LMFDB - Embedded newform 770.2.w.b.139.14

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			139.14
Character	$\chi$	$=$	770.139
Dual form			770.2.w.b.349.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 + 0.587785i) q^{2} +(0.208297 - 0.641072i) q^{3} +(0.309017 + 0.951057i) q^{4} +(1.77458 - 1.36046i) q^{5} +(0.545328 - 0.396204i) q^{6} +(-0.482283 - 2.60142i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(2.05947 + 1.49629i) q^{9} +O(q^{10})$	\(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} +(-0.482283 - 2.60142i) 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} +(1.13890 - 2.38807i) 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} +(2.32507 - 1.26256i) 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} +(-4.39499 - 3.96031i) 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} +(-1.29370 - 1.22755i) 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} +(-6.53481 + 2.50924i) 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} +(2.89924 - 6.07918i) 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} +(-1.22781 - 5.78727i) 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} +(7.84149 + 3.93840i) 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} +(-0.325089 - 1.75352i) 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} +(-5.69282 - 2.71498i) 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	−0.872748	−	0.488172i	$-0.837664\pi$
$3$	0.208297	−	0.641072i	0.120260	−	0.370123i	0.993008	+	0.118049i	$0.0376640\pi$
$4$	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
$7$	−0.482283	−	2.60142i	−0.182286	−	0.983246i
$7$	−0.482283	−	2.60142i	−0.182286	−	0.983246i
$8$	−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	−0.569222	−	0.822184i	$-0.692755\pi$
$13$	1.40119	−	1.92858i	0.388621	−	0.534891i	0.957843	+	0.287293i	$0.0927553\pi$
$14$	1.13890	−	2.38807i	0.304385	−	0.638240i
$15$	−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	$0.0374364\pi$
$17$	3.28944	+	4.52752i	0.797806	+	1.09809i	−0.195286	+	0.980746i	$0.562564\pi$
$18$	0.786646	+	2.42105i	0.185414	+	0.570646i
$19$	1.51734	−	4.66989i	0.348101	−	1.07135i	−0.611801	−	0.791012i	$-0.709555\pi$
$19$	1.51734	−	4.66989i	0.348101	−	1.07135i	0.959902	−	0.280334i	$-0.0904453\pi$
$20$	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
$28$	2.32507	−	1.26256i	0.439396	−	0.238602i
$29$	−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	$-0.524394\pi$
$31$	4.98516	−	6.86149i	0.895362	−	1.23236i	0.971924	−	0.235295i	$-0.0756056\pi$
$32$	−1.00000			−0.176777
$33$	1.27682	+	1.83513i	0.222266	+	0.319455i
$34$			5.59632i			0.959762i
$35$	−4.39499	−	3.96031i	−0.742889	−	0.669414i
$36$	−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	$0.351964\pi$
$41$	−2.81548	+	8.66515i	−0.439704	+	1.35327i	−0.888189	+	0.459479i	$0.848036\pi$
$42$	−1.29370	−	1.22755i	−0.199622	−	0.189415i
$43$	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	$-0.771599\pi$
$47$	1.66317	−	5.11870i	0.242598	−	0.746639i	0.996022	−	0.0891045i	$-0.0284005\pi$
$48$	0.208297	+	0.641072i	0.0300651	+	0.0925307i
$49$	−6.53481	+	2.50924i	−0.933544	+	0.358463i
$50$	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	−0.951950	−	0.306253i	$-0.900925\pi$
$59$	−11.8450	+	3.84866i	−1.54208	+	0.501053i	−0.590133	+	0.807306i	$0.700925\pi$
$60$	1.19618	−	0.917038i	0.154426	−	0.118389i
$61$	−1.97745	+	1.43670i	−0.253186	+	0.183951i	−0.707138	−	0.707076i	$-0.750014\pi$
$61$	−1.97745	+	1.43670i	−0.253186	+	0.183951i	0.453951	+	0.891026i	$0.350014\pi$
$62$	8.06616	−	2.62086i	1.02440	−	0.332849i
$63$	2.89924	−	6.07918i	0.365270	−	0.765904i
$64$	−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
$70$	−1.22781	−	5.78727i	−0.146752	−	0.691711i
