LMFDB - Embedded newform 231.2.s.a.8.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(8,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 0, 3]))

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

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

chi := DirichletCharacter("231.8");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.s (of order $10$, 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:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			8.2
Character	$\chi$	$=$	231.8
Dual form			231.2.s.a.29.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.11971 + 1.54006i) q^{2} +(0.569669 + 1.63569i) q^{3} +(1.50336 - 4.62686i) q^{4} +(0.853755 - 1.17509i) q^{5} +(-3.72660 - 2.58986i) q^{6} +(0.951057 + 0.309017i) q^{7} +(2.31965 + 7.13914i) q^{8} +(-2.35095 + 1.86360i) q^{9} +O(q^{10})$	\(q+(-2.11971 + 1.54006i) q^{2} +(0.569669 + 1.63569i) q^{3} +(1.50336 - 4.62686i) q^{4} +(0.853755 - 1.17509i) q^{5} +(-3.72660 - 2.58986i) q^{6} +(0.951057 + 0.309017i) q^{7} +(2.31965 + 7.13914i) q^{8} +(-2.35095 + 1.86360i) q^{9} +3.80570i q^{10} +(0.416755 + 3.29034i) q^{11} +(8.42452 - 0.176756i) q^{12} +(1.47393 + 2.02869i) q^{13} +(-2.49187 + 0.809658i) q^{14} +(2.40844 + 0.727063i) q^{15} +(-8.04002 - 5.84142i) q^{16} +(4.08973 + 2.97136i) q^{17} +(2.11328 - 7.57092i) q^{18} +(-5.94635 + 1.93209i) q^{19} +(-4.15349 - 5.71679i) q^{20} +(0.0363323 + 1.73167i) q^{21} +(-5.95072 - 6.33274i) q^{22} -6.44053i q^{23} +(-10.3560 + 7.86117i) q^{24} +(0.893139 + 2.74880i) q^{25} +(-6.24862 - 2.03030i) q^{26} +(-4.38754 - 2.78379i) q^{27} +(2.85956 - 3.93585i) q^{28} +(-1.37385 + 4.22826i) q^{29} +(-6.22493 + 2.16799i) q^{30} +(5.54823 - 4.03103i) q^{31} +11.0256 q^{32} +(-5.14455 + 2.55609i) q^{33} -13.2451 q^{34} +(1.17509 - 0.853755i) q^{35} +(5.08831 + 13.6792i) q^{36} +(-1.17258 + 3.60882i) q^{37} +(9.62902 - 13.2532i) q^{38} +(-2.47865 + 3.56657i) q^{39} +(10.3696 + 3.36928i) q^{40} +(0.338748 + 1.04256i) q^{41} +(-2.74389 - 3.61469i) q^{42} -4.14120i q^{43} +(15.8505 + 3.01829i) q^{44} +(0.182769 + 4.35365i) q^{45} +(9.91881 + 13.6521i) q^{46} +(4.21702 - 1.37019i) q^{47} +(4.97458 - 16.4786i) q^{48} +(0.809017 + 0.587785i) q^{49} +(-6.12652 - 4.45118i) q^{50} +(-2.53043 + 8.38221i) q^{51} +(11.6023 - 3.76982i) q^{52} +(0.860250 + 1.18403i) q^{53} +(13.5875 - 0.856249i) q^{54} +(4.22226 + 2.31942i) q^{55} +7.50654i q^{56} +(-6.54775 - 8.62573i) q^{57} +(-3.59962 - 11.0785i) q^{58} +(-10.7464 - 3.49172i) q^{59} +(6.98478 - 10.0505i) q^{60} +(3.19884 - 4.40283i) q^{61} +(-5.55263 + 17.0892i) q^{62} +(-2.81177 + 1.04591i) q^{63} +(-7.29105 + 5.29726i) q^{64} +3.64228 q^{65} +(6.96844 - 13.3411i) q^{66} +11.6236 q^{67} +(19.8964 - 14.4556i) q^{68} +(10.5347 - 3.66897i) q^{69} +(-1.17602 + 3.61943i) q^{70} +(0.493561 - 0.679329i) q^{71} +(-18.7579 - 12.4609i) q^{72} +(1.62164 + 0.526902i) q^{73} +(-3.07228 - 9.45550i) q^{74} +(-3.98739 + 3.02680i) q^{75} +30.4176i q^{76} +(-0.620412 + 3.25808i) q^{77} +(-0.238710 - 11.3774i) q^{78} +(-1.30582 - 1.79731i) q^{79} +(-13.7284 + 4.46063i) q^{80} +(2.05396 - 8.76249i) q^{81} +(-2.32365 - 1.68823i) q^{82} +(-5.63425 - 4.09352i) q^{83} +(8.06682 + 2.43522i) q^{84} +(6.98325 - 2.26900i) q^{85} +(6.37771 + 8.77816i) q^{86} +(-7.69876 + 0.161528i) q^{87} +(-22.5235 + 10.6077i) q^{88} +12.3634i q^{89} +(-7.09231 - 8.94701i) q^{90} +(0.774891 + 2.38487i) q^{91} +(-29.7994 - 9.68242i) q^{92} +(9.75416 + 6.77883i) q^{93} +(-6.82869 + 9.39889i) q^{94} +(-2.80635 + 8.63704i) q^{95} +(6.28094 + 18.0344i) q^{96} +(-7.64536 + 5.55468i) q^{97} -2.62011 q^{98} +(-7.11166 - 6.95876i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 6 q^{3} - 24 q^{4} - 10 q^{6} - 20 q^{9}+O(q^{10}) $ 96 * q + 6 * q^3 - 24 * q^4 - 10 * q^6 - 20 * q^9	$ 96 q + 6 q^{3} - 24 q^{4} - 10 q^{6} - 20 q^{9} - 20 q^{12} - 32 q^{16} - 10 q^{18} - 60 q^{19} + 30 q^{24} + 12 q^{25} - 40 q^{28} + 60 q^{30} + 40 q^{31} - 44 q^{33} + 8 q^{34} + 2 q^{36} + 16 q^{37} - 10 q^{39} - 96 q^{45} - 40 q^{46} + 48 q^{48} + 24 q^{49} - 30 q^{51} - 40 q^{52} + 28 q^{55} - 30 q^{57} + 36 q^{58} - 32 q^{60} + 40 q^{61} - 28 q^{64} + 118 q^{66} - 56 q^{67} + 26 q^{69} + 20 q^{70} + 150 q^{72} + 40 q^{73} + 2 q^{75} - 20 q^{78} - 40 q^{79} + 8 q^{81} - 16 q^{82} + 40 q^{84} - 60 q^{85} - 156 q^{88} + 100 q^{90} + 36 q^{91} - 36 q^{93} + 160 q^{96} - 88 q^{97} - 94 q^{99}+O(q^{100}) $ 96 * q + 6 * q^3 - 24 * q^4 - 10 * q^6 - 20 * q^9 - 20 * q^12 - 32 * q^16 - 10 * q^18 - 60 * q^19 + 30 * q^24 + 12 * q^25 - 40 * q^28 + 60 * q^30 + 40 * q^31 - 44 * q^33 + 8 * q^34 + 2 * q^36 + 16 * q^37 - 10 * q^39 - 96 * q^45 - 40 * q^46 + 48 * q^48 + 24 * q^49 - 30 * q^51 - 40 * q^52 + 28 * q^55 - 30 * q^57 + 36 * q^58 - 32 * q^60 + 40 * q^61 - 28 * q^64 + 118 * q^66 - 56 * q^67 + 26 * q^69 + 20 * q^70 + 150 * q^72 + 40 * q^73 + 2 * q^75 - 20 * q^78 - 40 * q^79 + 8 * q^81 - 16 * q^82 + 40 * q^84 - 60 * q^85 - 156 * q^88 + 100 * q^90 + 36 * q^91 - 36 * q^93 + 160 * q^96 - 88 * q^97 - 94 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{10}\right)$

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 $

$2$	−2.11971	+	1.54006i	−1.49886	+	1.08899i	−0.528032	+	0.849224i	$0.677070\pi$
$2$	−2.11971	+	1.54006i	−1.49886	+	1.08899i	−0.970831	+	0.239763i	$0.922930\pi$
$3$	0.569669	+	1.63569i	0.328899	+	0.944365i
$3$	0.569669	+	1.63569i	0.328899	+	0.944365i
$4$	1.50336	−	4.62686i	0.751680	−	2.31343i
$5$	0.853755	−	1.17509i	0.381811	−	0.525518i	−0.574252	−	0.818678i	$-0.694707\pi$
$5$	0.853755	−	1.17509i	0.381811	−	0.525518i	0.956063	+	0.293161i	$0.0947071\pi$
$6$	−3.72660	−	2.58986i	−1.52138	−	1.05731i
$7$	0.951057	+	0.309017i	0.359466	+	0.116797i
$7$	0.951057	+	0.309017i	0.359466	+	0.116797i
$8$	2.31965	+	7.13914i	0.820120	+	2.52407i
$9$	−2.35095	+	1.86360i	−0.783651	+	0.621201i
$10$			3.80570i			1.20347i
$11$	0.416755	+	3.29034i	0.125656	+	0.992074i
$11$	0.416755	+	3.29034i	0.125656	+	0.992074i
$12$	8.42452	−	0.176756i	2.43195	−	0.0510250i
$13$	1.47393	+	2.02869i	0.408795	+	0.562658i	0.962924	−	0.269773i	$-0.0869487\pi$
$13$	1.47393	+	2.02869i	0.408795	+	0.562658i	−0.554129	+	0.832431i	$0.686949\pi$
$14$	−2.49187	+	0.809658i	−0.665981	+	0.216390i
$15$	2.40844	+	0.727063i	0.621858	+	0.187727i
$16$	−8.04002	−	5.84142i	−2.01000	−	1.46035i
$17$	4.08973	+	2.97136i	0.991904	+	0.720661i	0.960337	−	0.278841i	$-0.0899502\pi$
$17$	4.08973	+	2.97136i	0.991904	+	0.720661i	0.0315672	+	0.999502i	$0.489950\pi$
$18$	2.11328	−	7.57092i	0.498105	−	1.78448i
$19$	−5.94635	+	1.93209i	−1.36419	+	0.443251i	−0.897439	−	0.441139i	$-0.854574\pi$
$19$	−5.94635	+	1.93209i	−1.36419	+	0.443251i	−0.466748	+	0.884390i	$0.654574\pi$
$20$	−4.15349	−	5.71679i	−0.928750	−	1.27831i
$21$	0.0363323	+	1.73167i	0.00792836	+	0.377881i
$22$	−5.95072	−	6.33274i	−1.26870	−	1.35014i
$23$		−	6.44053i		−	1.34294i	−0.741031	−	0.671471i	$-0.765663\pi$
$23$		−	6.44053i		−	1.34294i	0.741031	−	0.671471i	$-0.234337\pi$
$24$	−10.3560	+	7.86117i	−2.11391	+	1.60466i
$25$	0.893139	+	2.74880i	0.178628	+	0.549760i
$26$	−6.24862	−	2.03030i	−1.22545	−	0.398174i
$27$	−4.38754	−	2.78379i	−0.844383	−	0.535741i
$28$	2.85956	−	3.93585i	0.540406	−	0.743805i
$29$	−1.37385	+	4.22826i	−0.255117	+	0.785168i	0.738690	+	0.674045i	$0.235445\pi$
$29$	−1.37385	+	4.22826i	−0.255117	+	0.785168i	−0.993807	+	0.111123i	$0.964555\pi$
$30$	−6.22493	+	2.16799i	−1.13651	+	0.395819i
$31$	5.54823	−	4.03103i	0.996492	−	0.723994i	0.0351589	−	0.999382i	$-0.488806\pi$
$31$	5.54823	−	4.03103i	0.996492	−	0.723994i	0.961333	+	0.275388i	$0.0888063\pi$
$32$	11.0256			1.94907
$33$	−5.14455	+	2.55609i	−0.895552	+	0.444958i
$34$	−13.2451			−2.27152
$35$	1.17509	−	0.853755i	0.198627	−	0.144311i
$36$	5.08831	+	13.6792i	0.848052	+	2.27987i
$37$	−1.17258	+	3.60882i	−0.192770	+	0.593286i	0.807225	+	0.590244i	$0.200968\pi$
$37$	−1.17258	+	3.60882i	−0.192770	+	0.593286i	−0.999995	+	0.00304242i	$0.999032\pi$
$38$	9.62902	−	13.2532i	1.56203	−	2.14996i
$39$	−2.47865	+	3.56657i	−0.396902	+	0.571109i
$40$	10.3696	+	3.36928i	1.63957	+	0.532730i
$41$	0.338748	+	1.04256i	0.0529035	+	0.162820i	0.974018	−	0.226473i	$-0.0727194\pi$
$41$	0.338748	+	1.04256i	0.0529035	+	0.162820i	−0.921114	+	0.389293i	$0.872719\pi$
$42$	−2.74389	−	3.61469i	−0.423392	−	0.557759i
$43$		−	4.14120i		−	0.631528i	−0.948838	−	0.315764i	$-0.897739\pi$
$43$		−	4.14120i		−	0.631528i	0.948838	−	0.315764i	$-0.102261\pi$
$44$	15.8505	+	3.01829i	2.38955	+	0.455024i
$45$	0.182769	+	4.35365i	0.0272456	+	0.649004i
$46$	9.91881	+	13.6521i	1.46245	+	2.01289i
$47$	4.21702	−	1.37019i	0.615116	−	0.199863i	0.0151453	−	0.999885i	$-0.495179\pi$
$47$	4.21702	−	1.37019i	0.615116	−	0.199863i	0.599971	+	0.800022i	$0.295179\pi$
$48$	4.97458	−	16.4786i	0.718019	−	2.37849i
$49$	0.809017	+	0.587785i	0.115574	+	0.0839693i
$50$	−6.12652	−	4.45118i	−0.866421	−	0.629491i
$51$	−2.53043	+	8.38221i	−0.354331	+	1.17374i
$52$	11.6023	−	3.76982i	1.60895	−	0.522780i
$53$	0.860250	+	1.18403i	0.118164	+	0.162639i	0.864002	−	0.503489i	$-0.167950\pi$
$53$	0.860250	+	1.18403i	0.118164	+	0.162639i	−0.745837	+	0.666128i	$0.767950\pi$
$54$	13.5875	−	0.856249i	1.84903	−	0.116521i
$55$	4.22226	+	2.31942i	0.569329	+	0.312750i
$56$			7.50654i			1.00310i
$57$	−6.54775	−	8.62573i	−0.867270	−	1.14251i
$58$	−3.59962	−	11.0785i	−0.472654	−	1.45468i
