LMFDB - Embedded newform 31.4.g.a.7.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [31,4,Mod(7,31)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(31, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([28])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("31.7"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 31 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	31.g (of order $15$, 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:	$1.82905921018$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$7$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			7.5
Character	$\chi$	$=$	31.7
Dual form			31.4.g.a.9.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.529206 + 1.62873i) q^{2} +(3.53631 - 0.751666i) q^{3} +(4.09944 - 2.97842i) q^{4} +(-3.32346 + 5.75640i) q^{5} +(3.09570 + 5.36190i) q^{6} +(-2.35128 - 1.04686i) q^{7} +(18.1043 + 13.1535i) q^{8} +(-12.7252 + 5.66564i) q^{9} +(-11.1344 - 2.36669i) q^{10} +(-1.78038 - 16.9392i) q^{11} +(12.2581 - 13.6140i) q^{12} +(-53.2061 - 59.0914i) q^{13} +(0.460734 - 4.38360i) q^{14} +(-7.42590 + 22.8546i) q^{15} +(0.684133 - 2.10555i) q^{16} +(-1.58563 + 15.0862i) q^{17} +(-15.9620 - 17.7276i) q^{18} +(-13.4236 + 14.9084i) q^{19} +(3.52064 + 33.4967i) q^{20} +(-9.10174 - 1.93463i) q^{21} +(26.6472 - 11.8641i) q^{22} +(26.6455 + 19.3591i) q^{23} +(73.9095 + 32.9066i) q^{24} +(40.4092 + 69.9908i) q^{25} +(68.0868 - 117.930i) q^{26} +(-119.713 + 86.9764i) q^{27} +(-12.7569 + 2.71156i) q^{28} +(32.2755 + 99.3338i) q^{29} -41.1537 q^{30} +(150.679 - 84.1835i) q^{31} +182.817 q^{32} +(-19.0286 - 58.5640i) q^{33} +(-25.4105 + 5.40116i) q^{34} +(13.8405 - 10.0557i) q^{35} +(-35.2917 + 61.1270i) q^{36} +(-58.3471 - 101.060i) q^{37} +(-31.3855 - 13.9737i) q^{38} +(-232.570 - 168.972i) q^{39} +(-135.886 + 60.5004i) q^{40} +(164.892 + 35.0490i) q^{41} +(-1.66570 - 15.8481i) q^{42} +(-149.710 + 166.270i) q^{43} +(-57.7506 - 64.1385i) q^{44} +(9.67811 - 92.0810i) q^{45} +(-17.4297 + 53.6432i) q^{46} +(-62.7846 + 193.231i) q^{47} +(0.836641 - 7.96010i) q^{48} +(-225.079 - 249.976i) q^{49} +(-92.6112 + 102.855i) q^{50} +(5.73254 + 54.5415i) q^{51} +(-394.114 - 83.7715i) q^{52} +(614.773 - 273.715i) q^{53} +(-205.013 - 148.951i) q^{54} +(103.426 + 46.0482i) q^{55} +(-28.7984 - 49.8803i) q^{56} +(-36.2638 + 62.8107i) q^{57} +(-144.707 + 105.136i) q^{58} +(413.502 - 87.8925i) q^{59} +(37.6284 + 115.808i) q^{60} +671.787 q^{61} +(216.852 + 200.865i) q^{62} +35.8517 q^{63} +(91.2745 + 280.914i) q^{64} +(516.982 - 109.888i) q^{65} +(85.3148 - 61.9848i) q^{66} +(-328.276 + 568.591i) q^{67} +(38.4329 + 66.5678i) q^{68} +(108.778 + 48.4312i) q^{69} +(23.7025 + 17.2209i) q^{70} +(-694.938 + 309.406i) q^{71} +(-304.905 - 64.8095i) q^{72} +(-55.1261 - 524.490i) q^{73} +(133.722 - 148.513i) q^{74} +(195.509 + 217.135i) q^{75} +(-10.6257 + 101.097i) q^{76} +(-13.5467 + 41.6926i) q^{77} +(152.132 - 468.215i) q^{78} +(41.4502 - 394.372i) q^{79} +(9.84667 + 10.9358i) q^{80} +(-106.307 + 118.065i) q^{81} +(30.1768 + 287.113i) q^{82} +(-1326.16 - 281.884i) q^{83} +(-43.0742 + 19.1779i) q^{84} +(-81.5726 - 59.2660i) q^{85} +(-350.036 - 155.846i) q^{86} +(188.802 + 327.015i) q^{87} +(190.578 - 330.091i) q^{88} +(-197.885 + 143.772i) q^{89} +(155.097 - 32.9668i) q^{90} +(63.2422 + 194.639i) q^{91} +166.891 q^{92} +(469.570 - 410.959i) q^{93} -347.947 q^{94} +(-41.2060 - 126.819i) q^{95} +(646.497 - 137.417i) q^{96} +(-616.184 + 447.684i) q^{97} +(288.029 - 498.881i) q^{98} +(118.627 + 205.468i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 6 q^{2} + q^{3} - 42 q^{4} - 53 q^{6} - 71 q^{7} - 7 q^{8} + 4 q^{9} + 48 q^{10} - 25 q^{11} + 319 q^{12} - 45 q^{13} - 50 q^{14} + 217 q^{15} - 322 q^{16} + 61 q^{17} + 285 q^{18} - 143 q^{19}+ \cdots - 6383 q^{99}+O(q^{100}) $ 56 * q - 6 * q^2 + q^3 - 42 * q^4 - 53 * q^6 - 71 * q^7 - 7 * q^8 + 4 * q^9 + 48 * q^10 - 25 * q^11 + 319 * q^12 - 45 * q^13 - 50 * q^14 + 217 * q^15 - 322 * q^16 + 61 * q^17 + 285 * q^18 - 143 * q^19 + 95 * q^20 - 257 * q^21 - 1147 * q^22 - 244 * q^23 - 226 * q^24 - 96 * q^25 - 1019 * q^26 + 124 * q^27 + 1920 * q^28 - 142 * q^29 + 2430 * q^30 + 112 * q^31 + 618 * q^32 + 134 * q^33 + 2488 * q^34 + 813 * q^35 - 857 * q^36 - 866 * q^37 - 1186 * q^38 - 1090 * q^39 - 663 * q^40 - 333 * q^41 - 3347 * q^42 + 703 * q^43 + 1327 * q^44 - 1201 * q^45 - 818 * q^46 + 1886 * q^47 - 3046 * q^48 + 1346 * q^49 - 4015 * q^50 - 3179 * q^51 - 4447 * q^52 - 1613 * q^53 + 1276 * q^54 + 2486 * q^55 + 4558 * q^56 + 104 * q^57 + 415 * q^58 + 863 * q^59 + 9839 * q^60 + 6180 * q^61 + 427 * q^62 + 3128 * q^63 + 2807 * q^64 + 5398 * q^65 + 7976 * q^66 + 1026 * q^67 - 4992 * q^68 - 4882 * q^69 - 7786 * q^70 + 583 * q^71 - 299 * q^72 - 3709 * q^73 - 5029 * q^74 - 5668 * q^75 - 9928 * q^76 - 9614 * q^77 - 4597 * q^78 + 2323 * q^79 - 2582 * q^80 - 1715 * q^81 - 4314 * q^82 - 2399 * q^83 - 1740 * q^84 + 733 * q^85 + 11232 * q^86 + 4919 * q^87 + 3611 * q^88 - 2244 * q^89 + 10029 * q^90 + 9776 * q^91 + 15424 * q^92 - 2975 * q^93 + 988 * q^94 + 5791 * q^95 + 20204 * q^96 + 10170 * q^97 + 2332 * q^98 - 6383 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/31\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{14}{15}\right)$

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 $

$2$	0.529206	+	1.62873i	0.187102	+	0.575842i	0.999978	−	0.00659493i	$-0.00209925\pi$
$2$	0.529206	+	1.62873i	0.187102	+	0.575842i	−0.812876	+	0.582437i	$0.802099\pi$
$3$	3.53631	−	0.751666i	0.680563	−	0.144658i	0.145357	−	0.989379i	$-0.453567\pi$
$3$	3.53631	−	0.751666i	0.680563	−	0.144658i	0.535207	+	0.844721i	$0.320234\pi$
$4$	4.09944	−	2.97842i	0.512430	−	0.372302i
$5$	−3.32346	+	5.75640i	−0.297259	+	0.514868i	−0.975508	−	0.219964i	$-0.929406\pi$
$5$	−3.32346	+	5.75640i	−0.297259	+	0.514868i	0.678249	+	0.734832i	$0.262739\pi$
$6$	3.09570	+	5.36190i	0.210635	+	0.364831i
$7$	−2.35128	−	1.04686i	−0.126957	−	0.0565250i	0.342275	−	0.939600i	$-0.388803\pi$
$7$	−2.35128	−	1.04686i	−0.126957	−	0.0565250i	−0.469232	+	0.883075i	$0.655469\pi$
$8$	18.1043	+	13.1535i	0.800105	+	0.581310i
$9$	−12.7252	+	5.66564i	−0.471305	+	0.209838i
$10$	−11.1344	−	2.36669i	−0.352101	−	0.0748413i
$11$	−1.78038	−	16.9392i	−0.0488005	−	0.464306i	−0.991447	−	0.130512i	$-0.958338\pi$
$11$	−1.78038	−	16.9392i	−0.0488005	−	0.464306i	0.942646	−	0.333793i	$-0.108329\pi$
$12$	12.2581	−	13.6140i	0.294885	−	0.327503i
$13$	−53.2061	−	59.0914i	−1.13513	−	1.26069i	−0.961175	−	0.275939i	$-0.911011\pi$
$13$	−53.2061	−	59.0914i	−1.13513	−	1.26069i	−0.173957	−	0.984753i	$-0.555655\pi$
$14$	0.460734	−	4.38360i	0.00879546	−	0.0836832i
$15$	−7.42590	+	22.8546i	−0.127824	+	0.393401i
$16$	0.684133	−	2.10555i	0.0106896	−	0.0328991i
$17$	−1.58563	+	15.0862i	−0.0226218	+	0.215232i	0.977371	+	0.211531i	$0.0678449\pi$
