LMFDB - Embedded newform 429.2.n.d.157.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(157,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 8, 0]))

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

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

chi := DirichletCharacter("429.157");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.n (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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$9$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			157.2
Character	$\chi$	$=$	429.157
Dual form			429.2.n.d.235.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.61703 + 1.17484i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.616508 - 1.89742i) q^{4} +(2.77955 + 2.01946i) q^{5} +(-1.61703 - 1.17484i) q^{6} +(-1.25981 + 3.87730i) q^{7} +(-0.00305069 - 0.00938907i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(-1.61703 + 1.17484i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.616508 - 1.89742i) q^{4} +(2.77955 + 2.01946i) q^{5} +(-1.61703 - 1.17484i) q^{6} +(-1.25981 + 3.87730i) q^{7} +(-0.00305069 - 0.00938907i) q^{8} +(-0.809017 + 0.587785i) q^{9} -6.86718 q^{10} +(3.24652 + 0.678334i) q^{11} +1.99506 q^{12} +(0.809017 - 0.587785i) q^{13} +(-2.51807 - 7.74981i) q^{14} +(-1.06169 + 3.26756i) q^{15} +(3.24404 + 2.35693i) q^{16} +(-2.73891 - 1.98994i) q^{17} +(0.617652 - 1.90094i) q^{18} +(1.10836 + 3.41118i) q^{19} +(5.54537 - 4.02895i) q^{20} -4.07684 q^{21} +(-6.04666 + 2.71726i) q^{22} +4.32532 q^{23} +(0.00798682 - 0.00580277i) q^{24} +(2.10259 + 6.47110i) q^{25} +(-0.617652 + 1.90094i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(6.58017 + 4.78077i) q^{28} +(2.67758 - 8.24076i) q^{29} +(-2.12208 - 6.53108i) q^{30} +(-2.49022 + 1.80925i) q^{31} -7.99501 q^{32} +(0.358095 + 3.29724i) q^{33} +6.76679 q^{34} +(-11.3318 + 8.23301i) q^{35} +(0.616508 + 1.89742i) q^{36} +(0.558643 - 1.71933i) q^{37} +(-5.79987 - 4.21385i) q^{38} +(0.809017 + 0.587785i) q^{39} +(0.0104813 - 0.0322581i) q^{40} +(-0.446241 - 1.37339i) q^{41} +(6.59238 - 4.78965i) q^{42} -8.33614 q^{43} +(3.28858 - 5.74179i) q^{44} -3.43571 q^{45} +(-6.99419 + 5.08158i) q^{46} +(-2.68545 - 8.26497i) q^{47} +(-1.23911 + 3.81360i) q^{48} +(-7.78322 - 5.65484i) q^{49} +(-11.0025 - 7.99378i) q^{50} +(1.04617 - 3.21979i) q^{51} +(-0.616508 - 1.89742i) q^{52} +(-9.29785 + 6.75528i) q^{53} +1.99876 q^{54} +(7.65398 + 8.44167i) q^{55} +0.0402476 q^{56} +(-2.90173 + 2.10823i) q^{57} +(5.35186 + 16.4713i) q^{58} +(3.90781 - 12.0270i) q^{59} +(5.54537 + 4.02895i) q^{60} +(-3.06616 - 2.22770i) q^{61} +(1.90118 - 5.85123i) q^{62} +(-1.25981 - 3.87730i) q^{63} +(6.44013 - 4.67903i) q^{64} +3.43571 q^{65} +(-4.45279 - 4.91104i) q^{66} +2.21940 q^{67} +(-5.46430 + 3.97005i) q^{68} +(1.33660 + 4.11362i) q^{69} +(8.65135 - 26.6261i) q^{70} +(8.82688 + 6.41310i) q^{71} +(0.00798682 + 0.00580277i) q^{72} +(0.579305 - 1.78292i) q^{73} +(1.11660 + 3.43653i) q^{74} +(-5.50464 + 3.99936i) q^{75} +7.15575 q^{76} +(-6.72010 + 11.7331i) q^{77} -1.99876 q^{78} +(0.988798 - 0.718404i) q^{79} +(4.25724 + 13.1024i) q^{80} +(0.309017 - 0.951057i) q^{81} +(2.33510 + 1.69655i) q^{82} +(11.9794 + 8.70351i) q^{83} +(-2.51340 + 7.73545i) q^{84} +(-3.59435 - 11.0623i) q^{85} +(13.4798 - 9.79367i) q^{86} +8.66484 q^{87} +(-0.00353520 - 0.0325512i) q^{88} +10.1104 q^{89} +(5.55566 - 4.03643i) q^{90} +(1.25981 + 3.87730i) q^{91} +(2.66659 - 8.20693i) q^{92} +(-2.49022 - 1.80925i) q^{93} +(14.0525 + 10.2098i) q^{94} +(-3.80801 + 11.7198i) q^{95} +(-2.47059 - 7.60371i) q^{96} +(-6.50703 + 4.72763i) q^{97} +19.2293 q^{98} +(-3.02520 + 1.35947i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 3 q^{2} - 9 q^{3} - 11 q^{4} + 3 q^{6} + q^{7} - q^{8} - 9 q^{9}+O(q^{10}) $ 36 * q + 3 * q^2 - 9 * q^3 - 11 * q^4 + 3 * q^6 + q^7 - q^8 - 9 * q^9	\( 36 q + 3 q^{2} - 9 q^{3} - 11 q^{4} + 3 q^{6} + q^{7} - q^{8} - 9 q^{9} + 6 q^{10} - 10 q^{11} + 54 q^{12} + 9 q^{13} - 5 q^{14} - 10 q^{15} - 13 q^{16} - 2 q^{18} + 10 q^{19} + 37 q^{20} - 14 q^{21} - 9 q^{22} + 18 q^{23} + 4 q^{24} - 31 q^{25} + 2 q^{26} - 9 q^{27} + 12 q^{28} + 10 q^{29} + q^{30} - 28 q^{31} - 74 q^{32} + 5 q^{33} + 40 q^{34} - 14 q^{35} - 11 q^{36} - 26 q^{37} + 7 q^{38} + 9 q^{39} - 72 q^{40} + 26 q^{41} - 5 q^{42} + 4 q^{43} - 68 q^{44} + 20 q^{45} - 57 q^{46} - 28 q^{48} - 18 q^{49} + 11 q^{50} - 5 q^{51} + 11 q^{52} + 11 q^{53} - 2 q^{54} - 32 q^{55} + 72 q^{56} + 50 q^{58} + 55 q^{59} + 37 q^{60} + 14 q^{61} - 50 q^{62} + q^{63} - q^{64} - 20 q^{65} - 14 q^{66} + 104 q^{67} - 9 q^{68} + 8 q^{69} + 44 q^{70} - 8 q^{71} + 4 q^{72} - 3 q^{73} + 69 q^{74} - 21 q^{75} - 52 q^{76} + 2 q^{77} + 2 q^{78} - 19 q^{79} - 159 q^{80} - 9 q^{81} + 58 q^{82} + 12 q^{83} - 8 q^{84} + 63 q^{86} - 97 q^{88} + 118 q^{89} - 4 q^{90} - q^{91} + 98 q^{92} - 28 q^{93} - 99 q^{94} - 45 q^{95} + q^{96} + 50 q^{97} - 186 q^{98}+O(q^{100}) \) 36 * q + 3 * q^2 - 9 * q^3 - 11 * q^4 + 3 * q^6 + q^7 - q^8 - 9 * q^9 + 6 * q^10 - 10 * q^11 + 54 * q^12 + 9 * q^13 - 5 * q^14 - 10 * q^15 - 13 * q^16 - 2 * q^18 + 10 * q^19 + 37 * q^20 - 14 * q^21 - 9 * q^22 + 18 * q^23 + 4 * q^24 - 31 * q^25 + 2 * q^26 - 9 * q^27 + 12 * q^28 + 10 * q^29 + q^30 - 28 * q^31 - 74 * q^32 + 5 * q^33 + 40 * q^34 - 14 * q^35 - 11 * q^36 - 26 * q^37 + 7 * q^38 + 9 * q^39 - 72 * q^40 + 26 * q^41 - 5 * q^42 + 4 * q^43 - 68 * q^44 + 20 * q^45 - 57 * q^46 - 28 * q^48 - 18 * q^49 + 11 * q^50 - 5 * q^51 + 11 * q^52 + 11 * q^53 - 2 * q^54 - 32 * q^55 + 72 * q^56 + 50 * q^58 + 55 * q^59 + 37 * q^60 + 14 * q^61 - 50 * q^62 + q^63 - q^64 - 20 * q^65 - 14 * q^66 + 104 * q^67 - 9 * q^68 + 8 * q^69 + 44 * q^70 - 8 * q^71 + 4 * q^72 - 3 * q^73 + 69 * q^74 - 21 * q^75 - 52 * q^76 + 2 * q^77 + 2 * q^78 - 19 * q^79 - 159 * q^80 - 9 * q^81 + 58 * q^82 + 12 * q^83 - 8 * q^84 + 63 * q^86 - 97 * q^88 + 118 * q^89 - 4 * q^90 - q^91 + 98 * q^92 - 28 * q^93 - 99 * q^94 - 45 * q^95 + q^96 + 50 * q^97 - 186 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.61703	+	1.17484i	−1.14342	+	0.830741i	−0.987592	−	0.157044i	$-0.949803\pi$
$2$	−1.61703	+	1.17484i	−1.14342	+	0.830741i	−0.155825	+	0.987785i	$0.549803\pi$
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$4$	0.616508	−	1.89742i	0.308254	−	0.948708i
$5$	2.77955	+	2.01946i	1.24305	+	0.903130i	0.997798	−	0.0663285i	$-0.0211285\pi$
$5$	2.77955	+	2.01946i	1.24305	+	0.903130i	0.245254	+	0.969459i	$0.421129\pi$
$6$	−1.61703	−	1.17484i	−0.660152	−	0.479628i
$7$	−1.25981	+	3.87730i	−0.476164	+	1.46548i	0.368218	+	0.929740i	$0.379968\pi$
$7$	−1.25981	+	3.87730i	−0.476164	+	1.46548i	−0.844382	+	0.535742i	$0.820032\pi$
$8$	−0.00305069	−	0.00938907i	−0.00107858	−	0.00331954i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	−6.86718			−2.17159
$11$	3.24652	+	0.678334i	0.978861	+	0.204525i
$11$	3.24652	+	0.678334i	0.978861	+	0.204525i
$12$	1.99506			0.575924
$13$	0.809017	−	0.587785i	0.224381	−	0.163022i
$13$	0.809017	−	0.587785i	0.224381	−	0.163022i
$14$	−2.51807	−	7.74981i	−0.672982	−	2.07122i
$15$	−1.06169	+	3.26756i	−0.274128	+	0.843679i
$16$	3.24404	+	2.35693i	0.811010	+	0.589233i
$17$	−2.73891	−	1.98994i	−0.664284	−	0.482631i	0.203823	−	0.979008i	$-0.434663\pi$
$17$	−2.73891	−	1.98994i	−0.664284	−	0.482631i	−0.868107	+	0.496377i	$0.834663\pi$
$18$	0.617652	−	1.90094i	0.145582	−	0.448055i
$19$	1.10836	+	3.41118i	0.254275	+	0.782579i	0.993972	+	0.109638i	$0.0349692\pi$
$19$	1.10836	+	3.41118i	0.254275	+	0.782579i	−0.739696	+	0.672941i	$0.765031\pi$
$20$	5.54537	−	4.02895i	1.23998	−	0.900900i
$21$	−4.07684			−0.889638
$22$	−6.04666	+	2.71726i	−1.28915	+	0.579322i
$23$	4.32532			0.901892			0.450946	−	0.892551i	$-0.351087\pi$
$23$	4.32532			0.901892			0.450946	+	0.892551i	$0.351087\pi$
$24$	0.00798682	−	0.00580277i	0.00163030	−	0.00118448i
$25$	2.10259	+	6.47110i	0.420517	+	1.29422i
$26$	−0.617652	+	1.90094i	−0.121132	+	0.372805i
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$	6.58017	+	4.78077i	1.24353	+	0.903481i
$29$	2.67758	−	8.24076i	0.497215	−	1.53027i	−0.316261	−	0.948672i	$-0.602428\pi$
$29$	2.67758	−	8.24076i	0.497215	−	1.53027i	0.813476	−	0.581598i	$-0.197572\pi$
$30$	−2.12208	−	6.53108i	−0.387436	−	1.19241i
$31$	−2.49022	+	1.80925i	−0.447256	+	0.324950i	−0.788511	−	0.615020i	$-0.789148\pi$
$31$	−2.49022	+	1.80925i	−0.447256	+	0.324950i	0.341255	+	0.939971i	$0.389148\pi$
$32$	−7.99501			−1.41333
$33$	0.358095	+	3.29724i	0.0623363	+	0.573975i
$34$	6.76679			1.16049
$35$	−11.3318	+	8.23301i	−1.91542	+	1.39163i
$36$	0.616508	+	1.89742i	0.102751	+	0.316236i
$37$	0.558643	−	1.71933i	0.0918404	−	0.282656i	−0.894577	−	0.446914i	$-0.852523\pi$
$37$	0.558643	−	1.71933i	0.0918404	−	0.282656i	0.986417	+	0.164258i	$0.0525230\pi$
$38$	−5.79987	−	4.21385i	−0.940863	−	0.683577i
$39$	0.809017	+	0.587785i	0.129546	+	0.0941210i
$40$	0.0104813	−	0.0322581i	0.00165724	−	0.00510046i
$41$	−0.446241	−	1.37339i	−0.0696911	−	0.214487i	0.910145	−	0.414290i	$-0.135970\pi$
$41$	−0.446241	−	1.37339i	−0.0696911	−	0.214487i	−0.979836	+	0.199803i	$0.935970\pi$
$42$	6.59238	−	4.78965i	1.01723	−	0.739059i
$43$	−8.33614			−1.27125			−0.635625	−	0.771998i	$-0.719257\pi$
$43$	−8.33614			−1.27125			−0.635625	+	0.771998i	$0.719257\pi$
$44$	3.28858	−	5.74179i	0.495772	−	0.865608i
$45$	−3.43571			−0.512166
$46$	−6.99419	+	5.08158i	−1.03124	+	0.749238i
$47$	−2.68545	−	8.26497i	−0.391714	−	1.20557i	−0.931492	−	0.363763i	$-0.881492\pi$
