LMFDB - Embedded newform 547.2.c.a.40.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [547,2,Mod(40,547)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(547, 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("547.40");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 547 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	547.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:	$4.36781699056$
Analytic rank:	$0$
Dimension:	$90$
Relative dimension:	$45$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			40.9
Character	$\chi$	$=$	547.40
Dual form			547.2.c.a.506.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.958903 - 1.66087i) q^{2} -2.13159 q^{3} +(-0.838990 + 1.45317i) q^{4} +(0.601954 - 1.04261i) q^{5} +(2.04398 + 3.54028i) q^{6} +(0.787639 + 1.36423i) q^{7} -0.617573 q^{8} +1.54366 q^{9} +O(q^{10})$	\(q+(-0.958903 - 1.66087i) q^{2} -2.13159 q^{3} +(-0.838990 + 1.45317i) q^{4} +(0.601954 - 1.04261i) q^{5} +(2.04398 + 3.54028i) q^{6} +(0.787639 + 1.36423i) q^{7} -0.617573 q^{8} +1.54366 q^{9} -2.30886 q^{10} +(0.652725 + 1.13055i) q^{11} +(1.78838 - 3.09756i) q^{12} +(0.727380 + 1.25986i) q^{13} +(1.51054 - 2.61633i) q^{14} +(-1.28312 + 2.22242i) q^{15} +(2.27017 + 3.93205i) q^{16} +(3.07104 + 5.31919i) q^{17} +(-1.48022 - 2.56382i) q^{18} +(3.81409 - 6.60620i) q^{19} +(1.01007 + 1.74949i) q^{20} +(-1.67892 - 2.90798i) q^{21} +(1.25180 - 2.16818i) q^{22} +(-0.962776 + 1.66758i) q^{23} +1.31641 q^{24} +(1.77530 + 3.07492i) q^{25} +(1.39497 - 2.41617i) q^{26} +3.10431 q^{27} -2.64328 q^{28} -9.18870 q^{29} +4.92153 q^{30} +6.89434 q^{31} +(3.73618 - 6.47125i) q^{32} +(-1.39134 - 2.40987i) q^{33} +(5.88966 - 10.2012i) q^{34} +1.89649 q^{35} +(-1.29511 + 2.24320i) q^{36} +(-2.91336 - 5.04608i) q^{37} -14.6294 q^{38} +(-1.55047 - 2.68550i) q^{39} +(-0.371751 + 0.643891i) q^{40} +(-2.73595 - 4.73881i) q^{41} +(-3.21984 + 5.57693i) q^{42} +(4.10040 + 7.10211i) q^{43} -2.19052 q^{44} +(0.929212 - 1.60944i) q^{45} +3.69284 q^{46} +(5.76095 - 9.97826i) q^{47} +(-4.83907 - 8.38151i) q^{48} +(2.25925 - 3.91313i) q^{49} +(3.40469 - 5.89709i) q^{50} +(-6.54618 - 11.3383i) q^{51} -2.44106 q^{52} +(-2.19809 - 3.80720i) q^{53} +(-2.97674 - 5.15586i) q^{54} +1.57164 q^{55} +(-0.486425 - 0.842513i) q^{56} +(-8.13007 + 14.0817i) q^{57} +(8.81107 + 15.2612i) q^{58} +(-0.582111 - 1.00825i) q^{59} +(-2.15304 - 3.72918i) q^{60} +(-3.58568 - 6.21058i) q^{61} +(-6.61100 - 11.4506i) q^{62} +(1.21585 + 2.10591i) q^{63} -5.24983 q^{64} +1.75140 q^{65} +(-2.66832 + 4.62166i) q^{66} +(2.68657 + 4.65328i) q^{67} -10.3063 q^{68} +(2.05224 - 3.55459i) q^{69} +(-1.81855 - 3.14982i) q^{70} +(6.83368 + 11.8363i) q^{71} -0.953323 q^{72} +(4.77755 + 8.27495i) q^{73} +(-5.58725 + 9.67740i) q^{74} +(-3.78421 - 6.55445i) q^{75} +(6.39997 + 11.0851i) q^{76} +(-1.02822 + 1.78094i) q^{77} +(-2.97351 + 5.15027i) q^{78} +12.3394 q^{79} +5.46615 q^{80} -11.2481 q^{81} +(-5.24703 + 9.08812i) q^{82} +(6.42156 + 11.1225i) q^{83} +5.63439 q^{84} +7.39449 q^{85} +(7.86378 - 13.6205i) q^{86} +19.5865 q^{87} +(-0.403106 - 0.698199i) q^{88} +8.80502 q^{89} -3.56410 q^{90} +(-1.14583 + 1.98463i) q^{91} +(-1.61552 - 2.79816i) q^{92} -14.6959 q^{93} -22.0968 q^{94} +(-4.59181 - 7.95325i) q^{95} +(-7.96398 + 13.7940i) q^{96} +(-9.69705 + 16.7958i) q^{97} -8.66560 q^{98} +(1.00759 + 1.74519i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 90 q - q^{2} - 4 q^{3} - 47 q^{4} + q^{5} - 3 q^{6} + 2 q^{7} - 30 q^{8} + 82 q^{9}+O(q^{10}) $ 90 * q - q^2 - 4 * q^3 - 47 * q^4 + q^5 - 3 * q^6 + 2 * q^7 - 30 * q^8 + 82 * q^9	\( 90 q - q^{2} - 4 q^{3} - 47 q^{4} + q^{5} - 3 q^{6} + 2 q^{7} - 30 q^{8} + 82 q^{9} - 10 q^{10} + q^{11} + 4 q^{12} - 3 q^{13} + 2 q^{14} - 7 q^{15} - 39 q^{16} - 4 q^{17} - 11 q^{18} - 2 q^{19} + 25 q^{20} - 27 q^{21} - 7 q^{22} + q^{23} + 32 q^{24} - 40 q^{25} - 10 q^{26} - 34 q^{27} - 28 q^{28} + 26 q^{29} - 40 q^{30} - 24 q^{31} + 19 q^{32} + q^{33} - 6 q^{34} - 8 q^{35} - 36 q^{36} - 10 q^{37} + 24 q^{38} + 22 q^{39} + 20 q^{40} + 3 q^{41} + 38 q^{42} - 12 q^{43} - 30 q^{44} - 2 q^{45} - 40 q^{46} + 32 q^{47} + 14 q^{48} - 43 q^{49} + 14 q^{50} + 13 q^{51} + 46 q^{52} + 9 q^{53} - 8 q^{54} + 4 q^{55} - 8 q^{56} - 8 q^{57} + 4 q^{58} + 22 q^{59} - 2 q^{60} - 12 q^{61} + 11 q^{62} + 8 q^{63} + 22 q^{64} + 18 q^{65} + 12 q^{66} - 22 q^{67} + 6 q^{68} - q^{69} - 6 q^{70} - 4 q^{71} - 140 q^{72} + 17 q^{73} + 17 q^{74} + 39 q^{75} + 84 q^{76} - 4 q^{77} + 33 q^{78} - 72 q^{79} - 40 q^{80} + 18 q^{81} - 9 q^{82} + 24 q^{83} + 114 q^{84} + 40 q^{85} - 72 q^{86} - 78 q^{87} - 22 q^{88} + 14 q^{89} + 96 q^{90} - 8 q^{92} - 76 q^{93} + 108 q^{94} - 11 q^{95} - 34 q^{96} - 74 q^{98} - 62 q^{99}+O(q^{100}) \) 90 * q - q^2 - 4 * q^3 - 47 * q^4 + q^5 - 3 * q^6 + 2 * q^7 - 30 * q^8 + 82 * q^9 - 10 * q^10 + q^11 + 4 * q^12 - 3 * q^13 + 2 * q^14 - 7 * q^15 - 39 * q^16 - 4 * q^17 - 11 * q^18 - 2 * q^19 + 25 * q^20 - 27 * q^21 - 7 * q^22 + q^23 + 32 * q^24 - 40 * q^25 - 10 * q^26 - 34 * q^27 - 28 * q^28 + 26 * q^29 - 40 * q^30 - 24 * q^31 + 19 * q^32 + q^33 - 6 * q^34 - 8 * q^35 - 36 * q^36 - 10 * q^37 + 24 * q^38 + 22 * q^39 + 20 * q^40 + 3 * q^41 + 38 * q^42 - 12 * q^43 - 30 * q^44 - 2 * q^45 - 40 * q^46 + 32 * q^47 + 14 * q^48 - 43 * q^49 + 14 * q^50 + 13 * q^51 + 46 * q^52 + 9 * q^53 - 8 * q^54 + 4 * q^55 - 8 * q^56 - 8 * q^57 + 4 * q^58 + 22 * q^59 - 2 * q^60 - 12 * q^61 + 11 * q^62 + 8 * q^63 + 22 * q^64 + 18 * q^65 + 12 * q^66 - 22 * q^67 + 6 * q^68 - q^69 - 6 * q^70 - 4 * q^71 - 140 * q^72 + 17 * q^73 + 17 * q^74 + 39 * q^75 + 84 * q^76 - 4 * q^77 + 33 * q^78 - 72 * q^79 - 40 * q^80 + 18 * q^81 - 9 * q^82 + 24 * q^83 + 114 * q^84 + 40 * q^85 - 72 * q^86 - 78 * q^87 - 22 * q^88 + 14 * q^89 + 96 * q^90 - 8 * q^92 - 76 * q^93 + 108 * q^94 - 11 * q^95 - 34 * q^96 - 74 * q^98 - 62 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/547\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.958903	−	1.66087i	−0.678047	−	1.17441i	−0.975568	−	0.219696i	$-0.929493\pi$
$2$	−0.958903	−	1.66087i	−0.678047	−	1.17441i	0.297522	−	0.954715i	$-0.403840\pi$
$3$	−2.13159			−1.23067			−0.615336	−	0.788265i	$-0.710980\pi$
$3$	−2.13159			−1.23067			−0.615336	+	0.788265i	$0.710980\pi$
$4$	−0.838990	+	1.45317i	−0.419495	+	0.726586i
$5$	0.601954	−	1.04261i	0.269202	−	0.466271i	−0.699454	−	0.714678i	$-0.746573\pi$
$5$	0.601954	−	1.04261i	0.269202	−	0.466271i	0.968656	+	0.248406i	$0.0799068\pi$
$6$	2.04398	+	3.54028i	0.834453	+	1.44532i
$7$	0.787639	+	1.36423i	0.297700	+	0.515631i	0.975609	−	0.219514i	$-0.0704473\pi$
$7$	0.787639	+	1.36423i	0.297700	+	0.515631i	−0.677910	+	0.735145i	$0.737114\pi$
$8$	−0.617573			−0.218345
$9$	1.54366			0.514553
$10$	−2.30886			−0.730126
$11$	0.652725	+	1.13055i	0.196804	+	0.340874i	0.947490	−	0.319784i	$-0.103610\pi$
$11$	0.652725	+	1.13055i	0.196804	+	0.340874i	−0.750686	+	0.660659i	$0.770277\pi$
$12$	1.78838	−	3.09756i	0.516260	−	0.894189i
$13$	0.727380	+	1.25986i	0.201739	+	0.349422i	0.949089	−	0.315009i	$-0.102007\pi$
$13$	0.727380	+	1.25986i	0.201739	+	0.349422i	−0.747350	+	0.664431i	$0.768674\pi$
$14$	1.51054	−	2.61633i	0.403709	−	0.699244i
$15$	−1.28312	+	2.22242i	−0.331299	+	0.573827i
$16$	2.27017	+	3.93205i	0.567543	+	0.983013i
$17$	3.07104	+	5.31919i	0.744836	+	1.29009i	0.950271	+	0.311423i	$0.100806\pi$
$17$	3.07104	+	5.31919i	0.744836	+	1.29009i	−0.205435	+	0.978671i	$0.565861\pi$
$18$	−1.48022	−	2.56382i	−0.348891	−	0.604297i
$19$	3.81409	−	6.60620i	0.875013	−	1.51557i	0.0182633	−	0.999833i	$-0.494186\pi$
$19$	3.81409	−	6.60620i	0.875013	−	1.51557i	0.856749	−	0.515733i	$-0.172480\pi$
$20$	1.01007	+	1.74949i	0.225858	+	0.391197i
$21$	−1.67892	−	2.90798i	−0.366371	−	0.634573i
$22$	1.25180	−	2.16818i	0.266885	−	0.462258i
$23$	−0.962776	+	1.66758i	−0.200753	+	0.347714i	−0.948771	−	0.315964i	$-0.897672\pi$
$23$	−0.962776	+	1.66758i	−0.200753	+	0.347714i	0.748018	+	0.663678i	$0.231005\pi$
$24$	1.31641			0.268711
$25$	1.77530	+	3.07492i	0.355061	+	0.614983i
$26$	1.39497	−	2.41617i	0.273577	−	0.473849i
$27$	3.10431			0.597426
$28$	−2.64328			−0.499534
$29$	−9.18870			−1.70630			−0.853150	−	0.521666i	$-0.825311\pi$
$29$	−9.18870			−1.70630			−0.853150	+	0.521666i	$0.825311\pi$
$30$	4.92153			0.898545
$31$	6.89434			1.23826			0.619130	−	0.785289i	$-0.287486\pi$
$31$	6.89434			1.23826			0.619130	+	0.785289i	$0.287486\pi$
$32$	3.73618	−	6.47125i	0.660469	−	1.14397i
$33$	−1.39134	−	2.40987i	−0.242201	−	0.419505i
$34$	5.88966	−	10.2012i	1.01007	−	1.74949i
$35$	1.89649			0.320565
$36$	−1.29511	+	2.24320i	−0.215852	+	0.373867i
$37$	−2.91336	−	5.04608i	−0.478953	−	0.829570i	0.520756	−	0.853706i	$-0.325650\pi$
$37$	−2.91336	−	5.04608i	−0.478953	−	0.829570i	−0.999709	+	0.0241352i	$0.992317\pi$
$38$	−14.6294			−2.37320
$39$	−1.55047	−	2.68550i	−0.248274	−	0.430024i
$40$	−0.371751	+	0.643891i	−0.0587789	+	0.101808i
