LMFDB - Embedded newform 370.2.n.e.359.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(269,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

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

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

chi := DirichletCharacter("370.269");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.n (of order $6$, degree $2$, 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:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.303595776.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 5x^{6} + 16x^{4} + 45x^{2} + 81 $ x^8 + 5x^6 + 16x^4 + 45*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			359.2
Root			$0.396143 - 1.68614i$ of defining polynomial
Character	$\chi$	$=$	370.359
Dual form			370.2.n.e.269.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(1.73205 + 1.00000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.469882 - 2.18614i) q^{5} -2.00000 q^{6} +(-2.00626 - 1.15831i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(1.73205 + 1.00000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.469882 - 2.18614i) q^{5} -2.00000 q^{6} +(-2.00626 - 1.15831i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(1.50000 + 1.65831i) q^{10} +4.31662 q^{11} +(1.73205 - 1.00000i) q^{12} +(3.46410 + 2.00000i) q^{13} +2.31662 q^{14} +(1.37228 - 4.25639i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(4.60433 - 2.65831i) q^{17} +(-0.866025 - 0.500000i) q^{18} +(2.15831 - 3.73831i) q^{19} +(-2.12819 - 0.686141i) q^{20} +(-2.31662 - 4.01251i) q^{21} +(-3.73831 + 2.15831i) q^{22} +6.00000i q^{23} +(-1.00000 + 1.73205i) q^{24} +(-4.55842 + 2.05446i) q^{25} -4.00000 q^{26} -4.00000i q^{27} +(-2.00626 + 1.15831i) q^{28} -3.31662 q^{29} +(0.939764 + 4.37228i) q^{30} +2.31662 q^{31} +(0.866025 + 0.500000i) q^{32} +(7.47661 + 4.31662i) q^{33} +(-2.65831 + 4.60433i) q^{34} +(-1.58953 + 4.93023i) q^{35} +1.00000 q^{36} +(-2.59808 - 5.50000i) q^{37} +4.31662i q^{38} +(4.00000 + 6.92820i) q^{39} +(2.18614 - 0.469882i) q^{40} +(-3.81662 + 6.61059i) q^{41} +(4.01251 + 2.31662i) q^{42} -8.94987i q^{43} +(2.15831 - 3.73831i) q^{44} +(1.65831 - 1.50000i) q^{45} +(-3.00000 - 5.19615i) q^{46} +4.31662i q^{47} -2.00000i q^{48} +(-0.816625 - 1.41444i) q^{49} +(2.92048 - 4.05842i) q^{50} +10.6332 q^{51} +(3.46410 - 2.00000i) q^{52} +(-7.47661 + 4.31662i) q^{53} +(2.00000 + 3.46410i) q^{54} +(-2.02830 - 9.43675i) q^{55} +(1.15831 - 2.00626i) q^{56} +(7.47661 - 4.31662i) q^{57} +(2.87228 - 1.65831i) q^{58} +(6.31662 + 10.9407i) q^{59} +(-3.00000 - 3.31662i) q^{60} +(-5.97494 + 10.3489i) q^{61} +(-2.00626 + 1.15831i) q^{62} -2.31662i q^{63} -1.00000 q^{64} +(2.74456 - 8.51278i) q^{65} -8.63325 q^{66} +(-1.45785 - 0.841688i) q^{67} -5.31662i q^{68} +(-6.00000 + 10.3923i) q^{69} +(-1.08854 - 5.06447i) q^{70} +(3.84169 - 6.65400i) q^{71} +(-0.866025 + 0.500000i) q^{72} -2.63325i q^{73} +(5.00000 + 3.46410i) q^{74} +(-9.94987 - 1.00000i) q^{75} +(-2.15831 - 3.73831i) q^{76} +(-8.66025 - 5.00000i) q^{77} +(-6.92820 - 4.00000i) q^{78} +(-5.47494 + 9.48287i) q^{79} +(-1.65831 + 1.50000i) q^{80} +(5.50000 - 9.52628i) q^{81} -7.63325i q^{82} +(-5.74456 + 3.31662i) q^{83} -4.63325 q^{84} +(-7.97494 - 8.81662i) q^{85} +(4.47494 + 7.75082i) q^{86} +(-5.74456 - 3.31662i) q^{87} +4.31662i q^{88} +(5.81662 + 10.0747i) q^{89} +(-0.686141 + 2.12819i) q^{90} +(-4.63325 - 8.02502i) q^{91} +(5.19615 + 3.00000i) q^{92} +(4.01251 + 2.31662i) q^{93} +(-2.15831 - 3.73831i) q^{94} +(-9.18662 - 2.96181i) q^{95} +(1.00000 + 1.73205i) q^{96} +9.94987i q^{97} +(1.41444 + 0.816625i) q^{98} +(2.15831 + 3.73831i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4} - 16 q^{6} + 4 q^{9}+O(q^{10}) $ 8 * q + 4 * q^4 - 16 * q^6 + 4 * q^9	$ 8 q + 4 q^{4} - 16 q^{6} + 4 q^{9} + 12 q^{10} + 8 q^{11} - 8 q^{14} - 12 q^{15} - 4 q^{16} + 4 q^{19} + 8 q^{21} - 8 q^{24} - 2 q^{25} - 32 q^{26} - 8 q^{31} - 8 q^{34} - 6 q^{35} + 8 q^{36} + 32 q^{39} + 6 q^{40} - 4 q^{41} + 4 q^{44} - 24 q^{46} + 20 q^{49} + 32 q^{51} + 16 q^{54} + 22 q^{55} - 4 q^{56} + 24 q^{59} - 24 q^{60} - 8 q^{61} - 8 q^{64} - 24 q^{65} - 16 q^{66} - 48 q^{69} + 22 q^{70} + 44 q^{71} + 40 q^{74} - 4 q^{76} - 4 q^{79} + 44 q^{81} + 16 q^{84} - 24 q^{85} - 4 q^{86} + 20 q^{89} + 6 q^{90} + 16 q^{91} - 4 q^{94} - 22 q^{95} + 8 q^{96} + 4 q^{99}+O(q^{100}) $ 8 * q + 4 * q^4 - 16 * q^6 + 4 * q^9 + 12 * q^10 + 8 * q^11 - 8 * q^14 - 12 * q^15 - 4 * q^16 + 4 * q^19 + 8 * q^21 - 8 * q^24 - 2 * q^25 - 32 * q^26 - 8 * q^31 - 8 * q^34 - 6 * q^35 + 8 * q^36 + 32 * q^39 + 6 * q^40 - 4 * q^41 + 4 * q^44 - 24 * q^46 + 20 * q^49 + 32 * q^51 + 16 * q^54 + 22 * q^55 - 4 * q^56 + 24 * q^59 - 24 * q^60 - 8 * q^61 - 8 * q^64 - 24 * q^65 - 16 * q^66 - 48 * q^69 + 22 * q^70 + 44 * q^71 + 40 * q^74 - 4 * q^76 - 4 * q^79 + 44 * q^81 + 16 * q^84 - 24 * q^85 - 4 * q^86 + 20 * q^89 + 6 * q^90 + 16 * q^91 - 4 * q^94 - 22 * q^95 + 8 * q^96 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	1.73205	+	1.00000i	1.00000	+	0.577350i	0.908248	−	0.418432i	$-0.137420\pi$
$3$	1.73205	+	1.00000i	1.00000	+	0.577350i	0.0917517	+	0.995782i	$0.470753\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−0.469882	−	2.18614i	−0.210138	−	0.977672i
$5$	−0.469882	−	2.18614i	−0.210138	−	0.977672i
$6$	−2.00000			−0.816497
$7$	−2.00626	−	1.15831i	−0.758293	−	0.437801i	0.0703892	−	0.997520i	$-0.477576\pi$
$7$	−2.00626	−	1.15831i	−0.758293	−	0.437801i	−0.828683	+	0.559719i	$0.810909\pi$
$8$			1.00000i			0.353553i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	1.50000	+	1.65831i	0.474342	+	0.524404i
$11$	4.31662			1.30151			0.650756	−	0.759287i	$-0.274452\pi$
$11$	4.31662			1.30151			0.650756	+	0.759287i	$0.274452\pi$
$12$	1.73205	−	1.00000i	0.500000	−	0.288675i
$13$	3.46410	+	2.00000i	0.960769	+	0.554700i	0.896410	−	0.443227i	$-0.146166\pi$
$13$	3.46410	+	2.00000i	0.960769	+	0.554700i	0.0643593	+	0.997927i	$0.479500\pi$
$14$	2.31662			0.619144
$15$	1.37228	−	4.25639i	0.354322	−	1.09899i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	4.60433	−	2.65831i	1.11671	−	0.644735i	0.176154	−	0.984363i	$-0.443634\pi$
$17$	4.60433	−	2.65831i	1.11671	−	0.644735i	0.940560	+	0.339627i	$0.110301\pi$
$18$	−0.866025	−	0.500000i	−0.204124	−	0.117851i
$19$	2.15831	−	3.73831i	0.495151	−	0.857626i	−0.504834	−	0.863217i	$-0.668446\pi$
$19$	2.15831	−	3.73831i	0.495151	−	0.857626i	0.999984	+	0.00559033i	$0.00177947\pi$
$20$	−2.12819	−	0.686141i	−0.475879	−	0.153426i
$21$	−2.31662	−	4.01251i	−0.505529	−	0.875602i
$22$	−3.73831	+	2.15831i	−0.797010	+	0.460154i
$23$			6.00000i			1.25109i	0.780189	+	0.625543i	$0.215123\pi$
$23$			6.00000i			1.25109i	−0.780189	+	0.625543i	$0.784877\pi$
$24$	−1.00000	+	1.73205i	−0.204124	+	0.353553i
$25$	−4.55842	+	2.05446i	−0.911684	+	0.410891i
$26$	−4.00000			−0.784465
$27$		−	4.00000i		−	0.769800i
$28$	−2.00626	+	1.15831i	−0.379147	+	0.218900i
$29$	−3.31662			−0.615882			−0.307941	−	0.951405i	$-0.599640\pi$
$29$	−3.31662			−0.615882			−0.307941	+	0.951405i	$0.599640\pi$
$30$	0.939764	+	4.37228i	0.171577	+	0.798266i
$31$	2.31662			0.416078			0.208039	−	0.978121i	$-0.433292\pi$
$31$	2.31662			0.416078			0.208039	+	0.978121i	$0.433292\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	7.47661	+	4.31662i	1.30151	+	0.751428i
$34$	−2.65831	+	4.60433i	−0.455897	+	0.789636i
$35$	−1.58953	+	4.93023i	−0.268680	+	0.833361i
$36$	1.00000			0.166667
$37$	−2.59808	−	5.50000i	−0.427121	−	0.904194i
$37$	−2.59808	−	5.50000i	−0.427121	−	0.904194i
$38$			4.31662i			0.700249i
$39$	4.00000	+	6.92820i	0.640513	+	1.10940i
$40$	2.18614	−	0.469882i	0.345659	−	0.0742949i
$41$	−3.81662	+	6.61059i	−0.596057	+	1.03240i	0.397340	+	0.917671i	$0.369933\pi$
$41$	−3.81662	+	6.61059i	−0.596057	+	1.03240i	−0.993397	+	0.114729i	$0.963400\pi$
$42$	4.01251	+	2.31662i	0.619144	+	0.357463i
$43$		−	8.94987i		−	1.36484i	−0.730959	−	0.682422i	$-0.760927\pi$
$43$		−	8.94987i		−	1.36484i	0.730959	−	0.682422i	$-0.239073\pi$
$44$	2.15831	−	3.73831i	0.325378	−	0.563571i
$45$	1.65831	−	1.50000i	0.247207	−	0.223607i
$46$	−3.00000	−	5.19615i	−0.442326	−	0.766131i
$47$			4.31662i			0.629644i	0.949151	+	0.314822i	$0.101945\pi$
$47$			4.31662i			0.629644i	−0.949151	+	0.314822i	$0.898055\pi$
$48$		−	2.00000i		−	0.288675i
$49$	−0.816625	−	1.41444i	−0.116661	−	0.202062i
$50$	2.92048	−	4.05842i	0.413018	−	0.573948i
$51$	10.6332			1.48895
$52$	3.46410	−	2.00000i	0.480384	−	0.277350i
$53$	−7.47661	+	4.31662i	−1.02699	+	0.592934i	−0.916121	−	0.400901i	$-0.868697\pi$
$53$	−7.47661	+	4.31662i	−1.02699	+	0.592934i	−0.110870	+	0.993835i	$0.535364\pi$
$54$	2.00000	+	3.46410i	0.272166	+	0.471405i
$55$	−2.02830	−	9.43675i	−0.273496	−	1.27245i
$56$	1.15831	−	2.00626i	0.154786	−	0.268097i
$57$	7.47661	−	4.31662i	0.990302	−	0.571751i
$58$	2.87228	−	1.65831i	0.377149	−	0.217747i
$59$	6.31662	+	10.9407i	0.822355	+	1.42436i	0.903924	+	0.427692i	$0.140673\pi$
