LMFDB - Embedded newform 300.2.w.a.223.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,2,Mod(67,300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 0, 13]))

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

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

chi := DirichletCharacter("300.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	300.w (of order $20$, degree $8$, 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:	$2.39551206064$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			223.2
Character	$\chi$	$=$	300.223
Dual form			300.2.w.a.187.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.38012 - 0.308664i) q^{2} +(-0.453990 - 0.891007i) q^{3} +(1.80945 + 0.851985i) q^{4} +(-0.600764 - 2.15385i) q^{5} +(0.351539 + 1.36982i) q^{6} +(-0.972204 - 0.972204i) q^{7} +(-2.23428 - 1.73435i) q^{8} +(-0.587785 + 0.809017i) q^{9} +O(q^{10})$	\(q+(-1.38012 - 0.308664i) q^{2} +(-0.453990 - 0.891007i) q^{3} +(1.80945 + 0.851985i) q^{4} +(-0.600764 - 2.15385i) q^{5} +(0.351539 + 1.36982i) q^{6} +(-0.972204 - 0.972204i) q^{7} +(-2.23428 - 1.73435i) q^{8} +(-0.587785 + 0.809017i) q^{9} +(0.164308 + 3.15801i) q^{10} +(-0.162076 - 0.223079i) q^{11} +(-0.0623506 - 1.99903i) q^{12} +(0.0801385 + 0.505975i) q^{13} +(1.04167 + 1.64184i) q^{14} +(-1.64636 + 1.51311i) q^{15} +(2.54824 + 3.08325i) q^{16} +(-4.63639 - 2.36236i) q^{17} +(1.06093 - 0.935111i) q^{18} +(-0.118004 - 0.363178i) q^{19} +(0.747997 - 4.40914i) q^{20} +(-0.424869 + 1.30761i) q^{21} +(0.154828 + 0.357902i) q^{22} +(0.0164778 - 0.104037i) q^{23} +(-0.530976 + 2.77814i) q^{24} +(-4.27817 + 2.58791i) q^{25} +(0.0455754 - 0.723041i) q^{26} +(0.987688 + 0.156434i) q^{27} +(-0.930855 - 2.58746i) q^{28} +(-5.13240 - 1.66762i) q^{29} +(2.73921 - 1.58010i) q^{30} +(-4.03574 + 1.31129i) q^{31} +(-2.56519 - 5.04181i) q^{32} +(-0.125183 + 0.245686i) q^{33} +(5.66959 + 4.69142i) q^{34} +(-1.50992 + 2.67805i) q^{35} +(-1.75284 + 0.963094i) q^{36} +(-9.32402 + 1.47678i) q^{37} +(0.0507592 + 0.537652i) q^{38} +(0.414445 - 0.301112i) q^{39} +(-2.39326 + 5.85425i) q^{40} +(-0.259624 - 0.188628i) q^{41} +(0.989981 - 1.67352i) q^{42} +(6.23345 - 6.23345i) q^{43} +(-0.103210 - 0.541737i) q^{44} +(2.09562 + 0.779975i) q^{45} +(-0.0548538 + 0.138497i) q^{46} +(-2.85131 + 1.45282i) q^{47} +(1.59032 - 3.67027i) q^{48} -5.10964i q^{49} +(6.70317 - 2.25111i) q^{50} +5.20354i q^{51} +(-0.286076 + 0.983815i) q^{52} +(8.32407 - 4.24132i) q^{53} +(-1.31484 - 0.520762i) q^{54} +(-0.383109 + 0.483105i) q^{55} +(0.486034 + 3.85832i) q^{56} +(-0.270021 + 0.270021i) q^{57} +(6.56858 + 3.88569i) q^{58} +(11.0613 + 8.03648i) q^{59} +(-4.26815 + 1.33524i) q^{60} +(9.38530 - 6.81882i) q^{61} +(5.97455 - 0.564051i) q^{62} +(1.35798 - 0.215082i) q^{63} +(1.98404 + 7.75007i) q^{64} +(1.04165 - 0.476578i) q^{65} +(0.248602 - 0.300437i) q^{66} +(1.33244 - 2.61505i) q^{67} +(-6.37663 - 8.22471i) q^{68} +(-0.100178 + 0.0325500i) q^{69} +(2.91048 - 3.22997i) q^{70} +(-11.5226 - 3.74393i) q^{71} +(2.71640 - 0.788146i) q^{72} +(3.09545 + 0.490271i) q^{73} +(13.3241 + 0.839856i) q^{74} +(4.24809 + 2.63699i) q^{75} +(0.0959000 - 0.757691i) q^{76} +(-0.0593069 + 0.374449i) q^{77} +(-0.664925 + 0.287646i) q^{78} +(4.72943 - 14.5557i) q^{79} +(5.10998 - 7.34085i) q^{80} +(-0.309017 - 0.951057i) q^{81} +(0.300090 + 0.340466i) q^{82} +(12.6001 + 6.42005i) q^{83} +(-1.88284 + 2.00408i) q^{84} +(-2.30280 + 11.4053i) q^{85} +(-10.5269 + 6.67886i) q^{86} +(0.844202 + 5.33008i) q^{87} +(-0.0247731 + 0.779518i) q^{88} +(-2.29797 - 3.16288i) q^{89} +(-2.65146 - 1.72330i) q^{90} +(0.414000 - 0.569822i) q^{91} +(0.118454 - 0.174211i) q^{92} +(3.00056 + 3.00056i) q^{93} +(4.38358 - 1.12496i) q^{94} +(-0.711340 + 0.472347i) q^{95} +(-3.32771 + 4.57453i) q^{96} +(5.80431 + 11.3916i) q^{97} +(-1.57716 + 7.05191i) q^{98} +0.275740 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 12 q^{8}+O(q^{10}) $ 240 * q + 12 * q^8	$ 240 q + 12 q^{8} + 8 q^{10} + 8 q^{12} + 4 q^{13} + 20 q^{17} - 20 q^{20} - 12 q^{22} + 20 q^{25} + 4 q^{28} - 8 q^{30} - 20 q^{32} - 8 q^{33} - 4 q^{37} - 76 q^{38} - 92 q^{40} - 20 q^{42} - 140 q^{44} - 4 q^{45} - 16 q^{48} - 164 q^{50} - 172 q^{52} - 4 q^{53} - 120 q^{58} + 20 q^{60} - 44 q^{62} - 60 q^{64} - 20 q^{65} + 16 q^{68} - 44 q^{70} + 12 q^{72} - 44 q^{73} - 48 q^{77} + 24 q^{78} - 4 q^{80} + 60 q^{81} + 24 q^{82} + 80 q^{84} - 64 q^{85} + 60 q^{88} - 260 q^{89} + 48 q^{90} + 144 q^{92} - 64 q^{93} + 40 q^{94} - 20 q^{96} - 180 q^{97} + 256 q^{98}+O(q^{100}) $ 240 * q + 12 * q^8 + 8 * q^10 + 8 * q^12 + 4 * q^13 + 20 * q^17 - 20 * q^20 - 12 * q^22 + 20 * q^25 + 4 * q^28 - 8 * q^30 - 20 * q^32 - 8 * q^33 - 4 * q^37 - 76 * q^38 - 92 * q^40 - 20 * q^42 - 140 * q^44 - 4 * q^45 - 16 * q^48 - 164 * q^50 - 172 * q^52 - 4 * q^53 - 120 * q^58 + 20 * q^60 - 44 * q^62 - 60 * q^64 - 20 * q^65 + 16 * q^68 - 44 * q^70 + 12 * q^72 - 44 * q^73 - 48 * q^77 + 24 * q^78 - 4 * q^80 + 60 * q^81 + 24 * q^82 + 80 * q^84 - 64 * q^85 + 60 * q^88 - 260 * q^89 + 48 * q^90 + 144 * q^92 - 64 * q^93 + 40 * q^94 - 20 * q^96 - 180 * q^97 + 256 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$1$	$-1$	$e\left(\frac{11}{20}\right)$

Coefficient data

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

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

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

$2$	−1.38012	−	0.308664i	−0.975891	−	0.218258i
$2$	−1.38012	−	0.308664i	−0.975891	−	0.218258i
$3$	−0.453990	−	0.891007i	−0.262112	−	0.514423i
$3$	−0.453990	−	0.891007i	−0.262112	−	0.514423i
$4$	1.80945	+	0.851985i	0.904727	+	0.425992i
$5$	−0.600764	−	2.15385i	−0.268670	−	0.963232i
$5$	−0.600764	−	2.15385i	−0.268670	−	0.963232i
$6$	0.351539	+	1.36982i	0.143515	+	0.559229i
$7$	−0.972204	−	0.972204i	−0.367458	−	0.367458i	0.499091	−	0.866550i	$-0.333667\pi$
$7$	−0.972204	−	0.972204i	−0.367458	−	0.367458i	−0.866550	+	0.499091i	$0.833667\pi$
$8$	−2.23428	−	1.73435i	−0.789938	−	0.613186i
$9$	−0.587785	+	0.809017i	−0.195928	+	0.269672i
$10$	0.164308	+	3.15801i	0.0519589	+	0.998649i
$11$	−0.162076	−	0.223079i	−0.0488678	−	0.0672607i	0.783884	−	0.620908i	$-0.213236\pi$
$11$	−0.162076	−	0.223079i	−0.0488678	−	0.0672607i	−0.832752	+	0.553647i	$0.813236\pi$
$12$	−0.0623506	−	1.99903i	−0.0179991	−	0.577070i
$13$	0.0801385	+	0.505975i	0.0222264	+	0.140332i	0.996306	−	0.0858731i	$-0.0273680\pi$
$13$	0.0801385	+	0.505975i	0.0222264	+	0.140332i	−0.974080	+	0.226205i	$0.927368\pi$
$14$	1.04167	+	1.64184i	0.278399	+	0.438800i
$15$	−1.64636	+	1.51311i	−0.425087	+	0.390684i
$16$	2.54824	+	3.08325i	0.637061	+	0.770814i
$17$	−4.63639	−	2.36236i	−1.12449	−	0.572956i	−0.210055	−	0.977690i	$-0.567364\pi$
$17$	−4.63639	−	2.36236i	−1.12449	−	0.572956i	−0.914435	+	0.404734i	$0.867364\pi$
$18$	1.06093	−	0.935111i	0.250063	−	0.220408i
$19$	−0.118004	−	0.363178i	−0.0270719	−	0.0833187i	0.936608	−	0.350380i	$-0.113947\pi$
$19$	−0.118004	−	0.363178i	−0.0270719	−	0.0833187i	−0.963680	+	0.267061i	$0.913947\pi$
$20$	0.747997	−	4.40914i	0.167257	−	0.985913i
$21$	−0.424869	+	1.30761i	−0.0927139	+	0.285344i
$22$	0.154828	+	0.357902i	0.0330094	+	0.0763049i
$23$	0.0164778	−	0.104037i	0.00343587	−	0.0216932i	−0.985911	−	0.167272i	$-0.946504\pi$
$23$	0.0164778	−	0.104037i	0.00343587	−	0.0216932i	0.989347	+	0.145578i	$0.0465043\pi$
$24$	−0.530976	+	2.77814i	−0.108385	+	0.567086i
$25$	−4.27817	+	2.58791i	−0.855633	+	0.517583i
$26$	0.0455754	−	0.723041i	0.00893807	−	0.141800i
$27$	0.987688	+	0.156434i	0.190081	+	0.0301058i
$28$	−0.930855	−	2.58746i	−0.175915	−	0.488984i
$29$	−5.13240	−	1.66762i	−0.953062	−	0.309669i	−0.209103	−	0.977894i	$-0.567054\pi$
$29$	−5.13240	−	1.66762i	−0.953062	−	0.309669i	−0.743959	+	0.668225i	$0.767054\pi$
$30$	2.73921	−	1.58010i	0.500109	−	0.288486i
$31$	−4.03574	+	1.31129i	−0.724840	+	0.235515i	−0.648121	−	0.761538i	$-0.724445\pi$
$31$	−4.03574	+	1.31129i	−0.724840	+	0.235515i	−0.0767199	+	0.997053i	$0.524445\pi$
$32$	−2.56519	−	5.04181i	−0.453466	−	0.891274i
$33$	−0.125183	+	0.245686i	−0.0217916	+	0.0427685i
$34$	5.66959	+	4.69142i	0.972327	+	0.804571i
$35$	−1.50992	+	2.67805i	−0.255223	+	0.452673i
$36$	−1.75284	+	0.963094i	−0.292140	+	0.160516i
$37$	−9.32402	+	1.47678i	−1.53286	+	0.242781i	−0.865101	−	0.501597i	$-0.832746\pi$
$37$	−9.32402	+	1.47678i	−1.53286	+	0.242781i	−0.667758	+	0.744378i	$0.732746\pi$
$38$	0.0507592	+	0.537652i	0.00823423	+	0.0872187i
$39$	0.414445	−	0.301112i	0.0663643	−	0.0482165i
$40$	−2.39326	+	5.85425i	−0.378408	+	0.925639i
$41$	−0.259624	−	0.188628i	−0.0405465	−	0.0294588i	0.567327	−	0.823492i	$-0.307977\pi$
$41$	−0.259624	−	0.188628i	−0.0405465	−	0.0294588i	−0.607874	+	0.794034i	$0.707977\pi$
$42$	0.989981	−	1.67352i	0.152757	−	0.258229i
$43$	6.23345	−	6.23345i	0.950592	−	0.950592i	−0.0482434	−	0.998836i	$-0.515362\pi$
$43$	6.23345	−	6.23345i	0.950592	−	0.950592i	0.998836	+	0.0482434i	$0.0153623\pi$
$44$	−0.103210	−	0.541737i	−0.0155594	−	0.0816699i
$45$	2.09562	+	0.779975i	0.312397	+	0.116272i
$46$	−0.0548538	+	0.138497i	−0.00808776	+	0.0204203i
$47$	−2.85131	+	1.45282i	−0.415906	+	0.211915i	−0.649406	−	0.760442i	$-0.724982\pi$
$47$	−2.85131	+	1.45282i	−0.415906	+	0.211915i	0.233499	+	0.972357i	$0.424982\pi$
$48$	1.59032	−	3.67027i	0.229543	−	0.529758i
$49$		−	5.10964i		−	0.729949i
$50$	6.70317	−	2.25111i	0.947971	−	0.318355i
$51$			5.20354i			0.728641i
$52$	−0.286076	+	0.983815i	−0.0396716	+	0.136431i
$53$	8.32407	−	4.24132i	1.14340	−	0.582591i	0.223483	−	0.974708i	$-0.428257\pi$
$53$	8.32407	−	4.24132i	1.14340	−	0.582591i	0.919915	+	0.392117i	$0.128257\pi$
$54$	−1.31484	−	0.520762i	−0.178927	−	0.0708667i
$55$	−0.383109	+	0.483105i	−0.0516584	+	0.0651419i
$56$	0.486034	+	3.85832i	0.0649491	+	0.515590i
$57$	−0.270021	+	0.270021i	−0.0357652	+	0.0357652i
