LMFDB - Embedded newform 322.2.g.a.45.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [322,2,Mod(45,322)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(322, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 3]))

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

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

chi := DirichletCharacter("322.45");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 322 = 2 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	322.g (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:	$2.57118294509$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 18x^{14} + 226x^{12} + 1434x^{10} + 6585x^{8} + 14406x^{6} + 22423x^{4} + 8085x^{2} + 2401 $ x^16 + 18x^14 + 226x^12 + 1434x^10 + 6585x^8 + 14406x^6 + 22423x^4 + 8085*x^2 + 2401
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 7 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			45.3
Root			$-0.768626 - 1.33130i$ of defining polynomial
Character	$\chi$	$=$	322.45
Dual form			322.2.g.a.229.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.508912 - 0.293820i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.863449 - 1.49554i) q^{5} +0.587641i q^{6} +(1.63208 + 2.08239i) q^{7} +1.00000 q^{8} +(-1.32734 - 2.29902i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.508912 - 0.293820i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.863449 - 1.49554i) q^{5} +0.587641i q^{6} +(1.63208 + 2.08239i) q^{7} +1.00000 q^{8} +(-1.32734 - 2.29902i) q^{9} +(-0.863449 + 1.49554i) q^{10} +(-3.46919 - 2.00294i) q^{11} +(0.508912 - 0.293820i) q^{12} -5.60127i q^{13} +(0.987361 - 2.45461i) q^{14} +1.01480i q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.91929 + 5.05637i) q^{17} +(-1.32734 + 2.29902i) q^{18} +(-0.863449 - 1.49554i) q^{19} +1.72690 q^{20} +(-0.218735 - 1.53929i) q^{21} +4.00587i q^{22} +(-4.78761 - 0.280648i) q^{23} +(-0.508912 - 0.293820i) q^{24} +(1.00891 - 1.74749i) q^{25} +(-4.85084 + 2.80063i) q^{26} +3.32292i q^{27} +(-2.61944 + 0.372226i) q^{28} -9.71950 q^{29} +(0.878839 - 0.507398i) q^{30} +(3.47311 + 2.00520i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(1.17701 + 2.03864i) q^{33} +5.83859 q^{34} +(1.70507 - 4.23886i) q^{35} +2.65468 q^{36} +(7.43623 - 4.29331i) q^{37} +(-0.863449 + 1.49554i) q^{38} +(-1.64577 + 2.85055i) q^{39} +(-0.863449 - 1.49554i) q^{40} -5.60127i q^{41} +(-1.22369 + 0.959074i) q^{42} -3.11579i q^{43} +(3.46919 - 2.00294i) q^{44} +(-2.29218 + 3.97017i) q^{45} +(2.15076 + 4.28652i) q^{46} +(6.35084 - 3.66666i) q^{47} +0.587641i q^{48} +(-1.67266 + 6.79722i) q^{49} -2.01782 q^{50} +(2.97133 - 1.71550i) q^{51} +(4.85084 + 2.80063i) q^{52} +(-2.09249 - 1.20810i) q^{53} +(2.87773 - 1.66146i) q^{54} +6.91773i q^{55} +(1.63208 + 2.08239i) q^{56} +1.01480i q^{57} +(4.85975 + 8.41733i) q^{58} +(5.45528 + 3.14961i) q^{59} +(-0.878839 - 0.507398i) q^{60} +(-1.19240 - 2.06529i) q^{61} -4.01040i q^{62} +(2.62113 - 6.51620i) q^{63} +1.00000 q^{64} +(-8.37690 + 4.83641i) q^{65} +(1.17701 - 2.03864i) q^{66} +(-9.25574 - 5.34380i) q^{67} +(-2.91929 - 5.05637i) q^{68} +(2.35401 + 1.54952i) q^{69} +(-4.52350 + 0.642796i) q^{70} +11.7373 q^{71} +(-1.32734 - 2.29902i) q^{72} +(3.47311 + 2.00520i) q^{73} +(-7.43623 - 4.29331i) q^{74} +(-1.02689 + 0.592878i) q^{75} +1.72690 q^{76} +(-1.49109 - 10.4931i) q^{77} +3.29153 q^{78} +(8.75788 - 5.05637i) q^{79} +(-0.863449 + 1.49554i) q^{80} +(-3.00568 + 5.20598i) q^{81} +(-4.85084 + 2.80063i) q^{82} +14.8417 q^{83} +(1.44243 + 0.580214i) q^{84} +10.0826 q^{85} +(-2.69835 + 1.55789i) q^{86} +(4.94637 + 2.85579i) q^{87} +(-3.46919 - 2.00294i) q^{88} +(7.80182 + 13.5131i) q^{89} +4.58436 q^{90} +(11.6640 - 9.14169i) q^{91} +(2.63685 - 4.00587i) q^{92} +(-1.17834 - 2.04094i) q^{93} +(-6.35084 - 3.66666i) q^{94} +(-1.49109 + 2.58264i) q^{95} +(0.508912 - 0.293820i) q^{96} -15.4996 q^{97} +(6.72290 - 1.95004i) q^{98} +10.6343i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{2} + 6 q^{3} - 8 q^{4} + 16 q^{8} + 10 q^{9}+O(q^{10}) $ 16 * q - 8 * q^2 + 6 * q^3 - 8 * q^4 + 16 * q^8 + 10 * q^9	$ 16 q - 8 q^{2} + 6 q^{3} - 8 q^{4} + 16 q^{8} + 10 q^{9} - 6 q^{12} - 8 q^{16} + 10 q^{18} - 4 q^{23} + 6 q^{24} + 2 q^{25} - 6 q^{26} + 16 q^{29} - 24 q^{31} - 8 q^{32} + 4 q^{35} - 20 q^{36} + 22 q^{39} - 4 q^{46} + 30 q^{47} - 58 q^{49} - 4 q^{50} + 6 q^{52} + 54 q^{54} - 8 q^{58} + 36 q^{59} + 16 q^{64} - 32 q^{70} - 12 q^{71} + 10 q^{72} - 24 q^{73} - 96 q^{75} - 38 q^{77} - 44 q^{78} - 36 q^{81} - 6 q^{82} + 24 q^{85} + 42 q^{87} + 8 q^{92} - 38 q^{93} - 30 q^{94} - 38 q^{95} - 6 q^{96} + 56 q^{98}+O(q^{100}) $ 16 * q - 8 * q^2 + 6 * q^3 - 8 * q^4 + 16 * q^8 + 10 * q^9 - 6 * q^12 - 8 * q^16 + 10 * q^18 - 4 * q^23 + 6 * q^24 + 2 * q^25 - 6 * q^26 + 16 * q^29 - 24 * q^31 - 8 * q^32 + 4 * q^35 - 20 * q^36 + 22 * q^39 - 4 * q^46 + 30 * q^47 - 58 * q^49 - 4 * q^50 + 6 * q^52 + 54 * q^54 - 8 * q^58 + 36 * q^59 + 16 * q^64 - 32 * q^70 - 12 * q^71 + 10 * q^72 - 24 * q^73 - 96 * q^75 - 38 * q^77 - 44 * q^78 - 36 * q^81 - 6 * q^82 + 24 * q^85 + 42 * q^87 + 8 * q^92 - 38 * q^93 - 30 * q^94 - 38 * q^95 - 6 * q^96 + 56 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/322\mathbb{Z}\right)^\times$.

$n$	$185$	$281$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	−0.508912	−	0.293820i	−0.293820	−	0.169637i	0.345843	−	0.938292i	$-0.387593\pi$
$3$	−0.508912	−	0.293820i	−0.293820	−	0.169637i	−0.639663	+	0.768655i	$0.720926\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.863449	−	1.49554i	−0.386146	−	0.668825i	0.605781	−	0.795631i	$-0.292861\pi$
$5$	−0.863449	−	1.49554i	−0.386146	−	0.668825i	−0.991927	+	0.126806i	$0.959527\pi$
$6$			0.587641i			0.239903i
$7$	1.63208	+	2.08239i	0.616866	+	0.787068i
$7$	1.63208	+	2.08239i	0.616866	+	0.787068i
$8$	1.00000			0.353553
$9$	−1.32734	−	2.29902i	−0.442446	−	0.766340i
$10$	−0.863449	+	1.49554i	−0.273047	+	0.472930i
$11$	−3.46919	−	2.00294i	−1.04600	−	0.603908i	−0.124472	−	0.992223i	$-0.539724\pi$
$11$	−3.46919	−	2.00294i	−1.04600	−	0.603908i	−0.921527	+	0.388315i	$0.873057\pi$
$12$	0.508912	−	0.293820i	0.146910	−	0.0848187i
$13$		−	5.60127i		−	1.55351i	−0.629802	−	0.776756i	$-0.716864\pi$
$13$		−	5.60127i		−	1.55351i	0.629802	−	0.776756i	$-0.283136\pi$
$14$	0.987361	−	2.45461i	0.263883	−	0.656023i
$15$			1.01480i			0.262019i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.91929	+	5.05637i	−0.708033	+	1.22635i	0.257553	+	0.966264i	$0.417084\pi$
$17$	−2.91929	+	5.05637i	−0.708033	+	1.22635i	−0.965586	+	0.260085i	$0.916249\pi$
$18$	−1.32734	+	2.29902i	−0.312857	+	0.541884i
$19$	−0.863449	−	1.49554i	−0.198089	−	0.343100i	0.749820	−	0.661642i	$-0.230140\pi$
$19$	−0.863449	−	1.49554i	−0.198089	−	0.343100i	−0.947909	+	0.318542i	$0.896807\pi$
$20$	1.72690			0.386146
$21$	−0.218735	−	1.53929i	−0.0477319	−	0.335900i
$22$			4.00587i			0.854054i
$23$	−4.78761	−	0.280648i	−0.998286	−	0.0585191i
$23$	−4.78761	−	0.280648i	−0.998286	−	0.0585191i
$24$	−0.508912	−	0.293820i	−0.103881	−	0.0599758i
$25$	1.00891	−	1.74749i	0.201782	−	0.349497i
$26$	−4.85084	+	2.80063i	−0.951328	+	0.549249i
$27$			3.32292i			0.639496i
$28$	−2.61944	+	0.372226i	−0.495027	+	0.0703441i
$29$	−9.71950			−1.80487			−0.902433	−	0.430830i	$-0.858221\pi$
$29$	−9.71950			−1.80487			−0.902433	+	0.430830i	$0.858221\pi$
$30$	0.878839	−	0.507398i	0.160453	−	0.0926378i
$31$	3.47311	+	2.00520i	0.623788	+	0.360144i	0.778342	−	0.627840i	$-0.216061\pi$
$31$	3.47311	+	2.00520i	0.623788	+	0.360144i	−0.154554	+	0.987984i	$0.549394\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	1.17701	+	2.03864i	0.204891	+	0.354881i
$34$	5.83859			1.00131
$35$	1.70507	−	4.23886i	0.288210	−	0.716499i
$36$	2.65468			0.442446
$37$	7.43623	−	4.29331i	1.22251	−	0.705816i	0.257057	−	0.966396i	$-0.417247\pi$
$37$	7.43623	−	4.29331i	1.22251	−	0.705816i	0.965452	+	0.260581i	$0.0839140\pi$
$38$	−0.863449	+	1.49554i	−0.140070	+	0.242608i
$39$	−1.64577	+	2.85055i	−0.263534	+	0.456453i
$40$	−0.863449	−	1.49554i	−0.136523	−	0.236465i
$41$		−	5.60127i		−	0.874771i	−0.899274	−	0.437385i	$-0.855905\pi$
$41$		−	5.60127i		−	0.874771i	0.899274	−	0.437385i	$-0.144095\pi$
$42$	−1.22369	+	0.959074i	−0.188820	+	0.147988i
$43$		−	3.11579i		−	0.475153i	−0.971369	−	0.237577i	$-0.923647\pi$
$43$		−	3.11579i		−	0.475153i	0.971369	−	0.237577i	$-0.0763531\pi$
$44$	3.46919	−	2.00294i	0.522999	−	0.301954i
$45$	−2.29218	+	3.97017i	−0.341698	+	0.591838i
$46$	2.15076	+	4.28652i	0.317112	+	0.632013i
$47$	6.35084	−	3.66666i	0.926365	−	0.534837i	0.0407049	−	0.999171i	$-0.487040\pi$
$47$	6.35084	−	3.66666i	0.926365	−	0.534837i	0.885660	+	0.464334i	$0.153706\pi$
$48$			0.587641i			0.0848187i
$49$	−1.67266	+	6.79722i	−0.238952	+	0.971031i
$50$	−2.01782			−0.285363
$51$	2.97133	−	1.71550i	0.416069	−	0.240218i
$52$	4.85084	+	2.80063i	0.672690	+	0.388378i
$53$	−2.09249	−	1.20810i	−0.287425	−	0.165945i	0.349355	−	0.936991i	$-0.386401\pi$
