LMFDB - Embedded newform 875.2.u.a.599.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [875,2,Mod(74,875)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(875, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([9, 20]))

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

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

chi := DirichletCharacter("875.74");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 875 = 5^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	875.u (of order $30$, degree $8$, 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:	$6.98691017686$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$18$ over $\Q(\zeta_{30})$
Twist minimal:	no (minimal twist has level 175)
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			599.15
Character	$\chi$	$=$	875.599
Dual form			875.2.u.a.149.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.32048 + 1.18897i) q^{2} +(-0.135384 + 0.0142295i) q^{3} +(0.120974 + 1.15099i) q^{4} +(-0.195691 - 0.142178i) q^{6} +(1.92211 + 1.81810i) q^{7} +(0.880110 - 1.21137i) q^{8} +(-2.91632 + 0.619882i) q^{9} +O(q^{10})$	\(q+(1.32048 + 1.18897i) q^{2} +(-0.135384 + 0.0142295i) q^{3} +(0.120974 + 1.15099i) q^{4} +(-0.195691 - 0.142178i) q^{6} +(1.92211 + 1.81810i) q^{7} +(0.880110 - 1.21137i) q^{8} +(-2.91632 + 0.619882i) q^{9} +(0.876154 + 0.186232i) q^{11} +(-0.0327559 - 0.154104i) q^{12} +(5.62497 + 1.82766i) q^{13} +(0.376443 + 4.68611i) q^{14} +(4.86653 - 1.03441i) q^{16} +(-0.831108 - 1.86670i) q^{17} +(-4.58797 - 2.64887i) q^{18} +(-0.385351 + 3.66637i) q^{19} +(-0.286094 - 0.218792i) q^{21} +(0.935524 + 1.28764i) q^{22} +(-0.145934 - 0.131400i) q^{23} +(-0.101916 + 0.176524i) q^{24} +(5.25465 + 9.10133i) q^{26} +(0.774405 - 0.251619i) q^{27} +(-1.86009 + 2.43227i) q^{28} +(-1.19212 + 0.866123i) q^{29} +(-1.46865 + 0.653883i) q^{31} +(5.06260 + 2.92289i) q^{32} +(-0.121268 - 0.0127457i) q^{33} +(1.12198 - 3.45311i) q^{34} +(-1.06627 - 3.28166i) q^{36} +(1.81514 + 8.53955i) q^{37} +(-4.86805 + 4.38322i) q^{38} +(-0.787540 - 0.167397i) q^{39} +(1.96439 - 6.04579i) q^{41} +(-0.117645 - 0.629069i) q^{42} +11.5179i q^{43} +(-0.108360 + 1.03097i) q^{44} +(-0.0364735 - 0.347022i) q^{46} +(4.89753 - 11.0000i) q^{47} +(-0.644132 + 0.209291i) q^{48} +(0.388997 + 6.98918i) q^{49} +(0.139081 + 0.240896i) q^{51} +(-1.42315 + 6.69538i) q^{52} +(-2.08734 + 0.219388i) q^{53} +(1.32176 + 0.588484i) q^{54} +(3.89406 - 0.728248i) q^{56} -0.501852i q^{57} +(-2.60397 - 0.273688i) q^{58} +(-5.44105 - 6.04289i) q^{59} +(1.69386 - 1.88122i) q^{61} +(-2.71677 - 0.882733i) q^{62} +(-6.73248 - 4.11069i) q^{63} +(0.134982 + 0.415431i) q^{64} +(-0.144978 - 0.161014i) q^{66} +(-4.13775 - 9.29355i) q^{67} +(2.04801 - 1.18242i) q^{68} +(0.0216269 + 0.0157129i) q^{69} +(-9.11276 + 6.62080i) q^{71} +(-1.81577 + 4.07830i) q^{72} +(2.07918 - 9.78179i) q^{73} +(-7.75640 + 13.4345i) q^{74} -4.26657 q^{76} +(1.34547 + 1.95090i) q^{77} +(-0.840905 - 1.15741i) q^{78} +(-3.29105 - 1.46527i) q^{79} +(8.06986 - 3.59293i) q^{81} +(9.78221 - 5.64776i) q^{82} +(1.57843 - 2.17252i) q^{83} +(0.217217 - 0.355759i) q^{84} +(-13.6945 + 15.2092i) q^{86} +(0.149069 - 0.134223i) q^{87} +(0.996708 - 0.897440i) q^{88} +(4.43903 - 4.93004i) q^{89} +(7.48892 + 13.7398i) q^{91} +(0.133585 - 0.183864i) q^{92} +(0.189527 - 0.109424i) q^{93} +(19.5458 - 8.70236i) q^{94} +(-0.726988 - 0.323676i) q^{96} +(-10.3597 - 14.2589i) q^{97} +(-7.79626 + 9.69161i) q^{98} -2.67059 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 5 q^{2} + 5 q^{3} - 19 q^{4} - 12 q^{6} + 50 q^{8} - 17 q^{9}+O(q^{10}) $ 144 * q + 5 * q^2 + 5 * q^3 - 19 * q^4 - 12 * q^6 + 50 * q^8 - 17 * q^9	$ 144 q + 5 q^{2} + 5 q^{3} - 19 q^{4} - 12 q^{6} + 50 q^{8} - 17 q^{9} + 5 q^{12} + 20 q^{13} - 18 q^{14} + 5 q^{16} - 5 q^{17} - 11 q^{19} - 9 q^{21} + 60 q^{22} - 25 q^{23} + 50 q^{24} - 60 q^{26} - 40 q^{27} - 24 q^{29} + 15 q^{31} - 20 q^{33} - 20 q^{34} + 16 q^{36} + 5 q^{37} + 20 q^{38} + 13 q^{39} - 62 q^{41} - 40 q^{42} - 15 q^{44} - 27 q^{46} + 5 q^{47} - 38 q^{49} - 8 q^{51} + 130 q^{52} - 25 q^{53} - 29 q^{54} + 32 q^{56} + 65 q^{58} - 39 q^{59} + 7 q^{61} + 20 q^{62} + 45 q^{63} + 34 q^{64} + 11 q^{66} - 25 q^{67} + 74 q^{69} - 46 q^{71} - 60 q^{72} - 35 q^{73} + 6 q^{74} + 180 q^{76} + 5 q^{77} - 10 q^{78} + 9 q^{79} - 59 q^{81} - 90 q^{83} - 51 q^{84} + 11 q^{86} + 5 q^{87} - 140 q^{88} - 42 q^{89} + 22 q^{91} - 10 q^{92} + 5 q^{94} + 53 q^{96} - 120 q^{97} + 180 q^{98} - 44 q^{99}+O(q^{100}) $ 144 * q + 5 * q^2 + 5 * q^3 - 19 * q^4 - 12 * q^6 + 50 * q^8 - 17 * q^9 + 5 * q^12 + 20 * q^13 - 18 * q^14 + 5 * q^16 - 5 * q^17 - 11 * q^19 - 9 * q^21 + 60 * q^22 - 25 * q^23 + 50 * q^24 - 60 * q^26 - 40 * q^27 - 24 * q^29 + 15 * q^31 - 20 * q^33 - 20 * q^34 + 16 * q^36 + 5 * q^37 + 20 * q^38 + 13 * q^39 - 62 * q^41 - 40 * q^42 - 15 * q^44 - 27 * q^46 + 5 * q^47 - 38 * q^49 - 8 * q^51 + 130 * q^52 - 25 * q^53 - 29 * q^54 + 32 * q^56 + 65 * q^58 - 39 * q^59 + 7 * q^61 + 20 * q^62 + 45 * q^63 + 34 * q^64 + 11 * q^66 - 25 * q^67 + 74 * q^69 - 46 * q^71 - 60 * q^72 - 35 * q^73 + 6 * q^74 + 180 * q^76 + 5 * q^77 - 10 * q^78 + 9 * q^79 - 59 * q^81 - 90 * q^83 - 51 * q^84 + 11 * q^86 + 5 * q^87 - 140 * q^88 - 42 * q^89 + 22 * q^91 - 10 * q^92 + 5 * q^94 + 53 * q^96 - 120 * q^97 + 180 * q^98 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/875\mathbb{Z}\right)^\times$.

$n$	$127$	$626$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.32048	+	1.18897i	0.933724	+	0.840728i	0.987467	−	0.157826i	$-0.0504486\pi$
$2$	1.32048	+	1.18897i	0.933724	+	0.840728i	−0.0537433	+	0.998555i	$0.517115\pi$
$3$	−0.135384	+	0.0142295i	−0.0781642	+	0.00821539i	−0.143530	−	0.989646i	$-0.545845\pi$
$3$	−0.135384	+	0.0142295i	−0.0781642	+	0.00821539i	0.0653656	+	0.997861i	$0.479179\pi$
$4$	0.120974	+	1.15099i	0.0604869	+	0.575494i
$5$		0			0
$5$		0			0
$6$	−0.195691	−	0.142178i	−0.0798906	−	0.0580439i
$7$	1.92211	+	1.81810i	0.726488	+	0.687179i
$7$	1.92211	+	1.81810i	0.726488	+	0.687179i
$8$	0.880110	−	1.21137i	0.311166	−	0.428283i
$9$	−2.91632	+	0.619882i	−0.972105	+	0.206627i
$10$		0			0
$11$	0.876154	+	0.186232i	0.264170	+	0.0561512i	0.338093	−	0.941113i	$-0.390218\pi$
$11$	0.876154	+	0.186232i	0.264170	+	0.0561512i	−0.0739221	+	0.997264i	$0.523552\pi$
$12$	−0.0327559	−	0.154104i	−0.00945581	−	0.0444861i
$13$	5.62497	+	1.82766i	1.56009	+	0.506903i	0.956831	−	0.290645i	$-0.0938697\pi$
$13$	5.62497	+	1.82766i	1.56009	+	0.506903i	0.603256	+	0.797548i	$0.293870\pi$
$14$	0.376443	+	4.68611i	0.100609	+	1.25241i
$15$		0			0
$16$	4.86653	−	1.03441i	1.21663	−	0.258603i
$17$	−0.831108	−	1.86670i	−0.201573	−	0.452741i	0.784268	−	0.620422i	$-0.213039\pi$
$17$	−0.831108	−	1.86670i	−0.201573	−	0.452741i	−0.985841	+	0.167681i	$0.946372\pi$
$18$	−4.58797	−	2.64887i	−1.08140	−	0.624344i
$19$	−0.385351	+	3.66637i	−0.0884056	+	0.841123i	0.857020	+	0.515284i	$0.172314\pi$
$19$	−0.385351	+	3.66637i	−0.0884056	+	0.841123i	−0.945425	+	0.325839i	$0.894353\pi$
$20$		0			0
$21$	−0.286094	−	0.218792i	−0.0624308	−	0.0477444i
$22$	0.935524	+	1.28764i	0.199454	+	0.274525i
$23$	−0.145934	−	0.131400i	−0.0304293	−	0.0273987i	0.653776	−	0.756688i	$-0.273184\pi$
$23$	−0.145934	−	0.131400i	−0.0304293	−	0.0273987i	−0.684205	+	0.729290i	$0.739851\pi$
$24$	−0.101916	+	0.176524i	−0.0208035	+	0.0360328i
$25$		0			0
$26$	5.25465	+	9.10133i	1.03052	+	1.78492i
$27$	0.774405	−	0.251619i	0.149034	−	0.0484242i
$28$	−1.86009	+	2.43227i	−0.351524	+	0.459655i
$29$	−1.19212	+	0.866123i	−0.221370	+	0.160835i	−0.692943	−	0.720992i	$-0.743686\pi$
$29$	−1.19212	+	0.866123i	−0.221370	+	0.160835i	0.471573	+	0.881827i	$0.343686\pi$
$30$		0			0
$31$	−1.46865	+	0.653883i	−0.263777	+	0.117441i	−0.534364	−	0.845255i	$-0.679449\pi$
$31$	−1.46865	+	0.653883i	−0.263777	+	0.117441i	0.270587	+	0.962695i	$0.412782\pi$
$32$	5.06260	+	2.92289i	0.894950	+	0.516700i
$33$	−0.121268	−	0.0127457i	−0.0211100	−	0.00221875i
$34$	1.12198	−	3.45311i	0.192419	−	0.592204i
$35$		0			0
$36$	−1.06627	−	3.28166i	−0.177712	−	0.546943i
$37$	1.81514	+	8.53955i	0.298407	+	1.40389i	0.830411	+	0.557151i	$0.188106\pi$
$37$	1.81514	+	8.53955i	0.298407	+	1.40389i	−0.532004	+	0.846742i	$0.678561\pi$
$38$	−4.86805	+	4.38322i	−0.789703	+	0.711051i
$39$	−0.787540	−	0.167397i	−0.126107	−	0.0268049i
$40$		0			0
$41$	1.96439	−	6.04579i	0.306787	−	0.944193i	−0.672217	−	0.740354i	$-0.734658\pi$
$41$	1.96439	−	6.04579i	0.306787	−	0.944193i	0.979004	−	0.203839i	$-0.0653420\pi$
$42$	−0.117645	−	0.629069i	−0.0181531	−	0.0970674i
$43$			11.5179i			1.75647i	0.478232	+	0.878233i	$0.341278\pi$
$43$			11.5179i			1.75647i	−0.478232	+	0.878233i	$0.658722\pi$
$44$	−0.108360	+	1.03097i	−0.0163358	+	0.155425i
$45$		0			0
$46$	−0.0364735	−	0.347022i	−0.00537772	−	0.0511656i
$47$	4.89753	−	11.0000i	0.714379	−	1.60452i	−0.0797819	−	0.996812i	$-0.525422\pi$
$47$	4.89753	−	11.0000i	0.714379	−	1.60452i	0.794160	−	0.607708i	$-0.207911\pi$
$48$	−0.644132	+	0.209291i	−0.0929725	+	0.0302086i
