LMFDB - Embedded newform 370.2.m.c.249.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(159,370)]

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, 5]))

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

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

chi := DirichletCharacter("370.159");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.m (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:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 37x^{14} + 559x^{12} + 4431x^{10} + 19684x^{8} + 48248x^{6} + 58656x^{4} + 25392x^{2} + 256 $ x^16 + 37x^14 + 559x^12 + 4431x^10 + 19684x^8 + 48248x^6 + 58656x^4 + 25392*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			249.5
Root			$-0.926756i$ of defining polynomial
Character	$\chi$	$=$	370.249
Dual form			370.2.m.c.159.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(0.802594 - 0.463378i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.82024 + 1.29873i) q^{5} +0.926756i q^{6} +(-3.13584 + 1.81048i) q^{7} +1.00000 q^{8} +(-1.07056 + 1.85427i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(0.802594 - 0.463378i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.82024 + 1.29873i) q^{5} +0.926756i q^{6} +(-3.13584 + 1.81048i) q^{7} +1.00000 q^{8} +(-1.07056 + 1.85427i) q^{9} +(-2.03486 + 0.927011i) q^{10} -2.25810 q^{11} +(-0.802594 - 0.463378i) q^{12} +(2.51617 + 4.35814i) q^{13} -3.62096i q^{14} +(2.06272 + 0.198895i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.941511 + 1.63075i) q^{17} +(-1.07056 - 1.85427i) q^{18} +(4.77801 - 2.75859i) q^{19} +(0.214614 - 2.22574i) q^{20} +(-1.67787 + 2.90616i) q^{21} +(1.12905 - 1.95557i) q^{22} +3.62975 q^{23} +(0.802594 - 0.463378i) q^{24} +(1.62658 + 4.72803i) q^{25} -5.03234 q^{26} +4.76457i q^{27} +(3.13584 + 1.81048i) q^{28} -0.243433i q^{29} +(-1.20361 + 1.68692i) q^{30} -6.15831i q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.81234 + 1.04635i) q^{33} +(-0.941511 - 1.63075i) q^{34} +(-8.05933 - 0.777110i) q^{35} +2.14112 q^{36} +(-5.63910 - 2.28048i) q^{37} +5.51718i q^{38} +(4.03893 + 2.33188i) q^{39} +(1.82024 + 1.29873i) q^{40} +(4.85186 + 8.40367i) q^{41} +(-1.67787 - 2.90616i) q^{42} +2.54413 q^{43} +(1.12905 + 1.95557i) q^{44} +(-4.35688 + 1.98484i) q^{45} +(-1.81488 + 3.14346i) q^{46} -4.91549i q^{47} +0.926756i q^{48} +(3.05568 - 5.29258i) q^{49} +(-4.90788 - 0.955354i) q^{50} +1.74510i q^{51} +(2.51617 - 4.35814i) q^{52} +(-10.6289 - 6.13660i) q^{53} +(-4.12624 - 2.38228i) q^{54} +(-4.11030 - 2.93267i) q^{55} +(-3.13584 + 1.81048i) q^{56} +(2.55654 - 4.42805i) q^{57} +(0.210819 + 0.121716i) q^{58} +(-1.09602 - 0.632789i) q^{59} +(-0.859113 - 1.88582i) q^{60} +(6.70938 - 3.87366i) q^{61} +(5.33325 + 3.07915i) q^{62} -7.75292i q^{63} +1.00000 q^{64} +(-1.08001 + 11.2007i) q^{65} -2.09271i q^{66} +(-5.14397 + 2.96987i) q^{67} +1.88302 q^{68} +(2.91322 - 1.68195i) q^{69} +(4.70266 - 6.59103i) q^{70} +(2.93377 + 5.08144i) q^{71} +(-1.07056 + 1.85427i) q^{72} -13.0609i q^{73} +(4.79450 - 3.74336i) q^{74} +(3.49635 + 3.04097i) q^{75} +(-4.77801 - 2.75859i) q^{76} +(7.08105 - 4.08825i) q^{77} +(-4.03893 + 2.33188i) q^{78} +(9.17120 - 5.29499i) q^{79} +(-2.03486 + 0.927011i) q^{80} +(-1.00389 - 1.73879i) q^{81} -9.70373 q^{82} +(7.77888 + 4.49114i) q^{83} +3.35575 q^{84} +(-3.83168 + 1.74558i) q^{85} +(-1.27206 + 2.20328i) q^{86} +(-0.112801 - 0.195378i) q^{87} -2.25810 q^{88} +(11.0224 + 6.36378i) q^{89} +(0.459516 - 4.76559i) q^{90} +(-15.7806 - 9.11095i) q^{91} +(-1.81488 - 3.14346i) q^{92} +(-2.85362 - 4.94262i) q^{93} +(4.25694 + 2.45775i) q^{94} +(12.2798 + 1.18407i) q^{95} +(-0.802594 - 0.463378i) q^{96} +16.1820 q^{97} +(3.05568 + 5.29258i) q^{98} +(2.41744 - 4.18712i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{2} + 3 q^{3} - 8 q^{4} + 6 q^{5} + 12 q^{7} + 16 q^{8} + 13 q^{9}+O(q^{10}) $ 16 * q - 8 * q^2 + 3 * q^3 - 8 * q^4 + 6 * q^5 + 12 * q^7 + 16 * q^8 + 13 * q^9	$ 16 q - 8 q^{2} + 3 q^{3} - 8 q^{4} + 6 q^{5} + 12 q^{7} + 16 q^{8} + 13 q^{9} - 6 q^{10} - 6 q^{11} - 3 q^{12} + 6 q^{13} - 9 q^{15} - 8 q^{16} + 13 q^{18} - 3 q^{19} - 6 q^{21} + 3 q^{22} + 22 q^{23} + 3 q^{24} - 6 q^{25} - 12 q^{26} - 12 q^{28} - 9 q^{30} - 8 q^{32} - 6 q^{33} + 12 q^{35} - 26 q^{36} - 16 q^{37} + 15 q^{39} + 6 q^{40} + 7 q^{41} - 6 q^{42} + 22 q^{43} + 3 q^{44} - 4 q^{45} - 11 q^{46} + 4 q^{49} - 6 q^{50} + 6 q^{52} - 3 q^{53} + 9 q^{54} - 25 q^{55} + 12 q^{56} - 18 q^{57} - 36 q^{58} + 15 q^{59} + 18 q^{60} + 12 q^{61} + 33 q^{62} + 16 q^{64} - 26 q^{65} - 24 q^{67} + 42 q^{69} - 18 q^{70} - 4 q^{71} + 13 q^{72} + 5 q^{74} - 10 q^{75} + 3 q^{76} + 24 q^{77} - 15 q^{78} - 6 q^{80} + 10 q^{81} - 14 q^{82} - 6 q^{83} + 12 q^{84} - 26 q^{85} - 11 q^{86} - 50 q^{87} - 6 q^{88} + 9 q^{89} + 5 q^{90} - 24 q^{91} - 11 q^{92} + 25 q^{93} - 27 q^{94} + 49 q^{95} - 3 q^{96} - 68 q^{97} + 4 q^{98} + 37 q^{99}+O(q^{100}) $ 16 * q - 8 * q^2 + 3 * q^3 - 8 * q^4 + 6 * q^5 + 12 * q^7 + 16 * q^8 + 13 * q^9 - 6 * q^10 - 6 * q^11 - 3 * q^12 + 6 * q^13 - 9 * q^15 - 8 * q^16 + 13 * q^18 - 3 * q^19 - 6 * q^21 + 3 * q^22 + 22 * q^23 + 3 * q^24 - 6 * q^25 - 12 * q^26 - 12 * q^28 - 9 * q^30 - 8 * q^32 - 6 * q^33 + 12 * q^35 - 26 * q^36 - 16 * q^37 + 15 * q^39 + 6 * q^40 + 7 * q^41 - 6 * q^42 + 22 * q^43 + 3 * q^44 - 4 * q^45 - 11 * q^46 + 4 * q^49 - 6 * q^50 + 6 * q^52 - 3 * q^53 + 9 * q^54 - 25 * q^55 + 12 * q^56 - 18 * q^57 - 36 * q^58 + 15 * q^59 + 18 * q^60 + 12 * q^61 + 33 * q^62 + 16 * q^64 - 26 * q^65 - 24 * q^67 + 42 * q^69 - 18 * q^70 - 4 * q^71 + 13 * q^72 + 5 * q^74 - 10 * q^75 + 3 * q^76 + 24 * q^77 - 15 * q^78 - 6 * q^80 + 10 * q^81 - 14 * q^82 - 6 * q^83 + 12 * q^84 - 26 * q^85 - 11 * q^86 - 50 * q^87 - 6 * q^88 + 9 * q^89 + 5 * q^90 - 24 * q^91 - 11 * q^92 + 25 * q^93 - 27 * q^94 + 49 * q^95 - 3 * q^96 - 68 * q^97 + 4 * q^98 + 37 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	0.802594	−	0.463378i	0.463378	−	0.267531i	−0.250086	−	0.968224i	$-0.580459\pi$
$3$	0.802594	−	0.463378i	0.463378	−	0.267531i	0.713464	+	0.700692i	$0.247125\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	1.82024	+	1.29873i	0.814038	+	0.580812i
$5$	1.82024	+	1.29873i	0.814038	+	0.580812i
$6$			0.926756i			0.378347i
$7$	−3.13584	+	1.81048i	−1.18524	+	0.684297i	−0.957220	−	0.289360i	$-0.906558\pi$
$7$	−3.13584	+	1.81048i	−1.18524	+	0.684297i	−0.228017	+	0.973657i	$0.573224\pi$
$8$	1.00000			0.353553
$9$	−1.07056	+	1.85427i	−0.356854	+	0.618089i
$10$	−2.03486	+	0.927011i	−0.643479	+	0.293147i
$11$	−2.25810			−0.680843			−0.340421	−	0.940273i	$-0.610570\pi$
$11$	−2.25810			−0.680843			−0.340421	+	0.940273i	$0.610570\pi$
$12$	−0.802594	−	0.463378i	−0.231689	−	0.133766i
$13$	2.51617	+	4.35814i	0.697860	+	1.20873i	0.969207	+	0.246248i	$0.0791976\pi$
$13$	2.51617	+	4.35814i	0.697860	+	1.20873i	−0.271347	+	0.962482i	$0.587469\pi$
$14$		−	3.62096i		−	0.967742i
$15$	2.06272	+	0.198895i	0.532593	+	0.0513545i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−0.941511	+	1.63075i	−0.228350	+	0.395514i	−0.957319	−	0.289033i	$-0.906666\pi$
$17$	−0.941511	+	1.63075i	−0.228350	+	0.395514i	0.728969	+	0.684546i	$0.240000\pi$
$18$	−1.07056	−	1.85427i	−0.252334	−	0.437055i
$19$	4.77801	−	2.75859i	1.09615	−	0.632863i	0.160944	−	0.986964i	$-0.448546\pi$
$19$	4.77801	−	2.75859i	1.09615	−	0.632863i	0.935208	+	0.354100i	$0.115213\pi$
$20$	0.214614	−	2.22574i	0.0479893	−	0.497692i
$21$	−1.67787	+	2.90616i	−0.366142	+	0.634177i
$22$	1.12905	−	1.95557i	0.240714	−	0.416929i
$23$	3.62975			0.756856			0.378428	−	0.925631i	$-0.376465\pi$
$23$	3.62975			0.756856			0.378428	+	0.925631i	$0.376465\pi$
$24$	0.802594	−	0.463378i	0.163829	−	0.0945867i
$25$	1.62658	+	4.72803i	0.325316	+	0.945605i
$26$	−5.03234			−0.986923
$27$			4.76457i			0.916941i
$28$	3.13584	+	1.81048i	0.592619	+	0.342149i
$29$		−	0.243433i		−	0.0452043i	−0.999745	−	0.0226021i	$-0.992805\pi$
$29$		−	0.243433i		−	0.0452043i	0.999745	−	0.0226021i	$-0.00719510\pi$
$30$	−1.20361	+	1.68692i	−0.219748	+	0.307989i
$31$		−	6.15831i		−	1.10606i	−0.833160	−	0.553032i	$-0.813471\pi$
$31$		−	6.15831i		−	1.10606i	0.833160	−	0.553032i	$-0.186529\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−1.81234	+	1.04635i	−0.315488	+	0.182147i
$34$	−0.941511	−	1.63075i	−0.161468	−	0.279670i
$35$	−8.05933	−	0.777110i	−1.36228	−	0.131356i
$36$	2.14112			0.356854
$37$	−5.63910	−	2.28048i	−0.927062	−	0.374908i
$37$	−5.63910	−	2.28048i	−0.927062	−	0.374908i
$38$			5.51718i			0.895004i
$39$	4.03893	+	2.33188i	0.646746	+	0.373399i
$40$	1.82024	+	1.29873i	0.287806	+	0.205348i
$41$	4.85186	+	8.40367i	0.757734	+	1.31243i	0.944004	+	0.329935i	$0.107027\pi$
$41$	4.85186	+	8.40367i	0.757734	+	1.31243i	−0.186270	+	0.982499i	$0.559640\pi$
$42$	−1.67787	−	2.90616i	−0.258901	−	0.448431i
$43$	2.54413			0.387976			0.193988	−	0.981004i	$-0.437858\pi$
$43$	2.54413			0.387976			0.193988	+	0.981004i	$0.437858\pi$
$44$	1.12905	+	1.95557i	0.170211	+	0.294814i
$45$	−4.35688	+	1.98484i	−0.649486	+	0.295883i
$46$	−1.81488	+	3.14346i	−0.267589	+	0.463478i
$47$		−	4.91549i		−	0.716998i	−0.933530	−	0.358499i	$-0.883289\pi$
$47$		−	4.91549i		−	0.716998i	0.933530	−	0.358499i	$-0.116711\pi$
