LMFDB - Embedded newform 297.2.n.a.64.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [297,2,Mod(37,297)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(297, 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("297.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 297 = 3^{3} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	297.n (of order $15$, degree $8$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.37155694003$
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:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			64.1
Root			$0.669131 + 0.743145i$ of defining polynomial
Character	$\chi$	$=$	297.64
Dual form			297.2.n.a.181.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.373619 + 0.0794152i) q^{2} +(-1.69381 + 0.754131i) q^{4} +(-1.20906 - 0.256993i) q^{5} +(0.104528 - 0.994522i) q^{7} +(1.19098 - 0.865300i) q^{8} +0.472136 q^{10} +(3.01430 - 1.38348i) q^{11} +(-4.33070 - 4.80973i) q^{13} +(0.0399263 + 0.379874i) q^{14} +(2.10502 - 2.33786i) q^{16} +(-1.50000 - 4.61653i) q^{17} +(-0.809017 + 0.587785i) q^{19} +(2.24171 - 0.476491i) q^{20} +(-1.01633 + 0.756276i) q^{22} +(2.30902 - 3.99933i) q^{23} +(-3.17195 - 1.41224i) q^{25} +(2.00000 + 1.45309i) q^{26} +(0.572949 + 1.76336i) q^{28} +(-0.507392 + 4.82751i) q^{29} +(0.413545 + 0.459289i) q^{31} +(-2.07295 + 3.59045i) q^{32} +(0.927051 + 1.60570i) q^{34} +(-0.381966 + 1.17557i) q^{35} +(4.11803 + 2.99193i) q^{37} +(0.255585 - 0.283856i) q^{38} +(-1.66234 + 0.740122i) q^{40} +(-0.264234 - 2.51402i) q^{41} +(-0.927051 - 1.60570i) q^{43} +(-4.06231 + 4.61653i) q^{44} +(-0.545085 + 1.67760i) q^{46} +(-10.9116 - 4.85817i) q^{47} +(5.86889 + 1.24747i) q^{49} +(1.29726 + 0.275740i) q^{50} +(10.9625 + 4.88084i) q^{52} +(-1.26393 + 3.88998i) q^{53} +(-4.00000 + 0.898056i) q^{55} +(-0.736068 - 1.27491i) q^{56} +(-0.193806 - 1.84395i) q^{58} +(-1.47815 + 0.658114i) q^{59} +(7.26281 - 8.06617i) q^{61} +(-0.190983 - 0.138757i) q^{62} +(-1.45492 + 4.47777i) q^{64} +(4.00000 + 6.92820i) q^{65} +(-3.00000 + 5.19615i) q^{67} +(6.02218 + 6.68830i) q^{68} +(0.0493516 - 0.469550i) q^{70} +(0.899187 + 2.76741i) q^{71} +(0.118034 + 0.0857567i) q^{73} +(-1.77618 - 0.790807i) q^{74} +(0.927051 - 1.60570i) q^{76} +(-1.06082 - 3.14240i) q^{77} +(-10.3315 + 2.19603i) q^{79} +(-3.14590 + 2.28563i) q^{80} +(0.298374 + 0.918300i) q^{82} +(6.53335 - 7.25602i) q^{83} +(0.627171 + 5.96713i) q^{85} +(0.473881 + 0.526298i) q^{86} +(2.39285 - 4.25597i) q^{88} +6.76393 q^{89} +(-5.23607 + 3.80423i) q^{91} +(-0.895005 + 8.51540i) q^{92} +(4.46261 + 0.948557i) q^{94} +(1.12920 - 0.502754i) q^{95} +(-5.86889 + 1.24747i) q^{97} -2.29180 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} - 6 q^{4} - 6 q^{5} - q^{7} + 14 q^{8} - 32 q^{10} - q^{11} + 8 q^{13} + q^{14} + 14 q^{16} - 12 q^{17} - 2 q^{19} - 24 q^{20} + 11 q^{22} + 14 q^{23} - 9 q^{25} + 16 q^{26} + 18 q^{28}+ \cdots - 72 q^{98}+O(q^{100}) $ 8 * q + 4 * q^2 - 6 * q^4 - 6 * q^5 - q^7 + 14 * q^8 - 32 * q^10 - q^11 + 8 * q^13 + q^14 + 14 * q^16 - 12 * q^17 - 2 * q^19 - 24 * q^20 + 11 * q^22 + 14 * q^23 - 9 * q^25 + 16 * q^26 + 18 * q^28 + 9 * q^29 - 3 * q^31 - 30 * q^32 - 6 * q^34 - 12 * q^35 + 24 * q^37 + 4 * q^38 + 12 * q^40 - 3 * q^41 + 6 * q^43 + 48 * q^44 + 18 * q^46 - 23 * q^47 - 6 * q^49 + 24 * q^50 + 12 * q^52 - 28 * q^53 - 32 * q^55 + 12 * q^56 + 6 * q^58 - 3 * q^59 - 6 * q^62 - 34 * q^64 + 32 * q^65 - 24 * q^67 + 9 * q^68 - 6 * q^70 - 42 * q^71 - 8 * q^73 - 13 * q^74 - 6 * q^76 + 11 * q^77 - 22 * q^79 - 52 * q^80 - 96 * q^82 + 17 * q^83 - 6 * q^85 - 21 * q^86 + 37 * q^88 + 72 * q^89 - 24 * q^91 + 21 * q^92 + 28 * q^94 + 4 * q^95 + 6 * q^97 - 72 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/297\mathbb{Z}\right)^\times$.

$n$	$56$	$244$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{5}\right)$

Coefficient data

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

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

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

$2$	−0.373619	+	0.0794152i	−0.264189	+	0.0561550i	−0.338101	−	0.941110i	$-0.609785\pi$
$2$	−0.373619	+	0.0794152i	−0.264189	+	0.0561550i	0.0739128	+	0.997265i	$0.476451\pi$
$3$		0			0
$3$		0			0
$4$	−1.69381	+	0.754131i	−0.846903	+	0.377066i
$5$	−1.20906	−	0.256993i	−0.540707	−	0.114931i	−0.0705409	−	0.997509i	$-0.522473\pi$
$5$	−1.20906	−	0.256993i	−0.540707	−	0.114931i	−0.470166	+	0.882578i	$0.655806\pi$
$6$		0			0
$7$	0.104528	−	0.994522i	0.0395080	−	0.375894i	−0.956847	−	0.290592i	$-0.906148\pi$
$7$	0.104528	−	0.994522i	0.0395080	−	0.375894i	0.996355	−	0.0853021i	$-0.0271855\pi$
$8$	1.19098	−	0.865300i	0.421076	−	0.305930i
$9$		0			0
$10$	0.472136			0.149302
$11$	3.01430	−	1.38348i	0.908844	−	0.417136i
$11$	3.01430	−	1.38348i	0.908844	−	0.417136i
$12$		0			0
$13$	−4.33070	−	4.80973i	−1.20112	−	1.33398i	−0.928262	−	0.371926i	$-0.878697\pi$
$13$	−4.33070	−	4.80973i	−1.20112	−	1.33398i	−0.272859	−	0.962054i	$-0.587969\pi$
$14$	0.0399263	+	0.379874i	0.0106708	+	0.101525i
$15$		0			0
$16$	2.10502	−	2.33786i	0.526254	−	0.584464i
$17$	−1.50000	−	4.61653i	−0.363803	−	1.11967i	−0.950727	−	0.310029i	$-0.899661\pi$
$17$	−1.50000	−	4.61653i	−0.363803	−	1.11967i	0.586924	−	0.809642i	$-0.300339\pi$
$18$		0			0
$19$	−0.809017	+	0.587785i	−0.185601	+	0.134847i	−0.676706	−	0.736253i	$-0.736593\pi$
$19$	−0.809017	+	0.587785i	−0.185601	+	0.134847i	0.491105	+	0.871100i	$0.336593\pi$
$20$	2.24171	−	0.476491i	0.501263	−	0.106547i
$21$		0			0
$22$	−1.01633	+	0.756276i	−0.216682	+	0.161239i
$23$	2.30902	−	3.99933i	0.481463	−	0.833919i	−0.518310	−	0.855193i	$-0.673439\pi$
$23$	2.30902	−	3.99933i	0.481463	−	0.833919i	0.999774	+	0.0212736i	$0.00677212\pi$
$24$		0			0
$25$	−3.17195	−	1.41224i	−0.634391	−	0.282449i
$26$	2.00000	+	1.45309i	0.392232	+	0.284973i
$27$		0			0
$28$	0.572949	+	1.76336i	0.108277	+	0.333243i
$29$	−0.507392	+	4.82751i	−0.0942203	+	0.896446i	0.840679	+	0.541534i	$0.182156\pi$
$29$	−0.507392	+	4.82751i	−0.0942203	+	0.896446i	−0.934899	+	0.354913i	$0.884511\pi$
$30$		0			0
$31$	0.413545	+	0.459289i	0.0742750	+	0.0824907i	0.779137	−	0.626854i	$-0.215658\pi$
$31$	0.413545	+	0.459289i	0.0742750	+	0.0824907i	−0.704862	+	0.709345i	$0.748991\pi$
$32$	−2.07295	+	3.59045i	−0.366449	+	0.634708i
$33$		0			0
$34$	0.927051	+	1.60570i	0.158988	+	0.275375i
$35$	−0.381966	+	1.17557i	−0.0645640	+	0.198708i
$36$		0			0
$37$	4.11803	+	2.99193i	0.677001	+	0.491870i	0.872361	−	0.488862i	$-0.162588\pi$
$37$	4.11803	+	2.99193i	0.677001	+	0.491870i	−0.195361	+	0.980731i	$0.562588\pi$
$38$	0.255585	−	0.283856i	0.0414614	−	0.0460475i
$39$		0			0
$40$	−1.66234	+	0.740122i	−0.262839	+	0.117024i
$41$	−0.264234	−	2.51402i	−0.0412664	−	0.392623i	−0.995587	−	0.0938399i	$-0.970086\pi$
$41$	−0.264234	−	2.51402i	−0.0412664	−	0.392623i	0.954321	−	0.298783i	$-0.0965808\pi$
$42$		0			0
$43$	−0.927051	−	1.60570i	−0.141374	−	0.244867i	0.786640	−	0.617412i	$-0.211819\pi$
$43$	−0.927051	−	1.60570i	−0.141374	−	0.244867i	−0.928014	+	0.372545i	$0.878485\pi$
$44$	−4.06231	+	4.61653i	−0.612416	+	0.695967i
$45$		0			0
$46$	−0.545085	+	1.67760i	−0.0803684	+	0.247348i
$47$	−10.9116	−	4.85817i	−1.59163	−	0.708637i	−0.596081	−	0.802925i	$-0.703276\pi$
$47$	−10.9116	−	4.85817i	−1.59163	−	0.708637i	−0.995545	+	0.0942873i	$0.969943\pi$
$48$		0			0
$49$	5.86889	+	1.24747i	0.838412	+	0.178210i
$50$	1.29726	+	0.275740i	0.183460	+	0.0389956i
$51$		0			0
$52$	10.9625	+	4.88084i	1.52023	+	0.676851i
$53$	−1.26393	+	3.88998i	−0.173614	+	0.534330i	−0.999567	−	0.0294087i	$-0.990638\pi$
$53$	−1.26393	+	3.88998i	−0.173614	+	0.534330i	0.825953	+	0.563739i	$0.190638\pi$
$54$		0			0
$55$	−4.00000	+	0.898056i	−0.539360	+	0.121094i
$56$	−0.736068	−	1.27491i	−0.0983612	−	0.170367i
$57$		0			0
$58$	−0.193806	−	1.84395i	−0.0254480	−	0.242122i
$59$	−1.47815	+	0.658114i	−0.192438	+	0.0856791i	−0.500694	−	0.865625i	$-0.666922\pi$
$59$	−1.47815	+	0.658114i	−0.192438	+	0.0856791i	0.308255	+	0.951304i	$0.400255\pi$
