LMFDB - Embedded newform 625.2.d.q.501.4

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			501.4
Root			$1.51514i$ of defining polynomial
Character	$\chi$	$=$	625.501
Dual form			625.2.d.q.126.4

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

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{5}\right)$

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	−0.447869	−	0.894099i	$-0.647817\pi$
$2$	0.622258	−	1.91511i	0.440003	−	1.35419i	0.887872	−	0.460091i	$-0.152183\pi$
$3$	2.44781	+	1.77844i	1.41325	+	1.02678i	0.992841	+	0.119447i	$0.0381122\pi$
$3$	2.44781	+	1.77844i	1.41325	+	1.02678i	0.420406	+	0.907336i	$0.361888\pi$
$4$	−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	−0.998860	−	0.0477321i	$-0.984801\pi$
$11$	−0.539645	+	1.66086i	−0.162709	+	0.500767i	0.836151	+	0.548499i	$0.184801\pi$
$12$	−1.92126	−	5.91304i	−0.554621	−	1.70695i
$13$	−0.344932	−	1.06159i	−0.0956668	−	0.294432i	0.891760	−	0.452509i	$-0.149471\pi$
$13$	−0.344932	−	1.06159i	−0.0956668	−	0.294432i	−0.987427	+	0.158076i	$0.949471\pi$
$14$	−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	0.0997024	−	0.995017i	$-0.468211\pi$
$17$	4.43988	−	3.22576i	1.07683	−	0.782363i	0.977127	+	0.212655i	$0.0682109\pi$
$18$	12.3934			2.92116
$19$	3.03559	−	2.20548i	0.696411	−	0.505972i	−0.182350	−	0.983234i	$-0.558370\pi$
$19$	3.03559	−	2.20548i	0.696411	−	0.505972i	0.878761	+	0.477261i	$0.158370\pi$
$20$		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	0.389666	+	0.920956i	$0.372590\pi$
$23$	−2.23920	+	6.89154i	−0.466905	+	1.43699i	−0.856571	+	0.516029i	$0.827410\pi$
$24$	−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	0.226470	−	0.974018i	$-0.427281\pi$
$29$	−3.39208	−	2.46449i	−0.629893	−	0.457644i	−0.856363	+	0.516374i	$0.827281\pi$
$30$		0			0
$31$	−0.247303	+	0.179676i	−0.0444170	+	0.0322708i	−0.609772	−	0.792577i	$-0.708739\pi$
$31$	−0.247303	+	0.179676i	−0.0444170	+	0.0322708i	0.565355	+	0.824848i	$0.308739\pi$
$32$	−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	0.854690	+	0.519138i	$0.173747\pi$
$37$	2.84900	+	8.76833i	0.468373	+	1.44150i	−0.386317	+	0.922366i	$0.626253\pi$
$38$	−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	−0.999822	−	0.0188649i	$-0.993995\pi$
$41$	−1.29367	−	3.98151i	−0.202038	−	0.621808i	0.797785	−	0.602943i	$-0.206005\pi$
$42$	−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	0.634567	−	0.772868i	$-0.281178\pi$
$47$	0.655524	+	0.476266i	0.0956181	+	0.0694706i	−0.538949	+	0.842338i	$0.681178\pi$
$48$	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	0.348602	−	0.937271i	$-0.386657\pi$
$53$	−3.16737	−	2.30123i	−0.435072	−	0.316098i	−0.783674	+	0.621173i	$0.786657\pi$
$54$	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	0.906718	−	0.421738i	$-0.138580\pi$
$59$	−0.573962	−	1.76647i	−0.0747235	−	0.229975i	−0.981441	+	0.191762i	$0.938580\pi$
$60$		0			0
$61$	2.99399	−	9.21454i	0.383341	−	1.17980i	−0.554336	−	0.832293i	$-0.687028\pi$
$61$	2.99399	−	9.21454i	0.383341	−	1.17980i	0.937677	−	0.347508i	$-0.112972\pi$
$62$	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	−0.997075	−	0.0764234i	$-0.975650\pi$
$67$	−10.0885	+	7.32972i	−1.23251	+	0.895468i	−0.235430	+	0.971891i	$0.575650\pi$
$68$	−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	−0.136735	−	0.990608i	$-0.543661\pi$
$71$	−9.44666	−	6.86340i	−1.12111	−	0.814535i	−0.984377	+	0.176072i	$0.943661\pi$
