LMFDB - Embedded newform 330.2.m.f.91.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [330,2,Mod(31,330)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(330, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("330.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 330 = 2 \cdot 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	330.m (of order $5$, degree $4$, 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:	$2.63506326670$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.2769390625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 2x^{6} + 5x^{5} + 21x^{4} + 75x^{3} - 198x^{2} - 87x + 841 $ x^8 - x^7 - 2x^6 + 5x^5 + 21x^4 + 75x^3 - 198x^2 - 87x + 841
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			91.2
Root			$-1.07877 + 2.33544i$ of defining polynomial
Character	$\chi$	$=$	330.91
Dual form			330.2.m.f.301.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.809017 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.809017 + 0.587785i) q^{5} +(0.809017 + 0.587785i) q^{6} +(1.57877 - 4.85894i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} +1.00000 q^{10} +(1.45132 + 2.98223i) q^{11} +1.00000 q^{12} +(-1.07877 + 0.783769i) q^{13} +(-1.57877 - 4.85894i) q^{14} +(-0.309017 + 0.951057i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-0.627445 - 0.455866i) q^{17} +(-0.309017 + 0.951057i) q^{18} +(-0.0242693 - 0.0746932i) q^{19} +(0.809017 - 0.587785i) q^{20} +5.10899 q^{21} +(2.92705 + 1.55961i) q^{22} +6.64849 q^{23} +(0.809017 - 0.587785i) q^{24} +(0.309017 + 0.951057i) q^{25} +(-0.412052 + 1.26816i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(-4.13326 - 3.00299i) q^{28} +(-0.623850 + 1.92001i) q^{29} +(0.309017 + 0.951057i) q^{30} +(-6.86933 + 4.99086i) q^{31} -1.00000 q^{32} +(-2.38778 + 2.30185i) q^{33} -0.775565 q^{34} +(4.13326 - 3.00299i) q^{35} +(0.309017 + 0.951057i) q^{36} +(-1.21539 + 3.74060i) q^{37} +(-0.0635378 - 0.0461629i) q^{38} +(-1.07877 - 0.783769i) q^{39} +(0.309017 - 0.951057i) q^{40} +(-3.67612 - 11.3139i) q^{41} +(4.13326 - 3.00299i) q^{42} -6.01163 q^{43} +(3.28475 - 0.458729i) q^{44} -1.00000 q^{45} +(5.37874 - 3.90788i) q^{46} +(2.03009 + 6.24796i) q^{47} +(0.309017 - 0.951057i) q^{48} +(-15.4537 - 11.2278i) q^{49} +(0.809017 + 0.587785i) q^{50} +(0.239663 - 0.737606i) q^{51} +(0.412052 + 1.26816i) q^{52} +(-8.36933 + 6.08067i) q^{53} -1.00000 q^{54} +(-0.578765 + 3.26574i) q^{55} -5.10899 q^{56} +(0.0635378 - 0.0461629i) q^{57} +(0.623850 + 1.92001i) q^{58} +(-1.64590 + 5.06555i) q^{59} +(0.809017 + 0.587785i) q^{60} +(3.03046 + 2.20175i) q^{61} +(-2.62385 + 8.07538i) q^{62} +(1.57877 + 4.85894i) q^{63} +(-0.809017 + 0.587785i) q^{64} -1.33343 q^{65} +(-0.578765 + 3.26574i) q^{66} +0.588036 q^{67} +(-0.627445 + 0.455866i) q^{68} +(2.05450 + 6.32309i) q^{69} +(1.57877 - 4.85894i) q^{70} +(1.87292 + 1.36076i) q^{71} +(0.809017 + 0.587785i) q^{72} +(3.38197 - 10.4086i) q^{73} +(1.21539 + 3.74060i) q^{74} +(-0.809017 + 0.587785i) q^{75} -0.0785371 q^{76} +(16.7818 - 2.34364i) q^{77} -1.33343 q^{78} +(-9.97251 + 7.24545i) q^{79} +(-0.309017 - 0.951057i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-9.62422 - 6.99241i) q^{82} +(6.47214 + 4.70228i) q^{83} +(1.57877 - 4.85894i) q^{84} +(-0.239663 - 0.737606i) q^{85} +(-4.86351 + 3.53355i) q^{86} -2.01882 q^{87} +(2.38778 - 2.30185i) q^{88} -9.67821 q^{89} +(-0.809017 + 0.587785i) q^{90} +(2.10517 + 6.47904i) q^{91} +(2.05450 - 6.32309i) q^{92} +(-6.86933 - 4.99086i) q^{93} +(5.31483 + 3.86145i) q^{94} +(0.0242693 - 0.0746932i) q^{95} +(-0.309017 - 0.951057i) q^{96} +(10.8846 - 7.90809i) q^{97} -19.1018 q^{98} +(-2.92705 - 1.55961i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{5} + 2 q^{6} + 3 q^{7} + 2 q^{8} - 2 q^{9} + 8 q^{10} + 10 q^{11} + 8 q^{12} + q^{13} - 3 q^{14} + 2 q^{15} - 2 q^{16} + 3 q^{17} + 2 q^{18} - 12 q^{19} + 2 q^{20}+ \cdots - 10 q^{99}+O(q^{100}) $ 8 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^5 + 2 * q^6 + 3 * q^7 + 2 * q^8 - 2 * q^9 + 8 * q^10 + 10 * q^11 + 8 * q^12 + q^13 - 3 * q^14 + 2 * q^15 - 2 * q^16 + 3 * q^17 + 2 * q^18 - 12 * q^19 + 2 * q^20 - 2 * q^21 + 10 * q^22 + 2 * q^24 - 2 * q^25 - q^26 - 2 * q^27 - 2 * q^28 + 27 * q^29 - 2 * q^30 - 6 * q^31 - 8 * q^32 - 5 * q^33 + 22 * q^34 + 2 * q^35 - 2 * q^36 - 4 * q^37 - 13 * q^38 + q^39 - 2 * q^40 - 23 * q^41 + 2 * q^42 - 2 * q^43 + 10 * q^44 - 8 * q^45 - 5 * q^46 + 5 * q^47 - 2 * q^48 - 53 * q^49 + 2 * q^50 + 8 * q^51 + q^52 - 18 * q^53 - 8 * q^54 + 5 * q^55 + 2 * q^56 + 13 * q^57 - 27 * q^58 - 40 * q^59 + 2 * q^60 - 20 * q^61 + 11 * q^62 + 3 * q^63 - 2 * q^64 + 4 * q^65 + 5 * q^66 + 18 * q^67 + 3 * q^68 - 5 * q^69 + 3 * q^70 - 10 * q^71 + 2 * q^72 + 36 * q^73 + 4 * q^74 - 2 * q^75 - 2 * q^76 + 50 * q^77 + 4 * q^78 - 11 * q^79 + 2 * q^80 - 2 * q^81 - 12 * q^82 + 16 * q^83 + 3 * q^84 - 8 * q^85 - 13 * q^86 - 18 * q^87 + 5 * q^88 - 46 * q^89 - 2 * q^90 - 39 * q^91 - 5 * q^92 - 6 * q^93 + 15 * q^94 + 12 * q^95 + 2 * q^96 + 16 * q^97 - 62 * q^98 - 10 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/330\mathbb{Z}\right)^\times$.

$n$	$67$	$211$	$221$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$	$1$

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 $

$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	0.809017	+	0.587785i	0.361803	+	0.262866i
$5$	0.809017	+	0.587785i	0.361803	+	0.262866i
$6$	0.809017	+	0.587785i	0.330280	+	0.239962i
$7$	1.57877	−	4.85894i	0.596717	−	1.83651i	0.0507316	−	0.998712i	$-0.483845\pi$
$7$	1.57877	−	4.85894i	0.596717	−	1.83651i	0.545986	−	0.837795i	$-0.316155\pi$
$8$	−0.309017	−	0.951057i	−0.109254	−	0.336249i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	1.00000			0.316228
$11$	1.45132	+	2.98223i	0.437590	+	0.899175i
$11$	1.45132	+	2.98223i	0.437590	+	0.899175i
$12$	1.00000			0.288675
$13$	−1.07877	+	0.783769i	−0.299196	+	0.217378i	−0.727247	−	0.686376i	$-0.759200\pi$
$13$	−1.07877	+	0.783769i	−0.299196	+	0.217378i	0.428051	+	0.903755i	$0.359200\pi$
$14$	−1.57877	−	4.85894i	−0.421943	−	1.29861i
$15$	−0.309017	+	0.951057i	−0.0797878	+	0.245562i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−0.627445	−	0.455866i	−0.152178	−	0.110564i	0.509091	−	0.860713i	$-0.329982\pi$
$17$	−0.627445	−	0.455866i	−0.152178	−	0.110564i	−0.661269	+	0.750149i	$0.729982\pi$
$18$	−0.309017	+	0.951057i	−0.0728360	+	0.224166i
$19$	−0.0242693	−	0.0746932i	−0.00556776	−	0.0171358i	0.948234	−	0.317572i	$-0.102868\pi$
$19$	−0.0242693	−	0.0746932i	−0.00556776	−	0.0171358i	−0.953802	+	0.300437i	$0.902868\pi$
$20$	0.809017	−	0.587785i	0.180902	−	0.131433i
$21$	5.10899			1.11487
$22$	2.92705	+	1.55961i	0.624049	+	0.332509i
$23$	6.64849			1.38631			0.693153	−	0.720791i	$-0.256221\pi$
$23$	6.64849			1.38631			0.693153	+	0.720791i	$0.256221\pi$
$24$	0.809017	−	0.587785i	0.165140	−	0.119981i
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$	−0.412052	+	1.26816i	−0.0808100	+	0.248708i
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$	−4.13326	−	3.00299i	−0.781113	−	0.567512i
$29$	−0.623850	+	1.92001i	−0.115846	+	0.356538i	−0.992123	−	0.125271i	$-0.960020\pi$
$29$	−0.623850	+	1.92001i	−0.115846	+	0.356538i	0.876276	+	0.481809i	$0.160020\pi$
$30$	0.309017	+	0.951057i	0.0564185	+	0.173638i
$31$	−6.86933	+	4.99086i	−1.23377	+	0.896385i	−0.997167	−	0.0752219i	$-0.976033\pi$
$31$	−6.86933	+	4.99086i	−1.23377	+	0.896385i	−0.236601	+	0.971607i	$0.576033\pi$
$32$	−1.00000			−0.176777
$33$	−2.38778	+	2.30185i	−0.415660	+	0.400700i
$34$	−0.775565			−0.133008
$35$	4.13326	−	3.00299i	0.698649	−	0.507598i
$36$	0.309017	+	0.951057i	0.0515028	+	0.158509i
$37$	−1.21539	+	3.74060i	−0.199809	+	0.614950i	0.800077	+	0.599897i	$0.204792\pi$
$37$	−1.21539	+	3.74060i	−0.199809	+	0.614950i	−0.999887	+	0.0150533i	$0.995208\pi$
$38$	−0.0635378	−	0.0461629i	−0.0103072	−	0.00748862i
$39$	−1.07877	−	0.783769i	−0.172741	−	0.125503i
$40$	0.309017	−	0.951057i	0.0488599	−	0.150375i
$41$	−3.67612	−	11.3139i	−0.574114	−	1.76694i	−0.639176	−	0.769061i	$-0.720724\pi$
$41$	−3.67612	−	11.3139i	−0.574114	−	1.76694i	0.0650614	−	0.997881i	$-0.479276\pi$
$42$	4.13326	−	3.00299i	0.637776	−	0.463371i
$43$	−6.01163			−0.916765			−0.458383	−	0.888755i	$-0.651571\pi$
$43$	−6.01163			−0.916765			−0.458383	+	0.888755i	$0.651571\pi$
$44$	3.28475	−	0.458729i	0.495194	−	0.0691560i
$45$	−1.00000			−0.149071
$46$	5.37874	−	3.90788i	0.793052	−	0.576186i
$47$	2.03009	+	6.24796i	0.296118	+	0.911359i	0.982843	+	0.184442i	$0.0590476\pi$
$47$	2.03009	+	6.24796i	0.296118	+	0.911359i	−0.686725	+	0.726917i	$0.740952\pi$
$48$	0.309017	−	0.951057i	0.0446028	−	0.137273i
$49$	−15.4537	−	11.2278i	−2.20767	−	1.60397i
$50$	0.809017	+	0.587785i	0.114412	+	0.0831254i
$51$	0.239663	−	0.737606i	0.0335595	−	0.103286i
$52$	0.412052	+	1.26816i	0.0571413	+	0.175863i
$53$	−8.36933	+	6.08067i	−1.14962	+	0.835245i	−0.988430	−	0.151679i	$-0.951532\pi$
$53$	−8.36933	+	6.08067i	−1.14962	+	0.835245i	−0.161186	+	0.986924i	$0.551532\pi$
$54$	−1.00000			−0.136083
$55$	−0.578765	+	3.26574i	−0.0780407	+	0.440352i
$56$	−5.10899			−0.682718
$57$	0.0635378	−	0.0461629i	0.00841579	−	0.00611443i
$58$	0.623850	+	1.92001i	0.0819156	+	0.252110i
$59$	−1.64590	+	5.06555i	−0.214278	+	0.659479i	0.784926	+	0.619589i	$0.212701\pi$