$47$	−2.68545	−	8.26497i	−0.391714	−	1.20557i	0.539778	−	0.841807i	$-0.318508\pi$
$48$	−1.23911	+	3.81360i	−0.178851	+	0.550445i
$49$	−7.78322	−	5.65484i	−1.11189	−	0.807834i
$50$	−11.0025	−	7.99378i	−1.55599	−	1.13049i
$51$	1.04617	−	3.21979i	0.146493	−	0.450860i
$52$	−0.616508	−	1.89742i	−0.0854942	−	0.263124i
$53$	−9.29785	+	6.75528i	−1.27716	+	0.927909i	−0.999463	−	0.0327605i	$-0.989570\pi$
$53$	−9.29785	+	6.75528i	−1.27716	+	0.927909i	−0.277694	+	0.960670i	$0.589570\pi$
$54$	1.99876			0.271997
$55$	7.65398	+	8.44167i	1.03206	+	1.13827i
$56$	0.0402476			0.00537831
$57$	−2.90173	+	2.10823i	−0.384343	+	0.279242i
$58$	5.35186	+	16.4713i	0.702734	+	2.16279i
$59$	3.90781	−	12.0270i	0.508753	−	1.56578i	−0.285616	−	0.958344i	$-0.592198\pi$
$59$	3.90781	−	12.0270i	0.508753	−	1.56578i	0.794368	−	0.607436i	$-0.207802\pi$
$60$	5.54537	+	4.02895i	0.715904	+	0.520135i
$61$	−3.06616	−	2.22770i	−0.392582	−	0.285227i	0.373931	−	0.927457i	$-0.378010\pi$
$61$	−3.06616	−	2.22770i	−0.392582	−	0.285227i	−0.766513	+	0.642229i	$0.778010\pi$
$62$	1.90118	−	5.85123i	0.241450	−	0.743107i
$63$	−1.25981	−	3.87730i	−0.158721	−	0.488494i
$64$	6.44013	−	4.67903i	0.805016	−	0.584879i
$65$	3.43571			0.426148
$66$	−4.45279	−	4.91104i	−0.548101	−	0.604507i
$67$	2.21940			0.271143			0.135572	−	0.990768i	$-0.456713\pi$
$67$	2.21940			0.271143			0.135572	+	0.990768i	$0.456713\pi$
$68$	−5.46430	+	3.97005i	−0.662644	+	0.481439i
$69$	1.33660	+	4.11362i	0.160907	+	0.495222i
$70$	8.65135	−	26.6261i	1.03403	−	3.18243i
$71$	8.82688	+	6.41310i	1.04756	+	0.761095i	0.971747	−	0.236027i	$-0.0758453\pi$
$71$	8.82688	+	6.41310i	1.04756	+	0.761095i	0.0758113	+	0.997122i	$0.475845\pi$
$72$	0.00798682	+	0.00580277i	0.000941256	+	0.000683862i
$73$	0.579305	−	1.78292i	0.0678025	−	0.208675i	−0.911415	−	0.411489i	$-0.865009\pi$
$73$	0.579305	−	1.78292i	0.0678025	−	0.208675i	0.979217	+	0.202814i	$0.0650088\pi$
$74$	1.11660	+	3.43653i	0.129802	+	0.399489i
$75$	−5.50464	+	3.99936i	−0.635622	+	0.461806i
$76$	7.15575			0.820820
$77$	−6.72010	+	11.7331i	−0.765827	+	1.33712i
$78$	−1.99876			−0.226316
$79$	0.988798	−	0.718404i	0.111249	−	0.0808268i	−0.530770	−	0.847516i	$-0.678097\pi$
$79$	0.988798	−	0.718404i	0.111249	−	0.0808268i	0.642019	+	0.766689i	$0.278097\pi$
$80$	4.25724	+	13.1024i	0.475973	+	1.46490i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	2.33510	+	1.69655i	0.257869	+	0.187353i
$83$	11.9794	+	8.70351i	1.31490	+	0.955334i	0.999981	+	0.00621718i	$0.00197900\pi$
$83$	11.9794	+	8.70351i	1.31490	+	0.955334i	0.314924	+	0.949117i	$0.398021\pi$
$84$	−2.51340	+	7.73545i	−0.274234	+	0.844007i
$85$	−3.59435	−	11.0623i	−0.389862	−	1.19987i
$86$	13.4798	−	9.79367i	1.45357	−	1.05608i
$87$	8.66484			0.928969
$88$	−0.00353520	−	0.0325512i	−0.000376854	−	0.00346996i
$89$	10.1104			1.07170			0.535848	−	0.844314i	$-0.319992\pi$
$89$	10.1104			1.07170			0.535848	+	0.844314i	$0.319992\pi$
$90$	5.55566	−	4.03643i	0.585619	−	0.425477i
$91$	1.25981	+	3.87730i	0.132064	+	0.406452i
$92$	2.66659	−	8.20693i	0.278012	−	0.855632i
$93$	−2.49022	−	1.80925i	−0.258223	−	0.187610i
$94$	14.0525	+	10.2098i	1.44941	+	1.05306i
$95$	−3.80801	+	11.7198i	−0.390693	+	1.20243i
$96$	−2.47059	−	7.60371i	−0.252154	−	0.776050i
$97$	−6.50703	+	4.72763i	−0.660689	+	0.480018i	−0.866895	−	0.498490i	$-0.833888\pi$
$97$	−6.50703	+	4.72763i	−0.660689	+	0.480018i	0.206207	+	0.978508i	$0.433888\pi$
$98$	19.2293			1.94245
$99$	−3.02520	+	1.35947i	−0.304044	+	0.136632i
$100$	13.5746			1.35746
$101$	−9.88464	+	7.18161i	−0.983559	+	0.714597i	−0.958501	−	0.285089i	$-0.907977\pi$
$101$	−9.88464	+	7.18161i	−0.983559	+	0.714597i	−0.0250575	+	0.999686i	$0.507977\pi$
$102$	2.09105	+	6.43560i	0.207045	+	0.637219i
$103$	1.81642	−	5.59037i	0.178977	−	0.550836i	−0.820815	−	0.571194i	$-0.806481\pi$
$103$	1.81642	−	5.59037i	0.178977	−	0.550836i	0.999793	+	0.0203579i	$0.00648058\pi$
$104$	−0.00798682	−	0.00580277i	−0.000783172	−	0.000569008i
$105$	−11.3318	−	8.23301i	−1.10587	−	0.803459i
$106$	7.09853	−	21.8470i	0.689471	−	2.12197i
$107$	4.98716	+	15.3489i	0.482127	+	1.48384i	0.836099	+	0.548579i	$0.184831\pi$
$107$	4.98716	+	15.3489i	0.482127	+	1.48384i	−0.353971	+	0.935256i	$0.615169\pi$
$108$	−1.61404	+	1.17267i	−0.155311	+	0.112840i
$109$	9.40364			0.900705			0.450353	−	0.892851i	$-0.351298\pi$
$109$	9.40364			0.900705			0.450353	+	0.892851i	$0.351298\pi$
$110$	−22.2944	−	4.65824i	−2.12569	−	0.444146i
$111$	1.80781			0.171590
$112$	−13.2254	+	9.60883i	−1.24968	+	0.907949i
$113$	−3.46964	−	10.6785i	−0.326397	−	1.00455i	−0.970806	−	0.239865i	$-0.922897\pi$
$113$	−3.46964	−	10.6785i	−0.326397	−	1.00455i	0.644410	−	0.764680i	$-0.277103\pi$
$114$	2.21535	−	6.81815i	0.207487	−	0.638579i
$115$	12.0224	+	8.73481i	1.12110	+	0.814526i
$116$	−13.9854	−	10.1610i	−1.29851	−	0.943423i
$117$	−0.309017	+	0.951057i	−0.0285686	+	0.0879252i
$118$	7.81078	+	24.0391i	0.719041	+	2.21298i
$119$	11.1661	−	8.11265i	1.02359	−	0.743685i
$120$	0.0339182			0.00309630
$121$	10.0797	+	4.40444i	0.916339	+	0.400404i
$122$	7.57529			0.685835
$123$	1.16827	−	0.848800i	0.105340	−	0.0765337i
$124$	1.89766	+	5.84039i	0.170415	+	0.524482i
$125$	−1.91542	+	5.89504i	−0.171320	+	0.527269i
$126$	6.59238	+	4.78965i	0.587296	+	0.426696i
$127$	4.32906	+	3.14525i	0.384142	+	0.279096i	0.763051	−	0.646338i	$-0.223701\pi$
$127$	4.32906	+	3.14525i	0.384142	+	0.279096i	−0.378909	+	0.925434i	$0.623701\pi$
$128$	0.0244055	−	0.0751123i	0.00215716	−	0.00663906i
$129$	−2.57601	−	7.92814i	−0.226805	−	0.698034i
$130$	−5.55566	+	4.03643i	−0.487264	+	0.354018i
$131$	13.9811			1.22154			0.610769	−	0.791809i	$-0.290861\pi$
$131$	13.9811			1.22154			0.610769	+	0.791809i	$0.290861\pi$
$132$	6.47700	+	1.35332i	0.563750	+	0.117791i
$133$	−14.6225			−1.26793
$134$	−3.58885	+	2.60745i	−0.310029	+	0.225250i
$135$	−1.06169	−	3.26756i	−0.0913760	−	0.281226i
$136$	−0.0103281	+	0.0317866i	−0.000885625	+	0.00272567i
$137$	0.759685	+	0.551944i	0.0649043	+	0.0471557i	0.619764	−	0.784788i	$-0.287228\pi$
$137$	0.759685	+	0.551944i	0.0649043	+	0.0471557i	−0.554860	+	0.831944i	$0.687228\pi$
$138$	−6.99419	−	5.08158i	−0.595385	−	0.432573i
$139$	2.65279	−	8.16444i	0.225006	−	0.692499i	−0.773284	−	0.634059i	$-0.781388\pi$
$139$	2.65279	−	8.16444i	0.225006	−	0.692499i	0.998291	−	0.0584395i	$-0.0186125\pi$
$140$	8.63532	+	26.5768i	0.729818	+	2.24615i
$141$	7.03061	−	5.10803i	0.592084	−	0.430174i
$142$	−21.8078			−1.83007
$143$	3.02520	−	1.35947i	0.252980	−	0.113685i
$144$	−4.00985			−0.334154
$145$	24.0844	−	17.4983i	2.00010	−	1.45316i
$146$	1.15789	+	3.56363i	0.0958281	+	0.294928i
$147$	2.97292	−	9.14972i	0.245203	−	0.754656i
$148$	−2.91787	−	2.11996i	−0.239847	−	0.174259i
$149$	−13.6546	−	9.92066i	−1.11863	−	0.812732i	−0.134629	−	0.990896i	$-0.542984\pi$
$149$	−13.6546	−	9.92066i	−1.11863	−	0.812732i	−0.984001	+	0.178164i	$0.942984\pi$
$150$	4.20258	−	12.9342i	0.343139	−	1.05607i
$151$	−2.76801	−	8.51905i	−0.225257	−	0.693270i	−0.998265	−	0.0588744i	$-0.981249\pi$
$151$	−2.76801	−	8.51905i	−0.225257	−	0.693270i	0.773008	−	0.634396i	$-0.218751\pi$
$152$	0.0286466	−	0.0208130i	0.00232354	−	0.00168815i
$153$	3.38548			0.273700
$154$	−2.91799	−	26.8680i	−0.235138	−	2.16508i
$155$	−10.5754			−0.849435
$156$	1.61404	−	1.17267i	0.129226	−	0.0938885i
$157$	3.17496	+	9.77153i	0.253390	+	0.779853i	0.994143	+	0.108076i	$0.0344689\pi$
$157$	3.17496	+	9.77153i	0.253390	+	0.779853i	−0.740753	+	0.671777i	$0.765531\pi$
$158$	−0.754908	+	2.32337i	−0.0600573	+	0.184837i
$159$	−9.29785	−	6.75528i	−0.737367	−	0.535729i
$160$	−22.2225	−	16.1456i	−1.75684	−	1.27642i
$161$	−5.44909	+	16.7706i	−0.429448	+	1.32171i
$162$	0.617652	+	1.90094i	0.0485273	+	0.149352i
$163$	−8.92941	+	6.48759i	−0.699405	+	0.508148i	−0.879738	−	0.475458i	$-0.842282\pi$
$163$	−8.92941	+	6.48759i	−0.699405	+	0.508148i	0.180333	+	0.983606i	$0.442282\pi$
$164$	−2.88100			−0.224968
$165$	−5.66330	+	9.88799i	−0.440887	+	0.769779i
$166$	−29.5963			−2.29712
$167$	18.2943	−	13.2916i	1.41565	−	1.02853i	0.423183	−	0.906044i	$-0.360913\pi$
$167$	18.2943	−	13.2916i	1.41565	−	1.02853i	0.992470	−	0.122488i	$-0.0390872\pi$
$168$	0.0124372	+	0.0382777i	0.000959549	+	0.00295319i
$169$	0.309017	−	0.951057i	0.0237705	−	0.0731582i
$170$	18.8086	+	13.6653i	1.44255	+	1.04808i
$171$	−2.90173	−	2.10823i	−0.221901	−	0.161220i
$172$	−5.13929	+	15.8171i	−0.391868	+	1.20604i
$173$	−2.21740	−	6.82445i	−0.168586	−	0.518853i	0.830697	−	0.556725i	$-0.187942\pi$
$173$	−2.21740	−	6.82445i	−0.168586	−	0.518853i	−0.999283	+	0.0378717i	$0.987942\pi$
$174$	−14.0114	+	10.1798i	−1.06220	+	0.771732i
$175$	−27.7393			−2.09689
$176$	8.93304	+	9.85236i	0.673353	+	0.742650i
$177$	12.6459			0.950526
$178$	−16.3488	+	11.8781i	−1.22539	+	0.890301i
$179$	0.684051	+	2.10529i	0.0511283	+	0.157357i	0.973361	−	0.229279i	$-0.0736369\pi$
$179$	0.684051	+	2.10529i	0.0511283	+	0.157357i	−0.922232	+	0.386636i	$0.873637\pi$
$180$	−2.11814	+	6.51897i	−0.157877	+	0.485896i
$181$	14.6109	+	10.6154i	1.08602	+	0.789037i	0.978722	−	0.205190i	$-0.0657812\pi$
$181$	14.6109	+	10.6154i	1.08602	+	0.789037i	0.107295	+	0.994227i	$0.465781\pi$
$182$	−6.59238	−	4.78965i	−0.488660	−	0.355032i
$183$	1.17117	−	3.60449i	0.0865754	−	0.266452i
$184$	−0.0131952	−	0.0406107i	−0.000972765	−	0.00299386i
$185$	5.02489	−	3.65080i	0.369437	−	0.268412i
$186$	6.15235			0.451112
$187$	−7.54209	−	8.31826i	−0.551532	−	0.608291i