$72$	−0.550127	−	0.399691i	−0.0648331	−	0.0471040i
$73$	−1.06035	+	3.26343i	−0.124105	+	0.381955i	−0.993737	−	0.111745i	$-0.964356\pi$
$73$	−1.06035	+	3.26343i	−0.124105	+	0.381955i	0.869632	+	0.493700i	$0.164356\pi$
$74$	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	0.297709	−	0.954657i	$-0.403778\pi$
$79$	−4.60610	−	3.34653i	−0.518227	−	0.376514i	−0.815936	+	0.578143i	$0.803778\pi$
$80$		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	−0.224123	−	0.974561i	$-0.571952\pi$
$83$	5.77129	−	4.19309i	0.633482	−	0.460251i	0.857605	+	0.514309i	$0.171952\pi$
$84$	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	−0.922867	−	0.385120i	$-0.874160\pi$
$89$	0.472794	−	1.45511i	0.0501160	−	0.154241i	0.972983	+	0.230879i	$0.0741601\pi$
$90$		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	0.818673	−	0.574259i	$-0.194710\pi$
$97$	5.17562	+	3.76031i	0.525504	+	0.381801i	−0.293169	+	0.956061i	$0.594710\pi$
$98$	−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	0.238638	−	0.971109i	$-0.423299\pi$
$103$	−6.20298	−	4.50673i	−0.611197	−	0.444061i	−0.849836	+	0.527048i	$0.823299\pi$
$104$	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	0.890964	−	0.454075i	$-0.150030\pi$
$109$	−1.00999	−	3.10843i	−0.0967394	−	0.297733i	−0.987703	+	0.156341i	$0.950030\pi$
$110$		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	0.937975	−	0.346704i	$-0.112699\pi$
$113$	−0.262033	−	0.806455i	−0.0246500	−	0.0758649i	−0.962625	+	0.270839i	$0.912699\pi$
$114$	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	0.537976	+	0.842960i	$0.319189\pi$
$127$	−4.42590	+	13.6215i	−0.392735	+	1.20872i	−0.930711	+	0.365755i	$0.880811\pi$
$128$	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	0.183608	−	0.983000i	$-0.441222\pi$
$131$	13.4512	−	9.77284i	1.17523	−	0.853857i	0.991626	+	0.129142i	$0.0412224\pi$
$132$	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	0.983383	−	0.181543i	$-0.0581091\pi$
$137$	0.949265	+	2.92154i	0.0811012	+	0.249604i	−0.902282	+	0.431147i	$0.858109\pi$
$138$	13.6427	+	41.9880i	1.16135	+	3.57426i
$139$	−4.85775	+	14.9506i	−0.412029	+	1.26809i	0.502852	+	0.864372i	$0.332284\pi$
$139$	−4.85775	+	14.9506i	−0.412029	+	1.26809i	−0.914881	+	0.403723i	$0.867716\pi$
$140$		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	0.974259	+	0.225430i	$0.0723788\pi$
$163$	4.06725	+	12.5177i	0.318572	+	0.980462i	−0.655688	+	0.755032i	$0.727621\pi$
$164$	−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	−0.212226	−	0.977221i	$-0.568071\pi$
$167$	8.42033	−	6.11773i	0.651585	−	0.473404i	0.863811	+	0.503816i	$0.168071\pi$
$168$	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	−0.783114	−	0.621878i	$-0.786370\pi$
$173$	2.84063	−	8.74256i	0.215969	−	0.664684i	0.999083	−	0.0428065i	$-0.0136299\pi$
$174$	−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	0.999997	+	0.00251665i	$0.000801074\pi$
$179$	17.5454	+	12.7475i	1.31141	+	0.952792i	0.311409	+	0.950276i	$0.399199\pi$
$180$		0			0
$181$	−8.71149	+	6.32927i	−0.647520	+	0.470451i	−0.862425	−	0.506184i	$-0.831056\pi$
$181$	−8.71149	+	6.32927i	−0.647520	+	0.470451i	0.214906	+	0.976635i	$0.431056\pi$
$182$	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	0.898913	−	0.438128i	$-0.144358\pi$
$191$	−1.18644	−	3.65150i	−0.0858480	−	0.264213i	−0.984761	+	0.173915i	$0.944358\pi$
$192$	−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	0.273739	−	0.961804i	$-0.411740\pi$
