LMFDB - Embedded newform 117.2.t.c.103.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,2,Mod(25,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 3]))

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

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

chi := DirichletCharacter("117.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	117.t (of order $6$, 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:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 6x^{16} + 9x^{14} + 54x^{12} + 81x^{10} + 486x^{8} + 729x^{6} - 4374x^{4} + 59049 $ x^20 - 6x^16 + 9x^14 + 54x^12 + 81x^10 + 486x^8 + 729x^6 - 4374*x^4 + 59049
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			103.8
Root			$-0.651881 + 1.60470i$ of defining polynomial
Character	$\chi$	$=$	117.103
Dual form			117.2.t.c.25.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.41717 - 0.818205i) q^{2} +(0.471101 - 1.66675i) q^{3} +(0.338918 - 0.587023i) q^{4} +(0.950358 + 0.548689i) q^{5} +(-0.696113 - 2.74753i) q^{6} +(-2.77942 + 1.60470i) q^{7} +2.16360i q^{8} +(-2.55613 - 1.57042i) q^{9} +1.79576 q^{10} +(-1.52289 + 0.879239i) q^{11} +(-0.818757 - 0.841439i) q^{12} +(2.19891 - 2.85741i) q^{13} +(-2.62594 + 4.54826i) q^{14} +(1.36224 - 1.32552i) q^{15} +(2.44810 + 4.24024i) q^{16} +1.47360 q^{17} +(-4.90740 - 0.134118i) q^{18} -3.61452i q^{19} +(0.644186 - 0.371921i) q^{20} +(1.36525 + 5.38857i) q^{21} +(-1.43879 + 2.49207i) q^{22} +(-2.34599 + 4.06337i) q^{23} +(3.60619 + 1.01928i) q^{24} +(-1.89788 - 3.28722i) q^{25} +(0.778285 - 5.84860i) q^{26} +(-3.82169 + 3.52060i) q^{27} +2.17544i q^{28} +(0.959085 + 1.66118i) q^{29} +(0.845985 - 2.99309i) q^{30} +(5.68224 + 3.28064i) q^{31} +(3.19130 + 1.84250i) q^{32} +(0.748040 + 2.95249i) q^{33} +(2.08834 - 1.20570i) q^{34} -3.52192 q^{35} +(-1.78819 + 0.968262i) q^{36} -11.6237i q^{37} +(-2.95742 - 5.12239i) q^{38} +(-3.72669 - 5.01117i) q^{39} +(-1.18715 + 2.05620i) q^{40} +(-4.68013 - 2.70208i) q^{41} +(6.34374 + 6.51948i) q^{42} +(0.889142 + 1.54004i) q^{43} +1.19196i q^{44} +(-1.56756 - 2.89498i) q^{45} +7.67798i q^{46} +(-8.90053 + 5.13872i) q^{47} +(8.22074 - 2.08280i) q^{48} +(1.65010 - 2.85806i) q^{49} +(-5.37925 - 3.10571i) q^{50} +(0.694213 - 2.45612i) q^{51} +(-0.932116 - 2.25924i) q^{52} +11.7738 q^{53} +(-2.53542 + 8.11623i) q^{54} -1.92972 q^{55} +(-3.47193 - 6.01355i) q^{56} +(-6.02451 - 1.70280i) q^{57} +(2.71838 + 1.56946i) q^{58} +(4.78585 + 2.76311i) q^{59} +(-0.316423 - 1.24891i) q^{60} +(-0.985148 - 1.70633i) q^{61} +10.7370 q^{62} +(9.62459 + 0.263038i) q^{63} -3.76225 q^{64} +(3.65758 - 1.50905i) q^{65} +(3.47584 + 3.57213i) q^{66} +(-7.15434 - 4.13056i) q^{67} +(0.499428 - 0.865034i) q^{68} +(5.66743 + 5.82443i) q^{69} +(-4.99117 + 2.88165i) q^{70} -5.84860i q^{71} +(3.39776 - 5.53044i) q^{72} -1.24694i q^{73} +(-9.51060 - 16.4728i) q^{74} +(-6.37308 + 1.61468i) q^{75} +(-2.12180 - 1.22502i) q^{76} +(2.82182 - 4.88754i) q^{77} +(-9.38152 - 4.05249i) q^{78} +(-0.242912 - 0.420735i) q^{79} +5.37300i q^{80} +(4.06757 + 8.02838i) q^{81} -8.84340 q^{82} +(13.4351 - 7.75677i) q^{83} +(3.62592 + 1.02485i) q^{84} +(1.40044 + 0.808546i) q^{85} +(2.52014 + 1.45500i) q^{86} +(3.22061 - 0.815971i) q^{87} +(-1.90232 - 3.29492i) q^{88} +13.4245i q^{89} +(-4.59019 - 2.82010i) q^{90} +(-1.52640 + 11.4705i) q^{91} +(1.59019 + 2.75429i) q^{92} +(8.14493 - 7.92538i) q^{93} +(-8.40905 + 14.5649i) q^{94} +(1.98325 - 3.43508i) q^{95} +(4.57442 - 4.45111i) q^{96} +(-5.15756 + 2.97772i) q^{97} -5.40048i q^{98} +(5.27346 + 0.144123i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{3} + 12 q^{4} - 2 q^{9} - 16 q^{10} - 2 q^{12} - 4 q^{13} - 18 q^{14} + 4 q^{16} - 12 q^{17} - 10 q^{22} + 24 q^{23} - 12 q^{25} - 12 q^{26} - 22 q^{27} + 12 q^{29} - 54 q^{30} - 12 q^{35} + 50 q^{36}+ \cdots + 24 q^{95}+O(q^{100}) $ 20 * q + 2 * q^3 + 12 * q^4 - 2 * q^9 - 16 * q^10 - 2 * q^12 - 4 * q^13 - 18 * q^14 + 4 * q^16 - 12 * q^17 - 10 * q^22 + 24 * q^23 - 12 * q^25 - 12 * q^26 - 22 * q^27 + 12 * q^29 - 54 * q^30 - 12 * q^35 + 50 * q^36 + 12 * q^38 - 8 * q^39 - 8 * q^40 + 6 * q^42 + 4 * q^43 + 38 * q^48 - 10 * q^49 - 78 * q^51 + 108 * q^53 + 20 * q^55 + 36 * q^56 - 2 * q^61 - 72 * q^62 + 8 * q^64 - 24 * q^65 + 78 * q^66 + 24 * q^68 + 72 * q^69 - 42 * q^74 - 8 * q^75 - 6 * q^77 + 66 * q^78 - 14 * q^79 + 46 * q^81 - 4 * q^82 - 54 * q^87 + 22 * q^88 + 24 * q^90 - 72 * q^91 - 84 * q^92 + 20 * q^94 + 24 * q^95

Character values

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

$n$	$28$	$92$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	1.41717	−	0.818205i	1.00209	−	0.578558i	0.0932254	−	0.995645i	$-0.470282\pi$
$2$	1.41717	−	0.818205i	1.00209	−	0.578558i	0.908867	+	0.417087i	$0.136949\pi$
$3$	0.471101	−	1.66675i	0.271990	−	0.962300i
$3$	0.471101	−	1.66675i	0.271990	−	0.962300i
$4$	0.338918	−	0.587023i	0.169459	−	0.293511i
$5$	0.950358	+	0.548689i	0.425013	+	0.245381i	0.697220	−	0.716857i	$-0.254420\pi$
$5$	0.950358	+	0.548689i	0.425013	+	0.245381i	−0.272207	+	0.962239i	$0.587754\pi$
$6$	−0.696113	−	2.74753i	−0.284187	−	1.12168i
$7$	−2.77942	+	1.60470i	−1.05052	+	0.606518i	−0.922795	−	0.385291i	$-0.874101\pi$
$7$	−2.77942	+	1.60470i	−1.05052	+	0.606518i	−0.127725	+	0.991810i	$0.540768\pi$
$8$			2.16360i			0.764949i
$9$	−2.55613	−	1.57042i	−0.852042	−	0.523473i
$10$	1.79576			0.567869
$11$	−1.52289	+	0.879239i	−0.459168	+	0.265101i	−0.711694	−	0.702489i	$-0.752072\pi$
$11$	−1.52289	+	0.879239i	−0.459168	+	0.265101i	0.252527	+	0.967590i	$0.418738\pi$
$12$	−0.818757	−	0.841439i	−0.236355	−	0.242903i
$13$	2.19891	−	2.85741i	0.609868	−	0.792503i
$13$	2.19891	−	2.85741i	0.609868	−	0.792503i
$14$	−2.62594	+	4.54826i	−0.701812	+	1.21557i
$15$	1.36224	−	1.32552i	0.351730	−	0.342248i
$16$	2.44810	+	4.24024i	0.612026	+	1.06006i
$17$	1.47360			0.357399			0.178700	−	0.983904i	$-0.442811\pi$
$17$	1.47360			0.357399			0.178700	+	0.983904i	$0.442811\pi$
$18$	−4.90740	−	0.134118i	−1.15668	−	0.0316120i
$19$		−	3.61452i		−	0.829227i	−0.909998	−	0.414614i	$-0.863917\pi$
$19$		−	3.61452i		−	0.829227i	0.909998	−	0.414614i	$-0.136083\pi$
$20$	0.644186	−	0.371921i	0.144044	−	0.0831641i
$21$	1.36525	+	5.38857i	0.297921	+	1.17588i
$22$	−1.43879	+	2.49207i	−0.306752	+	0.531310i
$23$	−2.34599	+	4.06337i	−0.489172	+	0.847270i	−0.999922	−	0.0124586i	$-0.996034\pi$
$23$	−2.34599	+	4.06337i	−0.489172	+	0.847270i	0.510751	+	0.859729i	$0.329368\pi$
$24$	3.60619	+	1.01928i	0.736110	+	0.208059i
$25$	−1.89788	−	3.28722i	−0.379576	−	0.657445i
$26$	0.778285	−	5.84860i	0.152634	−	1.14700i
$27$	−3.82169	+	3.52060i	−0.735485	+	0.677541i
$28$			2.17544i			0.411120i
$29$	0.959085	+	1.66118i	0.178098	+	0.308474i	0.941229	−	0.337769i	$-0.109672\pi$
$29$	0.959085	+	1.66118i	0.178098	+	0.308474i	−0.763131	+	0.646244i	$0.776339\pi$
$30$	0.845985	−	2.99309i	0.154455	−	0.546461i
$31$	5.68224	+	3.28064i	1.02056	+	0.589221i	0.914266	−	0.405114i	$-0.132768\pi$
$31$	5.68224	+	3.28064i	1.02056	+	0.589221i	0.106294	+	0.994335i	$0.466101\pi$
$32$	3.19130	+	1.84250i	0.564148	+	0.325711i
$33$	0.748040	+	2.95249i	0.130217	+	0.513962i
$34$	2.08834	−	1.20570i	0.358147	−	0.206776i
$35$	−3.52192			−0.595313
$36$	−1.78819	+	0.968262i	−0.298031	+	0.161377i
$37$		−	11.6237i		−	1.91093i	−0.295103	−	0.955465i	$-0.595354\pi$
$37$		−	11.6237i		−	1.91093i	0.295103	−	0.955465i	$-0.404646\pi$
$38$	−2.95742	−	5.12239i	−0.479756	−	0.830962i
$39$	−3.72669	−	5.01117i	−0.596748	−	0.802429i
$40$	−1.18715	+	2.05620i	−0.187704	+	0.325113i
$41$	−4.68013	−	2.70208i	−0.730914	−	0.421993i	0.0878426	−	0.996134i	$-0.472003\pi$
$41$	−4.68013	−	2.70208i	−0.730914	−	0.421993i	−0.818756	+	0.574141i	$0.805336\pi$
$42$	6.34374	+	6.51948i	0.978861	+	1.00598i
$43$	0.889142	+	1.54004i	0.135593	+	0.234854i	0.925824	−	0.377955i	$-0.123373\pi$
$43$	0.889142	+	1.54004i	0.135593	+	0.234854i	−0.790231	+	0.612809i	$0.790039\pi$
$44$			1.19196i			0.179695i
$45$	−1.56756	−	2.89498i	−0.233679	−	0.431558i
$46$			7.67798i			1.13206i
$47$	−8.90053	+	5.13872i	−1.29828	+	0.749559i	−0.980106	−	0.198475i	$-0.936401\pi$
$47$	−8.90053	+	5.13872i	−1.29828	+	0.749559i	−0.318169	+	0.948034i	$0.603068\pi$
$48$	8.22074	−	2.08280i	1.18656	−	0.300626i
$49$	1.65010	−	2.85806i	0.235729	−	0.408294i
$50$	−5.37925	−	3.10571i	−0.760740	−	0.439214i
$51$	0.694213	−	2.45612i	0.0972093	−	0.343925i
$52$	−0.932116	−	2.25924i	−0.129261	−	0.313300i
$53$	11.7738			1.61726			0.808628	−	0.588320i	$-0.200211\pi$
$53$	11.7738			1.61726			0.808628	+	0.588320i	$0.200211\pi$
$54$	−2.53542	+	8.11623i	−0.345027	+	1.10448i
$55$	−1.92972			−0.260203
$56$	−3.47193	−	6.01355i	−0.463956	−	0.803595i
$57$	−6.02451	−	1.70280i	−0.797965	−	0.225542i
$58$	2.71838	+	1.56946i	0.356940	+	0.206080i
$59$	4.78585	+	2.76311i	0.623064	+	0.359726i	0.778061	−	0.628189i	$-0.216203\pi$
$59$	4.78585	+	2.76311i	0.623064	+	0.359726i	−0.154997	+	0.987915i	$0.549537\pi$
$60$	−0.316423	−	1.24891i	−0.0408501	−	0.161234i
$61$	−0.985148	−	1.70633i	−0.126135	−	0.218473i	0.796041	−	0.605243i	$-0.206924\pi$
