LMFDB - Embedded newform 547.2.c.a.40.1

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			40.1
Character	$\chi$	$=$	547.40
Dual form			547.2.c.a.506.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.33767 - 2.31692i) q^{2} +0.0966282 q^{3} +(-2.57874 + 4.46650i) q^{4} +(1.37326 - 2.37856i) q^{5} +(-0.129257 - 0.223879i) q^{6} +(1.47773 + 2.55950i) q^{7} +8.44732 q^{8} -2.99066 q^{9} +O(q^{10})$	\(q+(-1.33767 - 2.31692i) q^{2} +0.0966282 q^{3} +(-2.57874 + 4.46650i) q^{4} +(1.37326 - 2.37856i) q^{5} +(-0.129257 - 0.223879i) q^{6} +(1.47773 + 2.55950i) q^{7} +8.44732 q^{8} -2.99066 q^{9} -7.34791 q^{10} +(2.52005 + 4.36485i) q^{11} +(-0.249179 + 0.431590i) q^{12} +(-2.62031 - 4.53851i) q^{13} +(3.95343 - 6.84754i) q^{14} +(0.132696 - 0.229836i) q^{15} +(-6.14228 - 10.6387i) q^{16} +(-2.40693 - 4.16892i) q^{17} +(4.00053 + 6.92912i) q^{18} +(3.74402 - 6.48483i) q^{19} +(7.08257 + 12.2674i) q^{20} +(0.142790 + 0.247320i) q^{21} +(6.74200 - 11.6775i) q^{22} +(3.99818 - 6.92506i) q^{23} +0.816250 q^{24} +(-1.27171 - 2.20266i) q^{25} +(-7.01024 + 12.1421i) q^{26} -0.578867 q^{27} -15.2427 q^{28} +3.44196 q^{29} -0.710015 q^{30} -1.07924 q^{31} +(-7.98540 + 13.8311i) q^{32} +(0.243508 + 0.421768i) q^{33} +(-6.43936 + 11.1533i) q^{34} +8.11724 q^{35} +(7.71213 - 13.3578i) q^{36} +(-2.55362 - 4.42299i) q^{37} -20.0331 q^{38} +(-0.253196 - 0.438548i) q^{39} +(11.6004 - 20.0925i) q^{40} +(0.995306 + 1.72392i) q^{41} +(0.382013 - 0.661666i) q^{42} +(-2.86295 - 4.95878i) q^{43} -25.9942 q^{44} +(-4.10697 + 7.11348i) q^{45} -21.3930 q^{46} +(-2.56592 + 4.44430i) q^{47} +(-0.593518 - 1.02800i) q^{48} +(-0.867357 + 1.50231i) q^{49} +(-3.40225 + 5.89287i) q^{50} +(-0.232577 - 0.402835i) q^{51} +27.0284 q^{52} +(-2.37517 - 4.11391i) q^{53} +(0.774334 + 1.34119i) q^{54} +13.8428 q^{55} +(12.4828 + 21.6209i) q^{56} +(0.361778 - 0.626618i) q^{57} +(-4.60421 - 7.97473i) q^{58} +(2.75948 + 4.77956i) q^{59} +(0.684376 + 1.18537i) q^{60} +(2.42552 + 4.20113i) q^{61} +(1.44366 + 2.50050i) q^{62} +(-4.41939 - 7.65460i) q^{63} +18.1583 q^{64} -14.3935 q^{65} +(0.651468 - 1.12837i) q^{66} +(4.86120 + 8.41984i) q^{67} +24.8273 q^{68} +(0.386337 - 0.669156i) q^{69} +(-10.8582 - 18.8070i) q^{70} +(3.06217 + 5.30384i) q^{71} -25.2631 q^{72} +(-6.87493 - 11.9077i) q^{73} +(-6.83180 + 11.8330i) q^{74} +(-0.122883 - 0.212839i) q^{75} +(19.3097 + 33.4453i) q^{76} +(-7.44789 + 12.9001i) q^{77} +(-0.677387 + 1.17327i) q^{78} +8.49561 q^{79} -33.7399 q^{80} +8.91605 q^{81} +(2.66279 - 4.61208i) q^{82} +(0.180806 + 0.313165i) q^{83} -1.47287 q^{84} -13.2214 q^{85} +(-7.65939 + 13.2664i) q^{86} +0.332590 q^{87} +(21.2877 + 36.8713i) q^{88} +1.60520 q^{89} +21.9751 q^{90} +(7.74421 - 13.4134i) q^{91} +(20.6205 + 35.7158i) q^{92} -0.104285 q^{93} +13.7294 q^{94} +(-10.2831 - 17.8108i) q^{95} +(-0.771615 + 1.33648i) q^{96} +(3.61170 - 6.25565i) q^{97} +4.64096 q^{98} +(-7.53662 - 13.0538i) 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 $

$2$	−1.33767	−	2.31692i	−0.945877	−	1.63831i	−0.753985	−	0.656892i	$-0.771871\pi$
$2$	−1.33767	−	2.31692i	−0.945877	−	1.63831i	−0.191892	−	0.981416i	$-0.561462\pi$
$3$	0.0966282			0.0557883			0.0278942	−	0.999611i	$-0.491120\pi$
$3$	0.0966282			0.0557883			0.0278942	+	0.999611i	$0.491120\pi$
$4$	−2.57874	+	4.46650i	−1.28937	+	2.23325i
$5$	1.37326	−	2.37856i	0.614142	−	1.06373i	−0.376392	−	0.926460i	$-0.622835\pi$
$5$	1.37326	−	2.37856i	0.614142	−	1.06373i	0.990534	−	0.137265i	$-0.0438312\pi$
$6$	−0.129257	−	0.223879i	−0.0527689	−	0.0913984i
$7$	1.47773	+	2.55950i	0.558529	+	0.967400i	0.997620	+	0.0689572i	$0.0219672\pi$
$7$	1.47773	+	2.55950i	0.558529	+	0.967400i	−0.439091	+	0.898443i	$0.644699\pi$
$8$	8.44732			2.98658
$9$	−2.99066			−0.996888
$10$	−7.34791			−2.32361
$11$	2.52005	+	4.36485i	0.759824	+	1.31605i	0.942940	+	0.332962i	$0.108048\pi$
$11$	2.52005	+	4.36485i	0.759824	+	1.31605i	−0.183117	+	0.983091i	$0.558619\pi$
$12$	−0.249179	+	0.431590i	−0.0719317	+	0.124589i
$13$	−2.62031	−	4.53851i	−0.726744	−	1.25876i	−0.958252	−	0.285924i	$-0.907700\pi$
$13$	−2.62031	−	4.53851i	−0.726744	−	1.25876i	0.231509	−	0.972833i	$-0.425634\pi$
$14$	3.95343	−	6.84754i	1.05660	−	1.83008i
$15$	0.132696	−	0.229836i	0.0342620	−	0.0593434i
$16$	−6.14228	−	10.6387i	−1.53557	−	2.65969i
$17$	−2.40693	−	4.16892i	−0.583765	−	1.01111i	−0.995028	−	0.0995942i	$-0.968246\pi$
$17$	−2.40693	−	4.16892i	−0.583765	−	1.01111i	0.411263	−	0.911517i	$-0.365088\pi$
$18$	4.00053	+	6.92912i	0.942933	+	1.63321i
$19$	3.74402	−	6.48483i	0.858937	−	1.48772i	−0.0140065	−	0.999902i	$-0.504459\pi$
$19$	3.74402	−	6.48483i	0.858937	−	1.48772i	0.872944	−	0.487821i	$-0.162208\pi$
$20$	7.08257	+	12.2674i	1.58371	+	2.74307i
$21$	0.142790	+	0.247320i	0.0311594	+	0.0539696i
$22$	6.74200	−	11.6775i	1.43740	−	2.48965i
$23$	3.99818	−	6.92506i	0.833679	−	1.44397i	−0.0614222	−	0.998112i	$-0.519564\pi$
$23$	3.99818	−	6.92506i	0.833679	−	1.44397i	0.895101	−	0.445863i	$-0.147103\pi$
$24$	0.816250			0.166616
$25$	−1.27171	−	2.20266i	−0.254341	−	0.440532i
$26$	−7.01024	+	12.1421i	−1.37482	+	2.38126i
$27$	−0.578867			−0.111403
$28$	−15.2427			−2.88059
$29$	3.44196			0.639156			0.319578	−	0.947560i	$-0.396459\pi$
$29$	3.44196			0.639156			0.319578	+	0.947560i	$0.396459\pi$
$30$	−0.710015			−0.129630
$31$	−1.07924			−0.193837			−0.0969183	−	0.995292i	$-0.530899\pi$
$31$	−1.07924			−0.193837			−0.0969183	+	0.995292i	$0.530899\pi$
$32$	−7.98540	+	13.8311i	−1.41163	+	2.44502i
$33$	0.243508	+	0.421768i	0.0423893	+	0.0734204i
$34$	−6.43936	+	11.1533i	−1.10434	+	1.91277i
$35$	8.11724			1.37206
$36$	7.71213	−	13.3578i	1.28535	−	2.22630i
$37$	−2.55362	−	4.42299i	−0.419812	−	0.727136i	0.576108	−	0.817373i	$-0.304571\pi$
$37$	−2.55362	−	4.42299i	−0.419812	−	0.727136i	−0.995920	+	0.0902378i	$0.971237\pi$
$38$	−20.0331			−3.24980
$39$	−0.253196	−	0.438548i	−0.0405438	−	0.0702239i
$40$	11.6004	−	20.0925i	1.83418	−	3.17690i
$41$	0.995306	+	1.72392i	0.155441	+	0.269231i	0.933219	−	0.359307i	$-0.116987\pi$
$41$	0.995306	+	1.72392i	0.155441	+	0.269231i	−0.777779	+	0.628538i	$0.783654\pi$
$42$	0.382013	−	0.661666i	0.0589459	−	0.102097i
$43$	−2.86295	−	4.95878i	−0.436596	−	0.756207i	0.560828	−	0.827932i	$-0.310483\pi$
$43$	−2.86295	−	4.95878i	−0.436596	−	0.756207i	−0.997424	+	0.0717253i	$0.977150\pi$
$44$	−25.9942			−3.91877
$45$	−4.10697	+	7.11348i	−0.612231	+	1.06041i
$46$	−21.3930			−3.15423
$47$	−2.56592	+	4.44430i	−0.374278	+	0.648269i	−0.990219	−	0.139524i	$-0.955443\pi$
$47$	−2.56592	+	4.44430i	−0.374278	+	0.648269i	0.615941	+	0.787793i	$0.288776\pi$
$48$	−0.593518	−	1.02800i	−0.0856669	−	0.148379i
$49$	−0.867357	+	1.50231i	−0.123908	+	0.214615i
$50$	−3.40225	+	5.89287i	−0.481151	+	0.833378i
$51$	−0.232577	−	0.402835i	−0.0325673	−	0.0564082i
$52$	27.0284			3.74816
$53$	−2.37517	−	4.11391i	−0.326254	−	0.565089i	0.655511	−	0.755185i	$-0.272453\pi$
$53$	−2.37517	−	4.11391i	−0.326254	−	0.565089i	−0.981765	+	0.190097i	$0.939120\pi$
$54$	0.774334	+	1.34119i	0.105374	+	0.182512i
$55$	13.8428			1.86656
$56$	12.4828	+	21.6209i	1.66809	+	2.88922i
$57$	0.361778	−	0.626618i	0.0479187	−	0.0829976i
$58$	−4.60421	−	7.97473i	−0.604563	−	1.04713i
$59$	2.75948	+	4.77956i	0.359254	+	0.622246i	0.987836	−	0.155497i	$-0.0496980\pi$
$59$	2.75948	+	4.77956i	0.359254	+	0.622246i	−0.628583	+	0.777743i	$0.716365\pi$
$60$	0.684376	+	1.18537i	0.0883525	+	0.153031i
$61$	2.42552	+	4.20113i	0.310556	+	0.537899i	0.978483	−	0.206328i	$-0.0661513\pi$
$61$	2.42552	+	4.20113i	0.310556	+	0.537899i	−0.667927	+	0.744227i	$0.732818\pi$
$62$	1.44366	+	2.50050i	0.183346	+	0.317564i
$63$	−4.41939	−	7.65460i	−0.556790	−	0.964389i
$64$	18.1583			2.26978
$65$	−14.3935			−1.78530
$66$	0.651468	−	1.12837i	0.0801901	−	0.138893i
$67$	4.86120	+	8.41984i	0.593890	+	1.02865i	0.993702	+	0.112051i	$0.0357419\pi$
$67$	4.86120	+	8.41984i	0.593890	+	1.02865i	−0.399813	+	0.916597i	$0.630925\pi$
$68$	24.8273			3.01075
$69$	0.386337	−	0.669156i	0.0465096	−	0.0805569i
$70$	−10.8582	−	18.8070i	−1.29780	−	2.24786i
$71$	3.06217	+	5.30384i	0.363413	+	0.629450i	0.988520	−	0.151089i	$-0.0482780\pi$
$71$	3.06217	+	5.30384i	0.363413	+	0.629450i	−0.625107	+	0.780539i	$0.714945\pi$
$72$	−25.2631			−2.97728
