LMFDB - Embedded newform 241.2.c.a.225.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [241,2,Mod(15,241)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(241, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("241.15");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 241 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	241.c (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.92439468871$
Analytic rank:	$0$
Dimension:	$38$
Relative dimension:	$19$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			225.15
Character	$\chi$	$=$	241.225
Dual form			241.2.c.a.15.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.820137 - 1.42052i) q^{2} +(-1.19817 - 2.07530i) q^{3} +(-0.345250 - 0.597991i) q^{4} -4.29952 q^{5} -3.93067 q^{6} +(-0.578431 + 1.00187i) q^{7} +2.14794 q^{8} +(-1.37125 + 2.37507i) q^{9} +O(q^{10})$	\(q+(0.820137 - 1.42052i) q^{2} +(-1.19817 - 2.07530i) q^{3} +(-0.345250 - 0.597991i) q^{4} -4.29952 q^{5} -3.93067 q^{6} +(-0.578431 + 1.00187i) q^{7} +2.14794 q^{8} +(-1.37125 + 2.37507i) q^{9} +(-3.52620 + 6.10755i) q^{10} +(-0.0451539 + 0.0782089i) q^{11} +(-0.827340 + 1.43300i) q^{12} +(-2.65056 - 4.59090i) q^{13} +(0.948786 + 1.64335i) q^{14} +(5.15157 + 8.92279i) q^{15} +(2.45211 - 4.24717i) q^{16} -1.64306 q^{17} +(2.24922 + 3.89576i) q^{18} +(1.20168 - 2.08136i) q^{19} +(1.48441 + 2.57107i) q^{20} +2.77225 q^{21} +(0.0740648 + 0.128284i) q^{22} -7.62049 q^{23} +(-2.57361 - 4.45762i) q^{24} +13.4859 q^{25} -8.69528 q^{26} -0.617081 q^{27} +0.798814 q^{28} +(3.30454 - 5.72364i) q^{29} +16.9000 q^{30} +(2.44152 - 4.22884i) q^{31} +(-1.87419 - 3.24619i) q^{32} +0.216409 q^{33} +(-1.34753 + 2.33399i) q^{34} +(2.48698 - 4.30757i) q^{35} +1.89369 q^{36} +(-3.76545 + 6.52195i) q^{37} +(-1.97108 - 3.41401i) q^{38} +(-6.35166 + 11.0014i) q^{39} -9.23510 q^{40} -0.316578 q^{41} +(2.27362 - 3.93803i) q^{42} +4.02686 q^{43} +0.0623576 q^{44} +(5.89570 - 10.2116i) q^{45} +(-6.24985 + 10.8251i) q^{46} -1.08055 q^{47} -11.7522 q^{48} +(2.83083 + 4.90315i) q^{49} +(11.0603 - 19.1569i) q^{50} +(1.96867 + 3.40984i) q^{51} +(-1.83021 + 3.17002i) q^{52} +(-4.62703 - 8.01425i) q^{53} +(-0.506091 + 0.876576i) q^{54} +(0.194140 - 0.336261i) q^{55} +(-1.24243 + 2.15196i) q^{56} -5.75927 q^{57} +(-5.42036 - 9.38833i) q^{58} +(2.07761 - 3.59852i) q^{59} +(3.55716 - 6.16119i) q^{60} +10.5427 q^{61} +(-4.00477 - 6.93646i) q^{62} +(-1.58634 - 2.74763i) q^{63} +3.66006 q^{64} +(11.3961 + 19.7387i) q^{65} +(0.177485 - 0.307413i) q^{66} +(3.71258 - 6.43038i) q^{67} +(0.567266 + 0.982533i) q^{68} +(9.13068 + 15.8148i) q^{69} +(-4.07932 - 7.06559i) q^{70} +(7.25388 - 12.5641i) q^{71} +(-2.94535 + 5.10150i) q^{72} +9.21934 q^{73} +(6.17637 + 10.6978i) q^{74} +(-16.1584 - 27.9872i) q^{75} -1.65951 q^{76} +(-0.0522369 - 0.0904769i) q^{77} +(10.4185 + 18.0453i) q^{78} -9.74235 q^{79} +(-10.5429 + 18.2608i) q^{80} +(4.85311 + 8.40583i) q^{81} +(-0.259637 + 0.449705i) q^{82} +(-3.84438 + 6.65867i) q^{83} +(-0.957119 - 1.65778i) q^{84} +7.06435 q^{85} +(3.30258 - 5.72023i) q^{86} -15.8377 q^{87} +(-0.0969879 + 0.167988i) q^{88} +(-2.61828 + 4.53499i) q^{89} +(-9.67056 - 16.7499i) q^{90} +6.13266 q^{91} +(2.63098 + 4.55698i) q^{92} -11.7015 q^{93} +(-0.886195 + 1.53494i) q^{94} +(-5.16662 + 8.94886i) q^{95} +(-4.49121 + 7.77900i) q^{96} +(-1.12438 - 1.94749i) q^{97} +9.28669 q^{98} +(-0.123834 - 0.214487i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q + q^{2} + 2 q^{3} - 21 q^{4} - 4 q^{5} - 5 q^{7} - 12 q^{8} - 13 q^{9}+O(q^{10}) $ 38 * q + q^2 + 2 * q^3 - 21 * q^4 - 4 * q^5 - 5 * q^7 - 12 * q^8 - 13 * q^9	\( 38 q + q^{2} + 2 q^{3} - 21 q^{4} - 4 q^{5} - 5 q^{7} - 12 q^{8} - 13 q^{9} - 8 q^{10} - 4 q^{11} + 21 q^{12} - 9 q^{13} + 6 q^{14} + 4 q^{15} - 25 q^{16} - 18 q^{17} + 5 q^{18} + 3 q^{19} - 5 q^{20} + 10 q^{21} - 7 q^{22} - 10 q^{23} - 9 q^{24} + 54 q^{25} + 20 q^{26} - 4 q^{27} + 8 q^{28} + 25 q^{29} - 22 q^{30} - 8 q^{31} + 23 q^{32} - 28 q^{33} - 4 q^{34} - 7 q^{35} + 18 q^{36} + 12 q^{37} + 30 q^{38} + 20 q^{39} - 4 q^{40} - 20 q^{41} - 30 q^{42} + 12 q^{43} - 2 q^{44} - 9 q^{45} - 19 q^{46} - 42 q^{47} - 84 q^{48} + 6 q^{49} + 31 q^{50} + 11 q^{51} - 16 q^{52} + q^{53} + 42 q^{54} - 11 q^{55} - 5 q^{56} - 22 q^{57} - 2 q^{58} + 22 q^{59} + 48 q^{60} - 26 q^{61} - 44 q^{62} - q^{63} + 72 q^{64} - 19 q^{65} + 55 q^{66} + 18 q^{67} - 25 q^{68} + 3 q^{69} + 68 q^{70} - 14 q^{71} - 8 q^{72} - 38 q^{73} + 27 q^{74} + 26 q^{75} + 70 q^{76} + 17 q^{77} + 2 q^{78} + 12 q^{79} - 56 q^{80} + 5 q^{81} - 27 q^{82} + 14 q^{83} - 17 q^{84} - 50 q^{85} + 35 q^{86} + 44 q^{87} - 20 q^{88} - 32 q^{89} - 44 q^{90} + 56 q^{91} + 28 q^{92} + 10 q^{93} + 14 q^{94} + 17 q^{95} - 70 q^{96} - 35 q^{97} - 10 q^{98} - 10 q^{99}+O(q^{100}) \) 38 * q + q^2 + 2 * q^3 - 21 * q^4 - 4 * q^5 - 5 * q^7 - 12 * q^8 - 13 * q^9 - 8 * q^10 - 4 * q^11 + 21 * q^12 - 9 * q^13 + 6 * q^14 + 4 * q^15 - 25 * q^16 - 18 * q^17 + 5 * q^18 + 3 * q^19 - 5 * q^20 + 10 * q^21 - 7 * q^22 - 10 * q^23 - 9 * q^24 + 54 * q^25 + 20 * q^26 - 4 * q^27 + 8 * q^28 + 25 * q^29 - 22 * q^30 - 8 * q^31 + 23 * q^32 - 28 * q^33 - 4 * q^34 - 7 * q^35 + 18 * q^36 + 12 * q^37 + 30 * q^38 + 20 * q^39 - 4 * q^40 - 20 * q^41 - 30 * q^42 + 12 * q^43 - 2 * q^44 - 9 * q^45 - 19 * q^46 - 42 * q^47 - 84 * q^48 + 6 * q^49 + 31 * q^50 + 11 * q^51 - 16 * q^52 + q^53 + 42 * q^54 - 11 * q^55 - 5 * q^56 - 22 * q^57 - 2 * q^58 + 22 * q^59 + 48 * q^60 - 26 * q^61 - 44 * q^62 - q^63 + 72 * q^64 - 19 * q^65 + 55 * q^66 + 18 * q^67 - 25 * q^68 + 3 * q^69 + 68 * q^70 - 14 * q^71 - 8 * q^72 - 38 * q^73 + 27 * q^74 + 26 * q^75 + 70 * q^76 + 17 * q^77 + 2 * q^78 + 12 * q^79 - 56 * q^80 + 5 * q^81 - 27 * q^82 + 14 * q^83 - 17 * q^84 - 50 * q^85 + 35 * q^86 + 44 * q^87 - 20 * q^88 - 32 * q^89 - 44 * q^90 + 56 * q^91 + 28 * q^92 + 10 * q^93 + 14 * q^94 + 17 * q^95 - 70 * q^96 - 35 * q^97 - 10 * q^98 - 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/241\mathbb{Z}\right)^\times$.

$n$	$7$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.820137	−	1.42052i	0.579925	−	1.00446i	−0.415563	−	0.909565i	$-0.636415\pi$
$2$	0.820137	−	1.42052i	0.579925	−	1.00446i	0.995487	−	0.0948944i	$-0.0302513\pi$
$3$	−1.19817	−	2.07530i	−0.691767	−	1.19817i	−0.971259	−	0.238027i	$-0.923499\pi$
$3$	−1.19817	−	2.07530i	−0.691767	−	1.19817i	0.279492	−	0.960148i	$-0.409834\pi$
$4$	−0.345250	−	0.597991i	−0.172625	−	0.298995i
$5$	−4.29952			−1.92280			−0.961402	−	0.275149i	$-0.911273\pi$
$5$	−4.29952			−1.92280			−0.961402	+	0.275149i	$0.911273\pi$
$6$	−3.93067			−1.60469
$7$	−0.578431	+	1.00187i	−0.218626	+	0.378672i	−0.954388	−	0.298568i	$-0.903491\pi$
$7$	−0.578431	+	1.00187i	−0.218626	+	0.378672i	0.735762	+	0.677240i	$0.236824\pi$
$8$	2.14794			0.759411
$9$	−1.37125	+	2.37507i	−0.457082	+	0.791689i
$10$	−3.52620	+	6.10755i	−1.11508	+	1.93138i
$11$	−0.0451539	+	0.0782089i	−0.0136144	+	0.0235809i	−0.872752	−	0.488163i	$-0.837667\pi$
$11$	−0.0451539	+	0.0782089i	−0.0136144	+	0.0235809i	0.859138	+	0.511744i	$0.171000\pi$
$12$	−0.827340	+	1.43300i	−0.238833	+	0.413670i
$13$	−2.65056	−	4.59090i	−0.735132	−	1.27329i	−0.954665	−	0.297682i	$-0.903787\pi$
$13$	−2.65056	−	4.59090i	−0.735132	−	1.27329i	0.219533	−	0.975605i	$-0.429547\pi$
$14$	0.948786	+	1.64335i	0.253574	+	0.439203i
$15$	5.15157	+	8.92279i	1.33013	+	2.30385i
$16$	2.45211	−	4.24717i	0.613026	−	1.06179i
$17$	−1.64306			−0.398500			−0.199250	−	0.979949i	$-0.563851\pi$
$17$	−1.64306			−0.398500			−0.199250	+	0.979949i	$0.563851\pi$
$18$	2.24922	+	3.89576i	0.530146	+	0.918240i
$19$	1.20168	−	2.08136i	0.275683	−	0.477497i	−0.694624	−	0.719373i	$-0.744429\pi$
$19$	1.20168	−	2.08136i	0.275683	−	0.477497i	0.970307	+	0.241876i	$0.0777626\pi$
$20$	1.48441	+	2.57107i	0.331924	+	0.574909i
$21$	2.77225			0.604954
$22$	0.0740648	+	0.128284i	0.0157907	+	0.0273503i
$23$	−7.62049			−1.58898			−0.794491	−	0.607276i	$-0.792262\pi$
$23$	−7.62049			−1.58898			−0.794491	+	0.607276i	$0.792262\pi$
$24$	−2.57361	−	4.45762i	−0.525335	−	0.909907i
$25$	13.4859			2.69717
$26$	−8.69528			−1.70529
$27$	−0.617081			−0.118757
$28$	0.798814			0.150962
$29$	3.30454	−	5.72364i	0.613638	−	1.06285i	−0.376984	−	0.926220i	$-0.623039\pi$
$29$	3.30454	−	5.72364i	0.613638	−	1.06285i	0.990622	−	0.136633i	$-0.0436280\pi$
$30$	16.9000			3.08550
$31$	2.44152	−	4.22884i	0.438510	−	0.759522i	−0.559064	−	0.829124i	$-0.688840\pi$
$31$	2.44152	−	4.22884i	0.438510	−	0.759522i	0.997575	+	0.0696019i	$0.0221729\pi$
$32$	−1.87419	−	3.24619i	−0.331312	−	0.573850i
$33$	0.216409			0.0376720
$34$	−1.34753	+	2.33399i	−0.231100	+	0.400277i
$35$	2.48698	−	4.30757i	0.420376	−	0.728112i
$36$	1.89369			0.315615
$37$	−3.76545	+	6.52195i	−0.619036	+	1.07220i	0.370626	+	0.928782i	$0.379143\pi$
$37$	−3.76545	+	6.52195i	−0.619036	+	1.07220i	−0.989662	+	0.143420i	$0.954190\pi$
$38$	−1.97108	−	3.41401i	−0.319751	−	0.553825i
$39$	−6.35166	+	11.0014i	−1.01708	+	1.76163i
