LMFDB - Embedded newform 110.4.g.b.71.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [110,4,Mod(31,110)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(110, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 6])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("110.31"); S:= CuspForms(chi, 4); N := Newforms(S);

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

Newform invariants

comment:select newform

sage:traces = [12,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$6.49021010063$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 18 x^{10} + 56 x^{9} + 1903 x^{8} + 4434 x^{7} + 95917 x^{6} + 226101 x^{5} + \cdots + 14641 $ x^12 - 3x^11 + 18x^10 + 56x^9 + 1903x^8 + 4434x^7 + 95917x^6 + 226101x^5 + 2006313x^4 + 1418439x^3 + 529133x^2 + 103818*x + 14641
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			71.1
Root			$6.54616 + 4.75606i$ of defining polynomial
Character	$\chi$	$=$	110.71
Dual form			110.4.g.b.31.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.618034 + 1.90211i) q^{2} +(-3.92812 - 2.85395i) q^{3} +(-3.23607 + 2.35114i) q^{4} +(-1.54508 + 4.75528i) q^{5} +(3.00082 - 9.23557i) q^{6} +(5.32223 - 3.86683i) q^{7} +(-6.47214 - 4.70228i) q^{8} +(-1.05833 - 3.25720i) q^{9} -10.0000 q^{10} +(18.0044 - 31.7307i) q^{11} +19.4217 q^{12} +(-18.7225 - 57.6219i) q^{13} +(10.6445 + 7.73366i) q^{14} +(19.6406 - 14.2697i) q^{15} +(4.94427 - 15.2169i) q^{16} +(26.5889 - 81.8322i) q^{17} +(5.54149 - 4.02613i) q^{18} +(2.21395 + 1.60853i) q^{19} +(-6.18034 - 19.0211i) q^{20} -31.9421 q^{21} +(71.4828 + 14.6358i) q^{22} -70.7450 q^{23} +(12.0033 + 36.9423i) q^{24} +(-20.2254 - 14.6946i) q^{25} +(98.0323 - 71.2246i) q^{26} +(-45.6497 + 140.495i) q^{27} +(-8.13165 + 25.0266i) q^{28} +(-2.67723 + 1.94512i) q^{29} +(39.2812 + 28.5395i) q^{30} +(30.9596 + 95.2839i) q^{31} +32.0000 q^{32} +(-161.282 + 73.2586i) q^{33} +172.087 q^{34} +(10.1646 + 31.2833i) q^{35} +(11.0830 + 8.05225i) q^{36} +(264.070 - 191.858i) q^{37} +(-1.69130 + 5.20530i) q^{38} +(-90.9058 + 279.779i) q^{39} +(32.3607 - 23.5114i) q^{40} +(-16.6730 - 12.1137i) q^{41} +(-19.7413 - 60.7575i) q^{42} -469.247 q^{43} +(16.3399 + 145.014i) q^{44} +17.1241 q^{45} +(-43.7228 - 134.565i) q^{46} +(-238.941 - 173.601i) q^{47} +(-62.8500 + 45.6632i) q^{48} +(-92.6190 + 285.052i) q^{49} +(15.4508 - 47.5528i) q^{50} +(-337.989 + 245.563i) q^{51} +(196.065 + 142.449i) q^{52} +(-121.473 - 373.856i) q^{53} -295.451 q^{54} +(123.070 + 134.643i) q^{55} -52.6291 q^{56} +(-4.10600 - 12.6370i) q^{57} +(-5.35446 - 3.89024i) q^{58} +(477.662 - 347.041i) q^{59} +(-30.0082 + 92.3557i) q^{60} +(-70.0266 + 215.520i) q^{61} +(-162.107 + 117.777i) q^{62} +(-18.2277 - 13.2432i) q^{63} +(19.7771 + 60.8676i) q^{64} +302.936 q^{65} +(-239.024 - 261.499i) q^{66} -177.400 q^{67} +(106.356 + 327.329i) q^{68} +(277.895 + 201.902i) q^{69} +(-53.2223 + 38.6683i) q^{70} +(-163.903 + 504.441i) q^{71} +(-8.46664 + 26.0576i) q^{72} +(734.346 - 533.534i) q^{73} +(528.139 + 383.716i) q^{74} +(37.5102 + 115.445i) q^{75} -10.9464 q^{76} +(-26.8736 - 238.499i) q^{77} -588.354 q^{78} +(260.871 + 802.880i) q^{79} +(64.7214 + 47.0228i) q^{80} +(505.474 - 367.248i) q^{81} +(12.7371 - 39.2007i) q^{82} +(149.514 - 460.157i) q^{83} +(103.367 - 75.1004i) q^{84} +(348.053 + 252.875i) q^{85} +(-290.011 - 892.561i) q^{86} +16.0678 q^{87} +(-265.734 + 120.704i) q^{88} -60.8377 q^{89} +(10.5833 + 32.5720i) q^{90} +(-322.460 - 234.281i) q^{91} +(228.935 - 166.331i) q^{92} +(150.322 - 462.644i) q^{93} +(182.535 - 561.785i) q^{94} +(-11.0697 + 8.04263i) q^{95} +(-125.700 - 91.3264i) q^{96} +(79.2841 + 244.011i) q^{97} -599.443 q^{98} +(-122.408 - 25.0625i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{2} + 15 q^{3} - 12 q^{4} + 15 q^{5} - 20 q^{6} + 15 q^{7} - 24 q^{8} + 62 q^{9} - 120 q^{10} + 34 q^{11} - 40 q^{12} - 114 q^{13} + 30 q^{14} - 75 q^{15} - 48 q^{16} - 17 q^{17} - 166 q^{18}+ \cdots - 3855 q^{99}+O(q^{100}) $ 12 * q - 6 * q^2 + 15 * q^3 - 12 * q^4 + 15 * q^5 - 20 * q^6 + 15 * q^7 - 24 * q^8 + 62 * q^9 - 120 * q^10 + 34 * q^11 - 40 * q^12 - 114 * q^13 + 30 * q^14 - 75 * q^15 - 48 * q^16 - 17 * q^17 - 166 * q^18 - 162 * q^19 + 60 * q^20 + 148 * q^21 - 142 * q^22 - 210 * q^23 - 80 * q^24 - 75 * q^25 + 342 * q^26 - 147 * q^27 + 40 * q^28 - 57 * q^29 - 150 * q^30 + 816 * q^31 + 384 * q^32 - 1188 * q^33 + 696 * q^34 - 50 * q^35 - 332 * q^36 + 870 * q^37 + 466 * q^38 - 413 * q^39 + 120 * q^40 + 754 * q^41 + 586 * q^42 + 136 * q^43 - 204 * q^44 - 210 * q^45 - 430 * q^46 - 792 * q^47 + 240 * q^48 + 1008 * q^49 - 150 * q^50 - 504 * q^51 + 684 * q^52 + 359 * q^53 - 1364 * q^54 - 220 * q^55 - 400 * q^56 - 1242 * q^57 - 114 * q^58 + 1252 * q^59 + 200 * q^60 + 1346 * q^61 - 1858 * q^62 + 3469 * q^63 - 192 * q^64 + 570 * q^65 - 2336 * q^66 + 376 * q^67 - 68 * q^68 - 889 * q^69 - 150 * q^70 + 2038 * q^71 + 496 * q^72 + 945 * q^73 + 1740 * q^74 - 250 * q^75 - 568 * q^76 - 754 * q^77 + 1364 * q^78 - 149 * q^79 + 240 * q^80 - 1346 * q^81 + 368 * q^82 - 614 * q^83 - 1468 * q^84 + 785 * q^85 + 22 * q^86 - 4442 * q^87 + 352 * q^88 - 3122 * q^89 - 620 * q^90 - 4694 * q^91 + 1280 * q^92 + 1487 * q^93 + 2326 * q^94 + 810 * q^95 + 480 * q^96 + 1617 * q^97 + 1956 * q^98 - 3855 * q^99

Character values

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

$n$	$67$	$101$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.618034	+	1.90211i	0.218508	+	0.672499i
$2$	0.618034	+	1.90211i	0.218508	+	0.672499i
$3$	−3.92812	−	2.85395i	−0.755968	−	0.549243i	0.141703	−	0.989909i	$-0.454742\pi$
$3$	−3.92812	−	2.85395i	−0.755968	−	0.549243i	−0.897671	+	0.440667i	$0.854742\pi$
$4$	−3.23607	+	2.35114i	−0.404508	+	0.293893i
$5$	−1.54508	+	4.75528i	−0.138197	+	0.425325i
$5$	−1.54508	+	4.75528i	−0.138197	+	0.425325i
$6$	3.00082	−	9.23557i	0.204180	−	0.628401i
$7$	5.32223	−	3.86683i	0.287374	−	0.208789i	−0.434754	−	0.900549i	$-0.643165\pi$
$7$	5.32223	−	3.86683i	0.287374	−	0.208789i	0.722127	+	0.691760i	$0.243165\pi$
$8$	−6.47214	−	4.70228i	−0.286031	−	0.207813i
$9$	−1.05833	−	3.25720i	−0.0391974	−	0.120637i
$10$	−10.0000			−0.316228
$11$	18.0044	−	31.7307i	0.493504	−	0.869744i
$11$	18.0044	−	31.7307i	0.493504	−	0.869744i
$12$	19.4217			0.467214
$13$	−18.7225	−	57.6219i	−0.399438	−	1.22934i	−0.925451	−	0.378866i	$-0.876314\pi$
$13$	−18.7225	−	57.6219i	−0.399438	−	1.22934i	0.526014	−	0.850476i	$-0.323686\pi$
$14$	10.6445	+	7.73366i	0.203204	+	0.147636i
$15$	19.6406	−	14.2697i	0.338079	−	0.245629i
$16$	4.94427	−	15.2169i	0.0772542	−	0.237764i
$17$	26.5889	−	81.8322i	0.379338	−	1.16748i	−0.561167	−	0.827703i	$-0.689647\pi$
$17$	26.5889	−	81.8322i	0.379338	−	1.16748i	0.940505	−	0.339780i	$-0.110353\pi$
$18$	5.54149	−	4.02613i	0.0725634	−	0.0527204i
$19$	2.21395	+	1.60853i	0.0267323	+	0.0194222i	0.601071	−	0.799195i	$-0.294741\pi$
$19$	2.21395	+	1.60853i	0.0267323	+	0.0194222i	−0.574339	+	0.818618i	$0.694741\pi$
$20$	−6.18034	−	19.0211i	−0.0690983	−	0.212663i
$21$	−31.9421			−0.331921
$22$	71.4828	+	14.6358i	0.692736	+	0.141835i
$23$	−70.7450			−0.641363			−0.320681	−	0.947187i	$-0.603912\pi$
$23$	−70.7450			−0.641363			−0.320681	+	0.947187i	$0.603912\pi$
$24$	12.0033	+	36.9423i	0.102090	+	0.314201i
$25$	−20.2254	−	14.6946i	−0.161803	−	0.117557i
$26$	98.0323	−	71.2246i	0.739451	−	0.537242i
$27$	−45.6497	+	140.495i	−0.325381	+	1.00142i
$28$	−8.13165	+	25.0266i	−0.0548835	+	0.168914i
$29$	−2.67723	+	1.94512i	−0.0171431	+	0.0124552i	−0.596324	−	0.802744i	$-0.703373\pi$
$29$	−2.67723	+	1.94512i	−0.0171431	+	0.0124552i	0.579181	+	0.815199i	$0.303373\pi$
$30$	39.2812	+	28.5395i	0.239058	+	0.173686i
$31$	30.9596	+	95.2839i	0.179371	+	0.552048i	0.999806	−	0.0196919i	$-0.00626854\pi$
$31$	30.9596	+	95.2839i	0.179371	+	0.552048i	−0.820435	+	0.571740i	$0.806269\pi$
$32$	32.0000			0.176777
$33$	−161.282	+	73.2586i	−0.850773	+	0.386445i
$34$	172.087			0.868019
$35$	10.1646	+	31.2833i	0.0490893	+	0.151081i
$36$	11.0830	+	8.05225i	0.0513101	+	0.0372789i
$37$	264.070	−	191.858i	1.17332	−	0.852466i	0.181916	−	0.983314i	$-0.441770\pi$
$37$	264.070	−	191.858i	1.17332	−	0.852466i	0.991402	+	0.130849i	$0.0417702\pi$
$38$	−1.69130	+	5.20530i	−0.00722015	+	0.0222213i
$39$	−90.9058	+	279.779i	−0.373245	+	1.14873i
$40$	32.3607	−	23.5114i	0.127917	−	0.0929370i
$41$	−16.6730	−	12.1137i	−0.0635096	−	0.0461424i	0.555578	−	0.831465i	$-0.312497\pi$
$41$	−16.6730	−	12.1137i	−0.0635096	−	0.0461424i	−0.619087	+	0.785322i	$0.712497\pi$
$42$	−19.7413	−	60.7575i	−0.0725274	−	0.223216i
$43$	−469.247			−1.66417			−0.832087	−	0.554645i	$-0.812854\pi$
$43$	−469.247			−1.66417			−0.832087	+	0.554645i	$0.812854\pi$
$44$	16.3399	+	145.014i	0.0559848	+	0.496856i
$45$	17.1241			0.0567270
$46$	−43.7228	−	134.565i	−0.140143	−	0.431315i
$47$	−238.941	−	173.601i	−0.741557	−	0.538773i	0.151641	−	0.988436i	$-0.451544\pi$
$47$	−238.941	−	173.601i	−0.741557	−	0.538773i	−0.893198	+	0.449663i	$0.851544\pi$
$48$	−62.8500	+	45.6632i	−0.188992	+	0.137311i
$49$	−92.6190	+	285.052i	−0.270026	+	0.831056i
$50$	15.4508	−	47.5528i	0.0437016	−	0.134500i
$51$	−337.989	+	245.563i	−0.927999	+	0.674231i
$52$	196.065	+	142.449i	0.522871	+	0.379888i
