LMFDB - Embedded newform 231.2.j.g.190.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(64,231)]

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([0, 0, 6]))

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

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

chi := DirichletCharacter("231.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.j (of order $5$, 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:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 12 x^{18} - 3 x^{17} + 94 x^{16} - 10 x^{15} + 662 x^{14} - 153 x^{13} + 4638 x^{12} + \cdots + 121 $ x^20 + 12x^18 - 3x^17 + 94x^16 - 10x^15 + 662x^14 - 153x^13 + 4638x^12 - 1174x^11 + 15808x^10 - 3393x^9 + 26062x^8 - 15494x^7 + 11660x^6 - 33295x^5 + 67756x^4 - 43696x^3 + 13084x^2 - 1155x + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			190.1
Root			$2.13576 + 1.55172i$ of defining polynomial
Character	$\chi$	$=$	231.190
Dual form			231.2.j.g.169.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.13576 + 1.55172i) q^{2} +(0.309017 + 0.951057i) q^{3} +(1.53559 - 4.72606i) q^{4} +(-2.49476 - 1.81255i) q^{5} +(-2.13576 - 1.55172i) q^{6} +(-0.309017 + 0.951057i) q^{7} +(2.42230 + 7.45506i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(-2.13576 + 1.55172i) q^{2} +(0.309017 + 0.951057i) q^{3} +(1.53559 - 4.72606i) q^{4} +(-2.49476 - 1.81255i) q^{5} +(-2.13576 - 1.55172i) q^{6} +(-0.309017 + 0.951057i) q^{7} +(2.42230 + 7.45506i) q^{8} +(-0.809017 + 0.587785i) q^{9} +8.14075 q^{10} +(1.45539 - 2.98024i) q^{11} +4.96928 q^{12} +(4.56364 - 3.31568i) q^{13} +(-0.815786 - 2.51073i) q^{14} +(0.952912 - 2.93276i) q^{15} +(-8.70112 - 6.32173i) q^{16} +(4.53118 + 3.29210i) q^{17} +(0.815786 - 2.51073i) q^{18} +(0.0379017 + 0.116649i) q^{19} +(-12.3971 + 9.00705i) q^{20} -1.00000 q^{21} +(1.51613 + 8.62342i) q^{22} +1.67325 q^{23} +(-6.34165 + 4.60748i) q^{24} +(1.39340 + 4.28844i) q^{25} +(-4.60183 + 14.1630i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(4.02023 + 2.92087i) q^{28} +(2.73492 - 8.41721i) q^{29} +(2.51563 + 7.74231i) q^{30} +(-1.29259 + 0.939120i) q^{31} +12.7156 q^{32} +(3.28412 + 0.463217i) q^{33} -14.7859 q^{34} +(2.49476 - 1.81255i) q^{35} +(1.53559 + 4.72606i) q^{36} +(1.28943 - 3.96845i) q^{37} +(-0.261956 - 0.190322i) q^{38} +(4.56364 + 3.31568i) q^{39} +(7.46960 - 22.9891i) q^{40} +(1.07803 + 3.31785i) q^{41} +(2.13576 - 1.55172i) q^{42} -5.10698 q^{43} +(-11.8499 - 11.4547i) q^{44} +3.08369 q^{45} +(-3.57364 + 2.59640i) q^{46} +(-0.492574 - 1.51599i) q^{47} +(3.32353 - 10.2288i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(-9.63040 - 6.99690i) q^{50} +(-1.73076 + 5.32673i) q^{51} +(-8.66223 - 26.6596i) q^{52} +(9.59206 - 6.96904i) q^{53} +2.63994 q^{54} +(-9.03267 + 4.79700i) q^{55} -7.83871 q^{56} +(-0.0992279 + 0.0720933i) q^{57} +(7.22002 + 22.2209i) q^{58} +(2.04398 - 6.29072i) q^{59} +(-12.3971 - 9.00705i) q^{60} +(6.86789 + 4.98982i) q^{61} +(1.30340 - 4.01146i) q^{62} +(-0.309017 - 0.951057i) q^{63} +(-9.75511 + 7.08750i) q^{64} -17.3950 q^{65} +(-7.73285 + 4.10670i) q^{66} -8.04949 q^{67} +(22.5167 - 16.3593i) q^{68} +(0.517061 + 1.59135i) q^{69} +(-2.51563 + 7.74231i) q^{70} +(-5.05133 - 3.67001i) q^{71} +(-6.34165 - 4.60748i) q^{72} +(1.08466 - 3.33825i) q^{73} +(3.40401 + 10.4765i) q^{74} +(-3.64796 + 2.65040i) q^{75} +0.609494 q^{76} +(2.38464 + 2.30511i) q^{77} -14.8918 q^{78} +(7.60289 - 5.52382i) q^{79} +(10.2487 + 31.5424i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-7.45078 - 5.41331i) q^{82} +(7.63216 + 5.54509i) q^{83} +(-1.53559 + 4.72606i) q^{84} +(-5.33712 - 16.4260i) q^{85} +(10.9073 - 7.92458i) q^{86} +8.85038 q^{87} +(25.7433 + 3.63102i) q^{88} -8.45556 q^{89} +(-6.58600 + 4.78501i) q^{90} +(1.74316 + 5.36488i) q^{91} +(2.56942 - 7.90787i) q^{92} +(-1.29259 - 0.939120i) q^{93} +(3.40440 + 2.47344i) q^{94} +(0.116877 - 0.359710i) q^{95} +(3.92933 + 12.0932i) q^{96} +(4.59909 - 3.34143i) q^{97} +2.63994 q^{98} +(0.574303 + 3.26652i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 5 q^{3} - 14 q^{4} - 5 q^{5} + 5 q^{7} - 9 q^{8} - 5 q^{9}+O(q^{10}) $ 20 * q - 5 * q^3 - 14 * q^4 - 5 * q^5 + 5 * q^7 - 9 * q^8 - 5 * q^9	\( 20 q - 5 q^{3} - 14 q^{4} - 5 q^{5} + 5 q^{7} - 9 q^{8} - 5 q^{9} + 12 q^{10} - q^{11} + 36 q^{12} + 13 q^{13} - 24 q^{16} - q^{17} + 10 q^{19} - 46 q^{20} - 20 q^{21} + 26 q^{22} + 6 q^{24} - 8 q^{25} - 53 q^{26} - 5 q^{27} + 4 q^{28} + 3 q^{29} - 3 q^{30} - 13 q^{31} + 82 q^{32} + 9 q^{33} + 42 q^{34} + 5 q^{35} - 14 q^{36} - 32 q^{37} + 16 q^{38} + 13 q^{39} + 20 q^{40} - 3 q^{41} + 12 q^{43} + 25 q^{44} + 10 q^{45} - 13 q^{46} + 20 q^{47} - 14 q^{48} - 5 q^{49} - 83 q^{50} + 9 q^{51} - 80 q^{52} + 3 q^{53} - 28 q^{55} - 6 q^{56} - 10 q^{57} + 2 q^{58} - 9 q^{59} - 46 q^{60} - 15 q^{61} - 37 q^{62} + 5 q^{63} - 49 q^{64} + 58 q^{65} - 4 q^{66} + 76 q^{67} + 51 q^{68} + 3 q^{70} + 37 q^{71} + 6 q^{72} + 27 q^{73} - 32 q^{74} - 23 q^{75} + 4 q^{76} + 6 q^{77} + 2 q^{78} + 5 q^{79} + 137 q^{80} - 5 q^{81} - 55 q^{82} - 42 q^{83} + 14 q^{84} - 48 q^{85} + 3 q^{86} + 28 q^{87} + 151 q^{88} - 18 q^{89} - 3 q^{90} + 7 q^{91} + 39 q^{92} - 13 q^{93} - 35 q^{94} - 96 q^{95} - 48 q^{96} - 27 q^{97} - q^{99}+O(q^{100}) \) 20 * q - 5 * q^3 - 14 * q^4 - 5 * q^5 + 5 * q^7 - 9 * q^8 - 5 * q^9 + 12 * q^10 - q^11 + 36 * q^12 + 13 * q^13 - 24 * q^16 - q^17 + 10 * q^19 - 46 * q^20 - 20 * q^21 + 26 * q^22 + 6 * q^24 - 8 * q^25 - 53 * q^26 - 5 * q^27 + 4 * q^28 + 3 * q^29 - 3 * q^30 - 13 * q^31 + 82 * q^32 + 9 * q^33 + 42 * q^34 + 5 * q^35 - 14 * q^36 - 32 * q^37 + 16 * q^38 + 13 * q^39 + 20 * q^40 - 3 * q^41 + 12 * q^43 + 25 * q^44 + 10 * q^45 - 13 * q^46 + 20 * q^47 - 14 * q^48 - 5 * q^49 - 83 * q^50 + 9 * q^51 - 80 * q^52 + 3 * q^53 - 28 * q^55 - 6 * q^56 - 10 * q^57 + 2 * q^58 - 9 * q^59 - 46 * q^60 - 15 * q^61 - 37 * q^62 + 5 * q^63 - 49 * q^64 + 58 * q^65 - 4 * q^66 + 76 * q^67 + 51 * q^68 + 3 * q^70 + 37 * q^71 + 6 * q^72 + 27 * q^73 - 32 * q^74 - 23 * q^75 + 4 * q^76 + 6 * q^77 + 2 * q^78 + 5 * q^79 + 137 * q^80 - 5 * q^81 - 55 * q^82 - 42 * q^83 + 14 * q^84 - 48 * q^85 + 3 * q^86 + 28 * q^87 + 151 * q^88 - 18 * q^89 - 3 * q^90 + 7 * q^91 + 39 * q^92 - 13 * q^93 - 35 * q^94 - 96 * q^95 - 48 * q^96 - 27 * q^97 - q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−2.13576	+	1.55172i	−1.51021	+	1.09723i	−0.544122	+	0.839006i	$0.683137\pi$
$2$	−2.13576	+	1.55172i	−1.51021	+	1.09723i	−0.966085	+	0.258224i	$0.916863\pi$
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$4$	1.53559	−	4.72606i	0.767796	−	2.36303i
$5$	−2.49476	−	1.81255i	−1.11569	−	0.810595i	−0.132139	−	0.991231i	$-0.542184\pi$
$5$	−2.49476	−	1.81255i	−1.11569	−	0.810595i	−0.983550	+	0.180636i	$0.942184\pi$
$6$	−2.13576	−	1.55172i	−0.871919	−	0.633486i
$7$	−0.309017	+	0.951057i	−0.116797	+	0.359466i
$7$	−0.309017	+	0.951057i	−0.116797	+	0.359466i
$8$	2.42230	+	7.45506i	0.856411	+	2.63576i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	8.14075			2.57433
$11$	1.45539	−	2.98024i	0.438818	−	0.898576i
$11$	1.45539	−	2.98024i	0.438818	−	0.898576i
$12$	4.96928			1.43451
$13$	4.56364	−	3.31568i	1.26573	−	0.919604i	0.266703	−	0.963779i	$-0.414066\pi$
$13$	4.56364	−	3.31568i	1.26573	−	0.919604i	0.999024	+	0.0441746i	$0.0140658\pi$
$14$	−0.815786	−	2.51073i	−0.218028	−	0.671021i
$15$	0.952912	−	2.93276i	0.246041	−	0.757236i
$16$	−8.70112	−	6.32173i	−2.17528	−	1.58043i
$17$	4.53118	+	3.29210i	1.09897	+	0.798451i	0.980892	−	0.194553i	$-0.0623256\pi$
$17$	4.53118	+	3.29210i	1.09897	+	0.798451i	0.118081	+	0.993004i	$0.462326\pi$
$18$	0.815786	−	2.51073i	0.192283	−	0.591785i
$19$	0.0379017	+	0.116649i	0.00869524	+	0.0267612i	0.955310	−	0.295606i	$-0.0955215\pi$
$19$	0.0379017	+	0.116649i	0.00869524	+	0.0267612i	−0.946615	+	0.322367i	$0.895521\pi$
$20$	−12.3971	+	9.00705i	−2.77208	+	2.01404i
$21$	−1.00000			−0.218218
$22$	1.51613	+	8.62342i	0.323239	+	1.83852i
$23$	1.67325			0.348896			0.174448	−	0.984666i	$-0.444186\pi$
$23$	1.67325			0.348896			0.174448	+	0.984666i	$0.444186\pi$
$24$	−6.34165	+	4.60748i	−1.29448	+	0.940498i
$25$	1.39340	+	4.28844i	0.278680	+	0.857688i
$26$	−4.60183	+	14.1630i	−0.902492	+	2.77759i
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$	4.02023	+	2.92087i	0.759752	+	0.551992i
$29$	2.73492	−	8.41721i	0.507861	−	1.56304i	−0.288045	−	0.957617i	$-0.593005\pi$
$29$	2.73492	−	8.41721i	0.507861	−	1.56304i	0.795906	−	0.605420i	$-0.206995\pi$
$30$	2.51563	+	7.74231i	0.459289	+	1.41355i
$31$	−1.29259	+	0.939120i	−0.232156	+	0.168671i	−0.697781	−	0.716311i	$-0.745829\pi$
$31$	−1.29259	+	0.939120i	−0.232156	+	0.168671i	0.465626	+	0.884982i	$0.345829\pi$
$32$	12.7156			2.24782
$33$	3.28412	+	0.463217i	0.571692	+	0.0806357i
$34$	−14.7859			−2.53576
$35$	2.49476	−	1.81255i	0.421691	−	0.306376i
$36$	1.53559	+	4.72606i	0.255932	+	0.787677i
$37$	1.28943	−	3.96845i	0.211981	−	0.652409i	−0.787374	−	0.616476i	$-0.788560\pi$
$37$	1.28943	−	3.96845i	0.211981	−	0.652409i	0.999354	−	0.0359331i	$-0.0114403\pi$
$38$	−0.261956	−	0.190322i	−0.0424948	−	0.0308743i
$39$	4.56364	+	3.31568i	0.730768	+	0.530934i
$40$	7.46960	−	22.9891i	1.18105	−	3.63489i
$41$	1.07803	+	3.31785i	0.168361	+	0.518161i	0.999268	−	0.0382497i	$-0.0121782\pi$
$41$	1.07803	+	3.31785i	0.168361	+	0.518161i	−0.830908	+	0.556411i	$0.812178\pi$
$42$	2.13576	−	1.55172i	0.329554	−	0.239435i
$43$	−5.10698			−0.778807			−0.389403	−	0.921067i	$-0.627319\pi$
