LMFDB - Embedded newform 285.2.k.d.248.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [285,2,Mod(77,285)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(285, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("285.77");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 285 = 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	285.k (of order $4$, degree $2$, 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:	$2.27573645761$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			248.7
Character	$\chi$	$=$	285.248
Dual form			285.2.k.d.77.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.631220 - 0.631220i) q^{2} +(-1.41501 - 0.998873i) q^{3} -1.20312i q^{4} +(1.34140 + 1.78903i) q^{5} +(0.262674 + 1.52369i) q^{6} +(-3.10938 + 3.10938i) q^{7} +(-2.02187 + 2.02187i) q^{8} +(1.00451 + 2.82683i) q^{9} +O(q^{10})$	\(q+(-0.631220 - 0.631220i) q^{2} +(-1.41501 - 0.998873i) q^{3} -1.20312i q^{4} +(1.34140 + 1.78903i) q^{5} +(0.262674 + 1.52369i) q^{6} +(-3.10938 + 3.10938i) q^{7} +(-2.02187 + 2.02187i) q^{8} +(1.00451 + 2.82683i) q^{9} +(0.282552 - 1.97599i) q^{10} +0.484934i q^{11} +(-1.20177 + 1.70243i) q^{12} +(-1.71998 - 1.71998i) q^{13} +3.92540 q^{14} +(-0.111085 - 3.87139i) q^{15} +0.146246 q^{16} +(5.25692 + 5.25692i) q^{17} +(1.15029 - 2.41841i) q^{18} -1.00000i q^{19} +(2.15243 - 1.61387i) q^{20} +(7.50568 - 1.29393i) q^{21} +(0.306100 - 0.306100i) q^{22} +(-2.66096 + 2.66096i) q^{23} +(4.88057 - 0.841377i) q^{24} +(-1.40127 + 4.79963i) q^{25} +2.17137i q^{26} +(1.40226 - 5.00337i) q^{27} +(3.74097 + 3.74097i) q^{28} -6.46492 q^{29} +(-2.37358 + 2.51382i) q^{30} +3.84489 q^{31} +(3.95144 + 3.95144i) q^{32} +(0.484388 - 0.686187i) q^{33} -6.63654i q^{34} +(-9.73372 - 1.39185i) q^{35} +(3.40103 - 1.20855i) q^{36} +(-1.24679 + 1.24679i) q^{37} +(-0.631220 + 0.631220i) q^{38} +(0.715749 + 4.15184i) q^{39} +(-6.32935 - 0.905048i) q^{40} +10.2468i q^{41} +(-5.55449 - 3.92098i) q^{42} +(-1.78437 - 1.78437i) q^{43} +0.583436 q^{44} +(-3.70984 + 5.58902i) q^{45} +3.35930 q^{46} +(-4.00816 - 4.00816i) q^{47} +(-0.206939 - 0.146081i) q^{48} -12.3365i q^{49} +(3.91413 - 2.14511i) q^{50} +(-2.18760 - 12.6896i) q^{51} +(-2.06935 + 2.06935i) q^{52} +(2.13230 - 2.13230i) q^{53} +(-4.04335 + 2.27309i) q^{54} +(-0.867563 + 0.650493i) q^{55} -12.5736i q^{56} +(-0.998873 + 1.41501i) q^{57} +(4.08078 + 4.08078i) q^{58} -4.08854 q^{59} +(-4.65776 + 0.133649i) q^{60} -0.395747 q^{61} +(-2.42697 - 2.42697i) q^{62} +(-11.9131 - 5.66630i) q^{63} -5.28094i q^{64} +(0.769913 - 5.38430i) q^{65} +(-0.738890 + 0.127380i) q^{66} +(-0.787783 + 0.787783i) q^{67} +(6.32472 - 6.32472i) q^{68} +(6.42324 - 1.10732i) q^{69} +(5.26555 + 7.02267i) q^{70} +7.63110i q^{71} +(-7.74648 - 3.68451i) q^{72} +(-0.661154 - 0.661154i) q^{73} +1.57399 q^{74} +(6.77703 - 5.39183i) q^{75} -1.20312 q^{76} +(-1.50785 - 1.50785i) q^{77} +(2.16893 - 3.07252i) q^{78} +7.50129i q^{79} +(0.196174 + 0.261638i) q^{80} +(-6.98193 + 5.67914i) q^{81} +(6.46798 - 6.46798i) q^{82} +(-6.64986 + 6.64986i) q^{83} +(-1.55676 - 9.03026i) q^{84} +(-2.35314 + 16.4564i) q^{85} +2.25266i q^{86} +(9.14792 + 6.45763i) q^{87} +(-0.980476 - 0.980476i) q^{88} +8.36904 q^{89} +(5.86962 - 1.18617i) q^{90} +10.6962 q^{91} +(3.20146 + 3.20146i) q^{92} +(-5.44056 - 3.84055i) q^{93} +5.06005i q^{94} +(1.78903 - 1.34140i) q^{95} +(-1.64434 - 9.53830i) q^{96} +(-7.06303 + 7.06303i) q^{97} +(-7.78704 + 7.78704i) q^{98} +(-1.37083 + 0.487120i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 2 q^{3} + 4 q^{6} + 4 q^{7}+O(q^{10}) $ 36 * q - 2 * q^3 + 4 * q^6 + 4 * q^7	$ 36 q - 2 q^{3} + 4 q^{6} + 4 q^{7} - 4 q^{10} - 18 q^{12} - 8 q^{13} - 8 q^{15} - 84 q^{16} + 8 q^{21} + 40 q^{22} - 20 q^{25} - 14 q^{27} + 36 q^{28} + 28 q^{30} - 28 q^{33} + 92 q^{36} - 4 q^{37} - 20 q^{40} - 100 q^{42} + 16 q^{43} + 28 q^{45} - 24 q^{46} - 58 q^{48} + 32 q^{51} + 148 q^{52} - 72 q^{55} - 2 q^{57} - 12 q^{58} + 58 q^{60} - 112 q^{61} - 64 q^{63} + 92 q^{66} - 8 q^{67} + 8 q^{70} - 88 q^{72} + 76 q^{73} + 80 q^{75} + 36 q^{76} - 36 q^{78} + 4 q^{81} + 20 q^{82} - 28 q^{85} - 4 q^{87} + 140 q^{88} + 76 q^{90} - 24 q^{91} - 48 q^{93} + 32 q^{96} + 32 q^{97}+O(q^{100}) $ 36 * q - 2 * q^3 + 4 * q^6 + 4 * q^7 - 4 * q^10 - 18 * q^12 - 8 * q^13 - 8 * q^15 - 84 * q^16 + 8 * q^21 + 40 * q^22 - 20 * q^25 - 14 * q^27 + 36 * q^28 + 28 * q^30 - 28 * q^33 + 92 * q^36 - 4 * q^37 - 20 * q^40 - 100 * q^42 + 16 * q^43 + 28 * q^45 - 24 * q^46 - 58 * q^48 + 32 * q^51 + 148 * q^52 - 72 * q^55 - 2 * q^57 - 12 * q^58 + 58 * q^60 - 112 * q^61 - 64 * q^63 + 92 * q^66 - 8 * q^67 + 8 * q^70 - 88 * q^72 + 76 * q^73 + 80 * q^75 + 36 * q^76 - 36 * q^78 + 4 * q^81 + 20 * q^82 - 28 * q^85 - 4 * q^87 + 140 * q^88 + 76 * q^90 - 24 * q^91 - 48 * q^93 + 32 * q^96 + 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/285\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$211$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

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 $

$2$	−0.631220	−	0.631220i	−0.446340	−	0.446340i	0.447796	−	0.894136i	$-0.352209\pi$
$2$	−0.631220	−	0.631220i	−0.446340	−	0.446340i	−0.894136	+	0.447796i	$0.852209\pi$
$3$	−1.41501	−	0.998873i	−0.816956	−	0.576699i
$3$	−1.41501	−	0.998873i	−0.816956	−	0.576699i
$4$		−	1.20312i		−	0.601562i
$5$	1.34140	+	1.78903i	0.599894	+	0.800079i
$5$	1.34140	+	1.78903i	0.599894	+	0.800079i
$6$	0.262674	+	1.52369i	0.107236	+	0.622044i
$7$	−3.10938	+	3.10938i	−1.17524	+	1.17524i	−0.194292	+	0.980944i	$0.562241\pi$
$7$	−3.10938	+	3.10938i	−1.17524	+	1.17524i	−0.980944	+	0.194292i	$0.937759\pi$
$8$	−2.02187	+	2.02187i	−0.714841	+	0.714841i
$9$	1.00451	+	2.82683i	0.334836	+	0.942277i
$10$	0.282552	−	1.97599i	0.0893507	−	0.624864i
$11$			0.484934i			0.146213i	0.997324	+	0.0731066i	$0.0232913\pi$
$11$			0.484934i			0.146213i	−0.997324	+	0.0731066i	$0.976709\pi$
$12$	−1.20177	+	1.70243i	−0.346920	+	0.491450i
$13$	−1.71998	−	1.71998i	−0.477037	−	0.477037i	0.427146	−	0.904183i	$-0.359519\pi$
$13$	−1.71998	−	1.71998i	−0.477037	−	0.477037i	−0.904183	+	0.427146i	$0.859519\pi$
$14$	3.92540			1.04911
$15$	−0.111085	−	3.87139i	−0.0286820	−	0.999589i
$16$	0.146246			0.0365614
$17$	5.25692	+	5.25692i	1.27499	+	1.27499i	0.943437	+	0.331553i	$0.107572\pi$
$17$	5.25692	+	5.25692i	1.27499	+	1.27499i	0.331553	+	0.943437i	$0.392428\pi$
$18$	1.15029	−	2.41841i	0.271125	−	0.570026i
$19$		−	1.00000i		−	0.229416i
$19$		−	1.00000i		−	0.229416i
$20$	2.15243	−	1.61387i	0.481297	−	0.360873i
$21$	7.50568	−	1.29393i	1.63787	−	0.282359i
$22$	0.306100	−	0.306100i	0.0652607	−	0.0652607i
$23$	−2.66096	+	2.66096i	−0.554848	+	0.554848i	−0.927836	−	0.372988i	$-0.878333\pi$
$23$	−2.66096	+	2.66096i	−0.554848	+	0.554848i	0.372988	+	0.927836i	$0.378333\pi$
$24$	4.88057	−	0.841377i	0.996242	−	0.171745i
$25$	−1.40127	+	4.79963i	−0.280254	+	0.959926i
$26$			2.17137i			0.425841i
$27$	1.40226	−	5.00337i	0.269864	−	0.962898i
$28$	3.74097	+	3.74097i	0.706977	+	0.706977i
$29$	−6.46492			−1.20050			−0.600252	−	0.799811i	$-0.704933\pi$
$29$	−6.46492			−1.20050			−0.600252	+	0.799811i	$0.704933\pi$
$30$	−2.37358	+	2.51382i	−0.433354	+	0.458958i
$31$	3.84489			0.690562			0.345281	−	0.938499i	$-0.387784\pi$
$31$	3.84489			0.690562			0.345281	+	0.938499i	$0.387784\pi$
$32$	3.95144	+	3.95144i	0.698522	+	0.698522i
$33$	0.484388	−	0.686187i	0.0843211	−	0.119450i
$34$		−	6.63654i		−	1.13816i
$35$	−9.73372	−	1.39185i	−1.64530	−	0.235265i
$36$	3.40103	−	1.20855i	0.566838	−	0.201424i
$37$	−1.24679	+	1.24679i	−0.204971	+	0.204971i	−0.802126	−	0.597155i	$-0.796298\pi$
$37$	−1.24679	+	1.24679i	−0.204971	+	0.204971i	0.597155	+	0.802126i	$0.296298\pi$
$38$	−0.631220	+	0.631220i	−0.102397	+	0.102397i
$39$	0.715749	+	4.15184i	0.114612	+	0.664826i
$40$	−6.32935	−	0.905048i	−1.00076	−	0.143101i
$41$			10.2468i			1.60028i	0.599812	+	0.800141i	$0.295242\pi$
$41$			10.2468i			1.60028i	−0.599812	+	0.800141i	$0.704758\pi$
$42$	−5.55449	−	3.92098i	−0.857076	−	0.605020i
$43$	−1.78437	−	1.78437i	−0.272115	−	0.272115i	0.557836	−	0.829951i	$-0.311632\pi$
$43$	−1.78437	−	1.78437i	−0.272115	−	0.272115i	−0.829951	+	0.557836i	$0.811632\pi$
$44$	0.583436			0.0879563
$45$	−3.70984	+	5.58902i	−0.553030	+	0.833161i
$46$	3.35930			0.495301
$47$	−4.00816	−	4.00816i	−0.584650	−	0.584650i	0.351528	−	0.936177i	$-0.385662\pi$
$47$	−4.00816	−	4.00816i	−0.584650	−	0.584650i	−0.936177	+	0.351528i	$0.885662\pi$
$48$	−0.206939	−	0.146081i	−0.0298691	−	0.0210849i
$49$		−	12.3365i		−	1.76236i
$50$	3.91413	−	2.14511i	0.553541	−	0.303364i
$51$	−2.18760	−	12.6896i	−0.306325	−	1.77690i
$52$	−2.06935	+	2.06935i	−0.286968	+	0.286968i
$53$	2.13230	−	2.13230i	0.292893	−	0.292893i	−0.545329	−	0.838222i	$-0.683595\pi$
$53$	2.13230	−	2.13230i	0.292893	−	0.292893i	0.838222	+	0.545329i	$0.183595\pi$
$54$	−4.04335	+	2.27309i	−0.550231	+	0.309329i
$55$	−0.867563	+	0.650493i	−0.116982	+	0.0877124i
