LMFDB - Embedded newform 117.2.i.a.8.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,2,Mod(8,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("117.8");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	117.i (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.934249703649$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.26525057735983104.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 16x^{10} + 103x^{8} - 260x^{6} + 259x^{4} + 356x^{2} + 169 $ x^12 - 16x^10 + 103x^8 - 260x^6 + 259x^4 + 356*x^2 + 169
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{5}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			8.2
Root			$0.248859 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	117.8
Dual form			117.2.i.a.44.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.47512 + 1.47512i) q^{2} -2.35194i q^{4} +(-0.955965 + 0.955965i) q^{5} +(-3.08613 + 3.08613i) q^{7} +(0.519151 + 0.519151i) q^{8} -2.82032i q^{10} +(0.955965 + 0.955965i) q^{11} +(-3.43807 - 1.08613i) q^{13} -9.10481i q^{14} +3.17226 q^{16} -4.24264 q^{17} +(2.43807 + 2.43807i) q^{19} +(2.24837 + 2.24837i) q^{20} -2.82032 q^{22} +7.81240 q^{23} +3.17226i q^{25} +(6.67372 - 3.46939i) q^{26} +(7.25839 + 7.25839i) q^{28} +8.23118i q^{29} +(1.73419 + 1.73419i) q^{31} +(-5.71776 + 5.71776i) q^{32} +(6.25839 - 6.25839i) q^{34} -5.90047i q^{35} +(1.00000 - 1.00000i) q^{37} -7.19287 q^{38} -0.992582 q^{40} +(3.28668 - 3.28668i) q^{41} -7.46838i q^{43} +(2.24837 - 2.24837i) q^{44} +(-11.5242 + 11.5242i) q^{46} +(0.955965 + 0.955965i) q^{47} -12.0484i q^{49} +(-4.67945 - 4.67945i) q^{50} +(-2.55451 + 8.08613i) q^{52} +5.48169i q^{53} -1.82774 q^{55} -3.20434 q^{56} +(-12.1419 - 12.1419i) q^{58} +(-1.57549 - 1.57549i) q^{59} -6.87614 q^{61} -5.11627 q^{62} -10.5242i q^{64} +(4.32498 - 2.24837i) q^{65} +(2.91387 + 2.91387i) q^{67} +9.97843i q^{68} +(8.70388 + 8.70388i) q^{70} +(-6.23691 + 6.23691i) q^{71} +(-3.82032 + 3.82032i) q^{73} +2.95023i q^{74} +(5.73419 - 5.73419i) q^{76} -5.90047 q^{77} +5.64064 q^{79} +(-3.03257 + 3.03257i) q^{80} +9.69646i q^{82} +(10.0608 - 10.0608i) q^{83} +(4.05582 - 4.05582i) q^{85} +(11.0167 + 11.0167i) q^{86} +0.992582i q^{88} +(-6.85643 - 6.85643i) q^{89} +(13.9623 - 7.25839i) q^{91} -18.3743i q^{92} -2.82032 q^{94} -4.66142 q^{95} +(6.52420 + 6.52420i) q^{97} +(17.7728 + 17.7728i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 8 q^{7} - 4 q^{13} - 20 q^{16} - 8 q^{19} + 16 q^{22} - 12 q^{34} + 12 q^{37} + 96 q^{40} - 72 q^{46} + 40 q^{52} - 80 q^{55} - 92 q^{58} - 8 q^{61} + 64 q^{67} + 88 q^{70} + 4 q^{73} + 48 q^{76}+ \cdots + 12 q^{97}+O(q^{100}) $ 12 * q - 8 * q^7 - 4 * q^13 - 20 * q^16 - 8 * q^19 + 16 * q^22 - 12 * q^34 + 12 * q^37 + 96 * q^40 - 72 * q^46 + 40 * q^52 - 80 * q^55 - 92 * q^58 - 8 * q^61 + 64 * q^67 + 88 * q^70 + 4 * q^73 + 48 * q^76 - 32 * q^79 + 24 * q^85 + 64 * q^91 + 16 * q^94 + 12 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.47512	+	1.47512i	−1.04307	+	1.04307i	−0.0440351	+	0.999030i	$0.514021\pi$
$2$	−1.47512	+	1.47512i	−1.04307	+	1.04307i	−0.999030	+	0.0440351i	$0.985979\pi$
$3$		0			0
$3$		0			0
$4$		−	2.35194i		−	1.17597i
$5$	−0.955965	+	0.955965i	−0.427521	+	0.427521i	−0.887783	−	0.460262i	$-0.847755\pi$
$5$	−0.955965	+	0.955965i	−0.427521	+	0.427521i	0.460262	+	0.887783i	$0.347755\pi$
$6$		0			0
$7$	−3.08613	+	3.08613i	−1.16645	+	1.16645i	−0.183411	+	0.983036i	$0.558714\pi$
$7$	−3.08613	+	3.08613i	−1.16645	+	1.16645i	−0.983036	+	0.183411i	$0.941286\pi$
$8$	0.519151	+	0.519151i	0.183548	+	0.183548i
$9$		0			0
$10$		−	2.82032i		−	0.891864i
$11$	0.955965	+	0.955965i	0.288234	+	0.288234i	0.836382	−	0.548147i	$-0.184667\pi$
$11$	0.955965	+	0.955965i	0.288234	+	0.288234i	−0.548147	+	0.836382i	$0.684667\pi$
$12$		0			0
$13$	−3.43807	−	1.08613i	−0.953549	−	0.301238i
$13$	−3.43807	−	1.08613i	−0.953549	−	0.301238i
$14$		−	9.10481i		−	2.43336i
$15$		0			0
$16$	3.17226			0.793065
$17$	−4.24264			−1.02899			−0.514496	−	0.857493i	$-0.672021\pi$
$17$	−4.24264			−1.02899			−0.514496	+	0.857493i	$0.672021\pi$
$18$		0			0
$19$	2.43807	+	2.43807i	0.559331	+	0.559331i	0.929117	−	0.369786i	$-0.120569\pi$
$19$	2.43807	+	2.43807i	0.559331	+	0.559331i	−0.369786	+	0.929117i	$0.620569\pi$
$20$	2.24837	+	2.24837i	0.502751	+	0.502751i
$21$		0			0
$22$	−2.82032			−0.601294
$23$	7.81240			1.62900			0.814499	−	0.580165i	$-0.197012\pi$
$23$	7.81240			1.62900			0.814499	+	0.580165i	$0.197012\pi$
$24$		0			0
$25$			3.17226i			0.634452i
$26$	6.67372	−	3.46939i	1.30882	−	0.680402i
$27$		0			0
$28$	7.25839	+	7.25839i	1.37171	+	1.37171i
$29$			8.23118i			1.52849i	0.644925	+	0.764246i	$0.276888\pi$
$29$			8.23118i			1.52849i	−0.644925	+	0.764246i	$0.723112\pi$
$30$		0			0
$31$	1.73419	+	1.73419i	0.311470	+	0.311470i	0.845479	−	0.534009i	$-0.179315\pi$
$31$	1.73419	+	1.73419i	0.311470	+	0.311470i	−0.534009	+	0.845479i	$0.679315\pi$
$32$	−5.71776	+	5.71776i	−1.01077	+	1.01077i
$33$		0			0
$34$	6.25839	−	6.25839i	1.07331	−	1.07331i
$35$		−	5.90047i		−	0.997361i
$36$		0			0
$37$	1.00000	−	1.00000i	0.164399	−	0.164399i	−0.620113	−	0.784512i	$-0.712913\pi$
$37$	1.00000	−	1.00000i	0.164399	−	0.164399i	0.784512	+	0.620113i	$0.212913\pi$
$38$	−7.19287			−1.16684
$39$		0			0
$40$	−0.992582			−0.156941
$41$	3.28668	−	3.28668i	0.513292	−	0.513292i	−0.402241	−	0.915534i	$-0.631769\pi$
$41$	3.28668	−	3.28668i	0.513292	−	0.513292i	0.915534	+	0.402241i	$0.131769\pi$
$42$		0			0
$43$		−	7.46838i		−	1.13892i	−0.822020	−	0.569459i	$-0.807153\pi$
$43$		−	7.46838i		−	1.13892i	0.822020	−	0.569459i	$-0.192847\pi$
$44$	2.24837	−	2.24837i	0.338955	−	0.338955i
$45$		0			0
$46$	−11.5242	+	11.5242i	−1.69915	+	1.69915i
$47$	0.955965	+	0.955965i	0.139442	+	0.139442i	0.773382	−	0.633940i	$-0.218563\pi$
$47$	0.955965	+	0.955965i	0.139442	+	0.139442i	−0.633940	+	0.773382i	$0.718563\pi$
$48$		0			0
$49$		−	12.0484i		−	1.72120i
$50$	−4.67945	−	4.67945i	−0.661775	−	0.661775i
$51$		0			0
$52$	−2.55451	+	8.08613i	−0.354247	+	1.12134i
$53$			5.48169i			0.752968i	0.926423	+	0.376484i	$0.122867\pi$
$53$			5.48169i			0.752968i	−0.926423	+	0.376484i	$0.877133\pi$
$54$		0			0
$55$	−1.82774			−0.246452
$56$	−3.20434			−0.428198
$57$		0			0
$58$	−12.1419	−	12.1419i	−1.59432	−	1.59432i
$59$	−1.57549	−	1.57549i	−0.205111	−	0.205111i	0.597075	−	0.802186i	$-0.296330\pi$
$59$	−1.57549	−	1.57549i	−0.205111	−	0.205111i	−0.802186	+	0.597075i	$0.796330\pi$
$60$		0			0
$61$	−6.87614			−0.880399			−0.440200	−	0.897900i	$-0.645092\pi$
$61$	−6.87614			−0.880399			−0.440200	+	0.897900i	$0.645092\pi$
$62$	−5.11627			−0.649767
$63$		0			0
$64$		−	10.5242i		−	1.31552i
$65$	4.32498	−	2.24837i	0.536448	−	0.278876i
$66$		0			0
$67$	2.91387	+	2.91387i	0.355986	+	0.355986i	0.862331	−	0.506345i	$-0.169004\pi$
$67$	2.91387	+	2.91387i	0.355986	+	0.355986i	−0.506345	+	0.862331i	$0.669004\pi$