$60$		0			0
$61$	7.26281	−	8.06617i	0.929908	−	1.03277i	−0.0694731	−	0.997584i	$-0.522132\pi$
$61$	7.26281	−	8.06617i	0.929908	−	1.03277i	0.999381	−	0.0351834i	$-0.0112015\pi$
$62$	−0.190983	−	0.138757i	−0.0242549	−	0.0176222i
$63$		0			0
$64$	−1.45492	+	4.47777i	−0.181864	+	0.559721i
$65$	4.00000	+	6.92820i	0.496139	+	0.859338i
$66$		0			0
$67$	−3.00000	+	5.19615i	−0.366508	+	0.634811i	−0.989017	−	0.147802i	$-0.952780\pi$
$67$	−3.00000	+	5.19615i	−0.366508	+	0.634811i	0.622509	+	0.782613i	$0.286114\pi$
$68$	6.02218	+	6.68830i	0.730296	+	0.811076i
$69$		0			0
$70$	0.0493516	−	0.469550i	0.00589865	−	0.0561219i
$71$	0.899187	+	2.76741i	0.106714	+	0.328431i	0.990129	−	0.140160i	$-0.0447617\pi$
$71$	0.899187	+	2.76741i	0.106714	+	0.328431i	−0.883415	+	0.468591i	$0.844762\pi$
$72$		0			0
$73$	0.118034	+	0.0857567i	0.0138148	+	0.0100371i	0.594671	−	0.803969i	$-0.297282\pi$
$73$	0.118034	+	0.0857567i	0.0138148	+	0.0100371i	−0.580856	+	0.814006i	$0.697282\pi$
$74$	−1.77618	−	0.790807i	−0.206477	−	0.0919294i
$75$		0			0
$76$	0.927051	−	1.60570i	0.106340	−	0.184186i
$77$	−1.06082	−	3.14240i	−0.120892	−	0.358109i
$78$		0			0
$79$	−10.3315	+	2.19603i	−1.16238	+	0.247072i	−0.748423	−	0.663222i	$-0.769188\pi$
$79$	−10.3315	+	2.19603i	−1.16238	+	0.247072i	−0.413961	+	0.910294i	$0.635855\pi$
$80$	−3.14590	+	2.28563i	−0.351722	+	0.255541i
$81$		0			0
$82$	0.298374	+	0.918300i	0.0329499	+	0.101409i
$83$	6.53335	−	7.25602i	0.717128	−	0.796451i	−0.268876	−	0.963175i	$-0.586652\pi$
$83$	6.53335	−	7.25602i	0.717128	−	0.796451i	0.986004	+	0.166724i	$0.0533188\pi$
$84$		0			0
$85$	0.627171	+	5.96713i	0.0680262	+	0.647226i
$86$	0.473881	+	0.526298i	0.0510999	+	0.0567522i
$87$		0			0
$88$	2.39285	−	4.25597i	0.255078	−	0.453688i
$89$	6.76393			0.716975			0.358488	−	0.933534i	$-0.383293\pi$
$89$	6.76393			0.716975			0.358488	+	0.933534i	$0.383293\pi$
$90$		0			0
$91$	−5.23607	+	3.80423i	−0.548889	+	0.398791i
$92$	−0.895005	+	8.51540i	−0.0933107	+	0.887792i
$93$		0			0
$94$	4.46261	+	0.948557i	0.460283	+	0.0978362i
$95$	1.12920	−	0.502754i	0.115854	−	0.0515815i
$96$		0			0
$97$	−5.86889	+	1.24747i	−0.595895	+	0.126661i	−0.495979	−	0.868334i	$-0.665191\pi$
$97$	−5.86889	+	1.24747i	−0.595895	+	0.126661i	−0.0999160	+	0.994996i	$0.531857\pi$
$98$	−2.29180			−0.231506
$99$		0			0
$100$	6.43769			0.643769
$101$	−8.28700	+	1.76146i	−0.824587	+	0.175271i	−0.600833	−	0.799374i	$-0.705165\pi$
$101$	−8.28700	+	1.76146i	−0.824587	+	0.175271i	−0.223754	+	0.974646i	$0.571831\pi$
$102$		0			0
$103$	−9.35111	+	4.16338i	−0.921393	+	0.410230i	−0.811926	−	0.583760i	$-0.801581\pi$
$103$	−9.35111	+	4.16338i	−0.921393	+	0.410230i	−0.109466	+	0.993990i	$0.534914\pi$
$104$	−9.31966	−	1.98095i	−0.913868	−	0.194249i
$105$		0			0
$106$	0.163305	−	1.55375i	0.0158616	−	0.150913i
$107$	11.3541	−	8.24924i	1.09764	−	0.797484i	0.116969	−	0.993136i	$-0.462682\pi$
$107$	11.3541	−	8.24924i	1.09764	−	0.797484i	0.980673	+	0.195652i	$0.0626822\pi$
$108$		0			0
$109$	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
$111$		0			0
$112$	−2.10502	−	2.33786i	−0.198905	−	0.220907i
$113$	1.80166	+	17.1416i	0.169486	+	1.61255i	0.666975	+	0.745080i	$0.267589\pi$
$113$	1.80166	+	17.1416i	0.169486	+	1.61255i	−0.497489	+	0.867470i	$0.665745\pi$
$114$		0			0
$115$	−3.81953	+	4.24202i	−0.356173	+	0.395571i
$116$	−2.78115	−	8.55951i	−0.258224	−	0.794730i
$117$		0			0
$118$	0.500000	−	0.363271i	0.0460287	−	0.0334418i
$119$	−4.74803	+	1.00922i	−0.435251	+	0.0925155i
$120$		0			0
$121$	7.17195	−	8.34045i	0.651996	−	0.758223i
$122$	−2.07295	+	3.59045i	−0.187676	+	0.325064i
$123$		0			0
$124$	−1.04683	−	0.466079i	−0.0940081	−	0.0418551i
$125$	8.47214	+	6.15537i	0.757771	+	0.550553i
$126$		0			0
$127$	−3.26393	−	10.0453i	−0.289627	−	0.891381i	−0.984973	−	0.172706i	$-0.944749\pi$
$127$	−3.26393	−	10.0453i	−0.289627	−	0.891381i	0.695346	−	0.718675i	$-0.255251\pi$
$128$	1.05471	−	10.0349i	0.0932241	−	0.886968i
$129$		0			0
$130$	−2.04468	−	2.27085i	−0.179330	−	0.199167i
$131$	10.6180	−	18.3910i	0.927702	−	1.60683i	0.140545	−	0.990074i	$-0.455115\pi$
$131$	10.6180	−	18.3910i	0.927702	−	1.60683i	0.787157	−	0.616753i	$-0.211552\pi$
$132$		0			0
$133$	0.500000	+	0.866025i	0.0433555	+	0.0750939i
$134$	0.708204	−	2.17963i	0.0611795	−	0.188291i
$135$		0			0
$136$	−5.78115	−	4.20025i	−0.495730	−	0.360169i
$137$	5.76659	−	6.40445i	0.492673	−	0.547169i	−0.444616	−	0.895721i	$-0.646660\pi$
$137$	5.76659	−	6.40445i	0.492673	−	0.547169i	0.937289	+	0.348552i	$0.113327\pi$
$138$		0			0
$139$	8.86889	−	3.94868i	0.752249	−	0.334923i	0.00546112	−	0.999985i	$-0.498262\pi$
$139$	8.86889	−	3.94868i	0.752249	−	0.334923i	0.746788	+	0.665062i	$0.231595\pi$
$140$	−0.239558	−	2.27924i	−0.0202463	−	0.192631i
$141$		0			0
$142$	−0.555728	−	0.962549i	−0.0466357	−	0.0807753i
$143$	−19.7082	−	8.50651i	−1.64808	−	0.711350i
$144$		0			0
$145$	1.85410	−	5.70634i	0.153975	−	0.473886i
$146$	−0.0509101	−	0.0226667i	−0.00421335	−	0.00187591i
$147$		0			0
$148$	−9.23146	−	1.96221i	−0.758821	−	0.161292i
$149$	−14.8486	−	3.15617i	−1.21645	−	0.258564i	−0.445393	−	0.895335i	$-0.646936\pi$
$149$	−14.8486	−	3.15617i	−1.21645	−	0.258564i	−0.771053	+	0.636772i	$0.780269\pi$
$150$		0			0
$151$	3.95222	+	1.75964i	0.321627	+	0.143197i	0.561199	−	0.827681i	$-0.310340\pi$
$151$	3.95222	+	1.75964i	0.321627	+	0.143197i	−0.239572	+	0.970879i	$0.577007\pi$
$152$	−0.454915	+	1.40008i	−0.0368985	+	0.113562i
$153$		0			0
$154$	0.645898	+	1.08981i	0.0520479	+	0.0878197i
$155$	−0.381966	−	0.661585i	−0.0306802	−	0.0531397i
$156$		0			0
$157$	−0.746950	−	7.10675i	−0.0596131	−	0.567181i	−0.983038	−	0.183402i	$-0.941289\pi$
$157$	−0.746950	−	7.10675i	−0.0596131	−	0.567181i	0.923425	−	0.383779i	$-0.125378\pi$
$158$	3.68565	−	1.64096i	0.293214	−	0.130547i
$159$		0			0
$160$	3.42903	−	3.80833i	0.271089	−	0.301075i
$161$	−3.73607	−	2.71441i	−0.294443	−	0.213926i
$162$		0			0
$163$	6.39919	−	19.6947i	0.501223	−	1.54261i	−0.305806	−	0.952094i	$-0.598926\pi$
$163$	6.39919	−	19.6947i	0.501223	−	1.54261i	0.807029	−	0.590512i	$-0.201074\pi$
$164$	2.34346	+	4.05899i	0.182993	+	0.316954i
$165$		0			0
$166$	−1.86475	+	3.22983i	−0.144732	+	0.250684i
$167$	3.85682	+	4.28344i	0.298450	+	0.331462i	0.873654	−	0.486548i	$-0.161744\pi$
$167$	3.85682	+	4.28344i	0.298450	+	0.331462i	−0.575204	+	0.818010i	$0.695077\pi$
$168$		0			0
$169$	−3.01968	+	28.7303i	−0.232283	+	2.21002i
$170$	−0.708204	−	2.17963i	−0.0543168	−	0.167170i
$171$		0			0
$172$	2.78115	+	2.02063i	0.212061	+	0.154071i
$173$	21.0939	+	9.39162i	1.60374	+	0.714032i	0.996741	−	0.0806702i	$-0.0257060\pi$
$173$	21.0939	+	9.39162i	1.60374	+	0.714032i	0.607000	+	0.794702i	$0.292373\pi$
$174$		0			0
$175$	−1.73607	+	3.00696i	−0.131234	+	0.227305i
$176$	3.11076	−	9.95925i	0.234482	−	0.750707i
$177$		0			0
$178$	−2.52713	+	0.537159i	−0.189417	+	0.0402618i
$179$	−4.09017	+	2.97168i	−0.305714	+	0.222114i	−0.730055	−	0.683388i	$-0.760506\pi$
$179$	−4.09017	+	2.97168i	−0.305714	+	0.222114i	0.424341	+	0.905502i	$0.360506\pi$
$180$		0			0
$181$	−3.06231	−	9.42481i	−0.227619	−	0.700540i	−0.998015	−	0.0629745i	$-0.979941\pi$
$181$	−3.06231	−	9.42481i	−0.227619	−	0.700540i	0.770396	−	0.637566i	$-0.220059\pi$
$182$	1.65418	−	1.83716i	0.122616	−	0.136179i
$183$		0			0
$184$	−0.710624	−	6.76113i	−0.0523879	−	0.498437i
$185$	−4.21003	−	4.67572i	−0.309528	−	0.343765i
$186$		0			0
$187$	−10.9083	−	11.8403i	−0.797696	−	0.865852i
$188$	22.1459			1.61516
$189$		0			0
$190$	−0.381966	+	0.277515i	−0.0277107	+	0.0201330i
$191$	0.621346	−	5.91171i	0.0449590	−	0.427756i	−0.948772	−	0.315961i	$-0.897673\pi$
$191$	0.621346	−	5.91171i	0.0449590	−	0.427756i	0.993731	−	0.111795i	$-0.0356601\pi$
$192$		0			0
$193$	10.7596	+	2.28703i	0.774495	+	0.164624i	0.578171	−	0.815915i	$-0.303766\pi$
$193$	10.7596	+	2.28703i	0.774495	+	0.164624i	0.196323	+	0.980539i	$0.437100\pi$
$194$	2.09366	−	0.932157i	0.150316	−	0.0669250i