$56$		−	12.5736i		−	1.68021i
$57$	−0.998873	+	1.41501i	−0.132304	+	0.187423i
$58$	4.08078	+	4.08078i	0.535833	+	0.535833i
$59$	−4.08854			−0.532283			−0.266141	−	0.963934i	$-0.585749\pi$
$59$	−4.08854			−0.532283			−0.266141	+	0.963934i	$0.585749\pi$
$60$	−4.65776	+	0.133649i	−0.601314	+	0.0172540i
$61$	−0.395747			−0.0506703			−0.0253351	−	0.999679i	$-0.508065\pi$
$61$	−0.395747			−0.0506703			−0.0253351	+	0.999679i	$0.508065\pi$
$62$	−2.42697	−	2.42697i	−0.308225	−	0.308225i
$63$	−11.9131	−	5.66630i	−1.50091	−	0.713886i
$64$		−	5.28094i		−	0.660117i
$65$	0.769913	−	5.38430i	0.0954959	−	0.667840i
$66$	−0.738890	+	0.127380i	−0.0909510	+	0.0156794i
$67$	−0.787783	+	0.787783i	−0.0962430	+	0.0962430i	−0.753589	−	0.657346i	$-0.771679\pi$
$67$	−0.787783	+	0.787783i	−0.0962430	+	0.0962430i	0.657346	+	0.753589i	$0.271679\pi$
$68$	6.32472	−	6.32472i	0.766985	−	0.766985i
$69$	6.42324	−	1.10732i	0.773267	−	0.133306i
$70$	5.26555	+	7.02267i	0.629354	+	0.839370i
$71$			7.63110i			0.905645i	0.891601	+	0.452822i	$0.149583\pi$
$71$			7.63110i			0.905645i	−0.891601	+	0.452822i	$0.850417\pi$
$72$	−7.74648	−	3.68451i	−0.912932	−	0.434223i
$73$	−0.661154	−	0.661154i	−0.0773822	−	0.0773822i	0.667356	−	0.744739i	$-0.267426\pi$
$73$	−0.661154	−	0.661154i	−0.0773822	−	0.0773822i	−0.744739	+	0.667356i	$0.767426\pi$
$74$	1.57399			0.182973
$75$	6.77703	−	5.39183i	0.782544	−	0.622595i
$76$	−1.20312			−0.138008
$77$	−1.50785	−	1.50785i	−0.171835	−	0.171835i
$78$	2.16893	−	3.07252i	0.245582	−	0.347894i
$79$			7.50129i			0.843961i	0.906605	+	0.421980i	$0.138665\pi$
$79$			7.50129i			0.843961i	−0.906605	+	0.421980i	$0.861335\pi$
$80$	0.196174	+	0.261638i	0.0219330	+	0.0292520i
$81$	−6.98193	+	5.67914i	−0.775770	+	0.631015i
$82$	6.46798	−	6.46798i	0.714269	−	0.714269i
$83$	−6.64986	+	6.64986i	−0.729917	+	0.729917i	−0.970603	−	0.240686i	$-0.922628\pi$
$83$	−6.64986	+	6.64986i	−0.729917	+	0.729917i	0.240686	+	0.970603i	$0.422628\pi$
$84$	−1.55676	−	9.03026i	−0.169856	−	0.985283i
$85$	−2.35314	+	16.4564i	−0.255234	+	1.78495i
$86$			2.25266i			0.242911i
$87$	9.14792	+	6.45763i	0.980760	+	0.692330i
$88$	−0.980476	−	0.980476i	−0.104519	−	0.104519i
$89$	8.36904			0.887116			0.443558	−	0.896246i	$-0.353716\pi$
$89$	8.36904			0.887116			0.443558	+	0.896246i	$0.353716\pi$
$90$	5.86962	−	1.18617i	0.618712	−	0.125034i
$91$	10.6962			1.12126
$92$	3.20146	+	3.20146i	0.333775	+	0.333775i
$93$	−5.44056	−	3.84055i	−0.564159	−	0.398247i
$94$			5.06005i			0.521904i
$95$	1.78903	−	1.34140i	0.183551	−	0.137625i
$96$	−1.64434	−	9.53830i	−0.167825	−	0.973499i
$97$	−7.06303	+	7.06303i	−0.717142	+	0.717142i	−0.968019	−	0.250877i	$-0.919281\pi$
$97$	−7.06303	+	7.06303i	−0.717142	+	0.717142i	0.250877	+	0.968019i	$0.419281\pi$
$98$	−7.78704	+	7.78704i	−0.786610	+	0.786610i
$99$	−1.37083	+	0.487120i	−0.137773	+	0.0489574i
$100$	5.77455	+	1.68590i	0.577455	+	0.168590i
$101$			0.402110i			0.0400115i	0.999800	+	0.0200057i	$0.00636845\pi$
$101$			0.402110i			0.0400115i	−0.999800	+	0.0200057i	$0.993632\pi$
$102$	−6.62905	+	9.39077i	−0.656374	+	0.929824i
$103$	−9.11315	−	9.11315i	−0.897946	−	0.897946i	0.0973085	−	0.995254i	$-0.468977\pi$
$103$	−9.11315	−	9.11315i	−0.897946	−	0.897946i	−0.995254	+	0.0973085i	$0.968977\pi$
$104$	6.95518			0.682011
$105$	12.3830	+	11.6922i	1.20846	+	1.14104i
$106$	−2.69189			−0.261460
$107$	−8.57439	−	8.57439i	−0.828918	−	0.828918i	0.158449	−	0.987367i	$-0.449351\pi$
$107$	−8.57439	−	8.57439i	−0.828918	−	0.828918i	−0.987367	+	0.158449i	$0.949351\pi$
$108$	−6.01967	−	1.68709i	−0.579243	−	0.162340i
$109$		−	2.94223i		−	0.281814i	−0.990023	−	0.140907i	$-0.954998\pi$
$109$		−	2.94223i		−	0.281814i	0.990023	−	0.140907i	$-0.0450019\pi$
$110$	0.958226	+	0.137019i	0.0913633	+	0.0130642i
$111$	3.00960	−	0.518835i	0.285659	−	0.0492457i
$112$	−0.454733	+	0.454733i	−0.0429683	+	0.0429683i
$113$	13.6558	−	13.6558i	1.28463	−	1.28463i	0.346632	−	0.938001i	$-0.387325\pi$
$113$	13.6558	−	13.6558i	1.28463	−	1.28463i	0.938001	−	0.346632i	$-0.112675\pi$
$114$	1.52369	−	0.262674i	0.142707	−	0.0246017i
$115$	−8.32995	−	1.19112i	−0.776772	−	0.111072i
$116$			7.77809i			0.722178i
$117$	3.13436	−	6.58983i	0.289772	−	0.609230i
$118$	2.58077	+	2.58077i	0.237579	+	0.237579i
$119$	−32.6915			−2.99683
$120$	8.05206	+	7.60286i	0.735049	+	0.694043i
$121$	10.7648			0.978622
$122$	0.249803	+	0.249803i	0.0226161	+	0.0226161i
$123$	10.2353	−	14.4993i	0.922882	−	1.30736i
$124$		−	4.62588i		−	0.415416i
$125$	−10.4664	+	3.93132i	−0.936140	+	0.351628i
$126$	3.94310	+	11.0964i	0.351279	+	0.988550i
$127$	12.4056	−	12.4056i	1.10082	−	1.10082i	0.106507	−	0.994312i	$-0.466033\pi$
$127$	12.4056	−	12.4056i	1.10082	−	1.10082i	0.994312	−	0.106507i	$-0.0339665\pi$
$128$	4.56944	−	4.56944i	0.403885	−	0.403885i
$129$	0.742545	+	4.30727i	0.0653774	+	0.379234i
$130$	−3.88466	+	2.91269i	−0.340707	+	0.255460i
$131$		−	2.18846i		−	0.191206i	−0.995420	−	0.0956032i	$-0.969522\pi$
$131$		−	2.18846i		−	0.191206i	0.995420	−	0.0956032i	$-0.0304780\pi$
$132$	−0.825568	−	0.582778i	−0.0718565	−	0.0507243i
$133$	3.10938	+	3.10938i	0.269618	+	0.269618i
$134$	0.994528			0.0859141
$135$	10.8322	−	4.20286i	0.932285	−	0.361724i
$136$	−21.2576			−1.82283
$137$	13.4491	+	13.4491i	1.14903	+	1.14903i	0.986744	+	0.162287i	$0.0518870\pi$
$137$	13.4491	+	13.4491i	1.14903	+	1.14903i	0.162287	+	0.986744i	$0.448113\pi$
$138$	−4.75344	−	3.35551i	−0.404639	−	0.285640i
$139$			19.8345i			1.68234i	0.540769	+	0.841171i	$0.318133\pi$
$139$			19.8345i			1.68234i	−0.540769	+	0.841171i	$0.681867\pi$
$140$	−1.67456	+	11.7109i	−0.141526	+	0.989749i
$141$	1.66794	+	9.67522i	0.140466	+	0.814800i
$142$	4.81690	−	4.81690i	0.404225	−	0.404225i
$143$	0.834079	−	0.834079i	0.0697492	−	0.0697492i
$144$	0.146905	+	0.413411i	0.0122421	+	0.0344510i
$145$	−8.67206	−	11.5659i	−0.720176	−	0.960499i
$146$			0.834667i			0.0690775i
$147$	−12.3226	+	17.4563i	−1.01635	+	1.43977i
$148$	1.50004	+	1.50004i	0.123303	+	0.123303i
$149$	0.129352			0.0105970			0.00529848	−	0.999986i	$-0.498313\pi$
$149$	0.129352			0.0105970			0.00529848	+	0.999986i	$0.498313\pi$
$150$	−7.68122	−	0.874364i	−0.627169	−	0.0713916i
$151$	9.09129			0.739839			0.369920	−	0.929064i	$-0.379385\pi$
$151$	9.09129			0.739839			0.369920	+	0.929064i	$0.379385\pi$
$152$	2.02187	+	2.02187i	0.163996	+	0.163996i
$153$	−9.57980	+	20.1410i	−0.774481	+	1.62830i
$154$			1.90356i			0.153394i
$155$	5.15755	+	6.87863i	0.414264	+	0.552505i
$156$	4.99517	−	0.861135i	0.399934	−	0.0689460i
$157$	17.5751	−	17.5751i	1.40265	−	1.40265i	0.611078	−	0.791571i	$-0.290736\pi$
$157$	17.5751	−	17.5751i	1.40265	−	1.40265i	0.791571	−	0.611078i	$-0.209264\pi$
$158$	4.73496	−	4.73496i	0.376693	−	0.376693i
$159$	−5.14711	+	0.887328i	−0.408193	+	0.0703697i
$160$	−1.76877	+	12.3697i	−0.139834	+	0.977912i
$161$		−	16.5479i		−	1.30415i
$162$	7.99192	+	0.822348i	0.627904	+	0.0646098i
$163$	11.1001	+	11.1001i	0.869425	+	0.869425i	0.992409	−	0.122984i	$-0.0392463\pi$
$163$	11.1001	+	11.1001i	0.869425	+	0.869425i	−0.122984	+	0.992409i	$0.539246\pi$
$164$	12.3282			0.962669
$165$	1.87737	−	0.0538689i	0.146153	−	0.00419369i
$166$	8.39505			0.651582
$167$	2.27559	+	2.27559i	0.176091	+	0.176091i	0.789649	−	0.613559i	$-0.210263\pi$
$167$	2.27559	+	2.27559i	0.176091	+	0.176091i	−0.613559	+	0.789649i	$0.710263\pi$
$168$	−12.5594	+	17.7917i	−0.968977	+	1.37266i
$169$		−	7.08332i		−	0.544871i
$170$	11.8730	−	8.90228i	0.910616	−	0.682773i
$171$	2.82683	−	1.00451i	0.216173	−	0.0768166i
$172$	−2.14682	+	2.14682i	−0.163694	+	0.163694i
$173$	8.75419	−	8.75419i	0.665568	−	0.665568i	−0.291119	−	0.956687i	$-0.594027\pi$
$173$	8.75419	−	8.75419i	0.665568	−	0.665568i	0.956687	+	0.291119i	$0.0940274\pi$
$174$	−1.69817	−	9.85053i	−0.128738	−	0.746767i
$175$	−10.5668	−	19.2810i	−0.798774	−	1.45750i
$176$			0.0709195i			0.00534576i
$177$	5.78533	+	4.08393i	0.434852	+	0.306967i
$178$	−5.28270	−	5.28270i	−0.395955	−	0.395955i
$179$	10.7138			0.800787			0.400394	−	0.916343i	$-0.368873\pi$
$179$	10.7138			0.800787			0.400394	+	0.916343i	$0.368873\pi$
$180$	6.72428	+	4.46340i	0.501198	+	0.332682i
$181$	−21.0414			−1.56400			−0.781999	−	0.623280i	$-0.785800\pi$
$181$	−21.0414			−1.56400			−0.781999	+	0.623280i	$0.785800\pi$
$182$	−6.75163	−	6.75163i	−0.500464	−	0.500464i
$183$	0.559987	+	0.395301i	0.0413954	+	0.0292215i
$184$		−	10.7602i		−	0.793255i
$185$	−3.90299	−	0.558098i	−0.286954	−	0.0410322i
$186$	1.00995	+	5.85842i	0.0740533	+	0.429560i
$187$	−2.54926	+	2.54926i	−0.186420	+	0.186420i
$188$	−4.82231	+	4.82231i	−0.351703	+	0.351703i
$189$	11.1972	+	19.9175i	0.814478	+	1.44879i
$190$	−1.97599	−	0.282552i	−0.143354	−	0.0204984i
$191$			2.14074i			0.154899i	0.996996	+	0.0774493i	$0.0246776\pi$
$191$			2.14074i			0.154899i	−0.996996	+	0.0774493i	$0.975322\pi$
$192$	−5.27498	+	7.47258i	−0.380689	+	0.539287i
$193$	6.90598	+	6.90598i	0.497104	+	0.497104i	0.910535	−	0.413432i	$-0.135670\pi$
