LMFDB - Embedded newform 99.2.m.a.16.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [99,2,Mod(4,99)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(99, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([10, 6]))

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

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

chi := DirichletCharacter("99.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 99 = 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	99.m (of order $15$, 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:	$0.790518980011$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{15})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 $ x^8 - x^7 + x^5 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			16.1
Root			$-0.104528 + 0.994522i$ of defining polynomial
Character	$\chi$	$=$	99.16
Dual form			99.2.m.a.31.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.373619 + 0.0794152i) q^{2} +(1.72256 + 0.181049i) q^{3} +(-1.69381 - 0.754131i) q^{4} +(1.20906 - 0.256993i) q^{5} +(0.629204 + 0.204441i) q^{6} +(0.104528 + 0.994522i) q^{7} +(-1.19098 - 0.865300i) q^{8} +(2.93444 + 0.623735i) q^{9} +0.472136 q^{10} +(-3.01430 - 1.38348i) q^{11} +(-2.78115 - 1.60570i) q^{12} +(-4.33070 + 4.80973i) q^{13} +(-0.0399263 + 0.379874i) q^{14} +(2.12920 - 0.223788i) q^{15} +(2.10502 + 2.33786i) q^{16} +(1.50000 - 4.61653i) q^{17} +(1.04683 + 0.466079i) q^{18} +(-0.809017 - 0.587785i) q^{19} +(-2.24171 - 0.476491i) q^{20} +1.73205i q^{21} +(-1.01633 - 0.756276i) q^{22} +(-2.30902 - 3.99933i) q^{23} +(-1.89488 - 1.70616i) q^{24} +(-3.17195 + 1.41224i) q^{25} +(-2.00000 + 1.45309i) q^{26} +(4.94183 + 1.60570i) q^{27} +(0.572949 - 1.76336i) q^{28} +(0.507392 + 4.82751i) q^{29} +(0.813284 + 0.0854796i) q^{30} +(0.413545 - 0.459289i) q^{31} +(2.07295 + 3.59045i) q^{32} +(-4.94183 - 2.92887i) q^{33} +(0.927051 - 1.60570i) q^{34} +(0.381966 + 1.17557i) q^{35} +(-4.50000 - 3.26944i) q^{36} +(4.11803 - 2.99193i) q^{37} +(-0.255585 - 0.283856i) q^{38} +(-8.33070 + 7.50100i) q^{39} +(-1.66234 - 0.740122i) q^{40} +(0.264234 - 2.51402i) q^{41} +(-0.137551 + 0.647127i) q^{42} +(-0.927051 + 1.60570i) q^{43} +(4.06231 + 4.61653i) q^{44} +3.70820 q^{45} +(-0.545085 - 1.67760i) q^{46} +(10.9116 - 4.85817i) q^{47} +(3.20276 + 4.40822i) q^{48} +(5.86889 - 1.24747i) q^{49} +(-1.29726 + 0.275740i) q^{50} +(3.41966 - 7.68068i) q^{51} +(10.9625 - 4.88084i) q^{52} +(1.26393 + 3.88998i) q^{53} +(1.71885 + 0.992377i) q^{54} +(-4.00000 - 0.898056i) q^{55} +(0.736068 - 1.27491i) q^{56} +(-1.28716 - 1.15897i) q^{57} +(-0.193806 + 1.84395i) q^{58} +(1.47815 + 0.658114i) q^{59} +(-3.77523 - 1.22665i) q^{60} +(7.26281 + 8.06617i) q^{61} +(0.190983 - 0.138757i) q^{62} +(-0.313585 + 2.98357i) q^{63} +(-1.45492 - 4.47777i) q^{64} +(-4.00000 + 6.92820i) q^{65} +(-1.61377 - 1.48674i) q^{66} +(-3.00000 - 5.19615i) q^{67} +(-6.02218 + 6.68830i) q^{68} +(-3.25335 - 7.30715i) q^{69} +(0.0493516 + 0.469550i) q^{70} +(-0.899187 + 2.76741i) q^{71} +(-2.95515 - 3.28203i) q^{72} +(0.118034 - 0.0857567i) q^{73} +(1.77618 - 0.790807i) q^{74} +(-5.71957 + 1.85840i) q^{75} +(0.927051 + 1.60570i) q^{76} +(1.06082 - 3.14240i) q^{77} +(-3.70820 + 2.14093i) q^{78} +(-10.3315 - 2.19603i) q^{79} +(3.14590 + 2.28563i) q^{80} +(8.22191 + 3.66063i) q^{81} +(0.298374 - 0.918300i) q^{82} +(-6.53335 - 7.25602i) q^{83} +(1.30619 - 2.93376i) q^{84} +(0.627171 - 5.96713i) q^{85} +(-0.473881 + 0.526298i) q^{86} +8.40755i q^{87} +(2.39285 + 4.25597i) q^{88} -6.76393 q^{89} +(1.38546 + 0.294488i) q^{90} +(-5.23607 - 3.80423i) q^{91} +(0.895005 + 8.51540i) q^{92} +(0.795511 - 0.716282i) q^{93} +(4.46261 - 0.948557i) q^{94} +(-1.12920 - 0.502754i) q^{95} +(2.92074 + 6.56008i) q^{96} +(-5.86889 - 1.24747i) q^{97} +2.29180 q^{98} +(-7.98235 - 5.93987i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} + 3 q^{3} - 6 q^{4} + 6 q^{5} - q^{7} - 14 q^{8} - 3 q^{9} - 32 q^{10} + q^{11} + 18 q^{12} + 8 q^{13} - q^{14} + 12 q^{15} + 14 q^{16} + 12 q^{17} - 3 q^{18} - 2 q^{19} + 24 q^{20} + 11 q^{22}+ \cdots - 3 q^{99}+O(q^{100}) $ 8 * q - 4 * q^2 + 3 * q^3 - 6 * q^4 + 6 * q^5 - q^7 - 14 * q^8 - 3 * q^9 - 32 * q^10 + q^11 + 18 * q^12 + 8 * q^13 - q^14 + 12 * q^15 + 14 * q^16 + 12 * q^17 - 3 * q^18 - 2 * q^19 + 24 * q^20 + 11 * q^22 - 14 * q^23 - 39 * q^24 - 9 * q^25 - 16 * q^26 + 18 * q^28 - 9 * q^29 + 18 * q^30 - 3 * q^31 + 30 * q^32 - 6 * q^34 + 12 * q^35 - 36 * q^36 + 24 * q^37 - 4 * q^38 - 24 * q^39 + 12 * q^40 + 3 * q^41 - 12 * q^42 + 6 * q^43 - 48 * q^44 - 24 * q^45 + 18 * q^46 + 23 * q^47 - 6 * q^49 - 24 * q^50 + 27 * q^51 + 12 * q^52 + 28 * q^53 + 54 * q^54 - 32 * q^55 - 12 * q^56 + 3 * q^57 + 6 * q^58 + 3 * q^59 + 6 * q^62 + 3 * q^63 - 34 * q^64 - 32 * q^65 + 12 * q^66 - 24 * q^67 - 9 * q^68 - 18 * q^69 - 6 * q^70 + 42 * q^71 + 39 * q^72 - 8 * q^73 + 13 * q^74 - 6 * q^76 - 11 * q^77 + 24 * q^78 - 22 * q^79 + 52 * q^80 + 9 * q^81 - 96 * q^82 - 17 * q^83 + 18 * q^84 - 6 * q^85 + 21 * q^86 + 37 * q^88 - 72 * q^89 + 42 * q^90 - 24 * q^91 - 21 * q^92 + 9 * q^93 + 28 * q^94 - 4 * q^95 + 6 * q^97 + 72 * q^98 - 3 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

$n$	$46$	$56$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	0.373619	+	0.0794152i	0.264189	+	0.0561550i	0.338101	−	0.941110i	$-0.390215\pi$
$2$	0.373619	+	0.0794152i	0.264189	+	0.0561550i	−0.0739128	+	0.997265i	$0.523549\pi$
$3$	1.72256	+	0.181049i	0.994522	+	0.104528i
$3$	1.72256	+	0.181049i	0.994522	+	0.104528i
$4$	−1.69381	−	0.754131i	−0.846903	−	0.377066i
$5$	1.20906	−	0.256993i	0.540707	−	0.114931i	0.0705409	−	0.997509i	$-0.477527\pi$
$5$	1.20906	−	0.256993i	0.540707	−	0.114931i	0.470166	+	0.882578i	$0.344194\pi$
$6$	0.629204	+	0.204441i	0.256872	+	0.0834626i
$7$	0.104528	+	0.994522i	0.0395080	+	0.375894i	0.996355	+	0.0853021i	$0.0271855\pi$
$7$	0.104528	+	0.994522i	0.0395080	+	0.375894i	−0.956847	+	0.290592i	$0.906148\pi$
$8$	−1.19098	−	0.865300i	−0.421076	−	0.305930i
$9$	2.93444	+	0.623735i	0.978148	+	0.207912i
$10$	0.472136			0.149302
$11$	−3.01430	−	1.38348i	−0.908844	−	0.417136i
$11$	−3.01430	−	1.38348i	−0.908844	−	0.417136i
$12$	−2.78115	−	1.60570i	−0.802850	−	0.463525i
$13$	−4.33070	+	4.80973i	−1.20112	+	1.33398i	−0.272859	+	0.962054i	$0.587969\pi$
$13$	−4.33070	+	4.80973i	−1.20112	+	1.33398i	−0.928262	+	0.371926i	$0.878697\pi$
$14$	−0.0399263	+	0.379874i	−0.0106708	+	0.101525i
$15$	2.12920	−	0.223788i	0.549758	−	0.0577819i
$16$	2.10502	+	2.33786i	0.526254	+	0.584464i
$17$	1.50000	−	4.61653i	0.363803	−	1.11967i	−0.586924	−	0.809642i	$-0.699661\pi$
$17$	1.50000	−	4.61653i	0.363803	−	1.11967i	0.950727	−	0.310029i	$-0.100339\pi$
$18$	1.04683	+	0.466079i	0.246740	+	0.109856i
$19$	−0.809017	−	0.587785i	−0.185601	−	0.134847i	0.491105	−	0.871100i	$-0.336593\pi$
$19$	−0.809017	−	0.587785i	−0.185601	−	0.134847i	−0.676706	+	0.736253i	$0.736593\pi$
$20$	−2.24171	−	0.476491i	−0.501263	−	0.106547i
$21$			1.73205i			0.377964i
$22$	−1.01633	−	0.756276i	−0.216682	−	0.161239i
$23$	−2.30902	−	3.99933i	−0.481463	−	0.833919i	0.518310	−	0.855193i	$-0.326561\pi$
$23$	−2.30902	−	3.99933i	−0.481463	−	0.833919i	−0.999774	+	0.0212736i	$0.993228\pi$
$24$	−1.89488	−	1.70616i	−0.386791	−	0.348268i
$25$	−3.17195	+	1.41224i	−0.634391	+	0.282449i
$26$	−2.00000	+	1.45309i	−0.392232	+	0.284973i
$27$	4.94183	+	1.60570i	0.951057	+	0.309017i
$28$	0.572949	−	1.76336i	0.108277	−	0.333243i
$29$	0.507392	+	4.82751i	0.0942203	+	0.896446i	0.934899	+	0.354913i	$0.115489\pi$
$29$	0.507392	+	4.82751i	0.0942203	+	0.896446i	−0.840679	+	0.541534i	$0.817844\pi$
$30$	0.813284	+	0.0854796i	0.148485	+	0.0156064i
$31$	0.413545	−	0.459289i	0.0742750	−	0.0824907i	−0.704862	−	0.709345i	$-0.748991\pi$
$31$	0.413545	−	0.459289i	0.0742750	−	0.0824907i	0.779137	+	0.626854i	$0.215658\pi$
$32$	2.07295	+	3.59045i	0.366449	+	0.634708i
$33$	−4.94183	−	2.92887i	−0.860263	−	0.509851i
$34$	0.927051	−	1.60570i	0.158988	−	0.275375i
$35$	0.381966	+	1.17557i	0.0645640	+	0.198708i
$36$	−4.50000	−	3.26944i	−0.750000	−	0.544907i
$37$	4.11803	−	2.99193i	0.677001	−	0.491870i	−0.195361	−	0.980731i	$-0.562588\pi$
$37$	4.11803	−	2.99193i	0.677001	−	0.491870i	0.872361	+	0.488862i	$0.162588\pi$
$38$	−0.255585	−	0.283856i	−0.0414614	−	0.0460475i
$39$	−8.33070	+	7.50100i	−1.33398	+	1.20112i
$40$	−1.66234	−	0.740122i	−0.262839	−	0.117024i
$41$	0.264234	−	2.51402i	0.0412664	−	0.392623i	−0.954321	−	0.298783i	$-0.903419\pi$
$41$	0.264234	−	2.51402i	0.0412664	−	0.392623i	0.995587	−	0.0938399i	$-0.0299142\pi$
$42$	−0.137551	+	0.647127i	−0.0212246	+	0.0998539i
$43$	−0.927051	+	1.60570i	−0.141374	+	0.244867i	−0.928014	−	0.372545i	$-0.878485\pi$
$43$	−0.927051	+	1.60570i	−0.141374	+	0.244867i	0.786640	+	0.617412i	$0.211819\pi$
$44$	4.06231	+	4.61653i	0.612416	+	0.695967i
$45$	3.70820			0.552786
$46$	−0.545085	−	1.67760i	−0.0803684	−	0.247348i
$47$	10.9116	−	4.85817i	1.59163	−	0.708637i	0.596081	−	0.802925i	$-0.296724\pi$
$47$	10.9116	−	4.85817i	1.59163	−	0.708637i	0.995545	+	0.0942873i	$0.0300572\pi$
$48$	3.20276	+	4.40822i	0.462278	+	0.636271i
$49$	5.86889	−	1.24747i	0.838412	−	0.178210i
$50$	−1.29726	+	0.275740i	−0.183460	+	0.0389956i
$51$	3.41966	−	7.68068i	0.478848	−	1.07551i
$52$	10.9625	−	4.88084i	1.52023	−	0.676851i
$53$	1.26393	+	3.88998i	0.173614	+	0.534330i	0.999567	−	0.0294087i	$-0.00936242\pi$
$53$	1.26393	+	3.88998i	0.173614	+	0.534330i	−0.825953	+	0.563739i	$0.809362\pi$
$54$	1.71885	+	0.992377i	0.233905	+	0.135045i
$55$	−4.00000	−	0.898056i	−0.539360	−	0.121094i
$56$	0.736068	−	1.27491i	0.0983612	−	0.170367i
$57$	−1.28716	−	1.15897i	−0.170489	−	0.153509i
$58$	−0.193806	+	1.84395i	−0.0254480	+	0.242122i
$59$	1.47815	+	0.658114i	0.192438	+	0.0856791i	0.500694	−	0.865625i	$-0.333078\pi$
