LMFDB - Embedded newform 370.2.m.d.159.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("370.159");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.m (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 37x^{14} + 559x^{12} + 4431x^{10} + 19684x^{8} + 48248x^{6} + 58656x^{4} + 25392x^{2} + 256 $ x^16 + 37x^14 + 559x^12 + 4431x^10 + 19684x^8 + 48248x^6 + 58656x^4 + 25392*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			159.7
Root			$-2.06794i$ of defining polynomial
Character	$\chi$	$=$	370.159
Dual form			370.2.m.d.249.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(1.79089 + 1.03397i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.99857 + 1.00285i) q^{5} +2.06794i q^{6} +(1.25580 + 0.725037i) q^{7} -1.00000 q^{8} +(0.638185 + 1.10537i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(1.79089 + 1.03397i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.99857 + 1.00285i) q^{5} +2.06794i q^{6} +(1.25580 + 0.725037i) q^{7} -1.00000 q^{8} +(0.638185 + 1.10537i) q^{9} +(0.130790 + 2.23224i) q^{10} -5.11315 q^{11} +(-1.79089 + 1.03397i) q^{12} +(2.79761 - 4.84561i) q^{13} +1.45007i q^{14} +(2.54230 + 3.86246i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.19476 - 3.80144i) q^{17} +(-0.638185 + 1.10537i) q^{18} +(-0.736136 - 0.425009i) q^{19} +(-1.86778 + 1.22939i) q^{20} +(1.49933 + 2.59692i) q^{21} +(-2.55658 - 4.42812i) q^{22} -1.02299 q^{23} +(-1.79089 - 1.03397i) q^{24} +(2.98858 + 4.00854i) q^{25} +5.59523 q^{26} -3.56436i q^{27} +(-1.25580 + 0.725037i) q^{28} -3.13550i q^{29} +(-2.07384 + 4.13292i) q^{30} +6.98211i q^{31} +(0.500000 - 0.866025i) q^{32} +(-9.15708 - 5.28684i) q^{33} +(2.19476 - 3.80144i) q^{34} +(1.78270 + 2.70842i) q^{35} -1.27637 q^{36} +(0.667738 + 6.04600i) q^{37} -0.850017i q^{38} +(10.0204 - 5.78529i) q^{39} +(-1.99857 - 1.00285i) q^{40} +(-5.10397 + 8.84034i) q^{41} +(-1.49933 + 2.59692i) q^{42} -3.37607 q^{43} +(2.55658 - 4.42812i) q^{44} +(0.166937 + 2.84916i) q^{45} +(-0.511494 - 0.885933i) q^{46} -3.87763i q^{47} -2.06794i q^{48} +(-2.44864 - 4.24117i) q^{49} +(-1.97721 + 4.59245i) q^{50} -9.07727i q^{51} +(2.79761 + 4.84561i) q^{52} +(9.19294 - 5.30755i) q^{53} +(3.08683 - 1.78218i) q^{54} +(-10.2190 - 5.12774i) q^{55} +(-1.25580 - 0.725037i) q^{56} +(-0.878892 - 1.52228i) q^{57} +(2.71542 - 1.56775i) q^{58} +(1.97628 - 1.14100i) q^{59} +(-4.61613 + 0.270466i) q^{60} +(-0.743664 - 0.429355i) q^{61} +(-6.04669 + 3.49106i) q^{62} +1.85083i q^{63} +1.00000 q^{64} +(10.4507 - 6.87870i) q^{65} -10.5737i q^{66} +(9.48697 + 5.47730i) q^{67} +4.38952 q^{68} +(-1.83205 - 1.05774i) q^{69} +(-1.45421 + 2.89808i) q^{70} +(-4.71899 + 8.17352i) q^{71} +(-0.638185 - 1.10537i) q^{72} +10.2364i q^{73} +(-4.90212 + 3.60128i) q^{74} +(1.20749 + 10.2689i) q^{75} +(0.736136 - 0.425009i) q^{76} +(-6.42110 - 3.70723i) q^{77} +(10.0204 + 5.78529i) q^{78} +(-5.04391 - 2.91210i) q^{79} +(-0.130790 - 2.23224i) q^{80} +(5.59999 - 9.69948i) q^{81} -10.2079 q^{82} +(-0.0647311 + 0.0373725i) q^{83} -2.99866 q^{84} +(-0.574107 - 9.79847i) q^{85} +(-1.68804 - 2.92376i) q^{86} +(3.24201 - 5.61533i) q^{87} +5.11315 q^{88} +(12.1149 - 6.99456i) q^{89} +(-2.38398 + 1.56915i) q^{90} +(7.02649 - 4.05675i) q^{91} +(0.511494 - 0.885933i) q^{92} +(-7.21929 + 12.5042i) q^{93} +(3.35813 - 1.93882i) q^{94} +(-1.04500 - 1.58765i) q^{95} +(1.79089 - 1.03397i) q^{96} +2.26494 q^{97} +(2.44864 - 4.24117i) q^{98} +(-3.26314 - 5.65192i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{2} - 3 q^{3} - 8 q^{4} - 12 q^{7} - 16 q^{8} + 13 q^{9}+O(q^{10}) $ 16 * q + 8 * q^2 - 3 * q^3 - 8 * q^4 - 12 * q^7 - 16 * q^8 + 13 * q^9	$ 16 q + 8 q^{2} - 3 q^{3} - 8 q^{4} - 12 q^{7} - 16 q^{8} + 13 q^{9} - 6 q^{10} - 6 q^{11} + 3 q^{12} - 6 q^{13} + 9 q^{15} - 8 q^{16} - 13 q^{18} - 3 q^{19} - 6 q^{20} - 6 q^{21} - 3 q^{22} - 22 q^{23} + 3 q^{24} - 6 q^{25} - 12 q^{26} + 12 q^{28} - 9 q^{30} + 8 q^{32} + 6 q^{33} + 18 q^{35} - 26 q^{36} + 16 q^{37} + 15 q^{39} + 7 q^{41} + 6 q^{42} - 22 q^{43} + 3 q^{44} + 4 q^{45} - 11 q^{46} + 4 q^{49} + 6 q^{50} - 6 q^{52} + 3 q^{53} + 9 q^{54} - 35 q^{55} + 12 q^{56} + 18 q^{57} + 36 q^{58} + 15 q^{59} - 18 q^{60} + 12 q^{61} - 33 q^{62} + 16 q^{64} + 46 q^{65} + 24 q^{67} + 42 q^{69} + 12 q^{70} - 4 q^{71} - 13 q^{72} + 5 q^{74} - 10 q^{75} + 3 q^{76} - 24 q^{77} + 15 q^{78} + 6 q^{80} + 10 q^{81} + 14 q^{82} + 6 q^{83} + 12 q^{84} - 26 q^{85} - 11 q^{86} + 50 q^{87} + 6 q^{88} + 9 q^{89} - q^{90} - 24 q^{91} + 11 q^{92} - 25 q^{93} - 27 q^{94} - 53 q^{95} - 3 q^{96} + 68 q^{97} - 4 q^{98} + 37 q^{99}+O(q^{100}) $ 16 * q + 8 * q^2 - 3 * q^3 - 8 * q^4 - 12 * q^7 - 16 * q^8 + 13 * q^9 - 6 * q^10 - 6 * q^11 + 3 * q^12 - 6 * q^13 + 9 * q^15 - 8 * q^16 - 13 * q^18 - 3 * q^19 - 6 * q^20 - 6 * q^21 - 3 * q^22 - 22 * q^23 + 3 * q^24 - 6 * q^25 - 12 * q^26 + 12 * q^28 - 9 * q^30 + 8 * q^32 + 6 * q^33 + 18 * q^35 - 26 * q^36 + 16 * q^37 + 15 * q^39 + 7 * q^41 + 6 * q^42 - 22 * q^43 + 3 * q^44 + 4 * q^45 - 11 * q^46 + 4 * q^49 + 6 * q^50 - 6 * q^52 + 3 * q^53 + 9 * q^54 - 35 * q^55 + 12 * q^56 + 18 * q^57 + 36 * q^58 + 15 * q^59 - 18 * q^60 + 12 * q^61 - 33 * q^62 + 16 * q^64 + 46 * q^65 + 24 * q^67 + 42 * q^69 + 12 * q^70 - 4 * q^71 - 13 * q^72 + 5 * q^74 - 10 * q^75 + 3 * q^76 - 24 * q^77 + 15 * q^78 + 6 * q^80 + 10 * q^81 + 14 * q^82 + 6 * q^83 + 12 * q^84 - 26 * q^85 - 11 * q^86 + 50 * q^87 + 6 * q^88 + 9 * q^89 - q^90 - 24 * q^91 + 11 * q^92 - 25 * q^93 - 27 * q^94 - 53 * q^95 - 3 * q^96 + 68 * q^97 - 4 * q^98 + 37 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	1.79089	+	1.03397i	1.03397	+	0.596962i	0.918119	−	0.396304i	$-0.129707\pi$
$3$	1.79089	+	1.03397i	1.03397	+	0.596962i	0.115850	+	0.993267i	$0.463041\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	1.99857	+	1.00285i	0.893788	+	0.448489i
$5$	1.99857	+	1.00285i	0.893788	+	0.448489i
$6$			2.06794i			0.844232i
$7$	1.25580	+	0.725037i	0.474648	+	0.274038i	0.718183	−	0.695854i	$-0.244974\pi$
$7$	1.25580	+	0.725037i	0.474648	+	0.274038i	−0.243535	+	0.969892i	$0.578307\pi$
$8$	−1.00000			−0.353553
$9$	0.638185	+	1.10537i	0.212728	+	0.368456i
$10$	0.130790	+	2.23224i	0.0413595	+	0.705896i
$11$	−5.11315			−1.54167			−0.770837	−	0.637032i	$-0.780162\pi$
$11$	−5.11315			−1.54167			−0.770837	+	0.637032i	$0.780162\pi$
$12$	−1.79089	+	1.03397i	−0.516985	+	0.298481i
$13$	2.79761	−	4.84561i	0.775918	−	1.34393i	−0.158358	−	0.987382i	$-0.550620\pi$
$13$	2.79761	−	4.84561i	0.775918	−	1.34393i	0.934277	−	0.356549i	$-0.116047\pi$
$14$			1.45007i			0.387549i
$15$	2.54230	+	3.86246i	0.656418	+	0.997282i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.19476	−	3.80144i	−0.532308	−	0.921984i	−0.999288	−	0.0377168i	$-0.987992\pi$
$17$	−2.19476	−	3.80144i	−0.532308	−	0.921984i	0.466981	−	0.884268i	$-0.345342\pi$
$18$	−0.638185	+	1.10537i	−0.150422	+	0.260538i
$19$	−0.736136	−	0.425009i	−0.168881	−	0.0975036i	0.413177	−	0.910651i	$-0.364419\pi$
$19$	−0.736136	−	0.425009i	−0.168881	−	0.0975036i	−0.582058	+	0.813147i	$0.697752\pi$
$20$	−1.86778	+	1.22939i	−0.417649	+	0.274899i
$21$	1.49933	+	2.59692i	0.327181	+	0.566694i
$22$	−2.55658	−	4.42812i	−0.545064	−	0.944079i
$23$	−1.02299			−0.213308			−0.106654	−	0.994296i	$-0.534014\pi$
$23$	−1.02299			−0.213308			−0.106654	+	0.994296i	$0.534014\pi$
$24$	−1.79089	−	1.03397i	−0.365563	−	0.211058i
$25$	2.98858	+	4.00854i	0.597715	+	0.801709i
$26$	5.59523			1.09731
$27$		−	3.56436i		−	0.685962i
$28$	−1.25580	+	0.725037i	−0.237324	+	0.137019i
$29$		−	3.13550i		−	0.582248i	−0.956685	−	0.291124i	$-0.905971\pi$
$29$		−	3.13550i		−	0.582248i	0.956685	−	0.291124i	$-0.0940292\pi$
$30$	−2.07384	+	4.13292i	−0.378629	+	0.754565i
$31$			6.98211i			1.25402i	0.779009	+	0.627012i	$0.215722\pi$
$31$			6.98211i			1.25402i	−0.779009	+	0.627012i	$0.784278\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−9.15708	−	5.28684i	−1.59404	−	0.920321i
$34$	2.19476	−	3.80144i	0.376399	−	0.651941i
$35$	1.78270	+	2.70842i	0.301332	+	0.457807i
$36$	−1.27637			−0.212728
$37$	0.667738	+	6.04600i	0.109775	+	0.993956i
$37$	0.667738	+	6.04600i	0.109775	+	0.993956i
$38$		−	0.850017i		−	0.137891i
$39$	10.0204	−	5.78529i	1.60455	−	0.926388i
$40$	−1.99857	−	1.00285i	−0.316002	−	0.158565i
$41$	−5.10397	+	8.84034i	−0.797107	+	1.38063i	0.124386	+	0.992234i	$0.460304\pi$
$41$	−5.10397	+	8.84034i	−0.797107	+	1.38063i	−0.921493	+	0.388395i	$0.873030\pi$
$42$	−1.49933	+	2.59692i	−0.231352	+	0.400713i
$43$	−3.37607			−0.514846			−0.257423	−	0.966299i	$-0.582873\pi$
$43$	−3.37607			−0.514846			−0.257423	+	0.966299i	$0.582873\pi$
$44$	2.55658	−	4.42812i	0.385418	−	0.667564i
$45$	0.166937	+	2.84916i	0.0248855	+	0.424728i
$46$	−0.511494	−	0.885933i	−0.0754156	−	0.130624i
$47$		−	3.87763i		−	0.565611i	−0.959177	−	0.282806i	$-0.908735\pi$
$47$		−	3.87763i		−	0.565611i	0.959177	−	0.282806i	$-0.0912651\pi$
$48$		−	2.06794i		−	0.298481i
$49$	−2.44864	−	4.24117i	−0.349806	−	0.605882i
$50$	−1.97721	+	4.59245i	−0.279620	+	0.649471i
$51$		−	9.07727i		−	1.27107i
$52$	2.79761	+	4.84561i	0.387959	+	0.671965i