$53$	−121.473	−	373.856i	−0.314823	−	0.968926i	−0.975827	−	0.218544i	$-0.929869\pi$
$53$	−121.473	−	373.856i	−0.314823	−	0.968926i	0.661004	−	0.750382i	$-0.270131\pi$
$54$	−295.451			−0.744552
$55$	123.070	+	134.643i	0.301724	+	0.330095i
$56$	−52.6291			−0.125587
$57$	−4.10600	−	12.6370i	−0.00954129	−	0.0293651i
$58$	−5.35446	−	3.89024i	−0.0121220	−	0.00880714i
$59$	477.662	−	347.041i	1.05400	−	0.765779i	0.0810343	−	0.996711i	$-0.474178\pi$
$59$	477.662	−	347.041i	1.05400	−	0.765779i	0.972970	+	0.230933i	$0.0741777\pi$
$60$	−30.0082	+	92.3557i	−0.0645673	+	0.198718i
$61$	−70.0266	+	215.520i	−0.146983	+	0.452368i	−0.997261	−	0.0739667i	$-0.976434\pi$
$61$	−70.0266	+	215.520i	−0.146983	+	0.452368i	0.850277	+	0.526335i	$0.176434\pi$
$62$	−162.107	+	117.777i	−0.332058	+	0.241254i
$63$	−18.2277	−	13.2432i	−0.0364520	−	0.0264840i
$64$	19.7771	+	60.8676i	0.0386271	+	0.118882i
$65$	302.936			0.578071
$66$	−239.024	−	261.499i	−0.445784	−	0.487702i
$67$	−177.400			−0.323476			−0.161738	−	0.986834i	$-0.551710\pi$
$67$	−177.400			−0.323476			−0.161738	+	0.986834i	$0.551710\pi$
$68$	106.356	+	327.329i	0.189669	+	0.583742i
$69$	277.895	+	201.902i	0.484849	+	0.352264i
$70$	−53.2223	+	38.6683i	−0.0908755	+	0.0660249i
$71$	−163.903	+	504.441i	−0.273968	+	0.843186i	0.715523	+	0.698589i	$0.246188\pi$
$71$	−163.903	+	504.441i	−0.273968	+	0.843186i	−0.989491	+	0.144597i	$0.953812\pi$
$72$	−8.46664	+	26.0576i	−0.0138584	+	0.0426517i
$73$	734.346	−	533.534i	1.17738	−	0.855417i	0.185506	−	0.982643i	$-0.440607\pi$
$73$	734.346	−	533.534i	1.17738	−	0.855417i	0.991874	+	0.127226i	$0.0406075\pi$
$74$	528.139	+	383.716i	0.829661	+	0.602784i
$75$	37.5102	+	115.445i	0.0577508	+	0.177739i
$76$	−10.9464			−0.0165215
$77$	−26.8736	−	238.499i	−0.0397731	−	0.352980i
$78$	−588.354			−0.854077
$79$	260.871	+	802.880i	0.371523	+	1.14343i	0.945795	+	0.324766i	$0.105285\pi$
$79$	260.871	+	802.880i	0.371523	+	1.14343i	−0.574271	+	0.818665i	$0.694715\pi$
$80$	64.7214	+	47.0228i	0.0904508	+	0.0657164i
$81$	505.474	−	367.248i	0.693380	−	0.503770i
$82$	12.7371	−	39.2007i	0.0171533	−	0.0527926i
$83$	149.514	−	460.157i	0.197726	−	0.608539i	−0.802208	−	0.597045i	$-0.796341\pi$
$83$	149.514	−	460.157i	0.197726	−	0.608539i	0.999934	−	0.0114940i	$-0.00365873\pi$
$84$	103.367	−	75.1004i	0.134265	−	0.0975491i
$85$	348.053	+	252.875i	0.444137	+	0.322684i
$86$	−290.011	−	892.561i	−0.363635	−	1.11915i
$87$	16.0678			0.0198005
$88$	−265.734	+	120.704i	−0.321902	+	0.146217i
$89$	−60.8377			−0.0724583			−0.0362291	−	0.999344i	$-0.511535\pi$
$89$	−60.8377			−0.0724583			−0.0362291	+	0.999344i	$0.511535\pi$
$90$	10.5833	+	32.5720i	0.0123953	+	0.0381488i
$91$	−322.460	−	234.281i	−0.371461	−	0.269882i
$92$	228.935	−	166.331i	0.259437	−	0.188492i
$93$	150.322	−	462.644i	0.167610	−	0.515849i
$94$	182.535	−	561.785i	0.200288	−	0.616422i
$95$	−11.0697	+	8.04263i	−0.0119551	+	0.00868586i
$96$	−125.700	−	91.3264i	−0.133637	−	0.0970933i
$97$	79.2841	+	244.011i	0.0829905	+	0.255419i	0.983938	−	0.178509i	$-0.0571274\pi$
$97$	79.2841	+	244.011i	0.0829905	+	0.255419i	−0.900948	+	0.433928i	$0.857127\pi$
$98$	−599.443			−0.617887
$99$	−122.408	−	25.0625i	−0.124267	−	0.0254432i
$100$	100.000			0.100000
$101$	−58.6143	−	180.396i	−0.0577460	−	0.177724i	0.918023	−	0.396527i	$-0.129785\pi$
$101$	−58.6143	−	180.396i	−0.0577460	−	0.177724i	−0.975769	+	0.218803i	$0.929785\pi$
$102$	−675.978	−	491.127i	−0.656194	−	0.476753i
$103$	1266.85	−	920.420i	1.21191	−	0.880502i	0.216504	−	0.976282i	$-0.430534\pi$
$103$	1266.85	−	920.420i	1.21191	−	0.880502i	0.995403	+	0.0957797i	$0.0305344\pi$
$104$	−149.780	+	460.976i	−0.141223	+	0.434638i
$105$	49.3533	−	151.894i	0.0458704	−	0.141174i
$106$	636.042	−	462.112i	0.582810	−	0.423436i
$107$	−501.491	−	364.355i	−0.453093	−	0.329192i	0.337722	−	0.941246i	$-0.390343\pi$
$107$	−501.491	−	364.355i	−0.453093	−	0.329192i	−0.790816	+	0.612054i	$0.790343\pi$
$108$	−182.599	−	561.981i	−0.162691	−	0.500710i
$109$	2106.14			1.85075			0.925376	−	0.379050i	$-0.123749\pi$
$109$	2106.14			1.85075			0.925376	+	0.379050i	$0.123749\pi$
$110$	−180.044	+	317.307i	−0.156060	+	0.275037i
$111$	−1584.85			−1.35520
$112$	−32.5266	−	100.107i	−0.0274417	−	0.0844570i
$113$	−1154.52	−	838.805i	−0.961130	−	0.698302i	−0.00771744	−	0.999970i	$-0.502457\pi$
$113$	−1154.52	−	838.805i	−0.961130	−	0.698302i	−0.953413	+	0.301668i	$0.902457\pi$
$114$	21.4993	−	15.6202i	0.0176631	−	0.0128330i
$115$	109.307	−	336.412i	0.0886342	−	0.272788i
$116$	4.09045	−	12.5891i	0.00327404	−	0.0100765i
$117$	−167.872	+	121.966i	−0.132647	+	0.0963740i
$118$	955.323	+	694.083i	0.745293	+	0.541487i
$119$	−174.919	−	538.344i	−0.134746	−	0.414706i
$120$	−194.217			−0.147746
$121$	−682.681	−	1142.59i	−0.512908	−	0.858443i
$122$	−453.221			−0.336334
$123$	30.9220	+	95.1680i	0.0226678	+	0.0697643i
$124$	−324.213	−	235.555i	−0.234800	−	0.170592i
$125$	101.127	−	73.4732i	0.0723607	−	0.0525731i
$126$	13.9247	−	42.8560i	0.00984536	−	0.0303009i
$127$	−520.568	+	1602.14i	−0.363724	+	1.11943i	0.587053	+	0.809549i	$0.300288\pi$
$127$	−520.568	+	1602.14i	−0.363724	+	1.11943i	−0.950776	+	0.309878i	$0.899712\pi$
$128$	−103.554	+	75.2365i	−0.0715077	+	0.0519534i
$129$	1843.26	+	1339.21i	1.25806	+	0.914036i
$130$	187.225	+	576.219i	0.126313	+	0.388752i
$131$	569.413			0.379770			0.189885	−	0.981806i	$-0.439189\pi$
$131$	569.413			0.379770			0.189885	+	0.981806i	$0.439189\pi$
$132$	349.677	−	616.265i	0.230572	−	0.406356i
$133$	18.0030			0.0117373
$134$	−109.640	−	337.436i	−0.0706822	−	0.217537i
$135$	−597.562	−	434.154i	−0.380963	−	0.276786i
$136$	−556.885	+	404.600i	−0.351121	+	0.255104i
$137$	−731.554	+	2251.49i	−0.456211	+	1.40407i	0.413497	+	0.910505i	$0.364307\pi$
$137$	−731.554	+	2251.49i	−0.456211	+	1.40407i	−0.869708	+	0.493567i	$0.835693\pi$
$138$	−212.293	+	653.370i	−0.130953	+	0.403033i
$139$	−191.799	+	139.350i	−0.117037	+	0.0850325i	−0.644764	−	0.764382i	$-0.723044\pi$
$139$	−191.799	+	139.350i	−0.117037	+	0.0850325i	0.527727	+	0.849414i	$0.323044\pi$
$140$	−106.445	−	77.3366i	−0.0642587	−	0.0466867i
$141$	443.143	+	1363.85i	0.264676	+	0.814590i
$142$	−1060.80			−0.626905
$143$	−2165.48	−	443.371i	−1.26634	−	0.259277i
$144$	−54.7972			−0.0317114
$145$	−5.11306	−	15.7364i	−0.00292839	−	0.00901265i
$146$	1468.69	+	1067.07i	0.832533	+	0.604871i
$147$	1177.34	−	855.390i	0.660582	−	0.479941i
$148$	−403.462	+	1241.73i	−0.224084	+	0.689659i
$149$	638.072	−	1963.78i	0.350825	−	1.07973i	−0.607566	−	0.794269i	$-0.707854\pi$
$149$	638.072	−	1963.78i	0.350825	−	1.07973i	0.958391	−	0.285458i	$-0.0921459\pi$
$150$	−196.406	+	142.697i	−0.106910	+	0.0776746i
$151$	2342.08	+	1701.62i	1.26223	+	0.917060i	0.998865	−	0.0476371i	$-0.0151691\pi$
$151$	2342.08	+	1701.62i	1.26223	+	0.917060i	0.263361	+	0.964697i	$0.415169\pi$
$152$	−6.76522	−	20.8212i	−0.00361008	−	0.0111107i
$153$	−294.684			−0.155711
$154$	437.042	−	198.517i	0.228688	−	0.103876i
$155$	−500.937			−0.259589
$156$	−363.623	−	1119.12i	−0.186623	−	0.574366i
$157$	1329.64	+	966.043i	0.675906	+	0.491074i	0.871997	−	0.489512i	$-0.162825\pi$
$157$	1329.64	+	966.043i	0.675906	+	0.491074i	−0.196091	+	0.980586i	$0.562825\pi$
$158$	−1365.94	+	992.414i	−0.687775	+	0.499697i
$159$	−589.804	+	1815.23i	−0.294179	+	0.905391i
$160$	−49.4427	+	152.169i	−0.0244299	+	0.0751876i
$161$	−376.521	+	273.559i	−0.184311	+	0.133910i
$162$	1010.95	+	734.497i	0.490294	+	0.356219i
$163$	936.756	+	2883.04i	0.450137	+	1.38538i	0.876750	+	0.480946i	$0.159707\pi$
$163$	936.756	+	2883.04i	0.450137	+	1.38538i	−0.426613	+	0.904434i	$0.640293\pi$
$164$	82.4361			0.0392511
$165$	−99.1715	−	880.130i	−0.0467908	−	0.415261i
$166$	967.675			0.452447
$167$	529.982	+	1631.12i	0.245576	+	0.755807i	0.995541	+	0.0943287i	$0.0300705\pi$
$167$	529.982	+	1631.12i	0.245576	+	0.755807i	−0.749965	+	0.661478i	$0.769930\pi$
$168$	206.734	+	150.201i	0.0949396	+	0.0689777i
$169$	−1192.35	+	866.290i	−0.542715	+	0.394306i
$170$	−265.889	+	818.322i	−0.119957	+	0.369191i
$171$	2.89621	−	8.91363i	0.00129520	−	0.00398621i
$172$	1518.52	−	1103.27i	0.673173	−	0.489089i
$173$	−1541.80	−	1120.18i	−0.677576	−	0.492288i	0.194976	−	0.980808i	$-0.437537\pi$
$173$	−1541.80	−	1120.18i	−0.677576	−	0.492288i	−0.872553	+	0.488520i	$0.837537\pi$
$174$	9.93043	+	30.5627i	0.00432657	+	0.0133158i
$175$	−164.466			−0.0710427
$176$	−393.825	−	430.857i	−0.168669	−	0.184529i
$177$	−2866.75			−1.21739
$178$	−37.5998	−	115.720i	−0.0158327	−	0.0487281i
$179$	−2790.65	−	2027.52i	−1.16527	−	0.846616i	−0.174832	−	0.984598i	$-0.555938\pi$
$179$	−2790.65	−	2027.52i	−1.16527	−	0.846616i	−0.990435	+	0.137982i	$0.955938\pi$
$180$	−55.4149	+	40.2613i	−0.0229466	+	0.0166716i
$181$	337.512	−	1038.75i	0.138602	−	0.426575i	−0.857530	−	0.514433i	$-0.828002\pi$
$181$	337.512	−	1038.75i	0.138602	−	0.426575i	0.996133	+	0.0878586i	$0.0280024\pi$
$182$	246.337	−	758.148i	0.100328	−	0.308779i
$183$	890.155	−	646.735i	0.359574	−	0.261246i
$184$	457.871	+	332.663i	0.183449	+	0.133284i
$185$	504.328	+	1552.16i	0.200427	+	0.616850i
$186$	972.906			0.383532
$187$	−2117.88	−	2317.03i	−0.828206	−	0.906084i
$188$	1181.39			0.458308
$189$	300.313	+	924.269i	0.115580	+	0.355718i
$190$	−22.1395	−	16.0853i	−0.00845350	−	0.00614183i
