+	0.419001i	0.814896	−	0.579607i	$-0.196794\pi$
$929$	23.2303	+	12.7709i	0.762160	+	0.419001i	−0.0527356	+	0.998609i	$0.516794\pi$
$930$		0			0
$931$	12.0340	−	25.5735i	0.394397	−	0.838137i
$932$	−43.7339			−1.43255
$933$	−15.3139	+	32.5436i	−0.501353	+	1.06543i
$934$	5.05502	−	80.3472i	0.165405	−	2.62904i
$935$		0			0
$936$	3.43790	−	5.41727i	0.112371	−	0.177069i
$937$	0.315613	−	0.381511i	0.0103106	−	0.0124634i	−0.765333	−	0.643635i	$-0.777426\pi$
$937$	0.315613	−	0.381511i	0.0103106	−	0.0124634i	0.775643	+	0.631171i	$0.217426\pi$
$938$	−9.60862	+	11.6148i	−0.313733	+	0.379238i
$939$	−11.2481	+	17.7241i	−0.367067	+	0.578405i
$940$		0			0
$941$	−3.61488	+	57.4569i	−0.117842	+	1.87304i	0.286021	+	0.958223i	$0.407667\pi$
$941$	−3.61488	+	57.4569i	−0.117842	+	1.87304i	−0.403863	+	0.914820i	$0.632333\pi$
$942$	−2.93040	+	6.22742i	−0.0954776	+	0.202900i
$943$	−62.1306			−2.02325
$944$	2.17665	−	4.62562i	0.0708440	−	0.150551i
$945$		0			0
$946$	−33.6508	−	18.4997i	−1.09408	−	0.601476i
$947$	22.0805	−	20.7350i	0.717519	−	0.673796i	−0.237147	−	0.971474i	$-0.576212\pi$
$947$	22.0805	−	20.7350i	0.717519	−	0.673796i	0.954666	+	0.297678i	$0.0962123\pi$
$948$	0.654642	+	10.4052i	0.0212618	+	0.337946i
$949$	9.90931	+	30.4977i	0.321670	+	0.989998i
$950$		0			0
$951$	−4.69430	+	14.4476i	−0.152223	+	0.468495i
$952$	−3.12704	−	0.802888i	−0.101348	−	0.0260217i
$953$	−34.9205	−	19.1977i	−1.13118	−	0.621874i	−0.197619	−	0.980279i	$-0.563321\pi$
$953$	−34.9205	−	19.1977i	−1.13118	−	0.621874i	−0.933566	+	0.358405i	$0.883321\pi$
$954$	−15.0453	+	1.90066i	−0.487109	+	0.0615362i
$955$		0			0
$956$	14.1855	−	7.79854i	0.458792	−	0.252223i
$957$	−14.7504	+	45.3970i	−0.476812	+	1.46748i
$958$	45.7691	+	5.78198i	1.47873	+	0.186807i
$959$	−5.62249	−	8.85962i	−0.181560	−	0.286092i
$960$		0			0
$961$	28.8229	−	11.4118i	0.929772	−	0.368123i
$962$	26.0194	+	41.0000i	0.838899	+	1.32189i
$963$	−52.4207	−	20.7548i	−1.68923	−	0.668815i
$964$	2.80431	+	44.5732i	0.0903207	+	1.43561i
$965$		0			0
$966$	−13.5860	+	16.4227i	−0.437123	+	0.528390i
$967$	36.8089	+	34.5659i	1.18369	+	1.11156i	0.991487	+	0.130209i	$0.0415649\pi$
$967$	36.8089	+	34.5659i	1.18369	+	1.11156i	0.192208	+	0.981354i	$0.438435\pi$
$968$	0.113558	+	0.349495i	0.00364989	+	0.0112332i
$969$	12.6376	+	66.2489i	0.405980	+	2.12822i
$970$		0			0