$48$			0.926756i			0.133766i
$49$	3.05568	−	5.29258i	0.436525	−	0.756083i
$50$	−4.90788	−	0.955354i	−0.694079	−	0.135107i
$51$			1.74510i			0.244363i
$52$	2.51617	−	4.35814i	0.348930	−	0.604365i
$53$	−10.6289	−	6.13660i	−1.45999	−	0.842927i	−0.460982	−	0.887409i	$-0.652503\pi$
$53$	−10.6289	−	6.13660i	−1.45999	−	0.842927i	−0.999010	+	0.0444826i	$0.985836\pi$
$54$	−4.12624	−	2.38228i	−0.561510	−	0.324188i
$55$	−4.11030	−	2.93267i	−0.554232	−	0.395441i
$56$	−3.13584	+	1.81048i	−0.419045	+	0.241936i
$57$	2.55654	−	4.42805i	0.338622	−	0.586510i
$58$	0.210819	+	0.121716i	0.0276819	+	0.0159821i
$59$	−1.09602	−	0.632789i	−0.142690	−	0.0823822i	0.426955	−	0.904273i	$-0.359586\pi$
$59$	−1.09602	−	0.632789i	−0.142690	−	0.0823822i	−0.569645	+	0.821891i	$0.692919\pi$
$60$	−0.859113	−	1.88582i	−0.110911	−	0.243458i
$61$	6.70938	−	3.87366i	0.859048	−	0.495971i	−0.00464566	−	0.999989i	$-0.501479\pi$
$61$	6.70938	−	3.87366i	0.859048	−	0.495971i	0.863693	+	0.504018i	$0.168145\pi$
$62$	5.33325	+	3.07915i	0.677323	+	0.391053i
$63$		−	7.75292i		−	0.976776i
$64$	1.00000			0.125000
$65$	−1.08001	+	11.2007i	−0.133959	+	1.38928i
$66$		−	2.09271i		−	0.257595i
$67$	−5.14397	+	2.96987i	−0.628436	+	0.362828i	−0.780146	−	0.625597i	$-0.784855\pi$
$67$	−5.14397	+	2.96987i	−0.628436	+	0.362828i	0.151710	+	0.988425i	$0.451522\pi$
$68$	1.88302			0.228350
$69$	2.91322	−	1.68195i	0.350710	−	0.202483i
$70$	4.70266	−	6.59103i	0.562076	−	0.787779i
$71$	2.93377	+	5.08144i	0.348175	+	0.603056i	0.985925	−	0.167187i	$-0.0534683\pi$
$71$	2.93377	+	5.08144i	0.348175	+	0.603056i	−0.637751	+	0.770243i	$0.720135\pi$
$72$	−1.07056	+	1.85427i	−0.126167	+	0.218527i
$73$		−	13.0609i		−	1.52866i	−0.644825	−	0.764330i	$-0.723070\pi$
$73$		−	13.0609i		−	1.52866i	0.644825	−	0.764330i	$-0.276930\pi$
$74$	4.79450	−	3.74336i	0.557349	−	0.435157i
$75$	3.49635	+	3.04097i	0.403723	+	0.351141i
$76$	−4.77801	−	2.75859i	−0.548076	−	0.316432i
$77$	7.08105	−	4.08825i	0.806960	−	0.465899i
$78$	−4.03893	+	2.33188i	−0.457319	+	0.264033i
$79$	9.17120	−	5.29499i	1.03184	−	0.595733i	0.114329	−	0.993443i	$-0.463528\pi$
$79$	9.17120	−	5.29499i	1.03184	−	0.595733i	0.917511	+	0.397710i	$0.130195\pi$
$80$	−2.03486	+	0.927011i	−0.227504	+	0.103643i
$81$	−1.00389	−	1.73879i	−0.111543	−	0.193198i
$82$	−9.70373			−1.07160
$83$	7.77888	+	4.49114i	0.853843	+	0.492966i	0.861946	−	0.507001i	$-0.169246\pi$
$83$	7.77888	+	4.49114i	0.853843	+	0.492966i	−0.00810266	+	0.999967i	$0.502579\pi$
$84$	3.35575			0.366142
$85$	−3.83168	+	1.74558i	−0.415605	+	0.189335i
$86$	−1.27206	+	2.20328i	−0.137170	+	0.237586i
$87$	−0.112801	−	0.195378i	−0.0120936	−	0.0209467i
$88$	−2.25810			−0.240714
$89$	11.0224	+	6.36378i	1.16837	+	0.674559i	0.953296	−	0.302039i	$-0.0976672\pi$
$89$	11.0224	+	6.36378i	1.16837	+	0.674559i	0.215075	+	0.976598i	$0.431001\pi$
$90$	0.459516	−	4.76559i	0.0484372	−	0.502338i
$91$	−15.7806	−	9.11095i	−1.65426	−	0.955087i
$92$	−1.81488	−	3.14346i	−0.189214	−	0.327728i
$93$	−2.85362	−	4.94262i	−0.295907	−	0.512526i
$94$	4.25694	+	2.45775i	0.439070	+	0.253497i
$95$	12.2798	+	1.18407i	1.25988	+	0.121483i
$96$	−0.802594	−	0.463378i	−0.0819144	−	0.0472933i
$97$	16.1820			1.64303			0.821516	−	0.570185i	$-0.193128\pi$
$97$	16.1820			1.64303			0.821516	+	0.570185i	$0.193128\pi$
$98$	3.05568	+	5.29258i	0.308670	+	0.534632i
$99$	2.41744	−	4.18712i	0.242961	−	0.420822i
$100$	3.28130	−	3.77267i	0.328130	−	0.377267i
$101$	9.63711			0.958928			0.479464	−	0.877561i	$-0.340831\pi$
$101$	9.63711			0.958928			0.479464	+	0.877561i	$0.340831\pi$
$102$	−1.51130	−	0.872551i	−0.149641	−	0.0863955i
$103$	−10.3945			−1.02420			−0.512102	−	0.858925i	$-0.671133\pi$
$103$	−10.3945			−1.02420			−0.512102	+	0.858925i	$0.671133\pi$
$104$	2.51617	+	4.35814i	0.246731	+	0.427350i
$105$	−6.82847	+	3.11081i	−0.666391	+	0.303584i
$106$	10.6289	−	6.13660i	1.03237	−	0.596039i
$107$	−1.23783	+	0.714663i	−0.119666	+	0.0690891i	−0.558638	−	0.829412i	$-0.688676\pi$
$107$	−1.23783	+	0.714663i	−0.119666	+	0.0690891i	0.438972	+	0.898501i	$0.355343\pi$
$108$	4.12624	−	2.38228i	0.397047	−	0.229235i
$109$	−7.23804	−	4.17889i	−0.693279	−	0.400265i	0.111560	−	0.993758i	$-0.464415\pi$
$109$	−7.23804	−	4.17889i	−0.693279	−	0.400265i	−0.804839	+	0.593493i	$0.797748\pi$
$110$	4.59492	−	2.09328i	0.438108	−	0.199587i
$111$	−5.58263	+	0.782735i	−0.529880	+	0.0742939i
$112$		−	3.62096i		−	0.342149i
$113$	4.25810	−	7.37525i	0.400568	−	0.693805i	−0.593226	−	0.805036i	$-0.702146\pi$
$113$	4.25810	−	7.37525i	0.400568	−	0.693805i	0.993795	+	0.111231i	$0.0354793\pi$
$114$	2.55654	+	4.42805i	0.239442	+	0.414725i
$115$	6.60704	+	4.71408i	0.616109	+	0.439591i
$116$	−0.210819	+	0.121716i	−0.0195740	+	0.0113011i
$117$	−10.7749			−0.996136
$118$	1.09602	−	0.632789i	0.100897	−	0.0582530i
$119$		−	6.81835i		−	0.625037i
$120$	2.06272	+	0.198895i	0.188300	+	0.0181566i
$121$	−5.90098			−0.536453
$122$			7.74732i			0.701409i
$123$	7.78816	+	4.49649i	0.702234	+	0.405435i
$124$	−5.33325	+	3.07915i	−0.478940	+	0.276516i
$125$	−3.17968	+	10.7187i	−0.284399	+	0.958706i
$126$	6.71423	+	3.87646i	0.598151	+	0.345343i
$127$	−2.98727	−	1.72470i	−0.265077	−	0.153042i	0.361571	−	0.932344i	$-0.382240\pi$
$127$	−2.98727	−	1.72470i	−0.265077	−	0.153042i	−0.626648	+	0.779302i	$0.715574\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	2.04190	−	1.17889i	0.179780	−	0.103796i
$130$	−9.16009	−	6.53567i	−0.803393	−	0.573216i
$131$	−6.00535	−	3.46719i	−0.524690	−	0.302930i	0.214161	−	0.976798i	$-0.431298\pi$
$131$	−6.00535	−	3.46719i	−0.524690	−	0.302930i	−0.738851	+	0.673868i	$0.764632\pi$
$132$	1.81234	+	1.04635i	0.157744	+	0.0910735i
$133$	−9.98874	+	17.3010i	−0.866133	+	1.50019i
$134$		−	5.93975i		−	0.513116i
$135$	−6.18791	+	8.67268i	−0.532570	+	0.746425i
$136$	−0.941511	+	1.63075i	−0.0807339	+	0.139835i
$137$			10.9288i			0.933714i	0.884333	+	0.466857i	$0.154614\pi$
$137$			10.9288i			0.933714i	−0.884333	+	0.466857i	$0.845386\pi$
$138$			3.36390i			0.286354i
$139$	10.6422	−	18.4329i	0.902663	−	1.56346i	0.0786387	−	0.996903i	$-0.474943\pi$
$139$	10.6422	−	18.4329i	0.902663	−	1.56346i	0.824024	−	0.566555i	$-0.191724\pi$
$140$	3.35667	+	7.36814i	0.283690	+	0.622722i
$141$	−2.27773	−	3.94515i	−0.191820	−	0.332241i
$142$	−5.86754			−0.492393
$143$	−5.68177	−	9.84111i	−0.475133	−	0.822955i
$144$	−1.07056	−	1.85427i	−0.0892135	−	0.154522i
$145$	0.316154	−	0.443107i	0.0262552	−	0.0367980i
$146$	11.3111	+	6.53044i	0.936110	+	0.540463i
$147$		−	5.66373i		−	0.467137i
$148$	0.844597	+	6.02384i	0.0694254	+	0.495157i
$149$	−2.92539			−0.239658			−0.119829	−	0.992795i	$-0.538235\pi$
$149$	−2.92539			−0.239658			−0.119829	+	0.992795i	$0.538235\pi$
$150$	−4.38173	+	1.50744i	−0.357767	+	0.123082i
$151$	−7.02685	−	12.1709i	−0.571837	−	0.990451i	−0.996377	−	0.0850418i	$-0.972898\pi$
$151$	−7.02685	−	12.1709i	−0.571837	−	0.990451i	0.424540	−	0.905409i	$-0.360436\pi$
$152$	4.77801	−	2.75859i	0.387548	−	0.223751i
$153$	−2.01589	−	3.49163i	−0.162975	−	0.282281i
$154$			8.17649i			0.658880i
$155$	7.99800	−	11.2096i	0.642415	−	0.900378i
$156$		−	4.66375i		−	0.373399i
$157$	−5.02816	−	2.90301i	−0.401291	−	0.231685i	0.285750	−	0.958304i	$-0.407757\pi$
$157$	−5.02816	−	2.90301i	−0.401291	−	0.231685i	−0.687041	+	0.726619i	$0.741091\pi$
$158$			10.5900i			0.842494i
$159$	−11.3743			−0.902038
$160$	0.214614	−	2.22574i	0.0169668	−	0.175961i
$161$	−11.3823	+	6.57160i	−0.897054	+	0.517914i
$162$	2.00778			0.157746
$163$	3.68887	−	6.38931i	0.288935	−	0.500450i	−0.684621	−	0.728899i	$-0.740032\pi$
$163$	3.68887	−	6.38931i	0.288935	−	0.500450i	0.973556	+	0.228450i	$0.0733656\pi$
$164$	4.85186	−	8.40367i	0.378867	−	0.656217i
$165$	−4.65784	−	0.449126i	−0.362612	−	0.0349644i
$166$	−7.77888	+	4.49114i	−0.603758	+	0.348580i
$167$	11.3660	+	19.6864i	0.879525	+	1.52338i	0.851863	+	0.523765i	$0.175473\pi$
$167$	11.3660	+	19.6864i	0.879525	+	1.52338i	0.0276621	+	0.999617i	$0.491194\pi$
$168$	−1.67787	+	2.90616i	−0.129451	+	0.224215i
$169$	−6.16223	+	10.6733i	−0.474017	+	0.821022i
$170$	0.404124	−	4.19113i	0.0309949	−	0.321445i
$171$			11.8130i			0.903359i
$172$	−1.27206	−	2.20328i	−0.0969940	−	0.167999i
$173$	2.10249	+	1.21388i	0.159850	+	0.0922893i	0.577791	−	0.816185i	$-0.303915\pi$
$173$	2.10249	+	1.21388i	0.159850	+	0.0922893i	−0.417941	+	0.908474i	$0.637248\pi$
$174$	0.225603			0.0171029
$175$	−13.6607	−	11.8815i	−1.03265	−	0.898154i
$176$	1.12905	−	1.95557i	0.0851054	−	0.147407i
$177$	−1.17288			−0.0881593
$178$	−11.0224	+	6.36378i	−0.826162	+	0.476985i
$179$		−	1.36176i		−	0.101783i	−0.998704	−	0.0508914i	$-0.983794\pi$
$179$		−	1.36176i		−	0.101783i	0.998704	−	0.0508914i	$-0.0162063\pi$
$180$	3.89737	+	2.78075i	0.290493	+	0.207265i
$181$	6.98424	+	12.0971i	0.519135	+	0.899168i	0.999753	+	0.0222376i	$0.00707902\pi$
$181$	6.98424	+	12.0971i	0.519135	+	0.899168i	−0.480618	+	0.876930i	$0.659588\pi$
$182$	15.7806	−	9.11095i	1.16974	−	0.675349i
$183$	3.58994	−	6.21796i	0.265376	−	0.459645i
$184$	3.62975			0.267589
$185$	−7.30280	−	11.4747i	−0.536913	−	0.843638i
$186$	5.70725			0.418476
$187$	2.12603	−	3.68239i	0.155470	−	0.269283i
$188$	−4.25694	+	2.45775i	−0.310469	+	0.179250i