$59$	−1.64590	+	5.06555i	−0.214278	+	0.659479i	−0.999204	+	0.0398899i	$0.987299\pi$
$60$	0.809017	+	0.587785i	0.104444	+	0.0758827i
$61$	3.03046	+	2.20175i	0.388010	+	0.281906i	0.764640	−	0.644458i	$-0.222917\pi$
$61$	3.03046	+	2.20175i	0.388010	+	0.281906i	−0.376630	+	0.926364i	$0.622917\pi$
$62$	−2.62385	+	8.07538i	−0.333229	+	1.02557i
$63$	1.57877	+	4.85894i	0.198906	+	0.612169i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	−1.33343			−0.165391
$66$	−0.578765	+	3.26574i	−0.0712411	+	0.401984i
$67$	0.588036			0.0718400			0.0359200	−	0.999355i	$-0.488564\pi$
$67$	0.588036			0.0718400			0.0359200	+	0.999355i	$0.488564\pi$
$68$	−0.627445	+	0.455866i	−0.0760889	+	0.0552818i
$69$	2.05450	+	6.32309i	0.247332	+	0.761210i
$70$	1.57877	−	4.85894i	0.188699	−	0.580754i
$71$	1.87292	+	1.36076i	0.222275	+	0.161492i	0.693350	−	0.720601i	$-0.256134\pi$
$71$	1.87292	+	1.36076i	0.222275	+	0.161492i	−0.471075	+	0.882093i	$0.656134\pi$
$72$	0.809017	+	0.587785i	0.0953436	+	0.0692712i
$73$	3.38197	−	10.4086i	0.395829	−	1.21824i	−0.532485	−	0.846440i	$-0.678742\pi$
$73$	3.38197	−	10.4086i	0.395829	−	1.21824i	0.928314	−	0.371797i	$-0.121258\pi$
$74$	1.21539	+	3.74060i	0.141287	+	0.434836i
$75$	−0.809017	+	0.587785i	−0.0934172	+	0.0678716i
$76$	−0.0785371			−0.00900882
$77$	16.7818	−	2.34364i	1.91246	−	0.267083i
$78$	−1.33343			−0.150981
$79$	−9.97251	+	7.24545i	−1.12199	+	0.815177i	−0.984510	−	0.175327i	$-0.943902\pi$
$79$	−9.97251	+	7.24545i	−1.12199	+	0.815177i	−0.137484	+	0.990504i	$0.543902\pi$
$80$	−0.309017	−	0.951057i	−0.0345492	−	0.106331i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	−9.62422	−	6.99241i	−1.06282	−	0.772182i
$83$	6.47214	+	4.70228i	0.710409	+	0.516143i	0.883306	−	0.468798i	$-0.155313\pi$
$83$	6.47214	+	4.70228i	0.710409	+	0.516143i	−0.172896	+	0.984940i	$0.555313\pi$
$84$	1.57877	−	4.85894i	0.172257	−	0.530154i
$85$	−0.239663	−	0.737606i	−0.0259951	−	0.0800046i
$86$	−4.86351	+	3.53355i	−0.524446	+	0.381032i
$87$	−2.01882			−0.216440
$88$	2.38778	−	2.30185i	0.254538	−	0.245378i
$89$	−9.67821			−1.02589			−0.512944	−	0.858422i	$-0.671445\pi$
$89$	−9.67821			−1.02589			−0.512944	+	0.858422i	$0.671445\pi$
$90$	−0.809017	+	0.587785i	−0.0852779	+	0.0619580i
$91$	2.10517	+	6.47904i	0.220682	+	0.679188i
$92$	2.05450	−	6.32309i	0.214196	−	0.659228i
$93$	−6.86933	−	4.99086i	−0.712316	−	0.517528i
$94$	5.31483	+	3.86145i	0.548183	+	0.398278i
$95$	0.0242693	−	0.0746932i	0.00248998	−	0.00766336i
$96$	−0.309017	−	0.951057i	−0.0315389	−	0.0970668i
$97$	10.8846	−	7.90809i	1.10516	−	0.802945i	0.123265	−	0.992374i	$-0.460664\pi$
$97$	10.8846	−	7.90809i	1.10516	−	0.802945i	0.981895	+	0.189429i	$0.0606635\pi$
$98$	−19.1018			−1.92957
$99$	−2.92705	−	1.55961i	−0.294180	−	0.156746i
$100$	1.00000			0.100000
$101$	8.60862	−	6.25453i	0.856590	−	0.622349i	−0.0703651	−	0.997521i	$-0.522416\pi$
$101$	8.60862	−	6.25453i	0.856590	−	0.622349i	0.926955	+	0.375172i	$0.122416\pi$
$102$	−0.239663	−	0.737606i	−0.0237301	−	0.0730339i
$103$	5.16326	−	15.8909i	0.508751	−	1.56577i	−0.285620	−	0.958343i	$-0.592200\pi$
$103$	5.16326	−	15.8909i	0.508751	−	1.56577i	0.794372	−	0.607432i	$-0.207800\pi$
$104$	1.07877	+	0.783769i	0.105782	+	0.0768549i
$105$	4.13326	+	3.00299i	0.403365	+	0.293062i
$106$	−3.19680	+	9.83874i	−0.310501	+	0.955623i
$107$	5.42360	+	16.6921i	0.524319	+	1.61369i	0.765659	+	0.643247i	$0.222413\pi$
$107$	5.42360	+	16.6921i	0.524319	+	1.61369i	−0.241340	+	0.970441i	$0.577587\pi$
$108$	−0.809017	+	0.587785i	−0.0778477	+	0.0565597i
$109$	−8.94427			−0.856706			−0.428353	−	0.903612i	$-0.640906\pi$
$109$	−8.94427			−0.856706			−0.428353	+	0.903612i	$0.640906\pi$
$110$	1.45132	+	2.98223i	0.138378	+	0.284344i
$111$	−3.93310			−0.373313
$112$	−4.13326	+	3.00299i	−0.390557	+	0.283756i
$113$	−1.76975	−	5.44673i	−0.166484	−	0.512385i	0.832659	−	0.553787i	$-0.186818\pi$
$113$	−1.76975	−	5.44673i	−0.166484	−	0.512385i	−0.999143	+	0.0414017i	$0.986818\pi$
$114$	0.0242693	−	0.0746932i	0.00227303	−	0.00699566i
$115$	5.37874	+	3.90788i	0.501570	+	0.364412i
$116$	1.63326	+	1.18663i	0.151645	+	0.110176i
$117$	0.412052	−	1.26816i	0.0380942	−	0.117242i
$118$	1.64590	+	5.06555i	0.151517	+	0.466322i
$119$	−3.20561	+	2.32901i	−0.293858	+	0.213500i
$120$	1.00000			0.0912871
$121$	−6.78734	+	8.65633i	−0.617031	+	0.786939i
$122$	3.74585			0.339133
$123$	9.62422	−	6.99241i	0.867787	−	0.630484i
$124$	2.62385	+	8.07538i	0.235629	+	0.725191i
$125$	−0.309017	+	0.951057i	−0.0276393	+	0.0850651i
$126$	4.13326	+	3.00299i	0.368220	+	0.267528i
$127$	5.63303	+	4.09264i	0.499851	+	0.363163i	0.808960	−	0.587864i	$-0.200031\pi$
$127$	5.63303	+	4.09264i	0.499851	+	0.363163i	−0.309109	+	0.951027i	$0.600031\pi$
$128$	−0.309017	+	0.951057i	−0.0273135	+	0.0840623i
$129$	−1.85770	−	5.71740i	−0.163561	−	0.503389i
$130$	−1.07877	+	0.783769i	−0.0946140	+	0.0687411i
$131$	−2.19916			−0.192142			−0.0960709	−	0.995374i	$-0.530628\pi$
$131$	−2.19916			−0.192142			−0.0960709	+	0.995374i	$0.530628\pi$
$132$	1.45132	+	2.98223i	0.126321	+	0.259569i
$133$	−0.401245			−0.0347924
$134$	0.475731	−	0.345639i	0.0410969	−	0.0298586i
$135$	−0.309017	−	0.951057i	−0.0265959	−	0.0818539i
$136$	−0.239663	+	0.737606i	−0.0205509	+	0.0632492i
$137$	1.76034	+	1.27896i	0.150396	+	0.109269i	0.660438	−	0.750880i	$-0.270370\pi$
$137$	1.76034	+	1.27896i	0.150396	+	0.109269i	−0.510043	+	0.860149i	$0.670370\pi$
$138$	5.37874	+	3.90788i	0.457869	+	0.332661i
$139$	3.18517	−	9.80293i	0.270162	−	0.831474i	−0.720297	−	0.693666i	$-0.755994\pi$
$139$	3.18517	−	9.80293i	0.270162	−	0.831474i	0.990459	−	0.137808i	$-0.0440057\pi$
$140$	−1.57877	−	4.85894i	−0.133430	−	0.410655i
$141$	−5.31483	+	3.86145i	−0.447590	+	0.325193i
$142$	2.31506			0.194276
$143$	−3.90301	−	2.07962i	−0.326386	−	0.173907i
$144$	1.00000			0.0833333
$145$	−1.63326	+	1.18663i	−0.135635	+	0.0985446i
$146$	−3.38197	−	10.4086i	−0.279893	−	0.861424i
$147$	5.90278	−	18.1669i	0.486853	−	1.49838i
$148$	3.18194	+	2.31182i	0.261554	+	0.190030i
$149$	12.3356	+	8.96237i	1.01058	+	0.734226i	0.964330	−	0.264704i	$-0.0852742\pi$
$149$	12.3356	+	8.96237i	1.01058	+	0.734226i	0.0462460	+	0.998930i	$0.485274\pi$
$150$	−0.309017	+	0.951057i	−0.0252311	+	0.0776534i
$151$	2.03000	+	6.24769i	0.165199	+	0.508430i	0.999051	−	0.0435581i	$-0.0138694\pi$
$151$	2.03000	+	6.24769i	0.165199	+	0.508430i	−0.833852	+	0.551988i	$0.813869\pi$
$152$	−0.0635378	+	0.0461629i	−0.00515360	+	0.00374431i
$153$	0.775565			0.0627007
$154$	12.1992	−	11.7601i	0.983037	−	0.947657i
$155$	−8.49096			−0.682010
$156$	−1.07877	+	0.783769i	−0.0863704	+	0.0627517i
$157$	−2.87638	−	8.85258i	−0.229560	−	0.706513i	−0.997797	−	0.0663469i	$-0.978866\pi$
$157$	−2.87638	−	8.85258i	−0.229560	−	0.706513i	0.768237	−	0.640166i	$-0.221134\pi$
$158$	−3.80916	+	11.7234i	−0.303040	+	0.932662i
$159$	−8.36933	−	6.08067i	−0.663731	−	0.482229i
$160$	−0.809017	−	0.587785i	−0.0639584	−	0.0464685i
$161$	10.4964	−	32.3046i	0.827233	−	2.54596i
$162$	−0.309017	−	0.951057i	−0.0242787	−	0.0747221i
$163$	15.1300	−	10.9926i	1.18508	−	0.861008i	0.192341	−	0.981328i	$-0.438392\pi$
$163$	15.1300	−	10.9926i	1.18508	−	0.861008i	0.992735	+	0.120320i	$0.0383921\pi$
$164$	−11.8962			−0.928936
$165$	−3.28475	+	0.458729i	−0.255717	+	0.0357120i
$166$	8.00000			0.620920
$167$	1.92123	−	1.39586i	0.148670	−	0.108015i	−0.510964	−	0.859602i	$-0.670711\pi$
$167$	1.92123	−	1.39586i	0.148670	−	0.108015i	0.659634	+	0.751587i	$0.270711\pi$
$168$	−1.57877	−	4.85894i	−0.121804	−	0.374875i
$169$	−3.46778	+	10.6727i	−0.266752	+	0.820979i
$170$	−0.627445	−	0.455866i	−0.0481228	−	0.0349633i
$171$	0.0635378	+	0.0461629i	0.00485886	+	0.00353017i
$172$	−1.85770	+	5.71740i	−0.141648	+	0.435948i
$173$	0.900560	+	2.77164i	0.0684683	+	0.210724i	0.979436	−	0.201753i	$-0.0646638\pi$
$173$	0.900560	+	2.77164i	0.0684683	+	0.210724i	−0.910968	+	0.412477i	$0.864664\pi$
$174$	−1.63326	+	1.18663i	−0.123817	+	0.0899585i
$175$	5.10899			0.386204
$176$	0.578765	−	3.26574i	0.0436261	−	0.246164i
$177$	−5.32624			−0.400345
$178$	−7.82983	+	5.68871i	−0.586871	+	0.426387i
$179$	0.482779	+	1.48584i	0.0360846	+	0.111057i	0.967476	−	0.252961i	$-0.0814045\pi$
$179$	0.482779	+	1.48584i	0.0360846	+	0.111057i	−0.931392	+	0.364018i	$0.881405\pi$
$180$	−0.309017	+	0.951057i	−0.0230328	+	0.0708876i
$181$	−14.9443	−	10.8576i	−1.11080	−	0.807043i	−0.128010	−	0.991773i	$-0.540859\pi$
$181$	−14.9443	−	10.8576i	−1.11080	−	0.807043i	−0.982789	+	0.184730i	$0.940859\pi$
$182$	5.51140	+	4.00427i	0.408532	+	0.296816i
$183$	−1.15753	+	3.56251i	−0.0855671	+	0.263349i
$184$	−2.05450	−	6.32309i	−0.151459	−	0.466144i
$185$	−3.18194	+	2.31182i	−0.233941	+	0.169968i
$186$	−8.49096			−0.622587
$187$	0.448870	−	2.53279i	0.0328246	−	0.185216i
$188$	6.56950			0.479130
$189$	−4.13326	+	3.00299i	−0.300651	+	0.218435i
$190$	−0.0242693	−	0.0746932i	−0.00176068	−	0.00541881i
$191$	6.40523	−	19.7133i	0.463466	−	1.42640i	−0.397435	−	0.917630i	$-0.630100\pi$
$191$	6.40523	−	19.7133i	0.463466	−	1.42640i	0.860901	−	0.508772i	$-0.169900\pi$
$192$	−0.809017	−	0.587785i	−0.0583858	−	0.0424197i
$193$	−1.10899	−	0.805730i	−0.0798270	−	0.0579977i	0.547156	−	0.837031i	$-0.315710\pi$