$53$	9.19294	−	5.30755i	1.26275	−	0.729048i	0.289143	−	0.957286i	$-0.406630\pi$
$53$	9.19294	−	5.30755i	1.26275	−	0.729048i	0.973605	+	0.228238i	$0.0732965\pi$
$54$	3.08683	−	1.78218i	0.420064	−	0.242524i
$55$	−10.2190	−	5.12774i	−1.37793	−	0.691424i
$56$	−1.25580	−	0.725037i	−0.167813	−	0.0968871i
$57$	−0.878892	−	1.52228i	−0.116412	−	0.201632i
$58$	2.71542	−	1.56775i	0.356552	−	0.205856i
$59$	1.97628	−	1.14100i	0.257289	−	0.148546i	−0.365808	−	0.930690i	$-0.619207\pi$
$59$	1.97628	−	1.14100i	0.257289	−	0.148546i	0.623097	+	0.782144i	$0.285874\pi$
$60$	−4.61613	+	0.270466i	−0.595940	+	0.0349170i
$61$	−0.743664	−	0.429355i	−0.0952165	−	0.0549733i	0.451636	−	0.892202i	$-0.350841\pi$
$61$	−0.743664	−	0.429355i	−0.0952165	−	0.0549733i	−0.546852	+	0.837229i	$0.684174\pi$
$62$	−6.04669	+	3.49106i	−0.767930	+	0.443365i
$63$			1.85083i			0.233183i
$64$	1.00000			0.125000
$65$	10.4507	−	6.87870i	1.29624	−	0.853198i
$66$		−	10.5737i		−	1.30153i
$67$	9.48697	+	5.47730i	1.15902	+	0.669159i	0.951068	−	0.308981i	$-0.0999879\pi$
$67$	9.48697	+	5.47730i	1.15902	+	0.669159i	0.207949	+	0.978140i	$0.433321\pi$
$68$	4.38952			0.532308
$69$	−1.83205	−	1.05774i	−0.220553	−	0.127337i
$70$	−1.45421	+	2.89808i	−0.173811	+	0.346386i
$71$	−4.71899	+	8.17352i	−0.560041	+	0.970019i	0.437452	+	0.899242i	$0.355881\pi$
$71$	−4.71899	+	8.17352i	−0.560041	+	0.970019i	−0.997492	+	0.0707769i	$0.977452\pi$
$72$	−0.638185	−	1.10537i	−0.0752108	−	0.130269i
$73$			10.2364i			1.19808i	0.800721	+	0.599038i	$0.204450\pi$
$73$			10.2364i			1.19808i	−0.800721	+	0.599038i	$0.795550\pi$
$74$	−4.90212	+	3.60128i	−0.569860	+	0.418640i
$75$	1.20749	+	10.2689i	0.139429	+	1.18576i
$76$	0.736136	−	0.425009i	0.0844406	−	0.0487518i
$77$	−6.42110	−	3.70723i	−0.731753	−	0.422478i
$78$	10.0204	+	5.78529i	1.13459	+	0.655055i
$79$	−5.04391	−	2.91210i	−0.567484	−	0.327637i	0.188660	−	0.982042i	$-0.439586\pi$
$79$	−5.04391	−	2.91210i	−0.567484	−	0.327637i	−0.756144	+	0.654406i	$0.772919\pi$
$80$	−0.130790	−	2.23224i	−0.0146228	−	0.249572i
$81$	5.59999	−	9.69948i	0.622222	−	1.07772i
$82$	−10.2079			−1.12728
$83$	−0.0647311	+	0.0373725i	−0.00710516	+	0.00410217i	−0.503548	−	0.863967i	$-0.667972\pi$
$83$	−0.0647311	+	0.0373725i	−0.00710516	+	0.00410217i	0.496443	+	0.868069i	$0.334639\pi$
$84$	−2.99866			−0.327181
$85$	−0.574107	−	9.79847i	−0.0622706	−	1.06279i
$86$	−1.68804	−	2.92376i	−0.182026	−	0.315277i
$87$	3.24201	−	5.61533i	0.347580	−	0.602026i
$88$	5.11315			0.545064
$89$	12.1149	−	6.99456i	1.28418	−	0.741422i	0.306571	−	0.951848i	$-0.400818\pi$
$89$	12.1149	−	6.99456i	1.28418	−	0.741422i	0.977610	+	0.210426i	$0.0674850\pi$
$90$	−2.38398	+	1.56915i	−0.251293	+	0.165403i
$91$	7.02649	−	4.05675i	0.736577	−	0.425263i
$92$	0.511494	−	0.885933i	0.0533269	−	0.0923649i
$93$	−7.21929	+	12.5042i	−0.748606	+	1.29662i
$94$	3.35813	−	1.93882i	0.346365	−	0.199974i
$95$	−1.04500	−	1.58765i	−0.107215	−	0.162889i
$96$	1.79089	−	1.03397i	0.182782	−	0.105529i
$97$	2.26494			0.229970			0.114985	−	0.993367i	$-0.463318\pi$
$97$	2.26494			0.229970			0.114985	+	0.993367i	$0.463318\pi$
$98$	2.44864	−	4.24117i	0.247350	−	0.428423i
$99$	−3.26314	−	5.65192i	−0.327958	−	0.568039i
$100$	−4.96579	+	0.583910i	−0.496579	+	0.0583910i
$101$	−18.4477			−1.83561			−0.917805	−	0.397031i	$-0.870041\pi$
$101$	−18.4477			−1.83561			−0.917805	+	0.397031i	$0.870041\pi$
$102$	7.86114	−	4.53863i	0.778369	−	0.449392i
$103$	2.26780			0.223453			0.111727	−	0.993739i	$-0.464362\pi$
$103$	2.26780			0.223453			0.111727	+	0.993739i	$0.464362\pi$
$104$	−2.79761	+	4.84561i	−0.274329	+	0.475151i
$105$	0.392196	+	6.69374i	0.0382744	+	0.653242i
$106$	9.19294	+	5.30755i	0.892898	+	0.515515i
$107$	−3.36674	−	1.94379i	−0.325475	−	0.187913i	0.328355	−	0.944554i	$-0.393506\pi$
$107$	−3.36674	−	1.94379i	−0.325475	−	0.187913i	−0.653830	+	0.756641i	$0.726839\pi$
$108$	3.08683	+	1.78218i	0.297030	+	0.171490i
$109$	14.2463	−	8.22510i	1.36455	−	0.787822i	0.374322	−	0.927299i	$-0.377875\pi$
$109$	14.2463	−	8.22510i	1.36455	−	0.787822i	0.990225	+	0.139477i	$0.0445421\pi$
$110$	−0.668751	−	11.4138i	−0.0637629	−	1.08826i
$111$	−5.05554	+	11.5181i	−0.479850	+	1.09325i
$112$		−	1.45007i		−	0.137019i
$113$	−7.11315	−	12.3203i	−0.669149	−	1.15900i	−0.978142	−	0.207936i	$-0.933325\pi$
$113$	−7.11315	−	12.3203i	−0.669149	−	1.15900i	0.308993	−	0.951064i	$-0.400008\pi$
$114$	0.878892	−	1.52228i	0.0823157	−	0.142575i
$115$	−2.04451	−	1.02590i	−0.190652	−	0.0956661i
$116$	2.71542	+	1.56775i	0.252121	+	0.145562i
$117$	7.14158			0.660239
$118$	1.97628	+	1.14100i	0.181931	+	0.105038i
$119$		−	6.36513i		−	0.583491i
$120$	−2.54230	−	3.86246i	−0.232079	−	0.352592i
$121$	15.1443			1.37676
$122$		−	0.858710i		−	0.0777439i
$123$	−18.2813	+	10.5547i	−1.64837	+	0.951685i
$124$	−6.04669	−	3.49106i	−0.543009	−	0.313506i
$125$	1.95290	+	11.0085i	0.174673	+	0.984626i
$126$	−1.60287	+	0.925415i	−0.142795	+	0.0824425i
$127$	−3.05413	+	1.76330i	−0.271010	+	0.156468i	−0.629346	−	0.777125i	$-0.716677\pi$
$127$	−3.05413	+	1.76330i	−0.271010	+	0.156468i	0.358337	+	0.933592i	$0.383344\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−6.04616	−	3.49075i	−0.532335	−	0.307344i
$130$	11.1825	+	5.61119i	0.980767	+	0.492134i
$131$	−5.04314	+	2.91166i	−0.440621	+	0.254393i	−0.703861	−	0.710338i	$-0.748542\pi$
$131$	−5.04314	+	2.91166i	−0.440621	+	0.254393i	0.263240	+	0.964730i	$0.415209\pi$
$132$	9.15708	−	5.28684i	0.797022	−	0.460161i
$133$	−0.616294	−	1.06745i	−0.0534395	−	0.0925598i
$134$			10.9546i			0.946334i
$135$	3.57453	−	7.12363i	0.307646	−	0.613105i
$136$	2.19476	+	3.80144i	0.188199	+	0.325971i
$137$			0.860765i			0.0735401i	0.999324	+	0.0367700i	$0.0117069\pi$
$137$			0.860765i			0.0735401i	−0.999324	+	0.0367700i	$0.988293\pi$
$138$		−	2.11547i		−	0.180081i
$139$	0.0744527	+	0.128956i	0.00631500	+	0.0109379i	0.869166	−	0.494521i	$-0.164657\pi$
$139$	0.0744527	+	0.128956i	0.00631500	+	0.0109379i	−0.862851	+	0.505459i	$0.831323\pi$
$140$	−3.23691	+	0.189656i	−0.273569	+	0.0160288i
$141$	4.00935	−	6.94440i	0.337649	−	0.584824i
$142$	−9.43797			−0.792017
$143$	−14.3046	+	24.7763i	−1.19621	+	2.07190i
$144$	0.638185	−	1.10537i	0.0531821	−	0.0921140i
$145$	3.14444	−	6.26652i	0.261132	−	0.520406i
$146$	−8.86495	+	5.11818i	−0.733669	+	0.423584i
$147$		−	10.1273i		−	0.835284i
$148$	−5.56986	−	2.44472i	−0.457840	−	0.200955i
$149$	−17.9677			−1.47197			−0.735985	−	0.676998i	$-0.763280\pi$
$149$	−17.9677			−1.47197			−0.735985	+	0.676998i	$0.763280\pi$
$150$	−8.28942	+	6.18019i	−0.676828	+	0.504610i
$151$	8.19838	−	14.2000i	0.667175	−	1.15558i	−0.311516	−	0.950241i	$-0.600837\pi$
$151$	8.19838	−	14.2000i	0.667175	−	1.15558i	0.978691	−	0.205340i	$-0.0658300\pi$
$152$	0.736136	+	0.425009i	0.0597085	+	0.0344727i
$153$	2.80133	−	4.85204i	0.226474	−	0.392264i
$154$		−	7.41445i		−	0.597474i
$155$	−7.00203	+	13.9543i	−0.562416	+	1.12083i
$156$			11.5706i			0.926388i
$157$	−4.94939	+	2.85753i	−0.395004	+	0.228056i	−0.684326	−	0.729176i	$-0.739904\pi$
$157$	−4.94939	+	2.85753i	−0.395004	+	0.228056i	0.289322	+	0.957232i	$0.406570\pi$
$158$		−	5.82420i		−	0.463349i
$159$	21.9514			1.74086
$160$	1.86778	−	1.22939i	0.147661	−	0.0971916i
$161$	−1.28467	−	0.741704i	−0.101246	−	0.0584544i
$162$	11.2000			0.879954
$163$	8.26847	+	14.3214i	0.647637	+	1.12174i	0.983686	+	0.179895i	$0.0575759\pi$
$163$	8.26847	+	14.3214i	0.647637	+	1.12174i	−0.336049	+	0.941845i	$0.609091\pi$
$164$	−5.10397	−	8.84034i	−0.398553	−	0.690315i
$165$	−12.9992	−	19.7493i	−1.01198	−	1.53748i
$166$	−0.0647311	−	0.0373725i	−0.00502411	−	0.00290067i
$167$	−5.85478	+	10.1408i	−0.453057	+	0.784717i	−0.998574	−	0.0533822i	$-0.983000\pi$
$167$	−5.85478	+	10.1408i	−0.453057	+	0.784717i	0.545517	+	0.838099i	$0.316333\pi$
$168$	−1.49933	−	2.59692i	−0.115676	−	0.200357i
$169$	−9.15329	−	15.8540i	−0.704099	−	1.21954i
$170$	8.19867	−	5.39643i	0.628809	−	0.413887i
$171$		−	1.08494i		−	0.0829671i
$172$	1.68804	−	2.92376i	0.128711	−	0.222935i
$173$	6.50565	−	3.75604i	0.494615	−	0.285566i	−0.231872	−	0.972746i	$-0.574485\pi$
$173$	6.50565	−	3.75604i	0.494615	−	0.285566i	0.726487	+	0.687180i	$0.241152\pi$
$174$	6.48402			0.491552
$175$	0.846713	+	7.20076i	0.0640055	+	0.544326i
$176$	2.55658	+	4.42812i	0.192709	+	0.333782i
$177$	4.71905			0.354706
$178$	12.1149	+	6.99456i	0.908053	+	0.524265i
$179$			26.0641i			1.94812i	0.226288	+	0.974060i	$0.427341\pi$
$179$			26.0641i			1.94812i	−0.226288	+	0.974060i	$0.572659\pi$
$180$	−2.55092	−	1.28001i	−0.190134	−	0.0954063i
$181$	−7.89544	+	13.6753i	−0.586863	+	1.01648i	0.407777	+	0.913081i	$0.366304\pi$
$181$	−7.89544	+	13.6753i	−0.586863	+	1.01648i	−0.994640	+	0.103395i	$0.967029\pi$
$182$	7.02649	+	4.05675i	0.520838	+	0.300706i
$183$	−0.887879	−	1.53785i	−0.0656339	−	0.113681i
$184$	1.02299			0.0754156
$185$	−4.72872	+	12.7530i	−0.347663	+	0.937620i
$186$	−14.4386			−1.05869
$187$	11.2222	+	19.4373i	0.820645	+	1.42140i
$188$	3.35813	+	1.93882i	0.244917	+	0.141403i
$189$	2.58429	−	4.47613i	0.187980	−	0.325590i
$190$	0.852441	−	1.69882i	0.0618426	−	0.123245i
$191$			10.0828i			0.729565i	0.931093	+	0.364783i	$0.118857\pi$