$43$	−5.10698			−0.778807			−0.389403	+	0.921067i	$0.627319\pi$
$44$	−11.8499	−	11.4547i	−1.78644	−	1.72686i
$45$	3.08369			0.459689
$46$	−3.57364	+	2.59640i	−0.526905	+	0.382819i
$47$	−0.492574	−	1.51599i	−0.0718494	−	0.221130i	0.908683	−	0.417486i	$-0.137089\pi$
$47$	−0.492574	−	1.51599i	−0.0718494	−	0.221130i	−0.980532	+	0.196357i	$0.937089\pi$
$48$	3.32353	−	10.2288i	0.479710	−	1.47640i
$49$	−0.809017	−	0.587785i	−0.115574	−	0.0839693i
$50$	−9.63040	−	6.99690i	−1.36194	−	0.989511i
$51$	−1.73076	+	5.32673i	−0.242355	+	0.745891i
$52$	−8.66223	−	26.6596i	−1.20123	−	3.69702i
$53$	9.59206	−	6.96904i	1.31757	−	0.957271i	0.317611	−	0.948221i	$-0.397119\pi$
$53$	9.59206	−	6.96904i	1.31757	−	0.957271i	0.999959	−	0.00904978i	$-0.00288068\pi$
$54$	2.63994			0.359250
$55$	−9.03267	+	4.79700i	−1.21797	+	0.646828i
$56$	−7.83871			−1.04749
$57$	−0.0992279	+	0.0720933i	−0.0131431	+	0.00954899i
$58$	7.22002	+	22.2209i	0.948035	+	2.91775i
$59$	2.04398	−	6.29072i	0.266103	−	0.818982i	−0.725334	−	0.688397i	$-0.758315\pi$
$59$	2.04398	−	6.29072i	0.266103	−	0.818982i	0.991437	−	0.130584i	$-0.0416853\pi$
$60$	−12.3971	−	9.00705i	−1.60046	−	1.16280i
$61$	6.86789	+	4.98982i	0.879344	+	0.638880i	0.933078	−	0.359675i	$-0.117112\pi$
$61$	6.86789	+	4.98982i	0.879344	+	0.638880i	−0.0537342	+	0.998555i	$0.517112\pi$
$62$	1.30340	−	4.01146i	0.165532	−	0.509456i
$63$	−0.309017	−	0.951057i	−0.0389325	−	0.119822i
$64$	−9.75511	+	7.08750i	−1.21939	+	0.885938i
$65$	−17.3950			−2.15758
$66$	−7.73285	+	4.10670i	−0.951849	+	0.505500i
$67$	−8.04949			−0.983402			−0.491701	−	0.870764i	$-0.663625\pi$
$67$	−8.04949			−0.983402			−0.491701	+	0.870764i	$0.663625\pi$
$68$	22.5167	−	16.3593i	2.73055	−	1.98386i
$69$	0.517061	+	1.59135i	0.0622469	+	0.191576i
$70$	−2.51563	+	7.74231i	−0.300675	+	0.925383i
$71$	−5.05133	−	3.67001i	−0.599483	−	0.435550i	0.246213	−	0.969216i	$-0.420814\pi$
$71$	−5.05133	−	3.67001i	−0.599483	−	0.435550i	−0.845695	+	0.533666i	$0.820814\pi$
$72$	−6.34165	−	4.60748i	−0.747371	−	0.542997i
$73$	1.08466	−	3.33825i	0.126950	−	0.390713i	−0.867301	−	0.497784i	$-0.834147\pi$
$73$	1.08466	−	3.33825i	0.126950	−	0.390713i	0.994251	+	0.107071i	$0.0341472\pi$
$74$	3.40401	+	10.4765i	0.395708	+	1.21786i
$75$	−3.64796	+	2.65040i	−0.421231	+	0.306042i
$76$	0.609494			0.0699138
$77$	2.38464	+	2.30511i	0.271754	+	0.262691i
$78$	−14.8918			−1.68617
$79$	7.60289	−	5.52382i	0.855392	−	0.621479i	−0.0712355	−	0.997460i	$-0.522694\pi$
$79$	7.60289	−	5.52382i	0.855392	−	0.621479i	0.926627	+	0.375981i	$0.122694\pi$
$80$	10.2487	+	31.5424i	1.14584	+	3.52654i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	−7.45078	−	5.41331i	−0.822801	−	0.597800i
$83$	7.63216	+	5.54509i	0.837738	+	0.608652i	0.921738	−	0.387814i	$-0.126770\pi$
$83$	7.63216	+	5.54509i	0.837738	+	0.608652i	−0.0839999	+	0.996466i	$0.526770\pi$
$84$	−1.53559	+	4.72606i	−0.167547	+	0.515656i
$85$	−5.33712	−	16.4260i	−0.578892	−	1.78165i
$86$	10.9073	−	7.92458i	1.17616	−	0.854530i
$87$	8.85038			0.948860
$88$	25.7433	+	3.63102i	2.74424	+	0.387068i
$89$	−8.45556			−0.896288			−0.448144	−	0.893961i	$-0.647915\pi$
$89$	−8.45556			−0.896288			−0.448144	+	0.893961i	$0.647915\pi$
$90$	−6.58600	+	4.78501i	−0.694226	+	0.504385i
$91$	1.74316	+	5.36488i	0.182732	+	0.562393i
$92$	2.56942	−	7.90787i	0.267881	−	0.824452i
$93$	−1.29259	−	0.939120i	−0.134035	−	0.0973822i
$94$	3.40440	+	2.47344i	0.351137	+	0.255116i
$95$	0.116877	−	0.359710i	0.0119913	−	0.0369055i
$96$	3.92933	+	12.0932i	0.401035	+	1.23426i
$97$	4.59909	−	3.34143i	0.466966	−	0.339271i	−0.329291	−	0.944228i	$-0.606810\pi$
$97$	4.59909	−	3.34143i	0.466966	−	0.339271i	0.796258	+	0.604957i	$0.206810\pi$
$98$	2.63994			0.266674
$99$	0.574303	+	3.26652i	0.0577196	+	0.328298i
$100$	22.4071			2.24071
$101$	−13.6542	+	9.92038i	−1.35865	+	0.987115i	−0.360117	+	0.932907i	$0.617263\pi$
$101$	−13.6542	+	9.92038i	−1.35865	+	0.987115i	−0.998530	+	0.0542078i	$0.982737\pi$
$102$	−4.56910	−	14.0622i	−0.452408	−	1.39237i
$103$	−4.08433	+	12.5703i	−0.402441	+	1.23859i	0.520572	+	0.853818i	$0.325719\pi$
$103$	−4.08433	+	12.5703i	−0.402441	+	1.23859i	−0.923013	+	0.384768i	$0.874281\pi$
$104$	35.7731	+	25.9907i	3.50784	+	2.54859i
$105$	2.49476	+	1.81255i	0.243463	+	0.176886i
$106$	−9.67231	+	29.7683i	−0.939458	+	2.89135i
$107$	3.42221	+	10.5325i	0.330838	+	1.01821i	0.968736	+	0.248093i	$0.0798039\pi$
$107$	3.42221	+	10.5325i	0.330838	+	1.01821i	−0.637899	+	0.770120i	$0.720196\pi$
$108$	−4.02023	+	2.92087i	−0.386847	+	0.281061i
$109$	−4.87369			−0.466815			−0.233407	−	0.972379i	$-0.574988\pi$
$109$	−4.87369			−0.466815			−0.233407	+	0.972379i	$0.574988\pi$
$110$	11.8480	−	24.2614i	1.12966	−	2.31323i
$111$	4.17268			0.396053
$112$	8.70112	−	6.32173i	0.822178	−	0.597347i
$113$	−1.63242	−	5.02408i	−0.153565	−	0.472626i	0.844447	−	0.535639i	$-0.179929\pi$
$113$	−1.63242	−	5.02408i	−0.153565	−	0.472626i	−0.998013	+	0.0630130i	$0.979929\pi$
$114$	0.100058	−	0.307947i	0.00937130	−	0.0288419i
$115$	−4.17434	−	3.03284i	−0.389259	−	0.282813i
$116$	−35.5806	−	25.8508i	−3.30357	−	2.40019i
$117$	−1.74316	+	5.36488i	−0.161155	+	0.495984i
$118$	5.39598	+	16.6071i	0.496740	+	1.52881i
$119$	−4.53118	+	3.29210i	−0.415373	+	0.301786i
$120$	24.1721			2.20661
$121$	−6.76366	−	8.67484i	−0.614878	−	0.788622i
$122$	−22.4109			−2.02899
$123$	−2.82233	+	2.05054i	−0.254481	+	0.184891i
$124$	2.45346	+	7.55096i	0.220327	+	0.678096i
$125$	−0.467754	+	1.43960i	−0.0418372	+	0.128762i
$126$	2.13576	+	1.55172i	0.190268	+	0.138238i
$127$	9.17429	+	6.66551i	0.814086	+	0.591468i	0.915012	−	0.403426i	$-0.132181\pi$
$127$	9.17429	+	6.66551i	0.814086	+	0.591468i	−0.100926	+	0.994894i	$0.532181\pi$
$128$	1.97808	−	6.08791i	0.174839	−	0.538100i
$129$	−1.57814	−	4.85702i	−0.138948	−	0.427637i
$130$	37.1515	−	26.9921i	3.25840	−	2.36737i
$131$	−0.970284			−0.0847741			−0.0423870	−	0.999101i	$-0.513496\pi$
$131$	−0.970284			−0.0847741			−0.0423870	+	0.999101i	$0.513496\pi$
$132$	7.23226	−	14.8096i	0.629487	−	1.28901i
$133$	−0.122652			−0.0106353
$134$	17.1918	−	12.4905i	1.48514	−	1.07902i
$135$	0.952912	+	2.93276i	0.0820136	+	0.252412i
$136$	−13.5669	+	41.7547i	−1.16335	+	3.58043i
$137$	0.101208	+	0.0735323i	0.00864682	+	0.00628229i	0.592100	−	0.805864i	$-0.298299\pi$
$137$	0.101208	+	0.0735323i	0.00864682	+	0.00628229i	−0.583453	+	0.812147i	$0.698299\pi$
$138$	−3.57364	−	2.59640i	−0.304209	−	0.221021i
$139$	−0.518637	+	1.59620i	−0.0439902	+	0.135388i	−0.970639	−	0.240539i	$-0.922676\pi$
$139$	−0.518637	+	1.59620i	−0.0439902	+	0.135388i	0.926649	+	0.375927i	$0.122676\pi$
$140$	−4.73529	−	14.5737i	−0.400205	−	1.23170i
$141$	1.28958	−	0.936932i	0.108602	−	0.0789039i
$142$	16.4832			1.38324
$143$	−3.23963	−	18.4264i	−0.270911	−	1.54089i
$144$	10.7552			0.896264
$145$	−22.0795	+	16.0417i	−1.83361	+	1.33219i
$146$	2.86345	+	8.81278i	0.236981	+	0.729351i
$147$	0.309017	−	0.951057i	0.0254873	−	0.0784418i
$148$	−16.7751	−	12.1878i	−1.37891	−	1.00183i
$149$	−11.4712	−	8.33429i	−0.939754	−	0.682771i	0.00860721	−	0.999963i	$-0.497260\pi$
$149$	−11.4712	−	8.33429i	−0.939754	−	0.682771i	−0.948362	+	0.317191i	$0.897260\pi$
$150$	3.67849	−	11.3212i	0.300347	−	0.924374i
$151$	4.90791	+	15.1050i	0.399400	+	1.22923i	0.925482	+	0.378793i	$0.123661\pi$
$151$	4.90791	+	15.1050i	0.399400	+	1.22923i	−0.526082	+	0.850434i	$0.676339\pi$
$152$	−0.777819	+	0.565119i	−0.0630895	+	0.0458372i
$153$	−5.60085			−0.452802
$154$	−8.66987	−	1.22286i	−0.698638	−	0.0985412i
$155$	4.92689			0.395737
$156$	22.6780	−	16.4765i	1.81569	−	1.31918i
$157$	−2.84251	−	8.74833i	−0.226857	−	0.698193i	−0.998098	−	0.0616500i	$-0.980364\pi$
$157$	−2.84251	−	8.74833i	−0.226857	−	0.698193i	0.771241	−	0.636543i	$-0.219636\pi$
$158$	−7.66650	+	23.5951i	−0.609914	+	1.87712i
$159$	9.59206	+	6.96904i	0.760700	+	0.552681i
$160$	−31.7222	−	23.0476i	−2.50786	−	1.82207i
$161$	−0.517061	+	1.59135i	−0.0407501	+	0.125416i
$162$	0.815786	+	2.51073i	0.0640942	+	0.197262i
$163$	−7.90363	+	5.74232i	−0.619060	+	0.449773i	−0.852593	−	0.522575i	$-0.824971\pi$
$163$	−7.90363	+	5.74232i	−0.619060	+	0.449773i	0.233533	+	0.972349i	$0.424971\pi$
$164$	17.3358			1.35370
$165$	−7.35347	−	7.10823i	−0.572467	−	0.553375i
$166$	−24.9048			−1.93299
$167$	−4.93691	+	3.58688i	−0.382030	+	0.277561i	−0.762182	−	0.647363i	$-0.775872\pi$
$167$	−4.93691	+	3.58688i	−0.382030	+	0.277561i	0.380152	+	0.924924i	$0.375872\pi$
$168$	−2.42230	−	7.45506i	−0.186884	−	0.575170i
$169$	5.81587	−	17.8994i	0.447375	−	1.37688i
$170$	36.8872	+	26.8001i	2.82912	+	2.05548i
$171$	−0.0992279	−	0.0720933i	−0.00758815	−	0.00551311i
$172$	−7.84223	+	24.1359i	−0.597964	+	1.84035i
$173$	2.08221	+	6.40839i	0.158308	+	0.487221i	0.998481	−	0.0550972i	$-0.0175469\pi$
$173$	2.08221	+	6.40839i	0.158308	+	0.487221i	−0.840173	+	0.542318i	$0.817547\pi$
$174$	−18.9022	+	13.7333i	−1.43298	+	1.04112i
$175$	−4.50913			−0.340858
$176$	−31.5038	+	16.7308i	−2.37469	+	1.26113i
$177$	6.61445			0.497173
$178$	18.0590	−	13.1206i	1.35358	−	0.983433i
$179$	4.01523	+	12.3576i	0.300112	+	0.923651i	0.981456	+	0.191687i	$0.0613959\pi$
$179$	4.01523	+	12.3576i	0.300112	+	0.923651i	−0.681344	+	0.731964i	$0.738604\pi$
$180$	4.73529	−	14.5737i	0.352947	−	1.08626i
$181$	3.31550	+	2.40886i	0.246440	+	0.179049i	0.704147	−	0.710054i	$-0.251329\pi$
$181$	3.31550	+	2.40886i	0.246440	+	0.179049i	−0.457708	+	0.889103i	$0.651329\pi$
$182$	−12.0477	−	8.75319i	−0.893038	−	0.648830i