$59$	6.31662	+	10.9407i	0.822355	+	1.42436i	−0.0815699	+	0.996668i	$0.525993\pi$
$60$	−3.00000	−	3.31662i	−0.387298	−	0.428174i
$61$	−5.97494	+	10.3489i	−0.765012	+	1.32504i	0.175228	+	0.984528i	$0.443934\pi$
$61$	−5.97494	+	10.3489i	−0.765012	+	1.32504i	−0.940240	+	0.340512i	$0.889400\pi$
$62$	−2.00626	+	1.15831i	−0.254795	+	0.147106i
$63$		−	2.31662i		−	0.291867i
$64$	−1.00000			−0.125000
$65$	2.74456	−	8.51278i	0.340421	−	1.05588i
$66$	−8.63325			−1.06268
$67$	−1.45785	−	0.841688i	−0.178104	−	0.102829i	0.408297	−	0.912849i	$-0.366123\pi$
$67$	−1.45785	−	0.841688i	−0.178104	−	0.102829i	−0.586402	+	0.810020i	$0.699456\pi$
$68$		−	5.31662i		−	0.644735i
$69$	−6.00000	+	10.3923i	−0.722315	+	1.25109i
$70$	−1.08854	−	5.06447i	−0.130105	−	0.605320i
$71$	3.84169	−	6.65400i	0.455924	−	0.789684i	−0.542816	−	0.839851i	$-0.682642\pi$
$71$	3.84169	−	6.65400i	0.455924	−	0.789684i	0.998741	+	0.0501671i	$0.0159754\pi$
$72$	−0.866025	+	0.500000i	−0.102062	+	0.0589256i
$73$		−	2.63325i		−	0.308199i	−0.988055	−	0.154099i	$-0.950752\pi$
$73$		−	2.63325i		−	0.308199i	0.988055	−	0.154099i	$-0.0492476\pi$
$74$	5.00000	+	3.46410i	0.581238	+	0.402694i
$75$	−9.94987	−	1.00000i	−1.14891	−	0.115470i
$76$	−2.15831	−	3.73831i	−0.247575	−	0.428813i
$77$	−8.66025	−	5.00000i	−0.986928	−	0.569803i
$78$	−6.92820	−	4.00000i	−0.784465	−	0.452911i
$79$	−5.47494	+	9.48287i	−0.615979	+	1.06691i	0.374233	+	0.927335i	$0.377906\pi$
$79$	−5.47494	+	9.48287i	−0.615979	+	1.06691i	−0.990212	+	0.139572i	$0.955427\pi$
$80$	−1.65831	+	1.50000i	−0.185405	+	0.167705i
$81$	5.50000	−	9.52628i	0.611111	−	1.05848i
$82$		−	7.63325i		−	0.842951i
$83$	−5.74456	+	3.31662i	−0.630548	+	0.364047i	−0.780964	−	0.624576i	$-0.785272\pi$
$83$	−5.74456	+	3.31662i	−0.630548	+	0.364047i	0.150416	+	0.988623i	$0.451939\pi$
$84$	−4.63325			−0.505529
$85$	−7.97494	−	8.81662i	−0.865003	−	0.956297i
$86$	4.47494	+	7.75082i	0.482545	+	0.835792i
$87$	−5.74456	−	3.31662i	−0.615882	−	0.355580i
$88$			4.31662i			0.460154i
$89$	5.81662	+	10.0747i	0.616561	+	1.06791i	0.990108	+	0.140304i	$0.0448080\pi$
$89$	5.81662	+	10.0747i	0.616561	+	1.06791i	−0.373547	+	0.927611i	$0.621859\pi$
$90$	−0.686141	+	2.12819i	−0.0723256	+	0.224331i
$91$	−4.63325	−	8.02502i	−0.485697	−	0.841251i
$92$	5.19615	+	3.00000i	0.541736	+	0.312772i
$93$	4.01251	+	2.31662i	0.416078	+	0.240223i
$94$	−2.15831	−	3.73831i	−0.222613	−	0.385577i
$95$	−9.18662	−	2.96181i	−0.942527	−	0.303875i
$96$	1.00000	+	1.73205i	0.102062	+	0.176777i
$97$			9.94987i			1.01026i	0.863044	+	0.505128i	$0.168555\pi$
$97$			9.94987i			1.01026i	−0.863044	+	0.505128i	$0.831445\pi$
$98$	1.41444	+	0.816625i	0.142880	+	0.0824916i
$99$	2.15831	+	3.73831i	0.216919	+	0.375714i
$100$	−0.500000	+	4.97494i	−0.0500000	+	0.497494i
$101$	−15.3166			−1.52406			−0.762031	−	0.647541i	$-0.775797\pi$
$101$	−15.3166			−1.52406			−0.762031	+	0.647541i	$0.775797\pi$
$102$	−9.20866	+	5.31662i	−0.911794	+	0.526424i
$103$		−	9.68338i		−	0.954131i	−0.878868	−	0.477066i	$-0.841700\pi$
$103$		−	9.68338i		−	0.954131i	0.878868	−	0.477066i	$-0.158300\pi$
$104$	−2.00000	+	3.46410i	−0.196116	+	0.339683i
$105$	−7.68338	+	6.94987i	−0.749821	+	0.678238i
$106$	4.31662	−	7.47661i	0.419268	−	0.726193i
$107$	−0.274205	−	0.158312i	−0.0265084	−	0.0153046i	0.486687	−	0.873576i	$-0.338205\pi$
$107$	−0.274205	−	0.158312i	−0.0265084	−	0.0153046i	−0.513196	+	0.858272i	$0.671538\pi$
$108$	−3.46410	−	2.00000i	−0.333333	−	0.192450i
$109$	1.97494	+	3.42069i	0.189165	+	0.327643i	0.944972	−	0.327151i	$-0.106089\pi$
$109$	1.97494	+	3.42069i	0.189165	+	0.327643i	−0.755807	+	0.654794i	$0.772755\pi$
$110$	6.47494	+	7.15831i	0.617361	+	0.682518i
$111$	1.00000	−	12.1244i	0.0949158	−	1.15079i
$112$			2.31662i			0.218900i
$113$	4.64774	−	2.68338i	0.437223	−	0.252431i	−0.265196	−	0.964195i	$-0.585437\pi$
$113$	4.64774	−	2.68338i	0.437223	−	0.252431i	0.702419	+	0.711764i	$0.252103\pi$
$114$	−4.31662	+	7.47661i	−0.404289	+	0.700249i
$115$	13.1168	−	2.81929i	1.22315	−	0.262900i
$116$	−1.65831	+	2.87228i	−0.153970	+	0.266685i
$117$			4.00000i			0.369800i
$118$	−10.9407	−	6.31662i	−1.00717	−	0.581492i
$119$	−12.3166			−1.12906
$120$	4.25639	+	1.37228i	0.388553	+	0.125272i
$121$	7.63325			0.693932
$122$		−	11.9499i		−	1.08189i
$123$	−13.2212	+	7.63325i	−1.19211	+	0.688267i
$124$	1.15831	−	2.00626i	0.104020	−	0.180167i
$125$	6.63325	+	9.00000i	0.593296	+	0.804984i
$126$	1.15831	+	2.00626i	0.103191	+	0.178731i
$127$	1.18364	−	0.683375i	0.105031	−	0.0606397i	−0.446564	−	0.894752i	$-0.647353\pi$
$127$	1.18364	−	0.683375i	0.105031	−	0.0606397i	0.551595	+	0.834112i	$0.314019\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	8.94987	−	15.5016i	0.787993	−	1.36484i
$130$	1.87953	+	8.74456i	0.164845	+	0.766949i
$131$	0.683375	+	1.18364i	0.0597068	+	0.103415i	0.894334	−	0.447400i	$-0.147650\pi$
$131$	0.683375	+	1.18364i	0.0597068	+	0.103415i	−0.834627	+	0.550816i	$0.814317\pi$
$132$	7.47661	−	4.31662i	0.650756	−	0.375714i
$133$	−8.66025	+	5.00000i	−0.750939	+	0.433555i
$134$	1.68338			0.145421
$135$	−8.74456	+	1.87953i	−0.752612	+	0.161764i
$136$	2.65831	+	4.60433i	0.227948	+	0.394818i
$137$			11.3166i			0.966845i	0.875387	+	0.483422i	$0.160606\pi$
$137$			11.3166i			0.966845i	−0.875387	+	0.483422i	$0.839394\pi$
$138$		−	12.0000i		−	1.02151i
$139$	−9.94987	−	17.2337i	−0.843937	−	1.46174i	−0.886541	−	0.462650i	$-0.846899\pi$
$139$	−9.94987	−	17.2337i	−0.843937	−	1.46174i	0.0426035	−	0.999092i	$-0.486435\pi$
$140$	3.47494	+	3.84169i	0.293686	+	0.324682i
$141$	−4.31662	+	7.47661i	−0.363525	+	0.629644i
$142$			7.68338i			0.644775i
$143$	14.9532	+	8.63325i	1.25045	+	0.721949i
$144$	0.500000	−	0.866025i	0.0416667	−	0.0721688i
$145$	1.55842	+	7.25061i	0.129420	+	0.602130i
$146$	1.31662	+	2.28046i	0.108965	+	0.188732i
$147$		−	3.26650i		−	0.269416i
$148$	−6.06218	−	0.500000i	−0.498308	−	0.0410997i
$149$	15.9499			1.30666			0.653332	−	0.757071i	$-0.273370\pi$
$149$	15.9499			1.30666			0.653332	+	0.757071i	$0.273370\pi$
$150$	9.11684	−	4.10891i	0.744387	−	0.335491i
$151$	−5.31662	+	9.20866i	−0.432661	+	0.749390i	−0.997101	−	0.0760832i	$-0.975759\pi$
$151$	−5.31662	+	9.20866i	−0.432661	+	0.749390i	0.564441	+	0.825474i	$0.309092\pi$
$152$	3.73831	+	2.15831i	0.303217	+	0.175062i
$153$	4.60433	+	2.65831i	0.372238	+	0.214912i
$154$	10.0000			0.805823
$155$	−1.08854	−	5.06447i	−0.0874336	−	0.406788i
$156$	8.00000			0.640513
$157$	2.59808	−	1.50000i	0.207349	−	0.119713i	−0.392730	−	0.919654i	$-0.628469\pi$
$157$	2.59808	−	1.50000i	0.207349	−	0.119713i	0.600079	+	0.799941i	$0.295136\pi$
$158$		−	10.9499i		−	0.871125i
$159$	−17.2665			−1.36932
$160$	0.686141	−	2.12819i	0.0542442	−	0.168249i
$161$	6.94987	−	12.0375i	0.547727	−	0.948691i
$162$			11.0000i			0.864242i
$163$	19.2399	−	11.1082i	1.50699	−	0.870060i	0.507022	−	0.861933i	$-0.330746\pi$
$163$	19.2399	−	11.1082i	1.50699	−	0.870060i	0.999967	−	0.00812707i	$-0.00258695\pi$
$164$	3.81662	+	6.61059i	0.298028	+	0.516200i
$165$	5.92362	−	18.3732i	0.461153	−	1.43035i
$166$	3.31662	−	5.74456i	0.257420	−	0.445865i
$167$	−8.02502	−	4.63325i	−0.620995	−	0.358532i	0.156261	−	0.987716i	$-0.450056\pi$
$167$	−8.02502	−	4.63325i	−0.620995	−	0.358532i	−0.777256	+	0.629184i	$0.783389\pi$
$168$	4.01251	−	2.31662i	0.309572	−	0.178731i
$169$	1.50000	+	2.59808i	0.115385	+	0.199852i
$170$	11.3148	+	3.64795i	0.867806	+	0.279785i
$171$	4.31662			0.330101
$172$	−7.75082	−	4.47494i	−0.590994	−	0.341211i
$173$	10.6231	−	6.13325i	0.807659	−	0.466302i	−0.0384830	−	0.999259i	$-0.512253\pi$
$173$	10.6231	−	6.13325i	0.807659	−	0.466302i	0.846142	+	0.532957i	$0.178919\pi$
$174$	6.63325			0.502865
$175$	11.5251	+	1.15831i	0.871213	+	0.0875602i
$176$	−2.15831	−	3.73831i	−0.162689	−	0.281785i
$177$			25.2665i			1.89915i
$178$	−10.0747	−	5.81662i	−0.755130	−	0.435974i
$179$	5.26650			0.393637			0.196818	−	0.980440i	$-0.436939\pi$
$179$	5.26650			0.393637			0.196818	+	0.980440i	$0.436939\pi$
$180$	−0.469882	−	2.18614i	−0.0350229	−	0.162945i
$181$	−6.65831	+	11.5325i	−0.494908	+	0.857207i	−0.999983	−	0.00586926i	$-0.998132\pi$
$181$	−6.65831	+	11.5325i	−0.494908	+	0.857207i	0.505074	+	0.863076i	$0.331465\pi$
$182$	8.02502	+	4.63325i	0.594854	+	0.343439i
$183$	−20.6978	+	11.9499i	−1.53002	+	0.883360i
$184$	−6.00000			−0.442326
$185$	−10.8030	+	8.26411i	−0.794251	+	0.607589i
$186$	−4.63325			−0.339726
$187$	19.8752	−	11.4749i	1.45342	−	0.839131i
$188$	3.73831	+	2.15831i	0.272644	+	0.157411i
$189$	−4.63325	+	8.02502i	−0.337019	+	0.583735i
$190$	9.43675	−	2.02830i	0.684614	−	0.147149i
$191$	6.63325			0.479965			0.239983	−	0.970777i	$-0.422858\pi$
$191$	6.63325			0.479965			0.239983	+	0.970777i	$0.422858\pi$
$192$	−1.73205	−	1.00000i	−0.125000	−	0.0721688i
$193$			1.31662i			0.0947727i	0.998877	+	0.0473864i	$0.0150892\pi$
$193$			1.31662i			0.0947727i	−0.998877	+	0.0473864i	$0.984911\pi$
$194$	−4.97494	−	8.61684i	−0.357180	−	0.618653i