$49$	0.388997	+	6.98918i	0.0555710	+	0.998455i
$50$		0			0
$51$	0.139081	+	0.240896i	0.0194753	+	0.0337321i
$52$	−1.42315	+	6.69538i	−0.197355	+	0.928482i
$53$	−2.08734	+	0.219388i	−0.286718	+	0.0301353i	−0.246796	−	0.969067i	$-0.579378\pi$
$53$	−2.08734	+	0.219388i	−0.286718	+	0.0301353i	−0.0399223	+	0.999203i	$0.512711\pi$
$54$	1.32176	+	0.588484i	0.179868	+	0.0800826i
$55$		0			0
$56$	3.89406	−	0.728248i	0.520366	−	0.0973162i
$57$		−	0.501852i		−	0.0664720i
$58$	−2.60397	−	0.273688i	−0.341917	−	0.0359370i
$59$	−5.44105	−	6.04289i	−0.708364	−	0.786718i	0.276320	−	0.961066i	$-0.410885\pi$
$59$	−5.44105	−	6.04289i	−0.708364	−	0.786718i	−0.984684	+	0.174348i	$0.944218\pi$
$60$		0			0
$61$	1.69386	−	1.88122i	0.216876	−	0.240865i	−0.624883	−	0.780718i	$-0.714853\pi$
$61$	1.69386	−	1.88122i	0.216876	−	0.240865i	0.841759	+	0.539853i	$0.181520\pi$
$62$	−2.71677	−	0.882733i	−0.345030	−	0.112107i
$63$	−6.73248	−	4.11069i	−0.848213	−	0.517898i
$64$	0.134982	+	0.415431i	0.0168727	+	0.0519289i
$65$		0			0
$66$	−0.144978	−	0.161014i	−0.0178455	−	0.0198194i
$67$	−4.13775	−	9.29355i	−0.505507	−	1.13539i	−0.968497	−	0.249024i	$-0.919890\pi$
$67$	−4.13775	−	9.29355i	−0.505507	−	1.13539i	0.462990	−	0.886363i	$-0.346777\pi$
$68$	2.04801	−	1.18242i	0.248357	−	0.143389i
$69$	0.0216269	+	0.0157129i	0.00260358	+	0.00189161i
$70$		0			0
$71$	−9.11276	+	6.62080i	−1.08149	+	0.785745i	−0.977941	−	0.208880i	$-0.933018\pi$
$71$	−9.11276	+	6.62080i	−1.08149	+	0.785745i	−0.103544	+	0.994625i	$0.533018\pi$
$72$	−1.81577	+	4.07830i	−0.213991	+	0.480632i
$73$	2.07918	−	9.78179i	0.243350	−	1.14487i	−0.671477	−	0.741026i	$-0.734340\pi$
$73$	2.07918	−	9.78179i	0.243350	−	1.14487i	0.914827	−	0.403846i	$-0.132327\pi$
$74$	−7.75640	+	13.4345i	−0.901663	+	1.56173i
$75$		0			0
$76$	−4.26657			−0.489409
$77$	1.34547	+	1.95090i	0.153331	+	0.222325i
$78$	−0.840905	−	1.15741i	−0.0952137	−	0.131050i
$79$	−3.29105	−	1.46527i	−0.370272	−	0.164856i	0.213161	−	0.977017i	$-0.431624\pi$
$79$	−3.29105	−	1.46527i	−0.370272	−	0.164856i	−0.583433	+	0.812161i	$0.698291\pi$
$80$		0			0
$81$	8.06986	−	3.59293i	0.896651	−	0.399215i
$82$	9.78221	−	5.64776i	1.08026	−	0.623691i
$83$	1.57843	−	2.17252i	0.173255	−	0.238465i	−0.713555	−	0.700599i	$-0.752916\pi$
$83$	1.57843	−	2.17252i	0.173255	−	0.238465i	0.886810	+	0.462134i	$0.152916\pi$
$84$	0.217217	−	0.355759i	0.0237004	−	0.0388165i
$85$		0			0
$86$	−13.6945	+	15.2092i	−1.47671	+	1.64005i
$87$	0.149069	−	0.134223i	0.0159819	−	0.0143902i
$88$	0.996708	−	0.897440i	0.106249	−	0.0956674i
$89$	4.43903	−	4.93004i	0.470536	−	0.522584i	−0.460426	−	0.887698i	$-0.652303\pi$
$89$	4.43903	−	4.93004i	0.470536	−	0.522584i	0.930963	+	0.365114i	$0.118970\pi$
$90$		0			0
$91$	7.48892	+	13.7398i	0.785052	+	1.44032i
$92$	0.133585	−	0.183864i	0.0139272	−	0.0191692i
$93$	0.189527	−	0.109424i	0.0196531	−	0.0113467i
$94$	19.5458	−	8.70236i	2.01600	−	0.897580i
$95$		0			0
$96$	−0.726988	−	0.323676i	−0.0741979	−	0.0330350i
$97$	−10.3597	−	14.2589i	−1.05187	−	1.44777i	−0.887179	−	0.461425i	$-0.847338\pi$
$97$	−10.3597	−	14.2589i	−1.05187	−	1.44777i	−0.164688	−	0.986346i	$-0.552662\pi$
$98$	−7.79626	+	9.69161i	−0.787541	+	0.979001i
$99$	−2.67059			−0.268404
$100$		0			0
$101$	−4.58094	+	7.93442i	−0.455820	+	0.789504i	−0.998735	−	0.0502839i	$-0.983987\pi$
$101$	−4.58094	+	7.93442i	−0.455820	+	0.789504i	0.542915	+	0.839788i	$0.317321\pi$
$102$	−0.102763	+	0.483462i	−0.0101751	+	0.0478699i
$103$	−1.15107	+	2.58534i	−0.113418	+	0.254741i	−0.961332	−	0.275393i	$-0.911192\pi$
$103$	−1.15107	+	2.58534i	−0.113418	+	0.254741i	0.847914	+	0.530135i	$0.177859\pi$
$104$	7.16457	−	5.20537i	0.702544	−	0.510428i
$105$		0			0
$106$	−3.01715	−	2.19209i	−0.293051	−	0.212914i
$107$	9.66149	−	5.57806i	0.934011	−	0.539252i	0.0459333	−	0.998945i	$-0.485374\pi$
$107$	9.66149	−	5.57806i	0.934011	−	0.539252i	0.888078	+	0.459693i	$0.152040\pi$
$108$	0.383294	+	0.860892i	0.0368824	+	0.0828393i
$109$	−4.07926	−	4.53048i	−0.390722	−	0.433941i	0.515405	−	0.856947i	$-0.327642\pi$
$109$	−4.07926	−	4.53048i	−0.390722	−	0.433941i	−0.906127	+	0.423006i	$0.860975\pi$
$110$		0			0
$111$	−0.367254	−	1.13029i	−0.0348582	−	0.107283i
$112$	11.2347	+	6.85960i	1.06158	+	0.648171i
$113$	5.18982	+	1.68628i	0.488217	+	0.158631i	0.542773	−	0.839879i	$-0.317374\pi$
$113$	5.18982	+	1.68628i	0.488217	+	0.158631i	−0.0545558	+	0.998511i	$0.517374\pi$
$114$	0.596687	−	0.662688i	0.0558849	−	0.0620665i
$115$		0			0
$116$	−1.14111	−	1.26733i	−0.105950	−	0.117669i
$117$	−17.5371	−	1.84323i	−1.62131	−	0.170406i
$118$		−	14.4488i		−	1.33012i
$119$	1.79637	−	5.09904i	0.164673	−	0.467428i
$120$		0			0
$121$	−9.31604	−	4.14777i	−0.846912	−	0.377070i
$122$	4.47342	−	0.470176i	0.405005	−	0.0425677i
$123$	−0.179920	+	0.846457i	−0.0162228	+	0.0763224i
$124$	−0.930280	−	1.61129i	−0.0835416	−	0.144698i
$125$		0			0
$126$	−4.00266	−	13.4328i	−0.356585	−	1.19669i
$127$	−11.8243	+	3.84194i	−1.04923	+	0.340917i	−0.782368	−	0.622817i	$-0.785988\pi$
$127$	−11.8243	+	3.84194i	−1.04923	+	0.340917i	−0.266866	+	0.963734i	$0.585988\pi$
$128$	4.43970	−	9.97173i	0.392418	−	0.881384i
$129$	−0.163894	−	1.55935i	−0.0144301	−	0.137293i
$130$		0			0
$131$	0.335067	−	3.18795i	0.0292749	−	0.278532i	−0.970085	−	0.242765i	$-0.921946\pi$
$131$	0.335067	−	3.18795i	0.0292749	−	0.278532i	0.999360	−	0.0357675i	$-0.0113876\pi$
$132$		−	0.141119i		−	0.0122829i
$133$	−7.40653	+	6.34655i	−0.642228	+	0.550316i
$134$	5.58591	−	17.1916i	0.482549	−	1.48513i
$135$		0			0
$136$	−2.99273	−	0.636124i	−0.256624	−	0.0545472i
$137$	−1.24907	+	1.12467i	−0.106716	+	0.0960871i	−0.720761	−	0.693183i	$-0.756208\pi$
$137$	−1.24907	+	1.12467i	−0.106716	+	0.0960871i	0.614046	+	0.789270i	$0.289541\pi$
$138$	0.00987588	+	0.0464624i	0.000840691	+	0.00395514i
$139$	0.0192250	+	0.0591686i	0.00163065	+	0.00501861i	0.951869	−	0.306507i	$-0.0991602\pi$
$139$	0.0192250	+	0.0591686i	0.00163065	+	0.00501861i	−0.950238	+	0.311525i	$0.899160\pi$
$140$		0			0
$141$	−0.506524	+	1.55892i	−0.0426571	+	0.131285i
$142$	−19.9052	−	2.09212i	−1.67041	−	0.175567i
$143$	4.58797	+	2.64887i	0.383666	+	0.221510i
$144$	−13.5511	+	6.03335i	−1.12926	+	0.502779i
$145$		0			0
$146$	14.3758	−	10.4446i	1.18975	−	0.864403i
$147$	−0.152116	−	0.940691i	−0.0125464	−	0.0775868i
$148$	−9.60933	+	3.12226i	−0.789882	+	0.256648i
$149$	−10.9267	−	18.9256i	−0.895149	−	1.55044i	−0.833620	−	0.552339i	$-0.813735\pi$
$149$	−10.9267	−	18.9256i	−0.895149	−	1.55044i	−0.0615297	−	0.998105i	$-0.519598\pi$
$150$		0			0
$151$	2.73477	−	4.73676i	0.222552	−	0.385472i	−0.733030	−	0.680196i	$-0.761894\pi$
$151$	2.73477	−	4.73676i	0.222552	−	0.385472i	0.955582	+	0.294724i	$0.0952278\pi$
$152$	4.10217	+	3.69361i	0.332730	+	0.299592i
$153$	3.58091	+	4.92870i	0.289499	+	0.398462i
$154$	−0.542882	+	4.17586i	−0.0437467	+	0.336500i
$155$		0			0
$156$	0.0974001	−	0.926700i	0.00779825	−	0.0741954i
$157$	−6.75475	−	3.89986i	−0.539088	−	0.311243i	0.205621	−	0.978632i	$-0.434078\pi$
$157$	−6.75475	−	3.89986i	−0.539088	−	0.311243i	−0.744709	+	0.667389i	$0.767412\pi$
$158$	−2.60362	−	5.84783i	−0.207133	−	0.465228i
$159$	0.279471	−	0.0594035i	0.0221635	−	0.00471100i
$160$		0			0
$161$	−0.0416028	−	0.517887i	−0.00327876	−	0.0408152i
$162$	14.9280	+	4.85041i	1.17286	+	0.381084i
$163$	−3.68779	−	17.3497i	−0.288850	−	1.35893i	−0.848057	−	0.529905i	$-0.822227\pi$
$163$	−3.68779	−	17.3497i	−0.288850	−	1.35893i	0.559206	−	0.829028i	$-0.311106\pi$
$164$	7.19627	+	1.52961i	0.561934	+	0.119443i
$165$		0			0
$166$	4.66735	−	0.992076i	0.362257	−	0.0770000i
$167$	5.78918	−	7.96812i	0.447980	−	0.616591i	−0.523982	−	0.851729i	$-0.675554\pi$
$167$	5.78918	−	7.96812i	0.447980	−	0.616591i	0.971962	+	0.235138i	$0.0755541\pi$
$168$	−0.516832	+	0.154004i	−0.0398745	+	0.0118816i
$169$	17.7828	+	12.9199i	1.36790	+	0.993841i
$170$		0			0
$171$	−1.14891	−	10.9312i	−0.0878595	−	0.835927i
$172$	−13.2570	+	1.39337i	−1.01084	+	0.106243i
$173$	14.7742	+	13.3027i	1.12326	+	1.01139i	0.999819	+	0.0190351i	$0.00605943\pi$
$173$	14.7742	+	13.3027i	1.12326	+	1.01139i	0.123440	+	0.992352i	$0.460607\pi$
$174$	0.356431			0.0270209
$175$		0			0
$176$	4.45647			0.335919
$177$	0.822620	+	0.740690i	0.0618319	+	0.0556737i
$178$	11.7233	−	1.23217i	0.878702	−	0.0923553i
$179$	1.87236	+	17.8143i	0.139947	+	1.33150i	0.808789	+	0.588099i	$0.200124\pi$
$179$	1.87236	+	17.8143i	0.139947	+	1.33150i	−0.668842	+	0.743405i	$0.733210\pi$
$180$		0			0
$181$	−6.41485	−	4.66066i	−0.476812	−	0.346424i	0.323278	−	0.946304i	$-0.395215\pi$
$181$	−6.41485	−	4.66066i	−0.476812	−	0.346424i	−0.800090	+	0.599880i	$0.795215\pi$
$182$	−6.44715	+	27.0472i	−0.477894	+	2.00487i
$183$	−0.202553	+	0.278790i	−0.0149731	+	0.0206088i
$184$	−0.287611	+	0.0611337i	−0.0212030	+	0.00450683i
$185$		0			0
$186$	0.380369	+	0.0808500i	0.0278900	+	0.00592821i
$187$	−0.380539	−	1.79030i	−0.0278278	−	0.130919i
$188$	13.2534	+	4.30629i	0.966602	+	0.314068i
$189$	1.94596	+	0.924309i	0.141548	+	0.0672336i
$190$		0			0
