LMFDB - Embedded newform 625.2.d.c.376.1

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:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			376.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	625.376
Dual form			625.2.d.c.251.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.30902 - 0.951057i) q^{2} +(0.809017 + 2.48990i) q^{3} +(0.190983 + 0.587785i) q^{4} +(1.30902 - 4.02874i) q^{6} +3.85410 q^{7} +(-0.690983 + 2.12663i) q^{8} +(-3.11803 + 2.26538i) q^{9} +O(q^{10})$	\(q+(-1.30902 - 0.951057i) q^{2} +(0.809017 + 2.48990i) q^{3} +(0.190983 + 0.587785i) q^{4} +(1.30902 - 4.02874i) q^{6} +3.85410 q^{7} +(-0.690983 + 2.12663i) q^{8} +(-3.11803 + 2.26538i) q^{9} +(-0.500000 - 0.363271i) q^{11} +(-1.30902 + 0.951057i) q^{12} +(4.42705 - 3.21644i) q^{13} +(-5.04508 - 3.66547i) q^{14} +(3.92705 - 2.85317i) q^{16} +(-0.454915 + 1.40008i) q^{17} +6.23607 q^{18} +(-0.263932 + 0.812299i) q^{19} +(3.11803 + 9.59632i) q^{21} +(0.309017 + 0.951057i) q^{22} +(1.50000 + 1.08981i) q^{23} -5.85410 q^{24} -8.85410 q^{26} +(-1.80902 - 1.31433i) q^{27} +(0.736068 + 2.26538i) q^{28} +(-0.854102 - 2.62866i) q^{29} +(0.618034 - 1.90211i) q^{31} -3.38197 q^{32} +(0.500000 - 1.53884i) q^{33} +(1.92705 - 1.40008i) q^{34} +(-1.92705 - 1.40008i) q^{36} +(-2.42705 + 1.76336i) q^{37} +(1.11803 - 0.812299i) q^{38} +(11.5902 + 8.42075i) q^{39} +(-5.23607 + 3.80423i) q^{41} +(5.04508 - 15.5272i) q^{42} -0.472136 q^{43} +(0.118034 - 0.363271i) q^{44} +(-0.927051 - 2.85317i) q^{46} +(3.59017 + 11.0494i) q^{47} +(10.2812 + 7.46969i) q^{48} +7.85410 q^{49} -3.85410 q^{51} +(2.73607 + 1.98787i) q^{52} +(2.61803 + 8.05748i) q^{53} +(1.11803 + 3.44095i) q^{54} +(-2.66312 + 8.19624i) q^{56} -2.23607 q^{57} +(-1.38197 + 4.25325i) q^{58} +(11.2812 - 8.19624i) q^{59} +(7.16312 + 5.20431i) q^{61} +(-2.61803 + 1.90211i) q^{62} +(-12.0172 + 8.73102i) q^{63} +(-3.42705 - 2.48990i) q^{64} +(-2.11803 + 1.53884i) q^{66} +(-3.54508 + 10.9106i) q^{67} -0.909830 q^{68} +(-1.50000 + 4.61653i) q^{69} +(-1.02786 - 3.16344i) q^{71} +(-2.66312 - 8.19624i) q^{72} +(0.118034 + 0.0857567i) q^{73} +4.85410 q^{74} -0.527864 q^{76} +(-1.92705 - 1.40008i) q^{77} +(-7.16312 - 22.0458i) q^{78} +(-2.07295 - 6.37988i) q^{79} +(-1.76393 + 5.42882i) q^{81} +10.4721 q^{82} +(4.00000 - 12.3107i) q^{83} +(-5.04508 + 3.66547i) q^{84} +(0.618034 + 0.449028i) q^{86} +(5.85410 - 4.25325i) q^{87} +(1.11803 - 0.812299i) q^{88} +(-2.92705 - 2.12663i) q^{89} +(17.0623 - 12.3965i) q^{91} +(-0.354102 + 1.08981i) q^{92} +5.23607 q^{93} +(5.80902 - 17.8783i) q^{94} +(-2.73607 - 8.42075i) q^{96} +(-3.28115 - 10.0984i) q^{97} +(-10.2812 - 7.46969i) q^{98} +2.38197 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 3 q^{2} + q^{3} + 3 q^{4} + 3 q^{6} + 2 q^{7} - 5 q^{8} - 8 q^{9}+O(q^{10}) $ 4 * q - 3 * q^2 + q^3 + 3 * q^4 + 3 * q^6 + 2 * q^7 - 5 * q^8 - 8 * q^9	$ 4 q - 3 q^{2} + q^{3} + 3 q^{4} + 3 q^{6} + 2 q^{7} - 5 q^{8} - 8 q^{9} - 2 q^{11} - 3 q^{12} + 11 q^{13} - 9 q^{14} + 9 q^{16} - 13 q^{17} + 16 q^{18} - 10 q^{19} + 8 q^{21} - q^{22} + 6 q^{23} - 10 q^{24} - 22 q^{26} - 5 q^{27} - 6 q^{28} + 10 q^{29} - 2 q^{31} - 18 q^{32} + 2 q^{33} + q^{34} - q^{36} - 3 q^{37} + 24 q^{39} - 12 q^{41} + 9 q^{42} + 16 q^{43} - 4 q^{44} + 3 q^{46} - 8 q^{47} + 21 q^{48} + 18 q^{49} - 2 q^{51} + 2 q^{52} + 6 q^{53} + 5 q^{56} - 10 q^{58} + 25 q^{59} + 13 q^{61} - 6 q^{62} - 19 q^{63} - 7 q^{64} - 4 q^{66} - 3 q^{67} - 26 q^{68} - 6 q^{69} - 22 q^{71} + 5 q^{72} - 4 q^{73} + 6 q^{74} - 20 q^{76} - q^{77} - 13 q^{78} - 15 q^{79} - 16 q^{81} + 24 q^{82} + 16 q^{83} - 9 q^{84} - 2 q^{86} + 10 q^{87} - 5 q^{89} + 28 q^{91} + 12 q^{92} + 12 q^{93} + 21 q^{94} - 2 q^{96} + 7 q^{97} - 21 q^{98} + 14 q^{99}+O(q^{100}) $ 4 * q - 3 * q^2 + q^3 + 3 * q^4 + 3 * q^6 + 2 * q^7 - 5 * q^8 - 8 * q^9 - 2 * q^11 - 3 * q^12 + 11 * q^13 - 9 * q^14 + 9 * q^16 - 13 * q^17 + 16 * q^18 - 10 * q^19 + 8 * q^21 - q^22 + 6 * q^23 - 10 * q^24 - 22 * q^26 - 5 * q^27 - 6 * q^28 + 10 * q^29 - 2 * q^31 - 18 * q^32 + 2 * q^33 + q^34 - q^36 - 3 * q^37 + 24 * q^39 - 12 * q^41 + 9 * q^42 + 16 * q^43 - 4 * q^44 + 3 * q^46 - 8 * q^47 + 21 * q^48 + 18 * q^49 - 2 * q^51 + 2 * q^52 + 6 * q^53 + 5 * q^56 - 10 * q^58 + 25 * q^59 + 13 * q^61 - 6 * q^62 - 19 * q^63 - 7 * q^64 - 4 * q^66 - 3 * q^67 - 26 * q^68 - 6 * q^69 - 22 * q^71 + 5 * q^72 - 4 * q^73 + 6 * q^74 - 20 * q^76 - q^77 - 13 * q^78 - 15 * q^79 - 16 * q^81 + 24 * q^82 + 16 * q^83 - 9 * q^84 - 2 * q^86 + 10 * q^87 - 5 * q^89 + 28 * q^91 + 12 * q^92 + 12 * q^93 + 21 * q^94 - 2 * q^96 + 7 * q^97 - 21 * q^98 + 14 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−1.30902	−	0.951057i	−0.925615	−	0.672499i	0.0193004	−	0.999814i	$-0.493856\pi$
$2$	−1.30902	−	0.951057i	−0.925615	−	0.672499i	−0.944915	+	0.327315i	$0.893856\pi$
$3$	0.809017	+	2.48990i	0.467086	+	1.43754i	0.856340	+	0.516413i	$0.172733\pi$
$3$	0.809017	+	2.48990i	0.467086	+	1.43754i	−0.389254	+	0.921131i	$0.627267\pi$
$4$	0.190983	+	0.587785i	0.0954915	+	0.293893i
$5$		0			0
$5$		0			0
$6$	1.30902	−	4.02874i	0.534404	−	1.64473i
$7$	3.85410			1.45671			0.728357	−	0.685198i	$-0.240284\pi$
$7$	3.85410			1.45671			0.728357	+	0.685198i	$0.240284\pi$
$8$	−0.690983	+	2.12663i	−0.244299	+	0.751876i
$9$	−3.11803	+	2.26538i	−1.03934	+	0.755128i
$10$		0			0
$11$	−0.500000	−	0.363271i	−0.150756	−	0.109530i	0.509851	−	0.860263i	$-0.329701\pi$
$11$	−0.500000	−	0.363271i	−0.150756	−	0.109530i	−0.660606	+	0.750733i	$0.729701\pi$
$12$	−1.30902	+	0.951057i	−0.377881	+	0.274546i
$13$	4.42705	−	3.21644i	1.22784	−	0.892080i	0.231116	−	0.972926i	$-0.425762\pi$
$13$	4.42705	−	3.21644i	1.22784	−	0.892080i	0.996727	+	0.0808459i	$0.0257622\pi$
$14$	−5.04508	−	3.66547i	−1.34836	−	0.979638i
$15$		0			0
$16$	3.92705	−	2.85317i	0.981763	−	0.713292i
$17$	−0.454915	+	1.40008i	−0.110333	+	0.339570i	−0.990945	−	0.134268i	$-0.957132\pi$
$17$	−0.454915	+	1.40008i	−0.110333	+	0.339570i	0.880612	+	0.473838i	$0.157132\pi$
$18$	6.23607			1.46986
$19$	−0.263932	+	0.812299i	−0.0605502	+	0.186354i	−0.976756	−	0.214353i	$-0.931236\pi$
$19$	−0.263932	+	0.812299i	−0.0605502	+	0.186354i	0.916206	+	0.400707i	$0.131236\pi$
$20$		0			0
$21$	3.11803	+	9.59632i	0.680411	+	2.09409i
$22$	0.309017	+	0.951057i	0.0658826	+	0.202766i
$23$	1.50000	+	1.08981i	0.312772	+	0.227242i	0.733085	−	0.680137i	$-0.238080\pi$
$23$	1.50000	+	1.08981i	0.312772	+	0.227242i	−0.420313	+	0.907379i	$0.638080\pi$
$24$	−5.85410			−1.19496
$25$		0			0
$26$	−8.85410			−1.73643
$27$	−1.80902	−	1.31433i	−0.348145	−	0.252942i
$28$	0.736068	+	2.26538i	0.139104	+	0.428117i
$29$	−0.854102	−	2.62866i	−0.158603	−	0.488129i	0.839905	−	0.542733i	$-0.182610\pi$
$29$	−0.854102	−	2.62866i	−0.158603	−	0.488129i	−0.998508	+	0.0546038i	$0.982610\pi$
$30$		0			0
$31$	0.618034	−	1.90211i	0.111002	−	0.341630i	−0.880090	−	0.474807i	$-0.842518\pi$
$31$	0.618034	−	1.90211i	0.111002	−	0.341630i	0.991092	+	0.133177i	$0.0425179\pi$
$32$	−3.38197			−0.597853
$33$	0.500000	−	1.53884i	0.0870388	−	0.267878i
$34$	1.92705	−	1.40008i	0.330487	−	0.240113i
$35$		0			0
$36$	−1.92705	−	1.40008i	−0.321175	−	0.233347i
$37$	−2.42705	+	1.76336i	−0.399005	+	0.289894i	−0.769135	−	0.639086i	$-0.779313\pi$
$37$	−2.42705	+	1.76336i	−0.399005	+	0.289894i	0.370131	+	0.928980i	$0.379313\pi$
$38$	1.11803	−	0.812299i	0.181369	−	0.131772i
$39$	11.5902	+	8.42075i	1.85591	+	1.34840i
$40$		0			0
$41$	−5.23607	+	3.80423i	−0.817736	+	0.594120i	−0.916063	−	0.401034i	$-0.868651\pi$
$41$	−5.23607	+	3.80423i	−0.817736	+	0.594120i	0.0983268	+	0.995154i	$0.468651\pi$
$42$	5.04508	−	15.5272i	0.778474	−	2.39590i
$43$	−0.472136			−0.0720001			−0.0360000	−	0.999352i	$-0.511462\pi$
$43$	−0.472136			−0.0720001			−0.0360000	+	0.999352i	$0.511462\pi$
$44$	0.118034	−	0.363271i	0.0177943	−	0.0547652i
$45$		0			0
$46$	−0.927051	−	2.85317i	−0.136686	−	0.420677i
$47$	3.59017	+	11.0494i	0.523680	+	1.61172i	0.766911	+	0.641753i	$0.221793\pi$
$47$	3.59017	+	11.0494i	0.523680	+	1.61172i	−0.243231	+	0.969968i	$0.578207\pi$
$48$	10.2812	+	7.46969i	1.48396	+	1.07816i
$49$	7.85410			1.12201
$50$		0			0
$51$	−3.85410			−0.539682
$52$	2.73607	+	1.98787i	0.379424	+	0.275668i
$53$	2.61803	+	8.05748i	0.359615	+	1.10678i	0.953285	+	0.302072i	$0.0976782\pi$
$53$	2.61803	+	8.05748i	0.359615	+	1.10678i	−0.593671	+	0.804708i	$0.702322\pi$
$54$	1.11803	+	3.44095i	0.152145	+	0.468255i
$55$		0			0
$56$	−2.66312	+	8.19624i	−0.355874	+	1.09527i
$57$	−2.23607			−0.296174