$40$	−9.23510			−1.46020
$41$	−0.316578			−0.0494412			−0.0247206	−	0.999694i	$-0.507870\pi$
$41$	−0.316578			−0.0494412			−0.0247206	+	0.999694i	$0.507870\pi$
$42$	2.27362	−	3.93803i	0.350828	−	0.607651i
$43$	4.02686			0.614090			0.307045	−	0.951695i	$-0.400660\pi$
$43$	4.02686			0.614090			0.307045	+	0.951695i	$0.400660\pi$
$44$	0.0623576			0.00940076
$45$	5.89570	−	10.2116i	0.878878	−	1.52226i
$46$	−6.24985	+	10.8251i	−0.921490	+	1.59607i
$47$	−1.08055			−0.157614			−0.0788069	−	0.996890i	$-0.525111\pi$
$47$	−1.08055			−0.157614			−0.0788069	+	0.996890i	$0.525111\pi$
$48$	−11.7522			−1.69628
$49$	2.83083	+	4.90315i	0.404405	+	0.700450i
$50$	11.0603	−	19.1569i	1.56416	−	2.70920i
$51$	1.96867	+	3.40984i	0.275669	+	0.477472i
$52$	−1.83021	+	3.17002i	−0.253805	+	0.439603i
$53$	−4.62703	−	8.01425i	−0.635572	−	1.10084i	−0.986394	−	0.164400i	$-0.947431\pi$
$53$	−4.62703	−	8.01425i	−0.635572	−	1.10084i	0.350822	−	0.936442i	$-0.385902\pi$
$54$	−0.506091	+	0.876576i	−0.0688703	+	0.119287i
$55$	0.194140	−	0.336261i	0.0261779	−	0.0453414i
$56$	−1.24243	+	2.15196i	−0.166027	+	0.287568i
$57$	−5.75927			−0.762834
$58$	−5.42036	−	9.38833i	−0.711728	−	1.23275i
$59$	2.07761	−	3.59852i	0.270481	−	0.468488i	−0.698504	−	0.715606i	$-0.746150\pi$
$59$	2.07761	−	3.59852i	0.270481	−	0.468488i	0.968985	+	0.247119i	$0.0794838\pi$
$60$	3.55716	−	6.16119i	0.459228	−	0.795406i
$61$	10.5427			1.34986			0.674930	−	0.737882i	$-0.264174\pi$
$61$	10.5427			1.34986			0.674930	+	0.737882i	$0.264174\pi$
$62$	−4.00477	−	6.93646i	−0.508606	−	0.880931i
$63$	−1.58634	−	2.74763i	−0.199860	−	0.346168i
$64$	3.66006			0.457507
$65$	11.3961	+	19.7387i	1.41352	+	2.44828i
$66$	0.177485	−	0.307413i	0.0218469	−	0.0378400i
$67$	3.71258	−	6.43038i	0.453564	−	0.785596i	−0.545040	−	0.838410i	$-0.683486\pi$
$67$	3.71258	−	6.43038i	0.453564	−	0.785596i	0.998604	+	0.0528135i	$0.0168189\pi$
$68$	0.567266	+	0.982533i	0.0687911	+	0.119150i
$69$	9.13068	+	15.8148i	1.09920	+	1.90388i
$70$	−4.07932	−	7.06559i	−0.487572	−	0.844500i
$71$	7.25388	−	12.5641i	0.860878	−	1.49108i	−0.0102052	−	0.999948i	$-0.503248\pi$
$71$	7.25388	−	12.5641i	0.860878	−	1.49108i	0.871083	−	0.491136i	$-0.163418\pi$
$72$	−2.94535	+	5.10150i	−0.347113	+	0.601217i
$73$	9.21934			1.07904			0.539521	−	0.841972i	$-0.318605\pi$
$73$	9.21934			1.07904			0.539521	+	0.841972i	$0.318605\pi$
$74$	6.17637	+	10.6978i	0.717989	+	1.24359i
$75$	−16.1584	−	27.9872i	−1.86581	−	3.23168i
$76$	−1.65951			−0.190359
$77$	−0.0522369	−	0.0904769i	−0.00595295	−	0.0103108i
$78$	10.4185	+	18.0453i	1.17966	+	2.04323i
$79$	−9.74235			−1.09610			−0.548050	−	0.836446i	$-0.684630\pi$
$79$	−9.74235			−1.09610			−0.548050	+	0.836446i	$0.684630\pi$
$80$	−10.5429	+	18.2608i	−1.17873	+	2.04162i
$81$	4.85311	+	8.40583i	0.539234	+	0.933981i
$82$	−0.259637	+	0.449705i	−0.0286721	+	0.0496616i
$83$	−3.84438	+	6.65867i	−0.421976	+	0.730884i	−0.996133	−	0.0878615i	$-0.971997\pi$
$83$	−3.84438	+	6.65867i	−0.421976	+	0.730884i	0.574157	+	0.818745i	$0.305330\pi$
$84$	−0.957119	−	1.65778i	−0.104430	−	0.180878i
$85$	7.06435			0.766237
$86$	3.30258	−	5.72023i	0.356126	−	0.616828i
$87$	−15.8377			−1.69798
$88$	−0.0969879	+	0.167988i	−0.0103389	+	0.0179076i
$89$	−2.61828	+	4.53499i	−0.277537	+	0.480708i	−0.970772	−	0.240004i	$-0.922851\pi$
$89$	−2.61828	+	4.53499i	−0.277537	+	0.480708i	0.693235	+	0.720711i	$0.256185\pi$
$90$	−9.67056	−	16.7499i	−1.01937	−	1.76559i
$91$	6.13266			0.642878
$92$	2.63098	+	4.55698i	0.274298	+	0.475098i
$93$	−11.7015			−1.21339
$94$	−0.886195	+	1.53494i	−0.0914041	+	0.158317i
$95$	−5.16662	+	8.94886i	−0.530085	+	0.918133i
$96$	−4.49121	+	7.77900i	−0.458382	+	0.793941i
$97$	−1.12438	−	1.94749i	−0.114164	−	0.197738i	0.803281	−	0.595600i	$-0.203086\pi$
$97$	−1.12438	−	1.94749i	−0.114164	−	0.197738i	−0.917445	+	0.397862i	$0.869752\pi$
$98$	9.28669			0.938098
$99$	−0.123834	−	0.214487i	−0.0124458	−	0.0215568i
$100$	−4.65600	−	8.06442i	−0.465600	−	0.806442i
$101$	5.68725			0.565902			0.282951	−	0.959134i	$-0.408687\pi$
$101$	5.68725			0.565902			0.282951	+	0.959134i	$0.408687\pi$
$102$	6.45832			0.639469
$103$	3.27870			0.323060			0.161530	−	0.986868i	$-0.448357\pi$
$103$	3.27870			0.323060			0.161530	+	0.986868i	$0.448357\pi$
$104$	−5.69324	−	9.86097i	−0.558268	−	0.966948i
$105$	−11.9193			−1.16321
$106$	−15.1792			−1.47433
$107$	−1.79273	−	3.10510i	−0.173310	−	0.300181i	0.766265	−	0.642524i	$-0.222113\pi$
$107$	−1.79273	−	3.10510i	−0.173310	−	0.300181i	−0.939575	+	0.342343i	$0.888780\pi$
$108$	0.213047	+	0.369009i	0.0205005	+	0.0355079i
$109$	−3.39723	−	5.88418i	−0.325396	−	0.563602i	0.656196	−	0.754590i	$-0.272164\pi$
$109$	−3.39723	−	5.88418i	−0.325396	−	0.563602i	−0.981592	+	0.190988i	$0.938831\pi$
$110$	−0.318443	−	0.551560i	−0.0303624	−	0.0525892i
$111$	18.0467			1.71291
$112$	2.83675	+	4.91339i	0.268047	+	0.464272i
$113$	−10.3195	+	17.8738i	−0.970774	+	1.68143i	−0.277545	+	0.960713i	$0.589521\pi$
$113$	−10.3195	+	17.8738i	−0.970774	+	1.68143i	−0.693229	+	0.720718i	$0.743812\pi$
$114$	−4.72339	+	8.18115i	−0.442386	+	0.766235i
$115$	32.7644			3.05530
$116$	−4.56358			−0.423717
$117$	14.5383			1.34406
$118$	−3.40785	−	5.90256i	−0.313718	−	0.543375i
$119$	0.950395	−	1.64613i	0.0871226	−	0.150901i
$120$	11.0653	+	19.1656i	1.01012	+	1.74957i
$121$	5.49592	+	9.51922i	0.499629	+	0.865383i
$122$	8.64649	−	14.9762i	0.782817	−	1.35588i
$123$	0.379316	+	0.656994i	0.0342017	+	0.0592391i
$124$	−3.37174			−0.302792
$125$	−36.4851			−3.26333
$126$	−5.20407			−0.463616
$127$	−7.10717	+	12.3100i	−0.630659	+	1.09233i	0.356758	+	0.934197i	$0.383882\pi$
$127$	−7.10717	+	12.3100i	−0.630659	+	1.09233i	−0.987417	+	0.158137i	$0.949451\pi$
$128$	6.75012	−	11.6916i	0.596632	−	1.03340i
$129$	−4.82488	−	8.35694i	−0.424807	−	0.735787i
$130$	37.3855			3.27893
$131$	0.856334	+	1.48321i	0.0748182	+	0.129589i	0.901007	−	0.433804i	$-0.142829\pi$
$131$	0.856334	+	1.48321i	0.0748182	+	0.129589i	−0.826189	+	0.563393i	$0.809496\pi$
$132$	−0.0747153	−	0.129411i	−0.00650313	−	0.0112638i
$133$	1.39017	+	2.40785i	0.120543	+	0.208787i
$134$	−6.08966	−	10.5476i	−0.526066	−	0.911173i
$135$	2.65315			0.228347
$136$	−3.52919			−0.302625
$137$	−5.55249	−	9.61719i	−0.474381	−	0.821652i	0.525189	−	0.850986i	$-0.323995\pi$
$137$	−5.55249	−	9.61719i	−0.474381	−	0.821652i	−0.999570	+	0.0293338i	$0.990661\pi$
$138$	29.9536			2.54982
$139$	−18.9875			−1.61050			−0.805248	−	0.592938i	$-0.797968\pi$
$139$	−18.9875			−1.61050			−0.805248	+	0.592938i	$0.797968\pi$
$140$	−3.43452			−0.290270
$141$	1.29468	+	2.24246i	0.109032	+	0.188849i
$142$	−11.8984	−	20.6086i	−0.998488	−	1.72943i
$143$	0.478732			0.0400336
$144$	6.72488	+	11.6478i	0.560406	+	0.970652i
$145$	−14.2079	+	24.6089i	−1.17991	+	2.04366i
$146$	7.56112	−	13.0962i	0.625763	−	1.08385i
$147$	6.78367	−	11.7497i	0.559508	−	0.969096i
$148$	5.20009			0.427445
$149$	1.61547	+	2.79808i	0.132344	+	0.229227i	0.924580	−	0.380988i	$-0.124416\pi$
$149$	1.61547	+	2.79808i	0.132344	+	0.229227i	−0.792235	+	0.610216i	$0.791083\pi$
$150$	−53.0085			−4.32812
$151$	−9.81435	−	16.9990i	−0.798680	−	1.38335i	−0.920476	−	0.390800i	$-0.872198\pi$
$151$	−9.81435	−	16.9990i	−0.798680	−	1.38335i	0.121795	−	0.992555i	$-0.461135\pi$
$152$	2.58112	−	4.47064i	0.209357	−	0.362617i
$153$	2.25303	−	3.90237i	0.182147	−	0.315488i
$154$	−0.171366			−0.0138090
$155$	−10.4974	+	18.1820i	−0.843169	+	1.46041i
$156$	8.77165			0.702294
$157$	−2.59744	−	4.49890i	−0.207298	−	0.359051i	0.743564	−	0.668664i	$-0.233134\pi$
$157$	−2.59744	−	4.49890i	−0.207298	−	0.359051i	−0.950863	+	0.309613i	$0.899800\pi$
$158$	−7.99007	+	13.8392i	−0.635655	+	1.10099i
$159$	−11.0880	+	19.2049i	−0.879334	+	1.52305i
$160$	8.05810	+	13.9570i	0.637049	+	1.10340i
$161$	4.40793	−	7.63476i	0.347393	−	0.601703i
$162$	15.9209			1.25086
$163$	−9.24647	−	16.0153i	−0.724239	−	1.25442i	−0.959286	−	0.282435i	$-0.908858\pi$
$163$	−9.24647	−	16.0153i	−0.724239	−	1.25442i	0.235047	−	0.971984i	$-0.424476\pi$
$164$	0.109299	+	0.189311i	0.00853478	+	0.0147827i
$165$	−0.930455			−0.0724359
$166$	6.30585	+	10.9220i	0.489429	+	0.847715i
$167$	5.26704	+	9.12278i	0.407576	+	0.705942i	0.994618	−	0.103615i	$-0.0330409\pi$
$167$	5.26704	+	9.12278i	0.407576	+	0.705942i	−0.587042	+	0.809557i	$0.699708\pi$
$168$	5.95462			0.459409
$169$	−7.55091	+	13.0786i	−0.580840	+	1.00604i
$170$	5.79374	−	10.0351i	0.444360	−	0.769653i
$171$	3.29558	+	5.70812i	0.252020	+	0.436511i
$172$	−1.39027	−	2.40802i	−0.106007	−	0.183610i
$173$	2.55325	+	4.42236i	0.194120	+	0.336225i	0.946612	−	0.322376i	$-0.104482\pi$
$173$	2.55325	+	4.42236i	0.194120	+	0.336225i	−0.752492	+	0.658602i	$0.771148\pi$
$174$	−12.9891	+	22.4977i	−0.984699	+	1.70555i
$175$	−7.80064	+	13.5111i	−0.589673	+	1.02134i
$176$	0.221444	+	0.383553i	0.0166920	+	0.0289114i
$177$	−9.95735			−0.748440
$178$	4.29469	+	7.43863i	0.321901	+	0.557549i
$179$	1.84215	+	3.19069i	0.137688	+	0.238483i	0.926621	−	0.375996i	$-0.122699\pi$