$58$	6.56858	+	3.88569i	0.862497	+	0.510217i
$59$	11.0613	+	8.03648i	1.44005	+	1.04626i	0.988031	+	0.154254i	$0.0492976\pi$
$59$	11.0613	+	8.03648i	1.44005	+	1.04626i	0.452023	+	0.892006i	$0.350702\pi$
$60$	−4.26815	+	1.33524i	−0.551016	+	0.172378i
$61$	9.38530	−	6.81882i	1.20166	−	0.873060i	0.207217	−	0.978295i	$-0.433559\pi$
$61$	9.38530	−	6.81882i	1.20166	−	0.873060i	0.994447	+	0.105235i	$0.0335594\pi$
$62$	5.97455	−	0.564051i	0.758768	−	0.0716346i
$63$	1.35798	−	0.215082i	0.171089	−	0.0270978i
$64$	1.98404	+	7.75007i	0.248005	+	0.968759i
$65$	1.04165	−	0.476578i	0.129201	−	0.0591122i
$66$	0.248602	−	0.300437i	0.0306008	−	0.0369812i
$67$	1.33244	−	2.61505i	0.162783	−	0.319480i	−0.795179	−	0.606375i	$-0.792623\pi$
$67$	1.33244	−	2.61505i	0.162783	−	0.319480i	0.957962	+	0.286895i	$0.0926231\pi$
$68$	−6.37663	−	8.22471i	−0.773280	−	0.997392i
$69$	−0.100178	+	0.0325500i	−0.0120601	+	0.00391855i
$70$	2.91048	−	3.22997i	0.347869	−	0.386055i
$71$	−11.5226	−	3.74393i	−1.36748	−	0.444322i	−0.468949	−	0.883225i	$-0.655367\pi$
$71$	−11.5226	−	3.74393i	−1.36748	−	0.444322i	−0.898535	+	0.438903i	$0.855367\pi$
$72$	2.71640	−	0.788146i	0.320131	−	0.0928839i
$73$	3.09545	+	0.490271i	0.362295	+	0.0573819i	0.334928	−	0.942244i	$-0.391288\pi$
$73$	3.09545	+	0.490271i	0.362295	+	0.0573819i	0.0273666	+	0.999625i	$0.491288\pi$
$74$	13.3241	+	0.839856i	1.54889	+	0.0976312i
$75$	4.24809	+	2.63699i	0.490528	+	0.304493i
$76$	0.0959000	−	0.757691i	0.0110005	−	0.0869131i
$77$	−0.0593069	+	0.374449i	−0.00675864	+	0.0426724i
$78$	−0.664925	+	0.287646i	−0.0752879	+	0.0325695i
$79$	4.72943	−	14.5557i	0.532103	−	1.63764i	−0.217725	−	0.976010i	$-0.569864\pi$
$79$	4.72943	−	14.5557i	0.532103	−	1.63764i	0.749828	−	0.661633i	$-0.230136\pi$
$80$	5.10998	−	7.34085i	0.571314	−	0.820732i
$81$	−0.309017	−	0.951057i	−0.0343352	−	0.105673i
$82$	0.300090	+	0.340466i	0.0331394	+	0.0375982i
$83$	12.6001	+	6.42005i	1.38304	+	0.704692i	0.977804	−	0.209522i	$-0.0671909\pi$
$83$	12.6001	+	6.42005i	1.38304	+	0.704692i	0.405231	+	0.914214i	$0.367191\pi$
$84$	−1.88284	+	2.00408i	−0.205435	+	0.218663i
$85$	−2.30280	+	11.4053i	−0.249774	+	1.23708i
$86$	−10.5269	+	6.67886i	−1.13515	+	0.720200i
$87$	0.844202	+	5.33008i	0.0905080	+	0.571445i
$88$	−0.0247731	+	0.779518i	−0.00264082	+	0.0830969i
$89$	−2.29797	−	3.16288i	−0.243584	−	0.335265i	0.669667	−	0.742661i	$-0.266437\pi$
$89$	−2.29797	−	3.16288i	−0.243584	−	0.335265i	−0.913251	+	0.407397i	$0.866437\pi$
$90$	−2.65146	−	1.72330i	−0.279488	−	0.181652i
$91$	0.414000	−	0.569822i	0.0433990	−	0.0597335i
$92$	0.118454	−	0.174211i	0.0123497	−	0.0181628i
$93$	3.00056	+	3.00056i	0.311143	+	0.311143i
$94$	4.38358	−	1.12496i	0.452132	−	0.116031i
$95$	−0.711340	+	0.472347i	−0.0729819	+	0.0484617i
$96$	−3.32771	+	4.57453i	−0.339633	+	0.466886i
$97$	5.80431	+	11.3916i	0.589339	+	1.15664i	0.972487	+	0.232956i	$0.0748398\pi$
$97$	5.80431	+	11.3916i	0.589339	+	1.15664i	−0.383148	+	0.923687i	$0.625160\pi$
$98$	−1.57716	+	7.05191i	−0.159317	+	0.712350i
$99$	0.275740			0.0277129
$100$	−9.94601	+	1.03777i	−0.994601	+	0.103777i
$101$	4.33372			0.431221			0.215611	−	0.976479i	$-0.430826\pi$
$101$	4.33372			0.431221			0.215611	+	0.976479i	$0.430826\pi$
$102$	1.60614	−	7.18150i	0.159032	−	0.711074i
$103$	−7.23931	−	14.2079i	−0.713310	−	1.39995i	−0.907951	−	0.419075i	$-0.862354\pi$
$103$	−7.23931	−	14.2079i	−0.713310	−	1.39995i	0.194641	−	0.980874i	$-0.437646\pi$
$104$	0.698487	−	1.26948i	0.0684922	−	0.124483i
$105$	3.07165	+	0.129540i	0.299762	+	0.0126418i
$106$	−12.7973	+	3.28419i	−1.24299	+	0.318989i
$107$	−8.31112	−	8.31112i	−0.803466	−	0.803466i	0.180170	−	0.983636i	$-0.442335\pi$
$107$	−8.31112	−	8.31112i	−0.803466	−	0.803466i	−0.983636	+	0.180170i	$0.942335\pi$
$108$	1.65390	+	1.12456i	0.159146	+	0.108210i
$109$	2.37234	−	3.26524i	0.227229	−	0.312754i	−0.680145	−	0.733077i	$-0.738083\pi$
$109$	2.37234	−	3.26524i	0.227229	−	0.312754i	0.907374	+	0.420324i	$0.138083\pi$
$110$	0.677853	−	0.548491i	0.0646307	−	0.0522965i
$111$	5.54884	+	7.63732i	0.526672	+	0.724902i
$112$	0.520139	−	5.47496i	0.0491485	−	0.517335i
$113$	1.80343	+	11.3864i	0.169653	+	1.07114i	0.914700	+	0.404133i	$0.132427\pi$
$113$	1.80343	+	11.3864i	0.169653	+	1.07114i	−0.745047	+	0.667012i	$0.767573\pi$
$114$	0.456007	−	0.289316i	0.0427090	−	0.0270969i
$115$	−0.233980	+	0.0270108i	−0.0218187	+	0.00251877i
$116$	−7.86605	−	7.39020i	−0.730344	−	0.686163i
$117$	−0.456447	−	0.232571i	−0.0421985	−	0.0215012i
$118$	−12.7853	−	14.5055i	−1.17698	−	1.33534i
$119$	2.21082	+	6.80421i	0.202666	+	0.623741i
$120$	6.30270	−	0.525361i	0.575355	−	0.0479587i
$121$	3.37569	−	10.3893i	0.306881	−	0.944483i
$122$	−15.0575	+	6.51388i	−1.36325	+	0.589739i
$123$	−0.0502019	+	0.316962i	−0.00452655	+	0.0285795i
$124$	−8.41969	−	1.06567i	−0.756110	−	0.0956999i
$125$	8.14415	+	7.65982i	0.728435	+	0.685115i
$126$	−1.94056	−	0.122319i	−0.172878	−	0.0108970i
$127$	−2.02875	−	0.321322i	−0.180022	−	0.0285127i	0.0657724	−	0.997835i	$-0.479049\pi$
$127$	−2.02875	−	0.321322i	−0.180022	−	0.0285127i	−0.245795	+	0.969322i	$0.579049\pi$
$128$	−0.346048	−	11.3084i	−0.0305866	−	0.999532i
$129$	−8.38397	−	2.72412i	−0.738168	−	0.239845i
$130$	−1.58470	+	0.336214i	−0.138988	+	0.0294879i
$131$	−10.1344	+	3.29288i	−0.885450	+	0.287700i	−0.716219	−	0.697876i	$-0.754129\pi$
$131$	−10.1344	+	3.29288i	−0.885450	+	0.287700i	−0.169232	+	0.985576i	$0.554129\pi$
$132$	−0.435835	+	0.337904i	−0.0379345	+	0.0294107i
$133$	−0.238359	+	0.467807i	−0.0206684	+	0.0405640i
$134$	−2.64609	+	3.19781i	−0.228587	+	0.276249i
$135$	−0.256430	−	2.22132i	−0.0220700	−	0.191180i
$136$	6.26184	+	13.3193i	0.536948	+	1.14212i
$137$	−11.2331	+	1.77914i	−0.959705	+	0.152002i	−0.616584	−	0.787289i	$-0.711484\pi$
$137$	−11.2331	+	1.77914i	−0.959705	+	0.152002i	−0.343121	+	0.939291i	$0.611484\pi$
$138$	0.148305	−	0.0140013i	0.0126246	−	0.00119187i
$139$	−0.779173	+	0.566102i	−0.0660886	+	0.0480161i	−0.620339	−	0.784334i	$-0.713005\pi$
$139$	−0.779173	+	0.566102i	−0.0660886	+	0.0480161i	0.554250	+	0.832350i	$0.313005\pi$
$140$	−5.01379	+	3.55938i	−0.423742	+	0.300822i
$141$	2.58894	+	1.88097i	0.218028	+	0.158406i
$142$	14.7470	+	8.72368i	1.23754	+	0.732075i
$143$	0.0998836	−	0.0998836i	0.00835269	−	0.00835269i
$144$	−3.99222	+	0.249281i	−0.332685	+	0.0207734i
$145$	−0.508445	+	12.0563i	−0.0422240	+	1.00122i
$146$	−4.12076	−	1.63209i	−0.341036	−	0.135072i
$147$	−4.55272	+	2.31973i	−0.375502	+	0.191328i
$148$	−18.1296	−	5.27176i	−1.49024	−	0.433336i
$149$		−	11.5761i		−	0.948348i	−0.880431	−	0.474174i	$-0.842747\pi$
$149$		−	11.5761i		−	0.948348i	0.880431	−	0.474174i	$-0.157253\pi$
$150$	−5.04893	−	4.95059i	−0.412243	−	0.404214i
$151$		−	5.11520i		−	0.416269i	−0.978100	−	0.208135i	$-0.933261\pi$
$151$		−	5.11520i		−	0.416269i	0.978100	−	0.208135i	$-0.0667392\pi$
$152$	−0.366225	+	1.01610i	−0.0297048	+	0.0824168i
$153$	4.63639	−	2.36236i	0.374830	−	0.190985i
$154$	0.197429	−	0.498478i	0.0159093	−	0.0401685i
$155$	5.24886	+	7.90462i	0.421598	+	0.634914i
$156$	1.00646	−	0.191747i	0.0805814	−	0.0153520i
$157$	−2.84702	+	2.84702i	−0.227217	+	0.227217i	−0.811529	−	0.584312i	$-0.801364\pi$
$157$	−2.84702	+	2.84702i	−0.227217	+	0.227217i	0.584312	+	0.811529i	$0.301364\pi$
$158$	−11.0200	+	18.6288i	−0.876703	+	1.48203i
$159$	−7.55809	−	5.49128i	−0.599396	−	0.435487i
$160$	−9.31824	+	8.55397i	−0.736671	+	0.676251i
$161$	−0.117165	+	0.0851254i	−0.00923390	+	0.00670882i
$162$	0.132923	+	1.40795i	0.0104434	+	0.110619i
$163$	−13.7961	+	2.18509i	−1.08060	+	0.171150i	−0.671252	−	0.741230i	$-0.734243\pi$
$163$	−13.7961	+	2.18509i	−1.08060	+	0.171150i	−0.409346	+	0.912379i	$0.634243\pi$
$164$	−0.309070	−	0.562510i	−0.0241343	−	0.0439246i
$165$	0.604378	+	0.122027i	0.0470508	+	0.00949982i
$166$	−15.4079	−	12.7496i	−1.19589	−	0.989561i
$167$	6.05807	−	11.8896i	0.468787	−	0.920047i	−0.528673	−	0.848826i	$-0.677310\pi$
$167$	6.05807	−	11.8896i	0.468787	−	0.920047i	0.997461	−	0.0712216i	$-0.0226897\pi$
$168$	3.21714	−	2.18470i	0.248207	−	0.168553i
$169$	12.1141	−	3.93612i	0.931857	−	0.302779i
$170$	6.69854	−	15.0299i	0.513755	−	1.15274i
$171$	0.363178	+	0.118004i	0.0277729	+	0.00902397i
$172$	16.5899	−	5.96833i	1.26497	−	0.455081i
$173$	20.0285	+	3.17220i	1.52274	+	0.241178i	0.861019	−	0.508573i	$-0.169827\pi$
$173$	20.0285	+	3.17220i	1.52274	+	0.241178i	0.661720	+	0.749751i	$0.269827\pi$
$174$	0.480104	−	7.61672i	0.0363966	−	0.577422i
$175$	6.67523	+	1.64327i	0.504600	+	0.124220i
$176$	0.274799	−	1.06818i	0.0207137	−	0.0805171i
$177$	2.13885	−	13.5041i	0.160766	−	1.01503i
$178$	2.19520	+	5.07445i	0.164537	+	0.380346i
$179$	−5.28624	+	16.2694i	−0.395112	+	1.21603i	0.533762	+	0.845635i	$0.320778\pi$
$179$	−5.28624	+	16.2694i	−0.395112	+	1.21603i	−0.928874	+	0.370395i	$0.879222\pi$
$180$	3.12741	+	3.19677i	0.233103	+	0.238273i
$181$	−5.36665	−	16.5169i	−0.398900	−	1.22769i	−0.925882	−	0.377812i	$-0.876676\pi$
$181$	−5.36665	−	16.5169i	−0.398900	−	1.22769i	0.526982	−	0.849877i	$-0.323324\pi$
$182$	−0.747252	+	0.658635i	−0.0553900	+	0.0488212i
$183$	−10.3364	−	5.26668i	−0.764092	−	0.389324i
$184$	−0.217253	+	0.203870i	−0.0160161	+	0.0150295i
$185$	8.78230	+	19.1954i	0.645687	+	1.41127i
$186$	−3.21496	−	5.06729i	−0.235732	−	0.371552i
$187$	0.224456	+	1.41716i	0.0164139	+	0.103633i
$188$	−6.39709	+	0.199528i	−0.466556	+	0.0145521i
$189$	−0.808148	−	1.11232i	−0.0587841	−	0.0809094i
$190$	1.12753	−	0.432330i	0.0817996	−	0.0313645i
$191$	13.3352	−	18.3544i	0.964903	−	1.32808i	0.0203238	−	0.999793i	$-0.493530\pi$
$191$	13.3352	−	18.3544i	0.964903	−	1.32808i	0.944580	−	0.328282i	$-0.106470\pi$
$192$	6.00463	−	5.28625i	0.433347	−	0.381502i
$193$	−8.92702	−	8.92702i	−0.642581	−	0.642581i	0.308608	−	0.951189i	$-0.400137\pi$
$193$	−8.92702	−	8.92702i	−0.642581	−	0.642581i	−0.951189	+	0.308608i	$0.900137\pi$
