LMFDB - Embedded newform 117.2.z.a.5.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,2,Mod(5,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 9]))

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

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

chi := DirichletCharacter("117.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	117.z (of order $12$, degree $4$, 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:	$1$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			5.1
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	117.5
Dual form			117.2.z.a.47.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.633975 + 2.36603i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-3.46410 - 2.00000i) q^{4} +(-2.36603 + 0.633975i) q^{5} +(3.00000 - 3.00000i) q^{6} +(0.732051 - 2.73205i) q^{7} +(3.46410 - 3.46410i) q^{8} +(1.50000 + 2.59808i) q^{9} -6.00000i q^{10} +(-4.73205 - 1.26795i) q^{11} +(3.46410 + 6.00000i) q^{12} +(-3.23205 + 1.59808i) q^{13} +(6.00000 + 3.46410i) q^{14} +(4.09808 + 1.09808i) q^{15} +(2.00000 + 3.46410i) q^{16} +1.73205 q^{17} +(-7.09808 + 1.90192i) q^{18} +(-4.00000 + 4.00000i) q^{19} +(9.46410 + 2.53590i) q^{20} +(-3.46410 + 3.46410i) q^{21} +(6.00000 - 10.3923i) q^{22} +(0.866025 - 1.50000i) q^{23} +(-8.19615 + 2.19615i) q^{24} +(0.866025 - 0.500000i) q^{25} +(-1.73205 - 8.66025i) q^{26} -5.19615i q^{27} +(-8.00000 + 8.00000i) q^{28} +(-3.00000 + 1.73205i) q^{29} +(-5.19615 + 9.00000i) q^{30} +(0.366025 + 1.36603i) q^{31} +(6.00000 + 6.00000i) q^{33} +(-1.09808 + 4.09808i) q^{34} +6.92820i q^{35} -12.0000i q^{36} +(1.00000 + 1.00000i) q^{37} +(-6.92820 - 12.0000i) q^{38} +(6.23205 + 0.401924i) q^{39} +(-6.00000 + 10.3923i) q^{40} +(-7.09808 + 1.90192i) q^{41} +(-6.00000 - 10.3923i) q^{42} +(7.79423 - 4.50000i) q^{43} +(13.8564 + 13.8564i) q^{44} +(-5.19615 - 5.19615i) q^{45} +(3.00000 + 3.00000i) q^{46} +(2.36603 + 0.633975i) q^{47} -6.92820i q^{48} +(-0.866025 - 0.500000i) q^{49} +(0.633975 + 2.36603i) q^{50} +(-2.59808 - 1.50000i) q^{51} +(14.3923 + 0.928203i) q^{52} -1.73205i q^{53} +(12.2942 + 3.29423i) q^{54} +12.0000 q^{55} +(-6.92820 - 12.0000i) q^{56} +(9.46410 - 2.53590i) q^{57} +(-2.19615 - 8.19615i) q^{58} +(-1.90192 - 7.09808i) q^{59} +(-12.0000 - 12.0000i) q^{60} +(-1.50000 - 2.59808i) q^{61} -3.46410 q^{62} +(8.19615 - 2.19615i) q^{63} +8.00000i q^{64} +(6.63397 - 5.83013i) q^{65} +(-18.0000 + 10.3923i) q^{66} +(2.92820 + 10.9282i) q^{67} +(-6.00000 - 3.46410i) q^{68} +(-2.59808 + 1.50000i) q^{69} +(-16.3923 - 4.39230i) q^{70} +(-3.46410 - 3.46410i) q^{71} +(14.1962 + 3.80385i) q^{72} +(-7.00000 - 7.00000i) q^{73} +(-3.00000 + 1.73205i) q^{74} -1.73205 q^{75} +(21.8564 - 5.85641i) q^{76} +(-6.92820 + 12.0000i) q^{77} +(-4.90192 + 14.4904i) q^{78} +(-1.50000 - 2.59808i) q^{79} +(-6.92820 - 6.92820i) q^{80} +(-4.50000 + 7.79423i) q^{81} -18.0000i q^{82} +(0.633975 - 2.36603i) q^{83} +(18.9282 - 5.07180i) q^{84} +(-4.09808 + 1.09808i) q^{85} +(5.70577 + 21.2942i) q^{86} +6.00000 q^{87} +(-20.7846 + 12.0000i) q^{88} +(-10.3923 + 10.3923i) q^{89} +(15.5885 - 9.00000i) q^{90} +(2.00000 + 10.0000i) q^{91} +(-6.00000 + 3.46410i) q^{92} +(0.633975 - 2.36603i) q^{93} +(-3.00000 + 5.19615i) q^{94} +(6.92820 - 12.0000i) q^{95} +(-13.6603 - 3.66025i) q^{97} +(1.73205 - 1.73205i) q^{98} +(-3.80385 - 14.1962i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 6 q^{2} - 6 q^{3} - 6 q^{5} + 12 q^{6} - 4 q^{7} + 6 q^{9} - 12 q^{11} - 6 q^{13} + 24 q^{14} + 6 q^{15} + 8 q^{16} - 18 q^{18} - 16 q^{19} + 24 q^{20} + 24 q^{22} - 12 q^{24} - 32 q^{28} - 12 q^{29}+ \cdots - 36 q^{99}+O(q^{100}) $ 4 * q - 6 * q^2 - 6 * q^3 - 6 * q^5 + 12 * q^6 - 4 * q^7 + 6 * q^9 - 12 * q^11 - 6 * q^13 + 24 * q^14 + 6 * q^15 + 8 * q^16 - 18 * q^18 - 16 * q^19 + 24 * q^20 + 24 * q^22 - 12 * q^24 - 32 * q^28 - 12 * q^29 - 2 * q^31 + 24 * q^33 + 6 * q^34 + 4 * q^37 + 18 * q^39 - 24 * q^40 - 18 * q^41 - 24 * q^42 + 12 * q^46 + 6 * q^47 + 6 * q^50 + 16 * q^52 + 18 * q^54 + 48 * q^55 + 24 * q^57 + 12 * q^58 - 18 * q^59 - 48 * q^60 - 6 * q^61 + 12 * q^63 + 30 * q^65 - 72 * q^66 - 16 * q^67 - 24 * q^68 - 24 * q^70 + 36 * q^72 - 28 * q^73 - 12 * q^74 + 32 * q^76 - 30 * q^78 - 6 * q^79 - 18 * q^81 + 6 * q^83 + 48 * q^84 - 6 * q^85 + 54 * q^86 + 24 * q^87 + 8 * q^91 - 24 * q^92 + 6 * q^93 - 12 * q^94 - 20 * q^97 - 36 * q^99

Character values

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

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−0.633975	+	2.36603i	−0.448288	+	1.67303i	0.258819	+	0.965926i	$0.416667\pi$
$2$	−0.633975	+	2.36603i	−0.448288	+	1.67303i	−0.707107	+	0.707107i	$0.750000\pi$
$3$	−1.50000	−	0.866025i	−0.866025	−	0.500000i
$3$	−1.50000	−	0.866025i	−0.866025	−	0.500000i
$4$	−3.46410	−	2.00000i	−1.73205	−	1.00000i
$5$	−2.36603	+	0.633975i	−1.05812	+	0.283522i	−0.745603	−	0.666390i	$-0.767838\pi$
$5$	−2.36603	+	0.633975i	−1.05812	+	0.283522i	−0.312516	+	0.949913i	$0.601172\pi$
$6$	3.00000	−	3.00000i	1.22474	−	1.22474i
$7$	0.732051	−	2.73205i	0.276689	−	1.03262i	−0.678012	−	0.735051i	$-0.737158\pi$
$7$	0.732051	−	2.73205i	0.276689	−	1.03262i	0.954701	−	0.297567i	$-0.0961752\pi$
$8$	3.46410	−	3.46410i	1.22474	−	1.22474i
$9$	1.50000	+	2.59808i	0.500000	+	0.866025i
$10$		−	6.00000i		−	1.89737i
$11$	−4.73205	−	1.26795i	−1.42677	−	0.382301i	−0.538888	−	0.842378i	$-0.681155\pi$
$11$	−4.73205	−	1.26795i	−1.42677	−	0.382301i	−0.887879	+	0.460077i	$0.847822\pi$
$12$	3.46410	+	6.00000i	1.00000	+	1.73205i
$13$	−3.23205	+	1.59808i	−0.896410	+	0.443227i
$13$	−3.23205	+	1.59808i	−0.896410	+	0.443227i
$14$	6.00000	+	3.46410i	1.60357	+	0.925820i
$15$	4.09808	+	1.09808i	1.05812	+	0.283522i
$16$	2.00000	+	3.46410i	0.500000	+	0.866025i
$17$	1.73205			0.420084			0.210042	−	0.977692i	$-0.432640\pi$
$17$	1.73205			0.420084			0.210042	+	0.977692i	$0.432640\pi$
$18$	−7.09808	+	1.90192i	−1.67303	+	0.448288i
$19$	−4.00000	+	4.00000i	−0.917663	+	0.917663i	−0.996859	−	0.0791961i	$-0.974765\pi$
$19$	−4.00000	+	4.00000i	−0.917663	+	0.917663i	0.0791961	+	0.996859i	$0.474765\pi$
$20$	9.46410	+	2.53590i	2.11624	+	0.567044i
$21$	−3.46410	+	3.46410i	−0.755929	+	0.755929i
$22$	6.00000	−	10.3923i	1.27920	−	2.21565i
$23$	0.866025	−	1.50000i	0.180579	−	0.312772i	−0.761499	−	0.648166i	$-0.775536\pi$
$23$	0.866025	−	1.50000i	0.180579	−	0.312772i	0.942078	+	0.335394i	$0.108870\pi$
$24$	−8.19615	+	2.19615i	−1.67303	+	0.448288i
$25$	0.866025	−	0.500000i	0.173205	−	0.100000i
$26$	−1.73205	−	8.66025i	−0.339683	−	1.69842i
$27$		−	5.19615i		−	1.00000i
$28$	−8.00000	+	8.00000i	−1.51186	+	1.51186i
$29$	−3.00000	+	1.73205i	−0.557086	+	0.321634i	−0.751975	−	0.659192i	$-0.770899\pi$
$29$	−3.00000	+	1.73205i	−0.557086	+	0.321634i	0.194889	+	0.980825i	$0.437565\pi$
$30$	−5.19615	+	9.00000i	−0.948683	+	1.64317i
$31$	0.366025	+	1.36603i	0.0657401	+	0.245345i	0.990974	−	0.134051i	$-0.0427985\pi$
$31$	0.366025	+	1.36603i	0.0657401	+	0.245345i	−0.925234	+	0.379396i	$0.876132\pi$
$32$		0			0
$33$	6.00000	+	6.00000i	1.04447	+	1.04447i
$34$	−1.09808	+	4.09808i	−0.188319	+	0.702814i
$35$			6.92820i			1.17108i
$36$		−	12.0000i		−	2.00000i
$37$	1.00000	+	1.00000i	0.164399	+	0.164399i	0.784512	−	0.620113i	$-0.212913\pi$
$37$	1.00000	+	1.00000i	0.164399	+	0.164399i	−0.620113	+	0.784512i	$0.712913\pi$
$38$	−6.92820	−	12.0000i	−1.12390	−	1.94666i
$39$	6.23205	+	0.401924i	0.997927	+	0.0643593i
$40$	−6.00000	+	10.3923i	−0.948683	+	1.64317i
$41$	−7.09808	+	1.90192i	−1.10853	+	0.297031i	−0.766235	−	0.642561i	$-0.777872\pi$
$41$	−7.09808	+	1.90192i	−1.10853	+	0.297031i	−0.342298	+	0.939591i	$0.611205\pi$
$42$	−6.00000	−	10.3923i	−0.925820	−	1.60357i
$43$	7.79423	−	4.50000i	1.18861	−	0.686244i	0.230618	−	0.973044i	$-0.425925\pi$
$43$	7.79423	−	4.50000i	1.18861	−	0.686244i	0.957990	+	0.286801i	$0.0925917\pi$
$44$	13.8564	+	13.8564i	2.08893	+	2.08893i
$45$	−5.19615	−	5.19615i	−0.774597	−	0.774597i
$46$	3.00000	+	3.00000i	0.442326	+	0.442326i
$47$	2.36603	+	0.633975i	0.345120	+	0.0924747i	0.427216	−	0.904150i	$-0.359495\pi$
$47$	2.36603	+	0.633975i	0.345120	+	0.0924747i	−0.0820953	+	0.996624i	$0.526161\pi$
$48$		−	6.92820i		−	1.00000i
$49$	−0.866025	−	0.500000i	−0.123718	−	0.0714286i
$50$	0.633975	+	2.36603i	0.0896575	+	0.334607i
$51$	−2.59808	−	1.50000i	−0.363803	−	0.210042i
$52$	14.3923	+	0.928203i	1.99585	+	0.128719i
$53$		−	1.73205i		−	0.237915i	−0.992899	−	0.118958i	$-0.962045\pi$
$53$		−	1.73205i		−	0.237915i	0.992899	−	0.118958i	$-0.0379553\pi$
$54$	12.2942	+	3.29423i	1.67303	+	0.448288i
$55$	12.0000			1.61808
$56$	−6.92820	−	12.0000i	−0.925820	−	1.60357i
$57$	9.46410	−	2.53590i	1.25355	−	0.335888i
$58$	−2.19615	−	8.19615i	−0.288369	−	1.07621i
$59$	−1.90192	−	7.09808i	−0.247609	−	0.924091i	−0.972054	−	0.234758i	$-0.924570\pi$
$59$	−1.90192	−	7.09808i	−0.247609	−	0.924091i	0.724445	−	0.689333i	$-0.242096\pi$
$60$	−12.0000	−	12.0000i	−1.54919	−	1.54919i
$61$	−1.50000	−	2.59808i	−0.192055	−	0.332650i	0.753876	−	0.657017i	$-0.228182\pi$