$58$	−1.38197	+	4.25325i	−0.181461	+	0.558480i
$59$	11.2812	−	8.19624i	1.46868	−	1.06706i	0.487688	−	0.873018i	$-0.337841\pi$
$59$	11.2812	−	8.19624i	1.46868	−	1.06706i	0.980993	−	0.194041i	$-0.0621595\pi$
$60$		0			0
$61$	7.16312	+	5.20431i	0.917143	+	0.666344i	0.942811	−	0.333327i	$-0.108171\pi$
$61$	7.16312	+	5.20431i	0.917143	+	0.666344i	−0.0256679	+	0.999671i	$0.508171\pi$
$62$	−2.61803	+	1.90211i	−0.332491	+	0.241569i
$63$	−12.0172	+	8.73102i	−1.51403	+	1.10001i
$64$	−3.42705	−	2.48990i	−0.428381	−	0.311237i
$65$		0			0
$66$	−2.11803	+	1.53884i	−0.260712	+	0.189418i
$67$	−3.54508	+	10.9106i	−0.433101	+	1.33295i	0.461919	+	0.886922i	$0.347161\pi$
$67$	−3.54508	+	10.9106i	−0.433101	+	1.33295i	−0.895020	+	0.446026i	$0.852839\pi$
$68$	−0.909830			−0.110333
$69$	−1.50000	+	4.61653i	−0.180579	+	0.555764i
$70$		0			0
$71$	−1.02786	−	3.16344i	−0.121985	−	0.375431i	0.871355	−	0.490654i	$-0.163242\pi$
$71$	−1.02786	−	3.16344i	−0.121985	−	0.375431i	−0.993340	+	0.115222i	$0.963242\pi$
$72$	−2.66312	−	8.19624i	−0.313852	−	0.965936i
$73$	0.118034	+	0.0857567i	0.0138148	+	0.0100371i	0.594671	−	0.803969i	$-0.297282\pi$
$73$	0.118034	+	0.0857567i	0.0138148	+	0.0100371i	−0.580856	+	0.814006i	$0.697282\pi$
$74$	4.85410			0.564278
$75$		0			0
$76$	−0.527864			−0.0605502
$77$	−1.92705	−	1.40008i	−0.219608	−	0.159554i
$78$	−7.16312	−	22.0458i	−0.811064	−	2.49620i
$79$	−2.07295	−	6.37988i	−0.233225	−	0.717793i	−0.997352	−	0.0727268i	$-0.976830\pi$
$79$	−2.07295	−	6.37988i	−0.233225	−	0.717793i	0.764127	−	0.645066i	$-0.223170\pi$
$80$		0			0
$81$	−1.76393	+	5.42882i	−0.195992	+	0.603203i
$82$	10.4721			1.15645
$83$	4.00000	−	12.3107i	0.439057	−	1.35128i	−0.449814	−	0.893122i	$-0.648510\pi$
$83$	4.00000	−	12.3107i	0.439057	−	1.35128i	0.888871	−	0.458157i	$-0.151490\pi$
$84$	−5.04508	+	3.66547i	−0.550464	+	0.399935i
$85$		0			0
$86$	0.618034	+	0.449028i	0.0666443	+	0.0484199i
$87$	5.85410	−	4.25325i	0.627626	−	0.455997i
$88$	1.11803	−	0.812299i	0.119183	−	0.0865914i
$89$	−2.92705	−	2.12663i	−0.310267	−	0.225422i	0.421744	−	0.906715i	$-0.361418\pi$
$89$	−2.92705	−	2.12663i	−0.310267	−	0.225422i	−0.732011	+	0.681293i	$0.761418\pi$
$90$		0			0
$91$	17.0623	−	12.3965i	1.78862	−	1.29951i
$92$	−0.354102	+	1.08981i	−0.0369177	+	0.113621i
$93$	5.23607			0.542955
$94$	5.80902	−	17.8783i	0.599154	−	1.84401i
$95$		0			0
$96$	−2.73607	−	8.42075i	−0.279249	−	0.859439i
$97$	−3.28115	−	10.0984i	−0.333151	−	1.02533i	−0.967626	−	0.252389i	$-0.918784\pi$
$97$	−3.28115	−	10.0984i	−0.333151	−	1.02533i	0.634475	−	0.772943i	$-0.281216\pi$
$98$	−10.2812	−	7.46969i	−1.03855	−	0.754553i
$99$	2.38197			0.239397
$100$		0			0
$101$	9.76393			0.971548			0.485774	−	0.874085i	$-0.338538\pi$
$101$	9.76393			0.971548			0.485774	+	0.874085i	$0.338538\pi$
$102$	5.04508	+	3.66547i	0.499538	+	0.362935i
$103$	−1.59017	−	4.89404i	−0.156684	−	0.482224i	0.841644	−	0.540033i	$-0.181588\pi$
$103$	−1.59017	−	4.89404i	−0.156684	−	0.482224i	−0.998328	+	0.0578094i	$0.981588\pi$
$104$	3.78115	+	11.6372i	0.370773	+	1.14112i
$105$		0			0
$106$	4.23607	−	13.0373i	0.411443	−	1.26629i
$107$	−11.7984			−1.14059			−0.570296	−	0.821439i	$-0.693171\pi$
$107$	−11.7984			−1.14059			−0.570296	+	0.821439i	$0.693171\pi$
$108$	0.427051	−	1.31433i	0.0410930	−	0.126471i
$109$	−12.8262	+	9.31881i	−1.22853	+	0.892580i	−0.996779	−	0.0801951i	$-0.974446\pi$
$109$	−12.8262	+	9.31881i	−1.22853	+	0.892580i	−0.231752	+	0.972775i	$0.574446\pi$
$110$		0			0
$111$	−6.35410	−	4.61653i	−0.603105	−	0.438181i
$112$	15.1353	−	10.9964i	1.43015	−	1.03906i
$113$	−0.572949	+	0.416272i	−0.0538985	+	0.0391596i	−0.614408	−	0.788988i	$-0.710605\pi$
$113$	−0.572949	+	0.416272i	−0.0538985	+	0.0391596i	0.560510	+	0.828148i	$0.310605\pi$
$114$	2.92705	+	2.12663i	0.274143	+	0.199177i
$115$		0			0
$116$	1.38197	−	1.00406i	0.128312	−	0.0932244i
$117$	−6.51722	+	20.0579i	−0.602517	+	1.85436i
$118$	−22.5623			−2.07703
$119$	−1.75329	+	5.39607i	−0.160724	+	0.494657i
$120$		0			0
$121$	−3.28115	−	10.0984i	−0.298287	−	0.918032i
$122$	−4.42705	−	13.6251i	−0.400806	−	1.23356i
$123$	−13.7082	−	9.95959i	−1.23603	−	0.898026i
$124$	1.23607			0.111002
$125$		0			0
$126$	24.0344			2.14116
$127$	−5.78115	−	4.20025i	−0.512994	−	0.372712i	0.300964	−	0.953636i	$-0.402692\pi$
$127$	−5.78115	−	4.20025i	−0.512994	−	0.372712i	−0.813958	+	0.580923i	$0.802692\pi$
$128$	4.20820	+	12.9515i	0.371956	+	1.14476i
$129$	−0.381966	−	1.17557i	−0.0336302	−	0.103503i
$130$		0			0
$131$	−0.236068	+	0.726543i	−0.0206254	+	0.0634783i	−0.960839	−	0.277106i	$-0.910625\pi$
$131$	−0.236068	+	0.726543i	−0.0206254	+	0.0634783i	0.940214	+	0.340584i	$0.110625\pi$
$132$	1.00000			0.0870388
$133$	−1.01722	+	3.13068i	−0.0882042	+	0.271465i
$134$	15.0172	−	10.9106i	1.29729	−	0.942537i
$135$		0			0
$136$	−2.66312	−	1.93487i	−0.228361	−	0.165914i
$137$	−16.3713	+	11.8945i	−1.39870	+	1.01621i	−0.403849	+	0.914825i	$0.632328\pi$
$137$	−16.3713	+	11.8945i	−1.39870	+	1.01621i	−0.994847	+	0.101387i	$0.967672\pi$
$138$	6.35410	−	4.61653i	0.540897	−	0.392985i
$139$	−6.80902	−	4.94704i	−0.577533	−	0.419602i	0.260301	−	0.965528i	$-0.416178\pi$
$139$	−6.80902	−	4.94704i	−0.577533	−	0.419602i	−0.837834	+	0.545925i	$0.816178\pi$
$140$		0			0
$141$	−24.6074	+	17.8783i	−2.07232	+	1.50563i
$142$	−1.66312	+	5.11855i	−0.139566	+	0.429539i
$143$	−3.38197			−0.282814
$144$	−5.78115	+	17.7926i	−0.481763	+	1.48271i
$145$		0			0
$146$	−0.0729490	−	0.224514i	−0.00603730	−	0.0185809i
$147$	6.35410	+	19.5559i	0.524077	+	1.61294i
$148$	−1.50000	−	1.08981i	−0.123299	−	0.0895821i
$149$	−13.6180			−1.11563			−0.557816	−	0.829964i	$-0.688361\pi$
$149$	−13.6180			−1.11563			−0.557816	+	0.829964i	$0.688361\pi$
$150$		0			0
$151$	15.9443			1.29753			0.648763	−	0.760990i	$-0.275287\pi$
$151$	15.9443			1.29753			0.648763	+	0.760990i	$0.275287\pi$
$152$	−1.54508	−	1.12257i	−0.125323	−	0.0910524i
$153$	−1.75329	−	5.39607i	−0.141745	−	0.436246i
$154$	1.19098	+	3.66547i	0.0959721	+	0.295372i
$155$		0			0
$156$	−2.73607	+	8.42075i	−0.219061	+	0.674200i
$157$	13.0000			1.03751			0.518756	−	0.854922i	$-0.326395\pi$
$157$	13.0000			1.03751			0.518756	+	0.854922i	$0.326395\pi$
$158$	−3.35410	+	10.3229i	−0.266838	+	0.821243i
$159$	−17.9443	+	13.0373i	−1.42307	+	1.03392i
$160$		0			0
$161$	5.78115	+	4.20025i	0.455619	+	0.331026i
$162$	7.47214	−	5.42882i	0.587066	−	0.426529i
$163$	1.50000	−	1.08981i	0.117489	−	0.0853608i	−0.527489	−	0.849562i	$-0.676866\pi$
$163$	1.50000	−	1.08981i	0.117489	−	0.0853608i	0.644978	+	0.764201i	$0.276866\pi$
$164$	−3.23607	−	2.35114i	−0.252694	−	0.183593i
$165$		0			0
$166$	−16.9443	+	12.3107i	−1.31513	+	0.955498i
$167$	5.39919	−	16.6170i	0.417802	−	1.28586i	−0.491919	−	0.870641i	$-0.663704\pi$
$167$	5.39919	−	16.6170i	0.417802	−	1.28586i	0.909721	−	0.415220i	$-0.136296\pi$
$168$	−22.5623			−1.74072
$169$	5.23607	−	16.1150i	0.402774	−	1.23961i
$170$		0			0
$171$	−1.01722	−	3.13068i	−0.0777888	−	0.239409i
$172$	−0.0901699	−	0.277515i	−0.00687539	−	0.0211603i
$173$	−12.7082	−	9.23305i	−0.966187	−	0.701976i	−0.0116075	−	0.999933i	$-0.503695\pi$
$173$	−12.7082	−	9.23305i	−0.966187	−	0.701976i	−0.954579	+	0.297957i	$0.903695\pi$
$174$	−11.7082			−0.887597
$175$		0			0
$176$	−3.00000			−0.226134
$177$	29.5344	+	21.4580i	2.21994	+	1.61288i
$178$	1.80902	+	5.56758i	0.135592	+	0.417308i
$179$	−6.21885	−	19.1396i	−0.464818	−	1.43056i	−0.859211	−	0.511622i	$-0.829045\pi$
$179$	−6.21885	−	19.1396i	−0.464818	−	1.43056i	0.394392	−	0.918942i	$-0.370955\pi$
$180$		0			0
$181$	−4.11803	+	12.6740i	−0.306091	+	0.942051i	0.673177	+	0.739482i	$0.264929\pi$
$181$	−4.11803	+	12.6740i	−0.306091	+	0.942051i	−0.979268	+	0.202570i	$0.935071\pi$
$182$	−34.1246			−2.52948
$183$	−7.16312	+	22.0458i	−0.529513	+	1.62967i
$184$	−3.35410	+	2.43690i	−0.247268	+	0.179650i
$185$		0			0
$186$	−6.85410	−	4.97980i	−0.502567	−	0.365136i
$187$	0.736068	−	0.534785i	0.0538266	−	0.0391073i
$188$	−5.80902	+	4.22050i	−0.423666	+	0.307811i
$189$	−6.97214	−	5.06555i	−0.507148	−	0.368465i
$190$		0			0
$191$	2.42705	−	1.76336i	0.175615	−	0.127592i	−0.496505	−	0.868034i	$-0.665384\pi$
$191$	2.42705	−	1.76336i	0.175615	−	0.127592i	0.672121	+	0.740442i	$0.265384\pi$
$192$	3.42705	−	10.5474i	0.247326	−	0.761191i
$193$	22.9443			1.65156			0.825782	−	0.563989i	$-0.190734\pi$
$193$	22.9443			1.65156			0.825782	+	0.563989i	$0.190734\pi$
$194$	−5.30902	+	16.3395i	−0.381165	+	1.17311i
$195$		0			0