$194$	−4.49447	−	17.5134i	−0.322684	−	1.25739i
$195$	−0.897534	−	0.711756i	−0.0642737	−	0.0509699i
$196$	4.35334	−	9.24566i	0.310953	−	0.660404i
$197$	3.87872	+	7.61241i	0.276347	+	0.542362i	0.986910	−	0.161272i	$-0.0515596\pi$
$197$	3.87872	+	7.61241i	0.276347	+	0.542362i	−0.710563	+	0.703634i	$0.751560\pi$
$198$	−0.380554	−	0.0851110i	−0.0270448	−	0.00604858i
$199$	−22.4725			−1.59303			−0.796515	−	0.604619i	$-0.793325\pi$
$199$	−22.4725			−1.59303			−0.796515	+	0.604619i	$0.793325\pi$
$200$	14.0470	+	1.63772i	0.993272	+	0.115804i
$201$	−2.93494			−0.207015
$202$	−5.98105	−	1.33766i	−0.420825	−	0.0941176i
$203$	3.36847	+	6.61100i	0.236420	+	0.464001i
$204$	−4.43334	+	9.41556i	−0.310396	+	0.659221i
$205$	−0.250304	+	0.672514i	−0.0174820	+	0.0469704i
$206$	5.60562	+	21.8431i	0.390562	+	1.52188i
$207$	0.0744823	+	0.0744823i	0.00517688	+	0.00517688i
$208$	−1.35584	+	1.53643i	−0.0940103	+	0.106533i
$209$	−0.0618916	+	0.0851865i	−0.00428113	+	0.00589248i
$210$	−4.19925	−	1.12689i	−0.289776	−	0.0777625i
$211$	9.06187	+	12.4726i	0.623845	+	0.858649i	0.997626	−	0.0688681i	$-0.0219388\pi$
$211$	9.06187	+	12.4726i	0.623845	+	0.858649i	−0.373781	+	0.927517i	$0.621939\pi$
$212$	18.6756	−	0.582499i	1.28264	−	0.0400062i
$213$	1.89530	+	11.9664i	0.129864	+	0.819927i
$214$	8.90499	+	14.0357i	0.608732	+	0.959458i
$215$	−17.1708	−	9.68111i	−1.17104	−	0.660246i
$216$	−1.93546	−	2.06252i	−0.131692	−	0.140337i
$217$	5.19841	+	2.64872i	0.352891	+	0.179807i
$218$	−4.28197	+	3.77417i	−0.290012	+	0.255619i
$219$	−0.968470	−	2.98064i	−0.0654432	−	0.201413i
$220$	−1.10482	+	0.547754i	−0.0744867	+	0.0369295i
$221$	0.823740	−	2.53521i	0.0554108	−	0.170537i
$222$	−5.30069	−	12.2531i	−0.355759	−	0.822376i
$223$	−2.98548	+	18.8496i	−0.199923	+	1.26226i	0.659776	+	0.751462i	$0.270651\pi$
$223$	−2.98548	+	18.8496i	−0.199923	+	1.26226i	−0.859699	+	0.510801i	$0.829349\pi$
$224$	−2.40778	+	7.39555i	−0.160876	+	0.494136i
$225$	0.420978	−	4.98225i	0.0280652	−	0.332150i
$226$	1.02563	−	16.2713i	0.0682236	−	1.08235i
$227$	15.2762	+	2.41951i	1.01391	+	0.160588i	0.641213	−	0.767363i	$-0.278431\pi$
$227$	15.2762	+	2.41951i	1.01391	+	0.160588i	0.372702	+	0.927951i	$0.378431\pi$
$228$	−0.718645	+	0.258537i	−0.0475934	+	0.0171220i
$229$	−7.81332	−	2.53870i	−0.516318	−	0.167762i	0.0392554	−	0.999229i	$-0.487501\pi$
$229$	−7.81332	−	2.53870i	−0.516318	−	0.167762i	−0.555574	+	0.831467i	$0.687501\pi$
$230$	0.331257	+	0.0349430i	0.0218424	+	0.00230407i
$231$	0.360561	−	0.117153i	0.0237232	−	0.00770813i
$232$	8.57499	+	12.6273i	0.562976	+	0.829024i
$233$	−10.3149	+	20.2442i	−0.675752	+	1.32624i	0.257242	+	0.966347i	$0.417186\pi$
$233$	−10.3149	+	20.2442i	−0.675752	+	1.32624i	−0.932994	+	0.359892i	$0.882814\pi$
$234$	0.558164	+	0.461864i	0.0364883	+	0.0301930i
$235$	4.84212	+	5.26851i	0.315865	+	0.343680i
$236$	13.1679	+	23.9657i	0.857156	+	1.56003i
$237$	−15.1163	+	2.39419i	−0.981911	+	0.155519i
$238$	−0.950983	−	10.0730i	−0.0616430	−	0.652936i
$239$	−4.25763	+	3.09335i	−0.275403	+	0.200092i	−0.716910	−	0.697166i	$-0.754444\pi$
$239$	−4.25763	+	3.09335i	−0.275403	+	0.200092i	0.441507	+	0.897258i	$0.354444\pi$
$240$	−8.86063	−	1.22035i	−0.571951	−	0.0787735i
$241$	7.21982	+	5.24551i	0.465070	+	0.337893i	0.795517	−	0.605932i	$-0.207199\pi$
$241$	7.21982	+	5.24551i	0.465070	+	0.337893i	−0.330447	+	0.943825i	$0.607199\pi$
$242$	−7.86566	+	13.2965i	−0.505624	+	0.854733i
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$	22.7918	−	4.34220i	1.45909	−	0.277981i
$245$	−11.0054	+	3.06969i	−0.703110	+	0.196115i
$246$	0.167119	−	0.421950i	0.0106551	−	0.0269026i
$247$	0.174302	−	0.0888115i	0.0110906	−	0.00565094i
$248$	11.2912	+	4.06960i	0.716994	+	0.258420i
$249$		−	14.1414i		−	0.896173i
$250$	−8.87558	−	13.0853i	−0.561341	−	0.827584i
$251$		−	23.7666i		−	1.50013i	−0.661361	−	0.750067i	$-0.730021\pi$
$251$		−	23.7666i		−	1.50013i	0.661361	−	0.750067i	$-0.269979\pi$
$252$	2.64044	+	0.767794i	0.166332	+	0.0483665i
$253$	−0.0258791	+	0.0131861i	−0.00162700	+	0.000829000i
$254$	2.70073	+	1.06966i	0.169459	+	0.0671166i
$255$	11.2077	−	3.12610i	0.701851	−	0.195764i
$256$	−3.01291	+	15.7138i	−0.188307	+	0.982110i
$257$	9.94201	−	9.94201i	0.620166	−	0.620166i	−0.325408	−	0.945574i	$-0.605502\pi$
$257$	9.94201	−	9.94201i	0.620166	−	0.620166i	0.945574	+	0.325408i	$0.105502\pi$
$258$	10.7300	+	6.34743i	0.668023	+	0.395174i
$259$	10.5006	+	7.62912i	0.652474	+	0.474050i
$260$	2.29086	+	0.0251256i	0.142073	+	0.00155822i
$261$	4.36588	−	3.17200i	0.270241	−	0.196342i
$262$	15.0031	−	1.41643i	0.926896	−	0.0875073i
$263$	2.12166	−	0.336038i	0.130827	−	0.0207210i	−0.0906774	−	0.995880i	$-0.528903\pi$
$263$	2.12166	−	0.336038i	0.130827	−	0.0207210i	0.221505	+	0.975159i	$0.428903\pi$
$264$	0.705802	−	0.331821i	0.0434391	−	0.0204221i
$265$	−14.1360	−	15.3808i	−0.868366	−	0.944834i
$266$	0.473359	−	0.572056i	0.0290235	−	0.0350750i
$267$	−1.77489	+	3.48342i	−0.108622	+	0.213182i
$268$	4.63897	−	3.59660i	0.283370	−	0.219697i
$269$	−7.62107	+	2.47624i	−0.464665	+	0.150979i	−0.531987	−	0.846753i	$-0.678554\pi$
$269$	−7.62107	+	2.47624i	−0.464665	+	0.150979i	0.0673221	+	0.997731i	$0.478554\pi$
$270$	−0.331735	+	3.14483i	−0.0201888	+	0.191388i
$271$	20.8517	+	6.77512i	1.26665	+	0.411559i	0.863859	−	0.503734i	$-0.168041\pi$
$271$	20.8517	+	6.77512i	1.26665	+	0.411559i	0.402789	+	0.915293i	$0.368041\pi$
$272$	−4.53090	−	20.3150i	−0.274726	−	1.23178i
$273$	−0.695667	−	0.110183i	−0.0421037	−	0.00666857i
$274$	16.0521	+	1.01181i	0.969743	+	0.0611258i
$275$	1.27070	+	0.534928i	0.0766259	+	0.0322574i
$276$	−0.209000	−	0.0264529i	−0.0125803	−	0.00159228i
$277$	0.324059	−	2.04602i	0.0194708	−	0.122934i	−0.976038	−	0.217598i	$-0.930178\pi$
$277$	0.324059	−	2.04602i	0.0194708	−	0.122934i	0.995509	+	0.0946644i	$0.0301778\pi$
$278$	1.25009	−	0.540785i	0.0749751	−	0.0324342i
$279$	1.31129	−	4.03574i	0.0785050	−	0.241613i
$280$	8.01827	−	3.36479i	0.479183	−	0.201084i
$281$	0.736040	+	2.26530i	0.0439085	+	0.135136i	0.970608	−	0.240668i	$-0.0773665\pi$
$281$	0.736040	+	2.26530i	0.0439085	+	0.135136i	−0.926699	+	0.375804i	$0.877366\pi$
$282$	−2.99245	−	3.39508i	−0.178198	−	0.202174i
$283$	10.5127	+	5.35651i	0.624917	+	0.318411i	0.737619	−	0.675218i	$-0.235950\pi$
$283$	10.5127	+	5.35651i	0.624917	+	0.318411i	−0.112701	+	0.993629i	$0.535950\pi$
$284$	−17.6599	−	16.5916i	−1.04792	−	0.984528i
$285$	0.743805	+	0.419367i	0.0440592	+	0.0248412i
$286$	−0.168682	+	0.107021i	−0.00997435	+	0.00632827i
$287$	0.0690228	+	0.435793i	0.00407429	+	0.0257240i
$288$	5.58669	+	0.888218i	0.329199	+	0.0523387i
$289$	5.92300	+	8.15232i	0.348412	+	0.479548i
$290$	4.42305	−	16.4821i	0.259730	−	0.967865i
$291$	7.51489	−	10.3434i	0.440531	−	0.606339i
$292$	5.18337	+	3.52440i	0.303334	+	0.206250i
$293$	−11.7557	−	11.7557i	−0.686776	−	0.686776i	0.274742	−	0.961518i	$-0.411408\pi$
$293$	−11.7557	−	11.7557i	−0.686776	−	0.686776i	−0.961518	+	0.274742i	$0.911408\pi$
$294$	6.99931	−	1.79624i	0.408208	−	0.104759i
$295$	10.6642	−	28.6524i	0.620893	−	1.66821i
$296$	23.3938	+	12.8716i	1.35973	+	0.748146i
$297$	−0.125183	−	0.245686i	−0.00726388	−	0.0142562i
$298$	−3.57311	+	15.9763i	−0.206985	+	0.925484i
$299$	0.0539606			0.00312062
$300$	5.44006	+	8.39082i	0.314082	+	0.484444i
$301$	−12.1204			−0.698606
$302$	−1.57888	+	7.05959i	−0.0908542	+	0.406234i
$303$	−1.96747	−	3.86137i	−0.113028	−	0.221830i
$304$	0.819068	−	1.28930i	0.0469768	−	0.0739465i
$305$	−20.3251	−	16.1181i	−1.16381	−	0.922917i
$306$	−7.12794	+	1.82925i	−0.407477	+	0.104571i
$307$	14.1630	+	14.1630i	0.808325	+	0.808325i	0.984380	−	0.176055i	$-0.0563337\pi$
$307$	14.1630	+	14.1630i	0.808325	+	0.808325i	−0.176055	+	0.984380i	$0.556334\pi$
$308$	−0.426338	+	0.627019i	−0.0242928	+	0.0357277i
$309$	−9.37279	+	12.9005i	−0.533199	+	0.733886i
$310$	−4.80417	−	12.5294i	−0.272859	−	0.711624i
$311$	7.62109	+	10.4895i	0.432152	+	0.594807i	0.968446	−	0.249225i	$-0.0801758\pi$
$311$	7.62109	+	10.4895i	0.432152	+	0.594807i	−0.536293	+	0.844032i	$0.680176\pi$
$312$	−1.44822	−	0.0460245i	−0.0819894	−	0.00260562i
$313$	−1.82136	−	11.4996i	−0.102950	−	0.649998i	−0.984161	−	0.177276i	$-0.943271\pi$
$313$	−1.82136	−	11.4996i	−0.102950	−	0.649998i	0.881212	−	0.472722i	$-0.156729\pi$
$314$	4.80800	−	3.05045i	0.271331	−	0.172147i
$315$	−1.27908	−	2.79567i	−0.0720679	−	0.157518i
$316$	20.9589	−	22.3084i	1.17903	−	1.25495i
$317$	−22.7192	−	11.5760i	−1.27604	−	0.650173i	−0.321118	−	0.947039i	$-0.604059\pi$
$317$	−22.7192	−	11.5760i	−1.27604	−	0.650173i	−0.954919	+	0.296866i	$0.904059\pi$
$318$	8.73611	+	9.91152i	0.489896	+	0.555810i
$319$	0.459829	+	1.41521i	0.0257455	+	0.0792365i
$320$	15.5006	−	8.92929i	0.866508	−	0.499163i
$321$	−3.63209	+	11.1784i	−0.202724	+	0.623919i
$322$	0.187977	−	0.0813185i	0.0104755	−	0.00453170i
$323$	−0.310845	+	1.96260i	−0.0172959	+	0.109202i
$324$	0.251134	−	1.98417i	0.0139519	−	0.110232i
$325$	−1.65226	−	1.95725i	−0.0916512	−	0.108569i
$326$	19.7148	+	1.24268i	1.09190	+	0.0688257i
$327$	−3.98637	−	0.631379i	−0.220447	−	0.0349154i
$328$	0.252927	+	0.871729i	0.0139655	+	0.0481332i
$329$	4.18449	+	1.35962i	0.230698	+	0.0749584i
$330$	−0.796448	−	0.354962i	−0.0438430	−	0.0195400i
$331$	−10.7128	+	3.48080i	−0.588829	+	0.191322i	−0.588252	−	0.808678i	$-0.700184\pi$
$331$	−10.7128	+	3.48080i	−0.588829	+	0.191322i	−0.000577233		1.00000i	$0.500184\pi$
$332$	17.3294	+	22.3518i	0.951076	+	1.22672i
$333$	4.28578	−	8.41132i	0.234859	−	0.460937i
$334$	−12.0307	+	14.5392i	−0.658293	+	0.795549i
$335$	−6.43292	−	1.29884i	−0.351468	−	0.0709634i
$336$	−5.11437	+	2.02213i	−0.279012	+	0.110316i
$337$	−19.2296	+	3.04567i	−1.04750	+	0.165908i	−0.656380	−	0.754431i	$-0.727913\pi$
$337$	−19.2296	+	3.04567i	−1.04750	+	0.165908i	−0.391122	+	0.920339i	$0.627913\pi$
$338$	−17.9339	+	1.69312i	−0.975475	+	0.0920936i