$191$	−5.30465	+	1.12754i	−0.383831	+	0.0815858i	−0.395786	−	0.918343i	$-0.629528\pi$
$191$	−5.30465	+	1.12754i	−0.383831	+	0.0815858i	0.0119551	+	0.999929i	$0.496194\pi$
$192$	−0.0241858	−	0.0543221i	−0.00174546	−	0.00392036i
$193$	6.52619	+	3.76790i	0.469765	+	0.271219i	0.716142	−	0.697955i	$-0.245907\pi$
$193$	6.52619	+	3.76790i	0.469765	+	0.271219i	−0.246376	+	0.969174i	$0.579240\pi$
$194$	3.27358	−	31.1460i	0.235029	−	2.23615i
$195$		0			0
$196$	−7.99741	+	1.29324i	−0.571243	+	0.0923742i
$197$	7.01503	+	9.65536i	0.499800	+	0.687916i	0.982158	−	0.188059i	$-0.0602195\pi$
$197$	7.01503	+	9.65536i	0.499800	+	0.687916i	−0.482358	+	0.875974i	$0.660219\pi$
$198$	−3.52647	−	3.17524i	−0.250615	−	0.225655i
$199$	−10.1092	+	17.5097i	−0.716623	+	1.24123i	0.245708	+	0.969344i	$0.420980\pi$
$199$	−10.1092	+	17.5097i	−0.716623	+	1.24123i	−0.962330	+	0.271883i	$0.912354\pi$
$200$		0			0
$201$	0.692429	+	1.19932i	0.0488402	+	0.0845937i
$202$	−15.4828	+	5.03068i	−1.08937	+	0.353957i
$203$	−3.86608	−	0.502609i	−0.271346	−	0.0352762i
$204$	−0.260443	+	0.189223i	−0.0182346	+	0.0132482i
$205$		0			0
$206$	−4.59386	+	2.04532i	−0.320069	+	0.142504i
$207$	0.507042	+	0.292741i	0.0352419	+	0.0203469i
$208$	29.2646	+	3.07584i	2.02914	+	0.213271i
$209$	−1.02042	+	3.14054i	−0.0705842	+	0.217236i
$210$		0			0
$211$	−0.0373383	−	0.114915i	−0.00257047	−	0.00791110i	0.949763	−	0.312970i	$-0.101324\pi$
$211$	−0.0373383	−	0.114915i	−0.00257047	−	0.00791110i	−0.952334	+	0.305059i	$0.901324\pi$
$212$	−0.505027	−	2.37596i	−0.0346854	−	0.163182i
$213$	1.13951	−	1.02602i	0.0780782	−	0.0703019i
$214$	19.3900	+	4.12147i	1.32547	+	0.281738i
$215$		0			0
$216$	0.376758	−	1.15954i	0.0256351	−	0.0788969i
$217$	−4.01172	−	1.41332i	−0.272334	−	0.0959422i
$218$		−	10.8325i		−	0.733672i
$219$	−0.142299	+	1.35389i	−0.00961569	+	0.0914872i
$220$		0			0
$221$	−1.26326	−	12.0191i	−0.0849761	−	0.808494i
$222$	0.858930	−	1.92919i	0.0576476	−	0.129479i
$223$	18.2310	−	5.92362i	1.22084	−	0.396675i	0.373452	−	0.927650i	$-0.378174\pi$
$223$	18.2310	−	5.92362i	1.22084	−	0.396675i	0.847388	+	0.530975i	$0.178174\pi$
$224$	4.41674	+	14.8225i	0.295106	+	0.990367i
$225$		0			0
$226$	4.84815	+	8.39724i	0.322494	+	0.558576i
$227$	2.48639	−	11.6976i	0.165028	−	0.776394i	−0.815303	−	0.579034i	$-0.803430\pi$
$227$	2.48639	−	11.6976i	0.165028	−	0.776394i	0.980331	−	0.197360i	$-0.0632368\pi$
$228$	0.577626	−	0.0607110i	0.0382542	−	0.00402068i
$229$	−12.4325	−	5.53533i	−0.821566	−	0.365785i	−0.0474854	−	0.998872i	$-0.515121\pi$
$229$	−12.4325	−	5.53533i	−0.821566	−	0.365785i	−0.774080	+	0.633087i	$0.781787\pi$
$230$		0			0
$231$	−0.209916	−	0.244976i	−0.0138115	−	0.0161182i
$232$			2.20638i			0.144856i
$233$	−3.60218	−	0.378605i	−0.235987	−	0.0248032i	−0.0142032	−	0.999899i	$-0.504521\pi$
$233$	−3.60218	−	0.378605i	−0.235987	−	0.0248032i	−0.221784	+	0.975096i	$0.571188\pi$
$234$	−20.9660	−	23.2851i	−1.37059	−	1.52219i
$235$		0			0
$236$	6.29708	−	6.99361i	0.409905	−	0.455245i
$237$	0.466407	+	0.151545i	0.0302964	+	0.00984389i
$238$	8.43469	−	4.59737i	0.546740	−	0.298003i
$239$	5.63387	+	17.3393i	0.364425	+	1.12158i	0.950341	+	0.311212i	$0.100735\pi$
$239$	5.63387	+	17.3393i	0.364425	+	1.12158i	−0.585916	+	0.810372i	$0.699265\pi$
$240$		0			0
$241$	−9.80898	−	10.8940i	−0.631852	−	0.701743i	0.339172	−	0.940724i	$-0.389853\pi$
$241$	−9.80898	−	10.8940i	−0.631852	−	0.701743i	−0.971024	+	0.238981i	$0.923186\pi$
$242$	−7.37011	−	16.5535i	−0.473769	−	1.06410i
$243$	−3.15691	+	1.82264i	−0.202516	+	0.116923i
$244$	2.37017	+	1.72203i	0.151735	+	0.110242i
$245$		0			0
$246$	−1.24399	+	0.903814i	−0.0793141	+	0.0576251i
$247$	−8.86849	+	19.9189i	−0.564288	+	1.26741i
$248$	−0.500477	+	2.35456i	−0.0317803	+	0.149515i
$249$	−0.182781	+	0.316585i	−0.0115833	+	0.0200628i
$250$		0			0
$251$	3.37510			0.213034			0.106517	−	0.994311i	$-0.466030\pi$
$251$	3.37510			0.213034			0.106517	+	0.994311i	$0.466030\pi$
$252$	3.91690	−	8.24629i	0.246741	−	0.519468i
$253$	−0.103390	−	0.142304i	−0.00650006	−	0.00894657i
$254$	−20.1817	−	8.98547i	−1.26631	−	0.563799i
$255$		0			0
$256$	18.5167	−	8.24418i	1.15730	−	0.515261i
$257$	6.11524	−	3.53064i	0.381458	−	0.220235i	−0.296994	−	0.954879i	$-0.595984\pi$
$257$	6.11524	−	3.53064i	0.381458	−	0.220235i	0.678453	+	0.734644i	$0.262651\pi$
$258$	1.63760	−	2.25396i	0.101952	−	0.140325i
$259$	−12.0369	+	19.7140i	−0.747936	+	1.22497i
$260$		0			0
$261$	2.93969	−	3.26486i	0.181963	−	0.202090i
$262$	4.23282	−	3.81125i	0.261505	−	0.235460i
$263$	−21.1346	+	19.0297i	−1.30322	+	1.17342i	−0.329886	+	0.944021i	$0.607010\pi$
$263$	−21.1346	+	19.0297i	−1.30322	+	1.17342i	−0.973332	+	0.229402i	$0.926323\pi$
$264$	−0.122169	+	0.135682i	−0.00751896	+	0.00835065i
$265$		0			0
$266$	−17.3261	−	0.425615i	−1.06233	−	0.0260961i
$267$	−0.530823	+	0.730616i	−0.0324859	+	0.0447130i
$268$	10.1962	−	5.88678i	0.622832	−	0.359592i
$269$	14.4783	−	6.44613i	0.882755	−	0.393028i	0.0852637	−	0.996358i	$-0.472827\pi$
$269$	14.4783	−	6.44613i	0.882755	−	0.393028i	0.797491	+	0.603331i	$0.206160\pi$
$270$		0			0
$271$	9.27705	+	4.13041i	0.563540	+	0.250904i	0.668676	−	0.743553i	$-0.266861\pi$
$271$	9.27705	+	4.13041i	0.563540	+	0.250904i	−0.105136	+	0.994458i	$0.533528\pi$
$272$	−5.97555	−	8.22464i	−0.362321	−	0.498692i
$273$	−1.20939	−	1.75358i	−0.0731957	−	0.106132i
$274$	−2.98658			−0.180426
$275$		0			0
$276$	−0.0154690	+	0.0267932i	−0.000931127	+	0.00161276i
$277$	−4.41649	+	20.7779i	−0.265361	+	1.24842i	0.620401	+	0.784285i	$0.286970\pi$
$277$	−4.41649	+	20.7779i	−0.265361	+	1.24842i	−0.885762	+	0.464140i	$0.846363\pi$
$278$	−0.0449633	+	0.100989i	−0.00269672	+	0.00605693i
$279$	3.87771	−	2.81732i	0.232152	−	0.168668i
$280$		0			0
$281$	−16.1276	−	11.7174i	−0.962094	−	0.699003i	−0.00845822	−	0.999964i	$-0.502692\pi$
$281$	−16.1276	−	11.7174i	−0.962094	−	0.699003i	−0.953636	+	0.300962i	$0.902692\pi$
$282$	−2.52237	+	1.45629i	−0.150205	+	0.0867208i
$283$	5.64634	+	12.6819i	0.335640	+	0.753860i	0.999979	+	0.00642906i	$0.00204645\pi$
$283$	5.64634	+	12.6819i	0.335640	+	0.753860i	−0.664339	+	0.747431i	$0.731287\pi$
$284$	−8.72287	−	9.68773i	−0.517607	−	0.574861i
$285$		0			0
$286$	2.90893	+	8.95275i	0.172008	+	0.529387i
$287$	14.7676	−	8.04918i	0.871706	−	0.475128i
$288$	−16.5760	−	5.38587i	−0.976750	−	0.317365i
$289$	8.58139	−	9.53060i	0.504788	−	0.560624i
$290$		0			0
$291$	1.60544	+	1.78302i	0.0941123	+	0.104522i
$292$	11.5103	+	1.20978i	0.673587	+	0.0707968i
$293$			8.17516i			0.477598i	0.971069	+	0.238799i	$0.0767537\pi$
$293$			8.17516i			0.477598i	−0.971069	+	0.238799i	$0.923246\pi$
$294$	0.917585	−	1.42303i	0.0535146	−	0.0829927i
$295$		0			0
$296$	11.9421	+	5.31694i	0.694118	+	0.309041i
$297$	0.725358	−	0.0762382i	0.0420895	−	0.00442379i
$298$	8.07342	−	37.9824i	0.467680	−	2.20026i
$299$	−0.580721	−	1.00584i	−0.0335839	−	0.0581691i
$300$		0			0
$301$	−20.9408	+	22.1387i	−1.20701	+	1.27605i
$302$	9.24309	−	3.00326i	0.531880	−	0.172818i
$303$	0.507285	−	1.13938i	0.0291427	−	0.0654557i
$304$	1.91722	+	18.2411i	0.109960	+	1.04620i
$305$		0			0
$306$	−1.13154	+	10.7659i	−0.0646857	+	0.615443i
$307$			21.6183i			1.23382i	0.787033	+	0.616911i	$0.211616\pi$
$307$			21.6183i			1.23382i	−0.787033	+	0.616911i	$0.788384\pi$
$308$	−2.08269	+	1.78463i	−0.118672	+	0.101689i
$309$	0.119049	−	0.366394i	0.00677244	−	0.0208434i
$310$		0			0
$311$	6.07359	+	1.29098i	0.344402	+	0.0732049i	0.376865	−	0.926268i	$-0.377002\pi$
$311$	6.07359	+	1.29098i	0.344402	+	0.0732049i	−0.0324635	+	0.999473i	$0.510335\pi$
$312$	−0.895901	+	0.806673i	−0.0507204	+	0.0456689i
$313$	−2.02280	−	9.51653i	−0.114335	−	0.537906i	−0.997613	−	0.0690553i	$-0.978002\pi$
$313$	−2.02280	−	9.51653i	−0.114335	−	0.537906i	0.883277	−	0.468851i	$-0.155332\pi$
$314$	−4.28273	−	13.1809i	−0.241689	−	0.743841i
$315$		0			0
$316$	1.28838	−	3.96522i	0.0724770	−	0.223061i
$317$	20.6737	+	2.17289i	1.16115	+	0.122042i	0.665444	−	0.746448i	$-0.268242\pi$
$317$	20.6737	+	2.17289i	1.16115	+	0.122042i	0.495707	+	0.868490i	$0.334909\pi$
$318$	0.439666	+	0.253842i	0.0246553	+	0.0142347i
$319$	−1.20578	+	0.536847i	−0.0675106	+	0.0300577i
$320$		0			0
$321$	−1.22864	+	0.892660i	−0.0685761	+	0.0498234i
$322$	0.560816	−	0.733327i	0.0312531	−	0.0408667i
$323$	7.16428	−	2.32782i	0.398631	−	0.129523i
$324$	5.11166	+	8.85366i	0.283981	+	0.491870i
$325$		0			0
$326$	15.7586	−	27.2947i	0.872788	−	1.51171i
$327$	0.616734	+	0.555310i	0.0341055	+	0.0307087i
$328$	−5.59479	−	7.70056i	−0.308920	−	0.425192i
$329$	29.4128	−	12.2390i	1.62158	−	0.674760i
$330$		0			0
$331$	−0.772681	+	7.35156i	−0.0424704	+	0.404079i	0.952548	+	0.304388i	$0.0984519\pi$
$331$	−0.772681	+	7.35156i	−0.0424704	+	0.404079i	−0.995018	+	0.0996905i	$0.968215\pi$
$332$	2.69149	+	1.55393i	0.147715	+	0.0852832i
$333$	−10.5870	−	23.7788i	−0.580165	−	1.30307i
$334$	17.1184	−	3.63862i	0.936675	−	0.199097i
$335$		0			0
$336$	−1.61860	−	0.768819i	−0.0883021	−	0.0419425i
$337$	−27.2953	−	8.86877i	−1.48687	−	0.483113i	−0.550711	−	0.834696i	$-0.685643\pi$