$191$	−2033.24	+	1477.23i	−0.770262	+	0.559628i	−0.902041	−	0.431651i	$-0.857931\pi$
$191$	−2033.24	+	1477.23i	−0.770262	+	0.559628i	0.131779	+	0.991279i	$0.457931\pi$
$192$	96.0262	−	295.538i	0.0360942	−	0.111087i
$193$	1536.74	−	4729.58i	0.573143	−	1.76395i	−0.0692738	−	0.997598i	$-0.522068\pi$
$193$	1536.74	−	4729.58i	0.573143	−	1.76395i	0.642417	−	0.766355i	$-0.277932\pi$
$194$	−415.137	+	301.615i	−0.153635	+	0.111622i
$195$	−1189.97	−	864.565i	−0.437003	−	0.317501i
$196$	−370.476	−	1140.21i	−0.135013	−	0.415528i
$197$	1856.61			0.671463			0.335731	−	0.941958i	$-0.391017\pi$
$197$	1856.61			0.671463			0.335731	+	0.941958i	$0.391017\pi$
$198$	−27.9807	−	248.324i	−0.0100429	−	0.0891292i
$199$	−2935.58			−1.04572			−0.522858	−	0.852420i	$-0.675134\pi$
$199$	−2935.58			−1.04572			−0.522858	+	0.852420i	$0.675134\pi$
$200$	61.8034	+	190.211i	0.0218508	+	0.0672499i
$201$	696.851	+	506.292i	0.244538	+	0.177667i
$202$	306.908	−	222.982i	0.106901	−	0.0776681i
$203$	−6.72739	+	20.7048i	−0.00232596	+	0.00715858i
$204$	516.401	−	1589.32i	0.177232	−	0.545464i
$205$	83.3652	−	60.5684i	0.0284023	−	0.0206355i
$206$	2533.70	+	1840.84i	0.856948	+	0.622609i
$207$	74.8715	+	230.431i	0.0251398	+	0.0773722i
$208$	−969.397			−0.323152
$209$	90.9006	−	41.2896i	0.0300848	−	0.0136654i
$210$	319.421			0.104963
$211$	266.101	+	818.973i	0.0868205	+	0.267206i	0.985036	−	0.172350i	$-0.0551359\pi$
$211$	266.101	+	818.973i	0.0868205	+	0.267206i	−0.898215	+	0.439556i	$0.855136\pi$
$212$	1272.08	+	924.223i	0.412109	+	0.299415i
$213$	2083.48	−	1513.74i	0.670224	−	0.486946i
$214$	383.105	−	1179.08i	0.122376	−	0.376636i
$215$	725.027	−	2231.40i	0.229983	−	0.707816i
$216$	956.100	−	694.647i	0.301178	−	0.218818i
$217$	533.221	+	387.408i	0.166808	+	0.121193i
$218$	1301.67	+	4006.12i	0.404404	+	1.24463i
$219$	−4407.28			−1.35989
$220$	−714.828	−	146.358i	−0.219062	−	0.0448520i
$221$	−5213.14			−1.58676
$222$	−979.491	−	3014.56i	−0.296122	−	0.911371i
$223$	3758.37	+	2730.62i	1.12861	+	0.819980i	0.985491	−	0.169726i	$-0.0542882\pi$
$223$	3758.37	+	2730.62i	1.12861	+	0.819980i	0.143115	+	0.989706i	$0.454288\pi$
$224$	170.311	−	123.739i	0.0508010	−	0.0369091i
$225$	−26.4582	+	81.4301i	−0.00783948	+	0.0241274i
$226$	881.972	−	2714.43i	0.259592	−	0.798943i
$227$	303.468	−	220.482i	0.0887307	−	0.0644666i	−0.542535	−	0.840033i	$-0.682536\pi$
$227$	303.468	−	220.482i	0.0887307	−	0.0644666i	0.631266	+	0.775566i	$0.282536\pi$
$228$	42.9986	+	31.2403i	0.0124897	+	0.00907430i
$229$	−1195.04	−	3677.97i	−0.344850	−	1.06134i	−0.961664	−	0.274231i	$-0.911577\pi$
$229$	−1195.04	−	3677.97i	−0.344850	−	1.06134i	0.616814	−	0.787109i	$-0.288423\pi$
$230$	707.450			0.202817
$231$	−575.100	+	1013.55i	−0.163804	+	0.288686i
$232$	26.4739			0.00749180
$233$	899.234	+	2767.56i	0.252836	+	0.778149i	0.994248	+	0.107099i	$0.0341562\pi$
$233$	899.234	+	2767.56i	0.252836	+	0.778149i	−0.741412	+	0.671050i	$0.765844\pi$
$234$	−335.744	−	243.932i	−0.0937959	−	0.0681467i
$235$	1194.71	−	868.006i	0.331635	−	0.240947i
$236$	−729.802	+	2246.10i	−0.201297	+	0.619528i
$237$	1266.64	−	3898.32i	0.347161	−	1.06845i
$238$	915.886	−	665.430i	0.249446	−	0.181233i
$239$	173.901	+	126.347i	0.0470658	+	0.0341953i	0.611069	−	0.791577i	$-0.290740\pi$
$239$	173.901	+	126.347i	0.0470658	+	0.0341953i	−0.564004	+	0.825772i	$0.690740\pi$
$240$	−120.033	−	369.423i	−0.0322837	−	0.0993589i
$241$	3769.44			1.00751			0.503757	−	0.863846i	$-0.331951\pi$
$241$	3769.44			1.00751			0.503757	+	0.863846i	$0.331951\pi$
$242$	1751.41	−	2004.69i	0.465227	−	0.532507i
$243$	954.917			0.252090
$244$	−280.106	−	862.078i	−0.0734916	−	0.226184i
$245$	−1212.40	−	880.859i	−0.316152	−	0.229698i
$246$	−161.910	+	117.634i	−0.0419633	+	0.0304881i
$247$	51.2358	−	157.688i	0.0131986	−	0.0406211i
$248$	247.677	−	762.271i	0.0634173	−	0.195179i
$249$	−1900.57	+	1380.85i	−0.483710	+	0.351436i
$250$	202.254	+	146.946i	0.0511667	+	0.0371748i
$251$	−231.969	−	713.927i	−0.0583336	−	0.179532i	0.917644	−	0.397404i	$-0.130089\pi$
$251$	−231.969	−	713.927i	−0.0583336	−	0.179532i	−0.975978	+	0.217871i	$0.930089\pi$
$252$	90.1228			0.0225286
$253$	−1273.72	+	2244.79i	−0.316515	+	0.557821i
$254$	−3369.18			−0.832289
$255$	−645.502	−	1986.65i	−0.158521	−	0.487878i
$256$	−207.108	−	150.473i	−0.0505636	−	0.0367366i
$257$	1708.52	−	1241.31i	0.414687	−	0.301288i	−0.360810	−	0.932639i	$-0.617500\pi$
$257$	1708.52	−	1241.31i	0.414687	−	0.301288i	0.775497	+	0.631352i	$0.217500\pi$
$258$	−1408.13	+	4333.76i	−0.339791	+	1.04577i
$259$	663.559	−	2042.22i	0.159195	−	0.489952i
$260$	−980.323	+	712.246i	−0.233835	+	0.169891i
$261$	9.16905	+	6.66171i	0.00217452	+	0.00157988i
$262$	351.917	+	1083.09i	0.0829827	+	0.255395i
$263$	826.868			0.193866			0.0969332	−	0.995291i	$-0.469097\pi$
$263$	826.868			0.193866			0.0969332	+	0.995291i	$0.469097\pi$
$264$	1388.32	+	284.252i	0.323656	+	0.0662670i
$265$	1965.48			0.455616
$266$	11.1265	+	34.2438i	0.00256469	+	0.00789332i
$267$	238.978	+	173.628i	0.0547761	+	0.0397972i
$268$	574.080	−	417.094i	0.130849	−	0.0950673i
$269$	1940.94	−	5973.61i	0.439931	−	1.35397i	−0.448018	−	0.894025i	$-0.647870\pi$
$269$	1940.94	−	5973.61i	0.439931	−	1.35397i	0.887948	−	0.459943i	$-0.152130\pi$
$270$	456.497	−	1404.95i	0.102895	−	0.316677i
$271$	1838.97	−	1336.09i	0.412213	−	0.299490i	−0.362284	−	0.932068i	$-0.618003\pi$
$271$	1838.97	−	1336.09i	0.412213	−	0.299490i	0.774497	+	0.632577i	$0.218003\pi$
$272$	−1113.77	−	809.201i	−0.248280	−	0.180386i
$273$	598.036	+	1840.57i	0.132582	+	0.408045i
$274$	−4734.72			−1.04392
$275$	−830.419	+	377.199i	−0.182095	+	0.0827126i
$276$	−1373.99			−0.299653
$277$	1653.97	+	5090.38i	0.358762	+	1.10416i	0.953796	+	0.300456i	$0.0971388\pi$
$277$	1653.97	+	5090.38i	0.358762	+	1.10416i	−0.595033	+	0.803701i	$0.702861\pi$
$278$	−383.598	−	278.700i	−0.0827578	−	0.0601270i
$279$	277.594	−	201.684i	0.0595667	−	0.0432777i
$280$	81.3165	−	250.266i	0.0173557	−	0.0534153i
$281$	−996.700	+	3067.53i	−0.211595	+	0.651222i	0.787783	+	0.615953i	$0.211229\pi$
$281$	−996.700	+	3067.53i	−0.211595	+	0.651222i	−0.999378	+	0.0352690i	$0.988771\pi$
$282$	−2320.33	+	1685.82i	−0.489977	+	0.355989i
$283$	2059.14	+	1496.05i	0.432519	+	0.314244i	0.782655	−	0.622455i	$-0.213865\pi$
$283$	2059.14	+	1496.05i	0.432519	+	0.314244i	−0.350136	+	0.936699i	$0.613865\pi$
$284$	−655.612	−	2017.77i	−0.136984	−	0.421593i
$285$	66.4365			0.0138083
$286$	−494.995	−	4393.00i	−0.102341	−	0.908264i
$287$	−135.579			−0.0278850
$288$	−33.8666	−	104.231i	−0.00692919	−	0.0213258i
$289$	−2014.83	−	1463.86i	−0.410102	−	0.297957i
$290$	26.7723	−	19.4512i	0.00542112	−	0.00393867i
$291$	384.958	−	1184.78i	0.0775486	−	0.238670i
$292$	−1121.98	+	3453.10i	−0.224860	+	0.692047i
$293$	6284.90	−	4566.25i	1.25313	−	0.910454i	0.254733	−	0.967011i	$-0.418012\pi$
$293$	6284.90	−	4566.25i	1.25313	−	0.910454i	0.998399	+	0.0565575i	$0.0180124\pi$
$294$	2354.69	+	1710.78i	0.467102	+	0.339370i
$295$	912.252	+	2807.62i	0.180045	+	0.554123i
$296$	−2611.26			−0.512759
$297$	3636.12	+	3978.04i	0.710402	+	0.777203i
$298$	4129.69			0.802773
$299$	1324.52	+	4076.46i	0.256184	+	0.788454i
$300$	−392.812	−	285.395i	−0.0755968	−	0.0549243i
$301$	−2497.44	+	1814.50i	−0.478240	+	0.347462i
$302$	−1789.19	+	5506.57i	−0.340915	+	1.04923i
$303$	−284.597	+	875.901i	−0.0539594	+	0.166070i
$304$	35.4231	−	25.7364i	0.00668308	−	0.00485554i
$305$	−916.659	−	665.992i	−0.172091	−	0.125031i
$306$	−182.125	−	560.522i	−0.0340241	−	0.104715i
$307$	4801.35			0.892599			0.446299	−	0.894884i	$-0.352742\pi$
$307$	4801.35			0.892599			0.446299	+	0.894884i	$0.352742\pi$
$308$	647.708	+	708.614i	0.119827	+	0.131094i
$309$	−7603.17			−1.39977
$310$	−309.596	−	952.839i	−0.0567222	−	0.174573i
$311$	7628.35	+	5542.32i	1.39088	+	1.01053i	0.995768	+	0.0919022i	$0.0292947\pi$
$311$	7628.35	+	5542.32i	1.39088	+	1.01053i	0.395113	+	0.918632i	$0.370705\pi$
$312$	1903.95	−	1383.30i	0.345481	−	0.251007i
$313$	−1017.72	+	3132.22i	−0.183786	+	0.565635i	−0.999925	−	0.0122202i	$-0.996110\pi$
$313$	−1017.72	+	3132.22i	−0.183786	+	0.565635i	0.816139	+	0.577855i	$0.196110\pi$
$314$	−1015.76	+	3126.18i	−0.182556	+	0.561849i
$315$	91.1386	−	66.2161i	0.0163018	−	0.0118440i
$316$	−2731.88	−	1984.83i	−0.486330	−	0.353339i
$317$	−1801.38	−	5544.08i	−0.319166	−	0.982292i	−0.974006	−	0.226524i	$-0.927264\pi$
$317$	−1801.38	−	5544.08i	−0.319166	−	0.982292i	0.654840	−	0.755768i	$-0.272736\pi$
$318$	−3817.29			−0.673155
$319$	13.5182	+	119.971i	0.00237264	+	0.0210568i
$320$	−320.000			−0.0559017
$321$	930.070	+	2862.46i	0.161718	+	0.497716i
$322$	−753.042	−	547.117i	−0.130327	−	0.0946884i
$323$	190.496	−	138.403i	0.0328156	−	0.0238420i
$324$	−772.296	+	2376.88i	−0.132424	+	0.407559i
$325$	−468.063	+	1440.55i	−0.0798875	+	0.245868i
$326$	−4904.92	+	3563.63i	−0.833307	+	0.605433i
$327$	−8273.19	−	6010.83i	−1.39911	−	1.01651i
$328$	50.9483	+	156.803i	0.00857667	+	0.0263963i
$329$	−1942.99			−0.325594
$330$	1612.82	−	732.586i	0.269038	−	0.122205i
$331$	−7825.06			−1.29941			−0.649704	−	0.760187i	$-0.725107\pi$
$331$	−7825.06			−1.29941			−0.649704	+	0.760187i	$0.725107\pi$
$332$	598.056	+	1840.63i	0.0988632	+	0.304270i
$333$	−904.393	−	657.080i	−0.148830	−	0.108131i
