LMFDB - Embedded newform 770.2.w.b.139.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(139,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 5, 7]))

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

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

chi := DirichletCharacter("770.139");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.w (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			139.11
Character	$\chi$	$=$	770.139
Dual form			770.2.w.b.349.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 + 0.587785i) q^{2} +(-0.208297 + 0.641072i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-1.77458 + 1.36046i) q^{5} +(-0.545328 + 0.396204i) q^{6} +(-1.13890 - 2.38807i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(2.05947 + 1.49629i) q^{9} +O(q^{10})$	\(q+(0.809017 + 0.587785i) q^{2} +(-0.208297 + 0.641072i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-1.77458 + 1.36046i) q^{5} +(-0.545328 + 0.396204i) q^{6} +(-1.13890 - 2.38807i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(2.05947 + 1.49629i) q^{9} +(-2.23533 + 0.0575660i) q^{10} +(-2.00389 + 2.64280i) q^{11} -0.674063 q^{12} +(-1.40119 + 1.92858i) q^{13} +(0.482283 - 2.60142i) q^{14} +(-0.502515 - 1.42101i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-3.28944 - 4.52752i) q^{17} +(0.786646 + 2.42105i) q^{18} +(-1.51734 + 4.66989i) q^{19} +(-1.84225 - 1.26732i) q^{20} +(1.76816 - 0.232690i) q^{21} +(-3.17459 + 0.960214i) q^{22} -3.09144i q^{23} +(-0.545328 - 0.396204i) q^{24} +(1.29828 - 4.82851i) q^{25} +(-2.26718 + 0.736651i) q^{26} +(-3.02419 + 2.19720i) q^{27} +(1.91925 - 1.82112i) q^{28} +(-5.39874 + 1.75416i) q^{29} +(0.428707 - 1.44500i) q^{30} +(-4.98516 + 6.86149i) q^{31} -1.00000 q^{32} +(-1.27682 - 1.83513i) q^{33} -5.59632i q^{34} +(5.26997 + 2.68839i) q^{35} +(-0.786646 + 2.42105i) q^{36} +(-0.465541 + 0.151263i) q^{37} +(-3.97244 + 2.88615i) q^{38} +(-0.944492 - 1.29998i) q^{39} +(-0.745503 - 2.10813i) q^{40} +(2.81548 - 8.66515i) q^{41} +(1.56724 + 0.851046i) q^{42} +5.13743 q^{43} +(-3.13269 - 1.08915i) q^{44} +(-5.69034 + 0.146542i) q^{45} +(1.81710 - 2.50102i) q^{46} +(-1.66317 + 5.11870i) q^{47} +(-0.208297 - 0.641072i) q^{48} +(-4.40580 + 5.43957i) q^{49} +(3.88845 - 3.14324i) q^{50} +(3.58764 - 1.16570i) q^{51} +(-2.26718 - 0.736651i) q^{52} +(-3.44170 + 4.73710i) q^{53} -3.73811 q^{54} +(-0.0393670 - 7.41609i) q^{55} +(2.62313 - 0.345206i) q^{56} +(-2.67768 - 1.94545i) q^{57} +(-5.39874 - 1.75416i) q^{58} +(11.8450 - 3.84866i) q^{59} +(1.19618 - 0.917038i) q^{60} +(1.97745 - 1.43670i) q^{61} +(-8.06616 + 2.62086i) q^{62} +(1.22772 - 6.62229i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(-0.137229 - 5.32869i) q^{65} +(0.0456902 - 2.23515i) q^{66} +13.4008i q^{67} +(3.28944 - 4.52752i) q^{68} +(1.98183 + 0.643936i) q^{69} +(2.68329 + 5.27256i) q^{70} +(10.9414 - 7.94941i) q^{71} +(-2.05947 + 1.49629i) q^{72} +(-0.782563 + 0.254270i) q^{73} +(-0.465541 - 0.151263i) q^{74} +(2.82499 + 1.83805i) q^{75} -4.91021 q^{76} +(8.59345 + 1.77555i) q^{77} -1.60687i q^{78} +(-9.46039 + 13.0211i) q^{79} +(0.636005 - 2.14371i) q^{80} +(1.58130 + 4.86675i) q^{81} +(7.37102 - 5.35536i) q^{82} +(-2.44284 - 3.36228i) q^{83} +(0.767692 + 1.60971i) q^{84} +(11.9969 + 3.55929i) q^{85} +(4.15627 + 3.01970i) q^{86} -3.82636i q^{87} +(-1.89422 - 2.72249i) q^{88} -10.6875i q^{89} +(-4.68971 - 3.22614i) q^{90} +(6.20141 + 1.14969i) q^{91} +(2.94013 - 0.955306i) q^{92} +(-3.36031 - 4.62507i) q^{93} +(-4.35422 + 3.16353i) q^{94} +(-3.66058 - 10.3514i) q^{95} +(0.208297 - 0.641072i) q^{96} +(5.14075 + 3.73498i) q^{97} +(-6.76167 + 1.81104i) q^{98} +(-8.08135 + 2.44436i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 24 q^{2} - 24 q^{4} + 3 q^{7} + 24 q^{8} - 18 q^{9}+O(q^{10}) $ 96 * q + 24 * q^2 - 24 * q^4 + 3 * q^7 + 24 * q^8 - 18 * q^9	$ 96 q + 24 q^{2} - 24 q^{4} + 3 q^{7} + 24 q^{8} - 18 q^{9} + 4 q^{11} - 3 q^{14} - 6 q^{15} - 24 q^{16} + 28 q^{18} - 4 q^{22} + 38 q^{25} - 2 q^{28} + 6 q^{30} - 96 q^{32} + 46 q^{35} - 28 q^{36} + 10 q^{39} - 24 q^{43} - 16 q^{44} + 37 q^{49} - 8 q^{50} - 30 q^{51} + 40 q^{53} + 2 q^{56} - 20 q^{57} + 14 q^{60} + 63 q^{63} - 24 q^{64} - 40 q^{65} + 39 q^{70} - 20 q^{71} + 18 q^{72} - 16 q^{77} - 126 q^{81} + 60 q^{85} - 36 q^{86} - 14 q^{88} - 31 q^{91} - 10 q^{92} + 20 q^{93} - 44 q^{95} + 18 q^{98} + 100 q^{99}+O(q^{100}) $ 96 * q + 24 * q^2 - 24 * q^4 + 3 * q^7 + 24 * q^8 - 18 * q^9 + 4 * q^11 - 3 * q^14 - 6 * q^15 - 24 * q^16 + 28 * q^18 - 4 * q^22 + 38 * q^25 - 2 * q^28 + 6 * q^30 - 96 * q^32 + 46 * q^35 - 28 * q^36 + 10 * q^39 - 24 * q^43 - 16 * q^44 + 37 * q^49 - 8 * q^50 - 30 * q^51 + 40 * q^53 + 2 * q^56 - 20 * q^57 + 14 * q^60 + 63 * q^63 - 24 * q^64 - 40 * q^65 + 39 * q^70 - 20 * q^71 + 18 * q^72 - 16 * q^77 - 126 * q^81 + 60 * q^85 - 36 * q^86 - 14 * q^88 - 31 * q^91 - 10 * q^92 + 20 * q^93 - 44 * q^95 + 18 * q^98 + 100 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$3$	−0.208297	+	0.641072i	−0.120260	+	0.370123i	−0.993008	−	0.118049i	$-0.962336\pi$
$3$	−0.208297	+	0.641072i	−0.120260	+	0.370123i	0.872748	+	0.488172i	$0.162336\pi$
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	−1.77458	+	1.36046i	−0.793617	+	0.608418i
$5$	−1.77458	+	1.36046i	−0.793617	+	0.608418i
$6$	−0.545328	+	0.396204i	−0.222629	+	0.161750i
$7$	−1.13890	−	2.38807i	−0.430465	−	0.902607i
$7$	−1.13890	−	2.38807i	−0.430465	−	0.902607i
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$	2.05947	+	1.49629i	0.686489	+	0.498763i
$10$	−2.23533	+	0.0575660i	−0.706872	+	0.0182040i
$11$	−2.00389	+	2.64280i	−0.604197	+	0.796835i
$11$	−2.00389	+	2.64280i	−0.604197	+	0.796835i
$12$	−0.674063			−0.194585
$13$	−1.40119	+	1.92858i	−0.388621	+	0.534891i	−0.957843	−	0.287293i	$-0.907245\pi$
$13$	−1.40119	+	1.92858i	−0.388621	+	0.534891i	0.569222	+	0.822184i	$0.307245\pi$
$14$	0.482283	−	2.60142i	0.128895	−	0.695260i
$15$	−0.502515	−	1.42101i	−0.129749	−	0.366904i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−3.28944	−	4.52752i	−0.797806	−	1.09809i	−0.993092	−	0.117339i	$-0.962564\pi$
$17$	−3.28944	−	4.52752i	−0.797806	−	1.09809i	0.195286	−	0.980746i	$-0.437436\pi$
$18$	0.786646	+	2.42105i	0.185414	+	0.570646i
$19$	−1.51734	+	4.66989i	−0.348101	+	1.07135i	0.611801	+	0.791012i	$0.290445\pi$
$19$	−1.51734	+	4.66989i	−0.348101	+	1.07135i	−0.959902	+	0.280334i	$0.909555\pi$
$20$	−1.84225	−	1.26732i	−0.411940	−	0.283381i
$21$	1.76816	−	0.232690i	0.385843	−	0.0507772i
$22$	−3.17459	+	0.960214i	−0.676824	+	0.204718i
$23$		−	3.09144i		−	0.644609i	−0.946636	−	0.322304i	$-0.895543\pi$
$23$		−	3.09144i		−	0.644609i	0.946636	−	0.322304i	$-0.104457\pi$
$24$	−0.545328	−	0.396204i	−0.111315	−	0.0808748i
$25$	1.29828	−	4.82851i	0.259655	−	0.965701i
$26$	−2.26718	+	0.736651i	−0.444630	+	0.144469i
$27$	−3.02419	+	2.19720i	−0.582006	+	0.422852i
$28$	1.91925	−	1.82112i	0.362705	−	0.344159i
$29$	−5.39874	+	1.75416i	−1.00252	+	0.325739i	−0.763872	−	0.645368i	$-0.776704\pi$
$29$	−5.39874	+	1.75416i	−1.00252	+	0.325739i	−0.238648	+	0.971106i	$0.576704\pi$
$30$	0.428707	−	1.44500i	0.0782709	−	0.263819i
$31$	−4.98516	+	6.86149i	−0.895362	+	1.23236i	0.0765621	+	0.997065i	$0.475606\pi$
$31$	−4.98516	+	6.86149i	−0.895362	+	1.23236i	−0.971924	+	0.235295i	$0.924394\pi$
$32$	−1.00000			−0.176777
$33$	−1.27682	−	1.83513i	−0.222266	−	0.319455i
$34$		−	5.59632i		−	0.959762i
$35$	5.26997	+	2.68839i	0.890787	+	0.454422i
$36$	−0.786646	+	2.42105i	−0.131108	+	0.403508i
$37$	−0.465541	+	0.151263i	−0.0765345	+	0.0248676i	−0.347034	−	0.937853i	$-0.612811\pi$
$37$	−0.465541	+	0.151263i	−0.0765345	+	0.0248676i	0.270500	+	0.962720i	$0.412811\pi$
$38$	−3.97244	+	2.88615i	−0.644416	+	0.468195i
$39$	−0.944492	−	1.29998i	−0.151240	−	0.208164i
$40$	−0.745503	−	2.10813i	−0.117874	−	0.333325i
$41$	2.81548	−	8.66515i	0.439704	−	1.35327i	−0.448485	−	0.893790i	$-0.648036\pi$
$41$	2.81548	−	8.66515i	0.439704	−	1.35327i	0.888189	−	0.459479i	$-0.151964\pi$
$42$	1.56724	+	0.851046i	0.241830	+	0.131319i
$43$	5.13743			0.783450			0.391725	−	0.920082i	$-0.371878\pi$
$43$	5.13743			0.783450			0.391725	+	0.920082i	$0.371878\pi$
$44$	−3.13269	−	1.08915i	−0.472271	−	0.164195i
$45$	−5.69034	+	0.146542i	−0.848265	+	0.0218452i
$46$	1.81710	−	2.50102i	0.267917	−	0.368756i
$47$	−1.66317	+	5.11870i	−0.242598	+	0.746639i	0.753425	+	0.657534i	$0.228401\pi$
$47$	−1.66317	+	5.11870i	−0.242598	+	0.746639i	−0.996022	+	0.0891045i	$0.971599\pi$
$48$	−0.208297	−	0.641072i	−0.0300651	−	0.0925307i
$49$	−4.40580	+	5.43957i	−0.629400	+	0.777082i
$50$	3.88845	−	3.14324i	0.549910	−	0.444521i
$51$	3.58764	−	1.16570i	0.502371	−	0.163230i
$52$	−2.26718	−	0.736651i	−0.314401	−	0.102155i
$53$	−3.44170	+	4.73710i	−0.472754	+	0.650690i	−0.977092	−	0.212816i	$-0.931736\pi$
$53$	−3.44170	+	4.73710i	−0.472754	+	0.650690i	0.504338	+	0.863506i	$0.331736\pi$
$54$	−3.73811			−0.508692
$55$	−0.0393670	−	7.41609i	−0.00530824	−	0.999986i
$56$	2.62313	−	0.345206i	0.350531	−	0.0461301i
$57$	−2.67768	−	1.94545i	−0.354667	−	0.257681i
$58$	−5.39874	−	1.75416i	−0.708889	−	0.230332i
$59$	11.8450	−	3.84866i	1.54208	−	0.501053i	0.590133	−	0.807306i	$-0.299075\pi$
$59$	11.8450	−	3.84866i	1.54208	−	0.501053i	0.951950	+	0.306253i	$0.0990753\pi$
$60$	1.19618	−	0.917038i	0.154426	−	0.118389i
$61$	1.97745	−	1.43670i	0.253186	−	0.183951i	−0.453951	−	0.891026i	$-0.649986\pi$