$197$	−7.80946	−	5.67390i	−0.556401	−	0.404249i	−0.830140	+	0.557555i	$0.811740\pi$
$198$	−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	−0.843828	−	0.536613i	$-0.819704\pi$
$211$	2.24070	−	6.89617i	0.154256	−	0.474752i	0.998085	+	0.0618609i	$0.0197035\pi$
$212$	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	0.375264	+	0.926918i	$0.377552\pi$
$223$	−7.06578	+	21.7462i	−0.473159	+	1.45624i	−0.848424	+	0.529317i	$0.822448\pi$
$224$	2.97776			0.198960
$225$		0			0
$226$	−1.70751			−0.113582
$227$	0.205626	−	0.632850i	0.0136478	−	0.0420037i	−0.944001	−	0.329944i	$-0.892970\pi$
$227$	0.205626	−	0.632850i	0.0136478	−	0.0420037i	0.957649	+	0.287940i	$0.0929703\pi$
$228$	−18.8733	−	13.7122i	−1.24991	−	0.908115i
$229$	18.9902	+	13.7972i	1.25491	+	0.911744i	0.998496	−	0.0548231i	$-0.0174595\pi$
$229$	18.9902	+	13.7972i	1.25491	+	0.911744i	0.256412	+	0.966567i	$0.417459\pi$
$230$		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	−0.00465012	−	0.999989i	$-0.501480\pi$
$233$	14.4242	−	10.4798i	0.944959	−	0.686553i	0.949609	+	0.313436i	$0.101480\pi$
$234$	−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	0.365909	+	0.930651i	$0.380758\pi$
$239$	−7.37641	+	22.7023i	−0.477140	+	1.46849i	−0.843049	+	0.537837i	$0.819242\pi$
$240$		0			0
$241$	−1.30197	−	4.00704i	−0.0838670	−	0.258116i	0.900326	−	0.435217i	$-0.143328\pi$
$241$	−1.30197	−	4.00704i	−0.0838670	−	0.258116i	−0.984193	+	0.177101i	$0.943328\pi$
$242$	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	0.983766	−	0.179453i	$-0.0574329\pi$
$263$	1.33635	+	4.11285i	0.0824026	+	0.253609i	−0.901364	+	0.433063i	$0.857433\pi$
$264$	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	−0.698497	−	0.715613i	$-0.746148\pi$
$269$	−3.83389	+	2.78548i	−0.233756	+	0.169834i	0.464741	+	0.885447i	$0.346148\pi$
$270$		0			0
$271$	−8.06208	−	5.85745i	−0.489737	−	0.355815i	0.315346	−	0.948977i	$-0.397879\pi$
$271$	−8.06208	−	5.85745i	−0.489737	−	0.355815i	−0.805083	+	0.593162i	$0.797879\pi$
$272$	−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	−0.643601	−	0.765361i	$-0.722560\pi$
$277$	5.44155	−	16.7474i	0.326951	−	1.00625i	0.970552	−	0.240891i	$-0.0774396\pi$
$278$	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	0.233577	−	0.972338i	$-0.424957\pi$
$281$	20.6270	−	14.9864i	1.23051	−	0.894014i	0.996928	+	0.0783239i	$0.0249568\pi$
$282$	4.93674			0.293979
$283$	−13.0255	+	9.46360i	−0.774287	+	0.562553i	−0.903259	−	0.429096i	$-0.858832\pi$
$283$	−13.0255	+	9.46360i	−0.774287	+	0.562553i	0.128972	+	0.991648i	$0.458832\pi$
$284$	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	−0.652033	−	0.758190i	$-0.726084\pi$
$311$	5.66312	−	17.4293i	0.321126	−	0.988324i	0.973159	−	0.230133i	$-0.0739162\pi$
$312$	0.115307	+	0.354879i	0.00652798	+	0.0200911i
$313$	−1.02210	−	3.14569i	−0.0577724	−	0.177805i	0.918006	−	0.396566i	$-0.129798\pi$
$313$	−1.02210	−	3.14569i	−0.0577724	−	0.177805i	−0.975778	+	0.218761i	$0.929798\pi$
$314$	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	−0.610252	−	0.792208i	$-0.708932\pi$
$317$	−0.808243	+	0.587223i	−0.0453954	+	0.0329817i	0.564856	+	0.825189i	$0.308932\pi$
$318$	−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	−0.225431	−	0.974259i	$-0.572379\pi$
$331$	11.4888	−	8.34711i	0.631482	−	0.458798i	0.856913	+	0.515461i	$0.172379\pi$
$332$	−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	−0.998636	−	0.0522040i	$-0.983375\pi$
