LMFDB - Embedded newform 112.3.x.a.101.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [112,3,Mod(5,112)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("112.5"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(112, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 3, 10])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 112 = 2^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	112.x (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$3.05177896084$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$30$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			101.4
Character	$\chi$	$=$	112.101
Dual form			112.3.x.a.61.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.92758 - 0.533333i) q^{2} +(1.33491 - 0.357687i) q^{3} +(3.43111 + 2.05608i) q^{4} +(3.10820 + 0.832839i) q^{5} +(-2.76390 - 0.0224802i) q^{6} +(0.367625 + 6.99034i) q^{7} +(-5.51716 - 5.79318i) q^{8} +(-6.14019 + 3.54504i) q^{9} +(-5.54711 - 3.26307i) q^{10} +(13.7381 - 3.68111i) q^{11} +(5.31565 + 1.51741i) q^{12} +(5.71174 + 5.71174i) q^{13} +(3.01955 - 13.6705i) q^{14} +4.44705 q^{15} +(7.54505 + 14.1093i) q^{16} +(14.2404 + 8.22168i) q^{17} +(13.7264 - 3.55858i) q^{18} +(3.02729 - 11.2980i) q^{19} +(8.95219 + 9.24827i) q^{20} +(2.99110 + 9.19996i) q^{21} +(-28.4445 - 0.231353i) q^{22} +(23.3127 - 13.4596i) q^{23} +(-9.43704 - 5.75994i) q^{24} +(-12.6834 - 7.32274i) q^{25} +(-7.96356 - 14.0561i) q^{26} +(-15.7235 + 15.7235i) q^{27} +(-13.1114 + 24.7405i) q^{28} +(-3.82071 + 3.82071i) q^{29} +(-8.57203 - 2.37176i) q^{30} +(-7.03276 - 4.06036i) q^{31} +(-7.01872 - 31.2208i) q^{32} +(17.0224 - 9.82788i) q^{33} +(-23.0645 - 23.4428i) q^{34} +(-4.67918 + 22.0335i) q^{35} +(-28.3566 - 0.461306i) q^{36} +(-8.14184 + 30.3858i) q^{37} +(-11.8609 + 20.1632i) q^{38} +(9.66765 + 5.58162i) q^{39} +(-12.3236 - 22.6013i) q^{40} -76.1736 q^{41} +(-0.858936 - 19.3289i) q^{42} +(-42.8805 - 42.8805i) q^{43} +(54.7056 + 15.6163i) q^{44} +(-22.0374 + 5.90490i) q^{45} +(-52.1155 + 13.5110i) q^{46} +(75.7287 - 43.7220i) q^{47} +(15.1187 + 16.1358i) q^{48} +(-48.7297 + 5.13965i) q^{49} +(20.5427 + 20.8796i) q^{50} +(21.9503 + 5.88158i) q^{51} +(7.85381 + 31.3414i) q^{52} +(4.83847 - 1.29646i) q^{53} +(38.6942 - 21.9225i) q^{54} +45.7665 q^{55} +(38.4681 - 40.6965i) q^{56} -16.1646i q^{57} +(9.40243 - 5.32700i) q^{58} +(-13.3885 - 49.9666i) q^{59} +(15.2583 + 9.14350i) q^{60} +(-10.6701 + 39.8212i) q^{61} +(11.3907 + 11.5775i) q^{62} +(-27.0383 - 41.6188i) q^{63} +(-3.12195 + 63.9238i) q^{64} +(12.9963 + 22.5102i) q^{65} +(-38.0535 + 9.86540i) q^{66} +(20.5587 + 76.7262i) q^{67} +(31.9558 + 57.4889i) q^{68} +(26.3060 - 26.3060i) q^{69} +(20.7707 - 39.9758i) q^{70} +8.01424i q^{71} +(54.4135 + 16.0127i) q^{72} +(11.0908 - 19.2098i) q^{73} +(31.8998 - 54.2286i) q^{74} +(-19.5504 - 5.23850i) q^{75} +(33.6166 - 32.5403i) q^{76} +(30.7827 + 94.6807i) q^{77} +(-15.6583 - 15.9151i) q^{78} +(-27.0689 - 46.8846i) q^{79} +(11.7007 + 50.1383i) q^{80} +(16.5400 - 28.6482i) q^{81} +(146.830 + 40.6259i) q^{82} +(-36.2707 - 36.2707i) q^{83} +(-8.65307 + 37.7160i) q^{84} +(37.4145 + 37.4145i) q^{85} +(59.7859 + 105.525i) q^{86} +(-3.73367 + 6.46691i) q^{87} +(-97.1206 - 59.2780i) q^{88} +(-70.7447 - 122.533i) q^{89} +(45.6280 + 0.371115i) q^{90} +(-37.8272 + 42.0268i) q^{91} +(107.663 + 1.75146i) q^{92} +(-10.8404 - 2.90468i) q^{93} +(-169.291 + 43.8889i) q^{94} +(18.8188 - 32.5952i) q^{95} +(-20.5366 - 39.1663i) q^{96} -102.304i q^{97} +(96.6714 + 16.0821i) q^{98} +(-71.3049 + 71.3049i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 2 q^{2} - 6 q^{3} + 4 q^{4} - 6 q^{5} + 4 q^{8} - 60 q^{10} - 18 q^{11} - 6 q^{12} - 28 q^{14} - 16 q^{15} + 8 q^{16} - 12 q^{17} + 2 q^{18} - 6 q^{19} + 14 q^{21} - 20 q^{22} - 6 q^{24} - 6 q^{26}+ \cdots - 848 q^{99}+O(q^{100}) $ 120 * q - 2 * q^2 - 6 * q^3 + 4 * q^4 - 6 * q^5 + 4 * q^8 - 60 * q^10 - 18 * q^11 - 6 * q^12 - 28 * q^14 - 16 * q^15 + 8 * q^16 - 12 * q^17 + 2 * q^18 - 6 * q^19 + 14 * q^21 - 20 * q^22 - 6 * q^24 - 6 * q^26 - 6 * q^28 + 24 * q^29 + 10 * q^30 - 12 * q^31 - 92 * q^32 - 12 * q^33 + 94 * q^35 + 128 * q^36 + 46 * q^37 - 6 * q^38 - 66 * q^40 - 78 * q^42 + 88 * q^43 - 182 * q^44 - 60 * q^45 - 108 * q^46 - 12 * q^47 - 8 * q^49 - 8 * q^50 - 118 * q^51 - 564 * q^52 - 82 * q^53 - 306 * q^54 + 400 * q^56 + 346 * q^58 - 198 * q^59 - 186 * q^60 - 6 * q^61 - 204 * q^63 + 16 * q^64 - 4 * q^65 + 870 * q^66 + 222 * q^67 + 384 * q^68 + 556 * q^70 - 52 * q^72 + 126 * q^74 - 156 * q^75 - 102 * q^77 - 28 * q^78 - 4 * q^79 + 300 * q^80 + 248 * q^81 - 810 * q^82 - 288 * q^84 - 108 * q^85 - 196 * q^86 + 366 * q^88 + 88 * q^91 + 172 * q^92 - 38 * q^93 + 606 * q^94 - 388 * q^95 + 996 * q^96 - 848 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/112\mathbb{Z}\right)^\times$.

$n$	$15$	$17$	$85$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.92758	−	0.533333i	−0.963789	−	0.266667i
$2$	−1.92758	−	0.533333i	−0.963789	−	0.266667i
$3$	1.33491	−	0.357687i	0.444969	−	0.119229i	−0.0293755	−	0.999568i	$-0.509352\pi$
$3$	1.33491	−	0.357687i	0.444969	−	0.119229i	0.474344	+	0.880339i	$0.342685\pi$
$4$	3.43111	+	2.05608i	0.857778	+	0.514021i
$5$	3.10820	+	0.832839i	0.621640	+	0.166568i	0.555873	−	0.831267i	$-0.312384\pi$
$5$	3.10820	+	0.832839i	0.621640	+	0.166568i	0.0657665	+	0.997835i	$0.479051\pi$
$6$	−2.76390	−	0.0224802i	−0.460650	−	0.00374669i
$7$	0.367625	+	6.99034i	0.0525179	+	0.998620i
$7$	0.367625	+	6.99034i	0.0525179	+	0.998620i
$8$	−5.51716	−	5.79318i	−0.689645	−	0.724148i
$9$	−6.14019	+	3.54504i	−0.682244	+	0.393894i
$10$	−5.54711	−	3.26307i	−0.554711	−	0.326307i
$11$	13.7381	−	3.68111i	1.24892	−	0.334646i	0.426999	−	0.904252i	$-0.359571\pi$
$11$	13.7381	−	3.68111i	1.24892	−	0.334646i	0.821918	+	0.569605i	$0.192904\pi$
$12$	5.31565	+	1.51741i	0.442971	+	0.126451i
$13$	5.71174	+	5.71174i	0.439365	+	0.439365i	0.891798	−	0.452434i	$-0.149444\pi$
$13$	5.71174	+	5.71174i	0.439365	+	0.439365i	−0.452434	+	0.891798i	$0.649444\pi$
$14$	3.01955	−	13.6705i	0.215682	−	0.976464i
$15$	4.44705			0.296470
$16$	7.54505	+	14.1093i	0.471566	+	0.881831i
$17$	14.2404	+	8.22168i	0.837669	+	0.483628i	0.856471	−	0.516195i	$-0.172652\pi$
$17$	14.2404	+	8.22168i	0.837669	+	0.483628i	−0.0188025	+	0.999823i	$0.505985\pi$
$18$	13.7264	−	3.55858i	0.762577	−	0.197699i
$19$	3.02729	−	11.2980i	0.159331	−	0.594632i	−0.839364	−	0.543569i	$-0.817073\pi$
$19$	3.02729	−	11.2980i	0.159331	−	0.594632i	0.998695	−	0.0510625i	$-0.0162608\pi$
$20$	8.95219	+	9.24827i	0.447609	+	0.462414i
$21$	2.99110	+	9.19996i	0.142433	+	0.438093i
$22$	−28.4445	−	0.231353i	−1.29293	−	0.0105160i
$23$	23.3127	−	13.4596i	1.01360	−	0.585200i	0.101353	−	0.994850i	$-0.467683\pi$
$23$	23.3127	−	13.4596i	1.01360	−	0.585200i	0.912243	+	0.409651i	$0.134349\pi$
$24$	−9.43704	−	5.75994i	−0.393210	−	0.239998i
$25$	−12.6834	−	7.32274i	−0.507335	−	0.292910i
$26$	−7.96356	−	14.0561i	−0.306291	−	0.540618i
$27$	−15.7235	+	15.7235i	−0.582353	+	0.582353i
$28$	−13.1114	+	24.7405i	−0.468263	+	0.883589i
$29$	−3.82071	+	3.82071i	−0.131749	+	0.131749i	−0.769906	−	0.638157i	$-0.779697\pi$
$29$	−3.82071	+	3.82071i	−0.131749	+	0.131749i	0.638157	+	0.769906i	$0.279697\pi$
$30$	−8.57203	−	2.37176i	−0.285734	−	0.0790586i
$31$	−7.03276	−	4.06036i	−0.226863	−	0.130980i	0.382261	−	0.924054i	$-0.375146\pi$
$31$	−7.03276	−	4.06036i	−0.226863	−	0.130980i	−0.609124	+	0.793075i	$0.708479\pi$
$32$	−7.01872	−	31.2208i	−0.219335	−	0.975650i
$33$	17.0224	−	9.82788i	0.515830	−	0.297815i
$34$	−23.0645	−	23.4428i	−0.678368	−	0.689494i
$35$	−4.67918	+	22.0335i	−0.133691	+	0.629529i
$36$	−28.3566	−	0.461306i	−0.787683	−	0.0128141i
$37$	−8.14184	+	30.3858i	−0.220050	+	0.821237i	0.764278	+	0.644887i	$0.223096\pi$
$37$	−8.14184	+	30.3858i	−0.220050	+	0.821237i	−0.984328	+	0.176350i	$0.943571\pi$
$38$	−11.8609	+	20.1632i	−0.312130	+	0.530611i
$39$	9.66765	+	5.58162i	0.247889	+	0.143119i
$40$	−12.3236	−	22.6013i	−0.308091	−	0.565032i
$41$	−76.1736			−1.85789			−0.928946	−	0.370215i	$-0.879284\pi$
$41$	−76.1736			−1.85789			−0.928946	+	0.370215i	$0.879284\pi$
$42$	−0.858936	−	19.3289i	−0.0204509	−	0.460212i
$43$	−42.8805	−	42.8805i	−0.997220	−	0.997220i	0.00277584	−	0.999996i	$-0.499116\pi$
$43$	−42.8805	−	42.8805i	−0.997220	−	0.997220i	−0.999996	+	0.00277584i	$0.999116\pi$
$44$	54.7056	+	15.6163i	1.24331	+	0.354917i
$45$	−22.0374	+	5.90490i	−0.489720	+	0.131220i
$46$	−52.1155	+	13.5110i	−1.13295	+	0.293717i
$47$	75.7287	−	43.7220i	1.61125	−	0.930255i	0.622168	−	0.782884i	$-0.286252\pi$
$47$	75.7287	−	43.7220i	1.61125	−	0.930255i	0.989081	−	0.147372i	$-0.0470813\pi$
$48$	15.1187	+	16.1358i	0.314972	+	0.336163i
$49$	−48.7297	+	5.13965i	−0.994484	+	0.104891i
$50$	20.5427	+	20.8796i	0.410854	+	0.417592i
$51$	21.9503	+	5.88158i	0.430399	+	0.115325i
$52$	7.85381	+	31.3414i	0.151035	+	0.602720i
$53$	4.83847	−	1.29646i	0.0912919	−	0.0244616i	−0.212884	−	0.977077i	$-0.568286\pi$
$53$	4.83847	−	1.29646i	0.0912919	−	0.0244616i	0.304176	+	0.952616i	$0.401619\pi$
$54$	38.6942	−	21.9225i	0.716560	−	0.405972i
$55$	45.7665			0.832118
$56$	38.4681	−	40.6965i	0.686930	−	0.726724i
$57$		−	16.1646i		−	0.283589i
$58$	9.40243	−	5.32700i	0.162111	−	0.0918449i
$59$	−13.3885	−	49.9666i	−0.226924	−	0.846891i	−0.981625	−	0.190822i	$-0.938885\pi$
$59$	−13.3885	−	49.9666i	−0.226924	−	0.846891i	0.754701	−	0.656069i	$-0.227782\pi$
$60$	15.2583	+	9.14350i	0.254305	+	0.152392i
