LMFDB - Embedded newform 162.4.g.a.7.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [162,4,Mod(7,162)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(162, base_ring=CyclotomicField(54)) chi = DirichletCharacter(H, H._module([16])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("162.7"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	162.g (of order $27$, degree $18$, minimal)

Newform invariants

comment:select newform

sage:traces = [234] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$9.55830942093$
Analytic rank:	$0$
Dimension:	$234$
Relative dimension:	$13$ over $\Q(\zeta_{27})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			7.11
Character	$\chi$	$=$	162.7
Dual form			162.4.g.a.139.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.19432 + 1.60425i) q^{2} +(4.33355 + 2.86711i) q^{3} +(-1.14721 + 3.83196i) q^{4} +(12.9644 - 8.52679i) q^{5} +(0.576086 + 10.3763i) q^{6} +(-19.6582 + 20.8365i) q^{7} +(-7.51754 + 2.73616i) q^{8} +(10.5594 + 24.8495i) q^{9} +(29.1626 + 10.6143i) q^{10} +(-6.06658 + 3.04675i) q^{11} +(-15.9582 + 13.3168i) q^{12} +(12.2060 + 28.2967i) q^{13} +(-56.9050 - 6.65124i) q^{14} +(80.6290 + 0.218936i) q^{15} +(-13.3678 - 8.79214i) q^{16} +(79.2426 - 66.4924i) q^{17} +(-27.2536 + 46.6181i) q^{18} +(89.9218 + 75.4533i) q^{19} +(17.8014 + 59.4609i) q^{20} +(-144.930 + 33.9338i) q^{21} +(-12.1332 - 6.09350i) q^{22} +(-80.8818 - 85.7296i) q^{23} +(-40.4225 - 9.69632i) q^{24} +(45.8584 - 106.312i) q^{25} +(-30.8170 + 53.3766i) q^{26} +(-25.4868 + 137.962i) q^{27} +(-57.2924 - 99.2334i) q^{28} +(63.2551 - 7.39346i) q^{29} +(95.9453 + 129.610i) q^{30} +(-268.821 + 63.7118i) q^{31} +(-1.86063 - 31.9459i) q^{32} +(-35.0252 - 4.19030i) q^{33} +(201.311 + 47.7116i) q^{34} +(-77.1877 + 437.753i) q^{35} +(-107.336 + 11.9553i) q^{36} +(-48.8343 - 276.953i) q^{37} +(-13.6506 + 234.372i) q^{38} +(-28.2344 + 157.621i) q^{39} +(-74.1294 + 99.5731i) q^{40} +(165.318 - 222.061i) q^{41} +(-227.531 - 191.976i) q^{42} +(27.0653 - 464.692i) q^{43} +(-4.71536 - 26.7421i) q^{44} +(348.782 + 232.121i) q^{45} +(40.9330 - 232.143i) q^{46} +(217.317 + 51.5050i) q^{47} +(-32.7220 - 76.4282i) q^{48} +(-27.7703 - 476.797i) q^{49} +(225.320 - 53.4017i) q^{50} +(534.043 - 60.9512i) q^{51} +(-122.435 + 14.3105i) q^{52} +(129.277 + 223.915i) q^{53} +(-251.764 + 123.883i) q^{54} +(-52.6703 + 91.2276i) q^{55} +(90.7695 - 210.427i) q^{56} +(173.348 + 584.797i) q^{57} +(87.4076 + 92.6467i) q^{58} +(-694.783 - 348.933i) q^{59} +(-93.3376 + 308.716i) q^{60} +(81.2422 + 271.368i) q^{61} +(-423.267 - 355.163i) q^{62} +(-725.356 - 268.478i) q^{63} +(49.0268 - 41.1384i) q^{64} +(399.523 + 262.770i) q^{65} +(-35.1089 - 61.1936i) q^{66} +(350.594 + 40.9786i) q^{67} +(163.888 + 379.935i) q^{68} +(-104.709 - 603.411i) q^{69} +(-794.451 + 398.988i) q^{70} +(697.092 + 253.721i) q^{71} +(-147.373 - 157.915i) q^{72} +(656.547 - 238.963i) q^{73} +(385.978 - 409.112i) q^{74} +(503.537 - 329.226i) q^{75} +(-392.293 + 258.015i) q^{76} +(55.7745 - 186.300i) q^{77} +(-286.584 + 142.955i) q^{78} +(-791.295 - 1062.89i) q^{79} -248.274 q^{80} +(-506.000 + 524.791i) q^{81} +553.683 q^{82} +(-372.612 - 500.505i) q^{83} +(36.2333 - 594.297i) q^{84} +(460.362 - 1537.72i) q^{85} +(777.806 - 511.571i) q^{86} +(295.317 + 149.319i) q^{87} +(37.2694 - 39.5032i) q^{88} +(90.2159 - 32.8359i) q^{89} +(44.1774 + 836.759i) q^{90} +(-829.552 - 301.932i) q^{91} +(421.301 - 211.585i) q^{92} +(-1347.62 - 494.641i) q^{93} +(176.918 + 410.143i) q^{94} +(1809.15 + 211.460i) q^{95} +(83.5291 - 143.774i) q^{96} +(-124.085 - 81.6118i) q^{97} +(731.733 - 613.997i) q^{98} +(-139.770 - 118.580i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 234 q + 36 q^{6} - 90 q^{13} - 162 q^{18} - 144 q^{20} - 405 q^{21} - 756 q^{23} - 846 q^{25} + 702 q^{26} + 702 q^{27} + 504 q^{28} + 540 q^{29} + 1098 q^{30} + 2214 q^{31} + 684 q^{33} - 1242 q^{35} - 576 q^{36}+ \cdots + 18567 q^{99}+O(q^{100}) $ 234 * q + 36 * q^6 - 90 * q^13 - 162 * q^18 - 144 * q^20 - 405 * q^21 - 756 * q^23 - 846 * q^25 + 702 * q^26 + 702 * q^27 + 504 * q^28 + 540 * q^29 + 1098 * q^30 + 2214 * q^31 + 684 * q^33 - 1242 * q^35 - 576 * q^36 - 72 * q^38 - 927 * q^41 - 774 * q^42 + 900 * q^43 - 3843 * q^45 + 2088 * q^46 + 297 * q^47 + 144 * q^48 + 810 * q^51 + 720 * q^52 + 1431 * q^53 + 2970 * q^55 + 1485 * q^57 - 126 * q^58 - 1179 * q^59 - 2259 * q^63 + 3627 * q^65 + 4680 * q^66 - 8046 * q^67 + 2304 * q^68 - 594 * q^69 + 1530 * q^70 + 720 * q^71 + 864 * q^72 - 3204 * q^73 - 3384 * q^74 - 9918 * q^75 - 144 * q^76 - 9792 * q^77 - 7524 * q^78 + 4527 * q^79 - 1440 * q^80 + 5832 * q^81 - 5904 * q^82 - 9621 * q^83 - 1224 * q^84 + 4059 * q^85 - 3600 * q^86 - 117 * q^87 - 576 * q^88 + 531 * q^89 + 1440 * q^90 - 4473 * q^91 + 1872 * q^92 + 135 * q^93 + 666 * q^94 + 8037 * q^95 + 1728 * q^96 - 16560 * q^97 + 8136 * q^98 + 18567 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{8}{27}\right)$

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 $

$2$	1.19432	+	1.60425i	0.422255	+	0.567187i
$2$	1.19432	+	1.60425i	0.422255	+	0.567187i
$3$	4.33355	+	2.86711i	0.833993	+	0.551776i
$3$	4.33355	+	2.86711i	0.833993	+	0.551776i
$4$	−1.14721	+	3.83196i	−0.143402	+	0.478995i
$5$	12.9644	−	8.52679i	1.15957	−	0.762659i	0.184122	−	0.982903i	$-0.441056\pi$
$5$	12.9644	−	8.52679i	1.15957	−	0.762659i	0.975445	+	0.220244i	$0.0706853\pi$
$6$	0.576086	+	10.3763i	0.0391977	+	0.706020i
$7$	−19.6582	+	20.8365i	−1.06144	+	1.12506i	−0.0696041	+	0.997575i	$0.522174\pi$
$7$	−19.6582	+	20.8365i	−1.06144	+	1.12506i	−0.991840	+	0.127490i	$0.959308\pi$
$8$	−7.51754	+	2.73616i	−0.332232	+	0.120922i
$9$	10.5594	+	24.8495i	0.391087	+	0.920354i
$10$	29.1626	+	10.6143i	0.922203	+	0.335655i
$11$	−6.06658	+	3.04675i	−0.166286	+	0.0835118i	−0.529995	−	0.848001i	$-0.677806\pi$
$11$	−6.06658	+	3.04675i	−0.166286	+	0.0835118i	0.363710	+	0.931512i	$0.381510\pi$
$12$	−15.9582	+	13.3168i	−0.383894	+	0.320353i
$13$	12.2060	+	28.2967i	0.260410	+	0.603699i	0.997389	−	0.0722171i	$-0.0230074\pi$
$13$	12.2060	+	28.2967i	0.260410	+	0.603699i	−0.736979	+	0.675916i	$0.763748\pi$
$14$	−56.9050	−	6.65124i	−1.08632	−	0.126973i
$15$	80.6290	+	0.218936i	1.38789	+	0.00376861i
$16$	−13.3678	−	8.79214i	−0.208872	−	0.137377i
$17$	79.2426	−	66.4924i	1.13054	−	0.948634i	0.131450	−	0.991323i	$-0.458037\pi$
$17$	79.2426	−	66.4924i	1.13054	−	0.948634i	0.999088	+	0.0426888i	$0.0135924\pi$
$18$	−27.2536	+	46.6181i	−0.356874	+	0.610443i
$19$	89.9218	+	75.4533i	1.08576	+	0.911062i	0.996386	−	0.0849360i	$-0.0270686\pi$
$19$	89.9218	+	75.4533i	1.08576	+	0.911062i	0.0893751	+	0.995998i	$0.471513\pi$
$20$	17.8014	+	59.4609i	0.199026	+	0.664793i
$21$	−144.930	+	33.9338i	−1.50602	+	0.352617i
$22$	−12.1332	−	6.09350i	−0.117582	−	0.0590518i
$23$	−80.8818	−	85.7296i	−0.733261	−	0.777212i	0.248233	−	0.968700i	$-0.420150\pi$
$23$	−80.8818	−	85.7296i	−0.733261	−	0.777212i	−0.981495	+	0.191489i	$0.938668\pi$
$24$	−40.4225	−	9.69632i	−0.343801	−	0.0824689i
$25$	45.8584	−	106.312i	0.366867	−	0.850494i
$26$	−30.8170	+	53.3766i	−0.232451	+	0.402616i
$27$	−25.4868	+	137.962i	−0.181665	+	0.983361i
$28$	−57.2924	−	99.2334i	−0.386687	−	0.669762i
$29$	63.2551	−	7.39346i	0.405041	−	0.0473425i	0.0888664	−	0.996044i	$-0.471676\pi$
$29$	63.2551	−	7.39346i	0.405041	−	0.0473425i	0.316174	+	0.948701i	$0.397602\pi$
$30$	95.9453	+	129.610i	0.583905	+	0.788783i
$31$	−268.821	+	63.7118i	−1.55747	+	0.369128i	−0.917011	−	0.398861i	$-0.869406\pi$
$31$	−268.821	+	63.7118i	−1.55747	+	0.369128i	−0.640463	+	0.767989i	$0.721257\pi$
$32$	−1.86063	−	31.9459i	−0.0102787	−	0.176478i
$33$	−35.0252	−	4.19030i	−0.184761	−	0.0221041i
$34$	201.311	+	47.7116i	1.01543	+	0.240661i
$35$	−77.1877	+	437.753i	−0.372774	+	2.11411i
$36$	−107.336	+	11.9553i	−0.496927	+	0.0553486i
$37$	−48.8343	−	276.953i	−0.216982	−	1.23056i	−0.877435	−	0.479696i	$-0.840747\pi$
$37$	−48.8343	−	276.953i	−0.216982	−	1.23056i	0.660453	−	0.750867i	$-0.270364\pi$
$38$	−13.6506	+	234.372i	−0.0582742	+	1.00053i
$39$	−28.2344	+	157.621i	−0.115926	+	0.647169i
$40$	−74.1294	+	99.5731i	−0.293022	+	0.393597i
$41$	165.318	−	222.061i	0.629716	−	0.845855i	−0.366709	−	0.930336i	$-0.619516\pi$
$41$	165.318	−	222.061i	0.629716	−	0.845855i	0.996425	+	0.0844803i	$0.0269230\pi$
$42$	−227.531	−	191.976i	−0.835924	−	0.705300i
$43$	27.0653	−	464.692i	0.0959863	−	1.64802i	−0.515589	−	0.856836i	$-0.672427\pi$
$43$	27.0653	−	464.692i	0.0959863	−	1.64802i	0.611576	−	0.791186i	$-0.290536\pi$
$44$	−4.71536	−	26.7421i	−0.0161561	−	0.0916257i
$45$	348.782	+	232.121i	1.15541	+	0.768945i
$46$	40.9330	−	232.143i	0.131201	−	0.744078i
$47$	217.317	+	51.5050i	0.674444	+	0.159846i	0.553546	−	0.832819i	$-0.313274\pi$
$47$	217.317	+	51.5050i	0.674444	+	0.159846i	0.120898	+	0.992665i	$0.461422\pi$
$48$	−32.7220	−	76.4282i	−0.0983963	−	0.229822i
$49$	−27.7703	−	476.797i	−0.0809628	−	1.39008i
$50$	225.320	−	53.4017i	0.637300	−	0.151043i
$51$	534.043	−	60.9512i	1.46629	−	0.167351i
$52$	−122.435	+	14.3105i	−0.326512	+	0.0381638i
$53$	129.277	+	223.915i	0.335049	+	0.580321i	0.983494	−	0.180940i	$-0.0579139\pi$
$53$	129.277	+	223.915i	0.335049	+	0.580321i	−0.648446	+	0.761261i	$0.724581\pi$
$54$	−251.764	+	123.883i	−0.634458	+	0.312191i
$55$	−52.6703	+	91.2276i	−0.129128	+	0.223657i
$56$	90.7695	−	210.427i	0.216600	−	0.502134i
$57$	173.348	+	584.797i	0.402815	+	1.35892i
$58$	87.4076	+	92.6467i	0.197882	+	0.209743i
$59$	−694.783	−	348.933i	−1.53310	−	0.769953i	−0.535871	−	0.844300i	$-0.680017\pi$
$59$	−694.783	−	348.933i	−1.53310	−	0.769953i	−0.997232	+	0.0743465i	$0.976313\pi$
