LMFDB - Embedded newform 625.2.g.a.601.10

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			601.10
Character	$\chi$	$=$	625.601
Dual form			625.2.g.a.26.10

$q$-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 $\left(\mathbb{Z}/625\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{18}{25}\right)$

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	−0.0540360	−	0.998539i	$-0.517209\pi$
$2$	1.32504	−	1.60169i	0.936941	−	1.13257i	0.990977	−	0.134029i	$-0.0427914\pi$
$3$	2.43590	+	0.307726i	1.40637	+	0.177666i	0.791600	−	0.611040i	$-0.209249\pi$
$3$	2.43590	+	0.307726i	1.40637	+	0.177666i	0.614771	+	0.788706i	$0.289249\pi$
$4$	−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	0.462416	−	0.886663i	$-0.346983\pi$
$7$	−0.629574	−	0.457412i	−0.237956	−	0.172885i	−0.700372	+	0.713778i	$0.746983\pi$
$8$	−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	−0.362192	−	0.932104i	$-0.617971\pi$
$11$	2.06052	−	2.49074i	0.621270	−	0.750986i	0.983461	+	0.181118i	$0.0579715\pi$
$12$	−0.357844	−	5.68776i	−0.103301	−	1.64192i
$13$	−3.07406	−	0.789285i	−0.852592	−	0.218908i	−0.202988	−	0.979181i	$-0.565065\pi$
$13$	−3.07406	−	0.789285i	−0.852592	−	0.218908i	−0.649604	+	0.760273i	$0.725065\pi$
$14$	−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	0.504429	+	0.863453i	$0.331703\pi$
$17$	−1.16451	+	6.10458i	−0.282436	+	1.48058i	−0.786864	+	0.617126i	$0.788297\pi$
$18$	5.09284	−	3.70016i	1.20039	−	0.872137i
$19$	−4.38516	+	0.553975i	−1.00603	+	0.127091i	−0.611042	−	0.791598i	$-0.709250\pi$
$19$	−4.38516	+	0.553975i	−1.00603	+	0.127091i	−0.394983	+	0.918688i	$0.629250\pi$
$20$		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	0.999600	+	0.0282655i	$0.00899838\pi$
$23$	2.87542	+	4.53094i	0.599567	+	0.944766i	−0.400034	+	0.916500i	$0.631002\pi$
$24$	−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	−0.512864	−	0.858470i	$-0.671416\pi$
$29$	2.56070	−	5.44177i	0.475510	−	1.01051i	0.988374	−	0.152041i	$-0.0485845\pi$
$30$		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	$0.0596362\pi$
$32$	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	−0.855635	−	0.517579i	$-0.826833\pi$
$37$	−6.84347	+	2.70952i	−1.12506	+	0.445443i	−0.269424	+	0.963022i	$0.586833\pi$
$38$	−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	−0.123596	+	0.992333i	$0.539443\pi$
$41$	−6.20373	+	9.77552i	−0.968861	+	1.52668i	−0.845265	+	0.534347i	$0.820557\pi$
$42$	−3.94047	+	0.497797i	−0.608028	+	0.0768118i
$43$	−1.76593	−	5.43498i	−0.269302	−	0.828827i	−0.990671	−	0.136276i	$-0.956487\pi$
$43$	−1.76593	−	5.43498i	−0.269302	−	0.828827i	0.721369	−	0.692551i	$-0.243513\pi$
$44$	−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	0.00693559	−	0.999976i	$-0.497792\pi$
$47$	5.86131	−	3.22228i	0.854959	−	0.470018i	0.848024	+	0.529958i	$0.177792\pi$
$48$	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	0.554504	−	0.832181i	$-0.312908\pi$
$53$	−1.75608	−	1.64907i	−0.241217	−	0.226518i	−0.795721	+	0.605663i	$0.792908\pi$
$54$	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	0.999216	+	0.0395840i	$0.0126033\pi$
$59$	0.0986283	+	1.56765i	0.0128403	+	0.204091i	−0.986376	+	0.164507i	$0.947397\pi$
$60$		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	$0.493193\pi$
$62$	−0.0168634	−	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	0.986298	+	0.164972i	$0.0527534\pi$
$67$	3.96761	+	8.43161i	0.484721	+	1.03009i	−0.501577	+	0.865113i	$0.667247\pi$
$68$	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	−0.193697	−	0.981061i	$-0.562048\pi$
$71$	4.47304	−	2.45907i	0.530852	−	0.291838i	0.724549	+	0.689223i	$0.242048\pi$
$72$	−1.47368	−	1.38387i	−0.173674	−	0.163091i