$188$	−17.3377			−1.26448
$189$	3.29823	−	2.39630i	0.239911	−	0.174305i
$190$	−7.61131	−	23.4252i	−0.552183	−	1.69944i
$191$	2.69251	−	8.28669i	0.194823	−	0.599604i	−0.805155	−	0.593064i	$-0.797918\pi$
$191$	2.69251	−	8.28669i	0.194823	−	0.599604i	0.999979	−	0.00654021i	$-0.00208183\pi$
$192$	6.44013	+	4.67903i	0.464776	+	0.337680i
$193$	7.53342	+	5.47335i	0.542267	+	0.393980i	0.824926	−	0.565240i	$-0.191217\pi$
$193$	7.53342	+	5.47335i	0.542267	+	0.393980i	−0.282659	+	0.959220i	$0.591217\pi$
$194$	4.96786	−	15.2895i	0.356671	−	1.09772i
$195$	1.06169	+	3.26756i	0.0760294	+	0.233995i
$196$	−15.5280	+	11.2817i	−1.10914	+	0.805839i
$197$	−22.9741			−1.63684			−0.818419	−	0.574621i	$-0.805149\pi$
$197$	−22.9741			−1.63684			−0.818419	+	0.574621i	$0.805149\pi$
$198$	3.29469	−	5.75245i	0.234143	−	0.408809i
$199$	−6.35697			−0.450633			−0.225317	−	0.974286i	$-0.572342\pi$
$199$	−6.35697			−0.450633			−0.225317	+	0.974286i	$0.572342\pi$
$200$	0.0543432	−	0.0394827i	0.00384265	−	0.00279185i
$201$	0.685833	+	2.11078i	0.0483749	+	0.148883i
$202$	7.54653	−	23.2258i	0.530972	−	1.63416i
$203$	28.5786	+	20.7636i	2.00583	+	1.45732i
$204$	−5.46430	−	3.97005i	−0.382578	−	0.277959i
$205$	1.53315	−	4.71856i	0.107080	−	0.329559i
$206$	3.63060	+	11.1738i	0.252956	+	0.778518i
$207$	−3.49926	+	2.54236i	−0.243215	+	0.176706i
$208$	4.00985			0.278033
$209$	1.28439	+	11.8263i	0.0888431	+	0.818042i
$210$	27.9964			1.93193
$211$	−3.62844	+	2.63622i	−0.249792	+	0.181485i	−0.705635	−	0.708576i	$-0.749338\pi$
$211$	−3.62844	+	2.63622i	−0.249792	+	0.181485i	0.455842	+	0.890061i	$0.349338\pi$
$212$	7.08538	+	21.8066i	0.486626	+	1.49768i
$213$	−3.37157	+	10.3766i	−0.231016	+	0.710994i
$214$	−26.0970	−	18.9606i	−1.78395	−	1.29612i
$215$	−23.1707	−	16.8345i	−1.58023	−	1.14810i
$216$	−0.00305069	+	0.00938907i	−0.000207573	+	0.000638845i
$217$	−3.87780	−	11.9346i	−0.263242	−	0.810175i
$218$	−15.2060	+	11.0478i	−1.02988	+	0.748253i
$219$	1.87467			0.126679
$220$	20.7361	−	9.31843i	1.39803	−	0.628248i
$221$	−3.38548			−0.227732
$222$	−2.92329	+	2.12389i	−0.196198	+	0.142546i
$223$	5.07197	+	15.6099i	0.339645	+	1.04532i	0.964389	+	0.264489i	$0.0852033\pi$
$223$	5.07197	+	15.6099i	0.339645	+	1.04532i	−0.624744	+	0.780830i	$0.714797\pi$
$224$	10.0722	−	30.9991i	0.672978	−	2.07121i
$225$	−5.50464	−	3.99936i	−0.366976	−	0.266624i
$226$	18.1561	+	13.1912i	1.20772	+	0.877462i
$227$	−5.41481	+	16.6651i	−0.359394	+	1.10610i	0.594024	+	0.804447i	$0.297538\pi$
$227$	−5.41481	+	16.6651i	−0.359394	+	1.10610i	−0.953418	+	0.301653i	$0.902462\pi$
$228$	2.21125	+	6.80552i	0.146443	+	0.450706i
$229$	−4.55207	+	3.30727i	−0.300809	+	0.218551i	−0.727943	−	0.685638i	$-0.759523\pi$
$229$	−4.55207	+	3.30727i	−0.300809	+	0.218551i	0.427134	+	0.904189i	$0.359523\pi$
$230$	−29.7028			−1.95854
$231$	−13.2355	−	2.76545i	−0.870833	−	0.181954i
$232$	−0.0855415			−0.00561608
$233$	13.0937	−	9.51310i	0.857795	−	0.623224i	−0.0694895	−	0.997583i	$-0.522137\pi$
$233$	13.0937	−	9.51310i	0.857795	−	0.623224i	0.927284	+	0.374358i	$0.122137\pi$
$234$	−0.617652	−	1.90094i	−0.0403772	−	0.124268i
$235$	9.22644	−	28.3961i	0.601867	−	1.85236i
$236$	−20.4110	−	14.8295i	−1.32864	−	0.965316i
$237$	0.988798	+	0.718404i	0.0642294	+	0.0466654i
$238$	−8.52487	+	26.2369i	−0.552586	+	1.70068i
$239$	4.19715	+	12.9175i	0.271491	+	0.835564i	0.990127	+	0.140177i	$0.0447670\pi$
$239$	4.19715	+	12.9175i	0.271491	+	0.835564i	−0.718635	+	0.695387i	$0.755233\pi$
$240$	−11.1456	+	8.09774i	−0.719444	+	0.522707i
$241$	23.8962			1.53929			0.769645	−	0.638472i	$-0.220433\pi$
$241$	23.8962			1.53929			0.769645	+	0.638472i	$0.220433\pi$
$242$	−21.4738	+	4.71998i	−1.38039	+	0.303412i
$243$	1.00000			0.0641500
$244$	−6.11718	+	4.44439i	−0.391612	+	0.284523i
$245$	−10.2141	−	31.4358i	−0.652556	−	2.00836i
$246$	−0.891930	+	2.74508i	−0.0568674	+	0.175020i
$247$	2.90173	+	2.10823i	0.184632	+	0.134143i
$248$	0.0245840	+	0.0178614i	0.00156109	+	0.00113420i
$249$	−4.57570	+	14.0826i	−0.289974	+	0.892447i
$250$	−3.82847	−	11.7828i	−0.242133	−	0.745210i
$251$	−9.12030	+	6.62629i	−0.575668	+	0.418248i	−0.837160	−	0.546958i	$-0.815786\pi$
$251$	−9.12030	+	6.62629i	−0.575668	+	0.418248i	0.261491	+	0.965206i	$0.415786\pi$
$252$	−8.13353			−0.512364
$253$	14.0422	+	2.93401i	0.882827	+	0.184460i
$254$	−10.6954			−0.671091
$255$	9.41012	−	6.83685i	0.589285	−	0.428140i
$256$	4.96860	+	15.2918i	0.310538	+	0.955737i
$257$	0.0137476	−	0.0423108i	0.000857552	−	0.00263927i	−0.950627	−	0.310336i	$-0.899558\pi$
$257$	0.0137476	−	0.0423108i	0.000857552	−	0.00263927i	0.951484	+	0.307697i	$0.0995583\pi$
$258$	13.4798	+	9.79367i	0.839217	+	0.609727i
$259$	5.96256	+	4.33206i	0.370496	+	0.269181i
$260$	2.11814	−	6.51897i	0.131362	−	0.404290i
$261$	2.67758	+	8.24076i	0.165738	+	0.510090i
$262$	−22.6080	+	16.4257i	−1.39673	+	1.01478i
$263$	−29.8568			−1.84105			−0.920523	−	0.390688i	$-0.872237\pi$
$263$	−29.8568			−1.84105			−0.920523	+	0.390688i	$0.872237\pi$
$264$	0.0298656	−	0.0134210i	0.00183810	−	0.000826008i
$265$	−39.4858			−2.42560
$266$	23.6451	−	17.1792i	1.44977	−	1.05332i
$267$	3.12427	+	9.61552i	0.191202	+	0.588460i
$268$	1.36828	−	4.21113i	0.0835809	−	0.257236i
$269$	−22.6762	−	16.4753i	−1.38259	−	1.00451i	−0.996632	−	0.0819992i	$-0.973869\pi$
$269$	−22.6762	−	16.4753i	−1.38259	−	1.00451i	−0.385962	−	0.922515i	$-0.626131\pi$
$270$	5.55566	+	4.03643i	0.338107	+	0.245649i
$271$	−7.37220	+	22.6893i	−0.447829	+	1.37828i	0.431522	+	0.902102i	$0.357977\pi$
$271$	−7.37220	+	22.6893i	−0.447829	+	1.37828i	−0.879351	+	0.476174i	$0.842023\pi$
$272$	−4.19500	−	12.9109i	−0.254359	−	0.782837i
$273$	−3.29823	+	2.39630i	−0.199618	+	0.145031i
$274$	−1.87689			−0.113387
$275$	2.43652	+	22.4348i	0.146928	+	1.35287i
$276$	8.62928			0.519421
$277$	7.94050	−	5.76911i	0.477099	−	0.346632i	−0.323103	−	0.946364i	$-0.604726\pi$
$277$	7.94050	−	5.76911i	0.477099	−	0.346632i	0.800201	+	0.599731i	$0.204726\pi$
$278$	5.30230	+	16.3188i	0.318011	+	0.978736i
$279$	0.951178	−	2.92742i	0.0569455	−	0.175260i
$280$	0.111870	+	0.0812783i	0.00668551	+	0.00485731i
$281$	2.25865	+	1.64100i	0.134740	+	0.0978940i	0.653113	−	0.757260i	$-0.273462\pi$
$281$	2.25865	+	1.64100i	0.134740	+	0.0978940i	−0.518374	+	0.855154i	$0.673462\pi$
$282$	−5.36759	+	16.5197i	−0.319635	+	0.983736i
$283$	1.74620	+	5.37426i	0.103801	+	0.319467i	0.989447	−	0.144894i	$-0.0462841\pi$
$283$	1.74620	+	5.37426i	0.103801	+	0.319467i	−0.885646	+	0.464361i	$0.846284\pi$
$284$	17.6102	−	12.7945i	1.04497	−	0.759216i
$285$	−12.3230			−0.729950
$286$	−3.29469	+	5.75245i	−0.194819	+	0.340150i
$287$	5.88722			0.347511
$288$	6.46810	−	4.69935i	0.381136	−	0.276912i
$289$	−1.71149	−	5.26742i	−0.100676	−	0.309848i
$290$	−18.3875	+	56.5908i	−1.07975	+	3.32312i
$291$	−6.50703	−	4.72763i	−0.381449	−	0.277139i
$292$	−3.02579	−	2.19837i	−0.177071	−	0.128650i
$293$	−0.918351	+	2.82639i	−0.0536507	+	0.165120i	−0.974292	−	0.225291i	$-0.927667\pi$
$293$	−0.918351	+	2.82639i	−0.0536507	+	0.165120i	0.920641	+	0.390410i	$0.127667\pi$
$294$	5.94218	+	18.2881i	0.346555	+	1.06659i
$295$	35.1500	−	25.5379i	2.04651	−	1.48688i
$296$	−0.0178471			−0.00103734
$297$	−2.22777	−	2.45704i	−0.129268	−	0.142572i
$298$	33.7352			1.95423
$299$	3.49926	−	2.54236i	0.202367	−	0.147028i
$300$	4.19479	+	12.9102i	0.242186	+	0.745373i
$301$	10.5020	−	32.3217i	0.605323	−	1.86299i
$302$	14.4845	+	10.5236i	0.833491	+	0.605566i
$303$	−9.88464	−	7.18161i	−0.567858	−	0.412573i
$304$	−4.44436	+	13.6783i	−0.254902	+	0.784507i
$305$	−4.02380	−	12.3840i	−0.230402	−	0.709105i
$306$	−5.47445	+	3.97742i	−0.312953	+	0.227374i
$307$	7.61899			0.434839			0.217419	−	0.976078i	$-0.430236\pi$
$307$	7.61899			0.434839			0.217419	+	0.976078i	$0.430236\pi$
$308$	18.1197	+	19.9844i	1.03246	+	1.13872i
$309$	5.87806			0.334391
$310$	17.1008	−	12.4244i	0.971258	−	0.705660i
$311$	−1.55371	−	4.78182i	−0.0881027	−	0.271152i	0.897292	−	0.441437i	$-0.145531\pi$
$311$	−1.55371	−	4.78182i	−0.0881027	−	0.271152i	−0.985395	+	0.170285i	$0.945531\pi$
$312$	0.00305069	−	0.00938907i	0.000172712	−	0.000531552i
$313$	−18.9563	−	13.7726i	−1.07147	−	0.778471i	−0.0952969	−	0.995449i	$-0.530380\pi$
$313$	−18.9563	−	13.7726i	−1.07147	−	0.778471i	−0.976177	+	0.216978i	$0.930380\pi$
$314$	−16.6141	−	12.0708i	−0.937585	−	0.681196i
$315$	4.32835	−	13.3213i	0.243875	−	0.750569i
$316$	−0.753509	−	2.31906i	−0.0423882	−	0.130458i
$317$	10.4319	−	7.57921i	0.585913	−	0.425691i	−0.254938	−	0.966957i	$-0.582055\pi$
$317$	10.4319	−	7.57921i	0.585913	−	0.425691i	0.840851	+	0.541267i	$0.182055\pi$
$318$	22.9713			1.28817
$319$	14.2828	−	24.9375i	0.799683	−	1.39623i
$320$	27.3498			1.52890
$321$	−13.0566	+	9.48615i	−0.728747	+	0.529465i
$322$	−10.8914	−	33.5204i	−0.606956	−	1.86802i
$323$	3.75234	−	11.5485i	0.208786	−	0.642576i
$324$	−1.61404	−	1.17267i	−0.0896688	−	0.0651482i
$325$	5.50464	+	3.99936i	0.305343	+	0.221844i
$326$	6.81725	−	20.9813i	0.377572	−	1.16205i
$327$	2.90588	+	8.94339i	0.160696	+	0.494571i
$328$	−0.0115335	+	0.00837957i	−0.000636831	+	0.000462684i
$329$	35.4290			1.95326
$330$	−2.45910	−	22.6427i	−0.135369	−	1.24644i
$331$	14.0472			0.772104			0.386052	−	0.922477i	$-0.373839\pi$
$331$	14.0472			0.772104			0.386052	+	0.922477i	$0.373839\pi$
$332$	23.8995	−	17.3640i	1.31166	−	0.952975i
$333$	0.558643	+	1.71933i	0.0306135	+	0.0942185i
$334$	−13.9669	+	42.9858i	−0.764237	+	2.35208i
$335$	6.16894	+	4.48200i	0.337045	+	0.244878i
