LMFDB - Embedded newform 625.2.d.q.126.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [625,2,Mod(126,625)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(625, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("625.126");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 625 = 5^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	625.d (of order $5$, degree $4$, 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:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 25x^{14} + 239x^{12} + 1165x^{10} + 3166x^{8} + 4820x^{6} + 3809x^{4} + 1205x^{2} + 1 $ x^16 + 25x^14 + 239x^12 + 1165x^10 + 3166x^8 + 4820x^6 + 3809x^4 + 1205*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			126.4
Root			$-1.51514i$ of defining polynomial
Character	$\chi$	$=$	625.126
Dual form			625.2.d.q.501.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.622258 + 1.91511i) q^{2} +(2.44781 - 1.77844i) q^{3} +(-1.66242 + 1.20782i) q^{4} +(4.92909 + 3.58119i) q^{6} -0.369971 q^{7} +(-0.0893841 - 0.0649413i) q^{8} +(1.90189 - 5.85342i) q^{9} +O(q^{10})$	\(q+(0.622258 + 1.91511i) q^{2} +(2.44781 - 1.77844i) q^{3} +(-1.66242 + 1.20782i) q^{4} +(4.92909 + 3.58119i) q^{6} -0.369971 q^{7} +(-0.0893841 - 0.0649413i) q^{8} +(1.90189 - 5.85342i) q^{9} +(-0.539645 - 1.66086i) q^{11} +(-1.92126 + 5.91304i) q^{12} +(-0.344932 + 1.06159i) q^{13} +(-0.230218 - 0.708537i) q^{14} +(-1.20123 + 3.69700i) q^{16} +(4.43988 + 3.22576i) q^{17} +12.3934 q^{18} +(3.03559 + 2.20548i) q^{19} +(-0.905621 + 0.657972i) q^{21} +(2.84493 - 2.06696i) q^{22} +(-2.23920 - 6.89154i) q^{23} -0.334290 q^{24} -2.24770 q^{26} +(-2.94954 - 9.07774i) q^{27} +(0.615049 - 0.446859i) q^{28} +(-3.39208 + 2.46449i) q^{29} +(-0.247303 - 0.179676i) q^{31} -8.04862 q^{32} +(-4.27469 - 3.10574i) q^{33} +(-3.41495 + 10.5101i) q^{34} +(3.90813 + 12.0280i) q^{36} +(2.84900 - 8.76833i) q^{37} +(-2.33483 + 7.18587i) q^{38} +(1.04365 + 3.21202i) q^{39} +(-1.29367 + 3.98151i) q^{41} +(-1.82362 - 1.32494i) q^{42} -7.17118 q^{43} +(2.90314 + 2.10925i) q^{44} +(11.8047 - 8.57663i) q^{46} +(0.655524 - 0.476266i) q^{47} +(3.63451 + 11.1859i) q^{48} -6.86312 q^{49} +16.6048 q^{51} +(-0.708789 - 2.18143i) q^{52} +(-3.16737 + 2.30123i) q^{53} +(15.5495 - 11.2974i) q^{54} +(0.0330695 + 0.0240264i) q^{56} +11.3529 q^{57} +(-6.83052 - 4.96266i) q^{58} +(-0.573962 + 1.76647i) q^{59} +(2.99399 + 9.21454i) q^{61} +(0.190214 - 0.585419i) q^{62} +(-0.703645 + 2.16560i) q^{63} +(-2.60586 - 8.02002i) q^{64} +(3.28789 - 10.1191i) q^{66} +(-10.0885 - 7.32972i) q^{67} -11.2771 q^{68} +(-17.7373 - 12.8869i) q^{69} +(-9.44666 + 6.86340i) q^{71} +(-0.550127 + 0.399691i) q^{72} +(-1.06035 - 3.26343i) q^{73} +18.5652 q^{74} -7.71026 q^{76} +(0.199653 + 0.614470i) q^{77} +(-5.50196 + 3.99741i) q^{78} +(-4.60610 + 3.34653i) q^{79} +(-8.42651 - 6.12222i) q^{81} -8.43005 q^{82} +(5.77129 + 4.19309i) q^{83} +(0.710813 - 2.18766i) q^{84} +(-4.46232 - 13.7336i) q^{86} +(-3.92023 + 12.0652i) q^{87} +(-0.0596226 + 0.183499i) q^{88} +(0.472794 + 1.45511i) q^{89} +(0.127615 - 0.392758i) q^{91} +(12.0462 + 8.75210i) q^{92} -0.924896 q^{93} +(1.32001 + 0.959043i) q^{94} +(-19.7015 + 14.3140i) q^{96} +(5.17562 - 3.76031i) q^{97} +(-4.27063 - 13.1437i) q^{98} -10.7480 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 5 q^{2} - 3 q^{4} + 7 q^{6} - 20 q^{7} + 5 q^{8} - 12 q^{9}+O(q^{10}) $ 16 * q + 5 * q^2 - 3 * q^4 + 7 * q^6 - 20 * q^7 + 5 * q^8 - 12 * q^9	$ 16 q + 5 q^{2} - 3 q^{4} + 7 q^{6} - 20 q^{7} + 5 q^{8} - 12 q^{9} - 3 q^{11} - 15 q^{12} + 5 q^{13} - q^{14} + q^{16} + 25 q^{17} + 10 q^{18} + 10 q^{19} + 7 q^{21} + 35 q^{22} + 15 q^{23} + 10 q^{24} + 22 q^{26} - 35 q^{28} - 8 q^{31} - 60 q^{32} - 6 q^{34} + q^{36} + 5 q^{37} + 35 q^{38} + q^{39} - 8 q^{41} + 10 q^{42} - 31 q^{44} + 42 q^{46} + 5 q^{47} + 25 q^{48} - 8 q^{49} - 28 q^{51} - 15 q^{52} + 10 q^{53} + 50 q^{54} + 35 q^{56} + 20 q^{57} - 35 q^{58} - 15 q^{59} + 17 q^{61} - 5 q^{62} - 10 q^{63} + 37 q^{64} + 44 q^{66} + 10 q^{67} - 80 q^{68} - 9 q^{69} - 13 q^{71} - 20 q^{72} - 40 q^{73} - 36 q^{74} - 20 q^{76} + 45 q^{77} - 5 q^{78} - 55 q^{79} - 19 q^{81} + 90 q^{82} + 15 q^{83} + 59 q^{84} + 7 q^{86} + 60 q^{87} - 40 q^{88} - 28 q^{91} - 45 q^{92} + 80 q^{93} + 4 q^{94} - 43 q^{96} - 40 q^{97} - 45 q^{98} - 44 q^{99}+O(q^{100}) $ 16 * q + 5 * q^2 - 3 * q^4 + 7 * q^6 - 20 * q^7 + 5 * q^8 - 12 * q^9 - 3 * q^11 - 15 * q^12 + 5 * q^13 - q^14 + q^16 + 25 * q^17 + 10 * q^18 + 10 * q^19 + 7 * q^21 + 35 * q^22 + 15 * q^23 + 10 * q^24 + 22 * q^26 - 35 * q^28 - 8 * q^31 - 60 * q^32 - 6 * q^34 + q^36 + 5 * q^37 + 35 * q^38 + q^39 - 8 * q^41 + 10 * q^42 - 31 * q^44 + 42 * q^46 + 5 * q^47 + 25 * q^48 - 8 * q^49 - 28 * q^51 - 15 * q^52 + 10 * q^53 + 50 * q^54 + 35 * q^56 + 20 * q^57 - 35 * q^58 - 15 * q^59 + 17 * q^61 - 5 * q^62 - 10 * q^63 + 37 * q^64 + 44 * q^66 + 10 * q^67 - 80 * q^68 - 9 * q^69 - 13 * q^71 - 20 * q^72 - 40 * q^73 - 36 * q^74 - 20 * q^76 + 45 * q^77 - 5 * q^78 - 55 * q^79 - 19 * q^81 + 90 * q^82 + 15 * q^83 + 59 * q^84 + 7 * q^86 + 60 * q^87 - 40 * q^88 - 28 * q^91 - 45 * q^92 + 80 * q^93 + 4 * q^94 - 43 * q^96 - 40 * q^97 - 45 * q^98 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{2}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.622258	+	1.91511i	0.440003	+	1.35419i	0.887872	+	0.460091i	$0.152183\pi$
$2$	0.622258	+	1.91511i	0.440003	+	1.35419i	−0.447869	+	0.894099i	$0.647817\pi$
$3$	2.44781	−	1.77844i	1.41325	−	1.02678i	0.420406	−	0.907336i	$-0.361888\pi$
$3$	2.44781	−	1.77844i	1.41325	−	1.02678i	0.992841	−	0.119447i	$-0.0381122\pi$
$4$	−1.66242	+	1.20782i	−0.831211	+	0.603910i
$5$		0			0
$5$		0			0
$6$	4.92909	+	3.58119i	2.01229	+	1.46202i
$7$	−0.369971			−0.139836			−0.0699180	−	0.997553i	$-0.522274\pi$
$7$	−0.369971			−0.139836			−0.0699180	+	0.997553i	$0.522274\pi$
$8$	−0.0893841	−	0.0649413i	−0.0316020	−	0.0229602i
$9$	1.90189	−	5.85342i	0.633964	−	1.95114i
$10$		0			0
$11$	−0.539645	−	1.66086i	−0.162709	−	0.500767i	0.836151	−	0.548499i	$-0.184801\pi$
$11$	−0.539645	−	1.66086i	−0.162709	−	0.500767i	−0.998860	+	0.0477321i	$0.984801\pi$
$12$	−1.92126	+	5.91304i	−0.554621	+	1.70695i
$13$	−0.344932	+	1.06159i	−0.0956668	+	0.294432i	−0.987427	−	0.158076i	$-0.949471\pi$
$13$	−0.344932	+	1.06159i	−0.0956668	+	0.294432i	0.891760	+	0.452509i	$0.149471\pi$
$14$	−0.230218	−	0.708537i	−0.0615283	−	0.189365i
$15$		0			0
$16$	−1.20123	+	3.69700i	−0.300307	+	0.924250i
$17$	4.43988	+	3.22576i	1.07683	+	0.782363i	0.977127	−	0.212655i	$-0.0682109\pi$
$17$	4.43988	+	3.22576i	1.07683	+	0.782363i	0.0997024	+	0.995017i	$0.468211\pi$
$18$	12.3934			2.92116
$19$	3.03559	+	2.20548i	0.696411	+	0.505972i	0.878761	−	0.477261i	$-0.158370\pi$
$19$	3.03559	+	2.20548i	0.696411	+	0.505972i	−0.182350	+	0.983234i	$0.558370\pi$
$20$		0			0
$21$	−0.905621	+	0.657972i	−0.197623	+	0.143581i
$22$	2.84493	−	2.06696i	0.606541	−	0.440678i
$23$	−2.23920	−	6.89154i	−0.466905	−	1.43699i	−0.856571	−	0.516029i	$-0.827410\pi$
$23$	−2.23920	−	6.89154i	−0.466905	−	1.43699i	0.389666	−	0.920956i	$-0.372590\pi$
$24$	−0.334290			−0.0682366
$25$		0			0
$26$	−2.24770			−0.440811
$27$	−2.94954	−	9.07774i	−0.567639	−	1.74701i
$28$	0.615049	−	0.446859i	0.116233	−	0.0844484i
$29$	−3.39208	+	2.46449i	−0.629893	+	0.457644i	−0.856363	−	0.516374i	$-0.827281\pi$
$29$	−3.39208	+	2.46449i	−0.629893	+	0.457644i	0.226470	+	0.974018i	$0.427281\pi$
$30$		0			0
$31$	−0.247303	−	0.179676i	−0.0444170	−	0.0322708i	0.565355	−	0.824848i	$-0.308739\pi$
$31$	−0.247303	−	0.179676i	−0.0444170	−	0.0322708i	−0.609772	+	0.792577i	$0.708739\pi$
$32$	−8.04862			−1.42281
$33$	−4.27469	−	3.10574i	−0.744127	−	0.540640i
$34$	−3.41495	+	10.5101i	−0.585659	+	1.80247i
$35$		0			0
$36$	3.90813	+	12.0280i	0.651355	+	2.00467i
$37$	2.84900	−	8.76833i	0.468373	−	1.44150i	−0.386317	−	0.922366i	$-0.626253\pi$
$37$	2.84900	−	8.76833i	0.468373	−	1.44150i	0.854690	−	0.519138i	$-0.173747\pi$
$38$	−2.33483	+	7.18587i	−0.378760	+	1.16570i
$39$	1.04365	+	3.21202i	0.167117	+	0.514334i
$40$		0			0
$41$	−1.29367	+	3.98151i	−0.202038	+	0.621808i	0.797785	+	0.602943i	$0.206005\pi$
$41$	−1.29367	+	3.98151i	−0.202038	+	0.621808i	−0.999822	+	0.0188649i	$0.993995\pi$
$42$	−1.82362	−	1.32494i	−0.281391	−	0.204443i
$43$	−7.17118			−1.09359			−0.546797	−	0.837265i	$-0.684153\pi$
$43$	−7.17118			−1.09359			−0.546797	+	0.837265i	$0.684153\pi$
$44$	2.90314	+	2.10925i	0.437664	+	0.317982i
$45$		0			0
$46$	11.8047	−	8.57663i	1.74051	−	1.26456i
$47$	0.655524	−	0.476266i	0.0956181	−	0.0694706i	−0.538949	−	0.842338i	$-0.681178\pi$