$61$	−1.50000	−	2.59808i	−0.192055	−	0.332650i	−0.945931	+	0.324367i	$0.894849\pi$
$62$	−3.46410			−0.439941
$63$	8.19615	−	2.19615i	1.03262	−	0.276689i
$64$			8.00000i			1.00000i
$65$	6.63397	−	5.83013i	0.822843	−	0.723138i
$66$	−18.0000	+	10.3923i	−2.21565	+	1.27920i
$67$	2.92820	+	10.9282i	0.357737	+	1.33509i	0.877005	+	0.480481i	$0.159538\pi$
$67$	2.92820	+	10.9282i	0.357737	+	1.33509i	−0.519268	+	0.854611i	$0.673795\pi$
$68$	−6.00000	−	3.46410i	−0.727607	−	0.420084i
$69$	−2.59808	+	1.50000i	−0.312772	+	0.180579i
$70$	−16.3923	−	4.39230i	−1.95926	−	0.524981i
$71$	−3.46410	−	3.46410i	−0.411113	−	0.411113i	0.471013	−	0.882126i	$-0.343888\pi$
$71$	−3.46410	−	3.46410i	−0.411113	−	0.411113i	−0.882126	+	0.471013i	$0.843888\pi$
$72$	14.1962	+	3.80385i	1.67303	+	0.448288i
$73$	−7.00000	−	7.00000i	−0.819288	−	0.819288i	0.166717	−	0.986005i	$-0.446683\pi$
$73$	−7.00000	−	7.00000i	−0.819288	−	0.819288i	−0.986005	+	0.166717i	$0.946683\pi$
$74$	−3.00000	+	1.73205i	−0.348743	+	0.201347i
$75$	−1.73205			−0.200000
$76$	21.8564	−	5.85641i	2.50710	−	0.671776i
$77$	−6.92820	+	12.0000i	−0.789542	+	1.36753i
$78$	−4.90192	+	14.4904i	−0.555034	+	1.64071i
$79$	−1.50000	−	2.59808i	−0.168763	−	0.292306i	0.769222	−	0.638982i	$-0.220644\pi$
$79$	−1.50000	−	2.59808i	−0.168763	−	0.292306i	−0.937985	+	0.346675i	$0.887311\pi$
$80$	−6.92820	−	6.92820i	−0.774597	−	0.774597i
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$		−	18.0000i		−	1.98777i
$83$	0.633975	−	2.36603i	0.0695878	−	0.259705i	−0.922364	−	0.386322i	$-0.873745\pi$
$83$	0.633975	−	2.36603i	0.0695878	−	0.259705i	0.991952	+	0.126617i	$0.0404120\pi$
$84$	18.9282	−	5.07180i	2.06524	−	0.553378i
$85$	−4.09808	+	1.09808i	−0.444499	+	0.119103i
$86$	5.70577	+	21.2942i	0.615269	+	2.29622i
$87$	6.00000			0.643268
$88$	−20.7846	+	12.0000i	−2.21565	+	1.27920i
$89$	−10.3923	+	10.3923i	−1.10158	+	1.10158i	−0.107362	+	0.994220i	$0.534240\pi$
$89$	−10.3923	+	10.3923i	−1.10158	+	1.10158i	−0.994220	+	0.107362i	$0.965760\pi$
$90$	15.5885	−	9.00000i	1.64317	−	0.948683i
$91$	2.00000	+	10.0000i	0.209657	+	1.04828i
$92$	−6.00000	+	3.46410i	−0.625543	+	0.361158i
$93$	0.633975	−	2.36603i	0.0657401	−	0.245345i
$94$	−3.00000	+	5.19615i	−0.309426	+	0.535942i
$95$	6.92820	−	12.0000i	0.710819	−	1.23117i
$96$		0			0
$97$	−13.6603	−	3.66025i	−1.38699	−	0.371642i	−0.513334	−	0.858189i	$-0.671590\pi$
$97$	−13.6603	−	3.66025i	−1.38699	−	0.371642i	−0.873655	+	0.486546i	$0.838256\pi$
$98$	1.73205	−	1.73205i	0.174964	−	0.174964i
$99$	−3.80385	−	14.1962i	−0.382301	−	1.42677i
$100$	−4.00000			−0.400000
$101$	6.06218	+	10.5000i	0.603209	+	1.04479i	0.992332	+	0.123603i	$0.0394449\pi$
$101$	6.06218	+	10.5000i	0.603209	+	1.04479i	−0.389123	+	0.921186i	$0.627222\pi$
$102$	5.19615	−	5.19615i	0.514496	−	0.514496i
$103$	−15.5885	−	9.00000i	−1.53598	−	0.886796i	−0.999068	−	0.0431555i	$-0.986259\pi$
$103$	−15.5885	−	9.00000i	−1.53598	−	0.886796i	−0.536908	−	0.843641i	$-0.680408\pi$
$104$	−5.66025	+	16.7321i	−0.555034	+	1.64071i
$105$	6.00000	−	10.3923i	0.585540	−	1.01419i
$106$	4.09808	+	1.09808i	0.398040	+	0.106655i
$107$		−	12.1244i		−	1.17211i	−0.810273	−	0.586053i	$-0.800681\pi$
$107$		−	12.1244i		−	1.17211i	0.810273	−	0.586053i	$-0.199319\pi$
$108$	−10.3923	+	18.0000i	−1.00000	+	1.73205i
$109$	8.00000	−	8.00000i	0.766261	−	0.766261i	−0.211185	−	0.977446i	$-0.567732\pi$
$109$	8.00000	−	8.00000i	0.766261	−	0.766261i	0.977446	+	0.211185i	$0.0677323\pi$
$110$	−7.60770	+	28.3923i	−0.725365	+	2.70710i
$111$	−0.633975	−	2.36603i	−0.0601742	−	0.224573i
$112$	10.9282	−	2.92820i	1.03262	−	0.276689i
$113$	−1.50000	−	0.866025i	−0.141108	−	0.0814688i	0.427784	−	0.903881i	$-0.359294\pi$
$113$	−1.50000	−	0.866025i	−0.141108	−	0.0814688i	−0.568892	+	0.822412i	$0.692628\pi$
$114$			24.0000i			2.24781i
$115$	−1.09808	+	4.09808i	−0.102396	+	0.382148i
$116$	13.8564			1.28654
$117$	−9.00000	−	6.00000i	−0.832050	−	0.554700i
$118$	18.0000			1.65703
$119$	1.26795	−	4.73205i	0.116233	−	0.433786i
$120$	18.0000	−	10.3923i	1.64317	−	0.948683i
$121$	11.2583	+	6.50000i	1.02348	+	0.590909i
$122$	7.09808	−	1.90192i	0.642630	−	0.172192i
$123$	12.2942	+	3.29423i	1.10853	+	0.297031i
$124$	1.46410	−	5.46410i	0.131480	−	0.490691i
$125$	6.92820	−	6.92820i	0.619677	−	0.619677i
$126$			20.7846i			1.85164i
$127$			4.00000i			0.354943i	0.984126	+	0.177471i	$0.0567917\pi$
$127$			4.00000i			0.354943i	−0.984126	+	0.177471i	$0.943208\pi$
$128$	−18.9282	−	5.07180i	−1.67303	−	0.448288i
$129$	−15.5885			−1.37249
$130$	9.58846	+	19.3923i	0.840963	+	1.70082i
$131$	−13.5000	−	7.79423i	−1.17950	−	0.680985i	−0.223602	−	0.974681i	$-0.571781\pi$
$131$	−13.5000	−	7.79423i	−1.17950	−	0.680985i	−0.955899	+	0.293696i	$0.905115\pi$
$132$	−8.78461	−	32.7846i	−0.764602	−	2.85353i
$133$	8.00000	+	13.8564i	0.693688	+	1.20150i
$134$	−27.7128			−2.39402
$135$	3.29423	+	12.2942i	0.283522	+	1.05812i
$136$	6.00000	−	6.00000i	0.514496	−	0.514496i
$137$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$137$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$138$	−1.90192	−	7.09808i	−0.161903	−	0.604228i
$139$	−5.50000	+	9.52628i	−0.466504	+	0.808008i	−0.999268	−	0.0382553i	$-0.987820\pi$
$139$	−5.50000	+	9.52628i	−0.466504	+	0.808008i	0.532764	+	0.846264i	$0.321153\pi$
$140$	13.8564	−	24.0000i	1.17108	−	2.02837i
$141$	−3.00000	−	3.00000i	−0.252646	−	0.252646i
$142$	10.3923	−	6.00000i	0.872103	−	0.503509i
$143$	17.3205	−	3.46410i	1.44841	−	0.289683i
$144$	−6.00000	+	10.3923i	−0.500000	+	0.866025i
$145$	6.00000	−	6.00000i	0.498273	−	0.498273i
$146$	21.0000	−	12.1244i	1.73797	−	1.00342i
$147$	0.866025	+	1.50000i	0.0714286	+	0.123718i
$148$	−1.46410	−	5.46410i	−0.120348	−	0.449146i
$149$	14.1962	−	3.80385i	1.16299	−	0.311623i	0.374833	−	0.927092i	$-0.377700\pi$
$149$	14.1962	−	3.80385i	1.16299	−	0.311623i	0.788161	+	0.615469i	$0.211033\pi$
$150$	1.09808	−	4.09808i	0.0896575	−	0.334607i
$151$	−4.02628	+	15.0263i	−0.327654	+	1.22282i	0.583963	+	0.811780i	$0.301501\pi$
$151$	−4.02628	+	15.0263i	−0.327654	+	1.22282i	−0.911617	+	0.411041i	$0.865165\pi$
$152$			27.7128i			2.24781i
$153$	2.59808	+	4.50000i	0.210042	+	0.363803i
$154$	−24.0000	−	24.0000i	−1.93398	−	1.93398i
$155$	−1.73205	−	3.00000i	−0.139122	−	0.240966i
$156$	−20.7846	−	13.8564i	−1.66410	−	1.10940i
$157$	−3.50000	+	6.06218i	−0.279330	+	0.483814i	−0.971219	−	0.238190i	$-0.923446\pi$
$157$	−3.50000	+	6.06218i	−0.279330	+	0.483814i	0.691888	+	0.722005i	$0.256779\pi$
$158$	7.09808	−	1.90192i	0.564693	−	0.151309i
$159$	−1.50000	+	2.59808i	−0.118958	+	0.206041i
$160$		0			0
$161$	−3.46410	−	3.46410i	−0.273009	−	0.273009i
$162$	−15.5885	−	15.5885i	−1.22474	−	1.22474i
$163$	1.00000	+	1.00000i	0.0783260	+	0.0783260i	0.745184	−	0.666858i	$-0.232361\pi$
$163$	1.00000	+	1.00000i	0.0783260	+	0.0783260i	−0.666858	+	0.745184i	$0.732361\pi$
$164$	28.3923	+	7.60770i	2.21707	+	0.594061i
$165$	−18.0000	−	10.3923i	−1.40130	−	0.809040i
$166$	5.19615	+	3.00000i	0.403300	+	0.232845i
$167$	3.16987	+	11.8301i	0.245292	+	0.915443i	0.973236	+	0.229806i	$0.0738093\pi$
$167$	3.16987	+	11.8301i	0.245292	+	0.915443i	−0.727944	+	0.685636i	$0.759524\pi$
$168$			24.0000i			1.85164i
$169$	7.89230	−	10.3301i	0.607100	−	0.794625i
$170$		−	10.3923i		−	0.797053i
$171$	−16.3923	−	4.39230i	−1.25355	−	0.335888i
$172$	−36.0000			−2.74497
$173$	0.866025	+	1.50000i	0.0658427	+	0.114043i	0.897067	−	0.441894i	$-0.145693\pi$
$173$	0.866025	+	1.50000i	0.0658427	+	0.114043i	−0.831225	+	0.555936i	$0.812360\pi$
$174$	−3.80385	+	14.1962i	−0.288369	+	1.07621i
$175$	−0.732051	−	2.73205i	−0.0553378	−	0.206524i
$176$	−5.07180	−	18.9282i	−0.382301	−	1.42677i
$177$	−3.29423	+	12.2942i	−0.247609	+	0.924091i
$178$	−18.0000	−	31.1769i	−1.34916	−	2.33681i
$179$	−8.66025			−0.647298			−0.323649	−	0.946177i	$-0.604910\pi$
$179$	−8.66025			−0.647298			−0.323649	+	0.946177i	$0.604910\pi$
$180$	7.60770	+	28.3923i	0.567044	+	2.11624i
$181$			3.00000i			0.222988i	0.993765	+	0.111494i	$0.0355636\pi$
$181$			3.00000i			0.222988i	−0.993765	+	0.111494i	$0.964436\pi$
$182$	−24.9282	−	1.60770i	−1.84780	−	0.119170i
$183$			5.19615i			0.384111i
$184$	−2.19615	−	8.19615i	−0.161903	−	0.604228i
$185$	−3.00000	−	1.73205i	−0.220564	−	0.127343i
$186$	5.19615	+	3.00000i	0.381000	+	0.219971i
$187$	−8.19615	−	2.19615i	−0.599362	−	0.160599i
$188$	−6.92820	−	6.92820i	−0.505291	−	0.505291i
$189$	−14.1962	−	3.80385i	−1.03262	−	0.276689i
$190$	24.0000	+	24.0000i	1.74114	+	1.74114i
$191$	4.50000	−	2.59808i	0.325609	−	0.187990i	−0.328281	−	0.944580i	$-0.606469\pi$
$191$	4.50000	−	2.59808i	0.325609	−	0.187990i	0.653890	+	0.756590i	$0.273136\pi$
$192$	6.92820	−	12.0000i	0.500000	−	0.866025i
$193$	−2.73205	+	0.732051i	−0.196657	+	0.0526942i	−0.355803	−	0.934561i	$-0.615793\pi$
$193$	−2.73205	+	0.732051i	−0.196657	+	0.0526942i	0.159146	+	0.987255i	$0.449126\pi$
$194$	17.3205	−	30.0000i	1.24354	−	2.15387i
$195$	−15.0000	+	3.00000i	−1.07417	+	0.214834i
$196$	2.00000	+	3.46410i	0.142857	+	0.247436i
