LMFDB - Embedded newform 56.3.j.a.45.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [56,3,Mod(5,56)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(56, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("56.5");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 56 = 2^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	56.j (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:	$1.52588948042$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			45.1
Character	$\chi$	$=$	56.45
Dual form			56.3.j.a.5.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.97030 - 0.343404i) q^{2} +(-1.94818 + 3.37434i) q^{3} +(3.76415 + 1.35322i) q^{4} +(-4.42985 - 7.67272i) q^{5} +(4.99725 - 5.97944i) q^{6} +(-6.92329 - 1.03347i) q^{7} +(-6.95179 - 3.95886i) q^{8} +(-3.09078 - 5.35338i) q^{9} +O(q^{10})$	\(q+(-1.97030 - 0.343404i) q^{2} +(-1.94818 + 3.37434i) q^{3} +(3.76415 + 1.35322i) q^{4} +(-4.42985 - 7.67272i) q^{5} +(4.99725 - 5.97944i) q^{6} +(-6.92329 - 1.03347i) q^{7} +(-6.95179 - 3.95886i) q^{8} +(-3.09078 - 5.35338i) q^{9} +(6.09327 + 16.6388i) q^{10} +(-3.15749 - 1.82298i) q^{11} +(-11.8994 + 10.0652i) q^{12} -7.79378 q^{13} +(13.2860 + 4.41373i) q^{14} +34.5205 q^{15} +(12.3376 + 10.1874i) q^{16} +(-9.07152 - 5.23744i) q^{17} +(4.25138 + 11.6091i) q^{18} +(5.39264 + 9.34032i) q^{19} +(-6.29174 - 34.8758i) q^{20} +(16.9751 - 21.3482i) q^{21} +(5.59518 + 4.67610i) q^{22} +(6.45553 + 11.1813i) q^{23} +(26.9019 - 15.7451i) q^{24} +(-26.7471 + 46.3273i) q^{25} +(15.3561 + 2.67642i) q^{26} -10.9817 q^{27} +(-24.6618 - 13.2588i) q^{28} +17.2327i q^{29} +(-68.0156 - 11.8545i) q^{30} +(-26.1797 - 15.1148i) q^{31} +(-20.8104 - 24.3090i) q^{32} +(12.3027 - 7.10296i) q^{33} +(16.0750 + 13.4345i) q^{34} +(22.7396 + 57.6986i) q^{35} +(-4.38985 - 24.3334i) q^{36} +(34.2810 - 19.7922i) q^{37} +(-7.41760 - 20.2551i) q^{38} +(15.1837 - 26.2989i) q^{39} +(0.420114 + 70.8763i) q^{40} -73.6801i q^{41} +(-40.7770 + 36.2329i) q^{42} -40.8501i q^{43} +(-9.41837 - 11.1347i) q^{44} +(-27.3833 + 47.4293i) q^{45} +(-8.87961 - 24.2474i) q^{46} +(-36.2025 + 20.9015i) q^{47} +(-58.4116 + 21.7844i) q^{48} +(46.8639 + 14.3100i) q^{49} +(68.6087 - 82.0935i) q^{50} +(35.3458 - 20.4069i) q^{51} +(-29.3369 - 10.5467i) q^{52} +(-5.55272 - 3.20586i) q^{53} +(21.6371 + 3.77115i) q^{54} +32.3020i q^{55} +(44.0379 + 34.5928i) q^{56} -42.0232 q^{57} +(5.91778 - 33.9535i) q^{58} +(-7.95742 + 13.7827i) q^{59} +(129.940 + 46.7137i) q^{60} +(-6.07848 - 10.5282i) q^{61} +(46.3912 + 38.7709i) q^{62} +(15.8658 + 40.2572i) q^{63} +(32.6548 + 55.0424i) q^{64} +(34.5253 + 59.7995i) q^{65} +(-26.6792 + 9.77016i) q^{66} +(6.75274 + 3.89870i) q^{67} +(-27.0591 - 31.9902i) q^{68} -50.3060 q^{69} +(-24.9899 - 121.492i) q^{70} -41.3627 q^{71} +(0.293120 + 49.4516i) q^{72} +(77.6038 + 44.8046i) q^{73} +(-74.3406 + 27.2242i) q^{74} +(-104.216 - 180.507i) q^{75} +(7.65920 + 42.4557i) q^{76} +(19.9762 + 15.8842i) q^{77} +(-38.9475 + 46.6025i) q^{78} +(-35.3975 - 61.3103i) q^{79} +(23.5115 - 139.792i) q^{80} +(49.2112 - 85.2363i) q^{81} +(-25.3020 + 145.172i) q^{82} -60.8673 q^{83} +(92.7853 - 57.3866i) q^{84} +92.8043i q^{85} +(-14.0281 + 80.4868i) q^{86} +(-58.1489 - 33.5723i) q^{87} +(14.7333 + 25.1730i) q^{88} +(-23.4004 + 13.5102i) q^{89} +(70.2407 - 84.0463i) q^{90} +(53.9586 + 8.05463i) q^{91} +(9.16883 + 50.8238i) q^{92} +(102.005 - 58.8927i) q^{93} +(78.5073 - 28.7501i) q^{94} +(47.7771 - 82.7524i) q^{95} +(122.569 - 22.8630i) q^{96} +3.26608i q^{97} +(-87.4217 - 44.2882i) q^{98} +22.5377i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 2 q^{2} - 4 q^{4} - 4 q^{7} - 20 q^{8} - 32 q^{9}+O(q^{10}) $ 28 * q - 2 * q^2 - 4 * q^4 - 4 * q^7 - 20 * q^8 - 32 * q^9	$ 28 q - 2 q^{2} - 4 q^{4} - 4 q^{7} - 20 q^{8} - 32 q^{9} + 24 q^{10} - 18 q^{12} + 24 q^{14} + 28 q^{15} + 16 q^{16} - 6 q^{17} - 42 q^{18} - 92 q^{22} + 30 q^{23} - 30 q^{24} - 32 q^{25} - 30 q^{26} - 42 q^{28} + 22 q^{30} - 6 q^{31} + 88 q^{32} - 6 q^{33} + 256 q^{36} + 6 q^{38} - 20 q^{39} + 102 q^{40} + 18 q^{42} - 42 q^{44} + 68 q^{46} - 294 q^{47} - 20 q^{49} + 400 q^{50} - 168 q^{52} + 330 q^{54} - 96 q^{56} + 124 q^{57} - 22 q^{58} - 62 q^{60} + 432 q^{63} - 520 q^{64} - 52 q^{65} - 306 q^{66} - 456 q^{68} - 324 q^{70} - 136 q^{71} + 96 q^{72} + 234 q^{73} - 138 q^{74} - 956 q^{78} - 162 q^{79} + 276 q^{80} - 18 q^{81} - 642 q^{82} + 504 q^{84} + 168 q^{86} + 48 q^{87} + 50 q^{88} - 150 q^{89} + 1020 q^{92} + 618 q^{94} + 290 q^{95} + 1044 q^{96} + 424 q^{98}+O(q^{100}) $ 28 * q - 2 * q^2 - 4 * q^4 - 4 * q^7 - 20 * q^8 - 32 * q^9 + 24 * q^10 - 18 * q^12 + 24 * q^14 + 28 * q^15 + 16 * q^16 - 6 * q^17 - 42 * q^18 - 92 * q^22 + 30 * q^23 - 30 * q^24 - 32 * q^25 - 30 * q^26 - 42 * q^28 + 22 * q^30 - 6 * q^31 + 88 * q^32 - 6 * q^33 + 256 * q^36 + 6 * q^38 - 20 * q^39 + 102 * q^40 + 18 * q^42 - 42 * q^44 + 68 * q^46 - 294 * q^47 - 20 * q^49 + 400 * q^50 - 168 * q^52 + 330 * q^54 - 96 * q^56 + 124 * q^57 - 22 * q^58 - 62 * q^60 + 432 * q^63 - 520 * q^64 - 52 * q^65 - 306 * q^66 - 456 * q^68 - 324 * q^70 - 136 * q^71 + 96 * q^72 + 234 * q^73 - 138 * q^74 - 956 * q^78 - 162 * q^79 + 276 * q^80 - 18 * q^81 - 642 * q^82 + 504 * q^84 + 168 * q^86 + 48 * q^87 + 50 * q^88 - 150 * q^89 + 1020 * q^92 + 618 * q^94 + 290 * q^95 + 1044 * q^96 + 424 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/56\mathbb{Z}\right)^\times$.

$n$	$15$	$17$	$29$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	−1.97030	−	0.343404i	−0.985149	−	0.171702i
$2$	−1.97030	−	0.343404i	−0.985149	−	0.171702i
$3$	−1.94818	+	3.37434i	−0.649392	+	1.12478i	0.333876	+	0.942617i	$0.391643\pi$
$3$	−1.94818	+	3.37434i	−0.649392	+	1.12478i	−0.983268	+	0.182163i	$0.941690\pi$
$4$	3.76415	+	1.35322i	0.941037	+	0.338304i
$5$	−4.42985	−	7.67272i	−0.885969	−	1.53454i	−0.844599	−	0.535400i	$-0.820161\pi$
$5$	−4.42985	−	7.67272i	−0.885969	−	1.53454i	−0.0413705	−	0.999144i	$-0.513172\pi$
$6$	4.99725	−	5.97944i	0.832875	−	0.996574i
$7$	−6.92329	−	1.03347i	−0.989041	−	0.147638i
$7$	−6.92329	−	1.03347i	−0.989041	−	0.147638i
$8$	−6.95179	−	3.95886i	−0.868974	−	0.494858i
$9$	−3.09078	−	5.35338i	−0.343420	−	0.594820i
$10$	6.09327	+	16.6388i	0.609327	+	1.66388i
$11$	−3.15749	−	1.82298i	−0.287045	−	0.165725i	0.349564	−	0.936913i	$-0.386330\pi$
$11$	−3.15749	−	1.82298i	−0.287045	−	0.165725i	−0.636608	+	0.771187i	$0.719663\pi$
$12$	−11.8994	+	10.0652i	−0.991619	+	0.838767i
$13$	−7.79378			−0.599522			−0.299761	−	0.954014i	$-0.596907\pi$
$13$	−7.79378			−0.599522			−0.299761	+	0.954014i	$0.596907\pi$
$14$	13.2860	+	4.41373i	0.949003	+	0.315266i
$15$	34.5205			2.30136
$16$	12.3376	+	10.1874i	0.771101	+	0.636713i
$17$	−9.07152	−	5.23744i	−0.533619	−	0.308085i	0.208870	−	0.977943i	$-0.433021\pi$
$17$	−9.07152	−	5.23744i	−0.533619	−	0.308085i	−0.742489	+	0.669858i	$0.766355\pi$
$18$	4.25138	+	11.6091i	0.236188	+	0.644952i
$19$	5.39264	+	9.34032i	0.283823	+	0.491596i	0.972323	−	0.233640i	$-0.0750639\pi$
$19$	5.39264	+	9.34032i	0.283823	+	0.491596i	−0.688500	+	0.725236i	$0.741731\pi$
$20$	−6.29174	−	34.8758i	−0.314587	−	1.74379i
$21$	16.9751	−	21.3482i	0.808336	−	1.01658i
$22$	5.59518	+	4.67610i	0.254326	+	0.212550i
$23$	6.45553	+	11.1813i	0.280675	+	0.486144i	0.971551	−	0.236829i	$-0.0761083\pi$
$23$	6.45553	+	11.1813i	0.280675	+	0.486144i	−0.690876	+	0.722973i	$0.742775\pi$
$24$	26.9019	−	15.7451i	1.12091	−	0.656047i
$25$	−26.7471	+	46.3273i	−1.06988	+	1.85309i
$26$	15.3561	+	2.67642i	0.590618	+	0.102939i
$27$	−10.9817			−0.406728
$28$	−24.6618	−	13.2588i	−0.880778	−	0.473530i
$29$			17.2327i			0.594231i	0.954842	+	0.297115i	$0.0960246\pi$
$29$			17.2327i			0.594231i	−0.954842	+	0.297115i	$0.903975\pi$
$30$	−68.0156	−	11.8545i	−2.26719	−	0.395149i
$31$	−26.1797	−	15.1148i	−0.844505	−	0.487575i	0.0142878	−	0.999898i	$-0.495452\pi$
$31$	−26.1797	−	15.1148i	−0.844505	−	0.487575i	−0.858793	+	0.512323i	$0.828785\pi$
$32$	−20.8104	−	24.3090i	−0.650324	−	0.759657i
$33$	12.3027	−	7.10296i	0.372809	−	0.215241i
$34$	16.0750	+	13.4345i	0.472795	+	0.395133i
$35$	22.7396	+	57.6986i	0.649703	+	1.64853i
$36$	−4.38985	−	24.3334i	−0.121940	−	0.675928i
$37$	34.2810	−	19.7922i	0.926515	−	0.534924i	0.0408071	−	0.999167i	$-0.487007\pi$
$37$	34.2810	−	19.7922i	0.926515	−	0.534924i	0.885708	+	0.464244i	$0.153674\pi$
$38$	−7.41760	−	20.2551i	−0.195200	−	0.533028i
$39$	15.1837	−	26.2989i	0.389324	−	0.674330i
$40$	0.420114	+	70.8763i	0.0105029	+	1.77191i
$41$		−	73.6801i		−	1.79707i	−0.438897	−	0.898537i	$-0.644631\pi$
$41$		−	73.6801i		−	1.79707i	0.438897	−	0.898537i	$-0.355369\pi$
$42$	−40.7770	+	36.2329i	−0.970880	+	0.862688i
$43$		−	40.8501i		−	0.950002i	−0.879985	−	0.475001i	$-0.842448\pi$
$43$		−	40.8501i		−	0.950002i	0.879985	−	0.475001i	$-0.157552\pi$
$44$	−9.41837	−	11.1347i	−0.214054	−	0.253062i
$45$	−27.3833	+	47.4293i	−0.608518	+	1.05398i
$46$	−8.87961	−	24.2474i	−0.193035	−	0.527117i
$47$	−36.2025	+	20.9015i	−0.770266	+	0.444713i	−0.832969	−	0.553319i	$-0.813361\pi$
$47$	−36.2025	+	20.9015i	−0.770266	+	0.444713i	0.0627038	+	0.998032i	$0.480028\pi$
$48$	−58.4116	+	21.7844i	−1.21691	+	0.453842i
$49$	46.8639	+	14.3100i	0.956406	+	0.292041i
$50$	68.6087	−	82.0935i	1.37217	−	1.64187i
$51$	35.3458	−	20.4069i	0.693055	−	0.400136i
$52$	−29.3369	−	10.5467i	−0.564172	−	0.202821i
$53$	−5.55272	−	3.20586i	−0.104768	−	0.0604880i	0.446700	−	0.894684i	$-0.352599\pi$
$53$	−5.55272	−	3.20586i	−0.104768	−	0.0604880i	−0.551469	+	0.834196i	$0.685932\pi$