$59$	−10.7464	−	3.49172i	−1.39906	−	0.454583i	−0.490175	−	0.871624i	$-0.663067\pi$
$59$	−10.7464	−	3.49172i	−1.39906	−	0.454583i	−0.908888	+	0.417041i	$0.863067\pi$
$60$	6.98478	−	10.0505i	0.901731	−	1.29751i
$61$	3.19884	−	4.40283i	0.409570	−	0.563724i	−0.553544	−	0.832820i	$-0.686725\pi$
$61$	3.19884	−	4.40283i	0.409570	−	0.563724i	0.963113	+	0.269096i	$0.0867248\pi$
$62$	−5.55263	+	17.0892i	−0.705185	+	2.17034i
$63$	−2.81177	+	1.04591i	−0.354250	+	0.131772i
$64$	−7.29105	+	5.29726i	−0.911381	+	0.662157i
$65$	3.64228			0.451769
$66$	6.96844	−	13.3411i	0.857756	−	1.64218i
$67$	11.6236			1.42005			0.710023	−	0.704179i	$-0.248685\pi$
$67$	11.6236			1.42005			0.710023	+	0.704179i	$0.248685\pi$
$68$	19.8964	−	14.4556i	2.41279	−	1.75300i
$69$	10.5347	−	3.66897i	1.26823	−	0.441692i
$70$	−1.17602	+	3.61943i	−0.140562	+	0.432605i
$71$	0.493561	−	0.679329i	0.0585749	−	0.0806215i	−0.778725	−	0.627366i	$-0.784133\pi$
$71$	0.493561	−	0.679329i	0.0585749	−	0.0806215i	0.837300	+	0.546744i	$0.184133\pi$
$72$	−18.7579	−	12.4609i	−2.21064	−	1.46853i
$73$	1.62164	+	0.526902i	0.189798	+	0.0616692i	0.402374	−	0.915475i	$-0.368185\pi$
$73$	1.62164	+	0.526902i	0.189798	+	0.0616692i	−0.212576	+	0.977145i	$0.568185\pi$
$74$	−3.07228	−	9.45550i	−0.357145	−	1.09918i
$75$	−3.98739	+	3.02680i	−0.460424	+	0.349505i
$76$			30.4176i			3.48914i
$77$	−0.620412	+	3.25808i	−0.0707025	+	0.371293i
$78$	−0.238710	−	11.3774i	−0.0270286	−	1.28824i
$79$	−1.30582	−	1.79731i	−0.146917	−	0.202213i	0.729216	−	0.684284i	$-0.239885\pi$
$79$	−1.30582	−	1.79731i	−0.146917	−	0.202213i	−0.876133	+	0.482070i	$0.839885\pi$
$80$	−13.7284	+	4.46063i	−1.53488	+	0.498714i
$81$	2.05396	−	8.76249i	0.228218	−	0.973610i
$82$	−2.32365	−	1.68823i	−0.256604	−	0.186434i
$83$	−5.63425	−	4.09352i	−0.618439	−	0.449322i	0.233937	−	0.972252i	$-0.424839\pi$
$83$	−5.63425	−	4.09352i	−0.618439	−	0.449322i	−0.852376	+	0.522930i	$0.824839\pi$
$84$	8.06682	+	2.43522i	0.880162	+	0.265704i
$85$	6.98325	−	2.26900i	0.757440	−	0.246107i
$86$	6.37771	+	8.77816i	0.687726	+	0.946574i
$87$	−7.69876	+	0.161528i	−0.825393	+	0.0173176i
$88$	−22.5235	+	10.6077i	−2.40101	+	1.13078i
$89$			12.3634i			1.31052i	0.755404	+	0.655260i	$0.227441\pi$
$89$			12.3634i			1.31052i	−0.755404	+	0.655260i	$0.772559\pi$
$90$	−7.09231	−	8.94701i	−0.747595	−	0.943098i
$91$	0.774891	+	2.38487i	0.0812306	+	0.250002i
$92$	−29.7994	−	9.68242i	−3.10681	−	1.00946i
$93$	9.75416	+	6.77883i	1.01146	+	0.702932i
$94$	−6.82869	+	9.39889i	−0.704326	+	0.969422i
$95$	−2.80635	+	8.63704i	−0.287925	+	0.886142i
$96$	6.28094	+	18.0344i	0.641046	+	1.84063i
$97$	−7.64536	+	5.55468i	−0.776268	+	0.563992i	−0.903857	−	0.427835i	$-0.859276\pi$
$97$	−7.64536	+	5.55468i	−0.776268	+	0.563992i	0.127588	+	0.991827i	$0.459276\pi$
$98$	−2.62011			−0.264671
$99$	−7.11166	−	6.95876i	−0.714748	−	0.699382i
$100$	14.0610			1.40610
$101$	6.49503	−	4.71891i	0.646279	−	0.469549i	−0.215722	−	0.976455i	$-0.569211\pi$
$101$	6.49503	−	4.71891i	0.646279	−	0.469549i	0.862002	+	0.506905i	$0.169211\pi$
$102$	−7.54534	−	21.6649i	−0.747100	−	2.14514i
$103$	−0.940077	+	2.89326i	−0.0926286	+	0.285081i	−0.986628	−	0.162986i	$-0.947887\pi$
$103$	−0.940077	+	2.89326i	−0.0926286	+	0.285081i	0.894000	+	0.448067i	$0.147887\pi$
$104$	−11.0641	+	15.2284i	−1.08493	+	1.49327i
$105$	2.06589	+	1.43573i	0.201610	+	0.140113i
$106$	−3.64696	−	1.18497i	−0.354224	−	0.115095i
$107$	−3.81182	−	11.7316i	−0.368503	−	1.13414i	−0.947758	−	0.318989i	$-0.896657\pi$
$107$	−3.81182	−	11.7316i	−0.368503	−	1.13414i	0.579255	−	0.815146i	$-0.303343\pi$
$108$	−19.4763	+	16.1155i	−1.87410	+	1.55072i
$109$		−	17.5981i		−	1.68559i	−0.538236	−	0.842794i	$-0.680909\pi$
$109$		−	17.5981i		−	1.68559i	0.538236	−	0.842794i	$-0.319091\pi$
$110$	−12.5220	+	1.58604i	−1.19393	+	0.151223i
$111$	−6.57089	+	0.137864i	−0.623681	+	0.0130855i
$112$	−5.84142	−	8.04002i	−0.551962	−	0.759710i
$113$	15.6171	−	5.07430i	1.46913	−	0.477350i	0.538286	−	0.842762i	$-0.319072\pi$
$113$	15.6171	−	5.07430i	1.46913	−	0.477350i	0.930846	+	0.365412i	$0.119072\pi$
$114$	27.1635	+	8.20013i	2.54409	+	0.768013i
$115$	−7.56822	−	5.49863i	−0.705740	−	0.512750i
$116$	17.4982	+	12.7132i	1.62467	+	1.18039i
$117$	−7.24582	−	2.02254i	−0.669876	−	0.186984i
$118$	28.1567	−	9.14868i	2.59204	−	0.842204i
$119$	2.97136	+	4.08973i	0.272384	+	0.374905i
$120$	0.396139	+	18.8808i	0.0361624	+	1.72357i
$121$	−10.6526	+	2.74253i	−0.968421	+	0.249321i
$122$			14.2591i			1.29096i
$123$	−1.51233	+	1.14800i	−0.136362	+	0.103512i
$124$	−10.3100	−	31.7310i	−0.925868	−	2.84953i
$125$	10.8996	+	3.54151i	0.974893	+	0.316762i
$126$	4.34939	−	6.54733i	0.387475	−	0.583283i
$127$	12.5993	−	17.3415i	1.11801	−	1.53881i	0.308950	−	0.951078i	$-0.400023\pi$
$127$	12.5993	−	17.3415i	1.11801	−	1.53881i	0.809059	−	0.587728i	$-0.199977\pi$
$128$	0.482639	−	1.48541i	0.0426597	−	0.131293i
$129$	6.77372	−	2.35912i	0.596393	−	0.207709i
$130$	−7.72058	+	5.60933i	−0.677140	+	0.491971i
$131$	−0.927041			−0.0809959			−0.0404980	−	0.999180i	$-0.512894\pi$
$131$	−0.927041			−0.0809959			−0.0404980	+	0.999180i	$0.512894\pi$
$132$	4.09255	+	27.6459i	0.356211	+	2.40626i
$133$	−6.25236			−0.542149
$134$	−24.6386	+	17.9010i	−2.12845	+	1.54641i
$135$	−7.01710	+	2.77909i	−0.603936	+	0.239186i
$136$	−11.7262	+	36.0897i	−1.00552	+	3.09466i
$137$	12.0157	−	16.5382i	1.02657	−	1.41295i	0.119080	−	0.992885i	$-0.462005\pi$
$137$	12.0157	−	16.5382i	1.02657	−	1.41295i	0.907492	−	0.420070i	$-0.137995\pi$
$138$	−16.6801	+	24.0012i	−1.41990	+	2.04312i
$139$	3.32678	+	1.08094i	0.282174	+	0.0916839i	0.446685	−	0.894691i	$-0.352605\pi$
$139$	3.32678	+	1.08094i	0.282174	+	0.0916839i	−0.164511	+	0.986375i	$0.552605\pi$
$140$	−2.18362	−	6.72050i	−0.184550	−	0.567986i
$141$	4.64352	+	6.11718i	0.391055	+	0.515159i
$142$			2.20010i			0.184628i
$143$	−6.06081	+	5.69519i	−0.506830	+	0.476256i
$144$	29.7878	−	1.25051i	2.48232	−	0.104209i
$145$	3.79567	+	5.22430i	0.315213	+	0.433854i
$146$	−4.24886	+	1.38054i	−0.351639	+	0.114254i
$147$	−0.500561	+	1.65814i	−0.0412856	+	0.136761i
$148$	14.9347	+	10.8507i	1.22763	+	0.891922i
$149$	−14.3260	−	10.4084i	−1.17363	−	0.852693i	−0.182193	−	0.983263i	$-0.558319\pi$
$149$	−14.3260	−	10.4084i	−1.17363	−	0.852693i	−0.991439	+	0.130570i	$0.958319\pi$
$150$	3.79065	−	12.5568i	0.309505	−	1.02526i
$151$	−3.83064	+	1.24465i	−0.311733	+	0.101288i	−0.460705	−	0.887553i	$-0.652403\pi$
$151$	−3.83064	+	1.24465i	−0.311733	+	0.101288i	0.148972	+	0.988841i	$0.452403\pi$
$152$	−27.5869	−	37.9701i	−2.23759	−	3.07978i
$153$	−15.1522	+	0.636099i	−1.22498	+	0.0514256i
$154$	−3.70255	−	7.86167i	−0.298360	−	0.633511i
$155$		−	9.96120i		−	0.800103i
$156$	12.7757	+	16.8302i	1.02288	+	1.34750i
$157$	−1.53911	−	4.73690i	−0.122835	−	0.378046i	0.870666	−	0.491875i	$-0.163688\pi$
$157$	−1.53911	−	4.73690i	−0.122835	−	0.378046i	−0.993500	+	0.113829i	$0.963688\pi$
$158$	5.53594	+	1.79874i	0.440416	+	0.143100i
$159$	−1.44665	+	2.08161i	−0.114727	+	0.165082i
$160$	9.41315	−	12.9561i	0.744175	−	1.02427i
$161$	1.99023	−	6.12531i	0.156852	−	0.482742i
$162$	9.14096	+	21.7372i	0.718182	+	1.70784i
$163$	4.91370	−	3.57001i	0.384871	−	0.279625i	−0.378480	−	0.925610i	$-0.623553\pi$
$163$	4.91370	−	3.57001i	0.384871	−	0.279625i	0.763350	+	0.645985i	$0.223553\pi$
$164$	5.33303			0.416440
$165$	−1.38855	+	8.22760i	−0.108098	+	0.640518i
$166$	18.2473			1.41626
$167$	5.96661	−	4.33500i	0.461711	−	0.335452i	−0.332491	−	0.943106i	$-0.607889\pi$
$167$	5.96661	−	4.33500i	0.461711	−	0.335452i	0.794202	+	0.607654i	$0.207889\pi$
$168$	−12.2784	+	4.27625i	−0.947296	+	0.329920i
$169$	2.07410	−	6.38344i	0.159547	−	0.491034i
$170$	−11.3081	+	15.5643i	−0.867291	+	1.19372i
$171$	10.3790	−	15.6239i	0.793698	−	1.19479i
$172$	−19.1608	−	6.22572i	−1.46100	−	0.474706i
$173$	0.625970	+	1.92654i	0.0475916	+	0.146472i	0.972028	−	0.234863i	$-0.0754643\pi$
$173$	0.625970	+	1.92654i	0.0475916	+	0.146472i	−0.924437	+	0.381335i	$0.875464\pi$
$174$	16.0704	−	12.1990i	1.21829	−	0.924800i
$175$			2.89026i			0.218483i
$176$	15.8695	−	28.8888i	1.19621	−	2.17758i
$177$	−0.410535	−	19.5669i	−0.0308577	−	1.47074i
$178$	−19.0404	−	26.2069i	−1.42714	−	1.96429i
$179$	−2.57429	+	0.836439i	−0.192412	+	0.0625184i	−0.403638	−	0.914919i	$-0.632254\pi$
$179$	−2.57429	+	0.836439i	−0.192412	+	0.0625184i	0.211226	+	0.977437i	$0.432254\pi$
$180$	20.4185	+	5.69945i	1.52191	+	0.424812i
$181$	1.29243	+	0.939009i	0.0960659	+	0.0697960i	0.634781	−	0.772692i	$-0.281090\pi$
$181$	1.29243	+	0.939009i	0.0960659	+	0.0697960i	−0.538715	+	0.842488i	$0.681090\pi$
$182$	−5.31539	−	3.86186i	−0.394003	−	0.286260i
$183$	9.02394	+	2.72415i	0.667069	+	0.201375i
$184$	45.9798	−	14.9398i	3.38968	−	1.10137i
$185$	3.23961	+	4.45893i	0.238181	+	0.327827i
$186$	−31.1158	+	0.652844i	−2.28152	+	0.0478689i
$187$	−8.07236	+	14.6949i	−0.590309	+	1.07460i
$188$		−	21.5715i		−	1.57326i
$189$	−3.31256	−	4.00337i	−0.240953	−	0.291202i
$190$	−7.35293	−	22.6300i	−0.533438	−	1.64175i
$191$	4.73477	+	1.53842i	0.342596	+	0.111316i	0.475261	−	0.879845i	$-0.342354\pi$
$191$	4.73477	+	1.53842i	0.342596	+	0.111316i	−0.132665	+	0.991161i	$0.542354\pi$
$192$	−12.8182	−	8.90820i	−0.925070	−	0.642894i
$193$	−10.9939	+	15.1318i	−0.791357	+	1.08921i	0.202581	+	0.979266i	$0.435067\pi$
$193$	−10.9939	+	15.1318i	−0.791357	+	1.08921i	−0.993938	+	0.109944i	$0.964933\pi$