$197$	12.1244	+	12.1244i	0.863825	+	0.863825i	0.991780	−	0.127955i	$-0.0408414\pi$
$197$	12.1244	+	12.1244i	0.863825	+	0.863825i	−0.127955	+	0.991780i	$0.540841\pi$
$198$	36.0000			2.55841
$199$			13.0000i			0.921546i	0.887518	+	0.460773i	$0.152428\pi$
$199$			13.0000i			0.921546i	−0.887518	+	0.460773i	$0.847572\pi$
$200$	1.26795	−	4.73205i	0.0896575	−	0.334607i
$201$	5.07180	−	18.9282i	0.357737	−	1.33509i
$202$	−28.6865	+	7.68653i	−2.01838	+	0.540823i
$203$	2.53590	+	9.46410i	0.177985	+	0.664250i
$204$	6.00000	+	10.3923i	0.420084	+	0.727607i
$205$	15.5885	−	9.00000i	1.08875	−	0.628587i
$206$	31.1769	−	31.1769i	2.17220	−	2.17220i
$207$	5.19615			0.361158
$208$	−12.0000	−	8.00000i	−0.832050	−	0.554700i
$209$	24.0000	−	13.8564i	1.66011	−	0.958468i
$210$	20.7846	+	20.7846i	1.43427	+	1.43427i
$211$	4.50000	−	7.79423i	0.309793	−	0.536577i	−0.668524	−	0.743690i	$-0.733074\pi$
$211$	4.50000	−	7.79423i	0.309793	−	0.536577i	0.978317	+	0.207114i	$0.0664070\pi$
$212$	−3.46410	+	6.00000i	−0.237915	+	0.412082i
$213$	2.19615	+	8.19615i	0.150478	+	0.561591i
$214$	28.6865	+	7.68653i	1.96097	+	0.525441i
$215$	−15.5885	+	15.5885i	−1.06312	+	1.06312i
$216$	−18.0000	−	18.0000i	−1.22474	−	1.22474i
$217$	4.00000			0.271538
$218$	13.8564	+	24.0000i	0.938474	+	1.62549i
$219$	4.43782	+	16.5622i	0.299880	+	1.11917i
$220$	−41.5692	−	24.0000i	−2.80260	−	1.61808i
$221$	−5.59808	+	2.76795i	−0.376567	+	0.186192i
$222$	6.00000			0.402694
$223$	−2.73205	−	0.732051i	−0.182952	−	0.0490217i	0.166180	−	0.986095i	$-0.446857\pi$
$223$	−2.73205	−	0.732051i	−0.182952	−	0.0490217i	−0.349132	+	0.937074i	$0.613523\pi$
$224$		0			0
$225$	2.59808	+	1.50000i	0.173205	+	0.100000i
$226$	3.00000	−	3.00000i	0.199557	−	0.199557i
$227$	−0.633975	+	2.36603i	−0.0420784	+	0.157039i	−0.983768	−	0.179443i	$-0.942570\pi$
$227$	−0.633975	+	2.36603i	−0.0420784	+	0.157039i	0.941690	+	0.336482i	$0.109237\pi$
$228$	−37.8564	−	10.1436i	−2.50710	−	0.671776i
$229$	9.56218	−	2.56218i	0.631886	−	0.169313i	0.0713609	−	0.997451i	$-0.477266\pi$
$229$	9.56218	−	2.56218i	0.631886	−	0.169313i	0.560526	+	0.828137i	$0.310599\pi$
$230$	−9.00000	−	5.19615i	−0.593442	−	0.342624i
$231$	20.7846	−	12.0000i	1.36753	−	0.789542i
$232$	−4.39230	+	16.3923i	−0.288369	+	1.07621i
$233$	19.0526			1.24817			0.624087	−	0.781355i	$-0.285471\pi$
$233$	19.0526			1.24817			0.624087	+	0.781355i	$0.285471\pi$
$234$	19.9019	−	17.4904i	1.30103	−	1.14338i
$235$	−6.00000			−0.391397
$236$	−7.60770	+	28.3923i	−0.495219	+	1.84818i
$237$			5.19615i			0.337526i
$238$	10.3923	+	6.00000i	0.673633	+	0.388922i
$239$	−4.73205	+	1.26795i	−0.306091	+	0.0820168i	−0.408595	−	0.912716i	$-0.633981\pi$
$239$	−4.73205	+	1.26795i	−0.306091	+	0.0820168i	0.102504	+	0.994733i	$0.467315\pi$
$240$	4.39230	+	16.3923i	0.283522	+	1.05812i
$241$	−0.732051	+	2.73205i	−0.0471555	+	0.175987i	−0.985487	−	0.169749i	$-0.945704\pi$
$241$	−0.732051	+	2.73205i	−0.0471555	+	0.175987i	0.938332	+	0.345736i	$0.112371\pi$
$242$	−22.5167	+	22.5167i	−1.44743	+	1.44743i
$243$	13.5000	−	7.79423i	0.866025	−	0.500000i
$244$			12.0000i			0.768221i
$245$	2.36603	+	0.633975i	0.151160	+	0.0405032i
$246$	−15.5885	+	27.0000i	−0.993884	+	1.72146i
$247$	6.53590	−	19.3205i	0.415869	−	1.22933i
$248$	6.00000	+	3.46410i	0.381000	+	0.219971i
$249$	−3.00000	+	3.00000i	−0.190117	+	0.190117i
$250$	12.0000	+	20.7846i	0.758947	+	1.31453i
$251$	5.19615			0.327978			0.163989	−	0.986462i	$-0.447564\pi$
$251$	5.19615			0.327978			0.163989	+	0.986462i	$0.447564\pi$
$252$	−32.7846	−	8.78461i	−2.06524	−	0.553378i
$253$	−6.00000	+	6.00000i	−0.377217	+	0.377217i
$254$	−9.46410	−	2.53590i	−0.593831	−	0.159116i
$255$	7.09808	+	1.90192i	0.444499	+	0.119103i
$256$	16.0000	−	27.7128i	1.00000	−	1.73205i
$257$	−7.79423	+	13.5000i	−0.486191	+	0.842107i	−0.999874	−	0.0158730i	$-0.994947\pi$
$257$	−7.79423	+	13.5000i	−0.486191	+	0.842107i	0.513683	+	0.857980i	$0.328281\pi$
$258$	9.88269	−	36.8827i	0.615269	−	2.29622i
$259$	3.46410	−	2.00000i	0.215249	−	0.124274i
$260$	−34.6410	+	6.92820i	−2.14834	+	0.429669i
$261$	−9.00000	−	5.19615i	−0.557086	−	0.321634i
$262$	27.0000	−	27.0000i	1.66807	−	1.66807i
$263$	−1.50000	+	0.866025i	−0.0924940	+	0.0534014i	−0.545534	−	0.838089i	$-0.683673\pi$
$263$	−1.50000	+	0.866025i	−0.0924940	+	0.0534014i	0.453040	+	0.891490i	$0.350340\pi$
$264$	41.5692			2.55841
$265$	1.09808	+	4.09808i	0.0674543	+	0.251743i
$266$	−37.8564	+	10.1436i	−2.32113	+	0.621944i
$267$	24.5885	−	6.58846i	1.50479	−	0.403207i
$268$	11.7128	−	43.7128i	0.715474	−	2.67019i
$269$			10.3923i			0.633630i	0.948487	+	0.316815i	$0.102613\pi$
$269$			10.3923i			0.633630i	−0.948487	+	0.316815i	$0.897387\pi$
$270$	−31.1769			−1.89737
$271$	−14.0000	−	14.0000i	−0.850439	−	0.850439i	0.139748	−	0.990187i	$-0.455371\pi$
$271$	−14.0000	−	14.0000i	−0.850439	−	0.850439i	−0.990187	+	0.139748i	$0.955371\pi$
$272$	3.46410	+	6.00000i	0.210042	+	0.363803i
$273$	5.66025	−	16.7321i	0.342574	−	1.01267i
$274$		0			0
$275$	−4.73205	+	1.26795i	−0.285353	+	0.0764602i
$276$	12.0000			0.722315
$277$	−10.3923	+	6.00000i	−0.624413	+	0.360505i	−0.778585	−	0.627539i	$-0.784062\pi$
$277$	−10.3923	+	6.00000i	−0.624413	+	0.360505i	0.154172	+	0.988044i	$0.450729\pi$
$278$	−19.0526	−	19.0526i	−1.14270	−	1.14270i
$279$	−3.00000	+	3.00000i	−0.179605	+	0.179605i
$280$	24.0000	+	24.0000i	1.43427	+	1.43427i
$281$	−23.6603	−	6.33975i	−1.41145	−	0.378198i	−0.529009	−	0.848616i	$-0.677436\pi$
$281$	−23.6603	−	6.33975i	−1.41145	−	0.378198i	−0.882443	+	0.470419i	$0.844103\pi$
$282$	9.00000	−	5.19615i	0.535942	−	0.309426i
$283$	−19.9186	−	11.5000i	−1.18404	−	0.683604i	−0.227092	−	0.973873i	$-0.572922\pi$
$283$	−19.9186	−	11.5000i	−1.18404	−	0.683604i	−0.956945	+	0.290269i	$0.906255\pi$
$284$	5.07180	+	18.9282i	0.300956	+	1.12318i
$285$	−20.7846	+	12.0000i	−1.23117	+	0.710819i
$286$	−2.78461	+	43.1769i	−0.164657	+	2.55310i
$287$			20.7846i			1.22688i
$288$		0			0
$289$	−14.0000			−0.823529
$290$	10.3923	+	18.0000i	0.610257	+	1.05700i
$291$	17.3205	+	17.3205i	1.01535	+	1.01535i
$292$	10.2487	+	38.2487i	0.599760	+	2.23834i
$293$	−1.26795	−	4.73205i	−0.0740744	−	0.276449i	0.918947	−	0.394380i	$-0.129041\pi$
$293$	−1.26795	−	4.73205i	−0.0740744	−	0.276449i	−0.993022	+	0.117931i	$0.962374\pi$
$294$	−4.09808	+	1.09808i	−0.239005	+	0.0640411i
$295$	9.00000	+	15.5885i	0.524000	+	0.907595i
$296$	6.92820			0.402694
$297$	−6.58846	+	24.5885i	−0.382301	+	1.42677i
$298$			36.0000i			2.08542i
$299$	−0.401924	+	6.23205i	−0.0232439	+	0.360409i
$300$	6.00000	+	3.46410i	0.346410	+	0.200000i
$301$	−6.58846	−	24.5885i	−0.379752	−	1.41726i
$302$	−33.0000	−	19.0526i	−1.89894	−	1.09635i
$303$		−	21.0000i		−	1.20642i
$304$	−21.8564	−	5.85641i	−1.25355	−	0.335888i
$305$	5.19615	+	5.19615i	0.297531	+	0.297531i
$306$	−12.2942	+	3.29423i	−0.702814	+	0.188319i
$307$	−5.00000	−	5.00000i	−0.285365	−	0.285365i	0.549879	−	0.835244i	$-0.314674\pi$
$307$	−5.00000	−	5.00000i	−0.285365	−	0.285365i	−0.835244	+	0.549879i	$0.814674\pi$
$308$	48.0000	−	27.7128i	2.73505	−	1.57908i
$309$	15.5885	+	27.0000i	0.886796	+	1.53598i
$310$	8.19615	−	2.19615i	0.465510	−	0.124733i
$311$	12.1244	−	21.0000i	0.687509	−	1.19080i	−0.285132	−	0.958488i	$-0.592037\pi$
$311$	12.1244	−	21.0000i	0.687509	−	1.19080i	0.972641	−	0.232313i	$-0.0746292\pi$
$312$	22.9808	−	20.1962i	1.30103	−	1.14338i
$313$	−6.00000	−	10.3923i	−0.339140	−	0.587408i	0.645131	−	0.764072i	$-0.276803\pi$
$313$	−6.00000	−	10.3923i	−0.339140	−	0.587408i	−0.984271	+	0.176664i	$0.943469\pi$
$314$	−12.1244	−	12.1244i	−0.684217	−	0.684217i
$315$	−18.0000	+	10.3923i	−1.01419	+	0.585540i
$316$			12.0000i			0.675053i
$317$	0.633975	−	2.36603i	0.0356076	−	0.132889i	−0.945834	−	0.324651i	$-0.894753\pi$
$317$	0.633975	−	2.36603i	0.0356076	−	0.132889i	0.981442	+	0.191761i	$0.0614200\pi$
$318$	−5.19615	−	5.19615i	−0.291386	−	0.291386i
$319$	16.3923	−	4.39230i	0.917793	−	0.245922i
$320$	−5.07180	−	18.9282i	−0.283522	−	1.05812i
$321$	−10.5000	+	18.1865i	−0.586053	+	1.01507i
$322$	10.3923	−	6.00000i	0.579141	−	0.334367i
$323$	−6.92820	+	6.92820i	−0.385496	+	0.385496i
$324$	31.1769	−	18.0000i	1.73205	−	1.00000i
$325$	−2.00000	+	3.00000i	−0.110940	+	0.166410i
$326$	−3.00000	+	1.73205i	−0.166155	+	0.0959294i
$327$	−18.9282	+	5.07180i	−1.04673	+	0.280471i
$328$	−18.0000	+	31.1769i	−0.993884	+	1.72146i
$329$	3.46410	−	6.00000i	0.190982	−	0.330791i
$330$	36.0000	−	36.0000i	1.98173	−	1.98173i
$331$	−31.4186	−	8.41858i	−1.72692	−	0.462727i	−0.747451	−	0.664316i	$-0.768723\pi$
$331$	−31.4186	−	8.41858i	−1.72692	−	0.462727i	−0.979470	+	0.201589i	$0.935389\pi$
$332$	−6.92820	+	6.92820i	−0.380235	+	0.380235i
$333$	−1.09808	+	4.09808i	−0.0601742	+	0.224573i
$334$	−30.0000			−1.64153
$335$	−13.8564	−	24.0000i	−0.757056	−	1.31126i
$336$	−18.9282	−	5.07180i	−1.03262	−	0.276689i
$337$	16.4545	+	9.50000i	0.896333	+	0.517498i	0.876009	−	0.482295i	$-0.160197\pi$
$337$	16.4545	+	9.50000i	0.896333	+	0.517498i	0.0203242	+	0.999793i	$0.493530\pi$
$338$	19.4378	+	25.2224i	1.05728	+	1.37192i