$53$	−2.09249	−	1.20810i	−0.287425	−	0.165945i	−0.636780	+	0.771045i	$0.719734\pi$
$54$	2.87773	−	1.66146i	0.391610	−	0.226096i
$55$			6.91773i			0.932786i
$56$	1.63208	+	2.08239i	0.218095	+	0.278271i
$57$			1.01480i			0.134413i
$58$	4.85975	+	8.41733i	0.638116	+	1.10525i
$59$	5.45528	+	3.14961i	0.710217	+	0.410044i	0.811141	−	0.584850i	$-0.198847\pi$
$59$	5.45528	+	3.14961i	0.710217	+	0.410044i	−0.100924	+	0.994894i	$0.532180\pi$
$60$	−0.878839	−	0.507398i	−0.113458	−	0.0655048i
$61$	−1.19240	−	2.06529i	−0.152671	−	0.264433i	0.779538	−	0.626355i	$-0.215454\pi$
$61$	−1.19240	−	2.06529i	−0.152671	−	0.264433i	−0.932208	+	0.361922i	$0.882121\pi$
$62$		−	4.01040i		−	0.509321i
$63$	2.62113	−	6.51620i	0.330231	−	0.820964i
$64$	1.00000			0.125000
$65$	−8.37690	+	4.83641i	−1.03903	+	0.599882i
$66$	1.17701	−	2.03864i	0.144879	−	0.250939i
$67$	−9.25574	−	5.34380i	−1.13077	−	0.652850i	−0.186641	−	0.982428i	$-0.559760\pi$
$67$	−9.25574	−	5.34380i	−1.13077	−	0.652850i	−0.944128	+	0.329579i	$0.893093\pi$
$68$	−2.91929	−	5.05637i	−0.354016	−	0.613174i
$69$	2.35401	+	1.54952i	0.283390	+	0.186541i
$70$	−4.52350	+	0.642796i	−0.540662	+	0.0768288i
$71$	11.7373			1.39296			0.696482	−	0.717574i	$-0.254748\pi$
$71$	11.7373			1.39296			0.696482	+	0.717574i	$0.254748\pi$
$72$	−1.32734	−	2.29902i	−0.156428	−	0.270942i
$73$	3.47311	+	2.00520i	0.406496	+	0.234691i	0.689283	−	0.724492i	$-0.257926\pi$
$73$	3.47311	+	2.00520i	0.406496	+	0.234691i	−0.282787	+	0.959183i	$0.591259\pi$
$74$	−7.43623	−	4.29331i	−0.864444	−	0.499087i
$75$	−1.02689	+	0.592878i	−0.118576	+	0.0684596i
$76$	1.72690			0.198089
$77$	−1.49109	−	10.4931i	−0.169925	−	1.19580i
$78$	3.29153			0.372693
$79$	8.75788	−	5.05637i	0.985339	−	0.568886i	0.0814611	−	0.996677i	$-0.474041\pi$
$79$	8.75788	−	5.05637i	0.985339	−	0.568886i	0.903878	+	0.427791i	$0.140708\pi$
$80$	−0.863449	+	1.49554i	−0.0965365	+	0.167206i
$81$	−3.00568	+	5.20598i	−0.333964	+	0.578443i
$82$	−4.85084	+	2.80063i	−0.535686	+	0.309278i
$83$	14.8417			1.62909			0.814543	−	0.580103i	$-0.196988\pi$
$83$	14.8417			1.62909			0.814543	+	0.580103i	$0.196988\pi$
$84$	1.44243	+	0.580214i	0.157382	+	0.0633065i
$85$	10.0826			1.09362
$86$	−2.69835	+	1.55789i	−0.290971	+	0.167992i
$87$	4.94637	+	2.85579i	0.530306	+	0.306173i
$88$	−3.46919	−	2.00294i	−0.369816	−	0.213514i
$89$	7.80182	+	13.5131i	0.826991	+	1.43239i	0.900388	+	0.435088i	$0.143283\pi$
$89$	7.80182	+	13.5131i	0.826991	+	1.43239i	−0.0733966	+	0.997303i	$0.523384\pi$
$90$	4.58436			0.483234
$91$	11.6640	−	9.14169i	1.22272	−	0.958309i
$92$	2.63685	−	4.00587i	0.274911	−	0.417641i
$93$	−1.17834	−	2.04094i	−0.122188	−	0.211635i
$94$	−6.35084	−	3.66666i	−0.655039	−	0.378187i
$95$	−1.49109	+	2.58264i	−0.152982	+	0.264973i
$96$	0.508912	−	0.293820i	0.0519406	−	0.0299879i
$97$	−15.4996			−1.57374			−0.786872	−	0.617117i	$-0.788301\pi$
$97$	−15.4996			−1.57374			−0.786872	+	0.617117i	$0.788301\pi$
$98$	6.72290	−	1.95004i	0.679115	−	0.196984i
$99$			10.6343i			1.06879i
$100$	1.00891	+	1.74749i	0.100891	+	0.174749i
$101$	1.47326	+	0.850590i	0.146595	+	0.0846368i	0.571504	−	0.820600i	$-0.306360\pi$
$101$	1.47326	+	0.850590i	0.146595	+	0.0846368i	−0.424908	+	0.905236i	$0.639694\pi$
$102$	−2.97133	−	1.71550i	−0.294205	−	0.169859i
$103$	3.14024	+	5.43905i	0.309417	+	0.535926i	0.978235	−	0.207500i	$-0.0665328\pi$
$103$	3.14024	+	5.43905i	0.309417	+	0.535926i	−0.668818	+	0.743426i	$0.733199\pi$
$104$		−	5.60127i		−	0.549249i
$105$	−2.11320	+	1.65622i	−0.206227	+	0.161631i
$106$			2.41620i			0.234682i
$107$	9.14774	−	5.28145i	0.884345	−	0.510577i	0.0122565	−	0.999925i	$-0.496099\pi$
$107$	9.14774	−	5.28145i	0.884345	−	0.510577i	0.872089	+	0.489348i	$0.162765\pi$
$108$	−2.87773	−	1.66146i	−0.276910	−	0.159874i
$109$	−0.770835	−	0.445042i	−0.0738326	−	0.0426273i	0.462629	−	0.886552i	$-0.346906\pi$
$109$	−0.770835	−	0.445042i	−0.0738326	−	0.0426273i	−0.536462	+	0.843925i	$0.680239\pi$
$110$	5.99093	−	3.45886i	0.571213	−	0.329790i
$111$	−5.04585			−0.478931
$112$	0.987361	−	2.45461i	0.0932969	−	0.231939i
$113$		−	20.5509i		−	1.93327i	−0.256162	−	0.966634i	$-0.582458\pi$
$113$		−	20.5509i		−	1.93327i	0.256162	−	0.966634i	$-0.417542\pi$
$114$	0.878839	−	0.507398i	0.0823108	−	0.0475222i
$115$	3.71414	+	7.40238i	0.346345	+	0.690275i
$116$	4.85975	−	8.41733i	0.451216	−	0.781530i
$117$	−12.8774	+	7.43478i	−1.19052	+	0.687346i
$118$		−	6.29922i		−	0.579890i
$119$	−15.2938	+	2.17327i	−1.40198	+	0.199224i
$120$			1.01480i			0.0926378i
$121$	2.52350	+	4.37083i	0.229409	+	0.397348i
$122$	−1.19240	+	2.06529i	−0.107955	+	0.186983i
$123$	−1.64577	+	2.85055i	−0.148394	+	0.257026i
$124$	−3.47311	+	2.00520i	−0.311894	+	0.180072i
$125$	−12.1191			−1.08396
$126$	−6.95376	+	0.988140i	−0.619490	+	0.0880305i
$127$	−16.7195			−1.48362			−0.741808	−	0.670612i	$-0.766031\pi$
$127$	−16.7195			−1.48362			−0.741808	+	0.670612i	$0.766031\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−0.915482	+	1.58566i	−0.0806037	+	0.139610i
$130$	8.37690	+	4.83641i	0.734703	+	0.424181i
$131$	5.41948	−	3.12894i	0.473502	−	0.273376i	−0.244203	−	0.969724i	$-0.578526\pi$
$131$	5.41948	−	3.12894i	0.473502	−	0.273376i	0.717704	+	0.696348i	$0.245193\pi$
$132$	−2.35401			−0.204891
$133$	1.70507	−	4.23886i	0.147849	−	0.367556i
$134$			10.6876i			0.923269i
$135$	4.96955	−	2.86917i	0.427711	−	0.246939i
$136$	−2.91929	+	5.05637i	−0.250327	+	0.433580i
$137$	−6.55739	−	3.78591i	−0.560236	−	0.323452i	0.193004	−	0.981198i	$-0.438177\pi$
$137$	−6.55739	−	3.78591i	−0.560236	−	0.323452i	−0.753240	+	0.657746i	$0.771510\pi$
$138$	0.164920	−	2.81340i	0.0140389	−	0.239492i
$139$			11.0200i			0.934705i	0.884071	+	0.467352i	$0.154792\pi$
$139$			11.0200i			0.934705i	−0.884071	+	0.467352i	$0.845208\pi$
$140$	2.81843	+	3.59607i	0.238201	+	0.303923i
$141$	−4.30936			−0.362913
$142$	−5.86866	−	10.1648i	−0.492487	−	0.853013i
$143$	−11.2190	+	19.4318i	−0.938178	+	1.62497i
$144$	−1.32734	+	2.29902i	−0.110612	+	0.191585i
$145$	8.39229	+	14.5359i	0.696942	+	1.20714i
$146$		−	4.01040i		−	0.331903i
$147$	2.84840	−	2.96772i	0.234932	−	0.244774i
$148$			8.58662i			0.705816i
$149$	−6.93837	+	4.00587i	−0.568414	+	0.328174i	−0.756515	−	0.653976i	$-0.773100\pi$
$149$	−6.93837	+	4.00587i	−0.568414	+	0.328174i	0.188102	+	0.982150i	$0.439766\pi$
$150$	1.02689	+	0.592878i	0.0838456	+	0.0484083i
$151$	−5.15468	+	8.92816i	−0.419482	+	0.726564i	−0.995887	−	0.0906000i	$-0.971122\pi$
$151$	−5.15468	+	8.92816i	−0.419482	+	0.726564i	0.576406	+	0.817164i	$0.304455\pi$
$152$	−0.863449	−	1.49554i	−0.0700350	−	0.121304i
$153$	15.4996			1.25307
$154$	−8.34177	+	6.53788i	−0.672199	+	0.526838i
$155$		−	6.92555i		−	0.556273i
$156$	−1.64577	−	2.85055i	−0.131767	−	0.228227i
$157$	−4.04427	+	7.00488i	−0.322768	+	0.559050i	−0.981058	−	0.193714i	$-0.937947\pi$
$157$	−4.04427	+	7.00488i	−0.322768	+	0.559050i	0.658290	+	0.752764i	$0.271280\pi$
$158$	−8.75788	−	5.05637i	−0.696740	−	0.402263i
$159$	0.709928	+	1.22963i	0.0563010	+	0.0975161i
$160$	1.72690			0.136523
$161$	−7.22933	−	10.4277i	−0.569751	−	0.821817i
$162$	6.01135			0.472296
$163$	0.672661	+	1.16508i	0.0526869	+	0.0912563i	0.891166	−	0.453677i	$-0.149888\pi$
$163$	0.672661	+	1.16508i	0.0526869	+	0.0912563i	−0.838479	+	0.544934i	$0.816555\pi$
$164$	4.85084	+	2.80063i	0.378787	+	0.218693i
$165$	2.03257	−	3.52051i	0.158235	−	0.274072i
$166$	−7.42084	−	12.8533i	−0.575969	−	0.997607i
$167$		−	17.0172i		−	1.31683i	−0.752655	−	0.658415i	$-0.771227\pi$
$167$		−	17.0172i		−	1.31683i	0.752655	−	0.658415i	$-0.228773\pi$
$168$	−0.218735	−	1.53929i	−0.0168758	−	0.118759i
$169$	−18.3742			−1.41340
$170$	−5.04132	−	8.73183i	−0.386652	−	0.669701i
$171$	−2.29218	+	3.97017i	−0.175287	+	0.303607i
$172$	2.69835	+	1.55789i	0.205747	+	0.118788i
$173$	4.41072	−	2.54653i	0.335341	−	0.193609i	−0.322869	−	0.946444i	$-0.604647\pi$
$173$	4.41072	−	2.54653i	0.335341	−	0.193609i	0.658210	+	0.752834i	$0.271314\pi$
$174$		−	5.71158i		−	0.432993i
$175$	5.28556	−	0.751086i	0.399551	−	0.0567768i
$176$			4.00587i			0.301954i
$177$	−1.85084	−	3.20575i	−0.139118	−	0.240959i
$178$	7.80182	−	13.5131i	0.584771	−	1.01285i
$179$	−3.82734	+	6.62915i	−0.286069	+	0.495486i	−0.972868	−	0.231362i	$-0.925682\pi$
$179$	−3.82734	+	6.62915i	−0.286069	+	0.495486i	0.686799	+	0.726847i	$0.259015\pi$
$180$	−2.29218	−	3.97017i	−0.170849	−	0.295919i
$181$	10.9152			0.811322			0.405661	−	0.914024i	$-0.367041\pi$
$181$	10.9152			0.811322			0.405661	+	0.914024i	$0.367041\pi$
$182$	−13.7489	−	5.53047i	−1.01914	−	0.409946i
$183$			1.40140i			0.103595i
$184$	−4.78761	−	0.280648i	−0.352948	−	0.0206896i
$185$	−12.8416	−	7.41411i	−0.944134	−	0.545096i
$186$	−1.17834	+	2.04094i	−0.0863998	+	0.149649i
$187$	20.2551	−	11.6943i	1.48120	−	0.855173i
$188$			7.33332i			0.534837i
$189$	−6.91960	+	5.42326i	−0.503327	+	0.394484i
$190$	2.98218			0.216350
$191$	−8.64988	+	4.99401i	−0.625883	+	0.361354i	−0.779156	−	0.626830i	$-0.784352\pi$
$191$	−8.64988	+	4.99401i	−0.625883	+	0.361354i	0.153273	+	0.988184i	$0.451019\pi$