$194$	7.65142	−	23.5486i	0.549340	−	1.69069i
$195$	2.07489	+	5.95763i	0.148586	+	0.426635i
$196$	3.93585	−	2.85956i	0.281132	−	0.204254i
$197$	9.87372			0.703474			0.351737	−	0.936099i	$-0.385591\pi$
$197$	9.87372			0.703474			0.351737	+	0.936099i	$0.385591\pi$
$198$	25.7916	+	3.79819i	1.83293	+	0.269926i
$199$	−20.6993			−1.46734			−0.733669	−	0.679507i	$-0.762194\pi$
$199$	−20.6993			−1.46734			−0.733669	+	0.679507i	$0.762194\pi$
$200$	−17.5523	+	12.7525i	−1.24114	+	0.901738i
$201$	6.62159	+	19.0125i	0.467051	+	1.34104i
$202$	−6.50018	+	20.0055i	−0.457351	+	1.40758i
$203$	−2.61321	+	3.59677i	−0.183411	+	0.252444i
$204$	34.9792	+	24.3094i	2.44903	+	1.70200i
$205$	1.51431	+	0.492029i	0.105764	+	0.0343648i
$206$	−2.46310	−	7.58066i	−0.171613	−	0.528169i
$207$	12.0026	+	15.1414i	0.834238	+	1.05240i
$208$		−	24.9206i		−	1.72793i
$209$	−8.83539	−	18.7603i	−0.611157	−	1.29768i
$210$	−6.59021	+	0.138270i	−0.454767	+	0.00954152i
$211$	6.49549	+	8.94027i	0.447168	+	0.615474i	0.971786	−	0.235864i	$-0.0757920\pi$
$211$	6.49549	+	8.94027i	0.447168	+	0.615474i	−0.524618	+	0.851338i	$0.675792\pi$
$212$	6.77162	−	2.20023i	0.465077	−	0.151113i
$213$	1.39234	+	0.420319i	0.0954013	+	0.0287998i
$214$	26.1473	+	18.9972i	1.78740	+	1.29862i
$215$	−4.86630	−	3.53557i	−0.331879	−	0.241124i
$216$	9.69632	−	37.7807i	0.659751	−	2.57065i
$217$	6.52234	−	2.11924i	0.442765	−	0.143863i
$218$	27.1021	+	37.3028i	1.83559	+	2.52647i
$219$	0.0619498	+	2.95265i	0.00418618	+	0.199522i
$220$	17.0792	−	16.0489i	1.15148	−	1.08202i
$221$			12.6764i			0.852705i
$222$	13.7161	−	10.4118i	0.920562	−	0.698794i
$223$	6.70166	+	20.6256i	0.448776	+	1.38119i	0.878289	+	0.478130i	$0.158685\pi$
$223$	6.70166	+	20.6256i	0.448776	+	1.38119i	−0.429513	+	0.903061i	$0.641315\pi$
$224$	10.4860	+	3.40710i	0.700623	+	0.227646i
$225$	−7.22240	−	4.79784i	−0.481493	−	0.319856i
$226$	−25.2890	+	34.8073i	−1.68220	+	2.31535i
$227$	−5.05495	+	15.5575i	−0.335509	+	1.03259i	0.630962	+	0.775814i	$0.282660\pi$
$227$	−5.05495	+	15.5575i	−0.335509	+	1.03259i	−0.966471	+	0.256776i	$0.917340\pi$
$228$	−49.7537	+	17.3280i	−3.29502	+	1.14757i
$229$	−8.58044	+	6.23406i	−0.567012	+	0.411958i	−0.834018	−	0.551737i	$-0.813965\pi$
$229$	−8.58044	+	6.23406i	−0.567012	+	0.411958i	0.267007	+	0.963695i	$0.413965\pi$
$230$	24.5107			1.61619
$231$	−5.68263	+	0.841228i	−0.373890	+	0.0553488i
$232$	−33.3730			−2.19104
$233$	12.3771	−	8.99246i	0.810848	−	0.589116i	−0.103228	−	0.994658i	$-0.532917\pi$
$233$	12.3771	−	8.99246i	0.810848	−	0.589116i	0.914076	+	0.405542i	$0.132917\pi$
$234$	18.4739	−	6.87181i	1.20768	−	0.449224i
$235$	1.99020	−	6.12520i	0.129826	−	0.399564i
$236$	−32.3114	+	44.4728i	−2.10329	+	2.89493i
$237$	2.19595	−	3.15979i	0.142642	−	0.205251i
$238$	−12.5969	−	4.09297i	−0.816533	−	0.265308i
$239$	−1.28890	−	3.96682i	−0.0833719	−	0.256592i	0.900677	−	0.434489i	$-0.143071\pi$
$239$	−1.28890	−	3.96682i	−0.0833719	−	0.256592i	−0.984049	+	0.177896i	$0.943071\pi$
$240$	−15.1169	−	19.9143i	−0.975789	−	1.28546i
$241$			2.72135i			0.175298i	0.996151	+	0.0876489i	$0.0279353\pi$
$241$			2.72135i			0.175298i	−0.996151	+	0.0876489i	$0.972065\pi$
$242$	18.3568	−	22.2191i	1.18002	−	1.42830i
$243$	15.5028	−	1.63208i	0.994504	−	0.104698i
$244$	−15.5623	−	21.4196i	−0.996272	−	1.37125i
$245$	1.38140	−	0.448846i	0.0882547	−	0.0286757i
$246$	1.43771	−	4.76250i	0.0916649	−	0.303646i
$247$	−12.6841	−	9.21555i	−0.807071	−	0.586371i
$248$	41.6480	+	30.2591i	2.64465	+	1.92145i
$249$	3.48606	−	11.5478i	0.220920	−	0.731814i
$250$	−28.5582	+	9.27914i	−1.80618	+	0.586864i
$251$	−13.0604	−	17.9761i	−0.824363	−	1.13464i	−0.988946	−	0.148275i	$-0.952628\pi$
$251$	−13.0604	−	17.9761i	−0.824363	−	1.13464i	0.164583	−	0.986363i	$-0.447372\pi$
$252$	0.612165	+	14.5821i	0.0385628	+	0.918584i
$253$	21.1915	−	2.68412i	1.33230	−	0.168749i
$254$			56.1627i			3.52396i
$255$	7.68951	+	10.1298i	0.481536	+	0.634355i
$256$	−4.30530	−	13.2503i	−0.269081	−	0.828147i
$257$	−10.7436	−	3.49081i	−0.670168	−	0.217751i	−0.0458820	−	0.998947i	$-0.514610\pi$
$257$	−10.7436	−	3.49081i	−0.670168	−	0.217751i	−0.624286	+	0.781196i	$0.714610\pi$
$258$	−10.7252	+	15.4326i	−0.667719	+	0.960791i
$259$	−2.23037	+	3.06985i	−0.138589	+	0.190751i
$260$	5.47565	−	16.8523i	0.339585	−	1.04514i
$261$	−4.64996	−	12.5007i	−0.287825	−	0.773777i
$262$	1.96506	−	1.42770i	0.121402	−	0.0882036i
$263$	−14.7653			−0.910467			−0.455233	−	0.890372i	$-0.650444\pi$
$263$	−14.7653			−0.910467			−0.455233	+	0.890372i	$0.650444\pi$
$264$	−30.1818	−	30.7985i	−1.85756	−	1.89552i
$265$	2.12579			0.130586
$266$	13.2532	−	9.62902i	0.812607	−	0.590393i
$267$	−20.2227	+	7.04306i	−1.23761	+	0.431028i
$268$	17.4744	−	53.7807i	1.06742	−	3.28518i
$269$	−2.70743	+	3.72645i	−0.165075	+	0.227206i	−0.883539	−	0.468358i	$-0.844846\pi$
$269$	−2.70743	+	3.72645i	−0.165075	+	0.227206i	0.718464	+	0.695564i	$0.244846\pi$
$270$	10.5943	−	16.6976i	0.644746	−	1.01619i
$271$	−5.23895	−	1.70224i	−0.318244	−	0.103404i	0.145539	−	0.989352i	$-0.453508\pi$
$271$	−5.23895	−	1.70224i	−0.318244	−	0.103404i	−0.463783	+	0.885949i	$0.653508\pi$
$272$	−15.5245	−	47.7796i	−0.941313	−	2.89706i
$273$	−3.45947	+	2.62607i	−0.209377	+	0.158937i
$274$			53.5612i			3.23575i
$275$	−8.67225	+	4.08431i	−0.522957	+	0.246293i
$276$	−1.13840	−	54.2584i	−0.0685236	−	3.26597i
$277$	0.662374	+	0.911679i	0.0397982	+	0.0547775i	0.828452	−	0.560060i	$-0.189222\pi$
$277$	0.662374	+	0.911679i	0.0397982	+	0.0547775i	−0.788654	+	0.614837i	$0.789222\pi$
$278$	−8.71654	+	2.83217i	−0.522783	+	0.169863i
$279$	−5.53140	+	19.8165i	−0.331156	+	1.18638i
$280$	8.82088	+	6.40875i	0.527149	+	0.382996i
$281$	3.61575	+	2.62699i	0.215697	+	0.156713i	0.690388	−	0.723440i	$-0.257440\pi$
$281$	3.61575	+	2.62699i	0.215697	+	0.156713i	−0.474690	+	0.880153i	$0.657440\pi$
$282$	−19.2638	−	5.81535i	−1.14714	−	0.346299i
$283$	−5.62739	+	1.82845i	−0.334513	+	0.108690i	−0.471458	−	0.881889i	$-0.656272\pi$
$283$	−5.62739	+	1.82845i	−0.334513	+	0.108690i	0.136944	+	0.990579i	$0.456272\pi$
$284$	−2.40116	−	3.30491i	−0.142483	−	0.196111i
$285$	−15.7262	+	0.329953i	−0.931540	+	0.0195447i
$286$	4.07622	−	21.4062i	0.241032	−	1.26577i
$287$			1.09621i			0.0647072i
$288$	−25.9207	+	20.5473i	−1.52739	+	1.21076i
$289$	2.64359	+	8.13615i	0.155506	+	0.478597i
$290$	−16.0915	−	5.22844i	−0.944924	−	0.307024i
$291$	−13.4410	−	9.34109i	−0.787928	−	0.547585i
$292$	4.87580	−	6.71097i	0.285335	−	0.392730i
$293$	−9.95260	+	30.6310i	−0.581437	+	1.78948i	0.0316928	+	0.999498i	$0.489910\pi$
$293$	−9.95260	+	30.6310i	−0.581437	+	1.78948i	−0.613130	+	0.789982i	$0.710090\pi$
$294$	−1.49260	−	4.28568i	−0.0870500	−	0.249946i
$295$	−13.2779	+	9.64695i	−0.773069	+	0.561667i
$296$	−28.4838			−1.65559
$297$	7.33107	−	15.5966i	0.425392	−	0.905009i
$298$	46.3967			2.68769
$299$	13.0658	−	9.49289i	0.755617	−	0.548988i
$300$	8.01014	+	22.9995i	0.462466	+	1.32787i
$301$	1.27970	−	3.93852i	0.0737608	−	0.227012i
$302$	6.20302	−	8.53772i	0.356944	−	0.491291i
$303$	11.4187	+	7.93562i	0.655987	+	0.455889i
$304$	59.0949	+	19.2011i	3.38932	+	1.10126i
$305$	−2.44270	−	7.51787i	−0.139869	−	0.430472i
$306$	31.1387	−	24.6837i	1.78008	−	1.41107i
$307$			8.56138i			0.488624i	0.969697	+	0.244312i	$0.0785621\pi$
$307$			8.56138i			0.488624i	−0.969697	+	0.244312i	$0.921438\pi$
$308$	14.1420	+	7.76863i	0.805815	+	0.442659i
$309$	−5.26800	+	0.110528i	−0.299686	+	0.00628775i
$310$	15.3409	+	21.1149i	0.871302	+	1.19924i
$311$	8.01237	−	2.60338i	0.454340	−	0.147624i	−0.0729023	−	0.997339i	$-0.523226\pi$
$311$	8.01237	−	2.60338i	0.454340	−	0.147624i	0.527242	+	0.849715i	$0.323226\pi$
$312$	−31.2119	−	9.42226i	−1.76703	−	0.533431i
$313$	−1.11276	−	0.808471i	−0.0628972	−	0.0456975i	0.555892	−	0.831254i	$-0.312377\pi$
$313$	−1.11276	−	0.808471i	−0.0628972	−	0.0456975i	−0.618790	+	0.785557i	$0.712377\pi$
$314$	10.5576	+	7.67054i	0.595799	+	0.432874i
$315$	−1.17153	+	4.19705i	−0.0660081	+	0.236477i
$316$	−10.2790	+	3.33986i	−0.578241	+	0.187882i
$317$	8.17470	+	11.2515i	0.459137	+	0.631948i	0.974329	−	0.225127i	$-0.0722796\pi$
$317$	8.17470	+	11.2515i	0.459137	+	0.631948i	−0.515193	+	0.857074i	$0.672280\pi$
$318$	−0.139322	−	6.64034i	−0.00781276	−	0.372372i
$319$	−14.4850	−	2.75826i	−0.811002	−	0.154433i
$320$			13.0902i			0.731766i
$321$	17.0177	−	12.9181i	0.949838	−	0.721017i
$322$	5.21463	+	16.0490i	0.290600	+	0.894374i
$323$	−30.0599	−	9.76705i	−1.67258	−	0.543453i
$324$	−37.4550	−	22.6766i	−2.08083	−	1.25981i
$325$	−4.26004	+	5.86344i	−0.236304	+	0.325245i
$326$	−4.91760	+	15.1348i	−0.272361	+	0.838240i
$327$	28.7849	−	10.0251i	1.59181	−	0.554388i
$328$	−6.65719	+	4.83673i	−0.367582	+	0.267064i
$329$	4.43404			0.244457
$330$	−9.72769	−	19.5786i	−0.535491	−	1.07777i
$331$	−5.50646			−0.302662			−0.151331	−	0.988483i	$-0.548356\pi$
$331$	−5.50646			−0.302662			−0.151331	+	0.988483i	$0.548356\pi$
$332$	−27.4104	+	19.9149i	−1.50434	+	1.09297i
$333$	−3.96874	−	10.6694i	−0.217485	−	0.584679i
$334$	−5.97134	+	18.3779i	−0.326737	+	1.00559i
$335$	9.92368	−	13.6588i	0.542189	−	0.746259i
$336$	9.82329	−	14.1349i	0.535904	−	0.771121i
$337$	−0.896422	−	0.291265i	−0.0488312	−	0.0158662i	0.284500	−	0.958676i	$-0.408173\pi$
$337$	−0.896422	−	0.291265i	−0.0488312	−	0.0158662i	−0.333331	+	0.942810i	$0.608173\pi$