$337$	−27.2953	−	8.86877i	−1.48687	−	0.483113i	−0.936157	+	0.351583i	$0.885643\pi$
$338$	8.12045	+	38.2037i	0.441694	+	2.07801i
$339$	−0.726615	−	0.154447i	−0.0394643	−	0.00838840i
$340$		0			0
$341$	−1.40853	+	0.299393i	−0.0762764	+	0.0162131i
$342$	11.4797	−	15.8005i	0.620752	−	0.854391i
$343$	−11.9594	+	14.1412i	−0.645745	+	0.763553i
$344$	13.9524	+	10.1370i	0.752265	+	0.546553i
$345$		0			0
$346$	3.69253	+	35.1321i	0.198512	+	1.88871i
$347$	−15.8878	+	1.66988i	−0.852904	+	0.0896438i	−0.520883	−	0.853628i	$-0.674397\pi$
$347$	−15.8878	+	1.66988i	−0.852904	+	0.0896438i	−0.332021	+	0.943272i	$0.607731\pi$
$348$	0.172522	+	0.155340i	0.00924816	+	0.00832708i
$349$	−30.2549			−1.61951			−0.809754	−	0.586770i	$-0.800399\pi$
$349$	−30.2549			−1.61951			−0.809754	+	0.586770i	$0.800399\pi$
$350$		0			0
$351$	4.81588			0.257053
$352$	3.89128	+	3.50373i	0.207406	+	0.186749i
$353$	−9.05521	+	0.951741i	−0.481960	+	0.0506561i	−0.342394	−	0.939557i	$-0.611238\pi$
$353$	−9.05521	+	0.951741i	−0.481960	+	0.0506561i	−0.139567	+	0.990213i	$0.544571\pi$
$354$	0.205599	+	1.95614i	0.0109274	+	0.103968i
$355$		0			0
$356$	6.21143	+	4.51287i	0.329205	+	0.239181i
$357$	−0.170644	+	0.715892i	−0.00903146	+	0.0378890i
$358$	−18.7083	+	25.7497i	−0.988762	+	1.36091i
$359$	23.0329	−	4.89579i	1.21563	−	0.258390i	0.444916	−	0.895572i	$-0.353233\pi$
$359$	23.0329	−	4.89579i	1.21563	−	0.258390i	0.770713	+	0.637182i	$0.219900\pi$
$360$		0			0
$361$	5.29102	+	1.12464i	0.278475	+	0.0591917i
$362$	−2.92933	−	13.7814i	−0.153962	−	0.724334i
$363$	1.32027	+	0.428980i	0.0692960	+	0.0225156i
$364$	−14.9083	+	10.2818i	−0.781409	+	0.538913i
$365$		0			0
$366$	−0.598941	+	0.127309i	−0.0313072	+	0.00665454i
$367$	14.6279	+	32.8548i	0.763569	+	1.71500i	0.696833	+	0.717233i	$0.254592\pi$
$367$	14.6279	+	32.8548i	0.763569	+	1.71500i	0.0667361	+	0.997771i	$0.478741\pi$
$368$	−0.846113	−	0.488504i	−0.0441067	−	0.0254650i
$369$	−1.98112	+	18.8491i	−0.103133	+	0.981246i
$370$		0			0
$371$	−4.41096	−	3.37331i	−0.229006	−	0.175134i
$372$	0.148873	+	0.204906i	0.00771871	+	0.0106239i
$373$	−5.28729	−	4.76070i	−0.273765	−	0.246500i	0.520799	−	0.853679i	$-0.325634\pi$
$373$	−5.28729	−	4.76070i	−0.273765	−	0.246500i	−0.794564	+	0.607180i	$0.792301\pi$
$374$	1.62611	−	2.81651i	0.0840842	−	0.145638i
$375$		0			0
$376$	−9.01472	−	15.6140i	−0.464899	−	0.805229i
$377$	−8.28861	+	2.69313i	−0.426885	+	0.138703i
$378$	1.47063	+	3.53422i	0.0756413	+	0.181781i
$379$	7.76350	−	5.64052i	0.398784	−	0.289734i	−0.370261	−	0.928928i	$-0.620732\pi$
$379$	7.76350	−	5.64052i	0.398784	−	0.289734i	0.769046	+	0.639194i	$0.220732\pi$
$380$		0			0
$381$	1.54615	−	0.688391i	0.0792117	−	0.0352673i
$382$	−8.34532	−	4.81817i	−0.426983	−	0.246519i
$383$	−4.47665	−	0.470515i	−0.228746	−	0.0240422i	−0.0105382	−	0.999944i	$-0.503354\pi$
$383$	−4.47665	−	0.470515i	−0.228746	−	0.0240422i	−0.218208	+	0.975902i	$0.570021\pi$
$384$	−0.459173	+	1.41319i	−0.0234321	+	0.0721165i
$385$		0			0
$386$	4.13782	+	12.7349i	0.210609	+	0.648189i
$387$	−7.13976	−	33.5899i	−0.362934	−	1.70747i
$388$	15.1586	−	13.6488i	0.769559	−	0.692914i
$389$	−20.6389	−	4.38693i	−1.04643	−	0.222426i	−0.347549	−	0.937662i	$-0.612986\pi$
$389$	−20.6389	−	4.38693i	−1.04643	−	0.222426i	−0.698884	+	0.715235i	$0.746319\pi$
$390$		0			0
$391$	−0.123997	+	0.381622i	−0.00627078	+	0.0192995i
$392$	8.80883	+	5.68003i	0.444913	+	0.286885i
$393$			0.436366i			0.0220117i
$394$	−2.21669	+	21.0904i	−0.111675	+	1.06252i
$395$		0			0
$396$	−0.323071	−	3.07381i	−0.0162349	−	0.154465i
$397$	1.91039	−	4.29081i	0.0958799	−	0.215350i	−0.859238	−	0.511576i	$-0.829062\pi$
$397$	1.91039	−	4.29081i	0.0958799	−	0.215350i	0.955118	+	0.296227i	$0.0957284\pi$
$398$	−34.1675	+	11.1017i	−1.71266	+	0.556478i
$399$	0.912420	−	0.964615i	0.0456781	−	0.0482911i
$400$		0			0
$401$	−0.532582	−	0.922460i	−0.0265959	−	0.0460654i	0.852421	−	0.522856i	$-0.175133\pi$
$401$	−0.532582	−	0.922460i	−0.0265959	−	0.0460654i	−0.879017	+	0.476790i	$0.841800\pi$
$402$	−0.511616	+	2.40696i	−0.0255171	+	0.120048i
$403$	−9.45618	+	0.993884i	−0.471046	+	0.0495089i
$404$	−9.68659	−	4.31275i	−0.481926	−	0.214567i
$405$		0			0
$406$	−4.50751	−	5.26034i	−0.223704	−	0.261066i
$407$			7.82000i			0.387623i
$408$	0.414220	+	0.0435363i	0.0205069	+	0.00215537i
$409$	−11.4795	−	12.7492i	−0.567623	−	0.630410i	0.389174	−	0.921164i	$-0.372760\pi$
$409$	−11.4795	−	12.7492i	−0.567623	−	0.630410i	−0.956798	+	0.290755i	$0.906094\pi$
$410$		0			0
$411$	0.153102	−	0.170036i	0.00755194	−	0.00838728i
$412$	−3.11495	−	1.01211i	−0.153462	−	0.0498630i
$413$	0.528331	−	21.5075i	0.0259975	−	1.05831i
$414$	0.321481	+	0.989417i	0.0157999	+	0.0486272i
$415$		0			0
$416$	23.1349	+	25.6939i	1.13428	+	1.25975i
$417$	−0.00344471	−	0.00773694i	−0.000168688	−	0.000378879i
$418$	−5.08146	+	2.93378i	−0.248542	+	0.143496i
$419$	−20.0431	−	14.5622i	−0.979170	−	0.711409i	−0.0216469	−	0.999766i	$-0.506891\pi$
$419$	−20.0431	−	14.5622i	−0.979170	−	0.711409i	−0.957523	+	0.288357i	$0.906891\pi$
$420$		0			0
$421$	−8.45029	+	6.13949i	−0.411842	+	0.299221i	−0.774347	−	0.632761i	$-0.781921\pi$
$421$	−8.45029	+	6.13949i	−0.411842	+	0.299221i	0.362505	+	0.931982i	$0.381921\pi$
$422$	0.0873263	−	0.196138i	0.00425098	−	0.00954785i
$423$	−7.46403	+	35.1155i	−0.362913	+	1.70737i
$424$	−1.57133	+	2.72162i	−0.0763105	+	0.132174i
$425$		0			0
$426$	2.72462			0.132008
$427$	6.67603	−	0.536298i	0.323076	−	0.0259533i
$428$	7.58907	+	10.4455i	0.366832	+	0.504900i
$429$	−0.658832	−	0.293331i	−0.0318087	−	0.0141621i
$430$		0			0
$431$	−28.9662	+	12.8966i	−1.39525	+	0.621206i	−0.960229	−	0.279214i	$-0.909926\pi$
$431$	−28.9662	+	12.8966i	−1.39525	+	0.621206i	−0.435022	+	0.900420i	$0.643259\pi$
$432$	3.50838	−	2.02557i	0.168797	−	0.0974551i
$433$	−11.1442	+	15.3387i	−0.535556	+	0.737130i	−0.987964	−	0.154681i	$-0.950565\pi$
$433$	−11.1442	+	15.3387i	−0.535556	+	0.737130i	0.452408	+	0.891811i	$0.350565\pi$
$434$	−3.61703	−	6.63608i	−0.173623	−	0.318542i
$435$		0			0
$436$	4.72104	−	5.24325i	0.226097	−	0.251106i
$437$	0.537995	−	0.484413i	0.0257358	−	0.0231726i
$438$	−1.79763	+	1.61860i	−0.0858943	+	0.0773396i
$439$	3.34415	−	3.71405i	0.159608	−	0.177262i	−0.658037	−	0.752986i	$-0.728613\pi$
$439$	3.34415	−	3.71405i	0.159608	−	0.177262i	0.817644	+	0.575724i	$0.195280\pi$
$440$		0			0
$441$	−5.46691	−	20.1415i	−0.260329	−	0.959121i
$442$	12.6223	−	17.3731i	0.600380	−	0.826352i
$443$	2.82224	−	1.62942i	0.134089	−	0.0774162i	−0.431455	−	0.902134i	$-0.642000\pi$
$443$	2.82224	−	1.62942i	0.134089	−	0.0774162i	0.565544	+	0.824718i	$0.308666\pi$
$444$	1.25652	−	0.559441i	0.0596320	−	0.0265499i
$445$		0			0
$446$	31.1168	+	13.8541i	1.47342	+	0.656010i
$447$	1.74860	+	2.40675i	0.0827061	+	0.113835i
$448$	−0.495847	+	1.04391i	−0.0234266	+	0.0493203i
$449$	18.7348			0.884151			0.442076	−	0.896978i	$-0.354242\pi$
$449$	18.7348			0.884151			0.442076	+	0.896978i	$0.354242\pi$
$450$		0			0
$451$	2.84703	−	4.93121i	0.134062	−	0.232201i
$452$	−1.31305	+	6.17742i	−0.0617607	+	0.290561i
$453$	−0.302843	+	0.680198i	−0.0142288	+	0.0319585i
$454$	17.1913	−	12.4902i	0.806827	−	0.586194i
$455$		0			0
$456$	−0.607928	−	0.441686i	−0.0284688	−	0.0206838i
$457$	23.5235	−	13.5813i	1.10038	−	0.635306i	0.164061	−	0.986450i	$-0.447541\pi$
$457$	23.5235	−	13.5813i	1.10038	−	0.635306i	0.936322	+	0.351144i	$0.114207\pi$
$458$	−9.83565	−	22.0912i	−0.459590	−	1.03226i
$459$	−1.11331	−	1.23646i	−0.0519650	−	0.0577130i
$460$		0			0
$461$	−4.36190	−	13.4245i	−0.203154	−	0.625243i	−0.999784	−	0.0207762i	$-0.993386\pi$
$461$	−4.36190	−	13.4245i	−0.203154	−	0.625243i	0.796630	−	0.604467i	$-0.206614\pi$
$462$	0.0140775	−	0.573071i	0.000654943	−	0.0266617i
$463$	−17.1480	−	5.57173i	−0.796936	−	0.258940i	−0.117881	−	0.993028i	$-0.537610\pi$
$463$	−17.1480	−	5.57173i	−0.796936	−	0.258940i	−0.679055	+	0.734087i	$0.737610\pi$
$464$	−4.90554	+	5.44815i	−0.227734	+	0.252924i
$465$		0			0
$466$	−4.30648	−	4.78283i	−0.199494	−	0.221560i
$467$	18.4537	+	1.93956i	0.853935	+	0.0897522i	0.521373	−	0.853329i	$-0.325420\pi$
$467$	18.4537	+	1.93956i	0.853935	+	0.0897522i	0.332562	+	0.943081i	$0.392087\pi$
$468$		−	20.4080i		−	0.943361i
$469$	8.94343	−	25.3861i	0.412969	−	1.17222i
$470$		0			0
$471$	0.969980	+	0.431863i	0.0446943	+	0.0198992i
$472$	−12.1089	+	1.27270i	−0.557357	+	0.0585806i
$473$	−2.14501	+	10.0915i	−0.0986277	+	0.464007i
$474$	0.435701	+	0.754656i	0.0200124	+	0.0346625i
$475$		0			0
$476$	6.08625	+	1.45076i	0.278963	+	0.0664953i
$477$	5.95135	−	1.93371i	0.272494	−	0.0885385i
$478$	−13.1764	+	29.5947i	−0.602675	+	1.35363i
$479$	3.68019	+	35.0147i	0.168152	+	1.59986i	0.674994	+	0.737823i	$0.264146\pi$
$479$	3.68019	+	35.0147i	0.168152	+	1.59986i	−0.506842	+	0.862039i	$0.669187\pi$
$480$		0			0
$481$	−5.39733	+	51.3522i	−0.246097	+	2.34146i
$482$		−	26.0479i		−	1.18645i
$483$	0.0130016	+	0.0695218i	0.000591595	+	0.00316335i
$484$	3.64703	−	11.2244i	0.165774	−	0.510201i
$485$		0			0