$195$		0			0
$196$	−10.8815	+	2.31294i	−0.777251	+	0.165210i
$197$	−8.23607			−0.586796			−0.293398	−	0.955990i	$-0.594786\pi$
$197$	−8.23607			−0.586796			−0.293398	+	0.955990i	$0.594786\pi$
$198$		0			0
$199$	−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
$201$		0			0
$202$	2.95630	−	1.31623i	0.208004	−	0.0926094i
$203$	4.74803	+	1.00922i	0.333246	+	0.0708337i
$204$		0			0
$205$	−0.326611	+	3.10749i	−0.0228115	+	0.217037i
$206$	3.16312	−	2.29814i	0.220385	−	0.160119i
$207$		0			0
$208$	−20.3607			−1.41176
$209$	−1.62543	+	2.89102i	−0.112433	+	0.199976i
$210$		0			0
$211$	13.6985	+	15.2138i	0.943046	+	1.04736i	0.998803	+	0.0489142i	$0.0155761\pi$
$211$	13.6985	+	15.2138i	0.943046	+	1.04736i	−0.0557571	+	0.998444i	$0.517757\pi$
$212$	−0.792701	−	7.54205i	−0.0544429	−	0.517990i
$213$		0			0
$214$	−3.58699	+	3.98376i	−0.245202	+	0.272324i
$215$	0.708204	+	2.17963i	0.0482991	+	0.148649i
$216$		0			0
$217$	0.500000	−	0.363271i	0.0339422	−	0.0246605i
$218$	−2.66984	+	0.567493i	−0.180825	+	0.0384355i
$219$		0			0
$220$	6.09797	−	4.53766i	0.411125	−	0.305929i
$221$	−15.7082	+	27.2074i	−1.05665	+	1.83017i
$222$		0			0
$223$	−14.1660	−	6.30709i	−0.948623	−	0.422354i	−0.126693	−	0.991942i	$-0.540436\pi$
$223$	−14.1660	−	6.30709i	−0.948623	−	0.422354i	−0.821930	+	0.569588i	$0.807103\pi$
$224$	3.35410	+	2.43690i	0.224105	+	0.162822i
$225$		0			0
$226$	−2.03444	−	6.26137i	−0.135329	−	0.416500i
$227$	−1.73706	+	16.5270i	−0.115293	+	1.09694i	0.771966	+	0.635664i	$0.219273\pi$
$227$	−1.73706	+	16.5270i	−0.115293	+	1.09694i	−0.887259	+	0.461272i	$0.847393\pi$
$228$		0			0
$229$	6.81198	+	7.56547i	0.450148	+	0.499940i	0.924916	−	0.380171i	$-0.124135\pi$
$229$	6.81198	+	7.56547i	0.450148	+	0.499940i	−0.474768	+	0.880111i	$0.657468\pi$
$230$	1.09017	−	1.88823i	0.0718837	−	0.124506i
$231$		0			0
$232$	3.57295	+	6.18853i	0.234576	+	0.406297i
$233$	3.43769	−	10.5801i	0.225211	−	0.693128i	−0.773059	−	0.634334i	$-0.781275\pi$
$233$	3.43769	−	10.5801i	0.225211	−	0.693128i	0.998270	−	0.0587939i	$-0.0187255\pi$
$234$		0			0
$235$	11.9443	+	8.67802i	0.779158	+	0.566092i
$236$	2.00739	−	2.22943i	0.130670	−	0.145124i
$237$		0			0
$238$	1.69381	−	0.754131i	0.109793	−	0.0488831i
$239$	1.09464	+	10.4148i	0.0708061	+	0.673675i	0.971146	+	0.238487i	$0.0766515\pi$
$239$	1.09464	+	10.4148i	0.0708061	+	0.673675i	−0.900340	+	0.435188i	$0.856682\pi$
$240$		0			0
$241$	13.4164	+	23.2379i	0.864227	+	1.49688i	0.867813	+	0.496891i	$0.165525\pi$
$241$	13.4164	+	23.2379i	0.864227	+	1.49688i	−0.00358606	+	0.999994i	$0.501141\pi$
$242$	−2.01722	+	3.68571i	−0.129672	+	0.236927i
$243$		0			0
$244$	−6.21885	+	19.1396i	−0.398121	+	1.22529i
$245$	−6.77523	−	3.01652i	−0.432853	−	0.192719i
$246$		0			0
$247$	6.33070	+	1.34563i	0.402813	+	0.0856206i
$248$	0.889948	+	0.189164i	0.0565118	+	0.0120119i
$249$		0			0
$250$	−3.65418	−	1.62695i	−0.231111	−	0.102897i
$251$	−6.35410	+	19.5559i	−0.401067	+	1.23436i	0.523067	+	0.852291i	$0.324788\pi$
$251$	−6.35410	+	19.5559i	−0.401067	+	1.23436i	−0.924135	+	0.382067i	$0.875212\pi$
$252$		0			0
$253$	1.42705	−	15.2497i	0.0897179	−	0.958738i
$254$	2.01722	+	3.49393i	0.126572	+	0.219229i
$255$		0			0
$256$	−0.581419	−	5.53184i	−0.0363387	−	0.345740i
$257$	13.6208	−	6.06437i	0.849643	−	0.378285i	0.0647383	−	0.997902i	$-0.479379\pi$
$257$	13.6208	−	6.06437i	0.849643	−	0.378285i	0.784904	+	0.619617i	$0.212712\pi$
$258$		0			0
$259$	3.40599	−	3.78273i	0.211638	−	0.235048i
$260$	−12.0000	−	8.71851i	−0.744208	−	0.540699i
$261$		0			0
$262$	−2.50658	+	7.71445i	−0.154857	+	0.476601i
$263$	−6.35410	−	11.0056i	−0.391811	−	0.678636i	0.600878	−	0.799341i	$-0.294818\pi$
$263$	−6.35410	−	11.0056i	−0.391811	−	0.678636i	−0.992688	+	0.120705i	$0.961485\pi$
$264$		0			0
$265$	2.52786	−	4.37839i	0.155285	−	0.268962i
$266$	−0.255585	−	0.283856i	−0.0156709	−	0.0174043i
$267$		0			0
$268$	1.16284	−	11.0637i	0.0710317	−	0.675821i
$269$	6.57295	+	20.2295i	0.400760	+	1.23341i	0.924384	+	0.381463i	$0.124579\pi$
$269$	6.57295	+	20.2295i	0.400760	+	1.23341i	−0.523625	+	0.851949i	$0.675421\pi$
$270$		0			0
$271$	−8.70820	−	6.32688i	−0.528986	−	0.384331i	0.290993	−	0.956725i	$-0.406015\pi$
$271$	−8.70820	−	6.32688i	−0.528986	−	0.384331i	−0.819978	+	0.572395i	$0.806015\pi$
$272$	−13.9503	−	6.21108i	−0.845861	−	0.376602i
$273$		0			0
$274$	−1.64590	+	2.85078i	−0.0994323	+	0.172222i
$275$	−11.5150	+	0.131418i	−0.694382	+	0.00792483i
$276$		0			0
$277$	18.8157	−	3.99940i	1.13053	−	0.240301i	0.395584	−	0.918430i	$-0.370542\pi$
$277$	18.8157	−	3.99940i	1.13053	−	0.240301i	0.734943	+	0.678129i	$0.237209\pi$
$278$	−3.00000	+	2.17963i	−0.179928	+	0.130725i
$279$		0			0
$280$	0.562306	+	1.73060i	0.0336042	+	0.103423i
$281$	6.24047	−	6.93075i	0.372275	−	0.413454i	−0.527675	−	0.849446i	$-0.676936\pi$
$281$	6.24047	−	6.93075i	0.372275	−	0.413454i	0.899950	+	0.435993i	$0.143603\pi$
$282$		0			0
$283$	1.77698	+	16.9069i	0.105631	+	1.00501i	0.911048	+	0.412301i	$0.135275\pi$
$283$	1.77698	+	16.9069i	0.105631	+	1.00501i	−0.805417	+	0.592708i	$0.798059\pi$
$284$	−3.61004	−	4.00936i	−0.214217	−	0.237912i
$285$		0			0
$286$	8.03891	+	1.61306i	0.475351	+	0.0953824i
$287$	−2.52786			−0.149215
$288$		0			0
$289$	−5.30902	+	3.85723i	−0.312295	+	0.226896i
$290$	−0.239558	+	2.27924i	−0.0140673	+	0.133842i
$291$		0			0
$292$	−0.264599	−	0.0562422i	−0.0154845	−	0.00329132i
$293$	26.6576	−	11.8687i	1.55735	−	0.693378i	0.565975	−	0.824422i	$-0.308500\pi$
$293$	26.6576	−	11.8687i	1.55735	−	0.693378i	0.991376	+	0.131045i	$0.0418331\pi$
$294$		0			0
$295$	1.95630	−	0.415823i	0.113900	−	0.0242102i
$296$	7.49342			0.435546
$297$		0			0
$298$	5.79837			0.335891
$299$	−29.2354	+	6.21418i	−1.69073	+	0.359375i
$300$		0			0
$301$	−1.69381	+	0.754131i	−0.0976294	+	0.0434674i
$302$	−1.61637	−	0.343569i	−0.0930114	−	0.0197702i
$303$		0			0
$304$	−0.328836	+	3.12866i	−0.0188600	+	0.179441i
$305$	−10.8541	+	7.88597i	−0.621504	+	0.451549i
$306$		0			0
$307$	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
$309$		0			0
$310$	0.195250	+	0.216847i	0.0110894	+	0.0123161i
$311$	1.58678	+	15.0972i	0.0899779	+	0.856083i	0.942683	+	0.333690i	$0.108294\pi$
$311$	1.58678	+	15.0972i	0.0899779	+	0.856083i	−0.852705	+	0.522393i	$0.825040\pi$
$312$		0			0
$313$	2.32331	−	2.58030i	0.131321	−	0.145847i	−0.673898	−	0.738825i	$-0.735381\pi$
$313$	2.32331	−	2.58030i	0.131321	−	0.145847i	0.805219	+	0.592978i	$0.202048\pi$
$314$	0.843459	+	2.59590i	0.0475991	+	0.146495i
$315$		0			0
$316$	15.8435	−	11.5109i	0.891264	−	0.647541i
$317$	20.4866	−	4.35456i	1.15064	−	0.244576i	0.407175	−	0.913350i	$-0.366514\pi$
$317$	20.4866	−	4.35456i	1.15064	−	0.244576i	0.743466	+	0.668774i	$0.233180\pi$
$318$		0			0
$319$	5.14935	+	15.2535i	0.288308	+	0.854033i
$320$	2.90983	−	5.03997i	0.162664	−	0.281743i
$321$		0			0
$322$	1.61143	+	0.717456i	0.0898016	+	0.0399822i
$323$	3.92705	+	2.85317i	0.218507	+	0.158755i
$324$		0			0
$325$	6.94427	+	21.3723i	0.385199	+	1.18552i
$326$	−0.826802	+	7.86650i	−0.0457923	+	0.435685i
$327$		0			0
$328$	−2.49008	−	2.76551i	−0.137491	−	0.152700i
$329$	−5.97214	+	10.3440i	−0.329255	+	0.570286i
$330$		0			0
$331$	−7.20820	−	12.4850i	−0.396199	−	0.686236i	0.597055	−	0.802201i	$-0.296338\pi$
$331$	−7.20820	−	12.4850i	−0.396199	−	0.686236i	−0.993253	+	0.115964i	$0.963004\pi$
$332$	−5.59424	+	17.2173i	−0.307024	+	0.944921i
$333$		0			0
$334$	−1.78115	−	1.29408i	−0.0974604	−	0.0708091i
$335$	4.96255	−	5.51147i	0.271133	−	0.301124i
$336$		0			0
$337$	−10.4803	+	4.66614i	−0.570899	+	0.254181i	−0.671821	−	0.740714i	$-0.734488\pi$
$337$	−10.4803	+	4.66614i	−0.570899	+	0.254181i	0.100922	+	0.994894i	$0.467821\pi$
$338$	−1.15341	−	10.9740i	−0.0627374	−	0.596907i
$339$		0			0
$340$	−5.56231	−	9.63420i	−0.301658	−	0.522488i
$341$	1.88197	+	0.812299i	0.101914	+	0.0439885i
$342$		0			0
$343$	4.01722	−	12.3637i	0.216910	−	0.667579i
$344$	−2.49351	−	1.11018i	−0.134441	−	0.0598571i
$345$		0			0