$336$	−13.2254	−	9.60883i	−0.721506	−	0.524205i
$337$	10.6459	−	32.7648i	0.579921	−	1.78481i	−0.0388536	−	0.999245i	$-0.512371\pi$
$337$	10.6459	−	32.7648i	0.579921	−	1.78481i	0.618775	−	0.785569i	$-0.287629\pi$
$338$	0.617652	+	1.90094i	0.0335959	+	0.103397i
$339$	9.08364	−	6.59965i	0.493356	−	0.358444i
$340$	−23.2056			−1.25850
$341$	−9.31180	+	4.18455i	−0.504262	+	0.226606i
$342$	7.16903			0.387657
$343$	8.64329	−	6.27972i	0.466694	−	0.339073i
$344$	0.0254310	+	0.0782686i	0.00137115	+	0.00421996i
$345$	−4.59216	+	14.1332i	−0.247234	+	0.760907i
$346$	11.6033	+	8.43027i	0.623796	+	0.453214i
$347$	7.48485	+	5.43806i	0.401808	+	0.291930i	0.770277	−	0.637710i	$-0.220118\pi$
$347$	7.48485	+	5.43806i	0.401808	+	0.291930i	−0.368469	+	0.929640i	$0.620118\pi$
$348$	5.34194	−	16.4408i	0.286358	−	0.881320i
$349$	−1.98505	−	6.10935i	−0.106257	−	0.327026i	0.883766	−	0.467929i	$-0.155000\pi$
$349$	−1.98505	−	6.10935i	−0.106257	−	0.327026i	−0.990023	+	0.140903i	$0.955000\pi$
$350$	44.8553	−	32.5893i	2.39762	−	1.74197i
$351$	−1.00000			−0.0533761
$352$	−25.9559	−	5.42328i	−1.38346	−	0.289062i
$353$	28.3157			1.50709			0.753546	−	0.657395i	$-0.228342\pi$
$353$	28.3157			1.50709			0.753546	+	0.657395i	$0.228342\pi$
$354$	−20.4489	+	14.8570i	−1.08685	+	0.789640i
$355$	11.5837	+	35.6511i	0.614801	+	1.89216i
$356$	6.23311	−	19.1836i	0.330354	−	1.01673i
$357$	11.1661	+	8.11265i	0.590973	+	0.429367i
$358$	−3.57952	−	2.60068i	−0.189184	−	0.137450i
$359$	−6.66275	+	20.5058i	−0.351646	+	1.08226i	0.606282	+	0.795249i	$0.292660\pi$
$359$	−6.66275	+	20.5058i	−0.351646	+	1.08226i	−0.957929	+	0.287007i	$0.907340\pi$
$360$	0.0104813	+	0.0322581i	0.000552413	+	0.00170015i
$361$	4.96361	−	3.60628i	0.261243	−	0.189804i
$362$	−36.0977			−1.89725
$363$	−1.07407	+	10.9474i	−0.0563738	+	0.574591i
$364$	8.13353			0.426313
$365$	5.21074	−	3.78582i	0.272743	−	0.198159i
$366$	2.34089	+	7.20453i	0.122360	+	0.376587i
$367$	5.19139	−	15.9775i	0.270988	−	0.834016i	−0.719265	−	0.694736i	$-0.755521\pi$
$367$	5.19139	−	15.9775i	0.270988	−	0.834016i	0.990253	−	0.139280i	$-0.0444788\pi$
$368$	14.0315	+	10.1945i	0.731443	+	0.531425i
$369$	1.16827	+	0.848800i	0.0608179	+	0.0441868i
$370$	−3.83630	+	11.8069i	−0.199440	+	0.613813i
$371$	−14.4787	−	44.5609i	−0.751698	−	2.31349i
$372$	−4.96813	+	3.60956i	−0.257586	+	0.187147i
$373$	17.4598			0.904035			0.452017	−	0.892009i	$-0.350705\pi$
$373$	17.4598			0.904035			0.452017	+	0.892009i	$0.350705\pi$
$374$	21.9685	+	4.59014i	1.13596	+	0.237350i
$375$	−6.19842			−0.320085
$376$	−0.0694079	+	0.0504278i	−0.00357944	+	0.00260062i
$377$	−2.67758	−	8.24076i	−0.137903	−	0.424421i
$378$	−2.51807	+	7.74981i	−0.129515	+	0.398607i
$379$	−25.8184	−	18.7581i	−1.32620	−	0.963541i	−0.999833	−	0.0182987i	$-0.994175\pi$
$379$	−25.8184	−	18.7581i	−1.32620	−	0.963541i	−0.326368	−	0.945243i	$-0.605825\pi$
$380$	19.8897	+	14.4507i	1.02032	+	0.741308i
$381$	−1.65356	+	5.08912i	−0.0847142	+	0.260724i
$382$	5.38169	+	16.5631i	0.275351	+	0.847444i
$383$	−6.87201	+	4.99281i	−0.351143	+	0.255121i	−0.749349	−	0.662176i	$-0.769633\pi$
$383$	−6.87201	+	4.99281i	−0.351143	+	0.255121i	0.398205	+	0.917296i	$0.369633\pi$
$384$	0.0789778			0.00403032
$385$	−42.3735	+	19.0419i	−2.15955	+	0.970464i
$386$	−18.6121			−0.947333
$387$	6.74408	−	4.89986i	0.342821	−	0.249074i
$388$	4.95865	+	15.2612i	0.251737	+	0.774768i
$389$	−7.65150	+	23.5489i	−0.387947	+	1.19398i	0.546374	+	0.837542i	$0.316008\pi$
$389$	−7.65150	+	23.5489i	−0.387947	+	1.19398i	−0.934320	+	0.356435i	$0.883992\pi$
$390$	−5.55566	−	4.03643i	−0.281322	−	0.204392i
$391$	−11.8467	−	8.60712i	−0.599112	−	0.435281i
$392$	−0.0293495	+	0.0903284i	−0.00148237	+	0.00456227i
$393$	4.32041	+	13.2968i	0.217936	+	0.670737i
$394$	37.1500	−	26.9910i	1.87159	−	1.35979i
$395$	4.19920			0.211285
$396$	0.714421	+	6.57819i	0.0359010	+	0.330566i
$397$	−6.48408			−0.325427			−0.162713	−	0.986673i	$-0.552025\pi$
$397$	−6.48408			−0.325427			−0.162713	+	0.986673i	$0.552025\pi$
$398$	10.2794	−	7.46845i	0.515262	−	0.374359i
$399$	−4.51860	−	13.9068i	−0.226213	−	0.696212i
$400$	−8.43107	+	25.9482i	−0.421553	+	1.29741i
$401$	−28.1105	−	20.4235i	−1.40377	−	1.01990i	−0.994191	−	0.107626i	$-0.965675\pi$
$401$	−28.1105	−	20.4235i	−1.40377	−	1.01990i	−0.409580	−	0.912274i	$-0.634325\pi$
$402$	−3.58885	−	2.60745i	−0.178996	−	0.130048i
$403$	−0.951178	+	2.92742i	−0.0473815	+	0.145825i
$404$	7.53255	+	23.1828i	0.374758	+	1.15339i
$405$	2.77955	−	2.01946i	0.138117	−	0.100348i
$406$	−70.6067			−3.50415
$407$	2.97992	−	5.20288i	0.147709	−	0.257897i
$408$	−0.0334224			−0.00165465
$409$	−26.4872	+	19.2441i	−1.30971	+	0.951559i	−0.309709	+	0.950832i	$0.600232\pi$
$409$	−26.4872	+	19.2441i	−1.30971	+	0.951559i	−1.00000		0.000727318i	$0.999768\pi$
$410$	3.06441	+	9.43130i	0.151341	+	0.465779i
$411$	−0.290174	+	0.893064i	−0.0143132	+	0.0440516i
$412$	−9.48742	−	6.89301i	−0.467412	−	0.339594i
$413$	41.7092	+	30.3035i	2.05237	+	1.49114i
$414$	2.67154	−	8.22217i	0.131299	−	0.404097i
$415$	15.7208	+	48.3837i	0.771704	+	2.37506i
$416$	−6.46810	+	4.69935i	−0.317125	+	0.230405i
$417$	8.58460			0.420390
$418$	−15.9710	−	17.6146i	−0.781165	−	0.861557i
$419$	−33.0385			−1.61404			−0.807019	−	0.590526i	$-0.798920\pi$
$419$	−33.0385			−1.61404			−0.807019	+	0.590526i	$0.798920\pi$
$420$	−22.6076	+	16.4254i	−1.10314	+	0.801475i
$421$	−6.67060	−	20.5300i	−0.325105	−	1.00057i	−0.971393	−	0.237477i	$-0.923679\pi$
$421$	−6.67060	−	20.5300i	−0.325105	−	1.00057i	0.646288	−	0.763094i	$-0.276321\pi$
$422$	2.77017	−	8.52572i	0.134850	−	0.415025i
$423$	7.03061	+	5.10803i	0.341840	+	0.248361i
$424$	0.0917907	+	0.0666898i	0.00445775	+	0.00323874i
$425$	7.11827	−	21.9078i	0.345287	−	1.06268i
$426$	−6.73897	−	20.7404i	−0.326504	−	1.00488i
$427$	12.5002	−	9.08196i	0.604929	−	0.439507i
$428$	32.1979			1.55634
$429$	2.22777	+	2.45704i	0.107558	+	0.118627i
$430$	57.2458			2.76064
$431$	11.6433	−	8.45936i	0.560839	−	0.407473i	−0.270927	−	0.962600i	$-0.587330\pi$
$431$	11.6433	−	8.45936i	0.560839	−	0.407473i	0.831766	+	0.555127i	$0.187330\pi$
$432$	−1.23911	−	3.81360i	−0.0596169	−	0.183482i
$433$	−5.17112	+	15.9151i	−0.248508	+	0.764830i	0.746531	+	0.665350i	$0.231718\pi$
$433$	−5.17112	+	15.9151i	−0.248508	+	0.764830i	−0.995040	+	0.0994797i	$0.968282\pi$
$434$	20.2919	+	14.7429i	0.974040	+	0.707682i
$435$	24.0844	+	17.4983i	1.15476	+	0.838980i
$436$	5.79742	−	17.8426i	0.277646	−	0.854506i
$437$	4.79401	+	14.7545i	0.229329	+	0.705802i
$438$	−3.03141	+	2.20245i	−0.144846	+	0.105237i
$439$	−8.29724			−0.396006			−0.198003	−	0.980201i	$-0.563446\pi$
$439$	−8.29724			−0.396006			−0.198003	+	0.980201i	$0.563446\pi$
$440$	0.0559095	−	0.0976167i	0.00266538	−	0.00465370i
$441$	9.62059			0.458123
$442$	5.47445	−	3.97742i	0.260393	−	0.189186i
$443$	−3.61025	−	11.1112i	−0.171528	−	0.527909i	0.827930	−	0.560831i	$-0.189518\pi$
$443$	−3.61025	−	11.1112i	−0.171528	−	0.527909i	−0.999458	+	0.0329228i	$0.989518\pi$
$444$	1.11453	−	3.43016i	0.0528931	−	0.162788i
$445$	28.1022	+	20.4175i	1.33217	+	0.967881i
$446$	−26.5408	−	19.2830i	−1.25674	−	0.913078i
$447$	5.21560	−	16.0520i	0.246689	−	0.759232i
$448$	10.0287	+	30.8650i	0.473809	+	1.45823i
$449$	−22.0396	+	16.0127i	−1.04012	+	0.755688i	−0.970308	−	0.241872i	$-0.922238\pi$
$449$	−22.0396	+	16.0127i	−1.04012	+	0.755688i	−0.0698073	+	0.997560i	$0.522238\pi$
$450$	13.5998			0.641102
$451$	−0.517113	−	4.76142i	−0.0243499	−	0.224207i
$452$	−22.4005			−1.05363
$453$	7.24674	−	5.26506i	0.340481	−	0.247374i
$454$	−10.8229	−	33.3096i	−0.507946	−	1.56330i
$455$	−4.32835	+	13.3213i	−0.202916	+	0.624512i
$456$	0.0286466	+	0.0208130i	0.00134150	+	0.000974656i
$457$	3.27002	+	2.37581i	0.152965	+	0.111136i	0.661635	−	0.749826i	$-0.269863\pi$
$457$	3.27002	+	2.37581i	0.152965	+	0.111136i	−0.508670	+	0.860962i	$0.669863\pi$
$458$	3.47532	−	10.6960i	0.162391	−	0.499789i
$459$	1.04617	+	3.21979i	0.0488311	+	0.150287i
$460$	23.9855	−	17.4265i	1.11833	−	0.812514i
$461$	0.384811			0.0179224			0.00896122	−	0.999960i	$-0.497148\pi$
$461$	0.384811			0.0179224			0.00896122	+	0.999960i	$0.497148\pi$
$462$	24.6513	−	11.0778i	1.14688	−	0.515387i
$463$	−17.0160			−0.790799			−0.395399	−	0.918509i	$-0.629394\pi$
$463$	−17.0160			−0.790799			−0.395399	+	0.918509i	$0.629394\pi$
$464$	28.1091	−	20.4225i	1.30493	−	0.948089i
$465$	−3.26797	−	10.0578i	−0.151549	−	0.466419i
$466$	−9.99649	+	30.7660i	−0.463079	+	1.42521i
$467$	−19.5885	−	14.2319i	−0.906447	−	0.658572i	0.0336671	−	0.999433i	$-0.489281\pi$
$467$	−19.5885	−	14.2319i	−0.906447	−	0.658572i	−0.940114	+	0.340861i	$0.889281\pi$
$468$	1.61404	+	1.17267i	0.0746089	+	0.0542066i
$469$	−2.79603	+	8.60529i	−0.129109	+	0.397355i
$470$	18.4415	+	56.7571i	0.850642	+	2.61801i
$471$	−8.31216	+	6.03914i	−0.383004	+	0.278269i
$472$	−0.124844			−0.00574640
$473$	−27.0634	−	5.65468i	−1.24438	−	0.260003i
$474$	−2.44293			−0.112208
$475$	−19.7437	+	14.3446i	−0.905902	+	0.658176i
$476$	−8.50908	−	26.1882i	−0.390013	−	1.20034i
$477$	3.55146	−	10.9303i	0.162610	−	0.500463i
$478$	−21.9630	−	15.9570i	−1.00456	−	0.729858i
$479$	20.4966	+	14.8916i	0.936513	+	0.680416i	0.947579	−	0.319523i	$-0.103523\pi$
$479$	20.4966	+	14.8916i	0.936513	+	0.680416i	−0.0110661	+	0.999939i	$0.503523\pi$
$480$	8.48825	−	26.1241i	0.387434	−	1.19240i
$481$	−0.558643	−	1.71933i	−0.0254719	−	0.0783946i
$482$	−38.6410	+	28.0743i	−1.76005	+	1.27875i