$61$	−0.985148	−	1.70633i	−0.126135	−	0.218473i	−0.922176	+	0.386770i	$0.873591\pi$
$62$	10.7370			1.36359
$63$	9.62459	+	0.263038i	1.21258	+	0.0331397i
$64$	−3.76225			−0.470282
$65$	3.65758	−	1.50905i	0.453667	−	0.187174i
$66$	3.47584	+	3.57213i	0.427846	+	0.439699i
$67$	−7.15434	−	4.13056i	−0.874042	−	0.504628i	−0.00535270	−	0.999986i	$-0.501704\pi$
$67$	−7.15434	−	4.13056i	−0.874042	−	0.504628i	−0.868689	+	0.495357i	$0.835037\pi$
$68$	0.499428	−	0.865034i	0.0605645	−	0.104901i
$69$	5.66743	+	5.82443i	0.682278	+	0.701179i
$70$	−4.99117	+	2.88165i	−0.596558	+	0.344423i
$71$		−	5.84860i		−	0.694101i	−0.937846	−	0.347051i	$-0.887183\pi$
$71$		−	5.84860i		−	0.694101i	0.937846	−	0.347051i	$-0.112817\pi$
$72$	3.39776	−	5.53044i	0.400430	−	0.651769i
$73$		−	1.24694i		−	0.145943i	−0.997334	−	0.0729714i	$-0.976752\pi$
$73$		−	1.24694i		−	0.145943i	0.997334	−	0.0729714i	$-0.0232482\pi$
$74$	−9.51060	−	16.4728i	−1.10558	−	1.91493i
$75$	−6.37308	+	1.61468i	−0.735900	+	0.186447i
$76$	−2.12180	−	1.22502i	−0.243388	−	0.140520i
$77$	2.82182	−	4.88754i	0.321577	−	0.556987i
$78$	−9.38152	−	4.05249i	−1.06225	−	0.458854i
$79$	−0.242912	−	0.420735i	−0.0273297	−	0.0473364i	0.852037	−	0.523481i	$-0.175367\pi$
$79$	−0.242912	−	0.420735i	−0.0273297	−	0.0473364i	−0.879367	+	0.476145i	$0.842034\pi$
$80$			5.37300i			0.600719i
$81$	4.06757	+	8.02838i	0.451952	+	0.892042i
$82$	−8.84340			−0.976590
$83$	13.4351	−	7.75677i	1.47470	−	0.851417i	0.475103	−	0.879930i	$-0.342411\pi$
$83$	13.4351	−	7.75677i	1.47470	−	0.851417i	0.999593	+	0.0285134i	$0.00907732\pi$
$84$	3.62592	+	1.02485i	0.395620	+	0.111821i
$85$	1.40044	+	0.808546i	0.151899	+	0.0876991i
$86$	2.52014	+	1.45500i	0.271753	+	0.156897i
$87$	3.22061	−	0.815971i	0.345286	−	0.0874813i
$88$	−1.90232	−	3.29492i	−0.202788	−	0.351240i
$89$			13.4245i			1.42300i	0.702688	+	0.711498i	$0.251983\pi$
$89$			13.4245i			1.42300i	−0.702688	+	0.711498i	$0.748017\pi$
$90$	−4.59019	−	2.82010i	−0.483849	−	0.297264i
$91$	−1.52640	+	11.4705i	−0.160011	+	1.20244i
$92$	1.59019	+	2.75429i	0.165789	+	0.287155i
$93$	8.14493	−	7.92538i	0.844590	−	0.821823i
$94$	−8.40905	+	14.5649i	−0.867327	+	1.50225i
$95$	1.98325	−	3.43508i	0.203477	−	0.352432i
$96$	4.57442	−	4.45111i	0.466874	−	0.454289i
$97$	−5.15756	+	2.97772i	−0.523671	+	0.302342i	−0.738435	−	0.674324i	$-0.764435\pi$
$97$	−5.15756	+	2.97772i	−0.523671	+	0.302342i	0.214764	+	0.976666i	$0.431102\pi$
$98$		−	5.40048i		−	0.545531i
$99$	5.27346	+	0.144123i	0.530003	+	0.0144849i
$100$	−2.57290			−0.257290
$101$	7.94290	+	13.7575i	0.790348	+	1.36892i	0.925752	+	0.378132i	$0.123433\pi$
$101$	7.94290	+	13.7575i	0.790348	+	1.36892i	−0.135404	+	0.990790i	$0.543233\pi$
$102$	−1.02579	−	4.04875i	−0.101568	−	0.400886i
$103$	3.12594	−	5.41429i	0.308008	−	0.533486i	−0.669918	−	0.742435i	$-0.733671\pi$
$103$	3.12594	−	5.41429i	0.308008	−	0.533486i	0.977927	+	0.208949i	$0.0670043\pi$
$104$	6.18230	+	4.75756i	0.606225	+	0.466518i
$105$	−1.65918	+	5.87017i	−0.161919	+	0.572870i
$106$	16.6855	−	9.63338i	1.62064	−	0.935676i
$107$	−10.6339			−1.02802			−0.514010	−	0.857784i	$-0.671840\pi$
$107$	−10.6339			−1.02802			−0.514010	+	0.857784i	$0.671840\pi$
$108$	0.771435	+	3.43662i	0.0742314	+	0.330689i
$109$			16.0203i			1.53447i	0.641368	+	0.767234i	$0.278367\pi$
$109$			16.0203i			1.53447i	−0.641368	+	0.767234i	$0.721633\pi$
$110$	−2.73474	+	1.57890i	−0.260747	+	0.150542i
$111$	−19.3739	−	5.47596i	−1.83889	−	0.519755i
$112$	−13.6086	−	7.85693i	−1.28589	−	0.742410i
$113$	1.48868	−	2.57847i	0.140043	−	0.242562i	−0.787470	−	0.616354i	$-0.788609\pi$
$113$	1.48868	−	2.57847i	0.140043	−	0.242562i	0.927513	+	0.373792i	$0.121943\pi$
$114$	−9.93100	+	2.51611i	−0.930124	+	0.235656i
$115$	−4.45905	+	2.57443i	−0.415809	+	0.240067i
$116$	1.30020			0.120721
$117$	−10.1080	+	3.85070i	−0.934487	+	0.355997i
$118$	9.04316			0.832490
$119$	−4.09574	+	2.36467i	−0.375455	+	0.216769i
$120$	2.86790	+	2.94735i	0.261803	+	0.269055i
$121$	−3.95388	+	6.84832i	−0.359443	+	0.622574i
$122$	−2.79225	−	1.61211i	−0.252798	−	0.145953i
$123$	−6.70851	+	6.52767i	−0.604886	+	0.588580i
$124$	3.85162	−	2.22374i	0.345886	−	0.199697i
$125$		−	9.65228i		−	0.863326i
$126$	13.8549	−	7.50211i	1.23429	−	0.668341i
$127$	6.12947			0.543903			0.271951	−	0.962311i	$-0.412331\pi$
$127$	6.12947			0.543903			0.271951	+	0.962311i	$0.412331\pi$
$128$	−11.7144	+	6.76329i	−1.03541	+	0.597796i
$129$	2.98574	−	0.756465i	0.262880	−	0.0666031i
$130$	3.94871	−	5.13123i	0.346325	−	0.450038i
$131$	−4.21264	+	7.29650i	−0.368060	+	0.637498i	−0.989262	−	0.146152i	$-0.953311\pi$
$131$	−4.21264	+	7.29650i	−0.368060	+	0.637498i	0.621202	+	0.783650i	$0.286644\pi$
$132$	1.98670	+	0.561533i	0.172920	+	0.0488752i
$133$	5.80020	+	10.0462i	0.502941	+	0.871120i
$134$	−13.5186			−1.16783
$135$	−5.56369	+	1.24891i	−0.478847	+	0.107489i
$136$			3.18828i			0.273392i
$137$	6.70647	−	3.87198i	0.572973	−	0.330806i	−0.185363	−	0.982670i	$-0.559346\pi$
$137$	6.70647	−	3.87198i	0.572973	−	0.330806i	0.758336	+	0.651864i	$0.226013\pi$
$138$	12.7973	+	3.61711i	1.08938	+	0.307909i
$139$	−6.29796	+	10.9084i	−0.534186	+	0.925237i	0.465016	+	0.885302i	$0.346049\pi$
$139$	−6.29796	+	10.9084i	−0.534186	+	0.925237i	−0.999202	+	0.0399353i	$0.987285\pi$
$140$	−1.19364	+	2.06745i	−0.100881	+	0.174731i
$141$	4.37193	+	17.2558i	0.368183	+	1.45320i
$142$	−4.78535	−	8.28847i	−0.401578	−	0.695553i
$143$	−0.836341	+	6.28488i	−0.0699384	+	0.525568i
$144$	0.401288	−	14.6831i	0.0334407	−	1.22360i
$145$			2.10496i			0.174807i
$146$	−1.02025	−	1.76712i	−0.0844364	−	0.146248i
$147$	−3.98631	−	4.09675i	−0.328786	−	0.337894i
$148$	−6.82340	−	3.93949i	−0.560880	−	0.323824i
$149$	−6.76751	−	3.90722i	−0.554416	−	0.320092i	0.196485	−	0.980507i	$-0.437047\pi$
$149$	−6.76751	−	3.90722i	−0.554416	−	0.320092i	−0.750901	+	0.660415i	$0.770381\pi$
$150$	−7.71062	+	7.50277i	−0.629569	+	0.612598i
$151$	15.3081	−	8.83816i	1.24576	−	0.719239i	0.275498	−	0.961302i	$-0.411157\pi$
$151$	15.3081	−	8.83816i	1.24576	−	0.719239i	0.970261	+	0.242062i	$0.0778239\pi$
$152$	7.82038			0.634317
$153$	−3.76670	−	2.31416i	−0.304519	−	0.187089i
$154$		−	9.23532i		−	0.744203i
$155$	3.60011	+	6.23557i	0.289168	+	0.500853i
$156$	−4.20471	+	0.489277i	−0.336646	+	0.0391735i
$157$	8.89974	−	15.4148i	0.710277	−	1.23024i	−0.254477	−	0.967079i	$-0.581903\pi$
$157$	8.89974	−	15.4148i	0.710277	−	1.23024i	0.964753	−	0.263156i	$-0.0847635\pi$
$158$	−0.688495	−	0.397503i	−0.0547737	−	0.0316236i
$159$	5.54665	−	19.6240i	0.439878	−	1.55629i
$160$	2.02192	+	3.50207i	0.159847	+	0.276863i
$161$		−	15.0584i		−	1.18677i
$162$	12.3333	+	8.04949i	0.968996	+	0.632428i
$163$		−	16.7251i		−	1.31001i	−0.755624	−	0.655006i	$-0.772666\pi$
$163$		−	16.7251i		−	1.31001i	0.755624	−	0.655006i	$-0.227334\pi$
$164$	−3.17236	+	1.83156i	−0.247720	+	0.143021i
$165$	−0.909092	+	3.21636i	−0.0707727	+	0.250393i
$166$	12.6933	−	21.9854i	0.985188	−	1.70640i
$167$	4.62006	+	2.66739i	0.357511	+	0.206409i	0.667988	−	0.744172i	$-0.267156\pi$
$167$	4.62006	+	2.66739i	0.357511	+	0.206409i	−0.310477	+	0.950581i	$0.600489\pi$
$168$	−11.6587	+	2.95385i	−0.899491	+	0.227894i
$169$	−3.32960	−	12.5664i	−0.256123	−	0.966644i
$170$	2.64622			0.202956
$171$	−5.67631	+	9.23917i	−0.434078	+	0.706537i
$172$	1.20538			0.0919097
$173$	6.15330	+	10.6578i	0.467827	+	0.810299i	0.999324	−	0.0367604i	$-0.0117038\pi$
$173$	6.15330	+	10.6578i	0.467827	+	0.810299i	−0.531498	+	0.847060i	$0.678371\pi$
$174$	3.89653	−	3.79149i	0.295395	−	0.287432i
$175$	10.5500	+	6.09104i	0.797505	+	0.460440i
$176$	−7.45637	−	4.30494i	−0.562045	−	0.324497i
$177$	6.86004	−	6.67512i	0.515632	−	0.501732i
$178$	10.9840	+	19.0249i	0.823286	+	1.42597i
$179$	−18.8439			−1.40846			−0.704228	−	0.709974i	$-0.748707\pi$
$179$	−18.8439			−1.40846			−0.704228	+	0.709974i	$0.748707\pi$
$180$	−2.23069	−	0.0609645i	−0.166266	−	0.00454402i
$181$	10.8768			0.808469			0.404235	−	0.914655i	$-0.367538\pi$
$181$	10.8768			0.808469			0.404235	+	0.914655i	$0.367538\pi$
$182$	7.22205	+	17.5046i	0.535334	+	1.29753i
$183$	−3.30813	+	0.838146i	−0.244544	+	0.0619575i
$184$	−8.79151	−	5.07578i	−0.648119	−	0.374191i
$185$	6.37782	−	11.0467i	0.468907	−	0.812170i
$186$	5.05819	−	17.8958i	0.370885	−	1.31219i
$187$	−2.24412	+	1.29564i	−0.164106	+	0.0947468i
$188$			6.96641i			0.508078i
$189$	4.97258	−	15.9179i	0.361702	−	1.15786i
$190$		−	6.49081i		−	0.470893i
$191$	−9.29853	−	16.1055i	−0.672818	−	1.16536i	−0.977101	−	0.212774i	$-0.931750\pi$
$191$	−9.29853	−	16.1055i	−0.672818	−	1.16536i	0.304283	−	0.952582i	$-0.401583\pi$
$192$	−1.77240	+	6.27075i	−0.127912	+	0.452552i
$193$	11.2214	+	6.47868i	0.807735	+	0.466346i	0.846169	−	0.532915i	$-0.178904\pi$
$193$	11.2214	+	6.47868i	0.807735	+	0.466346i	−0.0384339	+	0.999261i	$0.512237\pi$
$194$	−4.87277	+	8.43989i	−0.349845	+	0.605949i
$195$	−0.792113	−	6.80719i	−0.0567244	−	0.487473i
$196$	−1.11850	−	1.93729i	−0.0798927	−	0.138378i
$197$			14.0963i			1.00432i	0.864774	+	0.502162i	$0.167462\pi$