$337$	−4.06450	−	12.5092i	−0.221407	−	0.681422i	0.777229	−	0.629218i	$-0.216625\pi$
$338$	−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	0.841732	−	0.539896i	$-0.181536\pi$
$347$	10.9601	+	7.96299i	0.588370	+	0.427476i	−0.253362	+	0.967372i	$0.581536\pi$
$348$	−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	0.907523	−	0.420002i	$-0.137971\pi$
$353$	14.8149	+	10.7637i	0.788518	+	0.572892i	−0.119005	+	0.992894i	$0.537971\pi$
$354$	−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	−0.997062	−	0.0766035i	$-0.975592\pi$
$359$	−4.46111	−	13.7299i	−0.235448	−	0.724635i	0.761613	−	0.648032i	$-0.224408\pi$
$360$		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	−0.345788	−	0.938312i	$-0.612389\pi$
$367$	8.42431	−	6.12062i	0.439745	−	0.319494i	0.785534	+	0.618819i	$0.212389\pi$
$368$	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	−0.998665	−	0.0516608i	$-0.983549\pi$
$373$	−3.09711	+	9.53194i	−0.160363	+	0.493545i	0.838302	+	0.545206i	$0.183549\pi$
$374$	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	0.249592	−	0.968351i	$-0.419703\pi$
$379$	−11.5685	−	8.40503i	−0.594236	−	0.431738i	−0.843828	+	0.536613i	$0.819703\pi$
$380$		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	−0.478785	−	0.877932i	$-0.658923\pi$
$383$	4.07506	−	2.96070i	0.208226	−	0.151285i	0.687011	+	0.726647i	$0.258923\pi$
$384$	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	−0.839767	−	0.542948i	$-0.817308\pi$
$389$	3.13115	−	9.63668i	0.158755	−	0.488599i	0.998522	+	0.0543486i	$0.0173082\pi$
$390$		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	0.910498	−	0.413513i	$-0.135698\pi$
$397$	15.9117	+	11.5605i	0.798584	+	0.580205i	−0.111914	+	0.993718i	$0.535698\pi$
$398$	−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	0.576762	+	0.816913i	$0.304316\pi$
$409$	11.9385	+	36.7429i	0.590321	+	1.81682i	0.0135592	+	0.999908i	$0.495684\pi$
$410$		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	−0.353797	−	0.935322i	$-0.615110\pi$
$419$	8.72857	−	6.34167i	0.426418	−	0.309811i	0.780215	+	0.625511i	$0.215110\pi$
$420$		0			0
$421$	−26.2567	−	19.0766i	−1.27967	−	0.929736i	−0.280128	−	0.959963i	$-0.590377\pi$
$421$	−26.2567	−	19.0766i	−1.27967	−	0.929736i	−0.999543	+	0.0302271i	$0.990377\pi$
$422$	−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	−0.823141	−	0.567836i	$-0.807781\pi$
$431$	−11.1580	+	8.10676i	−0.537462	+	0.390489i	0.285680	+	0.958325i	$0.407781\pi$
$432$	37.1035			1.78514
$433$	−17.0800	+	12.4093i	−0.820812	+	0.596355i	−0.916945	−	0.399014i	$-0.869353\pi$
$433$	−17.0800	+	12.4093i	−0.820812	+	0.596355i	0.0961332	+	0.995368i	$0.469353\pi$
$434$	−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	−0.205329	−	0.978693i	$-0.565827\pi$
$439$	11.2314	−	34.5668i	0.536047	−	1.64978i	0.741376	−	0.671090i	$-0.234173\pi$
$440$		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	−0.963707	−	0.266962i	$-0.913980\pi$
$461$	−0.582623	+	1.79313i	−0.0271355	+	0.0835144i	0.936572	+	0.350476i	$0.113980\pi$
$462$	−1.21643	−	3.74377i	−0.0565932	−	0.174176i
$463$	3.99100	+	12.2830i	0.185478	+	0.570842i	0.999956	−	0.00935195i	$-0.00297686\pi$
$463$	3.99100	+	12.2830i	0.185478	+	0.570842i	−0.814479	+	0.580194i	$0.802977\pi$
$464$	−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	−0.635714	−	0.771925i	$-0.719294\pi$
$467$	−2.11813	+	1.53891i	−0.0980155	+	0.0712125i	0.537698	+	0.843137i	$0.319294\pi$