$339$	1.50000	+	2.59808i	0.0814688	+	0.141108i
$340$	16.3923	+	4.39230i	0.888998	+	0.238206i
$341$		−	6.92820i		−	0.375183i
$342$	20.7846	−	36.0000i	1.12390	−	1.94666i
$343$	12.0000	−	12.0000i	0.647939	−	0.647939i
$344$	11.4115	−	42.5885i	0.615269	−	2.29622i
$345$	5.19615	−	5.19615i	0.279751	−	0.279751i
$346$	−4.09808	+	1.09808i	−0.220314	+	0.0590329i
$347$	−10.5000	−	6.06218i	−0.563670	−	0.325435i	0.190947	−	0.981600i	$-0.438844\pi$
$347$	−10.5000	−	6.06218i	−0.563670	−	0.325435i	−0.754617	+	0.656165i	$0.772177\pi$
$348$	−20.7846	−	12.0000i	−1.11417	−	0.643268i
$349$	6.22243	−	23.2224i	0.333079	−	1.24307i	−0.572857	−	0.819655i	$-0.694165\pi$
$349$	6.22243	−	23.2224i	0.333079	−	1.24307i	0.905937	−	0.423413i	$-0.139168\pi$
$350$	6.92820			0.370328
$351$	8.30385	+	16.7942i	0.443227	+	0.896410i
$352$		0			0
$353$	−1.26795	+	4.73205i	−0.0674861	+	0.251862i	−0.991425	−	0.130679i	$-0.958284\pi$
$353$	−1.26795	+	4.73205i	−0.0674861	+	0.251862i	0.923939	+	0.382541i	$0.124951\pi$
$354$	−27.0000	−	15.5885i	−1.43503	−	0.828517i
$355$	10.3923	+	6.00000i	0.551566	+	0.318447i
$356$	56.7846	−	15.2154i	3.00958	−	0.806414i
$357$	−6.00000	+	6.00000i	−0.317554	+	0.317554i
$358$	5.49038	−	20.4904i	0.290176	−	1.08295i
$359$	−17.3205	+	17.3205i	−0.914141	+	0.914141i	−0.996595	−	0.0824535i	$-0.973724\pi$
$359$	−17.3205	+	17.3205i	−0.914141	+	0.914141i	0.0824535	+	0.996595i	$0.473724\pi$
$360$	−36.0000			−1.89737
$361$		−	13.0000i		−	0.684211i
$362$	−7.09808	−	1.90192i	−0.373067	−	0.0999629i
$363$	−11.2583	−	19.5000i	−0.590909	−	1.02348i
$364$	13.0718	−	38.6410i	0.685148	−	2.02534i
$365$	21.0000	+	12.1244i	1.09919	+	0.634618i
$366$	−12.2942	−	3.29423i	−0.642630	−	0.172192i
$367$	11.5000	+	19.9186i	0.600295	+	1.03974i	0.992776	+	0.119982i	$0.0382835\pi$
$367$	11.5000	+	19.9186i	0.600295	+	1.03974i	−0.392481	+	0.919760i	$0.628383\pi$
$368$	6.92820			0.361158
$369$	−15.5885	−	15.5885i	−0.811503	−	0.811503i
$370$	6.00000	−	6.00000i	0.311925	−	0.311925i
$371$	−4.73205	−	1.26795i	−0.245676	−	0.0658286i
$372$	−6.92820	+	6.92820i	−0.359211	+	0.359211i
$373$	−1.50000	+	2.59808i	−0.0776671	+	0.134523i	−0.902243	−	0.431228i	$-0.858080\pi$
$373$	−1.50000	+	2.59808i	−0.0776671	+	0.134523i	0.824576	+	0.565751i	$0.191414\pi$
$374$	10.3923	−	18.0000i	0.537373	−	0.930758i
$375$	−16.3923	+	4.39230i	−0.846495	+	0.226818i
$376$	10.3923	−	6.00000i	0.535942	−	0.309426i
$377$	6.92820	−	10.3923i	0.356821	−	0.535231i
$378$	18.0000	−	31.1769i	0.925820	−	1.60357i
$379$	−20.0000	+	20.0000i	−1.02733	+	1.02733i	−0.0277151	+	0.999616i	$0.508823\pi$
$379$	−20.0000	+	20.0000i	−1.02733	+	1.02733i	−0.999616	+	0.0277151i	$0.991177\pi$
$380$	−48.0000	+	27.7128i	−2.46235	+	1.42164i
$381$	3.46410	−	6.00000i	0.177471	−	0.307389i
$382$	3.29423	+	12.2942i	0.168547	+	0.629027i
$383$	26.0263	−	6.97372i	1.32988	−	0.356340i	0.477210	−	0.878789i	$-0.341648\pi$
$383$	26.0263	−	6.97372i	1.32988	−	0.356340i	0.852671	+	0.522449i	$0.174981\pi$
$384$	24.0000	+	24.0000i	1.22474	+	1.22474i
$385$	8.78461	−	32.7846i	0.447705	−	1.67086i
$386$		−	6.92820i		−	0.352636i
$387$	23.3827	+	13.5000i	1.18861	+	0.686244i
$388$	40.0000	+	40.0000i	2.03069	+	2.03069i
$389$	9.52628	+	16.5000i	0.483002	+	0.836583i	0.999810	−	0.0195181i	$-0.00621321\pi$
$389$	9.52628	+	16.5000i	0.483002	+	0.836583i	−0.516808	+	0.856101i	$0.672880\pi$
$390$	2.41154	−	37.3923i	0.122113	−	1.89343i
$391$	1.50000	−	2.59808i	0.0758583	−	0.131390i
$392$	−4.73205	+	1.26795i	−0.239005	+	0.0640411i
$393$	13.5000	+	23.3827i	0.680985	+	1.17950i
$394$	−36.3731	+	21.0000i	−1.83245	+	1.05796i
$395$	5.19615	+	5.19615i	0.261447	+	0.261447i
$396$	−15.2154	+	56.7846i	−0.764602	+	2.85353i
$397$	2.00000	+	2.00000i	0.100377	+	0.100377i	0.755512	−	0.655135i	$-0.227388\pi$
$397$	2.00000	+	2.00000i	0.100377	+	0.100377i	−0.655135	+	0.755512i	$0.727388\pi$
$398$	−30.7583	−	8.24167i	−1.54178	−	0.413118i
$399$		−	27.7128i		−	1.38738i
$400$	3.46410	+	2.00000i	0.173205	+	0.100000i
$401$	2.53590	+	9.46410i	0.126637	+	0.472615i	0.999893	−	0.0146470i	$-0.00466245\pi$
$401$	2.53590	+	9.46410i	0.126637	+	0.472615i	−0.873256	+	0.487262i	$0.837996\pi$
$402$	41.5692	+	24.0000i	2.07328	+	1.19701i
$403$	−3.36603	−	3.83013i	−0.167674	−	0.190792i
$404$		−	48.4974i		−	2.41284i
$405$	5.70577	−	21.2942i	0.283522	−	1.05812i
$406$	−24.0000			−1.19110
$407$	−3.46410	−	6.00000i	−0.171709	−	0.297409i
$408$	−14.1962	+	3.80385i	−0.702814	+	0.188319i
$409$	6.22243	+	23.2224i	0.307679	+	1.14828i	0.930614	+	0.366002i	$0.119274\pi$
$409$	6.22243	+	23.2224i	0.307679	+	1.14828i	−0.622935	+	0.782274i	$0.714060\pi$
$410$	11.4115	+	42.5885i	0.563576	+	2.10329i
$411$		0			0
$412$	36.0000	+	62.3538i	1.77359	+	3.07195i
$413$	−20.7846			−1.02274
$414$	−3.29423	+	12.2942i	−0.161903	+	0.604228i
$415$			6.00000i			0.294528i
$416$		0			0
$417$	16.5000	−	9.52628i	0.808008	−	0.466504i
$418$	17.5692	+	65.5692i	0.859339	+	3.20710i
$419$	−1.50000	−	0.866025i	−0.0732798	−	0.0423081i	0.462912	−	0.886404i	$-0.346804\pi$
$419$	−1.50000	−	0.866025i	−0.0732798	−	0.0423081i	−0.536192	+	0.844096i	$0.680138\pi$
$420$	−41.5692	+	24.0000i	−2.02837	+	1.17108i
$421$	17.7583	+	4.75833i	0.865488	+	0.231907i	0.664136	−	0.747612i	$-0.268800\pi$
$421$	17.7583	+	4.75833i	0.865488	+	0.231907i	0.201352	+	0.979519i	$0.435466\pi$
$422$	15.5885	+	15.5885i	0.758834	+	0.758834i
$423$	1.90192	+	7.09808i	0.0924747	+	0.345120i
$424$	−6.00000	−	6.00000i	−0.291386	−	0.291386i
$425$	1.50000	−	0.866025i	0.0727607	−	0.0420084i
$426$	−20.7846			−1.00702
$427$	−8.19615	+	2.19615i	−0.396640	+	0.106279i
$428$	−24.2487	+	42.0000i	−1.17211	+	2.03015i
$429$	−28.9808	−	9.80385i	−1.39920	−	0.473334i
$430$	−27.0000	−	46.7654i	−1.30206	−	2.25523i
$431$	−20.7846	−	20.7846i	−1.00116	−	1.00116i	−0.999999	−	0.00116009i	$-0.999631\pi$
$431$	−20.7846	−	20.7846i	−1.00116	−	1.00116i	−0.00116009	−	0.999999i	$-0.500369\pi$
$432$	18.0000	−	10.3923i	0.866025	−	0.500000i
$433$		−	19.0000i		−	0.913082i	−0.889702	−	0.456541i	$-0.849088\pi$
$433$		−	19.0000i		−	0.913082i	0.889702	−	0.456541i	$-0.150912\pi$
$434$	−2.53590	+	9.46410i	−0.121727	+	0.454291i
$435$	−14.1962	+	3.80385i	−0.680653	+	0.182381i
$436$	−43.7128	+	11.7128i	−2.09346	+	0.560942i
$437$	2.53590	+	9.46410i	0.121308	+	0.452729i
$438$	−42.0000			−2.00684
$439$	−12.9904	+	7.50000i	−0.619997	+	0.357955i	−0.776868	−	0.629664i	$-0.783193\pi$
$439$	−12.9904	+	7.50000i	−0.619997	+	0.357955i	0.156871	+	0.987619i	$0.449859\pi$
$440$	41.5692	−	41.5692i	1.98173	−	1.98173i
$441$		−	3.00000i		−	0.142857i
$442$	−3.00000	−	15.0000i	−0.142695	−	0.713477i
$443$	−28.5000	+	16.4545i	−1.35408	+	0.781776i	−0.988818	−	0.149130i	$-0.952353\pi$
$443$	−28.5000	+	16.4545i	−1.35408	+	0.781776i	−0.365258	+	0.930906i	$0.619019\pi$
$444$	−2.53590	+	9.46410i	−0.120348	+	0.449146i
$445$	18.0000	−	31.1769i	0.853282	−	1.47793i
$446$	3.46410	−	6.00000i	0.164030	−	0.284108i
$447$	−24.5885	−	6.58846i	−1.16299	−	0.311623i
$448$	21.8564	+	5.85641i	1.03262	+	0.276689i
$449$	25.9808	−	25.9808i	1.22611	−	1.22611i	0.260684	−	0.965424i	$-0.416052\pi$
$449$	25.9808	−	25.9808i	1.22611	−	1.22611i	0.965424	−	0.260684i	$-0.0839480\pi$
$450$	−5.19615	+	5.19615i	−0.244949	+	0.244949i
$451$	36.0000			1.69517
$452$	3.46410	+	6.00000i	0.162938	+	0.282216i
$453$	19.0526	−	19.0526i	0.895167	−	0.895167i
$454$	−5.19615	−	3.00000i	−0.243868	−	0.140797i
$455$	−11.0718	−	22.3923i	−0.519054	−	1.04977i
$456$	24.0000	−	41.5692i	1.12390	−	1.94666i
$457$	−17.7583	−	4.75833i	−0.830700	−	0.222585i	−0.181681	−	0.983358i	$-0.558154\pi$
$457$	−17.7583	−	4.75833i	−0.830700	−	0.222585i	−0.649019	+	0.760772i	$0.724820\pi$
$458$			24.2487i			1.13307i
$459$		−	9.00000i		−	0.420084i
$460$	12.0000	−	12.0000i	0.559503	−	0.559503i
$461$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$461$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$462$	15.2154	+	56.7846i	0.707884	+	2.64186i
$463$	27.3205	−	7.32051i	1.26969	−	0.340213i	0.439779	−	0.898106i	$-0.355057\pi$
$463$	27.3205	−	7.32051i	1.26969	−	0.340213i	0.829913	+	0.557893i	$0.188390\pi$
$464$	−12.0000	−	6.92820i	−0.557086	−	0.321634i
$465$			6.00000i			0.278243i
$466$	−12.0788	+	45.0788i	−0.559541	+	2.08824i
$467$	−32.9090			−1.52285			−0.761423	−	0.648256i	$-0.775499\pi$
$467$	−32.9090			−1.52285			−0.761423	+	0.648256i	$0.775499\pi$
$468$	19.1769	+	38.7846i	0.886453	+	1.79282i
$469$	32.0000			1.47762
$470$	3.80385	−	14.1962i	0.175458	−	0.654820i
$471$	10.5000	−	6.06218i	0.483814	−	0.279330i
$472$	−31.1769	−	18.0000i	−1.43503	−	0.828517i
$473$	−42.5885	+	11.4115i	−1.95822	+	0.524703i
$474$	−12.2942	−	3.29423i	−0.564693	−	0.151309i
$475$	−1.46410	+	5.46410i	−0.0671776	+	0.250710i
$476$	−13.8564	+	13.8564i	−0.635107	+	0.635107i
$477$	4.50000	−	2.59808i	0.206041	−	0.118958i
$478$		−	12.0000i		−	0.548867i
$479$	35.4904	+	9.50962i	1.62160	+	0.434506i	0.951470	−	0.307741i	$-0.0995731\pi$
$479$	35.4904	+	9.50962i	1.62160	+	0.434506i	0.670127	+	0.742247i	$0.266240\pi$
$480$		0			0