$193$	−1.10899	−	0.805730i	−0.0798270	−	0.0579977i	−0.626983	+	0.779033i	$0.715710\pi$
$194$	4.15753	−	12.7956i	0.298493	−	0.918668i
$195$	−0.412052	−	1.26816i	−0.0295076	−	0.0908152i
$196$	−15.4537	+	11.2278i	−1.10383	+	0.801983i
$197$	−5.01135			−0.357044			−0.178522	−	0.983936i	$-0.557132\pi$
$197$	−5.01135			−0.357044			−0.178522	+	0.983936i	$0.557132\pi$
$198$	−3.28475	+	0.458729i	−0.233437	+	0.0326005i
$199$	23.3086			1.65230			0.826152	−	0.563448i	$-0.190525\pi$
$199$	23.3086			1.65230			0.826152	+	0.563448i	$0.190525\pi$
$200$	0.809017	−	0.587785i	0.0572061	−	0.0415627i
$201$	0.181713	+	0.559255i	0.0128170	+	0.0394468i
$202$	3.28820	−	10.1200i	0.231357	−	0.712044i
$203$	8.34432	+	6.06250i	0.585657	+	0.425504i
$204$	−0.627445	−	0.455866i	−0.0439300	−	0.0319170i
$205$	3.67612	−	11.3139i	0.256752	−	0.790200i
$206$	−5.16326	−	15.8909i	−0.359741	−	1.10717i
$207$	−5.37874	+	3.90788i	−0.373848	+	0.271617i
$208$	1.33343			0.0924566
$209$	0.187529	−	0.180780i	0.0129717	−	0.0125048i
$210$	5.10899			0.352554
$211$	16.2484	−	11.8052i	1.11859	−	0.812702i	0.134594	−	0.990901i	$-0.457027\pi$
$211$	16.2484	−	11.8052i	1.11859	−	0.812702i	0.983995	+	0.178199i	$0.0570269\pi$
$212$	3.19680	+	9.83874i	0.219557	+	0.675727i
$213$	−0.715393	+	2.20175i	−0.0490180	+	0.150862i
$214$	14.1992	+	10.3163i	0.970635	+	0.705207i
$215$	−4.86351	−	3.53355i	−0.331689	−	0.240986i
$216$	−0.309017	+	0.951057i	−0.0210259	+	0.0647112i
$217$	13.4052	+	41.2571i	0.910006	+	2.80071i
$218$	−7.23607	+	5.25731i	−0.490088	+	0.356070i
$219$	10.9443			0.739545
$220$	2.92705	+	1.55961i	0.197342	+	0.105149i
$221$	1.03416			0.0695651
$222$	−3.18194	+	2.31182i	−0.213558	+	0.155159i
$223$	2.81483	+	8.66317i	0.188495	+	0.580129i	0.999991	−	0.00422962i	$-0.00134633\pi$
$223$	2.81483	+	8.66317i	0.188495	+	0.580129i	−0.811496	+	0.584358i	$0.801346\pi$
$224$	−1.57877	+	4.85894i	−0.105486	+	0.324652i
$225$	−0.809017	−	0.587785i	−0.0539345	−	0.0391857i
$226$	−4.63326	−	3.36626i	−0.308200	−	0.223920i
$227$	6.39360	−	19.6775i	0.424358	−	1.30604i	−0.479250	−	0.877679i	$-0.659091\pi$
$227$	6.39360	−	19.6775i	0.424358	−	1.30604i	0.903608	−	0.428361i	$-0.140909\pi$
$228$	−0.0242693	−	0.0746932i	−0.00160727	−	0.00494668i
$229$	−8.88456	+	6.45501i	−0.587108	+	0.426559i	−0.841280	−	0.540600i	$-0.818197\pi$
$229$	−8.88456	+	6.45501i	−0.587108	+	0.426559i	0.254172	+	0.967159i	$0.418197\pi$
$230$	6.64849			0.438388
$231$	7.41478	+	15.2362i	0.487857	+	1.00247i
$232$	2.01882			0.132542
$233$	2.39719	−	1.74166i	0.157045	−	0.114100i	−0.506487	−	0.862247i	$-0.669056\pi$
$233$	2.39719	−	1.74166i	0.157045	−	0.114100i	0.663533	+	0.748147i	$0.269056\pi$
$234$	−0.412052	−	1.26816i	−0.0269367	−	0.0829025i
$235$	−2.03009	+	6.24796i	−0.132428	+	0.407572i
$236$	4.30902	+	3.13068i	0.280493	+	0.203790i
$237$	−9.97251	−	7.24545i	−0.647784	−	0.470643i
$238$	−1.22444	+	3.76842i	−0.0793683	+	0.244271i
$239$	2.64821	+	8.15034i	0.171298	+	0.527202i	0.999445	−	0.0333094i	$-0.0106047\pi$
$239$	2.64821	+	8.15034i	0.171298	+	0.527202i	−0.828147	+	0.560511i	$0.810605\pi$
$240$	0.809017	−	0.587785i	0.0522218	−	0.0379414i
$241$	7.97000			0.513393			0.256696	−	0.966492i	$-0.417366\pi$
$241$	7.97000			0.513393			0.256696	+	0.966492i	$0.417366\pi$
$242$	−0.403010	+	10.9926i	−0.0259065	+	0.706632i
$243$	1.00000			0.0641500
$244$	3.03046	−	2.20175i	0.194005	−	0.140953i
$245$	−5.90278	−	18.1669i	−0.377115	−	1.16064i
$246$	3.67612	−	11.3139i	0.234381	−	0.721351i
$247$	0.0847231	+	0.0615549i	0.00539080	+	0.00391665i
$248$	6.86933	+	4.99086i	0.436203	+	0.316920i
$249$	−2.47214	+	7.60845i	−0.156665	+	0.482166i
$250$	0.309017	+	0.951057i	0.0195440	+	0.0601501i
$251$	−16.3904	+	11.9083i	−1.03455	+	0.751645i	−0.969215	−	0.246218i	$-0.920812\pi$
$251$	−16.3904	+	11.9083i	−1.03455	+	0.751645i	−0.0653367	+	0.997863i	$0.520812\pi$
$252$	5.10899			0.321836
$253$	9.64909	+	19.8273i	0.606633	+	1.24653i
$254$	6.96281			0.436886
$255$	0.627445	−	0.455866i	0.0392921	−	0.0285474i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−6.16916	+	18.9867i	−0.384822	+	1.18436i	0.551788	+	0.833985i	$0.313946\pi$
$257$	−6.16916	+	18.9867i	−0.384822	+	1.18436i	−0.936609	+	0.350375i	$0.886054\pi$
$258$	−4.86351	−	3.53355i	−0.302789	−	0.219989i
$259$	16.2565	+	11.8110i	1.01013	+	0.733903i
$260$	−0.412052	+	1.26816i	−0.0255544	+	0.0786482i
$261$	−0.623850	−	1.92001i	−0.0386154	−	0.118846i
$262$	−1.77916	+	1.29264i	−0.109917	+	0.0798593i
$263$	−0.696114			−0.0429242			−0.0214621	−	0.999770i	$-0.506832\pi$
$263$	−0.696114			−0.0429242			−0.0214621	+	0.999770i	$0.506832\pi$
$264$	2.92705	+	1.55961i	0.180148	+	0.0959871i
$265$	−10.3451			−0.635492
$266$	−0.324614	+	0.235846i	−0.0199034	+	0.0144606i
$267$	−2.99073	−	9.20452i	−0.183030	−	0.563307i
$268$	0.181713	−	0.559255i	0.0110999	−	0.0341619i
$269$	−4.79079	−	3.48071i	−0.292100	−	0.212223i	0.432078	−	0.901836i	$-0.357781\pi$
$269$	−4.79079	−	3.48071i	−0.292100	−	0.212223i	−0.724178	+	0.689613i	$0.757781\pi$
$270$	−0.809017	−	0.587785i	−0.0492352	−	0.0357715i
$271$	−4.29983	+	13.2335i	−0.261196	+	0.803880i	0.731349	+	0.682003i	$0.238891\pi$
$271$	−4.29983	+	13.2335i	−0.261196	+	0.803880i	−0.992545	+	0.121876i	$0.961109\pi$
$272$	0.239663	+	0.737606i	0.0145317	+	0.0447239i
$273$	−5.51140	+	4.00427i	−0.333565	+	0.242349i
$274$	2.17590			0.131451
$275$	−2.38778	+	2.30185i	−0.143989	+	0.138807i
$276$	6.64849			0.400192
$277$	8.17313	−	5.93813i	0.491076	−	0.356787i	−0.314522	−	0.949250i	$-0.601844\pi$
$277$	8.17313	−	5.93813i	0.491076	−	0.356787i	0.805598	+	0.592463i	$0.201844\pi$
$278$	−3.18517	−	9.80293i	−0.191034	−	0.587941i
$279$	2.62385	−	8.07538i	0.157086	−	0.483460i
$280$	−4.13326	−	3.00299i	−0.247010	−	0.179463i
$281$	−23.3871	−	16.9918i	−1.39516	−	1.01364i	−0.995277	−	0.0970773i	$-0.969051\pi$
$281$	−23.3871	−	16.9918i	−1.39516	−	1.01364i	−0.399883	−	0.916566i	$-0.630949\pi$
$282$	−2.03009	+	6.24796i	−0.120890	+	0.372061i
$283$	−4.05464	−	12.4789i	−0.241023	−	0.741793i	−0.996265	−	0.0863469i	$-0.972481\pi$
$283$	−4.05464	−	12.4789i	−0.241023	−	0.741793i	0.755242	−	0.655446i	$-0.227519\pi$
$284$	1.87292	−	1.36076i	0.111138	−	0.0807462i
$285$	0.0785371			0.00465213
$286$	−4.37997	+	0.611682i	−0.258993	+	0.0361695i
$287$	−60.7775			−3.58759
$288$	0.809017	−	0.587785i	0.0476718	−	0.0346356i
$289$	−5.06741	−	15.5959i	−0.298083	−	0.917406i
$290$	−0.623850	+	1.92001i	−0.0366338	+	0.112747i
$291$	10.8846	+	7.90809i	0.638064	+	0.463581i
$292$	−8.85410	−	6.43288i	−0.518147	−	0.376456i
$293$	7.00236	−	21.5511i	0.409082	−	1.25903i	−0.508356	−	0.861147i	$-0.669746\pi$
$293$	7.00236	−	21.5511i	0.409082	−	1.25903i	0.917438	−	0.397879i	$-0.130254\pi$
$294$	−5.90278	−	18.1669i	−0.344257	−	1.05951i
$295$	−4.30902	+	3.13068i	−0.250881	+	0.182275i
$296$	3.93310			0.228607
$297$	0.578765	−	3.26574i	0.0335834	−	0.189497i
$298$	15.2477			0.883276
$299$	−7.17216	+	5.21088i	−0.414777	+	0.301353i
$300$	0.309017	+	0.951057i	0.0178411	+	0.0549093i
$301$	−9.49096	+	29.2102i	−0.547050	+	1.68365i
$302$	5.31461	+	3.86129i	0.305821	+	0.222192i
$303$	8.60862	+	6.25453i	0.494552	+	0.359313i
$304$	−0.0242693	+	0.0746932i	−0.00139194	+	0.00428395i
$305$	1.15753	+	3.56251i	0.0662800	+	0.203989i
$306$	0.627445	−	0.455866i	0.0358687	−	0.0260601i
$307$	−29.3158			−1.67314			−0.836571	−	0.547859i	$-0.815443\pi$
$307$	−29.3158			−1.67314			−0.836571	+	0.547859i	$0.815443\pi$
$308$	2.95691	−	16.6846i	0.168485	−	0.950694i
$309$	16.7087			0.950522
$310$	−6.86933	+	4.99086i	−0.390152	+	0.283462i
$311$	3.50950	+	10.8011i	0.199005	+	0.612476i	0.999906	+	0.0136789i	$0.00435427\pi$
$311$	3.50950	+	10.8011i	0.199005	+	0.612476i	−0.800901	+	0.598797i	$0.795646\pi$
$312$	−0.412052	+	1.26816i	−0.0233278	+	0.0717957i
$313$	2.56995	+	1.86718i	0.145262	+	0.105539i	0.658043	−	0.752980i	$-0.271385\pi$
$313$	2.56995	+	1.86718i	0.145262	+	0.105539i	−0.512781	+	0.858520i	$0.671385\pi$
$314$	−7.53046	−	5.47120i	−0.424968	−	0.308757i
$315$	−1.57877	+	4.85894i	−0.0889534	+	0.273770i
$316$	3.80916	+	11.7234i	0.214282	+	0.659492i
$317$	−3.82747	+	2.78082i	−0.214972	+	0.156186i	−0.690060	−	0.723752i	$-0.742416\pi$
$317$	−3.82747	+	2.78082i	−0.214972	+	0.156186i	0.475088	+	0.879938i	$0.342416\pi$
$318$	−10.3451			−0.580122
$319$	−6.63132	+	0.926093i	−0.371283	+	0.0518512i
$320$	−1.00000			−0.0559017
$321$	−14.1992	+	10.3163i	−0.792520	+	0.575799i
$322$	−10.4964	−	32.3046i	−0.584942	−	1.80027i
$323$	−0.0188224	+	0.0579294i	−0.00104731	+	0.00322328i
$324$	−0.809017	−	0.587785i	−0.0449454	−	0.0326547i
$325$	−1.07877	−	0.783769i	−0.0598391	−	0.0434757i
$326$	5.77916	−	17.7864i	0.320078	−	0.985099i
$327$	−2.76393	−	8.50651i	−0.152846	−	0.470411i
$328$	−9.62422	+	6.99241i	−0.531409	+	0.386091i
$329$	33.5635			1.85042
$330$	−2.38778	+	2.30185i	−0.131443	+	0.126712i
$331$	30.0424			1.65128			0.825639	−	0.564199i	$-0.190815\pi$
$331$	30.0424			1.65128			0.825639	+	0.564199i	$0.190815\pi$
$332$	6.47214	−	4.70228i	0.355205	−	0.258071i
$333$	−1.21539	−	3.74060i	−0.0666032	−	0.204983i
$334$	0.733846	−	2.25855i	0.0401543	−	0.123582i
$335$	0.475731	+	0.345639i	0.0259919	+	0.0188843i
$336$	−4.13326	−	3.00299i	−0.225488	−	0.163827i
$337$	−7.83574	+	24.1159i	−0.426840	+	1.31368i	0.474382	+	0.880319i	$0.342672\pi$
$337$	−7.83574	+	24.1159i	−0.426840	+	1.31368i	−0.901222	+	0.433359i	$0.857328\pi$