$334$	−2775.02	+	2016.17i	−0.454618	+	0.330300i
$335$	274.099	−	843.589i	0.0447033	−	0.137583i
$336$	−157.931	+	486.060i	−0.0256423	+	0.0789189i
$337$	−8900.52	+	6466.61i	−1.43870	+	1.04528i	−0.450389	+	0.892832i	$0.648715\pi$
$337$	−8900.52	+	6466.61i	−1.43870	+	1.04528i	−0.988312	+	0.152446i	$0.951285\pi$
$338$	−2384.69	−	1732.58i	−0.383758	−	0.278816i
$339$	2141.18	+	6589.86i	0.343046	+	1.05579i
$340$	−1720.87			−0.274492
$341$	3580.84	+	733.161i	0.568661	+	0.116431i
$342$	18.7447			0.00296373
$343$	1306.60	+	4021.29i	0.205684	+	0.633030i
$344$	3037.03	+	2206.53i	0.476005	+	0.345838i
$345$	−1389.47	+	1009.51i	−0.216831	+	0.157537i
$346$	1177.83	−	3624.98i	0.183007	−	0.563238i
$347$	161.440	−	496.860i	0.0249756	−	0.0768670i	−0.937792	−	0.347198i	$-0.887133\pi$
$347$	161.440	−	496.860i	0.0249756	−	0.0768670i	0.962767	+	0.270331i	$0.0871332\pi$
$348$	−51.9964	+	37.7776i	−0.00800948	+	0.00581923i
$349$	2673.40	+	1942.34i	0.410039	+	0.297911i	0.773618	−	0.633653i	$-0.218445\pi$
$349$	2673.40	+	1942.34i	0.410039	+	0.297911i	−0.363579	+	0.931564i	$0.618445\pi$
$350$	−101.646	−	312.833i	−0.0155234	−	0.0477761i
$351$	8950.29			1.36106
$352$	576.142	−	1015.38i	0.0872400	−	0.153750i
$353$	−1935.23			−0.291790			−0.145895	−	0.989300i	$-0.546606\pi$
$353$	−1935.23			−0.291790			−0.145895	+	0.989300i	$0.546606\pi$
$354$	−1771.75	−	5452.89i	−0.266010	−	0.818694i
$355$	−2145.52	−	1558.81i	−0.320767	−	0.233051i
$356$	196.875	−	143.038i	0.0293100	−	0.0212949i
$357$	−849.305	+	2613.89i	−0.125910	+	0.387512i
$358$	2131.86	−	6561.20i	0.314728	−	0.968632i
$359$	6399.55	−	4649.55i	0.940823	−	0.683548i	−0.00779550	−	0.999970i	$-0.502481\pi$
$359$	6399.55	−	4649.55i	0.940823	−	0.683548i	0.948619	+	0.316422i	$0.102481\pi$
$360$	−110.830	−	80.5225i	−0.0162257	−	0.0117886i
$361$	−2117.23	−	6516.17i	−0.308680	−	0.950018i
$362$	2184.42			0.317156
$363$	−579.234	+	6436.56i	−0.0837518	+	0.930667i
$364$	1594.33			0.229576
$365$	1402.48	+	4316.38i	0.201121	+	0.618985i
$366$	1780.31	+	1293.47i	0.254258	+	0.184729i
$367$	5264.60	−	3824.95i	0.748800	−	0.544035i	−0.146655	−	0.989188i	$-0.546851\pi$
$367$	5264.60	−	3824.95i	0.748800	−	0.544035i	0.895455	+	0.445153i	$0.146851\pi$
$368$	−349.782	+	1076.52i	−0.0495480	+	0.152493i
$369$	−21.8111	+	67.1278i	−0.00307708	+	0.00947028i
$370$	−2640.70	+	1918.58i	−0.371036	+	0.269573i
$371$	−2092.15	−	1520.03i	−0.292773	−	0.212712i
$372$	601.289	+	1850.58i	0.0838048	+	0.257925i
$373$	−11279.2			−1.56573			−0.782863	−	0.622194i	$-0.786242\pi$
$373$	−11279.2			−1.56573			−0.782863	+	0.622194i	$0.786242\pi$
$374$	3098.33	−	5460.44i	0.428371	−	0.754954i
$375$	−606.928			−0.0835777
$376$	730.140	+	2247.14i	0.100144	+	0.308211i
$377$	162.206	+	117.850i	0.0221593	+	0.0160997i
$378$	−1572.46	+	1142.46i	−0.213965	+	0.155454i
$379$	4247.48	−	13072.4i	0.575668	−	1.77172i	−0.0582246	−	0.998304i	$-0.518544\pi$
$379$	4247.48	−	13072.4i	0.575668	−	1.77172i	0.633893	−	0.773421i	$-0.281456\pi$
$380$	16.9130	−	52.0530i	0.00228321	−	0.00702701i
$381$	6617.29	−	4807.74i	0.889800	−	0.646478i
$382$	−4066.48	−	2954.47i	−0.544657	−	0.395717i
$383$	−2958.80	−	9106.26i	−0.394746	−	1.21490i	−0.929159	−	0.369680i	$-0.879467\pi$
$383$	−2958.80	−	9106.26i	−0.394746	−	1.21490i	0.534413	−	0.845224i	$-0.320533\pi$
$384$	621.495			0.0825925
$385$	1175.65	+	240.709i	0.155628	+	0.0318641i
$386$	9945.96			1.31149
$387$	496.618	+	1528.43i	0.0652313	+	0.200761i
$388$	−830.274	−	603.229i	−0.108636	−	0.0789287i
$389$	515.928	−	374.843i	0.0672457	−	0.0488568i	−0.553655	−	0.832746i	$-0.686767\pi$
$389$	515.928	−	374.843i	0.0672457	−	0.0488568i	0.620900	+	0.783890i	$0.286767\pi$
$390$	909.058	−	2797.79i	0.118031	−	0.363261i
$391$	−1881.03	+	5789.21i	−0.243293	+	0.748780i
$392$	1939.84	−	1409.37i	0.249940	−	0.181592i
$393$	−2236.72	−	1625.08i	−0.287094	−	0.208586i
$394$	1147.45	+	3531.49i	0.146720	+	0.451558i
$395$	−4220.99			−0.537673
$396$	455.047	−	206.695i	0.0577448	−	0.0262293i
$397$	3536.03			0.447023			0.223511	−	0.974701i	$-0.428248\pi$
$397$	3536.03			0.447023			0.223511	+	0.974701i	$0.428248\pi$
$398$	−1814.29	−	5583.80i	−0.228497	−	0.703242i
$399$	−70.7181	−	51.3797i	−0.00887302	−	0.00644663i
$400$	−323.607	+	235.114i	−0.0404508	+	0.0293893i
$401$	−3281.90	+	10100.6i	−0.408704	+	1.25786i	0.509059	+	0.860731i	$0.329993\pi$
$401$	−3281.90	+	10100.6i	−0.408704	+	1.25786i	−0.917763	+	0.397129i	$0.870007\pi$
$402$	−532.347	+	1638.39i	−0.0660474	+	0.203273i
$403$	4910.80	−	3567.91i	0.607009	−	0.441018i
$404$	613.817	+	445.964i	0.0755904	+	0.0549197i
$405$	965.369	+	2971.10i	0.118443	+	0.364531i
$406$	−43.5406			−0.00532237
$407$	−1333.37	−	11833.4i	−0.162390	−	1.44118i
$408$	3342.22			0.405550
$409$	2743.51	+	8443.66i	0.331682	+	1.02081i	0.968333	+	0.249661i	$0.0803191\pi$
$409$	2743.51	+	8443.66i	0.331682	+	1.02081i	−0.636651	+	0.771152i	$0.719681\pi$
$410$	166.730	+	121.137i	0.0200835	+	0.0145915i
$411$	9299.27	−	6756.32i	1.11606	−	0.810863i
$412$	−1935.57	+	5957.08i	−0.231454	+	0.712341i
$413$	1200.28	−	3694.07i	0.143007	−	0.440129i
$414$	−392.032	+	284.828i	−0.0465395	+	0.0338129i
$415$	1957.16	+	1421.96i	0.231502	+	0.168196i
$416$	−599.120	−	1843.90i	−0.0706113	−	0.217319i
$417$	1151.11			0.135180
$418$	134.717	+	147.385i	0.0157637	+	0.0172460i
$419$	12737.7			1.48514			0.742572	−	0.669766i	$-0.233606\pi$
$419$	12737.7			1.48514			0.742572	+	0.669766i	$0.233606\pi$
$420$	197.413	+	607.575i	0.0229352	+	0.0705872i
$421$	−9558.11	−	6944.37i	−1.10649	−	0.803914i	−0.124385	−	0.992234i	$-0.539696\pi$
$421$	−9558.11	−	6944.37i	−1.10649	−	0.803914i	−0.982108	+	0.188320i	$0.939696\pi$
$422$	−1393.32	+	1012.31i	−0.160725	+	0.116773i
$423$	−312.575	+	962.008i	−0.0359289	+	0.110578i
$424$	−971.786	+	2990.85i	−0.111307	+	0.342567i
$425$	−1740.26	+	1264.38i	−0.198624	+	0.144309i
$426$	4166.96	+	3027.47i	0.473920	+	0.344323i
$427$	460.680	+	1417.83i	0.0522104	+	0.160687i
$428$	2479.51			0.280027
$429$	7240.89	+	7921.77i	0.814904	+	0.891531i
$430$	4692.47			0.526258
$431$	−3934.52	−	12109.2i	−0.439720	−	1.35332i	−0.888172	−	0.459512i	$-0.848024\pi$
$431$	−3934.52	−	12109.2i	−0.439720	−	1.35332i	0.448452	−	0.893807i	$-0.351976\pi$
$432$	1912.20	+	1389.29i	0.212965	+	0.154728i
$433$	−11371.1	+	8261.61i	−1.26204	+	0.916923i	−0.998856	−	0.0478236i	$-0.984771\pi$
$433$	−11371.1	+	8261.61i	−1.26204	+	0.916923i	−0.263180	+	0.964747i	$0.584771\pi$
$434$	−407.345	+	1253.68i	−0.0450534	+	0.138660i
$435$	−24.8261	+	76.4068i	−0.00273637	+	0.00842167i
$436$	−6815.63	+	4951.84i	−0.748645	+	0.543923i
$437$	−156.626	−	113.795i	−0.0171451	−	0.0124567i
$438$	−2723.85	−	8383.15i	−0.297147	−	0.914526i
$439$	−6223.79			−0.676641			−0.338320	−	0.941031i	$-0.609859\pi$
$439$	−6223.79			−0.676641			−0.338320	+	0.941031i	$0.609859\pi$
$440$	−163.399	−	1450.14i	−0.0177040	−	0.157120i
$441$	1026.49			0.110841
$442$	−3221.90	−	9915.98i	−0.346719	−	1.06709i
$443$	−1921.62	−	1396.14i	−0.206092	−	0.149735i	0.479952	−	0.877295i	$-0.340654\pi$
$443$	−1921.62	−	1396.14i	−0.206092	−	0.149735i	−0.686044	+	0.727560i	$0.740654\pi$
$444$	5128.68	−	3726.21i	0.548190	−	0.398284i
$445$	93.9994	−	289.301i	0.0100135	−	0.0308183i
$446$	−2871.14	+	8836.46i	−0.304826	+	0.938158i
$447$	−8110.96	+	5892.96i	−0.858244	+	0.623551i
$448$	340.623	+	247.477i	0.0359217	+	0.0260986i
$449$	−3792.56	−	11672.3i	−0.398623	−	1.22684i	−0.926104	−	0.377269i	$-0.876863\pi$
$449$	−3792.56	−	11672.3i	−0.398623	−	1.22684i	0.527480	−	0.849567i	$-0.323137\pi$
$450$	−171.241			−0.0179387
$451$	−684.565	+	310.948i	−0.0714743	+	0.0324656i
$452$	5708.24			0.594011
$453$	−4343.65	−	13368.4i	−0.450513	−	1.38654i
$454$	606.935	+	440.964i	0.0627421	+	0.0455848i
$455$	1612.30	−	1171.40i	0.166122	−	0.120695i
$456$	−32.8480	+	101.096i	−0.00337335	+	0.0103821i
$457$	−4001.69	+	12315.9i	−0.409608	+	1.26064i	0.507377	+	0.861724i	$0.330615\pi$
$457$	−4001.69	+	12315.9i	−0.409608	+	1.26064i	−0.916985	+	0.398921i	$0.869385\pi$
$458$	6257.33	−	4546.22i	0.638397	−	0.463822i
$459$	10283.3	+	7471.23i	1.04571	+	0.759754i
$460$	437.228	+	1345.65i	0.0443171	+	0.136394i
$461$	13992.6			1.41367			0.706835	−	0.707379i	$-0.250123\pi$
$461$	13992.6			1.41367			0.706835	+	0.707379i	$0.250123\pi$
$462$	−2283.31	−	467.498i	−0.229934	−	0.0470779i
$463$	5749.62			0.577122			0.288561	−	0.957462i	$-0.406823\pi$
$463$	5749.62			0.577122			0.288561	+	0.957462i	$0.406823\pi$
$464$	16.3618	+	50.3564i	0.00163702	+	0.00503823i
$465$	1967.74	+	1429.65i	0.196241	+	0.142577i
$466$	−4708.45	+	3420.89i	−0.468057	+	0.340063i
$467$	5635.37	−	17343.9i	0.558402	−	1.71858i	−0.128384	−	0.991725i	$-0.540979\pi$
$467$	5635.37	−	17343.9i	0.558402	−	1.71858i	0.686786	−	0.726860i	$-0.259021\pi$
$468$	256.485	−	789.381i	0.0253334	−	0.0779682i
$469$	−944.167	+	685.977i	−0.0929586	+	0.0675384i
$470$	2389.41	+	1736.01i	0.234501	+	0.170375i
$471$	−2465.97	−	7589.47i	−0.241244	−	0.742472i
$472$	−4723.38			−0.460617
$473$	−8448.53	+	14889.6i	−0.821276	+	1.44741i
$474$	8197.88			0.794390
$475$	−21.1413	−	65.0663i	−0.00204217	−	0.00628515i
$476$	1831.77	+	1330.86i	0.176385	+	0.128151i
$477$	−1089.17	+	791.326i	−0.104548	+	0.0759588i
$478$	−132.849	+	408.866i	−0.0127120	+	0.0391236i