$339$	9.32664	−	6.77620i	0.506553	−	0.368033i
$340$	−13.8840	+	18.6754i	−0.752964	+	1.01282i
$341$	0.946618	+	0.687758i	0.0512622	+	0.0372442i
$342$	−0.464805	−	0.274959i	−0.0251338	−	0.0148681i
$343$	−11.7730	+	11.7730i	−0.635684	+	0.635684i
$344$	−24.7383	+	3.11629i	−1.33380	+	0.168019i
$345$	0.130291	+	0.196215i	0.00701465	+	0.0105639i
$346$	−26.6626	−	10.5601i	−1.43339	−	0.567714i
$347$	14.6796	−	7.47962i	0.788041	−	0.401527i	−0.0131665	−	0.999913i	$-0.504191\pi$
$347$	14.6796	−	7.47962i	0.788041	−	0.401527i	0.801208	+	0.598386i	$0.204191\pi$
$348$	−3.01360	+	10.3638i	−0.161546	+	0.555557i
$349$			10.3809i			0.555674i	0.960628	+	0.277837i	$0.0896176\pi$
$349$			10.3809i			0.555674i	−0.960628	+	0.277837i	$0.910382\pi$
$350$	−8.70539	−	4.32831i	−0.465322	−	0.231358i
$351$			0.512282i			0.0273436i
$352$	−0.708963	+	1.38939i	−0.0377879	+	0.0740550i
$353$	10.7453	−	5.47501i	0.571916	−	0.291406i	−0.144017	−	0.989575i	$-0.546002\pi$
$353$	10.7453	−	5.47501i	0.571916	−	0.291406i	0.715932	+	0.698170i	$0.246002\pi$
$354$	−7.12010	+	17.9771i	−0.378429	+	0.955474i
$355$	−1.14150	+	27.0673i	−0.0605844	+	1.43658i
$356$	−1.46334	−	7.68092i	−0.0775568	−	0.407088i
$357$	5.05890	−	5.05890i	0.267745	−	0.267745i
$358$	12.3174	−	20.8220i	0.650995	−	1.10048i
$359$	−26.5983	−	19.3248i	−1.40381	−	1.01993i	−0.994187	−	0.107670i	$-0.965661\pi$
$359$	−26.5983	−	19.3248i	−1.40381	−	1.01993i	−0.409620	−	0.912256i	$-0.634339\pi$
$360$	−3.32946	−	5.37724i	−0.175478	−	0.283405i
$361$	15.2533	−	11.0822i	0.802808	−	0.583274i
$362$	2.30846	+	24.4517i	0.121330	+	1.28515i
$363$	−10.7895	+	1.70888i	−0.566301	+	0.0896932i
$364$	1.23459	−	0.678344i	0.0647102	−	0.0355549i
$365$	−0.803662	−	6.96168i	−0.0420656	−	0.364391i
$366$	12.6399	+	10.4591i	0.660698	+	0.546708i
$367$	−15.9392	+	31.2824i	−0.832019	+	1.63293i	−0.0592491	+	0.998243i	$0.518871\pi$
$367$	−15.9392	+	31.2824i	−0.832019	+	1.63293i	−0.772770	+	0.634686i	$0.781129\pi$
$368$	0.362762	−	0.214306i	0.0189103	−	0.0111715i
$369$	0.305207	−	0.0991677i	0.0158884	−	0.00516246i
$370$	−6.19569	−	29.2027i	−0.322099	−	1.51817i
$371$	−12.2161	−	3.96926i	−0.634229	−	0.206074i
$372$	2.87294	+	7.98580i	0.148955	+	0.414044i
$373$	−8.04171	−	1.27368i	−0.416384	−	0.0659487i	−0.0552722	−	0.998471i	$-0.517603\pi$
$373$	−8.04171	−	1.27368i	−0.416384	−	0.0659487i	−0.361112	+	0.932523i	$0.617603\pi$
$374$	0.127650	−	2.02513i	0.00660062	−	0.104717i
$375$	3.12758	−	10.7340i	0.161508	−	0.554300i
$376$	8.89033	+	1.69918i	0.458484	+	0.0876284i
$377$	0.432469	−	2.73050i	0.0222733	−	0.140628i
$378$	0.772007	+	1.78458i	0.0397078	+	0.0917889i
$379$	4.56806	−	14.0590i	0.234645	−	0.722164i	−0.762523	−	0.646961i	$-0.776040\pi$
$379$	4.56806	−	14.0590i	0.234645	−	0.722164i	0.997168	−	0.0752030i	$-0.0239605\pi$
$380$	−1.68957	+	0.248639i	−0.0866730	+	0.0127549i
$381$	0.634732	+	1.95350i	0.0325183	+	0.100081i
$382$	−24.0695	+	21.2151i	−1.23150	+	1.08546i
$383$	9.74306	+	4.96434i	0.497847	+	0.253666i	0.684837	−	0.728696i	$-0.259873\pi$
$383$	9.74306	+	4.96434i	0.497847	+	0.253666i	−0.186990	+	0.982362i	$0.559873\pi$
$384$	−9.91877	+	5.44224i	−0.506165	+	0.277723i
$385$	0.842137	−	0.0972169i	0.0429193	−	0.00495463i
$386$	9.56490	+	15.0758i	0.486841	+	0.767338i
$387$	1.37904	+	8.70690i	0.0701004	+	0.442596i
$388$	0.797158	+	25.5578i	0.0404696	+	1.29750i
$389$	−6.96157	−	9.58178i	−0.352966	−	0.485816i	0.595206	−	0.803573i	$-0.297070\pi$
$389$	−6.96157	−	9.58178i	−0.352966	−	0.485816i	−0.948172	+	0.317757i	$0.897070\pi$
$390$	1.01901	+	1.25934i	0.0515996	+	0.0637694i
$391$	−0.322170	+	0.443429i	−0.0162929	+	0.0224252i
$392$	−8.86192	+	11.4164i	−0.447594	+	0.576614i
$393$	7.53492	+	7.53492i	0.380086	+	0.380086i
$394$	−3.00341	−	11.7033i	−0.151310	−	0.589601i
$395$	−34.1921	−	1.44197i	−1.72039	−	0.0725534i
$396$	0.498939	+	0.234927i	0.0250726	+	0.0118055i
$397$	11.9903	+	23.5324i	0.601778	+	1.18106i	0.968099	+	0.250567i	$0.0806171\pi$
$397$	11.9903	+	23.5324i	0.601778	+	1.18106i	−0.366321	+	0.930488i	$0.619383\pi$
$398$	31.0146	+	6.93643i	1.55462	+	0.347692i
$399$	0.525032			0.0262845
$400$	−18.8810	−	6.59604i	−0.944050	−	0.329802i
$401$	−19.3802			−0.967801			−0.483901	−	0.875123i	$-0.660780\pi$
$401$	−19.3802			−0.967801			−0.483901	+	0.875123i	$0.660780\pi$
$402$	4.05057	+	0.905910i	0.202024	+	0.0451827i
$403$	−0.986899	−	1.93690i	−0.0491609	−	0.0964838i
$404$	7.84167	+	3.69227i	0.390138	+	0.183697i
$405$	−1.86279	+	1.23694i	−0.0925628	+	0.0614639i
$406$	−2.60832	−	10.1637i	−0.129449	−	0.504415i
$407$	1.84064	+	1.84064i	0.0912370	+	0.0912370i
$408$	9.02477	−	11.6262i	0.446793	−	0.575582i
$409$	−3.14631	+	4.33052i	−0.155575	+	0.214130i	−0.879689	−	0.475550i	$-0.842249\pi$
$409$	−3.14631	+	4.33052i	−0.155575	+	0.214130i	0.724114	+	0.689681i	$0.242249\pi$
$410$	0.553030	−	0.850889i	0.0273122	−	0.0420224i
$411$	6.68493	+	9.20102i	0.329743	+	0.453853i
$412$	−0.994238	−	31.8764i	−0.0489826	−	1.57044i
$413$	−2.94071	−	18.5669i	−0.144703	−	0.913618i
$414$	−0.0798044	−	0.125784i	−0.00392217	−	0.00618196i
$415$	6.25819	−	30.9956i	0.307202	−	1.52151i
$416$	2.34546	−	1.70196i	0.114995	−	0.0834457i
$417$	0.858138	+	0.437243i	0.0420232	+	0.0214119i
$418$	0.111712	−	0.0984638i	0.00546400	−	0.00481602i
$419$	5.92697	+	18.2413i	0.289551	+	0.891147i	0.984997	+	0.172569i	$0.0552067\pi$
$419$	5.92697	+	18.2413i	0.289551	+	0.891147i	−0.695446	+	0.718578i	$0.744793\pi$
$420$	5.44764	+	2.85139i	0.265818	+	0.139134i
$421$	−9.26367	+	28.5106i	−0.451484	+	1.38952i	0.423731	+	0.905788i	$0.360720\pi$
$421$	−9.26367	+	28.5106i	−0.451484	+	1.38952i	−0.875214	+	0.483735i	$0.839280\pi$
$422$	−8.65662	−	20.0107i	−0.421398	−	0.974107i
$423$	0.500606	−	3.16070i	0.0243403	−	0.153679i
$424$	−25.9543	−	4.96055i	−1.26045	−	0.240906i
$425$	25.9488	−	1.89201i	1.25870	−	0.0917759i
$426$	1.07787	−	17.1001i	0.0522230	−	0.828503i
$427$	−15.7537	−	2.49514i	−0.762375	−	0.120748i
$428$	−7.95763	−	22.1195i	−0.384647	−	1.06919i
$429$	−0.134343	−	0.0436507i	−0.00648615	−	0.00210748i
$430$	20.7095	+	18.6611i	0.998700	+	0.899916i
$431$	−13.7926	+	4.48147i	−0.664364	+	0.215865i	−0.621737	−	0.783226i	$-0.713573\pi$
$431$	−13.7926	+	4.48147i	−0.664364	+	0.215865i	−0.0426269	+	0.999091i	$0.513573\pi$
$432$	2.03454	+	3.44393i	0.0978870	+	0.165696i
$433$	4.08174	−	8.01087i	0.196156	−	0.384978i	−0.771888	−	0.635759i	$-0.780687\pi$
$433$	4.08174	−	8.01087i	0.196156	−	0.384978i	0.968044	+	0.250781i	$0.0806874\pi$
$434$	−6.35685	−	5.26011i	−0.305139	−	0.252493i
$435$	10.9730	−	5.02041i	0.526117	−	0.240710i
$436$	7.07457	−	3.88711i	0.338811	−	0.186159i
$437$	−0.0397284	+	0.00629236i	−0.00190047	+	0.000301004i
$438$	0.416587	+	4.41257i	0.0199053	+	0.210841i
$439$	5.24758	−	3.81259i	0.250454	−	0.181965i	−0.455474	−	0.890249i	$-0.650530\pi$
$439$	5.24758	−	3.81259i	0.250454	−	0.181965i	0.705928	+	0.708284i	$0.250530\pi$
$440$	1.69385	−	0.414948i	0.0807511	−	0.0197819i
$441$	4.13379	+	3.00337i	0.196847	+	0.143018i
$442$	−1.91939	+	3.24463i	−0.0912959	+	0.154331i
$443$	18.9704	−	18.9704i	0.901311	−	0.901311i	−0.0942383	−	0.995550i	$-0.530042\pi$
$443$	18.9704	−	18.9704i	0.901311	−	0.901311i	0.995550	+	0.0942383i	$0.0300416\pi$
$444$	3.53348	+	18.5469i	0.167692	+	0.880197i
$445$	−5.43185	+	6.84963i	−0.257494	+	0.324703i
$446$	9.93851	−	25.0932i	0.470602	−	1.18820i
$447$	−10.3143	+	5.25542i	−0.487852	+	0.248573i
$448$	5.60575	−	9.46354i	0.264847	−	0.447110i
$449$			33.6046i			1.58590i	0.609286	+	0.792951i	$0.291456\pi$
$449$			33.6046i			1.58590i	−0.609286	+	0.792951i	$0.708544\pi$
$450$	−2.11884	+	6.74615i	−0.0998830	+	0.318017i
$451$			0.0884887i			0.00416677i
$452$	−6.43784	+	22.1397i	−0.302810	+	1.04136i
$453$	−4.55768	+	2.32225i	−0.214138	+	0.109109i
$454$	−20.3361	−	8.05441i	−0.954421	−	0.378012i
$455$	−1.47603	−	0.549366i	−0.0691973	−	0.0257547i
$456$	1.07162	−	0.134992i	0.0501830	−	0.00632158i
$457$	20.2739	−	20.2739i	0.948373	−	0.948373i	−0.0503586	−	0.998731i	$-0.516036\pi$
$457$	20.2739	−	20.2739i	0.948373	−	0.948373i	0.998731	+	0.0503586i	$0.0160364\pi$
$458$	9.99970	+	5.91539i	0.467255	+	0.276408i
$459$	−4.20975	−	3.05856i	−0.196494	−	0.142762i
$460$	−0.446388	−	0.150472i	−0.0208130	−	0.00701581i
$461$	17.2328	−	12.5204i	0.802613	−	0.583133i	−0.109066	−	0.994034i	$-0.534786\pi$
$461$	17.2328	−	12.5204i	0.802613	−	0.583133i	0.911680	+	0.410902i	$0.134786\pi$
$462$	−0.533778	+	0.0503934i	−0.0248336	+	0.00234451i
$463$	−26.7360	+	4.23456i	−1.24253	+	0.196797i	−0.742875	−	0.669430i	$-0.766539\pi$
$463$	−26.7360	+	4.23456i	−1.24253	+	0.196797i	−0.499651	+	0.866227i	$0.666539\pi$
$464$	−7.93691	−	20.0740i	−0.368462	−	0.931911i
$465$	4.66013	−	8.26539i	0.216109	−	0.383298i
$466$	20.4844	−	24.7555i	0.948923	−	1.14678i
$467$	10.4366	−	20.4830i	0.482949	−	0.947841i	−0.513040	−	0.858365i	$-0.671481\pi$
$467$	10.4366	−	20.4830i	0.482949	−	0.947841i	0.995989	−	0.0894762i	$-0.0285193\pi$
$468$	−0.627772	−	0.809712i	−0.0290188	−	0.0374290i
$469$	−3.83776	+	1.24697i	−0.177211	+	0.0575795i
$470$	−5.05650	−	8.76575i	−0.233239	−	0.404334i
$471$	3.82923	+	1.24419i	0.176442	+	0.0573294i
$472$	−10.7759	−	37.1399i	−0.496001	−	1.70950i
$473$	−2.40084	−	0.380256i	−0.110391	−	0.0174842i
$474$	21.6013	+	1.36160i	0.992182	+	0.0625401i
$475$	1.44471	+	1.24835i	0.0662879	+	0.0572783i
$476$	−1.79670	+	14.1955i	−0.0823518	+	0.650649i
$477$	−1.46146	+	9.22730i	−0.0669157	+	0.422489i
$478$	6.83083	−	2.95501i	0.312435	−	0.135159i
$479$	−3.08997	+	9.50994i	−0.141184	+	0.434520i	−0.996501	−	0.0835858i	$-0.973363\pi$
$479$	−3.08997	+	9.50994i	−0.141184	+	0.434520i	0.855316	+	0.518106i	$0.173363\pi$
$480$	11.8520	+	4.41919i	0.540969	+	0.201707i
$481$	−1.49443	−	4.59937i	−0.0681400	−	0.209713i
$482$	−8.34511	−	9.46792i	−0.380110	−	0.431252i
$483$	0.129039	+	0.0657487i	0.00587148	+	0.00299167i
$484$	14.9597	−	15.9229i	0.679986	−	0.723770i