$61$	−10.6701	+	39.8212i	−0.174919	+	0.652807i	0.821646	+	0.569998i	$0.193056\pi$
$61$	−10.6701	+	39.8212i	−0.174919	+	0.652807i	−0.996565	+	0.0828091i	$0.973611\pi$
$62$	11.3907	+	11.5775i	0.183720	+	0.186733i
$63$	−27.0383	−	41.6188i	−0.429180	−	0.660616i
$64$	−3.12195	+	63.9238i	−0.0487805	+	0.998810i
$65$	12.9963	+	22.5102i	0.199942	+	0.346310i
$66$	−38.0535	+	9.86540i	−0.576568	+	0.149476i
$67$	20.5587	+	76.7262i	0.306847	+	1.14517i	0.931344	+	0.364140i	$0.118637\pi$
$67$	20.5587	+	76.7262i	0.306847	+	1.14517i	−0.624497	+	0.781027i	$0.714696\pi$
$68$	31.9558	+	57.4889i	0.469939	+	0.845424i
$69$	26.3060	−	26.3060i	0.381246	−	0.381246i
$70$	20.7707	−	39.9758i	0.296724	−	0.571083i
$71$			8.01424i			0.112877i	0.998406	+	0.0564383i	$0.0179744\pi$
$71$			8.01424i			0.112877i	−0.998406	+	0.0564383i	$0.982026\pi$
$72$	54.4135	+	16.0127i	0.755743	+	0.222399i
$73$	11.0908	−	19.2098i	0.151929	−	0.263148i	−0.780008	−	0.625770i	$-0.784785\pi$
$73$	11.0908	−	19.2098i	0.151929	−	0.263148i	0.931936	+	0.362622i	$0.118118\pi$
$74$	31.8998	−	54.2286i	0.431078	−	0.732819i
$75$	−19.5504	−	5.23850i	−0.260671	−	0.0698467i
$76$	33.6166	−	32.5403i	0.442323	−	0.428162i
$77$	30.7827	+	94.6807i	0.399775	+	1.22962i
$78$	−15.6583	−	15.9151i	−0.200747	−	0.204040i
$79$	−27.0689	−	46.8846i	−0.342644	−	0.593477i	0.642279	−	0.766471i	$-0.277989\pi$
$79$	−27.0689	−	46.8846i	−0.342644	−	0.593477i	−0.984923	+	0.172994i	$0.944656\pi$
$80$	11.7007	+	50.1383i	0.146259	+	0.626729i
$81$	16.5400	−	28.6482i	0.204198	−	0.353681i
$82$	146.830	+	40.6259i	1.79062	+	0.495438i
$83$	−36.2707	−	36.2707i	−0.436997	−	0.436997i	0.454003	−	0.891000i	$-0.349995\pi$
$83$	−36.2707	−	36.2707i	−0.436997	−	0.436997i	−0.891000	+	0.454003i	$0.849995\pi$
$84$	−8.65307	+	37.7160i	−0.103013	+	0.449000i
$85$	37.4145	+	37.4145i	0.440171	+	0.440171i
$86$	59.7859	+	105.525i	0.695184	+	1.22704i
$87$	−3.73367	+	6.46691i	−0.0429158	+	0.0743323i
$88$	−97.1206	−	59.2780i	−1.10364	−	0.673614i
$89$	−70.7447	−	122.533i	−0.794884	−	1.37678i	−0.922913	−	0.385010i	$-0.874198\pi$
$89$	−70.7447	−	122.533i	−0.794884	−	1.37678i	0.128028	−	0.991771i	$-0.459135\pi$
$90$	45.6280	+	0.371115i	0.506978	+	0.00412350i
$91$	−37.8272	+	42.0268i	−0.415684	+	0.461833i
$92$	107.663	+	1.75146i	1.17024	+	0.0190376i
$93$	−10.8404	−	2.90468i	−0.116564	−	0.0312331i
$94$	−169.291	+	43.8889i	−1.80097	+	0.466903i
$95$	18.8188	−	32.5952i	0.198093	−	0.343107i
$96$	−20.5366	−	39.1663i	−0.213923	−	0.407983i
$97$		−	102.304i		−	1.05468i	−0.849655	−	0.527339i	$-0.823190\pi$
$97$		−	102.304i		−	1.05468i	0.849655	−	0.527339i	$-0.176810\pi$
$98$	96.6714	+	16.0821i	0.986443	+	0.164103i
$99$	−71.3049	+	71.3049i	−0.720251	+	0.720251i
$100$	−28.4619	−	51.2032i	−0.284619	−	0.512032i
$101$	−29.1172	−	108.667i	−0.288290	−	1.07591i	−0.946402	−	0.322992i	$-0.895311\pi$
$101$	−29.1172	−	108.667i	−0.288290	−	1.07591i	0.658112	−	0.752920i	$-0.271355\pi$
$102$	−39.1742	−	23.0440i	−0.384060	−	0.225922i
$103$	−29.8993	−	51.7872i	−0.290285	−	0.502788i	0.683592	−	0.729864i	$-0.260417\pi$
$103$	−29.8993	−	51.7872i	−0.290285	−	0.502788i	−0.973877	+	0.227076i	$0.927083\pi$
$104$	1.57659	−	64.6017i	0.0151595	−	0.621170i
$105$	1.63485	+	31.0864i	0.0155700	+	0.296061i
$106$	−10.0180	−	0.0814810i	−0.0945092	−	0.000768689i
$107$	−28.0616	+	104.727i	−0.262258	+	0.978761i	0.701649	+	0.712523i	$0.252447\pi$
$107$	−28.0616	+	104.727i	−0.262258	+	0.978761i	−0.963907	+	0.266238i	$0.914219\pi$
$108$	−86.2781	+	21.6203i	−0.798872	+	0.200188i
$109$	32.2120	+	120.217i	0.295523	+	1.10291i	0.940801	+	0.338959i	$0.110075\pi$
$109$	32.2120	+	120.217i	0.295523	+	1.10291i	−0.645278	+	0.763948i	$0.723259\pi$
$110$	−88.2185	−	24.4088i	−0.801986	−	0.221898i
$111$			43.4744i			0.391661i
$112$	−95.8550	+	57.9294i	−0.855848	+	0.517227i
$113$	89.7604			0.794340			0.397170	−	0.917745i	$-0.369992\pi$
$113$	89.7604			0.794340			0.397170	+	0.917745i	$0.369992\pi$
$114$	−8.62112	+	31.1585i	−0.0756238	+	0.273320i
$115$	83.6702	−	22.4194i	0.727567	−	0.194951i
$116$	−20.9650	+	5.25359i	−0.180733	+	0.0452896i
$117$	−55.3195	−	14.8228i	−0.472817	−	0.126691i
$118$	−0.841449	+	103.455i	−0.00713093	+	0.876737i
$119$	−52.2372	+	102.567i	−0.438968	+	0.861912i
$120$	−24.5351	−	25.7626i	−0.204459	−	0.214688i
$121$	70.3956	−	40.6429i	0.581782	−	0.335892i
$122$	41.8053	−	71.0678i	0.342667	−	0.582523i
$123$	−101.685	+	27.2463i	−0.826704	+	0.221515i
$124$	−15.7817	−	28.3915i	−0.127272	−	0.228964i
$125$	−90.2077	−	90.2077i	−0.721662	−	0.721662i
$126$	29.9218	+	94.6439i	0.237475	+	0.751142i
$127$	69.2095			0.544957			0.272478	−	0.962162i	$-0.412157\pi$
$127$	69.2095			0.544957			0.272478	+	0.962162i	$0.412157\pi$
$128$	40.1105	−	121.553i	0.313363	−	0.949633i
$129$	−72.5792	−	41.9036i	−0.562630	−	0.324834i
$130$	−13.0459	−	50.3214i	−0.100353	−	0.387088i
$131$	22.6779	−	84.6350i	0.173114	−	0.646069i	−0.823752	−	0.566951i	$-0.808123\pi$
$131$	22.6779	−	84.6350i	0.173114	−	0.646069i	0.996865	−	0.0791181i	$-0.0252104\pi$
$132$	78.6126	+	1.27887i	0.595550	+	0.00968844i
$133$	80.0898	+	17.0084i	0.602179	+	0.127882i
$134$	1.29209	−	158.860i	0.00964245	−	1.18553i
$135$	−61.9671	+	35.7767i	−0.459015	+	0.265013i
$136$	−30.9366	−	127.857i	−0.227475	−	0.940128i
$137$	190.226	+	109.827i	1.38851	+	0.801659i	0.993148	−	0.116865i	$-0.0372843\pi$
$137$	190.226	+	109.827i	1.38851	+	0.801659i	0.395366	+	0.918524i	$0.370618\pi$
$138$	−64.7366	+	36.6769i	−0.469106	+	0.265775i
$139$	−41.8824	+	41.8824i	−0.301312	+	0.301312i	−0.841527	−	0.540215i	$-0.818343\pi$
$139$	−41.8824	+	41.8824i	−0.301312	+	0.301312i	0.540215	+	0.841527i	$0.318343\pi$
$140$	−61.3575	+	65.9787i	−0.438268	+	0.471277i
$141$	85.4520	−	85.4520i	0.606042	−	0.606042i
$142$	4.27426	−	15.4481i	0.0301004	−	0.108789i
$143$	99.4940	+	57.4429i	0.695762	+	0.401698i
$144$	−96.3461	−	59.8863i	−0.669070	−	0.415877i
$145$	−15.0576	+	8.69349i	−0.103845	+	0.0599551i
$146$	−31.6236	+	31.1133i	−0.216600	+	0.213105i
$147$	−63.2112	+	24.2909i	−0.430008	+	0.165244i
$148$	−90.4112	+	87.5166i	−0.610886	+	0.591329i
$149$	−19.1489	+	71.4647i	−0.128516	+	0.479629i	−0.999941	−	0.0109010i	$-0.996530\pi$
$149$	−19.1489	+	71.4647i	−0.128516	+	0.479629i	0.871424	+	0.490530i	$0.163197\pi$
$150$	34.8910	+	20.5245i	0.232606	+	0.136830i
$151$	113.655	+	65.6188i	0.752682	+	0.434561i	0.826662	−	0.562698i	$-0.190237\pi$
$151$	113.655	+	65.6188i	0.752682	+	0.434561i	−0.0739800	+	0.997260i	$0.523570\pi$
$152$	−82.1534	+	44.7952i	−0.540483	+	0.294705i
$153$	−116.585			−0.761992
$154$	−8.83968	−	198.922i	−0.0574005	−	1.29170i
$155$	−18.4776	−	18.4776i	−0.119210	−	0.119210i
$156$	21.6945	+	39.0287i	0.139067	+	0.250184i
$157$	263.514	−	70.6084i	1.67843	−	0.449735i	0.711068	−	0.703123i	$-0.248212\pi$
$157$	263.514	−	70.6084i	1.67843	−	0.449735i	0.967365	+	0.253388i	$0.0815450\pi$
$158$	27.1722	+	104.811i	0.171976	+	0.663358i
$159$	5.99518	−	3.46132i	0.0377055	−	0.0217693i
$160$	4.18632	−	102.886i	0.0261645	−	0.643037i
$161$	102.658	+	158.016i	0.637624	+	0.981464i
$162$	−47.1612	+	46.4002i	−0.291119	+	0.286421i
$163$	63.6327	+	17.0503i	0.390384	+	0.104603i	0.448672	−	0.893697i	$-0.351897\pi$
$163$	63.6327	+	17.0503i	0.390384	+	0.104603i	−0.0582872	+	0.998300i	$0.518564\pi$
$164$	−261.360	−	156.619i	−1.59366	−	0.954995i
$165$	61.0940	−	16.3701i	0.370267	−	0.0992126i
$166$	50.5703	+	89.2590i	0.304640	+	0.537705i
$167$	−188.366			−1.12794			−0.563971	−	0.825795i	$-0.690727\pi$
$167$	−188.366			−1.12794			−0.563971	+	0.825795i	$0.690727\pi$
$168$	36.7947	−	68.0856i	0.219016	−	0.405271i
$169$		−	103.752i		−	0.613918i
$170$	−52.1650	−	92.0738i	−0.306853	−	0.541611i
$171$	21.4637	+	80.1038i	0.125519	+	0.468443i
$172$	−58.9619	−	235.293i	−0.342802	−	1.36799i
$173$	−58.6768	+	218.985i	−0.339172	+	1.26581i	0.560102	+	0.828423i	$0.310762\pi$
$173$	−58.6768	+	218.985i	−0.339172	+	1.26581i	−0.899275	+	0.437385i	$0.855905\pi$
$174$	10.6460	−	10.4742i	0.0611837	−	0.0601964i
$175$	46.5257	−	91.3530i	0.265861	−	0.522017i
$176$	155.593	+	166.061i	0.884048	+	0.943526i
$177$	−35.7448	−	61.9118i	−0.201948	−	0.349784i
$178$	71.0148	+	273.923i	0.398959	+	1.53889i
$179$	−42.0296	−	156.857i	−0.234802	−	0.876294i	−0.978238	−	0.207486i	$-0.933472\pi$
$179$	−42.0296	−	156.857i	−0.234802	−	0.876294i	0.743436	−	0.668807i	$-0.233195\pi$
$180$	−87.7537	−	25.0503i	−0.487520	−	0.139168i
$181$	129.217	−	129.217i	0.713905	−	0.713905i	−0.253445	−	0.967350i	$-0.581564\pi$
$181$	129.217	−	129.217i	0.713905	−	0.713905i	0.967350	+	0.253445i	$0.0815637\pi$
$182$	95.3292	−	60.8354i	0.523787	−	0.334260i
$183$			56.9741i			0.311334i
$184$	−206.594	−	60.7961i	−1.12279	−	0.330413i
$185$	−50.6129	+	87.6641i	−0.273583	+	0.473860i
$186$	19.3466	+	11.3806i	0.104014	+	0.0611858i
$187$	225.900	+	60.5298i	1.20802	+	0.323689i
$188$	349.730	+	5.68942i	1.86026	+	0.0302629i
$189$	−115.693	−	104.133i	−0.612134	−	0.550966i
$190$	−53.6588	+	52.7930i	−0.282415	+	0.277858i
$191$	−24.6493	−	42.6938i	−0.129054	−	0.223528i	0.794256	−	0.607583i	$-0.207861\pi$
$191$	−24.6493	−	42.6938i	−0.129054	−	0.223528i	−0.923310	+	0.384055i	$0.874527\pi$
$192$	18.6972	+	86.4490i	0.0973813	+	0.450255i
$193$	−41.8224	+	72.4384i	−0.216696	+	0.375329i	−0.953796	−	0.300455i	$-0.902861\pi$
$193$	−41.8224	+	72.4384i	−0.216696	+	0.375329i	0.737100	+	0.675784i	$0.236195\pi$
$194$	−54.5620	+	197.198i	−0.281247	+	1.01649i
$195$	25.4004	+	25.4004i	0.130258	+	0.130258i
$196$	−177.765	−	82.5576i	−0.906962	−	0.421212i