$191$			10.0828i			0.729565i	−0.931093	+	0.364783i	$0.881143\pi$
$192$	1.79089	+	1.03397i	0.129246	+	0.0746203i
$193$	−9.17733			−0.660599			−0.330299	−	0.943876i	$-0.607150\pi$
$193$	−9.17733			−0.660599			−0.330299	+	0.943876i	$0.607150\pi$
$194$	1.13247	+	1.96150i	0.0813067	+	0.140827i
$195$	25.8283	−	1.51332i	1.84960	−	0.108371i
$196$	4.89729			0.349806
$197$	−2.84877	+	1.64474i	−0.202967	+	0.117183i	−0.598039	−	0.801467i	$-0.704053\pi$
$197$	−2.84877	+	1.64474i	−0.202967	+	0.117183i	0.395072	+	0.918650i	$0.370720\pi$
$198$	3.26314	−	5.65192i	0.231901	−	0.401664i
$199$			16.6004i			1.17677i	0.808581	+	0.588385i	$0.200236\pi$
$199$			16.6004i			1.17677i	−0.808581	+	0.588385i	$0.799764\pi$
$200$	−2.98858	−	4.00854i	−0.211324	−	0.283447i
$201$	11.3267	+	19.6185i	0.798926	+	1.38378i
$202$	−9.22383	−	15.9761i	−0.648986	−	1.12408i
$203$	2.27335	−	3.93756i	0.159558	−	0.276363i
$204$	7.86114	+	4.53863i	0.550390	+	0.317768i
$205$	−19.0662	+	12.5495i	−1.33164	+	0.876497i
$206$	1.13390	+	1.96398i	0.0790027	+	0.136837i
$207$	−0.652855	−	1.13078i	−0.0453766	−	0.0785945i
$208$	−5.59523			−0.387959
$209$	3.76398	+	2.17313i	0.260360	+	0.150319i
$210$	−5.60085	+	3.68652i	−0.386495	+	0.254394i
$211$	13.9304			0.959009			0.479504	−	0.877539i	$-0.340816\pi$
$211$	13.9304			0.959009			0.479504	+	0.877539i	$0.340816\pi$
$212$			10.6151i			0.729048i
$213$	−16.9023	+	9.75857i	−1.15813	+	0.668646i
$214$		−	3.88757i		−	0.265749i
$215$	−6.74732	−	3.38570i	−0.460163	−	0.230903i
$216$			3.56436i			0.242524i
$217$	−5.06229	+	8.76815i	−0.343651	+	0.595220i
$218$	14.2463	+	8.22510i	0.964881	+	0.557074i
$219$	−10.5841	+	18.3322i	−0.715206	+	1.23877i
$220$	9.55025	−	6.28605i	0.643878	−	0.423805i
$221$	−24.5604			−1.65211
$222$	−12.5028	+	1.38084i	−0.839130	+	0.0926760i
$223$		−	28.0381i		−	1.87757i	−0.344499	−	0.938787i	$-0.611951\pi$
$223$		−	28.0381i		−	1.87757i	0.344499	−	0.938787i	$-0.388049\pi$
$224$	1.25580	−	0.725037i	0.0839067	−	0.0484436i
$225$	−2.52365	+	5.86167i	−0.168244	+	0.390778i
$226$	7.11315	−	12.3203i	0.473160	−	0.819537i
$227$	−2.97783	+	5.15775i	−0.197645	+	0.342332i	−0.947764	−	0.318971i	$-0.896663\pi$
$227$	−2.97783	+	5.15775i	−0.197645	+	0.342332i	0.750119	+	0.661303i	$0.229996\pi$
$228$	1.75778			0.116412
$229$	−1.81631	+	3.14593i	−0.120025	+	0.207889i	−0.919777	−	0.392441i	$-0.871631\pi$
$229$	−1.81631	+	3.14593i	−0.120025	+	0.207889i	0.799752	+	0.600330i	$0.204964\pi$
$230$	−0.133797	−	2.28355i	−0.00882230	−	0.150573i
$231$	−7.66631	−	13.2784i	−0.504406	−	0.873658i
$232$			3.13550i			0.205856i
$233$		−	21.1978i		−	1.38872i	−0.719630	−	0.694358i	$-0.755689\pi$
$233$		−	21.1978i		−	1.38872i	0.719630	−	0.694358i	$-0.244311\pi$
$234$	3.57079	+	6.18479i	0.233430	+	0.404312i
$235$	3.88869	−	7.74973i	0.253670	−	0.505536i
$236$			2.28201i			0.148546i
$237$	−6.02205	−	10.4305i	−0.391174	−	0.677533i
$238$	5.51237	−	3.18257i	0.357314	−	0.206295i
$239$	−17.3902	+	10.0402i	−1.12488	+	0.649447i	−0.942641	−	0.333808i	$-0.891666\pi$
$239$	−17.3902	+	10.0402i	−1.12488	+	0.649447i	−0.182235	+	0.983255i	$0.558333\pi$
$240$	2.07384	−	4.13292i	0.133866	−	0.266779i
$241$	13.9154	+	8.03405i	0.896369	+	0.517519i	0.876020	−	0.482274i	$-0.160189\pi$
$241$	13.9154	+	8.03405i	0.896369	+	0.517519i	0.0203486	+	0.999793i	$0.493522\pi$
$242$	7.57217	+	13.1154i	0.486758	+	0.843089i
$243$	10.7974	−	6.23390i	0.692656	−	0.399905i
$244$	0.743664	−	0.429355i	0.0476082	−	0.0274866i
$245$	−0.640517	−	10.9319i	−0.0409211	−	0.698414i
$246$	−18.2813	−	10.5547i	−1.16557	−	0.672943i
$247$	−4.11885	+	2.37802i	−0.262076	+	0.151310i
$248$		−	6.98211i		−	0.443365i
$249$	−0.154568			−0.00979536
$250$	−8.55715	+	7.19549i	−0.541202	+	0.455083i
$251$		−	4.58944i		−	0.289683i	−0.989455	−	0.144842i	$-0.953733\pi$
$251$		−	4.58944i		−	0.289683i	0.989455	−	0.144842i	$-0.0462673\pi$
$252$	−1.60287	−	0.925415i	−0.100971	−	0.0582957i
$253$	5.23069			0.328851
$254$	−3.05413	−	1.76330i	−0.191633	−	0.110639i
$255$	9.10315	−	18.1416i	0.570062	−	1.13607i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	6.81731	+	11.8079i	0.425252	+	0.736558i	0.996444	−	0.0842585i	$-0.0268522\pi$
$257$	6.81731	+	11.8079i	0.425252	+	0.736558i	−0.571192	+	0.820817i	$0.693519\pi$
$258$		−	6.98151i		−	0.434650i
$259$	−3.54503	+	8.07671i	−0.220277	+	0.501862i
$260$	0.731801	+	12.4899i	0.0453844	+	0.774590i
$261$	3.46588	−	2.00103i	0.214533	−	0.123861i
$262$	−5.04314	−	2.91166i	−0.311566	−	0.179883i
$263$	3.57092	+	2.06167i	0.220193	+	0.127128i	0.606039	−	0.795435i	$-0.292757\pi$
$263$	3.57092	+	2.06167i	0.220193	+	0.127128i	−0.385847	+	0.922563i	$0.626091\pi$
$264$	9.15708	+	5.28684i	0.563579	+	0.325383i
$265$	23.6954	−	1.38835i	1.45560	−	0.0852857i
$266$	0.616294	−	1.06745i	0.0377874	−	0.0654497i
$267$	28.9286			1.77040
$268$	−9.48697	+	5.47730i	−0.579509	+	0.334579i
$269$	14.8218			0.903703			0.451851	−	0.892093i	$-0.350764\pi$
$269$	14.8218			0.903703			0.451851	+	0.892093i	$0.350764\pi$
$270$	7.95651	−	0.466184i	0.484218	−	0.0283710i
$271$	−5.63808	−	9.76543i	−0.342489	−	0.593208i	0.642406	−	0.766365i	$-0.277937\pi$
$271$	−5.63808	−	9.76543i	−0.342489	−	0.593208i	−0.984894	+	0.173157i	$0.944603\pi$
$272$	−2.19476	+	3.80144i	−0.133077	+	0.230496i
$273$	16.7782			1.01546
$274$	−0.745444	+	0.430382i	−0.0450339	+	0.0260003i
$275$	−15.2810	−	20.4963i	−0.921482	−	1.23597i
$276$	1.83205	−	1.05774i	0.110277	−	0.0636683i
$277$	12.0388	−	20.8518i	0.723340	−	1.25286i	−0.236314	−	0.971677i	$-0.575939\pi$
$277$	12.0388	−	20.8518i	0.723340	−	1.25286i	0.959654	−	0.281185i	$-0.0907273\pi$
$278$	−0.0744527	+	0.128956i	−0.00446538	+	0.00773426i
$279$	−7.71781	+	4.45588i	−0.462053	+	0.266767i
$280$	−1.78270	−	2.70842i	−0.106537	−	0.161859i
$281$	22.1556	−	12.7915i	1.32169	−	0.763079i	0.337693	−	0.941256i	$-0.390354\pi$
$281$	22.1556	−	12.7915i	1.32169	−	0.763079i	0.983998	+	0.178178i	$0.0570202\pi$
$282$	8.01871			0.477507
$283$	−15.7571	+	27.2921i	−0.936662	+	1.62235i	−0.165018	+	0.986291i	$0.552768\pi$
$283$	−15.7571	+	27.2921i	−0.936662	+	1.62235i	−0.771644	+	0.636055i	$0.780565\pi$
$284$	−4.71899	−	8.17352i	−0.280020	−	0.485009i
$285$	−0.229901	−	3.92379i	−0.0136182	−	0.232425i
$286$	−28.6093			−1.69170
$287$	−12.8191	+	7.40114i	−0.756690	+	0.436875i
$288$	1.27637			0.0752108
$289$	−1.13396	+	1.96407i	−0.0667035	+	0.115534i
$290$	6.99919	−	0.410093i	0.411006	−	0.0240815i
$291$	4.05626	+	2.34188i	0.237782	+	0.137283i
$292$	−8.86495	−	5.11818i	−0.518782	−	0.299519i
$293$	−19.0530	−	11.0002i	−1.11309	−	0.642641i	−0.173460	−	0.984841i	$-0.555495\pi$
$293$	−19.0530	−	11.0002i	−1.11309	−	0.642641i	−0.939627	+	0.342200i	$0.888828\pi$
$294$	8.77049	−	5.06364i	0.511505	−	0.295318i
$295$	5.09399	−	0.298464i	0.296583	−	0.0173773i
$296$	−0.667738	−	6.04600i	−0.0388115	−	0.351417i
$297$			18.2251i			1.05753i
$298$	−8.98384	−	15.5605i	−0.520420	−	0.901393i
$299$	−2.86192	+	4.95700i	−0.165509	+	0.286671i
$300$	−9.49691	−	4.08875i	−0.548304	−	0.236064i
$301$	−4.23967	−	2.44778i	−0.244371	−	0.141087i
$302$	16.3968			0.943528
$303$	−33.0377	−	19.0743i	−1.89796	−	1.09579i
$304$			0.850017i			0.0487518i
$305$	−1.05569	−	1.60388i	−0.0604485	−	0.0918380i
$306$	5.60266			0.320282
$307$		−	15.5754i		−	0.888933i	−0.895796	−	0.444466i	$-0.853393\pi$
$307$		−	15.5754i		−	0.888933i	0.895796	−	0.444466i	$-0.146607\pi$
$308$	6.42110	−	3.70723i	0.365876	−	0.211239i
$309$	4.06138	+	2.34484i	0.231044	+	0.133393i
$310$	−15.5858	+	0.913192i	−0.885211	+	0.0518658i
$311$	15.8523	−	9.15233i	0.898901	−	0.518981i	0.0220576	−	0.999757i	$-0.492978\pi$
$311$	15.8523	−	9.15233i	0.898901	−	0.518981i	0.876844	+	0.480776i	$0.159645\pi$
$312$	−10.0204	+	5.78529i	−0.567295	+	0.327528i
$313$	−2.70484	−	4.68491i	−0.152886	−	0.264807i	0.779401	−	0.626525i	$-0.215524\pi$
$313$	−2.70484	−	4.68491i	−0.152886	−	0.264807i	−0.932287	+	0.361718i	$0.882190\pi$
$314$	−4.94939	−	2.85753i	−0.279310	−	0.161260i
$315$	−1.85611	+	3.69902i	−0.104580	+	0.208416i
$316$	5.04391	−	2.91210i	0.283742	−	0.163818i
$317$	−20.7120	+	11.9581i	−1.16330	+	0.671632i	−0.952093	−	0.305809i	$-0.901073\pi$
$317$	−20.7120	+	11.9581i	−1.16330	+	0.671632i	−0.211208	+	0.977441i	$0.567740\pi$
$318$	10.9757	+	19.0104i	0.615486	+	1.06605i
$319$			16.0323i			0.897636i
$320$	1.99857	+	1.00285i	0.111724	+	0.0560611i
$321$	−4.01963	−	6.96221i	−0.224354	−	0.388593i
$322$		−	1.48341i		−	0.0826671i
$323$			3.73117i			0.207608i
$324$	5.59999	+	9.69948i	0.311111	+	0.538860i
$325$	27.7847	−	3.26711i	1.54122	−	0.181227i
$326$	−8.26847	+	14.3214i	−0.457948	+	0.793190i
$327$	34.0180			1.88120
$328$	5.10397	−	8.84034i	0.281820	−	0.488126i
$329$	2.81143	−	4.86954i	0.154999	−	0.268466i
$330$	10.6038	−	21.1323i	0.583723	−	1.16329i
$331$	−0.538586	+	0.310953i	−0.0296034	+	0.0170915i	−0.514729	−	0.857353i	$-0.672107\pi$
$331$	−0.538586	+	0.310953i	−0.0296034	+	0.0170915i	0.485125	+	0.874445i	$0.338774\pi$
$332$		−	0.0747450i		−	0.00410217i
$333$	−6.25692	+	4.59656i	−0.342877	+	0.251890i
$334$	−11.7096			−0.640719
$335$	13.4675	+	20.4608i	0.735806	+	1.11789i
$336$	1.49933	−	2.59692i	0.0817953	−	0.141674i