$192$	−0.508912	−	0.293820i	−0.0367276	−	0.0212047i
$193$	10.3150	−	17.8662i	0.742492	−	1.28603i	−0.208865	−	0.977944i	$-0.566977\pi$
$193$	10.3150	−	17.8662i	0.742492	−	1.28603i	0.951357	−	0.308090i	$-0.0996897\pi$
$194$	7.74979	+	13.4230i	0.556402	+	0.963717i
$195$	5.68414			0.407050
$196$	−5.05024	−	4.84718i	−0.360731	−	0.346227i
$197$	5.41662			0.385918			0.192959	−	0.981207i	$-0.438192\pi$
$197$	5.41662			0.385918			0.192959	+	0.981207i	$0.438192\pi$
$198$	9.20957	−	5.31715i	0.654496	−	0.377873i
$199$	−3.50583	+	6.07227i	−0.248522	+	0.430452i	−0.963116	−	0.269087i	$-0.913278\pi$
$199$	−3.50583	+	6.07227i	−0.248522	+	0.430452i	0.714594	+	0.699539i	$0.246611\pi$
$200$	1.00891	−	1.74749i	0.0713408	−	0.123566i
$201$	3.14024	+	5.43905i	0.221495	+	0.383641i
$202$		−	1.70118i		−	0.119695i
$203$	−15.8630	−	20.2398i	−1.11336	−	1.42055i
$204$			3.43099i			0.240218i
$205$	−8.37690	+	4.83641i	−0.585068	+	0.337789i
$206$	3.14024	−	5.43905i	0.218791	−	0.378957i
$207$	5.70957	+	11.3793i	0.396843	+	0.790918i
$208$	−4.85084	+	2.80063i	−0.336345	+	0.194189i
$209$			6.91773i			0.478509i
$210$	2.49093	+	1.00197i	0.171890	+	0.0691425i
$211$	3.97539			0.273677			0.136838	−	0.990593i	$-0.456306\pi$
$211$	3.97539			0.273677			0.136838	+	0.990593i	$0.456306\pi$
$212$	2.09249	−	1.20810i	0.143713	−	0.0829726i
$213$	−5.97326	−	3.44867i	−0.409281	−	0.236299i
$214$	−9.14774	−	5.28145i	−0.625326	−	0.361032i
$215$	−4.65978	+	2.69032i	−0.317794	+	0.183479i
$216$			3.32292i			0.226096i
$217$	1.49277	+	10.5050i	0.101336	+	0.713124i
$218$			0.890083i			0.0602841i
$219$	−1.17834	−	2.04094i	−0.0796246	−	0.137914i
$220$	−5.99093	−	3.45886i	−0.403908	−	0.233197i
$221$	28.3221	+	16.3517i	1.90515	+	1.09994i
$222$	2.52292	+	4.36983i	0.169328	+	0.293284i
$223$			11.2439i			0.752946i	0.926428	+	0.376473i	$0.122863\pi$
$223$			11.2439i			0.752946i	−0.926428	+	0.376473i	$0.877137\pi$
$224$	−2.61944	+	0.372226i	−0.175018	+	0.0248704i
$225$	−5.35667			−0.357112
$226$	−17.7976	+	10.2755i	−1.18388	+	0.683513i
$227$	7.19990	−	12.4706i	0.477874	−	0.827702i	−0.521804	−	0.853065i	$-0.674741\pi$
$227$	7.19990	−	12.4706i	0.477874	−	0.827702i	0.999678	+	0.0253633i	$0.00807426\pi$
$228$	−0.878839	−	0.507398i	−0.0582025	−	0.0336032i
$229$	−10.6537	−	18.4527i	−0.704016	−	1.21939i	−0.967046	−	0.254603i	$-0.918055\pi$
$229$	−10.6537	−	18.4527i	−0.704016	−	1.21939i	0.263030	−	0.964788i	$-0.415278\pi$
$230$	4.55358	−	6.91773i	0.300254	−	0.456142i
$231$	−2.32426	+	5.77819i	−0.152925	+	0.380177i
$232$	−9.71950			−0.638116
$233$	3.74697	+	6.48995i	0.245472	+	0.425171i	0.962264	−	0.272116i	$-0.0877236\pi$
$233$	3.74697	+	6.48995i	0.245472	+	0.425171i	−0.716792	+	0.697287i	$0.754390\pi$
$234$	12.8774	+	7.43478i	0.841823	+	0.486027i
$235$	−10.9672	−	6.33194i	−0.715424	−	0.413051i
$236$	−5.45528	+	3.14961i	−0.355109	+	0.205022i
$237$	−5.94265			−0.386017
$238$	9.52902	+	12.1582i	0.617674	+	0.788099i
$239$	−8.53607			−0.552152			−0.276076	−	0.961136i	$-0.589034\pi$
$239$	−8.53607			−0.552152			−0.276076	+	0.961136i	$0.589034\pi$
$240$	0.878839	−	0.507398i	0.0567288	−	0.0327524i
$241$	14.1595	−	24.5250i	0.912095	−	1.57979i	0.100995	−	0.994887i	$-0.467797\pi$
$241$	14.1595	−	24.5250i	0.912095	−	1.57979i	0.811100	−	0.584908i	$-0.198869\pi$
$242$	2.52350	−	4.37083i	0.162217	−	0.280968i
$243$	11.6924	−	6.75064i	0.750071	−	0.433054i
$244$	2.38479			0.152671
$245$	11.6098	−	3.36753i	0.741720	−	0.215143i
$246$	3.29153			0.209860
$247$	−8.37690	+	4.83641i	−0.533010	+	0.307733i
$248$	3.47311	+	2.00520i	0.220542	+	0.127330i
$249$	−7.55311	−	4.36079i	−0.478659	−	0.276354i
$250$	6.05953	+	10.4954i	0.383238	+	0.663789i
$251$	−22.9918			−1.45123			−0.725614	−	0.688102i	$-0.758444\pi$
$251$	−22.9918			−1.45123			−0.725614	+	0.688102i	$0.758444\pi$
$252$	4.33263	+	5.52806i	0.272930	+	0.348235i
$253$	16.0470	+	10.5629i	1.00887	+	0.664084i
$254$	8.35975	+	14.4795i	0.524537	+	0.908525i
$255$	−5.13118	−	2.96249i	−0.321327	−	0.185518i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	24.3952	−	14.0846i	1.52173	−	0.878573i	0.522063	−	0.852907i	$-0.325163\pi$
$257$	24.3952	−	14.0846i	1.52173	−	0.878573i	0.999671	−	0.0256659i	$-0.00817062\pi$
$258$	1.83096			0.113991
$259$	21.0768	+	8.47810i	1.30965	+	0.526803i
$260$		−	9.67281i		−	0.599882i
$261$	12.9011	+	22.3453i	0.798556	+	1.38314i
$262$	−5.41948	−	3.12894i	−0.334816	−	0.193306i
$263$	−4.84588	−	2.79777i	−0.298810	−	0.172518i	0.343098	−	0.939300i	$-0.388524\pi$
$263$	−4.84588	−	2.79777i	−0.298810	−	0.172518i	−0.641908	+	0.766782i	$0.721857\pi$
$264$	1.17701	+	2.03864i	0.0724397	+	0.125469i
$265$			4.17253i			0.256316i
$266$	−4.52350	+	0.642796i	−0.277354	+	0.0394123i
$267$		−	9.16934i		−	0.561154i
$268$	9.25574	−	5.34380i	0.565384	−	0.326425i
$269$	−7.02689	−	4.05698i	−0.428437	−	0.247358i	0.270243	−	0.962792i	$-0.412896\pi$
$269$	−7.02689	−	4.05698i	−0.428437	−	0.247358i	−0.698681	+	0.715434i	$0.746229\pi$
$270$	−4.96955	−	2.86917i	−0.302437	−	0.174612i
$271$	−9.30596	+	5.37280i	−0.565297	+	0.326374i	−0.755269	−	0.655415i	$-0.772494\pi$
$271$	−9.30596	+	5.37280i	−0.565297	+	0.326374i	0.189972	+	0.981790i	$0.439160\pi$
$272$	5.83859			0.354016
$273$	−8.62196	+	1.22519i	−0.521825	+	0.0741521i
$274$			7.57182i			0.457431i
$275$	−7.00021	+	4.04157i	−0.422128	+	0.243716i
$276$	−2.51893	+	1.26387i	−0.151622	+	0.0760762i
$277$	−3.43136	+	5.94330i	−0.206171	+	0.357098i	−0.950505	−	0.310709i	$-0.899434\pi$
$277$	−3.43136	+	5.94330i	−0.206171	+	0.357098i	0.744334	+	0.667807i	$0.232767\pi$
$278$	9.54360	−	5.51000i	0.572387	−	0.330468i
$279$		−	10.6463i		−	0.637378i
$280$	1.70507	−	4.23886i	0.101898	−	0.253321i
$281$		−	4.76100i		−	0.284017i	−0.989865	−	0.142009i	$-0.954644\pi$
$281$		−	4.76100i		−	0.284017i	0.989865	−	0.142009i	$-0.0453561\pi$
$282$	2.15468	+	3.73201i	0.128309	+	0.222238i
$283$	4.69823	−	8.13756i	0.279280	−	0.483728i	−0.691926	−	0.721969i	$-0.743237\pi$
$283$	4.69823	−	8.13756i	0.279280	−	0.483728i	0.971206	+	0.238241i	$0.0765707\pi$
$284$	−5.86866	+	10.1648i	−0.348241	+	0.603171i
$285$	1.51766	−	0.876224i	0.0898987	−	0.0519030i
$286$	22.4379			1.32678
$287$	11.6640	−	9.14169i	0.688504	−	0.539617i
$288$	2.65468			0.156428
$289$	−8.54456	−	14.7996i	−0.502621	−	0.870565i
$290$	8.39229	−	14.5359i	0.492812	−	0.853576i
$291$	7.88792	+	4.55409i	0.462398	+	0.266966i
$292$	−3.47311	+	2.00520i	−0.203248	+	0.117345i
$293$	−10.7608			−0.628651			−0.314325	−	0.949315i	$-0.601778\pi$
$293$	−10.7608			−0.628651			−0.314325	+	0.949315i	$0.601778\pi$
$294$	−3.99432	−	0.982924i	−0.232954	−	0.0573253i
$295$		−	10.8781i		−	0.633348i
$296$	7.43623	−	4.29331i	0.432222	−	0.249544i
$297$	6.65559	−	11.5278i	0.386197	−	0.668912i
$298$	6.93837	+	4.00587i	0.401929	+	0.232054i
$299$	−1.57198	+	26.8167i	−0.0909101	+	1.55085i
$300$		−	1.18576i		−	0.0684596i
$301$	6.48827	−	5.08520i	0.373978	−	0.293106i
$302$	10.3094			0.593237
$303$	−0.499841	−	0.865750i	−0.0287151	−	0.0497361i
$304$	−0.863449	+	1.49554i	−0.0495222	+	0.0857750i
$305$	−2.05915	+	3.56655i	−0.117906	+	0.204220i
$306$	−7.74979	−	13.4230i	−0.443026	−	0.767343i
$307$		−	16.7244i		−	0.954510i	−0.878765	−	0.477255i	$-0.841632\pi$
$307$		−	16.7244i		−	0.954510i	0.878765	−	0.477255i	$-0.158368\pi$
$308$	9.83286	+	3.95524i	0.560279	+	0.225371i
$309$		−	3.69066i		−	0.209955i
$310$	−5.99770	+	3.46277i	−0.340646	+	0.196672i
$311$	18.8865	+	10.9041i	1.07095	+	0.618316i	0.928442	−	0.371477i	$-0.121149\pi$
$311$	18.8865	+	10.9041i	1.07095	+	0.618316i	0.142512	+	0.989793i	$0.454482\pi$
$312$	−1.64577	+	2.85055i	−0.0931732	+	0.161381i
$313$	−0.144647	−	0.250536i	−0.00817593	−	0.0141611i	0.861908	−	0.507064i	$-0.169269\pi$
$313$	−0.144647	−	0.250536i	−0.00817593	−	0.0141611i	−0.870084	+	0.492903i	$0.835936\pi$
$314$	8.08854			0.456462
$315$	−12.0084	+	1.70642i	−0.676599	+	0.0961457i
$316$			10.1127i			0.568886i
$317$	2.35651	+	4.08160i	0.132355	+	0.229246i	0.924584	−	0.380978i	$-0.124413\pi$
$317$	2.35651	+	4.08160i	0.132355	+	0.229246i	−0.792229	+	0.610224i	$0.791079\pi$
$318$	0.709928	−	1.22963i	0.0398108	−	0.0689543i
$319$	33.7188	+	19.4675i	1.88789	+	1.08997i
$320$	−0.863449	−	1.49554i	−0.0482683	−	0.0836031i
$321$	−6.20719			−0.346452
$322$	−5.41598	+	11.4746i	−0.301821	+	0.639456i
$323$	10.0826			0.561013
$324$	−3.00568	−	5.20598i	−0.166982	−	0.289221i
$325$	−9.78814	−	5.65118i	−0.542948	−	0.313471i
$326$	0.672661	−	1.16508i	0.0372552	−	0.0645280i
$327$	0.261525	+	0.452974i	0.0144623	+	0.0250495i
$328$		−	5.60127i		−	0.309278i
$329$	18.0004	+	7.24063i	0.992397	+	0.399189i
$330$	−4.06514			−0.223779
$331$	5.64237	+	9.77287i	0.310133	+	0.537166i	0.978391	−	0.206764i	$-0.0662932\pi$
$331$	5.64237	+	9.77287i	0.310133	+	0.537166i	−0.668258	+	0.743929i	$0.732960\pi$
$332$	−7.42084	+	12.8533i	−0.407271	+	0.705415i
$333$	−19.7408	−	11.3974i	−1.08179	−	0.624571i
$334$	−14.7373	+	8.50860i	−0.806391	+	0.465570i
$335$			18.4564i			1.00838i
$336$	−1.22369	+	0.959074i	−0.0667580	+	0.0523218i