$183$	−2.62330	+	8.07369i	−0.193920	+	0.596824i
$184$	4.05310	+	12.4741i	0.298798	+	0.919606i
$185$	−10.4098	+	7.56317i	−0.765344	+	0.556055i
$186$	4.21790			0.309271
$187$	16.4059	−	8.71272i	1.19972	−	0.637137i
$188$	−7.92105			−0.577702
$189$	0.809017	−	0.587785i	0.0588473	−	0.0427551i
$190$	0.308548	+	0.949613i	0.0223844	+	0.0688922i
$191$	6.64498	−	20.4511i	0.480814	−	1.47979i	−0.357139	−	0.934051i	$-0.616248\pi$
$191$	6.64498	−	20.4511i	0.480814	−	1.47979i	0.837953	−	0.545742i	$-0.183752\pi$
$192$	−9.75511	−	7.08750i	−0.704015	−	0.511497i
$193$	−14.3976	−	10.4604i	−1.03636	−	0.752960i	−0.0667882	−	0.997767i	$-0.521275\pi$
$193$	−14.3976	−	10.4604i	−1.03636	−	0.752960i	−0.969572	+	0.244808i	$0.921275\pi$
$194$	−4.63757	+	14.2730i	−0.332958	+	1.02474i
$195$	−5.37535	−	16.5436i	−0.384937	−	1.18471i
$196$	−4.02023	+	2.92087i	−0.287159	+	0.208633i
$197$	18.1083			1.29016			0.645080	−	0.764115i	$-0.276824\pi$
$197$	18.1083			1.29016			0.645080	+	0.764115i	$0.276824\pi$
$198$	−6.29529	−	6.08534i	−0.447387	−	0.432466i
$199$	2.67139			0.189370			0.0946848	−	0.995507i	$-0.469816\pi$
$199$	2.67139			0.189370			0.0946848	+	0.995507i	$0.469816\pi$
$200$	−28.5954	+	20.7757i	−2.02200	+	1.46907i
$201$	−2.48743	−	7.65552i	−0.175450	−	0.539979i
$202$	13.7685	−	42.3750i	0.968747	−	2.98150i
$203$	7.16011	+	5.20212i	0.502541	+	0.365117i
$204$	22.5167	+	16.3593i	1.57649	+	1.14538i
$205$	3.32432	−	10.2312i	0.232181	−	0.714579i
$206$	−10.7824	−	33.1848i	−0.751244	−	2.31209i
$207$	−1.35368	+	0.983509i	−0.0940876	+	0.0683586i
$208$	−60.6696			−4.20668
$209$	0.402805	+	0.0568146i	0.0278626	+	0.00392995i
$210$	−8.14075			−0.561765
$211$	6.59710	−	4.79308i	0.454163	−	0.329969i	−0.337074	−	0.941478i	$-0.609437\pi$
$211$	6.59710	−	4.79308i	0.454163	−	0.329969i	0.791237	+	0.611509i	$0.209437\pi$
$212$	−18.2066	−	56.0343i	−1.25044	−	3.84845i
$213$	1.92944	−	5.93819i	0.132203	−	0.406878i
$214$	−23.6524	−	17.1845i	−1.61685	−	1.17471i
$215$	12.7407	+	9.25663i	0.868906	+	0.631297i
$216$	2.42230	−	7.45506i	0.164816	−	0.507253i
$217$	−0.493725	−	1.51953i	−0.0335162	−	0.103152i
$218$	10.4090	−	7.56259i	0.704987	−	0.512203i
$219$	3.51005			0.237187
$220$	8.80045	+	50.0552i	0.593326	+	3.37472i
$221$	31.5942			2.12526
$222$	−8.91182	+	6.47481i	−0.598122	+	0.434561i
$223$	2.62282	+	8.07221i	0.175637	+	0.540555i	0.999662	−	0.0259982i	$-0.00827642\pi$
$223$	2.62282	+	8.07221i	0.175637	+	0.540555i	−0.824025	+	0.566554i	$0.808276\pi$
$224$	−3.92933	+	12.0932i	−0.262539	+	0.808012i
$225$	−3.64796	−	2.65040i	−0.243198	−	0.176693i
$226$	11.2824	+	8.19715i	0.750494	+	0.545266i
$227$	−6.84547	+	21.0682i	−0.454350	+	1.39835i	0.417546	+	0.908656i	$0.362890\pi$
$227$	−6.84547	+	21.0682i	−0.454350	+	1.39835i	−0.871897	+	0.489690i	$0.837110\pi$
$228$	0.188344	+	0.579663i	0.0124734	+	0.0383891i
$229$	7.26508	−	5.27839i	0.480090	−	0.348806i	−0.321270	−	0.946988i	$-0.604110\pi$
$229$	7.26508	−	5.27839i	0.480090	−	0.348806i	0.801361	+	0.598181i	$0.204110\pi$
$230$	13.6215			0.898173
$231$	−1.45539	+	2.98024i	−0.0957579	+	0.196085i
$232$	69.3756			4.55473
$233$	−16.0921	+	11.6916i	−1.05423	+	0.765940i	−0.973011	−	0.230757i	$-0.925880\pi$
$233$	−16.0921	+	11.6916i	−1.05423	+	0.765940i	−0.0812140	+	0.996697i	$0.525880\pi$
$234$	−4.60183	−	14.1630i	−0.300831	−	0.925862i
$235$	−1.51895	+	4.67483i	−0.0990851	+	0.304953i
$236$	−26.5916	−	19.3199i	−1.73097	−	1.25762i
$237$	7.60289	+	5.52382i	0.493861	+	0.358811i
$238$	4.56910	−	14.0622i	0.296170	−	0.911519i
$239$	−2.84906	−	8.76851i	−0.184291	−	0.567188i	0.815645	−	0.578553i	$-0.196382\pi$
$239$	−2.84906	−	8.76851i	−0.184291	−	0.567188i	−0.999935	+	0.0113649i	$0.996382\pi$
$240$	−26.8315	+	19.4942i	−1.73197	+	1.25835i
$241$	−0.802919			−0.0517206			−0.0258603	−	0.999666i	$-0.508233\pi$
$241$	−0.802919			−0.0517206			−0.0258603	+	0.999666i	$0.508233\pi$
$242$	27.9064	+	8.03206i	1.79389	+	0.516320i
$243$	1.00000			0.0641500
$244$	34.1285	−	24.7958i	2.18485	−	1.58739i
$245$	0.952912	+	2.93276i	0.0608793	+	0.187367i
$246$	2.84594	−	8.75892i	0.181451	−	0.558448i
$247$	0.559742	+	0.406676i	0.0356155	+	0.0258762i
$248$	−10.1322	−	7.36149i	−0.643397	−	0.467455i
$249$	−2.91522	+	8.97214i	−0.184745	+	0.568586i
$250$	−1.23484	−	3.80045i	−0.0780982	−	0.240362i
$251$	−0.371563	+	0.269956i	−0.0234528	+	0.0170395i	−0.599450	−	0.800412i	$-0.704614\pi$
$251$	−0.371563	+	0.269956i	−0.0234528	+	0.0170395i	0.575997	+	0.817452i	$0.304614\pi$
$252$	−4.96928			−0.313035
$253$	2.43523	−	4.98667i	0.153102	−	0.313509i
$254$	−29.9370			−1.87842
$255$	13.9728	−	10.1518i	0.875008	−	0.635730i
$256$	−2.23023	−	6.86394i	−0.139389	−	0.428996i
$257$	−7.21782	+	22.2142i	−0.450235	+	1.38568i	0.426404	+	0.904533i	$0.359780\pi$
$257$	−7.21782	+	22.2142i	−0.450235	+	1.38568i	−0.876639	+	0.481149i	$0.840220\pi$
$258$	10.9073	+	7.92458i	0.679056	+	0.493363i
$259$	3.37577	+	2.45264i	0.209760	+	0.152399i
$260$	−26.7116	+	82.2099i	−1.65658	+	5.09844i
$261$	2.73492	+	8.41721i	0.169287	+	0.521012i
$262$	2.07229	−	1.50561i	0.128026	−	0.0930166i
$263$	−4.96169			−0.305951			−0.152975	−	0.988230i	$-0.548886\pi$
$263$	−4.96169			−0.305951			−0.152975	+	0.988230i	$0.548886\pi$
$264$	4.50180	+	25.6053i	0.277066	+	1.57590i
$265$	−36.5615			−2.24596
$266$	0.261956	−	0.190322i	0.0160615	−	0.0116694i
$267$	−2.61291	−	8.04172i	−0.159908	−	0.492145i
$268$	−12.3607	+	38.0424i	−0.755052	+	2.32381i
$269$	−0.834929	−	0.606611i	−0.0509065	−	0.0369857i	0.562041	−	0.827109i	$-0.310016\pi$
$269$	−0.834929	−	0.606611i	−0.0509065	−	0.0369857i	−0.612948	+	0.790124i	$0.710016\pi$
$270$	−6.58600	−	4.78501i	−0.400811	−	0.291207i
$271$	4.67936	−	14.4016i	0.284251	−	0.874835i	−0.702371	−	0.711811i	$-0.747875\pi$
$271$	4.67936	−	14.4016i	0.284251	−	0.874835i	0.986622	−	0.163024i	$-0.0521247\pi$
$272$	−18.6146	−	57.2898i	−1.12868	−	3.47371i
$273$	−4.56364	+	3.31568i	−0.276204	+	0.200674i
$274$	−0.330258			−0.0199516
$275$	14.8085	+	2.08871i	0.892988	+	0.125954i
$276$	8.31482			0.500494
$277$	0.865659	−	0.628938i	0.0520124	−	0.0377892i	−0.561475	−	0.827494i	$-0.689766\pi$
$277$	0.865659	−	0.628938i	0.0520124	−	0.0377892i	0.613488	+	0.789704i	$0.289766\pi$
$278$	−1.36917	−	4.21387i	−0.0821174	−	0.252731i
$279$	0.493725	−	1.51953i	0.0295585	−	0.0909718i
$280$	19.5557	+	14.2080i	1.16868	+	0.849092i
$281$	25.3295	+	18.4029i	1.51103	+	1.09783i	0.965717	+	0.259596i	$0.0835892\pi$
$281$	25.3295	+	18.4029i	1.51103	+	1.09783i	0.545313	+	0.838232i	$0.316411\pi$
$282$	−1.30037	+	4.00212i	−0.0774357	+	0.238323i
$283$	9.87775	+	30.4006i	0.587171	+	1.80713i	0.590371	+	0.807132i	$0.298981\pi$
$283$	9.87775	+	30.4006i	0.587171	+	1.80713i	−0.00320001	+	0.999995i	$0.501019\pi$
$284$	−25.1015	+	18.2373i	−1.48950	+	1.08218i
$285$	0.378222			0.0224039
$286$	35.5116	+	34.3272i	2.09984	+	2.02981i
$287$	−3.48859			−0.205925
$288$	−10.2871	+	7.47402i	−0.606174	+	0.440411i
$289$	4.44043	+	13.6662i	0.261202	+	0.803896i
$290$	22.2643	−	68.5224i	1.30740	−	4.02377i
$291$	4.59909	+	3.34143i	0.269603	+	0.195878i
$292$	−14.1112	−	10.2524i	−0.825795	−	0.599975i
$293$	−0.146154	+	0.449814i	−0.00853838	+	0.0262784i	−0.955235	−	0.295848i	$-0.904398\pi$
$293$	−0.146154	+	0.449814i	−0.00853838	+	0.0262784i	0.946697	+	0.322127i	$0.104398\pi$
$294$	0.815786	+	2.51073i	0.0475776	+	0.146429i
$295$	−16.5014	+	11.9890i	−0.960751	+	0.698027i
$296$	32.7084			1.90114
$297$	−2.92918	+	1.55561i	−0.169968	+	0.0902654i
$298$	37.4321			2.16838
$299$	7.63609	−	5.54795i	0.441607	−	0.320846i
$300$	6.92419	+	21.3105i	0.399768	+	1.23036i
$301$	1.57814	−	4.85702i	0.0909626	−	0.279954i
$302$	−33.9208	−	24.6449i	−1.95192	−	1.41815i
$303$	−13.6542	−	9.92038i	−0.784415	−	0.569911i
$304$	0.407639	−	1.25458i	0.0233797	−	0.0719553i
$305$	−8.08944	−	24.8967i	−0.463200	−	1.42558i
$306$	11.9620	−	8.69094i	0.683825	−	0.496828i
$307$	−22.3522			−1.27571			−0.637854	−	0.770158i	$-0.720177\pi$
$307$	−22.3522			−1.27571			−0.637854	+	0.770158i	$0.720177\pi$
$308$	14.5559	−	7.73024i	0.829400	−	0.440471i
$309$	−13.2172			−0.751898
$310$	−10.5226	+	7.64514i	−0.597645	+	0.434215i
$311$	6.79337	+	20.9078i	0.385216	+	1.18557i	0.936323	+	0.351140i	$0.114206\pi$
$311$	6.79337	+	20.9078i	0.385216	+	1.18557i	−0.551107	+	0.834435i	$0.685794\pi$
$312$	−13.6641	+	42.0538i	−0.773578	+	2.38083i
$313$	6.43190	+	4.67305i	0.363553	+	0.264136i	0.754532	−	0.656263i	$-0.227864\pi$
$313$	6.43190	+	4.67305i	0.363553	+	0.264136i	−0.390980	+	0.920399i	$0.627864\pi$
$314$	19.6458	+	14.2735i	1.10868	+	0.805502i
$315$	−0.952912	+	2.93276i	−0.0536905	+	0.165242i
$316$	−14.4310	−	44.4141i	−0.811808	−	2.49849i
$317$	12.2345	−	8.88889i	0.687158	−	0.499250i	−0.188566	−	0.982060i	$-0.560384\pi$
$317$	12.2345	−	8.88889i	0.687158	−	0.499250i	0.875725	+	0.482811i	$0.160384\pi$
$318$	−31.3003			−1.75523
$319$	−21.1049	−	20.4011i	−1.18165	−	1.14224i
$320$	37.1831			2.07860
$321$	−8.95947	+	6.50943i	−0.500069	+	0.363321i
$322$	−1.36501	−	4.20107i	−0.0760691	−	0.234116i
$323$	−0.212282	+	0.653336i	−0.0118117	+	0.0363526i
$324$	−4.02023	−	2.92087i	−0.223346	−	0.162270i
$325$	20.5781	+	14.9508i	1.14147	+	0.829323i
$326$	7.96976	−	24.5284i	0.441404	−	1.35850i
$327$	−1.50605	−	4.63516i	−0.0832849	−	0.256325i
$328$	−22.1234	+	16.0736i	−1.22156	+	0.887517i
$329$	1.59400			0.0878803
$330$	26.7352	+	3.77093i	1.47172	+	0.207583i
$331$	−6.02542			−0.331187			−0.165594	−	0.986194i	$-0.552954\pi$
$331$	−6.02542			−0.331187			−0.165594	+	0.986194i	$0.552954\pi$