$71$	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	−0.262863	−	0.964833i	$-0.584667\pi$
$73$	0.782563	−	0.254270i	0.0915920	−	0.0297601i	0.354455	+	0.935073i	$0.384667\pi$
$74$	−0.465541	−	0.151263i	−0.0541180	−	0.0175840i
$75$	−2.82499	−	1.83805i	−0.326202	−	0.212240i
$76$	4.91021			0.563240
$77$	7.84149	+	3.93840i	0.893621	+	0.448822i
$78$		−	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	0.921759	−	0.387762i	$-0.126752\pi$
$83$	2.44284	+	3.36228i	0.268136	+	0.369058i	−0.653623	+	0.756820i	$0.726752\pi$
$84$	−0.325089	−	1.75352i	−0.0354701	−	0.191325i
$85$	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	$0.191679\pi$
$89$			10.6875i			1.13288i	−0.824104	+	0.566439i	$0.808321\pi$
$90$	4.68971	+	3.22614i	0.494339	+	0.340065i
$91$	−5.69282	−	2.71498i	−0.596770	−	0.284607i
$92$	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	0.295379	−	0.955380i	$-0.404554\pi$
$97$	−5.14075	−	3.73498i	−0.521964	−	0.379229i	−0.817343	+	0.576151i	$0.804554\pi$
$98$	−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	−0.186460	−	0.982463i	$-0.559701\pi$
$101$	−11.8433	−	8.60469i	−1.17846	−	0.856199i	−0.991997	+	0.126264i	$0.959701\pi$
$102$	3.58764	+	1.16570i	0.355230	+	0.115421i
$103$	−5.88324	−	18.1067i	−0.579693	−	1.78411i	−0.619613	−	0.784908i	$-0.712710\pi$
$103$	−5.88324	−	18.1067i	−0.579693	−	1.78411i	0.0399201	−	0.999203i	$-0.487290\pi$
$104$	1.40119	+	1.92858i	0.137398	+	0.189113i
$105$	−3.45430	+	1.99259i	−0.337106	+	0.194456i
$106$	−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
$112$	1.91925	+	1.82112i	0.181352	+	0.172079i
$113$	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
$119$	10.1916	−	10.7408i	0.934259	−	0.984604i
$120$	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
$126$	5.91878	−	3.21403i	0.527287	−	0.286328i
$127$	−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	$-0.519873\pi$
$131$	−1.42825			−0.124787			−0.0623935	+	0.998052i	$0.519873\pi$
$132$	−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	$0.0595214\pi$
$139$	3.50070	+	10.7740i	0.296926	+	0.913843i	−0.685642	+	0.727939i	$0.740479\pi$
$140$	2.40835	−	5.40369i	0.203543	−	0.456695i
$141$	−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
$147$	0.247425	+	4.71195i	0.0204073	+	0.388635i
$148$	−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
$154$	4.02897	+	7.79535i	0.324664	+	0.628167i
$155$	−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	−0.861718	−	0.507387i	$-0.830612\pi$
$157$	1.67477	−	5.15440i	0.133661	−	0.411366i	0.995379	+	0.0960207i	$0.0306115\pi$
$158$	−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
$161$	−8.04213	+	1.49095i	−0.633809	+	0.117503i
$162$	−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	$0.503661\pi$
$167$	−12.3923	+	17.0565i	−0.958941	+	1.31987i	−0.947439	+	0.319936i	$0.896339\pi$
$168$	0.767692	−	1.60971i	0.0592287	−	0.124192i
$169$	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	−0.346495	−	0.938052i	$-0.612628\pi$
$173$	−15.4967	−	5.03517i	−1.17819	−	0.382817i	−0.831694	+	0.555235i	$0.812628\pi$
$174$	−2.24908	+	3.09559i	−0.170502	+	0.234676i
$175$	−13.1871	−	1.04866i	−0.996853	−	0.0792711i
$176$	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	$0.156711\pi$
$181$	14.2401	+	19.5998i	1.05846	+	1.45684i	0.177221	+	0.984171i	$0.443289\pi$
$182$	−3.00976	−	5.54262i	−0.223098	−	0.410846i
$183$	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
$189$	−7.17438	−	6.80753i	−0.521859	−	0.495175i
$190$	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
$196$	−4.40580	−	5.43957i	−0.314700	−	0.388541i
$197$	−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	$-0.642046\pi$