$60$	−93.3376	+	308.716i	−0.200830	+	0.664250i
$61$	81.2422	+	271.368i	0.170524	+	0.569591i	0.999940	+	0.0109591i	$0.00348847\pi$
$61$	81.2422	+	271.368i	0.170524	+	0.569591i	−0.829415	+	0.558632i	$0.811326\pi$
$62$	−423.267	−	355.163i	−0.867016	−	0.727513i
$63$	−725.356	−	268.478i	−1.45057	−	0.536905i
$64$	49.0268	−	41.1384i	0.0957556	−	0.0803485i
$65$	399.523	+	262.770i	0.762380	+	0.501425i
$66$	−35.1089	−	61.1936i	−0.0654790	−	0.114127i
$67$	350.594	+	40.9786i	0.639282	+	0.0747214i	0.429558	−	0.903039i	$-0.358669\pi$
$67$	350.594	+	40.9786i	0.639282	+	0.0747214i	0.209724	+	0.977761i	$0.432743\pi$
$68$	163.888	+	379.935i	0.292270	+	0.677557i
$69$	−104.709	−	603.411i	−0.182688	−	1.05278i
$70$	−794.451	+	398.988i	−1.35650	+	0.681260i
$71$	697.092	+	253.721i	1.16520	+	0.424100i	0.850954	−	0.525240i	$-0.176024\pi$
$71$	697.092	+	253.721i	1.16520	+	0.424100i	0.314251	+	0.949340i	$0.398247\pi$
$72$	−147.373	−	157.915i	−0.241223	−	0.258479i
$73$	656.547	−	238.963i	1.05264	−	0.383131i	0.242984	−	0.970030i	$-0.421874\pi$
$73$	656.547	−	238.963i	1.05264	−	0.383131i	0.809660	+	0.586900i	$0.199652\pi$
$74$	385.978	−	409.112i	0.606338	−	0.642680i
$75$	503.537	−	329.226i	0.775246	−	0.506877i
$76$	−392.293	+	258.015i	−0.592094	+	0.389426i
$77$	55.7745	−	186.300i	0.0825467	−	0.275725i
$78$	−286.584	+	142.955i	−0.416016	+	0.207518i
$79$	−791.295	−	1062.89i	−1.12693	−	1.51373i	−0.829088	−	0.559118i	$-0.811140\pi$
$79$	−791.295	−	1062.89i	−1.12693	−	1.51373i	−0.297844	−	0.954615i	$-0.596268\pi$
$80$	−248.274			−0.346973
$81$	−506.000	+	524.791i	−0.694101	+	0.719877i
$82$	553.683			0.745659
$83$	−372.612	−	500.505i	−0.492765	−	0.661898i	0.484285	−	0.874911i	$-0.339080\pi$
$83$	−372.612	−	500.505i	−0.492765	−	0.661898i	−0.977049	+	0.213012i	$0.931673\pi$
$84$	36.2333	−	594.297i	0.0470640	−	0.771941i
$85$	460.362	−	1537.72i	0.587450	−	1.96222i
$86$	777.806	−	511.571i	0.975267	−	0.641443i
$87$	295.317	+	149.319i	0.363923	+	0.184008i
$88$	37.2694	−	39.5032i	0.0451469	−	0.0478529i
$89$	90.2159	−	32.8359i	0.107448	−	0.0391078i	−0.287737	−	0.957710i	$-0.592903\pi$
$89$	90.2159	−	32.8359i	0.107448	−	0.0391078i	0.395185	+	0.918602i	$0.370681\pi$
$90$	44.1774	+	836.759i	0.0517412	+	0.980023i
$91$	−829.552	−	301.932i	−0.955611	−	0.347814i
$92$	421.301	−	211.585i	0.477431	−	0.239775i
$93$	−1347.62	−	494.641i	−1.50260	−	0.551526i
$94$	176.918	+	410.143i	0.194125	+	0.450032i
$95$	1809.15	+	211.460i	1.95384	+	0.228372i
$96$	83.5291	−	143.774i	0.0888037	−	0.152853i
$97$	−124.085	−	81.6118i	−0.129885	−	0.0854270i	0.482904	−	0.875673i	$-0.339582\pi$
$97$	−124.085	−	81.6118i	−0.129885	−	0.0854270i	−0.612789	+	0.790246i	$0.709952\pi$
$98$	731.733	−	613.997i	0.754247	−	0.632888i
$99$	−139.770	−	118.580i	−0.141893	−	0.120381i
$100$	354.773	+	297.690i	0.354773	+	0.297690i
$101$	−21.6788	−	72.4121i	−0.0213576	−	0.0713393i	0.946646	−	0.322274i	$-0.104447\pi$
$101$	−21.6788	−	72.4121i	−0.0213576	−	0.0713393i	−0.968004	+	0.250935i	$0.919262\pi$
$102$	735.597	+	783.941i	0.714069	+	0.760998i
$103$	940.844	+	472.510i	0.900040	+	0.452017i	0.837758	−	0.546042i	$-0.183866\pi$
$103$	940.844	+	472.510i	0.900040	+	0.452017i	0.0622817	+	0.998059i	$0.480162\pi$
$104$	−169.183	−	179.324i	−0.159517	−	0.169078i
$105$	−1589.58	+	1675.72i	−1.47740	+	1.55746i
$106$	−204.816	+	474.817i	−0.187675	+	0.435079i
$107$	−110.128	+	190.747i	−0.0994997	+	0.172339i	−0.911478	−	0.411350i	$-0.865058\pi$
$107$	−110.128	+	190.747i	−0.0994997	+	0.172339i	0.811978	+	0.583688i	$0.198391\pi$
$108$	−499.424	−	255.936i	−0.444974	−	0.228032i
$109$	117.493	+	203.503i	0.103245	+	0.178826i	0.913020	−	0.407915i	$-0.133744\pi$
$109$	117.493	+	203.503i	0.103245	+	0.178826i	−0.809775	+	0.586741i	$0.800411\pi$
$110$	−209.257	+	24.4586i	−0.181380	+	0.0212003i
$111$	582.429	−	1340.21i	0.498034	−	1.14601i
$112$	445.985	−	105.700i	0.376264	−	0.0891762i
$113$	22.2127	+	381.377i	0.0184920	+	0.317495i	0.994852	+	0.101343i	$0.0323138\pi$
$113$	22.2127	+	381.377i	0.0184920	+	0.317495i	−0.976360	+	0.216153i	$0.930649\pi$
$114$	−731.126	+	976.525i	−0.600668	+	0.802280i
$115$	−1779.58	−	421.768i	−1.44301	−	0.342000i
$116$	−44.2357	+	250.873i	−0.0354067	+	0.200801i
$117$	−574.272	+	602.108i	−0.453773	+	0.475769i
$118$	−270.017	−	1531.34i	−0.210653	−	1.19467i
$119$	−172.299	+	2958.26i	−0.132728	+	2.27885i
$120$	−606.731	+	218.968i	−0.461556	+	0.166575i
$121$	−767.297	+	1030.66i	−0.576482	+	0.774350i
$122$	−338.312	+	454.432i	−0.251060	+	0.337232i
$123$	1353.09	−	488.327i	0.991901	−	0.357975i
$124$	64.2542	−	1103.20i	0.0465339	−	0.798956i
$125$	24.8416	+	140.884i	0.0177752	+	0.100808i
$126$	−435.600	−	1484.30i	−0.307987	−	1.04946i
$127$	−416.727	+	2363.38i	−0.291170	+	1.65131i	0.391205	+	0.920304i	$0.372058\pi$
$127$	−416.727	+	2363.38i	−0.291170	+	1.65131i	−0.682375	+	0.731003i	$0.739053\pi$
$128$	124.550	+	29.5188i	0.0860058	+	0.0203838i
$129$	1449.61	−	1936.17i	0.989390	−	1.32148i
$130$	55.6087	+	954.764i	0.0375169	+	0.644141i
$131$	−491.063	+	116.384i	−0.327514	+	0.0776223i	−0.391084	−	0.920355i	$-0.627900\pi$
$131$	−491.063	+	116.384i	−0.327514	+	0.0776223i	0.0635696	+	0.997977i	$0.479752\pi$
$132$	56.2384	−	129.408i	0.0370828	−	0.0853297i
$133$	−3339.88	+	390.376i	−2.17748	+	0.254511i
$134$	352.981	+	611.381i	0.227559	+	0.394144i
$135$	845.950	+	2005.91i	0.539317	+	1.27882i
$136$	−413.775	+	716.680i	−0.260889	+	0.451873i
$137$	56.3619	−	130.662i	0.0351483	−	0.0814830i	−0.899738	−	0.436431i	$-0.856242\pi$
$137$	56.3619	−	130.662i	0.0351483	−	0.0814830i	0.934886	+	0.354948i	$0.115501\pi$
$138$	842.964	−	888.643i	0.519984	−	0.548162i
$139$	−418.418	−	443.497i	−0.255322	−	0.270625i	0.587016	−	0.809575i	$-0.300303\pi$
$139$	−418.418	−	443.497i	−0.255322	−	0.270625i	−0.842338	+	0.538950i	$0.818821\pi$
$140$	−1588.90	−	797.976i	−0.959190	−	0.481724i
$141$	794.083	+	846.270i	0.474282	+	0.505453i
$142$	425.518	+	1421.33i	0.251470	+	0.839967i
$143$	−160.262	−	134.475i	−0.0937185	−	0.0786392i
$144$	77.3253	−	425.023i	0.0447484	−	0.245963i
$145$	757.019	−	635.215i	0.433566	−	0.363805i
$146$	1167.48	+	767.864i	0.661791	+	0.435266i
$147$	1246.69	−	2145.84i	0.699489	−	1.20399i
$148$	1117.30	+	130.593i	0.620549	+	0.0725318i
$149$	−833.443	−	1932.14i	−0.458244	−	1.06233i	−0.978112	−	0.208081i	$-0.933278\pi$
$149$	−833.443	−	1932.14i	−0.458244	−	1.06233i	0.519868	−	0.854247i	$-0.325981\pi$
$150$	1129.54	+	414.597i	0.614845	+	0.225678i
$151$	635.964	−	319.393i	0.342742	−	0.172131i	−0.269099	−	0.963113i	$-0.586726\pi$
$151$	635.964	−	319.393i	0.342742	−	0.172131i	0.611840	+	0.790981i	$0.290429\pi$
$152$	−882.443	−	321.183i	−0.470892	−	0.171391i
$153$	2489.06	+	1267.02i	1.31522	+	0.669496i
$154$	365.483	−	133.025i	0.191243	−	0.0696069i
$155$	−2941.84	+	3118.16i	−1.52448	+	1.61585i
$156$	−571.607	−	289.018i	−0.293366	−	0.148333i
$157$	−237.967	+	156.513i	−0.120967	+	0.0795612i	−0.608551	−	0.793515i	$-0.708249\pi$
$157$	−237.967	+	156.513i	−0.120967	+	0.0795612i	0.487584	+	0.873076i	$0.337878\pi$
$158$	760.086	−	2538.86i	0.382716	−	1.27836i
$159$	−81.7584	+	1341.00i	−0.0407790	+	0.668855i
$160$	−296.518	−	398.292i	−0.146511	−	0.196799i
$161$	3376.30			1.65273
$162$	−1446.22	−	184.982i	−0.701393	−	0.0897133i
$163$	666.132			0.320095			0.160047	−	0.987109i	$-0.448835\pi$
$163$	666.132			0.320095			0.160047	+	0.987109i	$0.448835\pi$
$164$	661.273	+	888.243i	0.314858	+	0.422928i
$165$	−489.809	+	244.328i	−0.231100	+	0.115278i
$166$	357.916	−	1195.52i	0.167347	−	0.558979i
$167$	−2361.58	+	1553.24i	−1.09428	+	0.719718i	−0.962424	−	0.271551i	$-0.912464\pi$
$167$	−2361.58	+	1553.24i	−1.09428	+	0.719718i	−0.131855	+	0.991269i	$0.542093\pi$
$168$	996.672	−	651.652i	0.457708	−	0.299262i
$169$	855.957	−	907.262i	0.389603	−	0.412955i
$170$	3016.69	−	1097.99i	1.36100	−	0.495363i
$171$	−925.464	+	3031.25i	−0.413872	+	1.35559i
$172$	1749.63	+	636.814i	0.775629	+	0.282306i
$173$	−3416.00	+	1715.58i	−1.50123	+	0.753948i	−0.994156	−	0.107952i	$-0.965571\pi$
$173$	−3416.00	+	1715.58i	−1.50123	+	0.753948i	−0.507078	+	0.861900i	$0.669274\pi$
$174$	113.157	+	652.096i	0.0493014	+	0.284111i
$175$	1313.67	+	3045.43i	0.567452	+	1.31550i
$176$	107.884	+	12.6099i	0.0462050	+	0.00540059i
$177$	−2010.45	−	3504.14i	−0.853755	−	1.48806i
$178$	160.423	+	105.512i	0.0675519	+	0.0444296i
$179$	1213.39	−	1018.15i	0.506663	−	0.425141i	−0.353290	−	0.935514i	$-0.614937\pi$
$179$	1213.39	−	1018.15i	0.506663	−	0.425141i	0.859953	+	0.510373i	$0.170493\pi$
$180$	−1289.60	+	1070.23i	−0.534008	+	0.443167i
$181$	−1145.94	−	961.560i	−0.470593	−	0.394874i	0.376418	−	0.926450i	$-0.377156\pi$
$181$	−1145.94	−	961.560i	−0.470593	−	0.394874i	−0.847011	+	0.531576i	$0.821600\pi$
$182$	−506.374	−	1691.41i	−0.206236	−	0.688876i
$183$	−425.974	+	1408.92i	−0.172070	+	0.569126i
$184$	842.602	+	423.171i	0.337595	+	0.169546i
$185$	−2994.63	−	3174.12i	−1.19011	−	1.26144i
$186$	−815.958	−	2752.67i	−0.321661	−	1.08514i
$187$	−278.145	+	644.814i	−0.108770	+	0.252157i
$188$	−446.673	+	773.661i	−0.173282	+	0.300133i
$189$	−2373.61	−	3243.14i	−0.913518	−	1.24817i
$190$	1821.47	+	3154.88i	0.695491	+	1.20463i
$191$	734.956	−	85.9041i	0.278427	−	0.0325435i	0.0242666	−	0.999706i	$-0.492275\pi$
$191$	734.956	−	85.9041i	0.278427	−	0.0325435i	0.254160	+	0.967162i	$0.418201\pi$
$192$	330.409	−	37.7101i	0.124194	−	0.0141744i
$193$	−192.593	+	45.6453i	−0.0718296	+	0.0170239i	−0.266374	−	0.963870i	$-0.585825\pi$
$193$	−192.593	+	45.6453i	−0.0718296	+	0.0170239i	0.194544	+	0.980894i	$0.437677\pi$
$194$	−17.2711	−	296.533i	−0.00639170	−	0.109741i
$195$	977.962	+	2284.20i	0.359145	+	0.838848i