$59$	1.47815	+	0.658114i	0.192438	+	0.0856791i	−0.308255	+	0.951304i	$0.599745\pi$
$60$	−3.77523	−	1.22665i	−0.487380	−	0.158359i
$61$	7.26281	+	8.06617i	0.929908	+	1.03277i	0.999381	+	0.0351834i	$0.0112015\pi$
$61$	7.26281	+	8.06617i	0.929908	+	1.03277i	−0.0694731	+	0.997584i	$0.522132\pi$
$62$	0.190983	−	0.138757i	0.0242549	−	0.0176222i
$63$	−0.313585	+	2.98357i	−0.0395080	+	0.375894i
$64$	−1.45492	−	4.47777i	−0.181864	−	0.559721i
$65$	−4.00000	+	6.92820i	−0.496139	+	0.859338i
$66$	−1.61377	−	1.48674i	−0.198641	−	0.183005i
$67$	−3.00000	−	5.19615i	−0.366508	−	0.634811i	0.622509	−	0.782613i	$-0.286114\pi$
$67$	−3.00000	−	5.19615i	−0.366508	−	0.634811i	−0.989017	+	0.147802i	$0.952780\pi$
$68$	−6.02218	+	6.68830i	−0.730296	+	0.811076i
$69$	−3.25335	−	7.30715i	−0.391658	−	0.879677i
$70$	0.0493516	+	0.469550i	0.00589865	+	0.0561219i
$71$	−0.899187	+	2.76741i	−0.106714	+	0.328431i	−0.990129	−	0.140160i	$-0.955238\pi$
$71$	−0.899187	+	2.76741i	−0.106714	+	0.328431i	0.883415	+	0.468591i	$0.155238\pi$
$72$	−2.95515	−	3.28203i	−0.348268	−	0.386791i
$73$	0.118034	−	0.0857567i	0.0138148	−	0.0100371i	−0.580856	−	0.814006i	$-0.697282\pi$
$73$	0.118034	−	0.0857567i	0.0138148	−	0.0100371i	0.594671	+	0.803969i	$0.297282\pi$
$74$	1.77618	−	0.790807i	0.206477	−	0.0919294i
$75$	−5.71957	+	1.85840i	−0.660440	+	0.214590i
$76$	0.927051	+	1.60570i	0.106340	+	0.184186i
$77$	1.06082	−	3.14240i	0.120892	−	0.358109i
$78$	−3.70820	+	2.14093i	−0.419871	+	0.242413i
$79$	−10.3315	−	2.19603i	−1.16238	−	0.247072i	−0.413961	−	0.910294i	$-0.635855\pi$
$79$	−10.3315	−	2.19603i	−1.16238	−	0.247072i	−0.748423	+	0.663222i	$0.769188\pi$
$80$	3.14590	+	2.28563i	0.351722	+	0.255541i
$81$	8.22191	+	3.66063i	0.913545	+	0.406737i
$82$	0.298374	−	0.918300i	0.0329499	−	0.101409i
$83$	−6.53335	−	7.25602i	−0.717128	−	0.796451i	0.268876	−	0.963175i	$-0.413348\pi$
$83$	−6.53335	−	7.25602i	−0.717128	−	0.796451i	−0.986004	+	0.166724i	$0.946681\pi$
$84$	1.30619	−	2.93376i	0.142517	−	0.320099i
$85$	0.627171	−	5.96713i	0.0680262	−	0.647226i
$86$	−0.473881	+	0.526298i	−0.0510999	+	0.0567522i
$87$			8.40755i			0.901384i
$88$	2.39285	+	4.25597i	0.255078	+	0.453688i
$89$	−6.76393			−0.716975			−0.358488	−	0.933534i	$-0.616707\pi$
$89$	−6.76393			−0.716975			−0.358488	+	0.933534i	$0.616707\pi$
$90$	1.38546	+	0.294488i	0.146040	+	0.0310417i
$91$	−5.23607	−	3.80423i	−0.548889	−	0.398791i
$92$	0.895005	+	8.51540i	0.0933107	+	0.887792i
$93$	0.795511	−	0.716282i	0.0824907	−	0.0742750i
$94$	4.46261	−	0.948557i	0.460283	−	0.0978362i
$95$	−1.12920	−	0.502754i	−0.115854	−	0.0515815i
$96$	2.92074	+	6.56008i	0.298097	+	0.669536i
$97$	−5.86889	−	1.24747i	−0.595895	−	0.126661i	−0.0999160	−	0.994996i	$-0.531857\pi$
$97$	−5.86889	−	1.24747i	−0.595895	−	0.126661i	−0.495979	+	0.868334i	$0.665191\pi$
$98$	2.29180			0.231506
$99$	−7.98235	−	5.93987i	−0.802256	−	0.596980i
$100$	6.43769			0.643769
$101$	8.28700	+	1.76146i	0.824587	+	0.175271i	0.600833	−	0.799374i	$-0.294835\pi$
$101$	8.28700	+	1.76146i	0.824587	+	0.175271i	0.223754	+	0.974646i	$0.428169\pi$
$102$	1.88761	−	2.59808i	0.186902	−	0.257248i
$103$	−9.35111	−	4.16338i	−0.921393	−	0.410230i	−0.109466	−	0.993990i	$-0.534914\pi$
$103$	−9.35111	−	4.16338i	−0.921393	−	0.410230i	−0.811926	+	0.583760i	$0.801581\pi$
$104$	9.31966	−	1.98095i	0.913868	−	0.194249i
$105$	0.445125	+	2.09415i	0.0434397	+	0.204368i
$106$	0.163305	+	1.55375i	0.0158616	+	0.150913i
$107$	−11.3541	−	8.24924i	−1.09764	−	0.797484i	−0.116969	−	0.993136i	$-0.537318\pi$
$107$	−11.3541	−	8.24924i	−1.09764	−	0.797484i	−0.980673	+	0.195652i	$0.937318\pi$
$108$	−7.15960	−	6.44654i	−0.688933	−	0.620318i
$109$	7.14590			0.684453			0.342226	−	0.939618i	$-0.388819\pi$
$109$	7.14590			0.684453			0.342226	+	0.939618i	$0.388819\pi$
$110$	−1.42316	−	0.653192i	−0.135693	−	0.0622794i
$111$	7.63525	−	4.40822i	0.724706	−	0.418409i
$112$	−2.10502	+	2.33786i	−0.198905	+	0.220907i
$113$	−1.80166	+	17.1416i	−0.169486	+	1.61255i	0.497489	+	0.867470i	$0.334255\pi$
$113$	−1.80166	+	17.1416i	−0.169486	+	1.61255i	−0.666975	+	0.745080i	$0.732411\pi$
$114$	−0.388870	−	0.535233i	−0.0364210	−	0.0501292i
$115$	−3.81953	−	4.24202i	−0.356173	−	0.395571i
$116$	2.78115	−	8.55951i	0.258224	−	0.794730i
$117$	−15.7082	+	11.4127i	−1.45222	+	1.05510i
$118$	0.500000	+	0.363271i	0.0460287	+	0.0334418i
$119$	4.74803	+	1.00922i	0.435251	+	0.0925155i
$120$	−2.72949	−	1.57587i	−0.249167	−	0.143857i
$121$	7.17195	+	8.34045i	0.651996	+	0.758223i
$122$	2.07295	+	3.59045i	0.187676	+	0.325064i
$123$	0.910318	−	4.28271i	0.0820806	−	0.386159i
$124$	−1.04683	+	0.466079i	−0.0940081	+	0.0418551i
$125$	−8.47214	+	6.15537i	−0.757771	+	0.550553i
$126$	−0.354102	+	1.08981i	−0.0315459	+	0.0970883i
$127$	−3.26393	+	10.0453i	−0.289627	+	0.891381i	0.695346	+	0.718675i	$0.255251\pi$
$127$	−3.26393	+	10.0453i	−0.289627	+	0.891381i	−0.984973	+	0.172706i	$0.944749\pi$
$128$	−1.05471	−	10.0349i	−0.0932241	−	0.886968i
$129$	−1.88761	+	2.59808i	−0.166195	+	0.228748i
$130$	−2.04468	+	2.27085i	−0.179330	+	0.199167i
$131$	−10.6180	−	18.3910i	−0.927702	−	1.60683i	−0.787157	−	0.616753i	$-0.788448\pi$
$131$	−10.6180	−	18.3910i	−0.927702	−	1.60683i	−0.140545	−	0.990074i	$-0.544885\pi$
$132$	6.16176	+	8.68773i	0.536312	+	0.756170i
$133$	0.500000	−	0.866025i	0.0433555	−	0.0750939i
$134$	−0.708204	−	2.17963i	−0.0611795	−	0.188291i
$135$	6.38761	+	0.671365i	0.549758	+	0.0577819i
$136$	−5.78115	+	4.20025i	−0.495730	+	0.360169i
$137$	−5.76659	−	6.40445i	−0.492673	−	0.547169i	0.444616	−	0.895721i	$-0.353340\pi$
$137$	−5.76659	−	6.40445i	−0.492673	−	0.547169i	−0.937289	+	0.348552i	$0.886673\pi$
$138$	−0.635216	−	2.98846i	−0.0540732	−	0.254394i
$139$	8.86889	+	3.94868i	0.752249	+	0.334923i	0.746788	−	0.665062i	$-0.231595\pi$
$139$	8.86889	+	3.94868i	0.752249	+	0.334923i	0.00546112	+	0.999985i	$0.498262\pi$
$140$	0.239558	−	2.27924i	0.0202463	−	0.192631i
$141$	19.6755	−	6.39297i	1.65698	−	0.538385i
$142$	−0.555728	+	0.962549i	−0.0466357	+	0.0807753i
$143$	19.7082	−	8.50651i	1.64808	−	0.711350i
$144$	4.71885	+	8.17328i	0.393237	+	0.681107i
$145$	1.85410	+	5.70634i	0.153975	+	0.473886i
$146$	0.0509101	−	0.0226667i	0.00421335	−	0.00187591i
$147$	10.3354	−	1.08629i	0.852447	−	0.0895958i
$148$	−9.23146	+	1.96221i	−0.758821	+	0.161292i
$149$	14.8486	−	3.15617i	1.21645	−	0.258564i	0.445393	−	0.895335i	$-0.353064\pi$
$149$	14.8486	−	3.15617i	1.21645	−	0.258564i	0.771053	+	0.636772i	$0.219731\pi$
$150$	−2.28453	+	0.240114i	−0.186531	+	0.0196052i
$151$	3.95222	−	1.75964i	0.321627	−	0.143197i	−0.239572	−	0.970879i	$-0.577007\pi$
$151$	3.95222	−	1.75964i	0.321627	−	0.143197i	0.561199	+	0.827681i	$0.310340\pi$
$152$	0.454915	+	1.40008i	0.0368985	+	0.113562i
$153$	7.28115	−	12.6113i	0.588646	−	1.01957i
$154$	0.645898	−	1.08981i	0.0520479	−	0.0878197i
$155$	0.381966	−	0.661585i	0.0306802	−	0.0531397i
$156$	19.7673	−	6.42280i	1.58265	−	0.514235i
$157$	−0.746950	+	7.10675i	−0.0596131	+	0.567181i	0.923425	+	0.383779i	$0.125378\pi$
$157$	−0.746950	+	7.10675i	−0.0596131	+	0.567181i	−0.983038	+	0.183402i	$0.941289\pi$
$158$	−3.68565	−	1.64096i	−0.293214	−	0.130547i
$159$	1.47293	+	6.92957i	0.116811	+	0.549551i
$160$	3.42903	+	3.80833i	0.271089	+	0.301075i
$161$	3.73607	−	2.71441i	0.294443	−	0.213926i
$162$	2.78115	+	2.02063i	0.218508	+	0.158755i
$163$	6.39919	+	19.6947i	0.501223	+	1.54261i	0.807029	+	0.590512i	$0.201074\pi$
$163$	6.39919	+	19.6947i	0.501223	+	1.54261i	−0.305806	+	0.952094i	$0.598926\pi$
$164$	−2.34346	+	4.05899i	−0.182993	+	0.316954i
$165$	−6.72766	−	2.27115i	−0.523747	−	0.176809i
$166$	−1.86475	−	3.22983i	−0.144732	−	0.250684i
$167$	−3.85682	+	4.28344i	−0.298450	+	0.331462i	−0.873654	−	0.486548i	$-0.838256\pi$
$167$	−3.85682	+	4.28344i	−0.298450	+	0.331462i	0.575204	+	0.818010i	$0.304923\pi$
$168$	1.49874	−	2.06284i	0.115631	−	0.159152i
$169$	−3.01968	−	28.7303i	−0.232283	−	2.21002i
$170$	0.708204	−	2.17963i	0.0543168	−	0.167170i
$171$	−2.00739	−	2.22943i	−0.153509	−	0.170489i
$172$	2.78115	−	2.02063i	0.212061	−	0.154071i
$173$	−21.0939	+	9.39162i	−1.60374	+	0.714032i	−0.996741	−	0.0806702i	$-0.974294\pi$
$173$	−21.0939	+	9.39162i	−1.60374	+	0.714032i	−0.607000	+	0.794702i	$0.707627\pi$
$174$	−0.667687	+	3.14122i	−0.0506172	+	0.238135i
$175$	−1.73607	−	3.00696i	−0.131234	−	0.227305i
$176$	−3.11076	−	9.95925i	−0.234482	−	0.750707i
$177$	2.42705	+	1.40126i	0.182428	+	0.105325i
$178$	−2.52713	−	0.537159i	−0.189417	−	0.0402618i
$179$	4.09017	+	2.97168i	0.305714	+	0.222114i	0.730055	−	0.683388i	$-0.239494\pi$
$179$	4.09017	+	2.97168i	0.305714	+	0.222114i	−0.424341	+	0.905502i	$0.639494\pi$
$180$	−6.28098	−	2.79647i	−0.468157	−	0.208437i
$181$	−3.06231	+	9.42481i	−0.227619	+	0.700540i	0.770396	+	0.637566i	$0.220059\pi$
$181$	−3.06231	+	9.42481i	−0.227619	+	0.700540i	−0.998015	+	0.0629745i	$0.979941\pi$
$182$	−1.65418	−	1.83716i	−0.122616	−	0.136179i
$183$	11.0503	+	15.2094i	0.816860	+	1.12431i
$184$	−0.710624	+	6.76113i	−0.0523879	+	0.498437i
$185$	4.21003	−	4.67572i	0.309528	−	0.343765i
$186$	0.354102	−	0.204441i	0.0259640	−	0.0149903i
$187$	−10.9083	+	11.8403i	−0.797696	+	0.865852i
$188$	−22.1459			−1.61516
$189$	−1.08034	+	5.08260i	−0.0785832	+	0.369705i
$190$	−0.381966	−	0.277515i	−0.0277107	−	0.0201330i
$191$	−0.621346	−	5.91171i	−0.0449590	−	0.427756i	−0.993731	−	0.111795i	$-0.964340\pi$
$191$	−0.621346	−	5.91171i	−0.0449590	−	0.427756i	0.948772	−	0.315961i	$-0.102327\pi$
$192$	−1.69549	−	7.97665i	−0.122361	−	0.575665i
$193$	10.7596	−	2.28703i	0.774495	−	0.164624i	0.196323	−	0.980539i	$-0.437100\pi$
$193$	10.7596	−	2.28703i	0.774495	−	0.164624i	0.578171	+	0.815915i	$0.303766\pi$
$194$	−2.09366	−	0.932157i	−0.150316	−	0.0669250i
$195$	−8.14459	+	11.2101i	−0.583246	+	0.802770i