$346$	−8.62693	−	1.83371i	−0.463787	−	0.0985809i
$347$	−8.69431	−	1.84803i	−0.466735	−	0.0992076i	−0.0314597	−	0.999505i	$-0.510016\pi$
$347$	−8.69431	−	1.84803i	−0.466735	−	0.0992076i	−0.435275	+	0.900297i	$0.643349\pi$
$348$		0			0
$349$	−3.78747	−	1.68629i	−0.202738	−	0.0902650i	0.302856	−	0.953036i	$-0.402060\pi$
$349$	−3.78747	−	1.68629i	−0.202738	−	0.0902650i	−0.505594	+	0.862771i	$0.668727\pi$
$350$	0.409830	−	1.26133i	0.0219063	−	0.0674208i
$351$		0			0
$352$	−1.28115	+	13.6906i	−0.0682857	+	0.729710i
$353$	−8.20820	−	14.2170i	−0.436879	−	0.756696i	0.560568	−	0.828108i	$-0.310583\pi$
$353$	−8.20820	−	14.2170i	−0.436879	−	0.756696i	−0.997447	+	0.0714123i	$0.977249\pi$
$354$		0			0
$355$	−0.375963	−	3.57704i	−0.0199540	−	0.189850i
$356$	−11.4568	+	5.10089i	−0.607209	+	0.270347i
$357$		0			0
$358$	1.29217	−	1.43510i	0.0682933	−	0.0758473i
$359$	−18.4894	−	13.4333i	−0.975831	−	0.708983i	−0.0190579	−	0.999818i	$-0.506067\pi$
$359$	−18.4894	−	13.4333i	−0.975831	−	0.708983i	−0.956773	+	0.290836i	$0.906067\pi$
$360$		0			0
$361$	−5.56231	+	17.1190i	−0.292753	+	0.901001i
$362$	1.89261	+	3.27810i	0.0994733	+	0.172293i
$363$		0			0
$364$	6.00000	−	10.3923i	0.314485	−	0.544705i
$365$	−0.120671	−	0.134019i	−0.00631621	−	0.00701486i
$366$		0			0
$367$	1.32837	−	12.6386i	0.0693403	−	0.659729i	−0.903553	−	0.428476i	$-0.859051\pi$
$367$	1.32837	−	12.6386i	0.0693403	−	0.659729i	0.972894	−	0.231253i	$-0.0742826\pi$
$368$	−4.48936	−	13.8168i	−0.234024	−	0.720252i
$369$		0			0
$370$	1.94427	+	1.41260i	0.101078	+	0.0734374i
$371$	3.73656	+	1.66362i	0.193992	+	0.0863710i
$372$		0			0
$373$	2.82624	−	4.89519i	0.146337	−	0.253463i	−0.783534	−	0.621349i	$-0.786585\pi$
$373$	2.82624	−	4.89519i	0.146337	−	0.253463i	0.929871	+	0.367886i	$0.119918\pi$
$374$	5.01586	+	3.55749i	0.259364	+	0.183954i
$375$		0			0
$376$	−17.1993	+	3.65583i	−0.886989	+	0.188535i
$377$	25.4164	−	18.4661i	1.30901	−	0.951053i
$378$		0			0
$379$	4.88197	+	15.0251i	0.250770	+	0.771790i	0.994634	+	0.103459i	$0.0329910\pi$
$379$	4.88197	+	15.0251i	0.250770	+	0.771790i	−0.743864	+	0.668331i	$0.767009\pi$
$380$	−1.53351	+	1.70314i	−0.0786674	+	0.0873691i
$381$		0			0
$382$	0.237333	+	2.25807i	0.0121430	+	0.115533i
$383$	−13.2850	−	14.7545i	−0.678831	−	0.753918i	0.301026	−	0.953616i	$-0.402671\pi$
$383$	−13.2850	−	14.7545i	−0.678831	−	0.753918i	−0.979858	+	0.199697i	$0.936004\pi$
$384$		0			0
$385$	0.475022	+	4.07196i	0.0242094	+	0.207526i
$386$	−4.20163			−0.213857
$387$		0			0
$388$	9.00000	−	6.53888i	0.456906	−	0.331961i
$389$	−2.36783	+	22.5284i	−0.120054	+	1.14223i	0.754159	+	0.656692i	$0.228045\pi$
$389$	−2.36783	+	22.5284i	−0.120054	+	1.14223i	−0.874213	+	0.485543i	$0.838622\pi$
$390$		0			0
$391$	−21.9266	−	4.66063i	−1.10887	−	0.235698i
$392$	8.06918	−	3.59263i	0.407555	−	0.181455i
$393$		0			0
$394$	3.07715	−	0.654069i	0.155025	−	0.0329515i
$395$	13.0557			0.656905
$396$		0			0
$397$	−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
$399$		0			0
$400$	−9.97864	+	4.44278i	−0.498932	+	0.222139i
$401$	14.2441	+	3.02767i	0.711316	+	0.151195i	0.549339	−	0.835600i	$-0.314880\pi$
$401$	14.2441	+	3.02767i	0.711316	+	0.151195i	0.161977	+	0.986795i	$0.448213\pi$
$402$		0			0
$403$	0.418114	−	3.97809i	0.0208277	−	0.198163i
$404$	12.7082	−	9.23305i	0.632257	−	0.459361i
$405$		0			0
$406$	−1.85410			−0.0920175
$407$	16.5522	+	3.32132i	0.820465	+	0.164632i
$408$		0			0
$409$	−22.5782	−	25.0757i	−1.11642	−	1.23991i	−0.967990	−	0.250990i	$-0.919244\pi$
$409$	−22.5782	−	25.0757i	−1.11642	−	1.23991i	−0.148432	−	0.988923i	$-0.547423\pi$
$410$	−0.124754	−	1.18696i	−0.00616117	−	0.0586196i
$411$		0			0
$412$	12.6992	−	14.1039i	0.625647	−	0.694851i
$413$	0.500000	+	1.53884i	0.0246034	+	0.0757215i
$414$		0			0
$415$	−9.76393	+	7.09391i	−0.479293	+	0.348226i
$416$	26.2465	−	5.57886i	1.28684	−	0.273526i
$417$		0			0
$418$	0.377699	−	1.20922i	0.0184739	−	0.0591451i
$419$	4.04508	−	7.00629i	0.197615	−	0.342280i	−0.750139	−	0.661280i	$-0.770014\pi$
$419$	4.04508	−	7.00629i	0.197615	−	0.342280i	0.947755	+	0.319000i	$0.103347\pi$
$420$		0			0
$421$	9.35111	+	4.16338i	0.455745	+	0.202911i	0.621753	−	0.783214i	$-0.286421\pi$
$421$	9.35111	+	4.16338i	0.455745	+	0.202911i	−0.166007	+	0.986125i	$0.553088\pi$
$422$	−6.32624	−	4.59628i	−0.307956	−	0.223743i
$423$		0			0
$424$	1.86068	+	5.72658i	0.0903626	+	0.278107i
$425$	−1.76173	+	16.7618i	−0.0854566	+	0.813065i
$426$		0			0
$427$	−7.26281	−	8.06617i	−0.351472	−	0.390349i
$428$	−13.0106	+	22.5351i	−0.628893	+	1.08927i
$429$		0			0
$430$	−0.437694	−	0.758108i	−0.0211075	−	0.0365592i
$431$	10.5279	−	32.4014i	0.507109	−	1.56072i	−0.290086	−	0.957001i	$-0.593684\pi$
$431$	10.5279	−	32.4014i	0.507109	−	1.56072i	0.797195	−	0.603722i	$-0.206316\pi$
$432$		0			0
$433$	−11.9271	−	8.66551i	−0.573177	−	0.416438i	0.263081	−	0.964774i	$-0.415261\pi$
$433$	−11.9271	−	8.66551i	−0.573177	−	0.416438i	−0.836258	+	0.548336i	$0.815261\pi$
$434$	−0.157960	+	0.175433i	−0.00758234	+	0.00842104i
$435$		0			0
$436$	−12.1038	+	5.38894i	−0.579665	+	0.258084i
$437$	0.482716	+	4.59274i	0.0230914	+	0.219700i
$438$		0			0
$439$	0.354102	+	0.613323i	0.0169004	+	0.0292723i	0.874352	−	0.485292i	$-0.161287\pi$
$439$	0.354102	+	0.613323i	0.0169004	+	0.0292723i	−0.857452	+	0.514565i	$0.827954\pi$
$440$	−3.98684	+	4.53077i	−0.190065	+	0.215996i
$441$		0			0
$442$	3.70820	−	11.4127i	0.176381	−	0.542846i
$443$	1.12920	+	0.502754i	0.0536501	+	0.0238866i	0.433386	−	0.901208i	$-0.357319\pi$
$443$	1.12920	+	0.502754i	0.0536501	+	0.0238866i	−0.379736	+	0.925095i	$0.623985\pi$
$444$		0			0
$445$	−8.17798	−	1.73828i	−0.387673	−	0.0824025i
$446$	5.79355	+	1.23146i	0.274333	+	0.0583112i
$447$		0			0
$448$	4.30116	+	1.91500i	0.203211	+	0.0904752i
$449$	−2.30902	+	7.10642i	−0.108969	+	0.335373i	−0.990642	−	0.136489i	$-0.956418\pi$
$449$	−2.30902	+	7.10642i	−0.108969	+	0.335373i	0.881672	+	0.471862i	$0.156418\pi$
$450$		0			0
$451$	−4.27458	−	7.21242i	−0.201282	−	0.339620i
$452$	−15.9787	−	27.6759i	−0.751575	−	1.30177i
$453$		0			0
$454$	−0.663497	−	6.31275i	−0.0311395	−	0.296272i
$455$	7.30836	−	3.25389i	0.342621	−	0.152545i
$456$		0			0
$457$	−0.669131	+	0.743145i	−0.0313006	+	0.0347628i	−0.758592	−	0.651566i	$-0.774112\pi$
$457$	−0.669131	+	0.743145i	−0.0313006	+	0.0347628i	0.727291	+	0.686329i	$0.240779\pi$
$458$	−3.14590	−	2.28563i	−0.146998	−	0.106800i
$459$		0			0
$460$	3.27051	−	10.0656i	0.152488	−	0.469311i
$461$	−8.07295	−	13.9828i	−0.375995	−	0.651242i	0.614481	−	0.788932i	$-0.289366\pi$
$461$	−8.07295	−	13.9828i	−0.375995	−	0.651242i	−0.990475	+	0.137690i	$0.956032\pi$
$462$		0			0
$463$	−8.50000	+	14.7224i	−0.395029	+	0.684209i	−0.993105	−	0.117230i	$-0.962599\pi$
$463$	−8.50000	+	14.7224i	−0.395029	+	0.684209i	0.598076	+	0.801439i	$0.295932\pi$
$464$	10.2180	+	11.3482i	0.474357	+	0.526827i
$465$		0			0
$466$	−0.444165	+	4.22595i	−0.0205755	+	0.195763i
$467$	0.236068	+	0.726543i	0.0109239	+	0.0336204i	0.956370	−	0.292159i	$-0.0943735\pi$
$467$	0.236068	+	0.726543i	0.0109239	+	0.0336204i	−0.945446	+	0.325779i	$0.894373\pi$
$468$		0			0
$469$	4.85410	+	3.52671i	0.224142	+	0.162848i
$470$	−5.15178	−	2.29372i	−0.237634	−	0.105801i
$471$		0			0
$472$	−1.19098	+	2.06284i	−0.0548194	+	0.0949500i
$473$	−5.01586	−	3.55749i	−0.230630	−	0.163574i
$474$		0			0
$475$	3.39626	−	0.721898i	0.155831	−	0.0331229i
$476$	7.28115	−	5.29007i	0.333731	−	0.242470i
$477$		0			0
$478$	−1.23607	−	3.80423i	−0.0565364	−	0.174001i
$479$	7.87161	−	8.74231i	0.359663	−	0.399446i	−0.535972	−	0.844236i	$-0.680055\pi$
$479$	7.87161	−	8.74231i	0.359663	−	0.399446i	0.895635	+	0.444789i	$0.146722\pi$
$480$		0			0
$481$	−3.44361	−	32.7638i	−0.157015	−	1.49390i
$482$	−6.85807	−	7.61666i	−0.312376	−	0.346929i
$483$		0			0
$484$	−5.85811	+	19.5357i	−0.266278	+	0.887986i
$485$	7.41641			0.336762
$486$		0			0
$487$	10.5000	−	7.62870i	0.475800	−	0.345689i	−0.323897	−	0.946092i	$-0.604993\pi$
