LMFDB - Embedded newform 110.4.k.a.7.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [110,4,Mod(7,110)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(110, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([5, 14])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("110.7"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 110 = 2 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	110.k (of order $20$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$6.49021010063$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$18$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			7.18
Character	$\chi$	$=$	110.7
Dual form			110.4.k.a.63.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.97538 - 0.312869i) q^{2} +(4.04090 + 7.93071i) q^{3} +(3.80423 - 1.23607i) q^{4} +(-8.78081 + 6.92079i) q^{5} +(10.4636 + 14.4019i) q^{6} +(0.860054 + 0.438219i) q^{7} +(7.12805 - 3.63192i) q^{8} +(-30.6971 + 42.2509i) q^{9} +(-15.1801 + 16.4184i) q^{10} +(21.5097 - 29.4675i) q^{11} +(25.1754 + 25.1754i) q^{12} +(2.67773 + 16.9065i) q^{13} +(1.83604 + 0.596564i) q^{14} +(-90.3691 - 41.6718i) q^{15} +(12.9443 - 9.40456i) q^{16} +(-1.25801 + 7.94273i) q^{17} +(-47.4193 + 93.0655i) q^{18} +(-10.9847 + 33.8073i) q^{19} +(-24.8496 + 37.1819i) q^{20} +8.59163i q^{21} +(33.2704 - 64.9391i) q^{22} +(119.284 - 119.284i) q^{23} +(57.6074 + 41.8543i) q^{24} +(29.2052 - 121.540i) q^{25} +(10.5791 + 32.5590i) q^{26} +(-221.759 - 35.1232i) q^{27} +(3.81351 + 0.604000i) q^{28} +(71.9845 + 221.546i) q^{29} +(-191.551 - 54.0438i) q^{30} +(130.218 + 94.6088i) q^{31} +(22.6274 - 22.6274i) q^{32} +(320.616 + 51.5123i) q^{33} +16.0835i q^{34} +(-10.5848 + 2.10433i) q^{35} +(-64.5536 + 198.675i) q^{36} +(156.811 - 307.758i) q^{37} +(-11.1216 + 70.2190i) q^{38} +(-123.260 + 89.5539i) q^{39} +(-37.4543 + 81.2230i) q^{40} +(178.801 + 58.0960i) q^{41} +(2.68806 + 16.9717i) q^{42} +(-239.269 - 239.269i) q^{43} +(45.4041 - 138.688i) q^{44} +(-22.8646 - 583.445i) q^{45} +(198.310 - 272.951i) q^{46} +(-57.1437 + 29.1161i) q^{47} +(126.891 + 64.6543i) q^{48} +(-201.063 - 276.739i) q^{49} +(19.6651 - 249.225i) q^{50} +(-68.0749 + 22.1189i) q^{51} +(31.0844 + 61.0065i) q^{52} +(-10.7551 + 1.70344i) q^{53} -449.046 q^{54} +(15.0655 + 407.613i) q^{55} +7.72209 q^{56} +(-312.504 + 49.4958i) q^{57} +(211.511 + 415.114i) q^{58} +(-581.899 + 189.071i) q^{59} +(-395.294 - 46.8266i) q^{60} +(-544.770 - 749.812i) q^{61} +(286.830 + 146.147i) q^{62} +(-44.9163 + 22.8860i) q^{63} +(37.6183 - 51.7771i) q^{64} +(-140.519 - 129.921i) q^{65} +(649.455 + 1.44528i) q^{66} +(-328.405 - 328.405i) q^{67} +(5.03202 + 31.7709i) q^{68} +(1428.02 + 463.992i) q^{69} +(-20.2506 + 7.46851i) q^{70} +(685.903 - 498.338i) q^{71} +(-65.3583 + 412.656i) q^{72} +(-311.753 + 611.849i) q^{73} +(213.472 - 657.000i) q^{74} +(1081.92 - 259.514i) q^{75} +142.189i q^{76} +(31.4127 - 15.9176i) q^{77} +(-215.467 + 215.467i) q^{78} +(1036.51 + 753.066i) q^{79} +(-48.5741 + 172.164i) q^{80} +(-181.817 - 559.574i) q^{81} +(371.376 + 58.8202i) q^{82} +(-424.483 - 67.2315i) q^{83} +(10.6198 + 32.6845i) q^{84} +(-43.9237 - 78.4500i) q^{85} +(-547.507 - 397.787i) q^{86} +(-1466.13 + 1466.13i) q^{87} +(46.2988 - 288.167i) q^{88} +38.4359i q^{89} +(-227.708 - 1145.37i) q^{90} +(-5.10578 + 15.7140i) q^{91} +(306.340 - 601.226i) q^{92} +(-224.118 + 1415.02i) q^{93} +(-103.771 + 75.3938i) q^{94} +(-137.519 - 372.878i) q^{95} +(270.886 + 88.0163i) q^{96} +(97.9096 + 618.177i) q^{97} +(-483.758 - 483.758i) q^{98} +(584.741 + 1813.37i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 8 q^{3} + 32 q^{5} - 40 q^{7} - 44 q^{11} + 128 q^{12} - 256 q^{15} + 576 q^{16} - 640 q^{17} - 64 q^{20} + 312 q^{22} - 984 q^{23} - 520 q^{25} + 304 q^{26} - 364 q^{27} + 240 q^{28} - 432 q^{31}+ \cdots + 7044 q^{97}+O(q^{100}) $ 144 * q + 8 * q^3 + 32 * q^5 - 40 * q^7 - 44 * q^11 + 128 * q^12 - 256 * q^15 + 576 * q^16 - 640 * q^17 - 64 * q^20 + 312 * q^22 - 984 * q^23 - 520 * q^25 + 304 * q^26 - 364 * q^27 + 240 * q^28 - 432 * q^31 + 2368 * q^33 + 1808 * q^36 - 960 * q^37 + 72 * q^38 + 740 * q^41 + 2440 * q^42 + 2656 * q^45 + 720 * q^46 - 1980 * q^47 - 128 * q^48 - 1360 * q^50 - 3880 * q^51 - 1920 * q^52 - 3060 * q^53 - 3044 * q^55 - 64 * q^56 - 4400 * q^57 - 2016 * q^58 - 1120 * q^60 - 960 * q^61 + 80 * q^62 + 1800 * q^63 + 1552 * q^66 + 10160 * q^67 + 2560 * q^68 + 2304 * q^70 + 1312 * q^71 - 2460 * q^73 + 8644 * q^75 - 1272 * q^77 - 5312 * q^78 + 768 * q^80 + 2116 * q^81 + 1280 * q^82 + 320 * q^85 - 5488 * q^86 + 1248 * q^88 - 8480 * q^90 + 11796 * q^91 - 704 * q^92 + 688 * q^93 - 1280 * q^95 + 7044 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/110\mathbb{Z}\right)^\times$.

$n$	$67$	$101$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{7}{10}\right)$

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 $

$2$	1.97538	−	0.312869i	0.698401	−	0.110616i
$2$	1.97538	−	0.312869i	0.698401	−	0.110616i
$3$	4.04090	+	7.93071i	0.777671	+	1.52627i	0.848750	+	0.528794i	$0.177356\pi$
$3$	4.04090	+	7.93071i	0.777671	+	1.52627i	−0.0710790	+	0.997471i	$0.522644\pi$
$4$	3.80423	−	1.23607i	0.475528	−	0.154508i
$5$	−8.78081	+	6.92079i	−0.785379	+	0.619015i
$5$	−8.78081	+	6.92079i	−0.785379	+	0.619015i
$6$	10.4636	+	14.4019i	0.711955	+	0.979923i
$7$	0.860054	+	0.438219i	0.0464385	+	0.0236616i	0.477056	−	0.878873i	$-0.341704\pi$
$7$	0.860054	+	0.438219i	0.0464385	+	0.0236616i	−0.430617	+	0.902535i	$0.641704\pi$
$8$	7.12805	−	3.63192i	0.315018	−	0.160510i
$9$	−30.6971	+	42.2509i	−1.13693	+	1.56485i
$10$	−15.1801	+	16.4184i	−0.480037	+	0.519196i
$11$	21.5097	−	29.4675i	0.589584	−	0.807707i
$11$	21.5097	−	29.4675i	0.589584	−	0.807707i
$12$	25.1754	+	25.1754i	0.605625	+	0.605625i
$13$	2.67773	+	16.9065i	0.0571285	+	0.360695i	0.999648	+	0.0265429i	$0.00844987\pi$
$13$	2.67773	+	16.9065i	0.0571285	+	0.360695i	−0.942519	+	0.334152i	$0.891550\pi$
$14$	1.83604	+	0.596564i	0.0350501	+	0.0113885i
$15$	−90.3691	−	41.6718i	−1.55555	−	0.717308i
$16$	12.9443	−	9.40456i	0.202254	−	0.146946i
$17$	−1.25801	+	7.94273i	−0.0179477	+	0.113317i	−0.995036	−	0.0995182i	$-0.968270\pi$
$17$	−1.25801	+	7.94273i	−0.0179477	+	0.113317i	0.977088	+	0.212836i	$0.0682699\pi$
$18$	−47.4193	+	93.0655i	−0.620935	+	1.21865i
$19$	−10.9847	+	33.8073i	−0.132635	+	0.408207i	−0.995215	−	0.0977135i	$-0.968847\pi$
$19$	−10.9847	+	33.8073i	−0.132635	+	0.408207i	0.862580	+	0.505921i	$0.168847\pi$
$20$	−24.8496	+	37.1819i	−0.277827	+	0.415707i
$21$			8.59163i			0.0892785i
$22$	33.2704	−	64.9391i	0.322421	−	0.629321i
$23$	119.284	−	119.284i	1.08141	−	1.08141i	0.0850307	−	0.996378i	$-0.472901\pi$
$23$	119.284	−	119.284i	1.08141	−	1.08141i	0.996378	−	0.0850307i	$-0.0270988\pi$
$24$	57.6074	+	41.8543i	0.489961	+	0.355978i
$25$	29.2052	−	121.540i	0.233642	−	0.972323i
$26$	10.5791	+	32.5590i	0.0797972	+	0.245590i
$27$	−221.759	−	35.1232i	−1.58065	−	0.250350i
$28$	3.81351	+	0.604000i	0.0257388	+	0.00407662i
$29$	71.9845	+	221.546i	0.460937	+	1.41862i	0.864021	+	0.503456i	$0.167939\pi$
$29$	71.9845	+	221.546i	0.460937	+	1.41862i	−0.403083	+	0.915163i	$0.632061\pi$
$30$	−191.551	−	54.0438i	−1.16574	−	0.328900i
$31$	130.218	+	94.6088i	0.754446	+	0.548137i	0.897202	−	0.441621i	$-0.145596\pi$
$31$	130.218	+	94.6088i	0.754446	+	0.548137i	−0.142756	+	0.989758i	$0.545596\pi$
$32$	22.6274	−	22.6274i	0.125000	−	0.125000i
$33$	320.616	+	51.5123i	1.69128	+	0.271732i
$34$			16.0835i			0.0811263i
$35$	−10.5848	+	2.10433i	−0.0511188	+	0.0101628i
$36$	−64.5536	+	198.675i	−0.298859	+	0.919794i
$37$	156.811	−	307.758i	0.696744	−	1.36744i	−0.222962	−	0.974827i	$-0.571572\pi$
$37$	156.811	−	307.758i	0.696744	−	1.36744i	0.919705	−	0.392609i	$-0.128428\pi$
$38$	−11.1216	+	70.2190i	−0.0474779	+	0.299764i
$39$	−123.260	+	89.5539i	−0.506089	+	0.367695i
$40$	−37.4543	+	81.2230i	−0.148051	+	0.321062i
$41$	178.801	+	58.0960i	0.681074	+	0.221294i	0.629065	−	0.777352i	$-0.283438\pi$
$41$	178.801	+	58.0960i	0.681074	+	0.221294i	0.0520084	+	0.998647i	$0.483438\pi$
$42$	2.68806	+	16.9717i	0.00987562	+	0.0623522i
$43$	−239.269	−	239.269i	−0.848563	−	0.848563i	0.141391	−	0.989954i	$-0.454843\pi$
$43$	−239.269	−	239.269i	−0.848563	−	0.848563i	−0.989954	+	0.141391i	$0.954843\pi$
$44$	45.4041	−	138.688i	0.155566	−	0.475183i
$45$	−22.8646	−	583.445i	−0.0757433	−	1.93277i
$46$	198.310	−	272.951i	0.635636	−	0.874878i
$47$	−57.1437	+	29.1161i	−0.177346	+	0.0903623i	−0.540410	−	0.841402i	$-0.681731\pi$
$47$	−57.1437	+	29.1161i	−0.177346	+	0.0903623i	0.363064	+	0.931764i	$0.381731\pi$
$48$	126.891	+	64.6543i	0.381566	+	0.194418i
$49$	−201.063	−	276.739i	−0.586189	−	0.806819i
$50$	19.6651	−	249.225i	0.0556214	−	0.704916i
$51$	−68.0749	+	22.1189i	−0.186910	+	0.0607307i
$52$	31.0844	+	61.0065i	0.0828966	+	0.162694i
$53$	−10.7551	+	1.70344i	−0.0278740	+	0.00441481i	−0.170356	−	0.985383i	$-0.554492\pi$
$53$	−10.7551	+	1.70344i	−0.0278740	+	0.00441481i	0.142482	+	0.989797i	$0.454492\pi$
$54$	−449.046			−1.13162
$55$	15.0655	+	407.613i	0.0369351	+	0.999318i
$56$	7.72209			0.0184269
$57$	−312.504	+	49.4958i	−0.726178	+	0.115015i
$58$	211.511	+	415.114i	0.478841	+	0.939779i
$59$	−581.899	+	189.071i	−1.28401	+	0.417202i	−0.869992	−	0.493065i	$-0.835876\pi$
$59$	−581.899	+	189.071i	−1.28401	+	0.417202i	−0.414022	+	0.910267i	$0.635876\pi$
$60$	−395.294	−	46.8266i	−0.850537	−	0.100755i
$61$	−544.770	−	749.812i	−1.14345	−	1.57383i	−0.759540	−	0.650461i	$-0.774576\pi$