$337$		−	8.65802i		−	0.471632i	−0.971798	−	0.235816i	$-0.924224\pi$
$337$		−	8.65802i		−	0.471632i	0.971798	−	0.235816i	$-0.0757763\pi$
$338$	9.18709	+	15.9125i	0.499712	+	0.865526i
$339$	−6.03828	+	10.4586i	−0.327954	+	0.568034i
$340$	−5.04132	+	8.73183i	−0.273404	+	0.473550i
$341$	−8.03257	−	13.9128i	−0.434988	−	0.753421i
$342$	4.58436			0.247894
$343$	−16.8843	+	7.61045i	−0.911669	+	0.410926i
$344$		−	3.11579i		−	0.167992i
$345$	0.284800	−	4.85845i	0.0153331	−	0.261570i
$346$	−4.41072	−	2.54653i	−0.237122	−	0.136902i
$347$	15.5647	−	26.9588i	0.835555	−	1.44722i	−0.0580229	−	0.998315i	$-0.518480\pi$
$347$	15.5647	−	26.9588i	0.835555	−	1.44722i	0.893578	−	0.448908i	$-0.148187\pi$
$348$	−4.94637	+	2.85579i	−0.265153	+	0.153086i
$349$		−	3.74843i		−	0.200649i	−0.994955	−	0.100324i	$-0.968012\pi$
$349$		−	3.74843i		−	0.200649i	0.994955	−	0.100324i	$-0.0319881\pi$
$350$	−3.29324	−	4.20189i	−0.176031	−	0.224600i
$351$	18.6126			0.993465
$352$	3.46919	−	2.00294i	0.184908	−	0.106757i
$353$	−1.18215	−	0.682515i	−0.0629195	−	0.0363266i	0.468210	−	0.883617i	$-0.344899\pi$
$353$	−1.18215	−	0.682515i	−0.0629195	−	0.0363266i	−0.531130	+	0.847291i	$0.678232\pi$
$354$	−1.85084	+	3.20575i	−0.0983710	+	0.170383i
$355$	−10.1346	−	17.5536i	−0.537888	−	0.931649i
$356$	−15.6036			−0.826991
$357$	8.42176	+	3.38763i	0.445727	+	0.179292i
$358$	7.65468			0.404562
$359$	2.92323	−	1.68773i	0.154282	−	0.0890749i	−0.420871	−	0.907120i	$-0.638276\pi$
$359$	2.92323	−	1.68773i	0.154282	−	0.0890749i	0.575154	+	0.818045i	$0.304942\pi$
$360$	−2.29218	+	3.97017i	−0.120808	+	0.209246i
$361$	8.00891	−	13.8718i	0.421522	−	0.730097i
$362$	−5.45761	−	9.45285i	−0.286846	−	0.496831i
$363$		−	2.96582i		−	0.155665i
$364$	2.08494	+	14.6722i	0.109280	+	0.769030i
$365$		−	6.92555i		−	0.362500i
$366$	1.21365	−	0.700701i	0.0634385	−	0.0366262i
$367$	6.79372	−	11.7671i	0.354630	−	0.614236i	−0.632425	−	0.774622i	$-0.717940\pi$
$367$	6.79372	−	11.7671i	0.354630	−	0.614236i	0.987054	+	0.160385i	$0.0512737\pi$
$368$	2.15076	+	4.28652i	0.112116	+	0.223450i
$369$	−12.8774	+	7.43478i	−0.670371	+	0.387039i
$370$			14.8282i			0.770882i
$371$	−0.899371	−	6.32908i	−0.0466930	−	0.328589i
$372$	2.35667			0.122188
$373$	−9.92344	+	5.72930i	−0.513816	+	0.296652i	−0.734401	−	0.678716i	$-0.762537\pi$
$373$	−9.92344	+	5.72930i	−0.513816	+	0.296652i	0.220585	+	0.975368i	$0.429203\pi$
$374$	−20.2551	−	11.6943i	−1.04737	−	0.604699i
$375$	6.16754	+	3.56083i	0.318490	+	0.183880i
$376$	6.35084	−	3.66666i	0.327519	−	0.189093i
$377$			54.4415i			2.80388i
$378$	8.15648	+	3.28092i	0.419524	+	0.168752i
$379$			3.50239i			0.179906i	0.995946	+	0.0899529i	$0.0286717\pi$
$379$			3.50239i			0.179906i	−0.995946	+	0.0899529i	$0.971328\pi$
$380$	−1.49109	−	2.58264i	−0.0764912	−	0.132487i
$381$	8.50875	+	4.91253i	0.435917	+	0.251677i
$382$	8.64988	+	4.99401i	0.442566	+	0.255516i
$383$	8.13077	+	14.0829i	0.415463	+	0.719603i	0.995477	−	0.0950037i	$-0.0302863\pi$
$383$	8.13077	+	14.0829i	0.415463	+	0.719603i	−0.580014	+	0.814606i	$0.696953\pi$
$384$			0.587641i			0.0299879i
$385$	−14.4054	+	11.2903i	−0.734166	+	0.575405i
$386$	−20.6301			−1.05004
$387$	−7.16325	+	4.13571i	−0.364129	+	0.210230i
$388$	7.74979	−	13.4230i	0.393436	−	0.681451i
$389$	16.3502	+	9.43980i	0.828989	+	0.478617i	0.853506	−	0.521083i	$-0.174472\pi$
$389$	16.3502	+	9.43980i	0.828989	+	0.478617i	−0.0245176	+	0.999699i	$0.507805\pi$
$390$	−2.84207	−	4.92261i	−0.143914	−	0.249266i
$391$	15.3955	−	23.3886i	0.778584	−	1.18281i
$392$	−1.67266	+	6.79722i	−0.0844821	+	0.343311i
$393$	−3.67738			−0.185499
$394$	−2.70831	−	4.69093i	−0.136443	−	0.236326i
$395$	−15.1240	−	8.73183i	−0.760969	−	0.439346i
$396$	−9.20957	−	5.31715i	−0.462798	−	0.267197i
$397$	−23.1989	+	13.3939i	−1.16432	+	0.672219i	−0.952335	−	0.305055i	$-0.901325\pi$
$397$	−23.1989	+	13.3939i	−1.16432	+	0.672219i	−0.211982	+	0.977273i	$0.567992\pi$
$398$	7.01166			0.351463
$399$	−2.11320	+	1.65622i	−0.105792	+	0.0829149i
$400$	−2.01782			−0.100891
$401$	3.02637	−	1.74728i	0.151130	−	0.0872548i	−0.422528	−	0.906350i	$-0.638857\pi$
$401$	3.02637	−	1.74728i	0.151130	−	0.0872548i	0.573658	+	0.819095i	$0.305524\pi$
$402$	3.14024	−	5.43905i	0.156621	−	0.271275i
$403$	11.2316	−	19.4538i	0.559488	−	0.969062i
$404$	−1.47326	+	0.850590i	−0.0732976	+	0.0423184i
$405$	10.3810			0.515836
$406$	−9.59666	+	23.8576i	−0.476274	+	1.18403i
$407$	−34.3969			−1.70499
$408$	2.97133	−	1.71550i	0.147103	−	0.0849297i
$409$	19.8178	+	11.4418i	0.979930	+	0.565763i	0.902249	−	0.431216i	$-0.141915\pi$
$409$	19.8178	+	11.4418i	0.979930	+	0.565763i	0.0776807	+	0.996978i	$0.475249\pi$
$410$	8.37690	+	4.83641i	0.413706	+	0.238853i
$411$	2.22476	+	3.85339i	0.109739	+	0.190074i
$412$	−6.28048			−0.309417
$413$	2.34473	+	16.5004i	0.115377	+	0.811932i
$414$	7.00000	−	10.6343i	0.344031	−	0.522647i
$415$	−12.8150	−	22.1963i	−0.629065	−	1.08957i
$416$	4.85084	+	2.80063i	0.237832	+	0.137312i
$417$	3.23790	−	5.60821i	0.158561	−	0.274635i
$418$	5.99093	−	3.45886i	0.293026	−	0.169179i
$419$	−13.9192			−0.680000			−0.340000	−	0.940425i	$-0.610427\pi$
$419$	−13.9192			−0.680000			−0.340000	+	0.940425i	$0.610427\pi$
$420$	−0.377733	−	2.65819i	−0.0184315	−	0.129707i
$421$			17.4351i			0.849736i	0.905255	+	0.424868i	$0.139680\pi$
$421$			17.4351i			0.849736i	−0.905255	+	0.424868i	$0.860320\pi$
$422$	−1.98769	−	3.44279i	−0.0967594	−	0.167592i
$423$	−16.8594	−	9.73380i	−0.819734	−	0.473273i
$424$	−2.09249	−	1.20810i	−0.101620	−	0.0586705i
$425$	5.89062	+	10.2029i	0.285737	+	0.494911i
$426$			6.89733i			0.334177i
$427$	2.35465	−	5.85374i	0.113950	−	0.283282i
$428$			10.5629i			0.510577i
$429$	11.4189	−	6.59273i	0.551312	−	0.318300i
$430$	4.65978	+	2.69032i	0.224714	+	0.129739i
$431$	−26.0665	−	15.0495i	−1.25558	−	0.724909i	−0.283368	−	0.959011i	$-0.591452\pi$
$431$	−26.0665	−	15.0495i	−1.25558	−	0.724909i	−0.972212	+	0.234102i	$0.924785\pi$
$432$	2.87773	−	1.66146i	0.138455	−	0.0799370i
$433$	−29.5615			−1.42064			−0.710319	−	0.703880i	$-0.751449\pi$
$433$	−29.5615			−1.42064			−0.710319	+	0.703880i	$0.751449\pi$
$434$	8.35119	−	6.54527i	0.400870	−	0.314183i
$435$		−	9.86331i		−	0.472909i
$436$	0.770835	−	0.445042i	0.0369163	−	0.0213136i
$437$	3.71414	+	7.40238i	0.177671	+	0.354104i
$438$	−1.17834	+	2.04094i	−0.0563031	+	0.0975198i
$439$	−13.2106	+	7.62714i	−0.630507	+	0.364023i	−0.780948	−	0.624596i	$-0.785264\pi$
$439$	−13.2106	+	7.62714i	−0.630507	+	0.364023i	0.150441	+	0.988619i	$0.451931\pi$
$440$			6.91773i			0.329790i
$441$	17.8471	−	5.17674i	0.849863	−	0.246511i
$442$		−	32.7035i		−	1.55555i
$443$	−4.24072	−	7.34514i	−0.201483	−	0.348978i	0.747524	−	0.664235i	$-0.231243\pi$
$443$	−4.24072	−	7.34514i	−0.201483	−	0.348978i	−0.949006	+	0.315257i	$0.897909\pi$
$444$	2.52292	−	4.36983i	0.119733	−	0.207383i
$445$	13.4729	−	23.3358i	0.638679	−	1.10622i
$446$	9.73748	−	5.62194i	0.461083	−	0.266207i
$447$	4.70803			0.222682
$448$	1.63208	+	2.08239i	0.0771083	+	0.0983835i
$449$	−4.82792			−0.227843			−0.113922	−	0.993490i	$-0.536341\pi$
$449$	−4.82792			−0.227843			−0.113922	+	0.993490i	$0.536341\pi$
$450$	2.67834	+	4.63901i	0.126258	+	0.218685i
$451$	−11.2190	+	19.4318i	−0.528281	+	0.915009i
$452$	17.7976	+	10.2755i	0.837129	+	0.483317i
$453$	5.24655	−	3.02910i	0.246505	−	0.142320i
$454$	−14.3998			−0.675816
$455$	−23.7430	−	9.55056i	−1.11309	−	0.447737i
$456$			1.01480i			0.0475222i
$457$	−8.59484	+	4.96223i	−0.402049	+	0.232123i	−0.687368	−	0.726309i	$-0.741234\pi$
$457$	−8.59484	+	4.96223i	−0.402049	+	0.232123i	0.285318	+	0.958433i	$0.407901\pi$
$458$	−10.6537	+	18.4527i	−0.497814	+	0.862240i
$459$	−16.8019	−	9.70058i	−0.784246	−	0.452784i
$460$	−8.26772	−	0.484650i	−0.385484	−	0.0225969i
$461$		−	24.1817i		−	1.12625i	−0.826370	−	0.563127i	$-0.809598\pi$
$461$		−	24.1817i		−	1.12625i	0.826370	−	0.563127i	$-0.190402\pi$
$462$	6.16619	−	0.876224i	0.286877	−	0.0407656i
$463$	−11.4928			−0.534115			−0.267058	−	0.963681i	$-0.586051\pi$
$463$	−11.4928			−0.534115			−0.267058	+	0.963681i	$0.586051\pi$
$464$	4.85975	+	8.41733i	0.225608	+	0.390765i
$465$	−2.03487	+	3.52449i	−0.0943647	+	0.163444i
$466$	3.74697	−	6.48995i	0.173575	−	0.300641i
$467$	0.441887	+	0.765371i	0.0204481	+	0.0354172i	0.876068	−	0.482187i	$-0.160157\pi$
$467$	0.441887	+	0.765371i	0.0204481	+	0.0354172i	−0.855620	+	0.517604i	$0.826824\pi$
$468$		−	14.8696i		−	0.687346i
$469$	−3.97820	−	27.9955i	−0.183696	−	1.29271i
$470$			12.6639i			0.584142i
$471$	4.11635	−	2.37658i	0.189672	−	0.109507i
$472$	5.45528	+	3.14961i	0.251100	+	0.144972i
$473$	−6.24072	+	10.8092i	−0.286949	+	0.497010i
$474$	2.97133	+	5.14649i	0.136478	+	0.236386i
$475$	−3.48458			−0.159883
$476$	5.76480	−	14.3315i	0.264229	−	0.656882i
$477$			6.41423i			0.293687i
$478$	4.26803	+	7.39245i	0.195215	+	0.338123i
$479$	−1.87154	+	3.24161i	−0.0855131	+	0.148113i	−0.905610	−	0.424112i	$-0.860586\pi$
$479$	−1.87154	+	3.24161i	−0.0855131	+	0.148113i	0.820097	+	0.572225i	$0.193920\pi$