$199$		−	25.4506i		−	1.80414i	0.431586	−	0.902072i	$-0.357954\pi$
$200$	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
$203$	7.16702	+	13.1984i	0.503026	+	0.926346i
$204$	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
$210$	−3.96580	−	0.418353i	−0.273666	−	0.0288691i
$211$	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
$217$	−20.2539	−	9.65934i	−1.37492	−	0.655719i
$218$	−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	−0.999581	−	0.0289486i	$-0.990784\pi$
$223$	−2.59669	+	7.99180i	−0.173887	+	0.535170i	0.825694	+	0.564119i	$0.190784\pi$
$224$	0.482283	+	2.60142i	0.0322239	+	0.173815i
$225$	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	0.166606	−	0.986024i	$-0.446719\pi$
$227$	13.2731	−	4.31268i	0.880963	−	0.286242i	0.714357	+	0.699781i	$0.246719\pi$
$228$	1.02278	−	3.14780i	0.0677353	−	0.208468i
$229$	−0.996049	+	1.37094i	−0.0658208	+	0.0905945i	−0.840658	−	0.541566i	$-0.817832\pi$
$229$	−0.996049	+	1.37094i	−0.0658208	+	0.0905945i	0.774837	+	0.632160i	$0.217832\pi$
$230$	−0.177962	−	6.91037i	−0.0117344	−	0.455656i
$231$	4.15815	−	4.20660i	0.273586	−	0.276774i
$232$		−	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
$238$	14.5584	−	2.69901i	0.943682	−	0.174951i
$239$	−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	$-0.631957\pi$
$241$	−12.5057			−0.805564			−0.402782	+	0.915296i	$0.631957\pi$
$242$	3.82388	−	10.3140i	0.245808	−	0.663007i
$243$	14.6636			0.940673
$244$	−1.97745	−	1.43670i	−0.126593	−	0.0919753i
$245$	−8.18281	+	13.3432i	−0.522781	+	0.852467i
$246$	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	−0.844219	−	0.535998i	$-0.819935\pi$
$251$	−1.16567	+	1.60440i	−0.0735762	+	0.101269i	0.770643	+	0.637267i	$0.219935\pi$
$252$	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	$-0.944479\pi$
$257$	−4.65049	−	14.3127i	−0.290090	−	0.892804i	0.694737	−	0.719264i	$-0.255521\pi$
$258$	2.80158	−	2.03547i	0.174419	−	0.126723i
$259$	0.618023	+	1.13812i	0.0384021	+	0.0707192i
$260$	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
$266$	−9.42394	−	8.94207i	−0.577819	−	0.548273i
$267$	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	$0.00289506\pi$
$269$	11.4744	+	15.7931i	0.699604	+	0.962923i	−0.300354	+	0.953828i	$0.597105\pi$
$270$	6.63358	−	5.08556i	0.403707	−	0.309497i
$271$	−2.08068	−	6.40368i	−0.126392	−	0.388996i	0.867760	−	0.496984i	$-0.165559\pi$
$271$	−2.08068	−	6.40368i	−0.126392	−	0.388996i	−0.994152	+	0.107988i	$0.965559\pi$
$272$	−5.32242	−	1.72936i	−0.322719	−	0.104858i
$273$	−2.92629	+	3.08398i	−0.177107	+	0.186651i
$274$		−	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
$280$	5.12460	−	2.95608i	0.306254	−	0.176660i
$281$	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	0.0736565	−	0.997284i	$-0.476533\pi$
$283$	−7.61968	−	2.47578i	−0.452943	−	0.147170i	−0.526599	+	0.850114i	$0.676533\pi$
$284$	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	0.579988	−	0.814625i	$-0.303057\pi$
$293$	26.1557	−	8.49850i	1.52803	−	0.496488i	0.948045	+	0.318138i	$0.103057\pi$
$294$	−2.56944	+	3.95748i	−0.149853	+	0.230805i
$295$	−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
$301$	−2.47769	−	13.3646i	−0.142812	−	0.770324i
$302$	−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	$0.0212313\pi$
$307$			2.33563i			0.133301i	−0.997776	+	0.0666506i	$0.978769\pi$
$308$	−1.32248	+	8.67474i	−0.0753555	+	0.494289i
$309$	−12.8332			−0.730054
$310$	10.7485	−	15.6246i	0.610473	−	0.887420i
$311$	−0.238158	−	0.0773821i	−0.0135047	−	0.00438794i	0.302257	−	0.953227i	$-0.402260\pi$
$311$	−0.238158	−	0.0773821i	−0.0135047	−	0.00438794i	−0.315762	+	0.948839i	$0.602260\pi$
$312$	1.52822	−	0.496549i	0.0865185	−	0.0281116i
