LMFDB - Embedded newform 56.3.k.c.11.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [56,3,Mod(11,56)]

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([3, 3, 4]))

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

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

chi := DirichletCharacter("56.11");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 56 = 2^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	56.k (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:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 2x^{10} - 12x^{9} + 12x^{8} - 12x^{7} + 148x^{6} - 48x^{5} + 192x^{4} - 768x^{3} + 512x^{2} + 4096 $ x^12 + 2x^10 - 12x^9 + 12x^8 - 12x^7 + 148x^6 - 48x^5 + 192x^4 - 768x^3 + 512*x^2 + 4096
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.5
Root			$0.0421483 - 1.99956i$ of defining polynomial
Character	$\chi$	$=$	56.11
Dual form			56.3.k.c.51.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.71059 + 1.03628i) q^{2} +(2.25274 - 3.90186i) q^{3} +(1.85225 + 3.54530i) q^{4} +(-6.07099 + 3.50509i) q^{5} +(7.89694 - 4.34002i) q^{6} +(2.51181 - 6.53382i) q^{7} +(-0.505481 + 7.98401i) q^{8} +(-5.64968 - 9.78553i) q^{9} +(-14.0172 - 0.295467i) q^{10} +(-7.90242 + 13.6874i) q^{11} +(18.0059 + 0.759426i) q^{12} -2.90039i q^{13} +(11.0675 - 8.57376i) q^{14} +31.5842i q^{15} +(-9.13834 + 13.1336i) q^{16} +(1.65516 - 2.86682i) q^{17} +(0.476249 - 22.5937i) q^{18} +(-8.10854 - 14.0444i) q^{19} +(-23.6716 - 15.0312i) q^{20} +(-19.8356 - 24.5197i) q^{21} +(-27.7018 + 15.2244i) q^{22} +(16.4804 - 9.51498i) q^{23} +(30.0138 + 19.9582i) q^{24} +(12.0713 - 20.9081i) q^{25} +(3.00561 - 4.96138i) q^{26} -10.3597 q^{27} +(27.8169 - 3.19714i) q^{28} -21.1392i q^{29} +(-32.7301 + 54.0277i) q^{30} +(23.6995 + 13.6829i) q^{31} +(-29.2420 + 12.9963i) q^{32} +(35.6042 + 61.6683i) q^{33} +(5.80213 - 3.18875i) q^{34} +(7.65245 + 48.4709i) q^{35} +(24.2280 - 38.1551i) q^{36} +(-15.2932 + 8.82951i) q^{37} +(0.683523 - 32.4270i) q^{38} +(-11.3169 - 6.53382i) q^{39} +(-24.9159 - 50.2427i) q^{40} +1.13482 q^{41} +(-8.52133 - 62.4985i) q^{42} +50.2084 q^{43} +(-63.1632 - 2.66400i) q^{44} +(68.5983 + 39.6053i) q^{45} +(38.0515 + 0.802081i) q^{46} +(-0.657646 + 0.379692i) q^{47} +(30.6591 + 65.2431i) q^{48} +(-36.3816 - 32.8234i) q^{49} +(42.3157 - 23.2560i) q^{50} +(-7.45728 - 12.9164i) q^{51} +(10.2828 - 5.37224i) q^{52} +(38.9677 + 22.4980i) q^{53} +(-17.7212 - 10.7355i) q^{54} -110.795i q^{55} +(50.8964 + 23.3570i) q^{56} -73.0658 q^{57} +(21.9061 - 36.1605i) q^{58} +(-1.19239 + 2.06529i) q^{59} +(-111.976 + 58.5019i) q^{60} +(-86.1653 + 49.7476i) q^{61} +(26.3608 + 47.9651i) q^{62} +(-78.1278 + 12.3346i) q^{63} +(-63.4890 - 8.07153i) q^{64} +(10.1661 + 17.6082i) q^{65} +(-3.00132 + 142.385i) q^{66} +(33.2440 - 57.5804i) q^{67} +(13.2295 + 0.557974i) q^{68} -85.7391i q^{69} +(-37.1392 + 90.8440i) q^{70} +44.4376i q^{71} +(80.9836 - 40.1607i) q^{72} +(-0.859703 + 1.48905i) q^{73} +(-35.3102 - 0.744298i) q^{74} +(-54.3870 - 94.2011i) q^{75} +(34.7726 - 54.7610i) q^{76} +(69.5816 + 86.0131i) q^{77} +(-12.5878 - 22.9042i) q^{78} +(-62.9171 + 36.3252i) q^{79} +(9.44446 - 111.765i) q^{80} +(27.5094 - 47.6476i) q^{81} +(1.94121 + 1.17599i) q^{82} -102.081 q^{83} +(50.1894 - 115.740i) q^{84} +23.2059i q^{85} +(85.8861 + 52.0299i) q^{86} +(-82.4821 - 47.6211i) q^{87} +(-105.286 - 70.0117i) q^{88} +(30.6865 + 53.1505i) q^{89} +(76.3016 + 138.835i) q^{90} +(-18.9506 - 7.28522i) q^{91} +(64.2594 + 40.8040i) q^{92} +(106.778 - 61.6480i) q^{93} +(-1.51843 - 0.0320068i) q^{94} +(98.4538 + 56.8423i) q^{95} +(-15.1649 + 143.376i) q^{96} -102.826 q^{97} +(-28.2199 - 93.8490i) q^{98} +178.584 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{3} - 4 q^{4} + 56 q^{6} + 36 q^{8} - 8 q^{9} - 30 q^{10} - 14 q^{11} - 14 q^{12} - 32 q^{14} - 40 q^{16} - 82 q^{17} + 38 q^{18} - 94 q^{19} - 56 q^{20} - 132 q^{22} - 38 q^{24} + 116 q^{25}+ \cdots + 872 q^{99}+O(q^{100}) $ 12 * q + 6 * q^3 - 4 * q^4 + 56 * q^6 + 36 * q^8 - 8 * q^9 - 30 * q^10 - 14 * q^11 - 14 * q^12 - 32 * q^14 - 40 * q^16 - 82 * q^17 + 38 * q^18 - 94 * q^19 - 56 * q^20 - 132 * q^22 - 38 * q^24 + 116 * q^25 + 22 * q^26 - 60 * q^27 + 50 * q^28 + 58 * q^30 - 60 * q^32 + 146 * q^33 + 188 * q^34 + 270 * q^35 + 200 * q^36 + 46 * q^38 - 142 * q^40 + 120 * q^41 - 38 * q^42 + 40 * q^43 - 86 * q^44 + 84 * q^46 + 184 * q^48 - 204 * q^49 - 256 * q^50 - 106 * q^51 + 20 * q^52 + 82 * q^54 + 440 * q^56 - 372 * q^57 - 130 * q^58 + 62 * q^59 - 290 * q^60 - 68 * q^62 - 328 * q^64 - 64 * q^65 - 208 * q^66 - 178 * q^67 + 4 * q^68 - 256 * q^70 + 52 * q^72 + 54 * q^73 + 120 * q^74 + 140 * q^75 - 172 * q^76 + 4 * q^78 - 12 * q^80 + 206 * q^81 + 54 * q^82 - 392 * q^83 - 176 * q^84 + 208 * q^86 + 90 * q^88 - 26 * q^89 + 156 * q^90 - 88 * q^91 + 388 * q^92 + 262 * q^94 + 64 * q^96 - 184 * q^97 + 498 * q^98 + 872 * q^99

Character values

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

$n$	$15$	$17$	$29$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	1.71059	+	1.03628i	0.855296	+	0.518140i
$2$	1.71059	+	1.03628i	0.855296	+	0.518140i
$3$	2.25274	−	3.90186i	0.750913	−	1.30062i	−0.196467	−	0.980510i	$-0.562947\pi$
$3$	2.25274	−	3.90186i	0.750913	−	1.30062i	0.947380	−	0.320110i	$-0.103720\pi$
$4$	1.85225	+	3.54530i	0.463062	+	0.886326i
$5$	−6.07099	+	3.50509i	−1.21420	+	0.701018i	−0.963671	−	0.267092i	$-0.913937\pi$
$5$	−6.07099	+	3.50509i	−1.21420	+	0.701018i	−0.250528	+	0.968109i	$0.580604\pi$
$6$	7.89694	−	4.34002i	1.31616	−	0.723337i
$7$	2.51181	−	6.53382i	0.358830	−	0.933403i
$7$	2.51181	−	6.53382i	0.358830	−	0.933403i
$8$	−0.505481	+	7.98401i	−0.0631851	+	0.998002i
$9$	−5.64968	−	9.78553i	−0.627742	−	1.08728i
$10$	−14.0172	−	0.295467i	−1.40172	−	0.0295467i
$11$	−7.90242	+	13.6874i	−0.718402	+	1.24431i	0.243231	+	0.969968i	$0.421793\pi$
$11$	−7.90242	+	13.6874i	−0.718402	+	1.24431i	−0.961633	+	0.274340i	$0.911541\pi$
$12$	18.0059	+	0.759426i	1.50049	+	0.0632855i
$13$		−	2.90039i		−	0.223107i	−0.993758	−	0.111553i	$-0.964417\pi$
$13$		−	2.90039i		−	0.223107i	0.993758	−	0.111553i	$-0.0355826\pi$
$14$	11.0675	−	8.57376i	0.790539	−	0.612412i
$15$			31.5842i			2.10562i
$16$	−9.13834	+	13.1336i	−0.571146	+	0.820848i
$17$	1.65516	−	2.86682i	0.0973623	−	0.168636i	−0.813230	−	0.581943i	$-0.802293\pi$
$17$	1.65516	−	2.86682i	0.0973623	−	0.168636i	0.910592	+	0.413306i	$0.135626\pi$
$18$	0.476249	−	22.5937i	0.0264583	−	1.25521i
$19$	−8.10854	−	14.0444i	−0.426765	−	0.739179i	0.569818	−	0.821771i	$-0.307014\pi$
$19$	−8.10854	−	14.0444i	−0.426765	−	0.739179i	−0.996583	+	0.0825915i	$0.973680\pi$
$20$	−23.6716	−	15.0312i	−1.18358	−	0.751560i
$21$	−19.8356	−	24.5197i	−0.944553	−	1.16761i
$22$	−27.7018	+	15.2244i	−1.25917	+	0.692019i
$23$	16.4804	−	9.51498i	0.716540	−	0.413695i	−0.0969377	−	0.995290i	$-0.530905\pi$
$23$	16.4804	−	9.51498i	0.716540	−	0.413695i	0.813478	+	0.581596i	$0.197571\pi$
$24$	30.0138	+	19.9582i	1.25057	+	0.831593i
$25$	12.0713	−	20.9081i	0.482852	−	0.836325i
$26$	3.00561	−	4.96138i	0.115600	−	0.190822i
$27$	−10.3597			−0.383693
$28$	27.8169	−	3.19714i	0.993460	−	0.114184i
$29$		−	21.1392i		−	0.728937i	−0.931216	−	0.364468i	$-0.881251\pi$
$29$		−	21.1392i		−	0.728937i	0.931216	−	0.364468i	$-0.118749\pi$
$30$	−32.7301	+	54.0277i	−1.09100	+	1.80092i
$31$	23.6995	+	13.6829i	0.764499	+	0.441384i	0.830909	−	0.556409i	$-0.187821\pi$
$31$	23.6995	+	13.6829i	0.764499	+	0.441384i	−0.0664095	+	0.997792i	$0.521154\pi$
$32$	−29.2420	+	12.9963i	−0.913813	+	0.406135i
$33$	35.6042	+	61.6683i	1.07891	+	1.86874i
$34$	5.80213	−	3.18875i	0.170651	−	0.0937868i
$35$	7.65245	+	48.4709i	0.218641	+	1.38488i
$36$	24.2280	−	38.1551i	0.673001	−	1.05986i
$37$	−15.2932	+	8.82951i	−0.413328	+	0.238635i	−0.692219	−	0.721688i	$-0.743367\pi$
$37$	−15.2932	+	8.82951i	−0.413328	+	0.238635i	0.278890	+	0.960323i	$0.410033\pi$
$38$	0.683523	−	32.4270i	0.0179875	−	0.853341i
$39$	−11.3169	−	6.53382i	−0.290177	−	0.167534i
$40$	−24.9159	−	50.2427i	−0.622898	−	1.25607i
$41$	1.13482			0.0276785			0.0138392	−	0.999904i	$-0.495595\pi$
$41$	1.13482			0.0276785			0.0138392	+	0.999904i	$0.495595\pi$
$42$	−8.52133	−	62.4985i	−0.202889	−	1.48806i
$43$	50.2084			1.16764			0.583818	−	0.811884i	$-0.301558\pi$
$43$	50.2084			1.16764			0.583818	+	0.811884i	$0.301558\pi$
$44$	−63.1632	−	2.66400i	−1.43553	−	0.0605454i
$45$	68.5983	+	39.6053i	1.52441	+	0.880117i
$46$	38.0515	+	0.802081i	0.827206	+	0.0174365i
$47$	−0.657646	+	0.379692i	−0.0139925	+	0.00807855i	−0.506980	−	0.861958i	$-0.669238\pi$
$47$	−0.657646	+	0.379692i	−0.0139925	+	0.00807855i	0.492987	+	0.870036i	$0.335905\pi$
$48$	30.6591	+	65.2431i	0.638730	+	1.35923i
$49$	−36.3816	−	32.8234i	−0.742482	−	0.669866i
$50$	42.3157	−	23.2560i	0.846315	−	0.465120i
$51$	−7.45728	−	12.9164i	−0.146221	−	0.253263i
$52$	10.2828	−	5.37224i	0.197745	−	0.103312i
$53$	38.9677	+	22.4980i	0.735240	+	0.424491i	0.820336	−	0.571882i	$-0.193786\pi$
$53$	38.9677	+	22.4980i	0.735240	+	0.424491i	−0.0850958	+	0.996373i	$0.527120\pi$
$54$	−17.7212	−	10.7355i	−0.328171	−	0.198806i
$55$		−	110.795i		−	2.01445i
$56$	50.8964	+	23.3570i	0.908865	+	0.417090i
$57$	−73.0658			−1.28186
$58$	21.9061	−	36.1605i	0.377691	−	0.623457i
$59$	−1.19239	+	2.06529i	−0.0202101	+	0.0350048i	−0.875954	−	0.482395i	$-0.839767\pi$