$193$	6.90598	+	6.90598i	0.497104	+	0.497104i	−0.413432	+	0.910535i	$0.635670\pi$
$194$	8.91665			0.640178
$195$	−6.46766	+	6.84979i	−0.463159	+	0.490523i
$196$	−14.8423			−1.06017
$197$	−4.53867	−	4.53867i	−0.323367	−	0.323367i	0.526690	−	0.850057i	$-0.323433\pi$
$197$	−4.53867	−	4.53867i	−0.323367	−	0.323367i	−0.850057	+	0.526690i	$0.823433\pi$
$198$	1.17277	+	0.557813i	0.0833453	+	0.0396420i
$199$		−	2.36288i		−	0.167500i	−0.996487	−	0.0837499i	$-0.973310\pi$
$199$		−	2.36288i		−	0.167500i	0.996487	−	0.0837499i	$-0.0266897\pi$
$200$	−6.87105	−	12.5374i	−0.485857	−	0.886531i
$201$	1.90162	−	0.327826i	0.134130	−	0.0231231i
$202$	0.253820	−	0.253820i	0.0178587	−	0.0178587i
$203$	20.1019	−	20.1019i	1.41088	−	1.41088i
$204$	−15.2671	+	2.63195i	−1.06891	+	0.184274i
$205$	−18.3319	+	13.7451i	−1.28035	+	0.960000i
$206$			11.5048i			0.801578i
$207$	−10.1950	−	4.84912i	−0.708603	−	0.337037i
$208$	−0.251540	−	0.251540i	−0.0174412	−	0.0174412i
$209$	0.484934			0.0335436
$210$	−0.436053	−	15.1968i	−0.0300905	−	1.04868i
$211$	8.32645			0.573217			0.286608	−	0.958048i	$-0.407472\pi$
$211$	8.32645			0.573217			0.286608	+	0.958048i	$0.407472\pi$
$212$	−2.56542	−	2.56542i	−0.176193	−	0.176193i
$213$	7.62249	−	10.7981i	0.522285	−	0.739872i
$214$			10.8247i			0.739958i
$215$	0.798736	−	5.58587i	0.0544733	−	0.380953i
$216$	7.28099	+	12.9514i	0.495409	+	0.881229i
$217$	−11.9552	+	11.9552i	−0.811574	+	0.811574i
$218$	−1.85719	+	1.85719i	−0.125785	+	0.125785i
$219$	0.275131	+	1.59595i	0.0185916	+	0.107844i
$220$	0.782623	+	1.04379i	0.0527645	+	0.0703720i
$221$		−	18.0836i		−	1.21644i
$222$	−2.22722	−	1.57222i	−0.149481	−	0.105521i
$223$	0.192204	+	0.192204i	0.0128709	+	0.0128709i	0.713513	−	0.700642i	$-0.247103\pi$
$223$	0.192204	+	0.192204i	0.0128709	+	0.0128709i	−0.700642	+	0.713513i	$0.747103\pi$
$224$	−24.5730			−1.64186
$225$	−14.9753	+	0.860106i	−0.998355	+	0.0573404i
$226$	−17.2397			−1.14677
$227$	7.27049	+	7.27049i	0.482559	+	0.482559i	0.905948	−	0.423389i	$-0.139160\pi$
$227$	7.27049	+	7.27049i	0.482559	+	0.482559i	−0.423389	+	0.905948i	$0.639160\pi$
$228$	1.70243	+	1.20177i	0.112746	+	0.0795890i
$229$		−	19.9414i		−	1.31776i	−0.752246	−	0.658882i	$-0.771030\pi$
$229$		−	19.9414i		−	1.31776i	0.752246	−	0.658882i	$-0.228970\pi$
$230$	4.50617	+	6.00989i	0.297128	+	0.396280i
$231$	0.627471	+	3.63976i	0.0412846	+	0.239479i
$232$	13.0712	−	13.0712i	0.858169	−	0.858169i
$233$	−8.00181	+	8.00181i	−0.524216	+	0.524216i	−0.918842	−	0.394626i	$-0.870874\pi$
$233$	−8.00181	+	8.00181i	−0.524216	+	0.524216i	0.394626	+	0.918842i	$0.370874\pi$
$234$	−6.13810	+	2.18116i	−0.401260	+	0.142587i
$235$	1.79416	−	12.5473i	0.117038	−	0.818494i
$236$			4.91902i			0.320201i
$237$	7.49283	−	10.6144i	0.486712	−	0.689479i
$238$	20.6355	+	20.6355i	1.33760	+	1.33760i
$239$	8.06309			0.521558			0.260779	−	0.965399i	$-0.416021\pi$
$239$	8.06309			0.521558			0.260779	+	0.965399i	$0.416021\pi$
$240$	−0.0162457	−	0.566174i	−0.00104865	−	0.0365464i
$241$	−3.28544			−0.211634			−0.105817	−	0.994386i	$-0.533746\pi$
$241$	−3.28544			−0.211634			−0.105817	+	0.994386i	$0.533746\pi$
$242$	−6.79498	−	6.79498i	−0.436798	−	0.436798i
$243$	15.5522	−	1.06198i	0.997677	−	0.0681259i
$244$			0.476133i			0.0304813i
$245$	22.0704	−	16.5482i	1.41003	−	1.05723i
$246$	−15.6130	+	2.69157i	−0.995446	+	0.171608i
$247$	−1.71998	+	1.71998i	−0.109440	+	0.109440i
$248$	−7.77388	+	7.77388i	−0.493642	+	0.493642i
$249$	16.0520	−	2.76726i	1.01725	−	0.175368i
$250$	9.08810	+	4.12504i	0.574782	+	0.260891i
$251$		−	5.94266i		−	0.375097i	−0.982255	−	0.187549i	$-0.939946\pi$
$251$		−	5.94266i		−	0.375097i	0.982255	−	0.187549i	$-0.0600542\pi$
$252$	−6.81726	+	14.3329i	−0.429447	+	0.902889i
$253$	−1.29039	−	1.29039i	−0.0811261	−	0.0811261i
$254$	−15.6613			−0.982678
$255$	19.7676	−	20.9355i	1.23790	−	1.31103i
$256$	−16.3305			−1.02066
$257$	−6.45234	−	6.45234i	−0.402486	−	0.402486i	0.476622	−	0.879108i	$-0.341861\pi$
$257$	−6.45234	−	6.45234i	−0.402486	−	0.402486i	−0.879108	+	0.476622i	$0.841861\pi$
$258$	2.25012	−	3.18754i	0.140087	−	0.198448i
$259$		−	7.75348i		−	0.481778i
$260$	−6.47797	−	0.926300i	−0.401747	−	0.0574467i
$261$	−6.49405	−	18.2752i	−0.401972	−	1.13121i
$262$	−1.38140	+	1.38140i	−0.0853430	+	0.0853430i
$263$	−16.6563	+	16.6563i	−1.02707	+	1.02707i	−0.0274500	+	0.999623i	$0.508739\pi$
$263$	−16.6563	+	16.6563i	−1.02707	+	1.02707i	−0.999623	+	0.0274500i	$0.991261\pi$
$264$	0.408013	+	2.36675i	0.0251115	+	0.145664i
$265$	6.67502	+	0.954475i	0.410043	+	0.0586330i
$266$		−	3.92540i		−	0.240682i
$267$	−11.8423	−	8.35960i	−0.724735	−	0.511599i
$268$	0.947801	+	0.947801i	0.0578961	+	0.0578961i
$269$	−23.6314			−1.44083			−0.720416	−	0.693543i	$-0.756049\pi$
$269$	−23.6314			−1.44083			−0.720416	+	0.693543i	$0.756049\pi$
$270$	−9.49040	−	4.18456i	−0.577568	−	0.254664i
$271$	−1.21408			−0.0737504			−0.0368752	−	0.999320i	$-0.511740\pi$
$271$	−1.21408			−0.0737504			−0.0368752	+	0.999320i	$0.511740\pi$
$272$	0.768801	+	0.768801i	0.0466154	+	0.0466154i
$273$	−15.1352	−	10.6841i	−0.916023	−	0.646632i
$274$		−	16.9786i		−	1.02572i
$275$	−2.32750	−	0.679524i	−0.140354	−	0.0409769i
$276$	−1.33225	−	7.72795i	−0.0801919	−	0.465168i
$277$	9.65826	−	9.65826i	0.580309	−	0.580309i	−0.354679	−	0.934988i	$-0.615410\pi$
$277$	9.65826	−	9.65826i	0.580309	−	0.580309i	0.934988	+	0.354679i	$0.115410\pi$
$278$	12.5199	−	12.5199i	0.750896	−	0.750896i
$279$	3.86222	+	10.8688i	0.231225	+	0.650701i
$280$	22.4945	−	16.8662i	1.34430	−	1.00795i
$281$			9.22464i			0.550296i	0.961402	+	0.275148i	$0.0887268\pi$
$281$			9.22464i			0.550296i	−0.961402	+	0.275148i	$0.911273\pi$
$282$	5.05435	−	7.16002i	0.300982	−	0.426373i
$283$	20.8970	+	20.8970i	1.24220	+	1.24220i	0.959087	+	0.283112i	$0.0913668\pi$
$283$	20.8970	+	20.8970i	1.24220	+	1.24220i	0.283112	+	0.959087i	$0.408633\pi$
$284$	9.18115			0.544801
$285$	−3.87139	+	0.111085i	−0.229321	+	0.00658010i
$286$	−1.05297			−0.0622636
$287$	−31.8612	−	31.8612i	−1.88071	−	1.88071i
$288$	−7.20079	+	15.1393i	−0.424311	+	0.892091i
$289$			38.2703i			2.25120i
$290$	−1.82667	+	12.7746i	−0.107266	+	0.750152i
$291$	17.0493	−	2.93919i	0.999450	−	0.172298i
$292$	−0.795450	+	0.795450i	−0.0465502	+	0.0465502i
$293$	−18.8428	+	18.8428i	−1.10081	+	1.10081i	−0.106498	+	0.994313i	$0.533964\pi$
$293$	−18.8428	+	18.8428i	−1.10081	+	1.10081i	−0.994313	+	0.106498i	$0.966036\pi$
$294$	18.7970	−	3.24048i	1.09626	−	0.188989i
$295$	−5.48439	−	7.31453i	−0.319313	−	0.425869i
$296$		−	5.04170i		−	0.293043i
$297$	2.42630	+	0.680002i	0.140788	+	0.0394577i
$298$	−0.0816498	−	0.0816498i	−0.00472985	−	0.00472985i
$299$	9.15360			0.529366
$300$	−6.48704	−	8.15361i	−0.374530	−	0.470749i
$301$	11.0966			0.639597
$302$	−5.73860	−	5.73860i	−0.330219	−	0.330219i
$303$	0.401657	−	0.568990i	0.0230746	−	0.0326876i
$304$		−	0.146246i		−	0.00838776i
$305$	−0.530857	−	0.708005i	−0.0303968	−	0.0405402i
$306$	18.7604	−	6.66645i	1.07246	−	0.381095i
$307$	1.57533	−	1.57533i	0.0899088	−	0.0899088i	−0.660722	−	0.750631i	$-0.729750\pi$
$307$	1.57533	−	1.57533i	0.0899088	−	0.0899088i	0.750631	+	0.660722i	$0.229750\pi$
$308$	−1.81412	+	1.81412i	−0.103369	+	0.103369i
$309$	3.79232	+	21.9981i	0.215738	+	1.25143i
$310$	1.08638	−	7.59747i	0.0617022	−	0.431507i
$311$		−	17.6141i		−	0.998804i	−0.866370	−	0.499402i	$-0.833553\pi$
$311$		−	17.6141i		−	0.998804i	0.866370	−	0.499402i	$-0.166447\pi$
$312$	−9.84165	−	6.94734i	−0.557174	−	0.393316i
$313$	−7.57967	−	7.57967i	−0.428428	−	0.428428i	0.459664	−	0.888093i	$-0.347970\pi$
$313$	−7.57967	−	7.57967i	−0.428428	−	0.428428i	−0.888093	+	0.459664i	$0.847970\pi$
$314$	−22.1875			−1.25212
$315$	−5.84307	−	28.9137i	−0.329220	−	1.62910i
$316$	9.02498			0.507695
$317$	6.04760	+	6.04760i	0.339667	+	0.339667i	0.856242	−	0.516575i	$-0.172793\pi$
$317$	6.04760	+	6.04760i	0.339667	+	0.339667i	−0.516575	+	0.856242i	$0.672793\pi$
$318$	3.80906	+	2.68886i	0.213601	+	0.150784i
$319$		−	3.13506i		−	0.175530i
$320$	9.44777	−	7.08387i	0.528146	−	0.396000i
$321$	3.56813	+	20.6976i	0.199153	+	1.15523i
$322$	−10.4453	+	10.4453i	−0.582096	+	0.582096i
$323$	5.25692	−	5.25692i	0.292503	−	0.292503i
$324$	6.83271	+	8.40013i	0.379595	+	0.466674i
$325$	10.6654	−	5.84512i	0.591612	−	0.324229i
$326$		−	14.0132i		−	0.776118i
$327$	−2.93891	+	4.16328i	−0.162522	+	0.230230i
$328$	−20.7178	−	20.7178i	−1.14395	−	1.14395i
$329$	24.9258			1.37420
$330$	−1.21904	−	1.15103i	−0.0671057	−	0.0633621i
$331$	−16.5043			−0.907157			−0.453579	−	0.891216i	$-0.649853\pi$
$331$	−16.5043			−0.907157			−0.453579	+	0.891216i	$0.649853\pi$
$332$	8.00061	+	8.00061i	0.439091	+	0.439091i
$333$	−4.77687	−	2.27205i	−0.261771	−	0.124508i
$334$		−	2.87280i		−	0.157192i
$335$	−2.46610	−	0.352634i	−0.134738	−	0.0192664i
$336$	1.09767	−	0.189232i	0.0598830	−	0.0103234i
$337$	−15.0634	+	15.0634i	−0.820555	+	0.820555i	−0.986188	−	0.165632i	$-0.947034\pi$