$179$	1.84215	+	3.19069i	0.137688	+	0.238483i	−0.788933	+	0.614479i	$0.789366\pi$
$180$	−8.14196			−0.606866
$181$	1.37596	−	2.38323i	0.102274	−	0.177144i	−0.810347	−	0.585950i	$-0.800721\pi$
$181$	1.37596	−	2.38323i	0.102274	−	0.177144i	0.912621	+	0.408806i	$0.134055\pi$
$182$	5.02962	−	8.71156i	0.372821	−	0.645744i
$183$	−12.6320	−	21.8793i	−0.933788	−	1.61737i
$184$	−16.3683			−1.20669
$185$	16.1896	−	28.0413i	1.19028	−	2.06163i
$186$	−9.59682	+	16.6222i	−0.703673	+	1.21880i
$187$	0.0741905	−	0.128502i	0.00542535	−	0.00939697i
$188$	0.373058	+	0.646156i	0.0272081	+	0.0471258i
$189$	0.356939	−	0.618237i	0.0259635	−	0.0449701i
$190$	8.47468	+	14.6786i	0.614818	+	1.06490i
$191$	4.44997	−	7.70758i	0.321989	−	0.557701i	−0.658909	−	0.752222i	$-0.728982\pi$
$191$	4.44997	−	7.70758i	0.321989	−	0.557701i	0.980898	+	0.194521i	$0.0623153\pi$
$192$	−4.38539	−	7.59572i	−0.316488	−	0.548174i
$193$	20.1406			1.44975			0.724877	−	0.688878i	$-0.241897\pi$
$193$	20.1406			1.44975			0.724877	+	0.688878i	$0.241897\pi$
$194$	−3.68860			−0.264826
$195$	27.3091	−	47.3007i	1.95564	−	3.38728i
$196$	1.95469	−	3.38563i	0.139621	−	0.241830i
$197$	12.5193			0.891962			0.445981	−	0.895042i	$-0.352855\pi$
$197$	12.5193			0.891962			0.445981	+	0.895042i	$0.352855\pi$
$198$	−0.406244			−0.0288705
$199$	−0.407338	+	0.705530i	−0.0288754	+	0.0500137i	−0.880102	−	0.474785i	$-0.842526\pi$
$199$	−0.407338	+	0.705530i	−0.0288754	+	0.0500137i	0.851227	+	0.524798i	$0.175859\pi$
$200$	28.9668			2.04826
$201$	−17.7933			−1.25504
$202$	4.66432	−	8.07884i	0.328181	−	0.568425i
$203$	3.82290	+	6.62146i	0.268315	+	0.464735i
$204$	1.35937	−	2.35449i	0.0951747	−	0.164847i
$205$	1.36113			0.0950656
$206$	2.68899	−	4.65746i	0.187351	−	0.324501i
$207$	10.4496	−	18.0992i	0.726295	−	1.25798i
$208$	−25.9978			−1.80262
$209$	0.108521	+	0.187963i	0.00750654	+	0.0130017i
$210$	−9.77548	+	16.9316i	−0.674572	+	1.16839i
$211$	10.4425			0.718892			0.359446	−	0.933166i	$-0.382966\pi$
$211$	10.4425			0.718892			0.359446	+	0.933166i	$0.382966\pi$
$212$	−3.19497	+	5.53384i	−0.219431	+	0.380066i
$213$	−34.7657			−2.38211
$214$	−5.88114			−0.402027
$215$	−17.3136			−1.18077
$216$	−1.32545			−0.0901856
$217$	2.82451	+	4.89219i	0.191740	+	0.332103i
$218$	−11.1448			−0.754821
$219$	−11.0464	−	19.1329i	−0.746445	−	1.29288i
$220$	−0.268108			−0.0180758
$221$	4.35502	+	7.54311i	0.292950	+	0.507405i
$222$	14.8007	−	25.6356i	0.993361	−	1.72055i
$223$	−2.21892	−	3.84328i	−0.148590	−	0.257365i	0.782117	−	0.623132i	$-0.214140\pi$
$223$	−2.21892	−	3.84328i	−0.148590	−	0.257365i	−0.930706	+	0.365767i	$0.880807\pi$
$224$	4.33635			0.289735
$225$	−18.4924	+	32.0298i	−1.23283	+	2.13532i
$226$	16.9268	+	29.3180i	1.12595	+	1.95021i
$227$	8.35490	+	14.4711i	0.554534	+	0.960481i	0.997940	+	0.0641603i	$0.0204369\pi$
$227$	8.35490	+	14.4711i	0.554534	+	0.960481i	−0.443405	+	0.896321i	$0.646230\pi$
$228$	1.98839	+	3.44399i	0.131684	+	0.228084i
$229$	−8.72600	+	15.1139i	−0.576631	+	0.998753i	0.419232	+	0.907879i	$0.362299\pi$
$229$	−8.72600	+	15.1139i	−0.576631	+	0.998753i	−0.995862	+	0.0908742i	$0.971034\pi$
$230$	26.8713	−	46.5425i	1.77184	−	3.06892i
$231$	−0.125178	+	0.216814i	−0.00823610	+	0.0142653i
$232$	7.09796	−	12.2940i	0.466004	−	0.807142i
$233$	4.72806			0.309745			0.154873	−	0.987934i	$-0.450503\pi$
$233$	4.72806			0.309745			0.154873	+	0.987934i	$0.450503\pi$
$234$	11.9234	−	20.6519i	0.779455	−	1.35006i
$235$	4.64582			0.303060
$236$	−2.86918			−0.186768
$237$	11.6730	+	20.2183i	0.758245	+	1.31332i
$238$	−1.55891	−	2.70011i	−0.101049	−	0.175022i
$239$	4.96075	−	8.59227i	0.320884	−	0.555787i	−0.659787	−	0.751453i	$-0.729353\pi$
$239$	4.96075	−	8.59227i	0.320884	−	0.555787i	0.980671	+	0.195666i	$0.0626867\pi$
$240$	50.5288			3.26162
$241$	11.1596	−	10.7918i	0.718855	−	0.695160i
$241$	11.1596	−	10.7918i	0.718855	−	0.695160i
$242$	18.0296			1.15899
$243$	10.7041	−	18.5401i	0.686670	−	1.18935i
$244$	−3.63988	−	6.30446i	−0.233020	−	0.403602i
$245$	−12.1712	−	21.0812i	−0.777591	−	1.34683i
$246$	1.24436			0.0793377
$247$	−12.7404			−0.810655
$248$	5.24424	−	9.08329i	0.333010	−	0.576790i
$249$	18.4250			1.16764
$250$	−29.9228	+	51.8278i	−1.89248	+	3.27788i
$251$	1.19974	−	2.07801i	0.0757271	−	0.131163i	−0.825675	−	0.564146i	$-0.809206\pi$
$251$	1.19974	−	2.07801i	0.0757271	−	0.131163i	0.901402	+	0.432983i	$0.142539\pi$
$252$	−1.09537	+	1.89724i	−0.0690018	+	0.119515i
$253$	0.344095	−	0.595990i	0.0216331	−	0.0374696i
$254$	11.6577	+	20.1917i	0.731470	+	1.26694i
$255$	−8.46433	−	14.6607i	−0.530057	−	0.918086i
$256$	−7.41200	−	12.8380i	−0.463250	−	0.802372i
$257$	11.6268	−	20.1383i	0.725262	−	1.25619i	−0.233605	−	0.972332i	$-0.575052\pi$
$257$	11.6268	−	20.1383i	0.725262	−	1.25619i	0.958866	−	0.283858i	$-0.0916145\pi$
$258$	−15.8283			−0.985424
$259$	−4.35611	−	7.54500i	−0.270675	−	0.468824i
$260$	7.86903	−	13.6296i	0.488016	−	0.845269i
$261$	9.06268	+	15.6970i	0.560966	+	0.971621i
$262$	2.80924			0.173556
$263$	−9.25296	−	16.0266i	−0.570562	−	0.988242i	−0.996508	−	0.0834937i	$-0.973392\pi$
$263$	−9.25296	−	16.0266i	−0.570562	−	0.988242i	0.425947	−	0.904748i	$-0.359941\pi$
$264$	0.464834			0.0286085
$265$	19.8940	+	34.4574i	1.22208	+	2.11670i
$266$	4.56053			0.279624
$267$	12.5486			0.767963
$268$	−5.12708			−0.313186
$269$	−13.5863			−0.828369			−0.414185	−	0.910193i	$-0.635933\pi$
$269$	−13.5863			−0.828369			−0.414185	+	0.910193i	$0.635933\pi$
$270$	2.17595	−	3.76885i	0.132424	−	0.229365i
$271$	−15.8122			−0.960523			−0.480261	−	0.877125i	$-0.659458\pi$
$271$	−15.8122			−0.960523			−0.480261	+	0.877125i	$0.659458\pi$
$272$	−4.02895	+	6.97834i	−0.244291	+	0.423124i
$273$	−7.34800	−	12.7271i	−0.444721	−	0.770280i
$274$	−18.2152			−1.10042
$275$	−0.608940	+	1.05471i	−0.0367204	+	0.0636017i
$276$	6.30474	−	10.9201i	0.379501	−	0.657314i
$277$	24.6245			1.47955			0.739773	−	0.672857i	$-0.234933\pi$
$277$	24.6245			1.47955			0.739773	+	0.672857i	$0.234933\pi$
$278$	−15.5723	+	26.9721i	−0.933966	+	1.61768i
$279$	6.69585	+	11.5976i	0.400870	+	0.694328i
$280$	5.34187	−	9.25239i	0.319238	−	0.552936i
$281$	8.59410			0.512681			0.256340	−	0.966587i	$-0.417483\pi$
$281$	8.59410			0.512681			0.256340	+	0.966587i	$0.417483\pi$
$282$	4.24727			0.252921
$283$	−0.986664	+	1.70895i	−0.0586511	+	0.101587i	−0.893860	−	0.448346i	$-0.852013\pi$
$283$	−0.986664	+	1.70895i	−0.0586511	+	0.101587i	0.835209	+	0.549933i	$0.185347\pi$
$284$	−10.0176			−0.594436
$285$	24.7621			1.46678
$286$	0.392626	−	0.680049i	0.0232165	−	0.0402121i
$287$	0.183119	−	0.317171i	0.0108091	−	0.0187220i
$288$	10.2799			0.605748
$289$	−14.3004			−0.841198
$290$	23.3049	+	40.3653i	1.36851	+	2.37033i
$291$	−2.69442	+	4.66687i	−0.157949	+	0.273577i
$292$	−3.18298	−	5.51308i	−0.186270	−	0.322629i
$293$	8.55612	−	14.8196i	0.499854	−	0.865773i	−0.500146	−	0.865941i	$-0.666720\pi$
$293$	8.55612	−	14.8196i	0.499854	−	0.865773i	1.00000		0.000168528i	$5.36440e-5\pi$
$294$	−11.1271	−	19.2727i	−0.648944	−	1.12400i
$295$	−8.93271	+	15.4719i	−0.520083	+	0.900810i
$296$	−8.08796	+	14.0088i	−0.470103	+	0.814242i
$297$	0.0278636	−	0.0482613i	0.00161681	−	0.00280040i
$298$	5.29963			0.306999
$299$	20.1985	+	34.9849i	1.16811	+	2.02323i
$300$	−11.1574	+	19.3252i	−0.644172	+	1.11574i
$301$	−2.32926	+	4.03440i	−0.134256	+	0.232539i
$302$	−32.1965			−1.85270
$303$	−6.81432	−	11.8027i	−0.391472	−	0.678050i
$304$	−5.89327	−	10.2074i	−0.338002	−	0.585437i
$305$	−45.3287			−2.59551
$306$	−3.69560	−	6.40096i	−0.211263	−	0.365918i
$307$	15.9840	−	27.6851i	0.912255	−	1.58007i	0.101383	−	0.994847i	$-0.467673\pi$
$307$	15.9840	−	27.6851i	0.912255	−	1.58007i	0.810872	−	0.585224i	$-0.198993\pi$
$308$	−0.0360696	+	0.0624744i	−0.00205526	+	0.00355981i
$309$	−3.92846	−	6.80429i	−0.223482	−	0.387083i
$310$	17.2186	+	29.8234i	0.977949	+	1.69386i
$311$	−3.45514	−	5.98449i	−0.195923	−	0.339349i	0.751280	−	0.659984i	$-0.229437\pi$
$311$	−3.45514	−	5.98449i	−0.195923	−	0.339349i	−0.947203	+	0.320635i	$0.896104\pi$
$312$	−13.6430	+	23.6303i	−0.772382	+	1.33780i
$313$	−0.475084	+	0.822869i	−0.0268533	+	0.0465113i	−0.879140	−	0.476564i	$-0.841882\pi$
$313$	−0.475084	+	0.822869i	−0.0268533	+	0.0465113i	0.852286	+	0.523075i	$0.175215\pi$
$314$	−8.52102			−0.480869
$315$	6.82051	+	11.8135i	0.384292	+	0.665614i
$316$	3.36355	+	5.82584i	0.189214	+	0.327729i
$317$	−1.30502			−0.0732970			−0.0366485	−	0.999328i	$-0.511668\pi$
$317$	−1.30502			−0.0732970			−0.0366485	+	0.999328i	$0.511668\pi$
$318$	18.1873	+	31.5014i	1.01990	+	1.76651i
$319$	0.298426	+	0.516889i	0.0167087	+	0.0289402i
$320$	−15.7365			−0.879697
$321$	−4.29601	+	7.44091i	−0.239780	+	0.415311i
$322$	−7.23021	−	12.5231i	−0.402924	−	0.697885i
$323$	−1.97442	+	3.41980i	−0.109860	+	0.190283i
$324$	3.35107	−	5.80423i	0.186171	−	0.322457i
$325$	−35.7451	−	61.9123i	−1.98278	−	3.43427i
$326$	−30.3335			−1.68002
$327$	−8.14096	+	14.1006i	−0.450196	+	0.779763i
$328$	−0.679990			−0.0375462