$197$	−37.9570	−	37.9570i	−0.192675	−	0.192675i	0.604176	−	0.796851i	$-0.293502\pi$
$197$	−37.9570	−	37.9570i	−0.192675	−	0.192675i	−0.796851	+	0.604176i	$0.793502\pi$
$198$	175.475	−	99.4164i	0.886237	−	0.502103i
$199$	94.7070	−	164.037i	0.475915	−	0.824309i	−0.523705	−	0.851900i	$-0.675450\pi$
$199$	94.7070	−	164.037i	0.475915	−	0.824309i	0.999619	+	0.0275915i	$0.00878375\pi$
$200$	27.5541	+	113.878i	0.137771	+	0.569389i
$201$	54.8880	+	95.0687i	0.273074	+	0.472979i
$202$	−1.82998	+	224.993i	−0.00905931	+	1.11383i
$203$	−28.1127	−	25.3035i	−0.138486	−	0.124648i
$204$	63.2211	+	65.3121i	0.309907	+	0.320157i
$205$	−236.763	−	63.4403i	−1.15494	−	0.309465i
$206$	30.0135	+	115.770i	0.145696	+	0.561991i
$207$	−95.4297	+	165.289i	−0.461013	+	0.798498i
$208$	−37.4932	+	123.684i	−0.180256	+	0.594635i
$209$		−	166.357i		−	0.795966i
$210$	13.4281	−	60.7933i	0.0639434	−	0.289492i
$211$	−249.436	+	249.436i	−1.18216	+	1.18216i	−0.202979	+	0.979183i	$0.565062\pi$
$211$	−249.436	+	249.436i	−1.18216	+	1.18216i	−0.979183	+	0.202979i	$0.934938\pi$
$212$	19.2670	+	5.49998i	0.0908819	+	0.0259433i
$213$	2.86659	+	10.6983i	0.0134582	+	0.0502266i
$214$	109.946	−	186.904i	0.513764	−	0.873383i
$215$	−97.5685	−	168.994i	−0.453807	−	0.786016i
$216$	177.839	+	4.34011i	0.823327	+	0.0200931i
$217$	25.7979	−	50.6541i	0.118884	−	0.233429i
$218$	2.02448	−	248.907i	0.00928661	−	1.14177i
$219$	7.93406	−	29.6103i	0.0362286	−	0.135207i
$220$	157.030	+	94.0997i	0.713772	+	0.427726i
$221$	34.3772	+	128.297i	0.155553	+	0.580531i
$222$	23.1863	−	83.8002i	0.104443	−	0.377479i
$223$			363.228i			1.62882i	0.580288	+	0.814412i	$0.302940\pi$
$223$			363.228i			1.62882i	−0.580288	+	0.814412i	$0.697060\pi$
$224$	215.664	−	60.5408i	0.962784	−	0.270271i
$225$	103.838			0.461501
$226$	−173.020	−	47.8722i	−0.765576	−	0.211824i
$227$	244.891	−	65.6183i	1.07881	−	0.289067i	0.324704	−	0.945816i	$-0.394735\pi$
$227$	244.891	−	65.6183i	1.07881	−	0.289067i	0.754110	+	0.656748i	$0.228069\pi$
$228$	33.2357	−	55.4625i	0.145771	−	0.243257i
$229$	151.004	+	40.4615i	0.659408	+	0.176688i	0.572979	−	0.819570i	$-0.305788\pi$
$229$	151.004	+	40.4615i	0.659408	+	0.176688i	0.0864292	+	0.996258i	$0.472454\pi$
$230$	−173.238	−	1.40903i	−0.753208	−	0.00612620i
$231$	74.9581	+	115.379i	0.324494	+	0.499477i
$232$	43.2135	+	1.05462i	0.186265	+	0.00454576i
$233$	145.131	−	83.7912i	0.622878	−	0.359619i	−0.155111	−	0.987897i	$-0.549573\pi$
$233$	145.131	−	83.7912i	0.622878	−	0.359619i	0.777989	+	0.628278i	$0.216240\pi$
$234$	98.7272	+	58.0759i	0.421911	+	0.248188i
$235$	271.793	−	72.8268i	1.15657	−	0.309901i
$236$	56.7979	−	198.969i	0.240669	−	0.843088i
$237$	−52.9044	−	52.9044i	−0.223225	−	0.223225i
$238$	155.394	−	169.847i	0.652916	−	0.713643i
$239$	−259.871			−1.08733			−0.543664	−	0.839303i	$-0.682963\pi$
$239$	−259.871			−1.08733			−0.543664	+	0.839303i	$0.682963\pi$
$240$	33.5532	+	62.7447i	0.139805	+	0.261436i
$241$	−16.8046	−	9.70212i	−0.0697285	−	0.0402578i	0.464730	−	0.885452i	$-0.346151\pi$
$241$	−16.8046	−	9.70212i	−0.0697285	−	0.0402578i	−0.534459	+	0.845194i	$0.679485\pi$
$242$	−157.369	+	40.7981i	−0.650286	+	0.168587i
$243$	63.6293	−	237.468i	0.261849	−	0.977233i
$244$	−118.486	+	114.692i	−0.485598	+	0.470051i
$245$	−155.742	−	24.6090i	−0.635682	−	0.100445i
$246$	210.536	+	1.71239i	0.855839	+	0.00696095i
$247$	81.8223	−	47.2401i	0.331264	−	0.191256i
$248$	15.2784	+	63.1437i	0.0616064	+	0.254612i
$249$	−61.3916	−	35.4445i	−0.246553	−	0.142347i
$250$	125.772	+	221.993i	0.503086	+	0.887972i
$251$	151.530	−	151.530i	0.603706	−	0.603706i	−0.337588	−	0.941294i	$-0.609611\pi$
$251$	151.530	−	151.530i	0.603706	−	0.603706i	0.941294	+	0.337588i	$0.109611\pi$
$252$	−7.19990	−	198.392i	−0.0285710	−	0.787269i
$253$	270.726	−	270.726i	1.07006	−	1.07006i
$254$	−133.407	−	36.9117i	−0.525223	−	0.145322i
$255$	63.3276	+	36.5622i	0.248344	+	0.143381i
$256$	−142.144	+	212.911i	−0.555251	+	0.831683i
$257$	−390.601	+	225.514i	−1.51985	+	0.877485i	−0.520123	+	0.854092i	$0.674114\pi$
$257$	−390.601	+	225.514i	−1.51985	+	0.877485i	−0.999726	+	0.0233936i	$0.992553\pi$
$258$	117.553	+	119.481i	0.455634	+	0.463106i
$259$	−215.400	−	45.7437i	−0.831660	−	0.176616i
$260$	−1.69117	+	103.956i	−0.00650448	+	0.399832i
$261$	9.91532	−	37.0045i	0.0379897	−	0.141780i
$262$	−88.8521	+	151.046i	−0.339130	+	0.576510i
$263$	−68.1696	−	39.3577i	−0.259200	−	0.149649i	0.364770	−	0.931098i	$-0.381148\pi$
$263$	−68.1696	−	39.3577i	−0.259200	−	0.149649i	−0.623970	+	0.781449i	$0.714481\pi$
$264$	−150.850	−	44.3919i	−0.571401	−	0.168151i
$265$	16.1187			0.0608252
$266$	−145.308	−	75.4995i	−0.546271	−	0.283833i
$267$	−138.266	−	138.266i	−0.517851	−	0.517851i
$268$	−87.2161	+	305.527i	−0.325433	+	1.14002i
$269$	−81.5329	+	21.8467i	−0.303096	+	0.0812144i	−0.407162	−	0.913356i	$-0.633482\pi$
$269$	−81.5329	+	21.8467i	−0.303096	+	0.0812144i	0.104066	+	0.994570i	$0.466815\pi$
$270$	138.527	−	35.9133i	0.513064	−	0.133012i
$271$	−372.592	+	215.116i	−1.37488	+	0.793786i	−0.991537	−	0.129822i	$-0.958559\pi$
$271$	−372.592	+	215.116i	−1.37488	+	0.793786i	−0.383340	+	0.923607i	$0.625226\pi$
$272$	−8.55778	+	262.955i	−0.0314624	+	0.966745i
$273$	−35.4634	+	69.6321i	−0.129902	+	0.255063i
$274$	−308.102	−	313.155i	−1.12446	−	1.14290i
$275$	−201.201	−	53.9117i	−0.731640	−	0.196042i
$276$	144.346	−	36.1715i	0.522992	−	0.131056i
$277$	−416.453	+	111.588i	−1.50344	+	0.402846i	−0.914251	−	0.405149i	$-0.867220\pi$
$277$	−416.453	+	111.588i	−1.50344	+	0.402846i	−0.589190	+	0.807995i	$0.700553\pi$
$278$	103.069	−	58.3943i	0.370751	−	0.210051i
$279$	57.5767			0.206368
$280$	153.460	−	94.4551i	0.548072	−	0.337340i
$281$			186.160i			0.662491i	0.943545	+	0.331245i	$0.107469\pi$
$281$			186.160i			0.662491i	−0.943545	+	0.331245i	$0.892531\pi$
$282$	−210.290	+	119.141i	−0.745708	+	0.422486i
$283$	−63.1162	−	235.553i	−0.223025	−	0.832342i	−0.983186	−	0.182607i	$-0.941546\pi$
$283$	−63.1162	−	235.553i	−0.223025	−	0.832342i	0.760161	−	0.649735i	$-0.225120\pi$
$284$	−16.4779	+	27.4977i	−0.0580209	+	0.0968231i
$285$	13.4625	−	50.2428i	0.0472369	−	0.176290i
$286$	−161.146	−	163.789i	−0.563448	−	0.572689i
$287$	−28.0033	−	532.479i	−0.0975725	−	1.85533i
$288$	153.775	+	166.820i	0.533942	+	0.579236i
$289$	−9.30799	−	16.1219i	−0.0322076	−	0.0557852i
$290$	33.6611	−	8.72668i	0.116073	−	0.0300920i
$291$	−36.5927	−	136.566i	−0.125748	−	0.469299i
$292$	77.5506	−	43.1074i	0.265584	−	0.147628i
$293$	−330.682	+	330.682i	−1.12861	+	1.12861i	−0.138203	+	0.990404i	$0.544133\pi$
$293$	−330.682	+	330.682i	−1.12861	+	1.12861i	−0.990404	+	0.138203i	$0.955867\pi$
$294$	134.800	−	13.1100i	0.458502	−	0.0445920i
$295$		−	166.456i		−	0.564259i
$296$	220.950	−	120.476i	0.746453	−	0.407013i
$297$	−158.131	+	273.892i	−0.532429	+	0.922194i
$298$	75.0255	−	127.541i	0.251763	−	0.427990i
$299$	210.034	+	56.2784i	0.702454	+	0.188222i
$300$	−56.3087	−	58.1710i	−0.187696	−	0.193903i
$301$	283.985	−	315.513i	0.943472	−	1.04822i
$302$	−184.082	−	187.101i	−0.609544	−	0.619541i
$303$	−77.7376	−	134.645i	−0.256560	−	0.444375i
$304$	182.248	−	42.5311i	0.599500	−	0.139905i
$305$	−66.3293	+	114.886i	−0.217473	+	0.376675i
$306$	224.726	+	62.1785i	0.734399	+	0.203198i
$307$	333.416	+	333.416i	1.08605	+	1.08605i	0.995931	+	0.0901140i	$0.0287231\pi$
$307$	333.416	+	333.416i	1.08605	+	1.08605i	0.0901140	+	0.995931i	$0.471277\pi$
$308$	−89.0524	+	388.152i	−0.289131	+	1.26023i
$309$	−58.4364	−	58.4364i	−0.189115	−	0.189115i
$310$	25.7623	+	45.4717i	0.0831040	+	0.146683i
$311$	−43.4292	+	75.2216i	−0.139644	+	0.241870i	−0.927362	−	0.374166i	$-0.877929\pi$
$311$	−43.4292	+	75.2216i	−0.139644	+	0.241870i	0.787718	+	0.616036i	$0.211262\pi$
$312$	−21.0026	−	86.8012i	−0.0673160	−	0.278209i
$313$	−54.5618	−	94.5038i	−0.174319	−	0.301929i	0.765607	−	0.643309i	$-0.222439\pi$
$313$	−54.5618	−	94.5038i	−0.174319	−	0.301929i	−0.939925	+	0.341380i	$0.889106\pi$
$314$	−545.601	−	4.43764i	−1.73758	−	0.0141326i
$315$	−49.3787	−	151.878i	−0.156758	−	0.482152i
$316$	3.52239	−	216.522i	0.0111468	−	0.685197i
$317$	−535.277	−	143.427i	−1.68857	−	0.452451i	−0.718550	−	0.695475i	$-0.755194\pi$
$317$	−535.277	−	143.427i	−1.68857	−	0.452451i	−0.970020	+	0.243024i	$0.921861\pi$
$318$	−13.4022	+	3.47453i	−0.0421453	+	0.0109262i
$319$	−38.4248	+	66.5537i	−0.120454	+	0.208632i
$320$	−62.9419	+	196.088i	−0.196693	+	0.612774i
$321$			149.839i			0.466787i
$322$	−113.605	−	359.338i	−0.352812	−	1.11596i
$323$	135.998	−	135.998i	0.421047	−	0.421047i
$324$	115.654	−	64.2874i	0.356956	−	0.198418i
$325$	−30.6185	−	114.270i	−0.0942107	−	0.351599i
$326$	−113.563	−	66.8032i	−0.348354	−	0.204918i
$327$	86.0000	+	148.956i	0.262997	+	0.455524i
$328$	420.262	+	441.288i	1.28129	+	1.34539i
$329$	333.471	+	513.296i	1.01359	+	1.56017i
$330$	−126.494	−	1.02884i	−0.383316	−	0.00311769i
$331$	−70.6071	+	263.509i	−0.213315	+	0.796101i	0.773438	+	0.633871i	$0.218535\pi$
$331$	−70.6071	+	263.509i	−0.213315	+	0.796101i	−0.986753	+	0.162230i	$0.948131\pi$
$332$	−49.8733	−	199.025i	−0.150221	−	0.599471i
$333$	−57.7263	−	215.438i	−0.173352	−	0.646960i
$334$	363.091	+	100.462i	1.08710	+	0.300784i
$335$			255.602i			0.762992i
$336$	−107.237	+	111.616i	−0.319157	+	0.332192i
$337$	167.261			0.496325			0.248162	−	0.968718i	$-0.420173\pi$
$337$	167.261			0.496325			0.248162	+	0.968718i	$0.420173\pi$
$338$	−55.3344	+	199.990i	−0.163711	+	0.591687i
$339$	119.822	−	32.1062i	0.353457	−	0.0947084i