$54$	21.6371	+	3.77115i	0.400688	+	0.0698361i
$55$			32.3020i			0.587310i
$56$	44.0379	+	34.5928i	0.786391	+	0.617729i
$57$	−42.0232			−0.737249
$58$	5.91778	−	33.9535i	0.102031	−	0.585406i
$59$	−7.95742	+	13.7827i	−0.134871	+	0.233604i	−0.925548	−	0.378629i	$-0.876395\pi$
$59$	−7.95742	+	13.7827i	−0.134871	+	0.233604i	0.790677	+	0.612234i	$0.209729\pi$
$60$	129.940	+	46.7137i	2.16567	+	0.778561i
$61$	−6.07848	−	10.5282i	−0.0996472	−	0.172594i	0.811891	−	0.583808i	$-0.198438\pi$
$61$	−6.07848	−	10.5282i	−0.0996472	−	0.172594i	−0.911539	+	0.411214i	$0.865105\pi$
$62$	46.3912	+	38.7709i	0.748246	+	0.625338i
$63$	15.8658	+	40.2572i	0.251838	+	0.639004i
$64$	32.6548	+	55.0424i	0.510231	+	0.860037i
$65$	34.5253	+	59.7995i	0.531158	+	0.919992i
$66$	−26.6792	+	9.77016i	−0.404230	+	0.148033i
$67$	6.75274	+	3.89870i	0.100787	+	0.0581895i	0.549546	−	0.835463i	$-0.314801\pi$
$67$	6.75274	+	3.89870i	0.100787	+	0.0581895i	−0.448759	+	0.893653i	$0.648134\pi$
$68$	−27.0591	−	31.9902i	−0.397928	−	0.470445i
$69$	−50.3060			−0.729073
$70$	−24.9899	−	121.492i	−0.356998	−	1.73560i
$71$	−41.3627			−0.582574			−0.291287	−	0.956636i	$-0.594083\pi$
$71$	−41.3627			−0.582574			−0.291287	+	0.956636i	$0.594083\pi$
$72$	0.293120	+	49.4516i	0.00407112	+	0.686827i
$73$	77.6038	+	44.8046i	1.06307	+	0.613761i	0.926279	−	0.376839i	$-0.122989\pi$
$73$	77.6038	+	44.8046i	1.06307	+	0.613761i	0.136787	+	0.990601i	$0.456322\pi$
$74$	−74.3406	+	27.2242i	−1.00460	+	0.367895i
$75$	−104.216	−	180.507i	−1.38955	−	2.40677i
$76$	7.65920	+	42.4557i	0.100779	+	0.558628i
$77$	19.9762	+	15.8842i	0.259432	+	0.206288i
$78$	−38.9475	+	46.6025i	−0.499326	+	0.597467i
$79$	−35.3975	−	61.3103i	−0.448070	−	0.776080i	0.550191	−	0.835039i	$-0.314555\pi$
$79$	−35.3975	−	61.3103i	−0.448070	−	0.776080i	−0.998260	+	0.0589594i	$0.981222\pi$
$80$	23.5115	−	139.792i	0.293893	−	1.74740i
$81$	49.2112	−	85.2363i	0.607546	−	1.05230i
$82$	−25.3020	+	145.172i	−0.308561	+	1.77039i
$83$	−60.8673			−0.733341			−0.366671	−	0.930351i	$-0.619502\pi$
$83$	−60.8673			−0.733341			−0.366671	+	0.930351i	$0.619502\pi$
$84$	92.7853	−	57.3866i	1.10459	−	0.683174i
$85$			92.8043i			1.09182i
$86$	−14.0281	+	80.4868i	−0.163117	+	0.935894i
$87$	−58.1489	−	33.5723i	−0.668379	−	0.385889i
$88$	14.7333	+	25.1730i	0.167424	+	0.286057i
$89$	−23.4004	+	13.5102i	−0.262926	+	0.151800i	−0.625668	−	0.780089i	$-0.715174\pi$
$89$	−23.4004	+	13.5102i	−0.262926	+	0.151800i	0.362743	+	0.931889i	$0.381840\pi$
$90$	70.2407	−	84.0463i	0.780453	−	0.933848i
$91$	53.9586	+	8.05463i	0.592952	+	0.0885124i
$92$	9.16883	+	50.8238i	0.0996612	+	0.552433i
$93$	102.005	−	58.8927i	1.09683	−	0.633255i
$94$	78.5073	−	28.7501i	0.835184	−	0.305852i
$95$	47.7771	−	82.7524i	0.502917	−	0.871078i
$96$	122.569	−	22.8630i	1.27676	−	0.238156i
$97$			3.26608i			0.0336710i	0.999858	+	0.0168355i	$0.00535916\pi$
$97$			3.26608i			0.0336710i	−0.999858	+	0.0168355i	$0.994641\pi$
$98$	−87.4217	−	44.2882i	−0.892058	−	0.451921i
$99$			22.5377i			0.227653i
$100$	−163.371	+	138.188i	−1.63371	+	1.38188i
$101$	−68.8571	+	119.264i	−0.681754	+	1.18083i	0.292691	+	0.956207i	$0.405449\pi$
$101$	−68.8571	+	119.264i	−0.681754	+	1.18083i	−0.974445	+	0.224625i	$0.927884\pi$
$102$	−76.6496	+	28.0698i	−0.751467	+	0.275194i
$103$	86.3243	−	49.8393i	0.838100	−	0.483877i	−0.0185182	−	0.999829i	$-0.505895\pi$
$103$	86.3243	−	49.8393i	0.838100	−	0.483877i	0.856618	+	0.515952i	$0.172562\pi$
$104$	54.1807	+	30.8545i	0.520969	+	0.296678i
$105$	−238.995	−	35.6758i	−2.27615	−	0.339770i
$106$	9.83960	+	8.22333i	0.0928265	+	0.0775786i
$107$	−81.4157	+	47.0054i	−0.760894	+	0.439302i	−0.829617	−	0.558333i	$-0.811441\pi$
$107$	−81.4157	+	47.0054i	−0.760894	+	0.439302i	0.0687226	+	0.997636i	$0.478108\pi$
$108$	−41.3366	−	14.8606i	−0.382746	−	0.137598i
$109$	−169.697	−	97.9745i	−1.55685	−	0.898849i	−0.997555	−	0.0698815i	$-0.977738\pi$
$109$	−169.697	−	97.9745i	−1.55685	−	0.898849i	−0.559297	−	0.828967i	$-0.688929\pi$
$110$	11.0927	−	63.6446i	0.100842	−	0.578588i
$111$			154.234i			1.38950i
$112$	−74.8885	−	83.2810i	−0.668647	−	0.743580i
$113$	101.873			0.901527			0.450763	−	0.892643i	$-0.351152\pi$
$113$	101.873			0.901527			0.450763	+	0.892643i	$0.351152\pi$
$114$	82.7982	+	14.4309i	0.726300	+	0.126587i
$115$	57.1940	−	99.0629i	0.497339	−	0.861417i
$116$	−23.3196	+	64.8664i	−0.201031	+	0.559193i
$117$	24.0888	+	41.7231i	0.205887	+	0.356608i
$118$	20.4115	−	24.4233i	0.172979	−	0.206977i
$119$	57.3920	+	45.6355i	0.482286	+	0.383491i
$120$	−239.979	−	136.662i	−1.99983	−	1.13885i
$121$	−53.8535	−	93.2770i	−0.445070	−	0.770884i
$122$	8.36098	+	22.8311i	0.0685326	+	0.187140i
$123$	248.622	+	143.542i	2.02131	+	1.16701i
$124$	−78.0905	−	92.3212i	−0.629762	−	0.744526i
$125$	252.449			2.01960
$126$	−17.4358	−	84.7671i	−0.138380	−	0.672755i
$127$	−139.079			−1.09511			−0.547554	−	0.836770i	$-0.684441\pi$
$127$	−139.079			−1.09511			−0.547554	+	0.836770i	$0.684441\pi$
$128$	−45.4379	−	119.664i	−0.354983	−	0.934873i
$129$	137.842	+	79.5831i	1.06854	+	0.616924i
$130$	−47.4896	−	129.679i	−0.365305	−	0.997530i
$131$	45.8526	+	79.4190i	0.350020	+	0.606252i	0.986252	−	0.165245i	$-0.0528416\pi$
$131$	45.8526	+	79.4190i	0.350020	+	0.606252i	−0.636233	+	0.771497i	$0.719508\pi$
$132$	55.9210	−	10.0884i	0.423644	−	0.0764272i
$133$	−27.6819	−	70.2389i	−0.208134	−	0.528112i
$134$	−11.9661	−	10.0005i	−0.0892991	−	0.0746307i
$135$	48.6471	+	84.2592i	0.360349	+	0.624142i
$136$	42.3290	+	72.3225i	0.311242	+	0.531783i
$137$	−99.7904	+	172.842i	−0.728397	+	1.26162i	0.229163	+	0.973388i	$0.426401\pi$
$137$	−99.7904	+	172.842i	−0.728397	+	1.26162i	−0.957560	+	0.288233i	$0.906932\pi$
$138$	99.1179	+	17.2753i	0.718245	+	0.125183i
$139$	−39.4768			−0.284006			−0.142003	−	0.989866i	$-0.545354\pi$
$139$	−39.4768			−0.284006			−0.142003	+	0.989866i	$0.545354\pi$
$140$	7.51653	+	247.957i	0.0536895	+	1.77112i
$141$		−	162.879i		−	1.15517i
$142$	81.4969	+	14.2041i	0.573922	+	0.100029i
$143$	24.6088	+	14.2079i	0.172089	+	0.0993559i
$144$	16.4043	−	97.5349i	0.113919	−	0.677326i
$145$	132.222	−	76.3382i	0.911873	−	0.526470i
$146$	−137.516	−	114.928i	−0.941894	−	0.787177i
$147$	−139.586	+	130.256i	−0.949564	+	0.886097i
$148$	155.822	−	28.1110i	1.05285	−	0.189939i
$149$	82.0846	−	47.3916i	0.550903	−	0.318064i	−0.198583	−	0.980084i	$-0.563634\pi$
$149$	82.0846	−	47.3916i	0.550903	−	0.318064i	0.749486	+	0.662020i	$0.230301\pi$
$150$	143.350	+	391.442i	0.955664	+	2.60961i
$151$	−33.2843	+	57.6501i	−0.220426	+	0.381789i	−0.954937	−	0.296807i	$-0.904078\pi$
$151$	−33.2843	+	57.6501i	−0.220426	+	0.381789i	0.734511	+	0.678596i	$0.237411\pi$
$152$	−0.511422	−	86.2807i	−0.00336462	−	0.567636i
$153$			64.7511i			0.423210i
$154$	−33.9044	−	38.1565i	−0.220159	−	0.247769i
$155$			267.826i			1.72791i
$156$	92.7416	−	78.4460i	0.594497	−	0.502859i
$157$	−12.7597	+	22.1004i	−0.0812720	+	0.140767i	−0.903797	−	0.427962i	$-0.859232\pi$
$157$	−12.7597	+	22.1004i	−0.0812720	+	0.140767i	0.822525	+	0.568730i	$0.192565\pi$
$158$	48.6894	+	132.955i	0.308161	+	0.841489i
$159$	21.6353	−	12.4912i	0.136071	−	0.0785608i
$160$	−94.3296	+	267.357i	−0.589560	+	1.67098i
$161$	−33.1380	−	84.0830i	−0.205826	−	0.522255i
$162$	−126.231	+	151.042i	−0.779205	+	0.932355i
$163$	166.364	−	96.0504i	1.02064	−	0.589267i	0.106350	−	0.994329i	$-0.466083\pi$
$163$	166.364	−	96.0504i	1.02064	−	0.589267i	0.914289	+	0.405062i	$0.132750\pi$
$164$	99.7051	−	277.343i	0.607958	−	1.69111i
$165$	−108.998	−	62.9301i	−0.660594	−	0.381394i
$166$	119.927	+	20.9021i	0.722450	+	0.125916i
$167$		−	184.150i		−	1.10269i	−0.834276	−	0.551346i	$-0.814114\pi$
$167$		−	184.150i		−	1.10269i	0.834276	−	0.551346i	$-0.185886\pi$
$168$	−202.521	+	81.2059i	−1.20548	+	0.483369i
$169$	−108.257			−0.640574
$170$	31.8694	−	182.852i	0.187467	−	1.07560i
$171$	33.3349	−	57.7377i	0.194941	−	0.337647i
$172$	55.2790	−	153.766i	0.321390	−	0.893987i
$173$	−34.9519	−	60.5384i	−0.202034	−	0.349933i	0.747150	−	0.664656i	$-0.231422\pi$
$173$	−34.9519	−	60.5384i	−0.202034	−	0.349933i	−0.949184	+	0.314723i	$0.898088\pi$
$174$	103.042	+	86.1160i	0.592195	+	0.494920i
$175$	233.056	−	293.095i	1.33175	−	1.67483i
$176$	−20.3844	−	54.6578i	−0.115821	−	0.310556i
$177$	−31.0049	−	53.7021i	−0.175169	−	0.303401i
$178$	50.7452	−	18.5834i	0.285085	−	0.104401i
$179$	−207.251	−	119.657i	−1.15783	−	0.668473i	−0.207047	−	0.978331i	$-0.566385\pi$
$179$	−207.251	−	119.657i	−1.15783	−	0.668473i	−0.950783	+	0.309858i	$0.899719\pi$
$180$	−167.257	+	141.475i	−0.929206	+	0.785974i
$181$	36.2834			0.200461			0.100230	−	0.994964i	$-0.468042\pi$
$181$	36.2834			0.200461			0.100230	+	0.994964i	$0.468042\pi$
$182$	−103.549	−	34.3996i	−0.568948	−	0.189009i
$183$	47.3678			0.258840
$184$	−0.612224	−	103.287i	−0.00332731	−	0.561341i
$185$	−303.720	−	175.353i	−1.64173	−	0.947852i
$186$	−221.205	+	81.0072i	−1.18927	+	0.435522i
$187$	19.0955	+	33.0744i	0.102115	+	0.176868i
$188$	−164.556	+	29.6866i	−0.875296	+	0.157907i
$189$	76.0292	+	11.3492i	0.402271	+	0.0600487i
$190$	−122.553	+	146.640i	−0.645014	+	0.771789i
$191$	162.622	+	281.669i	0.851422	+	1.47471i	0.879925	+	0.475113i	$0.157593\pi$
$191$	162.622	+	281.669i	0.851422	+	1.47471i	−0.0285024	+	0.999594i	$0.509074\pi$
$192$	−249.349	+	2.95610i	−1.29869	+	0.0153964i
$193$	−99.8198	+	172.893i	−0.517201	+	0.895818i	0.482599	+	0.875841i	$0.339693\pi$
$193$	−99.8198	+	172.893i	−0.517201	+	0.895818i	−0.999800	+	0.0199772i	$0.993641\pi$