$479$	−4158.70	+	12799.2i	−0.396693	+	1.22089i	0.530943	+	0.847408i	$0.321838\pi$
$479$	−4158.70	+	12799.2i	−0.396693	+	1.22089i	−0.927635	+	0.373487i	$0.878162\pi$
$480$	628.500	−	456.632i	0.0597645	−	0.0434214i
$481$	−15999.3	−	11624.1i	−1.51664	−	1.10190i
$482$	2329.64	+	7169.89i	0.220150	+	0.677551i
$483$	2259.74			0.212882
$484$	4895.59	+	2092.41i	0.459766	+	0.196508i
$485$	−1282.84			−0.120105
$486$	590.171	+	1816.36i	0.0550838	+	0.169530i
$487$	−7795.15	−	5663.51i	−0.725323	−	0.526978i	0.162758	−	0.986666i	$-0.447961\pi$
$487$	−7795.15	−	5663.51i	−0.725323	−	0.526978i	−0.888080	+	0.459688i	$0.847961\pi$
$488$	1466.66	−	1065.59i	0.136050	−	0.0988461i
$489$	4548.35	−	13998.4i	0.420621	−	1.29454i
$490$	926.190	−	2850.52i	0.0853898	−	0.262803i
$491$	−1302.40	+	946.249i	−0.119708	+	0.0869727i	−0.646028	−	0.763313i	$-0.723571\pi$
$491$	−1302.40	+	946.249i	−0.119708	+	0.0869727i	0.526321	+	0.850286i	$0.323571\pi$
$492$	−323.819	−	235.268i	−0.0296725	−	0.0215584i
$493$	87.9890	+	270.802i	0.00803818	+	0.0247390i
$494$	331.605			0.0302016
$495$	308.310	−	543.362i	0.0279950	−	0.0493380i
$496$	1603.00			0.145114
$497$	1078.26	+	3318.54i	0.0973170	+	0.299511i
$498$	−3801.15	−	2761.69i	−0.342035	−	0.248503i
$499$	−8410.54	+	6110.61i	−0.754524	+	0.548194i	−0.897226	−	0.441572i	$-0.854421\pi$
$499$	−8410.54	+	6110.61i	−0.754524	+	0.548194i	0.142702	+	0.989766i	$0.454421\pi$
$500$	−154.508	+	475.528i	−0.0138197	+	0.0425325i
$501$	2573.29	−	7919.77i	0.229473	−	0.706246i
$502$	1214.60	−	882.462i	0.107989	−	0.0784586i
$503$	−11410.9	−	8290.53i	−1.01151	−	0.734903i	−0.0469828	−	0.998896i	$-0.514961\pi$
$503$	−11410.9	−	8290.53i	−1.01151	−	0.734903i	−0.964525	+	0.263992i	$0.914961\pi$
$504$	55.6990	+	171.424i	0.00492268	+	0.0151504i
$505$	948.399			0.0835707
$506$	−5057.05	−	1035.41i	−0.444295	−	0.0909674i
$507$	7156.03			0.626845
$508$	−2082.27	−	6408.57i	−0.181862	−	0.559713i
$509$	−7153.35	−	5197.21i	−0.622921	−	0.452578i	0.231020	−	0.972949i	$-0.425794\pi$
$509$	−7153.35	−	5197.21i	−0.622921	−	0.452578i	−0.853941	+	0.520371i	$0.825794\pi$
$510$	3379.89	−	2455.63i	0.293459	−	0.213210i
$511$	1845.28	−	5679.18i	0.159746	−	0.491648i
$512$	158.217	−	486.941i	0.0136568	−	0.0420312i
$513$	−327.056	+	237.620i	−0.0281479	+	0.0204507i
$514$	3417.04	+	2482.62i	0.293228	+	0.213043i
$515$	2419.47	+	7446.36i	0.207018	+	0.637137i
$516$	−9113.58			−0.777525
$517$	−9810.50	+	4456.20i	−0.834556	+	0.379078i
$518$	4294.64			0.364278
$519$	2859.43	+	8800.42i	0.241840	+	0.744308i
$520$	−1960.65	−	1424.49i	−0.165346	−	0.120131i
$521$	−15305.2	+	11119.9i	−1.28701	+	0.935068i	−0.999740	−	0.0227817i	$-0.992748\pi$
$521$	−15305.2	+	11119.9i	−1.28701	+	0.935068i	−0.287270	+	0.957850i	$0.592748\pi$
$522$	−7.00453	+	21.5577i	−0.000587318	+	0.00180758i
$523$	−5642.54	+	17365.9i	−0.471761	+	1.45193i	0.378516	+	0.925595i	$0.376435\pi$
$523$	−5642.54	+	17365.9i	−0.471761	+	1.45193i	−0.850277	+	0.526336i	$0.823565\pi$
$524$	−1842.66	+	1338.77i	−0.153620	+	0.111612i
$525$	646.043	+	469.378i	0.0537060	+	0.0390197i
$526$	511.033	+	1572.80i	0.0423614	+	0.130375i
$527$	8620.47			0.712549
$528$	317.349	+	2816.42i	0.0261569	+	0.232138i
$529$	−7162.15			−0.588654
$530$	1214.73	+	3738.56i	0.0995558	+	0.306401i
$531$	−1635.91	−	1188.56i	−0.133696	−	0.0971355i
$532$	−58.2590	+	42.3277i	−0.00474784	+	0.00344951i
$533$	−385.852	+	1187.53i	−0.0313567	+	0.0965060i
$534$	−182.563	+	561.871i	−0.0147945	+	0.0455328i
$535$	2507.46	−	1821.77i	0.202630	−	0.147219i
$536$	1148.16	+	834.187i	0.0925242	+	0.0672228i
$537$	5175.56	+	15928.7i	0.415906	+	1.28003i
$538$	12562.0			1.00667
$539$	7377.36	+	8071.07i	0.589546	+	0.644983i
$540$	2954.51			0.235448
$541$	−4297.73	−	13227.0i	−0.341541	−	1.05115i	−0.963410	−	0.268033i	$-0.913626\pi$
$541$	−4297.73	−	13227.0i	−0.341541	−	1.05115i	0.621869	−	0.783122i	$-0.286374\pi$
$542$	3677.95	+	2672.19i	0.291479	+	0.211772i
$543$	−4290.34	+	3117.11i	−0.339072	+	0.246350i
$544$	850.844	−	2618.63i	0.0670582	−	0.206384i
$545$	−3254.17	+	10015.3i	−0.255768	+	0.787172i
$546$	−3131.36	+	2275.07i	−0.245439	+	0.178322i
$547$	−4602.92	−	3344.22i	−0.359793	−	0.261405i	0.393173	−	0.919465i	$-0.371377\pi$
$547$	−4602.92	−	3344.22i	−0.359793	−	0.261405i	−0.752966	+	0.658060i	$0.771377\pi$
$548$	−2926.22	−	9005.97i	−0.228105	−	0.702036i
$549$	776.102			0.0603338
$550$	−1230.70	−	1346.43i	−0.0954134	−	0.104385i
$551$	−9.05603			−0.000700181
$552$	−849.171	−	2613.48i	−0.0654767	−	0.201517i
$553$	4493.02	+	3264.37i	0.345502	+	0.251022i
$554$	−8660.28	+	6292.06i	−0.664151	+	0.482534i
$555$	2448.73	−	7536.41i	0.187284	−	0.576401i
$556$	293.042	−	901.892i	0.0223521	−	0.0687927i
$557$	−2992.24	+	2173.99i	−0.227622	+	0.165377i	−0.695751	−	0.718283i	$-0.744928\pi$
$557$	−2992.24	+	2173.99i	−0.227622	+	0.165377i	0.468129	+	0.883660i	$0.344928\pi$
$558$	555.187	+	403.367i	0.0421200	+	0.0306020i
$559$	8785.48	+	27038.9i	0.664734	+	2.04584i
$560$	526.291			0.0397141
$561$	1706.61	+	15145.9i	0.128437	+	1.13986i
$562$	−6450.78			−0.484181
$563$	1836.16	+	5651.11i	0.137451	+	0.423030i	0.995963	−	0.0897627i	$-0.0286109\pi$
$563$	1836.16	+	5651.11i	0.137451	+	0.423030i	−0.858512	+	0.512793i	$0.828611\pi$
$564$	−4640.65	−	3371.63i	−0.346466	−	0.251722i
$565$	5772.58	−	4194.03i	0.429831	−	0.312290i
$566$	−1573.04	+	4841.32i	−0.116819	+	0.359533i
$567$	1270.16	−	3909.16i	0.0940774	−	0.289540i
$568$	3432.83	−	2494.10i	0.253588	−	0.184243i
$569$	19564.6	+	14214.5i	1.44146	+	1.04728i	0.987734	+	0.156145i	$0.0499067\pi$
$569$	19564.6	+	14214.5i	1.44146	+	1.04728i	0.453729	+	0.891140i	$0.350093\pi$
$570$	41.0600	+	126.370i	0.00301722	+	0.00928605i
$571$	−8285.39			−0.607238			−0.303619	−	0.952794i	$-0.598195\pi$
$571$	−8285.39			−0.607238			−0.303619	+	0.952794i	$0.598195\pi$
$572$	8050.05	−	3656.56i	0.588443	−	0.267287i
$573$	12202.8			0.889665
$574$	−83.7927	−	257.887i	−0.00609310	−	0.0187526i
$575$	1430.85	+	1039.57i	0.103775	+	0.0753967i
$576$	177.328	−	128.836i	0.0128275	−	0.00931974i
$577$	1695.71	−	5218.87i	0.122346	−	0.376541i	−0.871062	−	0.491172i	$-0.836569\pi$
$577$	1695.71	−	5218.87i	0.122346	−	0.376541i	0.993408	+	0.114631i	$0.0365685\pi$
$578$	1539.19	−	4737.15i	0.110765	−	0.340899i
$579$	−19534.5	+	14192.6i	−1.40212	+	1.01870i
$580$	53.5446	+	38.9024i	0.00383331	+	0.00278506i
$581$	−983.599	−	3027.21i	−0.0702350	−	0.216161i
$582$	2491.50			0.177450
$583$	−14049.8	−	2876.63i	−0.998084	−	0.204353i
$584$	−7261.62			−0.514534
$585$	−320.607	−	986.726i	−0.0226589	−	0.0697369i
$586$	12569.8	+	9132.49i	0.886098	+	0.643788i
$587$	3366.78	−	2446.11i	0.236733	−	0.171996i	−0.463094	−	0.886309i	$-0.653261\pi$
$587$	3366.78	−	2446.11i	0.236733	−	0.171996i	0.699826	+	0.714313i	$0.253261\pi$
$588$	−1798.82	+	5536.20i	−0.126160	+	0.388281i
$589$	−84.7237	+	260.753i	−0.00592696	+	0.0182413i
$590$	−4776.62	+	3470.41i	−0.333305	+	0.242161i
$591$	−7293.00	−	5298.68i	−0.507604	−	0.368796i
$592$	−1613.85	−	4966.92i	−0.112042	−	0.344830i
$593$	20458.1			1.41672			0.708358	−	0.705853i	$-0.249436\pi$
$593$	20458.1			1.41672			0.708358	+	0.705853i	$0.249436\pi$
$594$	−5319.43	+	9374.88i	−0.367439	+	0.647569i
$595$	2830.24			0.195006
$596$	2552.29	+	7855.13i	0.175412	+	0.539864i
$597$	11531.3	+	8377.98i	0.790527	+	0.574352i
$598$	−6935.29	+	5038.78i	−0.474256	+	0.344567i
$599$	4714.00	−	14508.2i	0.321551	−	0.989632i	−0.651423	−	0.758715i	$-0.725828\pi$
$599$	4714.00	−	14508.2i	0.321551	−	0.989632i	0.972974	−	0.230917i	$-0.0741725\pi$
$600$	300.082	−	923.557i	0.0204180	−	0.0628401i
$601$	15496.6	−	11258.9i	1.05178	−	0.764160i	0.0792271	−	0.996857i	$-0.474755\pi$
$601$	15496.6	−	11258.9i	1.05178	−	0.764160i	0.972549	+	0.232696i	$0.0747548\pi$
$602$	−4994.88	−	3629.00i	−0.338167	−	0.245692i
$603$	187.748	+	577.830i	0.0126794	+	0.0390233i
$604$	−11579.9			−0.780098
$605$	6488.13	−	1480.94i	0.436000	−	0.0995189i
$606$	−1841.95			−0.123472
$607$	−4639.44	−	14278.7i	−0.310229	−	0.954787i	−0.977674	−	0.210127i	$-0.932612\pi$
$607$	−4639.44	−	14278.7i	−0.310229	−	0.954787i	0.667445	−	0.744659i	$-0.267388\pi$
$608$	70.8463	+	51.4728i	0.00472565	+	0.00343339i
$609$	85.5164	−	62.1313i	0.00569015	−	0.00413414i
$610$	700.266	−	2155.20i	0.0464802	−	0.143051i
$611$	−5529.65	+	17018.5i	−0.366131	+	1.12683i
$612$	953.617	−	692.843i	0.0629864	−	0.0457623i
$613$	−14244.9	−	10349.5i	−0.938576	−	0.681915i	0.00950179	−	0.999955i	$-0.496975\pi$
$613$	−14244.9	−	10349.5i	−0.938576	−	0.681915i	−0.948077	+	0.318040i	$0.896975\pi$
$614$	2967.40	+	9132.72i	0.195040	+	0.600271i
$615$	−500.328			−0.0328052
$616$	−947.558	+	1669.96i	−0.0619776	+	0.109228i
$617$	15674.4			1.02273			0.511367	−	0.859362i	$-0.329139\pi$
$617$	15674.4			1.02273			0.511367	+	0.859362i	$0.329139\pi$
$618$	−4699.02	−	14462.1i	−0.305861	−	0.941344i
$619$	3285.50	+	2387.06i	0.213337	+	0.154998i	0.689322	−	0.724455i	$-0.257908\pi$
$619$	3285.50	+	2387.06i	0.213337	+	0.154998i	−0.475985	+	0.879453i	$0.657908\pi$
$620$	1621.07	−	1177.77i	0.105006	−	0.0762912i
$621$	3229.49	−	9939.34i	0.208687	−	0.642273i
$622$	−5827.54	+	17935.3i	−0.375664	+	1.15618i
$623$	−323.793	+	235.249i	−0.0208226	+	0.0151285i
$624$	3807.91	+	2766.61i	0.244292	+	0.177489i
$625$	193.136	+	594.410i	0.0123607	+	0.0380423i