$487$	10.5000	−	7.62870i	0.475800	−	0.345689i	0.799698	+	0.600403i	$0.204993\pi$
$488$	1.67023	−	15.8912i	0.0756078	−	0.719360i
$489$		0			0
$490$	2.77091	+	0.588976i	0.125177	+	0.0266072i
$491$	−6.69285	+	2.97985i	−0.302044	+	0.134479i	−0.552162	−	0.833737i	$-0.686197\pi$
$491$	−6.69285	+	2.97985i	−0.302044	+	0.134479i	0.250118	+	0.968215i	$0.419531\pi$
$492$		0			0
$493$	23.0474	−	4.89888i	1.03800	−	0.220634i
$494$	−2.47214			−0.111227
$495$		0			0
$496$	1.94427			0.0873004
$497$	2.84624	−	0.604988i	0.127671	−	0.0271374i
$498$		0			0
$499$	35.0951	−	15.6254i	1.57107	−	0.699487i	0.577898	−	0.816109i	$-0.303873\pi$
$499$	35.0951	−	15.6254i	1.57107	−	0.699487i	0.993176	+	0.116622i	$0.0372066\pi$
$500$	−18.9921	−	4.03690i	−0.849353	−	0.180536i
$501$		0			0
$502$	0.820977	−	7.81108i	0.0366420	−	0.348625i
$503$	−7.70820	+	5.60034i	−0.343692	+	0.249707i	−0.746218	−	0.665702i	$-0.768132\pi$
$503$	−7.70820	+	5.60034i	−0.343692	+	0.249707i	0.402526	+	0.915409i	$0.368132\pi$
$504$		0			0
$505$	10.4721			0.466004
$506$	0.677881	+	5.81089i	0.0301355	+	0.258326i
$507$		0			0
$508$	13.1040	+	14.5534i	0.581395	+	0.645705i
$509$	−2.84112	−	27.0314i	−0.125930	−	1.19815i	−0.856807	−	0.515638i	$-0.827555\pi$
$509$	−2.84112	−	27.0314i	−0.125930	−	1.19815i	0.730876	−	0.682510i	$-0.239112\pi$
$510$		0			0
$511$	0.0976248	−	0.108423i	0.00431867	−	0.00479637i
$512$	6.89261	+	21.2133i	0.304613	+	0.937503i
$513$		0			0
$514$	−4.60739	+	3.34747i	−0.203223	+	0.147650i
$515$	12.3760	−	2.63060i	0.545351	−	0.115918i
$516$		0			0
$517$	−39.6121	+	0.452084i	−1.74214	+	0.0198826i
$518$	−0.972136	+	1.68379i	−0.0427132	+	0.0739814i
$519$		0			0
$520$	10.7589	+	4.79017i	0.471809	+	0.210063i
$521$	−32.6525	−	23.7234i	−1.43053	−	1.03934i	−0.989918	−	0.141645i	$-0.954761\pi$
$521$	−32.6525	−	23.7234i	−1.43053	−	1.03934i	−0.440613	−	0.897697i	$-0.645239\pi$
$522$		0			0
$523$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$523$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$524$	−4.11569	+	39.1581i	−0.179795	+	1.71063i
$525$		0			0
$526$	3.24803	+	3.60730i	0.141621	+	0.157286i
$527$	1.50000	−	2.59808i	0.0653410	−	0.113174i
$528$		0			0
$529$	0.836881	+	1.44952i	0.0363861	+	0.0630226i
$530$	−0.596748	+	1.83660i	−0.0259211	+	0.0797768i
$531$		0			0
$532$	−1.50000	−	1.08981i	−0.0650332	−	0.0472494i
$533$	−10.9474	+	12.1584i	−0.474186	+	0.526637i
$534$		0			0
$535$	−15.8478	+	7.05587i	−0.685158	+	0.305052i
$536$	0.923281	+	8.78443i	0.0398797	+	0.379430i
$537$		0			0
$538$	−4.06231	−	7.03612i	−0.175138	−	0.303349i
$539$	19.4164	−	4.35926i	0.836324	−	0.187766i
$540$		0			0
$541$	−3.68034	+	11.3269i	−0.158230	+	0.486982i	−0.998474	−	0.0552266i	$-0.982412\pi$
$541$	−3.68034	+	11.3269i	−0.158230	+	0.486982i	0.840244	+	0.542209i	$0.182412\pi$
$542$	3.75600	+	1.67228i	0.161334	+	0.0718306i
$543$		0			0
$544$	19.6848	+	4.18414i	0.843981	+	0.179394i
$545$	−8.63980	−	1.83645i	−0.370088	−	0.0786647i
$546$		0			0
$547$	−29.5315	−	13.1483i	−1.26268	−	0.562179i	−0.337359	−	0.941376i	$-0.609534\pi$
$547$	−29.5315	−	13.1483i	−1.26268	−	0.562179i	−0.925316	+	0.379197i	$0.876200\pi$
$548$	−4.93769	+	15.1967i	−0.210928	+	0.649169i
$549$		0			0
$550$	4.29180	−	0.963568i	0.183003	−	0.0410867i
$551$	−2.42705	−	4.20378i	−0.103396	−	0.179087i
$552$		0			0
$553$	1.10406	+	10.5044i	0.0469495	+	0.446694i
$554$	−6.71230	+	2.98851i	−0.285178	+	0.126970i
$555$		0			0
$556$	−12.0444	+	13.3766i	−0.510794	+	0.567294i
$557$	−0.527864	−	0.383516i	−0.0223663	−	0.0162501i	0.576546	−	0.817065i	$-0.304400\pi$
$557$	−0.527864	−	0.383516i	−0.0223663	−	0.0162501i	−0.598912	+	0.800815i	$0.704400\pi$
$558$		0			0
$559$	−3.70820	+	11.4127i	−0.156840	+	0.482705i
$560$	1.94427	+	3.36758i	0.0821605	+	0.142306i
$561$		0			0
$562$	−1.78115	+	3.08505i	−0.0751334	+	0.130135i
$563$	13.5867	+	15.0895i	0.572610	+	0.635947i	0.957987	−	0.286812i	$-0.0925954\pi$
$563$	13.5867	+	15.0895i	0.572610	+	0.635947i	−0.385377	+	0.922759i	$0.625929\pi$
$564$		0			0
$565$	2.22697	−	21.1882i	0.0936895	−	0.891396i
$566$	−2.00658	−	6.17561i	−0.0843428	−	0.259580i
$567$		0			0
$568$	3.46556	+	2.51788i	0.145412	+	0.105648i
$569$	−35.4441	−	15.7807i	−1.48589	−	0.661562i	−0.506264	−	0.862378i	$-0.668974\pi$
$569$	−35.4441	−	15.7807i	−1.48589	−	0.661562i	−0.979629	+	0.200816i	$0.935641\pi$
$570$		0			0
$571$	9.26393	−	16.0456i	0.387683	−	0.671488i	−0.604454	−	0.796640i	$-0.706609\pi$
$571$	9.26393	−	16.0456i	0.387683	−	0.671488i	0.992138	+	0.125153i	$0.0399420\pi$
$572$	39.7969	−	0.454194i	1.66399	−	0.0189908i
$573$		0			0
$574$	0.944458	−	0.200751i	0.0394209	−	0.00837918i
$575$	−12.9721	+	9.42481i	−0.540975	+	0.393042i
$576$		0			0
$577$	10.9443	+	33.6830i	0.455616	+	1.40224i	0.870410	+	0.492327i	$0.163853\pi$
$577$	10.9443	+	33.6830i	0.455616	+	1.40224i	−0.414794	+	0.909915i	$0.636147\pi$
$578$	1.67723	−	1.86275i	0.0697635	−	0.0774802i
$579$		0			0
$580$	1.16284	+	11.0637i	0.0482842	+	0.459394i
$581$	−6.53335	−	7.25602i	−0.271049	−	0.301030i
$582$		0			0
$583$	1.57186	+	13.4742i	0.0650997	+	0.558044i
$584$	0.214782			0.00888773
$585$		0			0
$586$	−9.01722	+	6.55139i	−0.372498	+	0.270636i
$587$	1.40240	−	13.3429i	0.0578831	−	0.550721i	−0.926700	−	0.375802i	$-0.877367\pi$
$587$	1.40240	−	13.3429i	0.0578831	−	0.550721i	0.984583	−	0.174918i	$-0.0559662\pi$
$588$		0			0
$589$	−0.604528	−	0.128496i	−0.0249092	−	0.00529461i
$590$	−0.697887	+	0.310719i	−0.0287315	+	0.0127921i
$591$		0			0
$592$	15.6632	−	3.32932i	0.643755	−	0.136834i
$593$	10.9443			0.449427			0.224714	−	0.974425i	$-0.427855\pi$
$593$	10.9443			0.449427			0.224714	+	0.974425i	$0.427855\pi$
$594$		0			0
$595$	6.00000			0.245976
$596$	27.5308	−	5.85186i	1.12771	−	0.239702i
$597$		0			0
$598$	10.4294	−	4.64347i	0.426490	−	0.189886i
$599$	−13.0687	−	2.77784i	−0.533973	−	0.113500i	−0.0669698	−	0.997755i	$-0.521333\pi$
$599$	−13.0687	−	2.77784i	−0.533973	−	0.113500i	−0.467003	+	0.884255i	$0.654666\pi$
$600$		0			0
$601$	1.82634	−	17.3764i	0.0744978	−	0.708799i	−0.891985	−	0.452066i	$-0.850687\pi$
$601$	1.82634	−	17.3764i	0.0744978	−	0.708799i	0.966482	−	0.256733i	$-0.0826461\pi$
$602$	0.572949	−	0.416272i	0.0233517	−	0.0169660i
$603$		0			0
$604$	−8.02129			−0.326382
$605$	−10.8147	+	8.24093i	−0.439682	+	0.335042i
$606$		0			0
$607$	−2.39789	−	2.66313i	−0.0973274	−	0.108093i	0.692513	−	0.721405i	$-0.256503\pi$
$607$	−2.39789	−	2.66313i	−0.0973274	−	0.108093i	−0.789841	+	0.613312i	$0.789837\pi$
$608$	−0.433364	−	4.12319i	−0.0175752	−	0.167217i
$609$		0			0
$610$	3.42903	−	3.80833i	0.138838	−	0.154195i
$611$	23.8885	+	73.5214i	0.966427	+	2.97436i
$612$		0			0
$613$	−16.0623	+	11.6699i	−0.648750	+	0.471345i	−0.862845	−	0.505468i	$-0.831320\pi$
$613$	−16.0623	+	11.6699i	−0.648750	+	0.471345i	0.214095	+	0.976813i	$0.431320\pi$
$614$	−2.93444	+	0.623735i	−0.118424	+	0.0251719i
$615$		0			0
$616$	−3.98254	−	2.82461i	−0.160461	−	0.113807i
$617$	−13.5795	+	23.5204i	−0.546691	+	0.946897i	0.451807	+	0.892116i	$0.350779\pi$
$617$	−13.5795	+	23.5204i	−0.546691	+	0.946897i	−0.998498	+	0.0547813i	$0.982554\pi$
$618$		0			0
$619$	25.1794	+	11.2106i	1.01205	+	0.450592i	0.844662	−	0.535300i	$-0.179801\pi$
$619$	25.1794	+	11.2106i	1.01205	+	0.450592i	0.167384	+	0.985892i	$0.446468\pi$
$620$	1.14590	+	0.832544i	0.0460204	+	0.0334358i
$621$		0			0
$622$	−1.79180	−	5.51458i	−0.0718445	−	0.221115i
$623$	0.707023	−	6.72688i	0.0283263	−	0.269507i
$624$		0			0
$625$	2.95515	+	3.28203i	0.118206	+	0.131281i
$626$	−0.663119	+	1.14856i	−0.0265036	+	0.0459055i
$627$		0			0
$628$	6.62461	+	11.4742i	0.264351	+	0.457869i
$629$	7.63525	−	23.4989i	0.304438	−	0.936962i
$630$		0			0
$631$	8.80902	+	6.40013i	0.350681	+	0.254785i	0.749155	−	0.662395i	$-0.230460\pi$
$631$	8.80902	+	6.40013i	0.350681	+	0.254785i	−0.398473	+	0.917180i	$0.630460\pi$
$632$	−10.4044	+	11.5553i	−0.413865	+	0.459644i
$633$		0			0
$634$	−7.30836	+	3.25389i	−0.290252	+	0.129229i
$635$	1.36470	+	12.9842i	0.0541563	+	0.515263i
$636$		0			0