$189$	−8.62615	−	14.9409i	−0.627460	−	1.08679i
$190$	−7.16534	+	10.0426i	−0.519829	+	0.728567i
$191$			19.3302i			1.39868i	0.714789	+	0.699340i	$0.246523\pi$
$191$			19.3302i			1.39868i	−0.714789	+	0.699340i	$0.753477\pi$
$192$	0.802594	−	0.463378i	0.0579223	−	0.0334414i
$193$	−4.64364			−0.334257			−0.167128	−	0.985935i	$-0.553449\pi$
$193$	−4.64364			−0.334257			−0.167128	+	0.985935i	$0.553449\pi$
$194$	−8.09100	+	14.0140i	−0.580900	+	1.00615i
$195$	4.32335	+	9.49008i	0.309602	+	0.679599i
$196$	−6.11135			−0.436525
$197$	−0.00951163	−	0.00549154i	−0.000677676	−	0.000391256i	0.499661	−	0.866221i	$-0.333458\pi$
$197$	−0.00951163	−	0.00549154i	−0.000677676	−	0.000391256i	−0.500339	+	0.865830i	$0.666791\pi$
$198$	2.41744	+	4.18712i	0.171800	+	0.297566i
$199$			22.1923i			1.57317i	0.617480	+	0.786586i	$0.288154\pi$
$199$			22.1923i			1.57317i	−0.617480	+	0.786586i	$0.711846\pi$
$200$	1.62658	+	4.72803i	0.115017	+	0.334322i
$201$	−2.75235	+	4.76721i	−0.194136	+	0.336253i
$202$	−4.81856	+	8.34598i	−0.339032	+	0.587221i
$203$	0.440730	+	0.763366i	0.0309332	+	0.0535778i
$204$	1.51130	−	0.872551i	0.105812	−	0.0610908i
$205$	−2.08256	+	21.5980i	−0.145452	+	1.50847i
$206$	5.19726	−	9.00193i	0.362111	−	0.627194i
$207$	−3.88587	+	6.73053i	−0.270087	+	0.467804i
$208$	−5.03234			−0.348930
$209$	−10.7892	+	6.22917i	−0.746307	+	0.430881i
$210$	0.720192	−	7.46904i	0.0496980	−	0.515413i
$211$	−1.02716			−0.0707129			−0.0353564	−	0.999375i	$-0.511257\pi$
$211$	−1.02716			−0.0707129			−0.0353564	+	0.999375i	$0.511257\pi$
$212$			12.2732i			0.842927i
$213$	4.70926	+	2.71889i	0.322673	+	0.186295i
$214$		−	1.42933i		−	0.0977067i
$215$	4.63094	+	3.30415i	0.315827	+	0.225341i
$216$			4.76457i			0.324188i
$217$	11.1495	+	19.3115i	0.756877	+	1.31095i
$218$	7.23804	−	4.17889i	0.490222	−	0.283030i
$219$	−6.05213	−	10.4826i	−0.408965	−	0.708348i
$220$	−0.484621	+	5.02596i	−0.0326731	+	0.338850i
$221$	−9.47601			−0.637425
$222$	2.11345	−	5.22607i	0.141845	−	0.350751i
$223$		−	19.2090i		−	1.28633i	−0.765728	−	0.643164i	$-0.777621\pi$
$223$		−	19.2090i		−	1.28633i	0.765728	−	0.643164i	$-0.222379\pi$
$224$	3.13584	+	1.81048i	0.209522	+	0.120968i
$225$	−10.5084	−	2.04553i	−0.700558	−	0.136369i
$226$	4.25810	+	7.37525i	0.283245	+	0.490594i
$227$	6.25789	+	10.8390i	0.415351	+	0.719409i	0.995465	−	0.0951263i	$-0.0303255\pi$
$227$	6.25789	+	10.8390i	0.415351	+	0.719409i	−0.580114	+	0.814535i	$0.696992\pi$
$228$	−5.11308			−0.338622
$229$	10.9023	+	18.8833i	0.720443	+	1.24784i	0.960822	+	0.277165i	$0.0893947\pi$
$229$	10.9023	+	18.8833i	0.720443	+	1.24784i	−0.240380	+	0.970679i	$0.577272\pi$
$230$	−7.38604	+	3.36482i	−0.487021	+	0.221870i
$231$	3.78881	−	6.56241i	0.249285	−	0.431775i
$232$		−	0.243433i		−	0.0159821i
$233$			12.8618i			0.842605i	0.906920	+	0.421303i	$0.138427\pi$
$233$			12.8618i			0.842605i	−0.906920	+	0.421303i	$0.861573\pi$
$234$	5.38743	−	9.33130i	0.352187	−	0.610006i
$235$	6.38392	−	8.94740i	0.416441	−	0.583664i
$236$			1.26558i			0.0823822i
$237$	4.90717	−	8.49946i	0.318755	−	0.552099i
$238$	5.90486	+	3.40917i	0.382755	+	0.220984i
$239$	−23.3924	−	13.5056i	−1.51313	−	0.873606i	−0.999882	−	0.0153660i	$-0.995109\pi$
$239$	−23.3924	−	13.5056i	−1.51313	−	0.873606i	−0.513248	−	0.858240i	$-0.671558\pi$
$240$	−1.20361	+	1.68692i	−0.0776927	+	0.108890i
$241$	22.6395	−	13.0709i	1.45834	−	0.841972i	0.459409	−	0.888225i	$-0.348061\pi$
$241$	22.6395	−	13.0709i	1.45834	−	0.841972i	0.998930	+	0.0462525i	$0.0147279\pi$
$242$	2.95049	−	5.11040i	0.189665	−	0.328509i
$243$	−13.9901	−	8.07721i	−0.897468	−	0.518153i
$244$	−6.70938	−	3.87366i	−0.429524	−	0.247986i
$245$	12.4357	−	5.66529i	0.794490	−	0.361942i
$246$	−7.78816	+	4.49649i	−0.496555	+	0.286686i
$247$	24.0446	+	13.8822i	1.52992	+	0.883300i
$248$		−	6.15831i		−	0.391053i
$249$	8.32438			0.527536
$250$	−7.69279	−	8.11301i	−0.486535	−	0.513112i
$251$			3.26731i			0.206231i	0.994669	+	0.103115i	$0.0328811\pi$
$251$			3.26731i			0.206231i	−0.994669	+	0.103115i	$0.967119\pi$
$252$	−6.71423	+	3.87646i	−0.422956	+	0.244194i
$253$	−8.19635			−0.515300
$254$	2.98727	−	1.72470i	0.187438	−	0.108217i
$255$	−2.26642	+	3.17651i	−0.141929	+	0.198921i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	6.74513	−	11.6829i	0.420750	−	0.728760i	−0.575263	−	0.817968i	$-0.695100\pi$
$257$	6.74513	−	11.6829i	0.420750	−	0.728760i	0.996013	+	0.0892084i	$0.0284337\pi$
$258$			2.35779i			0.146789i
$259$	21.8121	−	3.05825i	1.35534	−	0.190030i
$260$	10.2401	−	4.66503i	0.635064	−	0.289313i
$261$	0.451389	+	0.260609i	0.0279403	+	0.0161313i
$262$	6.00535	−	3.46719i	0.371012	−	0.214204i
$263$	−3.28354	+	1.89575i	−0.202472	+	0.116897i	−0.597808	−	0.801639i	$-0.703961\pi$
$263$	−3.28354	+	1.89575i	−0.202472	+	0.116897i	0.395336	+	0.918537i	$0.370628\pi$
$264$	−1.81234	+	1.04635i	−0.111542	+	0.0643987i
$265$	−11.3774	−	24.9742i	−0.698908	−	1.53415i
$266$	−9.98874	−	17.3010i	−0.612449	−	1.06079i
$267$	11.7953			0.721863
$268$	5.14397	+	2.96987i	0.314218	+	0.181414i
$269$	−31.4914			−1.92006			−0.960032	−	0.279889i	$-0.909702\pi$
$269$	−31.4914			−1.92006			−0.960032	+	0.279889i	$0.909702\pi$
$270$	−4.41681	−	9.69522i	−0.268798	−	0.590032i
$271$	14.1991	−	24.5936i	0.862534	−	1.49395i	−0.00694054	−	0.999976i	$-0.502209\pi$
$271$	14.1991	−	24.5936i	0.862534	−	1.49395i	0.869475	−	0.493977i	$-0.164457\pi$
$272$	−0.941511	−	1.63075i	−0.0570875	−	0.0988784i
$273$	−16.8873			−1.02206
$274$	−9.46466	−	5.46442i	−0.571781	−	0.330118i
$275$	−3.67298	−	10.6764i	−0.221489	−	0.643809i
$276$	−2.91322	−	1.68195i	−0.175355	−	0.101241i
$277$	4.20783	+	7.28818i	0.252824	+	0.437904i	0.964302	−	0.264804i	$-0.0853072\pi$
$277$	4.20783	+	7.28818i	0.252824	+	0.437904i	−0.711478	+	0.702708i	$0.751974\pi$
$278$	10.6422	+	18.4329i	0.638279	+	1.10553i
$279$	11.4191	+	6.59284i	0.683646	+	0.394703i
$280$	−8.05933	−	0.777110i	−0.481637	−	0.0464412i
$281$	2.41011	+	1.39148i	0.143775	+	0.0830087i	0.570162	−	0.821532i	$-0.306880\pi$
$281$	2.41011	+	1.39148i	0.143775	+	0.0830087i	−0.426387	+	0.904541i	$0.640214\pi$
$282$	4.55546			0.271274
$283$	4.95306	+	8.57896i	0.294429	+	0.509966i	0.974852	−	0.222854i	$-0.0715372\pi$
$283$	4.95306	+	8.57896i	0.294429	+	0.509966i	−0.680423	+	0.732820i	$0.738204\pi$
$284$	2.93377	−	5.08144i	0.174087	−	0.301528i
$285$	10.4044	−	4.73988i	0.616303	−	0.280766i
$286$	11.3635			0.671940
$287$	−30.4294	−	17.5684i	−1.79619	−	1.03703i
$288$	2.14112			0.126167
$289$	6.72711	+	11.6517i	0.395713	+	0.685394i
$290$	0.225665	+	0.495351i	0.0132515	+	0.0290880i
$291$	12.9876	−	7.49838i	0.761345	−	0.439563i
$292$	−11.3111	+	6.53044i	−0.661930	+	0.382165i
$293$	23.7479	−	13.7109i	1.38737	−	0.800998i	0.394352	−	0.918960i	$-0.370969\pi$
$293$	23.7479	−	13.7109i	1.38737	−	0.800998i	0.993018	+	0.117961i	$0.0376359\pi$
$294$	4.90494	+	2.83187i	0.286062	+	0.165158i
$295$	−1.17321	−	2.57527i	−0.0683066	−	0.149938i
$296$	−5.63910	−	2.28048i	−0.327766	−	0.132550i
$297$		−	10.7589i		−	0.624293i
$298$	1.46270	−	2.53347i	0.0847318	−	0.146760i
$299$	9.13308	+	15.8190i	0.528180	+	0.914834i
$300$	0.885380	−	4.54841i	0.0511175	−	0.262603i
$301$	−7.97799	+	4.60610i	−0.459844	+	0.265491i
$302$	14.0537			0.808700
$303$	7.73469	−	4.46563i	0.444346	−	0.256544i
$304$			5.51718i			0.316432i
$305$	17.2436	+	1.66269i	0.987363	+	0.0952052i
$306$	4.03178			0.230482
$307$		−	21.6669i		−	1.23660i	−0.785944	−	0.618298i	$-0.787822\pi$
$307$		−	21.6669i		−	1.23660i	0.785944	−	0.618298i	$-0.212178\pi$
$308$	−7.08105	−	4.08825i	−0.403480	−	0.232949i
$309$	−8.34259	+	4.81660i	−0.474593	+	0.274007i
$310$	5.70882	+	12.5313i	0.324239	+	0.711729i
$311$	−0.0824368	−	0.0475949i	−0.00467456	−	0.00269886i	0.497661	−	0.867372i	$-0.334192\pi$
$311$	−0.0824368	−	0.0475949i	−0.00467456	−	0.00269886i	−0.502335	+	0.864673i	$0.667526\pi$
$312$	4.03893	+	2.33188i	0.228659	+	0.132017i
$313$	3.36879	−	5.83491i	0.190415	−	0.329809i	−0.754973	−	0.655756i	$-0.772350\pi$
$313$	3.36879	−	5.83491i	0.190415	−	0.329809i	0.945388	+	0.325947i	$0.105683\pi$
$314$	5.02816	−	2.90301i	0.283755	−	0.163826i
$315$	10.0690	−	14.1122i	0.567323	−	0.795133i
$316$	−9.17120	−	5.29499i	−0.515920	−	0.297867i
$317$	−3.55048	−	2.04987i	−0.199415	−	0.115132i	0.396968	−	0.917833i	$-0.370062\pi$
$317$	−3.55048	−	2.04987i	−0.199415	−	0.115132i	−0.596382	+	0.802700i	$0.703396\pi$
$318$	5.68713	−	9.85040i	0.318919	−	0.552383i
$319$			0.549695i			0.0307770i
$320$	1.82024	+	1.29873i	0.101755	+	0.0726014i
$321$	−0.662318	+	1.14717i	−0.0369670	+	0.0640287i
$322$		−	13.1432i		−	0.732441i
$323$			10.3890i			0.578057i
$324$	−1.00389	+	1.73879i	−0.0557716	+	0.0965992i
$325$	−16.5126	+	18.9854i	−0.915956	+	1.05312i
$326$	3.68887	+	6.38931i	0.204308	+	0.353871i
$327$	−7.74562			−0.428334
$328$	4.85186	+	8.40367i	0.267899	+	0.464015i
$329$	8.89940	+	15.4142i	0.490640	+	0.849813i
$330$	2.71787	−	3.80924i	0.149614	−	0.209692i
$331$	−1.70092	−	0.982028i	−0.0934911	−	0.0539771i	0.452526	−	0.891751i	$-0.350523\pi$
$331$	−1.70092	−	0.982028i	−0.0934911	−	0.0539771i	−0.546017	+	0.837774i	$0.683856\pi$
$332$		−	8.98228i		−	0.492966i
$333$	10.2656	−	8.01500i	0.562552	−	0.439219i
