LMFDB - Embedded newform 143.2.h.c.27.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [143,2,Mod(14,143)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(143, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8, 0]))

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

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

chi := DirichletCharacter("143.14");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 143 = 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	143.h (of order $5$, degree $4$, 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:	$1.14186074890$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			27.1
Character	$\chi$	$=$	143.27
Dual form			143.2.h.c.53.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.778372 - 2.39558i) q^{2} +(1.03159 + 0.749493i) q^{3} +(-3.51492 + 2.55374i) q^{4} +(1.12792 - 3.47137i) q^{5} +(0.992512 - 3.05464i) q^{6} +(-1.20723 + 0.877107i) q^{7} +(4.77800 + 3.47142i) q^{8} +(-0.424616 - 1.30683i) q^{9} +O(q^{10})$	\(q+(-0.778372 - 2.39558i) q^{2} +(1.03159 + 0.749493i) q^{3} +(-3.51492 + 2.55374i) q^{4} +(1.12792 - 3.47137i) q^{5} +(0.992512 - 3.05464i) q^{6} +(-1.20723 + 0.877107i) q^{7} +(4.77800 + 3.47142i) q^{8} +(-0.424616 - 1.30683i) q^{9} -9.19388 q^{10} +(-0.00264842 - 3.31662i) q^{11} -5.53996 q^{12} +(0.309017 + 0.951057i) q^{13} +(3.04086 + 2.20932i) q^{14} +(3.76531 - 2.73566i) q^{15} +(1.91185 - 5.88408i) q^{16} +(-1.27792 + 3.93305i) q^{17} +(-2.80012 + 2.03441i) q^{18} +(4.53292 + 3.29336i) q^{19} +(4.90043 + 15.0820i) q^{20} -1.90275 q^{21} +(-7.94319 + 2.58791i) q^{22} +5.79470 q^{23} +(2.32712 + 7.16215i) q^{24} +(-6.73311 - 4.89189i) q^{25} +(2.03780 - 1.48055i) q^{26} +(1.72353 - 5.30447i) q^{27} +(2.00343 - 6.16593i) q^{28} +(-2.75946 + 2.00487i) q^{29} +(-9.48430 - 6.89075i) q^{30} +(1.53830 + 4.73440i) q^{31} -3.77207 q^{32} +(2.48305 - 3.42337i) q^{33} +10.4166 q^{34} +(1.68310 + 5.18006i) q^{35} +(4.82981 + 3.50906i) q^{36} +(6.27673 - 4.56031i) q^{37} +(4.36122 - 13.4225i) q^{38} +(-0.394032 + 1.21270i) q^{39} +(17.4398 - 12.6707i) q^{40} +(-4.76850 - 3.46452i) q^{41} +(1.48105 + 4.55821i) q^{42} +4.53367 q^{43} +(8.47910 + 11.6509i) q^{44} -5.01543 q^{45} +(-4.51044 - 13.8817i) q^{46} +(0.0678795 + 0.0493173i) q^{47} +(6.38232 - 4.63703i) q^{48} +(-1.47502 + 4.53965i) q^{49} +(-6.47806 + 19.9374i) q^{50} +(-4.26608 + 3.09949i) q^{51} +(-3.51492 - 2.55374i) q^{52} +(2.02033 + 6.21793i) q^{53} -14.0489 q^{54} +(-11.5162 - 3.73168i) q^{55} -8.81298 q^{56} +(2.20776 + 6.79478i) q^{57} +(6.95072 + 5.04999i) q^{58} +(-5.31074 + 3.85848i) q^{59} +(-6.24860 + 19.2312i) q^{60} +(0.0420253 - 0.129341i) q^{61} +(10.1443 - 7.37025i) q^{62} +(1.65885 + 1.20522i) q^{63} +(-0.887634 - 2.73186i) q^{64} +3.65001 q^{65} +(-10.1337 - 3.28370i) q^{66} +3.41442 q^{67} +(-5.55218 - 17.0878i) q^{68} +(5.97775 + 4.34309i) q^{69} +(11.0992 - 8.06402i) q^{70} +(-3.05319 + 9.39675i) q^{71} +(2.50776 - 7.71808i) q^{72} +(-9.97073 + 7.24416i) q^{73} +(-15.8102 - 11.4868i) q^{74} +(-3.27936 - 10.0928i) q^{75} -24.3432 q^{76} +(2.91223 + 4.00162i) q^{77} +3.21184 q^{78} +(1.08866 + 3.35054i) q^{79} +(-18.2694 - 13.2735i) q^{80} +(2.41866 - 1.75726i) q^{81} +(-4.58787 + 14.1200i) q^{82} +(4.89909 - 15.0779i) q^{83} +(6.68803 - 4.85914i) q^{84} +(12.2117 + 8.87229i) q^{85} +(-3.52889 - 10.8608i) q^{86} -4.34926 q^{87} +(11.5007 - 15.8560i) q^{88} -3.76228 q^{89} +(3.90387 + 12.0149i) q^{90} +(-1.20723 - 0.877107i) q^{91} +(-20.3679 + 14.7982i) q^{92} +(-1.96151 + 6.03689i) q^{93} +(0.0653082 - 0.200998i) q^{94} +(16.5452 - 12.0208i) q^{95} +(-3.89122 - 2.82714i) q^{96} +(-5.17046 - 15.9130i) q^{97} +12.0232 q^{98} +(-4.33315 + 1.41175i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 3 q^{2} - 7 q^{3} - 5 q^{4} - 7 q^{5} - 4 q^{6} - 7 q^{7} + q^{8} - 6 q^{9}+O(q^{10}) $ 28 * q - 3 * q^2 - 7 * q^3 - 5 * q^4 - 7 * q^5 - 4 * q^6 - 7 * q^7 + q^8 - 6 * q^9	\( 28 q - 3 q^{2} - 7 q^{3} - 5 q^{4} - 7 q^{5} - 4 q^{6} - 7 q^{7} + q^{8} - 6 q^{9} - 24 q^{10} - 5 q^{11} + 38 q^{12} - 7 q^{13} - 7 q^{14} + 8 q^{15} - 19 q^{16} + 7 q^{17} + 5 q^{18} + 5 q^{19} + 9 q^{20} - 33 q^{22} + 50 q^{23} - 7 q^{24} - 34 q^{25} + 2 q^{26} - 19 q^{27} + 30 q^{28} + 8 q^{29} - 6 q^{30} + 17 q^{31} + 24 q^{32} - 26 q^{33} + 26 q^{34} - 4 q^{35} - 27 q^{36} + 17 q^{37} - 51 q^{38} - 2 q^{39} + 39 q^{40} - 23 q^{41} + 80 q^{42} - 32 q^{43} + q^{44} + 78 q^{45} - 31 q^{46} - 29 q^{47} + 52 q^{48} - 52 q^{49} + 6 q^{50} + 7 q^{51} - 5 q^{52} - 16 q^{53} - 42 q^{54} - 5 q^{55} + 34 q^{56} - 7 q^{57} - 13 q^{58} - 11 q^{59} - 74 q^{60} + 37 q^{61} + 23 q^{62} - 38 q^{63} + 67 q^{64} + 18 q^{65} - 65 q^{66} + 58 q^{67} - 68 q^{68} - 28 q^{69} + 44 q^{70} - 47 q^{71} + 10 q^{72} + 44 q^{73} - 46 q^{74} + 17 q^{75} + 6 q^{76} + 21 q^{77} + 26 q^{78} + 51 q^{79} + 23 q^{80} - 14 q^{81} - 47 q^{82} - 13 q^{83} - 107 q^{84} - q^{85} + 38 q^{86} - 12 q^{87} + 9 q^{88} + 38 q^{89} - 74 q^{90} - 7 q^{91} - 41 q^{92} - 51 q^{93} - 5 q^{94} + 47 q^{95} - 71 q^{96} - 20 q^{97} + 162 q^{98} + 60 q^{99}+O(q^{100}) \) 28 * q - 3 * q^2 - 7 * q^3 - 5 * q^4 - 7 * q^5 - 4 * q^6 - 7 * q^7 + q^8 - 6 * q^9 - 24 * q^10 - 5 * q^11 + 38 * q^12 - 7 * q^13 - 7 * q^14 + 8 * q^15 - 19 * q^16 + 7 * q^17 + 5 * q^18 + 5 * q^19 + 9 * q^20 - 33 * q^22 + 50 * q^23 - 7 * q^24 - 34 * q^25 + 2 * q^26 - 19 * q^27 + 30 * q^28 + 8 * q^29 - 6 * q^30 + 17 * q^31 + 24 * q^32 - 26 * q^33 + 26 * q^34 - 4 * q^35 - 27 * q^36 + 17 * q^37 - 51 * q^38 - 2 * q^39 + 39 * q^40 - 23 * q^41 + 80 * q^42 - 32 * q^43 + q^44 + 78 * q^45 - 31 * q^46 - 29 * q^47 + 52 * q^48 - 52 * q^49 + 6 * q^50 + 7 * q^51 - 5 * q^52 - 16 * q^53 - 42 * q^54 - 5 * q^55 + 34 * q^56 - 7 * q^57 - 13 * q^58 - 11 * q^59 - 74 * q^60 + 37 * q^61 + 23 * q^62 - 38 * q^63 + 67 * q^64 + 18 * q^65 - 65 * q^66 + 58 * q^67 - 68 * q^68 - 28 * q^69 + 44 * q^70 - 47 * q^71 + 10 * q^72 + 44 * q^73 - 46 * q^74 + 17 * q^75 + 6 * q^76 + 21 * q^77 + 26 * q^78 + 51 * q^79 + 23 * q^80 - 14 * q^81 - 47 * q^82 - 13 * q^83 - 107 * q^84 - q^85 + 38 * q^86 - 12 * q^87 + 9 * q^88 + 38 * q^89 - 74 * q^90 - 7 * q^91 - 41 * q^92 - 51 * q^93 - 5 * q^94 + 47 * q^95 - 71 * q^96 - 20 * q^97 + 162 * q^98 + 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/143\mathbb{Z}\right)^\times$.

$n$	$67$	$79$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−0.778372	−	2.39558i	−0.550392	−	1.69393i	−0.707812	−	0.706401i	$-0.750318\pi$
$2$	−0.778372	−	2.39558i	−0.550392	−	1.69393i	0.157420	−	0.987532i	$-0.449682\pi$
$3$	1.03159	+	0.749493i	0.595588	+	0.432720i	0.844310	−	0.535855i	$-0.180011\pi$
$3$	1.03159	+	0.749493i	0.595588	+	0.432720i	−0.248722	+	0.968575i	$0.580011\pi$
$4$	−3.51492	+	2.55374i	−1.75746	+	1.27687i
$5$	1.12792	−	3.47137i	0.504419	−	1.55244i	−0.297326	−	0.954776i	$-0.596095\pi$
$5$	1.12792	−	3.47137i	0.504419	−	1.55244i	0.801745	−	0.597666i	$-0.203905\pi$
$6$	0.992512	−	3.05464i	0.405191	−	1.24705i
$7$	−1.20723	+	0.877107i	−0.456292	+	0.331515i	−0.792075	−	0.610424i	$-0.790999\pi$
$7$	−1.20723	+	0.877107i	−0.456292	+	0.331515i	0.335783	+	0.941939i	$0.390999\pi$
$8$	4.77800	+	3.47142i	1.68928	+	1.22733i
$9$	−0.424616	−	1.30683i	−0.141539	−	0.435612i
$10$	−9.19388			−2.90736
$11$	−0.00264842	−	3.31662i	−0.000798529	−	1.00000i
$11$	−0.00264842	−	3.31662i	−0.000798529	−	1.00000i
$12$	−5.53996			−1.59925
$13$	0.309017	+	0.951057i	0.0857059	+	0.263776i
$13$	0.309017	+	0.951057i	0.0857059	+	0.263776i
$14$	3.04086	+	2.20932i	0.812704	+	0.590464i
$15$	3.76531	−	2.73566i	0.972198	−	0.706343i
$16$	1.91185	−	5.88408i	0.477963	−	1.47102i
$17$	−1.27792	+	3.93305i	−0.309942	+	0.953904i	0.667844	+	0.744301i	$0.267217\pi$
$17$	−1.27792	+	3.93305i	−0.309942	+	0.953904i	−0.977787	+	0.209603i	$0.932783\pi$
$18$	−2.80012	+	2.03441i	−0.659995	+	0.479514i
$19$	4.53292	+	3.29336i	1.03992	+	0.755549i	0.970271	−	0.242022i	$-0.0778108\pi$
$19$	4.53292	+	3.29336i	1.03992	+	0.755549i	0.0696531	+	0.997571i	$0.477811\pi$
$20$	4.90043	+	15.0820i	1.09577	+	3.37243i
$21$	−1.90275			−0.415215
$22$	−7.94319	+	2.58791i	−1.69349	+	0.551745i
$23$	5.79470			1.20828			0.604140	−	0.796878i	$-0.293517\pi$
$23$	5.79470			1.20828			0.604140	+	0.796878i	$0.293517\pi$
$24$	2.32712	+	7.16215i	0.475022	+	1.46197i
$25$	−6.73311	−	4.89189i	−1.34662	−	0.978378i
$26$	2.03780	−	1.48055i	0.399646	−	0.290360i
$27$	1.72353	−	5.30447i	0.331693	−	1.02085i
$28$	2.00343	−	6.16593i	0.378613	−	1.16525i
$29$	−2.75946	+	2.00487i	−0.512419	+	0.372295i	−0.813741	−	0.581228i	$-0.802572\pi$
$29$	−2.75946	+	2.00487i	−0.512419	+	0.372295i	0.301321	+	0.953523i	$0.402572\pi$
$30$	−9.48430	−	6.89075i	−1.73159	−	1.25807i
$31$	1.53830	+	4.73440i	0.276287	+	0.850323i	0.988876	+	0.148742i	$0.0475223\pi$
$31$	1.53830	+	4.73440i	0.276287	+	0.850323i	−0.712589	+	0.701581i	$0.752478\pi$
$32$	−3.77207			−0.666814
$33$	2.48305	−	3.42337i	0.432244	−	0.595933i
$34$	10.4166			1.78644
$35$	1.68310	+	5.18006i	0.284496	+	0.875589i
$36$	4.82981	+	3.50906i	0.804968	+	0.584843i
$37$	6.27673	−	4.56031i	1.03189	−	0.749711i	0.0632027	−	0.998001i	$-0.479869\pi$
$37$	6.27673	−	4.56031i	1.03189	−	0.749711i	0.968686	+	0.248290i	$0.0798686\pi$
$38$	4.36122	−	13.4225i	0.707483	−	2.17741i
$39$	−0.394032	+	1.21270i	−0.0630955	+	0.194188i
$40$	17.4398	−	12.6707i	2.75747	−	2.00342i
$41$	−4.76850	−	3.46452i	−0.744714	−	0.541067i	0.149470	−	0.988766i	$-0.452243\pi$
$41$	−4.76850	−	3.46452i	−0.744714	−	0.541067i	−0.894184	+	0.447700i	$0.852243\pi$