$195$	13.2665	−	12.0000i	0.950034	−	0.859338i
$196$	−1.63325			−0.116661
$197$	−3.78172	+	2.18338i	−0.269436	+	0.155559i	−0.628631	−	0.777703i	$-0.716385\pi$
$197$	−3.78172	+	2.18338i	−0.269436	+	0.155559i	0.359195	+	0.933262i	$0.383051\pi$
$198$	−3.73831	−	2.15831i	−0.265670	−	0.153385i
$199$	16.9499			1.20154			0.600772	−	0.799420i	$-0.294860\pi$
$199$	16.9499			1.20154			0.600772	+	0.799420i	$0.294860\pi$
$200$	−2.05446	−	4.55842i	−0.145272	−	0.322329i
$201$	−1.68338	−	2.91569i	−0.118736	−	0.205657i
$202$	13.2646	−	7.65831i	0.933293	−	0.538837i
$203$	6.65400	+	3.84169i	0.467019	+	0.269634i
$204$	5.31662	−	9.20866i	0.372238	−	0.644735i
$205$	16.2450	+	5.23748i	1.13460	+	0.365802i
$206$	4.84169	+	8.38605i	0.337336	+	0.584284i
$207$	−5.19615	+	3.00000i	−0.361158	+	0.208514i
$208$		−	4.00000i		−	0.277350i
$209$	9.31662	−	16.1369i	0.644444	−	1.11621i
$210$	3.17906	−	9.86046i	0.219376	−	0.680436i
$211$	−14.3166			−0.985597			−0.492799	−	0.870143i	$-0.664026\pi$
$211$	−14.3166			−0.985597			−0.492799	+	0.870143i	$0.664026\pi$
$212$			8.63325i			0.592934i
$213$	13.3080	−	7.68338i	0.911849	−	0.526456i
$214$	0.316625			0.0216440
$215$	−19.5657	+	4.20538i	−1.33437	+	0.286805i
$216$	4.00000			0.272166
$217$	−4.64774	−	2.68338i	−0.315509	−	0.182159i
$218$	−3.42069	−	1.97494i	−0.231678	−	0.133760i
$219$	2.63325	−	4.56092i	0.177939	−	0.308199i
$220$	−9.18662	−	2.96181i	−0.619362	−	0.199685i
$221$	21.2665			1.43054
$222$	5.19615	+	11.0000i	0.348743	+	0.738272i
$223$			13.3668i			0.895104i	0.894258	+	0.447552i	$0.147704\pi$
$223$			13.3668i			0.895104i	−0.894258	+	0.447552i	$0.852296\pi$
$224$	−1.15831	−	2.00626i	−0.0773930	−	0.134049i
$225$	−4.05842	−	2.92048i	−0.270561	−	0.194699i
$226$	−2.68338	+	4.64774i	−0.178495	+	0.309163i
$227$	6.01877	+	3.47494i	0.399480	+	0.230640i	0.686259	−	0.727357i	$-0.259251\pi$
$227$	6.01877	+	3.47494i	0.399480	+	0.230640i	−0.286780	+	0.957997i	$0.592585\pi$
$228$		−	8.63325i		−	0.571751i
$229$	−1.97494	+	3.42069i	−0.130508	+	0.226046i	−0.923872	−	0.382701i	$-0.874994\pi$
$229$	−1.97494	+	3.42069i	−0.130508	+	0.226046i	0.793365	+	0.608746i	$0.208327\pi$
$230$	−9.94987	+	9.00000i	−0.656075	+	0.593442i
$231$	−10.0000	−	17.3205i	−0.657952	−	1.13961i
$232$		−	3.31662i		−	0.217747i
$233$			27.9499i			1.83106i	0.402253	+	0.915529i	$0.368227\pi$
$233$			27.9499i			1.83106i	−0.402253	+	0.915529i	$0.631773\pi$
$234$	−2.00000	−	3.46410i	−0.130744	−	0.226455i
$235$	9.43675	−	2.02830i	0.615586	−	0.132312i
$236$	12.6332			0.822355
$237$	−18.9657	+	10.9499i	−1.23196	+	0.711271i
$238$	10.6665	−	6.15831i	0.691407	−	0.399184i
$239$	−4.15831	−	7.20241i	−0.268979	−	0.465885i	0.699620	−	0.714516i	$-0.253353\pi$
$239$	−4.15831	−	7.20241i	−0.268979	−	0.465885i	−0.968598	+	0.248631i	$0.920020\pi$
$240$	−4.37228	+	0.939764i	−0.282230	+	0.0606615i
$241$	−14.6332	+	25.3455i	−0.942610	+	1.63265i	−0.182144	+	0.983272i	$0.558304\pi$
$241$	−14.6332	+	25.3455i	−0.942610	+	1.63265i	−0.760466	+	0.649377i	$0.775030\pi$
$242$	−6.61059	+	3.81662i	−0.424945	+	0.245342i
$243$	8.66025	−	5.00000i	0.555556	−	0.320750i
$244$	5.97494	+	10.3489i	0.382506	+	0.662520i
$245$	−2.70844	+	2.44987i	−0.173036	+	0.156517i
$246$	7.63325	−	13.2212i	0.486678	−	0.842951i
$247$	14.9532	−	8.63325i	0.951451	−	0.549321i
$248$			2.31662i			0.147106i
$249$	−13.2665			−0.840730
$250$	−10.2446	−	4.47760i	−0.647923	−	0.283189i
$251$	2.31662			0.146224			0.0731120	−	0.997324i	$-0.476707\pi$
$251$	2.31662			0.146224			0.0731120	+	0.997324i	$0.476707\pi$
$252$	−2.00626	−	1.15831i	−0.126382	−	0.0729668i
$253$			25.8997i			1.62830i
$254$	−0.683375	+	1.18364i	−0.0428788	+	0.0742682i
$255$	−4.99637	−	23.2458i	−0.312885	−	1.45571i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−20.1928	+	11.6583i	−1.25959	+	0.727226i	−0.972995	−	0.230826i	$-0.925857\pi$
$257$	−20.1928	+	11.6583i	−1.25959	+	0.727226i	−0.286597	+	0.958051i	$0.592524\pi$
$258$			17.8997i			1.11439i
$259$	−1.15831	+	14.0438i	−0.0719740	+	0.872639i
$260$	−6.00000	−	6.63325i	−0.372104	−	0.411377i
$261$	−1.65831	−	2.87228i	−0.102647	−	0.177790i
$262$	−1.18364	−	0.683375i	−0.0731256	−	0.0422191i
$263$	−11.4891	−	6.63325i	−0.708450	−	0.409024i	0.102037	−	0.994781i	$-0.467464\pi$
$263$	−11.4891	−	6.63325i	−0.708450	−	0.409024i	−0.810487	+	0.585757i	$0.800797\pi$
$264$	−4.31662	+	7.47661i	−0.265670	+	0.460154i
$265$	12.9499	+	14.3166i	0.795504	+	0.879463i
$266$	5.00000	−	8.66025i	0.306570	−	0.530994i
$267$			23.2665i			1.42389i
$268$	−1.45785	+	0.841688i	−0.0890521	+	0.0514143i
$269$	−1.26650			−0.0772198			−0.0386099	−	0.999254i	$-0.512293\pi$
$269$	−1.26650			−0.0772198			−0.0386099	+	0.999254i	$0.512293\pi$
$270$	6.63325	−	6.00000i	0.403687	−	0.365148i
$271$	−13.7916	−	23.8877i	−0.837778	−	1.45107i	−0.891749	−	0.452531i	$-0.850521\pi$
$271$	−13.7916	−	23.8877i	−0.837778	−	1.45107i	0.0539709	−	0.998543i	$-0.482812\pi$
$272$	−4.60433	−	2.65831i	−0.279179	−	0.161184i
$273$		−	18.5330i		−	1.12167i
$274$	−5.65831	−	9.80048i	−0.341831	−	0.592069i
$275$	−19.6770	+	8.86832i	−1.18657	+	0.534780i
$276$	6.00000	+	10.3923i	0.361158	+	0.625543i
$277$	4.87854	+	2.81662i	0.293123	+	0.169235i	0.639349	−	0.768916i	$-0.279204\pi$
$277$	4.87854	+	2.81662i	0.293123	+	0.169235i	−0.346226	+	0.938151i	$0.612537\pi$
$278$	17.2337	+	9.94987i	1.03361	+	0.596754i
$279$	1.15831	+	2.00626i	0.0693463	+	0.120111i
$280$	−4.93023	−	1.58953i	−0.294637	−	0.0949926i
$281$	−8.18338	−	14.1740i	−0.488179	−	0.845551i	0.511728	−	0.859147i	$-0.329005\pi$
$281$	−8.18338	−	14.1740i	−0.488179	−	0.845551i	−0.999908	+	0.0135961i	$0.995672\pi$
$282$		−	8.63325i		−	0.514103i
$283$	−7.20241	−	4.15831i	−0.428139	−	0.247186i	0.270415	−	0.962744i	$-0.412839\pi$
$283$	−7.20241	−	4.15831i	−0.428139	−	0.247186i	−0.698553	+	0.715558i	$0.746173\pi$
$284$	−3.84169	−	6.65400i	−0.227962	−	0.394842i
$285$	−12.9499	−	14.3166i	−0.767084	−	0.848044i
$286$	−17.2665			−1.02099
$287$	15.3143	−	8.84169i	0.903972	−	0.521908i
$288$			1.00000i			0.0589256i
$289$	5.63325	−	9.75707i	0.331368	−	0.573946i
$290$	−4.97494	−	5.50000i	−0.292138	−	0.322971i
$291$	−9.94987	+	17.2337i	−0.583272	+	1.01026i
$292$	−2.28046	−	1.31662i	−0.133454	−	0.0770496i
$293$	2.04967	+	1.18338i	0.119743	+	0.0691335i	0.558675	−	0.829387i	$-0.311310\pi$
$293$	2.04967	+	1.18338i	0.119743	+	0.0691335i	−0.438932	+	0.898520i	$0.644643\pi$
$294$	1.63325	+	2.82887i	0.0952530	+	0.164983i
$295$	20.9499	−	18.9499i	1.21975	−	1.10330i
$296$	5.50000	−	2.59808i	0.319681	−	0.151010i
$297$		−	17.2665i		−	1.00190i
$298$	−13.8130	+	7.97494i	−0.800165	+	0.461976i
$299$	−12.0000	+	20.7846i	−0.693978	+	1.20201i
$300$	−5.84096	+	8.11684i	−0.337228	+	0.468626i
$301$	−10.3668	+	17.9557i	−0.597530	+	1.03495i
$302$		−	10.6332i		−	0.611875i
$303$	−26.5292	−	15.3166i	−1.52406	−	0.879917i
$304$	−4.31662			−0.247575
$305$	25.4317	+	8.19929i	1.45621	+	0.469490i
$306$	−5.31662			−0.303931
$307$		−	15.6834i		−	0.895098i	−0.894260	−	0.447549i	$-0.852297\pi$
$307$		−	15.6834i		−	0.895098i	0.894260	−	0.447549i	$-0.147703\pi$
$308$	−8.66025	+	5.00000i	−0.493464	+	0.284901i
$309$	9.68338	−	16.7721i	0.550868	−	0.954131i
$310$	3.47494	+	3.84169i	0.197363	+	0.218193i
$311$	−4.79156	−	8.29923i	−0.271705	−	0.470606i	0.697594	−	0.716493i	$-0.254254\pi$
$311$	−4.79156	−	8.29923i	−0.271705	−	0.470606i	−0.969298	+	0.245887i	$0.920921\pi$
$312$	−6.92820	+	4.00000i	−0.392232	+	0.226455i
$313$	3.50751	−	2.02506i	0.198256	−	0.114463i	−0.397586	−	0.917565i	$-0.630152\pi$
$313$	3.50751	−	2.02506i	0.198256	−	0.114463i	0.595842	+	0.803102i	$0.296818\pi$
$314$	−1.50000	+	2.59808i	−0.0846499	+	0.146618i
$315$	−5.06447	+	1.08854i	−0.285350	+	0.0613323i
$316$	5.47494	+	9.48287i	0.307989	+	0.533453i
$317$	−7.24582	+	4.18338i	−0.406966	+	0.234962i	−0.689485	−	0.724300i	$-0.742163\pi$
$317$	−7.24582	+	4.18338i	−0.406966	+	0.234962i	0.282519	+	0.959262i	$0.408830\pi$
$318$	14.9532	−	8.63325i	0.838535	−	0.484129i
$319$	−14.3166			−0.801577
$320$	0.469882	+	2.18614i	0.0262672	+	0.122209i
$321$	−0.316625	−	0.548410i	−0.0176723	−	0.0306093i
$322$			13.8997i			0.774603i
$323$		−	22.9499i		−	1.27697i
$324$	−5.50000	−	9.52628i	−0.305556	−	0.529238i
$325$	−19.8997	−	2.00000i	−1.10384	−	0.110940i
$326$	−11.1082	+	19.2399i	−0.615226	+	1.06560i
$327$			7.89975i			0.436857i
$328$	−6.61059	−	3.81662i	−0.365009	−	0.210738i
$329$	5.00000	−	8.66025i	0.275659	−	0.477455i
$330$	4.05661	+	18.8735i	0.223309	+	1.03895i
$331$	16.9499	+	29.3580i	0.931649	+	1.61366i	0.780502	+	0.625153i	$0.214963\pi$
$331$	16.9499	+	29.3580i	0.931649	+	1.61366i	0.151147	+	0.988511i	$0.451703\pi$
$332$			6.63325i			0.364047i
$333$	3.46410	−	5.00000i	0.189832	−	0.273998i
$334$	9.26650			0.507040
$335$	−1.15503	+	3.58255i	−0.0631061	+	0.195736i
$336$	−2.31662	+	4.01251i	−0.126382	+	0.218900i
$337$	−10.3489	−	5.97494i	−0.563740	−	0.325476i	0.190905	−	0.981608i	$-0.438858\pi$