$337$	16.4751	+	9.51193i	0.897458	+	0.518148i	0.876375	−	0.481630i	$-0.159955\pi$
$337$	16.4751	+	9.51193i	0.897458	+	0.518148i	0.0210835	+	0.999778i	$0.493288\pi$
$338$	9.15329	−	15.8540i	0.497873	−	0.862342i
$339$		−	29.4191i		−	1.59783i
$340$	8.77278	+	4.40204i	0.475771	+	0.238734i
$341$		−	35.7006i		−	1.93330i
$342$	0.939582	−	0.542468i	0.0508068	−	0.0293333i
$343$		−	17.2519i		−	0.931517i
$344$	3.37607			0.182026
$345$	−2.60074	−	3.95124i	−0.140019	−	0.212728i
$346$	6.50565	+	3.75604i	0.349746	+	0.201926i
$347$	19.7918			1.06248			0.531241	−	0.847221i	$-0.321726\pi$
$347$	19.7918			1.06248			0.531241	+	0.847221i	$0.321726\pi$
$348$	3.24201	+	5.61533i	0.173790	+	0.301013i
$349$	−10.1429	−	17.5681i	−0.542939	−	0.940398i	−0.998734	−	0.0503130i	$-0.983978\pi$
$349$	−10.1429	−	17.5681i	−0.542939	−	0.940398i	0.455794	−	0.890085i	$-0.349355\pi$
$350$	−5.81268	+	4.33365i	−0.310701	+	0.231644i
$351$	−17.2715	−	9.97171i	−0.921885	−	0.532250i
$352$	−2.55658	+	4.42812i	−0.136266	+	0.236020i
$353$	−8.74971	−	15.1549i	−0.465700	−	0.806616i	0.533533	−	0.845779i	$-0.320864\pi$
$353$	−8.74971	−	15.1549i	−0.465700	−	0.806616i	−0.999233	+	0.0391633i	$0.987531\pi$
$354$	2.35953	+	4.08682i	0.125407	+	0.217212i
$355$	−17.6281	+	11.6029i	−0.935601	+	0.615819i
$356$			13.9891i			0.741422i
$357$	6.58135	−	11.3992i	0.348322	−	0.603312i
$358$	−22.5722	+	13.0320i	−1.19298	+	0.688765i
$359$	4.95683			0.261612			0.130806	−	0.991408i	$-0.458244\pi$
$359$	4.95683			0.261612			0.130806	+	0.991408i	$0.458244\pi$
$360$	−0.166937	−	2.84916i	−0.00879834	−	0.150164i
$361$	−9.13874	−	15.8288i	−0.480986	−	0.833092i
$362$	−15.7909			−0.829950
$363$	27.1218	+	15.6588i	1.42353	+	0.821873i
$364$			8.11349i			0.425263i
$365$	−10.2656	+	20.4581i	−0.537324	+	1.07083i
$366$	0.887879	−	1.53785i	0.0464102	−	0.0803848i
$367$	−19.9505	−	11.5184i	−1.04141	−	0.601257i	−0.121175	−	0.992631i	$-0.538666\pi$
$367$	−19.9505	−	11.5184i	−1.04141	−	0.601257i	−0.920231	+	0.391375i	$0.872000\pi$
$368$	0.511494	+	0.885933i	0.0266634	+	0.0461824i
$369$	−13.0291			−0.678268
$370$	−13.4088	+	2.28131i	−0.697090	+	0.118600i
$371$	15.3927			0.799148
$372$	−7.21929	−	12.5042i	−0.374303	−	0.648312i
$373$	13.3192	+	7.68983i	0.689641	+	0.398164i	0.803477	−	0.595335i	$-0.202981\pi$
$373$	13.3192	+	7.68983i	0.689641	+	0.398164i	−0.113837	+	0.993499i	$0.536314\pi$
$374$	−11.2222	+	19.4373i	−0.580284	+	1.00508i
$375$	−7.88498	+	21.7342i	−0.407178	+	1.12235i
$376$			3.87763i			0.199974i
$377$	−15.1934	−	8.77192i	−0.782500	−	0.451777i
$378$	5.16859			0.265843
$379$	6.96506	+	12.0638i	0.357771	+	0.619678i	0.987588	−	0.157066i	$-0.0502034\pi$
$379$	6.96506	+	12.0638i	0.357771	+	0.619678i	−0.629817	+	0.776744i	$0.716870\pi$
$380$	1.89744	−	0.111174i	0.0973367	−	0.00570310i
$381$	−7.29279			−0.373621
$382$	−8.73196	+	5.04140i	−0.446766	+	0.257940i
$383$	6.32698	−	10.9586i	0.323294	−	0.559961i	−0.657872	−	0.753130i	$-0.728543\pi$
$383$	6.32698	−	10.9586i	0.323294	−	0.559961i	0.981166	+	0.193169i	$0.0618765\pi$
$384$			2.06794i			0.105529i
$385$	−9.11523	−	13.8486i	−0.464555	−	0.705789i
$386$	−4.58866	−	7.94780i	−0.233557	−	0.404532i
$387$	−2.15456	−	3.73180i	−0.109522	−	0.189698i
$388$	−1.13247	+	1.96150i	−0.0574925	+	0.0995799i
$389$	17.4341	+	10.0656i	0.883945	+	0.510346i	0.871957	−	0.489583i	$-0.162851\pi$
$389$	17.4341	+	10.0656i	0.883945	+	0.510346i	0.0119875	+	0.999928i	$0.496184\pi$
$390$	14.2247	+	21.6113i	0.720297	+	1.09433i
$391$	2.24521	+	3.88882i	0.113545	+	0.196666i
$392$	2.44864	+	4.24117i	0.123675	+	0.214212i
$393$	−12.0423			−0.607452
$394$	−2.84877	−	1.64474i	−0.143519	−	0.0828608i
$395$	−7.16020	−	10.8783i	−0.360269	−	0.547348i
$396$	6.52627			0.327958
$397$			5.48424i			0.275246i	0.990485	+	0.137623i	$0.0439463\pi$
$397$			5.48424i			0.275246i	−0.990485	+	0.137623i	$0.956054\pi$
$398$	−14.3764	+	8.30019i	−0.720621	+	0.416051i
$399$		−	2.54892i		−	0.127605i
$400$	1.97721	−	4.59245i	0.0988606	−	0.229623i
$401$			17.6519i			0.881494i	0.897631	+	0.440747i	$0.145286\pi$
$401$			17.6519i			0.881494i	−0.897631	+	0.440747i	$0.854714\pi$
$402$	−11.3267	+	19.6185i	−0.564926	+	0.978480i
$403$	33.8326	+	19.5333i	1.68532	+	0.973021i
$404$	9.22383	−	15.9761i	0.458903	−	0.794843i
$405$	20.9191	−	13.7691i	1.03948	−	0.684193i
$406$	4.54671			0.225649
$407$	−3.41425	−	30.9141i	−0.169238	−	1.53236i
$408$			9.07727i			0.449392i
$409$	12.4970	−	7.21513i	0.617935	−	0.356765i	−0.158129	−	0.987418i	$-0.550546\pi$
$409$	12.4970	−	7.21513i	0.617935	−	0.356765i	0.776065	+	0.630653i	$0.217213\pi$
$410$	−20.4013	−	10.2371i	−1.00755	−	0.505572i
$411$	−0.890004	+	1.54153i	−0.0439007	+	0.0760382i
$412$	−1.13390	+	1.96398i	−0.0558633	+	0.0967581i
$413$	3.30908			0.162829
$414$	0.652855	−	1.13078i	0.0320861	−	0.0555747i
$415$	−0.166849	+	0.00977592i	−0.00819029	+	0.000479881i
$416$	−2.79761	−	4.84561i	−0.137164	−	0.237576i
$417$			0.307927i			0.0150793i
$418$			4.34627i			0.212583i
$419$	−3.15432	−	5.46344i	−0.154098	−	0.266906i	0.778632	−	0.627481i	$-0.215914\pi$
$419$	−3.15432	−	5.46344i	−0.154098	−	0.266906i	−0.932730	+	0.360575i	$0.882581\pi$
$420$	−5.99304	−	3.00722i	−0.292431	−	0.146737i
$421$			11.7094i			0.570682i	0.958426	+	0.285341i	$0.0921068\pi$
$421$			11.7094i			0.570682i	−0.958426	+	0.285341i	$0.907893\pi$
$422$	6.96520	+	12.0641i	0.339061	+	0.587271i
$423$	4.28621	−	2.47465i	0.208403	−	0.120321i
$424$	−9.19294	+	5.30755i	−0.446449	+	0.257757i
$425$	8.67902	−	20.1587i	0.420994	−	0.977840i
$426$	−16.9023	−	9.75857i	−0.818921	−	0.472804i
$427$	−0.622596	−	1.07837i	−0.0301295	−	0.0521859i
$428$	3.36674	−	1.94379i	0.162737	−	0.0939565i
$429$	−51.2360	+	29.5811i	−2.47370	+	1.42819i
$430$	−0.441557	−	7.53620i	−0.0212938	−	0.363428i
$431$	17.5027	+	10.1052i	0.843075	+	0.486750i	0.858308	−	0.513134i	$-0.171516\pi$
$431$	17.5027	+	10.1052i	0.843075	+	0.486750i	−0.0152332	+	0.999884i	$0.504849\pi$
$432$	−3.08683	+	1.78218i	−0.148515	+	0.0857452i
$433$		−	3.43048i		−	0.164858i	−0.996597	−	0.0824292i	$-0.973732\pi$
$433$		−	3.43048i		−	0.164858i	0.996597	−	0.0824292i	$-0.0262678\pi$
$434$	−10.1246			−0.485995
$435$	12.1107	−	7.97137i	0.580665	−	0.382198i
$436$			16.4502i			0.787822i
$437$	0.753058	+	0.434778i	0.0360237	+	0.0207983i
$438$	−21.1682			−1.01145
$439$	−10.6383	−	6.14204i	−0.507739	−	0.293143i	0.224165	−	0.974551i	$-0.428035\pi$
$439$	−10.6383	−	6.14204i	−0.507739	−	0.293143i	−0.731904	+	0.681408i	$0.761368\pi$
$440$	10.2190	+	5.12774i	0.487172	+	0.244455i
$441$	3.12537	−	5.41331i	0.148827	−	0.257776i
$442$	−12.2802	−	21.2699i	−0.584109	−	1.01171i
$443$		−	16.9591i		−	0.805751i	−0.915255	−	0.402875i	$-0.868011\pi$
$443$		−	16.9591i		−	0.805751i	0.915255	−	0.402875i	$-0.131989\pi$
$444$	−7.44722	−	10.1373i	−0.353430	−	0.481094i
$445$	31.2271	−	1.82964i	1.48031	−	0.0867333i
$446$	24.2817	−	14.0191i	1.14977	−	0.663822i
$447$	−32.1781	−	18.5780i	−1.52197	−	0.878710i
$448$	1.25580	+	0.725037i	0.0593310	+	0.0342548i
$449$	−12.1325	−	7.00470i	−0.572568	−	0.330572i	0.185606	−	0.982624i	$-0.440575\pi$
$449$	−12.1325	−	7.00470i	−0.572568	−	0.330572i	−0.758174	+	0.652052i	$0.773908\pi$
$450$	−6.33818	+	0.745285i	−0.298785	+	0.0351331i
$451$	26.0974	−	45.2020i	1.22888	−	2.12848i
$452$	14.2263			0.669149
$453$	29.3648	−	16.9538i	1.37968	−	0.796557i
$454$	−5.95565			−0.279513
$455$	18.1113	−	1.06117i	0.849069	−	0.0497482i
$456$	0.878892	+	1.52228i	0.0411579	+	0.0712875i
$457$	10.7887	−	18.6866i	0.504675	−	0.874123i	−0.495310	−	0.868716i	$-0.664946\pi$
$457$	10.7887	−	18.6866i	0.504675	−	0.874123i	0.999985	−	0.00540704i	$-0.00172112\pi$
$458$	−3.63261			−0.169741
$459$	−13.5497	+	7.82292i	−0.632446	+	0.365143i
$460$	1.91072	−	1.25765i	0.0890876	−	0.0586381i
$461$	12.7119	−	7.33924i	0.592054	−	0.341823i	−0.173855	−	0.984771i	$-0.555623\pi$
$461$	12.7119	−	7.33924i	0.592054	−	0.341823i	0.765909	+	0.642949i	$0.222289\pi$
$462$	7.66631	−	13.2784i	0.356669	−	0.617769i
$463$	−6.14006	+	10.6349i	−0.285353	+	0.494246i	−0.972695	−	0.232088i	$-0.925444\pi$
$463$	−6.14006	+	10.6349i	−0.285353	+	0.494246i	0.687342	+	0.726334i	$0.258777\pi$
$464$	−2.71542	+	1.56775i	−0.126060	+	0.0727810i
$465$	−26.9681	+	17.7506i	−1.25062	+	0.823165i
$466$	18.3579	−	10.5989i	0.850411	−	0.490985i
$467$	−24.1586			−1.11793			−0.558964	−	0.829192i	$-0.688801\pi$
$467$	−24.1586			−1.11793			−0.558964	+	0.829192i	$0.688801\pi$
$468$	−3.57079	+	6.18479i	−0.165060	+	0.285892i
$469$	7.94249	+	13.7568i	0.366750	+	0.635230i
$470$	8.65581	−	0.507157i	0.399263	−	0.0233934i
$471$	−11.8184			−0.544563
$472$	−1.97628	+	1.14100i	−0.0909655	+	0.0525189i
$473$	17.2624			0.793725
$474$	6.02205	−	10.4305i	0.276602	−	0.479088i
$475$	−0.496334	−	4.22100i	−0.0227734	−	0.193673i
$476$	5.51237	+	3.18257i	0.252659	+	0.145873i
$477$	11.7336	+	6.77439i	0.537244	+	0.310178i
$478$	−17.3902	−	10.0402i	−0.795407	−	0.459229i
$479$	−1.85947	+	1.07357i	−0.0849616	+	0.0490526i	−0.541879	−	0.840457i	$-0.682287\pi$
$479$	−1.85947	+	1.07357i	−0.0849616	+	0.0490526i	0.456917	+	0.889509i	$0.348954\pi$
$480$	4.61613	−	0.270466i	0.210697	−	0.0123450i
$481$	31.1646	+	13.6788i	1.42098	+	0.623699i