$194$	1.12159	−	6.43516i	0.00578138	−	0.0331709i
$195$	−269.045			−1.37972
$196$	157.038	+	117.282i	0.801214	+	0.598377i
$197$			15.5053i			0.0787071i	0.999225	+	0.0393536i	$0.0125299\pi$
$197$			15.5053i			0.0787071i	−0.999225	+	0.0393536i	$0.987470\pi$
$198$	7.73953	−	44.4059i	0.0390885	−	0.224272i
$199$	−48.6375	−	28.0809i	−0.244409	−	0.141110i	0.372792	−	0.927915i	$-0.378400\pi$
$199$	−48.6375	−	28.0809i	−0.244409	−	0.141110i	−0.617202	+	0.786805i	$0.711734\pi$
$200$	369.344	−	216.170i	1.84672	−	1.08085i
$201$	−26.3110	+	15.1907i	−0.130901	+	0.0755756i
$202$	176.625	−	211.340i	0.874380	−	1.04624i
$203$	17.8094	−	119.307i	0.0877312	−	0.587719i
$204$	160.662	−	28.9841i	0.787558	−	0.142079i
$205$	−565.326	+	326.391i	−2.75769	+	1.59215i
$206$	−187.200	+	68.5542i	−0.908736	+	0.332787i
$207$	39.9052	−	69.1178i	0.192779	−	0.333903i
$208$	−96.1566	−	79.3985i	−0.462291	−	0.381723i
$209$		−	39.3226i		−	0.188147i
$210$	458.641	+	152.364i	2.18400	+	0.725543i
$211$		−	370.470i		−	1.75578i	−0.478859	−	0.877892i	$-0.658949\pi$
$211$		−	370.470i		−	1.75578i	0.478859	−	0.877892i	$-0.341051\pi$
$212$	−16.5630	−	19.5814i	−0.0781275	−	0.0923650i
$213$	80.5819	−	139.572i	0.378319	−	0.655267i
$214$	176.555	−	64.6561i	0.825023	−	0.302131i
$215$	−313.431	+	180.960i	−1.45782	+	0.841673i
$216$	76.3422	+	43.4749i	0.353436	+	0.201273i
$217$	165.629	+	131.700i	0.763266	+	0.606914i
$218$	300.709	+	251.314i	1.37940	+	1.15281i
$219$	−302.372	+	174.574i	−1.38069	+	0.797143i
$220$	−43.7117	+	121.590i	−0.198689	+	0.552680i
$221$	70.7014	+	40.8195i	0.319916	+	0.184704i
$222$	52.9648	−	303.888i	0.238580	−	1.36886i
$223$		−	6.78533i		−	0.0304275i	−0.999884	−	0.0152137i	$-0.995157\pi$
$223$		−	6.78533i		−	0.0304275i	0.999884	−	0.0152137i	$-0.00484287\pi$
$224$	118.954	+	189.805i	0.531043	+	0.847345i
$225$	330.677			1.46968
$226$	−200.719	−	34.9834i	−0.888138	−	0.154794i
$227$	148.309	−	256.879i	0.653344	−	1.13163i	−0.328962	−	0.944343i	$-0.606699\pi$
$227$	148.309	−	256.879i	0.653344	−	1.13163i	0.982306	−	0.187282i	$-0.0599679\pi$
$228$	−158.182	−	56.8665i	−0.693779	−	0.249415i
$229$	89.0964	+	154.320i	0.389067	+	0.673885i	0.992324	−	0.123662i	$-0.0394640\pi$
$229$	89.0964	+	154.320i	0.389067	+	0.673885i	−0.603257	+	0.797547i	$0.706131\pi$
$230$	−146.708	+	175.543i	−0.637860	+	0.763230i
$231$	−92.5158	+	36.4614i	−0.400501	+	0.157842i
$232$	68.2219	−	119.798i	0.294060	−	0.516371i
$233$	−58.9011	−	102.020i	−0.252795	−	0.437853i	0.711500	−	0.702687i	$-0.248016\pi$
$233$	−58.9011	−	102.020i	−0.252795	−	0.437853i	−0.964294	+	0.264833i	$0.914683\pi$
$234$	−33.1343	−	90.4791i	−0.141600	−	0.386663i
$235$	320.743	+	185.181i	1.36486	+	0.788004i
$236$	−48.6038	+	41.1118i	−0.205948	+	0.174203i
$237$	275.842			1.16389
$238$	−97.4080	−	109.624i	−0.409277	−	0.460606i
$239$	46.3543			0.193951			0.0969755	−	0.995287i	$-0.469083\pi$
$239$	46.3543			0.193951			0.0969755	+	0.995287i	$0.469083\pi$
$240$	425.900	+	351.674i	1.77458	+	1.46531i
$241$	317.501	+	183.309i	1.31743	+	0.760619i	0.983315	−	0.181914i	$-0.0582291\pi$
$241$	317.501	+	183.309i	1.31743	+	0.760619i	0.334115	+	0.942532i	$0.391562\pi$
$242$	74.0757	+	202.277i	0.306098	+	0.835855i
$243$	142.327	+	246.517i	0.585706	+	1.01447i
$244$	−8.63331	−	47.8553i	−0.0353824	−	0.196128i
$245$	−97.8032	−	422.965i	−0.399197	−	1.72639i
$246$	−440.566	−	368.198i	−1.79092	−	1.49674i
$247$	−42.0290	−	72.7964i	−0.170158	−	0.294722i
$248$	122.158	+	208.717i	0.492572	+	0.841600i
$249$	118.580	−	205.387i	0.476226	−	0.824847i
$250$	−497.400	−	86.6922i	−1.98960	−	0.346769i
$251$	129.896			0.517513			0.258756	−	0.965943i	$-0.416687\pi$
$251$	129.896			0.517513			0.258756	+	0.965943i	$0.416687\pi$
$252$	5.24440	+	173.004i	0.0208111	+	0.686524i
$253$		−	47.0732i		−	0.186060i
$254$	274.027	+	47.7602i	1.07884	+	0.188032i
$255$	−313.153	−	180.799i	−1.22805	−	0.709016i
$256$	48.4332	+	251.377i	0.189192	+	0.981940i
$257$	232.394	−	134.173i	0.904256	−	0.522073i	0.0256776	−	0.999670i	$-0.491826\pi$
$257$	232.394	−	134.173i	0.904256	−	0.522073i	0.878579	+	0.477598i	$0.158492\pi$
$258$	−244.261	−	204.138i	−0.946747	−	0.791233i
$259$	−257.792	+	101.599i	−0.995337	+	0.392272i
$260$	49.0365	+	271.814i	0.188602	+	1.04544i
$261$	92.2532	−	53.2624i	0.353460	−	0.204070i
$262$	−63.0704	−	172.225i	−0.240727	−	0.657347i
$263$	117.691	−	203.847i	0.447495	−	0.775085i	−0.550727	−	0.834685i	$-0.685649\pi$
$263$	117.691	−	203.847i	0.447495	−	0.775085i	0.998222	+	0.0596008i	$0.0189828\pi$
$264$	−113.645	+	0.673625i	−0.430475	+	0.00255161i
$265$			56.8059i			0.214362i
$266$	30.4212	+	147.898i	0.114365	+	0.556006i
$267$		−	105.281i		−	0.394311i
$268$	20.1425	+	23.8132i	0.0751587	+	0.0888552i
$269$	−177.348	+	307.175i	−0.659285	+	1.14192i	0.321516	+	0.946904i	$0.395808\pi$
$269$	−177.348	+	307.175i	−0.659285	+	1.14192i	−0.980801	+	0.195011i	$0.937526\pi$
$270$	−66.9143	−	182.721i	−0.247831	−	0.676746i
$271$	−365.350	+	210.935i	−1.34816	+	0.778358i	−0.987988	−	0.154529i	$-0.950614\pi$
$271$	−365.350	+	210.935i	−1.34816	+	0.778358i	−0.360168	+	0.932888i	$0.617281\pi$
$272$	−58.5648	−	157.033i	−0.215312	−	0.577327i
$273$	−132.300	+	166.383i	−0.484615	+	0.609461i
$274$	255.972	−	306.282i	0.934203	−	1.11782i
$275$	168.907	−	97.5186i	0.614208	−	0.354613i
$276$	−189.359	−	68.0750i	−0.686084	−	0.246648i
$277$	319.155	+	184.264i	1.15218	+	0.665214i	0.949419	−	0.314013i	$-0.101674\pi$
$277$	319.155	+	184.264i	1.15218	+	0.665214i	0.202766	+	0.979227i	$0.435007\pi$
$278$	77.7810	+	13.5565i	0.279788	+	0.0487644i
$279$			186.866i			0.669772i
$280$	70.3398	−	491.131i	0.251214	−	1.75404i
$281$	−35.2868			−0.125576			−0.0627879	−	0.998027i	$-0.519999\pi$
$281$	−35.2868			−0.125576			−0.0627879	+	0.998027i	$0.519999\pi$
$282$	−55.9334	+	320.921i	−0.198345	+	1.13802i
$283$	98.3087	−	170.276i	0.347380	−	0.601681i	−0.638403	−	0.769702i	$-0.720405\pi$
$283$	98.3087	−	170.276i	0.347380	−	0.601681i	0.985783	+	0.168022i	$0.0537379\pi$
$284$	−155.695	−	55.9728i	−0.548223	−	0.197087i
$285$	186.156	+	322.432i	0.653180	+	1.13134i
$286$	−43.6076	−	36.4445i	−0.152474	−	0.127428i
$287$	−76.1460	+	510.108i	−0.265317	+	1.77738i
$288$	−65.8153	+	186.540i	−0.228525	+	0.647707i
$289$	−89.6384	−	155.258i	−0.310167	−	0.537226i
$290$	−286.731	+	105.003i	−0.988727	+	0.362081i
$291$	−11.0209	−	6.36291i	−0.0378724	−	0.0218657i
$292$	231.482	+	273.666i	0.792746	+	0.937211i
$293$	−317.573			−1.08387			−0.541933	−	0.840421i	$-0.682307\pi$
$293$	−317.573			−1.08387			−0.541933	+	0.840421i	$0.682307\pi$
$294$	319.756	−	208.709i	1.08761	−	0.709895i
$295$	141.001			0.477968
$296$	−316.669	+	1.87703i	−1.06983	+	0.00634133i
$297$	34.6745	+	20.0193i	0.116749	+	0.0674051i
$298$	−178.006	+	65.1873i	−0.597334	+	0.218749i
$299$	−50.3130	−	87.1447i	−0.168271	−	0.291454i
$300$	−148.019	−	820.483i	−0.493396	−	2.73494i
$301$	−42.2173	+	282.817i	−0.140257	+	0.939591i
$302$	85.3773	−	102.158i	0.282706	−	0.338271i
$303$	−268.292	−	464.695i	−0.885451	−	1.53365i
$304$	−28.6215	+	170.174i	−0.0941496	+	0.559784i
$305$	−53.8535	+	93.2769i	−0.176569	+	0.305826i
$306$	22.2358	−	127.579i	0.0726660	−	0.416924i
$307$	132.193			0.430596			0.215298	−	0.976548i	$-0.430928\pi$
$307$	132.193			0.430596			0.215298	+	0.976548i	$0.430928\pi$
$308$	53.6987	+	86.8225i	0.174347	+	0.281891i
$309$			388.383i			1.25690i
$310$	91.9724	−	527.696i	0.296685	−	1.70225i
$311$	400.453	+	231.202i	1.28763	+	0.743414i	0.978231	−	0.207518i	$-0.0665385\pi$
$311$	400.453	+	231.202i	1.28763	+	0.743414i	0.309400	+	0.950932i	$0.399872\pi$
$312$	−209.667	+	122.714i	−0.672010	+	0.393315i
$313$	−490.206	+	283.021i	−1.56615	+	0.904220i	−0.569544	+	0.821961i	$0.692880\pi$
$313$	−490.206	+	283.021i	−1.56615	+	0.904220i	−0.996611	+	0.0822589i	$0.973787\pi$
$314$	32.7298	−	39.1627i	0.104235	−	0.124722i
$315$	238.599	−	300.067i	0.757458	−	0.952594i
$316$	−50.2753	−	278.682i	−0.159099	−	0.881904i
$317$	153.315	−	88.5163i	0.483643	−	0.279231i	−0.238291	−	0.971194i	$-0.576587\pi$
$317$	153.315	−	88.5163i	0.483643	−	0.279231i	0.721933	+	0.691963i	$0.243254\pi$
$318$	−46.9176	+	17.1817i	−0.147540	+	0.0540304i
$319$	31.4148	−	54.4120i	0.0984790	−	0.170571i
$320$	277.669	−	494.380i	0.867716	−	1.54494i
$321$		−	366.299i		−	1.14112i
$322$	36.4172	+	177.048i	0.113097	+	0.549840i
$323$		−	112.975i		−	0.349766i
$324$	300.581	−	254.248i	0.927720	−	0.784718i
$325$	208.461	−	361.065i	0.641418	−	1.11097i
$326$	−360.771	+	132.118i	−1.10666	+	0.405269i
$327$	661.199	−	381.743i	2.02201	−	1.16741i
$328$	−291.689	+	512.208i	−0.889297	+	1.56161i
$329$	272.241	−	107.293i	0.827481	−	0.326119i
$330$	193.148	+	161.421i	0.585298	+	0.489156i
$331$	−429.688	+	248.080i	−1.29815	+	0.749487i	−0.980084	−	0.198582i	$-0.936366\pi$
$331$	−429.688	+	248.080i	−1.29815	+	0.749487i	−0.318065	+	0.948069i	$0.603033\pi$
$332$	−229.114	−	82.3667i	−0.690101	−	0.248092i
$333$	−211.910	−	122.346i	−0.636367	−	0.367406i
$334$	−63.2378	+	362.830i	−0.189335	+	1.08632i
$335$		−	69.0825i		−	0.206216i
$336$	426.914	−	90.4532i	1.27058	−	0.269206i
$337$	−206.191			−0.611843			−0.305922	−	0.952057i	$-0.598965\pi$
$337$	−206.191			−0.611843			−0.305922	+	0.952057i	$0.598965\pi$
$338$	213.298	+	37.1759i	0.631061	+	0.109988i
$339$	−198.466	+	343.752i	−0.585444	+	1.01402i
$340$	−125.584	+	349.329i	−0.369366	+	1.02744i
$341$	55.1080	+	95.4499i	0.161607	+	0.279912i
$342$	−85.5070	+	102.313i	−0.250020	+	0.299161i
$343$	−309.663	−	147.505i	−0.902809	−	0.430043i