$197$			14.0963i			1.00432i	−0.864774	+	0.502162i	$0.832538\pi$
$198$	7.59133	−	4.11053i	0.539492	−	0.292122i
$199$	16.6913			1.18321			0.591607	−	0.806226i	$-0.298494\pi$
$199$	16.6913			1.18321			0.591607	+	0.806226i	$0.298494\pi$
$200$	7.11225	−	4.10626i	0.502912	−	0.290356i
$201$	−10.2550	+	9.97860i	−0.723335	+	0.703836i
$202$	22.5129	+	12.9978i	1.58400	+	0.914524i
$203$	−5.33139	−	3.07808i	−0.374191	−	0.216039i
$204$	−1.20652	−	1.23994i	−0.0844731	−	0.0868132i
$205$	−2.96520	−	5.13588i	−0.207098	−	0.358705i
$206$		−	10.2306i		−	0.712802i
$207$	12.3778	−	6.70230i	0.860318	−	0.465842i
$208$	17.4993	+	2.32866i	1.21336	+	0.161464i
$209$	3.17802	+	5.50450i	0.219829	+	0.380754i
$210$	2.45165	+	9.67659i	0.169180	+	0.667748i
$211$	−2.74067	+	4.74698i	−0.188675	+	0.326795i	−0.944809	−	0.327622i	$-0.893753\pi$
$211$	−2.74067	+	4.74698i	−0.188675	+	0.326795i	0.756133	+	0.654417i	$0.227086\pi$
$212$	3.99035	−	6.91149i	0.274058	−	0.474683i
$213$	−9.74817	−	2.75528i	−0.667934	−	0.188789i
$214$	−15.0701	+	8.70072i	−1.03017	+	0.594769i
$215$			1.95145i			0.133088i
$216$	−7.61719	−	8.26863i	−0.518284	−	0.562609i
$217$	−21.0578			−1.42949
$218$	13.1079	+	22.7035i	0.887778	+	1.53768i
$219$	−2.07833	−	0.587433i	−0.140441	−	0.0396951i
$220$	−0.654015	+	1.13279i	−0.0440937	+	0.0763725i
$221$	3.24030	−	4.21067i	0.217966	−	0.283240i
$222$	−31.9366	+	8.09143i	−2.14344	+	0.543062i
$223$	−7.94603	+	4.58764i	−0.532105	+	0.307211i	−0.741873	−	0.670540i	$-0.766062\pi$
$223$	−7.94603	+	4.58764i	−0.532105	+	0.307211i	0.209768	+	0.977751i	$0.432729\pi$
$224$	−11.8266			−0.790198
$225$	−0.311096	+	11.3830i	−0.0207398	+	0.758869i
$226$		−	4.87217i		−	0.324092i
$227$	2.98340	−	1.72247i	0.198015	−	0.114324i	−0.397714	−	0.917509i	$-0.630196\pi$
$227$	2.98340	−	1.72247i	0.198015	−	0.114324i	0.595729	+	0.803185i	$0.296863\pi$
$228$	−3.04140	+	2.95941i	−0.201421	+	0.195992i
$229$	−10.8095	−	6.24088i	−0.714313	−	0.412409i	0.0983427	−	0.995153i	$-0.468646\pi$
$229$	−10.8095	−	6.24088i	−0.714313	−	0.412409i	−0.812656	+	0.582744i	$0.801979\pi$
$230$	−4.21283	+	7.29683i	−0.277786	+	0.481139i
$231$	−6.81696	−	7.00581i	−0.448523	−	0.460948i
$232$	−3.59414	+	2.07508i	−0.235967	+	0.136236i
$233$	−5.08821			−0.333340			−0.166670	−	0.986013i	$-0.553301\pi$
$233$	−5.08821			−0.333340			−0.166670	+	0.986013i	$0.553301\pi$
$234$	−11.1741	+	13.7275i	−0.730477	+	0.897397i
$235$	−11.2782			−0.735711
$236$	3.24402	−	1.87293i	0.211167	−	0.121918i
$237$	−0.815698	+	0.206665i	−0.0529852	+	0.0134243i
$238$	−3.86957	+	6.70230i	−0.250827	+	0.434446i
$239$	1.31463	+	0.759003i	0.0850365	+	0.0490958i	0.541915	−	0.840433i	$-0.317699\pi$
$239$	1.31463	+	0.759003i	0.0850365	+	0.0490958i	−0.456879	+	0.889529i	$0.651033\pi$
$240$	8.95545	+	2.53123i	0.578072	+	0.163390i
$241$	−16.5435	+	9.55141i	−1.06566	+	0.615260i	−0.926993	−	0.375079i	$-0.877616\pi$
$241$	−16.5435	+	9.55141i	−1.06566	+	0.615260i	−0.138669	+	0.990339i	$0.544282\pi$
$242$			12.9403i			0.831836i
$243$	15.2976	−	2.99745i	0.981339	−	0.192287i
$244$	−1.33554			−0.0854990
$245$	3.13637	−	1.81079i	0.200376	−	0.115687i
$246$	−4.16614	+	14.7398i	−0.265623	+	0.939773i
$247$	−10.3282	−	7.94799i	−0.657165	−	0.505719i
$248$	−7.09801	+	12.2941i	−0.450724	+	0.780677i
$249$	−6.59932	−	26.0473i	−0.418215	−	1.65068i
$250$	−7.89754	−	13.6789i	−0.499484	−	0.865132i
$251$	−7.96535			−0.502768			−0.251384	−	0.967887i	$-0.580886\pi$
$251$	−7.96535			−0.502768			−0.251384	+	0.967887i	$0.580886\pi$
$252$	3.41635	−	5.56070i	0.215210	−	0.350291i
$253$		−	8.25073i		−	0.518719i
$254$	8.68651	−	5.01516i	0.545040	−	0.314679i
$255$	2.00740	−	1.95328i	0.125708	−	0.122319i
$256$	−7.30526	+	12.6531i	−0.456579	+	0.790818i
$257$	10.5328	−	18.2433i	0.657017	−	1.13799i	−0.324367	−	0.945931i	$-0.605151\pi$
$257$	10.5328	−	18.2433i	0.657017	−	1.13799i	0.981384	−	0.192056i	$-0.0615155\pi$
$258$	3.61237	−	3.51499i	0.224896	−	0.218834i
$259$	18.6526	+	32.3072i	1.15901	+	2.00747i
$260$	0.353775	−	2.65852i	0.0219402	−	0.164875i
$261$	0.157211	−	5.75236i	0.00973113	−	0.356062i
$262$			13.7872i			0.851776i
$263$	−12.0525	−	20.8755i	−0.743187	−	1.28724i	−0.951037	−	0.309077i	$-0.899980\pi$
$263$	−12.0525	−	20.8755i	−0.743187	−	1.28724i	0.207850	−	0.978161i	$-0.433353\pi$
$264$	−6.38801	+	1.61846i	−0.393155	+	0.0996094i
$265$	11.1893	+	6.46016i	0.687355	+	0.396844i
$266$	16.4398	+	9.49151i	1.00799	+	0.581962i
$267$	22.3754	+	6.32431i	1.36935	+	0.387042i
$268$	−4.84947	+	2.79984i	−0.296228	+	0.171027i
$269$	−21.7780			−1.32783			−0.663913	−	0.747809i	$-0.731106\pi$
$269$	−21.7780			−1.32783			−0.663913	+	0.747809i	$0.731106\pi$
$270$	−6.86285	+	6.32216i	−0.417660	+	0.384755i
$271$		−	5.09950i		−	0.309773i	−0.987932	−	0.154886i	$-0.950499\pi$
$271$		−	5.09950i		−	0.309773i	0.987932	−	0.154886i	$-0.0495012\pi$
$272$	3.60752	+	6.24840i	0.218738	+	0.378865i
$273$	18.3994	+	7.94791i	1.11358	+	0.481030i
$274$	6.33615	−	10.9745i	0.382781	−	0.662996i
$275$	5.78051	+	3.33738i	0.348578	+	0.201252i
$276$	5.33987	−	1.35290i	0.321422	−	0.0814353i
$277$	−6.13878	−	10.6327i	−0.368844	−	0.638856i	0.620541	−	0.784174i	$-0.286913\pi$
$277$	−6.13878	−	10.6327i	−0.368844	−	0.638856i	−0.989385	+	0.145318i	$0.953580\pi$
$278$			20.6121i			1.23623i
$279$	−9.37255	−	17.3092i	−0.561120	−	1.03628i
$280$		−	7.62003i		−	0.455384i
$281$	6.33254	−	3.65609i	0.377768	−	0.218104i	−0.299079	−	0.954228i	$-0.596679\pi$
$281$	6.33254	−	3.65609i	0.377768	−	0.218104i	0.676847	+	0.736124i	$0.263346\pi$
$282$	20.3146	+	20.8773i	1.20972	+	1.24323i
$283$	−6.39883	+	11.0831i	−0.380371	+	0.658822i	−0.991115	−	0.133006i	$-0.957537\pi$
$283$	−6.39883	+	11.0831i	−0.380371	+	0.658822i	0.610744	+	0.791828i	$0.290870\pi$
$284$	−3.43326	−	1.98219i	−0.203727	−	0.117622i
$285$	−4.79113	−	4.92385i	−0.283802	−	0.291664i
$286$	3.95708	+	9.59105i	0.233987	+	0.567131i
$287$	17.3440			1.02379
$288$	−5.26388	−	9.72134i	−0.310177	−	0.572836i
$289$	−14.8285			−0.872266
$290$	1.72229	+	2.98309i	0.101136	+	0.175173i
$291$	2.53339	+	9.99919i	0.148510	+	0.586163i
$292$	−0.731980	−	0.422609i	−0.0428359	−	0.0247313i
$293$	5.69346	+	3.28712i	0.332616	+	0.192036i	0.657002	−	0.753889i	$-0.271824\pi$
$293$	5.69346	+	3.28712i	0.332616	+	0.192036i	−0.324386	+	0.945925i	$0.605158\pi$
$294$	−9.00127	−	2.54418i	−0.524965	−	0.148379i
$295$	3.03218	+	5.25188i	0.176540	+	0.305777i
$296$	25.1492			1.46176
$297$	2.72455	−	8.72166i	0.158095	−	0.506082i
$298$	−12.7876			−0.740768
$299$	6.45210	+	15.6384i	0.373135	+	0.904393i
$300$	−1.21210	+	4.28839i	−0.0699804	+	0.247590i
$301$	−4.94259	−	2.85361i	−0.284886	−	0.164479i
$302$	14.4628	−	25.0504i	0.832243	−	1.44149i
$303$	26.6723	−	6.75767i	1.53228	−	0.388218i
$304$	15.3264	−	8.84872i	0.879031	−	0.507509i
$305$		−	2.16216i		−	0.123805i
$306$	−7.23152	−	0.197636i	−0.413398	−	0.0112981i
$307$			24.3307i			1.38863i	0.719672	+	0.694315i	$0.244292\pi$
$307$			24.3307i			1.38863i	−0.719672	+	0.694315i	$0.755708\pi$
$308$	−1.91273	−	3.31295i	−0.108988	−	0.188773i
$309$	−7.55164	−	7.76085i	−0.429598	−	0.441499i
$310$	10.2039	+	5.89125i	0.579545	+	0.334601i
$311$	−5.58336	+	9.67066i	−0.316603	+	0.548373i	−0.979777	−	0.200093i	$-0.935876\pi$
$311$	−5.58336	+	9.67066i	−0.316603	+	0.548373i	0.663174	+	0.748465i	$0.269209\pi$
$312$	10.8422	−	8.06307i	0.613817	−	0.456482i
$313$	−8.90138	−	15.4176i	−0.503136	−	0.871456i	−0.999993	−	0.00362437i	$-0.998846\pi$
$313$	−8.90138	−	15.4176i	−0.503136	−	0.871456i	0.496858	−	0.867832i	$-0.334487\pi$
$314$		−	29.1272i		−	1.64374i
$315$	9.00247	+	5.53089i	0.507232	+	0.311630i
$316$	−0.329308			−0.0185250
$317$	−26.7276	+	15.4312i	−1.50117	+	0.866700i	−0.501170	+	0.865349i	$0.667097\pi$
$317$	−26.7276	+	15.4312i	−1.50117	+	0.866700i	−0.999999	+	0.00135144i	$0.999570\pi$
$318$	−8.19589	−	32.3489i	−0.459603	−	1.81404i
$319$	−2.92116	−	1.68653i	−0.163553	−	0.0944276i
$320$	−3.57549	−	2.06431i	−0.199876	−	0.115398i
$321$	−5.00965	+	17.7241i	−0.279611	+	0.989263i
$322$	−12.3208	−	21.3403i	−0.686613	−	1.18925i
$323$		−	5.32634i		−	0.296365i
$324$	6.09141	+	0.333203i	0.338412	+	0.0185113i
$325$	−13.5662	−	1.80528i	−0.752518	−	0.100139i
$326$	−13.6846	−	23.7024i	−0.757918	−	1.31275i
$327$	26.7019	+	7.54719i	1.47662	+	0.417361i
$328$	5.84622	−	10.1259i	0.322803	−	0.559112i
$329$	16.4922	−	28.5653i	0.909243	−	1.57486i
$330$	1.34330	+	5.30196i	0.0739462	+	0.291863i
$331$	15.0730	−	8.70242i	0.828489	−	0.478328i	−0.0248461	−	0.999691i	$-0.507910\pi$
$331$	15.0730	−	8.70242i	0.828489	−	0.478328i	0.853335	+	0.521363i	$0.174576\pi$
$332$		−	10.5156i		−	0.577120i
$333$	−18.2541	+	29.7118i	−1.00032	+	1.62819i
$334$	8.72989			0.477678
$335$	−4.53279	−	7.85102i	−0.247653	−	0.428947i
$336$	−19.5066	+	18.9808i	−1.06417	+	1.03549i
$337$	−4.37915	+	7.58491i	−0.238548	+	0.413176i	−0.960298	−	0.278977i	$-0.910005\pi$
$337$	−4.37915	+	7.58491i	−0.238548	+	0.413176i	0.721750	+	0.692154i	$0.243338\pi$
$338$	−15.0005	−	15.0844i	−0.815919	−	0.820484i
$339$	−3.59635	−	3.69598i	−0.195327	−	0.200738i