$68$			9.97843i			1.21006i
$69$		0			0
$70$	8.70388	+	8.70388i	1.04031	+	1.04031i
$71$	−6.23691	+	6.23691i	−0.740185	+	0.740185i	−0.972613	−	0.232429i	$-0.925333\pi$
$71$	−6.23691	+	6.23691i	−0.740185	+	0.740185i	0.232429	+	0.972613i	$0.425333\pi$
$72$		0			0
$73$	−3.82032	+	3.82032i	−0.447135	+	0.447135i	−0.894401	−	0.447266i	$-0.852398\pi$
$73$	−3.82032	+	3.82032i	−0.447135	+	0.447135i	0.447266	+	0.894401i	$0.352398\pi$
$74$			2.95023i			0.342958i
$75$		0			0
$76$	5.73419	−	5.73419i	0.657757	−	0.657757i
$77$	−5.90047			−0.672421
$78$		0			0
$79$	5.64064			0.634622			0.317311	−	0.948322i	$-0.397220\pi$
$79$	5.64064			0.634622			0.317311	+	0.948322i	$0.397220\pi$
$80$	−3.03257	+	3.03257i	−0.339052	+	0.339052i
$81$		0			0
$82$			9.69646i			1.07079i
$83$	10.0608	−	10.0608i	1.10431	−	1.10431i	0.110429	−	0.993884i	$-0.464778\pi$
$83$	10.0608	−	10.0608i	1.10431	−	1.10431i	0.993884	−	0.110429i	$-0.0352225\pi$
$84$		0			0
$85$	4.05582	−	4.05582i	0.439915	−	0.439915i
$86$	11.0167	+	11.0167i	1.18797	+	1.18797i
$87$		0			0
$88$			0.992582i			0.105810i
$89$	−6.85643	−	6.85643i	−0.726780	−	0.726780i	0.243197	−	0.969977i	$-0.421804\pi$
$89$	−6.85643	−	6.85643i	−0.726780	−	0.726780i	−0.969977	+	0.243197i	$0.921804\pi$
$90$		0			0
$91$	13.9623	−	7.25839i	1.46364	−	0.760886i
$92$		−	18.3743i		−	1.91565i
$93$		0			0
$94$	−2.82032			−0.290894
$95$	−4.66142			−0.478252
$96$		0			0
$97$	6.52420	+	6.52420i	0.662432	+	0.662432i	0.955953	−	0.293521i	$-0.0948269\pi$
$97$	6.52420	+	6.52420i	0.662432	+	0.662432i	−0.293521	+	0.955953i	$0.594827\pi$
$98$	17.7728	+	17.7728i	1.79532	+	1.79532i
$99$		0			0
$100$	7.46096			0.746096
$101$	−12.0550			−1.19952			−0.599761	−	0.800180i	$-0.704738\pi$
$101$	−12.0550			−1.19952			−0.599761	+	0.800180i	$0.704738\pi$
$102$		0			0
$103$			15.5800i			1.53514i	0.640962	+	0.767572i	$0.278535\pi$
$103$			15.5800i			1.53514i	−0.640962	+	0.767572i	$0.721465\pi$
$104$	−1.22101	−	2.34874i	−0.119730	−	0.230313i
$105$		0			0
$106$	−8.08613	−	8.08613i	−0.785394	−	0.785394i
$107$		−	5.22758i		−	0.505370i	−0.967549	−	0.252685i	$-0.918686\pi$
$107$		−	5.22758i		−	0.505370i	0.967549	−	0.252685i	$-0.0813136\pi$
$108$		0			0
$109$	−3.82032	−	3.82032i	−0.365920	−	0.365920i	0.500067	−	0.865987i	$-0.333309\pi$
$109$	−3.82032	−	3.82032i	−0.365920	−	0.365920i	−0.865987	+	0.500067i	$0.833309\pi$
$110$	2.69613	−	2.69613i	0.257066	−	0.257066i
$111$		0			0
$112$	−9.79001	+	9.79001i	−0.925069	+	0.925069i
$113$			8.23118i			0.774324i	0.922012	+	0.387162i	$0.126545\pi$
$113$			8.23118i			0.774324i	−0.922012	+	0.387162i	$0.873455\pi$
$114$		0			0
$115$	−7.46838	+	7.46838i	−0.696430	+	0.696430i
$116$	19.3592			1.79746
$117$		0			0
$118$	4.64806			0.427889
$119$	13.0933	−	13.0933i	1.20026	−	1.20026i
$120$		0			0
$121$		−	9.17226i		−	0.833842i
$122$	10.1431	−	10.1431i	0.918314	−	0.918314i
$123$		0			0
$124$	4.07871	−	4.07871i	0.366279	−	0.366279i
$125$	−7.81240	−	7.81240i	−0.698762	−	0.698762i
$126$		0			0
$127$			8.87614i			0.787630i	0.919190	+	0.393815i	$0.128845\pi$
$127$			8.87614i			0.787630i	−0.919190	+	0.393815i	$0.871155\pi$
$128$	4.08891	+	4.08891i	0.361412	+	0.361412i
$129$		0			0
$130$	−3.06324	+	9.69646i	−0.268664	+	0.850436i
$131$			3.98854i			0.348480i	0.984703	+	0.174240i	$0.0557469\pi$
$131$			3.98854i			0.348480i	−0.984703	+	0.174240i	$0.944253\pi$
$132$		0			0
$133$	−15.0484			−1.30486
$134$	−8.59660			−0.742633
$135$		0			0
$136$	−2.20257	−	2.20257i	−0.188869	−	0.188869i
$137$	−3.28668	−	3.28668i	−0.280800	−	0.280800i	0.552628	−	0.833428i	$-0.313625\pi$
$137$	−3.28668	−	3.28668i	−0.280800	−	0.280800i	−0.833428	+	0.552628i	$0.813625\pi$
$138$		0			0
$139$	4.11164			0.348744			0.174372	−	0.984680i	$-0.444210\pi$
$139$	4.11164			0.348744			0.174372	+	0.984680i	$0.444210\pi$
$140$	−13.8775			−1.17287
$141$		0			0
$142$		−	18.4003i		−	1.54412i
$143$	−2.24837	−	4.32498i	−0.188018	−	0.361673i
$144$		0			0
$145$	−7.86872	−	7.86872i	−0.653462	−	0.653462i
$146$		−	11.2708i		−	0.932781i
$147$		0			0
$148$	−2.35194	−	2.35194i	−0.193328	−	0.193328i
$149$	3.28668	−	3.28668i	0.269255	−	0.269255i	−0.559545	−	0.828800i	$-0.689024\pi$
$149$	3.28668	−	3.28668i	0.269255	−	0.269255i	0.828800	+	0.559545i	$0.189024\pi$
$150$		0			0
$151$	−4.78259	+	4.78259i	−0.389202	+	0.389202i	−0.874403	−	0.485201i	$-0.838746\pi$
$151$	−4.78259	+	4.78259i	−0.389202	+	0.389202i	0.485201	+	0.874403i	$0.338746\pi$
$152$			2.53145i			0.205328i
$153$		0			0
$154$	8.70388	−	8.70388i	0.701379	−	0.701379i
$155$	−3.31565			−0.266320
$156$		0			0
$157$	23.3929			1.86696			0.933479	−	0.358632i	$-0.116757\pi$
$157$	23.3929			1.86696			0.933479	+	0.358632i	$0.116757\pi$
$158$	−8.32061	+	8.32061i	−0.661952	+	0.661952i
$159$		0			0
$160$		−	10.9320i		−	0.864247i
$161$	−24.1101	+	24.1101i	−1.90014	+	1.90014i
$162$		0			0
$163$	3.20257	−	3.20257i	0.250845	−	0.250845i	−0.570472	−	0.821317i	$-0.693240\pi$
$163$	3.20257	−	3.20257i	0.250845	−	0.250845i	0.821317	+	0.570472i	$0.193240\pi$
$164$	−7.73006	−	7.73006i	−0.603616	−	0.603616i
$165$		0			0
$166$			29.6816i			2.30374i
$167$	17.2536	+	17.2536i	1.33513	+	1.33513i	0.900714	+	0.434414i	$0.143044\pi$
$167$	17.2536	+	17.2536i	1.33513	+	1.33513i	0.434414	+	0.900714i	$0.356956\pi$
$168$		0			0
$169$	10.6406	+	7.46838i	0.818511	+	0.574491i
$170$			11.9656i			0.917720i
$171$		0			0
$172$	−17.5652			−1.33933
$173$	5.64636			0.429285			0.214643	−	0.976693i	$-0.431141\pi$
$173$	5.64636			0.429285			0.214643	+	0.976693i	$0.431141\pi$
$174$		0			0
$175$	−9.79001	−	9.79001i	−0.740055	−	0.740055i
$176$	3.03257	+	3.03257i	0.228589	+	0.228589i
$177$		0			0
$178$	20.2281			1.51616
$179$	8.48528			0.634220			0.317110	−	0.948389i	$-0.397288\pi$
$179$	8.48528			0.634220			0.317110	+	0.948389i	$0.397288\pi$
$180$		0			0
$181$		−	8.11164i		−	0.602933i	−0.953477	−	0.301467i	$-0.902524\pi$
$181$		−	8.11164i		−	0.602933i	0.953477	−	0.301467i	$-0.0974762\pi$
$182$	−9.88900	+	31.3030i	−0.733022	+	2.32033i
$183$		0			0
$184$	4.05582	+	4.05582i	0.298999	+	0.298999i
$185$			1.91193i			0.140568i
$186$		0			0
$187$	−4.05582	−	4.05582i	−0.296591	−	0.296591i
$188$	2.24837	−	2.24837i	0.163979	−	0.163979i
$189$		0			0
$190$	6.87614	−	6.87614i	0.498848	−	0.498848i
$191$			9.72433i			0.703628i	0.936070	+	0.351814i	$0.114435\pi$
$191$			9.72433i			0.703628i	−0.936070	+	0.351814i	$0.885565\pi$
$192$		0			0
$193$	−6.40776	+	6.40776i	−0.461240	+	0.461240i	−0.899062	−	0.437821i	$-0.855750\pi$
$193$	−6.40776	+	6.40776i	−0.461240	+	0.461240i	0.437821	+	0.899062i	$0.355750\pi$
$194$	−19.2479			−1.38192
$195$		0			0
$196$	−28.3371			−2.02408
$197$	15.3417	−	15.3417i	1.09305	−	1.09305i	0.0978508	−	0.995201i	$-0.468803\pi$
$197$	15.3417	−	15.3417i	1.09305	−	1.09305i	0.995201	−	0.0978508i	$-0.0311968\pi$
$198$		0			0
$199$			0.764504i			0.0541942i	0.999633	+	0.0270971i	$0.00862633\pi$