$73$	−6.87493	−	11.9077i	−0.804650	−	1.39369i	−0.916527	−	0.399972i	$-0.869020\pi$
$73$	−6.87493	−	11.9077i	−0.804650	−	1.39369i	0.111877	−	0.993722i	$-0.464314\pi$
$74$	−6.83180	+	11.8330i	−0.794181	+	1.37556i
$75$	−0.122883	−	0.212839i	−0.0141893	−	0.0245765i
$76$	19.3097	+	33.4453i	2.21497	+	3.83644i
$77$	−7.44789	+	12.9001i	−0.848766	+	1.47011i
$78$	−0.677387	+	1.17327i	−0.0766989	+	0.132846i
$79$	8.49561			0.955831			0.477915	−	0.878406i	$-0.341393\pi$
$79$	8.49561			0.955831			0.477915	+	0.878406i	$0.341393\pi$
$80$	−33.7399			−3.77223
$81$	8.91605			0.990673
$82$	2.66279	−	4.61208i	0.294055	−	0.509319i
$83$	0.180806	+	0.313165i	0.0198460	+	0.0343743i	0.875778	−	0.482714i	$-0.160349\pi$
$83$	0.180806	+	0.313165i	0.0198460	+	0.0343743i	−0.855932	+	0.517089i	$0.827016\pi$
$84$	−1.47287			−0.160704
$85$	−13.2214			−1.43406
$86$	−7.65939	+	13.2664i	−0.825933	+	1.43056i
$87$	0.332590			0.0356574
$88$	21.2877	+	36.8713i	2.26927	+	3.93050i
$89$	1.60520			0.170151			0.0850756	−	0.996374i	$-0.472887\pi$
$89$	1.60520			0.170151			0.0850756	+	0.996374i	$0.472887\pi$
$90$	21.9751			2.31638
$91$	7.74421	−	13.4134i	0.811814	−	1.40610i
$92$	20.6205	+	35.7158i	2.14984	+	3.72363i
$93$	−0.104285			−0.0108138
$94$	13.7294			1.41608
$95$	−10.2831	−	17.8108i	−1.05502	−	1.82735i
$96$	−0.771615	+	1.33648i	−0.0787526	+	0.136403i
$97$	3.61170	−	6.25565i	0.366713	−	0.635165i	−0.622337	−	0.782750i	$-0.713816\pi$
$97$	3.61170	−	6.25565i	0.366713	−	0.635165i	0.989049	+	0.147584i	$0.0471498\pi$
$98$	4.64096			0.468808
$99$	−7.53662	−	13.0538i	−0.757459	−	1.31196i
$100$	13.1176			1.31176
$101$	10.4937			1.04416			0.522079	−	0.852897i	$-0.325156\pi$
$101$	10.4937			1.04416			0.522079	+	0.852897i	$0.325156\pi$
$102$	−0.622223	+	1.07772i	−0.0616093	+	0.106710i
$103$	−17.1788			−1.69267			−0.846337	−	0.532647i	$-0.821197\pi$
$103$	−17.1788			−1.69267			−0.846337	+	0.532647i	$0.821197\pi$
$104$	−22.1346	−	38.3383i	−2.17048	−	3.75938i
$105$	0.784354			0.0765451
$106$	−6.35439	+	11.0061i	−0.617193	+	1.06901i
$107$	14.7845			1.42927			0.714635	−	0.699498i	$-0.246593\pi$
$107$	14.7845			1.42927			0.714635	+	0.699498i	$0.246593\pi$
$108$	1.49274	−	2.58551i	0.143639	−	0.248791i
$109$	−2.62468	+	4.54608i	−0.251399	+	0.435436i	−0.963911	−	0.266224i	$-0.914224\pi$
$109$	−2.62468	+	4.54608i	−0.251399	+	0.435436i	0.712512	+	0.701660i	$0.247557\pi$
$110$	−18.5171	−	32.0725i	−1.76554	−	3.05800i
$111$	−0.246751	−	0.427386i	−0.0234206	−	0.0405657i
$112$	18.1532	−	31.4423i	1.71532	−	2.97102i
$113$	3.88163	−	6.72318i	0.365153	−	0.632463i	−0.623648	−	0.781705i	$-0.714350\pi$
$113$	3.88163	−	6.72318i	0.365153	−	0.632463i	0.988801	+	0.149242i	$0.0476834\pi$
$114$	−1.93576			−0.181301
$115$	−10.9811	−	19.0199i	−1.02399	−	1.77361i
$116$	−8.87590	+	15.3735i	−0.824107	+	1.42739i
$117$	7.83647	+	13.5732i	0.724482	+	1.25484i
$118$	7.38256	−	12.7870i	0.679620	−	1.17714i
$119$	7.11356	−	12.3210i	0.652099	−	1.12947i
$120$	1.12093	−	1.94150i	0.102326	−	0.177234i
$121$	−7.20130	+	12.4730i	−0.654664	+	1.13391i
$122$	6.48911	−	11.2395i	0.587496	−	1.01757i
$123$	0.0961746	+	0.166579i	0.00867177	+	0.0150199i
$124$	2.78306	−	4.82041i	0.249927	−	0.432886i
$125$	6.74709			0.603478
$126$	−11.8234	+	20.4787i	−1.05331	+	1.82439i
$127$	−6.39208	+	11.0714i	−0.567205	+	0.982428i	0.429636	+	0.903002i	$0.358642\pi$
$127$	−6.39208	+	11.0714i	−0.567205	+	0.982428i	−0.996841	+	0.0794257i	$0.974691\pi$
$128$	−8.31901	−	14.4090i	−0.735304	−	1.27358i
$129$	−0.276642	−	0.479158i	−0.0243570	−	0.0421875i
$130$	19.2538	+	33.3486i	1.68867	+	2.92486i
$131$	−15.2327			−1.33089			−0.665444	−	0.746448i	$-0.731758\pi$
$131$	−15.2327			−1.33089			−0.665444	+	0.746448i	$0.731758\pi$
$132$	−2.51177			−0.218621
$133$	22.1306			1.91896
$134$	13.0054	−	22.5260i	1.12349	−	1.94595i
$135$	−0.794937	+	1.37687i	−0.0684173	+	0.118502i
$136$	−20.3321	−	35.2162i	−1.74346	−	3.01976i
$137$	−5.18037	−	8.97266i	−0.442589	−	0.766586i	0.555292	−	0.831655i	$-0.312606\pi$
$137$	−5.18037	−	8.97266i	−0.442589	−	0.766586i	−0.997881	+	0.0650695i	$0.979273\pi$
$138$	−2.06717			−0.175969
$139$	−4.22334	−	7.31503i	−0.358219	−	0.620453i	0.629445	−	0.777045i	$-0.283282\pi$
$139$	−4.22334	−	7.31503i	−0.358219	−	0.620453i	−0.987663	+	0.156592i	$0.949949\pi$
$140$	−20.9322	+	36.2556i	−1.76909	+	3.06416i
$141$	−0.247940	+	0.429445i	−0.0208803	+	0.0361658i
$142$	8.19237	−	14.1896i	0.687489	−	1.19077i
$143$	13.2066	−	22.8746i	1.10439	−	1.91287i
$144$	18.3695	+	31.8169i	1.53079	+	2.65141i
$145$	4.72672	−	8.18691i	0.392532	−	0.679886i
$146$	−18.3928	+	31.8573i	−1.52220	+	2.63653i
$147$	−0.0838112	+	0.145165i	−0.00691263	+	0.0119730i
$148$	26.3404			2.16517
$149$	−9.06329			−0.742494			−0.371247	−	0.928534i	$-0.621070\pi$
$149$	−9.06329			−0.742494			−0.371247	+	0.928534i	$0.621070\pi$
$150$	−0.328753	+	0.569418i	−0.0268426	+	0.0464928i
$151$	−10.8994			−0.886984			−0.443492	−	0.896278i	$-0.646261\pi$
$151$	−10.8994			−0.886984			−0.443492	+	0.896278i	$0.646261\pi$
$152$	31.6270	−	54.7795i	2.56528	−	4.44320i
$153$	7.19830	+	12.4678i	0.581948	+	1.00796i
$154$	39.8514			3.21132
$155$	−1.48208	+	2.56703i	−0.119043	+	0.206189i
$156$	2.61170			0.209103
$157$	3.21555	+	5.56950i	0.256629	+	0.444494i	0.965337	−	0.261008i	$-0.0840549\pi$
$157$	3.21555	+	5.56950i	0.256629	+	0.444494i	−0.708708	+	0.705502i	$0.750722\pi$
$158$	−11.3643	−	19.6836i	−0.904098	−	1.56594i
$159$	−0.229508	−	0.397519i	−0.0182012	−	0.0315253i
$160$	21.9321	+	37.9875i	1.73389	+	3.00318i
$161$	23.6329			1.86253
$162$	−11.9268	−	20.6578i	−0.937055	−	1.62303i
$163$	9.73704	+	16.8650i	0.762663	+	1.32097i	0.941473	+	0.337088i	$0.109442\pi$
$163$	9.73704	+	16.8650i	0.762663	+	1.32097i	−0.178810	+	0.983884i	$0.557225\pi$
$164$	−10.2665			−0.801680
$165$	1.33760			0.104132
$166$	0.483717	−	0.837823i	0.0375438	−	0.0650277i
$167$	14.5586			1.12658			0.563289	−	0.826260i	$-0.309536\pi$
$167$	14.5586			1.12658			0.563289	+	0.826260i	$0.309536\pi$
$168$	1.20619	+	2.08919i	0.0930599	+	0.161185i
$169$	−7.23206	+	12.5263i	−0.556312	+	0.963561i
$170$	17.6859	+	30.6328i	1.35644	+	2.34943i
$171$	−11.1971	+	19.3940i	−0.856264	+	1.48309i
$172$	29.5312			2.25173
$173$	12.6653			0.962927			0.481464	−	0.876466i	$-0.340105\pi$
$173$	12.6653			0.962927			0.481464	+	0.876466i	$0.340105\pi$
$174$	−0.444897	−	0.770584i	−0.0337275	−	0.0584178i
$175$	3.75847	−	6.50986i	0.284114	−	0.492099i
$176$	30.9577	−	53.6203i	2.33353	−	4.04178i
$177$	0.266644	+	0.461840i	0.0200422	+	0.0347140i
$178$	−2.14724	−	3.71912i	−0.160942	−	0.278760i
$179$	−15.6788			−1.17189			−0.585944	−	0.810352i	$-0.699276\pi$
$179$	−15.6788			−1.17189			−0.585944	+	0.810352i	$0.699276\pi$
$180$	−21.1816	−	36.6876i	−1.57878	−	2.73453i
$181$	−5.23462	+	9.06662i	−0.389086	+	0.673917i	−0.992327	−	0.123642i	$-0.960542\pi$
$181$	−5.23462	+	9.06662i	−0.389086	+	0.673917i	0.603241	+	0.797559i	$0.293876\pi$
$182$	−41.4369			−3.07151
$183$	0.234374	+	0.405948i	0.0173254	+	0.0300085i
$184$	33.7740	−	58.4982i	2.48985	−	4.31255i
$185$	−14.0272			−1.03130
$186$	0.139499	+	0.241619i	0.0102285	+	0.0177164i
$187$	12.1311	−	21.0118i	0.887117	−	1.53653i
$188$	−13.2337	−	22.9214i	−0.965164	−	1.67171i
$189$	−0.855408	−	1.48161i	−0.0622218	−	0.107771i
$190$	−27.5107	+	47.6500i	−1.99584	+	3.45689i
$191$	−5.91405	+	10.2434i	−0.427925	+	0.741188i	−0.996689	−	0.0813128i	$-0.974089\pi$
$191$	−5.91405	+	10.2434i	−0.427925	+	0.741188i	0.568763	+	0.822501i	$0.307422\pi$
$192$	1.75460			0.126627
$193$	−10.2578	+	17.7670i	−0.738372	+	1.27890i	0.214855	+	0.976646i	$0.431072\pi$
$193$	−10.2578	+	17.7670i	−0.738372	+	1.27890i	−0.953228	+	0.302253i	$0.902261\pi$
$194$	−19.3251			−1.38746
$195$	−1.39082			−0.0995986
$196$	−4.47337	−	7.74811i	−0.319526	−	0.553436i
$197$	5.90377			0.420626			0.210313	−	0.977634i	$-0.432552\pi$
$197$	5.90377			0.420626			0.210313	+	0.977634i	$0.432552\pi$
$198$	−20.1631	+	34.9234i	−1.43293	+	2.48190i
$199$	0.00686276	−	0.0118867i	0.000486488	−	0.000842623i	−0.865782	−	0.500421i	$-0.833178\pi$
$199$	0.00686276	−	0.0118867i	0.000486488	−	0.000842623i	0.866269	+	0.499579i	$0.166512\pi$
$200$	−10.7425	−	18.6066i	−0.759610	−	1.31568i
$201$	0.469729	+	0.813594i	0.0331321	+	0.0573865i