$313$	14.3039	−	10.3924i	0.808504	−	0.587413i	−0.104892	−	0.994484i	$-0.533450\pi$
$313$	14.3039	−	10.3924i	0.808504	−	0.587413i	0.913397	+	0.407071i	$0.133450\pi$
$314$	4.38460	−	3.18560i	0.247437	−	0.179774i
$315$	−3.12557	−	14.7323i	−0.176106	−	0.830071i
$316$	−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
$322$	−7.38258	−	3.52085i	−0.411415	−	0.196209i
$323$	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
$336$	1.56724	−	0.851046i	0.0855000	−	0.0464284i
$337$	−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
$343$	9.67923	+	15.7896i	0.522629	+	0.852560i
$344$	−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	$0.367367\pi$
$349$	−8.59721	+	26.4595i	−0.460198	+	1.41634i	−0.864922	+	0.501905i	$0.832633\pi$
$350$	−10.0522	−	8.59958i	−0.537314	−	0.459667i
$351$		−	8.91110i		−	0.475639i
$352$	2.00389	−	2.64280i	0.106808	−	0.140862i
$353$	15.8096			0.841463			0.420731	−	0.907185i	$-0.361774\pi$
$353$	15.8096			0.841463			0.420731	+	0.907185i	$0.361774\pi$
$354$	−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
$357$	−4.76273	−	8.77079i	−0.252070	−	0.464199i
$358$	−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	$-0.836038\pi$
$367$	−8.73107	−	26.8715i	−0.455758	−	1.40268i	0.414484	−	0.910056i	$-0.363962\pi$
$368$	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
$371$	13.9831	+	6.66870i	0.725965	+	0.346222i
$372$	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
$378$	−1.80282	−	9.72440i	−0.0927273	−	0.500169i
$379$	−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	0.908835	−	0.417157i	$-0.136973\pi$
$383$	15.5181	+	11.2746i	0.792940	+	0.576105i	−0.115894	+	0.993262i	$0.536973\pi$
$384$	−0.674063			−0.0343981
$385$	19.2734	−	3.67906i	0.982264	−	0.187502i
$386$	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
$392$	−0.367065	−	6.99037i	−0.0185396	−	0.353067i
$393$	−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	$-0.311412\pi$
$397$	22.2524			1.11682			0.558409	+	0.829566i	$0.311412\pi$
$398$	14.9595	−	20.5899i	0.749851	−	1.03208i
$399$	−3.76953	+	7.90402i	−0.188713	+	0.395696i
$400$	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	0.658259	−	0.752791i	$-0.271293\pi$
$409$	2.94712	+	2.14121i	0.145726	+	0.105876i	−0.512534	+	0.858667i	$0.671293\pi$
$410$	−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
$413$	15.7246	+	28.9576i	0.773758	+	1.42491i
$414$	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	$0.0778550\pi$
$419$			9.91367i			0.484314i	−0.970237	+	0.242157i	$0.922145\pi$
$420$	−2.96250	−	2.66950i	−0.144555	−	0.130258i
$421$	−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
$427$	4.69115	+	4.45128i	0.227021	+	0.215413i
$428$	−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	0.963205	−	0.268769i	$-0.0866167\pi$
$433$	0.540557	+	1.66366i	0.0259775	+	0.0799505i	−0.937227	+	0.348719i	$0.886617\pi$
$434$	−10.7081	−	19.7195i	−0.514007	−	0.946567i
$435$	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	$-0.307117\pi$
$439$	23.8669			1.13910			0.569551	+	0.821956i	$0.307117\pi$
$440$	−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
$448$	−1.13890	+	2.38807i	−0.0538081	+	0.112826i
$449$	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
$455$	−13.7960	+	2.92693i	−0.646766	+	0.137216i
$456$	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	$-0.395528\pi$
$461$	13.8421			0.644692			0.322346	+	0.946622i	$0.395528\pi$
$462$	5.83660	−	0.959112i	0.271543	−	0.0446219i
$463$		−	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	−0.121824	−	0.992552i	$-0.538874\pi$
$467$	16.9533	−	12.3173i	0.784503	−	0.569975i	0.906327	+	0.422577i	$0.138874\pi$
$468$	3.56693	+	4.90946i	0.164882	+	0.226940i
$469$	34.8613	−	6.46300i	1.60974	−	0.298433i