$337$	−15.0634	+	15.0634i	−0.820555	+	0.820555i	0.165632	+	0.986188i	$0.447034\pi$
$338$	−4.47113	+	4.47113i	−0.243197	+	0.243197i
$339$	−32.9636	+	5.68270i	−1.79034	+	0.308642i
$340$	19.7991	+	2.83112i	1.07376	+	0.153539i
$341$			1.86452i			0.100969i
$342$	−2.41841	−	1.15029i	−0.130773	−	0.0622003i
$343$	16.5932	+	16.5932i	0.895950	+	0.895950i
$344$	7.21556			0.389037
$345$	10.5972	+	10.0060i	0.570534	+	0.538705i
$346$	−11.0516			−0.594139
$347$	16.3236	+	16.3236i	0.876298	+	0.876298i	0.993149	−	0.116851i	$-0.0372800\pi$
$347$	16.3236	+	16.3236i	0.876298	+	0.876298i	−0.116851	+	0.993149i	$0.537280\pi$
$348$	7.76933	−	11.0061i	0.416480	−	0.589988i
$349$		−	7.06087i		−	0.377960i	−0.981981	−	0.188980i	$-0.939482\pi$
$349$		−	7.06087i		−	0.377960i	0.981981	−	0.188980i	$-0.0605181\pi$
$350$	−5.50056	+	18.8405i	−0.294017	+	1.00707i
$351$	−11.0176	+	6.19385i	−0.588074	+	0.330603i
$352$	−1.91619	+	1.91619i	−0.102133	+	0.102133i
$353$	−15.7883	+	15.7883i	−0.840325	+	0.840325i	−0.988901	−	0.148576i	$-0.952531\pi$
$353$	−15.7883	+	15.7883i	−0.840325	+	0.840325i	0.148576	+	0.988901i	$0.452531\pi$
$354$	−1.07395	−	6.22967i	−0.0570800	−	0.331103i
$355$	−13.6523	+	10.2364i	−0.724588	+	0.543291i
$356$		−	10.0690i		−	0.533655i
$357$	46.2588	+	32.6547i	2.44828	+	1.72827i
$358$	−6.76276	−	6.76276i	−0.357423	−	0.357423i
$359$	25.8168			1.36256			0.681278	−	0.732025i	$-0.261424\pi$
$359$	25.8168			1.36256			0.681278	+	0.732025i	$0.261424\pi$
$360$	−3.79946	−	18.8011i	−0.200249	−	0.990906i
$361$	−1.00000			−0.0526316
$362$	13.2818	+	13.2818i	0.698074	+	0.698074i
$363$	−15.2324	−	10.7527i	−0.799491	−	0.564371i
$364$		−	12.8688i		−	0.674509i
$365$	0.295951	−	2.06970i	0.0154908	−	0.108333i
$366$	−0.103953	−	0.602996i	−0.00543369	−	0.0315191i
$367$	14.0056	−	14.0056i	0.731086	−	0.731086i	−0.239749	−	0.970835i	$-0.577065\pi$
$367$	14.0056	−	14.0056i	0.731086	−	0.731086i	0.970835	+	0.239749i	$0.0770651\pi$
$368$	−0.389153	+	0.389153i	−0.0202860	+	0.0202860i
$369$	−28.9660	+	10.2930i	−1.50791	+	0.535831i
$370$	2.11136	+	2.81593i	0.109765	+	0.146393i
$371$			13.2602i			0.688437i
$372$	−4.62066	+	6.54566i	−0.239570	+	0.339377i
$373$	18.1829	+	18.1829i	0.941476	+	0.941476i	0.998380	−	0.0569035i	$-0.0181227\pi$
$373$	18.1829	+	18.1829i	0.941476	+	0.941476i	−0.0569035	+	0.998380i	$0.518123\pi$
$374$	3.21828			0.166414
$375$	18.7369	+	4.89170i	0.967569	+	0.252606i
$376$	16.2080			0.835862
$377$	11.1195	+	11.1195i	0.572686	+	0.572686i
$378$	5.50442	−	19.6402i	0.283117	−	1.01018i
$379$			9.67090i			0.496761i	0.968663	+	0.248380i	$0.0798983\pi$
$379$			9.67090i			0.496761i	−0.968663	+	0.248380i	$0.920102\pi$
$380$	−1.61387	−	2.15243i	−0.0827900	−	0.110417i
$381$	−29.9457	+	5.16243i	−1.53416	+	0.264479i
$382$	1.35128	−	1.35128i	0.0691374	−	0.0691374i
$383$	−6.50293	+	6.50293i	−0.332284	+	0.332284i	−0.853453	−	0.521169i	$-0.825496\pi$
$383$	−6.50293	+	6.50293i	−0.332284	+	0.332284i	0.521169	+	0.853453i	$0.325496\pi$
$384$	−11.0301	+	1.90151i	−0.562877	+	0.0970363i
$385$	0.674954	−	4.72021i	0.0343988	−	0.240564i
$386$		−	8.71838i		−	0.443754i
$387$	3.25171	−	6.83654i	0.165294	−	0.347521i
$388$	8.49770	+	8.49770i	0.431406	+	0.431406i
$389$	−7.26031			−0.368112			−0.184056	−	0.982916i	$-0.558923\pi$
$389$	−7.26031			−0.368112			−0.184056	+	0.982916i	$0.558923\pi$
$390$	8.40623	−	0.241207i	0.425666	−	0.0122140i
$391$	−27.9768			−1.41485
$392$	24.9429	+	24.9429i	1.25980	+	1.25980i
$393$	−2.18599	+	3.09669i	−0.110269	+	0.156207i
$394$			5.72979i			0.288663i
$395$	−13.4200	+	10.0623i	−0.675236	+	0.506287i
$396$	0.586065	+	1.64927i	0.0294509	+	0.0828791i
$397$	13.5745	−	13.5745i	0.681287	−	0.681287i	−0.279003	−	0.960290i	$-0.590004\pi$
$397$	13.5745	−	13.5745i	0.681287	−	0.681287i	0.960290	+	0.279003i	$0.0900040\pi$
$398$	−1.49149	+	1.49149i	−0.0747618	+	0.0747618i
$399$	−1.29393	−	7.50568i	−0.0647775	−	0.375754i
$400$	−0.204930	+	0.701925i	−0.0102465	+	0.0350962i
$401$			26.8858i			1.34261i	0.741181	+	0.671306i	$0.234266\pi$
$401$			26.8858i			1.34261i	−0.741181	+	0.671306i	$0.765734\pi$
$402$	−1.40727	−	0.993407i	−0.0701881	−	0.0495466i
$403$	−6.61314	−	6.61314i	−0.329424	−	0.329424i
$404$	0.483789			0.0240694
$405$	−19.5258	−	4.87288i	−0.970242	−	0.242135i
$406$	−25.3774			−1.25946
$407$	−0.604611	−	0.604611i	−0.0299694	−	0.0299694i
$408$	30.0798	+	21.2337i	1.48917	+	1.05122i
$409$		−	9.24979i		−	0.457373i	−0.973500	−	0.228686i	$-0.926557\pi$
$409$		−	9.24979i		−	0.457373i	0.973500	−	0.228686i	$-0.0734430\pi$
$410$	20.2476	+	2.89525i	0.999958	+	0.142986i
$411$	−5.59666	−	32.4644i	−0.276063	−	1.60135i
$412$	−10.9643	+	10.9643i	−0.540170	+	0.540170i
$413$	12.7128	−	12.7128i	0.625558	−	0.625558i
$414$	3.37444	+	9.49616i	0.165844	+	0.466711i
$415$	−20.8170	−	2.97667i	−1.02187	−	0.146119i
$416$		−	13.5928i		−	0.666442i
$417$	19.8122	−	28.0660i	0.970206	−	1.37440i
$418$	−0.306100	−	0.306100i	−0.0149718	−	0.0149718i
$419$	27.3581			1.33653			0.668264	−	0.743924i	$-0.267038\pi$
$419$	27.3581			1.33653			0.668264	+	0.743924i	$0.267038\pi$
$420$	14.0672	−	14.8983i	0.686409	−	0.726964i
$421$	−13.7170			−0.668525			−0.334263	−	0.942480i	$-0.608487\pi$
$421$	−13.7170			−0.668525			−0.334263	+	0.942480i	$0.608487\pi$
$422$	−5.25582	−	5.25582i	−0.255849	−	0.255849i
$423$	7.30415	−	15.3566i	0.355140	−	0.746663i
$424$			8.62247i			0.418744i
$425$	−32.5976	+	17.8649i	−1.58122	+	0.866574i
$426$	−11.6274	+	2.00449i	−0.563351	+	0.0971179i
$427$	1.23053	−	1.23053i	0.0595495	−	0.0595495i
$428$	−10.3161	+	10.3161i	−0.498645	+	0.498645i
$429$	−2.01337	+	0.347091i	−0.0972063	+	0.0167577i
$430$	−4.03009	+	3.02173i	−0.194348	+	0.145721i
$431$		−	13.6763i		−	0.658766i	−0.944196	−	0.329383i	$-0.893159\pi$
$431$		−	13.6763i		−	0.658766i	0.944196	−	0.329383i	$-0.106841\pi$
$432$	0.205074	−	0.731720i	0.00986661	−	0.0352049i
$433$	−3.55520	−	3.55520i	−0.170852	−	0.170852i	0.616502	−	0.787354i	$-0.288549\pi$
$433$	−3.55520	−	3.55520i	−0.170852	−	0.170852i	−0.787354	+	0.616502i	$0.788549\pi$
$434$	15.0927			0.724475
$435$	0.718155	+	25.0282i	0.0344329	+	1.20001i
$436$	−3.53986			−0.169529
$437$	2.66096	+	2.66096i	0.127291	+	0.127291i
$438$	0.833726	−	1.18106i	0.0398370	−	0.0564333i
$439$			30.0669i			1.43502i	0.696551	+	0.717508i	$0.254717\pi$
$439$			30.0669i			1.43502i	−0.696551	+	0.717508i	$0.745283\pi$
$440$	0.438889	−	3.06932i	0.0209232	−	0.146324i
$441$	34.8732	−	12.3921i	1.66063	−	0.590100i
$442$	−11.4147	+	11.4147i	−0.542943	+	0.542943i
$443$	11.3303	−	11.3303i	0.538319	−	0.538319i	−0.384716	−	0.923035i	$-0.625700\pi$
$443$	11.3303	−	11.3303i	0.538319	−	0.538319i	0.923035	+	0.384716i	$0.125700\pi$
$444$	−0.624223	−	3.62092i	−0.0296243	−	0.171841i
$445$	11.2263	+	14.9725i	0.532176	+	0.709763i
$446$		−	0.242646i		−	0.0114896i
$447$	−0.183035	−	0.129207i	−0.00865726	−	0.00611126i
$448$	16.4204	+	16.4204i	0.775793	+	0.775793i
$449$	4.52307			0.213457			0.106728	−	0.994288i	$-0.465962\pi$
$449$	4.52307			0.213457			0.106728	+	0.994288i	$0.465962\pi$
$450$	9.99563	+	8.90980i	0.471199	+	0.420012i
$451$	−4.96903			−0.233982
$452$	−16.4297	−	16.4297i	−0.772786	−	0.772786i
$453$	−12.8643	−	9.08105i	−0.604416	−	0.426665i
$454$		−	9.17855i		−	0.430771i
$455$	14.3479	+	19.1358i	0.672639	+	0.897099i
$456$	−0.841377	−	4.88057i	−0.0394011	−	0.228554i
$457$	24.3285	−	24.3285i	1.13804	−	1.13804i	0.149240	−	0.988801i	$-0.452317\pi$
$457$	24.3285	−	24.3285i	1.13804	−	1.13804i	0.988801	−	0.149240i	$-0.0476828\pi$
$458$	−12.5874	+	12.5874i	−0.588170	+	0.588170i
$459$	33.6738	−	18.9307i	1.57176	−	0.883611i
$460$	−1.43306	+	10.0220i	−0.0668169	+	0.467277i
$461$			19.0723i			0.888284i	0.895957	+	0.444142i	$0.146491\pi$
$461$			19.0723i			0.888284i	−0.895957	+	0.444142i	$0.853509\pi$
$462$	1.90142	−	2.69356i	0.0884619	−	0.125316i
$463$	27.0456	+	27.0456i	1.25692	+	1.25692i	0.952557	+	0.304360i	$0.0984425\pi$
$463$	27.0456	+	27.0456i	1.25692	+	1.25692i	0.304360	+	0.952557i	$0.401558\pi$
$464$	−0.945466			−0.0438921
$465$	−0.427109	−	14.8851i	−0.0198067	−	0.690278i
$466$	10.1018			0.467957
$467$	14.7797	+	14.7797i	0.683924	+	0.683924i	0.960882	−	0.276958i	$-0.0893262\pi$
$467$	14.7797	+	14.7797i	0.683924	+	0.683924i	−0.276958	+	0.960882i	$0.589326\pi$
$468$	−7.92838	−	3.77103i	−0.366490	−	0.174316i
$469$		−	4.89904i		−	0.226216i
$470$	−9.05259	+	6.78757i	−0.417565	+	0.313087i
$471$	−42.4243	+	7.31367i	−1.95481	+	0.336996i
$472$	8.26652	−	8.26652i	0.380497	−	0.380497i
$473$	0.865304	−	0.865304i	0.0397867	−	0.0397867i
$474$	−11.4296	+	1.97039i	−0.524981	+	0.0905032i
$475$	4.79963	+	1.40127i	0.220222	+	0.0642947i
$476$			39.3319i			1.80278i
$477$	8.16954	+	3.88573i	0.374058	+	0.177915i
$478$	−5.08958	−	5.08958i	−0.232792	−	0.232792i
$479$	−28.2939			−1.29278			−0.646391	−	0.763006i	$-0.723723\pi$
$479$	−28.2939			−1.29278			−0.646391	+	0.763006i	$0.723723\pi$
$480$	14.8586	−	15.7365i	0.678199	−	0.718269i
$481$	4.28891			0.195557