$42$	1.48105	+	4.55821i	0.228531	+	0.703346i
$43$	4.53367			0.691379			0.345689	−	0.938349i	$-0.387645\pi$
$43$	4.53367			0.691379			0.345689	+	0.938349i	$0.387645\pi$
$44$	8.47910	+	11.6509i	1.27827	+	1.75644i
$45$	−5.01543			−0.747657
$46$	−4.51044	−	13.8817i	−0.665028	−	2.04674i
$47$	0.0678795	+	0.0493173i	0.00990124	+	0.00719367i	0.592725	−	0.805405i	$-0.298052\pi$
$47$	0.0678795	+	0.0493173i	0.00990124	+	0.00719367i	−0.582824	+	0.812599i	$0.698052\pi$
$48$	6.38232	−	4.63703i	0.921208	−	0.669297i
$49$	−1.47502	+	4.53965i	−0.210717	+	0.648521i
$50$	−6.47806	+	19.9374i	−0.916136	+	2.81958i
$51$	−4.26608	+	3.09949i	−0.597371	+	0.434015i
$52$	−3.51492	−	2.55374i	−0.487432	−	0.354140i
$53$	2.02033	+	6.21793i	0.277513	+	0.854098i	0.988543	+	0.150937i	$0.0482289\pi$
$53$	2.02033	+	6.21793i	0.277513	+	0.854098i	−0.711030	+	0.703162i	$0.751771\pi$
$54$	−14.0489			−1.91181
$55$	−11.5162	−	3.73168i	−1.55284	−	0.503179i
$56$	−8.81298			−1.17768
$57$	2.20776	+	6.79478i	0.292425	+	0.899991i
$58$	6.95072	+	5.04999i	0.912674	+	0.663096i
$59$	−5.31074	+	3.85848i	−0.691399	+	0.502331i	−0.877120	−	0.480272i	$-0.840538\pi$
$59$	−5.31074	+	3.85848i	−0.691399	+	0.502331i	0.185720	+	0.982603i	$0.440538\pi$
$60$	−6.24860	+	19.2312i	−0.806691	+	2.48274i
$61$	0.0420253	−	0.129341i	0.00538079	−	0.0165604i	−0.948330	−	0.317285i	$-0.897229\pi$
$61$	0.0420253	−	0.129341i	0.00538079	−	0.0165604i	0.953711	+	0.300725i	$0.0972287\pi$
$62$	10.1443	−	7.37025i	1.28832	−	0.936022i
$63$	1.65885	+	1.20522i	0.208995	+	0.151844i
$64$	−0.887634	−	2.73186i	−0.110954	−	0.341482i
$65$	3.65001			0.452728
$66$	−10.1337	−	3.28370i	−1.24737	−	0.404195i
$67$	3.41442			0.417138			0.208569	−	0.978008i	$-0.433119\pi$
$67$	3.41442			0.417138			0.208569	+	0.978008i	$0.433119\pi$
$68$	−5.55218	−	17.0878i	−0.673300	−	2.07220i
$69$	5.97775	+	4.34309i	0.719636	+	0.522846i
$70$	11.0992	−	8.06402i	1.32661	−	0.963835i
$71$	−3.05319	+	9.39675i	−0.362347	+	1.11519i	0.589279	+	0.807930i	$0.299412\pi$
$71$	−3.05319	+	9.39675i	−0.362347	+	1.11519i	−0.951626	+	0.307259i	$0.900588\pi$
$72$	2.50776	−	7.71808i	0.295542	−	0.909584i
$73$	−9.97073	+	7.24416i	−1.16699	+	0.847865i	−0.990645	−	0.136464i	$-0.956426\pi$
$73$	−9.97073	+	7.24416i	−1.16699	+	0.847865i	−0.176341	+	0.984329i	$0.556426\pi$
$74$	−15.8102	−	11.4868i	−1.83790	−	1.33531i
$75$	−3.27936	−	10.0928i	−0.378668	−	1.16542i
$76$	−24.3432			−2.79236
$77$	2.91223	+	4.00162i	0.331880	+	0.456027i
$78$	3.21184			0.363669
$79$	1.08866	+	3.35054i	0.122483	+	0.376965i	0.993434	−	0.114405i	$-0.0364962\pi$
$79$	1.08866	+	3.35054i	0.122483	+	0.376965i	−0.870951	+	0.491370i	$0.836496\pi$
$80$	−18.2694	−	13.2735i	−2.04258	−	1.48402i
$81$	2.41866	−	1.75726i	0.268740	−	0.195251i
$82$	−4.58787	+	14.1200i	−0.506646	+	1.55929i
$83$	4.89909	−	15.0779i	0.537745	−	1.65501i	−0.199896	−	0.979817i	$-0.564060\pi$
$83$	4.89909	−	15.0779i	0.537745	−	1.65501i	0.737641	−	0.675193i	$-0.235940\pi$
$84$	6.68803	−	4.85914i	0.729724	−	0.530175i
$85$	12.2117	+	8.87229i	1.32454	+	0.962335i
$86$	−3.52889	−	10.8608i	−0.380530	−	1.17115i
$87$	−4.34926			−0.466290
$88$	11.5007	−	15.8560i	1.22598	−	1.69026i
$89$	−3.76228			−0.398801			−0.199401	−	0.979918i	$-0.563900\pi$
$89$	−3.76228			−0.398801			−0.199401	+	0.979918i	$0.563900\pi$
$90$	3.90387	+	12.0149i	0.411504	+	1.26648i
$91$	−1.20723	−	0.877107i	−0.126553	−	0.0919458i
$92$	−20.3679	+	14.7982i	−2.12350	+	1.54282i
$93$	−1.96151	+	6.03689i	−0.203399	+	0.625997i
$94$	0.0653082	−	0.200998i	0.00673603	−	0.0207314i
$95$	16.5452	−	12.0208i	1.69750	−	1.23331i
$96$	−3.89122	−	2.82714i	−0.397146	−	0.288543i
$97$	−5.17046	−	15.9130i	−0.524980	−	1.61572i	−0.764355	−	0.644796i	$-0.776942\pi$
$97$	−5.17046	−	15.9130i	−0.524980	−	1.61572i	0.239374	−	0.970927i	$-0.423058\pi$
$98$	12.0232			1.21453
$99$	−4.33315	+	1.41175i	−0.435498	+	0.141887i
$100$	36.1589			3.61589
$101$	1.96499	+	6.04761i	0.195524	+	0.601760i	0.999970	+	0.00773462i	$0.00246203\pi$
$101$	1.96499	+	6.04761i	0.195524	+	0.601760i	−0.804446	+	0.594025i	$0.797538\pi$
$102$	10.7457	+	7.80720i	1.06398	+	0.773028i
$103$	−9.42386	+	6.84683i	−0.928560	+	0.674639i	−0.945640	−	0.325216i	$-0.894563\pi$
$103$	−9.42386	+	6.84683i	−0.928560	+	0.674639i	0.0170796	+	0.999854i	$0.494563\pi$
$104$	−1.82503	+	5.61688i	−0.178959	+	0.550780i
$105$	−2.14615	+	6.60516i	−0.209442	+	0.644597i
$106$	13.3230	−	9.67972i	1.29404	−	0.940178i
$107$	−1.88347	−	1.36842i	−0.182082	−	0.132290i	0.493011	−	0.870023i	$-0.335896\pi$
$107$	−1.88347	−	1.36842i	−0.182082	−	0.132290i	−0.675092	+	0.737733i	$0.735896\pi$
$108$	7.48818	+	23.0462i	0.720550	+	2.21763i
$109$	−9.33792			−0.894411			−0.447205	−	0.894431i	$-0.647581\pi$
$109$	−9.33792			−0.894411			−0.447205	+	0.894431i	$0.647581\pi$
$110$	0.0243493	+	30.4927i	0.00232161	+	2.90736i
$111$	9.89292			0.938995
$112$	2.85291	+	8.78037i	0.269575	+	0.829667i
$113$	−0.165936	−	0.120560i	−0.0156099	−	0.0113413i	0.579953	−	0.814650i	$-0.303071\pi$
$113$	−0.165936	−	0.120560i	−0.0156099	−	0.0113413i	−0.595563	+	0.803309i	$0.703071\pi$
$114$	14.5590	−	10.5777i	1.36358	−	0.990696i
$115$	6.53594	−	20.1155i	0.609479	−	1.87578i
$116$	4.57939	−	14.0939i	0.425185	−	1.30859i
$117$	1.11166	−	0.807668i	0.102773	−	0.0746689i
$118$	13.3770	+	9.71898i	1.23146	+	0.894705i
$119$	−1.90695	−	5.86899i	−0.174810	−	0.538009i
$120$	27.4873			2.50923
$121$	−11.0000	+	0.0175676i	−0.999999	+	0.00159706i
$122$	−0.342557			−0.0310137
$123$	−2.32250	−	7.14791i	−0.209412	−	0.644505i
$124$	−17.4974	−	12.7126i	−1.57131	−	1.14163i
$125$	−9.81131	+	7.12833i	−0.877550	+	0.637577i
$126$	1.59601	−	4.91201i	0.142184	−	0.437597i
$127$	1.39990	−	4.30844i	0.124221	−	0.382312i	−0.869537	−	0.493867i	$-0.835583\pi$
$127$	1.39990	−	4.30844i	0.124221	−	0.382312i	0.993758	+	0.111555i	$0.0355830\pi$
$128$	−11.9568	+	8.68714i	−1.05684	+	0.767842i
$129$	4.67688	+	3.39796i	0.411777	+	0.299173i
$130$	−2.84107	−	8.74390i	−0.249178	−	0.766891i
$131$	−11.0800			−0.968063			−0.484031	−	0.875051i	$-0.660828\pi$
$131$	−11.0800			−0.968063			−0.484031	+	0.875051i	$0.660828\pi$
$132$	0.0146721	+	18.3740i	0.00127705	+	1.59925i
$133$	−8.36093			−0.724985
$134$	−2.65769	−	8.17952i	−0.229589	−	0.706603i
$135$	−16.4698	−	11.9660i	−1.41749	−	1.02987i
$136$	−19.7592	+	14.3559i	−1.69434	+	1.23101i
$137$	5.76376	−	17.7390i	0.492431	−	1.51555i	−0.328490	−	0.944507i	$-0.606540\pi$
$137$	5.76376	−	17.7390i	0.492431	−	1.51555i	0.820922	−	0.571041i	$-0.193460\pi$
$138$	5.75132	−	17.7007i	0.489584	−	1.50679i
$139$	2.27625	−	1.65379i	0.193069	−	0.140273i	−0.487051	−	0.873373i	$-0.661928\pi$
$139$	2.27625	−	1.65379i	0.193069	−	0.140273i	0.680120	+	0.733101i	$0.261928\pi$
$140$	−19.1445	−	13.9093i	−1.61800	−	1.17555i
$141$	0.0330607	+	0.101750i	0.00278421	+	0.00856892i
$142$	24.8872			2.08849
$143$	3.15348	−	1.02741i	0.263707	−	0.0859165i
$144$	−8.50132			−0.708444
$145$	3.84719	+	11.8404i	0.319492	+	0.983294i
$146$	25.1149	+	18.2471i	2.07853	+	1.51014i
$147$	−4.92404	+	3.57753i	−0.406128	+	0.295070i
$148$	−10.4164	+	32.0583i	−0.856220	+	2.63517i
$149$	4.55103	−	14.0066i	0.372835	−	1.14747i	−0.572093	−	0.820189i	$-0.693868\pi$
$149$	4.55103	−	14.0066i	0.372835	−	1.14747i	0.944928	−	0.327279i	$-0.106132\pi$
$150$	−21.6256	+	15.7119i	−1.76573	+	1.28288i
$151$	−2.42879	−	1.76462i	−0.197652	−	0.143603i	0.484557	−	0.874760i	$-0.338981\pi$
$151$	−2.42879	−	1.76462i	−0.197652	−	0.143603i	−0.682209	+	0.731157i	$0.738981\pi$
$152$	10.2257	+	31.4714i	0.829411	+	2.55266i
$153$	5.68247			0.459401
$154$	7.31941	−	10.0912i	0.589815	−	0.813176i
$155$	18.1699			1.45944
$156$	−1.71194	−	5.26881i	−0.137065	−	0.421843i
$157$	−3.16280	−	2.29791i	−0.252419	−	0.183393i	0.454379	−	0.890808i	$-0.349861\pi$
$157$	−3.16280	−	2.29791i	−0.252419	−	0.183393i	−0.706798	+	0.707415i	$0.749861\pi$
$158$	7.17911	−	5.21593i	0.571140	−	0.414957i
$159$	−2.57615	+	7.92856i	−0.204302	+	0.628776i
$160$	−4.25457	+	13.0942i	−0.336354	+	1.03519i
$161$	−6.99557	+	5.08258i	−0.551328	+	0.400563i
$162$	−6.09227	−	4.42629i	−0.478654	−	0.347762i
$163$	4.67139	+	14.3770i	0.365891	+	1.12610i	0.949421	+	0.314006i	$0.101671\pi$
$163$	4.67139	+	14.3770i	0.365891	+	1.12610i	−0.583530	+	0.812092i	$0.698329\pi$
$164$	25.6084			1.99968
$165$	−9.08311	−	12.4809i	−0.707119	−	0.971634i
$166$	−39.9336			−3.09945
$167$	5.28231	+	16.2573i	0.408758	+	1.25803i	0.917717	+	0.397236i	$0.130030\pi$
$167$	5.28231	+	16.2573i	0.408758	+	1.25803i	−0.508959	+	0.860791i	$0.669970\pi$
$168$	−9.09136	−	6.60526i	−0.701414	−	0.509607i
$169$	−0.809017	+	0.587785i	−0.0622321	+	0.0452143i
$170$	11.7491	−	36.1600i	0.901114	−	2.77334i
$171$	2.37913	−	7.32219i	0.181936	−	0.559942i
$172$	−15.9355	+	11.5778i	−1.21507	+	0.882801i
$173$	2.89498	+	2.10332i	0.220101	+	0.159913i	0.692372	−	0.721541i	$-0.256566\pi$
$173$	2.89498	+	2.10332i	0.220101	+	0.159913i	−0.472271	+	0.881453i	$0.656566\pi$
$174$	3.38534	+	10.4190i	0.256642	+	0.789864i
$175$	12.4192			0.938800
$176$	−19.5203	−	6.32532i	−1.47140	−	0.476789i
$177$	−8.37040			−0.629157
$178$	2.92846	+	9.01286i	0.219497	+	0.675543i
$179$	1.69352	+	1.23042i	0.126580	+	0.0919656i	0.649274	−	0.760555i	$-0.275073\pi$
$179$	1.69352	+	1.23042i	0.126580	+	0.0919656i	−0.522694	+	0.852520i	$0.675073\pi$
$180$	17.6288	−	12.8081i	1.31398	−	0.954660i
$181$	−7.41845	+	22.8316i	−0.551409	+	1.69706i	0.153834	+	0.988097i	$0.450838\pi$