$196$	1858.92	+	440.573i	0.677450	+	0.160559i
$197$	−420.739	+	2386.13i	−0.152165	+	0.862969i	0.809168	+	0.587578i	$0.199918\pi$
$197$	−420.739	+	2386.13i	−0.152165	+	0.862969i	−0.961332	+	0.275391i	$0.911193\pi$
$198$	23.3024	−	365.847i	0.00836377	−	0.131311i
$199$	665.666	+	3775.18i	0.237125	+	1.34480i	0.838093	+	0.545527i	$0.183671\pi$
$199$	665.666	+	3775.18i	0.237125	+	1.34480i	−0.600968	+	0.799273i	$0.705218\pi$
$200$	−53.8564	+	924.678i	−0.0190411	+	0.326923i
$201$	1401.83	+	1182.78i	0.491927	+	0.415057i
$202$	90.2755	−	121.261i	0.0314444	−	0.0422371i
$203$	−1089.43	+	1463.36i	−0.376665	+	0.505948i
$204$	−379.098	+	2116.35i	−0.130109	+	0.726345i
$205$	249.777	−	4288.51i	0.0850985	−	1.46108i
$206$	365.644	+	2073.67i	0.123668	+	0.701357i
$207$	1276.28	−	2915.12i	0.428540	−	0.978817i
$208$	85.6211	−	485.581i	0.0285421	−	0.161870i
$209$	−775.405	−	183.774i	−0.256631	−	0.0608227i
$210$	−4586.74	−	548.741i	−1.50721	−	0.180318i
$211$	−21.2893	−	365.523i	−0.00694604	−	0.119259i	−0.999999	−	0.00158847i	$-0.999494\pi$
$211$	−21.2893	−	365.523i	−0.00694604	−	0.119259i	0.993053	−	0.117671i	$-0.0375427\pi$
$212$	−1006.34	+	238.507i	−0.326017	+	0.0772675i
$213$	2293.44	+	3098.15i	0.737764	+	0.996628i
$214$	−437.533	+	51.1403i	−0.139762	+	0.0163359i
$215$	−3611.45	−	6255.22i	−1.14558	−	1.98420i
$216$	−185.887	−	1106.87i	−0.0585556	−	0.348671i
$217$	3957.01	−	6853.75i	1.23788	−	2.14407i
$218$	−186.146	+	431.535i	−0.0578321	+	0.134070i
$219$	3530.31	+	846.831i	1.08930	+	0.261295i
$220$	−289.156	−	306.488i	−0.0886133	−	0.0939246i
$221$	2848.75	+	1430.70i	0.867093	+	0.435471i
$222$	2845.62	−	666.270i	0.860297	−	0.201428i
$223$	−75.0114	−	250.555i	−0.0225253	−	0.0752396i	0.945988	−	0.324202i	$-0.105096\pi$
$223$	−75.0114	−	250.555i	−0.0225253	−	0.0752396i	−0.968513	+	0.248962i	$0.919911\pi$
$224$	702.216	+	589.230i	0.209459	+	0.175757i
$225$	3126.03	+	16.9767i	0.926232	+	0.00503014i
$226$	−585.294	+	491.120i	−0.172271	+	0.144552i
$227$	−230.879	−	151.852i	−0.0675066	−	0.0443998i	0.515307	−	0.857006i	$-0.327678\pi$
$227$	−230.879	−	151.852i	−0.0675066	−	0.0443998i	−0.582814	+	0.812606i	$0.698048\pi$
$228$	−2439.78	−	6.62488i	−0.708678	−	0.00192431i
$229$	−1483.70	−	173.420i	−0.428148	−	0.0500433i	−0.100709	−	0.994916i	$-0.532111\pi$
$229$	−1483.70	−	173.420i	−0.428148	−	0.0500433i	−0.327438	+	0.944873i	$0.606185\pi$
$230$	−1448.76	−	3358.61i	−0.415341	−	0.962870i
$231$	775.844	−	647.429i	0.220982	−	0.184406i
$232$	−455.293	+	228.657i	−0.128843	+	0.0647072i
$233$	−3059.81	−	1113.68i	−0.860321	−	0.313131i	−0.126080	−	0.992020i	$-0.540240\pi$
$233$	−3059.81	−	1113.68i	−0.860321	−	0.313131i	−0.734241	+	0.678889i	$0.762462\pi$
$234$	−1651.79	−	202.166i	−0.461458	−	0.0564786i
$235$	3256.54	−	1185.28i	0.903972	−	0.329019i
$236$	2134.16	−	2262.08i	0.588653	−	0.623936i
$237$	−381.686	−	6874.83i	−0.104612	−	1.88426i
$238$	−4951.56	+	3256.69i	−1.34858	+	0.886974i
$239$	1282.77	−	4284.75i	0.347178	−	1.15965i	−0.589002	−	0.808132i	$-0.700479\pi$
$239$	1282.77	−	4284.75i	0.347178	−	1.15965i	0.936179	−	0.351522i	$-0.114336\pi$
$240$	−1075.91	−	711.828i	−0.289373	−	0.191451i
$241$	1777.15	+	2387.12i	0.475005	+	0.638042i	0.973456	−	0.228876i	$-0.0735050\pi$
$241$	1777.15	+	2387.12i	0.475005	+	0.638042i	−0.498451	+	0.866918i	$0.666098\pi$
$242$	−2569.83			−0.682623
$243$	−3697.41	+	823.450i	−0.976086	+	0.217384i
$244$	−1133.07			−0.297285
$245$	−4425.57	−	5944.57i	−1.15404	−	1.55014i
$246$	2399.41	+	1587.47i	0.621874	+	0.411436i
$247$	−1037.49	+	3465.47i	−0.267264	+	0.892723i
$248$	1846.55	−	1214.49i	0.472806	−	0.310969i
$249$	−179.731	−	3237.28i	−0.0457431	−	0.823914i
$250$	−196.343	+	208.112i	−0.0496714	+	0.0526486i
$251$	3158.82	−	1149.71i	0.794353	−	0.289121i	0.0872089	−	0.996190i	$-0.472205\pi$
$251$	3158.82	−	1149.71i	0.794353	−	0.289121i	0.707144	+	0.707069i	$0.249983\pi$
$252$	1860.93	−	2471.53i	0.465189	−	0.617825i
$253$	751.872	+	273.659i	0.186837	+	0.0680032i
$254$	−4289.15	+	2154.09i	−1.05955	+	0.532124i
$255$	6403.80	−	5343.87i	1.57263	−	1.31234i
$256$	101.396	+	235.063i	0.0247550	+	0.0573885i
$257$	−4882.33	−	570.662i	−1.18502	−	0.138509i	−0.499338	−	0.866407i	$-0.666424\pi$
$257$	−4882.33	−	570.662i	−1.18502	−	0.138509i	−0.685686	+	0.727898i	$0.740498\pi$
$258$	4837.39	+	13.1352i	1.16730	+	0.00316963i
$259$	6730.73	+	4426.87i	1.61478	+	1.06206i
$260$	−1465.26	+	1229.50i	−0.349507	+	0.293271i
$261$	851.658	+	1493.79i	0.201978	+	0.354266i
$262$	−773.193	−	648.786i	−0.182321	−	0.152985i
$263$	1998.31	+	6674.82i	0.468521	+	1.56497i	0.786946	+	0.617022i	$0.211661\pi$
$263$	1998.31	+	6674.82i	0.468521	+	1.56497i	−0.318425	+	0.947948i	$0.603154\pi$
$264$	274.769	−	64.3339i	0.0640562	−	0.0149980i
$265$	3585.27	+	1800.59i	0.831099	+	0.417394i
$266$	−4615.14	−	4891.76i	−1.06381	−	1.12757i
$267$	485.099	+	116.363i	0.111190	+	0.0266715i
$268$	−559.235	+	1296.45i	−0.127465	+	0.295498i
$269$	−29.2472	+	50.6576i	−0.00662912	+	0.0114820i	−0.869321	−	0.494248i	$-0.835443\pi$
$269$	−29.2472	+	50.6576i	−0.00662912	+	0.0114820i	0.862692	+	0.505730i	$0.168777\pi$
$270$	−2207.63	+	3752.80i	−0.497601	+	0.845882i
$271$	−3228.07	−	5591.18i	−0.723584	−	1.25328i	−0.959554	−	0.281524i	$-0.909160\pi$
$271$	−3228.07	−	5591.18i	−0.723584	−	1.25328i	0.235970	−	0.971760i	$-0.424173\pi$
$272$	−1643.91	+	192.146i	−0.366458	+	0.0428328i
$273$	−2729.23	−	3686.85i	−0.605058	−	0.817358i
$274$	276.927	−	65.6330i	0.0610577	−	0.0144709i
$275$	45.7017	+	784.667i	0.0100215	+	0.172063i
$276$	2432.37	+	291.000i	0.530476	+	0.0634643i
$277$	−8186.67	−	1940.28i	−1.77577	−	0.420866i	−0.793539	−	0.608519i	$-0.791764\pi$
$277$	−8186.67	−	1940.28i	−1.77577	−	0.420866i	−0.982235	+	0.187653i	$0.939912\pi$
$278$	211.755	−	1200.92i	0.0456842	−	0.259088i
$279$	−4421.79	−	6007.33i	−0.948837	−	1.28907i
$280$	−617.502	−	3502.03i	−0.131796	−	0.747450i
$281$	183.440	−	3149.55i	0.0389435	−	0.668635i	−0.921193	−	0.389105i	$-0.872784\pi$
$281$	183.440	−	3149.55i	0.0389435	−	0.668635i	0.960137	−	0.279530i	$-0.0901786\pi$
$282$	−409.240	+	2284.62i	−0.0864179	+	0.482437i
$283$	−1092.76	+	1467.82i	−0.229532	+	0.308315i	−0.901936	−	0.431869i	$-0.857854\pi$
$283$	−1092.76	+	1467.82i	−0.229532	+	0.308315i	0.672404	+	0.740184i	$0.265262\pi$
$284$	−1771.96	+	2380.15i	−0.370234	+	0.497310i
$285$	7233.78	+	6103.41i	1.50348	+	1.26854i
$286$	24.3286	−	417.705i	0.00502999	−	0.0863617i
$287$	1377.11	+	7809.97i	0.283234	+	1.60630i
$288$	774.193	−	383.564i	0.158402	−	0.0784782i
$289$	1005.01	−	5699.70i	0.204561	−	1.16013i
$290$	1923.16	+	455.798i	0.389421	+	0.0922944i
$291$	−303.738	−	709.433i	−0.0611870	−	0.142913i
$292$	162.499	+	2790.00i	0.0325669	+	0.559152i
$293$	−944.510	+	223.853i	−0.188324	+	0.0446336i	−0.323695	−	0.946161i	$-0.604925\pi$
$293$	−944.510	+	223.853i	−0.188324	+	0.0446336i	0.135372	+	0.990795i	$0.456777\pi$
$294$	4931.40	−	562.829i	0.978249	−	0.111649i
$295$	−11982.7	+	1400.58i	−2.36495	+	0.276423i
$296$	1124.90	+	1948.39i	0.220891	+	0.382594i
$297$	−265.717	−	914.607i	−0.0519140	−	0.178690i
$298$	2104.23	−	3644.63i	0.409043	−	0.708483i
$299$	1438.62	−	3335.10i	0.278253	−	0.645063i
$300$	683.917	+	2307.23i	0.131620	+	0.444026i
$301$	9150.51	+	9698.97i	1.75225	+	1.85727i
$302$	1271.93	+	638.786i	0.242355	+	0.121715i
$303$	113.667	−	375.957i	0.0215512	−	0.0712811i
$304$	−538.660	−	1799.25i	−0.101626	−	0.339454i
$305$	3367.15	+	2825.37i	0.632139	+	0.530427i
$306$	940.104	+	5506.29i	0.175628	+	1.02867i
$307$	−3502.42	+	2938.88i	−0.651120	+	0.546355i	−0.907411	−	0.420245i	$-0.861944\pi$
$307$	−3502.42	+	2938.88i	−0.651120	+	0.546355i	0.256290	+	0.966600i	$0.417500\pi$
$308$	649.908	+	427.451i	0.120234	+	0.0790789i
$309$	2722.46	+	4745.15i	0.501215	+	0.873599i
$310$	−8515.79	−	995.353i	−1.56021	−	0.182362i
$311$	3769.52	+	8738.74i	0.687299	+	1.59334i	0.800201	+	0.599732i	$0.204726\pi$
$311$	3769.52	+	8738.74i	0.687299	+	1.59334i	−0.112902	+	0.993606i	$0.536015\pi$
$312$	−219.024	−	1262.18i	−0.0397429	−	0.229028i
$313$	−4548.18	+	2284.18i	−0.821337	+	0.412491i	−0.809270	−	0.587436i	$-0.800137\pi$
$313$	−4548.18	+	2284.18i	−0.821337	+	0.412491i	−0.0120664	+	0.999927i	$0.503841\pi$
$314$	−535.294	−	194.831i	−0.0962050	−	0.0350158i
$315$	−11693.0	+	2704.31i	−2.09151	+	0.483717i
$316$	4980.75	−	1812.84i	0.886674	−	0.322723i
$317$	−2881.12	+	3053.81i	−0.510472	+	0.541069i	−0.930428	−	0.366476i	$-0.880564\pi$
$317$	−2881.12	+	3053.81i	−0.510472	+	0.541069i	0.419955	+	0.907545i	$0.362046\pi$
$318$	−2248.94	+	1470.42i	−0.396585	+	0.259298i
$319$	−361.216	+	237.576i	−0.0633988	+	0.0416981i
$320$	284.823	−	951.375i	0.0497565	−	0.166198i
$321$	−1024.14	+	510.864i	−0.178074	+	0.0888276i
$322$	4032.37	+	5416.41i	0.697873	+	0.937406i
$323$	12142.7			2.09176
$324$	−1430.49	−	2541.02i	−0.245282	−	0.435702i
$325$	3568.02			0.608978
$326$	795.572	+	1068.64i	0.135162	+	0.181554i
$327$	−74.3056	+	1218.76i	−0.0125661	+	0.206108i
$328$	−635.192	+	2121.69i	−0.106929	+	0.357167i
$329$	−5345.24	+	3515.62i	−0.895722	+	0.589126i
$330$	−976.950	−	493.969i	−0.162968	−	0.0824003i
$331$	7626.20	−	8083.30i	1.26639	−	1.34229i	0.352773	−	0.935709i	$-0.385239\pi$
$331$	7626.20	−	8083.30i	1.26639	−	1.34229i	0.913614	−	0.406583i	$-0.133280\pi$
$332$	2345.38	−	853.648i	0.387709	−	0.141115i
$333$	6366.50	−	4137.96i	1.04769	−	0.680957i
$334$	−5312.25	−	1933.50i	−0.870279	−	0.316756i
$335$	4894.65	−	2458.18i	0.798278	−	0.400910i
$336$	2235.75	+	820.629i	0.363007	+	0.133241i
$337$	2081.07	+	4824.45i	0.336388	+	0.779836i	0.999509	+	0.0313237i	$0.00997228\pi$
$337$	2081.07	+	4824.45i	0.336388	+	0.779836i	−0.663121	+	0.748512i	$0.730768\pi$