$202$	−14.0371	−	24.3130i	−0.987646	−	1.71065i
$203$	5.08628	+	8.80969i	0.356987	+	0.618319i
$204$	2.39902			0.167965
$205$	5.46727			0.381851
$206$	22.9796	+	39.8018i	1.60106	+	2.77312i
$207$	−11.9572	+	20.7105i	−0.831084	+	1.43948i
$208$	−32.1894	+	55.7536i	−2.23193	+	3.86582i
$209$	37.7405			2.61056
$210$	−1.04921	−	1.81728i	−0.0724023	−	0.125404i
$211$	4.79029	−	8.29702i	0.329777	−	0.571191i	−0.652690	−	0.757625i	$-0.726360\pi$
$211$	4.79029	−	8.29702i	0.329777	−	0.571191i	0.982467	+	0.186434i	$0.0596931\pi$
$212$	24.4997			1.68265
$213$	0.295892	+	0.512501i	0.0202742	+	0.0351160i
$214$	−19.7768	−	34.2544i	−1.35191	−	2.34158i
$215$	−15.7264			−1.07253
$216$	−4.88988			−0.332714
$217$	−1.59482	−	2.76230i	−0.108263	−	0.187517i
$218$	14.0439			0.951170
$219$	−0.664312	−	1.15062i	−0.0448901	−	0.0777519i
$220$	−35.6968	+	61.8287i	−2.40668	+	4.16849i
$221$	−12.6138	+	21.8477i	−0.848495	+	1.46964i
$222$	−0.660145	+	1.14340i	−0.0443060	+	0.0767403i
$223$	2.32492	−	4.02688i	0.155688	−	0.269660i	−0.777621	−	0.628733i	$-0.783574\pi$
$223$	2.32492	−	4.02688i	0.155688	−	0.269660i	0.933309	+	0.359073i	$0.116907\pi$
$224$	−47.2010			−3.15375
$225$	3.80324	+	6.58741i	0.253550	+	0.439161i
$226$	−20.7694			−1.38156
$227$	−10.5327	+	18.2431i	−0.699078	+	1.21084i	0.269708	+	0.962942i	$0.413073\pi$
$227$	−10.5327	+	18.2431i	−0.699078	+	1.21084i	−0.968786	+	0.247897i	$0.920261\pi$
$228$	1.86586	+	3.23176i	0.123570	+	0.214029i
$229$	−5.52118	+	9.56296i	−0.364850	+	0.631938i	−0.988752	−	0.149564i	$-0.952213\pi$
$229$	−5.52118	+	9.56296i	−0.364850	+	0.631938i	0.623902	+	0.781502i	$0.285546\pi$
$230$	−29.3783	+	50.8847i	−1.93715	+	3.35524i
$231$	−0.719677	+	1.24652i	−0.0473512	+	0.0820148i
$232$	29.0753			1.90889
$233$	−2.69050	+	4.66009i	−0.176261	+	0.305292i	−0.940597	−	0.339526i	$-0.889733\pi$
$233$	−2.69050	+	4.66009i	−0.176261	+	0.305292i	0.764336	+	0.644818i	$0.223067\pi$
$234$	20.9653	−	36.3129i	1.37054	−	2.37385i
$235$	7.04737	+	12.2064i	0.459720	+	0.796258i
$236$	−28.4639			−1.85284
$237$	0.820915			0.0533242
$238$	−38.0625			−2.46722
$239$	−6.00674	−	10.4040i	−0.388544	−	0.672978i	0.603710	−	0.797204i	$-0.293688\pi$
$239$	−6.00674	−	10.4040i	−0.388544	−	0.672978i	−0.992254	+	0.124226i	$0.960355\pi$
$240$	−3.26022			−0.210447
$241$	8.65749	−	14.9952i	0.557678	−	0.965927i	−0.440012	−	0.897992i	$-0.645026\pi$
$241$	8.65749	−	14.9952i	0.557678	−	0.965927i	0.997690	−	0.0679346i	$-0.0216409\pi$
$242$	38.5319			2.47693
$243$	2.59814			0.166671
$244$	−25.0191			−1.60169
$245$	2.38222	+	4.12613i	0.152194	+	0.263609i
$246$	0.257300	−	0.445657i	0.0164049	−	0.0284141i
$247$	−39.2420			−2.49691
$248$	−9.11666			−0.578908
$249$	0.0174709	+	0.0302605i	0.00110717	+	0.00191768i
$250$	−9.02539	−	15.6324i	−0.570816	−	0.988682i
$251$	1.20993	+	2.09566i	0.0763702	+	0.132277i	0.901681	−	0.432401i	$-0.142334\pi$
$251$	1.20993	+	2.09566i	0.0763702	+	0.132277i	−0.825311	+	0.564678i	$0.809000\pi$
$252$	45.5857			2.87163
$253$	40.3025			2.53380
$254$	34.2020			2.14603
$255$	−1.27756			−0.0800037
$256$	−4.09797	+	7.09789i	−0.256123	+	0.443618i
$257$	16.4906			1.02865			0.514327	−	0.857594i	$-0.328042\pi$
$257$	16.4906			1.02865			0.514327	+	0.857594i	$0.328042\pi$
$258$	−0.740113	+	1.28191i	−0.0460774	+	0.0798084i
$259$	7.54710	−	13.0720i	0.468954	−	0.812252i
$260$	37.1171	−	64.2886i	2.30190	−	3.98701i
$261$	−10.2937			−0.637166
$262$	20.3764	+	35.2929i	1.25886	+	2.18040i
$263$	18.6807			1.15190			0.575951	−	0.817484i	$-0.304632\pi$
$263$	18.6807			1.15190			0.575951	+	0.817484i	$0.304632\pi$
$264$	2.05699	+	3.56281i	0.126599	+	0.219276i
$265$	−13.0469			−0.801465
$266$	−29.6035	−	51.2747i	−1.81510	−	3.14385i
$267$	0.155108			0.00949245
$268$	−50.1430			−3.06297
$269$	2.61414	−	4.52782i	0.159387	−	0.276066i	−0.775261	−	0.631641i	$-0.782382\pi$
$269$	2.61414	−	4.52782i	0.159387	−	0.276066i	0.934648	+	0.355575i	$0.115715\pi$
$270$	4.25346			0.258857
$271$	−2.32291	−	4.02339i	−0.141106	−	0.244404i	0.786807	−	0.617199i	$-0.211733\pi$
$271$	−2.32291	−	4.02339i	−0.141106	−	0.244404i	−0.927914	+	0.372795i	$0.878399\pi$
$272$	−29.5680	+	51.2133i	−1.79282	+	3.10526i
$273$	0.748309	−	1.29611i	0.0452897	−	0.0784441i
$274$	−13.8593	+	24.0050i	−0.837269	+	1.45019i
$275$	6.40952	−	11.1016i	0.386509	−	0.669453i
$276$	1.99252	+	3.45115i	0.119936	+	0.207735i
$277$	−10.6767			−0.641502			−0.320751	−	0.947164i	$-0.603935\pi$
$277$	−10.6767			−0.641502			−0.320751	+	0.947164i	$0.603935\pi$
$278$	−11.2989	+	19.5702i	−0.677662	+	1.17374i
$279$	3.22763			0.193233
$280$	68.5689			4.09778
$281$	13.6960	+	23.7221i	0.817032	+	1.41514i	0.907860	+	0.419274i	$0.137715\pi$
$281$	13.6960	+	23.7221i	0.817032	+	1.41514i	−0.0908275	+	0.995867i	$0.528951\pi$
$282$	1.32665			0.0790010
$283$	−2.50898	−	4.34569i	−0.149144	−	0.258324i	0.781768	−	0.623570i	$-0.214318\pi$
$283$	−2.50898	−	4.34569i	−0.149144	−	0.258324i	−0.930911	+	0.365246i	$0.880985\pi$
$284$	−31.5862			−1.87429
$285$	−0.993633	−	1.72102i	−0.0588577	−	0.101945i
$286$	−70.6646			−4.17848
$287$	−2.94158	+	5.09497i	−0.173636	+	0.300746i
$288$	23.8816	−	41.3642i	1.40724	−	2.43741i
$289$	−3.08658	+	5.34611i	−0.181563	+	0.314477i
$290$	−25.2912			−1.48515
$291$	0.348992	−	0.604473i	0.0204583	−	0.0354348i
$292$	70.9145			4.14996
$293$	−3.74951			−0.219049			−0.109524	−	0.993984i	$-0.534933\pi$
$293$	−3.74951			−0.219049			−0.109524	+	0.993984i	$0.534933\pi$
$294$	0.448448			0.0261540
$295$	15.1580			0.882531
$296$	−21.5712	−	37.3625i	−1.25380	−	2.17165i
$297$	−1.45877	−	2.52667i	−0.0846466	−	0.146612i
$298$	12.1237	+	20.9989i	0.702308	+	1.21643i
$299$	−41.9060			−2.42348
$300$	1.26753			0.0731807
$301$	8.46133	−	14.6555i	0.487703	−	0.844726i
$302$	14.5799	+	25.2531i	0.838978	+	1.45315i
$303$	1.01398			0.0582519
$304$	−91.9873			−5.27583
$305$	13.3235			0.762903
$306$	19.2579	−	33.3557i	1.10090	−	1.90682i
$307$	20.9722			1.19695			0.598474	−	0.801143i	$-0.295774\pi$
$307$	20.9722			1.19695			0.598474	+	0.801143i	$0.295774\pi$
$308$	−38.4123	−	66.5320i	−2.18874	−	3.79102i
$309$	−1.65995			−0.0944315
$310$	7.93013			0.450401
$311$	25.2055			1.42927			0.714637	−	0.699496i	$-0.246592\pi$
$311$	25.2055			1.42927			0.714637	+	0.699496i	$0.246592\pi$
$312$	−2.13883	−	3.70456i	−0.121087	−	0.209729i
$313$	7.88544	−	13.6580i	0.445711	−	0.771995i	−0.552390	−	0.833586i	$-0.686284\pi$
$313$	7.88544	−	13.6580i	0.445711	−	0.771995i	0.998101	+	0.0615910i	$0.0196175\pi$
$314$	8.60271	−	14.9003i	0.485479	−	0.840874i
$315$	−24.2759			−1.36779
$316$	−21.9079	+	37.9456i	−1.23242	+	2.13461i
$317$	−16.7957	+	29.0911i	−0.943343	+	1.63392i	−0.184308	+	0.982869i	$0.559004\pi$
$317$	−16.7957	+	29.0911i	−0.943343	+	1.63392i	−0.759035	+	0.651050i	$0.774329\pi$
$318$	−0.614013	+	1.06350i	−0.0344321	+	0.0596382i
$319$	8.67391	+	15.0236i	0.485646	+	0.841163i
$320$	24.9361	−	43.1906i	1.39397	−	2.41443i
$321$	1.42860			0.0797365
$322$	−31.6131	−	54.7555i	−1.76173	−	3.05140i
$323$	−36.0463			−2.00567
$324$	−22.9921	+	39.8236i	−1.27734	+	2.21242i
$325$	−6.66453	+	11.5433i	−0.369682	+	0.640307i
$326$	26.0499	−	45.1198i	1.44277	−	2.49895i
$327$	−0.253618	+	0.439280i	−0.0140251	+	0.0242922i
$328$	8.40767	+	14.5625i	0.464236	+	0.804080i
$329$	−15.1669			−0.836180
$330$	−1.78927	−	3.09911i	−0.0984963	−	0.170601i
$331$	−3.96490			−0.217931			−0.108965	−	0.994046i	$-0.534754\pi$
$331$	−3.96490			−0.217931			−0.108965	+	0.994046i	$0.534754\pi$
$332$	−1.86500			−0.102355
$333$	7.63701	+	13.2277i	0.418505	+	0.724872i
$334$	−19.4746	−	33.7310i	−1.06560	−	1.84568i
$335$	26.7028			1.45893
$336$	1.75411	−	3.03822i	0.0956948	−	0.165748i
$337$	−8.92372	−	15.4563i	−0.486106	−	0.841960i	0.513766	−	0.857930i	$-0.328250\pi$
$337$	−8.92372	−	15.4563i	−0.486106	−	0.841960i	−0.999872	+	0.0159698i	$0.994916\pi$
$338$	38.6965			2.10481
$339$	0.375075	−	0.649649i	0.0203713	−	0.0352841i
$340$	34.0944	−	59.0533i	1.84903	−	3.20261i
$341$	−2.71973	−	4.71071i	−0.147282	−	0.255099i
$342$	59.9122			3.23968
$343$	15.5613			0.840232
$344$	−24.1843	−	41.8884i	−1.30393	−	2.25847i
$345$	−1.06109	−	1.83786i	−0.0571270	−	0.0989468i
$346$	−16.9421	−	29.3445i	−0.910811	−	1.57757i
$347$	−7.59411	−	13.1534i	−0.407673	−	0.706111i	0.586955	−	0.809619i	$-0.300326\pi$