$61$	−544.770	−	749.812i	−1.14345	−	1.57383i	−0.383915	−	0.923369i	$-0.625424\pi$
$62$	286.830	+	146.147i	0.587539	+	0.299366i
$63$	−44.9163	+	22.8860i	−0.0898241	+	0.0457677i
$64$	37.6183	−	51.7771i	0.0734732	−	0.101127i
$65$	−140.519	−	129.921i	−0.268143	−	0.247919i
$66$	649.455	+	1.44528i	1.21125	+	0.00269548i
$67$	−328.405	−	328.405i	−0.598822	−	0.598822i	0.341177	−	0.939999i	$-0.389174\pi$
$67$	−328.405	−	328.405i	−0.598822	−	0.598822i	−0.939999	+	0.341177i	$0.889174\pi$
$68$	5.03202	+	31.7709i	0.00897385	+	0.0566587i
$69$	1428.02	+	463.992i	2.49150	+	0.809537i
$70$	−20.2506	+	7.46851i	−0.0345772	+	0.0127522i
$71$	685.903	−	498.338i	1.14650	−	0.832984i	0.158491	−	0.987360i	$-0.449337\pi$
$71$	685.903	−	498.338i	1.14650	−	0.832984i	0.988012	+	0.154377i	$0.0493370\pi$
$72$	−65.3583	+	412.656i	−0.106980	+	0.675444i
$73$	−311.753	+	611.849i	−0.499834	+	0.980980i	0.493933	+	0.869500i	$0.335559\pi$
$73$	−311.753	+	611.849i	−0.499834	+	0.980980i	−0.993767	+	0.111479i	$0.964441\pi$
$74$	213.472	−	657.000i	0.335346	−	1.03209i
$75$	1081.92	−	259.514i	1.66572	−	0.399548i
$76$			142.189i			0.214607i
$77$	31.4127	−	15.9176i	0.0464911	−	0.0235582i
$78$	−215.467	+	215.467i	−0.312780	+	0.312780i
$79$	1036.51	+	753.066i	1.47615	+	1.07249i	0.978771	+	0.204957i	$0.0657055\pi$
$79$	1036.51	+	753.066i	1.47615	+	1.07249i	0.497383	+	0.867531i	$0.334294\pi$
$80$	−48.5741	+	172.164i	−0.0678844	+	0.240607i
$81$	−181.817	−	559.574i	−0.249406	−	0.767592i
$82$	371.376	+	58.8202i	0.500141	+	0.0792146i
$83$	−424.483	−	67.2315i	−0.561362	−	0.0889111i	−0.130696	−	0.991422i	$-0.541721\pi$
$83$	−424.483	−	67.2315i	−0.561362	−	0.0889111i	−0.430666	+	0.902511i	$0.641721\pi$
$84$	10.6198	+	32.6845i	0.0137943	+	0.0424544i
$85$	−43.9237	−	78.4500i	−0.0560493	−	0.100107i
$86$	−547.507	−	397.787i	−0.686502	−	0.498773i
$87$	−1466.13	+	1466.13i	−1.80673	+	1.80673i
$88$	46.2988	−	288.167i	0.0560849	−	0.349077i
$89$			38.4359i			0.0457775i	0.999738	+	0.0228888i	$0.00728636\pi$
$89$			38.4359i			0.0457775i	−0.999738	+	0.0228888i	$0.992714\pi$
$90$	−227.708	−	1145.37i	−0.266695	−	1.34147i
$91$	−5.10578	+	15.7140i	−0.00588166	+	0.0181019i
$92$	306.340	−	601.226i	0.347154	−	0.681327i
$93$	−224.118	+	1415.02i	−0.249892	+	1.57775i
$94$	−103.771	+	75.3938i	−0.113863	+	0.0827264i
$95$	−137.519	−	372.878i	−0.148518	−	0.402700i
$96$	270.886	+	88.0163i	0.287992	+	0.0935743i
$97$	97.9096	+	618.177i	0.102487	+	0.647076i	0.984438	+	0.175735i	$0.0562300\pi$
$97$	97.9096	+	618.177i	0.102487	+	0.647076i	−0.881951	+	0.471341i	$0.843770\pi$
$98$	−483.758	−	483.758i	−0.498642	−	0.498642i
$99$	584.741	+	1813.37i	0.593623	+	1.84091i
$100$	−39.1288	−	498.467i	−0.0391288	−	0.498467i
$101$	−116.174	+	159.899i	−0.114453	+	0.157531i	−0.862400	−	0.506228i	$-0.831040\pi$
$101$	−116.174	+	159.899i	−0.114453	+	0.157531i	0.747947	+	0.663758i	$0.231040\pi$
$102$	−127.553	+	64.9917i	−0.123820	+	0.0630896i
$103$	−818.652	−	417.124i	−0.783147	−	0.399033i	0.0162260	−	0.999868i	$-0.494835\pi$
$103$	−818.652	−	417.124i	−0.783147	−	0.399033i	−0.799373	+	0.600835i	$0.794835\pi$
$104$	80.4903	+	110.785i	0.0758916	+	0.104456i
$105$	−59.4609	−	75.4415i	−0.0552647	−	0.0701175i
$106$	−20.7124	+	6.72986i	−0.0189789	+	0.00616662i
$107$	609.269	+	1195.76i	0.550470	+	1.08036i	0.983825	+	0.179135i	$0.0573298\pi$
$107$	609.269	+	1195.76i	0.550470	+	1.08036i	−0.433355	+	0.901224i	$0.642670\pi$
$108$	−887.036	+	140.493i	−0.790325	+	0.125175i
$109$	−1546.47			−1.35895			−0.679474	−	0.733700i	$-0.737792\pi$
$109$	−1546.47			−1.35895			−0.679474	+	0.733700i	$0.737792\pi$
$110$	157.289	+	800.475i	0.136336	+	0.693839i
$111$	3074.40			2.62891
$112$	15.2540	−	2.41600i	0.0128694	−	0.00203831i
$113$	−558.102	−	1095.34i	−0.464618	−	0.911863i	−0.997828	−	0.0658804i	$-0.979014\pi$
$113$	−558.102	−	1095.34i	−0.464618	−	0.911863i	0.533210	−	0.845983i	$-0.320986\pi$
$114$	−601.827	+	195.546i	−0.494441	+	0.160654i
$115$	−221.870	+	1872.95i	−0.179908	+	1.51872i
$116$	547.691	+	753.832i	0.438378	+	0.603375i
$117$	−796.515	−	405.845i	−0.629383	−	0.320687i
$118$	−1090.32	+	555.544i	−0.850608	+	0.433406i
$119$	−4.56261	+	6.27989i	−0.00351474	+	0.00483762i
$120$	−795.505	+	31.1750i	−0.605161	+	0.0237156i
$121$	−405.664	−	1267.67i	−0.304781	−	0.952422i
$122$	−1310.72	−	1310.72i	−0.972680	−	0.972680i
$123$	261.774	+	1652.78i	0.191898	+	1.21159i
$124$	612.321	+	198.955i	0.443452	+	0.144086i
$125$	584.710	+	1269.35i	0.418384	+	0.908270i
$126$	−81.5662	+	59.2613i	−0.0576706	+	0.0419002i
$127$	184.312	−	1163.70i	0.128780	−	0.813084i	−0.835750	−	0.549110i	$-0.814967\pi$
$127$	184.312	−	1163.70i	0.128780	−	0.813084i	0.964530	−	0.263974i	$-0.0850333\pi$
$128$	58.1108	−	114.049i	0.0401275	−	0.0787546i
$129$	930.712	−	2864.44i	0.635229	−	1.95504i
$130$	−318.227	−	212.679i	−0.214695	−	0.143486i
$131$			2420.54i			1.61438i	0.590293	+	0.807189i	$0.299012\pi$
$131$			2420.54i			1.61438i	−0.590293	+	0.807189i	$0.700988\pi$
$132$	1283.37	−	200.339i	0.846235	−	0.132101i
$133$	−24.2624	+	24.2624i	−0.0158182	+	0.0158182i
$134$	−751.472	−	545.976i	−0.484457	−	0.351979i
$135$	2190.30	−	1226.34i	1.39638	−	0.781825i
$136$	19.8803	+	61.1852i	0.0125347	+	0.0385778i
$137$	−274.881	−	43.5369i	−0.171421	−	0.0271504i	0.0701338	−	0.997538i	$-0.477657\pi$
$137$	−274.881	−	43.5369i	−0.171421	−	0.0271504i	−0.241555	+	0.970387i	$0.577657\pi$
$138$	2966.04	+	469.775i	1.82961	+	0.289782i
$139$	−418.071	−	1286.69i	−0.255110	−	0.785149i	−0.993808	−	0.111112i	$-0.964559\pi$
$139$	−418.071	−	1286.69i	−0.255110	−	0.785149i	0.738697	−	0.674037i	$-0.235441\pi$
$140$	−37.6658	+	21.0889i	−0.0227382	+	0.0127310i
$141$	−461.823	−	335.534i	−0.275834	−	0.200405i
$142$	1199.00	−	1199.00i	0.708578	−	0.708578i
$143$	555.791	+	284.749i	0.325018	+	0.166517i
$144$			835.599i			0.483564i
$145$	−2165.35	−	1447.16i	−1.24016	−	0.828828i
$146$	−424.400	+	1306.17i	−0.240573	+	0.740407i
$147$	1382.26	−	2712.84i	0.775558	−	1.52212i
$148$	216.133	−	1364.61i	0.120041	−	0.757908i
$149$	793.688	−	576.648i	0.436386	−	0.317053i	−0.347811	−	0.937565i	$-0.613075\pi$
$149$	793.688	−	576.648i	0.436386	−	0.317053i	0.784197	+	0.620512i	$0.213075\pi$
$150$	2056.00	−	851.136i	1.11914	−	0.463300i
$151$	600.994	+	195.275i	0.323895	+	0.105240i	0.466452	−	0.884547i	$-0.345532\pi$
$151$	600.994	+	195.275i	0.323895	+	0.105240i	−0.142556	+	0.989787i	$0.545532\pi$
$152$	44.4864	+	280.876i	0.0237390	+	0.149882i
$153$	−296.970	−	296.970i	−0.156919	−	0.156919i
$154$	57.0719	−	41.2714i	0.0298635	−	0.0215957i
$155$	−1798.19	+	70.4690i	−0.931831	+	0.0365175i
$156$	−358.216	+	493.042i	−0.183848	+	0.253044i
$157$	−1549.12	+	789.315i	−0.787472	+	0.401237i	−0.800994	−	0.598672i	$-0.795695\pi$
$157$	−1549.12	+	789.315i	−0.787472	+	0.401237i	0.0135229	+	0.999909i	$0.495695\pi$
$158$	2283.10	+	1163.30i	1.14958	+	0.585741i
$159$	−56.9696	−	78.4119i	−0.0284150	−	0.0391099i
$160$	−42.0873	+	355.287i	−0.0207956	+	0.175549i
$161$	154.863	−	50.3181i	0.0758069	−	0.0246312i
$162$	−534.230	−	1048.49i	−0.259093	−	0.508499i
$163$	−3165.74	+	501.404i	−1.52123	+	0.240939i	−0.860407	−	0.509607i	$-0.829791\pi$
$163$	−3165.74	+	501.404i	−1.52123	+	0.240939i	−0.660819	+	0.750545i	$0.729791\pi$
$164$	752.010			0.358062
$165$	−3171.78	+	1766.60i	−1.49650	+	0.833513i
$166$	−859.549			−0.401891
$167$	1787.43	−	283.101i	0.828235	−	0.131180i	0.272097	−	0.962270i	$-0.412283\pi$
$167$	1787.43	−	283.101i	0.828235	−	0.131180i	0.556138	+	0.831090i	$0.312283\pi$
$168$	31.2042	+	61.2416i	0.0143301	+	0.0281244i
$169$	1810.81	−	588.368i	0.824219	−	0.267805i
$170$	−111.310	−	141.226i	−0.0502184	−	0.0637149i
$171$	−1091.19	−	1501.90i	−0.487986	−	0.671655i
$172$	−1205.99	−	614.481i	−0.534626	−	0.272406i
$173$	2015.14	−	1026.76i	0.885596	−	0.451234i	0.0488381	−	0.998807i	$-0.484448\pi$
$173$	2015.14	−	1026.76i	0.885596	−	0.451234i	0.836758	+	0.547573i	$0.184448\pi$
$174$	−2437.45	+	3354.87i	−1.06197	+	1.46168i
$175$	78.3794	−	91.7329i	0.0338567	−	0.0396249i
$176$	1.29901	−	583.725i	0.000556343	−	0.249999i
$177$	−3850.86	−	3850.86i	−1.63530	−	1.63530i
$178$	12.0254	+	75.9254i	0.00506372	+	0.0319711i
$179$	−1689.98	−	549.109i	−0.705672	−	0.229287i	−0.0658718	−	0.997828i	$-0.520983\pi$
$179$	−1689.98	−	549.109i	−0.705672	−	0.229287i	−0.639800	+	0.768541i	$0.720983\pi$
$180$	−808.159	−	2191.29i	−0.334648	−	0.907385i
$181$	1989.97	−	1445.79i	0.817199	−	0.593730i	−0.0987100	−	0.995116i	$-0.531472\pi$
$181$	1989.97	−	1445.79i	0.817199	−	0.593730i	0.915909	+	0.401387i	$0.131472\pi$
$182$	−5.16942	+	32.6385i	−0.00210540	+	0.0132930i
$183$	3745.18	−	7350.33i	1.51285	−	2.96914i
$184$	417.032	−	1283.49i	0.167087	−	0.514241i
$185$	753.007	+	3787.62i	0.299255	+	1.50525i
$186$			2865.33i			1.12955i
$187$	206.993	+	207.916i	0.0809455	+	0.0813066i
$188$	−181.398	+	181.398i	−0.0703713	+	0.0703713i
$189$	−175.333	−	127.387i	−0.0674794	−	0.0490266i
$190$	−388.314	−	693.550i	−0.148270	−	0.264818i
$191$	919.047	+	2828.53i	0.348167	+	1.07155i	0.959866	+	0.280457i	$0.0904861\pi$
$191$	919.047	+	2828.53i	0.348167	+	1.07155i	−0.611700	+	0.791090i	$0.709514\pi$
$192$	562.640	+	89.1135i	0.211485	+	0.0334959i
$193$	−4698.39	−	744.153i	−1.75232	−	0.277540i	−0.803948	−	0.594699i	$-0.797271\pi$
$193$	−4698.39	−	744.153i	−1.75232	−	0.277540i	−0.948372	+	0.317159i	$0.897271\pi$
$194$	386.817	+	1190.50i	0.143154	+	0.440582i
$195$	462.542	−	1639.42i	0.169863	−	0.602057i
$196$	−1106.96	−	804.251i	−0.403410	−	0.293094i
$197$	667.661	−	667.661i	0.241466	−	0.241466i	−0.575990	−	0.817457i	$-0.695383\pi$