$332$	37.9263	−	27.5551i	2.08148	−	1.51228i
$333$	1.28943	+	3.96845i	0.0706602	+	0.217470i
$334$	4.97822	−	15.3214i	0.272396	−	0.838349i
$335$	20.0815	+	14.5901i	1.09717	+	0.797141i
$336$	8.70112	+	6.32173i	0.474685	+	0.344879i
$337$	6.44281	−	19.8289i	0.350962	−	1.08015i	−0.607351	−	0.794433i	$-0.707768\pi$
$337$	6.44281	−	19.8289i	0.350962	−	1.08015i	0.958314	−	0.285718i	$-0.0922320\pi$
$338$	15.3536	+	47.2534i	0.835123	+	2.57025i
$339$	4.27374	−	3.10505i	0.232118	−	0.168643i
$340$	−85.8258			−4.65456
$341$	0.917579	+	5.21901i	0.0496897	+	0.282625i
$342$	0.323795			0.0175088
$343$	0.809017	−	0.587785i	0.0436828	−	0.0317374i
$344$	−12.3706	−	38.0728i	−0.666979	−	2.05275i
$345$	1.59446	−	4.90723i	0.0858426	−	0.264196i
$346$	−14.3911	−	10.4557i	−0.773670	−	0.562104i
$347$	−1.20810	−	0.877737i	−0.0648543	−	0.0471194i	0.554886	−	0.831927i	$-0.312762\pi$
$347$	−1.20810	−	0.877737i	−0.0648543	−	0.0471194i	−0.619740	+	0.784807i	$0.712762\pi$
$348$	13.5906	−	41.8275i	0.728531	−	2.24219i
$349$	−6.63753	−	20.4282i	−0.355299	−	1.09350i	−0.955836	−	0.293901i	$-0.905046\pi$
$349$	−6.63753	−	20.4282i	−0.355299	−	1.09350i	0.600537	−	0.799597i	$-0.294954\pi$
$350$	9.63040	−	6.99690i	0.514767	−	0.374000i
$351$	−5.64097			−0.301093
$352$	18.5062	−	37.8954i	0.986381	−	2.01983i
$353$	11.4760			0.610808			0.305404	−	0.952223i	$-0.401208\pi$
$353$	11.4760			0.610808			0.305404	+	0.952223i	$0.401208\pi$
$354$	−14.1269	+	10.2638i	−0.750834	+	0.545513i
$355$	5.94978	+	18.3115i	0.315782	+	0.971876i
$356$	−12.9843	+	39.9615i	−0.688166	+	2.11796i
$357$	−4.53118	−	3.29210i	−0.239816	−	0.174236i
$358$	−27.7511	−	20.1623i	−1.46669	−	1.06561i
$359$	−1.76906	+	5.44462i	−0.0933676	+	0.287356i	−0.986825	−	0.161792i	$-0.948273\pi$
$359$	−1.76906	+	5.44462i	−0.0933676	+	0.287356i	0.893457	+	0.449148i	$0.148273\pi$
$360$	7.46960	+	22.9891i	0.393683	+	1.21163i
$361$	15.3592	−	11.1591i	0.808376	−	0.587320i
$362$	−10.8190			−0.568632
$363$	6.16018	−	9.11330i	0.323326	−	0.478324i
$364$	28.0316			1.46925
$365$	−8.75671	+	6.36212i	−0.458347	+	0.333009i
$366$	−6.92536	−	21.3141i	−0.361994	−	1.11410i
$367$	5.40752	−	16.6426i	0.282270	−	0.868738i	−0.704933	−	0.709273i	$-0.749023\pi$
$367$	5.40752	−	16.6426i	0.282270	−	0.868738i	0.987204	−	0.159465i	$-0.0509768\pi$
$368$	−14.5591	−	10.5778i	−0.758946	−	0.551406i
$369$	−2.82233	−	2.05054i	−0.146925	−	0.106747i
$370$	10.4969	−	32.3062i	0.545708	−	1.67952i
$371$	3.66384	+	11.2761i	0.190217	+	0.585428i
$372$	−6.42323	+	4.66675i	−0.333029	+	0.241960i
$373$	−9.54362			−0.494150			−0.247075	−	0.968996i	$-0.579469\pi$
$373$	−9.54362			−0.494150			−0.247075	+	0.968996i	$0.579469\pi$
$374$	−21.5193	+	44.0655i	−1.11274	+	2.27857i
$375$	−1.51368			−0.0781662
$376$	10.1086	−	7.34434i	0.521312	−	0.378756i
$377$	−15.4276	−	47.4813i	−0.794562	−	2.44541i
$378$	−0.815786	+	2.51073i	−0.0419595	+	0.129138i
$379$	−25.8566	−	18.7859i	−1.32816	−	0.964967i	−0.999792	−	0.0204186i	$-0.993500\pi$
$379$	−25.8566	−	18.7859i	−1.32816	−	0.964967i	−0.328372	−	0.944549i	$-0.606500\pi$
$380$	−1.52054	−	1.10474i	−0.0780020	−	0.0566718i
$381$	−3.50427	+	10.7850i	−0.179529	+	0.552533i
$382$	17.5423	+	53.9898i	0.897545	+	2.76236i
$383$	7.94646	−	5.77344i	0.406045	−	0.295009i	−0.365954	−	0.930633i	$-0.619257\pi$
$383$	7.94646	−	5.77344i	0.406045	−	0.295009i	0.771999	+	0.635624i	$0.219257\pi$
$384$	6.40120			0.326660
$385$	−1.77097	−	10.0729i	−0.0902571	−	0.513365i
$386$	46.9814			2.39129
$387$	4.13163	−	3.00181i	0.210023	−	0.152590i
$388$	−8.72950	−	26.8666i	−0.443173	−	1.36395i
$389$	10.2593	−	31.5749i	0.520167	−	1.60091i	−0.253513	−	0.967332i	$-0.581586\pi$
$389$	10.2593	−	31.5749i	0.520167	−	1.60091i	0.773680	−	0.633577i	$-0.218414\pi$
$390$	37.1515	+	26.9921i	1.88124	+	1.36680i
$391$	7.58178	+	5.50849i	0.383427	+	0.278576i
$392$	2.42230	−	7.45506i	0.122344	−	0.376537i
$393$	−0.299834	−	0.922795i	−0.0151246	−	0.0465488i
$394$	−38.6748	+	28.0989i	−1.94841	+	1.41560i
$395$	−28.9795			−1.45812
$396$	16.3197	+	2.30185i	0.820096	+	0.115672i
$397$	23.6535			1.18713			0.593566	−	0.804785i	$-0.297719\pi$
$397$	23.6535			1.18713			0.593566	+	0.804785i	$0.297719\pi$
$398$	−5.70543	+	4.14524i	−0.285987	+	0.207782i
$399$	−0.0379017	−	0.116649i	−0.00189746	−	0.00583977i
$400$	14.9862	−	46.1229i	0.749312	−	2.30615i
$401$	−20.4469	−	14.8555i	−1.02107	−	0.741849i	−0.0545658	−	0.998510i	$-0.517377\pi$
$401$	−20.4469	−	14.8555i	−1.02107	−	0.741849i	−0.966501	+	0.256661i	$0.917377\pi$
$402$	17.1918	+	12.4905i	0.857447	+	0.622972i
$403$	−2.78509	+	8.57162i	−0.138735	+	0.426983i
$404$	25.9170	+	79.7644i	1.28942	+	3.96843i
$405$	−2.49476	+	1.81255i	−0.123965	+	0.0900662i
$406$	−23.3645			−1.15956
$407$	−9.95031	−	9.61846i	−0.493219	−	0.476769i
$408$	−43.9035			−2.17355
$409$	−11.3048	+	8.21344i	−0.558988	+	0.406129i	−0.831088	−	0.556140i	$-0.812282\pi$
$409$	−11.3048	+	8.21344i	−0.558988	+	0.406129i	0.272100	+	0.962269i	$0.412282\pi$
$410$	8.77601	+	27.0098i	0.433416	+	1.33392i
$411$	−0.0386582	+	0.118978i	−0.00190687	+	0.00586874i
$412$	53.1361	+	38.6056i	2.61783	+	1.90196i
$413$	5.35120	+	3.88788i	0.263315	+	0.191310i
$414$	1.36501	−	4.20107i	0.0670866	−	0.206471i
$415$	−8.98964	−	27.6673i	−0.441284	−	1.35813i
$416$	58.0293	−	42.1608i	2.84512	−	2.06710i
$417$	−1.67835			−0.0821889
$418$	−0.948453	+	0.503697i	−0.0463904	+	0.0246366i
$419$	29.7445			1.45311			0.726556	−	0.687107i	$-0.241120\pi$
$419$	29.7445			1.45311			0.726556	+	0.687107i	$0.241120\pi$
$420$	12.3971	−	9.00705i	0.604918	−	0.439499i
$421$	11.2073	+	34.4925i	0.546210	+	1.68106i	0.718096	+	0.695944i	$0.245014\pi$
$421$	11.2073	+	34.4925i	0.546210	+	1.68106i	−0.171887	+	0.985117i	$0.554986\pi$
$422$	−6.65230	+	20.4737i	−0.323829	+	0.996643i
$423$	1.28958	+	0.936932i	0.0627014	+	0.0455552i
$424$	75.1894	+	54.6283i	3.65152	+	2.65298i
$425$	−7.80422	+	24.0189i	−0.378560	+	1.16509i
$426$	5.09359	+	15.6765i	0.246785	+	0.759528i
$427$	−6.86789	+	4.98982i	−0.332361	+	0.241474i
$428$	55.0323			2.66009
$429$	16.5234	−	8.77513i	0.797758	−	0.423667i
$430$	−41.5746			−2.00491
$431$	−28.9682	+	21.0466i	−1.39535	+	1.01378i	−0.400093	+	0.916475i	$0.631022\pi$
$431$	−28.9682	+	21.0466i	−1.39535	+	1.01378i	−0.995255	+	0.0973046i	$0.968978\pi$
$432$	3.32353	+	10.2288i	0.159903	+	0.492132i
$433$	−7.13701	+	21.9655i	−0.342983	+	1.05559i	0.619672	+	0.784861i	$0.287266\pi$
$433$	−7.13701	+	21.9655i	−0.342983	+	1.05559i	−0.962655	+	0.270731i	$0.912734\pi$
$434$	3.41235	+	2.47922i	0.163798	+	0.119006i
$435$	−22.0795	−	16.0417i	−1.05863	−	0.769142i
$436$	−7.48400	+	23.0334i	−0.358419	+	1.10310i
$437$	0.0634188	+	0.195183i	0.00303373	+	0.00933687i
$438$	−7.49660	+	5.44660i	−0.358201	+	0.260249i
$439$	24.7837			1.18286			0.591431	−	0.806356i	$-0.298563\pi$
$439$	24.7837			1.18286			0.591431	+	0.806356i	$0.298563\pi$
$440$	−57.6418	−	55.7194i	−2.74796	−	2.65632i
$441$	1.00000			0.0476190
$442$	−67.4776	+	49.0253i	−3.20958	+	2.33190i
$443$	4.10823	+	12.6438i	0.195188	+	0.600727i	0.999974	+	0.00716250i	$0.00227992\pi$
$443$	4.10823	+	12.6438i	0.195188	+	0.600727i	−0.804786	+	0.593565i	$0.797720\pi$
$444$	6.40753	−	19.7203i	0.304088	−	0.935886i
$445$	21.0946	+	15.3261i	0.999978	+	0.726527i
$446$	−18.1275	−	13.1704i	−0.858362	−	0.623636i
$447$	4.38159	−	13.4852i	0.207242	−	0.637826i
$448$	−3.72612	−	11.4678i	−0.176043	−	0.541804i
$449$	−16.8853	+	12.2679i	−0.796866	+	0.578957i	−0.909993	−	0.414623i	$-0.863913\pi$
$449$	−16.8853	+	12.2679i	−0.796866	+	0.578957i	0.113127	+	0.993581i	$0.463913\pi$
$450$	11.9038			0.561152
$451$	11.4569	+	1.61597i	0.539487	+	0.0760932i
$452$	−26.2509			−1.23474
$453$	−12.8491	+	9.33540i	−0.603702	+	0.438615i
$454$	−18.0716	−	55.6188i	−0.848144	−	2.61032i
$455$	5.37535	−	16.5436i	0.252000	−	0.775577i
$456$	−0.777819	−	0.565119i	−0.0364247	−	0.0264641i
$457$	22.8421	+	16.5958i	1.06851	+	0.776317i	0.975644	−	0.219361i	$-0.0703973\pi$
$457$	22.8421	+	16.5958i	1.06851	+	0.776317i	0.0928655	+	0.995679i	$0.470397\pi$
$458$	−7.32587	+	22.5467i	−0.342316	+	1.05354i
$459$	−1.73076	−	5.32673i	−0.0807849	−	0.248630i
$460$	−20.7435	+	15.0710i	−0.967169	+	0.702689i
$461$	−13.5432			−0.630770			−0.315385	−	0.948964i	$-0.602134\pi$
$461$	−13.5432			−0.630770			−0.315385	+	0.948964i	$0.602134\pi$
$462$	−1.51613	−	8.62342i	−0.0705365	−	0.401198i
$463$	−33.9584			−1.57818			−0.789090	−	0.614277i	$-0.789448\pi$
$463$	−33.9584			−1.57818			−0.789090	+	0.614277i	$0.789448\pi$
$464$	−77.0082	+	55.9497i	−3.57502	+	2.59740i
$465$	1.52249	+	4.68575i	0.0706039	+	0.217296i
$466$	16.2267	−	49.9406i	0.751687	−	2.31346i
$467$	−10.1781	−	7.39484i	−0.470987	−	0.342192i	0.326839	−	0.945080i	$-0.394017\pi$
$467$	−10.1781	−	7.39484i	−0.470987	−	0.342192i	−0.797826	+	0.602888i	$0.794017\pi$
$468$	22.6780	+	16.4765i	1.04829	+	0.761628i
$469$	2.48743	−	7.65552i	0.114859	−	0.353499i
$470$	−4.00992	−	12.3413i	−0.184964	−	0.569261i
$471$	7.44178	−	5.40677i	0.342899	−	0.249131i
$472$	51.8488			2.38653
$473$	−7.43266	+	15.2200i	−0.341754	+	0.699817i
$474$	−24.8093			−1.13953
$475$	−0.447432	+	0.325078i	−0.0205296	+	0.0149156i
$476$	8.60062	+	26.4700i	0.394209	+	1.21325i
$477$	−3.66384	+	11.2761i	−0.167756	+	0.516299i
$478$	19.6912	+	14.3065i	0.900653	+	0.654362i
$479$	−23.3738	−	16.9821i	−1.06798	−	0.775931i	−0.0924293	−	0.995719i	$-0.529463\pi$
$479$	−23.3738	−	16.9821i	−1.06798	−	0.775931i	−0.975548	+	0.219789i	$0.929463\pi$
$480$	12.1168	−	37.2917i	0.553055	−	1.70213i