$47$	0.655524	−	0.476266i	0.0956181	−	0.0694706i	0.634567	+	0.772868i	$0.281178\pi$
$48$	3.63451	+	11.1859i	0.524597	+	1.61454i
$49$	−6.86312			−0.980446
$50$		0			0
$51$	16.6048			2.32514
$52$	−0.708789	−	2.18143i	−0.0982913	−	0.302510i
$53$	−3.16737	+	2.30123i	−0.435072	+	0.316098i	−0.783674	−	0.621173i	$-0.786657\pi$
$53$	−3.16737	+	2.30123i	−0.435072	+	0.316098i	0.348602	+	0.937271i	$0.386657\pi$
$54$	15.5495	−	11.2974i	2.11602	−	1.53738i
$55$		0			0
$56$	0.0330695	+	0.0240264i	0.00441910	+	0.00321067i
$57$	11.3529			1.50372
$58$	−6.83052	−	4.96266i	−0.896891	−	0.651630i
$59$	−0.573962	+	1.76647i	−0.0747235	+	0.229975i	−0.981441	−	0.191762i	$-0.938580\pi$
$59$	−0.573962	+	1.76647i	−0.0747235	+	0.229975i	0.906718	+	0.421738i	$0.138580\pi$
$60$		0			0
$61$	2.99399	+	9.21454i	0.383341	+	1.17980i	0.937677	+	0.347508i	$0.112972\pi$
$61$	2.99399	+	9.21454i	0.383341	+	1.17980i	−0.554336	+	0.832293i	$0.687028\pi$
$62$	0.190214	−	0.585419i	0.0241572	−	0.0743483i
$63$	−0.703645	+	2.16560i	−0.0886509	+	0.272840i
$64$	−2.60586	−	8.02002i	−0.325733	−	1.00250i
$65$		0			0
$66$	3.28789	−	10.1191i	0.404711	−	1.24557i
$67$	−10.0885	−	7.32972i	−1.23251	−	0.895468i	−0.235430	−	0.971891i	$-0.575650\pi$
$67$	−10.0885	−	7.32972i	−1.23251	−	0.895468i	−0.997075	+	0.0764234i	$0.975650\pi$
$68$	−11.2771			−1.36755
$69$	−17.7373	−	12.8869i	−2.13532	−	1.55140i
$70$		0			0
$71$	−9.44666	+	6.86340i	−1.12111	+	0.814535i	−0.984377	−	0.176072i	$-0.943661\pi$
$71$	−9.44666	+	6.86340i	−1.12111	+	0.814535i	−0.136735	+	0.990608i	$0.543661\pi$
$72$	−0.550127	+	0.399691i	−0.0648331	+	0.0471040i
$73$	−1.06035	−	3.26343i	−0.124105	−	0.381955i	0.869632	−	0.493700i	$-0.164356\pi$
$73$	−1.06035	−	3.26343i	−0.124105	−	0.381955i	−0.993737	+	0.111745i	$0.964356\pi$
$74$	18.5652			2.15816
$75$		0			0
$76$	−7.71026			−0.884427
$77$	0.199653	+	0.614470i	0.0227526	+	0.0700253i
$78$	−5.50196	+	3.99741i	−0.622974	+	0.452617i
$79$	−4.60610	+	3.34653i	−0.518227	+	0.376514i	−0.815936	−	0.578143i	$-0.803778\pi$
$79$	−4.60610	+	3.34653i	−0.518227	+	0.376514i	0.297709	+	0.954657i	$0.403778\pi$
$80$		0			0
$81$	−8.42651	−	6.12222i	−0.936279	−	0.680246i
$82$	−8.43005			−0.930943
$83$	5.77129	+	4.19309i	0.633482	+	0.460251i	0.857605	−	0.514309i	$-0.171952\pi$
$83$	5.77129	+	4.19309i	0.633482	+	0.460251i	−0.224123	+	0.974561i	$0.571952\pi$
$84$	0.710813	−	2.18766i	0.0775560	−	0.238693i
$85$		0			0
$86$	−4.46232	−	13.7336i	−0.481185	−	1.48093i
$87$	−3.92023	+	12.0652i	−0.420292	+	1.29353i
$88$	−0.0596226	+	0.183499i	−0.00635579	+	0.0195611i
$89$	0.472794	+	1.45511i	0.0501160	+	0.154241i	0.972983	−	0.230879i	$-0.0741601\pi$
$89$	0.472794	+	1.45511i	0.0501160	+	0.154241i	−0.922867	+	0.385120i	$0.874160\pi$
$90$		0			0
$91$	0.127615	−	0.392758i	0.0133777	−	0.0411722i
$92$	12.0462	+	8.75210i	1.25591	+	0.912470i
$93$	−0.924896			−0.0959072
$94$	1.32001	+	0.959043i	0.136149	+	0.0989178i
$95$		0			0
$96$	−19.7015	+	14.3140i	−2.01078	+	1.46092i
$97$	5.17562	−	3.76031i	0.525504	−	0.381801i	−0.293169	−	0.956061i	$-0.594710\pi$
$97$	5.17562	−	3.76031i	0.525504	−	0.381801i	0.818673	+	0.574259i	$0.194710\pi$
$98$	−4.27063	−	13.1437i	−0.431399	−	1.32771i
$99$	−10.7480			−1.08022
$100$		0			0
$101$	−12.2487			−1.21879			−0.609396	−	0.792866i	$-0.708588\pi$
$101$	−12.2487			−1.21879			−0.609396	+	0.792866i	$0.708588\pi$
$102$	10.3325	+	31.8002i	1.02307	+	3.14869i
$103$	−6.20298	+	4.50673i	−0.611197	+	0.444061i	−0.849836	−	0.527048i	$-0.823299\pi$
$103$	−6.20298	+	4.50673i	−0.611197	+	0.444061i	0.238638	+	0.971109i	$0.423299\pi$
$104$	0.0997725	−	0.0724889i	0.00978350	−	0.00710813i
$105$		0			0
$106$	−6.37804	−	4.63392i	−0.619490	−	0.450086i
$107$	0.758003			0.0732789			0.0366394	−	0.999329i	$-0.488335\pi$
$107$	0.758003			0.0732789			0.0366394	+	0.999329i	$0.488335\pi$
$108$	15.8677	+	11.5285i	1.52687	+	1.10933i
$109$	−1.00999	+	3.10843i	−0.0967394	+	0.297733i	−0.987703	−	0.156341i	$-0.950030\pi$
$109$	−1.00999	+	3.10843i	−0.0967394	+	0.297733i	0.890964	+	0.454075i	$0.150030\pi$
$110$		0			0
$111$	−8.62012	−	26.5300i	−0.818186	−	2.51812i
$112$	0.444420	−	1.36778i	0.0419937	−	0.129243i
$113$	−0.262033	+	0.806455i	−0.0246500	+	0.0758649i	−0.962625	−	0.270839i	$-0.912699\pi$
$113$	−0.262033	+	0.806455i	−0.0246500	+	0.0758649i	0.937975	+	0.346704i	$0.112699\pi$
$114$	7.06442	+	21.7420i	0.661644	+	2.03633i
$115$		0			0
$116$	2.66240	−	8.19404i	0.247198	−	0.760797i
$117$	5.55791	+	4.03806i	0.513829	+	0.373319i
$118$	−3.74015			−0.344309
$119$	−1.64263	−	1.19344i	−0.150580	−	0.109403i
$120$		0			0
$121$	6.43196	−	4.67309i	0.584723	−	0.424826i
$122$	−15.7839	+	11.4676i	−1.42900	+	1.03823i
$123$	3.91422	+	12.0467i	0.352933	+	1.08622i
$124$	0.628139			0.0564086
$125$		0			0
$126$	−4.58521			−0.408483
$127$	−4.42590	−	13.6215i	−0.392735	−	1.20872i	−0.930711	−	0.365755i	$-0.880811\pi$
$127$	−4.42590	−	13.6215i	−0.392735	−	1.20872i	0.537976	−	0.842960i	$-0.319189\pi$
$128$	0.714803	−	0.519335i	0.0631803	−	0.0459032i
$129$	−17.5537	+	12.7535i	−1.54552	+	1.12288i
$130$		0			0
$131$	13.4512	+	9.77284i	1.17523	+	0.853857i	0.991626	−	0.129142i	$-0.0412224\pi$
$131$	13.4512	+	9.77284i	1.17523	+	0.853857i	0.183608	+	0.983000i	$0.441222\pi$
$132$	10.8575			0.945025
$133$	−1.12308	−	0.815966i	−0.0973834	−	0.0707532i
$134$	7.75960	−	23.8816i	0.670327	−	2.06306i
$135$		0			0
$136$	−0.187369	−	0.576664i	−0.0160668	−	0.0494485i
$137$	0.949265	−	2.92154i	0.0811012	−	0.249604i	−0.902282	−	0.431147i	$-0.858109\pi$
$137$	0.949265	−	2.92154i	0.0811012	−	0.249604i	0.983383	+	0.181543i	$0.0581091\pi$
$138$	13.6427	−	41.9880i	1.16135	−	3.57426i
$139$	−4.85775	−	14.9506i	−0.412029	−	1.26809i	−0.914881	−	0.403723i	$-0.867716\pi$
$139$	−4.85775	−	14.9506i	−0.412029	−	1.26809i	0.502852	−	0.864372i	$-0.332284\pi$
$140$		0			0
$141$	0.757590	−	2.33162i	0.0638006	−	0.196358i
$142$	−19.0225	−	13.8206i	−1.59633	−	1.15980i
$143$	1.94929			0.163008
$144$	19.3555	+	14.0626i	1.61296	+	1.17188i
$145$		0			0
$146$	5.59002	−	4.06139i	0.462633	−	0.336123i
$147$	−16.7996	+	12.2057i	−1.38561	+	1.00671i
$148$	5.85432	+	18.0177i	0.481222	+	1.48105i
$149$	14.8504			1.21660			0.608298	−	0.793709i	$-0.291853\pi$
$149$	14.8504			1.21660			0.608298	+	0.793709i	$0.291853\pi$
$150$		0			0
$151$	−0.712013			−0.0579428			−0.0289714	−	0.999580i	$-0.509223\pi$
$151$	−0.712013			−0.0579428			−0.0289714	+	0.999580i	$0.509223\pi$
$152$	−0.128106	−	0.394270i	−0.0103908	−	0.0319795i
$153$	27.3259	−	19.8534i	2.20917	−	1.60506i
$154$	−1.05254	+	0.764717i	−0.0848164	+	0.0616227i
$155$		0			0
$156$	−5.61452	−	4.07919i	−0.449522	−	0.326597i
$157$	22.0704			1.76141			0.880704	−	0.473667i	$-0.157070\pi$
$157$	22.0704			1.76141			0.880704	+	0.473667i	$0.157070\pi$
$158$	−9.27517	−	6.73881i	−0.737893	−	0.536111i
$159$	−3.66053	+	11.2660i	−0.290299	+	0.893449i
$160$		0			0
$161$	0.828439	+	2.54967i	0.0652901	+	0.200942i
$162$	6.48128	−	19.9473i	0.509218	−	1.56721i
$163$	4.06725	−	12.5177i	0.318572	−	0.980462i	−0.655688	−	0.755032i	$-0.727621\pi$
$163$	4.06725	−	12.5177i	0.318572	−	0.980462i	0.974259	−	0.225430i	$-0.0723788\pi$
$164$	−2.65832	−	8.18148i	−0.207580	−	0.638866i
$165$		0			0
$166$	−4.43901	+	13.6619i	−0.344534	+	1.06037i
$167$	8.42033	+	6.11773i	0.651585	+	0.473404i	0.863811	−	0.503816i	$-0.168071\pi$
$167$	8.42033	+	6.11773i	0.651585	+	0.473404i	−0.212226	+	0.977221i	$0.568071\pi$
$168$	0.123678			0.00954194
$169$	9.50922	+	6.90886i	0.731479	+	0.531450i
$170$		0			0
$171$	18.6830	−	13.5740i	1.42872	−	1.03803i
$172$	11.9215	−	8.66149i	0.909008	−	0.660433i
$173$	2.84063	+	8.74256i	0.215969	+	0.664684i	0.999083	+	0.0428065i	$0.0136299\pi$
$173$	2.84063	+	8.74256i	0.215969	+	0.664684i	−0.783114	+	0.621878i	$0.786370\pi$
$174$	−25.5457			−1.93661
$175$		0			0
$176$	6.78842			0.511697
$177$	1.73662	+	5.34476i	0.130532	+	0.401736i
$178$	−2.49250	+	1.81091i	−0.186821	+	0.135733i
$179$	17.5454	−	12.7475i	1.31141	−	0.952792i	0.311409	−	0.950276i	$-0.399199\pi$
$179$	17.5454	−	12.7475i	1.31141	−	0.952792i	0.999997	−	0.00251665i	$-0.000801074\pi$
$180$		0			0
$181$	−8.71149	−	6.32927i	−0.647520	−	0.470451i	0.214906	−	0.976635i	$-0.431056\pi$
$181$	−8.71149	−	6.32927i	−0.647520	−	0.470451i	−0.862425	+	0.506184i	$0.831056\pi$
$182$	0.831586			0.0616413
$183$	23.7162	+	17.2309i	1.75315	+	1.27374i
$184$	−0.247397	+	0.761410i	−0.0182384	+	0.0561319i
$185$		0			0
$186$	−0.575524	−	1.77128i	−0.0421995	−	0.129877i
$187$	2.96157	−	9.11478i	0.216572	−	0.666539i
$188$	−0.514514	+	1.58351i	−0.0375248	+	0.115489i
$189$	1.09124	+	3.35851i	0.0793764	+	0.244295i
$190$		0			0