$485$	21.0488	−	19.3453i	0.955778	−	0.878425i
$486$	1.19415	−	0.757633i	0.0541677	−	0.0343669i
$487$	2.01824	+	12.7426i	0.0914551	+	0.577424i	0.990277	+	0.139110i	$0.0444243\pi$
$487$	2.01824	+	12.7426i	0.0914551	+	0.577424i	−0.898822	+	0.438314i	$0.855576\pi$
$488$	−32.7957	−	1.04225i	−1.48459	−	0.0471803i
$489$	8.21025	+	11.3004i	0.371280	+	0.511024i
$490$	16.1363	−	0.839557i	0.728963	−	0.0379273i
$491$	2.57773	−	3.54795i	0.116332	−	0.160117i	−0.746880	−	0.664959i	$-0.768449\pi$
$491$	2.57773	−	3.54795i	0.116332	−	0.160117i	0.863212	+	0.504842i	$0.168449\pi$
$492$	−0.360885	+	0.530757i	−0.0162700	+	0.0239284i
$493$	19.8563	+	19.8563i	0.894282	+	0.894282i
$494$	−0.267971	+	0.0687695i	−0.0120566	+	0.00309409i
$495$	−0.165655	−	0.593904i	−0.00744562	−	0.0266940i
$496$	−14.3271	−	9.10172i	−0.643306	−	0.408679i
$497$	7.56248	+	14.8422i	0.339223	+	0.665764i
$498$	−4.36493	+	19.5168i	−0.195597	+	0.874567i
$499$	−5.84058			−0.261460			−0.130730	−	0.991418i	$-0.541732\pi$
$499$	−5.84058			−0.261460			−0.130730	+	0.991418i	$0.541732\pi$
$500$	8.21041	+	20.7988i	0.367181	+	0.930150i
$501$	−13.3440			−0.596168
$502$	−7.33589	+	32.8007i	−0.327417	+	1.46397i
$503$	−3.61667	−	7.09811i	−0.161259	−	0.316489i	0.796212	−	0.605018i	$-0.206834\pi$
$503$	−3.61667	−	7.09811i	−0.161259	−	0.316489i	−0.957471	+	0.288529i	$0.906834\pi$
$504$	−3.40713	−	1.87466i	−0.151766	−	0.0835038i
$505$	−2.60354	−	9.33420i	−0.115856	−	0.415366i
$506$	0.0397863	−	0.0102104i	0.00176872	−	0.000453907i
$507$	−9.00682	−	9.00682i	−0.400007	−	0.400007i
$508$	−3.39716	−	2.30988i	−0.150725	−	0.102484i
$509$	5.13448	−	7.06700i	0.227582	−	0.313239i	−0.679921	−	0.733285i	$-0.737986\pi$
$509$	5.13448	−	7.06700i	0.227582	−	0.313239i	0.907503	+	0.420046i	$0.137986\pi$
$510$	−16.4328	+	0.854986i	−0.727657	+	0.0378594i
$511$	−2.53276	−	3.48605i	−0.112043	−	0.154214i
$512$	9.00844	−	20.7569i	0.398121	−	0.917333i
$513$	−0.0597373	−	0.377167i	−0.00263747	−	0.0166523i
$514$	−16.7899	+	10.6524i	−0.740570	+	0.469858i
$515$	−26.2527	+	24.1280i	−1.15683	+	1.06321i
$516$	−12.8495	−	12.0722i	−0.565668	−	0.531448i
$517$	0.786221	+	0.400600i	0.0345780	+	0.0176184i
$518$	−12.1372	−	13.7702i	−0.533278	−	0.605029i
$519$	−6.26629	−	19.2857i	−0.275060	−	0.846547i
$520$	−3.15390	−	0.741781i	−0.138308	−	0.0325292i
$521$	−13.6475	+	42.0028i	−0.597909	+	1.84018i	−0.0582333	+	0.998303i	$0.518547\pi$
$521$	−13.6475	+	42.0028i	−0.597909	+	1.84018i	−0.539676	+	0.841873i	$0.681453\pi$
$522$	−7.00451	+	3.03014i	−0.306579	+	0.132626i
$523$	−1.73126	+	10.9307i	−0.0757027	+	0.477968i	0.920488	+	0.390770i	$0.127791\pi$
$523$	−1.73126	+	10.9307i	−0.0757027	+	0.477968i	−0.996191	+	0.0871979i	$0.972209\pi$
$524$	−21.1433	−	2.67608i	−0.923649	−	0.116905i
$525$	−1.56632	−	6.69370i	−0.0683600	−	0.292137i
$526$	−3.03187	−	0.191108i	−0.132196	−	0.00833268i
$527$	21.8090	+	3.45421i	0.950015	+	0.150468i
$528$	−1.07651	+	0.240096i	−0.0468491	+	0.0104488i
$529$	21.8637	+	7.10396i	0.950598	+	0.308868i
$530$	14.7618	+	25.5906i	0.641213	+	1.11158i
$531$	−13.0033	+	4.22503i	−0.564295	+	0.183351i
$532$	−0.829864	+	0.643396i	−0.0359792	+	0.0278947i
$533$	0.0746352	−	0.146480i	0.00323281	−	0.00634474i
$534$	3.52477	−	4.25969i	0.152532	−	0.184335i
$535$	−12.9079	+	22.8939i	−0.558058	+	0.989791i
$536$	−7.51246	+	3.53185i	−0.324489	+	0.152553i
$537$	16.8960	−	2.67607i	0.729117	−	0.115481i
$538$	11.2823	−	1.06515i	0.486415	−	0.0459219i
$539$	−1.13985	+	0.828150i	−0.0490969	+	0.0356710i
$540$	1.42853	−	4.23784i	0.0614741	−	0.182368i
$541$	13.7726	+	10.0064i	0.592130	+	0.430208i	0.843077	−	0.537793i	$-0.180742\pi$
$541$	13.7726	+	10.0064i	0.592130	+	0.430208i	−0.250947	+	0.968001i	$0.580742\pi$
$542$	−26.6865	−	15.7866i	−1.14628	−	0.678093i
$543$	−12.2802	+	12.2802i	−0.526995	+	0.526995i
$544$	−0.0173373	+	29.4357i	−0.000743330	+	1.26204i
$545$	−8.45807	−	3.14803i	−0.362304	−	0.134847i
$546$	0.926093	+	0.366792i	0.0396331	+	0.0156973i
$547$	7.25427	−	3.69623i	0.310170	−	0.158040i	−0.291976	−	0.956426i	$-0.594313\pi$
$547$	7.25427	−	3.69623i	0.310170	−	0.158040i	0.602146	+	0.798386i	$0.294313\pi$
$548$	−21.8415	−	6.35112i	−0.933023	−	0.271307i
$549$			11.6009i			0.495113i
$550$	−1.58860	−	1.13048i	−0.0677380	−	0.0482039i
$551$			2.06076i			0.0877913i
$552$	0.280280	+	0.101019i	0.0119295	+	0.00429965i
$553$	−18.7491	+	9.55313i	−0.797292	+	0.406240i
$554$	−1.07877	+	2.72373i	−0.0458327	+	0.115720i
$555$	13.1161	−	16.5396i	0.556748	−	0.702067i
$556$	−1.89219	+	0.360492i	−0.0802466	+	0.0152883i
$557$	29.5580	−	29.5580i	1.25241	−	1.25241i	0.297777	−	0.954636i	$-0.403755\pi$
$557$	29.5580	−	29.5580i	1.25241	−	1.25241i	0.954636	−	0.297777i	$-0.0962451\pi$
$558$	−3.05542	+	5.16505i	−0.129346	+	0.218654i
$559$	3.65351	+	2.65443i	0.154527	+	0.112270i
$560$	−12.1047	+	2.16885i	−0.511519	+	0.0916508i
$561$	1.16080	−	0.843369i	0.0490089	−	0.0356071i
$562$	−0.316607	−	3.35357i	−0.0133553	−	0.141462i
$563$	41.5896	−	6.58714i	1.75279	−	0.277615i	0.804255	−	0.594284i	$-0.202564\pi$
$563$	41.5896	−	6.58714i	1.75279	−	0.277615i	0.948536	+	0.316669i	$0.102564\pi$
$564$	3.08200	+	5.60927i	0.129776	+	0.236193i
$565$	23.4413	−	10.7249i	0.986181	−	0.451199i
$566$	−12.8555	−	10.6375i	−0.540355	−	0.447128i
$567$	−0.624193	+	1.22505i	−0.0262137	+	0.0514472i
$568$	19.2515	+	28.3493i	0.807775	+	1.18951i
$569$	−9.87323	+	3.20801i	−0.413907	+	0.134487i	−0.508566	−	0.861023i	$-0.669824\pi$
$569$	−9.87323	+	3.20801i	−0.413907	+	0.134487i	0.0946585	+	0.995510i	$0.469824\pi$
$570$	−0.897096	−	0.808362i	−0.0375752	−	0.0338586i
$571$	5.75100	+	1.86861i	0.240672	+	0.0781991i	0.426869	−	0.904313i	$-0.359616\pi$
$571$	5.75100	+	1.86861i	0.240672	+	0.0781991i	−0.186197	+	0.982512i	$0.559616\pi$
$572$	0.265834	−	0.0956354i	0.0111151	−	0.00399872i
$573$	−22.4079	−	3.54907i	−0.936105	−	0.148264i
$574$	0.0392538	−	0.622751i	0.00163842	−	0.0259931i
$575$	0.198744	+	0.487731i	0.00828819	+	0.0203398i
$576$	−7.43613	−	2.95025i	−0.309839	−	0.122927i
$577$	1.53770	−	9.70868i	0.0640155	−	0.404178i	−0.934785	−	0.355214i	$-0.884408\pi$
$577$	1.53770	−	9.70868i	0.0640155	−	0.404178i	0.998801	−	0.0489639i	$-0.0155919\pi$
$578$	−5.65812	−	13.0794i	−0.235347	−	0.544030i
$579$	−3.90125	+	12.0068i	−0.162130	+	0.498986i
$580$	−11.1918	+	21.3821i	−0.464713	+	0.887842i
$581$	−6.00822	−	18.4914i	−0.249263	−	0.767153i
$582$	−13.5641	+	11.9555i	−0.562249	+	0.495571i
$583$	−2.29528	−	1.16950i	−0.0950608	−	0.0484359i
$584$	−6.06581	−	6.46401i	−0.251005	−	0.267483i
$585$	−0.226708	+	1.12284i	−0.00937321	+	0.0464237i
$586$	12.5957	+	19.8528i	0.520324	+	0.820113i
$587$	−4.67111	−	29.4922i	−0.192797	−	1.21728i	−0.874273	−	0.485434i	$-0.838661\pi$
$587$	−4.67111	−	29.4922i	−0.192797	−	1.21728i	0.681476	−	0.731841i	$-0.261339\pi$
$588$	−10.2143	+	0.318589i	−0.421231	+	0.0131384i
$589$	0.952465	+	1.31096i	0.0392456	+	0.0540170i
$590$	−23.5618	+	36.2520i	−0.970024	+	1.49247i
$591$	5.02181	−	6.91193i	0.206570	−	0.284319i
$592$	−28.3132	−	24.9851i	−1.16366	−	1.02688i
$593$	−23.7947	−	23.7947i	−0.977130	−	0.977130i	0.0226146	−	0.999744i	$-0.492801\pi$
$593$	−23.7947	−	23.7947i	−0.977130	−	0.977130i	−0.999744	+	0.0226146i	$0.992801\pi$
$594$	0.0969335	+	0.377716i	0.00397723	+	0.0154979i
$595$	13.3271	−	8.84950i	0.546357	−	0.362794i
$596$	9.86263	−	20.9463i	0.403989	−	0.857996i
$597$	10.2023	+	20.0231i	0.417552	+	0.819491i
$598$	−0.0744721	−	0.0166557i	−0.00304539	−	0.000681102i
$599$	10.7476			0.439135			0.219568	−	0.975597i	$-0.429535\pi$
$599$	10.7476			0.439135			0.219568	+	0.975597i	$0.429535\pi$
$600$	−4.91798	−	13.2595i	−0.200776	−	0.541315i
$601$	−11.2227			−0.457785			−0.228892	−	0.973452i	$-0.573510\pi$
$601$	−11.2227			−0.457785			−0.228892	+	0.973452i	$0.573510\pi$
$602$	16.7275	+	3.74112i	0.681764	+	0.152477i
$603$	1.33244	+	2.61505i	0.0542610	+	0.106493i
$604$	4.35808	−	9.25572i	0.177328	−	0.376610i
$605$	−24.4050	−	1.02923i	−0.992206	−	0.0418439i
$606$	1.52347	+	5.93644i	0.0618869	+	0.241151i
$607$	3.16391	+	3.16391i	0.128419	+	0.128419i	0.768395	−	0.639976i	$-0.221056\pi$
$607$	3.16391	+	3.16391i	0.128419	+	0.128419i	−0.639976	+	0.768395i	$0.721056\pi$
$608$	−1.52837	+	1.52657i	−0.0619836	+	0.0619107i
$609$	4.36119	−	6.00266i	0.176724	−	0.243240i
$610$	23.0760	+	28.5184i	0.934318	+	1.15468i
$611$	−0.963588	−	1.32627i	−0.0389826	−	0.0536549i
$612$	10.4020	−	0.324444i	0.420477	−	0.0131149i
$613$	1.70688	+	10.7768i	0.0689404	+	0.435272i	0.997882	+	0.0650467i	$0.0207196\pi$
$613$	1.70688	+	10.7768i	0.0689404	+	0.435272i	−0.928942	+	0.370226i	$0.879280\pi$
$614$	−15.1750	−	23.9182i	−0.612414	−	0.965261i
$615$	0.712850	−	0.0822919i	0.0287449	−	0.00331833i
$616$	0.781934	−	0.733765i	0.0315050	−	0.0295643i
$617$	18.9286	+	9.64461i	0.762037	+	0.388277i	0.791406	−	0.611291i	$-0.209350\pi$
$617$	18.9286	+	9.64461i	0.762037	+	0.388277i	−0.0293684	+	0.999569i	$0.509350\pi$
$618$	16.9175	−	14.9112i	0.680521	−	0.599818i
$619$	1.68151	+	5.17515i	0.0675855	+	0.208007i	0.979145	−	0.203160i	$-0.0651213\pi$
$619$	1.68151	+	5.17515i	0.0675855	+	0.208007i	−0.911560	+	0.411167i	$0.865121\pi$
$620$	2.76295	+	18.7750i	0.110963	+	0.754021i
$621$	0.0325500	−	0.100178i	0.00130618	−	0.00402002i
$622$	−7.28027	−	16.8292i	−0.291912	−	0.674788i
$623$	−0.840872	+	5.30906i	−0.0336888	+	0.212703i
$624$	1.98451	+	0.510532i	0.0794440	+	0.0204377i
$625$	11.6054	−	22.1430i	0.464217	−	0.885722i
$626$	−1.03582	+	16.4331i	−0.0413998	+	0.656797i
$627$	0.104000	+	0.0164720i	0.00415336	+	0.000657827i
$628$	−7.57717	+	2.72593i	−0.302362	+	0.108777i
$629$	46.7184	+	15.1797i	1.86279	+	0.605256i
$630$	0.902358	+	4.25316i	0.0359508	+	0.169450i
$631$	28.8977	−	9.38943i	1.15040	−	0.373787i	0.329105	−	0.944293i	$-0.393253\pi$
$631$	28.8977	−	9.38943i	1.15040	−	0.373787i	0.821293	+	0.570506i	$0.193253\pi$