$338$	2477.76	+	289.608i	0.398734	+	0.0466053i
$339$	−997.190	+	1716.40i	−0.159764	+	0.274992i
$340$	5364.33	+	3528.18i	0.855652	+	0.562771i
$341$	1436.71	−	1205.54i	0.228159	−	0.191448i
$342$	−5968.18	+	2135.61i	−0.943632	+	0.337662i
$343$	2953.81	+	2478.54i	0.464987	+	0.390170i
$344$	1068.01	+	3567.40i	0.167393	+	0.559132i
$345$	−6502.64	−	6930.00i	−1.01476	−	1.08145i
$346$	−6832.00	−	3431.16i	−1.06153	−	0.533122i
$347$	5250.00	+	5564.67i	0.812204	+	0.860886i	0.992439	−	0.122738i	$-0.0391674\pi$
$347$	5250.00	+	5564.67i	0.812204	+	0.860886i	−0.180235	+	0.983624i	$0.557686\pi$
$348$	−910.978	+	960.342i	−0.140326	+	0.147930i
$349$	−2096.75	+	4860.81i	−0.321594	+	0.745539i	0.678348	+	0.734741i	$0.262696\pi$
$349$	−2096.75	+	4860.81i	−0.321594	+	0.745539i	−0.999942	+	0.0107976i	$0.996563\pi$
$350$	−3316.68	+	5744.65i	−0.506525	+	0.877328i
$351$	−4214.95	+	962.767i	−0.640961	+	0.146406i
$352$	108.619	+	188.133i	0.0164472	+	0.0284873i
$353$	−94.4493	+	11.0395i	−0.0142409	+	0.00166452i	−0.123210	−	0.992381i	$-0.539319\pi$
$353$	−94.4493	+	11.0395i	−0.0142409	+	0.00166452i	0.108969	+	0.994045i	$0.465245\pi$
$354$	3220.39	−	7410.31i	0.483508	−	1.11258i
$355$	11200.8	−	2654.63i	1.67458	−	0.396882i
$356$	22.3289	+	383.373i	0.00332425	+	0.0570751i
$357$	−9228.32	+	12325.8i	−1.36811	+	1.82731i
$358$	3082.53	+	730.574i	0.455075	+	0.107855i
$359$	1971.09	−	11178.6i	0.289778	−	1.64341i	−0.397924	−	0.917418i	$-0.630269\pi$
$359$	1971.09	−	11178.6i	0.289778	−	1.64341i	0.687702	−	0.725993i	$-0.258620\pi$
$360$	−3257.10	−	790.654i	−0.476846	−	0.115753i
$361$	1201.67	+	6815.00i	0.175196	+	0.993584i
$362$	173.960	−	2986.78i	0.0252573	−	0.433651i
$363$	−6280.14	+	2266.49i	−0.908049	+	0.327713i
$364$	2108.66	−	2832.43i	0.303637	−	0.407856i
$365$	6474.11	−	8696.24i	0.928412	−	1.24707i
$366$	−2769.00	+	999.326i	−0.395458	+	0.142720i
$367$	567.445	−	9742.65i	0.0807095	−	1.38573i	−0.678365	−	0.734725i	$-0.737311\pi$
$367$	567.445	−	9742.65i	0.0807095	−	1.38573i	0.759075	−	0.651003i	$-0.225652\pi$
$368$	327.464	+	1857.14i	0.0463865	+	0.263071i
$369$	7263.76	+	1763.26i	1.02476	+	0.248758i
$370$	1515.54	−	8595.03i	0.212943	−	1.20766i
$371$	−7206.95	−	1708.08i	−1.00853	−	0.239027i
$372$	3441.45	−	4596.56i	0.479653	−	0.640647i
$373$	153.561	+	2636.54i	0.0213166	+	0.365992i	0.992051	+	0.125836i	$0.0401614\pi$
$373$	153.561	+	2636.54i	0.0213166	+	0.365992i	−0.970734	+	0.240156i	$0.922802\pi$
$374$	−1366.63	+	323.898i	−0.188949	+	0.0447818i
$375$	−296.277	+	681.750i	−0.0407991	+	0.0938812i
$376$	−1774.61	+	207.422i	−0.243401	+	0.0284495i
$377$	981.302	+	1699.67i	0.134057	+	0.232194i
$378$	2367.95	−	7681.19i	0.322206	−	1.04518i
$379$	−5266.33	+	9121.56i	−0.713756	+	1.23626i	0.249682	+	0.968328i	$0.419674\pi$
$379$	−5266.33	+	9121.56i	−0.713756	+	1.23626i	−0.963438	+	0.267933i	$0.913659\pi$
$380$	−2885.79	+	6690.01i	−0.389573	+	0.903132i
$381$	−8581.98	+	9047.02i	−1.15398	+	1.21652i
$382$	1015.58	+	1076.45i	0.136025	+	0.144178i
$383$	10861.0	+	5454.60i	1.44901	+	0.727721i	0.987234	−	0.159274i	$-0.0509154\pi$
$383$	10861.0	+	5454.60i	1.44901	+	0.727721i	0.461778	+	0.886996i	$0.347212\pi$
$384$	455.109	+	485.019i	0.0604810	+	0.0644558i
$385$	−865.459	−	2890.84i	−0.114566	−	0.382677i
$386$	−303.243	−	254.451i	−0.0399861	−	0.0335524i
$387$	11833.2	−	4234.30i	1.55430	−	0.556179i
$388$	455.084	−	381.861i	0.0595449	−	0.0499641i
$389$	−3028.94	−	1992.16i	−0.394790	−	0.259657i	0.336557	−	0.941663i	$-0.390738\pi$
$389$	−3028.94	−	1992.16i	−0.394790	−	0.259657i	−0.731347	+	0.682006i	$0.761108\pi$
$390$	−2496.43	+	4296.96i	−0.324132	+	0.557910i
$391$	−12109.6	−	1415.41i	−1.56627	−	0.183071i
$392$	1513.36	+	3508.36i	0.194990	+	0.452038i
$393$	−2461.73	−	903.574i	−0.315974	−	0.115978i
$394$	−4330.44	+	2174.83i	−0.553717	+	0.278087i
$395$	−19321.7	−	7032.52i	−2.46122	−	0.895809i
$396$	614.739	−	399.555i	0.0780096	−	0.0507030i
$397$	−659.092	+	239.890i	−0.0833221	+	0.0303268i	−0.383345	−	0.923605i	$-0.625228\pi$
$397$	−659.092	+	239.890i	−0.0833221	+	0.0303268i	0.300023	+	0.953932i	$0.403006\pi$
$398$	−5261.30	+	5576.65i	−0.662626	+	0.702342i
$399$	−15592.8	−	7884.10i	−1.95643	−	0.989220i
$400$	−1547.73	+	1017.96i	−0.193467	+	0.127245i
$401$	−1674.68	+	5593.83i	−0.208553	+	0.696615i	0.788151	+	0.615482i	$0.211039\pi$
$401$	−1674.68	+	5593.83i	−0.208553	+	0.696615i	−0.996703	+	0.0811322i	$0.974146\pi$
$402$	−223.235	+	3661.49i	−0.0276964	+	0.454275i
$403$	−5084.06	−	6829.08i	−0.628425	−	0.844121i
$404$	302.350			0.0372339
$405$	−2085.18	+	11118.1i	−0.255836	+	1.36411i
$406$	−3648.71			−0.446016
$407$	1140.06	+	1531.37i	0.138847	+	0.186505i
$408$	−3847.92	+	1919.43i	−0.466912	+	0.232907i
$409$	2814.46	−	9400.95i	0.340259	−	1.13655i	−0.601110	−	0.799167i	$-0.705274\pi$
$409$	2814.46	−	9400.95i	0.340259	−	1.13655i	0.941369	−	0.337379i	$-0.109540\pi$
$410$	7178.14	−	4721.14i	0.864641	−	0.568684i
$411$	618.869	−	404.633i	0.0742738	−	0.0485622i
$412$	−2889.98	+	3063.21i	−0.345581	+	0.366294i
$413$	20928.8	−	7617.44i	2.49355	−	0.907578i
$414$	6200.87	−	1434.11i	0.736125	−	0.170248i
$415$	−9098.37	−	3311.54i	−1.07620	−	0.391704i
$416$	881.251	−	442.581i	0.103863	−	0.0521618i
$417$	−541.681	−	3121.57i	−0.0636120	−	0.366580i
$418$	−631.260	−	1463.43i	−0.0738659	−	0.171240i
$419$	408.594	+	47.7578i	0.0476399	+	0.00556831i	0.139879	−	0.990169i	$-0.455328\pi$
$419$	408.594	+	47.7578i	0.0476399	+	0.00556831i	−0.0922396	+	0.995737i	$0.529403\pi$
$420$	−4597.70	−	8013.63i	−0.534154	−	0.931012i
$421$	−467.957	−	307.780i	−0.0541730	−	0.0356301i	0.522134	−	0.852864i	$-0.325136\pi$
$421$	−467.957	−	307.780i	−0.0541730	−	0.0356301i	−0.576307	+	0.817234i	$0.695507\pi$
$422$	560.963	−	470.704i	0.0647091	−	0.0542974i
$423$	1014.85	+	5944.08i	0.116652	+	0.683241i
$424$	−1584.51	−	1329.56i	−0.181488	−	0.152286i
$425$	−3434.98	−	11473.6i	−0.392050	−	1.30954i
$426$	−2231.10	+	7379.41i	−0.253750	+	0.839281i
$427$	−7251.43	−	3641.80i	−0.821829	−	0.412738i
$428$	−604.595	−	640.833i	−0.0682808	−	0.0723735i
$429$	−308.946	−	1042.24i	−0.0347694	−	0.117296i
$430$	5721.69	−	13264.4i	0.641685	−	1.48759i
$431$	4262.65	−	7383.12i	0.476391	−	0.825133i	−0.523243	−	0.852183i	$-0.675278\pi$
$431$	4262.65	−	7383.12i	0.476391	−	0.825133i	0.999634	+	0.0270503i	$0.00861144\pi$
$432$	1553.68	−	1620.16i	0.173036	−	0.180440i
$433$	5912.14	+	10240.1i	0.656164	+	1.13651i	0.981601	+	0.190946i	$0.0611555\pi$
$433$	5912.14	+	10240.1i	0.656164	+	1.13651i	−0.325436	+	0.945564i	$0.605511\pi$
$434$	15721.0	−	1837.53i	1.73879	−	0.203235i
$435$	5101.81	−	582.279i	0.562329	−	0.0641796i
$436$	−914.605	+	216.765i	−0.100462	+	0.0238100i
$437$	−804.443	−	13811.8i	−0.0880589	−	1.51191i
$438$	2857.79	+	6674.88i	0.311759	+	0.728169i
$439$	−8700.75	−	2062.12i	−0.945932	−	0.224190i	−0.271426	−	0.962459i	$-0.587495\pi$
$439$	−8700.75	−	2062.12i	−0.945932	−	0.224190i	−0.674506	+	0.738269i	$0.735643\pi$
$440$	146.338	−	829.922i	0.0158554	−	0.0899204i
$441$	11555.0	−	5724.75i	1.24770	−	0.618157i
$442$	1107.12	+	6278.80i	0.119141	+	0.675683i
$443$	−363.841	+	6246.92i	−0.0390217	+	0.669977i	0.920916	+	0.389762i	$0.127443\pi$
$443$	−363.841	+	6246.92i	−0.0390217	+	0.669977i	−0.959937	+	0.280215i	$0.909594\pi$
$444$	4467.44	+	3769.35i	0.477512	+	0.402895i
$445$	889.606	−	1194.95i	0.0947671	−	0.127294i
$446$	312.365	−	419.579i	0.0331635	−	0.0445463i
$447$	1927.88	−	10762.6i	0.203995	−	1.13882i
$448$	−106.600	+	1830.26i	−0.0112419	+	0.193017i
$449$	1255.25	+	7118.89i	0.131935	+	0.748243i	0.976945	+	0.213491i	$0.0684836\pi$
$449$	1255.25	+	7118.89i	0.131935	+	0.748243i	−0.845010	+	0.534751i	$0.820405\pi$
$450$	3706.24	+	5035.20i	0.388253	+	0.527470i
$451$	−326.352	+	1850.83i	−0.0340738	+	0.193242i
$452$	−1486.90	−	352.403i	−0.154730	−	0.0366717i
$453$	3671.72	+	439.272i	0.380822	+	0.0455602i
$454$	−32.1356	−	551.746i	−0.00332202	−	0.0570368i
$455$	−13329.1	+	3159.06i	−1.37336	+	0.325492i
$456$	−2903.25	−	3921.92i	−0.298151	−	0.402765i
$457$	16903.9	−	1975.78i	1.73026	−	0.202239i	0.808100	−	0.589045i	$-0.200496\pi$
$457$	16903.9	−	1975.78i	1.73026	−	0.202239i	0.922161	+	0.386806i	$0.126422\pi$
$458$	−1493.80	−	2587.34i	−0.152404	−	0.263971i
$459$	7153.76	+	12627.1i	0.727471	+	1.28406i
$460$	3657.75	−	6335.41i	0.370747	−	0.642153i
$461$	3871.10	−	8974.21i	0.391095	−	0.906661i	−0.602959	−	0.797773i	$-0.706012\pi$
$461$	3871.10	−	8974.21i	0.391095	−	0.906661i	0.994054	−	0.108889i	$-0.0347292\pi$
$462$	1965.24	+	471.410i	0.197903	+	0.0474718i
$463$	−3965.76	−	4203.46i	−0.398065	−	0.421925i	0.497076	−	0.867707i	$-0.334407\pi$
$463$	−3965.76	−	4203.46i	−0.398065	−	0.421925i	−0.895141	+	0.445782i	$0.852926\pi$
$464$	−910.587	−	457.314i	−0.0911054	−	0.0457549i
$465$	−21688.7	+	5078.16i	−2.16299	+	0.506439i
$466$	−1867.77	−	6238.78i	−0.185671	−	0.620184i
$467$	11598.6	+	9732.38i	1.14929	+	0.964370i	0.999703	−	0.0243782i	$-0.00776059\pi$
$467$	11598.6	+	9732.38i	1.14929	+	0.964370i	0.149589	+	0.988748i	$0.452205\pi$
$468$	−1648.44	−	2891.33i	−0.162819	−	0.285581i
$469$	−7745.91	+	6499.59i	−0.762629	+	0.639922i
$470$	5790.83	+	3808.69i	0.568322	+	0.373791i
$471$	−1479.98	−	4.01868i	−0.144786	−	0.000393144i
$472$	6177.80	+	722.081i	0.602450	+	0.0704163i
$473$	1251.61	+	2901.55i	0.121668	+	0.282058i
$474$	10573.1	−	8823.05i	1.02455	−	0.854971i
$475$	12145.2	−	6099.57i	1.17318	−	0.589194i
$476$	−11138.3	−	4054.00i	−1.07252	−	0.390367i
$477$	−4199.09	+	5576.87i	−0.403067	+	0.535320i
$478$	8405.83	−	3059.47i	0.804338	−	0.292755i
$479$	−4357.24	+	4618.40i	−0.415631	+	0.440543i	−0.901035	−	0.433747i	$-0.857191\pi$