$470$	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
$476$	13.3644	+	6.37367i	0.612558	+	0.292137i
$477$	−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	−0.338813	−	0.940854i	$-0.610025\pi$
$479$	9.87703	−	7.17608i	0.451293	−	0.327884i	0.790106	+	0.612970i	$0.210025\pi$
$480$	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
$490$	−14.4630	+	5.98516i	−0.653371	+	0.270382i
$491$	−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
$497$	−25.9566	−	24.6294i	−1.16431	−	1.10478i
$498$	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	−0.506198	−	0.862417i	$-0.668950\pi$
$503$	−31.9064	−	10.3670i	−1.42264	−	0.462243i	−0.916439	+	0.400174i	$0.868950\pi$
$504$	4.88573	+	4.63591i	0.217628	+	0.206500i
$505$	−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	0.388890	−	0.921284i	$-0.372859\pi$
$509$	3.65467	+	1.18747i	0.161990	+	0.0526339i	−0.226899	+	0.973918i	$0.572859\pi$
$510$	7.95245	−	2.81224i	0.352141	−	0.124528i
$511$	−1.03888	−	1.91315i	−0.0459574	−	0.0846326i
$512$	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	0.0650487	−	0.997882i	$-0.479280\pi$
$521$	16.0740	−	5.22276i	0.704215	−	0.228813i	0.639166	+	0.769069i	$0.279280\pi$
$522$	−8.49379	−	11.6907i	−0.371763	−	0.511688i
$523$	−10.9714	−	15.1009i	−0.479747	−	0.660315i	0.498710	−	0.866769i	$-0.333807\pi$
$523$	−10.9714	−	15.1009i	−0.479747	−	0.660315i	−0.978456	+	0.206455i	$0.933807\pi$
$524$	−0.441354	−	1.35835i	−0.0192807	−	0.0593397i
$525$	−3.41910	+	8.23546i	−0.149222	+	0.359425i
$526$	−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
$532$	−2.36811	−	12.7735i	−0.102671	−	0.553803i
$533$	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
$539$	6.46362	−	22.2985i	0.278408	−	0.960463i
$540$	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
$546$	−4.18014	+	0.774964i	−0.178893	+	0.0331654i
$547$	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
$553$	38.4360	+	18.3306i	1.63447	+	0.779498i
$554$	−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
$560$	5.88343	+	0.620645i	0.248620	+	0.0262270i
$561$	−4.10855	+	11.8174i	−0.173463	+	0.498930i
$562$			18.3351i			0.773418i
$563$	−0.949152	+	1.30640i	−0.0400020	+	0.0550580i	−0.828549	−	0.559916i	$-0.810833\pi$
$563$	−0.949152	+	1.30640i	−0.0400020	+	0.0550580i	0.788547	+	0.614974i	$0.210833\pi$
$564$	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
$567$	11.8978	−	6.46078i	0.499662	−	0.271327i
$568$	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
$574$	17.4865	+	16.5923i	0.729871	+	0.692551i
$575$	−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	−0.761108	−	0.648626i	$-0.775344\pi$
$577$	−9.11405	+	6.62175i	−0.379423	+	0.275667i	0.381685	+	0.924293i	$0.375344\pi$
$578$	−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
$581$	7.56857	−	7.97643i	0.313997	−	0.330918i
$582$	−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	$-0.939547\pi$
$587$	−7.23235	−	22.2589i	−0.298511	−	0.918722i	0.683509	−	0.729942i	$-0.260453\pi$
$588$	−4.40487	+	1.69139i	−0.181654	+	0.0697516i
$589$	−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	$-0.925330\pi$
$593$		−	11.3204i		−	0.464874i	0.972611	−	0.232437i	$-0.0746700\pi$
$594$	−7.49077	+	9.87908i	−0.307350	+	0.405344i
$595$	3.47333	−	32.9256i	0.142393	−	1.34982i
$596$	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	$-0.996016\pi$
$601$	−4.86199	−	14.9637i	−0.198325	−	0.610381i	0.801597	−	0.597865i	$-0.203984\pi$
$602$	5.85103	−	12.2686i	0.238470	−	0.500029i
$603$	−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	−0.911365	−	0.411598i	$-0.864971\pi$
$607$	−5.87071	+	8.08033i	−0.238285	+	0.327971i	0.673081	+	0.739569i	$0.264971\pi$
$608$	−1.51734	+	4.66989i	−0.0615362	+	0.189389i