$480$	−0.878839	−	0.507398i	−0.0401133	−	0.0231594i
$481$	−24.0480	−	41.6523i	−1.09649	−	1.89918i
$482$	−28.3190			−1.28990
$483$	0.615221	+	7.43090i	0.0279935	+	0.338118i
$484$	−5.04700			−0.229409
$485$	13.3831	+	23.1802i	0.607695	+	1.05256i
$486$	−11.6924	−	6.75064i	−0.530380	−	0.306215i
$487$	−15.4635	+	26.7835i	−0.700716	+	1.21368i	0.267499	+	0.963558i	$0.413803\pi$
$487$	−15.4635	+	26.7835i	−0.700716	+	1.21368i	−0.968215	+	0.250118i	$0.919531\pi$
$488$	−1.19240	−	2.06529i	−0.0539773	−	0.0934913i
$489$		−	0.790566i		−	0.0357506i
$490$	−8.72124	−	8.37058i	−0.393985	−	0.378144i
$491$	7.43932			0.335732			0.167866	−	0.985810i	$-0.446312\pi$
$491$	7.43932			0.335732			0.167866	+	0.985810i	$0.446312\pi$
$492$	−1.64577	−	2.85055i	−0.0741969	−	0.128513i
$493$	28.3741	−	49.1454i	1.27790	−	2.21340i
$494$	8.37690	+	4.83641i	0.376895	+	0.217600i
$495$	15.9040	−	9.18217i	0.714831	−	0.412708i
$496$		−	4.01040i		−	0.180072i
$497$	19.1562	+	24.4416i	0.859273	+	1.09636i
$498$			8.72158i			0.390823i
$499$	6.40771	+	11.0985i	0.286848	+	0.496836i	0.973056	−	0.230570i	$-0.0740591\pi$
$499$	6.40771	+	11.0985i	0.286848	+	0.496836i	−0.686207	+	0.727406i	$0.740726\pi$
$500$	6.05953	−	10.4954i	0.270991	−	0.469369i
$501$	−5.00000	+	8.66025i	−0.223384	+	0.386912i
$502$	11.4959	+	19.9115i	0.513087	+	0.888692i
$503$	1.59205			0.0709861			0.0354930	−	0.999370i	$-0.488700\pi$
$503$	1.59205			0.0709861			0.0354930	+	0.999370i	$0.488700\pi$
$504$	2.62113	−	6.51620i	0.116754	−	0.290255i
$505$		−	2.93776i		−	0.130729i
$506$	1.12424	−	19.1786i	0.0499785	−	0.852591i
$507$	9.35084	+	5.39871i	0.415285	+	0.239765i
$508$	8.35975	−	14.4795i	0.370904	−	0.642424i
$509$	0.851794	−	0.491784i	0.0377551	−	0.0217979i	−0.481004	−	0.876719i	$-0.659728\pi$
$509$	0.851794	−	0.491784i	0.0377551	−	0.0217979i	0.518759	+	0.854921i	$0.326394\pi$
$510$			5.92497i			0.262362i
$511$	1.49277	+	10.5050i	0.0660364	+	0.464713i
$512$	1.00000			0.0441942
$513$	4.96955	−	2.86917i	0.219411	−	0.126677i
$514$	−24.3952	−	14.0846i	−1.07603	−	0.621245i
$515$	5.42287	−	9.39269i	0.238960	−	0.413891i
$516$	−0.915482	−	1.58566i	−0.0403018	−	0.0698048i
$517$	−29.3763			−1.29197
$518$	−3.19616	−	22.4921i	−0.140431	−	0.988246i
$519$	−2.99289			−0.131373
$520$	−8.37690	+	4.83641i	−0.367351	+	0.212090i
$521$	4.51786	−	7.82517i	0.197931	−	0.342827i	−0.749926	−	0.661521i	$-0.769911\pi$
$521$	4.51786	−	7.82517i	0.197931	−	0.342827i	0.947857	+	0.318695i	$0.103244\pi$
$522$	12.9011	−	22.3453i	0.564665	−	0.978028i
$523$	−2.74946	−	4.76220i	−0.120225	−	0.208236i	0.799631	−	0.600492i	$-0.205028\pi$
$523$	−2.74946	−	4.76220i	−0.120225	−	0.208236i	−0.919856	+	0.392255i	$0.871695\pi$
$524$			6.25787i			0.273376i
$525$	−2.91057	−	1.17077i	−0.127028	−	0.0510966i
$526$			5.59554i			0.243977i
$527$	−20.2780	+	11.7075i	−0.883325	+	0.509988i
$528$	1.17701	−	2.03864i	0.0512226	−	0.0887202i
$529$	22.8425	+	2.68726i	0.993151	+	0.116838i
$530$	3.61351	−	2.08626i	0.156961	−	0.0906215i
$531$		−	16.7224i		−	0.725690i
$532$	2.81843	+	3.59607i	0.122194	+	0.155909i
$533$	−31.3742			−1.35897
$534$	−7.94088	+	4.58467i	−0.343635	+	0.198398i
$535$	−15.7972	−	9.12052i	−0.682973	−	0.394315i
$536$	−9.25574	−	5.34380i	−0.399787	−	0.230817i
$537$	3.89556	−	2.24910i	0.168106	−	0.0970559i
$538$			8.11396i			0.349818i
$539$	19.4172	−	20.2306i	0.836356	−	0.871393i
$540$			5.73834i			0.246939i
$541$	−1.91963	−	3.32490i	−0.0825315	−	0.142949i	0.821805	−	0.569769i	$-0.192967\pi$
$541$	−1.91963	−	3.32490i	−0.0825315	−	0.142949i	−0.904337	+	0.426820i	$0.859634\pi$
$542$	9.30596	+	5.37280i	0.399725	+	0.230781i
$543$	−5.55488	−	3.20711i	−0.238383	−	0.137630i
$544$	−2.91929	−	5.05637i	−0.125164	−	0.216790i
$545$			1.53708i			0.0658414i
$546$	5.37203	+	6.85424i	0.229902	+	0.293334i
$547$	28.7241			1.22815			0.614076	−	0.789247i	$-0.289529\pi$
$547$	28.7241			1.22815			0.614076	+	0.789247i	$0.289529\pi$
$548$	6.55739	−	3.78591i	0.280118	−	0.161726i
$549$	−3.16543	+	5.48268i	−0.135097	+	0.233995i
$550$	7.00021	+	4.04157i	0.298490	+	0.172333i
$551$	8.39229	+	14.5359i	0.357524	+	0.619249i
$552$	2.35401	+	1.54952i	0.100193	+	0.0659521i
$553$	24.8228	+	9.98492i	1.05557	+	0.424602i
$554$	6.86273			0.291569
$555$	4.35683	+	7.54625i	0.184937	+	0.320321i
$556$	−9.54360	−	5.51000i	−0.404739	−	0.233676i
$557$	38.8444	+	22.4268i	1.64589	+	0.950255i	0.978681	+	0.205384i	$0.0658445\pi$
$557$	38.8444	+	22.4268i	1.64589	+	0.950255i	0.667209	+	0.744871i	$0.267489\pi$
$558$	−9.21998	+	5.32316i	−0.390313	+	0.225347i
$559$	−17.4524			−0.738156
$560$	−4.52350	+	0.642796i	−0.191153	+	0.0271631i
$561$	−13.7441			−0.580277
$562$	−4.12314	+	2.38050i	−0.173924	+	0.100415i
$563$	2.20937	−	3.82673i	0.0931137	−	0.161278i	−0.815706	−	0.578467i	$-0.803651\pi$
$563$	2.20937	−	3.82673i	0.0931137	−	0.161278i	0.908820	+	0.417189i	$0.136985\pi$
$564$	2.15468	−	3.73201i	0.0907283	−	0.157146i
$565$	−30.7347	+	17.7447i	−1.29302	+	0.746524i
$566$	−9.39645			−0.394962
$567$	−15.7464	+	2.23758i	−0.661285	+	0.0939695i
$568$	11.7373			0.492487
$569$	−1.59671	+	0.921863i	−0.0669377	+	0.0386465i	−0.533095	−	0.846055i	$-0.678971\pi$
$569$	−1.59671	+	0.921863i	−0.0669377	+	0.0386465i	0.466158	+	0.884702i	$0.345638\pi$
$570$	−1.51766	−	0.876224i	−0.0635680	−	0.0367010i
$571$	−5.07756	−	2.93153i	−0.212489	−	0.122681i	0.389979	−	0.920824i	$-0.372482\pi$
$571$	−5.07756	−	2.93153i	−0.212489	−	0.122681i	−0.602468	+	0.798143i	$0.705816\pi$
$572$	−11.2190	−	19.4318i	−0.469089	−	0.812486i
$573$	5.86937			0.245196
$574$	−13.7489	−	5.53047i	−0.573869	−	0.230838i
$575$	−5.32071	+	8.08314i	−0.221889	+	0.337090i
$576$	−1.32734	−	2.29902i	−0.0553058	−	0.0957924i
$577$	−28.5416	−	16.4785i	−1.18820	−	0.686009i	−0.230304	−	0.973119i	$-0.573972\pi$
$577$	−28.5416	−	16.4785i	−1.18820	−	0.686009i	−0.957898	+	0.287110i	$0.907305\pi$
$578$	−8.54456	+	14.7996i	−0.355407	+	0.615583i
$579$	−10.4989	+	6.06153i	−0.436319	+	0.251909i
$580$	−16.7846			−0.696942
$581$	24.2227	+	30.9061i	1.00493	+	1.28220i
$582$		−	9.10818i		−	0.377546i
$583$	4.83949	+	8.38224i	0.200431	+	0.347157i
$584$	3.47311	+	2.00520i	0.143718	+	0.0829757i
$585$	22.2380	+	12.8391i	0.919427	+	0.530832i
$586$	5.38038	+	9.31910i	0.222262	+	0.384968i
$587$			26.6670i			1.10066i	0.834946	+	0.550331i	$0.185499\pi$
$587$			26.6670i			1.10066i	−0.834946	+	0.550331i	$0.814501\pi$
$588$	1.14593	+	3.95065i	0.0472572	+	0.162922i
$589$		−	6.92555i		−	0.285362i
$590$	−9.42071	+	5.43905i	−0.387845	+	0.223922i
$591$	−2.75658	−	1.59151i	−0.113391	−	0.0654661i
$592$	−7.43623	−	4.29331i	−0.305627	−	0.176454i
$593$	15.9371	−	9.20131i	0.654460	−	0.377853i	−0.135703	−	0.990750i	$-0.543329\pi$
$593$	15.9371	−	9.20131i	0.654460	−	0.377853i	0.790163	+	0.612897i	$0.209996\pi$
$594$	−13.3112			−0.546165
$595$	16.4556	+	20.9960i	0.674615	+	0.860750i
$596$		−	8.01174i		−	0.328174i
$597$	3.56832	−	2.06017i	0.146041	−	0.0843171i
$598$	24.0099	−	12.0470i	0.981839	−	0.492637i
$599$	−8.29477	+	14.3670i	−0.338915	+	0.587018i	−0.984229	−	0.176899i	$-0.943393\pi$
$599$	−8.29477	+	14.3670i	−0.338915	+	0.587018i	0.645314	+	0.763918i	$0.276727\pi$
$600$	−1.02689	+	0.592878i	−0.0419228	+	0.0242041i
$601$			19.4387i			0.792921i	0.918052	+	0.396460i	$0.129762\pi$
$601$			19.4387i			0.792921i	−0.918052	+	0.396460i	$0.870238\pi$
$602$	−7.64805	−	3.07641i	−0.311711	−	0.125385i
$603$			28.3722i			1.15540i
$604$	−5.15468	−	8.92816i	−0.209741	−	0.363282i
$605$	4.35783	−	7.54798i	0.177171	−	0.306869i
$606$	−0.499841	+	0.865750i	−0.0203047	+	0.0351687i
$607$	−12.4276	+	7.17507i	−0.504420	+	0.291227i	−0.730537	−	0.682873i	$-0.760730\pi$
$607$	−12.4276	+	7.17507i	−0.504420	+	0.291227i	0.226117	+	0.974100i	$0.427397\pi$
$608$	1.72690			0.0700350
$609$	2.12600	+	14.9611i	0.0861497	+	0.606255i
$610$	4.11829			0.166745
$611$	−20.5379	−	35.5727i	−0.830876	−	1.43912i
$612$	−7.74979	+	13.4230i	−0.313267	+	0.542594i
$613$	17.0749	+	9.85818i	0.689648	+	0.398168i	0.803480	−	0.595332i	$-0.202979\pi$
$613$	17.0749	+	9.85818i	0.689648	+	0.398168i	−0.113832	+	0.993500i	$0.536313\pi$
$614$	−14.4837	+	8.36218i	−0.584515	+	0.337470i
$615$	5.68414			0.229207
$616$	−1.49109	−	10.4931i	−0.0600777	−	0.422780i
$617$		−	27.5354i		−	1.10853i	−0.832339	−	0.554267i	$-0.812999\pi$
$617$		−	27.5354i		−	1.10853i	0.832339	−	0.554267i	$-0.187001\pi$
$618$	−3.19621	+	1.84533i	−0.128570	+	0.0742301i
$619$	−13.6801	+	23.6946i	−0.549848	+	0.952365i	0.448436	+	0.893815i	$0.351981\pi$
$619$	−13.6801	+	23.6946i	−0.549848	+	0.952365i	−0.998284	+	0.0585501i	$0.981352\pi$
$620$	5.99770	+	3.46277i	0.240873	+	0.139068i
$621$	0.932570	−	15.9089i	0.0374227	−	0.638400i
$622$		−	21.8082i		−	0.874431i
$623$	−15.4064	+	38.3009i	−0.617246	+	1.53449i
$624$	3.29153			0.131767
$625$	5.41963	+	9.38708i	0.216785	+	0.375483i
$626$	−0.144647	+	0.250536i	−0.00578126	+	0.0100134i
$627$	2.03257	−	3.52051i	0.0811730	−	0.140596i
$628$	−4.04427	−	7.00488i	−0.161384	−	0.279525i
$629$			50.1337i			1.99896i
$630$	7.48202	+	9.54640i	0.298091	+	0.380338i