$338$	5.43438	+	16.7253i	0.295591	+	0.909737i
$339$	17.1966	+	22.6540i	0.933989	+	1.23040i
$340$		−	35.7217i		−	1.93728i
$341$	15.5757	+	16.5756i	0.843471	+	0.897619i
$342$	2.06135	+	49.1024i	0.111465	+	2.65515i
$343$	0.587785	+	0.809017i	0.0317374	+	0.0436828i
$344$	29.5646	−	9.60614i	1.59402	−	0.517928i
$345$	4.68267	−	15.5116i	0.252106	−	0.835119i
$346$	−4.29386	−	3.11967i	−0.230839	−	0.167715i
$347$	−16.1319	−	11.7205i	−0.866005	−	0.629189i	0.0635072	−	0.997981i	$-0.479771\pi$
$347$	−16.1319	−	11.7205i	−0.866005	−	0.629189i	−0.929512	+	0.368792i	$0.879771\pi$
$348$	−10.8266	+	35.8639i	−0.580368	+	1.92251i
$349$	−26.8118	+	8.71169i	−1.43520	+	0.466326i	−0.920399	−	0.390981i	$-0.872136\pi$
$349$	−26.8118	+	8.71169i	−1.43520	+	0.466326i	−0.514806	+	0.857307i	$0.672136\pi$
$350$	−4.45118	−	6.12652i	−0.237925	−	0.327476i
$351$	−0.819481	−	13.0041i	−0.0437407	−	0.694106i
$352$	4.59497	+	36.2779i	0.244913	+	1.93362i
$353$		−	10.6380i		−	0.566206i	−0.959089	−	0.283103i	$-0.908636\pi$
$353$		−	10.6380i		−	0.566206i	0.959089	−	0.283103i	$-0.0913639\pi$
$354$	31.0044	+	40.8439i	1.64787	+	2.17083i
$355$	−0.376894	−	1.15996i	−0.0200035	−	0.0615643i
$356$	57.2038	+	18.5867i	3.03180	+	0.985091i
$357$	−4.99683	+	7.19001i	−0.264460	+	0.380536i
$358$	4.16860	−	5.73758i	0.220317	−	0.303241i
$359$	7.34213	−	22.5967i	0.387503	−	1.19261i	−0.547146	−	0.837037i	$-0.684286\pi$
$359$	7.34213	−	22.5967i	0.387503	−	1.19261i	0.934648	−	0.355573i	$-0.115714\pi$
$360$	−30.6574	+	11.4038i	−1.61579	+	0.601030i
$361$	16.2548	−	11.8098i	0.855516	−	0.621569i
$362$	−4.18572			−0.219997
$363$	−10.5544	−	15.8620i	−0.553963	−	0.832542i
$364$	12.1994			0.639422
$365$	2.00364	−	1.45573i	0.104875	−	0.0761963i
$366$	−23.3235	+	8.12300i	−1.21914	+	0.424596i
$367$	2.83444	−	8.72351i	0.147957	−	0.455364i	−0.849423	−	0.527713i	$-0.823050\pi$
$367$	2.83444	−	8.72351i	0.147957	−	0.455364i	0.997379	+	0.0723494i	$0.0230497\pi$
$368$	−37.6218	+	51.7820i	−1.96117	+	2.69932i
$369$	−2.73929	−	1.81971i	−0.142602	−	0.0947305i
$370$	−13.7341	−	4.46247i	−0.714000	−	0.231993i
$371$	0.452260	+	1.39191i	0.0234802	+	0.0722645i
$372$	46.0287	−	34.9402i	2.38648	−	1.81156i
$373$		−	8.91003i		−	0.461344i	−0.973032	−	0.230672i	$-0.925908\pi$
$373$		−	8.91003i		−	0.461344i	0.973032	−	0.230672i	$-0.0740924\pi$
$374$	−5.51998	−	43.5809i	−0.285431	−	2.25352i
$375$	0.416389	+	19.8459i	0.0215022	+	1.02484i
$376$	19.5640	+	26.9276i	1.00894	+	1.38868i
$377$	−10.6028	+	3.44505i	−0.546071	+	0.177429i
$378$	13.1871	+	3.38444i	0.678272	+	0.174077i
$379$	−5.37945	−	3.90840i	−0.276324	−	0.200761i	0.440989	−	0.897513i	$-0.354628\pi$
$379$	−5.37945	−	3.90840i	−0.276324	−	0.200761i	−0.717312	+	0.696752i	$0.754628\pi$
$380$	35.7435	+	25.9692i	1.83360	+	1.33219i
$381$	35.5427	+	10.7296i	1.82091	+	0.549697i
$382$	−12.4056	+	4.03083i	−0.634726	+	0.206235i
$383$	20.5030	+	28.2199i	1.04765	+	1.44197i	0.890826	+	0.454345i	$0.150127\pi$
$383$	20.5030	+	28.2199i	1.04765	+	1.44197i	0.156827	+	0.987626i	$0.449873\pi$
$384$	2.70461	−	0.0567457i	0.138019	−	0.00289579i
$385$	3.29887	+	3.51064i	0.168126	+	0.178919i
$386$		−	49.0063i		−	2.49435i
$387$	7.71756	+	9.73578i	0.392306	+	0.494897i
$388$	14.2070	+	43.7247i	0.721252	+	2.21979i
$389$	21.8293	+	7.09276i	1.10679	+	0.359617i	0.804711	−	0.593667i	$-0.202320\pi$
$389$	21.8293	+	7.09276i	1.10679	+	0.359617i	0.302076	+	0.953284i	$0.402320\pi$
$390$	−13.5733	−	9.43300i	−0.687310	−	0.477658i
$391$	19.1371	−	26.3400i	0.967806	−	1.33207i
$392$	−2.31965	+	7.13914i	−0.117160	+	0.360581i
$393$	−0.528107	−	1.51635i	−0.0266395	−	0.0764897i
$394$	−20.9295	+	15.2061i	−1.05441	+	0.766074i
$395$	−3.22686			−0.162361
$396$	−42.8886	+	22.4431i	−2.15523	+	1.12781i
$397$	−10.0308			−0.503430			−0.251715	−	0.967801i	$-0.580995\pi$
$397$	−10.0308			−0.503430			−0.251715	+	0.967801i	$0.580995\pi$
$398$	43.8767	−	31.8783i	2.19934	−	1.59791i
$399$	−3.56178	−	10.2269i	−0.178312	−	0.511986i
$400$	8.87602	−	27.3176i	0.443801	−	1.36588i
$401$	16.4533	−	22.6460i	0.821637	−	1.13089i	−0.167785	−	0.985824i	$-0.553662\pi$
$401$	16.4533	−	22.6460i	0.821637	−	1.13089i	0.989422	−	0.145063i	$-0.0463384\pi$
$402$	−43.3164	−	30.1035i	−2.16042	−	1.50142i
$403$	16.3554	+	5.31420i	0.814721	+	0.264719i
$404$	−12.0694	−	37.1458i	−0.600476	−	1.84807i
$405$	−8.54316	−	9.89462i	−0.424513	−	0.491668i
$406$		−	11.6486i		−	0.578112i
$407$	−12.3629	−	2.35418i	−0.612807	−	0.116692i
$408$	−65.7115	+	1.37870i	−3.25321	+	0.0682558i
$409$	−11.7100	−	16.1175i	−0.579024	−	0.796958i	0.414564	−	0.910020i	$-0.363934\pi$
$409$	−11.7100	−	16.1175i	−0.579024	−	0.796958i	−0.993588	+	0.113062i	$0.963934\pi$
$410$	−3.96766	+	1.28917i	−0.195949	+	0.0636676i
$411$	33.8963	+	10.2327i	1.67198	+	0.504739i
$412$	11.9734	+	8.69922i	0.589889	+	0.428580i
$413$	−9.14144	−	6.64164i	−0.449821	−	0.326814i
$414$	−48.7607	−	13.6107i	−2.39646	−	0.668927i
$415$	−9.62053	+	3.12590i	−0.472253	+	0.153444i
$416$	16.2510	+	22.3675i	0.796768	+	1.09666i
$417$	0.127090	+	6.05736i	0.00622362	+	0.296630i
$418$	47.6205	+	26.1594i	2.32919	+	1.27950i
$419$			28.1803i			1.37670i	0.725380	+	0.688349i	$0.241664\pi$
$419$			28.1803i			1.37670i	−0.725380	+	0.688349i	$0.758336\pi$
$420$	9.74869	−	7.40019i	0.475688	−	0.361092i
$421$	2.96828	+	9.13543i	0.144665	+	0.445234i	0.996968	−	0.0778153i	$-0.0247944\pi$
$421$	2.96828	+	9.13543i	0.144665	+	0.445234i	−0.852303	+	0.523049i	$0.824794\pi$
$422$	−27.5371	−	8.94736i	−1.34049	−	0.435551i
$423$	−7.36053	+	11.0801i	−0.357881	+	0.538734i
$424$	−6.45750	+	8.88798i	−0.313604	+	0.431639i
$425$	−4.51498	+	13.8957i	−0.219009	+	0.674039i
$426$	−3.59867	+	1.25333i	−0.174356	+	0.0607239i
$427$	4.40283	−	3.19884i	0.213068	−	0.154803i
$428$	−60.0110			−2.90074
$429$	−12.7682	−	6.66921i	−0.616455	−	0.321993i
$430$	15.7602			0.760022
$431$	−18.4535	+	13.4072i	−0.888872	+	0.645803i	−0.935584	−	0.353105i	$-0.885126\pi$
$431$	−18.4535	+	13.4072i	−0.888872	+	0.645803i	0.0467117	+	0.998908i	$0.485126\pi$
$432$	19.0146	+	48.0112i	0.914842	+	2.30994i
$433$	10.9045	−	33.5606i	0.524037	−	1.61282i	−0.242175	−	0.970233i	$-0.577861\pi$
$433$	10.9045	−	33.5606i	0.524037	−	1.61282i	0.766212	−	0.642588i	$-0.222139\pi$
$434$	−10.5617	+	14.5370i	−0.506979	+	0.697797i
$435$	−6.38304	+	9.18466i	−0.306043	+	0.440371i
$436$	−81.4238	−	26.4562i	−3.89949	−	1.26702i
$437$	12.4437	+	38.2976i	0.595261	+	1.83202i
$438$	−4.67858	−	6.16337i	−0.223551	−	0.294497i
$439$		−	21.2802i		−	1.01565i	−0.861461	−	0.507823i	$-0.830450\pi$
$439$		−	21.2802i		−	1.01565i	0.861461	−	0.507823i	$-0.169550\pi$
$440$	−6.76448	+	35.5235i	−0.322484	+	1.69352i
$441$	−2.99736	+	0.125831i	−0.142731	+	0.00599196i
$442$	−19.5224	−	26.8703i	−0.928585	−	1.27809i
$443$	−20.0395	+	6.51124i	−0.952107	+	0.309358i	−0.743572	−	0.668656i	$-0.766870\pi$
$443$	−20.0395	+	6.51124i	−0.952107	+	0.309358i	−0.208536	+	0.978015i	$0.566870\pi$
$444$	−9.24052	+	30.6099i	−0.438536	+	1.45268i
$445$	14.5282	+	10.5553i	0.688701	+	0.500371i
$446$	−45.9703	−	33.3993i	−2.17675	−	1.58150i
$447$	8.86389	−	29.3622i	0.419248	−	1.38879i
$448$	−8.57114	+	2.78493i	−0.404948	+	0.131576i
$449$	13.2534	+	18.2417i	0.625465	+	0.860879i	0.997736	−	0.0672452i	$-0.0214210\pi$
$449$	13.2534	+	18.2417i	0.625465	+	0.860879i	−0.372271	+	0.928124i	$0.621421\pi$
$450$	22.6984	−	0.952893i	1.07001	−	0.0449198i
$451$	−3.28919	+	1.54909i	−0.154882	+	0.0729436i
$452$		−	79.8866i		−	3.75755i
$453$	−4.21806	−	5.55669i	−0.198182	−	0.261076i
$454$	−13.2445	−	40.7624i	−0.621596	−	1.91308i
$455$	3.46401	+	1.12553i	0.162395	+	0.0527654i
$456$	46.3918	−	66.7540i	2.17250	−	3.12604i
$457$	−4.79040	+	6.59343i	−0.224086	+	0.308427i	−0.906226	−	0.422794i	$-0.861049\pi$
$457$	−4.79040	+	6.59343i	−0.224086	+	0.308427i	0.682140	+	0.731221i	$0.261049\pi$
$458$	8.58725	−	26.4288i	0.401256	−	1.23494i
$459$	−9.67220	−	24.4219i	−0.451460	−	1.13992i
$460$	−36.8192	+	26.7507i	−1.71670	+	1.24726i
$461$	−16.4341			−0.765410			−0.382705	−	0.923871i	$-0.625007\pi$
$461$	−16.4341			−0.765410			−0.382705	+	0.923871i	$0.625007\pi$
$462$	10.7500	−	10.5348i	0.500136	−	0.490122i
$463$	2.82165			0.131133			0.0655665	−	0.997848i	$-0.479115\pi$
$463$	2.82165			0.131133			0.0655665	+	0.997848i	$0.479115\pi$
$464$	35.7448	−	25.9701i	1.65941	−	1.20563i
$465$	16.2934	−	5.67459i	0.755589	−	0.263153i
$466$	−12.3869	+	38.1229i	−0.573811	+	1.76601i
$467$	14.4780	−	19.9272i	0.669962	−	0.922123i	−0.329798	−	0.944052i	$-0.606981\pi$
$467$	14.4780	−	19.9272i	0.669962	−	0.922123i	0.999760	+	0.0219285i	$0.00698060\pi$
$468$	−20.2511	+	30.4848i	−0.936106	+	1.40916i
$469$	11.0547	+	3.59188i	0.510457	+	0.165858i
$470$	5.21454	+	16.0487i	0.240529	+	0.740271i
$471$	6.87131	−	5.21597i	0.316613	−	0.240339i
$472$		−	84.8197i		−	3.90414i
$473$	13.6260	−	1.72587i	0.626522	−	0.0793555i
$474$	0.211484	+	10.0798i	0.00971379	+	0.462979i
$475$	−10.6218	−	14.6197i	−0.487363	−	0.670798i
$476$	23.3896	−	7.59975i	1.07206	−	0.348334i
$477$	−4.22897	−	1.18044i	−0.193631	−	0.0540486i
$478$	8.84124	+	6.42354i	0.404389	+	0.293806i
$479$	−3.73171	−	2.71124i	−0.170506	−	0.123880i	0.499260	−	0.866452i	$-0.333605\pi$
$479$	−3.73171	−	2.71124i	−0.170506	−	0.123880i	−0.669766	+	0.742573i	$0.733605\pi$
$480$	26.5545	+	8.01630i	1.21204	+	0.365892i
$481$	−9.04948	+	2.94035i	−0.412621	+	0.134069i
$482$	−4.19105	−	5.76849i	−0.190897	−	0.262747i