$329$	0.625021	−	1.08257i	0.0344585	−	0.0596839i
$330$	−0.763101	+	1.32173i	−0.0420073	+	0.0727588i
$331$	−7.93631	−	13.7461i	−0.436219	−	0.755554i	0.561175	−	0.827697i	$-0.310349\pi$
$331$	−7.93631	−	13.7461i	−0.436219	−	0.755554i	−0.997394	+	0.0721433i	$0.977016\pi$
$332$	5.30910			0.291375
$333$	−10.3267	−	17.8864i	−0.565900	−	0.980168i
$334$	17.2788			0.945453
$335$	−15.9623	+	27.6476i	−0.872115	+	1.51055i
$336$	6.79784	−	11.7742i	0.370853	−	0.642335i
$337$	12.5264	−	21.6963i	0.682356	−	1.18187i	−0.291904	−	0.956447i	$-0.594289\pi$
$337$	12.5264	−	21.6963i	0.682356	−	1.18187i	0.974260	−	0.225427i	$-0.0723777\pi$
$338$	12.3856	+	21.4524i	0.673686	+	1.16686i
$339$	49.4581			2.68620
$340$	−2.43897	−	4.22442i	−0.132272	−	0.229101i
$341$	0.220489	+	0.381898i	0.0119401	+	0.0206809i
$342$	10.8113			0.584609
$343$	−14.6478			−0.790907
$344$	8.64945			0.466347
$345$	−39.2575	−	67.9960i	−2.11355	−	3.66078i
$346$	8.37606			0.450300
$347$	3.55935			0.191076			0.0955379	−	0.995426i	$-0.469543\pi$
$347$	3.55935			0.191076			0.0955379	+	0.995426i	$0.469543\pi$
$348$	5.46796	+	9.47079i	0.293114	+	0.507688i
$349$	8.26310	+	14.3121i	0.442314	+	0.766109i	0.997861	−	0.0653755i	$-0.0208245\pi$
$349$	8.26310	+	14.3121i	0.442314	+	0.766109i	−0.555547	+	0.831485i	$0.687491\pi$
$350$	12.7952	+	22.1619i	0.683932	+	1.18460i
$351$	1.63561	+	2.83296i	0.0873024	+	0.151212i
$352$	0.338508			0.0180425
$353$	17.5329	+	30.3678i	0.933181	+	1.61632i	0.777845	+	0.628456i	$0.216313\pi$
$353$	17.5329	+	30.3678i	0.933181	+	1.61632i	0.155336	+	0.987862i	$0.450354\pi$
$354$	−8.16639	+	14.1446i	−0.434039	+	0.751777i
$355$	−31.1882	+	54.0196i	−1.65530	+	2.86706i
$356$	3.61584			0.191639
$357$	−4.55496			−0.241074
$358$	6.04325			0.319396
$359$	−7.37120	−	12.7673i	−0.389037	−	0.673832i	0.603283	−	0.797527i	$-0.293859\pi$
$359$	−7.37120	−	12.7673i	−0.389037	−	0.673832i	−0.992320	+	0.123695i	$0.960526\pi$
$360$	12.6636	−	21.9340i	0.667430	−	1.15602i
$361$	6.61195	+	11.4522i	0.347998	+	0.602749i
$362$	−2.25695	−	3.90915i	−0.118623	−	0.205460i
$363$	13.1702	−	22.8114i	0.691254	−	1.19729i
$364$	−2.11730	−	3.66728i	−0.110977	−	0.192217i
$365$	−39.6387			−2.07478
$366$	−41.4400			−2.16611
$367$	3.35392			0.175073			0.0875367	−	0.996161i	$-0.472101\pi$
$367$	3.35392			0.175073			0.0875367	+	0.996161i	$0.472101\pi$
$368$	−18.6862	+	32.3655i	−0.974087	+	1.68717i
$369$	0.434106	−	0.751894i	0.0225987	−	0.0391420i
$370$	−26.5554	−	45.9954i	−1.38055	−	2.39118i
$371$	10.7057			0.555811
$372$	4.03994	+	6.99738i	0.209461	+	0.362797i
$373$	9.76601	+	16.9152i	0.505665	+	0.875837i	0.999979	+	0.00655376i	$0.00208614\pi$
$373$	9.76601	+	16.9152i	0.505665	+	0.875837i	−0.494314	+	0.869284i	$0.664581\pi$
$374$	−0.121693	−	0.210778i	−0.00629258	−	0.0108991i
$375$	43.7156	+	75.7176i	2.25746	+	3.91004i
$376$	−2.32095			−0.119694
$377$	−35.0355			−1.80442
$378$	−0.585478	−	1.01408i	−0.0301137	−	0.0521585i
$379$	−30.0491			−1.54352			−0.771759	−	0.635915i	$-0.780623\pi$
$379$	−30.0491			−1.54352			−0.771759	+	0.635915i	$0.780623\pi$
$380$	7.13511			0.366024
$381$	34.0625			1.74508
$382$	−7.29918	−	12.6425i	−0.373458	−	0.646849i
$383$	−2.32304	−	4.02363i	−0.118702	−	0.205598i	0.800552	−	0.599264i	$-0.204540\pi$
$383$	−2.32304	−	4.02363i	−0.118702	−	0.205598i	−0.919254	+	0.393666i	$0.871207\pi$
$384$	−32.3513			−1.65092
$385$	0.224593	+	0.389007i	0.0114463	+	0.0198256i
$386$	16.5181	−	28.6102i	0.840748	−	1.45622i
$387$	−5.52181	+	9.56406i	−0.280689	+	0.486168i
$388$	−0.776387	+	1.34474i	−0.0394151	+	0.0682690i
$389$	3.30184			0.167410			0.0837050	−	0.996491i	$-0.473325\pi$
$389$	3.30184			0.167410			0.0837050	+	0.996491i	$0.473325\pi$
$390$	−44.7944	−	77.5862i	−2.26825	−	3.92873i
$391$	12.5209			0.633209
$392$	6.08046	+	10.5317i	0.307110	+	0.531929i
$393$	2.05207	−	3.55430i	0.103513	−	0.179291i
$394$	10.2675	−	17.7839i	0.517271	−	0.895939i
$395$	41.8874			2.10758
$396$	−0.0855076	+	0.148104i	−0.00429692	+	0.00744248i
$397$	−19.1459			−0.960904			−0.480452	−	0.877021i	$-0.659527\pi$
$397$	−19.1459			−0.960904			−0.480452	+	0.877021i	$0.659527\pi$
$398$	0.668146	+	1.15726i	0.0334911	+	0.0580083i
$399$	3.33134	−	5.77005i	0.166776	−	0.288864i
$400$	33.0687	−	57.2768i	1.65344	−	2.86384i
$401$	−10.3082	−	17.8543i	−0.514766	−	0.891601i	−0.999853	−	0.0171349i	$-0.994546\pi$
$401$	−10.3082	−	17.8543i	−0.514766	−	0.891601i	0.485087	−	0.874466i	$-0.338788\pi$
$402$	−14.5929	+	25.2757i	−0.727830	+	1.26064i
$403$	−25.8856			−1.28945
$404$	−1.96352	−	3.40092i	−0.0976889	−	0.169202i
$405$	−20.8660	−	36.1410i	−1.03684	−	1.79586i
$406$	12.5412			0.622410
$407$	−0.340050	−	0.588984i	−0.0168556	−	0.0291948i
$408$	4.22858	+	7.32412i	0.209346	+	0.362598i
$409$	−9.39333			−0.464470			−0.232235	−	0.972660i	$-0.574604\pi$
$409$	−9.39333			−0.464470			−0.232235	+	0.972660i	$0.574604\pi$
$410$	1.11632	−	1.93352i	0.0551309	−	0.0954895i
$411$	−13.3057	+	23.0462i	−0.656322	+	1.13678i
$412$	−1.13197	−	1.96064i	−0.0557683	−	0.0965936i
$413$	2.40351	+	4.16299i	0.118269	+	0.204848i
$414$	−17.1401	−	29.6876i	−0.842392	−	1.45907i
$415$	16.5290	−	28.6291i	0.811377	−	1.40535i
$416$	−9.93528	+	17.2084i	−0.487117	+	0.843712i
$417$	22.7503	+	39.4047i	1.11409	+	1.92966i
$418$	0.356008			0.0174129
$419$	−7.06199	−	12.2317i	−0.345001	−	0.597559i	0.640353	−	0.768081i	$-0.278788\pi$
$419$	−7.06199	−	12.2317i	−0.345001	−	0.597559i	−0.985354	+	0.170522i	$0.945455\pi$
$420$	4.11515	+	7.12765i	0.200799	+	0.347794i
$421$	12.5287			0.610611			0.305306	−	0.952254i	$-0.401241\pi$
$421$	12.5287			0.610611			0.305306	+	0.952254i	$0.401241\pi$
$422$	8.56429	−	14.8338i	0.416903	−	0.722098i
$423$	1.48169	−	2.56637i	0.0720424	−	0.124781i
$424$	−9.93858	−	17.2141i	−0.482660	−	0.835992i
$425$	−22.1580			−1.07482
$426$	−28.5126	+	49.3853i	−1.38144	+	2.39273i
$427$	−6.09825	+	10.5625i	−0.295115	+	0.511154i
$428$	−1.23788	+	2.14407i	−0.0598353	+	0.103638i
$429$	−0.573605	−	0.993513i	−0.0276939	−	0.0479673i
$430$	−14.1995	+	24.5942i	−0.684760	+	1.18604i
$431$	9.57080	+	16.5771i	0.461009	+	0.798491i	0.999012	−	0.0444521i	$-0.0141542\pi$
$431$	9.57080	+	16.5771i	0.461009	+	0.798491i	−0.538002	+	0.842943i	$0.680821\pi$
$432$	−1.51315	+	2.62085i	−0.0728014	+	0.126096i
$433$	9.84110	+	17.0453i	0.472933	+	0.819144i	0.999520	−	0.0309769i	$-0.00986184\pi$
$433$	9.84110	+	17.0453i	0.472933	+	0.819144i	−0.526587	+	0.850121i	$0.676529\pi$
$434$	9.26593			0.444779
$435$	68.0944			3.26488
$436$	−2.34579	+	4.06303i	−0.112343	+	0.194584i
$437$	−9.15735	+	15.8610i	−0.438056	+	0.758734i
$438$	−36.2382			−1.73153
$439$	33.9634			1.62098			0.810492	−	0.585750i	$-0.199200\pi$
$439$	33.9634			1.62098			0.810492	+	0.585750i	$0.199200\pi$
$440$	0.417001	−	0.722267i	0.0198798	−	0.0344327i
$441$	−15.5271			−0.739385
$442$	14.2868			0.679556
$443$	2.65655	−	4.60128i	0.126217	−	0.218613i	−0.795991	−	0.605308i	$-0.793050\pi$
$443$	2.65655	−	4.60128i	0.126217	−	0.218613i	0.922208	+	0.386695i	$0.126383\pi$
$444$	−6.23062	−	10.7917i	−0.295692	−	0.512154i
$445$	11.2573	−	19.4983i	0.533649	−	0.924307i
$446$	−7.27927			−0.344684
$447$	3.87123	−	6.70517i	0.183103	−	0.317144i
$448$	−2.11709	+	3.66691i	−0.100023	+	0.173245i
$449$	34.9719			1.65043			0.825214	−	0.564820i	$-0.191055\pi$
$449$	34.9719			1.65043			0.825214	+	0.564820i	$0.191055\pi$
$450$	30.3327	+	52.5377i	1.42990	+	2.47665i
$451$	0.0142947	−	0.0247592i	0.000673113	−	0.00116587i
$452$	14.2512			0.670320
$453$	−23.5186	+	40.7354i	−1.10500	+	1.91392i
$454$	27.4087			1.28635
$455$	−26.3675			−1.23613
$456$	−12.3706			−0.579304
$457$	−16.2143			−0.758472			−0.379236	−	0.925300i	$-0.623813\pi$
$457$	−16.2143			−0.758472			−0.379236	+	0.925300i	$0.623813\pi$
$458$	14.3130	+	24.7909i	0.668804	+	1.15840i
$459$	1.01390			0.0473248
$460$	−11.3119	−	19.5928i	−0.527421	−	0.913520i
$461$	4.64564			0.216369			0.108184	−	0.994131i	$-0.465496\pi$
$461$	4.64564			0.216369			0.108184	+	0.994131i	$0.465496\pi$
$462$	0.205326	+	0.355635i	0.00955263	+	0.0165456i
$463$	−7.57873	+	13.1267i	−0.352213	+	0.610051i	−0.986637	−	0.162934i	$-0.947904\pi$
$463$	−7.57873	+	13.1267i	−0.352213	+	0.610051i	0.634424	+	0.772986i	$0.281238\pi$
$464$	−16.2062	−	28.0699i	−0.752353	−	1.30311i
$465$	50.3107			2.33311
$466$	3.87766	−	6.71630i	0.179629	−	0.311126i
$467$	3.83598	+	6.64411i	0.177508	+	0.307453i	0.941026	−	0.338333i	$-0.109863\pi$
$467$	3.83598	+	6.64411i	0.177508	+	0.307453i	−0.763518	+	0.645786i	$0.776530\pi$
$468$	−5.01934	−	8.69375i	−0.232019	−	0.401869i
$469$	4.29495	+	7.43907i	0.198322	+	0.343504i
$470$	3.81021	−	6.59948i	0.175752	−	0.304412i
$471$	−6.22437	+	10.7809i	−0.286804	+	0.496759i
$472$	4.46257	−	7.72941i	0.205407	−	0.355775i
$473$	−0.181829	+	0.314936i	−0.00836048	+	0.0144808i
$474$	38.2940			1.75890
$475$	16.2056	−	28.0690i	0.743565	−	1.28789i
$476$	−1.31250			−0.0601582
$477$	25.3792			1.16203
$478$	−8.13699	−	14.0937i	−0.372177	−	0.644630i