$73$	−0.634423	+	10.0839i	−0.0742536	+	1.18023i	0.767748	+	0.640752i	$0.221377\pi$
$73$	−0.634423	+	10.0839i	−0.0742536	+	1.18023i	−0.842001	+	0.539476i	$0.818623\pi$
$74$	−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	0.226769	−	0.973949i	$-0.427184\pi$
$79$	1.81498	+	0.229286i	0.204201	+	0.0257966i	−0.0225670	+	0.999745i	$0.507184\pi$
$80$		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	−0.334473	−	0.942405i	$-0.608558\pi$
$83$	−3.86348	+	0.488071i	−0.424072	+	0.0535727i	−0.0895985	+	0.995978i	$0.528558\pi$
$84$	−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	−0.961186	−	0.275902i	$-0.911024\pi$
$89$	0.254721	−	4.04868i	0.0270004	−	0.429159i	0.988186	−	0.153257i	$-0.0489764\pi$
$90$		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	−0.861455	−	0.507834i	$-0.830446\pi$
$97$	0.777570	−	1.65242i	0.0789502	−	0.167778i	0.940405	+	0.340057i	$0.110446\pi$
$98$	−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	0.575673	−	0.817680i	$-0.304740\pi$
$101$	−0.242135	−	0.175921i	−0.0240933	−	0.0175048i	−0.599767	+	0.800175i	$0.704740\pi$
$102$	16.9957	+	26.7810i	1.68283	+	2.65171i
$103$	−2.99809	−	15.7165i	−0.295411	−	1.54860i	−0.752148	−	0.658995i	$-0.770982\pi$
$103$	−2.99809	−	15.7165i	−0.295411	−	1.54860i	0.456737	−	0.889602i	$-0.349018\pi$
$104$	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	−0.471726	+	0.881745i	$0.656369\pi$
$107$	−15.0619	+	10.9431i	−1.45609	+	1.05791i	−0.984361	+	0.176163i	$0.943631\pi$
$108$	0.0302518	−	0.158585i	0.00291098	−	0.0152599i
$109$	−4.84439	+	1.91803i	−0.464008	+	0.183714i	−0.588484	−	0.808509i	$-0.700275\pi$
$109$	−4.84439	+	1.91803i	−0.464008	+	0.183714i	0.124476	+	0.992223i	$0.460275\pi$
$110$		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	−0.913364	−	0.407144i	$-0.866525\pi$
$113$	−0.619002	−	9.83875i	−0.0582308	−	0.925552i	0.855133	−	0.518408i	$-0.173475\pi$
$114$	−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	−0.538185	−	0.842827i	$-0.680890\pi$
$127$	4.40137	−	5.32035i	0.390559	−	0.472104i	0.928744	+	0.370722i	$0.120890\pi$
$128$	−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	−0.854260	−	0.519845i	$-0.825990\pi$
$131$	−4.45323	+	4.18186i	−0.389080	+	0.365371i	0.465180	+	0.885216i	$0.345990\pi$
$132$	−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	−0.852002	−	0.523539i	$-0.824612\pi$
$137$	−0.846660	−	13.4573i	−0.0723351	−	1.14973i	0.779667	−	0.626195i	$-0.215388\pi$
$138$	26.5284	+	6.81134i	2.25825	+	0.579820i
$139$	5.66146	−	1.45362i	0.480199	−	0.123294i	−0.000828731	−	1.00000i	$-0.500264\pi$
$139$	5.66146	−	1.45362i	0.480199	−	0.123294i	0.481027	+	0.876706i	$0.340264\pi$
$140$		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	0.996544	−	0.0830697i	$-0.0264724\pi$
$149$	14.9590	+	10.8683i	1.22549	+	0.890370i	0.228945	+	0.973439i	$0.426472\pi$
$150$		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	$-0.000332383\pi$
$152$	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	−0.933050	−	0.359746i	$-0.882863\pi$
$157$	0.416703	−	1.28248i	0.0332566	−	0.102353i	0.966307	+	0.257393i	$0.0828634\pi$
$158$	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	−0.739823	−	0.672801i	$-0.765091\pi$
$163$	2.34847	−	3.70060i	0.183947	−	0.289854i	0.923770	+	0.382947i	$0.125091\pi$
$164$	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	0.0920922	−	0.995750i	$-0.470645\pi$
$167$	5.54292	−	0.700234i	0.428924	−	0.0541857i	0.336832	+	0.941565i	$0.390645\pi$
$168$	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	0.323463	−	0.946241i	$-0.395153\pi$
$173$	13.9786	−	3.58908i	1.06277	−	0.272873i	0.739308	+	0.673368i	$0.235153\pi$
$174$	−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	−0.531075	−	0.847325i	$-0.678212\pi$