$486$	−6.33572	−	1.34670i	−0.287394	−	0.0610875i
$487$	7.54091	−	6.78987i	0.341711	−	0.307678i	−0.480350	−	0.877077i	$-0.659490\pi$
$487$	7.54091	−	6.78987i	0.341711	−	0.307678i	0.822062	+	0.569398i	$0.192824\pi$
$488$	−0.788067	−	3.70756i	−0.0356741	−	0.167834i
$489$	0.746147	+	2.29640i	0.0337419	+	0.103847i
$490$		0			0
$491$	−5.28524	+	16.2663i	−0.238520	+	0.734088i	0.758115	+	0.652121i	$0.226120\pi$
$491$	−5.28524	+	16.2663i	−0.238520	+	0.734088i	−0.996635	+	0.0819676i	$0.973880\pi$
$492$	−0.996027	−	0.104687i	−0.0449044	−	0.00471964i
$493$	2.60757	+	1.50548i	0.117439	+	0.0678035i
$494$	−35.3937	+	15.7583i	−1.59244	+	0.709000i
$495$		0			0
$496$	−6.47082	+	4.70133i	−0.290548	+	0.211096i
$497$	−29.5530	−	3.84204i	−1.32563	−	0.172339i
$498$	−0.617769	+	0.200725i	−0.0276829	+	0.00899472i
$499$	7.24707	+	12.5523i	0.324423	+	0.561918i	0.981395	−	0.191997i	$-0.0614964\pi$
$499$	7.24707	+	12.5523i	0.324423	+	0.561918i	−0.656972	+	0.753915i	$0.728163\pi$
$500$		0			0
$501$	−0.670382	+	1.16114i	−0.0299504	+	0.0518757i
$502$	4.45676	+	4.01289i	0.198915	+	0.179104i
$503$	−11.7412	−	16.1604i	−0.523516	−	0.720558i	0.462609	−	0.886562i	$-0.346913\pi$
$503$	−11.7412	−	16.1604i	−0.523516	−	0.720558i	−0.986125	+	0.166005i	$0.946913\pi$
$504$	−10.9049	+	4.53766i	−0.485742	+	0.202123i
$505$		0			0
$506$	0.0326703	−	0.310838i	0.00145237	−	0.0138184i
$507$	−2.59135	−	1.49612i	−0.115086	−	0.0664449i
$508$	−5.85245	−	13.1448i	−0.259660	−	0.583207i
$509$	−4.10387	+	0.872305i	−0.181901	+	0.0386642i	−0.297961	−	0.954578i	$-0.596307\pi$
$509$	−4.10387	+	0.872305i	−0.181901	+	0.0386642i	0.116061	+	0.993242i	$0.462973\pi$
$510$		0			0
$511$	21.7807	−	15.0215i	0.963523	−	0.664511i
$512$	13.4908	+	4.38342i	0.596214	+	0.193722i
$513$	0.624112	+	2.93622i	0.0275552	+	0.129637i
$514$	12.2729	+	2.60869i	0.541335	+	0.115064i
$515$		0			0
$516$	1.77496	−	0.377280i	0.0781383	−	0.0166088i
$517$	6.33956	−	8.72565i	0.278813	−	0.383754i
$518$	−39.3339	+	11.7206i	−1.72823	+	0.514973i
$519$	−2.18948	−	1.59075i	−0.0961076	−	0.0698262i
$520$		0			0
$521$	−1.08972	−	10.3680i	−0.0477414	−	0.454229i	−0.992113	−	0.125348i	$-0.959995\pi$
$521$	−1.08972	−	10.3680i	−0.0477414	−	0.454229i	0.944371	−	0.328881i	$-0.106671\pi$
$522$	7.76364	−	0.815992i	0.339805	−	0.0357150i
$523$	13.4962	+	12.1520i	0.590146	+	0.531370i	0.909196	−	0.416368i	$-0.136697\pi$
$523$	13.4962	+	12.1520i	0.590146	+	0.531370i	−0.319050	+	0.947738i	$0.603364\pi$
$524$	3.70982			0.162064
$525$		0			0
$526$	−50.5337			−2.20337
$527$	2.44121	+	2.19807i	0.106341	+	0.0957496i
$528$	−0.603336	+	0.0634132i	−0.0262568	+	0.00275970i
$529$	−2.40012	−	22.8357i	−0.104353	−	0.992854i
$530$		0			0
$531$	19.6137	+	14.2502i	0.851162	+	0.618405i
$532$	−8.20080	−	7.75706i	−0.355550	−	0.336311i
$533$	22.0993	−	30.4171i	0.957229	−	1.31751i
$534$	−1.56962	+	0.333634i	−0.0679243	+	0.0144377i
$535$		0			0
$536$	−14.8996	−	3.16700i	−0.643564	−	0.136794i
$537$	−0.506976	−	2.38514i	−0.0218776	−	0.102926i
$538$	26.7826	+	8.70218i	1.15468	+	0.375178i
$539$	−0.960791	+	6.19605i	−0.0413842	+	0.266883i
$540$		0			0
$541$	7.24876	−	1.54077i	0.311649	−	0.0662429i	−0.0494322	−	0.998777i	$-0.515741\pi$
$541$	7.24876	−	1.54077i	0.311649	−	0.0662429i	0.361081	+	0.932535i	$0.382408\pi$
$542$	7.33927	+	16.4843i	0.315249	+	0.708060i
$543$	0.934789	+	0.539701i	0.0401156	+	0.0231608i
$544$	1.24860	−	11.8796i	0.0535331	−	0.509334i
$545$		0			0
$546$	0.487975	−	3.75351i	0.0208834	−	0.160635i
$547$	20.7804	+	28.6018i	0.888508	+	1.22293i	0.973991	+	0.226586i	$0.0727565\pi$
$547$	20.7804	+	28.6018i	0.888508	+	1.22293i	−0.0854834	+	0.996340i	$0.527243\pi$
$548$	−1.44559	−	1.30161i	−0.0617525	−	0.0556022i
$549$	−3.77369	+	6.53622i	−0.161057	+	0.278959i
$550$		0			0
$551$	−2.71615	−	4.70450i	−0.115712	−	0.200419i
$552$	0.0380681	−	0.0123691i	0.00162029	−	0.000526463i
$553$	−3.66174	−	8.79989i	−0.155713	−	0.374209i
$554$	−30.5362	+	22.1859i	−1.29736	+	0.942587i
$555$		0			0
$556$	−0.0657766	+	0.0292856i	−0.00278955	+	0.00124199i
$557$	−20.2649	−	11.6999i	−0.858650	−	0.495742i	0.00490988	−	0.999988i	$-0.498437\pi$
$557$	−20.2649	−	11.6999i	−0.858650	−	0.495742i	−0.863560	+	0.504246i	$0.831770\pi$
$558$	8.47016	+	0.890249i	0.358570	+	0.0376873i
$559$	−21.0509	+	64.7880i	−0.890358	+	2.74024i
$560$		0			0
$561$	0.0769940	+	0.236963i	0.00325069	+	0.0100046i
$562$	−7.36465	−	34.6479i	−0.310659	−	1.46154i
$563$	−13.3450	+	12.0159i	−0.562425	+	0.506409i	−0.900586	−	0.434679i	$-0.856862\pi$
$563$	−13.3450	+	12.0159i	−0.562425	+	0.506409i	0.338161	+	0.941088i	$0.390195\pi$
$564$	−1.85558	−	0.394415i	−0.0781339	−	0.0166079i
$565$		0			0
$566$	−7.62248	+	23.4596i	−0.320397	+	0.986080i
$567$	22.0435	+	7.76584i	0.925739	+	0.326135i
$568$			16.8659i			0.707679i
$569$	−4.49348	+	42.7526i	−0.188376	+	1.79228i	0.337095	+	0.941471i	$0.390556\pi$
$569$	−4.49348	+	42.7526i	−0.188376	+	1.79228i	−0.525471	+	0.850811i	$0.676111\pi$
$570$		0			0
$571$	2.31535	+	22.0290i	0.0968942	+	0.921887i	0.929699	+	0.368320i	$0.120067\pi$
$571$	2.31535	+	22.0290i	0.0968942	+	0.921887i	−0.832805	+	0.553567i	$0.813266\pi$
$572$	−2.49379	+	5.60115i	−0.104271	+	0.234196i
$573$	0.702122	−	0.228133i	0.0293316	−	0.00953040i
$574$	29.0707	+	6.92947i	1.21339	+	0.289230i
$575$		0			0
$576$	−0.651168	−	1.12786i	−0.0271320	−	0.0469940i
$577$	6.20020	−	29.1697i	0.258118	−	1.21435i	−0.637826	−	0.770181i	$-0.720166\pi$
$577$	6.20020	−	29.1697i	0.258118	−	1.21435i	0.895943	−	0.444168i	$-0.146501\pi$
$578$	22.6632	−	2.38200i	0.942664	−	0.0990780i
$579$	−0.937159	−	0.417250i	−0.0389470	−	0.0173403i
$580$		0			0
$581$	6.98378	−	1.30607i	0.289736	−	0.0541850i
$582$			4.26326i			0.176718i
$583$	−1.86969	−	0.196512i	−0.0774346	−	0.00813871i
$584$	−10.0194	−	11.1277i	−0.414607	−	0.460468i
$585$		0			0
$586$	−9.72002	+	10.7952i	−0.401530	+	0.445944i
$587$	38.4758	+	12.5015i	1.58807	+	0.515994i	0.964118	−	0.265473i	$-0.0855282\pi$
$587$	38.4758	+	12.5015i	1.58807	+	0.515994i	0.623947	+	0.781467i	$0.285528\pi$
$588$	1.06432	−	0.288883i	0.0438919	−	0.0119133i
$589$	−1.83143	−	5.63658i	−0.0754630	−	0.232251i
$590$		0			0
$591$	−1.08712	−	1.20736i	−0.0447179	−	0.0496643i
$592$	17.6668	+	39.6803i	0.726102	+	1.63085i
$593$	−0.540774	+	0.312216i	−0.0222069	+	0.0128212i	−0.511062	−	0.859544i	$-0.670748\pi$
$593$	−0.540774	+	0.312216i	−0.0222069	+	0.0128212i	0.488855	+	0.872365i	$0.337415\pi$
$594$	1.04847	+	0.761757i	0.0430192	+	0.0312553i
$595$		0			0
$596$	20.4613	−	14.8660i	0.838127	−	0.608935i
$597$	1.11947	−	2.51438i	0.0458171	−	0.102907i
$598$	0.429078	−	2.01865i	0.0175463	−	0.0825488i
$599$	6.69211	−	11.5911i	0.273432	−	0.473599i	−0.696306	−	0.717745i	$-0.745174\pi$
$599$	6.69211	−	11.5911i	0.273432	−	0.473599i	0.969738	+	0.244146i	$0.0785077\pi$
$600$		0			0
$601$	39.9880			1.63114			0.815572	−	0.578656i	$-0.196423\pi$
$601$	39.9880			1.63114			0.815572	+	0.578656i	$0.196423\pi$
$602$	−53.9742	+	4.33585i	−2.19982	+	0.176716i
$603$	17.8279	+	24.5380i	0.726008	+	0.999265i
$604$	5.78279	+	2.57466i	0.235298	+	0.104762i
$605$		0			0
$606$	2.02455	−	0.901388i	0.0822417	−	0.0366164i
$607$	−21.2227	+	12.2530i	−0.861405	+	0.497332i	−0.864482	−	0.502663i	$-0.832354\pi$
$607$	−21.2227	+	12.2530i	−0.861405	+	0.497332i	0.00307784	+	0.999995i	$0.499020\pi$
$608$	−12.6673	+	17.4350i	−0.513727	+	0.707084i
$609$	0.530558	+	0.0130332i	0.0214993	+	0.000528130i
$610$		0			0
$611$	47.6529	−	52.9239i	1.92783	−	2.14107i
$612$	−5.23968	+	4.71783i	−0.211801	+	0.190707i
$613$	24.9958	−	22.5063i	1.00957	−	0.909021i	0.0137084	−	0.999906i	$-0.495636\pi$
$613$	24.9958	−	22.5063i	1.00957	−	0.909021i	0.995861	+	0.0908854i	$0.0289697\pi$
$614$	−25.7035	+	28.5466i	−1.03731	+	1.15205i
$615$		0			0
$616$	3.54742	+	0.0871424i	0.142930	+	0.00351107i
$617$	−19.8937	+	27.3814i	−0.800891	+	1.10233i	0.191774	+	0.981439i	$0.438576\pi$
$617$	−19.8937	+	27.3814i	−0.800891	+	1.10233i	−0.992666	+	0.120893i	$0.961424\pi$
$618$	0.592833	−	0.342272i	0.0238472	−	0.0137682i
$619$	24.2226	−	10.7846i	0.973587	−	0.433469i	0.142612	−	0.989779i	$-0.454450\pi$
$619$	24.2226	−	10.7846i	0.973587	−	0.433469i	0.830975	+	0.556310i	$0.187783\pi$
$620$		0			0
$621$	−0.146075	−	0.0650366i	−0.00586178	−	0.00260983i
$622$	6.48515	+	8.92604i	0.260031	+	0.357902i
$623$	17.4956	−	1.40546i	0.700948	−	0.0563084i
$624$	−4.00574			−0.160358
$625$		0			0
$626$	8.64379	−	14.9715i	0.345475	−	0.598381i
$627$	0.0934612	−	0.439700i	0.00373248	−	0.0175599i
$628$	3.67154	−	8.24642i	0.146510	−	0.329068i
$629$	14.4322	−	10.4856i	0.575449	−	0.418088i
$630$		0			0
$631$	27.4224	+	19.9235i	1.09167	+	0.793144i	0.979680	−	0.200566i	$-0.0642781\pi$
$631$	27.4224	+	19.9235i	1.09167	+	0.793144i	0.111988	+	0.993710i	$0.464278\pi$
$632$	−4.67147	+	2.69708i	−0.185821	+	0.107284i
$633$	0.00669020	+	0.0150264i	0.000265912	+	0.000597247i
$634$	24.7158	+	27.4497i	0.981589	+	1.09017i
$635$		0			0
$636$	0.102181	+	0.314482i	0.00405175	+	0.0124700i
$637$	−10.5858	+	40.0249i	−0.419424	+	1.58585i
$638$	−2.23051	−	0.724735i	−0.0883066	−	0.0286925i