$631$			5.14760i			0.204923i	0.994737	+	0.102461i	$0.0326718\pi$
$631$			5.14760i			0.204923i	−0.994737	+	0.102461i	$0.967328\pi$
$632$	8.75788	−	5.05637i	0.348370	−	0.201131i
$633$	−2.02312	−	1.16805i	−0.0804118	−	0.0464258i
$634$	2.35651	−	4.08160i	0.0935891	−	0.162101i
$635$	14.4364	+	25.0046i	0.572892	+	0.992279i
$636$	−1.41986			−0.0563010
$637$	38.0730	+	9.36902i	1.50851	+	0.371214i
$638$		−	38.9351i		−	1.54145i
$639$	−15.5794	−	26.9843i	−0.616312	−	1.06748i
$640$	−0.863449	+	1.49554i	−0.0341308	+	0.0591163i
$641$	6.10570	+	3.52513i	0.241161	+	0.139234i	0.615710	−	0.787973i	$-0.288869\pi$
$641$	6.10570	+	3.52513i	0.241161	+	0.139234i	−0.374549	+	0.927207i	$0.622203\pi$
$642$	3.10360	+	5.37558i	0.122489	+	0.212157i
$643$	32.0178			1.26266			0.631329	−	0.775515i	$-0.282510\pi$
$643$	32.0178			1.26266			0.631329	+	0.775515i	$0.282510\pi$
$644$	12.6453	−	1.04693i	0.498295	−	0.0412550i
$645$	3.16189			0.124499
$646$	−5.04132	−	8.73183i	−0.198348	−	0.343549i
$647$	15.5852	+	8.99811i	0.612717	+	0.353752i	0.774028	−	0.633151i	$-0.218239\pi$
$647$	15.5852	+	8.99811i	0.612717	+	0.353752i	−0.161311	+	0.986904i	$0.551572\pi$
$648$	−3.00568	+	5.20598i	−0.118074	+	0.204510i
$649$	−12.6169	−	21.8532i	−0.495258	−	0.857811i
$650$			11.3024i			0.443315i
$651$	2.32689	−	5.78472i	0.0911979	−	0.226721i
$652$	−1.34532			−0.0526869
$653$	−8.72841	−	15.1181i	−0.341569	−	0.591615i	0.643155	−	0.765736i	$-0.277625\pi$
$653$	−8.72841	−	15.1181i	−0.341569	−	0.591615i	−0.984724	+	0.174121i	$0.944292\pi$
$654$	0.261525	−	0.452974i	0.0102264	−	0.0177127i
$655$	−9.35888	−	5.40335i	−0.365682	−	0.211126i
$656$	−4.85084	+	2.80063i	−0.189393	+	0.109346i
$657$		−	10.6463i		−	0.415352i
$658$	−2.72965	−	19.2092i	−0.106413	−	0.748851i
$659$		−	25.2564i		−	0.983849i	−0.870638	−	0.491924i	$-0.836294\pi$
$659$		−	25.2564i		−	0.983849i	0.870638	−	0.491924i	$-0.163706\pi$
$660$	2.03257	+	3.52051i	0.0791177	+	0.137036i
$661$	4.76959	−	8.26117i	0.185515	−	0.321322i	−0.758235	−	0.651982i	$-0.773938\pi$
$661$	4.76959	−	8.26117i	0.185515	−	0.321322i	0.943750	+	0.330660i	$0.107271\pi$
$662$	5.64237	−	9.77287i	0.219297	−	0.379834i
$663$	−9.60895	−	16.6432i	−0.373181	−	0.646368i
$664$	14.8417			0.575969
$665$	−7.81162	+	1.11004i	−0.302922	+	0.0430456i
$666$			22.7947i			0.883277i
$667$	46.5332	+	2.72775i	1.80177	+	0.105619i
$668$	14.7373	+	8.50860i	0.570204	+	0.329208i
$669$	3.30368	−	5.72214i	0.127728	−	0.221231i
$670$	15.9837	−	9.22821i	0.617505	−	0.356517i
$671$			9.55317i			0.368796i
$672$	1.44243	+	0.580214i	0.0556429	+	0.0223822i
$673$	27.5879			1.06344			0.531719	−	0.846921i	$-0.321546\pi$
$673$	27.5879			1.06344			0.531719	+	0.846921i	$0.321546\pi$
$674$	−7.49806	+	4.32901i	−0.288815	+	0.166747i
$675$	5.80676	+	3.35253i	0.223502	+	0.129039i
$676$	9.18709	−	15.9125i	0.353350	−	0.612019i
$677$	−8.61324	−	14.9186i	−0.331034	−	0.573367i	0.651681	−	0.758493i	$-0.274064\pi$
$677$	−8.61324	−	14.9186i	−0.331034	−	0.573367i	−0.982715	+	0.185126i	$0.940731\pi$
$678$	12.0766			0.463797
$679$	−25.2965	−	32.2761i	−0.970789	−	1.23864i
$680$	10.0826			0.386652
$681$	−7.32823	+	4.23095i	−0.280818	+	0.162130i
$682$	−8.03257	+	13.9128i	−0.307583	+	0.532749i
$683$	3.48865	−	6.04252i	0.133489	−	0.231210i	−0.791530	−	0.611130i	$-0.790715\pi$
$683$	3.48865	−	6.04252i	0.133489	−	0.231210i	0.925019	+	0.379920i	$0.124048\pi$
$684$	−2.29218	−	3.97017i	−0.0876437	−	0.151803i
$685$			13.0758i			0.499599i
$686$	15.0330	+	10.8170i	0.573963	+	0.412997i
$687$			12.5211i			0.477709i
$688$	−2.69835	+	1.55789i	−0.102874	+	0.0593941i
$689$	−6.76688	+	11.7206i	−0.257798	+	0.446519i
$690$	−4.34994	+	2.18258i	−0.165599	+	0.0830894i
$691$	−1.84914	+	1.06760i	−0.0703444	+	0.0406134i	−0.534760	−	0.845004i	$-0.679598\pi$
$691$	−1.84914	+	1.06760i	−0.0703444	+	0.0406134i	0.464415	+	0.885618i	$0.346265\pi$
$692$			5.09306i			0.193609i
$693$	−22.1447	+	17.3560i	−0.841208	+	0.659299i
$694$	−31.1293			−1.18165
$695$	16.4808	−	9.51521i	0.625153	−	0.360933i
$696$	4.94637	+	2.85579i	0.187492	+	0.108248i
$697$	28.3221	+	16.3517i	1.07277	+	0.619366i
$698$	−3.24624	+	1.87422i	−0.122872	+	0.0709401i
$699$		−	4.40375i		−	0.166565i
$700$	−1.99232	+	4.95297i	−0.0753027	+	0.187205i
$701$		−	15.7616i		−	0.595307i	−0.954674	−	0.297653i	$-0.903796\pi$
$701$		−	15.7616i		−	0.595307i	0.954674	−	0.297653i	$-0.0962040\pi$
$702$	−9.30628	−	16.1189i	−0.351243	−	0.608370i
$703$	−12.8416	−	7.41411i	−0.484330	−	0.279628i
$704$	−3.46919	−	2.00294i	−0.130750	−	0.0754885i
$705$	3.72091	+	6.44480i	0.140138	+	0.242725i
$706$			1.36503i			0.0513736i
$707$	0.633223	+	4.45613i	0.0238148	+	0.167590i
$708$	3.70168			0.139118
$709$	39.5534	−	22.8362i	1.48546	−	0.857630i	0.485596	−	0.874183i	$-0.338603\pi$
$709$	39.5534	−	22.8362i	1.48546	−	0.857630i	0.999863	+	0.0165529i	$0.00526919\pi$
$710$	−10.1346	+	17.5536i	−0.380344	+	0.658775i
$711$	−23.2494	−	13.4230i	−0.871919	−	0.503403i
$712$	7.80182	+	13.5131i	0.292386	+	0.506427i
$713$	−16.0651	−	10.5748i	−0.601644	−	0.396031i
$714$	−1.27710	−	8.98727i	−0.0477944	−	0.336340i
$715$	38.7480			1.44909
$716$	−3.82734	−	6.62915i	−0.143034	−	0.247743i
$717$	4.34411	+	2.50807i	0.162234	+	0.0936656i
$718$	−2.92323	−	1.68773i	−0.109094	−	0.0629855i
$719$	6.28093	−	3.62630i	0.234239	−	0.135238i	−0.378287	−	0.925688i	$-0.623487\pi$
$719$	6.28093	−	3.62630i	0.234239	−	0.135238i	0.612526	+	0.790450i	$0.290153\pi$
$720$	4.58436			0.170849
$721$	−6.20110	+	15.4161i	−0.230941	+	0.574127i
$722$	−16.0178			−0.596122
$723$	−14.4119	+	8.32071i	−0.535984	+	0.309451i
$724$	−5.45761	+	9.45285i	−0.202830	+	0.351313i
$725$	−9.80612	+	16.9847i	−0.364190	+	0.630796i
$726$	−2.56848	+	1.48291i	−0.0953252	+	0.0550360i
$727$	−12.5073			−0.463869			−0.231934	−	0.972731i	$-0.574505\pi$
$727$	−12.5073			−0.463869			−0.231934	+	0.972731i	$0.574505\pi$
$728$	11.6640	−	9.14169i	0.432296	−	0.338813i
$729$	10.1002			0.374080
$730$	−5.99770	+	3.46277i	−0.221985	+	0.128163i
$731$	15.7546	+	9.09590i	0.582703	+	0.336424i
$732$	−1.21365	−	0.700701i	−0.0448578	−	0.0258987i
$733$	−9.64817	−	16.7111i	−0.356363	−	0.617240i	0.630987	−	0.775793i	$-0.282650\pi$
$733$	−9.64817	−	16.7111i	−0.356363	−	0.617240i	−0.987350	+	0.158554i	$0.949317\pi$
$734$	−13.5874			−0.501522
$735$	−6.89779	−	1.69741i	−0.254429	−	0.0626099i
$736$	2.63685	−	4.00587i	0.0971957	−	0.147658i
$737$	21.4066	+	37.0773i	0.788522	+	1.36576i
$738$	12.8774	+	7.43478i	0.474024	+	0.273678i
$739$	−24.6924	+	42.7686i	−0.908326	+	1.57327i	−0.0919375	+	0.995765i	$0.529306\pi$
$739$	−24.6924	+	42.7686i	−0.908326	+	1.57327i	−0.816389	+	0.577503i	$0.804027\pi$
$740$	12.8416	−	7.41411i	0.472067	−	0.272548i
$741$	5.68414			0.208812
$742$	−5.03146	+	3.94342i	−0.184711	+	0.144767i
$743$			26.0648i			0.956225i	0.878299	+	0.478113i	$0.158679\pi$
$743$			26.0648i			0.956225i	−0.878299	+	0.478113i	$0.841321\pi$
$744$	−1.17834	−	2.04094i	−0.0431999	−	0.0748244i
$745$	11.9819	+	6.91773i	0.438981	+	0.253446i
$746$	9.92344	+	5.72930i	0.363323	+	0.209765i
$747$	−19.6999	−	34.1213i	−0.720783	−	1.24843i
$748$			23.3886i			0.855173i
$749$	25.9278	+	10.4294i	0.947382	+	0.381082i
$750$		−	7.12166i		−	0.260046i
$751$	39.4984	−	22.8044i	1.44132	−	0.832144i	0.443378	−	0.896335i	$-0.353780\pi$
$751$	39.4984	−	22.8044i	1.44132	−	0.832144i	0.997938	+	0.0641908i	$0.0204466\pi$
$752$	−6.35084	−	3.66666i	−0.231591	−	0.133709i
$753$	11.7008	+	6.75545i	0.426400	+	0.246182i
$754$	47.1477	−	27.2208i	1.71702	−	0.991321i
$755$	17.8032			0.647925
$756$	−1.23688	−	8.70418i	−0.0449848	−	0.316568i
$757$			48.0863i			1.74773i	0.486172	+	0.873863i	$0.338393\pi$
$757$			48.0863i			1.74773i	−0.486172	+	0.873863i	$0.661607\pi$
$758$	3.03316	−	1.75120i	0.110169	−	0.0636063i
$759$	−5.06291	−	10.0905i	−0.183772	−	0.366263i
$760$	−1.49109	+	2.58264i	−0.0540874	+	0.0936822i
$761$	−16.8605	+	9.73444i	−0.611194	+	0.352873i	−0.773433	−	0.633878i	$-0.781462\pi$
$761$	−16.8605	+	9.73444i	−0.611194	+	0.352873i	0.162238	+	0.986752i	$0.448129\pi$
$762$		−	9.82506i		−	0.355924i
$763$	−0.331312	−	2.33152i	−0.0119943	−	0.0844066i
$764$		−	9.98802i		−	0.361354i
$765$	−13.3831	−	23.1802i	−0.483867	−	0.838082i
$766$	8.13077	−	14.0829i	0.293777	−	0.508836i
$767$	17.6418	−	30.5565i	0.637008	−	1.10333i
$768$	0.508912	−	0.293820i	0.0183638	−	0.0106023i
$769$	−14.2164			−0.512657			−0.256329	−	0.966590i	$-0.582513\pi$
$769$	−14.2164			−0.512657			−0.256329	+	0.966590i	$0.582513\pi$
$770$	16.9803	+	6.83030i	0.611929	+	0.246147i
$771$	−16.5534			−0.596155
$772$	10.3150	+	17.8662i	0.371246	+	0.643017i
$773$	6.81004	−	11.7953i	0.244940	−	0.424249i	−0.717175	−	0.696894i	$-0.754565\pi$
$773$	6.81004	−	11.7953i	0.244940	−	0.424249i	0.962115	+	0.272645i	$0.0878983\pi$
$774$	7.16325	+	4.13571i	0.257478	+	0.148655i
$775$	7.00811	−	4.04614i	0.251739	−	0.145342i
$776$	−15.4996			−0.556402
$777$	−8.23520	−	10.5074i	−0.295436	−	0.376951i
$778$		−	18.8796i		−	0.676866i
$779$	−8.37690	+	4.83641i	−0.300134	+	0.173282i