$340$	0.949270	−	0.548061i	0.0514814	−	0.0297228i
$341$	−11.5379			−0.624811
$342$	−0.484773	+	17.7379i	−0.0262135	+	0.959154i
$343$		−	11.8741i		−	0.641141i
$344$	−3.33203	+	1.92375i	−0.179651	+	0.103722i
$345$	2.19028	+	8.64495i	0.117921	+	0.465429i
$346$	17.4406	+	10.0693i	0.937611	+	0.541330i
$347$	3.63878	−	6.30255i	0.195340	−	0.338339i	−0.751672	−	0.659537i	$-0.770752\pi$
$347$	3.63878	−	6.30255i	0.195340	−	0.338339i	0.947012	+	0.321198i	$0.104086\pi$
$348$	0.612528	−	2.16712i	0.0328349	−	0.116170i
$349$	−10.8475	+	6.26279i	−0.580652	+	0.335240i	−0.761392	−	0.648291i	$-0.775484\pi$
$349$	−10.8475	+	6.26279i	−0.580652	+	0.335240i	0.180740	+	0.983531i	$0.442151\pi$
$350$	19.9349			1.06556
$351$	1.65626	+	18.6616i	0.0884045	+	0.996085i
$352$	−6.47999			−0.345385
$353$	1.42107	−	0.820458i	0.0756361	−	0.0436686i	−0.461705	−	0.887034i	$-0.652762\pi$
$353$	1.42107	−	0.820458i	0.0756361	−	0.0436686i	0.537341	+	0.843365i	$0.319429\pi$
$354$	4.26024	−	15.0727i	0.226429	−	0.801105i
$355$	3.20906	−	5.55826i	0.170319	−	0.295002i
$356$	7.88050	+	4.54981i	0.417666	+	0.241139i
$357$	2.01182	+	7.94058i	0.106477	+	0.420260i
$358$	−26.7050	+	15.4181i	−1.41140	+	0.814874i
$359$			7.00788i			0.369862i	0.982752	+	0.184931i	$0.0592061\pi$
$359$			7.00788i			0.369862i	−0.982752	+	0.184931i	$0.940794\pi$
$360$	6.26358	−	3.39158i	0.330120	−	0.178752i
$361$	5.93526			0.312382
$362$	15.4144	−	8.89948i	0.810160	−	0.467746i
$363$	9.55177	+	9.81639i	0.501338	+	0.515227i
$364$	6.21613	+	4.78359i	0.325814	+	0.250728i
$365$	0.684180	−	1.18504i	0.0358116	−	0.0620276i
$366$	−4.00241	+	3.89452i	−0.209210	+	0.203570i
$367$	0.596340	+	1.03289i	0.0311287	+	0.0539165i	0.881170	−	0.472799i	$-0.156756\pi$
$367$	0.596340	+	1.03289i	0.0311287	+	0.0539165i	−0.850041	+	0.526716i	$0.823423\pi$
$368$	−22.9729			−1.19754
$369$	7.71962	+	14.2566i	0.401867	+	0.742170i
$370$		−	20.8735i		−	1.08516i
$371$	−32.7243	+	18.8934i	−1.69896	+	0.980895i
$372$	−1.89191	−	7.46731i	−0.0980911	−	0.387162i
$373$	−8.65200	+	14.9857i	−0.447984	+	0.775931i	−0.998255	−	0.0590555i	$-0.981191\pi$
$373$	−8.65200	+	14.9857i	−0.447984	+	0.775931i	0.550271	+	0.834986i	$0.314524\pi$
$374$	−2.12020	+	3.67230i	−0.109633	+	0.189890i
$375$	−16.0880	−	4.54720i	−0.830779	−	0.234816i
$376$	−11.1181	−	19.2572i	−0.573375	−	0.993114i
$377$	6.85563	+	0.912292i	0.353083	+	0.0469854i
$378$	−5.97709	−	26.6270i	−0.307428	−	1.36954i
$379$		−	1.54294i		−	0.0792554i	−0.999215	−	0.0396277i	$-0.987383\pi$
$379$		−	1.54294i		−	0.0792554i	0.999215	−	0.0396277i	$-0.0126172\pi$
$380$	−1.34431	−	2.32842i	−0.0689619	−	0.119446i
$381$	2.88760	−	10.2163i	0.147936	−	0.523397i
$382$	−26.3552	−	15.2162i	−1.34845	−	0.778529i
$383$	−20.4912	−	11.8306i	−1.04705	−	0.604515i	−0.125229	−	0.992128i	$-0.539967\pi$
$383$	−20.4912	−	11.8306i	−1.04705	−	0.604515i	−0.921822	+	0.387612i	$0.873300\pi$
$384$	5.75408	+	22.7111i	0.293637	+	1.15897i
$385$	5.36348	−	3.09661i	0.273348	−	0.157818i
$386$	21.2036			1.07923
$387$	0.145746	−	5.33286i	0.00740870	−	0.271085i
$388$			4.03681i			0.204938i
$389$	2.58336	+	4.47450i	0.130981	+	0.226866i	0.924055	−	0.382259i	$-0.124854\pi$
$389$	2.58336	+	4.47450i	0.130981	+	0.226866i	−0.793074	+	0.609126i	$0.791521\pi$
$390$	−6.69224	−	8.99886i	−0.338875	−	0.455675i
$391$	−3.45703	+	5.98776i	−0.174830	+	0.302814i
$392$	6.18371	+	3.57016i	0.312324	+	0.180321i
$393$	10.1769	+	10.4588i	0.513356	+	0.527577i
$394$	11.5337	+	19.9769i	0.581059	+	1.00642i
$395$		−	0.533132i		−	0.0268248i
$396$	1.87187	−	3.04680i	0.0940652	−	0.153107i
$397$		−	14.0455i		−	0.704926i	−0.935826	−	0.352463i	$-0.885344\pi$
$397$		−	14.0455i		−	0.704926i	0.935826	−	0.352463i	$-0.114656\pi$
$398$	23.6544	−	13.6569i	1.18569	−	0.684558i
$399$	19.4771	−	4.93470i	0.975074	−	0.247044i
$400$	9.29242	−	16.0949i	0.464621	−	0.804747i
$401$	−12.9801	−	7.49409i	−0.648198	−	0.374237i	0.139568	−	0.990213i	$-0.455429\pi$
$401$	−12.9801	−	7.49409i	−0.648198	−	0.374237i	−0.787765	+	0.615976i	$0.788762\pi$
$402$	−6.36862	+	22.5321i	−0.317638	+	1.12380i
$403$	21.8689	−	9.02267i	1.08937	−	0.449451i
$404$	10.7680			0.535726
$405$	−0.539438	+	9.86166i	−0.0268049	+	0.490030i
$406$	−10.0740			−0.499964
$407$	10.2200	+	17.7016i	0.506589	+	0.877438i
$408$	5.31407	+	1.50200i	0.263085	+	0.0743601i
$409$	−0.411886	−	0.237803i	−0.0203665	−	0.0117586i	0.489782	−	0.871845i	$-0.337076\pi$
$409$	−0.411886	−	0.237803i	−0.0203665	−	0.0117586i	−0.510149	+	0.860086i	$0.670410\pi$
$410$	−8.40439	−	4.85228i	−0.415063	−	0.239637i
$411$	−3.29421	−	13.0021i	−0.162491	−	0.641348i
$412$	−2.11887	−	3.67000i	−0.104389	−	0.180808i
$413$	−17.7358			−0.872722
$414$	12.0576	−	19.6259i	0.592601	−	0.964560i
$415$	17.0242			0.835687
$416$	12.2822	−	5.06738i	0.602182	−	0.248449i
$417$	15.2146	+	15.6361i	0.745062	+	0.765703i
$418$	9.00762	+	5.20055i	0.440577	+	0.254367i
$419$	−6.45908	+	11.1875i	−0.315547	+	0.546543i	−0.979554	−	0.201184i	$-0.935521\pi$
$419$	−6.45908	+	11.1875i	−0.315547	+	0.546543i	0.664007	+	0.747726i	$0.268855\pi$
$420$	2.88360	+	2.96348i	0.140705	+	0.144603i
$421$	27.3802	−	15.8080i	1.33443	−	0.770433i	0.348454	−	0.937326i	$-0.386707\pi$
$421$	27.3802	−	15.8080i	1.33443	−	0.770433i	0.985975	+	0.166893i	$0.0533735\pi$
$422$			8.96971i			0.436639i
$423$	30.8208	+	0.842328i	1.49856	+	0.0409554i
$424$			25.4738i			1.23712i
$425$	−2.79671	−	4.84404i	−0.135660	−	0.234970i
$426$	−16.0692	+	4.07129i	−0.778556	+	0.197254i
$427$	5.47627	+	3.16173i	0.265016	+	0.153007i
$428$	−3.60402	+	6.24235i	−0.174207	+	0.301735i
$429$	10.0813	+	4.35479i	0.486732	+	0.210251i
$430$	1.59669	+	2.76554i	0.0769991	+	0.133366i
$431$		−	12.5560i		−	0.604799i	−0.953181	−	0.302400i	$-0.902212\pi$
$431$		−	12.5560i		−	0.604799i	0.953181	−	0.302400i	$-0.0977877\pi$
$432$	−24.2841	−	7.58610i	−1.16837	−	0.364986i
$433$	−27.9766			−1.34447			−0.672235	−	0.740338i	$-0.734665\pi$
$433$	−27.9766			−1.34447			−0.672235	+	0.740338i	$0.734665\pi$
$434$	−29.8425	+	17.2296i	−1.43248	+	0.827045i
$435$	3.50845	+	0.991649i	0.168217	+	0.0475459i
$436$	9.40428	+	5.42957i	0.450384	+	0.260029i
$437$	14.6871	+	8.47960i	0.702580	+	0.405635i
$438$	−3.42600	+	0.868008i	−0.163700	+	0.0414750i
$439$	5.76780	+	9.99012i	0.275282	+	0.476802i	0.970206	−	0.242281i	$-0.0778955\pi$
$439$	5.76780	+	9.99012i	0.275282	+	0.476802i	−0.694924	+	0.719083i	$0.744562\pi$
$440$		−	4.17514i		−	0.199042i
$441$	−8.70622	+	4.71421i	−0.414582	+	0.224486i
$442$	1.14688	−	8.61847i	0.0545514	−	0.409939i
$443$	−13.1323	−	22.7457i	−0.623932	−	1.08068i	−0.988746	−	0.149602i	$-0.952201\pi$
$443$	−13.1323	−	22.7457i	−0.623932	−	1.08068i	0.364814	−	0.931080i	$-0.381132\pi$
$444$	−9.78067	+	9.51702i	−0.464170	+	0.451658i
$445$	−7.36589	+	12.7581i	−0.349177	+	0.604792i
$446$	−7.50726	+	13.0030i	−0.355479	+	0.615708i
$447$	−9.70056	+	9.43907i	−0.458821	+	0.446452i
$448$	10.4569	−	6.03728i	0.494041	−	0.285235i
$449$			29.9575i			1.41378i	0.707323	+	0.706891i	$0.249903\pi$
$449$			29.9575i			1.41378i	−0.707323	+	0.706891i	$0.750097\pi$
$450$	8.87277	+	16.3863i	0.418266	+	0.772455i
$451$	9.50308			0.447483
$452$	−1.00908	−	1.74778i	−0.0474631	−	0.0822085i
$453$	−7.51934	−	29.6786i	−0.353289	−	1.39442i
$454$	2.81866	−	4.88206i	0.132286	−	0.229127i
$455$	−7.74438	+	10.0636i	−0.363062	+	0.471788i
$456$	3.68419	−	13.0346i	0.172528	−	0.610403i
$457$	9.92475	−	5.73006i	0.464260	−	0.268041i	−0.249574	−	0.968356i	$-0.580290\pi$
$457$	9.92475	−	5.73006i	0.464260	−	0.268041i	0.713834	+	0.700315i	$0.246957\pi$
$458$	−20.4253			−0.954410
$459$	−5.63163	+	5.18795i	−0.262862	+	0.242153i
$460$			3.49008i			0.162726i
$461$	24.6926	−	14.2563i	1.15005	−	0.663981i	0.201149	−	0.979561i	$-0.435532\pi$
$461$	24.6926	−	14.2563i	1.15005	−	0.663981i	0.948899	+	0.315580i	$0.102199\pi$
$462$	−15.3930	−	4.35077i	−0.716147	−	0.202416i
$463$	1.46868	+	0.847942i	0.0682553	+	0.0394072i	0.533739	−	0.845649i	$-0.320786\pi$
$463$	1.46868	+	0.847942i	0.0682553	+	0.0394072i	−0.465484	+	0.885056i	$0.654120\pi$
$464$	−4.69588	+	8.13351i	−0.218001	+	0.377589i
$465$	12.0892	−	3.06290i	0.560622	−	0.142039i
$466$	−7.21086	+	4.16319i	−0.334037	+	0.192856i
$467$	14.1217			0.653476			0.326738	−	0.945115i	$-0.394051\pi$
$467$	14.1217			0.653476			0.326738	+	0.945115i	$0.394051\pi$
$468$	−1.16534	+	7.23871i	−0.0538679	+	0.334609i
$469$	26.5132			1.22427
$470$	−15.9832	+	9.22791i	−0.737251	+	0.425652i
$471$	−21.5000	−	22.0956i	−0.990667	−	1.01811i
$472$	−5.97827	+	10.3547i	−0.275172	+	0.476612i
$473$	−2.70813	−	1.56354i	−0.124520	−	0.0718915i
$474$	−0.986890	+	0.960287i	−0.0453293	+	0.0441074i
$475$	−11.8817	+	6.85992i	−0.545171	+	0.314755i
$476$			3.20572i			0.146934i
$477$	−30.0953	−	18.4898i	−1.37797	−	0.846590i
$478$	2.48408			0.113619
$479$	24.0438	−	13.8817i	1.09859	−	0.634272i	0.162740	−	0.986669i	$-0.447967\pi$
$479$	24.0438	−	13.8817i	1.09859	−	0.634272i	0.935850	+	0.352397i	$0.114633\pi$
$480$	6.78961	−	1.72021i	0.309902	−	0.0785165i
$481$	−33.2138	−	25.5595i	−1.51442	−	1.16541i
$482$	−15.6300	+	27.0720i	−0.711927	+	1.23309i