$482$	2.07384	+	2.07384i	0.0944606	+	0.0944606i
$483$	−16.5292	+	23.4154i	−0.752105	+	1.06544i
$484$		−	12.9514i		−	0.588702i
$485$	−22.1104	−	3.16161i	−1.00398	−	0.143561i
$486$	−10.4872	−	9.14654i	−0.475710	−	0.414895i
$487$	0.608543	−	0.608543i	0.0275757	−	0.0275757i	−0.693184	−	0.720760i	$-0.743793\pi$
$487$	0.608543	−	0.608543i	0.0275757	−	0.0275757i	0.720760	+	0.693184i	$0.243793\pi$
$488$	0.800152	−	0.800152i	0.0362212	−	0.0362212i
$489$	−4.61916	−	26.7943i	−0.208885	−	1.21168i
$490$	−24.3768	−	3.48570i	−1.10123	−	0.157468i
$491$			25.7171i			1.16060i	0.814403	+	0.580299i	$0.197064\pi$
$491$			25.7171i			1.16060i	−0.814403	+	0.580299i	$0.802936\pi$
$492$	−17.4445	−	12.3143i	−0.786458	−	0.555171i
$493$	−33.9855	−	33.9855i	−1.53063	−	1.53063i
$494$	2.17137			0.0976947
$495$	−2.71031	−	1.79903i	−0.121819	−	0.0808603i
$496$	0.562298			0.0252479
$497$	−23.7280	−	23.7280i	−1.06435	−	1.06435i
$498$	−11.8791	−	8.38558i	−0.532314	−	0.375767i
$499$		−	8.12902i		−	0.363905i	−0.983307	−	0.181952i	$-0.941758\pi$
$499$		−	8.12902i		−	0.363905i	0.983307	−	0.181952i	$-0.0582417\pi$
$500$	4.72987	+	12.5923i	0.211526	+	0.563146i
$501$	−0.946959	−	5.49301i	−0.0423070	−	0.245410i
$502$	−3.75112	+	3.75112i	−0.167421	+	0.167421i
$503$	−24.4871	+	24.4871i	−1.09182	+	1.09182i	−0.0964901	+	0.995334i	$0.530762\pi$
$503$	−24.4871	+	24.4871i	−1.09182	+	1.09182i	−0.995334	+	0.0964901i	$0.969238\pi$
$504$	35.5433	−	12.6302i	1.58322	−	0.562595i
$505$	−0.719388	+	0.539393i	−0.0320124	+	0.0240027i
$506$			1.62904i			0.0724196i
$507$	−7.07533	+	10.0230i	−0.314227	+	0.445136i
$508$	−14.9255	−	14.9255i	−0.662211	−	0.662211i
$509$	16.4424			0.728796			0.364398	−	0.931243i	$-0.381275\pi$
$509$	16.4424			0.728796			0.364398	+	0.931243i	$0.381275\pi$
$510$	−25.6926	+	0.737219i	−1.13769	+	0.0326446i
$511$	4.11156			0.181885
$512$	1.16926	+	1.16926i	0.0516745	+	0.0516745i
$513$	−5.00337	−	1.40226i	−0.220904	−	0.0619111i
$514$			8.14569i			0.359291i
$515$	4.07930	−	28.5281i	0.179756	−	1.25710i
$516$	5.18218	−	0.893373i	0.228133	−	0.0393286i
$517$	1.94369	−	1.94369i	0.0854835	−	0.0854835i
$518$	−4.89415	+	4.89415i	−0.215037	+	0.215037i
$519$	−21.1316	+	3.64294i	−0.927573	+	0.159907i
$520$	9.32970	+	12.4430i	0.409135	+	0.545663i
$521$			12.9898i			0.569094i	0.958662	+	0.284547i	$0.0918432\pi$
$521$			12.9898i			0.569094i	−0.958662	+	0.284547i	$0.908157\pi$
$522$	−7.43650	+	15.6348i	−0.325487	+	0.684319i
$523$	3.68860	+	3.68860i	0.161291	+	0.161291i	0.783138	−	0.621847i	$-0.213618\pi$
$523$	3.68860	+	3.68860i	0.161291	+	0.161291i	−0.621847	+	0.783138i	$0.713618\pi$
$524$	−2.63298			−0.115022
$525$	−4.30711	+	37.8376i	−0.187978	+	1.65137i
$526$	21.0276			0.916847
$527$	20.2123	+	20.2123i	0.880460	+	0.880460i
$528$	0.0708396	−	0.100352i	0.00308290	−	0.00436725i
$529$			8.83862i			0.384288i
$530$	−3.61092	−	4.81588i	−0.156848	−	0.209189i
$531$	−4.10697	−	11.5576i	−0.178227	−	0.501558i
$532$	3.74097	−	3.74097i	0.162192	−	0.162192i
$533$	17.6243	−	17.6243i	0.763394	−	0.763394i
$534$	2.19833	+	12.7518i	0.0951310	+	0.551825i
$535$	3.83814	−	26.8416i	0.165937	−	1.16046i
$536$		−	3.18560i		−	0.137597i
$537$	−15.1601	−	10.7017i	−0.654208	−	0.461813i
$538$	14.9166	+	14.9166i	0.643100	+	0.643100i
$539$	5.98239			0.257680
$540$	−5.05656	−	13.0324i	−0.217600	−	0.560827i
$541$	29.6270			1.27377			0.636883	−	0.770961i	$-0.280223\pi$
$541$	29.6270			1.27377			0.636883	+	0.770961i	$0.280223\pi$
$542$	0.766354	+	0.766354i	0.0329177	+	0.0329177i
$543$	29.7739	+	21.0177i	1.27772	+	0.901957i
$544$			41.5447i			1.78122i
$545$	5.26374	−	3.94671i	0.225474	−	0.169059i
$546$	2.80960	+	16.2976i	0.120240	+	0.697474i
$547$	24.9591	−	24.9591i	1.06717	−	1.06717i	0.0695973	−	0.997575i	$-0.477829\pi$
$547$	24.9591	−	24.9591i	1.06717	−	1.06717i	0.997575	−	0.0695973i	$-0.0221714\pi$
$548$	16.1809	−	16.1809i	0.691213	−	0.691213i
$549$	−0.397531	−	1.11871i	−0.0169662	−	0.0477454i
$550$	1.04024	+	1.89810i	0.0443559	+	0.0809351i
$551$			6.46492i			0.275415i
$552$	−10.7481	+	15.2258i	−0.457470	+	0.648055i
$553$	−23.3244	−	23.3244i	−0.991853	−	0.991853i
$554$	−12.1930			−0.518030
$555$	4.96531	+	4.68831i	0.210765	+	0.199008i
$556$	23.8634			1.01203
$557$	−11.3659	−	11.3659i	−0.481590	−	0.481590i	0.424049	−	0.905639i	$-0.360608\pi$
$557$	−11.3659	−	11.3659i	−0.481590	−	0.481590i	−0.905639	+	0.424049i	$0.860608\pi$
$558$	4.42272	−	9.29853i	0.187229	−	0.393638i
$559$			6.13819i			0.259618i
$560$	−1.42351	−	0.203551i	−0.0601544	−	0.00860162i
$561$	6.15361	−	1.06084i	0.259806	−	0.0447888i
$562$	5.82277	−	5.82277i	0.245619	−	0.245619i
$563$	−11.5917	+	11.5917i	−0.488530	+	0.488530i	−0.907842	−	0.419312i	$-0.862271\pi$
$563$	−11.5917	+	11.5917i	−0.488530	+	0.488530i	0.419312	+	0.907842i	$0.362271\pi$
$564$	11.6405	−	2.00674i	0.490153	−	0.0844991i
$565$	42.7487	+	6.11274i	1.79845	+	0.257165i
$566$		−	26.3812i		−	1.10889i
$567$	4.05088	−	39.3681i	0.170121	−	1.65330i
$568$	−15.4291	−	15.4291i	−0.647391	−	0.647391i
$569$	−16.0656			−0.673503			−0.336752	−	0.941593i	$-0.609328\pi$
$569$	−16.0656			−0.673503			−0.336752	+	0.941593i	$0.609328\pi$
$570$	2.51382	+	2.37358i	0.105292	+	0.0994182i
$571$	−3.13996			−0.131403			−0.0657017	−	0.997839i	$-0.520929\pi$
$571$	−3.13996			−0.131403			−0.0657017	+	0.997839i	$0.520929\pi$
$572$	−1.00350	−	1.00350i	−0.0419584	−	0.0419584i
$573$	2.13833	−	3.02917i	0.0893299	−	0.126545i
$574$			40.2229i			1.67887i
$575$	−9.04288	−	16.5003i	−0.377114	−	0.688111i
$576$	14.9283	−	5.30474i	0.622013	−	0.221031i
$577$	−26.5932	+	26.5932i	−1.10709	+	1.10709i	−0.113558	+	0.993531i	$0.536225\pi$
$577$	−26.5932	+	26.5932i	−1.10709	+	1.10709i	−0.993531	+	0.113558i	$0.963775\pi$
$578$	24.1570	−	24.1570i	1.00480	−	1.00480i
$579$	−2.87384	−	16.6702i	−0.119433	−	0.692791i
$580$	−13.9153	+	10.4336i	−0.577800	+	0.433230i
$581$		−	41.3539i		−	1.71565i
$582$	−12.6171	−	8.90660i	−0.522998	−	0.369190i
$583$	1.03402	+	1.03402i	0.0428249	+	0.0428249i
$584$	2.67354			0.110632
$585$	15.9939	−	3.23215i	0.661265	−	0.133633i
$586$	23.7879			0.982671
$587$	4.22727	+	4.22727i	0.174478	+	0.174478i	0.788944	−	0.614465i	$-0.210628\pi$
$587$	4.22727	+	4.22727i	0.174478	+	0.174478i	−0.614465	+	0.788944i	$0.710628\pi$
$588$	21.0021	+	14.8256i	0.866110	+	0.611398i
$589$		−	3.84489i		−	0.158426i
$590$	−1.15522	+	8.07893i	−0.0475598	+	0.332604i
$591$	1.88871	+	10.9558i	0.0776911	+	0.450662i
$592$	−0.182337	+	0.182337i	−0.00749402	+	0.00749402i
$593$	29.5108	−	29.5108i	1.21186	−	1.21186i	0.241447	−	0.970414i	$-0.422378\pi$
$593$	29.5108	−	29.5108i	1.21186	−	1.21186i	0.970414	−	0.241447i	$-0.0776221\pi$
$594$	−1.10230	−	1.96076i	−0.0452279	−	0.0804510i
$595$	−43.8525	−	58.4862i	−1.79778	−	2.39770i
$596$		−	0.155627i		−	0.00637473i
$597$	−2.36021	+	3.34349i	−0.0965970	+	0.136840i
$598$	−5.77793	−	5.77793i	−0.236277	−	0.236277i
$599$	4.56114			0.186363			0.0931815	−	0.995649i	$-0.470296\pi$
$599$	4.56114			0.186363			0.0931815	+	0.995649i	$0.470296\pi$
$600$	−2.80070	+	24.6039i	−0.114338	+	1.00445i
$601$	22.5632			0.920371			0.460186	−	0.887823i	$-0.347783\pi$
$601$	22.5632			0.920371			0.460186	+	0.887823i	$0.347783\pi$
$602$	−7.00439	−	7.00439i	−0.285478	−	0.285478i
$603$	−3.01826	−	1.43560i	−0.122913	−	0.0584620i
$604$		−	10.9380i		−	0.445059i
$605$	14.4400	+	19.2586i	0.587069	+	0.782975i
$606$	−0.612692	+	0.105624i	−0.0248889	+	0.00429068i
$607$	−29.4054	+	29.4054i	−1.19353	+	1.19353i	−0.217461	+	0.976069i	$0.569777\pi$
$607$	−29.4054	+	29.4054i	−1.19353	+	1.19353i	−0.976069	+	0.217461i	$0.930223\pi$
$608$	3.95144	−	3.95144i	0.160252	−	0.160252i
$609$	−48.5236	+	8.36515i	−1.96628	+	0.338973i
$610$	−0.111819	+	0.781994i	−0.00452742	+	0.0316620i
$611$			13.7879i			0.557799i
$612$	24.2321	+	11.5257i	0.979526	+	0.465898i
$613$	6.61155	+	6.61155i	0.267038	+	0.267038i	0.827905	−	0.560868i	$-0.189532\pi$
$613$	6.61155	+	6.61155i	0.267038	+	0.267038i	−0.560868	+	0.827905i	$0.689532\pi$
$614$	−1.98876			−0.0802597
$615$	39.6694	−	1.13827i	1.59962	−	0.0458993i
$616$	6.09735			0.245669
$617$	−16.4346	−	16.4346i	−0.661631	−	0.661631i	0.294133	−	0.955764i	$-0.404969\pi$
$617$	−16.4346	−	16.4346i	−0.661631	−	0.661631i	−0.955764	+	0.294133i	$0.904969\pi$
$618$	11.4918	−	16.2794i	0.462269	−	0.654854i
$619$		−	1.62695i		−	0.0653928i	−0.999465	−	0.0326964i	$-0.989591\pi$
$619$		−	1.62695i		−	0.0653928i	0.999465	−	0.0326964i	$-0.0104094\pi$
$620$	8.27584	−	6.20517i	0.332366	−	0.249206i
$621$	9.58240	+	17.0451i	0.384528	+	0.683996i
$622$	−11.1184	+	11.1184i	−0.445806	+	0.445806i
$623$	−26.0225	+	26.0225i	−1.04257	+	1.04257i
$624$	0.104675	+	0.607188i	0.00419036	+	0.0243070i
$625$	−21.0729	−	13.4512i	−0.842915	−	0.538046i
$626$			9.56888i			0.382449i
$627$	−0.686187	−	0.484388i	−0.0274037	−	0.0193446i
$628$	−21.1451	−	21.1451i	−0.843780	−	0.843780i
$629$	−13.1085			−0.522671
$630$	−14.5626	+	21.9391i	−0.580189	+	0.874076i