$334$	−22.7319			−1.24384
$335$	−13.2204	−	1.27476i	−0.722306	−	0.0696473i
$336$	−1.67787	−	2.90616i	−0.0915355	−	0.158544i
$337$	−2.72145	+	1.57123i	−0.148247	+	0.0855904i	−0.572289	−	0.820052i	$-0.693944\pi$
$337$	−2.72145	+	1.57123i	−0.148247	+	0.0855904i	0.424042	+	0.905643i	$0.360611\pi$
$338$	−6.16223	−	10.6733i	−0.335181	−	0.580550i
$339$		−	7.89244i		−	0.428659i
$340$	3.42756	+	2.44555i	0.185886	+	0.132628i
$341$			13.9061i			0.753056i
$342$	−10.2303	−	5.90648i	−0.553192	−	0.319386i
$343$		−	3.21777i		−	0.173743i
$344$	2.54413			0.137170
$345$	7.48718	+	0.721941i	0.403096	+	0.0388680i
$346$	−2.10249	+	1.21388i	−0.113031	+	0.0652584i
$347$	−22.5289			−1.20941			−0.604707	−	0.796448i	$-0.706710\pi$
$347$	−22.5289			−1.20941			−0.604707	+	0.796448i	$0.706710\pi$
$348$	−0.112801	+	0.195378i	−0.00604678	+	0.0104733i
$349$	−9.37813	+	16.2434i	−0.502000	+	0.869489i	0.497998	+	0.867178i	$0.334069\pi$
$349$	−9.37813	+	16.2434i	−0.502000	+	0.869489i	−0.999997	+	0.00231049i	$0.999265\pi$
$350$	17.1200	−	5.88978i	0.915102	−	0.314822i
$351$	−20.7646	+	11.9885i	−1.10833	+	0.639897i
$352$	1.12905	+	1.95557i	0.0601786	+	0.104232i
$353$	−10.6765	+	18.4922i	−0.568251	+	0.984240i	0.428488	+	0.903547i	$0.359046\pi$
$353$	−10.6765	+	18.4922i	−0.568251	+	0.984240i	−0.996739	+	0.0806922i	$0.974287\pi$
$354$	0.586441	−	1.01575i	0.0311690	−	0.0539863i
$355$	−1.25926	+	13.0597i	−0.0668346	+	0.693135i
$356$		−	12.7276i		−	0.674559i
$357$	−3.15947	−	5.47237i	−0.167217	−	0.289628i
$358$	1.17932	+	0.680881i	0.0623290	+	0.0359857i
$359$	−18.3277			−0.967301			−0.483650	−	0.875261i	$-0.660689\pi$
$359$	−18.3277			−0.967301			−0.483650	+	0.875261i	$0.660689\pi$
$360$	−4.35688	+	1.98484i	−0.229628	+	0.104610i
$361$	5.71961	−	9.90666i	0.301032	−	0.521403i
$362$	−13.9685			−0.734167
$363$	−4.73609	+	2.73439i	−0.248580	+	0.143518i
$364$			18.2219i			0.955087i
$365$	16.9626	−	23.7740i	0.887864	−	1.24439i
$366$	3.58994	+	6.21796i	0.187649	+	0.325018i
$367$	−21.4342	+	12.3750i	−1.11886	+	0.645972i	−0.941109	−	0.338104i	$-0.890214\pi$
$367$	−21.4342	+	12.3750i	−1.11886	+	0.645972i	−0.177747	+	0.984076i	$0.556881\pi$
$368$	−1.81488	+	3.14346i	−0.0946070	+	0.163864i
$369$	−20.7769			−1.08160
$370$	13.5888	−	0.587053i	0.706448	−	0.0305194i
$371$	44.4408			2.30725
$372$	−2.85362	+	4.94262i	−0.147953	+	0.256263i
$373$	22.9109	−	13.2276i	1.18628	−	0.684900i	0.228823	−	0.973468i	$-0.426512\pi$
$373$	22.9109	−	13.2276i	1.18628	−	0.684900i	0.957459	+	0.288568i	$0.0931790\pi$
$374$	2.12603	+	3.68239i	0.109934	+	0.190412i
$375$	2.41480	+	10.0761i	0.124700	+	0.520329i
$376$		−	4.91549i		−	0.253497i
$377$	1.06091	−	0.612518i	0.0546397	−	0.0315463i
$378$	17.2523			0.887363
$379$	9.58371	−	16.5995i	0.492282	−	0.852658i	−0.507678	−	0.861547i	$-0.669496\pi$
$379$	9.58371	−	16.5995i	0.492282	−	0.852658i	0.999960	+	0.00888907i	$0.00282952\pi$
$380$	−5.11448	−	11.2267i	−0.262367	−	0.575916i
$381$	−3.19675			−0.163774
$382$	−16.7404	−	9.66508i	−0.856514	−	0.494508i
$383$	−11.5490	−	20.0035i	−0.590127	−	1.02213i	−0.994215	−	0.107410i	$-0.965744\pi$
$383$	−11.5490	−	20.0035i	−0.590127	−	1.02213i	0.404088	−	0.914720i	$-0.367589\pi$
$384$			0.926756i			0.0472933i
$385$	18.1988	+	1.75479i	0.927496	+	0.0894326i
$386$	2.32182	−	4.02151i	0.118178	−	0.204690i
$387$	−2.72365	+	4.71750i	−0.138451	+	0.239804i
$388$	−8.09100	−	14.0140i	−0.410758	−	0.711454i
$389$	22.4950	−	12.9875i	1.14054	−	0.658492i	0.193977	−	0.981006i	$-0.437861\pi$
$389$	22.4950	−	12.9875i	1.14054	−	0.658492i	0.946565	+	0.322514i	$0.104528\pi$
$390$	−10.3803	−	1.00091i	−0.525628	−	0.0506830i
$391$	−3.41745	+	5.91920i	−0.172828	+	0.299347i
$392$	3.05568	−	5.29258i	0.154335	−	0.267316i
$393$	−6.42648			−0.324173
$394$	0.00951163	−	0.00549154i	0.000479189	−	0.000276660i
$395$	23.5706	+	2.27276i	1.18597	+	0.114355i
$396$	−4.83487			−0.242961
$397$			12.6422i			0.634492i	0.948343	+	0.317246i	$0.102758\pi$
$397$			12.6422i			0.634492i	−0.948343	+	0.317246i	$0.897242\pi$
$398$	−19.2191	−	11.0962i	−0.963368	−	0.556201i
$399$			18.5142i			0.926872i
$400$	−4.90788	−	0.955354i	−0.245394	−	0.0477677i
$401$			15.0083i			0.749480i	0.927130	+	0.374740i	$0.122268\pi$
$401$			15.0083i			0.749480i	−0.927130	+	0.374740i	$0.877732\pi$
$402$	−2.75235	−	4.76721i	−0.137275	−	0.237767i
$403$	26.8387	−	15.4953i	1.33693	−	0.771878i
$404$	−4.81856	−	8.34598i	−0.239732	−	0.415228i
$405$	0.430898	−	4.46880i	0.0214115	−	0.222056i
$406$	−0.881459			−0.0437461
$407$	12.7336	+	5.14955i	0.631184	+	0.255254i
$408$			1.74510i			0.0863955i
$409$	18.0019	+	10.3934i	0.890139	+	0.513922i	0.873988	−	0.485948i	$-0.161525\pi$
$409$	18.0019	+	10.3934i	0.890139	+	0.513922i	0.0161508	+	0.999870i	$0.494859\pi$
$410$	−17.6632	−	12.6026i	−0.872321	−	0.622396i
$411$	5.06419	+	8.77143i	0.249798	+	0.432663i
$412$	5.19726	+	9.00193i	0.256051	+	0.443493i
$413$	4.58261			0.225495
$414$	−3.88587	−	6.73053i	−0.190980	−	0.330788i
$415$	8.32667	+	18.2777i	0.408740	+	0.897215i
$416$	2.51617	−	4.35814i	0.123365	−	0.213675i
$417$		−	19.7255i		−	0.965963i
$418$		−	12.4583i		−	0.609357i
$419$	−8.93783	+	15.4808i	−0.436641	+	0.756285i	−0.997428	−	0.0716753i	$-0.977165\pi$
$419$	−8.93783	+	15.4808i	−0.436641	+	0.756285i	0.560787	+	0.827960i	$0.310499\pi$
$420$	6.10828	+	4.35822i	0.298054	+	0.212660i
$421$		−	29.8357i		−	1.45410i	−0.686583	−	0.727051i	$-0.740890\pi$
$421$		−	29.8357i		−	1.45410i	0.686583	−	0.727051i	$-0.259110\pi$
$422$	0.513582	−	0.889550i	0.0250008	−	0.0433026i
$423$	9.11463	+	5.26234i	0.443169	+	0.255864i
$424$	−10.6289	−	6.13660i	−0.516185	−	0.298020i
$425$	−9.24165	−	1.79895i	−0.448286	−	0.0872621i
$426$	−4.70926	+	2.71889i	−0.228164	+	0.131731i
$427$	−14.0264	+	24.2944i	−0.678783	+	1.17569i
$428$	1.23783	+	0.714663i	0.0598329	+	0.0345445i
$429$	−9.12031	−	5.26561i	−0.440333	−	0.254226i
$430$	−5.17695	+	2.35844i	−0.249654	+	0.113734i
$431$	−0.757968	+	0.437613i	−0.0365101	+	0.0210791i	−0.518144	−	0.855293i	$-0.673377\pi$
$431$	−0.757968	+	0.437613i	−0.0365101	+	0.0210791i	0.481634	+	0.876373i	$0.340044\pi$
$432$	−4.12624	−	2.38228i	−0.198524	−	0.114618i
$433$		−	7.02464i		−	0.337582i	−0.985652	−	0.168791i	$-0.946014\pi$
$433$		−	7.02464i		−	0.337582i	0.985652	−	0.168791i	$-0.0539864\pi$
$434$	−22.2990			−1.07039
$435$	0.0484176	−	0.502134i	0.00232145	−	0.0240755i
$436$			8.35777i			0.400265i
$437$	17.3430	−	10.0130i	0.829629	−	0.478986i
$438$	12.1043			0.578364
$439$	−31.4004	+	18.1290i	−1.49866	+	0.865251i	−0.999999	−	0.00154648i	$-0.999508\pi$
$439$	−31.4004	+	18.1290i	−1.49866	+	0.865251i	−0.498660	+	0.866798i	$0.666174\pi$
$440$	−4.11030	−	2.93267i	−0.195951	−	0.139810i
$441$	6.54258	+	11.3321i	0.311551	+	0.539623i
$442$	4.73801	−	8.20647i	0.225364	−	0.390342i
$443$			26.8433i			1.27536i	0.770299	+	0.637682i	$0.220107\pi$
$443$			26.8433i			1.27536i	−0.770299	+	0.637682i	$0.779893\pi$
$444$	3.46918	+	4.44333i	0.164640	+	0.210871i
$445$	11.7986	+	25.8988i	0.559306	+	1.22772i
$446$	16.6355	+	9.60449i	0.787712	+	0.454786i
$447$	−2.34791	+	1.35556i	−0.111052	+	0.0641160i
$448$	−3.13584	+	1.81048i	−0.148155	+	0.0855371i
$449$	−17.4410	+	10.0695i	−0.823089	+	0.475211i	−0.851481	−	0.524386i	$-0.824295\pi$
$449$	−17.4410	+	10.0695i	−0.823089	+	0.475211i	0.0283913	+	0.999597i	$0.490962\pi$
$450$	7.02567	−	8.07776i	0.331193	−	0.380789i
$451$	−10.9560	−	18.9763i	−0.515898	−	0.893561i
$452$	−8.51620			−0.400568
$453$	−11.2794	−	6.51218i	−0.529954	−	0.305969i
$454$	−12.5158			−0.587395
$455$	−16.8919	−	37.0790i	−0.791905	−	1.73829i
$456$	2.55654	−	4.42805i	0.119721	−	0.207363i
$457$	−6.88213	−	11.9202i	−0.321932	−	0.557603i	0.658954	−	0.752183i	$-0.270999\pi$
$457$	−6.88213	−	11.9202i	−0.321932	−	0.557603i	−0.980887	+	0.194580i	$0.937666\pi$
$458$	−21.8046			−1.01886
$459$	−7.76980	−	4.48589i	−0.362663	−	0.209384i
$460$	0.778998	−	8.07890i	0.0363210	−	0.376681i
$461$	−11.3932	−	6.57784i	−0.530632	−	0.306361i	0.210642	−	0.977563i	$-0.432445\pi$
$461$	−11.3932	−	6.57784i	−0.530632	−	0.306361i	−0.741274	+	0.671203i	$0.765778\pi$
$462$	3.78881	+	6.56241i	0.176271	+	0.305311i
$463$	−8.84138	−	15.3137i	−0.410894	−	0.711689i	0.584094	−	0.811686i	$-0.301450\pi$
$463$	−8.84138	−	15.3137i	−0.410894	−	0.711689i	−0.994988	+	0.0999970i	$0.968117\pi$
$464$	0.210819	+	0.121716i	0.00978702	+	0.00565054i
$465$	1.22486	−	12.7029i	0.0568014	−	0.589082i
$466$	−11.1387	−	6.43091i	−0.515988	−	0.297906i
$467$	−21.8479			−1.01100			−0.505500	−	0.862827i	$-0.668692\pi$
$467$	−21.8479			−1.01100			−0.505500	+	0.862827i	$0.668692\pi$
$468$	5.38743	+	9.33130i	0.249034	+	0.431340i
$469$	10.7538	−	18.6261i	0.496564	−	0.860074i
$470$	4.55671	+	10.0023i	0.210186	+	0.461373i
$471$	−5.38076			−0.247932
$472$	−1.09602	−	0.632789i	−0.0504486	−	0.0291265i
$473$	−5.74490			−0.264151
$474$	4.90717	+	8.49946i	0.225394	+	0.390393i
$475$	20.8145	+	18.1035i	0.955035	+	0.830646i
$476$	−5.90486	+	3.40917i	−0.270649	+	0.156259i
$477$	22.7578	−	13.1392i	1.04201	−	0.601603i
$478$	23.3924	−	13.5056i	1.06994	−	0.617733i
$479$	12.9567	+	7.48057i	0.592008	+	0.341796i	0.765891	−	0.642970i	$-0.222298\pi$
$479$	12.9567	+	7.48057i	0.592008	+	0.341796i	−0.173883	+	0.984766i	$0.555631\pi$