$191$	−1.18644	+	3.65150i	−0.0858480	+	0.264213i	−0.984761	−	0.173915i	$-0.944358\pi$
$191$	−1.18644	+	3.65150i	−0.0858480	+	0.264213i	0.898913	+	0.438128i	$0.144358\pi$
$192$	−20.6418	−	14.9972i	−1.48969	−	1.08233i
$193$	10.5334			0.758208			0.379104	−	0.925354i	$-0.376232\pi$
$193$	10.5334			0.758208			0.379104	+	0.925354i	$0.376232\pi$
$194$	10.4220	+	7.57202i	0.748255	+	0.543639i
$195$		0			0
$196$	11.4094	−	8.28942i	0.814958	−	0.592101i
$197$	−7.80946	+	5.67390i	−0.556401	+	0.404249i	−0.830140	−	0.557555i	$-0.811740\pi$
$197$	−7.80946	+	5.67390i	−0.556401	+	0.404249i	0.273739	+	0.961804i	$0.411740\pi$
$198$	−6.68805	−	20.5837i	−0.475299	−	1.46282i
$199$	−15.8462			−1.12331			−0.561654	−	0.827372i	$-0.689835\pi$
$199$	−15.8462			−1.12331			−0.561654	+	0.827372i	$0.689835\pi$
$200$		0			0
$201$	−37.7302			−2.66129
$202$	−7.62186	−	23.4577i	−0.536272	−	1.65048i
$203$	1.25497	−	0.911790i	0.0880817	−	0.0639951i
$204$	−27.6043	+	20.0557i	−1.93269	+	1.40418i
$205$		0			0
$206$	−12.4907	−	9.07506i	−0.870272	−	0.632289i
$207$	−44.5978			−3.09976
$208$	−3.51036	−	2.55042i	−0.243400	−	0.176840i
$209$	2.02485	−	6.23185i	0.140062	−	0.431066i
$210$		0			0
$211$	2.24070	+	6.89617i	0.154256	+	0.474752i	0.998085	−	0.0618609i	$-0.0197035\pi$
$211$	2.24070	+	6.89617i	0.154256	+	0.474752i	−0.843828	+	0.536613i	$0.819704\pi$
$212$	2.48603	−	7.65123i	0.170742	−	0.525489i
$213$	−10.9175	+	33.6006i	−0.748056	+	2.30228i
$214$	0.471674	+	1.45166i	0.0322429	+	0.0992336i
$215$		0			0
$216$	−0.325879	+	1.00295i	−0.0221733	+	0.0682423i
$217$	0.0914951	+	0.0664751i	0.00621109	+	0.00451262i
$218$	−6.58147			−0.445753
$219$	−8.39935	−	6.10249i	−0.567576	−	0.412368i
$220$		0			0
$221$	−4.95590	+	3.60067i	−0.333370	+	0.242207i
$222$	45.4441	−	33.0170i	3.05001	−	2.21596i
$223$	−7.06578	−	21.7462i	−0.473159	−	1.45624i	−0.848424	−	0.529317i	$-0.822448\pi$
$223$	−7.06578	−	21.7462i	−0.473159	−	1.45624i	0.375264	−	0.926918i	$-0.377552\pi$
$224$	2.97776			0.198960
$225$		0			0
$226$	−1.70751			−0.113582
$227$	0.205626	+	0.632850i	0.0136478	+	0.0420037i	0.957649	−	0.287940i	$-0.0929703\pi$
$227$	0.205626	+	0.632850i	0.0136478	+	0.0420037i	−0.944001	+	0.329944i	$0.892970\pi$
$228$	−18.8733	+	13.7122i	−1.24991	+	0.908115i
$229$	18.9902	−	13.7972i	1.25491	−	0.911744i	0.256412	−	0.966567i	$-0.417459\pi$
$229$	18.9902	−	13.7972i	1.25491	−	0.911744i	0.998496	+	0.0548231i	$0.0174595\pi$
$230$		0			0
$231$	1.58151	+	1.14904i	0.104056	+	0.0756010i
$232$	0.463245			0.0304135
$233$	14.4242	+	10.4798i	0.944959	+	0.686553i	0.949609	−	0.313436i	$-0.101480\pi$
$233$	14.4242	+	10.4798i	0.944959	+	0.686553i	−0.00465012	+	0.999989i	$0.501480\pi$
$234$	−4.27489	+	13.1567i	−0.279458	+	0.860083i
$235$		0			0
$236$	−1.17942	−	3.62987i	−0.0767734	−	0.236284i
$237$	−5.32328	+	16.3834i	−0.345784	+	1.06421i
$238$	1.26343	−	3.88845i	0.0818963	−	0.252051i
$239$	−7.37641	−	22.7023i	−0.477140	−	1.46849i	−0.843049	−	0.537837i	$-0.819242\pi$
$239$	−7.37641	−	22.7023i	−0.477140	−	1.46849i	0.365909	−	0.930651i	$-0.380758\pi$
$240$		0			0
$241$	−1.30197	+	4.00704i	−0.0838670	+	0.258116i	−0.984193	−	0.177101i	$-0.943328\pi$
$241$	−1.30197	+	4.00704i	−0.0838670	+	0.258116i	0.900326	+	0.435217i	$0.143328\pi$
$242$	12.9518	+	9.41006i	0.832576	+	0.604902i
$243$	−2.87982			−0.184741
$244$	−16.1068	−	11.7023i	−1.03113	−	0.749160i
$245$		0			0
$246$	−20.6352	+	14.9923i	−1.31565	+	0.955877i
$247$	−3.38839	+	2.46181i	−0.215598	+	0.156641i
$248$	0.0104365	+	0.0321204i	0.000662721	+	0.00203965i
$249$	21.5842			1.36784
$250$		0			0
$251$	19.5741			1.23551			0.617755	−	0.786371i	$-0.288042\pi$
$251$	19.5741			1.23551			0.617755	+	0.786371i	$0.288042\pi$
$252$	−1.44590	−	4.45001i	−0.0910830	−	0.280325i
$253$	−10.2375	+	7.43797i	−0.643625	+	0.467621i
$254$	23.3327	−	16.9522i	1.46403	−	1.06368i
$255$		0			0
$256$	−12.2051	−	8.86753i	−0.762819	−	0.554220i
$257$	18.4169			1.14881			0.574407	−	0.818570i	$-0.305233\pi$
$257$	18.4169			1.14881			0.574407	+	0.818570i	$0.305233\pi$
$258$	−35.3474	−	25.6814i	−2.20063	−	1.59885i
$259$	−1.05405	+	3.24403i	−0.0654954	+	0.201574i
$260$		0			0
$261$	7.97432	+	24.5424i	0.493598	+	1.51914i
$262$	−10.3460	+	31.8417i	−0.639179	+	1.96719i
$263$	1.33635	−	4.11285i	0.0824026	−	0.253609i	−0.901364	−	0.433063i	$-0.857433\pi$
$263$	1.33635	−	4.11285i	0.0824026	−	0.253609i	0.983766	+	0.179453i	$0.0574329\pi$
$264$	0.180398	+	0.555208i	0.0111027	+	0.0341707i
$265$		0			0
$266$	0.863821	−	2.65857i	0.0529643	−	0.163007i
$267$	3.74514	+	2.72100i	0.229199	+	0.166523i
$268$	25.6243			1.56526
$269$	−3.83389	−	2.78548i	−0.233756	−	0.169834i	0.464741	−	0.885447i	$-0.346148\pi$
$269$	−3.83389	−	2.78548i	−0.233756	−	0.169834i	−0.698497	+	0.715613i	$0.746148\pi$
$270$		0			0
$271$	−8.06208	+	5.85745i	−0.489737	+	0.355815i	−0.805083	−	0.593162i	$-0.797879\pi$
$271$	−8.06208	+	5.85745i	−0.489737	+	0.355815i	0.315346	+	0.948977i	$0.397879\pi$
$272$	−17.2590	+	12.5394i	−1.04648	+	0.760311i
$273$	−0.386120	−	1.18835i	−0.0233690	−	0.0719225i
$274$	6.18577			0.373696
$275$		0			0
$276$	45.0520			2.71181
$277$	5.44155	+	16.7474i	0.326951	+	1.00625i	0.970552	+	0.240891i	$0.0774396\pi$
$277$	5.44155	+	16.7474i	0.326951	+	1.00625i	−0.643601	+	0.765361i	$0.722560\pi$
$278$	25.6094	−	18.6063i	1.53595	−	1.11593i
$279$	−1.52206	+	1.10584i	−0.0911236	+	0.0662051i
$280$		0			0
$281$	20.6270	+	14.9864i	1.23051	+	0.894014i	0.996928	−	0.0783239i	$-0.0249568\pi$
$281$	20.6270	+	14.9864i	1.23051	+	0.894014i	0.233577	+	0.972338i	$0.424957\pi$
$282$	4.93674			0.293979
$283$	−13.0255	−	9.46360i	−0.774287	−	0.562553i	0.128972	−	0.991648i	$-0.458832\pi$
$283$	−13.0255	−	9.46360i	−0.774287	−	0.562553i	−0.903259	+	0.429096i	$0.858832\pi$
$284$	7.41458	−	22.8197i	0.439974	−	1.35410i
$285$		0			0
$286$	1.21296	+	3.73311i	0.0717240	+	0.220744i
$287$	0.478621	−	1.47305i	0.0282521	−	0.0869511i
$288$	−15.3076	+	47.1119i	−0.902008	+	2.77610i
$289$	4.05372	+	12.4761i	0.238454	+	0.733887i
$290$		0			0
$291$	5.98147	−	18.4091i	0.350640	−	1.07916i
$292$	5.70438	+	4.14448i	0.333824	+	0.242537i
$293$	−24.9049			−1.45496			−0.727481	−	0.686128i	$-0.759309\pi$
$293$	−24.9049			−1.45496			−0.727481	+	0.686128i	$0.759309\pi$
$294$	−33.8289	−	24.5782i	−1.97294	−	1.43343i
$295$		0			0
$296$	−0.824082	+	0.598731i	−0.0478988	+	0.0348005i
$297$	−13.4851	+	9.79752i	−0.782487	+	0.568510i
$298$	9.24081	+	28.4403i	0.535306	+	1.64750i
$299$	8.08836			0.467762
$300$		0			0
$301$	2.65313			0.152924
$302$	−0.443056	−	1.36359i	−0.0254950	−	0.0784655i
$303$	−29.9826	+	21.7836i	−1.72245	+	1.25144i
$304$	−11.8001	+	8.57327i	−0.676782	+	0.491711i
$305$		0			0
$306$	55.0254	+	39.9783i	3.14559	+	2.28541i
$307$	−1.74743			−0.0997311			−0.0498655	−	0.998756i	$-0.515879\pi$
$307$	−1.74743			−0.0997311			−0.0498655	+	0.998756i	$0.515879\pi$
$308$	−1.07408	−	0.780363i	−0.0612012	−	0.0444653i
$309$	−7.16879	+	22.0633i	−0.407818	+	1.25513i
$310$		0			0
$311$	5.66312	+	17.4293i	0.321126	+	0.988324i	0.973159	+	0.230133i	$0.0739162\pi$
$311$	5.66312	+	17.4293i	0.321126	+	0.988324i	−0.652033	+	0.758190i	$0.726084\pi$
$312$	0.115307	−	0.354879i	0.00652798	−	0.0200911i
$313$	−1.02210	+	3.14569i	−0.0577724	+	0.177805i	−0.975778	−	0.218761i	$-0.929798\pi$
$313$	−1.02210	+	3.14569i	−0.0577724	+	0.177805i	0.918006	+	0.396566i	$0.129798\pi$
$314$	13.7335	+	42.2673i	0.775025	+	2.38528i
$315$		0			0
$316$	3.61528	−	11.1267i	0.203375	−	0.625925i
$317$	−0.808243	−	0.587223i	−0.0453954	−	0.0329817i	0.564856	−	0.825189i	$-0.308932\pi$
$317$	−0.808243	−	0.587223i	−0.0453954	−	0.0329817i	−0.610252	+	0.792208i	$0.708932\pi$
$318$	−23.8534			−1.33763
$319$	5.92368	+	4.30380i	0.331662	+	0.240967i
$320$		0			0
$321$	1.85545	−	1.34806i	0.103561	−	0.0752416i
$322$	−4.36741	+	3.17311i	−0.243386	+	0.176830i
$323$	6.36328	+	19.5842i	0.354063	+	1.08969i
$324$	21.4030			1.18905
$325$		0			0
$326$	26.5037			1.46790
$327$	3.05589	+	9.40506i	0.168991	+	0.520101i
$328$	0.374198	−	0.271871i	0.0206616	−	0.0150116i
$329$	−0.242525	+	0.176205i	−0.0133709	+	0.00971449i
$330$		0			0
$331$	11.4888	+	8.34711i	0.631482	+	0.458798i	0.856913	−	0.515461i	$-0.172379\pi$
$331$	11.4888	+	8.34711i	0.631482	+	0.458798i	−0.225431	+	0.974259i	$0.572379\pi$
$332$	−14.6588			−0.804508
$333$	−45.9062	−	33.3528i	−2.51564	−	1.82772i
$334$	−6.47653	+	19.9327i	−0.354380	+	1.09067i
$335$		0			0
$336$	−1.34467	−	4.13846i	−0.0733575	−	0.225771i
$337$	−4.06450	+	12.5092i	−0.221407	+	0.681422i	0.777229	+	0.629218i	$0.216625\pi$
$337$	−4.06450	+	12.5092i	−0.221407	+	0.681422i	−0.998636	+	0.0522040i	$0.983375\pi$