$347$	−7.59411	−	13.1534i	−0.407673	−	0.706111i	−0.994629	+	0.103508i	$0.966993\pi$
$348$	−0.857662	+	1.48551i	−0.0459755	+	0.0796319i
$349$	6.56327	−	11.3679i	0.351324	−	0.608511i	−0.635158	−	0.772382i	$-0.719065\pi$
$349$	6.56327	−	11.3679i	0.351324	−	0.608511i	0.986482	+	0.163872i	$0.0523983\pi$
$350$	−20.1104			−1.07495
$351$	1.51681	+	2.62719i	0.0809614	+	0.140229i
$352$	−80.4944			−4.29037
$353$	0.152585			0.00812128			0.00406064	−	0.999992i	$-0.498707\pi$
$353$	0.152585			0.00812128			0.00406064	+	0.999992i	$0.498707\pi$
$354$	0.713363	−	1.23558i	0.0379148	−	0.0656704i
$355$	16.8207			0.892750
$356$	−4.13940	+	7.16964i	−0.219388	+	0.379990i
$357$	0.687370	−	1.19056i	0.0363795	−	0.0630111i
$358$	20.9731	+	36.3264i	1.10846	+	1.91991i
$359$	15.4967	+	26.8410i	0.817882	+	1.41661i	0.907240	+	0.420614i	$0.138185\pi$
$359$	15.4967	+	26.8410i	0.817882	+	1.41661i	−0.0893577	+	0.996000i	$0.528481\pi$
$360$	−34.6929	+	60.0899i	−1.82848	+	3.16701i
$361$	−18.5354	−	32.1042i	−0.975546	−	1.68970i
$362$	28.0088			1.47211
$363$	−0.695849	+	1.20525i	−0.0365226	+	0.0632590i
$364$	39.9405	+	69.1791i	2.09345	+	3.62597i
$365$	−37.7644			−1.97668
$366$	0.627031	−	1.08605i	0.0327754	−	0.0567687i
$367$	−1.90674	−	3.30257i	−0.0995311	−	0.172393i	0.811960	−	0.583714i	$-0.198401\pi$
$367$	−1.90674	−	3.30257i	−0.0995311	−	0.172393i	−0.911491	+	0.411321i	$0.865068\pi$
$368$	−98.2319			−5.12069
$369$	−2.97662	−	5.15566i	−0.154957	−	0.268393i
$370$	18.7637	+	32.4997i	0.975480	+	1.68958i
$371$	7.01969	−	12.1585i	0.364444	−	0.631236i
$372$	0.268923	−	0.465788i	0.0139430	−	0.0241500i
$373$	16.0992	+	27.8846i	0.833584	+	1.44381i	0.895178	+	0.445709i	$0.147048\pi$
$373$	16.0992	+	27.8846i	0.833584	+	1.44381i	−0.0615937	+	0.998101i	$0.519618\pi$
$374$	−64.9100			−3.35642
$375$	0.651959			0.0336670
$376$	−21.6752	+	37.5425i	−1.11781	+	1.93611i
$377$	−9.01900	−	15.6214i	−0.464502	−	0.804541i
$378$	−2.28851	+	3.96382i	−0.117708	+	0.203877i
$379$	5.36273	+	9.28852i	0.275465	+	0.477119i	0.970252	−	0.242096i	$-0.0778349\pi$
$379$	5.36273	+	9.28852i	0.275465	+	0.477119i	−0.694787	+	0.719215i	$0.744502\pi$
$380$	106.069			5.44123
$381$	−0.617655	+	1.06981i	−0.0316434	+	0.0548080i
$382$	31.6442			1.61906
$383$	−12.3911			−0.633158			−0.316579	−	0.948566i	$-0.602534\pi$
$383$	−12.3911			−0.633158			−0.316579	+	0.948566i	$0.602534\pi$
$384$	−0.803851	−	1.39231i	−0.0410214	−	0.0710511i
$385$	20.4558	+	35.4306i	1.04253	+	1.80571i
$386$	54.8863			2.79364
$387$	8.56213	+	14.8300i	0.435237	+	0.753853i
$388$	18.6273	+	32.2634i	0.945656	+	1.63792i
$389$	6.39243	+	11.0720i	0.324109	+	0.561373i	0.981332	−	0.192323i	$-0.0616022\pi$
$389$	6.39243	+	11.0720i	0.324109	+	0.561373i	−0.657223	+	0.753696i	$0.728269\pi$
$390$	1.86046	+	3.22241i	0.0942081	+	0.163173i
$391$	−38.4933			−1.94669
$392$	−7.32685	+	12.6905i	−0.370062	+	0.640966i
$393$	−1.47191			−0.0742480
$394$	−7.89731	−	13.6785i	−0.397861	−	0.689115i
$395$	11.6667	−	20.2073i	0.587016	−	1.01674i
$396$	77.7398			3.90657
$397$	−15.0548	+	26.0756i	−0.755577	+	1.30870i	0.189511	+	0.981879i	$0.439310\pi$
$397$	−15.0548	+	26.0756i	−0.755577	+	1.30870i	−0.945087	+	0.326818i	$0.894023\pi$
$398$	−0.0367205			−0.00184063
$399$	2.13844			0.107056
$400$	−15.6223	+	27.0587i	−0.781117	+	1.35293i
$401$	−5.10427	+	8.84086i	−0.254895	+	0.441492i	−0.964867	−	0.262739i	$-0.915374\pi$
$401$	−5.10427	+	8.84086i	−0.254895	+	0.441492i	0.709972	+	0.704230i	$0.248708\pi$
$402$	1.25669	−	2.17665i	0.0626778	−	0.108561i
$403$	2.82794	+	4.89813i	0.140869	+	0.243993i
$404$	−27.0604	+	46.8700i	−1.34630	+	2.33187i
$405$	12.2441	−	21.2074i	0.608414	−	1.05380i
$406$	13.6075	−	23.5690i	0.675331	−	1.16971i
$407$	12.8705	−	22.2923i	0.637966	−	1.10499i
$408$	−1.96465	−	3.40288i	−0.0972648	−	0.168468i
$409$	9.42172			0.465874			0.232937	−	0.972492i	$-0.425166\pi$
$409$	9.42172			0.465874			0.232937	+	0.972492i	$0.425166\pi$
$410$	−7.31341	−	12.6672i	−0.361184	−	0.625589i
$411$	−0.500569	−	0.867012i	−0.0246913	−	0.0427665i
$412$	44.2995	−	76.7290i	2.18248	−	3.78017i
$413$	−8.15552	+	14.1258i	−0.401307	+	0.695084i
$414$	63.9794			3.14442
$415$	0.993175			0.0487531
$416$	83.6969			4.10358
$417$	−0.408093	−	0.706838i	−0.0199844	−	0.0346140i
$418$	−50.4844	−	87.4415i	−2.46927	−	4.27691i
$419$	12.7406	+	22.0673i	0.622418	+	1.07806i	0.989034	+	0.147688i	$0.0471831\pi$
$419$	12.7406	+	22.0673i	0.622418	+	1.07806i	−0.366616	+	0.930373i	$0.619484\pi$
$420$	−2.02264	+	3.50332i	−0.0986948	+	0.170944i
$421$	−10.7097	+	18.5497i	−0.521958	+	0.904058i	0.477715	+	0.878515i	$0.341465\pi$
$421$	−10.7097	+	18.5497i	−0.521958	+	0.904058i	−0.999674	+	0.0255436i	$0.991868\pi$
$422$	−25.6313			−1.24771
$423$	7.67380	−	13.2914i	0.373113	−	0.646251i
$424$	−20.0638	−	34.7515i	−0.974384	−	1.68768i
$425$	−6.12180	+	10.6033i	−0.296951	+	0.514334i
$426$	0.791614	−	1.37112i	0.0383538	−	0.0664308i
$427$	−7.16852	+	12.4162i	−0.346909	+	0.600864i
$428$	−38.1253	+	66.0349i	−1.84285	+	3.19192i
$429$	1.27613	−	2.21033i	0.0616123	−	0.106716i
$430$	21.0367	+	36.4367i	1.01448	+	1.75713i
$431$	−4.70168	+	8.14354i	−0.226472	+	0.392261i	−0.956760	−	0.290879i	$-0.906052\pi$
$431$	−4.70168	+	8.14354i	−0.226472	+	0.392261i	0.730288	+	0.683139i	$0.239386\pi$
$432$	3.55556	+	6.15842i	0.171067	+	0.296297i
$433$	0.544620			0.0261728			0.0130864	−	0.999914i	$-0.495834\pi$
$433$	0.544620			0.0261728			0.0130864	+	0.999914i	$0.495834\pi$
$434$	−4.26669	+	7.39012i	−0.204808	+	0.354737i
$435$	0.456734	−	0.791087i	0.0218987	−	0.0379297i
$436$	−13.5367	−	23.4463i	−0.648291	−	1.12287i
$437$	−29.9386	−	51.8551i	−1.43216	−	2.48057i
$438$	−1.77726	+	3.07831i	−0.0849210	+	0.147087i
$439$	9.51476	−	16.4800i	0.454115	−	0.786549i	−0.544522	−	0.838746i	$-0.683289\pi$
$439$	9.51476	−	16.4800i	0.454115	−	0.786549i	0.998637	+	0.0521969i	$0.0166224\pi$
$440$	116.934			5.57463
$441$	2.59397	−	4.49289i	0.123523	−	0.213947i
$442$	67.4925			3.21029
$443$	2.74643	+	4.75696i	0.130487	+	0.226010i	0.923864	−	0.382720i	$-0.125013\pi$
$443$	2.74643	+	4.75696i	0.130487	+	0.226010i	−0.793378	+	0.608730i	$0.791679\pi$
$444$	2.54523			0.120791
$445$	2.20437	−	3.81808i	0.104497	−	0.180994i
$446$	−12.4399			−0.589047
$447$	−0.875769			−0.0414225
$448$	26.8330	+	46.4761i	1.26774	+	2.19579i
$449$	−3.17450			−0.149814			−0.0749069	−	0.997191i	$-0.523866\pi$
$449$	−3.17450			−0.149814			−0.0749069	+	0.997191i	$0.523866\pi$
$450$	10.1750	−	17.6236i	0.479653	−	0.830784i
$451$	−5.01644	+	8.68873i	−0.236215	+	0.409136i
$452$	20.0194	+	34.6746i	0.941633	+	1.63096i
$453$	−1.05319			−0.0494833
$454$	56.3571			2.64497
$455$	−21.2697	−	36.8402i	−0.997138	−	1.72709i
$456$	3.05606	−	5.29324i	0.143113	−	0.247879i
$457$	−18.1545			−0.849231			−0.424616	−	0.905374i	$-0.639591\pi$
$457$	−18.1545			−0.849231			−0.424616	+	0.905374i	$0.639591\pi$
$458$	29.5421			1.38041
$459$	1.39329	+	2.41325i	0.0650332	+	0.112641i
$460$	113.270			5.28122
$461$	−0.555196	+	0.961627i	−0.0258580	+	0.0447874i	−0.878665	−	0.477439i	$-0.841565\pi$
$461$	−0.555196	+	0.961627i	−0.0258580	+	0.0447874i	0.852807	+	0.522227i	$0.174898\pi$
$462$	3.85077			0.179154
$463$	−21.4321			−0.996032			−0.498016	−	0.867168i	$-0.665938\pi$
$463$	−21.4321			−0.996032			−0.498016	+	0.867168i	$0.665938\pi$
$464$	−21.1415	−	36.6181i	−0.981468	−	1.69995i
$465$	−0.143210	+	0.248048i	−0.00664122	+	0.0115029i
$466$	14.3960			0.666884
$467$	13.3112			0.615967			0.307984	−	0.951392i	$-0.400346\pi$
$467$	13.3112			0.615967			0.307984	+	0.951392i	$0.400346\pi$
$468$	−80.8327			−3.73649
$469$	−14.3671	+	24.8845i	−0.663409	+	1.14906i
$470$	18.8541	−	32.6563i	0.869677	−	1.50632i
$471$	0.310713	+	0.538170i	0.0143169	+	0.0247976i
$472$	23.3102	+	40.3745i	1.07294	+	1.85839i
$473$	14.4296	−	24.9927i	0.663472	−	1.14917i
$474$	−1.09812	−	1.90199i	−0.0504381	−	0.0873614i
$475$	−19.0452			−0.873852
$476$	36.6880	+	63.5454i	1.68159	+	2.91260i
$477$	7.10332	+	12.3033i	0.325239	+	0.563330i
$478$	−16.0701	+	27.8342i	−0.735030	+	1.27311i
$479$	−20.3177			−0.928338			−0.464169	−	0.885747i	$-0.653647\pi$
$479$	−20.3177			−0.928338			−0.464169	+	0.885747i	$0.653647\pi$
$480$	2.11926	+	3.67067i	0.0967306	+	0.167542i
$481$	−13.3825	+	23.1792i	−0.610191	+	1.05688i