$626$	−6586.83			−0.420547
$627$	−474.907	−	97.2351i	−0.0302487	−	0.00619329i
$628$	−6574.12			−0.417733
$629$	−8678.82	−	26710.7i	−0.550155	−	1.69320i
$630$	182.277	+	132.432i	0.0115271	+	0.00837496i
$631$	17179.1	−	12481.4i	1.08382	−	0.787440i	0.105474	−	0.994422i	$-0.466364\pi$
$631$	17179.1	−	12481.4i	1.08382	−	0.787440i	0.978345	+	0.206982i	$0.0663640\pi$
$632$	2086.97	−	6423.04i	0.131353	−	0.404264i
$633$	1292.03	−	3976.47i	0.0811274	−	0.249685i
$634$	9432.15	−	6852.86i	0.590850	−	0.429277i
$635$	−6814.32	−	4950.89i	−0.425855	−	0.309402i
$636$	−2359.22	−	7260.92i	−0.147090	−	0.452696i
$637$	18159.3			1.12951
$638$	−219.844	+	99.8594i	−0.0136422	+	0.00619667i
$639$	1816.53			0.112458
$640$	−197.771	−	608.676i	−0.0122150	−	0.0375938i
$641$	−7288.20	−	5295.19i	−0.449090	−	0.326283i	0.340147	−	0.940372i	$-0.389523\pi$
$641$	−7288.20	−	5295.19i	−0.449090	−	0.326283i	−0.789236	+	0.614090i	$0.789523\pi$
$642$	−4869.91	+	3538.20i	−0.299377	+	0.217510i
$643$	−1497.60	+	4609.12i	−0.0918498	+	0.282684i	−0.986420	−	0.164243i	$-0.947482\pi$
$643$	−1497.60	+	4609.12i	−0.0918498	+	0.282684i	0.894570	+	0.446928i	$0.147482\pi$
$644$	575.273	−	1770.51i	0.0352002	−	0.108335i
$645$	−9216.30	+	6696.03i	−0.562622	+	0.408769i
$646$	380.991	+	276.806i	0.0232042	+	0.0168588i
$647$	−7433.11	−	22876.8i	−0.451663	−	1.39008i	−0.875009	−	0.484107i	$-0.839144\pi$
$647$	−7433.11	−	22876.8i	−0.451663	−	1.39008i	0.423346	−	0.905968i	$-0.360856\pi$
$648$	−4998.40			−0.303018
$649$	−2411.86	−	21404.8i	−0.145876	−	1.29463i
$650$	−3029.36			−0.182802
$651$	−988.916	−	3043.57i	−0.0595371	−	0.183236i
$652$	−9809.83	−	7127.26i	−0.589237	−	0.428106i
$653$	3601.27	−	2616.47i	0.215817	−	0.156800i	−0.474625	−	0.880188i	$-0.657416\pi$
$653$	3601.27	−	2616.47i	0.215817	−	0.156800i	0.690442	+	0.723388i	$0.257416\pi$
$654$	6320.16	−	19451.4i	0.377886	−	1.16301i
$655$	−879.791	+	2707.72i	−0.0524829	+	0.161526i
$656$	−266.769	+	193.819i	−0.0158774	+	0.0115356i
$657$	−2515.01	−	1827.26i	−0.149345	−	0.108506i
$658$	−1200.83	−	3695.78i	−0.0711449	−	0.218961i
$659$	8920.20			0.527286			0.263643	−	0.964620i	$-0.415076\pi$
$659$	8920.20			0.527286			0.263643	+	0.964620i	$0.415076\pi$
$660$	2390.24	+	2614.99i	0.140969	+	0.154225i
$661$	25092.0			1.47650			0.738249	−	0.674528i	$-0.235653\pi$
$661$	25092.0			1.47650			0.738249	+	0.674528i	$0.235653\pi$
$662$	−4836.15	−	14884.1i	−0.283931	−	0.873850i
$663$	20477.8	+	14878.0i	1.19954	+	0.871515i
$664$	−3131.46	+	2275.14i	−0.183018	+	0.132971i
$665$	−27.8162	+	85.6095i	−0.00162206	+	0.00499217i
$666$	690.894	−	2126.35i	0.0401976	−	0.123716i
$667$	189.401	−	137.608i	0.0109949	−	0.00798829i
$668$	−5550.05	−	4032.35i	−0.321464	−	0.233557i
$669$	−6970.31	−	21452.4i	−0.402822	−	1.23976i
$670$	1774.00			0.102292
$671$	5577.81	+	6102.30i	0.320907	+	0.351083i
$672$	−1022.15			−0.0586759
$673$	2259.63	+	6954.44i	0.129424	+	0.398327i	0.994681	−	0.103002i	$-0.0328448\pi$
$673$	2259.63	+	6954.44i	0.129424	+	0.398327i	−0.865257	+	0.501329i	$0.832845\pi$
$674$	−17801.0	−	12933.2i	−1.01732	−	0.739123i
$675$	2987.81	−	2170.77i	0.170372	−	0.123782i
$676$	1821.74	−	5606.75i	0.103649	−	0.319000i
$677$	3984.70	−	12263.6i	0.226211	−	0.696204i	−0.771956	−	0.635676i	$-0.780721\pi$
$677$	3984.70	−	12263.6i	0.226211	−	0.696204i	0.998166	−	0.0605283i	$-0.0192786\pi$
$678$	−11211.3	+	8145.51i	−0.635057	+	0.461396i
$679$	1365.52	+	992.108i	0.0771779	+	0.0560730i
$680$	−1063.56	−	3273.29i	−0.0599786	−	0.184595i
$681$	−1821.30			−0.102485
$682$	818.526	+	7264.28i	0.0459575	+	0.407865i
$683$	−18812.8			−1.05395			−0.526977	−	0.849879i	$-0.676675\pi$
$683$	−18812.8			−1.05395			−0.526977	+	0.849879i	$0.676675\pi$
$684$	11.5849	+	35.6545i	0.000647599	+	0.00199311i
$685$	−9576.16	−	6957.49i	−0.534141	−	0.388076i
$686$	−6841.43	+	4970.59i	−0.380768	+	0.276644i
$687$	−5802.45	+	17858.1i	−0.322237	+	0.991745i
$688$	−2320.08	+	7140.49i	−0.128565	+	0.395681i
$689$	−19268.0	+	13999.0i	−1.06539	+	0.774051i
$690$	−2778.95	−	2019.02i	−0.153323	−	0.111396i
$691$	3440.05	+	10587.4i	0.189386	+	0.582870i	0.999996	−	0.00271614i	$-0.000864575\pi$
$691$	3440.05	+	10587.4i	0.189386	+	0.582870i	−0.810611	+	0.585586i	$0.800865\pi$
$692$	7623.07			0.418765
$693$	−748.397	+	339.943i	−0.0410235	+	0.0186340i
$694$	1044.86			0.0571503
$695$	−366.303	−	1127.37i	−0.0199923	−	0.0615301i
$696$	−103.993	−	75.5552i	−0.00566356	−	0.00411482i
$697$	−1434.61	+	1042.30i	−0.0779621	+	0.0566428i
$698$	−2042.29	+	6285.53i	−0.110748	+	0.340847i
$699$	4366.16	−	13437.7i	0.236257	−	0.727123i
$700$	532.223	−	386.683i	0.0287374	−	0.0208789i
$701$	22911.8	+	16646.4i	1.23448	+	0.896899i	0.997217	−	0.0745478i	$-0.0237513\pi$
$701$	22911.8	+	16646.4i	1.23448	+	0.896899i	0.237258	+	0.971447i	$0.423751\pi$
$702$	5531.58	+	17024.5i	0.297402	+	0.915309i
$703$	893.244			0.0479222
$704$	2287.45	+	468.345i	0.122460	+	0.0250730i
$705$	−7170.20			−0.383043
$706$	−1196.04	−	3681.03i	−0.0637585	−	0.196229i
$707$	−1009.52	−	733.460i	−0.0537015	−	0.0390164i
$708$	9277.00	−	6740.14i	0.492445	−	0.357782i
$709$	9896.93	−	30459.6i	0.524241	−	1.61345i	−0.241570	−	0.970383i	$-0.577662\pi$
$709$	9896.93	−	30459.6i	0.524241	−	1.61345i	0.765811	−	0.643065i	$-0.222338\pi$
$710$	1639.03	−	5044.41i	0.0866362	−	0.266639i
$711$	2339.05	−	1699.42i	0.123377	−	0.0896390i
$712$	393.750	+	286.076i	0.0207253	+	0.0150578i
$713$	−2190.24	−	6740.86i	−0.115042	−	0.354063i
$714$	−5496.82			−0.288114
$715$	5454.20	−	9612.40i	0.285280	−	0.502774i
$716$	13797.7			0.720174
$717$	−322.518	−	992.610i	−0.0167987	−	0.0517011i
$718$	12799.1	+	9299.10i	0.665262	+	0.483341i
$719$	−413.133	+	300.158i	−0.0214287	+	0.0155689i	−0.598448	−	0.801162i	$-0.704216\pi$
$719$	−413.133	+	300.158i	−0.0214287	+	0.0155689i	0.577019	+	0.816730i	$0.304216\pi$
$720$	84.6664	−	260.576i	0.00438240	−	0.0134876i
$721$	3183.36	−	9797.38i	0.164431	−	0.506066i
$722$	11086.0	−	8054.43i	0.571437	−	0.415173i
$723$	−14806.8	−	10757.8i	−0.761647	−	0.553369i
$724$	1350.05	+	4155.02i	0.0693012	+	0.213287i
$725$	82.7310			0.00423800
$726$	−12601.1	+	2876.25i	−0.644172	+	0.147035i
$727$	19171.8			0.978050			0.489025	−	0.872270i	$-0.337353\pi$
$727$	19171.8			0.978050			0.489025	+	0.872270i	$0.337353\pi$
$728$	985.349	+	3032.59i	0.0501641	+	0.154389i
$729$	−17398.8	−	12641.0i	−0.883952	−	0.642229i
$730$	−7343.46	+	5335.34i	−0.372320	+	0.270507i
$731$	−12476.8	+	38399.5i	−0.631285	+	1.94290i
$732$	−1360.04	+	4185.76i	−0.0686726	+	0.211353i
$733$	19423.0	−	14111.6i	0.978725	−	0.711085i	0.0213014	−	0.999773i	$-0.493219\pi$
$733$	19423.0	−	14111.6i	0.978725	−	0.711085i	0.957423	+	0.288688i	$0.0932191\pi$
$734$	10529.2	+	7649.90i	0.529482	+	0.384691i
$735$	2248.52	+	6920.25i	0.112841	+	0.347289i
$736$	−2263.84			−0.113378
$737$	−3194.00	+	5629.05i	−0.159637	+	0.281342i
$738$	−141.165			−0.00704111
$739$	9406.86	+	28951.3i	0.468250	+	1.44113i	0.854848	+	0.518878i	$0.173650\pi$
$739$	9406.86	+	28951.3i	0.468250	+	1.44113i	−0.386598	+	0.922248i	$0.626350\pi$
$740$	−5281.39	−	3837.16i	−0.262362	−	0.190617i
$741$	−651.293	+	473.192i	−0.0322886	+	0.0234590i
$742$	1598.26	−	4918.93i	0.0790753	−	0.243369i
$743$	−11493.0	+	35371.8i	−0.567480	+	1.74652i	0.0929855	+	0.995667i	$0.470359\pi$
$743$	−11493.0	+	35371.8i	−0.567480	+	1.74652i	−0.660465	+	0.750856i	$0.729641\pi$
$744$	−3148.39	+	2287.44i	−0.155142	+	0.112717i
$745$	8352.47	+	6068.42i	0.410753	+	0.298429i
$746$	−6970.94	−	21454.4i	−0.342124	−	1.05295i
$747$	−1657.06			−0.0811628
$748$	12301.3	+	2518.63i	0.601308	+	0.123115i
$749$	−4077.95			−0.198939
$750$	−375.102	−	1154.45i	−0.0182624	−	0.0562059i
$751$	14575.9	+	10590.0i	0.708234	+	0.514562i	0.882603	−	0.470118i	$-0.155789\pi$
$751$	14575.9	+	10590.0i	0.708234	+	0.514562i	−0.174370	+	0.984680i	$0.555789\pi$
$752$	−3823.06	+	2777.62i	−0.185389	+	0.134693i
$753$	−1126.31	+	3466.42i	−0.0545085	+	0.167760i
$754$	−123.915	+	381.370i	−0.00598501	+	0.0184200i
$755$	−11710.4	+	8508.12i	−0.564484	+	0.410122i
$756$	−3144.92	−	2284.92i	−0.151296	−	0.109923i
$757$	4713.53	+	14506.8i	0.226309	+	0.696509i	0.998156	+	0.0607001i	$0.0193333\pi$
$757$	4713.53	+	14506.8i	0.226309	+	0.696509i	−0.771847	+	0.635809i	$0.780667\pi$
$758$	27490.2			1.31727
$759$	11409.9	−	5182.67i	0.545654	−	0.247851i
$760$	109.464			0.00522455
$761$	5237.15	+	16118.3i	0.249470	+	0.767790i	0.994869	+	0.101171i	$0.0322589\pi$
$761$	5237.15	+	16118.3i	0.249470	+	0.767790i	−0.745399	+	0.666618i	$0.767741\pi$
$762$	13234.6	+	9615.48i	0.629184	+	0.457129i
$763$	11209.4	−	8144.10i	0.531857	−	0.386417i
$764$	3106.51	−	9560.86i	0.147107	−	0.452749i
$765$	455.312	−	1401.30i	0.0215187	−	0.0662278i
$766$	15492.5	−	11256.0i	0.730766	−	0.530932i
$767$	−28940.2	−	21026.3i	−1.36241	−	0.989851i
$768$	384.105	+	1182.15i	0.0180471	+	0.0555433i
$769$	−31515.1			−1.47784			−0.738922	−	0.673791i	$-0.764665\pi$
$769$	−31515.1			−1.47784			−0.738922	+	0.673791i	$0.764665\pi$
$770$	268.736	+	2384.99i	0.0125774	+	0.111622i
$771$	−10253.9			−0.478970
$772$	6146.94	+	18918.3i	0.286572	+	0.881977i
$773$	26498.4	+	19252.2i	1.23296	+	0.895801i	0.997109	−	0.0759877i	$-0.0242110\pi$
$773$	26498.4	+	19252.2i	1.23296	+	0.895801i	0.235855	+	0.971788i	$0.424211\pi$