$337$	−10.3489	−	5.97494i	−0.563740	−	0.325476i	−0.754645	+	0.656133i	$0.772191\pi$
$338$	−2.59808	−	1.50000i	−0.141317	−	0.0815892i
$339$	10.7335			0.582964
$340$	−11.6229	+	2.49819i	−0.630340	+	0.135483i
$341$	10.0000			0.541530
$342$	−3.73831	+	2.15831i	−0.202144	+	0.116708i
$343$			20.0000i			1.07990i
$344$	8.94987			0.482545
$345$	25.5383	+	8.23369i	1.37494	+	0.443287i
$346$	−6.13325	+	10.6231i	−0.329726	+	0.571101i
$347$		−	15.2665i		−	0.819549i	−0.912187	−	0.409774i	$-0.865607\pi$
$347$		−	15.2665i		−	0.819549i	0.912187	−	0.409774i	$-0.134393\pi$
$348$	−5.74456	+	3.31662i	−0.307941	+	0.177790i
$349$	−14.3417	−	24.8405i	−0.767693	−	1.32968i	−0.938811	−	0.344433i	$-0.888071\pi$
$349$	−14.3417	−	24.8405i	−0.767693	−	1.32968i	0.171118	−	0.985251i	$-0.445262\pi$
$350$	−10.5602	+	4.75940i	−0.564464	+	0.254401i
$351$	8.00000	−	13.8564i	0.427008	−	0.739600i
$352$	3.73831	+	2.15831i	0.199252	+	0.115038i
$353$	23.5701	−	13.6082i	1.25451	−	0.724291i	0.282507	−	0.959265i	$-0.408834\pi$
$353$	23.5701	−	13.6082i	1.25451	−	0.724291i	0.972002	+	0.234975i	$0.0755007\pi$
$354$	−12.6332	−	21.8814i	−0.671450	−	1.16298i
$355$	−16.3517	−	5.27188i	−0.867859	−	0.279802i
$356$	11.6332			0.616561
$357$	−21.3330	−	12.3166i	−1.12906	−	0.651865i
$358$	−4.56092	+	2.63325i	−0.241052	+	0.139172i
$359$	8.63325			0.455645			0.227823	−	0.973703i	$-0.426839\pi$
$359$	8.63325			0.455645			0.227823	+	0.973703i	$0.426839\pi$
$360$	1.50000	+	1.65831i	0.0790569	+	0.0874007i
$361$	0.183375	+	0.317615i	0.00965133	+	0.0167166i
$362$		−	13.3166i		−	0.699906i
$363$	13.2212	+	7.63325i	0.693932	+	0.400642i
$364$	−9.26650			−0.485697
$365$	−5.75665	+	1.23732i	−0.301317	+	0.0647641i
$366$	11.9499	−	20.6978i	0.624630	−	1.08189i
$367$	3.46410	+	2.00000i	0.180825	+	0.104399i	0.587680	−	0.809093i	$-0.300041\pi$
$367$	3.46410	+	2.00000i	0.180825	+	0.104399i	−0.406855	+	0.913493i	$0.633375\pi$
$368$	5.19615	−	3.00000i	0.270868	−	0.156386i
$369$	−7.63325			−0.397371
$370$	5.22360	−	12.5584i	0.271562	−	0.652881i
$371$	20.0000			1.03835
$372$	4.01251	−	2.31662i	0.208039	−	0.120111i
$373$	14.6356	+	8.44987i	0.757803	+	0.437518i	0.828506	−	0.559979i	$-0.189191\pi$
$373$	14.6356	+	8.44987i	0.757803	+	0.437518i	−0.0707032	+	0.997497i	$0.522524\pi$
$374$	−11.4749	+	19.8752i	−0.593355	+	1.02772i
$375$	2.48913	+	22.2217i	0.128538	+	1.14752i
$376$	−4.31662			−0.222613
$377$	−11.4891	−	6.63325i	−0.591720	−	0.341630i
$378$		−	9.26650i		−	0.476617i
$379$	6.52506	+	11.3017i	0.335170	+	0.580531i	0.983517	−	0.180813i	$-0.0578729\pi$
$379$	6.52506	+	11.3017i	0.335170	+	0.580531i	−0.648348	+	0.761345i	$0.724540\pi$
$380$	−7.15831	+	6.47494i	−0.367214	+	0.332157i
$381$	2.73350			0.140041
$382$	−5.74456	+	3.31662i	−0.293917	+	0.169693i
$383$	26.2550	+	15.1583i	1.34157	+	0.774554i	0.987037	−	0.160491i	$-0.0513079\pi$
$383$	26.2550	+	15.1583i	1.34157	+	0.774554i	0.354529	+	0.935045i	$0.384641\pi$
$384$	2.00000			0.102062
$385$	−6.86141	+	21.2819i	−0.349690	+	1.08463i
$386$	−0.658312	−	1.14023i	−0.0335072	−	0.0580362i
$387$	7.75082	−	4.47494i	0.393996	−	0.227474i
$388$	8.61684	+	4.97494i	0.437454	+	0.252564i
$389$	13.9749	−	24.2053i	0.708557	−	1.22726i	−0.256835	−	0.966455i	$-0.582680\pi$
$389$	13.9749	−	24.2053i	0.708557	−	1.22726i	0.965392	−	0.260802i	$-0.0839870\pi$
$390$	−5.48913	+	17.0256i	−0.277953	+	0.862122i
$391$	15.9499	+	27.6260i	0.806620	+	1.39711i
$392$	1.41444	−	0.816625i	0.0714398	−	0.0412458i
$393$			2.73350i			0.137887i
$394$	2.18338	−	3.78172i	0.109997	−	0.190520i
$395$	23.3035	+	7.51315i	1.17252	+	0.378028i
$396$	4.31662			0.216919
$397$		−	28.8997i		−	1.45044i	−0.688519	−	0.725218i	$-0.741739\pi$
$397$		−	28.8997i		−	1.45044i	0.688519	−	0.725218i	$-0.258261\pi$
$398$	−14.6790	+	8.47494i	−0.735793	+	0.424810i
$399$	−20.0000			−1.00125
$400$	4.05842	+	2.92048i	0.202921	+	0.146024i
$401$	−37.2665			−1.86100			−0.930500	−	0.366292i	$-0.880627\pi$
$401$	−37.2665			−1.86100			−0.930500	+	0.366292i	$0.880627\pi$
$402$	2.91569	+	1.68338i	0.145421	+	0.0839591i
$403$	8.02502	+	4.63325i	0.399755	+	0.230799i
$404$	−7.65831	+	13.2646i	−0.381015	+	0.659938i
$405$	−23.4101	−	7.54755i	−1.16326	−	0.375041i
$406$	−7.68338			−0.381320
$407$	−11.2149	−	23.7414i	−0.555903	−	1.17682i
$408$			10.6332i			0.526424i
$409$	−17.0831	−	29.5888i	−0.844706	−	1.46307i	−0.885876	−	0.463922i	$-0.846442\pi$
$409$	−17.0831	−	29.5888i	−0.844706	−	1.46307i	0.0411701	−	0.999152i	$-0.486891\pi$
$410$	−16.6874	+	3.58673i	−0.824130	+	0.177136i
$411$	−11.3166	+	19.6010i	−0.558208	+	0.966845i
$412$	−8.38605	−	4.84169i	−0.413151	−	0.238533i
$413$		−	29.2665i		−	1.44011i
$414$	3.00000	−	5.19615i	0.147442	−	0.255377i
$415$	9.94987	+	11.0000i	0.488420	+	0.539969i
$416$	2.00000	+	3.46410i	0.0980581	+	0.169842i
$417$		−	39.7995i		−	1.94899i
$418$			18.6332i			0.911382i
$419$	−8.52506	−	14.7658i	−0.416477	−	0.721359i	0.579106	−	0.815253i	$-0.303402\pi$
$419$	−8.52506	−	14.7658i	−0.416477	−	0.721359i	−0.995582	+	0.0938939i	$0.970069\pi$
$420$	2.17708	+	10.1289i	0.106231	+	0.494241i
$421$	21.9499			1.06977			0.534886	−	0.844924i	$-0.320355\pi$
$421$	21.9499			1.06977			0.534886	+	0.844924i	$0.320355\pi$
$422$	12.3986	−	7.15831i	0.603552	−	0.348461i
$423$	−3.73831	+	2.15831i	−0.181763	+	0.104941i
$424$	−4.31662	−	7.47661i	−0.209634	−	0.363096i
$425$	−15.5271	+	21.5771i	−0.753175	+	1.04664i
$426$	−7.68338	+	13.3080i	−0.372261	+	0.644775i
$427$	23.9745	−	13.8417i	1.16021	−	0.669846i
$428$	−0.274205	+	0.158312i	−0.0132542	+	0.00765232i
$429$	17.2665	+	29.9065i	0.833634	+	1.44390i
$430$	14.8417	−	13.4248i	0.715730	−	0.647402i
$431$	14.8417	−	25.7066i	0.714899	−	1.23824i	−0.248100	−	0.968735i	$-0.579806\pi$
$431$	14.8417	−	25.7066i	0.714899	−	1.23824i	0.962999	−	0.269507i	$-0.0868607\pi$
$432$	−3.46410	+	2.00000i	−0.166667	+	0.0962250i
$433$			15.9499i			0.766502i	0.923644	+	0.383251i	$0.125196\pi$
$433$			15.9499i			0.766502i	−0.923644	+	0.383251i	$0.874804\pi$
$434$	5.36675			0.257612
$435$	−4.55134	+	14.1168i	−0.218220	+	0.676851i
$436$	3.94987			0.189165
$437$	22.4298	+	12.9499i	1.07296	+	0.619477i
$438$			5.26650i			0.251643i
$439$	6.00000	−	10.3923i	0.286364	−	0.495998i	−0.686575	−	0.727059i	$-0.740887\pi$
$439$	6.00000	−	10.3923i	0.286364	−	0.495998i	0.972939	+	0.231062i	$0.0742199\pi$
$440$	9.43675	−	2.02830i	0.449879	−	0.0966956i
$441$	0.816625	−	1.41444i	0.0388869	−	0.0673541i
$442$	−18.4173	+	10.6332i	−0.876023	+	0.505772i
$443$			25.2665i			1.20045i	0.799832	+	0.600224i	$0.204922\pi$
$443$			25.2665i			1.20045i	−0.799832	+	0.600224i	$0.795078\pi$
$444$	−10.0000	−	6.92820i	−0.474579	−	0.328798i
$445$	19.2916	−	17.4499i	0.914508	−	0.827203i
$446$	−6.68338	−	11.5759i	−0.316467	−	0.548137i
$447$	27.6260	+	15.9499i	1.30666	+	0.754403i
$448$	2.00626	+	1.15831i	0.0947867	+	0.0547251i
$449$	−6.63325	+	11.4891i	−0.313042	+	0.542205i	−0.979019	−	0.203767i	$-0.934682\pi$
$449$	−6.63325	+	11.4891i	−0.313042	+	0.542205i	0.665977	+	0.745972i	$0.268015\pi$
$450$	4.97494	+	0.500000i	0.234521	+	0.0235702i
$451$	−16.4749	+	28.5354i	−0.775774	+	1.34368i
$452$		−	5.36675i		−	0.252431i
$453$	−18.4173	+	10.6332i	−0.865322	+	0.499594i
$454$	−6.94987			−0.326174
$455$	−15.3668	+	13.8997i	−0.720404	+	0.651630i
$456$	4.31662	+	7.47661i	0.202144	+	0.350125i
$457$	−8.70366	−	5.02506i	−0.407140	−	0.235063i	0.282420	−	0.959291i	$-0.408863\pi$
$457$	−8.70366	−	5.02506i	−0.407140	−	0.235063i	−0.689560	+	0.724228i	$0.742196\pi$
$458$		−	3.94987i		−	0.184566i
$459$	−10.6332	−	18.4173i	−0.496318	−	0.859647i
$460$	4.11684	−	12.7692i	0.191949	−	0.595365i
$461$	9.31662	+	16.1369i	0.433918	+	0.751569i	0.997207	−	0.0746916i	$-0.0237973\pi$
$461$	9.31662	+	16.1369i	0.433918	+	0.751569i	−0.563288	+	0.826260i	$0.690464\pi$
$462$	17.3205	+	10.0000i	0.805823	+	0.465242i
$463$	−31.3643	−	18.1082i	−1.45762	−	0.841559i	−0.458729	−	0.888576i	$-0.651695\pi$
$463$	−31.3643	−	18.1082i	−1.45762	−	0.841559i	−0.998894	+	0.0470176i	$0.985028\pi$
$464$	1.65831	+	2.87228i	0.0769852	+	0.133342i
$465$	3.17906	−	9.86046i	0.147425	−	0.457268i
$466$	−13.9749	−	24.2053i	−0.647376	−	1.12129i
$467$			25.8997i			1.19850i	0.800563	+	0.599249i	$0.204534\pi$
$467$			25.8997i			1.19850i	−0.800563	+	0.599249i	$0.795466\pi$
$468$	3.46410	+	2.00000i	0.160128	+	0.0924500i
$469$	1.94987	+	3.37728i	0.0900368	+	0.155948i
$470$	−7.15831	+	6.47494i	−0.330188	+	0.298667i
$471$	6.00000			0.276465
$472$	−10.9407	+	6.31662i	−0.503587	+	0.290746i
$473$		−	38.6332i		−	1.77636i
$474$	10.9499	−	18.9657i	0.502944	−	0.871125i
$475$	−2.15831	+	21.4749i	−0.0990302	+	0.985338i
$476$	−6.15831	+	10.6665i	−0.282266	+	0.488899i
$477$	−7.47661	−	4.31662i	−0.342331	−	0.197645i
$478$	7.20241	+	4.15831i	0.329430	+	0.190197i
$479$	−11.6834	−	20.2362i	−0.533827	−	0.924616i	−0.999219	−	0.0395109i	$-0.987420\pi$
$479$	−11.6834	−	20.2362i	−0.533827	−	0.924616i	0.465392	−	0.885105i	$-0.345913\pi$
$480$	3.31662	−	3.00000i	0.151383	−	0.136931i
