LMFDB - Embedded newform 370.2.n.e.359.1

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			359.1
Root			$-1.26217 + 1.18614i$ of defining polynomial
Character	$\chi$	$=$	370.359
Dual form			370.2.n.e.269.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(1.73205 + 1.00000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-2.12819 + 0.686141i) q^{5} -2.00000 q^{6} +(3.73831 + 2.15831i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(1.73205 + 1.00000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-2.12819 + 0.686141i) q^{5} -2.00000 q^{6} +(3.73831 + 2.15831i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(1.50000 - 1.65831i) q^{10} -2.31662 q^{11} +(1.73205 - 1.00000i) q^{12} +(3.46410 + 2.00000i) q^{13} -4.31662 q^{14} +(-4.37228 - 0.939764i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.14023 + 0.658312i) q^{17} +(-0.866025 - 0.500000i) q^{18} +(-1.15831 + 2.00626i) q^{19} +(-0.469882 + 2.18614i) q^{20} +(4.31662 + 7.47661i) q^{21} +(2.00626 - 1.15831i) q^{22} +6.00000i q^{23} +(-1.00000 + 1.73205i) q^{24} +(4.05842 - 2.92048i) q^{25} -4.00000 q^{26} -4.00000i q^{27} +(3.73831 - 2.15831i) q^{28} +3.31662 q^{29} +(4.25639 - 1.37228i) q^{30} -4.31662 q^{31} +(0.866025 + 0.500000i) q^{32} +(-4.01251 - 2.31662i) q^{33} +(0.658312 - 1.14023i) q^{34} +(-9.43675 - 2.02830i) q^{35} +1.00000 q^{36} +(-2.59808 - 5.50000i) q^{37} -2.31662i q^{38} +(4.00000 + 6.92820i) q^{39} +(-0.686141 - 2.12819i) q^{40} +(2.81662 - 4.87854i) q^{41} +(-7.47661 - 4.31662i) q^{42} +10.9499i q^{43} +(-1.15831 + 2.00626i) q^{44} +(-1.65831 - 1.50000i) q^{45} +(-3.00000 - 5.19615i) q^{46} -2.31662i q^{47} -2.00000i q^{48} +(5.81662 + 10.0747i) q^{49} +(-2.05446 + 4.55842i) q^{50} -2.63325 q^{51} +(3.46410 - 2.00000i) q^{52} +(4.01251 - 2.31662i) q^{53} +(2.00000 + 3.46410i) q^{54} +(4.93023 - 1.58953i) q^{55} +(-2.15831 + 3.73831i) q^{56} +(-4.01251 + 2.31662i) q^{57} +(-2.87228 + 1.65831i) q^{58} +(-0.316625 - 0.548410i) q^{59} +(-3.00000 + 3.31662i) q^{60} +(3.97494 - 6.88479i) q^{61} +(3.73831 - 2.15831i) q^{62} +4.31662i q^{63} -1.00000 q^{64} +(-8.74456 - 1.87953i) q^{65} +4.63325 q^{66} +(-7.20241 - 4.15831i) q^{67} +1.31662i q^{68} +(-6.00000 + 10.3923i) q^{69} +(9.18662 - 2.96181i) q^{70} +(7.15831 - 12.3986i) q^{71} +(-0.866025 + 0.500000i) q^{72} +10.6332i q^{73} +(5.00000 + 3.46410i) q^{74} +(9.94987 - 1.00000i) q^{75} +(1.15831 + 2.00626i) q^{76} +(-8.66025 - 5.00000i) q^{77} +(-6.92820 - 4.00000i) q^{78} +(4.47494 - 7.75082i) q^{79} +(1.65831 + 1.50000i) q^{80} +(5.50000 - 9.52628i) q^{81} +5.63325i q^{82} +(5.74456 - 3.31662i) q^{83} +8.63325 q^{84} +(1.97494 - 2.18338i) q^{85} +(-5.47494 - 9.48287i) q^{86} +(5.74456 + 3.31662i) q^{87} -2.31662i q^{88} +(-0.816625 - 1.41444i) q^{89} +(2.18614 + 0.469882i) q^{90} +(8.63325 + 14.9532i) q^{91} +(5.19615 + 3.00000i) q^{92} +(-7.47661 - 4.31662i) q^{93} +(1.15831 + 2.00626i) q^{94} +(1.08854 - 5.06447i) q^{95} +(1.00000 + 1.73205i) q^{96} -9.94987i q^{97} +(-10.0747 - 5.81662i) q^{98} +(-1.15831 - 2.00626i) 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
$5$	−2.12819	+	0.686141i	−0.951757	+	0.306851i
$5$	−2.12819	+	0.686141i	−0.951757	+	0.306851i
$6$	−2.00000			−0.816497
$7$	3.73831	+	2.15831i	1.41295	+	0.815765i	0.995665	−	0.0930116i	$-0.0296494\pi$
$7$	3.73831	+	2.15831i	1.41295	+	0.815765i	0.417282	+	0.908777i	$0.362983\pi$
$8$			1.00000i			0.353553i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	1.50000	−	1.65831i	0.474342	−	0.524404i
$11$	−2.31662			−0.698489			−0.349244	−	0.937032i	$-0.613562\pi$
$11$	−2.31662			−0.698489			−0.349244	+	0.937032i	$0.613562\pi$
$12$	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	$0.479500\pi$
$14$	−4.31662			−1.15367
$15$	−4.37228	−	0.939764i	−1.12892	−	0.242646i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.14023	+	0.658312i	−0.276547	+	0.159664i	−0.631859	−	0.775083i	$-0.717708\pi$
$17$	−1.14023	+	0.658312i	−0.276547	+	0.159664i	0.355312	+	0.934748i	$0.384374\pi$
$18$	−0.866025	−	0.500000i	−0.204124	−	0.117851i
$19$	−1.15831	+	2.00626i	−0.265735	+	0.460267i	−0.967756	−	0.251890i	$-0.918948\pi$
$19$	−1.15831	+	2.00626i	−0.265735	+	0.460267i	0.702021	+	0.712156i	$0.252281\pi$
$20$	−0.469882	+	2.18614i	−0.105069	+	0.488836i
$21$	4.31662	+	7.47661i	0.941965	+	1.63153i
$22$	2.00626	−	1.15831i	0.427735	−	0.246953i
$23$			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
$25$	4.05842	−	2.92048i	0.811684	−	0.584096i
$26$	−4.00000			−0.784465
$27$		−	4.00000i		−	0.769800i
$28$	3.73831	−	2.15831i	0.706474	−	0.407883i
$29$	3.31662			0.615882			0.307941	−	0.951405i	$-0.400360\pi$
$29$	3.31662			0.615882			0.307941	+	0.951405i	$0.400360\pi$
$30$	4.25639	−	1.37228i	0.777107	−	0.250543i
$31$	−4.31662			−0.775289			−0.387644	−	0.921809i	$-0.626711\pi$
$31$	−4.31662			−0.775289			−0.387644	+	0.921809i	$0.626711\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	−4.01251	−	2.31662i	−0.698489	−	0.403273i
$34$	0.658312	−	1.14023i	0.112900	−	0.195548i
$35$	−9.43675	−	2.02830i	−1.59510	−	0.342846i
$36$	1.00000			0.166667
$37$	−2.59808	−	5.50000i	−0.427121	−	0.904194i
$37$	−2.59808	−	5.50000i	−0.427121	−	0.904194i
$38$		−	2.31662i		−	0.375806i
$39$	4.00000	+	6.92820i	0.640513	+	1.10940i
$40$	−0.686141	−	2.12819i	−0.108488	−	0.336497i
$41$	2.81662	−	4.87854i	0.439883	−	0.761900i	−0.557797	−	0.829977i	$-0.688353\pi$
$41$	2.81662	−	4.87854i	0.439883	−	0.761900i	0.997680	+	0.0680778i	$0.0216866\pi$
$42$	−7.47661	−	4.31662i	−1.15367	−	0.666070i
$43$			10.9499i			1.66984i	0.550371	+	0.834920i	$0.314486\pi$
$43$			10.9499i			1.66984i	−0.550371	+	0.834920i	$0.685514\pi$
$44$	−1.15831	+	2.00626i	−0.174622	+	0.302454i
$45$	−1.65831	−	1.50000i	−0.247207	−	0.223607i
$46$	−3.00000	−	5.19615i	−0.442326	−	0.766131i
$47$		−	2.31662i		−	0.337914i	−0.985623	−	0.168957i	$-0.945960\pi$
$47$		−	2.31662i		−	0.337914i	0.985623	−	0.168957i	$-0.0540400\pi$
$48$		−	2.00000i		−	0.288675i
$49$	5.81662	+	10.0747i	0.830946	+	1.43924i
$50$	−2.05446	+	4.55842i	−0.290544	+	0.644658i
$51$	−2.63325			−0.368729
$52$	3.46410	−	2.00000i	0.480384	−	0.277350i
$53$	4.01251	−	2.31662i	0.551161	−	0.318213i	−0.198429	−	0.980115i	$-0.563584\pi$
$53$	4.01251	−	2.31662i	0.551161	−	0.318213i	0.749590	+	0.661902i	$0.230251\pi$
$54$	2.00000	+	3.46410i	0.272166	+	0.471405i
$55$	4.93023	−	1.58953i	0.664792	−	0.214332i
$56$	−2.15831	+	3.73831i	−0.288417	+	0.499552i
$57$	−4.01251	+	2.31662i	−0.531470	+	0.306844i
$58$	−2.87228	+	1.65831i	−0.377149	+	0.217747i
$59$	−0.316625	−	0.548410i	−0.0412210	−	0.0713969i	0.844679	−	0.535273i	$-0.179791\pi$
$59$	−0.316625	−	0.548410i	−0.0412210	−	0.0713969i	−0.885900	+	0.463877i	$0.846458\pi$
$60$	−3.00000	+	3.31662i	−0.387298	+	0.428174i
$61$	3.97494	−	6.88479i	0.508939	−	0.881507i	−0.491008	−	0.871155i	$-0.663371\pi$
$61$	3.97494	−	6.88479i	0.508939	−	0.881507i	0.999946	−	0.0103523i	$-0.00329530\pi$
$62$	3.73831	−	2.15831i	0.474765	−	0.274106i
$63$			4.31662i			0.543844i
$64$	−1.00000			−0.125000
$65$	−8.74456	−	1.87953i	−1.08463	−	0.233127i
$66$	4.63325			0.570314
$67$	−7.20241	−	4.15831i	−0.879914	−	0.508019i	−0.00928410	−	0.999957i	$-0.502955\pi$
$67$	−7.20241	−	4.15831i	−0.879914	−	0.508019i	−0.870630	+	0.491938i	$0.836289\pi$
$68$			1.31662i			0.159664i
$69$	−6.00000	+	10.3923i	−0.722315	+	1.25109i
$70$	9.18662	−	2.96181i	1.09801	−	0.354004i
$71$	7.15831	−	12.3986i	0.849535	−	1.47144i	−0.0320881	−	0.999485i	$-0.510216\pi$
$71$	7.15831	−	12.3986i	0.849535	−	1.47144i	0.881623	−	0.471953i	$-0.156451\pi$
$72$	−0.866025	+	0.500000i	−0.102062	+	0.0589256i
$73$			10.6332i			1.24453i	0.782808	+	0.622264i	$0.213787\pi$
$73$			10.6332i			1.24453i	−0.782808	+	0.622264i	$0.786213\pi$
$74$	5.00000	+	3.46410i	0.581238	+	0.402694i
$75$	9.94987	−	1.00000i	1.14891	−	0.115470i
$76$	1.15831	+	2.00626i	0.132868	+	0.230133i
$77$	−8.66025	−	5.00000i	−0.986928	−	0.569803i
$78$	−6.92820	−	4.00000i	−0.784465	−	0.452911i
$79$	4.47494	−	7.75082i	0.503470	−	0.872035i	−0.496522	−	0.868024i	$-0.665390\pi$
$79$	4.47494	−	7.75082i	0.503470	−	0.872035i	0.999992	−	0.00401119i	$-0.00127680\pi$
$80$	1.65831	+	1.50000i	0.185405	+	0.167705i
$81$	5.50000	−	9.52628i	0.611111	−	1.05848i
$82$			5.63325i			0.622088i