$479$	8.48232	+	14.6918i	0.387567	+	0.671286i	0.992122	−	0.125278i	$-0.0399822\pi$
$479$	8.48232	+	14.6918i	0.387567	+	0.671286i	−0.604555	+	0.796564i	$0.706649\pi$
$480$	19.3100	−	33.4459i	0.881378	−	1.52659i
$481$	39.9222			1.82029
$482$	−6.17752	−	24.7032i	−0.281378	−	1.12520i
$483$	−21.1259			−0.961260
$484$	3.79494	−	6.57302i	0.172497	−	0.298774i
$485$	4.83431	+	8.37327i	0.219515	+	0.380211i
$486$	−17.5577	−	30.4108i	−0.796433	−	1.37946i
$487$	30.8789			1.39926			0.699629	−	0.714506i	$-0.253348\pi$
$487$	30.8789			1.39926			0.699629	+	0.714506i	$0.253348\pi$
$488$	22.6452			1.02510
$489$	−22.1578	+	38.3784i	−1.00201	+	1.73553i
$490$	−39.9283			−1.80378
$491$	−17.8819	+	30.9724i	−0.807000	+	1.39777i	0.107932	+	0.994158i	$0.465577\pi$
$491$	−17.8819	+	30.9724i	−0.807000	+	1.39777i	−0.914932	+	0.403607i	$0.867756\pi$
$492$	0.261918	−	0.453655i	0.0118082	−	0.0204523i
$493$	−5.42955	+	9.40426i	−0.244535	+	0.423547i
$494$	−10.4489	+	18.0980i	−0.470119	+	0.814269i
$495$	0.532428	+	0.922192i	0.0239308	+	0.0414494i
$496$	−11.9737	−	20.7391i	−0.537637	−	0.931214i
$497$	8.39175	+	14.5349i	0.376421	+	0.651981i
$498$	15.1110	−	26.1730i	0.677141	−	1.17284i
$499$	−42.4545			−1.90052			−0.950262	−	0.311453i	$-0.899184\pi$
$499$	−42.4545			−1.90052			−0.950262	+	0.311453i	$0.899184\pi$
$500$	12.5965	+	21.8178i	0.563332	+	0.975720i
$501$	12.6217	−	21.8614i	0.563895	−	0.976694i
$502$	−1.96791	−	3.40851i	−0.0878320	−	0.152129i
$503$	26.7535			1.19288			0.596441	−	0.802657i	$-0.296581\pi$
$503$	26.7535			1.19288			0.596441	+	0.802657i	$0.296581\pi$
$504$	−3.40737	−	5.90173i	−0.151776	−	0.262884i
$505$	−24.4524			−1.08812
$506$	−0.564410	−	0.977587i	−0.0250911	−	0.0434591i
$507$	36.1893			1.60722
$508$	9.81501			0.435471
$509$	−15.7611			−0.698600			−0.349300	−	0.937011i	$-0.613581\pi$
$509$	−15.7611			−0.698600			−0.349300	+	0.937011i	$0.613581\pi$
$510$	−27.7677			−1.22957
$511$	−5.33275	+	9.23660i	−0.235907	+	0.408603i
$512$	2.68508			0.118665
$513$	−0.741531	+	1.28437i	−0.0327394	+	0.0567063i
$514$	−19.0712	−	33.0323i	−0.841194	−	1.45699i
$515$	−14.0969			−0.621182
$516$	−3.33158	+	5.77047i	−0.146665	+	0.254031i
$517$	0.0487909	−	0.0845083i	0.00214582	−	0.00371667i
$518$	−14.2904			−0.627885
$519$	6.11848	−	10.5975i	0.268571	−	0.465179i
$520$	24.4782	+	42.3974i	1.07344	+	1.85925i
$521$	−1.28159	+	2.21977i	−0.0561473	+	0.0972499i	−0.892733	−	0.450586i	$-0.851215\pi$
$521$	−1.28159	+	2.21977i	−0.0561473	+	0.0972499i	0.836586	+	0.547836i	$0.184548\pi$
$522$	29.7306			1.30127
$523$	31.8308			1.39187			0.695933	−	0.718107i	$-0.254991\pi$
$523$	31.8308			1.39187			0.695933	+	0.718107i	$0.254991\pi$
$524$	0.591299	−	1.02416i	0.0258310	−	0.0447406i
$525$	37.3861			1.63166
$526$	−30.3548			−1.32353
$527$	−4.01156	+	6.94823i	−0.174746	+	0.302670i
$528$	0.530658	−	0.919127i	0.0230939	−	0.0399999i
$529$	35.0718			1.52486
$530$	65.2633			2.83485
$531$	5.69782	+	9.86891i	0.247264	+	0.428274i
$532$	0.959915	−	1.66262i	0.0416176	−	0.0720838i
$533$	0.839108	+	1.45338i	0.0363458	+	0.0629528i
$534$	10.2916	−	17.8256i	0.445361	−	0.771387i
$535$	7.70788	+	13.3504i	0.333241	+	0.577190i
$536$	7.97440	−	13.8121i	0.344442	−	0.596591i
$537$	4.41443	−	7.64601i	0.190497	−	0.329950i
$538$	−11.1426	+	19.2996i	−0.480392	+	0.832063i
$539$	−0.511293			−0.0220230
$540$	−0.916001	−	1.58656i	−0.0394184	−	0.0682747i
$541$	10.7238	−	18.5742i	0.461053	−	0.798567i	−0.537961	−	0.842970i	$-0.680805\pi$
$541$	10.7238	−	18.5742i	0.461053	−	0.798567i	0.999014	+	0.0444027i	$0.0141385\pi$
$542$	−12.9682	+	22.4615i	−0.557031	+	0.964806i
$543$	−6.59455			−0.282999
$544$	3.07940	+	5.33367i	0.132028	+	0.228679i
$545$	14.6065	+	25.2992i	0.625672	+	1.08370i
$546$	−24.1055			−1.03162
$547$	−9.77321	−	16.9277i	−0.417872	−	0.723776i	0.577853	−	0.816141i	$-0.303891\pi$
$547$	−9.77321	−	16.9277i	−0.417872	−	0.723776i	−0.995725	+	0.0923647i	$0.970557\pi$
$548$	−3.83400	+	6.64067i	−0.163780	+	0.283676i
$549$	−14.4567	+	25.0397i	−0.616996	+	1.06867i
$550$	0.998828	+	1.73002i	0.0425902	+	0.0737684i
$551$	−7.94197	−	13.7559i	−0.338339	−	0.586021i
$552$	19.6121	+	33.9692i	0.834748	+	1.44583i
$553$	5.63528	−	9.76059i	0.239636	−	0.415063i
$554$	20.1955	−	34.9796i	0.858025	−	1.48614i
$555$	−77.5920			−3.29360
$556$	6.55543	+	11.3543i	0.278012	+	0.481531i
$557$	−0.142737	−	0.247229i	−0.00604798	−	0.0104754i	0.862986	−	0.505229i	$-0.168592\pi$
$557$	−0.142737	−	0.247229i	−0.00604798	−	0.0104754i	−0.869034	+	0.494753i	$0.835258\pi$
$558$	21.9661			0.929898
$559$	−10.6734	−	18.4869i	−0.451438	−	0.781913i
$560$	−12.1967	−	21.1252i	−0.515403	−	0.892703i
$561$	−0.355573			−0.0150123
$562$	7.04834	−	12.2081i	0.297316	−	0.514967i
$563$	4.83849	+	8.38051i	0.203918	+	0.353196i	0.949787	−	0.312896i	$-0.101299\pi$
$563$	4.83849	+	8.38051i	0.203918	+	0.353196i	−0.745870	+	0.666092i	$0.767966\pi$
$564$	0.893979	−	1.54842i	0.0376433	−	0.0652001i
$565$	44.3688	−	76.8489i	1.86661	−	3.23306i
$566$	1.61840	+	2.80315i	0.0680264	+	0.117825i
$567$	−11.2288			−0.471563
$568$	15.5809	−	26.9869i	0.653760	−	1.13235i
$569$	22.0217			0.923197			0.461598	−	0.887089i	$-0.347276\pi$
$569$	22.0217			0.923197			0.461598	+	0.887089i	$0.347276\pi$
$570$	20.3083	−	35.1750i	0.850621	−	1.47332i
$571$	−19.7217	+	34.1590i	−0.825328	+	1.42951i	0.0763397	+	0.997082i	$0.475677\pi$
$571$	−19.7217	+	34.1590i	−0.825328	+	1.42951i	−0.901668	+	0.432429i	$0.857657\pi$
$572$	−0.165282	−	0.286278i	−0.00691081	−	0.0119699i
$573$	−21.3274			−0.890964
$574$	−0.300365	−	0.520247i	−0.0125370	−	0.0217147i
$575$	−102.769			−4.28576
$576$	−5.01884	+	8.69289i	−0.209118	+	0.362204i
$577$	7.75662	−	13.4349i	0.322912	−	0.559300i	−0.658175	−	0.752865i	$-0.728672\pi$
$577$	7.75662	−	13.4349i	0.322912	−	0.559300i	0.981088	+	0.193564i	$0.0620048\pi$
$578$	−11.7283	+	20.3139i	−0.487831	+	0.844949i
$579$	−24.1320	−	41.7978i	−1.00289	−	1.73706i
$580$	19.6212			0.814725
$581$	−4.44742	−	7.70316i	−0.184510	−	0.319581i
$582$	4.41958	+	7.65494i	0.183198	+	0.317308i
$583$	0.835714			0.0346118
$584$	19.8026			0.819436
$585$	−62.5075			−2.58437
$586$	−14.0344	−	24.3083i	−0.579755	−	1.00417i
$587$	−33.1316			−1.36749			−0.683744	−	0.729722i	$-0.739649\pi$
$587$	−33.1316			−1.36749			−0.683744	+	0.729722i	$0.739649\pi$
$588$	−9.36825			−0.386340
$589$	−5.86783	−	10.1634i	−0.241780	−	0.418775i
$590$	14.6521	+	25.3782i	0.603217	+	1.04480i
$591$	−15.0003	−	25.9813i	−0.617029	−	1.06873i
$592$	18.4666	+	31.9850i	0.758971	+	1.31458i
$593$	−12.7907			−0.525251			−0.262625	−	0.964898i	$-0.584588\pi$
$593$	−12.7907			−0.525251			−0.262625	+	0.964898i	$0.584588\pi$
$594$	−0.0457040	−	0.0791617i	−0.00187526	−	0.00324804i
$595$	−4.08624	+	7.07758i	−0.167520	+	0.290153i
$596$	1.11548	−	1.93207i	0.0456919	−	0.0791408i
$597$	1.95225			0.0799002
$598$	66.2623			2.70967
$599$	13.2353			0.540778			0.270389	−	0.962751i	$-0.412848\pi$
$599$	13.2353			0.540778			0.270389	+	0.962751i	$0.412848\pi$
$600$	−34.7073	−	60.1148i	−1.41692	−	2.45418i
$601$	−3.41285	+	5.91122i	−0.139213	+	0.241124i	−0.927199	−	0.374569i	$-0.877791\pi$
$601$	−3.41285	+	5.91122i	−0.139213	+	0.241124i	0.787986	+	0.615693i	$0.211124\pi$
$602$	3.82063	+	6.61752i	0.155717	+	0.269710i
$603$	10.1817	+	17.6353i	0.414632	+	0.718164i
$604$	−6.77681	+	11.7378i	−0.275745	+	0.477604i
$605$	−23.6298	−	40.9281i	−0.960689	−	1.66396i
$606$	−22.3547			−0.908097
$607$	−44.0468			−1.78780			−0.893902	−	0.448262i	$-0.852043\pi$
$607$	−44.0468			−1.78780			−0.893902	+	0.448262i	$0.852043\pi$
$608$	−9.00865			−0.365349
$609$	9.16101	−	15.8673i	0.371223	−	0.642977i
$610$	−37.1758	+	64.3903i	−1.50520	+	2.60709i
$611$	2.86405	+	4.96068i	0.115867	+	0.200687i
$612$	−3.11144			−0.125773
$613$	1.76404	+	3.05541i	0.0712489	+	0.123407i	0.899449	−	0.437026i	$-0.143968\pi$
$613$	1.76404	+	3.05541i	0.0712489	+	0.123407i	−0.828200	+	0.560433i	$0.810635\pi$
$614$	−26.2181	−	45.4111i	−1.05808	−	1.83264i
$615$	−1.63087	−	2.82476i	−0.0657632	−	0.113905i
$616$	−0.112202	−	0.194339i	−0.00452073	−	0.00783014i
$617$	11.5683			0.465722			0.232861	−	0.972510i	$-0.425191\pi$
$617$	11.5683			0.465722			0.232861	+	0.972510i	$0.425191\pi$
$618$	−12.8875			−0.518412
$619$	5.00259	+	8.66473i	0.201071	+	0.348265i	0.948874	−	0.315656i	$-0.102225\pi$
$619$	5.00259	+	8.66473i	0.201071	+	0.348265i	−0.747803	+	0.663921i	$0.768891\pi$
$620$	14.4969			0.582209
$621$	4.70246			0.188703
$622$	−11.3348			−0.454483
$623$	−3.02899	−	5.24636i	−0.121354	−	0.210191i
$624$	31.1499	+	53.9532i	1.24699	+	2.15986i
$625$	89.4392			3.57757
$626$	0.779267	+	1.34973i	0.0311458	+	0.0539461i
$627$	0.260054	−	0.450426i	0.0103855	−	0.0179883i
$628$	−1.79353	+	3.10649i	−0.0715697	+	0.123962i
$629$	6.18685	−	10.7159i	0.246686	−	0.427272i
$630$	22.3750			0.891442
$631$	−9.12074	−	15.7976i	−0.363091	−	0.628892i	0.625377	−	0.780323i	$-0.284945\pi$
$631$	−9.12074	−	15.7976i	−0.363091	−	0.628892i	−0.988468	+	0.151431i	$0.951612\pi$
$632$	−20.9260			−0.832391