$181$	−7.41845	+	22.8316i	−0.551409	+	1.69706i	−0.705243	+	0.708965i	$0.749162\pi$
$182$	−1.16151	+	3.57475i	−0.0860965	+	0.264978i
$183$	0.140293	−	0.101928i	0.0103707	−	0.00753477i
$184$	27.6871	+	20.1159i	2.04112	+	1.48296i
$185$	−8.75089	−	26.9325i	−0.643379	−	1.98012i
$186$	15.9887			1.17235
$187$	13.0478	+	4.22798i	0.954152	+	0.309180i
$188$	−0.364534			−0.0265864
$189$	2.57189	+	7.91547i	0.187078	+	0.575765i
$190$	−41.6752	−	30.2788i	−3.02343	−	2.19665i
$191$	−6.50823	+	4.72851i	−0.470919	+	0.342143i	−0.797799	−	0.602923i	$-0.794003\pi$
$191$	−6.50823	+	4.72851i	−0.470919	+	0.342143i	0.326880	+	0.945066i	$0.394003\pi$
$192$	1.13183	−	3.48343i	0.0816831	−	0.251395i
$193$	−5.88879	+	18.1238i	−0.423885	+	1.30458i	0.480174	+	0.877173i	$0.340574\pi$
$193$	−5.88879	+	18.1238i	−0.423885	+	1.30458i	−0.904058	+	0.427409i	$0.859426\pi$
$194$	−34.0964	+	24.7725i	−2.44798	+	1.77856i
$195$	3.76531	+	2.73566i	0.269639	+	0.195904i
$196$	−6.40849	−	19.7233i	−0.457750	−	1.40881i
$197$	15.2634			1.08748			0.543738	−	0.839255i	$-0.317009\pi$
$197$	15.2634			1.08748			0.543738	+	0.839255i	$0.317009\pi$
$198$	6.75478	+	9.28156i	0.480041	+	0.659612i
$199$	25.0171			1.77341			0.886707	−	0.462331i	$-0.152987\pi$
$199$	25.0171			1.77341			0.886707	+	0.462331i	$0.152987\pi$
$200$	−15.1890	−	46.7469i	−1.07402	−	3.30550i
$201$	3.52227	+	2.55908i	0.248442	+	0.180504i
$202$	12.9581	−	9.41458i	0.911726	−	0.662408i
$203$	1.57284	−	4.84069i	0.110391	−	0.339750i
$204$	7.07965	−	21.7889i	0.495675	−	1.52553i
$205$	−17.4051	+	12.6455i	−1.21562	+	0.883202i
$206$	23.7374	+	17.2462i	1.65386	+	1.20160i
$207$	−2.46053	−	7.57272i	−0.171018	−	0.526340i
$208$	6.18689			0.428984
$209$	10.9108	−	15.0427i	0.754718	−	1.04053i
$210$	17.4937			1.20718
$211$	−4.11510	−	12.6650i	−0.283295	−	0.871893i	−0.986904	−	0.161306i	$-0.948429\pi$
$211$	−4.11510	−	12.6650i	−0.283295	−	0.871893i	0.703609	−	0.710587i	$-0.251571\pi$
$212$	−22.9803	−	16.6961i	−1.57829	−	1.14670i
$213$	−10.1924	+	7.40523i	−0.698374	+	0.507398i
$214$	−1.81212	+	5.57714i	−0.123874	+	0.381246i
$215$	5.11360	−	15.7380i	0.348745	−	1.07333i
$216$	26.6491	−	19.3617i	1.81324	−	1.31740i
$217$	−6.00966	−	4.36628i	−0.407963	−	0.296402i
$218$	7.26838	+	22.3698i	0.492277	+	1.51507i
$219$	−15.7151			−1.06193
$220$	50.0083	−	16.2928i	3.37156	−	1.09846i
$221$	−4.13545			−0.278181
$222$	−7.70037	−	23.6993i	−0.516815	−	1.59059i
$223$	5.52265	+	4.01244i	0.369824	+	0.268693i	0.757138	−	0.653255i	$-0.226597\pi$
$223$	5.52265	+	4.01244i	0.369824	+	0.268693i	−0.387314	+	0.921948i	$0.626597\pi$
$224$	4.55377	−	3.30851i	0.304262	−	0.221059i
$225$	−3.53390	+	10.8762i	−0.235593	+	0.725082i
$226$	−0.159650	+	0.491354i	−0.0106198	+	0.0326844i
$227$	−5.40067	+	3.92382i	−0.358455	+	0.260433i	−0.752407	−	0.658698i	$-0.771108\pi$
$227$	−5.40067	+	3.92382i	−0.358455	+	0.260433i	0.393952	+	0.919131i	$0.371108\pi$
$228$	−25.1122	−	18.2451i	−1.66310	−	1.20831i
$229$	−0.292667	−	0.900738i	−0.0193400	−	0.0595224i	0.940921	−	0.338627i	$-0.109962\pi$
$229$	−0.292667	−	0.900738i	−0.0193400	−	0.0595224i	−0.960261	+	0.279104i	$0.909962\pi$
$230$	−53.2758			−3.51290
$231$	0.00503929	+	6.31072i	0.000331561	+	0.415215i
$232$	−20.1445			−1.32255
$233$	−3.84200	−	11.8245i	−0.251698	−	0.774647i	−0.994462	−	0.105094i	$-0.966486\pi$
$233$	−3.84200	−	11.8245i	−0.251698	−	0.774647i	0.742764	−	0.669553i	$-0.233514\pi$
$234$	−2.80012	−	2.03441i	−0.183050	−	0.132993i
$235$	0.247761	−	0.180009i	0.0161621	−	0.0117425i
$236$	8.81328	−	27.1245i	0.573696	−	1.76565i
$237$	−1.38816	+	4.27231i	−0.0901706	+	0.277517i
$238$	−12.5753	+	9.13652i	−0.815138	+	0.592232i
$239$	−9.70260	−	7.04935i	−0.627609	−	0.455985i	0.227962	−	0.973670i	$-0.426794\pi$
$239$	−9.70260	−	7.04935i	−0.627609	−	0.455985i	−0.855571	+	0.517685i	$0.826794\pi$
$240$	−8.89810	−	27.3855i	−0.574370	−	1.76773i
$241$	−7.49754			−0.482959			−0.241479	−	0.970406i	$-0.577633\pi$
$241$	−7.49754			−0.482959			−0.241479	+	0.970406i	$0.577633\pi$
$242$	8.60417	+	26.3377i	0.553097	+	1.69305i
$243$	−12.9203			−0.828835
$244$	0.182586	+	0.561943i	0.0116889	+	0.0359747i
$245$	14.0951	+	10.2407i	0.900501	+	0.654253i
$246$	−15.3156	+	11.1275i	−0.976489	+	0.709461i
$247$	−1.73142	+	5.32877i	−0.110168	+	0.339062i
$248$	−9.08509	+	27.9610i	−0.576904	+	1.77553i
$249$	16.3546	−	11.8823i	1.03643	−	0.753010i
$250$	24.7134	+	17.9553i	1.56301	+	1.13559i
$251$	−0.509560	−	1.56826i	−0.0321631	−	0.0989879i	0.933686	−	0.358092i	$-0.116573\pi$
$251$	−0.509560	−	1.56826i	−0.0321631	−	0.0989879i	−0.965849	+	0.259104i	$0.916573\pi$
$252$	−8.90853			−0.561185
$253$	−0.0153468	−	19.2189i	−0.000964846	−	1.20828i
$254$	−11.4109			−0.715982
$255$	5.94769	+	18.3051i	0.372459	+	1.14631i
$256$	25.4699	+	18.5050i	1.59187	+	1.15656i
$257$	6.48398	−	4.71089i	0.404460	−	0.293857i	−0.366895	−	0.930262i	$-0.619579\pi$
$257$	6.48398	−	4.71089i	0.404460	−	0.293857i	0.771355	+	0.636405i	$0.219579\pi$
$258$	4.49973	−	13.8487i	0.280141	−	0.862185i
$259$	−3.57761	+	11.0107i	−0.222302	+	0.684174i
$260$	−12.8295	+	9.32118i	−0.795652	+	0.578075i
$261$	3.79174	+	2.75486i	0.234703	+	0.170522i
$262$	8.62435	+	26.5430i	0.532814	+	1.63983i
$263$	11.7101			0.722075			0.361037	−	0.932551i	$-0.382423\pi$
$263$	11.7101			0.722075			0.361037	+	0.932551i	$0.382423\pi$
$264$	23.7480	−	7.73716i	1.46159	−	0.476190i
$265$	23.8635			1.46592
$266$	6.50792	+	20.0293i	0.399026	+	1.22808i
$267$	−3.88113	−	2.81980i	−0.237521	−	0.172569i
$268$	−12.0014	+	8.71953i	−0.733103	+	0.532630i
$269$	−5.24914	+	16.1552i	−0.320046	+	0.985000i	0.653581	+	0.756856i	$0.273266\pi$
$269$	−5.24914	+	16.1552i	−0.320046	+	0.985000i	−0.973627	+	0.228144i	$0.926734\pi$
$270$	−15.8459	+	48.7687i	−0.964352	+	2.96797i
$271$	13.6116	−	9.88937i	0.826843	−	0.600736i	−0.0918215	−	0.995775i	$-0.529269\pi$
$271$	13.6116	−	9.88937i	0.826843	−	0.600736i	0.918664	+	0.395039i	$0.129269\pi$
$272$	20.6992	+	15.0388i	1.25507	+	0.911863i
$273$	−0.587983	−	1.80963i	−0.0355864	−	0.109524i
$274$	−46.9817			−2.83827
$275$	−16.2067	+	22.3441i	−0.977302	+	1.34740i
$276$	−32.1024			−1.93234
$277$	1.87097	+	5.75824i	0.112415	+	0.345979i	0.991399	−	0.130873i	$-0.0417779\pi$
$277$	1.87097	+	5.75824i	0.112415	+	0.345979i	−0.878984	+	0.476852i	$0.841778\pi$
$278$	−5.73357	−	4.16568i	−0.343876	−	0.249841i
$279$	5.53389	−	4.02061i	0.331305	−	0.240707i
$280$	−9.94029	+	30.5931i	−0.594046	+	1.82829i
$281$	3.04085	−	9.35876i	0.181402	−	0.558297i	−0.818466	−	0.574555i	$-0.805175\pi$
$281$	3.04085	−	9.35876i	0.181402	−	0.558297i	0.999868	+	0.0162579i	$0.00517528\pi$
$282$	0.218018	−	0.158399i	0.0129828	−	0.00943253i
$283$	−6.28268	−	4.56464i	−0.373467	−	0.271339i	0.385180	−	0.922841i	$-0.374139\pi$
$283$	−6.28268	−	4.56464i	−0.373467	−	0.271339i	−0.758647	+	0.651502i	$0.774139\pi$
$284$	−13.2651	−	40.8259i	−0.787141	−	2.42257i
$285$	26.0773			1.54469
$286$	−4.91583	−	6.75471i	−0.290679	−	0.399414i
$287$	8.79545			0.519179
$288$	1.60168	+	4.92947i	0.0943800	+	0.290472i
$289$	−0.0824894	−	0.0599320i	−0.00485231	−	0.00352541i
$290$	25.3702	−	18.4325i	1.48979	−	1.08239i
$291$	6.59292	−	20.2909i	0.386484	−	1.18947i
$292$	16.5466	−	50.9253i	0.968319	−	2.98018i
$293$	−9.70084	+	7.04807i	−0.566729	+	0.411753i	−0.833915	−	0.551892i	$-0.813906\pi$
$293$	−9.70084	+	7.04807i	−0.566729	+	0.411753i	0.267187	+	0.963645i	$0.413906\pi$
$294$	12.4030	+	9.01131i	0.723358	+	0.525550i
$295$	7.40413	+	22.7876i	0.431085	+	1.32674i
$296$	45.8210			2.66329
$297$	−17.5975	−	5.70225i	−1.02111	−	0.330878i
$298$	−37.0964			−2.14894
$299$	1.79066	+	5.51109i	0.103557	+	0.318715i
$300$	37.3011	+	27.1009i	2.15358	+	1.56467i
$301$	−5.47321	+	3.97652i	−0.315471	+	0.229203i
$302$	−2.33679	+	7.19190i	−0.134467	+	0.413847i
$303$	−2.50558	+	7.71139i	−0.143942	+	0.443008i
$304$	28.0447	−	20.3757i	1.60847	−	1.16862i
$305$	−0.401587	−	0.291770i	−0.0229948	−	0.0167067i
$306$	−4.42308	−	13.6128i	−0.252850	−	0.778194i
$307$	0.237591			0.0135600			0.00678001	−	0.999977i	$-0.497842\pi$
$307$	0.237591			0.0135600			0.00678001	+	0.999977i	$0.497842\pi$
$308$	−20.4554	−	6.62830i	−1.16555	−	0.377682i
$309$	−14.8532			−0.844968
$310$	−14.1429	−	43.5275i	−0.803265	−	2.47220i
$311$	0.898990	+	0.653155i	0.0509771	+	0.0370370i	0.612982	−	0.790097i	$-0.289970\pi$
$311$	0.898990	+	0.653155i	0.0509771	+	0.0370370i	−0.562005	+	0.827134i	$0.689970\pi$
$312$	−6.09249	+	4.42645i	−0.344919	+	0.250599i
$313$	−2.67032	+	8.21839i	−0.150935	+	0.464531i	−0.997726	−	0.0673947i	$-0.978531\pi$
$313$	−2.67032	+	8.21839i	−0.150935	+	0.464531i	0.846791	+	0.531925i	$0.178531\pi$
$314$	−3.04300	+	9.36539i	−0.171726	+	0.528520i
$315$	6.05481	−	4.39907i	0.341150	−	0.247860i
$316$	−12.3829	−	8.99673i	−0.696595	−	0.506106i
$317$	1.81719	+	5.59275i	0.102064	+	0.314120i	0.989030	−	0.147714i	$-0.0471915\pi$
$317$	1.81719	+	5.59275i	0.102064	+	0.314120i	−0.886966	+	0.461834i	$0.847192\pi$
$318$	20.9987			1.17755
$319$	6.65670	+	9.14679i	0.372704	+	0.512122i
$320$	−10.4845			−0.586099
$321$	−0.917342	−	2.82329i	−0.0512011	−	0.157581i
$322$	17.6209	+	12.8023i	0.981974	+	0.713446i
$323$	−18.7457	+	13.6195i	−1.04304	+	0.757811i
$324$	−4.01381	+	12.3532i	−0.222989	+	0.686291i
$325$	2.57182	−	7.91524i	0.142659	−	0.439059i
$326$	30.8053	−	22.3814i	1.70615	−	1.23959i
$327$	−9.63289	−	6.99870i	−0.532700	−	0.387029i
$328$	−10.7571	−	33.1069i	−0.593961	−	1.82802i
$329$	−0.125203			−0.00690267
$330$	−22.8289	+	31.4741i	−1.25669	+	1.73259i
$331$	12.8533			0.706481			0.353241	−	0.935532i	$-0.385080\pi$