$179$	−1.34083	+	0.737128i	−0.100218	+	0.0550956i	0.430856	+	0.902421i	$0.358212\pi$
$180$		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	$0.906594\pi$
$182$	5.13409			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	−0.829232	−	0.558904i	$-0.811222\pi$
$191$	−1.05847	−	16.8239i	−0.0765880	−	1.21733i	0.752644	−	0.658428i	$-0.228778\pi$
$192$	−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	0.361673	−	0.932305i	$-0.382206\pi$
$197$	−7.66463	−	7.19757i	−0.546082	−	0.512805i	−0.907756	+	0.419499i	$0.862206\pi$
$198$	1.27775	−	20.3092i	0.0908054	−	1.44331i
$199$	2.95165	−	9.08423i	0.209237	−	0.643964i	−0.790276	−	0.612751i	$-0.790063\pi$
$199$	2.95165	−	9.08423i	0.209237	−	0.643964i	0.999513	−	0.0312133i	$-0.00993711\pi$
$200$		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	0.572996	−	0.819558i	$-0.305781\pi$
$211$	6.24127	+	2.47110i	0.429667	+	0.170117i	−0.143329	+	0.989675i	$0.545781\pi$
$212$	−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	0.532809	−	0.846235i	$-0.321136\pi$
$223$	5.10599	+	2.02160i	0.341922	+	0.135377i	−0.190887	+	0.981612i	$0.561136\pi$
$224$	−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	−0.997090	−	0.0762352i	$-0.975710\pi$
$227$	−9.66561	−	15.2306i	−0.641529	−	1.01089i	0.355561	−	0.934653i	$-0.384290\pi$
$228$	4.72008	+	24.7435i	0.312595	+	1.63868i
$229$	11.3947	+	10.7003i	0.752984	+	0.707099i	0.962672	−	0.270669i	$-0.0872450\pi$
$229$	11.3947	+	10.7003i	0.752984	+	0.707099i	−0.209688	+	0.977768i	$0.567245\pi$
$230$		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	−0.657240	−	0.753681i	$-0.728276\pi$
$233$	3.53056	−	18.5079i	0.231295	−	1.21249i	0.888535	−	0.458809i	$-0.151724\pi$
$234$	−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	−0.894433	−	0.447202i	$-0.852421\pi$
$239$	−4.44545	+	5.37363i	−0.287552	+	0.347591i	0.606881	+	0.794793i	$0.292421\pi$
$240$		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	$0.367248\pi$
$242$	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	0.618496	−	0.785788i	$-0.287742\pi$
$257$	0.998633	+	0.725549i	0.0622930	+	0.0452585i	−0.556203	+	0.831046i	$0.687742\pi$
$258$	−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	−0.0679590	−	0.997688i	$-0.521649\pi$
$263$	−9.86257	−	2.53228i	−0.608152	−	0.156147i	−0.540193	+	0.841541i	$0.681649\pi$
$264$	−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	−0.996734	−	0.0807606i	$-0.974265\pi$
$269$	−31.8523	+	4.02388i	−1.94207	+	0.245340i	−0.945335	+	0.326101i	$0.894265\pi$
$270$		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	$0.812798\pi$
$272$	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	0.338558	−	0.940946i	$-0.390061\pi$
$277$	−0.978065	−	0.387243i	−0.0587662	−	0.0232672i	−0.397324	+	0.917678i	$0.630061\pi$
$278$	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	−0.941260	−	0.337684i	$-0.890357\pi$
$281$	0.975796	−	5.11530i	0.0582111	−	0.305153i	0.999471	+	0.0325303i	$0.0103566\pi$
$282$	10.5492	−	32.4670i	0.628194	−	1.93338i
$283$	−22.9620	+	21.5628i	−1.36495	+	1.28177i	−0.441914	+	0.897058i	$0.645700\pi$
$283$	−22.9620	+	21.5628i	−1.36495	+	1.28177i	−0.923035	+	0.384715i	$0.874300\pi$
$284$	−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	0.969420	−	0.245407i	$-0.0789217\pi$
$293$	0.700027	+	2.15446i	0.0408960	+	0.125865i	−0.928524	+	0.371272i	$0.878922\pi$
$294$	−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	0.545517	−	0.838100i	$-0.316333\pi$
$311$	−7.84921	−	12.3684i	−0.445088	−	0.701346i	−0.990605	+	0.136753i	$0.956333\pi$
$312$	3.31584	+	4.00816i	0.187722	+	0.226917i
$313$	−5.44984	−	6.58773i	−0.308043	−	0.372360i	0.593660	−	0.804716i	$-0.297682\pi$