$41$	−2.73595	−	4.73881i	−0.427284	−	0.740078i	0.569347	−	0.822098i	$-0.307196\pi$
$41$	−2.73595	−	4.73881i	−0.427284	−	0.740078i	−0.996631	+	0.0820197i	$0.973863\pi$
$42$	−3.21984	+	5.57693i	−0.496833	+	0.860540i
$43$	4.10040	+	7.10211i	0.625306	+	1.08306i	0.988482	+	0.151341i	$0.0483590\pi$
$43$	4.10040	+	7.10211i	0.625306	+	1.08306i	−0.363176	+	0.931721i	$0.618308\pi$
$44$	−2.19052			−0.330233
$45$	0.929212	−	1.60944i	0.138519	−	0.239921i
$46$	3.69284			0.544479
$47$	5.76095	−	9.97826i	0.840321	−	1.45548i	−0.0493027	−	0.998784i	$-0.515700\pi$
$47$	5.76095	−	9.97826i	0.840321	−	1.45548i	0.889624	−	0.456695i	$-0.150967\pi$
$48$	−4.83907	−	8.38151i	−0.698459	−	1.20977i
$49$	2.25925	−	3.91313i	0.322750	−	0.559019i
$50$	3.40469	−	5.89709i	0.481496	−	0.833975i
$51$	−6.54618	−	11.3383i	−0.916649	−	1.58768i
$52$	−2.44106			−0.338514
$53$	−2.19809	−	3.80720i	−0.301931	−	0.522959i	0.674642	−	0.738145i	$-0.264298\pi$
$53$	−2.19809	−	3.80720i	−0.301931	−	0.522959i	−0.976573	+	0.215185i	$0.930964\pi$
$54$	−2.97674	−	5.15586i	−0.405082	−	0.701623i
$55$	1.57164			0.211920
$56$	−0.486425	−	0.842513i	−0.0650013	−	0.112586i
$57$	−8.13007	+	14.0817i	−1.07685	+	1.86516i
$58$	8.81107	+	15.2612i	1.15695	+	2.00390i
$59$	−0.582111	−	1.00825i	−0.0757844	−	0.131262i	0.825643	−	0.564193i	$-0.190813\pi$
$59$	−0.582111	−	1.00825i	−0.0757844	−	0.131262i	−0.901427	+	0.432931i	$0.857479\pi$
$60$	−2.15304	−	3.72918i	−0.277957	−	0.481435i
$61$	−3.58568	−	6.21058i	−0.459099	−	0.795184i	0.539814	−	0.841784i	$-0.318495\pi$
$61$	−3.58568	−	6.21058i	−0.459099	−	0.795184i	−0.998914	+	0.0466006i	$0.985161\pi$
$62$	−6.61100	−	11.4506i	−0.839598	−	1.45423i
$63$	1.21585	+	2.10591i	0.153182	+	0.265320i
$64$	−5.24983			−0.656229
$65$	1.75140			0.217234
$66$	−2.66832	+	4.62166i	−0.328447	+	0.568888i
$67$	2.68657	+	4.65328i	0.328217	+	0.568489i	0.982158	−	0.188057i	$-0.0602189\pi$
$67$	2.68657	+	4.65328i	0.328217	+	0.568489i	−0.653941	+	0.756545i	$0.726886\pi$
$68$	−10.3063			−1.24982
$69$	2.05224	−	3.55459i	0.247061	−	0.427922i
$70$	−1.81855	−	3.14982i	−0.217358	−	0.376475i
$71$	6.83368	+	11.8363i	0.811008	+	1.40471i	0.912159	+	0.409836i	$0.134414\pi$
$71$	6.83368	+	11.8363i	0.811008	+	1.40471i	−0.101151	+	0.994871i	$0.532252\pi$
$72$	−0.953323			−0.112350
$73$	4.77755	+	8.27495i	0.559169	+	0.968510i	0.997566	+	0.0697282i	$0.0222132\pi$
$73$	4.77755	+	8.27495i	0.559169	+	0.968510i	−0.438397	+	0.898782i	$0.644453\pi$
$74$	−5.58725	+	9.67740i	−0.649505	+	1.12497i
$75$	−3.78421	−	6.55445i	−0.436963	−	0.756843i
$76$	6.39997	+	11.0851i	0.734127	+	1.27154i
$77$	−1.02822	+	1.78094i	−0.117177	+	0.202956i
$78$	−2.97351	+	5.15027i	−0.336683	+	0.583153i
$79$	12.3394			1.38829			0.694145	−	0.719835i	$-0.255783\pi$
$79$	12.3394			1.38829			0.694145	+	0.719835i	$0.255783\pi$
$80$	5.46615			0.611135
$81$	−11.2481			−1.24979
$82$	−5.24703	+	9.08812i	−0.579437	+	1.00361i
$83$	6.42156	+	11.1225i	0.704857	+	1.22085i	0.966743	+	0.255750i	$0.0823223\pi$
$83$	6.42156	+	11.1225i	0.704857	+	1.22085i	−0.261886	+	0.965099i	$0.584344\pi$
$84$	5.63439			0.614762
$85$	7.39449			0.802045
$86$	7.86378	−	13.6205i	0.847973	−	1.46873i
$87$	19.5865			2.09989
$88$	−0.403106	−	0.698199i	−0.0429712	−	0.0744283i
$89$	8.80502			0.933330			0.466665	−	0.884434i	$-0.345455\pi$
$89$	8.80502			0.933330			0.466665	+	0.884434i	$0.345455\pi$
$90$	−3.56410			−0.375689
$91$	−1.14583	+	1.98463i	−0.120115	+	0.208046i
$92$	−1.61552	−	2.79816i	−0.168429	−	0.291728i
$93$	−14.6959			−1.52389
$94$	−22.0968			−2.27911
$95$	−4.59181	−	7.95325i	−0.471110	−	0.815986i
$96$	−7.96398	+	13.7940i	−0.812820	+	1.40785i
$97$	−9.69705	+	16.7958i	−0.984586	+	1.70535i	−0.340826	+	0.940126i	$0.610707\pi$
$97$	−9.69705	+	16.7958i	−0.984586	+	1.70535i	−0.643760	+	0.765227i	$0.722627\pi$
$98$	−8.66560			−0.875358
$99$	1.00759	+	1.74519i	0.101266	+	0.175398i
$100$	−5.95785			−0.595785
$101$	−2.87603			−0.286176			−0.143088	−	0.989710i	$-0.545703\pi$
$101$	−2.87603			−0.286176			−0.143088	+	0.989710i	$0.545703\pi$
$102$	−12.5543	+	21.7447i	−1.24306	+	2.15305i
$103$	2.81046			0.276923			0.138462	−	0.990368i	$-0.455784\pi$
$103$	2.81046			0.276923			0.138462	+	0.990368i	$0.455784\pi$
$104$	−0.449211	−	0.778056i	−0.0440487	−	0.0762946i
$105$	−4.04253			−0.394511
$106$	−4.21551	+	7.30147i	−0.409446	+	0.709182i
$107$	5.29199			0.511596			0.255798	−	0.966730i	$-0.417662\pi$
$107$	5.29199			0.511596			0.255798	+	0.966730i	$0.417662\pi$
$108$	−2.60449	+	4.51110i	−0.250617	+	0.434081i
$109$	7.58571	−	13.1388i	0.726579	−	1.25847i	−0.231742	−	0.972777i	$-0.574442\pi$
$109$	7.58571	−	13.1388i	0.726579	−	1.25847i	0.958321	−	0.285694i	$-0.0922242\pi$
$110$	−1.50705	−	2.61029i	−0.143692	−	0.248881i
$111$	6.21007	+	10.7562i	0.589434	+	1.02093i
$112$	−3.57615	+	6.19408i	−0.337915	+	0.585286i
$113$	4.52023	−	7.82926i	0.425227	−	0.736515i	−0.571215	−	0.820801i	$-0.693528\pi$
$113$	4.52023	−	7.82926i	0.425227	−	0.736515i	0.996442	+	0.0842859i	$0.0268609\pi$
$114$	31.1838			2.92063
$115$	1.15909	+	2.00761i	0.108086	+	0.187210i
$116$	7.70923	−	13.3528i	0.715784	−	1.23977i
$117$	1.12283	+	1.94479i	0.103805	+	0.179796i
$118$	−1.11638	+	1.93362i	−0.102771	+	0.178004i
$119$	−4.83774	+	8.37921i	−0.443475	+	0.768121i
$120$	0.792418	−	1.37251i	0.0723376	−	0.125292i
$121$	4.64790	−	8.05040i	0.422536	−	0.731855i
$122$	−6.87664	+	11.9107i	−0.622582	+	1.07834i
$123$	5.83192	+	10.1012i	0.525847	+	0.910793i
$124$	−5.78428	+	10.0187i	−0.519443	+	0.899702i
$125$	10.2941			0.920736
$126$	2.33176	−	4.03873i	0.207730	−	0.359798i
$127$	3.33925	−	5.78375i	0.296310	−	0.513225i	−0.678979	−	0.734158i	$-0.737577\pi$
$127$	3.33925	−	5.78375i	0.296310	−	0.513225i	0.975289	+	0.220934i	$0.0709104\pi$
$128$	−2.43827	−	4.22321i	−0.215515	−	0.373283i
$129$	−8.74036	−	15.1388i	−0.769546	−	1.33289i
$130$	−1.67942	−	2.90884i	−0.147295	−	0.255122i
$131$	−10.8155			−0.944959			−0.472479	−	0.881342i	$-0.656641\pi$
$131$	−10.8155			−0.944959			−0.472479	+	0.881342i	$0.656641\pi$
$132$	4.66928			0.406408
$133$	12.0165			1.04196
$134$	5.15232	−	8.92409i	0.445093	−	0.770924i
$135$	1.86865	−	3.23660i	0.160828	−	0.278562i
$136$	−1.89659	−	3.28499i	−0.162631	−	0.281686i
$137$	5.89415	+	10.2090i	0.503572	+	0.872211i	0.999991	+	0.00412897i	$0.00131429\pi$
$137$	5.89415	+	10.2090i	0.503572	+	0.872211i	−0.496420	+	0.868083i	$0.665352\pi$
$138$	−7.87160			−0.670075
$139$	9.45103	+	16.3697i	0.801626	+	1.38846i	0.918545	+	0.395315i	$0.129365\pi$
$139$	9.45103	+	16.3697i	0.801626	+	1.38846i	−0.116919	+	0.993141i	$0.537302\pi$
$140$	−1.59113	+	2.75593i	−0.134475	+	0.232918i
$141$	−12.2800	+	21.2695i	−1.03416	+	1.79122i
$142$	13.1057	−	22.6997i	1.09980	−	1.90491i
$143$	−0.949558	+	1.64468i	−0.0794061	+	0.137535i
$144$	3.50437	+	6.06975i	0.292031	+	0.505813i
$145$	−5.53117	+	9.58027i	−0.459339	+	0.795598i
$146$	9.16240	−	15.8698i	0.758286	−	1.31339i
$147$	−4.81578	+	8.34118i	−0.397199	+	0.687969i
$148$	9.77710			0.803673
$149$	9.38536			0.768879			0.384439	−	0.923150i	$-0.374395\pi$
$149$	9.38536			0.768879			0.384439	+	0.923150i	$0.374395\pi$
$150$	−7.25739	+	12.5702i	−0.592563	+	1.02635i
$151$	−14.7172			−1.19767			−0.598834	−	0.800873i	$-0.704369\pi$
$151$	−14.7172			−1.19767			−0.598834	+	0.800873i	$0.704369\pi$
$152$	−2.35548	+	4.07981i	−0.191055	+	0.330917i
$153$	4.74064	+	8.21103i	0.383258	+	0.663822i
$154$	3.94387			0.317806
$155$	4.15007	−	7.18813i	0.333342	−	0.577365i
$156$	5.20333			0.416599
$157$	6.20550	+	10.7482i	0.495253	+	0.857803i	0.999985	−	0.00547305i	$-0.00174213\pi$
$157$	6.20550	+	10.7482i	0.495253	+	0.857803i	−0.504732	+	0.863276i	$0.668409\pi$
$158$	−11.8323	−	20.4941i	−0.941325	−	1.63042i
$159$	4.68542	+	8.11538i	0.371578	+	0.643591i
$160$	−4.49801	−	7.79078i	−0.355599	−	0.615915i
$161$	−3.03328			−0.239056
$162$	10.7858	+	18.6816i	0.847415	+	1.46777i
$163$	−0.294879	−	0.510746i	−0.0230967	−	0.0400047i	0.854246	−	0.519869i	$-0.174019\pi$
$163$	−0.294879	−	0.510746i	−0.0230967	−	0.0400047i	−0.877343	+	0.479864i	$0.840686\pi$
$164$	9.18175			0.716974
$165$	−3.35009			−0.260804
$166$	12.3153	−	21.3307i	0.955852	−	1.65559i
$167$	0.166304			0.0128690			0.00643448	−	0.999979i	$-0.497952\pi$
$167$	0.166304			0.0128690			0.00643448	+	0.999979i	$0.497952\pi$
$168$	1.03686	+	1.79589i	0.0799953	+	0.138556i
$169$	5.44184	−	9.42554i	0.418603	−	0.725041i
$170$	−7.09060	−	12.2813i	−0.543824	−	0.941931i
$171$	5.88766	−	10.1977i	0.450241	−	0.779840i
$172$	−13.7608			−1.04925
$173$	−14.7463			−1.12114			−0.560569	−	0.828107i	$-0.689418\pi$
$173$	−14.7463			−1.12114			−0.560569	+	0.828107i	$0.689418\pi$
$174$	−18.7816	−	32.5306i	−1.42383	−	2.46614i
$175$	−2.79660	+	4.84385i	−0.211403	+	0.366161i
$176$	−2.96360	+	5.13310i	−0.223389	+	0.386922i
$177$	1.24082	+	2.14916i	0.0932657	+	0.161541i
$178$	−8.44315	−	14.6240i	−0.632841	−	1.09611i
$179$	−3.07495			−0.229833			−0.114916	−	0.993375i	$-0.536660\pi$