$83$	5.74456	−	3.31662i	0.630548	−	0.364047i	−0.150416	−	0.988623i	$-0.548061\pi$
$83$	5.74456	−	3.31662i	0.630548	−	0.364047i	0.780964	+	0.624576i	$0.214728\pi$
$84$	8.63325			0.941965
$85$	1.97494	−	2.18338i	0.214212	−	0.236820i
$86$	−5.47494	−	9.48287i	−0.590378	−	1.02256i
$87$	5.74456	+	3.31662i	0.615882	+	0.355580i
$88$		−	2.31662i		−	0.246953i
$89$	−0.816625	−	1.41444i	−0.0865621	−	0.149930i	0.819494	−	0.573088i	$-0.194255\pi$
$89$	−0.816625	−	1.41444i	−0.0865621	−	0.149930i	−0.906056	+	0.423158i	$0.860921\pi$
$90$	2.18614	+	0.469882i	0.230439	+	0.0495299i
$91$	8.63325	+	14.9532i	0.905010	+	1.56752i
$92$	5.19615	+	3.00000i	0.541736	+	0.312772i
$93$	−7.47661	−	4.31662i	−0.775289	−	0.447613i
$94$	1.15831	+	2.00626i	0.119471	+	0.206929i
$95$	1.08854	−	5.06447i	0.111682	−	0.519603i
$96$	1.00000	+	1.73205i	0.102062	+	0.176777i
$97$		−	9.94987i		−	1.01026i	−0.863044	−	0.505128i	$-0.831445\pi$
$97$		−	9.94987i		−	1.01026i	0.863044	−	0.505128i	$-0.168555\pi$
$98$	−10.0747	−	5.81662i	−1.01770	−	0.587568i
$99$	−1.15831	−	2.00626i	−0.116415	−	0.201636i
$100$	−0.500000	−	4.97494i	−0.0500000	−	0.497494i
$101$	−8.68338			−0.864028			−0.432014	−	0.901867i	$-0.642197\pi$
$101$	−8.68338			−0.864028			−0.432014	+	0.901867i	$0.642197\pi$
$102$	2.28046	−	1.31662i	0.225799	−	0.130365i
$103$		−	16.3166i		−	1.60772i	−0.594815	−	0.803862i	$-0.702775\pi$
$103$		−	16.3166i		−	1.60772i	0.594815	−	0.803862i	$-0.297225\pi$
$104$	−2.00000	+	3.46410i	−0.196116	+	0.339683i
$105$	−14.3166	−	12.9499i	−1.39716	−	1.26378i
$106$	−2.31662	+	4.01251i	−0.225010	+	0.389730i
$107$	5.47036	+	3.15831i	0.528839	+	0.305326i	0.740544	−	0.672008i	$-0.234568\pi$
$107$	5.47036	+	3.15831i	0.528839	+	0.305326i	−0.211704	+	0.977334i	$0.567901\pi$
$108$	−3.46410	−	2.00000i	−0.333333	−	0.192450i
$109$	−7.97494	−	13.8130i	−0.763860	−	1.32305i	−0.940847	−	0.338832i	$-0.889968\pi$
$109$	−7.97494	−	13.8130i	−0.763860	−	1.32305i	0.176987	−	0.984213i	$-0.443365\pi$
$110$	−3.47494	+	3.84169i	−0.331322	+	0.366291i
$111$	1.00000	−	12.1244i	0.0949158	−	1.15079i
$112$		−	4.31662i		−	0.407883i
$113$	16.1369	−	9.31662i	1.51803	−	0.876434i	0.518254	−	0.855227i	$-0.326582\pi$
$113$	16.1369	−	9.31662i	1.51803	−	0.876434i	0.999775	−	0.0212074i	$-0.00675103\pi$
$114$	2.31662	−	4.01251i	0.216972	−	0.375806i
$115$	−4.11684	−	12.7692i	−0.383898	−	1.19073i
$116$	1.65831	−	2.87228i	0.153970	−	0.266685i
$117$			4.00000i			0.369800i
$118$	0.548410	+	0.316625i	0.0504853	+	0.0291477i
$119$	−5.68338			−0.520994
$120$	0.939764	−	4.37228i	0.0857883	−	0.399133i
$121$	−5.63325			−0.512114
$122$			7.94987i			0.719748i
$123$	9.75707	−	5.63325i	0.879766	−	0.507933i
$124$	−2.15831	+	3.73831i	−0.193822	+	0.335710i
$125$	−6.63325	+	9.00000i	−0.593296	+	0.804984i
$126$	−2.15831	−	3.73831i	−0.192278	−	0.333035i
$127$	12.6728	−	7.31662i	1.12453	−	0.649245i	0.181974	−	0.983303i	$-0.441751\pi$
$127$	12.6728	−	7.31662i	1.12453	−	0.649245i	0.942553	+	0.334058i	$0.108418\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−10.9499	+	18.9657i	−0.964083	+	1.66984i
$130$	8.51278	−	2.74456i	0.746620	−	0.240714i
$131$	7.31662	+	12.6728i	0.639256	+	1.10722i	0.985596	+	0.169116i	$0.0540911\pi$
$131$	7.31662	+	12.6728i	0.639256	+	1.10722i	−0.346340	+	0.938109i	$0.612576\pi$
$132$	−4.01251	+	2.31662i	−0.349244	+	0.201636i
$133$	−8.66025	+	5.00000i	−0.750939	+	0.433555i
$134$	8.31662			0.718447
$135$	2.74456	+	8.51278i	0.236214	+	0.732663i
$136$	−0.658312	−	1.14023i	−0.0564498	−	0.0977740i
$137$			4.68338i			0.400128i	0.979783	+	0.200064i	$0.0641150\pi$
$137$			4.68338i			0.400128i	−0.979783	+	0.200064i	$0.935885\pi$
$138$		−	12.0000i		−	1.02151i
$139$	9.94987	+	17.2337i	0.843937	+	1.46174i	0.886541	+	0.462650i	$0.153101\pi$
$139$	9.94987	+	17.2337i	0.843937	+	1.46174i	−0.0426035	+	0.999092i	$0.513565\pi$
$140$	−6.47494	+	7.15831i	−0.547232	+	0.604988i
$141$	2.31662	−	4.01251i	0.195095	−	0.337914i
$142$			14.3166i			1.20142i
$143$	−8.02502	−	4.63325i	−0.671086	−	0.387452i
$144$	0.500000	−	0.866025i	0.0416667	−	0.0721688i
$145$	−7.05842	+	2.27567i	−0.586170	+	0.188984i
$146$	−5.31662	−	9.20866i	−0.440007	−	0.762114i
$147$			23.2665i			1.91899i
$148$	−6.06218	−	0.500000i	−0.498308	−	0.0410997i
$149$	−3.94987			−0.323586			−0.161793	−	0.986825i	$-0.551728\pi$
$149$	−3.94987			−0.323586			−0.161793	+	0.986825i	$0.551728\pi$
$150$	−8.11684	+	5.84096i	−0.662738	+	0.476913i
$151$	1.31662	−	2.28046i	0.107145	−	0.185581i	−0.807467	−	0.589912i	$-0.799162\pi$
$151$	1.31662	−	2.28046i	0.107145	−	0.185581i	0.914613	+	0.404331i	$0.132496\pi$
$152$	−2.00626	−	1.15831i	−0.162729	−	0.0939515i
$153$	−1.14023	−	0.658312i	−0.0921822	−	0.0532214i
$154$	10.0000			0.805823
$155$	9.18662	−	2.96181i	0.737887	−	0.237898i
$156$	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	$0.295136\pi$
$158$			8.94987i			0.712014i
$159$	9.26650			0.734881
$160$	−2.18614	−	0.469882i	−0.172830	−	0.0371474i
$161$	−12.9499	+	22.4298i	−1.02059	+	1.76772i
$162$			11.0000i			0.864242i
$163$	−20.9720	+	12.1082i	−1.64265	+	0.948386i	−0.662768	+	0.748825i	$0.730618\pi$
$163$	−20.9720	+	12.1082i	−1.64265	+	0.948386i	−0.979885	+	0.199562i	$0.936048\pi$
$164$	−2.81662	−	4.87854i	−0.219941	−	0.380950i
$165$	10.1289	+	2.17708i	0.788537	+	0.169485i
$166$	−3.31662	+	5.74456i	−0.257420	+	0.445865i
$167$	14.9532	+	8.63325i	1.15712	+	0.668061i	0.950611	−	0.310385i	$-0.100458\pi$
$167$	14.9532	+	8.63325i	1.15712	+	0.668061i	0.206504	+	0.978446i	$0.433791\pi$
$168$	−7.47661	+	4.31662i	−0.576833	+	0.333035i
$169$	1.50000	+	2.59808i	0.115385	+	0.199852i
$170$	−0.618658	+	2.87833i	−0.0474489	+	0.220758i
$171$	−2.31662			−0.177157
$172$	9.48287	+	5.47494i	0.723062	+	0.417460i
$173$	−12.3552	+	7.13325i	−0.939345	+	0.542331i	−0.889755	−	0.456439i	$-0.849125\pi$
$173$	−12.3552	+	7.13325i	−0.939345	+	0.542331i	−0.0495899	+	0.998770i	$0.515791\pi$
$174$	−6.63325			−0.502865
$175$	21.4749	−	2.15831i	1.62335	−	0.163153i
$176$	1.15831	+	2.00626i	0.0873111	+	0.151227i
$177$		−	1.26650i		−	0.0951959i
$178$	1.41444	+	0.816625i	0.106016	+	0.0612086i
$179$	−21.2665			−1.58953			−0.794766	−	0.606915i	$-0.792407\pi$
$179$	−21.2665			−1.58953			−0.794766	+	0.606915i	$0.792407\pi$
$180$	−2.12819	+	0.686141i	−0.158626	+	0.0511419i
$181$	−3.34169	+	5.78797i	−0.248386	+	0.430217i	−0.963078	−	0.269222i	$-0.913233\pi$
$181$	−3.34169	+	5.78797i	−0.248386	+	0.430217i	0.714692	+	0.699439i	$0.246567\pi$
$182$	−14.9532	−	8.63325i	−1.10841	−	0.639939i
$183$	13.7696	−	7.94987i	1.01788	−	0.587672i
$184$	−6.00000			−0.442326
$185$	9.30298	+	9.92242i	0.683969	+	0.729511i
$186$	8.63325			0.633021
$187$	2.64149	−	1.52506i	0.193165	−	0.111524i
$188$	−2.00626	−	1.15831i	−0.146321	−	0.0844786i
$189$	8.63325	−	14.9532i	0.627977	−	1.08769i
$190$	1.58953	+	4.93023i	0.115317	+	0.357676i
$191$	−6.63325			−0.479965			−0.239983	−	0.970777i	$-0.577142\pi$
$191$	−6.63325			−0.479965			−0.239983	+	0.970777i	$0.577142\pi$
$192$	−1.73205	−	1.00000i	−0.125000	−	0.0721688i
$193$		−	5.31662i		−	0.382699i	−0.981522	−	0.191350i	$-0.938714\pi$
$193$		−	5.31662i		−	0.382699i	0.981522	−	0.191350i	$-0.0612864\pi$
$194$	4.97494	+	8.61684i	0.357180	+	0.618653i
$195$	−13.2665	−	12.0000i	−0.950034	−	0.859338i
$196$	11.6332			0.830946
$197$	−15.2708	+	8.81662i	−1.08800	+	0.628159i	−0.933044	−	0.359762i	$-0.882858\pi$
$197$	−15.2708	+	8.81662i	−1.08800	+	0.628159i	−0.154959	+	0.987921i	$0.549524\pi$
$198$	2.00626	+	1.15831i	0.142578	+	0.0823177i
$199$	−2.94987			−0.209111			−0.104556	−	0.994519i	$-0.533342\pi$
$199$	−2.94987			−0.209111			−0.104556	+	0.994519i	$0.533342\pi$
$200$	2.92048	+	4.05842i	0.206509	+	0.286974i
$201$	−8.31662	−	14.4048i	−0.586609	−	1.01604i
$202$	7.52002	−	4.34169i	0.529107	−	0.305480i
$203$	12.3986	+	7.15831i	0.870208	+	0.502415i
$204$	−1.31662	+	2.28046i	−0.0921822	+	0.159664i
$205$	−2.64696	+	12.3151i	−0.184872	+	0.860122i
$206$	8.15831	+	14.1306i	0.568417	+	0.984526i
$207$	−5.19615	+	3.00000i	−0.361158	+	0.208514i
$208$		−	4.00000i		−	0.277350i
$209$	2.68338	−	4.64774i	0.185613	−	0.321491i
$210$	18.8735	+	4.05661i	1.30240	+	0.279933i
$211$	−7.68338			−0.528945			−0.264473	−	0.964393i	$-0.585198\pi$
$211$	−7.68338			−0.528945			−0.264473	+	0.964393i	$0.585198\pi$
$212$		−	4.63325i		−	0.318213i