$313$	−5.44984	−	6.58773i	−0.308043	−	0.372360i	−0.901703	+	0.432356i	$0.857682\pi$
$314$	−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	0.817084	−	0.576519i	$-0.195589\pi$
$317$	−2.63436	−	5.59830i	−0.147960	−	0.314432i	−0.965044	+	0.262087i	$0.915589\pi$
$318$	−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	0.860331	−	0.509736i	$-0.170257\pi$
$331$	16.2091	+	8.91105i	0.890935	+	0.489796i	0.0306039	+	0.999532i	$0.490257\pi$
$332$	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	−0.979730	−	0.200321i	$-0.935801\pi$
$337$	−7.00020	+	11.0306i	−0.381325	+	0.600873i	0.598405	+	0.801194i	$0.295801\pi$
$338$	−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	−0.886017	−	0.463652i	$-0.846539\pi$
$347$	0.670629	−	1.42516i	0.0360013	−	0.0765066i	0.922019	+	0.387145i	$0.126539\pi$
$348$	−31.8678	−	12.6174i	−1.70829	−	0.676361i
$349$	7.85282	−	5.70541i	0.420352	−	0.305404i	−0.357427	−	0.933941i	$-0.616346\pi$
$349$	7.85282	−	5.70541i	0.420352	−	0.305404i	0.777779	+	0.628537i	$0.216346\pi$
$350$		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	−0.679486	−	0.733689i	$-0.737797\pi$
$353$	−5.97101	−	31.3011i	−0.317805	−	1.66599i	0.361681	−	0.932302i	$-0.382203\pi$
$354$	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	0.0607906	−	0.998151i	$-0.480638\pi$
$359$	14.9378	−	5.91429i	0.788386	−	0.312144i	0.727596	+	0.686006i	$0.240638\pi$
$360$		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	0.336239	−	0.941777i	$-0.390845\pi$
$367$	−5.34033	−	2.93587i	−0.278763	−	0.153251i	−0.615002	+	0.788525i	$0.710845\pi$
$368$	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	−0.999779	−	0.0210347i	$-0.993304\pi$
$373$	−15.2917	+	18.4846i	−0.791777	+	0.957094i	0.208002	+	0.978128i	$0.433304\pi$
$374$	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	0.835694	+	0.549196i	$0.185066\pi$
$379$	5.07836	+	26.6217i	0.260858	+	1.36746i	−0.574836	+	0.818269i	$0.694934\pi$
$380$		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	0.860827	−	0.508897i	$-0.169947\pi$
$383$	17.4647	+	9.60131i	0.892405	+	0.490604i	0.0315779	+	0.999501i	$0.489947\pi$
$384$	−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	0.566953	−	0.823750i	$-0.308122\pi$
$389$	28.8080	−	7.39663i	1.46062	−	0.375024i	0.893669	+	0.448726i	$0.148122\pi$
$390$		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	−0.986972	−	0.160892i	$-0.948563\pi$
$397$	−2.56108	−	13.4257i	−0.128537	−	0.673815i	0.858435	−	0.512922i	$-0.171437\pi$
$398$	−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	−0.290368	−	0.956915i	$-0.593778\pi$
$401$	10.6129	−	7.71074i	0.529984	−	0.385056i	0.820352	+	0.571859i	$0.193778\pi$
$402$	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	0.925997	−	0.377532i	$-0.123227\pi$
$409$	7.71814	+	9.32962i	0.381637	+	0.461320i	−0.544359	+	0.838852i	$0.683227\pi$
$410$		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	0.706053	−	0.708159i	$-0.250474\pi$
$419$	9.95753	+	5.47420i	0.486457	+	0.267432i	−0.219596	+	0.975591i	$0.570474\pi$
$420$		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	$0.737394\pi$
$422$	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	0.987400	+	0.158244i	$0.0505833\pi$
$431$	9.96374	+	21.1740i	0.479937	+	1.01992i	−0.507463	+	0.861673i	$0.669417\pi$
$432$	0.226371			0.0108913
$433$	−11.0497	−	23.4818i	−0.531014	−	1.12846i	−0.972865	−	0.231373i	$-0.925678\pi$
$433$	−11.0497	−	23.4818i	−0.531014	−	1.12846i	0.441851	−	0.897088i	$-0.354322\pi$
$434$	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	0.891140	−	0.453728i	$-0.149906\pi$
$439$	2.11965	+	3.34003i	0.101165	+	0.159411i	−0.789975	+	0.613139i	$0.789906\pi$