$637$	−19.4164	−	33.6302i	−0.769306	−	1.33248i
$638$	−3.13525	−	5.29007i	−0.124126	−	0.209436i
$639$		0			0
$640$	−3.85410	+	11.8617i	−0.152347	+	0.468875i
$641$	18.6828	+	8.31811i	0.737925	+	0.328546i	0.741050	−	0.671450i	$-0.234328\pi$
$641$	18.6828	+	8.31811i	0.737925	+	0.328546i	−0.00312481	+	0.999995i	$0.500995\pi$
$642$		0			0
$643$	6.70432	+	1.42505i	0.264393	+	0.0561984i	0.338200	−	0.941074i	$-0.390182\pi$
$643$	6.70432	+	1.42505i	0.264393	+	0.0561984i	−0.0738078	+	0.997272i	$0.523515\pi$
$644$	8.37520	+	1.78020i	0.330029	+	0.0701498i
$645$		0			0
$646$	−1.69381	−	0.754131i	−0.0666419	−	0.0296709i
$647$	1.29180	−	3.97574i	0.0507857	−	0.156302i	−0.922447	−	0.386123i	$-0.873814\pi$
$647$	1.29180	−	3.97574i	0.0507857	−	0.156302i	0.973233	+	0.229821i	$0.0738140\pi$
$648$		0			0
$649$	−3.54508	+	4.02874i	−0.139157	+	0.158142i
$650$	−4.29180	−	7.43361i	−0.168338	−	0.291570i
$651$		0			0
$652$	4.01338	+	38.1848i	0.157176	+	1.49543i
$653$	1.24304	−	0.553438i	0.0486440	−	0.0216577i	−0.382270	−	0.924050i	$-0.624858\pi$
$653$	1.24304	−	0.553438i	0.0486440	−	0.0216577i	0.430914	+	0.902393i	$0.358191\pi$
$654$		0			0
$655$	−17.5642	+	19.5070i	−0.686288	+	0.762201i
$656$	−6.43363	−	4.67430i	−0.251191	−	0.182501i
$657$		0			0
$658$	1.40983	−	4.33901i	0.0549609	−	0.169152i
$659$	4.98936	+	8.64182i	0.194358	+	0.336637i	0.946690	−	0.322147i	$-0.104404\pi$
$659$	4.98936	+	8.64182i	0.194358	+	0.336637i	−0.752332	+	0.658784i	$0.771071\pi$
$660$		0			0
$661$	2.14590	−	3.71680i	0.0834658	−	0.144567i	−0.821271	−	0.570539i	$-0.806734\pi$
$661$	2.14590	−	3.71680i	0.0834658	−	0.144567i	0.904736	+	0.425972i	$0.140068\pi$
$662$	3.68462	+	4.09218i	0.143207	+	0.159047i
$663$		0			0
$664$	1.50247	−	14.2951i	0.0583073	−	0.554757i
$665$	−0.381966	−	1.17557i	−0.0148120	−	0.0455867i
$666$		0			0
$667$	18.1353	+	13.1760i	0.702200	+	0.510178i
$668$	−9.76299	−	4.34676i	−0.377741	−	0.168181i
$669$		0			0
$670$	−1.41641	+	2.45329i	−0.0547206	+	0.0947789i
$671$	10.7329	−	34.3618i	0.414337	−	1.32652i
$672$		0			0
$673$	28.9163	−	6.14635i	1.11464	−	0.236924i	0.386458	−	0.922307i	$-0.373698\pi$
$673$	28.9163	−	6.14635i	1.11464	−	0.236924i	0.728183	+	0.685383i	$0.240365\pi$
$674$	3.54508	−	2.57565i	0.136552	−	0.0992105i
$675$		0			0
$676$	−16.5517	−	50.9408i	−0.636602	−	1.95926i
$677$	−4.05207	+	4.50028i	−0.155734	+	0.172960i	−0.815963	−	0.578105i	$-0.803793\pi$
$677$	−4.05207	+	4.50028i	−0.155734	+	0.172960i	0.660229	+	0.751064i	$0.270459\pi$
$678$		0			0
$679$	0.627171	+	5.96713i	0.0240686	+	0.228997i
$680$	5.91031	+	6.56406i	0.226650	+	0.251720i
$681$		0			0
$682$	−0.767647	−	0.154034i	−0.0293947	−	0.00589826i
$683$	5.52786			0.211518			0.105759	−	0.994392i	$-0.466273\pi$
$683$	5.52786			0.211518			0.105759	+	0.994392i	$0.466273\pi$
$684$		0			0
$685$	−8.61803	+	6.26137i	−0.329278	+	0.239235i
$686$	−0.519042	+	4.93836i	−0.0198171	+	0.188547i
$687$		0			0
$688$	−5.70535	−	1.21271i	−0.217515	−	0.0462342i
$689$	24.1835	−	10.7672i	0.921318	−	0.410197i
$690$		0			0
$691$	−14.2778	+	3.03483i	−0.543152	+	0.115451i	−0.471314	−	0.881966i	$-0.656220\pi$
$691$	−14.2778	+	3.03483i	−0.543152	+	0.115451i	−0.0718386	+	0.997416i	$0.522887\pi$
$692$	−42.8115			−1.62745
$693$		0			0
$694$	3.39512			0.128877
$695$	−11.7378	+	2.49494i	−0.445239	+	0.0946385i
$696$		0			0
$697$	−11.2097	+	4.99087i	−0.424596	+	0.189043i
$698$	1.54899	+	0.329247i	0.0586300	+	0.0124622i
$699$		0			0
$700$	0.672922	−	6.40243i	0.0254341	−	0.241989i
$701$	−38.6074	+	28.0499i	−1.45818	+	1.05943i	−0.474349	+	0.880337i	$0.657317\pi$
$701$	−38.6074	+	28.0499i	−1.45818	+	1.05943i	−0.983832	+	0.179094i	$0.942683\pi$
$702$		0			0
$703$	−5.09017			−0.191979
$704$	1.80937	+	15.5102i	0.0681931	+	0.584561i
$705$		0			0
$706$	4.19579	+	4.65990i	0.157911	+	0.175378i
$707$	0.885579	+	8.42572i	0.0333056	+	0.316882i
$708$		0			0
$709$	−17.2394	+	19.1463i	−0.647441	+	0.719056i	−0.974108	−	0.226084i	$-0.927408\pi$
$709$	−17.2394	+	19.1463i	−0.647441	+	0.719056i	0.326667	+	0.945139i	$0.394074\pi$
$710$	0.424538	+	1.30660i	0.0159326	+	0.0490356i
$711$		0			0
$712$	8.05573	−	5.85283i	0.301901	−	0.219344i
$713$	2.79173	−	0.593401i	0.104551	−	0.0222230i
$714$		0			0
$715$	21.6422	+	15.3497i	0.809373	+	0.574047i
$716$	4.68692	−	8.11798i	0.175158	−	0.303383i
$717$		0			0
$718$	7.97479	+	3.55060i	0.297616	+	0.132507i
$719$	−15.8541	−	11.5187i	−0.591258	−	0.429574i	0.251507	−	0.967855i	$-0.419074\pi$
$719$	−15.8541	−	11.5187i	−0.591258	−	0.429574i	−0.842765	+	0.538281i	$0.819074\pi$
$720$		0			0
$721$	3.16312	+	9.73508i	0.117801	+	0.362553i
$722$	0.718674	−	6.83772i	0.0267463	−	0.254474i
$723$		0			0
$724$	12.2945	+	13.6544i	0.456921	+	0.507463i
$725$	8.42705	−	14.5961i	0.312973	−	0.542085i
$726$		0			0
$727$	−9.41641	−	16.3097i	−0.349235	−	0.604893i	0.636879	−	0.770964i	$-0.280225\pi$
$727$	−9.41641	−	16.3097i	−0.349235	−	0.604893i	−0.986114	+	0.166071i	$0.946892\pi$
$728$	−2.94427	+	9.06154i	−0.109122	+	0.335843i
$729$		0			0
$730$	0.0557281	+	0.0404888i	0.00206259	+	0.00149856i
$731$	−6.02218	+	6.68830i	−0.222738	+	0.247376i
$732$		0			0
$733$	44.2815	−	19.7154i	1.63557	−	0.728205i	0.636502	−	0.771275i	$-0.280381\pi$
$733$	44.2815	−	19.7154i	1.63557	−	0.728205i	0.999072	+	0.0430700i	$0.0137138\pi$
$734$	0.507392	+	4.82751i	0.0187282	+	0.178187i
$735$		0			0
$736$	9.57295	+	16.5808i	0.352864	+	0.611178i
$737$	−1.85410	+	19.8132i	−0.0682967	+	0.729828i
$738$		0			0
$739$	13.1459	−	40.4589i	0.483580	−	1.48831i	−0.350448	−	0.936582i	$-0.613971\pi$
$739$	13.1459	−	40.4589i	0.483580	−	1.48831i	0.834027	−	0.551723i	$-0.186029\pi$
$740$	10.6571	+	4.74484i	0.391762	+	0.174424i
$741$		0			0
$742$	−1.52817	−	0.324822i	−0.0561007	−	0.0119246i
$743$	−41.4350	−	8.80728i	−1.52010	−	0.323108i	−0.629179	−	0.777261i	$-0.716609\pi$
$743$	−41.4350	−	8.80728i	−1.52010	−	0.323108i	−0.890924	+	0.454153i	$0.849942\pi$
$744$		0			0
$745$	17.1417	+	7.63198i	0.628023	+	0.279614i
$746$	−0.667184	+	2.05338i	−0.0244274	+	0.0751797i
$747$		0			0
$748$	27.4058	+	11.8290i	1.00205	+	0.432509i
$749$	−7.01722	−	12.1542i	−0.256404	−	0.444104i
$750$		0			0
$751$	3.26643	+	31.0780i	0.119194	+	1.13405i	0.876637	+	0.481152i	$0.159782\pi$
$751$	3.26643	+	31.0780i	0.119194	+	1.13405i	−0.757443	+	0.652901i	$0.773552\pi$
$752$	−34.3269	+	15.2833i	−1.25177	+	0.557325i
$753$		0			0
$754$	−8.02957	+	8.91774i	−0.292420	+	0.324765i
$755$	−4.32624	−	3.14320i	−0.157448	−	0.114393i
$756$		0			0
$757$	3.39919	−	10.4616i	0.123546	−	0.380234i	−0.870088	−	0.492897i	$-0.835938\pi$
$757$	3.39919	−	10.4616i	0.123546	−	0.380234i	0.993633	+	0.112663i	$0.0359380\pi$
$758$	−3.01722	−	5.22598i	−0.109590	−	0.189816i
$759$		0			0
$760$	0.909830	−	1.57587i	0.0330030	−	0.0571629i
$761$	−4.66967	−	5.18620i	−0.169275	−	0.187999i	0.652538	−	0.757756i	$-0.273704\pi$
$761$	−4.66967	−	5.18620i	−0.169275	−	0.187999i	−0.821814	+	0.569756i	$0.807038\pi$
$762$		0			0
$763$	0.746950	−	7.10675i	0.0270414	−	0.257282i
$764$	3.40576	+	10.4819i	0.123216	+	0.379221i
$765$		0			0
$766$	6.13525	+	4.45752i	0.221676	+	0.161057i
$767$	9.56677	+	4.25940i	0.345436	+	0.153798i
$768$		0			0
$769$	7.89919	−	13.6818i	0.284852	−	0.493378i	−0.687721	−	0.725975i	$-0.741389\pi$
$769$	7.89919	−	13.6818i	0.284852	−	0.493378i	0.972573	+	0.232597i	$0.0747222\pi$
$770$	−0.500853	−	1.48364i	−0.0180495	−	0.0534666i
$771$		0			0
$772$	−19.9494	+	4.24038i	−0.717996	+	0.152615i
$773$	19.1353	−	13.9026i	0.688247	−	0.500041i	−0.187836	−	0.982200i	$-0.560147\pi$
$773$	19.1353	−	13.9026i	0.688247	−	0.500041i	0.876083	+	0.482159i	$0.160147\pi$
$774$		0			0
$775$	−0.663119	−	2.04087i	−0.0238199	−	0.0733102i
$776$	−5.91031	+	6.56406i	−0.212168	+	0.235636i
$777$		0			0
$778$	−0.904430	−	8.60508i	−0.0324254	−	0.308507i
$779$	1.69147	+	1.87857i	0.0606032	+	0.0673067i
$780$		0			0
$781$	6.53908	+	7.09779i	0.233987	+	0.253979i
$782$	8.56231			0.306187
$783$		0			0
$784$	15.2705	−	11.0947i	0.545375	−	0.396238i