$483$	−17.6336			−0.802357
$484$	14.5713	−	16.4101i	0.662331	−	0.745912i
$485$	−27.6339			−1.25479
$486$	−1.61703	+	1.17484i	−0.0733502	+	0.0532920i
$487$	12.9548	+	39.8707i	0.587036	+	1.80671i	0.590935	+	0.806719i	$0.298759\pi$
$487$	12.9548	+	39.8707i	0.587036	+	1.80671i	−0.00389862	+	0.999992i	$0.501241\pi$
$488$	−0.0115621	+	0.0355845i	−0.000523391	+	0.00161083i
$489$	−8.92941	−	6.48759i	−0.403802	−	0.293379i
$490$	53.4487	+	38.8328i	2.41457	+	1.75429i
$491$	0.386353	−	1.18907i	0.0174359	−	0.0536621i	−0.941960	−	0.335725i	$-0.891019\pi$
$491$	0.386353	−	1.18907i	0.0174359	−	0.0536621i	0.959396	+	0.282063i	$0.0910187\pi$
$492$	−0.890277	−	2.73999i	−0.0401368	−	0.123528i
$493$	−23.7323	+	17.2425i	−1.06885	+	0.776563i
$494$	−7.16903			−0.322550
$495$	−11.1541	−	2.33056i	−0.501339	−	0.104751i
$496$	−12.3426			−0.554201
$497$	−35.9857	+	26.1452i	−1.61418	+	1.17277i
$498$	−9.14576	−	28.1477i	−0.409831	−	1.26133i
$499$	6.92852	−	21.3238i	0.310163	−	0.954583i	−0.667537	−	0.744577i	$-0.732651\pi$
$499$	6.92852	−	21.3238i	0.310163	−	0.954583i	0.977700	−	0.210007i	$-0.0673486\pi$
$500$	10.0045	+	7.26868i	0.447414	+	0.325065i
$501$	18.2943	+	13.2916i	0.817328	+	0.593823i
$502$	6.96299	−	21.4299i	0.310773	−	0.956462i
$503$	−6.14861	−	18.9235i	−0.274153	−	0.843756i	−0.989442	−	0.144928i	$-0.953705\pi$
$503$	−6.14861	−	18.9235i	−0.274153	−	0.843756i	0.715289	−	0.698828i	$-0.246295\pi$
$504$	−0.0325610	+	0.0236569i	−0.00145038	+	0.00105376i
$505$	−41.9778			−1.86799
$506$	−26.1538	+	11.7530i	−1.16268	+	0.522486i
$507$	1.00000			0.0444116
$508$	8.63675	−	6.27496i	0.383194	−	0.278406i
$509$	−8.61010	−	26.4992i	−0.381636	−	1.17456i	−0.938891	−	0.344214i	$-0.888145\pi$
$509$	−8.61010	−	26.4992i	−0.381636	−	1.17456i	0.557255	−	0.830341i	$-0.311855\pi$
$510$	−7.18425	+	22.1109i	−0.318124	+	0.979085i
$511$	6.18309	+	4.49228i	0.273524	+	0.198727i
$512$	−25.8721	−	18.7972i	−1.14340	−	0.830725i
$513$	1.10836	−	3.41118i	0.0489353	−	0.150607i
$514$	0.0274782	+	0.0845693i	0.00121201	+	0.00373019i
$515$	16.3384	−	11.8705i	0.719954	−	0.523078i
$516$	−16.6311			−0.732144
$517$	−3.11196	−	28.6540i	−0.136864	−	1.26020i
$518$	−14.7312			−0.647250
$519$	5.80522	−	4.21774i	0.254821	−	0.185138i
$520$	−0.0104813	−	0.0322581i	−0.000459636	−	0.00141461i
$521$	7.14597	−	21.9930i	0.313071	−	0.963533i	−0.663471	−	0.748202i	$-0.730917\pi$
$521$	7.14597	−	21.9930i	0.313071	−	0.963533i	0.976541	−	0.215330i	$-0.0690828\pi$
$522$	−14.0114	−	10.1798i	−0.613260	−	0.445560i
$523$	9.47788	+	6.88608i	0.414439	+	0.301107i	0.775396	−	0.631475i	$-0.217550\pi$
$523$	9.47788	+	6.88608i	0.414439	+	0.301107i	−0.360958	+	0.932582i	$0.617550\pi$
$524$	8.61948	−	26.5280i	0.376544	−	1.15888i
$525$	−8.57190	−	26.3816i	−0.374108	−	1.15139i
$526$	48.2794	−	35.0770i	2.10508	−	1.52943i
$527$	10.4208			0.453936
$528$	−6.60969	+	11.5404i	−0.287650	+	0.502230i
$529$	−4.29161			−0.186592
$530$	63.8500	−	46.3897i	2.77347	−	2.01504i
$531$	3.90781	+	12.0270i	0.169584	+	0.521927i
$532$	−9.01489	+	27.7450i	−0.390845	+	1.20290i
$533$	−1.16827	−	0.848800i	−0.0506035	−	0.0367656i
$534$	−16.3488	−	11.8781i	−0.707482	−	0.514016i
$535$	−17.1345	+	52.7344i	−0.740787	+	2.27991i
$536$	−0.00677072	−	0.0208381i	−0.000292450	−	0.000900070i
$537$	−1.79087	+	1.30114i	−0.0772816	+	0.0561484i
$538$	56.0241			2.41537
$539$	−21.4325	−	23.6381i	−0.923162	−	1.01817i
$540$	−6.85445			−0.294969
$541$	5.64249	−	4.09951i	0.242590	−	0.176252i	−0.459846	−	0.887998i	$-0.652096\pi$
$541$	5.64249	−	4.09951i	0.242590	−	0.176252i	0.702436	+	0.711747i	$0.252096\pi$
$542$	−14.7353	−	45.3506i	−0.632935	−	1.94797i
$543$	−5.58085	+	17.1761i	−0.239497	+	0.737097i
$544$	21.8976	+	15.9096i	0.938854	+	0.682117i
$545$	26.1379	+	18.9903i	1.11962	+	0.813454i
$546$	2.51807	−	7.74981i	0.107763	−	0.331661i
$547$	−13.3640	−	41.1302i	−0.571403	−	1.75860i	−0.648112	−	0.761545i	$-0.724441\pi$
$547$	−13.3640	−	41.1302i	−0.571403	−	1.75860i	0.0767089	−	0.997054i	$-0.475559\pi$
$548$	1.51562	−	1.10116i	0.0647440	−	0.0470393i
$549$	3.78999			0.161753
$550$	−30.2973	−	33.4153i	−1.29188	−	1.42483i
$551$	31.0785			1.32399
$552$	0.0345456	−	0.0250988i	0.00147036	−	0.00106828i
$553$	1.53977	+	4.73892i	0.0654777	+	0.201519i
$554$	−6.06226	+	18.6577i	−0.257561	+	0.792690i
$555$	5.02489	+	3.65080i	0.213295	+	0.154968i
$556$	−13.8559	−	10.0669i	−0.587620	−	0.426931i
$557$	3.29868	−	10.1523i	0.139770	−	0.430167i	−0.856532	−	0.516094i	$-0.827385\pi$
$557$	3.29868	−	10.1523i	0.139770	−	0.430167i	0.996301	+	0.0859276i	$0.0273854\pi$
$558$	1.90118	+	5.85123i	0.0804834	+	0.247702i
$559$	−6.74408	+	4.89986i	−0.285244	+	0.207242i
$560$	−56.1653			−2.37342
$561$	5.58050	−	9.74343i	0.235609	−	0.411368i
$562$	−5.58023			−0.235388
$563$	11.6911	−	8.49412i	0.492723	−	0.357984i	−0.313507	−	0.949586i	$-0.601504\pi$
$563$	11.6911	−	8.49412i	0.492723	−	0.357984i	0.806231	+	0.591601i	$0.201504\pi$
$564$	−5.35764	−	16.4891i	−0.225597	−	0.694317i
$565$	11.9207	−	36.6881i	0.501507	−	1.54348i
$566$	−9.13759	−	6.63885i	−0.384082	−	0.279052i
$567$	3.29823	+	2.39630i	0.138513	+	0.100635i
$568$	0.0332850	−	0.102441i	0.00139661	−	0.00429831i
$569$	−4.71294	−	14.5049i	−0.197577	−	0.608079i	−0.999937	−	0.0112385i	$-0.996423\pi$
$569$	−4.71294	−	14.5049i	−0.197577	−	0.608079i	0.802360	−	0.596840i	$-0.203577\pi$
$570$	19.9267	−	14.4776i	0.834637	−	0.606399i
$571$	36.0697			1.50947			0.754734	−	0.656030i	$-0.227766\pi$
$571$	36.0697			1.50947			0.754734	+	0.656030i	$0.227766\pi$
$572$	−0.714421	−	6.57819i	−0.0298715	−	0.275048i
$573$	8.71314			0.363997
$574$	−9.51983	+	6.91656i	−0.397350	+	0.288692i
$575$	9.09436	+	27.9896i	0.379261	+	1.16725i
$576$	−2.45991	+	7.57083i	−0.102496	+	0.315451i
$577$	−7.74509	−	5.62714i	−0.322432	−	0.234261i	0.414780	−	0.909922i	$-0.363858\pi$
$577$	−7.74509	−	5.62714i	−0.322432	−	0.234261i	−0.737213	+	0.675661i	$0.763858\pi$
$578$	8.95594	+	6.50687i	0.372518	+	0.270650i
$579$	−2.87751	+	8.85606i	−0.119585	+	0.368045i
$580$	−18.3534	−	56.4859i	−0.762082	−	2.34545i
$581$	−48.8378	+	35.4828i	−2.02613	+	1.47207i
$582$	16.0763			0.666385
$583$	−34.7679	+	15.6241i	−1.43994	+	0.647083i
$584$	−0.0185072			−0.000765835
$585$	−2.77955	+	2.01946i	−0.114920	+	0.0834944i
$586$	−1.83557	−	5.64930i	−0.0758266	−	0.233370i
$587$	6.87072	−	21.1459i	0.283585	−	0.872785i	−0.703234	−	0.710958i	$-0.748262\pi$
$587$	6.87072	−	21.1459i	0.283585	−	0.872785i	0.986819	−	0.161826i	$-0.0517385\pi$
$588$	−15.5280	−	11.2817i	−0.640364	−	0.465251i
$589$	−8.93173	−	6.48928i	−0.368026	−	0.267386i
$590$	−26.8356	+	82.5915i	−1.10480	+	3.40024i
$591$	−7.09940	−	21.8497i	−0.292030	−	0.898776i
$592$	5.86460	−	4.26088i	0.241034	−	0.175121i
$593$	21.0222			0.863279			0.431639	−	0.902046i	$-0.357935\pi$
$593$	21.0222			0.863279			0.431639	+	0.902046i	$0.357935\pi$
$594$	6.48902	+	1.35583i	0.266248	+	0.0556303i
$595$	47.4199			1.94403
$596$	−27.2418	+	19.7923i	−1.11587	+	0.810725i
$597$	−1.96441	−	6.04584i	−0.0803980	−	0.247440i
$598$	−2.67154	+	8.22217i	−0.109248	+	0.336229i
$599$	−8.61161	−	6.25670i	−0.351861	−	0.255642i	0.397788	−	0.917477i	$-0.369778\pi$
$599$	−8.61161	−	6.25670i	−0.351861	−	0.255642i	−0.749649	+	0.661835i	$0.769778\pi$
$600$	0.0543432	+	0.0394827i	0.00221855	+	0.00161187i
$601$	−2.33295	+	7.18007i	−0.0951628	+	0.292881i	−0.987296	−	0.158891i	$-0.949208\pi$
$601$	−2.33295	+	7.18007i	−0.0951628	+	0.292881i	0.892133	+	0.451772i	$0.149208\pi$
$602$	20.9910	+	64.6035i	0.855528	+	2.63304i
$603$	−1.79553	+	1.30453i	−0.0731198	+	0.0531246i
$604$	−17.8707			−0.727148
$605$	19.1225	+	32.5980i	0.777440	+	1.32530i
$606$	24.4211			0.992039
$607$	−12.8825	+	9.35971i	−0.522886	+	0.379899i	−0.817690	−	0.575659i	$-0.804746\pi$
$607$	−12.8825	+	9.35971i	−0.522886	+	0.379899i	0.294804	+	0.955558i	$0.404746\pi$
$608$	−8.86136	−	27.2724i	−0.359375	−	1.10604i
$609$	−10.9161	+	33.5962i	−0.442341	+	1.36139i
$610$	21.0559	+	15.2980i	0.852528	+	0.619398i
$611$	−7.03061	−	5.10803i	−0.284428	−	0.206649i
$612$	2.08718	−	6.42367i	0.0843691	−	0.259661i
$613$	4.08320	+	12.5668i	0.164919	+	0.507568i	0.999030	−	0.0440280i	$-0.0140191\pi$
$613$	4.08320	+	12.5668i	0.164919	+	0.507568i	−0.834111	+	0.551596i	$0.814019\pi$
$614$	−12.3202	+	8.95112i	−0.497201	+	0.361238i
$615$	4.96139			0.200063
$616$	0.130664	+	0.0273013i	0.00526462	+	0.00110000i
$617$	15.2150			0.612531			0.306265	−	0.951946i	$-0.400920\pi$
$617$	15.2150			0.612531			0.306265	+	0.951946i	$0.400920\pi$
$618$	−9.50503	+	6.90581i	−0.382349	+	0.277792i
$619$	14.3972	+	44.3099i	0.578671	+	1.78097i	0.623324	+	0.781963i	$0.285782\pi$
$619$	14.3972	+	44.3099i	0.578671	+	1.78097i	−0.0446533	+	0.999003i	$0.514218\pi$
$620$	−6.51980	+	20.0659i	−0.261842	+	0.805866i
$621$	−3.49926	−	2.54236i	−0.140420	−	0.102021i
$622$	8.13030	+	5.90701i	0.325995	+	0.236849i
$623$	−12.7371	+	39.2009i	−0.510303	+	1.57055i
$624$	1.23911	+	3.81360i	0.0496042	+	0.152666i
$625$	10.2944	−	7.47933i	0.411777	−	0.299173i
$626$	46.8336			1.87185
$627$	−10.8506	+	4.87605i	−0.433330	+	0.194731i
$628$	20.4980			0.817961
$629$	−4.95143	+	3.59742i	−0.197426	+	0.143439i
$630$	8.65135	+	26.6261i	0.344678	+	1.06081i
$631$	−1.50627	+	4.63583i	−0.0599638	+	0.184550i	−0.976551	−	0.215284i	$-0.930932\pi$
$631$	−1.50627	+	4.63583i	−0.0599638	+	0.184550i	0.916588	+	0.399834i	$0.130932\pi$
$632$	−0.00976167	−	0.00709227i	−0.000388298	−	0.000282115i
$633$	−3.62844	−	2.63622i	−0.144218	−	0.104780i