$481$	−4.83013	−	1.63397i	−0.220235	−	0.0745028i
$482$	−6.00000	−	3.46410i	−0.273293	−	0.157786i
$483$	2.19615	+	8.19615i	0.0999284	+	0.372938i
$484$	−26.0000	−	45.0333i	−1.18182	−	2.04697i
$485$	34.6410			1.57297
$486$	9.88269	+	36.8827i	0.448288	+	1.67303i
$487$	4.00000	−	4.00000i	0.181257	−	0.181257i	−0.610646	−	0.791904i	$-0.709090\pi$
$487$	4.00000	−	4.00000i	0.181257	−	0.181257i	0.791904	+	0.610646i	$0.209090\pi$
$488$	−14.1962	−	3.80385i	−0.642630	−	0.172192i
$489$	−0.633975	−	2.36603i	−0.0286693	−	0.106995i
$490$	−3.00000	+	5.19615i	−0.135526	+	0.234738i
$491$	6.92820	−	12.0000i	0.312665	−	0.541552i	−0.666273	−	0.745708i	$-0.732111\pi$
$491$	6.92820	−	12.0000i	0.312665	−	0.541552i	0.978938	+	0.204155i	$0.0654448\pi$
$492$	−36.0000	−	36.0000i	−1.62301	−	1.62301i
$493$	−5.19615	+	3.00000i	−0.234023	+	0.135113i
$494$	41.5692	+	27.7128i	1.87029	+	1.24686i
$495$	18.0000	+	31.1769i	0.809040	+	1.40130i
$496$	−4.00000	+	4.00000i	−0.179605	+	0.179605i
$497$	−12.0000	+	6.92820i	−0.538274	+	0.310772i
$498$	−5.19615	−	9.00000i	−0.232845	−	0.403300i
$499$	−5.12436	−	19.1244i	−0.229398	−	0.856124i	−0.980595	−	0.196046i	$-0.937190\pi$
$499$	−5.12436	−	19.1244i	−0.229398	−	0.856124i	0.751197	−	0.660078i	$-0.229477\pi$
$500$	−37.8564	+	10.1436i	−1.69299	+	0.453635i
$501$	5.49038	−	20.4904i	0.245292	−	0.915443i
$502$	−3.29423	+	12.2942i	−0.147029	+	0.548718i
$503$		−	1.73205i		−	0.0772283i	−0.999254	−	0.0386142i	$-0.987706\pi$
$503$		−	1.73205i		−	0.0772283i	0.999254	−	0.0386142i	$-0.0122943\pi$
$504$	20.7846	−	36.0000i	0.925820	−	1.60357i
$505$	−21.0000	−	21.0000i	−0.934488	−	0.934488i
$506$	−10.3923	−	18.0000i	−0.461994	−	0.800198i
$507$	−20.7846	+	8.66025i	−0.923077	+	0.384615i
$508$	8.00000	−	13.8564i	0.354943	−	0.614779i
$509$	23.6603	−	6.33975i	1.04872	−	0.281004i	0.306999	−	0.951710i	$-0.400675\pi$
$509$	23.6603	−	6.33975i	1.04872	−	0.281004i	0.741724	+	0.670706i	$0.234009\pi$
$510$	−9.00000	+	15.5885i	−0.398527	+	0.690268i
$511$	−24.2487	+	14.0000i	−1.07270	+	0.619324i
$512$	27.7128	+	27.7128i	1.22474	+	1.22474i
$513$	20.7846	+	20.7846i	0.917663	+	0.917663i
$514$	−27.0000	−	27.0000i	−1.19092	−	1.19092i
$515$	42.5885	+	11.4115i	1.87667	+	0.502853i
$516$	54.0000	+	31.1769i	2.37722	+	1.37249i
$517$	−10.3923	−	6.00000i	−0.457053	−	0.263880i
$518$	2.53590	+	9.46410i	0.111421	+	0.415829i
$519$		−	3.00000i		−	0.131685i
$520$	2.78461	−	43.1769i	0.122113	−	1.89343i
$521$			27.7128i			1.21412i	0.794656	+	0.607060i	$0.207651\pi$
$521$			27.7128i			1.21412i	−0.794656	+	0.607060i	$0.792349\pi$
$522$	18.0000	−	18.0000i	0.787839	−	0.787839i
$523$	16.0000			0.699631			0.349816	−	0.936819i	$-0.386244\pi$
$523$	16.0000			0.699631			0.349816	+	0.936819i	$0.386244\pi$
$524$	31.1769	+	54.0000i	1.36197	+	2.35900i
$525$	−1.26795	+	4.73205i	−0.0553378	+	0.206524i
$526$	−1.09808	−	4.09808i	−0.0478784	−	0.178685i
$527$	0.633975	+	2.36603i	0.0276164	+	0.103066i
$528$	−8.78461	+	32.7846i	−0.382301	+	1.42677i
$529$	10.0000	+	17.3205i	0.434783	+	0.753066i
$530$	−10.3923			−0.451413
$531$	15.5885	−	15.5885i	0.676481	−	0.676481i
$532$		−	64.0000i		−	2.77475i
$533$	19.9019	−	17.4904i	0.862048	−	0.757593i
$534$			62.3538i			2.69831i
$535$	7.68653	+	28.6865i	0.332318	+	1.24023i
$536$	48.0000	+	27.7128i	2.07328	+	1.19701i
$537$	12.9904	+	7.50000i	0.560576	+	0.323649i
$538$	−24.5885	−	6.58846i	−1.06008	−	0.284049i
$539$	3.46410	+	3.46410i	0.149209	+	0.149209i
$540$	13.1769	−	49.1769i	0.567044	−	2.11624i
$541$	−28.0000	−	28.0000i	−1.20381	−	1.20381i	−0.972997	−	0.230817i	$-0.925860\pi$
$541$	−28.0000	−	28.0000i	−1.20381	−	1.20381i	−0.230817	−	0.972997i	$-0.574140\pi$
$542$	42.0000	−	24.2487i	1.80405	−	1.04157i
$543$	2.59808	−	4.50000i	0.111494	−	0.193113i
$544$		0			0
$545$	−13.8564	+	24.0000i	−0.593543	+	1.02805i
$546$	36.0000	+	24.0000i	1.54066	+	1.02711i
$547$	−1.00000	−	1.73205i	−0.0427569	−	0.0740571i	0.843855	−	0.536571i	$-0.180281\pi$
$547$	−1.00000	−	1.73205i	−0.0427569	−	0.0740571i	−0.886612	+	0.462514i	$0.846947\pi$
$548$		0			0
$549$	4.50000	−	7.79423i	0.192055	−	0.332650i
$550$		−	12.0000i		−	0.511682i
$551$	5.07180	−	18.9282i	0.216066	−	0.806369i
$552$	−3.80385	+	14.1962i	−0.161903	+	0.604228i
$553$	−8.19615	+	2.19615i	−0.348536	+	0.0933899i
$554$	−7.60770	−	28.3923i	−0.323220	−	1.20627i
$555$	3.00000	+	5.19615i	0.127343	+	0.220564i
$556$	38.1051	−	22.0000i	1.61602	−	0.933008i
$557$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$557$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$558$	−5.19615	−	9.00000i	−0.219971	−	0.381000i
$559$	−18.0000	+	27.0000i	−0.761319	+	1.14198i
$560$	−24.0000	+	13.8564i	−1.01419	+	0.585540i
$561$	10.3923	+	10.3923i	0.438763	+	0.438763i
$562$	30.0000	−	51.9615i	1.26547	−	2.19186i
$563$	−4.33013	+	7.50000i	−0.182493	+	0.316087i	−0.942729	−	0.333560i	$-0.891750\pi$
$563$	−4.33013	+	7.50000i	−0.182493	+	0.316087i	0.760236	+	0.649647i	$0.225083\pi$
$564$	4.39230	+	16.3923i	0.184949	+	0.690241i
$565$	4.09808	+	1.09808i	0.172407	+	0.0461964i
$566$	39.8372	−	39.8372i	1.67448	−	1.67448i
$567$	18.0000	+	18.0000i	0.755929	+	0.755929i
$568$	−24.0000			−1.00702
$569$	−20.7846	−	36.0000i	−0.871336	−	1.50920i	−0.860615	−	0.509256i	$-0.829921\pi$
$569$	−20.7846	−	36.0000i	−0.871336	−	1.50920i	−0.0107211	−	0.999943i	$-0.503413\pi$
$570$	−15.2154	−	56.7846i	−0.637303	−	2.37845i
$571$	−8.66025	−	5.00000i	−0.362420	−	0.209243i	0.307722	−	0.951476i	$-0.400433\pi$
$571$	−8.66025	−	5.00000i	−0.362420	−	0.209243i	−0.670142	+	0.742233i	$0.733767\pi$
$572$	−66.9282	−	22.6410i	−2.79841	−	0.946668i
$573$	−9.00000			−0.375980
$574$	−49.1769	−	13.1769i	−2.05260	−	0.549994i
$575$		−	1.73205i		−	0.0722315i
$576$	−20.7846	+	12.0000i	−0.866025	+	0.500000i
$577$	−29.0000	+	29.0000i	−1.20729	+	1.20729i	−0.235383	+	0.971903i	$0.575634\pi$
$577$	−29.0000	+	29.0000i	−1.20729	+	1.20729i	−0.971903	+	0.235383i	$0.924366\pi$
$578$	8.87564	−	33.1244i	0.369178	−	1.37779i
$579$	4.73205	+	1.26795i	0.196657	+	0.0526942i
$580$	−32.7846	+	8.78461i	−1.36131	+	0.364761i
$581$	−6.00000	−	3.46410i	−0.248922	−	0.143715i
$582$	−51.9615	+	30.0000i	−2.15387	+	1.24354i
$583$	−2.19615	+	8.19615i	−0.0909553	+	0.339450i
$584$	−48.4974			−2.00684
$585$	25.0981	+	8.49038i	1.03768	+	0.351034i
$586$	12.0000			0.495715
$587$	1.90192	−	7.09808i	0.0785008	−	0.292969i	−0.915503	−	0.402310i	$-0.868207\pi$
$587$	1.90192	−	7.09808i	0.0785008	−	0.292969i	0.994004	+	0.109341i	$0.0348741\pi$
$588$		−	6.92820i		−	0.285714i
$589$	−6.92820	−	4.00000i	−0.285472	−	0.164817i
$590$	−42.5885	+	11.4115i	−1.75334	+	0.469806i
$591$	−7.68653	−	28.6865i	−0.316182	−	1.18001i
$592$	−1.46410	+	5.46410i	−0.0601742	+	0.224573i
$593$	27.7128	−	27.7128i	1.13803	−	1.13803i	0.149226	−	0.988803i	$-0.452322\pi$
$593$	27.7128	−	27.7128i	1.13803	−	1.13803i	0.988803	−	0.149226i	$-0.0476781\pi$
$594$	−54.0000	−	31.1769i	−2.21565	−	1.27920i
$595$			12.0000i			0.491952i
$596$	−56.7846	−	15.2154i	−2.32599	−	0.623247i
$597$	11.2583	−	19.5000i	0.460773	−	0.798082i
$598$	−14.4904	−	4.90192i	−0.592556	−	0.200455i
$599$	1.50000	+	0.866025i	0.0612883	+	0.0353848i	0.530331	−	0.847791i	$-0.322068\pi$
$599$	1.50000	+	0.866025i	0.0612883	+	0.0353848i	−0.469043	+	0.883175i	$0.655401\pi$
$600$	−6.00000	+	6.00000i	−0.244949	+	0.244949i
$601$	16.5000	+	28.5788i	0.673049	+	1.16576i	0.977035	+	0.213079i	$0.0683491\pi$
$601$	16.5000	+	28.5788i	0.673049	+	1.16576i	−0.303986	+	0.952676i	$0.598318\pi$
$602$	62.3538			2.54135
$603$	−24.0000	+	24.0000i	−0.977356	+	0.977356i
$604$	44.0000	−	44.0000i	1.79033	−	1.79033i
$605$	−30.7583	−	8.24167i	−1.25050	−	0.335072i
$606$	49.6865	+	13.3135i	2.01838	+	0.540823i
$607$	−0.500000	+	0.866025i	−0.0202944	+	0.0351509i	−0.875994	−	0.482322i	$-0.839794\pi$
$607$	−0.500000	+	0.866025i	−0.0202944	+	0.0351509i	0.855700	+	0.517472i	$0.173127\pi$
$608$		0			0
$609$	4.39230	−	16.3923i	0.177985	−	0.664250i
$610$	−15.5885	+	9.00000i	−0.631158	+	0.364399i
$611$	−8.66025	+	1.73205i	−0.350356	+	0.0700713i
$612$		−	20.7846i		−	0.840168i
$613$	25.0000	−	25.0000i	1.00974	−	1.00974i	0.00978840	−	0.999952i	$-0.496884\pi$
$613$	25.0000	−	25.0000i	1.00974	−	1.00974i	0.999952	−	0.00978840i	$-0.00311579\pi$
$614$	15.0000	−	8.66025i	0.605351	−	0.349499i
$615$	−31.1769			−1.25717
$616$	17.5692	+	65.5692i	0.707884	+	2.64186i
$617$	11.8301	−	3.16987i	0.476263	−	0.127614i	−0.0126990	−	0.999919i	$-0.504042\pi$
$617$	11.8301	−	3.16987i	0.476263	−	0.127614i	0.488962	+	0.872305i	$0.337376\pi$
$618$	−73.7654	+	19.7654i	−2.96728	+	0.795080i
$619$	−4.75833	+	17.7583i	−0.191253	+	0.713768i	0.801952	+	0.597389i	$0.203795\pi$
$619$	−4.75833	+	17.7583i	−0.191253	+	0.713768i	−0.993205	+	0.116378i	$0.962871\pi$
$620$			13.8564i			0.556487i
$621$	−7.79423	−	4.50000i	−0.312772	−	0.180579i
$622$	42.0000	+	42.0000i	1.68405	+	1.68405i
$623$	20.7846	+	36.0000i	0.832718	+	1.44231i
$624$	11.0718	+	22.3923i	0.443227	+	0.896410i
$625$	−14.5000	+	25.1147i	−0.580000	+	1.00459i
$626$	28.3923	−	7.60770i	1.13478	−	0.304065i
$627$	−48.0000			−1.91694