$480$	−0.859113	−	1.88582i	−0.0392130	−	0.0860754i
$481$	−4.25030	−	30.3140i	−0.193797	−	1.38220i
$482$			26.1419i			1.19073i
$483$	−6.09027	+	10.5487i	−0.277117	+	0.479980i
$484$	2.95049	+	5.11040i	0.134113	+	0.232291i
$485$	29.4552	+	21.0161i	1.33749	+	0.954293i
$486$	13.9901	−	8.07721i	0.634606	−	0.366390i
$487$	−20.9643			−0.949982			−0.474991	−	0.879991i	$-0.657549\pi$
$487$	−20.9643			−0.949982			−0.474991	+	0.879991i	$0.657549\pi$
$488$	6.70938	−	3.87366i	0.303719	−	0.175352i
$489$		−	6.83737i		−	0.309196i
$490$	−1.31158	+	13.6023i	−0.0592513	+	0.614490i
$491$	25.4588			1.14894			0.574469	−	0.818526i	$-0.305209\pi$
$491$	25.4588			1.14894			0.574469	+	0.818526i	$0.305209\pi$
$492$		−	8.99299i		−	0.405435i
$493$	0.396976	+	0.229194i	0.0178789	+	0.0103224i
$494$	−24.0446	+	13.8822i	−1.08182	+	0.624588i
$495$	9.83828	−	4.48198i	0.442198	−	0.201450i
$496$	5.33325	+	3.07915i	0.239470	+	0.138258i
$497$	−18.3997	−	10.6231i	−0.825339	−	0.476510i
$498$	−4.16219	+	7.20912i	−0.186512	+	0.323049i
$499$	−16.3730	+	9.45295i	−0.732956	+	0.423172i	−0.819503	−	0.573075i	$-0.805750\pi$
$499$	−16.3730	+	9.45295i	−0.732956	+	0.423172i	0.0865466	+	0.996248i	$0.472417\pi$
$500$	10.8725	−	2.60565i	0.486232	−	0.116528i
$501$	18.2445	+	10.5335i	0.815105	+	0.470601i
$502$	−2.82957	−	1.63365i	−0.126290	−	0.0729136i
$503$	−20.9214	+	36.2370i	−0.932841	+	1.61573i	−0.154402	+	0.988008i	$0.549345\pi$
$503$	−20.9214	+	36.2370i	−0.932841	+	1.61573i	−0.778439	+	0.627720i	$0.783988\pi$
$504$		−	7.75292i		−	0.345343i
$505$	17.5419	+	12.5160i	0.780604	+	0.556957i
$506$	4.09817	−	7.09825i	0.182186	−	0.315556i
$507$			11.4218i			0.507258i
$508$			3.44940i			0.153042i
$509$	19.3738	−	33.5564i	0.858729	−	1.48736i	−0.0144126	−	0.999896i	$-0.504588\pi$
$509$	19.3738	−	33.5564i	0.858729	−	1.48736i	0.873142	−	0.487466i	$-0.162079\pi$
$510$	−1.61773	−	3.55104i	−0.0716342	−	0.157243i
$511$	23.6465	+	40.9569i	1.04606	+	1.81183i
$512$	1.00000			0.0441942
$513$	13.1435	+	22.7652i	0.580299	+	1.00511i
$514$	6.74513	+	11.6829i	0.297515	+	0.515311i
$515$	−18.9206	−	13.4997i	−0.833741	−	0.594869i
$516$	−2.04190	−	1.17889i	−0.0898898	−	0.0518979i
$517$			11.0997i			0.488163i
$518$	−8.25752	+	20.4189i	−0.362815	+	0.897157i
$519$	2.24993			0.0987611
$520$	−1.08001	+	11.2007i	−0.0473617	+	0.491184i
$521$	−20.8258	−	36.0714i	−0.912395	−	1.58031i	−0.810671	−	0.585502i	$-0.800897\pi$
$521$	−20.8258	−	36.0714i	−0.912395	−	1.58031i	−0.101724	−	0.994813i	$-0.532436\pi$
$522$	−0.451389	+	0.260609i	−0.0197568	+	0.0114066i
$523$	1.53396	+	2.65690i	0.0670755	+	0.116178i	0.897613	−	0.440785i	$-0.145300\pi$
$523$	1.53396	+	2.65690i	0.0670755	+	0.116178i	−0.830537	+	0.556963i	$0.811967\pi$
$524$			6.93439i			0.302930i
$525$	−16.4696	−	3.20593i	−0.718793	−	0.139918i
$526$		−	3.79151i		−	0.165318i
$527$	10.0426	+	5.79811i	0.437464	+	0.252570i
$528$		−	2.09271i		−	0.0910735i
$529$	−9.82489			−0.427169
$530$	27.3170	+	2.63401i	1.18658	+	0.114414i
$531$	2.34672	−	1.35488i	0.101839	−	0.0587968i
$532$	19.9775			0.866133
$533$	−24.4162	+	42.2901i	−1.05758	+	1.83179i
$534$	−5.89767	+	10.2151i	−0.255217	+	0.442049i
$535$	−3.18131	−	0.306754i	−0.137540	−	0.0132621i
$536$	−5.14397	+	2.96987i	−0.222186	+	0.128279i
$537$	−0.631011	−	1.09294i	−0.0272301	−	0.0471640i
$538$	15.7457	−	27.2724i	0.678845	−	1.17579i
$539$	−6.90002	+	11.9512i	−0.297205	+	0.514774i
$540$	10.6047	+	1.02255i	0.456354	+	0.0440033i
$541$		−	29.2582i		−	1.25791i	−0.777442	−	0.628955i	$-0.783483\pi$
$541$		−	29.2582i		−	1.25791i	0.777442	−	0.628955i	$-0.216517\pi$
$542$	14.1991	+	24.5936i	0.609904	+	1.05638i
$543$	11.2110	+	6.47269i	0.481111	+	0.277770i
$544$	1.88302			0.0807339
$545$	−7.74774	−	17.0069i	−0.331877	−	0.728495i
$546$	8.44363	−	14.6248i	0.361354	−	0.625884i
$547$	9.65489			0.412813			0.206407	−	0.978466i	$-0.433823\pi$
$547$	9.65489			0.412813			0.206407	+	0.978466i	$0.433823\pi$
$548$	9.46466	−	5.46442i	0.404310	−	0.233429i
$549$			16.5880i			0.707957i
$550$	11.0825	+	2.15729i	0.472559	+	0.0919870i
$551$	−0.671530	−	1.16312i	−0.0286081	−	0.0495508i
$552$	2.91322	−	1.68195i	0.123995	−	0.0715885i
$553$	−19.1730	+	33.2085i	−0.815317	+	1.41217i
$554$	−8.41567			−0.357547
$555$	−11.1783	−	5.82558i	−0.474493	−	0.247282i
$556$	−21.2845			−0.902663
$557$	10.1286	−	17.5432i	0.429162	−	0.743330i	−0.567637	−	0.823279i	$-0.692142\pi$
$557$	10.1286	−	17.5432i	0.429162	−	0.743330i	0.996799	+	0.0799491i	$0.0254758\pi$
$558$	−11.4191	+	6.59284i	−0.483411	+	0.279097i
$559$	6.40146	+	11.0877i	0.270753	+	0.468958i
$560$	4.70266	−	6.59103i	0.198724	−	0.278522i
$561$		−	3.94062i		−	0.166373i
$562$	−2.41011	+	1.39148i	−0.101664	+	0.0586960i
$563$	25.8348			1.08881			0.544404	−	0.838823i	$-0.316756\pi$
$563$	25.8348			1.08881			0.544404	+	0.838823i	$0.316756\pi$
$564$	−2.27773	+	3.94515i	−0.0959098	+	0.166121i
$565$	17.3293	−	7.89461i	0.729048	−	0.332129i
$566$	−9.90612			−0.416385
$567$	6.29607	+	3.63504i	0.264410	+	0.152657i
$568$	2.93377	+	5.08144i	0.123098	+	0.213213i
$569$		−	22.5479i		−	0.945259i	−0.881261	−	0.472629i	$-0.843305\pi$
$569$		−	22.5479i		−	0.945259i	0.881261	−	0.472629i	$-0.156695\pi$
$570$	−1.09734	+	11.3804i	−0.0459625	+	0.476673i
$571$	−3.93155	+	6.80964i	−0.164530	+	0.284974i	−0.936488	−	0.350699i	$-0.885944\pi$
$571$	−3.93155	+	6.80964i	−0.164530	+	0.284974i	0.771958	+	0.635673i	$0.219277\pi$
$572$	−5.68177	+	9.84111i	−0.237567	+	0.411477i
$573$	8.95717	+	15.5143i	0.374191	+	0.648118i
$574$	30.4294	−	17.5684i	1.27010	−	0.733291i
$575$	5.90408	+	17.1616i	0.246217	+	0.715687i
$576$	−1.07056	+	1.85427i	−0.0446067	+	0.0772611i
$577$	17.2865	−	29.9411i	0.719646	−	1.24646i	−0.241494	−	0.970402i	$-0.577637\pi$
$577$	17.2865	−	29.9411i	0.719646	−	1.24646i	0.961140	−	0.276061i	$-0.0890293\pi$
$578$	−13.4542			−0.559622
$579$	−3.72696	+	2.15176i	−0.154887	+	0.0894242i
$580$	−0.541819	−	0.0522441i	−0.0224978	−	0.00216932i
$581$	−32.5245			−1.34934
$582$			14.9968i			0.621636i
$583$	24.0011	+	13.8571i	0.994025	+	0.573901i
$584$		−	13.0609i		−	0.540463i
$585$	−19.6129	−	13.9937i	−0.810893	−	0.578567i
$586$			27.4218i			1.13278i
$587$	−2.43100	−	4.21062i	−0.100338	−	0.173791i	0.811486	−	0.584372i	$-0.198659\pi$
$587$	−2.43100	−	4.21062i	−0.100338	−	0.173791i	−0.911824	+	0.410581i	$0.865326\pi$
$588$	−4.90494	+	2.83187i	−0.202276	+	0.116784i
$589$	−16.9882	−	29.4245i	−0.699988	−	1.21241i
$590$	2.81686	+	0.271612i	0.115968	+	0.0111821i
$591$	−0.0101786			−0.000418693
$592$	4.79450	−	3.74336i	0.197053	−	0.153851i
$593$		−	18.8663i		−	0.774746i	−0.921923	−	0.387373i	$-0.873383\pi$
$593$		−	18.8663i		−	0.774746i	0.921923	−	0.387373i	$-0.126617\pi$
$594$	9.31746	+	5.37944i	0.382300	+	0.220721i
$595$	8.85522	−	12.4111i	0.363029	−	0.508804i
$596$	1.46270	+	2.53347i	0.0599144	+	0.103775i
$597$	10.2834	+	17.8114i	0.420873	+	0.728974i
$598$	−18.2662			−0.746959
$599$	7.64354	+	13.2390i	0.312306	+	0.540931i	0.978861	−	0.204525i	$-0.0655651\pi$
$599$	7.64354	+	13.2390i	0.312306	+	0.540931i	−0.666555	+	0.745456i	$0.732232\pi$
$600$	3.49635	+	3.04097i	0.142738	+	0.124147i
$601$	−17.1292	+	29.6686i	−0.698714	+	1.21021i	0.270199	+	0.962804i	$0.412910\pi$
$601$	−17.1292	+	29.6686i	−0.698714	+	1.21021i	−0.968913	+	0.247403i	$0.920423\pi$
$602$		−	9.21219i		−	0.375461i
$603$		−	12.7177i		−	0.517906i
$604$	−7.02685	+	12.1709i	−0.285919	+	0.495225i
$605$	−10.7412	−	7.66381i	−0.436693	−	0.311578i
$606$			8.93125i			0.362807i
$607$	−12.8372	+	22.2347i	−0.521047	+	0.902480i	0.478653	+	0.878004i	$0.341125\pi$
$607$	−12.8372	+	22.2347i	−0.521047	+	0.902480i	−0.999700	+	0.0244759i	$0.992208\pi$
$608$	−4.77801	−	2.75859i	−0.193774	−	0.111876i
$609$	0.707454	+	0.408449i	0.0286675	+	0.0165512i
$610$	−10.0617	+	14.1020i	−0.407387	+	0.570974i
$611$	21.4224	−	12.3682i	0.866657	−	0.500364i
$612$	−2.01589	+	3.49163i	−0.0814876	+	0.141141i
$613$	1.42691	+	0.823827i	0.0576324	+	0.0332741i	0.528539	−	0.848909i	$-0.322740\pi$
$613$	1.42691	+	0.823827i	0.0576324	+	0.0332741i	−0.470907	+	0.882183i	$0.656073\pi$
$614$	18.7641	+	10.8335i	0.757257	+	0.437203i
$615$	8.33660	+	18.2995i	0.336164	+	0.737906i
$616$	7.08105	−	4.08825i	0.285304	−	0.164720i
$617$	4.12835	+	2.38351i	0.166201	+	0.0959563i	0.580793	−	0.814051i	$-0.302742\pi$
$617$	4.12835	+	2.38351i	0.166201	+	0.0959563i	−0.414592	+	0.910007i	$0.636076\pi$
$618$		−	9.63319i		−	0.387504i
$619$	−5.33041			−0.214247			−0.107124	−	0.994246i	$-0.534164\pi$
$619$	−5.33041			−0.214247			−0.107124	+	0.994246i	$0.534164\pi$
$620$	−13.7068	−	1.32166i	−0.550479	−	0.0530792i
$621$			17.2942i			0.693993i
$622$	0.0824368	−	0.0475949i	0.00330542	−	0.00190838i
$623$	−46.0859			−1.84639
$624$	−4.03893	+	2.33188i	−0.161687	+	0.0933498i
$625$	−19.7085	+	15.3810i	−0.788339	+	0.615241i
$626$	3.36879	+	5.83491i	0.134644	+	0.233210i
$627$	−5.77292	+	9.99899i	−0.230548	+	0.399321i
$628$			5.80602i			0.231685i
$629$	9.02815	−	7.04883i	0.359976	−	0.281055i
$630$	7.18704	+	15.7761i	0.286339	+	0.628535i
$631$	−33.5323	−	19.3599i	−1.33490	−	0.770705i	−0.348854	−	0.937177i	$-0.613429\pi$
$631$	−33.5323	−	19.3599i	−1.33490	−	0.770705i	−0.986046	+	0.166472i	$0.946762\pi$