$483$	−25.0986	−	7.09402i	−1.14203	−	0.322789i
$484$	2.68008	+	4.64203i	0.121822	+	0.211001i
$485$	−6.53537			−0.296756
$486$	19.2267	−	16.7644i	0.872143	−	0.760450i
$487$			27.5898i			1.25021i	0.780539	+	0.625107i	$0.214945\pi$
$487$			27.5898i			1.25021i	−0.780539	+	0.625107i	$0.785055\pi$
$488$	3.69181	−	2.13147i	0.167121	−	0.0964871i
$489$	−27.8766	−	7.87922i	−1.26062	−	0.356311i
$490$	2.96319	−	5.13239i	0.133863	−	0.231858i
$491$	−20.3683	+	35.2790i	−0.919210	+	1.59212i	−0.118591	+	0.992943i	$0.537838\pi$
$491$	−20.3683	+	35.2790i	−0.919210	+	1.59212i	−0.800618	+	0.599175i	$0.795496\pi$
$492$	1.55826	+	6.15039i	0.0702517	+	0.277281i
$493$	1.41330	+	2.44791i	0.0636520	+	0.110249i
$494$	−21.1399	−	2.81312i	−0.951128	−	0.126568i
$495$	4.93260	+	3.03046i	0.221704	+	0.136209i
$496$			32.1254i			1.44248i
$497$	9.38523	+	16.2557i	0.420985	+	0.729168i
$498$	−30.6644	−	31.5139i	−1.37410	−	1.41217i
$499$	−13.5293	−	7.81113i	−0.605654	−	0.349674i	0.165609	−	0.986192i	$-0.447041\pi$
$499$	−13.5293	−	7.81113i	−0.605654	−	0.349674i	−0.771262	+	0.636517i	$0.780374\pi$
$500$	−5.66611	−	3.27133i	−0.253396	−	0.146298i
$501$	6.62240	−	6.44388i	0.295867	−	0.287891i
$502$	−11.2883	+	6.51729i	−0.503820	+	0.290881i
$503$	30.2181			1.34736			0.673679	−	0.739024i	$-0.264713\pi$
$503$	30.2181			1.34736			0.673679	+	0.739024i	$0.264713\pi$
$504$	−0.569111	+	20.8238i	−0.0253502	+	0.927565i
$505$			17.4327i			0.775746i
$506$	−6.75078	−	11.6927i	−0.300109	−	0.519804i
$507$	−22.5136	−	0.370418i	−0.999865	−	0.0164509i
$508$	2.07739	−	3.59814i	0.0921691	−	0.159642i
$509$	13.0660	+	7.54366i	0.579140	+	0.334367i	0.760792	−	0.648996i	$-0.224811\pi$
$509$	13.0660	+	7.54366i	0.579140	+	0.334367i	−0.181651	+	0.983363i	$0.558144\pi$
$510$	1.24664	−	4.41060i	0.0552022	−	0.195305i
$511$	2.00095	+	3.46575i	0.0885170	+	0.153316i
$512$		−	3.14438i		−	0.138963i
$513$	12.7253	+	13.8136i	0.561835	+	0.609884i
$514$		−	34.4719i		−	1.52049i
$515$	5.94152	−	3.43034i	0.261815	−	0.151159i
$516$	0.567858	−	2.00908i	0.0249986	−	0.0884447i
$517$	9.03633	−	15.6514i	0.397417	−	0.688347i
$518$	52.8678	+	30.5232i	2.32288	+	1.34111i
$519$	20.6628	−	5.23511i	0.906996	−	0.229796i
$520$	3.26497	+	7.91355i	0.143179	+	0.347032i
$521$	26.8690			1.17715			0.588576	−	0.808442i	$-0.299689\pi$
$521$	26.8690			1.17715			0.588576	+	0.808442i	$0.299689\pi$
$522$	−4.48382	−	8.28072i	−0.196251	−	0.362437i
$523$	24.9855			1.09254			0.546270	−	0.837609i	$-0.316047\pi$
$523$	24.9855			1.09254			0.546270	+	0.837609i	$0.316047\pi$
$524$	2.85547	+	4.94583i	0.124742	+	0.216059i
$525$	15.1224	−	14.7147i	0.659995	−	0.642204i
$526$	−34.1608	−	19.7228i	−1.48948	−	0.859954i
$527$	8.37333	+	4.83434i	0.364748	+	0.210587i
$528$	−10.6880	+	10.3999i	−0.465134	+	0.452596i
$529$	0.492707	+	0.853394i	0.0214221	+	0.0371041i
$530$	21.1429			0.918390
$531$	−7.89399	−	14.5786i	−0.342570	−	0.632659i
$532$	7.86317			0.340911
$533$	−18.0121	+	7.43144i	−0.780192	+	0.321892i
$534$	36.8843	−	9.34498i	1.59614	−	0.404397i
$535$	−10.1060	−	5.83471i	−0.436921	−	0.252257i
$536$	8.93689	−	15.4792i	0.386015	−	0.668598i
$537$	−8.87737	+	31.4081i	−0.383087	+	1.35536i
$538$	−30.8631	+	17.8188i	−1.33060	+	0.768225i
$539$			5.80334i			0.249967i
$540$	−1.15250	+	3.68929i	−0.0495955	+	0.158762i
$541$			33.1735i			1.42624i	0.701042	+	0.713120i	$0.252719\pi$
$541$			33.1735i			1.42624i	−0.701042	+	0.713120i	$0.747281\pi$
$542$	−4.17244	−	7.22687i	−0.179222	−	0.310421i
$543$	5.12409	−	18.1290i	0.219896	−	0.777990i
$544$	4.70269	+	2.71510i	0.201626	+	0.116409i
$545$	−8.79017	+	15.2250i	−0.376530	+	0.652168i
$546$	32.5782	−	3.79093i	1.39422	−	0.162237i
$547$	−9.36201	−	16.2155i	−0.400291	−	0.693324i	0.593470	−	0.804856i	$-0.297758\pi$
$547$	−9.36201	−	16.2155i	−0.400291	−	0.693324i	−0.993761	+	0.111532i	$0.964424\pi$
$548$		−	5.24913i		−	0.224232i
$549$	−0.161483	+	5.90868i	−0.00689194	+	0.252177i
$550$	10.9226			0.465743
$551$	6.00438	−	3.46663i	0.255795	−	0.147683i
$552$	−12.6018	+	12.2621i	−0.536366	+	0.521908i
$553$	1.35030	+	0.779599i	0.0574208	+	0.0331519i
$554$	−17.3994	−	10.0456i	−0.739230	−	0.426795i
$555$	−15.4075	−	15.8344i	−0.654013	−	0.672132i
$556$	4.26898	+	7.39409i	0.181045	+	0.313579i
$557$		−	27.4258i		−	1.16207i	−0.813879	−	0.581035i	$-0.802648\pi$
$557$		−	27.4258i		−	1.16207i	0.813879	−	0.581035i	$-0.197352\pi$
$558$	−27.4450	−	16.8615i	−1.16184	−	0.713805i
$559$	6.35567	+	0.845762i	0.268816	+	0.0357719i
$560$	−8.62203	−	14.9338i	−0.364347	−	0.631068i
$561$	1.10231	+	4.35077i	0.0465395	+	0.183690i
$562$	5.98286	−	10.3626i	0.252372	−	0.437121i
$563$	9.85731	−	17.0734i	0.415436	−	0.719556i	−0.580038	−	0.814589i	$-0.696962\pi$
$563$	9.85731	−	17.0734i	0.415436	−	0.719556i	0.995474	+	0.0950331i	$0.0302957\pi$
$564$	11.6113	+	3.28189i	0.488923	+	0.138192i
$565$	2.82955	−	1.63364i	0.119040	−	0.0687279i
$566$			20.9422i			0.880267i
$567$	−24.1886	−	15.7870i	−1.01582	−	0.662991i
$568$	12.6540			0.530952
$569$	−9.70872	−	16.8160i	−0.407011	−	0.704963i	0.587543	−	0.809193i	$-0.300095\pi$
$569$	−9.70872	−	16.8160i	−0.407011	−	0.704963i	−0.994553	+	0.104230i	$0.966762\pi$
$570$	−10.8186	−	3.05783i	−0.453140	−	0.128078i
$571$	−4.99536	+	8.65223i	−0.209050	+	0.362084i	−0.951415	−	0.307910i	$-0.900370\pi$
$571$	−4.99536	+	8.65223i	−0.209050	+	0.362084i	0.742366	+	0.669995i	$0.233704\pi$
$572$	3.40592	+	2.62101i	0.142408	+	0.109590i
$573$	−31.2245	+	7.91101i	−1.30442	+	0.330487i
$574$	24.5795	−	14.1910i	1.02593	−	0.592320i
$575$	17.8096			0.742711
$576$	9.61680	+	5.90831i	0.400700	+	0.246180i
$577$		−	17.2976i		−	0.720107i	−0.932932	−	0.360054i	$-0.882758\pi$
$577$		−	17.2976i		−	0.720107i	0.932932	−	0.360054i	$-0.117242\pi$
$578$	−21.0146	+	12.1328i	−0.874090	+	0.504656i
$579$	16.0848	−	15.6512i	0.668461	−	0.650441i
$580$	1.23566	+	0.713408i	0.0513079	+	0.0296227i
$581$	−24.8945	+	43.1186i	−1.03280	+	1.78886i
$582$	11.7716	+	12.0977i	0.487950	+	0.501468i
$583$	−17.9302	+	10.3520i	−0.742591	+	0.428735i
$584$	2.69787			0.111639
$585$	−11.7191	−	1.88662i	−0.484524	−	0.0780022i
$586$	10.7582			0.444415
$587$	19.0473	−	10.9970i	0.786166	−	0.453893i	−0.0524453	−	0.998624i	$-0.516702\pi$
$587$	19.0473	−	10.9970i	0.786166	−	0.453893i	0.838611	+	0.544731i	$0.183368\pi$
$588$	−3.75592	+	0.951596i	−0.154891	+	0.0392432i
$589$	11.8579	−	20.5386i	0.488598	−	0.846277i
$590$	8.59423	+	4.96188i	0.353819	+	0.204277i
$591$	23.4951	+	6.64081i	0.966460	+	0.273166i
$592$	49.2875	−	28.4561i	2.02570	−	1.16954i
$593$		−	29.8711i		−	1.22666i	−0.789826	−	0.613330i	$-0.789829\pi$
$593$		−	29.8711i		−	1.22666i	0.789826	−	0.613330i	$-0.210171\pi$
$594$	−3.27494	−	14.5893i	−0.134373	−	0.598608i
$595$	−5.18988			−0.212765
$596$	−4.58726	+	2.64845i	−0.187901	+	0.108485i
$597$	7.86329	−	27.8202i	0.321823	−	1.13861i
$598$	21.9392	+	16.8832i	0.897159	+	0.690405i
$599$	0.00682877	−	0.0118278i	0.000279016	−	0.000483270i	−0.865886	−	0.500242i	$-0.833245\pi$
$599$	0.00682877	−	0.0118278i	0.000279016	−	0.000483270i	0.866165	+	0.499758i	$0.166578\pi$
$600$	−3.49353	−	13.7888i	−0.142623	−	0.562926i
$601$	−3.25799	−	5.64301i	−0.132896	−	0.230183i	0.791896	−	0.610657i	$-0.209094\pi$
$601$	−3.25799	−	5.64301i	−0.132896	−	0.230183i	−0.924792	+	0.380473i	$0.875761\pi$
$602$	−9.33934			−0.380643
$603$	11.8007	+	21.7936i	0.480562	+	0.887502i
$604$		−	11.9816i		−	0.487526i
$605$	−7.51520	+	4.33890i	−0.305536	+	0.176401i
$606$	32.2700	−	31.4001i	1.31088	−	1.27554i
$607$	17.7921	−	30.8168i	0.722158	−	1.25081i	−0.237975	−	0.971271i	$-0.576484\pi$
$607$	17.7921	−	30.8168i	0.722158	−	1.25081i	0.960133	−	0.279543i	$-0.0901831\pi$
$608$	6.65975	−	11.5350i	0.270088	−	0.467807i
$609$	−7.64203	+	7.43603i	−0.309671	+	0.301323i
$610$	−1.76909	−	3.06415i	−0.0716284	−	0.124064i
$611$	−4.88801	+	36.7320i	−0.197748	+	1.48602i
$612$	−2.63507	+	1.42683i	−0.106516	+	0.0576760i
$613$			2.03420i			0.0821607i	0.999156	+	0.0410803i	$0.0130800\pi$
$613$			2.03420i			0.0821607i	−0.999156	+	0.0410803i	$0.986920\pi$
$614$	19.9075	+	34.4809i	0.803403	+	1.39153i
$615$	−9.95714	+	2.52273i	−0.401511	+	0.101726i
$616$	10.5747	+	6.10530i	0.426067	+	0.245990i
$617$	−2.65725	−	1.53417i	−0.106977	−	0.0617632i	0.445557	−	0.895254i	$-0.353006\pi$
$617$	−2.65725	−	1.53417i	−0.106977	−	0.0617632i	−0.552534	+	0.833490i	$0.686339\pi$
$618$	−17.0519	−	4.81967i	−0.685929	−	0.193875i
$619$	3.43093	−	1.98085i	0.137901	−	0.0796169i	−0.429463	−	0.903085i	$-0.641297\pi$
$619$	3.43093	−	1.98085i	0.137901	−	0.0796169i	0.567363	+	0.823468i	$0.307964\pi$
$620$	4.88056			0.196008
$621$	−5.33987	−	23.7882i	−0.214281	−	0.954589i
$622$			18.2733i			0.732693i
$623$	−21.5423	−	37.3123i	−0.863074	−	1.49489i
$624$	12.1252	−	28.0699i	0.485398	−	1.12370i
$625$	−4.19330	+	7.26301i	−0.167732	+	0.290520i
$626$	−25.2296	−	14.5663i	−1.00838	−	0.582186i
$627$	10.6718	−	2.70380i	0.426191	−	0.107979i
$628$	−6.03256	−	10.4487i	−0.240725	−	0.416948i
$629$		−	17.1287i		−	0.682966i
$630$	17.2834	+	0.472354i	0.688589	+	0.0188190i