$196$	1.50000	+	4.61653i	0.107143	+	0.329752i
$197$	−5.09017	−	15.6659i	−0.362660	−	1.11615i	−0.951434	−	0.307854i	$-0.900389\pi$
$197$	−5.09017	−	15.6659i	−0.362660	−	1.11615i	0.588774	−	0.808298i	$-0.299611\pi$
$198$	−3.11803	−	2.26538i	−0.221589	−	0.160994i
$199$	−10.8541			−0.769427			−0.384713	−	0.923036i	$-0.625700\pi$
$199$	−10.8541			−0.769427			−0.384713	+	0.923036i	$0.625700\pi$
$200$		0			0
$201$	−30.0344			−2.11847
$202$	−12.7812	−	9.28605i	−0.899279	−	0.653364i
$203$	−3.29180	−	10.1311i	−0.231039	−	0.711064i
$204$	−0.736068	−	2.26538i	−0.0515351	−	0.158609i
$205$		0			0
$206$	−2.57295	+	7.91872i	−0.179266	+	0.551724i
$207$	−7.14590			−0.496674
$208$	8.20820	−	25.2623i	0.569137	−	1.75162i
$209$	0.427051	−	0.310271i	0.0295397	−	0.0214619i
$210$		0			0
$211$	−10.6631	−	7.74721i	−0.734079	−	0.533340i	0.156772	−	0.987635i	$-0.449891\pi$
$211$	−10.6631	−	7.74721i	−0.734079	−	0.533340i	−0.890851	+	0.454295i	$0.849891\pi$
$212$	−4.23607	+	3.07768i	−0.290934	+	0.211376i
$213$	7.04508	−	5.11855i	0.482721	−	0.350718i
$214$	15.4443	+	11.2209i	1.05575	+	0.767046i
$215$		0			0
$216$	4.04508	−	2.93893i	0.275233	−	0.199969i
$217$	2.38197	−	7.33094i	0.161698	−	0.497656i
$218$	25.6525			1.73740
$219$	−0.118034	+	0.363271i	−0.00797600	+	0.0245476i
$220$		0			0
$221$	2.48936	+	7.66145i	0.167452	+	0.515365i
$222$	3.92705	+	12.0862i	0.263566	+	0.811174i
$223$	0.118034	+	0.0857567i	0.00790414	+	0.00574269i	0.591730	−	0.806136i	$-0.298445\pi$
$223$	0.118034	+	0.0857567i	0.00790414	+	0.00574269i	−0.583826	+	0.811879i	$0.698445\pi$
$224$	−13.0344			−0.870900
$225$		0			0
$226$	1.14590			0.0762240
$227$	−0.618034	−	0.449028i	−0.0410204	−	0.0298030i	0.567086	−	0.823658i	$-0.308071\pi$
$227$	−0.618034	−	0.449028i	−0.0410204	−	0.0298030i	−0.608107	+	0.793855i	$0.708071\pi$
$228$	−0.427051	−	1.31433i	−0.0282821	−	0.0870435i
$229$	−1.01722	−	3.13068i	−0.0672199	−	0.206881i	0.911805	−	0.410624i	$-0.134689\pi$
$229$	−1.01722	−	3.13068i	−0.0672199	−	0.206881i	−0.979024	+	0.203743i	$0.934689\pi$
$230$		0			0
$231$	1.92705	−	5.93085i	0.126791	−	0.390221i
$232$	6.18034			0.405759
$233$	6.82624	−	21.0090i	0.447202	−	1.37635i	−0.432849	−	0.901466i	$-0.642492\pi$
$233$	6.82624	−	21.0090i	0.447202	−	1.37635i	0.880051	−	0.474879i	$-0.157508\pi$
$234$	27.6074	−	20.0579i	1.80475	−	1.31123i
$235$		0			0
$236$	6.97214	+	5.06555i	0.453847	+	0.329739i
$237$	14.2082	−	10.3229i	0.922922	−	0.670542i
$238$	7.42705	−	5.39607i	0.481424	−	0.349775i
$239$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$239$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$240$		0			0
$241$	11.2082	−	8.14324i	0.721984	−	0.524552i	−0.165034	−	0.986288i	$-0.552773\pi$
$241$	11.2082	−	8.14324i	0.721984	−	0.524552i	0.887017	+	0.461736i	$0.152773\pi$
$242$	−5.30902	+	16.3395i	−0.341277	+	1.05034i
$243$	−21.6525			−1.38901
$244$	−1.69098	+	5.20431i	−0.108254	+	0.333172i
$245$		0			0
$246$	8.47214	+	26.0746i	0.540164	+	1.66245i
$247$	1.44427	+	4.44501i	0.0918968	+	0.282829i
$248$	3.61803	+	2.62866i	0.229745	+	0.166920i
$249$	33.8885			2.14760
$250$		0			0
$251$	−9.18034			−0.579458			−0.289729	−	0.957109i	$-0.593565\pi$
$251$	−9.18034			−0.579458			−0.289729	+	0.957109i	$0.593565\pi$
$252$	−7.42705	−	5.39607i	−0.467860	−	0.339920i
$253$	−0.354102	−	1.08981i	−0.0222622	−	0.0685160i
$254$	3.57295	+	10.9964i	0.224187	+	0.689976i
$255$		0			0
$256$	4.19098	−	12.8985i	0.261936	−	0.806157i
$257$	−3.70820			−0.231311			−0.115656	−	0.993289i	$-0.536897\pi$
$257$	−3.70820			−0.231311			−0.115656	+	0.993289i	$0.536897\pi$
$258$	−0.618034	+	1.90211i	−0.0384771	+	0.118420i
$259$	−9.35410	+	6.79615i	−0.581236	+	0.422292i
$260$		0			0
$261$	8.61803	+	6.26137i	0.533443	+	0.387569i
$262$	1.00000	−	0.726543i	0.0617802	−	0.0448859i
$263$	−15.6353	+	11.3597i	−0.964111	+	0.700468i	−0.954102	−	0.299482i	$-0.903186\pi$
$263$	−15.6353	+	11.3597i	−0.964111	+	0.700468i	−0.0100092	+	0.999950i	$0.503186\pi$
$264$	2.92705	+	2.12663i	0.180148	+	0.130885i
$265$		0			0
$266$	4.30902	−	3.13068i	0.264203	−	0.191955i
$267$	2.92705	−	9.00854i	0.179133	−	0.551313i
$268$	−7.09017			−0.433101
$269$	1.18034	−	3.63271i	0.0719666	−	0.221490i	−0.908603	−	0.417660i	$-0.862850\pi$
$269$	1.18034	−	3.63271i	0.0719666	−	0.221490i	0.980570	+	0.196170i	$0.0628503\pi$
$270$		0			0
$271$	−4.01722	−	12.3637i	−0.244029	−	0.751043i	−0.995795	−	0.0916133i	$-0.970798\pi$
$271$	−4.01722	−	12.3637i	−0.244029	−	0.751043i	0.751766	−	0.659430i	$-0.229202\pi$
$272$	2.20820	+	6.79615i	0.133892	+	0.412077i
$273$	44.6697	+	32.4544i	2.70353	+	1.96423i
$274$	32.7426			1.97806
$275$		0			0
$276$	−3.00000			−0.180579
$277$	12.3713	+	8.98829i	0.743321	+	0.540054i	0.893749	−	0.448567i	$-0.148065\pi$
$277$	12.3713	+	8.98829i	0.743321	+	0.540054i	−0.150429	+	0.988621i	$0.548065\pi$
$278$	4.20820	+	12.9515i	0.252391	+	0.776781i
$279$	2.38197	+	7.33094i	0.142605	+	0.438892i
$280$		0			0
$281$	5.98278	−	18.4131i	0.356903	−	1.09843i	−0.597995	−	0.801500i	$-0.704036\pi$
$281$	5.98278	−	18.4131i	0.356903	−	1.09843i	0.954898	−	0.296934i	$-0.0959641\pi$
$282$	49.2148			2.93070
$283$	−7.21885	+	22.2173i	−0.429116	+	1.32068i	0.469882	+	0.882729i	$0.344297\pi$
$283$	−7.21885	+	22.2173i	−0.429116	+	1.32068i	−0.898998	+	0.437954i	$0.855703\pi$
$284$	1.66312	−	1.20833i	0.0986880	−	0.0717010i
$285$		0			0
$286$	4.42705	+	3.21644i	0.261777	+	0.190192i
$287$	−20.1803	+	14.6619i	−1.19121	+	0.865463i
$288$	10.5451	−	7.66145i	0.621375	−	0.451455i
$289$	12.0000	+	8.71851i	0.705882	+	0.512854i
$290$		0			0
$291$	22.4894	−	16.3395i	1.31835	−	0.957837i
$292$	−0.0278640	+	0.0857567i	−0.00163062	+	0.00501853i
$293$	14.3262			0.836948			0.418474	−	0.908229i	$-0.362565\pi$
$293$	14.3262			0.836948			0.418474	+	0.908229i	$0.362565\pi$
$294$	10.2812	−	31.6421i	0.599609	−	1.84541i
$295$		0			0
$296$	−2.07295	−	6.37988i	−0.120488	−	0.370823i
$297$	0.427051	+	1.31433i	0.0247800	+	0.0762650i
$298$	17.8262	+	12.9515i	1.03265	+	0.750261i
$299$	10.1459			0.586752
$300$		0			0
$301$	−1.81966			−0.104883
$302$	−20.8713	−	15.1639i	−1.20101	−	0.872585i
$303$	7.89919	+	24.3112i	0.453796	+	1.39664i
$304$	1.28115	+	3.94298i	0.0734792	+	0.226146i
$305$		0			0
$306$	−2.83688	+	8.73102i	−0.162174	+	0.499119i
$307$	13.9787			0.797807			0.398904	−	0.916993i	$-0.369391\pi$
$307$	13.9787			0.797807			0.398904	+	0.916993i	$0.369391\pi$
$308$	0.454915	−	1.40008i	0.0259212	−	0.0797772i
$309$	10.8992	−	7.91872i	0.620033	−	0.450480i
$310$		0			0
$311$	−11.7812	−	8.55951i	−0.668048	−	0.485365i	0.201323	−	0.979525i	$-0.435476\pi$
$311$	−11.7812	−	8.55951i	−0.668048	−	0.485365i	−0.869371	+	0.494160i	$0.835476\pi$
$312$	−25.9164	+	18.8294i	−1.46723	+	1.06600i
$313$	−17.0172	+	12.3637i	−0.961870	+	0.698840i	−0.953584	−	0.301126i	$-0.902638\pi$
$313$	−17.0172	+	12.3637i	−0.961870	+	0.698840i	−0.00828586	+	0.999966i	$0.502638\pi$
$314$	−17.0172	−	12.3637i	−0.960337	−	0.697726i
$315$		0			0
$316$	3.35410	−	2.43690i	0.188683	−	0.137086i
$317$	−2.10081	+	6.46564i	−0.117993	+	0.363146i	−0.992560	−	0.121760i	$-0.961146\pi$
$317$	−2.10081	+	6.46564i	−0.117993	+	0.363146i	0.874566	+	0.484906i	$0.161146\pi$
$318$	35.8885			2.01253
$319$	−0.527864	+	1.62460i	−0.0295547	+	0.0909601i
$320$		0			0
$321$	−9.54508	−	29.3768i	−0.532755	−	1.63965i
$322$	−3.57295	−	10.9964i	−0.199113	−	0.612806i
$323$	−1.01722	−	0.739054i	−0.0565997	−	0.0411221i
$324$	−3.52786			−0.195992
$325$		0			0
$326$	−3.00000			−0.166155
$327$	−33.5795	−	24.3970i	−1.85695	−	1.34915i
$328$	−4.47214	−	13.7638i	−0.246932	−	0.759980i
$329$	13.8369	+	42.5855i	0.762852	+	2.34782i
$330$		0			0
$331$	4.72542	−	14.5434i	0.259733	−	0.799375i	−0.733127	−	0.680091i	$-0.761940\pi$
$331$	4.72542	−	14.5434i	0.259733	−	0.799375i	0.992860	−	0.119284i	$-0.0380599\pi$
$332$	8.00000			0.439057
$333$	3.57295	−	10.9964i	0.195796	−	0.602599i
$334$	−22.8713	+	16.6170i	−1.25146	+	0.909241i
$335$		0			0
$336$	39.6246	+	28.7890i	2.16170	+	1.57057i
$337$	1.61803	−	1.17557i	0.0881399	−	0.0640374i	−0.542843	−	0.839834i	$-0.682652\pi$
$337$	1.61803	−	1.17557i	0.0881399	−	0.0640374i	0.630982	+	0.775797i	$0.282652\pi$
$338$	−22.1803	+	16.1150i	−1.20645	+	0.876538i
$339$	−1.50000	−	1.08981i	−0.0814688	−	0.0591906i
$340$		0			0
$341$	−1.00000	+	0.726543i	−0.0541530	+	0.0393445i
$342$	−1.64590	+	5.06555i	−0.0890000	+	0.273914i
$343$	3.29180			0.177740
$344$	0.326238	−	1.00406i	0.0175896	−	0.0541351i
$345$		0			0
$346$	7.85410	+	24.1724i	0.422239	+	1.29952i