$197$	667.661	−	667.661i	0.241466	−	0.241466i	0.817457	+	0.575990i	$0.195383\pi$
$198$	1722.43	+	3399.14i	0.618221	+	1.22003i
$199$		−	502.392i		−	0.178963i	−0.995988	−	0.0894814i	$-0.971479\pi$
$199$		−	502.392i		−	0.178963i	0.995988	−	0.0894814i	$-0.0285210\pi$
$200$	−233.249	−	972.417i	−0.0824659	−	0.343801i
$201$	1277.43	−	3931.54i	0.448275	−	1.37965i
$202$	−179.459	+	352.209i	−0.0625085	+	0.122680i
$203$	−35.1750	+	222.086i	−0.0121616	+	0.0767852i
$204$	−231.632	+	168.291i	−0.0794975	+	0.0577583i
$205$	−1972.09	+	727.315i	−0.671886	+	0.247795i
$206$	−1747.65	−	567.846i	−0.591090	−	0.192057i
$207$	1378.18	+	8701.51i	0.462756	+	2.92172i
$208$	193.660	+	193.660i	0.0645573	+	0.0645573i
$209$	759.939	+	1050.88i	0.251512	+	0.347802i
$210$	−141.061	−	130.422i	−0.0463530	−	0.0428570i
$211$	−2046.67	+	2817.00i	−0.667767	+	0.919102i	−0.999707	−	0.0241985i	$-0.992297\pi$
$211$	−2046.67	+	2817.00i	−0.667767	+	0.919102i	0.331941	+	0.943300i	$0.392297\pi$
$212$	−38.8092	+	19.7743i	−0.0125728	+	0.00640614i
$213$	6723.84	+	3425.97i	2.16296	+	1.10208i
$214$	1577.65	+	2171.45i	0.503954	+	0.693633i
$215$	3756.91	+	445.044i	1.19172	+	0.141171i
$216$	−1708.27	+	555.052i	−0.538117	+	0.174845i
$217$	70.5350	+	138.433i	0.0220656	+	0.0433061i
$218$	−3054.87	+	483.843i	−0.949090	+	0.150321i
$219$	−6112.15			−1.88594
$220$	561.149	+	1532.03i	0.171967	+	0.469497i
$221$	−137.653			−0.0418983
$222$	6073.09	−	961.883i	1.83603	−	0.290799i
$223$	113.387	+	222.534i	0.0340491	+	0.0668251i	0.907404	−	0.420259i	$-0.138061\pi$
$223$	113.387	+	222.534i	0.0340491	+	0.0668251i	−0.873355	+	0.487084i	$0.838061\pi$
$224$	29.3766	−	9.54503i	0.00876252	−	0.00284712i
$225$	4238.67	+	4964.88i	1.25590	+	1.47107i
$226$	−1445.16	−	1989.09i	−0.425356	−	0.585452i
$227$	1827.87	+	931.345i	0.534448	+	0.272315i	0.700316	−	0.713833i	$-0.253042\pi$
$227$	1827.87	+	931.345i	0.534448	+	0.272315i	−0.165868	+	0.986148i	$0.553042\pi$
$228$	−1127.66	+	574.569i	−0.327547	+	0.166894i
$229$	2293.08	−	3156.16i	0.661708	−	0.910762i	−0.337829	−	0.941208i	$-0.609692\pi$
$229$	2293.08	−	3156.16i	0.661708	−	0.910762i	0.999536	+	0.0304451i	$0.00969249\pi$
$230$	147.711	+	3769.19i	0.0423468	+	1.08058i
$231$	253.174	+	184.804i	0.0721108	+	0.0526372i
$232$	1317.75	+	1317.75i	0.372906	+	0.372906i
$233$	100.769	+	636.233i	0.0283331	+	0.178888i	0.997797	−	0.0663475i	$-0.0211346\pi$
$233$	100.769	+	636.233i	0.0283331	+	0.178888i	−0.969463	+	0.245236i	$0.921135\pi$
$234$	−1700.39	−	552.491i	−0.475035	−	0.154348i
$235$	300.261	−	651.143i	0.0833483	−	0.180748i
$236$	−1979.97	+	1438.53i	−0.546124	+	0.396782i
$237$	−1783.93	+	11263.3i	−0.488940	+	3.08704i
$238$	−7.04809	+	13.8327i	−0.00191958	+	0.00376739i
$239$	−743.209	+	2287.36i	−0.201147	+	0.619068i	0.798702	+	0.601726i	$0.205520\pi$
$239$	−743.209	+	2287.36i	−0.201147	+	0.619068i	−0.999850	+	0.0173414i	$0.994480\pi$
$240$	−1561.67	+	310.471i	−0.420022	+	0.0835034i
$241$		−	4161.87i		−	1.11241i	−0.831047	−	0.556203i	$-0.812258\pi$
$241$		−	4161.87i		−	1.11241i	0.831047	−	0.556203i	$-0.187742\pi$
$242$	−1197.95	−	2377.21i	−0.318212	−	0.631459i
$243$	−583.453	+	583.453i	−0.154027	+	0.154027i
$244$	−2999.25	−	2179.08i	−0.786915	−	0.571727i
$245$	3680.75	+	1038.48i	0.959813	+	0.270800i
$246$	1034.21	+	3182.96i	0.268043	+	0.824951i
$247$	−600.979	−	95.1858i	−0.154815	−	0.0245203i
$248$	1271.81	+	201.435i	0.325646	+	0.0515772i
$249$	−1182.10	−	3638.13i	−0.300853	−	0.925932i
$250$	1552.16	+	2324.50i	0.392669	+	0.588057i
$251$	−815.009	−	592.139i	−0.204952	−	0.148906i	0.480575	−	0.876954i	$-0.340428\pi$
$251$	−815.009	−	592.139i	−0.204952	−	0.148906i	−0.685527	+	0.728047i	$0.740428\pi$
$252$	−142.583	+	142.583i	−0.0356424	+	0.0356424i
$253$	−949.231	−	6080.76i	−0.235880	−	1.51104i
$254$		−	2356.41i		−	0.582104i
$255$	444.673	−	665.354i	0.109202	−	0.163396i
$256$	79.1084	−	243.470i	0.0193136	−	0.0594410i
$257$	2433.22	−	4775.46i	0.590584	−	1.15909i	−0.381482	−	0.924376i	$-0.624586\pi$
$257$	2433.22	−	4775.46i	0.590584	−	1.15909i	0.972066	−	0.234709i	$-0.0754139\pi$
$258$	942.313	−	5949.53i	0.227387	−	1.43567i
$259$	269.731	−	195.971i	0.0647115	−	0.0470157i
$260$	−695.159	−	320.558i	−0.165815	−	0.0764621i
$261$	−11570.2	−	3759.39i	−2.74398	−	0.891572i
$262$	757.312	+	4781.48i	0.178576	+	1.12748i
$263$	−3424.90	−	3424.90i	−0.802997	−	0.802997i	0.180566	−	0.983563i	$-0.442207\pi$
$263$	−3424.90	−	3424.90i	−0.802997	−	0.802997i	−0.983563	+	0.180566i	$0.942207\pi$
$264$	2472.46	−	797.272i	0.576399	−	0.185866i
$265$	82.6491	−	89.3912i	0.0191588	−	0.0207217i
$266$	−40.3365	+	55.5184i	−0.00929770	+	0.0127972i
$267$	−304.824	+	155.316i	−0.0698686	+	0.0355999i
$268$	−1655.26	−	843.396i	−0.377280	−	0.192234i
$269$	4002.74	+	5509.30i	0.907255	+	1.24873i	0.968096	+	0.250581i	$0.0806218\pi$
$269$	4002.74	+	5509.30i	0.907255	+	1.24873i	−0.0608409	+	0.998147i	$0.519378\pi$
$270$	3942.99	−	3107.76i	0.888751	−	0.700489i
$271$	−7727.26	+	2510.74i	−1.73209	+	0.562791i	−0.993749	−	0.111633i	$-0.964392\pi$
$271$	−7727.26	+	2510.74i	−1.73209	+	0.562791i	−0.738344	+	0.674424i	$0.764392\pi$
$272$	58.4140	+	114.644i	0.0130216	+	0.0255563i
$273$	−145.255	+	23.0061i	−0.0322023	+	0.00510034i
$274$	−556.616			−0.122724
$275$	−2953.29	−	3474.90i	−0.647600	−	0.761980i
$276$	6006.03			1.30986
$277$	5605.55	−	887.832i	1.21590	−	0.192580i	0.484663	−	0.874701i	$-0.338942\pi$
$277$	5605.55	−	887.832i	1.21590	−	0.192580i	0.731239	+	0.682121i	$0.238942\pi$
$278$	−1228.41	−	2410.90i	−0.265019	−	0.520130i
$279$	−7994.61	+	2597.61i	−1.71550	+	0.557400i
$280$	−67.8062	+	53.4430i	−0.0144721	+	0.0114065i
$281$	1108.74	+	1526.06i	0.235381	+	0.323975i	0.910325	−	0.413895i	$-0.135832\pi$
$281$	1108.74	+	1526.06i	0.235381	+	0.323975i	−0.674943	+	0.737870i	$0.735832\pi$
$282$	−1017.25	−	518.316i	−0.214810	−	0.109451i
$283$	−85.8698	+	43.7528i	−0.0180368	+	0.00919023i	−0.462986	−	0.886366i	$-0.653222\pi$
$283$	−85.8698	+	43.7528i	−0.0180368	+	0.00919023i	0.444949	+	0.895556i	$0.353222\pi$
$284$	1993.35	−	2743.61i	0.416492	−	0.573252i
$285$	2401.49	−	2597.39i	0.499129	−	0.539846i
$286$	1186.98	+	388.597i	0.245412	+	0.0803435i
$287$	128.320	+	128.320i	0.0263919	+	0.0263919i
$288$	261.433	+	1650.62i	0.0534899	+	0.337722i
$289$	4611.04	+	1498.22i	0.938538	+	0.304949i
$290$	−4730.16	−	2181.21i	−0.957809	−	0.441673i
$291$	−4506.94	+	3274.48i	−0.907908	+	0.659634i
$292$	−429.691	+	2712.96i	−0.0861155	+	0.543712i
$293$	785.488	−	1541.61i	0.156617	−	0.307378i	−0.799343	−	0.600875i	$-0.794819\pi$
$293$	785.488	−	1541.61i	0.156617	−	0.307378i	0.955960	+	0.293497i	$0.0948191\pi$
$294$	1881.72	−	5791.35i	0.373280	−	1.14884i
$295$	3801.03	−	5687.40i	0.750185	−	1.12249i
$296$		−	2763.24i		−	0.542602i
$297$	−5804.96	+	5779.19i	−1.13414	+	1.12910i
$298$	1387.42	−	1387.42i	0.269701	−	0.269701i
$299$	2336.09	+	1697.27i	0.451838	+	0.328279i
$300$	3795.08	−	2324.57i	0.730363	−	0.447364i
$301$	−100.932	−	310.637i	−0.0193277	−	0.0594844i
$302$	1248.28	+	197.709i	0.237850	+	0.0376717i
$303$	−1737.56	−	275.203i	−0.329440	−	0.0521781i
$304$	175.755	+	540.917i	0.0331586	+	0.102052i
$305$	9972.82	+	2813.71i	1.87227	+	0.528239i
$306$	−679.541	−	493.715i	−0.126950	−	0.0922347i
$307$	−3126.24	+	3126.24i	−0.581186	+	0.581186i	−0.935229	−	0.354043i	$-0.884807\pi$
$307$	−3126.24	+	3126.24i	−0.581186	+	0.581186i	0.354043	+	0.935229i	$0.384807\pi$
$308$	99.8259	−	99.3826i	0.0184679	−	0.0183859i
$309$		−	8178.04i		−	1.50561i
$310$	−3530.05	+	701.800i	−0.646753	+	0.128579i
$311$	−87.3294	+	268.772i	−0.0159228	+	0.0490054i	−0.958702	−	0.284412i	$-0.908202\pi$
$311$	−87.3294	+	268.772i	−0.0159228	+	0.0490054i	0.942779	+	0.333417i	$0.108202\pi$
$312$	−553.354	+	1086.02i	−0.100409	+	0.197063i
$313$	494.583	−	3122.67i	0.0893146	−	0.563910i	−0.901931	−	0.431880i	$-0.857850\pi$
$313$	494.583	−	3122.67i	0.0893146	−	0.563910i	0.991246	−	0.132030i	$-0.0421496\pi$
$314$	−2813.14	+	2043.86i	−0.505588	+	0.367331i
$315$	236.012	−	511.814i	0.0422151	−	0.0915474i
$316$	4873.95	+	1583.64i	0.867661	+	0.281920i
$317$	−635.834	−	4014.50i	−0.112656	−	0.711283i	−0.977766	−	0.209700i	$-0.932751\pi$
$317$	−635.834	−	4014.50i	−0.112656	−	0.711283i	0.865110	−	0.501583i	$-0.167249\pi$
$318$	−137.069	−	137.069i	−0.0241712	−	0.0241712i
$319$	8076.75	+	2644.18i	1.41759	+	0.464093i
$320$	28.0198	+	714.993i	0.00489486	+	0.124904i
$321$	−7021.21	+	9663.87i	−1.22083	+	1.68033i
$322$	290.170	−	147.849i	0.0502191	−	0.0255879i
$323$	−254.704	−	129.778i	−0.0438765	−	0.0223562i
$324$	−1383.34	−	1904.01i	−0.237199	−	0.326476i
$325$	2133.03	+	168.307i	0.364059	+	0.0287261i
$326$	−6096.66	+	1980.92i	−1.03577	+	0.336544i
$327$	−6249.14	−	12264.6i	−1.05681	−	2.07411i
$328$	1485.50	−	235.281i	0.250071	−	0.0396073i
$329$	−61.9059			−0.0103738
$330$	−5712.74	+	4482.05i	−0.952958	+	0.747663i
$331$	6854.45			1.13823			0.569116	−	0.822257i	$-0.307286\pi$
$331$	6854.45			1.13823			0.569116	+	0.822257i	$0.307286\pi$
$332$	−1697.93	+	268.926i	−0.280681	+	0.0444555i
$333$	8189.43	+	16072.7i	1.34768	+	2.64497i
$334$	3442.27	−	1118.46i	0.563930	−	0.183232i
$335$	5156.49	+	610.839i	0.840982	+	0.0996229i
$336$	80.8006	+	111.212i	0.0131191	+	0.0180570i
$337$	1288.00	+	656.267i	0.208195	+	0.106081i	0.554979	−	0.831864i	$-0.312726\pi$
$337$	1288.00	+	656.267i	0.208195	+	0.106081i	−0.346784	+	0.937945i	$0.612726\pi$
$338$	3392.95	−	1728.79i	0.546012	−	0.278207i
$339$	6431.56	−	8852.28i	1.03043	−	1.41826i