$338$	3.46778	+	10.6727i	0.188622	+	0.580520i
$339$	4.63326	−	3.36626i	0.251644	−	0.182830i
$340$	−0.775565			−0.0420609
$341$	−24.8535	−	13.2426i	−1.34589	−	0.717125i
$342$	0.0785371			0.00424680
$343$	−50.0199	+	36.3416i	−2.70082	+	1.96226i
$344$	1.85770	+	5.71740i	0.100160	+	0.308262i
$345$	−2.05450	+	6.32309i	−0.110610	+	0.340424i
$346$	2.35770	+	1.71297i	0.126751	+	0.0920897i
$347$	2.56995	+	1.86718i	0.137962	+	0.100235i	0.654626	−	0.755953i	$-0.272826\pi$
$347$	2.56995	+	1.86718i	0.137962	+	0.100235i	−0.516664	+	0.856189i	$0.672826\pi$
$348$	−0.623850	+	1.92001i	−0.0334419	+	0.102924i
$349$	−2.15034	−	6.61807i	−0.115105	−	0.354257i	0.876864	−	0.480739i	$-0.159632\pi$
$349$	−2.15034	−	6.61807i	−0.115105	−	0.354257i	−0.991969	+	0.126482i	$0.959632\pi$
$350$	4.13326	−	3.00299i	0.220932	−	0.160517i
$351$	1.33343			0.0711731
$352$	−1.45132	−	2.98223i	−0.0773556	−	0.158953i
$353$	8.01163			0.426416			0.213208	−	0.977007i	$-0.431609\pi$
$353$	8.01163			0.426416			0.213208	+	0.977007i	$0.431609\pi$
$354$	−4.30902	+	3.13068i	−0.229022	+	0.166394i
$355$	0.715393	+	2.20175i	0.0379691	+	0.116857i
$356$	−2.99073	+	9.20452i	−0.158508	+	0.487839i
$357$	−3.20561	−	2.32901i	−0.169659	−	0.123264i
$358$	1.26393	+	0.918300i	0.0668009	+	0.0485337i
$359$	−0.0557281	+	0.171513i	−0.00294122	+	0.00905213i	−0.952516	−	0.304487i	$-0.901515\pi$
$359$	−0.0557281	+	0.171513i	−0.00294122	+	0.00905213i	0.949575	+	0.313540i	$0.101515\pi$
$360$	0.309017	+	0.951057i	0.0162866	+	0.0501251i
$361$	15.3663	−	11.1643i	0.808754	−	0.587594i
$362$	−18.4721			−0.970874
$363$	−10.3301	−	3.78019i	−0.542188	−	0.198409i
$364$	6.81247			0.357070
$365$	8.85410	−	6.43288i	0.463445	−	0.336712i
$366$	1.15753	+	3.56251i	0.0605051	+	0.186216i
$367$	9.53950	−	29.3596i	0.497958	−	1.53256i	−0.314338	−	0.949311i	$-0.601783\pi$
$367$	9.53950	−	29.3596i	0.497958	−	1.53256i	0.812296	−	0.583245i	$-0.198217\pi$
$368$	−5.37874	−	3.90788i	−0.280386	−	0.203713i
$369$	9.62422	+	6.99241i	0.501017	+	0.364010i
$370$	−1.21539	+	3.74060i	−0.0631853	+	0.194464i
$371$	16.3324	+	50.2660i	0.847937	+	2.60968i
$372$	−6.86933	+	4.99086i	−0.356158	+	0.258764i
$373$	16.1018			0.833720			0.416860	−	0.908971i	$-0.363131\pi$
$373$	16.1018			0.833720			0.416860	+	0.908971i	$0.363131\pi$
$374$	−1.12559	−	2.31291i	−0.0582030	−	0.119598i
$375$	−1.00000			−0.0516398
$376$	5.31483	−	3.86145i	0.274092	−	0.199139i
$377$	−0.831859	−	2.56020i	−0.0428429	−	0.131857i
$378$	−1.57877	+	4.85894i	−0.0812029	+	0.249917i
$379$	−26.3324	−	19.1316i	−1.35261	−	0.982726i	−0.998877	−	0.0473775i	$-0.984914\pi$
$379$	−26.3324	−	19.1316i	−1.35261	−	0.982726i	−0.353729	−	0.935348i	$-0.615086\pi$
$380$	−0.0635378	−	0.0461629i	−0.00325942	−	0.00236811i
$381$	−2.15163	+	6.62203i	−0.110231	+	0.339257i
$382$	−6.40523	−	19.7133i	−0.327720	−	1.00862i
$383$	−1.70561	+	1.23920i	−0.0871527	+	0.0633202i	−0.630508	−	0.776182i	$-0.717154\pi$
$383$	−1.70561	+	1.23920i	−0.0871527	+	0.0633202i	0.543356	+	0.839503i	$0.317154\pi$
$384$	−1.00000			−0.0510310
$385$	14.9543	+	7.96802i	0.762141	+	0.406088i
$386$	−1.37079			−0.0697714
$387$	4.86351	−	3.53355i	0.247226	−	0.179620i
$388$	−4.15753	−	12.7956i	−0.211067	−	0.649596i
$389$	−3.89460	+	11.9864i	−0.197464	+	0.607732i	0.802475	+	0.596686i	$0.203516\pi$
$389$	−3.89460	+	11.9864i	−0.197464	+	0.607732i	−0.999939	+	0.0110463i	$0.996484\pi$
$390$	−1.07877	−	0.783769i	−0.0546254	−	0.0396877i
$391$	−4.17156	−	3.03082i	−0.210965	−	0.153275i
$392$	−5.90278	+	18.1669i	−0.298135	+	0.917567i
$393$	−0.679579	−	2.09153i	−0.0342802	−	0.105504i
$394$	−4.05427	+	2.94560i	−0.204251	+	0.148397i
$395$	−12.3267			−0.620223
$396$	−2.38778	+	2.30185i	−0.119991	+	0.115672i
$397$	−30.6341			−1.53748			−0.768741	−	0.639560i	$-0.779116\pi$
$397$	−30.6341			−1.53748			−0.768741	+	0.639560i	$0.779116\pi$
$398$	18.8571	−	13.7005i	0.945219	−	0.686742i
$399$	−0.123992	−	0.381607i	−0.00620734	−	0.0191042i
$400$	0.309017	−	0.951057i	0.0154508	−	0.0475528i
$401$	16.1537	+	11.7364i	0.806678	+	0.586086i	0.912865	−	0.408260i	$-0.133864\pi$
$401$	16.1537	+	11.7364i	0.806678	+	0.586086i	−0.106188	+	0.994346i	$0.533864\pi$
$402$	0.475731	+	0.345639i	0.0237273	+	0.0172389i
$403$	3.49871	−	10.7679i	0.174283	−	0.536389i
$404$	−3.28820	−	10.1200i	−0.163594	−	0.503491i
$405$	0.809017	−	0.587785i	0.0402004	−	0.0292073i
$406$	10.3141			0.511883
$407$	−12.9192	+	1.80423i	−0.640382	+	0.0894322i
$408$	−0.775565			−0.0383962
$409$	5.77608	−	4.19656i	0.285609	−	0.207507i	−0.435751	−	0.900067i	$-0.643517\pi$
$409$	5.77608	−	4.19656i	0.285609	−	0.207507i	0.721360	+	0.692560i	$0.243517\pi$
$410$	−3.67612	−	11.3139i	−0.181551	−	0.558756i
$411$	−0.672389	+	2.06940i	−0.0331665	+	0.102076i
$412$	−13.5176	−	9.82110i	−0.665964	−	0.483851i
$413$	22.0147	+	15.9946i	1.08327	+	0.787045i
$414$	−2.05450	+	6.32309i	−0.100973	+	0.310763i
$415$	2.47214	+	7.60845i	0.121352	+	0.373484i
$416$	1.07877	−	0.783769i	0.0528908	−	0.0384274i
$417$	10.3074			0.504756
$418$	0.0454545	−	0.256481i	0.00222325	−	0.0125449i
$419$	−22.3691			−1.09280			−0.546400	−	0.837524i	$-0.684002\pi$
$419$	−22.3691			−1.09280			−0.546400	+	0.837524i	$0.684002\pi$
$420$	4.13326	−	3.00299i	0.201683	−	0.146531i
$421$	−1.87292	−	5.76427i	−0.0912807	−	0.280933i	0.894986	−	0.446095i	$-0.147186\pi$
$421$	−1.87292	−	5.76427i	−0.0912807	−	0.280933i	−0.986267	+	0.165161i	$0.947186\pi$
$422$	6.20635	−	19.1012i	0.302120	−	0.929831i
$423$	−5.31483	−	3.86145i	−0.258416	−	0.187750i
$424$	8.36933	+	6.08067i	0.406451	+	0.295304i
$425$	0.239663	−	0.737606i	0.0116254	−	0.0357791i
$426$	0.715393	+	2.20175i	0.0346609	+	0.106675i
$427$	15.4826	−	11.2487i	0.749254	−	0.544365i
$428$	17.5511			0.848366
$429$	0.771742	−	4.35462i	0.0372600	−	0.210243i
$430$	−6.01163			−0.289907
$431$	−30.0649	+	21.8434i	−1.44818	+	1.05216i	−0.461922	+	0.886921i	$0.652840\pi$
$431$	−30.0649	+	21.8434i	−1.44818	+	1.05216i	−0.986253	+	0.165240i	$0.947160\pi$
$432$	0.309017	+	0.951057i	0.0148676	+	0.0457577i
$433$	9.47259	−	29.1536i	0.455224	−	1.40103i	−0.415649	−	0.909525i	$-0.636445\pi$
$433$	9.47259	−	29.1536i	0.455224	−	1.40103i	0.870872	−	0.491509i	$-0.163555\pi$
$434$	35.0954	+	25.4983i	1.68463	+	1.22396i
$435$	−1.63326	−	1.18663i	−0.0783089	−	0.0568947i
$436$	−2.76393	+	8.50651i	−0.132368	+	0.407388i
$437$	−0.161354	−	0.496597i	−0.00771861	−	0.0237554i
$438$	8.85410	−	6.43288i	0.423065	−	0.307375i
$439$	7.06017			0.336964			0.168482	−	0.985705i	$-0.446114\pi$
$439$	7.06017			0.336964			0.168482	+	0.985705i	$0.446114\pi$
$440$	3.28475	−	0.458729i	0.156594	−	0.0218691i
$441$	19.1018			0.909610
$442$	0.836653	−	0.607864i	0.0397955	−	0.0289131i
$443$	4.50932	+	13.8783i	0.214244	+	0.659377i	0.999206	+	0.0398326i	$0.0126825\pi$
$443$	4.50932	+	13.8783i	0.214244	+	0.659377i	−0.784962	+	0.619544i	$0.787318\pi$
$444$	−1.21539	+	3.74060i	−0.0576800	+	0.177521i
$445$	−7.82983	−	5.68871i	−0.371170	−	0.269671i
$446$	7.36933	+	5.35413i	0.348948	+	0.253525i
$447$	−4.71180	+	14.5014i	−0.222860	+	0.685894i
$448$	1.57877	+	4.85894i	0.0745897	+	0.229563i
$449$	−10.3301	+	7.50523i	−0.487506	+	0.354194i	−0.804224	−	0.594326i	$-0.797419\pi$
$449$	−10.3301	+	7.50523i	−0.487506	+	0.354194i	0.316719	+	0.948520i	$0.397419\pi$
$450$	−1.00000			−0.0471405
$451$	28.4055	−	27.3832i	1.33756	−	1.28942i
$452$	−5.72703			−0.269377
$453$	−5.31461	+	3.86129i	−0.249702	+	0.181419i
$454$	−6.39360	−	19.6775i	−0.300066	−	0.923510i
$455$	−2.10517	+	6.47904i	−0.0986919	+	0.303742i
$456$	−0.0635378	−	0.0461629i	−0.00297543	−	0.00216178i
$457$	14.0305	+	10.1937i	0.656317	+	0.476842i	0.865417	−	0.501052i	$-0.167053\pi$
$457$	14.0305	+	10.1937i	0.656317	+	0.476842i	−0.209100	+	0.977894i	$0.567053\pi$
$458$	−3.39360	+	10.4444i	−0.158572	+	0.488036i
$459$	0.239663	+	0.737606i	0.0111865	+	0.0344285i
$460$	5.37874	−	3.90788i	0.250785	−	0.182206i
$461$	−2.99355			−0.139424			−0.0697118	−	0.997567i	$-0.522208\pi$
$461$	−2.99355			−0.139424			−0.0697118	+	0.997567i	$0.522208\pi$
$462$	14.9543	+	7.96802i	0.695736	+	0.370706i
$463$	−16.2589			−0.755614			−0.377807	−	0.925884i	$-0.623322\pi$
$463$	−16.2589			−0.755614			−0.377807	+	0.925884i	$0.623322\pi$
$464$	1.63326	−	1.18663i	0.0758223	−	0.0550881i
$465$	−2.62385	−	8.07538i	−0.121678	−	0.374487i
$466$	0.915646	−	2.81807i	0.0424165	−	0.130545i
$467$	15.0240	+	10.9156i	0.695228	+	0.505113i	0.878375	−	0.477973i	$-0.158628\pi$
$467$	15.0240	+	10.9156i	0.695228	+	0.505113i	−0.183147	+	0.983086i	$0.558628\pi$
$468$	−1.07877	−	0.783769i	−0.0498660	−	0.0362297i
$469$	0.928370	−	2.85723i	0.0428682	−	0.131935i
$470$	2.03009	+	6.24796i	0.0936409	+	0.288197i
$471$	7.53046	−	5.47120i	0.346985	−	0.252099i
$472$	5.32624			0.245160
$473$	−8.72480	−	17.9280i	−0.401167	−	0.824332i
$474$	−12.3267			−0.566184
$475$	0.0635378	−	0.0461629i	0.00291531	−	0.00211810i
$476$	1.22444	+	3.76842i	0.0561219	+	0.172725i
$477$	3.19680	−	9.83874i	0.146371	−	0.450485i
$478$	6.93310	+	5.03719i	0.317112	+	0.230396i
$479$	24.7198	+	17.9600i	1.12948	+	0.820614i	0.985619	−	0.168984i	$-0.0540487\pi$
$479$	24.7198	+	17.9600i	1.12948	+	0.820614i	0.143859	+	0.989598i	$0.454049\pi$
$480$	0.309017	−	0.951057i	0.0141046	−	0.0434096i
$481$	−1.62064	−	4.98781i	−0.0738948	−	0.227425i