$61$	1.97745	−	1.43670i	0.253186	−	0.183951i	0.707138	+	0.707076i	$0.249986\pi$
$62$	−8.06616	+	2.62086i	−1.02440	+	0.332849i
$63$	1.22772	−	6.62229i	0.154678	−	0.834330i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−0.137229	−	5.32869i	−0.0170212	−	0.660943i
$66$	0.0456902	−	2.23515i	0.00562408	−	0.275127i
$67$			13.4008i			1.63717i	0.574383	+	0.818587i	$0.305242\pi$
$67$			13.4008i			1.63717i	−0.574383	+	0.818587i	$0.694758\pi$
$68$	3.28944	−	4.52752i	0.398903	−	0.549043i
$69$	1.98183	+	0.643936i	0.238584	+	0.0775208i
$70$	2.68329	+	5.27256i	0.320715	+	0.630192i
$71$	10.9414	−	7.94941i	1.29851	−	0.943421i	0.298568	−	0.954388i	$-0.403491\pi$
$71$	10.9414	−	7.94941i	1.29851	−	0.943421i	0.999940	+	0.0109676i	$0.00349115\pi$
$72$	−2.05947	+	1.49629i	−0.242710	+	0.176339i
$73$	−0.782563	+	0.254270i	−0.0915920	+	0.0297601i	−0.354455	−	0.935073i	$-0.615333\pi$
$73$	−0.782563	+	0.254270i	−0.0915920	+	0.0297601i	0.262863	+	0.964833i	$0.415333\pi$
$74$	−0.465541	−	0.151263i	−0.0541180	−	0.0175840i
$75$	2.82499	+	1.83805i	0.326202	+	0.212240i
$76$	−4.91021			−0.563240
$77$	8.59345	+	1.77555i	0.979315	+	0.202343i
$78$		−	1.60687i		−	0.181942i
$79$	−9.46039	+	13.0211i	−1.06438	+	1.46499i	−0.188736	+	0.982028i	$0.560439\pi$
$79$	−9.46039	+	13.0211i	−1.06438	+	1.46499i	−0.875641	+	0.482962i	$0.839561\pi$
$80$	0.636005	−	2.14371i	0.0711076	−	0.239674i
$81$	1.58130	+	4.86675i	0.175700	+	0.540750i
$82$	7.37102	−	5.35536i	0.813993	−	0.591400i
$83$	−2.44284	−	3.36228i	−0.268136	−	0.369058i	0.653623	−	0.756820i	$-0.273248\pi$
$83$	−2.44284	−	3.36228i	−0.268136	−	0.369058i	−0.921759	+	0.387762i	$0.873248\pi$
$84$	0.767692	+	1.60971i	0.0837621	+	0.175634i
$85$	11.9969	+	3.55929i	1.30125	+	0.386060i
$86$	4.15627	+	3.01970i	0.448182	+	0.325623i
$87$		−	3.82636i		−	0.410229i
$88$	−1.89422	−	2.72249i	−0.201924	−	0.290218i
$89$		−	10.6875i		−	1.13288i	−0.824104	−	0.566439i	$-0.808321\pi$
$89$		−	10.6875i		−	1.13288i	0.824104	−	0.566439i	$-0.191679\pi$
$90$	−4.68971	−	3.22614i	−0.494339	−	0.340065i
$91$	6.20141	+	1.14969i	0.650085	+	0.120520i
$92$	2.94013	−	0.955306i	0.306530	−	0.0995975i
$93$	−3.36031	−	4.62507i	−0.348448	−	0.479598i
$94$	−4.35422	+	3.16353i	−0.449104	+	0.326293i
$95$	−3.66058	−	10.3514i	−0.375567	−	1.06203i
$96$	0.208297	−	0.641072i	0.0212592	−	0.0654291i
$97$	5.14075	+	3.73498i	0.521964	+	0.379229i	0.817343	−	0.576151i	$-0.195446\pi$
$97$	5.14075	+	3.73498i	0.521964	+	0.379229i	−0.295379	+	0.955380i	$0.595446\pi$
$98$	−6.76167	+	1.81104i	−0.683031	+	0.182943i
$99$	−8.08135	+	2.44436i	−0.812206	+	0.245667i
$100$	4.99337	−	0.257358i	0.499337	−	0.0257358i
$101$	11.8433	+	8.60469i	1.17846	+	0.856199i	0.991997	−	0.126264i	$-0.0402987\pi$
$101$	11.8433	+	8.60469i	1.17846	+	0.856199i	0.186460	+	0.982463i	$0.440299\pi$
$102$	3.58764	+	1.16570i	0.355230	+	0.115421i
$103$	5.88324	+	18.1067i	0.579693	+	1.78411i	0.619613	+	0.784908i	$0.287290\pi$
$103$	5.88324	+	18.1067i	0.579693	+	1.78411i	−0.0399201	+	0.999203i	$0.512710\pi$
$104$	−1.40119	−	1.92858i	−0.137398	−	0.189113i
$105$	−2.82117	+	2.81844i	−0.275318	+	0.275052i
$106$	−5.56879	+	1.80941i	−0.540889	+	0.175745i
$107$	−2.95360	+	9.09025i	−0.285535	+	0.878787i	0.700702	+	0.713454i	$0.252870\pi$
$107$	−2.95360	+	9.09025i	−0.285535	+	0.878787i	−0.986238	+	0.165334i	$0.947130\pi$
$108$	−3.02419	−	2.19720i	−0.291003	−	0.211426i
$109$			5.78376i			0.553984i	0.960872	+	0.276992i	$0.0893376\pi$
$109$			5.78376i			0.553984i	−0.960872	+	0.276992i	$0.910662\pi$
$110$	4.32722	−	6.02289i	0.412584	−	0.574260i
$111$		−	0.329953i		−	0.0313177i
$112$	2.32507	+	1.26256i	0.219698	+	0.119301i
$113$	10.0055	+	3.25099i	0.941241	+	0.305828i	0.739152	−	0.673539i	$-0.235227\pi$
$113$	10.0055	+	3.25099i	0.941241	+	0.305828i	0.202090	+	0.979367i	$0.435227\pi$
$114$	−1.02278	−	3.14780i	−0.0957922	−	0.294818i
$115$	4.20579	+	5.48600i	0.392192	+	0.511572i
$116$	−3.33660	−	4.59244i	−0.309796	−	0.426397i
$117$	−5.77142	+	1.87525i	−0.533568	+	0.173367i
$118$	11.8450	+	3.84866i	1.09042	+	0.354298i
$119$	−7.06571	+	13.0118i	−0.647712	+	1.19279i
$120$	1.50675	−	0.0388031i	0.137547	−	0.00354222i
$121$	−2.96882	−	10.5918i	−0.269893	−	0.962890i
$122$	2.44426			0.221293
$123$	4.96853	+	3.60985i	0.447997	+	0.325489i
$124$	−8.06616	−	2.62086i	−0.724363	−	0.235360i
$125$	4.26512	+	10.3348i	0.381484	+	0.924376i
$126$	4.88573	−	4.63591i	0.435255	−	0.412999i
$127$	−12.1870	+	8.85437i	−1.08142	+	0.785698i	−0.977930	−	0.208933i	$-0.933001\pi$
$127$	−12.1870	+	8.85437i	−1.08142	+	0.785698i	−0.103490	+	0.994630i	$0.533001\pi$
$128$	−0.309017	−	0.951057i	−0.0273135	−	0.0840623i
$129$	−1.07011	+	3.29346i	−0.0942179	+	0.289973i
$130$	3.02111	−	4.39166i	0.264969	−	0.385174i
$131$	1.42825			0.124787			0.0623935	−	0.998052i	$-0.480127\pi$
$131$	1.42825			0.124787			0.0623935	+	0.998052i	$0.480127\pi$
$132$	1.35075	−	1.78141i	0.117568	−	0.155052i
$133$	12.8801	−	1.69503i	1.11685	−	0.146978i
$134$	−7.87682	+	10.8415i	−0.680454	+	0.936564i
$135$	2.37746	−	8.01342i	0.204619	−	0.689686i
$136$	5.32242	−	1.72936i	0.456394	−	0.148291i
$137$	−4.30254	−	5.92194i	−0.367591	−	0.505945i	0.584653	−	0.811283i	$-0.301231\pi$
$137$	−4.30254	−	5.92194i	−0.367591	−	0.505945i	−0.952244	+	0.305338i	$0.901231\pi$
$138$	1.22484	+	1.68585i	0.104265	+	0.143509i
$139$	−3.50070	−	10.7740i	−0.296926	−	0.913843i	−0.982568	−	0.185904i	$-0.940479\pi$
$139$	−3.50070	−	10.7740i	−0.296926	−	0.913843i	0.685642	−	0.727939i	$-0.259521\pi$
$140$	−0.928306	+	5.84279i	−0.0784562	+	0.493806i
$141$	−2.93502	−	2.13242i	−0.247173	−	0.179582i
$142$	13.5243			1.13494
$143$	−2.28901	−	7.56775i	−0.191416	−	0.632847i
$144$	−2.54564			−0.212137
$145$	7.19403	−	10.4577i	0.597432	−	0.868463i
$146$	−0.782563	−	0.254270i	−0.0647654	−	0.0210435i
$147$	−2.56944	−	3.95748i	−0.211924	−	0.326407i
$148$	−0.287720	−	0.396013i	−0.0236505	−	0.0325521i
$149$	−3.58142	−	4.92940i	−0.293401	−	0.403832i	0.636714	−	0.771100i	$-0.280293\pi$
$149$	−3.58142	−	4.92940i	−0.293401	−	0.403832i	−0.930115	+	0.367268i	$0.880293\pi$
$150$	1.20509	+	3.14750i	0.0983950	+	0.256992i
$151$	−3.88513	−	1.26235i	−0.316167	−	0.102729i	0.146635	−	0.989191i	$-0.453156\pi$
$151$	−3.88513	−	1.26235i	−0.316167	−	0.102729i	−0.462802	+	0.886462i	$0.653156\pi$
$152$	−3.97244	−	2.88615i	−0.322208	−	0.234098i
$153$		−	14.2462i		−	1.15174i
$154$	5.90861	+	6.48755i	0.476129	+	0.522782i
$155$	−0.488233	−	18.9584i	−0.0392158	−	1.52278i
$156$	0.944492	−	1.29998i	0.0756199	−	0.104082i
$157$	−1.67477	+	5.15440i	−0.133661	+	0.411366i	−0.995379	−	0.0960207i	$-0.969388\pi$
$157$	−1.67477	+	5.15440i	−0.133661	+	0.411366i	0.861718	+	0.507387i	$0.169388\pi$
$158$	−15.3072	+	4.97362i	−1.21778	+	0.395680i
$159$	−2.31992	−	3.19310i	−0.183982	−	0.253229i
$160$	1.77458	−	1.36046i	0.140293	−	0.107554i
$161$	−7.38258	+	3.52085i	−0.581829	+	0.277482i
$162$	−1.58130	+	4.86675i	−0.124239	+	0.382368i
$163$	2.94690	−	4.05606i	0.230819	−	0.317695i	−0.677860	−	0.735191i	$-0.737092\pi$
$163$	2.94690	−	4.05606i	0.230819	−	0.317695i	0.908679	+	0.417496i	$0.137092\pi$
$164$	9.11108			0.711456
$165$	4.76245	+	1.51951i	0.370756	+	0.118294i
$166$		−	4.15601i		−	0.322569i
$167$	12.3923	−	17.0565i	0.958941	−	1.31987i	0.0115022	−	0.999934i	$-0.496339\pi$
$167$	12.3923	−	17.0565i	0.958941	−	1.31987i	0.947439	−	0.319936i	$-0.103661\pi$
$168$	−0.325089	+	1.75352i	−0.0250811	+	0.135287i
$169$	2.26115	+	6.95911i	0.173935	+	0.535316i
$170$	7.61360	+	9.93113i	0.583936	+	0.761683i
$171$	−10.1124	+	7.34710i	−0.773316	+	0.561847i
$172$	1.58755	+	4.88598i	0.121050	+	0.372553i
$173$	15.4967	+	5.03517i	1.17819	+	0.382817i	0.831694	−	0.555235i	$-0.187372\pi$
$173$	15.4967	+	5.03517i	1.17819	+	0.382817i	0.346495	+	0.938052i	$0.387372\pi$
$174$	2.24908	−	3.09559i	0.170502	−	0.234676i
$175$	−13.0094	+	2.39883i	−0.983422	+	0.181334i
$176$	0.0677834	−	3.31593i	0.00510936	−	0.249948i
$177$			8.39514i			0.631017i
$178$	6.28198	−	8.64640i	0.470854	−	0.648075i
$179$	−3.08743	+	9.50214i	−0.230766	+	0.710224i	0.766889	+	0.641779i	$0.221804\pi$
$179$	−3.08743	+	9.50214i	−0.230766	+	0.710224i	−0.997655	+	0.0684442i	$0.978196\pi$
$180$	−1.89778	−	5.36655i	−0.141452	−	0.399999i
$181$	−14.2401	−	19.5998i	−1.05846	−	1.45684i	−0.881238	−	0.472673i	$-0.843289\pi$
$181$	−14.2401	−	19.5998i	−1.05846	−	1.45684i	−0.177221	−	0.984171i	$-0.556711\pi$
$182$	4.34128	+	4.57522i	0.321797	+	0.339138i
$183$	0.509132	+	1.56695i	0.0376361	+	0.115832i
$184$	2.94013	+	0.955306i	0.216749	+	0.0704261i
$185$	0.620352	−	0.901781i	0.0456092	−	0.0663003i
$186$		−	5.71690i		−	0.419184i
$187$	18.5570	+	0.379338i	1.35702	+	0.0277399i
$188$	−5.38212			−0.392531
$189$	8.69135	+	4.71959i	0.632203	+	0.343300i
$190$	3.12292	−	10.5261i	0.226561	−	0.763642i
$191$	3.20465	+	9.86290i	0.231880	+	0.713654i	0.997520	+	0.0703844i	$0.0224226\pi$
$191$	3.20465	+	9.86290i	0.231880	+	0.713654i	−0.765640	+	0.643270i	$0.777577\pi$
$192$	0.545328	−	0.396204i	0.0393557	−	0.0285936i
$193$	17.7314	−	12.8826i	1.27634	−	0.927313i	0.276901	−	0.960899i	$-0.410693\pi$
$193$	17.7314	−	12.8826i	1.27634	−	0.927313i	0.999436	+	0.0335860i	$0.0106928\pi$
$194$	1.96359	+	6.04332i	0.140978	+	0.433885i
$195$	3.44466	+	1.02198i	0.246677	+	0.0731852i
$196$	−6.53481	−	2.50924i	−0.466772	−	0.179232i
$197$	−6.70325			−0.477587			−0.238794	−	0.971070i	$-0.576752\pi$
$197$	−6.70325			−0.477587			−0.238794	+	0.971070i	$0.576752\pi$