$340$	−264.065	−	244.149i	−0.0421204	−	0.0389436i
$341$	5588.83	−	1802.18i	0.887544	−	0.286198i
$342$	−2625.41	−	2625.41i	−0.415105	−	0.415105i
$343$	−103.445	−	653.128i	−0.0162843	−	0.102815i
$344$	−2574.53	−	836.516i	−0.403516	−	0.131110i
$345$	−15750.4	+	5808.80i	−2.45789	+	0.906480i
$346$	3659.41	−	2658.72i	0.568588	−	0.413103i
$347$	929.286	−	5867.28i	0.143766	−	0.907701i	−0.805356	−	0.592791i	$-0.798026\pi$
$347$	929.286	−	5867.28i	0.143766	−	0.907701i	0.949122	−	0.314909i	$-0.101974\pi$
$348$	−3765.26	+	7389.73i	−0.579997	+	1.13831i
$349$	−2301.58	+	7083.53i	−0.353010	+	1.08645i	0.604144	+	0.796875i	$0.293515\pi$
$349$	−2301.58	+	7083.53i	−0.353010	+	1.08645i	−0.957154	+	0.289579i	$0.906485\pi$
$350$	126.128	−	205.730i	0.0192624	−	0.0314192i
$351$		−	3843.23i		−	0.584434i
$352$	−180.063	−	1153.48i	−0.0272653	−	0.174661i
$353$	1446.97	−	1446.97i	0.218171	−	0.218171i	−0.589556	−	0.807727i	$-0.700697\pi$
$353$	1446.97	−	1446.97i	0.218171	−	0.218171i	0.807727	+	0.589556i	$0.200697\pi$
$354$	−8811.71	−	6402.08i	−1.32299	−	0.961206i
$355$	−2573.89	+	9122.81i	−0.384811	+	1.36391i
$356$	47.5094	+	146.219i	0.00707302	+	0.0217685i
$357$	−68.2410	−	10.8083i	−0.0101168	−	0.00160234i
$358$	−3510.15	−	555.953i	−0.518205	−	0.0820756i
$359$	813.114	+	2502.51i	0.119539	+	0.367903i	0.992867	−	0.119230i	$-0.0380426\pi$
$359$	813.114	+	2502.51i	0.119539	+	0.367903i	−0.873328	+	0.487133i	$0.838043\pi$
$360$	−2282.01	−	4075.78i	−0.334090	−	0.596702i
$361$	4526.77	+	3288.89i	0.659976	+	0.479501i
$362$	3478.59	−	3478.59i	0.505057	−	0.505057i
$363$	8414.31	−	8339.74i	1.21663	−	1.20585i
$364$			66.0906i			0.00951673i
$365$	−1497.04	−	7530.10i	−0.214681	−	1.07985i
$366$	5098.45	−	15691.4i	0.728143	−	2.24099i
$367$	2417.44	−	4744.49i	0.343840	−	0.674824i	−0.652729	−	0.757591i	$-0.726376\pi$
$367$	2417.44	−	4744.49i	0.343840	−	0.674824i	0.996569	+	0.0827678i	$0.0263760\pi$
$368$	422.230	−	2665.86i	0.0598105	−	0.377629i
$369$	−7943.27	+	5771.12i	−1.12062	+	0.814181i
$370$	2672.50	+	7246.39i	0.375505	+	1.01817i
$371$	−9.99642	−	3.24803i	−0.00139889	−	0.000454527i
$372$	896.471	+	5660.10i	0.124946	+	0.788877i
$373$	1124.15	+	1124.15i	0.156049	+	0.156049i	0.780813	−	0.624764i	$-0.214805\pi$
$373$	1124.15	+	1124.15i	0.156049	+	0.156049i	−0.624764	+	0.780813i	$0.714805\pi$
$374$	473.939	+	345.951i	0.0655263	+	0.0478308i
$375$	−7704.06	+	9766.46i	−1.06090	+	1.34490i
$376$	−301.575	+	415.083i	−0.0413632	+	0.0569315i
$377$	−3552.82	+	1810.25i	−0.485356	+	0.247301i
$378$	−386.204	−	196.781i	−0.0525508	−	0.0267760i
$379$	−1243.84	−	1711.99i	−0.168579	−	0.232030i	0.716366	−	0.697725i	$-0.245804\pi$
$379$	−1243.84	−	1711.99i	−0.168579	−	0.232030i	−0.884945	+	0.465695i	$0.845804\pi$
$380$	−984.058	−	1248.53i	−0.132845	−	0.168548i
$381$	9973.75	−	3240.67i	1.34113	−	0.435760i
$382$	2700.42	+	5299.88i	0.361690	+	0.709857i
$383$	−452.988	+	71.7463i	−0.0604350	+	0.00957197i	−0.186579	−	0.982440i	$-0.559740\pi$
$383$	−452.988	+	71.7463i	−0.0604350	+	0.00957197i	0.126144	+	0.992012i	$0.459740\pi$
$384$	1139.31			0.151406
$385$	−165.667	+	357.171i	−0.0219303	+	0.0472808i
$386$	−9513.92			−1.25452
$387$	17454.2	−	2764.47i	2.29263	−	0.363116i
$388$	1136.58	+	2230.66i	0.148714	+	0.291868i
$389$	−6101.62	+	1982.54i	−0.795281	+	0.258403i	−0.678351	−	0.734738i	$-0.737305\pi$
$389$	−6101.62	+	1982.54i	−0.795281	+	0.258403i	−0.116930	+	0.993140i	$0.537305\pi$
$390$	400.772	−	3383.18i	0.0520356	−	0.439267i
$391$	797.380	+	1097.50i	0.103134	+	0.141951i
$392$	−2438.28	−	1242.37i	−0.314163	−	0.160074i
$393$	−19196.6	+	9781.15i	−2.46397	+	1.25545i
$394$	1109.99	−	1527.77i	0.141930	−	0.195350i
$395$	−14313.2	+	560.919i	−1.82323	+	0.0714503i
$396$	4465.93	+	6175.69i	0.566721	+	0.783687i
$397$	−4989.54	−	4989.54i	−0.630775	−	0.630775i	0.317487	−	0.948262i	$-0.397161\pi$
$397$	−4989.54	−	4989.54i	−0.630775	−	0.630775i	−0.948262	+	0.317487i	$0.897161\pi$
$398$	−157.183	−	992.413i	−0.0197961	−	0.124988i
$399$	−290.460	−	94.3762i	−0.0364441	−	0.0118414i
$400$	−764.994	−	1847.91i	−0.0956242	−	0.230989i
$401$	1851.42	−	1345.13i	0.230562	−	0.167513i	−0.466506	−	0.884518i	$-0.654488\pi$
$401$	1851.42	−	1345.13i	0.230562	−	0.167513i	0.697068	+	0.717005i	$0.254488\pi$
$402$	1293.36	−	8165.93i	0.160465	−	1.01313i
$403$	−1250.82	+	2454.87i	−0.154610	+	0.303439i
$404$	−244.305	+	751.892i	−0.0300857	+	0.0925941i
$405$	5469.20	+	3655.20i	0.671029	+	0.448465i
$406$			449.709i			0.0549721i
$407$	−5695.90	−	11240.6i	−0.693699	−	1.36898i
$408$	−404.908	+	404.908i	−0.0491321	+	0.0491321i
$409$	−8859.56	−	6436.85i	−1.07109	−	0.778194i	−0.0949844	−	0.995479i	$-0.530280\pi$
$409$	−8859.56	−	6436.85i	−1.07109	−	0.778194i	−0.976108	+	0.217284i	$0.930280\pi$
$410$	−3668.06	+	2053.73i	−0.441836	+	0.247381i
$411$	−765.489	−	2355.93i	−0.0918705	−	0.282748i
$412$	−3629.93	−	574.924i	−0.434063	−	0.0687488i
$413$	−583.319	−	92.3887i	−0.0694994	−	0.0110076i
$414$	5444.86	+	16757.6i	0.646378	+	1.98935i
$415$	4192.60	−	2347.41i	0.495920	−	0.277663i
$416$	443.142	+	321.961i	0.0522279	+	0.0379458i
$417$	8514.99	−	8514.99i	0.999954	−	0.999954i
$418$	1829.95	+	1838.12i	0.214129	+	0.215084i
$419$			14092.8i			1.64315i	0.570101	+	0.821575i	$0.306904\pi$
$419$			14092.8i			1.64315i	−0.570101	+	0.821575i	$0.693096\pi$
$420$	−319.454	−	213.499i	−0.0371137	−	0.0248040i
$421$	−3329.53	+	10247.2i	−0.385443	+	1.18627i	0.550716	+	0.834693i	$0.314355\pi$
$421$	−3329.53	+	10247.2i	−0.385443	+	1.18627i	−0.936159	+	0.351578i	$0.885645\pi$
$422$	−3161.60	+	6204.98i	−0.364702	+	0.715767i
$423$	523.959	−	3308.15i	0.0602264	−	0.380255i
$424$	−70.4760	+	51.2038i	−0.00807221	+	0.00586480i
$425$	928.622	+	384.868i	0.105988	+	0.0439266i
$426$	14354.0	+	4663.89i	1.63252	+	0.530437i
$427$	−139.950	−	883.608i	−0.0158610	−	0.100142i
$428$	3795.84	+	3795.84i	0.428689	+	0.428689i
$429$	−12.3696	+	5558.45i	−0.00139210	+	0.625559i
$430$	7560.55	−	296.290i	0.847912	−	0.0332288i
$431$	−5101.17	+	7021.16i	−0.570104	+	0.784681i	−0.992567	−	0.121699i	$-0.961166\pi$
$431$	−5101.17	+	7021.16i	−0.570104	+	0.784681i	0.422463	+	0.906380i	$0.361166\pi$
$432$	−3200.83	+	1630.90i	−0.356481	+	0.181636i
$433$	3489.72	+	1778.10i	0.387310	+	0.197344i	0.636793	−	0.771035i	$-0.280261\pi$
$433$	3489.72	+	1778.10i	0.387310	+	0.197344i	−0.249483	+	0.968379i	$0.580261\pi$
$434$	182.644	+	251.389i	0.0202010	+	0.0278042i
$435$	2727.03	−	23020.6i	0.300577	−	2.53736i
$436$	−5883.13	+	1911.55i	−0.646218	+	0.209969i
$437$	2722.38	+	5342.96i	0.298007	+	0.584871i
$438$	−12073.8	+	1912.30i	−1.31714	+	0.208615i
$439$	9102.45			0.989604			0.494802	−	0.869006i	$-0.335241\pi$
$439$	9102.45			0.989604			0.494802	+	0.869006i	$0.335241\pi$
$440$	1587.81	+	2850.77i	0.172036	+	0.308875i
$441$	17864.5			1.92900
$442$	−271.916	+	43.0673i	−0.0292618	+	0.00463462i
$443$	2612.04	+	5126.42i	0.280139	+	0.549805i	0.987608	−	0.156940i	$-0.0501630\pi$
$443$	2612.04	+	5126.42i	0.280139	+	0.549805i	−0.707469	+	0.706745i	$0.750163\pi$
$444$	11695.7	−	3800.16i	1.25012	−	0.406189i
$445$	−266.007	−	337.499i	−0.0283370	−	0.0359527i
$446$	293.606	+	404.114i	0.0311718	+	0.0429044i
$447$	7780.44	+	3964.33i	0.823271	+	0.419478i
$448$	55.0434	−	28.0460i	0.00580482	−	0.00295770i
$449$	2960.57	−	4074.88i	0.311176	−	0.428297i	−0.624571	−	0.780968i	$-0.714726\pi$
$449$	2960.57	−	4074.88i	0.311176	−	0.428297i	0.935748	+	0.352670i	$0.114726\pi$
$450$	9926.33	+	8481.35i	1.03985	+	0.888477i
$451$	5557.90	−	4019.19i	0.580291	−	0.419637i
$452$	−3477.06	−	3477.06i	−0.361829	−	0.361829i
$453$	879.887	+	5555.39i	0.0912599	+	0.576192i
$454$	3902.12	+	1267.87i	0.403382	+	0.131067i
$455$	−63.9203	−	173.317i	−0.00658600	−	0.0178577i
$456$	−2047.78	+	1487.80i	−0.210298	+	0.152791i
$457$	−1830.37	+	11556.5i	−0.187355	+	1.18291i	0.697340	+	0.716740i	$0.254367\pi$
$457$	−1830.37	+	11556.5i	−0.187355	+	1.18291i	−0.884695	+	0.466170i	$0.845633\pi$
$458$	3542.24	−	6952.03i	0.361393	−	0.709273i
$459$	557.948	−	1717.19i	0.0567381	−	0.174622i
$460$	1471.05	+	7399.36i	0.149104	+	0.749994i
$461$			4010.59i			0.405188i	0.979263	+	0.202594i	$0.0649372\pi$
$461$			4010.59i			0.405188i	−0.979263	+	0.202594i	$0.935063\pi$
$462$	557.933	+	285.847i	0.0561848	+	0.0287853i
$463$	−1443.73	+	1443.73i	−0.144915	+	0.144915i	−0.775842	−	0.630927i	$-0.782675\pi$
$463$	−1443.73	+	1443.73i	−0.144915	+	0.144915i	0.630927	+	0.775842i	$0.282675\pi$
$464$	3015.33	+	2190.76i	0.301688	+	0.219189i
$465$	−7825.16	−	13976.1i	−0.780393	−	1.39382i
$466$	398.115	+	1225.27i	0.0395758	+	0.121802i
$467$	−9793.22	−	1551.09i	−0.970399	−	0.153696i	−0.348942	−	0.937144i	$-0.613459\pi$
$467$	−9793.22	−	1551.09i	−0.970399	−	0.153696i	−0.621457	+	0.783448i	$0.713459\pi$
$468$	−3531.77	−	559.378i	−0.348838	−	0.0552506i
$469$	−138.533	−	426.360i	−0.0136393	−	0.0419775i
$470$	389.406	−	1380.19i	0.0382169	−	0.135455i
$471$	−12519.6	−	9096.06i	−1.22479	−	0.889860i
$472$	−3461.12	+	3461.12i	−0.337523	+	0.337523i
$473$	−12197.3	+	1904.04i	−1.18569	+	0.185091i
$474$			22807.4i			2.21008i
$475$	3788.15	+	2322.43i	0.365920	+	0.224338i
$476$	−9.59483	+	29.5298i	−0.000923904	+	0.00284348i
$477$	258.177	−	506.702i	0.0247822	−	0.0486379i
$478$	−752.473	+	4750.93i	−0.0720028	+	0.454608i
$479$	−4430.07	+	3218.63i	−0.422578	+	0.307021i	−0.778674	−	0.627428i	$-0.784108\pi$
$479$	−4430.07	+	3218.63i	−0.422578	+	0.307021i	0.356096	+	0.934449i	$0.384108\pi$
$480$	−2987.75	+	1101.89i	−0.284107	+	0.104780i
$481$	5623.03	+	1827.03i	0.533031	+	0.173192i