$631$	6.15817			0.245153			0.122576	−	0.992459i	$-0.460884\pi$
$631$	6.15817			0.245153			0.122576	+	0.992459i	$0.460884\pi$
$632$	−15.1667	−	15.1667i	−0.603298	−	0.603298i
$633$	−11.7820	−	8.31707i	−0.468293	−	0.330574i
$634$		−	7.63472i		−	0.303214i
$635$	38.8349	+	5.55309i	1.54112	+	0.220368i
$636$	1.06757	+	6.19261i	0.0423317	+	0.245553i
$637$	−21.2186	+	21.2186i	−0.840710	+	0.840710i
$638$	−1.97891	+	1.97891i	−0.0783458	+	0.0783458i
$639$	−21.5718	+	7.66549i	−0.853368	+	0.303242i
$640$	14.3043	+	2.04541i	0.565429	+	0.0808519i
$641$			4.36725i			0.172496i	0.996274	+	0.0862481i	$0.0274878\pi$
$641$			4.36725i			0.172496i	−0.996274	+	0.0862481i	$0.972512\pi$
$642$	10.8124	−	15.3170i	0.426733	−	0.604513i
$643$	−7.15001	−	7.15001i	−0.281969	−	0.281969i	0.551925	−	0.833894i	$-0.313893\pi$
$643$	−7.15001	−	7.15001i	−0.281969	−	0.281969i	−0.833894	+	0.551925i	$0.813893\pi$
$644$	−19.9091			−0.784529
$645$	−6.70979	+	7.10623i	−0.264198	+	0.279807i
$646$	−6.63654			−0.261111
$647$	−26.3863	−	26.3863i	−1.03735	−	1.03735i	−0.999275	−	0.0380774i	$-0.987877\pi$
$647$	−26.3863	−	26.3863i	−1.03735	−	1.03735i	−0.0380774	−	0.999275i	$-0.512123\pi$
$648$	2.63408	−	25.5991i	0.103477	−	1.00563i
$649$		−	1.98267i		−	0.0778268i
$650$	−10.4218	−	3.04268i	−0.408776	−	0.119344i
$651$	28.8585	−	4.97502i	1.13105	−	0.194986i
$652$	13.3548	−	13.3548i	0.523013	−	0.523013i
$653$	13.2064	−	13.2064i	0.516806	−	0.516806i	−0.399797	−	0.916604i	$-0.630920\pi$
$653$	13.2064	−	13.2064i	0.516806	−	0.516806i	0.916604	+	0.399797i	$0.130920\pi$
$654$	4.48304	−	0.772846i	0.175301	−	0.0302207i
$655$	3.91522	−	2.93560i	0.152980	−	0.114704i
$656$			1.49855i			0.0585086i
$657$	1.20484	−	2.53310i	0.0470051	−	0.0988258i
$658$	−15.7336	−	15.7336i	−0.613361	−	0.613361i
$659$	−25.5826			−0.996557			−0.498278	−	0.867017i	$-0.666034\pi$
$659$	−25.5826			−0.996557			−0.498278	+	0.867017i	$0.666034\pi$
$660$	−0.0648109	−	2.25871i	−0.00252276	−	0.0879201i
$661$	31.6395			1.23063			0.615317	−	0.788279i	$-0.289028\pi$
$661$	31.6395			1.23063			0.615317	+	0.788279i	$0.289028\pi$
$662$	10.4178	+	10.4178i	0.404900	+	0.404900i
$663$	−18.0632	+	25.5885i	−0.701517	+	0.993775i
$664$		−	26.8904i		−	1.04355i
$665$	−1.39185	+	9.73372i	−0.0539735	+	0.377457i
$666$	1.58109	+	4.44942i	0.0612659	+	0.172411i
$667$	17.2029	−	17.2029i	0.666097	−	0.666097i
$668$	2.73782	−	2.73782i	0.105929	−	0.105929i
$669$	−0.0799833	−	0.463958i	−0.00309233	−	0.0179377i
$670$	1.33406	+	1.77924i	0.0515394	+	0.0687381i
$671$		−	0.191911i		−	0.00740866i
$672$	34.7711	+	24.5453i	1.34132	+	0.946857i
$673$	−15.6709	−	15.6709i	−0.604069	−	0.604069i	0.337321	−	0.941390i	$-0.390479\pi$
$673$	−15.6709	−	15.6709i	−0.604069	−	0.604069i	−0.941390	+	0.337321i	$0.890479\pi$
$674$	19.0166			0.732493
$675$	22.0494	+	13.7414i	0.848680	+	0.528906i
$676$	−8.52211			−0.327773
$677$	−21.6627	−	21.6627i	−0.832564	−	0.832564i	0.155303	−	0.987867i	$-0.450365\pi$
$677$	−21.6627	−	21.6627i	−0.832564	−	0.832564i	−0.987867	+	0.155303i	$0.950365\pi$
$678$	24.3943	+	17.2202i	0.936857	+	0.661339i
$679$		−	43.9233i		−	1.68562i
$680$	−28.5151	−	38.0306i	−1.09350	−	1.45841i
$681$	−3.02552	−	17.5501i	−0.115938	−	0.672522i
$682$	1.17692	−	1.17692i	0.0450666	−	0.0450666i
$683$	22.3519	−	22.3519i	0.855271	−	0.855271i	−0.135506	−	0.990777i	$-0.543266\pi$
$683$	22.3519	−	22.3519i	0.855271	−	0.855271i	0.990777	+	0.135506i	$0.0432660\pi$
$684$	−1.20855	−	3.40103i	−0.0462099	−	0.130041i
$685$	−6.02018	+	42.1014i	−0.230019	+	1.60861i
$686$		−	20.9479i		−	0.799796i
$687$	−19.9189	+	28.2173i	−0.759954	+	1.07656i
$688$	−0.260957	−	0.260957i	−0.00994889	−	0.00994889i
$689$	−7.33502			−0.279442
$690$	−0.373167	−	13.0051i	−0.0142062	−	0.495097i
$691$	−26.6976			−1.01563			−0.507813	−	0.861468i	$-0.669546\pi$
$691$	−26.6976			−1.01563			−0.507813	+	0.861468i	$0.669546\pi$
$692$	−10.5324	−	10.5324i	−0.400381	−	0.400381i
$693$	2.74778	−	5.77706i	0.104380	−	0.219453i
$694$		−	20.6076i		−	0.782253i
$695$	−35.4846	+	26.6061i	−1.34601	+	1.00923i
$696$	−31.5525	+	5.43943i	−1.19599	+	0.206181i
$697$	−53.8666	+	53.8666i	−2.04034	+	2.04034i
$698$	−4.45696	+	4.45696i	−0.168698	+	0.168698i
$699$	19.3154	−	3.32985i	0.730576	−	0.125947i
$700$	−23.1974	+	12.7132i	−0.876779	+	0.480512i
$701$			7.96666i			0.300897i	0.988618	+	0.150448i	$0.0480717\pi$
$701$			7.96666i			0.300897i	−0.988618	+	0.150448i	$0.951928\pi$
$702$	10.8642	+	3.04482i	0.410042	+	0.114919i
$703$	1.24679	+	1.24679i	0.0470235	+	0.0470235i
$704$	2.56091			0.0965179
$705$	−15.0719	+	15.9624i	−0.567640	+	0.601178i
$706$	19.9317			0.750141
$707$	−1.25031	−	1.25031i	−0.0470229	−	0.0470229i
$708$	4.91348	−	6.96047i	0.184660	−	0.261590i
$709$			9.48047i			0.356046i	0.984026	+	0.178023i	$0.0569702\pi$
$709$			9.48047i			0.356046i	−0.984026	+	0.178023i	$0.943030\pi$
$710$	15.0790	+	2.15618i	0.565904	+	0.0809199i
$711$	−21.2049	+	7.53510i	−0.795245	+	0.282588i
$712$	−16.9211	+	16.9211i	−0.634147	+	0.634147i
$713$	−10.2311	+	10.2311i	−0.383157	+	0.383157i
$714$	−8.58721	−	49.8117i	−0.321368	−	1.86416i
$715$	2.61103	+	0.373357i	0.0976470	+	0.0139628i
$716$		−	12.8900i		−	0.481723i
$717$	−11.4093	−	8.05400i	−0.426090	−	0.300782i
$718$	−16.2960	−	16.2960i	−0.608163	−	0.608163i
$719$	−1.99830			−0.0745241			−0.0372621	−	0.999306i	$-0.511864\pi$
$719$	−1.99830			−0.0745241			−0.0372621	+	0.999306i	$0.511864\pi$
$720$	−0.542548	+	0.817369i	−0.0202196	+	0.0304615i
$721$	56.6725			2.11060
$722$	0.631220	+	0.631220i	0.0234916	+	0.0234916i
$723$	4.64893	+	3.28174i	0.172896	+	0.122049i
$724$			25.3155i			0.940842i
$725$	9.05910	−	31.0292i	0.336447	−	1.15240i
$726$	2.82764	+	16.4023i	0.104944	+	0.608746i
$727$	−8.30098	+	8.30098i	−0.307866	+	0.307866i	−0.844081	−	0.536215i	$-0.819854\pi$
$727$	−8.30098	+	8.30098i	−0.307866	+	0.307866i	0.536215	+	0.844081i	$0.319854\pi$
$728$	−21.6263	+	21.6263i	−0.801524	+	0.801524i
$729$	−23.0674	−	14.0320i	−0.854347	−	0.519704i
$730$	−1.49325	+	1.11963i	−0.0552675	+	0.0414392i
$731$		−	18.7606i		−	0.693886i
$732$	0.475596	−	0.673733i	0.0175785	−	0.0249019i
$733$	−3.73842	−	3.73842i	−0.138082	−	0.138082i	0.634687	−	0.772769i	$-0.281129\pi$
$733$	−3.73842	−	3.73842i	−0.138082	−	0.138082i	−0.772769	+	0.634687i	$0.781129\pi$
$734$	−17.6812			−0.652625
$735$	−47.7594	+	1.37040i	−1.76163	+	0.0505479i
$736$	−21.0292			−0.775146
$737$	−0.382023	−	0.382023i	−0.0140720	−	0.0140720i
$738$	24.7810	+	11.7868i	0.912202	+	0.433876i
$739$		−	15.4108i		−	0.566895i	−0.958988	−	0.283447i	$-0.908522\pi$
$739$		−	15.4108i		−	0.566895i	0.958988	−	0.283447i	$-0.0914781\pi$
$740$	−0.671461	+	4.69578i	−0.0246834	+	0.172620i
$741$	4.15184	−	0.715749i	0.152522	−	0.0262937i
$742$	8.37012	−	8.37012i	0.307277	−	0.307277i
$743$	−15.8667	+	15.8667i	−0.582092	+	0.582092i	−0.935478	−	0.353386i	$-0.885030\pi$
$743$	−15.8667	+	15.8667i	−0.582092	+	0.582092i	0.353386	+	0.935478i	$0.385030\pi$
$744$	18.7652	−	3.23500i	0.687967	−	0.118601i
$745$	0.173514	+	0.231416i	0.00635706	+	0.00847842i
$746$		−	22.9548i		−	0.840436i
$747$	−25.4779	−	12.1182i	−0.932186	−	0.443382i
$748$	3.06707	+	3.06707i	0.112143	+	0.112143i
$749$	53.3221			1.94835
$750$	−8.73936	−	14.9148i	−0.319116	−	0.544613i
$751$	−3.77036			−0.137583			−0.0687913	−	0.997631i	$-0.521914\pi$
$751$	−3.77036			−0.137583			−0.0687913	+	0.997631i	$0.521914\pi$
$752$	−0.586175	−	0.586175i	−0.0213756	−	0.0213756i
$753$	−5.93596	+	8.40892i	−0.216318	+	0.306438i
$754$		−	14.0377i		−	0.511225i
$755$	12.1951	+	16.2646i	0.443825	+	0.591930i
$756$	23.9632	−	13.4717i	0.871535	−	0.489959i
$757$	9.12642	−	9.12642i	0.331705	−	0.331705i	−0.521529	−	0.853234i	$-0.674638\pi$
$757$	9.12642	−	9.12642i	0.331705	−	0.331705i	0.853234	+	0.521529i	$0.174638\pi$
$758$	6.10446	−	6.10446i	0.221724	−	0.221724i
$759$	0.536979	+	3.11485i	0.0194911	+	0.113062i
$760$	−0.905048	+	6.32935i	−0.0328295	+	0.229590i
$761$		−	31.0451i		−	1.12538i	−0.826666	−	0.562692i	$-0.809766\pi$
$761$		−	31.0451i		−	1.12538i	0.826666	−	0.562692i	$-0.190234\pi$
$762$	22.1609	+	15.6437i	0.802805	+	0.566710i
$763$	9.14850	+	9.14850i	0.331198	+	0.331198i
$764$	2.57558			0.0931811
$765$	−48.8833	+	9.87867i	−1.76738	+	0.357164i
$766$	8.20955			0.296623
$767$	7.03222	+	7.03222i	0.253919	+	0.253919i
$768$	23.1078	+	16.3121i	0.833832	+	0.588612i
$769$		−	24.4566i		−	0.881927i	−0.897525	−	0.440964i	$-0.854637\pi$
$769$		−	24.4566i		−	0.881927i	0.897525	−	0.440964i	$-0.145363\pi$
$770$	−3.40554	+	2.55345i	−0.122727	+	0.0920199i
$771$	2.68506	+	15.5752i	0.0967001	+	0.560927i
$772$	8.30875	−	8.30875i	0.299039	−	0.299039i
$773$	−21.8454	+	21.8454i	−0.785726	+	0.785726i	−0.980790	−	0.195064i	$-0.937508\pi$
$773$	−21.8454	+	21.8454i	−0.785726	+	0.785726i	0.195064	+	0.980790i	$0.437508\pi$
$774$	−6.36790	+	2.26282i	−0.228889	+	0.0813353i
$775$	−5.38773	+	18.4540i	−0.193533	+	0.662889i
$776$		−	28.5611i		−	1.02528i
$777$	−7.74474	+	10.9713i	−0.277841	+	0.393592i
$778$	4.58285	+	4.58285i	0.164303	+	0.164303i