$338$	−7.31405	+	22.5103i	−0.397832	+	1.22440i
$339$	0.792825	+	2.44006i	0.0430603	+	0.132526i
$340$		0			0
$341$	−0.164961	+	0.507697i	−0.00893312	+	0.0274933i
$342$	37.6213	+	27.3335i	2.03433	+	1.47803i
$343$	5.12896			0.276938
$344$	0.640989	+	0.465706i	0.0345598	+	0.0251092i
$345$		0			0
$346$	−14.9754	+	10.8803i	−0.805082	+	0.584926i
$347$	10.9601	−	7.96299i	0.588370	−	0.427476i	−0.253362	−	0.967372i	$-0.581536\pi$
$347$	10.9601	−	7.96299i	0.588370	−	0.427476i	0.841732	+	0.539896i	$0.181536\pi$
$348$	−8.05554	−	24.7924i	−0.431822	−	1.32901i
$349$	−32.0976			−1.71814			−0.859072	−	0.511854i	$-0.828959\pi$
$349$	−32.0976			−1.71814			−0.859072	+	0.511854i	$0.828959\pi$
$350$		0			0
$351$	10.6542			0.568681
$352$	4.34340	+	13.3676i	0.231504	+	0.712496i
$353$	14.8149	−	10.7637i	0.788518	−	0.572892i	−0.119005	−	0.992894i	$-0.537971\pi$
$353$	14.8149	−	10.7637i	0.788518	−	0.572892i	0.907523	+	0.420002i	$0.137971\pi$
$354$	−9.15519	+	6.65164i	−0.486593	+	0.353531i
$355$		0			0
$356$	−2.54349	−	1.84796i	−0.134805	−	0.0979415i
$357$	−6.14332			−0.325139
$358$	35.3307	+	25.6692i	1.86728	+	1.35666i
$359$	−4.46111	+	13.7299i	−0.235448	+	0.724635i	0.761613	+	0.648032i	$0.224408\pi$
$359$	−4.46111	+	13.7299i	−0.235448	+	0.724635i	−0.997062	+	0.0766035i	$0.975592\pi$
$360$		0			0
$361$	−1.52069	−	4.68020i	−0.0800364	−	0.246327i
$362$	6.70047	−	20.6219i	0.352169	−	1.08386i
$363$	7.43342	−	22.8777i	0.390153	−	1.20077i
$364$	0.262232	+	0.807066i	0.0137447	+	0.0423017i
$365$		0			0
$366$	−18.2414	+	56.1413i	−0.953495	+	2.93455i
$367$	8.42431	+	6.12062i	0.439745	+	0.319494i	0.785534	−	0.618819i	$-0.212389\pi$
$367$	8.42431	+	6.12062i	0.439745	+	0.319494i	−0.345788	+	0.938312i	$0.612389\pi$
$368$	28.1678			1.46835
$369$	20.8450	+	15.1448i	1.08515	+	0.788407i
$370$		0			0
$371$	1.17184	−	0.851389i	0.0608387	−	0.0442019i
$372$	1.53757	−	1.11711i	0.0797192	−	0.0579194i
$373$	−3.09711	−	9.53194i	−0.160363	−	0.493545i	0.838302	−	0.545206i	$-0.183549\pi$
$373$	−3.09711	−	9.53194i	−0.160363	−	0.493545i	−0.998665	+	0.0516608i	$0.983549\pi$
$374$	19.2987			0.997912
$375$		0			0
$376$	−0.0895228			−0.00461679
$377$	−1.44624	−	4.45108i	−0.0744853	−	0.229242i
$378$	−5.75289	+	4.17972i	−0.295896	+	0.214981i
$379$	−11.5685	+	8.40503i	−0.594236	+	0.431738i	−0.843828	−	0.536613i	$-0.819703\pi$
$379$	−11.5685	+	8.40503i	−0.594236	+	0.431738i	0.249592	+	0.968351i	$0.419703\pi$
$380$		0			0
$381$	−35.0589	−	25.4718i	−1.79612	−	1.30496i
$382$	−7.73131			−0.395568
$383$	4.07506	+	2.96070i	0.208226	+	0.151285i	0.687011	−	0.726647i	$-0.258923\pi$
$383$	4.07506	+	2.96070i	0.208226	+	0.151285i	−0.478785	+	0.877932i	$0.658923\pi$
$384$	0.826099	−	2.54247i	0.0421567	−	0.129745i
$385$		0			0
$386$	6.55447	+	20.1726i	0.333614	+	1.02676i
$387$	−13.6388	+	41.9759i	−0.693299	+	2.13375i
$388$	−4.06229	+	12.5024i	−0.206231	+	0.634715i
$389$	3.13115	+	9.63668i	0.158755	+	0.488599i	0.998522	−	0.0543486i	$-0.0173082\pi$
$389$	3.13115	+	9.63668i	0.158755	+	0.488599i	−0.839767	+	0.542948i	$0.817308\pi$
$390$		0			0
$391$	12.2887	−	37.8207i	0.621467	−	1.91268i
$392$	0.613454	+	0.445700i	0.0309841	+	0.0225113i
$393$	50.3064			2.53762
$394$	−15.7257	−	11.4254i	−0.792248	−	0.575602i
$395$		0			0
$396$	17.8678	−	12.9817i	0.897889	−	0.652355i
$397$	15.9117	−	11.5605i	0.798584	−	0.580205i	−0.111914	−	0.993718i	$-0.535698\pi$
$397$	15.9117	−	11.5605i	0.798584	−	0.580205i	0.910498	+	0.413513i	$0.135698\pi$
$398$	−9.86044	−	30.3473i	−0.494259	−	1.52117i
$399$	−4.20024			−0.210275
$400$		0			0
$401$	−23.0931			−1.15321			−0.576606	−	0.817022i	$-0.695623\pi$
$401$	−23.0931			−1.15321			−0.576606	+	0.817022i	$0.695623\pi$
$402$	−23.4780	−	72.2577i	−1.17097	−	3.60389i
$403$	0.276045	−	0.200559i	0.0137508	−	0.00999054i
$404$	20.3625	−	14.7942i	1.01307	−	0.736041i
$405$		0			0
$406$	2.52710	+	1.83604i	0.125418	+	0.0911213i
$407$	−16.1004			−0.798066
$408$	−1.48421	−	1.07834i	−0.0734792	−	0.0533858i
$409$	11.9385	−	36.7429i	0.590321	−	1.81682i	0.0135592	−	0.999908i	$-0.495684\pi$
$409$	11.9385	−	36.7429i	0.590321	−	1.81682i	0.576762	−	0.816913i	$-0.304316\pi$
$410$		0			0
$411$	−2.87216	−	8.83959i	−0.141673	−	0.436025i
$412$	4.86865	−	14.9842i	0.239861	−	0.738217i
$413$	0.212349	−	0.653545i	0.0104490	−	0.0321588i
$414$	−27.7513	−	85.4098i	−1.36390	−	4.19766i
$415$		0			0
$416$	2.77622	−	8.54434i	0.136116	−	0.418921i
$417$	−38.4797	−	27.9571i	−1.88436	−	1.36907i
$418$	13.1947			0.645373
$419$	8.72857	+	6.34167i	0.426418	+	0.309811i	0.780215	−	0.625511i	$-0.215110\pi$
$419$	8.72857	+	6.34167i	0.426418	+	0.309811i	−0.353797	+	0.935322i	$0.615110\pi$
$420$		0			0
$421$	−26.2567	+	19.0766i	−1.27967	+	0.929736i	−0.999543	−	0.0302271i	$-0.990377\pi$
$421$	−26.2567	+	19.0766i	−1.27967	+	0.929736i	−0.280128	+	0.959963i	$0.590377\pi$
$422$	−11.8127	+	8.58240i	−0.575031	+	0.417785i
$423$	−1.54105	−	4.74286i	−0.0749284	−	0.230606i
$424$	0.432557			0.0210068
$425$		0			0
$426$	−71.1426			−3.44687
$427$	−1.10769	−	3.40912i	−0.0536048	−	0.164979i
$428$	−1.26012	+	0.915532i	−0.0609102	+	0.0442539i
$429$	4.77150	−	3.46670i	0.230370	−	0.167374i
$430$		0			0
$431$	−11.1580	−	8.10676i	−0.537462	−	0.390489i	0.285680	−	0.958325i	$-0.407781\pi$
$431$	−11.1580	−	8.10676i	−0.537462	−	0.390489i	−0.823141	+	0.567836i	$0.807781\pi$
$432$	37.1035			1.78514
$433$	−17.0800	−	12.4093i	−0.820812	−	0.596355i	0.0961332	−	0.995368i	$-0.469353\pi$
$433$	−17.0800	−	12.4093i	−0.820812	−	0.596355i	−0.916945	+	0.399014i	$0.869353\pi$
$434$	−0.0703738	+	0.216588i	−0.00337805	+	0.0103966i
$435$		0			0
$436$	−2.07539	−	6.38741i	−0.0993933	−	0.305901i
$437$	8.40189	−	25.8584i	0.401917	−	1.23697i
$438$	6.46039	−	19.8830i	0.308689	−	0.950048i
$439$	11.2314	+	34.5668i	0.536047	+	1.64978i	0.741376	+	0.671090i	$0.234173\pi$
$439$	11.2314	+	34.5668i	0.536047	+	1.64978i	−0.205329	+	0.978693i	$0.565827\pi$
$440$		0			0
$441$	−13.0529	+	40.1727i	−0.621567	+	1.91299i
$442$	−9.97954	−	7.25056i	−0.474678	−	0.344874i
$443$	−6.38810			−0.303508			−0.151754	−	0.988418i	$-0.548492\pi$
$443$	−6.38810			−0.303508			−0.151754	+	0.988418i	$0.548492\pi$
$444$	46.3738	+	33.6925i	2.20080	+	1.59898i
$445$		0			0
$446$	37.2498	−	27.0635i	1.76383	−	1.28150i
$447$	36.3511	−	26.4106i	1.71935	−	1.24918i
$448$	0.964095	+	2.96718i	0.0455492	+	0.140186i
$449$	−35.1628			−1.65943			−0.829717	−	0.558185i	$-0.811498\pi$
$449$	−35.1628			−1.65943			−0.829717	+	0.558185i	$0.811498\pi$
$450$		0			0
$451$	7.31084			0.344254
$452$	−0.538443	−	1.65716i	−0.0253262	−	0.0779462i
$453$	−1.74287	+	1.26627i	−0.0818874	+	0.0594947i
$454$	−1.08403	+	0.787593i	−0.0508760	+	0.0369636i
$455$		0			0
$456$	−1.01477	−	0.737271i	−0.0475208	−	0.0345259i
$457$	−22.2994			−1.04312			−0.521561	−	0.853214i	$-0.674650\pi$
$457$	−22.2994			−1.04312			−0.521561	+	0.853214i	$0.674650\pi$
$458$	38.2400	+	27.7830i	1.78684	+	1.29821i
$459$	16.1871	−	49.8186i	0.755547	−	2.32533i
$460$		0			0
$461$	−0.582623	−	1.79313i	−0.0271355	−	0.0835144i	0.936572	−	0.350476i	$-0.113980\pi$
$461$	−0.582623	−	1.79313i	−0.0271355	−	0.0835144i	−0.963707	+	0.266962i	$0.913980\pi$
$462$	−1.21643	+	3.74377i	−0.0565932	+	0.174176i
$463$	3.99100	−	12.2830i	0.185478	−	0.570842i	−0.814479	−	0.580194i	$-0.802977\pi$
$463$	3.99100	−	12.2830i	0.185478	−	0.570842i	0.999956	+	0.00935195i	$0.00297686\pi$
$464$	−5.03655	−	15.5009i	−0.233816	−	0.719612i
$465$		0			0
$466$	−11.0944	+	34.1451i	−0.513938	+	1.58174i
$467$	−2.11813	−	1.53891i	−0.0980155	−	0.0712125i	0.537698	−	0.843137i	$-0.319294\pi$
$467$	−2.11813	−	1.53891i	−0.0980155	−	0.0712125i	−0.635714	+	0.771925i	$0.719294\pi$
$468$	−14.1168			−0.652551
$469$	3.73245	+	2.71179i	0.172349	+	0.125219i
$470$		0			0
$471$	54.0242	−	39.2509i	2.48930	−	1.80858i
$472$	0.166020	−	0.120621i	0.00764170	−	0.00555202i
$473$	3.86989	+	11.9103i	0.177938	+	0.547636i
$474$	−34.6885			−1.59329
$475$		0			0
$476$	4.17221			0.191233
$477$	7.44606	+	22.9166i	0.340932	+	1.04928i
$478$	38.8874	−	28.2533i	1.77867	−	1.29228i
$479$	−5.44724	+	3.95765i	−0.248891	+	0.180830i	−0.705235	−	0.708974i	$-0.749159\pi$
$479$	−5.44724	+	3.95765i	−0.248891	+	0.180830i	0.456344	+	0.889803i	$0.349159\pi$
$480$		0			0
$481$	8.32566	+	6.04895i	0.379617	+	0.275808i
$482$	−8.48409			−0.386440
$483$	6.56231	+	4.76779i	0.298595	+	0.216942i
$484$	−5.04838	+	15.5373i	−0.229472	+	0.706241i
$485$		0			0
$486$	−1.79199	−	5.51519i	−0.0812865	−	0.250174i
$487$	1.71750	−	5.28592i	0.0778274	−	0.239528i	−0.904572	−	0.426321i	$-0.859809\pi$
$487$	1.71750	−	5.28592i	0.0778274	−	0.239528i	0.982399	+	0.186793i	$0.0598094\pi$