$199$			0.764504i			0.0541942i	−0.999633	+	0.0270971i	$0.991374\pi$
$200$	−1.64688	+	1.64688i	−0.116452	+	0.116452i
$201$		0			0
$202$	17.7826	−	17.7826i	1.25118	−	1.25118i
$203$	−25.4025	−	25.4025i	−1.78290	−	1.78290i
$204$		0			0
$205$			6.28390i			0.438886i
$206$	−22.9823	−	22.9823i	−1.60126	−	1.60126i
$207$		0			0
$208$	−10.9065	−	3.44549i	−0.756226	−	0.238902i
$209$			4.66142i			0.322437i
$210$		0			0
$211$	13.7523			0.946746			0.473373	−	0.880862i	$-0.343036\pi$
$211$	13.7523			0.946746			0.473373	+	0.880862i	$0.343036\pi$
$212$	12.8926			0.885467
$213$		0			0
$214$	7.71130	+	7.71130i	0.527133	+	0.527133i
$215$	7.13951	+	7.13951i	0.486911	+	0.486911i
$216$		0			0
$217$	−10.7039			−0.726627
$218$	11.2708			0.763358
$219$		0			0
$220$			4.29873i			0.289820i
$221$	14.5865	+	4.60806i	0.981194	+	0.309972i
$222$		0			0
$223$	−14.6103	−	14.6103i	−0.978380	−	0.978380i	0.0213911	−	0.999771i	$-0.493190\pi$
$223$	−14.6103	−	14.6103i	−0.978380	−	0.978380i	−0.999771	+	0.0213911i	$0.993190\pi$
$224$		−	35.2915i		−	2.35801i
$225$		0			0
$226$	−12.1419	−	12.1419i	−0.807670	−	0.807670i
$227$	−3.03257	+	3.03257i	−0.201279	+	0.201279i	−0.800548	−	0.599269i	$-0.795458\pi$
$227$	−3.03257	+	3.03257i	−0.201279	+	0.201279i	0.599269	+	0.800548i	$0.295458\pi$
$228$		0			0
$229$	−2.35194	+	2.35194i	−0.155421	+	0.155421i	−0.780534	−	0.625113i	$-0.785053\pi$
$229$	−2.35194	+	2.35194i	−0.155421	+	0.155421i	0.625113	+	0.780534i	$0.285053\pi$
$230$		−	22.0335i		−	1.45284i
$231$		0			0
$232$	−4.27323	+	4.27323i	−0.280551	+	0.280551i
$233$	27.6798			1.81337			0.906683	−	0.421812i	$-0.138606\pi$
$233$	27.6798			1.81337			0.906683	+	0.421812i	$0.138606\pi$
$234$		0			0
$235$	−1.82774			−0.119229
$236$	−3.70545	+	3.70545i	−0.241205	+	0.241205i
$237$		0			0
$238$			38.6284i			2.50391i
$239$	3.65209	−	3.65209i	0.236234	−	0.236234i	−0.579054	−	0.815289i	$-0.696578\pi$
$239$	3.65209	−	3.65209i	0.236234	−	0.236234i	0.815289	+	0.579054i	$0.196578\pi$
$240$		0			0
$241$	1.47580	−	1.47580i	0.0950647	−	0.0950647i	−0.657975	−	0.753040i	$-0.728587\pi$
$241$	1.47580	−	1.47580i	0.0950647	−	0.0950647i	0.753040	+	0.657975i	$0.228587\pi$
$242$	13.5302	+	13.5302i	0.869751	+	0.869751i
$243$		0			0
$244$			16.1723i			1.03532i
$245$	11.5179	+	11.5179i	0.735849	+	0.735849i
$246$		0			0
$247$	−5.73419	−	11.0303i	−0.364858	−	0.701842i
$248$			1.80062i			0.114339i
$249$		0			0
$250$	23.0484			1.45771
$251$	−5.73579			−0.362040			−0.181020	−	0.983479i	$-0.557940\pi$
$251$	−5.73579			−0.362040			−0.181020	+	0.983479i	$0.557940\pi$
$252$		0			0
$253$	7.46838	+	7.46838i	0.469533	+	0.469533i
$254$	−13.0933	−	13.0933i	−0.821549	−	0.821549i
$255$		0			0
$256$	8.98516			0.561573
$257$	3.56976			0.222675			0.111338	−	0.993783i	$-0.464486\pi$
$257$	3.56976			0.222675			0.111338	+	0.993783i	$0.464486\pi$
$258$		0			0
$259$			6.17226i			0.383526i
$260$	−5.28804	−	10.1721i	−0.327950	−	0.630846i
$261$		0			0
$262$	−5.88356	−	5.88356i	−0.363487	−	0.363487i
$263$			23.9454i			1.47654i	0.674507	+	0.738268i	$0.264356\pi$
$263$			23.9454i			1.47654i	−0.674507	+	0.738268i	$0.735644\pi$
$264$		0			0
$265$	−5.24030	−	5.24030i	−0.321909	−	0.321909i
$266$	22.1981	−	22.1981i	1.36106	−	1.36106i
$267$		0			0
$268$	6.85324	−	6.85324i	0.418629	−	0.418629i
$269$		−	0.984943i		−	0.0600530i	−0.999549	−	0.0300265i	$-0.990441\pi$
$269$		−	0.984943i		−	0.0600530i	0.999549	−	0.0300265i	$-0.00955918\pi$
$270$		0			0
$271$	−5.25839	+	5.25839i	−0.319424	+	0.319424i	−0.848546	−	0.529122i	$-0.822522\pi$
$271$	−5.25839	+	5.25839i	−0.319424	+	0.319424i	0.529122	+	0.848546i	$0.322522\pi$
$272$	−13.4588			−0.816057
$273$		0			0
$274$	9.69646			0.585785
$275$	−3.03257	+	3.03257i	−0.182871	+	0.182871i
$276$		0			0
$277$			5.04840i			0.303329i	0.988432	+	0.151664i	$0.0484633\pi$
$277$			5.04840i			0.303329i	−0.988432	+	0.151664i	$0.951537\pi$
$278$	−6.06514	+	6.06514i	−0.363763	+	0.363763i
$279$		0			0
$280$	3.06324	−	3.06324i	0.183063	−	0.183063i
$281$	10.9344	+	10.9344i	0.652292	+	0.652292i	0.953544	−	0.301253i	$-0.0974048\pi$
$281$	10.9344	+	10.9344i	0.652292	+	0.652292i	−0.301253	+	0.953544i	$0.597405\pi$
$282$		0			0
$283$		−	7.92454i		−	0.471065i	−0.971866	−	0.235532i	$-0.924317\pi$
$283$		−	7.92454i		−	0.471065i	0.971866	−	0.235532i	$-0.0756834\pi$
$284$	14.6688	+	14.6688i	0.870435	+	0.870435i
$285$		0			0
$286$	9.69646	+	3.06324i	0.573364	+	0.181133i
$287$			20.2862i			1.19746i
$288$		0			0
$289$	1.00000			0.0588235
$290$	23.2146			1.36321
$291$		0			0
$292$	8.98516	+	8.98516i	0.525817	+	0.525817i
$293$	−21.6610	−	21.6610i	−1.26545	−	1.26545i	−0.948415	−	0.317032i	$-0.897314\pi$
$293$	−21.6610	−	21.6610i	−1.26545	−	1.26545i	−0.317032	−	0.948415i	$-0.602686\pi$
$294$		0			0
$295$	3.01223			0.175379
$296$	1.03830			0.0603501
$297$		0			0
$298$			9.69646i			0.561701i
$299$	−26.8596	−	8.48528i	−1.55333	−	0.490716i
$300$		0			0
$301$	23.0484	+	23.0484i	1.32849	+	1.32849i
$302$		−	14.1098i		−	0.811925i
$303$		0			0
$304$	7.73419	+	7.73419i	0.443586	+	0.443586i
$305$	6.57335	−	6.57335i	0.376389	−	0.376389i
$306$		0			0
$307$	7.25839	−	7.25839i	0.414258	−	0.414258i	−0.468961	−	0.883219i	$-0.655371\pi$
$307$	7.25839	−	7.25839i	0.414258	−	0.414258i	0.883219	+	0.468961i	$0.155371\pi$
$308$			13.8775i			0.790746i
$309$		0			0
$310$	4.89098	−	4.89098i	0.277789	−	0.277789i
$311$	13.3114			0.754819			0.377409	−	0.926046i	$-0.376815\pi$
$311$	13.3114			0.754819			0.377409	+	0.926046i	$0.376815\pi$
$312$		0			0
$313$	−16.7645			−0.947586			−0.473793	−	0.880636i	$-0.657115\pi$
$313$	−16.7645			−0.947586			−0.473793	+	0.880636i	$0.657115\pi$
$314$	−34.5073	+	34.5073i	−1.94736	+	1.94736i
$315$		0			0
$316$		−	13.2664i		−	0.746296i
$317$	6.18355	−	6.18355i	0.347303	−	0.347303i	−0.511801	−	0.859104i	$-0.671022\pi$
$317$	6.18355	−	6.18355i	0.347303	−	0.347303i	0.859104	+	0.511801i	$0.171022\pi$
$318$		0			0
$319$	−7.86872	+	7.86872i	−0.440564	+	0.440564i
$320$	10.0608	+	10.0608i	0.562414	+	0.562414i
$321$		0			0
$322$		−	71.1304i		−	3.96394i
$323$	−10.3439	−	10.3439i	−0.575547	−	0.575547i
$324$		0			0
$325$	3.44549	−	10.9065i	0.191121	−	0.604981i
$326$			9.44834i			0.523295i
$327$		0			0
$328$	3.41256			0.188427
$329$	−5.90047			−0.325303
$330$		0			0
$331$	−0.666147	−	0.666147i	−0.0366148	−	0.0366148i	0.688562	−	0.725177i	$-0.258242\pi$
$331$	−0.666147	−	0.666147i	−0.0366148	−	0.0366148i	−0.725177	+	0.688562i	$0.758242\pi$
$332$	−23.6623	−	23.6623i	−1.29864	−	1.29864i
$333$		0			0
$334$	−50.9023			−2.78525
$335$	−5.57112			−0.304383
$336$		0			0
$337$			17.1090i			0.931988i	0.884788	+	0.465994i	$0.154303\pi$
$337$			17.1090i			0.931988i	−0.884788	+	0.465994i	$0.845697\pi$
$338$	−26.7129	+	4.67945i	−1.45299	+	0.254529i
$339$		0			0
$340$	−9.53904	−	9.53904i	−0.517327	−	0.517327i
$341$			3.31565i			0.179553i
$342$		0			0