$468$	−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	0.456344	−	0.889803i	$-0.349159\pi$
$479$	−5.44724	−	3.95765i	−0.248891	−	0.180830i	−0.705235	+	0.708974i	$0.749159\pi$
$480$		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	0.982399	−	0.186793i	$-0.0598094\pi$
$487$	1.71750	+	5.28592i	0.0778274	+	0.239528i	−0.904572	+	0.426321i	$0.859809\pi$
$488$	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	0.904850	−	0.425730i	$-0.139983\pi$
$491$	−1.71566	−	5.28026i	−0.0774266	−	0.238295i	−0.982277	+	0.187435i	$0.939983\pi$
$492$	−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	0.984794	−	0.173728i	$-0.0555814\pi$
$503$	25.2061	+	18.3133i	1.12389	+	0.816551i	0.139093	+	0.990279i	$0.455581\pi$
$504$	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	−0.984626	−	0.174674i	$-0.944113\pi$
$509$	−6.55889	−	20.1862i	−0.290718	−	0.894737i	0.693909	−	0.720063i	$-0.255887\pi$
$510$		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	0.0744320	−	0.997226i	$-0.476286\pi$
$521$	−19.4241	−	14.1124i	−0.850986	−	0.618277i	−0.925418	+	0.378949i	$0.876286\pi$
$522$	−42.0395	−	30.5434i	−1.84002	−	1.33685i
$523$	−7.05145	+	21.7021i	−0.308338	+	0.948968i	0.670072	+	0.742296i	$0.266263\pi$
$523$	−7.05145	+	21.7021i	−0.308338	+	0.948968i	−0.978410	+	0.206672i	$0.933737\pi$
$524$	−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	0.949697	+	0.313169i	$0.101391\pi$
$541$	8.50020	+	26.1609i	0.365452	+	1.12475i	−0.584245	+	0.811577i	$0.698609\pi$
$542$	−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	0.591984	−	0.805950i	$-0.298345\pi$
$547$	0.196772	+	0.142963i	0.00841338	+	0.00611267i	−0.583571	+	0.812062i	$0.698345\pi$
$548$	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	0.998766	−	0.0496637i	$-0.0158150\pi$
$563$	3.83333	+	11.7978i	0.161556	+	0.497217i	−0.837210	+	0.546881i	$0.815815\pi$
$564$	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	−0.0366734	−	0.999327i	$-0.511676\pi$
$569$	21.5259	−	15.6394i	0.902411	−	0.655640i	0.939084	+	0.343688i	$0.111676\pi$
$570$		0			0
$571$	−10.4540	−	7.59530i	−0.437488	−	0.317854i	0.347148	−	0.937810i	$-0.387150\pi$
$571$	−10.4540	−	7.59530i	−0.437488	−	0.317854i	−0.784636	+	0.619957i	$0.787150\pi$
$572$	−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	−0.585595	−	0.810604i	$-0.699139\pi$
$577$	8.75852	−	26.9560i	0.364622	−	1.12219i	0.950217	−	0.311588i	$-0.100861\pi$
$578$	−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	0.883198	−	0.469000i	$-0.155386\pi$
$587$	−2.59230	−	7.97827i	−0.106996	−	0.329299i	−0.990194	+	0.139702i	$0.955386\pi$
$588$	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	−0.936956	−	0.349449i	$-0.886369\pi$
$613$	−9.51589	−	29.2869i	−0.384343	−	1.18289i	0.552612	−	0.833439i	$-0.313631\pi$
$614$	−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	0.161943	−	0.986800i	$-0.448224\pi$
$617$	28.5776	−	20.7628i	1.15049	−	0.835879i	0.988546	+	0.150921i	$0.0482238\pi$
$618$	−46.7145			−1.87913
$619$	−3.19641	+	2.32233i	−0.128475	+	0.0933423i	−0.650167	−	0.759792i	$-0.725301\pi$
$619$	−3.19641	+	2.32233i	−0.128475	+	0.0933423i	0.521692	+	0.853134i	$0.325301\pi$
$620$		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	−0.783904	−	0.620882i	$-0.786775\pi$
$631$	−10.9434	+	7.95086i	−0.435651	+	0.316519i	0.348254	+	0.937400i	$0.386775\pi$
$632$	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	−0.886870	−	0.462019i	$-0.847125\pi$