$331$	12.8533			0.706481			0.353241	+	0.935532i	$0.385080\pi$
$332$	21.2850	+	65.5085i	1.16817	+	3.59525i
$333$	−8.62478	−	6.26627i	−0.472635	−	0.343389i
$334$	34.8341	−	25.3084i	1.90604	−	1.38482i
$335$	3.85117	−	11.8527i	0.210412	−	0.647582i
$336$	−3.63779	+	11.1960i	−0.198458	+	0.610790i
$337$	28.2121	−	20.4973i	1.53681	−	1.11656i	0.584517	−	0.811381i	$-0.301284\pi$
$337$	28.2121	−	20.4973i	1.53681	−	1.11656i	0.952295	−	0.305178i	$-0.0987160\pi$
$338$	2.03780	+	1.48055i	0.110842	+	0.0805314i
$339$	−0.0808191	−	0.248736i	−0.00438949	−	0.0135095i
$340$	−65.5805			−3.55660
$341$	15.6981	−	5.11450i	0.850102	−	0.276966i
$342$	−19.3928			−1.04864
$343$	−5.42892	−	16.7085i	−0.293134	−	0.902174i
$344$	21.6619	+	15.7383i	1.16793	+	0.848552i
$345$	21.8188	−	15.8523i	1.17469	−	0.853460i
$346$	2.78532	−	8.57233i	0.149740	−	0.460851i
$347$	−2.52305	+	7.76516i	−0.135445	+	0.416856i	−0.995659	−	0.0930771i	$-0.970330\pi$
$347$	−2.52305	+	7.76516i	−0.135445	+	0.416856i	0.860214	+	0.509933i	$0.170330\pi$
$348$	15.2873	−	11.1069i	0.819486	−	0.595391i
$349$	−22.1748	−	16.1109i	−1.18699	−	0.862399i	−0.194048	−	0.980992i	$-0.562162\pi$
$349$	−22.1748	−	16.1109i	−1.18699	−	0.862399i	−0.992943	+	0.118593i	$0.962162\pi$
$350$	−9.66672	−	29.7511i	−0.516708	−	1.59026i
$351$	5.57745			0.297703
$352$	0.00999002	+	12.5105i	0.000532470	+	0.666814i
$353$	17.2905			0.920280			0.460140	−	0.887846i	$-0.347799\pi$
$353$	17.2905			0.920280			0.460140	+	0.887846i	$0.347799\pi$
$354$	6.51528	+	20.0520i	0.346283	+	1.06575i
$355$	29.1758	+	21.1975i	1.54849	+	1.12505i
$356$	13.2241	−	9.60789i	0.700878	−	0.509217i
$357$	2.43158	−	7.48363i	0.128693	−	0.396075i
$358$	1.62937	−	5.01469i	0.0861150	−	0.265035i
$359$	−18.9504	+	13.7682i	−1.00016	+	0.726660i	−0.962123	−	0.272617i	$-0.912111\pi$
$359$	−18.9504	+	13.7682i	−1.00016	+	0.726660i	−0.0380385	+	0.999276i	$0.512111\pi$
$360$	−23.9637	−	17.4107i	−1.26300	−	0.917623i
$361$	3.82984	+	11.7870i	0.201570	+	0.620370i
$362$	60.4694			3.17820
$363$	−11.3606	−	8.22628i	−0.596278	−	0.431768i
$364$	6.48324			0.339814
$365$	13.9010	+	42.7829i	0.727611	+	2.23936i
$366$	−0.353378	−	0.256744i	−0.0184714	−	0.0134202i
$367$	−6.49547	+	4.71924i	−0.339061	+	0.246342i	−0.744265	−	0.667884i	$-0.767200\pi$
$367$	−6.49547	+	4.71924i	−0.339061	+	0.246342i	0.405205	+	0.914226i	$0.367200\pi$
$368$	11.0786	−	34.0965i	0.577513	−	1.77740i
$369$	−2.50277	+	7.70273i	−0.130289	+	0.400988i
$370$	−57.7075	+	41.9270i	−3.00007	+	2.17968i
$371$	−7.89280	−	5.73446i	−0.409774	−	0.297718i
$372$	−8.52211	−	26.2284i	−0.441851	−	1.35988i
$373$	−10.4876			−0.543025			−0.271513	−	0.962435i	$-0.587524\pi$
$373$	−10.4876			−0.543025			−0.271513	+	0.962435i	$0.587524\pi$
$374$	−0.0275877	−	34.5481i	−0.00142652	−	1.78644i
$375$	−15.4639			−0.798550
$376$	0.153127	+	0.471276i	0.00789692	+	0.0243042i
$377$	−2.75946	−	2.00487i	−0.142120	−	0.103256i
$378$	16.9603	−	12.3224i	0.872342	−	0.633794i
$379$	−8.43034	+	25.9459i	−0.433037	+	1.33275i	0.462047	+	0.886855i	$0.347115\pi$
$379$	−8.43034	+	25.9459i	−0.433037	+	1.33275i	−0.895084	+	0.445897i	$0.852885\pi$
$380$	−27.4571	+	84.5043i	−1.40852	+	4.33498i
$381$	4.67326	−	3.39532i	0.239419	−	0.173948i
$382$	16.3934	+	11.9105i	0.838757	+	0.609393i
$383$	5.15845	+	15.8761i	0.263584	+	0.811229i	0.992016	+	0.126111i	$0.0402495\pi$
$383$	5.15845	+	15.8761i	0.263584	+	0.811229i	−0.728432	+	0.685118i	$0.759751\pi$
$384$	−18.8455			−0.961703
$385$	17.1758	−	5.59594i	0.875362	−	0.285195i
$386$	48.0008			2.44318
$387$	−1.92507	−	5.92476i	−0.0978569	−	0.301173i
$388$	58.8115	+	42.7290i	2.98570	+	2.16924i
$389$	−6.14581	+	4.46519i	−0.311605	+	0.226394i	−0.732585	−	0.680676i	$-0.761686\pi$
$389$	−6.14581	+	4.46519i	−0.311605	+	0.226394i	0.420980	+	0.907070i	$0.361686\pi$
$390$	3.62268	−	11.1495i	0.183442	−	0.564575i
$391$	−7.40520	+	22.7909i	−0.374497	+	1.15258i
$392$	−22.8067	+	16.5700i	−1.15191	+	0.836912i
$393$	−11.4300	−	8.30436i	−0.576566	−	0.418900i
$394$	−11.8806	−	36.5648i	−0.598538	−	1.84211i
$395$	12.8589			0.646999
$396$	11.6254	−	16.0279i	0.584200	−	0.805435i
$397$	27.7259			1.39152			0.695761	−	0.718273i	$-0.255067\pi$
$397$	27.7259			1.39152			0.695761	+	0.718273i	$0.255067\pi$
$398$	−19.4726	−	59.9305i	−0.976074	−	3.00405i
$399$	−8.62504	−	6.26646i	−0.431792	−	0.313715i
$400$	−41.6570	+	30.2656i	−2.08285	+	1.51328i
$401$	7.46063	−	22.9615i	0.372566	−	1.14664i	−0.572540	−	0.819877i	$-0.694042\pi$
$401$	7.46063	−	22.9615i	0.372566	−	1.14664i	0.945106	−	0.326764i	$-0.105958\pi$
$402$	3.38885	−	10.4298i	0.169021	−	0.520192i
$403$	−4.02732	+	2.92602i	−0.200615	+	0.145755i
$404$	−22.3508	−	16.2388i	−1.11199	−	0.807911i
$405$	−3.37204	−	10.3781i	−0.167558	−	0.515691i
$406$	−12.8205			−0.636272
$407$	−15.1415	−	20.8055i	−0.750535	−	1.03129i
$408$	−31.1430			−1.54181
$409$	5.81439	+	17.8949i	0.287503	+	0.884844i	0.985637	+	0.168877i	$0.0540140\pi$
$409$	5.81439	+	17.8949i	0.287503	+	0.884844i	−0.698134	+	0.715967i	$0.745986\pi$
$410$	43.8410	+	31.8524i	2.16515	+	1.57308i
$411$	19.2411	−	13.9795i	0.949093	−	0.689557i
$412$	15.6391	−	48.1322i	0.770482	−	2.37130i
$413$	3.02701	−	9.31618i	0.148949	−	0.458419i
$414$	−16.2259	+	11.7888i	−0.797458	+	0.579387i
$415$	−46.8150	−	34.0131i	−2.29806	−	1.66964i
$416$	−1.16563	−	3.58745i	−0.0571499	−	0.175889i
$417$	3.58766			0.175688
$418$	−44.5288	−	14.4290i	−2.17797	−	0.705744i
$419$	−1.42696			−0.0697114			−0.0348557	−	0.999392i	$-0.511097\pi$
$419$	−1.42696			−0.0697114			−0.0348557	+	0.999392i	$0.511097\pi$
$420$	−9.32432	−	28.6973i	−0.454980	−	1.40028i
$421$	−24.0784	−	17.4940i	−1.17351	−	0.852603i	−0.182083	−	0.983283i	$-0.558284\pi$
$421$	−24.0784	−	17.4940i	−1.17351	−	0.852603i	−0.991425	+	0.130680i	$0.958284\pi$
$422$	−27.1369	+	19.7161i	−1.32101	+	0.959766i
$423$	0.0356268	−	0.109648i	0.00173224	−	0.00533128i
$424$	−11.9319	+	36.7227i	−0.579465	+	1.78341i
$425$	27.8444	−	20.2302i	1.35065	−	0.981307i
$426$	25.6733	+	18.6528i	1.24388	+	0.903730i
$427$	0.0627111	+	0.193005i	0.00303481	+	0.00934017i
$428$	10.1148			0.488918
$429$	4.02313	+	1.30364i	0.194238	+	0.0629405i
$430$	−41.6821			−2.01009
$431$	−5.39928	−	16.6173i	−0.260074	−	0.800426i	−0.992787	−	0.119888i	$-0.961746\pi$
$431$	−5.39928	−	16.6173i	−0.260074	−	0.800426i	0.732713	−	0.680538i	$-0.238254\pi$
$432$	−27.9168	−	20.2828i	−1.34315	−	0.975855i
$433$	6.26881	−	4.55456i	0.301260	−	0.218878i	−0.426877	−	0.904310i	$-0.640386\pi$
$433$	6.26881	−	4.55456i	0.301260	−	0.218878i	0.728137	+	0.685431i	$0.240386\pi$
$434$	−5.78202	+	17.7952i	−0.277546	+	0.854199i
$435$	−4.90560	+	15.0979i	−0.235205	+	0.723888i
$436$	32.8220	−	23.8466i	1.57189	−	1.14205i
$437$	26.2669	+	19.0841i	1.25652	+	0.912914i
$438$	12.2322	+	37.6469i	0.584478	+	1.79884i
$439$	0.371790			0.0177446			0.00887228	−	0.999961i	$-0.497176\pi$
$439$	0.371790			0.0177446			0.00887228	+	0.999961i	$0.497176\pi$
$440$	−42.0702	−	57.8075i	−2.00562	−	2.75587i
$441$	6.55888			0.312328
$442$	3.21892	+	9.90682i	0.153108	+	0.471219i
$443$	−24.7670	−	17.9943i	−1.17672	−	0.854935i	−0.184919	−	0.982754i	$-0.559202\pi$
$443$	−24.7670	−	17.9943i	−1.17672	−	0.854935i	−0.991798	+	0.127819i	$0.959202\pi$
$444$	−34.7728	+	25.2639i	−1.65025	+	1.19897i
$445$	−4.24354	+	13.0603i	−0.201163	+	0.619116i
$446$	5.31346	−	16.3532i	0.251600	−	0.774344i
$447$	15.1927	−	11.0381i	0.718588	−	0.522085i
$448$	3.46772	+	2.51944i	0.163834	+	0.119033i
$449$	−9.42525	−	29.0079i	−0.444805	−	1.36897i	−0.882697	−	0.469942i	$-0.844275\pi$
$449$	−9.42525	−	29.0079i	−0.444805	−	1.36897i	0.437892	−	0.899027i	$-0.355725\pi$
$450$	28.8056			1.35791
$451$	−11.4779	+	15.8245i	−0.540472	+	0.745146i
$452$	0.891129			0.0419152
$453$	−1.18294	−	3.64072i	−0.0555794	−	0.171056i
$454$	13.6036	+	9.88357i	0.638447	+	0.463859i
$455$	−4.40642	+	3.20145i	−0.206576	+	0.150086i
$456$	−13.0389	+	40.1295i	−0.610601	+	1.87924i
$457$	8.57108	−	26.3791i	0.400938	−	1.23396i	−0.523301	−	0.852148i	$-0.675300\pi$
$457$	8.57108	−	26.3791i	0.400938	−	1.23396i	0.924239	−	0.381813i	$-0.124700\pi$
$458$	−1.92999	+	1.40222i	−0.0901824	+	0.0655213i
$459$	18.6602	+	13.5574i	0.870984	+	0.632807i
$460$	28.3966	+	87.3956i	1.32400	+	4.07484i
$461$	−36.9630			−1.72154			−0.860769	−	0.508995i	$-0.830017\pi$
$461$	−36.9630			−1.72154			−0.860769	+	0.508995i	$0.830017\pi$
$462$	15.1139	−	4.92416i	0.703164	−	0.229093i
$463$	20.0131			0.930089			0.465044	−	0.885287i	$-0.346038\pi$
$463$	20.0131			0.930089			0.465044	+	0.885287i	$0.346038\pi$
$464$	6.52111	+	20.0699i	0.302735	+	0.931723i
$465$	18.7439	+	13.6182i	0.869225	+	0.631529i
$466$	−25.3360	+	18.4077i	−1.17367	+	0.852719i
$467$	−5.24802	+	16.1517i	−0.242849	+	0.747413i	0.753133	+	0.657868i	$0.228541\pi$
$467$	−5.24802	+	16.1517i	−0.242849	+	0.747413i	−0.995983	+	0.0895456i	$0.971459\pi$
$468$	−1.84482	+	5.67778i	−0.0852769	+	0.262455i
$469$	−4.12200	+	2.99481i	−0.190337	+	0.138288i
$470$	−0.624076	−	0.453418i	−0.0287865	−	0.0209146i
$471$	−1.54044	−	4.74100i	−0.0709799	−	0.218454i
$472$	−38.7691			−1.78449
$473$	−0.0120071	−	15.0365i	−0.000552086	−	0.691379i
$474$	11.3152			0.519724
$475$	−14.4099	−	44.3491i	−0.661171	−	2.03488i
$476$	21.6907	+	15.7592i	0.994189	+	0.722321i
$477$	7.26794	−	5.28047i	0.332776	−	0.241776i
$478$	−9.33508	+	28.7304i	−0.426976	+	1.31410i
$479$	−6.41826	+	19.7534i	−0.293258	+	0.902555i	0.690543	+	0.723291i	$0.257372\pi$
$479$	−6.41826	+	19.7534i	−0.293258	+	0.902555i	−0.983801	+	0.179264i	$0.942628\pi$