$343$	15.5800	+	15.5800i	0.841242	+	0.841242i
$344$	3.87722	−	3.87722i	0.209046	−	0.209046i
$345$		0			0
$346$	−8.32905	+	8.32905i	−0.447772	+	0.447772i
$347$			1.23905i			0.0665155i	0.999447	+	0.0332578i	$0.0105882\pi$
$347$			1.23905i			0.0665155i	−0.999447	+	0.0332578i	$0.989412\pi$
$348$		0			0
$349$	−14.8277	+	14.8277i	−0.793711	+	0.793711i	−0.982095	−	0.188385i	$-0.939675\pi$
$349$	−14.8277	+	14.8277i	−0.793711	+	0.793711i	0.188385	+	0.982095i	$0.439675\pi$
$350$	28.8828			1.54385
$351$		0			0
$352$	−10.9320			−0.582675
$353$	−4.52572	+	4.52572i	−0.240880	+	0.240880i	−0.817214	−	0.576334i	$-0.804483\pi$
$353$	−4.52572	+	4.52572i	−0.240880	+	0.240880i	0.576334	+	0.817214i	$0.304483\pi$
$354$		0			0
$355$		−	11.9245i		−	0.632889i
$356$	−16.1259	+	16.1259i	−0.854672	+	0.854672i
$357$		0			0
$358$	−12.5168	+	12.5168i	−0.661532	+	0.661532i
$359$	8.09548	+	8.09548i	0.427263	+	0.427263i	0.887695	−	0.460432i	$-0.152305\pi$
$359$	8.09548	+	8.09548i	0.427263	+	0.427263i	−0.460432	+	0.887695i	$0.652305\pi$
$360$		0			0
$361$		−	7.11164i		−	0.374297i
$362$	11.9656	+	11.9656i	0.628898	+	0.628898i
$363$		0			0
$364$	−17.0713	−	32.8384i	−0.894779	−	1.72120i
$365$		−	7.30419i		−	0.382319i
$366$		0			0
$367$	−13.6406			−0.712036			−0.356018	−	0.934479i	$-0.615866\pi$
$367$	−13.6406			−0.712036			−0.356018	+	0.934479i	$0.615866\pi$
$368$	24.7830			1.29190
$369$		0			0
$370$	−2.82032	−	2.82032i	−0.146622	−	0.146622i
$371$	−16.9172	−	16.9172i	−0.878297	−	0.878297i
$372$		0			0
$373$	−16.7645			−0.868033			−0.434017	−	0.900905i	$-0.642904\pi$
$373$	−16.7645			−0.868033			−0.434017	+	0.900905i	$0.642904\pi$
$374$	11.9656			0.618727
$375$		0			0
$376$			0.992582i			0.0511885i
$377$	8.94013	−	28.2994i	0.460440	−	1.45749i
$378$		0			0
$379$	11.3142	+	11.3142i	0.581172	+	0.581172i	0.935225	−	0.354053i	$-0.115197\pi$
$379$	11.3142	+	11.3142i	0.581172	+	0.581172i	−0.354053	+	0.935225i	$0.615197\pi$
$380$			10.9634i			0.562409i
$381$		0			0
$382$	−14.3445	−	14.3445i	−0.733930	−	0.733930i
$383$	−6.69176	+	6.69176i	−0.341933	+	0.341933i	−0.857094	−	0.515161i	$-0.827732\pi$
$383$	−6.69176	+	6.69176i	−0.341933	+	0.341933i	0.515161	+	0.857094i	$0.327732\pi$
$384$		0			0
$385$	5.64064	−	5.64064i	0.287474	−	0.287474i
$386$		−	18.9044i		−	0.962208i
$387$		0			0
$388$	15.3445	−	15.3445i	0.779000	−	0.779000i
$389$	−32.5059			−1.64812			−0.824058	−	0.566505i	$-0.808295\pi$
$389$	−32.5059			−1.64812			−0.824058	+	0.566505i	$0.808295\pi$
$390$		0			0
$391$	−33.1452			−1.67622
$392$	6.25494	−	6.25494i	0.315922	−	0.315922i
$393$		0			0
$394$			45.2616i			2.28025i
$395$	−5.39226	+	5.39226i	−0.271314	+	0.271314i
$396$		0			0
$397$	22.6406	−	22.6406i	1.13630	−	1.13630i	0.147194	−	0.989108i	$-0.452976\pi$
$397$	22.6406	−	22.6406i	1.13630	−	1.13630i	0.989108	−	0.147194i	$-0.0470240\pi$
$398$	−1.12773	−	1.12773i	−0.0565281	−	0.0565281i
$399$		0			0
$400$			10.0632i			0.503162i
$401$	−14.6688	−	14.6688i	−0.732526	−	0.732526i	0.238593	−	0.971120i	$-0.423314\pi$
$401$	−14.6688	−	14.6688i	−0.732526	−	0.732526i	−0.971120	+	0.238593i	$0.923314\pi$
$402$		0			0
$403$	−4.07871	−	7.84583i	−0.203175	−	0.390828i
$404$			28.3527i			1.41060i
$405$		0			0
$406$	74.9433			3.71937
$407$	1.91193			0.0947709
$408$		0			0
$409$	13.2281	+	13.2281i	0.654086	+	0.654086i	0.953974	−	0.299888i	$-0.0969493\pi$
$409$	13.2281	+	13.2281i	0.654086	+	0.654086i	−0.299888	+	0.953974i	$0.596949\pi$
$410$	−9.26948	−	9.26948i	−0.457787	−	0.457787i
$411$		0			0
$412$	36.6433			1.80528
$413$	9.72433			0.478503
$414$		0			0
$415$			19.2355i			0.944233i
$416$	25.8683	−	13.4478i	1.26830	−	0.659334i
$417$		0			0
$418$	−6.87614	−	6.87614i	−0.336323	−	0.336323i
$419$			20.9591i			1.02392i	0.859010	+	0.511960i	$0.171080\pi$
$419$			20.9591i			1.02392i	−0.859010	+	0.511960i	$0.828920\pi$
$420$		0			0
$421$	4.16484	+	4.16484i	0.202982	+	0.202982i	0.801276	−	0.598294i	$-0.204155\pi$
$421$	4.16484	+	4.16484i	0.202982	+	0.202982i	−0.598294	+	0.801276i	$0.704155\pi$
$422$	−20.2862	+	20.2862i	−0.987518	+	0.987518i
$423$		0			0
$424$	−2.84583	+	2.84583i	−0.138206	+	0.138206i
$425$		−	13.4588i		−	0.652846i
$426$		0			0
$427$	21.2207	−	21.2207i	1.02694	−	1.02694i
$428$	−12.2950			−0.594299
$429$		0			0
$430$	−21.0632			−1.01576
$431$	−10.8450	+	10.8450i	−0.522384	+	0.522384i	−0.918291	−	0.395907i	$-0.870430\pi$
$431$	−10.8450	+	10.8450i	−0.522384	+	0.522384i	0.395907	+	0.918291i	$0.370430\pi$
$432$		0			0
$433$		−	8.87614i		−	0.426560i	−0.976991	−	0.213280i	$-0.931585\pi$
$433$		−	8.87614i		−	0.426560i	0.976991	−	0.213280i	$-0.0684147\pi$
$434$	15.7895	−	15.7895i	0.757919	−	0.757919i
$435$		0			0
$436$	−8.98516	+	8.98516i	−0.430311	+	0.430311i
$437$	19.0472	+	19.0472i	0.911150	+	0.911150i
$438$		0			0
$439$		−	7.46838i		−	0.356446i	−0.983990	−	0.178223i	$-0.942965\pi$
$439$		−	7.46838i		−	0.356446i	0.983990	−	0.178223i	$-0.0570349\pi$
$440$	−0.948874	−	0.948874i	−0.0452358	−	0.0452358i
$441$		0			0
$442$	−28.3142	+	14.7194i	−1.34677	+	0.700128i
$443$		−	16.6992i		−	0.793401i	−0.917948	−	0.396701i	$-0.870155\pi$
$443$		−	16.6992i		−	0.793401i	0.917948	−	0.396701i	$-0.129845\pi$
$444$		0			0
$445$	13.1090			0.621427
$446$	43.1039			2.04103
$447$		0			0
$448$	32.4791	+	32.4791i	1.53449	+	1.53449i
$449$	10.8450	+	10.8450i	0.511806	+	0.511806i	0.915079	−	0.403274i	$-0.132128\pi$
$449$	10.8450	+	10.8450i	0.511806	+	0.511806i	−0.403274	+	0.915079i	$0.632128\pi$
$450$		0			0
$451$	6.28390			0.295897
$452$	19.3592			0.910582
$453$		0			0
$454$		−	8.94679i		−	0.419894i
$455$	−6.40868	+	20.2862i	−0.300443	+	0.951032i
$456$		0			0
$457$	27.1526	+	27.1526i	1.27015	+	1.27015i	0.946011	+	0.324135i	$0.105073\pi$
$457$	27.1526	+	27.1526i	1.27015	+	1.27015i	0.324135	+	0.946011i	$0.394927\pi$
$458$		−	6.93877i		−	0.324227i
$459$		0			0
$460$	17.5652	+	17.5652i	0.818981	+	0.818981i
$461$	23.1541	−	23.1541i	1.07839	−	1.07839i	0.0817409	−	0.996654i	$-0.473952\pi$
$461$	23.1541	−	23.1541i	1.07839	−	1.07839i	0.996654	−	0.0817409i	$-0.0260480\pi$
$462$		0			0
$463$	28.8384	−	28.8384i	1.34023	−	1.34023i	0.444412	−	0.895823i	$-0.353413\pi$
$463$	28.8384	−	28.8384i	1.34023	−	1.34023i	0.895823	−	0.444412i	$-0.146587\pi$
$464$			26.1114i			1.21219i
$465$		0			0
$466$	−40.8310	+	40.8310i	−1.89146	+	1.89146i
$467$	11.2348			0.519883			0.259942	−	0.965624i	$-0.416297\pi$
$467$	11.2348			0.519883			0.259942	+	0.965624i	$0.416297\pi$
$468$		0			0
$469$	−17.9852			−0.830478
$470$	2.69613	−	2.69613i	0.124363	−	0.124363i
$471$		0			0
$472$		−	1.63583i		−	0.0752954i
$473$	7.13951	−	7.13951i	0.328275	−	0.328275i
$474$		0			0
$475$	−7.73419	+	7.73419i	−0.354869	+	0.354869i
$476$	−30.7947	−	30.7947i	−1.41147	−	1.41147i
$477$		0			0
$478$			10.7745i			0.492816i
$479$	11.2998	+	11.2998i	0.516302	+	0.516302i	0.916450	−	0.400148i	$-0.131041\pi$