$628$	24.2487	−	14.0000i	0.967629	−	0.558661i
$629$	1.73205	+	1.73205i	0.0690614	+	0.0690614i
$630$	−13.1769	−	49.1769i	−0.524981	−	1.95926i
$631$	−25.0000	−	25.0000i	−0.995234	−	0.995234i	0.00475441	−	0.999989i	$-0.498487\pi$
$631$	−25.0000	−	25.0000i	−0.995234	−	0.995234i	−0.999989	+	0.00475441i	$0.998487\pi$
$632$	−14.1962	−	3.80385i	−0.564693	−	0.151309i
$633$	−13.5000	+	7.79423i	−0.536577	+	0.309793i
$634$	5.19615	+	3.00000i	0.206366	+	0.119145i
$635$	−2.53590	−	9.46410i	−0.100634	−	0.375571i
$636$	10.3923	−	6.00000i	0.412082	−	0.237915i
$637$	3.59808	+	0.232051i	0.142561	+	0.00919419i
$638$			41.5692i			1.64574i
$639$	3.80385	−	14.1962i	0.150478	−	0.561591i
$640$	48.0000			1.89737
$641$	15.5885	+	27.0000i	0.615707	+	1.06644i	0.990260	+	0.139230i	$0.0444629\pi$
$641$	15.5885	+	27.0000i	0.615707	+	1.06644i	−0.374553	+	0.927206i	$0.622204\pi$
$642$	−36.3731	−	36.3731i	−1.43553	−	1.43553i
$643$	6.22243	+	23.2224i	0.245389	+	0.915803i	0.973188	+	0.230013i	$0.0738768\pi$
$643$	6.22243	+	23.2224i	0.245389	+	0.915803i	−0.727799	+	0.685791i	$0.759457\pi$
$644$	5.07180	+	18.9282i	0.199857	+	0.745876i
$645$	36.8827	−	9.88269i	1.45225	−	0.389130i
$646$	−12.0000	−	20.7846i	−0.472134	−	0.817760i
$647$	−5.19615			−0.204282			−0.102141	−	0.994770i	$-0.532569\pi$
$647$	−5.19615			−0.204282			−0.102141	+	0.994770i	$0.532569\pi$
$648$	11.4115	+	42.5885i	0.448288	+	1.67303i
$649$			36.0000i			1.41312i
$650$	−5.83013	−	6.63397i	−0.228676	−	0.260206i
$651$	−6.00000	−	3.46410i	−0.235159	−	0.135769i
$652$	−1.46410	−	5.46410i	−0.0573386	−	0.213991i
$653$	−3.00000	−	1.73205i	−0.117399	−	0.0677804i	0.440151	−	0.897924i	$-0.354925\pi$
$653$	−3.00000	−	1.73205i	−0.117399	−	0.0677804i	−0.557550	+	0.830144i	$0.688258\pi$
$654$		−	48.0000i		−	1.87695i
$655$	36.8827	+	9.88269i	1.44113	+	0.386148i
$656$	−20.7846	−	20.7846i	−0.811503	−	0.811503i
$657$	7.68653	−	28.6865i	0.299880	−	1.11917i
$658$	12.0000	+	12.0000i	0.467809	+	0.467809i
$659$	−42.0000	+	24.2487i	−1.63609	+	0.944596i	−0.653926	+	0.756559i	$0.726879\pi$
$659$	−42.0000	+	24.2487i	−1.63609	+	0.944596i	−0.982162	+	0.188037i	$0.939788\pi$
$660$	41.5692	+	72.0000i	1.61808	+	2.80260i
$661$	27.3205	−	7.32051i	1.06264	−	0.284735i	0.315177	−	0.949033i	$-0.397936\pi$
$661$	27.3205	−	7.32051i	1.06264	−	0.284735i	0.747468	+	0.664298i	$0.231269\pi$
$662$	39.8372	−	69.0000i	1.54832	−	2.68176i
$663$	10.7942	+	0.696152i	0.419213	+	0.0270363i
$664$	−6.00000	−	10.3923i	−0.232845	−	0.403300i
$665$	−27.7128	−	27.7128i	−1.07466	−	1.07466i
$666$	−9.00000	−	5.19615i	−0.348743	−	0.201347i
$667$			6.00000i			0.232321i
$668$	12.6795	−	47.3205i	0.490584	−	1.83089i
$669$	3.46410	+	3.46410i	0.133930	+	0.133930i
$670$	65.5692	−	17.5692i	2.53316	−	0.678758i
$671$	3.80385	+	14.1962i	0.146846	+	0.548036i
$672$		0			0
$673$	23.3827	−	13.5000i	0.901336	−	0.520387i	0.0237028	−	0.999719i	$-0.492454\pi$
$673$	23.3827	−	13.5000i	0.901336	−	0.520387i	0.877633	+	0.479332i	$0.159121\pi$
$674$	−32.9090	+	32.9090i	−1.26761	+	1.26761i
$675$	−2.59808	−	4.50000i	−0.100000	−	0.173205i
$676$	−48.0000	+	20.0000i	−1.84615	+	0.769231i
$677$	−39.0000	+	22.5167i	−1.49889	+	0.865386i	−0.999999	−	0.00127827i	$-0.999593\pi$
$677$	−39.0000	+	22.5167i	−1.49889	+	0.865386i	−0.498893	+	0.866664i	$0.666260\pi$
$678$	−7.09808	+	1.90192i	−0.272600	+	0.0730429i
$679$	−20.0000	+	34.6410i	−0.767530	+	1.32940i
$680$	−10.3923	+	18.0000i	−0.398527	+	0.690268i
$681$	3.00000	−	3.00000i	0.114960	−	0.114960i
$682$	16.3923	+	4.39230i	0.627694	+	0.168190i
$683$	−10.3923	+	10.3923i	−0.397650	+	0.397650i	−0.877404	−	0.479753i	$-0.840726\pi$
$683$	−10.3923	+	10.3923i	−0.397650	+	0.397650i	0.479753	+	0.877404i	$0.340726\pi$
$684$	48.0000	+	48.0000i	1.83533	+	1.83533i
$685$		0			0
$686$	20.7846	+	36.0000i	0.793560	+	1.37449i
$687$	−16.5622	−	4.43782i	−0.631886	−	0.169313i
$688$	31.1769	+	18.0000i	1.18861	+	0.686244i
$689$	2.76795	+	5.59808i	0.105450	+	0.213270i
$690$	9.00000	+	15.5885i	0.342624	+	0.593442i
$691$	15.0263	+	4.02628i	0.571627	+	0.153167i	0.533042	−	0.846088i	$-0.321049\pi$
$691$	15.0263	+	4.02628i	0.571627	+	0.153167i	0.0385841	+	0.999255i	$0.487715\pi$
$692$		−	6.92820i		−	0.263371i
$693$	−41.5692			−1.57908
$694$	21.0000	−	21.0000i	0.797149	−	0.797149i
$695$	6.97372	−	26.0263i	0.264528	−	0.987233i
$696$	20.7846	−	20.7846i	0.787839	−	0.787839i
$697$	−12.2942	+	3.29423i	−0.465677	+	0.124778i
$698$	51.0000	+	29.4449i	1.93038	+	1.11450i
$699$	−28.5788	−	16.5000i	−1.08095	−	0.624087i
$700$	−2.92820	+	10.9282i	−0.110676	+	0.413047i
$701$	12.1244			0.457931			0.228965	−	0.973435i	$-0.426466\pi$
$701$	12.1244			0.457931			0.228965	+	0.973435i	$0.426466\pi$
$702$	−45.0000	+	9.00000i	−1.69842	+	0.339683i
$703$	−8.00000			−0.301726
$704$	10.1436	−	37.8564i	0.382301	−	1.42677i
$705$	9.00000	+	5.19615i	0.338960	+	0.195698i
$706$	−10.3923	−	6.00000i	−0.391120	−	0.225813i
$707$	33.1244	−	8.87564i	1.24577	−	0.333803i
$708$	36.0000	−	36.0000i	1.35296	−	1.35296i
$709$	−9.51666	+	35.5167i	−0.357406	+	1.33386i	0.520024	+	0.854151i	$0.325923\pi$
$709$	−9.51666	+	35.5167i	−0.357406	+	1.33386i	−0.877430	+	0.479705i	$0.840744\pi$
$710$	−20.7846	+	20.7846i	−0.780033	+	0.780033i
$711$	4.50000	−	7.79423i	0.168763	−	0.292306i
$712$			72.0000i			2.69831i
$713$	2.36603	+	0.633975i	0.0886083	+	0.0237425i
$714$	−10.3923	−	18.0000i	−0.388922	−	0.673633i
$715$	−38.7846	+	19.1769i	−1.45046	+	0.717176i
$716$	30.0000	+	17.3205i	1.12115	+	0.647298i
$717$	8.19615	+	2.19615i	0.306091	+	0.0820168i
$718$	−30.0000	−	51.9615i	−1.11959	−	1.93919i
$719$	6.92820			0.258378			0.129189	−	0.991620i	$-0.458763\pi$
$719$	6.92820			0.258378			0.129189	+	0.991620i	$0.458763\pi$
$720$	7.60770	−	28.3923i	0.283522	−	1.05812i
$721$	−36.0000	+	36.0000i	−1.34071	+	1.34071i
$722$	30.7583	+	8.24167i	1.14471	+	0.306723i
$723$	3.46410	−	3.46410i	0.128831	−	0.128831i
$724$	6.00000	−	10.3923i	0.222988	−	0.386227i
$725$	−1.73205	+	3.00000i	−0.0643268	+	0.111417i
$726$	53.2750	−	14.2750i	1.97722	−	0.529795i
$727$	40.7032	−	23.5000i	1.50960	−	0.871567i	0.509661	−	0.860376i	$-0.329771\pi$
$727$	40.7032	−	23.5000i	1.50960	−	0.871567i	0.999937	−	0.0111912i	$-0.00356233\pi$
$728$	41.5692	+	27.7128i	1.54066	+	1.02711i
$729$	−27.0000			−1.00000
$730$	−42.0000	+	42.0000i	−1.55449	+	1.55449i
$731$	13.5000	−	7.79423i	0.499316	−	0.288280i
$732$	10.3923	−	18.0000i	0.384111	−	0.665299i
$733$	−7.32051	−	27.3205i	−0.270389	−	1.00911i	−0.958869	−	0.283850i	$-0.908388\pi$
$733$	−7.32051	−	27.3205i	−0.270389	−	1.00911i	0.688480	−	0.725256i	$-0.258279\pi$
$734$	−54.4186	+	14.5814i	−2.00863	+	0.538210i
$735$	−3.00000	−	3.00000i	−0.110657	−	0.110657i
$736$		0			0
$737$		−	55.4256i		−	2.04163i
$738$	46.7654	−	27.0000i	1.72146	−	0.993884i
$739$	−31.0000	−	31.0000i	−1.14035	−	1.14035i	−0.988385	−	0.151968i	$-0.951439\pi$
$739$	−31.0000	−	31.0000i	−1.14035	−	1.14035i	−0.151968	−	0.988385i	$-0.548561\pi$
$740$	6.92820	+	12.0000i	0.254686	+	0.441129i
$741$	−26.5359	+	23.3205i	−0.974821	+	0.856700i
$742$	6.00000	−	10.3923i	0.220267	−	0.381514i
$743$	−37.8564	+	10.1436i	−1.38882	+	0.372132i	−0.874316	−	0.485357i	$-0.838689\pi$
$743$	−37.8564	+	10.1436i	−1.38882	+	0.372132i	−0.514501	+	0.857490i	$0.672023\pi$
$744$	−6.00000	−	10.3923i	−0.219971	−	0.381000i
$745$	−31.1769	+	18.0000i	−1.14223	+	0.659469i
$746$	−5.19615	−	5.19615i	−0.190245	−	0.190245i
$747$	7.09808	−	1.90192i	0.259705	−	0.0695878i
$748$	24.0000	+	24.0000i	0.877527	+	0.877527i
$749$	−33.1244	−	8.87564i	−1.21034	−	0.324309i
$750$		−	41.5692i		−	1.51789i
$751$	31.1769	+	18.0000i	1.13766	+	0.656829i	0.945851	−	0.324603i	$-0.105231\pi$
$751$	31.1769	+	18.0000i	1.13766	+	0.656829i	0.191811	+	0.981432i	$0.438564\pi$
$752$	2.53590	+	9.46410i	0.0924747	+	0.345120i
$753$	−7.79423	−	4.50000i	−0.284037	−	0.163989i
$754$	20.1962	+	22.9808i	0.735500	+	0.836910i
$755$		−	38.1051i		−	1.38679i
$756$	41.5692	+	41.5692i	1.51186	+	1.51186i
$757$	45.0000			1.63555			0.817776	−	0.575536i	$-0.195207\pi$
$757$	45.0000			1.63555			0.817776	+	0.575536i	$0.195207\pi$
$758$	−34.6410	−	60.0000i	−1.25822	−	2.17930i
$759$	14.1962	−	3.80385i	0.515288	−	0.138071i
$760$	−17.5692	−	65.5692i	−0.637303	−	2.37845i
$761$	3.80385	+	14.1962i	0.137889	+	0.514610i	0.999969	+	0.00783777i	$0.00249487\pi$
$761$	3.80385	+	14.1962i	0.137889	+	0.514610i	−0.862080	+	0.506772i	$0.830838\pi$
$762$	12.0000	+	12.0000i	0.434714	+	0.434714i
$763$	−16.0000	−	27.7128i	−0.579239	−	1.00327i
$764$	−20.7846			−0.751961
$765$	−9.00000	−	9.00000i	−0.325396	−	0.325396i
$766$			66.0000i			2.38468i
$767$	17.4904	+	19.9019i	0.631541	+	0.718617i
$768$	−48.0000	+	27.7128i	−1.73205	+	1.00000i
$769$	−7.32051	−	27.3205i	−0.263984	−	0.985203i	−0.962869	−	0.269969i	$-0.912987\pi$
$769$	−7.32051	−	27.3205i	−0.263984	−	0.985203i	0.698885	−	0.715234i	$-0.253680\pi$
$770$	72.0000	+	41.5692i	2.59470	+	1.49805i
$771$	23.3827	−	13.5000i	0.842107	−	0.486191i
$772$	10.9282	+	2.92820i	0.393315	+	0.105388i