$488$	0.330790	−	1.01807i	0.0149741	−	0.0460857i
$489$	−12.3061	−	37.8744i	−0.556503	−	1.71274i
$490$		0			0
$491$	−1.71566	+	5.28026i	−0.0774266	+	0.238295i	−0.982277	−	0.187435i	$-0.939983\pi$
$491$	−1.71566	+	5.28026i	−0.0774266	+	0.238295i	0.904850	+	0.425730i	$0.139983\pi$
$492$	−21.0574	−	15.2991i	−0.949339	−	0.689735i
$493$	−23.0103			−1.03633
$494$	−6.82310	−	4.95727i	−0.306986	−	0.223038i
$495$		0			0
$496$	0.961330	−	0.698447i	0.0431650	−	0.0313612i
$497$	3.49499	−	2.53926i	0.156772	−	0.113901i
$498$	13.4310	+	41.3362i	0.601856	+	1.85232i
$499$	19.2580			0.862107			0.431054	−	0.902326i	$-0.358142\pi$
$499$	19.2580			0.862107			0.431054	+	0.902326i	$0.358142\pi$
$500$		0			0
$501$	31.4914			1.40693
$502$	12.1802	+	37.4867i	0.543628	+	1.67311i
$503$	25.2061	−	18.3133i	1.12389	−	0.816551i	0.139093	−	0.990279i	$-0.455581\pi$
$503$	25.2061	−	18.3133i	1.12389	−	0.816551i	0.984794	+	0.173728i	$0.0555814\pi$
$504$	0.203531	−	0.147874i	0.00906601	−	0.00658684i
$505$		0			0
$506$	−20.6149	−	14.9776i	−0.916445	−	0.665836i
$507$	35.5638			1.57944
$508$	23.8101	+	17.2990i	1.05640	+	0.767521i
$509$	−6.55889	+	20.1862i	−0.290718	+	0.894737i	0.693909	+	0.720063i	$0.255887\pi$
$509$	−6.55889	+	20.1862i	−0.290718	+	0.894737i	−0.984626	+	0.174674i	$0.944113\pi$
$510$		0			0
$511$	0.392300	+	1.20737i	0.0173543	+	0.0534111i
$512$	9.93366	−	30.5727i	0.439010	−	1.35113i
$513$	11.0672	−	34.0614i	0.488630	−	1.50385i
$514$	11.4601	+	35.2704i	0.505482	+	1.55571i
$515$		0			0
$516$	13.7777	−	42.4035i	0.606530	−	1.86671i
$517$	−1.14476	−	0.831717i	−0.0503465	−	0.0365789i
$518$	−6.86858			−0.301788
$519$	22.5015	+	16.3483i	0.987704	+	0.717609i
$520$		0			0
$521$	−19.4241	+	14.1124i	−0.850986	+	0.618277i	−0.925418	−	0.378949i	$-0.876286\pi$
$521$	−19.4241	+	14.1124i	−0.850986	+	0.618277i	0.0744320	+	0.997226i	$0.476286\pi$
$522$	−42.0395	+	30.5434i	−1.84002	+	1.33685i
$523$	−7.05145	−	21.7021i	−0.308338	−	0.948968i	−0.978410	−	0.206672i	$-0.933737\pi$
$523$	−7.05145	−	21.7021i	−0.308338	−	0.948968i	0.670072	−	0.742296i	$-0.266263\pi$
$524$	−34.1654			−1.49252
$525$		0			0
$526$	8.70813			0.379692
$527$	−0.518404	−	1.59548i	−0.0225820	−	0.0695003i
$528$	16.6168	−	12.0728i	0.723153	−	0.525402i
$529$	−23.8719	+	17.3440i	−1.03791	+	0.754085i
$530$		0			0
$531$	9.24829	+	6.71928i	0.401342	+	0.291592i
$532$	2.85257			0.123675
$533$	−3.78051	−	2.74670i	−0.163752	−	0.118973i
$534$	−2.88058	+	8.86553i	−0.124655	+	0.383649i
$535$		0			0
$536$	0.425749	+	1.31032i	0.0183895	+	0.0565972i
$537$	20.2773	−	62.4070i	0.875028	−	2.69306i
$538$	2.94885	−	9.07562i	0.127134	−	0.391278i
$539$	3.70365	+	11.3987i	0.159527	+	0.490975i
$540$		0			0
$541$	8.50020	−	26.1609i	0.365452	−	1.12475i	−0.584245	−	0.811577i	$-0.698609\pi$
$541$	8.50020	−	26.1609i	0.365452	−	1.12475i	0.949697	−	0.313169i	$-0.101391\pi$
$542$	−16.2344	−	11.7950i	−0.697326	−	0.506637i
$543$	−32.5803			−1.39816
$544$	−35.7349	−	25.9629i	−1.53212	−	1.11315i
$545$		0			0
$546$	2.03557	−	1.47893i	0.0871143	−	0.0632922i
$547$	0.196772	−	0.142963i	0.00841338	−	0.00611267i	−0.583571	−	0.812062i	$-0.698345\pi$
$547$	0.196772	−	0.142963i	0.00841338	−	0.00611267i	0.591984	+	0.805950i	$0.298345\pi$
$548$	1.95061	+	6.00337i	0.0833261	+	0.256451i
$549$	59.6308			2.54498
$550$		0			0
$551$	−15.7323			−0.670220
$552$	0.748541	+	2.30377i	0.0318600	+	0.0980550i
$553$	1.70413	−	1.23812i	0.0724668	−	0.0526502i
$554$	−28.6871	+	20.8424i	−1.21880	+	0.885508i
$555$		0			0
$556$	26.1333	+	18.9870i	1.10830	+	0.805226i
$557$	−27.7280			−1.17487			−0.587436	−	0.809271i	$-0.699862\pi$
$557$	−27.7280			−1.17487			−0.587436	+	0.809271i	$0.699862\pi$
$558$	−3.06493	−	2.22680i	−0.129749	−	0.0942682i
$559$	2.47357	−	7.61285i	0.104621	−	0.321989i
$560$		0			0
$561$	−8.96072	−	27.5783i	−0.378322	−	1.16436i
$562$	−15.8654	+	48.8285i	−0.669239	+	2.05971i
$563$	3.83333	−	11.7978i	0.161556	−	0.497217i	−0.837210	−	0.546881i	$-0.815815\pi$
$563$	3.83333	−	11.7978i	0.161556	−	0.497217i	0.998766	+	0.0496637i	$0.0158150\pi$
$564$	1.55675	+	4.79118i	0.0655509	+	0.201745i
$565$		0			0
$566$	10.0186	−	30.8342i	0.421115	−	1.29606i
$567$	3.11757	+	2.26505i	0.130926	+	0.0951230i
$568$	1.29010			0.0541313
$569$	21.5259	+	15.6394i	0.902411	+	0.655640i	0.939084	−	0.343688i	$-0.111676\pi$
$569$	21.5259	+	15.6394i	0.902411	+	0.655640i	−0.0366734	+	0.999327i	$0.511676\pi$
$570$		0			0
$571$	−10.4540	+	7.59530i	−0.437488	+	0.317854i	−0.784636	−	0.619957i	$-0.787150\pi$
$571$	−10.4540	+	7.59530i	−0.437488	+	0.317854i	0.347148	+	0.937810i	$0.387150\pi$
$572$	−3.24054	+	2.35439i	−0.135494	+	0.0984421i
$573$	3.58978	+	11.0482i	0.149965	+	0.461545i
$574$	3.11888			0.130179
$575$		0			0
$576$	−51.9006			−2.16253
$577$	8.75852	+	26.9560i	0.364622	+	1.12219i	0.950217	+	0.311588i	$0.100861\pi$
$577$	8.75852	+	26.9560i	0.364622	+	1.12219i	−0.585595	+	0.810604i	$0.699139\pi$
$578$	−21.3706	+	15.5267i	−0.888901	+	0.645825i
$579$	25.7837	−	18.7330i	1.07153	−	0.778516i
$580$		0			0
$581$	−2.13521	−	1.55132i	−0.0885836	−	0.0643597i
$582$	38.9775			1.61567
$583$	5.53127	+	4.01870i	0.229082	+	0.166438i
$584$	−0.117153	+	0.360559i	−0.00484781	+	0.0149200i
$585$		0			0
$586$	−15.4973	−	47.6958i	−0.640187	−	1.97029i
$587$	−2.59230	+	7.97827i	−0.106996	+	0.329299i	−0.990194	−	0.139702i	$-0.955386\pi$
$587$	−2.59230	+	7.97827i	−0.106996	+	0.329299i	0.883198	+	0.469000i	$0.155386\pi$
$588$	13.1859	−	40.5819i	0.543776	−	1.67357i
$589$	−0.354437	−	1.09085i	−0.0146043	−	0.0449475i
$590$		0			0
$591$	−9.02540	+	27.7773i	−0.371255	+	1.14261i
$592$	28.9942	+	21.0655i	1.19165	+	0.865787i
$593$	30.9031			1.26904			0.634518	−	0.772908i	$-0.281199\pi$
$593$	30.9031			1.26904			0.634518	+	0.772908i	$0.281199\pi$
$594$	−27.1546	−	19.7290i	−1.11417	−	0.809490i
$595$		0			0
$596$	−24.6877	+	17.9367i	−1.01125	+	0.734714i
$597$	−38.7886	+	28.1816i	−1.58751	+	1.15339i
$598$	5.03305	+	15.4901i	0.205817	+	0.633439i
$599$	32.6384			1.33357			0.666784	−	0.745251i	$-0.267671\pi$
$599$	32.6384			1.33357			0.666784	+	0.745251i	$0.267671\pi$
$600$		0			0
$601$	16.9351			0.690796			0.345398	−	0.938456i	$-0.387744\pi$
$601$	16.9351			0.690796			0.345398	+	0.938456i	$0.387744\pi$
$602$	1.65093	+	5.08105i	0.0672870	+	0.207088i
$603$	−62.0911	+	45.1118i	−2.52855	+	1.83710i
$604$	1.18367	−	0.859984i	0.0481627	−	0.0349922i
$605$		0			0
$606$	−60.3750	−	43.8650i	−2.45257	−	1.78189i
$607$	36.3044			1.47355			0.736775	−	0.676138i	$-0.236348\pi$
$607$	36.3044			1.47355			0.736775	+	0.676138i	$0.236348\pi$
$608$	−24.4323	−	17.7511i	−0.990860	−	0.719902i
$609$	1.45037	−	4.46378i	0.0587720	−	0.180882i
$610$		0			0
$611$	0.279489	+	0.860178i	0.0113069	+	0.0347991i
$612$	−21.4478	+	66.0096i	−0.866977	+	2.66828i
$613$	−9.51589	+	29.2869i	−0.384343	+	1.18289i	0.552612	+	0.833439i	$0.313631\pi$
$613$	−9.51589	+	29.2869i	−0.384343	+	1.18289i	−0.936956	+	0.349449i	$0.886369\pi$
$614$	−1.08735	−	3.34653i	−0.0438820	−	0.135055i
$615$		0			0
$616$	0.0220586	−	0.0678895i	0.000888768	−	0.00273535i
$617$	28.5776	+	20.7628i	1.15049	+	0.835879i	0.988546	−	0.150921i	$-0.0482238\pi$
$617$	28.5776	+	20.7628i	1.15049	+	0.835879i	0.161943	+	0.986800i	$0.448224\pi$
$618$	−46.7145			−1.87913
$619$	−3.19641	−	2.32233i	−0.128475	−	0.0933423i	0.521692	−	0.853134i	$-0.325301\pi$
$619$	−3.19641	−	2.32233i	−0.128475	−	0.0933423i	−0.650167	+	0.759792i	$0.725301\pi$
$620$		0			0
$621$	−55.9550	+	40.6537i	−2.24540	+	1.63138i
$622$	−29.8551	+	21.6910i	−1.19708	+	0.869731i
$623$	−0.174920	−	0.538349i	−0.00700802	−	0.0215685i
$624$	−13.1285			−0.525560
$625$		0			0
$626$	−6.66037			−0.266202
$627$	−6.12652	−	18.8555i	−0.244670	−	0.753016i
$628$	−36.6903	+	26.6571i	−1.46410	+	1.06373i
$629$	40.9338	−	29.7401i	1.63214	−	1.18582i
$630$		0			0
$631$	−10.9434	−	7.95086i	−0.435651	−	0.316519i	0.348254	−	0.937400i	$-0.386775\pi$
$631$	−10.9434	−	7.95086i	−0.435651	−	0.316519i	−0.783904	+	0.620882i	$0.786775\pi$
$632$	0.629040			0.0250219
$633$	17.7493	+	12.8956i	0.705470	+	0.512554i
$634$	0.621663	−	1.91328i	0.0246894	−	0.0759861i
$635$		0			0
$636$	−7.52191	−	23.1501i	−0.298263	−	0.917959i
$637$	2.36731	−	7.28582i	0.0937962	−	0.288675i
$638$	−4.55622	+	14.0226i	−0.180382	+	0.555160i
$639$	22.2078	+	68.3487i	0.878528	+	2.70383i
$640$		0			0
$641$	−11.1638	+	34.3587i	−0.440945	+	1.35709i	0.445925	+	0.895070i	$0.352875\pi$
$641$	−11.1638	+	34.3587i	−0.440945	+	1.35709i	−0.886870	+	0.462019i	$0.847125\pi$
$642$	3.73626	+	2.71455i	0.147459	+	0.107135i
$643$	7.35135			0.289909			0.144954	−	0.989438i	$-0.453696\pi$