$179$	−3.07495			−0.229833			−0.114916	+	0.993375i	$0.536660\pi$
$180$	1.55920	+	2.70061i	0.116216	+	0.201292i
$181$	−1.32211	+	2.28996i	−0.0982715	+	0.170211i	−0.910969	−	0.412474i	$-0.864665\pi$
$181$	−1.32211	+	2.28996i	−0.0982715	+	0.170211i	0.812698	+	0.582685i	$0.197998\pi$
$182$	4.39495			0.325775
$183$	7.64319	+	13.2384i	0.565001	+	0.978610i
$184$	0.594585	−	1.02985i	0.0438334	−	0.0759217i
$185$	−7.01482			−0.515740
$186$	14.0919	+	24.4079i	1.03327	+	1.78967i
$187$	−4.00909	+	6.94394i	−0.293173	+	0.507791i
$188$	9.66675	+	16.7433i	0.705020	+	1.22113i
$189$	2.44508	+	4.23500i	0.177853	+	0.308051i
$190$	−8.80620	+	15.2528i	−0.638869	+	1.10655i
$191$	10.2867	−	17.8172i	0.744322	−	1.28920i	−0.206188	−	0.978512i	$-0.566106\pi$
$191$	10.2867	−	17.8172i	0.744322	−	1.28920i	0.950511	−	0.310692i	$-0.100561\pi$
$192$	11.1905			0.807603
$193$	−11.2138	+	19.4229i	−0.807189	+	1.39809i	0.107615	+	0.994193i	$0.465679\pi$
$193$	−11.2138	+	19.4229i	−0.807189	+	1.39809i	−0.914803	+	0.403899i	$0.867655\pi$
$194$	37.1941			2.67038
$195$	−3.73325			−0.267344
$196$	3.79097	+	6.56616i	0.270784	+	0.469011i
$197$	−8.32038			−0.592803			−0.296401	−	0.955063i	$-0.595787\pi$
$197$	−8.32038			−0.592803			−0.296401	+	0.955063i	$0.595787\pi$
$198$	1.93235	−	3.34693i	0.137326	−	0.237856i
$199$	−4.17822	+	7.23689i	−0.296186	+	0.513009i	−0.975260	−	0.221060i	$-0.929048\pi$
$199$	−4.17822	+	7.23689i	−0.296186	+	0.513009i	0.679074	+	0.734070i	$0.262382\pi$
$200$	−1.09638	−	1.89899i	−0.0775258	−	0.134279i
$201$	−5.72666	−	9.91887i	−0.403927	−	0.699623i
$202$	2.75784	+	4.77672i	0.194041	+	0.336088i
$203$	−7.23738	−	12.5355i	−0.507965	−	0.879821i
$204$	21.9687			1.53812
$205$	−6.58767			−0.460103
$206$	−2.69496	−	4.66781i	−0.187767	−	0.325222i
$207$	−1.48620	+	2.57417i	−0.103298	+	0.178917i
$208$	−3.30256	+	5.72020i	−0.228991	+	0.396624i
$209$	9.95821			0.688824
$210$	3.87639	+	6.71411i	0.267497	+	0.463318i
$211$	8.75839	−	15.1700i	0.602952	−	1.04434i	−0.389419	−	0.921061i	$-0.627324\pi$
$211$	8.75839	−	15.1700i	0.602952	−	1.04434i	0.992371	−	0.123284i	$-0.0393425\pi$
$212$	7.37670			0.506634
$213$	−14.5666	−	25.2300i	−0.998085	−	1.72873i
$214$	−5.07450	−	8.78930i	−0.346886	−	0.600824i
$215$	9.87301			0.673334
$216$	−1.91714			−0.130445
$217$	5.43025	+	9.40547i	0.368629	+	0.638485i
$218$	−29.0958			−1.97062
$219$	−10.1838	−	17.6388i	−0.688154	−	1.19192i
$220$	−1.31859	+	2.28386i	−0.0888993	+	0.153978i
$221$	−4.46763	+	7.73815i	−0.300525	+	0.520525i
$222$	11.9097	−	20.6282i	0.799327	−	1.38448i
$223$	−5.31413	+	9.20434i	−0.355860	+	0.616368i	−0.987265	−	0.159085i	$-0.949146\pi$
$223$	−5.31413	+	9.20434i	−0.355860	+	0.616368i	0.631404	+	0.775454i	$0.282479\pi$
$224$	11.7710			0.786485
$225$	2.74047	+	4.74663i	0.182698	+	0.316442i
$226$	−17.3378			−1.15330
$227$	11.3726	−	19.6979i	0.754827	−	1.30740i	−0.190634	−	0.981661i	$-0.561054\pi$
$227$	11.3726	−	19.6979i	0.754827	−	1.30740i	0.945460	−	0.325737i	$-0.105612\pi$
$228$	−13.6421	−	23.6288i	−0.903469	−	1.56485i
$229$	−5.01668	+	8.68915i	−0.331512	+	0.574195i	−0.982808	−	0.184628i	$-0.940892\pi$
$229$	−5.01668	+	8.68915i	−0.331512	+	0.574195i	0.651297	+	0.758823i	$0.274225\pi$
$230$	2.22292	−	3.85020i	0.146575	−	0.253875i
$231$	2.19175	−	3.79622i	0.144206	−	0.249773i
$232$	5.67470			0.372562
$233$	−8.40854	+	14.5640i	−0.550862	+	0.954120i	0.447351	+	0.894358i	$0.352367\pi$
$233$	−8.40854	+	14.5640i	−0.550862	+	0.954120i	−0.998213	+	0.0597618i	$0.980966\pi$
$234$	2.15337	−	3.72974i	0.140770	−	0.243821i
$235$	−6.93565	−	12.0129i	−0.452432	−	0.783635i
$236$	1.95354			0.127165
$237$	−26.3025			−1.70853
$238$	18.5557			1.20279
$239$	0.606712	+	1.05086i	0.0392449	+	0.0679742i	0.884981	−	0.465628i	$-0.154171\pi$
$239$	0.606712	+	1.05086i	0.0392449	+	0.0679742i	−0.845736	+	0.533602i	$0.820838\pi$
$240$	−11.6516			−0.752106
$241$	−4.43866	+	7.68799i	−0.285919	+	0.495227i	−0.972832	−	0.231513i	$-0.925632\pi$
$241$	−4.43866	+	7.68799i	−0.285919	+	0.495227i	0.686912	+	0.726740i	$0.258966\pi$
$242$	−17.8275			−1.14600
$243$	14.6633			0.940654
$244$	12.0334			0.770359
$245$	−2.71993	−	4.71105i	−0.173770	−	0.300978i
$246$	11.1845	−	19.3721i	0.713097	−	1.23512i
$247$	11.0972			0.706097
$248$	−4.25776			−0.270368
$249$	−13.6881	−	23.7085i	−0.867448	−	1.50246i
$250$	−9.87108	−	17.0972i	−0.624302	−	1.08132i
$251$	−2.98829	−	5.17587i	−0.188619	−	0.326698i	0.756171	−	0.654374i	$-0.227068\pi$
$251$	−2.98829	−	5.17587i	−0.188619	−	0.326698i	−0.944790	+	0.327676i	$0.893734\pi$
$252$	−4.08033			−0.257037
$253$	−2.51371			−0.158036
$254$	−12.8081			−0.803649
$255$	−15.7620			−0.987054
$256$	−9.92597	+	17.1923i	−0.620373	+	1.07452i
$257$	6.68542			0.417025			0.208512	−	0.978020i	$-0.433138\pi$
$257$	6.68542			0.417025			0.208512	+	0.978020i	$0.433138\pi$
$258$	−16.7623	+	29.0332i	−1.04358	+	1.80753i
$259$	4.58935	−	7.94898i	0.285168	−	0.493926i
$260$	−1.46940	+	2.54508i	−0.0911285	+	0.157839i
$261$	−14.1842			−0.877982
$262$	10.3711	+	17.9632i	0.640726	+	1.10977i
$263$	−14.0043			−0.863542			−0.431771	−	0.901983i	$-0.642111\pi$
$263$	−14.0043			−0.863542			−0.431771	+	0.901983i	$0.642111\pi$
$264$	0.859254	+	1.48827i	0.0528834	+	0.0915968i
$265$	−5.29259			−0.325121
$266$	−11.5227	−	19.9579i	−0.706500	−	1.22369i
$267$	−18.7686			−1.14862
$268$	−9.01602			−0.550741
$269$	−2.70954	+	4.69307i	−0.165204	+	0.286141i	−0.936728	−	0.350059i	$-0.886161\pi$
$269$	−2.70954	+	4.69307i	−0.165204	+	0.286141i	0.771524	+	0.636200i	$0.219495\pi$
$270$	−7.16743			−0.436196
$271$	−3.72607	−	6.45374i	−0.226343	−	0.392037i	0.730379	−	0.683042i	$-0.239344\pi$
$271$	−3.72607	−	6.45374i	−0.226343	−	0.392037i	−0.956721	+	0.291005i	$0.906010\pi$
$272$	−13.9436	+	24.1510i	−0.845453	+	1.46437i
$273$	2.44243	−	4.23041i	0.147822	−	0.256036i
$274$	11.3038	−	19.5788i	0.682890	−	1.18280i
$275$	−2.31757	+	4.01415i	−0.139755	+	0.242062i
$276$	3.44362	+	5.96452i	0.207281	+	0.359022i
$277$	9.22237			0.554119			0.277059	−	0.960853i	$-0.410640\pi$
$277$	9.22237			0.554119			0.277059	+	0.960853i	$0.410640\pi$
$278$	18.1252	−	31.3938i	1.08708	−	1.88288i
$279$	10.6425			0.637150
$280$	−1.17122			−0.0699939
$281$	2.92714	+	5.06995i	0.174618	+	0.302448i	0.940029	−	0.341094i	$-0.110798\pi$
$281$	2.92714	+	5.06995i	0.174618	+	0.302448i	−0.765411	+	0.643542i	$0.777464\pi$
$282$	47.1012			2.80483
$283$	−12.4007	−	21.4786i	−0.737144	−	1.27677i	−0.953776	−	0.300517i	$-0.902841\pi$
$283$	−12.4007	−	21.4786i	−0.737144	−	1.27677i	0.216633	−	0.976253i	$-0.430493\pi$
$284$	−22.9335			−1.36086
$285$	9.78784	+	16.9530i	0.579782	+	1.00421i
$286$	3.64214			0.215364
$287$	4.30989	−	7.46495i	0.254405	−	0.440642i
$288$	5.76739	−	9.98940i	0.339846	−	0.588631i
$289$	−10.3626	+	17.9485i	−0.609562	+	1.05579i
$290$	21.2154			1.24581
$291$	20.6701	−	35.8017i	1.21170	−	2.09873i
$292$	−16.0332			−0.938275
$293$	2.19432			0.128193			0.0640967	−	0.997944i	$-0.479583\pi$
$293$	2.19432			0.128193			0.0640967	+	0.997944i	$0.479583\pi$
$294$	18.4715			1.07728
$295$	−1.40162			−0.0816052
$296$	1.79921	+	3.11632i	0.104577	+	0.181133i
$297$	2.02626	+	3.50959i	0.117576	+	0.203647i
$298$	−8.99965	−	15.5879i	−0.521336	−	0.902980i
$299$	−2.80122			−0.161999
$300$	12.6997			0.733215
$301$	−6.45928	+	11.1878i	−0.372307	+	0.644854i
$302$	14.1124	+	24.4433i	0.812075	+	1.40656i
$303$	6.13052			0.352189
$304$	34.6346			1.98643
$305$	−8.63366			−0.494362
$306$	9.09163	−	15.7472i	0.519734	−	0.900205i
$307$	1.50613			0.0859592			0.0429796	−	0.999076i	$-0.486315\pi$
$307$	1.50613			0.0859592			0.0429796	+	0.999076i	$0.486315\pi$
$308$	−1.72534	−	2.98837i	−0.0983103	−	0.170278i
$309$	−5.99075			−0.340802
$310$	−15.9181			−0.904085
$311$	−7.17236			−0.406707			−0.203354	−	0.979105i	$-0.565184\pi$
$311$	−7.17236			−0.406707			−0.203354	+	0.979105i	$0.565184\pi$
$312$	0.957531	+	1.65849i	0.0542095	+	0.0938937i
$313$	−2.10654	+	3.64863i	−0.119069	+	0.206233i	−0.919399	−	0.393327i	$-0.871324\pi$
$313$	−2.10654	+	3.64863i	−0.119069	+	0.206233i	0.800330	+	0.599559i	$0.204657\pi$
$314$	11.9009	−	20.6130i	0.671609	−	1.16326i
$315$	2.92753			0.164948
$316$	−10.3526	+	17.9313i	−0.582380	+	1.00871i
$317$	11.5725	−	20.0442i	0.649977	−	1.12579i	−0.333150	−	0.942874i	$-0.608112\pi$
$317$	11.5725	−	20.0442i	0.649977	−	1.12579i	0.983128	−	0.182920i	$-0.0585550\pi$
$318$	8.98572	−	15.5637i	0.503894	−	0.872770i
$319$	−5.99769	−	10.3883i	−0.335806	−	0.581634i
$320$	−3.16016	+	5.47355i	−0.176658	+	0.305981i
$321$	−11.2803			−0.629607
$322$	2.90862	+	5.03788i	0.162091	+	0.280750i
$323$	46.8529			2.60696
$324$	9.43703	−	16.3454i	0.524280	−	0.908079i
$325$	−2.58264	+	4.47327i	−0.143259	+	0.248132i
$326$	−0.565521	+	0.979512i	−0.0313213	+	0.0542501i
$327$	−16.1696	+	28.0065i	−0.894180	+	1.54877i
$328$	1.68965	+	2.92656i	0.0932954	+	0.161592i
$329$	18.1502			1.00065
$330$	3.21241	+	5.56405i	0.176837	+	0.306291i
$331$	6.81981			0.374851			0.187425	−	0.982279i	$-0.439986\pi$