$479$	11.2998	+	11.2998i	0.516302	+	0.516302i	−0.400148	+	0.916450i	$0.631041\pi$
$480$		0			0
$481$	−4.52420	+	2.35194i	−0.206286	+	0.107239i
$482$			4.35396i			0.198317i
$483$		0			0
$484$	−21.5726			−0.980573
$485$	−12.4738			−0.566407
$486$		0			0
$487$	−6.68579	−	6.68579i	−0.302962	−	0.302962i	0.539210	−	0.842172i	$-0.318723\pi$
$487$	−6.68579	−	6.68579i	−0.302962	−	0.302962i	−0.842172	+	0.539210i	$0.818723\pi$
$488$	−3.56976	−	3.56976i	−0.161595	−	0.161595i
$489$		0			0
$490$	−33.9804			−1.53508
$491$	7.08156			0.319586			0.159793	−	0.987151i	$-0.448917\pi$
$491$	7.08156			0.319586			0.159793	+	0.987151i	$0.448917\pi$
$492$		0			0
$493$		−	34.9219i		−	1.57280i
$494$	24.7296	+	7.81240i	1.11264	+	0.351496i
$495$		0			0
$496$	5.50131	+	5.50131i	0.247016	+	0.247016i
$497$		−	38.4958i		−	1.72677i
$498$		0			0
$499$	−14.8384	−	14.8384i	−0.664258	−	0.664258i	0.292123	−	0.956381i	$-0.405638\pi$
$499$	−14.8384	−	14.8384i	−0.664258	−	0.664258i	−0.956381	+	0.292123i	$0.905638\pi$
$500$	−18.3743	+	18.3743i	−0.821723	+	0.821723i
$501$		0			0
$502$	8.46096	−	8.46096i	0.377631	−	0.377631i
$503$		−	42.1550i		−	1.87960i	−0.341726	−	0.939800i	$-0.611012\pi$
$503$		−	42.1550i		−	1.87960i	0.341726	−	0.939800i	$-0.388988\pi$
$504$		0			0
$505$	11.5242	−	11.5242i	0.512820	−	0.512820i
$506$	−22.0335			−0.979507
$507$		0			0
$508$	20.8761			0.926229
$509$	13.2651	−	13.2651i	0.587966	−	0.587966i	−0.349114	−	0.937080i	$-0.613518\pi$
$509$	13.2651	−	13.2651i	0.587966	−	0.587966i	0.937080	+	0.349114i	$0.113518\pi$
$510$		0			0
$511$		−	23.5800i		−	1.04312i
$512$	−21.4320	+	21.4320i	−0.947169	+	0.947169i
$513$		0			0
$514$	−5.26581	+	5.26581i	−0.232265	+	0.232265i
$515$	−14.8940	−	14.8940i	−0.656306	−	0.656306i
$516$		0			0
$517$			1.82774i			0.0803839i
$518$	−9.10481	−	9.10481i	−0.400042	−	0.400042i
$519$		0			0
$520$	3.41256	+	1.07807i	0.149651	+	0.0472766i
$521$			8.23118i			0.360614i	0.983610	+	0.180307i	$0.0577092\pi$
$521$			8.23118i			0.360614i	−0.983610	+	0.180307i	$0.942291\pi$
$522$		0			0
$523$	−33.7523			−1.47588			−0.737942	−	0.674864i	$-0.764202\pi$
$523$	−33.7523			−1.47588			−0.737942	+	0.674864i	$0.764202\pi$
$524$	9.38080			0.409802
$525$		0			0
$526$	−35.3223	−	35.3223i	−1.54012	−	1.54012i
$527$	−7.35755	−	7.35755i	−0.320500	−	0.320500i
$528$		0			0
$529$	38.0336			1.65363
$530$	15.4601			0.671545
$531$		0			0
$532$			35.3929i			1.53448i
$533$	−14.8696	+	7.73006i	−0.644073	+	0.334826i
$534$		0			0
$535$	4.99739	+	4.99739i	0.216056	+	0.216056i
$536$			3.02548i			0.130681i
$537$		0			0
$538$	1.45291	+	1.45291i	0.0626392	+	0.0626392i
$539$	11.5179	−	11.5179i	0.496109	−	0.496109i
$540$		0			0
$541$	−21.8203	+	21.8203i	−0.938129	+	0.938129i	−0.998194	−	0.0600656i	$-0.980869\pi$
$541$	−21.8203	+	21.8203i	−0.938129	+	0.938129i	0.0600656	+	0.998194i	$0.480869\pi$
$542$		−	15.5135i		−	0.666361i
$543$		0			0
$544$	24.2584	−	24.2584i	1.04007	−	1.04007i
$545$	7.30419			0.312877
$546$		0			0
$547$	16.1116			0.688884			0.344442	−	0.938808i	$-0.388068\pi$
$547$	16.1116			0.688884			0.344442	+	0.938808i	$0.388068\pi$
$548$	−7.73006	+	7.73006i	−0.330212	+	0.330212i
$549$		0			0
$550$		−	8.94679i		−	0.381493i
$551$	−20.0682	+	20.0682i	−0.854933	+	0.854933i
$552$		0			0
$553$	−17.4078	+	17.4078i	−0.740253	+	0.740253i
$554$	−7.44698	−	7.44698i	−0.316392	−	0.316392i
$555$		0			0
$556$		−	9.67032i		−	0.410113i
$557$	29.3087	+	29.3087i	1.24185	+	1.24185i	0.959233	+	0.282615i	$0.0912020\pi$
$557$	29.3087	+	29.3087i	1.24185	+	1.24185i	0.282615	+	0.959233i	$0.408798\pi$
$558$		0			0
$559$	−8.11164	+	25.6768i	−0.343086	+	1.08601i
$560$		−	18.7178i		−	0.790972i
$561$		0			0
$562$	−32.2590			−1.36077
$563$	−33.3262			−1.40453			−0.702266	−	0.711915i	$-0.747828\pi$
$563$	−33.3262			−1.40453			−0.702266	+	0.711915i	$0.747828\pi$
$564$		0			0
$565$	−7.86872	−	7.86872i	−0.331040	−	0.331040i
$566$	11.6896	+	11.6896i	0.491351	+	0.491351i
$567$		0			0
$568$	−6.47580			−0.271719
$569$	7.90183			0.331262			0.165631	−	0.986188i	$-0.447034\pi$
$569$	7.90183			0.331262			0.165631	+	0.986188i	$0.447034\pi$
$570$		0			0
$571$		−	35.3175i		−	1.47799i	−0.673711	−	0.738995i	$-0.735301\pi$
$571$		−	35.3175i		−	1.47799i	0.673711	−	0.738995i	$-0.264699\pi$
$572$	−10.1721	+	5.28804i	−0.425316	+	0.221104i
$573$		0			0
$574$	−29.9245	−	29.9245i	−1.24903	−	1.24903i
$575$			24.7830i			1.03352i
$576$		0			0
$577$	−19.6284	−	19.6284i	−0.817142	−	0.817142i	0.168551	−	0.985693i	$-0.446091\pi$
$577$	−19.6284	−	19.6284i	−0.817142	−	0.817142i	−0.985693	+	0.168551i	$0.946091\pi$
$578$	−1.47512	+	1.47512i	−0.0613568	+	0.0613568i
$579$		0			0
$580$	−18.5068	+	18.5068i	−0.768451	+	0.768451i
$581$			62.0977i			2.57625i
$582$		0			0
$583$	−5.24030	+	5.24030i	−0.217031	+	0.217031i
$584$	−3.96665			−0.164141
$585$		0			0
$586$	63.9049			2.63989
$587$	−9.89610	+	9.89610i	−0.408456	+	0.408456i	−0.881200	−	0.472744i	$-0.843263\pi$
$587$	−9.89610	+	9.89610i	−0.408456	+	0.408456i	0.472744	+	0.881200i	$0.343263\pi$
$588$		0			0
$589$			8.45616i			0.348430i
$590$	−4.44339	+	4.44339i	−0.182931	+	0.182931i
$591$		0			0
$592$	3.17226	−	3.17226i	0.130379	−	0.130379i
$593$	13.5945	+	13.5945i	0.558257	+	0.558257i	0.928811	−	0.370554i	$-0.120832\pi$
$593$	13.5945	+	13.5945i	0.558257	+	0.558257i	−0.370554	+	0.928811i	$0.620832\pi$
$594$		0			0
$595$			25.0336i			1.02628i
$596$	−7.73006	−	7.73006i	−0.316636	−	0.316636i
$597$		0			0
$598$	52.1378	−	27.1042i	2.13207	−	1.10837i
$599$		−	19.2118i		−	0.784975i	−0.919757	−	0.392487i	$-0.871615\pi$
$599$		−	19.2118i		−	0.784975i	0.919757	−	0.392487i	$-0.128385\pi$
$600$		0			0
$601$	44.2691			1.80577			0.902886	−	0.429879i	$-0.141444\pi$
$601$	44.2691			1.80577			0.902886	+	0.429879i	$0.141444\pi$
$602$	−67.9982			−2.77140
$603$		0			0
$604$	11.2484	+	11.2484i	0.457689	+	0.457689i
$605$	8.76836	+	8.76836i	0.356485	+	0.356485i
$606$		0			0
$607$	−17.8639			−0.725074			−0.362537	−	0.931969i	$-0.618089\pi$
$607$	−17.8639			−0.725074			−0.362537	+	0.931969i	$0.618089\pi$
$608$	−27.8806			−1.13071
$609$		0			0
$610$			19.3929i			0.785196i
$611$	−2.24837	−	4.32498i	−0.0909594	−	0.174970i
$612$		0			0
$613$	−7.11164	−	7.11164i	−0.287236	−	0.287236i	0.548750	−	0.835986i	$-0.315104\pi$
$613$	−7.11164	−	7.11164i	−0.287236	−	0.287236i	−0.835986	+	0.548750i	$0.815104\pi$
$614$			21.4139i			0.864197i
$615$		0			0
$616$	−3.06324	−	3.06324i	−0.123421	−	0.123421i
$617$	−7.94810	+	7.94810i	−0.319978	+	0.319978i	−0.848759	−	0.528780i	$-0.822650\pi$
$617$	−7.94810	+	7.94810i	−0.319978	+	0.319978i	0.528780	+	0.848759i	$0.322650\pi$
$618$		0			0
$619$	14.9139	−	14.9139i	0.599439	−	0.599439i	−0.340724	−	0.940163i	$-0.610672\pi$
$619$	14.9139	−	14.9139i	0.599439	−	0.599439i	0.940163	+	0.340724i	$0.110672\pi$
$620$			7.79821i			0.313184i
$621$		0			0
$622$	−19.6358	+	19.6358i	−0.787325	+	0.787325i
$623$	42.3197			1.69550
$624$		0			0