$17$	−1.58563	+	15.0862i	−0.0226218	+	0.215232i	−0.999993	+	0.00370144i	$0.998822\pi$
$18$	−15.9620	−	17.7276i	−0.209016	−	0.232136i
$19$	−13.4236	+	14.9084i	−0.162083	+	0.180012i	−0.818716	−	0.574199i	$-0.805314\pi$
$19$	−13.4236	+	14.9084i	−0.162083	+	0.180012i	0.656633	+	0.754211i	$0.271980\pi$
$20$	3.52064	+	33.4967i	0.0393620	+	0.374504i
$21$	−9.10174	−	1.93463i	−0.0945792	−	0.0201034i
$22$	26.6472	−	11.8641i	0.258236	−	0.114974i
$23$	26.6455	+	19.3591i	0.241564	+	0.175506i	0.701980	−	0.712197i	$-0.252300\pi$
$23$	26.6455	+	19.3591i	0.241564	+	0.175506i	−0.460416	+	0.887703i	$0.652300\pi$
$24$	73.9095	+	32.9066i	0.628613	+	0.279877i
$25$	40.4092	+	69.9908i	0.323274	+	0.559927i
$26$	68.0868	−	117.930i	0.513574	−	0.889535i
$27$	−119.713	+	86.9764i	−0.853286	+	0.619948i
$28$	−12.7569	+	2.71156i	−0.0861010	+	0.0183013i
$29$	32.2755	+	99.3338i	0.206669	+	0.636063i	0.999641	+	0.0268038i	$0.00853293\pi$
$29$	32.2755	+	99.3338i	0.206669	+	0.636063i	−0.792971	+	0.609259i	$0.791467\pi$
$30$	−41.1537			−0.250453
$31$	150.679	−	84.1835i	0.872991	−	0.487736i
$31$	150.679	−	84.1835i	0.872991	−	0.487736i
$32$	182.817			1.00993
$33$	−19.0286	−	58.5640i	−0.100377	−	0.308930i
$34$	−25.4105	+	5.40116i	−0.128172	+	0.0272439i
$35$	13.8405	−	10.0557i	0.0668421	−	0.0485636i
$36$	−35.2917	+	61.1270i	−0.163387	+	0.282995i
$37$	−58.3471	−	101.060i	−0.259249	−	0.449032i	0.706792	−	0.707421i	$-0.250142\pi$
$37$	−58.3471	−	101.060i	−0.259249	−	0.449032i	−0.966041	+	0.258389i	$0.916808\pi$
$38$	−31.3855	−	13.9737i	−0.133984	−	0.0596537i
$39$	−232.570	−	168.972i	−0.954899	−	0.693775i
$40$	−135.886	+	60.5004i	−0.537137	+	0.239149i
$41$	164.892	+	35.0490i	0.628095	+	0.133506i	0.510952	−	0.859609i	$-0.329293\pi$
$41$	164.892	+	35.0490i	0.628095	+	0.133506i	0.117143	+	0.993115i	$0.462626\pi$
$42$	−1.66570	−	15.8481i	−0.00611960	−	0.0582241i
$43$	−149.710	+	166.270i	−0.530944	+	0.589673i	−0.947627	−	0.319379i	$-0.896526\pi$
$43$	−149.710	+	166.270i	−0.530944	+	0.589673i	0.416683	+	0.909052i	$0.363192\pi$
$44$	−57.7506	−	64.1385i	−0.197869	−	0.219756i
$45$	9.67811	−	92.0810i	0.0320606	−	0.305036i
$46$	−17.4297	+	53.6432i	−0.0558668	+	0.171940i
$47$	−62.7846	+	193.231i	−0.194853	+	0.599695i	0.805126	+	0.593104i	$0.202098\pi$
$47$	−62.7846	+	193.231i	−0.194853	+	0.599695i	−0.999978	+	0.00659057i	$0.997902\pi$
$48$	0.836641	−	7.96010i	0.00251581	−	0.0239363i
$49$	−225.079	−	249.976i	−0.656208	−	0.728792i
$50$	−92.6112	+	102.855i	−0.261944	+	0.290918i
$51$	5.73254	+	54.5415i	0.0157395	+	0.149752i
$52$	−394.114	−	83.7715i	−1.05103	−	0.223404i
$53$	614.773	−	273.715i	1.59331	−	0.709389i	0.597593	−	0.801800i	$-0.296124\pi$
$53$	614.773	−	273.715i	1.59331	−	0.709389i	0.995721	+	0.0924110i	$0.0294574\pi$
$54$	−205.013	−	148.951i	−0.516644	−	0.375364i
$55$	103.426	+	46.0482i	0.253563	+	0.112893i
$56$	−28.7984	−	49.8803i	−0.0687205	−	0.119027i
$57$	−36.2638	+	62.8107i	−0.0842677	+	0.145956i
$58$	−144.707	+	105.136i	−0.327603	+	0.238018i
$59$	413.502	−	87.8925i	0.912429	−	0.193943i	0.272302	−	0.962212i	$-0.412215\pi$
$59$	413.502	−	87.8925i	0.912429	−	0.193943i	0.640127	+	0.768269i	$0.278882\pi$
$60$	37.6284	+	115.808i	0.0809635	+	0.249180i
$61$	671.787			1.41006			0.705028	−	0.709179i	$-0.250934\pi$
$61$	671.787			1.41006			0.705028	+	0.709179i	$0.250934\pi$
$62$	216.852	+	200.865i	0.444198	+	0.411449i
$63$	35.8517			0.0716966