$483$	11.1529	−	0.233999i	0.507473	−	0.0106473i
$484$	−3.32541	+	53.4113i	−0.151155	+	2.42779i
$485$			13.7263i			0.623281i
$486$	−30.3480	+	27.3348i	−1.37661	+	1.23993i
$487$	7.05032	+	21.6987i	0.319481	+	0.983260i	0.973871	+	0.227103i	$0.0729254\pi$
$487$	7.05032	+	21.6987i	0.319481	+	0.983260i	−0.654390	+	0.756157i	$0.727075\pi$
$488$	38.8526	+	12.6240i	1.75877	+	0.571461i
$489$	8.63862	+	6.00356i	0.390652	+	0.271490i
$490$	−2.23693	+	3.07887i	−0.101054	+	0.139089i
$491$	0.932465	−	2.86983i	0.0420816	−	0.129514i	−0.927809	−	0.373057i	$-0.878310\pi$
$491$	0.932465	−	2.86983i	0.0420816	−	0.129514i	0.969890	+	0.243543i	$0.0783097\pi$
$492$	3.03807	+	8.72318i	0.136967	+	0.393271i
$493$	−18.1823	+	13.2102i	−0.818891	+	0.594959i
$494$	41.0792			1.84824
$495$	−14.2488	+	2.41578i	−0.640436	+	0.108581i
$496$	−68.1548			−3.06024
$497$	0.679329	−	0.493561i	0.0304720	−	0.0221392i
$498$	10.3949	+	29.8468i	0.465807	+	1.33747i
$499$	−2.27349	+	6.99708i	−0.101775	+	0.313232i	−0.988960	−	0.148182i	$-0.952658\pi$
$499$	−2.27349	+	6.99708i	−0.101775	+	0.313232i	0.887185	+	0.461414i	$0.152658\pi$
$500$	32.7721	−	45.1070i	1.46561	−	2.01725i
$501$	10.4897	+	7.29001i	0.468646	+	0.325693i
$502$	55.3685	+	17.9903i	2.47122	+	0.802946i
$503$	9.88176	+	30.4129i	0.440606	+	1.35605i	0.887231	+	0.461325i	$0.152626\pi$
$503$	9.88176	+	30.4129i	0.440606	+	1.35605i	−0.446625	+	0.894721i	$0.647374\pi$
$504$	−13.9892	−	17.6475i	−0.623129	−	0.786083i
$505$		−	11.6611i		−	0.518910i
$506$	−40.7862	+	38.3258i	−1.81317	+	1.70379i
$507$	11.6229	−	0.243860i	0.516190	−	0.0108302i
$508$	−61.2953	−	84.3658i	−2.71954	−	3.74313i
$509$	−35.6442	+	11.5815i	−1.57990	+	0.513342i	−0.962032	−	0.272937i	$-0.912005\pi$
$509$	−35.6442	+	11.5815i	−1.57990	+	0.513342i	−0.617871	+	0.786279i	$0.712005\pi$
$510$	−31.9001	−	9.63004i	−1.41256	−	0.426425i
$511$	1.37945	+	1.00223i	0.0610231	+	0.0443359i
$512$	32.0595	+	23.2926i	1.41684	+	1.02940i
$513$	31.4684	+	8.07628i	1.38936	+	0.356576i
$514$	28.1494	−	9.14630i	1.24162	−	0.403426i
$515$	2.59725	+	3.57481i	0.114449	+	0.157525i
$516$	−0.731981	−	34.8877i	−0.0322237	−	1.53584i
$517$	6.26586	+	13.3044i	0.275572	+	0.585126i
$518$		−	9.94210i		−	0.436831i
$519$	−2.79462	+	2.12138i	−0.122670	+	0.0931183i
$520$	8.44880	+	26.0027i	0.370504	+	1.14030i
$521$	7.42841	+	2.41364i	0.325444	+	0.105743i	0.467183	−	0.884161i	$-0.345269\pi$
$521$	7.42841	+	2.41364i	0.325444	+	0.105743i	−0.141738	+	0.989904i	$0.545269\pi$
$522$	29.1085	+	19.3368i	1.27404	+	0.846348i
$523$	21.6163	−	29.7523i	0.945216	−	1.30098i	−0.00840438	−	0.999965i	$-0.502675\pi$
$523$	21.6163	−	29.7523i	0.945216	−	1.30098i	0.953620	−	0.301013i	$-0.0973248\pi$
$524$	−1.39368	+	4.28929i	−0.0608830	+	0.187379i
$525$	−4.72756	+	1.64649i	−0.206328	+	0.0718588i
$526$	31.2982	−	22.7395i	1.36467	−	0.991487i
$527$	34.6684			1.51018
$528$	56.2935	+	9.50049i	2.44986	+	0.413456i
$529$	−18.4804			−0.803495
$530$	−4.50606	+	3.27385i	−0.195731	+	0.142207i
$531$	31.7715	−	11.8182i	1.37876	−	0.512865i
$532$	−9.39955	+	28.9288i	−0.407522	+	1.25422i
$533$	−1.61574	+	2.22387i	−0.0699853	+	0.0963266i
$534$	32.0196	−	46.0735i	1.38562	−	1.99379i
$535$	−17.0401	−	5.53665i	−0.736707	−	0.239370i
$536$	26.9626	+	82.9823i	1.16461	+	3.58429i
$537$	−2.83465	−	3.73425i	−0.122324	−	0.161145i
$538$		−	12.0686i		−	0.520315i
$539$	−1.59685	+	2.90690i	−0.0687812	+	0.125209i
$540$	2.30928	+	36.6451i	0.0993754	+	1.57696i
$541$	−12.9628	−	17.8417i	−0.557313	−	0.767076i	0.433669	−	0.901072i	$-0.357219\pi$
$541$	−12.9628	−	17.8417i	−0.557313	−	0.767076i	−0.990982	+	0.133997i	$0.957219\pi$
$542$	13.7266	−	4.46005i	0.589609	−	0.191576i
$543$	−0.799665	+	2.64895i	−0.0343169	+	0.113677i
$544$	45.0917	+	32.7610i	1.93329	+	1.40462i
$545$	−20.6794	−	15.0244i	−0.885807	−	0.643576i
$546$	3.28878	−	10.8943i	0.140747	−	0.466233i
$547$	9.96807	−	3.23882i	0.426204	−	0.138482i	−0.0880578	−	0.996115i	$-0.528066\pi$
$547$	9.96807	−	3.23882i	0.426204	−	0.138482i	0.514262	+	0.857633i	$0.328066\pi$
$548$	−58.4561	−	80.4579i	−2.49712	−	3.43699i
$549$	0.684797	+	16.3122i	0.0292264	+	0.696188i
$550$	12.0926	−	22.0134i	0.515631	−	0.938653i
$551$		−	27.7971i		−	1.18420i
$552$	50.6301	+	66.6980i	2.15496	+	2.83885i
$553$	−0.686512	−	2.11287i	−0.0291934	−	0.0898482i
$554$	−2.80808	−	0.912402i	−0.119304	−	0.0387642i
$555$	−5.44792	+	7.83910i	−0.231251	+	0.332751i
$556$	10.0027	−	13.7675i	0.424209	−	0.583874i
$557$	−7.34726	+	22.6125i	−0.311314	+	0.958124i	0.665932	+	0.746013i	$0.268034\pi$
$557$	−7.34726	+	22.6125i	−0.311314	+	0.958124i	−0.977245	+	0.212112i	$0.931966\pi$
$558$	−18.7936	−	50.5239i	−0.795596	−	2.13885i
$559$	8.40122	−	6.10384i	0.355334	−	0.258165i
$560$	−14.4349			−0.609986
$561$	−28.6349	−	4.83263i	−1.20897	−	0.204034i
$562$	−11.7101			−0.493960
$563$	4.86565	−	3.53510i	0.205063	−	0.148987i	−0.480514	−	0.876987i	$-0.659550\pi$
$563$	4.86565	−	3.53510i	0.205063	−	0.148987i	0.685577	+	0.728000i	$0.259550\pi$
$564$	35.2842	−	12.2886i	1.48573	−	0.517444i
$565$	7.37039	−	22.6837i	0.310075	−	0.954312i
$566$	9.11252	−	12.5423i	0.383028	−	0.527193i
$567$	4.66119	−	7.69891i	0.195752	−	0.323324i
$568$	5.99471	+	1.94780i	0.251533	+	0.0817279i
$569$	−2.54914	−	7.84545i	−0.106866	−	0.328898i	0.883298	−	0.468811i	$-0.155318\pi$
$569$	−2.54914	−	7.84545i	−0.106866	−	0.328898i	−0.990164	+	0.139913i	$0.955318\pi$
$570$	32.8269	−	24.9187i	1.37497	−	1.04373i
$571$			14.2580i			0.596678i	0.954460	+	0.298339i	$0.0964326\pi$
$571$			14.2580i			0.596678i	−0.954460	+	0.298339i	$0.903567\pi$
$572$	17.2393	+	36.6044i	0.720812	+	1.53051i
$573$	0.180878	+	8.62100i	0.00755628	+	0.360147i
$574$	−1.68823	−	2.32365i	−0.0704654	−	0.0969873i
$575$	17.7037	−	5.75229i	0.738296	−	0.239887i
$576$	7.26893	−	26.0412i	0.302872	−	1.08505i
$577$	14.3738	+	10.4432i	0.598391	+	0.434756i	0.845307	−	0.534280i	$-0.179417\pi$
$577$	14.3738	+	10.4432i	0.598391	+	0.434756i	−0.246917	+	0.969037i	$0.579417\pi$
$578$	−18.1338	−	13.1750i	−0.754268	−	0.548008i
$579$	−31.0138	−	9.36245i	−1.28889	−	0.389090i
$580$	29.8784	−	9.70807i	1.24063	−	0.403106i
$581$	−4.09352	−	5.63425i	−0.169828	−	0.233748i
$582$	42.8770	−	0.899607i	1.77731	−	0.0372899i
$583$	−3.53735	+	3.32396i	−0.146502	+	0.137664i
$584$			12.7993i			0.529640i
$585$	−8.56282	+	6.78776i	−0.354029	+	0.280639i
$586$	−26.0769	−	80.2565i	−1.07723	−	3.31536i
$587$	−20.6768	−	6.71830i	−0.853423	−	0.277294i	−0.150544	−	0.988603i	$-0.548102\pi$
$587$	−20.6768	−	6.71830i	−0.853423	−	0.277294i	−0.702879	+	0.711310i	$0.748102\pi$
$588$	6.91948	+	4.80881i	0.285354	+	0.198312i
$589$	−25.2034	+	34.6896i	−1.03849	+	1.42936i
$590$	13.2884	−	40.8975i	0.547075	−	1.68372i
$591$	5.62476	+	16.1503i	0.231372	+	0.664336i
$592$	30.5082	−	22.1655i	1.25388	−	0.910995i
$593$	13.4873			0.553859			0.276929	−	0.960890i	$-0.410683\pi$
$593$	13.4873			0.553859			0.276929	+	0.960890i	$0.410683\pi$
$594$	8.48003	+	44.3507i	0.347940	+	1.81973i
$595$	7.34262			0.301018
$596$	−69.6956	+	50.6368i	−2.85484	+	2.07416i
$597$	−11.7918	−	33.8577i	−0.482606	−	1.38570i
$598$	−13.0762	+	40.2444i	−0.534725	+	1.64572i
$599$	−2.48243	+	3.41678i	−0.101430	+	0.139606i	−0.856715	−	0.515790i	$-0.827498\pi$
$599$	−2.48243	+	3.41678i	−0.101430	+	0.139606i	0.755285	+	0.655396i	$0.227498\pi$
$600$	−30.8581	−	21.4454i	−1.25978	−	0.875505i
$601$	16.3212	+	5.30307i	0.665755	+	0.216317i	0.622348	−	0.782741i	$-0.286179\pi$
$601$	16.3212	+	5.30307i	0.665755	+	0.216317i	0.0434066	+	0.999057i	$0.486179\pi$
$602$	3.35296	+	10.3193i	0.136656	+	0.420585i
$603$	−27.3265	+	21.6617i	−1.11282	+	0.882134i
$604$			19.5950i			0.797309i
$605$	−5.87201	+	14.8593i	−0.238731	+	0.604116i
$606$	−36.4257	+	0.764251i	−1.47969	+	0.0310456i
$607$	8.67717	+	11.9431i	0.352195	+	0.484755i	0.947954	−	0.318409i	$-0.103148\pi$
$607$	8.67717	+	11.9431i	0.352195	+	0.484755i	−0.595758	+	0.803164i	$0.703148\pi$
$608$	−65.5620	+	21.3024i	−2.65889	+	0.863926i
$609$	−7.37187	−	2.22542i	−0.298723	−	0.0901787i
$610$	16.7558	+	12.1738i	0.678423	+	0.492903i
$611$	8.99530	+	6.53546i	0.363911	+	0.264397i
$612$	−19.8360	+	71.0634i	−0.801825	+	2.87257i
$613$	30.1393	−	9.79284i	1.21731	−	0.395529i	0.371210	−	0.928549i	$-0.378943\pi$
$613$	30.1393	−	9.79284i	1.21731	−	0.395529i	0.846103	+	0.533020i	$0.178943\pi$
$614$	−13.1851	−	18.1477i	−0.532106	−	0.732381i
$615$	0.0578497	+	2.75723i	0.00233273	+	0.111182i
$616$	−24.6990	+	3.12839i	−0.995153	+	0.126046i
$617$		−	1.69946i		−	0.0684175i	−0.999415	−	0.0342087i	$-0.989109\pi$
$617$		−	1.69946i		−	0.0684175i	0.999415	−	0.0342087i	$-0.0108911\pi$
$618$	10.9964	−	8.34734i	0.442342	−	0.335779i
$619$	5.11063	+	15.7289i	0.205413	+	0.632198i	0.999696	+	0.0246492i	$0.00784689\pi$
$619$	5.11063	+	15.7289i	0.205413	+	0.632198i	−0.794283	+	0.607548i	$0.792153\pi$
$620$	−46.0891	−	14.9753i	−1.85098	−	0.601421i
$621$	−17.9291	+	28.2581i	−0.719469	+	1.13396i
$622$	−12.9746	+	17.8579i	−0.520232	+	0.716038i
$623$	−3.82051	+	11.7583i	−0.153065	+	0.471087i
$624$	40.7623	−	14.1965i	1.63180	−	0.568314i
$625$	1.77588	−	1.29025i	0.0710353	−	0.0516102i
$626$	3.60384			0.144038
$627$	25.6527	−	25.1391i	1.02447	−	1.00396i
$628$	−24.2308			−0.966915
$629$	−15.5186	+	11.2749i	−0.618768	+	0.449561i
$630$	−3.98041	−	10.7008i	−0.158583	−	0.426328i
$631$	−14.6270	+	45.0171i	−0.582290	+	1.79210i	0.0276010	+	0.999619i	$0.491213\pi$