$344$	−161.720	+	283.981i	−0.470116	+	0.825527i
$345$	222.848	+	385.984i	0.645936	+	1.11879i
$346$	48.0764	+	131.281i	0.138949	+	0.379426i
$347$	−524.976	−	303.095i	−1.51290	−	0.873472i	−0.999886	−	0.0150913i	$-0.995196\pi$
$347$	−524.976	−	303.095i	−1.51290	−	0.873472i	−0.513013	−	0.858381i	$-0.671471\pi$
$348$	−173.451	−	205.059i	−0.498421	−	0.589251i
$349$	−136.343			−0.390669			−0.195335	−	0.980737i	$-0.562579\pi$
$349$	−136.343			−0.390669			−0.195335	+	0.980737i	$0.562579\pi$
$350$	−559.839	+	497.452i	−1.59954	+	1.42129i
$351$	85.5887			0.243842
$352$	21.3937	+	114.692i	0.0607775	+	0.325831i
$353$	−8.72457	−	5.03713i	−0.0247155	−	0.0142695i	0.487591	−	0.873072i	$-0.337876\pi$
$353$	−8.72457	−	5.03713i	−0.0247155	−	0.0142695i	−0.512307	+	0.858802i	$0.671209\pi$
$354$	42.6474	+	116.456i	0.120473	+	0.328972i
$355$	183.231	+	317.365i	0.516143	+	0.893985i
$356$	−106.365	+	19.1887i	−0.298777	+	0.0539007i
$357$	−265.799	+	104.754i	−0.744536	+	0.293429i
$358$	367.257	+	306.930i	1.02586	+	0.857347i
$359$	−197.808	−	342.613i	−0.550997	−	0.954354i	−0.998203	−	0.0599236i	$-0.980914\pi$
$359$	−197.808	−	342.613i	−0.550997	−	0.954354i	0.447206	−	0.894431i	$-0.352419\pi$
$360$	378.129	−	221.312i	1.05036	−	0.614755i
$361$	122.339	−	211.897i	0.338889	−	0.586973i
$362$	−71.4890	−	12.4599i	−0.197483	−	0.0344195i
$363$	419.664			1.15610
$364$	192.208	+	103.336i	0.528045	+	0.283891i
$365$		−	793.909i		−	2.17509i
$366$	−93.3286	−	16.2663i	−0.254996	−	0.0444434i
$367$	164.486	+	94.9661i	0.448191	+	0.258763i	0.707066	−	0.707148i	$-0.250018\pi$
$367$	164.486	+	94.9661i	0.448191	+	0.258763i	−0.258875	+	0.965911i	$0.583352\pi$
$368$	−34.2628	+	203.716i	−0.0931055	+	0.553575i
$369$	−394.438	+	227.729i	−1.06894	+	0.617151i
$370$	538.201	+	449.795i	1.45460	+	1.21566i
$371$	35.1299	+	27.9337i	0.0946898	+	0.0752930i
$372$	463.657	−	83.6457i	1.24639	−	0.224854i
$373$	311.859	−	180.052i	0.836083	−	0.482713i	−0.0198479	−	0.999803i	$-0.506318\pi$
$373$	311.859	−	180.052i	0.836083	−	0.482713i	0.855931	+	0.517090i	$0.172985\pi$
$374$	−26.2659	−	71.7238i	−0.0702298	−	0.191775i
$375$	−491.816	+	851.850i	−1.31151	+	2.27160i
$376$	334.418	−	1.98224i	0.889410	−	0.00527192i
$377$		−	134.308i		−	0.356254i
$378$	−145.903	−	48.4700i	−0.385986	−	0.128228i
$379$			11.2929i			0.0297966i	0.999889	+	0.0148983i	$0.00474246\pi$
$379$			11.2929i			0.0297966i	−0.999889	+	0.0148983i	$0.995258\pi$
$380$	291.822	−	246.839i	0.767952	−	0.649577i
$381$	270.950	−	469.299i	0.711154	−	1.23176i
$382$	−223.687	−	610.817i	−0.585568	−	1.59900i
$383$	376.075	−	217.127i	0.981918	−	0.566910i	0.0790692	−	0.996869i	$-0.474805\pi$
$383$	376.075	−	217.127i	0.981918	−	0.566910i	0.902849	+	0.429959i	$0.141472\pi$
$384$	492.307	+	79.8031i	1.28205	+	0.207820i
$385$	33.3831	−	223.636i	0.0867095	−	0.580874i
$386$	256.047	−	306.372i	0.663334	−	0.793710i
$387$	−218.686	+	126.258i	−0.565080	+	0.326249i
$388$	−4.41972	+	12.2940i	−0.0113910	+	0.0316856i
$389$	−37.3803	−	21.5816i	−0.0960934	−	0.0554796i	0.451183	−	0.892431i	$-0.351002\pi$
$389$	−37.3803	−	21.5816i	−0.0960934	−	0.0554796i	−0.547277	+	0.836952i	$0.684335\pi$
$390$	530.099	+	92.3912i	1.35923	+	0.236900i
$391$		−	135.242i		−	0.345887i
$392$	−269.137	−	285.008i	−0.686573	−	0.727061i
$393$	−357.315			−0.909199
$394$	5.32458	−	30.5501i	0.0135142	−	0.0775382i
$395$	−313.611	+	543.190i	−0.793952	+	1.37517i
$396$	−30.4984	+	84.8351i	−0.0770160	+	0.214230i
$397$	−243.395	−	421.573i	−0.613086	−	1.06190i	−0.990717	−	0.135940i	$-0.956595\pi$
$397$	−243.395	−	421.573i	−0.613086	−	1.06190i	0.377631	−	0.925956i	$-0.376739\pi$
$398$	86.1872	+	72.0300i	0.216551	+	0.180980i
$399$	290.939	+	43.4297i	0.729170	+	0.108846i
$400$	−801.950	+	299.084i	−2.00488	+	0.747711i
$401$	273.457	+	473.641i	0.681938	+	1.18115i	0.974389	+	0.224870i	$0.0721958\pi$
$401$	273.457	+	473.641i	0.681938	+	1.18115i	−0.292451	+	0.956280i	$0.594471\pi$
$402$	57.0571	−	20.8949i	0.141933	−	0.0519773i
$403$	204.039	+	117.802i	0.506299	+	0.292312i
$404$	−420.579	+	355.749i	−1.04104	+	0.880566i
$405$	−871.992			−2.15307
$406$	−76.0604	+	228.954i	−0.187341	+	0.563927i
$407$	−144.323			−0.354601
$408$	−326.505	+	1.93533i	−0.800257	+	0.00474347i
$409$	57.8217	+	33.3834i	0.141373	+	0.0816220i	0.569018	−	0.822325i	$-0.307323\pi$
$409$	57.8217	+	33.3834i	0.141373	+	0.0816220i	−0.427645	+	0.903947i	$0.640657\pi$
$410$	1225.95	−	448.953i	2.99011	−	1.09501i
$411$	−388.819	−	673.453i	−0.946030	−	1.63857i
$412$	392.381	−	70.7871i	0.952380	−	0.171813i
$413$	69.3354	−	87.1976i	0.167882	−	0.211132i
$414$	−102.360	+	122.479i	−0.247248	+	0.295843i
$415$	269.633	+	467.018i	0.649718	+	1.12534i
$416$	162.191	+	189.459i	0.389883	+	0.455431i
$417$	76.9077	−	133.208i	0.184431	−	0.319444i
$418$	−13.5036	+	77.4773i	−0.0323052	+	0.185352i
$419$	550.169			1.31305			0.656527	−	0.754303i	$-0.272025\pi$
$419$	550.169			1.31305			0.656527	+	0.754303i	$0.272025\pi$
$420$	−851.336	−	457.701i	−2.02699	−	1.08977i
$421$			579.599i			1.37672i	0.725369	+	0.688360i	$0.241669\pi$
$421$			579.599i			1.37672i	−0.725369	+	0.688360i	$0.758331\pi$
$422$	−127.221	+	729.937i	−0.301472	+	1.72971i
$423$	223.788	+	129.204i	0.529049	+	0.305446i
$424$	25.9098	+	44.2690i	0.0611079	+	0.104408i
$425$	485.273	−	280.173i	1.14182	−	0.659230i
$426$	−206.700	+	247.326i	−0.485211	+	0.580578i
$427$	31.2025	+	79.1719i	0.0730737	+	0.185414i
$428$	−370.069	+	66.7620i	−0.864647	+	0.155986i
$429$	−95.8845	+	55.3589i	−0.223507	+	0.129042i
$430$	679.695	−	248.911i	1.58069	−	0.578862i
$431$	215.935	−	374.010i	0.501009	−	0.867773i	−0.498990	−	0.866607i	$-0.666296\pi$
$431$	215.935	−	374.010i	0.501009	−	0.867773i	0.999999	−	0.00116534i	$-0.000370939\pi$
$432$	−135.487	−	111.875i	−0.313628	−	0.258969i
$433$		−	0.143463i		−	0.000331322i	−1.00000		0.000165661i	$-0.999947\pi$
$433$		−	0.143463i		−	0.000331322i	1.00000		0.000165661i	$-5.27316e-5\pi$
$434$	−281.111	−	316.366i	−0.647722	−	0.728955i
$435$			594.881i			1.36754i
$436$	−506.183	−	598.427i	−1.16097	−	1.37254i
$437$	−69.6247	+	120.593i	−0.159324	+	0.275958i
$438$	655.712	−	240.128i	1.49706	−	0.548237i
$439$	−165.713	+	95.6744i	−0.377478	+	0.217937i	−0.676721	−	0.736240i	$-0.736599\pi$
$439$	−165.713	+	95.6744i	−0.377478	+	0.217937i	0.299242	+	0.954177i	$0.403266\pi$
$440$	127.879	−	224.557i	0.290635	−	0.510357i
$441$	−68.2389	−	295.109i	−0.154737	−	0.669182i
$442$	−125.285	−	104.706i	−0.283451	−	0.236891i
$443$	340.782	−	196.751i	0.769260	−	0.444133i	−0.0633505	−	0.997991i	$-0.520179\pi$
$443$	340.782	−	196.751i	0.769260	−	0.444133i	0.832611	+	0.553859i	$0.186845\pi$
$444$	−208.713	+	580.561i	−0.470074	+	1.30757i
$445$	207.320	+	119.696i	0.465888	+	0.268981i
$446$	−2.33011	+	13.3691i	−0.00522446	+	0.0299756i
$447$			369.308i			0.826193i
$448$	−169.194	−	414.822i	−0.377665	−	0.925942i
$449$	−725.831			−1.61655			−0.808275	−	0.588805i	$-0.799598\pi$
$449$	−725.831			−1.61655			−0.808275	+	0.588805i	$0.799598\pi$
$450$	−651.532	−	113.556i	−1.44785	−	0.252346i
$451$	−134.317	+	232.644i	−0.297821	+	0.515841i
$452$	383.463	+	137.856i	0.848370	+	0.304990i
$453$	−129.687	−	224.625i	−0.286286	−	0.495861i
$454$	−380.427	+	455.198i	−0.837944	+	1.00264i
$455$	−177.227	−	449.690i	−0.389511	−	0.988330i
$456$	292.137	+	166.364i	0.640650	+	0.364834i
$457$	34.6713	+	60.0525i	0.0758673	+	0.131406i	0.901463	−	0.432856i	$-0.142494\pi$
$457$	34.6713	+	60.0525i	0.0758673	+	0.131406i	−0.825596	+	0.564262i	$0.809161\pi$
$458$	−122.553	−	334.652i	−0.267582	−	0.730680i
$459$	99.6203	+	57.5158i	0.217038	+	0.125307i
$460$	349.340	−	295.492i	0.759436	−	0.642373i
$461$	768.006			1.66596			0.832978	−	0.553306i	$-0.186634\pi$
$461$	768.006			1.66596			0.832978	+	0.553306i	$0.186634\pi$
$462$	194.805	−	40.0696i	0.421655	−	0.0867306i
$463$	215.717			0.465911			0.232956	−	0.972487i	$-0.425160\pi$
$463$	215.717			0.465911			0.232956	+	0.972487i	$0.425160\pi$
$464$	−175.557	+	212.610i	−0.378355	+	0.458212i
$465$	−903.734	−	521.771i	−1.94351	−	1.12209i
$466$	81.0188	+	221.236i	0.173860	+	0.474756i
$467$	14.4688	+	25.0607i	0.0309824	+	0.0536631i	0.881101	−	0.472928i	$-0.156803\pi$
$467$	14.4688	+	25.0607i	0.0309824	+	0.0536631i	−0.850118	+	0.526592i	$0.823470\pi$
$468$	34.2135	+	189.649i	0.0731058	+	0.405233i
$469$	−42.7220	−	33.9705i	−0.0910917	−	0.0724319i
$470$	−568.367	−	475.006i	−1.20929	−	1.01065i
$471$	−49.7163	−	86.1111i	−0.105555	−	0.182826i
$472$	109.882	−	64.3118i	0.232801	−	0.136254i
$473$	−74.4688	+	128.984i	−0.157439	+	0.272693i
$474$	−543.492	−	94.7254i	−1.14661	−	0.199843i
$475$	−576.949			−1.21463
$476$	154.277	+	249.442i	0.324112	+	0.524039i
$477$			39.6344i			0.0830911i
$478$	−91.3317	−	15.9183i	−0.191071	−	0.0333018i
$479$	−695.377	−	401.476i	−1.45173	−	0.838154i	−0.453146	−	0.891436i	$-0.649698\pi$
$479$	−695.377	−	401.476i	−1.45173	−	0.838154i	−0.998580	+	0.0532818i	$0.983032\pi$
$480$	−718.384	−	839.159i	−1.49663	−	1.74825i
$481$	−267.179	+	154.256i	−0.555466	+	0.320698i
$482$	−562.622	−	470.205i	−1.16726	−	0.975528i
$483$	348.283	+	51.9897i	0.721083	+	0.107639i
$484$	−76.4885	−	423.984i	−0.158034	−	0.876000i
$485$	25.0598	−	14.4683i	0.0516696	−	0.0298315i
$486$	−195.771	−	534.587i	−0.402821	−	1.09997i
$487$	−9.96197	+	17.2546i	−0.0204558	+	0.0354305i	−0.876072	−	0.482180i	$-0.839845\pi$
$487$	−9.96197	+	17.2546i	−0.0204558	+	0.0354305i	0.855616	+	0.517611i	$0.173178\pi$
$488$	0.576466	+	97.2540i	0.00118128	+	0.199291i
$489$			748.493i			1.53066i
$490$	47.4537	+	866.952i	0.0968442	+	1.76929i