$482$			16.0681i			0.731882i
$483$	−1.53380	−	2.65662i	−0.0697902	−	0.120880i
$484$	−7.57217	+	13.1154i	−0.344190	+	0.596154i
$485$	4.52665	+	2.27140i	0.205544	+	0.103139i
$486$	10.7974	+	6.23390i	0.489782	+	0.282776i
$487$	−39.5376			−1.79162			−0.895810	−	0.444436i	$-0.853404\pi$
$487$	−39.5376			−1.79162			−0.895810	+	0.444436i	$0.853404\pi$
$488$	0.743664	+	0.429355i	0.0336641	+	0.0194360i
$489$			34.1974i			1.54646i
$490$	9.14706	−	6.02066i	0.413222	−	0.271986i
$491$	−37.2849			−1.68264			−0.841322	−	0.540535i	$-0.818222\pi$
$491$	−37.2849			−1.68264			−0.841322	+	0.540535i	$0.818222\pi$
$492$		−	21.1094i		−	0.951685i
$493$	−11.9194	+	6.88167i	−0.536823	+	0.309935i
$494$	−4.11885	−	2.37802i	−0.185316	−	0.106992i
$495$	−0.853573	−	14.5682i	−0.0383653	−	0.654792i
$496$	6.04669	−	3.49106i	0.271504	−	0.156753i
$497$	−11.8522	+	6.84288i	−0.531644	+	0.306945i
$498$	−0.0772841	−	0.133860i	−0.00346318	−	0.00599841i
$499$	1.96883	+	1.13670i	0.0881370	+	0.0508859i	0.543421	−	0.839460i	$-0.317129\pi$
$499$	1.96883	+	1.13670i	0.0881370	+	0.0508859i	−0.455284	+	0.890346i	$0.650462\pi$
$500$	−10.5101	−	3.81296i	−0.470024	−	0.170521i
$501$	−20.9705	+	12.1073i	−0.936893	+	0.540916i
$502$	3.97458	−	2.29472i	0.177394	−	0.102418i
$503$	−4.86299	−	8.42295i	−0.216830	−	0.375561i	0.737007	−	0.675885i	$-0.236238\pi$
$503$	−4.86299	−	8.42295i	−0.216830	−	0.375561i	−0.953837	+	0.300324i	$0.902905\pi$
$504$		−	1.85083i		−	0.0824425i
$505$	−36.8690	−	18.5003i	−1.64065	−	0.823251i
$506$	2.61535	+	4.52991i	0.116266	+	0.201379i
$507$		−	37.8569i		−	1.68128i
$508$		−	3.52660i		−	0.156468i
$509$	18.2656	+	31.6370i	0.809610	+	1.40229i	0.913135	+	0.407658i	$0.133655\pi$
$509$	18.2656	+	31.6370i	0.809610	+	1.40229i	−0.103525	+	0.994627i	$0.533012\pi$
$510$	20.2626	−	1.18722i	0.897244	−	0.0525709i
$511$	−7.42174	+	12.8548i	−0.328319	+	0.568665i
$512$	−1.00000			−0.0441942
$513$	−1.51488	+	2.62386i	−0.0668838	+	0.115846i
$514$	−6.81731	+	11.8079i	−0.300699	+	0.520825i
$515$	4.53237	+	2.27427i	0.199720	+	0.100216i
$516$	6.04616	−	3.49075i	0.266167	−	0.153672i
$517$			19.8269i			0.871988i
$518$	−8.76715	+	0.968270i	−0.385206	+	0.0425433i
$519$	15.5345			0.681890
$520$	−10.4507	+	6.87870i	−0.458292	+	0.301651i
$521$	−5.46423	+	9.46433i	−0.239392	+	0.414640i	−0.960540	−	0.278142i	$-0.910282\pi$
$521$	−5.46423	+	9.46433i	−0.239392	+	0.414640i	0.721148	+	0.692781i	$0.243615\pi$
$522$	3.46588	+	2.00103i	0.151698	+	0.0875826i
$523$	10.1816	−	17.6350i	0.445210	−	0.771126i	−0.552857	−	0.833276i	$-0.686462\pi$
$523$	10.1816	−	17.6350i	0.445210	−	0.771126i	0.998067	+	0.0621502i	$0.0197958\pi$
$524$		−	5.82332i		−	0.254393i
$525$	−5.92900	+	13.7712i	−0.258763	+	0.601026i
$526$			4.12335i			0.179787i
$527$	26.5421	−	15.3241i	1.15619	−	0.667527i
$528$			10.5737i			0.460161i
$529$	−21.9535			−0.954500
$530$	13.0501	+	19.8267i	0.566859	+	0.861216i
$531$	2.52246	+	1.45634i	0.109465	+	0.0631999i
$532$	1.23259			0.0534395
$533$	28.5579	+	49.4637i	1.23698	+	2.14251i
$534$	14.4643	+	25.0529i	0.625932	+	1.08415i
$535$	−4.77934	−	7.26114i	−0.206629	−	0.313926i
$536$	−9.48697	−	5.47730i	−0.409775	−	0.236583i
$537$	−26.9495	+	46.6778i	−1.16295	+	2.01430i
$538$	7.41091	+	12.8361i	0.319507	+	0.553403i
$539$	12.5203	+	21.6858i	0.539287	+	0.934072i
$540$	4.38198	+	6.65745i	0.188570	+	0.286491i
$541$		−	5.74756i		−	0.247107i	−0.992338	−	0.123554i	$-0.960571\pi$
$541$		−	5.74756i		−	0.247107i	0.992338	−	0.123554i	$-0.0394291\pi$
$542$	5.63808	−	9.76543i	0.242176	−	0.419461i
$543$	−28.2797	+	16.3273i	−1.21360	+	0.700671i
$544$	−4.38952			−0.188199
$545$	36.7208	−	2.15153i	1.57295	−	0.0921613i
$546$	8.38910	+	14.5304i	0.359020	+	0.621842i
$547$	43.8451			1.87468			0.937341	−	0.348413i	$-0.113279\pi$
$547$	43.8451			1.87468			0.937341	+	0.348413i	$0.113279\pi$
$548$	−0.745444	−	0.430382i	−0.0318438	−	0.0183850i
$549$		−	1.09603i		−	0.0467775i
$550$	10.1098	−	23.4819i	0.431083	−	1.00127i
$551$	−1.33261	+	2.30816i	−0.0567713	+	0.0983307i
$552$	1.83205	+	1.05774i	0.0779774	+	0.0450203i
$553$	−4.22276	−	7.31404i	−0.179570	−	0.311025i
$554$	24.0775			1.02296
$555$	−21.6548	+	17.9498i	−0.919196	+	0.761928i
$556$	−0.148905			−0.00631500
$557$	13.3274	+	23.0838i	0.564701	+	0.978091i	0.997077	+	0.0763977i	$0.0243419\pi$
$557$	13.3274	+	23.0838i	0.564701	+	0.978091i	−0.432376	+	0.901693i	$0.642325\pi$
$558$	−7.71781	−	4.45588i	−0.326721	−	0.188632i
$559$	−9.44494	+	16.3591i	−0.399478	+	0.691917i
$560$	1.45421	−	2.89808i	0.0614516	−	0.122466i
$561$			46.4135i			1.95958i
$562$	22.1556	+	12.7915i	0.934577	+	0.539578i
$563$	36.1030			1.52156			0.760781	−	0.649009i	$-0.224816\pi$
$563$	36.1030			1.52156			0.760781	+	0.649009i	$0.224816\pi$
$564$	4.00935	+	6.94440i	0.168824	+	0.292412i
$565$	−1.86066	−	31.7565i	−0.0782786	−	1.33601i
$566$	−31.5142			−1.32464
$567$	14.0650	−	8.12041i	0.590673	−	0.341025i
$568$	4.71899	−	8.17352i	0.198004	−	0.342953i
$569$			31.3674i			1.31499i	0.753459	+	0.657495i	$0.228384\pi$
$569$			31.3674i			1.31499i	−0.753459	+	0.657495i	$0.771616\pi$
$570$	3.28315	−	2.16100i	0.137516	−	0.0905142i
$571$	18.5786	+	32.1791i	0.777492	+	1.34666i	0.933383	+	0.358881i	$0.116842\pi$
$571$	18.5786	+	32.1791i	0.777492	+	1.34666i	−0.155891	+	0.987774i	$0.549825\pi$
$572$	−14.3046	−	24.7763i	−0.598107	−	1.03595i
$573$	−10.4253	+	18.0571i	−0.435523	+	0.754348i
$574$	−12.8191	−	7.40114i	−0.535061	−	0.308918i
$575$	−3.05727	−	4.10069i	−0.127497	−	0.171011i
$576$	0.638185	+	1.10537i	0.0265910	+	0.0460570i
$577$	5.46972	+	9.47383i	0.227707	+	0.394401i	0.957128	−	0.289665i	$-0.0935438\pi$
$577$	5.46972	+	9.47383i	0.227707	+	0.394401i	−0.729421	+	0.684065i	$0.760210\pi$
$578$	−2.26792			−0.0943330
$579$	−16.4356	−	9.48907i	−0.683039	−	0.394352i
$580$	3.85474	+	5.85643i	0.160060	+	0.243175i
$581$	−0.108386			−0.00449660
$582$			4.68376i			0.194148i
$583$	−47.0049	+	27.1383i	−1.94675	+	1.12395i
$584$		−	10.2364i		−	0.423584i
$585$	14.2730	+	7.16195i	0.590114	+	0.296110i
$586$		−	22.0005i		−	0.908832i
$587$	18.7763	−	32.5215i	0.774980	−	1.34230i	−0.159826	−	0.987145i	$-0.551093\pi$
$587$	18.7763	−	32.5215i	0.774980	−	1.34230i	0.934806	−	0.355159i	$-0.115573\pi$
$588$	8.77049	+	5.06364i	0.361689	+	0.208821i
$589$	2.96746	−	5.13979i	0.122272	−	0.211781i
$590$	2.80547	+	4.26229i	0.115499	+	0.175476i
$591$	−6.80244			−0.279815
$592$	4.90212	−	3.60128i	0.201476	−	0.148012i
$593$			40.8926i			1.67926i	0.543161	+	0.839629i	$0.317227\pi$
$593$			40.8926i			1.67926i	−0.543161	+	0.839629i	$0.682773\pi$
$594$	−15.7834	+	9.11256i	−0.647602	+	0.373893i
$595$	6.38329	−	12.7212i	0.261689	−	0.521517i
$596$	8.98384	−	15.5605i	0.367992	−	0.637381i
$597$	−17.1643	+	29.7294i	−0.702487	+	1.21674i
$598$	−5.72385			−0.234065
$599$	13.5131	−	23.4054i	0.552132	−	0.956320i	−0.445989	−	0.895038i	$-0.647148\pi$
$599$	13.5131	−	23.4054i	0.552132	−	0.956320i	0.998121	−	0.0612814i	$-0.0195187\pi$
$600$	−1.20749	−	10.2689i	−0.0492956	−	0.419228i
$601$	0.718472	+	1.24443i	0.0293071	+	0.0507613i	0.880307	−	0.474405i	$-0.157337\pi$
$601$	0.718472	+	1.24443i	0.0293071	+	0.0507613i	−0.851000	+	0.525166i	$0.824003\pi$
$602$		−	4.89555i		−	0.199528i
$603$			13.9821i			0.569396i
$604$	8.19838	+	14.2000i	0.333588	+	0.577791i
$605$	30.2671	+	15.1875i	1.23053	+	0.617461i
$606$		−	38.1486i		−	1.54968i
$607$	−17.5771	−	30.4444i	−0.713432	−	1.23570i	−0.963561	−	0.267488i	$-0.913806\pi$
$607$	−17.5771	−	30.4444i	−0.713432	−	1.23570i	0.250129	−	0.968212i	$-0.419527\pi$
$608$	−0.736136	+	0.425009i	−0.0298543	+	0.0172364i
$609$	8.14264	−	4.70115i	0.329956	−	0.190500i
$610$	0.861159	−	1.71619i	0.0348673	−	0.0694866i
$611$	−18.7895	−	10.8481i	−0.760142	−	0.438868i
$612$	2.80133	+	4.85204i	0.113237	+	0.196132i
$613$	34.9874	−	20.2000i	1.41313	−	0.815871i	0.417448	−	0.908701i	$-0.362925\pi$
$613$	34.9874	−	20.2000i	1.41313	−	0.815871i	0.995682	+	0.0928302i	$0.0295914\pi$
$614$	13.4887	−	7.78768i	0.544358	−	0.314285i
$615$	−47.1212	+	2.76090i	−1.90011	+	0.111330i
$616$	6.42110	+	3.70723i	0.258714	+	0.149368i
$617$	−25.0513	+	14.4634i	−1.00853	+	0.582274i	−0.910761	−	0.412935i	$-0.864504\pi$
$617$	−25.0513	+	14.4634i	−1.00853	+	0.582274i	−0.0977681	+	0.995209i	$0.531170\pi$
$618$			4.68968i			0.188647i
$619$	15.3746			0.617957			0.308978	−	0.951069i	$-0.400013\pi$
$619$	15.3746			0.617957			0.308978	+	0.951069i	$0.400013\pi$
$620$	−8.58372	−	13.0411i	−0.344731	−	0.523742i
$621$			3.64630i			0.146321i
$622$	15.8523	+	9.15233i	0.635619	+	0.366975i
$623$	20.2853			0.812712
$624$	−10.0204	−	5.78529i	−0.401138	−	0.231597i
$625$	−7.13684	+	23.9597i	−0.285474	+	0.958387i
$626$	2.70484	−	4.68491i	0.108107	−	0.187247i
$627$	4.49391	+	7.78368i	0.179469	+	0.310850i
$628$		−	5.71506i		−	0.228056i
$629$	21.5180	−	15.8079i	0.857978	−	0.630302i
$630$	−4.13150	+	0.242071i	−0.164603	+	0.00964432i
$631$	−17.6102	+	10.1673i	−0.701052	+	0.404753i	−0.807739	−	0.589540i	$-0.799309\pi$
$631$	−17.6102	+	10.1673i	−0.701052	+	0.404753i	0.106687	+	0.994293i	$0.465976\pi$
$632$	5.04391	+	2.91210i	0.200636	+	0.115837i
$633$	24.9478	+	14.4036i	0.991586	+	0.572492i