$347$	1.78115	+	5.48183i	0.0956173	+	0.294280i	0.987414	−	0.158156i	$-0.0505550\pi$
$347$	1.78115	+	5.48183i	0.0956173	+	0.294280i	−0.891797	+	0.452436i	$0.850555\pi$
$348$	3.61803	+	2.62866i	0.193947	+	0.140911i
$349$	−20.1246			−1.07725			−0.538623	−	0.842547i	$-0.681055\pi$
$349$	−20.1246			−1.07725			−0.538623	+	0.842547i	$0.681055\pi$
$350$		0			0
$351$	−12.2361			−0.653113
$352$	1.69098	+	1.22857i	0.0901297	+	0.0654831i
$353$	−2.05573	−	6.32688i	−0.109415	−	0.336746i	0.881326	−	0.472509i	$-0.156651\pi$
$353$	−2.05573	−	6.32688i	−0.109415	−	0.336746i	−0.990741	+	0.135763i	$0.956651\pi$
$354$	−18.2533	−	56.1778i	−0.970151	−	2.98582i
$355$		0			0
$356$	0.690983	−	2.12663i	0.0366220	−	0.112711i
$357$	−14.8541			−0.786162
$358$	−10.0623	+	30.9686i	−0.531809	+	1.63674i
$359$	20.7533	−	15.0781i	1.09532	−	0.795794i	0.115028	−	0.993362i	$-0.463304\pi$
$359$	20.7533	−	15.0781i	1.09532	−	0.795794i	0.980289	+	0.197568i	$0.0633044\pi$
$360$		0			0
$361$	14.7812	+	10.7391i	0.777955	+	0.565218i
$362$	17.4443	−	12.6740i	0.916851	−	0.666131i
$363$	22.4894	−	16.3395i	1.18039	−	0.857600i
$364$	10.5451	+	7.66145i	0.552713	+	0.401569i
$365$		0			0
$366$	30.3435	−	22.0458i	1.58608	−	1.15235i
$367$	5.56231	−	17.1190i	0.290350	−	0.893605i	−0.694394	−	0.719595i	$-0.744327\pi$
$367$	5.56231	−	17.1190i	0.290350	−	0.893605i	0.984744	−	0.174010i	$-0.0556726\pi$
$368$	9.00000			0.469157
$369$	7.70820	−	23.7234i	0.401273	−	1.23499i
$370$		0			0
$371$	10.0902	+	31.0543i	0.523856	+	1.61226i
$372$	1.00000	+	3.07768i	0.0518476	+	0.159570i
$373$	4.16312	+	3.02468i	0.215558	+	0.156612i	0.690325	−	0.723499i	$-0.257468\pi$
$373$	4.16312	+	3.02468i	0.215558	+	0.156612i	−0.474767	+	0.880112i	$0.657468\pi$
$374$	−1.47214			−0.0761223
$375$		0			0
$376$	−25.9787			−1.33975
$377$	−12.2361	−	8.89002i	−0.630190	−	0.457860i
$378$	4.30902	+	13.2618i	0.221632	+	0.682113i
$379$	0.854102	+	2.62866i	0.0438723	+	0.135025i	0.970593	−	0.240725i	$-0.0773852\pi$
$379$	0.854102	+	2.62866i	0.0438723	+	0.135025i	−0.926721	+	0.375750i	$0.877385\pi$
$380$		0			0
$381$	5.78115	−	17.7926i	0.296177	−	0.911540i
$382$	−4.85410			−0.248357
$383$	7.84346	−	24.1397i	0.400782	−	1.23348i	−0.523584	−	0.851974i	$-0.675405\pi$
$383$	7.84346	−	24.1397i	0.400782	−	1.23348i	0.924366	−	0.381506i	$-0.124595\pi$
$384$	−28.8435	+	20.9560i	−1.47191	+	1.06941i
$385$		0			0
$386$	−30.0344	−	21.8213i	−1.52871	−	1.11067i
$387$	1.47214	−	1.06957i	0.0748329	−	0.0543693i
$388$	5.30902	−	3.85723i	0.269525	−	0.195821i
$389$	−8.35410	−	6.06961i	−0.423570	−	0.307741i	0.355503	−	0.934675i	$-0.384310\pi$
$389$	−8.35410	−	6.06961i	−0.423570	−	0.307741i	−0.779073	+	0.626934i	$0.784310\pi$
$390$		0			0
$391$	−2.20820	+	1.60435i	−0.111674	+	0.0811357i
$392$	−5.42705	+	16.7027i	−0.274107	+	0.843616i
$393$	−2.00000			−0.100887
$394$	−8.23607	+	25.3480i	−0.414927	+	1.27701i
$395$		0			0
$396$	0.454915	+	1.40008i	0.0228603	+	0.0703569i
$397$	3.52786	+	10.8576i	0.177058	+	0.544930i	0.999721	−	0.0235994i	$-0.00751263\pi$
$397$	3.52786	+	10.8576i	0.177058	+	0.544930i	−0.822663	+	0.568529i	$0.807513\pi$
$398$	14.2082	+	10.3229i	0.712193	+	0.517438i
$399$	−8.61803			−0.431441
$400$		0			0
$401$	14.5623			0.727207			0.363603	−	0.931554i	$-0.381546\pi$
$401$	14.5623			0.727207			0.363603	+	0.931554i	$0.381546\pi$
$402$	39.3156	+	28.5645i	1.96088	+	1.42467i
$403$	−3.38197	−	10.4086i	−0.168468	−	0.518490i
$404$	1.86475	+	5.73910i	0.0927745	+	0.285531i
$405$		0			0
$406$	−5.32624	+	16.3925i	−0.264337	+	0.813545i
$407$	1.85410			0.0919044
$408$	2.66312	−	8.19624i	0.131844	−	0.405774i
$409$	25.6525	−	18.6376i	1.26843	−	0.921571i	0.269294	−	0.963058i	$-0.413210\pi$
$409$	25.6525	−	18.6376i	1.26843	−	0.921571i	0.999139	+	0.0414872i	$0.0132096\pi$
$410$		0			0
$411$	−42.8607	−	31.1401i	−2.11416	−	1.53603i
$412$	2.57295	−	1.86936i	0.126760	−	0.0920966i
$413$	43.4787	−	31.5891i	2.13945	−	1.55440i
$414$	9.35410	+	6.79615i	0.459729	+	0.334013i
$415$		0			0
$416$	−14.9721	+	10.8779i	−0.734069	+	0.533333i
$417$	6.80902	−	20.9560i	0.333439	−	1.02622i
$418$	−0.854102			−0.0417755
$419$	−9.96149	+	30.6583i	−0.486651	+	1.49776i	0.342925	+	0.939363i	$0.388582\pi$
$419$	−9.96149	+	30.6583i	−0.486651	+	1.49776i	−0.829576	+	0.558394i	$0.811418\pi$
$420$		0			0
$421$	4.07295	+	12.5352i	0.198503	+	0.610931i	0.999918	+	0.0128211i	$0.00408121\pi$
$421$	4.07295	+	12.5352i	0.198503	+	0.610931i	−0.801414	+	0.598109i	$0.795919\pi$
$422$	6.59017	+	20.2825i	0.320804	+	0.987335i
$423$	−36.2254	−	26.3193i	−1.76134	−	1.27969i
$424$	−18.9443			−0.920015
$425$		0			0
$426$	−14.0902			−0.682671
$427$	27.6074	+	20.0579i	1.33602	+	0.970672i
$428$	−2.25329	−	6.93491i	−0.108917	−	0.335212i
$429$	−2.73607	−	8.42075i	−0.132099	−	0.406558i
$430$		0			0
$431$	−1.41641	+	4.35926i	−0.0682260	+	0.209978i	−0.979357	−	0.202139i	$-0.935211\pi$
$431$	−1.41641	+	4.35926i	−0.0682260	+	0.209978i	0.911131	+	0.412117i	$0.135211\pi$
$432$	−10.8541			−0.522218
$433$	−0.0450850	+	0.138757i	−0.00216665	+	0.00666825i	−0.952134	−	0.305681i	$-0.901116\pi$
$433$	−0.0450850	+	0.138757i	−0.00216665	+	0.00666825i	0.949967	+	0.312349i	$0.101116\pi$
$434$	−10.0902	+	7.33094i	−0.484344	+	0.351896i
$435$		0			0
$436$	−7.92705	−	5.75934i	−0.379637	−	0.275822i
$437$	−1.28115	+	0.930812i	−0.0612859	+	0.0445268i
$438$	0.500000	−	0.363271i	0.0238909	−	0.0173578i
$439$	−7.50000	−	5.44907i	−0.357955	−	0.260070i	0.394243	−	0.919006i	$-0.371007\pi$
$439$	−7.50000	−	5.44907i	−0.357955	−	0.260070i	−0.752199	+	0.658936i	$0.771007\pi$
$440$		0			0
$441$	−24.4894	+	17.7926i	−1.16616	+	0.847265i
$442$	4.02786	−	12.3965i	0.191586	−	0.589641i
$443$	−27.7082			−1.31646			−0.658228	−	0.752818i	$-0.728694\pi$
$443$	−27.7082			−1.31646			−0.658228	+	0.752818i	$0.728694\pi$
$444$	1.50000	−	4.61653i	0.0711868	−	0.219091i
$445$		0			0
$446$	−0.0729490	−	0.224514i	−0.00345424	−	0.0106310i
$447$	−11.0172	−	33.9075i	−0.521097	−	1.60377i
$448$	−13.2082	−	9.59632i	−0.624029	−	0.453384i
$449$	29.0689			1.37185			0.685923	−	0.727674i	$-0.259399\pi$
$449$	29.0689			1.37185			0.685923	+	0.727674i	$0.259399\pi$
$450$		0			0
$451$	4.00000			0.188353
$452$	−0.354102	−	0.257270i	−0.0166556	−	0.0121010i
$453$	12.8992	+	39.6996i	0.606057	+	1.86525i
$454$	0.381966	+	1.17557i	0.0179266	+	0.0551723i
$455$		0			0
$456$	1.54508	−	4.75528i	0.0723552	−	0.222687i
$457$	−34.8885			−1.63202			−0.816009	−	0.578040i	$-0.803818\pi$
$457$	−34.8885			−1.63202			−0.816009	+	0.578040i	$0.803818\pi$
$458$	−1.64590	+	5.06555i	−0.0769078	+	0.236698i
$459$	2.66312	−	1.93487i	0.124304	−	0.0903120i
$460$		0			0
$461$	12.0623	+	8.76378i	0.561798	+	0.408170i	0.832116	−	0.554601i	$-0.187129\pi$
$461$	12.0623	+	8.76378i	0.561798	+	0.408170i	−0.270319	+	0.962771i	$0.587129\pi$
$462$	−8.16312	+	5.93085i	−0.379783	+	0.275928i
$463$	−2.97214	+	2.15938i	−0.138127	+	0.100355i	−0.654703	−	0.755886i	$-0.727206\pi$
$463$	−2.97214	+	2.15938i	−0.138127	+	0.100355i	0.516576	+	0.856241i	$0.327206\pi$
$464$	−10.8541	−	7.88597i	−0.503889	−	0.366097i
$465$		0			0
$466$	−28.9164	+	21.0090i	−1.33953	+	0.973223i
$467$	1.02786	−	3.16344i	0.0475639	−	0.146387i	−0.924454	−	0.381294i	$-0.875479\pi$
$467$	1.02786	−	3.16344i	0.0475639	−	0.146387i	0.972018	+	0.234907i	$0.0754786\pi$
$468$	−13.0344			−0.602517
$469$	−13.6631	+	42.0508i	−0.630904	+	1.94172i
$470$		0			0
$471$	10.5172	+	32.3687i	0.484608	+	1.49147i
$472$	9.63525	+	29.6543i	0.443499	+	1.36495i
$473$	0.236068	+	0.171513i	0.0108544	+	0.00788620i
$474$	−28.4164			−1.30521
$475$		0			0
$476$	−3.50658			−0.160724
$477$	−26.4164	−	19.1926i	−1.20952	−	0.878771i
$478$		0			0
$479$	7.03444	+	21.6498i	0.321412	+	0.989204i	0.973034	+	0.230660i	$0.0740887\pi$
$479$	7.03444	+	21.6498i	0.321412	+	0.989204i	−0.651622	+	0.758543i	$0.725911\pi$
$480$		0			0
$481$	−5.07295	+	15.6129i	−0.231307	+	0.711888i
$482$	−22.4164			−1.02104
$483$	−5.78115	+	17.7926i	−0.263052	+	0.809589i
$484$	5.30902	−	3.85723i	0.241319	−	0.175328i
$485$		0			0
$486$	28.3435	+	20.5927i	1.28569	+	0.934105i
$487$	−4.33688	+	3.15093i	−0.196523	+	0.142782i	−0.681695	−	0.731636i	$-0.738757\pi$
$487$	−4.33688	+	3.15093i	−0.196523	+	0.142782i	0.485172	+	0.874419i	$0.338757\pi$
$488$	−16.0172	+	11.6372i	−0.725066	+	0.526791i
$489$	3.92705	+	2.85317i	0.177587	+	0.129025i
$490$		0			0
$491$	−25.0344	+	18.1886i	−1.12979	+	0.820839i	−0.985664	−	0.168720i	$-0.946037\pi$
$491$	−25.0344	+	18.1886i	−1.12979	+	0.820839i	−0.144125	+	0.989560i	$0.546037\pi$