$340$	51.4461	+	205.301i	0.151312	+	0.603826i
$341$	−111.563	−	29.8933i	−0.327165	−	0.0876637i
$342$	1.34897	−	165.854i	0.00394435	−	0.484952i
$343$	−53.8421	−	338.748i	−0.156974	−	0.987603i
$344$	−11.8361	+	484.993i	−0.0344074	+	1.40986i
$345$	103.673	−	59.8555i	0.300501	−	0.173494i
$346$	229.896	−	390.816i	0.664439	−	1.12953i
$347$	511.104	−	136.950i	1.47292	−	0.394668i	0.568990	−	0.822344i	$-0.307334\pi$
$347$	511.104	−	136.950i	1.47292	−	0.394668i	0.903932	+	0.427676i	$0.140668\pi$
$348$	−26.1071	+	14.5120i	−0.0750205	+	0.0417010i
$349$	−214.626	−	214.626i	−0.614974	−	0.614974i	0.329264	−	0.944238i	$-0.393199\pi$
$349$	−214.626	−	214.626i	−0.614974	−	0.614974i	−0.944238	+	0.329264i	$0.893199\pi$
$350$	−138.404	+	151.276i	−0.395439	+	0.432218i
$351$	−179.618			−0.511731
$352$	−211.351	−	403.077i	−0.600429	−	1.14511i
$353$	−82.1082	−	47.4052i	−0.232601	−	0.134292i	0.379170	−	0.925327i	$-0.376209\pi$
$353$	−82.1082	−	47.4052i	−0.232601	−	0.134292i	−0.611771	+	0.791035i	$0.709543\pi$
$354$	35.8812	+	138.404i	0.101359	+	0.390971i
$355$	−6.67457	+	24.9098i	−0.0188016	+	0.0701686i
$356$	9.20581	−	565.883i	0.0258590	−	1.58956i
$357$	−33.0447	+	155.603i	−0.0925623	+	0.435862i
$358$	−2.64151	+	324.769i	−0.00737851	+	0.907176i
$359$	171.053	−	98.7573i	0.476470	−	0.275090i	−0.242474	−	0.970158i	$-0.577959\pi$
$359$	171.053	−	98.7573i	0.476470	−	0.275090i	0.718944	+	0.695068i	$0.244626\pi$
$360$	155.792	+	95.0884i	0.432755	+	0.264134i
$361$	194.155	+	112.095i	0.537825	+	0.310513i
$362$	−317.991	+	180.160i	−0.878428	+	0.497679i
$363$	79.4341	−	79.4341i	0.218827	−	0.218827i
$364$	−216.200	+	66.4227i	−0.593956	+	0.182480i
$365$	50.4710	−	50.4710i	0.138277	−	0.138277i
$366$	30.3862	−	109.822i	0.0830224	−	0.300060i
$367$	371.962	+	214.752i	1.01352	+	0.585157i	0.912221	−	0.409699i	$-0.134366\pi$
$367$	371.962	+	214.752i	1.01352	+	0.585157i	0.101300	+	0.994856i	$0.467700\pi$
$368$	365.801	+	227.372i	0.994025	+	0.617860i
$369$	467.720	−	270.039i	1.26754	−	0.731812i
$370$	144.314	−	141.986i	0.390039	−	0.383745i
$371$	10.8415	+	33.3459i	0.0292223	+	0.0898812i
$372$	−31.2224	−	32.2551i	−0.0839312	−	0.0867072i
$373$	−65.8172	+	245.633i	−0.176454	+	0.658534i	0.819846	+	0.572584i	$0.194059\pi$
$373$	−65.8172	+	245.633i	−0.176454	+	0.658534i	−0.996299	+	0.0859498i	$0.972608\pi$
$374$	−403.158	−	237.156i	−1.07796	−	0.634107i
$375$	−152.685	−	88.1527i	−0.407160	−	0.235074i
$376$	−671.097	−	197.489i	−1.78483	−	0.525237i
$377$	−43.6458			−0.115771
$378$	167.470	+	262.427i	0.443044	+	0.694250i
$379$	260.914	+	260.914i	0.688427	+	0.688427i	0.961884	−	0.273457i	$-0.0881672\pi$
$379$	260.914	+	260.914i	0.688427	+	0.688427i	−0.273457	+	0.961884i	$0.588167\pi$
$380$	131.588	−	73.1446i	0.346284	−	0.192486i
$381$	92.3882	−	24.7553i	0.242489	−	0.0649747i
$382$	24.7434	+	95.4419i	0.0647732	+	0.249848i
$383$	44.0445	−	25.4291i	0.114999	−	0.0663946i	−0.441397	−	0.897312i	$-0.645517\pi$
$383$	44.0445	−	25.4291i	0.114999	−	0.0663946i	0.556396	+	0.830917i	$0.312184\pi$
$384$	10.0658	−	176.609i	0.0262130	−	0.459919i
$385$	16.8249	+	319.923i	0.0437011	+	0.830970i
$386$	119.250	−	117.325i	0.308937	−	0.303952i
$387$	415.307	+	111.281i	1.07315	+	0.287549i
$388$	210.345	−	351.015i	0.542126	−	0.904679i
$389$	403.509	−	108.120i	1.03730	−	0.277943i	0.300305	−	0.953843i	$-0.402912\pi$
$389$	403.509	−	108.120i	1.03730	−	0.277943i	0.736993	+	0.675900i	$0.236245\pi$
$390$	−35.4144	−	62.5081i	−0.0908060	−	0.160277i
$391$	442.642			1.13208
$392$	298.624	+	253.944i	0.761797	+	0.647816i
$393$		−	121.091i		−	0.308121i
$394$	52.9214	+	93.4088i	0.134318	+	0.237078i
$395$	−45.0880	−	168.271i	−0.114147	−	0.426002i
$396$	−391.264	+	98.0463i	−0.988039	+	0.247592i
$397$	−186.551	+	696.216i	−0.469901	+	1.75369i	0.170207	+	0.985408i	$0.445556\pi$
$397$	−186.551	+	696.216i	−0.469901	+	1.75369i	−0.640108	+	0.768285i	$0.721110\pi$
$398$	−270.042	+	265.684i	−0.678497	+	0.667549i
$399$	112.996	−	5.94251i	0.283198	−	0.0148935i
$400$	7.62209	−	234.204i	0.0190552	−	0.585509i
$401$	109.161	+	189.072i	0.272221	+	0.471500i	0.969430	−	0.245367i	$-0.0789086\pi$
$401$	109.161	+	189.072i	0.272221	+	0.471500i	−0.697209	+	0.716867i	$0.745575\pi$
$402$	−55.0975	−	212.526i	−0.137058	−	0.528672i
$403$	−16.9775	−	63.3610i	−0.0421279	−	0.157223i
$404$	123.524	−	432.716i	0.305752	−	1.07108i
$405$	75.2690	−	75.2690i	0.185849	−	0.185849i
$406$	40.6941	+	63.7678i	0.100232	+	0.157064i
$407$			447.413i			1.09930i
$408$	−87.0305	−	159.612i	−0.213310	−	0.391206i
$409$	−203.218	+	351.984i	−0.496866	+	0.860597i	−0.999993	−	0.00361492i	$-0.998849\pi$
$409$	−203.218	+	351.984i	−0.496866	+	0.860597i	0.503127	+	0.864212i	$0.332183\pi$
$410$	422.543	+	248.559i	1.03059	+	0.606243i
$411$	293.218	+	78.5676i	0.713427	+	0.191162i
$412$	3.89072	−	239.163i	0.00944348	−	0.580493i
$413$	344.361	−	111.959i	0.833804	−	0.271087i
$414$	272.102	−	267.712i	0.657252	−	0.646647i
$415$	−82.5289	−	142.944i	−0.198865	−	0.344444i
$416$	138.236	−	218.414i	0.332298	−	0.525034i
$417$	−40.9283	+	70.8898i	−0.0981493	+	0.170000i
$418$	−88.7236	+	320.666i	−0.212257	+	0.767143i
$419$	−126.872	−	126.872i	−0.302797	−	0.302797i	0.539310	−	0.842107i	$-0.318685\pi$
$419$	−126.872	−	126.872i	−0.302797	−	0.302797i	−0.842107	+	0.539310i	$0.818685\pi$
$420$	−58.3068	+	110.022i	−0.138826	+	0.261958i
$421$	568.991	+	568.991i	1.35152	+	1.35152i	0.883960	+	0.467562i	$0.154868\pi$
$421$	568.991	+	568.991i	1.35152	+	1.35152i	0.467562	+	0.883960i	$0.345132\pi$
$422$	613.840	−	347.775i	1.45460	−	0.824112i
$423$	−309.993	+	536.923i	−0.732843	+	1.26932i
$424$	−34.2053	−	20.8773i	−0.0806728	−	0.0492390i
$425$	−120.410	−	208.557i	−0.283319	−	0.490723i
$426$	0.180161	−	22.1506i	0.000422914	−	0.0519967i
$427$	−282.286	−	59.9481i	−0.661092	−	0.140394i
$428$	−311.611	+	301.634i	−0.728062	+	0.704753i
$429$	153.362	+	41.0932i	0.357487	+	0.0957882i
$430$	97.9409	+	377.785i	0.227770	+	0.878569i
$431$	57.7637	−	100.050i	0.134022	−	0.232134i	−0.791201	−	0.611556i	$-0.790544\pi$
$431$	57.7637	−	100.050i	0.134022	−	0.232134i	0.925224	+	0.379422i	$0.123877\pi$
$432$	−340.483	−	103.213i	−0.788155	−	0.238919i
$433$		−	814.694i		−	1.88151i	−0.339086	−	0.940755i	$-0.610118\pi$
$433$		−	814.694i		−	1.88151i	0.339086	−	0.940755i	$-0.389882\pi$
$434$	−76.7430	+	83.8808i	−0.176827	+	0.193274i
$435$	−16.9909	+	16.9909i	−0.0390595	+	0.0390595i
$436$	−136.653	+	478.708i	−0.313424	+	1.09795i
$437$	−81.4922	−	304.133i	−0.186481	−	0.695957i
$438$	−31.0857	+	52.8447i	−0.0709719	+	0.120650i
$439$	−282.782	−	489.794i	−0.644151	−	1.11570i	−0.984497	−	0.175402i	$-0.943877\pi$
$439$	−282.782	−	489.794i	−0.644151	−	1.11570i	0.340345	−	0.940300i	$-0.389456\pi$
$440$	−252.501	−	265.134i	−0.573866	−	0.602577i
$441$	280.990	−	204.307i	0.637164	−	0.463282i
$442$	2.16056	−	265.638i	0.00488814	−	0.600990i
$443$	−151.447	+	565.208i	−0.341867	+	1.27586i	0.554364	+	0.832275i	$0.312962\pi$
$443$	−151.447	+	565.208i	−0.341867	+	1.27586i	−0.896230	+	0.443589i	$0.853705\pi$
$444$	−89.3869	+	149.165i	−0.201322	+	0.335958i
$445$	−117.838	−	439.777i	−0.264804	−	0.988263i
$446$	193.721	−	700.149i	0.434353	−	1.56984i
$447$			102.248i			0.228743i
$448$	−447.997	+	1.67650i	−0.999993	+	0.00374218i
$449$	−288.821			−0.643255			−0.321627	−	0.946866i	$-0.604230\pi$
$449$	−288.821			−0.643255			−0.321627	+	0.946866i	$0.604230\pi$
$450$	−200.155	−	55.3801i	−0.444790	−	0.123067i
$451$	−1046.48	+	280.403i	−2.32035	+	0.621737i
$452$	307.978	+	184.555i	0.681367	+	0.408307i
$453$	175.190	+	46.9420i	0.386733	+	0.103625i
$454$	−507.042	−	4.12402i	−1.11683	−	0.00908375i
$455$	−152.576	+	99.1235i	−0.335332	+	0.217854i
$456$	−93.6445	+	89.1826i	−0.205361	+	0.195576i
$457$	222.544	−	128.486i	0.486967	−	0.281151i	−0.236348	−	0.971668i	$-0.575951\pi$
$457$	222.544	−	128.486i	0.486967	−	0.281151i	0.723316	+	0.690518i	$0.242617\pi$
$458$	−269.493	−	158.528i	−0.588413	−	0.346132i
$459$	−353.183	+	94.6351i	−0.769462	+	0.206177i
$460$	333.178	+	95.1095i	0.724300	+	0.206760i
$461$	520.635	+	520.635i	1.12936	+	1.12936i	0.990281	+	0.139080i	$0.0444144\pi$
$461$	520.635	+	520.635i	1.12936	+	1.12936i	0.139080	+	0.990281i	$0.455586\pi$
$462$	−82.9519	−	262.380i	−0.179550	−	0.567922i
$463$	283.552			0.612422			0.306211	−	0.951964i	$-0.400939\pi$
$463$	283.552			0.612422			0.306211	+	0.951964i	$0.400939\pi$
$464$	−82.7350	−	25.0801i	−0.178308	−	0.0540519i
$465$	−31.2750	−	18.0566i	−0.0672581	−	0.0388315i
$466$	−324.439	+	84.1111i	−0.696221	+	0.180496i
$467$	145.137	−	541.660i	0.310787	−	1.15987i	−0.617062	−	0.786914i	$-0.711677\pi$
$467$	145.137	−	541.660i	0.310787	−	1.15987i	0.927849	−	0.372957i	$-0.121656\pi$
$468$	−159.331	−	164.600i	−0.340450	−	0.351710i
$469$	−528.784	+	171.919i	−1.12747	+	0.366565i
$470$	−562.743	−	4.57707i	−1.19733	−	0.00973844i
$471$	326.511	−	188.511i	0.693229	−	0.400236i
$472$	−215.599	+	353.235i	−0.456777	+	0.748380i
$473$	−746.944	−	431.248i	−1.57916	−	0.911730i
$474$	73.7617	+	130.193i	0.155615	+	0.274669i
$475$	−121.129	+	121.129i	−0.255008	+	0.255008i
$476$	−390.119	+	244.516i	−0.819578	+	0.513690i
$477$	−25.1131	+	25.1131i	−0.0526480	+	0.0526480i
$478$	500.922	+	138.598i	1.04795	+	0.289954i
$479$	239.747	+	138.418i	0.500515	+	0.288973i	0.728926	−	0.684592i	$-0.240020\pi$
$479$	239.747	+	138.418i	0.500515	+	0.288973i	−0.228411	+	0.973565i	$0.573353\pi$
$480$	−31.2126	−	138.840i	−0.0650262	−	0.289251i
$481$	−220.060	+	127.051i	−0.457504	+	0.264140i