$632$	−35.8116	+	24.3190i	−1.42451	+	0.967359i
$633$	6.99916	−	13.7366i	0.278192	−	0.545982i
$634$	27.7821	+	22.9888i	1.10337	+	0.913004i
$635$	0.526717	+	4.56266i	0.0209021	+	0.181064i
$636$	−8.99753	−	16.3756i	−0.356775	−	0.649334i
$637$	2.58535	−	0.409479i	0.102435	−	0.0162242i
$638$	−0.197795	−	2.09509i	−0.00783078	−	0.0829453i
$639$	9.80173	−	7.12137i	0.387750	−	0.281717i
$640$	−24.1488	+	7.53902i	−0.954564	+	0.298006i
$641$	17.1410	+	12.4537i	0.677030	+	0.491891i	0.872371	−	0.488844i	$-0.162581\pi$
$641$	17.1410	+	12.4537i	0.677030	+	0.491891i	−0.195341	+	0.980735i	$0.562581\pi$
$642$	8.46309	−	14.3065i	0.334012	−	0.564631i
$643$	35.5487	−	35.5487i	1.40191	−	1.40191i	0.607864	−	0.794041i	$-0.292026\pi$
$643$	35.5487	−	35.5487i	1.40191	−	1.40191i	0.794041	−	0.607864i	$-0.207974\pi$
$644$	−0.284530	+	0.0542076i	−0.0112121	+	0.00213608i
$645$	−0.830565	+	19.6944i	−0.0327034	+	0.775466i
$646$	1.03479	−	2.61267i	0.0407132	−	0.102794i
$647$	12.7159	−	6.47909i	0.499915	−	0.254719i	−0.185803	−	0.982587i	$-0.559489\pi$
$647$	12.7159	−	6.47909i	0.499915	−	0.254719i	0.685718	+	0.727868i	$0.259489\pi$
$648$	−0.959036	+	2.66087i	−0.0376745	+	0.104529i
$649$		−	3.77005i		−	0.147987i
$650$	1.67619	+	3.21124i	0.0657455	+	0.125955i
$651$		−	5.83431i		−	0.228665i
$652$	−26.8251	−	7.80028i	−1.05055	−	0.305483i
$653$	−15.9636	+	8.13386i	−0.624704	+	0.318303i	−0.737532	−	0.675312i	$-0.764009\pi$
$653$	−15.9636	+	8.13386i	−0.624704	+	0.318303i	0.112828	+	0.993615i	$0.464009\pi$
$654$	5.30678	+	2.10183i	0.207512	+	0.0821879i
$655$	13.1808	+	19.8499i	0.515016	+	0.775598i
$656$	−0.0799976	−	1.28116i	−0.00312338	−	0.0500208i
$657$	−2.21610	+	2.21610i	−0.0864582	+	0.0864582i
$658$	−5.35542	−	3.16804i	−0.208776	−	0.123503i
$659$	12.1686	+	8.84102i	0.474022	+	0.344397i	0.799007	−	0.601322i	$-0.205359\pi$
$659$	12.1686	+	8.84102i	0.474022	+	0.344397i	−0.324985	+	0.945719i	$0.605359\pi$
$660$	0.989628	+	0.735724i	0.0385212	+	0.0286380i
$661$	−12.7297	+	9.24865i	−0.495127	+	0.359731i	−0.807153	−	0.590343i	$-0.798993\pi$
$661$	−12.7297	+	9.24865i	−0.495127	+	0.359731i	0.312026	+	0.950074i	$0.398993\pi$
$662$	15.8593	−	1.49726i	0.616391	−	0.0581928i
$663$	−2.63286	+	0.417004i	−0.102252	+	0.0161951i
$664$	−17.0175	−	36.1971i	−0.660405	−	1.40472i
$665$	1.15078	+	0.232350i	0.0446255	+	0.00901014i
$666$	−8.51115	+	10.2858i	−0.329801	+	0.398565i
$667$	−0.258065	+	0.506481i	−0.00999231	+	0.0196110i
$668$	21.0916	−	16.3523i	0.816058	−	0.632691i
$669$	18.1505	−	5.89745i	0.701739	−	0.228009i
$670$	8.47728	+	3.77817i	0.327506	+	0.145963i
$671$	−3.04226	−	0.988492i	−0.117445	−	0.0381603i
$672$	7.68259	−	1.21216i	0.296362	−	0.0467603i
$673$	−19.7331	−	3.12542i	−0.760657	−	0.120476i	−0.235957	−	0.971764i	$-0.575822\pi$
$673$	−19.7331	−	3.12542i	−0.760657	−	0.120476i	−0.524700	+	0.851287i	$0.675822\pi$
$674$	27.4792	+	1.73209i	1.05846	+	0.0667177i
$675$	−4.63033	+	1.88680i	−0.178222	+	0.0726229i
$676$	25.2735	+	3.19884i	0.972058	+	0.123032i
$677$	1.09948	−	6.94183i	0.0422564	−	0.266796i	−0.957510	−	0.288399i	$-0.906877\pi$
$677$	1.09948	−	6.94183i	0.0422564	−	0.266796i	0.999767	+	0.0216030i	$0.00687698\pi$
$678$	−14.9634	+	6.47316i	−0.574667	+	0.248600i
$679$	5.43199	−	16.7179i	0.208461	−	0.641576i
$680$	24.9259	−	21.4888i	0.955866	−	0.824059i
$681$	−4.77944	−	14.7096i	−0.183148	−	0.563673i
$682$	−1.09416	−	1.24137i	−0.0418975	−	0.0475347i
$683$	0.600360	+	0.305899i	0.0229721	+	0.0117049i	0.465439	−	0.885080i	$-0.345897\pi$
$683$	0.600360	+	0.305899i	0.0229721	+	0.0117049i	−0.442467	+	0.896785i	$0.645897\pi$
$684$	0.556616	+	0.522944i	0.0212828	+	0.0199953i
$685$	10.5804	+	23.1255i	0.404257	+	0.883581i
$686$	19.8821	−	12.6143i	0.759102	−	0.481615i
$687$	1.28517	+	8.11426i	0.0490324	+	0.309578i
$688$	35.1037	+	3.33496i	1.33831	+	0.127144i
$689$	2.81308	+	3.87187i	0.107170	+	0.147507i
$690$	−0.119253	−	0.311016i	−0.00453989	−	0.0118402i
$691$	−24.8324	+	34.1789i	−0.944670	+	1.30023i	0.00918420	+	0.999958i	$0.497077\pi$
$691$	−24.8324	+	34.1789i	−0.944670	+	1.30023i	−0.953854	+	0.300269i	$0.902923\pi$
$692$	33.5380	+	22.8039i	1.27492	+	0.866875i
$693$	−0.268076	−	0.268076i	−0.0101834	−	0.0101834i
$694$	−22.5683	+	5.79171i	−0.856679	+	0.219850i
$695$	1.68740	+	1.33813i	0.0640067	+	0.0507582i
$696$	7.35805	−	13.3731i	0.278906	−	0.506904i
$697$	0.758112	+	1.48788i	0.0287155	+	0.0563574i
$698$	3.20419	−	14.3268i	0.121281	−	0.542278i
$699$	22.7205			0.859370
$700$	10.6785	+	8.66062i	0.403608	+	0.327341i
$701$	−27.0609			−1.02208			−0.511038	−	0.859558i	$-0.670739\pi$
$701$	−27.0609			−1.02208			−0.511038	+	0.859558i	$0.670739\pi$
$702$	0.158123	−	0.707010i	0.00596796	−	0.0266844i
$703$	1.63660	+	3.21201i	0.0617256	+	0.121143i
$704$	1.40731	−	1.69870i	0.0530399	−	0.0640221i
$705$	2.49600	−	6.70621i	0.0940048	−	0.252570i
$706$	−16.5198	+	4.23948i	−0.621729	+	0.159555i
$707$	−4.21326	−	4.21326i	−0.158456	−	0.158456i
$708$	15.3755	−	22.6129i	0.577846	−	0.849843i
$709$	7.52857	−	10.3622i	0.282741	−	0.389160i	−0.643898	−	0.765111i	$-0.722684\pi$
$709$	7.52857	−	10.3622i	0.282741	−	0.389160i	0.926639	+	0.375951i	$0.122684\pi$
$710$	9.93008	−	37.0037i	0.372669	−	1.38872i
$711$	8.99591	+	12.3818i	0.337373	+	0.464354i
$712$	−0.351241	+	11.0523i	−0.0131633	+	0.414201i
$713$	0.0699226	+	0.441474i	0.00261862	+	0.0165333i
$714$	−8.54338	+	5.42038i	−0.319728	+	0.202853i
$715$	−0.275141	−	0.155128i	−0.0102897	−	0.00580146i
$716$	−23.4265	+	24.9349i	−0.875488	+	0.931860i
$717$	4.68912	+	2.38922i	0.175118	+	0.0892272i
$718$	30.7440	+	34.8805i	1.14736	+	1.30173i
$719$	0.693869	+	2.13551i	0.0258770	+	0.0796411i	0.963161	−	0.268925i	$-0.0866685\pi$
$719$	0.693869	+	2.13551i	0.0258770	+	0.0796411i	−0.937284	+	0.348567i	$0.886669\pi$
$720$	2.93530	+	8.44891i	0.109392	+	0.314872i
$721$	−6.77493	+	20.8511i	−0.252312	+	0.776535i
$722$	−24.4721	+	10.5866i	−0.910757	+	0.393993i
$723$	1.39605	−	8.81432i	0.0519197	−	0.327808i
$724$	4.36141	−	34.4588i	0.162090	−	1.28065i
$725$	26.2729	−	6.14785i	0.975751	−	0.228326i
$726$	15.4182	+	0.971856i	0.572224	+	0.0360690i
$727$	−15.6953	−	2.48588i	−0.582105	−	0.0921964i	−0.141564	−	0.989929i	$-0.545213\pi$
$727$	−15.6953	−	2.48588i	−0.582105	−	0.0921964i	−0.440541	+	0.897733i	$0.645213\pi$
$728$	−1.91326	+	0.555121i	−0.0709103	+	0.0205742i
$729$	0.951057	+	0.309017i	0.0352243	+	0.0114451i
$730$	−1.03967	+	9.85601i	−0.0384799	+	0.364787i
$731$	−43.6263	+	14.1751i	−1.61358	+	0.524283i
$732$	−14.2162	−	18.3363i	−0.525445	−	0.677730i
$733$	8.07882	−	15.8556i	0.298398	−	0.585639i	−0.692317	−	0.721593i	$-0.743410\pi$
$733$	8.07882	−	15.8556i	0.298398	−	0.585639i	0.990715	+	0.135954i	$0.0434101\pi$
$734$	31.6537	−	38.2536i	1.16836	−	1.41197i
$735$	7.73146	+	8.41229i	0.285179	+	0.310292i
$736$	−0.566803	+	0.183797i	−0.0208926	+	0.00677483i
$737$	−0.799318	+	0.126600i	−0.0294433	+	0.00466336i
$738$	−0.451831	+	0.0426569i	−0.0166321	+	0.00157022i
$739$	−8.17498	+	5.93947i	−0.300721	+	0.218487i	−0.727905	−	0.685678i	$-0.759506\pi$
$739$	−8.17498	+	5.93947i	−0.300721	+	0.218487i	0.427184	+	0.904165i	$0.359506\pi$
$740$	−0.463010	+	42.2155i	−0.0170206	+	1.55187i
$741$	−0.158263	−	0.114985i	−0.00581394	−	0.00422408i
$742$	15.6345	+	9.24872i	0.573961	+	0.339531i
$743$	−7.67037	+	7.67037i	−0.281399	+	0.281399i	−0.833667	−	0.552268i	$-0.813763\pi$
$743$	−7.67037	+	7.67037i	−0.281399	+	0.281399i	0.552268	+	0.833667i	$0.313763\pi$
$744$	−1.50007	−	11.9081i	−0.0549952	−	0.436573i
$745$	−24.9331	+	6.95448i	−0.913479	+	0.254792i
$746$	10.7054	+	4.24001i	0.391951	+	0.155238i
$747$	−12.6001	+	6.42005i	−0.461012	+	0.234897i
$748$	−0.801256	+	2.75552i	−0.0292968	+	0.100752i
$749$			16.1602i			0.590481i
$750$	−7.62962	+	13.8488i	−0.278594	+	0.505686i
$751$			25.1511i			0.917777i	0.888494	+	0.458888i	$0.151752\pi$
$751$			25.1511i			0.917777i	−0.888494	+	0.458888i	$0.848248\pi$
$752$	−11.7452	−	5.08919i	−0.428305	−	0.185584i
$753$	−21.1762	+	10.7898i	−0.771704	+	0.393203i
$754$	−1.43967	+	3.63493i	−0.0524296	+	0.132376i
$755$	−11.0174	+	3.07303i	−0.400964	+	0.111839i
$756$	−0.514626	−	2.70122i	−0.0187168	−	0.0982425i
$757$	33.7621	−	33.7621i	1.22711	−	1.22711i	0.262051	−	0.965054i	$-0.415601\pi$
$757$	33.7621	−	33.7621i	1.22711	−	1.22711i	0.965054	−	0.262051i	$-0.0843989\pi$
$758$	−10.6440	+	17.9931i	−0.386607	+	0.653540i
$759$	0.0234977	+	0.0170721i	0.000852913	+	0.000619678i
$760$	2.40855	+	0.178358i	0.0873673	+	0.00646971i
$761$	−16.5093	+	11.9947i	−0.598462	+	0.434808i	−0.845332	−	0.534241i	$-0.820598\pi$
$761$	−16.5093	+	11.9947i	−0.598462	+	0.434808i	0.246871	+	0.969048i	$0.420598\pi$
$762$	−0.273029	−	2.89199i	−0.00989081	−	0.104766i
$763$	−5.48088	+	0.868086i	−0.198421	+	0.0314268i
$764$	39.7671	−	21.8500i	1.43872	−	0.790504i
$765$	−7.87354	−	8.56688i	−0.284669	−	0.309736i
$766$	−11.9143	−	9.85870i	−0.430480	−	0.356209i
$767$	−3.17982	+	6.24075i	−0.114817	+	0.225341i
$768$	15.3689	−	4.44938i	0.554577	−	0.160553i
$769$	−0.676656	+	0.219859i	−0.0244008	+	0.00792832i	−0.321192	−	0.947014i	$-0.604083\pi$
$769$	−0.676656	+	0.219859i	−0.0244008	+	0.00792832i	0.296791	+	0.954942i	$0.404083\pi$
$770$	−1.19226	−	0.125766i	−0.0429659	−	0.00453230i
$771$	−13.3720	−	4.34482i	−0.481580	−	0.156475i
$772$	−8.54734	−	23.7587i	−0.307626	−	0.855095i
$773$	−14.5667	−	2.30714i	−0.523928	−	0.0829821i	−0.111132	−	0.993806i	$-0.535448\pi$
$773$	−14.5667	−	2.30714i	−0.523928	−	0.0829821i	−0.412796	+	0.910824i	$0.635448\pi$
$774$	0.784269	−	12.4422i	0.0281900	−	0.447226i
$775$	13.8721	−	16.0541i	0.498299	−	0.576679i
$776$	6.78858	−	35.5188i	0.243696	−	1.27505i
$777$	2.03043	−	12.8196i	0.0728413	−	0.459902i
$778$	6.65024	+	15.3728i	0.238423	+	0.551141i
$779$	−0.0378690	+	0.116549i	−0.00135680	+	0.00417579i
$780$	−1.01764	−	2.05257i	−0.0364374	−	0.0734940i
$781$	1.03235	+	3.17725i	0.0369404	+	0.113691i