$625$	−0.924538			−0.0369815
$626$	24.7296	−	24.7296i	0.988394	−	0.988394i
$627$		0			0
$628$		−	55.0187i		−	2.19549i
$629$	−4.24264	+	4.24264i	−0.169165	+	0.169165i
$630$		0			0
$631$	23.0665	−	23.0665i	0.918262	−	0.918262i	−0.0786407	−	0.996903i	$-0.525058\pi$
$631$	23.0665	−	23.0665i	0.918262	−	0.918262i	0.996903	+	0.0786407i	$0.0250580\pi$
$632$	2.92835	+	2.92835i	0.116483	+	0.116483i
$633$		0			0
$634$			18.2429i			0.724519i
$635$	−8.48528	−	8.48528i	−0.336728	−	0.336728i
$636$		0			0
$637$	−13.0861	+	41.4232i	−0.518491	+	1.64125i
$638$		−	23.2146i		−	0.919073i
$639$		0			0
$640$	−7.81771			−0.309022
$641$	−34.7614			−1.37299			−0.686496	−	0.727133i	$-0.740852\pi$
$641$	−34.7614			−1.37299			−0.686496	+	0.727133i	$0.740852\pi$
$642$		0			0
$643$	11.0255	+	11.0255i	0.434803	+	0.434803i	0.890259	−	0.455455i	$-0.150523\pi$
$643$	11.0255	+	11.0255i	0.434803	+	0.434803i	−0.455455	+	0.890259i	$0.650523\pi$
$644$	56.7054	+	56.7054i	2.23451	+	2.23451i
$645$		0			0
$646$	30.5168			1.20067
$647$	−31.6857			−1.24569			−0.622846	−	0.782345i	$-0.714024\pi$
$647$	−31.6857			−1.24569			−0.622846	+	0.782345i	$0.714024\pi$
$648$		0			0
$649$		−	3.01223i		−	0.118240i
$650$	11.0058	+	21.1708i	0.431683	+	0.830387i
$651$		0			0
$652$	−7.53226	−	7.53226i	−0.294986	−	0.294986i
$653$		−	35.6569i		−	1.39536i	−0.716408	−	0.697681i	$-0.754215\pi$
$653$		−	35.6569i		−	1.39536i	0.716408	−	0.697681i	$-0.245785\pi$
$654$		0			0
$655$	−3.81290	−	3.81290i	−0.148982	−	0.148982i
$656$	10.4262	−	10.4262i	0.407074	−	0.407074i
$657$		0			0
$658$	8.70388	−	8.70388i	0.339313	−	0.339313i
$659$			18.2096i			0.709346i	0.934990	+	0.354673i	$0.115408\pi$
$659$			18.2096i			0.709346i	−0.934990	+	0.354673i	$0.884592\pi$
$660$		0			0
$661$	−10.5652	+	10.5652i	−0.410938	+	0.410938i	−0.882065	−	0.471127i	$-0.843847\pi$
$661$	−10.5652	+	10.5652i	−0.410938	+	0.410938i	0.471127	+	0.882065i	$0.343847\pi$
$662$	1.96529			0.0763832
$663$		0			0
$664$	10.4461			0.405388
$665$	14.3857	−	14.3857i	0.557855	−	0.557855i
$666$		0			0
$667$			64.3052i			2.48991i
$668$	40.5795	−	40.5795i	1.57007	−	1.57007i
$669$		0			0
$670$	8.21805	−	8.21805i	0.317491	−	0.317491i
$671$	−6.57335	−	6.57335i	−0.253761	−	0.253761i
$672$		0			0
$673$			30.0820i			1.15957i	0.814768	+	0.579787i	$0.196864\pi$
$673$			30.0820i			1.15957i	−0.814768	+	0.579787i	$0.803136\pi$
$674$	−25.2378	−	25.2378i	−0.972124	−	0.972124i
$675$		0			0
$676$	17.5652	−	25.0261i	0.675584	−	0.962544i
$677$		−	29.1903i		−	1.12187i	−0.827859	−	0.560937i	$-0.810441\pi$
$677$		−	29.1903i		−	1.12187i	0.827859	−	0.560937i	$-0.189559\pi$
$678$		0			0
$679$	−40.2691			−1.54538
$680$	4.21117			0.161491
$681$		0			0
$682$	−4.89098	−	4.89098i	−0.187285	−	0.187285i
$683$	30.5650	+	30.5650i	1.16954	+	1.16954i	0.982318	+	0.187220i	$0.0599477\pi$
$683$	30.5650	+	30.5650i	1.16954	+	1.16954i	0.187220	+	0.982318i	$0.440052\pi$
$684$		0			0
$685$	6.28390			0.240095
$686$	−45.9647			−1.75494
$687$		0			0
$688$		−	23.6917i		−	0.903236i
$689$	5.95383	−	18.8464i	0.226823	−	0.717992i
$690$		0			0
$691$	−26.1952	−	26.1952i	−0.996511	−	0.996511i	0.00348329	−	0.999994i	$-0.498891\pi$
$691$	−26.1952	−	26.1952i	−0.996511	−	0.996511i	−0.999994	+	0.00348329i	$0.998891\pi$
$692$		−	13.2799i		−	0.504826i
$693$		0			0
$694$	−1.82774	−	1.82774i	−0.0693800	−	0.0693800i
$695$	−3.93058	+	3.93058i	−0.149095	+	0.149095i
$696$		0			0
$697$	−13.9442	+	13.9442i	−0.528174	+	0.528174i
$698$		−	43.7453i		−	1.65578i
$699$		0			0
$700$	−23.0255	+	23.0255i	−0.870282	+	0.870282i
$701$	−29.6985			−1.12170			−0.560848	−	0.827919i	$-0.689525\pi$
$701$	−29.6985			−1.12170			−0.560848	+	0.827919i	$0.689525\pi$
$702$		0			0
$703$	4.87614			0.183907
$704$	10.0608	−	10.0608i	0.379180	−	0.379180i
$705$		0			0
$706$		−	13.3519i		−	0.502507i
$707$	37.2034	−	37.2034i	1.39918	−	1.39918i
$708$		0			0
$709$	4.10422	−	4.10422i	0.154137	−	0.154137i	−0.625826	−	0.779963i	$-0.715238\pi$
$709$	4.10422	−	4.10422i	0.154137	−	0.154137i	0.779963	+	0.625826i	$0.215238\pi$
$710$	17.5901	+	17.5901i	0.660144	+	0.660144i
$711$		0			0
$712$		−	7.11905i		−	0.266798i
$713$	13.5482	+	13.5482i	0.507384	+	0.507384i
$714$		0			0
$715$	6.28390	+	1.98516i	0.235004	+	0.0742409i
$716$		−	19.9569i		−	0.745823i
$717$		0			0
$718$	−23.8836			−0.891326
$719$	49.6239			1.85066			0.925329	−	0.379165i	$-0.123789\pi$
$719$	49.6239			1.85066			0.925329	+	0.379165i	$0.123789\pi$
$720$		0			0
$721$	−48.0820	−	48.0820i	−1.79067	−	1.79067i
$722$	10.4905	+	10.4905i	0.390416	+	0.390416i
$723$		0			0
$724$	−19.0781			−0.709031
$725$	−26.1114			−0.969754
$726$		0			0
$727$			26.1723i			0.970675i	0.874327	+	0.485338i	$0.161303\pi$
$727$			26.1723i			0.970675i	−0.874327	+	0.485338i	$0.838697\pi$
$728$	11.0167	+	3.48033i	0.408307	+	0.128990i
$729$		0			0
$730$	10.7745	+	10.7745i	0.398783	+	0.398783i
$731$			31.6857i			1.17194i
$732$		0			0
$733$	20.5094	+	20.5094i	0.757531	+	0.757531i	0.975872	−	0.218342i	$-0.0700648\pi$
$733$	20.5094	+	20.5094i	0.757531	+	0.757531i	−0.218342	+	0.975872i	$0.570065\pi$
$734$	20.1215	−	20.1215i	0.742700	−	0.742700i
$735$		0			0
$736$	−44.6694	+	44.6694i	−1.64654	+	1.64654i
$737$			5.57112i			0.205215i
$738$		0			0
$739$	20.7874	−	20.7874i	0.764677	−	0.764677i	−0.212487	−	0.977164i	$-0.568156\pi$
$739$	20.7874	−	20.7874i	0.764677	−	0.764677i	0.977164	+	0.212487i	$0.0681563\pi$
$740$	4.49674			0.165304
$741$		0			0
$742$	49.9097			1.83224
$743$	−16.7988	+	16.7988i	−0.616288	+	0.616288i	−0.944577	−	0.328289i	$-0.893528\pi$
$743$	−16.7988	+	16.7988i	−0.616288	+	0.616288i	0.328289	+	0.944577i	$0.393528\pi$
$744$		0			0
$745$			6.28390i			0.230224i
$746$	24.7296	−	24.7296i	0.905415	−	0.905415i
$747$		0			0
$748$	−9.53904	+	9.53904i	−0.348782	+	0.348782i
$749$	16.1330	+	16.1330i	0.589487	+	0.589487i
$750$		0			0
$751$			40.6136i			1.48201i	0.671499	+	0.741005i	$0.265651\pi$
$751$			40.6136i			1.48201i	−0.671499	+	0.741005i	$0.734349\pi$
$752$	3.03257	+	3.03257i	0.110586	+	0.110586i
$753$		0			0
$754$	28.5571	+	54.9326i	1.03999	+	2.00053i
$755$		−	9.14398i		−	0.332784i
$756$		0			0
$757$	−13.9097			−0.505557			−0.252778	−	0.967524i	$-0.581344\pi$
$757$	−13.9097			−0.505557			−0.252778	+	0.967524i	$0.581344\pi$
$758$	−33.3796			−1.21240
$759$		0			0
$760$	−2.41998	−	2.41998i	−0.0877820	−	0.0877820i
$761$	1.53942	+	1.53942i	0.0558039	+	0.0558039i	0.734458	−	0.678654i	$-0.237436\pi$
$761$	1.53942	+	1.53942i	0.0558039	+	0.0558039i	−0.678654	+	0.734458i	$0.737436\pi$
$762$		0			0
$763$	23.5800			0.853654
$764$	22.8710			0.827445
$765$		0			0
$766$		−	19.7422i		−	0.713316i
$767$	3.70545	+	7.12783i	0.133796	+	0.257371i
$768$		0			0
$769$	−8.58002	−	8.58002i	−0.309403	−	0.309403i	0.535275	−	0.844678i	$-0.320208\pi$
$769$	−8.58002	−	8.58002i	−0.309403	−	0.309403i	−0.844678	+	0.535275i	$0.820208\pi$
$770$			16.6412i			0.599708i