$482$	27.2176	+	27.6640i	0.0564681	+	0.0573942i
$483$	193.558	+	174.217i	0.400742	+	0.360697i
$484$	325.100	+	5.28875i	0.671695	+	0.0109272i
$485$	85.2025	−	317.980i	0.175675	−	0.655629i
$486$	−249.300	+	423.802i	−0.512962	+	0.872020i
$487$	−514.968	−	297.317i	−1.05743	−	0.610507i	−0.132709	−	0.991155i	$-0.542368\pi$
$487$	−514.968	−	297.317i	−1.05743	−	0.610507i	−0.924720	+	0.380648i	$0.875701\pi$
$488$	289.560	−	157.886i	0.593361	−	0.323537i
$489$	91.0424			0.186181
$490$	287.080	+	130.498i	0.585878	+	0.266323i
$491$	−350.792	−	350.792i	−0.714444	−	0.714444i	0.253017	−	0.967462i	$-0.418577\pi$
$491$	−350.792	−	350.792i	−0.714444	−	0.714444i	−0.967462	+	0.253017i	$0.918577\pi$
$492$	−404.912	−	115.587i	−0.822992	−	0.234932i
$493$	−85.8210	+	22.9957i	−0.174079	+	0.0466443i
$494$	−182.914	+	47.4205i	−0.370270	+	0.0959929i
$495$	−281.015	+	162.244i	−0.567707	+	0.327766i
$496$	4.22635	−	129.863i	0.00852087	−	0.261820i
$497$	−56.0223	+	2.94623i	−0.112721	+	0.00592804i
$498$	99.4334	+	101.064i	0.199665	+	0.202940i
$499$	110.941	+	29.7266i	0.222327	+	0.0595723i	0.368263	−	0.929722i	$-0.379953\pi$
$499$	110.941	+	29.7266i	0.222327	+	0.0595723i	−0.145936	+	0.989294i	$0.546619\pi$
$500$	−124.038	−	494.987i	−0.248076	−	0.989974i
$501$	−251.451	+	67.3762i	−0.501899	+	0.134483i
$502$	−372.902	+	211.270i	−0.742833	+	0.420857i
$503$	−0.944679			−0.00187809			−0.000939045	−	1.00000i	$-0.500299\pi$
$503$	−0.944679			−0.00187809			−0.000939045		1.00000i	$0.500299\pi$
$504$	−91.9305	+	386.255i	−0.182402	+	0.766380i
$505$		−	362.009i		−	0.716849i
$506$	−666.232	+	377.458i	−1.31666	+	0.745965i
$507$	−37.1108	−	138.499i	−0.0731968	−	0.273174i
$508$	237.466	+	142.300i	0.467452	+	0.280119i
$509$	−126.495	+	472.086i	−0.248517	+	0.927478i	0.723066	+	0.690779i	$0.242732\pi$
$509$	−126.495	+	472.086i	−0.248517	+	0.927478i	−0.971583	+	0.236699i	$0.923935\pi$
$510$	−102.569	−	104.251i	−0.201116	−	0.204414i
$511$	138.360	+	70.4663i	0.270764	+	0.137899i
$512$	387.547	−	334.592i	0.756927	−	0.653499i
$513$	130.045	+	225.244i	0.253499	+	0.439073i
$514$	873.188	−	226.375i	1.69881	−	0.440418i
$515$	−49.8027	−	185.866i	−0.0967042	−	0.360905i
$516$	−162.870	−	293.005i	−0.315640	−	0.567839i
$517$	879.423	−	879.423i	1.70101	−	1.70101i
$518$	390.803	+	203.054i	0.754447	+	0.391997i
$519$			313.312i			0.603684i
$520$	58.7032	−	199.482i	0.112891	−	0.383619i
$521$	−17.4782	+	30.2732i	−0.0335475	+	0.0581059i	−0.882312	−	0.470666i	$-0.844014\pi$
$521$	−17.4782	+	30.2732i	−0.0335475	+	0.0581059i	0.848764	+	0.528772i	$0.177347\pi$
$522$	−38.8483	+	66.0408i	−0.0744220	+	0.126515i
$523$	337.123	+	90.3318i	0.644594	+	0.172718i	0.566284	−	0.824211i	$-0.308381\pi$
$523$	337.123	+	90.3318i	0.644594	+	0.172718i	0.0783106	+	0.996929i	$0.475047\pi$
$524$	251.827	−	243.765i	0.480586	−	0.465200i
$525$	29.4317	−	138.589i	0.0560604	−	0.263980i
$526$	110.411	+	112.222i	0.209908	+	0.213350i
$527$	−66.7660	−	115.642i	−0.126691	−	0.219435i
$528$	267.099	+	166.022i	0.505870	+	0.314436i
$529$	97.8216	−	169.432i	0.184918	−	0.320287i
$530$	−31.0700	−	8.59662i	−0.0586226	−	0.0162200i
$531$	259.341	+	259.341i	0.488402	+	0.488402i
$532$	239.826	+	223.029i	0.450801	+	0.419227i
$533$	−435.084	−	435.084i	−0.816292	−	0.816292i
$534$	192.777	+	340.261i	0.361005	+	0.637193i
$535$	−174.442	+	302.143i	−0.326060	+	0.564753i
$536$	331.063	−	542.411i	0.617655	−	1.01196i
$537$	−112.211	−	194.355i	−0.208959	−	0.361928i
$538$	168.813	+	1.37303i	0.313778	+	0.00255211i
$539$	−650.534	+	249.988i	−1.20693	+	0.463800i
$540$	−286.176	−	4.65552i	−0.529955	−	0.00862134i
$541$	−195.448	−	52.3702i	−0.361272	−	0.0968027i	0.0736168	−	0.997287i	$-0.476546\pi$
$541$	−195.448	−	52.3702i	−0.361272	−	0.0968027i	−0.434889	+	0.900484i	$0.643212\pi$
$542$	832.928	−	215.937i	1.53677	−	0.398408i
$543$	126.273	−	218.711i	0.232547	−	0.402784i
$544$	156.738	−	502.301i	0.288122	−	0.923348i
$545$			400.485i			0.734835i
$546$	105.496	−	115.308i	0.193215	−	0.211186i
$547$	−141.272	+	141.272i	−0.258266	+	0.258266i	−0.824349	−	0.566083i	$-0.808458\pi$
$547$	−141.272	+	141.272i	−0.258266	+	0.258266i	0.566083	+	0.824349i	$0.308458\pi$
$548$	426.874	+	767.951i	0.778968	+	1.40137i
$549$	−75.6516	−	282.336i	−0.137799	−	0.514273i
$550$	359.078	+	211.226i	0.652869	+	0.384048i
$551$	31.6000	+	54.7328i	0.0573503	+	0.0993336i
$552$	−297.529	−	7.26114i	−0.539003	−	0.0131542i
$553$	317.788	−	206.457i	0.574663	−	0.373339i
$554$	862.259	+	7.01317i	1.55642	+	0.0126592i
$555$	−36.2072	+	135.127i	−0.0652381	+	0.243472i
$556$	−229.817	+	57.5895i	−0.413339	+	0.103578i
$557$	189.032	+	705.477i	0.339375	+	1.26656i	0.899048	+	0.437851i	$0.144260\pi$
$557$	189.032	+	705.477i	0.339375	+	1.26656i	−0.559673	+	0.828714i	$0.689073\pi$
$558$	−110.983	−	30.7075i	−0.198895	−	0.0550314i
$559$		−	489.844i		−	0.876287i
$560$	−346.182	+	100.224i	−0.618183	+	0.178972i
$561$	323.207			0.576126
$562$	99.2852	−	358.838i	0.176664	−	0.638501i
$563$	−512.650	+	137.364i	−0.910569	+	0.243986i	−0.683550	−	0.729904i	$-0.739565\pi$
$563$	−512.650	+	137.364i	−0.910569	+	0.243986i	−0.227019	+	0.973890i	$0.572898\pi$
$564$	468.892	−	117.499i	0.831368	−	0.208332i
$565$	278.993	+	74.7560i	0.493793	+	0.132312i
$566$	−3.96677	+	487.708i	−0.00700843	+	0.861676i
$567$	206.341	+	105.089i	0.363917	+	0.185341i
$568$	46.4280	−	44.2158i	0.0817394	−	0.0778447i
$569$	541.145	−	312.430i	0.951047	−	0.549087i	0.0576406	−	0.998337i	$-0.481642\pi$
$569$	541.145	−	312.430i	0.951047	−	0.549087i	0.893406	+	0.449250i	$0.148309\pi$
$570$	−52.7462	+	89.6668i	−0.0925371	+	0.157310i
$571$	−830.906	+	222.640i	−1.45518	+	0.389913i	−0.897821	−	0.440361i	$-0.854850\pi$
$571$	−830.906	+	222.640i	−1.45518	+	0.389913i	−0.557355	+	0.830274i	$0.688184\pi$
$572$	223.268	+	401.661i	0.390328	+	0.702204i
$573$	−48.1755	−	48.1755i	−0.0840759	−	0.0840759i
$574$	−230.010	+	1041.33i	−0.400715	+	1.81416i
$575$	−394.245			−0.685643
$576$	−207.443	−	403.572i	−0.360144	−	0.700646i
$577$	−837.578	−	483.576i	−1.45161	−	0.838087i	−0.453036	−	0.891492i	$-0.649659\pi$
$577$	−837.578	−	483.576i	−1.45161	−	0.838087i	−0.998573	+	0.0534056i	$0.982992\pi$
$578$	9.34353	+	36.0405i	0.0161653	+	0.0623538i
$579$	−29.9186	+	111.658i	−0.0516729	+	0.192846i
$580$	−69.5387	−	1.13126i	−0.119894	−	0.00195045i
$581$	240.211	−	266.879i	0.413444	−	0.459344i
$582$	−2.29980	+	282.757i	−0.00395155	+	0.485838i
$583$	61.6989	−	35.6219i	0.105830	−	0.0611010i
$584$	−172.475	+	41.7325i	−0.295335	+	0.0714598i
$585$	−159.599	−	92.1445i	−0.272819	−	0.157512i
$586$	813.779	−	461.052i	1.38870	−	0.786777i
$587$	−69.0441	+	69.0441i	−0.117622	+	0.117622i	−0.763468	−	0.645846i	$-0.776505\pi$
$587$	−69.0441	+	69.0441i	−0.117622	+	0.117622i	0.645846	+	0.763468i	$0.276505\pi$
$588$	−266.829	−	46.6225i	−0.453791	−	0.0792900i
$589$	−67.1642	+	67.1642i	−0.114031	+	0.114031i
$590$	−88.7767	+	320.858i	−0.150469	+	0.543826i
$591$	−64.2458	−	37.0923i	−0.108707	−	0.0627620i
$592$	−490.152	+	114.387i	−0.827960	+	0.193221i
$593$	677.043	−	390.891i	1.14173	−	0.659175i	0.194868	−	0.980830i	$-0.437572\pi$
$593$	677.043	−	390.891i	1.14173	−	0.659175i	0.946857	+	0.321654i	$0.104239\pi$
$594$	450.886	−	443.611i	0.759067	−	0.746819i
$595$	−247.786	+	275.295i	−0.416447	+	0.462680i
$596$	−212.639	+	205.832i	−0.356777	+	0.345355i
$597$	67.7510	−	252.850i	0.113486	−	0.423534i
$598$	−374.841	−	220.499i	−0.626825	−	0.368727i
$599$	335.973	+	193.974i	0.560889	+	0.323830i	0.753502	−	0.657445i	$-0.228363\pi$
$599$	335.973	+	193.974i	0.560889	+	0.323830i	−0.192613	+	0.981275i	$0.561696\pi$
$600$	77.5148	+	142.160i	0.129191	+	0.236934i
$601$	−410.330			−0.682745			−0.341372	−	0.939928i	$-0.610892\pi$
$601$	−410.330			−0.682745			−0.341372	+	0.939928i	$0.610892\pi$
$602$	−715.677	+	456.717i	−1.18883	+	0.758666i
$603$	−398.232	−	398.232i	−0.660418	−	0.660418i
$604$	255.046	+	458.829i	0.422261	+	0.759651i
$605$	252.652	−	67.6980i	0.417607	−	0.111898i
$606$	78.0344	+	301.000i	0.128770	+	0.496699i
$607$	−109.096	+	62.9866i	−0.179730	+	0.103767i	−0.587166	−	0.809467i	$-0.699756\pi$
$607$	−109.096	+	62.9866i	−0.179730	+	0.103767i	0.407436	+	0.913234i	$0.366423\pi$
$608$	−373.980	−	15.2169i	−0.615099	−	0.0250277i
$609$	−46.5785	−	23.7222i	−0.0764836	−	0.0389528i
$610$	189.127	−	186.076i	0.310045	−	0.305042i
$611$	682.271	+	182.814i	1.11665	+	0.299205i
$612$	−400.015	−	239.708i	−0.653620	−	0.391680i
$613$	497.402	−	133.278i	0.811422	−	0.217420i	0.170829	−	0.985301i	$-0.445355\pi$
$613$	497.402	−	133.278i	0.811422	−	0.217420i	0.640593	+	0.767881i	$0.278689\pi$
$614$	−464.863	−	820.507i	−0.757106	−	1.33633i
$615$	−338.748			−0.550809
$616$	378.670	−	700.698i	0.614723	−	1.13750i
$617$			931.104i			1.50908i	0.656253	+	0.754541i	$0.272141\pi$
$617$			931.104i			1.50908i	−0.656253	+	0.754541i	$0.727859\pi$
$618$	81.4747	+	143.807i	0.131836	+	0.232697i
$619$	−2.75654	−	10.2876i	−0.00445322	−	0.0166196i	0.963663	−	0.267119i	$-0.0860718\pi$
$619$	−2.75654	−	10.2876i	−0.00445322	−	0.0166196i	−0.968117	+	0.250500i	$0.919405\pi$
$620$	−25.4072	−	101.390i	−0.0409794	−	0.163532i
$621$	−154.926	+	578.191i	−0.249478	+	0.931064i
$622$	123.831	−	121.833i	0.199086	−	0.195873i
$623$	830.543	−	539.576i	1.33313	−	0.866093i
$624$	−5.80980	+	178.517i	−0.00931057	+	0.286086i
$625$	−22.1863	−	38.4278i	−0.0354981	−	0.0614845i
$626$	54.7701	+	211.263i	0.0874921	+	0.337481i
$627$	−59.5037	−	222.071i	−0.0949022	−	0.354180i