$479$	−4357.24	+	4618.40i	−0.415631	+	0.440543i	0.485404	+	0.874290i	$0.338673\pi$
$480$	−143.027	−	2576.17i	−0.0136005	−	0.244970i
$481$	7240.79	−	4762.34i	0.686386	−	0.451443i
$482$	−1707.06	+	5701.96i	−0.161316	+	0.538833i
$483$	14631.4	+	9680.21i	1.37836	+	0.911936i
$484$	−3069.19	−	4122.64i	−0.288241	−	0.387175i
$485$	−2304.56			−0.215763
$486$	−5736.90	−	4948.09i	−0.535455	−	0.461832i
$487$	−12180.6			−1.13338			−0.566688	−	0.823932i	$-0.691776\pi$
$487$	−12180.6			−1.13338			−0.566688	+	0.823932i	$0.691776\pi$
$488$	−1353.25	−	1817.73i	−0.125530	−	0.168616i
$489$	2886.72	+	1909.87i	0.266957	+	0.176621i
$490$	4251.03	−	14199.4i	0.391922	−	1.30911i
$491$	10813.4	−	7112.11i	0.993897	−	0.653696i	0.0552127	−	0.998475i	$-0.482416\pi$
$491$	10813.4	−	7112.11i	0.993897	−	0.653696i	0.938684	+	0.344778i	$0.112046\pi$
$492$	318.969	+	5745.19i	0.0292281	+	0.526450i
$493$	4520.89	−	4791.86i	0.413003	−	0.437758i
$494$	−6798.56	+	2474.48i	−0.619194	+	0.225368i
$495$	−2823.13	−	345.527i	−0.256344	−	0.0313744i
$496$	4153.71	+	1511.83i	0.376022	+	0.136861i
$497$	−18990.2	+	9537.25i	−1.71394	+	0.860773i
$498$	4978.74	−	4154.68i	0.447998	−	0.373846i
$499$	−5993.64	−	13894.8i	−0.537700	−	1.24653i	−0.943137	−	0.332406i	$-0.892140\pi$
$499$	−5993.64	−	13894.8i	−0.537700	−	1.24653i	0.405436	−	0.914123i	$-0.367120\pi$
$500$	−568.359	−	66.4316i	−0.0508356	−	0.00594182i
$501$	−14687.3	−	39.8813i	−1.30974	−	0.00355642i
$502$	5617.05	+	3694.39i	0.499405	+	0.328464i
$503$	11564.1	−	9703.46i	1.02509	−	0.860151i	0.0348296	−	0.999393i	$-0.488911\pi$
$503$	11564.1	−	9703.46i	1.02509	−	0.860151i	0.990258	+	0.139242i	$0.0444667\pi$
$504$	6187.49	+	33.6027i	0.546850	+	0.00296981i
$505$	−898.494	−	753.926i	−0.0791732	−	0.0664342i
$506$	458.957	+	1533.02i	0.0403224	+	0.134686i
$507$	6310.55	−	1477.54i	0.552784	−	0.129428i
$508$	−8578.29	−	4308.18i	−0.749213	−	0.376269i
$509$	800.780	+	848.778i	0.0697327	+	0.0739124i	0.761301	−	0.648399i	$-0.224561\pi$
$509$	800.780	+	848.778i	0.0697327	+	0.0739124i	−0.691568	+	0.722312i	$0.743080\pi$
$510$	16221.1	+	3891.01i	1.40839	+	0.337837i
$511$	−7927.38	+	18377.7i	−0.686275	+	1.59096i
$512$	−256.000	+	443.405i	−0.0220971	+	0.0382733i
$513$	−12701.5	+	10482.7i	−1.09315	+	0.902187i
$514$	−4915.56	−	8514.01i	−0.421822	−	0.730616i
$515$	16226.4	−	1896.60i	1.38839	−	0.162280i
$516$	5756.31	+	7776.06i	0.491100	+	0.663414i
$517$	−1475.29	+	349.650i	−0.125499	+	0.0297439i
$518$	936.835	+	16084.8i	0.0794637	+	1.36434i
$519$	−19722.2	−	2359.49i	−1.66803	−	0.199557i
$520$	−3722.41	−	882.227i	−0.313920	−	0.0744005i
$521$	−428.910	+	2432.47i	−0.0360670	+	0.204546i	−0.997516	−	0.0704362i	$-0.977561\pi$
$521$	−428.910	+	2432.47i	−0.0360670	+	0.204546i	0.961449	+	0.274982i	$0.0886720\pi$
$522$	−1379.26	+	3150.33i	−0.115649	+	0.264150i
$523$	−528.446	−	2996.97i	−0.0441823	−	0.250570i	0.954715	−	0.297522i	$-0.0961603\pi$
$523$	−528.446	−	2996.97i	−0.0441823	−	0.250570i	−0.998897	+	0.0469522i	$0.985049\pi$
$524$	117.375	−	2015.25i	0.00978539	−	0.168009i
$525$	−3038.72	+	16963.9i	−0.252611	+	1.41022i
$526$	−8321.44	+	11177.6i	−0.689795	+	0.926555i
$527$	−17065.7	+	22923.2i	−1.41062	+	1.89479i
$528$	431.368	+	363.962i	0.0355547	+	0.0299989i
$529$	−100.267	+	1721.51i	−0.00824087	+	0.141490i
$530$	1393.36	+	7902.13i	0.114195	+	0.647635i
$531$	1334.37	−	20949.6i	0.109052	−	1.71212i
$532$	2335.65	−	13246.1i	0.190345	−	1.07950i
$533$	8301.46	+	1967.48i	0.674627	+	0.159889i
$534$	392.688	+	917.193i	0.0318226	+	0.0743274i
$535$	198.724	+	3411.95i	0.0160590	+	0.275723i
$536$	−2747.73	+	651.224i	−0.221425	+	0.0524787i
$537$	8177.42	−	933.303i	0.657136	−	0.0750000i
$538$	−116.198	+	13.5816i	−0.00931159	+	0.00108837i
$539$	1621.15	+	2807.92i	0.129551	+	0.224389i
$540$	−8657.03	+	940.444i	−0.689887	+	0.0749449i
$541$	−1446.24	+	2504.96i	−0.114933	+	0.199070i	−0.917753	−	0.397152i	$-0.869999\pi$
$541$	−1446.24	+	2504.96i	−0.114933	+	0.199070i	0.802820	+	0.596221i	$0.203332\pi$
$542$	5114.29	−	11856.3i	0.405309	−	0.939613i
$543$	−2209.10	−	7452.52i	−0.174589	−	0.588984i
$544$	−2271.60	−	2407.75i	−0.179033	−	0.189764i
$545$	3258.45	+	1636.45i	0.256104	+	0.128620i
$546$	2655.05	−	8781.64i	0.208106	−	0.688314i
$547$	2873.00	+	9596.48i	0.224571	+	0.750120i	0.993804	+	0.111151i	$0.0354537\pi$
$547$	2873.00	+	9596.48i	0.224571	+	0.750120i	−0.769232	+	0.638969i	$0.779361\pi$
$548$	436.031	+	365.873i	0.0339896	+	0.0285207i
$549$	−5885.50	+	4884.30i	−0.457535	+	0.379703i
$550$	−1204.22	+	1010.46i	−0.0933600	+	0.0783383i
$551$	6245.87	+	4107.98i	0.482910	+	0.317615i
$552$	2438.18	+	4249.66i	0.188000	+	0.327677i
$553$	37702.4	+	4406.78i	2.89922	+	0.338871i
$554$	−6664.80	−	15450.7i	−0.511120	−	1.18491i
$555$	−3876.83	−	22341.2i	−0.296508	−	1.70870i
$556$	2179.47	−	1094.57i	0.166242	−	0.0834897i
$557$	−22817.5	−	8304.91i	−1.73575	−	0.631760i	−0.736733	−	0.676184i	$-0.763633\pi$
$557$	−22817.5	−	8304.91i	−1.73575	−	0.631760i	−0.999013	+	0.0444238i	$0.985855\pi$
$558$	4356.22	−	14268.3i	0.330490	−	1.08248i
$559$	13479.6	−	4906.18i	1.01990	−	0.371215i
$560$	4880.62	−	5173.15i	0.368293	−	0.390367i
$561$	−3054.11	+	1996.86i	−0.229848	+	0.150281i
$562$	5271.74	−	3467.28i	0.395685	−	0.260246i
$563$	3869.24	−	12924.2i	0.289643	−	0.967476i	−0.682065	−	0.731291i	$-0.738918\pi$
$563$	3869.24	−	12924.2i	0.289643	−	0.967476i	0.971708	−	0.236184i	$-0.0758969\pi$
$564$	−4153.85	+	2072.04i	−0.310122	+	0.154696i
$565$	3539.90	+	4754.91i	0.263583	+	0.354054i
$566$	−3659.85			−0.271793
$567$	−987.740	−	20859.7i	−0.0731591	−	1.54502i
$568$	−5934.64			−0.438401
$569$	−12614.6	−	16944.4i	−0.929405	−	1.24841i	−0.968459	−	0.249171i	$-0.919842\pi$
$569$	−12614.6	−	16944.4i	−0.929405	−	1.24841i	0.0390541	−	0.999237i	$-0.487566\pi$
$570$	−1151.95	+	18894.2i	−0.0846487	+	1.38840i
$571$	5293.01	−	17679.9i	0.387926	−	1.29576i	−0.511724	−	0.859150i	$-0.670993\pi$
$571$	5293.01	−	17679.9i	0.387926	−	1.29576i	0.899650	−	0.436612i	$-0.143822\pi$
$572$	699.158	−	459.844i	0.0511071	−	0.0336137i
$573$	3431.27	+	1734.93i	0.250163	+	0.126488i
$574$	−10884.4	+	11536.8i	−0.791475	+	0.838914i
$575$	−12823.2	+	4667.25i	−0.930023	+	0.338501i
$576$	1539.96	+	783.900i	0.111398	+	0.0567057i
$577$	−18691.9	−	6803.28i	−1.34862	−	0.490857i	−0.436102	−	0.899897i	$-0.643641\pi$
$577$	−18691.9	−	6803.28i	−1.34862	−	0.490857i	−0.912516	+	0.409041i	$0.865863\pi$
$578$	10344.0	−	5194.96i	0.744385	−	0.373844i
$579$	−965.480	−	354.378i	−0.0692988	−	0.0254360i
$580$	1565.65	+	3629.59i	0.112087	+	0.259846i
$581$	17753.7	+	2075.10i	1.26772	+	0.148175i
$582$	775.347	−	1334.56i	0.0552219	−	0.0950502i
$583$	−1466.48	−	964.520i	−0.104177	−	0.0685186i
$584$	−4281.77	+	3592.83i	−0.303392	+	0.254576i
$585$	−2311.02	+	12702.6i	−0.163331	+	0.897760i
$586$	−1487.16	−	1247.88i	−0.104836	−	0.0879680i
$587$	−2938.98	−	9816.88i	−0.206652	−	0.690266i	−0.996985	−	0.0775888i	$-0.975278\pi$
$587$	−2938.98	−	9816.88i	−0.206652	−	0.690266i	0.790333	−	0.612677i	$-0.209907\pi$
$588$	6792.57	+	7238.99i	0.476396	+	0.507705i
$589$	−28980.1	−	14554.4i	−2.02734	−	1.01817i
$590$	−16558.0	−	17550.5i	−1.15539	−	1.22465i
$591$	−8664.60	+	9134.12i	−0.603069	+	0.635749i
$592$	−1782.21	+	4131.62i	−0.123730	+	0.286838i
$593$	3209.83	−	5559.59i	0.222280	−	0.385000i	−0.733220	−	0.679992i	$-0.761983\pi$
$593$	3209.83	−	5559.59i	0.222280	−	0.385000i	0.955500	+	0.294991i	$0.0953168\pi$
$594$	1149.91	−	1518.61i	0.0794296	−	0.104898i
$595$	22990.7	+	39821.1i	1.58408	+	2.74371i
$596$	8360.01	−	977.145i	0.574562	−	0.0671567i
$597$	−7939.15	+	18268.5i	−0.544268	+	1.25239i
$598$	7068.49	−	1675.26i	0.483365	−	0.114560i
$599$	−1006.75	−	17285.2i	−0.0686720	−	1.17905i	−0.839990	−	0.542603i	$-0.817439\pi$
$599$	−1006.75	−	17285.2i	−0.0686720	−	1.17905i	0.771318	−	0.636451i	$-0.219598\pi$
$600$	−2884.54	+	3852.73i	−0.196268	+	0.262145i
$601$	22022.9	+	5219.51i	1.49473	+	0.354257i	0.895043	−	0.445980i	$-0.147145\pi$
$601$	22022.9	+	5219.51i	1.49473	+	0.354257i	0.599684	+	0.800237i	$0.295293\pi$
$602$	−4630.93	+	26263.3i	−0.313526	+	1.77809i
$603$	2683.75	+	9144.82i	0.181245	+	0.617588i
$604$	494.315	+	2803.40i	0.0333003	+	0.188855i
$605$	−1159.30	+	19904.4i	−0.0779046	+	1.33757i
$606$	738.883	−	266.661i	0.0495298	−	0.0178752i
$607$	−2045.32	+	2747.34i	−0.136766	+	0.183709i	−0.865230	−	0.501376i	$-0.832827\pi$
$607$	−2045.32	+	2747.34i	−0.136766	+	0.183709i	0.728463	+	0.685085i	$0.240235\pi$
$608$	2243.11	−	3013.02i	0.149622	−	0.200977i
$609$	−8916.70	+	3218.02i	−0.593306	+	0.214123i
$610$	−511.151	+	8776.13i	−0.0339277	+	0.582516i
$611$	1195.15	+	6778.01i	0.0791333	+	0.448787i
$612$	−7710.66	+	8084.41i	−0.509289	+	0.533976i
$613$	575.967	−	3266.47i	0.0379496	−	0.215223i	−0.959936	−	0.280220i	$-0.909593\pi$
$613$	575.967	−	3266.47i	0.0379496	−	0.215223i	0.997885	+	0.0649970i	$0.0207038\pi$
$614$	−8897.70	−	2108.79i	−0.584824	−	0.138606i
$615$	13378.0	−	17868.3i	0.877163	−	1.17158i
$616$	90.4592	+	1553.13i	0.00591673	+	0.101586i
$617$	1206.53	−	285.954i	0.0787248	−	0.0186581i	−0.191065	−	0.981577i	$-0.561194\pi$
$617$	1206.53	−	285.954i	0.0787248	−	0.0186581i	0.269790	+	0.962919i	$0.413046\pi$
$618$	−4360.91	+	10034.7i	−0.283853	+	0.653164i
$619$	−5786.76	+	676.375i	−0.375750	+	0.0439189i	−0.301872	−	0.953348i	$-0.597612\pi$
$619$	−5786.76	+	676.375i	−0.375750	+	0.0439189i	−0.0738781	+	0.997267i	$0.523538\pi$
$620$	−8573.76	−	14850.2i	−0.555372	−	0.961932i
$621$	13888.8	−	8973.60i	0.897487	−	0.579868i
$622$	−9517.08	+	16484.1i	−0.613505	+	1.06262i
$623$	−1089.30	+	2525.28i	−0.0700511	+	0.162397i
$624$	1763.26	−	1858.81i	0.113120	−	0.119250i