$782$	0.581504	−	0.512543i	0.0207945	−	0.0183285i
$783$	−4.80834	−	2.44997i	−0.171836	−	0.0875548i
$784$	15.7543	−	13.0206i	0.562654	−	0.465022i
$785$	7.84245	+	4.42168i	0.279909	+	0.157816i
$786$	−8.07332	−	12.7248i	−0.287966	−	0.453880i
$787$	−6.83311	−	43.1425i	−0.243574	−	1.53787i	−0.741683	−	0.670751i	$-0.765972\pi$
$787$	−6.83311	−	43.1425i	−0.243574	−	1.53787i	0.498109	−	0.867115i	$-0.334028\pi$
$788$	0.532699	+	17.0789i	0.0189766	+	0.608411i
$789$	−1.26263	−	1.73786i	−0.0449507	−	0.0618693i
$790$	46.7441	+	12.5439i	1.66308	+	0.446294i
$791$	9.31662	−	12.8232i	0.331261	−	0.455942i
$792$	−0.616082	−	0.478231i	−0.0218915	−	0.0169932i
$793$	4.20227	+	4.20227i	0.149227	+	0.149227i
$794$	−9.28450	−	36.1784i	−0.329495	−	1.28392i
$795$	−7.28678	+	19.5780i	−0.258435	+	0.694359i
$796$	−40.6629	−	19.1462i	−1.44126	−	0.678619i
$797$	16.4194	+	32.2249i	0.581605	+	1.14146i	0.975023	+	0.222104i	$0.0712924\pi$
$797$	16.4194	+	32.2249i	0.581605	+	1.14146i	−0.393418	+	0.919360i	$0.628708\pi$
$798$	−0.724606	−	0.162058i	−0.0256508	−	0.00573680i
$799$	16.6519			0.589100
$800$	24.0221	+	14.9312i	0.849308	+	0.527898i
$801$	3.90954			0.138137
$802$	26.7470	+	5.98197i	0.944469	+	0.211231i
$803$	−0.392329	−	0.769990i	−0.0138450	−	0.0271723i
$804$	−5.31064	−	2.50053i	−0.187292	−	0.0881868i
$805$	0.253736	+	0.201216i	0.00894302	+	0.00709193i
$806$	0.764187	+	2.97777i	0.0269173	+	0.104887i
$807$	5.66624	+	5.66624i	0.199461	+	0.199461i
$808$	−9.68276	−	7.51620i	−0.340638	−	0.264419i
$809$	7.03867	−	9.68790i	0.247466	−	0.340608i	−0.667155	−	0.744918i	$-0.732488\pi$
$809$	7.03867	−	9.68790i	0.247466	−	0.340608i	0.914622	+	0.404310i	$0.132488\pi$
$810$	2.95267	−	1.13214i	0.103746	−	0.0397795i
$811$	−31.6446	−	43.5551i	−1.11119	−	1.52943i	−0.819647	−	0.572870i	$-0.805830\pi$
$811$	−31.6446	−	43.5551i	−1.11119	−	1.52943i	−0.291547	−	0.956557i	$-0.594170\pi$
$812$	0.462622	+	14.8322i	0.0162349	+	0.520508i
$813$	−3.42978	−	21.6548i	−0.120288	−	0.759467i
$814$	−1.97216	−	3.10844i	−0.0691242	−	0.108951i
$815$	12.9946	+	28.4021i	0.455181	+	0.994884i
$816$	−16.0438	+	13.2599i	−0.561646	+	0.464189i
$817$	−2.99942	−	1.52828i	−0.104936	−	0.0534678i
$818$	5.67895	−	5.00548i	0.198560	−	0.175012i
$819$	0.217653	+	0.669866i	0.00760539	+	0.0234070i
$820$	−1.02589	+	1.00363i	−0.0358255	+	0.0350482i
$821$	3.06978	−	9.44782i	0.107136	−	0.329731i	−0.883090	−	0.469204i	$-0.844541\pi$
$821$	3.06978	−	9.44782i	0.107136	−	0.329731i	0.990226	+	0.139473i	$0.0445409\pi$
$822$	−6.38597	−	14.7619i	−0.222736	−	0.514880i
$823$	2.34435	−	14.8017i	0.0817190	−	0.515953i	−0.912543	−	0.408981i	$-0.865884\pi$
$823$	2.34435	−	14.8017i	0.0817190	−	0.515953i	0.994262	−	0.106972i	$-0.0341157\pi$
$824$	−8.46692	+	44.3001i	−0.294959	+	1.54327i
$825$	−0.100259	−	1.37505i	−0.00349058	−	0.0478731i
$826$	−1.67240	+	26.5322i	−0.0581903	+	0.923174i
$827$	−43.8653	−	6.94758i	−1.52535	−	0.241591i	−0.663274	−	0.748377i	$-0.730834\pi$
$827$	−43.8653	−	6.94758i	−1.52535	−	0.241591i	−0.862072	+	0.506785i	$0.830834\pi$
$828$	0.0713144	+	0.198230i	0.00247835	+	0.00688897i
$829$	−35.1668	−	11.4264i	−1.22139	−	0.396854i	−0.373803	−	0.927508i	$-0.621946\pi$
$829$	−35.1668	−	11.4264i	−1.22139	−	0.396854i	−0.847589	+	0.530654i	$0.821946\pi$
$830$	−18.2043	+	40.8459i	−0.631879	+	1.41778i
$831$	−1.97014	+	0.640138i	−0.0683434	+	0.0222061i
$832$	−3.76234	+	1.62495i	−0.130436	+	0.0563352i
$833$	−12.0708	+	23.6903i	−0.418228	+	0.820819i
$834$	−1.04937	−	0.868323i	−0.0363367	−	0.0300676i
$835$	−29.2480	−	5.90533i	−1.01217	−	0.204363i
$836$	−0.184568	+	0.101410i	−0.00638341	+	0.00350735i
$837$	−4.19119	+	0.663819i	−0.144869	+	0.0229449i
$838$	−2.54948	−	27.0046i	−0.0880703	−	0.932859i
$839$	−3.24459	+	2.35733i	−0.112016	+	0.0813842i	−0.642383	−	0.766384i	$-0.722054\pi$
$839$	−3.24459	+	2.35733i	−0.112016	+	0.0813842i	0.530367	+	0.847768i	$0.322054\pi$
$840$	−6.63826	−	5.61675i	−0.229042	−	0.193796i
$841$	0.0990611	+	0.0719721i	0.00341590	+	0.00248180i
$842$	21.5852	−	36.4887i	0.743874	−	1.25748i
$843$	1.68424	−	1.68424i	0.0580083	−	0.0580083i
$844$	5.77057	+	30.2892i	0.198631	+	1.04260i
$845$	−15.7556	−	23.7274i	−0.542008	−	0.816248i
$846$	−1.66649	+	4.20763i	−0.0572951	+	0.144661i
$847$	−13.3824	+	6.81867i	−0.459824	+	0.234292i
$848$	34.2888	+	14.8573i	1.17748	+	0.510201i
$849$		−	11.7987i		−	0.404931i
$850$	−36.3964	−	5.39826i	−1.24839	−	0.185159i
$851$			0.994377i			0.0340868i
$852$	−6.76577	+	23.2675i	−0.231792	+	0.797131i
$853$	−36.7113	+	18.7053i	−1.25697	+	0.640458i	−0.950294	−	0.311355i	$-0.899217\pi$
$853$	−36.7113	+	18.7053i	−1.25697	+	0.640458i	−0.306677	+	0.951814i	$0.599217\pi$
$854$	20.9718	+	8.30619i	0.717641	+	0.284232i
$855$	0.0359785	−	0.853124i	0.00123044	−	0.0291762i
$856$	4.15498	+	32.9838i	0.142014	+	1.12736i
$857$	−16.7685	+	16.7685i	−0.572802	+	0.572802i	−0.932911	−	0.360108i	$-0.882740\pi$
$857$	−16.7685	+	16.7685i	−0.572802	+	0.572802i	0.360108	+	0.932911i	$0.382740\pi$
$858$	0.171936	+	0.101710i	0.00586980	+	0.00347232i
$859$	16.4613	+	11.9598i	0.561652	+	0.408064i	0.832063	−	0.554681i	$-0.187160\pi$
$859$	16.4613	+	11.9598i	0.561652	+	0.408064i	−0.270411	+	0.962745i	$0.587160\pi$
$860$	−22.8215	−	32.1467i	−0.778208	−	1.09619i
$861$	0.356959	−	0.259346i	0.0121651	−	0.00883847i
$862$	20.4186	−	1.92770i	0.695461	−	0.0656578i
$863$	−12.3608	+	1.95776i	−0.420766	+	0.0666428i	−0.363227	−	0.931700i	$-0.618325\pi$
$863$	−12.3608	+	1.95776i	−0.420766	+	0.0666428i	−0.0575386	+	0.998343i	$0.518325\pi$
$864$	−1.74490	−	5.38102i	−0.0593625	−	0.183066i
$865$	−5.19993	−	45.0442i	−0.176803	−	1.53155i
$866$	−8.10595	+	9.79606i	−0.275451	+	0.332884i
$867$	4.57478	−	8.97851i	0.155368	−	0.304926i
$868$	7.14960	+	9.22170i	0.242673	+	0.313005i
$869$	−4.01359	+	1.30409i	−0.136152	+	0.0442384i
$870$	−16.6937	+	3.54177i	−0.565970	+	0.120077i
$871$	1.42993	+	0.464613i	0.0484514	+	0.0157428i
$872$	−10.9636	+	3.18101i	−0.371273	+	0.107723i
$873$	−12.6277	−	2.00003i	−0.427383	−	0.0676908i
$874$	0.0567721	+	0.00357851i	0.00192035	+	0.000121045i
$875$	−0.470869	−	15.3647i	−0.0159183	−	0.519421i
$876$	0.787063	−	6.21846i	0.0265924	−	0.210102i
$877$	4.21311	−	26.6005i	0.142267	−	0.898237i	−0.808538	−	0.588444i	$-0.799741\pi$
$877$	4.21311	−	26.6005i	0.142267	−	0.898237i	0.950804	−	0.309792i	$-0.100259\pi$
$878$	−8.41910	+	3.64209i	−0.284131	+	0.122915i
$879$	−5.13743	+	15.8114i	−0.173281	+	0.533305i
$880$	−2.46579	+	0.0498478i	−0.0831218	+	0.00168037i
$881$	1.67338	+	5.15014i	0.0563776	+	0.173513i	0.975280	−	0.220972i	$-0.0709231\pi$
$881$	1.67338	+	5.15014i	0.0563776	+	0.173513i	−0.918902	+	0.394485i	$0.870923\pi$
$882$	−4.77808	−	5.42096i	−0.160886	−	0.182533i
$883$	14.8981	+	7.59096i	0.501361	+	0.255456i	0.686333	−	0.727288i	$-0.259219\pi$
$883$	14.8981	+	7.59096i	0.501361	+	0.255456i	−0.184972	+	0.982744i	$0.559219\pi$
$884$	3.65048	−	3.88553i	0.122779	−	0.130685i
$885$	−30.3709	+	3.50604i	−1.02091	+	0.117854i
$886$	−32.0369	+	20.3259i	−1.07630	+	0.682863i
$887$	4.61394	+	29.1313i	0.154921	+	0.978132i	0.935565	+	0.353156i	$0.114891\pi$
$887$	4.61394	+	29.1313i	0.154921	+	0.978132i	−0.780644	+	0.624976i	$0.785109\pi$
$888$	0.848131	−	26.6876i	0.0284614	−	0.895576i
$889$	1.65997	+	2.28475i	0.0556735	+	0.0766279i
$890$	9.61082	−	7.77668i	0.322155	−	0.260675i
$891$	−0.162076	+	0.223079i	−0.00542975	+	0.00747341i
$892$	−21.4617	+	31.5639i	−0.718590	+	1.05684i
$893$	0.864096	+	0.864096i	0.0289159	+	0.0289159i
$894$	15.8572	−	4.06944i	0.530343	−	0.136102i
$895$	38.2176	+	1.61174i	1.27747	+	0.0538745i
$896$	−10.6577	+	11.3305i	−0.356047	+	0.378526i
$897$	−0.0244976	−	0.0480793i	−0.000817952	−	0.00160532i
$898$	10.3725	−	46.3784i	0.346136	−	1.54767i
$899$	22.8998			0.763750
$900$	5.00654	−	8.65648i	0.166885	−	0.288549i
$901$	−48.6131			−1.61954
$902$	0.0273133	−	0.122125i	0.000909432	−	0.00406632i
$903$	5.50253	+	10.7993i	0.183113	+	0.359379i
$904$	15.7187	−	28.5683i	0.522796	−	0.950167i
$905$	−32.3508	+	21.4817i	−1.07538	+	0.714076i
$906$	7.00693	−	1.79819i	0.232790	−	0.0597410i
$907$	−37.2479	−	37.2479i	−1.23680	−	1.23680i	−0.961303	−	0.275494i	$-0.911159\pi$
$907$	−37.2479	−	37.2479i	−1.23680	−	1.23680i	−0.275494	−	0.961303i	$-0.588841\pi$
$908$	25.5801	+	17.3931i	0.848907	+	0.577209i
$909$	−2.54730	+	3.50605i	−0.0844885	+	0.116288i
$910$	1.86752	+	1.21379i	0.0619078	+	0.0402366i
$911$	10.1575	+	13.9806i	0.336533	+	0.463198i	0.943425	−	0.331587i	$-0.107584\pi$
$911$	10.1575	+	13.9806i	0.336533	+	0.463198i	−0.606892	+	0.794784i	$0.707584\pi$
$912$	−1.52062	−	0.144464i	−0.0503529	−	0.00478369i
$913$	−0.609992	−	3.85134i	−0.0201878	−	0.127461i
$914$	−34.2382	+	21.7226i	−1.13250	+	0.718518i
$915$	−5.13390	+	25.4272i	−0.169722	+	0.840598i
$916$	−11.9749	−	11.2505i	−0.395662	−	0.371727i
$917$	13.0541	+	6.65139i	0.431084	+	0.219648i
$918$	4.86589	+	5.52058i	0.160598	+	0.182206i
$919$	−11.1918	−	34.4449i	−0.369185	−	1.13623i	−0.947319	−	0.320292i	$-0.896219\pi$
$919$	−11.1918	−	34.4449i	−0.369185	−	1.13623i	0.578134	−	0.815942i	$-0.303781\pi$
$920$	0.569623	+	0.345454i	0.0187799	+	0.0113893i
$921$	6.18946	−	19.0492i	0.203950	−	0.627692i
$922$	−27.6479	+	11.9605i	−0.910537	+	0.393897i
$923$	0.970927	−	6.13019i	0.0319584	−	0.201778i
$924$	0.752231	+	0.0952090i	0.0247466	+	0.00313215i
$925$	36.0679	−	30.4477i	1.18591	−	1.00111i
$926$	38.2059	+	2.40823i	1.25552	+	0.0791393i
$927$	15.7496	+	2.49449i	0.517285	+	0.0819300i
$928$	4.75777	+	30.1543i	0.156181	+	0.989863i
$929$	−5.15609	−	1.67531i	−0.169166	−	0.0549653i	0.223210	−	0.974770i	$-0.428347\pi$
$929$	−5.15609	−	1.67531i	−0.169166	−	0.0549653i	−0.392375	+	0.919805i	$0.628347\pi$
$930$	−8.98276	+	9.96880i	−0.294556	+	0.326890i
$931$	−1.85571	+	0.602956i	−0.0608184	+	0.0197611i
$932$	−35.9121	+	27.8427i	−1.17634	+	0.912018i
$933$	5.88634	−	11.5526i	0.192710	−	0.378215i