$213$	24.7971	−	14.3166i	1.69907	−	0.980959i
$214$	−6.31662			−0.431796
$215$	−7.51315	−	23.3035i	−0.512393	−	1.58928i
$216$	4.00000			0.272166
$217$	−16.1369	−	9.31662i	−1.09544	−	0.632454i
$218$	13.8130	+	7.97494i	0.935534	+	0.540131i
$219$	−10.6332	+	18.4173i	−0.718528	+	1.24453i
$220$	1.08854	−	5.06447i	0.0733894	−	0.341446i
$221$	−5.26650			−0.354263
$222$	5.19615	+	11.0000i	0.348743	+	0.738272i
$223$			26.6332i			1.78349i	0.452534	+	0.891747i	$0.350520\pi$
$223$			26.6332i			1.78349i	−0.452534	+	0.891747i	$0.649480\pi$
$224$	2.15831	+	3.73831i	0.144208	+	0.249776i
$225$	4.55842	+	2.05446i	0.303895	+	0.136964i
$226$	−9.31662	+	16.1369i	−0.619733	+	1.07341i
$227$	−11.2149	−	6.47494i	−0.744360	−	0.429757i	0.0792922	−	0.996851i	$-0.474734\pi$
$227$	−11.2149	−	6.47494i	−0.744360	−	0.429757i	−0.823653	+	0.567095i	$0.808067\pi$
$228$			4.63325i			0.306844i
$229$	7.97494	−	13.8130i	0.526999	−	0.912788i	−0.472506	−	0.881327i	$-0.656651\pi$
$229$	7.97494	−	13.8130i	0.526999	−	0.912788i	0.999505	−	0.0314612i	$-0.0100161\pi$
$230$	9.94987	+	9.00000i	0.656075	+	0.593442i
$231$	−10.0000	−	17.3205i	−0.657952	−	1.13961i
$232$			3.31662i			0.217747i
$233$			8.05013i			0.527381i	0.964607	+	0.263691i	$0.0849398\pi$
$233$			8.05013i			0.527381i	−0.964607	+	0.263691i	$0.915060\pi$
$234$	−2.00000	−	3.46410i	−0.130744	−	0.226455i
$235$	1.58953	+	4.93023i	0.103690	+	0.321613i
$236$	−0.633250			−0.0412210
$237$	15.5016	−	8.94987i	1.00694	−	0.581357i
$238$	4.92195	−	2.84169i	0.319042	−	0.184199i
$239$	−0.841688	−	1.45785i	−0.0544442	−	0.0943002i	0.837519	−	0.546409i	$-0.184005\pi$
$239$	−0.841688	−	1.45785i	−0.0544442	−	0.0943002i	−0.891963	+	0.452108i	$0.850672\pi$
$240$	1.37228	+	4.25639i	0.0885804	+	0.274749i
$241$	−1.36675	+	2.36728i	−0.0880401	+	0.152490i	−0.906683	−	0.421813i	$-0.861394\pi$
$241$	−1.36675	+	2.36728i	−0.0880401	+	0.152490i	0.818642	+	0.574303i	$0.194727\pi$
$242$	4.87854	−	2.81662i	0.313604	−	0.181059i
$243$	8.66025	−	5.00000i	0.555556	−	0.320750i
$244$	−3.97494	−	6.88479i	−0.254469	−	0.440754i
$245$	−19.2916	−	17.4499i	−1.23249	−	1.11483i
$246$	−5.63325	+	9.75707i	−0.359163	+	0.622088i
$247$	−8.02502	+	4.63325i	−0.510620	+	0.294807i
$248$		−	4.31662i		−	0.274106i
$249$	13.2665			0.840730
$250$	1.24456	−	11.1109i	0.0787131	−	0.702712i
$251$	−4.31662			−0.272463			−0.136231	−	0.990677i	$-0.543499\pi$
$251$	−4.31662			−0.272463			−0.136231	+	0.990677i	$0.543499\pi$
$252$	3.73831	+	2.15831i	0.235491	+	0.135961i
$253$		−	13.8997i		−	0.873870i
$254$	−7.31662	+	12.6728i	−0.459086	+	0.795160i
$255$	5.60407	−	1.80678i	0.350940	−	0.113145i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−14.4482	+	8.34169i	−0.901256	+	0.520340i	−0.877607	−	0.479380i	$-0.840862\pi$
$257$	−14.4482	+	8.34169i	−0.901256	+	0.520340i	−0.0236483	+	0.999720i	$0.507528\pi$
$258$		−	21.8997i		−	1.36342i
$259$	2.15831	−	26.1681i	0.134111	−	1.62601i
$260$	−6.00000	+	6.63325i	−0.372104	+	0.411377i
$261$	1.65831	+	2.87228i	0.102647	+	0.177790i
$262$	−12.6728	−	7.31662i	−0.782926	−	0.452023i
$263$	11.4891	+	6.63325i	0.708450	+	0.409024i	0.810487	−	0.585757i	$-0.199203\pi$
$263$	11.4891	+	6.63325i	0.708450	+	0.409024i	−0.102037	+	0.994781i	$0.532536\pi$
$264$	2.31662	−	4.01251i	0.142578	−	0.246953i
$265$	−6.94987	+	7.68338i	−0.426927	+	0.471986i
$266$	5.00000	−	8.66025i	0.306570	−	0.530994i
$267$		−	3.26650i		−	0.199907i
$268$	−7.20241	+	4.15831i	−0.439957	+	0.254009i
$269$	25.2665			1.54053			0.770263	−	0.637727i	$-0.220125\pi$
$269$	25.2665			1.54053			0.770263	+	0.637727i	$0.220125\pi$
$270$	−6.63325	−	6.00000i	−0.403687	−	0.365148i
$271$	2.79156	+	4.83513i	0.169575	+	0.293713i	0.938271	−	0.345902i	$-0.112427\pi$
$271$	2.79156	+	4.83513i	0.169575	+	0.293713i	−0.768695	+	0.639615i	$0.779094\pi$
$272$	1.14023	+	0.658312i	0.0691366	+	0.0399161i
$273$			34.5330i			2.09003i
$274$	−2.34169	−	4.05592i	−0.141467	−	0.245027i
$275$	−9.40184	+	6.76566i	−0.566952	+	0.407985i
$276$	6.00000	+	10.3923i	0.361158	+	0.625543i
$277$	−6.61059	−	3.81662i	−0.397192	−	0.229319i	0.288080	−	0.957606i	$-0.406983\pi$
$277$	−6.61059	−	3.81662i	−0.397192	−	0.229319i	−0.685272	+	0.728288i	$0.740316\pi$
$278$	−17.2337	−	9.94987i	−1.03361	−	0.596754i
$279$	−2.15831	−	3.73831i	−0.129215	−	0.223807i
$280$	2.02830	−	9.43675i	0.121214	−	0.563954i
$281$	−14.8166	−	25.6631i	−0.883886	−	1.53093i	−0.846985	−	0.531616i	$-0.821585\pi$
$281$	−14.8166	−	25.6631i	−0.883886	−	1.53093i	−0.0369003	−	0.999319i	$-0.511748\pi$
$282$			4.63325i			0.275906i
$283$	−1.45785	−	0.841688i	−0.0866599	−	0.0500331i	0.456044	−	0.889957i	$-0.349266\pi$
$283$	−1.45785	−	0.841688i	−0.0866599	−	0.0500331i	−0.542704	+	0.839924i	$0.682599\pi$
$284$	−7.15831	−	12.3986i	−0.424768	−	0.735719i
$285$	6.94987	−	7.68338i	0.411675	−	0.455124i
$286$	9.26650			0.547940
$287$	21.0588	−	12.1583i	1.24306	−	0.717682i
$288$			1.00000i			0.0589256i
$289$	−7.63325	+	13.2212i	−0.449015	+	0.777716i
$290$	4.97494	−	5.50000i	0.292138	−	0.322971i
$291$	9.94987	−	17.2337i	0.583272	−	1.01026i
$292$	9.20866	+	5.31662i	0.538896	+	0.311132i
$293$	13.5388	+	7.81662i	0.790945	+	0.456652i	0.840295	−	0.542129i	$-0.182382\pi$
$293$	13.5388	+	7.81662i	0.790945	+	0.456652i	−0.0493504	+	0.998782i	$0.515715\pi$
$294$	−11.6332	−	20.1494i	−0.678465	−	1.17514i
$295$	1.05013	+	0.949874i	0.0611407	+	0.0553038i
$296$	5.50000	−	2.59808i	0.319681	−	0.151010i
$297$			9.26650i			0.537697i
$298$	3.42069	−	1.97494i	0.198155	−	0.114405i
$299$	−12.0000	+	20.7846i	−0.693978	+	1.20201i
$300$	4.10891	−	9.11684i	0.237228	−	0.526361i
$301$	−23.6332	+	40.9340i	−1.36220	+	2.35940i
$302$			2.63325i			0.151526i
$303$	−15.0400	−	8.68338i	−0.864028	−	0.498847i
$304$	2.31662			0.132868
$305$	−3.73550	+	17.3795i	−0.213894	+	0.995150i
$306$	1.31662			0.0752664
$307$		−	22.3166i		−	1.27368i	−0.770997	−	0.636839i	$-0.780242\pi$
$307$		−	22.3166i		−	1.27368i	0.770997	−	0.636839i	$-0.219758\pi$
$308$	−8.66025	+	5.00000i	−0.493464	+	0.284901i
$309$	16.3166	−	28.2612i	0.928220	−	1.60772i
$310$	−6.47494	+	7.15831i	−0.367752	+	0.406565i
$311$	11.7916	+	20.4236i	0.668638	+	1.15812i	0.978285	+	0.207264i	$0.0664558\pi$
$311$	11.7916	+	20.4236i	0.668638	+	1.15812i	−0.309647	+	0.950852i	$0.600211\pi$
$312$	−6.92820	+	4.00000i	−0.392232	+	0.226455i
$313$	20.7412	−	11.9749i	1.17236	−	0.676863i	0.218127	−	0.975920i	$-0.430005\pi$
$313$	20.7412	−	11.9749i	1.17236	−	0.676863i	0.954235	+	0.299057i	$0.0966721\pi$
$314$	−1.50000	+	2.59808i	−0.0846499	+	0.146618i
$315$	−2.96181	−	9.18662i	−0.166879	−	0.517607i
$316$	−4.47494	−	7.75082i	−0.251735	−	0.436018i
$317$	−18.7349	+	10.8166i	−1.05226	+	0.607522i	−0.923281	−	0.384125i	$-0.874503\pi$
$317$	−18.7349	+	10.8166i	−1.05226	+	0.607522i	−0.128978	+	0.991647i	$0.541170\pi$
$318$	−8.02502	+	4.63325i	−0.450021	+	0.259820i
$319$	−7.68338			−0.430186
$320$	2.12819	−	0.686141i	0.118970	−	0.0383564i
$321$	6.31662	+	10.9407i	0.352560	+	0.610651i
$322$		−	25.8997i		−	1.44334i
$323$		−	3.05013i		−	0.169714i
$324$	−5.50000	−	9.52628i	−0.305556	−	0.529238i
$325$	19.8997	−	2.00000i	1.10384	−	0.110940i
$326$	12.1082	−	20.9720i	0.670610	−	1.16153i
$327$		−	31.8997i		−	1.76406i
$328$	4.87854	+	2.81662i	0.269372	+	0.155522i
$329$	5.00000	−	8.66025i	0.275659	−	0.477455i
$330$	−9.86046	+	3.17906i	−0.542800	+	0.175002i
$331$	−2.94987	−	5.10933i	−0.162140	−	0.280834i	0.773496	−	0.633801i	$-0.218506\pi$
$331$	−2.94987	−	5.10933i	−0.162140	−	0.280834i	−0.935636	+	0.352967i	$0.885173\pi$
$332$		−	6.63325i		−	0.364047i
$333$	3.46410	−	5.00000i	0.189832	−	0.273998i
$334$	−17.2665			−0.944781
$335$	18.1813	+	3.90783i	0.993351	+	0.213508i
$336$	4.31662	−	7.47661i	0.235491	−	0.407883i
$337$	6.88479	+	3.97494i	0.375039	+	0.216529i	0.675657	−	0.737216i	$-0.263860\pi$
$337$	6.88479	+	3.97494i	0.375039	+	0.216529i	−0.300619	+	0.953744i	$0.597193\pi$
$338$	−2.59808	−	1.50000i	−0.141317	−	0.0815892i
$339$	37.2665			2.02404
$340$	−0.903390	−	2.80203i	−0.0489932	−	0.151962i
$341$	10.0000			0.541530
$342$	2.00626	−	1.15831i	0.108486	−	0.0626344i
$343$			20.0000i			1.07990i
$344$	−10.9499			−0.590378
$345$	5.63858	−	26.2337i	0.303571	−	1.41237i
$346$	7.13325	−	12.3552i	0.383486	−	0.664217i
$347$			11.2665i			0.604817i	0.953178	+	0.302409i	$0.0977907\pi$