$632$	9.17120	−	5.29499i	0.364811	−	0.210623i
$633$	−0.824396	+	0.475965i	−0.0327668	+	0.0189179i
$634$	3.55048	−	2.04987i	0.141007	−	0.0814107i
$635$	−3.19763	−	7.01904i	−0.126894	−	0.278542i
$636$	5.68713	+	9.85040i	0.225509	+	0.390594i
$637$	30.7544			1.21853
$638$	−0.476050	−	0.274848i	−0.0188470	−	0.0108813i
$639$	−12.5631			−0.496990
$640$	−2.03486	+	0.927011i	−0.0804349	+	0.0366433i
$641$	−12.2108	+	21.1497i	−0.482298	+	0.835364i	−0.999793	−	0.0203216i	$-0.993531\pi$
$641$	−12.2108	+	21.1497i	−0.482298	+	0.835364i	0.517496	+	0.855686i	$0.326864\pi$
$642$	−0.662318	−	1.14717i	−0.0261396	−	0.0452751i
$643$	4.80535			0.189504			0.0947522	−	0.995501i	$-0.469794\pi$
$643$	4.80535			0.189504			0.0947522	+	0.995501i	$0.469794\pi$
$644$	11.3823	+	6.57160i	0.448527	+	0.258957i
$645$	5.24783	+	0.506015i	0.206633	+	0.0199243i
$646$	−8.99711	−	5.19448i	−0.353986	−	0.204374i
$647$	−19.9678	−	34.5853i	−0.785016	−	1.35969i	−0.928990	−	0.370105i	$-0.879322\pi$
$647$	−19.9678	−	34.5853i	−0.785016	−	1.35969i	0.143974	−	0.989581i	$-0.454012\pi$
$648$	−1.00389	−	1.73879i	−0.0394365	−	0.0683059i
$649$	2.47493	+	1.42890i	0.0971495	+	0.0560893i
$650$	−8.18550	−	23.7930i	−0.321062	−	0.933240i
$651$	17.8970	+	10.3329i	0.701440	+	0.404977i
$652$	−7.37774			−0.288935
$653$	−9.64037	−	16.6976i	−0.377257	−	0.653428i	0.613405	−	0.789768i	$-0.289799\pi$
$653$	−9.64037	−	16.6976i	−0.377257	−	0.653428i	−0.990662	+	0.136341i	$0.956466\pi$
$654$	3.87281	−	6.70790i	0.151439	−	0.262300i
$655$	−6.42825	−	14.1105i	−0.251173	−	0.551343i
$656$	−9.70373			−0.378867
$657$	24.2184	+	13.9825i	0.944848	+	0.545508i
$658$	−17.7988			−0.693869
$659$	13.7323	+	23.7851i	0.534936	+	0.926536i	0.999166	+	0.0408215i	$0.0129975\pi$
$659$	13.7323	+	23.7851i	0.534936	+	0.926536i	−0.464231	+	0.885714i	$0.653669\pi$
$660$	1.93996	+	4.25837i	0.0755130	+	0.165757i
$661$	−6.22869	+	3.59614i	−0.242268	+	0.139873i	−0.616219	−	0.787575i	$-0.711336\pi$
$661$	−6.22869	+	3.59614i	−0.242268	+	0.139873i	0.373951	+	0.927449i	$0.378003\pi$
$662$	1.70092	−	0.982028i	0.0661082	−	0.0381676i
$663$	−7.60539	+	4.39098i	−0.295369	+	0.170531i
$664$	7.77888	+	4.49114i	0.301879	+	0.174290i
$665$	−40.6513	+	18.5193i	−1.57639	+	0.718149i
$666$	1.80839	+	12.8978i	0.0700735	+	0.499779i
$667$		−	0.883600i		−	0.0342131i
$668$	11.3660	−	19.6864i	0.439763	−	0.761691i
$669$	−8.90102	−	15.4170i	−0.344133	−	0.596057i
$670$	7.71415	−	10.8118i	0.298024	−	0.417696i
$671$	−15.1504	+	8.74711i	−0.584876	+	0.337679i
$672$	3.35575			0.129451
$673$	31.8817	−	18.4069i	1.22895	−	0.709533i	0.262138	−	0.965030i	$-0.415573\pi$
$673$	31.8817	−	18.4069i	1.22895	−	0.709533i	0.966810	+	0.255497i	$0.0822392\pi$
$674$		−	3.14246i		−	0.121043i
$675$	−22.5270	+	7.74995i	−0.867065	+	0.298296i
$676$	12.3245			0.474017
$677$		−	5.49722i		−	0.211275i	−0.994405	−	0.105638i	$-0.966312\pi$
$677$		−	5.49722i		−	0.211275i	0.994405	−	0.105638i	$-0.0336884\pi$
$678$	6.83506	+	3.94622i	0.262499	+	0.151554i
$679$	−50.7442	+	29.2972i	−1.94738	+	1.12432i
$680$	−3.83168	+	1.74558i	−0.146938	+	0.0669400i
$681$	10.0451	+	5.79954i	0.384929	+	0.222239i
$682$	−12.0430	−	6.95304i	−0.461151	−	0.266246i
$683$	20.3464	−	35.2410i	0.778532	−	1.34846i	−0.154255	−	0.988031i	$-0.549298\pi$
$683$	20.3464	−	35.2410i	0.778532	−	1.34846i	0.932788	−	0.360427i	$-0.117369\pi$
$684$	10.2303	−	5.90648i	0.391166	−	0.225840i
$685$	−14.1937	+	19.8932i	−0.542312	+	0.760079i
$686$	2.78667	+	1.60888i	0.106395	+	0.0614274i
$687$	17.5002	+	10.1038i	0.667675	+	0.385482i
$688$	−1.27206	+	2.20328i	−0.0484970	+	0.0839993i
$689$		−	61.7629i		−	2.35298i
$690$	−4.36881	+	6.12311i	−0.166318	+	0.233103i
$691$	14.5580	−	25.2152i	0.553812	−	0.959231i	−0.444183	−	0.895936i	$-0.646506\pi$
$691$	14.5580	−	25.2152i	0.553812	−	0.959231i	0.997995	−	0.0632944i	$-0.0201607\pi$
$692$		−	2.42775i		−	0.0922893i
$693$			17.5069i			0.665031i
$694$	11.2644	−	19.5106i	0.427592	−	0.740612i
$695$	43.3109	−	19.7309i	1.64288	−	0.748437i
$696$	−0.112801	−	0.195378i	−0.00427572	−	0.00740577i
$697$	−18.2723			−0.692114
$698$	−9.37813	−	16.2434i	−0.354967	−	0.614821i
$699$	5.95988	+	10.3228i	0.225423	+	0.390445i
$700$	−3.45930	+	17.7712i	−0.130749	+	0.671690i
$701$	−5.47829	−	3.16289i	−0.206912	−	0.119461i	0.392963	−	0.919554i	$-0.371450\pi$
$701$	−5.47829	−	3.16289i	−0.206912	−	0.119461i	−0.599876	+	0.800093i	$0.704783\pi$
$702$		−	23.9769i		−	0.904951i
$703$	−33.2346	+	4.65979i	−1.25347	+	0.175747i
$704$	−2.25810			−0.0851054
$705$	0.977668	−	10.1393i	0.0368211	−	0.381868i
$706$	−10.6765	−	18.4922i	−0.401814	−	0.695963i
$707$	−30.2205	+	17.4478i	−1.13656	+	0.656192i
$708$	0.586441	+	1.01575i	0.0220398	+	0.0381741i
$709$			35.0427i			1.31605i	0.752994	+	0.658027i	$0.228609\pi$
$709$			35.0427i			1.31605i	−0.752994	+	0.658027i	$0.771391\pi$
$710$	−10.6804	−	7.62038i	−0.400827	−	0.285988i
$711$			22.6745i			0.850359i
$712$	11.0224	+	6.36378i	0.413081	+	0.238493i
$713$		−	22.3531i		−	0.837131i
$714$	6.31895			0.236481
$715$	2.43878	−	25.2923i	0.0912051	−	0.945879i
$716$	−1.17932	+	0.680881i	−0.0440733	+	0.0254457i
$717$	−25.0328			−0.934869
$718$	9.16386	−	15.8723i	0.341992	−	0.592348i
$719$	18.4292	−	31.9203i	0.687294	−	1.19043i	−0.285416	−	0.958404i	$-0.592132\pi$
$719$	18.4292	−	31.9203i	0.687294	−	1.19043i	0.972710	−	0.232024i	$-0.0745349\pi$
$720$	0.459516	−	4.76559i	0.0171252	−	0.177603i
$721$	32.5956	−	18.8191i	1.21392	−	0.700859i
$722$	5.71961	+	9.90666i	0.212862	+	0.368688i
$723$	12.1136	−	20.9813i	0.450508	−	0.780303i
$724$	6.98424	−	12.0971i	0.259567	−	0.449584i
$725$	1.15096	−	0.395962i	0.0427454	−	0.0147057i
$726$		−	5.46877i		−	0.202965i
$727$	−11.4755	−	19.8761i	−0.425601	−	0.737163i	0.570875	−	0.821037i	$-0.306604\pi$
$727$	−11.4755	−	19.8761i	−0.425601	−	0.737163i	−0.996476	+	0.0838739i	$0.973271\pi$
$728$	−15.7806	−	9.11095i	−0.584869	−	0.337674i
$729$	−8.94788			−0.331403
$730$	12.1076	+	26.5771i	0.448122	+	0.983661i
$731$	−2.39533	+	4.14883i	−0.0885944	+	0.153450i
$732$	−7.17988			−0.265376
$733$	−19.8366	+	11.4527i	−0.732681	+	0.423014i	−0.819402	−	0.573219i	$-0.805694\pi$
$733$	−19.8366	+	11.4527i	−0.732681	+	0.423014i	0.0867210	+	0.996233i	$0.472361\pi$
$734$		−	24.7501i		−	0.913542i
$735$	7.35568	−	10.3094i	0.271318	−	0.380267i
$736$	−1.81488	−	3.14346i	−0.0668972	−	0.115869i
$737$	11.6156	−	6.70627i	0.427866	−	0.247029i
$738$	10.3884	−	17.9933i	0.382404	−	0.662342i
$739$	2.03791			0.0749656			0.0374828	−	0.999297i	$-0.488066\pi$
$739$	2.03791			0.0749656			0.0374828	+	0.999297i	$0.488066\pi$
$740$	−6.28599	+	12.0618i	−0.231078	+	0.443399i
$741$	25.7307			0.945242
$742$	−22.2204	+	38.4868i	−0.815736	+	1.41290i
$743$	7.91455	−	4.56947i	0.290357	−	0.167638i	−0.347746	−	0.937589i	$-0.613053\pi$
$743$	7.91455	−	4.56947i	0.290357	−	0.167638i	0.638103	+	0.769951i	$0.279720\pi$
$744$	−2.85362	−	4.94262i	−0.104619	−	0.181205i
$745$	−5.32493	−	3.79931i	−0.195090	−	0.139196i
$746$			26.4552i			0.968595i
$747$	−16.6555	+	9.61608i	−0.609394	+	0.351834i
$748$	−4.25205			−0.155470
$749$	2.58777	−	4.48214i	0.0945549	−	0.163774i
$750$	−9.93358	−	2.94679i	−0.362723	−	0.107601i
$751$	−23.2533			−0.848525			−0.424262	−	0.905539i	$-0.639467\pi$
$751$	−23.2533			−0.848525			−0.424262	+	0.905539i	$0.639467\pi$
$752$	4.25694	+	2.45775i	0.155235	+	0.0896248i
$753$	1.51400	+	2.62232i	0.0551732	+	0.0955628i
$754$			1.22504i			0.0446132i
$755$	3.01613	−	31.2800i	0.109768	−	1.13839i
$756$	−8.62615	+	14.9409i	−0.313730	+	0.543397i
$757$	19.2812	−	33.3960i	0.700786	−	1.21380i	−0.267405	−	0.963584i	$-0.586166\pi$
$757$	19.2812	−	33.3960i	0.700786	−	1.21380i	0.968191	−	0.250213i	$-0.0805006\pi$
$758$	9.58371	+	16.5995i	0.348096	+	0.602920i
$759$	−6.57834	+	3.79801i	−0.238779	+	0.137859i
$760$	12.2798	+	1.18407i	0.445436	+	0.0429506i
$761$	6.39309	−	11.0731i	0.231749	−	0.401401i	−0.726574	−	0.687088i	$-0.758888\pi$
$761$	6.39309	−	11.0731i	0.231749	−	0.401401i	0.958323	+	0.285687i	$0.0922218\pi$
$762$	1.59838	−	2.76847i	0.0579030	−	0.100291i
$763$	30.2632			1.09560
$764$	16.7404	−	9.66508i	0.605647	−	0.349670i
$765$	0.865279	−	8.97372i	0.0312842	−	0.324445i
$766$	23.0980			0.834566
$767$		−	6.36882i		−	0.229965i
$768$	−0.802594	−	0.463378i	−0.0289611	−	0.0167207i
$769$			29.6480i			1.06913i	0.845126	+	0.534567i	$0.179525\pi$
$769$			29.6480i			1.06913i	−0.845126	+	0.534567i	$0.820475\pi$
$770$	−10.6191	+	14.8832i	−0.382685	+	0.536354i
$771$		−	12.5022i		−	0.450255i
$772$	2.32182	+	4.02151i	0.0835642	+	0.144737i
$773$	−14.0777	+	8.12774i	−0.506338	+	0.292335i	−0.731327	−	0.682027i	$-0.761099\pi$
$773$	−14.0777	+	8.12774i	−0.506338	+	0.292335i	0.224989	+	0.974361i	$0.427765\pi$
$774$	−2.72365	−	4.71750i	−0.0978995	−	0.169567i
$775$	29.1166	−	10.0170i	1.04590	−	0.359820i
$776$	16.1820			0.580900
$777$	16.0891	−	12.5618i	0.577194	−	0.450651i
$778$			25.9750i			0.931248i
$779$	46.3645	+	26.7686i	1.66118	+	0.959084i
$780$	6.05697	−	8.48917i	0.216874	−	0.303961i
$781$	−6.62475	−	11.4744i	−0.237052	−	0.410587i
$782$	−3.41745	−	5.91920i	−0.122208	−	0.211670i
$783$	1.15985			0.0414497
$784$	3.05568	+	5.29258i	0.109131	+	0.189021i
$785$	−5.38224	−	11.8144i	−0.192100	−	0.421675i