$198$	−7.97471	−	2.77257i	−0.566738	−	0.197038i
$199$			25.4506i			1.80414i	0.431586	+	0.902072i	$0.357954\pi$
$199$			25.4506i			1.80414i	−0.431586	+	0.902072i	$0.642046\pi$
$200$	4.19099	+	2.72682i	0.296348	+	0.192816i
$201$	−8.59090	−	2.79135i	−0.605955	−	0.196887i
$202$	4.52375	+	13.9227i	0.318290	+	0.979596i
$203$	10.3377	+	10.8948i	0.725564	+	0.764663i
$204$	2.21729	+	3.05183i	0.155241	+	0.213671i
$205$	6.79233	+	19.2074i	0.474397	+	1.34150i
$206$	−5.88324	+	18.1067i	−0.409905	+	1.26156i
$207$	4.62568	−	6.36670i	0.321507	−	0.442517i
$208$		−	2.38385i		−	0.165290i
$209$	−9.30101	−	13.3680i	−0.643364	−	0.924683i
$210$	−3.93901	+	0.621925i	−0.271818	+	0.0429169i
$211$	10.4445	−	14.3756i	0.719030	−	0.989660i	−0.280526	−	0.959847i	$-0.590509\pi$
$211$	10.4445	−	14.3756i	0.719030	−	0.989660i	0.999555	−	0.0298131i	$-0.00949122\pi$
$212$	−5.56879	−	1.80941i	−0.382466	−	0.124271i
$213$	2.81708	+	8.67007i	0.193023	+	0.594063i
$214$	−7.73262	+	5.61808i	−0.528591	+	0.384044i
$215$	−9.11678	+	6.98928i	−0.621759	+	0.476665i
$216$	−1.15514	−	3.55515i	−0.0785972	−	0.241897i
$217$	22.0634	+	4.09037i	1.49776	+	0.277672i
$218$	−3.39961	+	4.67916i	−0.230251	+	0.316913i
$219$		−	0.554642i		−	0.0374793i
$220$	7.04096	−	2.32914i	0.474701	−	0.157031i
$221$	13.3408			0.897400
$222$	0.193941	−	0.266937i	0.0130165	−	0.0179157i
$223$	2.59669	−	7.99180i	0.173887	−	0.535170i	−0.825694	−	0.564119i	$-0.809216\pi$
$223$	2.59669	−	7.99180i	0.173887	−	0.535170i	0.999581	+	0.0289486i	$0.00921593\pi$
$224$	1.13890	+	2.38807i	0.0760962	+	0.159560i
$225$	9.89860	−	8.00155i	0.659907	−	0.533437i
$226$	6.18376	+	8.51121i	0.411337	+	0.566157i
$227$	−13.2731	+	4.31268i	−0.880963	+	0.286242i	−0.714357	−	0.699781i	$-0.753281\pi$
$227$	−13.2731	+	4.31268i	−0.880963	+	0.286242i	−0.166606	+	0.986024i	$0.553281\pi$
$228$	1.02278	−	3.14780i	0.0677353	−	0.208468i
$229$	0.996049	−	1.37094i	0.0658208	−	0.0905945i	−0.774837	−	0.632160i	$-0.782168\pi$
$229$	0.996049	−	1.37094i	0.0658208	−	0.0905945i	0.840658	+	0.541566i	$0.182168\pi$
$230$	0.177962	+	6.91037i	0.0117344	+	0.455656i
$231$	−2.92824	+	5.13918i	−0.192664	+	0.338133i
$232$		−	5.67657i		−	0.372685i
$233$	−3.34376	−	2.42939i	−0.219057	−	0.159154i	0.472845	−	0.881146i	$-0.343227\pi$
$233$	−3.34376	−	2.42939i	−0.219057	−	0.159154i	−0.691902	+	0.721991i	$0.743227\pi$
$234$	−5.77142	−	1.87525i	−0.377290	−	0.122589i
$235$	−4.01238	−	11.3462i	−0.261739	−	0.740146i
$236$	7.32059	+	10.0759i	0.476530	+	0.655887i
$237$	−6.37690	−	8.77705i	−0.414224	−	0.570130i
$238$	−13.3644	+	6.37367i	−0.866288	+	0.413144i
$239$	−21.7162	−	7.05601i	−1.40470	−	0.456415i	−0.493994	−	0.869465i	$-0.664463\pi$
$239$	−21.7162	−	7.05601i	−1.40470	−	0.456415i	−0.910708	+	0.413050i	$0.864463\pi$
$240$	1.24179	+	0.854253i	0.0801575	+	0.0551418i
$241$	12.5057			0.805564			0.402782	−	0.915296i	$-0.368043\pi$
$241$	12.5057			0.805564			0.402782	+	0.915296i	$0.368043\pi$
$242$	3.82388	−	10.3140i	0.245808	−	0.663007i
$243$	−14.6636			−0.940673
$244$	1.97745	+	1.43670i	0.126593	+	0.0919753i
$245$	0.418103	−	15.6469i	0.0267116	−	0.999643i
$246$	1.89781	+	5.84085i	0.121000	+	0.372399i
$247$	−6.88016	−	9.46973i	−0.437774	−	0.602544i
$248$	−4.98516	−	6.86149i	−0.316558	−	0.435705i
$249$	2.66430	−	0.865683i	0.168843	−	0.0548604i
$250$	−2.62411	+	10.8680i	−0.165963	+	0.687354i
$251$	1.16567	−	1.60440i	0.0735762	−	0.101269i	−0.770643	−	0.637267i	$-0.780065\pi$
$251$	1.16567	−	1.60440i	0.0735762	−	0.101269i	0.844219	+	0.535998i	$0.180065\pi$
$252$	6.67755	−	0.878770i	0.420646	−	0.0553573i
$253$	8.17005	+	6.19491i	0.513647	+	0.389471i
$254$	−15.0639			−0.945196
$255$	−4.78068	+	6.94948i	−0.299378	+	0.435194i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	4.65049	+	14.3127i	0.290090	+	0.892804i	0.984827	+	0.173540i	$0.0555207\pi$
$257$	4.65049	+	14.3127i	0.290090	+	0.892804i	−0.694737	+	0.719264i	$0.744479\pi$
$258$	−2.80158	+	2.03547i	−0.174419	+	0.126723i
$259$	0.891435	+	0.939472i	0.0553911	+	0.0583760i
$260$	5.02548	−	1.77717i	0.311667	−	0.110215i
$261$	−13.7432	−	4.46545i	−0.850685	−	0.276404i
$262$	1.15548	+	0.839506i	0.0713858	+	0.0518648i
$263$	−1.21070			−0.0746547			−0.0373274	−	0.999303i	$-0.511884\pi$
$263$	−1.21070			−0.0746547			−0.0373274	+	0.999303i	$0.511884\pi$
$264$	2.13987	−	0.647244i	0.131700	−	0.0398351i
$265$	−0.337070	−	13.0887i	−0.0207061	−	0.804031i
$266$	11.4166	+	6.19945i	0.699995	+	0.380112i
$267$	6.85148	+	2.22618i	0.419304	+	0.136240i
$268$	−12.7450	+	4.14109i	−0.778522	+	0.252957i
$269$	−11.4744	−	15.7931i	−0.699604	−	0.962923i	−0.999959	−	0.00909498i	$-0.997105\pi$
$269$	−11.4744	−	15.7931i	−0.699604	−	0.962923i	0.300354	−	0.953828i	$-0.402895\pi$
$270$	6.63358	−	5.08556i	0.403707	−	0.309497i
$271$	2.08068	+	6.40368i	0.126392	+	0.388996i	0.994152	−	0.107988i	$-0.0344408\pi$
$271$	2.08068	+	6.40368i	0.126392	+	0.388996i	−0.867760	+	0.496984i	$0.834441\pi$
$272$	5.32242	+	1.72936i	0.322719	+	0.104858i
$273$	−2.02877	+	3.73607i	−0.122787	+	0.226117i
$274$		−	7.31992i		−	0.442212i
$275$	10.1592	+	13.1069i	0.612622	+	0.790376i
$276$			2.08382i			0.125431i
$277$	−12.2430	−	8.89509i	−0.735613	−	0.534454i	0.155721	−	0.987801i	$-0.450230\pi$
$277$	−12.2430	−	8.89509i	−0.735613	−	0.534454i	−0.891334	+	0.453347i	$0.850230\pi$
$278$	3.50070	−	10.7740i	0.209958	−	0.646184i
$279$	−20.5335	+	6.67175i	−1.22931	+	0.399427i
$280$	−4.18532	+	4.18128i	−0.250121	+	0.249879i
$281$	10.7771	+	14.8334i	0.642906	+	0.884885i	0.998766	−	0.0496545i	$-0.0158120\pi$
$281$	10.7771	+	14.8334i	0.642906	+	0.884885i	−0.355860	+	0.934539i	$0.615812\pi$
$282$	−1.12108	−	3.45032i	−0.0667592	−	0.205464i
$283$	7.61968	+	2.47578i	0.452943	+	0.147170i	0.526599	−	0.850114i	$-0.323467\pi$
$283$	7.61968	+	2.47578i	0.452943	+	0.147170i	−0.0736565	+	0.997284i	$0.523467\pi$
$284$	10.9414	+	7.94941i	0.649254	+	0.471710i
$285$	7.39846	−	0.190531i	0.438247	−	0.0112861i
$286$	2.59636	−	7.46788i	0.153526	−	0.441585i
$287$	−23.8996	+	3.14520i	−1.41075	+	0.185655i
$288$	−2.05947	−	1.49629i	−0.121355	−	0.0881697i
$289$	−4.42477	+	13.6180i	−0.260280	+	0.801061i
$290$	11.9670	−	4.23190i	0.702724	−	0.248505i
$291$	−3.46519	+	2.51761i	−0.203133	+	0.147585i
$292$	−0.483650	−	0.665688i	−0.0283035	−	0.0389564i
$293$	−26.1557	+	8.49850i	−1.52803	+	0.496488i	−0.948045	−	0.318138i	$-0.896943\pi$
$293$	−26.1557	+	8.49850i	−1.52803	+	0.496488i	−0.579988	+	0.814625i	$0.696943\pi$
$294$	0.247425	−	4.71195i	0.0144301	−	0.274806i
$295$	−15.7839	+	22.9444i	−0.918973	+	1.33588i
$296$		−	0.489499i		−	0.0284515i
$297$	0.253382	−	12.3953i	0.0147027	−	0.719249i
$298$		−	6.09308i		−	0.352963i
$299$	5.96207	+	4.33170i	0.344796	+	0.250509i
$300$	−0.875119	+	3.25472i	−0.0505250	+	0.187911i
$301$	−5.85103	−	12.2686i	−0.337248	−	0.707148i
$302$	−2.40114	−	3.30489i	−0.138170	−	0.190175i
$303$	−7.98315	+	5.80010i	−0.458620	+	0.333207i
$304$	−1.51734	−	4.66989i	−0.0870253	−	0.267836i
$305$	−1.55456	+	5.23979i	−0.0890140	+	0.300029i
$306$	8.37372	−	11.5254i	0.478694	−	0.658865i
$307$		−	2.33563i		−	0.133301i	−0.997776	−	0.0666506i	$-0.978769\pi$
$307$		−	2.33563i		−	0.133301i	0.997776	−	0.0666506i	$-0.0212313\pi$
$308$	0.966875	+	8.72153i	0.0550928	+	0.496956i
$309$	−12.8332			−0.730054
$310$	10.7485	−	15.6246i	0.610473	−	0.887420i
$311$	0.238158	+	0.0773821i	0.0135047	+	0.00438794i	0.315762	−	0.948839i	$-0.397740\pi$
$311$	0.238158	+	0.0773821i	0.0135047	+	0.00438794i	−0.302257	+	0.953227i	$0.597740\pi$
$312$	1.52822	−	0.496549i	0.0865185	−	0.0281116i
$313$	−14.3039	+	10.3924i	−0.808504	+	0.587413i	−0.913397	−	0.407071i	$-0.866550\pi$
$313$	−14.3039	+	10.3924i	−0.808504	+	0.587413i	0.104892	+	0.994484i	$0.466550\pi$
$314$	−4.38460	+	3.18560i	−0.247437	+	0.179774i
$315$	6.83070	+	13.4220i	0.384866	+	0.756247i
$316$	−15.3072	−	4.97362i	−0.861100	−	0.279788i
$317$	15.5342	−	21.3810i	0.872486	−	1.20087i	−0.105960	−	0.994370i	$-0.533791\pi$
$317$	15.5342	−	21.3810i	0.872486	−	1.20087i	0.978446	−	0.206504i	$-0.0662085\pi$
$318$		−	3.94689i		−	0.221330i
$319$	6.18261	−	17.7829i	0.346159	−	0.995654i
$320$	2.23533	−	0.0575660i	0.124959	−	0.00321804i
$321$	−5.21227	−	3.78694i	−0.290921	−	0.211366i
$322$	−8.04213	−	1.49095i	−0.448170	−	0.0830871i
$323$	26.1342	−	8.49152i	1.45415	−	0.472481i
$324$	−4.13990	+	3.00781i	−0.229995	+	0.167101i
$325$	7.49302	+	9.26950i	0.415638	+	0.514179i
$326$	4.76818	−	1.54928i	0.264085	−	0.0858065i
$327$	−3.70781	−	1.20474i	−0.205042	−	0.0666223i
$328$	7.37102	+	5.35536i	0.406996	+	0.295700i
$329$	14.1180	−	1.85794i	0.778351	−	0.102431i
$330$	2.95975	+	4.02861i	0.162929	+	0.221768i
$331$	−0.379546			−0.0208617			−0.0104309	−	0.999946i	$-0.503320\pi$
$331$	−0.379546			−0.0208617			−0.0104309	+	0.999946i	$0.503320\pi$
$332$	2.44284	−	3.36228i	0.134068	−	0.184529i
$333$	−1.18510	−	0.385062i	−0.0649431	−	0.0211013i
$334$	20.0511	−	6.51499i	1.09715	−	0.356485i
$335$	−18.2314	−	23.7809i	−0.996086	−	1.29929i
$336$	−1.29370	+	1.22755i	−0.0705769	+	0.0669682i
$337$	−7.03698	−	21.6576i	−0.383329	−	1.17976i	−0.937685	−	0.347486i	$-0.887036\pi$
$337$	−7.03698	−	21.6576i	−0.383329	−	1.17976i	0.554357	−	0.832279i	$-0.312964\pi$
$338$	−2.26115	+	6.95911i	−0.122990	+	0.378526i
$339$	−4.16824	+	5.73709i	−0.226388	+	0.311596i
$340$	0.322158	+	12.5096i	0.0174715	+	0.678429i
$341$	−8.14383	−	26.9245i	−0.441013	−	1.45804i
$342$	−12.4996			−0.675903
$343$	18.0079	+	4.32623i	0.972334	+	0.233594i