$347$			11.2665i			0.604817i	−0.953178	+	0.302409i	$0.902209\pi$
$348$	5.74456	−	3.31662i	0.307941	−	0.177790i
$349$	−17.6583	−	30.5851i	−0.945228	−	1.63718i	−0.755294	−	0.655386i	$-0.772506\pi$
$349$	−17.6583	−	30.5851i	−0.945228	−	1.63718i	−0.189933	−	0.981797i	$-0.560827\pi$
$350$	−17.5187	+	12.6066i	−0.936413	+	0.673852i
$351$	8.00000	−	13.8564i	0.427008	−	0.739600i
$352$	−2.00626	−	1.15831i	−0.106934	−	0.0617383i
$353$	−16.6419	+	9.60819i	−0.885757	+	0.511392i	−0.872552	−	0.488521i	$-0.837537\pi$
$353$	−16.6419	+	9.60819i	−0.885757	+	0.511392i	−0.0132049	+	0.999913i	$0.504203\pi$
$354$	0.633250	+	1.09682i	0.0336568	+	0.0582953i
$355$	−6.72712	+	31.2982i	−0.357039	+	1.66113i
$356$	−1.63325			−0.0865621
$357$	−9.84389	−	5.68338i	−0.520994	−	0.300796i
$358$	18.4173	−	10.6332i	0.973386	−	0.561985i
$359$	−4.63325			−0.244534			−0.122267	−	0.992497i	$-0.539016\pi$
$359$	−4.63325			−0.244534			−0.122267	+	0.992497i	$0.539016\pi$
$360$	1.50000	−	1.65831i	0.0790569	−	0.0874007i
$361$	6.81662	+	11.8067i	0.358770	+	0.621407i
$362$		−	6.68338i		−	0.351270i
$363$	−9.75707	−	5.63325i	−0.512114	−	0.295669i
$364$	17.2665			0.905010
$365$	−7.29590	−	22.6296i	−0.381885	−	1.18449i
$366$	−7.94987	+	13.7696i	−0.415547	+	0.719748i
$367$	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
$369$	5.63325			0.293255
$370$	−13.0178	−	3.94158i	−0.676765	−	0.204913i
$371$	20.0000			1.03835
$372$	−7.47661	+	4.31662i	−0.387644	+	0.223807i
$373$	−19.8318	−	11.4499i	−1.02685	−	0.592852i	−0.110769	−	0.993846i	$-0.535331\pi$
$373$	−19.8318	−	11.4499i	−1.02685	−	0.592852i	−0.916081	+	0.400994i	$0.868665\pi$
$374$	−1.52506	+	2.64149i	−0.0788591	+	0.136588i
$375$	−20.4891	+	8.95521i	−1.05805	+	0.462445i
$376$	2.31662			0.119471
$377$	11.4891	+	6.63325i	0.591720	+	0.341630i
$378$			17.2665i			0.888093i
$379$	16.4749	+	28.5354i	0.846261	+	1.46577i	0.884522	+	0.466499i	$0.154485\pi$
$379$	16.4749	+	28.5354i	0.846261	+	1.46577i	−0.0382612	+	0.999268i	$0.512182\pi$
$380$	−3.84169	−	3.47494i	−0.197074	−	0.178261i
$381$	29.2665			1.49937
$382$	5.74456	−	3.31662i	0.293917	−	0.169693i
$383$	20.5104	+	11.8417i	1.04803	+	0.605082i	0.922098	−	0.386957i	$-0.126474\pi$
$383$	20.5104	+	11.8417i	1.04803	+	0.605082i	0.125935	+	0.992039i	$0.459807\pi$
$384$	2.00000			0.102062
$385$	21.8614	+	4.69882i	1.11416	+	0.239474i
$386$	2.65831	+	4.60433i	0.135305	+	0.234354i
$387$	−9.48287	+	5.47494i	−0.482041	+	0.278307i
$388$	−8.61684	−	4.97494i	−0.437454	−	0.252564i
$389$	4.02506	−	6.97161i	0.204079	−	0.353475i	−0.745760	−	0.666215i	$-0.767913\pi$
$389$	4.02506	−	6.97161i	0.204079	−	0.353475i	0.949839	+	0.312740i	$0.101247\pi$
$390$	17.4891	+	3.75906i	0.885596	+	0.190347i
$391$	−3.94987	−	6.84138i	−0.199754	−	0.345984i
$392$	−10.0747	+	5.81662i	−0.508849	+	0.293784i
$393$			29.2665i			1.47630i
$394$	8.81662	−	15.2708i	0.444175	−	0.769334i
$395$	−4.20538	+	19.5657i	−0.211596	+	0.984456i
$396$	−2.31662			−0.116415
$397$			10.8997i			0.547043i	0.961866	+	0.273521i	$0.0881884\pi$
$397$			10.8997i			0.547043i	−0.961866	+	0.273521i	$0.911812\pi$
$398$	2.55467	−	1.47494i	0.128054	−	0.0739319i
$399$	−20.0000			−1.00125
$400$	−4.55842	−	2.05446i	−0.227921	−	0.102723i
$401$	−10.7335			−0.536005			−0.268003	−	0.963418i	$-0.586364\pi$
$401$	−10.7335			−0.536005			−0.268003	+	0.963418i	$0.586364\pi$
$402$	14.4048	+	8.31662i	0.718447	+	0.414796i
$403$	−14.9532	−	8.63325i	−0.744873	−	0.430053i
$404$	−4.34169	+	7.52002i	−0.216007	+	0.374135i
$405$	−5.16870	+	24.0475i	−0.256835	+	1.19493i
$406$	−14.3166			−0.710522
$407$	6.01877	+	12.7414i	0.298339	+	0.631570i
$408$		−	2.63325i		−	0.130365i
$409$	16.0831	+	27.8568i	0.795259	+	1.37743i	0.922674	+	0.385580i	$0.125999\pi$
$409$	16.0831	+	27.8568i	0.795259	+	1.37743i	−0.127415	+	0.991849i	$0.540668\pi$
$410$	−3.86520	−	11.9886i	−0.190889	−	0.592077i
$411$	−4.68338	+	8.11184i	−0.231014	+	0.400128i
$412$	−14.1306	−	8.15831i	−0.696165	−	0.401931i
$413$		−	2.73350i		−	0.134507i
$414$	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
$418$			5.36675i			0.262496i
$419$	−18.4749	−	31.9995i	−0.902560	−	1.56328i	−0.824160	−	0.566357i	$-0.808352\pi$
$419$	−18.4749	−	31.9995i	−0.902560	−	1.56328i	−0.0784000	−	0.996922i	$-0.524981\pi$
$420$	−18.3732	+	5.92362i	−0.896522	+	0.289043i
$421$	2.05013			0.0999170			0.0499585	−	0.998751i	$-0.484091\pi$
$421$	2.05013			0.0999170			0.0499585	+	0.998751i	$0.484091\pi$
$422$	6.65400	−	3.84169i	0.323912	−	0.187010i
$423$	2.00626	−	1.15831i	0.0975475	−	0.0563191i
$424$	2.31662	+	4.01251i	0.112505	+	0.194865i
$425$	−2.70495	+	6.00173i	−0.131209	+	0.291127i
$426$	−14.3166	+	24.7971i	−0.693643	+	1.20142i
$427$	29.7191	−	17.1583i	1.43821	−	0.830349i
$428$	5.47036	−	3.15831i	0.264420	−	0.152663i
$429$	−9.26650	−	16.0500i	−0.447391	−	0.774904i
$430$	18.1583	+	16.4248i	0.875672	+	0.792075i
$431$	18.1583	−	31.4511i	0.874655	−	1.51495i	0.0175255	−	0.999846i	$-0.494421\pi$
$431$	18.1583	−	31.4511i	0.874655	−	1.51495i	0.857130	−	0.515101i	$-0.172245\pi$
$432$	−3.46410	+	2.00000i	−0.166667	+	0.0962250i
$433$		−	3.94987i		−	0.189819i	−0.995486	−	0.0949094i	$-0.969744\pi$
$433$		−	3.94987i		−	0.189819i	0.995486	−	0.0949094i	$-0.0302561\pi$
$434$	18.6332			0.894425
$435$	−14.5012	−	3.11684i	−0.695280	−	0.149441i
$436$	−15.9499			−0.763860
$437$	−12.0375	−	6.94987i	−0.575833	−	0.332458i
$438$		−	21.2665i		−	1.01615i
$439$	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	$0.0742199\pi$
$440$	1.58953	+	4.93023i	0.0757779	+	0.235039i
$441$	−5.81662	+	10.0747i	−0.276982	+	0.479747i
$442$	4.56092	−	2.63325i	0.216941	−	0.125251i
$443$		−	1.26650i		−	0.0601732i	−0.999547	−	0.0300866i	$-0.990422\pi$
$443$		−	1.26650i		−	0.0601732i	0.999547	−	0.0300866i	$-0.00957831\pi$
$444$	−10.0000	−	6.92820i	−0.474579	−	0.328798i
$445$	2.70844	+	2.44987i	0.128392	+	0.116135i
$446$	−13.3166	−	23.0651i	−0.630560	−	1.09216i
$447$	−6.84138	−	3.94987i	−0.323586	−	0.186823i
$448$	−3.73831	−	2.15831i	−0.176618	−	0.101971i
$449$	6.63325	−	11.4891i	0.313042	−	0.542205i	−0.665977	−	0.745972i	$-0.731985\pi$
$449$	6.63325	−	11.4891i	0.313042	−	0.542205i	0.979019	+	0.203767i	$0.0653185\pi$
$450$	−4.97494	+	0.500000i	−0.234521	+	0.0235702i
$451$	−6.52506	+	11.3017i	−0.307253	+	0.532178i
$452$		−	18.6332i		−	0.876434i
$453$	4.56092	−	2.63325i	0.214291	−	0.123721i
$454$	12.9499			0.607768
$455$	−28.6332	−	25.8997i	−1.34235	−	1.21420i
$456$	−2.31662	−	4.01251i	−0.108486	−	0.187903i
$457$	−25.9374	−	14.9749i	−1.21330	−	0.700498i	−0.249822	−	0.968292i	$-0.580372\pi$
$457$	−25.9374	−	14.9749i	−1.21330	−	0.700498i	−0.963476	+	0.267794i	$0.913705\pi$
$458$			15.9499i			0.745289i
$459$	2.63325	+	4.56092i	0.122910	+	0.212886i
$460$	−13.1168	−	2.81929i	−0.611576	−	0.131450i
$461$	2.68338	+	4.64774i	0.124977	+	0.216467i	0.921724	−	0.387846i	$-0.126781\pi$
$461$	2.68338	+	4.64774i	0.124977	+	0.216467i	−0.796747	+	0.604313i	$0.793448\pi$
$462$	17.3205	+	10.0000i	0.805823	+	0.465242i
$463$	8.84764	+	5.10819i	0.411185	+	0.237398i	0.691299	−	0.722569i	$-0.257039\pi$
$463$	8.84764	+	5.10819i	0.411185	+	0.237398i	−0.280114	+	0.959967i	$0.590372\pi$
$464$	−1.65831	−	2.87228i	−0.0769852	−	0.133342i
$465$	18.8735	+	4.05661i	0.875238	+	0.188121i
$466$	−4.02506	−	6.97161i	−0.186457	−	0.322954i
$467$		−	13.8997i		−	0.643204i	−0.946875	−	0.321602i	$-0.895779\pi$
$467$		−	13.8997i		−	0.643204i	0.946875	−	0.321602i	$-0.104221\pi$
$468$	3.46410	+	2.00000i	0.160128	+	0.0924500i
$469$	−17.9499	−	31.0901i	−0.828848	−	1.43561i
$470$	−3.84169	−	3.47494i	−0.177204	−	0.160287i
$471$	6.00000			0.276465
$472$	0.548410	−	0.316625i	0.0252426	−	0.0145738i
$473$		−	25.3668i		−	1.16636i
$474$	−8.94987	+	15.5016i	−0.411081	+	0.712014i
$475$	1.15831	+	11.5251i	0.0531470	+	0.528806i
$476$	−2.84169	+	4.92195i	−0.130249	+	0.225597i
$477$	4.01251	+	2.31662i	0.183720	+	0.106071i
$478$	1.45785	+	0.841688i	0.0666803	+	0.0384979i
$479$	−18.3166	−	31.7253i	−0.836908	−	1.44957i	−0.892467	−	0.451112i	$-0.851028\pi$
$479$	−18.3166	−	31.7253i	−0.836908	−	1.44957i	0.0555595	−	0.998455i	$-0.482306\pi$
$480$	−3.31662	−	3.00000i	−0.151383	−	0.136931i
$481$	2.00000	−	24.2487i	0.0911922	−	1.10565i
$482$		−	2.73350i		−	0.124508i
$483$	−44.8597	+	25.8997i	−2.04119	+	1.17848i
$484$	−2.81662	+	4.87854i	−0.128028	+	0.221752i