$786$	3.21324	−	5.56550i	0.114613	−	0.198515i
$787$			2.72161i			0.0970148i	0.998823	+	0.0485074i	$0.0154464\pi$
$787$			2.72161i			0.0970148i	−0.998823	+	0.0485074i	$0.984554\pi$
$788$			0.0109831i			0.000391256i
$789$	−1.75690	+	3.04304i	−0.0625474	+	0.108335i
$790$	−13.7536	+	19.2764i	−0.489330	+	0.685822i
$791$			30.8368i			1.09643i
$792$	2.41744	−	4.18712i	0.0858998	−	0.148783i
$793$	33.7639	+	19.4936i	1.19899	+	0.692237i
$794$	−10.9484	−	6.32109i	−0.388546	−	0.224327i
$795$	−20.7039	−	14.7721i	−0.734293	−	0.523914i
$796$	19.2191	−	11.0962i	0.681204	−	0.393293i
$797$	−1.69524	+	2.93624i	−0.0600484	+	0.104007i	−0.894487	−	0.447094i	$-0.852459\pi$
$797$	−1.69524	+	2.93624i	−0.0600484	+	0.104007i	0.834438	+	0.551101i	$0.185792\pi$
$798$	−16.0338	−	9.25712i	−0.567591	−	0.327699i
$799$	8.01591	+	4.62799i	0.283583	+	0.163727i
$800$	3.28130	−	3.77267i	0.116012	−	0.133384i
$801$	−23.6003	+	13.6256i	−0.833875	+	0.481438i
$802$	−12.9976	−	7.50417i	−0.458961	−	0.264981i
$803$			29.4928i			1.04078i
$804$	5.50470			0.194136
$805$	−29.2534	−	2.82072i	−1.03105	−	0.0994173i
$806$			30.9907i			1.09160i
$807$	−25.2748	+	14.5924i	−0.889716	+	0.513678i
$808$	9.63711			0.339032
$809$	28.1719	−	16.2651i	0.990472	−	0.571849i	0.0850564	−	0.996376i	$-0.472893\pi$
$809$	28.1719	−	16.2651i	0.990472	−	0.571849i	0.905415	+	0.424527i	$0.139560\pi$
$810$	3.65464	+	2.60757i	0.128411	+	0.0916206i
$811$	−10.1732	−	17.6205i	−0.357229	−	0.618738i	0.630268	−	0.776378i	$-0.282945\pi$
$811$	−10.1732	−	17.6205i	−0.357229	−	0.618738i	−0.987497	+	0.157639i	$0.949612\pi$
$812$	0.440730	−	0.763366i	0.0154666	−	0.0267889i
$813$		−	26.3182i		−	0.923020i
$814$	−10.8265	+	8.45289i	−0.379467	+	0.296274i
$815$	15.0127	−	6.83925i	0.525871	−	0.239568i
$816$	−1.51130	−	0.872551i	−0.0529062	−	0.0305454i
$817$	12.1559	−	7.01821i	0.425281	−	0.245536i
$818$	−18.0019	+	10.3934i	−0.629423	+	0.363398i
$819$	33.7883	−	19.5077i	1.18066	−	0.681653i
$820$	19.7457	−	8.99546i	0.689550	−	0.314135i
$821$	−15.5606	−	26.9518i	−0.543069	−	0.940623i	−0.998726	−	0.0504676i	$-0.983929\pi$
$821$	−15.5606	−	26.9518i	−0.543069	−	0.940623i	0.455657	−	0.890156i	$-0.349404\pi$
$822$	−10.1284			−0.353268
$823$	−30.1015	−	17.3791i	−1.04927	−	0.605798i	−0.126827	−	0.991925i	$-0.540479\pi$
$823$	−30.1015	−	17.3791i	−1.04927	−	0.605798i	−0.922446	+	0.386127i	$0.873813\pi$
$824$	−10.3945			−0.362111
$825$	−7.89511	−	6.86681i	−0.274872	−	0.239072i
$826$	−2.29130	+	3.96866i	−0.0797247	+	0.138087i
$827$	−14.6665	−	25.4031i	−0.510003	−	0.883351i	−0.999933	−	0.0115891i	$-0.996311\pi$
$827$	−14.6665	−	25.4031i	−0.510003	−	0.883351i	0.489930	−	0.871762i	$-0.337022\pi$
$828$	7.77175			0.270087
$829$	−7.76593	−	4.48366i	−0.269722	−	0.155724i	0.359039	−	0.933322i	$-0.383104\pi$
$829$	−7.76593	−	4.48366i	−0.269722	−	0.155724i	−0.628761	+	0.777598i	$0.716438\pi$
$830$	−19.9923	−	1.92773i	−0.693941	−	0.0669124i
$831$	6.75437	+	3.89964i	0.234306	+	0.135277i
$832$	2.51617	+	4.35814i	0.0872325	+	0.151091i
$833$	5.75390	+	9.96605i	0.199361	+	0.345303i
$834$	17.0828	+	9.86276i	0.591529	+	0.341519i
$835$	−4.87860	+	50.5955i	−0.168831	+	1.75093i
$836$	10.7892	+	6.22917i	0.373154	+	0.215440i
$837$	29.3417			1.01420
$838$	−8.93783	−	15.4808i	−0.308752	−	0.534774i
$839$	−0.697910	+	1.20881i	−0.0240945	+	0.0417329i	−0.877821	−	0.478988i	$-0.841004\pi$
$839$	−0.697910	+	1.20881i	−0.0240945	+	0.0417329i	0.853727	+	0.520721i	$0.174337\pi$
$840$	−6.82847	+	3.11081i	−0.235605	+	0.107333i
$841$	28.9407			0.997957
$842$	25.8385	+	14.9178i	0.890452	+	0.514103i
$843$	2.57912			0.0888298
$844$	0.513582	+	0.889550i	0.0176782	+	0.0306196i
$845$	−25.0785	+	11.4249i	−0.862728	+	0.393029i
$846$	−9.11463	+	5.26234i	−0.313368	+	0.180923i
$847$	18.5046	−	10.6836i	0.635824	−	0.367093i
$848$	10.6289	−	6.13660i	0.364998	−	0.210732i
$849$	7.95060	+	4.59028i	0.272864	+	0.157538i
$850$	6.17876	−	7.10403i	0.211930	−	0.243666i
$851$	−20.4685	−	8.27757i	−0.701652	−	0.283752i
$852$		−	5.43778i		−	0.186295i
$853$	20.4030	−	35.3391i	0.698587	−	1.20999i	−0.270370	−	0.962757i	$-0.587146\pi$
$853$	20.4030	−	35.3391i	0.698587	−	1.20999i	0.968957	−	0.247231i	$-0.0795207\pi$
$854$	−14.0264	−	24.2944i	−0.479972	−	0.831337i
$855$	−15.3419	+	21.5025i	−0.524681	+	0.735369i
$856$	−1.23783	+	0.714663i	−0.0423082	+	0.0244267i
$857$	−34.4195			−1.17575			−0.587873	−	0.808953i	$-0.700035\pi$
$857$	−34.4195			−1.17575			−0.587873	+	0.808953i	$0.700035\pi$
$858$	9.12031	−	5.26561i	0.311362	−	0.179765i
$859$		−	55.8042i		−	1.90402i	−0.306074	−	0.952008i	$-0.599016\pi$
$859$		−	55.8042i		−	1.90402i	0.306074	−	0.952008i	$-0.400984\pi$
$860$	0.546007	−	5.66258i	0.0186187	−	0.193093i
$861$	−32.5632			−1.10975
$862$		−	0.875227i		−	0.0298103i
$863$	19.4588	+	11.2346i	0.662386	+	0.382429i	0.793186	−	0.608980i	$-0.208421\pi$
$863$	19.4588	+	11.2346i	0.662386	+	0.382429i	−0.130799	+	0.991409i	$0.541754\pi$
$864$	4.12624	−	2.38228i	0.140377	−	0.0810469i
$865$	2.25055	+	4.94013i	0.0765211	+	0.167970i
$866$	6.08351	+	3.51232i	0.206726	+	0.119353i
$867$	10.7983	+	6.23439i	0.366729	+	0.211731i
$868$	11.1495	−	19.3115i	0.378438	−	0.655474i
$869$	−20.7095	+	11.9566i	−0.702521	+	0.405601i
$870$	0.410652	+	0.292998i	0.0139224	+	0.00993356i
$871$	−25.8862	−	14.9454i	−0.877121	−	0.506406i
$872$	−7.23804	−	4.17889i	−0.245111	−	0.141515i
$873$	−17.3238	+	30.0057i	−0.586323	+	1.01554i
$874$			20.0260i			0.677389i
$875$	−9.43495	−	39.3688i	−0.318959	−	1.33091i
$876$	−6.05213	+	10.4826i	−0.204482	+	0.354174i
$877$			1.51387i			0.0511198i	0.999673	+	0.0255599i	$0.00813686\pi$
$877$			1.51387i			0.0511198i	−0.999673	+	0.0255599i	$0.991863\pi$
$878$		−	36.2580i		−	1.22365i
$879$	12.7066	−	22.0086i	0.428585	−	0.742330i
$880$	4.59492	−	2.09328i	0.154895	−	0.0705646i
$881$	19.9997	+	34.6405i	0.673806	+	1.16707i	0.976816	+	0.214079i	$0.0686751\pi$
$881$	19.9997	+	34.6405i	0.673806	+	1.16707i	−0.303010	+	0.952987i	$0.597992\pi$
$882$	−13.0852			−0.440600
$883$	11.0420	+	19.1253i	0.371593	+	0.643618i	0.989811	−	0.142389i	$-0.0454784\pi$
$883$	11.0420	+	19.1253i	0.371593	+	0.643618i	−0.618218	+	0.786007i	$0.712145\pi$
$884$	4.73801	+	8.20647i	0.159356	+	0.276013i
$885$	−2.13493	−	1.52326i	−0.0717650	−	0.0512039i
$886$	−23.2470	−	13.4217i	−0.780998	−	0.450910i
$887$			30.0892i			1.01030i	0.863032	+	0.505149i	$0.168562\pi$
$887$			30.0892i			1.01030i	−0.863032	+	0.505149i	$0.831438\pi$
$888$	−5.58263	+	0.782735i	−0.187341	+	0.0262669i
$889$	12.4901			0.418905
$890$	−28.3283	−	2.73152i	−0.949566	−	0.0915606i
$891$	2.26688	+	3.92635i	0.0759434	+	0.131538i
$892$	−16.6355	+	9.60449i	−0.556997	+	0.321582i
$893$	−13.5598	−	23.4863i	−0.453762	−	0.785939i
$894$		−	2.71113i		−	0.0906737i
$895$	1.76857	−	2.47874i	0.0591167	−	0.0828551i
$896$		−	3.62096i		−	0.120968i
$897$	14.6603	+	8.46414i	0.489494	+	0.282609i
$898$		−	20.1391i		−	0.672050i
$899$	−1.49913			−0.0499988
$900$	3.48271	+	10.1233i	0.116090	+	0.337443i
$901$	20.0145	−	11.5554i	0.666778	−	0.384965i
$902$	21.9120			0.729589
$903$	−4.26873	+	7.39365i	−0.142054	+	0.246045i
$904$	4.25810	−	7.37525i	0.141622	−	0.245297i
$905$	−2.99784	+	31.0903i	−0.0996515	+	1.03348i
$906$	11.2794	−	6.51218i	0.374734	−	0.216353i
$907$	−5.02826	−	8.70921i	−0.166961	−	0.289184i	0.770389	−	0.637574i	$-0.220062\pi$
$907$	−5.02826	−	8.70921i	−0.166961	−	0.289184i	−0.937350	+	0.348390i	$0.886729\pi$
$908$	6.25789	−	10.8390i	0.207675	−	0.359704i
$909$	−10.3171	+	17.8698i	−0.342197	+	0.592703i
$910$	40.5573	+	3.91068i	1.34446	+	0.129638i
$911$			33.6099i			1.11355i	0.830665	+	0.556773i	$0.187961\pi$
$911$			33.6099i			1.11355i	−0.830665	+	0.556773i	$0.812039\pi$
$912$	2.55654	+	4.42805i	0.0846554	+	0.146628i
$913$	−17.5655	−	10.1414i	−0.581333	−	0.335633i
$914$	13.7643			0.455281
$915$	14.6100	−	6.65582i	0.482993	−	0.220035i
$916$	10.9023	−	18.8833i	0.360221	−	0.623922i
$917$	25.1091			0.829177
$918$	7.76980	−	4.48589i	0.256441	−	0.148057i
$919$		−	15.1624i		−	0.500160i	−0.968225	−	0.250080i	$-0.919543\pi$
$919$		−	15.1624i		−	0.500160i	0.968225	−	0.250080i	$-0.0804569\pi$
$920$	6.60704	+	4.71408i	0.217828	+	0.155419i
$921$	−10.0400	−	17.3897i	−0.330828	−	0.573012i
$922$	11.3932	−	6.57784i	0.375214	−	0.216630i
$923$	−14.7637	+	25.5716i	−0.485955	+	0.841698i
$924$	−7.57761			−0.249285
$925$	1.60972	−	30.3712i	0.0529273	−	0.998598i
$926$	17.6828			0.581092
$927$	11.1280	−	19.2742i	0.365491	−	0.633049i
$928$	−0.210819	+	0.121716i	−0.00692046	+	0.00399553i
$929$	5.25368	+	9.09964i	0.172368	+	0.298550i	0.939247	−	0.343242i	$-0.111525\pi$
$929$	5.25368	+	9.09964i	0.172368	+	0.298550i	−0.766879	+	0.641791i	$0.778192\pi$
$930$	10.3886	+	7.41220i	0.340655	+	0.243056i
$931$		−	33.7174i		−	1.10504i
$932$	11.1387	−	6.43091i	0.364859	−	0.210651i
$933$	−0.0882178			−0.00288812
$934$	10.9239	−	18.9208i	0.357442	−	0.619108i
$935$	8.65233	−	3.94170i	0.282961	−	0.128907i
$936$	−10.7749			−0.352187
$937$	−15.9529	−	9.21042i	−0.521159	−	0.300891i	0.216250	−	0.976338i	$-0.430618\pi$
$937$	−15.9529	−	9.21042i	−0.521159	−	0.300891i	−0.737409	+	0.675447i	$0.763951\pi$
$938$	10.7538	+	18.6261i	0.351124	+	0.608164i
$939$		−	6.24409i		−	0.203768i
$940$	−10.9406	−	1.05494i	−0.356844	−	0.0344082i