$785$	−0.923281	+	8.78443i	−0.0329533	+	0.313530i
$786$		0			0
$787$	−35.2133	−	7.48482i	−1.25522	−	0.266805i	−0.468138	−	0.883655i	$-0.655075\pi$
$787$	−35.2133	−	7.48482i	−1.25522	−	0.266805i	−0.787081	+	0.616850i	$0.788408\pi$
$788$	13.9503	−	6.21108i	0.496959	−	0.221260i
$789$		0			0
$790$	−4.87787	+	1.03682i	−0.173547	+	0.0368885i
$791$	17.2361			0.612844
$792$		0			0
$793$	−70.2492			−2.49462
$794$	0.793796	−	0.168726i	0.0281708	−	0.00598788i
$795$		0			0
$796$	12.1038	−	5.38894i	0.429007	−	0.191006i
$797$	23.7401	+	5.04612i	0.840919	+	0.178743i	0.608183	−	0.793797i	$-0.291899\pi$
$797$	23.7401	+	5.04612i	0.840919	+	0.178743i	0.232736	+	0.972540i	$0.425232\pi$
$798$		0			0
$799$	−6.06043	+	57.6611i	−0.214402	+	2.03990i
$800$	11.6459	−	8.46124i	0.411745	−	0.299150i
$801$		0			0
$802$	−5.56231			−0.196412
$803$	0.474432	+	0.0951981i	0.0167423	+	0.00335947i
$804$		0			0
$805$	3.81953	+	4.24202i	0.134621	+	0.149512i
$806$	0.159705	+	1.51949i	0.00562538	+	0.0535219i
$807$		0			0
$808$	−8.34549	+	9.26860i	−0.293593	+	0.326068i
$809$	5.59017	+	17.2048i	0.196540	+	0.604888i	0.999955	+	0.00946853i	$0.00301397\pi$
$809$	5.59017	+	17.2048i	0.196540	+	0.604888i	−0.803415	+	0.595419i	$0.796986\pi$
$810$		0			0
$811$	−7.02786	+	5.10604i	−0.246782	+	0.179297i	−0.704299	−	0.709903i	$-0.748739\pi$
$811$	−7.02786	+	5.10604i	−0.246782	+	0.179297i	0.457518	+	0.889201i	$0.348739\pi$
$812$	−8.80333	+	1.87121i	−0.308936	+	0.0656664i
$813$		0			0
$814$	−6.44800	+	0.0735897i	−0.226002	+	0.00257932i
$815$	−12.7984	+	22.1674i	−0.448307	+	0.776491i
$816$		0			0
$817$	1.69381	+	0.754131i	0.0592588	+	0.0263837i
$818$	10.4271	+	7.57570i	0.364573	+	0.264878i
$819$		0			0
$820$	−1.79024	−	5.50980i	−0.0625180	−	0.192411i
$821$	3.99453	−	38.0054i	0.139410	−	1.32640i	−0.671402	−	0.741093i	$-0.734308\pi$
$821$	3.99453	−	38.0054i	0.139410	−	1.32640i	0.810813	−	0.585306i	$-0.199026\pi$
$822$		0			0
$823$	−28.2987	−	31.4289i	−0.986432	−	1.09554i	−0.995421	−	0.0955840i	$-0.969528\pi$
$823$	−28.2987	−	31.4289i	−0.986432	−	1.09554i	0.00898947	−	0.999960i	$-0.497139\pi$
$824$	−7.53444	+	13.0500i	−0.262475	+	0.454620i
$825$		0			0
$826$	−0.309017	−	0.535233i	−0.0107521	−	0.0186231i
$827$	17.6246	−	54.2430i	0.612868	−	1.88621i	0.183721	−	0.982978i	$-0.441186\pi$
$827$	17.6246	−	54.2430i	0.612868	−	1.88621i	0.429147	−	0.903235i	$-0.358814\pi$
$828$		0			0
$829$	−35.2254	−	25.5928i	−1.22343	−	0.888874i	−0.227049	−	0.973883i	$-0.572908\pi$
$829$	−35.2254	−	25.5928i	−1.22343	−	0.888874i	−0.996380	+	0.0850096i	$0.972908\pi$
$830$	3.08463	−	3.42583i	0.107069	−	0.118912i
$831$		0			0
$832$	27.8377	−	12.3941i	0.965098	−	0.429689i
$833$	−3.04435	−	28.9651i	−0.105481	−	1.00358i
$834$		0			0
$835$	−3.56231	−	6.17009i	−0.123279	−	0.213525i
$836$	0.572949	−	6.12261i	0.0198159	−	0.211755i
$837$		0			0
$838$	−0.954915	+	2.93893i	−0.0329870	+	0.101524i
$839$	15.7968	+	7.03321i	0.545368	+	0.242813i	0.660878	−	0.750493i	$-0.270184\pi$
$839$	15.7968	+	7.03321i	0.545368	+	0.242813i	−0.115511	+	0.993306i	$0.536851\pi$
$840$		0			0
$841$	5.31887	+	1.13056i	0.183409	+	0.0389848i
$842$	−3.82439	−	0.812899i	−0.131797	−	0.0280144i
$843$		0			0
$844$	−34.6758	−	15.4387i	−1.19359	−	0.531421i
$845$	11.0344	−	33.9605i	0.379596	−	1.16828i
$846$		0			0
$847$	−7.54508	−	8.00448i	−0.259252	−	0.275037i
$848$	6.43363	+	11.1434i	0.220932	+	0.382665i
$849$		0			0
$850$	−0.672922	−	6.40243i	−0.0230810	−	0.219601i
$851$	21.4743	−	9.56099i	0.736130	−	0.327746i
$852$		0			0
$853$	−23.7124	+	26.3353i	−0.811899	+	0.901705i	−0.996708	−	0.0810695i	$-0.974166\pi$
$853$	−23.7124	+	26.3353i	−0.811899	+	0.901705i	0.184810	+	0.982774i	$0.440833\pi$
$854$	3.35410	+	2.43690i	0.114775	+	0.0833889i
$855$		0			0
$856$	6.38448	−	19.6494i	0.218217	−	0.671603i
$857$	12.6803	+	21.9630i	0.433152	+	0.750242i	0.997143	−	0.0755396i	$-0.0240679\pi$
$857$	12.6803	+	21.9630i	0.433152	+	0.750242i	−0.563991	+	0.825781i	$0.690735\pi$
$858$		0			0
$859$	16.2812	−	28.1998i	0.555506	−	0.962164i	−0.442358	−	0.896838i	$-0.645858\pi$
$859$	16.2812	−	28.1998i	0.555506	−	0.962164i	0.997864	−	0.0653258i	$-0.0208087\pi$
$860$	−2.84329	−	3.15779i	−0.0969552	−	0.107680i
$861$		0			0
$862$	−1.36025	+	12.9419i	−0.0463301	+	0.440802i
$863$	−4.46556	−	13.7436i	−0.152009	−	0.467837i	0.845836	−	0.533443i	$-0.179102\pi$
$863$	−4.46556	−	13.7436i	−0.152009	−	0.467837i	−0.997846	+	0.0656059i	$0.979102\pi$
$864$		0			0
$865$	−23.0902	−	16.7760i	−0.785089	−	0.570401i
$866$	5.14435	+	2.29041i	0.174812	+	0.0778313i
$867$		0			0
$868$	−0.572949	+	0.992377i	−0.0194472	+	0.0336835i
$869$	−28.1040	+	20.9129i	−0.953363	+	0.709422i
$870$		0			0
$871$	37.9842	−	8.07380i	1.28705	−	0.273570i
$872$	8.51064	−	6.18334i	0.288207	−	0.209394i
$873$		0			0
$874$	−0.545085	−	1.67760i	−0.0184378	−	0.0567456i
$875$	7.00723	−	7.78231i	0.236887	−	0.263090i
$876$		0			0
$877$	−1.21219	−	11.5332i	−0.0409328	−	0.389449i	−0.995739	−	0.0922193i	$-0.970604\pi$
$877$	−1.21219	−	11.5332i	−0.0409328	−	0.389449i	0.954806	−	0.297230i	$-0.0960628\pi$
$878$	−0.181006	−	0.201028i	−0.00610867	−	0.00678437i
$879$		0			0
$880$	−6.32054	+	11.2419i	−0.213065	+	0.378963i
$881$	−1.81966			−0.0613059			−0.0306530	−	0.999530i	$-0.509759\pi$
$881$	−1.81966			−0.0613059			−0.0306530	+	0.999530i	$0.509759\pi$
$882$		0			0
$883$	28.8435	−	20.9560i	0.970660	−	0.705226i	0.0150579	−	0.999887i	$-0.495207\pi$
$883$	28.8435	−	20.9560i	0.970660	−	0.705226i	0.955602	+	0.294661i	$0.0952068\pi$
$884$	6.08870	−	57.9301i	0.204785	−	1.94840i
$885$		0			0
$886$	−0.461819	−	0.0981626i	−0.0155151	−	0.00329784i
$887$	3.68565	−	1.64096i	0.123752	−	0.0550979i	−0.343927	−	0.938997i	$-0.611757\pi$
$887$	3.68565	−	1.64096i	0.123752	−	0.0550979i	0.467679	+	0.883899i	$0.345090\pi$
$888$		0			0
$889$	−10.3315	+	2.19603i	−0.346507	+	0.0736524i
$890$	3.19350			0.107046
$891$		0			0
$892$	28.7508			0.962647
$893$	11.6833	−	2.48335i	0.390965	−	0.0831023i
$894$		0			0
$895$	5.70895	−	2.54179i	0.190829	−	0.0849626i
$896$	−9.86968	−	2.09786i	−0.329723	−	0.0700847i
$897$		0			0
$898$	0.298335	−	2.83847i	0.00995556	−	0.0947209i
$899$	−2.42705	+	1.76336i	−0.0809467	+	0.0588112i
$900$		0			0
$901$	19.8541			0.661436
$902$	2.16984	+	2.35523i	0.0722477	+	0.0784207i
$903$		0			0
$904$	16.9784	+	18.8564i	0.564694	+	0.627156i
$905$	1.28039	+	12.1821i	0.0425617	+	0.404947i
$906$		0			0
$907$	−9.75833	+	10.8377i	−0.324020	+	0.359861i	−0.883043	−	0.469291i	$-0.844509\pi$
$907$	−9.75833	+	10.8377i	−0.324020	+	0.359861i	0.559024	+	0.829152i	$0.311176\pi$
$908$	−9.52129	−	29.3035i	−0.315975	−	0.972471i
$909$		0			0
$910$	−2.47214	+	1.79611i	−0.0819505	+	0.0595405i
$911$	−18.7612	+	3.98782i	−0.621586	+	0.132122i	−0.507931	−	0.861398i	$-0.669589\pi$
$911$	−18.7612	+	3.98782i	−0.621586	+	0.132122i	−0.113656	+	0.993520i	$0.536256\pi$
$912$		0			0
$913$	9.65487	−	30.9105i	0.319529	−	1.02299i
$914$	0.190983	−	0.330792i	0.00631716	−	0.0109416i
$915$		0			0
$916$	−17.2435	−	7.67731i	−0.569742	−	0.253666i
$917$	−17.1803	−	12.4822i	−0.567345	−	0.412200i
$918$		0			0
$919$	−8.30244	−	25.5523i	−0.273872	−	0.842892i	−0.989516	−	0.144426i	$-0.953866\pi$
$919$	−8.30244	−	25.5523i	−0.273872	−	0.842892i	0.715643	−	0.698466i	$-0.246134\pi$
$920$	−0.878379	+	8.35722i	−0.0289593	+	0.275529i
$921$		0			0
$922$	4.12665	+	4.58311i	0.135904	+	0.150937i
$923$	9.41641	−	16.3097i	0.309945	−	0.536840i
$924$		0			0
$925$	−8.83688	−	15.3059i	−0.290555	−	0.503256i
$926$	2.00658	−	6.17561i	0.0659402	−	0.202943i
$927$		0			0
$928$	−16.2812	−	11.8290i	−0.534455	−	0.388304i
$929$	32.2993	−	35.8720i	1.05970	−	1.17692i	0.0760042	−	0.997107i	$-0.475784\pi$
$929$	32.2993	−	35.8720i	1.05970	−	1.17692i	0.983701	−	0.179814i	$-0.0575496\pi$
$930$		0			0
$931$	−5.48127	+	2.44042i	−0.179641	+	0.0799815i
$932$	2.15602	+	20.5132i	0.0706228	+	0.671931i
$933$		0			0
$934$	−0.145898	−	0.252703i	−0.00477393	−	0.00826869i
$935$	10.1459	+	17.1190i	0.331806	+	0.559852i
$936$		0			0