$609$	9.95399	−	1.84539i	0.403356	−	0.0747789i
$610$	−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
$616$	−6.16879	+	6.24067i	−0.248548	+	0.251444i
$617$			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	−0.277337	−	0.960773i	$-0.589452\pi$
$619$	−26.5326	−	8.62096i	−1.06644	−	0.346506i	−0.789098	+	0.614267i	$0.789452\pi$
$620$	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
$623$	27.8028	−	5.15442i	1.11390	−	0.206507i
$624$	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
$630$	6.13079	−	13.7558i	0.244257	−	0.548046i
$631$	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	−0.910940	−	0.412539i	$-0.864642\pi$
$643$	−20.2882	+	14.7402i	−0.800089	+	0.581298i	0.110852	+	0.993837i	$0.464642\pi$
$644$	−3.90313	−	7.18779i	−0.153805	−	0.283239i
$645$	−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	0.657818	−	0.753177i	$-0.271480\pi$
$647$	3.68269	+	2.67563i	0.144781	+	0.105190i	−0.513037	+	0.858367i	$0.671480\pi$
$648$	−5.11720			−0.201023
$649$	13.5648	−	39.0162i	0.532465	−	1.53152i
$650$	−0.613503	−	11.9035i	−0.0240636	−	0.466892i
$651$	−10.4112	+	10.9722i	−0.408045	+	0.430034i
$652$	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
$658$	−10.3296	−	9.80147i	−0.402692	−	0.382101i
$659$		−	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	$-0.761144\pi$
$661$		−	35.0644i		−	1.36385i	0.731423	−	0.681924i	$-0.238856\pi$
$662$	−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
$665$	−25.1629	+	14.5150i	−0.975775	+	0.562867i
$666$	−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	0.361441	−	0.932395i	$-0.382285\pi$
$677$	−16.5745	−	22.8129i	−0.637010	−	0.876770i	−0.998452	+	0.0556252i	$0.982285\pi$
$678$	6.74435	−	2.19137i	0.259015	−	0.0841592i
$679$	−7.23696	+	15.1746i	−0.277729	+	0.582347i
$680$	−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
$686$	−1.45026	+	18.4634i	−0.0553710	+	0.704935i
$687$	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	−0.360562	−	0.932735i	$-0.617415\pi$
$691$	16.7695	−	23.0812i	0.637942	−	0.878052i	0.998504	+	0.0546834i	$0.0174149\pi$
$692$		−	16.2941i		−	0.619411i
$693$	10.2563	+	19.8441i	0.389605	+	0.753817i
$694$	−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
$700$	−3.07771	−	12.8658i	−0.116327	−	0.486280i
$701$	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
$707$	−16.6726	+	34.9594i	−0.627038	+	1.31478i
$708$	−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	0.0317142	−	0.999497i	$-0.489903\pi$
$719$	17.2914	−	5.61832i	0.644861	−	0.209528i	0.613147	+	0.789969i	$0.289903\pi$
$720$	−4.51744	+	3.46325i	−0.168355	+	0.129068i
$721$	−44.2659	+	24.0374i	−1.64855	+	0.895198i
$722$	−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	$-0.677600\pi$
$727$	−28.5508			−1.05889			−0.529445	+	0.848344i	$0.677600\pi$
$728$	4.34128	−	4.57522i	0.160898	−	0.169569i
$729$	−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	−0.533254	−	0.845955i	$-0.679031\pi$
$733$	−12.6550	+	4.11187i	−0.467425	+	0.151876i	0.0658288	+	0.997831i	$0.479031\pi$
$734$	8.73107	−	26.8715i	0.322270	−	0.991844i
$735$	6.84951	+	8.02512i	0.252648	+	0.296011i
$736$			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
$742$	7.39277	+	13.6141i	0.271397	+	0.499791i
$743$	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
$756$	4.25734	−	8.92688i	0.154838	−	0.324667i
$757$	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	0.376391	−	0.926461i	$-0.377165\pi$
$761$	−10.7149	−	7.78483i	−0.388415	−	0.282200i	−0.764806	+	0.644261i	$0.777165\pi$
$762$	−3.13777	+	9.65707i	−0.113669	+	0.349839i
$763$	15.0460	−	2.78941i	0.544702	−	0.100983i
$764$	−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	$-0.744640\pi$