$440$		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	0.591088	+	0.806607i	$0.298698\pi$
$449$	−7.65420	+	23.5572i	−0.361224	+	1.11173i	−0.952312	+	0.305126i	$0.901302\pi$
$450$		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	0.998316	+	0.0580056i	$0.0184741\pi$
$457$	4.80474	+	14.7875i	0.224756	+	0.691729i	−0.773560	+	0.633723i	$0.781526\pi$
$458$	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	−0.0675514	−	0.997716i	$-0.521519\pi$
$461$	−17.1720	−	6.79886i	−0.799778	−	0.316654i	−0.732226	+	0.681061i	$0.761519\pi$
$462$	−6.87953	+	10.8404i	−0.320065	+	0.504341i
$463$	8.09227	−	3.20396i	0.376080	−	0.148900i	−0.172478	−	0.985013i	$-0.555177\pi$
$463$	8.09227	−	3.20396i	0.376080	−	0.148900i	0.548557	+	0.836113i	$0.315177\pi$
$464$	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	−0.349325	+	0.937002i	$0.613589\pi$
$467$	−28.2318	+	26.5114i	−1.30641	+	1.22680i	−0.957087	+	0.289801i	$0.906411\pi$
$468$	−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	0.959632	−	0.281259i	$-0.0907519\pi$
$479$	16.1778	+	15.1920i	0.739184	+	0.694140i	−0.220448	+	0.975399i	$0.570752\pi$
$480$		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	0.508291	−	0.861186i	$-0.330278\pi$
$487$	11.8909	+	3.05307i	0.538830	+	0.138348i	0.0305390	+	0.999534i	$0.490278\pi$
$488$	−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	0.216574	−	0.976266i	$-0.430512\pi$
$491$	−1.41728	−	0.363896i	−0.0639611	−	0.0164224i	−0.280535	+	0.959844i	$0.590512\pi$
$492$	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	−0.0324565	−	0.999473i	$-0.510333\pi$
$503$	−7.00757	−	0.885262i	−0.312452	−	0.0394719i	−0.279996	+	0.960001i	$0.590333\pi$
$504$	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	0.0178318	−	0.999841i	$-0.494324\pi$
$509$	−10.1123	−	2.59639i	−0.448219	−	0.115083i	−0.466051	+	0.884758i	$0.654324\pi$
$510$		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	0.581637	−	0.813449i	$-0.302413\pi$
$521$	−4.42096	−	4.15155i	−0.193686	−	0.181883i	−0.775322	+	0.631566i	$0.782413\pi$
$522$	−7.09419	−	37.1890i	−0.310504	−	1.62772i
$523$	14.1536	+	22.3024i	0.618892	+	0.975217i	0.998741	+	0.0501689i	$0.0159760\pi$
$523$	14.1536	+	22.3024i	0.618892	+	0.975217i	−0.379849	+	0.925049i	$0.624024\pi$
$524$	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	−0.232120	−	0.972687i	$-0.574566\pi$
$541$	17.3707	−	27.3719i	0.746826	−	1.17681i	0.978946	−	0.204122i	$-0.0654338\pi$
$542$	−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	−0.808530	−	0.588455i	$-0.799736\pi$
$547$	−17.4221	+	9.57786i	−0.744913	+	0.409520i	0.0636167	+	0.997974i	$0.479736\pi$
$548$	−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	0.875328	−	0.483529i	$-0.160645\pi$
$563$	5.60788	+	6.77876i	0.236344	+	0.285691i	−0.638984	+	0.769220i	$0.720645\pi$
$564$	−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	0.807646	−	0.589667i	$-0.200741\pi$
$569$	−3.85270	−	8.18740i	−0.161513	−	0.343234i	−0.969160	+	0.246434i	$0.920741\pi$
$570$		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	$0.443301\pi$
$572$	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	−0.252565	−	0.967580i	$-0.581274\pi$
$577$	−0.186241	+	0.0478187i	−0.00775333	+	0.00199072i	0.244811	+	0.969571i	$0.421274\pi$
$578$	−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	−0.970041	−	0.242942i	$-0.921888\pi$
$587$	−8.16964	+	12.8733i	−0.337197	+	0.531338i	0.632844	+	0.774280i	$0.281888\pi$
$588$	−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	−0.0476219	−	0.998865i	$-0.515164\pi$
$593$	14.0758	−	43.3208i	0.578023	−	1.77897i	0.625645	−	0.780108i	$-0.284836\pi$
$594$	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	−0.870244	−	0.492621i	$-0.836039\pi$