$480$	−14.2030	+	10.3191i	−0.648275	+	0.470999i
$481$	6.27673	+	4.56031i	0.286194	+	0.207932i
$482$	5.83587	+	17.9610i	0.265817	+	0.818100i
$483$	−11.0259			−0.501696
$484$	38.6192	−	28.1528i	1.75542	−	1.27967i
$485$	−61.0718			−2.77313
$486$	10.0568	+	30.9515i	0.456184	+	1.40399i
$487$	−20.1183	−	14.6168i	−0.911646	−	0.662350i	0.0297845	−	0.999556i	$-0.490518\pi$
$487$	−20.1183	−	14.6168i	−0.911646	−	0.662350i	−0.941431	+	0.337207i	$0.890518\pi$
$488$	0.649792	−	0.472102i	0.0294147	−	0.0213710i
$489$	−5.95654	+	18.3324i	−0.269364	+	0.829018i
$490$	13.5612	−	41.7370i	0.612631	−	1.88548i
$491$	−5.78390	+	4.20225i	−0.261024	+	0.189645i	−0.710598	−	0.703598i	$-0.751576\pi$
$491$	−5.78390	+	4.20225i	−0.261024	+	0.189645i	0.449574	+	0.893243i	$0.351576\pi$
$492$	26.4173	+	19.1933i	1.19098	+	0.865300i
$493$	−4.35885	−	13.4152i	−0.196313	−	0.604189i
$494$	14.1132			0.634983
$495$	0.0132830	+	16.6343i	0.000597025	+	0.747656i
$496$	30.7986			1.38290
$497$	−4.55604	−	14.0221i	−0.204366	−	0.628975i
$498$	−41.1950	−	29.9299i	−1.84599	−	1.34119i
$499$	−8.04669	+	5.84626i	−0.360219	+	0.261715i	−0.753144	−	0.657856i	$-0.771463\pi$
$499$	−8.04669	+	5.84626i	−0.360219	+	0.261715i	0.392924	+	0.919571i	$0.371463\pi$
$500$	16.2821	−	50.1110i	0.728156	−	2.24103i
$501$	−6.73554	+	20.7299i	−0.300922	+	0.926142i
$502$	−3.36028	+	2.44138i	−0.149976	+	0.108964i
$503$	3.33230	+	2.42106i	0.148580	+	0.107950i	0.659592	−	0.751624i	$-0.270729\pi$
$503$	3.33230	+	2.42106i	0.148580	+	0.107950i	−0.511012	+	0.859574i	$0.670729\pi$
$504$	3.74213	+	11.5171i	0.166688	+	0.513013i
$505$	23.2098			1.03282
$506$	−46.0284	+	14.9962i	−2.04621	+	0.666662i
$507$	−1.27511			−0.0566298
$508$	6.08211	+	18.7188i	0.269850	+	0.830513i
$509$	−9.71523	−	7.05853i	−0.430620	−	0.312864i	0.351277	−	0.936272i	$-0.385748\pi$
$509$	−9.71523	−	7.05853i	−0.430620	−	0.312864i	−0.781897	+	0.623408i	$0.785748\pi$
$510$	39.2219	−	28.4964i	1.73677	−	1.26184i
$511$	5.68311	−	17.4908i	0.251406	−	0.773748i
$512$	15.3709	−	47.3068i	0.679305	−	2.09069i
$513$	25.2822	−	18.3686i	1.11624	−	0.810992i
$514$	−16.3323	−	11.8661i	−0.720385	−	0.523391i
$515$	13.1386	+	40.4363i	0.578954	+	1.78184i
$516$	−25.1164			−1.10569
$517$	0.163387	−	0.225261i	0.00718576	−	0.00990698i
$518$	29.1618			1.28130
$519$	1.41000	+	4.33953i	0.0618921	+	0.190484i
$520$	17.4398	+	12.6707i	0.764784	+	0.555648i
$521$	4.05259	−	2.94438i	0.177547	−	0.128995i	−0.495462	−	0.868629i	$-0.665001\pi$
$521$	4.05259	−	2.94438i	0.177547	−	0.128995i	0.673009	+	0.739634i	$0.265001\pi$
$522$	3.64811	−	11.2277i	0.159674	−	0.491425i
$523$	1.03014	−	3.17044i	0.0450449	−	0.138634i	−0.926005	−	0.377512i	$-0.876780\pi$
$523$	1.03014	−	3.17044i	0.0450449	−	0.138634i	0.971050	+	0.238878i	$0.0767797\pi$
$524$	38.9453	−	28.2954i	1.70133	−	1.23609i
$525$	12.8114	+	9.30806i	0.559137	+	0.406237i
$526$	−9.11480	−	28.0525i	−0.397424	−	1.22315i
$527$	−20.5864			−0.896760
$528$	−15.3962	−	21.1555i	−0.670033	−	0.920674i
$529$	10.5786			0.459939
$530$	−18.5747	−	57.1669i	−0.806831	−	2.48317i
$531$	7.29742	+	5.30189i	0.316681	+	0.230082i
$532$	29.3880	−	21.3516i	1.27413	−	0.925711i
$533$	1.82140	−	5.60571i	0.0788938	−	0.242810i
$534$	−3.73411	+	11.4924i	−0.161591	+	0.497326i
$535$	−6.87468	+	4.99474i	−0.297218	+	0.215942i
$536$	16.3141	+	11.8529i	0.704662	+	0.511967i
$537$	0.824829	+	2.53856i	0.0355940	+	0.109547i
$538$	42.7869			1.84467
$539$	15.0602	+	4.88007i	0.648689	+	0.210199i
$540$	88.4480			3.80620
$541$	−8.81502	−	27.1298i	−0.378987	−	1.16640i	−0.940749	−	0.339103i	$-0.889876\pi$
$541$	−8.81502	−	27.1298i	−0.378987	−	1.16640i	0.561762	−	0.827299i	$-0.310124\pi$
$542$	−34.2857	−	24.9100i	−1.47270	−	1.06998i
$543$	−24.7649	+	17.9928i	−1.06276	+	0.772144i
$544$	4.82042	−	14.8357i	0.206674	−	0.636077i
$545$	−10.5324	+	32.4153i	−0.451158	+	1.38852i
$546$	−3.87744	+	2.81713i	−0.165939	+	0.120562i
$547$	35.1106	+	25.5094i	1.50122	+	1.09070i	0.969892	+	0.243536i	$0.0783073\pi$
$547$	35.1106	+	25.5094i	1.50122	+	1.09070i	0.531329	+	0.847165i	$0.321693\pi$
$548$	25.0417	+	77.0704i	1.06973	+	3.29229i
$549$	−0.186871			−0.00797547
$550$	66.1421	+	21.4325i	2.82031	+	0.913884i
$551$	−19.1112			−0.814164
$552$	13.4850	+	41.5026i	0.573960	+	1.76647i
$553$	−4.25305	−	3.09002i	−0.180858	−	0.131401i
$554$	12.3380	−	8.96410i	0.524193	−	0.380848i
$555$	11.1584	−	34.3420i	0.473647	−	1.45773i
$556$	−3.77748	+	11.6259i	−0.160201	+	0.493048i
$557$	7.80783	−	5.67272i	0.330828	−	0.240361i	−0.409954	−	0.912106i	$-0.634455\pi$
$557$	7.80783	−	5.67272i	0.330828	−	0.240361i	0.740782	+	0.671746i	$0.234455\pi$
$558$	−13.9391	−	10.1274i	−0.590090	−	0.428725i
$559$	1.40098	+	4.31178i	0.0592552	+	0.182369i
$560$	33.6977			1.42399
$561$	10.2911	+	14.1408i	0.434492	+	0.597024i
$562$	−24.7866			−1.04556
$563$	2.68558	+	8.26537i	0.113184	+	0.348344i	0.991564	−	0.129619i	$-0.0413754\pi$
$563$	2.68558	+	8.26537i	0.113184	+	0.348344i	−0.878380	+	0.477963i	$0.841375\pi$
$564$	−0.376049	−	0.273216i	−0.0158345	−	0.0115045i
$565$	−0.605668	+	0.440044i	−0.0254806	+	0.0185128i
$566$	−6.04470	+	18.6037i	−0.254078	+	0.781971i
$567$	−1.37858	+	4.24284i	−0.0578950	+	0.178183i
$568$	−47.2082	+	34.2988i	−1.98081	+	1.43914i
$569$	23.2158	+	16.8672i	0.973255	+	0.707111i	0.956191	−	0.292743i	$-0.0945680\pi$
$569$	23.2158	+	16.8672i	0.973255	+	0.707111i	0.0170642	+	0.999854i	$0.494568\pi$
$570$	−20.2979	−	62.4704i	−0.850185	−	2.61660i
$571$	20.8403			0.872139			0.436070	−	0.899913i	$-0.356370\pi$
$571$	20.8403			0.872139			0.436070	+	0.899913i	$0.356370\pi$
$572$	−8.46048	+	11.6644i	−0.353751	+	0.487714i
$573$	−10.2578			−0.428526
$574$	−6.84613	−	21.0702i	−0.285752	−	0.879454i
$575$	−39.0164	−	28.3470i	−1.62709	−	1.18215i
$576$	−3.19318	+	2.31998i	−0.133049	+	0.0966659i
$577$	5.70244	−	17.5503i	0.237396	−	0.730629i	−0.759399	−	0.650625i	$-0.774507\pi$
$577$	5.70244	−	17.5503i	0.237396	−	0.730629i	0.996795	−	0.0800035i	$-0.0254931\pi$
$578$	−0.0793647	+	0.244259i	−0.00330114	+	0.0101599i
$579$	−19.6585	+	14.2827i	−0.816979	+	0.593570i
$580$	−43.7599	−	31.7934i	−1.81703	−	1.32015i
$581$	7.31055	+	22.4995i	0.303293	+	0.933439i
$582$	−53.7403			−2.22761
$583$	20.6172	−	6.71713i	0.853876	−	0.278195i
$584$	−72.7877			−3.01198
$585$	−1.54985	−	4.76996i	−0.0640786	−	0.197214i
$586$	24.4351	+	17.7531i	1.00940	+	0.733375i
$587$	2.20104	−	1.59915i	0.0908465	−	0.0660039i	−0.541435	−	0.840743i	$-0.682119\pi$
$587$	2.20104	−	1.59915i	0.0908465	−	0.0660039i	0.632281	+	0.774739i	$0.282119\pi$
$588$	8.17155	−	25.1495i	0.336989	−	1.03715i
$589$	−8.61909	+	26.5268i	−0.355143	+	1.09302i
$590$	48.8263	−	35.4744i	2.01015	−	1.46046i
$591$	15.7456	+	11.4398i	0.647687	+	0.470572i
$592$	−14.8331	−	45.6514i	−0.609635	−	1.87626i
$593$	−33.2142			−1.36394			−0.681972	−	0.731378i	$-0.738877\pi$
$593$	−33.2142			−1.36394			−0.681972	+	0.731378i	$0.738877\pi$
$594$	0.0372073	+	46.5948i	0.00152663	+	1.91181i
$595$	−22.5243			−0.923406
$596$	19.7728	+	60.8543i	0.809924	+	2.49269i
$597$	25.8073	+	18.7501i	1.05622	+	0.767392i
$598$	11.8085	−	8.57936i	0.482884	−	0.350836i
$599$	8.60533	−	26.4845i	0.351604	−	1.08213i	−0.606348	−	0.795199i	$-0.707366\pi$
$599$	8.60533	−	26.4845i	0.351604	−	1.08213i	0.957952	−	0.286927i	$-0.0926338\pi$
$600$	19.3677	−	59.6076i	0.790682	−	2.43347i
$601$	−12.7478	+	9.26181i	−0.519993	+	0.377797i	−0.816601	−	0.577202i	$-0.804144\pi$
$601$	−12.7478	+	9.26181i	−0.519993	+	0.377797i	0.296608	+	0.954999i	$0.404144\pi$
$602$	13.7863	+	10.0163i	0.561887	+	0.408235i
$603$	−1.44982	−	4.46208i	−0.0590411	−	0.181710i
$604$	13.0434			0.530728
$605$	−12.3461	+	38.2048i	−0.501939	+	1.55325i
$606$	20.4235			0.829650
$607$	9.26937	+	28.5282i	0.376232	+	1.15792i	0.942644	+	0.333801i	$0.108331\pi$
$607$	9.26937	+	28.5282i	0.376232	+	1.15792i	−0.566412	+	0.824122i	$0.691669\pi$
$608$	−17.0985	−	12.4228i	−0.693436	−	0.503810i
$609$	5.25058	−	3.81477i	0.212764	−	0.154582i
$610$	−0.386376	+	1.18914i	−0.0156439	+	0.0481469i
$611$	−0.0259276	+	0.0797971i	−0.00104892	+	0.00322825i
$612$	−19.9734	+	14.5115i	−0.807378	+	0.586595i
$613$	−12.3122	−	8.94532i	−0.497284	−	0.361298i	0.310695	−	0.950510i	$-0.399438\pi$
$613$	−12.3122	−	8.94532i	−0.497284	−	0.361298i	−0.807979	+	0.589212i	$0.799438\pi$
$614$	−0.184934	−	0.569169i	−0.00746333	−	0.0229698i
$615$	−27.4326			−1.10619
$616$	0.0233405	+	29.2293i	0.000940414	+	1.17768i
$617$	−45.5660			−1.83442			−0.917209	−	0.398406i	$-0.869564\pi$
$617$	−45.5660			−1.83442			−0.917209	+	0.398406i	$0.869564\pi$
$618$	11.5613	+	35.5820i	0.465064	+	1.43132i
$619$	29.0373	+	21.0968i	1.16711	+	0.847954i	0.990660	−	0.136356i	$-0.0435392\pi$
$619$	29.0373	+	21.0968i	1.16711	+	0.847954i	0.176448	+	0.984310i	$0.443539\pi$
$620$	−63.8658	+	46.4012i	−2.56491	+	1.86352i
$621$	9.98734	−	30.7379i	0.400778	−	1.23347i
$622$	0.864937	−	2.66200i	0.0346808	−	0.106737i
$623$	4.54196	−	3.29993i	0.181970	−	0.132209i
$624$	6.38232	+	4.63703i	0.255497	+	0.185630i
$625$	0.819639	+	2.52259i	0.0327856	+	0.100904i
$626$	21.7663			0.869957
$627$	22.5299	−	7.34030i	0.899757	−	0.293143i
$628$	16.9853			0.677786
$629$	9.91474	+	30.5144i	0.395327	+	1.21669i
$630$	−15.2512	−	11.0807i	−0.607624	−	0.441465i
$631$	−24.6341	+	17.8977i	−0.980670	+	0.712498i	−0.957858	−	0.287242i	$-0.907262\pi$
$631$	−24.6341	+	17.8977i	−0.980670	+	0.712498i	−0.0228114	+	0.999740i	$0.507262\pi$
$632$	−6.42953	+	19.7881i	−0.255753	+	0.787127i