$937$	−7.11803	+	21.9071i	−0.232536	+	0.715672i	0.764903	+	0.644146i	$0.222787\pi$
$937$	−7.11803	+	21.9071i	−0.232536	+	0.715672i	−0.997439	+	0.0715265i	$0.977213\pi$
$938$	−2.09366	−	0.932157i	−0.0683604	−	0.0304360i
$939$		0			0
$940$	−26.7757	−	5.69134i	−0.873325	−	0.185631i
$941$	26.5656	+	5.64668i	0.866013	+	0.184077i	0.619436	−	0.785047i	$-0.287361\pi$
$941$	26.5656	+	5.64668i	0.866013	+	0.184077i	0.246576	+	0.969123i	$0.420694\pi$
$942$		0			0
$943$	−10.6645	−	4.74815i	−0.347284	−	0.154621i
$944$	−1.57295	+	4.84104i	−0.0511951	+	0.157562i
$945$		0			0
$946$	2.15654	+	0.930812i	0.0701152	+	0.0302633i
$947$	18.3541	+	31.7902i	0.596428	+	1.03304i	0.993344	+	0.115189i	$0.0367473\pi$
$947$	18.3541	+	31.7902i	0.596428	+	1.03304i	−0.396915	+	0.917855i	$0.629919\pi$
$948$		0			0
$949$	−0.0987033	−	0.939099i	−0.00320404	−	0.0304844i
$950$	−1.21158	+	0.539430i	−0.0393088	+	0.0175014i
$951$		0			0
$952$	−4.78154	+	5.31044i	−0.154971	+	0.172112i
$953$	−7.68034	−	5.58009i	−0.248791	−	0.180757i	0.456400	−	0.889775i	$-0.349139\pi$
$953$	−7.68034	−	5.58009i	−0.248791	−	0.180757i	−0.705191	+	0.709018i	$0.749139\pi$
$954$		0			0
$955$	−2.27051	+	6.98791i	−0.0734720	+	0.226123i
$956$	−9.70820	−	16.8151i	−0.313986	−	0.543839i
$957$		0			0
$958$	−2.24671	+	3.89142i	−0.0725879	+	0.125726i
$959$	−5.76659	−	6.40445i	−0.186213	−	0.206810i
$960$		0			0
$961$	3.20046	−	30.4503i	0.103241	−	0.982268i
$962$	3.88854	+	11.9677i	0.125372	+	0.385854i
$963$		0			0
$964$	−40.2492	−	29.2428i	−1.29634	−	0.941846i
$965$	−12.4212	−	5.53030i	−0.399854	−	0.178027i
$966$		0			0
$967$	−26.2426	+	45.4536i	−0.843907	+	1.46169i	0.0426608	+	0.999090i	$0.486417\pi$
$967$	−26.2426	+	45.4536i	−0.843907	+	1.46169i	−0.886567	+	0.462599i	$0.846917\pi$
$968$	1.32469	−	16.1392i	0.0425771	−	0.518734i
$969$		0			0
$970$	−2.77091	+	0.588976i	−0.0889686	+	0.0189109i
$971$	7.50000	−	5.44907i	0.240686	−	0.174869i	−0.460903	−	0.887451i	$-0.652474\pi$
$971$	7.50000	−	5.44907i	0.240686	−	0.174869i	0.701589	+	0.712582i	$0.252474\pi$
$972$		0			0
$973$	−3.00000	−	9.23305i	−0.0961756	−	0.295998i
$974$	−3.31717	+	3.68409i	−0.106289	+	0.118046i
$975$		0			0
$976$	−3.56922	−	33.9588i	−0.114248	−	1.08700i
$977$	−10.5481	−	11.7149i	−0.337465	−	0.374792i	0.550397	−	0.834903i	$-0.314476\pi$
$977$	−10.5481	−	11.7149i	−0.337465	−	0.374792i	−0.887862	+	0.460111i	$0.847810\pi$
$978$		0			0
$979$	20.3885	−	9.35778i	0.651619	−	0.299076i
$980$	13.7508			0.439252
$981$		0			0
$982$	2.26393	−	1.64484i	0.0722450	−	0.0524890i
$983$	0.967657	−	9.20664i	0.0308635	−	0.293646i	−0.968193	−	0.250206i	$-0.919502\pi$
$983$	0.967657	−	9.20664i	0.0308635	−	0.293646i	0.999056	−	0.0434400i	$-0.0138317\pi$
$984$		0			0
$985$	9.95788	+	2.11661i	0.317284	+	0.0674409i
$986$	−8.22191	+	3.66063i	−0.261839	+	0.116578i
$987$		0			0
$988$	−11.7378	+	2.49494i	−0.373428	+	0.0793746i
$989$	−8.56231			−0.272265
$990$		0			0
$991$	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
$993$		0			0
$994$	−1.01537	+	0.452070i	−0.0322054	+	0.0143388i
$995$	8.63980	+	1.83645i	0.273900	+	0.0582192i
$996$		0			0
$997$	−0.771626	+	7.34153i	−0.0244376	+	0.232508i	0.975485	+	0.220066i	$0.0706273\pi$
$997$	−0.771626	+	7.34153i	−0.0244376	+	0.232508i	−0.999923	+	0.0124424i	$0.996039\pi$
$998$	−11.8713	+	8.62502i	−0.375780	+	0.273020i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	297.2.n.a.64.1		8
3.2	odd	2		99.2.m.a.31.1	yes	8
9.2	odd	6		99.2.m.a.97.1	yes	8
9.4	even	3		891.2.f.a.163.1		4
9.5	odd	6		891.2.f.b.163.1		4
9.7	even	3	inner	297.2.n.a.262.1		8
11.5	even	5	inner	297.2.n.a.280.1		8
33.5	odd	10		99.2.m.a.49.1	yes	8
33.26	odd	10		1089.2.e.g.364.1		4
33.29	even	10		1089.2.e.d.364.2		4
99.4	even	15		9801.2.a.bb.1.1		2
99.5	odd	30		891.2.f.b.82.1		4
99.16	even	15	inner	297.2.n.a.181.1		8
99.29	even	30		1089.2.e.d.727.2		4
99.38	odd	30		99.2.m.a.16.1	✓	8
99.40	odd	30		9801.2.a.m.1.2		2
99.49	even	15		891.2.f.a.82.1		4
99.59	odd	30		9801.2.a.n.1.2		2
99.92	odd	30		1089.2.e.g.727.1		4
99.95	even	30		9801.2.a.bc.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.m.a.16.1	✓	8	99.38	odd	30
99.2.m.a.31.1	yes	8	3.2	odd	2
99.2.m.a.49.1	yes	8	33.5	odd	10
99.2.m.a.97.1	yes	8	9.2	odd	6
297.2.n.a.64.1		8	1.1	even	1	trivial
297.2.n.a.181.1		8	99.16	even	15	inner
297.2.n.a.262.1		8	9.7	even	3	inner
297.2.n.a.280.1		8	11.5	even	5	inner
891.2.f.a.82.1		4	99.49	even	15
891.2.f.a.163.1		4	9.4	even	3
891.2.f.b.82.1		4	99.5	odd	30
891.2.f.b.163.1		4	9.5	odd	6
1089.2.e.d.364.2		4	33.29	even	10
1089.2.e.d.727.2		4	99.29	even	30
1089.2.e.g.364.1		4	33.26	odd	10
1089.2.e.g.727.1		4	99.92	odd	30
9801.2.a.m.1.2		2	99.40	odd	30
9801.2.a.n.1.2		2	99.59	odd	30
9801.2.a.bb.1.1		2	99.4	even	15
9801.2.a.bc.1.1		2	99.95	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 297 = 3^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	297.n (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.373619 + 0.0794152i) q^{2} +(-1.69381 + 0.754131i) q^{4} +(-1.20906 - 0.256993i) q^{5} +(0.104528 - 0.994522i) q^{7} +(1.19098 - 0.865300i) q^{8} +0.472136 q^{10} +(3.01430 - 1.38348i) q^{11} +(-4.33070 - 4.80973i) q^{13} +(0.0399263 + 0.379874i) q^{14} +(2.10502 - 2.33786i) q^{16} +(-1.50000 - 4.61653i) q^{17} +(-0.809017 + 0.587785i) q^{19} +(2.24171 - 0.476491i) q^{20} +(-1.01633 + 0.756276i) q^{22} +(2.30902 - 3.99933i) q^{23} +(-3.17195 - 1.41224i) q^{25} +(2.00000 + 1.45309i) q^{26} +(0.572949 + 1.76336i) q^{28} +(-0.507392 + 4.82751i) q^{29} +(0.413545 + 0.459289i) q^{31} +(-2.07295 + 3.59045i) q^{32} +(0.927051 + 1.60570i) q^{34} +(-0.381966 + 1.17557i) q^{35} +(4.11803 + 2.99193i) q^{37} +(0.255585 - 0.283856i) q^{38} +(-1.66234 + 0.740122i) q^{40} +(-0.264234 - 2.51402i) q^{41} +(-0.927051 - 1.60570i) q^{43} +(-4.06231 + 4.61653i) q^{44} +(-0.545085 + 1.67760i) q^{46} +(-10.9116 - 4.85817i) q^{47} +(5.86889 + 1.24747i) q^{49} +(1.29726 + 0.275740i) q^{50} +(10.9625 + 4.88084i) q^{52} +(-1.26393 + 3.88998i) q^{53} +(-4.00000 + 0.898056i) q^{55} +(-0.736068 - 1.27491i) q^{56} +(-0.193806 - 1.84395i) q^{58} +(-1.47815 + 0.658114i) q^{59} +(7.26281 - 8.06617i) q^{61} +(-0.190983 - 0.138757i) q^{62} +(-1.45492 + 4.47777i) q^{64} +(4.00000 + 6.92820i) q^{65} +(-3.00000 + 5.19615i) q^{67} +(6.02218 + 6.68830i) q^{68} +(0.0493516 - 0.469550i) q^{70} +(0.899187 + 2.76741i) q^{71} +(0.118034 + 0.0857567i) q^{73} +(-1.77618 - 0.790807i) q^{74} +(0.927051 - 1.60570i) q^{76} +(-1.06082 - 3.14240i) q^{77} +(-10.3315 + 2.19603i) q^{79} +(-3.14590 + 2.28563i) q^{80} +(0.298374 + 0.918300i) q^{82} +(6.53335 - 7.25602i) q^{83} +(0.627171 + 5.96713i) q^{85} +(0.473881 + 0.526298i) q^{86} +(2.39285 - 4.25597i) q^{88} +6.76393 q^{89} +(-5.23607 + 3.80423i) q^{91} +(-0.895005 + 8.51540i) q^{92} +(4.46261 + 0.948557i) q^{94} +(1.12920 - 0.502754i) q^{95} +(-5.86889 + 1.24747i) q^{97} -2.29180 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} - 6 q^{4} - 6 q^{5} - q^{7} + 14 q^{8} - 32 q^{10} - q^{11} + 8 q^{13} + q^{14} + 14 q^{16} - 12 q^{17} - 2 q^{19} - 24 q^{20} + 11 q^{22} + 14 q^{23} - 9 q^{25} + 16 q^{26} + 18 q^{28}+ \cdots - 72 q^{98}+O(q^{100}) \) 8 * q + 4 * q^2 - 6 * q^4 - 6 * q^5 - q^7 + 14 * q^8 - 32 * q^10 - q^11 + 8 * q^13 + q^14 + 14 * q^16 - 12 * q^17 - 2 * q^19 - 24 * q^20 + 11 * q^22 + 14 * q^23 - 9 * q^25 + 16 * q^26 + 18 * q^28 + 9 * q^29 - 3 * q^31 - 30 * q^32 - 6 * q^34 - 12 * q^35 + 24 * q^37 + 4 * q^38 + 12 * q^40 - 3 * q^41 + 6 * q^43 + 48 * q^44 + 18 * q^46 - 23 * q^47 - 6 * q^49 + 24 * q^50 + 12 * q^52 - 28 * q^53 - 32 * q^55 + 12 * q^56 + 6 * q^58 - 3 * q^59 - 6 * q^62 - 34 * q^64 + 32 * q^65 - 24 * q^67 + 9 * q^68 - 6 * q^70 - 42 * q^71 - 8 * q^73 - 13 * q^74 - 6 * q^76 + 11 * q^77 - 22 * q^79 - 52 * q^80 - 96 * q^82 + 17 * q^83 - 6 * q^85 - 21 * q^86 + 37 * q^88 + 72 * q^89 - 24 * q^91 + 21 * q^92 + 28 * q^94 + 4 * q^95 + 6 * q^97 - 72 * q^98

Introduction

L-functions

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