$196$	−10.8815	−	2.31294i	−0.777251	−	0.165210i
$197$	8.23607			0.586796			0.293398	−	0.955990i	$-0.405214\pi$
$197$	8.23607			0.586796			0.293398	+	0.955990i	$0.405214\pi$
$198$	−2.51064	−	2.85317i	−0.178424	−	0.202766i
$199$	−7.14590			−0.506559			−0.253280	−	0.967393i	$-0.581509\pi$
$199$	−7.14590			−0.506559			−0.253280	+	0.967393i	$0.581509\pi$
$200$	4.99976	+	1.06273i	0.353536	+	0.0751465i
$201$	−4.22693	−	9.49384i	−0.298145	−	0.669644i
$202$	2.95630	+	1.31623i	0.208004	+	0.0926094i
$203$	−4.74803	+	1.00922i	−0.333246	+	0.0708337i
$204$	−11.5845	+	10.4307i	−0.811076	+	0.730296i
$205$	−0.326611	−	3.10749i	−0.0228115	−	0.217037i
$206$	−3.16312	−	2.29814i	−0.220385	−	0.160119i
$207$	−4.28115	−	13.1760i	−0.297561	−	0.915798i
$208$	−20.3607			−1.41176
$209$	1.62543	+	2.89102i	0.112433	+	0.199976i
$210$			0.817763i			0.0564310i
$211$	13.6985	−	15.2138i	0.943046	−	1.04736i	−0.0557571	−	0.998444i	$-0.517757\pi$
$211$	13.6985	−	15.2138i	0.943046	−	1.04736i	0.998803	−	0.0489142i	$-0.0155761\pi$
$212$	0.792701	−	7.54205i	0.0544429	−	0.517990i
$213$	−2.04994	+	4.60424i	−0.140460	+	0.315478i
$214$	−3.58699	−	3.98376i	−0.245202	−	0.272324i
$215$	−0.708204	+	2.17963i	−0.0482991	+	0.148649i
$216$	−4.49623	−	6.18853i	−0.305930	−	0.421076i
$217$	0.500000	+	0.363271i	0.0339422	+	0.0246605i
$218$	2.66984	+	0.567493i	0.180825	+	0.0384355i
$219$	0.218847	−	0.126351i	0.0147883	−	0.00853804i
$220$	6.09797	+	4.53766i	0.411125	+	0.305929i
$221$	15.7082	+	27.2074i	1.05665	+	1.83017i
$222$	3.20276	−	1.04064i	0.214955	−	0.0698431i
$223$	−14.1660	+	6.30709i	−0.948623	+	0.422354i	−0.821930	−	0.569588i	$-0.807103\pi$
$223$	−14.1660	+	6.30709i	−0.948623	+	0.422354i	−0.126693	+	0.991942i	$0.540436\pi$
$224$	−3.35410	+	2.43690i	−0.224105	+	0.162822i
$225$	−10.1888	+	2.16569i	−0.679252	+	0.144380i
$226$	−2.03444	+	6.26137i	−0.135329	+	0.416500i
$227$	1.73706	+	16.5270i	0.115293	+	1.09694i	0.887259	+	0.461272i	$0.152607\pi$
$227$	1.73706	+	16.5270i	0.115293	+	1.09694i	−0.771966	+	0.635664i	$0.780727\pi$
$228$	1.30619	+	2.93376i	0.0865048	+	0.194293i
$229$	6.81198	−	7.56547i	0.450148	−	0.499940i	−0.474768	−	0.880111i	$-0.657468\pi$
$229$	6.81198	−	7.56547i	0.450148	−	0.499940i	0.924916	+	0.380171i	$0.124135\pi$
$230$	−1.09017	−	1.88823i	−0.0718837	−	0.124506i
$231$	2.39626	−	5.22091i	0.157662	−	0.343511i
$232$	3.57295	−	6.18853i	0.234576	−	0.406297i
$233$	−3.43769	−	10.5801i	−0.225211	−	0.693128i	−0.998270	−	0.0587939i	$-0.981275\pi$
$233$	−3.43769	−	10.5801i	−0.225211	−	0.693128i	0.773059	−	0.634334i	$-0.218725\pi$
$234$	−6.77523	+	3.01652i	−0.442910	+	0.197196i
$235$	11.9443	−	8.67802i	0.779158	−	0.566092i
$236$	−2.00739	−	2.22943i	−0.130670	−	0.145124i
$237$	−17.3991	−	5.65330i	−1.13019	−	0.367221i
$238$	1.69381	+	0.754131i	0.109793	+	0.0488831i
$239$	−1.09464	+	10.4148i	−0.0708061	+	0.673675i	0.900340	+	0.435188i	$0.143318\pi$
$239$	−1.09464	+	10.4148i	−0.0708061	+	0.673675i	−0.971146	+	0.238487i	$0.923349\pi$
$240$	5.00520	+	4.50670i	0.323084	+	0.290906i
$241$	13.4164	−	23.2379i	0.864227	−	1.49688i	−0.00358606	−	0.999994i	$-0.501141\pi$
$241$	13.4164	−	23.2379i	0.864227	−	1.49688i	0.867813	−	0.496891i	$-0.165525\pi$
$242$	2.01722	+	3.68571i	0.129672	+	0.236927i
$243$	13.5000	+	7.79423i	0.866025	+	0.500000i
$244$	−6.21885	−	19.1396i	−0.398121	−	1.22529i
$245$	6.77523	−	3.01652i	0.432853	−	0.192719i
$246$	0.680225	−	1.52781i	0.0433695	−	0.0974096i
$247$	6.33070	−	1.34563i	0.402813	−	0.0856206i
$248$	−0.889948	+	0.189164i	−0.0565118	+	0.0120119i
$249$	−9.94040	−	13.6818i	−0.629948	−	0.867048i
$250$	−3.65418	+	1.62695i	−0.231111	+	0.102897i
$251$	6.35410	+	19.5559i	0.401067	+	1.23436i	0.924135	+	0.382067i	$0.124788\pi$
$251$	6.35410	+	19.5559i	0.401067	+	1.23436i	−0.523067	+	0.852291i	$0.675212\pi$
$252$	2.78115	−	4.81710i	0.175196	−	0.303449i
$253$	1.42705	+	15.2497i	0.0897179	+	0.958738i
$254$	−2.01722	+	3.49393i	−0.126572	+	0.219229i
$255$	2.16068	−	10.1652i	0.135307	−	0.636570i
$256$	−0.581419	+	5.53184i	−0.0363387	+	0.345740i
$257$	−13.6208	−	6.06437i	−0.849643	−	0.378285i	−0.0647383	−	0.997902i	$-0.520621\pi$
$257$	−13.6208	−	6.06437i	−0.849643	−	0.378285i	−0.784904	+	0.619617i	$0.787288\pi$
$258$	−0.911575	+	0.820786i	−0.0567522	+	0.0510999i
$259$	3.40599	+	3.78273i	0.211638	+	0.235048i
$260$	12.0000	−	8.71851i	0.744208	−	0.540699i
$261$	−1.52218	+	14.4825i	−0.0942203	+	0.896446i
$262$	−2.50658	−	7.71445i	−0.154857	−	0.476601i
$263$	6.35410	−	11.0056i	0.391811	−	0.678636i	−0.600878	−	0.799341i	$-0.705182\pi$
$263$	6.35410	−	11.0056i	0.391811	−	0.678636i	0.992688	+	0.120705i	$0.0385155\pi$
$264$	3.35129	+	7.76440i	0.206258	+	0.477866i
$265$	2.52786	+	4.37839i	0.155285	+	0.268962i
$266$	0.255585	−	0.283856i	0.0156709	−	0.0174043i
$267$	−11.6513	−	1.22460i	−0.713048	−	0.0749443i
$268$	1.16284	+	11.0637i	0.0710317	+	0.675821i
$269$	−6.57295	+	20.2295i	−0.400760	+	1.23341i	0.523625	+	0.851949i	$0.324579\pi$
$269$	−6.57295	+	20.2295i	−0.400760	+	1.23341i	−0.924384	+	0.381463i	$0.875421\pi$
$270$	2.33322	+	0.758108i	0.141995	+	0.0461370i
$271$	−8.70820	+	6.32688i	−0.528986	+	0.384331i	−0.819978	−	0.572395i	$-0.806015\pi$
$271$	−8.70820	+	6.32688i	−0.528986	+	0.384331i	0.290993	+	0.956725i	$0.406015\pi$
$272$	13.9503	−	6.21108i	0.845861	−	0.376602i
$273$	−8.33070	−	7.50100i	−0.504197	−	0.453981i
$274$	−1.64590	−	2.85078i	−0.0994323	−	0.172222i
$275$	11.5150	+	0.131418i	0.694382	+	0.00792483i
$276$			14.8303i			0.892682i
$277$	18.8157	+	3.99940i	1.13053	+	0.240301i	0.734943	−	0.678129i	$-0.237209\pi$
$277$	18.8157	+	3.99940i	1.13053	+	0.240301i	0.395584	+	0.918430i	$0.370542\pi$
$278$	3.00000	+	2.17963i	0.179928	+	0.130725i
$279$	1.50000	−	1.08981i	0.0898027	−	0.0652454i
$280$	0.562306	−	1.73060i	0.0336042	−	0.103423i
$281$	−6.24047	−	6.93075i	−0.372275	−	0.413454i	0.527675	−	0.849446i	$-0.323064\pi$
$281$	−6.24047	−	6.93075i	−0.372275	−	0.413454i	−0.899950	+	0.435993i	$0.856397\pi$
$282$	7.85886	−	0.825999i	0.467988	−	0.0491875i
$283$	1.77698	−	16.9069i	0.105631	−	1.00501i	−0.805417	−	0.592708i	$-0.798059\pi$
$283$	1.77698	−	16.9069i	0.105631	−	1.00501i	0.911048	−	0.412301i	$-0.135275\pi$
$284$	3.61004	−	4.00936i	0.214217	−	0.237912i
$285$	−1.85410	−	1.07047i	−0.109828	−	0.0634089i
$286$	8.03891	−	1.61306i	0.475351	−	0.0953824i
$287$	2.52786			0.149215
$288$	3.84346	+	11.8290i	0.226478	+	0.697028i
$289$	−5.30902	−	3.85723i	−0.312295	−	0.226896i
$290$	0.239558	+	2.27924i	0.0140673	+	0.133842i
$291$	−9.88367	−	3.21140i	−0.579391	−	0.188256i
$292$	−0.264599	+	0.0562422i	−0.0154845	+	0.00329132i
$293$	−26.6576	−	11.8687i	−1.55735	−	0.693378i	−0.565975	−	0.824422i	$-0.691500\pi$
$293$	−26.6576	−	11.8687i	−1.55735	−	0.693378i	−0.991376	+	0.131045i	$0.958167\pi$
$294$	3.94776	+	0.414926i	0.230238	+	0.0241990i
$295$	1.95630	+	0.415823i	0.113900	+	0.0242102i
$296$	−7.49342			−0.435546
$297$	−12.6747	−	11.6770i	−0.735460	−	0.677568i
$298$	5.79837			0.335891
$299$	29.2354	+	6.21418i	1.69073	+	0.359375i
$300$	11.0893	+	1.16554i	0.640243	+	0.0672922i
$301$	−1.69381	−	0.754131i	−0.0976294	−	0.0434674i
$302$	1.61637	−	0.343569i	0.0930114	−	0.0197702i
$303$	13.9560	+	4.53457i	0.801749	+	0.260504i
$304$	−0.328836	−	3.12866i	−0.0188600	−	0.179441i
$305$	10.8541	+	7.88597i	0.621504	+	0.451549i
$306$	3.72191	−	4.13360i	0.212767	−	0.236302i
$307$	7.85410			0.448257			0.224129	−	0.974560i	$-0.428046\pi$
$307$	7.85410			0.448257			0.224129	+	0.974560i	$0.428046\pi$
$308$	−4.16661	+	4.52261i	−0.237415	+	0.257700i
$309$	−15.3541	−	8.86469i	−0.873464	−	0.504295i
$310$	0.195250	−	0.216847i	0.0110894	−	0.0123161i
$311$	−1.58678	+	15.0972i	−0.0899779	+	0.856083i	0.852705	+	0.522393i	$0.174960\pi$
$311$	−1.58678	+	15.0972i	−0.0899779	+	0.856083i	−0.942683	+	0.333690i	$0.891706\pi$
$312$	16.4123	−	1.72501i	0.929166	−	0.0976593i
$313$	2.32331	+	2.58030i	0.131321	+	0.145847i	0.805219	−	0.592978i	$-0.202048\pi$
$313$	2.32331	+	2.58030i	0.131321	+	0.145847i	−0.673898	+	0.738825i	$0.735381\pi$
$314$	−0.843459	+	2.59590i	−0.0475991	+	0.146495i
$315$	0.387613	+	3.68789i	0.0218395	+	0.207789i
$316$	15.8435	+	11.5109i	0.891264	+	0.647541i
$317$	−20.4866	−	4.35456i	−1.15064	−	0.244576i	−0.407175	−	0.913350i	$-0.633486\pi$
$317$	−20.4866	−	4.35456i	−1.15064	−	0.244576i	−0.743466	+	0.668774i	$0.766820\pi$
$318$			2.70599i			0.151745i
$319$	5.14935	−	15.2535i	0.288308	−	0.854033i
$320$	−2.90983	−	5.03997i	−0.162664	−	0.281743i
$321$	−18.0646	−	16.2655i	−1.00827	−	0.907850i
$322$	1.61143	−	0.717456i	0.0898016	−	0.0399822i
$323$	−3.92705	+	2.85317i	−0.218507	+	0.158755i
$324$	−11.1657	−	12.4008i	−0.620318	−	0.688933i
$325$	6.94427	−	21.3723i	0.385199	−	1.18552i
$326$	0.826802	+	7.86650i	0.0457923	+	0.435685i
$327$	12.3093	+	1.29375i	0.680703	+	0.0715448i
$328$	−2.49008	+	2.76551i	−0.137491	+	0.152700i
$329$	5.97214	+	10.3440i	0.329255	+	0.570286i
$330$	−2.33322	−	1.38282i	−0.128439	−	0.0761220i
$331$	−7.20820	+	12.4850i	−0.396199	+	0.686236i	−0.993253	−	0.115964i	$-0.963004\pi$
$331$	−7.20820	+	12.4850i	−0.396199	+	0.686236i	0.597055	+	0.802201i	$0.296338\pi$
$332$	5.59424	+	17.2173i	0.307024	+	0.944921i
$333$	13.9503	−	6.21108i	0.764472	−	0.340365i
$334$	−1.78115	+	1.29408i	−0.0974604	+	0.0708091i
$335$	−4.96255	−	5.51147i	−0.271133	−	0.301124i
$336$	−4.04929	+	3.64600i	−0.220907	+	0.198905i
$337$	−10.4803	−	4.66614i	−0.570899	−	0.254181i	0.100922	−	0.994894i	$-0.467821\pi$
$337$	−10.4803	−	4.66614i	−0.570899	−	0.254181i	−0.671821	+	0.740714i	$0.734488\pi$
$338$	1.15341	−	10.9740i	0.0627374	−	0.596907i
$339$	−6.20694	+	29.2014i	−0.337115	+	1.58600i
$340$	−5.56231	+	9.63420i	−0.301658	+	0.522488i
$341$	−1.88197	+	0.812299i	−0.101914	+	0.0439885i
$342$	−0.572949	−	0.992377i	−0.0309815	−	0.0536616i
$343$	4.01722	+	12.3637i	0.216910	+	0.667579i