$344$	−1.58755	+	4.88598i	−0.0855951	+	0.263435i
$345$	−4.39297	+	1.55349i	−0.236510	+	0.0836373i
$346$	9.57746	+	13.1822i	0.514887	+	0.708682i
$347$	−9.01167	+	6.54736i	−0.483772	+	0.351481i	−0.802784	−	0.596270i	$-0.796649\pi$
$347$	−9.01167	+	6.54736i	−0.483772	+	0.351481i	0.319012	+	0.947751i	$0.396649\pi$
$348$	3.63909	−	1.18241i	0.195075	−	0.0633839i
$349$	8.59721	−	26.4595i	0.460198	−	1.41634i	−0.404724	−	0.914439i	$-0.632633\pi$
$349$	8.59721	−	26.4595i	0.460198	−	1.41634i	0.864922	−	0.501905i	$-0.167367\pi$
$350$	−11.9349	−	5.70607i	−0.637945	−	0.305002i
$351$		−	8.91110i		−	0.475639i
$352$	2.00389	−	2.64280i	0.106808	−	0.140862i
$353$	−15.8096			−0.841463			−0.420731	−	0.907185i	$-0.638226\pi$
$353$	−15.8096			−0.841463			−0.420731	+	0.907185i	$0.638226\pi$
$354$	−4.93454	+	6.79181i	−0.262268	+	0.360981i
$355$	−8.60155	+	28.9923i	−0.456523	+	1.53875i
$356$	10.1645	−	3.30263i	0.538715	−	0.175039i
$357$	−6.86975	−	7.23995i	−0.363586	−	0.383179i
$358$	−8.08301	+	5.87265i	−0.427200	+	0.310379i
$359$	6.03343	−	1.96038i	0.318432	−	0.103465i	−0.145440	−	0.989367i	$-0.546460\pi$
$359$	6.03343	−	1.96038i	0.318432	−	0.103465i	0.463872	+	0.885902i	$0.346460\pi$
$360$	1.61904	−	5.45712i	0.0853309	−	0.287615i
$361$	−4.13422	−	3.00369i	−0.217591	−	0.158089i
$362$		−	24.2267i		−	1.27333i
$363$	7.40849	+	0.303011i	0.388845	+	0.0159040i
$364$	0.822920	+	6.25317i	0.0431328	+	0.327755i
$365$	1.04280	−	1.51587i	0.0545824	−	0.0793443i
$366$	−0.509132	+	1.56695i	−0.0266127	+	0.0819056i
$367$	8.73107	+	26.8715i	0.455758	+	1.40268i	0.870243	+	0.492623i	$0.163962\pi$
$367$	8.73107	+	26.8715i	0.455758	+	1.40268i	−0.414484	+	0.910056i	$0.636038\pi$
$368$	1.81710	+	2.50102i	0.0947229	+	0.130375i
$369$	18.7640	−	13.6328i	0.976812	−	0.709696i
$370$	1.03193	−	0.364923i	0.0536474	−	0.0189714i
$371$	15.2323	+	2.82394i	0.790822	+	0.146612i
$372$	3.36031	−	4.62507i	0.174224	−	0.239799i
$373$	8.15506			0.422253			0.211126	−	0.977459i	$-0.432287\pi$
$373$	8.15506			0.422253			0.211126	+	0.977459i	$0.432287\pi$
$374$	14.7900	+	11.2144i	0.764772	+	0.579885i
$375$	−7.51378	+	0.581532i	−0.388010	+	0.0300302i
$376$	−4.35422	−	3.16353i	−0.224552	−	0.163147i
$377$	4.18165	−	12.8698i	0.215366	−	0.662828i
$378$	4.25734	+	8.92688i	0.218974	+	0.459149i
$379$	−23.0727	+	16.7633i	−1.18517	+	0.861075i	−0.992745	−	0.120238i	$-0.961634\pi$
$379$	−23.0727	+	16.7633i	−1.18517	+	0.861075i	−0.192422	+	0.981312i	$0.561634\pi$
$380$	8.71357	−	6.68017i	0.446997	−	0.342685i
$381$	−3.13777	−	9.65707i	−0.160753	−	0.494747i
$382$	−3.20465	+	9.86290i	−0.163964	+	0.504630i
$383$	−15.5181	−	11.2746i	−0.792940	−	0.576105i	0.115894	−	0.993262i	$-0.463027\pi$
$383$	−15.5181	−	11.2746i	−0.792940	−	0.576105i	−0.908835	+	0.417157i	$0.863027\pi$
$384$	0.674063			0.0343981
$385$	−17.6653	+	8.54023i	−0.900310	+	0.435250i
$386$	21.9173			1.11556
$387$	10.5804	+	7.68708i	0.537830	+	0.390756i
$388$	−1.96359	+	6.04332i	−0.0996863	+	0.306803i
$389$	0.0246554	+	0.0758815i	0.00125008	+	0.00384735i	0.951680	−	0.307093i	$-0.0993562\pi$
$389$	0.0246554	+	0.0758815i	0.00125008	+	0.00384735i	−0.950430	+	0.310940i	$0.899356\pi$
$390$	2.18608	+	2.85151i	0.110697	+	0.144392i
$391$	−13.9965	+	10.1691i	−0.707835	+	0.514273i
$392$	−3.81187	−	5.87108i	−0.192529	−	0.296534i
$393$	−0.297500	+	0.915612i	−0.0150069	+	0.0461865i
$394$	−5.42305	−	3.94007i	−0.273209	−	0.198498i
$395$	−0.926524	−	35.9776i	−0.0466185	−	1.81023i
$396$	−4.82200	−	6.93047i	−0.242314	−	0.348269i
$397$	−22.2524			−1.11682			−0.558409	−	0.829566i	$-0.688588\pi$
$397$	−22.2524			−1.11682			−0.558409	+	0.829566i	$0.688588\pi$
$398$	−14.9595	+	20.5899i	−0.749851	+	1.03208i
$399$	−1.59625	+	8.61016i	−0.0799127	+	0.431047i
$400$	1.78780	+	4.66945i	0.0893899	+	0.233473i
$401$	16.4261	−	11.9343i	0.820280	−	0.595969i	−0.0965125	−	0.995332i	$-0.530769\pi$
$401$	16.4261	−	11.9343i	0.820280	−	0.595969i	0.916793	+	0.399363i	$0.130769\pi$
$402$	−5.30947	−	7.30786i	−0.264812	−	0.364483i
$403$	−6.24774	−	19.2286i	−0.311222	−	0.957842i
$404$	−4.52375	+	13.9227i	−0.225065	+	0.692679i
$405$	−9.42718	−	6.48513i	−0.468440	−	0.322249i
$406$	1.95959	+	14.8904i	0.0972526	+	0.738998i
$407$	0.533135	−	1.53345i	0.0264265	−	0.0760103i
$408$			3.77227i			0.186755i
$409$	−2.94712	−	2.14121i	−0.145726	−	0.105876i	0.512534	−	0.858667i	$-0.328707\pi$
$409$	−2.94712	−	2.14121i	−0.145726	−	0.105876i	−0.658259	+	0.752791i	$0.728707\pi$
$410$	−5.79470	+	19.5315i	−0.286180	+	0.964593i
$411$	4.69259	−	1.52472i	0.231469	−	0.0752087i
$412$	−15.4025	+	11.1906i	−0.758828	+	0.551320i
$413$	−22.6812	−	23.9034i	−1.11607	−	1.17621i
$414$	7.48451	−	2.43186i	0.367844	−	0.119520i
$415$	8.90928	+	2.64324i	0.437339	+	0.129752i
$416$	1.40119	−	1.92858i	0.0686992	−	0.0945563i
$417$	7.63612			0.373942
$418$	0.332831	−	16.2819i	0.0162793	−	0.796375i
$419$		−	9.91367i		−	0.484314i	−0.970237	−	0.242157i	$-0.922145\pi$
$419$		−	9.91367i		−	0.484314i	0.970237	−	0.242157i	$-0.0778550\pi$
$420$	−3.55229	−	1.81215i	−0.173334	−	0.0884237i
$421$	−2.45217	+	7.54702i	−0.119512	+	0.367819i	−0.992861	−	0.119275i	$-0.961943\pi$
$421$	−2.45217	+	7.54702i	−0.119512	+	0.367819i	0.873350	+	0.487094i	$0.161943\pi$
$422$	16.8996	−	5.49100i	0.822658	−	0.267298i
$423$	−11.0843	+	8.05321i	−0.538936	+	0.391560i
$424$	−3.44170	−	4.73710i	−0.167144	−	0.230054i
$425$	−26.1318	+	10.0051i	−1.26758	+	0.485319i
$426$	−2.81708	+	8.67007i	−0.136488	+	0.420066i
$427$	−5.68307	−	3.08603i	−0.275023	−	0.149343i
$428$	−9.55805			−0.462006
$429$	5.32826	+	0.108919i	0.257251	+	0.00525865i
$430$	−11.4838	+	0.295741i	−0.553799	+	0.0142619i
$431$	0.394145	−	0.542494i	0.0189853	−	0.0261310i	−0.799419	−	0.600774i	$-0.794859\pi$
$431$	0.394145	−	0.542494i	0.0189853	−	0.0261310i	0.818404	+	0.574643i	$0.194859\pi$
$432$	1.15514	−	3.55515i	0.0555766	−	0.171047i
$433$	−0.540557	−	1.66366i	−0.0259775	−	0.0799505i	0.937227	−	0.348719i	$-0.113383\pi$
$433$	−0.540557	−	1.66366i	−0.0259775	−	0.0799505i	−0.963205	+	0.268769i	$0.913383\pi$
$434$	15.4454	+	16.2777i	0.741402	+	0.781355i
$435$	5.20563	+	6.79019i	0.249591	+	0.325565i
$436$	−5.50069	+	1.78728i	−0.263435	+	0.0855953i
$437$	14.4367	+	4.69075i	0.690599	+	0.224389i
$438$	0.326011	−	0.448715i	0.0155774	−	0.0214404i
$439$	−23.8669			−1.13910			−0.569551	−	0.821956i	$-0.692883\pi$
$439$	−23.8669			−1.13910			−0.569551	+	0.821956i	$0.692883\pi$
$440$	7.06529	+	2.25426i	0.336824	+	0.107468i
$441$	−17.2128	+	4.61026i	−0.819655	+	0.219536i
$442$	10.7929	+	7.84154i	0.513368	+	0.372984i
$443$	−21.0096	−	6.82644i	−0.998197	−	0.324334i	−0.236052	−	0.971740i	$-0.575854\pi$
$443$	−21.0096	−	6.82644i	−0.998197	−	0.324334i	−0.762145	+	0.647406i	$0.775854\pi$
$444$	0.313804	−	0.101961i	0.0148925	−	0.00483886i
$445$	14.5400	+	18.9659i	0.689263	+	0.899070i
$446$	6.79823	−	4.93920i	0.321905	−	0.233878i
$447$	3.90610	−	1.26917i	0.184752	−	0.0600296i
$448$	−0.482283	+	2.60142i	−0.0227857	+	0.122906i
$449$	12.7709	+	9.27860i	0.602696	+	0.437884i	0.846835	−	0.531856i	$-0.178505\pi$
$449$	12.7709	+	9.27860i	0.602696	+	0.437884i	−0.244139	+	0.969740i	$0.578505\pi$
$450$	12.7113	−	0.655140i	0.599218	−	0.0308836i
$451$	17.2584	+	24.8048i	0.812665	+	1.16801i
$452$			10.5204i			0.494840i
$453$	1.61852	−	2.22770i	0.0760447	−	0.104667i
$454$	−13.2731	−	4.31268i	−0.622935	−	0.202404i
$455$	−12.5690	+	6.39658i	−0.589245	+	0.299876i
$456$	2.67768	−	1.94545i	0.125394	−	0.0911038i
$457$	10.1325	−	7.36172i	0.473980	−	0.344367i	−0.325010	−	0.945710i	$-0.605368\pi$
$457$	10.1325	−	7.36172i	0.473980	−	0.344367i	0.798990	+	0.601344i	$0.205368\pi$
$458$	1.61164	−	0.523654i	0.0753071	−	0.0244687i
$459$	19.8958	+	6.46453i	0.928656	+	0.301739i
$460$	−3.91784	+	5.69521i	−0.182670	+	0.265540i
$461$	−13.8421			−0.644692			−0.322346	−	0.946622i	$-0.604472\pi$
$461$	−13.8421			−0.644692			−0.322346	+	0.946622i	$0.604472\pi$
$462$	−5.38973	+	2.43650i	−0.250753	+	0.113356i
$463$		−	6.40102i		−	0.297481i	−0.988876	−	0.148740i	$-0.952478\pi$
$463$		−	6.40102i		−	0.297481i	0.988876	−	0.148740i	$-0.0475219\pi$
$464$	3.33660	−	4.59244i	0.154898	−	0.213199i
$465$	12.2554	+	3.63598i	0.568330	+	0.168615i
$466$	−1.27720	−	3.93083i	−0.0591653	−	0.182092i
$467$	−16.9533	+	12.3173i	−0.784503	+	0.569975i	−0.906327	−	0.422577i	$-0.861126\pi$
$467$	−16.9533	+	12.3173i	−0.784503	+	0.569975i	0.121824	+	0.992552i	$0.461126\pi$
$468$	−3.56693	−	4.90946i	−0.164882	−	0.226940i
$469$	32.0022	−	15.2623i	1.47773	−	0.704746i
$470$	3.42306	−	11.5377i	0.157894	−	0.532195i
$471$	−2.95549	−	2.14729i	−0.136182	−	0.0989420i
$472$			12.4545i			0.573266i
$473$	−10.2949	+	13.5772i	−0.473358	+	0.624281i
$474$		−	10.8490i		−	0.498312i
$475$	20.5787	+	13.3893i	0.944214	+	0.614342i
$476$	−14.5584	−	2.69901i	−0.667284	−	0.123709i
$477$	−14.1761	+	4.60610i	−0.649081	+	0.210899i
$478$	−13.4213	−	18.4729i	−0.613877	−	0.844930i
$479$	−9.87703	+	7.17608i	−0.451293	+	0.327884i	−0.790106	−	0.612970i	$-0.789975\pi$
$479$	−9.87703	+	7.17608i	−0.451293	+	0.327884i	0.338813	+	0.940854i	$0.389975\pi$
$480$	0.502515	+	1.42101i	0.0229366	+	0.0648601i
$481$	0.360590	−	1.10978i	0.0164415	−	0.0506017i
$482$	10.1173	+	7.35068i	0.460832	+	0.334814i
$483$	−0.719347	−	5.46614i	−0.0327314	−	0.248718i
$484$	9.15598	−	6.09656i	0.416181	−	0.277116i
$485$	−14.2040	+	0.365793i	−0.644970	+	0.0166098i
$486$	−11.8631	−	8.61907i	−0.538123	−	0.390969i
$487$	−1.85492	−	0.602701i	−0.0840546	−	0.0273110i	0.266688	−	0.963783i	$-0.414071\pi$