$59$	−1.19239	+	2.06529i	−0.0202101	+	0.0350048i	0.855743	+	0.517400i	$0.173100\pi$
$60$	−111.976	+	58.5019i	−1.86626	+	0.975031i
$61$	−86.1653	+	49.7476i	−1.41255	+	0.815534i	−0.995628	−	0.0934097i	$-0.970223\pi$
$61$	−86.1653	+	49.7476i	−1.41255	+	0.815534i	−0.416919	+	0.908944i	$0.636890\pi$
$62$	26.3608	+	47.9651i	0.425175	+	0.773631i
$63$	−78.1278	+	12.3346i	−1.24012	+	0.195787i
$64$	−63.4890	−	8.07153i	−0.992015	−	0.126118i
$65$	10.1661	+	17.6082i	0.156402	+	0.270896i
$66$	−3.00132	+	142.385i	−0.0454745	+	2.15735i
$67$	33.2440	−	57.5804i	0.496180	−	0.859408i	−0.503811	−	0.863814i	$-0.668069\pi$
$67$	33.2440	−	57.5804i	0.496180	−	0.859408i	0.999990	+	0.00440572i	$0.00140239\pi$
$68$	13.2295	+	0.557974i	0.194552	+	0.00820549i
$69$		−	85.7391i		−	1.24260i
$70$	−37.1392	+	90.8440i	−0.530560	+	1.29777i
$71$			44.4376i			0.625882i	0.949773	+	0.312941i	$0.101314\pi$
$71$			44.4376i			0.625882i	−0.949773	+	0.312941i	$0.898686\pi$
$72$	80.9836	−	40.1607i	1.12477	−	0.557788i
$73$	−0.859703	+	1.48905i	−0.0117768	+	0.0203979i	−0.871854	−	0.489766i	$-0.837082\pi$
$73$	−0.859703	+	1.48905i	−0.0117768	+	0.0203979i	0.860077	+	0.510164i	$0.170415\pi$
$74$	−35.3102	−	0.744298i	−0.477165	−	0.0100581i
$75$	−54.3870	−	94.2011i	−0.725161	−	1.25602i
$76$	34.7726	−	54.7610i	0.457535	−	0.720539i
$77$	69.5816	+	86.0131i	0.903657	+	1.11705i
$78$	−12.5878	−	22.9042i	−0.161381	−	0.293643i
$79$	−62.9171	+	36.3252i	−0.796418	+	0.459812i	−0.842217	−	0.539138i	$-0.818750\pi$
$79$	−62.9171	+	36.3252i	−0.796418	+	0.459812i	0.0457989	+	0.998951i	$0.485417\pi$
$80$	9.44446	−	111.765i	0.118056	−	1.39706i
$81$	27.5094	−	47.6476i	0.339622	−	0.588243i
$82$	1.94121	+	1.17599i	0.0236733	+	0.0143413i
$83$	−102.081			−1.22990			−0.614948	−	0.788568i	$-0.710823\pi$
$83$	−102.081			−1.22990			−0.614948	+	0.788568i	$0.710823\pi$
$84$	50.1894	−	115.740i	0.597493	−	1.37786i
$85$			23.2059i			0.273011i
$86$	85.8861	+	52.0299i	0.998675	+	0.604999i
$87$	−82.4821	−	47.6211i	−0.948070	−	0.547369i
$88$	−105.286	−	70.0117i	−1.19643	−	0.795588i
$89$	30.6865	+	53.1505i	0.344792	+	0.597197i	0.985316	−	0.170741i	$-0.0546162\pi$
$89$	30.6865	+	53.1505i	0.344792	+	0.597197i	−0.640524	+	0.767938i	$0.721283\pi$
$90$	76.3016	+	138.835i	0.847796	+	1.54262i
$91$	−18.9506	−	7.28522i	−0.208249	−	0.0800574i
$92$	64.2594	+	40.8040i	0.698471	+	0.443522i
$93$	106.778	−	61.6480i	1.14815	−	0.662882i
$94$	−1.51843	−	0.0320068i	−0.0161535	−	0.000340498i
$95$	98.4538	+	56.8423i	1.03636	+	0.598340i
$96$	−15.1649	+	143.376i	−0.157968	+	1.49350i
$97$	−102.826			−1.06006			−0.530030	−	0.847979i	$-0.677819\pi$
$97$	−102.826			−1.06006			−0.530030	+	0.847979i	$0.677819\pi$
$98$	−28.2199	−	93.8490i	−0.287958	−	0.957643i
$99$	178.584			1.80388
$100$	96.4847	+	4.06938i	0.964847	+	0.0406938i
$101$	−157.651	−	91.0197i	−1.56090	−	0.901185i	−0.997166	−	0.0752264i	$-0.976032\pi$
$101$	−157.651	−	91.0197i	−1.56090	−	0.901185i	−0.563731	−	0.825958i	$-0.690635\pi$
$102$	0.628624	−	29.8225i	0.00616298	−	0.292378i
$103$	39.7104	−	22.9268i	0.385538	−	0.222591i	−0.294687	−	0.955594i	$-0.595215\pi$
$103$	39.7104	−	22.9268i	0.385538	−	0.222591i	0.680225	+	0.733003i	$0.261882\pi$
$104$	23.1567	+	1.46609i	0.222661	+	0.0140970i
$105$	206.366	+	79.3336i	1.96539	+	0.755558i
$106$	43.3437	+	78.8664i	0.408902	+	0.744023i
$107$	36.9463	+	63.9928i	0.345292	+	0.598064i	0.985407	−	0.170216i	$-0.0544465\pi$
$107$	36.9463	+	63.9928i	0.345292	+	0.598064i	−0.640115	+	0.768279i	$0.721113\pi$
$108$	−19.1888	−	36.7283i	−0.177674	−	0.340077i
$109$	104.724	+	60.4622i	0.960767	+	0.554699i	0.896409	−	0.443228i	$-0.146167\pi$
$109$	104.724	+	60.4622i	0.960767	+	0.554699i	0.0643577	+	0.997927i	$0.479500\pi$
$110$	114.814	−	189.525i	1.04377	−	1.72295i
$111$			79.5623i			0.716778i
$112$	62.8586	+	92.6973i	0.561238	+	0.827655i
$113$	−97.7663			−0.865188			−0.432594	−	0.901589i	$-0.642402\pi$
$113$	−97.7663			−0.865188			−0.432594	+	0.901589i	$0.642402\pi$
$114$	−124.986	−	75.7166i	−1.09637	−	0.664180i
$115$	−66.7017	+	115.531i	−0.580015	+	1.00462i
$116$	74.9448	−	39.1550i	0.646076	−	0.337543i
$117$	−28.3818	+	16.3863i	−0.242580	+	0.140053i
$118$	−4.17991	+	2.29721i	−0.0354230	+	0.0194679i
$119$	−14.5738	−	18.0154i	−0.122469	−	0.151390i
$120$	−252.169	−	15.9652i	−2.10141	−	0.133043i
$121$	−64.3964	−	111.538i	−0.532202	−	0.921801i
$122$	−198.946	−	4.19356i	−1.63071	−	0.0343734i
$123$	2.55645	−	4.42790i	0.0207841	−	0.0359992i
$124$	−4.61267	+	109.366i	−0.0371989	+	0.881984i
$125$		−	6.01041i		−	0.0480833i
$126$	−146.427	−	59.8628i	−1.16212	−	0.475101i
$127$		−	175.050i		−	1.37835i	−0.724595	−	0.689175i	$-0.757973\pi$
$127$		−	175.050i		−	1.37835i	0.724595	−	0.689175i	$-0.242027\pi$
$128$	−100.239	−	79.5994i	−0.783120	−	0.621870i
$129$	113.106	−	195.906i	0.876794	−	1.51865i
$130$	−0.856970	+	40.6554i	−0.00659208	+	0.312734i
$131$	4.30993	+	7.46501i	0.0329002	+	0.0569848i	0.882007	−	0.471237i	$-0.156192\pi$
$131$	4.30993	+	7.46501i	0.0329002	+	0.0569848i	−0.849106	+	0.528222i	$0.822859\pi$
$132$	−152.685	+	240.453i	−1.15670	+	1.82161i
$133$	−112.131	+	17.7029i	−0.843088	+	0.133104i
$134$	116.536	−	64.0464i	0.869674	−	0.477958i
$135$	62.8937	−	36.3117i	0.465879	−	0.268975i
$136$	22.0521	+	14.6639i	0.162148	+	0.107823i
$137$	−128.042	+	221.776i	−0.934615	+	1.61880i	−0.159295	+	0.987231i	$0.550922\pi$
$137$	−128.042	+	221.776i	−0.934615	+	1.61880i	−0.775320	+	0.631569i	$0.782411\pi$
$138$	88.8497	−	146.665i	0.643838	−	1.06279i
$139$	218.834			1.57434			0.787171	−	0.616735i	$-0.211545\pi$
$139$	218.834			1.57434			0.787171	+	0.616735i	$0.211545\pi$
$140$	−157.670	+	116.910i	−1.12621	+	0.835075i
$141$			3.42139i			0.0242652i
$142$	−46.0498	+	76.0147i	−0.324295	+	0.535315i
$143$	39.6987	+	22.9201i	0.277614	+	0.160280i
$144$	180.148	+	15.2231i	1.25103	+	0.105716i
$145$	74.0947	+	128.336i	0.510998	+	0.885074i
$146$	−3.01367	+	1.65626i	−0.0206416	+	0.0113443i
$147$	−210.031	+	68.0134i	−1.42878	+	0.462676i
$148$	−59.6300	−	37.8644i	−0.402906	−	0.255841i
$149$	20.6792	−	11.9391i	0.138786	−	0.0801284i	−0.428999	−	0.903305i	$-0.641134\pi$
$149$	20.6792	−	11.9391i	0.138786	−	0.0801284i	0.567785	+	0.823177i	$0.307800\pi$
$150$	4.58465	−	217.500i	0.0305643	−	1.45000i
$151$	158.916	+	91.7504i	1.05243	+	0.607619i	0.923328	−	0.384013i	$-0.125458\pi$
$151$	158.916	+	91.7504i	1.05243	+	0.607619i	0.129099	+	0.991632i	$0.458792\pi$
$152$	116.229	−	57.6395i	0.764668	−	0.379208i
$153$	−37.4044			−0.244474
$154$	29.8921	+	219.239i	0.194104	+	1.42363i
$155$	−191.839			−1.23767
$156$	2.20263	−	52.2241i	0.0141194	−	0.334770i
$157$	143.703	+	82.9671i	0.915307	+	0.528453i	0.882135	−	0.470997i	$-0.156106\pi$
$157$	143.703	+	82.9671i	0.915307	+	0.528453i	0.0331720	+	0.999450i	$0.489439\pi$
$158$	−145.268	−	3.06209i	−0.919420	−	0.0193803i
$159$	175.568	−	101.364i	1.10420	−	0.637512i
$160$	131.975	−	181.396i	0.824843	−	1.13373i
$161$	−20.7735	−	131.580i	−0.129028	−	0.817267i
$162$	96.4336	−	52.9983i	0.595269	−	0.327150i
$163$	5.05216	+	8.75059i	0.0309948	+	0.0536846i	0.881107	−	0.472917i	$-0.156799\pi$
$163$	5.05216	+	8.75059i	0.0309948	+	0.0536846i	−0.850112	+	0.526602i	$0.823466\pi$
$164$	2.10196	+	4.02327i	0.0128169	+	0.0245321i
$165$	−432.306	−	249.592i	−2.62003	−	1.51268i
$166$	−174.620	−	105.785i	−1.05193	−	0.637258i
$167$			285.049i			1.70688i	0.521190	+	0.853441i	$0.325488\pi$
$167$			285.049i			1.70688i	−0.521190	+	0.853441i	$0.674512\pi$
$168$	205.792	−	145.973i	1.22495	−	0.868890i
$169$	160.588			0.950223
$170$	−24.0478	+	39.6959i	−0.141458	+	0.233505i
$171$	−91.6213	+	158.693i	−0.535797	+	0.928028i
$172$	92.9985	+	178.004i	0.540689	+	1.03491i
$173$	84.3266	−	48.6860i	0.487437	−	0.281422i	−0.236074	−	0.971735i	$-0.575861\pi$
$173$	84.3266	−	48.6860i	0.487437	−	0.281422i	0.723511	+	0.690313i	$0.242527\pi$
$174$	−91.7445	−	166.935i	−0.527267	−	0.959395i
$175$	−106.289	−	131.389i	−0.607366	−	0.750794i
$176$	−107.549	−	228.867i	−0.611076	−	1.30038i
$177$	5.37230	+	9.30510i	0.0303520	+	0.0525712i
$178$	−2.58677	+	122.719i	−0.0145324	+	0.689430i
$179$	150.908	−	261.380i	0.843061	−	1.46022i	−0.0442343	−	0.999021i	$-0.514085\pi$
$179$	150.908	−	261.380i	0.843061	−	1.46022i	0.887295	−	0.461203i	$-0.152582\pi$
$180$	−13.3514	+	316.561i	−0.0741745	+	1.75867i
$181$			60.4535i			0.333997i	0.985957	+	0.166999i	$0.0534076\pi$
$181$			60.4535i			0.333997i	−0.985957	+	0.166999i	$0.946592\pi$
$182$	−24.8672	−	32.1002i	−0.136633	−	0.176375i
$183$			448.273i			2.44958i
$184$	67.6372	+	136.390i	0.367593	+	0.741248i
$185$	61.8964	−	107.208i	0.334575	−	0.579501i
$186$	246.537	+	5.19673i	1.32547	+	0.0279394i
$187$	26.1595	+	45.3096i	0.139890	+	0.242297i
$188$	−2.56425	−	1.62827i	−0.0136396	−	0.00866100i
$189$	−26.0216	+	67.6884i	−0.137680	+	0.358140i
$190$	109.510	+	199.260i	0.576367	+	1.04874i
$191$	63.5769	−	36.7062i	0.332864	−	0.192179i	−0.324248	−	0.945972i	$-0.605111\pi$
$191$	63.5769	−	36.7062i	0.332864	−	0.192179i	0.657112	+	0.753793i	$0.271778\pi$
$192$	−174.518	+	229.542i	−0.908949	+	1.19553i
$193$	−32.5446	+	56.3690i	−0.168625	+	0.292067i	−0.937937	−	0.346807i	$-0.887266\pi$
$193$	−32.5446	+	56.3690i	−0.168625	+	0.292067i	0.769312	+	0.638874i	$0.220599\pi$
$194$	−175.893	−	106.556i	−0.906665	−	0.549259i
$195$	91.6065			0.469777
$196$	48.9811	−	189.781i	0.249904	−	0.968271i