$331$	6.81981			0.374851			0.187425	+	0.982279i	$0.439986\pi$
$332$	−21.5505			−1.18274
$333$	−4.49723	−	7.78943i	−0.246447	−	0.426858i
$334$	−0.159469	−	0.276209i	−0.00872576	−	0.0151135i
$335$	6.46877			0.353427
$336$	7.62288	−	13.2032i	0.415862	−	0.720294i
$337$	−16.2252	−	28.1028i	−0.883842	−	1.53086i	−0.847035	−	0.531537i	$-0.821615\pi$
$337$	−16.2252	−	28.1028i	−0.883842	−	1.53086i	−0.0368073	−	0.999322i	$-0.511719\pi$
$338$	−20.8728			−1.13533
$339$	−9.63525	+	16.6887i	−0.523315	+	0.906408i
$340$	−6.20390	+	10.7455i	−0.336454	+	0.582755i
$341$	4.50010	+	7.79441i	0.243694	+	0.422091i
$342$	−22.5828			−1.22114
$343$	18.1448			0.979729
$344$	−2.53230	−	4.38607i	−0.136532	−	0.236481i
$345$	−2.47071	−	4.27939i	−0.133018	−	0.230395i
$346$	14.1402	+	24.4916i	0.760184	+	1.31668i
$347$	−3.17748	−	5.50356i	−0.170576	−	0.295447i	0.768045	−	0.640396i	$-0.221230\pi$
$347$	−3.17748	−	5.50356i	−0.170576	−	0.295447i	−0.938621	+	0.344949i	$0.887896\pi$
$348$	−16.4329	+	28.4626i	−0.880895	+	1.52575i
$349$	−6.85880	+	11.8798i	−0.367143	+	0.635911i	−0.989118	−	0.147127i	$-0.952997\pi$
$349$	−6.85880	+	11.8798i	−0.367143	+	0.635911i	0.621974	+	0.783038i	$0.286331\pi$
$350$	10.7267			0.573364
$351$	2.25802	+	3.91100i	0.120524	+	0.208754i
$352$	9.75478			0.519932
$353$	20.3360			1.08238			0.541189	−	0.840901i	$-0.317975\pi$
$353$	20.3360			1.08238			0.541189	+	0.840901i	$0.317975\pi$
$354$	2.37965	−	4.12168i	0.126477	−	0.219065i
$355$	16.4542			0.873300
$356$	−7.38732	+	12.7952i	−0.391527	+	0.678145i
$357$	10.3121	−	17.8610i	0.545772	−	0.945305i
$358$	2.94858	+	5.10709i	0.155837	+	0.269918i
$359$	10.1482	+	17.5773i	0.535603	+	0.927692i	0.999134	+	0.0416111i	$0.0132490\pi$
$359$	10.1482	+	17.5773i	0.535603	+	0.927692i	−0.463531	+	0.886081i	$0.653418\pi$
$360$	−0.573856	+	0.993948i	−0.0302449	+	0.0523857i
$361$	−19.5946	−	33.9388i	−1.03129	−	1.78625i
$362$	5.07109			0.266531
$363$	−9.90740	+	17.1601i	−0.520004	+	0.900673i
$364$	−1.92267	−	3.33017i	−0.100775	−	0.174548i
$365$	11.5034			0.602118
$366$	14.6582	−	25.3887i	0.766194	−	1.32709i
$367$	1.82425	+	3.15970i	0.0952252	+	0.164935i	0.909703	−	0.415260i	$-0.136310\pi$
$367$	1.82425	+	3.15970i	0.0952252	+	0.164935i	−0.814477	+	0.580195i	$0.802976\pi$
$368$	−8.74267			−0.455743
$369$	−4.22338	−	7.31511i	−0.219860	−	0.380810i
$370$	6.72653	+	11.6507i	0.349696	+	0.605691i
$371$	3.46260	−	5.99740i	0.179769	−	0.311370i
$372$	12.3297	−	21.3556i	0.639264	−	1.10724i
$373$	−13.7550	−	23.8243i	−0.712205	−	1.23357i	−0.964028	−	0.265802i	$-0.914363\pi$
$373$	−13.7550	−	23.8243i	−0.712205	−	1.23357i	0.251823	−	0.967773i	$-0.418970\pi$
$374$	15.3773			0.795141
$375$	−21.9428			−1.13312
$376$	−3.55781	+	6.16231i	−0.183480	+	0.317797i
$377$	−6.68368	−	11.5765i	−0.344227	−	0.596219i
$378$	4.68919	−	8.12191i	0.241186	−	0.417746i
$379$	17.3930	+	30.1256i	0.893420	+	1.54745i	0.835747	+	0.549114i	$0.185035\pi$
$379$	17.3930	+	30.1256i	0.893420	+	1.54745i	0.0576731	+	0.998336i	$0.481632\pi$
$380$	15.4099			0.790513
$381$	−7.11789	+	12.3286i	−0.364661	+	0.631611i
$382$	−39.4559			−2.01874
$383$	−12.4035			−0.633787			−0.316893	−	0.948461i	$-0.602640\pi$
$383$	−12.4035			−0.633787			−0.316893	+	0.948461i	$0.602640\pi$
$384$	5.19739	+	9.00214i	0.265228	+	0.459389i
$385$	1.23789	+	2.14408i	0.0630885	+	0.109272i
$386$	43.0119			2.18925
$387$	6.32963	+	10.9632i	0.321753	+	0.557293i
$388$	−16.2715	−	28.1830i	−0.826058	−	1.43077i
$389$	13.2635	+	22.9731i	0.672488	+	1.16478i	0.977196	+	0.212338i	$0.0681078\pi$
$389$	13.2635	+	22.9731i	0.672488	+	1.16478i	−0.304708	+	0.952446i	$0.598559\pi$
$390$	3.57983	+	6.20044i	0.181272	+	0.313972i
$391$	−11.8269			−0.598112
$392$	−1.39525	+	2.41665i	−0.0704709	+	0.122059i
$393$	23.0543			1.16293
$394$	7.97844	+	13.8191i	0.401948	+	0.696194i
$395$	7.42774	−	12.8652i	0.373730	−	0.647319i
$396$	−3.38141			−0.169922
$397$	1.79593	−	3.11064i	0.0901351	−	0.156119i	−0.817433	−	0.576024i	$-0.804603\pi$
$397$	1.79593	−	3.11064i	0.0901351	−	0.156119i	0.907568	+	0.419906i	$0.137937\pi$
$398$	16.0260			0.803312
$399$	−25.6142			−1.28232
$400$	−8.06049	+	13.9612i	−0.403024	+	0.698059i
$401$	−14.2800	+	24.7336i	−0.713107	+	1.23514i	0.250578	+	0.968096i	$0.419379\pi$
$401$	−14.2800	+	24.7336i	−0.713107	+	1.23514i	−0.963685	+	0.267041i	$0.913954\pi$
$402$	−10.9826	+	19.0225i	−0.547763	+	0.948754i
$403$	5.01480	+	8.68589i	0.249805	+	0.432675i
$404$	2.41296	−	4.17937i	0.120049	−	0.207932i
$405$	−6.77083	+	11.7274i	−0.336445	+	0.582740i
$406$	−13.8799	+	24.0407i	−0.688848	+	1.19312i
$407$	3.80324	−	6.58740i	0.188520	−	0.326525i
$408$	4.04275	+	7.00225i	0.200146	+	0.346663i
$409$	21.9694			1.08632			0.543158	−	0.839631i	$-0.317228\pi$
$409$	21.9694			1.08632			0.543158	+	0.839631i	$0.317228\pi$
$410$	6.31693	+	10.9413i	0.311971	+	0.540350i
$411$	−12.5639	−	21.7613i	−0.619731	−	1.07341i
$412$	−2.35795	+	4.08409i	−0.116168	+	0.201209i
$413$	0.916987	−	1.58827i	0.0451220	−	0.0781536i
$414$	5.70048			0.280164
$415$	15.4619			0.758996
$416$	10.8705			0.532969
$417$	−20.1457	−	34.8934i	−0.986539	−	1.70873i
$418$	−9.54896	−	16.5393i	−0.467055	−	0.808963i
$419$	−13.4079	−	23.2232i	−0.655019	−	1.13453i	−0.981889	−	0.189457i	$-0.939327\pi$
$419$	−13.4079	−	23.2232i	−0.655019	−	1.13453i	0.326870	−	0.945069i	$-0.394006\pi$
$420$	3.39164	−	5.87450i	0.165495	−	0.286646i
$421$	7.55360	−	13.0832i	0.368140	−	0.637637i	−0.621135	−	0.783704i	$-0.713328\pi$
$421$	7.55360	−	13.0832i	0.368140	−	0.637637i	0.989275	+	0.146067i	$0.0466614\pi$
$422$	−33.5938			−1.63532
$423$	8.89295	−	15.4030i	0.432390	−	0.748921i
$424$	1.35748	+	2.35123i	0.0659251	+	0.114186i
$425$	−10.9041	+	18.8864i	−0.528924	+	0.916124i
$426$	−27.9359	+	48.3863i	−1.35350	+	2.34433i
$427$	5.64845	−	9.78340i	0.273348	−	0.473452i
$428$	−4.43992	+	7.69017i	−0.214612	+	0.371719i
$429$	2.02407	−	3.50578i	0.0977228	−	0.169261i
$430$	−9.46726	−	16.3978i	−0.456552	−	0.790771i
$431$	−2.19311	+	3.79858i	−0.105639	+	0.182971i	−0.913999	−	0.405717i	$-0.867022\pi$
$431$	−2.19311	+	3.79858i	−0.105639	+	0.182971i	0.808360	+	0.588688i	$0.200355\pi$
$432$	7.04733	+	12.2063i	0.339065	+	0.587277i
$433$	−23.2895			−1.11922			−0.559611	−	0.828755i	$-0.689050\pi$
$433$	−23.2895			−1.11922			−0.559611	+	0.828755i	$0.689050\pi$
$434$	10.4142	−	18.0379i	0.499896	−	0.865845i
$435$	11.7902	−	20.4212i	0.565295	−	0.979120i
$436$	12.7287	+	22.0467i	0.609592	+	1.05584i
$437$	7.34424	+	12.7206i	0.351322	+	0.608508i
$438$	−19.5305	+	33.8277i	−0.933201	+	1.61635i
$439$	−4.42398	+	7.66256i	−0.211145	+	0.365714i	−0.952073	−	0.305870i	$-0.901053\pi$
$439$	−4.42398	+	7.66256i	−0.211145	+	0.365714i	0.740928	+	0.671584i	$0.234386\pi$
$440$	−0.970603			−0.0462717
$441$	3.48751	−	6.04055i	0.166072	−	0.287645i
$442$	17.1361			0.815080
$443$	8.91828	+	15.4469i	0.423720	+	0.733905i	0.996300	−	0.0859438i	$-0.0273905\pi$
$443$	8.91828	+	15.4469i	0.423720	+	0.733905i	−0.572579	+	0.819849i	$0.694057\pi$
$444$	−20.8407			−0.989057
$445$	5.30021	−	9.18023i	0.251254	−	0.435185i
$446$	20.3829			0.965160
$447$	−20.0057			−0.946237
$448$	−4.13497	−	7.16199i	−0.195359	−	0.338372i
$449$	−22.0399			−1.04013			−0.520064	−	0.854128i	$-0.674092\pi$
$449$	−22.0399			−1.04013			−0.520064	+	0.854128i	$0.674092\pi$
$450$	5.25568	−	9.10311i	0.247755	−	0.429125i
$451$	3.57165	−	6.18628i	0.168182	−	0.291301i
$452$	7.58484	+	13.1373i	0.356761	+	0.617928i
$453$	31.3710			1.47394
$454$	−43.6209			−2.04723
$455$	1.37947	+	2.38931i	0.0646705	+	0.112013i
$456$	5.02091	−	8.69647i	0.235126	−	0.407250i
$457$	38.5571			1.80363			0.901813	−	0.432127i	$-0.142237\pi$
$457$	38.5571			1.80363			0.901813	+	0.432127i	$0.142237\pi$
$458$	19.2420			0.899122
$459$	9.53347	+	16.5125i	0.444984	+	0.770735i
$460$	−3.88987			−0.181366
$461$	14.9512	−	25.8963i	0.696349	−	1.20611i	−0.273375	−	0.961908i	$-0.588140\pi$
$461$	14.9512	−	25.8963i	0.696349	−	1.20611i	0.969724	−	0.244204i	$-0.0785267\pi$
$462$	−8.40669			−0.391115
$463$	−19.1110			−0.888163			−0.444082	−	0.895986i	$-0.646470\pi$
$463$	−19.1110			−0.888163			−0.444082	+	0.895986i	$0.646470\pi$
$464$	−20.8599	−	36.1305i	−0.968398	−	1.67731i
$465$	−8.84623	+	15.3221i	−0.410234	+	0.710546i
$466$	32.2519			1.49404
$467$	−17.5940			−0.814153			−0.407076	−	0.913394i	$-0.633452\pi$
$467$	−17.5940			−0.814153			−0.407076	+	0.913394i	$0.633452\pi$
$468$	−3.76816			−0.174183
$469$	−4.23210	+	7.33021i	−0.195420	+	0.338478i
$470$	−13.3012	+	23.0384i	−0.613540	+	1.06268i
$471$	−13.2276	−	22.9108i	−0.609494	−	1.05567i
$472$	0.359496	+	0.622666i	0.0165472	+	0.0286605i
$473$	−5.35287	+	9.27144i	−0.246125	+	0.426301i
$474$	25.2215	+	43.6849i	1.15846	+	2.00652i
$475$	27.0847			1.24273
$476$	−8.11763	−	14.0601i	−0.372071	−	0.644446i
$477$	−3.39310	−	5.87703i	−0.155359	−	0.269091i
$478$	1.16356	−	2.01534i	0.0532198	−	0.0921794i
$479$	−9.75365			−0.445655			−0.222828	−	0.974858i	$-0.571529\pi$