$641$	−11.1638	−	34.3587i	−0.440945	−	1.35709i	0.445925	−	0.895070i	$-0.352875\pi$
$642$	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	0.995874	+	0.0907489i	$0.0289261\pi$
$647$	35.3544	+	25.6864i	1.38992	+	1.00984i	0.394049	+	0.919089i	$0.371074\pi$
$648$	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	−0.148424	−	0.988924i	$-0.547420\pi$
$653$	−28.9988	−	21.0689i	−1.13481	−	0.824489i	−0.986388	+	0.164435i	$0.947420\pi$
$654$	−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	0.951467	−	0.307751i	$-0.0995765\pi$
$659$	0.0211105	+	0.0649714i	0.000822348	+	0.00253093i	−0.950645	+	0.310282i	$0.899576\pi$
$660$		0			0
$661$	−8.14485	+	25.0673i	−0.316798	+	0.975003i	0.658210	+	0.752834i	$0.271314\pi$
$661$	−8.14485	+	25.0673i	−0.316798	+	0.975003i	−0.975008	+	0.222169i	$0.928686\pi$
$662$	−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	−0.916254	−	0.400597i	$-0.868803\pi$
$673$	1.56889	−	4.82854i	0.0604762	−	0.186126i	0.976730	+	0.214471i	$0.0688027\pi$
$674$	−26.4858			−1.02019
$675$		0			0
$676$	−24.1530			−0.928962
$677$	−11.9129	+	36.6640i	−0.457848	+	1.40911i	0.409910	+	0.912126i	$0.365560\pi$
$677$	−11.9129	+	36.6640i	−0.457848	+	1.40911i	−0.867758	+	0.496986i	$0.834440\pi$
$678$	−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	0.147220	−	0.989104i	$-0.452968\pi$
$683$	29.6208	−	21.5207i	1.13341	−	0.823468i	0.986187	+	0.165635i	$0.0529675\pi$
$684$	−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	0.961401	+	0.275151i	$0.0887280\pi$
$691$	9.07794	+	27.9390i	0.345341	+	1.06285i	−0.616060	+	0.787699i	$0.711272\pi$
$692$	−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	0.954798	−	0.297256i	$-0.0960714\pi$
$709$	0.203104	+	0.625089i	0.00762772	+	0.0234757i	−0.947170	+	0.320731i	$0.896071\pi$
$710$		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	−0.973934	−	0.226831i	$-0.927163\pi$
$719$	−28.4007	+	20.6343i	−1.05917	+	0.769530i	−0.0852327	+	0.996361i	$0.527163\pi$
$720$		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	−0.377052	−	0.926192i	$-0.623062\pi$
$727$	12.7371	−	39.2007i	0.472392	−	1.45387i	0.849443	−	0.527680i	$-0.176938\pi$
$728$	−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	−0.994137	−	0.108132i	$-0.965513\pi$
$733$	−32.4482	+	23.5750i	−1.19850	+	0.870763i	−0.204365	+	0.978895i	$0.565513\pi$
$734$	−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	0.647218	+	0.762305i	$0.275932\pi$
$739$	−8.82040	+	27.1464i	−0.324464	+	0.998597i	−0.971682	+	0.236292i	$0.924068\pi$
$740$		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	0.390958	+	0.920409i	$0.372144\pi$
$761$	−12.8645	+	39.5927i	−0.466336	+	1.43524i	−0.857294	+	0.514827i	$0.827856\pi$
$762$	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	−0.330718	−	0.943730i	$-0.607291\pi$
$769$	12.8845	−	9.36110i	0.464625	−	0.337570i	0.795343	+	0.606160i	$0.207291\pi$
$770$		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	−0.219184	−	0.975683i	$-0.570340\pi$
$773$	14.7809	−	45.4909i	0.531632	−	1.63619i	0.750816	−	0.660511i	$-0.229660\pi$
$774$	−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	−0.880569	−	0.473919i	$-0.842839\pi$
$787$	−12.5325	−	38.5711i	−0.446736	−	1.37491i	0.433832	−	0.900994i	$-0.357161\pi$
$788$	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	0.910199	−	0.414170i	$-0.135928\pi$
$797$	22.5163	+	16.3590i	0.797567	+	0.579466i	−0.112632	+	0.993637i	$0.535928\pi$