$482$	6.44787	−	4.68465i	0.293692	−	0.213380i
$483$	33.9671			1.54556
$484$	6.13525	+	9.13010i	0.278875	+	0.415004i
$485$	13.4541			0.610917
$486$	0.809017	−	0.587785i	0.0366978	−	0.0266625i
$487$	−0.157074	−	0.483424i	−0.00711771	−	0.0219061i	0.947435	−	0.319950i	$-0.103666\pi$
$487$	−0.157074	−	0.483424i	−0.00711771	−	0.0219061i	−0.954552	+	0.298043i	$0.903666\pi$
$488$	1.15753	−	3.56251i	0.0523990	−	0.161267i
$489$	15.1300	+	10.9926i	0.684204	+	0.497103i
$490$	−15.4537	−	11.2278i	−0.698126	−	0.507218i
$491$	12.1735	−	37.4662i	0.549383	−	1.69083i	−0.160950	−	0.986963i	$-0.551456\pi$
$491$	12.1735	−	37.4662i	0.549383	−	1.69083i	0.710333	−	0.703865i	$-0.248544\pi$
$492$	−3.67612	−	11.3139i	−0.165733	−	0.510072i
$493$	1.26670	−	0.920312i	0.0570493	−	0.0414488i
$494$	0.104723			0.00471173
$495$	−1.45132	−	2.98223i	−0.0652320	−	0.134041i
$496$	8.49096			0.381255
$497$	9.56876	−	6.95211i	0.429217	−	0.311845i
$498$	2.47214	+	7.60845i	0.110779	+	0.340943i
$499$	6.63175	−	20.4104i	0.296878	−	0.913696i	−0.685706	−	0.727878i	$-0.740507\pi$
$499$	6.63175	−	20.4104i	0.296878	−	0.913696i	0.982584	−	0.185818i	$-0.0594934\pi$
$500$	0.809017	+	0.587785i	0.0361803	+	0.0262866i
$501$	1.92123	+	1.39586i	0.0858344	+	0.0623624i
$502$	−6.26057	+	19.2680i	−0.279423	+	0.859975i
$503$	−7.27779	−	22.3987i	−0.324500	−	0.998710i	−0.971666	−	0.236360i	$-0.924046\pi$
$503$	−7.27779	−	22.3987i	−0.324500	−	0.998710i	0.647165	−	0.762350i	$-0.275954\pi$
$504$	4.13326	−	3.00299i	0.184110	−	0.133764i
$505$	10.6408			0.473511
$506$	19.4605	+	10.3690i	0.865123	+	0.460959i
$507$	−11.2220			−0.498385
$508$	5.63303	−	4.09264i	0.249925	−	0.181581i
$509$	11.9645	+	36.8228i	0.530316	+	1.63214i	0.753558	+	0.657381i	$0.228336\pi$
$509$	11.9645	+	36.8228i	0.530316	+	1.63214i	−0.223243	+	0.974763i	$0.571664\pi$
$510$	0.239663	−	0.737606i	0.0106124	−	0.0326617i
$511$	−45.2355	−	32.8655i	−2.00110	−	1.45389i
$512$	0.809017	+	0.587785i	0.0357538	+	0.0259767i
$513$	−0.0242693	+	0.0746932i	−0.00107152	+	0.00329778i
$514$	6.16916	+	18.9867i	0.272110	+	0.837469i
$515$	13.5176	−	9.82110i	0.595656	−	0.432770i
$516$	−6.01163			−0.264647
$517$	−15.6865	+	15.1220i	−0.689893	+	0.665063i
$518$	20.0942			0.882887
$519$	−2.35770	+	1.71297i	−0.103491	+	0.0751909i
$520$	0.412052	+	1.26816i	0.0180697	+	0.0556127i
$521$	0.784660	−	2.41494i	0.0343766	−	0.105800i	−0.932396	−	0.361439i	$-0.882286\pi$
$521$	0.784660	−	2.41494i	0.0343766	−	0.105800i	0.966772	+	0.255638i	$0.0822857\pi$
$522$	−1.63326	−	1.18663i	−0.0714859	−	0.0519376i
$523$	−30.1927	−	21.9363i	−1.32024	−	0.959207i	−0.999929	−	0.0118928i	$-0.996214\pi$
$523$	−30.1927	−	21.9363i	−1.32024	−	0.959207i	−0.320306	−	0.947314i	$-0.603786\pi$
$524$	−0.679579	+	2.09153i	−0.0296875	+	0.0913688i
$525$	1.57877	+	4.85894i	0.0689030	+	0.212062i
$526$	−0.563168	+	0.409166i	−0.0245553	+	0.0178405i
$527$	6.58529			0.286860
$528$	3.28475	−	0.458729i	0.142950	−	0.0199636i
$529$	21.2024			0.921844
$530$	−8.36933	+	6.08067i	−0.363540	+	0.264128i
$531$	−1.64590	−	5.06555i	−0.0714259	−	0.219826i
$532$	−0.123992	+	0.381607i	−0.00537572	+	0.0165448i
$533$	12.8332	+	9.32386i	0.555868	+	0.403861i
$534$	−7.82983	−	5.68871i	−0.338830	−	0.246174i
$535$	−5.42360	+	16.6921i	−0.234483	+	0.721663i
$536$	−0.181713	−	0.559255i	−0.00784880	−	0.0241561i
$537$	−1.26393	+	0.918300i	−0.0545427	+	0.0396276i
$538$	−5.92175			−0.255305
$539$	11.0555	−	62.3814i	0.476193	−	2.68696i
$540$	−1.00000			−0.0430331
$541$	7.47140	−	5.42829i	0.321220	−	0.233380i	−0.415476	−	0.909604i	$-0.636385\pi$
$541$	7.47140	−	5.42829i	0.321220	−	0.233380i	0.736696	+	0.676224i	$0.236385\pi$
$542$	4.29983	+	13.2335i	0.184694	+	0.568429i
$543$	5.70820	−	17.5680i	0.244962	−	0.753917i
$544$	0.627445	+	0.455866i	0.0269015	+	0.0195451i
$545$	−7.23607	−	5.25731i	−0.309959	−	0.225198i
$546$	−2.10517	+	6.47904i	−0.0900929	+	0.277278i
$547$	−7.84155	−	24.1338i	−0.335281	−	1.03189i	−0.966584	−	0.256351i	$-0.917480\pi$
$547$	−7.84155	−	24.1338i	−0.335281	−	1.03189i	0.631303	−	0.775536i	$-0.282520\pi$
$548$	1.76034	−	1.27896i	0.0751979	−	0.0546345i
$549$	−3.74585			−0.159869
$550$	−0.578765	+	3.26574i	−0.0246786	+	0.139251i
$551$	0.158552			0.00675456
$552$	5.37874	−	3.90788i	0.228934	−	0.166331i
$553$	19.4610	+	59.8947i	0.827564	+	2.54698i
$554$	3.12186	−	9.60809i	0.132635	−	0.408209i
$555$	−3.18194	−	2.31182i	−0.135066	−	0.0981311i
$556$	−8.33887	−	6.05855i	−0.353647	−	0.256940i
$557$	−3.27888	+	10.0913i	−0.138930	+	0.427584i	−0.996181	−	0.0873160i	$-0.972171\pi$
$557$	−3.27888	+	10.0913i	−0.138930	+	0.427584i	0.857250	+	0.514900i	$0.172171\pi$
$558$	−2.62385	−	8.07538i	−0.111076	−	0.341858i
$559$	6.48514	−	4.71173i	0.274292	−	0.199285i
$560$	−5.10899			−0.215894
$561$	2.54754	−	0.355774i	0.107557	−	0.0150208i
$562$	−28.9081			−1.21941
$563$	3.75748	−	2.72997i	0.158359	−	0.115055i	−0.505784	−	0.862660i	$-0.668797\pi$
$563$	3.75748	−	2.72997i	0.158359	−	0.115055i	0.664143	+	0.747606i	$0.268797\pi$
$564$	2.03009	+	6.24796i	0.0854820	+	0.263087i
$565$	1.76975	−	5.44673i	0.0744539	−	0.229145i
$566$	−10.6152	−	7.71238i	−0.446189	−	0.324175i
$567$	−4.13326	−	3.00299i	−0.173581	−	0.126114i
$568$	0.715393	−	2.20175i	0.0300172	−	0.0923836i
$569$	−10.8497	−	33.3920i	−0.454844	−	1.39987i	−0.871318	−	0.490719i	$-0.836734\pi$
$569$	−10.8497	−	33.3920i	−0.454844	−	1.39987i	0.416473	−	0.909148i	$-0.363266\pi$
$570$	0.0635378	−	0.0461629i	0.00266131	−	0.00193355i
$571$	17.7758			0.743896			0.371948	−	0.928254i	$-0.378690\pi$
$571$	17.7758			0.743896			0.371948	+	0.928254i	$0.378690\pi$
$572$	−3.18393	+	3.06934i	−0.133127	+	0.128336i
$573$	20.7278			0.865915
$574$	−49.1701	+	35.7241i	−2.05232	+	1.49110i
$575$	2.05450	+	6.32309i	0.0856784	+	0.263691i
$576$	0.309017	−	0.951057i	0.0128757	−	0.0396274i
$577$	−2.94029	−	2.13624i	−0.122406	−	0.0889329i	0.524898	−	0.851165i	$-0.324103\pi$
$577$	−2.94029	−	2.13624i	−0.122406	−	0.0889329i	−0.647304	+	0.762232i	$0.724103\pi$
$578$	−13.2667	−	9.63880i	−0.551820	−	0.400921i
$579$	0.423597	−	1.30370i	0.0176041	−	0.0541799i
$580$	0.623850	+	1.92001i	0.0259040	+	0.0797243i
$581$	33.0661	−	24.0239i	1.37181	−	0.996680i
$582$	13.4541			0.557688
$583$	−30.2805	−	16.1342i	−1.25409	−	0.668211i
$584$	−10.9443			−0.452877
$585$	1.07877	−	0.783769i	0.0446015	−	0.0324049i
$586$	−7.00236	−	21.5511i	−0.289265	−	0.890266i
$587$	2.28461	−	7.03130i	0.0942958	−	0.290213i	−0.892774	−	0.450505i	$-0.851244\pi$
$587$	2.28461	−	7.03130i	0.0942958	−	0.290213i	0.987070	+	0.160293i	$0.0512438\pi$
$588$	−15.4537	−	11.2278i	−0.637299	−	0.463025i
$589$	0.539497	+	0.391967i	0.0222296	+	0.0161507i
$590$	−1.64590	+	5.06555i	−0.0677605	+	0.208546i
$591$	−1.54859	−	4.76608i	−0.0637006	−	0.196050i
$592$	3.18194	−	2.31182i	0.130777	−	0.0950150i
$593$	−35.9315			−1.47553			−0.737766	−	0.675057i	$-0.764119\pi$
$593$	−35.9315			−1.47553			−0.737766	+	0.675057i	$0.764119\pi$
$594$	−1.45132	−	2.98223i	−0.0595484	−	0.122362i
$595$	−3.96236			−0.162441
$596$	12.3356	−	8.96237i	0.505288	−	0.367113i
$597$	7.20276	+	22.1678i	0.294789	+	0.907268i
$598$	−2.73952	+	8.43138i	−0.112027	+	0.344785i
$599$	16.6297	+	12.0822i	0.679470	+	0.493664i	0.873182	−	0.487395i	$-0.162053\pi$
$599$	16.6297	+	12.0822i	0.679470	+	0.493664i	−0.193712	+	0.981058i	$0.562053\pi$
$600$	0.809017	+	0.587785i	0.0330280	+	0.0239962i
$601$	−1.58259	+	4.87071i	−0.0645551	+	0.198680i	−0.978132	−	0.207986i	$-0.933309\pi$
$601$	−1.58259	+	4.87071i	−0.0645551	+	0.198680i	0.913577	+	0.406667i	$0.133309\pi$
$602$	9.49096	+	29.2102i	0.386823	+	1.19052i
$603$	−0.475731	+	0.345639i	−0.0193733	+	0.0140755i
$604$	6.56921			0.267297
$605$	−10.5791	+	3.01362i	−0.430103	+	0.122521i
$606$	10.6408			0.432255
$607$	30.2529	−	21.9800i	1.22793	−	0.892141i	0.231194	−	0.972908i	$-0.425737\pi$
$607$	30.2529	−	21.9800i	1.22793	−	0.892141i	0.996733	+	0.0807668i	$0.0257369\pi$
$608$	0.0242693	+	0.0746932i	0.000984249	+	0.00302921i
$609$	−3.18725	+	9.80934i	−0.129154	+	0.397494i
$610$	3.03046	+	2.20175i	0.122700	+	0.0891464i
$611$	−7.08694	−	5.14897i	−0.286707	−	0.208305i
$612$	0.239663	−	0.737606i	0.00968779	−	0.0298160i
$613$	−2.59477	−	7.98588i	−0.104802	−	0.322546i	0.884882	−	0.465815i	$-0.154239\pi$
$613$	−2.59477	−	7.98588i	−0.104802	−	0.322546i	−0.989684	+	0.143268i	$0.954239\pi$
$614$	−23.7170	+	17.2314i	−0.957139	+	0.695403i
$615$	11.8962			0.479701
$616$	−7.41478	−	15.2362i	−0.298750	−	0.613883i
$617$	−25.9029			−1.04281			−0.521406	−	0.853309i	$-0.674592\pi$
$617$	−25.9029			−1.04281			−0.521406	+	0.853309i	$0.674592\pi$
$618$	13.5176	−	9.82110i	0.543757	−	0.395063i
$619$	7.76994	+	23.9134i	0.312300	+	0.961162i	0.976851	+	0.213919i	$0.0686228\pi$
$619$	7.76994	+	23.9134i	0.312300	+	0.961162i	−0.664551	+	0.747243i	$0.731377\pi$
$620$	−2.62385	+	8.07538i	−0.105376	+	0.324315i
$621$	−5.37874	−	3.90788i	−0.215841	−	0.156818i
$622$	9.18799	+	6.67546i	0.368405	+	0.267662i
$623$	−15.2796	+	47.0258i	−0.612165	+	1.88405i
$624$	0.412052	+	1.26816i	0.0164953	+	0.0507672i
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$	3.17664			0.126964
$627$	0.229882	+	0.122487i	0.00918060	+	0.00489166i
$628$	−9.30815			−0.371436
$629$	2.46780	−	1.79296i	0.0983977	−	0.0714901i
$630$	1.57877	+	4.85894i	0.0628995	+	0.193585i