$634$	−20.7120	−	11.9581i	−0.822578	−	0.474915i
$635$	−7.87222	+	0.461245i	−0.312399	+	0.0183039i
$636$	−10.9757	+	19.0104i	−0.435214	+	0.753813i
$637$	−27.4014			−1.08568
$638$	−13.8844	+	8.01615i	−0.549688	+	0.317362i
$639$	−12.0463			−0.476546
$640$	0.130790	+	2.23224i	0.00516994	+	0.0882370i
$641$	−8.94409	−	15.4916i	−0.353270	−	0.611882i	0.633550	−	0.773702i	$-0.281597\pi$
$641$	−8.94409	−	15.4916i	−0.353270	−	0.611882i	−0.986820	+	0.161820i	$0.948264\pi$
$642$	4.01963	−	6.96221i	0.158642	−	0.274776i
$643$	11.1450			0.439516			0.219758	−	0.975554i	$-0.429473\pi$
$643$	11.1450			0.439516			0.219758	+	0.975554i	$0.429473\pi$
$644$	1.28467	−	0.741704i	0.0506230	−	0.0292272i
$645$	−8.58298	−	13.0399i	−0.337954	−	0.513447i
$646$	−3.23129	+	1.86559i	−0.127133	+	0.0734005i
$647$	8.64172	−	14.9679i	0.339741	−	0.588449i	−0.644643	−	0.764484i	$-0.722994\pi$
$647$	8.64172	−	14.9679i	0.339741	−	0.588449i	0.984384	+	0.176035i	$0.0563272\pi$
$648$	−5.59999	+	9.69948i	−0.219989	+	0.381031i
$649$	−10.1050	+	5.83413i	−0.396656	+	0.229009i
$650$	16.7218	+	22.4287i	0.655881	+	0.879726i
$651$	−18.1320	+	10.4685i	−0.710649	+	0.410293i
$652$	−16.5369			−0.647637
$653$	−2.35613	+	4.08093i	−0.0922023	+	0.159699i	−0.908438	−	0.418021i	$-0.862724\pi$
$653$	−2.35613	+	4.08093i	−0.0922023	+	0.159699i	0.816235	+	0.577720i	$0.196057\pi$
$654$	17.0090	+	29.4605i	0.665105	+	1.15200i
$655$	−12.9990	+	0.761633i	−0.507915	+	0.0297595i
$656$	10.2079			0.398553
$657$	−11.3150	+	6.53269i	−0.441439	+	0.254865i
$658$	5.62286			0.219202
$659$	7.22649	−	12.5166i	0.281504	−	0.487579i	−0.690251	−	0.723570i	$-0.742500\pi$
$659$	7.22649	−	12.5166i	0.281504	−	0.487579i	0.971755	+	0.235990i	$0.0758334\pi$
$660$	23.6030	−	1.38294i	0.918746	−	0.0538307i
$661$	22.5021	+	12.9916i	0.875230	+	0.505314i	0.869083	−	0.494667i	$-0.164710\pi$
$661$	22.5021	+	12.9916i	0.875230	+	0.505314i	0.00614743	+	0.999981i	$0.498043\pi$
$662$	−0.538586	−	0.310953i	−0.0209327	−	0.0120855i
$663$	−43.9849	−	25.3947i	−1.70823	−	0.986248i
$664$	0.0647311	−	0.0373725i	0.00251205	−	0.00145033i
$665$	−0.161210	−	2.75143i	−0.00625147	−	0.106696i
$666$	−7.10920	−	3.12037i	−0.275476	−	0.120912i
$667$			3.20758i			0.124198i
$668$	−5.85478	−	10.1408i	−0.226528	−	0.392359i
$669$	28.9906	−	50.2132i	1.12084	−	1.94135i
$670$	−10.9858	+	21.8936i	−0.424420	+	0.845822i
$671$	3.80247	+	2.19536i	0.146793	+	0.0847508i
$672$	2.99866			0.115676
$673$	1.69806	+	0.980376i	0.0654554	+	0.0377907i	0.532371	−	0.846511i	$-0.321301\pi$
$673$	1.69806	+	0.980376i	0.0654554	+	0.0377907i	−0.466915	+	0.884302i	$0.654635\pi$
$674$			19.0239i			0.732772i
$675$	14.2879	−	10.6524i	0.549941	−	0.410010i
$676$	18.3066			0.704099
$677$			7.45165i			0.286390i	0.989694	+	0.143195i	$0.0457377\pi$
$677$			7.45165i			0.286390i	−0.989694	+	0.143195i	$0.954262\pi$
$678$	25.4777	−	14.7096i	0.978466	−	0.564917i
$679$	2.84432	+	1.64217i	0.109155	+	0.0630206i
$680$	0.574107	+	9.79847i	0.0220160	+	0.375754i
$681$	−10.6659	+	6.15796i	−0.408718	+	0.235974i
$682$	30.9176	−	17.8503i	1.18390	−	0.683524i
$683$	0.00690727	+	0.0119637i	0.000264299	+	0.000457780i	0.866158	−	0.499771i	$-0.166583\pi$
$683$	0.00690727	+	0.0119637i	0.000264299	+	0.000457780i	−0.865893	+	0.500229i	$0.833249\pi$
$684$	0.939582	+	0.542468i	0.0359258	+	0.0207418i
$685$	−0.863220	+	1.72030i	−0.0329819	+	0.0657293i
$686$	14.9406	−	8.62597i	0.570436	−	0.329341i
$687$	−6.50560	+	3.75601i	−0.248204	+	0.143301i
$688$	1.68804	+	2.92376i	0.0643557	+	0.111467i
$689$		−	59.3939i		−	2.26273i
$690$	2.12151	−	4.22793i	0.0807644	−	0.160954i
$691$	−23.7796	−	41.1875i	−0.904619	−	1.56685i	−0.821427	−	0.570313i	$-0.806822\pi$
$691$	−23.7796	−	41.1875i	−0.904619	−	1.56685i	−0.0831921	−	0.996534i	$-0.526512\pi$
$692$			7.51208i			0.285566i
$693$		−	9.46358i		−	0.359492i
$694$	9.89592	+	17.1402i	0.375644	+	0.650635i
$695$	0.0194754	+	0.332393i	0.000738743	+	0.0126084i
$696$	−3.24201	+	5.61533i	−0.122888	+	0.212848i
$697$	44.8080			1.69722
$698$	10.1429	−	17.5681i	0.383916	−	0.664962i
$699$	21.9179	−	37.9629i	0.829011	−	1.43589i
$700$	−6.65940	−	2.86710i	−0.251702	−	0.108366i
$701$	−26.1651	+	15.1064i	−0.988243	+	0.570562i	−0.904749	−	0.425946i	$-0.859941\pi$
$701$	−26.1651	+	15.1064i	−0.988243	+	0.570562i	−0.0834941	+	0.996508i	$0.526608\pi$
$702$		−	19.9434i		−	0.752716i
$703$	2.07806	−	4.73448i	0.0783754	−	0.178564i
$704$	−5.11315			−0.192709
$705$	14.9772	−	9.85810i	0.564074	−	0.371278i
$706$	8.74971	−	15.1549i	0.329300	−	0.570364i
$707$	−23.1666	−	13.3752i	−0.871269	−	0.503027i
$708$	−2.35953	+	4.08682i	−0.0886764	+	0.153592i
$709$			25.8591i			0.971159i	0.874193	+	0.485579i	$0.161391\pi$
$709$			25.8591i			0.971159i	−0.874193	+	0.485579i	$0.838609\pi$
$710$	−18.8625	−	9.46489i	−0.707896	−	0.355211i
$711$		−	7.43383i		−	0.278791i
$712$	−12.1149	+	6.99456i	−0.454026	+	0.262132i
$713$		−	7.14261i		−	0.267493i
$714$	13.1627			0.492602
$715$	−53.4358	+	35.1719i	−1.99839	+	1.31535i
$716$	−22.5722	−	13.0320i	−0.843561	−	0.487030i
$717$	−41.5251			−1.55078
$718$	2.47842	+	4.29274i	0.0924936	+	0.160204i
$719$	3.91727	+	6.78492i	0.146090	+	0.253035i	0.929779	−	0.368118i	$-0.119998\pi$
$719$	3.91727	+	6.78492i	0.146090	+	0.253035i	−0.783689	+	0.621153i	$0.786665\pi$
$720$	2.38398	−	1.56915i	0.0888457	−	0.0584789i
$721$	2.84791	+	1.64424i	0.106062	+	0.0612348i
$722$	9.13874	−	15.8288i	0.340109	−	0.589085i
$723$	16.6139	+	28.7762i	0.617879	+	1.07020i
$724$	−7.89544	−	13.6753i	−0.293432	−	0.508238i
$725$	12.5688	−	9.37068i	0.466793	−	0.348018i
$726$			31.3176i			1.16230i
$727$	−7.31881	+	12.6765i	−0.271440	+	0.470147i	−0.969231	−	0.246154i	$-0.920833\pi$
$727$	−7.31881	+	12.6765i	−0.271440	+	0.470147i	0.697791	+	0.716301i	$0.254166\pi$
$728$	−7.02649	+	4.05675i	−0.260419	+	0.150353i
$729$	−7.81731			−0.289530
$730$	−22.8500	+	1.33882i	−0.845717	+	0.0495518i
$731$	7.40967	+	12.8339i	0.274057	+	0.474680i
$732$	1.77576			0.0656339
$733$	10.4907	+	6.05679i	0.387482	+	0.223713i	0.681068	−	0.732220i	$-0.261516\pi$
$733$	10.4907	+	6.05679i	0.387482	+	0.223713i	−0.293587	+	0.955932i	$0.594849\pi$
$734$		−	23.0368i		−	0.850305i
$735$	10.1562	−	20.2401i	0.374616	−	0.746567i
$736$	−0.511494	+	0.885933i	−0.0188539	+	0.0326559i
$737$	−48.5083	−	28.0063i	−1.78683	−	1.03162i
$738$	−6.51456	−	11.2835i	−0.239804	−	0.415353i
$739$	22.9087			0.842711			0.421356	−	0.906896i	$-0.361554\pi$
$739$	22.9087			0.842711			0.421356	+	0.906896i	$0.361554\pi$
$740$	−8.68007	−	10.4717i	−0.319086	−	0.384947i
$741$	−9.83520			−0.361305
$742$	7.69634	+	13.3304i	0.282541	+	0.489376i
$743$	−35.8997	−	20.7267i	−1.31703	−	0.760389i	−0.333783	−	0.942650i	$-0.608325\pi$
$743$	−35.8997	−	20.7267i	−1.31703	−	0.760389i	−0.983250	+	0.182261i	$0.941659\pi$
$744$	7.21929	−	12.5042i	0.264672	−	0.458425i
$745$	−35.9097	−	18.0189i	−1.31563	−	0.660162i
$746$			15.3797i			0.563089i
$747$	−0.0826208	−	0.0477011i	−0.00302294	−	0.00174529i
$748$	−22.4443			−0.820645
$749$	−2.81864	−	4.88202i	−0.102991	−	0.178385i
$750$	−22.7648	+	4.03849i	−0.831254	+	0.147465i
$751$	−1.67476			−0.0611127			−0.0305563	−	0.999533i	$-0.509728\pi$
$751$	−1.67476			−0.0611127			−0.0305563	+	0.999533i	$0.509728\pi$
$752$	−3.35813	+	1.93882i	−0.122458	+	0.0707014i
$753$	4.74534	−	8.21918i	0.172930	−	0.299523i
$754$		−	17.5438i		−	0.638909i
$755$	30.6256	−	20.1580i	1.11458	−	0.733624i
$756$	2.58429	+	4.47613i	0.0939899	+	0.162795i
$757$	4.96443	+	8.59864i	0.180435	+	0.312523i	0.942029	−	0.335532i	$-0.108916\pi$
$757$	4.96443	+	8.59864i	0.180435	+	0.312523i	−0.761594	+	0.648055i	$0.775583\pi$
$758$	−6.96506	+	12.0638i	−0.252983	+	0.438179i
$759$	9.36758	+	5.40837i	0.340022	+	0.196312i
$760$	1.04500	+	1.58765i	0.0379061	+	0.0575900i
$761$	−23.0153	−	39.8637i	−0.834305	−	1.44506i	−0.894595	−	0.446878i	$-0.852536\pi$
$761$	−23.0153	−	39.8637i	−0.834305	−	1.44506i	0.0602894	−	0.998181i	$-0.480798\pi$
$762$	−3.64640	−	6.31574i	−0.132095	−	0.228795i
$763$	23.8540			0.863573
$764$	−8.73196	−	5.04140i	−0.315911	−	0.182391i
$765$	10.4645	−	6.88783i	0.378346	−	0.249030i
$766$	12.6540			0.457206
$767$		−	12.7683i		−	0.461038i
$768$	−1.79089	+	1.03397i	−0.0646231	+	0.0373102i
$769$		−	17.4997i		−	0.631056i	−0.948916	−	0.315528i	$-0.897818\pi$
$769$		−	17.4997i		−	0.631056i	0.948916	−	0.315528i	$-0.102182\pi$
$770$	7.43560	−	14.8183i	0.267960	−	0.534015i
$771$			28.1955i			1.01544i
$772$	4.58866	−	7.94780i	0.165150	−	0.286048i
$773$	−36.3141	−	20.9660i	−1.30613	−	0.754094i	−0.324681	−	0.945824i	$-0.605257\pi$
$773$	−36.3141	−	20.9660i	−1.30613	−	0.754094i	−0.981448	+	0.191730i	$0.938590\pi$
$774$	2.15456	−	3.73180i	0.0774440	−	0.134137i
$775$	−27.9881	+	20.8666i	−1.00536	+	0.749549i
$776$	−2.26494			−0.0813067
$777$	−14.6998	+	10.7990i	−0.527353	+	0.387413i
$778$			20.1312i			0.721738i
$779$	7.51444	−	4.33846i	0.269233	−	0.155442i
$780$	−11.6036	+	23.1246i	−0.415475	+	0.827995i
$781$	24.1289	−	41.7925i	0.863400	−	1.49545i
$782$	−2.24521	+	3.88882i	−0.0802887	+	0.139064i
$783$	−11.1761			−0.399400
$784$	−2.44864	+	4.24117i	−0.0874515	+	0.151470i
$785$	−12.7574	+	0.747475i	−0.455331	+	0.0266785i