$634$	−7.96433	+	24.5117i	−0.316304	+	0.973484i
$635$	5.68114	+	17.4847i	0.225449	+	0.693861i
$636$	−18.5498	+	13.4772i	−0.735546	+	0.534406i
$637$	−9.62059			−0.381181
$638$	6.20184	+	57.1048i	0.245533	+	2.26080i
$639$	−10.9106			−0.431618
$640$	0.219523	−	0.159493i	0.00867739	−	0.00630450i
$641$	−8.21406	−	25.2803i	−0.324436	−	0.998511i	−0.971695	−	0.236241i	$-0.924085\pi$
$641$	−8.21406	−	25.2803i	−0.324436	−	0.998511i	0.647259	−	0.762271i	$-0.275915\pi$
$642$	9.96817	−	30.6789i	0.393412	−	1.21080i
$643$	9.61884	+	6.98850i	0.379330	+	0.275599i	0.761069	−	0.648671i	$-0.224675\pi$
$643$	9.61884	+	6.98850i	0.379330	+	0.275599i	−0.381739	+	0.924270i	$0.624675\pi$
$644$	28.4613	+	20.6784i	1.12153	+	0.814842i
$645$	8.85042	−	27.2388i	0.348485	−	1.07253i
$646$	7.50004	+	23.0828i	0.295085	+	0.908179i
$647$	−13.4290	+	9.75672i	−0.527948	+	0.383576i	−0.819589	−	0.572951i	$-0.805798\pi$
$647$	−13.4290	+	9.75672i	−0.527948	+	0.383576i	0.291642	+	0.956528i	$0.405798\pi$
$648$	−0.00987225			−0.000387819
$649$	20.8451	−	36.3950i	0.818240	−	1.42863i
$650$	−13.5998			−0.533429
$651$	10.1522	−	7.37600i	0.397896	−	0.289088i
$652$	6.80461	+	20.9424i	0.266489	+	0.820170i
$653$	−1.01629	+	3.12782i	−0.0397705	+	0.122401i	−0.968971	−	0.247176i	$-0.920497\pi$
$653$	−1.01629	+	3.12782i	−0.0397705	+	0.122401i	0.929200	+	0.369577i	$0.120497\pi$
$654$	−15.2060	−	11.0478i	−0.594602	−	0.432004i
$655$	38.8612	+	28.2343i	1.51843	+	1.10321i
$656$	1.78936	−	5.50708i	0.0698628	−	0.215016i
$657$	0.579305	+	1.78292i	0.0226008	+	0.0695583i
$658$	−57.2898	+	41.6235i	−2.23339	+	1.62265i
$659$	24.0044			0.935077			0.467539	−	0.883973i	$-0.345141\pi$
$659$	24.0044			0.935077			0.467539	+	0.883973i	$0.345141\pi$
$660$	15.2702	+	16.8416i	0.594390	+	0.655560i
$661$	18.5797			0.722667			0.361333	−	0.932437i	$-0.382322\pi$
$661$	18.5797			0.722667			0.361333	+	0.932437i	$0.382322\pi$
$662$	−22.7148	+	16.5033i	−0.882836	+	0.641418i
$663$	−1.04617	−	3.21979i	−0.0406300	−	0.125046i
$664$	0.0451725	−	0.139027i	0.00175303	−	0.00539528i
$665$	−40.6440	−	29.5296i	−1.57611	−	1.14511i
$666$	−2.92329	−	2.12389i	−0.113275	−	0.0822992i
$667$	11.5814	−	35.6439i	0.448434	−	1.38014i
$668$	−13.9411	−	42.9062i	−0.539396	−	1.66009i
$669$	−13.2786	+	9.64747i	−0.513380	+	0.372993i
$670$	−15.2410			−0.588813
$671$	−8.44322	−	9.31214i	−0.325947	−	0.359491i
$672$	32.5943			1.25735
$673$	−5.43018	+	3.94526i	−0.209318	+	0.152078i	−0.687505	−	0.726180i	$-0.741294\pi$
$673$	−5.43018	+	3.94526i	−0.209318	+	0.152078i	0.478187	+	0.878258i	$0.341294\pi$
$674$	21.2787	+	65.4892i	0.819626	+	2.52255i
$675$	2.10259	−	6.47110i	0.0809286	−	0.249073i
$676$	−1.61404	−	1.17267i	−0.0620784	−	0.0451026i
$677$	−16.4393	−	11.9438i	−0.631812	−	0.459039i	0.225215	−	0.974309i	$-0.427691\pi$
$677$	−16.4393	−	11.9438i	−0.631812	−	0.459039i	−0.857028	+	0.515270i	$0.827691\pi$
$678$	−6.93500	+	21.3437i	−0.266337	+	0.819701i
$679$	−10.1328	−	31.1856i	−0.388862	−	1.19679i
$680$	−0.0928991	+	0.0674951i	−0.00356252	+	0.00258832i
$681$	−17.5227			−0.671471
$682$	10.1413	−	17.7065i	0.388330	−	0.678016i
$683$	1.93616			0.0740850			0.0370425	−	0.999314i	$-0.488206\pi$
$683$	1.93616			0.0740850			0.0370425	+	0.999314i	$0.488206\pi$
$684$	−5.78912	+	4.20604i	−0.221353	+	0.160822i
$685$	0.996954	+	3.06831i	0.0380917	+	0.117234i
$686$	−6.59881	+	20.3090i	−0.251944	+	0.775403i
$687$	−4.55207	−	3.30727i	−0.173672	−	0.126180i
$688$	−27.0428	−	19.6477i	−1.03100	−	0.749063i
$689$	−3.55146	+	10.9303i	−0.135300	+	0.416410i
$690$	−9.17865	−	28.2490i	−0.349425	−	1.07542i
$691$	−22.9426	+	16.6688i	−0.872777	+	0.634109i	−0.931331	−	0.364175i	$-0.881351\pi$
$691$	−22.9426	+	16.6688i	−0.872777	+	0.634109i	0.0585539	+	0.998284i	$0.481351\pi$
$692$	−14.3159			−0.544207
$693$	−1.45989	−	13.4423i	−0.0554568	−	0.510630i
$694$	−18.4921			−0.701952
$695$	23.8613	−	17.3363i	0.905111	−	0.657602i
$696$	−0.0264338	−	0.0813548i	−0.00100197	−	0.00308375i
$697$	−1.51074	+	4.64958i	−0.0572234	+	0.176115i
$698$	10.3874	+	7.54691i	0.393170	+	0.285655i
$699$	13.0937	+	9.51310i	0.495248	+	0.359819i
$700$	−17.1015	+	52.6329i	−0.646375	+	1.98934i
$701$	−2.81893	−	8.67577i	−0.106469	−	0.327679i	0.883603	−	0.468237i	$-0.155111\pi$
$701$	−2.81893	−	8.67577i	−0.106469	−	0.327679i	−0.990073	+	0.140557i	$0.955111\pi$
$702$	1.61703	−	1.17484i	0.0610310	−	0.0443416i
$703$	6.48412			0.244553
$704$	24.0819	−	10.8220i	0.907622	−	0.407869i
$705$	29.8574			1.12449
$706$	−45.7875	+	33.2665i	−1.72323	+	1.25200i
$707$	−15.3925	−	47.3732i	−0.578894	−	1.78165i
$708$	7.79631	−	23.9946i	0.293003	−	0.901771i
$709$	−3.65651	−	2.65661i	−0.137323	−	0.0997711i	0.517003	−	0.855984i	$-0.327048\pi$
$709$	−3.65651	−	2.65661i	−0.137323	−	0.0997711i	−0.654326	+	0.756213i	$0.727048\pi$
$710$	−60.6158	−	44.0399i	−2.27487	−	1.65279i
$711$	−0.377687	+	1.16240i	−0.0141644	+	0.0435935i
$712$	−0.0308436	−	0.0949269i	−0.00115591	−	0.00355754i
$713$	−10.7710	+	7.82558i	−0.403376	+	0.293070i
$714$	−27.5871			−1.03242
$715$	11.1541	+	2.33056i	0.417139	+	0.0871579i
$716$	4.41633			0.165046
$717$	−10.9883	+	7.98345i	−0.410365	+	0.298148i
$718$	−13.3173	−	40.9863i	−0.496996	−	1.52960i
$719$	−0.461496	+	1.42034i	−0.0172109	+	0.0529697i	−0.959293	−	0.282412i	$-0.908865\pi$
$719$	−0.461496	+	1.42034i	−0.0172109	+	0.0529697i	0.942082	+	0.335382i	$0.108865\pi$
$720$	−11.1456	−	8.09774i	−0.415371	−	0.301785i
$721$	19.3872	+	14.0856i	0.722017	+	0.524576i
$722$	−3.78952	+	11.6629i	−0.141031	+	0.434050i
$723$	7.38433	+	22.7266i	0.274626	+	0.845213i
$724$	29.1496	−	21.1784i	1.08333	−	0.787089i
$725$	58.9566			2.18959
$726$	−11.1247	−	18.9642i	−0.412878	−	0.703829i
$727$	47.6792			1.76832			0.884162	−	0.467180i	$-0.154730\pi$
$727$	47.6792			1.76832			0.884162	+	0.467180i	$0.154730\pi$
$728$	0.0325610	−	0.0236569i	0.00120679	−	0.000876784i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	−3.97819	+	12.2436i	−0.147240	+	0.453157i
$731$	22.8320	+	16.5884i	0.844471	+	0.613544i
$732$	−6.11718	−	4.44439i	−0.226098	−	0.164269i
$733$	−6.60621	+	20.3318i	−0.244006	+	0.750973i	0.751792	+	0.659400i	$0.229190\pi$
$733$	−6.60621	+	20.3318i	−0.244006	+	0.750973i	−0.995798	+	0.0915732i	$0.970810\pi$
$734$	10.3764	+	31.9352i	0.382999	+	1.17875i
$735$	26.7409	−	19.4284i	0.986353	−	0.716627i
$736$	−34.5810			−1.27467
$737$	7.20532	+	1.50550i	0.265412	+	0.0554556i
$738$	−2.88635			−0.106248
$739$	35.9796	−	26.1407i	1.32353	−	0.961602i	0.323650	−	0.946177i	$-0.395090\pi$
$739$	35.9796	−	26.1407i	1.32353	−	0.961602i	0.999881	−	0.0154249i	$-0.00491008\pi$
$740$	−3.82919	−	11.7850i	−0.140764	−	0.433227i
$741$	−1.10836	+	3.41118i	−0.0407166	+	0.125313i
$742$	75.7647	+	55.0463i	2.78141	+	2.02081i
$743$	−38.8377	−	28.2173i	−1.42482	−	1.03519i	−0.990952	−	0.134213i	$-0.957149\pi$
$743$	−38.8377	−	28.2173i	−1.42482	−	1.03519i	−0.433865	−	0.900978i	$-0.642851\pi$
$744$	−0.00939027	+	0.0289003i	−0.000344264	+	0.00105954i
$745$	−17.9193	−	55.1499i	−0.656512	−	2.02054i
$746$	−28.2331	+	20.5126i	−1.03369	+	0.751018i
$747$	−14.8073			−0.541770
$748$	−20.4330	+	9.18220i	−0.747103	+	0.335734i
$749$	−65.7952			−2.40411
$750$	10.0231	−	7.28218i	0.365990	−	0.265907i
$751$	−1.33233	−	4.10047i	−0.0486172	−	0.149628i	0.923801	−	0.382874i	$-0.125066\pi$
$751$	−1.33233	−	4.10047i	−0.0486172	−	0.149628i	−0.972418	+	0.233245i	$0.925066\pi$
$752$	10.7683	−	33.1413i	0.392679	−	1.20854i
$753$	−9.12030	−	6.62629i	−0.332362	−	0.241475i
$754$	14.0114	+	10.1798i	0.510263	+	0.370728i
$755$	9.51007	−	29.2690i	0.346107	−	1.06521i
$756$	−2.51340	−	7.73545i	−0.0914115	−	0.281336i
$757$	13.5307	−	9.83066i	0.491783	−	0.357301i	−0.314087	−	0.949394i	$-0.601698\pi$
$757$	13.5307	−	9.83066i	0.491783	−	0.357301i	0.805870	+	0.592093i	$0.201698\pi$
$758$	63.7871			2.31685
$759$	1.54888	+	14.2616i	0.0562206	+	0.517663i
$760$	0.121656			0.00441291
$761$	−19.9360	+	14.4844i	−0.722680	+	0.525058i	−0.887239	−	0.461310i	$-0.847380\pi$
$761$	−19.9360	+	14.4844i	−0.722680	+	0.525058i	0.164559	+	0.986367i	$0.447380\pi$
$762$	−3.30507	−	10.1720i	−0.119730	−	0.368491i
$763$	−11.8468	+	36.4607i	−0.428883	+	1.31997i
$764$	−14.0633	−	10.2176i	−0.508794	−	0.369661i
$765$	9.41012	+	6.83685i	0.340224	+	0.247187i
$766$	5.24651	−	16.1471i	0.189564	−	0.583418i
$767$	−3.90781	−	12.0270i	−0.141103	−	0.434269i
$768$	−13.0080	+	9.45084i	−0.469385	+	0.341028i
$769$	−13.2261			−0.476945			−0.238473	−	0.971149i	$-0.576647\pi$
$769$	−13.2261			−0.476945			−0.238473	+	0.971149i	$0.576647\pi$
$770$	46.1481	−	80.5736i	1.66306	−	2.90367i
$771$	0.0444882			0.00160220
$772$	15.0296	−	10.9197i	0.540928	−	0.393007i
$773$	5.31978	+	16.3726i	0.191339	+	0.588882i	1.00000		0.000606172i	$0.000192951\pi$
$773$	5.31978	+	16.3726i	0.191339	+	0.588882i	−0.808661	+	0.588276i	$0.799807\pi$
$774$	−5.14884	+	15.8465i	−0.185071	+	0.569590i
$775$	−16.9437	−	12.3103i	−0.608636	−	0.442200i
$776$	0.0642391	+	0.0466724i	0.00230605	+	0.00167544i
$777$	−2.27750	+	7.00941i	−0.0817047	+	0.251461i
$778$	−15.2936	−	47.0687i	−0.548300	−	1.68750i
$779$	4.19028	−	3.04442i	0.150132	−	0.109078i
$780$	6.85445			0.245429
$781$	24.3064	+	26.8078i	0.869751	+	0.959259i
$782$	29.2685			1.04664
$783$	−7.01001	+	5.09307i	−0.250517	+	0.182011i
$784$	−11.9210	−	36.6890i	−0.425750	−	1.31032i
$785$	−10.9083	+	33.5722i	−0.389332	+	1.19824i
$786$	−22.6080	−	16.4257i	−0.806400	−	0.585884i
$787$	3.50185	+	2.54424i	0.124827	+	0.0906924i	0.648447	−	0.761260i	$-0.275419\pi$