$934$	−20.7261	+	25.0476i	−0.678180	+	0.819582i
$935$	2.91751	−	1.33482i	0.0954128	−	0.0436534i
$936$	0.616470	+	1.31127i	0.0201500	+	0.0428602i
$937$	−29.9700	+	4.74677i	−0.979076	+	0.155070i	−0.625406	−	0.780300i	$-0.715066\pi$
$937$	−29.9700	+	4.74677i	−0.979076	+	0.155070i	−0.353670	+	0.935370i	$0.615066\pi$
$938$	5.68146	−	0.536381i	0.185506	−	0.0175135i
$939$	−9.41937	+	6.84358i	−0.307390	+	0.223332i
$940$	4.27289	+	13.6585i	0.139366	+	0.445492i
$941$	16.6066	+	12.0654i	0.541361	+	0.393322i	0.824590	−	0.565730i	$-0.191406\pi$
$941$	16.6066	+	12.0654i	0.541361	+	0.393322i	−0.283229	+	0.959052i	$0.591406\pi$
$942$	−4.90076	−	2.89908i	−0.159675	−	0.0944571i
$943$	−0.0239024	+	0.0239024i	−0.000778368	+	0.000778368i
$944$	3.40829	+	54.5836i	0.110930	+	1.77655i
$945$	−1.91027	+	2.40887i	−0.0621411	+	0.0783607i
$946$	3.19607	+	1.26585i	0.103913	+	0.0411564i
$947$	0.673811	−	0.343324i	0.0218959	−	0.0111565i	−0.443008	−	0.896518i	$-0.646089\pi$
$947$	0.673811	−	0.343324i	0.0218959	−	0.0111565i	0.464904	+	0.885361i	$0.346089\pi$
$948$	−29.3921	−	8.54671i	−0.954612	−	0.277584i
$949$			1.60551i			0.0521170i
$950$	−1.60855	−	2.16880i	−0.0521883	−	0.0703653i
$951$			25.4983i			0.826840i
$952$	6.86129	−	19.0369i	0.222376	−	0.616988i
$953$	−8.95160	+	4.56107i	−0.289971	+	0.147747i	−0.592925	−	0.805258i	$-0.702027\pi$
$953$	−8.95160	+	4.56107i	−0.289971	+	0.147747i	0.302954	+	0.953005i	$0.402027\pi$
$954$	4.86512	−	12.2837i	0.157514	−	0.397698i
$955$	−47.5439	−	17.6955i	−1.53849	−	0.572613i
$956$	−10.3395	+	1.96983i	−0.334402	+	0.0637090i
$957$	1.05220	−	1.05220i	0.0340129	−	0.0340129i
$958$	7.19989	−	12.1711i	0.232618	−	0.393230i
$959$	12.6505	+	9.19113i	0.408506	+	0.296797i
$960$	−14.9932	−	9.75730i	−0.483903	−	0.314915i
$961$	−10.5118	+	7.63728i	−0.339091	+	0.246364i
$962$	0.642826	+	6.80895i	0.0207256	+	0.219529i
$963$	11.6090	−	1.83868i	0.374094	−	0.0592507i
$964$	8.59484	+	15.6427i	0.276821	+	0.503817i
$965$	−13.8645	+	24.5905i	−0.446313	+	0.791597i
$966$	−0.157795	−	0.130571i	−0.00507697	−	0.00420104i
$967$	12.3634	−	24.2645i	0.397580	−	0.780295i	−0.602258	−	0.798302i	$-0.705732\pi$
$967$	12.3634	−	24.2645i	0.397580	−	0.780295i	0.999838	+	0.0180068i	$0.00573205\pi$
$968$	−25.5610	+	17.3580i	−0.821561	+	0.557908i
$969$	1.88981	−	0.614037i	0.0607095	−	0.0197257i
$970$	−35.0211	+	20.2018i	−1.12446	+	0.648641i
$971$	−29.1197	−	9.46156i	−0.934495	−	0.303636i	−0.198096	−	0.980183i	$-0.563476\pi$
$971$	−29.1197	−	9.46156i	−0.934495	−	0.303636i	−0.736400	+	0.676547i	$0.763476\pi$
$972$	−1.88192	+	0.677032i	−0.0603626	+	0.0217158i
$973$	1.30788	+	0.207148i	0.0419287	+	0.00664086i
$974$	1.14779	−	18.2093i	0.0367775	−	0.583464i
$975$	−0.993813	+	2.36075i	−0.0318275	+	0.0756046i
$976$	44.9402	+	11.5613i	1.43850	+	0.370067i
$977$	5.90000	−	37.2511i	0.188758	−	1.19177i	−0.693308	−	0.720642i	$-0.743847\pi$
$977$	5.90000	−	37.2511i	0.188758	−	1.19177i	0.882065	−	0.471127i	$-0.156153\pi$
$978$	−7.84308	−	18.1302i	−0.250794	−	0.579738i
$979$	−0.333125	+	1.02525i	−0.0106467	+	0.0327673i
$980$	−22.5291	−	3.82199i	−0.719666	−	0.122089i
$981$	1.24721	+	3.83852i	0.0398204	+	0.122555i
$982$	−4.65270	+	4.10093i	−0.148474	+	0.130866i
$983$	−14.4955	−	7.38580i	−0.462333	−	0.235570i	0.207278	−	0.978282i	$-0.433539\pi$
$983$	−14.4955	−	7.38580i	−0.462333	−	0.235570i	−0.669612	+	0.742712i	$0.733539\pi$
$984$	0.661890	−	0.621116i	0.0211003	−	0.0198005i
$985$	14.0658	−	12.9274i	0.448174	−	0.411903i
$986$	−21.2751	−	33.5329i	−0.677537	−	1.06791i
$987$	−0.688285	−	4.34566i	−0.0219084	−	0.138324i
$988$	0.391058	−	0.0121973i	0.0124412	−	0.000388047i
$989$	−0.545796	−	0.751223i	−0.0173553	−	0.0238875i
$990$	0.0453065	+	0.870789i	0.00143993	+	0.0276755i
$991$	−5.22404	+	7.19027i	−0.165947	+	0.228407i	−0.883889	−	0.467696i	$-0.845084\pi$
$991$	−5.22404	+	7.19027i	−0.165947	+	0.228407i	0.717942	+	0.696103i	$0.245084\pi$
$992$	16.9637	+	16.9837i	0.538599	+	0.539233i
$993$	7.96493	+	7.96493i	0.252760	+	0.252760i
$994$	−5.85587	−	22.8183i	−0.185737	−	0.723751i
$995$	13.5006	+	48.4024i	0.427999	+	1.53446i
$996$	12.0482	−	25.5881i	0.381763	−	0.810791i
$997$	−0.844993	−	1.65839i	−0.0267612	−	0.0525218i	0.877239	−	0.480054i	$-0.159383\pi$
$997$	−0.844993	−	1.65839i	−0.0267612	−	0.0525218i	−0.904000	+	0.427532i	$0.859383\pi$
$998$	8.06069	+	1.80277i	0.255157	+	0.0570658i
$999$	−9.44024			−0.298676

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.2.w.a.223.2	yes	240
3.2	odd	2		900.2.bj.f.523.29		240
4.3	odd	2	inner	300.2.w.a.223.30	yes	240
12.11	even	2		900.2.bj.f.523.1		240
25.12	odd	20	inner	300.2.w.a.187.30	yes	240
75.62	even	20		900.2.bj.f.487.1		240
100.87	even	20	inner	300.2.w.a.187.2	✓	240
300.287	odd	20		900.2.bj.f.487.29		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.w.a.187.2	✓	240	100.87	even	20	inner
300.2.w.a.187.30	yes	240	25.12	odd	20	inner
300.2.w.a.223.2	yes	240	1.1	even	1	trivial
300.2.w.a.223.30	yes	240	4.3	odd	2	inner
900.2.bj.f.487.1		240	75.62	even	20
900.2.bj.f.487.29		240	300.287	odd	20
900.2.bj.f.523.1		240	12.11	even	2
900.2.bj.f.523.29		240	3.2	odd	2

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:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	300.w (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.38012 - 0.308664i) q^{2} +(-0.453990 - 0.891007i) q^{3} +(1.80945 + 0.851985i) q^{4} +(-0.600764 - 2.15385i) q^{5} +(0.351539 + 1.36982i) q^{6} +(-0.972204 - 0.972204i) q^{7} +(-2.23428 - 1.73435i) q^{8} +(-0.587785 + 0.809017i) q^{9} +O(q^{10})\)	\(q+(-1.38012 - 0.308664i) q^{2} +(-0.453990 - 0.891007i) q^{3} +(1.80945 + 0.851985i) q^{4} +(-0.600764 - 2.15385i) q^{5} +(0.351539 + 1.36982i) q^{6} +(-0.972204 - 0.972204i) q^{7} +(-2.23428 - 1.73435i) q^{8} +(-0.587785 + 0.809017i) q^{9} +(0.164308 + 3.15801i) q^{10} +(-0.162076 - 0.223079i) q^{11} +(-0.0623506 - 1.99903i) q^{12} +(0.0801385 + 0.505975i) q^{13} +(1.04167 + 1.64184i) q^{14} +(-1.64636 + 1.51311i) q^{15} +(2.54824 + 3.08325i) q^{16} +(-4.63639 - 2.36236i) q^{17} +(1.06093 - 0.935111i) q^{18} +(-0.118004 - 0.363178i) q^{19} +(0.747997 - 4.40914i) q^{20} +(-0.424869 + 1.30761i) q^{21} +(0.154828 + 0.357902i) q^{22} +(0.0164778 - 0.104037i) q^{23} +(-0.530976 + 2.77814i) q^{24} +(-4.27817 + 2.58791i) q^{25} +(0.0455754 - 0.723041i) q^{26} +(0.987688 + 0.156434i) q^{27} +(-0.930855 - 2.58746i) q^{28} +(-5.13240 - 1.66762i) q^{29} +(2.73921 - 1.58010i) q^{30} +(-4.03574 + 1.31129i) q^{31} +(-2.56519 - 5.04181i) q^{32} +(-0.125183 + 0.245686i) q^{33} +(5.66959 + 4.69142i) q^{34} +(-1.50992 + 2.67805i) q^{35} +(-1.75284 + 0.963094i) q^{36} +(-9.32402 + 1.47678i) q^{37} +(0.0507592 + 0.537652i) q^{38} +(0.414445 - 0.301112i) q^{39} +(-2.39326 + 5.85425i) q^{40} +(-0.259624 - 0.188628i) q^{41} +(0.989981 - 1.67352i) q^{42} +(6.23345 - 6.23345i) q^{43} +(-0.103210 - 0.541737i) q^{44} +(2.09562 + 0.779975i) q^{45} +(-0.0548538 + 0.138497i) q^{46} +(-2.85131 + 1.45282i) q^{47} +(1.59032 - 3.67027i) q^{48} -5.10964i q^{49} +(6.70317 - 2.25111i) q^{50} +5.20354i q^{51} +(-0.286076 + 0.983815i) q^{52} +(8.32407 - 4.24132i) q^{53} +(-1.31484 - 0.520762i) q^{54} +(-0.383109 + 0.483105i) q^{55} +(0.486034 + 3.85832i) q^{56} +(-0.270021 + 0.270021i) q^{57} +(6.56858 + 3.88569i) q^{58} +(11.0613 + 8.03648i) q^{59} +(-4.26815 + 1.33524i) q^{60} +(9.38530 - 6.81882i) q^{61} +(5.97455 - 0.564051i) q^{62} +(1.35798 - 0.215082i) q^{63} +(1.98404 + 7.75007i) q^{64} +(1.04165 - 0.476578i) q^{65} +(0.248602 - 0.300437i) q^{66} +(1.33244 - 2.61505i) q^{67} +(-6.37663 - 8.22471i) q^{68} +(-0.100178 + 0.0325500i) q^{69} +(2.91048 - 3.22997i) q^{70} +(-11.5226 - 3.74393i) q^{71} +(2.71640 - 0.788146i) q^{72} +(3.09545 + 0.490271i) q^{73} +(13.3241 + 0.839856i) q^{74} +(4.24809 + 2.63699i) q^{75} +(0.0959000 - 0.757691i) q^{76} +(-0.0593069 + 0.374449i) q^{77} +(-0.664925 + 0.287646i) q^{78} +(4.72943 - 14.5557i) q^{79} +(5.10998 - 7.34085i) q^{80} +(-0.309017 - 0.951057i) q^{81} +(0.300090 + 0.340466i) q^{82} +(12.6001 + 6.42005i) q^{83} +(-1.88284 + 2.00408i) q^{84} +(-2.30280 + 11.4053i) q^{85} +(-10.5269 + 6.67886i) q^{86} +(0.844202 + 5.33008i) q^{87} +(-0.0247731 + 0.779518i) q^{88} +(-2.29797 - 3.16288i) q^{89} +(-2.65146 - 1.72330i) q^{90} +(0.414000 - 0.569822i) q^{91} +(0.118454 - 0.174211i) q^{92} +(3.00056 + 3.00056i) q^{93} +(4.38358 - 1.12496i) q^{94} +(-0.711340 + 0.472347i) q^{95} +(-3.32771 + 4.57453i) q^{96} +(5.80431 + 11.3916i) q^{97} +(-1.57716 + 7.05191i) q^{98} +0.275740 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 12 q^{8}+O(q^{10}) \) 240 * q + 12 * q^8	\( 240 q + 12 q^{8} + 8 q^{10} + 8 q^{12} + 4 q^{13} + 20 q^{17} - 20 q^{20} - 12 q^{22} + 20 q^{25} + 4 q^{28} - 8 q^{30} - 20 q^{32} - 8 q^{33} - 4 q^{37} - 76 q^{38} - 92 q^{40} - 20 q^{42} - 140 q^{44} - 4 q^{45} - 16 q^{48} - 164 q^{50} - 172 q^{52} - 4 q^{53} - 120 q^{58} + 20 q^{60} - 44 q^{62} - 60 q^{64} - 20 q^{65} + 16 q^{68} - 44 q^{70} + 12 q^{72} - 44 q^{73} - 48 q^{77} + 24 q^{78} - 4 q^{80} + 60 q^{81} + 24 q^{82} + 80 q^{84} - 64 q^{85} + 60 q^{88} - 260 q^{89} + 48 q^{90} + 144 q^{92} - 64 q^{93} + 40 q^{94} - 20 q^{96} - 180 q^{97} + 256 q^{98}+O(q^{100}) \) 240 * q + 12 * q^8 + 8 * q^10 + 8 * q^12 + 4 * q^13 + 20 * q^17 - 20 * q^20 - 12 * q^22 + 20 * q^25 + 4 * q^28 - 8 * q^30 - 20 * q^32 - 8 * q^33 - 4 * q^37 - 76 * q^38 - 92 * q^40 - 20 * q^42 - 140 * q^44 - 4 * q^45 - 16 * q^48 - 164 * q^50 - 172 * q^52 - 4 * q^53 - 120 * q^58 + 20 * q^60 - 44 * q^62 - 60 * q^64 - 20 * q^65 + 16 * q^68 - 44 * q^70 + 12 * q^72 - 44 * q^73 - 48 * q^77 + 24 * q^78 - 4 * q^80 + 60 * q^81 + 24 * q^82 + 80 * q^84 - 64 * q^85 + 60 * q^88 - 260 * q^89 + 48 * q^90 + 144 * q^92 - 64 * q^93 + 40 * q^94 - 20 * q^96 - 180 * q^97 + 256 * q^98

Introduction

L-functions

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