$631$	−14.6270	+	45.0171i	−0.582290	+	1.79210i	−0.609891	+	0.792485i	$0.708787\pi$
$632$	9.80221	−	13.4916i	0.389911	−	0.536666i
$633$	−10.9232	+	15.7176i	−0.434159	+	0.624718i
$634$	−34.6560	−	11.2604i	−1.37637	−	0.447209i
$635$	−9.62111	−	29.6107i	−0.381802	−	1.17507i
$636$	7.45648	+	9.82285i	0.295669	+	0.389501i
$637$			2.50760i			0.0993547i
$638$	34.9518	−	16.4610i	1.38376	−	0.651697i
$639$	0.105660	+	2.51687i	0.00417984	+	0.0995659i
$640$	−1.33344	−	1.83532i	−0.0527088	−	0.0725475i
$641$	−19.5835	+	6.36308i	−0.773503	+	0.251326i	−0.669064	−	0.743205i	$-0.733305\pi$
$641$	−19.5835	+	6.36308i	−0.773503	+	0.251326i	−0.104439	+	0.994531i	$0.533305\pi$
$642$	−16.1781	+	53.5910i	−0.638498	+	2.11507i
$643$	8.00223	+	5.81396i	0.315577	+	0.229280i	0.734286	−	0.678840i	$-0.237517\pi$
$643$	8.00223	+	5.81396i	0.315577	+	0.229280i	−0.418709	+	0.908121i	$0.637517\pi$
$644$	−25.3489	−	18.4171i	−0.998887	−	0.725734i
$645$	3.01091	−	9.97386i	0.118555	−	0.392720i
$646$	78.7602	−	25.5907i	3.09878	−	1.00685i
$647$	−27.1905	−	37.4245i	−1.06897	−	1.47131i	−0.871115	−	0.491079i	$-0.836603\pi$
$647$	−27.1905	−	37.4245i	−1.06897	−	1.47131i	−0.197854	−	0.980231i	$-0.563397\pi$
$648$	67.3212	−	5.66235i	2.64462	−	0.222438i
$649$	7.01031	−	36.8145i	0.275179	−	1.44509i
$650$		−	18.9895i		−	0.744831i
$651$	7.18199	+	9.46125i	0.281484	+	0.370816i
$652$	−9.13091	−	28.1020i	−0.357594	−	1.10056i
$653$	−16.0077	−	5.20121i	−0.626429	−	0.203539i	−0.0214364	−	0.999770i	$-0.506824\pi$
$653$	−16.0077	−	5.20121i	−0.626429	−	0.203539i	−0.604993	+	0.796231i	$0.706824\pi$
$654$	−45.5766	+	65.5809i	−1.78219	+	2.56442i
$655$	−0.791466	+	1.08936i	−0.0309251	+	0.0425648i
$656$	3.36648	−	10.3609i	0.131439	−	0.404527i
$657$	−4.79433	+	1.78337i	−0.187045	+	0.0695757i
$658$	−9.39889	+	6.82869i	−0.366407	+	0.266210i
$659$	28.9420			1.12742			0.563710	−	0.825973i	$-0.309374\pi$
$659$	28.9420			1.12742			0.563710	+	0.825973i	$0.309374\pi$
$660$	35.9805	+	18.7937i	1.40054	+	0.731542i
$661$	−11.0213			−0.428680			−0.214340	−	0.976759i	$-0.568760\pi$
$661$	−11.0213			−0.428680			−0.214340	+	0.976759i	$0.568760\pi$
$662$	11.6721	−	8.48028i	0.453649	−	0.329596i
$663$	−20.7346	+	7.22134i	−0.805265	+	0.280454i
$664$	16.1548	−	49.7192i	0.626926	−	1.92948i
$665$	−5.33799	+	7.34711i	−0.206998	+	0.284909i
$666$	24.8441	+	16.5039i	0.962689	+	0.639515i
$667$	27.2322	+	8.84829i	1.05444	+	0.342607i
$668$	−11.0875	−	34.1238i	−0.428988	−	1.32029i
$669$	−29.9193	+	22.7116i	−1.15675	+	0.878081i
$670$			44.2358i			1.70898i
$671$	15.8199	+	8.69036i	0.610721	+	0.335488i
$672$	0.400585	+	19.0927i	0.0154529	+	0.736516i
$673$	9.25961	+	12.7448i	0.356932	+	0.491274i	0.949291	−	0.314400i	$-0.101803\pi$
$673$	9.25961	+	12.7448i	0.356932	+	0.491274i	−0.592359	+	0.805674i	$0.701803\pi$
$674$	2.34872	−	0.763146i	0.0904694	−	0.0293953i
$675$	3.73339	−	14.5468i	0.143698	−	0.559906i
$676$	−26.4172	−	19.1932i	−1.01605	−	0.738200i
$677$	10.3426	+	7.51434i	0.397499	+	0.288800i	0.768521	−	0.639824i	$-0.220993\pi$
$677$	10.3426	+	7.51434i	0.397499	+	0.288800i	−0.371023	+	0.928624i	$0.620993\pi$
$678$	−71.3403	−	21.5363i	−2.73981	−	0.827095i
$679$	−8.98766	+	2.92027i	−0.344915	+	0.112070i
$680$	32.3974	+	44.5912i	1.24238	+	1.70999i
$681$	−28.3269	+	0.594330i	−1.08549	+	0.0227748i
$682$	−58.5434	−	11.1480i	−2.24174	−	0.426879i
$683$			5.87416i			0.224769i	0.993665	+	0.112384i	$0.0358488\pi$
$683$			5.87416i			0.224769i	−0.993665	+	0.112384i	$0.964151\pi$
$684$	−56.6863	−	71.5103i	−2.16745	−	2.73426i
$685$	−9.17546	−	28.2392i	−0.350576	−	1.07896i
$686$	−2.49187	−	0.809658i	−0.0951401	−	0.0309129i
$687$	−15.0850	−	10.4836i	−0.575528	−	0.399974i
$688$	−24.1905	+	33.2954i	−0.922254	+	1.26937i
$689$	−1.13409	+	3.49036i	−0.0432053	+	0.132972i
$690$	13.9630	+	40.0918i	0.531562	+	1.52627i
$691$	−19.2066	+	13.9544i	−0.730652	+	0.530850i	−0.889770	−	0.456410i	$-0.849135\pi$
$691$	−19.2066	+	13.9544i	−0.730652	+	0.530850i	0.159118	+	0.987260i	$0.449135\pi$
$692$	9.85488			0.374626
$693$	−4.61321	−	8.81580i	−0.175241	−	0.334884i
$694$	52.2452			1.98320
$695$	4.11046	−	2.98642i	0.155919	−	0.113282i
$696$	−19.0116	−	54.5878i	−0.720632	−	2.06915i
$697$	−1.71243	+	5.27032i	−0.0648629	+	0.199628i
$698$	43.4169	−	59.7582i	1.64335	−	2.26188i
$699$	21.7597	+	15.1223i	0.823027	+	0.571977i
$700$	13.3728	+	4.34510i	0.505446	+	0.164229i
$701$	6.43734	+	19.8121i	0.243135	+	0.748293i	0.995938	+	0.0900464i	$0.0287015\pi$
$701$	6.43734	+	19.8121i	0.243135	+	0.748293i	−0.752802	+	0.658246i	$0.771298\pi$
$702$	21.7641	+	26.3029i	0.821435	+	0.992737i
$703$		−	23.7248i		−	0.894799i
$704$	−20.4683	−	21.7823i	−0.771430	−	0.820953i
$705$	11.1527	−	0.233995i	0.420034	−	0.00881277i
$706$	16.3832	+	22.5496i	0.616592	+	0.848666i
$707$	7.63536	−	2.48088i	0.287157	−	0.0933031i
$708$	−91.1505	−	27.5166i	−3.42565	−	1.03414i
$709$	18.2625	+	13.2685i	0.685864	+	0.498309i	0.875298	−	0.483584i	$-0.160665\pi$
$709$	18.2625	+	13.2685i	0.685864	+	0.498309i	−0.189434	+	0.981893i	$0.560665\pi$
$710$	2.58532	+	1.87834i	0.0970252	+	0.0704930i
$711$	6.41940	+	1.79186i	0.240746	+	0.0671999i
$712$	−88.2642	+	28.6788i	−3.30784	+	1.07478i
$713$	−25.9619	−	35.7335i	−0.972282	−	1.33823i
$714$	−0.481226	−	22.9362i	−0.0180094	−	0.858365i
$715$	1.51794	+	11.9843i	0.0567677	+	0.448188i
$716$			13.1684i			0.492125i
$717$	5.75423	−	4.36801i	0.214896	−	0.163126i
$718$	19.2372	+	59.2060i	0.717925	+	2.20955i
$719$	20.4297	+	6.63800i	0.761898	+	0.247556i	0.664093	−	0.747650i	$-0.268818\pi$
$719$	20.4297	+	6.63800i	0.761898	+	0.247556i	0.0978051	+	0.995206i	$0.468818\pi$
$720$	23.9620	−	36.0711i	0.893011	−	1.34429i
$721$	−1.78813	+	2.46115i	−0.0665936	+	0.0916582i
$722$	−16.2677	+	50.0668i	−0.605421	+	1.86329i
$723$	−4.45128	+	1.55027i	−0.165545	+	0.0576552i
$724$	6.28766	−	4.56825i	0.233679	−	0.169778i
$725$	−12.8497			−0.477225
$726$	46.8008	+	17.3686i	1.73694	+	0.644607i
$727$	−11.8154			−0.438209			−0.219105	−	0.975701i	$-0.570314\pi$
$727$	−11.8154			−0.438209			−0.219105	+	0.975701i	$0.570314\pi$
$728$	−15.2284	+	11.0641i	−0.564404	+	0.410063i
$729$	11.5010	+	24.4280i	0.425964	+	0.904740i
$730$	−2.00523	+	6.17145i	−0.0742168	+	0.228416i
$731$	12.3050	−	16.9364i	0.455117	−	0.626415i
$732$	26.1705	−	37.6571i	0.967289	−	1.39185i
$733$	10.5654	+	3.43292i	0.390243	+	0.126798i	0.497565	−	0.867427i	$-0.334228\pi$
$733$	10.5654	+	3.43292i	0.390243	+	0.126798i	−0.107322	+	0.994224i	$0.534228\pi$
$734$	7.42654	+	22.8565i	0.274119	+	0.843651i
$735$	1.52112	+	2.00385i	0.0561072	+	0.0739133i
$736$		−	71.0106i		−	2.61749i
$737$	4.84419	+	38.2455i	0.178438	+	1.40879i
$738$	8.60899	−	0.361411i	0.316901	−	0.0133037i
$739$	3.87698	+	5.33620i	0.142617	+	0.196295i	0.874350	−	0.485296i	$-0.161288\pi$
$739$	3.87698	+	5.33620i	0.142617	+	0.196295i	−0.731733	+	0.681591i	$0.761288\pi$
$740$	25.5012	−	8.28583i	0.937442	−	0.304593i
$741$	7.84801	−	25.9971i	0.288304	−	0.955026i
$742$	−3.10229	−	2.25395i	−0.113889	−	0.0827450i
$743$	−21.4467	−	15.5819i	−0.786802	−	0.571645i	0.120210	−	0.992748i	$-0.461643\pi$
$743$	−21.4467	−	15.5819i	−0.786802	−	0.571645i	−0.907013	+	0.421103i	$0.861643\pi$
$744$	−25.7688	+	85.3609i	−0.944730	+	3.12948i
$745$	−24.4618	+	7.94812i	−0.896211	+	0.291196i
$746$	13.7220	+	18.8867i	0.502398	+	0.691492i
$747$	20.8745	−	0.876327i	0.763760	−	0.0320631i
$748$	55.8557	+	59.4414i	2.04229	+	2.17339i
$749$		−	12.3353i		−	0.450723i
$750$	−31.4465	−	41.4264i	−1.14827	−	1.51268i
$751$	6.79637	+	20.9171i	0.248003	+	0.763275i	0.995128	+	0.0985911i	$0.0314336\pi$
$751$	6.79637	+	20.9171i	0.248003	+	0.763275i	−0.747125	+	0.664683i	$0.768566\pi$
$752$	−41.9088	−	13.6170i	−1.52826	−	0.496561i
$753$	21.9631	−	31.6031i	0.800381	−	1.15168i
$754$	17.1693	−	23.6315i	0.625268	−	0.860607i
$755$	−1.80785	+	5.56398i	−0.0657943	+	0.202494i
$756$	−23.5030	+	9.30827i	−0.854796	+	0.338539i
$757$	−5.08361	+	3.69346i	−0.184767	+	0.134241i	−0.676324	−	0.736604i	$-0.736428\pi$
$757$	−5.08361	+	3.69346i	−0.184767	+	0.134241i	0.491557	+	0.870846i	$0.336428\pi$
$758$	17.4221			0.632798
$759$	16.4625	+	33.1336i	0.597552	+	1.20267i
$760$	−68.1708			−2.47282
$761$	−43.1699	+	31.3648i	−1.56491	+	1.13697i	−0.633072	+	0.774093i	$0.718206\pi$
$761$	−43.1699	+	31.3648i	−1.56491	+	1.13697i	−0.931836	+	0.362879i	$0.881794\pi$
$762$	−91.8646	+	31.9941i	−3.32790	+	1.15903i
$763$	5.43810	−	16.7368i	0.196872	−	0.605911i
$764$	14.2361	−	19.5943i	0.515045	−	0.708898i
$765$	−12.1888	+	18.3483i	−0.440687	+	0.663385i
$766$	−86.9208	−	28.2423i	−3.14058	−	1.02044i
$767$	−8.75583	−	26.9477i	−0.316155	−	0.973024i
$768$	19.2208	−	14.5904i	0.693573	−	0.526487i
$769$		−	20.1378i		−	0.726189i	−0.931752	−	0.363095i	$-0.881720\pi$
$769$		−	20.1378i		−	0.726189i	0.931752	−	0.363095i	$-0.118280\pi$
$770$	−12.3993	−	2.36110i	−0.446838	−	0.0850881i
$771$	−0.410428	−	19.5618i	−0.0147812	−	0.704501i
$772$	53.4849	+	73.6157i	1.92496	+	2.64949i
$773$	3.87910	−	1.26040i	0.139522	−	0.0453333i	−0.238424	−	0.971161i	$-0.576631\pi$
$773$	3.87910	−	1.26040i	0.139522	−	0.0453333i	0.377945	+	0.925828i	$0.376631\pi$
$774$	−31.3527	−	8.75153i	−1.12695	−	0.314567i
$775$	16.0358	+	11.6507i	0.576024	+	0.418506i
$776$	−57.3902	−	41.6964i	−2.06019	−	1.49681i
$777$	−6.29189	−	1.89940i	−0.225720	−	0.0681405i
$778$	−57.1950	+	18.5838i	−2.05054	+	0.666261i