$771$		0			0
$772$	15.0707	+	15.0707i	0.542405	+	0.542405i
$773$	−20.8234	+	20.8234i	−0.748966	+	0.748966i	−0.974285	−	0.225319i	$-0.927657\pi$
$773$	−20.8234	+	20.8234i	−0.748966	+	0.748966i	0.225319	+	0.974285i	$0.427657\pi$
$774$		0			0
$775$	−5.50131	+	5.50131i	−0.197613	+	0.197613i
$776$			6.77410i			0.243176i
$777$		0			0
$778$	47.9500	−	47.9500i	1.71909	−	1.71909i
$779$	16.0263			0.574201
$780$		0			0
$781$	−11.9245			−0.426694
$782$	48.8930	−	48.8930i	1.74841	−	1.74841i
$783$		0			0
$784$		−	38.2207i		−	1.36502i
$785$	−22.3628	+	22.3628i	−0.798163	+	0.798163i
$786$		0			0
$787$	2.72677	−	2.72677i	0.0971989	−	0.0971989i	−0.656835	−	0.754034i	$-0.728105\pi$
$787$	2.72677	−	2.72677i	0.0971989	−	0.0971989i	0.754034	+	0.656835i	$0.228105\pi$
$788$	−36.0828	−	36.0828i	−1.28540	−	1.28540i
$789$		0			0
$790$		−	15.9084i		−	0.565996i
$791$	−25.4025	−	25.4025i	−0.903208	−	0.903208i
$792$		0			0
$793$	23.6406	+	7.46838i	0.839504	+	0.265210i
$794$			66.7952i			2.37047i
$795$		0			0
$796$	1.79807			0.0637308
$797$	−8.39585			−0.297396			−0.148698	−	0.988883i	$-0.547508\pi$
$797$	−8.39585			−0.297396			−0.148698	+	0.988883i	$0.547508\pi$
$798$		0			0
$799$	−4.05582	−	4.05582i	−0.143485	−	0.143485i
$800$	−18.1382	−	18.1382i	−0.641283	−	0.641283i
$801$		0			0
$802$	43.2765			1.52815
$803$	−7.30419			−0.257759
$804$		0			0
$805$		−	46.0968i		−	1.62470i
$806$	17.5901	+	5.55693i	0.619584	+	0.195735i
$807$		0			0
$808$	−6.25839	−	6.25839i	−0.220169	−	0.220169i
$809$		−	34.9261i		−	1.22794i	−0.789331	−	0.613968i	$-0.789573\pi$
$809$		−	34.9261i		−	1.22794i	0.789331	−	0.613968i	$-0.210427\pi$
$810$		0			0
$811$	32.9549	+	32.9549i	1.15720	+	1.15720i	0.985075	+	0.172126i	$0.0550638\pi$
$811$	32.9549	+	32.9549i	1.15720	+	1.15720i	0.172126	+	0.985075i	$0.444936\pi$
$812$	−59.7451	+	59.7451i	−2.09664	+	2.09664i
$813$		0			0
$814$	−2.82032	+	2.82032i	−0.0988522	+	0.0988522i
$815$			6.12310i			0.214483i
$816$		0			0
$817$	18.2084	−	18.2084i	0.637032	−	0.637032i
$818$	−39.0259			−1.36451
$819$		0			0
$820$	14.7793			0.516117
$821$	3.95956	−	3.95956i	0.138190	−	0.138190i	−0.634628	−	0.772818i	$-0.718847\pi$
$821$	3.95956	−	3.95956i	0.138190	−	0.138190i	0.772818	+	0.634628i	$0.218847\pi$
$822$		0			0
$823$			32.5019i			1.13295i	0.824080	+	0.566473i	$0.191693\pi$
$823$			32.5019i			1.13295i	−0.824080	+	0.566473i	$0.808307\pi$
$824$	−8.08839	+	8.08839i	−0.281772	+	0.281772i
$825$		0			0
$826$	−14.3445	+	14.3445i	−0.499110	+	0.499110i
$827$	−9.60592	−	9.60592i	−0.334031	−	0.334031i	0.520084	−	0.854115i	$-0.325901\pi$
$827$	−9.60592	−	9.60592i	−0.334031	−	0.334031i	−0.854115	+	0.520084i	$0.825901\pi$
$828$		0			0
$829$		−	34.9878i		−	1.21518i	−0.794253	−	0.607588i	$-0.792137\pi$
$829$		−	34.9878i		−	1.21518i	0.794253	−	0.607588i	$-0.207863\pi$
$830$	−28.3746	−	28.3746i	−0.984897	−	0.984897i
$831$		0			0
$832$	−11.4307	+	36.1829i	−0.396287	+	1.25442i
$833$			51.1170i			1.77110i
$834$		0			0
$835$	−32.9878			−1.14159
$836$	10.9634			0.379176
$837$		0			0
$838$	−30.9171	−	30.9171i	−1.06801	−	1.06801i
$839$	31.0199	+	31.0199i	1.07092	+	1.07092i	0.997285	+	0.0736399i	$0.0234616\pi$
$839$	31.0199	+	31.0199i	1.07092	+	1.07092i	0.0736399	+	0.997285i	$0.476538\pi$
$840$		0			0
$841$	−38.7523			−1.33629
$842$	−12.2873			−0.423447
$843$		0			0
$844$		−	32.3445i		−	1.11334i
$845$	−17.3116	+	3.03257i	−0.595537	+	0.104324i
$846$		0			0
$847$	28.3068	+	28.3068i	0.972633	+	0.972633i
$848$			17.3893i			0.597152i
$849$		0			0
$850$	19.8532	+	19.8532i	0.680961	+	0.680961i
$851$	7.81240	−	7.81240i	0.267806	−	0.267806i
$852$		0			0
$853$	22.4535	−	22.4535i	0.768795	−	0.768795i	−0.209100	−	0.977894i	$-0.567053\pi$
$853$	22.4535	−	22.4535i	0.768795	−	0.768795i	0.977894	+	0.209100i	$0.0670533\pi$
$854$			62.6059i			2.14233i
$855$		0			0
$856$	2.71391	−	2.71391i	0.0927595	−	0.0927595i
$857$	−5.82522			−0.198986			−0.0994929	−	0.995038i	$-0.531722\pi$
$857$	−5.82522			−0.198986			−0.0994929	+	0.995038i	$0.531722\pi$
$858$		0			0
$859$	−19.3929			−0.661678			−0.330839	−	0.943687i	$-0.607332\pi$
$859$	−19.3929			−0.661678			−0.330839	+	0.943687i	$0.607332\pi$
$860$	16.7917	−	16.7917i	0.572592	−	0.572592i
$861$		0			0
$862$		−	31.9952i		−	1.08976i
$863$	26.5765	−	26.5765i	0.904674	−	0.904674i	−0.0911620	−	0.995836i	$-0.529058\pi$
$863$	26.5765	−	26.5765i	0.904674	−	0.904674i	0.995836	+	0.0911620i	$0.0290581\pi$
$864$		0			0
$865$	−5.39773	+	5.39773i	−0.183528	+	0.183528i
$866$	13.0933	+	13.0933i	0.444930	+	0.444930i
$867$		0			0
$868$			25.1749i			0.854491i
$869$	5.39226	+	5.39226i	0.182920	+	0.182920i
$870$		0			0
$871$	−6.85324	−	13.1829i	−0.232213	−	0.446686i
$872$		−	3.96665i		−	0.134328i
$873$		0			0
$874$	−56.1936			−1.90078
$875$	48.2202			1.63014
$876$		0			0
$877$	2.16003	+	2.16003i	0.0729392	+	0.0729392i	0.742635	−	0.669696i	$-0.233576\pi$
$877$	2.16003	+	2.16003i	0.0729392	+	0.0729392i	−0.669696	+	0.742635i	$0.733576\pi$
$878$	11.0167	+	11.0167i	0.371797	+	0.371797i
$879$		0			0
$880$	−5.79807			−0.195453
$881$	−39.1514			−1.31904			−0.659522	−	0.751685i	$-0.729241\pi$
$881$	−39.1514			−1.31904			−0.659522	+	0.751685i	$0.729241\pi$
$882$		0			0
$883$			0.764504i			0.0257276i	0.999917	+	0.0128638i	$0.00409479\pi$
$883$			0.764504i			0.0257276i	−0.999917	+	0.0128638i	$0.995905\pi$
$884$	10.8379	−	34.3065i	0.364517	−	1.15385i
$885$		0			0
$886$	24.6332	+	24.6332i	0.827569	+	0.827569i
$887$		−	10.9634i		−	0.368114i	−0.982916	−	0.184057i	$-0.941077\pi$
$887$		−	10.9634i		−	0.368114i	0.982916	−	0.184057i	$-0.0589231\pi$
$888$		0			0
$889$	−27.3929	−	27.3929i	−0.918729	−	0.918729i
$890$	−19.3373	+	19.3373i	−0.648189	+	0.648189i
$891$		0			0
$892$	−34.3626	+	34.3626i	−1.15055	+	1.15055i
$893$			4.66142i			0.155988i
$894$		0			0
$895$	−8.11164	+	8.11164i	−0.271142	+	0.271142i
$896$	−25.2378			−0.843136
$897$		0			0
$898$	−31.9952			−1.06769
$899$	−14.2744	+	14.2744i	−0.476079	+	0.476079i
$900$		0			0
$901$		−	23.2568i		−	0.774797i
$902$	−9.26948	+	9.26948i	−0.308640	+	0.308640i
$903$		0			0
$904$	−4.27323	+	4.27323i	−0.142125	+	0.142125i
$905$	7.75444	+	7.75444i	0.257766	+	0.257766i
$906$		0			0
$907$		−	38.2542i		−	1.27021i	−0.772426	−	0.635105i	$-0.780957\pi$
$907$		−	38.2542i		−	1.27021i	0.772426	−	0.635105i	$-0.219043\pi$
$908$	7.13242	+	7.13242i	0.236698	+	0.236698i
$909$		0			0
$910$	−20.4710	−	39.3781i	−0.678607	−	1.30537i
$911$		−	44.9045i		−	1.48775i	−0.668317	−	0.743876i	$-0.732985\pi$
$911$		−	44.9045i		−	1.48775i	0.668317	−	0.743876i	$-0.267015\pi$
$912$		0			0
$913$	19.2355			0.636602
$914$	−80.1066			−2.64969
$915$		0			0
$916$	5.53162	+	5.53162i	0.182770	+	0.182770i
$917$	−12.3091	−	12.3091i	−0.406484	−	0.406484i
$918$		0			0
$919$	30.6742			1.01185			0.505924	−	0.862578i	$-0.331151\pi$
$919$	30.6742			1.01185			0.505924	+	0.862578i	$0.331151\pi$
$920$	−7.75444			−0.255656