$197$		−	348.324i		−	1.76814i	−0.467355	−	0.884070i	$-0.654793\pi$
$197$		−	348.324i		−	1.76814i	0.467355	−	0.884070i	$-0.345207\pi$
$198$	305.485	+	185.063i	1.54285	+	0.934664i
$199$	−225.265	−	130.057i	−1.13198	−	0.653551i	−0.187550	−	0.982255i	$-0.560055\pi$
$199$	−225.265	−	130.057i	−1.13198	−	0.653551i	−0.944433	+	0.328704i	$0.893388\pi$
$200$	160.829	+	106.946i	0.804145	+	0.534731i
$201$	−149.780	−	259.427i	−0.745176	−	1.29068i
$202$	−175.354	−	319.068i	−0.868090	−	1.57954i
$203$	−138.120	−	53.0976i	−0.680392	−	0.261564i
$204$	31.9798	−	50.3627i	0.156764	−	0.246876i
$205$	−6.88946	+	3.97763i	−0.0336071	+	0.0194031i
$206$	91.6869	+	1.93266i	0.445082	+	0.00938182i
$207$	−186.218	−	107.513i	−0.899605	−	0.519387i
$208$	38.0925	+	26.5047i	0.183137	+	0.127427i
$209$	256.308			1.22636
$210$	270.796	+	349.560i	1.28950	+	1.66457i
$211$	4.73025			0.0224182			0.0112091	−	0.999937i	$-0.496432\pi$
$211$	4.73025			0.0224182			0.0112091	+	0.999937i	$0.496432\pi$
$212$	−7.58435	+	179.824i	−0.0357753	+	0.848228i
$213$	173.390	+	100.106i	0.814035	+	0.469983i
$214$	−3.11445	+	147.752i	−0.0145535	+	0.690431i
$215$	−304.815	+	175.985i	−1.41774	+	0.818534i
$216$	5.23663	−	82.7120i	0.0242437	−	0.382926i
$217$	148.930	−	120.479i	0.686314	−	0.555204i
$218$	116.484	+	211.949i	0.534328	+	0.972243i
$219$	3.87337	+	6.70888i	0.0176866	+	0.0306342i
$220$	392.801	−	205.220i	1.78546	−	0.932816i
$221$	−8.31489	−	4.80060i	−0.0376239	−	0.0217222i
$222$	−82.4488	+	136.099i	−0.371391	+	0.613057i
$223$		−	109.315i		−	0.490200i	−0.969498	−	0.245100i	$-0.921179\pi$
$223$		−	109.315i		−	0.490200i	0.969498	−	0.245100i	$-0.0788209\pi$
$224$	11.4651	+	223.706i	0.0511837	+	0.998689i
$225$	−272.796			−1.21243
$226$	−167.238	−	101.313i	−0.739992	−	0.448288i
$227$	60.7205	−	105.171i	0.267491	−	0.463308i	−0.700722	−	0.713434i	$-0.747139\pi$
$227$	60.7205	−	105.171i	0.267491	−	0.463308i	0.968213	+	0.250126i	$0.0804721\pi$
$228$	−135.336	−	259.040i	−0.593579	−	1.13614i
$229$	−124.878	+	72.0983i	−0.545319	+	0.314840i	−0.747232	−	0.664564i	$-0.768617\pi$
$229$	−124.878	+	72.0983i	−0.545319	+	0.314840i	0.201913	+	0.979403i	$0.435284\pi$
$230$	−233.822	+	128.504i	−1.01662	+	0.558715i
$231$	492.360	−	77.7325i	2.13143	−	0.336504i
$232$	168.775	+	10.6854i	0.727480	+	0.0460579i
$233$	−97.1309	−	168.236i	−0.416871	−	0.722042i	0.578752	−	0.815504i	$-0.303540\pi$
$233$	−97.1309	−	168.236i	−0.416871	−	0.722042i	−0.995623	+	0.0934621i	$0.970207\pi$
$234$	−65.5305	−	1.38131i	−0.280045	−	0.00590302i
$235$	2.66171	−	4.61021i	0.0113264	−	0.0196179i
$236$	−9.53067	−	0.401970i	−0.0403842	−	0.00170326i
$237$			327.325i			1.38112i
$238$	−6.26089	−	45.9196i	−0.0263062	−	0.192939i
$239$		−	315.567i		−	1.32036i	−0.751106	−	0.660181i	$-0.770479\pi$
$239$		−	315.567i		−	1.32036i	0.751106	−	0.660181i	$-0.229521\pi$
$240$	−414.814	−	288.627i	−1.72839	−	1.20261i
$241$	−181.356	+	314.117i	−0.752513	+	1.30339i	0.194089	+	0.980984i	$0.437825\pi$
$241$	−181.356	+	314.117i	−0.752513	+	1.30339i	−0.946601	+	0.322406i	$0.895508\pi$
$242$	5.42841	−	257.529i	0.0224314	−	1.06417i
$243$	−170.562	−	295.421i	−0.701900	−	1.21573i
$244$	−335.970	−	213.337i	−1.37693	−	0.874333i
$245$	335.922	+	71.7499i	1.37111	+	0.292857i
$246$	8.96158	−	4.92513i	0.0364292	−	0.0200209i
$247$	−40.7342	+	23.5179i	−0.164916	+	0.0952143i
$248$	−121.224	+	182.301i	−0.488807	+	0.735083i
$249$	−229.963	+	398.307i	−0.923545	+	1.59963i
$250$	6.22847	−	10.2814i	0.0249139	−	0.0411254i
$251$	−9.04237			−0.0360254			−0.0180127	−	0.999838i	$-0.505734\pi$
$251$	−9.04237			−0.0360254			−0.0180127	+	0.999838i	$0.505734\pi$
$252$	−188.442	−	254.140i	−0.747786	−	1.00849i
$253$			300.765i			1.18880i
$254$	181.401	−	299.440i	0.714178	−	1.17890i
$255$	90.5463	+	52.2769i	0.355083	+	0.205007i
$256$	−88.9814	−	240.038i	−0.347584	−	0.937649i
$257$	185.539	+	321.363i	0.721942	+	1.25044i	0.960221	+	0.279243i	$0.0900834\pi$
$257$	185.539	+	321.363i	0.721942	+	1.25044i	−0.238279	+	0.971197i	$0.576583\pi$
$258$	396.492	−	217.906i	1.53679	−	0.844595i
$259$	19.2769	+	122.101i	0.0744283	+	0.471432i
$260$	−43.5963	+	68.6568i	−0.167678	+	0.264065i
$261$	−206.858	+	119.430i	−0.792559	+	0.457584i
$262$	−0.363313	+	17.2359i	−0.00138669	+	0.0657858i
$263$	−410.392	−	236.940i	−1.56043	−	0.900912i	−0.997214	−	0.0745993i	$-0.976232\pi$
$263$	−410.392	−	236.940i	−1.56043	−	0.900912i	−0.563212	−	0.826313i	$-0.690434\pi$
$264$	−510.358	+	253.092i	−1.93317	+	0.958683i
$265$	−315.431			−1.19030
$266$	−210.155	−	85.9164i	−0.790057	−	0.322994i
$267$	276.515			1.03563
$268$	265.716	+	11.2070i	0.991478	+	0.0418170i
$269$	81.5026	+	47.0556i	0.302984	+	0.174928i	0.643782	−	0.765209i	$-0.277364\pi$
$269$	81.5026	+	47.0556i	0.302984	+	0.174928i	−0.340799	+	0.940136i	$0.610697\pi$
$270$	145.214	+	3.06096i	0.537831	+	0.0113369i
$271$	137.021	−	79.1093i	0.505614	−	0.291916i	−0.225415	−	0.974263i	$-0.572374\pi$
$271$	137.021	−	79.1093i	0.505614	−	0.291916i	0.731029	+	0.682347i	$0.239041\pi$
$272$	22.5262	+	47.9361i	0.0828168	+	0.176236i
$273$	−71.1167	+	57.5309i	−0.260501	+	0.210736i
$274$	−448.849	+	246.680i	−1.63814	+	0.900292i
$275$	190.785	+	330.449i	0.693764	+	1.20163i
$276$	303.971	−	158.810i	1.10134	−	0.575399i
$277$	205.022	+	118.370i	0.740153	+	0.427328i	0.822125	−	0.569307i	$-0.192788\pi$
$277$	205.022	+	118.370i	0.740153	+	0.427328i	−0.0819717	+	0.996635i	$0.526122\pi$
$278$	374.335	+	226.773i	1.34653	+	0.815729i
$279$		−	309.216i		−	1.10830i
$280$	−390.861	+	36.5962i	−1.39593	+	0.130701i
$281$	241.948			0.861025			0.430512	−	0.902585i	$-0.358333\pi$
$281$	241.948			0.861025			0.430512	+	0.902585i	$0.358333\pi$
$282$	−3.54552	+	5.85260i	−0.0125728	+	0.0207539i
$283$	116.737	−	202.194i	0.412498	−	0.714468i	−0.582664	−	0.812713i	$-0.697990\pi$
$283$	116.737	−	202.194i	0.412498	−	0.714468i	0.995162	+	0.0982453i	$0.0313230\pi$
$284$	−157.545	+	82.3096i	−0.554736	+	0.289823i
$285$	443.582	−	256.102i	1.55643	−	0.898604i
$286$	44.1567	+	80.3459i	0.154394	+	0.280930i
$287$	2.85044	−	7.41469i	0.00993186	−	0.0258351i
$288$	292.384	+	212.724i	1.01522	+	0.738624i
$289$	139.021	+	240.791i	0.481041	+	0.833188i
$290$	−6.24594	+	296.313i	−0.0215377	+	1.02177i
$291$	−231.640	+	401.212i	−0.796014	+	1.37874i
$292$	−6.87151	−	0.289816i	−0.0235326	−	0.000992521i
$293$		−	216.492i		−	0.738882i	−0.929254	−	0.369441i	$-0.879549\pi$
$293$		−	216.492i		−	0.738882i	0.929254	−	0.369441i	$-0.120451\pi$
$294$	−429.758	−	101.307i	−1.46176	−	0.344583i
$295$		−	16.7178i		−	0.0566704i
$296$	−62.7645	−	126.564i	−0.212042	−	0.427581i
$297$	81.8667	−	141.797i	0.275645	−	0.477432i
$298$	47.7459	+	1.00643i	0.160221	+	0.00337728i
$299$	−27.5971	−	47.7996i	−0.0922981	−	0.159865i
$300$	233.233	−	367.303i	0.777444	−	1.22434i
$301$	126.114	−	328.053i	0.418983	−	1.08988i
$302$	176.762	+	321.629i	0.585305	+	1.06500i
$303$	−710.292	+	410.087i	−2.34420	+	1.35342i
$304$	258.552	+	21.8485i	0.850500	+	0.0718700i
$305$	348.739	−	604.034i	1.14341	−	1.98044i
$306$	−63.9838	−	38.7615i	−0.209097	−	0.126671i
$307$	173.487			0.565106			0.282553	−	0.959252i	$-0.408819\pi$
$307$	173.487			0.565106			0.282553	+	0.959252i	$0.408819\pi$
$308$	−176.060	+	406.006i	−0.571623	+	1.31820i
$309$		−	206.593i		−	0.668585i
$310$	−328.159	−	198.799i	−1.05858	−	0.641287i
$311$	100.205	+	57.8536i	0.322204	+	0.186024i	0.652374	−	0.757897i	$-0.273773\pi$
$311$	100.205	+	57.8536i	0.322204	+	0.186024i	−0.330171	+	0.943921i	$0.607106\pi$
$312$	57.8866	−	87.0517i	0.185534	−	0.279012i
$313$	−105.261	−	182.317i	−0.336297	−	0.582483i	0.647436	−	0.762120i	$-0.275841\pi$
$313$	−105.261	−	182.317i	−0.336297	−	0.582483i	−0.983733	+	0.179637i	$0.942508\pi$
$314$	159.840	+	290.839i	0.509046	+	0.926240i
$315$	431.080	−	348.728i	1.36851	−	1.10707i
$316$	−245.322	−	155.777i	−0.776335	−	0.492964i
$317$	−302.997	+	174.936i	−0.955828	+	0.551847i	−0.894886	−	0.446294i	$-0.852744\pi$
$317$	−302.997	+	174.936i	−0.955828	+	0.551847i	−0.0609413	+	0.998141i	$0.519410\pi$
$318$	405.368	+	8.54469i	1.27474	+	0.0268701i
$319$	289.340	+	167.051i	0.907022	+	0.523669i
$320$	413.733	−	173.532i	1.29291	−	0.542289i
$321$	332.921			1.03714
$322$	100.819	−	246.607i	0.313102	−	0.765860i
$323$	−53.6837			−0.166203
$324$	219.880	+	9.27374i	0.678641	+	0.0286227i
$325$	−60.6417	−	35.0115i	−0.186590	−	0.107728i
$326$	−0.425880	+	20.2041i	−0.00130638	+	0.0619759i
$327$	471.830	−	272.411i	1.44291	−	0.833062i
$328$	−0.573628	+	9.06039i	−0.00174887	+	0.0276231i
$329$	0.828958	+	5.25065i	0.00251963	+	0.0159594i
$330$	−480.852	−	874.939i	−1.45713	−	2.65133i
$331$	−107.055	−	185.425i	−0.323430	−	0.560196i	0.657764	−	0.753224i	$-0.271503\pi$
$331$	−107.055	−	185.425i	−0.323430	−	0.560196i	−0.981193	+	0.193028i	$0.938169\pi$
$332$	−189.080	−	361.909i	−0.569519	−	1.09009i
$333$	172.803	+	99.7677i	0.518927	+	0.299603i
$334$	−295.391	+	487.603i	−0.884403	+	1.45989i
$335$			466.093i			1.39132i
$336$	503.296	−	36.4426i	1.49791	−	0.108460i
$337$	−437.275			−1.29755			−0.648777	−	0.760979i	$-0.724719\pi$
$337$	−437.275			−1.29755			−0.648777	+	0.760979i	$0.724719\pi$
$338$	274.700	+	166.414i	0.812722	+	0.492348i
$339$	−220.242	+	381.470i	−0.649682	+	1.12528i
$340$	−82.2720	+	42.9832i	−0.241976	+	0.126421i
$341$	−374.566	+	216.256i	−1.09844	+	0.634182i
$342$	−321.177	+	176.513i	−0.939113	+	0.516121i