$344$	2.49351	−	1.11018i	0.134441	−	0.0598571i
$345$	−5.81137	−	7.99867i	−0.312874	−	0.430634i
$346$	−8.62693	+	1.83371i	−0.463787	+	0.0985809i
$347$	8.69431	−	1.84803i	0.466735	−	0.0992076i	0.0314597	−	0.999505i	$-0.489984\pi$
$347$	8.69431	−	1.84803i	0.466735	−	0.0992076i	0.435275	+	0.900297i	$0.356651\pi$
$348$	6.34040	−	14.2408i	0.339881	−	0.763385i
$349$	−3.78747	+	1.68629i	−0.202738	+	0.0902650i	−0.505594	−	0.862771i	$-0.668727\pi$
$349$	−3.78747	+	1.68629i	−0.202738	+	0.0902650i	0.302856	+	0.953036i	$0.402060\pi$
$350$	−0.409830	−	1.26133i	−0.0219063	−	0.0674208i
$351$	−29.1246	+	16.8151i	−1.55456	+	0.897524i
$352$	−1.28115	−	13.6906i	−0.0682857	−	0.729710i
$353$	8.20820	−	14.2170i	0.436879	−	0.756696i	−0.560568	−	0.828108i	$-0.689417\pi$
$353$	8.20820	−	14.2170i	0.436879	−	0.756696i	0.997447	+	0.0714123i	$0.0227506\pi$
$354$	0.795511	+	0.716282i	0.0422810	+	0.0380699i
$355$	−0.375963	+	3.57704i	−0.0199540	+	0.189850i
$356$	11.4568	+	5.10089i	0.607209	+	0.270347i
$357$	7.99606	+	2.59808i	0.423196	+	0.137505i
$358$	1.29217	+	1.43510i	0.0682933	+	0.0758473i
$359$	18.4894	−	13.4333i	0.975831	−	0.708983i	0.0190579	−	0.999818i	$-0.493933\pi$
$359$	18.4894	−	13.4333i	0.975831	−	0.708983i	0.956773	+	0.290836i	$0.0939333\pi$
$360$	−4.41641	−	3.20871i	−0.232765	−	0.169114i
$361$	−5.56231	−	17.1190i	−0.292753	−	0.901001i
$362$	−1.89261	+	3.27810i	−0.0994733	+	0.172293i
$363$	10.8441	+	15.6654i	0.569168	+	0.822221i
$364$	6.00000	+	10.3923i	0.314485	+	0.544705i
$365$	0.120671	−	0.134019i	0.00631621	−	0.00701486i
$366$	2.92074	+	6.56008i	0.152669	+	0.342901i
$367$	1.32837	+	12.6386i	0.0693403	+	0.659729i	0.972894	+	0.231253i	$0.0742826\pi$
$367$	1.32837	+	12.6386i	0.0693403	+	0.659729i	−0.903553	+	0.428476i	$0.859051\pi$
$368$	4.48936	−	13.8168i	0.234024	−	0.720252i
$369$	2.34346	−	7.21242i	0.121996	−	0.375464i
$370$	1.94427	−	1.41260i	0.101078	−	0.0734374i
$371$	−3.73656	+	1.66362i	−0.193992	+	0.0863710i
$372$	−1.88761	+	0.613323i	−0.0978682	+	0.0317993i
$373$	2.82624	+	4.89519i	0.146337	+	0.253463i	0.929871	−	0.367886i	$-0.119918\pi$
$373$	2.82624	+	4.89519i	0.146337	+	0.253463i	−0.783534	+	0.621349i	$0.786585\pi$
$374$	−5.01586	+	3.55749i	−0.259364	+	0.183954i
$375$	−15.7082	+	9.06914i	−0.811168	+	0.468328i
$376$	−17.1993	−	3.65583i	−0.886989	−	0.188535i
$377$	−25.4164	−	18.4661i	−1.30901	−	0.951053i
$378$	−0.807272	+	1.81316i	−0.0415216	+	0.0932590i
$379$	4.88197	−	15.0251i	0.250770	−	0.771790i	−0.743864	−	0.668331i	$-0.767009\pi$
$379$	4.88197	−	15.0251i	0.250770	−	0.771790i	0.994634	−	0.103459i	$-0.0329910\pi$
$380$	1.53351	+	1.70314i	0.0786674	+	0.0873691i
$381$	−7.44102	+	16.7128i	−0.381215	+	0.856223i
$382$	0.237333	−	2.25807i	0.0121430	−	0.115533i
$383$	13.2850	−	14.7545i	0.678831	−	0.753918i	−0.301026	−	0.953616i	$-0.597329\pi$
$383$	13.2850	−	14.7545i	0.678831	−	0.753918i	0.979858	+	0.199697i	$0.0639959\pi$
$384$		−	17.4767i		−	0.891853i
$385$	0.475022	−	4.07196i	0.0242094	−	0.207526i
$386$	4.20163			0.213857
$387$	−3.72191	+	4.13360i	−0.189195	+	0.210123i
$388$	9.00000	+	6.53888i	0.456906	+	0.331961i
$389$	2.36783	+	22.5284i	0.120054	+	1.14223i	0.874213	+	0.485543i	$0.161378\pi$
$389$	2.36783	+	22.5284i	0.120054	+	1.14223i	−0.754159	+	0.656692i	$0.771955\pi$
$390$	−3.93323	+	3.54149i	−0.199167	+	0.179330i
$391$	−21.9266	+	4.66063i	−1.10887	+	0.235698i
$392$	−8.06918	−	3.59263i	−0.407555	−	0.181455i
$393$	−14.9606	−	33.6020i	−0.754661	−	1.69500i
$394$	3.07715	+	0.654069i	0.155025	+	0.0329515i
$395$	−13.0557			−0.656905
$396$	9.04112	+	16.0807i	0.454333	+	0.808087i
$397$	−2.12461			−0.106631			−0.0533156	−	0.998578i	$-0.516979\pi$
$397$	−2.12461			−0.106631			−0.0533156	+	0.998578i	$0.516979\pi$
$398$	−2.66984	−	0.567493i	−0.133827	−	0.0284458i
$399$	1.01807	−	1.40126i	0.0509674	−	0.0701507i
$400$	−9.97864	−	4.44278i	−0.498932	−	0.222139i
$401$	−14.2441	+	3.02767i	−0.711316	+	0.151195i	−0.549339	−	0.835600i	$-0.685120\pi$
$401$	−14.2441	+	3.02767i	−0.711316	+	0.151195i	−0.161977	+	0.986795i	$0.551787\pi$
$402$	−0.825307	−	3.88276i	−0.0411626	−	0.193655i
$403$	0.418114	+	3.97809i	0.0208277	+	0.198163i
$404$	−12.7082	−	9.23305i	−0.632257	−	0.459361i
$405$	10.8815	+	2.31294i	0.540707	+	0.114931i
$406$	−1.85410			−0.0920175
$407$	−16.5522	+	3.32132i	−0.820465	+	0.164632i
$408$	−10.7188	+	6.18853i	−0.530662	+	0.306378i
$409$	−22.5782	+	25.0757i	−1.11642	+	1.23991i	−0.148432	+	0.988923i	$0.547423\pi$
$409$	−22.5782	+	25.0757i	−1.11642	+	1.23991i	−0.967990	+	0.250990i	$0.919244\pi$
$410$	0.124754	−	1.18696i	0.00616117	−	0.0586196i
$411$	−8.77380	−	12.0761i	−0.432779	−	0.595670i
$412$	12.6992	+	14.1039i	0.625647	+	0.694851i
$413$	−0.500000	+	1.53884i	−0.0246034	+	0.0757215i
$414$	−0.553143	−	5.26281i	−0.0271855	−	0.258653i
$415$	−9.76393	−	7.09391i	−0.479293	−	0.348226i
$416$	−26.2465	−	5.57886i	−1.28684	−	0.273526i
$417$	14.5623	+	8.40755i	0.713119	+	0.411720i
$418$	0.377699	+	1.20922i	0.0184739	+	0.0591451i
$419$	−4.04508	−	7.00629i	−0.197615	−	0.342280i	0.750139	−	0.661280i	$-0.229986\pi$
$419$	−4.04508	−	7.00629i	−0.197615	−	0.342280i	−0.947755	+	0.319000i	$0.896653\pi$
$420$	0.825307	−	3.88276i	0.0402709	−	0.189459i
$421$	9.35111	−	4.16338i	0.455745	−	0.202911i	−0.166007	−	0.986125i	$-0.553088\pi$
$421$	9.35111	−	4.16338i	0.455745	−	0.202911i	0.621753	+	0.783214i	$0.286421\pi$
$422$	6.32624	−	4.59628i	0.307956	−	0.223743i
$423$	35.0498	−	7.45006i	1.70418	−	0.362234i
$424$	1.86068	−	5.72658i	0.0903626	−	0.278107i
$425$	1.76173	+	16.7618i	0.0854566	+	0.813065i
$426$	−1.13154	+	1.55744i	−0.0548235	+	0.0754581i
$427$	−7.26281	+	8.06617i	−0.351472	+	0.390349i
$428$	13.0106	+	22.5351i	0.628893	+	1.08927i
$429$	35.4887	−	11.0848i	1.71341	−	0.535182i
$430$	−0.437694	+	0.758108i	−0.0211075	+	0.0365592i
$431$	−10.5279	−	32.4014i	−0.507109	−	1.56072i	−0.797195	−	0.603722i	$-0.793684\pi$
$431$	−10.5279	−	32.4014i	−0.507109	−	1.56072i	0.290086	−	0.957001i	$-0.406316\pi$
$432$	6.64875	+	14.9333i	0.319888	+	0.718480i
$433$	−11.9271	+	8.66551i	−0.573177	+	0.416438i	−0.836258	−	0.548336i	$-0.815261\pi$
$433$	−11.9271	+	8.66551i	−0.573177	+	0.416438i	0.263081	+	0.964774i	$0.415261\pi$
$434$	0.157960	+	0.175433i	0.00758234	+	0.00842104i
$435$	2.16068	+	10.1652i	0.103597	+	0.487384i
$436$	−12.1038	−	5.38894i	−0.579665	−	0.258084i
$437$	−0.482716	+	4.59274i	−0.0230914	+	0.219700i
$438$	0.0917997	−	0.0298275i	0.00438636	−	0.00142521i
$439$	0.354102	−	0.613323i	0.0169004	−	0.0292723i	−0.857452	−	0.514565i	$-0.827954\pi$
$439$	0.354102	−	0.613323i	0.0169004	−	0.0292723i	0.874352	+	0.485292i	$0.161287\pi$
$440$	3.98684	+	4.53077i	0.190065	+	0.215996i
$441$	18.0000			0.857143
$442$	3.70820	+	11.4127i	0.176381	+	0.542846i
$443$	−1.12920	+	0.502754i	−0.0536501	+	0.0238866i	−0.433386	−	0.901208i	$-0.642681\pi$
$443$	−1.12920	+	0.502754i	−0.0536501	+	0.0238866i	0.379736	+	0.925095i	$0.376015\pi$
$444$	−16.2570	+	1.70868i	−0.771524	+	0.0810904i
$445$	−8.17798	+	1.73828i	−0.387673	+	0.0824025i
$446$	−5.79355	+	1.23146i	−0.274333	+	0.0583112i
$447$	26.1491	−	2.74838i	1.23681	−	0.129994i
$448$	4.30116	−	1.91500i	0.203211	−	0.0904752i
$449$	2.30902	+	7.10642i	0.108969	+	0.335373i	0.990642	−	0.136489i	$-0.0435820\pi$
$449$	2.30902	+	7.10642i	0.108969	+	0.335373i	−0.881672	+	0.471862i	$0.843582\pi$
$450$	−3.97871			−0.187558
$451$	−4.27458	+	7.21242i	−0.201282	+	0.339620i
$452$	15.9787	−	27.6759i	0.751575	−	1.30177i
$453$	7.12652	−	2.31555i	0.334833	−	0.108794i
$454$	−0.663497	+	6.31275i	−0.0311395	+	0.296272i
$455$	−7.30836	−	3.25389i	−0.342621	−	0.152545i
$456$	0.530136	+	2.49409i	0.0248259	+	0.116797i
$457$	−0.669131	−	0.743145i	−0.0313006	−	0.0347628i	0.727291	−	0.686329i	$-0.240779\pi$
$457$	−0.669131	−	0.743145i	−0.0313006	−	0.0347628i	−0.758592	+	0.651566i	$0.774112\pi$
$458$	3.14590	−	2.28563i	0.146998	−	0.106800i
$459$	14.8255	−	20.4056i	0.691995	−	0.952450i
$460$	3.27051	+	10.0656i	0.152488	+	0.469311i
$461$	8.07295	−	13.9828i	0.375995	−	0.651242i	−0.614481	−	0.788932i	$-0.710634\pi$
$461$	8.07295	−	13.9828i	0.375995	−	0.651242i	0.990475	+	0.137690i	$0.0439677\pi$
$462$	1.30991	−	1.76033i	0.0609425	−	0.0818981i
$463$	−8.50000	−	14.7224i	−0.395029	−	0.684209i	0.598076	−	0.801439i	$-0.295932\pi$
$463$	−8.50000	−	14.7224i	−0.395029	−	0.684209i	−0.993105	+	0.117230i	$0.962599\pi$
$464$	−10.2180	+	11.3482i	−0.474357	+	0.526827i
$465$	0.777739	−	1.07047i	0.0360668	−	0.0496417i
$466$	−0.444165	−	4.22595i	−0.0205755	−	0.195763i
$467$	−0.236068	+	0.726543i	−0.0109239	+	0.0336204i	−0.956370	−	0.292159i	$-0.905627\pi$
$467$	−0.236068	+	0.726543i	−0.0109239	+	0.0336204i	0.945446	+	0.325779i	$0.105627\pi$
$468$	35.2133	−	7.48482i	1.62774	−	0.345986i
$469$	4.85410	−	3.52671i	0.224142	−	0.162848i
$470$	5.15178	−	2.29372i	0.237634	−	0.105801i
$471$	−2.57334	+	12.1066i	−0.118573	+	0.557842i
$472$	−1.19098	−	2.06284i	−0.0548194	−	0.0949500i
$473$	5.01586	−	3.55749i	0.230630	−	0.163574i
$474$	−6.05166	−	3.49393i	−0.277962	−	0.160481i
$475$	3.39626	+	0.721898i	0.155831	+	0.0331229i
$476$	−7.28115	−	5.29007i	−0.333731	−	0.242470i
$477$	1.28262	+	12.2033i	0.0587270	+	0.558750i
$478$	−1.23607	+	3.80423i	−0.0565364	+	0.174001i
$479$	−7.87161	−	8.74231i	−0.359663	−	0.399446i	0.535972	−	0.844236i	$-0.319945\pi$
$479$	−7.87161	−	8.74231i	−0.359663	−	0.399446i	−0.895635	+	0.444789i	$0.853278\pi$
$480$	5.21723	+	7.18091i	0.238133	+	0.327762i
$481$	−3.44361	+	32.7638i	−0.157015	+	1.49390i
$482$	6.85807	−	7.61666i	0.312376	−	0.346929i
$483$	6.92705	−	3.99933i	0.315192	−	0.181976i
$484$	−5.85811	−	19.5357i	−0.266278	−	0.887986i
$485$	−7.41641			−0.336762
$486$	4.42488	+	3.98418i	0.200717	+	0.180726i
$487$	10.5000	+	7.62870i	0.475800	+	0.345689i	0.799698	−	0.600403i	$-0.204993\pi$