$633$	5.24722	−	16.1493i	0.208558	−	0.641876i
$634$	11.9834	−	8.70648i	0.475923	−	0.345778i
$635$	−13.3772	−	9.71912i	−0.530859	−	0.385691i
$636$	−11.1925	−	34.4471i	−0.443813	−	1.36591i
$637$	−4.77327			−0.189124
$638$	16.7305	−	23.0663i	0.662367	−	0.913203i
$639$	13.5764			0.537075
$640$	16.6700	+	51.3048i	0.658938	+	2.02800i
$641$	−23.7870	−	17.2823i	−0.939530	−	0.682608i	0.00877763	−	0.999961i	$-0.497206\pi$
$641$	−23.7870	−	17.2823i	−0.939530	−	0.682608i	−0.948307	+	0.317353i	$0.897206\pi$
$642$	−6.04939	+	4.39514i	−0.238750	+	0.173462i
$643$	2.72406	−	8.38379i	0.107426	−	0.330624i	−0.882866	−	0.469625i	$-0.844389\pi$
$643$	2.72406	−	8.38379i	0.107426	−	0.330624i	0.990292	+	0.139001i	$0.0443890\pi$
$644$	11.6093	−	35.7297i	0.457470	−	1.40795i
$645$	17.0707	−	12.4026i	0.672157	−	0.488351i
$646$	47.2178	+	34.3058i	1.85776	+	1.34974i
$647$	−5.81753	−	17.9045i	−0.228711	−	0.703900i	−0.997894	−	0.0648709i	$-0.979336\pi$
$647$	−5.81753	−	17.9045i	−0.228711	−	0.703900i	0.769183	−	0.639029i	$-0.220664\pi$
$648$	17.6565			0.693613
$649$	12.8112	+	17.6035i	0.502883	+	0.690998i
$650$	−20.9634			−0.822254
$651$	−2.92701	−	9.00840i	−0.114718	−	0.353067i
$652$	−53.1348	−	38.6047i	−2.08092	−	1.51188i
$653$	11.8461	−	8.60668i	0.463573	−	0.336806i	−0.331358	−	0.943505i	$-0.607507\pi$
$653$	11.8461	−	8.60668i	0.463573	−	0.336806i	0.794931	+	0.606699i	$0.207507\pi$
$654$	−9.26800	+	28.5240i	−0.362407	+	1.11538i
$655$	−12.4973	+	38.4627i	−0.488309	+	1.50286i
$656$	−29.5022	+	21.4346i	−1.15187	+	0.836880i
$657$	13.7007	+	9.95411i	0.534514	+	0.388347i
$658$	0.0974546	+	0.299934i	0.00379917	+	0.0116927i
$659$	17.9316			0.698515			0.349258	−	0.937027i	$-0.386434\pi$
$659$	17.9316			0.698515			0.349258	+	0.937027i	$0.386434\pi$
$660$	63.7993	+	20.6733i	2.48338	+	0.804708i
$661$	3.85833			0.150072			0.0750358	−	0.997181i	$-0.476093\pi$
$661$	3.85833			0.150072			0.0750358	+	0.997181i	$0.476093\pi$
$662$	−10.0047	−	30.7912i	−0.388842	−	1.19673i
$663$	−4.26608	−	3.09949i	−0.165681	−	0.120374i
$664$	75.7495	−	55.0352i	2.93965	−	2.13578i
$665$	−9.43042	+	29.0239i	−0.365696	+	1.12550i
$666$	−8.29808	+	25.5389i	−0.321544	+	0.989611i
$667$	−15.9903	+	11.6176i	−0.619146	+	0.449836i
$668$	−60.0838	−	43.6534i	−2.32471	−	1.68900i
$669$	2.68981	+	8.27838i	0.103994	+	0.320061i
$670$	−31.3918			−1.21277
$671$	−0.429085	−	0.139040i	−0.0165646	−	0.00536756i
$672$	7.17732			0.276871
$673$	−8.51807	−	26.2159i	−0.328347	−	1.01055i	−0.969907	−	0.243476i	$-0.921712\pi$
$673$	−8.51807	−	26.2159i	−0.328347	−	1.01055i	0.641560	−	0.767073i	$-0.278288\pi$
$674$	−71.0625	−	51.6300i	−2.73723	−	1.98871i
$675$	−37.5536	+	27.2843i	−1.44544	+	1.05017i
$676$	1.34258	−	4.13204i	0.0516377	−	0.158924i
$677$	5.37049	−	16.5287i	0.206405	−	0.635248i	−0.793248	−	0.608898i	$-0.791612\pi$
$677$	5.37049	−	16.5287i	0.206405	−	0.635248i	0.999653	−	0.0263497i	$-0.00838833\pi$
$678$	−0.532959	+	0.387218i	−0.0204682	+	0.0148710i
$679$	20.1994	+	14.6757i	0.775182	+	0.563202i
$680$	27.5479	+	84.7836i	1.05641	+	3.25130i
$681$	−8.51214			−0.326186
$682$	−24.4712	−	33.6252i	−0.937051	−	1.28758i
$683$	−26.8739			−1.02830			−0.514152	−	0.857699i	$-0.671893\pi$
$683$	−26.8739			−1.02830			−0.514152	+	0.857699i	$0.671893\pi$
$684$	10.3365	+	31.8126i	0.395227	+	1.21639i
$685$	−55.0777	−	40.0163i	−2.10441	−	1.52894i
$686$	−35.8009	+	26.0109i	−1.36688	+	0.993099i
$687$	0.373184	−	1.14854i	0.0142379	−	0.0438196i
$688$	8.66772	−	26.6765i	0.330454	−	1.01703i
$689$	−5.28929	+	3.84289i	−0.201506	+	0.146402i
$690$	−54.9587	−	39.9298i	−2.09224	−	1.52010i
$691$	−1.80447	−	5.55358i	−0.0686452	−	0.211268i	0.910849	−	0.412739i	$-0.135428\pi$
$691$	−1.80447	−	5.55358i	−0.0686452	−	0.211268i	−0.979494	+	0.201471i	$0.935428\pi$
$692$	−15.5470			−0.591007
$693$	3.99287	−	5.50496i	0.151677	−	0.209116i
$694$	20.5660			0.780673
$695$	−3.17350	−	9.76704i	−0.120378	−	0.370485i
$696$	−20.7808	−	15.0981i	−0.787693	−	0.572293i
$697$	19.7199	−	14.3273i	0.746944	−	0.542687i
$698$	−21.3349	+	65.6619i	−0.807536	+	2.48534i
$699$	4.89899	−	15.0775i	0.185297	−	0.570285i
$700$	−43.6523	+	31.7153i	−1.64990	+	1.19872i
$701$	18.9469	+	13.7658i	0.715616	+	0.519925i	0.884981	−	0.465628i	$-0.154172\pi$
$701$	18.9469	+	13.7658i	0.715616	+	0.519925i	−0.169365	+	0.985553i	$0.554172\pi$
$702$	−4.34134	−	13.3613i	−0.163853	−	0.504288i
$703$	43.4707			1.63953
$704$	−9.05819	+	2.95118i	−0.341394	+	0.111227i
$705$	0.390502			0.0147072
$706$	−13.4584	−	41.4208i	−0.506515	−	1.55889i
$707$	−7.67661	−	5.57738i	−0.288708	−	0.209759i
$708$	29.4213	−	21.3758i	1.10572	−	0.803352i
$709$	−13.1237	+	40.3907i	−0.492872	+	1.51690i	0.327375	+	0.944895i	$0.393836\pi$
$709$	−13.1237	+	40.3907i	−0.492872	+	1.51690i	−0.820247	+	0.572010i	$0.806164\pi$
$710$	28.0707	−	86.3926i	1.05347	−	3.24226i
$711$	3.91634	−	2.84539i	0.146874	−	0.106710i
$712$	−17.9762	−	13.0605i	−0.673687	−	0.489462i
$713$	8.91399	+	27.4344i	0.333832	+	1.02743i
$714$	−19.8203			−0.741757
$715$	−0.00966676	−	12.1057i	−0.000361516	−	0.452728i
$716$	−9.09475			−0.339887
$717$	−4.72565	−	14.5441i	−0.176483	−	0.543158i
$718$	47.7334	+	34.6803i	1.78139	+	1.29426i
$719$	6.61777	−	4.80809i	0.246801	−	0.179311i	−0.457507	−	0.889206i	$-0.651257\pi$
$719$	6.61777	−	4.80809i	0.246801	−	0.179311i	0.704308	+	0.709895i	$0.251257\pi$
$720$	−9.58877	+	29.5112i	−0.357352	+	1.09982i
$721$	5.37140	−	16.5315i	0.200041	−	0.615664i
$722$	25.2558	−	18.3494i	0.939922	−	0.682893i
$723$	−7.73437	−	5.61935i	−0.287644	−	0.208986i
$724$	−32.2308	−	99.1962i	−1.19785	−	3.68660i
$725$	28.3873			1.05428
$726$	−10.8640	+	33.6184i	−0.403199	+	1.24770i
$727$	24.8891			0.923085			0.461543	−	0.887118i	$-0.347296\pi$
$727$	24.8891			0.923085			0.461543	+	0.887118i	$0.347296\pi$
$728$	−2.72336	−	8.38164i	−0.100934	−	0.310644i
$729$	−20.5843	−	14.9554i	−0.762383	−	0.553904i
$730$	91.6698	−	66.6020i	3.39285	−	2.46505i
$731$	−5.79370	+	17.8312i	−0.214288	+	0.659509i
$732$	−0.232818	+	0.716541i	−0.00860521	+	0.0264841i
$733$	4.85588	−	3.52801i	0.179356	−	0.130310i	−0.494485	−	0.869186i	$-0.664643\pi$
$733$	4.85588	−	3.52801i	0.179356	−	0.130310i	0.673841	+	0.738876i	$0.264643\pi$
$734$	16.3612	+	11.8871i	0.603903	+	0.438762i
$735$	6.86500	+	21.1283i	0.253219	+	0.779329i
$736$	−21.8580			−0.805697
$737$	−0.00904281	−	11.3243i	−0.000333096	−	0.417137i
$738$	20.4006			0.750957
$739$	−7.78192	−	23.9503i	−0.286263	−	0.881026i	−0.986017	−	0.166643i	$-0.946707\pi$
$739$	−7.78192	−	23.9503i	−0.286263	−	0.881026i	0.699755	−	0.714383i	$-0.253293\pi$
$740$	99.5372	+	72.3180i	3.65906	+	2.65846i
$741$	−5.77999	+	4.19941i	−0.212333	+	0.154269i
$742$	−7.59383	+	23.3714i	−0.278778	+	0.857991i
$743$	−1.45847	+	4.48871i	−0.0535061	+	0.164675i	−0.974239	−	0.225519i	$-0.927592\pi$
$743$	−1.45847	+	4.48871i	−0.0535061	+	0.164675i	0.920733	+	0.390194i	$0.127592\pi$
$744$	−30.3287	+	22.0351i	−1.11190	+	0.807845i
$745$	−43.4890	−	31.5966i	−1.59331	−	1.15761i
$746$	8.16322	+	25.1238i	0.298877	+	0.919848i
$747$	−21.7845			−0.797053
$748$	−56.6592	+	18.4597i	−2.07167	+	0.674955i
$749$	3.47404			0.126939
$750$	12.0366	+	37.0450i	0.439516	+	1.35269i
$751$	9.41744	+	6.84217i	0.343647	+	0.249674i	0.746199	−	0.665723i	$-0.231877\pi$
$751$	9.41744	+	6.84217i	0.343647	+	0.249674i	−0.402552	+	0.915397i	$0.631877\pi$
$752$	0.419963	−	0.305121i	0.0153145	−	0.0111266i
$753$	0.649746	−	1.99971i	0.0236781	−	0.0728736i
$754$	−2.65494	+	8.17106i	−0.0966871	+	0.297572i
$755$	−8.86511	+	6.44088i	−0.322634	+	0.234408i
$756$	−29.2540	−	21.2543i	−1.06396	−	0.773011i
$757$	2.07027	+	6.37163i	0.0752452	+	0.231581i	0.981604	−	0.190928i	$-0.0611496\pi$
$757$	2.07027	+	6.37163i	0.0752452	+	0.231581i	−0.906359	+	0.422509i	$0.861150\pi$
$758$	68.7175			2.49593
$759$	14.3886	−	19.8374i	0.522272	−	0.720054i
$760$	120.782			4.38123
$761$	−7.94335	−	24.4471i	−0.287946	−	0.886208i	−0.985500	−	0.169675i	$-0.945728\pi$
$761$	−7.94335	−	24.4471i	−0.287946	−	0.886208i	0.697554	−	0.716533i	$-0.254272\pi$
$762$	−11.7713	−	8.55236i	−0.426430	−	0.309819i
$763$	11.2731	−	8.19036i	0.408112	−	0.296511i
$764$	10.8005	−	33.2407i	0.390750	−	1.20260i
$765$	6.40935	−	19.7259i	0.231730	−	0.713193i
$766$	34.0172	−	24.7150i	1.22909	−	0.892988i
$767$	−5.31074	−	3.85848i	−0.191760	−	0.139322i
$768$	12.4051	+	38.1790i	0.447631	+	1.37767i
$769$	20.7793			0.749322			0.374661	−	0.927162i	$-0.377759\pi$
$769$	20.7793			0.749322			0.374661	+	0.927162i	$0.377759\pi$
$770$	−26.7747	−	36.7904i	−0.964894	−	1.32584i
$771$	10.2196			0.368049
$772$	−25.5849	−	78.7423i	−0.920822	−	2.83400i
$773$	−1.80601	−	1.31214i	−0.0649577	−	0.0471946i	0.554833	−	0.831962i	$-0.312782\pi$
$773$	−1.80601	−	1.31214i	−0.0649577	−	0.0471946i	−0.619790	+	0.784768i	$0.712782\pi$
$774$	−12.6948	+	9.22334i	−0.456306	+	0.331526i
$775$	12.8026	−	39.4024i	0.459883	−	1.41538i
$776$	30.5364	−	93.9813i	1.09619	−	3.37373i
$777$	−11.9431	+	8.67716i	−0.428456	+	0.311291i
$778$	15.4805	+	11.2472i	0.555002	+	0.403232i
$779$	−10.2053	−	31.4088i	−0.365644	−	1.12534i
$780$	−20.2209			−0.724025
$781$	31.1736	+	10.1014i	1.11548	+	0.361456i
$782$	60.3614			2.15852
$783$	5.87876	+	18.0929i	0.210090	+	0.646589i
$784$	23.8916	+	17.3583i	0.853272	+	0.619939i
$785$	−11.5443	+	8.38740i	−0.412033	+	0.299359i
$786$	−10.9970	+	33.8453i	−0.392251	+	1.20722i
$787$	−6.57151	+	20.2250i	−0.234249	+	0.720944i	0.762971	+	0.646433i	$0.223740\pi$
$787$	−6.57151	+	20.2250i	−0.234249	+	0.720944i	−0.997220	+	0.0745117i	$0.976260\pi$