$941$	0.706741	−	1.22411i	0.0230391	−	0.0399049i	−0.854276	−	0.519820i	$-0.825999\pi$
$941$	0.706741	−	1.22411i	0.0230391	−	0.0399049i	0.877315	+	0.479915i	$0.159332\pi$
$942$	2.69038	−	4.65988i	0.0876574	−	0.151827i
$943$	17.6111	+	30.5033i	0.573495	+	0.993323i
$944$	1.09602	−	0.632789i	0.0356725	−	0.0205955i
$945$	3.70260	−	38.3992i	0.120445	−	1.24913i
$946$	2.87245	−	4.97523i	0.0933914	−	0.161759i
$947$	20.2518	−	35.0771i	0.658094	−	1.13985i	−0.323015	−	0.946394i	$-0.604696\pi$
$947$	20.2518	−	35.0771i	0.658094	−	1.13985i	0.981109	−	0.193458i	$-0.0619704\pi$
$948$	−9.81433			−0.318755
$949$	56.9211	−	32.8634i	1.84774	−	1.06679i
$950$	−26.0854	+	8.97413i	−0.846321	+	0.291159i
$951$	−3.79946			−0.123206
$952$		−	6.81835i		−	0.220984i
$953$	24.9722	+	14.4177i	0.808930	+	0.467036i	0.846584	−	0.532255i	$-0.178655\pi$
$953$	24.9722	+	14.4177i	0.808930	+	0.467036i	−0.0376539	+	0.999291i	$0.511988\pi$
$954$			26.2784i			0.850796i
$955$	−25.1047	+	35.1856i	−0.812370	+	1.13858i
$956$			27.0112i			0.873606i
$957$	0.254717	+	0.441182i	0.00823382	+	0.0142614i
$958$	−12.9567	+	7.48057i	−0.418613	+	0.241686i
$959$	−19.7865	−	34.2711i	−0.638938	−	1.10667i
$960$	2.06272	+	0.198895i	0.0665741	+	0.00641932i
$961$	−6.92472			−0.223378
$962$	28.3779	+	11.4761i	0.914939	+	0.370006i
$963$		−	3.06036i		−	0.0986188i
$964$	−22.6395	−	13.0709i	−0.729169	−	0.420986i
$965$	−8.45257	−	6.03086i	−0.272098	−	0.194140i
$966$	−6.09027	−	10.5487i	−0.195951	−	0.339397i
$967$	13.0340	+	22.5756i	0.419146	+	0.725981i	0.995854	−	0.0909688i	$-0.0289964\pi$
$967$	13.0340	+	22.5756i	0.419146	+	0.725981i	−0.576708	+	0.816950i	$0.695663\pi$
$968$	−5.90098			−0.189665
$969$	4.81402	+	8.33812i	0.154649	+	0.267859i
$970$	−32.9281	+	15.0009i	−1.05726	+	0.481650i
$971$	−9.40165	+	16.2841i	−0.301713	+	0.522583i	−0.976524	−	0.215408i	$-0.930892\pi$
$971$	−9.40165	+	16.2841i	−0.301713	+	0.522583i	0.674811	+	0.737991i	$0.264225\pi$
$972$			16.1544i			0.518153i
$973$			77.0702i			2.47076i
$974$	10.4821	−	18.1556i	0.335870	−	0.581743i
$975$	−4.45554	+	22.8891i	−0.142691	+	0.733039i
$976$			7.74732i			0.247986i
$977$	14.4420	−	25.0143i	0.462041	−	0.800278i	−0.537022	−	0.843568i	$-0.680451\pi$
$977$	14.4420	−	25.0143i	0.462041	−	0.800278i	0.999063	+	0.0432904i	$0.0137841\pi$
$978$	5.92133	+	3.41868i	0.189343	+	0.109317i
$979$	−24.8896	−	14.3700i	−0.795477	−	0.459269i
$980$	−11.1242	−	7.93702i	−0.355348	−	0.253539i
$981$	15.4975	−	8.94751i	0.494798	−	0.285672i
$982$	−12.7294	+	22.0479i	−0.406211	+	0.703578i
$983$	−42.3647	−	24.4592i	−1.35122	−	0.780129i	−0.362802	−	0.931866i	$-0.618180\pi$
$983$	−42.3647	−	24.4592i	−1.35122	−	0.780129i	−0.988421	+	0.151738i	$0.951513\pi$
$984$	7.78816	+	4.49649i	0.248277	+	0.143343i
$985$	−0.0101814	−	0.0223490i	−0.000324408	−	0.000712099i
$986$	−0.396976	+	0.229194i	−0.0126423	+	0.00729904i
$987$	14.2852	+	8.24757i	0.454703	+	0.262523i
$988$		−	27.7643i		−	0.883300i
$989$	9.23456			0.293642
$990$	−1.03763	+	10.7612i	−0.0329782	+	0.342013i
$991$			46.2399i			1.46886i	0.678685	+	0.734429i	$0.262550\pi$
$991$			46.2399i			1.46886i	−0.678685	+	0.734429i	$0.737450\pi$
$992$	−5.33325	+	3.07915i	−0.169331	+	0.0977632i
$993$	−1.82020			−0.0577623
$994$	18.3997	−	10.6231i	0.583603	−	0.336943i
$995$	−28.8219	+	40.3955i	−0.913717	+	1.28062i
$996$	−4.16219	−	7.20912i	−0.131884	−	0.228430i
$997$	15.4729	−	26.7999i	0.490032	−	0.848761i	−0.509902	−	0.860233i	$-0.670318\pi$
$997$	15.4729	−	26.7999i	0.490032	−	0.848761i	0.999934	+	0.0114718i	$0.00365167\pi$
$998$		−	18.9059i		−	0.598456i
$999$	10.8655	−	26.8679i	0.343769	−	0.850061i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.m.c.249.5	yes	16
5.4	even	2		370.2.m.d.249.4	yes	16
37.11	even	6		370.2.m.d.159.4	yes	16
185.159	even	6	inner	370.2.m.c.159.5	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.m.c.159.5	✓	16	185.159	even	6	inner
370.2.m.c.249.5	yes	16	1.1	even	1	trivial
370.2.m.d.159.4	yes	16	37.11	even	6
370.2.m.d.249.4	yes	16	5.4	even	2

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.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.802594 - 0.463378i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.82024 + 1.29873i) q^{5} +0.926756i q^{6} +(-3.13584 + 1.81048i) q^{7} +1.00000 q^{8} +(-1.07056 + 1.85427i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.802594 - 0.463378i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.82024 + 1.29873i) q^{5} +0.926756i q^{6} +(-3.13584 + 1.81048i) q^{7} +1.00000 q^{8} +(-1.07056 + 1.85427i) q^{9} +(-2.03486 + 0.927011i) q^{10} -2.25810 q^{11} +(-0.802594 - 0.463378i) q^{12} +(2.51617 + 4.35814i) q^{13} -3.62096i q^{14} +(2.06272 + 0.198895i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.941511 + 1.63075i) q^{17} +(-1.07056 - 1.85427i) q^{18} +(4.77801 - 2.75859i) q^{19} +(0.214614 - 2.22574i) q^{20} +(-1.67787 + 2.90616i) q^{21} +(1.12905 - 1.95557i) q^{22} +3.62975 q^{23} +(0.802594 - 0.463378i) q^{24} +(1.62658 + 4.72803i) q^{25} -5.03234 q^{26} +4.76457i q^{27} +(3.13584 + 1.81048i) q^{28} -0.243433i q^{29} +(-1.20361 + 1.68692i) q^{30} -6.15831i q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.81234 + 1.04635i) q^{33} +(-0.941511 - 1.63075i) q^{34} +(-8.05933 - 0.777110i) q^{35} +2.14112 q^{36} +(-5.63910 - 2.28048i) q^{37} +5.51718i q^{38} +(4.03893 + 2.33188i) q^{39} +(1.82024 + 1.29873i) q^{40} +(4.85186 + 8.40367i) q^{41} +(-1.67787 - 2.90616i) q^{42} +2.54413 q^{43} +(1.12905 + 1.95557i) q^{44} +(-4.35688 + 1.98484i) q^{45} +(-1.81488 + 3.14346i) q^{46} -4.91549i q^{47} +0.926756i q^{48} +(3.05568 - 5.29258i) q^{49} +(-4.90788 - 0.955354i) q^{50} +1.74510i q^{51} +(2.51617 - 4.35814i) q^{52} +(-10.6289 - 6.13660i) q^{53} +(-4.12624 - 2.38228i) q^{54} +(-4.11030 - 2.93267i) q^{55} +(-3.13584 + 1.81048i) q^{56} +(2.55654 - 4.42805i) q^{57} +(0.210819 + 0.121716i) q^{58} +(-1.09602 - 0.632789i) q^{59} +(-0.859113 - 1.88582i) q^{60} +(6.70938 - 3.87366i) q^{61} +(5.33325 + 3.07915i) q^{62} -7.75292i q^{63} +1.00000 q^{64} +(-1.08001 + 11.2007i) q^{65} -2.09271i q^{66} +(-5.14397 + 2.96987i) q^{67} +1.88302 q^{68} +(2.91322 - 1.68195i) q^{69} +(4.70266 - 6.59103i) q^{70} +(2.93377 + 5.08144i) q^{71} +(-1.07056 + 1.85427i) q^{72} -13.0609i q^{73} +(4.79450 - 3.74336i) q^{74} +(3.49635 + 3.04097i) q^{75} +(-4.77801 - 2.75859i) q^{76} +(7.08105 - 4.08825i) q^{77} +(-4.03893 + 2.33188i) q^{78} +(9.17120 - 5.29499i) q^{79} +(-2.03486 + 0.927011i) q^{80} +(-1.00389 - 1.73879i) q^{81} -9.70373 q^{82} +(7.77888 + 4.49114i) q^{83} +3.35575 q^{84} +(-3.83168 + 1.74558i) q^{85} +(-1.27206 + 2.20328i) q^{86} +(-0.112801 - 0.195378i) q^{87} -2.25810 q^{88} +(11.0224 + 6.36378i) q^{89} +(0.459516 - 4.76559i) q^{90} +(-15.7806 - 9.11095i) q^{91} +(-1.81488 - 3.14346i) q^{92} +(-2.85362 - 4.94262i) q^{93} +(4.25694 + 2.45775i) q^{94} +(12.2798 + 1.18407i) q^{95} +(-0.802594 - 0.463378i) q^{96} +16.1820 q^{97} +(3.05568 + 5.29258i) q^{98} +(2.41744 - 4.18712i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{2} + 3 q^{3} - 8 q^{4} + 6 q^{5} + 12 q^{7} + 16 q^{8} + 13 q^{9}+O(q^{10}) \) 16 * q - 8 * q^2 + 3 * q^3 - 8 * q^4 + 6 * q^5 + 12 * q^7 + 16 * q^8 + 13 * q^9	\( 16 q - 8 q^{2} + 3 q^{3} - 8 q^{4} + 6 q^{5} + 12 q^{7} + 16 q^{8} + 13 q^{9} - 6 q^{10} - 6 q^{11} - 3 q^{12} + 6 q^{13} - 9 q^{15} - 8 q^{16} + 13 q^{18} - 3 q^{19} - 6 q^{21} + 3 q^{22} + 22 q^{23} + 3 q^{24} - 6 q^{25} - 12 q^{26} - 12 q^{28} - 9 q^{30} - 8 q^{32} - 6 q^{33} + 12 q^{35} - 26 q^{36} - 16 q^{37} + 15 q^{39} + 6 q^{40} + 7 q^{41} - 6 q^{42} + 22 q^{43} + 3 q^{44} - 4 q^{45} - 11 q^{46} + 4 q^{49} - 6 q^{50} + 6 q^{52} - 3 q^{53} + 9 q^{54} - 25 q^{55} + 12 q^{56} - 18 q^{57} - 36 q^{58} + 15 q^{59} + 18 q^{60} + 12 q^{61} + 33 q^{62} + 16 q^{64} - 26 q^{65} - 24 q^{67} + 42 q^{69} - 18 q^{70} - 4 q^{71} + 13 q^{72} + 5 q^{74} - 10 q^{75} + 3 q^{76} + 24 q^{77} - 15 q^{78} - 6 q^{80} + 10 q^{81} - 14 q^{82} - 6 q^{83} + 12 q^{84} - 26 q^{85} - 11 q^{86} - 50 q^{87} - 6 q^{88} + 9 q^{89} + 5 q^{90} - 24 q^{91} - 11 q^{92} + 25 q^{93} - 27 q^{94} + 49 q^{95} - 3 q^{96} - 68 q^{97} + 4 q^{98} + 37 q^{99}+O(q^{100}) \) 16 * q - 8 * q^2 + 3 * q^3 - 8 * q^4 + 6 * q^5 + 12 * q^7 + 16 * q^8 + 13 * q^9 - 6 * q^10 - 6 * q^11 - 3 * q^12 + 6 * q^13 - 9 * q^15 - 8 * q^16 + 13 * q^18 - 3 * q^19 - 6 * q^21 + 3 * q^22 + 22 * q^23 + 3 * q^24 - 6 * q^25 - 12 * q^26 - 12 * q^28 - 9 * q^30 - 8 * q^32 - 6 * q^33 + 12 * q^35 - 26 * q^36 - 16 * q^37 + 15 * q^39 + 6 * q^40 + 7 * q^41 - 6 * q^42 + 22 * q^43 + 3 * q^44 - 4 * q^45 - 11 * q^46 + 4 * q^49 - 6 * q^50 + 6 * q^52 - 3 * q^53 + 9 * q^54 - 25 * q^55 + 12 * q^56 - 18 * q^57 - 36 * q^58 + 15 * q^59 + 18 * q^60 + 12 * q^61 + 33 * q^62 + 16 * q^64 - 26 * q^65 - 24 * q^67 + 42 * q^69 - 18 * q^70 - 4 * q^71 + 13 * q^72 + 5 * q^74 - 10 * q^75 + 3 * q^76 + 24 * q^77 - 15 * q^78 - 6 * q^80 + 10 * q^81 - 14 * q^82 - 6 * q^83 + 12 * q^84 - 26 * q^85 - 11 * q^86 - 50 * q^87 - 6 * q^88 + 9 * q^89 + 5 * q^90 - 24 * q^91 - 11 * q^92 + 25 * q^93 - 27 * q^94 + 49 * q^95 - 3 * q^96 - 68 * q^97 + 4 * q^98 + 37 * q^99

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