$643$	7.35135			0.289909			0.144954	+	0.989438i	$0.453696\pi$
$644$	−4.45676	−	3.23803i	−0.175621	−	0.127596i
$645$		0			0
$646$	−33.5463	+	24.3728i	−1.31986	+	0.958936i
$647$	35.3544	−	25.6864i	1.38992	−	1.00984i	0.394049	−	0.919089i	$-0.371074\pi$
$647$	35.3544	−	25.6864i	1.38992	−	1.00984i	0.995874	−	0.0907489i	$-0.0289261\pi$
$648$	0.355611	+	1.09446i	0.0139697	+	0.0429943i
$649$	3.24359			0.127322
$650$		0			0
$651$	0.342185			0.0134113
$652$	8.35766	+	25.7222i	0.327311	+	1.00736i
$653$	−28.9988	+	21.0689i	−1.13481	+	0.824489i	−0.986388	−	0.164435i	$-0.947420\pi$
$653$	−28.9988	+	21.0689i	−1.13481	+	0.824489i	−0.148424	+	0.988924i	$0.547420\pi$
$654$	−16.1102	+	11.7048i	−0.629959	+	0.457692i
$655$		0			0
$656$	−13.1656	−	9.56540i	−0.514032	−	0.373466i
$657$	−21.1189			−0.823925
$658$	−0.488366	−	0.354819i	−0.0190385	−	0.0138323i
$659$	0.0211105	−	0.0649714i	0.000822348	−	0.00253093i	−0.950645	−	0.310282i	$-0.899576\pi$
$659$	0.0211105	−	0.0649714i	0.000822348	−	0.00253093i	0.951467	+	0.307751i	$0.0995765\pi$
$660$		0			0
$661$	−8.14485	−	25.0673i	−0.316798	−	0.975003i	−0.975008	−	0.222169i	$-0.928686\pi$
$661$	−8.14485	−	25.0673i	−0.316798	−	0.975003i	0.658210	−	0.752834i	$-0.271314\pi$
$662$	−8.83666	+	27.1964i	−0.343446	+	1.05702i
$663$	−5.72754	+	17.6275i	−0.222439	+	0.684597i
$664$	−0.243557	−	0.749591i	−0.00945184	−	0.0290898i
$665$		0			0
$666$	35.3089	−	108.670i	1.36819	−	4.21086i
$667$	24.5796	+	17.8581i	0.951727	+	0.691470i
$668$	−21.3873			−0.827498
$669$	−55.9701	−	40.6647i	−2.16393	−	1.57219i
$670$		0			0
$671$	13.6883	−	9.94516i	0.528433	−	0.383929i
$672$	7.28900	−	5.29577i	0.281179	−	0.204289i
$673$	1.56889	+	4.82854i	0.0604762	+	0.186126i	0.976730	−	0.214471i	$-0.0688027\pi$
$673$	1.56889	+	4.82854i	0.0604762	+	0.186126i	−0.916254	+	0.400597i	$0.868803\pi$
$674$	−26.4858			−1.02019
$675$		0			0
$676$	−24.1530			−0.928962
$677$	−11.9129	−	36.6640i	−0.457848	−	1.40911i	−0.867758	−	0.496986i	$-0.834440\pi$
$677$	−11.9129	−	36.6640i	−0.457848	−	1.40911i	0.409910	−	0.912126i	$-0.365560\pi$
$678$	−4.17966	+	3.03670i	−0.160519	+	0.116624i
$679$	−1.91483	+	1.39121i	−0.0734844	+	0.0533896i
$680$		0			0
$681$	1.62882	+	1.18341i	0.0624165	+	0.0453483i
$682$	−1.07494			−0.0411618
$683$	29.6208	+	21.5207i	1.13341	+	0.823468i	0.986187	−	0.165635i	$-0.0529675\pi$
$683$	29.6208	+	21.5207i	1.13341	+	0.823468i	0.147220	+	0.989104i	$0.452968\pi$
$684$	−14.6641	+	45.1313i	−0.560694	+	1.72564i
$685$		0			0
$686$	3.19154	+	9.82254i	0.121853	+	0.375026i
$687$	21.9470	−	67.5459i	0.837331	−	2.57704i
$688$	8.61421	−	26.5118i	0.328414	−	1.01075i
$689$	−1.35044	−	4.15622i	−0.0514475	−	0.158339i
$690$		0			0
$691$	9.07794	−	27.9390i	0.345341	−	1.06285i	−0.616060	−	0.787699i	$-0.711272\pi$
$691$	9.07794	−	27.9390i	0.345341	−	1.06285i	0.961401	−	0.275151i	$-0.0887280\pi$
$692$	−15.2818	−	11.1029i	−0.580926	−	0.422067i
$693$	3.97647			0.151053
$694$	22.0701	+	16.0348i	0.837768	+	0.608674i
$695$		0			0
$696$	1.13394	−	0.823853i	0.0429818	−	0.0312281i
$697$	−18.5872	+	13.5044i	−0.704039	+	0.511514i
$698$	−19.9730	−	61.4705i	−0.755989	−	2.32669i
$699$	53.9454			2.04040
$700$		0			0
$701$	−0.566147			−0.0213831			−0.0106915	−	0.999943i	$-0.503403\pi$
$701$	−0.566147			−0.0213831			−0.0106915	+	0.999943i	$0.503403\pi$
$702$	6.62969	+	20.4041i	0.250221	+	0.770102i
$703$	27.9868	−	20.3336i	1.05554	−	0.766896i
$704$	−11.9139	+	8.65593i	−0.449021	+	0.326233i
$705$		0			0
$706$	29.8323	+	21.6745i	1.12275	+	0.815729i
$707$	4.53167			0.170431
$708$	−9.34250	−	6.78772i	−0.351113	−	0.255098i
$709$	0.203104	−	0.625089i	0.00762772	−	0.0234757i	−0.947170	−	0.320731i	$-0.896071\pi$
$709$	0.203104	−	0.625089i	0.00762772	−	0.0234757i	0.954798	+	0.297256i	$0.0960714\pi$
$710$		0			0
$711$	10.8283	+	33.3262i	0.406094	+	1.24983i
$712$	0.0522365	−	0.160767i	0.00195764	−	0.00602501i
$713$	−0.684485	+	2.10663i	−0.0256342	+	0.0788939i
$714$	−3.82273	−	11.7652i	−0.143062	−	0.440300i
$715$		0			0
$716$	−13.7712	+	42.3834i	−0.514655	+	1.58394i
$717$	−58.4307	−	42.4524i	−2.18214	−	1.58541i
$718$	−29.0702			−1.08489
$719$	−28.4007	−	20.6343i	−1.05917	−	0.769530i	−0.0852327	−	0.996361i	$-0.527163\pi$
$719$	−28.4007	−	20.6343i	−1.05917	−	0.769530i	−0.973934	+	0.226831i	$0.927163\pi$
$720$		0			0
$721$	2.29492	−	1.66736i	0.0854674	−	0.0620957i
$722$	8.01686	−	5.82459i	0.298357	−	0.216769i
$723$	3.93931	+	12.1240i	0.146505	+	0.450895i
$724$	22.1268			0.822336
$725$		0			0
$726$	48.4389			1.79774
$727$	12.7371	+	39.2007i	0.472392	+	1.45387i	0.849443	+	0.527680i	$0.176938\pi$
$727$	12.7371	+	39.2007i	0.472392	+	1.45387i	−0.377052	+	0.926192i	$0.623062\pi$
$728$	−0.0369130	+	0.0268188i	−0.00136809	+	0.000993972i
$729$	18.2303	−	13.2451i	0.675195	−	0.490558i
$730$		0			0
$731$	−31.8392	−	23.1325i	−1.17761	−	0.855587i
$732$	−60.2382			−2.22647
$733$	−32.4482	−	23.5750i	−1.19850	−	0.870763i	−0.204365	−	0.978895i	$-0.565513\pi$
$733$	−32.4482	−	23.5750i	−1.19850	−	0.870763i	−0.994137	+	0.108132i	$0.965513\pi$
$734$	−6.47959	+	19.9421i	−0.239166	+	0.736077i
$735$		0			0
$736$	18.0224	+	55.4674i	0.664316	+	2.04455i
$737$	−6.72941	+	20.7110i	−0.247881	+	0.762899i
$738$	−16.0330	+	49.3446i	−0.590184	+	1.81640i
$739$	−8.82040	−	27.1464i	−0.324464	−	0.998597i	−0.971682	−	0.236292i	$-0.924068\pi$
$739$	−8.82040	−	27.1464i	−0.324464	−	0.998597i	0.647218	−	0.762305i	$-0.275932\pi$
$740$		0			0
$741$	−3.91597	+	12.0521i	−0.143857	+	0.442745i
$742$	2.35969	+	1.71442i	0.0866270	+	0.0629382i
$743$	−29.6851			−1.08904			−0.544520	−	0.838748i	$-0.683288\pi$
$743$	−29.6851			−1.08904			−0.544520	+	0.838748i	$0.683288\pi$
$744$	0.0826709	+	0.0600640i	0.00303086	+	0.00220205i
$745$		0			0
$746$	16.3275	−	11.8627i	0.597794	−	0.434323i
$747$	35.5203	−	25.8070i	1.29962	−	0.944228i
$748$	6.08564	+	18.7297i	0.222513	+	0.684824i
$749$	−0.280439			−0.0102470
$750$		0			0
$751$	45.2113			1.64978			0.824892	−	0.565290i	$-0.191236\pi$
$751$	45.2113			1.64978			0.824892	+	0.565290i	$0.191236\pi$
$752$	0.973322	+	2.99558i	0.0354934	+	0.109237i
$753$	47.9139	−	34.8115i	1.74608	−	1.26860i
$754$	7.62438	−	5.53944i	0.277664	−	0.201734i
$755$		0			0
$756$	−5.87058	−	4.26523i	−0.213511	−	0.155125i
$757$	−5.69813			−0.207102			−0.103551	−	0.994624i	$-0.533020\pi$
$757$	−5.69813			−0.207102			−0.103551	+	0.994624i	$0.533020\pi$
$758$	−23.2952	−	16.9250i	−0.846120	−	0.614742i
$759$	−11.8315	+	36.4135i	−0.429455	+	1.32173i
$760$		0			0
$761$	−12.8645	−	39.5927i	−0.466336	−	1.43524i	−0.857294	−	0.514827i	$-0.827856\pi$
$761$	−12.8645	−	39.5927i	−0.466336	−	1.43524i	0.390958	−	0.920409i	$-0.372144\pi$
$762$	26.9657	−	82.9917i	0.976863	−	3.00647i
$763$	0.373667	−	1.15003i	0.0135277	−	0.0416338i
$764$	−2.43798	−	7.50334i	−0.0882032	−	0.271461i
$765$		0			0
$766$	−3.13434	+	9.64652i	−0.113248	+	0.348543i
$767$	−1.67729	−	1.21863i	−0.0605636	−	0.0440020i
$768$	−45.6462			−1.64712
$769$	12.8845	+	9.36110i	0.464625	+	0.337570i	0.795343	−	0.606160i	$-0.207291\pi$
$769$	12.8845	+	9.36110i	0.464625	+	0.337570i	−0.330718	+	0.943730i	$0.607291\pi$
$770$		0			0
$771$	45.0811	−	32.7534i	1.62356	−	1.17958i
$772$	−17.5109	+	12.7224i	−0.630231	+	0.457890i
$773$	14.7809	+	45.4909i	0.531632	+	1.63619i	0.750816	+	0.660511i	$0.229660\pi$
$773$	14.7809	+	45.4909i	0.531632	+	1.63619i	−0.219184	+	0.975683i	$0.570340\pi$
$774$	−88.8755			−3.19456
$775$		0			0
$776$	−0.706817			−0.0253732
$777$	3.18920	+	9.81535i	0.114412	+	0.352124i
$778$	−16.5070	+	11.9930i	−0.591803	+	0.429970i
$779$	−12.7082	+	9.23305i	−0.455319	+	0.330808i
$780$		0			0
$781$	16.4970	+	11.9857i	0.590308	+	0.428884i
$782$	80.0778			2.86358
$783$	32.3770	+	23.5233i	1.15706	+	0.840654i
$784$	8.24417	−	25.3730i	0.294435	−	0.906177i
$785$		0			0
$786$	31.3036	+	96.3425i	1.11656	+	3.43642i
$787$	−12.5325	+	38.5711i	−0.446736	+	1.37491i	0.433832	+	0.900994i	$0.357161\pi$
$787$	−12.5325	+	38.5711i	−0.446736	+	1.37491i	−0.880569	+	0.473919i	$0.842839\pi$
$788$	6.12956	−	18.8649i	0.218357	−	0.672032i
$789$	−4.04333	−	12.4441i	−0.143946	−	0.443022i
$790$		0			0
$791$	0.0969448	−	0.298365i	0.00344696	−	0.0106087i
$792$	0.960703	+	0.697991i	0.0341371	+	0.0248020i
$793$	−10.8148			−0.384044
$794$	32.0409	+	23.2790i	1.13709	+	0.826142i
$795$		0			0
$796$	26.3431	−	19.1394i	0.933707	−	0.678378i
$797$	22.5163	−	16.3590i	0.797567	−	0.579466i	−0.112632	−	0.993637i	$-0.535928\pi$
$797$	22.5163	−	16.3590i	0.797567	−	0.579466i	0.910199	+	0.414170i	$0.135928\pi$
$798$	−2.61363	−	8.04394i	−0.0925216	−	0.284752i
$799$	4.44678			0.157316
$800$		0			0
$801$	9.41656			0.332718