$779$	10.2468			0.367130
$780$	8.24114	+	7.78140i	0.295080	+	0.278619i
$781$	−3.70058			−0.132417
$782$	17.6595	+	17.6595i	0.631504	+	0.631504i
$783$	−9.06547	+	32.3463i	−0.323973	+	1.15596i
$784$		−	1.80416i		−	0.0644343i
$785$	55.0178	+	7.86712i	1.96367	+	0.280790i
$786$	3.33453	−	0.574851i	0.118939	−	0.0205042i
$787$	−12.3097	+	12.3097i	−0.438792	+	0.438792i	−0.891605	−	0.452813i	$-0.850420\pi$
$787$	−12.3097	+	12.3097i	−0.438792	+	0.438792i	0.452813	+	0.891605i	$0.350420\pi$
$788$	−5.46058	+	5.46058i	−0.194525	+	0.194525i
$789$	40.2064	−	6.93132i	1.43139	−	0.246762i
$790$	14.8225	+	2.11950i	0.527361	+	0.0754085i
$791$			84.9224i			3.01949i
$792$	1.78674	−	3.75653i	0.0634892	−	0.133483i
$793$	0.680679	+	0.680679i	0.0241716	+	0.0241716i
$794$	−17.1370			−0.608171
$795$	−8.49181	−	8.01808i	−0.301174	−	0.284372i
$796$	−2.84283			−0.100761
$797$	2.92885	+	2.92885i	0.103745	+	0.103745i	0.757074	−	0.653329i	$-0.226628\pi$
$797$	2.92885	+	2.92885i	0.103745	+	0.103745i	−0.653329	+	0.757074i	$0.726628\pi$
$798$	−3.92098	+	5.55449i	−0.138801	+	0.196627i
$799$		−	42.1411i		−	1.49084i
$800$	−24.5025	+	13.4284i	−0.866293	+	0.474765i
$801$	8.40675	+	23.6578i	0.297038	+	0.835909i
$802$	16.9708	−	16.9708i	0.599261	−	0.599261i
$803$	0.320616	−	0.320616i	0.0113143	−	0.0113143i
$804$	−0.394415	−	2.28788i	−0.0139100	−	0.0806873i
$805$	29.6046	−	22.1974i	1.04343	−	0.782354i
$806$			8.34869i			0.294070i
$807$	33.4387	+	23.6047i	1.17710	+	0.830926i
$808$	−0.813017	−	0.813017i	−0.0286018	−	0.0286018i
$809$	7.39524			0.260003			0.130001	−	0.991514i	$-0.458502\pi$
$809$	7.39524			0.260003			0.130001	+	0.991514i	$0.458502\pi$
$810$	9.24918	+	15.4009i	0.324983	+	0.541132i
$811$	12.0994			0.424866			0.212433	−	0.977176i	$-0.431861\pi$
$811$	12.0994			0.424866			0.212433	+	0.977176i	$0.431861\pi$
$812$	−24.1851	−	24.1851i	−0.848729	−	0.848729i
$813$	1.71794	+	1.21272i	0.0602508	+	0.0425318i
$814$			0.763284i			0.0267531i
$815$	−4.96871	+	34.7481i	−0.174046	+	1.21717i
$816$	−0.319927	−	1.85580i	−0.0111997	−	0.0649658i
$817$	−1.78437	+	1.78437i	−0.0624274	+	0.0624274i
$818$	−5.83865	+	5.83865i	−0.204144	+	0.204144i
$819$	10.7444	+	30.2362i	0.375439	+	1.05654i
$820$	16.5371	+	22.0555i	0.577499	+	0.770212i
$821$			2.84476i			0.0992830i	0.998767	+	0.0496415i	$0.0158079\pi$
$821$			2.84476i			0.0992830i	−0.998767	+	0.0496415i	$0.984192\pi$
$822$	−16.9595	+	24.0249i	−0.591530	+	0.837965i
$823$	13.6012	+	13.6012i	0.474109	+	0.474109i	0.903242	−	0.429132i	$-0.141181\pi$
$823$	13.6012	+	13.6012i	0.474109	+	0.474109i	−0.429132	+	0.903242i	$0.641181\pi$
$824$	36.8513			1.28378
$825$	2.61468	+	3.28641i	0.0910316	+	0.114418i
$826$	−16.0492			−0.558423
$827$	10.4967	+	10.4967i	0.365007	+	0.365007i	0.865653	−	0.500645i	$-0.166904\pi$
$827$	10.4967	+	10.4967i	0.365007	+	0.365007i	−0.500645	+	0.865653i	$0.666904\pi$
$828$	−5.83409	+	12.2659i	−0.202749	+	0.426268i
$829$		−	15.0426i		−	0.522449i	−0.965278	−	0.261225i	$-0.915874\pi$
$829$		−	15.0426i		−	0.522449i	0.965278	−	0.261225i	$-0.0841264\pi$
$830$	11.2612	+	15.0190i	0.390880	+	0.521317i
$831$	−23.3139	+	4.01916i	−0.808751	+	0.139423i
$832$	−9.08312	+	9.08312i	−0.314901	+	0.314901i
$833$	64.8520	−	64.8520i	2.24699	−	2.24699i
$834$	−30.2217	+	5.21001i	−1.04649	+	0.180408i
$835$	−1.01862	+	7.12359i	−0.0352508	+	0.246522i
$836$		−	0.583436i		−	0.0201786i
$837$	5.39152	−	19.2374i	0.186358	−	0.664941i
$838$	−17.2689	−	17.2689i	−0.596546	−	0.596546i
$839$	45.3221			1.56469			0.782346	−	0.622844i	$-0.214023\pi$
$839$	45.3221			1.56469			0.782346	+	0.622844i	$0.214023\pi$
$840$	−48.6771	+	1.39673i	−1.67952	+	0.0481918i
$841$	12.7951			0.441212
$842$	8.65844	+	8.65844i	0.298389	+	0.298389i
$843$	9.21424	−	13.0530i	0.317355	−	0.449568i
$844$		−	10.0178i		−	0.344825i
$845$	12.6723	−	9.50159i	0.435940	−	0.326865i
$846$	−14.3039	+	5.08286i	−0.491778	+	0.174752i
$847$	−33.4720	+	33.4720i	−1.15011	+	1.15011i
$848$	0.311839	−	0.311839i	0.0107086	−	0.0107086i
$849$	−8.69603	−	50.4429i	−0.298447	−	1.73120i
$850$	31.8529	+	9.29959i	1.09255	+	0.318973i
$851$		−	6.63530i		−	0.227455i
$852$	−12.9914	−	9.17080i	−0.445079	−	0.314187i
$853$	18.7950	+	18.7950i	0.643529	+	0.643529i	0.951421	−	0.307892i	$-0.0996235\pi$
$853$	18.7950	+	18.7950i	0.643529	+	0.643529i	−0.307892	+	0.951421i	$0.599624\pi$
$854$	−1.55347			−0.0531586
$855$	5.58902	+	3.70984i	0.191140	+	0.126874i
$856$	34.6727			1.18509
$857$	0.880196	+	0.880196i	0.0300669	+	0.0300669i	0.721980	−	0.691914i	$-0.243232\pi$
$857$	0.880196	+	0.880196i	0.0300669	+	0.0300669i	−0.691914	+	0.721980i	$0.743232\pi$
$858$	1.48997	+	1.05179i	0.0508667	+	0.0359074i
$859$			28.5134i			0.972865i	0.873718	+	0.486432i	$0.161702\pi$
$859$			28.5134i			0.972865i	−0.873718	+	0.486432i	$0.838298\pi$
$860$	−6.72049	−	0.960978i	−0.229167	−	0.0327691i
$861$	13.2586	+	76.9093i	0.451854	+	2.62106i
$862$	−8.63278	+	8.63278i	−0.294034	+	0.294034i
$863$	20.4063	−	20.4063i	0.694639	−	0.694639i	−0.268610	−	0.963249i	$-0.586564\pi$
$863$	20.4063	−	20.4063i	0.694639	−	0.694639i	0.963249	+	0.268610i	$0.0865642\pi$
$864$	25.3114	−	14.2296i	0.861111	−	0.484099i
$865$	27.4044	+	3.91862i	0.931778	+	0.133237i
$866$			4.48822i			0.152516i
$867$	38.2272	−	54.1529i	1.29826	−	1.83913i
$868$	14.3836	+	14.3836i	0.488212	+	0.488212i
$869$	−3.63763			−0.123398
$870$	15.3450	−	16.2516i	0.520244	−	0.550981i
$871$	2.70995			0.0918230
$872$	5.94881	+	5.94881i	0.201452	+	0.201452i
$873$	−27.0609	−	12.8711i	−0.915871	−	0.435622i
$874$		−	3.35930i		−	0.113630i
$875$	20.3199	−	44.7679i	0.686939	−	1.51343i
$876$	1.92012	−	0.331017i	0.0648749	−	0.0111840i
$877$	−16.4879	+	16.4879i	−0.556756	+	0.556756i	−0.928382	−	0.371626i	$-0.878800\pi$
$877$	−16.4879	+	16.4879i	−0.556756	+	0.556756i	0.371626	+	0.928382i	$0.378800\pi$
$878$	18.9788	−	18.9788i	0.640504	−	0.640504i
$879$	45.4844	−	7.84121i	1.53415	−	0.264478i
$880$	−0.126877	+	0.0951317i	−0.00427703	+	0.00320689i
$881$		−	8.63341i		−	0.290867i	−0.989368	−	0.145434i	$-0.953542\pi$
$881$		−	8.63341i		−	0.290867i	0.989368	−	0.145434i	$-0.0464577\pi$
$882$	−29.8348	−	14.1905i	−1.00459	−	0.477819i
$883$	15.0747	+	15.0747i	0.507305	+	0.507305i	0.913698	−	0.406393i	$-0.133214\pi$
$883$	15.0747	+	15.0747i	0.507305	+	0.507305i	−0.406393	+	0.913698i	$0.633214\pi$
$884$	−21.7568			−0.731761
$885$	0.454175	+	15.8283i	0.0152669	+	0.532064i
$886$	−14.3038			−0.480547
$887$	29.5934	+	29.5934i	0.993650	+	0.993650i	0.999980	−	0.00632995i	$-0.00201490\pi$
$887$	29.5934	+	29.5934i	0.993650	+	0.993650i	−0.00632995	+	0.999980i	$0.502015\pi$
$888$	−5.03602	+	7.13406i	−0.168998	+	0.239403i
$889$			77.1475i			2.58744i
$890$	2.36468	−	16.5372i	0.0792644	−	0.554327i
$891$	−2.75401	−	3.38578i	−0.0922628	−	0.113428i
$892$	0.231245	−	0.231245i	0.00774267	−	0.00774267i
$893$	−4.00816	+	4.00816i	−0.134128	+	0.134128i
$894$	0.0339775	+	0.197093i	0.00113638	+	0.00659178i
$895$	14.3715	+	19.1673i	0.480387	+	0.640693i
$896$			28.4163i			0.949321i
$897$	−12.9524	−	9.14328i	−0.432469	−	0.305285i
$898$	−2.85505	−	2.85505i	−0.0952743	−	0.0952743i
$899$	−24.8569			−0.829023
$900$	1.03481	+	18.0172i	0.0344938	+	0.600572i
$901$	22.4186			0.746872
$902$	3.13655	+	3.13655i	0.104436	+	0.104436i
$903$	−15.7018	−	11.0841i	−0.522523	−	0.368855i
$904$			55.2208i			1.83662i
$905$	−28.2251	−	37.6438i	−0.938233	−	1.25132i
$906$	2.38805	+	13.8523i	0.0793376	+	0.460212i
$907$	2.10673	−	2.10673i	0.0699529	−	0.0699529i	−0.671265	−	0.741218i	$-0.734249\pi$
$907$	2.10673	−	2.10673i	0.0699529	−	0.0699529i	0.741218	+	0.671265i	$0.234249\pi$
$908$	8.74730	−	8.74730i	0.290289	−	0.290289i
$909$	−1.13670	+	0.403923i	−0.0377019	+	0.0133973i
$910$	3.02222	−	21.1355i	0.100186	−	0.700636i
$911$			17.3279i			0.574099i	0.957916	+	0.287050i	$0.0926744\pi$
$911$			17.3279i			0.574099i	−0.957916	+	0.287050i	$0.907326\pi$
$912$	−0.146081	+	0.206939i	−0.00483722	+	0.00685244i
$913$	−3.22475	−	3.22475i	−0.106724	−	0.106724i
$914$	−30.7133			−1.01591
$915$	0.0439616	+	1.53209i	0.00145332	+	0.0506494i
$916$	−23.9920			−0.792717
$917$	6.80475	+	6.80475i	0.224713	+	0.224713i
$918$	−33.2050	−	9.30612i	−1.09593	−	0.307148i
$919$		−	17.8632i		−	0.589252i	−0.955613	−	0.294626i	$-0.904805\pi$
$919$		−	17.8632i		−	0.589252i	0.955613	−	0.294626i	$-0.0951951\pi$
$920$	19.2504	−	14.4338i	0.634667	−	0.475869i
$921$	−3.80266	+	0.655554i	−0.125302	+	0.0216012i
$922$	12.0388	−	12.0388i	0.396476	−	0.396476i
$923$	13.1254	−	13.1254i	0.432026	−	0.432026i
$924$	4.37908	−	0.754925i	0.144061	−	0.0248352i
$925$	−4.23704	−	7.73121i	−0.139313	−	0.254201i
$926$		−	34.1435i		−	1.12202i
$927$	16.6071	−	34.9156i	0.545449	−	1.14678i
$928$	−25.5457	−	25.5457i	−0.838579	−	0.838579i
$929$	31.8731			1.04572			0.522862	−	0.852418i	$-0.324864\pi$
$929$	31.8731			1.04572			0.522862	+	0.852418i	$0.324864\pi$
$930$	−9.12614	+	9.66534i	−0.299258	+	0.316939i
$931$	−12.3365			−0.404313