$492$	3.23607	−	9.95959i	0.145893	−	0.449013i
$493$	4.06888			0.183253
$494$	2.33688	−	7.19218i	0.105141	−	0.323591i
$495$		0			0
$496$	−3.00000	−	9.23305i	−0.134704	−	0.414576i
$497$	−3.96149	−	12.1922i	−0.177697	−	0.546896i
$498$	−44.3607	−	32.2299i	−1.98785	−	1.44426i
$499$	−28.4164			−1.27209			−0.636047	−	0.771651i	$-0.719431\pi$
$499$	−28.4164			−1.27209			−0.636047	+	0.771651i	$0.719431\pi$
$500$		0			0
$501$	45.7426			2.04363
$502$	12.0172	+	8.73102i	0.536355	+	0.389685i
$503$	2.78115	+	8.55951i	0.124005	+	0.381650i	0.993719	−	0.111908i	$-0.0356962\pi$
$503$	2.78115	+	8.55951i	0.124005	+	0.381650i	−0.869713	+	0.493558i	$0.835696\pi$
$504$	−10.2639	−	31.5891i	−0.457192	−	1.40709i
$505$		0			0
$506$	−0.572949	+	1.76336i	−0.0254707	+	0.0783907i
$507$	44.3607			1.97013
$508$	1.36475	−	4.20025i	0.0605508	−	0.186356i
$509$	−25.3885	+	18.4459i	−1.12533	+	0.817598i	−0.985008	−	0.172508i	$-0.944813\pi$
$509$	−25.3885	+	18.4459i	−1.12533	+	0.817598i	−0.140319	+	0.990106i	$0.544813\pi$
$510$		0			0
$511$	0.454915	+	0.330515i	0.0201243	+	0.0146211i
$512$	4.28115	−	3.11044i	0.189202	−	0.137463i
$513$	1.54508	−	1.12257i	0.0682172	−	0.0495627i
$514$	4.85410	+	3.52671i	0.214105	+	0.155557i
$515$		0			0
$516$	0.618034	−	0.449028i	0.0272074	−	0.0197674i
$517$	2.21885	−	6.82891i	0.0975848	−	0.300335i
$518$	18.7082			0.821991
$519$	12.7082	−	39.1118i	0.557828	−	1.71682i
$520$		0			0
$521$	−10.1976	−	31.3849i	−0.446763	−	1.37500i	−0.880538	−	0.473975i	$-0.842819\pi$
$521$	−10.1976	−	31.3849i	−0.446763	−	1.37500i	0.433775	−	0.901021i	$-0.357181\pi$
$522$	−5.32624	−	16.3925i	−0.233123	−	0.717479i
$523$	17.0902	+	12.4167i	0.747301	+	0.542946i	0.894989	−	0.446088i	$-0.147183\pi$
$523$	17.0902	+	12.4167i	0.747301	+	0.542946i	−0.147688	+	0.989034i	$0.547183\pi$
$524$	−0.472136			−0.0206254
$525$		0			0
$526$	31.2705			1.36346
$527$	2.38197	+	1.73060i	0.103760	+	0.0753861i
$528$	−2.42705	−	7.46969i	−0.105624	−	0.325077i
$529$	−6.04508	−	18.6049i	−0.262830	−	0.808907i
$530$		0			0
$531$	−16.6074	+	51.1123i	−0.720699	+	2.21808i
$532$	−2.03444			−0.0882042
$533$	−10.9443	+	33.6830i	−0.474049	+	1.45897i
$534$	−12.3992	+	9.00854i	−0.536565	+	0.389838i
$535$		0			0
$536$	−20.7533	−	15.0781i	−0.896406	−	0.651277i
$537$	42.6246	−	30.9686i	1.83939	−	1.33639i
$538$	−5.00000	+	3.63271i	−0.215565	+	0.156617i
$539$	−3.92705	−	2.85317i	−0.169150	−	0.122895i
$540$		0			0
$541$	−19.1803	+	13.9353i	−0.824627	+	0.599127i	−0.918034	−	0.396501i	$-0.870224\pi$
$541$	−19.1803	+	13.9353i	−0.824627	+	0.599127i	0.0934070	+	0.995628i	$0.470224\pi$
$542$	−6.50000	+	20.0049i	−0.279199	+	0.859286i
$543$	−34.8885			−1.49721
$544$	1.53851	−	4.73504i	0.0659630	−	0.203013i
$545$		0			0
$546$	−27.6074	−	84.9668i	−1.18149	−	3.63624i
$547$	−1.63525	−	5.03280i	−0.0699185	−	0.215187i	0.909992	−	0.414627i	$-0.136088\pi$
$547$	−1.63525	−	5.03280i	−0.0699185	−	0.215187i	−0.979910	+	0.199440i	$0.936088\pi$
$548$	−10.1180	−	7.35118i	−0.432221	−	0.314027i
$549$	−34.1246			−1.45640
$550$		0			0
$551$	2.36068			0.100568
$552$	−8.78115	−	6.37988i	−0.373751	−	0.271546i
$553$	−7.98936	−	24.5887i	−0.339742	−	1.04562i
$554$	−7.64590	−	23.5317i	−0.324843	−	0.999764i
$555$		0			0
$556$	1.60739	−	4.94704i	0.0681686	−	0.209801i
$557$	14.3820			0.609383			0.304692	−	0.952451i	$-0.401447\pi$
$557$	14.3820			0.609383			0.304692	+	0.952451i	$0.401447\pi$
$558$	3.85410	−	11.8617i	0.163157	−	0.502146i
$559$	−2.09017	+	1.51860i	−0.0884048	+	0.0642298i
$560$		0			0
$561$	1.92705	+	1.40008i	0.0813602	+	0.0591116i
$562$	−25.3435	+	18.4131i	−1.06905	+	0.776710i
$563$	−28.9894	+	21.0620i	−1.22176	+	0.887657i	−0.996245	−	0.0865831i	$-0.972405\pi$
$563$	−28.9894	+	21.0620i	−1.22176	+	0.887657i	−0.225511	+	0.974241i	$0.572405\pi$
$564$	−15.2082	−	11.0494i	−0.640381	−	0.465264i
$565$		0			0
$566$	30.5795	−	22.2173i	1.28535	−	0.933864i
$567$	−6.79837	+	20.9232i	−0.285505	+	0.878694i
$568$	7.43769			0.312079
$569$	−3.78115	+	11.6372i	−0.158514	+	0.487856i	−0.998500	−	0.0547519i	$-0.982563\pi$
$569$	−3.78115	+	11.6372i	−0.158514	+	0.487856i	0.839986	+	0.542608i	$0.182563\pi$
$570$		0			0
$571$	4.72542	+	14.5434i	0.197753	+	0.608621i	0.999933	+	0.0115392i	$0.00367313\pi$
$571$	4.72542	+	14.5434i	0.197753	+	0.608621i	−0.802181	+	0.597082i	$0.796327\pi$
$572$	−0.645898	−	1.98787i	−0.0270064	−	0.0831170i
$573$	6.35410	+	4.61653i	0.265446	+	0.192858i
$574$	40.3607			1.68462
$575$		0			0
$576$	16.3262			0.680260
$577$	13.4271	+	9.75532i	0.558975	+	0.406119i	0.831084	−	0.556147i	$-0.187721\pi$
$577$	13.4271	+	9.75532i	0.558975	+	0.406119i	−0.272108	+	0.962267i	$0.587721\pi$
$578$	−7.41641	−	22.8254i	−0.308482	−	0.949410i
$579$	18.5623	+	57.1289i	0.771423	+	2.37420i
$580$		0			0
$581$	15.4164	−	47.4468i	0.639580	−	1.96843i
$582$	−44.9787			−1.86443
$583$	1.61803	−	4.97980i	0.0670121	−	0.206242i
$584$	−0.263932	+	0.191758i	−0.0109216	+	0.00793500i
$585$		0			0
$586$	−18.7533	−	13.6251i	−0.774691	−	0.562846i
$587$	0.927051	−	0.673542i	0.0382635	−	0.0278001i	−0.568489	−	0.822691i	$-0.692472\pi$
$587$	0.927051	−	0.673542i	0.0382635	−	0.0278001i	0.606753	+	0.794891i	$0.292472\pi$
$588$	−10.2812	+	7.46969i	−0.423988	+	0.308045i
$589$	1.38197	+	1.00406i	0.0569429	+	0.0413715i
$590$		0			0
$591$	34.8885	−	25.3480i	1.43512	−	1.04268i
$592$	−4.50000	+	13.8496i	−0.184949	+	0.569214i
$593$	−21.0000			−0.862367			−0.431183	−	0.902264i	$-0.641904\pi$
$593$	−21.0000			−0.862367			−0.431183	+	0.902264i	$0.641904\pi$
$594$	0.690983	−	2.12663i	0.0283514	−	0.0872566i
$595$		0			0
$596$	−2.60081	−	8.00448i	−0.106533	−	0.327876i
$597$	−8.78115	−	27.0256i	−0.359389	−	1.10608i
$598$	−13.2812	−	9.64932i	−0.543107	−	0.394590i
$599$	7.23607			0.295658			0.147829	−	0.989013i	$-0.452772\pi$
$599$	7.23607			0.295658			0.147829	+	0.989013i	$0.452772\pi$
$600$		0			0
$601$	−24.1803			−0.986337			−0.493168	−	0.869934i	$-0.664161\pi$
$601$	−24.1803			−0.986337			−0.493168	+	0.869934i	$0.664161\pi$
$602$	2.38197	+	1.73060i	0.0970817	+	0.0705340i
$603$	−13.6631	−	42.0508i	−0.556405	−	1.71244i
$604$	3.04508	+	9.37181i	0.123903	+	0.381333i
$605$		0			0
$606$	12.7812	−	39.3363i	0.519199	−	1.59793i
$607$	4.58359			0.186042			0.0930211	−	0.995664i	$-0.470348\pi$
$607$	4.58359			0.186042			0.0930211	+	0.995664i	$0.470348\pi$
$608$	0.892609	−	2.74717i	0.0362001	−	0.111412i
$609$	22.5623	−	16.3925i	0.914271	−	0.664257i
$610$		0			0
$611$	51.4336	+	37.3687i	2.08078	+	1.51178i
$612$	2.83688	−	2.06111i	0.114674	−	0.0833156i
$613$	22.4164	−	16.2865i	0.905390	−	0.657804i	−0.0344546	−	0.999406i	$-0.510969\pi$
$613$	22.4164	−	16.2865i	0.905390	−	0.657804i	0.939845	+	0.341602i	$0.110969\pi$
$614$	−18.2984	−	13.2945i	−0.738462	−	0.536524i
$615$		0			0
$616$	4.30902	−	3.13068i	0.173615	−	0.126139i
$617$	−13.0795	+	40.2546i	−0.526562	+	1.62059i	0.234644	+	0.972081i	$0.424607\pi$
$617$	−13.0795	+	40.2546i	−0.526562	+	1.62059i	−0.761206	+	0.648510i	$0.775393\pi$
$618$	−21.7984			−0.876859
$619$	8.12868	−	25.0175i	0.326719	−	1.00554i	−0.643940	−	0.765076i	$-0.722701\pi$
$619$	8.12868	−	25.0175i	0.326719	−	1.00554i	0.970659	−	0.240462i	$-0.0772988\pi$
$620$		0			0
$621$	−1.28115	−	3.94298i	−0.0514109	−	0.158226i
$622$	7.28115	+	22.4091i	0.291948	+	0.898522i
$623$	−11.2812	−	8.19624i	−0.451970	−	0.328375i
$624$	69.5410			2.78387
$625$		0			0
$626$	34.0344			1.36029
$627$	1.11803	+	0.812299i	0.0446500	+	0.0324401i
$628$	2.48278	+	7.64121i	0.0990737	+	0.304917i
$629$	−1.36475	−	4.20025i	−0.0544160	−	0.167475i
$630$		0			0
$631$	−14.6697	+	45.1487i	−0.583991	+	1.79734i	0.0192920	+	0.999814i	$0.493859\pi$
$631$	−14.6697	+	45.1487i	−0.583991	+	1.79734i	−0.603283	+	0.797527i	$0.706141\pi$
$632$	15.0000			0.596668
$633$	10.6631	−	32.8177i	0.423821	−	1.30439i
$634$	8.89919	−	6.46564i	0.353432	−	0.256783i
$635$		0			0
$636$	−11.0902	−	8.05748i	−0.439754	−	0.319500i
$637$	34.7705	−	25.2623i	1.37766	−	1.00093i
$638$	2.23607	−	1.62460i	0.0885268	−	0.0643185i
$639$	10.3713	+	7.53521i	0.410283	+	0.298088i
$640$		0			0
$641$	29.5623	−	21.4783i	1.16764	−	0.848341i	0.176916	−	0.984226i	$-0.443388\pi$
$641$	29.5623	−	21.4783i	1.16764	−	0.848341i	0.990725	+	0.135885i	$0.0433878\pi$
$642$	−15.4443	+	47.5326i	−0.609537	+	1.87596i
$643$	−18.2361			−0.719160			−0.359580	−	0.933114i	$-0.617080\pi$
$643$	−18.2361			−0.719160			−0.359580	+	0.933114i	$0.617080\pi$
$644$	−1.36475	+	4.20025i	−0.0537785	+	0.165513i
$645$		0			0
$646$	0.628677	+	1.93487i	0.0247350	+	0.0761264i