$599$	−16.4139	+	11.9254i	−0.670653	+	0.487258i	0.199590	+	0.979879i	$0.436039\pi$
$600$		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	$0.746978\pi$
$602$	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	−0.636303	−	0.771439i	$-0.719537\pi$
$607$	−2.44524	+	1.77657i	−0.0992490	+	0.0721087i	0.537054	+	0.843548i	$0.319537\pi$
$608$	−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	0.901783	+	0.432189i	$0.142259\pi$
$613$	1.51718	+	24.1150i	0.0612785	+	0.973994i	−0.840504	+	0.541805i	$0.817741\pi$
$614$	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	0.945200	−	0.326491i	$-0.105866\pi$
$617$	29.2112	+	16.0590i	1.17600	+	0.646511i	0.230798	+	0.973002i	$0.425866\pi$
$618$	−66.0653	−	47.9993i	−2.65754	−	1.93081i
$619$	−8.36904	+	7.85905i	−0.336380	+	0.315882i	−0.834268	−	0.551360i	$-0.814109\pi$
$619$	−8.36904	+	7.85905i	−0.336380	+	0.315882i	0.497888	+	0.867242i	$0.334109\pi$
$620$		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	−0.331605	−	0.943418i	$-0.607590\pi$
$631$	14.7988	−	13.8970i	0.589130	−	0.553230i	0.920735	+	0.390188i	$0.127590\pi$
$632$	−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	−0.663930	−	0.747795i	$-0.731113\pi$
$641$	−16.1026	+	6.37546i	−0.636014	+	0.251816i	0.0279163	+	0.999610i	$0.491113\pi$
$642$	−17.8051	+	93.3378i	−0.702713	+	3.68375i
$643$	−27.8652	+	20.2453i	−1.09890	+	0.798395i	−0.980879	−	0.194616i	$-0.937654\pi$
$643$	−27.8652	+	20.2453i	−1.09890	+	0.798395i	−0.118018	+	0.993012i	$0.537654\pi$
$644$	−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	0.737324	+	0.675539i	$0.236089\pi$
$647$	7.64256	+	40.0637i	0.300460	+	1.57507i	−0.436864	+	0.899528i	$0.643911\pi$
$648$	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	0.131646	+	0.991297i	$0.457974\pi$
$653$	−18.2985	+	38.8863i	−0.716075	+	1.52174i	−0.847722	+	0.530441i	$0.822026\pi$
$654$	−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	0.997762	+	0.0668697i	$0.0213012\pi$
$659$	22.5002	+	27.1981i	0.876485	+	1.05949i	−0.121277	+	0.992619i	$0.538699\pi$
$660$		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	$0.979534\pi$
$662$	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	−0.690598	−	0.723239i	$-0.742653\pi$
$673$	−24.5764	+	6.31015i	−0.947351	+	0.243238i	−0.256753	+	0.966477i	$0.582653\pi$
$674$	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	−0.766617	−	0.642105i	$-0.778061\pi$
$677$	1.93666	−	30.7824i	0.0744320	−	1.18306i	0.841049	−	0.540959i	$-0.181939\pi$
$678$	−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	0.899673	−	0.436564i	$-0.143805\pi$
$683$	−0.266017	−	0.565314i	−0.0101788	−	0.0216312i	−0.909852	+	0.414933i	$0.863805\pi$
$684$	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	0.816266	+	0.577676i	$0.196040\pi$
$691$	2.07242	+	32.9402i	0.0788386	+	1.25310i	−0.737427	+	0.675427i	$0.763960\pi$
$692$	−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	−0.991081	−	0.133264i	$-0.957454\pi$
$701$	−7.08536	−	21.8065i	−0.267610	−	0.823620i	0.723470	−	0.690356i	$-0.242546\pi$
$702$	−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	−0.902349	−	0.431005i	$-0.858159\pi$
$709$	−3.41258	+	5.37737i	−0.128162	+	0.201951i	0.774187	+	0.632957i	$0.218159\pi$
$710$		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	0.905599	+	0.424135i	$0.139422\pi$
$719$	−2.48139	+	13.0079i	−0.0925403	+	0.485113i	−0.998139	+	0.0609778i	$0.980578\pi$
$720$		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	0.999849	−	0.0173574i	$-0.00552532\pi$
$727$	15.0569	+	23.7258i	0.558429	+	0.879943i	−0.441421	+	0.897300i	$0.645525\pi$
$728$	−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	0.884191	+	0.467125i	$0.154710\pi$