$481$	2.00000	−	24.2487i	0.0911922	−	1.10565i
$482$		−	29.2665i		−	1.33305i
$483$	24.0751	−	13.8997i	1.09545	−	0.632460i
$484$	3.81662	−	6.61059i	0.173483	−	0.300481i
$485$	21.7518	−	4.67527i	0.987699	−	0.212293i
$486$	−5.00000	+	8.66025i	−0.226805	+	0.392837i
$487$			18.0000i			0.815658i	0.913058	+	0.407829i	$0.133714\pi$
$487$			18.0000i			0.815658i	−0.913058	+	0.407829i	$0.866286\pi$
$488$	−10.3489	−	5.97494i	−0.468472	−	0.270473i
$489$	44.4327			2.00932
$490$	1.12064	−	3.47587i	0.0506253	−	0.157024i
$491$	24.3166			1.09739			0.548697	−	0.836021i	$-0.315124\pi$
$491$	24.3166			1.09739			0.548697	+	0.836021i	$0.315124\pi$
$492$			15.2665i			0.688267i
$493$	−15.2708	+	8.81662i	−0.687764	+	0.397081i
$494$	−8.63325	+	14.9532i	−0.388428	+	0.672777i
$495$	7.15831	−	6.47494i	0.321742	−	0.291027i
$496$	−1.15831	−	2.00626i	−0.0520098	−	0.0900836i
$497$	−15.4148	+	8.89975i	−0.691449	+	0.399208i
$498$	11.4891	−	6.63325i	0.514840	−	0.297243i
$499$	−8.47494	+	14.6790i	−0.379390	+	0.657123i	−0.990974	−	0.134057i	$-0.957200\pi$
$499$	−8.47494	+	14.6790i	−0.379390	+	0.657123i	0.611583	+	0.791180i	$0.290533\pi$
$500$	11.1109	−	1.24456i	0.496892	−	0.0556585i
$501$	−9.26650	−	16.0500i	−0.413997	−	0.717063i
$502$	−2.00626	+	1.15831i	−0.0895436	+	0.0516980i
$503$	−22.1556	+	12.7916i	−0.987871	+	0.570348i	−0.904637	−	0.426182i	$-0.859858\pi$
$503$	−22.1556	+	12.7916i	−0.987871	+	0.570348i	−0.0832337	+	0.996530i	$0.526525\pi$
$504$	2.31662			0.103191
$505$	7.19700	+	33.4843i	0.320263	+	1.49003i
$506$	−12.9499	−	22.4298i	−0.575692	−	0.997128i
$507$			6.00000i			0.266469i
$508$		−	1.36675i		−	0.0606397i
$509$	−0.658312	−	1.14023i	−0.0291792	−	0.0505398i	0.851067	−	0.525057i	$-0.175956\pi$
$509$	−0.658312	−	1.14023i	−0.0291792	−	0.0505398i	−0.880246	+	0.474517i	$0.842623\pi$
$510$	15.9499	+	17.6332i	0.706272	+	0.780813i
$511$	−3.05013	+	5.28297i	−0.134930	+	0.233705i
$512$		−	1.00000i		−	0.0441942i
$513$	−14.9532	−	8.63325i	−0.660201	−	0.381167i
$514$	11.6583	−	20.1928i	0.514226	−	0.890666i
$515$	−21.1692	+	4.55004i	−0.932827	+	0.200499i
$516$	−8.94987	−	15.5016i	−0.393996	−	0.682422i
$517$			18.6332i			0.819489i
$518$	−6.01877	−	12.7414i	−0.264449	−	0.559827i
$519$	24.5330			1.07688
$520$	8.51278	+	2.74456i	0.373310	+	0.120357i
$521$	14.6332	−	25.3455i	0.641094	−	1.11041i	−0.344095	−	0.938935i	$-0.611814\pi$
$521$	14.6332	−	25.3455i	0.641094	−	1.11041i	0.985189	−	0.171473i	$-0.0548526\pi$
$522$	2.87228	+	1.65831i	0.125716	+	0.0725824i
$523$	−0.0868201	−	0.0501256i	−0.00379638	−	0.00219184i	0.498101	−	0.867119i	$-0.334031\pi$
$523$	−0.0868201	−	0.0501256i	−0.00379638	−	0.00219184i	−0.501897	+	0.864927i	$0.667364\pi$
$524$	1.36675			0.0597068
$525$	18.8037	+	13.5313i	0.820660	+	0.590555i
$526$	13.2665			0.578447
$527$	10.6665	−	6.15831i	0.464640	−	0.268260i
$528$		−	8.63325i		−	0.375714i
$529$	−13.0000			−0.565217
$530$	−18.3732	−	5.92362i	−0.798082	−	0.257306i
$531$	−6.31662	+	10.9407i	−0.274118	+	0.474787i
$532$			10.0000i			0.433555i
$533$	−26.4424	+	15.2665i	−1.14535	+	0.661265i
$534$	−11.6332	−	20.1494i	−0.503420	−	0.871949i
$535$	−0.217249	+	0.673839i	−0.00939250	+	0.0291326i
$536$	0.841688	−	1.45785i	0.0363554	−	0.0629693i
$537$	9.12184	+	5.26650i	0.393637	+	0.227266i
$538$	1.09682	−	0.633250i	0.0472873	−	0.0273013i
$539$	−3.52506	−	6.10559i	−0.151835	−	0.262986i
$540$	−2.74456	+	8.51278i	−0.118107	+	0.366332i
$541$	−2.05013			−0.0881418			−0.0440709	−	0.999028i	$-0.514033\pi$
$541$	−2.05013			−0.0881418			−0.0440709	+	0.999028i	$0.514033\pi$
$542$	23.8877	+	13.7916i	1.02606	+	0.592398i
$543$	−23.0651	+	13.3166i	−0.989817	+	0.571471i
$544$	5.31662			0.227948
$545$	6.55013	−	5.92481i	0.280577	−	0.253791i
$546$	9.26650	+	16.0500i	0.396570	+	0.686879i
$547$			21.6834i			0.927114i	0.886067	+	0.463557i	$0.153427\pi$
$547$			21.6834i			0.927114i	−0.886067	+	0.463557i	$0.846573\pi$
$548$	9.80048	+	5.65831i	0.418656	+	0.241711i
$549$	−11.9499			−0.510008
$550$	12.6066	−	17.5187i	0.537548	−	0.746999i
$551$	−7.15831	+	12.3986i	−0.304954	+	0.528196i
$552$	−10.3923	−	6.00000i	−0.442326	−	0.255377i
$553$	21.9683	−	12.6834i	0.934185	−	0.539352i
$554$	−5.63325			−0.239334
$555$	−26.9754	+	3.51087i	−1.14504	+	0.149028i
$556$	−19.8997			−0.843937
$557$	−12.3552	+	7.13325i	−0.523505	+	0.302245i	−0.738367	−	0.674399i	$-0.764403\pi$
$557$	−12.3552	+	7.13325i	−0.523505	+	0.302245i	0.214863	+	0.976644i	$0.431070\pi$
$558$	−2.00626	−	1.15831i	−0.0849316	−	0.0490353i
$559$	17.8997	−	31.0033i	0.757079	−	1.31130i
$560$	5.06447	−	1.08854i	0.214013	−	0.0459992i
$561$	45.8997			1.93789
$562$	14.1740	+	8.18338i	0.597895	+	0.345195i
$563$			8.53300i			0.359623i	0.983701	+	0.179812i	$0.0575488\pi$
$563$			8.53300i			0.359623i	−0.983701	+	0.179812i	$0.942451\pi$
$564$	4.31662	+	7.47661i	0.181763	+	0.314822i
$565$	−8.05013	−	8.89975i	−0.338671	−	0.374415i
$566$	8.31662			0.349574
$567$	−22.0688	+	12.7414i	−0.926803	+	0.535090i
$568$	6.65400	+	3.84169i	0.279196	+	0.161194i
$569$	−34.1662			−1.43232			−0.716162	−	0.697934i	$-0.754103\pi$
$569$	−34.1662			−1.43232			−0.716162	+	0.697934i	$0.754103\pi$
$570$	18.3732	+	5.92362i	0.769570	+	0.248113i
$571$	−8.26650	−	14.3180i	−0.345942	−	0.599190i	0.639582	−	0.768723i	$-0.279107\pi$
$571$	−8.26650	−	14.3180i	−0.345942	−	0.599190i	−0.985524	+	0.169533i	$0.945774\pi$
$572$	14.9532	−	8.63325i	0.625226	−	0.360974i
$573$	11.4891	+	6.63325i	0.479965	+	0.277108i
$574$	−8.84169	+	15.3143i	−0.369045	+	0.639205i
$575$	−12.3267	−	27.3505i	−0.514060	−	1.14060i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	15.5885	−	9.00000i	0.648956	−	0.374675i	−0.139100	−	0.990278i	$-0.544421\pi$
$577$	15.5885	−	9.00000i	0.648956	−	0.374675i	0.788056	+	0.615603i	$0.211088\pi$
$578$			11.2665i			0.468625i
$579$	−1.31662	+	2.28046i	−0.0547171	+	0.0947727i
$580$	7.05842	+	2.27567i	0.293085	+	0.0944921i
$581$	15.3668			0.637520
$582$		−	19.8997i		−	0.824871i
$583$	−32.2737	+	18.6332i	−1.33664	+	0.771710i
$584$	2.63325			0.108965
$585$	8.74456	−	1.87953i	0.361543	−	0.0777089i
$586$	−2.36675			−0.0977696
$587$	16.6853	+	9.63325i	0.688675	+	0.397607i	0.803116	−	0.595823i	$-0.203174\pi$
$587$	16.6853	+	9.63325i	0.688675	+	0.397607i	−0.114440	+	0.993430i	$0.536507\pi$
$588$	−2.82887	−	1.63325i	−0.116661	−	0.0673541i
$589$	5.00000	−	8.66025i	0.206021	−	0.356840i
$590$	−8.66819	+	26.8860i	−0.356864	+	1.10688i
$591$	−8.73350			−0.359248
$592$	−3.46410	+	5.00000i	−0.142374	+	0.205499i
$593$		−	29.8496i		−	1.22578i	−0.790169	−	0.612889i	$-0.790007\pi$
$593$		−	29.8496i		−	1.22578i	0.790169	−	0.612889i	$-0.209993\pi$
$594$	8.63325	+	14.9532i	0.354227	+	0.613538i
$595$	5.78736	+	26.9259i	0.237259	+	1.10385i
$596$	7.97494	−	13.8130i	0.326666	−	0.565802i
$597$	29.3580	+	16.9499i	1.20154	+	0.693712i
$598$		−	24.0000i		−	0.981433i
$599$	15.7916	−	27.3518i	0.645226	−	1.11756i	−0.339024	−	0.940778i	$-0.610097\pi$
$599$	15.7916	−	27.3518i	0.645226	−	1.11756i	0.984249	−	0.176786i	$-0.0565700\pi$
$600$	1.00000	−	9.94987i	0.0408248	−	0.406202i
$601$	−17.5000	−	30.3109i	−0.713840	−	1.23641i	−0.963405	−	0.268049i	$-0.913621\pi$
$601$	−17.5000	−	30.3109i	−0.713840	−	1.23641i	0.249565	−	0.968358i	$-0.419712\pi$
$602$		−	20.7335i		−	0.845034i
$603$		−	1.68338i		−	0.0685523i
$604$	5.31662	+	9.20866i	0.216330	+	0.374695i
$605$	−3.58673	−	16.6874i	−0.145821	−	0.678438i
$606$	30.6332			1.24439
$607$	36.0120	−	20.7916i	1.46168	−	0.843903i	0.462594	−	0.886570i	$-0.346919\pi$
$607$	36.0120	−	20.7916i	1.46168	−	0.843903i	0.999089	+	0.0426666i	$0.0135853\pi$
$608$	3.73831	−	2.15831i	0.151608	−	0.0875311i
$609$	7.68338	+	13.3080i	0.311346	+	0.539267i
$610$	−26.1241	+	5.61503i	−1.05773	+	0.227346i
$611$	−8.63325	+	14.9532i	−0.349264	+	0.604943i
$612$	4.60433	−	2.65831i	0.186119	−	0.107456i
$613$	11.8067	−	6.81662i	0.476870	−	0.275321i	−0.242241	−	0.970216i	$-0.577883\pi$
$613$	11.8067	−	6.81662i	0.476870	−	0.275321i	0.719111	+	0.694895i	$0.244549\pi$
$614$	7.84169	+	13.5822i	0.316465	+	0.548133i
$615$	22.8997	+	25.3166i	0.923407	+	1.02086i
$616$	5.00000	−	8.66025i	0.201456	−	0.348932i
$617$	−31.1769	+	18.0000i	−1.25514	+	0.724653i	−0.972125	−	0.234464i	$-0.924666\pi$
$617$	−31.1769	+	18.0000i	−1.25514	+	0.724653i	−0.283011	+	0.959117i	$0.591333\pi$
$618$			19.3668i			0.779045i
$619$	22.9499			0.922433			0.461217	−	0.887288i	$-0.347413\pi$
$619$	22.9499			0.922433			0.461217	+	0.887288i	$0.347413\pi$
$620$	−4.93023	−	1.58953i	−0.198003	−	0.0638371i
$621$	24.0000			0.963087
$622$	8.29923	+	4.79156i	0.332769	+	0.192124i
$623$		−	26.9499i		−	1.07972i
$624$	4.00000	−	6.92820i	0.160128	−	0.277350i
$625$	16.5584	−	18.7302i	0.662337	−	0.749206i
$626$	−2.02506	+	3.50751i	−0.0809378	+	0.140188i
$627$	32.2737	−	18.6332i	1.28889	−	0.744140i
$628$		−	3.00000i		−	0.119713i
$629$	−26.5831	−	18.4173i	−1.05994	−	0.734347i
$630$	3.84169	−	3.47494i	0.153056	−	0.138445i