$633$	−12.5120	−	21.6713i	−0.497306	−	0.861359i
$634$	−1.07029	+	1.85380i	−0.0425067	+	0.0736238i
$635$	30.5574	−	52.9270i	1.21263	−	2.10034i
$636$	15.3125			0.607181
$637$	15.0066	−	25.9922i	0.594582	−	1.02985i
$638$	0.979002			0.0387591
$639$	19.8937	+	34.4569i	0.786983	+	1.36309i
$640$	−29.0223	+	50.2681i	−1.14721	+	1.98702i
$641$	−6.12843	+	10.6147i	−0.242058	+	0.419257i	−0.961300	−	0.275502i	$-0.911156\pi$
$641$	−6.12843	+	10.6147i	−0.242058	+	0.419257i	0.719242	+	0.694760i	$0.244489\pi$
$642$	7.04663	+	12.2051i	0.278108	+	0.481698i
$643$	19.6171	−	33.9778i	0.773623	−	1.33995i	−0.161942	−	0.986800i	$-0.551776\pi$
$643$	19.6171	−	33.9778i	0.773623	−	1.33995i	0.935565	−	0.353154i	$-0.114891\pi$
$644$	−6.08735			−0.239875
$645$	20.7447	+	35.9308i	0.816820	+	1.41477i
$646$	3.23859	+	5.60941i	0.127421	+	0.220699i
$647$	−9.93362			−0.390531			−0.195265	−	0.980750i	$-0.562557\pi$
$647$	−9.93362			−0.390531			−0.195265	+	0.980750i	$0.562557\pi$
$648$	10.4242	+	18.0552i	0.409500	+	0.709276i
$649$	0.187624	+	0.324975i	0.00736490	+	0.0127564i
$650$	−117.263			−4.59945
$651$	6.76850	−	11.7234i	0.265279	−	0.459476i
$652$	−6.38469	+	11.0586i	−0.250044	+	0.433088i
$653$	0.132167	+	0.228920i	0.00517209	+	0.00895832i	0.868600	−	0.495514i	$-0.165020\pi$
$653$	0.132167	+	0.228920i	0.00517209	+	0.00895832i	−0.863428	+	0.504472i	$0.831687\pi$
$654$	13.3534	+	23.1288i	0.522160	+	0.904407i
$655$	−3.68182	−	6.37710i	−0.143861	−	0.249174i
$656$	−0.776282	+	1.34456i	−0.0303087	+	0.0524963i
$657$	−12.6420	+	21.8965i	−0.493210	+	0.854265i
$658$	−1.02521	−	1.77571i	−0.0399667	−	0.0692244i
$659$	31.5798			1.23017			0.615087	−	0.788459i	$-0.289121\pi$
$659$	31.5798			1.23017			0.615087	+	0.788459i	$0.289121\pi$
$660$	0.321240	+	0.556404i	0.0125042	+	0.0216580i
$661$	−7.07757	−	12.2587i	−0.275286	−	0.476809i	0.694921	−	0.719086i	$-0.255439\pi$
$661$	−7.07757	−	12.2587i	−0.275286	−	0.476809i	−0.970207	+	0.242277i	$0.922106\pi$
$662$	−26.0355			−1.01190
$663$	10.4361	−	18.0759i	0.405306	−	0.702011i
$664$	−8.25750	+	14.3024i	−0.320453	+	0.555041i
$665$	−5.97707	−	10.3526i	−0.231781	−	0.401456i
$666$	−33.8773			−1.31272
$667$	−25.1822	+	43.6169i	−0.975060	+	1.68885i
$668$	3.63689	−	6.29928i	0.140716	−	0.243727i
$669$	−5.31731	+	9.20984i	−0.205579	+	0.356073i
$670$	26.1826	+	45.3496i	1.01152	+	1.75201i
$671$	−0.476046	+	0.824536i	−0.0183776	+	0.0318309i
$672$	−5.19571	−	8.99923i	−0.200429	−	0.347153i
$673$	−9.21752	+	15.9652i	−0.355309	+	0.615414i	−0.987171	−	0.159667i	$-0.948958\pi$
$673$	−9.21752	+	15.9652i	−0.355309	+	0.615414i	0.631861	+	0.775081i	$0.282291\pi$
$674$	−20.5467	−	35.5879i	−0.791430	−	1.37080i
$675$	−8.32187			−0.320309
$676$	10.4278			0.401070
$677$	2.58725	−	4.48124i	0.0994360	−	0.172228i	−0.812015	−	0.583636i	$-0.801629\pi$
$677$	2.58725	−	4.48124i	0.0994360	−	0.172228i	0.911451	+	0.411408i	$0.134963\pi$
$678$	40.5624	−	70.2562i	1.55779	−	2.69817i
$679$	2.60151			0.0998370
$680$	15.1738			0.581889
$681$	20.0213	−	34.6778i	0.767216	−	1.32886i
$682$	0.723324			0.0276975
$683$	8.54870			0.327107			0.163553	−	0.986534i	$-0.447704\pi$
$683$	8.54870			0.327107			0.163553	+	0.986534i	$0.447704\pi$
$684$	2.27560	−	3.94146i	0.0870098	−	0.150705i
$685$	23.8730	+	41.3493i	0.912141	+	1.57988i
$686$	−12.0132	+	20.8075i	−0.458667	+	0.794434i
$687$	41.8211			1.59557
$688$	9.87428	−	17.1028i	0.376453	−	0.652036i
$689$	−24.5284	+	42.4845i	−0.934459	+	1.61853i
$690$	−128.786			−4.90281
$691$	−9.89997	−	17.1473i	−0.376613	−	0.652312i	0.613954	−	0.789342i	$-0.289578\pi$
$691$	−9.89997	−	17.1473i	−0.376613	−	0.652312i	−0.990567	+	0.137029i	$0.956245\pi$
$692$	1.76302	−	3.05364i	0.0670199	−	0.116082i
$693$	0.286518			0.0108839
$694$	2.91915	−	5.05612i	0.110810	−	0.191928i
$695$	81.6369			3.09667
$696$	−34.0184			−1.28946
$697$	0.520156			0.0197023
$698$	27.1075			1.02603
$699$	−5.66504	−	9.81214i	−0.214271	−	0.371129i
$700$	10.7727			0.407170
$701$	7.73917	+	13.4046i	0.292304	+	0.506286i	0.974354	−	0.225020i	$-0.0722447\pi$
$701$	7.73917	+	13.4046i	0.292304	+	0.506286i	−0.682050	+	0.731306i	$0.738911\pi$
$702$	5.36570			0.202515
$703$	9.04970	+	15.6745i	0.341316	+	0.591176i
$704$	−0.165266	+	0.286249i	−0.00622870	+	0.0107884i
$705$	−5.56651	−	9.64148i	−0.209647	−	0.363119i
$706$	57.5175			2.16470
$707$	−3.28968	+	5.69789i	−0.123721	+	0.214291i
$708$	3.43778	+	5.95440i	0.129200	+	0.223780i
$709$	14.7059	+	25.4713i	0.552290	+	0.956594i	0.998109	+	0.0614711i	$0.0195792\pi$
$709$	14.7059	+	25.4713i	0.552290	+	0.956594i	−0.445819	+	0.895123i	$0.647087\pi$
$710$	51.1572	+	88.6069i	1.91990	+	3.32536i
$711$	13.3592	−	23.1387i	0.501007	−	0.867770i
$712$	−5.62390	+	9.74088i	−0.210765	+	0.365055i
$713$	−18.6056	+	32.2258i	−0.696785	+	1.20687i
$714$	−3.73569	+	6.47041i	−0.139805	+	0.242149i
$715$	−2.05832			−0.0769768
$716$	1.27200	−	2.20317i	0.0475370	−	0.0823364i
$717$	−23.7754			−0.887907
$718$	−24.1816			−0.902449
$719$	24.1951	+	41.9071i	0.902324	+	1.56287i	0.824470	+	0.565906i	$0.191474\pi$
$719$	24.1951	+	41.9071i	0.902324	+	1.56287i	0.0778545	+	0.996965i	$0.475193\pi$
$720$	−28.9137	−	50.0801i	−1.07755	−	1.86637i
$721$	−1.89651	+	3.28484i	−0.0706295	+	0.122334i
$722$	21.6908			0.807249
$723$	−35.7674	−	10.2291i	−1.33020	−	0.380425i
$724$	−1.90020			−0.0706204
$725$	44.5646	−	77.1882i	1.65509	−	2.86670i
$726$	−21.6027	−	37.4169i	−0.801750	−	1.38867i
$727$	−13.1230	−	22.7298i	−0.486706	−	0.843000i	0.513177	−	0.858283i	$-0.328468\pi$
$727$	−13.1230	−	22.7298i	−0.486706	−	0.843000i	−0.999883	+	0.0152828i	$0.995135\pi$
$728$	13.1726			0.488208
$729$	−22.1830			−0.821592
$730$	−32.5092	+	56.3076i	−1.20322	+	2.08404i
$731$	−6.61636			−0.244715
$732$	−8.72243	+	15.1077i	−0.322390	+	0.558396i
$733$	7.34601	−	12.7237i	0.271331	−	0.469959i	−0.697872	−	0.716223i	$-0.745870\pi$
$733$	7.34601	−	12.7237i	0.271331	−	0.469959i	0.969203	+	0.246263i	$0.0792028\pi$
$734$	2.75068	−	4.76431i	0.101529	−	0.175854i
$735$	−29.1665	+	50.5179i	−1.07582	+	1.86338i
$736$	14.2822	+	24.7375i	0.526449	+	0.911837i
$737$	0.335276	+	0.580714i	0.0123500	+	0.0213909i
$738$	−0.712053	−	1.23331i	−0.0262110	−	0.0453988i
$739$	−21.0132	+	36.3960i	−0.772985	+	1.33885i	0.162936	+	0.986637i	$0.447904\pi$
$739$	−21.0132	+	36.3960i	−0.772985	+	1.33885i	−0.935920	+	0.352212i	$0.885430\pi$
$740$	−22.3579			−0.821892
$741$	15.2653	+	26.4402i	0.560784	+	0.971306i
$742$	8.78012	−	15.2076i	0.322328	−	0.558289i
$743$	0.0333676	+	0.0577944i	0.00122414	+	0.00212027i	0.866637	−	0.498939i	$-0.166277\pi$
$743$	0.0333676	+	0.0577944i	0.00122414	+	0.00212027i	−0.865413	+	0.501060i	$0.832944\pi$
$744$	−25.1341			−0.921460
$745$	−6.94574	−	12.0304i	−0.254472	−	0.440759i
$746$	32.0379			1.17299
$747$	−10.5432	−	18.2613i	−0.385755	−	0.668148i
$748$	−0.102457			−0.00374620
$749$	4.14789			0.151560
$750$	143.411			5.23663
$751$	−27.5221			−1.00430			−0.502149	−	0.864781i	$-0.667457\pi$
$751$	−27.5221			−1.00430			−0.502149	+	0.864781i	$0.667457\pi$
$752$	−2.64961	+	4.58926i	−0.0966214	+	0.167353i
$753$	−5.75000			−0.209542
$754$	−28.7339	+	49.7686i	−1.04643	+	1.81247i
$755$	42.1970	+	73.0873i	1.53571	+	2.65992i
$756$	−0.492933			−0.0179278
$757$	−8.42193	+	14.5872i	−0.306100	+	0.530181i	−0.977506	−	0.210909i	$-0.932358\pi$
$757$	−8.42193	+	14.5872i	−0.306100	+	0.530181i	0.671405	+	0.741090i	$0.265691\pi$
$758$	−24.6444	+	42.6853i	−0.895124	+	1.55040i
$759$	−1.64914			−0.0598601
$760$	−11.0976	+	19.2216i	−0.402552	+	0.697241i
$761$	−10.0795	−	17.4582i	−0.365382	−	0.632861i	0.623455	−	0.781859i	$-0.285728\pi$
$761$	−10.0795	−	17.4582i	−0.365382	−	0.632861i	−0.988837	+	0.148998i	$0.952395\pi$
$762$	27.9360	−	48.3865i	1.01201	−	1.75286i
$763$	7.86026			0.284561
$764$	−6.14542			−0.222333
$765$	−9.68696	+	16.7783i	−0.350233	+	0.606621i
$766$	−7.62086			−0.275353
$767$	−22.0273			−0.795359
$768$	−17.7617	+	30.7642i	−0.640921	+	1.11011i
$769$	20.6804	−	35.8195i	0.745754	−	1.29168i	−0.204087	−	0.978953i	$-0.565423\pi$
$769$	20.6804	−	35.8195i	0.745754	−	1.29168i	0.949841	−	0.312732i	$-0.101244\pi$
$770$	0.736790			0.0265521
$771$	−55.7239			−2.00685
$772$	−6.95356	−	12.0439i	−0.250264	−	0.433470i
$773$	−9.48547	+	16.4293i	−0.341169	+	0.590922i	−0.984650	−	0.174540i	$-0.944156\pi$
$773$	−9.48547	+	16.4293i	−0.341169	+	0.590922i	0.643481	+	0.765462i	$0.277489\pi$
$774$	9.05729	+	15.6877i	0.325557	+	0.563882i
$775$	32.9260	−	57.0296i	1.18274	−	2.04856i
$776$	−2.41511	−	4.18309i	−0.0866973	−	0.150164i
$777$	−10.4388	+	18.0805i	−0.374488	+	0.648633i
$778$	2.70796	−	4.69033i	0.0970851	−	0.168156i
$779$	−0.380424	+	0.658913i	−0.0136301	+	0.0236080i
$780$	−37.7139			−1.35037
$781$	0.655083	+	1.13464i	0.0234407	+	0.0406005i
$782$	10.2689	−	17.7862i	0.367213	−	0.636032i
$783$	−2.03917	+	3.53195i	−0.0728740	+	0.126222i
$784$	27.7660			0.991643
$785$	11.1677	+	19.3431i	0.398594	+	0.690384i
$786$	−3.36597	−	5.83002i	−0.120060	−	0.207950i
$787$	27.0008			0.962474			0.481237	−	0.876591i	$-0.340188\pi$