$631$	−12.9922	+	39.9858i	−0.517210	+	1.59181i	0.262014	+	0.965064i	$0.415613\pi$
$631$	−12.9922	+	39.9858i	−0.517210	+	1.59181i	−0.779224	+	0.626746i	$0.784387\pi$
$632$	9.97251	+	7.24545i	0.396685	+	0.288209i
$633$	16.2484	+	11.8052i	0.645818	+	0.469214i
$634$	−1.46196	+	4.49946i	−0.0580620	+	0.178696i
$635$	2.15163	+	6.62203i	0.0853847	+	0.262787i
$636$	−8.36933	+	6.08067i	−0.331866	+	0.241114i
$637$	25.4709			1.00919
$638$	−4.82051	+	4.64702i	−0.190846	+	0.183977i
$639$	−2.31506			−0.0915824
$640$	−0.809017	+	0.587785i	−0.0319792	+	0.0232343i
$641$	−0.653762	−	2.01207i	−0.0258220	−	0.0794720i	0.937315	−	0.348483i	$-0.113303\pi$
$641$	−0.653762	−	2.01207i	−0.0258220	−	0.0794720i	−0.963137	+	0.269011i	$0.913303\pi$
$642$	−5.42360	+	16.6921i	−0.214052	+	0.658785i
$643$	31.9422	+	23.2073i	1.25968	+	0.915208i	0.998742	−	0.0501487i	$-0.0159695\pi$
$643$	31.9422	+	23.2073i	1.25968	+	0.915208i	0.260934	+	0.965357i	$0.415970\pi$
$644$	−27.4799	−	19.9653i	−1.08286	−	0.786745i
$645$	1.85770	−	5.71740i	0.0731467	−	0.225123i
$646$	0.0188224	+	0.0579294i	0.000740558	+	0.00227920i
$647$	13.0619	−	9.49005i	0.513518	−	0.373092i	−0.300639	−	0.953738i	$-0.597200\pi$
$647$	13.0619	−	9.49005i	0.513518	−	0.373092i	0.814156	+	0.580646i	$0.197200\pi$
$648$	−1.00000			−0.0392837
$649$	−17.4953	+	2.44330i	−0.686752	+	0.0959080i
$650$	−1.33343			−0.0523013
$651$	−35.0954	+	25.4983i	−1.37550	+	0.999356i
$652$	−5.77916	−	17.7864i	−0.226329	−	0.696570i
$653$	−0.399046	+	1.22814i	−0.0156159	+	0.0480607i	−0.958561	−	0.284888i	$-0.908044\pi$
$653$	−0.399046	+	1.22814i	−0.0156159	+	0.0480607i	0.942945	+	0.332949i	$0.108044\pi$
$654$	−7.23607	−	5.25731i	−0.282953	−	0.205577i
$655$	−1.77916	−	1.29264i	−0.0695175	−	0.0505074i
$656$	−3.67612	+	11.3139i	−0.143529	+	0.441736i
$657$	3.38197	+	10.4086i	0.131943	+	0.406079i
$658$	27.1534	−	19.7281i	1.05855	−	0.769083i
$659$	−23.7015			−0.923278			−0.461639	−	0.887068i	$-0.652738\pi$
$659$	−23.7015			−0.923278			−0.461639	+	0.887068i	$0.652738\pi$
$660$	−0.578765	+	3.26574i	−0.0225284	+	0.127119i
$661$	−17.0796			−0.664318			−0.332159	−	0.943223i	$-0.607777\pi$
$661$	−17.0796			−0.664318			−0.332159	+	0.943223i	$0.607777\pi$
$662$	24.3048	−	17.6585i	0.944632	−	0.686316i
$663$	0.319573	+	0.983544i	0.0124112	+	0.0381977i
$664$	2.47214	−	7.60845i	0.0959375	−	0.295265i
$665$	−0.324614	−	0.235846i	−0.0125880	−	0.00914572i
$666$	−3.18194	−	2.31182i	−0.123298	−	0.0895810i
$667$	−4.14766	+	12.7652i	−0.160598	+	0.494270i
$668$	−0.733846	−	2.25855i	−0.0283934	−	0.0873858i
$669$	−7.36933	+	5.35413i	−0.284915	+	0.207003i
$670$	0.588036			0.0227178
$671$	−2.16797	+	12.2330i	−0.0836935	+	0.472248i
$672$	−5.10899			−0.197084
$673$	6.88530	−	5.00246i	0.265409	−	0.192831i	−0.447119	−	0.894474i	$-0.647550\pi$
$673$	6.88530	−	5.00246i	0.265409	−	0.192831i	0.712528	+	0.701644i	$0.247550\pi$
$674$	7.83574	+	24.1159i	0.301821	+	0.928910i
$675$	0.309017	−	0.951057i	0.0118941	−	0.0366062i
$676$	9.07877	+	6.59611i	0.349183	+	0.253697i
$677$	−18.3748	−	13.3501i	−0.706200	−	0.513084i	0.175746	−	0.984436i	$-0.443766\pi$
$677$	−18.3748	−	13.3501i	−0.706200	−	0.513084i	−0.881946	+	0.471351i	$0.843766\pi$
$678$	1.76975	−	5.44673i	0.0679668	−	0.209180i
$679$	−21.2408	−	65.3724i	−0.815147	−	2.50876i
$680$	−0.627445	+	0.455866i	−0.0240614	+	0.0174816i
$681$	20.6901			0.792847
$682$	−27.8907	+	3.89505i	−1.06799	+	0.149149i
$683$	−11.0419			−0.422507			−0.211254	−	0.977431i	$-0.567755\pi$
$683$	−11.0419			−0.422507			−0.211254	+	0.977431i	$0.567755\pi$
$684$	0.0635378	−	0.0461629i	0.00242943	−	0.00176508i
$685$	0.672389	+	2.06940i	0.0256907	+	0.0790677i
$686$	−19.1059	+	58.8019i	−0.729467	+	2.24507i
$687$	−8.88456	−	6.45501i	−0.338967	−	0.246274i
$688$	4.86351	+	3.53355i	0.185420	+	0.134715i
$689$	4.26270	−	13.1192i	0.162396	−	0.499803i
$690$	2.05450	+	6.32309i	0.0782133	+	0.240716i
$691$	−7.68513	+	5.58357i	−0.292356	+	0.212409i	−0.724289	−	0.689497i	$-0.757832\pi$
$691$	−7.68513	+	5.58357i	−0.292356	+	0.212409i	0.431933	+	0.901906i	$0.357832\pi$
$692$	2.91427			0.110784
$693$	−12.1992	+	11.7601i	−0.463408	+	0.446730i
$694$	3.17664			0.120583
$695$	8.33887	−	6.05855i	0.316312	−	0.229814i
$696$	0.623850	+	1.92001i	0.0236470	+	0.0727780i
$697$	−2.85107	+	8.77470i	−0.107992	+	0.332366i
$698$	−5.62967	−	4.09019i	−0.213086	−	0.154816i
$699$	2.39719	+	1.74166i	0.0906702	+	0.0658758i
$700$	1.57877	−	4.85894i	0.0596717	−	0.183651i
$701$	7.97028	+	24.5300i	0.301033	+	0.926486i	0.981128	+	0.193361i	$0.0619389\pi$
$701$	7.97028	+	24.5300i	0.301033	+	0.926486i	−0.680094	+	0.733125i	$0.738061\pi$
$702$	1.07877	−	0.783769i	0.0407154	−	0.0295815i
$703$	0.308894			0.0116501
$704$	−2.92705	−	1.55961i	−0.110317	−	0.0587799i
$705$	−6.56950			−0.247422
$706$	6.48155	−	4.70912i	0.243936	−	0.177230i
$707$	−16.7994	−	51.7032i	−0.631806	−	1.94450i
$708$	−1.64590	+	5.06555i	−0.0618566	+	0.190375i
$709$	11.1583	+	8.10696i	0.419058	+	0.304463i	0.777259	−	0.629181i	$-0.216610\pi$
$709$	11.1583	+	8.10696i	0.419058	+	0.304463i	−0.358201	+	0.933645i	$0.616610\pi$
$710$	1.87292	+	1.36076i	0.0702896	+	0.0510684i
$711$	3.80916	−	11.7234i	0.142855	−	0.439661i
$712$	2.99073	+	9.20452i	0.112082	+	0.344954i
$713$	−45.6707	+	33.1817i	−1.71038	+	1.24266i
$714$	−3.96236			−0.148287
$715$	−1.93523	−	3.97658i	−0.0723735	−	0.148716i
$716$	1.56231			0.0583861
$717$	−6.93310	+	5.03719i	−0.258921	+	0.188117i
$718$	0.0557281	+	0.171513i	0.00207975	+	0.00640082i
$719$	−5.99601	+	18.4538i	−0.223614	+	0.688212i	0.774816	+	0.632187i	$0.217843\pi$
$719$	−5.99601	+	18.4538i	−0.223614	+	0.688212i	−0.998429	+	0.0560248i	$0.982157\pi$
$720$	0.809017	+	0.587785i	0.0301503	+	0.0219055i
$721$	−69.0613	−	50.1759i	−2.57198	−	1.86865i
$722$	5.86942	−	18.0642i	0.218437	−	0.672280i
$723$	2.46287	+	7.57992i	0.0915950	+	0.281900i
$724$	−14.9443	+	10.8576i	−0.555399	+	0.403521i
$725$	−2.01882			−0.0749772
$726$	−10.5791	+	3.01362i	−0.392629	+	0.111846i
$727$	−1.37752			−0.0510895			−0.0255447	−	0.999674i	$-0.508132\pi$
$727$	−1.37752			−0.0510895			−0.0255447	+	0.999674i	$0.508132\pi$
$728$	5.51140	−	4.00427i	0.204266	−	0.148408i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	3.38197	−	10.4086i	0.125172	−	0.385240i
$731$	3.77197	+	2.74050i	0.139511	+	0.101361i
$732$	3.03046	+	2.20175i	0.112009	+	0.0813792i
$733$	6.76062	−	20.8070i	0.249709	−	0.768526i	−0.745117	−	0.666934i	$-0.767606\pi$
$733$	6.76062	−	20.8070i	0.249709	−	0.768526i	0.994826	−	0.101592i	$-0.0323936\pi$
$734$	−9.53950	−	29.3596i	−0.352109	−	1.08368i
$735$	15.4537	−	11.2278i	0.570018	−	0.414142i
$736$	−6.64849			−0.245067
$737$	0.853428	+	1.75365i	0.0314364	+	0.0645967i
$738$	11.8962			0.437905
$739$	−0.425058	+	0.308822i	−0.0156360	+	0.0113602i	−0.595576	−	0.803299i	$-0.703076\pi$
$739$	−0.425058	+	0.308822i	−0.0156360	+	0.0113602i	0.579940	+	0.814659i	$0.303076\pi$
$740$	1.21539	+	3.74060i	0.0446788	+	0.137507i
$741$	−0.0323613	+	0.0995979i	−0.00118882	+	0.00365882i
$742$	42.7588	+	31.0661i	1.56973	+	1.14047i
$743$	−38.7413	−	28.1472i	−1.42128	−	1.03262i	−0.991559	−	0.129657i	$-0.958612\pi$
$743$	−38.7413	−	28.1472i	−1.42128	−	1.03262i	−0.429720	−	0.902962i	$-0.641388\pi$
$744$	−2.62385	+	8.07538i	−0.0961950	+	0.296058i
$745$	4.71180	+	14.5014i	0.172627	+	0.531291i
$746$	13.0266	−	9.46440i	0.476939	−	0.346516i
$747$	−8.00000			−0.292705
$748$	−2.27012	−	1.20958i	−0.0830037	−	0.0442265i
$749$	89.6686			3.27642
$750$	−0.809017	+	0.587785i	−0.0295411	+	0.0214629i
$751$	11.1723	+	34.3848i	0.407683	+	1.25472i	0.918634	+	0.395110i	$0.129293\pi$
$751$	11.1723	+	34.3848i	0.407683	+	1.25472i	−0.510951	+	0.859610i	$0.670707\pi$
$752$	2.03009	−	6.24796i	0.0740296	−	0.227840i
$753$	−16.3904	−	11.9083i	−0.597298	−	0.433963i
$754$	−2.17784	−	1.58229i	−0.0793121	−	0.0576236i
$755$	−2.03000	+	6.24769i	−0.0738792	+	0.227377i
$756$	1.57877	+	4.85894i	0.0574191	+	0.176718i
$757$	35.2824	−	25.6341i	1.28236	−	0.931689i	0.282738	−	0.959197i	$-0.408757\pi$
$757$	35.2824	−	25.6341i	1.28236	−	0.931689i	0.999622	+	0.0275084i	$0.00875730\pi$
$758$	−32.5487			−1.18222
$759$	−15.8751	+	15.3038i	−0.576231	+	0.555493i
$760$	−0.0785371			−0.00284884
$761$	0.891747	−	0.647892i	0.0323258	−	0.0234861i	−0.571505	−	0.820599i	$-0.693640\pi$
$761$	0.891747	−	0.647892i	0.0323258	−	0.0234861i	0.603831	+	0.797112i	$0.293640\pi$
$762$	2.15163	+	6.62203i	0.0779452	+	0.239891i
$763$	−14.1209	+	43.4597i	−0.511211	+	1.57335i
$764$	−16.7691	−	12.1835i	−0.606685	−	0.440783i
$765$	0.627445	+	0.455866i	0.0226853	+	0.0164819i
$766$	−0.651486	+	2.00507i	−0.0235391	+	0.0724461i
$767$	−2.19469	−	6.75455i	−0.0792455	−	0.243893i
$768$	−0.809017	+	0.587785i	−0.0291929	+	0.0212099i
$769$	−26.9983			−0.973583			−0.486791	−	0.873518i	$-0.661833\pi$
$769$	−26.9983			−0.973583			−0.486791	+	0.873518i	$0.661833\pi$
$770$	16.7818	−	2.34364i	0.604772	−	0.0844591i
$771$	−19.9638			−0.718980
$772$	−1.10899	+	0.805730i	−0.0399135	+	0.0289989i
$773$	−7.26427	−	22.3571i	−0.261278	−	0.804130i	−0.992528	−	0.122020i	$-0.961063\pi$
$773$	−7.26427	−	22.3571i	−0.261278	−	0.804130i	0.731250	−	0.682109i	$-0.238937\pi$
$774$	1.85770	−	5.71740i	0.0667735	−	0.205508i
$775$	−6.86933	−	4.99086i	−0.246754	−	0.179277i
$776$	−10.8846	−	7.90809i	−0.390733	−	0.283884i