$482$	−1302.12	−	8221.26i	−0.123050	−	0.776905i
$483$	1024.84	+	1024.84i	0.0965466	+	0.0965466i
$484$	−3110.17	−	4321.09i	−0.292089	−	0.405813i
$485$	−5138.00	−	4750.48i	−0.481040	−	0.444759i
$486$	−969.995	+	1335.08i	−0.0905347	+	0.124610i
$487$	−15287.2	+	7789.20i	−1.42244	+	0.724769i	−0.984688	−	0.174328i	$-0.944225\pi$
$487$	−15287.2	+	7789.20i	−1.42244	+	0.724769i	−0.437751	+	0.899096i	$0.644225\pi$
$488$	−6606.41	−	3366.14i	−0.612824	−	0.312250i
$489$	−16768.9	−	23080.4i	−1.55075	−	2.13442i
$490$	7595.77	+	899.797i	0.700290	+	0.0829565i
$491$	8638.91	−	2806.95i	0.794030	−	0.257996i	0.116211	−	0.993225i	$-0.462925\pi$
$491$	8638.91	−	2806.95i	0.794030	−	0.257996i	0.677819	+	0.735229i	$0.262925\pi$
$492$	3038.80	+	5963.97i	0.278454	+	0.546497i
$493$	−1850.23	+	293.048i	−0.169027	+	0.0267713i
$494$	−1216.94			−0.110836
$495$	−17684.5	−	11876.0i	−1.60577	−	1.07835i
$496$	2575.33			0.233137
$497$	808.295	−	128.021i	0.0729517	−	0.0115544i
$498$	−3473.35	−	6816.83i	−0.312539	−	0.613392i
$499$	−2069.29	+	672.354i	−0.185640	+	0.0603180i	−0.400362	−	0.916357i	$-0.631116\pi$
$499$	−2069.29	+	672.354i	−0.185640	+	0.0603180i	0.214722	+	0.976675i	$0.431116\pi$
$500$	3793.37	+	4106.14i	0.339289	+	0.367264i
$501$	9468.00	+	13031.6i	0.844309	+	1.16209i
$502$	−1795.21	−	914.706i	−0.159610	−	0.0813254i
$503$	−1724.84	+	878.852i	−0.152897	+	0.0779047i	−0.528765	−	0.848768i	$-0.677345\pi$
$503$	−1724.84	+	878.852i	−0.152897	+	0.0779047i	0.375868	+	0.926673i	$0.377345\pi$
$504$	−237.045	+	326.265i	−0.0209501	+	0.0288353i
$505$	−86.5315	−	2208.06i	−0.00762496	−	0.194569i
$506$	−3777.57	−	11714.8i	−0.331884	−	1.02922i
$507$	11983.5	+	11983.5i	1.04971	+	1.04971i
$508$	−737.248	−	4654.80i	−0.0643899	−	0.406542i
$509$	−7406.90	−	2406.65i	−0.645000	−	0.209573i	−0.0317918	−	0.999495i	$-0.510121\pi$
$509$	−7406.90	−	2406.65i	−0.645000	−	0.209573i	−0.613208	+	0.789921i	$0.710121\pi$
$510$	670.228	−	1453.45i	0.0581925	−	0.126196i
$511$	−536.248	+	389.607i	−0.0464231	+	0.0337284i
$512$	80.0944	−	505.696i	0.00691349	−	0.0436501i
$513$	3623.37	−	7111.26i	0.311843	−	0.612027i
$514$	3312.43	−	10194.6i	0.284251	−	0.874835i
$515$	10075.3	−	2003.03i	0.862075	−	0.171387i
$516$		−	12047.4i		−	1.02782i
$517$	−371.165	+	2310.16i	−0.0315741	+	0.196520i
$518$	471.508	−	471.508i	0.0399939	−	0.0399939i
$519$	16285.9	+	11832.4i	1.37740	+	1.00074i
$520$	−1473.49	−	415.729i	−0.124263	−	0.0350595i
$521$	−6569.23	−	20218.0i	−0.552405	−	1.70013i	−0.702699	−	0.711487i	$-0.748022\pi$
$521$	−6569.23	−	20218.0i	−0.552405	−	1.70013i	0.150294	−	0.988641i	$-0.451978\pi$
$522$	−24031.7	−	3806.25i	−2.01502	−	0.319147i
$523$	2837.58	+	449.428i	0.237244	+	0.0375757i	0.273924	−	0.961751i	$-0.411678\pi$
$523$	2837.58	+	449.428i	0.237244	+	0.0375757i	−0.0366802	+	0.999327i	$0.511678\pi$
$524$	2991.95	+	9208.28i	0.249435	+	0.767682i
$525$	1044.23	+	250.921i	0.0868075	+	0.0208592i
$526$	−7837.01	−	5693.92i	−0.649638	−	0.471990i
$527$	−915.267	+	915.267i	−0.0756540	+	0.0756540i
$528$	4634.60	−	2348.47i	0.381998	−	0.193568i
$529$		−	16290.3i		−	1.33889i
$530$	135.295	−	202.440i	0.0110884	−	0.0165913i
$531$	9874.20	−	30389.7i	0.806975	−	2.48361i
$532$	−62.3098	+	122.290i	−0.00507795	+	0.00996604i
$533$	−503.421	+	3178.47i	−0.0409110	+	0.258302i
$534$	−553.549	+	402.177i	−0.0448584	+	0.0325916i
$535$	−13625.5	−	6283.10i	−1.10109	−	0.507742i
$536$	−3533.63	−	1148.15i	−0.284757	−	0.0925231i
$537$	−2474.23	−	15621.6i	−0.198828	−	1.25535i
$538$	9630.61	+	9630.61i	0.771757	+	0.771757i
$539$	−12479.6	−	27.7718i	−0.997281	−	0.00221933i
$540$	6816.57	−	7372.63i	0.543219	−	0.587532i
$541$	−3409.82	+	4693.21i	−0.270979	+	0.372970i	−0.922720	−	0.385471i	$-0.874039\pi$
$541$	−3409.82	+	4693.21i	−0.270979	+	0.372970i	0.651741	+	0.758442i	$0.274039\pi$
$542$	−14478.7	+	7377.27i	−1.14744	+	0.584651i
$543$	19507.4	+	9939.53i	1.54170	+	0.785536i
$544$	151.258	+	208.189i	0.0119212	+	0.0164081i
$545$	13579.3	−	10702.8i	1.06729	−	0.841208i
$546$	−279.735	+	90.8915i	−0.0219259	+	0.00712417i
$547$	11088.0	+	21761.5i	0.866709	+	1.70101i	0.698934	+	0.715187i	$0.253658\pi$
$547$	11088.0	+	21761.5i	0.866709	+	1.70101i	0.167775	+	0.985825i	$0.446342\pi$
$548$	−1099.53	+	174.148i	−0.0857106	+	0.0135752i
$549$	48403.1			3.76283
$550$	−6921.05	−	5940.25i	−0.536572	−	0.460533i
$551$	−8280.59			−0.640227
$552$	11864.2	−	1879.10i	0.914806	−	0.144891i
$553$	561.444	+	1101.89i	0.0431736	+	0.0847330i
$554$	10795.3	−	3507.61i	0.827885	−	0.268996i
$555$	−26995.7	+	21277.3i	−2.06469	+	1.62733i
$556$	−3180.88	−	4378.10i	−0.242624	−	0.333944i
$557$	3096.91	+	1577.95i	0.235584	+	0.120036i	0.567798	−	0.823168i	$-0.307796\pi$
$557$	3096.91	+	1577.95i	0.235584	+	0.120036i	−0.332214	+	0.943204i	$0.607796\pi$
$558$	−14979.7	+	7632.52i	−1.13645	+	0.579051i
$559$	3404.52	−	4685.92i	0.257595	−	0.354549i
$560$	−117.222	+	126.784i	−0.00884560	+	0.00956718i
$561$	−812.485	+	2481.77i	−0.0611465	+	0.186774i
$562$	2667.64	+	2667.64i	0.200227	+	0.200227i
$563$	−981.315	−	6195.78i	−0.0734591	−	0.463803i	−0.996808	−	0.0798398i	$-0.974559\pi$
$563$	−981.315	−	6195.78i	−0.0734591	−	0.463803i	0.923349	−	0.383963i	$-0.125441\pi$
$564$	−2171.62	−	705.603i	−0.162131	−	0.0526795i
$565$	12481.2	+	5755.43i	0.929358	+	0.428554i
$566$	−155.936	+	113.294i	−0.0115804	+	0.00841363i
$567$	88.8441	−	560.940i	0.00658043	−	0.0415472i
$568$	3079.23	−	6043.33i	0.227468	−	0.446430i
$569$	−5114.19	+	15739.9i	−0.376798	+	1.15966i	0.565460	+	0.824776i	$0.308699\pi$
$569$	−5114.19	+	15739.9i	−0.376798	+	1.15966i	−0.942258	+	0.334889i	$0.891301\pi$
$570$	3931.20	−	5882.17i	0.288877	−	0.432240i
$571$			15650.9i			1.14706i	0.819185	+	0.573529i	$0.194426\pi$
$571$			15650.9i			1.14706i	−0.819185	+	0.573529i	$0.805574\pi$
$572$	2466.32	+	396.255i	0.180283	+	0.0289655i
$573$	−18718.5	+	18718.5i	−1.36471	+	1.36471i
$574$	293.627	+	213.333i	0.0213515	+	0.0155128i
$575$	−11014.1	−	17981.5i	−0.798816	−	1.30414i
$576$	1032.86	+	3178.81i	0.0747148	+	0.229948i
$577$	20163.0	+	3193.50i	1.45476	+	0.230411i	0.833206	−	0.552962i	$-0.186503\pi$
$577$	20163.0	+	3193.50i	1.45476	+	0.230411i	0.621552	+	0.783373i	$0.286503\pi$
$578$	9577.28	+	1516.89i	0.689208	+	0.109160i
$579$	−13084.1	−	40268.6i	−0.939129	−	2.89034i
$580$	−10026.3	−	2828.80i	−0.717791	−	0.202516i
$581$	−335.616	−	243.839i	−0.0239651	−	0.0174116i
$582$	−7878.42	+	7878.42i	−0.561118	+	0.561118i
$583$	−181.143	+	353.565i	−0.0128682	+	0.0251169i
$584$			5493.55i			0.389255i
$585$	9802.81	−	1948.87i	0.692814	−	0.137737i
$586$	1069.31	−	3291.01i	0.0753805	−	0.231997i
$587$	6461.32	−	12681.0i	0.454322	−	0.891657i	−0.544285	−	0.838900i	$-0.683199\pi$
$587$	6461.32	−	12681.0i	0.454322	−	0.891657i	0.998607	−	0.0527571i	$-0.0168009\pi$
$588$	1905.18	−	12028.8i	0.133620	−	0.843641i
$589$	−4628.87	+	3363.07i	−0.323819	+	0.235268i
$590$	5729.05	−	12424.0i	0.399765	−	0.866927i
$591$	7992.97	+	2597.07i	0.556323	+	0.180760i
$592$	−864.533	−	5458.44i	−0.0600204	−	0.378954i
$593$	4221.97	+	4221.97i	0.292370	+	0.292370i	0.838016	−	0.545646i	$-0.183716\pi$
$593$	4221.97	+	4221.97i	0.292370	+	0.292370i	−0.545646	+	0.838016i	$0.683716\pi$
$594$	−9658.86	+	13232.3i	−0.667185	+	0.914017i
$595$	−3.39844	−	86.7194i	−0.000234156	−	0.00597504i
$596$	2306.59	−	3174.75i	0.158526	−	0.218193i
$597$	3984.32	−	2030.11i	0.273145	−	0.139174i
$598$	5145.68	+	2621.85i	0.351877	+	0.179290i
$599$	8615.75	+	11858.6i	0.587696	+	0.808894i	0.994513	−	0.104616i	$-0.0333612\pi$
$599$	8615.75	+	11858.6i	0.587696	+	0.808894i	−0.406817	+	0.913510i	$0.633361\pi$
$600$	6769.42	−	5779.27i	0.460601	−	0.393229i
$601$	20035.6	−	6509.95i	1.35985	−	0.441841i	0.463854	−	0.885911i	$-0.346466\pi$
$601$	20035.6	−	6509.95i	1.35985	−	0.441841i	0.895992	+	0.444071i	$0.146466\pi$
$602$	−296.567	−	582.046i	−0.0200784	−	0.0394060i
$603$	23956.5	−	3794.33i	1.61788	−	0.256247i
$604$	2527.69			0.170282
$605$	12335.4	+	8323.69i	0.828932	+	0.559349i
$606$	−3518.44			−0.235853
$607$	−26659.6	+	4222.46i	−1.78267	+	0.282347i	−0.958726	−	0.284331i	$-0.908229\pi$
$607$	−26659.6	+	4222.46i	−1.78267	+	0.282347i	−0.823940	+	0.566678i	$0.808229\pi$
$608$	516.418	+	1013.53i	0.0344466	+	0.0676052i
$609$	−1903.44	+	618.464i	−0.126652	+	0.0411518i
$610$	20580.4	+	2437.96i	1.36603	+	0.161820i
$611$	−645.269	−	888.137i	−0.0427247	−	0.0588055i
$612$	−1496.82	−	762.667i	−0.0988648	−	0.0503741i
$613$	−15195.2	+	7742.33i	−1.00119	+	0.510130i	−0.876159	−	0.482023i	$-0.839902\pi$
$613$	−15195.2	+	7742.33i	−1.00119	+	0.510130i	−0.125028	+	0.992153i	$0.539902\pi$
$614$	−5197.41	+	7153.61i	−0.341613	+	0.470190i
$615$	−13737.1	−	12701.0i	−0.900706	−	0.832773i
$616$	166.100	−	227.550i	0.0108642	−	0.0148835i
$617$	−9731.53	−	9731.53i	−0.634970	−	0.634970i	0.314340	−	0.949310i	$-0.398217\pi$
$617$	−9731.53	−	9731.53i	−0.634970	−	0.634970i	−0.949310	+	0.314340i	$0.898217\pi$
$618$	−2558.65	−	16154.7i	−0.166544	−	1.05152i
$619$	1185.61	+	385.229i	0.0769851	+	0.0250140i	0.347256	−	0.937770i	$-0.387113\pi$
$619$	1185.61	+	385.229i	0.0769851	+	0.0250140i	−0.270271	+	0.962784i	$0.587113\pi$
$620$	−6753.61	+	2490.76i	−0.437470	+	0.161341i
$621$	−30641.9	+	22262.6i	−1.98006	+	1.43860i
$622$	−88.4180	+	558.249i	−0.00569974	+	0.0359867i
$623$	−16.8434	+	33.0570i	−0.00108317	+	0.00212584i
$624$	−753.301	+	2318.42i	−0.0483272	+	0.148736i
$625$	−13919.1	−	7099.23i	−0.890823	−	0.454350i
$626$		−	6323.19i		−	0.403715i
$627$	−5263.36	+	10273.3i	−0.335244	+	0.654350i