$773$	1.73205	+	1.73205i	0.0622975	+	0.0622975i	0.737569	−	0.675272i	$-0.235974\pi$
$773$	1.73205	+	1.73205i	0.0622975	+	0.0622975i	−0.675272	+	0.737569i	$0.735974\pi$
$774$	−46.7654	+	46.7654i	−1.68095	+	1.68095i
$775$	1.00000	+	1.00000i	0.0359211	+	0.0359211i
$776$	−60.0000	+	34.6410i	−2.15387	+	1.24354i
$777$	−6.92820			−0.248548
$778$	−45.0788	+	12.0788i	−1.61615	+	0.433047i
$779$	20.7846	−	36.0000i	0.744686	−	1.28983i
$780$	57.9615	+	19.6077i	2.07536	+	0.702068i
$781$	12.0000	+	20.7846i	0.429394	+	0.743732i
$782$	5.19615	+	5.19615i	0.185814	+	0.185814i
$783$	9.00000	+	15.5885i	0.321634	+	0.557086i
$784$		−	4.00000i		−	0.142857i
$785$	4.43782	−	16.5622i	0.158393	−	0.591129i
$786$	−63.8827	+	17.1173i	−2.27862	+	0.610554i
$787$	35.5167	−	9.51666i	1.26603	−	0.339232i	0.437523	−	0.899207i	$-0.355856\pi$
$787$	35.5167	−	9.51666i	1.26603	−	0.339232i	0.828509	+	0.559975i	$0.189189\pi$
$788$	−17.7513	−	66.2487i	−0.632363	−	2.36001i
$789$	3.00000			0.106803
$790$	−15.5885	+	9.00000i	−0.554612	+	0.320206i
$791$	−3.46410	+	3.46410i	−0.123169	+	0.123169i
$792$	−62.3538	−	36.0000i	−2.21565	−	1.27920i
$793$	9.00000	+	6.00000i	0.319599	+	0.213066i
$794$	−6.00000	+	3.46410i	−0.212932	+	0.122936i
$795$	1.90192	−	7.09808i	0.0674543	−	0.251743i
$796$	26.0000	−	45.0333i	0.921546	−	1.59616i
$797$	−5.19615	+	9.00000i	−0.184057	+	0.318796i	−0.943258	−	0.332060i	$-0.892256\pi$
$797$	−5.19615	+	9.00000i	−0.184057	+	0.318796i	0.759201	+	0.650856i	$0.225590\pi$
$798$	65.5692	+	17.5692i	2.32113	+	0.621944i
$799$	4.09808	+	1.09808i	0.144980	+	0.0388471i
$800$		0			0
$801$	−42.5885	−	11.4115i	−1.50479	−	0.403207i
$802$	−24.0000			−0.847469
$803$	24.2487	+	42.0000i	0.855718	+	1.48215i
$804$	−55.4256	+	55.4256i	−1.95471	+	1.95471i
$805$	10.3923	+	6.00000i	0.366281	+	0.211472i
$806$	11.1962	−	5.53590i	0.394368	−	0.194994i
$807$	9.00000	−	15.5885i	0.316815	−	0.548740i
$808$	57.3731	+	15.3731i	2.01838	+	0.540823i
$809$		−	8.66025i		−	0.304478i	−0.988344	−	0.152239i	$-0.951352\pi$
$809$		−	8.66025i		−	0.304478i	0.988344	−	0.152239i	$-0.0486484\pi$
$810$	46.7654	+	27.0000i	1.64317	+	0.948683i
$811$	14.0000	−	14.0000i	0.491606	−	0.491606i	−0.417206	−	0.908812i	$-0.636991\pi$
$811$	14.0000	−	14.0000i	0.491606	−	0.491606i	0.908812	+	0.417206i	$0.136991\pi$
$812$	10.1436	−	37.8564i	0.355970	−	1.32850i
$813$	8.87564	+	33.1244i	0.311282	+	1.16172i
$814$	16.3923	−	4.39230i	0.574550	−	0.153950i
$815$	−3.00000	−	1.73205i	−0.105085	−	0.0606711i
$816$		−	12.0000i		−	0.420084i
$817$	−13.1769	+	49.1769i	−0.461002	+	1.72048i
$818$	−58.8897			−2.05903
$819$	−22.9808	+	20.1962i	−0.803013	+	0.705711i
$820$	−72.0000			−2.51435
$821$	−13.9474	+	52.0526i	−0.486769	+	1.81665i	0.0851901	+	0.996365i	$0.472850\pi$
$821$	−13.9474	+	52.0526i	−0.486769	+	1.81665i	−0.571959	+	0.820282i	$0.693816\pi$
$822$		0			0
$823$	−33.7750	−	19.5000i	−1.17732	−	0.679727i	−0.221929	−	0.975063i	$-0.571235\pi$
$823$	−33.7750	−	19.5000i	−1.17732	−	0.679727i	−0.955394	+	0.295336i	$0.904569\pi$
$824$	−85.1769	+	22.8231i	−2.96728	+	0.795080i
$825$	8.19615	+	2.19615i	0.285353	+	0.0764602i
$826$	13.1769	−	49.1769i	0.458483	−	1.71108i
$827$	24.2487	−	24.2487i	0.843210	−	0.843210i	−0.146065	−	0.989275i	$-0.546661\pi$
$827$	24.2487	−	24.2487i	0.843210	−	0.843210i	0.989275	+	0.146065i	$0.0466608\pi$
$828$	−18.0000	−	10.3923i	−0.625543	−	0.361158i
$829$			32.0000i			1.11141i	0.831381	+	0.555703i	$0.187551\pi$
$829$			32.0000i			1.11141i	−0.831381	+	0.555703i	$0.812449\pi$
$830$	−14.1962	−	3.80385i	−0.492756	−	0.132033i
$831$	20.7846			0.721010
$832$	−12.7846	−	25.8564i	−0.443227	−	0.896410i
$833$	−1.50000	−	0.866025i	−0.0519719	−	0.0300060i
$834$	12.0788	+	45.0788i	0.418256	+	1.56095i
$835$	−15.0000	−	25.9808i	−0.519096	−	0.899101i
$836$	−110.851			−3.83387
$837$	7.09808	−	1.90192i	0.245345	−	0.0657401i
$838$	3.00000	−	3.00000i	0.103633	−	0.103633i
$839$	14.1962	+	3.80385i	0.490106	+	0.131323i	0.495404	−	0.868663i	$-0.335020\pi$
$839$	14.1962	+	3.80385i	0.490106	+	0.131323i	−0.00529863	+	0.999986i	$0.501687\pi$
$840$	−15.2154	−	56.7846i	−0.524981	−	1.95926i
$841$	−8.50000	+	14.7224i	−0.293103	+	0.507670i
$842$	−22.5167	+	39.0000i	−0.775975	+	1.34403i
$843$	30.0000	+	30.0000i	1.03325	+	1.03325i
$844$	−31.1769	+	18.0000i	−1.07315	+	0.619586i
$845$	−12.1244	+	29.4449i	−0.417091	+	1.01293i
$846$	−18.0000			−0.618853
$847$	26.0000	−	26.0000i	0.893371	−	0.893371i
$848$	6.00000	−	3.46410i	0.206041	−	0.118958i
$849$	19.9186	+	34.5000i	0.683604	+	1.18404i
$850$	1.09808	+	4.09808i	0.0376637	+	0.140563i
$851$	2.36603	−	0.633975i	0.0811063	−	0.0217324i
$852$	8.78461	−	32.7846i	0.300956	−	1.12318i
$853$	2.56218	−	9.56218i	0.0877273	−	0.327403i	−0.908089	−	0.418776i	$-0.862459\pi$
$853$	2.56218	−	9.56218i	0.0877273	−	0.327403i	0.995817	+	0.0913737i	$0.0291258\pi$
$854$		−	20.7846i		−	0.711235i
$855$	41.5692			1.42164
$856$	−42.0000	−	42.0000i	−1.43553	−	1.43553i
$857$	−1.73205	−	3.00000i	−0.0591657	−	0.102478i	0.834925	−	0.550363i	$-0.185511\pi$
$857$	−1.73205	−	3.00000i	−0.0591657	−	0.102478i	−0.894091	+	0.447885i	$0.852177\pi$
$858$	41.5692	−	62.3538i	1.41915	−	2.12872i
$859$	−19.5000	+	33.7750i	−0.665331	+	1.15239i	0.313864	+	0.949468i	$0.398376\pi$
$859$	−19.5000	+	33.7750i	−0.665331	+	1.15239i	−0.979195	+	0.202920i	$0.934957\pi$
$860$	85.1769	−	22.8231i	2.90451	−	0.778261i
$861$	18.0000	−	31.1769i	0.613438	−	1.06251i
$862$	62.3538	−	36.0000i	2.12378	−	1.22616i
$863$	10.3923	+	10.3923i	0.353758	+	0.353758i	0.861506	−	0.507748i	$-0.169522\pi$
$863$	10.3923	+	10.3923i	0.353758	+	0.353758i	−0.507748	+	0.861506i	$0.669522\pi$
$864$		0			0
$865$	−3.00000	−	3.00000i	−0.102003	−	0.102003i
$866$	44.9545	+	12.0455i	1.52762	+	0.409323i
$867$	21.0000	+	12.1244i	0.713197	+	0.411765i
$868$	−13.8564	−	8.00000i	−0.470317	−	0.271538i
$869$	3.80385	+	14.1962i	0.129037	+	0.481571i
$870$		−	36.0000i		−	1.22051i
$871$	−26.9282	−	30.6410i	−0.912427	−	1.03823i
$872$		−	55.4256i		−	1.87695i
$873$	−10.9808	−	40.9808i	−0.371642	−	1.38699i
$874$	−24.0000			−0.811812
$875$	−13.8564	−	24.0000i	−0.468432	−	0.811348i
$876$	17.7513	−	66.2487i	0.599760	−	2.23834i
$877$	−2.92820	−	10.9282i	−0.0988784	−	0.369019i	0.898701	−	0.438563i	$-0.144512\pi$
$877$	−2.92820	−	10.9282i	−0.0988784	−	0.369019i	−0.997579	+	0.0695437i	$0.977846\pi$
$878$	−9.50962	−	35.4904i	−0.320934	−	1.19774i
$879$	−2.19615	+	8.19615i	−0.0740744	+	0.276449i
$880$	24.0000	+	41.5692i	0.809040	+	1.40130i
$881$	−8.66025			−0.291771			−0.145886	−	0.989301i	$-0.546603\pi$
$881$	−8.66025			−0.291771			−0.145886	+	0.989301i	$0.546603\pi$
$882$	7.09808	+	1.90192i	0.239005	+	0.0640411i
$883$		−	26.0000i		−	0.874970i	−0.899226	−	0.437485i	$-0.855869\pi$
$883$		−	26.0000i		−	0.874970i	0.899226	−	0.437485i	$-0.144131\pi$
$884$	24.9282	+	1.60770i	0.838426	+	0.0540726i
$885$		−	31.1769i		−	1.04800i
$886$	−20.8634	−	77.8634i	−0.700921	−	2.61587i
$887$	−43.5000	−	25.1147i	−1.46059	−	0.843270i	−0.461549	−	0.887115i	$-0.652706\pi$
$887$	−43.5000	−	25.1147i	−1.46059	−	0.843270i	−0.999038	+	0.0438445i	$0.986039\pi$
$888$	−10.3923	−	6.00000i	−0.348743	−	0.201347i
$889$	10.9282	+	2.92820i	0.366520	+	0.0982088i
$890$	62.3538	+	62.3538i	2.09011	+	2.09011i
$891$	31.1769	−	31.1769i	1.04447	−	1.04447i
$892$	8.00000	+	8.00000i	0.267860	+	0.267860i
$893$	−12.0000	+	6.92820i	−0.401565	+	0.231843i
$894$	31.1769	−	54.0000i	1.04271	−	1.80603i
$895$	20.4904	−	5.49038i	0.684918	−	0.183523i
$896$	−27.7128	+	48.0000i	−0.925820	+	1.60357i
$897$	6.00000	−	9.00000i	0.200334	−	0.300501i
$898$	45.0000	+	77.9423i	1.50167	+	2.60097i
$899$	−3.46410	−	3.46410i	−0.115534	−	0.115534i
$900$	−6.00000	−	10.3923i	−0.200000	−	0.346410i
$901$		−	3.00000i		−	0.0999445i
$902$	−22.8231	+	85.1769i	−0.759926	+	2.83608i
$903$	−11.4115	+	42.5885i	−0.379752	+	1.41726i
$904$	−8.19615	+	2.19615i	−0.272600	+	0.0730429i
$905$	−1.90192	−	7.09808i	−0.0632221	−	0.235948i
$906$	33.0000	+	57.1577i	1.09635	+	1.89894i
$907$	−19.9186	+	11.5000i	−0.661386	+	0.381851i	−0.792805	−	0.609476i	$-0.791380\pi$
$907$	−19.9186	+	11.5000i	−0.661386	+	0.381851i	0.131419	+	0.991327i	$0.458047\pi$
$908$	6.92820	−	6.92820i	0.229920	−	0.229920i
$909$	−18.1865	+	31.5000i	−0.603209	+	1.04479i
$910$	60.0000	−	12.0000i	1.98898	−	0.397796i
$911$	−13.5000	+	7.79423i	−0.447275	+	0.258234i	−0.706679	−	0.707535i	$-0.749807\pi$
$911$	−13.5000	+	7.79423i	−0.447275	+	0.258234i	0.259404	+	0.965769i	$0.416474\pi$
$912$	27.7128	+	27.7128i	0.917663	+	0.917663i
$913$	−6.00000	+	10.3923i	−0.198571	+	0.343935i
$914$	22.5167	−	39.0000i	0.744785	−	1.29001i
$915$	−3.29423	−	12.2942i	−0.108904	−	0.406435i
$916$	−38.2487	−	10.2487i	−1.26377	−	0.338627i
$917$	−31.1769	+	31.1769i	−1.02955	+	1.02955i
$918$	21.2942	+	5.70577i	0.702814	+	0.188319i
$919$	57.0000			1.88026			0.940128	−	0.340821i	$-0.110705\pi$
$919$	57.0000			1.88026			0.940128	+	0.340821i	$0.110705\pi$
$920$	10.3923	+	18.0000i	0.342624	+	0.593442i
$921$	3.16987	+	11.8301i	0.104451	+	0.389816i
$922$		0			0
$923$	16.7321	+	5.66025i	0.550742	+	0.186310i