$777$	−6.20944	+	19.1107i	−0.222762	+	0.685592i
$778$	3.89460	+	11.9864i	0.139628	+	0.429732i
$779$	−0.755858	+	0.549163i	−0.0270814	+	0.0196758i
$780$	−1.33343			−0.0477444
$781$	−1.33988	+	7.56038i	−0.0479446	+	0.270532i
$782$	−5.15633			−0.184390
$783$	1.63326	−	1.18663i	0.0583680	−	0.0424068i
$784$	5.90278	+	18.1669i	0.210814	+	0.648818i
$785$	2.87638	−	8.85258i	0.102662	−	0.315962i
$786$	−1.77916	−	1.29264i	−0.0634605	−	0.0461068i
$787$	26.1826	+	19.0227i	0.933308	+	0.678088i	0.946800	−	0.321821i	$-0.104295\pi$
$787$	26.1826	+	19.0227i	0.933308	+	0.678088i	−0.0134929	+	0.999909i	$0.504295\pi$
$788$	−1.54859	+	4.76608i	−0.0551663	+	0.169784i
$789$	−0.215111	−	0.662044i	−0.00765816	−	0.0235694i
$790$	−9.97251	+	7.24545i	−0.354806	+	0.257782i
$791$	−29.2593			−1.04034
$792$	−0.578765	+	3.26574i	−0.0205655	+	0.116043i
$793$	−4.99482			−0.177371
$794$	−24.7835	+	18.0063i	−0.879534	+	0.639019i
$795$	−3.19680	−	9.83874i	−0.113379	−	0.348944i
$796$	7.20276	−	22.1678i	0.255295	−	0.785717i
$797$	32.6868	+	23.7483i	1.15782	+	0.841209i	0.989501	−	0.144523i	$-0.0461649\pi$
$797$	32.6868	+	23.7483i	1.15782	+	0.841209i	0.168323	+	0.985732i	$0.446165\pi$
$798$	−0.324614	−	0.235846i	−0.0114912	−	0.00834886i
$799$	1.57446	−	4.84570i	0.0557005	−	0.171429i
$800$	−0.309017	−	0.951057i	−0.0109254	−	0.0336249i
$801$	7.82983	−	5.68871i	0.276654	−	0.201001i
$802$	19.9671			0.705062
$803$	35.9492	−	5.02046i	1.26862	−	0.177168i
$804$	0.588036			0.0207384
$805$	27.4799	−	19.9653i	0.968541	−	0.703686i
$806$	−3.49871	−	10.7679i	−0.123237	−	0.379284i
$807$	1.82992	−	5.63191i	0.0644162	−	0.198253i
$808$	−8.60862	−	6.25453i	−0.302850	−	0.220034i
$809$	−9.89956	−	7.19245i	−0.348050	−	0.252873i	0.400001	−	0.916515i	$-0.369010\pi$
$809$	−9.89956	−	7.19245i	−0.348050	−	0.252873i	−0.748050	+	0.663642i	$0.769010\pi$
$810$	0.309017	−	0.951057i	0.0108578	−	0.0334167i
$811$	−4.68730	−	14.4260i	−0.164593	−	0.506566i	0.834413	−	0.551140i	$-0.185807\pi$
$811$	−4.68730	−	14.4260i	−0.164593	−	0.506566i	−0.999006	+	0.0445737i	$0.985807\pi$
$812$	8.34432	−	6.06250i	0.292828	−	0.212752i
$813$	−13.9146			−0.488005
$814$	−9.39138	+	9.05338i	−0.329168	+	0.317321i
$815$	18.7018			0.655094
$816$	−0.627445	+	0.455866i	−0.0219650	+	0.0159585i
$817$	0.145898	+	0.449028i	0.00510433	+	0.0157095i
$818$	2.20626	−	6.79018i	0.0771402	−	0.237413i
$819$	−5.51140	−	4.00427i	−0.192584	−	0.139921i
$820$	−9.62422	−	6.99241i	−0.336092	−	0.244185i
$821$	−4.47242	+	13.7647i	−0.156088	+	0.480391i	−0.998270	−	0.0588039i	$-0.981271\pi$
$821$	−4.47242	+	13.7647i	−0.156088	+	0.480391i	0.842181	+	0.539195i	$0.181271\pi$
$822$	0.672389	+	2.06940i	0.0234523	+	0.0721786i
$823$	−2.86910	+	2.08452i	−0.100011	+	0.0726619i	−0.636667	−	0.771139i	$-0.719687\pi$
$823$	−2.86910	+	2.08452i	−0.100011	+	0.0726619i	0.536656	+	0.843801i	$0.319687\pi$
$824$	−16.7087			−0.582074
$825$	−2.92705	−	1.55961i	−0.101907	−	0.0542985i
$826$	27.2117			0.946816
$827$	30.1130	−	21.8784i	1.04713	−	0.760785i	0.0754661	−	0.997148i	$-0.475956\pi$
$827$	30.1130	−	21.8784i	1.04713	−	0.760785i	0.971665	+	0.236363i	$0.0759555\pi$
$828$	2.05450	+	6.32309i	0.0713987	+	0.219743i
$829$	−12.6297	+	38.8701i	−0.438646	+	1.35001i	0.450657	+	0.892697i	$0.351190\pi$
$829$	−12.6297	+	38.8701i	−0.438646	+	1.35001i	−0.889303	+	0.457318i	$0.848810\pi$
$830$	6.47214	+	4.70228i	0.224651	+	0.163219i
$831$	8.17313	+	5.93813i	0.283523	+	0.205991i
$832$	0.412052	−	1.26816i	0.0142853	−	0.0439657i
$833$	4.57799	+	14.0896i	0.158618	+	0.488176i
$834$	8.33887	−	6.05855i	0.288752	−	0.209790i
$835$	2.37478			0.0821825
$836$	−0.113982	−	0.234215i	−0.00394216	−	0.00810050i
$837$	8.49096			0.293490
$838$	−18.0970	+	13.1482i	−0.625149	+	0.454197i
$839$	−5.07209	−	15.6103i	−0.175108	−	0.538927i	0.824530	−	0.565818i	$-0.191439\pi$
$839$	−5.07209	−	15.6103i	−0.175108	−	0.538927i	−0.999638	+	0.0268909i	$0.991439\pi$
$840$	1.57877	−	4.85894i	0.0544726	−	0.167649i
$841$	20.1642	+	14.6502i	0.695318	+	0.505178i
$842$	−4.90338	−	3.56251i	−0.168982	−	0.122772i
$843$	8.93310	−	27.4932i	0.307672	−	0.946918i
$844$	−6.20635	−	19.1012i	−0.213631	−	0.657490i
$845$	−9.07877	+	6.59611i	−0.312319	+	0.226913i
$846$	−6.56950			−0.225864
$847$	31.3450	+	46.6456i	1.07703	+	1.60276i
$848$	10.3451			0.355251
$849$	10.6152	−	7.71238i	0.364312	−	0.264688i
$850$	−0.239663	−	0.737606i	−0.00822036	−	0.0252997i
$851$	−8.08053	+	24.8693i	−0.276997	+	0.852509i
$852$	1.87292	+	1.36076i	0.0641653	+	0.0466188i
$853$	−14.7144	−	10.6906i	−0.503811	−	0.366040i	0.306660	−	0.951819i	$-0.400789\pi$
$853$	−14.7144	−	10.6906i	−0.503811	−	0.366040i	−0.810471	+	0.585779i	$0.800789\pi$
$854$	5.91382	−	18.2009i	0.202367	−	0.622820i
$855$	0.0242693	+	0.0746932i	0.000829992	+	0.00255445i
$856$	14.1992	−	10.3163i	0.485317	−	0.352604i
$857$	48.5679			1.65905			0.829525	−	0.558470i	$-0.188611\pi$
$857$	48.5679			1.65905			0.829525	+	0.558470i	$0.188611\pi$
$858$	−1.93523	−	3.97658i	−0.0660677	−	0.135758i
$859$	−29.1564			−0.994805			−0.497402	−	0.867520i	$-0.665713\pi$
$859$	−29.1564			−0.994805			−0.497402	+	0.867520i	$0.665713\pi$
$860$	−4.86351	+	3.53355i	−0.165844	+	0.120493i
$861$	−18.7813	−	57.8029i	−0.640065	−	1.96992i
$862$	−11.4838	+	35.3434i	−0.391139	+	1.20380i
$863$	24.0405	+	17.4664i	0.818348	+	0.594564i	0.916239	−	0.400633i	$-0.131210\pi$
$863$	24.0405	+	17.4664i	0.818348	+	0.594564i	−0.0978910	+	0.995197i	$0.531210\pi$
$864$	0.809017	+	0.587785i	0.0275233	+	0.0199969i
$865$	−0.900560	+	2.77164i	−0.0306200	+	0.0942385i
$866$	−9.47259	−	29.1536i	−0.321892	−	0.990681i
$867$	13.2667	−	9.63880i	0.450560	−	0.327351i
$868$	43.3802			1.47242
$869$	−36.0809	−	19.2248i	−1.22396	−	0.652156i
$870$	−2.01882			−0.0684445
$871$	−0.634352	+	0.460884i	−0.0214942	+	0.0156165i
$872$	2.76393	+	8.50651i	0.0935985	+	0.288067i
$873$	−4.15753	+	12.7956i	−0.140711	+	0.433064i
$874$	−0.422430	−	0.306914i	−0.0142889	−	0.0103815i
$875$	4.13326	+	3.00299i	0.139730	+	0.101520i
$876$	3.38197	−	10.4086i	0.114266	−	0.351675i
$877$	8.25674	+	25.4116i	0.278810	+	0.858090i	0.988186	+	0.153259i	$0.0489770\pi$
$877$	8.25674	+	25.4116i	0.278810	+	0.858090i	−0.709376	+	0.704831i	$0.751023\pi$
$878$	5.71180	−	4.14986i	0.192764	−	0.140051i
$879$	22.6601			0.764307
$880$	2.38778	−	2.30185i	0.0804921	−	0.0775952i
$881$	2.72012			0.0916431			0.0458216	−	0.998950i	$-0.485409\pi$
$881$	2.72012			0.0916431			0.0458216	+	0.998950i	$0.485409\pi$
$882$	15.4537	−	11.2278i	0.520353	−	0.378058i
$883$	10.7306	+	33.0255i	0.361114	+	1.11140i	0.952379	+	0.304917i	$0.0986289\pi$
$883$	10.7306	+	33.0255i	0.361114	+	1.11140i	−0.591265	+	0.806478i	$0.701371\pi$
$884$	0.319573	−	0.983544i	0.0107484	−	0.0330802i
$885$	−4.30902	−	3.13068i	−0.144846	−	0.105237i
$886$	11.8056	+	8.57724i	0.396616	+	0.288158i
$887$	−11.5157	+	35.4418i	−0.386661	+	1.19002i	0.548608	+	0.836080i	$0.315158\pi$
$887$	−11.5157	+	35.4418i	−0.386661	+	1.19002i	−0.935268	+	0.353939i	$0.884842\pi$
$888$	1.21539	+	3.74060i	0.0407859	+	0.125526i
$889$	28.7791	−	20.9093i	0.965221	−	0.701274i
$890$	−9.67821			−0.324414
$891$	3.28475	−	0.458729i	0.110043	−	0.0153680i
$892$	9.10899			0.304992
$893$	0.417411	−	0.303267i	0.0139681	−	0.0101484i
$894$	4.71180	+	14.5014i	0.157586	+	0.485000i
$895$	−0.482779	+	1.48584i	−0.0161375	+	0.0496662i
$896$	4.13326	+	3.00299i	0.138083	+	0.100323i
$897$	−7.17216	−	5.21088i	−0.239471	−	0.173986i
$898$	−3.94573	+	12.1437i	−0.131671	+	0.405241i
$899$	−5.29709	−	16.3028i	−0.176668	−	0.543728i
$900$	−0.809017	+	0.587785i	−0.0269672	+	0.0195928i
$901$	8.02327			0.267294
$902$	6.88510	−	38.8498i	0.229249	−	1.29356i
$903$	−30.7134			−1.02208
$904$	−4.63326	+	3.36626i	−0.154100	+	0.111960i
$905$	−5.70820	−	17.5680i	−0.189747	−	0.583982i
$906$	−2.03000	+	6.24769i	−0.0674422	+	0.207566i
$907$	32.1937	+	23.3901i	1.06898	+	0.776656i	0.975728	−	0.218987i	$-0.0702752\pi$
$907$	32.1937	+	23.3901i	1.06898	+	0.776656i	0.0932477	+	0.995643i	$0.470275\pi$
$908$	−16.7387	−	12.1613i	−0.555492	−	0.403589i
$909$	−3.28820	+	10.1200i	−0.109063	+	0.335661i
$910$	2.10517	+	6.47904i	0.0697857	+	0.214778i
$911$	10.3743	−	7.53738i	0.343717	−	0.249725i	−0.402512	−	0.915415i	$-0.631863\pi$
$911$	10.3743	−	7.53738i	0.343717	−	0.249725i	0.746228	+	0.665690i	$0.231863\pi$
$912$	−0.0785371			−0.00260062
$913$	−4.63012	+	26.1259i	−0.153235	+	0.864641i
$914$	17.3426			0.573642
$915$	−3.03046	+	2.20175i	−0.100184	+	0.0727878i
$916$	3.39360	+	10.4444i	0.112128	+	0.345093i
$917$	−3.47196	+	10.6856i	−0.114654	+	0.352870i
$918$	0.627445	+	0.455866i	0.0207088	+	0.0150458i
$919$	30.0258	+	21.8150i	0.990459	+	0.719610i	0.960022	−	0.279926i	$-0.0903100\pi$
$919$	30.0258	+	21.8150i	0.990459	+	0.719610i	0.0304373	+	0.999537i	$0.490310\pi$
$920$	2.05450	−	6.32309i	0.0677347	−	0.208466i
$921$	−9.05908	−	27.8810i	−0.298507	−	0.918710i
$922$	−2.42183	+	1.75956i	−0.0797588	+	0.0579482i
$923$	−3.08697			−0.101609
$924$	16.7818	−	2.34364i	0.552079	−	0.0771002i
$925$	−3.93310			−0.129319
$926$	−13.1537	+	9.55673i	−0.432258	+	0.314054i
$927$	5.16326	+	15.8909i	0.169584	+	0.521925i
$928$	0.623850	−	1.92001i	0.0204789	−	0.0630276i
$929$	−8.06590	−	5.86022i	−0.264634	−	0.192268i	0.447554	−	0.894257i	$-0.352295\pi$