$64$	91.2745	+	280.914i	0.178271	+	0.548660i
$65$	516.982	−	109.888i	0.986519	−	0.209691i
$66$	85.3148	−	61.9848i	0.159114	−	0.115603i
$67$	−328.276	+	568.591i	−0.598587	+	1.03678i	0.394443	+	0.918921i	$0.370938\pi$
$67$	−328.276	+	568.591i	−0.598587	+	1.03678i	−0.993030	+	0.117863i	$0.962396\pi$
$68$	38.4329	+	66.5678i	0.0685394	+	0.118714i
$69$	108.778	+	48.4312i	0.189788	+	0.0844990i
$70$	23.7025	+	17.2209i	0.0404713	+	0.0294041i
$71$	−694.938	+	309.406i	−1.16161	+	0.517180i	−0.894755	−	0.446558i	$-0.852650\pi$
$71$	−694.938	+	309.406i	−1.16161	+	0.517180i	−0.266851	+	0.963738i	$0.585983\pi$
$72$	−304.905	−	64.8095i	−0.499075	−	0.106082i
$73$	−55.1261	−	524.490i	−0.0883838	−	0.840916i	−0.945463	−	0.325731i	$-0.894390\pi$
$73$	−55.1261	−	524.490i	−0.0883838	−	0.840916i	0.857079	−	0.515185i	$-0.172277\pi$
$74$	133.722	−	148.513i	0.210066	−	0.233301i
$75$	195.509	+	217.135i	0.301006	+	0.334301i
$76$	−10.6257	+	101.097i	−0.0160376	+	0.152587i
$77$	−13.5467	+	41.6926i	−0.0200493	+	0.0617054i
$78$	152.132	−	468.215i	0.220841	−	0.679678i
$79$	41.4502	−	394.372i	0.0590318	−	0.561650i	−0.924534	−	0.381100i	$-0.875546\pi$
$79$	41.4502	−	394.372i	0.0590318	−	0.561650i	0.983566	−	0.180550i	$-0.0577878\pi$
$80$	9.84667	+	10.9358i	0.0137611	+	0.0152833i
$81$	−106.307	+	118.065i	−0.145825	+	0.161955i
$82$	30.1768	+	287.113i	0.0406399	+	0.386663i
$83$	−1326.16	−	281.884i	−1.75379	−	0.372780i	−0.784777	−	0.619779i	$-0.787222\pi$
$83$	−1326.16	−	281.884i	−1.75379	−	0.372780i	−0.969016	+	0.246998i	$0.920556\pi$
$84$	−43.0742	+	19.1779i	−0.0559498	+	0.0249104i
$85$	−81.5726	−	59.2660i	−0.104092	−	0.0756270i
$86$	−350.036	−	155.846i	−0.438899	−	0.195411i
$87$	188.802	+	327.015i	0.232663	+	0.402985i
$88$	190.578	−	330.091i	0.230860	−	0.399861i
$89$	−197.885	+	143.772i	−0.235683	+	0.171234i	−0.699358	−	0.714772i	$-0.746531\pi$
$89$	−197.885	+	143.772i	−0.235683	+	0.171234i	0.463675	+	0.886005i	$0.346531\pi$
$90$	155.097	−	32.9668i	0.181651	−	0.0386112i
$91$	63.2422	+	194.639i	0.0728526	+	0.224217i
$92$	166.891			0.189126
$93$	469.570	−	410.959i	0.523571	−	0.458220i
$94$	−347.947			−0.381787
$95$	−41.2060	−	126.819i	−0.0445015	−	0.136962i
$96$	646.497	−	137.417i	0.687321	−	0.146095i
$97$	−616.184	+	447.684i	−0.644990	+	0.468612i	−0.861561	−	0.507655i	$-0.830513\pi$
$97$	−616.184	+	447.684i	−0.644990	+	0.468612i	0.216571	+	0.976267i	$0.430513\pi$
$98$	288.029	−	498.881i	0.296891	−	0.514231i
$99$	118.627	+	205.468i	0.120429	+	0.208589i
$100$	374.117	+	166.568i	0.374117	+	0.166568i
$101$	−1109.79	−	806.308i	−1.09335	−	0.794363i	−0.113385	−	0.993551i	$-0.536170\pi$
$101$	−1109.79	−	806.308i	−1.09335	−	0.794363i	−0.979961	+	0.199188i	$0.936170\pi$
$102$	−85.7995	+	38.2004i	−0.0832884	+	0.0370824i
$103$	−471.137	−	100.143i	−0.450704	−	0.0958001i	−0.0230332	−	0.999735i	$-0.507332\pi$
$103$	−471.137	−	100.143i	−0.450704	−	0.0958001i	−0.427671	+	0.903935i	$0.640666\pi$
$104$	−185.998	−	1769.66i	−0.175372	−	1.66855i
$105$	41.3858	−	45.9636i	0.0384652	−	0.0427199i
$106$	771.148	+	856.447i	0.706609	+	0.784769i
$107$	−217.340	+	2067.85i	−0.196365	+	1.86829i	0.243067	+	0.970010i	$0.421847\pi$
$107$	−217.340	+	2067.85i	−0.196365	+	1.86829i	−0.439431	+	0.898276i	$0.644820\pi$
$108$	−231.703	+	713.109i	−0.206441	+	0.635361i
$109$	547.732	−	1685.75i	0.481314	−	1.48133i	−0.355935	−	0.934511i	$-0.615838\pi$
$109$	547.732	−	1685.75i	0.481314	−	1.48133i	0.837249	−	0.546822i	$-0.184162\pi$