$343$	−305.846	+	155.265i	−0.891680	+	0.452667i
$344$	−25.3794	+	400.864i	−0.0737772	+	1.16530i
$345$	300.523	+	520.522i	0.871082	+	1.50876i
$346$	194.701	+	4.10407i	0.562719	+	0.0118615i
$347$	−188.694	+	326.827i	−0.543786	+	0.941865i	0.454896	+	0.890545i	$0.349676\pi$
$347$	−188.694	+	326.827i	−0.543786	+	0.941865i	−0.998682	+	0.0513208i	$0.983657\pi$
$348$	16.0536	−	380.630i	0.0461311	−	1.09376i
$349$		−	211.146i		−	0.605003i	−0.953149	−	0.302502i	$-0.902178\pi$
$349$		−	211.146i		−	0.605003i	0.953149	−	0.302502i	$-0.0978218\pi$
$350$	−45.6615	−	334.898i	−0.130462	−	0.956852i
$351$			30.0472i			0.0856044i
$352$	53.1972	−	502.949i	0.151128	−	1.42883i
$353$	−149.375	+	258.725i	−0.423159	+	0.732933i	−0.996247	−	0.0865610i	$-0.972412\pi$
$353$	−149.375	+	258.725i	−0.423159	+	0.732933i	0.573087	+	0.819494i	$0.305746\pi$
$354$	−0.452868	+	21.4844i	−0.00127929	+	0.0606905i
$355$	−155.758	−	269.781i	−0.438755	−	0.759946i
$356$	−131.596	+	207.241i	−0.369651	+	0.582137i
$357$	−103.125	+	16.2810i	−0.288865	+	0.0456051i
$358$	529.005	−	290.732i	1.47767	−	0.812100i
$359$	191.258	−	110.423i	0.532751	−	0.307584i	−0.209385	−	0.977833i	$-0.567146\pi$
$359$	191.258	−	110.423i	0.532751	−	0.307584i	0.742136	+	0.670249i	$0.233813\pi$
$360$	−350.884	+	527.670i	−0.974678	+	1.46575i
$361$	49.0031	−	84.8758i	0.135743	−	0.235113i
$362$	−62.6468	+	103.411i	−0.173057	+	0.285667i
$363$	−580.274			−1.59855
$364$	−9.27295	−	80.6797i	−0.0254751	−	0.221648i
$365$		−	12.0533i		−	0.0330229i
$366$	−464.537	+	766.813i	−1.26923	+	2.09512i
$367$	186.496	+	107.674i	0.508165	+	0.293389i	0.732079	−	0.681220i	$-0.238550\pi$
$367$	186.496	+	107.674i	0.508165	+	0.293389i	−0.223914	+	0.974609i	$0.571884\pi$
$368$	−25.6381	+	303.398i	−0.0696688	+	0.824451i
$369$	−6.41135	−	11.1048i	−0.0173749	−	0.0300943i
$370$	216.977	−	119.247i	0.586424	−	0.322288i
$371$	244.878	−	198.097i	0.660048	−	0.533955i
$372$	416.340	+	264.371i	1.11919	+	0.710675i
$373$	193.884	−	111.939i	0.519796	−	0.300104i	−0.217055	−	0.976159i	$-0.569645\pi$
$373$	193.884	−	111.939i	0.519796	−	0.300104i	0.736851	+	0.676055i	$0.236312\pi$
$374$	−2.20516	+	104.615i	−0.00589615	+	0.279719i
$375$	−23.4518	−	13.5399i	−0.0625381	−	0.0361064i
$376$	−2.69904	−	5.44258i	−0.00717830	−	0.0144749i
$377$	−61.3118			−0.162631
$378$	−114.656	+	88.8217i	−0.303324	+	0.234978i
$379$	−507.051			−1.33787			−0.668933	−	0.743323i	$-0.733249\pi$
$379$	−507.051			−1.33787			−0.668933	+	0.743323i	$0.733249\pi$
$380$	−19.1622	+	454.335i	−0.0504269	+	1.19562i
$381$	−683.023	−	394.343i	−1.79271	−	1.03502i
$382$	146.792	+	3.09421i	0.384272	+	0.00810002i
$383$	128.681	−	74.2939i	0.335981	−	0.193979i	−0.322512	−	0.946565i	$-0.604527\pi$
$383$	128.681	−	74.2939i	0.335981	−	0.193979i	0.658493	+	0.752586i	$0.271194\pi$
$384$	−536.399	+	211.803i	−1.39687	+	0.551571i
$385$	−723.913	−	278.295i	−1.88029	−	0.722845i
$386$	−114.085	+	62.6990i	−0.295556	+	0.162433i
$387$	−283.661	−	491.316i	−0.732975	−	1.26955i
$388$	−190.459	−	364.549i	−0.490874	−	0.939559i
$389$	−137.107	−	79.1586i	−0.352459	−	0.203493i	0.313309	−	0.949651i	$-0.398563\pi$
$389$	−137.107	−	79.1586i	−0.352459	−	0.203493i	−0.665768	+	0.746159i	$0.731896\pi$
$390$	156.701	+	94.9299i	0.401798	+	0.243410i
$391$		−	62.9952i		−	0.161113i
$392$	280.453	−	273.880i	0.715441	−	0.698673i
$393$	38.8366			0.0988208
$394$	360.960	−	595.839i	0.916143	−	1.51228i
$395$	254.646	−	441.060i	0.644673	−	1.11661i
$396$	330.783	+	633.136i	0.835311	+	1.59883i
$397$	−240.531	+	138.871i	−0.605872	+	0.349801i	−0.771348	−	0.636413i	$-0.780417\pi$
$397$	−240.531	+	138.871i	−0.605872	+	0.349801i	0.165476	+	0.986214i	$0.447084\pi$
$398$	−250.561	−	455.911i	−0.629550	−	1.14550i
$399$	−183.527	+	477.399i	−0.459968	+	1.19649i
$400$	164.287	+	349.605i	0.410716	+	0.874012i
$401$	−311.899	−	540.225i	−0.777803	−	1.34719i	−0.933205	−	0.359344i	$-0.883001\pi$
$401$	−311.899	−	540.225i	−0.777803	−	1.34719i	0.155402	−	0.987851i	$-0.450333\pi$
$402$	12.6260	−	598.988i	0.0314079	−	1.49002i
$403$	39.6857	−	68.7377i	0.0984757	−	0.170565i
$404$	30.6838	−	727.510i	0.0759500	−	1.80077i
$405$			385.691i			0.952324i
$406$	−181.242	−	233.959i	−0.446410	−	0.576253i
$407$		−	279.098i		−	0.685744i
$408$	106.894	−	53.0101i	0.261996	−	0.129927i
$409$	247.569	−	428.801i	0.605302	−	1.04841i	−0.386701	−	0.922205i	$-0.626386\pi$
$409$	247.569	−	428.801i	0.605302	−	1.04841i	0.992004	−	0.126209i	$-0.0402810\pi$
$410$	−15.9070	−	0.335301i	−0.0387976	−	0.000817808i
$411$	576.892	+	999.206i	1.40363	+	2.43116i
$412$	154.836	+	98.3193i	0.375816	+	0.238639i
$413$	10.4991	+	12.9785i	0.0254217	+	0.0314249i
$414$	−207.130	−	376.885i	−0.500313	−	0.910351i
$415$	619.735	−	357.804i	1.49334	−	0.862179i
$416$	37.6943	+	84.8132i	0.0906114	+	0.203878i
$417$	492.975	−	853.858i	1.18219	−	2.04762i
$418$	438.439	+	265.607i	1.04890	+	0.635424i
$419$	112.631			0.268810			0.134405	−	0.990927i	$-0.457088\pi$
$419$	112.631			0.268810			0.134405	+	0.990927i	$0.457088\pi$
$420$	100.979	+	878.574i	0.240427	+	2.09184i
$421$			821.936i			1.95234i	0.217003	+	0.976171i	$0.430372\pi$
$421$			821.936i			1.95234i	−0.217003	+	0.976171i	$0.569628\pi$
$422$	8.09152	+	4.90186i	0.0191742	+	0.0116158i
$423$	7.43097	+	4.29027i	0.0175673	+	0.0101425i
$424$	−199.322	+	299.747i	−0.470099	+	0.706950i
$425$	−39.9599	−	69.2125i	−0.0940232	−	0.162853i
$426$	192.860	+	350.921i	0.452724	+	0.823759i
$427$	108.611	+	687.945i	0.254358	+	1.61111i
$428$	−158.440	+	249.516i	−0.370187	+	0.582982i
$429$	178.862	−	103.266i	0.416928	−	0.240713i
$430$	−703.783	−	14.8349i	−1.63671	−	0.0344999i
$431$	−289.087	−	166.904i	−0.670735	−	0.387249i	0.125620	−	0.992078i	$-0.459908\pi$
$431$	−289.087	−	166.904i	−0.670735	−	0.387249i	−0.796355	+	0.604830i	$0.793241\pi$
$432$	94.6705	−	136.060i	0.219145	−	0.314953i
$433$	604.681			1.39649			0.698246	−	0.715858i	$-0.253964\pi$
$433$	604.681			1.39649			0.698246	+	0.715858i	$0.253964\pi$
$434$	379.609	−	51.7576i	0.874675	−	0.119257i
$435$	667.664			1.53486
$436$	−20.3825	+	483.268i	−0.0467489	+	1.10841i
$437$	−267.265	−	154.305i	−0.611589	−	0.353101i
$438$	−0.326513	+	15.4901i	−0.000745463	+	0.0353654i
$439$	−416.657	+	240.557i	−0.949105	+	0.547966i	−0.892803	−	0.450448i	$-0.851264\pi$
$439$	−416.657	+	240.557i	−0.949105	+	0.547966i	−0.0563019	+	0.998414i	$0.517931\pi$
$440$	884.587	+	56.0046i	2.01042	+	0.127283i
$441$	−115.650	+	541.455i	−0.262245	+	1.22779i
$442$	−9.24861	−	16.8284i	−0.0209245	−	0.0380733i
$443$	−92.3599	−	159.972i	−0.208487	−	0.361111i	0.742751	−	0.669568i	$-0.233521\pi$
$443$	−92.3599	−	159.972i	−0.208487	−	0.361111i	−0.951238	+	0.308457i	$0.900187\pi$
$444$	−282.073	+	147.369i	−0.635299	+	0.331913i
$445$	−372.595	−	215.118i	−0.837291	−	0.483410i
$446$	113.281	−	186.993i	0.253992	−	0.419266i
$447$		−	107.583i		−	0.240678i
$448$	−212.210	+	394.551i	−0.473683	+	0.880695i
$449$	115.894			0.258115			0.129057	−	0.991637i	$-0.458805\pi$
$449$	115.894			0.258115			0.129057	+	0.991637i	$0.458805\pi$
$450$	−466.643	−	282.693i	−1.03698	−	0.628206i
$451$	−8.96779	+	15.5327i	−0.0198842	+	0.0344405i
$452$	−181.088	−	346.611i	−0.400636	−	0.766839i
$453$	715.995	−	413.380i	1.58056	−	0.912538i
$454$	212.854	−	116.981i	0.468842	−	0.257668i
$455$	140.584	−	22.1951i	0.308977	−	0.0487804i
$456$	36.9333	−	583.358i	0.0809941	−	1.27929i
$457$	79.2311	+	137.232i	0.173372	+	0.300290i	0.939597	−	0.342283i	$-0.111200\pi$
$457$	79.2311	+	137.232i	0.173372	+	0.300290i	−0.766224	+	0.642573i	$0.777867\pi$
$458$	−288.329	−	6.07765i	−0.629540	−	0.0132700i
$459$	−17.1470	+	29.6994i	−0.0373572	+	0.0647046i
$460$	−533.140	−	22.4859i	−1.15900	−	0.0488825i
$461$			42.3829i			0.0919368i	0.998943	+	0.0459684i	$0.0146374\pi$
$461$			42.3829i			0.0919368i	−0.998943	+	0.0459684i	$0.985363\pi$
$462$	922.780	+	377.254i	1.99736	+	0.816568i
$463$			390.038i			0.842416i	0.906964	+	0.421208i	$0.138394\pi$
$463$			390.038i			0.842416i	−0.906964	+	0.421208i	$0.861606\pi$
$464$	277.633	+	193.177i	0.598347	+	0.416330i
$465$	−432.164	+	748.530i	−0.929385	+	1.60974i
$466$	8.18781	−	388.437i	0.0175704	−	0.833557i
$467$	−19.1723	−	33.2074i	−0.0410541	−	0.0711078i	0.844768	−	0.535132i	$-0.179738\pi$
$467$	−19.1723	−	33.2074i	−0.0410541	−	0.0711078i	−0.885822	+	0.464025i	$0.846405\pi$
$468$	−110.664	−	70.2707i	−0.236463	−	0.150151i
$469$	−292.717	−	361.841i	−0.624130	−	0.771517i
$470$	9.33057	−	5.12792i	0.0198523	−	0.0109105i
$471$	647.452	−	373.807i	1.37463	−	0.793644i
$472$	−15.8865	−	10.5640i	−0.0336579	−	0.0223815i
$473$	−396.768	+	687.222i	−0.838832	+	1.45290i
$474$	−339.200	+	559.919i	−0.715612	+	1.18126i
$475$	−391.523			−0.824259
$476$	36.8757	−	85.0377i	0.0774700	−	0.178651i
$477$		−	508.427i		−	1.06588i
$478$	327.015	−	539.806i	0.684132	−	1.12930i
$479$	561.326	+	324.082i	1.17187	+	0.676580i	0.954120	−	0.299424i	$-0.0967945\pi$
$479$	561.326	+	324.082i	1.17187	+	0.676580i	0.217751	+	0.976004i	$0.430128\pi$
$480$	−410.478	−	923.587i	−0.855163	−	1.92414i
$481$	25.6090	+	44.3561i	0.0532412	+	0.0922164i
$482$	−635.738	+	349.391i	−1.31896	+	0.724878i
$483$	−560.204	−	215.360i	−1.15984	−	0.445881i
$484$	276.157	−	434.901i	0.570573	−	0.898555i
$485$	624.255	−	360.414i	1.28712	−	0.743121i
$486$	14.3778	−	682.095i	0.0295839	−	1.40349i
$487$	303.304	+	175.113i	0.622800	+	0.359574i	0.777959	−	0.628316i	$-0.216255\pi$