$481$	−7.27363	−	22.3859i	−0.331649	−	1.02071i
$482$	1.71484	−	1.24590i	0.0781088	−	0.0567494i
$483$	−1.67325			−0.0761353
$484$	−51.3841	+	18.6445i	−2.33564	+	0.847476i
$485$	−17.5301			−0.796001
$486$	−2.13576	+	1.55172i	−0.0968798	+	0.0703873i
$487$	7.88232	+	24.2593i	0.357182	+	1.09929i	0.954734	+	0.297462i	$0.0961403\pi$
$487$	7.88232	+	24.2593i	0.357182	+	1.09929i	−0.597552	+	0.801830i	$0.703860\pi$
$488$	−20.5633	+	63.2874i	−0.930857	+	2.86488i
$489$	−7.90363	−	5.74232i	−0.357414	−	0.259677i
$490$	−6.58600	−	4.78501i	−0.297525	−	0.216165i
$491$	1.44187	−	4.43761i	0.0650705	−	0.200266i	−0.913235	−	0.407433i	$-0.866424\pi$
$491$	1.44187	−	4.43761i	0.0650705	−	0.200266i	0.978306	+	0.207166i	$0.0664241\pi$
$492$	5.35705	+	16.4873i	0.241515	+	0.743305i
$493$	40.1027	−	29.1363i	1.80613	−	1.31223i
$494$	−1.82652			−0.0821789
$495$	4.48798	−	9.19013i	0.201720	−	0.413066i
$496$	17.1838			0.771576
$497$	5.05133	−	3.67001i	0.226583	−	0.164622i
$498$	−7.69601	−	23.6859i	−0.344867	−	1.06139i
$499$	−5.71553	+	17.5906i	−0.255862	+	0.787463i	0.737796	+	0.675023i	$0.235866\pi$
$499$	−5.71553	+	17.5906i	−0.255862	+	0.787463i	−0.993659	+	0.112440i	$0.964134\pi$
$500$	6.08535	+	4.42127i	0.272145	+	0.197725i
$501$	−4.93691	−	3.58688i	−0.220565	−	0.160250i
$502$	0.374672	−	1.15312i	0.0167224	−	0.0514663i
$503$	−7.14065	−	21.9767i	−0.318386	−	0.979891i	−0.974338	−	0.225089i	$-0.927733\pi$
$503$	−7.14065	−	21.9767i	−0.318386	−	0.979891i	0.655952	−	0.754802i	$-0.272267\pi$
$504$	6.34165	−	4.60748i	0.282480	−	0.205233i
$505$	52.0451			2.31598
$506$	2.53685	+	14.4291i	0.112777	+	0.641452i
$507$	18.8206			0.835851
$508$	45.5896	−	33.1228i	2.02271	−	1.46959i
$509$	−8.85461	−	27.2517i	−0.392474	−	1.20791i	−0.930912	−	0.365245i	$-0.880985\pi$
$509$	−8.85461	−	27.2517i	−0.392474	−	1.20791i	0.538438	−	0.842665i	$-0.319015\pi$
$510$	−14.0897	+	43.3635i	−0.623901	+	1.92017i
$511$	2.83969	+	2.06315i	0.125620	+	0.0912685i
$512$	25.7715	+	18.7241i	1.13895	+	0.827495i
$513$	0.0379017	−	0.116649i	0.00167340	−	0.00515020i
$514$	−19.0546	−	58.6441i	−0.840463	−	2.58668i
$515$	32.9736	−	23.9567i	1.45299	−	1.05566i
$516$	−25.3780			−1.11720
$517$	−5.23490	−	0.738369i	−0.230231	−	0.0324734i
$518$	−11.0156			−0.483998
$519$	−5.45130	+	3.96060i	−0.239285	+	0.173851i
$520$	−42.1358	−	129.681i	−1.84778	−	5.68688i
$521$	−2.46972	+	7.60103i	−0.108201	+	0.333007i	−0.990468	−	0.137741i	$-0.956016\pi$
$521$	−2.46972	+	7.60103i	−0.108201	+	0.333007i	0.882268	+	0.470748i	$0.156016\pi$
$522$	−18.9022	−	13.7333i	−0.827329	−	0.601090i
$523$	−30.1277	−	21.8891i	−1.31739	−	0.957143i	−0.999961	−	0.00886223i	$-0.997179\pi$
$523$	−30.1277	−	21.8891i	−1.31739	−	0.957143i	−0.317433	−	0.948281i	$-0.602821\pi$
$524$	−1.48996	+	4.58562i	−0.0650892	+	0.200324i
$525$	−1.39340	−	4.28844i	−0.0608129	−	0.187163i
$526$	10.5970	−	7.69914i	0.462049	−	0.335699i
$527$	−8.94863			−0.389808
$528$	−25.6472	−	24.7918i	−1.11615	−	1.07893i
$529$	−20.2002			−0.878272
$530$	78.0865	−	56.7332i	3.39186	−	2.46433i
$531$	2.04398	+	6.29072i	0.0887011	+	0.272994i
$532$	−0.188344	+	0.579663i	−0.00816575	+	0.0251316i
$533$	15.9207	+	11.5671i	0.689601	+	0.501025i
$534$	18.0590	+	13.1206i	0.781490	+	0.567786i
$535$	10.5530	−	32.4789i	0.456247	−	1.40418i
$536$	−19.4983	−	60.0095i	−0.842196	−	2.59201i
$537$	−10.5120	+	7.63742i	−0.453627	+	0.329579i
$538$	2.72449			0.117461
$539$	−2.92918	+	1.55561i	−0.126169	+	0.0670047i
$540$	15.3237			0.659427
$541$	18.5985	−	13.5126i	0.799613	−	0.580953i	−0.111187	−	0.993799i	$-0.535465\pi$
$541$	18.5985	−	13.5126i	0.799613	−	0.580953i	0.910801	+	0.412846i	$0.135465\pi$
$542$	12.3532	+	38.0193i	0.530617	+	1.63307i
$543$	−1.26641	+	3.89761i	−0.0543469	+	0.167262i
$544$	57.6166	+	41.8609i	2.47029	+	1.79477i
$545$	12.1587	+	8.83379i	0.520820	+	0.378398i
$546$	4.60183	−	14.1630i	0.196940	−	0.606119i
$547$	9.40294	+	28.9393i	0.402041	+	1.23735i	0.923341	+	0.383981i	$0.125447\pi$
$547$	9.40294	+	28.9393i	0.402041	+	1.23735i	−0.521301	+	0.853373i	$0.674553\pi$
$548$	0.502933	−	0.365402i	0.0214842	−	0.0156092i
$549$	−8.48918			−0.362309
$550$	−34.8685	+	18.5177i	−1.48680	+	0.789596i
$551$	1.08552			0.0462447
$552$	−10.6111	+	7.70945i	−0.451640	+	0.328136i
$553$	2.90405	+	8.93773i	0.123493	+	0.380071i
$554$	−0.872902	+	2.68652i	−0.0370861	+	0.114139i
$555$	−10.4098	−	7.56317i	−0.441872	−	0.321039i
$556$	6.74734	+	4.90223i	0.286151	+	0.207901i
$557$	−13.1274	+	40.4020i	−0.556226	+	1.71189i	0.136459	+	0.990646i	$0.456428\pi$
$557$	−13.1274	+	40.4020i	−0.556226	+	1.71189i	−0.692684	+	0.721241i	$0.743572\pi$
$558$	1.30340	+	4.01146i	0.0551774	+	0.169819i
$559$	−23.3064	+	16.9331i	−0.985756	+	0.716194i
$560$	−33.1656			−1.40150
$561$	13.3560	+	12.9106i	0.563890	+	0.545084i
$562$	−82.6538			−3.48654
$563$	−9.78569	+	7.10972i	−0.412418	+	0.299639i	−0.774580	−	0.632476i	$-0.782039\pi$
$563$	−9.78569	+	7.10972i	−0.412418	+	0.299639i	0.362162	+	0.932115i	$0.382039\pi$
$564$	−2.44774	−	7.53337i	−0.103068	−	0.317212i
$565$	−5.03388	+	15.4927i	−0.211777	+	0.651783i
$566$	−68.2696	−	49.6007i	−2.86958	−	2.08487i
$567$	0.809017	+	0.587785i	0.0339755	+	0.0246847i
$568$	15.1243	−	46.5478i	0.634602	−	1.95310i
$569$	−10.5082	−	32.3410i	−0.440528	−	1.35581i	−0.887314	−	0.461165i	$-0.847432\pi$
$569$	−10.5082	−	32.3410i	−0.440528	−	1.35581i	0.446786	−	0.894641i	$-0.352568\pi$
$570$	−0.807789	+	0.586893i	−0.0338346	+	0.0245823i
$571$	16.0762			0.672767			0.336383	−	0.941725i	$-0.390796\pi$
$571$	16.0762			0.672767			0.336383	+	0.941725i	$0.390796\pi$
$572$	−92.0589	−	12.9847i	−3.84918	−	0.542917i
$573$	21.5036			0.898326
$574$	7.45078	−	5.41331i	0.310990	−	0.225947i
$575$	2.33150	+	7.17561i	0.0972302	+	0.299244i
$576$	3.72612	−	11.4678i	0.155255	−	0.477826i
$577$	−3.18808	−	2.31628i	−0.132722	−	0.0964278i	0.519444	−	0.854505i	$-0.326139\pi$
$577$	−3.18808	−	2.31628i	−0.132722	−	0.0964278i	−0.652165	+	0.758077i	$0.726139\pi$
$578$	−30.6898	−	22.2974i	−1.27653	−	0.927451i
$579$	5.49938	−	16.9254i	0.228547	−	0.703394i
$580$	41.9091	+	128.983i	1.74018	+	5.35572i
$581$	−7.63216	+	5.54509i	−0.316635	+	0.230049i
$582$	−15.0075			−0.622080
$583$	−6.80919	−	38.7293i	−0.282008	−	1.60400i
$584$	27.5142			1.13855
$585$	14.0728	−	10.2245i	0.581841	−	0.422732i
$586$	−0.385836	−	1.18748i	−0.0159388	−	0.0490544i
$587$	3.06798	−	9.44228i	0.126629	−	0.389725i	−0.867565	−	0.497324i	$-0.834316\pi$
$587$	3.06798	−	9.44228i	0.126629	−	0.389725i	0.994194	+	0.107599i	$0.0343162\pi$
$588$	−4.02023	−	2.92087i	−0.165792	−	0.120455i
$589$	−0.158539	−	0.115185i	−0.00653249	−	0.00474613i
$590$	16.6395	−	51.2111i	0.685038	−	2.10833i
$591$	5.59576	+	17.2220i	0.230179	+	0.708417i
$592$	−36.3069	+	26.3785i	−1.49221	+	1.08415i
$593$	1.35512			0.0556480			0.0278240	−	0.999613i	$-0.491142\pi$
$593$	1.35512			0.0556480			0.0278240	+	0.999613i	$0.491142\pi$
$594$	3.84215	−	7.86765i	0.157645	−	0.322814i
$595$	17.2713			0.708053
$596$	−57.0034	+	41.4154i	−2.33495	+	1.69644i
$597$	0.825504	+	2.54064i	0.0337856	+	0.103981i
$598$	−7.69999	+	23.6981i	−0.314876	+	0.969088i
$599$	24.8920	+	18.0851i	1.01706	+	0.738938i	0.965678	−	0.259742i	$-0.0836374\pi$
$599$	24.8920	+	18.0851i	1.01706	+	0.738938i	0.0513821	+	0.998679i	$0.483637\pi$
$600$	−28.5954	−	20.7757i	−1.16740	−	0.848166i
$601$	−4.08413	+	12.5697i	−0.166595	+	0.512727i	−0.999150	−	0.0412149i	$-0.986877\pi$
$601$	−4.08413	+	12.5697i	−0.166595	+	0.512727i	0.832555	+	0.553942i	$0.186877\pi$
$602$	4.16620	+	12.8222i	0.169802	+	0.522596i
$603$	6.51218	−	4.73137i	0.265196	−	0.192676i
$604$	78.9237			3.21136
$605$	1.15013	+	33.9011i	0.0467593	+	1.37827i
$606$	44.5557			1.80995
$607$	4.71906	−	3.42860i	0.191541	−	0.139162i	−0.487882	−	0.872910i	$-0.662230\pi$
$607$	4.71906	−	3.42860i	0.191541	−	0.139162i	0.679423	+	0.733747i	$0.262230\pi$
$608$	0.481941	+	1.48326i	0.0195453	+	0.0601543i
$609$	−2.73492	+	8.41721i	−0.110824	+	0.341083i
$610$	55.9098	+	40.6208i	2.26372	+	1.64469i
$611$	−7.27446	−	5.28521i	−0.294293	−	0.213817i
$612$	−8.60062	+	26.4700i	−0.347659	+	1.06999i
$613$	2.06340	+	6.35050i	0.0833400	+	0.256494i	0.984040	−	0.177947i	$-0.0569457\pi$
$613$	2.06340	+	6.35050i	0.0833400	+	0.256494i	−0.900700	+	0.434442i	$0.856946\pi$
$614$	47.7388	−	34.6843i	1.92658	−	1.39974i
$615$	10.7577			0.433794
$616$	−11.4084	+	23.3612i	−0.459658	+	0.941252i
$617$	15.1716			0.610785			0.305392	−	0.952227i	$-0.401212\pi$
$617$	15.1716			0.610785			0.305392	+	0.952227i	$0.401212\pi$
$618$	28.2286	−	20.5093i	1.13552	−	0.825005i
$619$	8.64944	+	26.6202i	0.347650	+	1.06996i	0.960150	+	0.279487i	$0.0901642\pi$
$619$	8.64944	+	26.6202i	0.347650	+	1.06996i	−0.612499	+	0.790471i	$0.709836\pi$
$620$	7.56569	−	23.2848i	0.303845	−	0.935140i
$621$	−1.35368	−	0.983509i	−0.0543215	−	0.0394669i
$622$	−46.9520	−	34.1126i	−1.88260	−	1.36779i
$623$	2.61291	−	8.04172i	0.104684	−	0.322185i
$624$	−18.7479	−	57.7002i	−0.750518	−	2.30986i
$625$	22.0161	−	15.9956i	0.880644	−	0.639825i
$626$	−20.9882			−0.838858
$627$	0.0704397	+	0.400647i	0.00281309	+	0.0160003i
$628$	−45.7101			−1.82403
$629$	18.9072	−	13.7369i	0.753878	−	0.547724i
$630$	−2.51563	−	7.74231i	−0.100225	−	0.308461i
$631$	−1.72442	+	5.30723i	−0.0686482	+	0.211277i	−0.979495	−	0.201466i	$-0.935429\pi$
$631$	−1.72442	+	5.30723i	−0.0686482	+	0.211277i	0.910847	+	0.412743i	$0.135429\pi$
$632$	59.5969	+	43.2997i	2.37064	+	1.72237i
$633$	6.59710	+	4.79308i	0.262211	+	0.190508i
$634$	−12.3369	+	37.9690i	−0.489960	+	1.50794i