$787$	3.50185	+	2.54424i	0.124827	+	0.0906924i	−0.523620	+	0.851952i	$0.675419\pi$
$788$	−14.1637	+	43.5915i	−0.504562	+	1.55288i
$789$	−9.22624	−	28.3955i	−0.328463	−	1.01091i
$790$	−6.79026	+	4.93341i	−0.241586	+	0.175523i
$791$	45.7747			1.62756
$792$	0.0219931	+	0.0242565i	0.000781492	+	0.000861917i
$793$	−3.78999			−0.134586
$794$	10.4850	−	7.61779i	0.372098	−	0.270345i
$795$	−12.2018	−	37.5533i	−0.432753	−	1.33188i
$796$	−3.91912	+	12.0618i	−0.138910	+	0.427520i
$797$	26.3974	+	19.1788i	0.935043	+	0.679349i	0.947222	−	0.320577i	$-0.103877\pi$
$797$	26.3974	+	19.1788i	0.935043	+	0.679349i	−0.0121791	+	0.999926i	$0.503877\pi$
$798$	23.6451	+	17.1792i	0.837028	+	0.608136i
$799$	−9.09156	+	27.9809i	−0.321636	+	0.989894i
$800$	−16.8102	−	51.7365i	−0.594331	−	1.82916i
$801$	−8.17945	+	5.94272i	−0.289007	+	0.209976i
$802$	69.4501			2.45237
$803$	3.09014	−	5.39531i	0.109049	−	0.190396i
$804$	4.42784			0.156158
$805$	−49.0135	+	35.6104i	−1.72750	+	1.25510i
$806$	−1.90118	−	5.85123i	−0.0669662	−	0.206101i
$807$	8.66155	−	26.6575i	0.304901	−	0.938389i
$808$	0.0975837	+	0.0708987i	0.00343298	+	0.00249421i
$809$	15.9540	+	11.5913i	0.560914	+	0.407528i	0.831794	−	0.555085i	$-0.187314\pi$
$809$	15.9540	+	11.5913i	0.560914	+	0.407528i	−0.270879	+	0.962613i	$0.587314\pi$
$810$	−2.12208	+	6.53108i	−0.0745621	+	0.229479i
$811$	−1.28244	−	3.94694i	−0.0450325	−	0.138596i	0.926012	−	0.377493i	$-0.123214\pi$
$811$	−1.28244	−	3.94694i	−0.0450325	−	0.138596i	−0.971045	+	0.238898i	$0.923214\pi$
$812$	57.0161	−	41.4246i	2.00087	−	1.45372i
$813$	−23.8569			−0.836699
$814$	1.29393	+	11.9142i	0.0453524	+	0.417592i
$815$	−37.9212			−1.32832
$816$	10.9826	−	7.97936i	0.384470	−	0.279333i
$817$	−9.23945	−	28.4361i	−0.323247	−	0.994853i
$818$	20.2219	−	62.2367i	0.707043	−	2.17606i
$819$	−3.29823	−	2.39630i	−0.115249	−	0.0837336i
$820$	−8.00788	−	5.81806i	−0.279647	−	0.203176i
$821$	4.30793	−	13.2584i	0.150348	−	0.462723i	−0.847312	−	0.531095i	$-0.821781\pi$
$821$	4.30793	−	13.2584i	0.150348	−	0.462723i	0.997660	+	0.0683724i	$0.0217806\pi$
$822$	−0.579989	−	1.78502i	−0.0202295	−	0.0622599i
$823$	−33.3382	+	24.2216i	−1.16210	+	0.844312i	−0.990041	−	0.140776i	$-0.955040\pi$
$823$	−33.3382	+	24.2216i	−1.16210	+	0.844312i	−0.172054	+	0.985088i	$0.555040\pi$
$824$	−0.0580297			−0.00202156
$825$	−20.5838	+	9.24999i	−0.716636	+	0.322043i
$826$	−103.047			−3.58546
$827$	−6.75483	+	4.90767i	−0.234889	+	0.170657i	−0.699003	−	0.715119i	$-0.746373\pi$
$827$	−6.75483	+	4.90767i	−0.234889	+	0.170657i	0.464114	+	0.885775i	$0.346373\pi$
$828$	2.66659	+	8.20693i	0.0926705	+	0.285211i
$829$	0.579253	−	1.78276i	0.0201183	−	0.0619177i	−0.940493	−	0.339812i	$-0.889637\pi$
$829$	0.579253	−	1.78276i	0.0201183	−	0.0619177i	0.960612	+	0.277894i	$0.0896365\pi$
$830$	−82.2644	−	59.7686i	−2.85544	−	2.07460i
$831$	7.94050	+	5.76911i	0.275453	+	0.200128i
$832$	2.45991	−	7.57083i	0.0852821	−	0.262471i
$833$	10.0648	+	30.9762i	0.348724	+	1.07326i
$834$	−13.8816	+	10.0856i	−0.480680	+	0.349235i
$835$	77.6916			2.68863
$836$	23.2312	+	4.85398i	0.803469	+	0.167878i
$837$	3.07808			0.106394
$838$	53.4244	−	38.8151i	1.84552	−	1.34085i
$839$	−3.24318	−	9.98147i	−0.111967	−	0.344599i	0.879335	−	0.476203i	$-0.157987\pi$
$839$	−3.24318	−	9.98147i	−0.111967	−	0.344599i	−0.991302	+	0.131604i	$0.957987\pi$
$840$	−0.0427306	+	0.131511i	−0.00147434	+	0.00453757i
$841$	−37.2791	−	27.0849i	−1.28549	−	0.933961i
$842$	34.9061	+	25.3608i	1.20295	+	0.873991i
$843$	−0.862726	+	2.65520i	−0.0297139	+	0.0914499i
$844$	2.76504	+	8.50992i	0.0951766	+	0.292923i
$845$	2.77955	−	2.01946i	0.0956194	−	0.0694716i
$846$	−17.3699			−0.597189
$847$	−29.7759	+	33.5334i	−1.02311	+	1.15222i
$848$	−46.0843			−1.58254
$849$	−4.57162	+	3.32148i	−0.156898	+	0.113993i
$850$	14.2278	+	43.7885i	0.488008	+	1.50193i
$851$	2.41631	−	7.43664i	0.0828301	−	0.254925i
$852$	17.6102	+	12.7945i	0.603314	+	0.438333i
$853$	−25.8142	−	18.7551i	−0.883861	−	0.642163i	0.0504091	−	0.998729i	$-0.483947\pi$
$853$	−25.8142	−	18.7551i	−0.883861	−	0.642163i	−0.934270	+	0.356566i	$0.883947\pi$
$854$	−9.54344	+	29.3717i	−0.326570	+	1.00508i
$855$	−3.80801	−	11.7198i	−0.130231	−	0.400810i
$856$	0.128898	−	0.0936497i	0.00440563	−	0.00320088i
$857$	19.7454			0.674489			0.337244	−	0.941417i	$-0.390505\pi$
$857$	19.7454			0.674489			0.337244	+	0.941417i	$0.390505\pi$
$858$	−6.48902	−	1.35583i	−0.221532	−	0.0462872i
$859$	15.5566			0.530785			0.265392	−	0.964141i	$-0.414499\pi$
$859$	15.5566			0.530785			0.265392	+	0.964141i	$0.414499\pi$
$860$	−46.2270	+	33.5859i	−1.57633	+	1.14527i
$861$	1.81925	+	5.59908i	0.0619999	+	0.190816i
$862$	−8.88921	+	27.3582i	−0.302768	+	0.931823i
$863$	−22.4360	−	16.3007i	−0.763730	−	0.554882i	0.136322	−	0.990665i	$-0.456472\pi$
$863$	−22.4360	−	16.3007i	−0.763730	−	0.554882i	−0.900052	+	0.435783i	$0.856472\pi$
$864$	6.46810	+	4.69935i	0.220049	+	0.159875i
$865$	7.61834	−	23.4468i	0.259031	−	0.797216i
$866$	−10.3359	−	31.8105i	−0.351227	−	1.08097i
$867$	4.48074	−	3.25545i	0.152174	−	0.110561i
$868$	−25.0356			−0.849765
$869$	3.69747	−	1.66158i	0.125428	−	0.0563651i
$870$	−59.5030			−2.01734
$871$	1.79553	−	1.30453i	0.0608394	−	0.0442024i
$872$	−0.0286876	−	0.0882915i	−0.000971486	−	0.00298993i
$873$	2.48546	−	7.64947i	0.0841202	−	0.258895i
$874$	−25.0863	−	18.2263i	−0.848556	−	0.616512i
$875$	−20.4438	−	14.8533i	−0.691127	−	0.502133i
$876$	1.15575	−	3.55703i	0.0390491	−	0.120181i
$877$	10.4317	+	32.1055i	0.352254	+	1.08412i	0.957585	+	0.288151i	$0.0930406\pi$
$877$	10.4317	+	32.1055i	0.352254	+	1.08412i	−0.605331	+	0.795974i	$0.706959\pi$
$878$	13.4169	−	9.74797i	0.452799	−	0.328978i
$879$	−2.97185			−0.100238
$880$	4.93337	+	45.4250i	0.166304	+	1.53128i
$881$	33.2521			1.12029			0.560146	−	0.828394i	$-0.310745\pi$
$881$	33.2521			1.12029			0.560146	+	0.828394i	$0.310745\pi$
$882$	−15.5568	+	11.3027i	−0.523825	+	0.380581i
$883$	−5.00710	−	15.4103i	−0.168502	−	0.518597i	0.830775	−	0.556608i	$-0.187898\pi$
$883$	−5.00710	−	15.4103i	−0.168502	−	0.518597i	−0.999277	+	0.0380118i	$0.987898\pi$
$884$	−2.08718	+	6.42367i	−0.0701994	+	0.216051i
$885$	35.1500	+	25.5379i	1.18155	+	0.858449i
$886$	18.8918	+	13.7257i	0.634683	+	0.461124i
$887$	−3.89187	+	11.9779i	−0.130676	+	0.402180i	−0.994892	−	0.100941i	$-0.967815\pi$
$887$	−3.89187	+	11.9779i	−0.130676	+	0.402180i	0.864216	+	0.503120i	$0.167815\pi$
$888$	−0.00551507	−	0.0169736i	−0.000185074	−	0.000569598i
$889$	−17.6489	+	12.8227i	−0.591924	+	0.430058i
$890$	−69.4297			−2.32729
$891$	1.64836	−	2.87800i	0.0552222	−	0.0964167i
$892$	32.7454			1.09640
$893$	25.2169	−	18.3211i	0.843851	−	0.613094i
$894$	10.4248	+	32.0841i	0.348656	+	1.07305i
$895$	−2.35020	+	7.23317i	−0.0785585	+	0.241778i
$896$	0.260487	+	0.189255i	0.00870225	+	0.00632256i
$897$	3.49926	+	2.54236i	0.116837	+	0.0848869i
$898$	16.8264	−	51.7863i	0.561504	−	1.72813i
$899$	8.24181	+	25.3657i	0.274880	+	0.845993i
$900$	−10.9821	+	7.97896i	−0.366070	+	0.265965i
$901$	38.9086			1.29623
$902$	6.43012	+	7.09186i	0.214100	+	0.236133i
$903$	33.9851			1.13095
$904$	−0.0896760	+	0.0651534i	−0.00298258	+	0.00216697i
$905$	19.1742	+	59.0121i	0.637372	+	1.96163i
$906$	−5.53260	+	17.0276i	−0.183808	+	0.565703i
$907$	−28.9200	−	21.0116i	−0.960272	−	0.697678i	−0.00705804	−	0.999975i	$-0.502247\pi$
$907$	−28.9200	−	21.0116i	−0.960272	−	0.697678i	−0.953214	+	0.302297i	$0.902247\pi$
$908$	28.2823	+	20.5483i	0.938581	+	0.681919i
$909$	3.77560	−	11.6201i	0.125229	−	0.385414i
$910$	−8.65135	−	26.6261i	−0.286789	−	0.882647i
$911$	−33.0460	+	24.0093i	−1.09486	+	0.795464i	−0.980214	−	0.197942i	$-0.936574\pi$
$911$	−33.0460	+	24.0093i	−1.09486	+	0.795464i	−0.114648	+	0.993406i	$0.536574\pi$
$912$	−14.3823			−0.476244
$913$	32.9873	+	36.3821i	1.09172	+	1.20407i
$914$	−8.07895			−0.267228
$915$	10.5345	−	7.65373i	0.348258	−	0.253024i
$916$	3.46888	+	10.6761i	0.114615	+	0.352749i
$917$	−17.6136	+	54.2091i	−0.581652	+	1.79014i
$918$	−5.47445	−	3.97742i	−0.180684	−	0.131274i
$919$	−6.30709	−	4.58237i	−0.208052	−	0.151158i	0.478880	−	0.877880i	$-0.341043\pi$
$919$	−6.30709	−	4.58237i	−0.208052	−	0.151158i	−0.686932	+	0.726722i	$0.741043\pi$
$920$	0.0453350	−	0.139527i	0.00149465	−	0.00460006i
$921$	2.35440	+	7.24609i	0.0775800	+	0.238767i
$922$	−0.622253	+	0.452093i	−0.0204928	+	0.0148889i
$923$	10.9106			0.359128
$924$	−13.4070	+	23.4083i	−0.441058	+	0.770078i
$925$	12.3005			0.404439
$926$	27.5154	−	19.9911i	0.904212	−	0.656948i
$927$	1.81642	+	5.59037i	0.0596591	+	0.183612i
$928$	−21.4073	+	65.8849i	−0.702729	+	2.16278i
$929$	31.0032	+	22.5252i	1.01718	+	0.739027i	0.965704	−	0.259647i	$-0.0836063\pi$
$929$	31.0032	+	22.5252i	1.01718	+	0.739027i	0.0514796	+	0.998674i	$0.483606\pi$
$930$	17.1008	+	12.4244i	0.560756	+	0.407413i
$931$	10.6631	−	32.8176i	0.349468	−	1.07555i
$932$	−9.97797	−	30.7090i	−0.326839	−	1.00591i
$933$	4.06766	−	2.95533i	0.133169	−	0.0967531i
$934$	48.3955			1.58355
$935$	−4.16520	−	38.3520i	−0.136217	−	1.25424i
$936$	0.00987225			0.000322685
$937$	−2.81977	+	2.04868i	−0.0921179	+	0.0669276i	−0.632891	−	0.774241i	$-0.718132\pi$
$937$	−2.81977	+	2.04868i	−0.0921179	+	0.0669276i	0.540773	+	0.841169i	$0.318132\pi$
$938$	−5.58860	−	17.2000i	−0.182474	−	0.561598i
$939$	7.24066	−	22.2845i	0.236290	−	0.727226i
$940$	−48.1910	−	35.0128i	−1.57182	−	1.14199i
$941$	35.0092	+	25.4357i	1.14127	+	0.829179i	0.987295	−	0.158897i	$-0.0507936\pi$