$625$	11455.0	+	12141.6i	0.733122	+	0.777064i
$626$	−9096.36	−	4568.37i	−0.580773	−	0.291675i
$627$	−2833.36	−	3019.57i	−0.180468	−	0.192328i
$628$	−326.754	−	1091.43i	−0.0207626	−	0.0693518i
$629$	−22285.1	−	18699.4i	−1.41266	−	1.18536i
$630$	−18303.6	−	15528.7i	−1.15751	−	0.982028i
$631$	−16133.6	+	13537.7i	−1.01786	+	0.854083i	−0.989357	−	0.145511i	$-0.953517\pi$
$631$	−16133.6	+	13537.7i	−1.01786	+	0.854083i	−0.0284996	+	0.999594i	$0.509073\pi$
$632$	8856.84	+	5825.24i	0.557446	+	0.366638i
$633$	955.737	−	1645.05i	0.0600112	−	0.103294i
$634$	−8340.03	−	974.809i	−0.522437	−	0.0610641i
$635$	14749.4	+	34193.0i	0.921753	+	2.13686i
$636$	−5044.85	−	1851.70i	−0.314530	−	0.115448i
$637$	13152.8	−	6605.59i	0.818105	−	0.410868i
$638$	−812.536	−	295.739i	−0.0504210	−	0.0183518i
$639$	1056.00	+	20001.5i	0.0653751	+	1.23826i
$640$	1866.41	−	679.317i	0.115275	−	0.0419568i
$641$	9531.46	−	10102.8i	0.587317	−	0.622519i	−0.363753	−	0.931495i	$-0.618505\pi$
$641$	9531.46	−	10102.8i	0.587317	−	0.622519i	0.951070	+	0.308976i	$0.0999863\pi$
$642$	−2042.70	−	1032.84i	−0.125575	−	0.0634935i
$643$	−13247.8	+	8713.23i	−0.812508	+	0.534395i	−0.886427	−	0.462869i	$-0.846820\pi$
$643$	−13247.8	+	8713.23i	−0.812508	+	0.534395i	0.0739183	+	0.997264i	$0.476450\pi$
$644$	−3873.33	+	12937.8i	−0.237004	+	0.791649i
$645$	2283.98	−	37461.8i	0.139429	−	2.28691i
$646$	14502.2	+	19479.9i	0.883255	+	1.18642i
$647$	−15119.7			−0.918726			−0.459363	−	0.888249i	$-0.651922\pi$
$647$	−15119.7			−0.918726			−0.459363	+	0.888249i	$0.651922\pi$
$648$	2367.96	−	5329.63i	0.143553	−	0.323098i
$649$	5278.07			0.319233
$650$	4261.34	+	5723.98i	0.257144	+	0.345404i
$651$	36798.4	−	18355.9i	2.21543	−	1.10511i
$652$	−764.195	+	2552.59i	−0.0459021	+	0.153324i
$653$	3991.15	−	2625.02i	0.239182	−	0.157312i	−0.424259	−	0.905541i	$-0.639466\pi$
$653$	3991.15	−	2625.02i	0.239182	−	0.157312i	0.663441	+	0.748228i	$0.269095\pi$
$654$	−2043.93	+	1336.38i	−0.122208	+	0.0799029i
$655$	−5373.93	+	5696.03i	−0.320575	+	0.339790i
$656$	−4162.33	+	1514.96i	−0.247731	+	0.0901668i
$657$	12870.8	+	13791.6i	0.764291	+	0.818966i
$658$	−12023.8	−	4376.32i	−0.712368	−	0.259281i
$659$	5439.48	−	2731.81i	0.321536	−	0.161481i	−0.280709	−	0.959793i	$-0.590569\pi$
$659$	5439.48	−	2731.81i	0.321536	−	0.161481i	0.602245	+	0.798312i	$0.294273\pi$
$660$	−374.340	−	2157.22i	−0.0220775	−	0.127227i
$661$	11295.6	+	26186.2i	0.664673	+	1.54089i	0.831875	+	0.554963i	$0.187268\pi$
$661$	11295.6	+	26186.2i	0.664673	+	1.54089i	−0.167202	+	0.985923i	$0.553473\pi$
$662$	22075.7	+	2580.28i	1.29607	+	0.151489i
$663$	8243.24	+	14367.7i	0.482867	+	0.841620i
$664$	4170.59	+	2743.04i	0.243750	+	0.160317i
$665$	−39970.8	+	33539.5i	−2.33083	+	1.95580i
$666$	14241.9	+	5271.40i	0.828624	+	0.306701i
$667$	−5750.02	−	4824.84i	−0.333796	−	0.280088i
$668$	−3242.70	−	10831.4i	−0.187820	−	0.627363i
$669$	393.304	−	1300.86i	0.0227295	−	0.0751781i
$670$	9789.29	+	4916.37i	0.564468	+	0.283486i
$671$	−1319.65	−	1398.75i	−0.0759234	−	0.0804741i
$672$	1353.71	+	4566.79i	0.0777088	+	0.262154i
$673$	−2454.64	+	5690.50i	−0.140594	+	0.325933i	−0.973935	−	0.226825i	$-0.927165\pi$
$673$	−2454.64	+	5690.50i	−0.140594	+	0.325933i	0.833342	+	0.552758i	$0.186425\pi$
$674$	−5254.16	+	9100.47i	−0.300271	+	0.520085i
$675$	13498.2	+	9036.25i	0.769695	+	0.515267i
$676$	2494.62	+	4320.81i	0.141933	+	0.245836i
$677$	29752.7	−	3477.59i	1.68905	−	0.197422i	0.783422	−	0.621491i	$-0.213473\pi$
$677$	29752.7	−	3477.59i	1.68905	−	0.197422i	0.905630	+	0.424069i	$0.139399\pi$
$678$	−3944.50	+	450.192i	−0.223433	+	0.0255008i
$679$	4139.79	−	981.147i	0.233977	−	0.0554536i
$680$	746.649	+	12819.5i	0.0421069	+	0.722947i
$681$	−565.152	−	1320.01i	−0.0318013	−	0.0742775i
$682$	3649.88	+	865.037i	0.204928	+	0.0485689i
$683$	−3408.14	+	19328.5i	−0.190935	+	1.08285i	0.727154	+	0.686475i	$0.240843\pi$
$683$	−3408.14	+	19328.5i	−0.190935	+	1.08285i	−0.918089	+	0.396374i	$0.870268\pi$
$684$	−10553.9	−	7023.83i	−0.589970	−	0.392636i
$685$	−383.428	−	2174.53i	−0.0213869	−	0.121291i
$686$	−448.404	+	7698.79i	−0.0249565	+	0.428486i
$687$	−5932.49	−	5005.46i	−0.329459	−	0.277977i
$688$	−4447.45	+	5973.96i	−0.246450	+	0.331039i
$689$	−4758.08	+	6391.21i	−0.263089	+	0.353390i
$690$	3351.21	−	18708.5i	0.184896	−	1.03220i
$691$	−608.978	+	10455.7i	−0.0335262	+	0.575623i	0.939157	+	0.343487i	$0.111608\pi$
$691$	−608.978	+	10455.7i	−0.0335262	+	0.575623i	−0.972683	+	0.232135i	$0.925429\pi$
$692$	−2655.15	−	15058.1i	−0.145858	−	0.827201i
$693$	5218.41	−	581.236i	0.286048	−	0.0318605i
$694$	−2656.94	+	15068.3i	−0.145326	+	0.824184i
$695$	−9206.12	−	2181.89i	−0.502458	−	0.119085i
$696$	−2628.62	−	314.479i	−0.143158	−	0.0171269i
$697$	−1665.12	−	28589.1i	−0.0904893	−	1.55364i
$698$	−10302.1	+	2441.65i	−0.558654	+	0.132403i
$699$	−10066.8	−	13599.0i	−0.544723	−	0.735853i
$700$	−13177.0	+	1540.17i	−0.711491	+	0.0831614i
$701$	−15357.5	−	26599.9i	−0.827451	−	1.43319i	−0.900032	−	0.435824i	$-0.856457\pi$
$701$	−15357.5	−	26599.9i	−0.827451	−	1.43319i	0.0725811	−	0.997363i	$-0.476876\pi$
$702$	−6578.50	−	5611.97i	−0.353689	−	0.301724i
$703$	16505.8	−	28588.8i	0.885529	−	1.53378i
$704$	−172.087	+	398.942i	−0.00921273	+	0.0213575i
$705$	17510.7	+	4200.37i	0.935451	+	0.224390i
$706$	−130.513	−	138.335i	−0.00695737	−	0.00737439i
$707$	1934.98	+	971.783i	0.102931	+	0.0516940i
$708$	15734.1	−	3683.96i	0.835205	−	0.195553i
$709$	−1676.93	−	5601.34i	−0.0888272	−	0.296704i	0.902019	−	0.431695i	$-0.142084\pi$
$709$	−1676.93	−	5601.34i	−0.0888272	−	0.296704i	−0.990847	+	0.134992i	$0.956899\pi$
$710$	17635.9	+	14798.3i	0.932205	+	0.782213i
$711$	18056.9	−	30886.8i	0.952440	−	1.62918i
$712$	−588.357	+	493.690i	−0.0309686	+	0.0259857i
$713$	27204.7	+	17892.8i	1.42893	+	0.939820i
$714$	−30795.1	−	83.6197i	−1.61412	−	0.00438290i
$715$	−3224.33	−	376.870i	−0.168648	−	0.0197121i
$716$	2509.50	+	5817.68i	0.130984	+	0.303655i
$717$	17843.8	−	14890.3i	0.929413	−	0.775579i
$718$	20287.4	−	10188.7i	1.05448	−	0.529581i
$719$	25901.2	+	9427.27i	1.34347	+	0.488982i	0.910903	−	0.412621i	$-0.135387\pi$
$719$	25901.2	+	9427.27i	1.34347	+	0.488982i	0.432564	+	0.901603i	$0.357609\pi$
$720$	−2621.61	−	6169.49i	−0.135697	−	0.319338i
$721$	−28340.8	+	10315.2i	−1.46389	+	0.532812i
$722$	−9497.76	+	10067.0i	−0.489571	+	0.518915i
$723$	857.217	+	15440.0i	0.0440944	+	0.794218i
$724$	4999.30	−	3288.09i	0.256626	−	0.168786i
$725$	2114.77	−	7063.81i	0.108332	−	0.361853i
$726$	−11136.5	−	7367.98i	−0.569303	−	0.376655i
$727$	6430.19	+	8637.25i	0.328037	+	0.440630i	0.935292	−	0.353877i	$-0.115137\pi$
$727$	6430.19	+	8637.25i	0.328037	+	0.440630i	−0.607255	+	0.794507i	$0.707729\pi$
$728$	7062.32			0.359543
$729$	−18383.8	−	7032.41i	−0.933996	−	0.357284i
$730$	21683.1			1.09935
$731$	−28753.8	−	38623.1i	−1.45485	−	1.95421i
$732$	−4910.23	−	3248.64i	−0.247933	−	0.164034i
$733$	8105.45	−	27074.1i	0.408433	−	1.36426i	−0.468421	−	0.883505i	$-0.655177\pi$
$733$	8105.45	−	27074.1i	0.408433	−	1.36426i	0.876854	−	0.480757i	$-0.159638\pi$
$734$	16307.3	−	10725.5i	0.820047	−	0.539353i
$735$	−2134.70	−	38449.7i	−0.107129	−	1.92958i
$736$	−2588.22	+	2743.35i	−0.129624	+	0.137393i
$737$	−2251.76	+	819.574i	−0.112544	+	0.0409625i
$738$	5846.53	+	13758.8i	0.291618	+	0.686270i
$739$	−20172.2	−	7342.06i	−1.00412	−	0.365470i	−0.212948	−	0.977064i	$-0.568306\pi$
$739$	−20172.2	−	7342.06i	−1.00412	−	0.365470i	−0.791172	+	0.611594i	$0.790529\pi$
$740$	15598.6	−	7833.90i	0.774885	−	0.389162i
$741$	−14431.9	+	12043.2i	−0.715479	+	0.597055i
$742$	−5867.21	−	13601.7i	−0.290286	−	0.672958i
$743$	−39863.5	−	4659.38i	−1.96830	−	0.230062i	−0.968486	−	0.249070i	$-0.919875\pi$
$743$	−39863.5	−	4659.38i	−1.96830	−	0.230062i	−0.999819	+	0.0190078i	$0.993949\pi$
$744$	11484.2	+	31.1837i	0.565902	+	0.00153663i
$745$	−27280.0	−	17942.3i	−1.34156	−	0.882357i
$746$	−4046.26	+	3395.22i	−0.198585	+	0.166632i
$747$	8502.77	−	14544.2i	0.416466	−	0.712378i
$748$	−2151.81	−	1805.58i	−0.105184	−	0.0882601i
$749$	−1809.58	−	6044.43i	−0.0882787	−	0.294871i
$750$	−1447.54	+	338.925i	−0.0704758	+	0.0165011i
$751$	−11052.6	−	5550.83i	−0.537038	−	0.269711i	0.159540	−	0.987191i	$-0.448999\pi$
$751$	−11052.6	−	5550.83i	−0.537038	−	0.269711i	−0.696578	+	0.717481i	$0.745295\pi$
$752$	−2452.21	−	2599.19i	−0.118913	−	0.126041i
$753$	16985.3	+	4074.32i	0.822015	+	0.197180i
$754$	−1554.70	+	3604.19i	−0.0750911	+	0.174081i
$755$	5521.46	−	9563.45i	0.266154	−	0.460993i
$756$	15150.6	−	5375.01i	0.728865	−	0.258581i
$757$	17331.4	+	30018.9i	0.832128	+	1.44129i	0.896347	+	0.443352i	$0.146211\pi$
$757$	17331.4	+	30018.9i	0.832128	+	1.44129i	−0.0642194	+	0.997936i	$0.520456\pi$
$758$	−20922.9	+	2445.54i	−1.00258	+	0.117185i
$759$	2473.67	+	3341.62i	0.118298	+	0.159806i
$760$	−14179.0	+	3360.48i	−0.676744	+	0.160391i
$761$	1101.98	+	18920.3i	0.0524926	+	0.901264i	0.917061	+	0.398748i	$0.130555\pi$
$761$	1101.98	+	18920.3i	0.0524926	+	0.901264i	−0.864568	+	0.502516i	$0.832408\pi$
$762$	−24763.3	−	2962.59i	−1.17727	−	0.140844i
$763$	−6549.99	−	1552.38i	−0.310781	−	0.0736563i
$764$	−513.971	+	2914.87i	−0.0243387	+	0.138032i
$765$	43072.7	−	4797.51i	2.03568	−	0.226738i
$766$	4220.96	+	23938.3i	0.199099	+	1.12914i
$767$	1393.13	−	23919.1i	0.0655842	−	1.12604i
$768$	−234.546	+	1309.37i	−0.0110201	+	0.0615208i
$769$	−17268.9	+	23196.1i	−0.809793	+	1.08774i	0.184685	+	0.982798i	$0.440873\pi$
$769$	−17268.9	+	23196.1i	−0.809793	+	1.08774i	−0.994478	+	0.104943i	$0.966534\pi$
$770$	3603.98	−	4840.99i	0.168673	−	0.226568i
$771$	−19521.7	−	16471.2i	−0.911875	−	0.769383i