$628$	−4917.55	+	4917.55i	−0.312471	+	0.312471i
$629$	2247.17	+	1632.67i	0.142449	+	0.103496i
$630$	306.082	−	1084.87i	0.0193565	−	0.0686065i
$631$	93.6225	+	288.141i	0.00590658	+	0.0181786i	0.953966	−	0.299914i	$-0.0969578\pi$
$631$	93.6225	+	288.141i	0.00590658	+	0.0181786i	−0.948060	+	0.318092i	$0.896958\pi$
$632$	10123.4	+	1603.38i	0.637161	+	0.100916i
$633$	−30611.2	−	4848.34i	−1.92210	−	0.304430i
$634$	−2512.02	−	7731.22i	−0.157358	−	0.484299i
$635$	6435.32	+	11493.8i	0.402170	+	0.718296i
$636$	−313.648	−	227.878i	−0.0195549	−	0.0142075i
$637$	4140.31	−	4140.31i	0.257528	−	0.257528i
$638$	16781.9	+	2696.29i	1.04138	+	0.167315i
$639$			44277.5i			2.74114i
$640$	279.049	+	1403.61i	0.0172350	+	0.0866917i
$641$	111.404	−	342.868i	0.00686461	−	0.0211271i	−0.947566	−	0.319561i	$-0.896464\pi$
$641$	111.404	−	342.868i	0.00686461	−	0.0211271i	0.954430	+	0.298434i	$0.0964644\pi$
$642$	−10846.0	+	21286.5i	−0.666757	+	1.30858i
$643$	2538.93	−	16030.2i	0.155717	−	0.983156i	−0.778809	−	0.627261i	$-0.784176\pi$
$643$	2538.93	−	16030.2i	0.155717	−	0.983156i	0.934526	−	0.355895i	$-0.115824\pi$
$644$	526.938	−	382.843i	0.0322426	−	0.0234256i
$645$	11651.8	+	31593.3i	0.711299	+	1.92866i
$646$	−543.739	−	176.672i	−0.0331163	−	0.0107601i
$647$	827.345	+	5223.65i	0.0502725	+	0.317408i	0.999991	+	0.00430219i	$0.00136943\pi$
$647$	827.345	+	5223.65i	0.0502725	+	0.317408i	−0.949718	+	0.313106i	$0.898631\pi$
$648$	−3328.33	−	3328.33i	−0.201773	−	0.201773i
$649$	−6945.06	+	21214.0i	−0.420058	+	1.28308i
$650$	4266.20	−	334.890i	0.257437	−	0.0202084i
$651$	−812.845	+	1118.78i	−0.0489368	+	0.0673558i
$652$	−11423.4	+	5820.52i	−0.686159	+	0.349615i
$653$	15847.4	+	8074.63i	0.949701	+	0.483897i	0.858997	−	0.511981i	$-0.171088\pi$
$653$	15847.4	+	8074.63i	0.949701	+	0.483897i	0.0907043	+	0.995878i	$0.471088\pi$
$654$	−16181.6	−	22272.1i	−0.967510	−	1.33166i
$655$	−16752.1	−	21254.3i	−0.999323	−	1.26790i
$656$	2860.82	−	929.536i	0.170268	−	0.0553236i
$657$	−16281.3	−	31953.8i	−0.966808	−	1.89747i
$658$	−122.287	+	19.3684i	−0.00724508	+	0.00114751i
$659$	−16699.2			−0.987112			−0.493556	−	0.869714i	$-0.664303\pi$
$659$	−16699.2			−0.987112			−0.493556	+	0.869714i	$0.664303\pi$
$660$	−9882.52	+	10641.1i	−0.582843	+	0.627581i
$661$	14106.9			0.830098			0.415049	−	0.909799i	$-0.363764\pi$
$661$	14106.9			0.830098			0.415049	+	0.909799i	$0.363764\pi$
$662$	13540.1	−	2144.55i	0.794942	−	0.125907i
$663$	−556.241	−	1091.68i	−0.0325831	−	0.0639479i
$664$	−3269.92	+	1062.46i	−0.191111	+	0.0620956i
$665$	45.1285	−	380.959i	0.00263159	−	0.0222150i
$666$	21205.8	+	29187.3i	1.23380	+	1.69818i
$667$	35013.4	+	17840.2i	2.03257	+	1.03565i
$668$	6449.85	−	3286.36i	0.373581	−	0.190349i
$669$	−1306.67	+	1798.48i	−0.0755138	+	0.103936i
$670$	10377.1	−	406.668i	0.598363	−	0.0234492i
$671$	−33812.9	−	75.2465i	−1.94536	−	0.00432915i
$672$	194.406	+	194.406i	0.0111598	+	0.0111598i
$673$	−2555.95	−	16137.7i	−0.146396	−	0.924310i	−0.946090	−	0.323903i	$-0.895005\pi$
$673$	−2555.95	−	16137.7i	−0.146396	−	0.924310i	0.799694	−	0.600408i	$-0.204995\pi$
$674$	2749.60	+	893.400i	0.157138	+	0.0510571i
$675$	−10745.4	+	25926.9i	−0.612727	+	1.47841i
$676$	6161.47	−	4476.57i	0.350561	−	0.254698i
$677$	2743.43	−	17321.3i	0.155744	−	0.983328i	−0.778746	−	0.627339i	$-0.784144\pi$
$677$	2743.43	−	17321.3i	0.155744	−	0.983328i	0.934490	−	0.355989i	$-0.115856\pi$
$678$	9935.15	−	19498.8i	0.562768	−	1.10450i
$679$	−186.690	+	574.571i	−0.0105515	+	0.0324743i
$680$	−598.015	−	399.668i	−0.0337247	−	0.0225391i
$681$			18259.7i			1.02748i
$682$	10476.2	−	5308.56i	0.588203	−	0.298058i
$683$	−11735.7	+	11735.7i	−0.657472	+	0.657472i	−0.954781	−	0.297309i	$-0.903911\pi$
$683$	−11735.7	+	11735.7i	−0.657472	+	0.657472i	0.297309	+	0.954781i	$0.403911\pi$
$684$	−6007.59	−	4364.77i	−0.335827	−	0.243993i
$685$	2714.99	−	1520.11i	0.151437	−	0.0847888i
$686$	−408.687	−	1257.81i	−0.0227460	−	0.0700050i
$687$	34296.6	+	5432.05i	1.90466	+	0.301668i
$688$	−5347.39	−	846.943i	−0.296319	−	0.0469323i
$689$	−57.5985	−	177.270i	−0.00318480	−	0.00980180i
$690$	−29295.5	+	16402.4i	−1.61632	+	0.904968i
$691$	69.5262	+	50.5137i	0.00382764	+	0.00278094i	0.589697	−	0.807624i	$-0.299247\pi$
$691$	69.5262	+	50.5137i	0.00382764	+	0.00278094i	−0.585870	+	0.810405i	$0.699247\pi$
$692$	6396.89	−	6396.89i	0.351407	−	0.351407i
$693$	−291.745	+	1815.84i	−0.0159920	+	0.0995354i
$694$		−	11880.8i		−	0.649842i
$695$	12575.9	+	8404.81i	0.686377	+	0.458723i
$696$	−5125.78	+	15775.5i	−0.279155	+	0.859152i
$697$	−686.373	+	1347.08i	−0.0373002	+	0.0732058i
$698$	−2330.27	+	14712.7i	−0.126364	+	0.797830i
$699$	−4638.58	+	3370.12i	−0.250997	+	0.182360i
$700$	184.785	−	445.855i	0.00997744	−	0.0240739i
$701$	32554.7	+	10577.7i	1.75403	+	0.569918i	0.996554	−	0.0829473i	$-0.0264333\pi$
$701$	32554.7	+	10577.7i	1.75403	+	0.569918i	0.757474	+	0.652865i	$0.226433\pi$
$702$	−1202.43	−	7591.82i	−0.0646477	−	0.408169i
$703$	8681.97	+	8681.97i	0.465785	+	0.465785i
$704$	−716.581	−	2222.23i	−0.0383625	−	0.118968i
$705$	6377.34	−	249.921i	0.340688	−	0.0133512i
$706$	2405.59	−	3311.02i	0.128238	−	0.176504i
$707$	−169.987	+	86.6125i	−0.00904244	+	0.00460735i
$708$	−19409.5	−	9889.61i	−1.03030	−	0.524964i
$709$	−13315.0	−	18326.5i	−0.705296	−	0.970757i	−0.999885	−	0.0151332i	$-0.995183\pi$
$709$	−13315.0	−	18326.5i	−0.705296	−	0.970757i	0.294589	−	0.955624i	$-0.404817\pi$
$710$	−2230.16	+	18826.3i	−0.117882	+	0.995123i
$711$	−63635.4	+	20676.4i	−3.35656	+	1.09061i
$712$	139.596	+	273.973i	0.00734775	+	0.0144208i
$713$	26818.2	−	4247.59i	1.40863	−	0.223104i
$714$	−138.183			−0.00724283
$715$	−6850.98	+	1346.18i	−0.358339	+	0.0704118i
$716$	−7107.81			−0.370994
$717$	−21143.6	+	3348.82i	−1.10129	+	0.174427i
$718$	2389.16	+	4689.00i	0.124182	+	0.243721i
$719$	−20569.9	+	6683.55i	−1.06693	+	0.346668i	−0.789293	−	0.614016i	$-0.789553\pi$
$719$	−20569.9	+	6683.55i	−1.06693	+	0.346668i	−0.277642	+	0.960685i	$0.589553\pi$
$720$	−5783.01	−	7337.24i	−0.299333	−	0.379781i
$721$	−521.293	−	717.498i	−0.0269264	−	0.0370611i
$722$	9971.08	+	5080.52i	0.513968	+	0.261880i
$723$	33006.6	−	16817.7i	1.69783	−	0.865085i
$724$	5783.18	−	7959.86i	0.296865	−	0.408599i
$725$	29029.0	−	2278.73i	1.48705	−	0.116731i
$726$	14012.2	−	19106.7i	0.716310	−	0.976744i
$727$	8034.09	+	8034.09i	0.409860	+	0.409860i	0.881690	−	0.471830i	$-0.156406\pi$
$727$	8034.09	+	8034.09i	0.409860	+	0.409860i	−0.471830	+	0.881690i	$0.656406\pi$
$728$	20.6777	+	130.554i	0.00105270	+	0.00664649i
$729$	−22093.4	−	7178.57i	−1.12246	−	0.364709i
$730$	−5313.15	−	14406.4i	−0.269382	−	0.730418i
$731$	2201.45	−	1599.45i	0.111387	−	0.0809272i
$732$	5162.00	−	32591.6i	0.260646	−	1.64566i
$733$	−8545.91	+	16772.3i	−0.430628	+	0.845156i	0.569110	+	0.822262i	$0.307288\pi$
$733$	−8545.91	+	16772.3i	−0.430628	+	0.845156i	−0.999738	+	0.0228940i	$0.992712\pi$
$734$	3290.95	−	10128.5i	0.165492	−	0.509332i
$735$	6637.64	+	33387.3i	0.333106	+	1.67552i
$736$		−	5398.17i		−	0.270352i
$737$	−16741.2	+	2613.36i	−0.836729	+	0.130617i
$738$	−13885.3	+	13885.3i	−0.692584	+	0.692584i
$739$	13968.9	+	10149.0i	0.695336	+	0.505191i	0.878410	−	0.477908i	$-0.158605\pi$
$739$	13968.9	+	10149.0i	0.695336	+	0.505191i	−0.183074	+	0.983099i	$0.558605\pi$
$740$	7546.37	+	13478.2i	0.374878	+	0.669552i
$741$	−1673.61	−	5150.83i	−0.0829709	−	0.255358i
$742$	−20.7629	−	3.28852i	−0.00102726	−	0.000162703i
$743$	27865.2	+	4413.41i	1.37587	+	0.217917i	0.800185	−	0.599753i	$-0.204734\pi$
$743$	27865.2	+	4413.41i	1.37587	+	0.217917i	0.575687	+	0.817670i	$0.304734\pi$
$744$	3541.74	+	10900.3i	0.174525	+	0.537132i
$745$	−2978.36	+	10556.4i	−0.146468	+	0.519136i
$746$	2572.33	+	1868.91i	0.126246	+	0.0917234i
$747$	15871.0	−	15871.0i	0.777361	−	0.777361i
$748$	1044.45	+	535.103i	0.0510545	+	0.0261568i
$749$			1295.41i			0.0631953i
$750$	−12162.8	+	21702.8i	−0.592163	+	1.05663i
$751$	2715.09	−	8356.18i	0.131924	−	0.406021i	−0.863175	−	0.504905i	$-0.831527\pi$
$751$	2715.09	−	8356.18i	0.131924	−	0.406021i	0.995099	+	0.0988846i	$0.0315275\pi$
$752$	−465.858	+	914.298i	−0.0225906	+	0.0443365i
$753$	1402.71	−	8856.37i	0.0678853	−	0.428611i
$754$	−6451.78	+	4687.49i	−0.311618	+	0.226404i
$755$	−6628.67	+	2444.68i	−0.319526	+	0.117843i
$756$	−824.465	−	267.885i	−0.0396634	−	0.0128874i
$757$	−5096.88	−	32180.4i	−0.244715	−	1.54507i	−0.737759	−	0.675064i	$-0.764116\pi$
$757$	−5096.88	−	32180.4i	−0.244715	−	1.54507i	0.493044	−	0.870004i	$-0.335884\pi$
$758$	−2992.68	−	2992.68i	−0.143402	−	0.143402i
$759$	44389.0	−	32099.8i	2.12282	−	1.53511i
$760$	−2334.51	−	2158.44i	−0.111423	−	0.103019i
$761$	−772.061	+	1062.65i	−0.0367769	+	0.0506190i	−0.827009	−	0.562188i	$-0.809960\pi$
$761$	−772.061	+	1062.65i	−0.0367769	+	0.0506190i	0.790233	+	0.612807i	$0.209960\pi$
$762$	18688.0	−	9522.01i	0.888445	−	0.452685i
$763$	−1330.05	−	677.694i	−0.0631075	−	0.0321549i
$764$	6992.52	+	9624.38i	0.331126	+	0.455756i
$765$	4662.91	+	552.369i	0.220376	+	0.0261058i
$766$	−872.375	+	283.452i	−0.0411491	+	0.0133701i
$767$	−4754.70	−	9331.63i	−0.223836	−	0.439303i
$768$	2250.56	−	356.454i	0.105742	−	0.0167479i
$769$	−10531.6			−0.493860			−0.246930	−	0.969033i	$-0.579422\pi$
$769$	−10531.6			−0.493860			−0.246930	+	0.969033i	$0.579422\pi$
$770$	−215.506	+	757.379i	−0.0100861	+	0.0354468i
$771$	47705.2			2.22835
$772$	−18793.6	+	2976.61i	−0.876160	+	0.138770i
$773$	4672.81	+	9170.91i	0.217425	+	0.426720i	0.973796	−	0.227422i	$-0.0730297\pi$