$733$	−2.97459	+	15.5934i	−0.109869	+	0.575954i	−0.994060	+	0.108829i	$0.965290\pi$
$734$	−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	−0.361009	+	0.932562i	$0.617568\pi$
$739$	−32.8772	+	39.7417i	−1.20941	+	1.46192i	−0.848398	+	0.529360i	$0.822432\pi$
$740$		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	0.870266	−	0.492582i	$-0.163947\pi$
$743$	18.2825	+	13.2830i	0.670720	+	0.487307i	−0.199546	+	0.979888i	$0.563947\pi$
$744$	−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	0.509383	−	0.860540i	$-0.329874\pi$
$757$	−4.17190	−	3.03106i	−0.151630	−	0.110166i	−0.661014	+	0.750374i	$0.729874\pi$
$758$	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	−0.536879	−	0.843659i	$-0.680397\pi$
$761$	10.8259	−	13.0862i	0.392437	−	0.474375i	0.929317	+	0.369284i	$0.120397\pi$
$762$	−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	0.157432	−	0.987530i	$-0.449679\pi$
$769$	15.4047	−	1.94606i	0.555507	−	0.0701768i	0.398075	+	0.917353i	$0.369679\pi$
$770$		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	0.915339	−	0.402683i	$-0.131922\pi$
$773$	4.48315	+	7.06432i	0.161248	+	0.254086i	−0.754091	+	0.656769i	$0.771922\pi$
$774$	−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	0.708006	−	0.706207i	$-0.249595\pi$
$787$	47.9028	−	18.9661i	1.70755	−	0.676067i	0.999546	+	0.0301394i	$0.00959512\pi$
$788$	−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	−0.709660	−	0.704545i	$-0.751151\pi$
$797$	−13.9758	+	7.68325i	−0.495047	+	0.272155i	0.214612	+	0.976699i	$0.431151\pi$
$798$	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	−0.795379	−	0.606113i	$-0.792728\pi$
$809$	−2.33909	−	37.1787i	−0.0822379	−	1.30713i	0.713141	−	0.701021i	$-0.247272\pi$
$810$		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	$0.645423\pi$
$812$	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	−0.820903	−	0.571067i	$-0.806530\pi$
$821$	−22.3092	+	12.2646i	−0.778598	+	0.428038i	0.0423058	+	0.999105i	$0.486530\pi$
$822$	−50.1674	−	47.1103i	−1.74979	−	1.64316i
$823$	−0.607457	+	9.65525i	−0.0211746	+	0.336561i	0.973150	+	0.230172i	$0.0739289\pi$
$823$	−0.607457	+	9.65525i	−0.0211746	+	0.336561i	−0.994325	+	0.106389i	$0.966071\pi$
$824$	−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	−0.882270	−	0.470744i	$-0.843986\pi$
$827$	−41.0839	+	10.5485i	−1.42863	+	0.366809i	−0.546356	+	0.837553i	$0.683986\pi$
$828$	33.0550	−	18.1721i	1.14874	−	0.631525i
$829$	0.209963	+	0.0265245i	0.00729232	+	0.000921234i	0.128979	−	0.991647i	$-0.458830\pi$
$829$	0.209963	+	0.0265245i	0.00729232	+	0.000921234i	−0.121686	+	0.992569i	$0.538830\pi$
$830$		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	0.525758	+	0.850634i	$0.323782\pi$
$839$	−2.96801	+	47.1751i	−0.102467	+	1.62867i	−0.628225	+	0.778032i	$0.716218\pi$
$840$		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	0.992670	−	0.120853i	$-0.0385630\pi$
$853$	0.736574	+	3.86126i	0.0252198	+	0.132207i	−0.967451	+	0.253060i	$0.918563\pi$
$854$	−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	−0.0931279	−	0.995654i	$-0.529687\pi$
$857$	24.1520	−	17.5475i	0.825017	−	0.599410i	0.918145	+	0.396244i	$0.129687\pi$
$858$	−9.81178	+	51.4351i	−0.334969	+	1.75597i
$859$	35.8707	−	14.2022i	1.22389	−	0.484574i	0.334796	−	0.942291i	$-0.391333\pi$
$859$	35.8707	−	14.2022i	1.22389	−	0.484574i	0.889098	+	0.457717i	$0.151333\pi$
$860$		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	−0.999311	−	0.0371194i	$-0.988182\pi$
$863$	−0.368155	−	5.85166i	−0.0125322	−	0.199193i	0.986779	−	0.162074i	$-0.0518182\pi$
$864$	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	−0.824908	−	0.565268i	$-0.808773\pi$