$971$	8.63645	+	18.3534i	0.277157	+	0.588988i	0.994140	−	0.108103i	$-0.0344775\pi$
$971$	8.63645	+	18.3534i	0.277157	+	0.588988i	−0.716983	+	0.697091i	$0.754477\pi$
$972$	−21.8367	−	46.4054i	−0.700414	−	1.48845i
$973$	−4.22921	+	1.67446i	−0.135582	+	0.0536808i
$974$	20.6460	+	15.0002i	0.661540	+	0.480637i
$975$		0			0
$976$	35.1898	−	25.5669i	1.12640	−	0.818375i
$977$	−11.0930	+	17.4798i	−0.354897	+	0.559228i	−0.974133	−	0.225977i	$-0.927442\pi$
$977$	−11.0930	+	17.4798i	−0.354897	+	0.559228i	0.619236	+	0.785205i	$0.287442\pi$
$978$	−4.19165	+	21.9734i	−0.134034	+	0.702632i
$979$	−9.55934	+	8.97682i	−0.305518	+	0.286900i
$980$		0			0
$981$	−15.6540	−	1.97756i	−0.499793	−	0.0631386i
$982$	−2.46080	−	1.78788i	−0.0785273	−	0.0570534i
$983$	9.32449	+	48.8807i	0.297405	+	1.55905i	0.746388	+	0.665511i	$0.231786\pi$
$983$	9.32449	+	48.8807i	0.297405	+	1.55905i	−0.448983	+	0.893540i	$0.648214\pi$
$984$	17.6440	+	6.98574i	0.562469	+	0.222697i
$985$		0			0
$986$	75.2537	+	19.3219i	2.39657	+	0.615333i
$987$	−12.3783	+	3.17822i	−0.394007	+	0.101164i
$988$	−2.04454	+	32.4970i	−0.0650453	+	1.03387i
$989$	19.5478	+	23.6292i	0.621583	+	0.751365i
$990$		0			0
$991$	−50.6629	+	13.0080i	−1.60936	+	0.413214i	−0.943101	−	0.332506i	$-0.892106\pi$
$991$	−50.6629	+	13.0080i	−1.60936	+	0.413214i	−0.666260	+	0.745720i	$0.732106\pi$
$992$	−0.0903417	+	0.0496658i	−0.00286835	+	0.00157689i
$993$	36.7418	−	26.6944i	1.16596	−	0.847123i
$994$	−6.01926	−	5.65246i	−0.190919	−	0.179285i
$995$		0			0
$996$	4.15855	−	21.7999i	0.131769	−	0.690756i
$997$	39.9545	−	5.04743i	1.26537	−	0.159854i	0.536145	−	0.844126i	$-0.319880\pi$
$997$	39.9545	−	5.04743i	1.26537	−	0.159854i	0.729226	+	0.684272i	$0.239880\pi$
$998$	15.2459	+	18.4291i	0.482600	+	0.583364i
$999$	−0.511943			−0.0161972

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
125.2.g.a.71.2	✓	220	125.54	even	50
125.2.g.a.81.2	yes	220	5.4	even	2
625.2.g.a.26.10		220	1.1	even	1	trivial
625.2.g.a.601.10		220	125.71	even	25	inner
625.2.h.b.24.4		440	125.78	odd	100
625.2.h.b.24.19		440	125.47	odd	100
625.2.h.b.599.4		440	5.2	odd	4
625.2.h.b.599.19		440	5.3	odd	4