$788$	−53.6498	+	38.9789i	−1.91119	+	1.38856i
$789$	12.0800	+	8.77662i	0.430059	+	0.312456i
$790$	−10.0090	−	30.8045i	−0.356103	−	1.09597i
$791$	0.306067			0.0108825
$792$	−25.6046	−	8.29684i	−0.909820	−	0.294815i
$793$	0.135997			0.00482938
$794$	−21.5811	−	66.4197i	−0.765883	−	2.35715i
$795$	24.6173	+	17.8855i	0.873084	+	0.634333i
$796$	−87.9331	+	63.8871i	−3.11671	+	2.26442i
$797$	−3.48197	+	10.7164i	−0.123338	+	0.379594i	−0.993595	−	0.113004i	$-0.963953\pi$
$797$	−3.48197	+	10.7164i	−0.123338	+	0.379594i	0.870257	+	0.492598i	$0.163953\pi$
$798$	−8.29833	+	25.5396i	−0.293758	+	0.904093i
$799$	−0.280712	+	0.203949i	−0.00993089	+	0.00721521i
$800$	25.3977	+	18.4525i	0.897946	+	0.652396i
$801$	1.59753	+	4.91668i	0.0564459	+	0.173722i
$802$	−60.8133			−2.14739
$803$	24.0526	+	33.0500i	0.848797	+	1.16631i
$804$	−18.9157			−0.667107
$805$	9.75308	+	30.0169i	0.343751	+	1.05796i
$806$	10.1443	+	7.37025i	0.357317	+	0.259606i
$807$	−17.5232	+	12.7313i	−0.616844	+	0.448164i
$808$	−11.6051	+	35.7168i	−0.408266	+	1.25651i
$809$	12.5735	−	38.6972i	0.442060	−	1.36052i	−0.443616	−	0.896217i	$-0.646304\pi$
$809$	12.5735	−	38.6972i	0.442060	−	1.36052i	0.885676	−	0.464304i	$-0.153696\pi$
$810$	−22.2368	+	16.1560i	−0.781323	+	0.567664i
$811$	−16.4969	−	11.9857i	−0.579286	−	0.420876i	0.259181	−	0.965829i	$-0.416548\pi$
$811$	−16.4969	−	11.9857i	−0.579286	−	0.420876i	−0.838467	+	0.544953i	$0.816548\pi$
$812$	6.83347	+	21.0313i	0.239808	+	0.738052i
$813$	21.4535			0.752408
$814$	−38.0556	+	52.4670i	−1.33385	+	1.83897i
$815$	55.1769			1.93276
$816$	10.0815	+	31.0277i	0.352924	+	1.08619i
$817$	20.5508	+	14.9310i	0.718981	+	0.522370i
$818$	38.3429	−	27.8577i	1.34063	−	0.974022i
$819$	−0.633623	+	1.95009i	−0.0221406	+	0.0681417i
$820$	28.8841	−	88.8960i	1.00868	−	3.10438i
$821$	6.36439	−	4.62400i	0.222119	−	0.161379i	−0.471161	−	0.882047i	$-0.656165\pi$
$821$	6.36439	−	4.62400i	0.222119	−	0.161379i	0.693280	+	0.720668i	$0.256165\pi$
$822$	−48.4657	−	35.2124i	−1.69044	−	1.22817i
$823$	5.28558	+	16.2673i	0.184244	+	0.567044i	0.999935	−	0.0114443i	$-0.00364291\pi$
$823$	5.28558	+	16.2673i	0.184244	+	0.567044i	−0.815691	+	0.578488i	$0.803643\pi$
$824$	−68.7954			−2.39660
$825$	−33.4654	+	10.9031i	−1.16512	+	0.379598i
$826$	−24.6738			−0.858512
$827$	−10.6335	−	32.7265i	−0.369762	−	1.13801i	−0.946945	−	0.321396i	$-0.895848\pi$
$827$	−10.6335	−	32.7265i	−0.369762	−	1.13801i	0.577182	−	0.816615i	$-0.304152\pi$
$828$	27.9873	+	20.3340i	0.972626	+	0.706654i
$829$	42.1387	−	30.6155i	1.46354	−	1.06332i	0.481113	−	0.876659i	$-0.340233\pi$
$829$	42.1387	−	30.6155i	1.46354	−	1.06332i	0.982424	−	0.186663i	$-0.0597672\pi$
$830$	−45.0417	+	138.624i	−1.56342	+	4.81171i
$831$	−2.38569	+	7.34240i	−0.0827587	+	0.254705i
$832$	2.32386	−	1.68838i	0.0805652	−	0.0585341i
$833$	−15.9697	−	11.6027i	−0.553317	−	0.402008i
$834$	−2.79253	−	8.59453i	−0.0966975	−	0.297604i
$835$	62.3930			2.15920
$836$	0.0644711	+	80.7374i	0.00222978	+	2.79236i
$837$	27.7648			0.959692
$838$	1.11070	+	3.41839i	0.0383686	+	0.118086i
$839$	−14.0150	−	10.1825i	−0.483850	−	0.351538i	0.318964	−	0.947767i	$-0.396665\pi$
$839$	−14.0150	−	10.1825i	−0.483850	−	0.351538i	−0.802814	+	0.596229i	$0.796665\pi$
$840$	−33.1836	+	24.1093i	−1.14494	+	0.831849i
$841$	−5.36635	+	16.5159i	−0.185047	+	0.569515i
$842$	−23.1663	+	71.2985i	−0.798363	+	2.45711i
$843$	10.1512	−	7.37529i	0.349627	−	0.254019i
$844$	46.8073	+	34.0075i	1.61117	+	1.17059i
$845$	1.12792	+	3.47137i	0.0388015	+	0.119419i
$846$	−0.290402			−0.00998423
$847$	13.2642	−	9.66938i	0.455762	−	0.332244i
$848$	40.4494			1.38904
$849$	−3.05998	−	9.41765i	−0.105018	−	0.323213i
$850$	−70.1364	−	50.9571i	−2.40566	−	1.74781i
$851$	36.3718	−	26.4257i	1.24681	−	0.905860i
$852$	16.9145	−	52.0576i	0.579483	−	1.78346i
$853$	−8.23011	+	25.3297i	−0.281793	+	0.867271i	0.705548	+	0.708662i	$0.250701\pi$
$853$	−8.23011	+	25.3297i	−0.281793	+	0.867271i	−0.987341	+	0.158609i	$0.949299\pi$
$854$	0.413547	−	0.300460i	0.0141513	−	0.0102815i
$855$	−22.7346	−	16.5176i	−0.777506	−	0.564891i
$856$	−4.24885	−	13.0766i	−0.145223	−	0.446949i
$857$	−28.1283			−0.960843			−0.480422	−	0.877038i	$-0.659516\pi$
$857$	−28.1283			−0.960843			−0.480422	+	0.877038i	$0.659516\pi$
$858$	−0.00850629	−	10.6525i	−0.000290400	−	0.363669i
$859$	−1.44763			−0.0493924			−0.0246962	−	0.999695i	$-0.507862\pi$
$859$	−1.44763			−0.0493924			−0.0246962	+	0.999695i	$0.507862\pi$
$860$	22.2170	+	68.3768i	0.757592	+	2.33163i
$861$	9.07328	+	6.59212i	0.309217	+	0.224659i
$862$	−35.6054	+	25.8688i	−1.21273	+	0.881096i
$863$	−14.8334	+	45.6525i	−0.504935	+	1.55403i	0.295946	+	0.955205i	$0.404365\pi$
$863$	−14.8334	+	45.6525i	−0.504935	+	1.55403i	−0.800880	+	0.598824i	$0.795635\pi$
$864$	−6.50127	+	20.0088i	−0.221178	+	0.680715i
$865$	10.5667	−	7.67716i	0.359279	−	0.261031i
$866$	−15.7903	−	11.4723i	−0.536576	−	0.389845i
$867$	−0.0401764	−	0.123650i	−0.00136446	−	0.00419938i
$868$	32.2738			1.09544
$869$	11.1096	−	3.61954i	0.376867	−	0.122784i
$870$	39.9866			1.35567
$871$	1.05511	+	3.24731i	0.0357512	+	0.110031i
$872$	−44.6166	−	32.4158i	−1.51091	−	1.09774i
$873$	−18.6002	+	13.5139i	−0.629523	+	0.457375i
$874$	25.2720	−	77.7791i	0.854837	−	2.63092i
$875$	5.59224	−	17.2111i	0.189052	−	0.581843i
$876$	55.2374	−	40.1324i	1.86630	−	1.35595i
$877$	−6.12668	−	4.45130i	−0.206883	−	0.150310i	0.479519	−	0.877531i	$-0.340811\pi$
$877$	−6.12668	−	4.45130i	−0.206883	−	0.150310i	−0.686402	+	0.727222i	$0.740811\pi$
$878$	−0.289391	−	0.890653i	−0.00976646	−	0.0300581i
$879$	−15.2897			−0.515710
$880$	−43.9748	+	60.6278i	−1.48239	+	2.04376i
$881$	−53.7190			−1.80984			−0.904920	−	0.425583i	$-0.860069\pi$
$881$	−53.7190			−1.80984			−0.904920	+	0.425583i	$0.860069\pi$
$882$	−5.10525	−	15.7124i	−0.171903	−	0.529062i
$883$	−9.98209	−	7.25241i	−0.335924	−	0.244063i	0.407016	−	0.913421i	$-0.366569\pi$
$883$	−9.98209	−	7.25241i	−0.335924	−	0.244063i	−0.742940	+	0.669358i	$0.766569\pi$
$884$	14.5358	−	10.5609i	0.488891	−	0.355200i
$885$	−9.44110	+	29.0567i	−0.317359	+	0.976731i
$886$	−23.8289	+	73.3377i	−0.800546	+	2.46383i
$887$	26.4206	−	19.1957i	0.887115	−	0.644527i	−0.0480089	−	0.998847i	$-0.515288\pi$
$887$	26.4206	−	19.1957i	0.887115	−	0.644527i	0.935124	+	0.354320i	$0.115288\pi$
$888$	47.2684	+	34.3425i	1.58622	+	1.15246i
$889$	2.08896	+	6.42916i	0.0700615	+	0.215627i
$890$	34.5900			1.15946
$891$	−5.83456	−	8.01712i	−0.195465	−	0.268584i
$892$	−29.6584			−0.993038
$893$	0.145273	+	0.447103i	0.00486136	+	0.0149617i
$894$	−38.2682	−	27.8035i	−1.27988	−	0.929888i
$895$	6.18137	−	4.49103i	0.206620	−	0.150119i
$896$	6.81513	−	20.9748i	0.227678	−	0.700720i
$897$	−2.28330	+	7.02726i	−0.0762371	+	0.234634i
$898$	−62.1546	+	45.1579i	−2.07413	+	1.50694i
$899$	−13.7367	−	9.98031i	−0.458145	−	0.332862i
$900$	−15.3537	−	47.2538i	−0.511789	−	1.57513i
$901$	−27.0372			−0.900741
$902$	46.8429	+	15.1788i	1.55970	+	0.505400i
$903$	−8.62647			−0.287071
$904$	−0.374329	−	1.15207i	−0.0124500	−	0.0383172i
$905$	70.8896	+	51.5043i	2.35645	+	1.71206i
$906$	−7.80088	+	5.66767i	−0.259167	+	0.188296i
$907$	−15.1341	+	46.5779i	−0.502519	+	1.54660i	0.302382	+	0.953187i	$0.402218\pi$
$907$	−15.1341	+	46.5779i	−0.502519	+	1.54660i	−0.804901	+	0.593409i	$0.797782\pi$
$908$	8.96252	−	27.5838i	0.297432	−	0.915401i
$909$	7.06886	−	5.13583i	0.234459	−	0.170345i
$910$	11.0992	+	8.06402i	0.367934	+	0.267320i
$911$	−11.9717	−	36.8450i	−0.396639	−	1.22073i	−0.927678	−	0.373382i	$-0.878198\pi$
$911$	−11.9717	−	36.8450i	−0.396639	−	1.22073i	0.531039	−	0.847347i	$-0.321802\pi$
$912$	44.2020			1.46367
$913$	−50.0206	−	16.2085i	−1.65544	−	0.536424i
$914$	−69.8648			−2.31092
$915$	−0.195593	−	0.601973i	−0.00646611	−	0.0199006i
$916$	3.32895	+	2.41863i	0.109992	+	0.0799136i
$917$	13.3761	−	9.71834i	0.441719	−	0.320928i
$918$	17.9534	−	55.2548i	0.592550	−	1.82368i
$919$	13.2338	−	40.7294i	0.436542	−	1.34354i	−0.454955	−	0.890514i	$-0.650345\pi$
$919$	13.2338	−	40.7294i	0.436542	−	1.34354i	0.891498	−	0.453025i	$-0.149655\pi$
$920$	101.058	−	73.4231i	3.33179	−	2.42069i
$921$	0.245096	+	0.178073i	0.00807618	+	0.00586769i
$922$	28.7710	+	88.5480i	0.947522	+	2.91617i
$923$	−9.88033			−0.325215
$924$	−16.1336	−	22.1688i	−0.530758	−	0.729300i
$925$	−64.5704			−2.12306
$926$	−15.5777	−	47.9431i	−0.511913	−	1.57551i
$927$	12.9492	+	9.40815i	0.425308	+	0.309004i
$928$	10.4089	−	7.56250i	0.341688	−	0.248251i
$929$	0.489315	−	1.50596i	0.0160539	−	0.0494089i	−0.942709	−	0.333617i	$-0.891731\pi$
$929$	0.489315	−	1.50596i	0.0160539	−	0.0494089i	0.958763	+	0.284208i	$0.0917307\pi$
$930$	18.0338	−	55.5025i	0.591353	−	1.82000i
$931$	−21.6368	+	15.7201i	−0.709119	+	0.515205i
$932$	43.7010	+	31.7506i	1.43147	+	1.04003i
$933$	0.437853	+	1.34757i	0.0143347	+	0.0441176i
$934$	42.7777			1.39973
$935$	29.3937	−	40.5250i	0.961277	−	1.32531i
$936$	8.11527			0.265256
$937$	−12.4215	−	38.2293i	−0.405792	−	1.24890i	−0.920232	−	0.391372i	$-0.872000\pi$
$937$	−12.4215	−	38.2293i	−0.405792	−	1.24890i	0.514441	−	0.857526i	$-0.328000\pi$
$938$	10.3828	+	7.54353i	0.339010	+	0.246305i
$939$	−8.91428	+	6.47661i	−0.290907	+	0.211356i
$940$	−0.411164	+	1.26543i	−0.0134107	+	0.0412739i
$941$	15.3475	−	47.2347i	0.500314	−	1.53981i	−0.308195	−	0.951323i	$-0.599725\pi$
$941$	15.3475	−	47.2347i	0.500314	−	1.53981i	0.808509	−	0.588484i	$-0.200275\pi$
$942$	−10.1584	+	7.38052i	−0.330979	+	0.240470i