$479$	−9.75365			−0.445655			−0.222828	+	0.974858i	$0.571529\pi$
$480$	9.58789	+	16.6067i	0.437626	+	0.757990i
$481$	4.23823	−	7.34084i	0.193247	−	0.334713i
$482$	17.0250			0.775467
$483$	6.46570			0.294200
$484$	7.79908	+	13.5084i	0.354504	+	0.614018i
$485$	11.6743	+	20.2206i	0.530105	+	0.918169i
$486$	−14.0607	−	24.3539i	−0.637807	−	1.10471i
$487$	−10.8224	−	18.7449i	−0.490409	−	0.849414i	0.509530	−	0.860453i	$-0.329819\pi$
$487$	−10.8224	−	18.7449i	−0.490409	−	0.849414i	−0.999939	+	0.0110392i	$0.996486\pi$
$488$	2.21442	+	3.83549i	0.100242	+	0.173624i
$489$	0.628561	+	1.08870i	0.0284245	+	0.0492327i
$490$	−5.21629	+	9.03488i	−0.235648	+	0.408154i
$491$	−11.9978	−	20.7808i	−0.541453	−	0.937825i	−0.998821	−	0.0485469i	$-0.984541\pi$
$491$	−11.9978	−	20.7808i	−0.541453	−	0.937825i	0.457368	−	0.889278i	$-0.348792\pi$
$492$	−19.5717			−0.882360
$493$	−28.2189	−	48.8765i	−1.27091	−	2.20129i
$494$	−10.6411	−	18.4310i	−0.478767	−	0.829248i
$495$	2.42608			0.109044
$496$	15.6513	+	27.1089i	0.702765	+	1.21723i
$497$	−10.7649	+	18.6454i	−0.482874	+	0.836362i
$498$	−26.2511	+	45.4683i	−1.17634	+	2.03748i
$499$	−20.4570	−	35.4325i	−0.915780	−	1.58618i	−0.805755	−	0.592249i	$-0.798240\pi$
$499$	−20.4570	−	35.4325i	−0.915780	−	1.58618i	−0.110025	−	0.993929i	$-0.535093\pi$
$500$	−8.63667	+	14.9592i	−0.386244	+	0.668994i
$501$	−0.354491			−0.0158375
$502$	−5.73096	+	9.92631i	−0.255785	+	0.443033i
$503$	−18.9177			−0.843500			−0.421750	−	0.906712i	$-0.638584\pi$
$503$	−18.9177			−0.843500			−0.421750	+	0.906712i	$0.638584\pi$
$504$	−0.750875	−	1.30055i	−0.0334466	−	0.0579313i
$505$	−1.73124	+	2.99859i	−0.0770391	+	0.133436i
$506$	2.41041	+	4.17495i	0.107156	+	0.185599i
$507$	−11.5997	+	20.0913i	−0.515163	+	0.892288i
$508$	5.60319	+	9.70501i	0.248601	+	0.430590i
$509$	−5.75984			−0.255300			−0.127650	−	0.991819i	$-0.540743\pi$
$509$	−5.75984			−0.255300			−0.127650	+	0.991819i	$0.540743\pi$
$510$	15.1142	+	26.1786i	0.669269	+	1.15921i
$511$	−7.52597	+	13.0354i	−0.332929	+	0.576650i
$512$	28.3191			1.25154
$513$	11.8401	−	20.5077i	0.522755	−	0.905438i
$514$	−6.41067	−	11.1036i	−0.282762	−	0.489759i
$515$	1.69177	−	2.93023i	0.0745483	−	0.129121i
$516$	29.3323			1.29128
$517$	15.0413			0.661514
$518$	−17.6030			−0.773429
$519$	31.4330			1.37975
$520$	−1.08162			−0.0474320
$521$	−7.74398	+	13.4130i	−0.339270	+	0.587632i	−0.984296	−	0.176528i	$-0.943513\pi$
$521$	−7.74398	+	13.4130i	−0.339270	+	0.587632i	0.645026	+	0.764161i	$0.276847\pi$
$522$	13.6013	+	23.5581i	0.595313	+	1.03111i
$523$	−14.6288			−0.639671			−0.319836	−	0.947473i	$-0.603628\pi$
$523$	−14.6288			−0.639671			−0.319836	+	0.947473i	$0.603628\pi$
$524$	9.07413	−	15.7169i	0.396405	−	0.686594i
$525$	5.96119	−	10.3251i	0.260168	−	0.450624i
$526$	13.4288	+	23.2593i	0.585522	+	1.01415i
$527$	21.1728	+	36.6723i	0.922300	+	1.59747i
$528$	6.31716	−	10.9416i	0.274919	−	0.476174i
$529$	9.64612	+	16.7076i	0.419397	+	0.726416i
$530$	5.07508	+	8.79030i	0.220447	+	0.381826i
$531$	−0.898582	−	1.55639i	−0.0389951	−	0.0675415i
$532$	−10.0817	+	17.4621i	−0.437098	+	0.757077i
$533$	3.98016	−	6.89383i	0.172400	−	0.298605i
$534$	17.9973	+	31.1723i	0.778820	+	1.34896i
$535$	3.18553	−	5.51750i	0.137723	−	0.238542i
$536$	−1.65916	−	2.87374i	−0.0716646	−	0.124127i
$537$	6.55452			0.282849
$538$	10.3928			0.448063
$539$	5.89867			0.254074
$540$	3.13556	+	5.43095i	0.134933	+	0.233711i
$541$	15.5738	+	26.9745i	0.669568	+	1.15973i	0.978025	+	0.208488i	$0.0668542\pi$
$541$	15.5738	+	26.9745i	0.669568	+	1.15973i	−0.308457	+	0.951238i	$0.599813\pi$
$542$	−7.14588	+	12.3770i	−0.306942	+	0.531639i
$543$	2.81819	−	4.88124i	0.120940	−	0.209474i
$544$	45.8958			1.96776
$545$	−9.13249	−	15.8179i	−0.391193	−	0.677566i
$546$	−9.36821			−0.400922
$547$	17.2949	+	15.7444i	0.739478	+	0.673180i
$547$	17.2949	+	15.7444i	0.739478	+	0.673180i
$548$	−19.7805			−0.844983
$549$	−5.53507	−	9.58703i	−0.236231	−	0.409164i
$550$	8.88930			0.379041
$551$	−35.0466	+	60.7024i	−1.49303	+	2.58601i
$552$	−1.26741	+	2.19522i	−0.0539445	+	0.0934347i
$553$	9.71899	+	16.8338i	0.413293	+	0.715845i
$554$	−8.84336	−	15.3172i	−0.375718	−	0.650763i
$555$	14.9527			0.634706
$556$	−31.7173			−1.34511
$557$	−40.9309			−1.73430			−0.867149	−	0.498049i	$-0.834050\pi$
$557$	−40.9309			−1.73430			−0.867149	+	0.498049i	$0.834050\pi$
$558$	−10.2051	−	17.6758i	−0.432018	−	0.748277i
$559$	−5.96510	+	10.3319i	−0.252297	+	0.436991i
$560$	4.30536	+	7.45710i	0.181935	+	0.315120i
$561$	8.54571	−	14.8016i	0.360800	−	0.624925i
$562$	5.61368	−	9.72318i	0.236799	−	0.410148i
$563$	−1.67257	−	2.89697i	−0.0704902	−	0.122093i	0.828626	−	0.559803i	$-0.189123\pi$
$563$	−1.67257	−	2.89697i	−0.0704902	−	0.122093i	−0.899116	+	0.437710i	$0.855790\pi$
$564$	−20.6055	−	35.6898i	−0.867649	−	1.50281i
$565$	−5.44193	−	9.42570i	−0.228944	−	0.396542i
$566$	−23.7821	+	41.1918i	−0.999636	+	1.73142i
$567$	−8.85944	−	15.3450i	−0.372062	−	0.644430i
$568$	−4.22030	−	7.30977i	−0.177080	−	0.306711i
$569$	−13.6228	+	23.5953i	−0.571096	+	0.989168i	0.425357	+	0.905026i	$0.360148\pi$
$569$	−13.6228	+	23.5953i	−0.571096	+	0.989168i	−0.996454	+	0.0841426i	$0.973185\pi$
$570$	18.7712	−	32.5126i	0.786238	−	1.36180i
$571$	24.9870			1.04567			0.522837	−	0.852433i	$-0.324874\pi$
$571$	24.9870			1.04567			0.522837	+	0.852433i	$0.324874\pi$
$572$	−1.59334	−	2.75974i	−0.0666209	−	0.115391i
$573$	−21.9271	+	37.9788i	−0.916017	+	1.58659i
$574$	−16.5311			−0.689993
$575$	−6.83688			−0.285118
$576$	−8.10396			−0.337665
$577$	−14.6274			−0.608948			−0.304474	−	0.952521i	$-0.598481\pi$
$577$	−14.6274			−0.608948			−0.304474	+	0.952521i	$0.598481\pi$
$578$	39.7467			1.65325
$579$	23.9032	−	41.4016i	0.993384	−	1.72059i
$580$	−9.28119	−	16.0755i	−0.385381	−	0.667499i
$581$	−10.1157	+	17.5210i	−0.419672	+	0.726893i
$582$	−79.2825			−3.28636
$583$	2.86950	−	4.97011i	0.118842	−	0.205841i
$584$	−2.95048	−	5.11039i	−0.122092	−	0.211469i
$585$	2.70356			0.111778
$586$	−2.10414	−	3.64447i	−0.0869211	−	0.150552i
$587$	−21.0609	+	36.4786i	−0.869278	+	1.50563i	−0.00654276	+	0.999979i	$0.502083\pi$
$587$	−21.0609	+	36.4786i	−0.869278	+	1.50563i	−0.862735	+	0.505655i	$0.831251\pi$
$588$	−8.08078	−	13.9963i	−0.333246	−	0.577199i
$589$	26.2956	−	45.5454i	1.08349	−	1.87666i
$590$	1.34401	+	2.32790i	0.0553321	+	0.0958381i
$591$	17.7356			0.729546
$592$	13.2276	−	22.9109i	0.543652	−	0.941634i
$593$	−6.71284			−0.275663			−0.137832	−	0.990456i	$-0.544013\pi$
$593$	−6.71284			−0.275663			−0.137832	+	0.990456i	$0.544013\pi$
$594$	3.88598	−	6.73071i	0.159444	−	0.276165i
$595$	5.82419	+	10.0878i	0.238769	+	0.413559i
$596$	−7.87422	+	13.6385i	−0.322541	+	0.558657i
$597$	8.90623	−	15.4261i	0.364508	−	0.631346i
$598$	2.68610	+	4.65246i	0.109843	+	0.190253i
$599$	−13.0537			−0.533359			−0.266680	−	0.963785i	$-0.585927\pi$
$599$	−13.0537			−0.533359			−0.266680	+	0.963785i	$0.585927\pi$
$600$	2.33703	+	4.04785i	0.0954088	+	0.165253i
$601$	−2.42767	−	4.20486i	−0.0990269	−	0.171520i	0.812255	−	0.583302i	$-0.198240\pi$
$601$	−2.42767	−	4.20486i	−0.0990269	−	0.171520i	−0.911282	+	0.411783i	$0.864906\pi$
$602$	24.7753			1.00977
$603$	4.14715	+	7.18308i	0.168885	+	0.292518i
$604$	12.3476	−	21.3866i	0.502416	−	0.870210i
$605$	−5.59564	−	9.69193i	−0.227495	−	0.394033i
$606$	−5.87857	−	10.1820i	−0.238801	−	0.413615i
$607$	0.389768	+	0.675098i	0.0158202	+	0.0274014i	0.873827	−	0.486237i	$-0.161631\pi$
$607$	0.389768	+	0.675098i	0.0158202	+	0.0274014i	−0.858007	+	0.513638i	$0.828297\pi$
$608$	−28.5002	−	49.3639i	−1.15584	−	2.00197i
$609$	15.4271	+	26.7205i	0.625138	+	1.08277i
$610$	8.27884	+	14.3394i	0.335200	+	0.580584i
$611$	16.7616			0.678102
$612$	−15.9094			−0.643099
$613$	−9.29105	+	16.0926i	−0.375262	+	0.649973i	−0.990366	−	0.138473i	$-0.955781\pi$
$613$	−9.29105	+	16.0926i	−0.375262	+	0.649973i	0.615104	+	0.788446i	$0.289114\pi$
$614$	−1.44423	−	2.50148i	−0.0582844	−	0.100951i
$615$	14.0422			0.566236
$616$	0.635004	−	1.09986i	0.0255850	−	0.0443146i
$617$	−24.0238	−	41.6104i	−0.967162	−	1.67517i	−0.703692	−	0.710505i	$-0.748466\pi$
$617$	−24.0238	−	41.6104i	−0.967162	−	1.67517i	−0.263470	−	0.964668i	$-0.584867\pi$
$618$	5.74454	+	9.94984i	0.231079	+	0.400241i
$619$	−11.2532			−0.452304			−0.226152	−	0.974092i	$-0.572615\pi$
$619$	−11.2532			−0.452304			−0.226152	+	0.974092i	$0.572615\pi$
$620$	6.96373	+	12.0615i	0.279670	+	0.484403i
$621$	−2.98876	+	5.17669i	−0.119935	+	0.207733i
$622$	6.87760	+	11.9124i	0.275767	+	0.477642i
$623$	6.93518	+	12.0121i	0.277852	+	0.481254i
$624$	7.03968	−	12.1931i	0.281813	−	0.488114i
$625$	−2.67992	+	4.64177i	−0.107197	+	0.185671i
$626$	8.07986			0.322936
$627$	−21.2268			−0.847716
$628$	−20.8254			−0.831024
$629$	17.8941	−	30.9934i	0.713483	−	1.23579i
$630$	−2.80722	−	4.86225i	−0.111842	−	0.193717i
$631$	−25.0767			−0.998289			−0.499145	−	0.866519i	$-0.666352\pi$