$647$	−5.12868	−	15.7844i	−0.201629	−	0.620551i	−0.999835	−	0.0181658i	$-0.994217\pi$
$647$	−5.12868	−	15.7844i	−0.201629	−	0.620551i	0.798206	−	0.602385i	$-0.205783\pi$
$648$	−10.3262	−	7.50245i	−0.405653	−	0.294724i
$649$	−8.61803			−0.338287
$650$		0			0
$651$	20.1803			0.790930
$652$	0.927051	+	0.673542i	0.0363061	+	0.0263779i
$653$	−10.7361	−	33.0422i	−0.420135	−	1.29304i	−0.907577	−	0.419887i	$-0.862070\pi$
$653$	−10.7361	−	33.0422i	−0.420135	−	1.29304i	0.487442	−	0.873155i	$-0.337930\pi$
$654$	20.7533	+	63.8721i	0.811518	+	2.49760i
$655$		0			0
$656$	−9.70820	+	29.8788i	−0.379042	+	1.16657i
$657$	−0.562306			−0.0219376
$658$	22.3885	−	68.9049i	0.872796	−	2.68619i
$659$	16.5451	−	12.0207i	0.644505	−	0.468260i	−0.216890	−	0.976196i	$-0.569591\pi$
$659$	16.5451	−	12.0207i	0.644505	−	0.468260i	0.861395	+	0.507936i	$0.169591\pi$
$660$		0			0
$661$	−16.4164	−	11.9272i	−0.638524	−	0.463915i	0.220819	−	0.975315i	$-0.429127\pi$
$661$	−16.4164	−	11.9272i	−0.638524	−	0.463915i	−0.859343	+	0.511400i	$0.829127\pi$
$662$	−20.0172	+	14.5434i	−0.777991	+	0.565244i
$663$	−17.0623	+	12.3965i	−0.662645	+	0.481440i
$664$	23.4164	+	17.0130i	0.908733	+	0.660233i
$665$		0			0
$666$	−15.1353	+	10.9964i	−0.586479	+	0.426102i
$667$	1.58359	−	4.87380i	0.0613169	−	0.188714i
$668$	10.7984			0.417802
$669$	−0.118034	+	0.363271i	−0.00456346	+	0.0140449i
$670$		0			0
$671$	−1.69098	−	5.20431i	−0.0652797	−	0.200910i
$672$	−10.5451	−	32.4544i	−0.406785	−	1.25196i
$673$	11.6631	+	8.47375i	0.449580	+	0.326639i	0.789430	−	0.613841i	$-0.210376\pi$
$673$	11.6631	+	8.47375i	0.449580	+	0.326639i	−0.339850	+	0.940480i	$0.610376\pi$
$674$	−3.23607			−0.124649
$675$		0			0
$676$	10.4721			0.402774
$677$	−11.7361	−	8.52675i	−0.451054	−	0.327710i	0.338958	−	0.940802i	$-0.389926\pi$
$677$	−11.7361	−	8.52675i	−0.451054	−	0.327710i	−0.790012	+	0.613092i	$0.789926\pi$
$678$	0.927051	+	2.85317i	0.0356032	+	0.109575i
$679$	−12.6459	−	38.9201i	−0.485305	−	1.49362i
$680$		0			0
$681$	0.618034	−	1.90211i	0.0236831	−	0.0728891i
$682$	2.00000			0.0765840
$683$	−3.29837	+	10.1514i	−0.126209	+	0.388431i	−0.994119	−	0.108290i	$-0.965463\pi$
$683$	−3.29837	+	10.1514i	−0.126209	+	0.388431i	0.867911	+	0.496720i	$0.165463\pi$
$684$	1.64590	−	1.19581i	0.0629325	−	0.0457231i
$685$		0			0
$686$	−4.30902	−	3.13068i	−0.164519	−	0.119530i
$687$	6.97214	−	5.06555i	0.266004	−	0.193263i
$688$	−1.85410	+	1.34708i	−0.0706870	+	0.0513571i
$689$	37.5066	+	27.2501i	1.42889	+	1.03815i
$690$		0			0
$691$	−12.5729	+	9.13478i	−0.478298	+	0.347503i	−0.800666	−	0.599111i	$-0.795521\pi$
$691$	−12.5729	+	9.13478i	−0.478298	+	0.347503i	0.322369	+	0.946614i	$0.395521\pi$
$692$	3.00000	−	9.23305i	0.114043	−	0.350988i
$693$	9.18034			0.348732
$694$	2.88197	−	8.86978i	0.109398	−	0.336692i
$695$		0			0
$696$	5.00000	+	15.3884i	0.189525	+	0.583296i
$697$	−2.94427	−	9.06154i	−0.111522	−	0.343230i
$698$	26.3435	+	19.1396i	0.997115	+	0.724446i
$699$	57.8328			2.18744
$700$		0			0
$701$	−11.9443			−0.451129			−0.225564	−	0.974228i	$-0.572423\pi$
$701$	−11.9443			−0.451129			−0.225564	+	0.974228i	$0.572423\pi$
$702$	16.0172	+	11.6372i	0.604531	+	0.439218i
$703$	−0.791796	−	2.43690i	−0.0298632	−	0.0919093i
$704$	0.809017	+	2.48990i	0.0304910	+	0.0938416i
$705$		0			0
$706$	−3.32624	+	10.2371i	−0.125185	+	0.385279i
$707$	37.6312			1.41527
$708$	−6.97214	+	21.4580i	−0.262029	+	0.806442i
$709$	−0.100813	+	0.0732450i	−0.00378611	+	0.00275077i	−0.589677	−	0.807639i	$-0.700745\pi$
$709$	−0.100813	+	0.0732450i	−0.00378611	+	0.00275077i	0.585891	+	0.810390i	$0.300745\pi$
$710$		0			0
$711$	20.9164	+	15.1967i	0.784427	+	0.569919i
$712$	6.54508	−	4.75528i	0.245287	−	0.178212i
$713$	3.00000	−	2.17963i	0.112351	−	0.0816277i
$714$	19.4443	+	14.1271i	0.727684	+	0.528693i
$715$		0			0
$716$	10.0623	−	7.31069i	0.376046	−	0.273213i
$717$		0			0
$718$	−41.5066			−1.54901
$719$	13.3541	−	41.0997i	0.498024	−	1.53276i	−0.314167	−	0.949368i	$-0.601725\pi$
$719$	13.3541	−	41.0997i	0.498024	−	1.53276i	0.812191	−	0.583392i	$-0.198275\pi$
$720$		0			0
$721$	−6.12868	−	18.8621i	−0.228244	−	0.702462i
$722$	−9.13525	−	28.1154i	−0.339979	−	1.04635i
$723$	29.3435	+	21.3193i	1.09129	+	0.792872i
$724$	−8.23607			−0.306091
$725$		0			0
$726$	−44.9787			−1.66932
$727$	−23.4443	−	17.0333i	−0.869500	−	0.631729i	0.0609528	−	0.998141i	$-0.480586\pi$
$727$	−23.4443	−	17.0333i	−0.869500	−	0.631729i	−0.930453	+	0.366412i	$0.880586\pi$
$728$	14.5729	+	44.8509i	0.540109	+	1.66229i
$729$	−12.2254	−	37.6260i	−0.452794	−	1.39356i
$730$		0			0
$731$	0.214782	−	0.661030i	0.00794399	−	0.0244491i
$732$	−14.3262			−0.529513
$733$	−8.60081	+	26.4706i	−0.317678	+	0.977713i	0.656960	+	0.753926i	$0.271842\pi$
$733$	−8.60081	+	26.4706i	−0.317678	+	0.977713i	−0.974638	+	0.223787i	$0.928158\pi$
$734$	−23.5623	+	17.1190i	−0.869701	+	0.631874i
$735$		0			0
$736$	−5.07295	−	3.68571i	−0.186991	−	0.135857i
$737$	5.73607	−	4.16750i	0.211291	−	0.153512i
$738$	−32.6525	+	23.7234i	−1.20195	+	0.873271i
$739$	−23.8435	−	17.3233i	−0.877096	−	0.637247i	0.0553857	−	0.998465i	$-0.482361\pi$
$739$	−23.8435	−	17.3233i	−0.877096	−	0.637247i	−0.932482	+	0.361218i	$0.882361\pi$
$740$		0			0
$741$	−9.89919	+	7.19218i	−0.363656	+	0.264211i
$742$	16.3262	−	50.2470i	0.599355	−	1.84463i
$743$	25.9098			0.950539			0.475270	−	0.879840i	$-0.342350\pi$
$743$	25.9098			0.950539			0.475270	+	0.879840i	$0.342350\pi$
$744$	−3.61803	+	11.1352i	−0.132644	+	0.408235i
$745$		0			0
$746$	−2.57295	−	7.91872i	−0.0942024	−	0.289925i
$747$	15.4164	+	47.4468i	0.564057	+	1.73599i
$748$	0.454915	+	0.330515i	0.0166333	+	0.0120848i
$749$	−45.4721			−1.66152
$750$		0			0
$751$	−20.0344			−0.731067			−0.365534	−	0.930798i	$-0.619113\pi$
$751$	−20.0344			−0.731067			−0.365534	+	0.930798i	$0.619113\pi$
$752$	45.6246	+	33.1482i	1.66376	+	1.20879i
$753$	−7.42705	−	22.8581i	−0.270657	−	0.832996i
$754$	7.56231	+	23.2744i	0.275403	+	0.847603i
$755$		0			0
$756$	1.64590	−	5.06555i	0.0598607	−	0.184232i
$757$	−53.8328			−1.95659			−0.978293	−	0.207224i	$-0.933557\pi$
$757$	−53.8328			−1.95659			−0.978293	+	0.207224i	$0.933557\pi$
$758$	1.38197	−	4.25325i	0.0501953	−	0.154485i
$759$	2.42705	−	1.76336i	0.0880964	−	0.0640058i
$760$		0			0
$761$	22.0623	+	16.0292i	0.799758	+	0.581058i	0.910843	−	0.412753i	$-0.135433\pi$
$761$	22.0623	+	16.0292i	0.799758	+	0.581058i	−0.111085	+	0.993811i	$0.535433\pi$
$762$	−24.4894	+	17.7926i	−0.887156	+	0.644556i
$763$	−49.4336	+	35.9156i	−1.78962	+	1.30023i
$764$	1.50000	+	1.08981i	0.0542681	+	0.0394281i
$765$		0			0
$766$	−33.2254	+	24.1397i	−1.20048	+	0.872202i
$767$	23.5795	−	72.5703i	0.851407	−	2.62036i
$768$	35.5066			1.28123
$769$	−10.3647	+	31.8994i	−0.373762	+	1.15032i	0.570548	+	0.821265i	$0.306731\pi$
$769$	−10.3647	+	31.8994i	−0.373762	+	1.15032i	−0.944310	+	0.329057i	$0.893269\pi$
$770$		0			0
$771$	−3.00000	−	9.23305i	−0.108042	−	0.332520i
$772$	4.38197	+	13.4863i	0.157710	+	0.485383i
$773$	−35.3713	−	25.6988i	−1.27222	−	0.924321i	−0.272929	−	0.962034i	$-0.587993\pi$
$773$	−35.3713	−	25.6988i	−1.27222	−	0.924321i	−0.999289	+	0.0377135i	$0.987993\pi$
$774$	−2.94427			−0.105830
$775$		0			0
$776$	23.7426			0.852311
$777$	−24.4894	−	17.7926i	−0.878551	−	0.638305i
$778$	5.16312	+	15.8904i	0.185107	+	0.569700i
$779$	−1.70820	−	5.25731i	−0.0612028	−	0.188363i
$780$		0			0
$781$	−0.635255	+	1.95511i	−0.0227312	+	0.0699595i
$782$	4.41641			0.157930
$783$	−1.90983	+	5.87785i	−0.0682518	+	0.210057i
$784$	30.8435	−	22.4091i	1.10155	−	0.800324i
$785$		0			0
$786$	2.61803	+	1.90211i	0.0933822	+	0.0678461i
$787$	−24.9894	+	18.1558i	−0.890774	+	0.647185i	−0.936080	−	0.351788i	$-0.885574\pi$
$787$	−24.9894	+	18.1558i	−0.890774	+	0.647185i	0.0453054	+	0.998973i	$0.485574\pi$
$788$	8.23607	−	5.98385i	0.293398	−	0.213166i
$789$	−40.9336	−	29.7400i	−1.45728	−	1.05877i
$790$		0			0
$791$	−2.20820	+	1.60435i	−0.0785147	+	0.0570443i
$792$	−1.64590	+	5.06555i	−0.0584844	+	0.179997i
$793$	48.4508			1.72054
$794$	5.70820	−	17.5680i	0.202577	−	0.623467i
$795$		0			0
$796$	−2.07295	−	6.37988i	−0.0734737	−	0.226129i
$797$	12.5729	+	38.6956i	0.445357	+	1.37067i	0.882092	+	0.471077i	$0.156135\pi$
$797$	12.5729	+	38.6956i	0.445357	+	1.37067i	−0.436735	+	0.899590i	$0.643865\pi$
$798$	11.2812	+	8.19624i	0.399348	+	0.290144i
$799$	−17.1033			−0.605072
$800$		0			0
$801$	13.9443			0.492697
$802$	−19.0623	−	13.8496i	−0.673113	−	0.489046i
$803$	−0.0278640	−	0.0857567i	−0.000983301	−	0.00302629i