$487$	303.304	+	175.113i	0.622800	+	0.359574i	−0.155158	+	0.987890i	$0.549589\pi$
$488$	−353.630	−	713.092i	−0.724653	−	1.46125i
$489$	45.5248			0.0930977
$490$	500.272	+	470.844i	1.02096	+	0.960905i
$491$	−453.547			−0.923722			−0.461861	−	0.886952i	$-0.652818\pi$
$491$	−453.547			−0.923722			−0.461861	+	0.886952i	$0.652818\pi$
$492$	20.4334	+	0.861809i	0.0415313	+	0.00175164i
$493$	−60.6022	−	34.9887i	−0.122925	−	0.0709710i
$494$	−94.0508	−	1.98248i	−0.190386	−	0.00401312i
$495$	−1084.19	+	625.955i	−2.19027	+	1.26455i
$496$	−396.279	+	186.220i	−0.798950	+	0.375443i
$497$	290.348	+	111.619i	0.584200	+	0.224585i
$498$	−806.130	+	443.035i	−1.61874	+	0.889629i
$499$	264.783	+	458.617i	0.530626	+	0.919072i	0.999361	+	0.0357329i	$0.0113766\pi$
$499$	264.783	+	458.617i	0.530626	+	0.919072i	−0.468735	+	0.883339i	$0.655290\pi$
$500$	21.3087	−	11.1328i	0.0426175	−	0.0222656i
$501$	1112.22	+	642.142i	2.22000	+	1.28172i
$502$	−15.4678	−	9.37042i	−0.0308124	−	0.0186662i
$503$		−	321.597i		−	0.639358i	−0.947526	−	0.319679i	$-0.896425\pi$
$503$		−	321.597i		−	0.639358i	0.947526	−	0.319679i	$-0.103575\pi$
$504$	−58.9875	−	630.008i	−0.117039	−	1.25002i
$505$	1276.13			2.52699
$506$	−311.677	+	514.487i	−0.615962	+	1.01677i
$507$	361.762	−	626.591i	0.713536	−	1.23588i
$508$	620.607	−	324.237i	1.22167	−	0.638262i
$509$	−623.464	+	359.957i	−1.22488	+	0.707185i	−0.965954	−	0.258712i	$-0.916702\pi$
$509$	−623.464	+	359.957i	−1.22488	+	0.707185i	−0.258926	+	0.965897i	$0.583369\pi$
$510$	100.714	+	183.256i	0.197479	+	0.359325i
$511$	7.56977	+	9.35735i	0.0148136	+	0.0183118i
$512$	96.5357	−	502.817i	0.188546	−	0.982064i
$513$	84.0021	+	145.496i	0.163747	+	0.283618i
$514$	−15.6403	+	741.991i	−0.0304286	+	1.44356i
$515$	−160.721	+	278.377i	−0.312080	+	0.540538i
$516$	904.048	+	38.1295i	1.75203	+	0.0738944i
$517$		−	12.0019i		−	0.0232146i
$518$	−93.5556	+	228.841i	−0.180609	+	0.441778i
$519$		−	438.708i		−	0.845294i
$520$	−145.723	+	72.2658i	−0.280237	+	0.138973i
$521$	−206.990	+	358.517i	−0.397294	+	0.688133i	−0.993391	−	0.114779i	$-0.963384\pi$
$521$	−206.990	+	358.517i	−0.397294	+	0.688133i	0.596097	+	0.802912i	$0.296717\pi$
$522$	−477.612	−	10.0675i	−0.914965	−	0.0192864i
$523$	174.324	+	301.938i	0.333316	+	0.577320i	0.983160	−	0.182747i	$-0.0584991\pi$
$523$	174.324	+	301.938i	0.333316	+	0.577320i	−0.649844	+	0.760068i	$0.725166\pi$
$524$	−18.4827	+	29.1071i	−0.0352723	+	0.0555478i
$525$	−752.103	+	118.740i	−1.43258	+	0.226171i
$526$	−456.477	−	830.588i	−0.867827	−	1.57906i
$527$	78.4528	−	45.2947i	0.148867	−	0.0859483i
$528$	−1135.29	−	95.9355i	−2.15017	−	0.181696i
$529$	−83.4303	+	144.506i	−0.157713	+	0.273167i
$530$	−539.573	−	326.874i	−1.01806	−	0.616744i
$531$	26.9466			0.0507468
$532$	−270.456	−	364.747i	−0.508376	−	0.685615i
$533$		−	3.29141i		−	0.00617525i
$534$	473.004	+	286.546i	0.885774	+	0.536604i
$535$	−448.601	−	259.000i	−0.838507	−	0.484112i
$536$	442.918	+	294.527i	0.826340	+	0.549490i
$537$	−679.912	−	1177.64i	−1.26613	−	2.19300i
$538$	90.6550	+	164.952i	0.168504	+	0.306603i
$539$	736.770	−	238.585i	1.36692	−	0.442644i
$540$	245.231	+	155.719i	0.454131	+	0.288368i
$541$	202.840	−	117.110i	0.374936	−	0.216469i	−0.300677	−	0.953726i	$-0.597213\pi$
$541$	202.840	−	117.110i	0.374936	−	0.216469i	0.675613	+	0.737257i	$0.263879\pi$
$542$	316.367	+	6.66865i	0.583703	+	0.0123038i
$543$	235.881	+	136.186i	0.434404	+	0.250803i
$544$	−11.1421	+	105.343i	−0.0204819	+	0.193644i
$545$	−847.701			−1.55542
$546$	−181.270	+	24.7152i	−0.331996	+	0.0452659i
$547$	−577.082			−1.05499			−0.527497	−	0.849557i	$-0.676870\pi$
$547$	−577.082			−1.05499			−0.527497	+	0.849557i	$0.676870\pi$
$548$	−1023.43	−	43.1645i	−1.86757	−	0.0787674i
$549$	973.613	+	562.116i	1.77343	+	1.02389i
$550$	−16.0825	+	762.971i	−0.0292410	+	1.38722i
$551$	−296.887	+	171.408i	−0.538815	+	0.311085i
$552$	684.542	+	43.3395i	1.24011	+	0.0785135i
$553$	79.3065	+	502.331i	0.143411	+	0.908374i
$554$	228.046	+	414.943i	0.411635	+	0.748995i
$555$	−278.873	−	483.022i	−0.502474	−	0.870311i
$556$	405.334	+	775.831i	0.729019	+	1.39538i
$557$	−36.7252	−	21.2033i	−0.0659339	−	0.0380670i	0.466671	−	0.884431i	$-0.345453\pi$
$557$	−36.7252	−	21.2033i	−0.0659339	−	0.0380670i	−0.532605	+	0.846364i	$0.678787\pi$
$558$	320.434	−	528.942i	0.574255	−	0.947925i
$559$		−	145.624i		−	0.260508i
$560$	−706.527	−	342.440i	−1.26165	−	0.611499i
$561$	235.722			0.420182
$562$	413.874	+	250.726i	0.736431	+	0.446131i
$563$	123.648	−	214.165i	0.219624	−	0.380399i	−0.735069	−	0.677992i	$-0.762850\pi$
$563$	123.648	−	214.165i	0.219624	−	0.380399i	0.954693	+	0.297593i	$0.0961837\pi$
$564$	−12.1299	+	6.33727i	−0.0215068	+	0.0112363i
$565$	593.539	−	342.680i	1.05051	−	0.606513i
$566$	409.219	−	224.900i	0.723002	−	0.397350i
$567$	−242.223	−	299.423i	−0.427201	−	0.528083i
$568$	−354.791	−	22.4624i	−0.624632	−	0.0395464i
$569$	−312.737	−	541.677i	−0.549626	−	0.951980i	−0.998300	−	0.0582847i	$-0.981437\pi$
$569$	−312.737	−	541.677i	−0.549626	−	0.951980i	0.448674	−	0.893696i	$-0.351896\pi$
$570$	1024.18	+	21.5886i	1.79681	+	0.0378747i
$571$	291.287	−	504.524i	0.510135	−	0.883579i	−0.489796	−	0.871837i	$-0.662929\pi$
$571$	291.287	−	504.524i	0.510135	−	0.883579i	0.999931	−	0.0117423i	$-0.00373777\pi$
$572$	−7.72663	+	183.198i	−0.0135081	+	0.320276i
$573$		−	330.758i		−	0.577239i
$574$	12.5596	−	9.72965i	0.0218809	−	0.0169506i
$575$		−	459.433i		−	0.799014i
$576$	279.708	+	666.875i	0.485604	+	1.15777i
$577$	198.380	−	343.605i	0.343814	−	0.595503i	−0.641324	−	0.767270i	$-0.721615\pi$
$577$	198.380	−	343.605i	0.343814	−	0.595503i	0.985137	+	0.171768i	$0.0549478\pi$
$578$	−11.7190	+	555.960i	−0.0202751	+	0.961869i
$579$	146.629	+	253.969i	0.253246	+	0.438634i
$580$	−317.747	+	500.398i	−0.547840	+	0.862755i
$581$	−256.409	+	666.981i	−0.441324	+	1.14799i
$582$	−812.009	+	446.267i	−1.39521	+	0.766781i
$583$	−615.879	+	355.578i	−1.05640	+	0.609910i
$584$	−11.4540	−	7.61657i	−0.0196131	−	0.0130421i
$585$	114.871	−	198.962i	0.196360	−	0.340106i
$586$	224.347	−	370.330i	0.382844	−	0.631963i
$587$	355.763			0.606070			0.303035	−	0.952979i	$-0.402000\pi$
$587$	355.763			0.606070			0.303035	+	0.952979i	$0.402000\pi$
$588$	−630.157	−	618.645i	−1.07170	−	1.05212i
$589$		−	443.794i		−	0.753470i
$590$	17.3243	−	28.5973i	0.0293632	−	0.0484700i
$591$	−1359.11	−	784.682i	−2.29968	−	1.32772i
$592$	23.7911	−	281.541i	0.0401877	−	0.475576i
$593$	89.8611	+	155.644i	0.151536	+	0.262469i	0.931792	−	0.362991i	$-0.118245\pi$
$593$	89.8611	+	155.644i	0.151536	+	0.262469i	−0.780256	+	0.625460i	$0.784911\pi$
$594$	286.982	−	157.721i	0.483135	−	0.265523i
$595$	151.623	+	58.2888i	0.254829	+	0.0979644i
$596$	80.6308	+	51.1997i	0.135287	+	0.0859055i
$597$	−1014.93	+	585.967i	−1.70004	+	0.981520i
$598$	2.32635	−	110.364i	0.00389021	−	0.184555i
$599$	−35.2310	−	20.3406i	−0.0588163	−	0.0339576i	0.470303	−	0.882505i	$-0.344144\pi$
$599$	−35.2310	−	20.3406i	−0.0588163	−	0.0339576i	−0.529120	+	0.848547i	$0.677478\pi$
$600$	779.595	−	386.610i	1.29932	−	0.644350i
$601$	−1020.79			−1.69849			−0.849245	−	0.527998i	$-0.822943\pi$
$601$	−1020.79			−1.69849			−0.849245	+	0.527998i	$0.822943\pi$
$602$	555.684	−	430.475i	0.923062	−	0.715075i
$603$	−751.272			−1.24589
$604$	−30.9302	+	733.351i	−0.0512089	+	1.21416i
$605$	781.901	+	451.431i	1.29240	+	0.746166i
$606$	−1639.98	−	34.5690i	−2.70625	−	0.0570446i
$607$	273.220	−	157.744i	0.450116	−	0.259874i	−0.257763	−	0.966208i	$-0.582986\pi$
$607$	273.220	−	157.744i	0.450116	−	0.259874i	0.707879	+	0.706334i	$0.249652\pi$
$608$	419.636	+	305.306i	0.690190	+	0.502148i
$609$	−518.327	+	419.308i	−0.851111	+	0.688519i
$610$	1222.50	−	671.865i	2.00410	−	1.10142i
$611$	1.10125	+	1.90743i	0.00180238	+	0.00312181i
$612$	−69.2824	−	132.610i	−0.113207	−	0.216683i
$613$	358.417	+	206.932i	0.584693	+	0.337572i	0.762996	−	0.646403i	$-0.223728\pi$
$613$	358.417	+	206.932i	0.584693	+	0.337572i	−0.178303	+	0.983976i	$0.557061\pi$
$614$	296.766	+	179.781i	0.483333	+	0.292804i
$615$			35.8423i			0.0582802i
$616$	−721.902	+	512.062i	−1.17192	+	0.831270i
$617$	139.167			0.225554			0.112777	−	0.993620i	$-0.464025\pi$
$617$	139.167			0.225554			0.112777	+	0.993620i	$0.464025\pi$
$618$	214.088	−	353.396i	0.346420	−	0.571838i
$619$	−167.006	+	289.264i	−0.269800	+	0.467308i	−0.968810	−	0.247804i	$-0.920291\pi$
$619$	−167.006	+	289.264i	−0.269800	+	0.467308i	0.699010	+	0.715112i	$0.253624\pi$
$620$	−355.334	−	680.128i	−0.573120	−	1.09698i
$621$	−170.732	+	98.5724i	−0.274931	+	0.158732i
$622$	111.458	+	202.805i	0.179193	+	0.326053i
$623$	424.354	−	66.9959i	0.681147	−	0.107538i
$624$	189.230	−	88.9232i	0.303254	−	0.142505i
$625$	322.850	+	559.192i	0.516560	+	0.894707i
$626$	8.87314	−	420.950i	0.0141743	−	0.672444i
$627$	577.396	−	1000.08i	0.920887	−	1.59502i
$628$	−27.9692	+	663.147i	−0.0445369	+	1.05597i
$629$			58.4569i			0.0929363i
$630$	1098.78	−	149.813i	1.74410	−	0.237798i
$631$			284.343i			0.450623i	0.974287	+	0.225311i	$0.0723399\pi$
$631$			284.343i			0.450623i	−0.974287	+	0.225311i	$0.927660\pi$
$632$	−258.217	−	520.692i	−0.408572	−	0.823880i
$633$	10.6560	−	18.4568i	0.0168342	−	0.0291576i
$634$	−699.587	−	14.7465i	−1.10345	−	0.0232595i
$635$	613.568	+	1062.73i	0.966248	+	1.67359i
$636$	684.564	+	434.691i	1.07636	+	0.683476i