$786$	−6.02113	−	10.4289i	−0.214767	−	0.371987i
$787$			6.57778i			0.234472i	0.993104	+	0.117236i	$0.0374035\pi$
$787$			6.57778i			0.234472i	−0.993104	+	0.117236i	$0.962597\pi$
$788$		−	3.28948i		−	0.117183i
$789$	4.26342	+	7.38445i	0.151782	+	0.262893i
$790$	5.84081	−	11.6401i	0.207807	−	0.414136i
$791$		−	20.6292i		−	0.733490i
$792$	3.26314	+	5.65192i	0.115951	+	0.200832i
$793$	−4.16097	+	2.40234i	−0.147760	+	0.0853095i
$794$	−4.74950	+	2.74212i	−0.168553	+	0.0973143i
$795$	43.8714	+	22.0140i	1.55596	+	0.780755i
$796$	−14.3764	−	8.30019i	−0.509556	−	0.294192i
$797$	22.0878	+	38.2572i	0.782391	+	1.35514i	0.930545	+	0.366177i	$0.119333\pi$
$797$	22.0878	+	38.2572i	0.782391	+	1.35514i	−0.148154	+	0.988964i	$0.547333\pi$
$798$	2.20743	−	1.27446i	0.0781420	−	0.0451153i
$799$	−14.7406	+	8.51048i	−0.521485	+	0.301079i
$800$	4.96579	−	0.583910i	0.175567	−	0.0206443i
$801$	15.4631	+	8.92765i	0.546363	+	0.315443i
$802$	−15.2870	+	8.82596i	−0.539803	+	0.311655i
$803$		−	52.3401i		−	1.84704i
$804$	−22.6534			−0.798926
$805$	−1.82368	−	2.77068i	−0.0642764	−	0.0976536i
$806$			39.0665i			1.37606i
$807$	26.5442	+	15.3253i	0.934401	+	0.539477i
$808$	18.4477			0.648986
$809$	−18.4547	−	10.6548i	−0.648832	−	0.374603i	0.139177	−	0.990268i	$-0.455554\pi$
$809$	−18.4547	−	10.6548i	−0.648832	−	0.374603i	−0.788008	+	0.615664i	$0.788888\pi$
$810$	22.3840	+	11.2319i	0.786493	+	0.394650i
$811$	−16.8382	+	29.1646i	−0.591268	+	1.02411i	0.402794	+	0.915291i	$0.368039\pi$
$811$	−16.8382	+	29.1646i	−0.591268	+	1.02411i	−0.994062	+	0.108816i	$0.965294\pi$
$812$	2.27335	+	3.93756i	0.0797791	+	0.138181i
$813$		−	23.3184i		−	0.817812i
$814$	25.0653	−	18.4139i	0.878538	−	0.645407i
$815$	2.16287	+	36.9144i	0.0757621	+	1.29306i
$816$	−7.86114	+	4.53863i	−0.275195	+	0.158884i
$817$	2.48525	+	1.43486i	0.0869478	+	0.0501994i
$818$	12.4970	+	7.21513i	0.436946	+	0.252271i
$819$	8.96840	+	5.17791i	0.313381	+	0.180931i
$820$	−1.33510	−	22.7866i	−0.0466237	−	0.795742i
$821$	1.57960	−	2.73595i	0.0551286	−	0.0954855i	−0.837144	−	0.546982i	$-0.815776\pi$
$821$	1.57960	−	2.73595i	0.0551286	−	0.0954855i	0.892273	+	0.451497i	$0.149110\pi$
$822$	−1.78001			−0.0620849
$823$	−16.8000	+	9.69947i	−0.585610	+	0.338102i	−0.763360	−	0.645974i	$-0.776452\pi$
$823$	−16.8000	+	9.69947i	−0.585610	+	0.338102i	0.177750	+	0.984076i	$0.443118\pi$
$824$	−2.26780			−0.0790027
$825$	−6.17409	−	52.5067i	−0.214954	−	1.82805i
$826$	1.65454	+	2.86575i	0.0575688	+	0.0997121i
$827$	24.1617	−	41.8494i	0.840186	−	1.45524i	−0.0495511	−	0.998772i	$-0.515779\pi$
$827$	24.1617	−	41.8494i	0.840186	−	1.45524i	0.889737	−	0.456473i	$-0.150888\pi$
$828$	1.30571			0.0453766
$829$	−10.4300	+	6.02174i	−0.362247	+	0.209144i	−0.670066	−	0.742301i	$-0.733734\pi$
$829$	−10.4300	+	6.02174i	−0.362247	+	0.209144i	0.307819	+	0.951445i	$0.400401\pi$
$830$	−0.0918906	−	0.139607i	−0.00318957	−	0.00484584i
$831$	43.1202	−	24.8954i	1.49582	−	0.863613i
$832$	2.79761	−	4.84561i	0.0969898	−	0.167991i
$833$	−10.7484	+	18.6167i	−0.372409	+	0.645032i
$834$	−0.266673	+	0.153964i	−0.00923413	+	0.00533133i
$835$	−21.8709	+	14.3956i	−0.756874	+	0.498180i
$836$	−3.76398	+	2.17313i	−0.130180	+	0.0751594i
$837$	24.8868			0.860213
$838$	3.15432	−	5.46344i	0.108964	−	0.188731i
$839$	−16.4354	−	28.4670i	−0.567413	−	0.982788i	−0.996821	−	0.0796775i	$-0.974611\pi$
$839$	−16.4354	−	28.4670i	−0.567413	−	0.982788i	0.429408	−	0.903111i	$-0.358722\pi$
$840$	−0.392196	−	6.69374i	−0.0135320	−	0.230956i
$841$	19.1686			0.660988
$842$	−10.1406	+	5.85470i	−0.349470	+	0.201766i
$843$	52.9042			1.82212
$844$	−6.96520	+	12.0641i	−0.239752	+	0.415263i
$845$	−2.39432	−	40.8647i	−0.0823671	−	1.40579i
$846$	4.28621	+	2.47465i	0.147363	+	0.0850801i
$847$	19.0183	+	10.9802i	0.653476	+	0.377284i
$848$	−9.19294	−	5.30755i	−0.315687	−	0.182262i
$849$	−56.4383	+	32.5847i	−1.93696	+	1.11830i
$850$	21.7974	−	2.56309i	0.747646	−	0.0879132i
$851$	−0.683088	−	6.18498i	−0.0234159	−	0.212018i
$852$		−	19.5171i		−	0.668646i
$853$	−23.7304	−	41.1023i	−0.812515	−	1.40732i	−0.911099	−	0.412188i	$-0.864765\pi$
$853$	−23.7304	−	41.1023i	−0.812515	−	1.40732i	0.0985844	−	0.995129i	$-0.468569\pi$
$854$	0.622596	−	1.07837i	0.0213048	−	0.0369010i
$855$	1.08803	−	2.16832i	0.0372099	−	0.0741551i
$856$	3.36674	+	1.94379i	0.115073	+	0.0664373i
$857$	29.2935			1.00065			0.500323	−	0.865839i	$-0.333215\pi$
$857$	29.2935			1.00065			0.500323	+	0.865839i	$0.333215\pi$
$858$	−51.2360	−	29.5811i	−1.74917	−	1.00988i
$859$		−	14.2975i		−	0.487823i	−0.969798	−	0.243911i	$-0.921569\pi$
$859$		−	14.2975i		−	0.487823i	0.969798	−	0.243911i	$-0.0784306\pi$
$860$	6.30576	−	4.15050i	0.215025	−	0.141531i
$861$	−30.6102			−1.04319
$862$			20.2104i			0.688368i
$863$	33.5767	−	19.3855i	1.14296	−	0.659890i	0.195800	−	0.980644i	$-0.437270\pi$
$863$	33.5767	−	19.3855i	1.14296	−	0.659890i	0.947163	+	0.320754i	$0.103936\pi$
$864$	−3.08683	−	1.78218i	−0.105016	−	0.0606310i
$865$	16.7688	−	0.982506i	0.570155	−	0.0334062i
$866$	2.97088	−	1.71524i	0.100955	−	0.0582862i
$867$	−4.06159	+	2.34496i	−0.137939	+	0.0796389i
$868$	−5.06229	−	8.76815i	−0.171825	−	0.297610i
$869$	25.7903	+	14.8900i	0.874875	+	0.505109i
$870$	12.9588	+	6.50251i	0.439344	+	0.220456i
$871$	53.0817	−	30.6468i	1.79861	−	1.03843i
$872$	−14.2463	+	8.22510i	−0.482440	+	0.278537i
$873$	1.44545	+	2.50360i	0.0489211	+	0.0847339i
$874$			0.869557i			0.0294132i
$875$	−5.52908	+	15.2404i	−0.186917	+	0.515218i
$876$	−10.5841	−	18.3322i	−0.357603	−	0.619387i
$877$			46.3476i			1.56505i	0.622622	+	0.782523i	$0.286068\pi$
$877$			46.3476i			1.56505i	−0.622622	+	0.782523i	$0.713932\pi$
$878$		−	12.2841i		−	0.414567i
$879$	−22.7478	−	39.4004i	−0.767265	−	1.32894i
$880$	0.668751	+	11.4138i	0.0225436	+	0.384759i
$881$	−1.33327	+	2.30929i	−0.0449190	+	0.0778021i	−0.887611	−	0.460594i	$-0.847636\pi$
$881$	−1.33327	+	2.30929i	−0.0449190	+	0.0778021i	0.842692	+	0.538396i	$0.180970\pi$
$882$	6.25075			0.210474
$883$	−28.7929	+	49.8708i	−0.968960	+	1.67829i	−0.270382	+	0.962753i	$0.587150\pi$
$883$	−28.7929	+	49.8708i	−0.968960	+	1.67829i	−0.698578	+	0.715534i	$0.746183\pi$
$884$	12.2802	−	21.2699i	0.413028	−	0.715385i
$885$	9.43136	+	4.73251i	0.317032	+	0.159082i
$886$	14.6870	−	8.47955i	0.493420	−	0.284876i
$887$			35.8043i			1.20219i	0.799177	+	0.601095i	$0.205269\pi$
$887$			35.8043i			1.20219i	−0.799177	+	0.601095i	$0.794731\pi$
$888$	5.05554	−	11.5181i	0.169653	−	0.386523i
$889$	−5.11383			−0.171512
$890$	17.1981	+	26.1286i	0.576480	+	0.875833i
$891$	−28.6336	+	49.5949i	−0.959263	+	1.66149i
$892$	24.2817	+	14.0191i	0.813013	+	0.469393i
$893$	−1.64803	+	2.85447i	−0.0551491	+	0.0955211i
$894$		−	37.1560i		−	1.24268i
$895$	−26.1384	+	52.0909i	−0.873711	+	1.74121i
$896$			1.45007i			0.0484436i
$897$	−10.2508	+	5.91828i	−0.342263	+	0.197606i
$898$		−	14.0094i		−	0.467500i
$899$	21.8924			0.730153
$900$	−3.81453	−	5.11638i	−0.127151	−	0.170546i
$901$	−40.3526	−	23.2976i	−1.34434	−	0.776156i
$902$	52.1948			1.73790
$903$	−5.06185	−	8.76738i	−0.168448	−	0.291760i
$904$	7.11315	+	12.3203i	0.236580	+	0.409769i
$905$	−29.4939	+	19.4131i	−0.980410	+	0.645313i
$906$	29.3648	+	16.9538i	0.975579	+	0.563251i
$907$	−3.92642	+	6.80076i	−0.130375	+	0.225816i	−0.923821	−	0.382825i	$-0.874951\pi$
$907$	−3.92642	+	6.80076i	−0.130375	+	0.225816i	0.793446	+	0.608640i	$0.208285\pi$
$908$	−2.97783	−	5.15775i	−0.0988226	−	0.171166i
$909$	−11.7730	−	20.3915i	−0.390486	−	0.676342i
$910$	9.97463	+	15.1542i	0.330656	+	0.502358i
$911$		−	22.9123i		−	0.759120i	−0.925167	−	0.379560i	$-0.876075\pi$
$911$		−	22.9123i		−	0.759120i	0.925167	−	0.379560i	$-0.123925\pi$
$912$	−0.878892	+	1.52228i	−0.0291030	+	0.0504079i
$913$	0.330980	−	0.191091i	0.0109538	−	0.00632420i
$914$	21.5775			0.713719
$915$	−0.232252	−	3.96392i	−0.00767801	−	0.131043i
$916$	−1.81631	−	3.14593i	−0.0600124	−	0.103945i
$917$	−8.44424			−0.278853
$918$	−13.5497	−	7.82292i	−0.447207	−	0.258195i
$919$		−	46.5712i		−	1.53624i	−0.640304	−	0.768121i	$-0.721192\pi$
$919$		−	46.5712i		−	1.53624i	0.640304	−	0.768121i	$-0.278808\pi$
$920$	2.04451	+	1.02590i	0.0674056	+	0.0338231i
$921$	16.1044	−	27.8937i	0.530659	−	0.919129i
$922$	12.7119	+	7.33924i	0.418645	+	0.241705i
$923$	26.4038	+	45.7327i	0.869092	+	1.50531i
$924$	15.3326			0.504406
$925$	−22.2401	+	20.7456i	−0.731249	+	0.682111i
$926$	−12.2801			−0.403550
$927$	1.44728	+	2.50676i	0.0475348	+	0.0823328i
$928$	−2.71542	−	1.56775i	−0.0891381	−	0.0514639i
$929$	11.3707	−	19.6947i	0.373061	−	0.646161i	−0.616973	−	0.786984i	$-0.711641\pi$
$929$	11.3707	−	19.6947i	0.373061	−	0.646161i	0.990035	+	0.140823i	$0.0449747\pi$
$930$	−28.8565	−	14.4798i	−0.946243	−	0.474810i
$931$			4.16278i			0.136429i
$932$	18.3579	+	10.5989i	0.601331	+	0.347179i
$933$	37.8529			1.23925
$934$	−12.0793	−	20.9220i	−0.395247	−	0.684588i
$935$	2.93550	+	50.1011i	0.0960010	+	1.63848i
$936$	−7.14158			−0.233430
$937$	0.597945	−	0.345224i	0.0195340	−	0.0112780i	−0.490201	−	0.871609i	$-0.663077\pi$
$937$	0.597945	−	0.345224i	0.0195340	−	0.0112780i	0.509735	+	0.860331i	$0.329743\pi$