$779$	−4.02862	−	5.54492i	−0.144340	−	0.198668i
$780$	30.6844	−	0.643793i	1.09868	−	0.0230515i
$781$	2.44091	+	1.34087i	0.0873428	+	0.0479800i
$782$			85.3056i			3.05052i
$783$	17.7984	−	14.7272i	0.636063	−	0.526306i
$784$	−3.07101	−	9.45161i	−0.109679	−	0.337557i
$785$	−6.88032	−	2.23555i	−0.245569	−	0.0797903i
$786$	3.45471	+	2.40091i	0.123225	+	0.0856376i
$787$	−24.4236	+	33.6161i	−0.870606	+	1.19829i	0.108330	+	0.994115i	$0.465450\pi$
$787$	−24.4236	+	33.6161i	−0.870606	+	1.19829i	−0.978935	+	0.204171i	$0.934550\pi$
$788$	14.8438	−	45.6844i	0.528787	−	1.62744i
$789$	−8.41133	−	24.1514i	−0.299451	−	0.859813i
$790$	6.84002	−	4.96956i	0.243357	−	0.176809i
$791$	16.4208			0.583856
$792$	33.1831	−	66.9130i	1.17911	−	2.37765i
$793$	13.6468			0.484614
$794$	21.2624	−	15.4480i	0.754573	−	0.548230i
$795$	1.21100	+	3.47713i	0.0429497	+	0.123321i
$796$	−31.1185	+	95.7730i	−1.10297	+	3.39459i
$797$	−13.4616	+	18.5283i	−0.476834	+	0.656305i	−0.977893	−	0.209108i	$-0.932944\pi$
$797$	−13.4616	+	18.5283i	−0.476834	+	0.656305i	0.501059	+	0.865413i	$0.332944\pi$
$798$	23.3000	+	16.1928i	0.824812	+	0.573218i
$799$	21.3178	+	6.92658i	0.754170	+	0.245045i
$800$	9.84739	+	30.3071i	0.348158	+	1.07152i
$801$	−23.0405	−	29.0658i	−0.814096	−	1.02699i
$802$			73.3420i			2.58980i
$803$	−1.05786	+	5.55532i	−0.0373310	+	0.196043i
$804$	97.9231	−	2.05453i	3.45348	−	0.0724578i
$805$	−5.49863	−	7.56822i	−0.193801	−	0.266745i
$806$	−42.8530	+	13.9238i	−1.50943	+	0.490444i
$807$	−7.63766	−	2.30566i	−0.268858	−	0.0811631i
$808$	48.7552	+	35.4227i	1.71520	+	1.24617i
$809$	−2.61138	−	1.89728i	−0.0918113	−	0.0667048i	0.540933	−	0.841066i	$-0.318071\pi$
$809$	−2.61138	−	1.89728i	−0.0918113	−	0.0667048i	−0.632744	+	0.774361i	$0.718071\pi$
$810$	33.3474	+	7.81676i	1.17171	+	0.274653i
$811$	47.4019	−	15.4018i	1.66451	−	0.540831i	0.682697	−	0.730702i	$-0.260807\pi$
$811$	47.4019	−	15.4018i	1.66451	−	0.540831i	0.981809	+	0.189871i	$0.0608070\pi$
$812$	12.7132	+	17.4982i	0.446145	+	0.614067i
$813$	−0.200139	−	9.53901i	−0.00701918	−	0.334548i
$814$	29.8314	−	14.0495i	1.04559	−	0.492433i
$815$		−	8.82198i		−	0.309020i
$816$	69.3087	−	52.6119i	2.42629	−	1.84178i
$817$	8.00116	+	24.6251i	0.279925	+	0.861521i
$818$	49.6438	+	16.1303i	1.73576	+	0.563981i
$819$	−6.26618	−	4.16263i	−0.218958	−	0.145454i
$820$	4.55310	−	6.26681i	0.159001	−	0.218846i
$821$	7.52157	−	23.1490i	0.262504	−	0.807906i	−0.729753	−	0.683711i	$-0.760365\pi$
$821$	7.52157	−	23.1490i	0.262504	−	0.807906i	0.992258	−	0.124195i	$-0.0396349\pi$
$822$	−87.6094	+	30.5122i	−3.05573	+	1.06423i
$823$	44.7176	−	32.4892i	1.55876	−	1.13250i	0.621736	−	0.783227i	$-0.286428\pi$
$823$	44.7176	−	32.4892i	1.55876	−	1.13250i	0.937020	−	0.349276i	$-0.113572\pi$
$824$	−22.8360			−0.795531
$825$	−11.6210	−	11.8584i	−0.404590	−	0.412857i
$826$	29.6058			1.03012
$827$	−31.6318	+	22.9819i	−1.09995	+	0.799158i	−0.981051	−	0.193749i	$-0.937935\pi$
$827$	−31.6318	+	22.9819i	−1.09995	+	0.799158i	−0.118895	+	0.992907i	$0.537935\pi$
$828$	88.1013	−	32.7714i	3.06173	−	1.13889i
$829$	2.27836	−	7.01206i	0.0791306	−	0.243539i	−0.903664	−	0.428243i	$-0.859133\pi$
$829$	2.27836	−	7.01206i	0.0791306	−	0.243539i	0.982794	+	0.184704i	$0.0591327\pi$
$830$	15.5787	−	21.4422i	0.540744	−	0.744270i
$831$	−1.11389	+	1.60279i	−0.0386404	+	0.0556003i
$832$	−21.4930	−	6.98350i	−0.745136	−	0.242109i
$833$	1.56214	+	4.80776i	0.0541248	+	0.166579i
$834$	−9.59810	−	12.6441i	−0.332355	−	0.437831i
$835$		−	10.7124i		−	0.370716i
$836$	−100.084	+	12.6767i	−3.46148	+	0.438432i
$837$	−35.5646	+	2.24119i	−1.22929	+	0.0774667i
$838$	−43.3994	−	59.7341i	−1.49921	−	2.06348i
$839$	53.0945	−	17.2515i	1.83303	−	0.595587i	0.833987	−	0.551784i	$-0.186053\pi$
$839$	53.0945	−	17.2515i	1.83303	−	0.595587i	0.999040	−	0.0438029i	$-0.0139473\pi$
$840$	−5.45773	+	18.0791i	−0.188309	+	0.623788i
$841$	7.47075	+	5.42782i	0.257612	+	0.187166i
$842$	−20.3610	−	14.7932i	−0.701688	−	0.509806i
$843$	−2.23716	+	7.41076i	−0.0770520	+	0.255240i
$844$	51.1305	−	16.6133i	1.75998	−	0.571853i
$845$	−5.73036	−	7.88716i	−0.197130	−	0.271326i
$846$	−1.46186	−	34.8223i	−0.0502599	−	1.19722i
$847$	−10.9787	−	0.683541i	−0.377234	−	0.0234868i
$848$		−	14.5447i		−	0.499468i
$849$	−6.19652	−	8.16304i	−0.212664	−	0.280155i
$850$	−11.8297	−	36.4082i	−0.405757	−	1.24879i
$851$	23.2427	+	7.55201i	0.796750	+	0.258880i
$852$	4.03794	−	5.81026i	0.138338	−	0.199056i
$853$	0.119852	−	0.164963i	0.00410366	−	0.00564821i	−0.806960	−	0.590606i	$-0.798889\pi$
$853$	0.119852	−	0.164963i	0.00410366	−	0.00564821i	0.811064	+	0.584958i	$0.198889\pi$
$854$	−4.40632	+	13.5612i	−0.150781	+	0.464056i
$855$	−9.49844	−	25.5352i	−0.324840	−	0.873286i
$856$	74.9114	−	54.4263i	2.56042	−	1.86025i
$857$	0.861204			0.0294182			0.0147091	−	0.999892i	$-0.495318\pi$
$857$	0.861204			0.0294182			0.0147091	+	0.999892i	$0.495318\pi$
$858$	37.3360	−	5.52703i	1.27463	−	0.188690i
$859$	−27.3194			−0.932126			−0.466063	−	0.884752i	$-0.654328\pi$
$859$	−27.3194			−0.932126			−0.466063	+	0.884752i	$0.654328\pi$
$860$	−23.6744	+	17.2005i	−0.807291	+	0.586531i
$861$	−1.79306	+	0.624477i	−0.0611073	+	0.0212821i
$862$	18.4681	−	56.8389i	0.629026	−	1.93594i
$863$	−7.05329	+	9.70802i	−0.240097	+	0.330465i	−0.912012	−	0.410163i	$-0.865472\pi$
$863$	−7.05329	+	9.70802i	−0.240097	+	0.330465i	0.671915	+	0.740628i	$0.265472\pi$
$864$	−48.3752	−	30.6929i	−1.64576	−	1.04419i
$865$	2.79829	+	0.909218i	0.0951446	+	0.0309143i
$866$	28.5710	+	87.9325i	0.970882	+	2.98807i
$867$	−11.8022	+	8.95901i	−0.400825	+	0.304264i
$868$		−	33.3639i		−	1.13245i
$869$	5.36955	−	5.04564i	0.182149	−	0.171161i
$870$	−0.614727	−	29.2991i	−0.0208412	−	0.993333i
$871$	17.1323	+	23.5806i	0.580507	+	0.798999i
$872$	125.635	−	40.8213i	4.25454	−	1.38238i
$873$	7.62216	−	27.3067i	0.257971	−	0.924192i
$874$	−85.3577	−	62.0160i	−2.88727	−	2.09772i
$875$	9.27179	+	6.73635i	0.313444	+	0.227730i
$876$	13.7546	+	4.15226i	0.464727	+	0.140292i
$877$	−7.03934	+	2.28722i	−0.237702	+	0.0772339i	−0.425445	−	0.904984i	$-0.639883\pi$
$877$	−7.03934	+	2.28722i	−0.237702	+	0.0772339i	0.187744	+	0.982218i	$0.439883\pi$
$878$	32.7728	+	45.1078i	1.10603	+	1.52232i
$879$	−55.7724	+	1.17017i	−1.88116	+	0.0394687i
$880$	−20.3984	−	43.3121i	−0.687629	−	1.46005i
$881$		−	4.86775i		−	0.163999i	−0.996632	−	0.0819993i	$-0.973869\pi$
$881$		−	4.86775i		−	0.163999i	0.996632	−	0.0819993i	$-0.0261305\pi$
$882$	6.15975	−	4.88284i	0.207410	−	0.164414i
$883$	−7.36651	−	22.6718i	−0.247903	−	0.762967i	−0.995145	−	0.0984153i	$-0.968623\pi$
$883$	−7.36651	−	22.6718i	−0.247903	−	0.762967i	0.747242	−	0.664551i	$-0.231377\pi$
$884$	58.6518	+	19.0571i	1.97267	+	0.640961i
$885$	−23.3434	−	16.2229i	−0.784680	−	0.545327i
$886$	32.4504	−	44.6641i	1.09019	−	1.50052i
$887$	7.88020	−	24.2528i	0.264591	−	0.814328i	−0.727196	−	0.686430i	$-0.759177\pi$
$887$	7.88020	−	24.2528i	0.264591	−	0.814328i	0.991787	−	0.127898i	$-0.0408231\pi$
$888$	−16.2264	−	46.5907i	−0.544522	−	1.56348i
$889$	17.3415	−	12.5993i	0.581614	−	0.422567i
$890$	−47.0514			−1.57717
$891$	29.6875	+	3.10642i	0.994570	+	0.104069i
$892$	105.507			3.53263
$893$	−22.4286	+	16.2953i	−0.750543	+	0.545302i
$894$	26.4308	+	75.8905i	0.883977	+	2.53816i
$895$	−1.21492	+	3.73915i	−0.0406104	+	0.124986i
$896$	0.918034	−	1.26357i	0.0306694	−	0.0422128i
$897$	22.9706	+	15.9638i	0.766966	+	0.533017i
$898$	−56.1867	−	18.2562i	−1.87497	−	0.609216i
$899$	9.42182	+	28.9974i	0.314235	+	0.967117i
$900$	−33.0568	+	26.2042i	−1.10189	+	0.873473i
$901$			7.39848i			0.246479i
$902$	4.58645	−	8.34917i	0.152712	−	0.277997i
$903$	7.17120	−	0.150460i	0.238642	−	0.00500698i
$904$	72.4523	+	99.7221i	2.40973	+	3.31671i
$905$	2.20685	−	0.717048i	0.0733580	−	0.0238355i
$906$	17.4987	+	5.28253i	0.581356	+	0.175500i
$907$	−44.1234	−	32.0575i	−1.46509	−	1.06445i	−0.982000	−	0.188883i	$-0.939513\pi$
$907$	−44.1234	−	32.0575i	−1.46509	−	1.06445i	−0.483093	−	0.875569i	$-0.660487\pi$
$908$	64.3832	+	46.7771i	2.13663	+	1.55235i
$909$	−6.47532	+	23.1981i	−0.214773	+	0.769432i
$910$	−9.07608	+	2.94900i	−0.300869	+	0.0977584i
$911$	−20.1681	−	27.7590i	−0.668198	−	0.919696i	0.331520	−	0.943448i	$-0.392439\pi$
$911$	−20.1681	−	27.7590i	−0.668198	−	0.919696i	−0.999718	+	0.0237524i	$0.992439\pi$
$912$	2.25755	+	107.599i	0.0747548	+	3.56296i
$913$	11.1210	−	20.2446i	0.368050	−	0.669997i
$914$		−	21.3537i		−	0.706317i
$915$	10.9054	−	8.27821i	0.360520	−	0.273669i
$916$	15.9446	+	49.0726i	0.526826	+	1.62140i
$917$	−0.881668	−	0.286471i	−0.0291153	−	0.00946012i
$918$	58.1135	+	36.8716i	1.91803	+	1.21695i
$919$	26.4722	−	36.4358i	0.873237	−	1.20191i	−0.105011	−	0.994471i	$-0.533488\pi$
$919$	26.4722	−	36.4358i	0.873237	−	1.20191i	0.978248	−	0.207437i	$-0.0665121\pi$
$920$	21.6999	−	66.7855i	0.715425	−	2.20185i
$921$	−14.0038	+	4.87716i	−0.461439	+	0.160708i
$922$	34.8355	−	25.3095i	1.14725	−	0.833522i
$923$	2.10562			0.0693074
$924$	−4.65079	+	27.5574i	−0.153000	+	0.906573i
$925$	−10.9672			−0.360599
$926$	−5.98108	+	4.34551i	−0.196551	+	0.142802i
$927$	−3.18181	−	8.55385i	−0.104504	−	0.280945i
$928$	−15.1475	+	46.6191i	−0.497240	+	1.53035i
$929$	10.1858	−	14.0195i	0.334185	−	0.459966i	−0.608547	−	0.793518i	$-0.708247\pi$
$929$	10.1858	−	14.0195i	0.334185	−	0.459966i	0.942732	+	0.333552i	$0.108247\pi$
$930$	−25.7982	+	37.1214i	−0.845955	+	1.21726i