$628$	1049.32	+	299.541i	1.67090	+	0.476976i
$629$	−365.765	+	365.765i	−0.581502	+	0.581502i
$630$	14.1798	+	319.092i	0.0225076	+	0.506495i
$631$			316.786i			0.502038i	0.967982	+	0.251019i	$0.0807656\pi$
$631$			316.786i			0.502038i	−0.967982	+	0.251019i	$0.919234\pi$
$632$	−122.268	+	415.485i	−0.193462	+	0.657413i
$633$	−243.754	+	422.194i	−0.385077	+	0.666974i
$634$	955.293	+	561.948i	1.50677	+	0.886353i
$635$	215.117	+	57.6404i	0.338767	+	0.0907722i
$636$	27.6869	+	0.450411i	0.0435328	+	0.000708194i
$637$	−307.688	−	248.975i	−0.483026	−	0.390856i
$638$	109.562	−	107.794i	0.171728	−	0.168957i
$639$	−28.4108	−	49.2090i	−0.0444614	−	0.0770093i
$640$	225.905	−	344.405i	0.352977	−	0.538133i
$641$	324.494	−	562.040i	0.506231	−	0.876818i	−0.493743	−	0.869608i	$-0.664372\pi$
$641$	324.494	−	562.040i	0.506231	−	0.876818i	0.999974	−	0.00721021i	$-0.00229510\pi$
$642$	79.9139	−	288.826i	0.124476	−	0.449884i
$643$	−468.828	−	468.828i	−0.729126	−	0.729126i	0.241319	−	0.970446i	$-0.422420\pi$
$643$	−468.828	−	468.828i	−0.729126	−	0.729126i	−0.970446	+	0.241319i	$0.922420\pi$
$644$	27.3361	+	753.242i	0.0424474	+	1.16963i
$645$	−190.692	−	190.692i	−0.295646	−	0.295646i
$646$	−334.680	+	189.615i	−0.518080	+	0.293521i
$647$	201.347	−	348.744i	0.311201	−	0.539017i	−0.667421	−	0.744680i	$-0.732602\pi$
$647$	201.347	−	348.744i	0.311201	−	0.539017i	0.978623	+	0.205664i	$0.0659353\pi$
$648$	−257.218	+	62.2370i	−0.396941	+	0.0960448i
$649$	−367.865	−	637.161i	−0.566818	−	0.981758i
$650$	−1.92433	+	236.593i	−0.00296051	+	0.363990i
$651$	16.3195	−	76.8460i	0.0250684	−	0.118043i
$652$	183.274	+	189.336i	0.281095	+	0.290392i
$653$	253.657	+	67.9672i	0.388449	+	0.104085i	0.447757	−	0.894155i	$-0.352223\pi$
$653$	253.657	+	67.9672i	0.388449	+	0.104085i	−0.0593084	+	0.998240i	$0.518890\pi$
$654$	−86.3283	−	332.992i	−0.132000	−	0.509162i
$655$	140.975	−	244.175i	0.215229	−	0.372787i
$656$	−574.734	−	1074.76i	−0.876118	−	1.63835i
$657$			157.269i			0.239375i
$658$	−369.034	−	1167.27i	−0.560842	−	1.77397i
$659$	167.587	−	167.587i	0.254305	−	0.254305i	−0.568428	−	0.822733i	$-0.692448\pi$
$659$	167.587	−	167.587i	0.254305	−	0.254305i	0.822733	+	0.568428i	$0.192448\pi$
$660$	243.279	+	69.4467i	0.368604	+	0.105222i
$661$	277.765	+	1036.63i	0.420219	+	1.56828i	0.774146	+	0.633006i	$0.218179\pi$
$661$	277.765	+	1036.63i	0.420219	+	1.56828i	−0.353927	+	0.935273i	$0.615154\pi$
$662$	276.639	−	470.278i	0.417884	−	0.710389i
$663$	91.7806	+	158.969i	0.138432	+	0.239772i
$664$	−10.0117	+	410.234i	−0.0150778	+	0.617823i
$665$	234.770	+	119.567i	0.353037	+	0.179800i
$666$	−3.62802	+	446.060i	−0.00544748	+	0.669760i
$667$	−37.6459	+	140.496i	−0.0564406	+	0.210639i
$668$	−646.306	−	387.296i	−0.967523	−	0.579785i
$669$	129.922	+	484.875i	0.194203	+	0.724776i
$670$	136.321	−	492.693i	0.203464	−	0.735363i
$671$			586.345i			0.873838i
$672$	266.236	−	157.956i	0.396185	−	0.235054i
$673$	−1057.27			−1.57097			−0.785487	−	0.618878i	$-0.787587\pi$
$673$	−1057.27			−1.57097			−0.785487	+	0.618878i	$0.787587\pi$
$674$	−322.409	−	89.2061i	−0.478352	−	0.132353i
$675$	314.567	−	84.2879i	0.466025	−	0.124871i
$676$	213.323	−	355.985i	0.315566	−	0.526605i
$677$	362.745	+	97.1972i	0.535812	+	0.143570i	0.516571	−	0.856244i	$-0.327208\pi$
$677$	362.745	+	97.1972i	0.535812	+	0.143570i	0.0192414	+	0.999815i	$0.493875\pi$
$678$	−248.089	−	2.01783i	−0.365913	−	0.00297615i
$679$	715.138	−	37.6094i	1.05322	−	0.0553894i
$680$	10.3274	−	423.171i	0.0151873	−	0.622311i
$681$	303.436	−	175.189i	0.445573	−	0.257252i
$682$	199.104	+	117.122i	0.291941	+	0.171733i
$683$	62.5296	−	16.7548i	0.0915514	−	0.0245311i	−0.212753	−	0.977106i	$-0.568243\pi$
$683$	62.5296	−	16.7548i	0.0915514	−	0.0245311i	0.304304	+	0.952575i	$0.401576\pi$
$684$	−91.0554	+	318.976i	−0.133122	+	0.466339i
$685$	499.793	+	499.793i	0.729625	+	0.729625i
$686$	−76.8805	+	681.678i	−0.112071	+	0.993700i
$687$	216.049			0.314482
$688$	281.478	−	928.549i	0.409125	−	1.34963i
$689$	35.0411	+	20.2310i	0.0508580	+	0.0293629i
$690$	−231.760	+	60.0840i	−0.335884	+	0.0870783i
$691$	−138.124	+	515.487i	−0.199890	+	0.746001i	0.791056	+	0.611744i	$0.209532\pi$
$691$	−138.124	+	515.487i	−0.199890	+	0.746001i	−0.990946	+	0.134257i	$0.957135\pi$
$692$	−651.577	+	630.717i	−0.941586	+	0.911441i
$693$	−524.659	−	472.232i	−0.757083	−	0.681431i
$694$	−1058.23	−	8.60712i	−1.52483	−	0.0124022i
$695$	−165.060	+	95.2974i	−0.237496	+	0.137119i
$696$	58.0633	−	14.0491i	0.0834242	−	0.0201855i
$697$	−1084.74	−	626.275i	−1.55630	−	0.898529i
$698$	299.241	+	528.175i	0.428712	+	0.756698i
$699$	163.765	−	163.765i	0.234284	−	0.234284i
$700$	347.464	−	217.782i	0.496378	−	0.311117i
$701$	128.165	−	128.165i	0.182832	−	0.182832i	−0.609757	−	0.792589i	$-0.708733\pi$
$701$	128.165	−	128.165i	0.182832	−	0.182832i	0.792589	+	0.609757i	$0.208733\pi$
$702$	346.227	+	95.7960i	0.493201	+	0.136462i
$703$	318.651	+	183.973i	0.453273	+	0.261697i
$704$	192.421	+	889.684i	0.273325	+	1.26376i
$705$	336.769	−	194.434i	0.477687	−	0.275793i
$706$	132.987	+	135.168i	0.188367	+	0.191456i
$707$	748.915	−	243.488i	1.05929	−	0.344396i
$708$	4.65137	−	285.920i	0.00656973	−	0.403842i
$709$	−340.257	+	1269.85i	−0.479911	+	1.79105i	0.122049	+	0.992524i	$0.461053\pi$
$709$	−340.257	+	1269.85i	−0.479911	+	1.79105i	−0.601960	+	0.798527i	$0.705613\pi$
$710$	26.1510	−	44.4559i	0.0368324	−	0.0626139i
$711$	332.416	+	191.921i	0.467533	+	0.269930i
$712$	−319.549	+	1085.87i	−0.448805	+	1.52510i
$713$	−218.604			−0.306597
$714$	146.684	−	282.312i	0.205440	−	0.395395i
$715$	261.406	+	261.406i	0.365603	+	0.365603i
$716$	178.302	−	624.609i	0.249025	−	0.872359i
$717$	−346.904	+	92.9526i	−0.483827	+	0.129641i
$718$	−382.388	+	99.1343i	−0.532574	+	0.138070i
$719$	174.142	−	100.541i	0.242200	−	0.139834i	−0.373987	−	0.927434i	$-0.622010\pi$
$719$	174.142	−	100.541i	0.242200	−	0.139834i	0.616188	+	0.787599i	$0.288676\pi$
$720$	−249.587	−	266.379i	−0.346649	−	0.369971i
$721$	351.018	−	228.045i	0.486849	−	0.316290i
$722$	−314.464	−	319.622i	−0.435546	−	0.442689i
$723$	−25.9028	−	6.94065i	−0.0358269	−	0.00959979i
$724$	709.037	−	177.677i	0.979333	−	0.245410i
$725$	76.4375	−	20.4814i	0.105431	−	0.0282502i
$726$	−195.480	+	110.751i	−0.269257	+	0.152549i
$727$	−386.126			−0.531122			−0.265561	−	0.964094i	$-0.585557\pi$
$727$	−386.126			−0.531122			−0.265561	+	0.964094i	$0.585557\pi$
$728$	452.168	−	12.7283i	0.621109	−	0.0174839i
$729$		−	42.0360i		−	0.0576625i
$730$	−124.205	+	70.3689i	−0.170143	+	0.0963958i
$731$	−258.084	−	963.183i	−0.353056	−	1.31762i
$732$	−117.143	+	195.485i	−0.160032	+	0.267055i
$733$	105.748	−	394.657i	0.144268	−	0.538414i	−0.855519	−	0.517771i	$-0.826762\pi$
$733$	105.748	−	394.657i	0.144268	−	0.538414i	0.999787	−	0.0206431i	$-0.00657137\pi$
$734$	−602.451	−	612.332i	−0.820779	−	0.834240i
$735$	−216.703	+	22.8563i	−0.294835	+	0.0310970i
$736$	−583.845	−	633.372i	−0.793267	−	0.860560i
$737$	564.875	+	978.393i	0.766453	+	1.32753i
$738$	−1045.59	+	271.069i	−1.41679	+	0.367303i
$739$	174.365	+	650.738i	0.235947	+	0.880566i	0.977720	+	0.209915i	$0.0673186\pi$
$739$	174.365	+	650.738i	0.235947	+	0.880566i	−0.741773	+	0.670651i	$0.766015\pi$
$740$	−353.903	+	196.721i	−0.478247	+	0.265839i
$741$	92.3280	−	92.3280i	0.124599	−	0.124599i
$742$	−3.11328	−	70.0590i	−0.00419579	−	0.0944191i
$743$		−	1027.49i		−	1.38290i	−0.722425	−	0.691450i	$-0.756972\pi$
$743$		−	1027.49i		−	1.38290i	0.722425	−	0.691450i	$-0.243028\pi$
$744$	42.9809	+	78.8261i	0.0577701	+	0.105949i
$745$	−119.037	+	206.178i	−0.159781	+	0.276750i
$746$	257.872	−	438.375i	0.345673	−	0.587634i
$747$	351.291	+	94.1280i	0.470268	+	0.126008i
$748$	650.635	+	672.154i	0.869833	+	0.898602i
$749$	−742.396	−	157.660i	−0.991183	−	0.210494i
$750$	247.297	+	251.353i	0.329730	+	0.335138i
$751$	−672.978	−	1165.63i	−0.896109	−	1.55211i	−0.832426	−	0.554136i	$-0.813049\pi$
$751$	−672.978	−	1165.63i	−0.896109	−	1.55211i	−0.0636829	−	0.997970i	$-0.520285\pi$
$752$	1188.26	+	738.594i	1.58014	+	0.982173i
$753$	148.078	−	256.479i	0.196651	−	0.340610i
$754$	84.1307	+	23.2778i	0.111579	+	0.0308724i
$755$	298.612	+	298.612i	0.395513	+	0.395513i
$756$	−182.851	−	595.165i	−0.241867	−	0.787256i
$757$	−18.1716	−	18.1716i	−0.0240048	−	0.0240048i	0.695003	−	0.719007i	$-0.255403\pi$
$757$	−18.1716	−	18.1716i	−0.0240048	−	0.0240048i	−0.719007	+	0.695003i	$0.755403\pi$
$758$	−363.778	−	642.086i	−0.479918	−	0.847079i
$759$	264.559	−	458.229i	0.348562	−	0.603727i
$760$	−292.656	+	70.8117i	−0.385074	+	0.0931734i
$761$	−513.120	−	888.750i	−0.674271	−	1.16787i	−0.976681	−	0.214693i	$-0.931125\pi$
$761$	−513.120	−	888.750i	−0.674271	−	1.16787i	0.302411	−	0.953178i	$-0.402209\pi$
$762$	−191.288	−	1.55584i	−0.251035	−	0.00204179i
$763$	−828.514	+	269.367i	−1.08586	+	0.353037i
$764$	3.20754	−	197.168i	0.00419835	−	0.258073i
$765$	−362.369	−	97.0964i	−0.473684	−	0.126923i
$766$	−98.4615	+	25.5262i	−0.128540	+	0.0333240i
$767$	208.924	−	361.868i	0.272392	−	0.471796i
$768$	−113.594	+	335.059i	−0.147909	+	0.436275i
$769$			389.923i			0.507052i	0.967329	+	0.253526i	$0.0815903\pi$
$769$			389.923i			0.507052i	−0.967329	+	0.253526i	$0.918410\pi$
$770$	138.194	−	625.650i	0.179473	−	0.812533i
$771$	−440.753	+	440.753i	−0.571664	+	0.571664i
$772$	−292.437	+	162.554i	−0.378804	+	0.210562i
$773$	98.3331	+	366.984i	0.127210	+	0.474753i	0.999909	−	0.0135053i	$-0.00429899\pi$
$773$	98.3331	+	366.984i	0.127210	+	0.474753i	−0.872699	+	0.488258i	$0.837632\pi$