$487$	−1.85492	−	0.602701i	−0.0840546	−	0.0273110i	−0.350742	+	0.936472i	$0.614071\pi$
$488$	0.755318	+	2.32463i	0.0341916	+	0.105231i
$489$	1.98639	+	2.73404i	0.0898278	+	0.123637i
$490$	9.53526	−	12.4128i	0.430759	−	0.560755i
$491$	−8.20805	+	2.66696i	−0.370424	+	0.120358i	−0.488313	−	0.872669i	$-0.662387\pi$
$491$	−8.20805	+	2.66696i	−0.370424	+	0.120358i	0.117889	+	0.993027i	$0.462387\pi$
$492$	−1.89781	+	5.84085i	−0.0855598	+	0.263326i
$493$	25.7008	+	18.6727i	1.15751	+	0.840977i
$494$		−	11.7052i		−	0.526643i
$495$	11.0155	−	15.3321i	0.495112	−	0.689126i
$496$		−	8.48127i		−	0.380820i
$497$	−31.4450	−	17.0753i	−1.41050	−	0.765933i
$498$	2.66430	+	0.865683i	0.119390	+	0.0387922i
$499$	−3.79657	−	11.6846i	−0.169958	−	0.523076i	0.829410	−	0.558641i	$-0.188677\pi$
$499$	−3.79657	−	11.6846i	−0.169958	−	0.523076i	−0.999367	+	0.0355646i	$0.988677\pi$
$500$	−8.51102	+	7.25001i	−0.380624	+	0.324230i
$501$	8.35316	+	11.4971i	0.373191	+	0.513654i
$502$	1.88609	−	0.612827i	0.0841802	−	0.0273518i
$503$	31.9064	+	10.3670i	1.42264	+	0.462243i	0.916439	−	0.400174i	$-0.131050\pi$
$503$	31.9064	+	10.3670i	1.42264	+	0.462243i	0.506198	+	0.862417i	$0.331050\pi$
$504$	5.91878	+	3.21403i	0.263644	+	0.143164i
$505$	−32.7233	+	0.842719i	−1.45617	+	0.0375005i
$506$	2.96844	+	9.81402i	0.131963	+	0.436287i
$507$	−4.93228			−0.219050
$508$	−12.1870	−	8.85437i	−0.540710	−	0.392849i
$509$	−3.65467	−	1.18747i	−0.161990	−	0.0526339i	0.226899	−	0.973918i	$-0.427141\pi$
$509$	−3.65467	−	1.18747i	−0.161990	−	0.0526339i	−0.388890	+	0.921284i	$0.627141\pi$
$510$	−7.95245	+	2.81224i	−0.352141	+	0.124528i
$511$	1.49848	+	1.57923i	0.0662888	+	0.0698610i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	−5.67198	−	17.4565i	−0.250424	−	0.770725i
$514$	−4.65049	+	14.3127i	−0.205124	+	0.631308i
$515$	−35.0739	−	24.1280i	−1.54554	−	1.06320i
$516$	−3.46295			−0.152448
$517$	−10.1949	−	14.6527i	−0.448371	−	0.644427i
$518$	0.168978	+	1.28402i	0.00742446	+	0.0564166i
$519$	−6.45581	+	8.88566i	−0.283378	+	0.390037i
$520$	5.11029	+	1.51614i	0.224101	+	0.0664873i
$521$	−16.0740	+	5.22276i	−0.704215	+	0.228813i	−0.639166	−	0.769069i	$-0.720720\pi$
$521$	−16.0740	+	5.22276i	−0.704215	+	0.228813i	−0.0650487	+	0.997882i	$0.520720\pi$
$522$	−8.49379	−	11.6907i	−0.371763	−	0.511688i
$523$	10.9714	+	15.1009i	0.479747	+	0.660315i	0.978456	−	0.206455i	$-0.0661926\pi$
$523$	10.9714	+	15.1009i	0.479747	+	0.660315i	−0.498710	+	0.866769i	$0.666193\pi$
$524$	0.441354	+	1.35835i	0.0192807	+	0.0593397i
$525$	1.17201	−	8.83965i	0.0511506	−	0.385794i
$526$	−0.979474	−	0.711629i	−0.0427071	−	0.0310285i
$527$	47.4639			2.06756
$528$	2.11163	+	0.734152i	0.0918969	+	0.0319499i
$529$	13.4430			0.584480
$530$	7.42063	−	10.7871i	0.322332	−	0.468561i
$531$	30.1530	+	9.79731i	1.30853	+	0.425167i
$532$	5.59226	+	11.7260i	0.242455	+	0.508384i
$533$	12.7664	+	17.5714i	0.552974	+	0.761103i
$534$	4.23445	+	5.82822i	0.183242	+	0.252212i
$535$	−7.12555	−	20.1496i	−0.308064	−	0.871145i
$536$	−12.7450	−	4.14109i	−0.550498	−	0.178868i
$537$	−5.44845	−	3.95853i	−0.235118	−	0.170823i
$538$		−	19.5214i		−	0.841625i
$539$	−5.54697	−	22.5440i	−0.238925	−	0.971038i
$540$	8.35589	−	0.215188i	0.359580	−	0.00926022i
$541$	−6.83863	+	9.41257i	−0.294016	+	0.404678i	−0.930313	−	0.366766i	$-0.880465\pi$
$541$	−6.83863	+	9.41257i	−0.294016	+	0.404678i	0.636298	+	0.771444i	$0.280465\pi$
$542$	−2.08068	+	6.40368i	−0.0893730	+	0.275062i
$543$	15.5311	−	5.04635i	0.666502	−	0.216560i
$544$	3.28944	+	4.52752i	0.141033	+	0.194116i
$545$	−7.86860	−	10.2638i	−0.337054	−	0.439651i
$546$	−3.83732	+	1.83007i	−0.164222	+	0.0783196i
$547$	0.584504	−	1.79892i	0.0249916	−	0.0769161i	−0.937783	−	0.347222i	$-0.887125\pi$
$547$	0.584504	−	1.79892i	0.0249916	−	0.0769161i	0.962774	+	0.270306i	$0.0871249\pi$
$548$	4.30254	−	5.92194i	0.183795	−	0.252973i
$549$	6.22221			0.265557
$550$	0.514913	+	16.5751i	0.0219560	+	0.706766i
$551$		−	27.8731i		−	1.18744i
$552$	−1.22484	+	1.68585i	−0.0521326	+	0.0717544i
$553$	41.8699	+	7.76233i	1.78049	+	0.330088i
$554$	−4.67643	−	14.3926i	−0.198682	−	0.611481i
$555$	0.448889	+	0.585528i	0.0190543	+	0.0248543i
$556$	9.16495	−	6.65873i	0.388681	−	0.282393i
$557$	11.7403	+	36.1330i	0.497453	+	1.53100i	0.813098	+	0.582126i	$0.197779\pi$
$557$	11.7403	+	36.1330i	0.497453	+	1.53100i	−0.315645	+	0.948877i	$0.602221\pi$
$558$	−20.5335	−	6.67175i	−0.869254	−	0.282438i
$559$	−7.19853	+	9.90793i	−0.304465	+	0.419061i
$560$	−5.84369	+	0.922652i	−0.246941	+	0.0389891i
$561$	−4.10855	+	11.8174i	−0.173463	+	0.498930i
$562$			18.3351i			0.773418i
$563$	0.949152	−	1.30640i	0.0400020	−	0.0550580i	−0.788547	−	0.614974i	$-0.789167\pi$
$563$	0.949152	−	1.30640i	0.0400020	−	0.0550580i	0.828549	+	0.559916i	$0.189167\pi$
$564$	1.12108	−	3.45032i	0.0472059	−	0.145285i
$565$	−22.1785	+	7.84301i	−0.933056	+	0.329958i
$566$	4.70922	+	6.48168i	0.197943	+	0.272445i
$567$	9.82120	−	9.31902i	0.412452	−	0.391362i
$568$	4.17925	+	12.8624i	0.175357	+	0.539695i
$569$	−13.3128	−	4.32559i	−0.558101	−	0.181338i	0.0163654	−	0.999866i	$-0.494791\pi$
$569$	−13.3128	−	4.32559i	−0.558101	−	0.181338i	−0.574467	+	0.818528i	$0.694791\pi$
$570$	6.09747	+	4.19456i	0.255395	+	0.175691i
$571$			21.3396i			0.893036i	0.894775	+	0.446518i	$0.147336\pi$
$571$			21.3396i			0.893036i	−0.894775	+	0.446518i	$0.852664\pi$
$572$	6.49001	−	4.51554i	0.271361	−	0.188804i
$573$	−6.99034			−0.292026
$574$	−21.1839	−	11.5033i	−0.884198	−	0.480139i
$575$	−14.9270	−	4.01353i	−0.622500	−	0.167376i
$576$	−0.786646	−	2.42105i	−0.0327769	−	0.100877i
$577$	9.11405	−	6.62175i	0.379423	−	0.275667i	−0.381685	−	0.924293i	$-0.624656\pi$
$577$	9.11405	−	6.62175i	0.379423	−	0.275667i	0.761108	+	0.648626i	$0.224656\pi$
$578$	−11.5842	+	8.41641i	−0.481839	+	0.350076i
$579$	4.56529	+	14.0505i	0.189727	+	0.583920i
$580$	12.1689	+	3.61033i	0.505287	+	0.149911i
$581$	−5.24722	+	9.66299i	−0.217691	+	0.400888i
$582$	−4.28321			−0.177545
$583$	−5.62241	−	18.5884i	−0.232856	−	0.769852i
$584$		−	0.822835i		−	0.0340492i
$585$	7.69065	−	11.1796i	0.317969	−	0.462219i
$586$	−26.1557	−	8.49850i	−1.08048	−	0.351070i
$587$	7.23235	+	22.2589i	0.298511	+	0.918722i	0.982019	+	0.188780i	$0.0604532\pi$
$587$	7.23235	+	22.2589i	0.298511	+	0.918722i	−0.683509	+	0.729942i	$0.739547\pi$
$588$	2.96978	−	3.66661i	0.122472	−	0.151209i
$589$	−24.4782	−	33.6914i	−1.00861	−	1.38823i
$590$	−26.2558	+	9.28489i	−1.08094	+	0.382253i
$591$	1.39627	−	4.29727i	0.0574347	−	0.176766i
$592$	0.287720	−	0.396013i	0.0118252	−	0.0162760i
$593$			11.3204i			0.464874i	0.972611	+	0.232437i	$0.0746700\pi$
$593$			11.3204i			0.464874i	−0.972611	+	0.232437i	$0.925330\pi$
$594$	7.49077	−	9.87908i	0.307350	−	0.405344i
$595$	−5.16346	−	32.7032i	−0.211681	−	1.34070i
$596$	3.58142	−	4.92940i	0.146701	−	0.201916i
$597$	−16.3156	−	5.30127i	−0.667755	−	0.216967i
$598$	2.27731	+	7.00884i	0.0931261	+	0.286613i
$599$	9.17756	−	6.66789i	0.374985	−	0.272442i	−0.384290	−	0.923212i	$-0.625554\pi$
$599$	9.17756	−	6.66789i	0.374985	−	0.272442i	0.759275	+	0.650770i	$0.225554\pi$
$600$	−2.62106	+	2.11874i	−0.107004	+	0.0864971i
$601$	4.86199	+	14.9637i	0.198325	+	0.610381i	0.999922	+	0.0125160i	$0.00398407\pi$
$601$	4.86199	+	14.9637i	0.198325	+	0.610381i	−0.801597	+	0.597865i	$0.796016\pi$
$602$	2.47769	−	13.3646i	0.100983	−	0.544701i
$603$	−20.0515	+	27.5986i	−0.816562	+	1.12390i
$604$		−	4.08507i		−	0.166219i
$605$	19.6782	+	14.7570i	0.800031	+	0.599958i
$606$	−9.86772			−0.400849
$607$	5.87071	−	8.08033i	0.238285	−	0.327971i	−0.673081	−	0.739569i	$-0.735029\pi$
$607$	5.87071	−	8.08033i	0.238285	−	0.327971i	0.911365	+	0.411598i	$0.135029\pi$
$608$	1.51734	−	4.66989i	0.0615362	−	0.189389i
$609$	−9.13764	+	4.35786i	−0.370276	+	0.176589i
$610$	−4.33754	+	3.32533i	−0.175622	+	0.134639i
$611$	−7.54139	−	10.3798i	−0.305092	−	0.419923i
$612$	13.5490	−	4.40233i	0.547684	−	0.177953i
$613$	3.64951	−	11.2320i	0.147402	−	0.453658i	−0.849910	−	0.526928i	$-0.823344\pi$
$613$	3.64951	−	11.2320i	0.147402	−	0.453658i	0.997312	+	0.0732703i	$0.0233436\pi$
$614$	1.37285	−	1.88956i	0.0554036	−	0.0762565i
$615$	−13.7281	+	0.353538i	−0.553571	+	0.0142560i
$616$	−4.34417	+	7.62418i	−0.175032	+	0.307187i
$617$			3.15658i			0.127079i	0.997979	+	0.0635396i	$0.0202389\pi$
$617$			3.15658i			0.127079i	−0.997979	+	0.0635396i	$0.979761\pi$
$618$	−10.3823	−	7.54315i	−0.417636	−	0.303430i
$619$	26.5326	+	8.62096i	1.06644	+	0.346506i	0.789098	−	0.614267i	$-0.210548\pi$
$619$	26.5326	+	8.62096i	1.06644	+	0.346506i	0.277337	+	0.960773i	$0.410548\pi$
$620$	17.8796	−	6.32281i	0.718064	−	0.253930i
$621$	6.79252	+	9.34910i	0.272574	+	0.375166i
$622$	0.147190	+	0.202589i	0.00590176	+	0.00812308i
$623$	−25.5226	+	12.1721i	−1.02254	+	0.487664i
$624$	1.52822	+	0.496549i	0.0611778	+	0.0198779i
$625$	−21.6290	−	12.5375i	−0.865159	−	0.501498i
$626$	−17.6806			−0.706658
$627$	10.5072	−	3.17811i	0.419618	−	0.126921i
$628$	−5.41966			−0.216268
$629$	2.21622	+	1.61018i	0.0883663	+	0.0642019i
$630$	−2.36313	+	14.8736i	−0.0941494	+	0.592580i
$631$	5.55946	+	17.1102i	0.221318	+	0.681148i	0.998644	+	0.0520501i	$0.0165756\pi$
$631$	5.55946	+	17.1102i	0.221318	+	0.681148i	−0.777326	+	0.629098i	$0.783424\pi$
$632$	−9.46039	−	13.0211i	−0.376314	−	0.517952i
$633$	7.04025	+	9.69008i	0.279825	+	0.385146i
$634$	25.1348	−	8.16680i	0.998231	−	0.324345i