$637$	−95.2007	+	105.521i	−0.149452	+	0.165653i
$638$	321.832	+	585.593i	0.504438	+	0.917857i
$639$	434.846	−	251.058i	0.680510	−	0.392893i
$640$	887.556	+	131.900i	1.38681	+	0.206093i
$641$	−32.4545	+	56.2128i	−0.0506310	+	0.0876955i	−0.890230	−	0.455511i	$-0.849457\pi$
$641$	−32.4545	+	56.2128i	−0.0506310	+	0.0876955i	0.839599	+	0.543206i	$0.182790\pi$
$642$	569.493	+	345.000i	0.887060	+	0.537382i
$643$	683.365			1.06278			0.531388	−	0.847128i	$-0.321671\pi$
$643$	683.365			1.06278			0.531388	+	0.847128i	$0.321671\pi$
$644$	428.013	−	317.367i	0.664617	−	0.492806i
$645$			1585.79i			2.45859i
$646$	−91.8309	−	55.6313i	−0.142153	−	0.0861166i
$647$	1103.61	+	637.171i	1.70574	+	0.984808i	0.939691	+	0.342024i	$0.111112\pi$
$647$	1103.61	+	637.171i	1.70574	+	0.984808i	0.766047	+	0.642785i	$0.222221\pi$
$648$	366.514	+	243.720i	0.565608	+	0.376112i
$649$	−18.8456	−	32.6415i	−0.0290379	−	0.0502951i
$650$	−67.4515	−	122.732i	−0.103771	−	0.188819i
$651$	−134.592	−	852.514i	−0.206747	−	1.30954i
$652$	−21.6656	+	34.1197i	−0.0332295	+	0.0523308i
$653$	−472.891	+	273.024i	−0.724182	+	0.418107i	−0.816290	−	0.577642i	$-0.803973\pi$
$653$	−472.891	+	273.024i	−0.724182	+	0.418107i	0.0921079	+	0.995749i	$0.470640\pi$
$654$	1089.40	+	22.9634i	1.66575	+	0.0351122i
$655$	−52.3311	−	30.2134i	−0.0798948	−	0.0461273i
$656$	−10.3703	+	14.9042i	−0.0158084	+	0.0227198i
$657$	19.4282			0.0295710
$658$	−4.02313	+	9.84076i	−0.00611419	+	0.0149556i
$659$	−398.883			−0.605285			−0.302642	−	0.953104i	$-0.597869\pi$
$659$	−398.883			−0.605285			−0.302642	+	0.953104i	$0.597869\pi$
$660$	84.1404	−	1994.96i	0.127485	−	3.02267i
$661$	−718.146	−	414.622i	−1.08645	−	0.627264i	−0.153824	−	0.988098i	$-0.549159\pi$
$661$	−718.146	−	414.622i	−1.08645	−	0.627264i	−0.932630	+	0.360834i	$0.882492\pi$
$662$	9.02440	−	428.126i	0.0136320	−	0.646716i
$663$	−37.4626	+	21.6290i	−0.0565046	+	0.0326230i
$664$	51.6002	−	815.019i	0.0777111	−	1.22744i
$665$	618.695	−	500.502i	0.930368	−	0.752635i
$666$	192.208	+	349.734i	0.288600	+	0.525126i
$667$	−201.139	−	348.383i	−0.301557	−	0.522313i
$668$	−1010.59	+	527.982i	−1.51285	+	0.790393i
$669$	−426.531	−	246.258i	−0.637565	−	0.368098i
$670$	−483.003	+	797.296i	−0.720900	+	1.18999i
$671$		−	1572.50i		−	2.34352i
$672$	898.699	+	459.217i	1.33735	+	0.683359i
$673$	946.218			1.40597			0.702985	−	0.711205i	$-0.251850\pi$
$673$	946.218			1.40597			0.702985	+	0.711205i	$0.251850\pi$
$674$	−748.000	−	453.140i	−1.10979	−	0.672314i
$675$	−125.055	+	216.602i	−0.185267	+	0.320892i
$676$	297.449	+	569.332i	0.440013	+	0.842207i
$677$	987.793	−	570.303i	1.45907	−	0.842397i	0.460108	−	0.887863i	$-0.347811\pi$
$677$	987.793	−	570.303i	1.45907	−	0.842397i	0.998966	+	0.0454660i	$0.0144773\pi$
$678$	−772.054	+	424.308i	−1.13872	+	0.625823i
$679$	−258.279	+	671.846i	−0.380381	+	0.989463i
$680$	−185.276	−	11.7301i	−0.272465	−	0.0172502i
$681$	−273.575	−	473.846i	−0.401725	−	0.695809i
$682$	−864.832	−	18.2297i	−1.26808	−	0.0267297i
$683$	−58.7041	+	101.678i	−0.0859504	+	0.148870i	−0.905796	−	0.423715i	$-0.860726\pi$
$683$	−58.7041	+	101.678i	−0.0859504	+	0.148870i	0.819845	+	0.572585i	$0.194059\pi$
$684$	−732.319	−	30.8866i	−1.07064	−	0.0451559i
$685$		−	1795.20i		−	2.62073i
$686$	−684.076	−	51.3473i	−0.997195	−	0.0748503i
$687$			649.675i			0.945670i
$688$	−458.821	+	659.415i	−0.666892	+	0.958453i
$689$	65.2530	−	113.022i	0.0947069	−	0.164037i
$690$	−25.3331	+	1201.83i	−0.0367147	+	1.74178i
$691$	−477.961	−	827.853i	−0.691695	−	1.19805i	−0.971282	−	0.237930i	$-0.923531\pi$
$691$	−477.961	−	827.853i	−0.691695	−	1.19805i	0.279588	−	0.960120i	$-0.409802\pi$
$692$	328.801	+	208.785i	0.475145	+	0.301712i
$693$	448.570	−	1166.84i	0.647287	−	1.68375i
$694$	−661.463	+	363.529i	−0.953116	+	0.523816i
$695$	−1328.54	+	767.031i	−1.91156	+	1.10364i
$696$	421.900	−	634.467i	0.606179	−	0.911590i
$697$	1.87830	−	3.25331i	0.00269484	−	0.00466759i
$698$	218.806	−	361.185i	0.313476	−	0.517457i
$699$	−875.243			−1.25214
$700$	268.940	−	620.192i	0.384200	−	0.885989i
$701$			824.950i			1.17682i	0.808563	+	0.588410i	$0.200246\pi$
$701$			824.950i			1.17682i	−0.808563	+	0.588410i	$0.799754\pi$
$702$	−31.1373	+	51.3984i	−0.0443551	+	0.0732171i
$703$	248.010	+	143.189i	0.352789	+	0.203683i
$704$	612.195	−	805.214i	0.869595	−	1.14377i
$705$	−11.9923	−	20.7712i	−0.0170103	−	0.0294627i
$706$	−523.632	+	287.779i	−0.741688	+	0.407619i
$707$	−990.695	+	801.437i	−1.40127	+	1.13357i
$708$	−23.0386	+	36.2818i	−0.0325403	+	0.0512455i
$709$	−112.576	+	64.9959i	−0.158782	+	0.0916726i	−0.577285	−	0.816542i	$-0.695888\pi$
$709$	−112.576	+	64.9959i	−0.158782	+	0.0916726i	0.418504	+	0.908215i	$0.362555\pi$
$710$	13.1299	−	622.893i	0.0184928	−	0.877315i
$711$	710.922	+	410.451i	0.999890	+	0.577287i
$712$	−439.866	+	218.135i	−0.617789	+	0.306369i
$713$	520.770			0.730393
$714$	−193.276	−	79.0158i	−0.270695	−	0.110666i
$715$	−321.348			−0.449437
$716$	1206.19	+	50.8728i	1.68462	+	0.0710514i
$717$	−1231.30	−	710.890i	−1.71729	−	0.991478i
$718$	441.593	+	9.30827i	0.615032	+	0.0129642i
$719$	−438.623	+	253.239i	−0.610046	+	0.352210i	−0.772984	−	0.634426i	$-0.781237\pi$
$719$	−438.623	+	253.239i	−0.610046	+	0.352210i	0.162937	+	0.986636i	$0.447903\pi$
$720$	−1147.03	+	539.015i	−1.59310	+	0.748631i
$721$	−50.0547	−	317.049i	−0.0694240	−	0.439735i
$722$	171.779	−	94.4070i	0.237921	−	0.130758i
$723$	817.094	+	1415.25i	1.13014	+	1.95747i
$724$	−214.326	+	111.975i	−0.296031	+	0.154662i
$725$	−441.980	−	255.177i	−0.609628	−	0.351969i
$726$	−992.612	−	601.326i	−1.36723	−	0.828272i
$727$			1272.41i			1.75022i	0.483924	+	0.875110i	$0.339211\pi$
$727$			1272.41i			1.75022i	−0.483924	+	0.875110i	$0.660789\pi$
$728$	67.7445	−	147.619i	0.0930556	−	0.202774i
$729$	−1041.76			−1.42902
$730$	12.4906	−	20.6184i	0.0171105	−	0.0282443i
$731$	83.1028	−	143.938i	0.113684	−	0.196906i
$732$	−1589.27	+	830.314i	−2.17113	+	1.13431i
$733$	615.475	−	355.345i	0.839666	−	0.484781i	−0.0174847	−	0.999847i	$-0.505566\pi$
$733$	615.475	−	355.345i	0.839666	−	0.484781i	0.857151	+	0.515066i	$0.172233\pi$
$734$	207.439	+	377.448i	0.282615	+	0.514235i
$735$	1036.70	−	1149.09i	1.41048	−	1.56338i
$736$	−358.261	+	492.422i	−0.486768	+	0.669052i
$737$	525.417	+	910.048i	0.712913	+	1.23480i
$738$	0.540455	−	25.6397i	0.000732324	−	0.0347421i
$739$	105.509	−	182.748i	0.142773	−	0.247291i	−0.785767	−	0.618523i	$-0.787731\pi$
$739$	105.509	−	182.748i	0.142773	−	0.247291i	0.928540	+	0.371232i	$0.121065\pi$
$740$	494.732	+	20.8660i	0.668556	+	0.0281973i
$741$			211.919i			0.285991i
$742$	624.170	−	85.1022i	0.841200	−	0.114693i
$743$		−	244.355i		−	0.328876i	−0.986387	−	0.164438i	$-0.947419\pi$
$743$		−	244.355i		−	0.328876i	0.986387	−	0.164438i	$-0.0525811\pi$
$744$	438.225	+	883.675i	0.589012	+	1.18774i
$745$	−83.6954	+	144.965i	−0.112343	+	0.194583i
$746$	447.656	+	9.43608i	0.600075	+	0.0126489i
$747$	576.727	+	998.920i	0.772057	+	1.33724i
$748$	−112.182	+	176.668i	−0.149976	+	0.236187i
$749$	510.919	−	80.6625i	0.682136	−	0.107694i
$750$	−26.0853	−	47.4638i	−0.0347804	−	0.0632851i
$751$	262.737	−	151.692i	0.349850	−	0.201986i	−0.314769	−	0.949168i	$-0.601927\pi$
$751$	262.737	−	151.692i	0.349850	−	0.201986i	0.664619	+	0.747182i	$0.268594\pi$
$752$	1.02308	−	12.1070i	0.00136048	−	0.0160997i
$753$	−20.3701	+	35.2821i	−0.0270519	+	0.0468553i
$754$	−104.879	−	63.5362i	−0.139097	−	0.0842655i
$755$	−1286.37			−1.70381
$756$	−288.175	+	33.1215i	−0.381183	+	0.0438114i
$757$		−	668.225i		−	0.882728i	−0.897328	−	0.441364i	$-0.854495\pi$
$757$		−	668.225i		−	0.882728i	0.897328	−	0.441364i	$-0.145505\pi$
$758$	−867.358	−	525.447i	−1.14427	−	0.693201i
$759$	1173.54	+	677.546i	1.54617	+	0.892683i
$760$	−503.597	+	757.324i	−0.662627	+	0.996479i
$761$	−45.4152	−	78.6615i	−0.0596784	−	0.103366i	0.834643	−	0.550792i	$-0.185674\pi$
$761$	−45.4152	−	78.6615i	−0.0596784	−	0.103366i	−0.894321	+	0.447426i	$0.852341\pi$
$762$	−759.723	−	1382.36i	−0.997012	−	1.81412i
$763$	658.095	−	532.375i	0.862509	−	0.697740i
$764$	247.895	+	157.410i	0.324470	+	0.206035i
$765$	227.082	−	131.106i	0.296839	−	0.171380i
$766$	297.110	+	6.26273i	0.387872	+	0.00817589i
$767$	5.99013	+	3.45840i	0.00780982	+	0.00450900i
$768$	−1137.05	−	193.550i	−1.48053	−	0.252019i
$769$	421.091			0.547582			0.273791	−	0.961789i	$-0.411722\pi$
$769$	421.091			0.547582			0.273791	+	0.961789i	$0.411722\pi$
$770$	−949.928	−	1226.23i	−1.23367	−	1.59250i
$771$	1671.88			2.16846
$772$	−260.126	−	10.9712i	−0.336951	−	0.0142114i
$773$	508.100	+	293.352i	0.657309	+	0.379498i	0.791251	−	0.611492i	$-0.209430\pi$
$773$	508.100	+	293.352i	0.657309	+	0.379498i	−0.133942	+	0.990989i	$0.542763\pi$
$774$	23.9117	−	1134.39i	0.0308937	−	1.46562i
$775$	572.167	−	330.341i	0.738281	−	0.426247i
$776$	51.9765	−	820.963i	0.0669800	−	1.05794i
$777$	519.846	+	199.845i	0.669043	+	0.257201i
$778$	−152.503	−	277.489i	−0.196020	−	0.356670i
$779$	−9.20171	−	15.9378i	−0.0118122	−	0.0204593i
$780$	169.678	+	324.773i	0.217536	+	0.416375i
$781$	−608.235	−	351.165i	−0.778791	−	0.449635i
$782$	65.2806	−	107.759i	0.0834791	−	0.137799i
$783$			218.996i			0.279688i
$784$	763.557	−	177.869i	0.973924	−	0.226874i
$785$	−1163.23			−1.48182
$786$	66.4335	+	40.2455i	0.0845210	+	0.0512030i