$491$			76.2017i			0.155197i	0.996985	+	0.0775985i	$0.0247252\pi$
$491$			76.2017i			0.155197i	−0.996985	+	0.0775985i	$0.975275\pi$
$492$	741.605	+	876.751i	1.50733	+	1.78201i
$493$	90.2552	−	156.327i	0.183073	−	0.317093i
$494$	57.8111	+	157.864i	0.117027	+	0.319562i
$495$	172.925	−	99.8384i	0.349344	−	0.201694i
$496$	−169.013	−	453.184i	−0.340753	−	0.913677i
$497$	286.366	+	42.7471i	0.576190	+	0.0860102i
$498$	−304.169	+	363.953i	−0.610781	+	0.730828i
$499$	452.819	−	261.435i	0.907454	−	0.523919i	0.0278428	−	0.999612i	$-0.491136\pi$
$499$	452.819	−	261.435i	0.907454	−	0.523919i	0.879611	+	0.475694i	$0.157803\pi$
$500$	950.257	+	341.619i	1.90051	+	0.683238i
$501$	621.384	+	358.756i	1.24029	+	0.716080i
$502$	−255.933	−	44.6067i	−0.509827	−	0.0888581i
$503$		−	132.060i		−	0.262545i	−0.991346	−	0.131273i	$-0.958094\pi$
$503$		−	132.060i		−	0.262545i	0.991346	−	0.131273i	$-0.0419064\pi$
$504$	49.0773	−	342.670i	0.0973755	−	0.679902i
$505$	1220.11			2.41605
$506$	−16.1651	+	92.7481i	−0.0319469	+	0.183297i
$507$	210.904	−	365.296i	0.415983	−	0.720504i
$508$	−523.513	−	188.204i	−1.03054	−	0.370480i
$509$	−155.079	−	268.604i	−0.304673	−	0.527709i	0.672515	−	0.740083i	$-0.265214\pi$
$509$	−155.079	−	268.604i	−0.304673	−	0.527709i	−0.977189	+	0.212374i	$0.931881\pi$
$510$	554.918	+	463.766i	1.08807	+	0.909345i
$511$	−490.969	−	390.396i	−0.960801	−	0.763984i
$512$	−9.10394	−	511.919i	−0.0177811	−	0.999842i
$513$	−59.2201	−	102.572i	−0.115439	−	0.199946i
$514$	−503.961	+	184.555i	−0.980468	+	0.359057i
$515$	−764.806	−	441.561i	−1.48506	−	0.857400i
$516$	411.165	+	486.093i	0.796830	+	0.942040i
$517$	152.412			0.294801
$518$	542.817	−	111.653i	1.04791	−	0.215545i
$519$	272.369			0.524797
$520$	−3.27428	−	552.394i	−0.00629669	−	1.06230i
$521$	52.9121	+	30.5488i	0.101559	+	0.0586349i	0.549919	−	0.835218i	$-0.314659\pi$
$521$	52.9121	+	30.5488i	0.101559	+	0.0586349i	−0.448360	+	0.893853i	$0.647992\pi$
$522$	−200.057	+	73.2626i	−0.383250	+	0.140350i
$523$	256.923	+	445.004i	0.491249	+	0.850868i	0.999949	−	0.0100759i	$-0.00320730\pi$
$523$	256.923	+	445.004i	0.491249	+	0.850868i	−0.508701	+	0.860944i	$0.669874\pi$
$524$	65.1247	+	360.993i	0.124284	+	0.688918i
$525$	534.969	+	1357.41i	1.01899	+	2.58554i
$526$	−301.889	+	361.224i	−0.573933	+	0.686738i
$527$	158.326	+	274.229i	0.300429	+	0.520359i
$528$	224.147	+	37.6991i	0.424520	+	0.0713997i
$529$	181.152	−	313.765i	0.342443	−	0.593128i
$530$	19.5074	−	111.925i	0.0368064	−	0.211179i
$531$	98.3784			0.185270
$532$	−9.15018	−	301.849i	−0.0171996	−	0.567385i
$533$			574.246i			1.07739i
$534$	−36.1540	+	207.435i	−0.0677041	+	0.388455i
$535$	721.318	+	416.453i	1.34826	+	0.778417i
$536$	−31.5092	−	53.8361i	−0.0587859	−	0.100440i
$537$	807.525	−	466.225i	1.50377	−	0.868202i
$538$	454.913	−	544.325i	0.845563	−	1.01176i
$539$	−121.885	−	130.616i	−0.226133	−	0.242329i
$540$	69.0938	+	382.994i	0.127951	+	0.709248i
$541$	−92.7322	+	53.5390i	−0.171409	+	0.0989630i	−0.583250	−	0.812293i	$-0.698219\pi$
$541$	−92.7322	+	53.5390i	−0.171409	+	0.0989630i	0.411841	+	0.911256i	$0.364886\pi$
$542$	792.285	−	290.142i	1.46178	−	0.535318i
$543$	−70.6863	+	122.432i	−0.130177	+	0.225474i
$544$	61.4644	+	329.513i	0.112986	+	0.605722i
$545$			1736.05i			3.18541i
$546$	317.807	−	282.391i	0.582064	−	0.517200i
$547$		−	43.3240i		−	0.0792030i	−0.999216	−	0.0396015i	$-0.987391\pi$
$547$		−	43.3240i		−	0.0792030i	0.999216	−	0.0396015i	$-0.0126088\pi$
$548$	−609.519	+	515.565i	−1.11226	+	0.940812i
$549$	−37.5744	+	65.0808i	−0.0684416	+	0.118544i
$550$	−366.286	+	134.137i	−0.665974	+	0.243886i
$551$	−160.959	+	92.9296i	−0.292121	+	0.168656i
$552$	349.717	+	199.155i	0.633545	+	0.360788i
$553$	181.705	+	461.051i	0.328581	+	0.833727i
$554$	−565.553	−	472.655i	−1.02085	−	0.853167i
$555$	1183.40	−	683.235i	2.13225	−	1.23105i
$556$	−148.596	−	53.4207i	−0.267260	−	0.0960803i
$557$	−62.7878	−	36.2506i	−0.112725	−	0.0650818i	0.442577	−	0.896730i	$-0.354064\pi$
$557$	−62.7878	−	36.2506i	−0.112725	−	0.0650818i	−0.555302	+	0.831648i	$0.687397\pi$
$558$	64.1707	−	368.182i	0.115001	−	0.659825i
$559$			318.377i			0.569547i
$560$	−307.247	+	943.520i	−0.548655	+	1.68486i
$561$	−148.805			−0.265250
$562$	69.5255	+	12.1176i	0.123711	+	0.0215616i
$563$	−292.471	+	506.575i	−0.519487	+	0.899779i	0.480256	+	0.877128i	$0.340544\pi$
$563$	−292.471	+	506.575i	−0.519487	+	0.899779i	−0.999743	+	0.0226503i	$0.992790\pi$
$564$	220.411	−	613.102i	0.390800	−	1.08706i
$565$	−451.280	−	781.639i	−0.798725	−	1.38343i
$566$	−252.171	+	301.734i	−0.445531	+	0.533099i
$567$	−428.792	+	539.257i	−0.756247	+	0.951071i
$568$	287.545	+	163.749i	0.506241	+	0.288291i
$569$	−371.765	−	643.915i	−0.653365	−	1.13166i	−0.982301	−	0.187309i	$-0.940023\pi$
$569$	−371.765	−	643.915i	−0.653365	−	1.13166i	0.328936	−	0.944352i	$-0.393310\pi$
$570$	−256.059	−	699.215i	−0.449226	−	1.22669i
$571$	−893.793	−	516.031i	−1.56531	−	0.903733i	−0.996704	−	0.0811234i	$-0.974149\pi$
$571$	−893.793	−	516.031i	−1.56531	−	0.903733i	−0.568607	−	0.822609i	$-0.692517\pi$
$572$	73.4047	+	86.7816i	0.128330	+	0.151716i
$573$	−1267.26			−2.21163
$574$	325.204	−	978.917i	0.566557	−	1.70543i
$575$	−690.666			−1.20116
$576$	193.734	−	344.937i	0.336344	−	0.598849i
$577$	−825.404	−	476.547i	−1.43051	−	0.825905i	−0.433350	−	0.901226i	$-0.642668\pi$
$577$	−825.404	−	476.547i	−1.43051	−	0.825905i	−0.997159	+	0.0753213i	$0.976002\pi$
$578$	123.298	+	336.687i	0.213318	+	0.582504i
$579$	−388.933	−	673.652i	−0.671732	−	1.16347i
$580$	601.004	−	108.424i	1.03621	−	0.186937i
$581$	421.402	+	62.9044i	0.725305	+	0.108269i
$582$	19.5294	+	16.3214i	0.0335556	+	0.0280437i
$583$	11.6884	+	20.2450i	0.0200488	+	0.0347255i
$584$	−362.110	−	618.695i	−0.620051	−	1.05941i
$585$	213.420	−	369.654i	0.364820	−	0.631887i
$586$	625.713	+	109.056i	1.06777	+	0.186102i
$587$	96.2876			0.164033			0.0820167	−	0.996631i	$-0.473864\pi$
$587$	96.2876			0.164033			0.0820167	+	0.996631i	$0.473864\pi$
$588$	−701.687	+	301.414i	−1.19334	+	0.512608i
$589$		−	326.035i		−	0.553540i
$590$	−277.813	−	48.4202i	−0.470870	−	0.0820681i
$591$	−52.3201	−	30.2071i	−0.0885282	−	0.0511118i
$592$	624.577	+	105.047i	1.05503	+	0.177445i
$593$	44.1840	−	25.5096i	0.0745092	−	0.0430179i	−0.462283	−	0.886733i	$-0.652969\pi$
$593$	44.1840	−	25.5096i	0.0745092	−	0.0430179i	0.536792	+	0.843715i	$0.319636\pi$
$594$	−61.4443	−	51.3514i	−0.103442	−	0.0864501i
$595$	95.9103	−	642.511i	0.161194	−	1.07985i
$596$	373.109	−	67.3105i	0.626023	−	0.112937i
$597$	189.509	−	109.413i	0.317435	−	0.183271i
$598$	69.2058	+	188.979i	0.115729	+	0.316018i
$599$	−451.118	+	781.359i	−0.753119	+	1.30444i	0.193186	+	0.981162i	$0.438118\pi$
$599$	−451.118	+	781.359i	−0.753119	+	1.30444i	−0.946304	+	0.323277i	$0.895215\pi$
$600$	9.88355	+	1667.43i	0.0164726	+	2.77904i
$601$		−	903.595i		−	1.50349i	−0.659456	−	0.751743i	$-0.729213\pi$
$601$		−	903.595i		−	1.50349i	0.659456	−	0.751743i	$-0.270787\pi$
$602$	180.301	−	542.736i	0.299504	−	0.901555i
$603$		−	48.2000i		−	0.0799337i
$604$	−203.300	+	171.963i	−0.336590	+	0.284706i
$605$	−477.125	+	826.406i	−0.788637	+	1.36596i
$606$	369.036	+	1007.72i	0.608971	+	1.66290i
$607$	−306.928	+	177.205i	−0.505648	+	0.291936i	−0.731043	−	0.682332i	$-0.760966\pi$
$607$	−306.928	+	177.205i	−0.505648	+	0.291936i	0.225395	+	0.974267i	$0.427633\pi$
$608$	114.831	−	325.465i	0.188867	−	0.535305i
$609$	367.886	+	292.526i	0.604082	+	0.480338i
$610$	138.139	−	165.290i	0.226457	−	0.270967i
$611$	282.154	−	162.902i	0.461791	−	0.266615i
$612$	−87.6222	+	243.733i	−0.143174	+	0.398256i
$613$	290.984	+	168.000i	0.474688	+	0.274061i	0.718200	−	0.695837i	$-0.244966\pi$
$613$	290.984	+	168.000i	0.474688	+	0.274061i	−0.243512	+	0.969898i	$0.578300\pi$
$614$	−260.460	−	45.3956i	−0.424201	−	0.0739342i
$615$		−	2543.47i		−	4.13573i
$616$	−75.9873	−	189.507i	−0.123356	−	0.307641i
$617$	223.359			0.362008			0.181004	−	0.983482i	$-0.442065\pi$
$617$	223.359			0.362008			0.181004	+	0.983482i	$0.442065\pi$
$618$	133.372	−	765.230i	0.215813	−	1.23824i
$619$	−363.026	+	628.780i	−0.586472	+	1.01580i	0.408218	+	0.912885i	$0.366150\pi$
$619$	−363.026	+	628.780i	−0.586472	+	1.01580i	−0.994690	+	0.102915i	$0.967183\pi$
$620$	−362.426	+	1008.13i	−0.584558	+	1.62602i
$621$	−70.8925	−	122.789i	−0.114159	−	0.197728i
$622$	−709.617	−	593.054i	−1.14086	−	0.953463i
$623$	175.970	−	69.3516i	0.282456	−	0.111319i
$624$	455.247	−	169.783i	0.729563	−	0.272088i
$625$	−449.635	−	778.791i	−0.719416	−	1.24607i
$626$	1063.04	−	389.296i	1.69815	−	0.621879i
$627$	132.688	+	76.6074i	0.211623	+	0.122181i
$628$	−77.9361	+	65.9227i	−0.124102	+	0.104972i
$629$	−414.642			−0.659208
$630$	−573.156	+	509.286i	−0.909772	+	0.808390i
$631$	−326.157			−0.516888			−0.258444	−	0.966026i	$-0.583210\pi$
$631$	−326.157			−0.516888			−0.258444	+	0.966026i	$0.583210\pi$
$632$	3.35700	+	566.350i	0.00531171	+	0.896124i
$633$	1250.09	+	721.741i	1.97487	+	1.14019i
$634$	−332.473	+	121.755i	−0.524405	+	0.192042i
$635$	616.097	+	1067.11i	0.970232	+	1.68049i
$636$	98.3419	−	17.7413i	0.154626	−	0.0278951i
$637$	−365.247	−	111.529i	−0.573386	−	0.175085i
$638$	−80.5818	+	96.4200i	−0.126304	+	0.151128i
$639$	127.843	+	221.431i	0.200067	+	0.346527i
$640$	−716.863	+	878.724i	−1.12010	+	1.37301i
$641$	299.187	−	518.208i	0.466751	−	0.808436i	−0.532528	−	0.846413i	$-0.678758\pi$
$641$	299.187	−	518.208i	0.466751	−	0.808436i	0.999279	+	0.0379764i	$0.0120912\pi$