$635$	9.58075	−	32.2927i	0.380201	−	1.28150i
$636$	2.31992	−	3.19310i	0.0919909	−	0.126615i
$637$	−4.31726	−	16.1188i	−0.171056	−	0.638651i
$638$	15.4544	−	10.7527i	0.611845	−	0.425702i
$639$	34.4281			1.36195
$640$	1.84225	+	1.26732i	0.0728215	+	0.0500952i
$641$	6.03684	−	18.5795i	0.238441	−	0.733845i	−0.758206	−	0.652016i	$-0.773924\pi$
$641$	6.03684	−	18.5795i	0.238441	−	0.733845i	0.996646	−	0.0818296i	$-0.0260763\pi$
$642$	−1.99091	−	6.12739i	−0.0785750	−	0.241829i
$643$	20.2882	−	14.7402i	0.800089	−	0.581298i	−0.110852	−	0.993837i	$-0.535358\pi$
$643$	20.2882	−	14.7402i	0.800089	−	0.581298i	0.910940	+	0.412539i	$0.135358\pi$
$644$	−5.62987	−	5.93325i	−0.221848	−	0.233803i
$645$	−2.58164	−	7.30035i	−0.101652	−	0.287451i
$646$	26.1342	+	8.49152i	1.02824	+	0.334094i
$647$	−3.68269	−	2.67563i	−0.144781	−	0.105190i	0.513037	−	0.858367i	$-0.328520\pi$
$647$	−3.68269	−	2.67563i	−0.144781	−	0.105190i	−0.657818	+	0.753177i	$0.728520\pi$
$648$	−5.11720			−0.201023
$649$	−13.5648	+	39.0162i	−0.532465	+	1.53152i
$650$	0.613503	+	11.9035i	0.0240636	+	0.466892i
$651$	−7.21795	+	13.2922i	−0.282894	+	0.520962i
$652$	4.76818	+	1.54928i	0.186736	+	0.0606743i
$653$	−32.5923	+	10.5899i	−1.27544	+	0.414414i	−0.866970	−	0.498360i	$-0.833936\pi$
$653$	−32.5923	+	10.5899i	−1.27544	+	0.414414i	−0.408465	+	0.912774i	$0.633936\pi$
$654$	−2.29155	−	3.15405i	−0.0896067	−	0.123333i
$655$	−2.53455	+	1.94309i	−0.0990330	+	0.0759227i
$656$	2.81548	+	8.66515i	0.109926	+	0.338317i
$657$	−1.99212	−	0.647280i	−0.0777201	−	0.0252528i
$658$	12.5138	+	6.79526i	0.487838	+	0.264907i
$659$		−	5.73814i		−	0.223526i	−0.993735	−	0.111763i	$-0.964350\pi$
$659$		−	5.73814i		−	0.223526i	0.993735	−	0.111763i	$-0.0356498\pi$
$660$	0.0265358	+	4.99891i	0.00103291	+	0.194582i
$661$			35.0644i			1.36385i	0.731423	+	0.681924i	$0.238856\pi$
$661$			35.0644i			1.36385i	−0.731423	+	0.681924i	$0.761144\pi$
$662$	−0.307059	−	0.223091i	−0.0119342	−	0.00867069i
$663$	−2.77885	+	8.55242i	−0.107922	+	0.332148i
$664$	3.95260	−	1.28428i	0.153390	−	0.0498396i
$665$	−20.5508	+	20.5309i	−0.796927	+	0.796156i
$666$	−0.732432	−	1.00811i	−0.0283812	−	0.0390633i
$667$	5.42286	+	16.6898i	0.209974	+	0.646233i
$668$	20.0511	+	6.51499i	0.775800	+	0.252073i
$669$	4.58243	+	3.32933i	0.177167	+	0.128719i
$670$	−0.771433	−	29.9553i	−0.0298031	−	1.15727i
$671$	−0.165680	+	8.10500i	−0.00639601	+	0.312890i
$672$	−1.76816	+	0.232690i	−0.0682081	+	0.00897623i
$673$	36.7847	+	26.7256i	1.41795	+	1.03020i	0.992106	+	0.125399i	$0.0400212\pi$
$673$	36.7847	+	26.7256i	1.41795	+	1.03020i	0.425840	+	0.904799i	$0.359979\pi$
$674$	7.03698	−	21.6576i	0.271054	−	0.834220i
$675$	6.68298	+	17.4549i	0.257228	+	0.671840i
$676$	−5.91977	+	4.30097i	−0.227684	+	0.165422i
$677$	16.5745	+	22.8129i	0.637010	+	0.876770i	0.998452	−	0.0556252i	$-0.0177152\pi$
$677$	16.5745	+	22.8129i	0.637010	+	0.876770i	−0.361441	+	0.932395i	$0.617715\pi$
$678$	−6.74435	+	2.19137i	−0.259015	+	0.0841592i
$679$	3.06458	−	16.5303i	0.117608	−	0.634374i
$680$	−7.09234	+	10.3099i	−0.271979	+	0.395365i
$681$		−	9.40729i		−	0.360488i
$682$	9.23733	−	26.5692i	0.353716	−	1.01739i
$683$		−	6.09685i		−	0.233289i	−0.993174	−	0.116645i	$-0.962786\pi$
$683$		−	6.09685i		−	0.233289i	0.993174	−	0.116645i	$-0.0372139\pi$
$684$	−10.1124	−	7.34710i	−0.386658	−	0.280923i
$685$	15.6918	+	4.65551i	0.599553	+	0.177878i
$686$	12.0258	+	14.0848i	0.459147	+	0.537759i
$687$	0.671400	+	0.924102i	0.0256155	+	0.0352567i
$688$	−4.15627	+	3.01970i	−0.158456	+	0.115125i
$689$	−4.31337	−	13.2752i	−0.164326	−	0.505744i
$690$	−4.46711	−	1.32532i	−0.170060	−	0.0504541i
$691$	−16.7695	+	23.0812i	−0.637942	+	0.878052i	−0.998504	−	0.0546834i	$-0.982585\pi$
$691$	−16.7695	+	23.0812i	−0.637942	+	0.878052i	0.360562	+	0.932735i	$0.382585\pi$
$692$			16.2941i			0.619411i
$693$	15.0412	+	16.5150i	0.571367	+	0.627352i
$694$	−11.1390			−0.422832
$695$	20.8700	+	14.3568i	0.791643	+	0.544586i
$696$	3.63909	+	1.18241i	0.137939	+	0.0448192i
$697$	−48.4930	+	15.7563i	−1.83680	+	0.596813i
$698$	22.5078	−	16.3529i	0.851932	−	0.618965i
$699$	2.25391	−	1.63756i	0.0852505	−	0.0619381i
$700$	−6.30156	−	11.6314i	−0.238177	−	0.439627i
$701$	16.9830	+	5.51812i	0.641440	+	0.208416i	0.611636	−	0.791139i	$-0.290512\pi$
$701$	16.9830	+	5.51812i	0.641440	+	0.208416i	0.0298038	+	0.999556i	$0.490512\pi$
$702$	5.23781	−	7.20923i	0.197689	−	0.272095i
$703$		−	2.40354i		−	0.0906513i
$704$	3.17459	−	0.960214i	0.119647	−	0.0361894i
$705$	8.10951	−	0.208843i	0.305422	−	0.00786547i
$706$	−12.7903	−	9.29268i	−0.481368	−	0.349735i
$707$	7.06022	−	38.0827i	0.265527	−	1.43225i
$708$	−7.98425	+	2.59424i	−0.300066	+	0.0974975i
$709$	−15.6175	+	11.3468i	−0.586529	+	0.426138i	−0.841072	−	0.540923i	$-0.818075\pi$
$709$	−15.6175	+	11.3468i	−0.586529	+	0.426138i	0.254543	+	0.967061i	$0.418075\pi$
$710$	−24.0000	+	18.3994i	−0.900705	+	0.690516i
$711$	−38.9667	+	12.6611i	−1.46137	+	0.474827i
$712$	10.1645	+	3.30263i	0.380929	+	0.123771i
$713$	21.2118	+	15.4113i	0.794390	+	0.577158i
$714$	−1.30221	−	9.89518i	−0.0487340	−	0.370318i
$715$	14.3577	+	10.3155i	0.536947	+	0.385776i
$716$	−9.99114			−0.373387
$717$	9.04682	−	12.4519i	0.337860	−	0.465024i
$718$	6.03343	+	1.96038i	0.225166	+	0.0731608i
$719$	−17.2914	+	5.61832i	−0.644861	+	0.209528i	−0.613147	−	0.789969i	$-0.710097\pi$
$719$	−17.2914	+	5.61832i	−0.644861	+	0.209528i	−0.0317142	+	0.999497i	$0.510097\pi$
$720$	4.51744	−	3.46325i	0.168355	−	0.129068i
$721$	36.5398	−	34.6714i	1.36081	−	1.29123i
$722$	−1.57913	−	4.86007i	−0.0587692	−	0.180873i
$723$	−2.60490	+	8.01706i	−0.0968773	+	0.298158i
$724$	14.2401	−	19.5998i	0.529230	−	0.728422i
$725$	1.46091	+	28.3452i	0.0542568	+	1.05271i
$726$	5.81549	+	4.59975i	0.215833	+	0.170713i
$727$	28.5508			1.05889			0.529445	−	0.848344i	$-0.322400\pi$
$727$	28.5508			1.05889			0.529445	+	0.848344i	$0.322400\pi$
$728$	−3.00976	+	5.54262i	−0.111549	+	0.205423i
$729$	−1.68952	+	5.19980i	−0.0625747	+	0.192585i
$730$	1.73465	−	0.613426i	0.0642021	−	0.0227039i
$731$	−16.8992	−	23.2598i	−0.625041	−	0.860295i
$732$	−1.33292	+	0.968426i	−0.0492663	+	0.0357940i
$733$	12.6550	−	4.11187i	0.467425	−	0.151876i	−0.0658288	−	0.997831i	$-0.520969\pi$
$733$	12.6550	−	4.11187i	0.467425	−	0.151876i	0.533254	+	0.845955i	$0.320969\pi$
$734$	−8.73107	+	26.8715i	−0.322270	+	0.991844i
$735$	9.94369	+	3.52723i	0.366778	+	0.130104i
$736$			3.09144i			0.113952i
$737$	−35.4158	−	26.8539i	−1.30456	−	0.989175i
$738$	23.1935			0.853765
$739$	17.7106	−	24.3765i	0.651493	−	0.896704i	−0.347669	−	0.937617i	$-0.613027\pi$
$739$	17.7106	−	24.3765i	0.651493	−	0.896704i	0.999163	+	0.0409136i	$0.0130268\pi$
$740$	1.04934	+	0.311324i	0.0385747	+	0.0114445i
$741$	7.50389	−	2.43816i	0.275662	−	0.0895681i
$742$	10.6633	+	11.2379i	0.391463	+	0.412558i
$743$	35.8797	−	26.0682i	1.31630	−	0.956348i	0.316330	−	0.948649i	$-0.397549\pi$
$743$	35.8797	−	26.0682i	1.31630	−	0.956348i	0.999970	−	0.00769861i	$-0.00245057\pi$
$744$	5.43710	−	1.76662i	0.199334	−	0.0647675i
$745$	13.0618	+	3.87523i	0.478547	+	0.141977i
$746$	6.59758	+	4.79342i	0.241555	+	0.175500i
$747$		−	10.5797i		−	0.387091i
$748$	5.37367	+	17.7660i	0.196481	+	0.649590i
$749$	25.0720	−	3.29950i	0.916113	−	0.120561i
$750$	−6.42059	−	3.94602i	−0.234447	−	0.144088i
$751$	0.760696	−	2.34118i	0.0277582	−	0.0854309i	−0.936218	−	0.351421i	$-0.885699\pi$
$751$	0.760696	−	2.34118i	0.0277582	−	0.0854309i	0.963976	+	0.265990i	$0.0856987\pi$
$752$	−1.66317	−	5.11870i	−0.0606494	−	0.186660i
$753$	0.785732	+	1.08147i	0.0286337	+	0.0394108i
$754$	10.9477	−	7.95397i	0.398692	−	0.289667i
$755$	8.61186	−	3.04543i	0.313418	−	0.110834i
$756$	−1.80282	+	9.72440i	−0.0655681	+	0.353673i
$757$	16.1397	−	22.2144i	0.586608	−	0.807396i	−0.407793	−	0.913075i	$-0.633701\pi$
$757$	16.1397	−	22.2144i	0.586608	−	0.807396i	0.994400	+	0.105678i	$0.0337013\pi$
$758$	−28.5195			−1.03587
$759$	−5.67318	+	3.94721i	−0.205923	+	0.143275i
$760$	10.9759	−	0.282661i	0.398139	−	0.0102532i
$761$	10.7149	+	7.78483i	0.388415	+	0.282200i	0.764806	−	0.644261i	$-0.222835\pi$
$761$	10.7149	+	7.78483i	0.388415	+	0.282200i	−0.376391	+	0.926461i	$0.622835\pi$
$762$	3.13777	−	9.65707i	0.113669	−	0.349839i
$763$	13.8121	−	6.58715i	0.500030	−	0.238471i
$764$	−8.38988	+	6.09560i	−0.303535	+	0.220531i
$765$	19.3815	+	25.2811i	0.700739	+	0.914039i
$766$	−5.92740	−	18.2427i	−0.214166	−	0.659135i
$767$	−9.17465	+	28.2367i	−0.331277	+	1.01957i
$768$	0.545328	+	0.396204i	0.0196778	+	0.0142968i
$769$	38.5514			1.39020			0.695100	−	0.718913i	$-0.255360\pi$
$769$	38.5514			1.39020			0.695100	+	0.718913i	$0.255360\pi$
$770$	−19.3114	−	3.47424i	−0.695934	−	0.125203i
$771$	−10.1442			−0.365333
$772$	17.7314	+	12.8826i	0.638168	+	0.463656i
$773$	10.8560	−	33.4112i	0.390462	−	1.20172i	−0.541978	−	0.840393i	$-0.682324\pi$
$773$	10.8560	−	33.4112i	0.390462	−	1.20172i	0.932440	−	0.361325i	$-0.117676\pi$
$774$	4.04134	+	12.4380i	0.145263	+	0.447073i
$775$	26.6586	+	32.9790i	0.957606	+	1.18464i
$776$	−5.14075	+	3.73498i	−0.184542	+	0.134078i
$777$	−0.787952	+	0.375784i	−0.0282676	+	0.0134812i
$778$	−0.0246554	+	0.0758815i	−0.000883939	+	0.00272049i
$779$	36.1933	+	26.2959i	1.29676	+	0.942150i
$780$	0.0925009	+	3.59187i	0.00331206	+	0.128610i
$781$	−0.916725	+	44.8458i	−0.0328030	+	1.60471i
$782$	−17.3007			−0.618671
$783$	12.4726	−	17.1670i	0.445734	−	0.613500i