$482$	−46.3235			−2.10998
$483$	2.28361			0.103908
$484$	−37.1405	−	64.3292i	−1.68820	−	2.92406i
$485$	−9.91964	−	17.1813i	−0.450428	−	0.780164i
$486$	−3.47546	−	6.01968i	−0.157650	−	0.273058i
$487$	−3.29495	−	5.70702i	−0.149308	−	0.258610i	0.781664	−	0.623700i	$-0.214371\pi$
$487$	−3.29495	−	5.70702i	−0.149308	−	0.258610i	−0.930972	+	0.365091i	$0.881038\pi$
$488$	20.4892	+	35.4883i	0.927501	+	1.60648i
$489$	0.940872	+	1.62964i	0.0425477	+	0.0736948i
$490$	6.37326	−	11.0388i	0.287915	−	0.498683i
$491$	−12.4213	−	21.5143i	−0.560565	−	0.970926i	−0.997447	−	0.0714079i	$-0.977251\pi$
$491$	−12.4213	−	21.5143i	−0.560565	−	0.970926i	0.436883	−	0.899519i	$-0.356083\pi$
$492$	−0.992035			−0.0447244
$493$	−8.28454	−	14.3492i	−0.373117	−	0.646257i
$494$	52.4929	+	90.9204i	2.36177	+	4.09070i
$495$	−41.3991			−1.86075
$496$	6.62897	+	11.4817i	0.297650	+	0.515544i
$497$	−9.05012	+	15.6753i	−0.405953	+	0.703132i
$498$	0.0467407	−	0.0809574i	0.00209450	−	0.00362779i
$499$	−8.27869	−	14.3391i	−0.370605	−	0.641907i	0.619054	−	0.785349i	$-0.287516\pi$
$499$	−8.27869	−	14.3391i	−0.370605	−	0.641907i	−0.989659	+	0.143442i	$0.954183\pi$
$500$	−17.3990	+	30.1359i	−0.778105	+	1.34772i
$501$	1.40677			0.0628499
$502$	3.23698	−	5.60662i	0.144474	−	0.250236i
$503$	−0.874823			−0.0390064			−0.0195032	−	0.999810i	$-0.506208\pi$
$503$	−0.874823			−0.0390064			−0.0195032	+	0.999810i	$0.506208\pi$
$504$	−37.3320	−	64.6609i	−1.66290	−	2.88022i
$505$	14.4106	−	24.9598i	0.641262	−	1.11070i
$506$	−53.9115	−	93.3775i	−2.39666	−	4.15114i
$507$	−0.698821	+	1.21039i	−0.0310357	+	0.0537555i
$508$	−32.9669	−	57.1004i	−1.46267	−	2.53342i
$509$	9.36812			0.415235			0.207617	−	0.978210i	$-0.433429\pi$
$509$	9.36812			0.415235			0.207617	+	0.978210i	$0.433429\pi$
$510$	1.70895	+	2.95999i	0.0756737	+	0.131071i
$511$	20.3186	−	35.1928i	0.898840	−	1.55684i
$512$	−11.3491			−0.501564
$513$	−2.16729	+	3.75386i	−0.0956882	+	0.165737i
$514$	−22.0590	−	38.2073i	−0.972981	−	1.68525i
$515$	−23.5910	+	40.8608i	−1.03954	+	1.80054i
$516$	2.85355			0.125620
$517$	−25.8650			−1.13754
$518$	−40.3822			−1.77429
$519$	1.22383			0.0537201
$520$	−121.587			−5.33193
$521$	1.78317	−	3.08854i	0.0781220	−	0.135311i	−0.824318	−	0.566128i	$-0.808441\pi$
$521$	1.78317	−	3.08854i	0.0781220	−	0.135311i	0.902440	+	0.430816i	$0.141774\pi$
$522$	13.7696	+	23.8497i	0.602681	+	1.04387i
$523$	−11.4536			−0.500829			−0.250414	−	0.968139i	$-0.580567\pi$
$523$	−11.4536			−0.500829			−0.250414	+	0.968139i	$0.580567\pi$
$524$	39.2811	−	68.0369i	1.71600	−	2.97221i
$525$	0.363174	−	0.629036i	0.0158502	−	0.0274534i
$526$	−24.9887	−	43.2817i	−1.08956	−	1.88717i
$527$	2.59764	+	4.49925i	0.113155	+	0.195990i
$528$	2.99139	−	5.18124i	0.130183	−	0.225484i
$529$	−20.4710	−	35.4567i	−0.890042	−	1.54160i
$530$	17.4525	+	30.2286i	0.758088	+	1.31305i
$531$	−8.25267	−	14.2941i	−0.358136	−	0.620309i
$532$	−57.0689	+	98.8462i	−2.47425	+	4.28553i
$533$	5.21602	−	9.03441i	0.225931	−	0.391324i
$534$	−0.207484	−	0.359372i	−0.00897870	−	0.0155516i
$535$	20.3030	−	35.1658i	0.877775	−	1.52035i
$536$	41.0641	+	71.1251i	1.77370	+	3.07214i
$537$	−1.51501			−0.0653776
$538$	−13.9875			−0.603042
$539$	−8.74314			−0.376594
$540$	−4.09986	−	7.10117i	−0.176430	−	0.305586i
$541$	−6.99621	−	12.1178i	−0.300791	−	0.520985i	0.675525	−	0.737337i	$-0.263917\pi$
$541$	−6.99621	−	12.1178i	−0.300791	−	0.520985i	−0.976315	+	0.216353i	$0.930584\pi$
$542$	−6.21457	+	10.7640i	−0.266939	+	0.462351i
$543$	−0.505812	+	0.876092i	−0.0217065	+	0.0375967i
$544$	76.8810			3.29625
$545$	7.20876	+	12.4859i	0.308789	+	0.534839i
$546$	−4.00397			−0.171354
$547$	−15.7975	+	17.2464i	−0.675452	+	0.737404i
$547$	−15.7975	+	17.2464i	−0.675452	+	0.737404i
$548$	53.4352			2.28264
$549$	−7.25392	−	12.5642i	−0.309590	−	0.536225i
$550$	−34.2954			−1.46236
$551$	12.8868	−	22.3205i	0.548995	−	0.950886i
$552$	3.26352	−	5.65258i	0.138905	−	0.240590i
$553$	12.5542	+	21.7445i	0.533859	+	0.924670i
$554$	14.2820	+	24.7371i	0.606782	+	1.05098i
$555$	−1.35542			−0.0575343
$556$	43.5635			1.84750
$557$	−0.360236			−0.0152637			−0.00763185	−	0.999971i	$-0.502429\pi$
$557$	−0.360236			−0.0152637			−0.00763185	+	0.999971i	$0.502429\pi$
$558$	−4.31751	−	7.47816i	−0.182775	−	0.316576i
$559$	−15.0037	+	25.9871i	−0.634587	+	1.09914i
$560$	−49.8584	−	86.3572i	−2.10690	−	3.64926i
$561$	1.17221	−	2.03033i	0.0494908	−	0.0857205i
$562$	36.6414	−	63.4648i	1.54562	−	2.67710i
$563$	19.5508	+	33.8629i	0.823967	+	1.42715i	0.902706	+	0.430257i	$0.141577\pi$
$563$	19.5508	+	33.8629i	0.823967	+	1.42715i	−0.0787398	+	0.996895i	$0.525090\pi$
$564$	−1.27874	−	2.21485i	−0.0538449	−	0.0932621i
$565$	−10.6610	−	18.4654i	−0.448512	−	0.776845i
$566$	−6.71240	+	11.6262i	−0.282143	+	0.488686i
$567$	13.1755	+	22.8206i	0.553319	+	0.958377i
$568$	25.8672	+	44.8033i	1.08536	+	1.87990i
$569$	7.21051	−	12.4890i	0.302280	−	0.523565i	−0.674372	−	0.738392i	$-0.735585\pi$
$569$	7.21051	−	12.4890i	0.302280	−	0.523565i	0.976652	+	0.214827i	$0.0689188\pi$
$570$	−2.65831	+	4.60433i	−0.111344	+	0.192854i
$571$	22.4116			0.937897			0.468949	−	0.883225i	$-0.344633\pi$
$571$	22.4116			0.937897			0.468949	+	0.883225i	$0.344633\pi$
$572$	68.1128	+	117.975i	2.84794	+	4.93278i
$573$	−0.571464	+	0.989804i	−0.0238732	+	0.0413497i
$574$	15.7395			0.656953
$575$	−20.3381			−0.848156
$576$	−54.3053			−2.26272
$577$	19.3664			0.806235			0.403118	−	0.915148i	$-0.367927\pi$
$577$	19.3664			0.806235			0.403118	+	0.915148i	$0.367927\pi$
$578$	16.5153			0.686947
$579$	−0.991192	+	1.71680i	−0.0411926	+	0.0713476i
$580$	24.3779	+	42.2238i	1.01224	+	1.75325i
$581$	−0.534363	+	0.925544i	−0.0221691	+	0.0383980i
$582$	−1.86735			−0.0774042
$583$	11.9711	−	20.7345i	0.495791	−	0.858735i
$584$	−58.0748	−	100.588i	−2.40315	−	4.16238i
$585$	43.0461			1.77974
$586$	5.01561	+	8.68730i	0.207193	+	0.358869i
$587$	3.98553	−	6.90314i	0.164500	−	0.284923i	−0.771977	−	0.635650i	$-0.780732\pi$
$587$	3.98553	−	6.90314i	0.164500	−	0.284923i	0.936478	+	0.350727i	$0.114065\pi$
$588$	−0.432254	−	0.748685i	−0.0178258	−	0.0308753i
$589$	−4.04068	+	6.99867i	−0.166493	+	0.288375i
$590$	−20.2764	−	35.1198i	−0.834766	−	1.44586i
$591$	0.570470			0.0234660
$592$	−31.3701	+	54.3345i	−1.28930	+	2.23314i
$593$	34.0679			1.39900			0.699501	−	0.714631i	$-0.253405\pi$
$593$	34.0679			1.39900			0.699501	+	0.714631i	$0.253405\pi$
$594$	−3.90272	+	6.75971i	−0.160131	+	0.277354i
$595$	−19.5376	−	33.8401i	−0.800963	−	1.38731i
$596$	23.3718	−	40.4812i	0.957347	−	1.65817i
$597$	0.000663136	−	0.00114859i	2.71404e−5	−	4.70085e-5i
$598$	56.0564	+	97.0926i	2.29232	+	3.97041i
$599$	−26.4704			−1.08155			−0.540775	−	0.841167i	$-0.681869\pi$
$599$	−26.4704			−1.08155			−0.540775	+	0.841167i	$0.681869\pi$
$600$	−1.03803	−	1.79792i	−0.0423774	−	0.0733998i
$601$	19.9729	+	34.5941i	0.814712	+	1.41112i	0.909534	+	0.415628i	$0.136438\pi$
$601$	19.9729	+	34.5941i	0.814712	+	1.41112i	−0.0948224	+	0.995494i	$0.530228\pi$
$602$	−45.2740			−1.84523
$603$	−14.5382	−	25.1809i	−0.592042	−	1.02545i
$604$	28.1068	−	48.6824i	1.14365	−	1.98086i
$605$	19.7786	+	34.2575i	0.804113	+	1.39277i
$606$	−1.35638	−	2.34932i	−0.0550991	−	0.0954345i
$607$	16.1491	+	27.9711i	0.655472	+	1.13531i	0.981775	+	0.190046i	$0.0608638\pi$
$607$	16.1491	+	27.9711i	0.655472	+	1.13531i	−0.326303	+	0.945265i	$0.605803\pi$
$608$	59.7950	+	103.568i	2.42501	+	4.20024i
$609$	0.491478	+	0.851264i	0.0199157	+	0.0344950i
$610$	−17.8225	−	30.8695i	−0.721613	−	1.24987i
$611$	26.8940			1.08802
$612$	−74.2501			−3.00138
$613$	10.8429	−	18.7805i	0.437943	−	0.758539i	−0.559588	−	0.828771i	$-0.689041\pi$
$613$	10.8429	−	18.7805i	0.437943	−	0.758539i	0.997531	+	0.0702321i	$0.0223740\pi$
$614$	−28.0539	−	48.5909i	−1.13217	−	1.96097i
$615$	0.528292			0.0213028
$616$	−62.9148	+	108.972i	−2.53491	+	4.39059i
$617$	−12.5639	−	21.7614i	−0.505805	−	0.876080i	−0.999977	−	0.00671606i	$-0.997862\pi$
$617$	−12.5639	−	21.7614i	−0.505805	−	0.876080i	0.494172	−	0.869364i	$-0.335471\pi$
$618$	2.22047	+	3.84598i	0.0893206	+	0.154708i
$619$	4.91382			0.197503			0.0987516	−	0.995112i	$-0.468515\pi$
$619$	4.91382			0.197503			0.0987516	+	0.995112i	$0.468515\pi$
$620$	−7.64376	−	13.2394i	−0.306981	−	0.531707i