$802$	−14.3698	−	44.2258i	−0.507417	−	1.56167i
$803$	−4.84787	+	3.52218i	−0.171078	+	0.124295i
$804$	62.7236	−	45.5714i	2.21209	−	1.60718i
$805$		0			0
$806$	0.555864	+	0.403859i	0.0195795	+	0.0142253i
$807$	−14.3385			−0.504738
$808$	1.09484	+	0.795447i	0.0385163	+	0.0279837i
$809$	−2.54848	+	7.84342i	−0.0895998	+	0.275760i	−0.985809	−	0.167872i	$-0.946310\pi$
$809$	−2.54848	+	7.84342i	−0.0895998	+	0.275760i	0.896209	+	0.443632i	$0.146310\pi$
$810$		0			0
$811$	−5.67232	−	17.4576i	−0.199182	−	0.613019i	−0.999902	−	0.0139809i	$-0.995550\pi$
$811$	−5.67232	−	17.4576i	−0.199182	−	0.613019i	0.800720	−	0.599039i	$-0.204450\pi$
$812$	−0.985014	+	3.03156i	−0.0345672	+	0.106387i
$813$	−9.31736	+	28.6759i	−0.326774	+	1.00571i
$814$	−10.0186	−	30.8341i	−0.351152	−	1.08073i
$815$		0			0
$816$	−19.9462	+	61.3881i	−0.698257	+	2.14901i
$817$	−21.7687	−	15.8159i	−0.761591	−	0.553328i
$818$	77.7957			2.72006
$819$	−2.05627	−	1.49397i	−0.0718518	−	0.0522034i
$820$		0			0
$821$	12.8338	−	9.32434i	0.447904	−	0.325422i	−0.340863	−	0.940113i	$-0.610719\pi$
$821$	12.8338	−	9.32434i	0.447904	−	0.325422i	0.788768	+	0.614691i	$0.210719\pi$
$822$	15.1416	−	11.0010i	0.528124	−	0.383705i
$823$	10.0339	+	30.8812i	0.349761	+	1.07645i	0.958986	+	0.283455i	$0.0914807\pi$
$823$	10.0339	+	30.8812i	0.349761	+	1.07645i	−0.609225	+	0.792998i	$0.708519\pi$
$824$	0.847120			0.0295108
$825$		0			0
$826$	1.38375			0.0481468
$827$	−8.89801	−	27.3853i	−0.309414	−	0.952279i	−0.977993	−	0.208638i	$-0.933097\pi$
$827$	−8.89801	−	27.3853i	−0.309414	−	0.952279i	0.668579	−	0.743641i	$-0.266903\pi$
$828$	74.1403	−	53.8661i	2.57655	−	1.87198i
$829$	6.95127	−	5.05039i	0.241428	−	0.175407i	−0.460491	−	0.887664i	$-0.652327\pi$
$829$	6.95127	−	5.05039i	0.241428	−	0.175407i	0.701919	+	0.712257i	$0.252327\pi$
$830$		0			0
$831$	43.1041	+	31.3170i	1.49527	+	1.08637i
$832$	9.41283			0.326331
$833$	−30.4715	−	22.1388i	−1.05577	−	0.767064i
$834$	29.5968	−	91.0895i	1.02485	−	3.15417i
$835$		0			0
$836$	4.16080	+	12.8056i	0.143904	+	0.442892i
$837$	−0.901625	+	2.77492i	−0.0311647	+	0.0959151i
$838$	−6.71361	+	20.6624i	−0.231918	+	0.713769i
$839$	−14.5405	−	44.7511i	−0.501994	−	1.54498i	−0.805766	−	0.592235i	$-0.798246\pi$
$839$	−14.5405	−	44.7511i	−0.501994	−	1.54498i	0.303771	−	0.952745i	$-0.401754\pi$
$840$		0			0
$841$	−3.52901	+	10.8612i	−0.121690	+	0.374524i
$842$	−52.8722	−	38.4139i	−1.82210	−	1.32383i
$843$	77.1436			2.65697
$844$	−12.0543	−	8.75799i	−0.414927	−	0.301462i
$845$		0			0
$846$	8.12420	−	5.90257i	0.279316	−	0.202935i
$847$	−2.37964	+	1.72891i	−0.0817654	+	0.0594061i
$848$	−4.70291	−	14.4741i	−0.161499	−	0.497041i
$849$	−48.7145			−1.67188
$850$		0			0
$851$	−66.8067			−2.29011
$852$	−22.4340	−	69.0449i	−0.768577	−	2.36544i
$853$	−15.1198	+	10.9852i	−0.517693	+	0.376126i	−0.815734	−	0.578427i	$-0.803667\pi$
$853$	−15.1198	+	10.9852i	−0.517693	+	0.376126i	0.298041	+	0.954553i	$0.403667\pi$
$854$	5.83958	−	4.24270i	0.199826	−	0.145182i
$855$		0			0
$856$	−0.0677534	−	0.0492257i	−0.00231576	−	0.00168250i
$857$	−3.06228			−0.104606			−0.0523028	−	0.998631i	$-0.516656\pi$
$857$	−3.06228			−0.104606			−0.0523028	+	0.998631i	$0.516656\pi$
$858$	9.60823	+	6.98079i	0.328020	+	0.238320i
$859$	5.24289	−	16.1360i	0.178885	−	0.550552i	−0.820904	−	0.571066i	$-0.806530\pi$
$859$	5.24289	−	16.1360i	0.178885	−	0.550552i	0.999790	+	0.0205136i	$0.00653012\pi$
$860$		0			0
$861$	−1.44815	−	4.45694i	−0.0493527	−	0.151892i
$862$	8.58221	−	26.4133i	0.292311	−	0.899642i
$863$	6.76653	−	20.8252i	0.230335	−	0.708899i	−0.767371	−	0.641204i	$-0.778435\pi$
$863$	6.76653	−	20.8252i	0.230335	−	0.708899i	0.997706	−	0.0676953i	$-0.0215646\pi$
$864$	23.7397	+	73.0633i	0.807641	+	2.48566i
$865$		0			0
$866$	13.1371	−	40.4319i	0.446418	−	1.37393i
$867$	32.1107	+	23.3298i	1.09054	+	0.792322i
$868$	−0.232393			−0.00788795
$869$	8.04377	+	5.84414i	0.272866	+	0.198249i
$870$		0			0
$871$	11.2610	−	8.18160i	0.381565	−	0.277223i
$872$	0.292142	−	0.212254i	0.00989319	−	0.00718782i
$873$	−12.1672	−	37.4467i	−0.411797	−	1.26738i
$874$	54.7499			1.85194
$875$		0			0
$876$	21.3340			0.720808
$877$	−14.4719	−	44.5399i	−0.488681	−	1.50401i	−0.826578	−	0.562823i	$-0.809715\pi$
$877$	−14.4719	−	44.5399i	−0.488681	−	1.50401i	0.337896	−	0.941183i	$-0.390285\pi$
$878$	−59.2105	+	43.0189i	−1.99826	+	1.45182i
$879$	−60.9626	+	44.2919i	−2.05622	+	1.49393i
$880$		0			0
$881$	−0.0227639	−	0.0165389i	−0.000766934	−	0.000557210i	0.587402	−	0.809296i	$-0.300151\pi$
$881$	−0.0227639	−	0.0165389i	−0.000766934	−	0.000557210i	−0.588169	+	0.808738i	$0.700151\pi$
$882$	−85.0576			−2.86404
$883$	−23.6813	−	17.2055i	−0.796938	−	0.579010i	0.113076	−	0.993586i	$-0.463930\pi$
$883$	−23.6813	−	17.2055i	−0.796938	−	0.579010i	−0.910014	+	0.414577i	$0.863930\pi$
$884$	3.88983	−	11.9717i	0.130829	−	0.402651i
$885$		0			0
$886$	−3.97505	−	12.2339i	−0.133544	−	0.411007i
$887$	−6.14316	+	18.9067i	−0.206267	+	0.634825i	0.793392	+	0.608711i	$0.208313\pi$
$887$	−6.14316	+	18.9067i	−0.206267	+	0.634825i	−0.999659	+	0.0261137i	$0.991687\pi$
$888$	−0.952392	+	2.93116i	−0.0319602	+	0.0983634i
$889$	1.63746	+	5.03958i	0.0549186	+	0.169022i
$890$		0			0
$891$	−5.62080	+	17.2991i	−0.188304	+	0.579540i
$892$	38.0119	+	27.6172i	1.27273	+	0.924693i
$893$	3.04030			0.101740
$894$	73.1991	+	53.1823i	2.44815	+	1.77868i
$895$		0			0
$896$	−0.264457	+	0.192139i	−0.00883488	+	0.00641892i
$897$	19.7988	−	14.3847i	0.661063	−	0.480290i
$898$	−21.8803	−	67.3407i	−0.730156	−	2.24719i
$899$	1.28168			0.0427465
$900$		0			0
$901$	−21.4860			−0.715801
$902$	4.54923	+	14.0011i	0.151473	+	0.466186i
$903$	6.49437	−	4.71843i	0.216119	−	0.157020i
$904$	0.0757939	−	0.0550675i	0.00252087	−	0.00183152i
$905$		0			0
$906$	−3.50957	−	2.54986i	−0.116598	−	0.0847133i
$907$	14.2958			0.474685			0.237343	−	0.971426i	$-0.423724\pi$
$907$	14.2958			0.474685			0.237343	+	0.971426i	$0.423724\pi$
$908$	−1.10621	−	0.803706i	−0.0367107	−	0.0266719i
$909$	−23.2957	+	71.6968i	−0.772670	+	2.37803i
$910$		0			0
$911$	5.99507	+	18.4509i	0.198626	+	0.611307i	0.999915	+	0.0130299i	$0.00414767\pi$
$911$	5.99507	+	18.4509i	0.198626	+	0.611307i	−0.801290	+	0.598277i	$0.795852\pi$
$912$	−13.6374	+	41.9716i	−0.451579	+	1.38982i
$913$	3.84967	−	11.8481i	0.127406	−	0.392114i
$914$	−13.8760	−	42.7059i	−0.458977	−	1.41258i
$915$		0			0
$916$	−14.9052	+	45.8735i	−0.492482	+	1.51570i
$917$	−4.97655	−	3.61567i	−0.164340	−	0.119400i
$918$	105.481			3.48139
$919$	−3.47808	−	2.52697i	−0.114731	−	0.0833571i	0.528940	−	0.848659i	$-0.322590\pi$
$919$	−3.47808	−	2.52697i	−0.114731	−	0.0833571i	−0.643671	+	0.765302i	$0.722590\pi$
$920$		0			0
$921$	−4.27738	+	3.10770i	−0.140945	+	0.102402i
$922$	3.07151	−	2.23158i	0.101155	−	0.0734932i
$923$	−4.02767	−	12.3959i	−0.132572	−	0.408016i
$924$	−4.01697			−0.132149
$925$		0			0
$926$	26.0069			0.854639
$927$	14.5824	+	44.8799i	0.478948	+	1.47405i
$928$	27.3015	−	19.8357i	0.896216	−	0.651139i
$929$	−34.8134	+	25.2934i	−1.14219	+	0.829849i	−0.987423	−	0.158102i	$-0.949462\pi$
$929$	−34.8134	+	25.2934i	−1.14219	+	0.829849i	−0.154766	+	0.987951i	$0.549462\pi$
$930$		0			0
$931$	−20.8336	−	15.1365i	−0.682794	−	0.496079i
$932$	−36.6368			−1.20008
$933$	44.8592	+	32.5921i	1.46862	+	1.06702i
$934$	1.62917	−	5.01407i	0.0533081	−	0.164065i
$935$		0			0
$936$	−0.234552	−	0.721876i	−0.00766656	−	0.0235953i
$937$	−5.24737	+	16.1497i	−0.171424	+	0.527589i	−0.999452	−	0.0330976i	$-0.989463\pi$
$937$	−5.24737	+	16.1497i	−0.171424	+	0.527589i	0.828028	+	0.560687i	$0.189463\pi$
$938$	−2.87083	+	8.83551i	−0.0937359	+	0.288490i
$939$	3.09253	+	9.51781i	0.100921	+	0.310602i
$940$		0			0
$941$	−5.57614	+	17.1616i	−0.181777	+	0.559452i	−0.999878	−	0.0156227i	$-0.995027\pi$
$941$	−5.57614	+	17.1616i	−0.181777	+	0.559452i	0.818101	+	0.575074i	$0.195027\pi$
$942$	108.787	+	79.0383i	3.54447	+	2.57521i
$943$	30.3355			0.987860
$944$	−5.84119	−	4.24387i	−0.190115	−	0.138126i
$945$		0			0
$946$	−20.4015	+	14.8226i	−0.663310	+	0.481923i
$947$	5.83198	−	4.23718i	0.189514	−	0.137690i	−0.488983	−	0.872294i	$-0.662632\pi$
$947$	5.83198	−	4.23718i	0.189514	−	0.137690i	0.678496	+	0.734604i	$0.262632\pi$
$948$	−10.9386	−	33.6656i	−0.355270	−	1.09341i
$949$	3.83017			0.124333
$950$		0			0
$951$	−3.02277			−0.0980200
$952$	0.0693213	+	0.213349i	0.00224672	+	0.00691468i
$953$	11.1644	−	8.11145i	0.361652	−	0.262755i	−0.392089	−	0.919927i	$-0.628247\pi$
$953$	11.1644	−	8.11145i	0.361652	−	0.262755i	0.753741	+	0.657172i	$0.228247\pi$
$954$	−39.2546	+	28.5201i	−1.27091	+	0.923373i
$955$		0			0
$956$	39.6830	+	28.8314i	1.28344	+	0.932473i