$941$	35.0092	+	25.4357i	1.14127	+	0.829179i	0.153971	+	0.988075i	$0.450794\pi$
$942$	6.34600	−	19.5310i	0.206764	−	0.636354i
$943$	−1.93013	−	5.94034i	−0.0628538	−	0.193444i
$944$	41.0239	−	29.8056i	1.33521	−	0.970090i
$945$	14.0068			0.455642
$946$	50.4058	−	22.6515i	1.63884	−	0.736463i
$947$	−32.7033			−1.06272			−0.531358	−	0.847148i	$-0.678318\pi$
$947$	−32.7033			−1.06272			−0.531358	+	0.847148i	$0.678318\pi$
$948$	1.97271	−	1.43326i	0.0640707	−	0.0465501i
$949$	−0.579305	−	1.78292i	−0.0188050	−	0.0578760i
$950$	15.0735	−	46.3915i	0.489049	−	1.50514i
$951$	10.4319	+	7.57921i	0.338277	+	0.245773i
$952$	−0.110235	−	0.0800901i	−0.00357272	−	0.00259574i
$953$	12.4523	−	38.3242i	0.403369	−	1.24144i	−0.518880	−	0.854847i	$-0.673651\pi$
$953$	12.4523	−	38.3242i	0.403369	−	1.24144i	0.922249	−	0.386596i	$-0.126349\pi$
$954$	7.09853	+	21.8470i	0.229824	+	0.707324i
$955$	24.2186	−	17.5959i	0.783696	−	0.569388i
$956$	27.0974			0.876394
$957$	28.1306	+	5.87765i	0.909332	+	0.189998i
$958$	−50.6390			−1.63607
$959$	−3.09711	+	2.25018i	−0.100011	+	0.0726622i
$960$	8.45154	+	26.0112i	0.272772	+	0.839507i
$961$	−6.65173	+	20.4719i	−0.214572	+	0.660384i
$962$	2.92329	+	2.12389i	0.0942506	+	0.0684771i
$963$	−13.0566	−	9.48615i	−0.420742	−	0.305687i
$964$	14.7322	−	45.3410i	0.474492	−	1.46034i
$965$	9.88629	+	30.4269i	0.318251	+	0.979476i
$966$	28.5142	−	20.7168i	0.917428	−	0.666551i
$967$	−16.9000			−0.543468			−0.271734	−	0.962372i	$-0.587597\pi$
$967$	−16.9000			−0.543468			−0.271734	+	0.962372i	$0.587597\pi$
$968$	0.0106034	−	0.108076i	0.000340808	−	0.00347369i
$969$	12.1428			0.390084
$970$	44.6849	−	32.4655i	1.43475	−	1.04240i
$971$	4.98031	+	15.3278i	0.159826	+	0.491893i	0.998618	−	0.0525588i	$-0.0167377\pi$
$971$	4.98031	+	15.3278i	0.159826	+	0.491893i	−0.838792	+	0.544452i	$0.816738\pi$
$972$	0.616508	−	1.89742i	0.0197745	−	0.0608596i
$973$	28.3140	+	20.5713i	0.907704	+	0.659486i
$974$	−67.7901	−	49.2524i	−2.17214	−	1.57815i
$975$	−2.10259	+	6.47110i	−0.0673367	+	0.207241i
$976$	−4.69622	−	14.4535i	−0.150322	−	0.462645i
$977$	16.1310	−	11.7199i	0.516077	−	0.374952i	−0.299047	−	0.954238i	$-0.596669\pi$
$977$	16.1310	−	11.7199i	0.516077	−	0.374952i	0.815124	+	0.579286i	$0.196669\pi$
$978$	22.0611			0.705435
$979$	32.8234	+	6.85820i	1.04904	+	0.219189i
$980$	−65.9439			−2.10650
$981$	−7.60771	+	5.52732i	−0.242895	+	0.176474i
$982$	0.772230	+	2.37668i	0.0246428	+	0.0758429i
$983$	8.50465	−	26.1746i	0.271256	−	0.834841i	−0.718929	−	0.695083i	$-0.755368\pi$
$983$	8.50465	−	26.1746i	0.271256	−	0.834841i	0.990186	−	0.139758i	$-0.0446324\pi$
$984$	−0.0115335	−	0.00837957i	−0.000367674	−	0.000267131i
$985$	−63.8577	−	46.3953i	−2.03468	−	1.47828i
$986$	18.1186	−	55.7634i	0.577015	−	1.77587i
$987$	10.9481	+	33.6949i	0.348483	+	1.07252i
$988$	5.78912	−	4.20604i	0.184176	−	0.133812i
$989$	−36.0565			−1.14653
$990$	20.7746	−	9.33573i	0.660260	−	0.296709i
$991$	−59.2324			−1.88158			−0.940789	−	0.338993i	$-0.889914\pi$
$991$	−59.2324			−1.88158			−0.940789	+	0.338993i	$0.889914\pi$
$992$	19.9093	−	14.4650i	0.632121	−	0.459263i
$993$	4.34082	+	13.3597i	0.137752	+	0.423957i
$994$	27.4737	−	84.5553i	0.871412	−	2.68193i
$995$	−17.6695	−	12.8376i	−0.560161	−	0.406981i
$996$	23.8995	+	17.3640i	0.757286	+	0.550200i
$997$	6.10073	−	18.7761i	0.193212	−	0.594645i	−0.806781	−	0.590851i	$-0.798792\pi$
$997$	6.10073	−	18.7761i	0.193212	−	0.594645i	0.999993	−	0.00379458i	$-0.00120785\pi$
$998$	13.8485	+	42.6212i	0.438366	+	1.34915i
$999$	−1.46255	+	1.06260i	−0.0462729	+	0.0336193i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.n.d.157.2	✓	36
11.2	odd	10		4719.2.a.br.1.4		18
11.4	even	5	inner	429.2.n.d.235.2	yes	36
11.9	even	5		4719.2.a.bq.1.15		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.n.d.157.2	✓	36	1.1	even	1	trivial
429.2.n.d.235.2	yes	36	11.4	even	5	inner
4719.2.a.bq.1.15		18	11.9	even	5
4719.2.a.br.1.4		18	11.2	odd	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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.61703 + 1.17484i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.616508 - 1.89742i) q^{4} +(2.77955 + 2.01946i) q^{5} +(-1.61703 - 1.17484i) q^{6} +(-1.25981 + 3.87730i) q^{7} +(-0.00305069 - 0.00938907i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(-1.61703 + 1.17484i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.616508 - 1.89742i) q^{4} +(2.77955 + 2.01946i) q^{5} +(-1.61703 - 1.17484i) q^{6} +(-1.25981 + 3.87730i) q^{7} +(-0.00305069 - 0.00938907i) q^{8} +(-0.809017 + 0.587785i) q^{9} -6.86718 q^{10} +(3.24652 + 0.678334i) q^{11} +1.99506 q^{12} +(0.809017 - 0.587785i) q^{13} +(-2.51807 - 7.74981i) q^{14} +(-1.06169 + 3.26756i) q^{15} +(3.24404 + 2.35693i) q^{16} +(-2.73891 - 1.98994i) q^{17} +(0.617652 - 1.90094i) q^{18} +(1.10836 + 3.41118i) q^{19} +(5.54537 - 4.02895i) q^{20} -4.07684 q^{21} +(-6.04666 + 2.71726i) q^{22} +4.32532 q^{23} +(0.00798682 - 0.00580277i) q^{24} +(2.10259 + 6.47110i) q^{25} +(-0.617652 + 1.90094i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(6.58017 + 4.78077i) q^{28} +(2.67758 - 8.24076i) q^{29} +(-2.12208 - 6.53108i) q^{30} +(-2.49022 + 1.80925i) q^{31} -7.99501 q^{32} +(0.358095 + 3.29724i) q^{33} +6.76679 q^{34} +(-11.3318 + 8.23301i) q^{35} +(0.616508 + 1.89742i) q^{36} +(0.558643 - 1.71933i) q^{37} +(-5.79987 - 4.21385i) q^{38} +(0.809017 + 0.587785i) q^{39} +(0.0104813 - 0.0322581i) q^{40} +(-0.446241 - 1.37339i) q^{41} +(6.59238 - 4.78965i) q^{42} -8.33614 q^{43} +(3.28858 - 5.74179i) q^{44} -3.43571 q^{45} +(-6.99419 + 5.08158i) q^{46} +(-2.68545 - 8.26497i) q^{47} +(-1.23911 + 3.81360i) q^{48} +(-7.78322 - 5.65484i) q^{49} +(-11.0025 - 7.99378i) q^{50} +(1.04617 - 3.21979i) q^{51} +(-0.616508 - 1.89742i) q^{52} +(-9.29785 + 6.75528i) q^{53} +1.99876 q^{54} +(7.65398 + 8.44167i) q^{55} +0.0402476 q^{56} +(-2.90173 + 2.10823i) q^{57} +(5.35186 + 16.4713i) q^{58} +(3.90781 - 12.0270i) q^{59} +(5.54537 + 4.02895i) q^{60} +(-3.06616 - 2.22770i) q^{61} +(1.90118 - 5.85123i) q^{62} +(-1.25981 - 3.87730i) q^{63} +(6.44013 - 4.67903i) q^{64} +3.43571 q^{65} +(-4.45279 - 4.91104i) q^{66} +2.21940 q^{67} +(-5.46430 + 3.97005i) q^{68} +(1.33660 + 4.11362i) q^{69} +(8.65135 - 26.6261i) q^{70} +(8.82688 + 6.41310i) q^{71} +(0.00798682 + 0.00580277i) q^{72} +(0.579305 - 1.78292i) q^{73} +(1.11660 + 3.43653i) q^{74} +(-5.50464 + 3.99936i) q^{75} +7.15575 q^{76} +(-6.72010 + 11.7331i) q^{77} -1.99876 q^{78} +(0.988798 - 0.718404i) q^{79} +(4.25724 + 13.1024i) q^{80} +(0.309017 - 0.951057i) q^{81} +(2.33510 + 1.69655i) q^{82} +(11.9794 + 8.70351i) q^{83} +(-2.51340 + 7.73545i) q^{84} +(-3.59435 - 11.0623i) q^{85} +(13.4798 - 9.79367i) q^{86} +8.66484 q^{87} +(-0.00353520 - 0.0325512i) q^{88} +10.1104 q^{89} +(5.55566 - 4.03643i) q^{90} +(1.25981 + 3.87730i) q^{91} +(2.66659 - 8.20693i) q^{92} +(-2.49022 - 1.80925i) q^{93} +(14.0525 + 10.2098i) q^{94} +(-3.80801 + 11.7198i) q^{95} +(-2.47059 - 7.60371i) q^{96} +(-6.50703 + 4.72763i) q^{97} +19.2293 q^{98} +(-3.02520 + 1.35947i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 3 q^{2} - 9 q^{3} - 11 q^{4} + 3 q^{6} + q^{7} - q^{8} - 9 q^{9}+O(q^{10}) \) 36 * q + 3 * q^2 - 9 * q^3 - 11 * q^4 + 3 * q^6 + q^7 - q^8 - 9 * q^9	\( 36 q + 3 q^{2} - 9 q^{3} - 11 q^{4} + 3 q^{6} + q^{7} - q^{8} - 9 q^{9} + 6 q^{10} - 10 q^{11} + 54 q^{12} + 9 q^{13} - 5 q^{14} - 10 q^{15} - 13 q^{16} - 2 q^{18} + 10 q^{19} + 37 q^{20} - 14 q^{21} - 9 q^{22} + 18 q^{23} + 4 q^{24} - 31 q^{25} + 2 q^{26} - 9 q^{27} + 12 q^{28} + 10 q^{29} + q^{30} - 28 q^{31} - 74 q^{32} + 5 q^{33} + 40 q^{34} - 14 q^{35} - 11 q^{36} - 26 q^{37} + 7 q^{38} + 9 q^{39} - 72 q^{40} + 26 q^{41} - 5 q^{42} + 4 q^{43} - 68 q^{44} + 20 q^{45} - 57 q^{46} - 28 q^{48} - 18 q^{49} + 11 q^{50} - 5 q^{51} + 11 q^{52} + 11 q^{53} - 2 q^{54} - 32 q^{55} + 72 q^{56} + 50 q^{58} + 55 q^{59} + 37 q^{60} + 14 q^{61} - 50 q^{62} + q^{63} - q^{64} - 20 q^{65} - 14 q^{66} + 104 q^{67} - 9 q^{68} + 8 q^{69} + 44 q^{70} - 8 q^{71} + 4 q^{72} - 3 q^{73} + 69 q^{74} - 21 q^{75} - 52 q^{76} + 2 q^{77} + 2 q^{78} - 19 q^{79} - 159 q^{80} - 9 q^{81} + 58 q^{82} + 12 q^{83} - 8 q^{84} + 63 q^{86} - 97 q^{88} + 118 q^{89} - 4 q^{90} - q^{91} + 98 q^{92} - 28 q^{93} - 99 q^{94} - 45 q^{95} + q^{96} + 50 q^{97} - 186 q^{98}+O(q^{100}) \) 36 * q + 3 * q^2 - 9 * q^3 - 11 * q^4 + 3 * q^6 + q^7 - q^8 - 9 * q^9 + 6 * q^10 - 10 * q^11 + 54 * q^12 + 9 * q^13 - 5 * q^14 - 10 * q^15 - 13 * q^16 - 2 * q^18 + 10 * q^19 + 37 * q^20 - 14 * q^21 - 9 * q^22 + 18 * q^23 + 4 * q^24 - 31 * q^25 + 2 * q^26 - 9 * q^27 + 12 * q^28 + 10 * q^29 + q^30 - 28 * q^31 - 74 * q^32 + 5 * q^33 + 40 * q^34 - 14 * q^35 - 11 * q^36 - 26 * q^37 + 7 * q^38 + 9 * q^39 - 72 * q^40 + 26 * q^41 - 5 * q^42 + 4 * q^43 - 68 * q^44 + 20 * q^45 - 57 * q^46 - 28 * q^48 - 18 * q^49 + 11 * q^50 - 5 * q^51 + 11 * q^52 + 11 * q^53 - 2 * q^54 - 32 * q^55 + 72 * q^56 + 50 * q^58 + 55 * q^59 + 37 * q^60 + 14 * q^61 - 50 * q^62 + q^63 - q^64 - 20 * q^65 - 14 * q^66 + 104 * q^67 - 9 * q^68 + 8 * q^69 + 44 * q^70 - 8 * q^71 + 4 * q^72 - 3 * q^73 + 69 * q^74 - 21 * q^75 - 52 * q^76 + 2 * q^77 + 2 * q^78 - 19 * q^79 - 159 * q^80 - 9 * q^81 + 58 * q^82 + 12 * q^83 - 8 * q^84 + 63 * q^86 - 97 * q^88 + 118 * q^89 - 4 * q^90 - q^91 + 98 * q^92 - 28 * q^93 - 99 * q^94 - 45 * q^95 + q^96 + 50 * q^97 - 186 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more