$798$	−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	0.896209	−	0.443632i	$-0.146310\pi$
$809$	−2.54848	−	7.84342i	−0.0895998	−	0.275760i	−0.985809	+	0.167872i	$0.946310\pi$
$810$		0			0
$811$	−5.67232	+	17.4576i	−0.199182	+	0.613019i	0.800720	+	0.599039i	$0.204450\pi$
$811$	−5.67232	+	17.4576i	−0.199182	+	0.613019i	−0.999902	+	0.0139809i	$0.995550\pi$
$812$	−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	0.788768	−	0.614691i	$-0.210719\pi$
$821$	12.8338	+	9.32434i	0.447904	+	0.325422i	−0.340863	+	0.940113i	$0.610719\pi$
$822$	15.1416	+	11.0010i	0.528124	+	0.383705i
$823$	10.0339	−	30.8812i	0.349761	−	1.07645i	−0.609225	−	0.792998i	$-0.708519\pi$
$823$	10.0339	−	30.8812i	0.349761	−	1.07645i	0.958986	−	0.283455i	$-0.0914807\pi$
$824$	0.847120			0.0295108
$825$		0			0
$826$	1.38375			0.0481468
$827$	−8.89801	+	27.3853i	−0.309414	+	0.952279i	0.668579	+	0.743641i	$0.266903\pi$
$827$	−8.89801	+	27.3853i	−0.309414	+	0.952279i	−0.977993	+	0.208638i	$0.933097\pi$
$828$	74.1403	+	53.8661i	2.57655	+	1.87198i
$829$	6.95127	+	5.05039i	0.241428	+	0.175407i	0.701919	−	0.712257i	$-0.252327\pi$
$829$	6.95127	+	5.05039i	0.241428	+	0.175407i	−0.460491	+	0.887664i	$0.652327\pi$
$830$		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	0.303771	+	0.952745i	$0.401754\pi$
$839$	−14.5405	+	44.7511i	−0.501994	+	1.54498i	−0.805766	+	0.592235i	$0.798246\pi$
$840$		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	0.298041	−	0.954553i	$-0.403667\pi$
$853$	−15.1198	−	10.9852i	−0.517693	−	0.376126i	−0.815734	+	0.578427i	$0.803667\pi$
$854$	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	0.999790	−	0.0205136i	$-0.00653012\pi$
$859$	5.24289	+	16.1360i	0.178885	+	0.550552i	−0.820904	+	0.571066i	$0.806530\pi$
$860$		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	0.997706	+	0.0676953i	$0.0215646\pi$
$863$	6.76653	+	20.8252i	0.230335	+	0.708899i	−0.767371	+	0.641204i	$0.778435\pi$
$864$	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	0.337896	+	0.941183i	$0.390285\pi$
$877$	−14.4719	+	44.5399i	−0.488681	+	1.50401i	−0.826578	+	0.562823i	$0.809715\pi$
$878$	−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	−0.588169	−	0.808738i	$-0.700151\pi$
$881$	−0.0227639	+	0.0165389i	−0.000766934	+	0.000557210i	0.587402	+	0.809296i	$0.300151\pi$
$882$	−85.0576			−2.86404
$883$	−23.6813	+	17.2055i	−0.796938	+	0.579010i	−0.910014	−	0.414577i	$-0.863930\pi$
$883$	−23.6813	+	17.2055i	−0.796938	+	0.579010i	0.113076	+	0.993586i	$0.463930\pi$
$884$	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	−0.999659	−	0.0261137i	$-0.991687\pi$
$887$	−6.14316	−	18.9067i	−0.206267	−	0.634825i	0.793392	−	0.608711i	$-0.208313\pi$
$888$	−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	−0.801290	−	0.598277i	$-0.795852\pi$
$911$	5.99507	−	18.4509i	0.198626	−	0.611307i	0.999915	−	0.0130299i	$-0.00414767\pi$
$912$	−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	−0.643671	−	0.765302i	$-0.722590\pi$
$919$	−3.47808	+	2.52697i	−0.114731	+	0.0833571i	0.528940	+	0.848659i	$0.322590\pi$
$920$		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	−0.154766	−	0.987951i	$-0.549462\pi$
$929$	−34.8134	−	25.2934i	−1.14219	−	0.829849i	−0.987423	+	0.158102i	$0.949462\pi$
$930$		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	0.828028	−	0.560687i	$-0.189463\pi$
$937$	−5.24737	−	16.1497i	−0.171424	−	0.527589i	−0.999452	+	0.0330976i	$0.989463\pi$