$635$	−10.8061	−	33.2576i	−0.428826	−	1.31979i
$636$	47.6656	−	34.6311i	1.89006	−	1.37321i
$637$	−5.64097			−0.223503
$638$	76.7317	+	10.8228i	3.03784	+	0.428479i
$639$	6.24379			0.247000
$640$	−15.9694	+	11.6025i	−0.631248	+	0.458628i
$641$	3.38889	+	10.4299i	0.133853	+	0.411958i	0.995410	−	0.0957036i	$-0.0305101\pi$
$641$	3.38889	+	10.4299i	0.133853	+	0.411958i	−0.861557	+	0.507661i	$0.830510\pi$
$642$	9.03443	−	27.8051i	0.356560	−	1.09738i
$643$	−0.322913	−	0.234610i	−0.0127344	−	0.00925212i	0.581400	−	0.813618i	$-0.302505\pi$
$643$	−0.322913	−	0.234610i	−0.0127344	−	0.00925212i	−0.594134	+	0.804366i	$0.702505\pi$
$644$	6.72683	+	4.88733i	0.265074	+	0.192588i
$645$	−4.86650	+	14.9775i	−0.191618	+	0.589740i
$646$	−0.560411	−	1.72477i	−0.0220491	−	0.0678600i
$647$	−25.3186	+	18.3951i	−0.995378	+	0.723185i	−0.961092	−	0.276227i	$-0.910916\pi$
$647$	−25.3186	+	18.3951i	−0.995378	+	0.723185i	−0.0342860	+	0.999412i	$0.510916\pi$
$648$	7.83871			0.307934
$649$	−15.7731	−	15.2470i	−0.619146	−	0.598498i
$650$	−67.1492			−2.63381
$651$	1.29259	−	0.939120i	0.0506605	−	0.0368070i
$652$	15.0018	+	46.1709i	0.587518	+	1.80819i
$653$	−8.08970	+	24.8975i	−0.316574	+	0.974316i	0.658527	+	0.752557i	$0.271180\pi$
$653$	−8.08970	+	24.8975i	−0.316574	+	0.974316i	−0.975102	+	0.221759i	$0.928820\pi$
$654$	10.4090	+	7.56259i	0.407025	+	0.295721i
$655$	2.42062	+	1.75868i	0.0945815	+	0.0687175i
$656$	11.5944	−	35.6840i	0.452687	−	1.39323i
$657$	1.08466	+	3.33825i	0.0423168	+	0.130238i
$658$	−3.40440	+	2.47344i	−0.132717	+	0.0964249i
$659$	−5.84482			−0.227682			−0.113841	−	0.993499i	$-0.536315\pi$
$659$	−5.84482			−0.227682			−0.113841	+	0.993499i	$0.536315\pi$
$660$	−44.8859	+	23.8376i	−1.74718	+	0.927879i
$661$	−6.32811			−0.246135			−0.123067	−	0.992398i	$-0.539273\pi$
$661$	−6.32811			−0.246135			−0.123067	+	0.992398i	$0.539273\pi$
$662$	12.8688	−	9.34975i	0.500161	−	0.363388i
$663$	9.76316	+	30.0479i	0.379170	+	1.16696i
$664$	−22.8516	+	70.3300i	−0.886814	+	2.72933i
$665$	0.305988	+	0.222313i	0.0118657	+	0.00862094i
$666$	−8.91182	−	6.47481i	−0.345326	−	0.250894i
$667$	4.57619	−	14.0841i	0.177191	−	0.545337i
$668$	9.37073	+	28.8401i	0.362565	+	1.11586i
$669$	−6.86663	+	4.98890i	−0.265479	+	0.192882i
$670$	−65.5289			−2.53160
$671$	24.8663	−	13.2058i	0.959954	−	0.509805i
$672$	−12.7156			−0.490514
$673$	−3.41334	+	2.47994i	−0.131575	+	0.0955946i	−0.651626	−	0.758540i	$-0.725913\pi$
$673$	−3.41334	+	2.47994i	−0.131575	+	0.0955946i	0.520051	+	0.854135i	$0.325913\pi$
$674$	17.0086	+	52.3472i	0.655148	+	2.01634i
$675$	1.39340	−	4.28844i	0.0536319	−	0.165062i
$676$	−75.6630	−	54.9724i	−2.91012	−	2.11432i
$677$	−14.5014	−	10.5359i	−0.557333	−	0.404926i	0.273149	−	0.961972i	$-0.411935\pi$
$677$	−14.5014	−	10.5359i	−0.557333	−	0.404926i	−0.830482	+	0.557045i	$0.811935\pi$
$678$	−4.30950	+	13.2633i	−0.165505	+	0.509373i
$679$	1.75669	+	5.40655i	0.0674157	+	0.207484i
$680$	109.528	−	79.5771i	4.20022	−	3.05164i
$681$	−22.1524			−0.848883
$682$	−10.0582	−	9.72271i	−0.385147	−	0.372302i
$683$	−5.96513			−0.228249			−0.114125	−	0.993466i	$-0.536406\pi$
$683$	−5.96513			−0.228249			−0.114125	+	0.993466i	$0.536406\pi$
$684$	−0.493091	+	0.358252i	−0.0188538	+	0.0136981i
$685$	−0.119210	−	0.366890i	−0.00455477	−	0.0140182i
$686$	−0.815786	+	2.51073i	−0.0311469	+	0.0958602i
$687$	7.26508	+	5.27839i	0.277180	+	0.201383i
$688$	44.4364	+	32.2849i	1.69412	+	1.23085i
$689$	20.6676	−	63.6084i	0.787373	−	2.42329i
$690$	4.20927	+	12.9548i	0.160244	+	0.493180i
$691$	31.8821	−	23.1637i	1.21285	−	0.881188i	0.217365	−	0.976090i	$-0.430254\pi$
$691$	31.8821	−	23.1637i	1.21285	−	0.881188i	0.995487	+	0.0949021i	$0.0302538\pi$
$692$	33.4839			1.27287
$693$	−3.28412	−	0.463217i	−0.124753	−	0.0175961i
$694$	3.94221			0.149644
$695$	4.18706	−	3.04208i	0.158824	−	0.115393i
$696$	21.4382	+	65.9801i	0.812614	+	2.50097i
$697$	−6.03791	+	18.5828i	−0.228702	+	0.703873i
$698$	45.8750	+	33.3301i	1.73639	+	1.26156i
$699$	−16.0921	−	11.6916i	−0.608657	−	0.442215i
$700$	−6.92419	+	21.3105i	−0.261710	+	0.805459i
$701$	−7.85780	−	24.1838i	−0.296785	−	0.913410i	−0.982616	−	0.185650i	$-0.940561\pi$
$701$	−7.85780	−	24.1838i	−0.296785	−	0.913410i	0.685831	−	0.727761i	$-0.259439\pi$
$702$	12.0477	−	8.75319i	0.454713	−	0.330368i
$703$	0.511789			0.0193025
$704$	6.92494	+	39.3877i	0.260993	+	1.48448i
$705$	−4.91541			−0.185125
$706$	−24.5100	+	17.8076i	−0.922447	+	0.670197i
$707$	−5.21545	−	16.0515i	−0.196147	−	0.603679i
$708$	10.1571	−	31.2603i	0.381727	−	1.17483i
$709$	−5.72839	−	4.16192i	−0.215134	−	0.156304i	0.474999	−	0.879986i	$-0.342448\pi$
$709$	−5.72839	−	4.16192i	−0.215134	−	0.156304i	−0.690134	+	0.723682i	$0.742448\pi$
$710$	−41.1216	−	29.8766i	−1.54327	−	1.12125i
$711$	−2.90405	+	8.93773i	−0.108910	+	0.335191i
$712$	−20.4819	−	63.0367i	−0.767590	−	2.36240i
$713$	−2.16282	+	1.57138i	−0.0809981	+	0.0588486i
$714$	14.7859			0.553349
$715$	−25.3166	+	51.8413i	−0.946786	+	1.93875i
$716$	64.5686			2.41304
$717$	7.45894	−	5.41924i	0.278559	−	0.202385i
$718$	−4.67022	−	14.3735i	−0.174291	−	0.536413i
$719$	−6.66894	+	20.5249i	−0.248709	+	0.765449i	0.746295	+	0.665616i	$0.231831\pi$
$719$	−6.66894	+	20.5249i	−0.248709	+	0.765449i	−0.995004	+	0.0998332i	$0.968169\pi$
$720$	−26.8315	−	19.4942i	−0.999952	−	0.726508i
$721$	−10.6929	−	7.76886i	−0.398225	−	0.289327i
$722$	−15.4877	+	47.6661i	−0.576391	+	1.77395i
$723$	−0.248116	−	0.763622i	−0.00922752	−	0.0283994i
$724$	16.4757	−	11.9703i	0.612313	−	0.444872i
$725$	39.9075			1.48213
$726$	0.984621	+	29.0226i	0.0365427	+	1.07713i
$727$	35.7114			1.32446			0.662231	−	0.749300i	$-0.269610\pi$
$727$	35.7114			1.32446			0.662231	+	0.749300i	$0.269610\pi$
$728$	−35.7731	+	25.9907i	−1.32584	+	0.963278i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	8.82998	−	27.1759i	0.326812	−	1.00582i
$731$	−23.1406	−	16.8127i	−0.855888	−	0.621839i
$732$	34.1285	+	24.7958i	1.26142	+	0.916479i
$733$	1.96072	−	6.03446i	0.0724207	−	0.222888i	−0.908294	−	0.418332i	$-0.862615\pi$
$733$	1.96072	−	6.03446i	0.0724207	−	0.222888i	0.980715	+	0.195444i	$0.0626148\pi$
$734$	14.2755	+	43.9355i	0.526919	+	1.62169i
$735$	−2.49476	+	1.81255i	−0.0920205	+	0.0668568i
$736$	21.2763			0.784254
$737$	−11.7152	+	23.9894i	−0.431534	+	0.883662i
$738$	9.20967			0.339013
$739$	−8.88336	+	6.45414i	−0.326780	+	0.237419i	−0.739063	−	0.673636i	$-0.764731\pi$
$739$	−8.88336	+	6.45414i	−0.326780	+	0.237419i	0.412283	+	0.911056i	$0.364731\pi$
$740$	19.7588	+	60.8114i	0.726348	+	2.23547i
$741$	−0.213802	+	0.658016i	−0.00785422	+	0.0241728i
$742$	−25.3224	−	18.3978i	−0.929616	−	0.675406i
$743$	14.9009	+	10.8262i	0.546662	+	0.397173i	0.826553	−	0.562859i	$-0.190298\pi$
$743$	14.9009	+	10.8262i	0.546662	+	0.397173i	−0.279891	+	0.960032i	$0.590298\pi$
$744$	3.87017	−	11.9111i	0.141887	−	0.436684i
$745$	13.5115	+	41.5840i	0.495022	+	1.52352i
$746$	20.3828	−	14.8090i	0.746268	−	0.542196i
$747$	−9.43386			−0.345167
$748$	−15.9841	−	90.9145i	−0.584437	−	3.32416i
$749$	−11.0745			−0.404654
$750$	3.23286	−	2.34881i	0.118047	−	0.0857663i
$751$	1.53447	+	4.72263i	0.0559938	+	0.172331i	0.975142	−	0.221581i	$-0.0711216\pi$
$751$	1.53447	+	4.72263i	0.0559938	+	0.172331i	−0.919148	+	0.393912i	$0.871122\pi$
$752$	−5.29772	+	16.3047i	−0.193188	+	0.594572i
$753$	−0.371563	−	0.269956i	−0.0135405	−	0.00983775i
$754$	106.627	+	77.4691i	3.88313	+	2.82126i
$755$	15.1345	−	46.5791i	0.550799	−	1.69519i
$756$	−1.53559	−	4.72606i	−0.0558489	−	0.171885i
$757$	0.842244	−	0.611926i	0.0306119	−	0.0222408i	−0.572374	−	0.819993i	$-0.693977\pi$
$757$	0.842244	−	0.611926i	0.0306119	−	0.0222408i	0.602986	+	0.797752i	$0.293977\pi$
$758$	84.3737			3.06459
$759$	5.49514	+	0.775075i	0.199461	+	0.0281334i
$760$	2.96477			0.107544
$761$	34.0015	−	24.7035i	1.23255	−	0.895502i	0.235474	−	0.971881i	$-0.424336\pi$
$761$	34.0015	−	24.7035i	1.23255	−	0.895502i	0.997079	+	0.0763782i	$0.0243356\pi$
$762$	−9.25105	−	28.4718i	−0.335130	−	1.03142i
$763$	1.50605	−	4.63516i	0.0545228	−	0.167804i
$764$	−86.4495	−	62.8092i	−3.12763	−	2.27236i
$765$	13.9728	+	10.1518i	0.505186	+	0.367039i
$766$	−8.01295	+	24.6613i	−0.289520	+	0.891050i
$767$	−11.5300	−	35.4858i	−0.416325	−	1.28132i
$768$	5.83882	−	4.24215i	0.210690	−	0.153075i
$769$	44.1300			1.59137			0.795684	−	0.605712i	$-0.207112\pi$
$769$	44.1300			1.59137			0.795684	+	0.605712i	$0.207112\pi$
$770$	19.4127	+	18.7653i	0.699586	+	0.676254i
$771$	−23.3574			−0.841195
$772$	−71.5455	+	51.9809i	−2.57498	+	1.87083i
$773$	−11.5272	−	35.4770i	−0.414603	−	1.27602i	−0.912605	−	0.408842i	$-0.865933\pi$
$773$	−11.5272	−	35.4770i	−0.414603	−	1.27602i	0.498002	−	0.867176i	$-0.334067\pi$
$774$	−4.16620	+	12.8222i	−0.149751	+	0.460886i
$775$	−5.82845	−	4.23462i	−0.209364	−	0.152112i
$776$	36.0509	+	26.1925i	1.29415	+	0.940257i
$777$	−1.28943	+	3.96845i	−0.0462580	+	0.142367i
$778$	27.0839	+	83.3557i	0.971005	+	2.98845i
$779$	−0.346166	+	0.251504i	−0.0124027	+	0.00901107i
$780$	−86.4406			−3.09507
$781$	−18.2892	+	9.71287i	−0.654438	+	0.347554i
$782$	−24.7404			−0.884717
$783$	−7.16011	+	5.20212i	−0.255881	+	0.185909i
$784$	3.32353	+	10.2288i	0.118698	+	0.365313i
$785$	−8.76540	+	26.9771i	−0.312851	+	0.962855i
$786$	2.07229	+	1.50561i	0.0739161	+	0.0537032i
$787$	−5.95282	−	4.32498i	−0.212195	−	0.154169i	0.476611	−	0.879114i	$-0.341865\pi$
$787$	−5.95282	−	4.32498i	−0.212195	−	0.154169i	−0.688806	+	0.724945i	$0.741865\pi$