$772$	46.0339	−	790.371i	0.00214611	−	0.0368473i
$773$	2709.08	+	15363.9i	0.126053	+	0.714881i	0.980677	+	0.195634i	$0.0626764\pi$
$773$	2709.08	+	15363.9i	0.126053	+	0.714881i	−0.854624	+	0.519247i	$0.826212\pi$
$774$	20925.4	+	13926.3i	0.971769	+	0.646730i
$775$	−5554.40	+	31500.5i	−0.257445	+	1.46004i
$776$	1156.11	+	274.004i	0.0534821	+	0.0126755i
$777$	16475.7	+	38481.8i	0.760696	+	1.77674i
$778$	−421.591	−	7238.44i	−0.0194277	−	0.333561i
$779$	31620.9	−	7494.30i	1.45435	−	0.344687i
$780$	−9874.91	+	1127.04i	−0.453306	+	0.0517365i
$781$	−5001.98	+	584.648i	−0.229174	+	0.0267866i
$782$	−12192.1	−	21117.3i	−0.557530	−	0.965670i
$783$	−592.159	+	8915.22i	−0.0270269	+	0.406902i
$784$	−3820.84	+	6617.89i	−0.174054	+	0.301471i
$785$	−1750.53	+	4058.19i	−0.0795912	+	0.184513i
$786$	−1490.53	−	5028.38i	−0.0676406	−	0.228189i
$787$	−17382.1	−	18424.0i	−0.787302	−	0.834491i	0.202150	−	0.979355i	$-0.435207\pi$
$787$	−17382.1	−	18424.0i	−0.787302	−	0.834491i	−0.989452	+	0.144864i	$0.953726\pi$
$788$	−8660.88	−	4349.66i	−0.391537	−	0.196637i
$789$	−10477.7	+	34655.1i	−0.472769	+	1.56369i
$790$	−11794.3	−	39395.8i	−0.531169	−	1.77423i
$791$	−8383.22	−	7034.36i	−0.376831	−	0.316199i
$792$	1375.18	+	508.998i	0.0616980	+	0.0228364i
$793$	−6687.16	+	5611.20i	−0.299455	+	0.251273i
$794$	−1172.01	−	770.842i	−0.0523841	−	0.0344536i
$795$	10374.5	+	18082.3i	0.462823	+	0.806683i
$796$	−15230.0	−	1780.13i	−0.678156	−	0.0792651i
$797$	14756.9	+	34210.3i	0.655855	+	1.52044i	0.842888	+	0.538089i	$0.180854\pi$
$797$	14756.9	+	34210.3i	0.655855	+	1.52044i	−0.187033	+	0.982354i	$0.559887\pi$
$798$	−5974.73	−	34430.8i	−0.265042	−	1.52737i
$799$	20645.4	−	10368.5i	0.914121	−	0.459089i
$800$	−3481.54	−	1267.18i	−0.153864	−	0.0560019i
$801$	1768.58	+	1895.10i	0.0780146	+	0.0835955i
$802$	−10974.0	+	3994.20i	−0.483173	+	0.175861i
$803$	−3254.93	+	3450.02i	−0.143044	+	0.151617i
$804$	−6140.54	+	4014.85i	−0.269354	+	0.176111i
$805$	43771.5	−	28789.0i	1.91645	−	1.26047i
$806$	4883.54	−	16312.2i	0.213419	−	0.712868i
$807$	−271.985	+	135.673i	−0.0118641	+	0.00591809i
$808$	361.102	+	485.044i	0.0157222	+	0.0211186i
$809$	−9488.61			−0.412363			−0.206182	−	0.978514i	$-0.566104\pi$
$809$	−9488.61			−0.412363			−0.206182	+	0.978514i	$0.566104\pi$
$810$	−20326.6	+	9933.42i	−0.881733	+	0.430895i
$811$	27550.6			1.19289			0.596443	−	0.802655i	$-0.296580\pi$
$811$	27550.6			1.19289			0.596443	+	0.802655i	$0.296580\pi$
$812$	−4357.72	−	5853.43i	−0.188332	−	0.252974i
$813$	2041.52	−	33484.9i	0.0880679	−	1.44449i
$814$	−1095.10	+	3657.89i	−0.0471539	+	0.157505i
$815$	8635.97	−	5679.97i	0.371171	−	0.244123i
$816$	−7674.87	−	3880.60i	−0.329258	−	0.166481i
$817$	37496.3	−	39743.8i	1.60567	−	1.70191i
$818$	18442.8	−	6712.63i	0.788310	−	0.286921i
$819$	−1256.66	−	23802.2i	−0.0536156	−	1.01553i
$820$	16146.8	+	5876.97i	0.687649	+	0.250284i
$821$	−18654.6	+	9368.69i	−0.792996	+	0.398258i	−0.798702	−	0.601726i	$-0.794480\pi$
$821$	−18654.6	+	9368.69i	−0.792996	+	0.398258i	0.00570650	+	0.999984i	$0.498184\pi$
$822$	1388.26	+	509.557i	0.0589063	+	0.0216215i
$823$	13107.5	+	30386.7i	0.555164	+	1.28701i	0.932578	+	0.360969i	$0.117554\pi$
$823$	13107.5	+	30386.7i	0.555164	+	1.28701i	−0.377414	+	0.926045i	$0.623187\pi$
$824$	−8365.69	−	977.809i	−0.353681	−	0.0413393i
$825$	−2051.68	+	3531.43i	−0.0865821	+	0.149029i
$826$	37215.8	+	24477.2i	1.56768	+	1.03108i
$827$	18839.1	−	15807.9i	0.792140	−	0.664684i	−0.154134	−	0.988050i	$-0.549259\pi$
$827$	18839.1	−	15807.9i	0.792140	−	0.664684i	0.946274	+	0.323365i	$0.104814\pi$
$828$	9706.47	+	8234.93i	0.407395	+	0.345632i
$829$	−7867.55	−	6601.66i	−0.329615	−	0.276580i	0.462928	−	0.886396i	$-0.346799\pi$
$829$	−7867.55	−	6601.66i	−0.329615	−	0.276580i	−0.792543	+	0.609816i	$0.791243\pi$
$830$	−5553.82	−	18551.1i	−0.232260	−	0.775803i
$831$	−29914.4	−	31880.4i	−1.24876	−	1.33083i
$832$	1762.50	+	885.162i	0.0734420	+	0.0368840i
$833$	−33904.0	−	35936.1i	−1.41021	−	1.49473i
$834$	4360.82	−	4597.13i	0.181059	−	0.190870i
$835$	−17372.2	+	40273.4i	−0.719990	+	1.66912i
$836$	1593.77	−	2760.49i	0.0659350	−	0.114203i
$837$	−1938.38	−	38710.8i	−0.0800481	−	1.59862i
$838$	411.376	+	712.524i	0.0169579	+	0.0293720i
$839$	−3680.37	+	430.174i	−0.151443	+	0.0177011i	−0.191477	−	0.981497i	$-0.561328\pi$
$839$	−3680.37	+	430.174i	−0.151443	+	0.0177011i	0.0400336	+	0.999198i	$0.487254\pi$
$840$	7364.72	−	16946.7i	0.302508	−	0.696090i
$841$	−19785.0	+	4689.14i	−0.811228	+	0.192265i
$842$	−65.1339	−	1118.31i	−0.00266587	−	0.0457712i
$843$	9825.05	−	13122.8i	0.401415	−	0.536148i
$844$	1425.09	+	337.753i	0.0581205	+	0.0137748i
$845$	3360.90	−	19060.6i	0.136827	−	0.775983i
$846$	−8323.72	+	8727.18i	−0.338269	+	0.354665i
$847$	−6391.63	−	36248.7i	−0.259290	−	1.47051i
$848$	240.537	−	4129.87i	0.00974067	−	0.167241i
$849$	−8943.93	+	3227.85i	−0.361549	+	0.130482i
$850$	14304.1	−	19213.7i	0.577208	−	0.775324i
$851$	−19793.3	+	26587.0i	−0.797304	+	1.07097i
$852$	−14503.0	+	5234.12i	−0.583176	+	0.210467i
$853$	−1462.94	+	25117.8i	−0.0587225	+	1.00823i	0.832317	+	0.554300i	$0.187014\pi$
$853$	−1462.94	+	25117.8i	−0.0587225	+	1.00823i	−0.891039	+	0.453926i	$0.850023\pi$
$854$	−2818.15	−	15982.5i	−0.112922	−	0.640411i
$855$	13848.8	+	47189.5i	0.553941	+	1.88754i
$856$	305.976	−	1735.28i	0.0122173	−	0.0692880i
$857$	−143.831	−	34.0885i	−0.00573298	−	0.00135874i	0.227748	−	0.973720i	$-0.426864\pi$
$857$	−143.831	−	34.0885i	−0.00573298	−	0.00135874i	−0.233481	+	0.972361i	$0.575012\pi$
$858$	1303.04	−	1740.40i	0.0518472	−	0.0692496i
$859$	1298.67	+	22297.4i	0.0515834	+	0.885653i	0.920512	+	0.390715i	$0.127772\pi$
$859$	1298.67	+	22297.4i	0.0515834	+	0.885653i	−0.868928	+	0.494938i	$0.835191\pi$
$860$	28112.8	−	6662.87i	1.11470	−	0.264188i
$861$	−16424.3	+	37793.2i	−0.650102	+	1.49592i
$862$	16935.3	−	1979.45i	0.669163	−	0.0782139i
$863$	−9926.41	−	17193.1i	−0.391540	−	0.678167i	0.601113	−	0.799164i	$-0.294724\pi$
$863$	−9926.41	−	17193.1i	−0.391540	−	0.678167i	−0.992653	+	0.120997i	$0.961391\pi$
$864$	4454.73	+	557.503i	0.175408	+	0.0219521i
$865$	−29657.8	+	51368.9i	−1.16578	+	2.01918i
$866$	−9366.71	+	21714.5i	−0.367545	+	0.852065i
$867$	20696.9	−	21818.5i	0.810732	−	0.854664i
$868$	21723.7	+	23025.8i	0.849484	+	0.900400i
$869$	8038.82	+	4037.25i	0.313807	+	0.157600i
$870$	7027.30	+	7489.14i	0.273848	+	0.291846i
$871$	3119.79	+	10420.8i	0.121366	+	0.405392i
$872$	−1440.07	−	1208.37i	−0.0559255	−	0.0469271i
$873$	717.761	−	3945.22i	0.0278265	−	0.152950i
$874$	21196.7	−	17786.1i	0.820354	−	0.688359i
$875$	−3423.86	−	2251.91i	−0.132283	−	0.0870039i
$876$	−7295.04	+	12556.5i	−0.281366	+	0.484298i
$877$	−5400.14	−	631.186i	−0.207924	−	0.0243029i	0.0114930	−	0.999934i	$-0.496342\pi$
$877$	−5400.14	−	631.186i	−0.207924	−	0.0243029i	−0.219417	+	0.975631i	$0.570416\pi$
$878$	−7083.32	−	16421.0i	−0.272267	−	0.631186i
$879$	−4734.90	−	1737.94i	−0.181688	−	0.0666884i
$880$	1506.17	−	756.428i	0.0576967	−	0.0289763i
$881$	23140.2	+	8422.35i	0.884919	+	0.322084i	0.744193	−	0.667964i	$-0.232834\pi$
$881$	23140.2	+	8422.35i	0.884919	+	0.322084i	0.140726	+	0.990049i	$0.455056\pi$
$882$	22984.2	+	11699.8i	0.877458	+	0.446659i
$883$	12801.7	−	4659.45i	0.487897	−	0.177580i	−0.0863456	−	0.996265i	$-0.527519\pi$
$883$	12801.7	−	4659.45i	0.487897	−	0.177580i	0.574242	+	0.818685i	$0.305297\pi$
$884$	−8750.49	+	9274.97i	−0.332931	+	0.352886i
$885$	−55943.3	−	28286.3i	−2.12487	−	1.07439i
$886$	−10456.1	+	6877.11i	−0.396479	+	0.260769i
$887$	−3027.31	+	10111.9i	−0.114596	+	0.382779i	−0.995975	−	0.0896320i	$-0.971431\pi$
$887$	−3027.31	+	10111.9i	−0.114596	+	0.382779i	0.881379	+	0.472411i	$0.156616\pi$
$888$	−711.420	+	11668.7i	−0.0268848	+	0.440963i
$889$	−41052.4	−	55142.9i	−1.54877	−	2.08035i
$890$	2979.46			0.112216
$891$	1470.78	−	4725.34i	0.0553008	−	0.177671i
$892$	1046.17			0.0392695
$893$	15655.3	+	21028.7i	0.586656	+	0.788016i
$894$	19568.4	−	9761.15i	0.732062	−	0.365170i
$895$	7049.20	−	23546.0i	0.263272	−	0.879391i
$896$	−3063.49	+	2014.89i	−0.114223	+	0.0751259i
$897$	15796.4	−	10328.1i	0.587991	−	0.384445i
$898$	−9921.28	+	10515.9i	−0.368683	+	0.390781i
$899$	−16533.3	+	6017.62i	−0.613365	+	0.223247i
$900$	−3651.28	+	11959.3i	−0.135233	+	0.442939i
$901$	25132.9	+	9147.62i	0.929298	+	0.338237i
$902$	−3358.96	+	1686.93i	−0.123992	+	0.0622713i
$903$	11846.2	+	68266.5i	0.436563	+	2.51580i
$904$	−1210.49	−	2806.24i	−0.0445359	−	0.103246i
$905$	−23055.4	−	2694.79i	−0.846838	−	0.0989812i
$906$	3680.49	+	6414.97i	0.134963	+	0.235235i
$907$	−11739.6	−	7721.23i	−0.429775	−	0.282667i	0.316135	−	0.948714i	$-0.397615\pi$
$907$	−11739.6	−	7721.23i	−0.429775	−	0.282667i	−0.745910	+	0.666047i	$0.767985\pi$
$908$	846.757	−	710.513i	0.0309478	−	0.0259683i
$909$	1570.49	−	1303.33i	0.0573047	−	0.0475564i
$910$	−20987.1	−	17610.3i	−0.764523	−	0.641511i
$911$	3143.91	+	10501.4i	0.114339	+	0.381917i	0.995934	−	0.0900890i	$-0.0287151\pi$
$911$	3143.91	+	10501.4i	0.114339	+	0.381917i	−0.881595	+	0.472006i	$0.843530\pi$
$912$	2824.34	−	9341.54i	0.102547	−	0.339177i
$913$	3785.39	+	1901.10i	0.137216	+	0.0689125i
$914$	23358.2	+	24758.3i	0.845318	+	0.895985i
$915$	6491.06	+	21897.9i	0.234522	+	0.791171i
$916$	2366.66	−	5486.53i	0.0853675	−	0.197904i
$917$	7228.38	−	12519.9i	0.260308	−	0.450866i
$918$	−11713.1	+	26557.2i	−0.421124	+	0.954812i
$919$	−24403.0	−	42267.2i	−0.875931	−	1.51716i	−0.855768	−	0.517360i	$-0.826915\pi$
$919$	−24403.0	−	42267.2i	−0.875931	−	1.51716i	−0.0201630	−	0.999797i	$-0.506419\pi$
$920$	14532.1	−	1698.56i	0.520770	−	0.0608693i
$921$	−23604.0	+	2693.97i	−0.844495	+	0.0963836i