$774$	−2600.33	+	1889.25i	−0.120758	+	0.0877359i
$775$	773.990	−	2382.10i	0.0358743	−	0.110410i
$776$	634.273	−	1952.09i	0.0293416	−	0.0903041i
$777$	−8434.94	+	6128.34i	−0.389449	+	0.282951i
$778$	1031.86	+	749.687i	0.0475499	+	0.0345470i
$779$	−17.4281	−	53.6381i	−0.000801573	−	0.00246699i
$780$	5883.54			0.270083
$781$	13055.3	+	14282.9i	0.598151	+	0.654397i
$782$	−12174.3			−0.556715
$783$	−151.066	−	464.933i	−0.00689483	−	0.0212201i
$784$	3879.68	+	2818.75i	0.176735	+	0.128405i
$785$	−6648.22	+	4830.22i	−0.302274	+	0.219615i
$786$	1708.71	−	5258.85i	0.0775413	−	0.238648i
$787$	1150.98	−	3542.34i	0.0521320	−	0.160446i	−0.921601	−	0.388139i	$-0.873118\pi$
$787$	1150.98	−	3542.34i	0.0521320	−	0.160446i	0.973733	+	0.227693i	$0.0731182\pi$
$788$	−6008.13	+	4365.16i	−0.271612	+	0.197338i
$789$	−3248.04	−	2359.84i	−0.146557	−	0.106480i
$790$	−2608.71	−	8028.80i	−0.117486	−	0.361584i
$791$	−9388.12			−0.422001
$792$	674.391	+	737.806i	0.0302569	+	0.0331020i
$793$	13729.7			0.614826
$794$	2185.38	+	6725.92i	0.0976781	+	0.300622i
$795$	−7720.64	−	5609.37i	−0.344431	−	0.250244i
$796$	9499.72	−	6901.95i	0.423001	−	0.307328i
$797$	−10320.2	+	31762.2i	−0.458669	+	1.41164i	0.408103	+	0.912936i	$0.366190\pi$
$797$	−10320.2	+	31762.2i	−0.458669	+	1.41164i	−0.866773	+	0.498703i	$0.833810\pi$
$798$	54.0239	−	166.268i	0.00239652	−	0.00737573i
$799$	−20559.3	+	14937.2i	−0.910309	+	0.661378i
$800$	−647.214	−	470.228i	−0.0286031	−	0.0207813i
$801$	64.3864	+	198.161i	0.00284018	+	0.00874116i
$802$	−21240.9			−0.935214
$803$	−3707.94	−	32907.3i	−0.162952	−	1.44617i
$804$	−3445.42			−0.151133
$805$	−719.091	−	2213.14i	−0.0314840	−	0.0968979i
$806$	9821.60	+	7135.81i	0.429220	+	0.311847i
$807$	−24672.6	+	17925.7i	−1.07623	+	0.781927i
$808$	−468.914	+	1443.17i	−0.0204163	+	0.0628348i
$809$	2649.98	−	8155.81i	0.115165	−	0.354441i	−0.876816	−	0.480825i	$-0.840337\pi$
$809$	2649.98	−	8155.81i	0.115165	−	0.354441i	0.991981	+	0.126384i	$0.0403371\pi$
$810$	−5054.74	+	3672.48i	−0.219266	+	0.159306i
$811$	−24851.1	−	18055.4i	−1.07600	−	0.781763i	−0.0990225	−	0.995085i	$-0.531572\pi$
$811$	−24851.1	−	18055.4i	−1.07600	−	0.781763i	−0.976982	+	0.213322i	$0.931572\pi$
$812$	−26.9096	−	82.8192i	−0.00116298	−	0.00357929i
$813$	−11036.9			−0.476113
$814$	21684.4	−	9849.67i	0.933709	−	0.424116i
$815$	−15157.0			−0.651445
$816$	2065.61	+	6357.28i	0.0886160	+	0.272732i
$817$	−1038.89	−	754.796i	−0.0444872	−	0.0323219i
$818$	−14365.2	+	10436.9i	−0.614020	+	0.446111i
$819$	−421.831	+	1298.26i	−0.0179975	+	0.0553907i
$820$	−127.371	+	392.007i	−0.00542436	+	0.0166945i
$821$	7489.01	−	5441.08i	0.318353	−	0.231297i	−0.417119	−	0.908852i	$-0.636960\pi$
$821$	7489.01	−	5441.08i	0.318353	−	0.231297i	0.735473	+	0.677555i	$0.236960\pi$
$822$	18598.5	+	13512.6i	0.789171	+	0.573367i
$823$	−4358.76	−	13414.9i	−0.184613	−	0.568182i	0.815328	−	0.578999i	$-0.196557\pi$
$823$	−4358.76	−	13414.9i	−0.184613	−	0.568182i	−0.999941	+	0.0108176i	$0.996557\pi$
$824$	−12527.3			−0.529623
$825$	4338.50	+	888.287i	0.183087	+	0.0374863i
$826$	7768.35			0.327234
$827$	−4530.67	−	13944.0i	−0.190504	−	0.586311i	0.809496	−	0.587126i	$-0.199741\pi$
$827$	−4530.67	−	13944.0i	−0.190504	−	0.586311i	−1.00000		0.000814781i	$0.999741\pi$
$828$	−784.064	−	569.656i	−0.0329084	−	0.0239093i
$829$	−8555.36	+	6215.84i	−0.358432	+	0.260416i	−0.752398	−	0.658709i	$-0.771103\pi$
$829$	−8555.36	+	6215.84i	−0.358432	+	0.260416i	0.393966	+	0.919125i	$0.371103\pi$
$830$	−1495.14	+	4601.57i	−0.0625266	+	0.192437i
$831$	8030.71	−	24716.0i	0.335237	−	1.03175i
$832$	3137.03	−	2279.19i	0.130718	−	0.0949719i
$833$	20863.8	+	15158.4i	0.867812	+	0.630502i
$834$	711.423	+	2189.54i	0.0295379	+	0.0909082i
$835$	−8575.29			−0.355402
$836$	−197.083	+	347.336i	−0.00815341	+	0.0143695i
$837$	−14800.2			−0.611196
$838$	7872.31	+	24228.5i	0.324516	+	0.998758i
$839$	−16781.7	−	12192.6i	−0.690547	−	0.501712i	0.186293	−	0.982494i	$-0.440353\pi$
$839$	−16781.7	−	12192.6i	−0.690547	−	0.501712i	−0.876840	+	0.480783i	$0.840353\pi$
$840$	−1033.67	+	751.004i	−0.0424583	+	0.0308477i
$841$	−7533.23	+	23184.9i	−0.308878	+	0.950629i
$842$	7301.74	−	22472.5i	0.298854	−	0.919777i
$843$	12669.7	−	9205.09i	0.517638	−	0.376086i
$844$	−2786.64	−	2024.61i	−0.113649	−	0.0825712i
$845$	−2277.18	−	7008.43i	−0.0927068	−	0.285322i
$846$	−2023.03			−0.0822142
$847$	−8051.58	−	3441.31i	−0.326630	−	0.139604i
$848$	−6289.53			−0.254697
$849$	−3818.89	−	11753.3i	−0.154375	−	0.475116i
$850$	−3480.53	−	2528.75i	−0.140448	−	0.102042i
$851$	−18681.6	+	13573.0i	−0.752523	+	0.546740i
$852$	−3183.28	+	9797.11i	−0.128001	+	0.393948i
$853$	−622.873	+	1917.01i	−0.0250021	+	0.0769484i	−0.962779	−	0.270290i	$-0.912880\pi$
$853$	−622.873	+	1917.01i	−0.0250021	+	0.0769484i	0.937777	+	0.347238i	$0.112880\pi$
$854$	−2412.15	+	1752.53i	−0.0966535	+	0.0702229i
$855$	37.9119	+	27.5446i	0.00151644	+	0.00110176i
$856$	1532.42	+	4716.31i	0.0611882	+	0.188318i
$857$	202.599			0.00807544			0.00403772	−	0.999992i	$-0.498715\pi$
$857$	202.599			0.00807544			0.00403772	+	0.999992i	$0.498715\pi$
$858$	−10593.0	+	18668.9i	−0.421490	+	0.742828i
$859$	5408.70			0.214834			0.107417	−	0.994214i	$-0.465742\pi$
$859$	5408.70			0.214834			0.107417	+	0.994214i	$0.465742\pi$
$860$	2900.11	+	8925.61i	0.114992	+	0.353908i
$861$	532.572	+	386.937i	0.0210802	+	0.0153156i
$862$	20601.4	−	14967.8i	0.814022	−	0.591422i
$863$	−5773.94	+	17770.4i	−0.227749	+	0.700939i	0.770252	+	0.637740i	$0.220130\pi$
$863$	−5773.94	+	17770.4i	−0.227749	+	0.700939i	−0.998001	+	0.0631996i	$0.979870\pi$
$864$	−1460.79	+	4495.85i	−0.0575198	+	0.177028i
$865$	7708.99	−	5600.91i	0.303021	−	0.220158i
$866$	−22742.3	−	16523.2i	−0.892394	−	0.648362i
$867$	3736.72	+	11500.5i	0.146373	+	0.450491i
$868$	−2636.39			−0.103093
$869$	30172.8	+	6177.75i	1.17784	+	0.241157i
$870$	−160.678			−0.00626148
$871$	3321.38	+	10222.2i	0.129209	+	0.397663i
$872$	−13631.3	−	9903.68i	−0.529372	−	0.384611i
$873$	710.886	−	516.489i	0.0275600	−	0.0200235i
$874$	119.651	−	368.249i	0.00463074	−	0.0142519i
$875$	254.114	−	782.083i	0.00981785	−	0.0302162i
$876$	14262.3	−	10362.1i	0.550088	−	0.399662i
$877$	19103.3	+	13879.4i	0.735545	+	0.534405i	0.891313	−	0.453389i	$-0.149785\pi$
$877$	19103.3	+	13879.4i	0.735545	+	0.534405i	−0.155768	+	0.987794i	$0.549785\pi$
$878$	−3846.51	−	11838.4i	−0.147851	−	0.455040i
$879$	−37719.7			−1.44739
$880$	2657.34	−	1207.04i	0.101794	−	0.0462378i
$881$	−10589.0			−0.404939			−0.202469	−	0.979289i	$-0.564897\pi$
$881$	−10589.0			−0.404939			−0.202469	+	0.979289i	$0.564897\pi$
$882$	634.408	+	1952.51i	0.0242195	+	0.0745401i
$883$	34484.9	+	25054.8i	1.31428	+	0.954881i	0.999985	+	0.00555628i	$0.00176863\pi$
$883$	34484.9	+	25054.8i	1.31428	+	0.954881i	0.314297	+	0.949325i	$0.398231\pi$
$884$	16870.1	−	12256.8i	0.641857	−	0.466337i
$885$	4429.38	−	13632.2i	0.168239	−	0.517787i
$886$	1467.98	−	4517.99i	0.0556635	−	0.171315i
$887$	1102.29	−	800.862i	0.0417264	−	0.0303160i	−0.566727	−	0.823906i	$-0.691790\pi$
$887$	1102.29	−	800.862i	0.0417264	−	0.0303160i	0.608453	+	0.793590i	$0.291790\pi$
$888$	10257.4	+	7452.41i	0.387629	+	0.281629i
$889$	3424.63	+	10539.9i	0.129200	+	0.397635i
$890$	608.377			0.0229133
$891$	−2552.29	−	22651.2i	−0.0959652	−	0.851675i
$892$	−18582.4			−0.697517
$893$	−249.762	−	768.687i	−0.00935941	−	0.0288053i
$894$	−16221.9	−	11785.9i	−0.606870	−	0.440917i
$895$	13953.2	−	10137.6i	0.521123	−	0.378618i
$896$	−260.213	+	800.853i	−0.00970212	+	0.0298601i
$897$	6431.12	−	19793.0i	0.239386	−	0.736753i
$898$	19858.1	−	14427.7i	0.737943	−	0.536147i
$899$	−268.225	−	194.877i	−0.00995084	−	0.00722971i
$900$	−105.833	−	325.720i	−0.00391974	−	0.0120637i
$901$	−33823.3			−1.25063
$902$	−1014.54	−	1109.94i	−0.0374508	−	0.0409723i
$903$	14988.7			0.552375
$904$	3527.89	+	10857.7i	0.129796	+	0.399472i
$905$	4418.09	+	3209.93i	0.162279	+	0.117902i
$906$	22743.6	−	16524.2i	0.834003	−	0.605938i
$907$	−2637.90	+	8118.62i	−0.0965711	+	0.297215i	−0.987660	−	0.156614i	$-0.949942\pi$
$907$	−2637.90	+	8118.62i	−0.0965711	+	0.297215i	0.891089	+	0.453829i	$0.149942\pi$
$908$	−463.657	+	1426.99i	−0.0169460	+	0.0521546i
$909$	−525.554	+	381.837i	−0.0191766	+	0.0139326i
$910$	3224.60	+	2342.81i	0.117466	+	0.0853443i
$911$	12312.7	+	37894.6i	0.447792	+	1.37816i	0.879393	+	0.476097i	$0.157949\pi$
$911$	12312.7	+	37894.6i	0.447792	+	1.37816i	−0.431601	+	0.902064i	$0.642051\pi$
$912$	−212.597			−0.00771906
$913$	−11909.2	−	13029.1i	−0.431694	−	0.472288i
$914$	−25899.5			−0.937285
$915$	1700.04	+	5232.20i	0.0614227	+	0.189039i
$916$	12514.7	+	9092.43i	0.451415	+	0.327972i
$917$	3030.55	−	2201.82i	0.109136	−	0.0792918i
$918$	−7855.71	+	24177.4i	−0.282437	+	0.869252i
$919$	14556.2	−	44799.3i	0.522485	−	1.60804i	−0.246750	−	0.969079i	$-0.579363\pi$
$919$	14556.2	−	44799.3i	0.522485	−	1.60804i	0.769235	−	0.638966i	$-0.220637\pi$
$920$	−2289.35	+	1663.31i	−0.0820411	+	0.0596063i
$921$	−18860.3	−	13702.8i	−0.674776	−	0.490253i
$922$	8647.92	+	26615.6i	0.308898	+	0.950690i
$923$	32135.6			1.14600
$924$	−521.931	−	4632.05i	−0.0185825	−	0.164917i
$925$	−8160.20			−0.290060
$926$	3553.46	+	10936.4i	0.126106	+	0.388114i
$927$	−4338.74	−	3152.28i	−0.153725	−	0.111688i