$957$	22.1541			0.716141
$958$	−10.9689	−	7.96941i	−0.354391	−	0.257480i
$959$	−0.351201	+	1.08089i	−0.0113409	+	0.0349036i
$960$		0			0
$961$	−9.55065	−	29.3939i	−0.308086	−	0.948190i
$962$	−6.40371	+	19.7086i	−0.206464	+	0.635431i
$963$	1.44164	−	4.43691i	0.0464561	−	0.142977i
$964$	−2.67537	−	8.23393i	−0.0861677	−	0.265197i
$965$		0			0
$966$	−5.04742	+	15.5344i	−0.162398	+	0.499810i
$967$	12.0508	+	8.75541i	0.387527	+	0.281555i	0.764441	−	0.644693i	$-0.223015\pi$
$967$	12.0508	+	8.75541i	0.387527	+	0.281555i	−0.376914	+	0.926248i	$0.623015\pi$
$968$	−0.878391			−0.0282326
$969$	50.4054	+	36.6217i	1.61926	+	1.17646i
$970$		0			0
$971$	−32.1938	+	23.3902i	−1.03315	+	0.750627i	−0.968937	−	0.247309i	$-0.920454\pi$
$971$	−32.1938	+	23.3902i	−1.03315	+	0.750627i	−0.0642130	+	0.997936i	$0.520454\pi$
$972$	4.78748	−	3.47831i	0.153559	−	0.111567i
$973$	1.79723	+	5.53130i	0.0576165	+	0.177325i
$974$	11.1919			0.358611
$975$		0			0
$976$	−37.6626			−1.20555
$977$	−9.56800	−	29.4473i	−0.306107	−	0.942102i	−0.979262	−	0.202600i	$-0.935061\pi$
$977$	−9.56800	−	29.4473i	−0.306107	−	0.942102i	0.673154	−	0.739502i	$-0.264939\pi$
$978$	64.8762	−	47.1353i	2.07451	−	1.50722i
$979$	2.16159	−	1.57048i	0.0690846	−	0.0501929i
$980$		0			0
$981$	16.2740	+	11.8238i	0.519590	+	0.377504i
$982$	−11.1799			−0.356764
$983$	−22.4542	−	16.3139i	−0.716177	−	0.520333i	0.168984	−	0.985619i	$-0.445951\pi$
$983$	−22.4542	−	16.3139i	−0.716177	−	0.520333i	−0.885160	+	0.465286i	$0.845951\pi$
$984$	0.432461	−	1.33098i	0.0137864	−	0.0424301i
$985$		0			0
$986$	−14.3183	−	44.0673i	−0.455989	−	1.40339i
$987$	−0.280287	+	0.862634i	−0.00892163	+	0.0274579i
$988$	2.65951	−	8.18513i	0.0846103	−	0.260404i
$989$	16.0577	+	49.4204i	0.510604	+	1.57148i
$990$		0			0
$991$	4.64082	−	14.2830i	0.147420	−	0.453713i	−0.849894	−	0.526954i	$-0.823334\pi$
$991$	4.64082	−	14.2830i	0.147420	−	0.453713i	0.997314	+	0.0732405i	$0.0233341\pi$
$992$	1.99045	+	1.44615i	0.0631968	+	0.0459152i
$993$	42.9673			1.36353
$994$	7.03776	+	5.11323i	0.223224	+	0.162182i
$995$		0			0
$996$	−35.8821	+	26.0699i	−1.13697	+	0.826055i
$997$	−14.4926	+	10.5295i	−0.458984	+	0.333471i	−0.793133	−	0.609049i	$-0.791551\pi$
$997$	−14.4926	+	10.5295i	−0.458984	+	0.333471i	0.334149	+	0.942520i	$0.391551\pi$
$998$	11.9835	+	36.8813i	0.379330	+	1.16746i
$999$	−87.9999			−2.78419

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	625.2.d.q.126.4		16
5.2	odd	4		625.2.e.j.499.2		32
5.3	odd	4		625.2.e.j.499.7		32
5.4	even	2		625.2.d.m.126.1		16
25.2	odd	20		625.2.b.d.624.13		16
25.3	odd	20		625.2.e.j.124.2		32
25.4	even	10		625.2.d.m.501.1		16
25.6	even	5		625.2.d.p.376.1		16
25.8	odd	20		625.2.e.k.249.2		32
25.9	even	10		625.2.d.n.251.4		16
25.11	even	5		625.2.a.e.1.8	✓	8
25.12	odd	20		625.2.e.k.374.2		32
25.13	odd	20		625.2.e.k.374.7		32
25.14	even	10		625.2.a.g.1.1	yes	8
25.16	even	5		625.2.d.p.251.1		16
25.17	odd	20		625.2.e.k.249.7		32
25.19	even	10		625.2.d.n.376.4		16
25.21	even	5	inner	625.2.d.q.501.4		16
25.22	odd	20		625.2.e.j.124.7		32
25.23	odd	20		625.2.b.d.624.4		16
75.11	odd	10		5625.2.a.be.1.1		8
75.14	odd	10		5625.2.a.s.1.8		8
100.11	odd	10		10000.2.a.bn.1.7		8
100.39	odd	10		10000.2.a.be.1.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
625.2.a.e.1.8	✓	8	25.11	even	5
625.2.a.g.1.1	yes	8	25.14	even	10
625.2.b.d.624.4		16	25.23	odd	20
625.2.b.d.624.13		16	25.2	odd	20
625.2.d.m.126.1		16	5.4	even	2
625.2.d.m.501.1		16	25.4	even	10
625.2.d.n.251.4		16	25.9	even	10
625.2.d.n.376.4		16	25.19	even	10
625.2.d.p.251.1		16	25.16	even	5
625.2.d.p.376.1		16	25.6	even	5
625.2.d.q.126.4		16	1.1	even	1	trivial
625.2.d.q.501.4		16	25.21	even	5	inner
625.2.e.j.124.2		32	25.3	odd	20
625.2.e.j.124.7		32	25.22	odd	20
625.2.e.j.499.2		32	5.2	odd	4
625.2.e.j.499.7		32	5.3	odd	4
625.2.e.k.249.2		32	25.8	odd	20
625.2.e.k.249.7		32	25.17	odd	20
625.2.e.k.374.2		32	25.12	odd	20
625.2.e.k.374.7		32	25.13	odd	20
5625.2.a.s.1.8		8	75.14	odd	10
5625.2.a.be.1.1		8	75.11	odd	10
10000.2.a.be.1.2		8	100.39	odd	10
10000.2.a.bn.1.7		8	100.11	odd	10

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.d (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.622258 + 1.91511i) q^{2} +(2.44781 - 1.77844i) q^{3} +(-1.66242 + 1.20782i) q^{4} +(4.92909 + 3.58119i) q^{6} -0.369971 q^{7} +(-0.0893841 - 0.0649413i) q^{8} +(1.90189 - 5.85342i) q^{9} +O(q^{10})\)	\(q+(0.622258 + 1.91511i) q^{2} +(2.44781 - 1.77844i) q^{3} +(-1.66242 + 1.20782i) q^{4} +(4.92909 + 3.58119i) q^{6} -0.369971 q^{7} +(-0.0893841 - 0.0649413i) q^{8} +(1.90189 - 5.85342i) q^{9} +(-0.539645 - 1.66086i) q^{11} +(-1.92126 + 5.91304i) q^{12} +(-0.344932 + 1.06159i) q^{13} +(-0.230218 - 0.708537i) q^{14} +(-1.20123 + 3.69700i) q^{16} +(4.43988 + 3.22576i) q^{17} +12.3934 q^{18} +(3.03559 + 2.20548i) q^{19} +(-0.905621 + 0.657972i) q^{21} +(2.84493 - 2.06696i) q^{22} +(-2.23920 - 6.89154i) q^{23} -0.334290 q^{24} -2.24770 q^{26} +(-2.94954 - 9.07774i) q^{27} +(0.615049 - 0.446859i) q^{28} +(-3.39208 + 2.46449i) q^{29} +(-0.247303 - 0.179676i) q^{31} -8.04862 q^{32} +(-4.27469 - 3.10574i) q^{33} +(-3.41495 + 10.5101i) q^{34} +(3.90813 + 12.0280i) q^{36} +(2.84900 - 8.76833i) q^{37} +(-2.33483 + 7.18587i) q^{38} +(1.04365 + 3.21202i) q^{39} +(-1.29367 + 3.98151i) q^{41} +(-1.82362 - 1.32494i) q^{42} -7.17118 q^{43} +(2.90314 + 2.10925i) q^{44} +(11.8047 - 8.57663i) q^{46} +(0.655524 - 0.476266i) q^{47} +(3.63451 + 11.1859i) q^{48} -6.86312 q^{49} +16.6048 q^{51} +(-0.708789 - 2.18143i) q^{52} +(-3.16737 + 2.30123i) q^{53} +(15.5495 - 11.2974i) q^{54} +(0.0330695 + 0.0240264i) q^{56} +11.3529 q^{57} +(-6.83052 - 4.96266i) q^{58} +(-0.573962 + 1.76647i) q^{59} +(2.99399 + 9.21454i) q^{61} +(0.190214 - 0.585419i) q^{62} +(-0.703645 + 2.16560i) q^{63} +(-2.60586 - 8.02002i) q^{64} +(3.28789 - 10.1191i) q^{66} +(-10.0885 - 7.32972i) q^{67} -11.2771 q^{68} +(-17.7373 - 12.8869i) q^{69} +(-9.44666 + 6.86340i) q^{71} +(-0.550127 + 0.399691i) q^{72} +(-1.06035 - 3.26343i) q^{73} +18.5652 q^{74} -7.71026 q^{76} +(0.199653 + 0.614470i) q^{77} +(-5.50196 + 3.99741i) q^{78} +(-4.60610 + 3.34653i) q^{79} +(-8.42651 - 6.12222i) q^{81} -8.43005 q^{82} +(5.77129 + 4.19309i) q^{83} +(0.710813 - 2.18766i) q^{84} +(-4.46232 - 13.7336i) q^{86} +(-3.92023 + 12.0652i) q^{87} +(-0.0596226 + 0.183499i) q^{88} +(0.472794 + 1.45511i) q^{89} +(0.127615 - 0.392758i) q^{91} +(12.0462 + 8.75210i) q^{92} -0.924896 q^{93} +(1.32001 + 0.959043i) q^{94} +(-19.7015 + 14.3140i) q^{96} +(5.17562 - 3.76031i) q^{97} +(-4.27063 - 13.1437i) q^{98} -10.7480 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 5 q^{2} - 3 q^{4} + 7 q^{6} - 20 q^{7} + 5 q^{8} - 12 q^{9}+O(q^{10}) \) 16 * q + 5 * q^2 - 3 * q^4 + 7 * q^6 - 20 * q^7 + 5 * q^8 - 12 * q^9	\( 16 q + 5 q^{2} - 3 q^{4} + 7 q^{6} - 20 q^{7} + 5 q^{8} - 12 q^{9} - 3 q^{11} - 15 q^{12} + 5 q^{13} - q^{14} + q^{16} + 25 q^{17} + 10 q^{18} + 10 q^{19} + 7 q^{21} + 35 q^{22} + 15 q^{23} + 10 q^{24} + 22 q^{26} - 35 q^{28} - 8 q^{31} - 60 q^{32} - 6 q^{34} + q^{36} + 5 q^{37} + 35 q^{38} + q^{39} - 8 q^{41} + 10 q^{42} - 31 q^{44} + 42 q^{46} + 5 q^{47} + 25 q^{48} - 8 q^{49} - 28 q^{51} - 15 q^{52} + 10 q^{53} + 50 q^{54} + 35 q^{56} + 20 q^{57} - 35 q^{58} - 15 q^{59} + 17 q^{61} - 5 q^{62} - 10 q^{63} + 37 q^{64} + 44 q^{66} + 10 q^{67} - 80 q^{68} - 9 q^{69} - 13 q^{71} - 20 q^{72} - 40 q^{73} - 36 q^{74} - 20 q^{76} + 45 q^{77} - 5 q^{78} - 55 q^{79} - 19 q^{81} + 90 q^{82} + 15 q^{83} + 59 q^{84} + 7 q^{86} + 60 q^{87} - 40 q^{88} - 28 q^{91} - 45 q^{92} + 80 q^{93} + 4 q^{94} - 43 q^{96} - 40 q^{97} - 45 q^{98} - 44 q^{99}+O(q^{100}) \) 16 * q + 5 * q^2 - 3 * q^4 + 7 * q^6 - 20 * q^7 + 5 * q^8 - 12 * q^9 - 3 * q^11 - 15 * q^12 + 5 * q^13 - q^14 + q^16 + 25 * q^17 + 10 * q^18 + 10 * q^19 + 7 * q^21 + 35 * q^22 + 15 * q^23 + 10 * q^24 + 22 * q^26 - 35 * q^28 - 8 * q^31 - 60 * q^32 - 6 * q^34 + q^36 + 5 * q^37 + 35 * q^38 + q^39 - 8 * q^41 + 10 * q^42 - 31 * q^44 + 42 * q^46 + 5 * q^47 + 25 * q^48 - 8 * q^49 - 28 * q^51 - 15 * q^52 + 10 * q^53 + 50 * q^54 + 35 * q^56 + 20 * q^57 - 35 * q^58 - 15 * q^59 + 17 * q^61 - 5 * q^62 - 10 * q^63 + 37 * q^64 + 44 * q^66 + 10 * q^67 - 80 * q^68 - 9 * q^69 - 13 * q^71 - 20 * q^72 - 40 * q^73 - 36 * q^74 - 20 * q^76 + 45 * q^77 - 5 * q^78 - 55 * q^79 - 19 * q^81 + 90 * q^82 + 15 * q^83 + 59 * q^84 + 7 * q^86 + 60 * q^87 - 40 * q^88 - 28 * q^91 - 45 * q^92 + 80 * q^93 + 4 * q^94 - 43 * q^96 - 40 * q^97 - 45 * q^98 - 44 * q^99

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