$774$	−741.187	−	436.001i	−0.957606	−	0.563308i
$775$	59.4660	+	102.998i	0.0767303	+	0.132901i
$776$	−592.664	+	564.426i	−0.763742	+	0.727353i
$777$	−303.901	+	15.9823i	−0.391121	+	0.0205692i
$778$	−835.459	−	6.79519i	−1.07385	−	0.00873418i
$779$	−230.600	+	860.609i	−0.296020	+	1.10476i
$780$	34.9263	+	139.377i	0.0447773	+	0.178688i
$781$	29.5013	+	110.100i	0.0377738	+	0.140974i
$782$	−853.227	−	236.076i	−1.09108	−	0.301887i
$783$		−	120.150i		−	0.153449i
$784$	−440.185	−	648.763i	−0.561460	−	0.827504i
$785$	877.859			1.11829
$786$	−64.5821	+	233.413i	−0.0821655	+	0.296963i
$787$	−9.06903	+	2.43004i	−0.0115235	+	0.00308772i	−0.264576	−	0.964365i	$-0.585232\pi$
$787$	−9.06903	+	2.43004i	−0.0115235	+	0.00308772i	0.253053	+	0.967453i	$0.418565\pi$
$788$	−52.1920	−	208.278i	−0.0662335	−	0.264312i
$789$	−105.078	−	28.1555i	−0.133178	−	0.0356850i
$790$	−2.83372	+	348.402i	−0.00358699	+	0.441015i
$791$	32.9982	+	627.456i	0.0417170	+	0.793244i
$792$	806.482	+	19.6820i	1.01829	+	0.0248510i
$793$	−288.393	+	166.504i	−0.363673	+	0.209967i
$794$	730.906	−	1242.52i	0.920536	−	1.56488i
$795$	21.5169	−	5.76544i	0.0270653	−	0.00725213i
$796$	662.225	−	368.105i	0.831941	−	0.462444i
$797$	65.7242	+	65.7242i	0.0824645	+	0.0824645i	0.747136	−	0.664671i	$-0.231428\pi$
$797$	65.7242	+	65.7242i	0.0824645	+	0.0824645i	−0.664671	+	0.747136i	$0.731428\pi$
$798$	−220.978	−	48.8099i	−0.276915	−	0.0611653i
$799$	1437.87			1.79959
$800$	−139.601	+	447.381i	−0.174501	+	0.559226i
$801$	868.772	+	501.586i	1.08461	+	0.626200i
$802$	−109.577	−	422.669i	−0.136630	−	0.527019i
$803$	81.6528	−	304.732i	0.101685	−	0.379492i
$804$	−7.14242	+	439.046i	−0.00888360	+	0.546077i
$805$	187.478	+	576.641i	0.232892	+	0.716324i
$806$	−1.06702	+	131.188i	−0.00132384	+	0.162764i
$807$	−101.025	+	58.3266i	−0.125185	+	0.0722758i
$808$	−468.884	+	768.215i	−0.580302	+	0.950761i
$809$	885.324	+	511.142i	1.09434	+	0.631820i	0.934730	−	0.355360i	$-0.115642\pi$
$809$	885.324	+	511.142i	1.09434	+	0.631820i	0.159614	+	0.987179i	$0.448975\pi$
$810$	−185.230	+	104.943i	−0.228679	+	0.129560i
$811$	938.812	−	938.812i	1.15760	−	1.15760i	0.172608	−	0.984991i	$-0.444781\pi$
$811$	938.812	−	938.812i	1.15760	−	1.15760i	0.984991	−	0.172608i	$-0.0552194\pi$
$812$	−44.4316	−	144.621i	−0.0547188	−	0.178105i
$813$	−420.431	+	420.431i	−0.517135	+	0.517135i
$814$	238.620	−	862.424i	0.293145	−	1.05949i
$815$	183.583	+	105.992i	0.225255	+	0.130051i
$816$	82.6316	+	354.081i	0.101264	+	0.433922i
$817$	−614.275	+	354.652i	−0.751867	+	0.434091i
$818$	579.444	−	570.094i	0.708367	−	0.696937i
$819$	83.2797	−	392.152i	0.101685	−	0.478818i
$820$	−681.920	−	704.474i	−0.831610	−	0.859115i
$821$	−41.7129	+	155.675i	−0.0508075	+	0.189616i	−0.986665	−	0.162761i	$-0.947960\pi$
$821$	−41.7129	+	155.675i	−0.0508075	+	0.189616i	0.935858	+	0.352377i	$0.114627\pi$
$822$	−523.298	−	307.828i	−0.636616	−	0.374487i
$823$	−687.784	−	397.092i	−0.835704	−	0.482494i	0.0200978	−	0.999798i	$-0.493602\pi$
$823$	−687.784	−	397.092i	−0.835704	−	0.482494i	−0.855802	+	0.517304i	$0.826936\pi$
$824$	−135.053	+	458.930i	−0.163900	+	0.556954i
$825$	−287.868			−0.348931
$826$	−723.495	+	32.1506i	−0.875901	+	0.0389233i
$827$	117.766	+	117.766i	0.142401	+	0.142401i	0.774713	−	0.632312i	$-0.217894\pi$
$827$	117.766	+	117.766i	0.142401	+	0.142401i	−0.632312	+	0.774713i	$0.717894\pi$
$828$	−667.278	+	370.914i	−0.805891	+	0.447964i
$829$	1086.17	−	291.037i	1.31021	−	0.351070i	0.464910	−	0.885358i	$-0.346087\pi$
$829$	1086.17	−	291.037i	1.31021	−	0.351070i	0.845303	+	0.534288i	$0.179420\pi$
$830$	82.8440	+	319.552i	0.0998120	+	0.385002i
$831$	−516.012	+	297.920i	−0.620953	+	0.358507i
$832$	−382.948	+	347.284i	−0.460274	+	0.417409i
$833$	−736.185	−	327.450i	−0.883776	−	0.393097i
$834$	116.700	−	114.817i	0.139928	−	0.137671i
$835$	−585.480	−	156.879i	−0.701173	−	0.187879i
$836$	342.043	−	570.789i	0.409143	−	0.682762i
$837$	174.423	−	46.7366i	0.208391	−	0.0558382i
$838$	176.891	+	312.221i	0.211087	+	0.372578i
$839$	393.596			0.469126			0.234563	−	0.972101i	$-0.424634\pi$
$839$	393.596			0.469126			0.234563	+	0.972101i	$0.424634\pi$
$840$	171.069	−	180.979i	0.203654	−	0.215452i
$841$			811.804i			0.965285i
$842$	−793.313	−	1400.24i	−0.942176	−	1.66299i
$843$	66.5870	+	248.506i	0.0789881	+	0.294788i
$844$	−1368.71	+	342.982i	−1.62169	+	0.406377i
$845$	86.4088	−	322.482i	0.102259	−	0.381635i
$846$	883.894	−	869.631i	1.04479	−	1.02793i
$847$	309.987	+	477.148i	0.365982	+	0.563339i
$848$	54.7987	+	58.4855i	0.0646211	+	0.0689687i
$849$	−168.508	−	291.865i	−0.198479	−	0.343775i
$850$	120.870	+	466.229i	0.142200	+	0.548505i
$851$	219.172	+	817.960i	0.257546	+	0.961175i
$852$	−12.1609	+	42.6009i	−0.0142734	+	0.0500010i
$853$	−533.322	+	533.322i	−0.625232	+	0.625232i	−0.946864	−	0.321633i	$-0.895768\pi$
$853$	−533.322	+	533.322i	−0.625232	+	0.625232i	0.321633	+	0.946864i	$0.395768\pi$
$854$	512.157	+	266.107i	0.599715	+	0.311601i
$855$			266.854i			0.312110i
$856$	761.525	−	415.231i	0.889633	−	0.485083i
$857$	85.8259	−	148.655i	0.100147	−	0.173460i	−0.811598	−	0.584216i	$-0.801402\pi$
$857$	85.8259	−	148.655i	0.100147	−	0.173460i	0.911745	+	0.410757i	$0.134735\pi$
$858$	−273.700	−	161.003i	−0.318998	−	0.187649i
$859$	−80.6202	−	21.6021i	−0.0938536	−	0.0251480i	0.211587	−	0.977359i	$-0.432137\pi$
$859$	−80.6202	−	21.6021i	−0.0938536	−	0.0251480i	−0.305440	+	0.952211i	$0.598804\pi$
$860$	12.6963	−	780.444i	0.0147631	−	0.907493i
$861$	−227.843	−	700.794i	−0.264626	−	0.813930i
$862$	−164.704	+	162.046i	−0.191072	+	0.187989i
$863$	−664.894	−	1151.63i	−0.770445	−	1.33445i	−0.937319	−	0.348472i	$-0.886701\pi$
$863$	−664.894	−	1151.63i	−0.770445	−	1.33445i	0.166874	−	0.985978i	$-0.446633\pi$
$864$	601.261	+	380.542i	0.695903	+	0.440442i
$865$	−364.758	+	631.780i	−0.421686	+	0.730381i
$866$	−434.503	+	1570.39i	−0.501736	+	1.81338i
$867$	−18.1919	−	18.1919i	−0.0209826	−	0.0209826i
$868$	192.664	−	120.757i	0.221964	−	0.139121i
$869$	−544.462	−	544.462i	−0.626539	−	0.626539i
$870$	41.8131	−	23.6895i	0.0480610	−	0.0272293i
$871$	−320.814	+	555.666i	−0.368328	+	0.637964i
$872$	518.719	−	849.865i	0.594862	−	0.974616i
$873$	362.671	+	628.164i	0.415431	+	0.719547i
$874$	−5.12168	+	629.703i	−0.00586004	+	0.720484i
$875$	597.420	−	663.745i	0.682766	−	0.758566i
$876$	88.1039	−	85.2832i	0.100575	−	0.0973553i
$877$	−835.552	−	223.886i	−0.952739	−	0.255286i	−0.251215	−	0.967931i	$-0.580830\pi$
$877$	−835.552	−	223.886i	−0.952739	−	0.255286i	−0.701524	+	0.712646i	$0.747497\pi$
$878$	283.862	+	1094.93i	0.323305	+	1.24708i
$879$	−323.149	+	559.710i	−0.367632	+	0.636758i
$880$	345.311	+	645.733i	0.392398	+	0.733787i
$881$			6.44588i			0.00731655i	0.999993	+	0.00365827i	$0.00116447\pi$
$881$			6.44588i			0.00731655i	−0.999993	+	0.00365827i	$0.998836\pi$
$882$	−650.593	+	243.957i	−0.737634	+	0.276595i
$883$	529.179	−	529.179i	0.599297	−	0.599297i	−0.340829	−	0.940125i	$-0.610708\pi$
$883$	529.179	−	529.179i	0.599297	−	0.599297i	0.940125	+	0.340829i	$0.110708\pi$
$884$	−145.838	+	510.885i	−0.164975	+	0.577924i
$885$	−59.5393	−	222.204i	−0.0672761	−	0.251078i
$886$	593.370	−	1008.71i	0.669717	−	1.13850i
$887$	364.311	+	631.005i	0.410723	+	0.711392i	0.994969	−	0.100184i	$-0.0319432\pi$
$887$	364.311	+	631.005i	0.410723	+	0.711392i	−0.584246	+	0.811576i	$0.698610\pi$
$888$	251.855	−	239.855i	0.283621	−	0.270107i
$889$	25.4431	+	483.798i	0.0286200	+	0.544205i
$890$	−7.40596	+	910.551i	−0.00832130	+	1.02309i
$891$	121.771	−	454.457i	0.136668	−	0.510053i
$892$	−746.826	+	1246.27i	−0.837249	+	1.39717i
$893$	−264.718	−	987.942i	−0.296437	−	1.10632i
$894$	54.5322	−	197.091i	0.0609980	−	0.220460i
$895$		−	522.545i		−	0.583849i
$896$	864.443	+	235.700i	0.964780	+	0.263058i
$897$	300.506			0.335012
$898$	556.726	+	154.038i	0.619962	+	0.171534i
$899$	42.3836	−	11.3567i	0.0471453	−	0.0126325i
$900$	356.279	+	213.499i	0.395865	+	0.237221i
$901$	79.5607	+	21.3182i	0.0883026	+	0.0236606i
$902$	2166.72	+	17.6230i	2.40213	+	0.0195377i
$903$	266.239	−	522.758i	0.294838	−	0.578913i
$904$	−495.222	−	519.999i	−0.547812	−	0.575220i
$905$	509.248	−	294.014i	0.562705	−	0.324878i
$906$	−312.656	−	183.919i	−0.345095	−	0.203001i
$907$	144.057	−	38.5999i	0.158828	−	0.0425577i	−0.178529	−	0.983935i	$-0.557134\pi$
$907$	144.057	−	38.5999i	0.158828	−	0.0425577i	0.337357	+	0.941377i	$0.390467\pi$
$908$	975.164	+	278.372i	1.07397	+	0.306577i
$909$	564.015	+	564.015i	0.620478	+	0.620478i
$910$	346.968	−	109.694i	0.381284	−	0.120543i
$911$	233.157			0.255935			0.127967	−	0.991778i	$-0.459155\pi$
$911$	233.157			0.255935			0.127967	+	0.991778i	$0.459155\pi$
$912$	228.071	−	121.963i	0.250078	−	0.133731i
$913$	−631.807	−	364.774i	−0.692012	−	0.399534i
$914$	−497.497	+	128.976i	−0.544307	+	0.141112i
$915$	−47.4503	+	177.087i	−0.0518582	+	0.193538i
$916$	434.921	+	449.306i	0.474805	+	0.490508i
$917$	599.965	+	127.412i	0.654269	+	0.138945i
$918$	731.260	+	5.94769i	0.796579	+	0.00647897i
$919$	1262.56	−	728.937i	1.37384	−	0.793185i	0.382429	−	0.923985i	$-0.375088\pi$
$919$	1262.56	−	728.937i	1.37384	−	0.793185i	0.991409	+	0.130800i	$0.0417545\pi$
$920$	−591.501	−	361.026i	−0.642936	−	0.392419i
$921$	564.338	+	325.821i	0.612745	+	0.353768i
$922$	−725.893	−	1281.24i	−0.787303	−	1.38963i
$923$	−45.7752	+	45.7752i	−0.0495940	+	0.0495940i
$924$	19.9602	+	549.999i	0.0216020	+	0.595237i
$925$	325.773	−	325.773i	0.352187	−	0.352187i