$631$	−25.0767			−0.998289			−0.499145	+	0.866519i	$0.666352\pi$
$632$	−7.62048			−0.303126
$633$	−18.6693	+	32.3361i	−0.742037	+	1.28525i
$634$	−44.3877			−1.76286
$635$	−4.02014	−	6.96309i	−0.159535	−	0.276322i
$636$	−15.7241			−0.623500
$637$	6.57333			0.260445
$638$	−11.5024	+	19.9228i	−0.455385	+	0.788750i
$639$	10.5489	+	18.2712i	0.417307	+	0.722797i
$640$	−5.87091			−0.232068
$641$	10.4589			0.413101			0.206550	−	0.978436i	$-0.433776\pi$
$641$	10.4589			0.413101			0.206550	+	0.978436i	$0.433776\pi$
$642$	10.8167	+	18.7351i	0.426903	+	0.739417i
$643$	−1.74877	+	3.02895i	−0.0689646	+	0.119450i	−0.898446	−	0.439084i	$-0.855303\pi$
$643$	−1.74877	+	3.02895i	−0.0689646	+	0.119450i	0.829481	+	0.558535i	$0.188636\pi$
$644$	2.54489	−	4.40788i	0.100283	−	0.173695i
$645$	−21.0452			−0.828653
$646$	−44.9274	−	77.8165i	−1.76764	−	3.06165i
$647$	27.4810			1.08039			0.540194	−	0.841540i	$-0.318351\pi$
$647$	27.4810			1.08039			0.540194	+	0.841540i	$0.318351\pi$
$648$	6.94652			0.272885
$649$	0.759917	−	1.31621i	0.0298293	−	0.0516659i
$650$	9.90601			0.388546
$651$	−11.5750	−	20.0486i	−0.453662	−	0.785765i
$652$	0.989603			0.0387558
$653$	11.7356	−	20.3266i	0.459249	−	0.795443i	−0.539672	−	0.841875i	$-0.681452\pi$
$653$	11.7356	−	20.3266i	0.459249	−	0.795443i	0.998921	+	0.0464323i	$0.0147852\pi$
$654$	62.0203			2.42518
$655$	−6.51046	+	11.2764i	−0.254385	+	0.440607i
$656$	12.4222	−	21.5158i	0.485004	−	0.840052i
$657$	7.37491	+	12.7737i	0.287722	+	0.498350i
$658$	−17.4043	−	30.1451i	−0.678490	−	1.17518i
$659$	−7.86650	+	13.6252i	−0.306435	+	0.530761i	−0.977580	−	0.210565i	$-0.932470\pi$
$659$	−7.86650	+	13.6252i	−0.306435	+	0.530761i	0.671145	+	0.741326i	$0.265803\pi$
$660$	2.81069	−	4.86826i	0.109406	−	0.189497i
$661$	29.5134			1.14794			0.573969	−	0.818877i	$-0.305403\pi$
$661$	29.5134			1.14794			0.573969	+	0.818877i	$0.305403\pi$
$662$	−6.53954	−	11.3268i	−0.254166	−	0.440229i
$663$	9.52313	−	16.4945i	0.369848	−	0.640595i
$664$	−3.96578	−	6.86894i	−0.153902	−	0.266566i
$665$	7.23338	−	12.5286i	0.280499	−	0.485838i
$666$	−8.62481	+	14.9386i	−0.334205	+	0.578860i
$667$	8.84667	−	15.3229i	0.342544	−	0.593304i
$668$	−0.139527	+	0.241668i	−0.00539847	+	0.00935042i
$669$	11.3275	−	19.6199i	0.437948	−	0.758547i
$670$	−6.20292	−	10.7438i	−0.239640	−	0.415068i
$671$	4.68093	−	8.10760i	0.180705	−	0.312991i
$672$	−25.0910			−0.967906
$673$	11.3097	−	19.5891i	0.435959	−	0.755102i	−0.561415	−	0.827535i	$-0.689743\pi$
$673$	11.3097	−	19.5891i	0.435959	−	0.755102i	0.997373	+	0.0724321i	$0.0230761\pi$
$674$	−31.1168	+	53.8958i	−1.19857	+	2.07599i
$675$	5.51110	+	9.54551i	0.212122	+	0.367407i
$676$	9.13129	+	15.8159i	0.351203	+	0.608302i
$677$	20.8550	+	36.1220i	0.801525	+	1.38828i	0.918612	+	0.395160i	$0.129311\pi$
$677$	20.8550	+	36.1220i	0.801525	+	1.38828i	−0.117088	+	0.993122i	$0.537356\pi$
$678$	36.9571			1.41933
$679$	−30.5511			−1.17244
$680$	−4.56664			−0.175123
$681$	−24.2417	+	41.9879i	−0.928944	+	1.60898i
$682$	8.63033	−	14.9482i	0.330472	−	0.572395i
$683$	−9.11216	−	15.7827i	−0.348667	−	0.603909i	0.637346	−	0.770578i	$-0.280032\pi$
$683$	−9.11216	−	15.7827i	−0.348667	−	0.603909i	−0.986013	+	0.166669i	$0.946699\pi$
$684$	9.87937	+	17.1116i	0.377747	+	0.654277i
$685$	14.1920			0.542250
$686$	−17.3991	−	30.1362i	−0.664302	−	1.15061i
$687$	10.6935	−	18.5217i	0.407982	−	0.706646i
$688$	−18.6172	+	32.2460i	−0.709776	+	1.22937i
$689$	3.19769	−	5.53857i	0.121822	−	0.211003i
$690$	−4.73834	+	8.20704i	−0.180385	+	0.312437i
$691$	−12.3750	−	21.4341i	−0.470765	−	0.815390i	0.528675	−	0.848824i	$-0.322689\pi$
$691$	−12.3750	−	21.4341i	−0.470765	−	0.815390i	−0.999441	+	0.0334343i	$0.989356\pi$
$692$	12.3720	−	21.4289i	0.470312	−	0.814604i
$693$	−1.58723	+	2.74916i	−0.0602938	+	0.104432i
$694$	−6.09380	+	10.5548i	−0.231317	+	0.400654i
$695$	22.7563			0.863197
$696$	−12.0961			−0.458502
$697$	16.8044	−	29.1061i	0.636513	−	1.10247i
$698$	26.3077			0.995761
$699$	17.9235	−	31.0444i	0.677930	−	1.17421i
$700$	−4.69263	−	8.12788i	−0.177365	−	0.307205i
$701$	10.3464			0.390780			0.195390	−	0.980726i	$-0.437403\pi$
$701$	10.3464			0.390780			0.195390	+	0.980726i	$0.437403\pi$
$702$	4.33044	−	7.50054i	0.163442	−	0.283090i
$703$	−44.4472			−1.67636
$704$	−3.42670	−	5.93521i	−0.129148	−	0.223692i
$705$	14.7839	+	25.6065i	0.556795	+	0.964398i
$706$	−19.5003	−	33.7755i	−0.733902	−	1.27116i
$707$	−2.26528	−	3.92358i	−0.0851945	−	0.147561i
$708$	−4.16414			−0.156498
$709$	−19.3399	−	33.4978i	−0.726327	−	1.25803i	−0.958426	−	0.285342i	$-0.907893\pi$
$709$	−19.3399	−	33.4978i	−0.726327	−	1.25803i	0.232099	−	0.972692i	$-0.425441\pi$
$710$	−15.7780	−	27.3283i	−0.592138	−	1.02561i
$711$	19.0478			0.714349
$712$	−5.43774			−0.203788
$713$	−6.63770	+	11.4968i	−0.248584	+	0.430560i
$714$	−39.5531			−1.48024
$715$	1.14318	+	1.98005i	0.0427525	+	0.0740495i
$716$	2.57985	−	4.46843i	0.0964136	−	0.166993i
$717$	−1.29326	−	2.23999i	−0.0482976	−	0.0836539i
$718$	19.4623	−	33.7098i	0.726328	−	1.25804i
$719$	17.1636			0.640095			0.320047	−	0.947402i	$-0.396301\pi$
$719$	17.1636			0.640095			0.320047	+	0.947402i	$0.396301\pi$
$720$	8.43788			0.314461
$721$	2.21363	+	3.83412i	0.0824400	+	0.142790i
$722$	−37.5786	+	65.0881i	−1.39853	+	2.42233i
$723$	9.46139	−	16.3876i	0.351873	−	0.609462i
$724$	−2.21847	−	3.84250i	−0.0824487	−	0.142805i
$725$	−16.3127	−	28.2545i	−0.605840	−	1.04935i
$726$	38.0009			1.41035
$727$	−6.39778	−	11.0813i	−0.237281	−	0.410982i	0.722652	−	0.691212i	$-0.242923\pi$
$727$	−6.39778	−	11.0813i	−0.237281	−	0.410982i	−0.959933	+	0.280229i	$0.909589\pi$
$728$	0.707632	−	1.22565i	0.0262266	−	0.0454258i
$729$	2.48811			0.0921522
$730$	−11.0307	−	19.1057i	−0.408264	−	0.707134i
$731$	−25.1850	+	43.6217i	−0.931501	+	1.61341i
$732$	−25.6502			−0.948060
$733$	−18.2488	−	31.6078i	−0.674034	−	1.16746i	−0.976750	−	0.214381i	$-0.931227\pi$
$733$	−18.2488	−	31.6078i	−0.674034	−	1.16746i	0.302716	−	0.953081i	$-0.402107\pi$
$734$	3.49856	−	6.05969i	0.129134	−	0.223667i
$735$	5.79776	+	10.0420i	0.213853	+	0.370405i
$736$	7.19420	+	12.4607i	0.265182	+	0.459309i
$737$	−3.50719	+	6.07462i	−0.129189	+	0.223762i
$738$	−8.09963	+	14.0290i	−0.298151	+	0.516413i
$739$	24.3438			0.895500			0.447750	−	0.894159i	$-0.352225\pi$
$739$	24.3438			0.895500			0.447750	+	0.894159i	$0.352225\pi$
$740$	5.88536	−	10.1937i	0.216350	−	0.374729i
$741$	−23.6546			−0.868973
$742$	−13.2812			−0.487568
$743$	18.5973	+	32.2115i	0.682269	+	1.18173i	0.974287	+	0.225312i	$0.0723402\pi$
$743$	18.5973	+	32.2115i	0.682269	+	1.18173i	−0.292017	+	0.956413i	$0.594326\pi$
$744$	9.07578			0.332734
$745$	5.64955	−	9.78531i	0.206984	−	0.358506i
$746$	−26.3793	+	45.6904i	−0.965816	+	1.67284i
$747$	9.91270	+	17.1693i	0.362687	+	0.628192i
$748$	−6.72716	−	11.6518i	−0.245969	−	0.426032i
$749$	4.16818	+	7.21950i	0.152302	+	0.263795i
$750$	21.0411	+	36.4442i	0.768311	+	1.33075i
$751$	−18.3498			−0.669594			−0.334797	−	0.942290i	$-0.608668\pi$
$751$	−18.3498			−0.669594			−0.334797	+	0.942290i	$0.608668\pi$
$752$	52.3134			1.90767
$753$	6.36979	+	11.0328i	0.232128	+	0.402058i
$754$	−12.8180	+	22.2014i	−0.466804	+	0.808528i
$755$	−8.85907	+	15.3444i	−0.322415	+	0.558438i
$756$	−8.20559			−0.298434
$757$	−8.24006	−	14.2722i	−0.299490	−	0.518732i	0.676529	−	0.736416i	$-0.263483\pi$
$757$	−8.24006	−	14.2722i	−0.299490	−	0.518732i	−0.976019	+	0.217684i	$0.930150\pi$
$758$	33.3565	−	57.7751i	1.21156	−	2.09849i
$759$	5.35820			0.194490
$760$	2.83578	+	4.91172i	0.102865	+	0.178167i
$761$	0.338488	+	0.586278i	0.0122702	+	0.0212526i	0.872095	−	0.489336i	$-0.162761\pi$
$761$	0.338488	+	0.586278i	0.0122702	+	0.0212526i	−0.859825	+	0.510589i	$0.829428\pi$
$762$	27.3015			0.989028
$763$	23.8992			0.865209
$764$	17.2609	+	29.8968i	0.624479	+	1.08163i
$765$	11.4146			0.412695
$766$	11.8937	+	20.6005i	0.429737	+	0.744327i
$767$	0.846832	−	1.46676i	0.0305773	−	0.0529615i
$768$	21.1581	−	36.6468i	0.763475	−	1.32238i
$769$	−16.8175	+	29.1288i	−0.606455	+	1.05041i	0.385365	+	0.922764i	$0.374076\pi$
$769$	−16.8175	+	29.1288i	−0.606455	+	1.05041i	−0.991820	+	0.127646i	$0.959258\pi$
$770$	2.37402	−	4.11193i	0.0855539	−	0.148184i
$771$	−14.2505			−0.513221
$772$	−18.8166	−	32.5912i	−0.677223	−	1.17298i
$773$	32.3577			1.16382			0.581912	−	0.813252i	$-0.302305\pi$
$773$	32.3577			1.16382			0.581912	+	0.813252i	$0.302305\pi$
$774$	12.1390	−	21.0254i	0.436327	−	0.755741i
$775$	12.2395	+	21.1995i	0.439657	+	0.761509i
$776$	5.98864	−	10.3726i	0.214980	−	0.372356i
$777$	−9.78259	+	16.9439i	−0.350948	+	0.607860i
$778$	25.4369	−	44.0580i	0.911957	−	1.57956i
$779$	−41.7407			−1.49552
$780$	3.13216	−	5.42506i	0.112149	−	0.194248i
$781$	−8.92102	+	15.4517i	−0.319219	+	0.552904i
$782$	11.3408	+	19.6429i	0.405548	+	0.702429i
$783$	−28.5246			−1.01939
$784$	20.5155			0.732698
$785$	14.9417			0.533292
$786$	−22.1068	−	38.2901i	−0.788524	−	1.36576i