$110$	−20.2664	+	192.821i	−0.0175666	+	0.167135i
$111$	−282.297	−	313.523i	−0.241392	−	0.268092i
$112$	−3.81279	+	4.23454i	−0.00321674	+	0.00357255i
$113$	128.919	+	1226.58i	0.107324	+	1.02112i	0.907126	+	0.420858i	$0.138271\pi$
$113$	128.919	+	1226.58i	0.107324	+	1.02112i	−0.799802	+	0.600264i	$0.795062\pi$
$114$	−121.493	−	25.8240i	−0.0998142	−	0.0212162i
$115$	−199.994	+	89.0430i	−0.162170	+	0.0722026i
$116$	428.169	+	311.083i	0.342711	+	0.248994i
$117$	1011.85	+	450.505i	0.799535	+	0.355976i
$118$	361.980	+	626.968i	0.282398	+	0.489128i
$119$	19.5214	−	33.8120i	0.0150380	−	0.0260466i
$120$	−435.059	+	316.089i	−0.330961	+	0.240457i
$121$	1018.15	−	216.414i	0.764949	−	0.162595i
$122$	355.513	+	1094.16i	0.263825	+	0.811970i
$123$	609.456			0.446771
$124$	366.966	−	793.890i	0.265762	−	0.574947i
$125$	−1368.06			−0.978903
$126$	18.9729	+	58.3926i	0.0134146	+	0.0412859i
$127$	2008.38	−	426.894i	1.40327	−	0.298273i	0.556769	−	0.830668i	$-0.312041\pi$
$127$	2008.38	−	426.894i	1.40327	−	0.298273i	0.846496	+	0.532394i	$0.178708\pi$
$128$	773.985	−	562.333i	0.534463	−	0.388310i
$129$	−404.442	+	700.515i	−0.276040	+	0.478115i
$130$	452.567	+	783.869i	0.305329	+	0.528845i
$131$	−1239.63	−	551.919i	−0.826771	−	0.368102i	−0.0506734	−	0.998715i	$-0.516137\pi$
$131$	−1239.63	−	551.919i	−0.826771	−	0.368102i	−0.776097	+	0.630613i	$0.782803\pi$
$132$	−252.435	−	183.405i	−0.166452	−	0.120934i
$133$	47.1695	−	21.0012i	0.0307527	−	0.0136920i
$134$	−1099.81	−	233.771i	−0.709021	−	0.150707i
$135$	−102.811	−	978.177i	−0.0655446	−	0.623615i
$136$	−227.144	+	252.269i	−0.143217	+	0.159058i
$137$	650.906	+	722.905i	0.405917	+	0.450817i	0.911094	−	0.412199i	$-0.135239\pi$
$137$	650.906	+	722.905i	0.405917	+	0.450817i	−0.505176	+	0.863016i	$0.668573\pi$
$138$	−21.3152	+	202.800i	−0.0131483	+	0.125098i
$139$	840.338	−	2586.29i	0.512781	−	1.57818i	−0.274503	−	0.961586i	$-0.588513\pi$
$139$	840.338	−	2586.29i	0.512781	−	1.57818i	0.787284	−	0.616591i	$-0.211487\pi$
$140$	26.7882	−	82.4457i	0.0161716	−	0.0497709i
$141$	−76.7806	+	730.519i	−0.0458588	+	0.436318i
$142$	−871.704	−	968.126i	−0.515153	−	0.572136i
$143$	−906.233	+	1006.47i	−0.529951	+	0.588571i
$144$	3.22351	+	30.6696i	0.00186545	+	0.0177486i
$145$	−679.071	−	144.341i	−0.388923	−	0.0826681i
$146$	825.077	−	367.348i	0.467698	−	0.208233i
$147$	−983.848	−	714.808i	−0.552017	−	0.401064i
$148$	−540.190	−	240.508i	−0.300023	−	0.133579i
$149$	−1355.31	−	2347.47i	−0.745179	−	1.29069i	−0.950111	−	0.311912i	$-0.899031\pi$
$149$	−1355.31	−	2347.47i	−0.745179	−	1.29069i	0.204932	−	0.978776i	$-0.434303\pi$
$150$	−250.189	+	433.341i	−0.136186	+	0.235881i
$151$	−934.747	+	679.133i	−0.503766	+	0.366007i	−0.810454	−	0.585803i	$-0.800779\pi$
$151$	−934.747	+	679.133i	−0.503766	+	0.366007i	0.306688	+	0.951810i	$0.400779\pi$
$152$	−439.123	+	93.3384i	−0.234326	+	0.0498075i
$153$	−65.2957	−	200.959i	−0.0345022	−	0.106187i
$154$	−75.0749			−0.0392838
$155$	−16.1814	+	1147.15i	−0.00838529	+	0.594459i
$156$	−1456.68			−0.747613
$157$	770.556	+	2371.53i	0.391701	+	1.20553i	0.931501	+	0.363738i	$0.118500\pi$
$157$	770.556	+	2371.53i	0.391701	+	1.20553i	−0.539800	+	0.841793i	$0.681500\pi$
$158$	664.260	−	141.193i	0.334467	−	0.0710931i
$159$	1968.29	−	1430.04i	0.981732	−	0.713270i
$160$	−607.584	+	1052.37i	−0.300211	+	0.519980i
$161$	−42.3848	−	73.4126i	−0.0207478	−	0.0359362i