$926$	−546.568	−	151.227i	−0.590246	−	0.163313i
$927$	367.175	+	211.989i	0.396090	+	0.228683i
$928$	146.102	+	92.4691i	0.157438	+	0.0996434i
$929$	−147.357	+	85.0763i	−0.158618	+	0.0915784i	−0.577208	−	0.816597i	$-0.695858\pi$
$929$	−147.357	+	85.0763i	−0.158618	+	0.0915784i	0.418590	+	0.908175i	$0.362525\pi$
$930$	50.6548	+	51.4856i	0.0544676	+	0.0553608i
$931$	−89.4512	+	566.107i	−0.0960808	+	0.608064i
$932$	670.241	+	10.9035i	0.719143	+	0.0116990i
$933$	−31.0682	+	115.948i	−0.0332992	+	0.124274i
$934$	−568.649	+	966.685i	−0.608831	+	1.03499i
$935$	651.732	+	376.277i	0.697039	+	0.402436i
$936$	219.335	+	402.256i	0.234333	+	0.429761i
$937$	436.868			0.466241			0.233121	−	0.972448i	$-0.425106\pi$
$937$	436.868			0.466241			0.233121	+	0.972448i	$0.425106\pi$
$938$	1110.96	−	49.3689i	1.18440	−	0.0526321i
$939$	−106.638	−	106.638i	−0.113565	−	0.113565i
$940$	1082.29	+	308.952i	1.15137	+	0.328673i
$941$	1006.04	−	269.569i	1.06912	−	0.286471i	0.318990	−	0.947758i	$-0.396656\pi$
$941$	1006.04	−	269.569i	1.06912	−	0.286471i	0.750133	+	0.661287i	$0.229990\pi$
$942$	−729.914	+	189.231i	−0.774856	+	0.200882i
$943$	−1775.81	+	1025.27i	−1.88315	+	1.08724i
$944$	603.976	−	565.903i	0.639805	−	0.599473i
$945$	−272.872	−	420.018i	−0.288753	−	0.444464i
$946$	1209.79	+	1229.63i	1.27885	+	1.29982i
$947$	375.839	+	100.706i	0.396873	+	0.106342i	0.451735	−	0.892152i	$-0.350805\pi$
$947$	375.839	+	100.706i	0.396873	+	0.106342i	−0.0548621	+	0.998494i	$0.517472\pi$
$948$	−72.7452	−	290.297i	−0.0767354	−	0.306220i
$949$	173.069	−	46.3737i	0.182370	−	0.0488659i
$950$	298.087	−	168.883i	0.313775	−	0.177771i
$951$	−765.847			−0.805307
$952$	882.393	−	263.261i	0.926884	−	0.276535i
$953$		−	160.455i		−	0.168368i	−0.996450	−	0.0841839i	$-0.973172\pi$
$953$		−	160.455i		−	0.168368i	0.996450	−	0.0841839i	$-0.0268283\pi$
$954$	61.8011	−	35.0138i	0.0647811	−	0.0367021i
$955$	−41.0578	−	153.230i	−0.0429924	−	0.160450i
$956$	−891.648	−	534.317i	−0.932686	−	0.558909i
$957$	−27.4881	+	102.587i	−0.0287232	+	0.107197i
$958$	−388.308	−	394.676i	−0.405332	−	0.411979i
$959$	−697.798	+	1370.12i	−0.727631	+	1.42870i
$960$	−13.8835	+	284.272i	−0.0144619	+	0.296117i
$961$	−447.527	−	775.139i	−0.465689	−	0.806597i
$962$	491.943	−	127.536i	0.511375	−	0.132574i
$963$	−198.959	−	742.526i	−0.206604	−	0.771055i
$964$	−37.7100	−	67.8406i	−0.0391182	−	0.0703741i
$965$	−190.322	+	190.322i	−0.197225	+	0.197225i
$966$	−280.183	−	439.048i	−0.290045	−	0.454501i
$967$		−	956.667i		−	0.989315i	−0.869088	−	0.494657i	$-0.835294\pi$
$967$		−	956.667i		−	0.989315i	0.869088	−	0.494657i	$-0.164706\pi$
$968$	−623.835	−	183.581i	−0.644458	−	0.189650i
$969$	132.900	−	230.190i	0.137152	−	0.237554i
$970$	−333.824	+	567.490i	−0.344148	+	0.585041i
$971$	−248.423	−	66.5647i	−0.255842	−	0.0685527i	0.128618	−	0.991694i	$-0.458946\pi$
$971$	−248.423	−	66.5647i	−0.255842	−	0.0685527i	−0.384460	+	0.923141i	$0.625612\pi$
$972$	706.572	−	683.951i	0.726926	−	0.703653i
$973$	−308.169	−	277.375i	−0.316720	−	0.285072i
$974$	834.072	+	847.751i	0.856337	+	0.870381i
$975$	−81.7456	−	141.587i	−0.0838416	−	0.145218i
$976$	−642.355	+	149.906i	−0.658151	+	0.153592i
$977$	−128.826	+	223.132i	−0.131858	+	0.228385i	−0.924393	−	0.381442i	$-0.875428\pi$
$977$	−128.826	+	223.132i	−0.131858	+	0.228385i	0.792535	+	0.609827i	$0.208761\pi$
$978$	−175.491	−	48.5559i	−0.179439	−	0.0496482i
$979$	−1422.96	−	1422.96i	−1.45348	−	1.45348i
$980$	−483.770	−	404.655i	−0.493643	−	0.412913i
$981$	−623.961	−	623.961i	−0.636046	−	0.636046i
$982$	489.090	+	863.268i	0.498055	+	0.879092i
$983$	−36.8020	+	63.7429i	−0.0374384	+	0.0648453i	−0.884137	−	0.467227i	$-0.845253\pi$
$983$	−36.8020	+	63.7429i	−0.0374384	+	0.0648453i	0.846699	+	0.532072i	$0.178586\pi$
$984$	718.853	+	438.755i	0.730542	+	0.445890i
$985$	−86.3658	−	149.590i	−0.0876810	−	0.151868i
$986$	177.691	+	1.44525i	0.180214	+	0.00146577i
$987$	628.753	+	565.924i	0.637034	+	0.573378i
$988$	377.871	+	6.14723i	0.382461	+	0.00622189i
$989$	−1576.81	−	422.506i	−1.59435	−	0.427205i
$990$	628.209	−	162.864i	0.634554	−	0.164509i
$991$	−530.205	+	918.342i	−0.535020	+	0.926682i	0.464142	+	0.885761i	$0.346363\pi$
$991$	−530.205	+	918.342i	−0.535020	+	0.926682i	−0.999162	+	0.0409214i	$0.986971\pi$
$992$	−77.4068	+	248.067i	−0.0780311	+	0.250067i
$993$			377.016i			0.379673i
$994$	109.559	+	24.1994i	0.110220	+	0.0243455i
$995$	430.985	−	430.985i	0.433151	−	0.433151i
$996$	−137.765	−	247.840i	−0.138318	−	0.248835i
$997$	−276.601	−	1032.29i	−0.277433	−	1.03539i	−0.954193	−	0.299190i	$-0.903283\pi$
$997$	−276.601	−	1032.29i	−0.277433	−	1.03539i	0.676761	−	0.736203i	$-0.263383\pi$
$998$	−197.993	−	116.469i	−0.198390	−	0.116702i
$999$	−349.753	−	605.790i	−0.350103	−	0.606397i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	112.3.x.a.101.4	yes	120
7.5	odd	6	inner	112.3.x.a.5.17	✓	120
16.13	even	4	inner	112.3.x.a.45.17	yes	120
112.61	odd	12	inner	112.3.x.a.61.4	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.3.x.a.5.17	✓	120	7.5	odd	6	inner
112.3.x.a.45.17	yes	120	16.13	even	4	inner
112.3.x.a.61.4	yes	120	112.61	odd	12	inner
112.3.x.a.101.4	yes	120	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 112 = 2^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	112.x (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.92758 - 0.533333i) q^{2} +(1.33491 - 0.357687i) q^{3} +(3.43111 + 2.05608i) q^{4} +(3.10820 + 0.832839i) q^{5} +(-2.76390 - 0.0224802i) q^{6} +(0.367625 + 6.99034i) q^{7} +(-5.51716 - 5.79318i) q^{8} +(-6.14019 + 3.54504i) q^{9} +(-5.54711 - 3.26307i) q^{10} +(13.7381 - 3.68111i) q^{11} +(5.31565 + 1.51741i) q^{12} +(5.71174 + 5.71174i) q^{13} +(3.01955 - 13.6705i) q^{14} +4.44705 q^{15} +(7.54505 + 14.1093i) q^{16} +(14.2404 + 8.22168i) q^{17} +(13.7264 - 3.55858i) q^{18} +(3.02729 - 11.2980i) q^{19} +(8.95219 + 9.24827i) q^{20} +(2.99110 + 9.19996i) q^{21} +(-28.4445 - 0.231353i) q^{22} +(23.3127 - 13.4596i) q^{23} +(-9.43704 - 5.75994i) q^{24} +(-12.6834 - 7.32274i) q^{25} +(-7.96356 - 14.0561i) q^{26} +(-15.7235 + 15.7235i) q^{27} +(-13.1114 + 24.7405i) q^{28} +(-3.82071 + 3.82071i) q^{29} +(-8.57203 - 2.37176i) q^{30} +(-7.03276 - 4.06036i) q^{31} +(-7.01872 - 31.2208i) q^{32} +(17.0224 - 9.82788i) q^{33} +(-23.0645 - 23.4428i) q^{34} +(-4.67918 + 22.0335i) q^{35} +(-28.3566 - 0.461306i) q^{36} +(-8.14184 + 30.3858i) q^{37} +(-11.8609 + 20.1632i) q^{38} +(9.66765 + 5.58162i) q^{39} +(-12.3236 - 22.6013i) q^{40} -76.1736 q^{41} +(-0.858936 - 19.3289i) q^{42} +(-42.8805 - 42.8805i) q^{43} +(54.7056 + 15.6163i) q^{44} +(-22.0374 + 5.90490i) q^{45} +(-52.1155 + 13.5110i) q^{46} +(75.7287 - 43.7220i) q^{47} +(15.1187 + 16.1358i) q^{48} +(-48.7297 + 5.13965i) q^{49} +(20.5427 + 20.8796i) q^{50} +(21.9503 + 5.88158i) q^{51} +(7.85381 + 31.3414i) q^{52} +(4.83847 - 1.29646i) q^{53} +(38.6942 - 21.9225i) q^{54} +45.7665 q^{55} +(38.4681 - 40.6965i) q^{56} -16.1646i q^{57} +(9.40243 - 5.32700i) q^{58} +(-13.3885 - 49.9666i) q^{59} +(15.2583 + 9.14350i) q^{60} +(-10.6701 + 39.8212i) q^{61} +(11.3907 + 11.5775i) q^{62} +(-27.0383 - 41.6188i) q^{63} +(-3.12195 + 63.9238i) q^{64} +(12.9963 + 22.5102i) q^{65} +(-38.0535 + 9.86540i) q^{66} +(20.5587 + 76.7262i) q^{67} +(31.9558 + 57.4889i) q^{68} +(26.3060 - 26.3060i) q^{69} +(20.7707 - 39.9758i) q^{70} +8.01424i q^{71} +(54.4135 + 16.0127i) q^{72} +(11.0908 - 19.2098i) q^{73} +(31.8998 - 54.2286i) q^{74} +(-19.5504 - 5.23850i) q^{75} +(33.6166 - 32.5403i) q^{76} +(30.7827 + 94.6807i) q^{77} +(-15.6583 - 15.9151i) q^{78} +(-27.0689 - 46.8846i) q^{79} +(11.7007 + 50.1383i) q^{80} +(16.5400 - 28.6482i) q^{81} +(146.830 + 40.6259i) q^{82} +(-36.2707 - 36.2707i) q^{83} +(-8.65307 + 37.7160i) q^{84} +(37.4145 + 37.4145i) q^{85} +(59.7859 + 105.525i) q^{86} +(-3.73367 + 6.46691i) q^{87} +(-97.1206 - 59.2780i) q^{88} +(-70.7447 - 122.533i) q^{89} +(45.6280 + 0.371115i) q^{90} +(-37.8272 + 42.0268i) q^{91} +(107.663 + 1.75146i) q^{92} +(-10.8404 - 2.90468i) q^{93} +(-169.291 + 43.8889i) q^{94} +(18.8188 - 32.5952i) q^{95} +(-20.5366 - 39.1663i) q^{96} -102.304i q^{97} +(96.6714 + 16.0821i) q^{98} +(-71.3049 + 71.3049i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 2 q^{2} - 6 q^{3} + 4 q^{4} - 6 q^{5} + 4 q^{8} - 60 q^{10} - 18 q^{11} - 6 q^{12} - 28 q^{14} - 16 q^{15} + 8 q^{16} - 12 q^{17} + 2 q^{18} - 6 q^{19} + 14 q^{21} - 20 q^{22} - 6 q^{24} - 6 q^{26}+ \cdots - 848 q^{99}+O(q^{100}) \) 120 * q - 2 * q^2 - 6 * q^3 + 4 * q^4 - 6 * q^5 + 4 * q^8 - 60 * q^10 - 18 * q^11 - 6 * q^12 - 28 * q^14 - 16 * q^15 + 8 * q^16 - 12 * q^17 + 2 * q^18 - 6 * q^19 + 14 * q^21 - 20 * q^22 - 6 * q^24 - 6 * q^26 - 6 * q^28 + 24 * q^29 + 10 * q^30 - 12 * q^31 - 92 * q^32 - 12 * q^33 + 94 * q^35 + 128 * q^36 + 46 * q^37 - 6 * q^38 - 66 * q^40 - 78 * q^42 + 88 * q^43 - 182 * q^44 - 60 * q^45 - 108 * q^46 - 12 * q^47 - 8 * q^49 - 8 * q^50 - 118 * q^51 - 564 * q^52 - 82 * q^53 - 306 * q^54 + 400 * q^56 + 346 * q^58 - 198 * q^59 - 186 * q^60 - 6 * q^61 - 204 * q^63 + 16 * q^64 - 4 * q^65 + 870 * q^66 + 222 * q^67 + 384 * q^68 + 556 * q^70 - 52 * q^72 + 126 * q^74 - 156 * q^75 - 102 * q^77 - 28 * q^78 - 4 * q^79 + 300 * q^80 + 248 * q^81 - 810 * q^82 - 288 * q^84 - 108 * q^85 - 196 * q^86 + 366 * q^88 + 88 * q^91 + 172 * q^92 - 38 * q^93 + 606 * q^94 - 388 * q^95 + 996 * q^96 - 848 * q^99

Introduction

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