$631$	−5.00000	−	8.66025i	−0.199047	−	0.344759i	0.749173	−	0.662375i	$-0.230451\pi$
$631$	−5.00000	−	8.66025i	−0.199047	−	0.344759i	−0.948220	+	0.317615i	$0.897118\pi$
$632$	−9.48287	−	5.47494i	−0.377208	−	0.217781i
$633$	−24.7971	−	14.3166i	−0.985597	−	0.569035i
$634$	4.18338	−	7.24582i	0.166143	−	0.287768i
$635$	−2.05013	−	2.26650i	−0.0813568	−	0.0899433i
$636$	−8.63325	+	14.9532i	−0.342331	+	0.592934i
$637$		−	6.53300i		−	0.258847i
$638$	12.3986	−	7.15831i	0.490864	−	0.283400i
$639$	7.68338			0.303950
$640$	−1.50000	−	1.65831i	−0.0592927	−	0.0655506i
$641$	5.13325	+	8.89105i	0.202751	+	0.351175i	0.949414	−	0.314027i	$-0.101678\pi$
$641$	5.13325	+	8.89105i	0.202751	+	0.351175i	−0.746663	+	0.665203i	$0.768345\pi$
$642$	0.548410	+	0.316625i	0.0216440	+	0.0124962i
$643$		−	36.8496i		−	1.45321i	−0.687057	−	0.726604i	$-0.741098\pi$
$643$		−	36.8496i		−	1.45321i	0.687057	−	0.726604i	$-0.258902\pi$
$644$	−6.94987	−	12.0375i	−0.273863	−	0.474345i
$645$	−38.0941	−	12.2817i	−1.49996	−	0.483593i
$646$	11.4749	+	19.8752i	0.451475	+	0.781978i
$647$	−26.8034	−	15.4749i	−1.05375	−	0.608383i	−0.130053	−	0.991507i	$-0.541515\pi$
$647$	−26.8034	−	15.4749i	−1.05375	−	0.608383i	−0.923697	+	0.383125i	$0.874848\pi$
$648$	9.52628	+	5.50000i	0.374228	+	0.216060i
$649$	27.2665	+	47.2270i	1.07030	+	1.85382i
$650$	18.2337	−	8.21782i	0.715184	−	0.322330i
$651$	−5.36675	−	9.29548i	−0.210340	−	0.364319i
$652$		−	22.2164i		−	0.870060i
$653$	−25.0279	−	14.4499i	−0.979418	−	0.565467i	−0.0773237	−	0.997006i	$-0.524637\pi$
$653$	−25.0279	−	14.4499i	−0.979418	−	0.565467i	−0.902094	+	0.431539i	$0.857971\pi$
$654$	−3.94987	−	6.84138i	−0.154452	−	0.267519i
$655$	2.26650	−	2.05013i	0.0885595	−	0.0801050i
$656$	7.63325			0.298028
$657$	2.28046	−	1.31662i	0.0889693	−	0.0513664i
$658$			10.0000i			0.389841i
$659$	−7.68338	+	13.3080i	−0.299302	+	0.518406i	−0.975976	−	0.217876i	$-0.930087\pi$
$659$	−7.68338	+	13.3080i	−0.299302	+	0.518406i	0.676675	+	0.736282i	$0.263420\pi$
$660$	−12.9499	−	14.3166i	−0.504073	−	0.557274i
$661$	−10.0251	+	17.3639i	−0.389930	+	0.675378i	−0.992440	−	0.122733i	$-0.960834\pi$
$661$	−10.0251	+	17.3639i	−0.389930	+	0.675378i	0.602510	+	0.798111i	$0.294167\pi$
$662$	−29.3580	−	16.9499i	−1.14103	−	0.658776i
$663$	36.8347	+	21.2665i	1.43054	+	0.825922i
$664$	−3.31662	−	5.74456i	−0.128710	−	0.222932i
$665$	15.0000	+	16.5831i	0.581675	+	0.643066i
$666$	−0.500000	+	6.06218i	−0.0193746	+	0.234905i
$667$		−	19.8997i		−	0.770521i
$668$	−8.02502	+	4.63325i	−0.310497	+	0.179266i
$669$	−13.3668	+	23.1519i	−0.516788	+	0.895104i
$670$	−0.790988	−	3.68009i	−0.0305585	−	0.142174i
$671$	−25.7916	+	44.6723i	−0.995672	+	1.72455i
$672$		−	4.63325i		−	0.178731i
$673$	−7.01502	−	4.05013i	−0.270409	−	0.156121i	0.358664	−	0.933467i	$-0.383232\pi$
$673$	−7.01502	−	4.05013i	−0.270409	−	0.156121i	−0.629074	+	0.777346i	$0.716566\pi$
$674$	11.9499			0.460292
$675$	8.21782	+	18.2337i	0.316304	+	0.701815i
$676$	3.00000			0.115385
$677$		−	8.36675i		−	0.321560i	−0.986990	−	0.160780i	$-0.948599\pi$
$677$		−	8.36675i		−	0.321560i	0.986990	−	0.160780i	$-0.0514010\pi$
$678$	−9.29548	+	5.36675i	−0.356991	+	0.206109i
$679$	11.5251	−	19.9620i	0.442291	−	0.766071i
$680$	8.81662	−	7.97494i	0.338102	−	0.305825i
$681$	6.94987	+	12.0375i	0.266320	+	0.461279i
$682$	−8.66025	+	5.00000i	−0.331618	+	0.191460i
$683$	34.1932	−	19.7414i	1.30837	−	0.755385i	0.326542	−	0.945183i	$-0.394117\pi$
$683$	34.1932	−	19.7414i	1.30837	−	0.755385i	0.981823	+	0.189798i	$0.0607832\pi$
$684$	2.15831	−	3.73831i	0.0825251	−	0.142938i
$685$	24.7397	−	5.31748i	0.945257	−	0.203170i
$686$	−10.0000	−	17.3205i	−0.381802	−	0.661300i
$687$	−6.84138	+	3.94987i	−0.261015	+	0.150697i
$688$	−7.75082	+	4.47494i	−0.295497	+	0.170605i
$689$	−34.5330			−1.31560
$690$	−26.2337	+	5.63858i	−0.998699	+	0.214657i
$691$	13.8417	+	23.9745i	0.526563	+	0.912033i	0.999521	+	0.0309484i	$0.00985276\pi$
$691$	13.8417	+	23.9745i	0.526563	+	0.912033i	−0.472958	+	0.881085i	$0.656814\pi$
$692$		−	12.2665i		−	0.466302i
$693$		−	10.0000i		−	0.379869i
$694$	7.63325	+	13.2212i	0.289754	+	0.501869i
$695$	−33.0000	+	29.8496i	−1.25176	+	1.13226i
$696$	3.31662	−	5.74456i	0.125716	−	0.217747i
$697$			40.5831i			1.53720i
$698$	24.8405	+	14.3417i	0.940228	+	0.542841i
$699$	−27.9499	+	48.4106i	−1.05716	+	1.83106i
$700$	6.76566	−	9.40184i	0.255718	−	0.355356i
$701$	−18.2665	−	31.6385i	−0.689916	−	1.19497i	−0.971865	−	0.235540i	$-0.924314\pi$
$701$	−18.2665	−	31.6385i	−0.689916	−	1.19497i	0.281948	−	0.959430i	$-0.409019\pi$
$702$			16.0000i			0.603881i
$703$	−26.1681	−	2.15831i	−0.986950	−	0.0814023i
$704$	−4.31662			−0.162689
$705$	18.3732	+	5.92362i	0.691976	+	0.223097i
$706$	−13.6082	+	23.5701i	−0.512151	+	0.887071i
$707$	30.7291	+	17.7414i	1.15569	+	0.667235i
$708$	21.8814	+	12.6332i	0.822355	+	0.474787i
$709$	34.5330			1.29691			0.648457	−	0.761251i	$-0.275415\pi$
$709$	34.5330			1.29691			0.648457	+	0.761251i	$0.275415\pi$
$710$	16.7969	−	3.61028i	0.630378	−	0.135491i
$711$	−10.9499			−0.410652
$712$	−10.0747	+	5.81662i	−0.377565	+	0.217987i
$713$			13.8997i			0.520550i
$714$	24.6332			0.921876
$715$	11.8472	−	36.7465i	0.443062	−	1.37424i
$716$	2.63325	−	4.56092i	0.0984092	−	0.170450i
$717$		−	16.6332i		−	0.621180i
$718$	−7.47661	+	4.31662i	−0.279025	+	0.161095i
$719$	−22.5831	−	39.1151i	−0.842208	−	1.45875i	−0.888024	−	0.459798i	$-0.847922\pi$
$719$	−22.5831	−	39.1151i	−0.842208	−	1.45875i	0.0458152	−	0.998950i	$-0.485411\pi$
$720$	−2.12819	−	0.686141i	−0.0793131	−	0.0255710i
$721$	−11.2164	+	19.4273i	−0.417720	+	0.723512i
$722$	−0.317615	−	0.183375i	−0.0118204	−	0.00682452i
$723$	−50.6911	+	29.2665i	−1.88522	+	1.08843i
$724$	6.65831	+	11.5325i	0.247454	+	0.428603i
$725$	15.1186	−	6.81386i	0.561490	−	0.253060i
$726$	−15.2665			−0.566593
$727$	2.91569	+	1.68338i	0.108137	+	0.0624329i	0.553093	−	0.833119i	$-0.313447\pi$
$727$	2.91569	+	1.68338i	0.108137	+	0.0624329i	−0.444956	+	0.895552i	$0.646781\pi$
$728$	8.02502	−	4.63325i	0.297427	−	0.171720i
$729$	−13.0000			−0.481481
$730$	4.36675	−	3.94987i	0.161621	−	0.146191i
$731$	−23.7916	−	41.2082i	−0.879963	−	1.52414i
$732$			23.8997i			0.883360i
$733$	31.1769	+	18.0000i	1.15155	+	0.664845i	0.949263	−	0.314482i	$-0.101831\pi$
$733$	31.1769	+	18.0000i	1.15155	+	0.664845i	0.202282	+	0.979327i	$0.435164\pi$
$734$	−4.00000			−0.147643
$735$	−7.14103	+	1.53487i	−0.263401	+	0.0566145i
$736$	−3.00000	+	5.19615i	−0.110581	+	0.191533i
$737$	−6.29297	−	3.63325i	−0.231805	−	0.133832i
$738$	6.61059	−	3.81662i	0.243339	−	0.140492i
$739$	−27.8997			−1.02631			−0.513154	−	0.858296i	$-0.671523\pi$
$739$	−27.8997			−1.02631			−0.513154	+	0.858296i	$0.671523\pi$
$740$	1.75544	+	13.4877i	0.0645312	+	0.495818i
$741$	34.5330			1.26860
$742$	−17.3205	+	10.0000i	−0.635856	+	0.367112i
$743$	37.6573	+	21.7414i	1.38151	+	0.797616i	0.992338	−	0.123549i	$-0.0394276\pi$
$743$	37.6573	+	21.7414i	1.38151	+	0.797616i	0.389173	+	0.921165i	$0.372761\pi$
$744$	−2.31662	+	4.01251i	−0.0849316	+	0.147106i
$745$	−7.49456	−	34.8687i	−0.274579	−	1.27749i
$746$	−16.8997			−0.618744
$747$	−5.74456	−	3.31662i	−0.210183	−	0.121349i
$748$		−	22.9499i		−	0.839131i
$749$	0.366750	+	0.635230i	0.0134008	+	0.0232108i
$750$	−13.2665	−	18.0000i	−0.484424	−	0.657267i
$751$	22.2164			0.810687			0.405343	−	0.914164i	$-0.367152\pi$
$751$	22.2164			0.810687			0.405343	+	0.914164i	$0.367152\pi$
$752$	3.73831	−	2.15831i	0.136322	−	0.0787056i
$753$	4.01251	+	2.31662i	0.146224	+	0.0844225i
$754$	13.2665			0.483137
$755$	22.6296	+	7.29590i	0.823576	+	0.265525i
$756$	4.63325	+	8.02502i	0.168510	+	0.291867i
$757$	−44.0805	+	25.4499i	−1.60213	+	0.924991i	−0.611072	+	0.791575i	$0.709261\pi$
$757$	−44.0805	+	25.4499i	−1.60213	+	0.924991i	−0.991060	+	0.133416i	$0.957405\pi$
$758$	−11.3017	−	6.52506i	−0.410498	−	0.237001i
$759$	−25.8997	+	44.8597i	−0.940101	+	1.62830i
$760$	2.96181	−	9.18662i	0.107436	−	0.333234i
$761$	−3.13325	−	5.42695i	−0.113580	−	0.196727i	0.803631	−	0.595128i	$-0.202899\pi$
$761$	−3.13325	−	5.42695i	−0.113580	−	0.196727i	−0.917211	+	0.398401i	$0.869565\pi$
$762$	−2.36728	+	1.36675i	−0.0857575	+	0.0495121i
$763$		−	9.15038i		−	0.331266i
$764$	3.31662	−	5.74456i	0.119991	−	0.207831i
$765$	3.64795	−	11.3148i	0.131892	−	0.409088i
$766$	−30.3166			−1.09538
$767$			50.5330i			1.82464i
$768$	−1.73205	+	1.00000i	−0.0625000	+	0.0360844i
$769$	29.2665			1.05538			0.527688	−	0.849438i	$-0.323059\pi$
$769$	29.2665			1.05538			0.527688	+	0.849438i	$0.323059\pi$
$770$	−4.69882	−	21.8614i	−0.169334	−	0.787830i
$771$	−46.6332			−1.67946
$772$	1.14023	+	0.658312i	0.0410378	+	0.0236932i
$773$	−26.1247	−	15.0831i	−0.939641	−	0.542502i	−0.0497936	−	0.998760i	$-0.515856\pi$
$773$	−26.1247	−	15.0831i	−0.939641	−	0.542502i	−0.889848	+	0.456257i	$0.849190\pi$
$774$	−4.47494	+	7.75082i	−0.160848	+	0.278597i
$775$	−10.5602	+	4.75940i	−0.379332	+	0.170963i
$776$	−9.94987			−0.357180