$787$	−681.137	+	1179.76i	−0.865485	+	1.49906i	0.00107958	+	0.999999i	$0.499656\pi$
$787$	−681.137	+	1179.76i	−0.865485	+	1.49906i	−0.866565	+	0.499065i	$0.833677\pi$
$788$	1234.91	−	645.182i	1.56715	−	0.818759i
$789$	−1849.01	+	1067.53i	−2.34349	+	1.35301i
$790$	892.657	−	490.589i	1.12995	−	0.620999i
$791$	−245.570	+	638.787i	−0.310456	+	0.807569i
$792$	−90.2710	+	1425.82i	−0.113979	+	1.80028i
$793$	144.287	+	249.913i	0.181951	+	0.315149i
$794$	−555.360	−	11.7064i	−0.699446	−	0.0147435i
$795$	−710.583	+	1230.77i	−0.893815	+	1.54813i
$796$	43.8436	−	1039.53i	0.0550799	−	1.30594i
$797$			874.598i			1.09736i	0.836032	+	0.548681i	$0.184870\pi$
$797$			874.598i			1.09736i	−0.836032	+	0.548681i	$0.815130\pi$
$798$	−808.659	+	626.449i	−1.01336	+	0.785023i
$799$			2.51380i			0.00314618i
$800$	−81.2611	+	768.278i	−0.101576	+	0.960348i
$801$	346.737	−	600.567i	0.432880	−	0.749771i
$802$	26.2921	−	1247.32i	0.0327831	−	1.55526i
$803$	−13.5875	−	23.5342i	−0.0169209	−	0.0293078i
$804$	642.317	−	1011.54i	0.798902	−	1.25814i
$805$	587.315	+	726.008i	0.729584	+	0.901874i
$806$	139.118	−	76.4566i	0.172602	−	0.0948594i
$807$	367.208	−	212.008i	0.455029	−	0.262711i
$808$	806.392	−	1212.68i	0.998009	−	1.50084i
$809$	27.9415	−	48.3961i	0.0345383	−	0.0598222i	−0.848240	−	0.529613i	$-0.822337\pi$
$809$	27.9415	−	48.3961i	0.0345383	−	0.0598222i	0.882778	+	0.469791i	$0.155671\pi$
$810$	−399.684	+	659.761i	−0.493437	+	0.814519i
$811$	917.924			1.13184			0.565921	−	0.824459i	$-0.308521\pi$
$811$	917.924			1.13184			0.565921	+	0.824459i	$0.308521\pi$
$812$	−67.5850	−	588.026i	−0.0832327	−	0.724169i
$813$		−	712.850i		−	0.876815i
$814$	289.223	−	477.422i	0.355311	−	0.586514i
$815$	−61.3432	−	35.4165i	−0.0752677	−	0.0434559i
$816$	237.786	+	20.0936i	0.291404	+	0.0246246i
$817$	−407.117	−	705.147i	−0.498307	−	0.863093i
$818$	867.847	−	476.954i	1.06094	−	0.583073i
$819$	35.7751	+	226.601i	0.0436815	+	0.276680i
$820$	−26.8629	−	17.0577i	−0.0327597	−	0.0208020i
$821$	1178.10	−	680.176i	1.43496	−	0.828472i	0.437463	−	0.899237i	$-0.355877\pi$
$821$	1178.10	−	680.176i	1.43496	−	0.828472i	0.997493	+	0.0707646i	$0.0225439\pi$
$822$	−48.6301	+	2307.05i	−0.0591607	+	2.80664i
$823$	−488.057	−	281.780i	−0.593022	−	0.342382i	0.173269	−	0.984874i	$-0.444567\pi$
$823$	−488.057	−	281.780i	−0.593022	−	0.342382i	−0.766292	+	0.642493i	$0.777900\pi$
$824$	162.975	+	328.638i	0.197785	+	0.398832i
$825$	1719.16			2.08383
$826$	4.51041	+	33.0809i	0.00546054	+	0.0400496i
$827$	63.4180			0.0766844			0.0383422	−	0.999265i	$-0.487792\pi$
$827$	63.4180			0.0766844			0.0383422	+	0.999265i	$0.487792\pi$
$828$	36.2440	−	859.341i	0.0437729	−	1.03785i
$829$	252.620	+	145.850i	0.304728	+	0.175935i	0.644565	−	0.764549i	$-0.277038\pi$
$829$	252.620	+	145.850i	0.304728	+	0.175935i	−0.339837	+	0.940484i	$0.610372\pi$
$830$	1430.90	+	30.1617i	1.72398	+	0.0363394i
$831$	923.725	−	533.313i	1.11158	−	0.641772i
$832$	−23.4106	+	184.143i	−0.0281377	+	0.221325i
$833$	−154.316	+	49.9715i	−0.185254	+	0.0599899i
$834$	1728.11	−	949.743i	2.07208	−	1.13878i
$835$	−999.123	−	1730.53i	−1.19655	−	2.07249i
$836$	474.747	+	908.691i	0.567879	+	1.08695i
$837$	−245.520	−	141.751i	−0.293333	−	0.169356i
$838$	192.666	+	116.717i	0.229912	+	0.139281i
$839$		−	463.917i		−	0.552940i	−0.961023	−	0.276470i	$-0.910835\pi$
$839$		−	463.917i		−	0.552940i	0.961023	−	0.276470i	$-0.0891646\pi$
$840$	−737.714	+	1607.53i	−0.878231	+	1.91372i
$841$	394.135			0.468651
$842$	−851.755	+	1406.00i	−1.01159	+	1.66983i
$843$	545.046	−	944.047i	0.646555	−	1.11987i
$844$	8.76160	+	16.7702i	0.0103810	+	0.0198699i
$845$	−974.927	+	562.874i	−1.15376	+	0.666124i
$846$	8.26544	+	15.0395i	0.00977002	+	0.0177772i
$847$	−890.520	+	140.593i	−1.05138	+	0.165989i
$848$	−651.580	+	306.191i	−0.768373	+	0.361074i
$849$	−525.956	−	910.983i	−0.619501	−	1.07301i
$850$	3.36848	−	159.804i	0.00396292	−	0.188005i
$851$	−168.025	+	291.028i	−0.197444	+	0.341984i
$852$	−33.7471	+	800.141i	−0.0396093	+	0.939132i
$853$			649.909i			0.761909i	0.924594	+	0.380955i	$0.124405\pi$
$853$			649.909i			0.761909i	−0.924594	+	0.380955i	$0.875595\pi$
$854$	−527.115	+	1289.34i	−0.617230	+	1.50977i
$855$		−	1284.56i		−	1.50241i
$856$	−529.595	+	262.632i	−0.618686	+	0.306814i
$857$	−584.140	+	1011.76i	−0.681610	+	1.18058i	0.292880	+	0.956149i	$0.405386\pi$
$857$	−584.140	+	1011.76i	−0.681610	+	1.18058i	−0.974489	+	0.224433i	$0.927947\pi$
$858$	412.972	+	8.70498i	0.481320	+	0.0101457i
$859$	−733.208	−	1269.95i	−0.853560	−	1.47841i	−0.877974	−	0.478708i	$-0.841105\pi$
$859$	−733.208	−	1269.95i	−0.853560	−	1.47841i	0.0244139	−	0.999702i	$-0.492228\pi$
$860$	−1188.51	−	754.693i	−1.38199	−	0.877550i
$861$	−22.5098	−	27.8254i	−0.0261438	−	0.0323175i
$862$	−321.550	−	585.080i	−0.373028	−	0.678747i
$863$	36.9921	−	21.3574i	0.0428646	−	0.0247479i	−0.478415	−	0.878134i	$-0.658788\pi$
$863$	36.9921	−	21.3574i	0.0428646	−	0.0247479i	0.521279	+	0.853386i	$0.325455\pi$
$864$	302.939	−	134.638i	0.350623	−	0.155831i
$865$	−341.298	+	591.145i	−0.394564	+	0.683404i
$866$	1034.36	+	626.618i	1.19441	+	0.723578i
$867$	1252.71			1.44488
$868$	702.992	+	304.845i	0.809898	+	0.351204i
$869$		−	1148.23i		−	1.32132i
$870$	1142.10	+	691.887i	1.31276	+	0.795272i
$871$	−167.005	−	96.4206i	−0.191740	−	0.110701i
$872$	−535.667	+	805.552i	−0.614297	+	0.923798i
$873$	580.933	+	1006.21i	0.665444	+	1.15258i
$874$	−297.277	−	540.914i	−0.340134	−	0.618895i
$875$	−39.2709	−	15.0970i	−0.0448811	−	0.0172537i
$876$	−16.6106	+	26.1588i	−0.0189618	+	0.0298617i
$877$	−842.217	+	486.254i	−0.960338	+	0.554452i	−0.896277	−	0.443494i	$-0.853739\pi$
$877$	−842.217	+	486.254i	−0.960338	+	0.554452i	−0.0640612	+	0.997946i	$0.520405\pi$
$878$	−962.014	−	20.2782i	−1.09569	−	0.0230959i
$879$	−844.723	−	487.701i	−0.961005	−	0.554836i
$880$	1455.13	+	1012.48i	1.65356	+	1.15055i
$881$	−110.722			−0.125678			−0.0628390	−	0.998024i	$-0.520015\pi$
$881$	−110.722			−0.125678			−0.0628390	+	0.998024i	$0.520015\pi$
$882$	−758.929	+	806.363i	−0.860464	+	0.914244i
$883$	1283.66			1.45375			0.726874	−	0.686770i	$-0.240972\pi$
$883$	1283.66			1.45375			0.726874	+	0.686770i	$0.240972\pi$
$884$	1.61834	−	38.3707i	0.00183070	−	0.0434058i
$885$	−65.2305	−	37.6608i	−0.0737067	−	0.0425546i
$886$	7.78563	−	369.357i	0.00878739	−	0.416882i
$887$	429.755	−	248.119i	0.484504	−	0.279729i	−0.237788	−	0.971317i	$-0.576422\pi$
$887$	429.755	−	248.119i	0.484504	−	0.279729i	0.722292	+	0.691589i	$0.243089\pi$
$888$	−635.227	−	40.2172i	−0.715346	−	0.0452897i
$889$	−1143.75	−	439.693i	−1.28656	−	0.494593i
$890$	−414.435	−	754.091i	−0.465658	−	0.847293i
$891$	434.781	+	753.063i	0.487970	+	0.845189i
$892$	387.554	−	202.478i	0.434477	−	0.226993i
$893$	10.6651	+	6.15750i	0.0119430	+	0.00689529i
$894$	111.486	−	184.031i	0.124705	−	0.205851i
$895$			2115.78i			2.36400i
$896$	−771.871	+	455.008i	−0.861463	+	0.507821i
$897$	−248.677			−0.277232
$898$	198.247	+	120.098i	0.220765	+	0.133740i
$899$	289.245	−	500.987i	0.321741	−	0.557272i
$900$	−505.286	−	967.144i	−0.561429	−	1.07460i
$901$	128.996	−	74.4756i	0.143169	−	0.0826589i
$902$	−31.4364	+	17.2769i	−0.0348519	+	0.0191540i
$903$	−995.914	−	1231.10i	−1.10289	−	1.36334i
$904$	49.4190	−	780.568i	0.0546670	−	0.863460i
$905$	−211.895	−	367.013i	−0.234138	−	0.405539i
$906$	1653.15	+	34.8465i	1.82467	+	0.0384620i
$907$	−796.131	+	1378.94i	−0.877763	+	1.52033i	−0.0239725	+	0.999713i	$0.507631\pi$
$907$	−796.131	+	1378.94i	−0.877763	+	1.52033i	−0.853790	+	0.520617i	$0.825702\pi$
$908$	485.332	+	20.4696i	0.534507	+	0.0225436i
$909$			2056.93i			2.26285i
$910$	263.483	+	107.718i	0.289542	+	0.118371i
$911$			663.197i			0.727988i	0.931401	+	0.363994i	$0.118587\pi$
$911$			663.197i			0.727988i	−0.931401	+	0.363994i	$0.881413\pi$
$912$	667.700	−	959.615i	0.732127	−	1.05221i
$913$	806.690	−	1397.23i	0.883559	−	1.53037i
$914$	−6.67892	+	316.854i	−0.00730736	+	0.346668i
$915$	−1571.24	−	2721.47i	−1.71720	−	2.97428i
$916$	−486.916	−	309.186i	−0.531567	−	0.337539i
$917$	59.6008	−	9.40960i	0.0649954	−	0.0102613i
$918$	−60.1083	+	33.0345i	−0.0654775	+	0.0359853i
$919$	−441.371	+	254.826i	−0.480273	+	0.277286i	−0.720530	−	0.693424i	$-0.756102\pi$
$919$	−441.371	+	254.826i	−0.480273	+	0.277286i	0.240257	+	0.970709i	$0.422768\pi$
$920$	−888.683	−	590.946i	−0.965960	−	0.642333i
$921$	390.822	−	676.924i	0.424345	−	0.734988i
$922$	−43.9205	+	72.4998i	−0.0476361	+	0.0786332i
$923$	128.886			0.139639
$924$	1187.56	+	1601.59i	1.28524	+	1.73332i
$925$			426.335i			0.460902i
$926$	−404.189	+	667.197i	−0.436489	+	0.720515i
$927$	−448.702	−	259.058i	−0.484037	−	0.279459i
$928$	274.731	+	618.152i	0.296047	+	0.666112i
$929$	161.143	+	279.108i	0.173459	+	0.300439i	0.939627	−	0.342201i	$-0.111172\pi$
$929$	161.143	+	279.108i	0.173459	+	0.300439i	−0.766168	+	0.642640i	$0.777839\pi$
$930$	−1514.94	+	832.587i	−1.62897	+	0.895254i
$931$	−165.984	+	777.109i	−0.178285	+	0.834703i
$932$	416.536	−	655.973i	0.446927	−	0.703834i
$933$	451.473	−	260.658i	0.483894	−	0.279376i
$934$	1.61616	−	76.6721i	0.00173036	−	0.0820900i
$935$	−317.628	−	183.383i	−0.339710	−	0.196131i
$936$	−116.482	−	234.884i	−0.124446	−	0.250944i
$937$	−1077.79			−1.15026			−0.575130	−	0.818062i	$-0.695048\pi$
$937$	−1077.79			−1.15026			−0.575130	+	0.818062i	$0.695048\pi$
$938$	−125.751	−	922.300i	−0.134062	−	0.983262i