$639$	22.4716	−	24.9572i	0.888961	−	0.987291i
$640$		0			0
$641$	−23.8022	−	26.4350i	−0.940131	−	1.04412i	−0.998948	−	0.0458523i	$-0.985400\pi$
$641$	−23.8022	−	26.4350i	−0.940131	−	1.04412i	0.0588174	−	0.998269i	$-0.481267\pi$
$642$	−2.68375	−	0.282073i	−0.105919	−	0.0111325i
$643$		−	32.5951i		−	1.28542i	−0.766108	−	0.642712i	$-0.777809\pi$
$643$		−	32.5951i		−	1.28542i	0.766108	−	0.642712i	$-0.222191\pi$
$644$	0.591049	−	0.110535i	0.0232906	−	0.00435569i
$645$		0			0
$646$	12.2280	+	5.44427i	0.481105	+	0.214202i
$647$	39.1547	−	4.11533i	1.53933	−	0.161790i	0.703467	−	0.710728i	$-0.251634\pi$
$647$	39.1547	−	4.11533i	1.53933	−	0.161790i	0.835864	+	0.548937i	$0.184967\pi$
$648$	2.75000	−	12.9377i	0.108030	−	0.508243i
$649$	−3.64181	−	6.30781i	−0.142954	−	0.247603i
$650$		0			0
$651$	0.563235	+	0.134256i	0.0220749	+	0.00526192i
$652$	19.5232	−	6.34347i	0.764587	−	0.248429i
$653$	11.6251	−	26.1104i	0.454926	−	1.02178i	−0.529872	−	0.848078i	$-0.677760\pi$
$653$	11.6251	−	26.1104i	0.454926	−	1.02178i	0.984798	−	0.173703i	$-0.0555733\pi$
$654$	0.154141	+	1.46656i	0.00602740	+	0.0573469i
$655$		0			0
$656$	3.30595	−	31.4540i	0.129075	−	1.22807i
$657$			29.8156i			1.16322i
$658$	53.3910	+	18.8095i	2.08140	+	0.733269i
$659$	3.08756	−	9.50254i	0.120274	−	0.370166i	−0.872736	−	0.488192i	$-0.837657\pi$
$659$	3.08756	−	9.50254i	0.120274	−	0.370166i	0.993011	+	0.118026i	$0.0376565\pi$
$660$		0			0
$661$	−8.30978	−	1.76630i	−0.323213	−	0.0687010i	0.0434480	−	0.999056i	$-0.486166\pi$
$661$	−8.30978	−	1.76630i	−0.323213	−	0.0687010i	−0.366661	+	0.930355i	$0.619499\pi$
$662$	−9.76110	+	8.78893i	−0.379376	+	0.341592i
$663$	0.342051	+	1.60923i	0.0132842	+	0.0624971i
$664$	−1.24253	−	3.82412i	−0.0482195	−	0.148404i
$665$		0			0
$666$	14.2923	−	43.9873i	0.553816	−	1.70447i
$667$	0.287779	+	0.0302467i	0.0111428	+	0.00117116i
$668$	9.87155	+	5.69934i	0.381942	+	0.220514i
$669$	−2.38390	+	1.06138i	−0.0921671	+	0.0410354i
$670$		0			0
$671$	1.83442	−	1.33279i	0.0708172	−	0.0514517i
$672$	−0.808873	−	1.94388i	−0.0312029	−	0.0749868i
$673$	16.7937	−	5.45660i	0.647349	−	0.210336i	0.0331038	−	0.999452i	$-0.489461\pi$
$673$	16.7937	−	5.45660i	0.647349	−	0.210336i	0.614245	+	0.789116i	$0.289461\pi$
$674$	−25.4983	−	44.1643i	−0.982157	−	1.70115i
$675$		0			0
$676$	−12.7194	+	22.0307i	−0.489209	+	0.847335i
$677$	2.96788	+	2.67229i	0.114065	+	0.102704i	0.724190	−	0.689601i	$-0.242214\pi$
$677$	2.96788	+	2.67229i	0.114065	+	0.102704i	−0.610125	+	0.792305i	$0.708881\pi$
$678$	−0.775852	−	1.06787i	−0.0297964	−	0.0410112i
$679$	6.01170	−	46.2421i	0.230708	−	1.77461i
$680$		0			0
$681$	−0.170169	+	1.61905i	−0.00652087	+	0.0620419i
$682$	−2.21592	−	1.27936i	−0.0848519	−	0.0489893i
$683$	−3.92101	−	8.80674i	−0.150033	−	0.336980i	0.822857	−	0.568249i	$-0.192379\pi$
$683$	−3.92101	−	8.80674i	−0.150033	−	0.336980i	−0.972890	+	0.231269i	$0.925712\pi$
$684$	12.4427	−	2.64477i	0.475757	−	0.101125i
$685$		0			0
$686$	−32.6056	+	4.45391i	−1.24489	+	0.170051i
$687$	1.76194	+	0.572488i	0.0672221	+	0.0218418i
$688$	11.9143	+	56.0523i	0.454228	+	2.13697i
$689$	−12.1422	−	2.58090i	−0.462581	−	0.0983246i
$690$		0			0
$691$	−6.25348	+	1.32922i	−0.237894	+	0.0505658i	−0.325315	−	0.945606i	$-0.605470\pi$
$691$	−6.25348	+	1.32922i	−0.237894	+	0.0505658i	0.0874219	+	0.996171i	$0.472137\pi$
$692$	−13.5240	+	18.6142i	−0.514105	+	0.707605i
$693$	−5.13315	−	4.85540i	−0.194992	−	0.184441i
$694$	−22.9651	−	16.6851i	−0.871743	−	0.633358i
$695$		0			0
$696$	−0.0313955	−	0.298709i	−0.00119004	−	0.0113225i
$697$	−12.9183	+	1.35777i	−0.489315	+	0.0514291i
$698$	−39.9511	−	35.9721i	−1.51217	−	1.36157i
$699$	0.493066			0.0186495
$700$		0			0
$701$	13.7697			0.520075			0.260037	−	0.965599i	$-0.416265\pi$
$701$	13.7697			0.520075			0.260037	+	0.965599i	$0.416265\pi$
$702$	6.35930	+	5.72594i	0.240016	+	0.216112i
$703$	−32.0086	+	3.36424i	−1.20723	+	0.126885i
$704$	0.0408981	+	0.389120i	0.00154141	+	0.0146655i
$705$		0			0
$706$	−13.0889	−	9.50961i	−0.492606	−	0.357899i
$707$	−23.2307	+	6.92219i	−0.873679	+	0.260336i
$708$	−0.753010	+	1.03643i	−0.0282998	+	0.0389514i
$709$	47.0675	−	10.0045i	1.76766	−	0.375727i	0.794752	−	0.606934i	$-0.207601\pi$
$709$	47.0675	−	10.0045i	1.76766	−	0.375727i	0.972905	+	0.231207i	$0.0742673\pi$
$710$		0			0
$711$	10.5060	+	2.23313i	0.394008	+	0.0837489i
$712$	−2.06526	−	9.71628i	−0.0773989	−	0.364133i
$713$	0.300245	+	0.0975556i	0.0112443	+	0.00365349i
$714$	−1.07651	+	0.742433i	−0.0402872	+	0.0277848i
$715$		0			0
$716$	−20.2776	+	4.31013i	−0.757808	+	0.161077i
$717$	−1.00947	−	2.26730i	−0.0376992	−	0.0846738i
$718$	36.2355	+	20.9206i	1.35230	+	0.780750i
$719$	−0.565884	+	5.38402i	−0.0211039	+	0.200790i	−0.999994	−	0.00359939i	$-0.998854\pi$
$719$	−0.565884	+	5.38402i	−0.0211039	+	0.200790i	0.978890	+	0.204390i	$0.0655209\pi$
$720$		0			0
$721$	−6.91290	+	2.87654i	−0.257450	+	0.107128i
$722$	5.64955	+	7.77594i	0.210254	+	0.289390i
$723$	1.48300	+	1.33530i	0.0551533	+	0.0496602i
$724$	4.58834	−	7.94723i	0.170524	−	0.295357i
$725$		0			0
$726$	1.23335	+	2.13622i	0.0457738	+	0.0792825i
$727$	−1.54580	+	0.502260i	−0.0573305	+	0.0186278i	−0.337542	−	0.941311i	$-0.609595\pi$
$727$	−1.54580	+	0.502260i	−0.0573305	+	0.0186278i	0.280211	+	0.959938i	$0.409595\pi$
$728$	23.2350	+	3.02066i	0.861146	+	0.111953i
$729$	−21.0380	+	15.2850i	−0.779187	+	0.566112i
$730$		0			0
$731$	21.5005	−	9.57264i	0.795225	−	0.354057i
$732$	−0.345388	−	0.199410i	−0.0127659	−	0.00737040i
$733$	−18.3810	−	1.93192i	−0.678919	−	0.0713572i	−0.241208	−	0.970473i	$-0.577544\pi$
$733$	−18.3810	−	1.93192i	−0.678919	−	0.0713572i	−0.437710	+	0.899116i	$0.644210\pi$
$734$	−19.7474	+	60.7763i	−0.728890	+	2.24329i
$735$		0			0
$736$	−0.354739	−	1.09177i	−0.0130758	−	0.0402433i
$737$	−1.89455	−	8.91317i	−0.0697867	−	0.328321i
$738$	−25.0271	+	22.5345i	−0.921259	+	0.829505i
$739$	−3.91680	−	0.832542i	−0.144082	−	0.0306256i	0.135306	−	0.990804i	$-0.456798\pi$
$739$	−3.91680	−	0.832542i	−0.144082	−	0.0306256i	−0.279388	+	0.960178i	$0.590132\pi$
$740$		0			0
$741$	0.917218	−	2.82291i	0.0336948	−	0.103702i
$742$	−1.81384	−	9.69891i	−0.0665882	−	0.356058i
$743$			20.9549i			0.768760i	0.923175	+	0.384380i	$0.125585\pi$
$743$			20.9549i			0.768760i	−0.923175	+	0.384380i	$0.874415\pi$
$744$	0.0342526	−	0.325892i	0.00125576	−	0.0119478i
$745$		0			0
$746$	−1.32146	−	12.5729i	−0.0483821	−	0.460325i
$747$	−3.25649	+	7.31420i	−0.119149	+	0.267612i
$748$	2.01457	−	0.654575i	0.0736601	−	0.0239336i
$749$	28.7119	+	6.84395i	1.04911	+	0.250073i
$750$		0			0
$751$	1.95354	+	3.38362i	0.0712855	+	0.123470i	0.899465	−	0.436993i	$-0.143957\pi$
$751$	1.95354	+	3.38362i	0.0712855	+	0.123470i	−0.828179	+	0.560463i	$0.810623\pi$
$752$	12.4554	−	58.5980i	0.454202	−	2.13685i
$753$	−0.456935	+	0.0480258i	−0.0166516	+	0.00175016i
$754$	−14.1470	−	6.29866i	−0.515204	−	0.229384i
$755$		0			0
$756$	−0.828459	+	2.35159i	−0.0301307	+	0.0855266i
$757$		−	28.1928i		−	1.02469i	−0.858781	−	0.512343i	$-0.828778\pi$
$757$		−	28.1928i		−	1.02469i	0.858781	−	0.512343i	$-0.171222\pi$
$758$	16.9580	+	1.78236i	0.615942	+	0.0647381i
$759$	0.0160223	+	0.0177945i	0.000581572	+	0.000645901i
$760$		0			0
$761$	1.56426	−	1.73728i	0.0567043	−	0.0629765i	−0.714125	−	0.700018i	$-0.753175\pi$
$761$	1.56426	−	1.73728i	0.0567043	−	0.0629765i	0.770830	+	0.637041i	$0.219842\pi$
$762$	2.86014	+	0.929317i	0.103612	+	0.0336656i
$763$	0.396100	−	16.1246i	0.0143398	−	0.583749i
$764$	−1.93951	−	5.96919i	−0.0701689	−	0.215958i
$765$		0			0
$766$	−5.35192	−	5.94391i	−0.193373	−	0.214762i
$767$	−19.5614	−	43.9355i	−0.706320	−	1.58642i
$768$	−2.38956	+	1.37962i	−0.0862260	+	0.0497826i
$769$	4.40134	+	3.19776i	0.158716	+	0.115314i	0.664309	−	0.747458i	$-0.268726\pi$
$769$	4.40134	+	3.19776i	0.158716	+	0.115314i	−0.505592	+	0.862772i	$0.668726\pi$
$770$		0			0
$771$	−0.777669	+	0.565009i	−0.0280071	+	0.0203483i
$772$	−3.54731	+	7.96738i	−0.127670	+	0.286752i
$773$	6.36875	−	29.9626i	0.229068	−	1.07768i	−0.701814	−	0.712360i	$-0.747626\pi$
$773$	6.36875	−	29.9626i	0.229068	−	1.07768i	0.930882	−	0.365320i	$-0.119040\pi$
$774$	30.5094	−	52.8439i	1.09664	−	1.89944i
$775$		0			0
$776$	−26.3904			−0.947361
$777$	1.34909	−	2.84025i	0.0483982	−	0.101893i
$778$	−22.0374	−	30.3319i	−0.790079	−	1.08745i
$779$	21.4091	+	9.53195i	0.767061	+	0.341518i
$780$		0			0
$781$	−9.21719	+	4.10376i	−0.329817	+	0.146844i
$782$	−0.617473	+	0.356498i	−0.0220808	+	0.0127483i
$783$	−0.705247	+	0.970690i	−0.0252035	+	0.0346896i
$784$	9.12276	+	33.6107i	0.325813	+	1.20038i
$785$		0			0
$786$	−0.518825	+	0.576214i	−0.0185059	+	0.0205529i
$787$	−14.2925	+	12.8691i	−0.509474	+	0.458733i	−0.883328	−	0.468755i	$-0.844703\pi$
$787$	−14.2925	+	12.8691i	−0.509474	+	0.458733i	0.373854	+	0.927488i	$0.378036\pi$
$788$	−10.2646	+	9.24226i	−0.365660	+	0.329242i
$789$	2.59052	−	2.87706i	0.0922248	−	0.102426i
$790$		0			0
$791$	6.90958	+	12.6768i	0.245676	+	0.450737i
$792$	−2.35041	+	3.23506i	−0.0835182	+	0.114953i