$621$	−2.31442	+	4.00869i	−0.0928744	+	0.160863i
$622$	−33.7167	−	58.3991i	−1.35192	−	2.34159i
$623$	2.37205	+	4.10852i	0.0950343	+	0.164604i
$624$	−3.11040	+	5.38737i	−0.124516	+	0.215668i
$625$	15.6241	−	27.0617i	0.624962	−	1.08247i
$626$	−42.1925			−1.68635
$627$	3.64679			0.145639
$628$	−33.1682			−1.32356
$629$	−12.2927	+	21.2916i	−0.490143	+	0.848953i
$630$	32.4732	+	56.2453i	1.29376	+	2.24087i
$631$	12.8515			0.511609			0.255804	−	0.966729i	$-0.417660\pi$
$631$	12.8515			0.511609			0.255804	+	0.966729i	$0.417660\pi$
$632$	71.7652			2.85466
$633$	0.462877	−	0.801726i	0.0183977	−	0.0318658i
$634$	89.8688			3.56915
$635$	17.5560	+	30.4079i	0.696689	+	1.20670i
$636$	2.36736			0.0938720
$637$	9.09099			0.360198
$638$	23.2057	−	40.1934i	0.918722	−	1.59127i
$639$	−9.15793	−	15.8620i	−0.362282	−	0.627491i
$640$	−45.6968			−1.80632
$641$	14.5805			0.575896			0.287948	−	0.957646i	$-0.407027\pi$
$641$	14.5805			0.575896			0.287948	+	0.957646i	$0.407027\pi$
$642$	−1.91100	−	3.30994i	−0.0754210	−	0.130633i
$643$	6.80648	−	11.7892i	0.268422	−	0.464920i	−0.700033	−	0.714111i	$-0.746831\pi$
$643$	6.80648	−	11.7892i	0.268422	−	0.464920i	0.968454	+	0.249191i	$0.0801647\pi$
$644$	−60.9430	+	105.556i	−2.40149	+	4.15951i
$645$	−1.51961			−0.0598346
$646$	48.2182	+	83.5163i	1.89712	+	3.28590i
$647$	24.0591			0.945860			0.472930	−	0.881100i	$-0.343196\pi$
$647$	24.0591			0.945860			0.472930	+	0.881100i	$0.343196\pi$
$648$	75.3168			2.95872
$649$	−13.9081	+	24.0895i	−0.545939	+	0.945594i
$650$	35.6598			1.39869
$651$	−0.154104	−	0.266917i	−0.00603982	−	0.0104613i
$652$	−100.437			−3.93341
$653$	−0.537062	+	0.930218i	−0.0210168	+	0.0364022i	−0.876343	−	0.481688i	$-0.840024\pi$
$653$	−0.537062	+	0.930218i	−0.0210168	+	0.0364022i	0.855326	+	0.518091i	$0.173357\pi$
$654$	1.35703			0.0530642
$655$	−20.9185	+	36.2319i	−0.817354	+	1.41570i
$656$	12.2269	−	21.1776i	0.477380	−	0.826846i
$657$	20.5606	+	35.6120i	0.802146	+	1.38936i
$658$	20.2884	+	35.1405i	0.790923	+	1.36992i
$659$	5.60301	−	9.70471i	0.218262	−	0.378042i	−0.736014	−	0.676966i	$-0.763294\pi$
$659$	5.60301	−	9.70471i	0.218262	−	0.378042i	0.954277	+	0.298924i	$0.0966278\pi$
$660$	−3.44932	+	5.97440i	−0.134265	+	0.232553i
$661$	3.00316			0.116810			0.0584048	−	0.998293i	$-0.481399\pi$
$661$	3.00316			0.116810			0.0584048	+	0.998293i	$0.481399\pi$
$662$	5.30374	+	9.18635i	0.206136	+	0.357038i
$663$	−1.21885	+	2.11111i	−0.0473361	+	0.0819886i
$664$	1.52732	+	2.64540i	0.0592717	+	0.102662i
$665$	30.3911	−	52.6389i	1.17852	−	2.04125i
$666$	20.4316	−	35.3886i	0.791709	−	1.37128i
$667$	13.7616	−	23.8358i	0.532851	−	0.922924i
$668$	−37.5428	+	65.0260i	−1.45257	+	2.51593i
$669$	0.224653	−	0.389110i	0.00868557	−	0.0150439i
$670$	−35.7196	−	61.8682i	−1.37997	−	2.39018i
$671$	−12.2249	+	21.1741i	−0.471936	+	0.817417i
$672$	−4.56094			−0.175942
$673$	−25.0139	+	43.3253i	−0.964215	+	1.67007i	−0.252505	+	0.967596i	$0.581254\pi$
$673$	−25.0139	+	43.3253i	−0.964215	+	1.67007i	−0.711710	+	0.702474i	$0.752079\pi$
$674$	−23.8740	+	41.3510i	−0.919593	+	1.59278i
$675$	0.736148	+	1.27505i	0.0283344	+	0.0490766i
$676$	−37.2991	−	64.6040i	−1.43458	−	2.48477i
$677$	−9.00280	−	15.5933i	−0.346006	−	0.599300i	0.639530	−	0.768766i	$-0.279129\pi$
$677$	−9.00280	−	15.5933i	−0.346006	−	0.599300i	−0.985536	+	0.169466i	$0.945796\pi$
$678$	−2.00691			−0.0770749
$679$	21.3485			0.819279
$680$	−111.685			−4.28293
$681$	−1.01775	+	1.76280i	−0.0390004	+	0.0675507i
$682$	−7.27621	+	12.6028i	−0.278621	+	0.482585i
$683$	−14.8798	−	25.7726i	−0.569360	−	0.986160i	−0.996629	−	0.0820355i	$-0.973858\pi$
$683$	−14.8798	−	25.7726i	−0.569360	−	0.986160i	0.427270	−	0.904124i	$-0.359475\pi$
$684$	−57.7487	−	100.024i	−2.20808	−	3.82450i
$685$	−28.4560			−1.08725
$686$	−20.8159	−	36.0543i	−0.794756	−	1.37656i
$687$	−0.533501	+	0.924052i	−0.0203544	+	0.0352548i
$688$	−35.1701	+	60.9165i	−1.34085	+	2.32242i
$689$	−12.4473	+	21.5594i	−0.474206	+	0.821349i
$690$	−2.83877	+	4.91690i	−0.108070	+	0.187183i
$691$	−4.51565	−	7.82133i	−0.171783	−	0.297537i	0.767260	−	0.641336i	$-0.221620\pi$
$691$	−4.51565	−	7.82133i	−0.171783	−	0.297537i	−0.939043	+	0.343799i	$0.888286\pi$
$692$	−32.6605	+	56.5697i	−1.24157	+	2.15046i
$693$	22.2741	−	38.5799i	0.846125	−	1.46553i
$694$	−20.3169	+	35.1899i	−0.771218	+	1.33579i
$695$	−23.1990			−0.879989
$696$	2.80950			0.106494
$697$	4.79125	−	8.29869i	0.181482	−	0.314335i
$698$	−35.1180			−1.32924
$699$	−0.259978	+	0.450296i	−0.00983328	+	0.0170317i
$700$	19.3842	+	33.5744i	0.732654	+	1.26899i
$701$	24.5337			0.926625			0.463313	−	0.886195i	$-0.346661\pi$
$701$	24.5337			0.926625			0.463313	+	0.886195i	$0.346661\pi$
$702$	4.05799	−	7.02865i	0.153159	−	0.265279i
$703$	−38.2432			−1.44237
$704$	45.7597	+	79.2582i	1.72463	+	2.98716i
$705$	0.680975	+	1.17948i	0.0256470	+	0.0444219i
$706$	−0.204109	−	0.353527i	−0.00768173	−	0.0133051i
$707$	15.5068	+	26.8585i	0.583192	+	1.01012i
$708$	−2.75041			−0.103367
$709$	−10.8973	−	18.8747i	−0.409258	−	0.708855i	0.585549	−	0.810637i	$-0.300879\pi$
$709$	−10.8973	−	18.8747i	−0.409258	−	0.708855i	−0.994807	+	0.101782i	$0.967546\pi$
$710$	−22.5006	−	38.9721i	−0.844432	−	1.46260i
$711$	−25.4075			−0.952856
$712$	13.5597			0.508170
$713$	−4.31499	+	7.47378i	−0.161598	+	0.279895i
$714$	−3.67791			−0.137642
$715$	−36.2724	−	62.8256i	−1.35651	−	2.34954i
$716$	40.4314	−	70.0293i	1.51099	−	2.61712i
$717$	−0.580421	−	1.00532i	−0.0216762	−	0.0375443i
$718$	41.4589	−	71.8089i	1.54723	−	2.67988i
$719$	45.4860			1.69634			0.848171	−	0.529723i	$-0.177704\pi$
$719$	45.4860			1.69634			0.848171	+	0.529723i	$0.177704\pi$
$720$	100.905			3.76049
$721$	−25.3855	−	43.9691i	−0.945407	−	1.63749i
$722$	−49.5885	+	85.8899i	−1.84549	+	3.19649i
$723$	0.836558	−	1.44896i	0.0311119	−	0.0538874i
$724$	−26.9974	−	46.7608i	−1.00335	−	1.73785i
$725$	−4.37716	−	7.58146i	−0.162564	−	0.281568i
$726$	3.72327			0.138184
$727$	−11.9960	−	20.7778i	−0.444909	−	0.770605i	0.553137	−	0.833090i	$-0.313431\pi$
$727$	−11.9960	−	20.7778i	−0.444909	−	0.770605i	−0.998046	+	0.0624857i	$0.980097\pi$
$728$	65.4179	−	113.307i	2.42455	−	4.19944i
$729$	−26.4971			−0.981374
$730$	50.5164	+	87.4969i	1.86969	+	3.23841i
$731$	−13.7818	+	23.8708i	−0.509739	+	0.882894i
$732$	−2.41755			−0.0893553
$733$	−4.83696	−	8.37786i	−0.178657	−	0.309443i	0.762764	−	0.646677i	$-0.223842\pi$
$733$	−4.83696	−	8.37786i	−0.178657	−	0.309443i	−0.941421	+	0.337234i	$0.890509\pi$
$734$	−5.10119	+	8.83552i	−0.188288	+	0.326125i
$735$	0.230190	+	0.398700i	0.00849067	+	0.0147063i
$736$	63.8542	+	110.599i	2.35370	+	4.07672i
$737$	−24.5009	+	42.4368i	−0.902503	+	1.56318i
$738$	−7.96349	+	13.7932i	−0.293140	+	0.507734i
$739$	4.14022			0.152300			0.0761502	−	0.997096i	$-0.475737\pi$
$739$	4.14022			0.152300			0.0761502	+	0.997096i	$0.475737\pi$
$740$	36.1723	−	62.6523i	1.32972	−	2.30314i
$741$	−3.79188			−0.139298
$742$	−37.5602			−1.37888
$743$	20.5213	+	35.5438i	0.752852	+	1.30398i	0.946435	+	0.322894i	$0.104656\pi$
$743$	20.5213	+	35.5438i	0.752852	+	1.30398i	−0.193584	+	0.981084i	$0.562011\pi$
$744$	−0.880926			−0.0322963
$745$	−12.4463	+	21.5576i	−0.455997	+	0.789809i
$746$	43.0709	−	74.6009i	1.57694	−	2.73133i
$747$	−0.540729	−	0.936570i	−0.0197842	−	0.0342673i
$748$	62.5660	+	108.368i	2.28764	+	3.96231i
$749$	21.8474	+	37.8409i	0.798288	+	1.38267i
$750$	−0.872108	−	1.51053i	−0.0318449	−	0.0551569i
$751$	−37.5641			−1.37073			−0.685367	−	0.728198i	$-0.740358\pi$
$751$	−37.5641			−1.37073			−0.685367	+	0.728198i	$0.740358\pi$
$752$	63.0424			2.29892
$753$	0.116914	+	0.202500i	0.00426057	+	0.00737952i
$754$	−24.1289	+	41.7926i	−0.878724	+	1.52199i
$755$	−14.9678	+	25.9250i	−0.544734	+	0.943507i
$756$	8.82348			0.320907
$757$	−17.3520	−	30.0546i	−0.630671	−	1.09235i	−0.987415	−	0.158151i	$-0.949447\pi$
$757$	−17.3520	−	30.0546i	−0.630671	−	1.09235i	0.356744	−	0.934202i	$-0.383887\pi$
$758$	14.3472	−	24.8500i	0.521112	−	0.902592i
$759$	3.89436			0.141356
$760$	−86.8643	−	150.453i	−3.15090	−	5.45752i
$761$	26.6496	+	46.1585i	0.966048	+	1.67324i	0.706773	+	0.707440i	$0.250150\pi$
$761$	26.6496	+	46.1585i	0.966048	+	1.67324i	0.259275	+	0.965804i	$0.416517\pi$
$762$	3.30488			0.119723
$763$	−15.5143			−0.561654