$804$	−5.73607	−	17.6538i	−0.202296	−	0.622602i
$805$		0			0
$806$	−5.47214	+	16.8415i	−0.192748	+	0.593217i
$807$	10.0000			0.352017
$808$	−6.74671	+	20.7642i	−0.237348	+	0.730483i
$809$	28.6803	−	20.8375i	1.00835	−	0.732607i	0.0444853	−	0.999010i	$-0.485835\pi$
$809$	28.6803	−	20.8375i	1.00835	−	0.732607i	0.963862	+	0.266403i	$0.0858352\pi$
$810$		0			0
$811$	−1.71885	−	1.24882i	−0.0603569	−	0.0438518i	0.557198	−	0.830380i	$-0.311877\pi$
$811$	−1.71885	−	1.24882i	−0.0603569	−	0.0438518i	−0.617555	+	0.786528i	$0.711877\pi$
$812$	5.32624	−	3.86974i	0.186914	−	0.135801i
$813$	27.5344	−	20.0049i	0.965675	−	0.701604i
$814$	−2.42705	−	1.76336i	−0.0850681	−	0.0618056i
$815$		0			0
$816$	−15.1353	+	10.9964i	−0.529840	+	0.384951i
$817$	0.124612	−	0.383516i	0.00435961	−	0.0134175i
$818$	−51.3050			−1.79384
$819$	−25.1180	+	77.3054i	−0.877695	+	2.70127i
$820$		0			0
$821$	−6.94427	−	21.3723i	−0.242357	−	0.745897i	−0.996060	−	0.0886825i	$-0.971734\pi$
$821$	−6.94427	−	21.3723i	−0.242357	−	0.745897i	0.753703	−	0.657215i	$-0.228266\pi$
$822$	26.4894	+	81.5259i	0.923922	+	2.84354i
$823$	−0.572949	−	0.416272i	−0.0199717	−	0.0145103i	0.577755	−	0.816211i	$-0.303929\pi$
$823$	−0.572949	−	0.416272i	−0.0199717	−	0.0145103i	−0.597726	+	0.801700i	$0.703929\pi$
$824$	11.5066			0.400851
$825$		0			0
$826$	−86.9574			−3.02564
$827$	5.56231	+	4.04125i	0.193420	+	0.140528i	0.680281	−	0.732952i	$-0.261858\pi$
$827$	5.56231	+	4.04125i	0.193420	+	0.140528i	−0.486860	+	0.873480i	$0.661858\pi$
$828$	−1.36475	−	4.20025i	−0.0474282	−	0.145969i
$829$	−4.59675	−	14.1473i	−0.159652	−	0.491357i	0.838951	−	0.544207i	$-0.183169\pi$
$829$	−4.59675	−	14.1473i	−0.159652	−	0.491357i	−0.998602	+	0.0528500i	$0.983169\pi$
$830$		0			0
$831$	−12.3713	+	38.0750i	−0.429156	+	1.32081i
$832$	−23.1803			−0.803634
$833$	−3.57295	+	10.9964i	−0.123795	+	0.381003i
$834$	−28.8435	+	20.9560i	−0.998767	+	0.725647i
$835$		0			0
$836$	0.263932	+	0.191758i	0.00912828	+	0.00663208i
$837$	−3.61803	+	2.62866i	−0.125058	+	0.0908596i
$838$	42.1976	−	30.6583i	1.45769	−	1.05907i
$839$	21.4443	+	15.5802i	0.740338	+	0.537887i	0.892817	−	0.450419i	$-0.148726\pi$
$839$	21.4443	+	15.5802i	0.740338	+	0.537887i	−0.152479	+	0.988307i	$0.548726\pi$
$840$		0			0
$841$	17.2812	−	12.5555i	0.595902	−	0.432948i
$842$	6.59017	−	20.2825i	0.227112	−	0.698980i
$843$	50.6869			1.74575
$844$	2.51722	−	7.74721i	0.0866463	−	0.266670i
$845$		0			0
$846$	22.3885	+	68.9049i	0.769734	+	2.36900i
$847$	−12.6459	−	38.9201i	−0.434518	−	1.33731i
$848$	33.2705	+	24.1724i	1.14251	+	0.830085i
$849$	−61.1591			−2.09897
$850$		0			0
$851$	−5.56231			−0.190673
$852$	4.35410	+	3.16344i	0.149169	+	0.108378i
$853$	15.9721	+	49.1572i	0.546876	+	1.68311i	0.716488	+	0.697599i	$0.245748\pi$
$853$	15.9721	+	49.1572i	0.546876	+	1.68311i	−0.169613	+	0.985511i	$0.554252\pi$
$854$	−17.0623	−	52.5124i	−0.583860	−	1.79694i
$855$		0			0
$856$	8.15248	−	25.0907i	0.278646	−	0.857584i
$857$	22.0689			0.753859			0.376929	−	0.926242i	$-0.376980\pi$
$857$	22.0689			0.753859			0.376929	+	0.926242i	$0.376980\pi$
$858$	−4.42705	+	13.6251i	−0.151137	+	0.465152i
$859$	6.28115	−	4.56352i	0.214310	−	0.155705i	−0.475452	−	0.879742i	$-0.657715\pi$
$859$	6.28115	−	4.56352i	0.214310	−	0.155705i	0.689762	+	0.724036i	$0.257715\pi$
$860$		0			0
$861$	−52.8328	−	38.3853i	−1.80054	−	1.30817i
$862$	6.00000	−	4.35926i	0.204361	−	0.148477i
$863$	25.2812	−	18.3678i	0.860580	−	0.625248i	−0.0674624	−	0.997722i	$-0.521490\pi$
$863$	25.2812	−	18.3678i	0.860580	−	0.625248i	0.928043	+	0.372474i	$0.121490\pi$
$864$	6.11803	+	4.44501i	0.208140	+	0.151222i
$865$		0			0
$866$	0.190983	−	0.138757i	0.00648987	−	0.00471516i
$867$	−12.0000	+	36.9322i	−0.407541	+	1.25428i
$868$	4.76393			0.161698
$869$	−1.28115	+	3.94298i	−0.0434601	+	0.133757i
$870$		0			0
$871$	19.3992	+	59.7046i	0.657316	+	2.02301i
$872$	−10.9549	−	33.7158i	−0.370980	−	1.14176i
$873$	33.1074	+	24.0539i	1.12052	+	0.814102i
$874$	2.56231			0.0866713
$875$		0			0
$876$	−0.236068			−0.00797600
$877$	14.5451	+	10.5676i	0.491153	+	0.356843i	0.805627	−	0.592423i	$-0.201828\pi$
$877$	14.5451	+	10.5676i	0.491153	+	0.356843i	−0.314475	+	0.949266i	$0.601828\pi$
$878$	4.63525	+	14.2658i	0.156432	+	0.481449i
$879$	11.5902	+	35.6709i	0.390927	+	1.20315i
$880$		0			0
$881$	10.0279	−	30.8626i	0.337847	−	1.03979i	−0.627455	−	0.778653i	$-0.715903\pi$
$881$	10.0279	−	30.8626i	0.337847	−	1.03979i	0.965302	−	0.261134i	$-0.0840966\pi$
$882$	48.9787			1.64920
$883$	−3.39919	+	10.4616i	−0.114392	+	0.352062i	−0.991820	−	0.127647i	$-0.959258\pi$
$883$	−3.39919	+	10.4616i	−0.114392	+	0.352062i	0.877428	+	0.479708i	$0.159258\pi$
$884$	−4.02786	+	2.92641i	−0.135472	+	0.0984260i
$885$		0			0
$886$	36.2705	+	26.3521i	1.21853	+	0.885315i
$887$	13.0000	−	9.44505i	0.436497	−	0.317134i	−0.347744	−	0.937589i	$-0.613052\pi$
$887$	13.0000	−	9.44505i	0.436497	−	0.317134i	0.784242	+	0.620456i	$0.213052\pi$
$888$	14.2082	−	10.3229i	0.476796	−	0.346413i
$889$	−22.2812	−	16.1882i	−0.747286	−	0.542935i
$890$		0			0
$891$	2.85410	−	2.07363i	0.0956160	−	0.0694691i
$892$	−0.0278640	+	0.0857567i	−0.000932957	+	0.00287135i
$893$	−9.92299			−0.332060
$894$	−17.8262	+	54.8635i	−0.596199	+	1.83491i
$895$		0			0
$896$	16.2188	+	49.9165i	0.541834	+	1.66759i
$897$	8.20820	+	25.2623i	0.274064	+	0.843482i
$898$	−38.0517	−	27.6462i	−1.26980	−	0.922564i
$899$	−5.52786			−0.184365
$900$		0			0
$901$	−12.4721			−0.415507
$902$	−5.23607	−	3.80423i	−0.174342	−	0.126667i
$903$	−1.47214	−	4.53077i	−0.0489896	−	0.150775i
$904$	−0.489357	−	1.50609i	−0.0162758	−	0.0500917i
$905$		0			0
$906$	20.8713	−	64.2353i	0.693403	−	2.13408i
$907$	−52.8541			−1.75499			−0.877496	−	0.479584i	$-0.840787\pi$
$907$	−52.8541			−1.75499			−0.877496	+	0.479584i	$0.840787\pi$
$908$	0.145898	−	0.449028i	0.00484180	−	0.0149015i
$909$	−30.4443	+	22.1191i	−1.00977	+	0.733643i
$910$		0			0
$911$	−26.3156	−	19.1194i	−0.871875	−	0.633454i	0.0592147	−	0.998245i	$-0.481140\pi$
$911$	−26.3156	−	19.1194i	−0.871875	−	0.633454i	−0.931089	+	0.364791i	$0.881140\pi$
$912$	−8.78115	+	6.37988i	−0.290773	+	0.211259i
$913$	−6.47214	+	4.70228i	−0.214196	+	0.155623i
$914$	45.6697	+	33.1810i	1.51062	+	1.09753i
$915$		0			0
$916$	1.64590	−	1.19581i	0.0543820	−	0.0395108i
$917$	−0.909830	+	2.80017i	−0.0300452	+	0.0924697i
$918$	−5.32624			−0.175792
$919$	17.7254	−	54.5532i	0.584708	−	1.79955i	−0.0157328	−	0.999876i	$-0.505008\pi$
$919$	17.7254	−	54.5532i	0.584708	−	1.79955i	0.600441	−	0.799669i	$-0.294992\pi$
$920$		0			0
$921$	11.3090	+	34.8056i	0.372645	+	1.14688i
$922$	−7.45492	−	22.9439i	−0.245515	−	0.755616i
$923$	−14.7254	−	10.6986i	−0.484693	−	0.352150i
$924$	3.85410			0.126791
$925$		0			0
$926$	5.94427			0.195341
$927$	16.0451	+	11.6574i	0.526990	+	0.382880i
$928$	2.88854	+	8.89002i	0.0948211	+	0.291829i
$929$	4.83688	+	14.8864i	0.158693	+	0.488407i	0.998516	−	0.0544531i	$-0.0173415\pi$
$929$	4.83688	+	14.8864i	0.158693	+	0.488407i	−0.839823	+	0.542860i	$0.817342\pi$
$930$		0			0
$931$	−2.07295	+	6.37988i	−0.0679382	+	0.209092i
$932$	13.6525			0.447202
$933$	11.7812	−	36.2587i	0.385698	−	1.18706i
$934$	−4.35410	+	3.16344i	−0.142471	+	0.103511i
$935$		0			0
$936$	−38.1525	−	27.7194i	−1.24705	−	0.906037i
$937$	−3.80902	+	2.76741i	−0.124435	+	0.0904074i	−0.648262	−	0.761417i	$-0.724504\pi$
$937$	−3.80902	+	2.76741i	−0.124435	+	0.0904074i	0.523827	+	0.851825i	$0.324504\pi$
$938$	57.8779	−	42.0508i	1.88978	−	1.37301i
$939$	−44.5517	−	32.3687i	−1.45389	−	1.05631i
$940$		0			0
$941$	−0.864745	+	0.628274i	−0.0281899	+	0.0204811i	−0.601791	−	0.798654i	$-0.705546\pi$
$941$	−0.864745	+	0.628274i	−0.0281899	+	0.0204811i	0.573601	+	0.819135i	$0.305546\pi$
$942$	17.0172	−	52.3736i	0.554451	−	1.70642i
$943$	−12.0000			−0.390774
$944$	20.9164	−	64.3741i	0.680771	−	2.09520i
$945$		0			0
$946$	−0.145898	−	0.449028i	−0.00474355	−	0.0145992i
$947$	0.927051	+	2.85317i	0.0301251	+	0.0927156i	0.964989	−	0.262292i	$-0.0844783\pi$
$947$	0.927051	+	2.85317i	0.0301251	+	0.0927156i	−0.934863	+	0.355007i	$0.884478\pi$
$948$	8.78115	+	6.37988i	0.285199	+	0.207209i
$949$	0.798374			0.0259163
$950$		0			0
$951$	−17.7984			−0.577152
$952$	−10.2639	−	7.45718i	−0.332656	−	0.241689i
$953$	13.5729	+	41.7732i	0.439671	+	1.35317i	0.888224	+	0.459412i	$0.151940\pi$
$953$	13.5729	+	41.7732i	0.439671	+	1.35317i	−0.448553	+	0.893756i	$0.648060\pi$
$954$	16.3262	+	50.2470i	0.528581	+	1.62681i
$955$		0			0