$793$	12.9661	−	7.48601i	0.460441	−	0.265836i
$794$	7.62429	−	3.39455i	0.270576	−	0.120468i
$795$		0			0
$796$	−21.3764	−	9.51737i	−0.757665	−	0.337334i
$797$	16.0174	+	22.0460i	0.567365	+	0.780911i	0.992240	−	0.124341i	$-0.0396818\pi$
$797$	16.0174	+	22.0460i	0.567365	+	0.780911i	−0.424874	+	0.905252i	$0.639682\pi$
$798$	2.35173	−	0.188919i	0.0832505	−	0.00668766i
$799$	−24.6042			−0.870432
$800$		0			0
$801$	−9.88957	+	17.1292i	−0.349431	+	0.605232i
$802$	0.393510	−	1.85132i	0.0138953	−	0.0653723i
$803$	3.64337	−	8.18315i	0.128572	−	0.288777i
$804$	−1.29664	+	0.942064i	−0.0457290	+	0.0332240i
$805$		0			0
$806$	−13.6684	−	9.93070i	−0.481450	−	0.349794i
$807$	−1.86840	+	1.07872i	−0.0657709	+	0.0379729i
$808$	5.57977	+	12.5324i	0.196296	+	0.440887i
$809$	−10.3329	−	11.4759i	−0.363287	−	0.403471i	0.533596	−	0.845740i	$-0.320840\pi$
$809$	−10.3329	−	11.4759i	−0.363287	−	0.403471i	−0.896883	+	0.442269i	$0.854174\pi$
$810$		0			0
$811$	7.57398	+	23.3103i	0.265958	+	0.818536i	0.991471	+	0.130327i	$0.0416027\pi$
$811$	7.57398	+	23.3103i	0.265958	+	0.818536i	−0.725513	+	0.688209i	$0.758397\pi$
$812$	0.110803	−	4.51061i	0.00388843	−	0.158291i
$813$	−1.31474	−	0.427185i	−0.0461099	−	0.0149820i
$814$	−9.29774	+	10.3262i	−0.325886	+	0.361933i
$815$		0			0
$816$	0.926028	+	1.02846i	0.0324175	+	0.0360032i
$817$	−42.2290	−	4.43845i	−1.47741	−	0.155282i
$818$		−	30.4839i		−	1.06585i
$819$	−30.3571	−	35.4272i	−1.06076	−	1.23793i
$820$		0			0
$821$	−26.9382	−	11.9937i	−0.940151	−	0.418582i	−0.121318	−	0.992614i	$-0.538712\pi$
$821$	−26.9382	−	11.9937i	−0.940151	−	0.418582i	−0.818833	+	0.574032i	$0.805379\pi$
$822$	0.404336	−	0.0424975i	0.0141029	−	0.00148227i
$823$	1.59736	−	7.51501i	0.0556806	−	0.261957i	−0.941498	−	0.337018i	$-0.890582\pi$
$823$	1.59736	−	7.51501i	0.0556806	−	0.261957i	0.997179	+	0.0750609i	$0.0239151\pi$
$824$	2.11873	+	3.66975i	0.0738096	+	0.127842i
$825$		0			0
$826$	26.2694	−	27.7721i	0.914029	−	0.966316i
$827$	−5.39373	+	1.75253i	−0.187558	+	0.0609414i	−0.401290	−	0.915951i	$-0.631438\pi$
$827$	−5.39373	+	1.75253i	−0.187558	+	0.0609414i	0.213732	+	0.976892i	$0.431438\pi$
$828$	−0.275602	+	0.619013i	−0.00957785	+	0.0215122i
$829$	1.61187	+	15.3359i	0.0559824	+	0.532637i	0.986192	+	0.165608i	$0.0529585\pi$
$829$	1.61187	+	15.3359i	0.0559824	+	0.532637i	−0.930209	+	0.367030i	$0.880375\pi$
$830$		0			0
$831$	0.302264	−	2.87585i	0.0104854	−	0.0997621i
$832$			2.58349i			0.0895664i
$833$	12.7234	−	6.53491i	0.440840	−	0.226421i
$834$	0.00465030	−	0.0143122i	0.000161027	−	0.000495589i
$835$		0			0
$836$	−3.73817	−	0.794573i	−0.129287	−	0.0274809i
$837$	−0.972797	+	0.875911i	−0.0336248	+	0.0302759i
$838$	−9.15264	−	43.0598i	−0.316173	−	1.48747i
$839$	−12.6424	−	38.9093i	−0.436464	−	1.34330i	−0.891579	−	0.452865i	$-0.850402\pi$
$839$	−12.6424	−	38.9093i	−0.436464	−	1.34330i	0.455115	−	0.890433i	$-0.349598\pi$
$840$		0			0
$841$	−8.29052	+	25.5156i	−0.285880	+	0.879848i
$842$	−18.4581	−	1.94003i	−0.636110	−	0.0668578i
$843$	2.35016	+	1.35687i	0.0809439	+	0.0467330i
$844$	0.127749	−	0.0568777i	0.00439731	−	0.00195781i
$845$		0			0
$846$	−51.6074	+	37.4950i	−1.77430	+	1.28910i
$847$	−10.3654	−	24.9100i	−0.356158	−	0.855917i
$848$	−9.93116	+	3.22683i	−0.341037	+	0.110810i
$849$	−0.944883	−	1.63659i	−0.0324283	−	0.0561675i
$850$		0			0
$851$	0.857203	−	1.48472i	0.0293845	−	0.0508955i
$852$	1.31879	+	1.18744i	0.0451810	+	0.0406812i
$853$	10.1441	+	13.9621i	0.347326	+	0.478053i	0.946563	−	0.322519i	$-0.104529\pi$
$853$	10.1441	+	13.9621i	0.347326	+	0.478053i	−0.599237	+	0.800571i	$0.704529\pi$
$854$	9.45323	+	7.22942i	0.323483	+	0.247386i
$855$		0			0
$856$	1.74609	−	16.6129i	0.0596801	−	0.567818i
$857$	−37.5323	−	21.6693i	−1.28208	−	0.740208i	−0.304850	−	0.952400i	$-0.598606\pi$
$857$	−37.5323	−	21.6693i	−1.28208	−	0.740208i	−0.977228	+	0.212192i	$0.931940\pi$
$858$	−0.521216	−	1.17067i	−0.0177940	−	0.0399660i
$859$	17.4422	−	3.70745i	0.595120	−	0.126497i	0.0995020	−	0.995037i	$-0.468275\pi$
$859$	17.4422	−	3.70745i	0.595120	−	0.126497i	0.495618	+	0.868541i	$0.334942\pi$
$860$		0			0
$861$	−1.88477	+	1.29987i	−0.0642329	+	0.0442994i
$862$	−53.5830	−	17.4102i	−1.82504	−	0.592993i
$863$	−7.29125	−	34.3026i	−0.248197	−	1.16768i	−0.908895	−	0.417024i	$-0.863073\pi$
$863$	−7.29125	−	34.3026i	−0.248197	−	1.16768i	0.660698	−	0.750652i	$-0.270260\pi$
$864$	4.65596	+	0.989655i	0.158399	+	0.0336687i
$865$		0			0
$866$	−32.9530	+	7.00437i	−1.11979	+	0.238018i
$867$	−1.02617	+	1.41240i	−0.0348506	+	0.0479677i
$868$	1.14140	−	4.78842i	0.0387416	−	0.162530i
$869$	−2.61059	−	1.89670i	−0.0885582	−	0.0643413i
$870$		0			0
$871$	−6.28927	−	59.8384i	−0.213104	−	2.02755i
$872$	−9.07827	+	0.954165i	−0.307429	+	0.0323121i
$873$	39.0510	+	35.1616i	1.32167	+	1.19004i
$874$	1.28637			0.0435120
$875$		0			0
$876$	−1.57552			−0.0532320
$877$	29.8620	+	26.8879i	1.00837	+	0.907940i	0.995761	−	0.0919803i	$-0.0293197\pi$
$877$	29.8620	+	26.8879i	1.00837	+	0.907940i	0.0126089	+	0.999921i	$0.495986\pi$
$878$	8.83180	−	0.928259i	0.298059	−	0.0313272i
$879$	−0.116328	−	1.10679i	−0.00392365	−	0.0373310i
$880$		0			0
$881$	−13.0284	−	9.46567i	−0.438937	−	0.318907i	0.346275	−	0.938133i	$-0.387446\pi$
$881$	−13.0284	−	9.46567i	−0.438937	−	0.318907i	−0.785213	+	0.619226i	$0.787446\pi$
$882$	16.7287	−	33.0966i	0.563285	−	1.11442i
$883$	−0.925642	+	1.27404i	−0.0311503	+	0.0428748i	−0.824308	−	0.566141i	$-0.808436\pi$
$883$	−0.925642	+	1.27404i	−0.0311503	+	0.0428748i	0.793158	+	0.609016i	$0.208436\pi$
$884$	13.6811	−	2.90800i	0.460144	−	0.0978065i
$885$		0			0
$886$	5.66406	+	1.20393i	0.190288	+	0.0404469i
$887$	2.05844	+	9.68421i	0.0691157	+	0.325164i	0.999099	−	0.0424376i	$-0.0135124\pi$
$887$	2.05844	+	9.68421i	0.0691157	+	0.325164i	−0.929983	+	0.367602i	$0.880179\pi$
$888$	−1.69242	−	0.549902i	−0.0567940	−	0.0184535i
$889$	−29.7125	−	14.1131i	−0.996527	−	0.473339i
$890$		0			0
$891$	7.73956	−	1.64509i	0.259285	−	0.0551127i
$892$	9.02349	+	20.2671i	0.302129	+	0.678592i
$893$	38.4430	+	22.1950i	1.28644	+	0.742729i
$894$	−0.552544	+	5.25711i	−0.0184798	+	0.175824i
$895$		0			0
$896$	26.6632	−	11.0949i	0.890755	−	0.370655i
$897$	0.0929330	+	0.127911i	0.00310294	+	0.00427083i
$898$	24.7390	+	22.2751i	0.825553	+	0.743331i
$899$	1.18445	−	2.05153i	0.0395037	−	0.0684225i
$900$		0			0
$901$	2.14434	+	3.71410i	0.0714383	+	0.123735i
$902$	9.62252	−	3.12655i	0.320395	−	0.104103i
$903$	2.52003	−	3.29521i	0.0838614	−	0.109658i
$904$	6.61032	−	4.80268i	0.219856	−	0.159735i
$905$		0			0
$906$	−1.20863	+	0.538119i	−0.0401542	+	0.0178778i
$907$	25.1973	+	14.5476i	0.836661	+	0.483047i	0.856128	−	0.516764i	$-0.172864\pi$
$907$	25.1973	+	14.5476i	0.836661	+	0.483047i	−0.0194668	+	0.999811i	$0.506197\pi$
$908$	13.7645	+	1.44671i	0.456792	+	0.0480108i
$909$	8.44106	−	25.9789i	0.279972	−	0.861666i
$910$		0			0
$911$	10.9862	+	33.8121i	0.363989	+	1.12024i	0.950612	+	0.310383i	$0.100457\pi$
$911$	10.9862	+	33.8121i	0.363989	+	1.12024i	−0.586622	+	0.809861i	$0.699543\pi$
$912$	−0.519122	−	2.44228i	−0.0171899	−	0.0808719i
$913$	1.78754	−	1.60951i	0.0591590	−	0.0532670i
$914$	47.2102	+	10.0348i	1.56157	+	0.331923i
$915$		0			0
$916$	4.86708	−	14.9793i	0.160813	−	0.494931i
$917$	6.44005	−	5.51839i	0.212669	−	0.182233i
$918$		−	2.95642i		−	0.0975764i
$919$	−3.05900	+	29.1044i	−0.100907	+	0.960067i	0.820547	+	0.571579i	$0.193669\pi$
$919$	−3.05900	+	29.1044i	−0.100907	+	0.960067i	−0.921454	+	0.388488i	$0.872998\pi$
$920$		0			0
$921$	−0.307617	−	2.92678i	−0.0101363	−	0.0964407i
$922$	10.2015	−	22.9131i	0.335970	−	0.754601i
$923$	−63.3596	+	20.5868i	−2.08551	+	0.677623i
$924$	0.256570	−	0.271247i	0.00844052	−	0.00892336i
$925$		0			0
$926$	−16.0191	−	27.7459i	−0.526420	−	0.911786i
$927$	1.75427	−	8.25320i	0.0576178	−	0.271071i
$928$	−8.56680	+	0.900407i	−0.281219	+	0.0295573i
$929$	−31.7179	−	14.1217i	−1.04063	−	0.463319i	−0.185997	−	0.982550i	$-0.559552\pi$
$929$	−31.7179	−	14.1217i	−1.04063	−	0.463319i	−0.854634	+	0.519231i	$0.826218\pi$
$930$		0			0
$931$	−25.7748	−	1.26708i	−0.844736	−	0.0415269i
$932$		−	4.19187i		−	0.137309i
$933$	−0.840639	−	0.0883548i	−0.0275213	−	0.00289260i
$934$	22.0617	+	24.5020i	0.721882	+	0.801731i
$935$		0			0
$936$	−17.6674	+	19.6217i	−0.577479	+	0.641355i
$937$	4.44214	+	1.44334i	0.145119	+	0.0471519i	0.380676	−	0.924709i	$-0.375691\pi$
$937$	4.44214	+	1.44334i	0.145119	+	0.0471519i	−0.235557	+	0.971861i	$0.575691\pi$
$938$	41.9929	−	22.8884i	1.37112	−	0.747334i
$939$	0.409271	+	1.25961i	0.0133560	+	0.0411057i
$940$		0			0
$941$	24.7415	+	27.4782i	0.806550	+	0.895765i	0.996289	−	0.0860698i	$-0.0274308\pi$
$941$	24.7415	+	27.4782i	0.806550	+	0.895765i	−0.189739	+	0.981835i	$0.560764\pi$
$942$	0.767372	+	1.72355i	0.0250023	+	0.0561562i
$943$	−1.08109	+	0.624165i	−0.0352050	+	0.0203256i
$944$	−32.7298	−	23.7796i	−1.06527	−	0.773961i
$945$		0			0
$946$	−14.8309	+	10.7753i	−0.482195	+	0.350335i
$947$	17.5261	−	39.3642i	0.569521	−	1.27916i	−0.367543	−	0.930006i	$-0.619801\pi$