$777$	−16.0500	+	23.1662i	−0.575792	+	0.831085i
$778$			27.9499i			1.00205i
$779$	16.4749	+	28.5354i	0.590276	+	1.02239i
$780$	−3.75906	−	17.4891i	−0.134596	−	0.626211i
$781$	16.5831	−	28.7228i	0.593391	−	1.02778i
$782$	−27.6260	−	15.9499i	−0.987903	−	0.570366i
$783$			13.2665i			0.474106i
$784$	−0.816625	+	1.41444i	−0.0291652	+	0.0505156i
$785$	−4.50000	−	4.97494i	−0.160612	−	0.177563i
$786$	−1.36675	−	2.36728i	−0.0487504	−	0.0844381i
$787$			24.0000i			0.855508i	0.903895	+	0.427754i	$0.140695\pi$
$787$			24.0000i			0.855508i	−0.903895	+	0.427754i	$0.859305\pi$
$788$			4.36675i			0.155559i
$789$	−13.2665	−	22.9783i	−0.472300	−	0.818047i
$790$	−23.9380	+	5.14515i	−0.851675	+	0.183056i
$791$	−12.4327			−0.442058
$792$	−3.73831	+	2.15831i	−0.132835	+	0.0766923i
$793$	−41.3956	+	23.8997i	−1.47000	+	0.848705i
$794$	14.4499	+	25.0279i	0.512807	+	0.888208i
$795$	8.11322	+	37.7470i	0.287746	+	1.33875i
$796$	8.47494	−	14.6790i	0.300386	−	0.520284i
$797$	33.9190	−	19.5831i	1.20147	−	0.693670i	0.240589	−	0.970627i	$-0.422659\pi$
$797$	33.9190	−	19.5831i	1.20147	−	0.693670i	0.960882	+	0.276957i	$0.0893260\pi$
$798$	17.3205	−	10.0000i	0.613139	−	0.353996i
$799$	11.4749	+	19.8752i	0.405954	+	0.703133i
$800$	−4.97494	−	0.500000i	−0.175891	−	0.0176777i
$801$	−5.81662	+	10.0747i	−0.205520	+	0.355972i
$802$	32.2737	−	18.6332i	1.13963	−	0.657963i
$803$		−	11.3668i		−	0.401124i
$804$	−3.36675			−0.118736
$805$	−29.5814	−	9.53718i	−1.04261	−	0.336142i
$806$	−9.26650			−0.326399
$807$	−2.19364	−	1.26650i	−0.0772198	−	0.0445829i
$808$		−	15.3166i		−	0.538837i
$809$	−18.9499	+	32.8221i	−0.666242	+	1.15397i	0.312705	+	0.949850i	$0.398765\pi$
$809$	−18.9499	+	32.8221i	−0.666242	+	1.15397i	−0.978947	+	0.204115i	$0.934568\pi$
$810$	24.0475	−	5.16870i	0.844945	−	0.181610i
$811$	6.94987	−	12.0375i	0.244043	−	0.422695i	−0.717819	−	0.696230i	$-0.754859\pi$
$811$	6.94987	−	12.0375i	0.244043	−	0.422695i	0.961862	+	0.273535i	$0.0881928\pi$
$812$	6.65400	−	3.84169i	0.233510	−	0.134817i
$813$		−	55.1662i		−	1.93476i
$814$	21.5831	+	14.9532i	0.756488	+	0.524110i
$815$	−33.3246	−	36.8417i	−1.16731	−	1.29051i
$816$	−5.31662	−	9.20866i	−0.186119	−	0.322368i
$817$	−33.4574	−	19.3166i	−1.17053	−	0.675803i
$818$	29.5888	+	17.0831i	1.03455	+	0.597297i
$819$	4.63325	−	8.02502i	0.161899	−	0.280417i
$820$	12.6583	−	11.4499i	0.442047	−	0.399847i
$821$	−21.2665	+	36.8347i	−0.742206	+	1.28554i	0.209283	+	0.977855i	$0.432887\pi$
$821$	−21.2665	+	36.8347i	−0.742206	+	1.28554i	−0.951489	+	0.307683i	$0.900446\pi$
$822$		−	22.6332i		−	0.789425i
$823$	12.1244	−	7.00000i	0.422628	−	0.244005i	−0.273573	−	0.961851i	$-0.588205\pi$
$823$	12.1244	−	7.00000i	0.422628	−	0.244005i	0.696201	+	0.717847i	$0.254872\pi$
$824$	9.68338			0.337336
$825$	−42.9499	−	4.31662i	−1.49532	−	0.150286i
$826$	14.6332	+	25.3455i	0.509156	+	0.881884i
$827$	−22.9783	−	13.2665i	−0.799032	−	0.461321i	0.0441005	−	0.999027i	$-0.485958\pi$
$827$	−22.9783	−	13.2665i	−0.799032	−	0.461321i	−0.843133	+	0.537706i	$0.819291\pi$
$828$			6.00000i			0.208514i
$829$	−8.05013	−	13.9432i	−0.279592	−	0.484268i	0.691691	−	0.722194i	$-0.256866\pi$
$829$	−8.05013	−	13.9432i	−0.279592	−	0.484268i	−0.971283	+	0.237925i	$0.923533\pi$
$830$	−14.1168	−	4.55134i	−0.490003	−	0.157979i
$831$	5.63325	+	9.75707i	0.195415	+	0.338469i
$832$	−3.46410	−	2.00000i	−0.120096	−	0.0693375i
$833$	−7.52002	−	4.34169i	−0.260553	−	0.150431i
$834$	19.8997	+	34.4674i	0.689072	+	1.19351i
$835$	−6.35812	+	19.7209i	−0.220032	+	0.682470i
$836$	−9.31662	−	16.1369i	−0.322222	−	0.558105i
$837$		−	9.26650i		−	0.320297i
$838$	14.7658	+	8.52506i	0.510078	+	0.294493i
$839$	9.94987	+	17.2337i	0.343508	+	0.594973i	0.985082	−	0.172088i	$-0.0550515\pi$
$839$	9.94987	+	17.2337i	0.343508	+	0.594973i	−0.641574	+	0.767061i	$0.721718\pi$
$840$	−6.94987	−	7.68338i	−0.239793	−	0.265102i
$841$	−18.0000			−0.620690
$842$	−19.0091	+	10.9749i	−0.655099	+	0.378221i
$843$		−	32.7335i		−	1.12740i
$844$	−7.15831	+	12.3986i	−0.246399	+	0.426776i
$845$	4.97494	−	4.50000i	0.171143	−	0.154805i
$846$	2.15831	−	3.73831i	0.0742043	−	0.128526i
$847$	−15.3143	−	8.84169i	−0.526204	−	0.303804i
$848$	7.47661	+	4.31662i	0.256748	+	0.148234i
$849$	−8.31662	−	14.4048i	−0.285426	−	0.494372i
$850$	2.65831	−	26.4499i	0.0911794	−	0.907223i
$851$	33.0000	−	15.5885i	1.13123	−	0.534365i
$852$		−	15.3668i		−	0.526456i
$853$	8.80423	−	5.08312i	0.301451	−	0.174043i	−0.341644	−	0.939830i	$-0.610984\pi$
$853$	8.80423	−	5.08312i	0.301451	−	0.174043i	0.643095	+	0.765787i	$0.277650\pi$
$854$	−13.8417	+	23.9745i	−0.473653	+	0.820391i
$855$	−2.02830	−	9.43675i	−0.0693665	−	0.322730i
$856$	0.158312	−	0.274205i	0.00541101	−	0.00937214i
$857$		−	6.58312i		−	0.224875i	−0.993659	−	0.112438i	$-0.964134\pi$
$857$		−	6.58312i		−	0.224875i	0.993659	−	0.112438i	$-0.0358658\pi$
$858$	−29.9065	−	17.2665i	−1.02099	−	0.589469i
$859$	5.05013			0.172308			0.0861540	−	0.996282i	$-0.472542\pi$
$859$	5.05013			0.172308			0.0861540	+	0.996282i	$0.472542\pi$
$860$	−6.14087	+	19.0471i	−0.209402	+	0.649500i
$861$	35.3668			1.20530
$862$			29.6834i			1.01102i
$863$	17.8689	−	10.3166i	0.608265	−	0.351182i	−0.164021	−	0.986457i	$-0.552447\pi$
$863$	17.8689	−	10.3166i	0.608265	−	0.351182i	0.772286	+	0.635275i	$0.219113\pi$
$864$	2.00000	−	3.46410i	0.0680414	−	0.117851i
$865$	−18.3997	−	20.3417i	−0.625610	−	0.691638i
$866$	−7.97494	−	13.8130i	−0.270999	−	0.469385i
$867$	19.5141	−	11.2665i	0.662735	−	0.382630i
$868$	−4.64774	+	2.68338i	−0.157755	+	0.0910797i
$869$	−23.6332	+	40.9340i	−0.801703	+	1.38859i
$870$	−3.11684	−	14.5012i	−0.105671	−	0.491637i
$871$	−3.36675	−	5.83138i	−0.114078	−	0.197589i
$872$	−3.42069	+	1.97494i	−0.115839	+	0.0668798i
$873$	−8.61684	+	4.97494i	−0.291636	+	0.168376i
$874$	−25.8997			−0.876072
$875$	−2.88318	−	25.7397i	−0.0974694	−	0.870160i
$876$	−2.63325	−	4.56092i	−0.0889693	−	0.154099i
$877$		−	15.0000i		−	0.506514i	−0.967399	−	0.253257i	$-0.918498\pi$
$877$		−	15.0000i		−	0.506514i	0.967399	−	0.253257i	$-0.0815018\pi$
$878$			12.0000i			0.404980i
$879$	2.36675	+	4.09933i	0.0798285	+	0.138267i
$880$	−7.15831	+	6.47494i	−0.241307	+	0.218270i
$881$	12.1834	−	21.1022i	0.410468	−	0.710952i	−0.584473	−	0.811413i	$-0.698699\pi$
$881$	12.1834	−	21.1022i	0.410468	−	0.710952i	0.994941	+	0.100461i	$0.0320319\pi$
$882$			1.63325i			0.0549944i
$883$	−6.84138	−	3.94987i	−0.230231	−	0.132924i	0.380448	−	0.924802i	$-0.375770\pi$
$883$	−6.84138	−	3.94987i	−0.230231	−	0.132924i	−0.610679	+	0.791879i	$0.709103\pi$
$884$	10.6332	−	18.4173i	0.357635	−	0.619442i
$885$	55.2361	−	11.8723i	1.85674	−	0.399082i
$886$	−12.6332	−	21.8814i	−0.424422	−	0.735121i
$887$		−	4.73350i		−	0.158935i	−0.996837	−	0.0794677i	$-0.974678\pi$
$887$		−	4.73350i		−	0.158935i	0.996837	−	0.0794677i	$-0.0253221\pi$
$888$	12.1244	+	1.00000i	0.406867	+	0.0335578i
$889$	−3.16625			−0.106193
$890$	−7.98205	+	24.7578i	−0.267559	+	0.829884i
$891$	23.7414	−	41.1214i	0.795368	−	1.37762i
$892$	11.5759	+	6.68338i	0.387591	+	0.223776i
$893$	16.1369	+	9.31662i	0.540000	+	0.311769i
$894$	−31.8997			−1.06689
$895$	−2.47463	−	11.5133i	−0.0827178	−	0.384847i
$896$	−2.31662			−0.0773930
$897$	−41.5692	+	24.0000i	−1.38796	+	0.801337i
$898$		−	13.2665i		−	0.442709i
$899$	−7.68338			−0.256255
$900$	−4.55842	+	2.05446i	−0.151947	+	0.0684819i
$901$	−22.9499	+	39.7503i	−0.764571	+	1.32428i
$902$		−	32.9499i		−	1.09711i
$903$	−35.9115	+	20.7335i	−1.19506	+	0.689968i
$904$	2.68338	+	4.64774i	0.0892477	+	0.154582i
$905$	28.3404	+	9.13708i	0.942066	+	0.303727i
$906$	10.6332	−	18.4173i	0.353266	−	0.611875i
$907$	10.5797	+	6.10819i	0.351293	+	0.202819i	0.665255	−	0.746617i	$-0.268323\pi$
$907$	10.5797	+	6.10819i	0.351293	+	0.202819i	−0.313962	+	0.949436i	$0.601656\pi$
$908$	6.01877	−	3.47494i	0.199740	−	0.115320i
$909$	−7.65831	−	13.2646i	−0.254010	−	0.439959i
$910$	6.35812	−	19.7209i	0.210770	−	0.653742i
$911$	−18.0000			−0.596367			−0.298183	−	0.954509i	$-0.596381\pi$
$911$	−18.0000			−0.596367			−0.298183	+	0.954509i	$0.596381\pi$
$912$	−7.47661	−	4.31662i	−0.247575	−	0.142938i
$913$	−24.7971	+	14.3166i	−0.820665	+	0.473811i
$914$	10.0501			0.332429
$915$	35.8496	+	39.6332i	1.18515	+	1.31023i
$916$	1.97494	+	3.42069i	0.0652538	+	0.113023i
$917$		−	3.16625i		−	0.104559i
$918$	18.4173	+	10.6332i	0.607862	+	0.350950i
$919$	16.1003			0.531098			0.265549	−	0.964097i	$-0.414447\pi$
$919$	16.1003			0.531098			0.265549	+	0.964097i	$0.414447\pi$
$920$	2.81929	+	13.1168i	0.0929493	+	0.432450i
$921$	15.6834	−	27.1644i	0.516785	−	0.895098i
$922$	−16.1369	−	9.31662i	−0.531439	−	0.306827i
$923$	26.6160	−	15.3668i	0.876076	−	0.505803i
$924$	−20.0000			−0.657952
$925$	23.1426	+	19.7337i	0.760925	+	0.648840i
$926$	36.2164			1.19014
$927$	8.38605	−	4.84169i	0.275434	−	0.159022i
$928$	−2.87228	−	1.65831i	−0.0942873	−	0.0544368i
$929$	−11.4499	+	19.8318i	−0.375658	+	0.650659i	−0.990425	−	0.138050i	$-0.955917\pi$