$769$	−38.5514			−1.39020			−0.695100	+	0.718913i	$0.744640\pi$
$770$	17.7550	+	8.35220i	0.639846	+	0.300993i
$771$	−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	$0.317676\pi$
$773$	−10.8560	+	33.4112i	−0.390462	+	1.20172i	−0.932440	+	0.361325i	$0.882324\pi$
$774$	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
$777$	0.858347	−	0.159131i	0.0307930	−	0.00570878i
$778$	−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
$784$	3.81187	−	5.87108i	0.136138	−	0.209682i
$785$	−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	0.627207	−	0.778852i	$-0.284198\pi$
$787$	−8.62206	−	11.8672i	−0.307343	−	0.423022i	−0.934550	+	0.355831i	$0.884198\pi$
$788$	−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	−0.761587	−	0.648063i	$-0.775579\pi$
$797$	−10.7444	+	7.80626i	−0.380586	+	0.276512i	0.381001	+	0.924575i	$0.375579\pi$
$798$	−7.69548	+	4.17882i	−0.272417	+	0.147928i
$799$	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
$805$	−12.2430	+	13.5868i	−0.431510	+	0.478873i
$806$	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	$0.259529\pi$
$811$	−8.45624	+	26.0256i	−0.296939	+	0.913883i	−0.982563	+	0.185928i	$0.940471\pi$
$812$	−10.3377	+	10.8948i	−0.362782	+	0.382331i
$813$	−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
$819$	−7.66177	−	14.1095i	−0.267724	−	0.493026i
$820$	−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	−0.803373	−	0.595476i	$-0.796964\pi$
$829$	−31.7667	+	10.3216i	−1.10330	+	0.358485i	−0.299931	+	0.953961i	$0.596964\pi$
$830$	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
$833$	−32.8565	−	21.3325i	−1.13841	−	0.739127i
$834$	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	−0.215299	−	0.976548i	$-0.569073\pi$
$839$	−27.9077	−	9.06775i	−0.963480	−	0.313054i	−0.748181	+	0.663495i	$0.769073\pi$
$840$	−0.827623	−	3.90098i	−0.0285557	−	0.134597i
$841$	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
$847$	−26.1219	+	12.8314i	−0.897560	+	0.440892i
$848$		−	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	0.976392	−	0.216005i	$-0.0693027\pi$
$853$	13.7046	+	18.8628i	0.469238	+	0.645850i	−0.507155	+	0.861855i	$0.669303\pi$
$854$	1.17882	+	6.35856i	0.0403385	+	0.217585i
$855$	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	$-0.947637\pi$
$857$		−	9.58814i		−	0.327525i	0.986500	−	0.163762i	$-0.0523630\pi$
$858$	4.24663	+	3.21999i	0.144978	+	0.109929i
$859$		−	9.92918i		−	0.338779i	−0.985549	−	0.169390i	$-0.945820\pi$
$859$		−	9.92918i		−	0.338779i	0.985549	−	0.169390i	$-0.0541796\pi$
$860$	9.46444	+	6.51076i	0.322735	+	0.222015i
$861$	6.99450	−	14.6662i	0.238372	−	0.499823i
$862$	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
$875$	−24.8283	+	16.0797i	−0.839349	+	0.543593i
$876$	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	$-0.699998\pi$
$881$		−	48.0261i		−	1.61804i	0.587780	−	0.809021i	$-0.300002\pi$
$882$	−11.2156	−	13.8472i	−0.377648	−	0.466259i
$883$	−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	−0.525879	−	0.850560i	$-0.676263\pi$
$887$	−13.4431	+	4.36794i	−0.451377	+	0.146661i	0.0745018	+	0.997221i	$0.476263\pi$
$888$	−0.313804	−	0.101961i	−0.0105306	−	0.00342159i
$889$	28.9115	+	27.4332i	0.969661	+	0.920080i
$890$	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
$896$	−2.32507	+	1.26256i	−0.0776750	+	0.0421792i
$897$	−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
$910$	−12.8816	−	5.74115i	−0.427021	−	0.190317i
$911$	−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
$917$	0.688821	+	3.71549i	0.0227469	+	0.122696i
$918$	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
$924$	5.28566	+	2.65473i	0.173885	+	0.0873341i
$925$	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	0.985266	−	0.171029i	$-0.0547090\pi$