$780$	−2.84207	+	4.92261i	−0.101762	+	0.176258i
$781$	−40.7190	−	23.5091i	−1.45704	−	0.841222i
$782$	−27.9529	−	1.63859i	−0.999594	−	0.0585957i
$783$		−	32.2971i		−	1.15421i
$784$	6.72290	−	1.95004i	0.240103	−	0.0696444i
$785$	13.9681			0.498542
$786$	1.83869	+	3.18470i	0.0655839	+	0.113595i
$787$	19.3595	−	33.5317i	0.690093	−	1.19528i	−0.281714	−	0.959498i	$-0.590903\pi$
$787$	19.3595	−	33.5317i	0.690093	−	1.19528i	0.971807	−	0.235778i	$-0.0757638\pi$
$788$	−2.70831	+	4.69093i	−0.0964795	+	0.167107i
$789$	1.64408	+	2.84764i	0.0585310	+	0.101379i
$790$			17.4637i			0.621329i
$791$	42.7949	−	33.5406i	1.52161	−	1.19257i
$792$			10.6343i			0.377873i
$793$	−11.5682	+	6.67893i	−0.410800	+	0.237176i
$794$	23.1989	+	13.3939i	0.823297	+	0.475331i
$795$	1.22597	−	2.12345i	0.0434808	−	0.0753110i
$796$	−3.50583	−	6.07227i	−0.124261	−	0.215226i
$797$	−3.41129			−0.120834			−0.0604170	−	0.998173i	$-0.519243\pi$
$797$	−3.41129			−0.120834			−0.0604170	+	0.998173i	$0.519243\pi$
$798$	2.49093	+	1.00197i	0.0881779	+	0.0354694i
$799$			42.8162i			1.51473i
$800$	1.00891	+	1.74749i	0.0356704	+	0.0617830i
$801$	20.7113	−	35.8731i	0.731799	−	1.26751i
$802$	−3.02637	−	1.74728i	−0.106865	−	0.0616985i
$803$	−8.03257	−	13.9128i	−0.283463	−	0.490972i
$804$	−6.28048			−0.221495
$805$	−9.35285	+	19.8155i	−0.329645	+	0.698405i
$806$	−22.4633			−0.791236
$807$	2.38405	+	4.12929i	0.0839224	+	0.145358i
$808$	1.47326	+	0.850590i	0.0518293	+	0.0299236i
$809$	9.17552	−	15.8925i	0.322594	−	0.558749i	−0.658428	−	0.752643i	$-0.728778\pi$
$809$	9.17552	−	15.8925i	0.322594	−	0.558749i	0.981022	+	0.193894i	$0.0621118\pi$
$810$	−5.19049	−	8.99020i	−0.182375	−	0.315883i
$811$			35.8682i			1.25950i	0.776796	+	0.629752i	$0.216844\pi$
$811$			35.8682i			1.25950i	−0.776796	+	0.629752i	$0.783156\pi$
$812$	25.4596	−	3.61785i	0.893457	−	0.126962i
$813$	6.31455			0.221461
$814$	17.1984	+	29.7886i	0.602805	+	1.04409i
$815$	1.16162	−	2.01198i	0.0406897	−	0.0704766i
$816$	−2.97133	−	1.71550i	−0.104017	−	0.0600544i
$817$	−4.65978	+	2.69032i	−0.163025	+	0.0941225i
$818$		−	22.8837i		−	0.800109i
$819$	−36.4990	−	14.6816i	−1.27538	−	0.513018i
$820$		−	9.67281i		−	0.337789i
$821$	2.19048	+	3.79403i	0.0764484	+	0.132413i	0.901715	−	0.432330i	$-0.142309\pi$
$821$	2.19048	+	3.79403i	0.0764484	+	0.132413i	−0.825267	+	0.564743i	$0.808975\pi$
$822$	2.22476	−	3.85339i	0.0775973	−	0.134402i
$823$	8.31445	−	14.4011i	0.289824	−	0.501989i	−0.683944	−	0.729535i	$-0.739737\pi$
$823$	8.31445	−	14.4011i	0.289824	−	0.501989i	0.973767	+	0.227545i	$0.0730700\pi$
$824$	3.14024	+	5.43905i	0.109395	+	0.189478i
$825$	4.74998			0.165373
$826$	13.1174	−	10.2808i	0.456413	−	0.357715i
$827$			9.43925i			0.328235i	0.986441	+	0.164118i	$0.0524776\pi$
$827$			9.43925i			0.328235i	−0.986441	+	0.164118i	$0.947522\pi$
$828$	−12.7096	−	0.745029i	−0.441688	−	0.0258916i
$829$	19.9373	+	11.5108i	0.692451	+	0.399787i	0.804530	−	0.593913i	$-0.202418\pi$
$829$	19.9373	+	11.5108i	0.692451	+	0.399787i	−0.112079	+	0.993699i	$0.535751\pi$
$830$	−12.8150	+	22.1963i	−0.444816	+	0.770444i
$831$	3.49252	−	2.01641i	0.121154	−	0.0699485i
$832$		−	5.60127i		−	0.194189i
$833$	−29.4862	−	28.3007i	−1.02164	−	0.980560i
$834$	−6.47580			−0.224239
$835$	−25.4499	+	14.6935i	−0.880729	+	0.508489i
$836$	−5.99093	−	3.45886i	−0.207201	−	0.119627i
$837$	−6.66311	+	11.5409i	−0.230311	+	0.398910i
$838$	6.95962	+	12.0544i	0.240416	+	0.416413i
$839$	19.7349			0.681326			0.340663	−	0.940186i	$-0.389349\pi$
$839$	19.7349			0.681326			0.340663	+	0.940186i	$0.389349\pi$
$840$	−2.11320	+	1.65622i	−0.0729122	+	0.0571451i
$841$	65.4687			2.25754
$842$	15.0993	−	8.71757i	0.520355	−	0.300427i
$843$	−1.39888	+	2.42293i	−0.0481799	+	0.0834500i
$844$	−1.98769	+	3.44279i	−0.0684192	+	0.118506i
$845$	15.8652	+	27.4793i	0.545778	+	0.945316i
$846$			19.4676i			0.669310i
$847$	−4.98321	+	12.3884i	−0.171225	+	0.425671i
$848$			2.41620i			0.0829726i
$849$	−4.78197	+	2.76087i	−0.164117	+	0.0947528i
$850$	5.89062	−	10.2029i	0.202047	−	0.349955i
$851$	−36.8067	+	18.4677i	−1.26172	+	0.633066i
$852$	5.97326	−	3.44867i	0.204641	−	0.118149i
$853$		−	52.6163i		−	1.80155i	−0.434289	−	0.900774i	$-0.643000\pi$
$853$		−	52.6163i		−	1.80155i	0.434289	−	0.900774i	$-0.357000\pi$
$854$	−6.24681	+	0.887681i	−0.213762	+	0.0303758i
$855$	7.91672			0.270746
$856$	9.14774	−	5.28145i	0.312663	−	0.180516i
$857$	−12.8671	−	7.42883i	−0.439532	−	0.253764i	0.263867	−	0.964559i	$-0.415002\pi$
$857$	−12.8671	−	7.42883i	−0.439532	−	0.253764i	−0.703399	+	0.710795i	$0.748335\pi$
$858$	−11.4189	−	6.59273i	−0.389836	−	0.225072i
$859$	22.5159	−	12.9996i	0.768233	−	0.443540i	−0.0640109	−	0.997949i	$-0.520389\pi$
$859$	22.5159	−	12.9996i	0.768233	−	0.443540i	0.832244	+	0.554410i	$0.187056\pi$
$860$		−	5.38065i		−	0.183479i
$861$	−8.62196	+	1.22519i	−0.293836	+	0.0417545i
$862$			30.0990i			1.02518i
$863$	10.4134	+	18.0365i	0.354476	+	0.613970i	0.987028	−	0.160548i	$-0.0513261\pi$
$863$	10.4134	+	18.0365i	0.354476	+	0.613970i	−0.632552	+	0.774518i	$0.717993\pi$
$864$	−2.87773	−	1.66146i	−0.0979025	−	0.0565240i
$865$	−7.61687	−	4.39760i	−0.258981	−	0.149523i
$866$	14.7808	+	25.6010i	0.502271	+	0.869959i
$867$			10.0423i			0.341053i
$868$	−9.84397	−	3.95971i	−0.334126	−	0.134401i
$869$	−40.5103			−1.37422
$870$	−8.54188	+	4.93165i	−0.289597	+	0.167199i
$871$	−29.9321	+	51.8439i	−1.01421	+	1.75666i
$872$	−0.770835	−	0.445042i	−0.0261038	−	0.0150710i
$873$	20.5732	+	35.6338i	0.696297	+	1.20602i
$874$	4.55358	−	6.91773i	0.154027	−	0.233996i
$875$	−19.7792	−	25.2366i	−0.668660	−	0.853152i
$876$	2.35667			0.0796246
$877$	−21.9447	−	38.0093i	−0.741019	−	1.28348i	−0.952032	−	0.305999i	$-0.901009\pi$
$877$	−21.9447	−	38.0093i	−0.741019	−	1.28348i	0.211013	−	0.977483i	$-0.432324\pi$
$878$	13.2106	+	7.62714i	0.445836	+	0.257403i
$879$	5.47628	+	3.16173i	0.184710	+	0.106643i
$880$	5.99093	−	3.45886i	0.201954	−	0.116598i
$881$	32.5912			1.09803			0.549013	−	0.835814i	$-0.315004\pi$
$881$	32.5912			1.09803			0.549013	+	0.835814i	$0.315004\pi$
$882$	−13.4067	−	12.8677i	−0.451429	−	0.433278i
$883$	−43.1588			−1.45241			−0.726205	−	0.687478i	$-0.758718\pi$
$883$	−43.1588			−1.45241			−0.726205	+	0.687478i	$0.758718\pi$
$884$	−28.3221	+	16.3517i	−0.952574	+	0.549969i
$885$	−3.19621	+	5.53600i	−0.107439	+	0.186090i
$886$	−4.24072	+	7.34514i	−0.142470	+	0.246765i
$887$	−41.7550	+	24.1073i	−1.40200	+	0.809442i	−0.994597	−	0.103808i	$-0.966897\pi$
$887$	−41.7550	+	24.1073i	−1.40200	+	0.809442i	−0.407398	+	0.913251i	$0.633564\pi$
$888$	−5.04585			−0.169328
$889$	−27.2875	−	34.8165i	−0.915193	−	1.16771i
$890$	−26.9459			−0.903228
$891$	20.8545	−	12.0403i	0.698652	−	0.403367i
$892$	−9.73748	−	5.62194i	−0.326035	−	0.188236i
$893$	−10.9672	−	6.33194i	−0.367005	−	0.211890i
$894$	−2.35401	−	4.07727i	−0.0787300	−	0.136364i
$895$	13.2188			0.441857
$896$	0.987361	−	2.45461i	0.0329854	−	0.0820028i
$897$	8.67929	−	13.1855i	0.289793	−	0.440249i
$898$	2.41396	+	4.18110i	0.0805548	+	0.139525i
$899$	−33.7569	−	19.4895i	−1.12585	−	0.650012i
$900$	2.67834	−	4.63901i	0.0892779	−	0.154634i
$901$	12.2172	−	7.05359i	0.407013	−	0.234989i
$902$	22.4379			0.747102
$903$	−4.79609	+	0.681532i	−0.159604	+	0.0226800i
$904$		−	20.5509i		−	0.683513i
$905$	−9.42473	−	16.3241i	−0.313289	−	0.542632i
$906$	−5.24655	−	3.02910i	−0.174305	−	0.100635i
$907$	−4.14576	−	2.39355i	−0.137658	−	0.0794766i	0.429590	−	0.903024i	$-0.358658\pi$
$907$	−4.14576	−	2.39355i	−0.137658	−	0.0794766i	−0.567247	+	0.823548i	$0.691992\pi$
$908$	7.19990	+	12.4706i	0.238937	+	0.413851i
$909$		−	4.51608i		−	0.149789i
$910$	3.60047	+	25.3373i	0.119354	+	0.839924i
$911$			12.5267i			0.415028i	0.978232	+	0.207514i	$0.0665373\pi$
$911$			12.5267i			0.415028i	−0.978232	+	0.207514i	$0.933463\pi$
$912$	0.878839	−	0.507398i	0.0291013	−	0.0168016i
$913$	−51.4885	−	29.7269i	−1.70402	−	0.983818i
$914$	8.59484	+	4.96223i	0.284292	+	0.164136i
$915$	2.09585	−	1.21004i	0.0692866	−	0.0400027i
$916$	21.3074			0.704016
$917$	15.3606	+	6.17878i	0.507253	+	0.204041i
$918$			19.4012i			0.640334i
$919$	−22.5796	+	13.0363i	−0.744832	+	0.430029i	−0.823823	−	0.566846i	$-0.808163\pi$
$919$	−22.5796	+	13.0363i	−0.744832	+	0.430029i	0.0789917	+	0.996875i	$0.474830\pi$
$920$	3.71414	+	7.40238i	0.122452	+	0.244049i
$921$	−4.91396	+	8.51123i	−0.161920	+	0.280454i
$922$	−20.9420	+	12.0909i	−0.689687	+	0.398191i
$923$		−	65.7439i		−	2.16399i
$924$	−3.84193	−	4.90196i	−0.126390	−	0.161263i
$925$		−	17.3263i		−	0.569685i
$926$	5.74640	+	9.95305i	0.188838	+	0.327077i
$927$	8.33632	−	14.4389i	0.273801	−	0.474237i
$928$	4.85975	−	8.41733i	0.159529	−	0.276313i
$929$	30.1479	−	17.4059i	0.989120	−	0.571069i	0.0841089	−	0.996457i	$-0.473196\pi$
$929$	30.1479	−	17.4059i	0.989120	−	0.571069i	0.905011	+	0.425388i	$0.139862\pi$
$930$	4.06973			0.133452
$931$	11.6098	−	3.36753i	0.380494	−	0.110366i
$932$	−7.49395			−0.245472
$933$	−6.40771	−	11.0985i	−0.209779	−	0.363348i