$642$	−125.788	+	721.718i	−0.195932	+	1.12417i
$643$	−1008.20			−1.56796			−0.783979	−	0.620787i	$-0.786813\pi$
$643$	−1008.20			−1.56796			−0.783979	+	0.620787i	$0.786813\pi$
$644$	−10.9537	−	361.344i	−0.0170088	−	0.561093i
$645$		−	1410.16i		−	2.18630i
$646$	−38.7959	+	222.593i	−0.0600556	+	0.344572i
$647$	574.378	+	331.617i	0.887756	+	0.512546i	0.873208	−	0.487348i	$-0.162036\pi$
$647$	574.378	+	331.617i	0.887756	+	0.512546i	0.0145481	+	0.999894i	$0.495369\pi$
$648$	−679.545	+	397.724i	−1.04868	+	0.613772i
$649$	50.2509	−	29.0124i	0.0774283	−	0.0447032i
$650$	−534.721	+	639.819i	−0.822648	+	0.984337i
$651$	−767.075	+	302.312i	−1.17830	+	0.464381i
$652$	756.197	−	136.421i	1.15981	−	0.209235i
$653$	−857.892	+	495.304i	−1.31377	+	0.758506i	−0.982718	−	0.185107i	$-0.940737\pi$
$653$	−857.892	+	495.304i	−1.31377	+	0.758506i	−0.331052	+	0.943612i	$0.607404\pi$
$654$	−1433.85	+	525.089i	−2.19243	+	0.802889i
$655$	406.240	−	703.628i	0.620213	−	1.07424i
$656$	750.609	−	909.036i	1.14422	−	1.38573i
$657$		−	553.924i		−	0.843110i
$658$	−573.241	+	117.911i	−0.871187	+	0.179195i
$659$			82.2318i			0.124783i	0.998052	+	0.0623914i	$0.0198727\pi$
$659$			82.2318i			0.124783i	−0.998052	+	0.0623914i	$0.980127\pi$
$660$	−325.127	−	384.376i	−0.492616	−	0.582388i
$661$	313.110	−	542.322i	0.473691	−	0.820457i	−0.525855	−	0.850574i	$-0.676255\pi$
$661$	313.110	−	542.322i	0.473691	−	0.820457i	0.999546	+	0.0301171i	$0.00958802\pi$
$662$	931.804	−	341.235i	1.40756	−	0.515461i
$663$	−275.478	+	159.047i	−0.415502	+	0.239890i
$664$	423.137	+	240.965i	0.637254	+	0.362900i
$665$	−416.297	+	523.543i	−0.626010	+	0.787282i
$666$	375.512	+	313.830i	0.563831	+	0.471216i
$667$	−192.684	+	111.246i	−0.288882	+	0.166786i
$668$	249.195	−	693.167i	0.373046	−	1.03767i
$669$	22.8960	+	13.2190i	0.0342242	+	0.0197594i
$670$	−23.7232	+	136.113i	−0.0354078	+	0.203154i
$671$			44.3237i			0.0660562i
$672$	−872.210	+	31.6156i	−1.29793	+	0.0470470i
$673$	−150.211			−0.223196			−0.111598	−	0.993753i	$-0.535597\pi$
$673$	−150.211			−0.223196			−0.111598	+	0.993753i	$0.535597\pi$
$674$	406.258	+	70.8069i	0.602757	+	0.105055i
$675$	293.727	−	508.751i	0.435152	−	0.753705i
$676$	−407.495	−	146.495i	−0.602804	−	0.216709i
$677$	278.207	+	481.869i	0.410941	+	0.711771i	0.994993	−	0.0999455i	$-0.0318668\pi$
$677$	278.207	+	481.869i	0.410941	+	0.711771i	−0.584052	+	0.811716i	$0.698533\pi$
$678$	509.082	−	609.141i	0.750859	−	0.898438i
$679$	3.37540	−	22.6121i	0.00497113	−	0.0333020i
$680$	367.400	−	645.156i	0.540293	−	0.948759i
$681$	577.865	+	1000.89i	0.848553	+	1.46974i
$682$	−75.8013	−	206.989i	−0.111146	−	0.303503i
$683$	685.334	+	395.678i	1.00342	+	0.579323i	0.909258	−	0.416234i	$-0.136650\pi$
$683$	685.334	+	395.678i	1.00342	+	0.579323i	0.0941597	+	0.995557i	$0.469984\pi$
$684$	203.609	−	172.224i	0.297674	−	0.251789i
$685$	1768.22			2.58135
$686$	559.475	+	396.968i	0.815562	+	0.578670i
$687$	−694.302			−1.01063
$688$	416.157	−	503.992i	0.604879	−	0.732547i
$689$	43.2767	+	24.9858i	0.0628109	+	0.0362639i
$690$	−306.528	−	837.030i	−0.444244	−	1.21309i
$691$	−488.267	−	845.703i	−0.706609	−	1.22388i	−0.966108	−	0.258139i	$-0.916891\pi$
$691$	−488.267	−	845.703i	−0.706609	−	1.22388i	0.259499	−	0.965743i	$-0.416443\pi$
$692$	−49.6424	−	275.173i	−0.0717375	−	0.397649i
$693$	23.2920	−	156.035i	0.0336103	−	0.225158i
$694$	930.275	+	777.466i	1.34045	+	1.12027i
$695$	174.876	+	302.894i	0.251620	+	0.435819i
$696$	271.331	+	463.591i	0.389843	+	0.666080i
$697$	−385.895	+	668.390i	−0.553652	+	0.958953i
$698$	268.637	+	46.8209i	0.384867	+	0.0670787i
$699$	458.999			0.656651
$700$	1273.88	−	787.878i	1.81982	−	1.12554i
$701$			855.098i			1.21983i	0.792468	+	0.609913i	$0.208796\pi$
$701$			855.098i			1.21983i	−0.792468	+	0.609913i	$0.791204\pi$
$702$	−168.635	−	29.3915i	−0.240221	−	0.0418682i
$703$	369.730	+	213.464i	0.525932	+	0.303647i
$704$	−2.76613	−	233.325i	−0.00392916	−	0.331427i
$705$	−1249.73	+	721.530i	−1.77266	+	1.02345i
$706$	15.4602	+	12.9207i	0.0218983	+	0.0183013i
$707$	599.974	−	754.538i	0.848619	−	1.06724i
$708$	−44.0365	−	244.099i	−0.0621984	−	0.344772i
$709$	288.794	−	166.735i	0.407326	−	0.235170i	−0.282314	−	0.959322i	$-0.591102\pi$
$709$	288.794	−	166.735i	0.407326	−	0.235170i	0.689640	+	0.724152i	$0.257769\pi$
$710$	−252.035	−	688.225i	−0.354978	−	0.969331i
$711$	−218.812	+	378.993i	−0.307752	+	0.533042i
$712$	216.160	−	1.28127i	0.303595	−	0.00179954i
$713$		−	390.297i		−	0.547401i
$714$	559.677	−	115.120i	0.783861	−	0.161233i
$715$		−	251.755i		−	0.352105i
$716$	−618.204	−	730.862i	−0.863413	−	1.02076i
$717$	−90.3063	+	156.415i	−0.125950	+	0.218152i
$718$	272.086	+	742.978i	0.378949	+	1.03479i
$719$	−34.4877	+	19.9115i	−0.0479662	+	0.0276933i	−0.523791	−	0.851847i	$-0.675483\pi$
$719$	−34.4877	+	19.9115i	−0.0479662	+	0.0276933i	0.475825	+	0.879540i	$0.342150\pi$
$720$	−821.027	+	306.199i	−1.14032	+	0.425276i
$721$	−649.155	+	255.839i	−0.900354	+	0.354839i
$722$	−313.811	+	375.489i	−0.434641	+	0.520068i
$723$	−1237.09	+	714.237i	−1.71106	+	0.987879i
$724$	136.576	+	49.0992i	0.188641	+	0.0678166i
$725$	−798.344	−	460.924i	−1.10116	−	0.635757i
$726$	−826.864	−	144.114i	−1.13893	−	0.198505i
$727$			489.402i			0.673180i	0.941651	+	0.336590i	$0.109274\pi$
$727$			489.402i			0.673180i	−0.941651	+	0.336590i	$0.890726\pi$
$728$	−343.222	−	269.609i	−0.471459	−	0.370342i
$729$	−223.307			−0.306320
$730$	−272.632	+	1564.24i	−0.373468	+	2.14279i
$731$	−213.950	+	370.572i	−0.292681	+	0.506939i
$732$	178.299	+	64.0989i	0.243578	+	0.0875668i
$733$	−89.1592	−	154.428i	−0.121636	−	0.210680i	0.798777	−	0.601627i	$-0.205481\pi$
$733$	−89.1592	−	154.428i	−0.121636	−	0.210680i	−0.920413	+	0.390948i	$0.872147\pi$
$734$	−291.475	−	243.597i	−0.397105	−	0.331876i
$735$	1617.76	+	493.988i	2.20104	+	0.672093i
$736$	137.465	−	389.615i	0.186773	−	0.529368i
$737$	−14.2145	−	24.6202i	−0.0192869	−	0.0334060i
$738$	855.362	−	313.242i	1.15903	−	0.424447i
$739$	764.182	+	441.200i	1.03408	+	0.597024i	0.918149	−	0.396234i	$-0.129683\pi$
$739$	764.182	+	441.200i	1.03408	+	0.597024i	0.115926	+	0.993258i	$0.463017\pi$
$740$	−905.955	−	1071.05i	−1.22426	−	1.44737i
$741$	327.520			0.441997
$742$	−59.6239	−	67.1014i	−0.0803556	−	0.0904332i
$743$	1404.00			1.88964			0.944819	−	0.327591i	$-0.106237\pi$
$743$	1404.00			1.88964			0.944819	+	0.327591i	$0.106237\pi$
$744$	−942.267	+	5.58522i	−1.26649	+	0.00750701i
$745$	−727.244	−	419.875i	−0.976167	−	0.563590i
$746$	−676.286	+	247.662i	−0.906549	+	0.331987i
$747$	188.127	+	325.846i	0.251844	+	0.436206i
$748$	27.1215	+	150.337i	0.0362586	+	0.200985i
$749$	612.243	−	241.291i	0.817414	−	0.322151i
$750$	1261.55	−	1509.51i	1.68207	−	2.01268i
$751$	−102.840	−	178.124i	−0.136938	−	0.237183i	0.789398	−	0.613881i	$-0.210393\pi$
$751$	−102.840	−	178.124i	−0.136938	−	0.237183i	−0.926336	+	0.376698i	$0.877059\pi$
$752$	−659.584	−	110.935i	−0.877107	−	0.147520i
$753$	−253.060	+	438.312i	−0.336069	+	0.582088i
$754$	−46.1219	+	264.626i	−0.0611696	+	0.350963i
$755$	589.777			0.781162
$756$	270.827	+	145.604i	0.358237	+	0.192598i
$757$			15.0345i			0.0198606i	0.999951	+	0.00993032i	$0.00316097\pi$
$757$			15.0345i			0.0198606i	−0.999951	+	0.00993032i	$0.996839\pi$
$758$	3.87804	−	22.2504i	0.00511614	−	0.0293541i
$759$	158.841	+	91.7068i	0.209276	+	0.120826i
$760$	−659.742	+	386.134i	−0.868081	+	0.508071i
$761$	−544.290	+	314.246i	−0.715229	+	0.412938i	−0.812994	−	0.582272i	$-0.802164\pi$
$761$	−544.290	+	314.246i	−0.715229	+	0.412938i	0.0977649	+	0.995210i	$0.468831\pi$
$762$	−695.011	+	831.613i	−0.912088	+	1.09136i
$763$	1073.61	+	853.682i	1.40709	+	1.11885i
$764$	230.973	+	1280.31i	0.302320	+	1.67579i
$765$	496.817	−	286.837i	0.649434	−	0.374951i
$766$	−815.541	+	298.659i	−1.06467	+	0.389894i
$767$	62.0184	−	107.419i	0.0808584	−	0.140051i
$768$	−942.586	−	326.296i	−1.22733	−	0.424865i
$769$		−	442.918i		−	0.575967i	−0.957635	−	0.287983i	$-0.907015\pi$
$769$		−	442.918i		−	0.575967i	0.957635	−	0.287983i	$-0.0929848\pi$
$770$	−142.572	+	429.166i	−0.185159	+	0.557359i
$771$			1045.57i			1.35612i
$772$	−609.698	+	515.717i	−0.789764	+	0.668027i
$773$	84.5990	−	146.530i	0.109442	−	0.189560i	−0.806102	−	0.591777i	$-0.798427\pi$
$773$	84.5990	−	146.530i	0.109442	−	0.189560i	0.915545	+	0.402217i	$0.131760\pi$
$774$	474.234	−	173.669i	0.612706	−	0.224379i
$775$	1400.46	−	808.555i	1.80704	−	1.04330i
$776$	12.9300	−	22.7051i	0.0166624	−	0.0292592i
$777$	159.396	−	1067.81i	0.205143	−	1.37427i
$778$	66.2392	+	55.3586i	0.0851404	+	0.0711551i
$779$	688.196	−	397.330i	0.883435	−	0.510051i
$780$	−1012.73	−	364.076i	−1.29837	−	0.466764i
$781$	130.602	+	75.4034i	0.167225	+	0.0965472i
$782$	−46.4426	+	266.467i	−0.0593896	+	0.340750i
$783$		−	189.244i		−	0.241690i
$784$	432.406	+	653.973i	0.551539	+	0.834149i
$785$	226.094			0.288018
$786$	704.018	+	122.704i	0.895697	+	0.156111i
$787$	23.2437	−	40.2593i	0.0295346	−	0.0511554i	−0.850880	−	0.525360i	$-0.823931\pi$
$787$	23.2437	−	40.2593i	0.0295346	−	0.0511554i	0.880415	+	0.474204i	$0.157264\pi$
$788$	−20.9820	+	58.3642i	−0.0266269	+	0.0740663i
$789$	458.567	+	794.261i	0.581200	+	1.00667i
$790$	804.441	−	962.551i	1.01828	−	1.21842i
$791$	−705.293	−	105.282i	−0.891647	−	0.133100i
$792$	89.2236	−	156.677i	0.112656	−	0.197825i
$793$	47.3743	+	82.0548i	0.0597407	+	0.103474i
$794$	334.791	+	914.206i	0.421651	+	1.15139i
$795$	−191.683	−	110.668i	−0.241110	−	0.139205i
$796$	−145.079	−	171.518i	−0.182260	−	0.215474i