$929$	15.7928	+	21.7369i	0.518144	+	0.713164i	−0.467122	+	0.884193i	$0.654709\pi$
$930$	−7.77764	−	10.1451i	−0.255039	−	0.332671i
$931$	1.80237	+	34.3242i	0.0590702	+	1.12493i
$932$	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	−0.552570	−	0.833467i	$-0.686353\pi$
$937$	12.5765	−	17.3101i	0.410858	−	0.565497i	0.963427	+	0.267969i	$0.0863526\pi$
$938$	32.0022	+	15.2623i	1.04491	+	0.498331i
$939$	−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	0.188950	−	0.981987i	$-0.439492\pi$
$941$	36.2361	−	26.3271i	1.18126	−	0.858238i	0.992314	+	0.123749i	$0.0394917\pi$
$942$	−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
$945$	−21.9929	−	2.32004i	−0.715430	−	0.0754708i
$946$	−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
$952$	7.06571	+	13.0118i	0.229001	+	0.421716i
$953$	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
$959$	−13.3304	+	14.0488i	−0.430462	+	0.453659i
$960$	−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
$966$	−3.79488	+	3.99938i	−0.122098	+	0.128678i
$967$	−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	−0.455058	−	0.890462i	$-0.650381\pi$
$971$	−41.9615	−	13.6341i	−1.34661	−	0.437539i	−0.891550	+	0.452923i	$0.850381\pi$
$972$	4.53131	+	13.9459i	0.145342	+	0.447316i
$973$	26.3395	−	14.3029i	0.844407	−	0.458531i
$974$	−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
$980$	−15.2188	−	3.65903i	−0.486146	−	0.116883i
$981$	−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	0.986591	−	0.163212i	$-0.0521854\pi$
$983$	2.89978	+	8.92461i	0.0924887	+	0.284651i	−0.894102	+	0.447863i	$0.852185\pi$
$984$	−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
$987$	−4.13181	+	8.66366i	−0.131517	+	0.275767i
$988$	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
$994$	−6.52255	−	35.1825i	−0.206883	−	1.11592i
$995$	−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	−0.261897	−	0.965096i	$-0.584348\pi$
$997$	2.95208	−	0.959189i	0.0934933	−	0.0303778i	0.355390	+	0.934718i	$0.384348\pi$
$998$	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.139.14	yes	96
5.4	even	2		770.2.w.a.139.11	✓	96
7.6	odd	2	inner	770.2.w.b.139.11	yes	96
11.8	odd	10		770.2.w.a.349.14	yes	96
35.34	odd	2		770.2.w.a.139.14	yes	96
55.19	odd	10	inner	770.2.w.b.349.11	yes	96
77.41	even	10		770.2.w.a.349.11	yes	96
385.349	even	10	inner	770.2.w.b.349.14	yes	96

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

\(f(q)\)	\(=\)	\(q+(0.809017 + 0.587785i) q^{2} +(0.208297 - 0.641072i) q^{3} +(0.309017 + 0.951057i) q^{4} +(1.77458 - 1.36046i) q^{5} +(0.545328 - 0.396204i) q^{6} +(-0.482283 - 2.60142i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(2.05947 + 1.49629i) q^{9} +O(q^{10})\)	\(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} +(-0.482283 - 2.60142i) 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} +(1.13890 - 2.38807i) 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} +(2.32507 - 1.26256i) 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} +(-4.39499 - 3.96031i) 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} +(-1.29370 - 1.22755i) 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} +(-6.53481 + 2.50924i) 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} +(2.89924 - 6.07918i) 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} +(-1.22781 - 5.78727i) 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} +(7.84149 + 3.93840i) 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} +(-0.325089 - 1.75352i) 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} +(-5.69282 - 2.71498i) 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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