$929$	−11.4499	+	19.8318i	−0.375658	+	0.650659i	0.614767	+	0.788709i	$0.289250\pi$
$930$	2.17708	+	10.1289i	0.0713893	+	0.332141i
$931$	−7.05013			−0.231059
$932$	24.2053	+	13.9749i	0.792871	+	0.457764i
$933$		−	19.1662i		−	0.627475i
$934$	−12.9499	−	22.4298i	−0.423733	−	0.733927i
$935$	−34.4248	−	38.0581i	−1.12581	−	1.24463i
$936$	−4.00000			−0.130744
$937$	5.15274	−	2.97494i	0.168333	−	0.0971870i	−0.413467	−	0.910519i	$-0.635682\pi$
$937$	5.15274	−	2.97494i	0.168333	−	0.0971870i	0.581799	+	0.813332i	$0.302349\pi$
$938$	−3.37728	−	1.94987i	−0.110272	−	0.0636657i
$939$	8.10025			0.264342
$940$	2.96181	−	9.18662i	0.0966036	−	0.299634i
$941$	18.2916	+	31.6819i	0.596288	+	1.03280i	0.993364	+	0.115015i	$0.0366916\pi$
$941$	18.2916	+	31.6819i	0.596288	+	1.03280i	−0.397076	+	0.917786i	$0.629975\pi$
$942$	−5.19615	+	3.00000i	−0.169300	+	0.0977453i
$943$	−39.6635	−	22.8997i	−1.29162	−	0.745718i
$944$	6.31662	−	10.9407i	0.205589	−	0.356090i
$945$	19.7209	+	6.35812i	0.641521	+	0.206830i
$946$	19.3166	+	33.4574i	0.628038	+	1.08779i
$947$	−4.56092	+	2.63325i	−0.148210	+	0.0855691i	−0.572271	−	0.820064i	$-0.693938\pi$
$947$	−4.56092	+	2.63325i	−0.148210	+	0.0855691i	0.424061	+	0.905634i	$0.360604\pi$
$948$			21.8997i			0.711271i
$949$	5.26650	−	9.12184i	0.170958	−	0.296108i
$950$	−8.86832	−	19.6770i	−0.287726	−	0.638406i
$951$	−16.7335			−0.542621
$952$		−	12.3166i		−	0.399184i
$953$	34.0058	−	19.6332i	1.10156	−	0.635983i	0.164926	−	0.986306i	$-0.447261\pi$
$953$	34.0058	−	19.6332i	1.10156	−	0.635983i	0.936629	+	0.350323i	$0.113928\pi$
$954$	8.63325			0.279512
$955$	−3.11684	−	14.5012i	−0.100859	−	0.469248i
$956$	−8.31662			−0.268979
$957$	−24.7971	−	14.3166i	−0.801577	−	0.462791i
$958$	20.2362	+	11.6834i	0.653802	+	0.377473i
$959$	13.1082	−	22.7040i	0.423285	−	0.733152i
$960$	−1.37228	+	4.25639i	−0.0442902	+	0.137374i
$961$	−25.6332			−0.826879
$962$	10.3923	+	22.0000i	0.335061	+	0.709308i
$963$		−	0.316625i		−	0.0102031i
$964$	14.6332	+	25.3455i	0.471305	+	0.816325i
$965$	2.87833	−	0.618658i	0.0926566	−	0.0199153i
$966$	−13.8997	+	24.0751i	−0.447217	+	0.774603i
$967$	25.3455	+	14.6332i	0.815057	+	0.470574i	0.848709	−	0.528860i	$-0.177380\pi$
$967$	25.3455	+	14.6332i	0.815057	+	0.470574i	−0.0336517	+	0.999434i	$0.510714\pi$
$968$			7.63325i			0.245342i
$969$	22.9499	−	39.7503i	0.737256	−	1.27697i
$970$	−16.5000	+	14.9248i	−0.529783	+	0.479207i
$971$	9.94987	+	17.2337i	0.319307	+	0.553055i	0.980344	−	0.197298i	$-0.0632167\pi$
$971$	9.94987	+	17.2337i	0.319307	+	0.553055i	−0.661037	+	0.750353i	$0.729883\pi$
$972$		−	10.0000i		−	0.320750i
$973$			46.1003i			1.47791i
$974$	−9.00000	−	15.5885i	−0.288379	−	0.499486i
$975$	−32.4674	−	23.3639i	−1.03979	−	0.748242i
$976$	11.9499			0.382506
$977$	51.7011	−	29.8496i	1.65406	−	0.954974i	0.678687	−	0.734428i	$-0.262549\pi$
$977$	51.7011	−	29.8496i	1.65406	−	0.954974i	0.975376	−	0.220547i	$-0.0707841\pi$
$978$	−38.4799	+	22.2164i	−1.23045	+	0.710401i
$979$	25.1082	+	43.4887i	0.802461	+	1.38990i
$980$	0.767434	+	3.57051i	0.0245148	+	0.114056i
$981$	−1.97494	+	3.42069i	−0.0630549	+	0.109214i
$982$	−21.0588	+	12.1583i	−0.672014	+	0.387987i
$983$	−20.5104	+	11.8417i	−0.654180	+	0.377691i	−0.790056	−	0.613035i	$-0.789949\pi$
$983$	−20.5104	+	11.8417i	−0.654180	+	0.377691i	0.135876	+	0.990726i	$0.456615\pi$
$984$	−7.63325	−	13.2212i	−0.243339	−	0.421476i
$985$	6.55013	+	7.24144i	0.208704	+	0.230731i
$986$	8.81662	−	15.2708i	0.280779	−	0.486323i
$987$	17.3205	−	10.0000i	0.551318	−	0.318304i
$988$		−	17.2665i		−	0.549321i
$989$	53.6992			1.70754
$990$	−2.96181	+	9.18662i	−0.0941326	+	0.291970i
$991$	39.6834			1.26058			0.630292	−	0.776358i	$-0.282935\pi$
$991$	39.6834			1.26058			0.630292	+	0.776358i	$0.282935\pi$
$992$	2.00626	+	1.15831i	0.0636987	+	0.0367765i
$993$			67.7995i			2.15155i
$994$	8.89975	−	15.4148i	0.282283	−	0.488928i
$995$	−7.96444	−	37.0548i	−0.252490	−	1.17472i
$996$	−6.63325	+	11.4891i	−0.210183	+	0.364047i
$997$	−41.3956	+	23.8997i	−1.31101	+	0.756913i	−0.982264	−	0.187505i	$-0.939960\pi$
$997$	−41.3956	+	23.8997i	−1.31101	+	0.756913i	−0.328748	+	0.944418i	$0.606627\pi$
$998$		−	16.9499i		−	0.536539i
$999$	−22.0000	+	10.3923i	−0.696049	+	0.328798i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.n.e.359.2	yes	8
5.4	even	2	inner	370.2.n.e.359.4	yes	8
37.10	even	3	inner	370.2.n.e.269.4	yes	8
185.84	even	6	inner	370.2.n.e.269.2	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.n.e.269.2	✓	8	185.84	even	6	inner
370.2.n.e.269.4	yes	8	37.10	even	3	inner
370.2.n.e.359.2	yes	8	1.1	even	1	trivial
370.2.n.e.359.4	yes	8	5.4	even	2	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:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(1.73205 + 1.00000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.469882 - 2.18614i) q^{5} -2.00000 q^{6} +(-2.00626 - 1.15831i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(1.73205 + 1.00000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.469882 - 2.18614i) q^{5} -2.00000 q^{6} +(-2.00626 - 1.15831i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(1.50000 + 1.65831i) q^{10} +4.31662 q^{11} +(1.73205 - 1.00000i) q^{12} +(3.46410 + 2.00000i) q^{13} +2.31662 q^{14} +(1.37228 - 4.25639i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(4.60433 - 2.65831i) q^{17} +(-0.866025 - 0.500000i) q^{18} +(2.15831 - 3.73831i) q^{19} +(-2.12819 - 0.686141i) q^{20} +(-2.31662 - 4.01251i) q^{21} +(-3.73831 + 2.15831i) q^{22} +6.00000i q^{23} +(-1.00000 + 1.73205i) q^{24} +(-4.55842 + 2.05446i) q^{25} -4.00000 q^{26} -4.00000i q^{27} +(-2.00626 + 1.15831i) q^{28} -3.31662 q^{29} +(0.939764 + 4.37228i) q^{30} +2.31662 q^{31} +(0.866025 + 0.500000i) q^{32} +(7.47661 + 4.31662i) q^{33} +(-2.65831 + 4.60433i) q^{34} +(-1.58953 + 4.93023i) q^{35} +1.00000 q^{36} +(-2.59808 - 5.50000i) q^{37} +4.31662i q^{38} +(4.00000 + 6.92820i) q^{39} +(2.18614 - 0.469882i) q^{40} +(-3.81662 + 6.61059i) q^{41} +(4.01251 + 2.31662i) q^{42} -8.94987i q^{43} +(2.15831 - 3.73831i) q^{44} +(1.65831 - 1.50000i) q^{45} +(-3.00000 - 5.19615i) q^{46} +4.31662i q^{47} -2.00000i q^{48} +(-0.816625 - 1.41444i) q^{49} +(2.92048 - 4.05842i) q^{50} +10.6332 q^{51} +(3.46410 - 2.00000i) q^{52} +(-7.47661 + 4.31662i) q^{53} +(2.00000 + 3.46410i) q^{54} +(-2.02830 - 9.43675i) q^{55} +(1.15831 - 2.00626i) q^{56} +(7.47661 - 4.31662i) q^{57} +(2.87228 - 1.65831i) q^{58} +(6.31662 + 10.9407i) q^{59} +(-3.00000 - 3.31662i) q^{60} +(-5.97494 + 10.3489i) q^{61} +(-2.00626 + 1.15831i) q^{62} -2.31662i q^{63} -1.00000 q^{64} +(2.74456 - 8.51278i) q^{65} -8.63325 q^{66} +(-1.45785 - 0.841688i) q^{67} -5.31662i q^{68} +(-6.00000 + 10.3923i) q^{69} +(-1.08854 - 5.06447i) q^{70} +(3.84169 - 6.65400i) q^{71} +(-0.866025 + 0.500000i) q^{72} -2.63325i q^{73} +(5.00000 + 3.46410i) q^{74} +(-9.94987 - 1.00000i) q^{75} +(-2.15831 - 3.73831i) q^{76} +(-8.66025 - 5.00000i) q^{77} +(-6.92820 - 4.00000i) q^{78} +(-5.47494 + 9.48287i) q^{79} +(-1.65831 + 1.50000i) q^{80} +(5.50000 - 9.52628i) q^{81} -7.63325i q^{82} +(-5.74456 + 3.31662i) q^{83} -4.63325 q^{84} +(-7.97494 - 8.81662i) q^{85} +(4.47494 + 7.75082i) q^{86} +(-5.74456 - 3.31662i) q^{87} +4.31662i q^{88} +(5.81662 + 10.0747i) q^{89} +(-0.686141 + 2.12819i) q^{90} +(-4.63325 - 8.02502i) q^{91} +(5.19615 + 3.00000i) q^{92} +(4.01251 + 2.31662i) q^{93} +(-2.15831 - 3.73831i) q^{94} +(-9.18662 - 2.96181i) q^{95} +(1.00000 + 1.73205i) q^{96} +9.94987i q^{97} +(1.41444 + 0.816625i) q^{98} +(2.15831 + 3.73831i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4} - 16 q^{6} + 4 q^{9}+O(q^{10}) \) 8 * q + 4 * q^4 - 16 * q^6 + 4 * q^9	\( 8 q + 4 q^{4} - 16 q^{6} + 4 q^{9} + 12 q^{10} + 8 q^{11} - 8 q^{14} - 12 q^{15} - 4 q^{16} + 4 q^{19} + 8 q^{21} - 8 q^{24} - 2 q^{25} - 32 q^{26} - 8 q^{31} - 8 q^{34} - 6 q^{35} + 8 q^{36} + 32 q^{39} + 6 q^{40} - 4 q^{41} + 4 q^{44} - 24 q^{46} + 20 q^{49} + 32 q^{51} + 16 q^{54} + 22 q^{55} - 4 q^{56} + 24 q^{59} - 24 q^{60} - 8 q^{61} - 8 q^{64} - 24 q^{65} - 16 q^{66} - 48 q^{69} + 22 q^{70} + 44 q^{71} + 40 q^{74} - 4 q^{76} - 4 q^{79} + 44 q^{81} + 16 q^{84} - 24 q^{85} - 4 q^{86} + 20 q^{89} + 6 q^{90} + 16 q^{91} - 4 q^{94} - 22 q^{95} + 8 q^{96} + 4 q^{99}+O(q^{100}) \) 8 * q + 4 * q^4 - 16 * q^6 + 4 * q^9 + 12 * q^10 + 8 * q^11 - 8 * q^14 - 12 * q^15 - 4 * q^16 + 4 * q^19 + 8 * q^21 - 8 * q^24 - 2 * q^25 - 32 * q^26 - 8 * q^31 - 8 * q^34 - 6 * q^35 + 8 * q^36 + 32 * q^39 + 6 * q^40 - 4 * q^41 + 4 * q^44 - 24 * q^46 + 20 * q^49 + 32 * q^51 + 16 * q^54 + 22 * q^55 - 4 * q^56 + 24 * q^59 - 24 * q^60 - 8 * q^61 - 8 * q^64 - 24 * q^65 - 16 * q^66 - 48 * q^69 + 22 * q^70 + 44 * q^71 + 40 * q^74 - 4 * q^76 - 4 * q^79 + 44 * q^81 + 16 * q^84 - 24 * q^85 - 4 * q^86 + 20 * q^89 + 6 * q^90 + 16 * q^91 - 4 * q^94 - 22 * q^95 + 8 * q^96 + 4 * q^99

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