$934$	0.441887	−	0.765371i	0.0144590	−	0.0250437i
$935$	−34.9786	−	20.1949i	−1.14392	−	0.660443i
$936$	−12.8774	+	7.43478i	−0.420911	+	0.243013i
$937$	51.8954			1.69535			0.847675	−	0.530516i	$-0.178002\pi$
$937$	51.8954			1.69535			0.847675	+	0.530516i	$0.178002\pi$
$938$	−22.2557	+	17.4430i	−0.726675	+	0.569534i
$939$			0.170001i			0.00554777i
$940$	10.9672	−	6.33194i	0.357712	−	0.206525i
$941$	−9.23148	+	15.9894i	−0.300938	+	0.521239i	−0.976349	−	0.216202i	$-0.930633\pi$
$941$	−9.23148	+	15.9894i	−0.300938	+	0.521239i	0.675411	+	0.737442i	$0.263966\pi$
$942$	−4.11635	−	2.37658i	−0.134118	−	0.0774331i
$943$	−1.57198	+	26.8167i	−0.0511908	+	0.873272i
$944$		−	6.29922i		−	0.205022i
$945$	14.0854	+	5.66582i	0.458198	+	0.184309i
$946$	12.4814			0.405807
$947$	7.30936	+	12.6602i	0.237522	+	0.411400i	0.960003	−	0.279991i	$-0.0903314\pi$
$947$	7.30936	+	12.6602i	0.237522	+	0.411400i	−0.722481	+	0.691391i	$0.756998\pi$
$948$	2.97133	−	5.14649i	0.0965042	−	0.167150i
$949$	11.2316	−	19.4538i	0.364595	−	0.631497i
$950$	1.74229	+	3.01773i	0.0565273	+	0.0979081i
$951$		−	2.76957i		−	0.0898094i
$952$	−15.2938	+	2.17327i	−0.495675	+	0.0704362i
$953$		−	8.39051i		−	0.271795i	−0.990723	−	0.135898i	$-0.956608\pi$
$953$		−	8.39051i		−	0.271795i	0.990723	−	0.135898i	$-0.0433918\pi$
$954$	5.55488	−	3.20711i	0.179846	−	0.103834i
$955$	14.9375	+	8.62415i	0.483365	+	0.279071i
$956$	4.26803	−	7.39245i	0.138038	−	0.239089i
$957$	−11.4399	−	19.8145i	−0.369800	−	0.640512i
$958$	3.74309			0.120934
$959$	−2.81843	−	19.8339i	−0.0910118	−	0.640470i
$960$			1.01480i			0.0327524i
$961$	−7.45836	−	12.9183i	−0.240592	−	0.416718i
$962$	−24.0480	+	41.6523i	−0.775338	+	1.34292i
$963$	−24.2843	−	14.0205i	−0.782551	−	0.451806i
$964$	14.1595	+	24.5250i	0.456047	+	0.789897i
$965$	−35.6260			−1.14684
$966$	6.12774	−	4.24825i	0.197157	−	0.136685i
$967$	9.30511			0.299232			0.149616	−	0.988744i	$-0.452196\pi$
$967$	9.30511			0.299232			0.149616	+	0.988744i	$0.452196\pi$
$968$	2.52350	+	4.37083i	0.0811083	+	0.140484i
$969$	−5.13118	−	2.96249i	−0.164837	−	0.0951688i
$970$	13.3831	−	23.1802i	0.429705	−	0.744271i
$971$	29.3514	+	50.8381i	0.941931	+	1.63147i	0.761782	+	0.647834i	$0.224325\pi$
$971$	29.3514	+	50.8381i	0.941931	+	1.63147i	0.180149	+	0.983639i	$0.442342\pi$
$972$			13.5013i			0.433054i
$973$	−22.9479	+	17.9855i	−0.735676	+	0.576588i
$974$	30.9269			0.990962
$975$	3.32087	+	5.75191i	0.106353	+	0.184209i
$976$	−1.19240	+	2.06529i	−0.0381677	+	0.0661084i
$977$	−3.52423	−	2.03471i	−0.112750	−	0.0650963i	0.442564	−	0.896737i	$-0.354069\pi$
$977$	−3.52423	−	2.03471i	−0.112750	−	0.0650963i	−0.555315	+	0.831640i	$0.687402\pi$
$978$	−0.684650	+	0.395283i	−0.0218927	+	0.0126398i
$979$		−	62.5062i		−	1.99771i
$980$	−2.88851	+	11.7381i	−0.0922702	+	0.374960i
$981$			2.36289i			0.0754411i
$982$	−3.71966	−	6.44264i	−0.118699	−	0.205593i
$983$	−17.4483	+	30.2214i	−0.556516	+	0.963914i	0.441268	+	0.897375i	$0.354529\pi$
$983$	−17.4483	+	30.2214i	−0.556516	+	0.963914i	−0.997784	+	0.0665382i	$0.978805\pi$
$984$	−1.64577	+	2.85055i	−0.0524651	+	0.0908722i
$985$	−4.67697	−	8.10075i	−0.149021	−	0.258111i
$986$	−56.7482			−1.80723
$987$	−7.03319	−	8.97374i	−0.223869	−	0.285637i
$988$		−	9.67281i		−	0.307733i
$989$	−0.874438	+	14.9172i	−0.0278055	+	0.474339i
$990$	−15.9040	−	9.18217i	−0.505462	−	0.291829i
$991$	−26.3316	+	45.6076i	−0.836450	+	1.44877i	0.0563939	+	0.998409i	$0.482040\pi$
$991$	−26.3316	+	45.6076i	−0.836450	+	1.44877i	−0.892844	+	0.450366i	$0.851294\pi$
$992$	−3.47311	+	2.00520i	−0.110271	+	0.0636651i
$993$		−	6.63138i		−	0.210440i
$994$	11.5890	−	28.8106i	0.367580	−	0.913816i
$995$	12.1084			0.383863
$996$	7.55311	−	4.36079i	0.239329	−	0.138177i
$997$	−29.0078	−	16.7477i	−0.918686	−	0.530404i	−0.0354705	−	0.999371i	$-0.511293\pi$
$997$	−29.0078	−	16.7477i	−0.918686	−	0.530404i	−0.883216	+	0.468967i	$0.844626\pi$
$998$	6.40771	−	11.0985i	0.202832	−	0.351316i
$999$	14.2663	+	24.7100i	0.451366	+	0.781790i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	322.2.g.a.45.3	✓	16
7.3	odd	6		2254.2.c.c.2253.7		16
7.4	even	3		2254.2.c.c.2253.10		16
7.5	odd	6	inner	322.2.g.a.229.4	yes	16
23.22	odd	2	inner	322.2.g.a.45.4	yes	16
161.45	even	6		2254.2.c.c.2253.8		16
161.68	even	6	inner	322.2.g.a.229.3	yes	16
161.137	odd	6		2254.2.c.c.2253.9		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
322.2.g.a.45.3	✓	16	1.1	even	1	trivial
322.2.g.a.45.4	yes	16	23.22	odd	2	inner
322.2.g.a.229.3	yes	16	161.68	even	6	inner
322.2.g.a.229.4	yes	16	7.5	odd	6	inner
2254.2.c.c.2253.7		16	7.3	odd	6
2254.2.c.c.2253.8		16	161.45	even	6
2254.2.c.c.2253.9		16	161.137	odd	6
2254.2.c.c.2253.10		16	7.4	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:	\( N \)	\(=\)	\( 322 = 2 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	322.g (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.508912 - 0.293820i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.863449 - 1.49554i) q^{5} +0.587641i q^{6} +(1.63208 + 2.08239i) q^{7} +1.00000 q^{8} +(-1.32734 - 2.29902i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.508912 - 0.293820i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.863449 - 1.49554i) q^{5} +0.587641i q^{6} +(1.63208 + 2.08239i) q^{7} +1.00000 q^{8} +(-1.32734 - 2.29902i) q^{9} +(-0.863449 + 1.49554i) q^{10} +(-3.46919 - 2.00294i) q^{11} +(0.508912 - 0.293820i) q^{12} -5.60127i q^{13} +(0.987361 - 2.45461i) q^{14} +1.01480i q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.91929 + 5.05637i) q^{17} +(-1.32734 + 2.29902i) q^{18} +(-0.863449 - 1.49554i) q^{19} +1.72690 q^{20} +(-0.218735 - 1.53929i) q^{21} +4.00587i q^{22} +(-4.78761 - 0.280648i) q^{23} +(-0.508912 - 0.293820i) q^{24} +(1.00891 - 1.74749i) q^{25} +(-4.85084 + 2.80063i) q^{26} +3.32292i q^{27} +(-2.61944 + 0.372226i) q^{28} -9.71950 q^{29} +(0.878839 - 0.507398i) q^{30} +(3.47311 + 2.00520i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(1.17701 + 2.03864i) q^{33} +5.83859 q^{34} +(1.70507 - 4.23886i) q^{35} +2.65468 q^{36} +(7.43623 - 4.29331i) q^{37} +(-0.863449 + 1.49554i) q^{38} +(-1.64577 + 2.85055i) q^{39} +(-0.863449 - 1.49554i) q^{40} -5.60127i q^{41} +(-1.22369 + 0.959074i) q^{42} -3.11579i q^{43} +(3.46919 - 2.00294i) q^{44} +(-2.29218 + 3.97017i) q^{45} +(2.15076 + 4.28652i) q^{46} +(6.35084 - 3.66666i) q^{47} +0.587641i q^{48} +(-1.67266 + 6.79722i) q^{49} -2.01782 q^{50} +(2.97133 - 1.71550i) q^{51} +(4.85084 + 2.80063i) q^{52} +(-2.09249 - 1.20810i) q^{53} +(2.87773 - 1.66146i) q^{54} +6.91773i q^{55} +(1.63208 + 2.08239i) q^{56} +1.01480i q^{57} +(4.85975 + 8.41733i) q^{58} +(5.45528 + 3.14961i) q^{59} +(-0.878839 - 0.507398i) q^{60} +(-1.19240 - 2.06529i) q^{61} -4.01040i q^{62} +(2.62113 - 6.51620i) q^{63} +1.00000 q^{64} +(-8.37690 + 4.83641i) q^{65} +(1.17701 - 2.03864i) q^{66} +(-9.25574 - 5.34380i) q^{67} +(-2.91929 - 5.05637i) q^{68} +(2.35401 + 1.54952i) q^{69} +(-4.52350 + 0.642796i) q^{70} +11.7373 q^{71} +(-1.32734 - 2.29902i) q^{72} +(3.47311 + 2.00520i) q^{73} +(-7.43623 - 4.29331i) q^{74} +(-1.02689 + 0.592878i) q^{75} +1.72690 q^{76} +(-1.49109 - 10.4931i) q^{77} +3.29153 q^{78} +(8.75788 - 5.05637i) q^{79} +(-0.863449 + 1.49554i) q^{80} +(-3.00568 + 5.20598i) q^{81} +(-4.85084 + 2.80063i) q^{82} +14.8417 q^{83} +(1.44243 + 0.580214i) q^{84} +10.0826 q^{85} +(-2.69835 + 1.55789i) q^{86} +(4.94637 + 2.85579i) q^{87} +(-3.46919 - 2.00294i) q^{88} +(7.80182 + 13.5131i) q^{89} +4.58436 q^{90} +(11.6640 - 9.14169i) q^{91} +(2.63685 - 4.00587i) q^{92} +(-1.17834 - 2.04094i) q^{93} +(-6.35084 - 3.66666i) q^{94} +(-1.49109 + 2.58264i) q^{95} +(0.508912 - 0.293820i) q^{96} -15.4996 q^{97} +(6.72290 - 1.95004i) q^{98} +10.6343i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{2} + 6 q^{3} - 8 q^{4} + 16 q^{8} + 10 q^{9}+O(q^{10}) \) 16 * q - 8 * q^2 + 6 * q^3 - 8 * q^4 + 16 * q^8 + 10 * q^9	\( 16 q - 8 q^{2} + 6 q^{3} - 8 q^{4} + 16 q^{8} + 10 q^{9} - 6 q^{12} - 8 q^{16} + 10 q^{18} - 4 q^{23} + 6 q^{24} + 2 q^{25} - 6 q^{26} + 16 q^{29} - 24 q^{31} - 8 q^{32} + 4 q^{35} - 20 q^{36} + 22 q^{39} - 4 q^{46} + 30 q^{47} - 58 q^{49} - 4 q^{50} + 6 q^{52} + 54 q^{54} - 8 q^{58} + 36 q^{59} + 16 q^{64} - 32 q^{70} - 12 q^{71} + 10 q^{72} - 24 q^{73} - 96 q^{75} - 38 q^{77} - 44 q^{78} - 36 q^{81} - 6 q^{82} + 24 q^{85} + 42 q^{87} + 8 q^{92} - 38 q^{93} - 30 q^{94} - 38 q^{95} - 6 q^{96} + 56 q^{98}+O(q^{100}) \) 16 * q - 8 * q^2 + 6 * q^3 - 8 * q^4 + 16 * q^8 + 10 * q^9 - 6 * q^12 - 8 * q^16 + 10 * q^18 - 4 * q^23 + 6 * q^24 + 2 * q^25 - 6 * q^26 + 16 * q^29 - 24 * q^31 - 8 * q^32 + 4 * q^35 - 20 * q^36 + 22 * q^39 - 4 * q^46 + 30 * q^47 - 58 * q^49 - 4 * q^50 + 6 * q^52 + 54 * q^54 - 8 * q^58 + 36 * q^59 + 16 * q^64 - 32 * q^70 - 12 * q^71 + 10 * q^72 - 24 * q^73 - 96 * q^75 - 38 * q^77 - 44 * q^78 - 36 * q^81 - 6 * q^82 + 24 * q^85 + 42 * q^87 + 8 * q^92 - 38 * q^93 - 30 * q^94 - 38 * q^95 - 6 * q^96 + 56 * q^98

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