$487$	10.5000	+	7.62870i	0.475800	+	0.345689i	−0.323897	+	0.946092i	$0.604993\pi$
$488$	−1.67023	−	15.8912i	−0.0756078	−	0.719360i
$489$	7.45731	+	35.0839i	0.337231	+	1.58655i
$490$	2.77091	−	0.588976i	0.125177	−	0.0266072i
$491$	6.69285	+	2.97985i	0.302044	+	0.134479i	0.552162	−	0.833737i	$-0.313803\pi$
$491$	6.69285	+	2.97985i	0.302044	+	0.134479i	−0.250118	+	0.968215i	$0.580469\pi$
$492$	−4.77163	+	6.56758i	−0.215122	+	0.296090i
$493$	23.0474	+	4.89888i	1.03800	+	0.220634i
$494$	2.47214			0.111227
$495$	−11.1776	−	5.13023i	−0.502397	−	0.230587i
$496$	1.94427			0.0873004
$497$	−2.84624	−	0.604988i	−0.127671	−	0.0271374i
$498$	−2.62738	−	5.90120i	−0.117736	−	0.264439i
$499$	35.0951	+	15.6254i	1.57107	+	0.699487i	0.993176	−	0.116622i	$-0.0372066\pi$
$499$	35.0951	+	15.6254i	1.57107	+	0.699487i	0.577898	+	0.816109i	$0.303873\pi$
$500$	18.9921	−	4.03690i	0.849353	−	0.180536i
$501$	−7.41913	+	6.68021i	−0.331462	+	0.298450i
$502$	0.820977	+	7.81108i	0.0366420	+	0.348625i
$503$	7.70820	+	5.60034i	0.343692	+	0.249707i	0.746218	−	0.665702i	$-0.231868\pi$
$503$	7.70820	+	5.60034i	0.343692	+	0.249707i	−0.402526	+	0.915409i	$0.631868\pi$
$504$	2.95515	−	3.28203i	0.131633	−	0.146193i
$505$	10.4721			0.466004
$506$	−0.677881	+	5.81089i	−0.0301355	+	0.258326i
$507$		−	50.0364i		−	2.22220i
$508$	13.1040	−	14.5534i	0.581395	−	0.645705i
$509$	2.84112	−	27.0314i	0.125930	−	1.19815i	−0.730876	−	0.682510i	$-0.760888\pi$
$509$	2.84112	−	27.0314i	0.125930	−	1.19815i	0.856807	−	0.515638i	$-0.172445\pi$
$510$	1.61454	−	3.62633i	0.0714932	−	0.160576i
$511$	0.0976248	+	0.108423i	0.00431867	+	0.00479637i
$512$	−6.89261	+	21.2133i	−0.304613	+	0.937503i
$513$	−3.05422	−	4.20378i	−0.134847	−	0.185601i
$514$	−4.60739	−	3.34747i	−0.203223	−	0.147650i
$515$	−12.3760	−	2.63060i	−0.545351	−	0.115918i
$516$	5.15654	−	2.97713i	0.227004	−	0.131061i
$517$	−39.6121	−	0.452084i	−1.74214	−	0.0198826i
$518$	0.972136	+	1.68379i	0.0427132	+	0.0739814i
$519$	−38.0359	+	12.3586i	−1.66959	+	0.542483i
$520$	10.7589	−	4.79017i	0.471809	−	0.210063i
$521$	32.6525	−	23.7234i	1.43053	−	1.03934i	0.440613	−	0.897697i	$-0.354761\pi$
$521$	32.6525	−	23.7234i	1.43053	−	1.03934i	0.989918	−	0.141645i	$-0.0452390\pi$
$522$	−1.71885	+	5.29007i	−0.0752319	+	0.231540i
$523$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$523$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$524$	4.11569	+	39.1581i	0.179795	+	1.71063i
$525$	−2.44608	−	5.49399i	−0.106756	−	0.239777i
$526$	3.24803	−	3.60730i	0.141621	−	0.157286i
$527$	−1.50000	−	2.59808i	−0.0653410	−	0.113174i
$528$	−3.55537	−	17.7186i	−0.154727	−	0.771104i
$529$	0.836881	−	1.44952i	0.0363861	−	0.0630226i
$530$	0.596748	+	1.83660i	0.0259211	+	0.0797768i
$531$	3.92705	+	2.85317i	0.170419	+	0.123817i
$532$	−1.50000	+	1.08981i	−0.0650332	+	0.0472494i
$533$	10.9474	+	12.1584i	0.474186	+	0.526637i
$534$	−4.25590	−	1.38282i	−0.184171	−	0.0598407i
$535$	−15.8478	−	7.05587i	−0.685158	−	0.305052i
$536$	−0.923281	+	8.78443i	−0.0398797	+	0.379430i
$537$	6.50755	+	5.85943i	0.280822	+	0.252853i
$538$	−4.06231	+	7.03612i	−0.175138	+	0.303349i
$539$	−19.4164	−	4.35926i	−0.836324	−	0.187766i
$540$	−10.3131	−	5.95426i	−0.443804	−	0.256231i
$541$	−3.68034	−	11.3269i	−0.158230	−	0.486982i	0.840244	−	0.542209i	$-0.182412\pi$
$541$	−3.68034	−	11.3269i	−0.158230	−	0.486982i	−0.998474	+	0.0552266i	$0.982412\pi$
$542$	−3.75600	+	1.67228i	−0.161334	+	0.0718306i
$543$	−6.98136	+	15.6804i	−0.299599	+	0.672910i
$544$	19.6848	−	4.18414i	0.843981	−	0.179394i
$545$	8.63980	−	1.83645i	0.370088	−	0.0786647i
$546$	−2.51682	−	3.46410i	−0.107710	−	0.148250i
$547$	−29.5315	+	13.1483i	−1.26268	+	0.562179i	−0.925316	−	0.379197i	$-0.876200\pi$
$547$	−29.5315	+	13.1483i	−1.26268	+	0.562179i	−0.337359	+	0.941376i	$0.609534\pi$
$548$	4.93769	+	15.1967i	0.210928	+	0.649169i
$549$	16.2812	+	28.1998i	0.694863	+	1.20354i
$550$	4.29180	+	0.963568i	0.183003	+	0.0410867i
$551$	2.42705	−	4.20378i	0.103396	−	0.179087i
$552$	−2.44819	+	11.5178i	−0.104202	+	0.490231i
$553$	1.10406	−	10.5044i	0.0469495	−	0.446694i
$554$	6.71230	+	2.98851i	0.285178	+	0.126970i
$555$	8.09858	−	7.29199i	0.343765	−	0.309528i
$556$	−12.0444	−	13.3766i	−0.510794	−	0.567294i
$557$	0.527864	−	0.383516i	0.0223663	−	0.0162501i	−0.576546	−	0.817065i	$-0.695600\pi$
$557$	0.527864	−	0.383516i	0.0223663	−	0.0162501i	0.598912	+	0.800815i	$0.295600\pi$
$558$	0.646976	−	0.288052i	0.0273887	−	0.0121942i
$559$	−3.70820	−	11.4127i	−0.156840	−	0.482705i
$560$	−1.94427	+	3.36758i	−0.0821605	+	0.142306i
$561$	−20.9339	+	18.4208i	−0.883832	+	0.777727i
$562$	−1.78115	−	3.08505i	−0.0751334	−	0.130135i
$563$	−13.5867	+	15.0895i	−0.572610	+	0.635947i	−0.957987	−	0.286812i	$-0.907405\pi$
$563$	−13.5867	+	15.0895i	−0.572610	+	0.635947i	0.385377	+	0.922759i	$0.374071\pi$
$564$	−38.1477	−	4.00948i	−1.60631	−	0.168830i
$565$	2.22697	+	21.1882i	0.0936895	+	0.891396i
$566$	2.00658	−	6.17561i	0.0843428	−	0.259580i
$567$	−2.78115	+	8.55951i	−0.116797	+	0.359466i
$568$	3.46556	−	2.51788i	0.145412	−	0.105648i
$569$	35.4441	−	15.7807i	1.48589	−	0.661562i	0.506264	−	0.862378i	$-0.331026\pi$
$569$	35.4441	−	15.7807i	1.48589	−	0.661562i	0.979629	+	0.200816i	$0.0643594\pi$
$570$	−0.607717	−	0.547191i	−0.0254545	−	0.0229193i
$571$	9.26393	+	16.0456i	0.387683	+	0.671488i	0.992138	−	0.125153i	$-0.0399420\pi$
$571$	9.26393	+	16.0456i	0.387683	+	0.671488i	−0.604454	+	0.796640i	$0.706609\pi$
$572$	−39.7969	−	0.454194i	−1.66399	−	0.0189908i
$573$		−	10.2958i		−	0.430112i
$574$	0.944458	+	0.200751i	0.0394209	+	0.00837918i
$575$	12.9721	+	9.42481i	0.540975	+	0.393042i
$576$	−1.47642	−	14.0472i	−0.0615177	−	0.585301i
$577$	10.9443	−	33.6830i	0.455616	−	1.40224i	−0.414794	−	0.909915i	$-0.636147\pi$
$577$	10.9443	−	33.6830i	0.455616	−	1.40224i	0.870410	−	0.492327i	$-0.163853\pi$
$578$	−1.67723	−	1.86275i	−0.0697635	−	0.0774802i
$579$	18.9482	−	1.99153i	0.787460	−	0.0827654i
$580$	1.16284	−	11.0637i	0.0482842	−	0.459394i
$581$	6.53335	−	7.25602i	0.271049	−	0.301030i
$582$	−3.43769	−	1.98475i	−0.142497	−	0.0822707i
$583$	1.57186	−	13.4742i	0.0650997	−	0.558044i
$584$	−0.214782			−0.00888773
$585$	−16.0591	+	17.8355i	−0.663963	+	0.737406i
$586$	−9.01722	−	6.55139i	−0.372498	−	0.270636i
$587$	−1.40240	−	13.3429i	−0.0578831	−	0.550721i	−0.984583	−	0.174918i	$-0.944034\pi$
$587$	−1.40240	−	13.3429i	−0.0578831	−	0.550721i	0.926700	−	0.375802i	$-0.122633\pi$
$588$	−18.3253	−	5.95426i	−0.755724	−	0.245550i
$589$	−0.604528	+	0.128496i	−0.0249092	+	0.00529461i
$590$	0.697887	+	0.310719i	0.0287315	+	0.0127921i
$591$	14.1871	+	1.49113i	0.583581	+	0.0613368i
$592$	15.6632	+	3.32932i	0.643755	+	0.136834i
$593$	−10.9443			−0.449427			−0.224714	−	0.974425i	$-0.572145\pi$
$593$	−10.9443			−0.449427			−0.224714	+	0.974425i	$0.572145\pi$
$594$	−3.80818	−	5.36931i	−0.156251	−	0.220306i
$595$	6.00000			0.245976
$596$	−27.5308	−	5.85186i	−1.12771	−	0.239702i
$597$	−12.3093	−	1.29375i	−0.503784	−	0.0529499i
$598$	10.4294	+	4.64347i	0.426490	+	0.189886i
$599$	13.0687	−	2.77784i	0.533973	−	0.113500i	0.0669698	−	0.997755i	$-0.478667\pi$
$599$	13.0687	−	2.77784i	0.533973	−	0.113500i	0.467003	+	0.884255i	$0.345334\pi$
$600$	8.41999	+	2.73582i	0.343745	+	0.111689i
$601$	1.82634	+	17.3764i	0.0744978	+	0.708799i	0.966482	+	0.256733i	$0.0826461\pi$
$601$	1.82634	+	17.3764i	0.0744978	+	0.708799i	−0.891985	+	0.452066i	$0.850687\pi$
$602$	−0.572949	−	0.416272i	−0.0233517	−	0.0169660i
$603$	−5.56231	−	17.1190i	−0.226515	−	0.697140i
$604$	−8.02129			−0.326382
$605$	10.8147	+	8.24093i	0.439682	+	0.335042i
$606$	4.85410	+	2.80252i	0.197184	+	0.113844i
$607$	−2.39789	+	2.66313i	−0.0973274	+	0.108093i	−0.789841	−	0.613312i	$-0.789837\pi$
$607$	−2.39789	+	2.66313i	−0.0973274	+	0.108093i	0.692513	+	0.721405i	$0.256503\pi$
$608$	0.433364	−	4.12319i	0.0175752	−	0.167217i
$609$	−8.36149	+	0.878828i	−0.338825	+	0.0356119i
$610$	3.42903	+	3.80833i	0.138838	+	0.154195i
$611$	−23.8885	+	73.5214i	−0.966427	+	2.97436i
$612$	−21.8435	+	15.8702i	−0.882969	+	0.641515i
$613$	−16.0623	−	11.6699i	−0.648750	−	0.471345i	0.214095	−	0.976813i	$-0.431320\pi$
$613$	−16.0623	−	11.6699i	−0.648750	−	0.471345i	−0.862845	+	0.505468i	$0.831320\pi$
$614$	2.93444	+	0.623735i	0.118424	+	0.0251719i
$615$		−	5.41199i		−	0.218232i
$616$	−3.98254	+	2.82461i	−0.160461	+	0.113807i
$617$	13.5795	+	23.5204i	0.546691	+	0.946897i	0.998498	+	0.0547813i	$0.0174462\pi$
$617$	13.5795	+	23.5204i	0.546691	+	0.946897i	−0.451807	+	0.892116i	$0.649221\pi$
$618$	−5.03259	−	4.53137i	−0.202441	−	0.182278i
$619$	25.1794	−	11.2106i	1.01205	−	0.450592i	0.167384	−	0.985892i	$-0.446468\pi$
$619$	25.1794	−	11.2106i	1.01205	−	0.450592i	0.844662	+	0.535300i	$0.179801\pi$
$620$	−1.14590	+	0.832544i	−0.0460204	+	0.0334358i
$621$	−4.98905	−	23.4716i	−0.200204	−	0.941884i
$622$	−1.79180	+	5.51458i	−0.0718445	+	0.221115i
$623$	−0.707023	−	6.72688i	−0.0283263	−	0.269507i
$624$	−35.0725	−	3.68627i	−1.40403	−	0.147569i
$625$	2.95515	−	3.28203i	0.118206	−	0.131281i
$626$	0.663119	+	1.14856i	0.0265036	+	0.0459055i
$627$	2.27648	+	5.27424i	0.0909140	+	0.210633i
$628$	6.62461	−	11.4742i	0.264351	−	0.457869i
$629$	−7.63525	−	23.4989i	−0.304438	−	0.936962i
$630$	−0.148055	+	1.40865i	−0.00589865	+	0.0561219i
$631$	8.80902	−	6.40013i	0.350681	−	0.254785i	−0.398473	−	0.917180i	$-0.630460\pi$
$631$	8.80902	−	6.40013i	0.350681	−	0.254785i	0.749155	+	0.662395i	$0.230460\pi$
$632$	10.4044	+	11.5553i	0.413865	+	0.459644i
$633$	26.3510	−	23.7266i	1.04736	−	0.943046i
$634$	−7.30836	−	3.25389i	−0.290252	−	0.129229i
$635$	−1.36470	+	12.9842i	−0.0541563	+	0.515263i
$636$	2.73095	−	12.8481i	0.108289	−	0.509462i
$637$	−19.4164	+	33.6302i	−0.769306	+	1.33248i
$638$	3.13525	−	5.29007i	0.124126	−	0.209436i