$921$		0			0
$922$			68.3100i			2.24967i
$923$	28.2170	−	14.6688i	0.928775	−	0.482830i
$924$		0			0
$925$	3.17226	+	3.17226i	0.104303	+	0.104303i
$926$			85.0800i			2.79590i
$927$		0			0
$928$	−47.0639	−	47.0639i	−1.54495	−	1.54495i
$929$	−13.7418	+	13.7418i	−0.450855	+	0.450855i	−0.895638	−	0.444783i	$-0.853281\pi$
$929$	−13.7418	+	13.7418i	−0.450855	+	0.450855i	0.444783	+	0.895638i	$0.353281\pi$
$930$		0			0
$931$	29.3748	−	29.3748i	0.962721	−	0.962721i
$932$		−	65.1013i		−	2.13246i
$933$		0			0
$934$	−16.5726	+	16.5726i	−0.542272	+	0.542272i
$935$	7.75444			0.253597
$936$		0			0
$937$	−23.0994			−0.754625			−0.377312	−	0.926086i	$-0.623152\pi$
$937$	−23.0994			−0.754625			−0.377312	+	0.926086i	$0.623152\pi$
$938$	26.5302	−	26.5302i	0.866242	−	0.866242i
$939$		0			0
$940$			4.29873i			0.140209i
$941$	23.7376	−	23.7376i	0.773823	−	0.773823i	−0.204950	−	0.978772i	$-0.565703\pi$
$941$	23.7376	−	23.7376i	0.773823	−	0.773823i	0.978772	+	0.204950i	$0.0657032\pi$
$942$		0			0
$943$	25.6768	−	25.6768i	0.836152	−	0.836152i
$944$	−4.99786	−	4.99786i	−0.162667	−	0.162667i
$945$		0			0
$946$			21.0632i			0.684825i
$947$	−26.3584	−	26.3584i	−0.856535	−	0.856535i	0.134394	−	0.990928i	$-0.457091\pi$
$947$	−26.3584	−	26.3584i	−0.856535	−	0.856535i	−0.990928	+	0.134394i	$0.957091\pi$
$948$		0			0
$949$	17.2839	−	8.98516i	0.561059	−	0.291671i
$950$		−	22.8177i		−	0.740303i
$951$		0			0
$952$	13.5949			0.440612
$953$	12.9647			0.419969			0.209984	−	0.977705i	$-0.432659\pi$
$953$	12.9647			0.419969			0.209984	+	0.977705i	$0.432659\pi$
$954$		0			0
$955$	−9.29612	−	9.29612i	−0.300815	−	0.300815i
$956$	−8.58950	−	8.58950i	−0.277804	−	0.277804i
$957$		0			0
$958$	−33.3371			−1.07707
$959$	20.2862			0.655076
$960$		0			0
$961$		−	24.9852i		−	0.805973i
$962$	3.20434	−	10.1431i	0.103312	−	0.327027i
$963$		0			0
$964$	−3.47099	−	3.47099i	−0.111793	−	0.111793i
$965$		−	12.2512i		−	0.394380i
$966$		0			0
$967$	−2.91868	−	2.91868i	−0.0938583	−	0.0938583i	0.658619	−	0.752477i	$-0.271141\pi$
$967$	−2.91868	−	2.91868i	−0.0938583	−	0.0938583i	−0.752477	+	0.658619i	$0.771141\pi$
$968$	4.76179	−	4.76179i	0.153050	−	0.153050i
$969$		0			0
$970$	18.4003	−	18.4003i	0.590799	−	0.590799i
$971$		−	17.1932i		−	0.551756i	−0.961193	−	0.275878i	$-0.911031\pi$
$971$		−	17.1932i		−	0.551756i	0.961193	−	0.275878i	$-0.0889685\pi$
$972$		0			0
$973$	−12.6890	+	12.6890i	−0.406792	+	0.406792i
$974$	19.7246			0.632018
$975$		0			0
$976$	−21.8129			−0.698214
$977$	−36.3588	+	36.3588i	−1.16322	+	1.16322i	−0.179454	+	0.983766i	$0.557433\pi$
$977$	−36.3588	+	36.3588i	−1.16322	+	1.16322i	−0.983766	+	0.179454i	$0.942567\pi$
$978$		0			0
$979$		−	13.1090i		−	0.418966i
$980$	27.0893	−	27.0893i	0.865336	−	0.865336i
$981$		0			0
$982$	−10.4461	+	10.4461i	−0.333349	+	0.333349i
$983$	−17.8732	−	17.8732i	−0.570066	−	0.570066i	0.362081	−	0.932147i	$-0.382066\pi$
$983$	−17.8732	−	17.8732i	−0.570066	−	0.570066i	−0.932147	+	0.362081i	$0.882066\pi$
$984$		0			0
$985$			29.3323i			0.934605i
$986$	51.5139	+	51.5139i	1.64054	+	1.64054i
$987$		0			0
$988$	−25.9426	+	13.4865i	−0.825345	+	0.429062i
$989$		−	58.3460i		−	1.85529i
$990$		0			0
$991$	25.2568			0.802310			0.401155	−	0.916010i	$-0.368609\pi$
$991$	25.2568			0.802310			0.401155	+	0.916010i	$0.368609\pi$
$992$	−19.8314			−0.629647
$993$		0			0
$994$	56.7858	+	56.7858i	1.80114	+	1.80114i
$995$	−0.730839	−	0.730839i	−0.0231692	−	0.0231692i
$996$		0			0
$997$	−3.75228			−0.118836			−0.0594179	−	0.998233i	$-0.518924\pi$
$997$	−3.75228			−0.118836			−0.0594179	+	0.998233i	$0.518924\pi$
$998$	43.7768			1.38573
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.2.i.a.8.2	✓	12
3.2	odd	2	inner	117.2.i.a.8.5	yes	12
4.3	odd	2		1872.2.bi.f.593.3		12
12.11	even	2		1872.2.bi.f.593.4		12
13.5	odd	4	inner	117.2.i.a.44.5	yes	12
13.8	odd	4		1521.2.i.g.746.2		12
13.12	even	2		1521.2.i.g.944.5		12
39.5	even	4	inner	117.2.i.a.44.2	yes	12
39.8	even	4		1521.2.i.g.746.5		12
39.38	odd	2		1521.2.i.g.944.2		12
52.31	even	4		1872.2.bi.f.161.4		12
156.83	odd	4		1872.2.bi.f.161.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.i.a.8.2	✓	12	1.1	even	1	trivial
117.2.i.a.8.5	yes	12	3.2	odd	2	inner
117.2.i.a.44.2	yes	12	39.5	even	4	inner
117.2.i.a.44.5	yes	12	13.5	odd	4	inner
1521.2.i.g.746.2		12	13.8	odd	4
1521.2.i.g.746.5		12	39.8	even	4
1521.2.i.g.944.2		12	39.38	odd	2
1521.2.i.g.944.5		12	13.12	even	2
1872.2.bi.f.161.3		12	156.83	odd	4
1872.2.bi.f.161.4		12	52.31	even	4
1872.2.bi.f.593.3		12	4.3	odd	2
1872.2.bi.f.593.4		12	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	117.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.47512 + 1.47512i) q^{2} -2.35194i q^{4} +(-0.955965 + 0.955965i) q^{5} +(-3.08613 + 3.08613i) q^{7} +(0.519151 + 0.519151i) q^{8} -2.82032i q^{10} +(0.955965 + 0.955965i) q^{11} +(-3.43807 - 1.08613i) q^{13} -9.10481i q^{14} +3.17226 q^{16} -4.24264 q^{17} +(2.43807 + 2.43807i) q^{19} +(2.24837 + 2.24837i) q^{20} -2.82032 q^{22} +7.81240 q^{23} +3.17226i q^{25} +(6.67372 - 3.46939i) q^{26} +(7.25839 + 7.25839i) q^{28} +8.23118i q^{29} +(1.73419 + 1.73419i) q^{31} +(-5.71776 + 5.71776i) q^{32} +(6.25839 - 6.25839i) q^{34} -5.90047i q^{35} +(1.00000 - 1.00000i) q^{37} -7.19287 q^{38} -0.992582 q^{40} +(3.28668 - 3.28668i) q^{41} -7.46838i q^{43} +(2.24837 - 2.24837i) q^{44} +(-11.5242 + 11.5242i) q^{46} +(0.955965 + 0.955965i) q^{47} -12.0484i q^{49} +(-4.67945 - 4.67945i) q^{50} +(-2.55451 + 8.08613i) q^{52} +5.48169i q^{53} -1.82774 q^{55} -3.20434 q^{56} +(-12.1419 - 12.1419i) q^{58} +(-1.57549 - 1.57549i) q^{59} -6.87614 q^{61} -5.11627 q^{62} -10.5242i q^{64} +(4.32498 - 2.24837i) q^{65} +(2.91387 + 2.91387i) q^{67} +9.97843i q^{68} +(8.70388 + 8.70388i) q^{70} +(-6.23691 + 6.23691i) q^{71} +(-3.82032 + 3.82032i) q^{73} +2.95023i q^{74} +(5.73419 - 5.73419i) q^{76} -5.90047 q^{77} +5.64064 q^{79} +(-3.03257 + 3.03257i) q^{80} +9.69646i q^{82} +(10.0608 - 10.0608i) q^{83} +(4.05582 - 4.05582i) q^{85} +(11.0167 + 11.0167i) q^{86} +0.992582i q^{88} +(-6.85643 - 6.85643i) q^{89} +(13.9623 - 7.25839i) q^{91} -18.3743i q^{92} -2.82032 q^{94} -4.66142 q^{95} +(6.52420 + 6.52420i) q^{97} +(17.7728 + 17.7728i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 8 q^{7} - 4 q^{13} - 20 q^{16} - 8 q^{19} + 16 q^{22} - 12 q^{34} + 12 q^{37} + 96 q^{40} - 72 q^{46} + 40 q^{52} - 80 q^{55} - 92 q^{58} - 8 q^{61} + 64 q^{67} + 88 q^{70} + 4 q^{73} + 48 q^{76}+ \cdots + 12 q^{97}+O(q^{100}) \) 12 * q - 8 * q^7 - 4 * q^13 - 20 * q^16 - 8 * q^19 + 16 * q^22 - 12 * q^34 + 12 * q^37 + 96 * q^40 - 72 * q^46 + 40 * q^52 - 80 * q^55 - 92 * q^58 - 8 * q^61 + 64 * q^67 + 88 * q^70 + 4 * q^73 + 48 * q^76 - 32 * q^79 + 24 * q^85 + 64 * q^91 + 16 * q^94 + 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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