$787$	−49.7273			−1.77259			−0.886293	−	0.463126i	$-0.846728\pi$
$787$	−49.7273			−1.77259			−0.886293	+	0.463126i	$0.846728\pi$
$788$	6.98071	−	12.0910i	0.248678	−	0.430722i
$789$	29.8514			1.06274
$790$	−28.4899			−1.01363
$791$	14.2412			0.506360
$792$	−0.622258	−	1.07778i	−0.0221110	−	0.0382973i
$793$	5.21631	−	9.03491i	0.185237	−	0.320839i
$794$	−6.88848			−0.244463
$795$	11.2816			0.400118
$796$	−7.01096	−	12.1433i	−0.248497	−	0.430410i
$797$	2.20117	+	3.81253i	0.0779694	+	0.135047i	0.902374	−	0.430954i	$-0.141823\pi$
$797$	2.20117	+	3.81253i	0.0779694	+	0.135047i	−0.824404	+	0.566001i	$0.808490\pi$
$798$	24.5616	+	42.5419i	0.869470	+	1.50597i
$799$	70.7684			2.50361
$800$	26.5314			0.938026
$801$	13.5920			0.480248
$802$	54.7724			1.93408
$803$	−6.23685	+	10.8025i	−0.220094	+	0.381213i
$804$	19.2184			0.677782
$805$	−1.82590	+	3.16254i	−0.0643544	+	0.111465i
$806$	9.61742	−	16.6579i	0.338759	−	0.586748i
$807$	5.77562	−	10.0037i	0.203312	−	0.352146i
$808$	1.77616			0.0624852
$809$	−1.41317	−	2.44769i	−0.0496846	−	0.0860562i	0.840114	−	0.542411i	$-0.182488\pi$
$809$	−1.41317	−	2.44769i	−0.0496846	−	0.0860562i	−0.889798	+	0.456354i	$0.849155\pi$
$810$	25.9703			0.912503
$811$	−16.4808	−	28.5456i	−0.578719	−	1.00237i	−0.995627	−	0.0934219i	$-0.970219\pi$
$811$	−16.4808	−	28.5456i	−0.578719	−	1.00237i	0.416908	−	0.908949i	$-0.363114\pi$
$812$	24.2884			0.852354
$813$	7.94244	+	13.7567i	0.278554	+	0.482469i
$814$	−14.5877			−0.511300
$815$	−0.710015			−0.0248707
$816$	29.7219	−	51.4799i	1.04048	−	1.80216i
$817$	62.5573			2.18860
$818$	−21.0665	−	36.4883i	−0.736573	−	1.27578i
$819$	−1.76877	+	3.06359i	−0.0618057	+	0.107051i
$820$	5.52699	−	9.57302i	0.193011	−	0.334304i
$821$	−16.1400	+	27.9554i	−0.563292	+	0.975650i	0.433915	+	0.900954i	$0.357132\pi$
$821$	−16.1400	+	27.9554i	−0.563292	+	0.975650i	−0.997206	+	0.0746956i	$0.976201\pi$
$822$	−24.0951	+	41.7340i	−0.840414	+	1.45564i
$823$	4.18824	+	7.25425i	0.145993	+	0.252867i	0.929743	−	0.368209i	$-0.120029\pi$
$823$	4.18824	+	7.25425i	0.145993	+	0.252867i	−0.783750	+	0.621076i	$0.786696\pi$
$824$	−1.73567			−0.0604649
$825$	4.94010	−	8.55650i	0.171992	−	0.297899i
$826$	−3.51721			−0.122379
$827$	34.0420			1.18376			0.591878	−	0.806027i	$-0.298387\pi$
$827$	34.0420			1.18376			0.591878	+	0.806027i	$0.298387\pi$
$828$	−2.49381	−	4.31941i	−0.0866660	−	0.150110i
$829$	27.0962			0.941090			0.470545	−	0.882376i	$-0.344057\pi$
$829$	27.0962			0.941090			0.470545	+	0.882376i	$0.344057\pi$
$830$	−14.8265	−	25.6802i	−0.514635	−	0.891373i
$831$	−19.6583			−0.681938
$832$	−3.81862	−	6.61405i	−0.132387	−	0.229301i
$833$	27.7530			0.961583
$834$	−38.6355	+	66.9187i	−1.33784	+	2.31720i
$835$	0.100107	−	0.173391i	0.00346435	−	0.00600043i
$836$	−8.35484	+	14.4710i	−0.288958	+	0.500490i
$837$	21.4022			0.739768
$838$	−25.7138	+	44.5376i	−0.888267	+	1.53852i
$839$	22.6577			0.782230			0.391115	−	0.920342i	$-0.372089\pi$
$839$	22.6577			0.782230			0.391115	+	0.920342i	$0.372089\pi$
$840$	2.49656			0.0861395
$841$	55.4322			1.91146
$842$	−28.9727			−0.998464
$843$	−6.23944	−	10.8070i	−0.214898	−	0.372214i
$844$	14.6964	+	25.4549i	0.505871	+	0.876194i
$845$	−6.55147	−	11.3475i	−0.225377	−	0.390365i
$846$	−34.1099			−1.17272
$847$	14.6435			0.503156
$848$	9.98008	−	17.2860i	0.342717	−	0.593604i
$849$	26.4331	+	45.7835i	0.907182	+	1.57129i
$850$	41.8237			1.43454
$851$	11.2196			0.384604
$852$	48.8848			1.67477
$853$	−26.8157	+	46.4461i	−0.918152	+	1.59029i	−0.115932	+	0.993257i	$0.536985\pi$
$853$	−26.8157	+	46.4461i	−0.918152	+	1.59029i	−0.802220	+	0.597029i	$0.796348\pi$
$854$	−21.6653			−0.741370
$855$	−7.08820	−	12.2771i	−0.242411	−	0.419869i
$856$	−3.26819			−0.111704
$857$	−39.9007			−1.36298			−0.681491	−	0.731827i	$-0.738668\pi$
$857$	−39.9007			−1.36298			−0.681491	+	0.731827i	$0.738668\pi$
$858$	−7.76353			−0.265043
$859$	−4.13928	−	7.16945i	−0.141231	−	0.244618i	0.786730	−	0.617298i	$-0.211773\pi$
$859$	−4.13928	−	7.16945i	−0.141231	−	0.244618i	−0.927960	+	0.372679i	$0.878439\pi$
$860$	−8.28335	+	14.3472i	−0.282460	+	0.489235i
$861$	−9.18690	+	15.9122i	−0.313089	+	0.542286i
$862$	8.41193			0.286512
$863$	9.16388	−	15.8723i	0.311942	−	0.540299i	−0.666841	−	0.745200i	$-0.732354\pi$
$863$	9.16388	−	15.8723i	0.311942	−	0.540299i	0.978783	+	0.204901i	$0.0656872\pi$
$864$	11.5983	−	20.0888i	0.394581	−	0.683434i
$865$	−8.87657	+	15.3747i	−0.301813	+	0.522755i
$866$	22.3324	+	38.6808i	0.758885	+	1.31443i
$867$	22.0887	−	38.2587i	0.750171	−	1.29933i
$868$	−18.2237			−0.618552
$869$	8.05422	+	13.9503i	0.273221	+	0.473232i
$870$	−45.2225			−1.53319
$871$	−3.90832	+	6.76941i	−0.132428	+	0.229373i
$872$	−4.68473	+	8.11419i	−0.158645	+	0.274781i
$873$	−14.9690	+	25.9270i	−0.506622	+	0.877495i
$874$	14.0848	−	24.3956i	0.476426	−	0.825194i
$875$	8.10807	+	14.0436i	0.274103	+	0.474760i
$876$	34.1762			1.15471
$877$	−22.7148	−	39.3432i	−0.767024	−	1.32852i	−0.939170	−	0.343453i	$-0.888403\pi$
$877$	−22.7148	−	39.3432i	−0.767024	−	1.32852i	0.172146	−	0.985072i	$-0.444930\pi$
$878$	16.9687			0.572665
$879$	−4.67738			−0.157764
$880$	3.56789	+	6.17977i	0.120274	+	0.208320i
$881$	−5.73746	−	9.93757i	−0.193300	−	0.334805i	0.753042	−	0.657972i	$-0.228586\pi$
$881$	−5.73746	−	9.93757i	−0.193300	−	0.334805i	−0.946342	+	0.323167i	$0.895252\pi$
$882$	−13.3767			−0.450418
$883$	−18.6012	+	32.2182i	−0.625979	+	1.08423i	0.362371	+	0.932034i	$0.381967\pi$
$883$	−18.6012	+	32.2182i	−0.625979	+	1.08423i	−0.988351	+	0.152194i	$0.951366\pi$
$884$	−7.49658	−	12.9845i	−0.252137	−	0.436715i
$885$	2.98766			0.100429
$886$	17.1035	−	29.6242i	0.574605	−	0.995244i
$887$	10.5012	−	18.1885i	0.352595	−	0.610712i	−0.634109	−	0.773244i	$-0.718633\pi$
$887$	10.5012	−	18.1885i	0.352595	−	0.610712i	0.986703	+	0.162532i	$0.0519662\pi$
$888$	−3.83517	−	6.64271i	−0.128700	−	0.222915i
$889$	10.5205			0.352846
$890$	−20.3296			−0.681448
$891$	−7.34191	−	12.7166i	−0.245963	−	0.426021i
$892$	−8.91700	−	15.4447i	−0.298563	−	0.517127i
$893$	−43.9456	−	76.1160i	−1.47058	−	2.54712i
$894$	19.1835	+	33.2268i	0.641593	+	1.11127i
$895$	−1.85098	+	3.20599i	−0.0618714	+	0.107164i
$896$	3.84096	−	6.65274i	0.128317	−	0.222252i
$897$	5.97104			0.199367
$898$	21.1341	+	36.6054i	0.705255	+	1.22154i
$899$	−63.3500			−2.11284
$900$	−9.19689			−0.306563
$901$	13.5008	−	23.3841i	0.449778	−	0.779038i
$902$	−13.6995			−0.456142
$903$	13.7685	−	23.8478i	0.458187	−	0.793604i
$904$	−2.79157	+	4.83514i	−0.0928463	+	0.160814i
$905$	1.59169	+	2.75690i	0.0529097	+	0.0916423i
$906$	−30.0817	−	52.1031i	−0.999398	−	1.73101i
$907$	−15.1797	+	26.2919i	−0.504032	+	0.873009i	0.495957	+	0.868347i	$0.334817\pi$
$907$	−15.1797	+	26.2919i	−0.504032	+	0.873009i	−0.999989	+	0.00466226i	$0.998516\pi$
$908$	19.0830	+	33.0527i	0.633292	+	1.09689i
$909$	−4.43962			−0.147253
$910$	2.64555	−	4.58223i	0.0876992	−	0.151900i
$911$	23.5411	+	40.7744i	0.779952	+	1.35092i	0.931969	+	0.362539i	$0.118090\pi$
$911$	23.5411	+	40.7744i	0.779952	+	1.35092i	−0.152017	+	0.988378i	$0.548577\pi$
$912$	−73.8266			−2.44464
$913$	−8.38302	+	14.5198i	−0.277437	+	0.480536i
$914$	−36.9725	−	64.0383i	−1.22294	−	2.11820i
$915$	18.4034			0.608397
$916$	−8.41789	−	14.5802i	−0.278135	−	0.481744i
$917$	−8.51875	−	14.7549i	−0.281314	−	0.487250i
$918$	18.2833	−	31.6677i	0.603440	−	1.04519i
$919$	8.95788	−	15.5155i	0.295493	−	0.511809i	−0.679606	−	0.733577i	$-0.737849\pi$
$919$	8.95788	−	15.5155i	0.295493	−	0.511809i	0.975099	+	0.221768i	$0.0711827\pi$
$920$	−0.715825	−	1.23985i	−0.0236001	−	0.0408765i
$921$	−3.21044			−0.105788
$922$	−57.3472			−1.88863
$923$	−9.94136	+	17.2189i	−0.327224	+	0.566768i
$924$	3.67771	+	6.36997i	0.120988	+	0.209557i
$925$	10.3442	−	17.9166i	0.340115	−	0.589096i
$926$	18.3256	+	31.7408i	0.602216	+	1.04307i
$927$	4.33840			0.142492
$928$	−34.3306	+	59.4624i	−1.12696	+	1.95195i
$929$	30.5377			1.00191			0.500955	−	0.865474i	$-0.332982\pi$
$929$	30.5377			1.00191			0.500955	+	0.865474i	$0.332982\pi$
$930$	33.9307			1.11263
$931$	−17.2340	−	29.8501i	−0.564820	−	0.978297i
$932$	−14.1093	−	24.4381i	−0.462167	−	0.800497i
$933$	15.2885			0.500523
$934$	16.8709	+	29.2213i	0.552034	+	0.956150i
$935$	4.82657	+	8.35986i	0.157846	+	0.273397i
$936$	−0.693428	−	1.20105i	−0.0226654	−	0.0392577i
$937$	−5.97566	−	10.3502i	−0.195216	−	0.338125i	0.751755	−	0.659442i	$-0.229208\pi$
$937$	−5.97566	−	10.3502i	−0.195216	−	0.338125i	−0.946971	+	0.321318i	$0.895874\pi$
$938$	16.2327			0.530016
$939$	4.49027	−	7.77737i	0.146534	−	0.253805i
$940$	23.2758			0.759171
$941$	−7.75989	−	13.4405i	−0.252965	−	0.438149i	0.711376	−	0.702812i	$-0.248072\pi$
$941$	−7.75989	−	13.4405i	−0.252965	−	0.438149i	−0.964341	+	0.264663i	$0.914739\pi$
$942$	−25.3679	+	43.9385i	−0.826530	+	1.43159i
$943$	10.5364			0.343114
$944$	2.64298	−	4.57778i	0.0860218	−	0.148994i
$945$	5.88730			0.191514
$946$	20.5315			0.667538