$797$	−1351.86			−1.69618			−0.848092	−	0.529850i	$-0.822248\pi$
$797$	−1351.86			−1.69618			−0.848092	+	0.529850i	$0.822248\pi$
$798$	−558.322	−	185.479i	−0.699652	−	0.232430i
$799$	437.882			0.548038
$800$	1682.79	−	313.892i	2.10348	−	0.392365i
$801$	144.651	+	83.5141i	0.180588	+	0.104262i
$802$	−376.141	−	1027.12i	−0.469004	−	1.28070i
$803$	−163.355	−	282.940i	−0.203431	−	0.352354i
$804$	−119.595	+	21.5754i	−0.148750	+	0.0268351i
$805$	−498.349	+	626.733i	−0.619067	+	0.778551i
$806$	−361.563	−	302.172i	−0.448590	−	0.374903i
$807$	−691.009	−	1196.86i	−0.856269	−	1.48310i
$808$	950.831	−	556.503i	1.17677	−	0.688741i
$809$	701.563	−	1215.14i	0.867198	−	1.50203i	0.00235012	−	0.999997i	$-0.499252\pi$
$809$	701.563	−	1215.14i	0.867198	−	1.50203i	0.864848	−	0.502034i	$-0.167415\pi$
$810$	1718.08	+	299.446i	2.12109	+	0.369686i
$811$	−689.037			−0.849614			−0.424807	−	0.905284i	$-0.639658\pi$
$811$	−689.037			−0.849614			−0.424807	+	0.905284i	$0.639658\pi$
$812$	228.485	−	424.989i	0.281386	−	0.523385i
$813$		−	1643.75i		−	2.02184i
$814$	284.359	+	49.5610i	0.349335	+	0.0608858i
$815$	−1473.94	−	850.977i	−1.80851	−	1.04414i
$816$	643.977	+	108.310i	0.789187	+	0.132733i
$817$	381.553	−	220.290i	0.467017	−	0.269632i
$818$	−102.462	−	85.6314i	−0.125259	−	0.104684i
$819$	−123.655	−	313.756i	−0.150982	−	0.383097i
$820$	−2569.65	+	463.576i	−3.13372	+	0.565336i
$821$	19.3490	−	11.1711i	0.0235675	−	0.0136067i	−0.488170	−	0.872749i	$-0.662335\pi$
$821$	19.3490	−	11.1711i	0.0235675	−	0.0136067i	0.511737	+	0.859142i	$0.329002\pi$
$822$	534.822	+	1460.43i	0.650635	+	1.77667i
$823$	−512.111	+	887.003i	−0.622249	+	1.07777i	0.366816	+	0.930293i	$0.380448\pi$
$823$	−512.111	+	887.003i	−0.622249	+	1.07777i	−0.989066	+	0.147474i	$0.952886\pi$
$824$	−797.415	+	4.72662i	−0.967737	+	0.00573619i
$825$			759.934i			0.921132i
$826$	−166.555	+	147.995i	−0.201641	+	0.179171i
$827$			466.377i			0.563938i	0.959424	+	0.281969i	$0.0909875\pi$
$827$			466.377i			0.563938i	−0.959424	+	0.281969i	$0.909012\pi$
$828$	243.741	−	206.169i	0.294373	−	0.248997i
$829$	750.350	−	1299.64i	0.905126	−	1.56773i	0.0843791	−	0.996434i	$-0.473109\pi$
$829$	750.350	−	1299.64i	0.905126	−	1.56773i	0.820747	−	0.571291i	$-0.193557\pi$
$830$	−370.881	−	1012.76i	−0.446845	−	1.22019i
$831$	−1243.54	+	717.958i	−1.49644	+	0.863969i
$832$	−254.504	−	428.988i	−0.305895	−	0.515611i
$833$	−350.179	−	375.260i	−0.420383	−	0.450493i
$834$	−197.275	+	236.049i	−0.236541	+	0.283033i
$835$	−1412.93	+	815.755i	−1.69213	+	0.976952i
$836$	53.2120	−	148.016i	0.0636508	−	0.177053i
$837$	287.496	+	165.986i	0.343484	+	0.198311i
$838$	−1084.00	−	188.930i	−1.29355	−	0.225454i
$839$			1068.18i			1.27316i	0.771212	+	0.636579i	$0.219651\pi$
$839$			1068.18i			1.27316i	−0.771212	+	0.636579i	$0.780349\pi$
$840$	1520.21	+	1194.16i	1.80977	+	1.42162i
$841$	544.034			0.646890
$842$	199.037	−	1141.98i	0.236386	−	1.35627i
$843$	68.7449	−	119.070i	0.0815479	−	0.141245i
$844$	501.327	−	1394.51i	0.593989	−	1.65226i
$845$	479.562	+	830.625i	0.567529	+	0.982988i
$846$	−396.559	−	331.420i	−0.468746	−	0.391749i
$847$	276.445	+	701.440i	0.326381	+	0.828146i
$848$	−35.8478	−	96.1206i	−0.0422734	−	0.113350i
$849$	383.045	+	663.453i	0.451172	+	0.781453i
$850$	−1052.35	+	385.379i	−1.23805	+	0.453387i
$851$	442.605	+	255.538i	0.520100	+	0.300280i
$852$	492.193	−	416.325i	0.577692	−	0.488644i
$853$	−918.640			−1.07695			−0.538476	−	0.842641i	$-0.681000\pi$
$853$	−918.640			−1.07695			−0.538476	+	0.842641i	$0.681000\pi$
$854$	−34.2902	−	166.707i	−0.0401525	−	0.195208i
$855$	−590.673			−0.690846
$856$	752.072	−	4.45785i	0.878589	−	0.00520777i
$857$	−438.167	−	252.976i	−0.511280	−	0.295188i	0.222080	−	0.975029i	$-0.428716\pi$
$857$	−438.167	−	252.976i	−0.511280	−	0.295188i	−0.733360	+	0.679841i	$0.762049\pi$
$858$	207.931	−	76.1465i	0.242344	−	0.0887488i
$859$	688.516	+	1192.54i	0.801532	+	1.38829i	0.918607	+	0.395171i	$0.129315\pi$
$859$	688.516	+	1192.54i	0.801532	+	1.38829i	−0.117075	+	0.993123i	$0.537352\pi$
$860$	−1424.68	+	257.018i	−1.65660	+	0.298858i
$861$	−1572.93	−	1250.72i	−1.82687	−	1.45264i
$862$	−553.893	+	662.758i	−0.642567	+	0.768861i
$863$	−458.817	−	794.695i	−0.531654	−	0.920852i	−0.999317	−	0.0369450i	$-0.988237\pi$
$863$	−458.817	−	794.695i	−0.531654	−	0.920852i	0.467663	−	0.883907i	$-0.345096\pi$
$864$	228.532	+	266.953i	0.264505	+	0.308974i
$865$	−309.663	+	536.352i	−0.357992	+	0.620060i
$866$	−0.0492657	+	0.282664i	−5.68888e−5	+	0.000326402i
$867$	698.525			0.805681
$868$	445.232	+	719.871i	0.512940	+	0.829344i
$869$			258.116i			0.297026i
$870$	204.284	−	1172.09i	0.234810	−	1.34723i
$871$	−52.6294	−	30.3856i	−0.0604241	−	0.0348859i
$872$	791.829	+	1352.91i	0.908061	+	1.55150i
$873$	17.4846	−	10.0947i	0.0200282	−	0.0115633i
$874$	178.594	−	213.696i	0.204341	−	0.244503i
$875$	−1747.78	−	260.898i	−1.99746	−	0.298170i
$876$	−1374.41	+	247.949i	−1.56896	+	0.283047i
$877$	606.173	−	349.974i	0.691189	−	0.399058i	−0.112868	−	0.993610i	$-0.536004\pi$
$877$	606.173	−	349.974i	0.691189	−	0.399058i	0.804057	+	0.594552i	$0.202671\pi$
$878$	359.359	−	131.601i	0.409293	−	0.149887i
$879$	618.688	−	1071.60i	0.703854	−	1.21911i
$880$	−329.074	+	398.530i	−0.373948	+	0.452875i
$881$			6.37652i			0.00723783i	0.999993	+	0.00361891i	$0.00115194\pi$
$881$			6.37652i			0.00723783i	−0.999993	+	0.00361891i	$0.998848\pi$
$882$	33.1092	+	604.887i	0.0375388	+	0.685813i
$883$		−	1548.35i		−	1.75351i	−0.480935	−	0.876756i	$-0.659703\pi$
$883$		−	1548.35i		−	1.75351i	0.480935	−	0.876756i	$-0.340297\pi$
$884$	210.893	+	249.325i	0.238567	+	0.282042i
$885$	−274.694	+	475.784i	−0.310389	+	0.537609i
$886$	−739.008	+	270.631i	−0.834094	+	0.305453i
$887$	634.250	−	366.185i	0.715051	−	0.412835i	−0.0978774	−	0.995198i	$-0.531205\pi$
$887$	634.250	−	366.185i	0.715051	−	0.412835i	0.812928	+	0.582364i	$0.197872\pi$
$888$	610.593	−	1072.21i	0.687605	−	1.20744i
$889$	962.882	+	143.733i	1.08311	+	0.161680i
$890$	−367.378	−	307.032i	−0.412785	−	0.344980i
$891$	−310.768	+	179.422i	−0.348785	+	0.201371i
$892$	9.18203	−	25.5410i	0.0102938	−	0.0286334i
$893$	−390.454	−	225.429i	−0.437238	−	0.252440i
$894$	126.822	−	727.647i	0.141859	−	0.813923i
$895$			2120.24i			2.36899i
$896$	190.911	+	875.425i	0.213070	+	0.977037i
$897$	392.074			0.437095
$898$	1430.10	+	249.253i	1.59254	+	0.277565i
$899$	260.469	−	451.146i	0.289732	−	0.501831i
$900$	1244.72	+	447.478i	1.38302	+	0.497197i
$901$	33.5811	+	58.1641i	0.0372709	+	0.0645551i
$902$	344.536	−	412.253i	0.381969	−	0.457043i
$903$	−872.074	−	693.433i	−0.965752	−	0.767921i
$904$	−708.197	−	403.299i	−0.783403	−	0.446128i
$905$	−160.730	−	278.392i	−0.177602	−	0.307615i
$906$	178.386	+	487.113i	0.196894	+	0.537653i
$907$	−626.862	−	361.919i	−0.691138	−	0.399029i	0.112900	−	0.993606i	$-0.463986\pi$
$907$	−626.862	−	361.919i	−0.691138	−	0.399029i	−0.804038	+	0.594578i	$0.797319\pi$
$908$	905.870	−	766.236i	0.997655	−	0.843872i
$909$	851.288			0.936511
$910$	194.765	+	946.884i	0.214028	+	1.04053i
$911$	1600.04			1.75636			0.878179	−	0.478332i	$-0.158758\pi$
$911$	1600.04			1.75636			0.878179	+	0.478332i	$0.158758\pi$
$912$	−518.466	−	428.108i	−0.568493	−	0.469417i
$913$	192.188	+	110.960i	0.210502	+	0.121533i
$914$	−47.6906	−	130.228i	−0.0521779	−	0.142481i
$915$	−209.832	−	363.440i	−0.229325	−	0.397202i
$916$	126.544	+	701.448i	0.138149	+	0.765773i
$917$	−235.374	−	597.228i	−0.256678	−	0.651284i
$918$	−176.531	−	147.533i	−0.192299	−	0.160712i
$919$	262.042	+	453.871i	0.285139	+	0.493875i	0.972643	−	0.232306i	$-0.0746270\pi$
$919$	262.042	+	453.871i	0.285139	+	0.493875i	−0.687504	+	0.726180i	$0.741294\pi$
$920$	−789.778	+	462.242i	−0.858454	+	0.502436i
$921$	−257.535	+	446.064i	−0.279626	+	0.484326i
$922$	−1513.20	−	263.736i	−1.64122	−	0.286048i
$923$	322.372			0.349266
$924$	−397.583	+	12.0522i	−0.430285	+	0.0130436i
$925$			2117.53i			2.28922i
$926$	−425.027	−	74.0781i	−0.458992	−	0.0799980i
$927$	−533.618	−	308.084i	−0.575640	−	0.332346i
$928$	418.910	−	358.618i	0.451412	−	0.386442i
$929$	551.791	−	318.577i	0.593962	−	0.342924i	−0.172700	−	0.984974i	$-0.555249\pi$
$929$	551.791	−	318.577i	0.593962	−	0.342924i	0.766663	+	0.642050i	$0.221916\pi$
$930$	1601.45	+	1338.39i	1.72199	+	1.43913i
$931$	119.060	+	514.892i	0.127884	+	0.553053i
$932$	−83.6577	−	463.723i	−0.0897615	−	0.497557i
$933$	−1560.31	+	900.844i	−1.67235	+	0.965534i
$934$	−19.9019	−	54.3456i	−0.0213082	−	0.0581859i
$935$	169.180	−	293.029i	0.180941	−	0.313400i
$936$	−2.28452	−	385.415i	−0.00244072	−	0.411768i
$937$			383.587i			0.409378i	0.978827	+	0.204689i	$0.0656182\pi$
$937$			383.587i			0.409378i	−0.978827	+	0.204689i	$0.934382\pi$
$938$	72.5094	+	81.6030i	0.0773022	+	0.0869968i
$939$		−	2205.50i		−	2.34877i
$940$	956.733	+	1131.08i	1.01780	+	1.20328i
$941$	130.295	−	225.678i	0.138465	−	0.239828i	−0.788451	−	0.615098i	$-0.789117\pi$
$941$	130.295	−	225.678i	0.138465	−	0.239828i	0.926916	+	0.375270i	$0.122450\pi$
$942$	68.3850	+	186.737i	0.0725955	+	0.198235i
$943$	823.840	−	475.644i	0.873637	−	0.504394i
$944$	−238.585	+	88.9794i	−0.252738	+	0.0942579i
$945$	−249.719	−	633.626i	−0.264252	−	0.670504i
$946$	191.019	−	228.564i	0.201923	−	0.241610i
$947$	−851.444	+	491.581i	−0.899096	+	0.519093i	−0.876907	−	0.480660i	$-0.840397\pi$
$947$	−851.444	+	491.581i	−0.899096	+	0.519093i	−0.0221894	+	0.999754i	$0.507064\pi$
$948$	1038.31	+	373.274i	1.09526	+	0.393749i
$949$	−604.827	−	349.197i	−0.637331	−	0.367963i