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.g (of order \(25\), degree \(20\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.32504 + 1.60169i) q^{2} +(2.43590 - 0.307726i) q^{3} +(-0.434938 + 2.28002i) q^{4} +(3.72054 + 3.49382i) q^{6} +(-0.629574 + 0.457412i) q^{7} +(-0.584987 + 0.321599i) q^{8} +(2.93319 - 0.753115i) q^{9} +O(q^{10})\)	\(q+(1.32504 + 1.60169i) q^{2} +(2.43590 - 0.307726i) q^{3} +(-0.434938 + 2.28002i) q^{4} +(3.72054 + 3.49382i) q^{6} +(-0.629574 + 0.457412i) q^{7} +(-0.584987 + 0.321599i) q^{8} +(2.93319 - 0.753115i) q^{9} +(2.06052 + 2.49074i) q^{11} +(-0.357844 + 5.68776i) q^{12} +(-3.07406 + 0.789285i) q^{13} +(-1.56684 - 0.402296i) q^{14} +(3.02605 + 1.19810i) q^{16} +(-1.16451 - 6.10458i) q^{17} +(5.09284 + 3.70016i) q^{18} +(-4.38516 - 0.553975i) q^{19} +(-1.39282 + 1.30795i) q^{21} +(-1.25914 + 6.60063i) q^{22} +(2.87542 - 4.53094i) q^{23} +(-1.32601 + 0.963402i) q^{24} +(-5.33743 - 3.87787i) q^{26} +(0.0646699 - 0.0256046i) q^{27} +(-0.769085 - 1.63439i) q^{28} +(2.56070 + 5.44177i) q^{29} +(0.00238475 + 0.0125013i) q^{31} +(2.50321 + 7.70409i) q^{32} +(5.78569 + 5.43313i) q^{33} +(8.23465 - 9.95398i) q^{34} +(0.441365 + 7.01530i) q^{36} +(-6.84347 - 2.70952i) q^{37} +(-4.92320 - 7.75772i) q^{38} +(-7.24524 + 2.86859i) q^{39} +(-6.20373 - 9.77552i) q^{41} +(-3.94047 - 0.497797i) q^{42} +(-1.76593 + 5.43498i) q^{43} +(-6.57514 + 3.61471i) q^{44} +(11.0672 - 1.39811i) q^{46} +(5.86131 + 3.22228i) q^{47} +(7.73985 + 1.98725i) q^{48} +(-1.97598 + 6.08145i) q^{49} +(-4.71518 - 14.5118i) q^{51} +(-0.462563 - 7.35223i) q^{52} +(-1.75608 + 1.64907i) q^{53} +(0.126701 + 0.0696543i) q^{54} +(0.221189 - 0.470051i) q^{56} -10.8523 q^{57} +(-5.32302 + 11.3120i) q^{58} +(0.0986283 - 1.56765i) q^{59} +(7.16121 - 11.2843i) q^{61} +(-0.0168634 + 0.0203843i) q^{62} +(-1.50217 + 1.81582i) q^{63} +(-5.53494 + 8.72167i) q^{64} +(-1.03595 + 16.4660i) q^{66} +(3.96761 - 8.43161i) q^{67} +14.4251 q^{68} +(5.60996 - 11.9218i) q^{69} +(4.47304 + 2.45907i) q^{71} +(-1.47368 + 1.38387i) q^{72} +(-0.634423 - 10.0839i) q^{73} +(-4.72802 - 14.5513i) q^{74} +(3.17035 - 9.75733i) q^{76} +(-2.43654 - 0.625598i) q^{77} +(-14.1948 - 7.80366i) q^{78} +(1.81498 - 0.229286i) q^{79} +(-7.81158 + 4.29445i) q^{81} +(7.43721 - 22.8894i) q^{82} +(-3.86348 - 0.488071i) q^{83} +(-2.37636 - 3.74455i) q^{84} +(-11.0451 + 4.37306i) q^{86} +(7.91220 + 12.4676i) q^{87} +(-2.00640 - 0.794389i) q^{88} +(0.254721 + 4.04868i) q^{89} +(1.57432 - 1.90303i) q^{91} +(9.08002 + 8.52670i) q^{92} +(0.00965601 + 0.0297182i) q^{93} +(2.60534 + 13.6576i) q^{94} +(8.46833 + 17.9961i) q^{96} +(0.777570 + 1.65242i) q^{97} +(-12.3589 + 4.89322i) q^{98} +(7.91970 + 5.75400i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 220 q + 20 q^{2} + 20 q^{3} - 20 q^{4} - 20 q^{6} + 15 q^{7} + 5 q^{8} - 20 q^{9}+O(q^{10}) \) 220 * q + 20 * q^2 + 20 * q^3 - 20 * q^4 - 20 * q^6 + 15 * q^7 + 5 * q^8 - 20 * q^9	\( 220 q + 20 q^{2} + 20 q^{3} - 20 q^{4} - 20 q^{6} + 15 q^{7} + 5 q^{8} - 20 q^{9} - 15 q^{11} + 100 q^{12} + 20 q^{13} - 10 q^{14} + 15 q^{17} - 10 q^{18} - 10 q^{19} - 5 q^{21} - 25 q^{22} + 90 q^{23} + 15 q^{24} + 15 q^{26} - 10 q^{27} - 30 q^{28} - 10 q^{29} - 10 q^{31} - 20 q^{32} - 15 q^{33} + 5 q^{34} - 210 q^{36} - 20 q^{37} - 30 q^{38} - 5 q^{41} - 70 q^{42} - 25 q^{43} + 15 q^{44} + 100 q^{47} - 105 q^{48} - 20 q^{49} + 25 q^{51} - 85 q^{52} - 20 q^{53} + 60 q^{54} - 105 q^{56} - 40 q^{57} + 225 q^{58} + 5 q^{59} - 65 q^{62} - 85 q^{63} + 45 q^{64} + 55 q^{66} + 105 q^{67} - 80 q^{68} + 40 q^{69} - 85 q^{71} - 160 q^{72} - 40 q^{73} + 35 q^{74} + 35 q^{76} - 75 q^{77} + 10 q^{78} + 55 q^{81} + 95 q^{82} - 50 q^{83} + 115 q^{84} + 40 q^{86} - 95 q^{87} - 165 q^{88} + 55 q^{89} - 105 q^{91} - 155 q^{92} + 185 q^{93} + 60 q^{94} + 135 q^{96} - 65 q^{97} - 135 q^{98} + 45 q^{99}+O(q^{100}) \) 220 * q + 20 * q^2 + 20 * q^3 - 20 * q^4 - 20 * q^6 + 15 * q^7 + 5 * q^8 - 20 * q^9 - 15 * q^11 + 100 * q^12 + 20 * q^13 - 10 * q^14 + 15 * q^17 - 10 * q^18 - 10 * q^19 - 5 * q^21 - 25 * q^22 + 90 * q^23 + 15 * q^24 + 15 * q^26 - 10 * q^27 - 30 * q^28 - 10 * q^29 - 10 * q^31 - 20 * q^32 - 15 * q^33 + 5 * q^34 - 210 * q^36 - 20 * q^37 - 30 * q^38 - 5 * q^41 - 70 * q^42 - 25 * q^43 + 15 * q^44 + 100 * q^47 - 105 * q^48 - 20 * q^49 + 25 * q^51 - 85 * q^52 - 20 * q^53 + 60 * q^54 - 105 * q^56 - 40 * q^57 + 225 * q^58 + 5 * q^59 - 65 * q^62 - 85 * q^63 + 45 * q^64 + 55 * q^66 + 105 * q^67 - 80 * q^68 + 40 * q^69 - 85 * q^71 - 160 * q^72 - 40 * q^73 + 35 * q^74 + 35 * q^76 - 75 * q^77 + 10 * q^78 + 55 * q^81 + 95 * q^82 - 50 * q^83 + 115 * q^84 + 40 * q^86 - 95 * q^87 - 165 * q^88 + 55 * q^89 - 105 * q^91 - 155 * q^92 + 185 * q^93 + 60 * q^94 + 135 * q^96 - 65 * q^97 - 135 * q^98 + 45 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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