$784$	0.367065	−	6.99037i	0.0131095	−	0.249656i
$785$	−4.04037	−	11.4254i	−0.144207	−	0.407789i
$786$	−0.778866	+	0.565879i	−0.0277812	+	0.0201842i
$787$	8.62206	+	11.8672i	0.307343	+	0.423022i	0.934550	−	0.355831i	$-0.115802\pi$
$787$	8.62206	+	11.8672i	0.307343	+	0.423022i	−0.627207	+	0.778852i	$0.715802\pi$
$788$	−2.07142	−	6.37517i	−0.0737913	−	0.227106i
$789$	0.252184	−	0.776143i	0.00897799	−	0.0276314i
$790$	20.3975	−	29.6510i	0.725710	−	1.05494i
$791$	−3.63172	−	27.5965i	−0.129129	−	0.981219i
$792$	0.172552	−	8.44117i	0.00613137	−	0.299944i
$793$			5.82676i			0.206914i
$794$	−18.0026	−	13.0797i	−0.638888	−	0.464180i
$795$	8.46099	+	2.51024i	0.300080	+	0.0890291i
$796$	−24.2049	+	7.86466i	−0.857921	+	0.278755i
$797$	10.7444	−	7.80626i	0.380586	−	0.276512i	−0.381001	−	0.924575i	$-0.624421\pi$
$797$	10.7444	−	7.80626i	0.380586	−	0.276512i	0.761587	+	0.648063i	$0.224421\pi$
$798$	−6.35232	+	6.02751i	−0.224870	+	0.213372i
$799$	28.6459	−	9.30762i	1.01342	−	0.329280i
$800$	−1.29828	+	4.82851i	−0.0459010	+	0.170714i
$801$	15.9917	−	22.0106i	0.565037	−	0.777707i
$802$	20.3038			0.716951
$803$	0.896187	−	2.57769i	0.0316257	−	0.0909647i
$804$		−	9.03301i		−	0.318570i
$805$	8.31100	−	16.2918i	0.292924	−	0.574209i
$806$	6.24774	−	19.2286i	0.220067	−	0.677297i
$807$	12.5146	−	4.06624i	0.440534	−	0.143138i
$808$	−11.8433	+	8.60469i	−0.416647	+	0.302712i
$809$	−10.1565	−	13.9793i	−0.357085	−	0.491485i	0.592249	−	0.805755i	$-0.298240\pi$
$809$	−10.1565	−	13.9793i	−0.357085	−	0.491485i	−0.949334	+	0.314270i	$0.898240\pi$
$810$	−3.81489	−	10.7877i	−0.134041	−	0.379043i
$811$	8.45624	−	26.0256i	0.296939	−	0.913883i	−0.685625	−	0.727955i	$-0.740471\pi$
$811$	8.45624	−	26.0256i	0.296939	−	0.913883i	0.982563	−	0.185928i	$-0.0595291\pi$
$812$	−7.16702	+	13.1984i	−0.251513	+	0.463173i
$813$	−4.53862			−0.159176
$814$	1.33265	−	0.927218i	0.0467095	−	0.0324990i
$815$	0.288611	+	11.2070i	0.0101096	+	0.392562i
$816$	−2.21729	+	3.05183i	−0.0776205	+	0.106836i
$817$	−7.79522	+	23.9912i	−0.272720	+	0.839346i
$818$	−1.12570	−	3.46454i	−0.0393591	−	0.121135i
$819$	11.0513	+	11.6469i	0.386165	+	0.406974i
$820$	−16.1683	+	12.3953i	−0.564623	+	0.432862i
$821$	7.72752	−	2.51082i	0.269692	−	0.0876283i	−0.171049	−	0.985263i	$-0.554716\pi$
$821$	7.72752	−	2.51082i	0.269692	−	0.0876283i	0.440741	+	0.897634i	$0.354716\pi$
$822$	4.69259	+	1.52472i	0.163673	+	0.0531806i
$823$	5.64902	−	7.77521i	0.196912	−	0.271027i	−0.699131	−	0.714994i	$-0.746429\pi$
$823$	5.64902	−	7.77521i	0.196912	−	0.271027i	0.896043	+	0.443967i	$0.146429\pi$
$824$	−19.0386			−0.663240
$825$	−10.5186	+	3.78264i	−0.366210	+	0.131695i
$826$	−4.29938	−	32.6699i	−0.149595	−	1.13673i
$827$	17.9007	+	13.0056i	0.622468	+	0.452249i	0.853783	−	0.520629i	$-0.174303\pi$
$827$	17.9007	+	13.0056i	0.622468	+	0.452249i	−0.231315	+	0.972879i	$0.574303\pi$
$828$	7.48451	+	2.43186i	0.260105	+	0.0845131i
$829$	31.7667	−	10.3216i	1.10330	−	0.358485i	0.299931	−	0.953961i	$-0.403036\pi$
$829$	31.7667	−	10.3216i	1.10330	−	0.358485i	0.803373	+	0.595476i	$0.203036\pi$
$830$	5.65410	+	7.37517i	0.196257	+	0.255996i
$831$	8.25258	−	5.99585i	0.286279	−	0.207994i
$832$	2.26718	−	0.736651i	0.0786003	−	0.0255388i
$833$	39.1204	+	2.05422i	1.35544	+	0.0711744i
$834$	6.17775	+	4.48840i	0.213918	+	0.155421i
$835$	1.21366	+	47.1273i	0.0420005	+	1.63091i
$836$	9.83954	−	12.9767i	0.340308	−	0.448809i
$837$		−	31.7039i		−	1.09585i
$838$	5.82711	−	8.02033i	0.201294	−	0.277058i
$839$	27.9077	+	9.06775i	0.963480	+	0.313054i	0.748181	−	0.663495i	$-0.230927\pi$
$839$	27.9077	+	9.06775i	0.963480	+	0.313054i	0.215299	+	0.976548i	$0.430927\pi$
$840$	−1.80871	−	3.55404i	−0.0624063	−	0.122626i
$841$	2.60780	−	1.89468i	0.0899241	−	0.0653337i
$842$	−6.41988	+	4.66431i	−0.221244	+	0.160743i
$843$	−11.7541	+	3.81913i	−0.404832	+	0.131538i
$844$	16.8996	+	5.49100i	0.581707	+	0.189008i
$845$	−13.4802	−	9.27329i	−0.463734	−	0.319011i
$846$	−13.7009			−0.471048
$847$	−21.9128	+	19.1528i	−0.752933	+	0.658098i
$848$		−	5.85537i		−	0.201074i
$849$	−3.17431	+	4.36906i	−0.108942	+	0.149946i
$850$	−27.0219	−	7.26557i	−0.926843	−	0.249207i
$851$	0.467621	+	1.43919i	0.0160298	+	0.0493348i
$852$	−7.37520	+	5.35840i	−0.252670	+	0.183576i
$853$	−13.7046	−	18.8628i	−0.469238	−	0.645850i	0.507155	−	0.861855i	$-0.330697\pi$
$853$	−13.7046	−	18.8628i	−0.469238	−	0.645850i	−0.976392	+	0.216005i	$0.930697\pi$
$854$	−2.78378	−	5.83707i	−0.0952589	−	0.199741i
$855$	7.94983	−	26.7956i	0.271879	−	0.916390i
$856$	−7.73262	−	5.61808i	−0.264296	−	0.192022i
$857$			9.58814i			0.327525i	0.986500	+	0.163762i	$0.0523630\pi$
$857$			9.58814i			0.327525i	−0.986500	+	0.163762i	$0.947637\pi$
$858$	4.24663	+	3.21999i	0.144978	+	0.109929i
$859$			9.92918i			0.338779i	0.985549	+	0.169390i	$0.0541796\pi$
$859$			9.92918i			0.338779i	−0.985549	+	0.169390i	$0.945820\pi$
$860$	−9.46444	−	6.51076i	−0.322735	−	0.222015i
$861$	2.96191	−	15.9765i	0.100942	−	0.544477i
$862$	0.637740	−	0.207214i	0.0217215	−	0.00705775i
$863$	−14.5321	−	20.0017i	−0.494678	−	0.680865i	0.486564	−	0.873645i	$-0.338250\pi$
$863$	−14.5321	−	20.0017i	−0.494678	−	0.680865i	−0.981242	+	0.192779i	$0.938250\pi$
$864$	3.02419	−	2.19720i	0.102885	−	0.0747504i
$865$	−34.3502	+	12.1473i	−1.16794	+	0.413022i
$866$	0.540557	−	1.66366i	0.0183689	−	0.0565336i
$867$	−7.80847	−	5.67319i	−0.265190	−	0.192671i
$868$	2.92778	+	22.2475i	0.0993755	+	0.755129i
$869$	−15.4546	−	51.0949i	−0.524262	−	1.73328i
$870$	0.220268	+	8.55317i	0.00746780	+	0.289980i
$871$	−25.8446	−	18.7772i	−0.875710	−	0.636241i
$872$	−5.50069	−	1.78728i	−0.186277	−	0.0605250i
$873$	4.99860	+	15.3841i	0.169177	+	0.520673i
$874$	8.92234	+	12.2806i	0.301803	+	0.415396i
$875$	19.8228	−	21.9558i	0.670133	−	0.742241i
$876$	0.527496	−	0.171394i	0.0178224	−	0.00579086i
$877$	−6.01498	+	18.5122i	−0.203112	+	0.625113i	0.796674	+	0.604409i	$0.206591\pi$
$877$	−6.01498	+	18.5122i	−0.203112	+	0.625113i	−0.999786	+	0.0207040i	$0.993409\pi$
$878$	−19.3087	−	14.0286i	−0.651637	−	0.473442i
$879$		−	18.5379i		−	0.625267i
$880$	4.39092	+	5.97661i	0.148018	+	0.201471i
$881$			48.0261i			1.61804i	0.587780	+	0.809021i	$0.300002\pi$
$881$			48.0261i			1.61804i	−0.587780	+	0.809021i	$0.699998\pi$
$882$	−16.6353	−	6.38763i	−0.560138	−	0.215083i
$883$	−30.2083	−	9.81527i	−1.01659	−	0.330310i	−0.247115	−	0.968986i	$-0.579482\pi$
$883$	−30.2083	−	9.81527i	−1.01659	−	0.330310i	−0.769476	+	0.638676i	$0.779482\pi$
$884$	4.12254	+	12.6879i	0.138656	+	0.426739i
$885$	−11.4213	−	14.8978i	−0.383922	−	0.500786i
$886$	−12.9847	−	17.8719i	−0.436228	−	0.600417i
$887$	13.4431	−	4.36794i	0.451377	−	0.146661i	−0.0745018	−	0.997221i	$-0.523737\pi$
$887$	13.4431	−	4.36794i	0.451377	−	0.146661i	0.525879	+	0.850560i	$0.323737\pi$
$888$	0.313804	+	0.101961i	0.0105306	+	0.00342159i
$889$	35.0247	+	19.0192i	1.17469	+	0.637882i
$890$	0.615239	+	23.8902i	0.0206229	+	0.800800i
$891$	−16.0306	−	5.57337i	−0.537046	−	0.186715i
$892$	8.40307			0.281356
$893$	−21.3802	−	15.5336i	−0.715460	−	0.519812i
$894$	3.90610	+	1.26917i	0.130640	+	0.0424473i
$895$	−7.44842	−	21.0627i	−0.248973	−	0.704047i
$896$	−1.91925	+	1.82112i	−0.0641177	+	0.0608393i
$897$	−4.01881	+	2.91984i	−0.134184	+	0.0974905i
$898$	4.87805	+	15.0131i	0.162783	+	0.500993i
$899$	14.8775	−	45.7881i	0.496191	−	1.52712i
$900$	10.6688	+	6.94151i	0.355625	+	0.231384i
$901$	32.7686			1.09168
$902$	−0.617580	+	30.2117i	−0.0205631	+	1.00594i
$903$	9.08377	−	1.19543i	0.302289	−	0.0397814i
$904$	−6.18376	+	8.51121i	−0.205669	+	0.283079i
$905$	51.9351	+	15.4083i	1.72638	+	0.512190i
$906$	2.61882	−	0.850906i	0.0870045	−	0.0282695i
$907$	−8.73489	−	12.0225i	−0.290037	−	0.399202i	0.638989	−	0.769216i	$-0.279353\pi$
$907$	−8.73489	−	12.0225i	−0.290037	−	0.399202i	−0.929026	+	0.370014i	$0.879353\pi$
$908$	−8.20320	−	11.2907i	−0.272233	−	0.374696i
$909$	11.5158	+	35.4421i	0.381956	+	1.17554i
$910$	−13.9284	−	2.21294i	−0.461721	−	0.0733584i
$911$	−9.55408	−	6.94145i	−0.316541	−	0.229980i	0.418157	−	0.908375i	$-0.362676\pi$
$911$	−9.55408	−	6.94145i	−0.316541	−	0.229980i	−0.734698	+	0.678394i	$0.762676\pi$
$912$	3.30979			0.109598
$913$	13.7810	+	0.281708i	0.456086	+	0.00932318i
$914$	12.5245			0.414274
$915$	−3.03527	−	2.08802i	−0.100343	−	0.0690277i
$916$	1.61164	+	0.523654i	0.0532501	+	0.0173020i
$917$	−1.62664	−	3.41077i	−0.0537164	−	0.112634i
$918$	12.2963	+	16.9244i	0.405837	+	0.558587i
$919$	−18.3938	−	25.3169i	−0.606755	−	0.835126i	0.389551	−	0.921005i	$-0.372630\pi$
$919$	−18.3938	−	25.3169i	−0.606755	−	0.835126i	−0.996306	+	0.0858786i	$0.972630\pi$
$920$	−6.51716	+	2.30467i	−0.214864	+	0.0759828i
$921$	1.49730	+	0.486504i	0.0493379	+	0.0160308i
$922$	−11.1985	−	8.13620i	−0.368804	−	0.267952i
$923$			32.2400i			1.06119i
$924$	−5.79252	−	1.19683i	−0.190560	−	0.0393729i
$925$	0.125976	+	2.44425i	0.00414207	+	0.0803664i
$926$	3.76243	−	5.17854i	0.123641	−	0.170177i
$927$	−14.9766	+	46.0932i	−0.491896	+	1.51390i
$928$	5.39874	−	1.75416i	0.177222	−	0.0575830i
$929$	−15.7928	−	21.7369i	−0.518144	−	0.713164i	0.467122	−	0.884193i	$-0.345291\pi$
$929$	−15.7928	−	21.7369i	−0.518144	−	0.713164i	−0.985266	+	0.171029i	$0.945291\pi$
$930$	7.77764	+	10.1451i	0.255039	+	0.332671i
$931$	−18.7171	−	28.8283i	−0.613428	−	0.944808i
$932$	1.27720	−	3.93083i	0.0418362	−	0.128759i
$933$	−0.0992150	+	0.136558i	−0.00324815	+	0.00447070i
$934$	−20.9554			−0.685681