$639$	−4.36475	+	7.55996i	−0.172667	+	0.299067i
$640$	−3.85410	−	11.8617i	−0.152347	−	0.468875i
$641$	−18.6828	+	8.31811i	−0.737925	+	0.328546i	−0.741050	−	0.671450i	$-0.765672\pi$
$641$	−18.6828	+	8.31811i	−0.737925	+	0.328546i	0.00312481	+	0.999995i	$0.499005\pi$
$642$	−5.45757	−	7.51170i	−0.215393	−	0.296463i
$643$	6.70432	−	1.42505i	0.264393	−	0.0561984i	−0.0738078	−	0.997272i	$-0.523515\pi$
$643$	6.70432	−	1.42505i	0.264393	−	0.0561984i	0.338200	+	0.941074i	$0.390182\pi$
$644$	−8.37520	+	1.78020i	−0.330029	+	0.0701498i
$645$	−1.61454	+	3.62633i	−0.0635726	+	0.142786i
$646$	−1.69381	+	0.754131i	−0.0666419	+	0.0296709i
$647$	−1.29180	−	3.97574i	−0.0507857	−	0.156302i	0.922447	−	0.386123i	$-0.126186\pi$
$647$	−1.29180	−	3.97574i	−0.0507857	−	0.156302i	−0.973233	+	0.229821i	$0.926186\pi$
$648$	−6.62461	−	11.4742i	−0.260239	−	0.450748i
$649$	−3.54508	−	4.02874i	−0.139157	−	0.158142i
$650$	4.29180	−	7.43361i	0.168338	−	0.291570i
$651$	0.795511	+	0.716282i	0.0311786	+	0.0280733i
$652$	4.01338	−	38.1848i	0.157176	−	1.49543i
$653$	−1.24304	−	0.553438i	−0.0486440	−	0.0216577i	0.382270	−	0.924050i	$-0.375142\pi$
$653$	−1.24304	−	0.553438i	−0.0486440	−	0.0216577i	−0.430914	+	0.902393i	$0.641809\pi$
$654$	4.49623	+	1.46091i	0.175816	+	0.0571262i
$655$	−17.5642	−	19.5070i	−0.686288	−	0.762201i
$656$	6.43363	−	4.67430i	0.251191	−	0.182501i
$657$	0.399853	−	0.178026i	0.0155998	−	0.00694546i
$658$	1.40983	+	4.33901i	0.0549609	+	0.169152i
$659$	−4.98936	+	8.64182i	−0.194358	+	0.336637i	−0.946690	−	0.322147i	$-0.895596\pi$
$659$	−4.98936	+	8.64182i	−0.194358	+	0.336637i	0.752332	+	0.658784i	$0.228929\pi$
$660$	9.68260	+	8.92043i	0.376895	+	0.347227i
$661$	2.14590	+	3.71680i	0.0834658	+	0.144567i	0.904736	−	0.425972i	$-0.140068\pi$
$661$	2.14590	+	3.71680i	0.0834658	+	0.144567i	−0.821271	+	0.570539i	$0.806734\pi$
$662$	−3.68462	+	4.09218i	−0.143207	+	0.159047i
$663$	22.1325	+	49.7104i	0.859555	+	1.93059i
$664$	1.50247	+	14.2951i	0.0583073	+	0.554757i
$665$	0.381966	−	1.17557i	0.0148120	−	0.0455867i
$666$	5.70535	−	1.21271i	0.221078	−	0.0469916i
$667$	18.1353	−	13.1760i	0.702200	−	0.510178i
$668$	9.76299	−	4.34676i	0.377741	−	0.168181i
$669$	−25.5436	+	8.29963i	−0.987574	+	0.320882i
$670$	−1.41641	−	2.45329i	−0.0547206	−	0.0947789i
$671$	−10.7329	−	34.3618i	−0.414337	−	1.32652i
$672$	−6.21885	+	3.59045i	−0.239897	+	0.138505i
$673$	28.9163	+	6.14635i	1.11464	+	0.236924i	0.728183	−	0.685383i	$-0.240365\pi$
$673$	28.9163	+	6.14635i	1.11464	+	0.236924i	0.386458	+	0.922307i	$0.373698\pi$
$674$	−3.54508	−	2.57565i	−0.136552	−	0.0992105i
$675$	−17.9429	+	1.88588i	−0.690623	+	0.0725874i
$676$	−16.5517	+	50.9408i	−0.636602	+	1.95926i
$677$	4.05207	+	4.50028i	0.155734	+	0.172960i	0.815963	−	0.578105i	$-0.196207\pi$
$677$	4.05207	+	4.50028i	0.155734	+	0.172960i	−0.660229	+	0.751064i	$0.729541\pi$
$678$	−4.63807	+	10.4173i	−0.178124	+	0.400073i
$679$	0.627171	−	5.96713i	0.0240686	−	0.228997i
$680$	−5.91031	+	6.56406i	−0.226650	+	0.251720i
$681$			28.7833i			1.10298i
$682$	−0.767647	+	0.154034i	−0.0293947	+	0.00589826i
$683$	−5.52786			−0.211518			−0.105759	−	0.994392i	$-0.533727\pi$
$683$	−5.52786			−0.211518			−0.105759	+	0.994392i	$0.533727\pi$
$684$	1.71885	+	5.29007i	0.0657218	+	0.202271i
$685$	−8.61803	−	6.26137i	−0.329278	−	0.239235i
$686$	0.519042	+	4.93836i	0.0198171	+	0.188547i
$687$	13.1038	−	11.7987i	0.499940	−	0.450148i
$688$	−5.70535	+	1.21271i	−0.217515	+	0.0462342i
$689$	−24.1835	−	10.7672i	−0.921318	−	0.410197i
$690$	−1.53602	−	3.44997i	−0.0584755	−	0.131338i
$691$	−14.2778	−	3.03483i	−0.543152	−	0.115451i	−0.0718386	−	0.997416i	$-0.522887\pi$
$691$	−14.2778	−	3.03483i	−0.543152	−	0.115451i	−0.471314	+	0.881966i	$0.656220\pi$
$692$	42.8115			1.62745
$693$	5.07295	−	8.55951i	0.192705	−	0.325149i
$694$	3.39512			0.128877
$695$	11.7378	+	2.49494i	0.445239	+	0.0946385i
$696$	7.27505	−	10.0133i	0.275760	−	0.379551i
$697$	−11.2097	−	4.99087i	−0.424596	−	0.189043i
$698$	−1.54899	+	0.329247i	−0.0586300	+	0.0124622i
$699$	−4.00612	−	18.8473i	−0.151526	−	0.712872i
$700$	0.672922	+	6.40243i	0.0254341	+	0.241989i
$701$	38.6074	+	28.0499i	1.45818	+	1.05943i	0.983832	+	0.179094i	$0.0573165\pi$
$701$	38.6074	+	28.0499i	1.45818	+	1.05943i	0.474349	+	0.880337i	$0.342683\pi$
$702$	−12.2169	+	3.96951i	−0.461097	+	0.149819i
$703$	−5.09017			−0.191979
$704$	−1.80937	+	15.5102i	−0.0681931	+	0.584561i
$705$	22.1459	−	12.7859i	0.834063	−	0.481546i
$706$	4.19579	−	4.65990i	0.157911	−	0.175378i
$707$	−0.885579	+	8.42572i	−0.0333056	+	0.316882i
$708$	−3.05422	−	4.20378i	−0.114785	−	0.157988i
$709$	−17.2394	−	19.1463i	−0.647441	−	0.719056i	0.326667	−	0.945139i	$-0.394074\pi$
$709$	−17.2394	−	19.1463i	−0.647441	−	0.719056i	−0.974108	+	0.226084i	$0.927408\pi$
$710$	−0.424538	+	1.30660i	−0.0159326	+	0.0490356i
$711$	−28.9474	−	12.8882i	−1.08561	−	0.483346i
$712$	8.05573	+	5.85283i	0.301901	+	0.219344i
$713$	−2.79173	−	0.593401i	−0.104551	−	0.0222230i
$714$	2.78115	+	1.60570i	0.104082	+	0.0600918i
$715$	21.6422	−	15.3497i	0.809373	−	0.574047i
$716$	−4.68692	−	8.11798i	−0.175158	−	0.303383i
$717$	−3.77116	+	17.7419i	−0.140837	+	0.662584i
$718$	7.97479	−	3.55060i	0.297616	−	0.132507i
$719$	15.8541	−	11.5187i	0.591258	−	0.429574i	−0.251507	−	0.967855i	$-0.580926\pi$
$719$	15.8541	−	11.5187i	0.591258	−	0.429574i	0.842765	+	0.538281i	$0.180926\pi$
$720$	7.80583	+	8.66925i	0.290906	+	0.323084i
$721$	3.16312	−	9.73508i	0.117801	−	0.362553i
$722$	−0.718674	−	6.83772i	−0.0267463	−	0.254474i
$723$	27.3178	−	37.5997i	1.01596	−	1.39835i
$724$	12.2945	−	13.6544i	0.456921	−	0.507463i
$725$	−8.42705	−	14.5961i	−0.312973	−	0.542085i
$726$	2.80750	+	6.71409i	0.104196	+	0.249183i
$727$	−9.41641	+	16.3097i	−0.349235	+	0.604893i	−0.986114	−	0.166071i	$-0.946892\pi$
$727$	−9.41641	+	16.3097i	−0.349235	+	0.604893i	0.636879	+	0.770964i	$0.280225\pi$
$728$	2.94427	+	9.06154i	0.109122	+	0.335843i
$729$	21.8435	+	15.8702i	0.809017	+	0.587785i
$730$	0.0557281	−	0.0404888i	0.00206259	−	0.00149856i
$731$	6.02218	+	6.68830i	0.222738	+	0.247376i
$732$	−7.24715	−	34.0951i	−0.267862	−	1.26019i
$733$	44.2815	+	19.7154i	1.63557	+	0.728205i	0.999072	−	0.0430700i	$-0.0137138\pi$
$733$	44.2815	+	19.7154i	1.63557	+	0.728205i	0.636502	+	0.771275i	$0.280381\pi$
$734$	−0.507392	+	4.82751i	−0.0187282	+	0.178187i
$735$	12.2169	−	3.96951i	0.450627	−	0.146417i
$736$	9.57295	−	16.5808i	0.352864	−	0.611178i
$737$	1.85410	+	19.8132i	0.0682967	+	0.729828i
$738$	1.44834	−	2.50859i	0.0533140	−	0.0923426i
$739$	13.1459	+	40.4589i	0.483580	+	1.48831i	0.834027	+	0.551723i	$0.186029\pi$
$739$	13.1459	+	40.4589i	0.483580	+	1.48831i	−0.350448	+	0.936582i	$0.613971\pi$
$740$	−10.6571	+	4.74484i	−0.391762	+	0.174424i
$741$	11.1487	−	1.17177i	0.409556	−	0.0430461i
$742$	−1.52817	+	0.324822i	−0.0561007	+	0.0119246i
$743$	41.4350	−	8.80728i	1.52010	−	0.323108i	0.629179	−	0.777261i	$-0.283391\pi$
$743$	41.4350	−	8.80728i	1.52010	−	0.323108i	0.890924	+	0.454153i	$0.150058\pi$
$744$	−1.56724	+	0.164723i	−0.0574578	+	0.00603906i
$745$	17.1417	−	7.63198i	0.628023	−	0.279614i
$746$	0.667184	+	2.05338i	0.0244274	+	0.0751797i
$747$	−14.6459	−	25.3674i	−0.535865	−	0.928146i
$748$	27.4058	−	11.8290i	1.00205	−	0.432509i
$749$	7.01722	−	12.1542i	0.256404	−	0.444104i
$750$	−6.58911	+	2.14093i	−0.240600	+	0.0781758i
$751$	3.26643	−	31.0780i	0.119194	−	1.13405i	−0.757443	−	0.652901i	$-0.773552\pi$
$751$	3.26643	−	31.0780i	0.119194	−	1.13405i	0.876637	−	0.481152i	$-0.159782\pi$
$752$	34.3269	+	15.2833i	1.25177	+	0.557325i
$753$	7.40477	+	34.8367i	0.269845	+	1.26952i
$754$	−8.02957	−	8.91774i	−0.292420	−	0.324765i
$755$	4.32624	−	3.14320i	0.157448	−	0.114393i
$756$	5.66284	−	7.79423i	0.205955	−	0.283473i
$757$	3.39919	+	10.4616i	0.123546	+	0.380234i	0.993633	−	0.112663i	$-0.0359380\pi$
$757$	3.39919	+	10.4616i	0.123546	+	0.380234i	−0.870088	+	0.492897i	$0.835938\pi$
$758$	3.01722	−	5.22598i	0.109590	−	0.189816i
$759$	−0.302745	+	26.5269i	−0.0109890	+	0.962864i
$760$	0.909830	+	1.57587i	0.0330030	+	0.0571629i
$761$	4.66967	−	5.18620i	0.169275	−	0.187999i	−0.652538	−	0.757756i	$-0.726296\pi$
$761$	4.66967	−	5.18620i	0.169275	−	0.187999i	0.821814	+	0.569756i	$0.192962\pi$
$762$	−4.10736	+	5.65330i	−0.148794	+	0.204797i
$763$	0.746950	+	7.10675i	0.0270414	+	0.257282i
$764$	−3.40576	+	10.4819i	−0.123216	+	0.379221i
$765$	5.56231	−	17.1190i	0.201106	−	0.618939i
$766$	6.13525	−	4.45752i	0.221676	−	0.161057i
$767$	−9.56677	+	4.25940i	−0.345436	+	0.153798i
$768$	−2.00306	+	9.42367i	−0.0722793	+	0.340047i
$769$	7.89919	+	13.6818i	0.284852	+	0.493378i	0.972573	−	0.232597i	$-0.0747222\pi$
$769$	7.89919	+	13.6818i	0.284852	+	0.493378i	−0.687721	+	0.725975i	$0.741389\pi$
$770$	0.500853	−	1.48364i	0.0180495	−	0.0534666i
$771$	−22.3647	−	12.9123i	−0.805447	−	0.465025i
$772$	−19.9494	−	4.24038i	−0.717996	−	0.152615i
$773$	−19.1353	−	13.9026i	−0.688247	−	0.500041i	0.187836	−	0.982200i	$-0.439853\pi$
$773$	−19.1353	−	13.9026i	−0.688247	−	0.500041i	−0.876083	+	0.482159i	$0.839853\pi$
$774$	−1.71885	+	1.24882i	−0.0617827	+	0.0448877i
$775$	−0.663119	+	2.04087i	−0.0238199	+	0.0733102i
$776$	5.91031	+	6.56406i	0.212168	+	0.235636i
$777$	5.18217	+	7.13264i	0.185909	+	0.255882i
$778$	−0.904430	+	8.60508i	−0.0324254	+	0.308507i
$779$	−1.69147	+	1.87857i	−0.0606032	+	0.0673067i
$780$	22.2492	−	12.8456i	0.796650	−	0.459946i
$781$	6.53908	−	7.09779i	0.233987	−	0.253979i
$782$	−8.56231			−0.306187
$783$	−5.24408	+	24.6715i	−0.187408	+	0.881687i
$784$	15.2705	+	11.0947i	0.545375	+	0.396238i
$785$	0.923281	+	8.78443i	0.0329533	+	0.313530i
$786$	−2.92105	−	13.7424i	−0.104190	−	0.490177i
$787$	−35.2133	+	7.48482i	−1.25522	+	0.266805i	−0.787081	−	0.616850i	$-0.788408\pi$