$485$	6.82701	+	21.1753i	0.309999	+	0.961519i
$486$	−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	$0.866286\pi$
$488$	6.88479	+	3.97494i	0.311660	+	0.179937i
$489$	−48.4327			−2.19020
$490$	25.4319	+	5.46625i	1.14890	+	0.246940i
$491$	17.6834			0.798040			0.399020	−	0.916942i	$-0.369350\pi$
$491$	17.6834			0.798040			0.399020	+	0.916942i	$0.369350\pi$
$492$		−	11.2665i		−	0.507933i
$493$	−3.78172	+	2.18338i	−0.170320	+	0.0983343i
$494$	4.63325	−	8.02502i	0.208460	−	0.361063i
$495$	3.84169	+	3.47494i	0.172671	+	0.156187i
$496$	2.15831	+	3.73831i	0.0969111	+	0.167855i
$497$	53.5199	−	30.8997i	2.40070	−	1.38604i
$498$	−11.4891	+	6.63325i	−0.514840	+	0.297243i
$499$	1.47494	−	2.55467i	0.0660273	−	0.114363i	−0.831122	−	0.556090i	$-0.812301\pi$
$499$	1.47494	−	2.55467i	0.0660273	−	0.114363i	0.897149	+	0.441728i	$0.145634\pi$
$500$	4.47760	+	10.2446i	0.200245	+	0.458151i
$501$	17.2665	+	29.9065i	0.771410	+	1.33612i
$502$	3.73831	−	2.15831i	0.166849	−	0.0963302i
$503$	6.56718	−	3.79156i	0.292816	−	0.169057i	−0.346395	−	0.938089i	$-0.612594\pi$
$503$	6.56718	−	3.79156i	0.292816	−	0.169057i	0.639211	+	0.769031i	$0.279261\pi$
$504$	−4.31662			−0.192278
$505$	18.4799	−	5.95802i	0.822345	−	0.265128i
$506$	6.94987	+	12.0375i	0.308960	+	0.535134i
$507$			6.00000i			0.266469i
$508$		−	14.6332i		−	0.649245i
$509$	2.65831	+	4.60433i	0.117828	+	0.204083i	0.918907	−	0.394475i	$-0.129074\pi$
$509$	2.65831	+	4.60433i	0.117828	+	0.204083i	−0.801079	+	0.598559i	$0.795740\pi$
$510$	−3.94987	+	4.36675i	−0.174903	+	0.193363i
$511$	−22.9499	+	39.7503i	−1.01524	+	1.75845i
$512$		−	1.00000i		−	0.0441942i
$513$	8.02502	+	4.63325i	0.354313	+	0.204563i
$514$	8.34169	−	14.4482i	0.367936	−	0.637284i
$515$	11.1955	+	34.7249i	0.493333	+	1.53016i
$516$	10.9499	+	18.9657i	0.482041	+	0.834920i
$517$			5.36675i			0.236029i
$518$	11.2149	+	23.7414i	0.492755	+	1.04314i
$519$	−28.5330			−1.25246
$520$	1.87953	−	8.74456i	0.0824227	−	0.383474i
$521$	1.36675	−	2.36728i	0.0598784	−	0.103712i	−0.834532	−	0.550959i	$-0.814262\pi$
$521$	1.36675	−	2.36728i	0.0598784	−	0.103712i	0.894411	+	0.447247i	$0.147595\pi$
$522$	−2.87228	−	1.65831i	−0.125716	−	0.0725824i
$523$	−34.5542	−	19.9499i	−1.51095	−	0.872347i	−0.999918	−	0.0127850i	$-0.995930\pi$
$523$	−34.5542	−	19.9499i	−1.51095	−	0.872347i	−0.511031	−	0.859562i	$-0.670736\pi$
$524$	14.6332			0.639256
$525$	39.3540	+	17.7366i	1.71755	+	0.774090i
$526$	−13.2665			−0.578447
$527$	4.92195	−	2.84169i	0.214403	−	0.123786i
$528$			4.63325i			0.201636i
$529$	−13.0000			−0.565217
$530$	2.17708	−	10.1289i	0.0945663	−	0.439973i
$531$	0.316625	−	0.548410i	0.0137403	−	0.0237990i
$532$			10.0000i			0.433555i
$533$	19.5141	−	11.2665i	0.845252	−	0.488006i
$534$	1.63325	+	2.82887i	0.0706776	+	0.122417i
$535$	−13.8090	−	2.96807i	−0.597016	−	0.128321i
$536$	4.15831	−	7.20241i	0.179612	−	0.311097i
$537$	−36.8347	−	21.2665i	−1.58953	−	0.917717i
$538$	−21.8814	+	12.6332i	−0.943375	+	0.544658i
$539$	−13.4749	−	23.3393i	−0.580407	−	1.00529i
$540$	8.74456	+	1.87953i	0.376306	+	0.0808820i
$541$	−21.9499			−0.943699			−0.471849	−	0.881679i	$-0.656413\pi$
$541$	−21.9499			−0.943699			−0.471849	+	0.881679i	$0.656413\pi$
$542$	−4.83513	−	2.79156i	−0.207686	−	0.119908i
$543$	−11.5759	+	6.68338i	−0.496771	+	0.286811i
$544$	−1.31662			−0.0564498
$545$	26.4499	+	23.9248i	1.13299	+	1.02483i
$546$	−17.2665	−	29.9065i	−0.738938	−	1.27988i
$547$			28.3166i			1.21073i	0.795947	+	0.605366i	$0.206973\pi$
$547$			28.3166i			1.21073i	−0.795947	+	0.605366i	$0.793027\pi$
$548$	4.05592	+	2.34169i	0.173260	+	0.100032i
$549$	7.94987			0.339292
$550$	4.75940	−	10.5602i	0.202942	−	0.450286i
$551$	−3.84169	+	6.65400i	−0.163661	+	0.283470i
$552$	−10.3923	−	6.00000i	−0.442326	−	0.255377i
$553$	33.4574	−	19.3166i	1.42275	−	0.821426i
$554$	7.63325			0.324306
$555$	6.19082	+	26.4891i	0.262786	+	1.12440i
$556$	19.8997			0.843937
$557$	10.6231	−	6.13325i	0.450115	−	0.259874i	−0.257764	−	0.966208i	$-0.582986\pi$
$557$	10.6231	−	6.13325i	0.450115	−	0.259874i	0.707879	+	0.706334i	$0.249652\pi$
$558$	3.73831	+	2.15831i	0.158255	+	0.0913686i
$559$	−21.8997	+	37.9315i	−0.926261	+	1.60433i
$560$	2.96181	+	9.18662i	0.125159	+	0.388205i
$561$	6.10025			0.257553
$562$	25.6631	+	14.8166i	1.08253	+	0.625002i
$563$		−	44.5330i		−	1.87684i	−0.345494	−	0.938421i	$-0.612289\pi$
$563$		−	44.5330i		−	1.87684i	0.345494	−	0.938421i	$-0.387711\pi$
$564$	−2.31662	−	4.01251i	−0.0975475	−	0.168957i
$565$	−27.9499	+	30.8997i	−1.17586	+	1.29996i
$566$	1.68338			0.0707575
$567$	41.1214	−	23.7414i	1.72694	−	0.997047i
$568$	12.3986	+	7.15831i	0.520232	+	0.300356i
$569$	32.1662			1.34848			0.674240	−	0.738513i	$-0.264471\pi$
$569$	32.1662			1.34848			0.674240	+	0.738513i	$0.264471\pi$
$570$	−2.17708	+	10.1289i	−0.0911879	+	0.424254i
$571$	18.2665	+	31.6385i	0.764429	+	1.32403i	0.940548	+	0.339661i	$0.110312\pi$
$571$	18.2665	+	31.6385i	0.764429	+	1.32403i	−0.176119	+	0.984369i	$0.556354\pi$
$572$	−8.02502	+	4.63325i	−0.335543	+	0.193726i
$573$	−11.4891	−	6.63325i	−0.479965	−	0.277108i
$574$	−12.1583	+	21.0588i	−0.507478	+	0.878978i
$575$	17.5229	+	24.3505i	0.730755	+	1.01549i
$576$	−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	$0.211088\pi$
$578$		−	15.2665i		−	0.635003i
$579$	5.31662	−	9.20866i	0.220951	−	0.382699i
$580$	−1.55842	+	7.25061i	−0.0647100	+	0.301065i
$581$	28.6332			1.18791
$582$			19.8997i			0.824871i
$583$	−9.29548	+	5.36675i	−0.384980	+	0.222268i
$584$	−10.6332			−0.440007
$585$	−2.74456	−	8.51278i	−0.113474	−	0.351960i
$586$	−15.6332			−0.645804
$587$	−6.29297	−	3.63325i	−0.259739	−	0.149960i	0.364477	−	0.931213i	$-0.381248\pi$
$587$	−6.29297	−	3.63325i	−0.259739	−	0.149960i	−0.624215	+	0.781252i	$0.714581\pi$
$588$	20.1494	+	11.6332i	0.830946	+	0.479747i
$589$	5.00000	−	8.66025i	0.206021	−	0.356840i
$590$	−1.38437	−	0.297553i	−0.0569937	−	0.0122500i
$591$	−35.2665			−1.45067
$592$	−3.46410	+	5.00000i	−0.142374	+	0.205499i
$593$			29.8496i			1.22578i	0.790169	+	0.612889i	$0.209993\pi$
$593$			29.8496i			1.22578i	−0.790169	+	0.612889i	$0.790007\pi$
$594$	−4.63325	−	8.02502i	−0.190105	−	0.329271i
$595$	12.0953	−	3.89959i	0.495860	−	0.159868i
$596$	−1.97494	+	3.42069i	−0.0808966	+	0.140117i
$597$	−5.10933	−	2.94987i	−0.209111	−	0.120730i
$598$		−	24.0000i		−	0.981433i
$599$	−0.791562	+	1.37103i	−0.0323423	+	0.0560186i	−0.881744	−	0.471729i	$-0.843630\pi$
$599$	−0.791562	+	1.37103i	−0.0323423	+	0.0560186i	0.849401	+	0.527748i	$0.176963\pi$
$600$	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	$-0.419712\pi$
$602$		−	47.2665i		−	1.92644i
$603$		−	8.31662i		−	0.338679i
$604$	−1.31662	−	2.28046i	−0.0535727	−	0.0927906i
$605$	11.9886	−	3.86520i	0.487408	−	0.157143i
$606$	17.3668			0.705476
$607$	7.28923	−	4.20844i	0.295861	−	0.170815i	−0.344721	−	0.938705i	$-0.612027\pi$
$607$	7.28923	−	4.20844i	0.295861	−	0.170815i	0.640582	+	0.767890i	$0.278693\pi$
$608$	−2.00626	+	1.15831i	−0.0813644	+	0.0469758i
$609$	14.3166	+	24.7971i	0.580139	+	1.00483i
$610$	−5.45473	−	16.9189i	−0.220856	−	0.685025i
$611$	4.63325	−	8.02502i	0.187441	−	0.324658i
$612$	−1.14023	+	0.658312i	−0.0460911	+	0.0266107i
$613$	0.317615	−	0.183375i	0.0128284	−	0.00740645i	−0.493572	−	0.869705i	$-0.664309\pi$
$613$	0.317615	−	0.183375i	0.0128284	−	0.00740645i	0.506400	+	0.862298i	$0.330976\pi$
$614$	11.1583	+	19.3268i	0.450313	+	0.779965i
$615$	−16.8997	+	18.6834i	−0.681464	+	0.753386i
$616$	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	$0.591333\pi$
$618$			32.6332i			1.31270i
$619$	3.05013			0.122595			0.0612974	−	0.998120i	$-0.480476\pi$
$619$	3.05013			0.122595			0.0612974	+	0.998120i	$0.480476\pi$
$620$	2.02830	−	9.43675i	0.0814586	−	0.378989i
$621$	24.0000			0.963087
$622$	−20.4236	−	11.7916i	−0.818911	−	0.472799i
$623$		−	7.05013i		−	0.282457i
$624$	4.00000	−	6.92820i	0.160128	−	0.277350i
$625$	7.94158	−	23.7051i	0.317663	−	0.948204i
$626$	−11.9749	+	20.7412i	−0.478615	+	0.828985i
$627$	9.29548	−	5.36675i	0.371226	−	0.214327i
$628$		−	3.00000i		−	0.119713i
$629$	6.58312	+	4.56092i	0.262486	+	0.181856i
$630$	7.15831	+	6.47494i	0.285194	+	0.257968i
$631$	−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	$0.897118\pi$
$632$	7.75082	+	4.47494i	0.308311	+	0.178003i