$939$	−948.502			−1.01012
$940$	21.2748	+	0.897294i	0.0226327	+	0.000954568i
$941$	−63.5953	−	36.7168i	−0.0675827	−	0.0390189i	0.465828	−	0.884875i	$-0.345757\pi$
$941$	−63.5953	−	36.7168i	−0.0675827	−	0.0390189i	−0.533411	+	0.845856i	$0.679090\pi$
$942$	1494.89	+	31.5107i	1.58694	+	0.0334508i
$943$	18.7023	−	10.7978i	0.0198327	−	0.0114504i
$944$	−16.2281	−	34.5337i	−0.0171908	−	0.0365823i
$945$	−79.2771	−	502.144i	−0.0838911	−	0.531369i
$946$	−1390.86	+	764.394i	−1.47026	+	0.808027i
$947$	−38.4077	−	66.5241i	−0.0405572	−	0.0702472i	0.845034	−	0.534712i	$-0.179580\pi$
$947$	−38.4077	−	66.5241i	−0.0405572	−	0.0702472i	−0.885591	+	0.464465i	$0.846247\pi$
$948$	−1160.47	+	606.287i	−1.22412	+	0.639543i
$949$	4.31882	+	2.49347i	0.00455092	+	0.00262747i
$950$	−669.736	−	405.727i	−0.704985	−	0.427081i
$951$			1576.34i			1.65756i
$952$	151.202	−	107.251i	0.158826	−	0.112659i
$953$	−1329.39			−1.39495			−0.697477	−	0.716607i	$-0.745694\pi$
$953$	−1329.39			−1.39495			−0.697477	+	0.716607i	$0.745694\pi$
$954$	526.872	−	869.710i	0.552277	−	0.911646i
$955$	−257.317	+	445.686i	−0.269442	+	0.466687i
$956$	1118.78	−	584.508i	1.17027	−	0.611410i
$957$	1303.62	−	752.643i	1.36219	−	0.786461i
$958$	624.361	+	1136.06i	0.651734	+	1.18587i
$959$	1127.42	+	1393.66i	1.17563	+	1.45325i
$960$	254.933	−	2005.25i	0.265555	−	2.08880i
$961$	−106.056	−	183.695i	−0.110360	−	0.191150i
$962$	−2.15875	+	102.413i	−0.00224403	+	0.106459i
$963$	417.469	−	723.077i	0.433509	−	0.750859i
$964$	−1449.56	−	61.1371i	−1.50369	−	0.0634202i
$965$		−	456.288i		−	0.472837i
$966$	−735.107	−	948.922i	−0.760980	−	0.982320i
$967$		−	601.743i		−	0.622279i	−0.950364	−	0.311139i	$-0.899289\pi$
$967$		−	601.743i		−	0.622279i	0.950364	−	0.311139i	$-0.100711\pi$
$968$	923.071	−	457.762i	0.953586	−	0.472894i
$969$	−120.935	+	209.466i	−0.124804	+	0.216167i
$970$	1441.34	+	30.3817i	1.48591	+	0.0313213i
$971$	−213.139	−	369.168i	−0.219505	−	0.380193i	0.735152	−	0.677902i	$-0.237111\pi$
$971$	−213.139	−	369.168i	−0.219505	−	0.380193i	−0.954657	+	0.297709i	$0.903777\pi$
$972$	731.436	−	1151.89i	0.752506	−	1.18507i
$973$	549.668	−	1429.82i	0.564921	−	1.46950i
$974$	337.364	+	613.854i	0.346369	+	0.630240i
$975$	−273.220	+	157.744i	−0.280225	+	0.161788i
$976$	134.045	−	1586.27i	0.137341	−	1.62528i
$977$	−109.928	+	190.401i	−0.112516	+	0.194884i	−0.916784	−	0.399383i	$-0.869224\pi$
$977$	−109.928	+	190.401i	−0.112516	+	0.194884i	0.804268	+	0.594267i	$0.202558\pi$
$978$	77.8743	+	47.1764i	0.0796261	+	0.0482376i
$979$	−969.989			−0.990796
$980$	367.836	+	1323.84i	0.375342	+	1.35086i
$981$		−	1366.37i		−	1.39283i
$982$	−775.834	−	470.002i	−0.790055	−	0.478617i
$983$	−1444.72	−	834.112i	−1.46971	−	0.848537i	−0.470286	−	0.882514i	$-0.655849\pi$
$983$	−1444.72	−	834.112i	−1.46971	−	0.848537i	−0.999423	+	0.0339771i	$0.989183\pi$
$984$	34.0602	+	22.6489i	0.0346140	+	0.0230172i
$985$	1220.91	+	2114.67i	1.23950	+	2.14687i
$986$	−67.4075	−	122.652i	−0.0683646	−	0.124394i
$987$	22.3547	+	8.59388i	0.0226492	+	0.00870707i
$988$	−158.828	−	100.854i	−0.160757	−	0.102079i
$989$	827.456	−	477.732i	0.836659	−	0.483045i
$990$	−2503.26	−	52.7659i	−2.52855	−	0.0532989i
$991$	−1184.20	−	683.697i	−1.19495	−	0.689906i	−0.235527	−	0.971868i	$-0.575682\pi$
$991$	−1184.20	−	683.697i	−1.19495	−	0.689906i	−0.959426	+	0.281962i	$0.909015\pi$
$992$	−870.848	−	92.1100i	−0.877871	−	0.0928528i
$993$	−964.670			−0.971471
$994$	380.998	+	491.816i	0.383298	+	0.494784i
$995$	1823.44			1.83260
$996$	−1838.07	−	77.5232i	−1.84545	−	0.0778345i
$997$	803.308	+	463.790i	0.805725	+	0.465186i	0.845469	−	0.534024i	$-0.179321\pi$
$997$	803.308	+	463.790i	0.805725	+	0.465186i	−0.0397440	+	0.999210i	$0.512654\pi$
$998$	−22.3203	+	1058.89i	−0.0223650	+	1.06102i
$999$	158.433	−	91.4711i	0.158591	−	0.0915626i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	56.3.k.c.11.5	yes	12
4.3	odd	2		224.3.o.c.207.1		12
7.2	even	3	inner	56.3.k.c.51.4	yes	12
7.3	odd	6		392.3.g.l.99.2		6
7.4	even	3		392.3.g.k.99.2		6
7.5	odd	6		392.3.k.k.275.4		12
7.6	odd	2		392.3.k.k.67.5		12
8.3	odd	2	inner	56.3.k.c.11.4	✓	12
8.5	even	2		224.3.o.c.207.2		12
28.3	even	6		1568.3.g.i.687.2		6
28.11	odd	6		1568.3.g.k.687.5		6
28.23	odd	6		224.3.o.c.79.2		12
56.3	even	6		392.3.g.l.99.1		6
56.11	odd	6		392.3.g.k.99.1		6
56.19	even	6		392.3.k.k.275.5		12
56.27	even	2		392.3.k.k.67.4		12
56.37	even	6		224.3.o.c.79.1		12
56.45	odd	6		1568.3.g.i.687.1		6
56.51	odd	6	inner	56.3.k.c.51.5	yes	12
56.53	even	6		1568.3.g.k.687.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.3.k.c.11.4	✓	12	8.3	odd	2	inner
56.3.k.c.11.5	yes	12	1.1	even	1	trivial
56.3.k.c.51.4	yes	12	7.2	even	3	inner
56.3.k.c.51.5	yes	12	56.51	odd	6	inner
224.3.o.c.79.1		12	56.37	even	6
224.3.o.c.79.2		12	28.23	odd	6
224.3.o.c.207.1		12	4.3	odd	2
224.3.o.c.207.2		12	8.5	even	2
392.3.g.k.99.1		6	56.11	odd	6
392.3.g.k.99.2		6	7.4	even	3
392.3.g.l.99.1		6	56.3	even	6
392.3.g.l.99.2		6	7.3	odd	6
392.3.k.k.67.4		12	56.27	even	2
392.3.k.k.67.5		12	7.6	odd	2
392.3.k.k.275.4		12	7.5	odd	6
392.3.k.k.275.5		12	56.19	even	6
1568.3.g.i.687.1		6	56.45	odd	6
1568.3.g.i.687.2		6	28.3	even	6
1568.3.g.k.687.5		6	28.11	odd	6
1568.3.g.k.687.6		6	56.53	even	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.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.71059 + 1.03628i) q^{2} +(2.25274 - 3.90186i) q^{3} +(1.85225 + 3.54530i) q^{4} +(-6.07099 + 3.50509i) q^{5} +(7.89694 - 4.34002i) q^{6} +(2.51181 - 6.53382i) q^{7} +(-0.505481 + 7.98401i) q^{8} +(-5.64968 - 9.78553i) q^{9} +(-14.0172 - 0.295467i) q^{10} +(-7.90242 + 13.6874i) q^{11} +(18.0059 + 0.759426i) q^{12} -2.90039i q^{13} +(11.0675 - 8.57376i) q^{14} +31.5842i q^{15} +(-9.13834 + 13.1336i) q^{16} +(1.65516 - 2.86682i) q^{17} +(0.476249 - 22.5937i) q^{18} +(-8.10854 - 14.0444i) q^{19} +(-23.6716 - 15.0312i) q^{20} +(-19.8356 - 24.5197i) q^{21} +(-27.7018 + 15.2244i) q^{22} +(16.4804 - 9.51498i) q^{23} +(30.0138 + 19.9582i) q^{24} +(12.0713 - 20.9081i) q^{25} +(3.00561 - 4.96138i) q^{26} -10.3597 q^{27} +(27.8169 - 3.19714i) q^{28} -21.1392i q^{29} +(-32.7301 + 54.0277i) q^{30} +(23.6995 + 13.6829i) q^{31} +(-29.2420 + 12.9963i) q^{32} +(35.6042 + 61.6683i) q^{33} +(5.80213 - 3.18875i) q^{34} +(7.65245 + 48.4709i) q^{35} +(24.2280 - 38.1551i) q^{36} +(-15.2932 + 8.82951i) q^{37} +(0.683523 - 32.4270i) q^{38} +(-11.3169 - 6.53382i) q^{39} +(-24.9159 - 50.2427i) q^{40} +1.13482 q^{41} +(-8.52133 - 62.4985i) q^{42} +50.2084 q^{43} +(-63.1632 - 2.66400i) q^{44} +(68.5983 + 39.6053i) q^{45} +(38.0515 + 0.802081i) q^{46} +(-0.657646 + 0.379692i) q^{47} +(30.6591 + 65.2431i) q^{48} +(-36.3816 - 32.8234i) q^{49} +(42.3157 - 23.2560i) q^{50} +(-7.45728 - 12.9164i) q^{51} +(10.2828 - 5.37224i) q^{52} +(38.9677 + 22.4980i) q^{53} +(-17.7212 - 10.7355i) q^{54} -110.795i q^{55} +(50.8964 + 23.3570i) q^{56} -73.0658 q^{57} +(21.9061 - 36.1605i) q^{58} +(-1.19239 + 2.06529i) q^{59} +(-111.976 + 58.5019i) q^{60} +(-86.1653 + 49.7476i) q^{61} +(26.3608 + 47.9651i) q^{62} +(-78.1278 + 12.3346i) q^{63} +(-63.4890 - 8.07153i) q^{64} +(10.1661 + 17.6082i) q^{65} +(-3.00132 + 142.385i) q^{66} +(33.2440 - 57.5804i) q^{67} +(13.2295 + 0.557974i) q^{68} -85.7391i q^{69} +(-37.1392 + 90.8440i) q^{70} +44.4376i q^{71} +(80.9836 - 40.1607i) q^{72} +(-0.859703 + 1.48905i) q^{73} +(-35.3102 - 0.744298i) q^{74} +(-54.3870 - 94.2011i) q^{75} +(34.7726 - 54.7610i) q^{76} +(69.5816 + 86.0131i) q^{77} +(-12.5878 - 22.9042i) q^{78} +(-62.9171 + 36.3252i) q^{79} +(9.44446 - 111.765i) q^{80} +(27.5094 - 47.6476i) q^{81} +(1.94121 + 1.17599i) q^{82} -102.081 q^{83} +(50.1894 - 115.740i) q^{84} +23.2059i q^{85} +(85.8861 + 52.0299i) q^{86} +(-82.4821 - 47.6211i) q^{87} +(-105.286 - 70.0117i) q^{88} +(30.6865 + 53.1505i) q^{89} +(76.3016 + 138.835i) q^{90} +(-18.9506 - 7.28522i) q^{91} +(64.2594 + 40.8040i) q^{92} +(106.778 - 61.6480i) q^{93} +(-1.51843 - 0.0320068i) q^{94} +(98.4538 + 56.8423i) q^{95} +(-15.1649 + 143.376i) q^{96} -102.826 q^{97} +(-28.2199 - 93.8490i) q^{98} +178.584 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{3} - 4 q^{4} + 56 q^{6} + 36 q^{8} - 8 q^{9} - 30 q^{10} - 14 q^{11} - 14 q^{12} - 32 q^{14} - 40 q^{16} - 82 q^{17} + 38 q^{18} - 94 q^{19} - 56 q^{20} - 132 q^{22} - 38 q^{24} + 116 q^{25}+ \cdots + 872 q^{99}+O(q^{100}) \) 12 * q + 6 * q^3 - 4 * q^4 + 56 * q^6 + 36 * q^8 - 8 * q^9 - 30 * q^10 - 14 * q^11 - 14 * q^12 - 32 * q^14 - 40 * q^16 - 82 * q^17 + 38 * q^18 - 94 * q^19 - 56 * q^20 - 132 * q^22 - 38 * q^24 + 116 * q^25 + 22 * q^26 - 60 * q^27 + 50 * q^28 + 58 * q^30 - 60 * q^32 + 146 * q^33 + 188 * q^34 + 270 * q^35 + 200 * q^36 + 46 * q^38 - 142 * q^40 + 120 * q^41 - 38 * q^42 + 40 * q^43 - 86 * q^44 + 84 * q^46 + 184 * q^48 - 204 * q^49 - 256 * q^50 - 106 * q^51 + 20 * q^52 + 82 * q^54 + 440 * q^56 - 372 * q^57 - 130 * q^58 + 62 * q^59 - 290 * q^60 - 68 * q^62 - 328 * q^64 - 64 * q^65 - 208 * q^66 - 178 * q^67 + 4 * q^68 - 256 * q^70 + 52 * q^72 + 54 * q^73 + 120 * q^74 + 140 * q^75 - 172 * q^76 + 4 * q^78 - 12 * q^80 + 206 * q^81 + 54 * q^82 - 392 * q^83 - 176 * q^84 + 208 * q^86 + 90 * q^88 - 26 * q^89 + 156 * q^90 - 88 * q^91 + 388 * q^92 + 262 * q^94 + 64 * q^96 - 184 * q^97 + 498 * q^98 + 872 * q^99

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