$787$	27.0008			0.962474			0.481237	+	0.876591i	$0.340188\pi$
$788$	−4.32228	−	7.48642i	−0.153975	−	0.266693i
$789$	−22.1733	+	38.4053i	−0.789391	+	1.36727i
$790$	34.3534	−	59.5019i	1.22224	−	2.11698i
$791$	−11.9382	−	20.6776i	−0.424474	−	0.735210i
$792$	−0.265988	−	0.460705i	−0.00945149	−	0.0163705i
$793$	−27.9441	−	48.4007i	−0.992325	−	1.71876i
$794$	−15.7022	+	27.1971i	−0.557252	+	0.965189i
$795$	47.6730	−	82.5720i	1.69079	−	2.92853i
$796$	0.562534			0.0199385
$797$	23.2739	+	40.3116i	0.824403	+	1.42791i	0.902374	+	0.430953i	$0.141822\pi$
$797$	23.2739	+	40.3116i	0.824403	+	1.42791i	−0.0779711	+	0.996956i	$0.524844\pi$
$798$	−5.46431	−	9.46447i	−0.193435	−	0.335038i
$799$	1.77540			0.0628091
$800$	−25.2750	−	43.7776i	−0.893607	−	1.54777i
$801$	−7.18060	−	12.4372i	−0.253714	−	0.439446i
$802$	−33.8165			−1.19410
$803$	−0.416289	+	0.721034i	−0.0146905	+	0.0254447i
$804$	6.14314	+	10.6402i	0.216652	+	0.375252i
$805$	−18.9520	+	32.8258i	−0.667969	+	1.15696i
$806$	−21.2297	+	36.7710i	−0.747786	+	1.29520i
$807$	16.2787	+	28.1956i	0.573038	+	0.992531i
$808$	12.2159			0.429752
$809$	9.33892	−	16.1755i	0.328339	−	0.568700i	−0.653843	−	0.756630i	$-0.726844\pi$
$809$	9.33892	−	16.1755i	0.328339	−	0.568700i	0.982182	+	0.187930i	$0.0601778\pi$
$810$	−68.4520			−2.40516
$811$	5.85160	−	10.1353i	0.205478	−	0.355898i	−0.744807	−	0.667280i	$-0.767459\pi$
$811$	5.85160	−	10.1353i	0.205478	−	0.355898i	0.950285	+	0.311382i	$0.100792\pi$
$812$	2.63971	−	4.57212i	0.0926358	−	0.160450i
$813$	18.9458	+	32.8151i	0.664458	+	1.15087i
$814$	−1.11555			−0.0391000
$815$	39.7554	+	68.8583i	1.39257	+	2.41200i
$816$	19.3095			0.675969
$817$	4.83898	−	8.38135i	0.169294	−	0.293226i
$818$	−7.70382	+	13.3434i	−0.269358	+	0.466541i
$819$	−8.40938	+	14.5655i	−0.293848	+	0.508959i
$820$	−0.469931	−	0.813945i	−0.0164107	−	0.0284242i
$821$	6.39468			0.223176			0.111588	−	0.993755i	$-0.464406\pi$
$821$	6.39468			0.223176			0.111588	+	0.993755i	$0.464406\pi$
$822$	21.8250	+	37.8020i	0.761234	+	1.31850i
$823$	4.61846	+	7.99941i	0.160989	+	0.278842i	0.935224	−	0.354057i	$-0.115198\pi$
$823$	4.61846	+	7.99941i	0.160989	+	0.278842i	−0.774234	+	0.632899i	$0.781865\pi$
$824$	7.04246			0.245336
$825$	2.91846			0.101608
$826$	7.88482			0.274348
$827$	−6.13183	−	10.6206i	−0.213225	−	0.369316i	0.739497	−	0.673160i	$-0.235063\pi$
$827$	−6.13183	−	10.6206i	−0.213225	−	0.369316i	−0.952722	+	0.303844i	$0.901730\pi$
$828$	−14.4309			−0.501507
$829$	−53.1162			−1.84480			−0.922400	−	0.386236i	$-0.873775\pi$
$829$	−53.1162			−1.84480			−0.922400	+	0.386236i	$0.873775\pi$
$830$	−27.1121	−	46.9595i	−0.941075	−	1.62999i
$831$	−29.5045	−	51.1033i	−1.02350	−	1.77275i
$832$	−9.70120	−	16.8030i	−0.336329	−	0.582538i
$833$	−4.65122	−	8.05615i	−0.161155	−	0.279129i
$834$	74.6335			2.58435
$835$	−22.6457	−	39.2236i	−0.783688	−	1.35739i
$836$	0.0749336	−	0.129789i	0.00259163	−	0.00448884i
$837$	−1.50662	+	2.60954i	−0.0520763	+	0.0901989i
$838$	−23.1672			−0.800297
$839$	1.64179			0.0566809			0.0283405	−	0.999598i	$-0.490978\pi$
$839$	1.64179			0.0566809			0.0283405	+	0.999598i	$0.490978\pi$
$840$	−25.6020			−0.883352
$841$	−7.34000	−	12.7133i	−0.253104	−	0.438388i
$842$	10.2753	−	17.7973i	0.354109	−	0.613334i
$843$	−10.2972	−	17.8353i	−0.354655	−	0.614281i
$844$	−3.60528	−	6.24453i	−0.124099	−	0.214946i
$845$	32.4653	−	56.2315i	1.11684	−	1.93442i
$846$	−2.43038	−	4.20955i	−0.0835583	−	0.144727i
$847$	−12.7161			−0.436929
$848$	−45.3839			−1.55849
$849$	4.72879			0.162292
$850$	−18.1726	+	31.4759i	−0.623316	+	1.07962i
$851$	28.6946	−	49.7005i	0.983637	−	1.70371i
$852$	12.0029	+	20.7896i	0.411211	+	0.712239i
$853$	−3.12352			−0.106947			−0.0534736	−	0.998569i	$-0.517029\pi$
$853$	−3.12352			−0.106947			−0.0534736	+	0.998569i	$0.517029\pi$
$854$	10.0028	+	17.3254i	0.342289	+	0.592862i
$855$	−14.1694	−	24.5422i	−0.484584	−	0.839324i
$856$	−3.85068	−	6.66957i	−0.131613	−	0.227961i
$857$	−26.3721	−	45.6778i	−0.900854	−	1.56033i	−0.826388	−	0.563102i	$-0.809608\pi$
$857$	−26.3721	−	45.6778i	−0.900854	−	1.56033i	−0.0744665	−	0.997224i	$-0.523725\pi$
$858$	−1.88174			−0.0642415
$859$	11.9733			0.408524			0.204262	−	0.978916i	$-0.434521\pi$
$859$	11.9733			0.408524			0.204262	+	0.978916i	$0.434521\pi$
$860$	5.97751	+	10.3533i	0.203831	+	0.353046i
$861$	−0.877632			−0.0299096
$862$	31.3975			1.06940
$863$	30.9314			1.05292			0.526458	−	0.850201i	$-0.323520\pi$
$863$	30.9314			1.05292			0.526458	+	0.850201i	$0.323520\pi$
$864$	1.15653	+	2.00316i	0.0393458	+	0.0681489i
$865$	−10.9777	−	19.0140i	−0.373254	−	0.646495i
$866$	32.2842			1.09706
$867$	17.1343	+	29.6775i	0.581913	+	1.00790i
$868$	1.95032	−	3.37806i	0.0661983	−	0.114659i
$869$	0.439905	−	0.761939i	0.0149228	−	0.0258470i
$870$	55.8468	−	96.7294i	1.89338	−	3.27943i
$871$	−39.3617			−1.33372
$872$	−7.29705	−	12.6389i	−0.247109	−	0.428006i
$873$	6.16722			0.208729
$874$	15.0206	+	26.0164i	0.508078	+	0.880018i
$875$	21.1041	−	36.5534i	0.713450	−	1.23573i
$876$	−7.62753	+	13.2113i	−0.257710	+	0.446367i
$877$	−13.7122			−0.463030			−0.231515	−	0.972831i	$-0.574368\pi$
$877$	−13.7122			−0.463030			−0.231515	+	0.972831i	$0.574368\pi$
$878$	27.8546	−	48.2456i	0.940048	−	1.62821i
$879$	−41.0069			−1.38313
$880$	−0.952104	−	1.64909i	−0.0320954	−	0.0555909i
$881$	14.0603	−	24.3531i	0.473703	−	0.820478i	−0.525843	−	0.850581i	$-0.676250\pi$
$881$	14.0603	−	24.3531i	0.473703	−	0.820478i	0.999547	+	0.0301031i	$0.00958357\pi$
$882$	−12.7343	+	22.0565i	−0.428787	+	0.742682i
$883$	−12.5366	−	21.7141i	−0.421891	−	0.730736i	0.574234	−	0.818691i	$-0.305300\pi$
$883$	−12.5366	−	21.7141i	−0.421891	−	0.730736i	−0.996124	+	0.0879553i	$0.971967\pi$
$884$	3.00714	−	5.20852i	0.101141	−	0.175182i
$885$	42.8118			1.43910
$886$	−4.35747	−	7.54736i	−0.146392	−	0.253559i
$887$	4.89266	+	8.47433i	0.164279	+	0.284540i	0.936399	−	0.350937i	$-0.114137\pi$
$887$	4.89266	+	8.47433i	0.164279	+	0.284540i	−0.772120	+	0.635477i	$0.780804\pi$
$888$	38.7631			1.30081
$889$	−8.22202	−	14.2410i	−0.275758	−	0.477626i
$890$	−18.4651	−	31.9825i	−0.618952	−	1.07206i
$891$	−0.876548			−0.0293655
$892$	−1.53216	+	2.65379i	−0.0513007	+	0.0888554i
$893$	−1.29846	+	2.24901i	−0.0434515	+	0.0752601i
$894$	−6.34988	−	10.9983i	−0.212372	−	0.367839i
$895$	−7.92034	−	13.7184i	−0.264748	−	0.458557i
$896$	7.80896	+	13.5255i	0.260879	+	0.451856i
$897$	48.4028	−	83.8361i	1.61612	−	2.79920i
$898$	28.6818	−	49.6783i	0.957124	−	1.65779i
$899$	−16.1362	−	27.9488i	−0.538173	−	0.932144i
$900$	25.5381			0.851269
$901$	7.60247	+	13.1679i	0.253275	+	0.438685i
$902$	−0.0234473	−	0.0406119i	−0.000780709	−	0.00135223i
$903$	11.1634			0.371496
$904$	−22.1656	+	38.3919i	−0.737217	+	1.27690i
$905$	−5.91596	+	10.2467i	−0.196653	+	0.340613i
$906$	38.5770	+	66.8173i	1.28163	+	2.21986i
$907$	3.15903			0.104894			0.0524470	−	0.998624i	$-0.483298\pi$
$907$	3.15903			0.104894			0.0524470	+	0.998624i	$0.483298\pi$
$908$	5.76906	−	9.99231i	0.191453	−	0.331606i
$909$	−7.79861	+	13.5076i	−0.258664	+	0.448019i
$910$	−21.6250	+	37.4555i	−0.716861	+	1.24164i
$911$	21.4479	+	37.1488i	0.710600	+	1.23080i	0.964632	+	0.263599i	$0.0849097\pi$
$911$	21.4479	+	37.1488i	0.710600	+	1.23080i	−0.254032	+	0.967196i	$0.581757\pi$
$912$	−14.1223	+	24.4606i	−0.467637	+	0.809971i
$913$	−0.347178	−	0.601330i	−0.0114899	−	0.0199011i
$914$	−13.2979	+	23.0327i	−0.439857	+	0.761854i
$915$	54.3117	+	94.0706i	1.79549	+	3.10988i
$916$	12.0506			0.398164
$917$	−1.98132			−0.0654290
$918$	0.831537	−	1.44026i	0.0274448	−	0.0475358i
$919$	−4.62491	+	8.01058i	−0.152562	+	0.264245i	−0.932168	−	0.362025i	$-0.882086\pi$
$919$	−4.62491	+	8.01058i	−0.152562	+	0.264245i	0.779607	+	0.626269i	$0.215419\pi$
$920$	70.3760			2.32023
$921$	−76.6065			−2.52427
$922$	3.81006	−	6.59922i	0.125478	−	0.217334i
$923$	−76.9074			−2.53144
$924$	0.172871			0.00568703
$925$	−50.7803	+	87.9541i	−1.66965	+	2.89191i
$926$	12.4312	+	21.5315i	0.408514	+	0.707568i
$927$	−4.49591	+	7.78714i	−0.147665	+	0.255763i
$928$	−24.7733			−0.813224
$929$	−15.9273	+	27.5869i	−0.522558	+	0.905097i	0.477098	+	0.878850i	$0.341689\pi$
$929$	−15.9273	+	27.5869i	−0.522558	+	0.905097i	−0.999656	+	0.0262464i	$0.991645\pi$
$930$	41.2617	−	71.4674i	1.35303	−	2.34351i
$931$	13.6070			0.445951
$932$	−1.63236	−	2.82734i	−0.0534698	−	0.0926125i
$933$	−8.27973	+	14.3409i	−0.271066	+	0.469501i
$934$	12.5841			0.411765
$935$	−0.318983	+	0.552495i	−0.0104319	+	0.0180685i
$936$	31.2273			1.02070
$937$	20.8821			0.682190			0.341095	−	0.940029i	$-0.389202\pi$
$937$	20.8821			0.682190			0.341095	+	0.940029i	$0.389202\pi$
$938$	14.0898			0.460048
$939$	2.27693			0.0743049
$940$	−1.60397	−	2.77816i	−0.0523158	−	0.0906136i
$941$	−40.8680			−1.33226			−0.666130	−	0.745836i	$-0.732050\pi$
$941$	−40.8680			−1.33226			−0.666130	+	0.745836i	$0.732050\pi$
$942$	10.2097	+	17.6837i	0.332649	+	0.576165i
$943$	2.41248			0.0785611
$944$	−10.1890	−	17.6479i	−0.331624	−	0.574390i