$633$	−13.3080	−	7.68338i	−0.528945	−	0.305387i
$634$	10.8166	−	18.7349i	0.429583	−	0.744060i
$635$	−21.9499	+	24.2665i	−0.871054	+	0.962987i
$636$	4.63325	−	8.02502i	0.183720	−	0.318213i
$637$			46.5330i			1.84370i
$638$	6.65400	−	3.84169i	0.263434	−	0.152094i
$639$	14.3166			0.566357
$640$	−1.50000	+	1.65831i	−0.0592927	+	0.0655506i
$641$	−8.13325	−	14.0872i	−0.321244	−	0.556411i	0.659501	−	0.751704i	$-0.270768\pi$
$641$	−8.13325	−	14.0872i	−0.321244	−	0.556411i	−0.980745	+	0.195293i	$0.937434\pi$
$642$	−10.9407	−	6.31662i	−0.431796	−	0.249297i
$643$			22.8496i			0.901101i	0.892751	+	0.450551i	$0.148772\pi$
$643$			22.8496i			0.901101i	−0.892751	+	0.450551i	$0.851228\pi$
$644$	12.9499	+	22.4298i	0.510297	+	0.883860i
$645$	10.2903	−	47.8759i	0.405180	−	1.88511i
$646$	1.52506	+	2.64149i	0.0600028	+	0.103928i
$647$	−9.56969	−	5.52506i	−0.376223	−	0.217213i	0.299950	−	0.953955i	$-0.403030\pi$
$647$	−9.56969	−	5.52506i	−0.376223	−	0.217213i	−0.676174	+	0.736742i	$0.736363\pi$
$648$	9.52628	+	5.50000i	0.374228	+	0.216060i
$649$	0.733501	+	1.27046i	0.0287924	+	0.0498699i
$650$	−16.2337	+	11.6819i	−0.636738	+	0.458203i
$651$	−18.6332	−	32.2737i	−0.730295	−	1.26491i
$652$			24.2164i			0.948386i
$653$	9.43946	+	5.44987i	0.369395	+	0.213270i	0.673194	−	0.739466i	$-0.264922\pi$
$653$	9.43946	+	5.44987i	0.369395	+	0.213270i	−0.303799	+	0.952736i	$0.598255\pi$
$654$	15.9499	+	27.6260i	0.623689	+	1.08026i
$655$	−24.2665	−	21.9499i	−0.948171	−	0.857653i
$656$	−5.63325			−0.219941
$657$	−9.20866	+	5.31662i	−0.359264	+	0.207421i
$658$			10.0000i			0.389841i
$659$	−14.3166	+	24.7971i	−0.557697	+	0.965959i	0.439992	+	0.898002i	$0.354981\pi$
$659$	−14.3166	+	24.7971i	−0.557697	+	0.965959i	−0.997688	+	0.0679569i	$0.978352\pi$
$660$	6.94987	−	7.68338i	0.270523	−	0.299075i
$661$	−19.9749	+	34.5976i	−0.776935	+	1.34569i	0.156765	+	0.987636i	$0.449893\pi$
$661$	−19.9749	+	34.5976i	−0.776935	+	1.34569i	−0.933700	+	0.358055i	$0.883440\pi$
$662$	5.10933	+	2.94987i	0.198580	+	0.114650i
$663$	−9.12184	−	5.26650i	−0.354263	−	0.204534i
$664$	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
$668$	14.9532	−	8.63325i	0.578558	−	0.334030i
$669$	−26.6332	+	46.1301i	−1.02970	+	1.78349i
$670$	−17.6994	+	5.70637i	−0.683787	+	0.220456i
$671$	−9.20844	+	15.9495i	−0.355488	+	0.615723i
$672$			8.63325i			0.333035i
$673$	−41.4824	−	23.9499i	−1.59903	−	0.923200i	−0.991675	−	0.128769i	$-0.958898\pi$
$673$	−41.4824	−	23.9499i	−1.59903	−	0.923200i	−0.607354	−	0.794431i	$-0.707769\pi$
$674$	−7.94987			−0.306218
$675$	−11.6819	−	16.2337i	−0.449638	−	0.624835i
$676$	3.00000			0.115385
$677$		−	21.6332i		−	0.831433i	−0.909494	−	0.415717i	$-0.863531\pi$
$677$		−	21.6332i		−	0.831433i	0.909494	−	0.415717i	$-0.136469\pi$
$678$	−32.2737	+	18.6332i	−1.23947	+	0.715606i
$679$	21.4749	−	37.1957i	0.824132	−	1.42744i
$680$	2.18338	+	1.97494i	0.0837286	+	0.0757354i
$681$	−12.9499	−	22.4298i	−0.496240	−	0.859513i
$682$	−8.66025	+	5.00000i	−0.331618	+	0.191460i
$683$	−28.9970	+	16.7414i	−1.10954	+	0.640593i	−0.938710	−	0.344707i	$-0.887978\pi$
$683$	−28.9970	+	16.7414i	−1.10954	+	0.640593i	−0.170830	+	0.985301i	$0.554645\pi$
$684$	−1.15831	+	2.00626i	−0.0442892	+	0.0767111i
$685$	−3.21345	−	9.96713i	−0.122780	−	0.380825i
$686$	−10.0000	−	17.3205i	−0.381802	−	0.661300i
$687$	27.6260	−	15.9499i	1.05400	−	0.608526i
$688$	9.48287	−	5.47494i	0.361531	−	0.208730i
$689$	18.5330			0.706051
$690$	8.23369	+	25.5383i	0.313451	+	0.972228i
$691$	17.1583	+	29.7191i	0.652733	+	1.13057i	0.982457	+	0.186489i	$0.0597110\pi$
$691$	17.1583	+	29.7191i	0.652733	+	1.13057i	−0.329724	+	0.944077i	$0.606956\pi$
$692$			14.2665i			0.542331i
$693$		−	10.0000i		−	0.379869i
$694$	−5.63325	−	9.75707i	−0.213835	−	0.370373i
$695$	−33.0000	−	29.8496i	−1.25176	−	1.13226i
$696$	−3.31662	+	5.74456i	−0.125716	+	0.217747i
$697$			7.41688i			0.280934i
$698$	30.5851	+	17.6583i	1.15766	+	0.668377i
$699$	−8.05013	+	13.9432i	−0.304484	+	0.527381i
$700$	8.86832	−	19.6770i	0.335191	−	0.743721i
$701$	8.26650	+	14.3180i	0.312221	+	0.540783i	0.978843	−	0.204613i	$-0.0655936\pi$
$701$	8.26650	+	14.3180i	0.312221	+	0.540783i	−0.666622	+	0.745396i	$0.732260\pi$
$702$			16.0000i			0.603881i
$703$	14.0438	+	1.15831i	0.529672	+	0.0436866i
$704$	2.31662			0.0873111
$705$	−2.17708	+	10.1289i	−0.0819936	+	0.381478i
$706$	9.60819	−	16.6419i	0.361609	−	0.626325i
$707$	−32.4611	−	18.7414i	−1.22083	−	0.704844i
$708$	−1.09682	−	0.633250i	−0.0412210	−	0.0237990i
$709$	−18.5330			−0.696021			−0.348011	−	0.937491i	$-0.613143\pi$
$709$	−18.5330			−0.696021			−0.348011	+	0.937491i	$0.613143\pi$
$710$	−9.82322	−	30.4686i	−0.368659	−	1.14346i
$711$	8.94987			0.335647
$712$	1.41444	−	0.816625i	0.0530082	−	0.0306043i
$713$		−	25.8997i		−	0.969953i
$714$	11.3668			0.425390
$715$	20.2579	+	4.35416i	0.757601	+	0.162836i
$716$	−10.6332	+	18.4173i	−0.397383	+	0.688288i
$717$		−	3.36675i		−	0.125734i
$718$	4.01251	−	2.31662i	0.149746	−	0.0864557i
$719$	10.5831	+	18.3305i	0.394684	+	0.683613i	0.993061	−	0.117602i	$-0.0375208\pi$
$719$	10.5831	+	18.3305i	0.394684	+	0.683613i	−0.598377	+	0.801215i	$0.704187\pi$
$720$	−0.469882	+	2.18614i	−0.0175115	+	0.0814727i
$721$	35.2164	−	60.9965i	1.31153	−	2.27163i
$722$	−11.8067	−	6.81662i	−0.439401	−	0.253689i
$723$	−4.73456	+	2.73350i	−0.176080	+	0.101660i
$724$	3.34169	+	5.78797i	0.124193	+	0.215108i
$725$	13.4603	−	9.68614i	0.499902	−	0.359734i
$726$	11.2665			0.418139
$727$	14.4048	+	8.31662i	0.534245	+	0.308447i	0.742743	−	0.669576i	$-0.233524\pi$
$727$	14.4048	+	8.31662i	0.534245	+	0.308447i	−0.208498	+	0.978023i	$0.566858\pi$
$728$	−14.9532	+	8.63325i	−0.554203	+	0.319970i
$729$	−13.0000			−0.481481
$730$	17.6332	+	15.9499i	0.652636	+	0.590331i
$731$	−7.20844	−	12.4854i	−0.266614	−	0.461788i
$732$		−	15.8997i		−	0.587672i
$733$	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
$735$	−15.9641	−	49.5156i	−0.588844	−	1.82641i
$736$	−3.00000	+	5.19615i	−0.110581	+	0.191533i
$737$	16.6853	+	9.63325i	0.614610	+	0.354845i
$738$	−4.87854	+	2.81662i	−0.179581	+	0.103681i
$739$	11.8997			0.437739			0.218870	−	0.975754i	$-0.429763\pi$
$739$	11.8997			0.437739			0.218870	+	0.975754i	$0.429763\pi$
$740$	13.2446	−	3.09541i	0.486880	−	0.113790i
$741$	−18.5330			−0.680827
$742$	−17.3205	+	10.0000i	−0.635856	+	0.367112i
$743$	−25.5329	−	14.7414i	−0.936712	−	0.540811i	−0.0477838	−	0.998858i	$-0.515216\pi$
$743$	−25.5329	−	14.7414i	−0.936712	−	0.540811i	−0.888928	+	0.458047i	$0.848549\pi$
$744$	4.31662	−	7.47661i	0.158255	−	0.274106i
$745$	8.40610	−	2.71017i	0.307976	−	0.0992929i
$746$	22.8997			0.838419
$747$	5.74456	+	3.31662i	0.210183	+	0.121349i
$748$		−	3.05013i		−	0.111524i
$749$	13.6332	+	23.6135i	0.498148	+	0.862818i
$750$	13.2665	−	18.0000i	0.484424	−	0.657267i
$751$	−24.2164			−0.883668			−0.441834	−	0.897097i	$-0.645672\pi$
$751$	−24.2164			−0.883668			−0.441834	+	0.897097i	$0.645672\pi$
$752$	−2.00626	+	1.15831i	−0.0731606	+	0.0422393i
$753$	−7.47661	−	4.31662i	−0.272463	−	0.157307i
$754$	−13.2665			−0.483137
$755$	−1.23732	+	5.75665i	−0.0450306	+	0.209506i
$756$	−8.63325	−	14.9532i	−0.313988	−	0.543844i
$757$	−9.61310	+	5.55013i	−0.349394	+	0.201723i	−0.664418	−	0.747361i	$-0.731321\pi$
$757$	−9.61310	+	5.55013i	−0.349394	+	0.201723i	0.315024	+	0.949084i	$0.397987\pi$
$758$	−28.5354	−	16.4749i	−1.03645	−	0.598397i
$759$	13.8997	−	24.0751i	0.504529	−	0.873870i
$760$	5.06447	+	1.08854i	0.183708	+	0.0394855i
$761$	10.1332	+	17.5513i	0.367330	+	0.636234i	0.989147	−	0.146928i	$-0.0469386\pi$
$761$	10.1332	+	17.5513i	0.367330	+	0.636234i	−0.621817	+	0.783162i	$0.713605\pi$
$762$	−25.3455	+	14.6332i	−0.918172	+	0.530107i
$763$		−	68.8496i		−	2.49252i
$764$	−3.31662	+	5.74456i	−0.119991	+	0.207831i
$765$	2.87833	+	0.618658i	0.104066	+	0.0223676i
$766$	−23.6834			−0.855715
$767$		−	2.53300i		−	0.0914613i
$768$	−1.73205	+	1.00000i	−0.0625000	+	0.0360844i
$769$	2.73350			0.0985726			0.0492863	−	0.998785i	$-0.484305\pi$
$769$	2.73350			0.0985726			0.0492863	+	0.998785i	$0.484305\pi$
$770$	−21.2819	+	6.86141i	−0.766948	+	0.247268i
$771$	−33.3668			−1.20167
$772$	−4.60433	−	2.65831i	−0.165714	−	0.0956748i
$773$	31.3209	+	18.0831i	1.12653	+	0.650405i	0.943061	−	0.332620i	$-0.107933\pi$