$950$	1136.76	+	198.127i	1.19659	+	0.208554i
$951$			689.781i			0.725322i
$952$	−218.313	−	544.455i	−0.229320	−	0.571907i
$953$	−1137.60			−1.19370			−0.596851	−	0.802352i	$-0.703582\pi$
$953$	−1137.60			−1.19370			−0.596851	+	0.802352i	$0.703582\pi$
$954$	13.6106	−	78.0916i	0.0142669	−	0.0818571i
$955$	1440.78	−	2495.50i	1.50867	−	2.61309i
$956$	174.484	+	62.7274i	0.182515	+	0.0656144i
$957$	122.403	+	212.008i	0.127903	+	0.221534i
$958$	1232.23	+	1029.82i	1.28625	+	1.07497i
$959$	869.505	−	1093.51i	0.906679	−	1.14026i
$960$	1127.26	+	1900.09i	1.17423	+	1.97926i
$961$	−23.5835	−	40.8479i	−0.0245406	−	0.0425056i
$962$	579.394	−	212.180i	0.602281	−	0.220561i
$963$	503.275	+	290.566i	0.522612	+	0.301730i
$964$	947.062	+	1119.65i	0.982430	+	1.16146i
$965$	1768.75			1.83290
$966$	−668.368	−	222.037i	−0.691893	−	0.229852i
$967$	−1296.35			−1.34059			−0.670297	−	0.742093i	$-0.733833\pi$
$967$	−1296.35			−1.34059			−0.670297	+	0.742093i	$0.733833\pi$
$968$	5.10731	+	861.641i	0.00527615	+	0.890125i
$969$	381.214	+	220.094i	0.393410	+	0.227135i
$970$	−54.3436	+	19.9011i	−0.0560244	+	0.0205166i
$971$	−665.237	−	1152.22i	−0.685105	−	1.18664i	−0.973404	−	0.229096i	$-0.926423\pi$
$971$	−665.237	−	1152.22i	−0.685105	−	1.18664i	0.288299	−	0.957540i	$-0.406910\pi$
$972$	202.147	+	1120.52i	0.207971	+	1.15280i
$973$	273.309	+	40.7980i	0.280893	+	0.0419301i
$974$	25.5534	−	30.5758i	0.0262355	−	0.0313920i
$975$	812.237	+	1406.84i	0.833063	+	1.44291i
$976$	32.2616	−	191.817i	0.0330549	−	0.196534i
$977$	−693.081	+	1200.45i	−0.709397	+	1.22871i	0.255684	+	0.966760i	$0.417699\pi$
$977$	−693.081	+	1200.45i	−0.709397	+	1.22871i	−0.965081	+	0.261952i	$0.915634\pi$
$978$	257.035	−	1474.75i	0.262817	−	1.50793i
$979$	98.5153			0.100629
$980$	204.217	−	1724.45i	0.208385	−	1.75964i
$981$			1211.27i			1.23473i
$982$	26.1680	−	150.140i	0.0266476	−	0.152892i
$983$	−601.161	−	347.081i	−0.611558	−	0.353083i	0.162017	−	0.986788i	$-0.448200\pi$
$983$	−601.161	−	347.081i	−0.611558	−	0.353083i	−0.773575	+	0.633705i	$0.781533\pi$
$984$	−1160.10	−	1982.13i	−1.17897	−	2.01436i
$985$	118.968	−	68.6861i	0.120780	−	0.0697321i
$986$	−231.513	+	277.016i	−0.234800	+	0.280949i
$987$	−168.331	+	1127.66i	−0.170548	+	1.14251i
$988$	−59.6941	−	330.891i	−0.0604192	−	0.334910i
$989$	456.757	−	263.709i	0.461838	−	0.266642i
$990$	−374.999	+	137.328i	−0.378787	+	0.138715i
$991$	467.257	−	809.312i	0.471500	−	0.816662i	−0.527968	−	0.849264i	$-0.677046\pi$
$991$	467.257	−	809.312i	0.471500	−	0.816662i	0.999468	+	0.0326018i	$0.0103793\pi$
$992$	177.381	+	950.947i	0.178812	+	0.958616i
$993$		−	1933.22i		−	1.94684i
$994$	−549.547	−	182.564i	−0.552865	−	0.183666i
$995$			497.576i			0.500076i
$996$	724.287	−	612.642i	0.727195	−	0.615102i
$997$	−769.103	+	1332.12i	−0.771417	+	1.33613i	0.165370	+	0.986232i	$0.447118\pi$
$997$	−769.103	+	1332.12i	−0.771417	+	1.33613i	−0.936786	+	0.349902i	$0.886215\pi$
$998$	−981.967	+	359.606i	−0.983935	+	0.360326i
$999$	−376.463	+	217.351i	−0.376840	+	0.217568i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	56.3.j.a.45.1	yes	28
4.3	odd	2		224.3.n.a.17.13		28
7.2	even	3		392.3.j.e.117.10		28
7.3	odd	6		392.3.h.a.293.17		28
7.4	even	3		392.3.h.a.293.18		28
7.5	odd	6	inner	56.3.j.a.5.10	yes	28
7.6	odd	2		392.3.j.e.325.1		28
8.3	odd	2		224.3.n.a.17.2		28
8.5	even	2	inner	56.3.j.a.45.10	yes	28
28.3	even	6		1568.3.h.a.881.25		28
28.11	odd	6		1568.3.h.a.881.3		28
28.19	even	6		224.3.n.a.145.2		28
56.3	even	6		1568.3.h.a.881.4		28
56.5	odd	6	inner	56.3.j.a.5.1	✓	28
56.11	odd	6		1568.3.h.a.881.26		28
56.13	odd	2		392.3.j.e.325.10		28
56.19	even	6		224.3.n.a.145.13		28
56.37	even	6		392.3.j.e.117.1		28
56.45	odd	6		392.3.h.a.293.20		28
56.53	even	6		392.3.h.a.293.19		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.3.j.a.5.1	✓	28	56.5	odd	6	inner
56.3.j.a.5.10	yes	28	7.5	odd	6	inner
56.3.j.a.45.1	yes	28	1.1	even	1	trivial
56.3.j.a.45.10	yes	28	8.5	even	2	inner
224.3.n.a.17.2		28	8.3	odd	2
224.3.n.a.17.13		28	4.3	odd	2
224.3.n.a.145.2		28	28.19	even	6
224.3.n.a.145.13		28	56.19	even	6
392.3.h.a.293.17		28	7.3	odd	6
392.3.h.a.293.18		28	7.4	even	3
392.3.h.a.293.19		28	56.53	even	6
392.3.h.a.293.20		28	56.45	odd	6
392.3.j.e.117.1		28	56.37	even	6
392.3.j.e.117.10		28	7.2	even	3
392.3.j.e.325.1		28	7.6	odd	2
392.3.j.e.325.10		28	56.13	odd	2
1568.3.h.a.881.3		28	28.11	odd	6
1568.3.h.a.881.4		28	56.3	even	6
1568.3.h.a.881.25		28	28.3	even	6
1568.3.h.a.881.26		28	56.11	odd	6

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:	\( N \)	\(=\)	\( 56 = 2^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	56.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.97030 - 0.343404i) q^{2} +(-1.94818 + 3.37434i) q^{3} +(3.76415 + 1.35322i) q^{4} +(-4.42985 - 7.67272i) q^{5} +(4.99725 - 5.97944i) q^{6} +(-6.92329 - 1.03347i) q^{7} +(-6.95179 - 3.95886i) q^{8} +(-3.09078 - 5.35338i) q^{9} +O(q^{10})\)	\(q+(-1.97030 - 0.343404i) q^{2} +(-1.94818 + 3.37434i) q^{3} +(3.76415 + 1.35322i) q^{4} +(-4.42985 - 7.67272i) q^{5} +(4.99725 - 5.97944i) q^{6} +(-6.92329 - 1.03347i) q^{7} +(-6.95179 - 3.95886i) q^{8} +(-3.09078 - 5.35338i) q^{9} +(6.09327 + 16.6388i) q^{10} +(-3.15749 - 1.82298i) q^{11} +(-11.8994 + 10.0652i) q^{12} -7.79378 q^{13} +(13.2860 + 4.41373i) q^{14} +34.5205 q^{15} +(12.3376 + 10.1874i) q^{16} +(-9.07152 - 5.23744i) q^{17} +(4.25138 + 11.6091i) q^{18} +(5.39264 + 9.34032i) q^{19} +(-6.29174 - 34.8758i) q^{20} +(16.9751 - 21.3482i) q^{21} +(5.59518 + 4.67610i) q^{22} +(6.45553 + 11.1813i) q^{23} +(26.9019 - 15.7451i) q^{24} +(-26.7471 + 46.3273i) q^{25} +(15.3561 + 2.67642i) q^{26} -10.9817 q^{27} +(-24.6618 - 13.2588i) q^{28} +17.2327i q^{29} +(-68.0156 - 11.8545i) q^{30} +(-26.1797 - 15.1148i) q^{31} +(-20.8104 - 24.3090i) q^{32} +(12.3027 - 7.10296i) q^{33} +(16.0750 + 13.4345i) q^{34} +(22.7396 + 57.6986i) q^{35} +(-4.38985 - 24.3334i) q^{36} +(34.2810 - 19.7922i) q^{37} +(-7.41760 - 20.2551i) q^{38} +(15.1837 - 26.2989i) q^{39} +(0.420114 + 70.8763i) q^{40} -73.6801i q^{41} +(-40.7770 + 36.2329i) q^{42} -40.8501i q^{43} +(-9.41837 - 11.1347i) q^{44} +(-27.3833 + 47.4293i) q^{45} +(-8.87961 - 24.2474i) q^{46} +(-36.2025 + 20.9015i) q^{47} +(-58.4116 + 21.7844i) q^{48} +(46.8639 + 14.3100i) q^{49} +(68.6087 - 82.0935i) q^{50} +(35.3458 - 20.4069i) q^{51} +(-29.3369 - 10.5467i) q^{52} +(-5.55272 - 3.20586i) q^{53} +(21.6371 + 3.77115i) q^{54} +32.3020i q^{55} +(44.0379 + 34.5928i) q^{56} -42.0232 q^{57} +(5.91778 - 33.9535i) q^{58} +(-7.95742 + 13.7827i) q^{59} +(129.940 + 46.7137i) q^{60} +(-6.07848 - 10.5282i) q^{61} +(46.3912 + 38.7709i) q^{62} +(15.8658 + 40.2572i) q^{63} +(32.6548 + 55.0424i) q^{64} +(34.5253 + 59.7995i) q^{65} +(-26.6792 + 9.77016i) q^{66} +(6.75274 + 3.89870i) q^{67} +(-27.0591 - 31.9902i) q^{68} -50.3060 q^{69} +(-24.9899 - 121.492i) q^{70} -41.3627 q^{71} +(0.293120 + 49.4516i) q^{72} +(77.6038 + 44.8046i) q^{73} +(-74.3406 + 27.2242i) q^{74} +(-104.216 - 180.507i) q^{75} +(7.65920 + 42.4557i) q^{76} +(19.9762 + 15.8842i) q^{77} +(-38.9475 + 46.6025i) q^{78} +(-35.3975 - 61.3103i) q^{79} +(23.5115 - 139.792i) q^{80} +(49.2112 - 85.2363i) q^{81} +(-25.3020 + 145.172i) q^{82} -60.8673 q^{83} +(92.7853 - 57.3866i) q^{84} +92.8043i q^{85} +(-14.0281 + 80.4868i) q^{86} +(-58.1489 - 33.5723i) q^{87} +(14.7333 + 25.1730i) q^{88} +(-23.4004 + 13.5102i) q^{89} +(70.2407 - 84.0463i) q^{90} +(53.9586 + 8.05463i) q^{91} +(9.16883 + 50.8238i) q^{92} +(102.005 - 58.8927i) q^{93} +(78.5073 - 28.7501i) q^{94} +(47.7771 - 82.7524i) q^{95} +(122.569 - 22.8630i) q^{96} +3.26608i q^{97} +(-87.4217 - 44.2882i) q^{98} +22.5377i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 2 q^{2} - 4 q^{4} - 4 q^{7} - 20 q^{8} - 32 q^{9}+O(q^{10}) \) 28 * q - 2 * q^2 - 4 * q^4 - 4 * q^7 - 20 * q^8 - 32 * q^9	\( 28 q - 2 q^{2} - 4 q^{4} - 4 q^{7} - 20 q^{8} - 32 q^{9} + 24 q^{10} - 18 q^{12} + 24 q^{14} + 28 q^{15} + 16 q^{16} - 6 q^{17} - 42 q^{18} - 92 q^{22} + 30 q^{23} - 30 q^{24} - 32 q^{25} - 30 q^{26} - 42 q^{28} + 22 q^{30} - 6 q^{31} + 88 q^{32} - 6 q^{33} + 256 q^{36} + 6 q^{38} - 20 q^{39} + 102 q^{40} + 18 q^{42} - 42 q^{44} + 68 q^{46} - 294 q^{47} - 20 q^{49} + 400 q^{50} - 168 q^{52} + 330 q^{54} - 96 q^{56} + 124 q^{57} - 22 q^{58} - 62 q^{60} + 432 q^{63} - 520 q^{64} - 52 q^{65} - 306 q^{66} - 456 q^{68} - 324 q^{70} - 136 q^{71} + 96 q^{72} + 234 q^{73} - 138 q^{74} - 956 q^{78} - 162 q^{79} + 276 q^{80} - 18 q^{81} - 642 q^{82} + 504 q^{84} + 168 q^{86} + 48 q^{87} + 50 q^{88} - 150 q^{89} + 1020 q^{92} + 618 q^{94} + 290 q^{95} + 1044 q^{96} + 424 q^{98}+O(q^{100}) \) 28 * q - 2 * q^2 - 4 * q^4 - 4 * q^7 - 20 * q^8 - 32 * q^9 + 24 * q^10 - 18 * q^12 + 24 * q^14 + 28 * q^15 + 16 * q^16 - 6 * q^17 - 42 * q^18 - 92 * q^22 + 30 * q^23 - 30 * q^24 - 32 * q^25 - 30 * q^26 - 42 * q^28 + 22 * q^30 - 6 * q^31 + 88 * q^32 - 6 * q^33 + 256 * q^36 + 6 * q^38 - 20 * q^39 + 102 * q^40 + 18 * q^42 - 42 * q^44 + 68 * q^46 - 294 * q^47 - 20 * q^49 + 400 * q^50 - 168 * q^52 + 330 * q^54 - 96 * q^56 + 124 * q^57 - 22 * q^58 - 62 * q^60 + 432 * q^63 - 520 * q^64 - 52 * q^65 - 306 * q^66 - 456 * q^68 - 324 * q^70 - 136 * q^71 + 96 * q^72 + 234 * q^73 - 138 * q^74 - 956 * q^78 - 162 * q^79 + 276 * q^80 - 18 * q^81 - 642 * q^82 + 504 * q^84 + 168 * q^86 + 48 * q^87 + 50 * q^88 - 150 * q^89 + 1020 * q^92 + 618 * q^94 + 290 * q^95 + 1044 * q^96 + 424 * q^98

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