$773$	4672.81	+	9170.91i	0.217425	+	0.426720i	−0.756372	+	0.654142i	$0.773030\pi$
$774$	33613.7	−	10921.7i	1.56101	−	0.507202i
$775$	15301.8	−	13063.7i	0.709236	−	0.605497i
$776$	2943.08	+	4050.80i	0.136147	+	0.187391i
$777$	2644.15	+	1347.26i	0.122083	+	0.0622042i
$778$	−11432.7	+	5825.26i	−0.526842	+	0.268439i
$779$	−3928.14	+	5406.62i	−0.180668	+	0.248668i
$780$	−266.816	−	6808.44i	−0.0122481	−	0.312540i
$781$	68.8330	−	30930.9i	0.00315370	−	1.41715i
$782$	1918.50	+	1918.50i	0.0877307	+	0.0877307i
$783$	−8181.83	−	51658.0i	−0.373429	−	2.35774i
$784$	−5205.22	−	1691.28i	−0.237118	−	0.0770444i
$785$	8139.82	−	17651.9i	0.370093	−	0.802580i
$786$	−34860.3	+	25327.5i	−1.58197	+	1.14936i
$787$	4223.79	−	26668.0i	0.191311	−	1.20789i	−0.685867	−	0.727727i	$-0.740577\pi$
$787$	4223.79	−	26668.0i	0.191311	−	1.20789i	0.877178	−	0.480165i	$-0.159423\pi$
$788$	1714.66	−	3365.21i	0.0775154	−	0.152133i
$789$	13322.2	−	41001.5i	0.601119	−	1.85005i
$790$	−28098.4	+	5586.18i	−1.26544	+	0.251579i
$791$		−	1186.62i		−	0.0533392i
$792$	10754.1	+	10802.1i	0.482487	+	0.484639i
$793$	11218.0	−	11218.0i	0.502348	−	0.502348i
$794$	−11417.3	−	8295.14i	−0.510308	−	0.370760i
$795$	1042.91	+	294.245i	0.0465261	+	0.0131268i
$796$	−620.990	−	1911.21i	−0.0276513	−	0.0851019i
$797$	−7799.37	−	1235.30i	−0.346635	−	0.0549016i	−0.0193103	−	0.999814i	$-0.506147\pi$
$797$	−7799.37	−	1235.30i	−0.346635	−	0.0549016i	−0.327325	+	0.944912i	$0.606147\pi$
$798$	−603.296	−	95.5527i	−0.0267625	−	0.00423876i
$799$	−159.375	−	490.505i	−0.00705666	−	0.0217182i
$800$	−2089.31	−	3410.98i	−0.0923351	−	0.150746i
$801$	−1623.95	−	1179.87i	−0.0716348	−	0.0520457i
$802$	3236.39	−	3236.39i	0.142495	−	0.142495i
$803$	11323.9	+	22347.3i	0.497650	+	0.982089i
$804$		−	16535.4i		−	0.725324i
$805$	−1011.58	+	1513.61i	−0.0442902	+	0.0662704i
$806$	−1702.79	+	5240.64i	−0.0744146	+	0.229024i
$807$	−27518.0	+	54007.1i	−1.20035	+	2.35581i
$808$	−247.350	+	1561.71i	−0.0107695	+	0.0679958i
$809$	−12513.6	+	9091.67i	−0.543826	+	0.395112i	−0.825504	−	0.564397i	$-0.809109\pi$
$809$	−12513.6	+	9091.67i	−0.543826	+	0.395112i	0.281678	+	0.959509i	$0.409109\pi$
$810$	11947.3	+	5509.26i	0.518255	+	0.238982i
$811$	−41109.8	−	13357.4i	−1.77998	−	0.578349i	−0.781041	−	0.624480i	$-0.785311\pi$
$811$	−41109.8	−	13357.4i	−1.77998	−	0.578349i	−0.998935	+	0.0461305i	$0.985311\pi$
$812$	140.700	+	888.344i	0.00608079	+	0.0383926i
$813$	−51137.0	−	51137.0i	−2.20597	−	2.20597i
$814$	−14768.4	−	20422.4i	−0.635911	−	0.879366i
$815$	24327.6	−	26312.2i	1.04560	−	1.13089i
$816$	−673.162	+	926.528i	−0.0288791	+	0.0397487i
$817$	10717.3	−	5460.76i	0.458938	−	0.233841i
$818$	−19514.9	−	9943.31i	−0.834133	−	0.425012i
$819$	−507.197	−	698.096i	−0.0216397	−	0.0297844i
$820$	−6603.26	+	5204.51i	−0.281214	+	0.221645i
$821$	−33831.2	+	10992.4i	−1.43815	+	0.467282i	−0.921319	−	0.388807i	$-0.872887\pi$
$821$	−33831.2	+	10992.4i	−1.43815	+	0.467282i	−0.516827	+	0.856090i	$0.672887\pi$
$822$	−2249.23	−	4414.35i	−0.0954389	−	0.187309i
$823$	−14910.0	+	2361.51i	−0.631507	+	0.100021i	−0.463979	−	0.885846i	$-0.653579\pi$
$823$	−14910.0	+	2361.51i	−0.631507	+	0.100021i	−0.167529	+	0.985867i	$0.553579\pi$
$824$	−7350.35			−0.310755
$825$	15624.5	−	37463.4i	0.659364	−	1.58098i
$826$	−1181.18			−0.0497561
$827$	−38338.9	+	6072.29i	−1.61206	+	0.255326i	−0.896441	−	0.443163i	$-0.853856\pi$
$827$	−38338.9	+	6072.29i	−1.61206	+	0.255326i	−0.715621	+	0.698489i	$0.753856\pi$
$828$	15998.6	+	31399.0i	0.671484	+	1.31786i
$829$	7033.66	−	2285.37i	0.294679	−	0.0957470i	−0.157947	−	0.987448i	$-0.550487\pi$
$829$	7033.66	−	2285.37i	0.294679	−	0.0957470i	0.452626	+	0.891701i	$0.350487\pi$
$830$	7547.54	−	5948.76i	0.315637	−	0.248777i
$831$	29692.6	+	40868.3i	1.23950	+	1.70603i
$832$	976.104	+	497.350i	0.0406734	+	0.0207242i
$833$	2451.00	−	1248.85i	0.101947	−	0.0519448i
$834$	14156.2	−	19484.4i	0.587758	−	0.808980i
$835$	−13735.8	+	14856.3i	−0.569277	+	0.615715i
$836$	4189.94	+	3058.44i	0.173340	+	0.126529i
$837$	−25554.0	−	25554.0i	−1.05529	−	1.05529i
$838$	4409.21	+	27838.6i	0.181758	+	1.14758i
$839$	21187.0	+	6884.08i	0.871821	+	0.283272i	0.710557	−	0.703640i	$-0.248443\pi$
$839$	21187.0	+	6884.08i	0.871821	+	0.283272i	0.161264	+	0.986911i	$0.448443\pi$
$840$	−697.838	−	321.793i	−0.0286639	−	0.0132178i
$841$	−24169.5	+	17560.2i	−0.991002	+	0.720005i
$842$	−3371.03	+	21283.9i	−0.137973	+	0.871129i
$843$	−7622.38	+	14959.8i	−0.311422	+	0.611200i
$844$	−4304.00	+	13246.3i	−0.175533	+	0.540234i
$845$	−11828.4	+	17698.6i	−0.481550	+	0.720532i
$846$		−	6698.77i		−	0.272232i
$847$	206.627	−	1268.04i	0.00838227	−	0.0514407i
$848$	−123.197	+	123.197i	−0.00498890	+	0.00498890i
$849$	−693.982	−	504.207i	−0.0280535	−	0.0203820i
$850$	1954.79	+	469.722i	0.0788809	+	0.0189545i
$851$	−18005.6	−	55415.6i	−0.725293	−	2.23222i
$852$	29813.7	+	4722.03i	1.19883	+	0.189876i
$853$	−17735.3	−	2808.99i	−0.711892	−	0.112753i	−0.210023	−	0.977696i	$-0.567354\pi$
$853$	−17735.3	−	2808.99i	−0.711892	−	0.112753i	−0.501869	+	0.864944i	$0.667354\pi$
$854$	−552.907	−	1701.67i	−0.0221547	−	0.0681850i
$855$	19975.9	+	5635.96i	0.799018	+	0.225434i
$856$	8685.81	+	6310.61i	0.346816	+	0.251977i
$857$	−19791.8	+	19791.8i	−0.788886	+	0.788886i	−0.981312	−	0.192426i	$-0.938365\pi$
$857$	−19791.8	+	19791.8i	−0.788886	+	0.788886i	0.192426	+	0.981312i	$0.438365\pi$
$858$	1714.63	+	10983.9i	0.0682245	+	0.437045i
$859$		−	27225.7i		−	1.08141i	−0.841213	−	0.540705i	$-0.818158\pi$
$859$		−	27225.7i		−	1.08141i	0.841213	−	0.540705i	$-0.181842\pi$
$860$	14842.2	−	2950.75i	0.588507	−	0.117000i
$861$	−499.139	+	1536.19i	−0.0197568	+	0.0608052i
$862$	−7880.04	+	15465.4i	−0.311363	+	0.611085i
$863$	5831.80	−	36820.5i	0.230031	−	1.45236i	−0.554456	−	0.832213i	$-0.687074\pi$
$863$	5831.80	−	36820.5i	0.230031	−	1.45236i	0.784487	−	0.620145i	$-0.212926\pi$
$864$	−5812.58	+	4223.09i	−0.228875	+	0.166287i
$865$	−10588.5	+	22962.2i	−0.416209	+	0.902587i
$866$	7449.82	+	2420.59i	0.292327	+	0.0949828i
$867$	6750.81	+	42622.9i	0.264440	+	1.66961i
$868$	439.443	+	439.443i	0.0171840	+	0.0171840i
$869$	44485.9	−	14345.0i	1.73657	−	0.559977i
$870$	−1815.53	−	46327.6i	−0.0707496	−	1.80535i
$871$	4672.82	−	6431.58i	0.181782	−	0.250202i
$872$	−11023.3	+	5616.67i	−0.428093	+	0.218124i
$873$	−29124.1	−	14839.4i	−1.12909	−	0.575303i
$874$	7049.37	+	9702.62i	0.272824	+	0.375510i
$875$	−53.3697	+	1347.94i	−0.00206197	+	0.0520784i
$876$	−23252.0	+	7555.04i	−0.896818	+	0.291394i
$877$	1823.55	+	3578.91i	0.0702130	+	0.137801i	0.923445	−	0.383731i	$-0.125361\pi$
$877$	1823.55	+	3578.91i	0.0702130	+	0.137801i	−0.853232	+	0.521531i	$0.825361\pi$
$878$	17980.8	−	2847.87i	0.691141	−	0.109466i
$879$	15400.1			0.590936
$880$	4028.43	+	5134.56i	0.154316	+	0.196689i
$881$	−7171.08			−0.274233			−0.137117	−	0.990555i	$-0.543784\pi$
$881$	−7171.08			−0.274233			−0.137117	+	0.990555i	$0.543784\pi$
$882$	35289.1	−	5589.25i	1.34722	−	0.213378i
$883$	−2497.69	−	4901.99i	−0.0951913	−	0.186823i	0.838501	−	0.544900i	$-0.183433\pi$
$883$	−2497.69	−	4901.99i	−0.0951913	−	0.186823i	−0.933692	+	0.358077i	$0.883433\pi$
$884$	−523.662	+	170.148i	−0.0199238	+	0.00647365i
$885$	60464.6	+	7162.66i	2.29661	+	0.272057i
$886$	6763.66	+	9309.38i	0.256467	+	0.352996i
$887$	2804.40	+	1428.92i	0.106159	+	0.0540905i	0.506264	−	0.862379i	$-0.331026\pi$
$887$	2804.40	+	1428.92i	0.106159	+	0.0540905i	−0.400105	+	0.916469i	$0.631026\pi$
$888$	21914.5	−	11166.0i	0.828154	−	0.421966i
$889$	668.474	−	920.076i	0.0252192	−	0.0347113i
$890$	−631.057	−	583.461i	−0.0237675	−	0.0219749i
$891$	−20400.1	−	6678.61i	−0.767035	−	0.251113i
$892$	706.417	+	706.417i	0.0265163	+	0.0265163i
$893$	−356.635	−	2251.71i	−0.0133643	−	0.0843790i
$894$	16609.6	+	5396.79i	0.621374	+	0.201897i
$895$	18639.7	−	6874.40i	0.696152	−	0.256744i
$896$	99.9568	−	72.6229i	0.00372692	−	0.00270777i
$897$	−4020.64	+	25385.3i	−0.149660	+	0.944918i
$898$	4573.34	−	8975.69i	0.169949	−	0.333544i
$899$	−11586.5	+	35659.6i	−0.429846	+	1.32293i
$900$	22261.8	+	13648.2i	0.824511	+	0.505490i
$901$		−	87.5676i		−	0.00323785i
$902$	9721.47	−	9678.30i	0.358858	−	0.357264i
$903$	2055.71	−	2055.71i	0.0757584	−	0.0757584i
$904$	−7956.36	−	5780.63i	−0.292726	−	0.212678i
$905$	−7467.46	+	26467.4i	−0.274284	+	0.972161i
$906$	3476.22	+	10698.7i	0.127472	+	0.392318i
$907$	203.950	+	32.3026i	0.00746644	+	0.00118257i	0.160167	−	0.987090i	$-0.448797\pi$
$907$	203.950	+	32.3026i	0.00746644	+	0.00118257i	−0.152700	+	0.988273i	$0.548797\pi$
$908$	8104.83	+	1283.68i	0.296220	+	0.0469167i
$909$	−3189.70	−	9816.88i	−0.116387	−	0.358202i
$910$	−180.492	−	322.369i	−0.00657501	−	0.0117433i
$911$	22235.6	+	16155.1i	0.808668	+	0.587532i	0.913444	−	0.406964i	$-0.133413\pi$
$911$	22235.6	+	16155.1i	0.808668	+	0.587532i	−0.104776	+	0.994496i	$0.533413\pi$
$912$	−3579.65	+	3579.65i	−0.129972	+	0.129972i
$913$	−11111.7	+	11062.3i	−0.402785	+	0.400996i
$914$			23401.1i			0.846871i
$915$	17984.4	+	90461.4i	0.649777	+	3.26837i
$916$	4822.18	−	14841.1i	0.173940	−	0.535333i
$917$	−1060.73	+	2081.79i	−0.0381988	+	0.0749694i
$918$	564.903	−	3566.65i	0.0203100	−	0.128232i
$919$	−6793.74	+	4935.94i	−0.243857	+	0.177173i	−0.703000	−	0.711190i	$-0.748157\pi$
$919$	−6793.74	+	4935.94i	−0.243857	+	0.177173i	0.459143	+	0.888363i	$0.348157\pi$
$920$	5220.91	+	14156.3i	0.187096	+	0.507303i
$921$	−37426.2	−	12160.5i	−1.33902	−	0.435073i
$922$	1254.79	+	7922.42i	0.0448202	+	0.282984i
$923$	10261.8	+	10261.8i	0.365951	+	0.365951i