$788$	27.8069	−	85.5808i	0.990579	−	3.04869i
$789$	−1.53325	−	4.71885i	−0.0545850	−	0.167995i
$790$	61.8932	−	44.9681i	2.20206	−	1.59989i
$791$	5.28263			0.187829
$792$	−22.9610	+	12.1940i	−0.815884	+	0.433293i
$793$	47.8872			1.70053
$794$	−50.5180	+	36.7035i	−1.79282	+	1.30256i
$795$	−11.2981	−	34.7721i	−0.400704	−	1.23324i
$796$	4.10216	−	12.6251i	0.145397	−	0.447486i
$797$	−4.85553	−	3.52775i	−0.171992	−	0.124959i	0.498459	−	0.866913i	$-0.333899\pi$
$797$	−4.85553	−	3.52775i	−0.171992	−	0.124959i	−0.670451	+	0.741954i	$0.733899\pi$
$798$	0.261956	+	0.190322i	0.00927313	+	0.00673732i
$799$	2.75884	−	8.49082i	0.0976006	−	0.300384i
$800$	17.7179	+	54.5299i	0.626421	+	1.92792i
$801$	6.84069	−	4.97005i	0.241704	−	0.175608i
$802$	66.7210			2.35600
$803$	−8.37018	−	8.09103i	−0.295377	−	0.285526i
$804$	−40.0002			−1.41070
$805$	4.17434	−	3.03284i	0.147126	−	0.106893i
$806$	−7.35246	−	22.6285i	−0.258979	−	0.797056i
$807$	0.318914	−	0.981518i	0.0112263	−	0.0345511i
$808$	−107.032	−	77.7630i	−3.76536	−	2.73569i
$809$	22.9712	+	16.6895i	0.807624	+	0.586773i	0.913141	−	0.407645i	$-0.133650\pi$
$809$	22.9712	+	16.6895i	0.807624	+	0.586773i	−0.105517	+	0.994418i	$0.533650\pi$
$810$	2.51563	−	7.74231i	0.0883902	−	0.272037i
$811$	9.85967	+	30.3450i	0.346220	+	1.06556i	0.960927	+	0.276800i	$0.0892741\pi$
$811$	9.85967	+	30.3450i	0.346220	+	1.06556i	−0.614707	+	0.788755i	$0.710726\pi$
$812$	35.5806	−	25.8508i	1.24863	−	0.907185i
$813$	15.1427			0.531079
$814$	36.1766	+	5.10261i	1.26799	+	0.178847i
$815$	30.1259			1.05526
$816$	48.7336	−	35.4071i	1.70602	−	1.23950i
$817$	−0.193563	−	0.595726i	−0.00677191	−	0.0208418i
$818$	11.3994	−	35.0838i	0.398571	−	1.22668i
$819$	−4.56364	−	3.31568i	−0.159467	−	0.115859i
$820$	−43.2486	−	31.4219i	−1.51031	−	1.09730i
$821$	−1.40894	+	4.33626i	−0.0491722	+	0.151337i	−0.972628	−	0.232369i	$-0.925352\pi$
$821$	−1.40894	+	4.33626i	−0.0491722	+	0.151337i	0.923455	+	0.383706i	$0.125352\pi$
$822$	−0.102055	−	0.314094i	−0.00355959	−	0.0109553i
$823$	−37.6947	+	27.3868i	−1.31396	+	0.954644i	−0.313969	+	0.949433i	$0.601659\pi$
$823$	−37.6947	+	27.3868i	−1.31396	+	0.954644i	−0.999986	+	0.00521085i	$0.998341\pi$
$824$	−103.606			−3.60927
$825$	2.58961	+	14.7292i	0.0901586	+	0.512804i
$826$	−17.4617			−0.607572
$827$	0.811006	−	0.589230i	0.0282014	−	0.0204895i	−0.573595	−	0.819139i	$-0.694452\pi$
$827$	0.811006	−	0.589230i	0.0282014	−	0.0204895i	0.601797	+	0.798649i	$0.294452\pi$
$828$	2.56942	+	7.90787i	0.0892936	+	0.274817i
$829$	−15.6006	+	48.0136i	−0.541830	+	1.66758i	0.186580	+	0.982440i	$0.440260\pi$
$829$	−15.6006	+	48.0136i	−0.541830	+	1.66758i	−0.728410	+	0.685141i	$0.759740\pi$
$830$	62.1315	+	45.1411i	2.15661	+	1.56687i
$831$	0.865659	+	0.628938i	0.0300294	+	0.0218176i
$832$	−21.0189	+	64.6897i	−0.728701	+	2.24271i
$833$	−1.73076	−	5.32673i	−0.0599672	−	0.184560i
$834$	3.58454	−	2.60432i	0.124122	−	0.0901801i
$835$	18.8178			0.651216
$836$	0.887054	−	1.81644i	0.0306794	−	0.0628228i
$837$	1.59773			0.0552255
$838$	−63.5269	+	46.1550i	−2.19450	+	1.59440i
$839$	−8.05341	−	24.7858i	−0.278035	−	0.855703i	−0.988400	−	0.151870i	$-0.951471\pi$
$839$	−8.05341	−	24.7858i	−0.278035	−	0.855703i	0.710366	−	0.703833i	$-0.248529\pi$
$840$	−7.46960	+	22.9891i	−0.257726	+	0.793199i
$841$	−39.9082	−	28.9950i	−1.37614	−	0.999827i
$842$	−77.4586	−	56.2770i	−2.66940	−	1.93943i
$843$	−9.67500	+	29.7766i	−0.333225	+	1.02556i
$844$	−12.5219	−	38.5385i	−0.431023	−	1.32655i
$845$	−46.9527	+	34.1131i	−1.61522	+	1.17353i
$846$	−4.20807			−0.144677
$847$	10.3404	−	3.75195i	0.355299	−	0.128918i
$848$	−127.518			−4.37898
$849$	−25.8603	+	18.7886i	−0.887522	+	0.644823i
$850$	−20.6027	−	63.4085i	−0.706665	−	2.17489i
$851$	2.15753	−	6.64019i	0.0739592	−	0.227623i
$852$	−25.1015	−	18.2373i	−0.859962	−	0.624799i
$853$	24.4232	+	17.7445i	0.836235	+	0.607560i	0.921316	−	0.388814i	$-0.127115\pi$
$853$	24.4232	+	17.7445i	0.836235	+	0.607560i	−0.0850814	+	0.996374i	$0.527115\pi$
$854$	6.92536	−	21.3141i	0.236981	−	0.729352i
$855$	0.116877	+	0.359710i	0.00399711	+	0.0123018i
$856$	−70.2307	+	51.0256i	−2.40044	+	1.74402i
$857$	−25.3151			−0.864748			−0.432374	−	0.901694i	$-0.642324\pi$
$857$	−25.3151			−0.864748			−0.432374	+	0.901694i	$0.642324\pi$
$858$	−21.6735	+	44.3812i	−0.739920	+	1.51515i
$859$	−10.7680			−0.367399			−0.183699	−	0.982982i	$-0.558807\pi$
$859$	−10.7680			−0.367399			−0.183699	+	0.982982i	$0.558807\pi$
$860$	63.3119	−	45.9988i	2.15892	−	1.56855i
$861$	−1.07803	−	3.31785i	−0.0367393	−	0.113072i
$862$	29.2105	−	89.9008i	0.994915	−	3.06203i
$863$	28.5585	+	20.7490i	0.972143	+	0.706303i	0.955939	−	0.293566i	$-0.0948419\pi$
$863$	28.5585	+	20.7490i	0.972143	+	0.706303i	0.0162040	+	0.999869i	$0.494842\pi$
$864$	−10.2871	−	7.47402i	−0.349975	−	0.254271i
$865$	6.42089	−	19.7615i	0.218317	−	0.671910i
$866$	−18.8413	−	57.9875i	−0.640252	−	1.97049i
$867$	−11.6252	+	8.44620i	−0.394812	+	0.286848i
$868$	−7.93955			−0.269486
$869$	−5.39712	−	30.6978i	−0.183085	−	1.04135i
$870$	72.0487			2.44268
$871$	−36.7350	+	26.6896i	−1.24472	+	0.904341i
$872$	−11.8055	−	36.3337i	−0.399785	−	1.23041i
$873$	−1.75669	+	5.40655i	−0.0594551	+	0.182984i
$874$	−0.438316	−	0.318455i	−0.0148263	−	0.0107719i
$875$	−1.22459	−	0.889720i	−0.0413989	−	0.0300780i
$876$	5.39000	−	16.5887i	0.182111	−	0.560480i
$877$	−1.28769	−	3.96311i	−0.0434823	−	0.133825i	0.926959	−	0.375164i	$-0.122413\pi$
$877$	−1.28769	−	3.96311i	−0.0434823	−	0.133825i	−0.970441	+	0.241339i	$0.922413\pi$
$878$	−52.9319	+	38.4573i	−1.78637	+	1.29787i
$879$	−0.472963			−0.0159526
$880$	108.920	+	15.3629i	3.67168	+	0.517882i
$881$	−40.6561			−1.36974			−0.684870	−	0.728665i	$-0.740141\pi$
$881$	−40.6561			−1.36974			−0.684870	+	0.728665i	$0.740141\pi$
$882$	−2.13576	+	1.55172i	−0.0719146	+	0.0522490i
$883$	−5.92377	−	18.2315i	−0.199351	−	0.613539i	−0.999898	−	0.0142692i	$-0.995458\pi$
$883$	−5.92377	−	18.2315i	−0.199351	−	0.613539i	0.800547	−	0.599269i	$-0.204542\pi$
$884$	48.5158	−	149.316i	1.63176	−	5.02205i
$885$	−16.5014	−	11.9890i	−0.554690	−	0.403006i
$886$	−28.3939	−	20.6293i	−0.953910	−	0.693056i
$887$	−11.4454	+	35.2253i	−0.384298	+	1.18275i	0.552690	+	0.833387i	$0.313602\pi$
$887$	−11.4454	+	35.2253i	−0.384298	+	1.18275i	−0.936988	+	0.349362i	$0.886398\pi$
$888$	10.1075	+	31.1076i	0.339184	+	1.04390i
$889$	−9.17429	+	6.66551i	−0.307696	+	0.223554i
$890$	−68.8346			−2.30734
$891$	−2.38464	−	2.30511i	−0.0798883	−	0.0772240i
$892$	42.1774			1.41220
$893$	0.158170	−	0.114917i	0.00529295	−	0.00384555i
$894$	11.5671	+	35.6000i	0.386863	+	1.19064i
$895$	12.3817	−	38.1070i	0.413875	−	1.27378i
$896$	5.17868	+	3.76253i	0.173008	+	0.125697i
$897$	7.63609	+	5.54795i	0.254962	+	0.185241i
$898$	17.0266	−	52.4024i	0.568184	−	1.74869i
$899$	4.36965	+	13.4484i	0.145736	+	0.448529i
$900$	−18.1278	+	13.1706i	−0.604258	+	0.439019i
$901$	66.4061			2.21231
$902$	−26.9768	+	14.3266i	−0.898228	+	0.477024i
$903$	5.10698			0.169950
$904$	33.5006	−	24.3396i	1.11421	−	0.809523i
$905$	−3.90521	−	12.0190i	−0.129814	−	0.399525i
$906$	12.9566	−	39.8763i	0.430454	−	1.32480i
$907$	23.2660	+	16.9037i	0.772534	+	0.561279i	0.902729	−	0.430209i	$-0.141560\pi$
$907$	23.2660	+	16.9037i	0.772534	+	0.561279i	−0.130195	+	0.991488i	$0.541560\pi$
$908$	89.0578	+	64.7043i	2.95549	+	2.14729i
$909$	5.21545	−	16.0515i	0.172986	−	0.532395i
$910$	14.1906	+	43.6742i	0.470414	+	1.44778i
$911$	−36.2210	+	26.3161i	−1.20006	+	0.871892i	−0.994290	−	0.106710i	$-0.965968\pi$
$911$	−36.2210	+	26.3161i	−1.20006	+	0.871892i	−0.205765	+	0.978601i	$0.565968\pi$
$912$	1.31915			0.0436813
$913$	27.6335	−	14.6754i	0.914535	−	0.485684i
$914$	−74.5371			−2.46547
$915$	21.1784	−	15.3870i	0.700138	−	0.508680i
$916$	−13.7898	−	42.4407i	−0.455629	−	1.40228i
$917$	0.299834	−	0.922795i	0.00990140	−	0.0304734i
$918$	11.9620	+	8.69094i	0.394806	+	0.286844i
$919$	−15.6458	−	11.3673i	−0.516107	−	0.374973i	0.299029	−	0.954244i	$-0.403337\pi$
$919$	−15.6458	−	11.3673i	−0.516107	−	0.374973i	−0.815135	+	0.579271i	$0.803337\pi$
$920$	12.4985	−	38.4664i	0.412063	−	1.26820i
$921$	−6.90721	−	21.2582i	−0.227600	−	0.700481i
$922$	28.9250	−	21.0152i	0.952594	−	0.692100i
$923$	−35.2210			−1.15931
$924$	11.8499	+	11.4547i	0.389834	+	0.376832i
$925$	18.8152			0.618638
$926$	72.5268	−	52.6938i	2.38338	−	1.73163i
$927$	−4.08433	−	12.5703i	−0.134147	−	0.412862i
$928$	34.7760	−	107.030i	1.14158	−	3.51342i
$929$	21.7730	+	15.8190i	0.714350	+	0.519006i	0.884574	−	0.466400i	$-0.154449\pi$
$929$	21.7730	+	15.8190i	0.714350	+	0.519006i	−0.170224	+	0.985405i	$0.554449\pi$
$930$	−10.5226	−	7.64514i	−0.345051	−	0.250694i
$931$	0.0379017	−	0.116649i	0.00124218	−	0.00382303i
$932$	30.5443	+	94.0055i	1.00051	+	3.07925i
$933$	−17.7853	+	12.9217i	−0.582263	+	0.423039i
$934$	33.2127			1.08675
$935$	−56.7209	−	8.00034i	−1.85497	−	0.261639i
$936$	−44.2180			−1.44531
$937$	−34.4115	+	25.0014i	−1.12417	+	0.816760i	−0.984837	−	0.173484i	$-0.944497\pi$
$937$	−34.4115	+	25.0014i	−1.12417	+	0.816760i	−0.139338	+	0.990245i	$0.544497\pi$
$938$	6.56667	+	20.2101i	0.214409	+	0.659884i
$939$	−2.45677	+	7.56115i	−0.0801736	+	0.246749i
$940$	19.7611	+	14.3573i	0.644536	+	0.468283i
$941$	39.4561	+	28.6665i	1.28623	+	0.934502i	0.999722	−	0.0235760i	$-0.00750517\pi$
$941$	39.4561	+	28.6665i	1.28623	+	0.934502i	0.286509	+	0.958078i	$0.407505\pi$
$942$	−7.50404	+	23.0951i	−0.244495	+	0.752478i
$943$	1.80382	+	5.55158i	0.0587403	+	0.180784i