$956$		0			0
$957$	−4.47214			−0.144564
$958$	11.3820	−	35.0301i	0.367735	−	1.13177i
$959$	−63.0967	+	45.8425i	−2.03750	+	1.48033i
$960$		0			0
$961$	21.8435	+	15.8702i	0.704628	+	0.511942i
$962$	21.4894	−	15.6129i	0.692845	−	0.503381i
$963$	36.7877	−	26.7279i	1.18547	−	0.861293i
$964$	6.92705	+	5.03280i	0.223105	+	0.162095i
$965$		0			0
$966$	24.4894	−	17.7926i	0.787932	−	0.572466i
$967$	−9.60081	+	29.5483i	−0.308741	+	0.950208i	0.669513	+	0.742800i	$0.266503\pi$
$967$	−9.60081	+	29.5483i	−0.308741	+	0.950208i	−0.978255	+	0.207408i	$0.933497\pi$
$968$	23.7426			0.763118
$969$	1.01722	−	3.13068i	0.0326778	−	0.100572i
$970$		0			0
$971$	1.44834	+	4.45752i	0.0464794	+	0.143049i	0.971603	−	0.236618i	$-0.0760388\pi$
$971$	1.44834	+	4.45752i	0.0464794	+	0.143049i	−0.925124	+	0.379666i	$0.876039\pi$
$972$	−4.13525	−	12.7270i	−0.132638	−	0.408219i
$973$	−26.2426	−	19.0664i	−0.841301	−	0.611241i
$974$	8.67376			0.277925
$975$		0			0
$976$	42.9787			1.37572
$977$	−21.8992	−	15.9107i	−0.700617	−	0.509028i	0.179516	−	0.983755i	$-0.442547\pi$
$977$	−21.8992	−	15.9107i	−0.700617	−	0.509028i	−0.880133	+	0.474727i	$0.842547\pi$
$978$	−2.42705	−	7.46969i	−0.0776085	−	0.238855i
$979$	0.690983	+	2.12663i	0.0220839	+	0.0679673i
$980$		0			0
$981$	18.8820	−	58.1127i	0.602855	−	1.85540i
$982$	50.0689			1.59776
$983$	10.8328	−	33.3400i	0.345513	−	1.06338i	−0.615795	−	0.787906i	$-0.711165\pi$
$983$	10.8328	−	33.3400i	0.345513	−	1.06338i	0.961309	−	0.275474i	$-0.0888348\pi$
$984$	30.6525	−	22.2703i	0.977165	−	0.709952i
$985$		0			0
$986$	−5.32624	−	3.86974i	−0.169622	−	0.123238i
$987$	−94.8394	+	68.9049i	−3.01877	+	2.19327i
$988$	−2.33688	+	1.69784i	−0.0743461	+	0.0540156i
$989$	−0.708204	−	0.514540i	−0.0225196	−	0.0163614i
$990$		0			0
$991$	29.5623	−	21.4783i	0.939078	−	0.682280i	−0.00912086	−	0.999958i	$-0.502903\pi$
$991$	29.5623	−	21.4783i	0.939078	−	0.682280i	0.948198	+	0.317679i	$0.102903\pi$
$992$	−2.09017	+	6.43288i	−0.0663630	+	0.204244i
$993$	40.0344			1.27045
$994$	−6.40983	+	19.7274i	−0.203307	+	0.625716i
$995$		0			0
$996$	6.47214	+	19.9192i	0.205077	+	0.631164i
$997$	1.68034	+	5.17155i	0.0532169	+	0.163785i	0.974133	−	0.225977i	$-0.0725574\pi$
$997$	1.68034	+	5.17155i	0.0532169	+	0.163785i	−0.920916	+	0.389762i	$0.872557\pi$
$998$	37.1976	+	27.0256i	1.17747	+	0.855481i
$999$	6.70820			0.212238

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	625.2.d.c.376.1		4
5.2	odd	4		625.2.e.e.249.2		8
5.3	odd	4		625.2.e.e.249.1		8
5.4	even	2		625.2.d.i.376.1		4
25.2	odd	20		625.2.e.e.374.1		8
25.3	odd	20		625.2.e.f.499.2		8
25.4	even	10		625.2.d.e.126.1		4
25.6	even	5		625.2.a.d.1.2	yes	2
25.8	odd	20		625.2.b.b.624.1		4
25.9	even	10		625.2.d.e.501.1		4
25.11	even	5	inner	625.2.d.c.251.1		4
25.12	odd	20		625.2.e.f.124.2		8
25.13	odd	20		625.2.e.f.124.1		8
25.14	even	10		625.2.d.i.251.1		4
25.16	even	5		625.2.d.f.501.1		4
25.17	odd	20		625.2.b.b.624.4		4
25.19	even	10		625.2.a.a.1.1	✓	2
25.21	even	5		625.2.d.f.126.1		4
25.22	odd	20		625.2.e.f.499.1		8
25.23	odd	20		625.2.e.e.374.2		8
75.44	odd	10		5625.2.a.e.1.2		2
75.56	odd	10		5625.2.a.c.1.1		2
100.19	odd	10		10000.2.a.m.1.2		2
100.31	odd	10		10000.2.a.b.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
625.2.a.a.1.1	✓	2	25.19	even	10
625.2.a.d.1.2	yes	2	25.6	even	5
625.2.b.b.624.1		4	25.8	odd	20
625.2.b.b.624.4		4	25.17	odd	20
625.2.d.c.251.1		4	25.11	even	5	inner
625.2.d.c.376.1		4	1.1	even	1	trivial
625.2.d.e.126.1		4	25.4	even	10
625.2.d.e.501.1		4	25.9	even	10
625.2.d.f.126.1		4	25.21	even	5
625.2.d.f.501.1		4	25.16	even	5
625.2.d.i.251.1		4	25.14	even	10
625.2.d.i.376.1		4	5.4	even	2
625.2.e.e.249.1		8	5.3	odd	4
625.2.e.e.249.2		8	5.2	odd	4
625.2.e.e.374.1		8	25.2	odd	20
625.2.e.e.374.2		8	25.23	odd	20
625.2.e.f.124.1		8	25.13	odd	20
625.2.e.f.124.2		8	25.12	odd	20
625.2.e.f.499.1		8	25.22	odd	20
625.2.e.f.499.2		8	25.3	odd	20
5625.2.a.c.1.1		2	75.56	odd	10
5625.2.a.e.1.2		2	75.44	odd	10
10000.2.a.b.1.1		2	100.31	odd	10
10000.2.a.m.1.2		2	100.19	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)

\(f(q)\)	\(=\)	\(q+(-1.30902 - 0.951057i) q^{2} +(0.809017 + 2.48990i) q^{3} +(0.190983 + 0.587785i) q^{4} +(1.30902 - 4.02874i) q^{6} +3.85410 q^{7} +(-0.690983 + 2.12663i) q^{8} +(-3.11803 + 2.26538i) q^{9} +O(q^{10})\)	\(q+(-1.30902 - 0.951057i) q^{2} +(0.809017 + 2.48990i) q^{3} +(0.190983 + 0.587785i) q^{4} +(1.30902 - 4.02874i) q^{6} +3.85410 q^{7} +(-0.690983 + 2.12663i) q^{8} +(-3.11803 + 2.26538i) q^{9} +(-0.500000 - 0.363271i) q^{11} +(-1.30902 + 0.951057i) q^{12} +(4.42705 - 3.21644i) q^{13} +(-5.04508 - 3.66547i) q^{14} +(3.92705 - 2.85317i) q^{16} +(-0.454915 + 1.40008i) q^{17} +6.23607 q^{18} +(-0.263932 + 0.812299i) q^{19} +(3.11803 + 9.59632i) q^{21} +(0.309017 + 0.951057i) q^{22} +(1.50000 + 1.08981i) q^{23} -5.85410 q^{24} -8.85410 q^{26} +(-1.80902 - 1.31433i) q^{27} +(0.736068 + 2.26538i) q^{28} +(-0.854102 - 2.62866i) q^{29} +(0.618034 - 1.90211i) q^{31} -3.38197 q^{32} +(0.500000 - 1.53884i) q^{33} +(1.92705 - 1.40008i) q^{34} +(-1.92705 - 1.40008i) q^{36} +(-2.42705 + 1.76336i) q^{37} +(1.11803 - 0.812299i) q^{38} +(11.5902 + 8.42075i) q^{39} +(-5.23607 + 3.80423i) q^{41} +(5.04508 - 15.5272i) q^{42} -0.472136 q^{43} +(0.118034 - 0.363271i) q^{44} +(-0.927051 - 2.85317i) q^{46} +(3.59017 + 11.0494i) q^{47} +(10.2812 + 7.46969i) q^{48} +7.85410 q^{49} -3.85410 q^{51} +(2.73607 + 1.98787i) q^{52} +(2.61803 + 8.05748i) q^{53} +(1.11803 + 3.44095i) q^{54} +(-2.66312 + 8.19624i) q^{56} -2.23607 q^{57} +(-1.38197 + 4.25325i) q^{58} +(11.2812 - 8.19624i) q^{59} +(7.16312 + 5.20431i) q^{61} +(-2.61803 + 1.90211i) q^{62} +(-12.0172 + 8.73102i) q^{63} +(-3.42705 - 2.48990i) q^{64} +(-2.11803 + 1.53884i) q^{66} +(-3.54508 + 10.9106i) q^{67} -0.909830 q^{68} +(-1.50000 + 4.61653i) q^{69} +(-1.02786 - 3.16344i) q^{71} +(-2.66312 - 8.19624i) q^{72} +(0.118034 + 0.0857567i) q^{73} +4.85410 q^{74} -0.527864 q^{76} +(-1.92705 - 1.40008i) q^{77} +(-7.16312 - 22.0458i) q^{78} +(-2.07295 - 6.37988i) q^{79} +(-1.76393 + 5.42882i) q^{81} +10.4721 q^{82} +(4.00000 - 12.3107i) q^{83} +(-5.04508 + 3.66547i) q^{84} +(0.618034 + 0.449028i) q^{86} +(5.85410 - 4.25325i) q^{87} +(1.11803 - 0.812299i) q^{88} +(-2.92705 - 2.12663i) q^{89} +(17.0623 - 12.3965i) q^{91} +(-0.354102 + 1.08981i) q^{92} +5.23607 q^{93} +(5.80902 - 17.8783i) q^{94} +(-2.73607 - 8.42075i) q^{96} +(-3.28115 - 10.0984i) q^{97} +(-10.2812 - 7.46969i) q^{98} +2.38197 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 3 q^{2} + q^{3} + 3 q^{4} + 3 q^{6} + 2 q^{7} - 5 q^{8} - 8 q^{9}+O(q^{10}) \) 4 * q - 3 * q^2 + q^3 + 3 * q^4 + 3 * q^6 + 2 * q^7 - 5 * q^8 - 8 * q^9	\( 4 q - 3 q^{2} + q^{3} + 3 q^{4} + 3 q^{6} + 2 q^{7} - 5 q^{8} - 8 q^{9} - 2 q^{11} - 3 q^{12} + 11 q^{13} - 9 q^{14} + 9 q^{16} - 13 q^{17} + 16 q^{18} - 10 q^{19} + 8 q^{21} - q^{22} + 6 q^{23} - 10 q^{24} - 22 q^{26} - 5 q^{27} - 6 q^{28} + 10 q^{29} - 2 q^{31} - 18 q^{32} + 2 q^{33} + q^{34} - q^{36} - 3 q^{37} + 24 q^{39} - 12 q^{41} + 9 q^{42} + 16 q^{43} - 4 q^{44} + 3 q^{46} - 8 q^{47} + 21 q^{48} + 18 q^{49} - 2 q^{51} + 2 q^{52} + 6 q^{53} + 5 q^{56} - 10 q^{58} + 25 q^{59} + 13 q^{61} - 6 q^{62} - 19 q^{63} - 7 q^{64} - 4 q^{66} - 3 q^{67} - 26 q^{68} - 6 q^{69} - 22 q^{71} + 5 q^{72} - 4 q^{73} + 6 q^{74} - 20 q^{76} - q^{77} - 13 q^{78} - 15 q^{79} - 16 q^{81} + 24 q^{82} + 16 q^{83} - 9 q^{84} - 2 q^{86} + 10 q^{87} - 5 q^{89} + 28 q^{91} + 12 q^{92} + 12 q^{93} + 21 q^{94} - 2 q^{96} + 7 q^{97} - 21 q^{98} + 14 q^{99}+O(q^{100}) \) 4 * q - 3 * q^2 + q^3 + 3 * q^4 + 3 * q^6 + 2 * q^7 - 5 * q^8 - 8 * q^9 - 2 * q^11 - 3 * q^12 + 11 * q^13 - 9 * q^14 + 9 * q^16 - 13 * q^17 + 16 * q^18 - 10 * q^19 + 8 * q^21 - q^22 + 6 * q^23 - 10 * q^24 - 22 * q^26 - 5 * q^27 - 6 * q^28 + 10 * q^29 - 2 * q^31 - 18 * q^32 + 2 * q^33 + q^34 - q^36 - 3 * q^37 + 24 * q^39 - 12 * q^41 + 9 * q^42 + 16 * q^43 - 4 * q^44 + 3 * q^46 - 8 * q^47 + 21 * q^48 + 18 * q^49 - 2 * q^51 + 2 * q^52 + 6 * q^53 + 5 * q^56 - 10 * q^58 + 25 * q^59 + 13 * q^61 - 6 * q^62 - 19 * q^63 - 7 * q^64 - 4 * q^66 - 3 * q^67 - 26 * q^68 - 6 * q^69 - 22 * q^71 + 5 * q^72 - 4 * q^73 + 6 * q^74 - 20 * q^76 - q^77 - 13 * q^78 - 15 * q^79 - 16 * q^81 + 24 * q^82 + 16 * q^83 - 9 * q^84 - 2 * q^86 + 10 * q^87 - 5 * q^89 + 28 * q^91 + 12 * q^92 + 12 * q^93 + 21 * q^94 - 2 * q^96 + 7 * q^97 - 21 * q^98 + 14 * q^99

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