$945$	−1.53467	+	2.65812i	−0.0499227	+	0.0864686i
$946$	0.298249	+	0.516582i	0.00969690	+	0.0167955i
$947$	3.73700			0.121436			0.0607181	−	0.998155i	$-0.480661\pi$
$947$	3.73700			0.121436			0.0607181	+	0.998155i	$0.480661\pi$
$948$	8.06024	−	13.9607i	0.261784	−	0.453424i
$949$	−24.4364	−	42.3251i	−0.793239	−	1.37393i
$950$	−26.5817	−	46.0408i	−0.862423	−	1.49376i
$951$	1.56364	+	2.70830i	0.0507044	+	0.0878226i
$952$	2.04139	−	3.53579i	0.0661619	−	0.114596i
$953$	24.8171	−	42.9844i	0.803903	−	1.39240i	−0.113126	−	0.993581i	$-0.536086\pi$
$953$	24.8171	−	42.9844i	0.803903	−	1.39240i	0.917029	−	0.398821i	$-0.130580\pi$
$954$	20.8144	−	36.0516i	0.673891	−	1.16721i
$955$	−19.1327	+	33.1389i	−0.619121	+	1.07235i
$956$	−6.85080			−0.221571
$957$	0.715133	−	1.23865i	0.0231170	−	0.0400398i
$958$	27.8267			0.899039
$959$	12.8469			0.414849
$960$	18.8551	+	32.6579i	0.608545	+	1.05403i
$961$	3.57793	+	6.19716i	0.115417	+	0.199908i
$962$	32.7417	−	56.7102i	1.05563	−	1.82841i
$963$	9.83310			0.316867
$964$	−10.3063	−	2.94749i	−0.331942	−	0.0949322i
$965$	−86.5950			−2.78759
$966$	−17.3261	+	30.0097i	−0.557459	+	0.965547i
$967$	12.5369	+	21.7146i	0.403161	+	0.698295i	0.994105	−	0.108417i	$-0.0345783\pi$
$967$	12.5369	+	21.7146i	0.403161	+	0.698295i	−0.590945	+	0.806712i	$0.701245\pi$
$968$	11.8049	+	20.4467i	0.379424	+	0.657182i
$969$	9.46280			0.303989
$970$	15.8592			0.509208
$971$	4.37687	−	7.58096i	0.140460	−	0.243284i	−0.787210	−	0.616685i	$-0.788475\pi$
$971$	4.37687	−	7.58096i	0.140460	−	0.243284i	0.927670	+	0.373401i	$0.121808\pi$
$972$	−14.7824			−0.474146
$973$	10.9829	−	19.0230i	0.352097	−	0.609850i
$974$	25.3250	−	43.8641i	0.811465	−	1.40550i
$975$	−85.6576	+	148.363i	−2.74324	+	4.75143i
$976$	25.8519	−	44.7768i	0.827499	−	1.43327i
$977$	−28.1104	−	48.6887i	−0.899332	−	1.55769i	−0.828350	−	0.560211i	$-0.810720\pi$
$977$	−28.1104	−	48.6887i	−0.899332	−	1.55769i	−0.0709815	−	0.997478i	$-0.522613\pi$
$978$	36.3448	+	62.9511i	1.16218	+	2.01295i
$979$	−0.236451	−	0.409545i	−0.00755701	−	0.0130891i
$980$	−8.40424	+	14.5566i	−0.268464	+	0.464992i
$981$	18.6338			0.594930
$982$	29.3313	+	50.8033i	0.935999	+	1.62120i
$983$	−7.90132	+	13.6855i	−0.252013	+	0.436499i	−0.964080	−	0.265612i	$-0.914426\pi$
$983$	−7.90132	+	13.6855i	−0.252013	+	0.436499i	0.712067	+	0.702111i	$0.247759\pi$
$984$	0.814747	+	1.41118i	0.0259732	+	0.0449869i
$985$	−53.8269			−1.71507
$986$	8.90596	+	15.4256i	0.283623	+	0.491250i
$987$	−2.99554			−0.0953490
$988$	4.39864	+	7.61867i	0.139939	+	0.242382i
$989$	−30.6866			−0.975778
$990$	1.74666			0.0555123
$991$	39.6990			1.26108			0.630540	−	0.776157i	$-0.282834\pi$
$991$	39.6990			1.26108			0.630540	+	0.776157i	$0.282834\pi$
$992$	−18.3035			−0.581136
$993$	−19.0182	+	32.9405i	−0.603524	+	1.04533i
$994$	27.5295			0.873184
$995$	1.75136	−	3.03344i	0.0555218	−	0.0961665i
$996$	−6.36123	−	11.0180i	−0.201563	−	0.349118i
$997$	−9.25494			−0.293107			−0.146554	−	0.989203i	$-0.546818\pi$
$997$	−9.25494			−0.293107			−0.146554	+	0.989203i	$0.546818\pi$
$998$	−34.8185	+	60.3074i	−1.10216	+	1.90900i
$999$	2.32359	−	4.02457i	0.0735151	−	0.127332i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	241.2.c.a.225.15	yes	38
241.15	even	3	inner	241.2.c.a.15.15	✓	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
241.2.c.a.15.15	✓	38	241.15	even	3	inner
241.2.c.a.225.15	yes	38	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 241 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	241.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.820137 - 1.42052i) q^{2} +(-1.19817 - 2.07530i) q^{3} +(-0.345250 - 0.597991i) q^{4} -4.29952 q^{5} -3.93067 q^{6} +(-0.578431 + 1.00187i) q^{7} +2.14794 q^{8} +(-1.37125 + 2.37507i) q^{9} +O(q^{10})\)	\(q+(0.820137 - 1.42052i) q^{2} +(-1.19817 - 2.07530i) q^{3} +(-0.345250 - 0.597991i) q^{4} -4.29952 q^{5} -3.93067 q^{6} +(-0.578431 + 1.00187i) q^{7} +2.14794 q^{8} +(-1.37125 + 2.37507i) q^{9} +(-3.52620 + 6.10755i) q^{10} +(-0.0451539 + 0.0782089i) q^{11} +(-0.827340 + 1.43300i) q^{12} +(-2.65056 - 4.59090i) q^{13} +(0.948786 + 1.64335i) q^{14} +(5.15157 + 8.92279i) q^{15} +(2.45211 - 4.24717i) q^{16} -1.64306 q^{17} +(2.24922 + 3.89576i) q^{18} +(1.20168 - 2.08136i) q^{19} +(1.48441 + 2.57107i) q^{20} +2.77225 q^{21} +(0.0740648 + 0.128284i) q^{22} -7.62049 q^{23} +(-2.57361 - 4.45762i) q^{24} +13.4859 q^{25} -8.69528 q^{26} -0.617081 q^{27} +0.798814 q^{28} +(3.30454 - 5.72364i) q^{29} +16.9000 q^{30} +(2.44152 - 4.22884i) q^{31} +(-1.87419 - 3.24619i) q^{32} +0.216409 q^{33} +(-1.34753 + 2.33399i) q^{34} +(2.48698 - 4.30757i) q^{35} +1.89369 q^{36} +(-3.76545 + 6.52195i) q^{37} +(-1.97108 - 3.41401i) q^{38} +(-6.35166 + 11.0014i) q^{39} -9.23510 q^{40} -0.316578 q^{41} +(2.27362 - 3.93803i) q^{42} +4.02686 q^{43} +0.0623576 q^{44} +(5.89570 - 10.2116i) q^{45} +(-6.24985 + 10.8251i) q^{46} -1.08055 q^{47} -11.7522 q^{48} +(2.83083 + 4.90315i) q^{49} +(11.0603 - 19.1569i) q^{50} +(1.96867 + 3.40984i) q^{51} +(-1.83021 + 3.17002i) q^{52} +(-4.62703 - 8.01425i) q^{53} +(-0.506091 + 0.876576i) q^{54} +(0.194140 - 0.336261i) q^{55} +(-1.24243 + 2.15196i) q^{56} -5.75927 q^{57} +(-5.42036 - 9.38833i) q^{58} +(2.07761 - 3.59852i) q^{59} +(3.55716 - 6.16119i) q^{60} +10.5427 q^{61} +(-4.00477 - 6.93646i) q^{62} +(-1.58634 - 2.74763i) q^{63} +3.66006 q^{64} +(11.3961 + 19.7387i) q^{65} +(0.177485 - 0.307413i) q^{66} +(3.71258 - 6.43038i) q^{67} +(0.567266 + 0.982533i) q^{68} +(9.13068 + 15.8148i) q^{69} +(-4.07932 - 7.06559i) q^{70} +(7.25388 - 12.5641i) q^{71} +(-2.94535 + 5.10150i) q^{72} +9.21934 q^{73} +(6.17637 + 10.6978i) q^{74} +(-16.1584 - 27.9872i) q^{75} -1.65951 q^{76} +(-0.0522369 - 0.0904769i) q^{77} +(10.4185 + 18.0453i) q^{78} -9.74235 q^{79} +(-10.5429 + 18.2608i) q^{80} +(4.85311 + 8.40583i) q^{81} +(-0.259637 + 0.449705i) q^{82} +(-3.84438 + 6.65867i) q^{83} +(-0.957119 - 1.65778i) q^{84} +7.06435 q^{85} +(3.30258 - 5.72023i) q^{86} -15.8377 q^{87} +(-0.0969879 + 0.167988i) q^{88} +(-2.61828 + 4.53499i) q^{89} +(-9.67056 - 16.7499i) q^{90} +6.13266 q^{91} +(2.63098 + 4.55698i) q^{92} -11.7015 q^{93} +(-0.886195 + 1.53494i) q^{94} +(-5.16662 + 8.94886i) q^{95} +(-4.49121 + 7.77900i) q^{96} +(-1.12438 - 1.94749i) q^{97} +9.28669 q^{98} +(-0.123834 - 0.214487i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q + q^{2} + 2 q^{3} - 21 q^{4} - 4 q^{5} - 5 q^{7} - 12 q^{8} - 13 q^{9}+O(q^{10}) \) 38 * q + q^2 + 2 * q^3 - 21 * q^4 - 4 * q^5 - 5 * q^7 - 12 * q^8 - 13 * q^9	\( 38 q + q^{2} + 2 q^{3} - 21 q^{4} - 4 q^{5} - 5 q^{7} - 12 q^{8} - 13 q^{9} - 8 q^{10} - 4 q^{11} + 21 q^{12} - 9 q^{13} + 6 q^{14} + 4 q^{15} - 25 q^{16} - 18 q^{17} + 5 q^{18} + 3 q^{19} - 5 q^{20} + 10 q^{21} - 7 q^{22} - 10 q^{23} - 9 q^{24} + 54 q^{25} + 20 q^{26} - 4 q^{27} + 8 q^{28} + 25 q^{29} - 22 q^{30} - 8 q^{31} + 23 q^{32} - 28 q^{33} - 4 q^{34} - 7 q^{35} + 18 q^{36} + 12 q^{37} + 30 q^{38} + 20 q^{39} - 4 q^{40} - 20 q^{41} - 30 q^{42} + 12 q^{43} - 2 q^{44} - 9 q^{45} - 19 q^{46} - 42 q^{47} - 84 q^{48} + 6 q^{49} + 31 q^{50} + 11 q^{51} - 16 q^{52} + q^{53} + 42 q^{54} - 11 q^{55} - 5 q^{56} - 22 q^{57} - 2 q^{58} + 22 q^{59} + 48 q^{60} - 26 q^{61} - 44 q^{62} - q^{63} + 72 q^{64} - 19 q^{65} + 55 q^{66} + 18 q^{67} - 25 q^{68} + 3 q^{69} + 68 q^{70} - 14 q^{71} - 8 q^{72} - 38 q^{73} + 27 q^{74} + 26 q^{75} + 70 q^{76} + 17 q^{77} + 2 q^{78} + 12 q^{79} - 56 q^{80} + 5 q^{81} - 27 q^{82} + 14 q^{83} - 17 q^{84} - 50 q^{85} + 35 q^{86} + 44 q^{87} - 20 q^{88} - 32 q^{89} - 44 q^{90} + 56 q^{91} + 28 q^{92} + 10 q^{93} + 14 q^{94} + 17 q^{95} - 70 q^{96} - 35 q^{97} - 10 q^{98} - 10 q^{99}+O(q^{100}) \) 38 * q + q^2 + 2 * q^3 - 21 * q^4 - 4 * q^5 - 5 * q^7 - 12 * q^8 - 13 * q^9 - 8 * q^10 - 4 * q^11 + 21 * q^12 - 9 * q^13 + 6 * q^14 + 4 * q^15 - 25 * q^16 - 18 * q^17 + 5 * q^18 + 3 * q^19 - 5 * q^20 + 10 * q^21 - 7 * q^22 - 10 * q^23 - 9 * q^24 + 54 * q^25 + 20 * q^26 - 4 * q^27 + 8 * q^28 + 25 * q^29 - 22 * q^30 - 8 * q^31 + 23 * q^32 - 28 * q^33 - 4 * q^34 - 7 * q^35 + 18 * q^36 + 12 * q^37 + 30 * q^38 + 20 * q^39 - 4 * q^40 - 20 * q^41 - 30 * q^42 + 12 * q^43 - 2 * q^44 - 9 * q^45 - 19 * q^46 - 42 * q^47 - 84 * q^48 + 6 * q^49 + 31 * q^50 + 11 * q^51 - 16 * q^52 + q^53 + 42 * q^54 - 11 * q^55 - 5 * q^56 - 22 * q^57 - 2 * q^58 + 22 * q^59 + 48 * q^60 - 26 * q^61 - 44 * q^62 - q^63 + 72 * q^64 - 19 * q^65 + 55 * q^66 + 18 * q^67 - 25 * q^68 + 3 * q^69 + 68 * q^70 - 14 * q^71 - 8 * q^72 - 38 * q^73 + 27 * q^74 + 26 * q^75 + 70 * q^76 + 17 * q^77 + 2 * q^78 + 12 * q^79 - 56 * q^80 + 5 * q^81 - 27 * q^82 + 14 * q^83 - 17 * q^84 - 50 * q^85 + 35 * q^86 + 44 * q^87 - 20 * q^88 - 32 * q^89 - 44 * q^90 + 56 * q^91 + 28 * q^92 + 10 * q^93 + 14 * q^94 + 17 * q^95 - 70 * q^96 - 35 * q^97 - 10 * q^98 - 10 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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