$787$	−35.2133	+	7.48482i	−1.25522	+	0.266805i	−0.468138	+	0.883655i	$0.655075\pi$
$788$	−13.9503	−	6.21108i	−0.496959	−	0.221260i
$789$	12.9379	−	17.8075i	0.460601	−	0.633963i
$790$	−4.87787	−	1.03682i	−0.173547	−	0.0368885i
$791$	−17.2361			−0.612844
$792$	4.36708	+	13.9814i	0.155177	+	0.496808i
$793$	−70.2492			−2.49462
$794$	−0.793796	−	0.168726i	−0.0281708	−	0.00598788i
$795$	3.56170	+	7.99971i	0.126321	+	0.283721i
$796$	12.1038	+	5.38894i	0.429007	+	0.191006i
$797$	−23.7401	+	5.04612i	−0.840919	+	0.178743i	−0.608183	−	0.793797i	$-0.708101\pi$
$797$	−23.7401	+	5.04612i	−0.840919	+	0.178743i	−0.232736	+	0.972540i	$0.574768\pi$
$798$	0.491653	−	0.442686i	0.0174043	−	0.0156709i
$799$	−6.06043	−	57.6611i	−0.214402	−	2.03990i
$800$	−11.6459	−	8.46124i	−0.411745	−	0.299150i
$801$	−19.8484	−	4.21890i	−0.701308	−	0.149068i
$802$	−5.56231			−0.196412
$803$	−0.474432	+	0.0951981i	−0.0167423	+	0.00335947i
$804$			19.2684i			0.679544i
$805$	3.81953	−	4.24202i	0.134621	−	0.149512i
$806$	−0.159705	+	1.51949i	−0.00562538	+	0.0535219i
$807$	−14.9848	+	33.6565i	−0.527491	+	1.18476i
$808$	−8.34549	−	9.26860i	−0.293593	−	0.326068i
$809$	−5.59017	+	17.2048i	−0.196540	+	0.604888i	0.803415	+	0.595419i	$0.203014\pi$
$809$	−5.59017	+	17.2048i	−0.196540	+	0.604888i	−0.999955	+	0.00946853i	$0.996986\pi$
$810$	3.88186	+	1.72831i	0.136395	+	0.0607268i
$811$	−7.02786	−	5.10604i	−0.246782	−	0.179297i	0.457518	−	0.889201i	$-0.348739\pi$
$811$	−7.02786	−	5.10604i	−0.246782	−	0.179297i	−0.704299	+	0.709903i	$0.748739\pi$
$812$	8.80333	+	1.87121i	0.308936	+	0.0656664i
$813$	−16.1459	+	9.32184i	−0.566261	+	0.326931i
$814$	−6.44800	−	0.0735897i	−0.226002	−	0.00257932i
$815$	12.7984	+	22.1674i	0.448307	+	0.776491i
$816$	25.1548	−	8.17328i	0.880593	−	0.286122i
$817$	1.69381	−	0.754131i	0.0592588	−	0.0263837i
$818$	−10.4271	+	7.57570i	−0.364573	+	0.264878i
$819$	−12.9921	−	14.4292i	−0.453981	−	0.504197i
$820$	−1.79024	+	5.50980i	−0.0625180	+	0.192411i
$821$	−3.99453	−	38.0054i	−0.139410	−	1.32640i	−0.810813	−	0.585306i	$-0.800974\pi$
$821$	−3.99453	−	38.0054i	−0.139410	−	1.32640i	0.671402	−	0.741093i	$-0.265692\pi$
$822$	−2.31903	−	5.20863i	−0.0808855	−	0.181672i
$823$	−28.2987	+	31.4289i	−0.986432	+	1.09554i	0.00898947	+	0.999960i	$0.497139\pi$
$823$	−28.2987	+	31.4289i	−0.986432	+	1.09554i	−0.995421	+	0.0955840i	$0.969528\pi$
$824$	7.53444	+	13.0500i	0.262475	+	0.454620i
$825$	19.8116	+	2.31116i	0.689750	+	0.0804641i
$826$	−0.309017	+	0.535233i	−0.0107521	+	0.0186231i
$827$	−17.6246	−	54.2430i	−0.612868	−	1.88621i	−0.429147	−	0.903235i	$-0.641186\pi$
$827$	−17.6246	−	54.2430i	−0.612868	−	1.88621i	−0.183721	−	0.982978i	$-0.558814\pi$
$828$	−2.68501	+	25.5462i	−0.0933107	+	0.887792i
$829$	−35.2254	+	25.5928i	−1.22343	+	0.888874i	−0.996380	−	0.0850096i	$-0.972908\pi$
$829$	−35.2254	+	25.5928i	−1.22343	+	0.888874i	−0.227049	+	0.973883i	$0.572908\pi$
$830$	−3.08463	−	3.42583i	−0.107069	−	0.118912i
$831$	31.6872	+	10.2958i	1.09922	+	0.357157i
$832$	27.8377	+	12.3941i	0.965098	+	0.429689i
$833$	3.04435	−	28.9651i	0.105481	−	1.00358i
$834$	4.77307	+	4.29769i	0.165278	+	0.148817i
$835$	−3.56231	+	6.17009i	−0.123279	+	0.213525i
$836$	−0.572949	−	6.12261i	−0.0198159	−	0.211755i
$837$	2.78115	−	1.60570i	0.0961307	−	0.0555011i
$838$	−0.954915	−	2.93893i	−0.0329870	−	0.101524i
$839$	−15.7968	+	7.03321i	−0.545368	+	0.242813i	−0.660878	−	0.750493i	$-0.729816\pi$
$839$	−15.7968	+	7.03321i	−0.545368	+	0.242813i	0.115511	+	0.993306i	$0.463149\pi$
$840$	1.28193	−	2.87926i	0.0442308	−	0.0993439i
$841$	5.31887	−	1.13056i	0.183409	−	0.0389848i
$842$	3.82439	−	0.812899i	0.131797	−	0.0280144i
$843$	−9.49480	−	13.0685i	−0.327018	−	0.450102i
$844$	−34.6758	+	15.4387i	−1.19359	+	0.531421i
$845$	−11.0344	−	33.9605i	−0.379596	−	1.16828i
$846$	13.6869			0.470566
$847$	−7.54508	+	8.00448i	−0.259252	+	0.275037i
$848$	−6.43363	+	11.1434i	−0.220932	+	0.382665i
$849$	6.12193	−	28.8014i	0.210104	−	0.988462i
$850$	−0.672922	+	6.40243i	−0.0230810	+	0.219601i
$851$	−21.4743	−	9.56099i	−0.736130	−	0.327746i
$852$	6.94441	−	6.25277i	0.237912	−	0.214217i
$853$	−23.7124	−	26.3353i	−0.811899	−	0.901705i	0.184810	−	0.982774i	$-0.440833\pi$
$853$	−23.7124	−	26.3353i	−0.811899	−	0.901705i	−0.996708	+	0.0810695i	$0.974166\pi$
$854$	−3.35410	+	2.43690i	−0.114775	+	0.0833889i
$855$	−3.00000	−	2.17963i	−0.102598	−	0.0745417i
$856$	6.38448	+	19.6494i	0.218217	+	0.671603i
$857$	−12.6803	+	21.9630i	−0.433152	+	0.750242i	−0.997143	−	0.0755396i	$-0.975932\pi$
$857$	−12.6803	+	21.9630i	−0.433152	+	0.750242i	0.563991	+	0.825781i	$0.309265\pi$
$858$	14.1396	−	1.32317i	0.482717	−	0.0451722i
$859$	16.2812	+	28.1998i	0.555506	+	0.962164i	0.997864	+	0.0653258i	$0.0208087\pi$
$859$	16.2812	+	28.1998i	0.555506	+	0.962164i	−0.442358	+	0.896838i	$0.645858\pi$
$860$	2.84329	−	3.15779i	0.0969552	−	0.107680i
$861$	4.35440	+	0.457666i	0.148398	+	0.0155972i
$862$	−1.36025	−	12.9419i	−0.0463301	−	0.440802i
$863$	4.46556	−	13.7436i	0.152009	−	0.467837i	−0.845836	−	0.533443i	$-0.820898\pi$
$863$	4.46556	−	13.7436i	0.152009	−	0.467837i	0.997846	+	0.0656059i	$0.0208980\pi$
$864$	4.47898	+	21.0720i	0.152378	+	0.716883i
$865$	−23.0902	+	16.7760i	−0.785089	+	0.570401i
$866$	−5.14435	+	2.29041i	−0.174812	+	0.0778313i
$867$	−8.44677	−	7.60550i	−0.286867	−	0.258296i
$868$	−0.572949	−	0.992377i	−0.0194472	−	0.0336835i
$869$	28.1040	+	20.9129i	0.953363	+	0.709422i
$870$			3.96951i			0.134579i
$871$	37.9842	+	8.07380i	1.28705	+	0.273570i
$872$	−8.51064	−	6.18334i	−0.288207	−	0.209394i
$873$	−16.4438	−	7.32126i	−0.556539	−	0.247787i
$874$	−0.545085	+	1.67760i	−0.0184378	+	0.0567456i
$875$	−7.00723	−	7.78231i	−0.236887	−	0.263090i
$876$	−0.465970	+	0.0489754i	−0.0157437	+	0.00165473i
$877$	−1.21219	+	11.5332i	−0.0409328	+	0.389449i	0.954806	+	0.297230i	$0.0960628\pi$
$877$	−1.21219	+	11.5332i	−0.0409328	+	0.389449i	−0.995739	+	0.0922193i	$0.970604\pi$
$878$	0.181006	−	0.201028i	0.00610867	−	0.00678437i
$879$	−43.7705	−	25.2709i	−1.47634	−	0.852367i
$880$	−6.32054	−	11.2419i	−0.213065	−	0.378963i
$881$	1.81966			0.0613059			0.0306530	−	0.999530i	$-0.490241\pi$
$881$	1.81966			0.0613059			0.0306530	+	0.999530i	$0.490241\pi$
$882$	6.72514	+	1.42947i	0.226447	+	0.0481329i
$883$	28.8435	+	20.9560i	0.970660	+	0.705226i	0.955602	−	0.294661i	$-0.0952068\pi$
$883$	28.8435	+	20.9560i	0.970660	+	0.705226i	0.0150579	+	0.999887i	$0.495207\pi$
$884$	−6.08870	−	57.9301i	−0.204785	−	1.94840i
$885$	3.29456	+	1.07047i	0.110745	+	0.0359833i
$886$	−0.461819	+	0.0981626i	−0.0155151	+	0.00329784i
$887$	−3.68565	−	1.64096i	−0.123752	−	0.0550979i	0.343927	−	0.938997i	$-0.388243\pi$
$887$	−3.68565	−	1.64096i	−0.123752	−	0.0550979i	−0.467679	+	0.883899i	$0.654910\pi$
$888$	−12.9079	−	1.35667i	−0.433160	−	0.0455270i
$889$	−10.3315	−	2.19603i	−0.346507	−	0.0736524i
$890$	−3.19350			−0.107046
$891$	−19.7188	−	22.4091i	−0.660606	−	0.750733i
$892$	28.7508			0.962647
$893$	−11.6833	−	2.48335i	−0.390965	−	0.0831023i
$894$	9.98806	+	1.04979i	0.334051	+	0.0351101i
$895$	5.70895	+	2.54179i	0.190829	+	0.0849626i
$896$	9.86968	−	2.09786i	0.329723	−	0.0700847i
$897$	49.2347	+	15.9973i	1.64390	+	0.534136i
$898$	0.298335	+	2.83847i	0.00995556	+	0.0947209i
$899$	2.42705	+	1.76336i	0.0809467	+	0.0588112i
$900$	18.8910	+	4.01542i	0.629702	+	0.133847i
$901$	19.8541			0.661436
$902$	−2.16984	+	2.35523i	−0.0722477	+	0.0784207i
$903$	−2.78115	−	1.60570i	−0.0925510	−	0.0534343i
$904$	16.9784	−	18.8564i	0.564694	−	0.627156i
$905$	−1.28039	+	12.1821i	−0.0425617	+	0.404947i
$906$	2.84649	−	0.299178i	0.0945684	−	0.00993954i
$907$	−9.75833	−	10.8377i	−0.324020	−	0.359861i	0.559024	−	0.829152i	$-0.311176\pi$
$907$	−9.75833	−	10.8377i	−0.324020	−	0.359861i	−0.883043	+	0.469291i	$0.844509\pi$
$908$	9.52129	−	29.3035i	0.315975	−	0.972471i
$909$	23.2190	+	10.3378i	0.770127	+	0.342883i
$910$	−2.47214	−	1.79611i	−0.0819505	−	0.0595405i
$911$	18.7612	+	3.98782i	0.621586	+	0.132122i	0.507931	−	0.861398i	$-0.330411\pi$
$911$	18.7612	+	3.98782i	0.621586	+	0.132122i	0.113656	+	0.993520i	$0.463744\pi$
$912$		−	5.44886i		−	0.180430i
$913$	9.65487	+	30.9105i	0.319529	+	1.02299i
$914$	−0.190983	−	0.330792i	−0.00631716	−	0.0109416i
$915$	17.2691	+	15.5492i	0.570900	+	0.514040i
$916$	−17.2435	+	7.67731i	−0.569742	+	0.253666i
$917$	17.1803	−	12.4822i	0.567345	−	0.412200i
$918$	7.15960	−	6.44654i	0.236302	−	0.212767i
$919$	−8.30244	+	25.5523i	−0.273872	+	0.842892i	0.715643	+	0.698466i	$0.246134\pi$
$919$	−8.30244	+	25.5523i	−0.273872	+	0.842892i	−0.989516	+	0.144426i	$0.953866\pi$
$920$	0.878379	+	8.35722i	0.0289593	+	0.275529i
$921$	13.5292	+	1.42197i	0.445802	+	0.0468556i
$922$	4.12665	−	4.58311i	0.135904	−	0.150937i
$923$	−9.41641	−	16.3097i	−0.309945	−	0.536840i
$924$	−7.99606	+	7.03612i	−0.263051	+	0.231471i
$925$	−8.83688	+	15.3059i	−0.290555	+	0.503256i
$926$	−2.00658	−	6.17561i	−0.0659402	−	0.202943i
$927$	−24.8435	−	18.0498i	−0.815966	−	0.592834i
$928$	−16.2812	+	11.8290i	−0.534455	+	0.388304i
$929$	−32.2993	−	35.8720i	−1.05970	−	1.17692i	−0.983701	−	0.179814i	$-0.942450\pi$
$929$	−32.2993	−	35.8720i	−1.05970	−	1.17692i	−0.0760042	−	0.997107i	$-0.524216\pi$
$930$	0.375590	−	0.338182i	0.0123161	−	0.0110894i
$931$	−5.48127	−	2.44042i	−0.179641	−	0.0799815i
$932$	−2.15602	+	20.5132i	−0.0706228	+	0.671931i
$933$	−5.46665	+	25.7186i	−0.178970	+	0.841988i
$934$	−0.145898	+	0.252703i	−0.00477393	+	0.00826869i
$935$	−10.1459	+	17.1190i	−0.331806	+	0.559852i
$936$	28.5836			0.934284
$937$	−7.11803	−	21.9071i	−0.232536	−	0.715672i	−0.997439	−	0.0715265i	$-0.977213\pi$
$937$	−7.11803	−	21.9071i	−0.232536	−	0.715672i	0.764903	−	0.644146i	$-0.222787\pi$
$938$	2.09366	−	0.932157i	0.0683604	−	0.0304360i
$939$	3.53489	+	4.86536i	0.115357	+	0.158775i
$940$	−26.7757	+	5.69134i	−0.873325	+	0.185631i