$922$	19020.2	−	4507.86i	0.679388	−	0.161018i
$923$	1329.25	+	22822.3i	0.0474027	+	0.813873i
$924$	1590.86	+	3715.74i	0.0566401	+	0.132293i
$925$	−31682.8	−	7508.97i	−1.12619	−	0.266912i
$926$	2007.01	−	11382.3i	0.0712250	−	0.403937i
$927$	−1806.94	+	28368.9i	−0.0640212	+	1.00513i
$928$	−353.885	−	2006.98i	−0.0125182	−	0.0709940i
$929$	1176.78	−	20204.5i	0.0415595	−	0.713550i	−0.911599	−	0.411080i	$-0.865152\pi$
$929$	1176.78	−	20204.5i	0.0415595	−	0.713550i	0.953159	−	0.302470i	$-0.0978112\pi$
$930$	−34049.8	−	28729.1i	−1.20058	−	1.01297i
$931$	33478.8	−	44969.8i	1.17854	−	1.58306i
$932$	7777.83	−	10447.4i	0.273360	−	0.367186i
$933$	−8719.49	+	48677.4i	−0.305963	+	1.70807i
$934$	−1760.73	+	30230.6i	−0.0616840	+	1.05907i
$935$	1892.21	+	10731.3i	0.0661840	+	0.375348i
$936$	2669.65	−	6097.67i	0.0932267	−	0.212937i
$937$	6855.67	−	38880.4i	0.239023	−	1.35557i	−0.594949	−	0.803763i	$-0.702828\pi$
$937$	6855.67	−	38880.4i	0.239023	−	1.35557i	0.833973	−	0.551806i	$-0.186061\pi$
$938$	−19678.0	−	4663.78i	−0.684979	−	0.162343i
$939$	−26258.8	−	3141.51i	−0.912591	−	0.109179i
$940$	806.013	+	13838.7i	0.0279673	+	0.480180i
$941$	−1486.05	+	352.199i	−0.0514811	+	0.0122012i	−0.256276	−	0.966604i	$-0.582495\pi$
$941$	−1486.05	+	352.199i	−0.0514811	+	0.0122012i	0.204795	+	0.978805i	$0.434347\pi$
$942$	−1761.12	−	2379.06i	−0.0609134	−	0.0822864i
$943$	−32408.4	+	3788.00i	−1.11915	+	0.130810i
$944$	6219.86	+	10773.1i	0.214448	+	0.371435i
$945$	−58425.9	−	21805.9i	−2.01121	−	0.750630i
$946$	−3159.99	+	5473.26i	−0.108605	+	0.188109i
$947$	−10500.3	+	24342.4i	−0.360310	+	0.835294i	0.637581	+	0.770384i	$0.279935\pi$
$947$	−10500.3	+	24342.4i	−0.360310	+	0.835294i	−0.997891	+	0.0649099i	$0.979324\pi$
$948$	26782.0	+	6424.30i	0.917550	+	0.220096i
$949$	14775.7	+	15661.3i	0.505415	+	0.535708i
$950$	24290.5	+	12199.1i	0.829565	+	0.416623i
$951$	−21241.1	+	4973.35i	−0.724279	+	0.169581i
$952$	−6799.01	−	22710.3i	−0.231468	−	0.773156i
$953$	39207.3	+	32898.8i	1.33268	+	1.11826i	0.983442	+	0.181223i	$0.0580055\pi$
$953$	39207.3	+	32898.8i	1.33268	+	1.11826i	0.349243	+	0.937032i	$0.386439\pi$
$954$	−13961.7	−	75.8227i	−0.473823	−	0.00257322i
$955$	8795.75	−	7380.51i	0.298035	−	0.250081i
$956$	14947.4	+	9831.04i	0.505682	+	0.332593i
$957$	−2246.50	−	6.10006i	−0.0758821	−	0.000206047i
$958$	−12613.0	−	1474.25i	−0.425372	−	0.0497189i
$959$	1614.56	+	3742.96i	0.0543657	+	0.126034i
$960$	3961.99	−	3306.21i	0.133201	−	0.111154i
$961$	41583.4	−	20884.0i	1.39584	−	0.701016i
$962$	16287.8	+	5928.26i	0.545882	+	0.198685i
$963$	−5902.86	−	722.461i	−0.197525	−	0.0241755i
$964$	−11186.1	+	4071.42i	−0.373735	+	0.136029i
$965$	−2107.63	+	2233.96i	−0.0703078	+	0.0745219i
$966$	1945.04	+	35033.5i	0.0647831	+	1.16686i
$967$	21643.0	−	14234.8i	0.719742	−	0.473382i	−0.136050	−	0.990702i	$-0.543441\pi$
$967$	21643.0	−	14234.8i	0.719742	−	0.473382i	0.855792	+	0.517320i	$0.173070\pi$
$968$	2948.14	−	9847.47i	0.0978893	−	0.326973i
$969$	52621.1	+	34814.5i	1.74451	+	1.15418i
$970$	−2752.38	−	3697.09i	−0.0911068	−	0.122378i
$971$	−16600.4			−0.548644			−0.274322	−	0.961638i	$-0.588453\pi$
$971$	−16600.4			−0.548644			−0.274322	+	0.961638i	$0.588453\pi$
$972$	1086.29	−	15113.0i	0.0358464	−	0.498713i
$973$	17466.3			0.575481
$974$	−14547.5	−	19540.6i	−0.478574	−	0.642836i
$975$	15462.2	+	10229.9i	0.507883	+	0.336019i
$976$	1299.87	−	4341.88i	0.0426311	−	0.142398i
$977$	−17085.6	+	11237.4i	−0.559487	+	0.367980i	−0.797535	−	0.603273i	$-0.793863\pi$
$977$	−17085.6	+	11237.4i	−0.559487	+	0.367980i	0.238048	+	0.971253i	$0.423492\pi$
$978$	383.749	+	6912.00i	0.0125470	+	0.225993i
$979$	−447.259	+	474.067i	−0.0146011	+	0.0154762i
$980$	27856.4	−	10138.9i	0.908001	−	0.330485i
$981$	−3816.32	+	5068.50i	−0.124206	+	0.164959i
$982$	24324.2	+	8853.30i	0.790446	+	0.287699i
$983$	−11437.4	+	5744.09i	−0.371106	+	0.186376i	−0.624571	−	0.780968i	$-0.714726\pi$
$983$	−11437.4	+	5744.09i	−0.371106	+	0.186376i	0.253465	+	0.967345i	$0.418430\pi$
$984$	−8835.75	+	7373.28i	−0.286253	+	0.238874i
$985$	14891.4	+	34522.2i	0.481706	+	1.11672i
$986$	13086.7	+	1529.62i	0.422683	+	0.0494046i
$987$	−33243.6	−	90.2681i	−1.07209	−	0.00291111i
$988$	−12089.3	−	7951.26i	−0.389284	−	0.256036i
$989$	−42027.0	+	35264.8i	−1.35124	+	1.13383i
$990$	−2817.40	−	4941.66i	−0.0904473	−	0.158643i
$991$	−818.014	−	686.395i	−0.0262211	−	0.0220021i	0.629583	−	0.776933i	$-0.283226\pi$
$991$	−818.014	−	686.395i	−0.0262211	−	0.0220021i	−0.655804	+	0.754931i	$0.727670\pi$
$992$	2535.51	+	8469.18i	0.0811516	+	0.271065i
$993$	56224.3	−	13164.3i	1.79680	−	0.420700i
$994$	−37980.5	−	19074.5i	−1.21194	−	0.608658i
$995$	40820.1	+	43266.8i	1.30059	+	1.37854i
$996$	12611.3	+	3025.13i	0.401210	+	0.0962399i
$997$	7028.74	−	16294.5i	0.223272	−	0.517603i	−0.769353	−	0.638823i	$-0.779421\pi$
$997$	7028.74	−	16294.5i	0.223272	−	0.517603i	0.992626	+	0.121220i	$0.0386807\pi$
$998$	15132.4	−	26210.1i	0.479968	−	0.831329i
$999$	39453.6	+	321.398i	1.24951	+	0.0101788i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.4.g.a.7.11	✓	234
81.58	even	27	inner	162.4.g.a.139.11	yes	234

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
162.4.g.a.7.11	✓	234	1.1	even	1	trivial
162.4.g.a.139.11	yes	234	81.58	even	27	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	162.g (of order \(27\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(1.19432 + 1.60425i) q^{2} +(4.33355 + 2.86711i) q^{3} +(-1.14721 + 3.83196i) q^{4} +(12.9644 - 8.52679i) q^{5} +(0.576086 + 10.3763i) q^{6} +(-19.6582 + 20.8365i) q^{7} +(-7.51754 + 2.73616i) q^{8} +(10.5594 + 24.8495i) q^{9} +(29.1626 + 10.6143i) q^{10} +(-6.06658 + 3.04675i) q^{11} +(-15.9582 + 13.3168i) q^{12} +(12.2060 + 28.2967i) q^{13} +(-56.9050 - 6.65124i) q^{14} +(80.6290 + 0.218936i) q^{15} +(-13.3678 - 8.79214i) q^{16} +(79.2426 - 66.4924i) q^{17} +(-27.2536 + 46.6181i) q^{18} +(89.9218 + 75.4533i) q^{19} +(17.8014 + 59.4609i) q^{20} +(-144.930 + 33.9338i) q^{21} +(-12.1332 - 6.09350i) q^{22} +(-80.8818 - 85.7296i) q^{23} +(-40.4225 - 9.69632i) q^{24} +(45.8584 - 106.312i) q^{25} +(-30.8170 + 53.3766i) q^{26} +(-25.4868 + 137.962i) q^{27} +(-57.2924 - 99.2334i) q^{28} +(63.2551 - 7.39346i) q^{29} +(95.9453 + 129.610i) q^{30} +(-268.821 + 63.7118i) q^{31} +(-1.86063 - 31.9459i) q^{32} +(-35.0252 - 4.19030i) q^{33} +(201.311 + 47.7116i) q^{34} +(-77.1877 + 437.753i) q^{35} +(-107.336 + 11.9553i) q^{36} +(-48.8343 - 276.953i) q^{37} +(-13.6506 + 234.372i) q^{38} +(-28.2344 + 157.621i) q^{39} +(-74.1294 + 99.5731i) q^{40} +(165.318 - 222.061i) q^{41} +(-227.531 - 191.976i) q^{42} +(27.0653 - 464.692i) q^{43} +(-4.71536 - 26.7421i) q^{44} +(348.782 + 232.121i) q^{45} +(40.9330 - 232.143i) q^{46} +(217.317 + 51.5050i) q^{47} +(-32.7220 - 76.4282i) q^{48} +(-27.7703 - 476.797i) q^{49} +(225.320 - 53.4017i) q^{50} +(534.043 - 60.9512i) q^{51} +(-122.435 + 14.3105i) q^{52} +(129.277 + 223.915i) q^{53} +(-251.764 + 123.883i) q^{54} +(-52.6703 + 91.2276i) q^{55} +(90.7695 - 210.427i) q^{56} +(173.348 + 584.797i) q^{57} +(87.4076 + 92.6467i) q^{58} +(-694.783 - 348.933i) q^{59} +(-93.3376 + 308.716i) q^{60} +(81.2422 + 271.368i) q^{61} +(-423.267 - 355.163i) q^{62} +(-725.356 - 268.478i) q^{63} +(49.0268 - 41.1384i) q^{64} +(399.523 + 262.770i) q^{65} +(-35.1089 - 61.1936i) q^{66} +(350.594 + 40.9786i) q^{67} +(163.888 + 379.935i) q^{68} +(-104.709 - 603.411i) q^{69} +(-794.451 + 398.988i) q^{70} +(697.092 + 253.721i) q^{71} +(-147.373 - 157.915i) q^{72} +(656.547 - 238.963i) q^{73} +(385.978 - 409.112i) q^{74} +(503.537 - 329.226i) q^{75} +(-392.293 + 258.015i) q^{76} +(55.7745 - 186.300i) q^{77} +(-286.584 + 142.955i) q^{78} +(-791.295 - 1062.89i) q^{79} -248.274 q^{80} +(-506.000 + 524.791i) q^{81} +553.683 q^{82} +(-372.612 - 500.505i) q^{83} +(36.2333 - 594.297i) q^{84} +(460.362 - 1537.72i) q^{85} +(777.806 - 511.571i) q^{86} +(295.317 + 149.319i) q^{87} +(37.2694 - 39.5032i) q^{88} +(90.2159 - 32.8359i) q^{89} +(44.1774 + 836.759i) q^{90} +(-829.552 - 301.932i) q^{91} +(421.301 - 211.585i) q^{92} +(-1347.62 - 494.641i) q^{93} +(176.918 + 410.143i) q^{94} +(1809.15 + 211.460i) q^{95} +(83.5291 - 143.774i) q^{96} +(-124.085 - 81.6118i) q^{97} +(731.733 - 613.997i) q^{98} +(-139.770 - 118.580i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 234 q + 36 q^{6} - 90 q^{13} - 162 q^{18} - 144 q^{20} - 405 q^{21} - 756 q^{23} - 846 q^{25} + 702 q^{26} + 702 q^{27} + 504 q^{28} + 540 q^{29} + 1098 q^{30} + 2214 q^{31} + 684 q^{33} - 1242 q^{35} - 576 q^{36}+ \cdots + 18567 q^{99}+O(q^{100}) \) 234 * q + 36 * q^6 - 90 * q^13 - 162 * q^18 - 144 * q^20 - 405 * q^21 - 756 * q^23 - 846 * q^25 + 702 * q^26 + 702 * q^27 + 504 * q^28 + 540 * q^29 + 1098 * q^30 + 2214 * q^31 + 684 * q^33 - 1242 * q^35 - 576 * q^36 - 72 * q^38 - 927 * q^41 - 774 * q^42 + 900 * q^43 - 3843 * q^45 + 2088 * q^46 + 297 * q^47 + 144 * q^48 + 810 * q^51 + 720 * q^52 + 1431 * q^53 + 2970 * q^55 + 1485 * q^57 - 126 * q^58 - 1179 * q^59 - 2259 * q^63 + 3627 * q^65 + 4680 * q^66 - 8046 * q^67 + 2304 * q^68 - 594 * q^69 + 1530 * q^70 + 720 * q^71 + 864 * q^72 - 3204 * q^73 - 3384 * q^74 - 9918 * q^75 - 144 * q^76 - 9792 * q^77 - 7524 * q^78 + 4527 * q^79 - 1440 * q^80 + 5832 * q^81 - 5904 * q^82 - 9621 * q^83 - 1224 * q^84 + 4059 * q^85 - 3600 * q^86 - 117 * q^87 - 576 * q^88 + 531 * q^89 + 1440 * q^90 - 4473 * q^91 + 1872 * q^92 + 135 * q^93 + 666 * q^94 + 8037 * q^95 + 1728 * q^96 - 16560 * q^97 + 8136 * q^98 + 18567 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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