$944$	−57.5531	+	41.8148i	−1.87319	+	1.36096i
$945$	−3.08369			−0.100312
$946$	−7.74282	−	44.0396i	−0.251741	−	1.43185i
$947$	0.641845			0.0208572			0.0104286	−	0.999946i	$-0.496680\pi$
$947$	0.641845			0.0208572			0.0104286	+	0.999946i	$0.496680\pi$
$948$	37.7809	−	27.4494i	1.22707	−	0.891516i
$949$	−6.11856	−	18.8310i	−0.198617	−	0.611280i
$950$	0.451175	−	1.38858i	0.0146381	−	0.0450513i
$951$	12.2345	+	8.88889i	0.396731	+	0.288242i
$952$	−35.5186	−	25.8058i	−1.15117	−	0.836371i
$953$	2.36690	−	7.28456i	0.0766713	−	0.235970i	−0.905374	−	0.424615i	$-0.860409\pi$
$953$	2.36690	−	7.28456i	0.0766713	−	0.235970i	0.982045	+	0.188645i	$0.0604095\pi$
$954$	−9.67231	−	29.7683i	−0.313153	−	0.963785i
$955$	−53.6463	+	38.9763i	−1.73595	+	1.26124i
$956$	−45.8156			−1.48178
$957$	12.8808	−	26.3763i	0.416377	−	0.852623i
$958$	76.2721			2.46424
$959$	−0.101208	+	0.0735323i	−0.00326819	+	0.00237448i
$960$	11.4902	+	35.3632i	0.370845	+	1.14134i
$961$	−8.79069	+	27.0550i	−0.283571	+	0.872741i
$962$	50.2713	+	36.5242i	1.62081	+	1.17759i
$963$	−8.95947	−	6.50943i	−0.288715	−	0.209764i
$964$	−1.23296	+	3.79465i	−0.0397108	+	0.122217i
$965$	16.9584	+	52.1925i	0.545910	+	1.68014i
$966$	3.57364	−	2.59640i	0.114980	−	0.0835379i
$967$	−29.7387			−0.956333			−0.478166	−	0.878269i	$-0.658698\pi$
$967$	−29.7387			−0.956333			−0.478166	+	0.878269i	$0.658698\pi$
$968$	48.2879	−	71.4365i	1.55203	−	2.29606i
$969$	−0.686958			−0.0220683
$970$	37.4400	−	27.2018i	1.20213	−	0.873396i
$971$	−10.7905	−	33.2097i	−0.346284	−	1.06575i	−0.960893	−	0.276920i	$-0.910686\pi$
$971$	−10.7905	−	33.2097i	−0.346284	−	1.06575i	0.614609	−	0.788832i	$-0.289314\pi$
$972$	1.53559	−	4.72606i	0.0492541	−	0.151589i
$973$	−1.35781	−	0.986507i	−0.0435294	−	0.0316259i
$974$	−54.4782	−	39.5808i	−1.74560	−	1.26825i
$975$	−7.86012	+	24.1910i	−0.251725	+	0.774731i
$976$	−28.2141	−	86.8339i	−0.903110	−	2.77949i
$977$	−25.8353	+	18.7704i	−0.826543	+	0.600519i	−0.918579	−	0.395237i	$-0.870662\pi$
$977$	−25.8353	+	18.7704i	−0.826543	+	0.600519i	0.0920361	+	0.995756i	$0.470662\pi$
$978$	25.7907			0.824695
$979$	−12.3062	+	25.1996i	−0.393307	+	0.805383i
$980$	15.3237			0.489498
$981$	3.94290	−	2.86468i	0.125887	−	0.0914623i
$982$	3.80644	+	11.7150i	0.121468	+	0.373841i
$983$	−10.4791	+	32.2513i	−0.334231	+	1.02866i	0.632868	+	0.774259i	$0.281877\pi$
$983$	−10.4791	+	32.2513i	−0.334231	+	1.02866i	−0.967100	+	0.254398i	$0.918123\pi$
$984$	−22.1234	−	16.0736i	−0.705270	−	0.512408i
$985$	−45.1757	−	32.8221i	−1.43942	−	1.04580i
$986$	−40.4382	+	124.456i	−1.28782	+	3.96349i
$987$	0.492574	+	1.51599i	0.0156788	+	0.0482544i
$988$	2.78151	−	2.02089i	0.0884917	−	0.0642930i
$989$	−8.54523			−0.271722
$990$	4.67526	+	26.5919i	0.148589	+	0.845148i
$991$	−13.3101			−0.422809			−0.211404	−	0.977399i	$-0.567804\pi$
$991$	−13.3101			−0.422809			−0.211404	+	0.977399i	$0.567804\pi$
$992$	−16.4360	+	11.9414i	−0.521843	+	0.379141i
$993$	−1.86196	−	5.73052i	−0.0590874	−	0.181852i
$994$	−5.09359	+	15.6765i	−0.161559	+	0.497228i
$995$	−6.66446	−	4.84201i	−0.211278	−	0.153502i
$996$	37.9263	+	27.5551i	1.20174	+	0.873116i
$997$	−0.912394	+	2.80806i	−0.0288958	+	0.0889322i	−0.964464	−	0.264213i	$-0.914888\pi$
$997$	−0.912394	+	2.80806i	−0.0288958	+	0.0889322i	0.935569	+	0.353145i	$0.114888\pi$
$998$	−15.0886	−	46.4381i	−0.477623	−	1.46997i
$999$	−3.37577	+	2.45264i	−0.106805	+	0.0775980i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.j.g.190.1	yes	20
3.2	odd	2		693.2.m.j.190.5		20
11.2	odd	10		2541.2.a.br.1.2		10
11.4	even	5	inner	231.2.j.g.169.1	✓	20
11.9	even	5		2541.2.a.bq.1.9		10
33.2	even	10		7623.2.a.cy.1.9		10
33.20	odd	10		7623.2.a.cx.1.2		10
33.26	odd	10		693.2.m.j.631.5		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.j.g.169.1	✓	20	11.4	even	5	inner
231.2.j.g.190.1	yes	20	1.1	even	1	trivial
693.2.m.j.190.5		20	3.2	odd	2
693.2.m.j.631.5		20	33.26	odd	10
2541.2.a.bq.1.9		10	11.9	even	5
2541.2.a.br.1.2		10	11.2	odd	10
7623.2.a.cx.1.2		10	33.20	odd	10
7623.2.a.cy.1.9		10	33.2	even	10

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.j (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.13576 + 1.55172i) q^{2} +(0.309017 + 0.951057i) q^{3} +(1.53559 - 4.72606i) q^{4} +(-2.49476 - 1.81255i) q^{5} +(-2.13576 - 1.55172i) q^{6} +(-0.309017 + 0.951057i) q^{7} +(2.42230 + 7.45506i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(-2.13576 + 1.55172i) q^{2} +(0.309017 + 0.951057i) q^{3} +(1.53559 - 4.72606i) q^{4} +(-2.49476 - 1.81255i) q^{5} +(-2.13576 - 1.55172i) q^{6} +(-0.309017 + 0.951057i) q^{7} +(2.42230 + 7.45506i) q^{8} +(-0.809017 + 0.587785i) q^{9} +8.14075 q^{10} +(1.45539 - 2.98024i) q^{11} +4.96928 q^{12} +(4.56364 - 3.31568i) q^{13} +(-0.815786 - 2.51073i) q^{14} +(0.952912 - 2.93276i) q^{15} +(-8.70112 - 6.32173i) q^{16} +(4.53118 + 3.29210i) q^{17} +(0.815786 - 2.51073i) q^{18} +(0.0379017 + 0.116649i) q^{19} +(-12.3971 + 9.00705i) q^{20} -1.00000 q^{21} +(1.51613 + 8.62342i) q^{22} +1.67325 q^{23} +(-6.34165 + 4.60748i) q^{24} +(1.39340 + 4.28844i) q^{25} +(-4.60183 + 14.1630i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(4.02023 + 2.92087i) q^{28} +(2.73492 - 8.41721i) q^{29} +(2.51563 + 7.74231i) q^{30} +(-1.29259 + 0.939120i) q^{31} +12.7156 q^{32} +(3.28412 + 0.463217i) q^{33} -14.7859 q^{34} +(2.49476 - 1.81255i) q^{35} +(1.53559 + 4.72606i) q^{36} +(1.28943 - 3.96845i) q^{37} +(-0.261956 - 0.190322i) q^{38} +(4.56364 + 3.31568i) q^{39} +(7.46960 - 22.9891i) q^{40} +(1.07803 + 3.31785i) q^{41} +(2.13576 - 1.55172i) q^{42} -5.10698 q^{43} +(-11.8499 - 11.4547i) q^{44} +3.08369 q^{45} +(-3.57364 + 2.59640i) q^{46} +(-0.492574 - 1.51599i) q^{47} +(3.32353 - 10.2288i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(-9.63040 - 6.99690i) q^{50} +(-1.73076 + 5.32673i) q^{51} +(-8.66223 - 26.6596i) q^{52} +(9.59206 - 6.96904i) q^{53} +2.63994 q^{54} +(-9.03267 + 4.79700i) q^{55} -7.83871 q^{56} +(-0.0992279 + 0.0720933i) q^{57} +(7.22002 + 22.2209i) q^{58} +(2.04398 - 6.29072i) q^{59} +(-12.3971 - 9.00705i) q^{60} +(6.86789 + 4.98982i) q^{61} +(1.30340 - 4.01146i) q^{62} +(-0.309017 - 0.951057i) q^{63} +(-9.75511 + 7.08750i) q^{64} -17.3950 q^{65} +(-7.73285 + 4.10670i) q^{66} -8.04949 q^{67} +(22.5167 - 16.3593i) q^{68} +(0.517061 + 1.59135i) q^{69} +(-2.51563 + 7.74231i) q^{70} +(-5.05133 - 3.67001i) q^{71} +(-6.34165 - 4.60748i) q^{72} +(1.08466 - 3.33825i) q^{73} +(3.40401 + 10.4765i) q^{74} +(-3.64796 + 2.65040i) q^{75} +0.609494 q^{76} +(2.38464 + 2.30511i) q^{77} -14.8918 q^{78} +(7.60289 - 5.52382i) q^{79} +(10.2487 + 31.5424i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-7.45078 - 5.41331i) q^{82} +(7.63216 + 5.54509i) q^{83} +(-1.53559 + 4.72606i) q^{84} +(-5.33712 - 16.4260i) q^{85} +(10.9073 - 7.92458i) q^{86} +8.85038 q^{87} +(25.7433 + 3.63102i) q^{88} -8.45556 q^{89} +(-6.58600 + 4.78501i) q^{90} +(1.74316 + 5.36488i) q^{91} +(2.56942 - 7.90787i) q^{92} +(-1.29259 - 0.939120i) q^{93} +(3.40440 + 2.47344i) q^{94} +(0.116877 - 0.359710i) q^{95} +(3.92933 + 12.0932i) q^{96} +(4.59909 - 3.34143i) q^{97} +2.63994 q^{98} +(0.574303 + 3.26652i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 5 q^{3} - 14 q^{4} - 5 q^{5} + 5 q^{7} - 9 q^{8} - 5 q^{9}+O(q^{10}) \) 20 * q - 5 * q^3 - 14 * q^4 - 5 * q^5 + 5 * q^7 - 9 * q^8 - 5 * q^9	\( 20 q - 5 q^{3} - 14 q^{4} - 5 q^{5} + 5 q^{7} - 9 q^{8} - 5 q^{9} + 12 q^{10} - q^{11} + 36 q^{12} + 13 q^{13} - 24 q^{16} - q^{17} + 10 q^{19} - 46 q^{20} - 20 q^{21} + 26 q^{22} + 6 q^{24} - 8 q^{25} - 53 q^{26} - 5 q^{27} + 4 q^{28} + 3 q^{29} - 3 q^{30} - 13 q^{31} + 82 q^{32} + 9 q^{33} + 42 q^{34} + 5 q^{35} - 14 q^{36} - 32 q^{37} + 16 q^{38} + 13 q^{39} + 20 q^{40} - 3 q^{41} + 12 q^{43} + 25 q^{44} + 10 q^{45} - 13 q^{46} + 20 q^{47} - 14 q^{48} - 5 q^{49} - 83 q^{50} + 9 q^{51} - 80 q^{52} + 3 q^{53} - 28 q^{55} - 6 q^{56} - 10 q^{57} + 2 q^{58} - 9 q^{59} - 46 q^{60} - 15 q^{61} - 37 q^{62} + 5 q^{63} - 49 q^{64} + 58 q^{65} - 4 q^{66} + 76 q^{67} + 51 q^{68} + 3 q^{70} + 37 q^{71} + 6 q^{72} + 27 q^{73} - 32 q^{74} - 23 q^{75} + 4 q^{76} + 6 q^{77} + 2 q^{78} + 5 q^{79} + 137 q^{80} - 5 q^{81} - 55 q^{82} - 42 q^{83} + 14 q^{84} - 48 q^{85} + 3 q^{86} + 28 q^{87} + 151 q^{88} - 18 q^{89} - 3 q^{90} + 7 q^{91} + 39 q^{92} - 13 q^{93} - 35 q^{94} - 96 q^{95} - 48 q^{96} - 27 q^{97} - q^{99}+O(q^{100}) \) 20 * q - 5 * q^3 - 14 * q^4 - 5 * q^5 + 5 * q^7 - 9 * q^8 - 5 * q^9 + 12 * q^10 - q^11 + 36 * q^12 + 13 * q^13 - 24 * q^16 - q^17 + 10 * q^19 - 46 * q^20 - 20 * q^21 + 26 * q^22 + 6 * q^24 - 8 * q^25 - 53 * q^26 - 5 * q^27 + 4 * q^28 + 3 * q^29 - 3 * q^30 - 13 * q^31 + 82 * q^32 + 9 * q^33 + 42 * q^34 + 5 * q^35 - 14 * q^36 - 32 * q^37 + 16 * q^38 + 13 * q^39 + 20 * q^40 - 3 * q^41 + 12 * q^43 + 25 * q^44 + 10 * q^45 - 13 * q^46 + 20 * q^47 - 14 * q^48 - 5 * q^49 - 83 * q^50 + 9 * q^51 - 80 * q^52 + 3 * q^53 - 28 * q^55 - 6 * q^56 - 10 * q^57 + 2 * q^58 - 9 * q^59 - 46 * q^60 - 15 * q^61 - 37 * q^62 + 5 * q^63 - 49 * q^64 + 58 * q^65 - 4 * q^66 + 76 * q^67 + 51 * q^68 + 3 * q^70 + 37 * q^71 + 6 * q^72 + 27 * q^73 - 32 * q^74 - 23 * q^75 + 4 * q^76 + 6 * q^77 + 2 * q^78 + 5 * q^79 + 137 * q^80 - 5 * q^81 - 55 * q^82 - 42 * q^83 + 14 * q^84 - 48 * q^85 + 3 * q^86 + 28 * q^87 + 151 * q^88 - 18 * q^89 - 3 * q^90 + 7 * q^91 + 39 * q^92 - 13 * q^93 - 35 * q^94 - 96 * q^95 - 48 * q^96 - 27 * q^97 - q^99

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