$932$	9.62716	+	9.62716i	0.315348	+	0.315348i
$933$	−17.5942	+	24.9241i	−0.576010	+	0.815979i
$934$		−	18.6585i		−	0.610525i
$935$	−7.98029	−	1.14112i	−0.260983	−	0.0373186i
$936$	6.98652	+	19.6611i	0.228362	+	0.642643i
$937$	−33.0659	+	33.0659i	−1.08022	+	1.08022i	−0.0837278	+	0.996489i	$0.526683\pi$
$937$	−33.0659	+	33.0659i	−1.08022	+	1.08022i	−0.996489	+	0.0837278i	$0.973317\pi$
$938$	−3.09237	+	3.09237i	−0.100969	+	0.100969i
$939$	3.15419	+	18.2964i	0.102933	+	0.597082i
$940$	−15.0959	−	2.15860i	−0.492375	−	0.0704058i
$941$		−	36.7158i		−	1.19690i	−0.801160	−	0.598451i	$-0.795783\pi$
$941$		−	36.7158i		−	1.19690i	0.801160	−	0.598451i	$-0.204217\pi$
$942$	31.3956	+	22.1625i	1.02292	+	0.722094i
$943$	−27.2663	−	27.2663i	−0.887913	−	0.887913i
$944$	−0.597931			−0.0194610
$945$	−20.6131	+	46.7496i	−0.670544	+	1.52077i
$946$	−1.09239			−0.0355168
$947$	23.4841	+	23.4841i	0.763131	+	0.763131i	0.976887	−	0.213756i	$-0.0685698\pi$
$947$	23.4841	+	23.4841i	0.763131	+	0.763131i	−0.213756	+	0.976887i	$0.568570\pi$
$948$	−12.7704	−	9.01481i	−0.414764	−	0.292787i
$949$			2.27435i			0.0738284i
$950$	−2.14511	−	3.91413i	−0.0695966	−	0.126991i
$951$	−2.51663	−	14.5982i	−0.0816073	−	0.473379i
$952$	66.0981	−	66.0981i	2.14225	−	2.14225i
$953$	−6.80443	+	6.80443i	−0.220417	+	0.220417i	−0.808674	−	0.588257i	$-0.799814\pi$
$953$	−6.80443	+	6.80443i	−0.220417	+	0.220417i	0.588257	+	0.808674i	$0.299814\pi$
$954$	−2.70403	−	7.60952i	−0.0875461	−	0.246367i
$955$	−3.82985	+	2.87160i	−0.123931	+	0.0929227i
$956$		−	9.70089i		−	0.313749i
$957$	−3.13153	+	4.43614i	−0.101228	+	0.143400i
$958$	17.8597	+	17.8597i	0.577020	+	0.577020i
$959$	−83.6365			−2.70076
$960$	−20.4446	+	0.586632i	−0.659846	+	0.0189335i
$961$	−16.2168			−0.523124
$962$	−2.70724	−	2.70724i	−0.0872851	−	0.0872851i
$963$	15.6253	−	32.8514i	0.503519	−	1.05862i
$964$			3.95279i			0.127311i
$965$	−3.09131	+	21.6187i	−0.0995129	+	0.695932i
$966$	25.2138	−	4.34669i	0.811241	−	0.139853i
$967$	−16.8127	+	16.8127i	−0.540659	+	0.540659i	−0.923722	−	0.383063i	$-0.874869\pi$
$967$	−16.8127	+	16.8127i	−0.540659	+	0.540659i	0.383063	+	0.923722i	$0.374869\pi$
$968$	−21.7652	+	21.7652i	−0.699558	+	0.699558i
$969$	−12.6896	+	2.18760i	−0.407648	+	0.0702758i
$970$	11.9608	+	15.9522i	0.384039	+	0.512193i
$971$		−	9.36157i		−	0.300427i	−0.988654	−	0.150214i	$-0.952004\pi$
$971$		−	9.36157i		−	0.300427i	0.988654	−	0.150214i	$-0.0479961\pi$
$972$	−1.27769	−	18.7113i	−0.0409820	−	0.600164i
$973$	−61.6731	−	61.6731i	−1.97715	−	1.97715i
$974$	−0.768249			−0.0246163
$975$	−20.9302	−	2.38252i	−0.670304	−	0.0763016i
$976$	−0.0578763			−0.00185258
$977$	−27.6008	−	27.6008i	−0.883029	−	0.883029i	0.110813	−	0.993841i	$-0.464655\pi$
$977$	−27.6008	−	27.6008i	−0.883029	−	0.883029i	−0.993841	+	0.110813i	$0.964655\pi$
$978$	−13.9974	+	19.8288i	−0.447587	+	0.634054i
$979$			4.05843i			0.129708i
$980$	−19.9096	−	26.5534i	−0.635988	−	0.848218i
$981$	8.31717	−	2.95549i	0.265547	−	0.0943614i
$982$	16.2332	−	16.2332i	0.518021	−	0.518021i
$983$	−12.8794	+	12.8794i	−0.410791	+	0.410791i	−0.882014	−	0.471223i	$-0.843813\pi$
$983$	−12.8794	+	12.8794i	−0.410791	+	0.410791i	0.471223	+	0.882014i	$0.343813\pi$
$984$	8.62143	+	50.0102i	0.274841	+	1.59427i
$985$	2.03164	−	14.2080i	0.0647333	−	0.452705i
$986$			42.9047i			1.36636i
$987$	−35.2702	−	24.8977i	−1.12266	−	0.792501i
$988$	2.06935	+	2.06935i	0.0658349	+	0.0658349i
$989$	9.49629			0.301964
$990$	0.575216	+	2.84638i	0.0182816	+	0.0904639i
$991$	−15.7575			−0.500552			−0.250276	−	0.968175i	$-0.580521\pi$
$991$	−15.7575			−0.500552			−0.250276	+	0.968175i	$0.580521\pi$
$992$	15.1928	+	15.1928i	0.482373	+	0.482373i
$993$	23.3537	+	16.4857i	0.741108	+	0.523157i
$994$			29.9551i			0.950119i
$995$	4.22726	−	3.16957i	0.134013	−	0.100482i
$996$	−3.32935	−	19.3125i	−0.105495	−	0.611941i
$997$	−2.79020	+	2.79020i	−0.0883664	+	0.0883664i	−0.749908	−	0.661542i	$-0.769902\pi$
$997$	−2.79020	+	2.79020i	−0.0883664	+	0.0883664i	0.661542	+	0.749908i	$0.269902\pi$
$998$	−5.13120	+	5.13120i	−0.162425	+	0.162425i
$999$	4.48983	+	7.98646i	0.142052	+	0.252680i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	285.2.k.d.248.7	yes	36
3.2	odd	2	inner	285.2.k.d.248.12	yes	36
5.2	odd	4	inner	285.2.k.d.77.12	yes	36
15.2	even	4	inner	285.2.k.d.77.7	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
285.2.k.d.77.7	✓	36	15.2	even	4	inner
285.2.k.d.77.12	yes	36	5.2	odd	4	inner
285.2.k.d.248.7	yes	36	1.1	even	1	trivial
285.2.k.d.248.12	yes	36	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 285 = 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	285.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.631220 - 0.631220i) q^{2} +(-1.41501 - 0.998873i) q^{3} -1.20312i q^{4} +(1.34140 + 1.78903i) q^{5} +(0.262674 + 1.52369i) q^{6} +(-3.10938 + 3.10938i) q^{7} +(-2.02187 + 2.02187i) q^{8} +(1.00451 + 2.82683i) q^{9} +O(q^{10})\)	\(q+(-0.631220 - 0.631220i) q^{2} +(-1.41501 - 0.998873i) q^{3} -1.20312i q^{4} +(1.34140 + 1.78903i) q^{5} +(0.262674 + 1.52369i) q^{6} +(-3.10938 + 3.10938i) q^{7} +(-2.02187 + 2.02187i) q^{8} +(1.00451 + 2.82683i) q^{9} +(0.282552 - 1.97599i) q^{10} +0.484934i q^{11} +(-1.20177 + 1.70243i) q^{12} +(-1.71998 - 1.71998i) q^{13} +3.92540 q^{14} +(-0.111085 - 3.87139i) q^{15} +0.146246 q^{16} +(5.25692 + 5.25692i) q^{17} +(1.15029 - 2.41841i) q^{18} -1.00000i q^{19} +(2.15243 - 1.61387i) q^{20} +(7.50568 - 1.29393i) q^{21} +(0.306100 - 0.306100i) q^{22} +(-2.66096 + 2.66096i) q^{23} +(4.88057 - 0.841377i) q^{24} +(-1.40127 + 4.79963i) q^{25} +2.17137i q^{26} +(1.40226 - 5.00337i) q^{27} +(3.74097 + 3.74097i) q^{28} -6.46492 q^{29} +(-2.37358 + 2.51382i) q^{30} +3.84489 q^{31} +(3.95144 + 3.95144i) q^{32} +(0.484388 - 0.686187i) q^{33} -6.63654i q^{34} +(-9.73372 - 1.39185i) q^{35} +(3.40103 - 1.20855i) q^{36} +(-1.24679 + 1.24679i) q^{37} +(-0.631220 + 0.631220i) q^{38} +(0.715749 + 4.15184i) q^{39} +(-6.32935 - 0.905048i) q^{40} +10.2468i q^{41} +(-5.55449 - 3.92098i) q^{42} +(-1.78437 - 1.78437i) q^{43} +0.583436 q^{44} +(-3.70984 + 5.58902i) q^{45} +3.35930 q^{46} +(-4.00816 - 4.00816i) q^{47} +(-0.206939 - 0.146081i) q^{48} -12.3365i q^{49} +(3.91413 - 2.14511i) q^{50} +(-2.18760 - 12.6896i) q^{51} +(-2.06935 + 2.06935i) q^{52} +(2.13230 - 2.13230i) q^{53} +(-4.04335 + 2.27309i) q^{54} +(-0.867563 + 0.650493i) q^{55} -12.5736i q^{56} +(-0.998873 + 1.41501i) q^{57} +(4.08078 + 4.08078i) q^{58} -4.08854 q^{59} +(-4.65776 + 0.133649i) q^{60} -0.395747 q^{61} +(-2.42697 - 2.42697i) q^{62} +(-11.9131 - 5.66630i) q^{63} -5.28094i q^{64} +(0.769913 - 5.38430i) q^{65} +(-0.738890 + 0.127380i) q^{66} +(-0.787783 + 0.787783i) q^{67} +(6.32472 - 6.32472i) q^{68} +(6.42324 - 1.10732i) q^{69} +(5.26555 + 7.02267i) q^{70} +7.63110i q^{71} +(-7.74648 - 3.68451i) q^{72} +(-0.661154 - 0.661154i) q^{73} +1.57399 q^{74} +(6.77703 - 5.39183i) q^{75} -1.20312 q^{76} +(-1.50785 - 1.50785i) q^{77} +(2.16893 - 3.07252i) q^{78} +7.50129i q^{79} +(0.196174 + 0.261638i) q^{80} +(-6.98193 + 5.67914i) q^{81} +(6.46798 - 6.46798i) q^{82} +(-6.64986 + 6.64986i) q^{83} +(-1.55676 - 9.03026i) q^{84} +(-2.35314 + 16.4564i) q^{85} +2.25266i q^{86} +(9.14792 + 6.45763i) q^{87} +(-0.980476 - 0.980476i) q^{88} +8.36904 q^{89} +(5.86962 - 1.18617i) q^{90} +10.6962 q^{91} +(3.20146 + 3.20146i) q^{92} +(-5.44056 - 3.84055i) q^{93} +5.06005i q^{94} +(1.78903 - 1.34140i) q^{95} +(-1.64434 - 9.53830i) q^{96} +(-7.06303 + 7.06303i) q^{97} +(-7.78704 + 7.78704i) q^{98} +(-1.37083 + 0.487120i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 2 q^{3} + 4 q^{6} + 4 q^{7}+O(q^{10}) \) 36 * q - 2 * q^3 + 4 * q^6 + 4 * q^7	\( 36 q - 2 q^{3} + 4 q^{6} + 4 q^{7} - 4 q^{10} - 18 q^{12} - 8 q^{13} - 8 q^{15} - 84 q^{16} + 8 q^{21} + 40 q^{22} - 20 q^{25} - 14 q^{27} + 36 q^{28} + 28 q^{30} - 28 q^{33} + 92 q^{36} - 4 q^{37} - 20 q^{40} - 100 q^{42} + 16 q^{43} + 28 q^{45} - 24 q^{46} - 58 q^{48} + 32 q^{51} + 148 q^{52} - 72 q^{55} - 2 q^{57} - 12 q^{58} + 58 q^{60} - 112 q^{61} - 64 q^{63} + 92 q^{66} - 8 q^{67} + 8 q^{70} - 88 q^{72} + 76 q^{73} + 80 q^{75} + 36 q^{76} - 36 q^{78} + 4 q^{81} + 20 q^{82} - 28 q^{85} - 4 q^{87} + 140 q^{88} + 76 q^{90} - 24 q^{91} - 48 q^{93} + 32 q^{96} + 32 q^{97}+O(q^{100}) \) 36 * q - 2 * q^3 + 4 * q^6 + 4 * q^7 - 4 * q^10 - 18 * q^12 - 8 * q^13 - 8 * q^15 - 84 * q^16 + 8 * q^21 + 40 * q^22 - 20 * q^25 - 14 * q^27 + 36 * q^28 + 28 * q^30 - 28 * q^33 + 92 * q^36 - 4 * q^37 - 20 * q^40 - 100 * q^42 + 16 * q^43 + 28 * q^45 - 24 * q^46 - 58 * q^48 + 32 * q^51 + 148 * q^52 - 72 * q^55 - 2 * q^57 - 12 * q^58 + 58 * q^60 - 112 * q^61 - 64 * q^63 + 92 * q^66 - 8 * q^67 + 8 * q^70 - 88 * q^72 + 76 * q^73 + 80 * q^75 + 36 * q^76 - 36 * q^78 + 4 * q^81 + 20 * q^82 - 28 * q^85 - 4 * q^87 + 140 * q^88 + 76 * q^90 - 24 * q^91 - 48 * q^93 + 32 * q^96 + 32 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more