$941$	−26.5656	+	5.64668i	−0.866013	+	0.184077i	−0.619436	−	0.785047i	$-0.712639\pi$
$941$	−26.5656	+	5.64668i	−0.866013	+	0.184077i	−0.246576	+	0.969123i	$0.579306\pi$
$942$	−1.92289	+	4.31889i	−0.0626513	+	0.140717i
$943$	−10.6645	+	4.74815i	−0.347284	+	0.154621i
$944$	1.57295	+	4.84104i	0.0511951	+	0.157562i
$945$			6.42280i			0.208934i
$946$	2.15654	−	0.930812i	0.0701152	−	0.0302633i
$947$	−18.3541	+	31.7902i	−0.596428	+	1.03304i	0.396915	+	0.917855i	$0.370081\pi$
$947$	−18.3541	+	31.7902i	−0.596428	+	1.03304i	−0.993344	+	0.115189i	$0.963253\pi$
$948$	25.2073	+	22.6968i	0.818695	+	0.737157i
$949$	−0.0987033	+	0.939099i	−0.00320404	+	0.0304844i
$950$	1.21158	+	0.539430i	0.0393088	+	0.0175014i
$951$	−34.5010	−	11.2101i	−1.11877	−	0.363511i
$952$	−4.78154	−	5.31044i	−0.154971	−	0.172112i
$953$	7.68034	−	5.58009i	0.248791	−	0.180757i	−0.456400	−	0.889775i	$-0.650861\pi$
$953$	7.68034	−	5.58009i	0.248791	−	0.180757i	0.705191	+	0.709018i	$0.250861\pi$
$954$	−0.489916	+	4.66124i	−0.0158616	+	0.150913i
$955$	−2.27051	−	6.98791i	−0.0734720	−	0.226123i
$956$	9.70820	−	16.8151i	0.313986	−	0.543839i
$957$	11.6317	−	25.3428i	0.375999	−	0.819218i
$958$	−2.24671	−	3.89142i	−0.0725879	−	0.125726i
$959$	5.76659	−	6.40445i	0.186213	−	0.206810i
$960$	−4.09988	−	9.20849i	−0.132323	−	0.297203i
$961$	3.20046	+	30.4503i	0.103241	+	0.982268i
$962$	−3.88854	+	11.9677i	−0.125372	+	0.385854i
$963$	−28.1726	−	31.2889i	−0.907850	−	1.00827i
$964$	−40.2492	+	29.2428i	−1.29634	+	0.941846i
$965$	12.4212	−	5.53030i	0.399854	−	0.178027i
$966$	2.90569	−	0.944115i	0.0934889	−	0.0303764i
$967$	−26.2426	−	45.4536i	−0.843907	−	1.46169i	−0.886567	−	0.462599i	$-0.846917\pi$
$967$	−26.2426	−	45.4536i	−0.843907	−	1.46169i	0.0426608	−	0.999090i	$-0.486417\pi$
$968$	−1.32469	−	16.1392i	−0.0425771	−	0.518734i
$969$	−7.28115	+	4.20378i	−0.233904	+	0.135045i
$970$	−2.77091	−	0.588976i	−0.0889686	−	0.0189109i
$971$	−7.50000	−	5.44907i	−0.240686	−	0.174869i	0.460903	−	0.887451i	$-0.347526\pi$
$971$	−7.50000	−	5.44907i	−0.240686	−	0.174869i	−0.701589	+	0.712582i	$0.747526\pi$
$972$	−16.9885	−	23.3827i	−0.544907	−	0.750000i
$973$	−3.00000	+	9.23305i	−0.0961756	+	0.295998i
$974$	3.31717	+	3.68409i	0.106289	+	0.118046i
$975$	15.8314	−	35.5578i	0.507009	−	1.13876i
$976$	−3.56922	+	33.9588i	−0.114248	+	1.08700i
$977$	10.5481	−	11.7149i	0.337465	−	0.374792i	−0.550397	−	0.834903i	$-0.685524\pi$
$977$	10.5481	−	11.7149i	0.337465	−	0.374792i	0.887862	+	0.460111i	$0.152190\pi$
$978$			13.7002i			0.438085i
$979$	20.3885	+	9.35778i	0.651619	+	0.299076i
$980$	−13.7508			−0.439252
$981$	20.9692	+	4.45715i	0.669496	+	0.142306i
$982$	2.26393	+	1.64484i	0.0722450	+	0.0524890i
$983$	−0.967657	−	9.20664i	−0.0308635	−	0.293646i	−0.999056	−	0.0434400i	$-0.986168\pi$
$983$	−0.967657	−	9.20664i	−0.0308635	−	0.293646i	0.968193	−	0.250206i	$-0.0804984\pi$
$984$	−4.79000	+	4.31294i	−0.152700	+	0.137491i
$985$	9.95788	−	2.11661i	0.317284	−	0.0674409i
$986$	8.22191	+	3.66063i	0.261839	+	0.116578i
$987$	8.41460	+	18.8995i	0.267840	+	0.601578i
$988$	−11.7378	−	2.49494i	−0.373428	−	0.0793746i
$989$	8.56231			0.272265
$990$	−3.76876	−	2.80443i	−0.119779	−	0.0891305i
$991$	20.5967			0.654277			0.327139	−	0.944976i	$-0.393916\pi$
$991$	20.5967			0.654277			0.327139	+	0.944976i	$0.393916\pi$
$992$	2.50631	+	0.532733i	0.0795755	+	0.0169143i
$993$	−14.6770	+	20.2011i	−0.465760	+	0.641063i
$994$	−1.01537	−	0.452070i	−0.0322054	−	0.0143388i
$995$	−8.63980	+	1.83645i	−0.273900	+	0.0582192i
$996$	6.51925	+	30.6707i	0.206570	+	0.971838i
$997$	−0.771626	−	7.34153i	−0.0244376	−	0.232508i	−0.999923	−	0.0124424i	$-0.996039\pi$
$997$	−0.771626	−	7.34153i	−0.0244376	−	0.232508i	0.975485	−	0.220066i	$-0.0706273\pi$
$998$	11.8713	+	8.62502i	0.375780	+	0.273020i
$999$	25.1548	−	8.17328i	0.795862	−	0.258591i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.2.m.a.16.1	✓	8
3.2	odd	2		297.2.n.a.181.1		8
9.2	odd	6		891.2.f.a.82.1		4
9.4	even	3	inner	99.2.m.a.49.1	yes	8
9.5	odd	6		297.2.n.a.280.1		8
9.7	even	3		891.2.f.b.82.1		4
11.3	even	5		1089.2.e.g.727.1		4
11.8	odd	10		1089.2.e.d.727.2		4
11.9	even	5	inner	99.2.m.a.97.1	yes	8
33.20	odd	10		297.2.n.a.262.1		8
99.20	odd	30		891.2.f.a.163.1		4
99.25	even	15		9801.2.a.n.1.2		2
99.31	even	15	inner	99.2.m.a.31.1	yes	8
99.47	odd	30		9801.2.a.bb.1.1		2
99.52	odd	30		9801.2.a.bc.1.1		2
99.58	even	15		1089.2.e.g.364.1		4
99.74	even	30		9801.2.a.m.1.2		2
99.85	odd	30		1089.2.e.d.364.2		4
99.86	odd	30		297.2.n.a.64.1		8
99.97	even	15		891.2.f.b.163.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.m.a.16.1	✓	8	1.1	even	1	trivial
99.2.m.a.31.1	yes	8	99.31	even	15	inner
99.2.m.a.49.1	yes	8	9.4	even	3	inner
99.2.m.a.97.1	yes	8	11.9	even	5	inner
297.2.n.a.64.1		8	99.86	odd	30
297.2.n.a.181.1		8	3.2	odd	2
297.2.n.a.262.1		8	33.20	odd	10
297.2.n.a.280.1		8	9.5	odd	6
891.2.f.a.82.1		4	9.2	odd	6
891.2.f.a.163.1		4	99.20	odd	30
891.2.f.b.82.1		4	9.7	even	3
891.2.f.b.163.1		4	99.97	even	15
1089.2.e.d.364.2		4	99.85	odd	30
1089.2.e.d.727.2		4	11.8	odd	10
1089.2.e.g.364.1		4	99.58	even	15
1089.2.e.g.727.1		4	11.3	even	5
9801.2.a.m.1.2		2	99.74	even	30
9801.2.a.n.1.2		2	99.25	even	15
9801.2.a.bb.1.1		2	99.47	odd	30
9801.2.a.bc.1.1		2	99.52	odd	30

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:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	99.m (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.373619 + 0.0794152i) q^{2} +(1.72256 + 0.181049i) q^{3} +(-1.69381 - 0.754131i) q^{4} +(1.20906 - 0.256993i) q^{5} +(0.629204 + 0.204441i) q^{6} +(0.104528 + 0.994522i) q^{7} +(-1.19098 - 0.865300i) q^{8} +(2.93444 + 0.623735i) q^{9} +0.472136 q^{10} +(-3.01430 - 1.38348i) q^{11} +(-2.78115 - 1.60570i) q^{12} +(-4.33070 + 4.80973i) q^{13} +(-0.0399263 + 0.379874i) q^{14} +(2.12920 - 0.223788i) q^{15} +(2.10502 + 2.33786i) q^{16} +(1.50000 - 4.61653i) q^{17} +(1.04683 + 0.466079i) q^{18} +(-0.809017 - 0.587785i) q^{19} +(-2.24171 - 0.476491i) q^{20} +1.73205i q^{21} +(-1.01633 - 0.756276i) q^{22} +(-2.30902 - 3.99933i) q^{23} +(-1.89488 - 1.70616i) q^{24} +(-3.17195 + 1.41224i) q^{25} +(-2.00000 + 1.45309i) q^{26} +(4.94183 + 1.60570i) q^{27} +(0.572949 - 1.76336i) q^{28} +(0.507392 + 4.82751i) q^{29} +(0.813284 + 0.0854796i) q^{30} +(0.413545 - 0.459289i) q^{31} +(2.07295 + 3.59045i) q^{32} +(-4.94183 - 2.92887i) q^{33} +(0.927051 - 1.60570i) q^{34} +(0.381966 + 1.17557i) q^{35} +(-4.50000 - 3.26944i) q^{36} +(4.11803 - 2.99193i) q^{37} +(-0.255585 - 0.283856i) q^{38} +(-8.33070 + 7.50100i) q^{39} +(-1.66234 - 0.740122i) q^{40} +(0.264234 - 2.51402i) q^{41} +(-0.137551 + 0.647127i) q^{42} +(-0.927051 + 1.60570i) q^{43} +(4.06231 + 4.61653i) q^{44} +3.70820 q^{45} +(-0.545085 - 1.67760i) q^{46} +(10.9116 - 4.85817i) q^{47} +(3.20276 + 4.40822i) q^{48} +(5.86889 - 1.24747i) q^{49} +(-1.29726 + 0.275740i) q^{50} +(3.41966 - 7.68068i) q^{51} +(10.9625 - 4.88084i) q^{52} +(1.26393 + 3.88998i) q^{53} +(1.71885 + 0.992377i) q^{54} +(-4.00000 - 0.898056i) q^{55} +(0.736068 - 1.27491i) q^{56} +(-1.28716 - 1.15897i) q^{57} +(-0.193806 + 1.84395i) q^{58} +(1.47815 + 0.658114i) q^{59} +(-3.77523 - 1.22665i) q^{60} +(7.26281 + 8.06617i) q^{61} +(0.190983 - 0.138757i) q^{62} +(-0.313585 + 2.98357i) q^{63} +(-1.45492 - 4.47777i) q^{64} +(-4.00000 + 6.92820i) q^{65} +(-1.61377 - 1.48674i) q^{66} +(-3.00000 - 5.19615i) q^{67} +(-6.02218 + 6.68830i) q^{68} +(-3.25335 - 7.30715i) q^{69} +(0.0493516 + 0.469550i) q^{70} +(-0.899187 + 2.76741i) q^{71} +(-2.95515 - 3.28203i) q^{72} +(0.118034 - 0.0857567i) q^{73} +(1.77618 - 0.790807i) q^{74} +(-5.71957 + 1.85840i) q^{75} +(0.927051 + 1.60570i) q^{76} +(1.06082 - 3.14240i) q^{77} +(-3.70820 + 2.14093i) q^{78} +(-10.3315 - 2.19603i) q^{79} +(3.14590 + 2.28563i) q^{80} +(8.22191 + 3.66063i) q^{81} +(0.298374 - 0.918300i) q^{82} +(-6.53335 - 7.25602i) q^{83} +(1.30619 - 2.93376i) q^{84} +(0.627171 - 5.96713i) q^{85} +(-0.473881 + 0.526298i) q^{86} +8.40755i q^{87} +(2.39285 + 4.25597i) q^{88} -6.76393 q^{89} +(1.38546 + 0.294488i) q^{90} +(-5.23607 - 3.80423i) q^{91} +(0.895005 + 8.51540i) q^{92} +(0.795511 - 0.716282i) q^{93} +(4.46261 - 0.948557i) q^{94} +(-1.12920 - 0.502754i) q^{95} +(2.92074 + 6.56008i) q^{96} +(-5.86889 - 1.24747i) q^{97} +2.29180 q^{98} +(-7.98235 - 5.93987i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} + 3 q^{3} - 6 q^{4} + 6 q^{5} - q^{7} - 14 q^{8} - 3 q^{9} - 32 q^{10} + q^{11} + 18 q^{12} + 8 q^{13} - q^{14} + 12 q^{15} + 14 q^{16} + 12 q^{17} - 3 q^{18} - 2 q^{19} + 24 q^{20} + 11 q^{22}+ \cdots - 3 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 + 3 * q^3 - 6 * q^4 + 6 * q^5 - q^7 - 14 * q^8 - 3 * q^9 - 32 * q^10 + q^11 + 18 * q^12 + 8 * q^13 - q^14 + 12 * q^15 + 14 * q^16 + 12 * q^17 - 3 * q^18 - 2 * q^19 + 24 * q^20 + 11 * q^22 - 14 * q^23 - 39 * q^24 - 9 * q^25 - 16 * q^26 + 18 * q^28 - 9 * q^29 + 18 * q^30 - 3 * q^31 + 30 * q^32 - 6 * q^34 + 12 * q^35 - 36 * q^36 + 24 * q^37 - 4 * q^38 - 24 * q^39 + 12 * q^40 + 3 * q^41 - 12 * q^42 + 6 * q^43 - 48 * q^44 - 24 * q^45 + 18 * q^46 + 23 * q^47 - 6 * q^49 - 24 * q^50 + 27 * q^51 + 12 * q^52 + 28 * q^53 + 54 * q^54 - 32 * q^55 - 12 * q^56 + 3 * q^57 + 6 * q^58 + 3 * q^59 + 6 * q^62 + 3 * q^63 - 34 * q^64 - 32 * q^65 + 12 * q^66 - 24 * q^67 - 9 * q^68 - 18 * q^69 - 6 * q^70 + 42 * q^71 + 39 * q^72 - 8 * q^73 + 13 * q^74 - 6 * q^76 - 11 * q^77 + 24 * q^78 - 22 * q^79 + 52 * q^80 + 9 * q^81 - 96 * q^82 - 17 * q^83 + 18 * q^84 - 6 * q^85 + 21 * q^86 + 37 * q^88 - 72 * q^89 + 42 * q^90 - 24 * q^91 - 21 * q^92 + 9 * q^93 + 28 * q^94 - 4 * q^95 + 6 * q^97 + 72 * q^98 - 3 * q^99

Introduction

L-functions

Modular forms

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