$943$	−27.6320	−	20.0759i	−0.899823	−	0.653760i
$944$	12.5502	+	38.6257i	0.408475	+	1.25716i
$945$	30.3784			0.988208
$946$	−36.0118	+	11.7327i	−1.17085	+	0.381465i
$947$	2.67488			0.0869219			0.0434610	−	0.999055i	$-0.486162\pi$
$947$	2.67488			0.0869219			0.0434610	+	0.999055i	$0.486162\pi$
$948$	−6.03111	−	18.5618i	−0.195881	−	0.602861i
$949$	−9.97073	−	7.24416i	−0.323664	−	0.235155i
$950$	−95.0257	+	69.0402i	−3.08304	+	2.23996i
$951$	−2.31713	+	7.13139i	−0.0751380	+	0.231251i
$952$	11.2623	−	34.6619i	0.365014	−	1.12340i
$953$	37.3504	−	27.1367i	1.20990	−	0.879043i	0.214677	−	0.976685i	$-0.431130\pi$
$953$	37.3504	−	27.1367i	1.20990	−	0.879043i	0.995222	+	0.0976421i	$0.0311301\pi$
$954$	−18.3070	−	13.3008i	−0.592710	−	0.430629i
$955$	9.07365	+	27.9258i	0.293616	+	0.903658i
$956$	52.1061			1.68523
$957$	0.0115187	+	14.4249i	0.000372346	+	0.466290i
$958$	52.3166			1.69027
$959$	8.60082	+	26.4706i	0.277735	+	0.854781i
$960$	−10.8156	−	7.85802i	−0.349073	−	0.253617i
$961$	5.03137	−	3.65550i	0.162302	−	0.117919i
$962$	6.03897	−	18.5861i	0.194704	−	0.599238i
$963$	−0.988546	+	3.04243i	−0.0318555	+	0.0980410i
$964$	26.3532	−	19.1468i	0.848781	−	0.616675i
$965$	56.2724	+	40.8843i	1.81147	+	1.31611i
$966$	8.58225	+	26.4135i	0.276129	+	0.849839i
$967$	−43.8306			−1.40950			−0.704748	−	0.709457i	$-0.748940\pi$
$967$	−43.8306			−1.40950			−0.704748	+	0.709457i	$0.748940\pi$
$968$	−52.6189	−	38.1016i	−1.69124	−	1.22463i
$969$	−29.5456			−0.949140
$970$	47.5366	+	146.303i	1.52631	+	4.69749i
$971$	35.6274	+	25.8848i	1.14334	+	0.830683i	0.987581	−	0.157113i	$-0.0502186\pi$
$971$	35.6274	+	25.8848i	1.14334	+	0.830683i	0.155756	+	0.987796i	$0.450219\pi$
$972$	45.4137	−	32.9950i	1.45664	−	1.05831i
$973$	−1.29741	+	3.99303i	−0.0415932	+	0.128011i
$974$	−19.3562	+	59.5723i	−0.620213	+	1.90882i
$975$	8.58547	−	6.23771i	0.274955	−	0.199767i
$976$	−0.680704	−	0.494560i	−0.0217888	−	0.0158305i
$977$	16.9534	+	52.1773i	0.542388	+	1.66930i	0.727120	+	0.686510i	$0.240858\pi$
$977$	16.9534	+	52.1773i	0.542388	+	1.66930i	−0.184732	+	0.982789i	$0.559142\pi$
$978$	48.5531			1.55256
$979$	0.00996411	+	12.4781i	0.000318454	+	0.398801i
$980$	−75.6951			−2.41799
$981$	3.96503	+	12.2031i	0.126594	+	0.389616i
$982$	14.5689	+	10.5849i	0.464911	+	0.337778i
$983$	44.2906	−	32.1790i	1.41265	−	1.02635i	0.419720	−	0.907654i	$-0.362128\pi$
$983$	44.2906	−	32.1790i	1.41265	−	1.02635i	0.992930	−	0.118697i	$-0.0378718\pi$
$984$	13.7165	−	42.2151i	0.437266	−	1.34577i
$985$	17.2159	−	52.9850i	0.548543	−	1.68824i
$986$	−28.7443	+	20.8840i	−0.915407	+	0.665082i
$987$	−0.129158	−	0.0938387i	−0.00411114	−	0.00298692i
$988$	−7.52248	−	23.1518i	−0.239322	−	0.736557i
$989$	26.2713			0.835379
$990$	39.8385	−	12.9795i	1.26615	−	0.412516i
$991$	−9.45835			−0.300454			−0.150227	−	0.988652i	$-0.548001\pi$
$991$	−9.45835			−0.300454			−0.150227	+	0.988652i	$0.548001\pi$
$992$	−5.80257	−	17.8585i	−0.184232	−	0.567007i
$993$	13.2593	+	9.63346i	0.420772	+	0.305708i
$994$	−30.0447	+	21.8288i	−0.952960	+	0.692366i
$995$	28.2172	−	86.8435i	0.894544	−	2.75312i
$996$	−27.1408	+	83.5307i	−0.859988	+	2.64677i
$997$	2.90408	−	2.10994i	0.0919732	−	0.0668224i	−0.540848	−	0.841120i	$-0.681897\pi$
$997$	2.90408	−	2.10994i	0.0919732	−	0.0668224i	0.632821	+	0.774298i	$0.281897\pi$
$998$	20.2685	+	14.7259i	0.641589	+	0.466142i
$999$	−13.3719	−	41.1546i	−0.423069	−	1.30207i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.2.h.c.27.1	✓	28
11.3	even	5		1573.2.a.s.1.1		14
11.8	odd	10		1573.2.a.r.1.14		14
11.9	even	5	inner	143.2.h.c.53.1	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.2.h.c.27.1	✓	28	1.1	even	1	trivial
143.2.h.c.53.1	yes	28	11.9	even	5	inner
1573.2.a.r.1.14		14	11.8	odd	10
1573.2.a.s.1.1		14	11.3	even	5

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:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	143.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.778372 - 2.39558i) q^{2} +(1.03159 + 0.749493i) q^{3} +(-3.51492 + 2.55374i) q^{4} +(1.12792 - 3.47137i) q^{5} +(0.992512 - 3.05464i) q^{6} +(-1.20723 + 0.877107i) q^{7} +(4.77800 + 3.47142i) q^{8} +(-0.424616 - 1.30683i) q^{9} +O(q^{10})\)	\(q+(-0.778372 - 2.39558i) q^{2} +(1.03159 + 0.749493i) q^{3} +(-3.51492 + 2.55374i) q^{4} +(1.12792 - 3.47137i) q^{5} +(0.992512 - 3.05464i) q^{6} +(-1.20723 + 0.877107i) q^{7} +(4.77800 + 3.47142i) q^{8} +(-0.424616 - 1.30683i) q^{9} -9.19388 q^{10} +(-0.00264842 - 3.31662i) q^{11} -5.53996 q^{12} +(0.309017 + 0.951057i) q^{13} +(3.04086 + 2.20932i) q^{14} +(3.76531 - 2.73566i) q^{15} +(1.91185 - 5.88408i) q^{16} +(-1.27792 + 3.93305i) q^{17} +(-2.80012 + 2.03441i) q^{18} +(4.53292 + 3.29336i) q^{19} +(4.90043 + 15.0820i) q^{20} -1.90275 q^{21} +(-7.94319 + 2.58791i) q^{22} +5.79470 q^{23} +(2.32712 + 7.16215i) q^{24} +(-6.73311 - 4.89189i) q^{25} +(2.03780 - 1.48055i) q^{26} +(1.72353 - 5.30447i) q^{27} +(2.00343 - 6.16593i) q^{28} +(-2.75946 + 2.00487i) q^{29} +(-9.48430 - 6.89075i) q^{30} +(1.53830 + 4.73440i) q^{31} -3.77207 q^{32} +(2.48305 - 3.42337i) q^{33} +10.4166 q^{34} +(1.68310 + 5.18006i) q^{35} +(4.82981 + 3.50906i) q^{36} +(6.27673 - 4.56031i) q^{37} +(4.36122 - 13.4225i) q^{38} +(-0.394032 + 1.21270i) q^{39} +(17.4398 - 12.6707i) q^{40} +(-4.76850 - 3.46452i) q^{41} +(1.48105 + 4.55821i) q^{42} +4.53367 q^{43} +(8.47910 + 11.6509i) q^{44} -5.01543 q^{45} +(-4.51044 - 13.8817i) q^{46} +(0.0678795 + 0.0493173i) q^{47} +(6.38232 - 4.63703i) q^{48} +(-1.47502 + 4.53965i) q^{49} +(-6.47806 + 19.9374i) q^{50} +(-4.26608 + 3.09949i) q^{51} +(-3.51492 - 2.55374i) q^{52} +(2.02033 + 6.21793i) q^{53} -14.0489 q^{54} +(-11.5162 - 3.73168i) q^{55} -8.81298 q^{56} +(2.20776 + 6.79478i) q^{57} +(6.95072 + 5.04999i) q^{58} +(-5.31074 + 3.85848i) q^{59} +(-6.24860 + 19.2312i) q^{60} +(0.0420253 - 0.129341i) q^{61} +(10.1443 - 7.37025i) q^{62} +(1.65885 + 1.20522i) q^{63} +(-0.887634 - 2.73186i) q^{64} +3.65001 q^{65} +(-10.1337 - 3.28370i) q^{66} +3.41442 q^{67} +(-5.55218 - 17.0878i) q^{68} +(5.97775 + 4.34309i) q^{69} +(11.0992 - 8.06402i) q^{70} +(-3.05319 + 9.39675i) q^{71} +(2.50776 - 7.71808i) q^{72} +(-9.97073 + 7.24416i) q^{73} +(-15.8102 - 11.4868i) q^{74} +(-3.27936 - 10.0928i) q^{75} -24.3432 q^{76} +(2.91223 + 4.00162i) q^{77} +3.21184 q^{78} +(1.08866 + 3.35054i) q^{79} +(-18.2694 - 13.2735i) q^{80} +(2.41866 - 1.75726i) q^{81} +(-4.58787 + 14.1200i) q^{82} +(4.89909 - 15.0779i) q^{83} +(6.68803 - 4.85914i) q^{84} +(12.2117 + 8.87229i) q^{85} +(-3.52889 - 10.8608i) q^{86} -4.34926 q^{87} +(11.5007 - 15.8560i) q^{88} -3.76228 q^{89} +(3.90387 + 12.0149i) q^{90} +(-1.20723 - 0.877107i) q^{91} +(-20.3679 + 14.7982i) q^{92} +(-1.96151 + 6.03689i) q^{93} +(0.0653082 - 0.200998i) q^{94} +(16.5452 - 12.0208i) q^{95} +(-3.89122 - 2.82714i) q^{96} +(-5.17046 - 15.9130i) q^{97} +12.0232 q^{98} +(-4.33315 + 1.41175i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 3 q^{2} - 7 q^{3} - 5 q^{4} - 7 q^{5} - 4 q^{6} - 7 q^{7} + q^{8} - 6 q^{9}+O(q^{10}) \) 28 * q - 3 * q^2 - 7 * q^3 - 5 * q^4 - 7 * q^5 - 4 * q^6 - 7 * q^7 + q^8 - 6 * q^9	\( 28 q - 3 q^{2} - 7 q^{3} - 5 q^{4} - 7 q^{5} - 4 q^{6} - 7 q^{7} + q^{8} - 6 q^{9} - 24 q^{10} - 5 q^{11} + 38 q^{12} - 7 q^{13} - 7 q^{14} + 8 q^{15} - 19 q^{16} + 7 q^{17} + 5 q^{18} + 5 q^{19} + 9 q^{20} - 33 q^{22} + 50 q^{23} - 7 q^{24} - 34 q^{25} + 2 q^{26} - 19 q^{27} + 30 q^{28} + 8 q^{29} - 6 q^{30} + 17 q^{31} + 24 q^{32} - 26 q^{33} + 26 q^{34} - 4 q^{35} - 27 q^{36} + 17 q^{37} - 51 q^{38} - 2 q^{39} + 39 q^{40} - 23 q^{41} + 80 q^{42} - 32 q^{43} + q^{44} + 78 q^{45} - 31 q^{46} - 29 q^{47} + 52 q^{48} - 52 q^{49} + 6 q^{50} + 7 q^{51} - 5 q^{52} - 16 q^{53} - 42 q^{54} - 5 q^{55} + 34 q^{56} - 7 q^{57} - 13 q^{58} - 11 q^{59} - 74 q^{60} + 37 q^{61} + 23 q^{62} - 38 q^{63} + 67 q^{64} + 18 q^{65} - 65 q^{66} + 58 q^{67} - 68 q^{68} - 28 q^{69} + 44 q^{70} - 47 q^{71} + 10 q^{72} + 44 q^{73} - 46 q^{74} + 17 q^{75} + 6 q^{76} + 21 q^{77} + 26 q^{78} + 51 q^{79} + 23 q^{80} - 14 q^{81} - 47 q^{82} - 13 q^{83} - 107 q^{84} - q^{85} + 38 q^{86} - 12 q^{87} + 9 q^{88} + 38 q^{89} - 74 q^{90} - 7 q^{91} - 41 q^{92} - 51 q^{93} - 5 q^{94} + 47 q^{95} - 71 q^{96} - 20 q^{97} + 162 q^{98} + 60 q^{99}+O(q^{100}) \) 28 * q - 3 * q^2 - 7 * q^3 - 5 * q^4 - 7 * q^5 - 4 * q^6 - 7 * q^7 + q^8 - 6 * q^9 - 24 * q^10 - 5 * q^11 + 38 * q^12 - 7 * q^13 - 7 * q^14 + 8 * q^15 - 19 * q^16 + 7 * q^17 + 5 * q^18 + 5 * q^19 + 9 * q^20 - 33 * q^22 + 50 * q^23 - 7 * q^24 - 34 * q^25 + 2 * q^26 - 19 * q^27 + 30 * q^28 + 8 * q^29 - 6 * q^30 + 17 * q^31 + 24 * q^32 - 26 * q^33 + 26 * q^34 - 4 * q^35 - 27 * q^36 + 17 * q^37 - 51 * q^38 - 2 * q^39 + 39 * q^40 - 23 * q^41 + 80 * q^42 - 32 * q^43 + q^44 + 78 * q^45 - 31 * q^46 - 29 * q^47 + 52 * q^48 - 52 * q^49 + 6 * q^50 + 7 * q^51 - 5 * q^52 - 16 * q^53 - 42 * q^54 - 5 * q^55 + 34 * q^56 - 7 * q^57 - 13 * q^58 - 11 * q^59 - 74 * q^60 + 37 * q^61 + 23 * q^62 - 38 * q^63 + 67 * q^64 + 18 * q^65 - 65 * q^66 + 58 * q^67 - 68 * q^68 - 28 * q^69 + 44 * q^70 - 47 * q^71 + 10 * q^72 + 44 * q^73 - 46 * q^74 + 17 * q^75 + 6 * q^76 + 21 * q^77 + 26 * q^78 + 51 * q^79 + 23 * q^80 - 14 * q^81 - 47 * q^82 - 13 * q^83 - 107 * q^84 - q^85 + 38 * q^86 - 12 * q^87 + 9 * q^88 + 38 * q^89 - 74 * q^90 - 7 * q^91 - 41 * q^92 - 51 * q^93 - 5 * q^94 + 47 * q^95 - 71 * q^96 - 20 * q^97 + 162 * q^98 + 60 * q^99

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