$631$		−	8.56943i		−	0.341144i	−0.985345	−	0.170572i	$-0.945438\pi$
$631$		−	8.56943i		−	0.341144i	0.985345	−	0.170572i	$-0.0545615\pi$
$632$	0.910304	−	0.525564i	0.0362099	−	0.0209058i
$633$	6.62090	+	6.80432i	0.263157	+	0.270448i
$634$	−25.2517	+	43.7372i	−1.00287	+	1.73703i
$635$	5.82519	+	3.36317i	0.231166	+	0.133464i
$636$	−9.63988	−	9.90693i	−0.382246	−	0.392835i
$637$	−4.53823	−	10.9996i	−0.179811	−	0.435821i
$638$	−5.51971			−0.218527
$639$	−9.18475	+	14.9498i	−0.363343	+	0.591404i
$640$	−14.8438			−0.586752
$641$	5.45756	+	9.45277i	0.215561	+	0.373362i	0.953446	−	0.301564i	$-0.0975088\pi$
$641$	5.45756	+	9.45277i	0.215561	+	0.373362i	−0.737885	+	0.674926i	$0.764175\pi$
$642$	7.40240	+	29.2170i	0.292150	+	1.15310i
$643$	25.3834	+	14.6551i	1.00102	+	0.577941i	0.908551	−	0.417774i	$-0.137190\pi$
$643$	25.3834	+	14.6551i	1.00102	+	0.577941i	0.0924728	+	0.995715i	$0.470523\pi$
$644$	−8.83961	−	5.10355i	−0.348329	−	0.201108i
$645$	3.25259	+	0.919332i	0.128070	+	0.0361986i
$646$	−4.35803	−	7.54834i	−0.171465	−	0.296985i
$647$	−5.27064			−0.207210			−0.103605	−	0.994619i	$-0.533038\pi$
$647$	−5.27064			−0.207210			−0.103605	+	0.994619i	$0.533038\pi$
$648$	−17.3702	+	8.80061i	−0.682367	+	0.345720i
$649$	−9.71773			−0.381454
$650$	−20.7028	+	8.54155i	−0.812029	+	0.335027i
$651$	−9.92034	+	35.0981i	−0.388809	+	1.37560i
$652$	−9.81802	−	5.66843i	−0.384503	−	0.221993i
$653$	−10.5317	+	18.2414i	−0.412137	+	0.713842i	−0.995123	−	0.0986399i	$-0.968551\pi$
$653$	−10.5317	+	18.2414i	−0.412137	+	0.713842i	0.582986	+	0.812482i	$0.301884\pi$
$654$	44.0163	−	11.1519i	1.72117	−	0.436075i
$655$	−8.00702	+	4.62286i	−0.312860	+	0.180630i
$656$		−	26.4599i		−	1.03308i
$657$	−1.95821	+	3.18733i	−0.0763971	+	0.124349i
$658$		−	53.9759i		−	2.10420i
$659$	−4.60414	−	7.97460i	−0.179352	−	0.310646i	0.762307	−	0.647216i	$-0.224067\pi$
$659$	−4.60414	−	7.97460i	−0.179352	−	0.310646i	−0.941659	+	0.336569i	$0.890733\pi$
$660$	1.57997	+	1.62374i	0.0615002	+	0.0632039i
$661$	8.39767	+	4.84840i	0.326632	+	0.188581i	0.654345	−	0.756196i	$-0.272945\pi$
$661$	8.39767	+	4.84840i	0.326632	+	0.188581i	−0.327713	+	0.944777i	$0.606278\pi$
$662$	14.2407	−	24.6657i	0.553481	−	0.958658i
$663$	−5.49163	−	7.38443i	−0.213277	−	0.286788i
$664$	16.7826	+	29.0683i	0.651290	+	1.12807i
$665$			12.7300i			0.493650i
$666$	−1.55896	+	57.0423i	−0.0604083	+	2.21034i
$667$	−9.00000			−0.348481
$668$	3.13164	−	1.80805i	0.121167	−	0.0699557i
$669$	3.90308	+	15.4053i	0.150902	+	0.595603i
$670$	−12.8475	−	7.41750i	−0.496342	−	0.286563i
$671$	3.00054	+	1.73236i	0.115835	+	0.0668771i
$672$	−5.57153	+	19.7120i	−0.214926	+	0.760408i
$673$	13.8136	+	23.9259i	0.532475	+	0.922275i	0.999281	+	0.0379146i	$0.0120715\pi$
$673$	13.8136	+	23.9259i	0.532475	+	0.922275i	−0.466805	+	0.884360i	$0.654595\pi$
$674$			14.3322i			0.552054i
$675$	18.8261	+	5.88108i	0.724618	+	0.226363i
$676$	−8.50521	−	2.30442i	−0.327123	−	0.0886314i
$677$	11.4941	+	19.9084i	0.441755	+	0.765141i	0.997820	−	0.0659973i	$-0.0210229\pi$
$677$	11.4941	+	19.9084i	0.441755	+	0.765141i	−0.556065	+	0.831139i	$0.687690\pi$
$678$	−8.12071	−	2.29529i	−0.311874	−	0.0881500i
$679$	9.55668	−	16.5527i	0.366752	−	0.635232i
$680$	−1.74937	+	3.03000i	−0.0670854	+	0.116195i
$681$	−1.46544	−	5.78405i	−0.0561559	−	0.221645i
$682$	−16.3512	+	9.44035i	−0.626118	+	0.361490i
$683$		−	19.2616i		−	0.737023i	−0.929623	−	0.368512i	$-0.879867\pi$
$683$		−	19.2616i		−	0.737023i	0.929623	−	0.368512i	$-0.120133\pi$
$684$	3.49980	+	6.46344i	0.133818	+	0.247136i
$685$	8.49806			0.324694
$686$	−9.71544	−	16.8276i	−0.370937	−	0.642482i
$687$	−15.4944	+	15.0767i	−0.591148	+	0.575212i
$688$	−4.35343	+	7.54036i	−0.165973	+	0.287473i
$689$	25.8895	−	33.6426i	0.986312	−	1.28168i
$690$	10.1773	+	10.4593i	0.387445	+	0.398178i
$691$	0.829355	−	0.478828i	0.0315502	−	0.0182155i	−0.484142	−	0.874989i	$-0.660868\pi$
$691$	0.829355	−	0.478828i	0.0315502	−	0.0182155i	0.515692	+	0.856774i	$0.327535\pi$
$692$	8.34185			0.317109
$693$	−14.8884	+	8.06173i	−0.565565	+	0.306240i
$694$		−	11.9091i		−	0.452062i
$695$	−11.9706	+	6.91125i	−0.454072	+	0.262159i
$696$	1.76544	+	6.96812i	0.0669188	+	0.264126i
$697$	−6.89662	−	3.98177i	−0.261228	−	0.150820i
$698$	−10.2485	+	17.7509i	−0.387911	+	0.671882i
$699$	−2.39706	+	8.48078i	−0.0906652	+	0.320773i
$700$	7.15116	−	4.12872i	0.270288	−	0.156051i
$701$	−5.78079			−0.218337			−0.109169	−	0.994023i	$-0.534819\pi$
$701$	−5.78079			−0.218337			−0.109169	+	0.994023i	$0.534819\pi$
$702$	17.6162	+	25.0916i	0.664882	+	0.947021i
$703$	−42.0142			−1.58460
$704$	5.72949	−	3.30792i	0.215938	−	0.124672i
$705$	−5.31320	+	18.7980i	−0.200107	+	0.707975i
$706$	1.34260	−	2.32546i	0.0505296	−	0.0875198i
$707$	−44.1532	−	25.4919i	−1.66055	−	0.958721i
$708$	−1.59346	−	6.28931i	−0.0598857	−	0.236367i
$709$	−4.84652	+	2.79814i	−0.182015	+	0.105086i	−0.588239	−	0.808687i	$-0.700179\pi$
$709$	−4.84652	+	2.79814i	−0.182015	+	0.105086i	0.406224	+	0.913773i	$0.366845\pi$
$710$		−	10.5027i		−	0.394159i
$711$	−0.0398175	+	1.45693i	−0.00149327	+	0.0546390i
$712$	−29.0453			−1.08852
$713$	−26.6609	+	15.3927i	−0.998459	+	0.576461i
$714$	9.34811	+	9.60708i	0.349844	+	0.359536i
$715$	−4.24327	+	5.51399i	−0.158689	+	0.206212i
$716$	−6.38652	+	11.0618i	−0.238675	+	0.413398i
$717$	1.88440	−	1.83360i	0.0703740	−	0.0684770i
$718$	5.73388	+	9.93137i	0.213987	+	0.370636i
$719$	17.4320			0.650102			0.325051	−	0.945696i	$-0.394618\pi$
$719$	17.4320			0.650102			0.325051	+	0.945696i	$0.394618\pi$
$720$	8.43785	−	13.7341i	0.314460	−	0.511838i
$721$			20.0647i			0.747250i
$722$	8.41129	−	4.85626i	0.313036	−	0.180731i
$723$	8.12615	+	32.0736i	0.302215	+	1.19283i
$724$	3.68635	−	6.38495i	0.137002	−	0.237295i
$725$	3.64046	−	6.30546i	0.135203	−	0.234179i
$726$	21.5683	+	6.09620i	0.800475	+	0.226251i
$727$	−12.0213	−	20.8215i	−0.445845	−	0.772225i	0.552266	−	0.833668i	$-0.313763\pi$
$727$	−12.0213	−	20.8215i	−0.445845	−	0.772225i	−0.998111	+	0.0614425i	$0.980430\pi$
$728$	−24.8176	−	3.30253i	−0.919803	−	0.122400i
$729$	2.21069	−	26.9093i	0.0818774	−	0.996642i
$730$		−	2.23920i		−	0.0828764i
$731$	1.31024	+	2.26940i	0.0484608	+	0.0839367i
$732$	−0.629173	+	2.22601i	−0.0232549	+	0.0822757i
$733$	11.8926	+	6.86619i	0.439263	+	0.253608i	0.703285	−	0.710908i	$-0.251716\pi$
$733$	11.8926	+	6.86619i	0.439263	+	0.253608i	−0.264022	+	0.964517i	$0.585049\pi$
$734$	1.69023	+	0.975856i	0.0623876	+	0.0360195i
$735$	−1.54058	−	6.08062i	−0.0568252	−	0.224287i
$736$	−14.9735	+	8.64495i	−0.551930	+	0.318657i
$737$	14.5270			0.535109
$738$	22.6049	+	13.8878i	0.832096	+	0.511219i
$739$			13.1229i			0.482732i	0.970434	+	0.241366i	$0.0775954\pi$
$739$			13.1229i			0.482732i	−0.970434	+	0.241366i	$0.922405\pi$
$740$	−4.32311	−	7.48785i	−0.158921	−	0.275259i
$741$	−18.1130	+	13.4702i	−0.665396	+	0.494839i
$742$	−30.9173	+	53.5503i	−1.13501	+	1.96589i
$743$	30.7672	+	17.7634i	1.12874	+	0.651677i	0.943617	−	0.331039i	$-0.107399\pi$
$743$	30.7672	+	17.7634i	1.12874	+	0.651677i	0.185120	+	0.982716i	$0.440732\pi$
$744$	17.1474	+	17.6224i	0.628653	+	0.646068i
$745$	−4.28770	−	7.42652i	−0.157089	−	0.272087i
$746$			28.3164i			1.03674i
$747$	−46.5233	−	1.27147i	−1.70220	−	0.0465208i
$748$			1.75646i			0.0642227i
$749$	29.5561	−	17.0642i	1.07996	−	0.623512i
$750$	−26.5199	+	6.71908i	−0.968371	+	0.245346i
$751$	−11.7119	+	20.2856i	−0.427374	+	0.740233i	−0.996639	−	0.0819210i	$-0.973894\pi$
$751$	−11.7119	+	20.2856i	−0.427374	+	0.740233i	0.569265	+	0.822154i	$0.307228\pi$
$752$	−43.5788	−	25.1603i	−1.58916	−	0.917500i
$753$	−3.75249	+	13.2763i	−0.136748	+	0.483814i
$754$	10.4620	−	4.31643i	0.381005	−	0.157195i
$755$	19.3976			0.705951
$756$	−7.65886	−	8.31387i	−0.278550	−	0.302372i
$757$	18.7868			0.682817			0.341409	−	0.939915i	$-0.389096\pi$
$757$	18.7868			0.682817			0.341409	+	0.939915i	$0.389096\pi$
$758$	−1.26244	−	2.18661i	−0.0458538	−	0.0794212i
$759$	−13.7519	−	3.88693i	−0.499163	−	0.141087i
$760$	7.43216	+	4.29096i	0.269593	+	0.155649i
$761$	−14.6714	−	8.47054i	−0.531838	−	0.307057i	0.209927	−	0.977717i	$-0.432677\pi$
$761$	−14.6714	−	8.47054i	−0.531838	−	0.307057i	−0.741765	+	0.670660i	$0.766011\pi$
$762$	−4.26680	−	16.8409i	−0.154570	−	0.610082i
$763$	−25.7077	−	44.5271i	−0.930682	−	1.61199i
$764$	−12.6057			−0.456060
$765$	−2.30995	−	4.26603i	−0.0835166	−	0.154239i
$766$	−38.7194			−1.39899
$767$	18.4190	−	7.59930i	0.665071	−	0.274395i
$768$	17.6480	+	18.1369i	0.636819	+	0.654461i
$769$	33.2707	+	19.2088i	1.19977	+	0.692688i	0.960504	−	0.278266i	$-0.0897595\pi$
$769$	33.2707	+	19.2088i	1.19977	+	0.692688i	0.239267	+	0.970954i	$0.423093\pi$
$770$	5.06732	−	8.77685i	0.182613	−	0.316296i
$771$	−25.4451	−	26.1500i	−0.916383	−	0.941770i
$772$	7.60627	−	4.39148i	0.273756	−	0.158053i
$773$			21.1236i			0.759761i	0.925036	+	0.379881i	$0.124035\pi$
$773$			21.1236i			0.759761i	−0.925036	+	0.379881i	$0.875965\pi$
$774$	−4.15683	−	7.67684i	−0.149414	−	0.275938i
$775$		−	24.9051i		−	0.894617i
$776$	−6.44261	−	11.1589i	−0.231276	−	0.400582i