$931$	−5.94635	−	1.93209i	−0.194884	−	0.0633216i
$932$	−22.9997	−	70.7859i	−0.753381	−	2.31867i
$933$	8.82271	+	11.6227i	0.288843	+	0.380509i
$934$			64.5370i			2.11172i
$935$	10.3761	+	22.0316i	0.339334	+	0.720511i
$936$	−2.36857	−	56.4205i	−0.0774191	−	1.84416i
$937$	35.2819	+	48.5613i	1.15261	+	1.58643i	0.735425	+	0.677607i	$0.236983\pi$
$937$	35.2819	+	48.5613i	1.15261	+	1.58643i	0.417184	+	0.908822i	$0.363017\pi$
$938$	−28.9645	+	9.41112i	−0.945723	+	0.307284i
$939$	0.688498	−	2.28070i	0.0224683	−	0.0744277i
$940$	−25.3485	−	18.4168i	−0.826777	−	0.600688i
$941$	31.8407	+	23.1336i	1.03798	+	0.754133i	0.969889	−	0.243546i	$-0.0783107\pi$
$941$	31.8407	+	23.1336i	1.03798	+	0.754133i	0.0680863	+	0.997679i	$0.478311\pi$
$942$	−6.53228	+	21.6386i	−0.212833	+	0.705024i
$943$	6.71462	−	2.18171i	0.218658	−	0.0710463i
$944$	66.0047	+	90.8477i	2.14827	+	2.95684i
$945$	−7.53244	+	0.474674i	−0.245030	+	0.0154411i
$946$	−26.2252	+	24.6432i	−0.852654	+	0.801218i
$947$		−	23.9920i		−	0.779636i	−0.920892	−	0.389818i	$-0.872538\pi$
$947$		−	23.9920i		−	0.779636i	0.920892	−	0.389818i	$-0.127462\pi$
$948$	−11.3186	−	14.9107i	−0.367612	−	0.484276i
$949$	1.32126	+	4.06642i	0.0428899	+	0.132001i
$950$	45.0305	+	14.6313i	1.46098	+	0.474702i
$951$	−13.7471	+	19.7809i	−0.445780	+	0.641440i
$952$	−22.3046	+	30.6997i	−0.722897	+	0.994983i
$953$	7.87127	−	24.2253i	0.254976	−	0.784734i	−0.738859	−	0.673860i	$-0.764635\pi$
$953$	7.87127	−	24.2253i	0.254976	−	0.784734i	0.993834	−	0.110874i	$-0.0353650\pi$
$954$	10.7822	−	4.01068i	0.349085	−	0.129851i
$955$	5.85012	−	4.25036i	0.189305	−	0.137538i
$956$	−20.2916			−0.656277
$957$	−3.73998	−	25.2642i	−0.120896	−	0.816675i
$958$	12.0856			0.390469
$959$	16.5382	−	12.0157i	0.534047	−	0.388008i
$960$	−21.4115	+	7.45710i	−0.691054	+	0.240677i
$961$	4.95418	−	15.2474i	0.159812	−	0.491852i
$962$	14.6540	−	20.1695i	0.472463	−	0.650289i
$963$	30.8245	+	20.4767i	0.993304	+	0.659852i
$964$	12.5913	+	4.09117i	0.405539	+	0.131768i
$965$	8.39517	+	25.8377i	0.270250	+	0.831744i
$966$	−23.2805	+	17.6721i	−0.749038	+	0.568591i
$967$			4.29267i			0.138043i	0.997615	+	0.0690216i	$0.0219877\pi$
$967$			4.29267i			0.138043i	−0.997615	+	0.0690216i	$0.978012\pi$
$968$	−44.2897	−	69.6889i	−1.42352	−	2.23989i
$969$	−1.14835	−	54.7326i	−0.0368903	−	1.75826i
$970$	−21.1394	−	29.0959i	−0.678746	−	0.934213i
$971$	6.10236	−	1.98278i	0.195834	−	0.0636303i	−0.209458	−	0.977818i	$-0.567170\pi$
$971$	6.10236	−	1.98278i	0.195834	−	0.0636303i	0.405292	+	0.914187i	$0.367170\pi$
$972$	15.7549	−	74.1829i	0.505337	−	2.37942i
$973$	2.82993	+	2.05607i	0.0907234	+	0.0659144i
$974$	−48.3619	−	35.1370i	−1.54962	−	1.12586i
$975$	−12.0176	−	3.62787i	−0.384870	−	0.116185i
$976$	−51.4375	+	16.7131i	−1.64647	+	0.534972i
$977$	−15.1289	−	20.8231i	−0.484016	−	0.666190i	0.495255	−	0.868748i	$-0.335075\pi$
$977$	−15.1289	−	20.8231i	−0.484016	−	0.666190i	−0.979270	+	0.202557i	$0.935075\pi$
$978$	−27.5572	+	0.578181i	−0.881183	+	0.0184882i
$979$	−40.6798	+	5.15252i	−1.30013	+	0.164675i
$980$		−	7.06635i		−	0.225726i
$981$	32.7958	+	41.3722i	1.04709	+	1.32091i
$982$	2.44316	+	7.51927i	0.0779644	+	0.239950i
$983$	−43.2573	−	14.0551i	−1.37969	−	0.448289i	−0.477124	−	0.878836i	$-0.658321\pi$
$983$	−43.2573	−	14.0551i	−1.37969	−	0.448289i	−0.902568	+	0.430547i	$0.858321\pi$
$984$	−11.7038	−	8.13376i	−0.373103	−	0.259295i
$985$	8.42974	−	11.6025i	0.268594	−	0.369688i
$986$	18.1968	−	56.0038i	0.579503	−	1.78353i
$987$	2.52594	+	7.25271i	0.0804015	+	0.230856i
$988$	−61.7079	+	44.8334i	−1.96319	+	1.42634i
$989$	−26.6715			−0.848105
$990$	26.4829	−	27.0648i	0.841683	−	0.860176i
$991$	−36.1724			−1.14905			−0.574527	−	0.818486i	$-0.694814\pi$
$991$	−36.1724			−1.14905			−0.574527	+	0.818486i	$0.694814\pi$
$992$	61.1725	−	44.4445i	1.94223	−	1.41111i
$993$	−3.13686	−	9.00685i	−0.0995452	−	0.285824i
$994$	−0.679867	+	2.09242i	−0.0215641	+	0.0663674i
$995$	−17.6722	+	24.3237i	−0.560245	+	0.771112i
$996$	−48.1894	−	33.4901i	−1.52694	−	1.06117i
$997$	8.55998	+	2.78131i	0.271097	+	0.0880849i	0.441411	−	0.897305i	$-0.354478\pi$
$997$	8.55998	+	2.78131i	0.271097	+	0.0880849i	−0.170314	+	0.985390i	$0.554478\pi$
$998$	−5.95679	−	18.3331i	−0.188559	−	0.580325i
$999$	15.1909	−	12.5696i	0.480620	−	0.397686i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.s.a.8.2	✓	96
3.2	odd	2	inner	231.2.s.a.8.23	yes	96
11.7	odd	10	inner	231.2.s.a.29.23	yes	96
33.29	even	10	inner	231.2.s.a.29.2	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.s.a.8.2	✓	96	1.1	even	1	trivial
231.2.s.a.8.23	yes	96	3.2	odd	2	inner
231.2.s.a.29.2	yes	96	33.29	even	10	inner
231.2.s.a.29.23	yes	96	11.7	odd	10	inner

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:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.s (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.11971 + 1.54006i) q^{2} +(0.569669 + 1.63569i) q^{3} +(1.50336 - 4.62686i) q^{4} +(0.853755 - 1.17509i) q^{5} +(-3.72660 - 2.58986i) q^{6} +(0.951057 + 0.309017i) q^{7} +(2.31965 + 7.13914i) q^{8} +(-2.35095 + 1.86360i) q^{9} +O(q^{10})\)	\(q+(-2.11971 + 1.54006i) q^{2} +(0.569669 + 1.63569i) q^{3} +(1.50336 - 4.62686i) q^{4} +(0.853755 - 1.17509i) q^{5} +(-3.72660 - 2.58986i) q^{6} +(0.951057 + 0.309017i) q^{7} +(2.31965 + 7.13914i) q^{8} +(-2.35095 + 1.86360i) q^{9} +3.80570i q^{10} +(0.416755 + 3.29034i) q^{11} +(8.42452 - 0.176756i) q^{12} +(1.47393 + 2.02869i) q^{13} +(-2.49187 + 0.809658i) q^{14} +(2.40844 + 0.727063i) q^{15} +(-8.04002 - 5.84142i) q^{16} +(4.08973 + 2.97136i) q^{17} +(2.11328 - 7.57092i) q^{18} +(-5.94635 + 1.93209i) q^{19} +(-4.15349 - 5.71679i) q^{20} +(0.0363323 + 1.73167i) q^{21} +(-5.95072 - 6.33274i) q^{22} -6.44053i q^{23} +(-10.3560 + 7.86117i) q^{24} +(0.893139 + 2.74880i) q^{25} +(-6.24862 - 2.03030i) q^{26} +(-4.38754 - 2.78379i) q^{27} +(2.85956 - 3.93585i) q^{28} +(-1.37385 + 4.22826i) q^{29} +(-6.22493 + 2.16799i) q^{30} +(5.54823 - 4.03103i) q^{31} +11.0256 q^{32} +(-5.14455 + 2.55609i) q^{33} -13.2451 q^{34} +(1.17509 - 0.853755i) q^{35} +(5.08831 + 13.6792i) q^{36} +(-1.17258 + 3.60882i) q^{37} +(9.62902 - 13.2532i) q^{38} +(-2.47865 + 3.56657i) q^{39} +(10.3696 + 3.36928i) q^{40} +(0.338748 + 1.04256i) q^{41} +(-2.74389 - 3.61469i) q^{42} -4.14120i q^{43} +(15.8505 + 3.01829i) q^{44} +(0.182769 + 4.35365i) q^{45} +(9.91881 + 13.6521i) q^{46} +(4.21702 - 1.37019i) q^{47} +(4.97458 - 16.4786i) q^{48} +(0.809017 + 0.587785i) q^{49} +(-6.12652 - 4.45118i) q^{50} +(-2.53043 + 8.38221i) q^{51} +(11.6023 - 3.76982i) q^{52} +(0.860250 + 1.18403i) q^{53} +(13.5875 - 0.856249i) q^{54} +(4.22226 + 2.31942i) q^{55} +7.50654i q^{56} +(-6.54775 - 8.62573i) q^{57} +(-3.59962 - 11.0785i) q^{58} +(-10.7464 - 3.49172i) q^{59} +(6.98478 - 10.0505i) q^{60} +(3.19884 - 4.40283i) q^{61} +(-5.55263 + 17.0892i) q^{62} +(-2.81177 + 1.04591i) q^{63} +(-7.29105 + 5.29726i) q^{64} +3.64228 q^{65} +(6.96844 - 13.3411i) q^{66} +11.6236 q^{67} +(19.8964 - 14.4556i) q^{68} +(10.5347 - 3.66897i) q^{69} +(-1.17602 + 3.61943i) q^{70} +(0.493561 - 0.679329i) q^{71} +(-18.7579 - 12.4609i) q^{72} +(1.62164 + 0.526902i) q^{73} +(-3.07228 - 9.45550i) q^{74} +(-3.98739 + 3.02680i) q^{75} +30.4176i q^{76} +(-0.620412 + 3.25808i) q^{77} +(-0.238710 - 11.3774i) q^{78} +(-1.30582 - 1.79731i) q^{79} +(-13.7284 + 4.46063i) q^{80} +(2.05396 - 8.76249i) q^{81} +(-2.32365 - 1.68823i) q^{82} +(-5.63425 - 4.09352i) q^{83} +(8.06682 + 2.43522i) q^{84} +(6.98325 - 2.26900i) q^{85} +(6.37771 + 8.77816i) q^{86} +(-7.69876 + 0.161528i) q^{87} +(-22.5235 + 10.6077i) q^{88} +12.3634i q^{89} +(-7.09231 - 8.94701i) q^{90} +(0.774891 + 2.38487i) q^{91} +(-29.7994 - 9.68242i) q^{92} +(9.75416 + 6.77883i) q^{93} +(-6.82869 + 9.39889i) q^{94} +(-2.80635 + 8.63704i) q^{95} +(6.28094 + 18.0344i) q^{96} +(-7.64536 + 5.55468i) q^{97} -2.62011 q^{98} +(-7.11166 - 6.95876i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 6 q^{3} - 24 q^{4} - 10 q^{6} - 20 q^{9}+O(q^{10}) \) 96 * q + 6 * q^3 - 24 * q^4 - 10 * q^6 - 20 * q^9	\( 96 q + 6 q^{3} - 24 q^{4} - 10 q^{6} - 20 q^{9} - 20 q^{12} - 32 q^{16} - 10 q^{18} - 60 q^{19} + 30 q^{24} + 12 q^{25} - 40 q^{28} + 60 q^{30} + 40 q^{31} - 44 q^{33} + 8 q^{34} + 2 q^{36} + 16 q^{37} - 10 q^{39} - 96 q^{45} - 40 q^{46} + 48 q^{48} + 24 q^{49} - 30 q^{51} - 40 q^{52} + 28 q^{55} - 30 q^{57} + 36 q^{58} - 32 q^{60} + 40 q^{61} - 28 q^{64} + 118 q^{66} - 56 q^{67} + 26 q^{69} + 20 q^{70} + 150 q^{72} + 40 q^{73} + 2 q^{75} - 20 q^{78} - 40 q^{79} + 8 q^{81} - 16 q^{82} + 40 q^{84} - 60 q^{85} - 156 q^{88} + 100 q^{90} + 36 q^{91} - 36 q^{93} + 160 q^{96} - 88 q^{97} - 94 q^{99}+O(q^{100}) \) 96 * q + 6 * q^3 - 24 * q^4 - 10 * q^6 - 20 * q^9 - 20 * q^12 - 32 * q^16 - 10 * q^18 - 60 * q^19 + 30 * q^24 + 12 * q^25 - 40 * q^28 + 60 * q^30 + 40 * q^31 - 44 * q^33 + 8 * q^34 + 2 * q^36 + 16 * q^37 - 10 * q^39 - 96 * q^45 - 40 * q^46 + 48 * q^48 + 24 * q^49 - 30 * q^51 - 40 * q^52 + 28 * q^55 - 30 * q^57 + 36 * q^58 - 32 * q^60 + 40 * q^61 - 28 * q^64 + 118 * q^66 - 56 * q^67 + 26 * q^69 + 20 * q^70 + 150 * q^72 + 40 * q^73 + 2 * q^75 - 20 * q^78 - 40 * q^79 + 8 * q^81 - 16 * q^82 + 40 * q^84 - 60 * q^85 - 156 * q^88 + 100 * q^90 + 36 * q^91 - 36 * q^93 + 160 * q^96 - 88 * q^97 - 94 * q^99

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