$935$	−33.4470	+	24.5730i	−1.09383	+	0.803623i
$936$		−	6.06843i		−	0.198353i
$937$	−12.5765	+	17.3101i	−0.410858	+	0.565497i	−0.963427	−	0.267969i	$-0.913647\pi$
$937$	−12.5765	+	17.3101i	−0.410858	+	0.565497i	0.552570	+	0.833467i	$0.313647\pi$
$938$	34.8613	+	6.46300i	1.13826	+	0.211024i
$939$	−3.68281	−	11.3345i	−0.120184	−	0.369888i
$940$	9.55100	−	7.32218i	0.311519	−	0.238823i
$941$	−36.2361	+	26.3271i	−1.18126	+	0.858238i	−0.992314	−	0.123749i	$-0.960508\pi$
$941$	−36.2361	+	26.3271i	−1.18126	+	0.858238i	−0.188950	+	0.981987i	$0.560508\pi$
$942$	−1.12890	−	3.47439i	−0.0367815	−	0.113202i
$943$	−26.7877	−	8.70387i	−0.872329	−	0.283437i
$944$	−7.32059	+	10.0759i	−0.238265	+	0.327944i
$945$	−21.8443	+	3.44897i	−0.710597	+	0.112195i
$946$	−16.3092	+	4.93303i	−0.530258	+	0.160387i
$947$			50.7539i			1.64928i	0.565657	+	0.824641i	$0.308623\pi$
$947$			50.7539i			1.64928i	−0.565657	+	0.824641i	$0.691377\pi$
$948$	6.37690	−	8.77705i	0.207112	−	0.285065i
$949$	0.606143	−	1.86551i	0.0196762	−	0.0605572i
$950$	8.77847	+	22.9280i	0.284811	+	0.743882i
$951$	10.4710	+	14.4121i	0.339546	+	0.467344i
$952$	−10.1916	−	10.7408i	−0.330310	−	0.348110i
$953$	2.59026	+	7.97199i	0.0839066	+	0.258238i	0.984204	−	0.177037i	$-0.0566512\pi$
$953$	2.59026	+	7.97199i	0.0839066	+	0.258238i	−0.900298	+	0.435275i	$0.856651\pi$
$954$	−14.1761	−	4.60610i	−0.458969	−	0.149128i
$955$	−19.1050	−	13.1427i	−0.618224	−	0.425288i
$956$		−	22.8337i		−	0.738496i
$957$	10.1123	+	7.66762i	0.326885	+	0.247859i
$958$	−12.2087			−0.394445
$959$	−9.24185	+	17.0193i	−0.298435	+	0.549582i
$960$	−0.428707	+	1.44500i	−0.0138365	+	0.0466370i
$961$	−12.6487	−	38.9285i	−0.408021	−	1.25576i
$962$	0.944037	−	0.685883i	0.0304370	−	0.0221137i
$963$	−19.6845	+	14.3016i	−0.634323	+	0.460863i
$964$	3.86448	+	11.8936i	0.124467	+	0.383069i
$965$	−13.9395	+	46.9843i	−0.448728	+	1.51248i
$966$	2.63095	−	4.84502i	0.0846495	−	0.155886i
$967$	−1.80329			−0.0579899			−0.0289950	−	0.999580i	$-0.509231\pi$
$967$	−1.80329			−0.0579899			−0.0289950	+	0.999580i	$0.509231\pi$
$968$	10.9908	+	0.449530i	0.353258	+	0.0144484i
$969$			18.5227i			0.595033i
$970$	−11.7063	−	8.05296i	−0.375866	−	0.258565i
$971$	41.9615	+	13.6341i	1.34661	+	0.437539i	0.891550	−	0.452923i	$-0.149619\pi$
$971$	41.9615	+	13.6341i	1.34661	+	0.437539i	0.455058	+	0.890462i	$0.349619\pi$
$972$	−4.53131	−	13.9459i	−0.145342	−	0.447316i
$973$	−21.7423	+	20.6305i	−0.697025	+	0.661384i
$974$	−1.14641	−	1.57789i	−0.0367332	−	0.0505589i
$975$	−7.50318	+	2.87275i	−0.240294	+	0.0920017i
$976$	−0.755318	+	2.32463i	−0.0241771	+	0.0744096i
$977$	28.6389	−	39.4181i	0.916240	−	1.26110i	−0.0487501	−	0.998811i	$-0.515524\pi$
$977$	28.6389	−	39.4181i	0.916240	−	1.26110i	0.964990	−	0.262286i	$-0.0844762\pi$
$978$			3.37945i			0.108063i
$979$	28.2451	+	21.4167i	0.902716	+	0.684481i
$980$	15.0103	−	4.43752i	0.479486	−	0.141751i
$981$	−8.65419	+	11.9115i	−0.276307	+	0.380304i
$982$	−8.20805	−	2.66696i	−0.261929	−	0.0851060i
$983$	−2.89978	−	8.92461i	−0.0924887	−	0.284651i	0.894102	−	0.447863i	$-0.147815\pi$
$983$	−2.89978	−	8.92461i	−0.0924887	−	0.284651i	−0.986591	+	0.163212i	$0.947815\pi$
$984$	−4.96853	+	3.60985i	−0.158391	+	0.115078i
$985$	11.8955	−	9.11954i	0.379021	−	0.290573i
$986$	9.81683	+	30.2131i	0.312631	+	0.962181i
$987$	−1.74967	+	9.43766i	−0.0556925	+	0.300404i
$988$	6.88016	−	9.46973i	0.218887	−	0.301272i
$989$		−	15.8820i		−	0.505019i
$990$	17.9237	−	5.92915i	0.569654	−	0.188441i
$991$	−25.4782			−0.809341			−0.404670	−	0.914463i	$-0.632614\pi$
$991$	−25.4782			−0.809341			−0.404670	+	0.914463i	$0.632614\pi$
$992$	4.98516	−	6.86149i	0.158279	−	0.217853i
$993$	0.0790582	−	0.243316i	0.00250884	−	0.00772140i
$994$	−15.4029	−	32.2971i	−0.488551	−	1.02440i
$995$	−34.6246	−	45.1641i	−1.09767	−	1.43180i
$996$	1.64663	+	2.26639i	0.0521753	+	0.0718132i
$997$	−2.95208	+	0.959189i	−0.0934933	+	0.0303778i	−0.355390	−	0.934718i	$-0.615652\pi$
$997$	−2.95208	+	0.959189i	−0.0934933	+	0.0303778i	0.261897	+	0.965096i	$0.415652\pi$
$998$	3.79657	−	11.6846i	0.120178	−	0.369871i
$999$	1.07553	−	1.48034i	0.0340282	−	0.0468359i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.w.b.139.11	yes	96
5.4	even	2		770.2.w.a.139.14	yes	96
7.6	odd	2	inner	770.2.w.b.139.14	yes	96
11.8	odd	10		770.2.w.a.349.11	yes	96
35.34	odd	2		770.2.w.a.139.11	✓	96
55.19	odd	10	inner	770.2.w.b.349.14	yes	96
77.41	even	10		770.2.w.a.349.14	yes	96
385.349	even	10	inner	770.2.w.b.349.11	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.w.a.139.11	✓	96	35.34	odd	2
770.2.w.a.139.14	yes	96	5.4	even	2
770.2.w.a.349.11	yes	96	11.8	odd	10
770.2.w.a.349.14	yes	96	77.41	even	10
770.2.w.b.139.11	yes	96	1.1	even	1	trivial
770.2.w.b.139.14	yes	96	7.6	odd	2	inner
770.2.w.b.349.11	yes	96	385.349	even	10	inner
770.2.w.b.349.14	yes	96	55.19	odd	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.w (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 + 0.587785i) q^{2} +(-0.208297 + 0.641072i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-1.77458 + 1.36046i) q^{5} +(-0.545328 + 0.396204i) q^{6} +(-1.13890 - 2.38807i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(2.05947 + 1.49629i) q^{9} +O(q^{10})\)	\(q+(0.809017 + 0.587785i) q^{2} +(-0.208297 + 0.641072i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-1.77458 + 1.36046i) q^{5} +(-0.545328 + 0.396204i) q^{6} +(-1.13890 - 2.38807i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(2.05947 + 1.49629i) q^{9} +(-2.23533 + 0.0575660i) q^{10} +(-2.00389 + 2.64280i) q^{11} -0.674063 q^{12} +(-1.40119 + 1.92858i) q^{13} +(0.482283 - 2.60142i) q^{14} +(-0.502515 - 1.42101i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-3.28944 - 4.52752i) q^{17} +(0.786646 + 2.42105i) q^{18} +(-1.51734 + 4.66989i) q^{19} +(-1.84225 - 1.26732i) q^{20} +(1.76816 - 0.232690i) q^{21} +(-3.17459 + 0.960214i) q^{22} -3.09144i q^{23} +(-0.545328 - 0.396204i) q^{24} +(1.29828 - 4.82851i) q^{25} +(-2.26718 + 0.736651i) q^{26} +(-3.02419 + 2.19720i) q^{27} +(1.91925 - 1.82112i) q^{28} +(-5.39874 + 1.75416i) q^{29} +(0.428707 - 1.44500i) q^{30} +(-4.98516 + 6.86149i) q^{31} -1.00000 q^{32} +(-1.27682 - 1.83513i) q^{33} -5.59632i q^{34} +(5.26997 + 2.68839i) q^{35} +(-0.786646 + 2.42105i) q^{36} +(-0.465541 + 0.151263i) q^{37} +(-3.97244 + 2.88615i) q^{38} +(-0.944492 - 1.29998i) q^{39} +(-0.745503 - 2.10813i) q^{40} +(2.81548 - 8.66515i) q^{41} +(1.56724 + 0.851046i) q^{42} +5.13743 q^{43} +(-3.13269 - 1.08915i) q^{44} +(-5.69034 + 0.146542i) q^{45} +(1.81710 - 2.50102i) q^{46} +(-1.66317 + 5.11870i) q^{47} +(-0.208297 - 0.641072i) q^{48} +(-4.40580 + 5.43957i) q^{49} +(3.88845 - 3.14324i) q^{50} +(3.58764 - 1.16570i) q^{51} +(-2.26718 - 0.736651i) q^{52} +(-3.44170 + 4.73710i) q^{53} -3.73811 q^{54} +(-0.0393670 - 7.41609i) q^{55} +(2.62313 - 0.345206i) q^{56} +(-2.67768 - 1.94545i) q^{57} +(-5.39874 - 1.75416i) q^{58} +(11.8450 - 3.84866i) q^{59} +(1.19618 - 0.917038i) q^{60} +(1.97745 - 1.43670i) q^{61} +(-8.06616 + 2.62086i) q^{62} +(1.22772 - 6.62229i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(-0.137229 - 5.32869i) q^{65} +(0.0456902 - 2.23515i) q^{66} +13.4008i q^{67} +(3.28944 - 4.52752i) q^{68} +(1.98183 + 0.643936i) q^{69} +(2.68329 + 5.27256i) q^{70} +(10.9414 - 7.94941i) q^{71} +(-2.05947 + 1.49629i) q^{72} +(-0.782563 + 0.254270i) q^{73} +(-0.465541 - 0.151263i) q^{74} +(2.82499 + 1.83805i) q^{75} -4.91021 q^{76} +(8.59345 + 1.77555i) q^{77} -1.60687i q^{78} +(-9.46039 + 13.0211i) q^{79} +(0.636005 - 2.14371i) q^{80} +(1.58130 + 4.86675i) q^{81} +(7.37102 - 5.35536i) q^{82} +(-2.44284 - 3.36228i) q^{83} +(0.767692 + 1.60971i) q^{84} +(11.9969 + 3.55929i) q^{85} +(4.15627 + 3.01970i) q^{86} -3.82636i q^{87} +(-1.89422 - 2.72249i) q^{88} -10.6875i q^{89} +(-4.68971 - 3.22614i) q^{90} +(6.20141 + 1.14969i) q^{91} +(2.94013 - 0.955306i) q^{92} +(-3.36031 - 4.62507i) q^{93} +(-4.35422 + 3.16353i) q^{94} +(-3.66058 - 10.3514i) q^{95} +(0.208297 - 0.641072i) q^{96} +(5.14075 + 3.73498i) q^{97} +(-6.76167 + 1.81104i) q^{98} +(-8.08135 + 2.44436i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 24 q^{2} - 24 q^{4} + 3 q^{7} + 24 q^{8} - 18 q^{9}+O(q^{10}) \) 96 * q + 24 * q^2 - 24 * q^4 + 3 * q^7 + 24 * q^8 - 18 * q^9	\( 96 q + 24 q^{2} - 24 q^{4} + 3 q^{7} + 24 q^{8} - 18 q^{9} + 4 q^{11} - 3 q^{14} - 6 q^{15} - 24 q^{16} + 28 q^{18} - 4 q^{22} + 38 q^{25} - 2 q^{28} + 6 q^{30} - 96 q^{32} + 46 q^{35} - 28 q^{36} + 10 q^{39} - 24 q^{43} - 16 q^{44} + 37 q^{49} - 8 q^{50} - 30 q^{51} + 40 q^{53} + 2 q^{56} - 20 q^{57} + 14 q^{60} + 63 q^{63} - 24 q^{64} - 40 q^{65} + 39 q^{70} - 20 q^{71} + 18 q^{72} - 16 q^{77} - 126 q^{81} + 60 q^{85} - 36 q^{86} - 14 q^{88} - 31 q^{91} - 10 q^{92} + 20 q^{93} - 44 q^{95} + 18 q^{98} + 100 q^{99}+O(q^{100}) \) 96 * q + 24 * q^2 - 24 * q^4 + 3 * q^7 + 24 * q^8 - 18 * q^9 + 4 * q^11 - 3 * q^14 - 6 * q^15 - 24 * q^16 + 28 * q^18 - 4 * q^22 + 38 * q^25 - 2 * q^28 + 6 * q^30 - 96 * q^32 + 46 * q^35 - 28 * q^36 + 10 * q^39 - 24 * q^43 - 16 * q^44 + 37 * q^49 - 8 * q^50 - 30 * q^51 + 40 * q^53 + 2 * q^56 - 20 * q^57 + 14 * q^60 + 63 * q^63 - 24 * q^64 - 40 * q^65 + 39 * q^70 - 20 * q^71 + 18 * q^72 - 16 * q^77 - 126 * q^81 + 60 * q^85 - 36 * q^86 - 14 * q^88 - 31 * q^91 - 10 * q^92 + 20 * q^93 - 44 * q^95 + 18 * q^98 + 100 * q^99

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