$947$	17.5261	−	39.3642i	0.569521	−	1.27916i	0.937064	−	0.349158i	$-0.113532\pi$
$948$	−0.118003	+	0.555162i	−0.00383257	+	0.0180308i
$949$	29.5732	−	51.2223i	0.959986	−	1.66275i
$950$		0			0
$951$	−2.82981			−0.0917630
$952$	−4.59581	−	6.66379i	−0.148951	−	0.215975i
$953$	−10.2390	−	14.0927i	−0.331672	−	0.456508i	0.610314	−	0.792160i	$-0.291043\pi$
$953$	−10.2390	−	14.0927i	−0.331672	−	0.456508i	−0.941986	+	0.335652i	$0.891043\pi$
$954$	10.1578	+	4.52254i	0.328871	+	0.146423i
$955$		0			0
$956$	−19.2757	+	8.58211i	−0.623422	+	0.277565i
$957$	0.155604	−	0.0898382i	0.00502998	−	0.00290406i
$958$	−36.7718	+	50.6120i	−1.18804	+	1.63520i
$959$	−4.44562	−	0.109207i	−0.143557	−	0.00352647i
$960$		0			0
$961$	−19.0137	+	21.1168i	−0.613345	+	0.681188i
$962$	−68.1833	+	61.3925i	−2.19832	+	1.97937i
$963$	−24.7182	+	22.2564i	−0.796533	+	0.717202i
$964$	11.3522	−	12.6079i	0.365630	−	0.406073i
$965$		0			0
$966$	−0.0654909	+	0.107261i	−0.00210713	+	0.00345107i
$967$	4.31454	−	5.93845i	0.138746	−	0.190968i	−0.733989	−	0.679161i	$-0.762344\pi$
$967$	4.31454	−	5.93845i	0.138746	−	0.190968i	0.872736	+	0.488193i	$0.162344\pi$
$968$	−13.2236	+	7.63466i	−0.425023	+	0.245387i
$969$	−0.936808	+	0.417094i	−0.0300946	+	0.0133990i
$970$		0			0
$971$	−27.1712	−	12.0974i	−0.871966	−	0.388224i	−0.0785541	−	0.996910i	$-0.525030\pi$
$971$	−27.1712	−	12.0974i	−0.871966	−	0.388224i	−0.793411	+	0.608686i	$0.791697\pi$
$972$	−2.47974	−	3.41307i	−0.0795378	−	0.109474i
$973$	−0.0706220	+	0.148682i	−0.00226404	+	0.00476651i
$974$	18.0306			0.577738
$975$		0			0
$976$	6.29725	−	10.9071i	0.201570	−	0.349129i
$977$	7.14936	−	33.6351i	0.228728	−	1.07608i	−0.702511	−	0.711673i	$-0.747938\pi$
$977$	7.14936	−	33.6351i	0.228728	−	1.07608i	0.931239	−	0.364408i	$-0.118729\pi$
$978$	−1.74508	+	3.91951i	−0.0558014	+	0.125332i
$979$	4.80741	−	3.49279i	0.153646	−	0.111630i
$980$		0			0
$981$	14.7048	+	10.6836i	0.469487	+	0.341103i
$982$	−26.3192	+	15.1954i	−0.839880	+	0.484905i
$983$	−4.69953	−	10.5553i	−0.149892	−	0.336662i	0.822957	−	0.568103i	$-0.192323\pi$
$983$	−4.69953	−	10.5553i	−0.149892	−	0.336662i	−0.972849	+	0.231441i	$0.925656\pi$
$984$	0.867021	+	0.962925i	0.0276396	+	0.0306969i
$985$		0			0
$986$	1.65328	+	5.08829i	0.0526513	+	0.162044i
$987$	−3.80788	+	2.07550i	−0.121206	+	0.0660640i
$988$	−23.9993	−	7.79785i	−0.763520	−	0.248083i
$989$	1.51345	−	1.68086i	0.0481249	−	0.0534481i
$990$		0			0
$991$	15.4926	+	17.2063i	0.492138	+	0.546575i	0.937139	−	0.348955i	$-0.113463\pi$
$991$	15.4926	+	17.2063i	0.492138	+	0.546575i	−0.445001	+	0.895530i	$0.646797\pi$
$992$	−9.34640	−	0.982346i	−0.296749	−	0.0311895i
$993$		−	1.00628i		−	0.0319334i
$994$	−34.4562	−	40.2110i	−1.09289	−	1.27541i
$995$		0			0
$996$	−0.386498	−	0.172080i	−0.0122466	−	0.00545256i
$997$	52.2869	−	5.49557i	1.65594	−	0.174047i	0.770065	−	0.637966i	$-0.220224\pi$
$997$	52.2869	−	5.49557i	1.65594	−	0.174047i	0.885877	+	0.463919i	$0.153557\pi$
$998$	−5.35465	+	25.1917i	−0.169499	+	0.797428i
$999$	3.55437	+	6.15634i	0.112455	+	0.194778i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	875.2.u.a.599.15		144
5.2	odd	4		875.2.q.b.151.8		288
5.3	odd	4		875.2.q.b.151.29		288
5.4	even	2		175.2.t.a.144.4	yes	144
7.2	even	3	inner	875.2.u.a.849.15		144
25.3	odd	20		875.2.q.b.851.8		288
25.4	even	10	inner	875.2.u.a.774.15		144
25.21	even	5		175.2.t.a.4.4	✓	144
25.22	odd	20		875.2.q.b.851.29		288
35.2	odd	12		875.2.q.b.401.29		288
35.9	even	6		175.2.t.a.44.4	yes	144
35.23	odd	12		875.2.q.b.401.8		288
175.72	odd	60		875.2.q.b.226.8		288
175.79	even	30	inner	875.2.u.a.149.15		144
175.121	even	15		175.2.t.a.79.4	yes	144
175.128	odd	60		875.2.q.b.226.29		288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.t.a.4.4	✓	144	25.21	even	5
175.2.t.a.44.4	yes	144	35.9	even	6
175.2.t.a.79.4	yes	144	175.121	even	15
175.2.t.a.144.4	yes	144	5.4	even	2
875.2.q.b.151.8		288	5.2	odd	4
875.2.q.b.151.29		288	5.3	odd	4
875.2.q.b.226.8		288	175.72	odd	60
875.2.q.b.226.29		288	175.128	odd	60
875.2.q.b.401.8		288	35.23	odd	12
875.2.q.b.401.29		288	35.2	odd	12
875.2.q.b.851.8		288	25.3	odd	20
875.2.q.b.851.29		288	25.22	odd	20
875.2.u.a.149.15		144	175.79	even	30	inner
875.2.u.a.599.15		144	1.1	even	1	trivial
875.2.u.a.774.15		144	25.4	even	10	inner
875.2.u.a.849.15		144	7.2	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 875 = 5^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	875.u (of order \(30\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.32048 + 1.18897i) q^{2} +(-0.135384 + 0.0142295i) q^{3} +(0.120974 + 1.15099i) q^{4} +(-0.195691 - 0.142178i) q^{6} +(1.92211 + 1.81810i) q^{7} +(0.880110 - 1.21137i) q^{8} +(-2.91632 + 0.619882i) q^{9} +O(q^{10})\)	\(q+(1.32048 + 1.18897i) q^{2} +(-0.135384 + 0.0142295i) q^{3} +(0.120974 + 1.15099i) q^{4} +(-0.195691 - 0.142178i) q^{6} +(1.92211 + 1.81810i) q^{7} +(0.880110 - 1.21137i) q^{8} +(-2.91632 + 0.619882i) q^{9} +(0.876154 + 0.186232i) q^{11} +(-0.0327559 - 0.154104i) q^{12} +(5.62497 + 1.82766i) q^{13} +(0.376443 + 4.68611i) q^{14} +(4.86653 - 1.03441i) q^{16} +(-0.831108 - 1.86670i) q^{17} +(-4.58797 - 2.64887i) q^{18} +(-0.385351 + 3.66637i) q^{19} +(-0.286094 - 0.218792i) q^{21} +(0.935524 + 1.28764i) q^{22} +(-0.145934 - 0.131400i) q^{23} +(-0.101916 + 0.176524i) q^{24} +(5.25465 + 9.10133i) q^{26} +(0.774405 - 0.251619i) q^{27} +(-1.86009 + 2.43227i) q^{28} +(-1.19212 + 0.866123i) q^{29} +(-1.46865 + 0.653883i) q^{31} +(5.06260 + 2.92289i) q^{32} +(-0.121268 - 0.0127457i) q^{33} +(1.12198 - 3.45311i) q^{34} +(-1.06627 - 3.28166i) q^{36} +(1.81514 + 8.53955i) q^{37} +(-4.86805 + 4.38322i) q^{38} +(-0.787540 - 0.167397i) q^{39} +(1.96439 - 6.04579i) q^{41} +(-0.117645 - 0.629069i) q^{42} +11.5179i q^{43} +(-0.108360 + 1.03097i) q^{44} +(-0.0364735 - 0.347022i) q^{46} +(4.89753 - 11.0000i) q^{47} +(-0.644132 + 0.209291i) q^{48} +(0.388997 + 6.98918i) q^{49} +(0.139081 + 0.240896i) q^{51} +(-1.42315 + 6.69538i) q^{52} +(-2.08734 + 0.219388i) q^{53} +(1.32176 + 0.588484i) q^{54} +(3.89406 - 0.728248i) q^{56} -0.501852i q^{57} +(-2.60397 - 0.273688i) q^{58} +(-5.44105 - 6.04289i) q^{59} +(1.69386 - 1.88122i) q^{61} +(-2.71677 - 0.882733i) q^{62} +(-6.73248 - 4.11069i) q^{63} +(0.134982 + 0.415431i) q^{64} +(-0.144978 - 0.161014i) q^{66} +(-4.13775 - 9.29355i) q^{67} +(2.04801 - 1.18242i) q^{68} +(0.0216269 + 0.0157129i) q^{69} +(-9.11276 + 6.62080i) q^{71} +(-1.81577 + 4.07830i) q^{72} +(2.07918 - 9.78179i) q^{73} +(-7.75640 + 13.4345i) q^{74} -4.26657 q^{76} +(1.34547 + 1.95090i) q^{77} +(-0.840905 - 1.15741i) q^{78} +(-3.29105 - 1.46527i) q^{79} +(8.06986 - 3.59293i) q^{81} +(9.78221 - 5.64776i) q^{82} +(1.57843 - 2.17252i) q^{83} +(0.217217 - 0.355759i) q^{84} +(-13.6945 + 15.2092i) q^{86} +(0.149069 - 0.134223i) q^{87} +(0.996708 - 0.897440i) q^{88} +(4.43903 - 4.93004i) q^{89} +(7.48892 + 13.7398i) q^{91} +(0.133585 - 0.183864i) q^{92} +(0.189527 - 0.109424i) q^{93} +(19.5458 - 8.70236i) q^{94} +(-0.726988 - 0.323676i) q^{96} +(-10.3597 - 14.2589i) q^{97} +(-7.79626 + 9.69161i) q^{98} -2.67059 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 5 q^{2} + 5 q^{3} - 19 q^{4} - 12 q^{6} + 50 q^{8} - 17 q^{9}+O(q^{10}) \) 144 * q + 5 * q^2 + 5 * q^3 - 19 * q^4 - 12 * q^6 + 50 * q^8 - 17 * q^9	\( 144 q + 5 q^{2} + 5 q^{3} - 19 q^{4} - 12 q^{6} + 50 q^{8} - 17 q^{9} + 5 q^{12} + 20 q^{13} - 18 q^{14} + 5 q^{16} - 5 q^{17} - 11 q^{19} - 9 q^{21} + 60 q^{22} - 25 q^{23} + 50 q^{24} - 60 q^{26} - 40 q^{27} - 24 q^{29} + 15 q^{31} - 20 q^{33} - 20 q^{34} + 16 q^{36} + 5 q^{37} + 20 q^{38} + 13 q^{39} - 62 q^{41} - 40 q^{42} - 15 q^{44} - 27 q^{46} + 5 q^{47} - 38 q^{49} - 8 q^{51} + 130 q^{52} - 25 q^{53} - 29 q^{54} + 32 q^{56} + 65 q^{58} - 39 q^{59} + 7 q^{61} + 20 q^{62} + 45 q^{63} + 34 q^{64} + 11 q^{66} - 25 q^{67} + 74 q^{69} - 46 q^{71} - 60 q^{72} - 35 q^{73} + 6 q^{74} + 180 q^{76} + 5 q^{77} - 10 q^{78} + 9 q^{79} - 59 q^{81} - 90 q^{83} - 51 q^{84} + 11 q^{86} + 5 q^{87} - 140 q^{88} - 42 q^{89} + 22 q^{91} - 10 q^{92} + 5 q^{94} + 53 q^{96} - 120 q^{97} + 180 q^{98} - 44 q^{99}+O(q^{100}) \) 144 * q + 5 * q^2 + 5 * q^3 - 19 * q^4 - 12 * q^6 + 50 * q^8 - 17 * q^9 + 5 * q^12 + 20 * q^13 - 18 * q^14 + 5 * q^16 - 5 * q^17 - 11 * q^19 - 9 * q^21 + 60 * q^22 - 25 * q^23 + 50 * q^24 - 60 * q^26 - 40 * q^27 - 24 * q^29 + 15 * q^31 - 20 * q^33 - 20 * q^34 + 16 * q^36 + 5 * q^37 + 20 * q^38 + 13 * q^39 - 62 * q^41 - 40 * q^42 - 15 * q^44 - 27 * q^46 + 5 * q^47 - 38 * q^49 - 8 * q^51 + 130 * q^52 - 25 * q^53 - 29 * q^54 + 32 * q^56 + 65 * q^58 - 39 * q^59 + 7 * q^61 + 20 * q^62 + 45 * q^63 + 34 * q^64 + 11 * q^66 - 25 * q^67 + 74 * q^69 - 46 * q^71 - 60 * q^72 - 35 * q^73 + 6 * q^74 + 180 * q^76 + 5 * q^77 - 10 * q^78 + 9 * q^79 - 59 * q^81 - 90 * q^83 - 51 * q^84 + 11 * q^86 + 5 * q^87 - 140 * q^88 - 42 * q^89 + 22 * q^91 - 10 * q^92 + 5 * q^94 + 53 * q^96 - 120 * q^97 + 180 * q^98 - 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more