$777$	62.6354	−	15.8693i	2.24703	−	0.569306i
$778$	7.32212	+	4.22743i	0.262511	+	0.151561i
$779$	−9.76670	+	16.9164i	−0.349928	+	0.606094i
$780$	−4.26444	−	1.84209i	−0.152691	−	0.0659574i
$781$	5.14232	+	8.90676i	0.184007	+	0.318709i
$782$			11.3142i			0.404597i
$783$	−9.51370	−	2.97198i	−0.339992	−	0.106210i
$784$	16.1585			0.577089
$785$	16.9159	−	9.76638i	0.603753	−	0.348577i
$786$	22.9798	+	6.49517i	0.819664	+	0.231675i
$787$	2.57534	+	1.48688i	0.0918011	+	0.0530014i	0.545198	−	0.838307i	$-0.316455\pi$
$787$	2.57534	+	1.48688i	0.0918011	+	0.0530014i	−0.453397	+	0.891309i	$0.649788\pi$
$788$	8.27487	+	4.77750i	0.294780	+	0.170191i
$789$	−40.4722	+	10.2540i	−1.44085	+	0.365052i
$790$	−0.436211	−	0.755540i	−0.0155197	−	0.0268809i
$791$			9.55551i			0.339755i
$792$	−0.311825	+	11.4097i	−0.0110802	+	0.405425i
$793$	−7.04193	−	0.937084i	−0.250066	−	0.0332768i
$794$	−11.4921	−	19.9049i	−0.407840	−	0.706400i
$795$	16.0388	−	15.6064i	0.568837	−	0.553503i
$796$	5.65697	−	9.79816i	0.200506	−	0.347287i
$797$	14.8513	−	25.7233i	0.526061	−	0.911165i	−0.473478	−	0.880806i	$-0.657002\pi$
$797$	14.8513	−	25.7233i	0.526061	−	0.911165i	0.999539	−	0.0303591i	$-0.00966508\pi$
$798$	23.5648	−	22.9296i	0.834185	−	0.811698i
$799$	−13.1158	+	7.57240i	−0.464003	+	0.267892i
$800$		−	13.9874i		−	0.494528i
$801$	21.0821	−	34.3148i	0.744900	−	1.21245i
$802$	−24.5268			−0.866071
$803$	1.09635	+	1.89894i	0.0386895	+	0.0670122i
$804$	2.38205	+	9.40187i	0.0840085	+	0.331578i
$805$	8.26237	−	14.3108i	0.291210	−	0.504391i
$806$	23.6096	−	30.6799i	0.831612	−	1.08065i
$807$	−10.2596	+	36.2985i	−0.361156	+	1.27777i
$808$	−29.7658	+	17.1853i	−1.04716	+	0.604576i
$809$	1.78891			0.0628946			0.0314473	−	0.999505i	$-0.489988\pi$
$809$	1.78891			0.0628946			0.0314473	+	0.999505i	$0.489988\pi$
$810$	7.30438	+	14.4170i	0.256650	+	0.506563i
$811$		−	17.3429i		−	0.608991i	−0.952514	−	0.304496i	$-0.901512\pi$
$811$		−	17.3429i		−	0.608991i	0.952514	−	0.304496i	$-0.0984879\pi$
$812$	−3.61381	+	2.08643i	−0.126820	+	0.0732194i
$813$	−8.49961	−	2.40238i	−0.298094	−	0.0842553i
$814$	28.9671	+	16.7242i	1.01530	+	0.586182i
$815$	9.17689	−	15.8948i	0.321452	−	0.556772i
$816$	12.1140	−	3.06921i	0.424076	−	0.107444i
$817$	5.56650	−	3.21382i	0.194747	−	0.112437i
$818$	−0.778285			−0.0272121
$819$	21.9152	−	26.9230i	0.765779	−	0.940766i
$820$	−4.01983			−0.140379
$821$	−30.1046	+	17.3809i	−1.05066	+	0.606598i	−0.922834	−	0.385198i	$-0.874133\pi$
$821$	−30.1046	+	17.3809i	−1.05066	+	0.606598i	−0.127825	+	0.991797i	$0.540800\pi$
$822$	−15.3069	−	15.7309i	−0.533888	−	0.548678i
$823$	10.0169	−	17.3498i	0.349167	−	0.604776i	−0.636934	−	0.770918i	$-0.719798\pi$
$823$	10.0169	−	17.3498i	0.349167	−	0.604776i	0.986102	+	0.166142i	$0.0531311\pi$
$824$	11.7144	+	6.76329i	0.408089	+	0.235610i
$825$	8.28579	−	8.06244i	0.288474	−	0.280698i
$826$	−25.1347	+	14.5115i	−0.874548	+	0.504920i
$827$		−	11.7034i		−	0.406966i	−0.979078	−	0.203483i	$-0.934774\pi$
$827$		−	11.7034i		−	0.406966i	0.979078	−	0.203483i	$-0.0652262\pi$
$828$	0.260661	−	9.53759i	0.00905859	−	0.331454i
$829$	25.2016			0.875287			0.437644	−	0.899149i	$-0.355813\pi$
$829$	25.2016			0.875287			0.437644	+	0.899149i	$0.355813\pi$
$830$	24.1263	−	13.9293i	0.837435	−	0.483493i
$831$	−20.6140	+	5.22276i	−0.715093	+	0.181175i
$832$	−8.27285	+	10.7503i	−0.286810	+	0.372700i
$833$	2.43158	−	4.21163i	0.0842494	−	0.145924i
$834$	34.3552	+	9.71038i	1.18962	+	0.336243i
$835$	2.92714	+	5.06995i	0.101298	+	0.175453i
$836$	4.30836			0.149008
$837$	−33.2656	+	7.46731i	−1.14983	+	0.258108i
$838$			21.1394i			0.730248i
$839$	10.9918	−	6.34609i	0.379478	−	0.219091i	−0.298113	−	0.954530i	$-0.596357\pi$
$839$	10.9918	−	6.34609i	0.379478	−	0.219091i	0.677591	+	0.735439i	$0.263024\pi$
$840$	−12.7007	−	3.58981i	−0.438216	−	0.123860i
$841$	12.6603	−	21.9283i	0.436562	−	0.756148i
$842$	25.8683	−	44.8052i	0.891480	−	1.54409i
$843$	−3.11053	−	12.2772i	−0.107132	−	0.422848i
$844$	1.85772	+	3.21767i	0.0639454	+	0.110757i
$845$	3.73072	−	13.7695i	0.128341	−	0.473684i
$846$	44.3676	−	24.0240i	1.52539	−	0.825962i
$847$		−	25.3791i		−	0.872036i
$848$	28.8235	+	49.9238i	0.989803	+	1.71439i
$849$	15.4583	+	15.8865i	0.530527	+	0.545225i
$850$	−7.92683	−	4.57656i	−0.271888	−	0.156975i
$851$	47.2315	+	27.2691i	1.61908	+	0.934773i
$852$	−4.92124	+	4.78858i	−0.168599	+	0.164054i
$853$	5.60579	−	3.23650i	0.191939	−	0.110816i	−0.400951	−	0.916099i	$-0.631320\pi$
$853$	5.60579	−	3.23650i	0.191939	−	0.110816i	0.592890	+	0.805284i	$0.297987\pi$
$854$	10.3478			0.354093
$855$	−10.4640	+	5.66598i	−0.357860	+	0.193773i
$856$		−	23.0076i		−	0.786382i
$857$	−13.2153	−	22.8895i	−0.451425	−	0.781890i	0.547050	−	0.837100i	$-0.315751\pi$
$857$	−13.2153	−	22.8895i	−0.451425	−	0.781890i	−0.998475	+	0.0552094i	$0.982417\pi$
$858$	17.8501	−	2.07711i	0.609392	−	0.0709114i
$859$	1.49096	−	2.58242i	0.0508710	−	0.0881112i	−0.839469	−	0.543408i	$-0.817134\pi$
$859$	1.49096	−	2.58242i	0.0508710	−	0.0881112i	0.890340	+	0.455297i	$0.150467\pi$
$860$	1.14555	+	0.661381i	0.0390628	+	0.0225529i
$861$	8.17080	−	28.9082i	0.278460	−	0.985190i
$862$	−10.2733	−	17.7940i	−0.349911	−	0.606064i
$863$		−	3.40827i		−	0.116019i	−0.998316	−	0.0580095i	$-0.981525\pi$
$863$		−	3.40827i		−	0.116019i	0.998316	−	0.0580095i	$-0.0184754\pi$
$864$	−18.6829	+	4.19384i	−0.635605	+	0.142677i
$865$			13.5050i			0.459184i
$866$	−39.6476	+	22.8906i	−1.34728	+	0.777853i
$867$	−6.98573	+	24.7155i	−0.237248	+	0.839381i
$868$	−7.13684	+	12.3614i	−0.242240	+	0.419572i
$869$	0.739854	+	0.427155i	0.0250978	+	0.0144902i
$870$	5.78344	−	1.46529i	0.196077	−	0.0496780i
$871$	−27.5345	+	11.3602i	−0.932970	+	0.384925i
$872$	−34.6616			−1.17379
$873$	17.8597	+	0.488102i	0.604458	+	0.0165197i
$874$	27.7522			0.938732
$875$	15.4890	+	26.8277i	0.523623	+	0.906942i
$876$	−1.04922	+	1.02094i	−0.0354499	+	0.0344943i
$877$	−13.8761	−	8.01136i	−0.468562	−	0.270524i	0.247076	−	0.968996i	$-0.420530\pi$
$877$	−13.8761	−	8.01136i	−0.468562	−	0.270524i	−0.715638	+	0.698472i	$0.753864\pi$
$878$	16.3479	+	9.43847i	0.551715	+	0.318533i
$879$	8.16101	−	7.94102i	0.275264	−	0.267844i
$880$	−4.72415	−	8.18246i	−0.159251	−	0.275831i
$881$	−26.8852			−0.905787			−0.452894	−	0.891565i	$-0.649608\pi$
$881$	−26.8852			−0.905787			−0.452894	+	0.891565i	$0.649608\pi$
$882$	−8.48102	+	13.8043i	−0.285571	+	0.464816i
$883$	−16.3368			−0.549778			−0.274889	−	0.961476i	$-0.588641\pi$
$883$	−16.3368			−0.549778			−0.274889	+	0.961476i	$0.588641\pi$
$884$	−1.37356	−	3.32920i	−0.0461979	−	0.111973i
$885$	10.1821	−	2.57972i	0.342266	−	0.0867163i
$886$	−37.2213	−	21.4897i	−1.25047	−	0.721962i
$887$	−12.4100	+	21.4947i	−0.416686	+	0.721721i	−0.995604	−	0.0936651i	$-0.970142\pi$
$887$	−12.4100	+	21.4947i	−0.416686	+	0.721721i	0.578918	+	0.815386i	$0.303475\pi$
$888$	11.8478	−	41.9174i	0.397586	−	1.40666i
$889$	−17.0363	+	9.83594i	−0.571381	+	0.329887i
$890$			24.1072i			0.808076i
$891$	−13.2533	−	8.64994i	−0.444003	−	0.289784i
$892$			6.21933i			0.208239i
$893$	18.5740	+	32.1711i	0.621555	+	1.07656i
$894$	−6.02427	+	21.3138i	−0.201482	+	0.712841i
$895$	−17.9084	−	10.3394i	−0.598612	−	0.345609i
$896$	21.7061	−	37.5960i	0.725149	−	1.25599i
$897$	29.1050	−	3.38677i	0.971786	−	0.113081i
$898$	24.5114	+	42.4549i	0.817955	+	1.41674i
$899$			12.5857i			0.419756i
$900$	6.57666	+	4.04053i	0.219222	+	0.134684i
$901$	17.3498			0.578006
$902$	13.4675	−	7.77546i	0.448419	−	0.258895i
$903$	−7.08472	+	6.89374i	−0.235765	+	0.229409i
$904$	5.57878	+	3.22091i	0.185547	+	0.107126i
$905$	10.3369	+	5.96800i	0.343610	+	0.198383i
$906$	−34.9393	−	35.9073i	−1.16078	−	1.19294i
$907$	14.4337	+	25.0000i	0.479265	+	0.830111i	0.999717	−	0.0237800i	$-0.00757011\pi$
$907$	14.4337	+	25.0000i	0.479265	+	0.830111i	−0.520453	+	0.853891i	$0.674237\pi$
$908$		−	2.33510i		−	0.0774930i
$909$	1.30198	−	47.6396i	0.0431840	−	1.58011i
$910$	−2.74106	+	20.5983i	−0.0908651	+	0.682827i
$911$	−6.64094	−	11.5024i	−0.220024	−	0.381093i	0.734791	−	0.678294i	$-0.237280\pi$
$911$	−6.64094	−	11.5024i	−0.220024	−	0.381093i	−0.954815	+	0.297201i	$0.903947\pi$
$912$	−7.52832	−	29.7140i	−0.249288	−	0.983929i
$913$	−13.6401	+	23.6254i	−0.451422	+	0.781886i
$914$	9.37672	−	16.2410i	0.310154	−	0.537203i
$915$	−3.60379	−	1.01860i	−0.119138	−	0.0336738i
$916$	−7.32708	+	4.23029i	−0.242093	+	0.139773i
$917$		−	27.0400i		−	0.892940i
$918$	−3.73619	+	11.9600i	−0.123313	+	0.394740i
$919$	−3.98083			−0.131316			−0.0656578	−	0.997842i	$-0.520915\pi$
$919$	−3.98083			−0.131316			−0.0656578	+	0.997842i	$0.520915\pi$
$920$	−5.57005	−	9.64761i	−0.183639	−	0.318072i
$921$	40.5533	+	11.4622i	1.33628	+	0.377694i
$922$	23.3291	−	40.4072i	0.768303	−	1.33074i
$923$	−16.7119	−	12.8605i	−0.550078	−	0.423310i
$924$	−6.42296	+	1.62732i	−0.211300	+	0.0535348i
$925$	−38.2098	+	22.0605i	−1.25633	+	0.725344i
$926$	2.77516			0.0911975
$927$	−16.4930	+	8.93057i	−0.541701	+	0.293318i
$928$			7.06846i			0.232033i