$938$	−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	0.818101	−	0.575074i	$-0.195027\pi$
$941$	−5.57614	−	17.1616i	−0.181777	−	0.559452i	−0.999878	+	0.0156227i	$0.995027\pi$
$942$	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	0.678496	−	0.734604i	$-0.262632\pi$
$947$	5.83198	+	4.23718i	0.189514	+	0.137690i	−0.488983	+	0.872294i	$0.662632\pi$
$948$	−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	0.753741	−	0.657172i	$-0.228247\pi$
$953$	11.1644	+	8.11145i	0.361652	+	0.262755i	−0.392089	+	0.919927i	$0.628247\pi$
$954$	−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	−0.376914	−	0.926248i	$-0.623015\pi$
$967$	12.0508	−	8.75541i	0.387527	−	0.281555i	0.764441	+	0.644693i	$0.223015\pi$
$968$	−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	−0.0642130	−	0.997936i	$-0.520454\pi$
$971$	−32.1938	−	23.3902i	−1.03315	−	0.750627i	−0.968937	+	0.247309i	$0.920454\pi$
$972$	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	0.673154	+	0.739502i	$0.264939\pi$
$977$	−9.56800	+	29.4473i	−0.306107	+	0.942102i	−0.979262	+	0.202600i	$0.935061\pi$
$978$	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	−0.885160	−	0.465286i	$-0.845951\pi$
$983$	−22.4542	+	16.3139i	−0.716177	+	0.520333i	0.168984	+	0.985619i	$0.445951\pi$
$984$	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	0.997314	−	0.0732405i	$-0.0233341\pi$
$991$	4.64082	+	14.2830i	0.147420	+	0.453713i	−0.849894	+	0.526954i	$0.823334\pi$
$992$	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	0.334149	−	0.942520i	$-0.391551\pi$
$997$	−14.4926	−	10.5295i	−0.458984	−	0.333471i	−0.793133	+	0.609049i	$0.791551\pi$
$998$	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.501.4		16
5.2	odd	4		625.2.e.j.124.7		32
5.3	odd	4		625.2.e.j.124.2		32
5.4	even	2		625.2.d.m.501.1		16
25.2	odd	20		625.2.e.k.249.7		32
25.3	odd	20		625.2.e.k.374.7		32
25.4	even	10		625.2.d.n.251.4		16
25.6	even	5	inner	625.2.d.q.126.4		16
25.8	odd	20		625.2.e.j.499.7		32
25.9	even	10		625.2.a.g.1.1	yes	8
25.11	even	5		625.2.d.p.376.1		16
25.12	odd	20		625.2.b.d.624.13		16
25.13	odd	20		625.2.b.d.624.4		16
25.14	even	10		625.2.d.n.376.4		16
25.16	even	5		625.2.a.e.1.8	✓	8
25.17	odd	20		625.2.e.j.499.2		32
25.19	even	10		625.2.d.m.126.1		16
25.21	even	5		625.2.d.p.251.1		16
25.22	odd	20		625.2.e.k.374.2		32
25.23	odd	20		625.2.e.k.249.2		32
75.41	odd	10		5625.2.a.be.1.1		8
75.59	odd	10		5625.2.a.s.1.8		8
100.59	odd	10		10000.2.a.be.1.2		8
100.91	odd	10		10000.2.a.bn.1.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
625.2.a.e.1.8	✓	8	25.16	even	5
625.2.a.g.1.1	yes	8	25.9	even	10
625.2.b.d.624.4		16	25.13	odd	20
625.2.b.d.624.13		16	25.12	odd	20
625.2.d.m.126.1		16	25.19	even	10
625.2.d.m.501.1		16	5.4	even	2
625.2.d.n.251.4		16	25.4	even	10
625.2.d.n.376.4		16	25.14	even	10
625.2.d.p.251.1		16	25.21	even	5
625.2.d.p.376.1		16	25.11	even	5
625.2.d.q.126.4		16	25.6	even	5	inner
625.2.d.q.501.4		16	1.1	even	1	trivial
625.2.e.j.124.2		32	5.3	odd	4
625.2.e.j.124.7		32	5.2	odd	4
625.2.e.j.499.2		32	25.17	odd	20
625.2.e.j.499.7		32	25.8	odd	20
625.2.e.k.249.2		32	25.23	odd	20
625.2.e.k.249.7		32	25.2	odd	20
625.2.e.k.374.2		32	25.22	odd	20
625.2.e.k.374.7		32	25.3	odd	20
5625.2.a.s.1.8		8	75.59	odd	10
5625.2.a.be.1.1		8	75.41	odd	10
10000.2.a.be.1.2		8	100.59	odd	10
10000.2.a.bn.1.7		8	100.91	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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