$877$	−3.40800	+	4.11957i	−0.115080	+	0.139108i	0.709828	+	0.704376i	$0.248773\pi$
$878$	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	−0.847010	−	0.531577i	$-0.821600\pi$
$881$	−10.9723	+	10.3037i	−0.369666	+	0.347139i	0.477344	+	0.878717i	$0.341600\pi$
$882$	−32.5657	−	23.6604i	−1.09654	−	0.796686i
$883$	36.0582	+	19.8232i	1.21345	+	0.667102i	0.954334	−	0.298743i	$-0.0965672\pi$
$883$	36.0582	+	19.8232i	1.21345	+	0.667102i	0.259121	+	0.965845i	$0.416567\pi$
$884$	−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	1.00000		0.000828554i	$-0.000263737\pi$
$887$	0.231751	+	3.68358i	0.00778145	+	0.123683i	−0.992218	+	0.124511i	$0.960264\pi$
$888$	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	−0.0971061	−	0.995274i	$-0.530959\pi$
$907$	17.0598	−	52.5047i	0.566462	−	1.74339i	0.663568	−	0.748116i	$-0.269041\pi$
$908$	−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	0.988984	+	0.148020i	$0.0472899\pi$
$911$	−0.324565	+	5.15882i	−0.0107533	+	0.170919i	−0.999738	+	0.0228998i	$0.992710\pi$
$912$	−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	0.935637	−	0.352964i	$-0.114826\pi$
$919$	34.5276	+	18.9817i	1.13896	+	0.626148i	0.203322	+	0.979112i	$0.434826\pi$
$920$		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	−0.0527356	−	0.998609i	$-0.516794\pi$
$929$	23.2303	−	12.7709i	0.762160	−	0.419001i	0.814896	+	0.579607i	$0.196794\pi$
$930$		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	0.775643	−	0.631171i	$-0.217426\pi$
$937$	0.315613	+	0.381511i	0.0103106	+	0.0124634i	−0.765333	+	0.643635i	$0.777426\pi$
$938$	−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	−0.403863	−	0.914820i	$-0.632333\pi$
$941$	−3.61488	−	57.4569i	−0.117842	−	1.87304i	0.286021	−	0.958223i	$-0.407667\pi$
$942$	−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	0.954666	−	0.297678i	$-0.0962123\pi$
$947$	22.0805	+	20.7350i	0.717519	+	0.673796i	−0.237147	+	0.971474i	$0.576212\pi$
$948$	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	−0.933566	−	0.358405i	$-0.883321\pi$
$953$	−34.9205	+	19.1977i	−1.13118	+	0.621874i	−0.197619	+	0.980279i	$0.563321\pi$
$954$	−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	0.192208	−	0.981354i	$-0.438435\pi$
$967$	36.8089	−	34.5659i	1.18369	−	1.11156i	0.991487	−	0.130209i	$-0.0415649\pi$
$968$	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	−0.716983	−	0.697091i	$-0.754477\pi$
$971$	8.63645	−	18.3534i	0.277157	−	0.588988i	0.994140	+	0.108103i	$0.0344775\pi$
$972$	−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	0.619236	−	0.785205i	$-0.287442\pi$
$977$	−11.0930	−	17.4798i	−0.354897	−	0.559228i	−0.974133	+	0.225977i	$0.927442\pi$
$978$	−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	−0.448983	−	0.893540i	$-0.648214\pi$
$983$	9.32449	−	48.8807i	0.297405	−	1.55905i	0.746388	−	0.665511i	$-0.231786\pi$
$984$	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	−0.666260	−	0.745720i	$-0.732106\pi$
$991$	−50.6629	−	13.0080i	−1.60936	−	0.413214i	−0.943101	+	0.332506i	$0.892106\pi$
$992$	−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	0.729226	−	0.684272i	$-0.239880\pi$
$997$	39.9545	+	5.04743i	1.26537	+	0.159854i	0.536145	+	0.844126i	$0.319880\pi$
$998$	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.601.10		220
5.2	odd	4		625.2.h.b.24.19		440
5.3	odd	4		625.2.h.b.24.4		440
5.4	even	2		125.2.g.a.71.2	✓	220
125.8	odd	100		625.2.h.b.599.19		440
125.44	even	50		125.2.g.a.81.2	yes	220
125.81	even	25	inner	625.2.g.a.26.10		220
125.117	odd	100		625.2.h.b.599.4		440

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

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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