$924$	−96.0000			−3.15817
$925$	1.36603	+	0.366025i	0.0449146	+	0.0120348i
$926$			69.2820i			2.27675i
$927$		−	54.0000i		−	1.77359i
$928$		0			0
$929$	12.6795	−	47.3205i	0.416001	−	1.55254i	−0.366822	−	0.930291i	$-0.619554\pi$
$929$	12.6795	−	47.3205i	0.416001	−	1.55254i	0.782823	−	0.622244i	$-0.213779\pi$
$930$	−14.1962	−	3.80385i	−0.465510	−	0.124733i
$931$	5.46410	−	1.46410i	0.179079	−	0.0479840i
$932$	−66.0000	−	38.1051i	−2.16190	−	1.24817i
$933$	−36.3731	+	21.0000i	−1.19080	+	0.687509i
$934$	20.8634	−	77.8634i	0.682673	−	2.54777i
$935$	20.7846			0.679729
$936$	−51.9615	+	10.3923i	−1.69842	+	0.339683i
$937$	−3.00000			−0.0980057			−0.0490029	−	0.998799i	$-0.515604\pi$
$937$	−3.00000			−0.0980057			−0.0490029	+	0.998799i	$0.515604\pi$
$938$	−20.2872	+	75.7128i	−0.662400	+	2.47211i
$939$			20.7846i			0.678280i
$940$	20.7846	+	12.0000i	0.677919	+	0.391397i
$941$	11.8301	−	3.16987i	0.385651	−	0.103335i	−0.0607839	−	0.998151i	$-0.519360\pi$
$941$	11.8301	−	3.16987i	0.385651	−	0.103335i	0.446435	+	0.894816i	$0.352693\pi$
$942$	7.68653	+	28.6865i	0.250441	+	0.934658i
$943$	−3.29423	+	12.2942i	−0.107275	+	0.400355i
$944$	20.7846	−	20.7846i	0.676481	−	0.676481i
$945$	36.0000			1.17108
$946$		−	108.000i		−	3.51138i
$947$	−4.73205	−	1.26795i	−0.153771	−	0.0412028i	0.181112	−	0.983462i	$-0.442030\pi$
$947$	−4.73205	−	1.26795i	−0.153771	−	0.0412028i	−0.334883	+	0.942260i	$0.608697\pi$
$948$	10.3923	−	18.0000i	0.337526	−	0.584613i
$949$	33.8109	+	11.4378i	1.09755	+	0.371287i
$950$	−12.0000	−	6.92820i	−0.389331	−	0.224781i
$951$	−3.00000	+	3.00000i	−0.0972817	+	0.0972817i
$952$	−12.0000	−	20.7846i	−0.388922	−	0.673633i
$953$	−24.2487			−0.785493			−0.392746	−	0.919647i	$-0.628475\pi$
$953$	−24.2487			−0.785493			−0.392746	+	0.919647i	$0.628475\pi$
$954$	3.29423	+	12.2942i	0.106655	+	0.398040i
$955$	−9.00000	+	9.00000i	−0.291233	+	0.291233i
$956$	18.9282	+	5.07180i	0.612182	+	0.164034i
$957$	−28.3923	−	7.60770i	−0.917793	−	0.245922i
$958$	−45.0000	+	77.9423i	−1.45388	+	2.51820i
$959$		0			0
$960$	−8.78461	+	32.7846i	−0.283522	+	1.05812i
$961$	25.1147	−	14.5000i	0.810153	−	0.467742i
$962$	6.92820	−	10.3923i	0.223374	−	0.335061i
$963$	31.5000	−	18.1865i	1.01507	−	0.586053i
$964$	8.00000	−	8.00000i	0.257663	−	0.257663i
$965$	6.00000	−	3.46410i	0.193147	−	0.111513i
$966$	−20.7846			−0.668734
$967$	−0.366025	−	1.36603i	−0.0117706	−	0.0439284i	0.959791	−	0.280716i	$-0.0905720\pi$
$967$	−0.366025	−	1.36603i	−0.0117706	−	0.0439284i	−0.971561	+	0.236788i	$0.923905\pi$
$968$	61.5167	−	16.4833i	1.97722	−	0.529795i
$969$	16.3923	−	4.39230i	0.526597	−	0.141101i
$970$	−21.9615	+	81.9615i	−0.705142	+	2.63163i
$971$			24.2487i			0.778178i	0.921200	+	0.389089i	$0.127210\pi$
$971$			24.2487i			0.778178i	−0.921200	+	0.389089i	$0.872790\pi$
$972$	−62.3538			−2.00000
$973$	22.0000	+	22.0000i	0.705288	+	0.705288i
$974$	6.92820	+	12.0000i	0.221994	+	0.384505i
$975$	5.59808	−	2.76795i	0.179282	−	0.0886453i
$976$	6.00000	−	10.3923i	0.192055	−	0.332650i
$977$	11.8301	−	3.16987i	0.378479	−	0.101413i	−0.0645637	−	0.997914i	$-0.520566\pi$
$977$	11.8301	−	3.16987i	0.378479	−	0.101413i	0.443043	+	0.896500i	$0.353899\pi$
$978$	6.00000			0.191859
$979$	62.3538	−	36.0000i	1.99284	−	1.15056i
$980$	−6.92820	−	6.92820i	−0.221313	−	0.221313i
$981$	32.7846	+	8.78461i	1.04673	+	0.280471i
$982$	24.0000	+	24.0000i	0.765871	+	0.765871i
$983$	21.2942	+	5.70577i	0.679180	+	0.181986i	0.581887	−	0.813270i	$-0.302315\pi$
$983$	21.2942	+	5.70577i	0.679180	+	0.181986i	0.0972937	+	0.995256i	$0.468981\pi$
$984$	54.0000	−	31.1769i	1.72146	−	0.993884i
$985$	−36.3731	−	21.0000i	−1.15894	−	0.669116i
$986$	−3.80385	−	14.1962i	−0.121139	−	0.452098i
$987$	−10.3923	+	6.00000i	−0.330791	+	0.190982i
$988$	−61.2820	+	53.8564i	−1.94964	+	1.71340i
$989$		−	15.5885i		−	0.495684i
$990$	−85.1769	+	22.8231i	−2.70710	+	0.725365i
$991$	−31.0000			−0.984747			−0.492374	−	0.870384i	$-0.663871\pi$
$991$	−31.0000			−0.984747			−0.492374	+	0.870384i	$0.663871\pi$
$992$		0			0
$993$	39.8372	+	39.8372i	1.26419	+	1.26419i
$994$	−8.78461	−	32.7846i	−0.278631	−	1.03986i
$995$	−8.24167	−	30.7583i	−0.261278	−	0.975105i
$996$	16.3923	−	4.39230i	0.519410	−	0.139176i
$997$	−21.5000	−	37.2391i	−0.680912	−	1.17937i	−0.974703	−	0.223504i	$-0.928250\pi$
$997$	−21.5000	−	37.2391i	−0.680912	−	1.17937i	0.293791	−	0.955870i	$-0.405083\pi$
$998$	48.4974			1.53516
$999$	5.19615	−	5.19615i	0.164399	−	0.164399i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.2.z.a.5.1	✓	4
3.2	odd	2		351.2.bc.a.44.1		4
9.2	odd	6	inner	117.2.z.a.83.1	yes	4
9.7	even	3		351.2.bc.a.278.1		4
13.8	odd	4	inner	117.2.z.a.86.1	yes	4
39.8	even	4		351.2.bc.a.125.1		4
117.34	odd	12		351.2.bc.a.8.1		4
117.47	even	12	inner	117.2.z.a.47.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.z.a.5.1	✓	4	1.1	even	1	trivial
117.2.z.a.47.1	yes	4	117.47	even	12	inner
117.2.z.a.83.1	yes	4	9.2	odd	6	inner
117.2.z.a.86.1	yes	4	13.8	odd	4	inner
351.2.bc.a.8.1		4	117.34	odd	12
351.2.bc.a.44.1		4	3.2	odd	2
351.2.bc.a.125.1		4	39.8	even	4
351.2.bc.a.278.1		4	9.7	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.z (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.633975 + 2.36603i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-3.46410 - 2.00000i) q^{4} +(-2.36603 + 0.633975i) q^{5} +(3.00000 - 3.00000i) q^{6} +(0.732051 - 2.73205i) q^{7} +(3.46410 - 3.46410i) q^{8} +(1.50000 + 2.59808i) q^{9} -6.00000i q^{10} +(-4.73205 - 1.26795i) q^{11} +(3.46410 + 6.00000i) q^{12} +(-3.23205 + 1.59808i) q^{13} +(6.00000 + 3.46410i) q^{14} +(4.09808 + 1.09808i) q^{15} +(2.00000 + 3.46410i) q^{16} +1.73205 q^{17} +(-7.09808 + 1.90192i) q^{18} +(-4.00000 + 4.00000i) q^{19} +(9.46410 + 2.53590i) q^{20} +(-3.46410 + 3.46410i) q^{21} +(6.00000 - 10.3923i) q^{22} +(0.866025 - 1.50000i) q^{23} +(-8.19615 + 2.19615i) q^{24} +(0.866025 - 0.500000i) q^{25} +(-1.73205 - 8.66025i) q^{26} -5.19615i q^{27} +(-8.00000 + 8.00000i) q^{28} +(-3.00000 + 1.73205i) q^{29} +(-5.19615 + 9.00000i) q^{30} +(0.366025 + 1.36603i) q^{31} +(6.00000 + 6.00000i) q^{33} +(-1.09808 + 4.09808i) q^{34} +6.92820i q^{35} -12.0000i q^{36} +(1.00000 + 1.00000i) q^{37} +(-6.92820 - 12.0000i) q^{38} +(6.23205 + 0.401924i) q^{39} +(-6.00000 + 10.3923i) q^{40} +(-7.09808 + 1.90192i) q^{41} +(-6.00000 - 10.3923i) q^{42} +(7.79423 - 4.50000i) q^{43} +(13.8564 + 13.8564i) q^{44} +(-5.19615 - 5.19615i) q^{45} +(3.00000 + 3.00000i) q^{46} +(2.36603 + 0.633975i) q^{47} -6.92820i q^{48} +(-0.866025 - 0.500000i) q^{49} +(0.633975 + 2.36603i) q^{50} +(-2.59808 - 1.50000i) q^{51} +(14.3923 + 0.928203i) q^{52} -1.73205i q^{53} +(12.2942 + 3.29423i) q^{54} +12.0000 q^{55} +(-6.92820 - 12.0000i) q^{56} +(9.46410 - 2.53590i) q^{57} +(-2.19615 - 8.19615i) q^{58} +(-1.90192 - 7.09808i) q^{59} +(-12.0000 - 12.0000i) q^{60} +(-1.50000 - 2.59808i) q^{61} -3.46410 q^{62} +(8.19615 - 2.19615i) q^{63} +8.00000i q^{64} +(6.63397 - 5.83013i) q^{65} +(-18.0000 + 10.3923i) q^{66} +(2.92820 + 10.9282i) q^{67} +(-6.00000 - 3.46410i) q^{68} +(-2.59808 + 1.50000i) q^{69} +(-16.3923 - 4.39230i) q^{70} +(-3.46410 - 3.46410i) q^{71} +(14.1962 + 3.80385i) q^{72} +(-7.00000 - 7.00000i) q^{73} +(-3.00000 + 1.73205i) q^{74} -1.73205 q^{75} +(21.8564 - 5.85641i) q^{76} +(-6.92820 + 12.0000i) q^{77} +(-4.90192 + 14.4904i) q^{78} +(-1.50000 - 2.59808i) q^{79} +(-6.92820 - 6.92820i) q^{80} +(-4.50000 + 7.79423i) q^{81} -18.0000i q^{82} +(0.633975 - 2.36603i) q^{83} +(18.9282 - 5.07180i) q^{84} +(-4.09808 + 1.09808i) q^{85} +(5.70577 + 21.2942i) q^{86} +6.00000 q^{87} +(-20.7846 + 12.0000i) q^{88} +(-10.3923 + 10.3923i) q^{89} +(15.5885 - 9.00000i) q^{90} +(2.00000 + 10.0000i) q^{91} +(-6.00000 + 3.46410i) q^{92} +(0.633975 - 2.36603i) q^{93} +(-3.00000 + 5.19615i) q^{94} +(6.92820 - 12.0000i) q^{95} +(-13.6603 - 3.66025i) q^{97} +(1.73205 - 1.73205i) q^{98} +(-3.80385 - 14.1962i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 6 q^{2} - 6 q^{3} - 6 q^{5} + 12 q^{6} - 4 q^{7} + 6 q^{9} - 12 q^{11} - 6 q^{13} + 24 q^{14} + 6 q^{15} + 8 q^{16} - 18 q^{18} - 16 q^{19} + 24 q^{20} + 24 q^{22} - 12 q^{24} - 32 q^{28} - 12 q^{29}+ \cdots - 36 q^{99}+O(q^{100}) \) 4 * q - 6 * q^2 - 6 * q^3 - 6 * q^5 + 12 * q^6 - 4 * q^7 + 6 * q^9 - 12 * q^11 - 6 * q^13 + 24 * q^14 + 6 * q^15 + 8 * q^16 - 18 * q^18 - 16 * q^19 + 24 * q^20 + 24 * q^22 - 12 * q^24 - 32 * q^28 - 12 * q^29 - 2 * q^31 + 24 * q^33 + 6 * q^34 + 4 * q^37 + 18 * q^39 - 24 * q^40 - 18 * q^41 - 24 * q^42 + 12 * q^46 + 6 * q^47 + 6 * q^50 + 16 * q^52 + 18 * q^54 + 48 * q^55 + 24 * q^57 + 12 * q^58 - 18 * q^59 - 48 * q^60 - 6 * q^61 + 12 * q^63 + 30 * q^65 - 72 * q^66 - 16 * q^67 - 24 * q^68 - 24 * q^70 + 36 * q^72 - 28 * q^73 - 12 * q^74 + 32 * q^76 - 30 * q^78 - 6 * q^79 - 18 * q^81 + 6 * q^83 + 48 * q^84 - 6 * q^85 + 54 * q^86 + 24 * q^87 + 8 * q^91 - 24 * q^92 + 6 * q^93 - 12 * q^94 - 20 * q^97 - 36 * q^99

Introduction

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