$162$	−248.554	−	110.663i	−0.120545	−	0.0536700i
$163$	235.608	+	171.180i	0.113216	+	0.0822566i	0.642953	−	0.765906i	$-0.277709\pi$
$163$	235.608	+	171.180i	0.113216	+	0.0822566i	−0.529736	+	0.848162i	$0.677709\pi$
$164$	780.357	−	347.438i	0.371559	−	0.165429i
$165$	400.359	+	85.0989i	0.188896	+	0.0401512i
$166$	−242.699	−	2309.12i	−0.113476	−	1.07966i
$167$	−552.315	+	613.408i	−0.255925	+	0.284233i	−0.857392	−	0.514665i	$-0.827916\pi$
$167$	−552.315	+	613.408i	−0.255925	+	0.284233i	0.601467	+	0.798898i	$0.294583\pi$
$168$	−139.333	−	154.745i	−0.0639869	−	0.0710647i
$169$	−431.251	+	4103.08i	−0.196291	+	1.86758i
$170$	53.3594	−	164.223i	0.0240734	−	0.0740904i
$171$	86.3525	−	265.766i	0.0386172	−	0.118852i
$172$	−118.506	+	1127.51i	−0.0525351	+	0.499838i
$173$	−2227.99	−	2474.43i	−0.979137	−	1.08744i	−0.996157	−	0.0875864i	$-0.972085\pi$
$173$	−2227.99	−	2474.43i	−0.979137	−	1.08744i	0.0170202	−	0.999855i	$-0.494582\pi$
$174$	−432.703	+	480.565i	−0.188524	+	0.209377i
$175$	−21.7430	−	206.871i	−0.00939209	−	0.0893597i
$176$	−36.8843	−	7.84000i	−0.0157969	−	0.00335774i
$177$	1396.20	−	621.630i	0.592911	−	0.263981i
$178$	−338.887	−	246.216i	−0.142700	−	0.103678i
$179$	2894.37	+	1288.65i	1.20858	+	0.538093i	0.909327	−	0.416083i	$-0.136597\pi$
$179$	2894.37	+	1288.65i	1.20858	+	0.538093i	0.299249	+	0.954175i	$0.403264\pi$
$180$	−234.581	−	406.306i	−0.0971369	−	0.168246i
$181$	1269.36	−	2198.60i	0.521275	−	0.902875i	−0.478418	−	0.878132i	$-0.658790\pi$
$181$	1269.36	−	2198.60i	0.521275	−	0.902875i	0.999694	−	0.0247434i	$-0.00787688\pi$
$182$	−283.547	+	206.009i	−0.115483	+	0.0839032i
$183$	2375.65	−	504.959i	0.959633	−	0.203976i
$184$	227.757	+	700.965i	0.0912527	+	0.280847i
$185$	775.657			0.308257
$186$	917.840	+	547.319i	0.361824	+	0.215760i
$187$	258.372			0.101037
$188$	318.141	+	979.139i	0.123419	+	0.379846i
$189$	372.530	−	79.1836i	0.143373	−	0.0304749i
$190$	184.747	−	134.227i	0.0705419	−	0.0512517i
$191$	536.000	−	928.379i	0.203056	−	0.351702i	−0.746456	−	0.665435i	$-0.768246\pi$
$191$	536.000	−	928.379i	0.203056	−	0.351702i	0.949511	+	0.313732i	$0.101579\pi$
$192$	533.929	+	924.792i	0.200693	+	0.347610i
$193$	−988.462	−	440.092i	−0.368658	−	0.164137i	0.214042	−	0.976825i	$-0.431337\pi$
$193$	−988.462	−	440.092i	−0.368658	−	0.164137i	−0.582700	+	0.812687i	$0.698004\pi$
$194$	−1055.24	−	766.679i	−0.390526	−	0.283734i
$195$	1745.61	−	777.196i	0.641055	−	0.285416i
$196$	−1667.23	−	354.381i	−0.607592	−	0.129148i
$197$	205.280	+	1953.11i	0.0742416	+	0.706362i	0.966818	+	0.255466i	$0.0822288\pi$
$197$	205.280	+	1953.11i	0.0742416	+	0.706362i	−0.892576	+	0.450896i	$0.851104\pi$
$198$	−271.874	+	301.946i	−0.0975819	+	0.108376i
$199$	2211.82	+	2456.48i	0.787898	+	0.875050i	0.994646	−	0.103345i	$-0.0329545\pi$
$199$	2211.82	+	2456.48i	0.787898	+	0.875050i	−0.206747	+	0.978394i	$0.566288\pi$
$200$	−189.047	+	1798.66i	−0.0668381	+	0.635923i
$201$	−733.497	+	2257.47i	−0.257397	+	0.792187i
$202$	725.950	−	2234.24i	0.252860	−	0.778222i
$203$	28.0995	−	267.349i	0.00971527	−	0.0924347i
$204$	185.948	+	206.516i	0.0638183	+	0.0708774i
$205$	−749.769	+	832.703i	−0.255445	+	0.283700i
$206$	−86.2223	−	820.350i	−0.0291621	−	0.277459i
$207$	−448.751	−	95.3851i	−0.150678	−	0.0320276i
$208$	−160.820	+	71.6015i	−0.0536098	+	0.0238686i
$209$	276.435	+	200.842i	0.0914901	+	0.0664714i
$210$	96.7638	+	43.0820i	0.0317968	+	0.0141569i