$928$	−85.6714	+	62.2439i	−0.00303050	+	0.00220179i
$929$	3987.12	−	12271.1i	0.140811	−	0.433371i	−0.855638	−	0.517575i	$-0.826835\pi$
$929$	3987.12	−	12271.1i	0.140811	−	0.433371i	0.996449	+	0.0842040i	$0.0268347\pi$
$930$	−1503.22	+	4626.44i	−0.0530028	+	0.163126i
$931$	−663.567	+	482.110i	−0.0233593	+	0.0169715i
$932$	−9416.90	−	6841.78i	−0.330966	−	0.240461i
$933$	−14147.6	−	43541.8i	−0.496433	−	1.52786i
$934$	36472.9			1.27776
$935$	14290.4	−	6491.10i	0.499836	−	0.227039i
$936$	1660.01			0.0579691
$937$	13678.6	+	42098.3i	0.476904	+	1.46776i	0.843373	+	0.537329i	$0.180567\pi$
$937$	13678.6	+	42098.3i	0.476904	+	1.46776i	−0.366469	+	0.930430i	$0.619433\pi$
$938$	−1888.33	−	1371.95i	−0.0657316	−	0.0477568i
$939$	12936.9	−	9399.23i	0.449607	−	0.326659i
$940$	−1825.35	+	5617.85i	−0.0633366	+	0.194930i
$941$	−6865.26	+	21129.1i	−0.237833	+	0.731975i	0.758900	+	0.651207i	$0.225737\pi$
$941$	−6865.26	+	21129.1i	−0.237833	+	0.731975i	−0.996733	+	0.0807677i	$0.974263\pi$
$942$	12912.0	−	9381.10i	0.446598	−	0.324472i
$943$	1179.53	+	856.982i	0.0407327	+	0.0295940i
$944$	−2919.21	−	8984.40i	−0.100648	−	0.309764i
$945$	−4859.17			−0.167268
$946$	−33543.1	−	6867.80i	−1.15283	−	0.236037i
$947$	−14244.5			−0.488790			−0.244395	−	0.969676i	$-0.578589\pi$
$947$	−14244.5			−0.488790			−0.244395	+	0.969676i	$0.578589\pi$
$948$	5066.57	+	15593.3i	0.173581	+	0.534226i
$949$	−44492.1	−	32325.4i	−1.52189	−	1.10572i
$950$	110.697	−	80.4263i	0.00378052	−	0.00274671i
$951$	−8746.47	+	26918.9i	−0.298237	+	0.917881i
$952$	−1399.35	+	4306.76i	−0.0476399	+	0.146621i
$953$	43624.4	−	31694.9i	1.48282	−	1.07733i	0.506191	−	0.862421i	$-0.331053\pi$
$953$	43624.4	−	31694.9i	1.48282	−	1.07733i	0.976633	−	0.214914i	$-0.0689470\pi$
$954$	−2178.33	−	1582.65i	−0.0739268	−	0.0537110i
$955$	−3883.14	−	11951.1i	−0.131576	−	0.404951i
$956$	−859.814			−0.0290883
$957$	289.291	−	509.842i	0.00977163	−	0.0172214i
$958$	−26915.7			−0.907730
$959$	4812.63	+	14811.8i	0.162052	+	0.498745i
$960$	1257.00	+	913.264i	0.0422599	+	0.0307036i
$961$	15980.9	−	11610.8i	0.536434	−	0.389742i
$962$	12222.3	−	37616.5i	0.409630	−	1.26071i
$963$	−656.035	+	2019.07i	−0.0219527	+	0.0675634i
$964$	−12198.2	+	8862.48i	−0.407548	+	0.296101i
$965$	20116.1	+	14615.2i	0.671048	+	0.487545i
$966$	1396.60	+	4298.29i	0.0465164	+	0.143163i
$967$	−26362.3			−0.876684			−0.438342	−	0.898808i	$-0.644434\pi$
$967$	−26362.3			−0.876684			−0.438342	+	0.898808i	$0.644434\pi$
$968$	−954.369	+	10605.1i	−0.0316886	+	0.352130i
$969$	−1143.29			−0.0379026
$970$	−792.841	−	2440.11i	−0.0262439	−	0.0807705i
$971$	−44111.6	−	32049.0i	−1.45789	−	1.05922i	−0.983907	−	0.178683i	$-0.942816\pi$
$971$	−44111.6	−	32049.0i	−1.45789	−	1.05922i	−0.473981	−	0.880535i	$-0.657184\pi$
$972$	−3090.18	+	2245.15i	−0.101973	+	0.0740875i
$973$	−481.955	+	1483.31i	−0.0158795	+	0.0488722i
$974$	5954.97	−	18327.5i	0.195903	−	0.602927i
$975$	5949.86	−	4322.83i	0.195434	−	0.141991i
$976$	2933.31	+	2131.17i	0.0962018	+	0.0698947i
$977$	−12493.5	−	38451.2i	−0.409114	−	1.25912i	−0.917411	−	0.397941i	$-0.869725\pi$
$977$	−12493.5	−	38451.2i	−0.409114	−	1.25912i	0.508298	−	0.861181i	$-0.330275\pi$
$978$	29437.5			0.962483
$979$	−1095.35	+	1930.43i	−0.0357584	+	0.0630201i
$980$	5994.43			0.195393
$981$	−2229.00	−	6860.14i	−0.0725447	−	0.223270i
$982$	−2604.80	−	1892.50i	−0.0846461	−	0.0614990i
$983$	−5572.07	+	4048.35i	−0.180795	+	0.131355i	−0.674502	−	0.738273i	$-0.735642\pi$
$983$	−5572.07	+	4048.35i	−0.180795	+	0.131355i	0.493707	+	0.869628i	$0.335642\pi$
$984$	247.376	−	761.344i	0.00801428	−	0.0246654i
$985$	−2868.62	+	8828.72i	−0.0927939	+	0.285590i
$986$	−460.716	+	334.730i	−0.0148805	+	0.0108113i
$987$	7632.30	+	5545.19i	0.246138	+	0.178830i
$988$	204.943	+	630.750i	0.00659930	+	0.0203106i
$989$	33196.9			1.06734
$990$	1224.08	+	250.625i	0.0392968	+	0.00804585i
$991$	38999.3			1.25011			0.625053	−	0.780582i	$-0.285077\pi$
$991$	38999.3			1.25011			0.625053	+	0.780582i	$0.285077\pi$
$992$	990.708	+	3049.09i	0.0317087	+	0.0975893i
$993$	30737.8	+	22332.3i	0.982310	+	0.713690i
$994$	−5645.84	+	4101.94i	−0.180156	+	0.130891i
$995$	4535.71	−	13959.5i	0.144514	−	0.444770i
$996$	2903.82	−	8937.03i	0.0923805	−	0.284318i
$997$	32624.4	−	23703.0i	1.03633	−	0.752941i	0.0667678	−	0.997769i	$-0.478731\pi$
$997$	32624.4	−	23703.0i	1.03633	−	0.752941i	0.969567	+	0.244827i	$0.0787313\pi$
$998$	−16821.1	−	12221.2i	−0.533529	−	0.387631i
$999$	14900.4	+	45858.8i	0.471900	+	1.45236i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	110.4.g.b.71.1	yes	12
11.3	even	5		1210.4.a.bf.1.5		6
11.8	odd	10		1210.4.a.bc.1.5		6
11.9	even	5	inner	110.4.g.b.31.1	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.4.g.b.31.1	✓	12	11.9	even	5	inner
110.4.g.b.71.1	yes	12	1.1	even	1	trivial
1210.4.a.bc.1.5		6	11.8	odd	10
1210.4.a.bf.1.5		6	11.3	even	5

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.618034 + 1.90211i) q^{2} +(-3.92812 - 2.85395i) q^{3} +(-3.23607 + 2.35114i) q^{4} +(-1.54508 + 4.75528i) q^{5} +(3.00082 - 9.23557i) q^{6} +(5.32223 - 3.86683i) q^{7} +(-6.47214 - 4.70228i) q^{8} +(-1.05833 - 3.25720i) q^{9} -10.0000 q^{10} +(18.0044 - 31.7307i) q^{11} +19.4217 q^{12} +(-18.7225 - 57.6219i) q^{13} +(10.6445 + 7.73366i) q^{14} +(19.6406 - 14.2697i) q^{15} +(4.94427 - 15.2169i) q^{16} +(26.5889 - 81.8322i) q^{17} +(5.54149 - 4.02613i) q^{18} +(2.21395 + 1.60853i) q^{19} +(-6.18034 - 19.0211i) q^{20} -31.9421 q^{21} +(71.4828 + 14.6358i) q^{22} -70.7450 q^{23} +(12.0033 + 36.9423i) q^{24} +(-20.2254 - 14.6946i) q^{25} +(98.0323 - 71.2246i) q^{26} +(-45.6497 + 140.495i) q^{27} +(-8.13165 + 25.0266i) q^{28} +(-2.67723 + 1.94512i) q^{29} +(39.2812 + 28.5395i) q^{30} +(30.9596 + 95.2839i) q^{31} +32.0000 q^{32} +(-161.282 + 73.2586i) q^{33} +172.087 q^{34} +(10.1646 + 31.2833i) q^{35} +(11.0830 + 8.05225i) q^{36} +(264.070 - 191.858i) q^{37} +(-1.69130 + 5.20530i) q^{38} +(-90.9058 + 279.779i) q^{39} +(32.3607 - 23.5114i) q^{40} +(-16.6730 - 12.1137i) q^{41} +(-19.7413 - 60.7575i) q^{42} -469.247 q^{43} +(16.3399 + 145.014i) q^{44} +17.1241 q^{45} +(-43.7228 - 134.565i) q^{46} +(-238.941 - 173.601i) q^{47} +(-62.8500 + 45.6632i) q^{48} +(-92.6190 + 285.052i) q^{49} +(15.4508 - 47.5528i) q^{50} +(-337.989 + 245.563i) q^{51} +(196.065 + 142.449i) q^{52} +(-121.473 - 373.856i) q^{53} -295.451 q^{54} +(123.070 + 134.643i) q^{55} -52.6291 q^{56} +(-4.10600 - 12.6370i) q^{57} +(-5.35446 - 3.89024i) q^{58} +(477.662 - 347.041i) q^{59} +(-30.0082 + 92.3557i) q^{60} +(-70.0266 + 215.520i) q^{61} +(-162.107 + 117.777i) q^{62} +(-18.2277 - 13.2432i) q^{63} +(19.7771 + 60.8676i) q^{64} +302.936 q^{65} +(-239.024 - 261.499i) q^{66} -177.400 q^{67} +(106.356 + 327.329i) q^{68} +(277.895 + 201.902i) q^{69} +(-53.2223 + 38.6683i) q^{70} +(-163.903 + 504.441i) q^{71} +(-8.46664 + 26.0576i) q^{72} +(734.346 - 533.534i) q^{73} +(528.139 + 383.716i) q^{74} +(37.5102 + 115.445i) q^{75} -10.9464 q^{76} +(-26.8736 - 238.499i) q^{77} -588.354 q^{78} +(260.871 + 802.880i) q^{79} +(64.7214 + 47.0228i) q^{80} +(505.474 - 367.248i) q^{81} +(12.7371 - 39.2007i) q^{82} +(149.514 - 460.157i) q^{83} +(103.367 - 75.1004i) q^{84} +(348.053 + 252.875i) q^{85} +(-290.011 - 892.561i) q^{86} +16.0678 q^{87} +(-265.734 + 120.704i) q^{88} -60.8377 q^{89} +(10.5833 + 32.5720i) q^{90} +(-322.460 - 234.281i) q^{91} +(228.935 - 166.331i) q^{92} +(150.322 - 462.644i) q^{93} +(182.535 - 561.785i) q^{94} +(-11.0697 + 8.04263i) q^{95} +(-125.700 - 91.3264i) q^{96} +(79.2841 + 244.011i) q^{97} -599.443 q^{98} +(-122.408 - 25.0625i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{2} + 15 q^{3} - 12 q^{4} + 15 q^{5} - 20 q^{6} + 15 q^{7} - 24 q^{8} + 62 q^{9} - 120 q^{10} + 34 q^{11} - 40 q^{12} - 114 q^{13} + 30 q^{14} - 75 q^{15} - 48 q^{16} - 17 q^{17} - 166 q^{18}+ \cdots - 3855 q^{99}+O(q^{100}) \) 12 * q - 6 * q^2 + 15 * q^3 - 12 * q^4 + 15 * q^5 - 20 * q^6 + 15 * q^7 - 24 * q^8 + 62 * q^9 - 120 * q^10 + 34 * q^11 - 40 * q^12 - 114 * q^13 + 30 * q^14 - 75 * q^15 - 48 * q^16 - 17 * q^17 - 166 * q^18 - 162 * q^19 + 60 * q^20 + 148 * q^21 - 142 * q^22 - 210 * q^23 - 80 * q^24 - 75 * q^25 + 342 * q^26 - 147 * q^27 + 40 * q^28 - 57 * q^29 - 150 * q^30 + 816 * q^31 + 384 * q^32 - 1188 * q^33 + 696 * q^34 - 50 * q^35 - 332 * q^36 + 870 * q^37 + 466 * q^38 - 413 * q^39 + 120 * q^40 + 754 * q^41 + 586 * q^42 + 136 * q^43 - 204 * q^44 - 210 * q^45 - 430 * q^46 - 792 * q^47 + 240 * q^48 + 1008 * q^49 - 150 * q^50 - 504 * q^51 + 684 * q^52 + 359 * q^53 - 1364 * q^54 - 220 * q^55 - 400 * q^56 - 1242 * q^57 - 114 * q^58 + 1252 * q^59 + 200 * q^60 + 1346 * q^61 - 1858 * q^62 + 3469 * q^63 - 192 * q^64 + 570 * q^65 - 2336 * q^66 + 376 * q^67 - 68 * q^68 - 889 * q^69 - 150 * q^70 + 2038 * q^71 + 496 * q^72 + 945 * q^73 + 1740 * q^74 - 250 * q^75 - 568 * q^76 - 754 * q^77 + 1364 * q^78 - 149 * q^79 + 240 * q^80 - 1346 * q^81 + 368 * q^82 - 614 * q^83 - 1468 * q^84 + 785 * q^85 + 22 * q^86 - 4442 * q^87 + 352 * q^88 - 3122 * q^89 - 620 * q^90 - 4694 * q^91 + 1280 * q^92 + 1487 * q^93 + 2326 * q^94 + 810 * q^95 + 480 * q^96 + 1617 * q^97 + 1956 * q^98 - 3855 * q^99

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