$924$	1191.56	+	390.095i	0.0424236	+	0.0138887i
$925$	−32825.4	−	28047.0i	−1.16680	−	0.996950i
$926$	−2400.21	+	3303.61i	−0.0851791	+	0.117239i
$927$	42754.0	−	21784.3i	1.51481	−	0.771833i
$928$	6641.83	+	3384.18i	0.234945	+	0.119710i
$929$	−17076.7	−	23504.1i	−0.603088	−	0.830080i	0.392898	−	0.919582i	$-0.371472\pi$
$929$	−17076.7	−	23504.1i	−0.603088	−	0.830080i	−0.995987	+	0.0895021i	$0.971472\pi$
$930$	−19830.3	−	25159.9i	−0.699207	−	0.887124i
$931$	11564.4	−	3757.51i	0.407098	−	0.132274i
$932$	1169.78	+	2295.82i	0.0411130	+	0.0806888i
$933$	−2484.44	+	393.497i	−0.0871780	+	0.0138076i
$934$	−19830.6			−0.694729
$935$	−3256.51	−	393.118i	−0.113903	−	0.0137501i
$936$	−7151.60			−0.249741
$937$	6223.94	−	985.776i	0.216998	−	0.0343691i	−0.0469886	−	0.998895i	$-0.514962\pi$
$937$	6223.94	−	985.776i	0.216998	−	0.0343691i	0.263987	+	0.964526i	$0.414962\pi$
$938$	−407.049	−	798.878i	−0.0141691	−	0.0278084i
$939$	26763.5	−	8696.00i	0.930133	−	0.302219i
$940$	337.403	−	2848.24i	0.0117073	−	0.0988290i
$941$	952.079	+	1310.42i	0.0329829	+	0.0453970i	0.825190	−	0.564855i	$-0.191068\pi$
$941$	952.079	+	1310.42i	0.0329829	+	0.0453970i	−0.792207	+	0.610252i	$0.791068\pi$
$942$	−27576.9	−	14051.1i	−0.953826	−	0.485998i
$943$	28258.0	−	14398.2i	0.975829	−	0.497210i
$944$	−5754.14	+	7919.89i	−0.198391	+	0.273062i
$945$	2421.18	−	94.8836i	0.0833451	−	0.00326621i
$946$	−23498.5	+	7577.35i	−0.807613	+	0.260424i
$947$	−1314.23	−	1314.23i	−0.0450969	−	0.0450969i	0.684199	−	0.729296i	$-0.260152\pi$
$947$	−1314.23	−	1314.23i	−0.0450969	−	0.0450969i	−0.729296	+	0.684199i	$0.760152\pi$
$948$	7135.72	+	45053.2i	0.244470	+	1.54352i
$949$	−11179.0	−	3632.29i	−0.382389	−	0.124246i
$950$	8209.63	+	3402.48i	0.280374	+	0.116201i
$951$	29268.5	−	21264.8i	0.997997	−	0.725088i
$952$	−9.71443	+	61.3345i	−0.000330721	+	0.00208809i
$953$	6910.85	−	13563.3i	0.234905	−	0.461027i	−0.743219	−	0.669048i	$-0.766702\pi$
$953$	6910.85	−	13563.3i	0.234905	−	0.461027i	0.978124	+	0.208021i	$0.0667022\pi$
$954$	351.466	−	1081.70i	0.0119278	−	0.0367101i
$955$	−27645.7	−	18476.3i	−0.936747	−	0.626051i
$956$			9620.30i			0.325463i
$957$	11667.1	+	74739.2i	0.394089	+	2.52453i
$958$	−7744.05	+	7744.05i	−0.261168	+	0.261168i
$959$	−217.334	−	157.902i	−0.00731813	−	0.00531693i
$960$	−5557.17	+	3111.43i	−0.186830	+	0.104605i
$961$	−1200.06	−	3693.39i	−0.0402825	−	0.123977i
$962$	11679.2	+	1849.81i	0.391427	+	0.0619960i
$963$	−69224.6	−	10964.1i	−2.31644	−	0.366888i
$964$	−5144.36	−	15832.7i	−0.171876	−	0.528980i
$965$	46405.8	−	25982.4i	1.54804	−	0.866738i
$966$	2345.09	+	1703.81i	0.0781078	+	0.0567486i
$967$	4017.35	−	4017.35i	0.133598	−	0.133598i	−0.637145	−	0.770744i	$-0.719885\pi$
$967$	4017.35	−	4017.35i	0.133598	−	0.133598i	0.770744	+	0.637145i	$0.219885\pi$
$968$	−7495.69	−	7562.71i	−0.248885	−	0.251110i
$969$		−	2544.40i		−	0.0843529i
$970$	−11635.8	−	7776.47i	−0.385157	−	0.257410i
$971$	−7196.81	+	22149.5i	−0.237854	+	0.732041i	0.758876	+	0.651236i	$0.225749\pi$
$971$	−7196.81	+	22149.5i	−0.237854	+	0.732041i	−0.996730	+	0.0808049i	$0.974251\pi$
$972$	−1498.40	+	2940.77i	−0.0494457	+	0.0970426i
$973$	204.289	−	1289.83i	0.00673094	−	0.0424975i
$974$	−27760.9	+	20169.5i	−0.913262	+	0.663523i
$975$	7284.57	+	17596.6i	0.239275	+	0.577991i
$976$	−14103.3	−	4582.44i	−0.462537	−	0.150287i
$977$	−3136.45	−	19802.8i	−0.102706	−	0.648462i	−0.984307	−	0.176466i	$-0.943534\pi$
$977$	−3136.45	−	19802.8i	−0.102706	−	0.648462i	0.881601	−	0.471996i	$-0.156466\pi$
$978$	−40346.1	−	40346.1i	−1.31915	−	1.31915i
$979$	1132.61	+	826.746i	0.0369748	+	0.0269897i
$980$	15286.0	−	599.043i	0.498259	−	0.0195263i
$981$	47472.2	−	65339.8i	1.54503	−	2.12654i
$982$	16186.9	−	8247.64i	0.526013	−	0.268017i
$983$	−43283.5	−	22054.1i	−1.40441	−	0.715580i	−0.422750	−	0.906246i	$-0.638935\pi$
$983$	−43283.5	−	22054.1i	−1.40441	−	0.715580i	−0.981655	+	0.190666i	$0.938935\pi$
$984$	7868.71	+	10830.3i	0.254924	+	0.350873i
$985$	−1241.86	+	10483.3i	−0.0401715	+	0.339114i
$986$	−3563.22	+	1157.76i	−0.115087	+	0.0373941i
$987$	−250.155	−	490.957i	−0.00806741	−	0.0158332i
$988$	−2403.92	+	380.743i	−0.0774077	+	0.0122602i
$989$	−57081.9			−1.83529
$990$	−38649.1	−	17926.6i	−1.24076	−	0.575500i
$991$	22241.5			0.712940			0.356470	−	0.934307i	$-0.383980\pi$
$991$	22241.5			0.712940			0.356470	+	0.934307i	$0.383980\pi$
$992$	5087.25	−	805.741i	0.162823	−	0.0257886i
$993$	27698.1	+	54360.6i	0.885170	+	1.73724i
$994$	1556.63	−	505.781i	0.0496714	−	0.0161392i
$995$	3476.95	+	4411.41i	0.110781	+	0.140554i
$996$	−8993.95	−	12379.1i	−0.286129	−	0.393822i
$997$	−13891.7	−	7078.19i	−0.441279	−	0.224843i	0.219211	−	0.975677i	$-0.429652\pi$
$997$	−13891.7	−	7078.19i	−0.441279	−	0.224843i	−0.660490	+	0.750834i	$0.729652\pi$
$998$	−3877.27	+	1975.57i	−0.122979	+	0.0626609i
$999$	−45583.6	+	62740.5i	−1.44365	+	1.98701i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	110.4.k.a.7.18	✓	144
5.3	odd	4	inner	110.4.k.a.73.1	yes	144
11.8	odd	10	inner	110.4.k.a.107.1	yes	144
55.8	even	20	inner	110.4.k.a.63.18	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.4.k.a.7.18	✓	144	1.1	even	1	trivial
110.4.k.a.63.18	yes	144	55.8	even	20	inner
110.4.k.a.73.1	yes	144	5.3	odd	4	inner
110.4.k.a.107.1	yes	144	11.8	odd	10	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:	\( N \)	\(=\)	\( 110 = 2 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	110.k (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.97538 - 0.312869i) q^{2} +(4.04090 + 7.93071i) q^{3} +(3.80423 - 1.23607i) q^{4} +(-8.78081 + 6.92079i) q^{5} +(10.4636 + 14.4019i) q^{6} +(0.860054 + 0.438219i) q^{7} +(7.12805 - 3.63192i) q^{8} +(-30.6971 + 42.2509i) q^{9} +(-15.1801 + 16.4184i) q^{10} +(21.5097 - 29.4675i) q^{11} +(25.1754 + 25.1754i) q^{12} +(2.67773 + 16.9065i) q^{13} +(1.83604 + 0.596564i) q^{14} +(-90.3691 - 41.6718i) q^{15} +(12.9443 - 9.40456i) q^{16} +(-1.25801 + 7.94273i) q^{17} +(-47.4193 + 93.0655i) q^{18} +(-10.9847 + 33.8073i) q^{19} +(-24.8496 + 37.1819i) q^{20} +8.59163i q^{21} +(33.2704 - 64.9391i) q^{22} +(119.284 - 119.284i) q^{23} +(57.6074 + 41.8543i) q^{24} +(29.2052 - 121.540i) q^{25} +(10.5791 + 32.5590i) q^{26} +(-221.759 - 35.1232i) q^{27} +(3.81351 + 0.604000i) q^{28} +(71.9845 + 221.546i) q^{29} +(-191.551 - 54.0438i) q^{30} +(130.218 + 94.6088i) q^{31} +(22.6274 - 22.6274i) q^{32} +(320.616 + 51.5123i) q^{33} +16.0835i q^{34} +(-10.5848 + 2.10433i) q^{35} +(-64.5536 + 198.675i) q^{36} +(156.811 - 307.758i) q^{37} +(-11.1216 + 70.2190i) q^{38} +(-123.260 + 89.5539i) q^{39} +(-37.4543 + 81.2230i) q^{40} +(178.801 + 58.0960i) q^{41} +(2.68806 + 16.9717i) q^{42} +(-239.269 - 239.269i) q^{43} +(45.4041 - 138.688i) q^{44} +(-22.8646 - 583.445i) q^{45} +(198.310 - 272.951i) q^{46} +(-57.1437 + 29.1161i) q^{47} +(126.891 + 64.6543i) q^{48} +(-201.063 - 276.739i) q^{49} +(19.6651 - 249.225i) q^{50} +(-68.0749 + 22.1189i) q^{51} +(31.0844 + 61.0065i) q^{52} +(-10.7551 + 1.70344i) q^{53} -449.046 q^{54} +(15.0655 + 407.613i) q^{55} +7.72209 q^{56} +(-312.504 + 49.4958i) q^{57} +(211.511 + 415.114i) q^{58} +(-581.899 + 189.071i) q^{59} +(-395.294 - 46.8266i) q^{60} +(-544.770 - 749.812i) q^{61} +(286.830 + 146.147i) q^{62} +(-44.9163 + 22.8860i) q^{63} +(37.6183 - 51.7771i) q^{64} +(-140.519 - 129.921i) q^{65} +(649.455 + 1.44528i) q^{66} +(-328.405 - 328.405i) q^{67} +(5.03202 + 31.7709i) q^{68} +(1428.02 + 463.992i) q^{69} +(-20.2506 + 7.46851i) q^{70} +(685.903 - 498.338i) q^{71} +(-65.3583 + 412.656i) q^{72} +(-311.753 + 611.849i) q^{73} +(213.472 - 657.000i) q^{74} +(1081.92 - 259.514i) q^{75} +142.189i q^{76} +(31.4127 - 15.9176i) q^{77} +(-215.467 + 215.467i) q^{78} +(1036.51 + 753.066i) q^{79} +(-48.5741 + 172.164i) q^{80} +(-181.817 - 559.574i) q^{81} +(371.376 + 58.8202i) q^{82} +(-424.483 - 67.2315i) q^{83} +(10.6198 + 32.6845i) q^{84} +(-43.9237 - 78.4500i) q^{85} +(-547.507 - 397.787i) q^{86} +(-1466.13 + 1466.13i) q^{87} +(46.2988 - 288.167i) q^{88} +38.4359i q^{89} +(-227.708 - 1145.37i) q^{90} +(-5.10578 + 15.7140i) q^{91} +(306.340 - 601.226i) q^{92} +(-224.118 + 1415.02i) q^{93} +(-103.771 + 75.3938i) q^{94} +(-137.519 - 372.878i) q^{95} +(270.886 + 88.0163i) q^{96} +(97.9096 + 618.177i) q^{97} +(-483.758 - 483.758i) q^{98} +(584.741 + 1813.37i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 8 q^{3} + 32 q^{5} - 40 q^{7} - 44 q^{11} + 128 q^{12} - 256 q^{15} + 576 q^{16} - 640 q^{17} - 64 q^{20} + 312 q^{22} - 984 q^{23} - 520 q^{25} + 304 q^{26} - 364 q^{27} + 240 q^{28} - 432 q^{31}+ \cdots + 7044 q^{97}+O(q^{100}) \) 144 * q + 8 * q^3 + 32 * q^5 - 40 * q^7 - 44 * q^11 + 128 * q^12 - 256 * q^15 + 576 * q^16 - 640 * q^17 - 64 * q^20 + 312 * q^22 - 984 * q^23 - 520 * q^25 + 304 * q^26 - 364 * q^27 + 240 * q^28 - 432 * q^31 + 2368 * q^33 + 1808 * q^36 - 960 * q^37 + 72 * q^38 + 740 * q^41 + 2440 * q^42 + 2656 * q^45 + 720 * q^46 - 1980 * q^47 - 128 * q^48 - 1360 * q^50 - 3880 * q^51 - 1920 * q^52 - 3060 * q^53 - 3044 * q^55 - 64 * q^56 - 4400 * q^57 - 2016 * q^58 - 1120 * q^60 - 960 * q^61 + 80 * q^62 + 1800 * q^63 + 1552 * q^66 + 10160 * q^67 + 2560 * q^68 + 2304 * q^70 + 1312 * q^71 - 2460 * q^73 + 8644 * q^75 - 1272 * q^77 - 5312 * q^78 + 768 * q^80 + 2116 * q^81 + 1280 * q^82 + 320 * q^85 - 5488 * q^86 + 1248 * q^88 - 8480 * q^90 + 11796 * q^91 - 704 * q^92 + 688 * q^93 - 1280 * q^95 + 7044 * q^97

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