$773$	31.3209	+	18.0831i	1.12653	+	0.650405i	0.183473	+	0.983025i	$0.441266\pi$
$774$	5.47494	−	9.48287i	0.196793	−	0.340855i
$775$	−17.5187	+	12.6066i	−0.629290	+	0.452843i
$776$	9.94987			0.357180
$777$	29.9065	−	43.1662i	1.07289	−	1.54858i
$778$			8.05013i			0.288611i
$779$	6.52506	+	11.3017i	0.233785	+	0.404927i
$780$	−17.0256	+	5.48913i	−0.609613	+	0.196542i
$781$	−16.5831	+	28.7228i	−0.593391	+	1.02778i
$782$	6.84138	+	3.94987i	0.244647	+	0.141247i
$783$		−	13.2665i		−	0.474106i
$784$	5.81662	−	10.0747i	0.207737	−	0.359810i
$785$	−4.50000	+	4.97494i	−0.160612	+	0.177563i
$786$	−14.6332	−	25.3455i	−0.521951	−	0.904045i
$787$			24.0000i			0.855508i	0.903895	+	0.427754i	$0.140695\pi$
$787$			24.0000i			0.855508i	−0.903895	+	0.427754i	$0.859305\pi$
$788$			17.6332i			0.628159i
$789$	13.2665	+	22.9783i	0.472300	+	0.818047i
$790$	−6.14087	−	19.0471i	−0.218482	−	0.677664i
$791$	80.4327			2.85986
$792$	2.00626	−	1.15831i	0.0712892	−	0.0411588i
$793$	27.5392	−	15.8997i	0.977945	−	0.564617i
$794$	−5.44987	−	9.43946i	−0.193409	−	0.334994i
$795$	−19.7209	+	6.35812i	−0.699429	+	0.225499i
$796$	−1.47494	+	2.55467i	−0.0522778	+	0.0905477i
$797$	−23.5267	+	13.5831i	−0.833357	+	0.481139i	−0.855001	−	0.518627i	$-0.826443\pi$
$797$	−23.5267	+	13.5831i	−0.833357	+	0.481139i	0.0216436	+	0.999766i	$0.493110\pi$
$798$	17.3205	−	10.0000i	0.613139	−	0.353996i
$799$	1.52506	+	2.64149i	0.0539528	+	0.0934491i
$800$	4.97494	−	0.500000i	0.175891	−	0.0176777i
$801$	0.816625	−	1.41444i	0.0288540	−	0.0499766i
$802$	9.29548	−	5.36675i	0.328235	−	0.189507i
$803$		−	24.6332i		−	0.869289i
$804$	−16.6332			−0.586609
$805$	12.1698	−	56.6205i	0.428930	−	1.99561i
$806$	17.2665			0.608186
$807$	43.7629	+	25.2665i	1.54053	+	0.889423i
$808$		−	8.68338i		−	0.305480i
$809$	0.949874	−	1.64523i	0.0333958	−	0.0578432i	−0.848844	−	0.528643i	$-0.822701\pi$
$809$	0.949874	−	1.64523i	0.0333958	−	0.0578432i	0.882240	+	0.470799i	$0.156034\pi$
$810$	−7.54755	−	23.4101i	−0.265194	−	0.822548i
$811$	−12.9499	+	22.4298i	−0.454732	+	0.787618i	−0.998673	−	0.0515052i	$-0.983598\pi$
$811$	−12.9499	+	22.4298i	−0.454732	+	0.787618i	0.543941	+	0.839123i	$0.316931\pi$
$812$	12.3986	−	7.15831i	0.435104	−	0.251208i
$813$			11.1662i			0.391617i
$814$	−11.5831	−	8.02502i	−0.405988	−	0.281277i
$815$	36.3246	−	40.1583i	1.27239	−	1.40668i
$816$	1.31662	+	2.28046i	0.0460911	+	0.0798321i
$817$	−21.9683	−	12.6834i	−0.768572	−	0.443735i
$818$	−27.8568	−	16.0831i	−0.973990	−	0.562333i
$819$	−8.63325	+	14.9532i	−0.301670	+	0.522508i
$820$	9.34169	+	8.44987i	0.326226	+	0.295082i
$821$	5.26650	−	9.12184i	0.183802	−	0.318355i	−0.759370	−	0.650659i	$-0.774493\pi$
$821$	5.26650	−	9.12184i	0.183802	−	0.318355i	0.943172	+	0.332304i	$0.107826\pi$
$822$		−	9.36675i		−	0.326703i
$823$	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	$0.254872\pi$
$824$	16.3166			0.568417
$825$	−23.0501	+	2.31662i	−0.802502	+	0.0806545i
$826$	1.36675	+	2.36728i	0.0475553	+	0.0823682i
$827$	22.9783	+	13.2665i	0.799032	+	0.461321i	0.843133	−	0.537706i	$-0.180709\pi$
$827$	22.9783	+	13.2665i	0.799032	+	0.461321i	−0.0441005	+	0.999027i	$0.514042\pi$
$828$			6.00000i			0.208514i
$829$	−27.9499	−	48.4106i	−0.970739	−	1.68137i	−0.693333	−	0.720617i	$-0.743859\pi$
$829$	−27.9499	−	48.4106i	−0.970739	−	1.68137i	−0.277406	−	0.960753i	$-0.589475\pi$
$830$	3.11684	−	14.5012i	0.108187	−	0.503345i
$831$	−7.63325	−	13.2212i	−0.264794	−	0.458638i
$832$	−3.46410	−	2.00000i	−0.120096	−	0.0693375i
$833$	−13.2646	−	7.65831i	−0.459591	−	0.265345i
$834$	−19.8997	−	34.4674i	−0.689072	−	1.19351i
$835$	−37.7470	−	8.11322i	−1.30629	−	0.280769i
$836$	−2.68338	−	4.64774i	−0.0928065	−	0.160746i
$837$			17.2665i			0.596818i
$838$	31.9995	+	18.4749i	1.10541	+	0.638206i
$839$	−9.94987	−	17.2337i	−0.343508	−	0.594973i	0.641574	−	0.767061i	$-0.278282\pi$
$839$	−9.94987	−	17.2337i	−0.343508	−	0.594973i	−0.985082	+	0.172088i	$0.944949\pi$
$840$	12.9499	−	14.3166i	0.446813	−	0.493970i
$841$	−18.0000			−0.620690
$842$	−1.77546	+	1.02506i	−0.0611864	+	0.0353260i
$843$		−	59.2665i		−	2.04125i
$844$	−3.84169	+	6.65400i	−0.132236	+	0.229040i
$845$	−4.97494	−	4.50000i	−0.171143	−	0.154805i
$846$	−1.15831	+	2.00626i	−0.0398236	+	0.0689765i
$847$	−21.0588	−	12.1583i	−0.723589	−	0.417765i
$848$	−4.01251	−	2.31662i	−0.137790	−	0.0795532i
$849$	−1.68338	−	2.91569i	−0.0577733	−	0.100066i
$850$	−0.658312	−	6.55013i	−0.0225799	−	0.224667i
$851$	33.0000	−	15.5885i	1.13123	−	0.534365i
$852$		−	28.6332i		−	0.980959i
$853$	−48.6414	+	28.0831i	−1.66545	+	0.961548i	−0.695406	+	0.718617i	$0.744775\pi$
$853$	−48.6414	+	28.0831i	−1.66545	+	0.961548i	−0.970044	+	0.242931i	$0.921891\pi$
$854$	−17.1583	+	29.7191i	−0.587145	+	1.01697i
$855$	4.93023	−	1.58953i	0.168610	−	0.0543608i
$856$	−3.15831	+	5.47036i	−0.107949	+	0.186973i
$857$			26.5831i			0.908062i	0.890986	+	0.454031i	$0.150015\pi$
$857$			26.5831i			0.908062i	−0.890986	+	0.454031i	$0.849985\pi$
$858$	16.0500	+	9.26650i	0.547940	+	0.316353i
$859$	24.9499			0.851279			0.425639	−	0.904893i	$-0.360049\pi$
$859$	24.9499			0.851279			0.425639	+	0.904893i	$0.360049\pi$
$860$	−23.9380	−	5.14515i	−0.816278	−	0.175448i
$861$	48.6332			1.65742
$862$			36.3166i			1.23695i
$863$	6.37979	−	3.68338i	0.217171	−	0.125384i	−0.387469	−	0.921883i	$-0.626651\pi$
$863$	6.37979	−	3.68338i	0.217171	−	0.125384i	0.604640	+	0.796499i	$0.293317\pi$
$864$	2.00000	−	3.46410i	0.0680414	−	0.117851i
$865$	21.3997	−	23.6583i	0.727613	−	0.804407i
$866$	1.97494	+	3.42069i	0.0671111	+	0.116240i
$867$	−26.4424	+	15.2665i	−0.898029	+	0.518477i
$868$	−16.1369	+	9.31662i	−0.547721	+	0.316227i
$869$	−10.3668	+	17.9557i	−0.351668	+	0.609107i
$870$	14.1168	−	4.55134i	0.478606	−	0.154305i
$871$	−16.6332	−	28.8096i	−0.563596	−	0.976177i
$872$	13.8130	−	7.97494i	0.467767	−	0.270065i
$873$	8.61684	−	4.97494i	0.291636	−	0.168376i
$874$	13.8997			0.470166
$875$	−44.2219	+	19.3281i	−1.49497	+	0.653410i
$876$	10.6332	+	18.4173i	0.359264	+	0.622264i
$877$		−	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
$879$	15.6332	+	27.0776i	0.527296	+	0.913304i
$880$	−3.84169	−	3.47494i	−0.129503	−	0.117140i
$881$	18.8166	−	32.5914i	0.633948	−	1.09803i	−0.352789	−	0.935703i	$-0.614767\pi$
$881$	18.8166	−	32.5914i	0.633948	−	1.09803i	0.986737	−	0.162327i	$-0.0519001\pi$
$882$		−	11.6332i		−	0.391712i
$883$	27.6260	+	15.9499i	0.929689	+	0.536756i	0.886713	−	0.462320i	$-0.152983\pi$
$883$	27.6260	+	15.9499i	0.929689	+	0.536756i	0.0429756	+	0.999076i	$0.486316\pi$
$884$	−2.63325	+	4.56092i	−0.0885658	+	0.153400i
$885$	0.868997	+	2.69536i	0.0292110	+	0.0906034i
$886$	0.633250	+	1.09682i	0.0212744	+	0.0368484i
$887$		−	31.2665i		−	1.04983i	−0.851156	−	0.524913i	$-0.824098\pi$
$887$		−	31.2665i		−	1.04983i	0.851156	−	0.524913i	$-0.175902\pi$
$888$	12.1244	+	1.00000i	0.406867	+	0.0335578i
$889$	63.1662			2.11853
$890$	−3.57051	−	0.767434i	−0.119684	−	0.0257245i
$891$	−12.7414	+	22.0688i	−0.426854	+	0.739333i
$892$	23.0651	+	13.3166i	0.772276	+	0.445874i
$893$	4.64774	+	2.68338i	0.155531	+	0.0897957i
$894$	7.89975			0.264207
$895$	45.2592	−	14.5918i	1.51285	−	0.487750i
$896$	4.31662			0.144208
$897$	−41.5692	+	24.0000i	−1.38796	+	0.801337i
$898$			13.2665i			0.442709i
$899$	−14.3166			−0.477486
$900$	4.05842	−	2.92048i	0.135281	−	0.0973494i
$901$	−3.05013	+	5.28297i	−0.101614	+	0.176001i
$902$		−	13.0501i		−	0.434522i
$903$	−81.8680	+	47.2665i	−2.72440	+	1.57293i
$904$	9.31662	+	16.1369i	0.309866	+	0.536704i
$905$	3.14040	−	14.6108i	0.104390	−	0.485679i
$906$	−2.63325	+	4.56092i	−0.0874839	+	0.151526i
$907$	−29.6322	−	17.1082i	−0.983923	−	0.568068i	−0.0804705	−	0.996757i	$-0.525642\pi$
$907$	−29.6322	−	17.1082i	−0.983923	−	0.568068i	−0.903452	+	0.428689i	$0.858976\pi$
$908$	−11.2149	+	6.47494i	−0.372180	+	0.214878i
$909$	−4.34169	−	7.52002i	−0.144005	−	0.249423i
$910$	37.7470	+	8.11322i	1.25130	+	0.268950i
$911$	−18.0000			−0.596367			−0.298183	−	0.954509i	$-0.596381\pi$
$911$	−18.0000			−0.596367			−0.298183	+	0.954509i	$0.596381\pi$
$912$	4.01251	+	2.31662i	0.132868	+	0.0767111i
$913$	−13.3080	+	7.68338i	−0.440430	+	0.254283i
$914$	29.9499			0.990654
$915$	−23.8496	+	26.3668i	−0.788444	+	0.871658i
$916$	−7.97494	−	13.8130i	−0.263499	−	0.456394i