$938$	−7.94249	+	13.7568i	−0.259332	+	0.449176i
$939$		−	11.1869i		−	0.365070i
$940$	4.76711	+	7.24257i	0.155486	+	0.236227i
$941$	17.0364	+	29.5080i	0.555372	+	0.961932i	0.997875	+	0.0651647i	$0.0207573\pi$
$941$	17.0364	+	29.5080i	0.555372	+	0.961932i	−0.442503	+	0.896767i	$0.645909\pi$
$942$	−5.90920	−	10.2350i	−0.192532	−	0.333475i
$943$	5.22130	−	9.04356i	0.170029	−	0.294499i
$944$	−1.97628	−	1.14100i	−0.0643223	−	0.0371365i
$945$	9.65379	−	6.35420i	0.314038	−	0.206702i
$946$	8.63118	+	14.9496i	0.280624	+	0.486055i
$947$	4.22773	+	7.32264i	0.137383	+	0.237954i	0.926505	−	0.376282i	$-0.122798\pi$
$947$	4.22773	+	7.32264i	0.137383	+	0.237954i	−0.789122	+	0.614236i	$0.789464\pi$
$948$	12.0441			0.391174
$949$	49.6014	+	28.6374i	1.61013	+	0.929609i
$950$	3.40733	−	2.54034i	0.110548	−	0.0824195i
$951$	−49.4571			−1.60376
$952$			6.36513i			0.206295i
$953$	31.5720	−	18.2281i	1.02272	−	0.590466i	0.107827	−	0.994170i	$-0.465611\pi$
$953$	31.5720	−	18.2281i	1.02272	−	0.590466i	0.914890	+	0.403704i	$0.132277\pi$
$954$			13.5488i			0.438658i
$955$	−10.1116	+	20.1512i	−0.327202	+	0.652077i
$956$		−	20.0804i		−	0.649447i
$957$	−16.5769	+	28.7120i	−0.535855	+	0.928128i
$958$	−1.85947	−	1.07357i	−0.0600769	−	0.0346854i
$959$	−0.624086	+	1.08095i	−0.0201528	+	0.0349057i
$960$	2.54230	+	3.86246i	0.0820523	+	0.124660i
$961$	−17.7499			−0.572578
$962$	3.73615	+	33.8288i	0.120458	+	1.09068i
$963$		−	4.96198i		−	0.159898i
$964$	−13.9154	+	8.03405i	−0.448184	+	0.258759i
$965$	−18.3415	−	9.20350i	−0.590435	−	0.296271i
$966$	1.53380	−	2.65662i	0.0493491	−	0.0854752i
$967$	25.3622	−	43.9286i	0.815592	−	1.41265i	−0.0933095	−	0.995637i	$-0.529745\pi$
$967$	25.3622	−	43.9286i	0.815592	−	1.41265i	0.908902	−	0.417010i	$-0.136922\pi$
$968$	−15.1443			−0.486758
$969$	−3.85792	+	6.68211i	−0.123934	+	0.214660i
$970$	0.296232	+	5.05589i	0.00951144	+	0.162335i
$971$	14.0719	+	24.3732i	0.451587	+	0.782172i	0.998485	−	0.0550273i	$-0.0175246\pi$
$971$	14.0719	+	24.3732i	0.451587	+	0.782172i	−0.546897	+	0.837200i	$0.684191\pi$
$972$			12.4678i			0.399905i
$973$			0.215924i			0.00692220i
$974$	−19.7688	−	34.2406i	−0.633434	−	1.09714i
$975$	53.1374	+	22.8775i	1.70176	+	0.732667i
$976$			0.858710i			0.0274866i
$977$	4.63887	+	8.03476i	0.148411	+	0.257055i	0.930640	−	0.365936i	$-0.119251\pi$
$977$	4.63887	+	8.03476i	0.148411	+	0.257055i	−0.782230	+	0.622990i	$0.785918\pi$
$978$	−29.6158	+	17.0987i	−0.947009	+	0.546756i
$979$	−61.9455	+	35.7643i	−1.97979	+	1.14303i
$980$	9.78757	+	4.91125i	0.312653	+	0.156884i
$981$	18.1835	+	10.4983i	0.580556	+	0.335184i
$982$	−18.6424	−	32.2897i	−0.594904	−	1.03040i
$983$	19.9482	−	11.5171i	0.636250	−	0.367339i	−0.146919	−	0.989149i	$-0.546936\pi$
$983$	19.9482	−	11.5171i	0.636250	−	0.367339i	0.783169	+	0.621809i	$0.213602\pi$
$984$	18.2813	−	10.5547i	0.582786	−	0.336472i
$985$	−7.34291	+	0.430232i	−0.233965	+	0.0137083i
$986$	−11.9194	−	6.88167i	−0.379591	−	0.219157i
$987$	10.0699	−	5.81386i	0.320528	−	0.185057i
$988$		−	4.75604i		−	0.151310i
$989$	3.45368			0.109821
$990$	12.1897	−	8.02332i	0.387413	−	0.254998i
$991$			54.3969i			1.72797i	0.503514	+	0.863987i	$0.332040\pi$
$991$			54.3969i			1.72797i	−0.503514	+	0.863987i	$0.667960\pi$
$992$	6.04669	+	3.49106i	0.191983	+	0.110841i
$993$	−1.28606			−0.0408119
$994$	−11.8522	−	6.84288i	−0.375929	−	0.217043i
$995$	−16.6477	+	33.1770i	−0.527768	+	1.05178i
$996$	0.0772841	−	0.133860i	0.00244884	−	0.00424151i
$997$	−4.65769	−	8.06736i	−0.147511	−	0.255496i	0.782796	−	0.622278i	$-0.213793\pi$
$997$	−4.65769	−	8.06736i	−0.147511	−	0.255496i	−0.930307	+	0.366782i	$0.880459\pi$
$998$			2.27341i			0.0719635i
$999$	21.5501	−	2.38006i	0.681816	−	0.0753018i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.m.d.159.7	yes	16
5.4	even	2		370.2.m.c.159.2	✓	16
37.27	even	6		370.2.m.c.249.2	yes	16
185.64	even	6	inner	370.2.m.d.249.7	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.m.c.159.2	✓	16	5.4	even	2
370.2.m.c.249.2	yes	16	37.27	even	6
370.2.m.d.159.7	yes	16	1.1	even	1	trivial
370.2.m.d.249.7	yes	16	185.64	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(1.79089 + 1.03397i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.99857 + 1.00285i) q^{5} +2.06794i q^{6} +(1.25580 + 0.725037i) q^{7} -1.00000 q^{8} +(0.638185 + 1.10537i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(1.79089 + 1.03397i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.99857 + 1.00285i) q^{5} +2.06794i q^{6} +(1.25580 + 0.725037i) q^{7} -1.00000 q^{8} +(0.638185 + 1.10537i) q^{9} +(0.130790 + 2.23224i) q^{10} -5.11315 q^{11} +(-1.79089 + 1.03397i) q^{12} +(2.79761 - 4.84561i) q^{13} +1.45007i q^{14} +(2.54230 + 3.86246i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.19476 - 3.80144i) q^{17} +(-0.638185 + 1.10537i) q^{18} +(-0.736136 - 0.425009i) q^{19} +(-1.86778 + 1.22939i) q^{20} +(1.49933 + 2.59692i) q^{21} +(-2.55658 - 4.42812i) q^{22} -1.02299 q^{23} +(-1.79089 - 1.03397i) q^{24} +(2.98858 + 4.00854i) q^{25} +5.59523 q^{26} -3.56436i q^{27} +(-1.25580 + 0.725037i) q^{28} -3.13550i q^{29} +(-2.07384 + 4.13292i) q^{30} +6.98211i q^{31} +(0.500000 - 0.866025i) q^{32} +(-9.15708 - 5.28684i) q^{33} +(2.19476 - 3.80144i) q^{34} +(1.78270 + 2.70842i) q^{35} -1.27637 q^{36} +(0.667738 + 6.04600i) q^{37} -0.850017i q^{38} +(10.0204 - 5.78529i) q^{39} +(-1.99857 - 1.00285i) q^{40} +(-5.10397 + 8.84034i) q^{41} +(-1.49933 + 2.59692i) q^{42} -3.37607 q^{43} +(2.55658 - 4.42812i) q^{44} +(0.166937 + 2.84916i) q^{45} +(-0.511494 - 0.885933i) q^{46} -3.87763i q^{47} -2.06794i q^{48} +(-2.44864 - 4.24117i) q^{49} +(-1.97721 + 4.59245i) q^{50} -9.07727i q^{51} +(2.79761 + 4.84561i) q^{52} +(9.19294 - 5.30755i) q^{53} +(3.08683 - 1.78218i) q^{54} +(-10.2190 - 5.12774i) q^{55} +(-1.25580 - 0.725037i) q^{56} +(-0.878892 - 1.52228i) q^{57} +(2.71542 - 1.56775i) q^{58} +(1.97628 - 1.14100i) q^{59} +(-4.61613 + 0.270466i) q^{60} +(-0.743664 - 0.429355i) q^{61} +(-6.04669 + 3.49106i) q^{62} +1.85083i q^{63} +1.00000 q^{64} +(10.4507 - 6.87870i) q^{65} -10.5737i q^{66} +(9.48697 + 5.47730i) q^{67} +4.38952 q^{68} +(-1.83205 - 1.05774i) q^{69} +(-1.45421 + 2.89808i) q^{70} +(-4.71899 + 8.17352i) q^{71} +(-0.638185 - 1.10537i) q^{72} +10.2364i q^{73} +(-4.90212 + 3.60128i) q^{74} +(1.20749 + 10.2689i) q^{75} +(0.736136 - 0.425009i) q^{76} +(-6.42110 - 3.70723i) q^{77} +(10.0204 + 5.78529i) q^{78} +(-5.04391 - 2.91210i) q^{79} +(-0.130790 - 2.23224i) q^{80} +(5.59999 - 9.69948i) q^{81} -10.2079 q^{82} +(-0.0647311 + 0.0373725i) q^{83} -2.99866 q^{84} +(-0.574107 - 9.79847i) q^{85} +(-1.68804 - 2.92376i) q^{86} +(3.24201 - 5.61533i) q^{87} +5.11315 q^{88} +(12.1149 - 6.99456i) q^{89} +(-2.38398 + 1.56915i) q^{90} +(7.02649 - 4.05675i) q^{91} +(0.511494 - 0.885933i) q^{92} +(-7.21929 + 12.5042i) q^{93} +(3.35813 - 1.93882i) q^{94} +(-1.04500 - 1.58765i) q^{95} +(1.79089 - 1.03397i) q^{96} +2.26494 q^{97} +(2.44864 - 4.24117i) q^{98} +(-3.26314 - 5.65192i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{2} - 3 q^{3} - 8 q^{4} - 12 q^{7} - 16 q^{8} + 13 q^{9}+O(q^{10}) \) 16 * q + 8 * q^2 - 3 * q^3 - 8 * q^4 - 12 * q^7 - 16 * q^8 + 13 * q^9	\( 16 q + 8 q^{2} - 3 q^{3} - 8 q^{4} - 12 q^{7} - 16 q^{8} + 13 q^{9} - 6 q^{10} - 6 q^{11} + 3 q^{12} - 6 q^{13} + 9 q^{15} - 8 q^{16} - 13 q^{18} - 3 q^{19} - 6 q^{20} - 6 q^{21} - 3 q^{22} - 22 q^{23} + 3 q^{24} - 6 q^{25} - 12 q^{26} + 12 q^{28} - 9 q^{30} + 8 q^{32} + 6 q^{33} + 18 q^{35} - 26 q^{36} + 16 q^{37} + 15 q^{39} + 7 q^{41} + 6 q^{42} - 22 q^{43} + 3 q^{44} + 4 q^{45} - 11 q^{46} + 4 q^{49} + 6 q^{50} - 6 q^{52} + 3 q^{53} + 9 q^{54} - 35 q^{55} + 12 q^{56} + 18 q^{57} + 36 q^{58} + 15 q^{59} - 18 q^{60} + 12 q^{61} - 33 q^{62} + 16 q^{64} + 46 q^{65} + 24 q^{67} + 42 q^{69} + 12 q^{70} - 4 q^{71} - 13 q^{72} + 5 q^{74} - 10 q^{75} + 3 q^{76} - 24 q^{77} + 15 q^{78} + 6 q^{80} + 10 q^{81} + 14 q^{82} + 6 q^{83} + 12 q^{84} - 26 q^{85} - 11 q^{86} + 50 q^{87} + 6 q^{88} + 9 q^{89} - q^{90} - 24 q^{91} + 11 q^{92} - 25 q^{93} - 27 q^{94} - 53 q^{95} - 3 q^{96} + 68 q^{97} - 4 q^{98} + 37 q^{99}+O(q^{100}) \) 16 * q + 8 * q^2 - 3 * q^3 - 8 * q^4 - 12 * q^7 - 16 * q^8 + 13 * q^9 - 6 * q^10 - 6 * q^11 + 3 * q^12 - 6 * q^13 + 9 * q^15 - 8 * q^16 - 13 * q^18 - 3 * q^19 - 6 * q^20 - 6 * q^21 - 3 * q^22 - 22 * q^23 + 3 * q^24 - 6 * q^25 - 12 * q^26 + 12 * q^28 - 9 * q^30 + 8 * q^32 + 6 * q^33 + 18 * q^35 - 26 * q^36 + 16 * q^37 + 15 * q^39 + 7 * q^41 + 6 * q^42 - 22 * q^43 + 3 * q^44 + 4 * q^45 - 11 * q^46 + 4 * q^49 + 6 * q^50 - 6 * q^52 + 3 * q^53 + 9 * q^54 - 35 * q^55 + 12 * q^56 + 18 * q^57 + 36 * q^58 + 15 * q^59 - 18 * q^60 + 12 * q^61 - 33 * q^62 + 16 * q^64 + 46 * q^65 + 24 * q^67 + 42 * q^69 + 12 * q^70 - 4 * q^71 - 13 * q^72 + 5 * q^74 - 10 * q^75 + 3 * q^76 - 24 * q^77 + 15 * q^78 + 6 * q^80 + 10 * q^81 + 14 * q^82 + 6 * q^83 + 12 * q^84 - 26 * q^85 - 11 * q^86 + 50 * q^87 + 6 * q^88 + 9 * q^89 - q^90 - 24 * q^91 + 11 * q^92 - 25 * q^93 - 27 * q^94 - 53 * q^95 - 3 * q^96 + 68 * q^97 - 4 * q^98 + 37 * q^99

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