$947$	13.6913	−	23.7141i	0.444908	−	0.770603i	−0.553138	−	0.833090i	$-0.686570\pi$
$947$	13.6913	−	23.7141i	0.444908	−	0.770603i	0.998046	+	0.0624864i	$0.0199030\pi$
$948$	22.0675	−	38.2220i	0.716719	−	1.24139i
$949$	−6.95018	+	12.0381i	−0.225613	+	0.390772i
$950$	−25.9716	−	44.9841i	−0.842629	−	1.45948i
$951$	−24.6678	+	42.7259i	−0.799909	+	1.38548i
$952$	2.98766	−	5.17478i	0.0968306	−	0.167716i
$953$	0.738898	−	1.27981i	0.0239353	−	0.0414571i	−0.853810	−	0.520585i	$-0.825714\pi$
$953$	0.738898	−	1.27981i	0.0239353	−	0.0414571i	0.877745	+	0.479128i	$0.159047\pi$
$954$	−6.50731	+	11.2710i	−0.210682	+	0.364912i
$955$	−12.3843	−	21.4502i	−0.400746	−	0.694112i
$956$	−2.03610			−0.0658522
$957$	12.7846	+	22.1436i	0.413268	+	0.715800i
$958$	9.35280	+	16.1995i	0.302175	+	0.523383i
$959$	−9.28493	+	16.0820i	−0.299826	+	0.519314i
$960$	6.73614	−	11.6673i	0.217408	−	0.376562i
$961$	16.5319			0.533286
$962$	−16.2562			−0.524122
$963$	8.16903			0.263243
$964$	−7.44798	−	12.9003i	−0.239883	−	0.415490i
$965$	13.5004	+	23.3834i	0.434593	+	0.752738i
$966$	−6.19998	−	10.7387i	−0.199481	−	0.345511i
$967$	3.35150	−	5.80497i	0.107777	−	0.186675i	−0.807092	−	0.590425i	$-0.798960\pi$
$967$	3.35150	−	5.80497i	0.107777	−	0.186675i	0.914869	+	0.403750i	$0.132293\pi$
$968$	−2.87042	+	4.97171i	−0.0922588	+	0.159797i
$969$	−99.8710			−3.20832
$970$	22.3891	−	38.7791i	0.718872	−	1.24512i
$971$	7.35106	+	12.7324i	0.235907	+	0.408602i	0.959536	−	0.281587i	$-0.0908607\pi$
$971$	7.35106	+	12.7324i	0.235907	+	0.408602i	−0.723629	+	0.690189i	$0.757527\pi$
$972$	−12.3024	+	21.3084i	−0.394599	+	0.683466i
$973$	−14.8880	+	25.7868i	−0.477288	+	0.826686i
$974$	−20.7552	+	35.9491i	−0.665041	+	1.15188i
$975$	5.50512	−	9.53515i	0.176305	−	0.305369i
$976$	16.2802	−	28.1982i	0.521117	−	0.902602i
$977$	−19.6565	−	34.0461i	−0.628867	−	1.08923i	−0.987779	−	0.155859i	$-0.950186\pi$
$977$	−19.6565	−	34.0461i	−0.628867	−	1.08923i	0.358912	−	0.933371i	$-0.383148\pi$
$978$	1.20546	−	2.08791i	0.0385463	−	0.0667641i
$979$	5.74725	+	9.95453i	0.183683	+	0.318148i
$980$	9.12796			0.291582
$981$	11.7098	−	20.2819i	0.373864	−	0.647551i
$982$	−23.0095	+	39.8536i	−0.734261	+	1.27178i
$983$	11.0120	+	19.0734i	0.351229	+	0.608347i	0.986465	−	0.163971i	$-0.0524305\pi$
$983$	11.0120	+	19.0734i	0.351229	+	0.608347i	−0.635236	+	0.772318i	$0.719097\pi$
$984$	−3.60164	−	6.23822i	−0.114816	−	0.198867i
$985$	−5.00848	+	8.67495i	−0.159584	+	0.276407i
$986$	−54.1183	+	93.7356i	−1.72348	+	2.98515i
$987$	−38.6887			−1.23148
$988$	−9.31042	+	16.1261i	−0.296204	+	0.513040i
$989$	−15.7911			−0.502127
$990$	−2.32637	−	4.02940i	−0.0739370	−	0.128063i
$991$	−44.6240			−1.41753			−0.708765	−	0.705445i	$-0.750747\pi$
$991$	−44.6240			−1.41753			−0.708765	+	0.705445i	$0.750747\pi$
$992$	25.7585	−	44.6149i	0.817832	−	1.41653i
$993$	−14.5370			−0.461318
$994$	41.2902			1.30964
$995$	5.03019	+	8.71254i	0.159468	+	0.276206i
$996$	45.9367			1.45556
$997$	−9.96561	+	17.2609i	−0.315614	+	0.546660i	−0.979568	−	0.201114i	$-0.935544\pi$
$997$	−9.96561	+	17.2609i	−0.315614	+	0.546660i	0.663954	+	0.747774i	$0.268877\pi$
$998$	−39.2325	+	67.9527i	−1.24188	+	2.15101i
$999$	−9.04397	−	15.6646i	−0.286139	−	0.495607i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.2.c.a.40.9	✓	90
547.506	even	3	inner	547.2.c.a.506.9	yes	90

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.2.c.a.40.9	✓	90	1.1	even	1	trivial
547.2.c.a.506.9	yes	90	547.506	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 547 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	547.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.958903 - 1.66087i) q^{2} -2.13159 q^{3} +(-0.838990 + 1.45317i) q^{4} +(0.601954 - 1.04261i) q^{5} +(2.04398 + 3.54028i) q^{6} +(0.787639 + 1.36423i) q^{7} -0.617573 q^{8} +1.54366 q^{9} +O(q^{10})\)	\(q+(-0.958903 - 1.66087i) q^{2} -2.13159 q^{3} +(-0.838990 + 1.45317i) q^{4} +(0.601954 - 1.04261i) q^{5} +(2.04398 + 3.54028i) q^{6} +(0.787639 + 1.36423i) q^{7} -0.617573 q^{8} +1.54366 q^{9} -2.30886 q^{10} +(0.652725 + 1.13055i) q^{11} +(1.78838 - 3.09756i) q^{12} +(0.727380 + 1.25986i) q^{13} +(1.51054 - 2.61633i) q^{14} +(-1.28312 + 2.22242i) q^{15} +(2.27017 + 3.93205i) q^{16} +(3.07104 + 5.31919i) q^{17} +(-1.48022 - 2.56382i) q^{18} +(3.81409 - 6.60620i) q^{19} +(1.01007 + 1.74949i) q^{20} +(-1.67892 - 2.90798i) q^{21} +(1.25180 - 2.16818i) q^{22} +(-0.962776 + 1.66758i) q^{23} +1.31641 q^{24} +(1.77530 + 3.07492i) q^{25} +(1.39497 - 2.41617i) q^{26} +3.10431 q^{27} -2.64328 q^{28} -9.18870 q^{29} +4.92153 q^{30} +6.89434 q^{31} +(3.73618 - 6.47125i) q^{32} +(-1.39134 - 2.40987i) q^{33} +(5.88966 - 10.2012i) q^{34} +1.89649 q^{35} +(-1.29511 + 2.24320i) q^{36} +(-2.91336 - 5.04608i) q^{37} -14.6294 q^{38} +(-1.55047 - 2.68550i) q^{39} +(-0.371751 + 0.643891i) q^{40} +(-2.73595 - 4.73881i) q^{41} +(-3.21984 + 5.57693i) q^{42} +(4.10040 + 7.10211i) q^{43} -2.19052 q^{44} +(0.929212 - 1.60944i) q^{45} +3.69284 q^{46} +(5.76095 - 9.97826i) q^{47} +(-4.83907 - 8.38151i) q^{48} +(2.25925 - 3.91313i) q^{49} +(3.40469 - 5.89709i) q^{50} +(-6.54618 - 11.3383i) q^{51} -2.44106 q^{52} +(-2.19809 - 3.80720i) q^{53} +(-2.97674 - 5.15586i) q^{54} +1.57164 q^{55} +(-0.486425 - 0.842513i) q^{56} +(-8.13007 + 14.0817i) q^{57} +(8.81107 + 15.2612i) q^{58} +(-0.582111 - 1.00825i) q^{59} +(-2.15304 - 3.72918i) q^{60} +(-3.58568 - 6.21058i) q^{61} +(-6.61100 - 11.4506i) q^{62} +(1.21585 + 2.10591i) q^{63} -5.24983 q^{64} +1.75140 q^{65} +(-2.66832 + 4.62166i) q^{66} +(2.68657 + 4.65328i) q^{67} -10.3063 q^{68} +(2.05224 - 3.55459i) q^{69} +(-1.81855 - 3.14982i) q^{70} +(6.83368 + 11.8363i) q^{71} -0.953323 q^{72} +(4.77755 + 8.27495i) q^{73} +(-5.58725 + 9.67740i) q^{74} +(-3.78421 - 6.55445i) q^{75} +(6.39997 + 11.0851i) q^{76} +(-1.02822 + 1.78094i) q^{77} +(-2.97351 + 5.15027i) q^{78} +12.3394 q^{79} +5.46615 q^{80} -11.2481 q^{81} +(-5.24703 + 9.08812i) q^{82} +(6.42156 + 11.1225i) q^{83} +5.63439 q^{84} +7.39449 q^{85} +(7.86378 - 13.6205i) q^{86} +19.5865 q^{87} +(-0.403106 - 0.698199i) q^{88} +8.80502 q^{89} -3.56410 q^{90} +(-1.14583 + 1.98463i) q^{91} +(-1.61552 - 2.79816i) q^{92} -14.6959 q^{93} -22.0968 q^{94} +(-4.59181 - 7.95325i) q^{95} +(-7.96398 + 13.7940i) q^{96} +(-9.69705 + 16.7958i) q^{97} -8.66560 q^{98} +(1.00759 + 1.74519i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 90 q - q^{2} - 4 q^{3} - 47 q^{4} + q^{5} - 3 q^{6} + 2 q^{7} - 30 q^{8} + 82 q^{9}+O(q^{10}) \) 90 * q - q^2 - 4 * q^3 - 47 * q^4 + q^5 - 3 * q^6 + 2 * q^7 - 30 * q^8 + 82 * q^9	\( 90 q - q^{2} - 4 q^{3} - 47 q^{4} + q^{5} - 3 q^{6} + 2 q^{7} - 30 q^{8} + 82 q^{9} - 10 q^{10} + q^{11} + 4 q^{12} - 3 q^{13} + 2 q^{14} - 7 q^{15} - 39 q^{16} - 4 q^{17} - 11 q^{18} - 2 q^{19} + 25 q^{20} - 27 q^{21} - 7 q^{22} + q^{23} + 32 q^{24} - 40 q^{25} - 10 q^{26} - 34 q^{27} - 28 q^{28} + 26 q^{29} - 40 q^{30} - 24 q^{31} + 19 q^{32} + q^{33} - 6 q^{34} - 8 q^{35} - 36 q^{36} - 10 q^{37} + 24 q^{38} + 22 q^{39} + 20 q^{40} + 3 q^{41} + 38 q^{42} - 12 q^{43} - 30 q^{44} - 2 q^{45} - 40 q^{46} + 32 q^{47} + 14 q^{48} - 43 q^{49} + 14 q^{50} + 13 q^{51} + 46 q^{52} + 9 q^{53} - 8 q^{54} + 4 q^{55} - 8 q^{56} - 8 q^{57} + 4 q^{58} + 22 q^{59} - 2 q^{60} - 12 q^{61} + 11 q^{62} + 8 q^{63} + 22 q^{64} + 18 q^{65} + 12 q^{66} - 22 q^{67} + 6 q^{68} - q^{69} - 6 q^{70} - 4 q^{71} - 140 q^{72} + 17 q^{73} + 17 q^{74} + 39 q^{75} + 84 q^{76} - 4 q^{77} + 33 q^{78} - 72 q^{79} - 40 q^{80} + 18 q^{81} - 9 q^{82} + 24 q^{83} + 114 q^{84} + 40 q^{85} - 72 q^{86} - 78 q^{87} - 22 q^{88} + 14 q^{89} + 96 q^{90} - 8 q^{92} - 76 q^{93} + 108 q^{94} - 11 q^{95} - 34 q^{96} - 74 q^{98} - 62 q^{99}+O(q^{100}) \) 90 * q - q^2 - 4 * q^3 - 47 * q^4 + q^5 - 3 * q^6 + 2 * q^7 - 30 * q^8 + 82 * q^9 - 10 * q^10 + q^11 + 4 * q^12 - 3 * q^13 + 2 * q^14 - 7 * q^15 - 39 * q^16 - 4 * q^17 - 11 * q^18 - 2 * q^19 + 25 * q^20 - 27 * q^21 - 7 * q^22 + q^23 + 32 * q^24 - 40 * q^25 - 10 * q^26 - 34 * q^27 - 28 * q^28 + 26 * q^29 - 40 * q^30 - 24 * q^31 + 19 * q^32 + q^33 - 6 * q^34 - 8 * q^35 - 36 * q^36 - 10 * q^37 + 24 * q^38 + 22 * q^39 + 20 * q^40 + 3 * q^41 + 38 * q^42 - 12 * q^43 - 30 * q^44 - 2 * q^45 - 40 * q^46 + 32 * q^47 + 14 * q^48 - 43 * q^49 + 14 * q^50 + 13 * q^51 + 46 * q^52 + 9 * q^53 - 8 * q^54 + 4 * q^55 - 8 * q^56 - 8 * q^57 + 4 * q^58 + 22 * q^59 - 2 * q^60 - 12 * q^61 + 11 * q^62 + 8 * q^63 + 22 * q^64 + 18 * q^65 + 12 * q^66 - 22 * q^67 + 6 * q^68 - q^69 - 6 * q^70 - 4 * q^71 - 140 * q^72 + 17 * q^73 + 17 * q^74 + 39 * q^75 + 84 * q^76 - 4 * q^77 + 33 * q^78 - 72 * q^79 - 40 * q^80 + 18 * q^81 - 9 * q^82 + 24 * q^83 + 114 * q^84 + 40 * q^85 - 72 * q^86 - 78 * q^87 - 22 * q^88 + 14 * q^89 + 96 * q^90 - 8 * q^92 - 76 * q^93 + 108 * q^94 - 11 * q^95 - 34 * q^96 - 74 * q^98 - 62 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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