$211$	429.261	+	743.502i	0.140055	+	0.242582i	0.927517	−	0.373781i	$-0.121939\pi$
$211$	429.261	+	743.502i	0.140055	+	0.242582i	−0.787462	+	0.616363i	$0.788605\pi$
$212$	1704.99	−	2953.13i	0.552355	−	0.956707i
$213$	−2224.95	+	1616.52i	−0.715732	+	0.520010i
$214$	−3482.98	+	740.331i	−1.11258	+	0.236486i
$215$	−459.561	−	1414.38i	−0.145776	−	0.448652i
$216$	−3311.36			−1.04310
$217$	−442.416	+	40.1996i	−0.138402	+	0.0125757i
$218$	3035.48			0.943069
$219$	−589.184	−	1813.32i	−0.181796	−	0.559511i
$220$	561.139	−	119.274i	0.171964	−	0.0365520i
$221$	975.831	−	708.983i	0.297020	−	0.215798i
$222$	361.250	−	625.703i	0.109214	−	0.189164i
$223$	−2245.70	−	3889.66i	−0.674363	−	1.16803i	−0.976655	−	0.214816i	$-0.931085\pi$
$223$	−2245.70	−	3889.66i	−0.674363	−	1.16803i	0.302291	−	0.953216i	$-0.402249\pi$
$224$	−429.853	−	191.383i	−0.128218	−	0.0570862i
$225$	−910.760	−	661.706i	−0.269855	−	0.196061i
$226$	−1929.54	+	859.086i	−0.567925	+	0.252856i
$227$	−1867.82	−	397.018i	−0.546131	−	0.116084i	−0.0734195	−	0.997301i	$-0.523391\pi$
$227$	−1867.82	−	397.018i	−0.546131	−	0.116084i	−0.472711	+	0.881218i	$0.656725\pi$
$228$	38.4154	+	365.498i	0.0111584	+	0.106165i
$229$	−893.612	+	992.457i	−0.257867	+	0.286390i	−0.858152	−	0.513396i	$-0.828387\pi$
$229$	−893.612	+	992.457i	−0.257867	+	0.286390i	0.600285	+	0.799786i	$0.295054\pi$
$230$	−250.865	−	278.613i	−0.0719197	−	0.0798749i
$231$	−16.5666	+	157.621i	−0.00471862	+	0.0448947i
$232$	−722.266	+	2222.91i	−0.204393	+	0.629056i
$233$	−316.343	+	973.603i	−0.0889456	+	0.273746i	−0.985629	−	0.168927i	$-0.945970\pi$
$233$	−316.343	+	973.603i	−0.0889456	+	0.273746i	0.896683	+	0.442673i	$0.145970\pi$
$234$	−198.273	+	1886.44i	−0.0553910	+	0.527010i
$235$	−903.654	−	1003.61i	−0.250842	−	0.278588i
$236$	1433.35	−	1591.89i	0.395351	−	0.439082i
$237$	−149.855	−	1425.78i	−0.0410724	−	0.390778i
$238$	65.4014	+	13.9015i	0.0178124	+	0.00378613i
$239$	−2001.78	+	891.248i	−0.541774	+	0.241214i	−0.659331	−	0.751853i	$-0.729160\pi$
$239$	−2001.78	+	891.248i	−0.541774	+	0.241214i	0.117557	+	0.993066i	$0.462494\pi$
$240$	43.0410	+	31.2711i	0.0115762	+	0.00841059i
$241$	−2480.60	−	1104.43i	−0.663026	−	0.295198i	0.0474978	−	0.998871i	$-0.484875\pi$
$241$	−2480.60	−	1104.43i	−0.663026	−	0.295198i	−0.710524	+	0.703673i	$0.751542\pi$
$242$	891.289	+	1543.76i	0.236753	+	0.410068i
$243$	1710.45	−	2962.58i	0.451545	−	0.782098i
$244$	2753.95	−	2000.86i	0.722556	−	0.524967i
$245$	2187.00	−	464.862i	0.570296	−	0.121220i
$246$	322.528	+	992.638i	0.0835919	+	0.257269i
$247$	1595.17			0.410925
$248$	3835.25	+	457.879i	0.982010	+	0.117239i
$249$	−4901.59			−1.24749
$250$	−723.984	−	2228.19i	−0.183155	−	0.563694i
$251$	2074.80	−	441.013i	0.521755	−	0.110902i	0.0604967	−	0.998168i	$-0.480732\pi$
$251$	2074.80	−	441.013i	0.521755	−	0.110902i	0.461258	+	0.887266i	$0.347398\pi$
$252$	146.972	−	106.781i	0.0367395	−	0.0266928i
$253$	280.488	−	485.820i	0.0697002	−	0.120724i
$254$	1758.14	+	3045.18i	0.434313	+	0.752252i
$255$	−333.014	−	148.268i	−0.0817811	−	0.0364113i
$256$	3237.16	+	2351.94i	0.790323	+	0.574203i
$257$	−639.254	+	284.614i	−0.155158	+	0.0690807i	−0.482846	−	0.875705i	$-0.660397\pi$
$257$	−639.254	+	284.614i	−0.155158	+	0.0690807i	0.327688	+	0.944786i	$0.393730\pi$
$258$	−1354.98	−	288.010i	−0.326967	−	0.0694989i
$259$	31.3948	+	298.702i	0.00753197	+	0.0716619i
$260$	1792.04	−	1990.27i	0.427453	−	0.474735i