$929$	−8.06590	−	5.86022i	−0.264634	−	0.192268i	−0.712187	+	0.701989i	$0.752295\pi$
$930$	−6.86933	−	4.99086i	−0.225254	−	0.163657i
$931$	−0.463587	+	1.42677i	−0.0151935	+	0.0467606i
$932$	−0.915646	−	2.81807i	−0.0299930	−	0.0923090i
$933$	−9.18799	+	6.67546i	−0.300801	+	0.218545i
$934$	18.5707			0.607652
$935$	1.85188	−	1.78523i	0.0605630	−	0.0583833i
$936$	−1.33343			−0.0435844
$937$	−9.68938	+	7.03975i	−0.316538	+	0.229979i	−0.734697	−	0.678395i	$-0.762676\pi$
$937$	−9.68938	+	7.03975i	−0.316538	+	0.229979i	0.418159	+	0.908374i	$0.362676\pi$
$938$	−0.928370	−	2.85723i	−0.0303124	−	0.0932919i
$939$	−0.981634	+	3.02116i	−0.0320344	+	0.0985918i
$940$	5.31483	+	3.86145i	0.173351	+	0.125947i
$941$	−4.45765	−	3.23867i	−0.145315	−	0.105578i	0.512752	−	0.858537i	$-0.328626\pi$
$941$	−4.45765	−	3.23867i	−0.145315	−	0.105578i	−0.658068	+	0.752959i	$0.728626\pi$
$942$	2.87638	−	8.85258i	0.0937175	−	0.288433i
$943$	−24.4407	−	75.2207i	−0.795898	−	2.44952i
$944$	4.30902	−	3.13068i	0.140247	−	0.101895i
$945$	−5.10899			−0.166196
$946$	−17.5964	−	9.37578i	−0.572107	−	0.304833i
$947$	−27.3946			−0.890206			−0.445103	−	0.895479i	$-0.646833\pi$
$947$	−27.3946			−0.890206			−0.445103	+	0.895479i	$0.646833\pi$
$948$	−9.97251	+	7.24545i	−0.323892	+	0.235321i
$949$	4.50961	+	13.8791i	0.146388	+	0.450536i
$950$	0.0242693	−	0.0746932i	0.000787400	−	0.00242337i
$951$	−3.82747	−	2.78082i	−0.124114	−	0.0901743i
$952$	3.20561	+	2.32901i	0.103895	+	0.0754838i
$953$	2.46900	−	7.59879i	0.0799787	−	0.246149i	−0.903070	−	0.429493i	$-0.858692\pi$
$953$	2.46900	−	7.59879i	0.0799787	−	0.246149i	0.983049	+	0.183344i	$0.0586922\pi$
$954$	−3.19680	−	9.83874i	−0.103500	−	0.318541i
$955$	16.7691	−	12.1835i	0.542636	−	0.394248i
$956$	8.56978			0.277166
$957$	−2.92996	−	6.02058i	−0.0947121	−	0.194618i
$958$	30.5554			0.987200
$959$	8.99355	−	6.53420i	0.290417	−	0.211000i
$960$	−0.309017	−	0.951057i	−0.00997348	−	0.0306952i
$961$	12.6995	−	39.0850i	0.409661	−	1.26081i
$962$	−4.24289	−	3.08264i	−0.136796	−	0.0993883i
$963$	−14.1992	−	10.3163i	−0.457562	−	0.332438i
$964$	2.46287	−	7.57992i	0.0793236	−	0.244133i
$965$	−0.423597	−	1.30370i	−0.0136361	−	0.0419675i
$966$	27.4799	−	19.9653i	0.884153	−	0.642375i
$967$	−19.0966			−0.614106			−0.307053	−	0.951692i	$-0.599343\pi$
$967$	−19.0966			−0.614106			−0.307053	+	0.951692i	$0.599343\pi$
$968$	10.3301	+	3.78019i	0.332021	+	0.121500i
$969$	−0.0609106			−0.00195673
$970$	10.8846	−	7.90809i	0.349482	−	0.253914i
$971$	0.0462836	+	0.142446i	0.00148531	+	0.00457131i	0.951796	−	0.306730i	$-0.0992350\pi$
$971$	0.0462836	+	0.142446i	0.00148531	+	0.00457131i	−0.950311	+	0.311302i	$0.899235\pi$
$972$	0.309017	−	0.951057i	0.00991172	−	0.0305052i
$973$	−42.6032	−	30.9531i	−1.36580	−	0.992310i
$974$	−0.411225	−	0.298773i	−0.0131765	−	0.00957330i
$975$	0.412052	−	1.26816i	0.0131962	−	0.0406138i
$976$	−1.15753	−	3.56251i	−0.0370517	−	0.114033i
$977$	15.4833	−	11.2493i	0.495355	−	0.359897i	−0.311885	−	0.950120i	$-0.600960\pi$
$977$	15.4833	−	11.2493i	0.495355	−	0.359897i	0.807240	+	0.590223i	$0.200960\pi$
$978$	18.7018			0.598016
$979$	−14.0462	−	28.8626i	−0.448918	−	0.922452i
$980$	−19.1018			−0.610185
$981$	7.23607	−	5.25731i	0.231030	−	0.167853i
$982$	−12.1735	−	37.4662i	−0.388473	−	1.19560i
$983$	2.65314	−	8.16553i	0.0846221	−	0.260440i	−0.899788	−	0.436327i	$-0.856279\pi$
$983$	2.65314	−	8.16553i	0.0846221	−	0.260440i	0.984410	+	0.175887i	$0.0562792\pi$
$984$	−9.62422	−	6.99241i	−0.306809	−	0.222910i
$985$	−4.05427	−	2.94560i	−0.129180	−	0.0938546i
$986$	0.483837	−	1.48910i	0.0154085	−	0.0474225i
$987$	10.3717	+	31.9208i	0.330135	+	1.01605i
$988$	0.0847231	−	0.0615549i	0.00269540	−	0.00195832i
$989$	−39.9683			−1.27092
$990$	−2.92705	−	1.55961i	−0.0930278	−	0.0495675i
$991$	−11.3086			−0.359230			−0.179615	−	0.983737i	$-0.557485\pi$
$991$	−11.3086			−0.359230			−0.179615	+	0.983737i	$0.557485\pi$
$992$	6.86933	−	4.99086i	0.218101	−	0.158460i
$993$	9.28360	+	28.5720i	0.294606	+	0.906705i
$994$	3.65494	−	11.2487i	0.115928	−	0.356789i
$995$	18.8571	+	13.7005i	0.597809	+	0.434334i
$996$	6.47214	+	4.70228i	0.205077	+	0.148998i
$997$	−11.4436	+	35.2196i	−0.362421	+	1.11542i	0.589159	+	0.808017i	$0.299459\pi$
$997$	−11.4436	+	35.2196i	−0.362421	+	1.11542i	−0.951580	+	0.307400i	$0.900541\pi$
$998$	−6.63175	−	20.4104i	−0.209924	−	0.646081i
$999$	3.18194	−	2.31182i	0.100672	−	0.0731426i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	330.2.m.f.91.2	✓	8
3.2	odd	2		990.2.n.i.91.2		8
11.2	odd	10		3630.2.a.bs.1.1		4
11.4	even	5	inner	330.2.m.f.301.2	yes	8
11.9	even	5		3630.2.a.bq.1.4		4
33.26	odd	10		990.2.n.i.631.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
330.2.m.f.91.2	✓	8	1.1	even	1	trivial
330.2.m.f.301.2	yes	8	11.4	even	5	inner
990.2.n.i.91.2		8	3.2	odd	2
990.2.n.i.631.2		8	33.26	odd	10
3630.2.a.bq.1.4		4	11.9	even	5
3630.2.a.bs.1.1		4	11.2	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:	\( N \)	\(=\)	\( 330 = 2 \cdot 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	330.m (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 - 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.809017 + 0.587785i) q^{5} +(0.809017 + 0.587785i) q^{6} +(1.57877 - 4.85894i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.809017 + 0.587785i) q^{9} +1.00000 q^{10} +(1.45132 + 2.98223i) q^{11} +1.00000 q^{12} +(-1.07877 + 0.783769i) q^{13} +(-1.57877 - 4.85894i) q^{14} +(-0.309017 + 0.951057i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-0.627445 - 0.455866i) q^{17} +(-0.309017 + 0.951057i) q^{18} +(-0.0242693 - 0.0746932i) q^{19} +(0.809017 - 0.587785i) q^{20} +5.10899 q^{21} +(2.92705 + 1.55961i) q^{22} +6.64849 q^{23} +(0.809017 - 0.587785i) q^{24} +(0.309017 + 0.951057i) q^{25} +(-0.412052 + 1.26816i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(-4.13326 - 3.00299i) q^{28} +(-0.623850 + 1.92001i) q^{29} +(0.309017 + 0.951057i) q^{30} +(-6.86933 + 4.99086i) q^{31} -1.00000 q^{32} +(-2.38778 + 2.30185i) q^{33} -0.775565 q^{34} +(4.13326 - 3.00299i) q^{35} +(0.309017 + 0.951057i) q^{36} +(-1.21539 + 3.74060i) q^{37} +(-0.0635378 - 0.0461629i) q^{38} +(-1.07877 - 0.783769i) q^{39} +(0.309017 - 0.951057i) q^{40} +(-3.67612 - 11.3139i) q^{41} +(4.13326 - 3.00299i) q^{42} -6.01163 q^{43} +(3.28475 - 0.458729i) q^{44} -1.00000 q^{45} +(5.37874 - 3.90788i) q^{46} +(2.03009 + 6.24796i) q^{47} +(0.309017 - 0.951057i) q^{48} +(-15.4537 - 11.2278i) q^{49} +(0.809017 + 0.587785i) q^{50} +(0.239663 - 0.737606i) q^{51} +(0.412052 + 1.26816i) q^{52} +(-8.36933 + 6.08067i) q^{53} -1.00000 q^{54} +(-0.578765 + 3.26574i) q^{55} -5.10899 q^{56} +(0.0635378 - 0.0461629i) q^{57} +(0.623850 + 1.92001i) q^{58} +(-1.64590 + 5.06555i) q^{59} +(0.809017 + 0.587785i) q^{60} +(3.03046 + 2.20175i) q^{61} +(-2.62385 + 8.07538i) q^{62} +(1.57877 + 4.85894i) q^{63} +(-0.809017 + 0.587785i) q^{64} -1.33343 q^{65} +(-0.578765 + 3.26574i) q^{66} +0.588036 q^{67} +(-0.627445 + 0.455866i) q^{68} +(2.05450 + 6.32309i) q^{69} +(1.57877 - 4.85894i) q^{70} +(1.87292 + 1.36076i) q^{71} +(0.809017 + 0.587785i) q^{72} +(3.38197 - 10.4086i) q^{73} +(1.21539 + 3.74060i) q^{74} +(-0.809017 + 0.587785i) q^{75} -0.0785371 q^{76} +(16.7818 - 2.34364i) q^{77} -1.33343 q^{78} +(-9.97251 + 7.24545i) q^{79} +(-0.309017 - 0.951057i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-9.62422 - 6.99241i) q^{82} +(6.47214 + 4.70228i) q^{83} +(1.57877 - 4.85894i) q^{84} +(-0.239663 - 0.737606i) q^{85} +(-4.86351 + 3.53355i) q^{86} -2.01882 q^{87} +(2.38778 - 2.30185i) q^{88} -9.67821 q^{89} +(-0.809017 + 0.587785i) q^{90} +(2.10517 + 6.47904i) q^{91} +(2.05450 - 6.32309i) q^{92} +(-6.86933 - 4.99086i) q^{93} +(5.31483 + 3.86145i) q^{94} +(0.0242693 - 0.0746932i) q^{95} +(-0.309017 - 0.951057i) q^{96} +(10.8846 - 7.90809i) q^{97} -19.1018 q^{98} +(-2.92705 - 1.55961i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{5} + 2 q^{6} + 3 q^{7} + 2 q^{8} - 2 q^{9} + 8 q^{10} + 10 q^{11} + 8 q^{12} + q^{13} - 3 q^{14} + 2 q^{15} - 2 q^{16} + 3 q^{17} + 2 q^{18} - 12 q^{19} + 2 q^{20}+ \cdots - 10 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^5 + 2 * q^6 + 3 * q^7 + 2 * q^8 - 2 * q^9 + 8 * q^10 + 10 * q^11 + 8 * q^12 + q^13 - 3 * q^14 + 2 * q^15 - 2 * q^16 + 3 * q^17 + 2 * q^18 - 12 * q^19 + 2 * q^20 - 2 * q^21 + 10 * q^22 + 2 * q^24 - 2 * q^25 - q^26 - 2 * q^27 - 2 * q^28 + 27 * q^29 - 2 * q^30 - 6 * q^31 - 8 * q^32 - 5 * q^33 + 22 * q^34 + 2 * q^35 - 2 * q^36 - 4 * q^37 - 13 * q^38 + q^39 - 2 * q^40 - 23 * q^41 + 2 * q^42 - 2 * q^43 + 10 * q^44 - 8 * q^45 - 5 * q^46 + 5 * q^47 - 2 * q^48 - 53 * q^49 + 2 * q^50 + 8 * q^51 + q^52 - 18 * q^53 - 8 * q^54 + 5 * q^55 + 2 * q^56 + 13 * q^57 - 27 * q^58 - 40 * q^59 + 2 * q^60 - 20 * q^61 + 11 * q^62 + 3 * q^63 - 2 * q^64 + 4 * q^65 + 5 * q^66 + 18 * q^67 + 3 * q^68 - 5 * q^69 + 3 * q^70 - 10 * q^71 + 2 * q^72 + 36 * q^73 + 4 * q^74 - 2 * q^75 - 2 * q^76 + 50 * q^77 + 4 * q^78 - 11 * q^79 + 2 * q^80 - 2 * q^81 - 12 * q^82 + 16 * q^83 + 3 * q^84 - 8 * q^85 - 13 * q^86 - 18 * q^87 + 5 * q^88 - 46 * q^89 - 2 * q^90 - 39 * q^91 - 5 * q^92 - 6 * q^93 + 15 * q^94 + 12 * q^95 + 2 * q^96 + 16 * q^97 - 62 * q^98 - 10 * q^99

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