$764$	−30.5015	−	52.8302i	−1.10351	−	1.91133i
$765$	39.5407			1.42960
$766$	16.5753	+	28.7092i	0.598890	+	1.03731i
$767$	14.4614	−	25.0479i	0.522171	−	0.904426i
$768$	−0.395979	+	0.685856i	−0.0142887	+	0.0247487i
$769$	−25.2464	+	43.7281i	−0.910409	+	1.57687i	−0.0969211	+	0.995292i	$0.530899\pi$
$769$	−25.2464	+	43.7281i	−0.910409	+	1.57687i	−0.813488	+	0.581582i	$0.802434\pi$
$770$	54.7264	−	94.7890i	1.97220	−	3.41596i
$771$	1.59346			0.0573869
$772$	−52.9043	−	91.6329i	−1.90407	−	3.29794i
$773$	−26.5511			−0.954978			−0.477489	−	0.878638i	$-0.658453\pi$
$773$	−26.5511			−0.954978			−0.477489	+	0.878638i	$0.658453\pi$
$774$	22.9066	−	39.6755i	0.823362	−	1.42611i
$775$	1.37247	+	2.37719i	0.0493006	+	0.0853912i
$776$	30.5092	−	52.8435i	1.09522	−	1.89697i
$777$	0.729262	−	1.26312i	0.0261621	−	0.0453142i
$778$	17.1020	−	29.6214i	0.613135	−	1.06198i
$779$	14.9058			0.534055
$780$	3.58655	−	6.21209i	0.128419	−	0.222429i
$781$	−15.4337	+	26.7319i	−0.552260	+	0.956542i
$782$	51.4915	+	89.1858i	1.84133	+	3.18928i
$783$	−1.99244			−0.0712039
$784$	21.3102			0.761079
$785$	17.6632			0.630426
$786$	1.96893	+	3.41029i	0.0702295	+	0.121641i
$787$	0.0396028			0.00141169			0.000705844	−	1.00000i	$-0.499775\pi$
$787$	0.0396028			0.00141169			0.000705844		1.00000i	$0.499775\pi$
$788$	−15.2243	+	26.3692i	−0.542342	+	0.939363i
$789$	1.80508			0.0642627
$790$	−62.4249			−2.22098
$791$	22.9440			0.815793
$792$	−63.6643	−	110.270i	−2.26221	−	3.91826i
$793$	12.7112	−	22.0165i	0.451390	−	0.781830i
$794$	80.5533			2.85873
$795$	−1.26070			−0.0447124
$796$	0.0353945	+	0.0613051i	0.00125452	+	0.00217290i
$797$	−21.9517	−	38.0214i	−0.777567	−	1.34679i	−0.933340	−	0.358993i	$-0.883120\pi$
$797$	−21.9517	−	38.0214i	−0.777567	−	1.34679i	0.155773	−	0.987793i	$-0.450213\pi$
$798$	−2.86053	−	4.95458i	−0.101262	−	0.175390i
$799$	24.7039			0.873962
$800$	40.6203			1.43614
$801$	−4.80062			−0.169622
$802$	27.3114			0.964399
$803$	34.6503	−	60.0162i	1.22278	−	2.11792i
$804$	−4.84523			−0.170878
$805$	32.4542	−	56.2123i	1.14386	−	1.98122i
$806$	7.56570	−	13.1042i	0.266490	−	0.461575i
$807$	0.252600	−	0.437515i	0.00889193	−	0.0154013i
$808$	88.6434			3.11846
$809$	−3.28660	−	5.69256i	−0.115551	−	0.200140i	0.802449	−	0.596721i	$-0.203530\pi$
$809$	−3.28660	−	5.69256i	−0.115551	−	0.200140i	−0.918000	+	0.396581i	$0.870197\pi$
$810$	−65.5143			−2.30194
$811$	−0.307091	−	0.531898i	−0.0107834	−	0.0186775i	0.860583	−	0.509310i	$-0.170099\pi$
$811$	−0.307091	−	0.531898i	−0.0107834	−	0.0186775i	−0.871367	+	0.490632i	$0.836766\pi$
$812$	−52.4646			−1.84115
$813$	−0.224458	−	0.388773i	−0.00787209	−	0.0136349i
$814$	−68.8659			−2.41375
$815$	53.4861			1.87354
$816$	−2.85711	+	4.94865i	−0.100019	+	0.173237i
$817$	−42.8758			−1.50004
$818$	−12.6032	−	21.8293i	−0.440660	−	0.763245i
$819$	−23.1603	+	40.1149i	−0.809287	+	1.40173i
$820$	−14.0986	+	24.4196i	−0.492346	+	0.852768i
$821$	−4.43405	+	7.67999i	−0.154749	+	0.268034i	−0.932968	−	0.359960i	$-0.882790\pi$
$821$	−4.43405	+	7.67999i	−0.154749	+	0.268034i	0.778218	+	0.627994i	$0.216124\pi$
$822$	−1.33920	+	2.31956i	−0.0467098	+	0.0809038i
$823$	19.6146	+	33.9735i	0.683722	+	1.18424i	0.973837	+	0.227249i	$0.0729732\pi$
$823$	19.6146	+	33.9735i	0.683722	+	1.18424i	−0.290115	+	0.956992i	$0.593694\pi$
$824$	−145.115			−5.05531
$825$	0.619341	−	1.07273i	0.0215627	−	0.0373476i
$826$	43.6376			1.51835
$827$	−10.5553			−0.367044			−0.183522	−	0.983016i	$-0.558750\pi$
$827$	−10.5553			−0.367044			−0.183522	+	0.983016i	$0.558750\pi$
$828$	−61.6690	−	106.814i	−2.14315	−	3.71204i
$829$	−30.6417			−1.06423			−0.532114	−	0.846673i	$-0.678602\pi$
$829$	−30.6417			−1.06423			−0.532114	+	0.846673i	$0.678602\pi$
$830$	−1.32854	−	2.30110i	−0.0461144	−	0.0798725i
$831$	−1.03167			−0.0357883
$832$	−47.5803	−	82.4115i	−1.64955	−	2.85710i
$833$	8.35066			0.289333
$834$	−1.09179	+	1.89104i	−0.0378056	+	0.0654812i
$835$	19.9928	−	34.6285i	0.691879	−	1.19837i
$836$	−97.3227	+	168.568i	−3.36598	+	5.83004i
$837$	0.624734			0.0215940
$838$	34.0855	−	59.0378i	1.17746	−	2.03943i
$839$	−12.0106			−0.414652			−0.207326	−	0.978272i	$-0.566476\pi$
$839$	−12.0106			−0.414652			−0.207326	+	0.978272i	$0.566476\pi$
$840$	6.62569			0.228608
$841$	−17.1529			−0.591480
$842$	57.3042			1.97483
$843$	1.32342	+	2.29222i	0.0455808	+	0.0789483i
$844$	24.7058	+	42.7917i	0.850408	+	1.47295i
$845$	19.8631	+	34.4038i	0.683310	+	1.18353i
$846$	−41.0601			−1.41168
$847$	−42.5662			−1.46259
$848$	−29.1779	+	50.5376i	−1.00197	+	1.73547i
$849$	−0.242439	−	0.419916i	−0.00832047	−	0.0144115i
$850$	32.7559			1.12352
$851$	−40.8393			−1.39995
$852$	−3.05211			−0.104564
$853$	4.25793	−	7.37495i	0.145789	−	0.252513i	−0.783878	−	0.620915i	$-0.786761\pi$
$853$	4.25793	−	7.37495i	0.145789	−	0.252513i	0.929667	+	0.368401i	$0.120095\pi$
$854$	38.3565			1.31253
$855$	30.7531	+	53.2660i	1.05174	+	1.82166i
$856$	124.889			4.26863
$857$	43.5319			1.48702			0.743510	−	0.668724i	$-0.233159\pi$
$857$	43.5319			1.48702			0.743510	+	0.668724i	$0.233159\pi$
$858$	−6.82819			−0.233111
$859$	3.41877	+	5.92148i	0.116647	+	0.202038i	0.918437	−	0.395568i	$-0.129452\pi$
$859$	3.41877	+	5.92148i	0.116647	+	0.202038i	−0.801790	+	0.597606i	$0.796119\pi$
$860$	40.5541	−	70.2418i	1.38288	−	2.39523i
$861$	−0.284240	+	0.492318i	−0.00968686	+	0.0167781i
$862$	25.1572			0.856858
$863$	18.7424	−	32.4629i	0.638000	−	1.10505i	−0.347871	−	0.937542i	$-0.613095\pi$
$863$	18.7424	−	32.4629i	0.638000	−	1.10505i	0.985871	−	0.167506i	$-0.0535714\pi$
$864$	4.62248	−	8.00638i	0.157260	−	0.272382i
$865$	17.3928	−	30.1253i	0.591374	−	1.02429i
$866$	−0.728524	−	1.26184i	−0.0247562	−	0.0428791i
$867$	−0.298251	+	0.516585i	−0.0101291	+	0.0175442i
$868$	16.4504			0.558365
$869$	21.4094	+	37.0821i	0.726263	+	1.25792i
$870$	−2.44384			−0.0828540
$871$	25.4757	−	44.1252i	0.863211	−	1.49513i
$872$	−22.1715	+	38.4022i	−0.750823	+	1.30046i
$873$	−10.8014	+	18.7086i	−0.365572	+	0.633189i
$874$	−80.0960	+	138.730i	−2.70929	+	4.69262i
$875$	9.97036	+	17.2692i	0.337060	+	0.583804i
$876$	6.85234			0.231519
$877$	7.52432	+	13.0325i	0.254078	+	0.440076i	0.964645	−	0.263554i	$-0.0848946\pi$
$877$	7.52432	+	13.0325i	0.254078	+	0.440076i	−0.710567	+	0.703630i	$0.751561\pi$
$878$	−50.9105			−1.71815
$879$	−0.362308			−0.0122203
$880$	−85.0262	−	147.270i	−2.86623	−	4.96446i
$881$	14.6729	+	25.4143i	0.494344	+	0.856228i	0.999979	−	0.00651920i	$-0.00207514\pi$
$881$	14.6729	+	25.4143i	0.494344	+	0.856228i	−0.505635	+	0.862747i	$0.668742\pi$
$882$	−13.8795			−0.467349
$883$	28.3369	−	49.0810i	0.953614	−	1.65171i	0.216104	−	0.976370i	$-0.430665\pi$
$883$	28.3369	−	49.0810i	0.953614	−	1.65171i	0.737509	−	0.675337i	$-0.236002\pi$
$884$	−65.0552	−	112.679i	−2.18804	−	3.78980i
$885$	1.46469			0.0492349
$886$	7.34765	−	12.7265i	0.246849	−	0.427555i
$887$	17.3418	−	30.0369i	0.582281	−	1.00854i	−0.412928	−	0.910764i	$-0.635494\pi$
$887$	17.3418	−	30.0369i	0.582281	−	1.00854i	0.995208	−	0.0977760i	$-0.0311729\pi$
$888$	−2.08439	−	3.61027i	−0.0699475	−	0.121153i
$889$	−37.7830			−1.26720
$890$	−11.7949			−0.395366
$891$	22.4689	+	38.9173i	0.752736	+	1.30378i
$892$	11.9907	+	20.7685i	0.401478	+	0.695381i
$893$	19.2137	+	33.2791i	0.642963	+	1.11364i
$894$	1.17149	+	2.02908i	0.0391806	+	0.0678628i
$895$	−21.5311	+	37.2930i	−0.719705	+	1.24657i
$896$	24.5865	−	42.5850i	0.821376	−	1.42267i
$897$	−4.04930			−0.135202
$898$	4.24644	+	7.35504i	0.141705	+	0.245441i
$899$	−3.71469			−0.123892
$900$	−39.2302			−1.30767
$901$	−11.4337	+	19.8037i	−0.380911	+	0.659758i
$902$	26.8414			0.893721
$903$	0.817603	−	1.41613i	0.0272081	−	0.0471259i
$904$	32.7894	−	56.7929i	1.09056	−	1.88890i
$905$	14.3770	+	24.9017i	0.477908	+	0.827761i
$906$	1.40883	+	2.44016i	0.0468052	+	0.0810689i
$907$	2.07910	−	3.60111i	0.0690354	−	0.119573i	−0.829442	−	0.558594i	$-0.811341\pi$
$907$	2.07910	−	3.60111i	0.0690354	−	0.119573i	0.898477	+	0.439021i	$0.144675\pi$
$908$	−54.3220	−	94.0884i	−1.80274	−	3.12243i
$909$	−31.3830			−1.04091
$910$	−56.9038	+	98.5602i	−1.88634	+	3.26724i
$911$	0.277908	+	0.481350i	0.00920750	+	0.0159479i	0.870592	−	0.492005i	$-0.163736\pi$
$911$	0.277908	+	0.481350i	0.00920750	+	0.0159479i	−0.861385	+	0.507953i	$0.830402\pi$