$917$			63.1662i			2.08593i
$918$	−4.56092	−	2.63325i	−0.150533	−	0.0869102i
$919$	55.8997			1.84396			0.921981	−	0.387234i	$-0.126570\pi$
$919$	55.8997			1.84396			0.921981	+	0.387234i	$0.126570\pi$
$920$	12.7692	−	4.11684i	0.420987	−	0.135728i
$921$	22.3166	−	38.6535i	0.735358	−	1.27368i
$922$	−4.64774	−	2.68338i	−0.153065	−	0.0883723i
$923$	49.5942	−	28.6332i	1.63241	−	0.942475i
$924$	−20.0000			−0.657952
$925$	−26.6067	−	14.7337i	−0.874824	−	0.484441i
$926$	−10.2164			−0.335731
$927$	14.1306	−	8.15831i	0.464110	−	0.267954i
$928$	2.87228	+	1.65831i	0.0942873	+	0.0544368i
$929$	8.44987	−	14.6356i	0.277231	−	0.480179i	−0.693464	−	0.720491i	$-0.743916\pi$
$929$	8.44987	−	14.6356i	0.277231	−	0.480179i	0.970696	+	0.240312i	$0.0772498\pi$
$930$	−18.3732	+	5.92362i	−0.602482	+	0.194243i
$931$	−26.9499			−0.883246
$932$	6.97161	+	4.02506i	0.228363	+	0.131845i
$933$			47.1662i			1.54415i
$934$	6.94987	+	12.0375i	0.227407	+	0.393880i
$935$	−4.57519	+	5.05806i	−0.149625	+	0.165416i
$936$	−4.00000			−0.130744
$937$	−12.0809	+	6.97494i	−0.394667	+	0.227861i	−0.684180	−	0.729313i	$-0.739840\pi$
$937$	−12.0809	+	6.97494i	−0.394667	+	0.227861i	0.289513	+	0.957174i	$0.406507\pi$
$938$	31.0901	+	17.9499i	1.01513	+	0.586084i
$939$	47.8997			1.56315
$940$	5.06447	+	1.08854i	0.165185	+	0.0355043i
$941$	1.70844	+	2.95910i	0.0556935	+	0.0964640i	0.892528	−	0.450992i	$-0.148930\pi$
$941$	1.70844	+	2.95910i	0.0556935	+	0.0964640i	−0.836835	+	0.547456i	$0.815596\pi$
$942$	−5.19615	+	3.00000i	−0.169300	+	0.0977453i
$943$	29.2712	+	16.8997i	0.953202	+	0.550332i
$944$	−0.316625	+	0.548410i	−0.0103053	+	0.0178492i
$945$	−8.11322	+	37.7470i	−0.263923	+	1.22791i
$946$	12.6834	+	21.9683i	0.412372	+	0.714249i
$947$	18.4173	−	10.6332i	0.598483	−	0.345534i	−0.169962	−	0.985451i	$-0.554364\pi$
$947$	18.4173	−	10.6332i	0.598483	−	0.345534i	0.768444	+	0.639916i	$0.221031\pi$
$948$		−	17.8997i		−	0.581357i
$949$	−21.2665	+	36.8347i	−0.690340	+	1.19570i
$950$	−6.76566	−	9.40184i	−0.219507	−	0.305036i
$951$	−43.2665			−1.40301
$952$		−	5.68338i		−	0.184199i
$953$	11.0275	−	6.36675i	0.357217	−	0.206239i	−0.310642	−	0.950527i	$-0.600544\pi$
$953$	11.0275	−	6.36675i	0.357217	−	0.206239i	0.667859	+	0.744288i	$0.267211\pi$
$954$	−4.63325			−0.150007
$955$	14.1168	−	4.55134i	0.456810	−	0.147278i
$956$	−1.68338			−0.0544442
$957$	−13.3080	−	7.68338i	−0.430186	−	0.248368i
$958$	31.7253	+	18.3166i	1.02500	+	0.591783i
$959$	−10.1082	+	17.5079i	−0.326410	+	0.565359i
$960$	4.37228	+	0.939764i	0.141115	+	0.0303307i
$961$	−12.3668			−0.398927
$962$	10.3923	+	22.0000i	0.335061	+	0.709308i
$963$			6.31662i			0.203550i
$964$	1.36675	+	2.36728i	0.0440201	+	0.0762450i
$965$	3.64795	+	11.3148i	0.117432	+	0.364237i
$966$	25.8997	−	44.8597i	0.833311	−	1.44334i
$967$	2.36728	+	1.36675i	0.0761266	+	0.0439517i	0.537580	−	0.843213i	$-0.319339\pi$
$967$	2.36728	+	1.36675i	0.0761266	+	0.0439517i	−0.461454	+	0.887164i	$0.652672\pi$
$968$		−	5.63325i		−	0.181059i
$969$	3.05013	−	5.28297i	0.0979842	−	0.169714i
$970$	−16.5000	−	14.9248i	−0.529783	−	0.479207i
$971$	−9.94987	−	17.2337i	−0.319307	−	0.553055i	0.661037	−	0.750353i	$-0.270117\pi$
$971$	−9.94987	−	17.2337i	−0.319307	−	0.553055i	−0.980344	+	0.197298i	$0.936783\pi$
$972$		−	10.0000i		−	0.320750i
$973$			85.8997i			2.75382i
$974$	−9.00000	−	15.5885i	−0.288379	−	0.499486i
$975$	36.4674	+	16.4356i	1.16789	+	0.526362i
$976$	−7.94987			−0.254469
$977$	−51.7011	+	29.8496i	−1.65406	+	0.954974i	−0.678687	+	0.734428i	$0.737451\pi$
$977$	−51.7011	+	29.8496i	−1.65406	+	0.954974i	−0.975376	+	0.220547i	$0.929216\pi$
$978$	41.9440	−	24.2164i	1.34122	−	0.774354i
$979$	1.89181	+	3.27672i	0.0604626	+	0.104724i
$980$	−24.7578	+	7.98205i	−0.790859	+	0.254977i
$981$	7.97494	−	13.8130i	0.254620	−	0.441015i
$982$	−15.3143	+	8.84169i	−0.488697	+	0.282150i
$983$	−26.2550	+	15.1583i	−0.837403	+	0.483475i	−0.856381	−	0.516345i	$-0.827292\pi$
$983$	−26.2550	+	15.1583i	−0.837403	+	0.483475i	0.0189774	+	0.999820i	$0.493959\pi$
$984$	5.63325	+	9.75707i	0.179581	+	0.311044i
$985$	26.4499	−	29.2414i	0.842763	−	0.931710i
$986$	2.18338	−	3.78172i	0.0695328	−	0.120434i
$987$	17.3205	−	10.0000i	0.551318	−	0.318304i
$988$			9.26650i			0.294807i
$989$	−65.6992			−2.08911
$990$	−5.06447	−	1.08854i	−0.160959	−	0.0345961i
$991$	46.3166			1.47130			0.735648	−	0.677364i	$-0.236878\pi$
$991$	46.3166			1.47130			0.735648	+	0.677364i	$0.236878\pi$
$992$	−3.73831	−	2.15831i	−0.118691	−	0.0685265i
$993$		−	11.7995i		−	0.374446i
$994$	−30.8997	+	53.5199i	−0.980081	+	1.69755i
$995$	6.27791	−	2.02403i	0.199023	−	0.0641660i
$996$	6.63325	−	11.4891i	0.210183	−	0.364047i
$997$	27.5392	−	15.8997i	0.872174	−	0.503550i	0.00410416	−	0.999992i	$-0.498694\pi$
$997$	27.5392	−	15.8997i	0.872174	−	0.503550i	0.868070	+	0.496441i	$0.165360\pi$
$998$			2.94987i			0.0933766i
$999$	−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.359.1	yes	8
5.4	even	2	inner	370.2.n.e.359.3	yes	8
37.10	even	3	inner	370.2.n.e.269.3	yes	8
185.84	even	6	inner	370.2.n.e.269.1	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.n.e.269.1	✓	8	185.84	even	6	inner
370.2.n.e.269.3	yes	8	37.10	even	3	inner
370.2.n.e.359.1	yes	8	1.1	even	1	trivial
370.2.n.e.359.3	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)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(1.73205 + 1.00000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-2.12819 + 0.686141i) q^{5} -2.00000 q^{6} +(3.73831 + 2.15831i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(1.73205 + 1.00000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-2.12819 + 0.686141i) q^{5} -2.00000 q^{6} +(3.73831 + 2.15831i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(1.50000 - 1.65831i) q^{10} -2.31662 q^{11} +(1.73205 - 1.00000i) q^{12} +(3.46410 + 2.00000i) q^{13} -4.31662 q^{14} +(-4.37228 - 0.939764i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.14023 + 0.658312i) q^{17} +(-0.866025 - 0.500000i) q^{18} +(-1.15831 + 2.00626i) q^{19} +(-0.469882 + 2.18614i) q^{20} +(4.31662 + 7.47661i) q^{21} +(2.00626 - 1.15831i) q^{22} +6.00000i q^{23} +(-1.00000 + 1.73205i) q^{24} +(4.05842 - 2.92048i) q^{25} -4.00000 q^{26} -4.00000i q^{27} +(3.73831 - 2.15831i) q^{28} +3.31662 q^{29} +(4.25639 - 1.37228i) q^{30} -4.31662 q^{31} +(0.866025 + 0.500000i) q^{32} +(-4.01251 - 2.31662i) q^{33} +(0.658312 - 1.14023i) q^{34} +(-9.43675 - 2.02830i) q^{35} +1.00000 q^{36} +(-2.59808 - 5.50000i) q^{37} -2.31662i q^{38} +(4.00000 + 6.92820i) q^{39} +(-0.686141 - 2.12819i) q^{40} +(2.81662 - 4.87854i) q^{41} +(-7.47661 - 4.31662i) q^{42} +10.9499i q^{43} +(-1.15831 + 2.00626i) q^{44} +(-1.65831 - 1.50000i) q^{45} +(-3.00000 - 5.19615i) q^{46} -2.31662i q^{47} -2.00000i q^{48} +(5.81662 + 10.0747i) q^{49} +(-2.05446 + 4.55842i) q^{50} -2.63325 q^{51} +(3.46410 - 2.00000i) q^{52} +(4.01251 - 2.31662i) q^{53} +(2.00000 + 3.46410i) q^{54} +(4.93023 - 1.58953i) q^{55} +(-2.15831 + 3.73831i) q^{56} +(-4.01251 + 2.31662i) q^{57} +(-2.87228 + 1.65831i) q^{58} +(-0.316625 - 0.548410i) q^{59} +(-3.00000 + 3.31662i) q^{60} +(3.97494 - 6.88479i) q^{61} +(3.73831 - 2.15831i) q^{62} +4.31662i q^{63} -1.00000 q^{64} +(-8.74456 - 1.87953i) q^{65} +4.63325 q^{66} +(-7.20241 - 4.15831i) q^{67} +1.31662i q^{68} +(-6.00000 + 10.3923i) q^{69} +(9.18662 - 2.96181i) q^{70} +(7.15831 - 12.3986i) q^{71} +(-0.866025 + 0.500000i) q^{72} +10.6332i q^{73} +(5.00000 + 3.46410i) q^{74} +(9.94987 - 1.00000i) q^{75} +(1.15831 + 2.00626i) q^{76} +(-8.66025 - 5.00000i) q^{77} +(-6.92820 - 4.00000i) q^{78} +(4.47494 - 7.75082i) q^{79} +(1.65831 + 1.50000i) q^{80} +(5.50000 - 9.52628i) q^{81} +5.63325i q^{82} +(5.74456 - 3.31662i) q^{83} +8.63325 q^{84} +(1.97494 - 2.18338i) q^{85} +(-5.47494 - 9.48287i) q^{86} +(5.74456 + 3.31662i) q^{87} -2.31662i q^{88} +(-0.816625 - 1.41444i) q^{89} +(2.18614 + 0.469882i) q^{90} +(8.63325 + 14.9532i) q^{91} +(5.19615 + 3.00000i) q^{92} +(-7.47661 - 4.31662i) q^{93} +(1.15831 + 2.00626i) q^{94} +(1.08854 - 5.06447i) q^{95} +(1.00000 + 1.73205i) q^{96} -9.94987i q^{97} +(-10.0747 - 5.81662i) q^{98} +(-1.15831 - 2.00626i) 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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