$929$	6.37258	−	3.67921i	0.209077	−	0.120711i	−0.391805	−	0.920048i	$-0.628149\pi$
$929$	6.37258	−	3.67921i	0.209077	−	0.120711i	0.600883	+	0.799337i	$0.294816\pi$
$930$	14.6263	−	14.2321i	0.479617	−	0.466688i
$931$	−10.3305	−	5.96432i	−0.338569	−	0.195473i
$932$	−1.72448	+	2.98689i	−0.0564873	+	0.0978389i
$933$	13.4883	+	13.8619i	0.441586	+	0.453819i
$934$	20.0129	−	11.5545i	0.654843	−	0.378074i
$935$	−2.84362			−0.0929964
$936$	−8.33138	−	21.8697i	−0.272320	−	0.714835i
$937$	8.02666			0.262220			0.131110	−	0.991368i	$-0.458146\pi$
$937$	8.02666			0.262220			0.131110	+	0.991368i	$0.458146\pi$
$938$	37.5738	−	21.6932i	1.22683	−	0.708309i
$939$	−29.8908	+	7.57312i	−0.975450	+	0.247139i
$940$	−3.82240	+	6.62058i	−0.124673	+	0.215940i
$941$	12.3516	+	7.13120i	0.402650	+	0.232470i	0.687627	−	0.726064i	$-0.258652\pi$
$941$	12.3516	+	7.13120i	0.402650	+	0.232470i	−0.284977	+	0.958534i	$0.591986\pi$
$942$	−48.5479	−	13.7219i	−1.58178	−	0.447083i
$943$	21.9590	−	12.6781i	0.715085	−	0.412854i
$944$			27.0575i			0.880648i
$945$	13.4597	−	12.3993i	0.437844	−	0.403349i
$946$	−5.11717			−0.166374
$947$	−7.11939	+	4.11038i	−0.231349	+	0.133569i	−0.611194	−	0.791481i	$-0.709311\pi$
$947$	−7.11939	+	4.11038i	−0.231349	+	0.133569i	0.379845	+	0.925050i	$0.375977\pi$
$948$	−0.155138	+	0.548875i	−0.00503863	+	0.0178266i
$949$	−3.56301	−	2.74190i	−0.115660	−	0.0890058i
$950$	−11.2256	+	19.4434i	−0.364208	+	0.630826i
$951$	13.1285	+	51.8179i	0.425722	+	1.68031i
$952$	−5.11621	−	8.86154i	−0.165817	−	0.287204i
$953$	−34.3915			−1.11405			−0.557025	−	0.830496i	$-0.688057\pi$
$953$	−34.3915			−1.11405			−0.557025	+	0.830496i	$0.688057\pi$
$954$	−57.7787	−	1.57908i	−1.87065	−	0.0511247i
$955$		−	20.4080i		−	0.660388i
$956$	0.891104	−	0.514479i	0.0288204	−	0.0166394i
$957$	−4.18719	+	4.07432i	−0.135353	+	0.131704i
$958$	22.7162	−	39.3455i	0.733926	−	1.27120i
$959$	−12.4267	+	21.5237i	−0.401280	+	0.695037i
$960$	−5.12511	+	4.98695i	−0.165412	+	0.160953i
$961$	6.02525	+	10.4360i	0.194363	+	0.336647i
$962$	−67.9826	−	9.04658i	−2.19185	−	0.291673i
$963$	27.1816	+	16.6997i	0.875916	+	0.538140i
$964$			12.9486i			0.417045i
$965$	7.10957	+	12.3141i	0.228865	+	0.396406i
$966$	−41.3734	+	10.4823i	−1.33117	+	0.337263i
$967$	43.1384	+	24.9059i	1.38724	+	0.800921i	0.993003	−	0.118089i	$-0.0376769\pi$
$967$	43.1384	+	24.9059i	1.38724	+	0.800921i	0.394233	+	0.919010i	$0.371010\pi$
$968$	−14.8170	−	8.55462i	−0.476238	−	0.274956i
$969$	−8.87769	−	2.50924i	−0.285192	−	0.0806086i
$970$	−9.26175	+	5.34727i	−0.297377	+	0.171691i
$971$	49.8192			1.59878			0.799388	−	0.600815i	$-0.205157\pi$
$971$	49.8192			1.59878			0.799388	+	0.600815i	$0.205157\pi$
$972$	3.42504	−	9.99590i	0.109858	−	0.320619i
$973$		−	40.4253i		−	1.29597i
$974$	22.5741	+	39.0995i	0.723322	+	1.25283i
$975$	−9.40003	+	21.7611i	−0.301042	+	0.696912i
$976$	4.82349	−	8.35454i	0.154396	−	0.267422i
$977$	−37.7814	−	21.8131i	−1.20873	−	0.697863i	−0.246252	−	0.969206i	$-0.579199\pi$
$977$	−37.7814	−	21.8131i	−1.20873	−	0.697863i	−0.962483	+	0.271343i	$0.912532\pi$
$978$	−45.9528	+	11.6426i	−1.46941	+	0.372288i
$979$	−11.8034	−	20.4440i	−0.377237	−	0.653394i
$980$		−	2.45483i		−	0.0784167i
$981$	25.1586	−	40.9499i	0.803252	−	1.30743i
$982$			66.6618i			2.12726i
$983$	−49.7372	+	28.7158i	−1.58637	+	0.915891i	−0.592472	+	0.805591i	$0.701848\pi$
$983$	−49.7372	+	28.7158i	−1.58637	+	0.915891i	−0.993898	+	0.110300i	$0.964819\pi$
$984$	−14.1233	−	14.5145i	−0.450234	−	0.462707i
$985$	−7.73451	+	13.3966i	−0.246442	+	0.426850i
$986$	4.00579	+	2.31274i	0.127570	+	0.0736528i
$987$	−39.8418	−	40.9455i	−1.26818	−	1.30331i
$988$	−8.16605	+	3.36915i	−0.259797	+	0.107187i
$989$	−8.34366			−0.265313
$990$	9.46988	+	0.258810i	0.300973	+	0.00822553i
$991$	7.92798			0.251841			0.125920	−	0.992040i	$-0.459812\pi$
$991$	7.92798			0.251841			0.125920	+	0.992040i	$0.459812\pi$
$992$	12.0892	+	20.9391i	0.383831	+	0.664816i
$993$	−7.40385	−	29.2227i	−0.234954	−	0.927356i
$994$	26.6010	+	15.3581i	0.843732	+	0.487129i
$995$	15.8627	+	9.15833i	0.502881	+	0.290339i
$996$	−17.5270	−	4.95393i	−0.555363	−	0.156971i
$997$	23.0997	+	40.0098i	0.731573	+	1.26712i	0.956210	+	0.292680i	$0.0945470\pi$
$997$	23.0997	+	40.0098i	0.731573	+	1.26712i	−0.224637	+	0.974443i	$0.572120\pi$
$998$	−25.5644			−0.809228
$999$	40.9226	+	44.4224i	1.29473	+	1.40546i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.2.t.c.103.8	yes	20
3.2	odd	2		351.2.t.c.64.3		20
9.2	odd	6		351.2.t.c.181.8		20
9.4	even	3		1053.2.b.j.649.8		10
9.5	odd	6		1053.2.b.i.649.3		10
9.7	even	3	inner	117.2.t.c.25.3	✓	20
13.12	even	2	inner	117.2.t.c.103.3	yes	20
39.38	odd	2		351.2.t.c.64.8		20
117.25	even	6	inner	117.2.t.c.25.8	yes	20
117.38	odd	6		351.2.t.c.181.3		20
117.77	odd	6		1053.2.b.i.649.8		10
117.103	even	6		1053.2.b.j.649.3		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.t.c.25.3	✓	20	9.7	even	3	inner
117.2.t.c.25.8	yes	20	117.25	even	6	inner
117.2.t.c.103.3	yes	20	13.12	even	2	inner
117.2.t.c.103.8	yes	20	1.1	even	1	trivial
351.2.t.c.64.3		20	3.2	odd	2
351.2.t.c.64.8		20	39.38	odd	2
351.2.t.c.181.3		20	117.38	odd	6
351.2.t.c.181.8		20	9.2	odd	6
1053.2.b.i.649.3		10	9.5	odd	6
1053.2.b.i.649.8		10	117.77	odd	6
1053.2.b.j.649.3		10	117.103	even	6
1053.2.b.j.649.8		10	9.4	even	3

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.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.41717 - 0.818205i) q^{2} +(0.471101 - 1.66675i) q^{3} +(0.338918 - 0.587023i) q^{4} +(0.950358 + 0.548689i) q^{5} +(-0.696113 - 2.74753i) q^{6} +(-2.77942 + 1.60470i) q^{7} +2.16360i q^{8} +(-2.55613 - 1.57042i) q^{9} +1.79576 q^{10} +(-1.52289 + 0.879239i) q^{11} +(-0.818757 - 0.841439i) q^{12} +(2.19891 - 2.85741i) q^{13} +(-2.62594 + 4.54826i) q^{14} +(1.36224 - 1.32552i) q^{15} +(2.44810 + 4.24024i) q^{16} +1.47360 q^{17} +(-4.90740 - 0.134118i) q^{18} -3.61452i q^{19} +(0.644186 - 0.371921i) q^{20} +(1.36525 + 5.38857i) q^{21} +(-1.43879 + 2.49207i) q^{22} +(-2.34599 + 4.06337i) q^{23} +(3.60619 + 1.01928i) q^{24} +(-1.89788 - 3.28722i) q^{25} +(0.778285 - 5.84860i) q^{26} +(-3.82169 + 3.52060i) q^{27} +2.17544i q^{28} +(0.959085 + 1.66118i) q^{29} +(0.845985 - 2.99309i) q^{30} +(5.68224 + 3.28064i) q^{31} +(3.19130 + 1.84250i) q^{32} +(0.748040 + 2.95249i) q^{33} +(2.08834 - 1.20570i) q^{34} -3.52192 q^{35} +(-1.78819 + 0.968262i) q^{36} -11.6237i q^{37} +(-2.95742 - 5.12239i) q^{38} +(-3.72669 - 5.01117i) q^{39} +(-1.18715 + 2.05620i) q^{40} +(-4.68013 - 2.70208i) q^{41} +(6.34374 + 6.51948i) q^{42} +(0.889142 + 1.54004i) q^{43} +1.19196i q^{44} +(-1.56756 - 2.89498i) q^{45} +7.67798i q^{46} +(-8.90053 + 5.13872i) q^{47} +(8.22074 - 2.08280i) q^{48} +(1.65010 - 2.85806i) q^{49} +(-5.37925 - 3.10571i) q^{50} +(0.694213 - 2.45612i) q^{51} +(-0.932116 - 2.25924i) q^{52} +11.7738 q^{53} +(-2.53542 + 8.11623i) q^{54} -1.92972 q^{55} +(-3.47193 - 6.01355i) q^{56} +(-6.02451 - 1.70280i) q^{57} +(2.71838 + 1.56946i) q^{58} +(4.78585 + 2.76311i) q^{59} +(-0.316423 - 1.24891i) q^{60} +(-0.985148 - 1.70633i) q^{61} +10.7370 q^{62} +(9.62459 + 0.263038i) q^{63} -3.76225 q^{64} +(3.65758 - 1.50905i) q^{65} +(3.47584 + 3.57213i) q^{66} +(-7.15434 - 4.13056i) q^{67} +(0.499428 - 0.865034i) q^{68} +(5.66743 + 5.82443i) q^{69} +(-4.99117 + 2.88165i) q^{70} -5.84860i q^{71} +(3.39776 - 5.53044i) q^{72} -1.24694i q^{73} +(-9.51060 - 16.4728i) q^{74} +(-6.37308 + 1.61468i) q^{75} +(-2.12180 - 1.22502i) q^{76} +(2.82182 - 4.88754i) q^{77} +(-9.38152 - 4.05249i) q^{78} +(-0.242912 - 0.420735i) q^{79} +5.37300i q^{80} +(4.06757 + 8.02838i) q^{81} -8.84340 q^{82} +(13.4351 - 7.75677i) q^{83} +(3.62592 + 1.02485i) q^{84} +(1.40044 + 0.808546i) q^{85} +(2.52014 + 1.45500i) q^{86} +(3.22061 - 0.815971i) q^{87} +(-1.90232 - 3.29492i) q^{88} +13.4245i q^{89} +(-4.59019 - 2.82010i) q^{90} +(-1.52640 + 11.4705i) q^{91} +(1.59019 + 2.75429i) q^{92} +(8.14493 - 7.92538i) q^{93} +(-8.40905 + 14.5649i) q^{94} +(1.98325 - 3.43508i) q^{95} +(4.57442 - 4.45111i) q^{96} +(-5.15756 + 2.97772i) q^{97} -5.40048i q^{98} +(5.27346 + 0.144123i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{3} + 12 q^{4} - 2 q^{9} - 16 q^{10} - 2 q^{12} - 4 q^{13} - 18 q^{14} + 4 q^{16} - 12 q^{17} - 10 q^{22} + 24 q^{23} - 12 q^{25} - 12 q^{26} - 22 q^{27} + 12 q^{29} - 54 q^{30} - 12 q^{35} + 50 q^{36}+ \cdots + 24 q^{95}+O(q^{100}) \) 20 * q + 2 * q^3 + 12 * q^4 - 2 * q^9 - 16 * q^10 - 2 * q^12 - 4 * q^13 - 18 * q^14 + 4 * q^16 - 12 * q^17 - 10 * q^22 + 24 * q^23 - 12 * q^25 - 12 * q^26 - 22 * q^27 + 12 * q^29 - 54 * q^30 - 12 * q^35 + 50 * q^36 + 12 * q^38 - 8 * q^39 - 8 * q^40 + 6 * q^42 + 4 * q^43 + 38 * q^48 - 10 * q^49 - 78 * q^51 + 108 * q^53 + 20 * q^55 + 36 * q^56 - 2 * q^61 - 72 * q^62 + 8 * q^64 - 24 * q^65 + 78 * q^66 + 24 * q^68 + 72 * q^69 - 42 * q^74 - 8 * q^75 - 6 * q^77 + 66 * q^78 - 14 * q^79 + 46 * q^81 - 4 * q^82 - 54 * q^87 + 22 * q^88 + 24 * q^90 - 72 * q^91 - 84 * q^92 + 20 * q^94 + 24 * q^95

Introduction

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