$912$	−8.88857			−0.294330
$913$	−0.911278	+	1.57838i	−0.0301589	+	0.0522368i
$914$	24.2848	+	42.0624i	0.803268	+	1.39130i
$915$	1.28743			0.0425611
$916$	−28.4753	−	49.3207i	−0.940851	−	1.62960i
$917$	−22.5098	−	38.9881i	−0.743339	−	1.28750i
$918$	3.72753	−	6.45627i	0.123027	−	0.213089i
$919$	18.4973	−	32.0383i	0.610169	−	1.05684i	−0.381042	−	0.924558i	$-0.624435\pi$
$919$	18.4973	−	32.0383i	0.610169	−	1.05684i	0.991211	−	0.132287i	$-0.0422320\pi$
$920$	−92.7611	−	160.667i	−3.05824	−	5.29703i
$921$	2.02651			0.0667757
$922$	2.97068			0.0978341
$923$	16.0477	−	27.7954i	0.528216	−	0.914898i
$924$	−3.71171	−	6.42887i	−0.122106	−	0.211494i
$925$	−6.49490	+	11.2495i	−0.213551	+	0.369881i
$926$	28.6691	+	49.6563i	0.942124	+	1.63181i
$927$	51.3759			1.68741
$928$	−27.4854	+	47.6061i	−0.902253	+	1.56275i
$929$	−52.8295			−1.73328			−0.866640	−	0.498934i	$-0.833725\pi$
$929$	−52.8295			−1.73328			−0.866640	+	0.498934i	$0.833725\pi$
$930$	0.766274			0.0251271
$931$	6.49481	+	11.2493i	0.212859	+	0.368682i
$932$	−13.8762	−	24.0343i	−0.454530	−	0.787268i
$933$	2.43556			0.0797368
$934$	−17.8060	−	30.8409i	−0.582630	−	1.00914i
$935$	−33.3185	−	57.7094i	−1.08963	−	1.88730i
$936$	66.1972	+	114.657i	2.16372	+	3.74768i
$937$	29.6814	+	51.4097i	0.969648	+	1.67948i	0.696571	+	0.717488i	$0.254708\pi$
$937$	29.6814	+	51.4097i	0.969648	+	1.67948i	0.273078	+	0.961992i	$0.411958\pi$
$938$	76.8737			2.51001
$939$	0.761956	−	1.31975i	0.0248655	−	0.0430683i
$940$	−72.6932			−2.37099
$941$	18.2800	+	31.6618i	0.595910	+	1.03215i	0.993418	+	0.114547i	$0.0365417\pi$
$941$	18.2800	+	31.6618i	0.595910	+	1.03215i	−0.397508	+	0.917599i	$0.630125\pi$
$942$	0.831264	−	1.43979i	0.0270840	−	0.0469109i
$943$	15.9177			0.518350
$944$	33.8990	−	58.7148i	1.10332	−	1.91100i
$945$	−4.69880			−0.152852
$946$	−77.2082			−2.51025
$947$	20.6211	−	35.7167i	0.670095	−	1.16064i	−0.307782	−	0.951457i	$-0.599587\pi$
$947$	20.6211	−	35.7167i	0.670095	−	1.16064i	0.977877	−	0.209181i	$-0.0670798\pi$
$948$	−2.11692	+	3.66662i	−0.0687545	+	0.119086i
$949$	−36.0289	+	62.4039i	−1.16955	+	2.02572i
$950$	25.4762	+	44.1261i	0.826557	+	1.43164i
$951$	−1.62294	+	2.81102i	−0.0526275	+	0.0911536i
$952$	60.0905	−	104.080i	1.94755	−	3.37325i
$953$	−7.48428	+	12.9632i	−0.242440	+	0.419918i	−0.961409	−	0.275124i	$-0.911281\pi$
$953$	−7.48428	+	12.9632i	−0.242440	+	0.419918i	0.718969	+	0.695042i	$0.244614\pi$
$954$	19.0038	−	32.9156i	0.615272	−	1.06568i
$955$	16.2431	+	28.1339i	0.525614	+	0.910390i
$956$	61.9592			2.00390
$957$	0.838144	+	1.45171i	0.0270933	+	0.0469271i
$958$	27.1784	+	47.0744i	0.878094	+	1.52090i
$959$	15.3103	−	26.5183i	0.494397	−	0.856320i
$960$	2.40953	−	4.17343i	0.0777672	−	0.134697i
$961$	−29.8352			−0.962427
$962$	71.6058			2.30866
$963$	−44.2154			−1.42482
$964$	44.6508	+	77.3374i	1.43810	+	2.49087i
$965$	28.1733	+	48.7976i	0.906931	+	1.57085i
$966$	−3.05472	−	5.29092i	−0.0982839	−	0.170233i
$967$	−18.2289	+	31.5734i	−0.586202	+	1.01533i	0.408522	+	0.912748i	$0.366044\pi$
$967$	−18.2289	+	31.5734i	−0.586202	+	1.01533i	−0.994724	+	0.102584i	$0.967289\pi$
$968$	−60.8317	+	105.364i	−1.95521	+	3.38652i
$969$	−3.48309			−0.111893
$970$	−26.5385	+	45.9660i	−0.852099	+	1.47588i
$971$	0.0409143	+	0.0708657i	0.00131300	+	0.00227419i	0.866681	−	0.498862i	$-0.166249\pi$
$971$	0.0409143	+	0.0708657i	0.00131300	+	0.00227419i	−0.865368	+	0.501137i	$0.832915\pi$
$972$	−6.69992	+	11.6046i	−0.214900	+	0.372218i
$973$	12.4819	−	21.6193i	0.400151	−	0.693081i
$974$	−8.81512	+	15.2682i	−0.282455	+	0.489226i
$975$	−0.643981	+	1.11541i	−0.0206239	+	0.0357217i
$976$	29.7965	−	51.6090i	0.953762	−	1.65196i
$977$	8.80173	+	15.2450i	0.281592	+	0.487732i	0.971777	−	0.235901i	$-0.0758042\pi$
$977$	8.80173	+	15.2450i	0.281592	+	0.487732i	−0.690185	+	0.723633i	$0.742471\pi$
$978$	2.51716	−	4.35985i	0.0804898	−	0.139412i
$979$	4.04519	+	7.00648i	0.129285	+	0.223928i
$980$	−24.5725			−0.784939
$981$	7.84954	−	13.5958i	0.250616	−	0.434080i
$982$	−33.2312	+	57.5582i	−1.06045	+	1.83675i
$983$	−20.5043	−	35.5145i	−0.653986	−	1.13274i	−0.982147	−	0.188115i	$-0.939762\pi$
$983$	−20.5043	−	35.5145i	−0.653986	−	1.13274i	0.328162	−	0.944622i	$-0.393571\pi$
$984$	0.812418	+	1.40715i	0.0258989	+	0.0448583i
$985$	8.10743	−	14.0425i	0.258324	−	0.447431i
$986$	−22.1640	+	38.3892i	−0.705845	+	1.22256i
$987$	−1.46555			−0.0466491
$988$	101.195	−	175.274i	3.21943	−	5.57622i
$989$	−45.7865			−1.45592
$990$	55.3784	+	95.9182i	1.76004	+	3.04848i
$991$	−59.2614			−1.88250			−0.941251	−	0.337709i	$-0.890348\pi$
$991$	−59.2614			−1.88250			−0.941251	+	0.337709i	$0.890348\pi$
$992$	8.61813	−	14.9270i	0.273626	−	0.473934i
$993$	−0.383121			−0.0121580
$994$	48.4244			1.53593
$995$	−0.0188488	−	0.0326470i	−0.000597546	−	0.00103498i
$996$	−0.180212			−0.00571022
$997$	19.8145	−	34.3196i	0.627530	−	1.08691i	−0.360516	−	0.932753i	$-0.617399\pi$
$997$	19.8145	−	34.3196i	0.627530	−	1.08691i	0.988046	−	0.154161i	$-0.0492674\pi$
$998$	−22.1483	+	38.3621i	−0.701094	+	1.21433i
$999$	1.47820	+	2.56032i	0.0467683	+	0.0810051i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	547.2.c.a.40.1	✓	90
547.506	even	3	inner	547.2.c.a.506.1	yes	90

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
547.2.c.a.40.1	✓	90	1.1	even	1	trivial
547.2.c.a.506.1	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)

\(f(q)\)	\(=\)	\(q+(-1.33767 - 2.31692i) q^{2} +0.0966282 q^{3} +(-2.57874 + 4.46650i) q^{4} +(1.37326 - 2.37856i) q^{5} +(-0.129257 - 0.223879i) q^{6} +(1.47773 + 2.55950i) q^{7} +8.44732 q^{8} -2.99066 q^{9} +O(q^{10})\)	\(q+(-1.33767 - 2.31692i) q^{2} +0.0966282 q^{3} +(-2.57874 + 4.46650i) q^{4} +(1.37326 - 2.37856i) q^{5} +(-0.129257 - 0.223879i) q^{6} +(1.47773 + 2.55950i) q^{7} +8.44732 q^{8} -2.99066 q^{9} -7.34791 q^{10} +(2.52005 + 4.36485i) q^{11} +(-0.249179 + 0.431590i) q^{12} +(-2.62031 - 4.53851i) q^{13} +(3.95343 - 6.84754i) q^{14} +(0.132696 - 0.229836i) q^{15} +(-6.14228 - 10.6387i) q^{16} +(-2.40693 - 4.16892i) q^{17} +(4.00053 + 6.92912i) q^{18} +(3.74402 - 6.48483i) q^{19} +(7.08257 + 12.2674i) q^{20} +(0.142790 + 0.247320i) q^{21} +(6.74200 - 11.6775i) q^{22} +(3.99818 - 6.92506i) q^{23} +0.816250 q^{24} +(-1.27171 - 2.20266i) q^{25} +(-7.01024 + 12.1421i) q^{26} -0.578867 q^{27} -15.2427 q^{28} +3.44196 q^{29} -0.710015 q^{30} -1.07924 q^{31} +(-7.98540 + 13.8311i) q^{32} +(0.243508 + 0.421768i) q^{33} +(-6.43936 + 11.1533i) q^{34} +8.11724 q^{35} +(7.71213 - 13.3578i) q^{36} +(-2.55362 - 4.42299i) q^{37} -20.0331 q^{38} +(-0.253196 - 0.438548i) q^{39} +(11.6004 - 20.0925i) q^{40} +(0.995306 + 1.72392i) q^{41} +(0.382013 - 0.661666i) q^{42} +(-2.86295 - 4.95878i) q^{43} -25.9942 q^{44} +(-4.10697 + 7.11348i) q^{45} -21.3930 q^{46} +(-2.56592 + 4.44430i) q^{47} +(-0.593518 - 1.02800i) q^{48} +(-0.867357 + 1.50231i) q^{49} +(-3.40225 + 5.89287i) q^{50} +(-0.232577 - 0.402835i) q^{51} +27.0284 q^{52} +(-2.37517 - 4.11391i) q^{53} +(0.774334 + 1.34119i) q^{54} +13.8428 q^{55} +(12.4828 + 21.6209i) q^{56} +(0.361778 - 0.626618i) q^{57} +(-4.60421 - 7.97473i) q^{58} +(2.75948 + 4.77956i) q^{59} +(0.684376 + 1.18537i) q^{60} +(2.42552 + 4.20113i) q^{61} +(1.44366 + 2.50050i) q^{62} +(-4.41939 - 7.65460i) q^{63} +18.1583 q^{64} -14.3935 q^{65} +(0.651468 - 1.12837i) q^{66} +(4.86120 + 8.41984i) q^{67} +24.8273 q^{68} +(0.386337 - 0.669156i) q^{69} +(-10.8582 - 18.8070i) q^{70} +(3.06217 + 5.30384i) q^{71} -25.2631 q^{72} +(-6.87493 - 11.9077i) q^{73} +(-6.83180 + 11.8330i) q^{74} +(-0.122883 - 0.212839i) q^{75} +(19.3097 + 33.4453i) q^{76} +(-7.44789 + 12.9001i) q^{77} +(-0.677387 + 1.17327i) q^{78} +8.49561 q^{79} -33.7399 q^{80} +8.91605 q^{81} +(2.66279 - 4.61208i) q^{82} +(0.180806 + 0.313165i) q^{83} -1.47287 q^{84} -13.2214 q^{85} +(-7.65939 + 13.2664i) q^{86} +0.332590 q^{87} +(21.2877 + 36.8713i) q^{88} +1.60520 q^{89} +21.9751 q^{90} +(7.74421 - 13.4134i) q^{91} +(20.6205 + 35.7158i) q^{92} -0.104285 q^{93} +13.7294 q^{94} +(-10.2831 - 17.8108i) q^{95} +(-0.771615 + 1.33648i) q^{96} +(3.61170 - 6.25565i) q^{97} +4.64096 q^{98} +(-7.53662 - 13.0538i) 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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