$261$	−973.502	−	1081.18i	−0.230875	−	0.256412i
$262$	242.906	−	2311.10i	0.0572778	−	0.544962i
$263$	−1613.87	+	4966.99i	−0.378387	+	1.16455i	0.562778	+	0.826608i	$0.309732\pi$
$263$	−1613.87	+	4966.99i	−0.378387	+	1.16455i	−0.941165	+	0.337947i	$0.890268\pi$
$264$	425.825	−	1310.56i	0.0992717	−	0.305527i
$265$	−467.563	+	4448.56i	−0.108385	+	1.03122i
$266$	59.1676	+	65.7123i	0.0136383	+	0.0151469i
$267$	−591.715	+	657.166i	−0.135627	+	0.150629i
$268$	347.753	+	3308.65i	0.0792627	+	0.754134i
$269$	3152.19	+	670.018i	0.714470	+	0.151865i	0.550785	−	0.834647i	$-0.314329\pi$
$269$	3152.19	+	670.018i	0.714470	+	0.151865i	0.163685	+	0.986513i	$0.447662\pi$
$270$	1538.78	−	685.107i	0.346840	−	0.154423i
$271$	173.915	+	126.357i	0.0389838	+	0.0283234i	0.607107	−	0.794620i	$-0.292330\pi$
$271$	173.915	+	126.357i	0.0389838	+	0.0283234i	−0.568123	+	0.822944i	$0.692330\pi$
$272$	30.6800	+	13.6596i	0.00683914	+	0.00304498i
$273$	369.948	+	640.769i	0.0820156	+	0.142055i
$274$	−832.951	+	1442.71i	−0.183651	+	0.318093i
$275$	1113.65	−	809.111i	0.244201	−	0.177423i
$276$	590.179	−	125.446i	0.128712	−	0.0273586i
$277$	−1673.55	−	5150.64i	−0.363009	−	1.11723i	−0.951218	−	0.308519i	$-0.900167\pi$
$277$	−1673.55	−	5150.64i	−0.363009	−	1.11723i	0.588209	−	0.808709i	$-0.299833\pi$
$278$	4657.08			1.00472
$279$	−1440.47	+	1924.95i	−0.309099	+	0.413059i
$280$	382.841			0.0817112
$281$	1918.58	+	5904.79i	0.407306	+	1.25356i	0.918954	+	0.394365i	$0.129035\pi$
$281$	1918.58	+	5904.79i	0.407306	+	1.25356i	−0.511648	+	0.859195i	$0.670965\pi$
$282$	−1230.45	+	261.540i	−0.259830	+	0.0552286i
$283$	−841.571	+	611.437i	−0.176771	+	0.128432i	−0.672652	−	0.739959i	$-0.734845\pi$
$283$	−841.571	+	611.437i	−0.176771	+	0.128432i	0.495881	+	0.868390i	$0.334845\pi$
$284$	−1927.32	+	3338.21i	−0.402694	+	0.697487i
$285$	−241.043	−	417.498i	−0.0500987	−	0.0867735i
$286$	−2118.86	−	943.375i	−0.438079	−	0.195045i
$287$	−351.017	−	255.029i	−0.0721947	−	0.0524525i
$288$	−2326.38	+	1035.77i	−0.475984	+	0.211922i
$289$	4580.56	+	973.628i	0.932334	+	0.198174i
$290$	−124.276	−	1182.41i	−0.0251646	−	0.239425i
$291$	−1842.51	+	2046.31i	−0.371168	+	0.412223i
$292$	−1788.14	−	1985.93i	−0.358365	−	0.398005i
$293$	727.266	−	6919.47i	0.145008	−	1.37966i	−0.643882	−	0.765125i	$-0.722677\pi$
$293$	727.266	−	6919.47i	0.145008	−	1.37966i	0.788890	−	0.614534i	$-0.210656\pi$
$294$	643.569	−	1980.70i	0.127666	−	0.392914i
$295$	−868.312	+	2672.39i	−0.171373	+	0.527432i
$296$	272.966	−	2597.10i	0.0536007	−	0.509977i
$297$	1686.44	+	1872.99i	0.329486	+	0.365932i
$298$	3106.15	−	3449.73i	0.603808	−	0.670596i
$299$	−273.748	−	2604.54i	−0.0529474	−	0.503760i
$300$	1448.20	+	307.824i	0.278706	+	0.0592408i
$301$	526.071	−	234.222i	0.100738	−	0.0448516i
$302$	−1600.80	−	1163.05i	−0.305018	−	0.221609i
$303$	−4530.63	−	2017.17i	−0.859003	−	0.382453i
$304$	22.2068	+	38.4633i	0.00418962	+	0.00725664i
$305$	−2232.66	+	3867.07i	−0.419152	+	0.725993i
$306$	292.753	−	212.698i	0.0546915	−	0.0397357i
$307$	5844.28	−	1242.24i	1.08648	−	0.230940i	0.370344	−	0.928895i	$-0.379240\pi$
$307$	5844.28	−	1242.24i	1.08648	−	0.230940i	0.716141	+	0.697955i	$0.245907\pi$
$308$	68.6439	+	211.264i	0.0126992	+	0.0390841i
$309$	−1741.36			−0.320591
$310$	−1876.96	+	580.723i	−0.343884	+	0.106396i
$311$	5209.21			0.949798			0.474899	−	0.880040i	$-0.342485\pi$
$311$	5209.21			0.949798			0.474899	+	0.880040i	$0.342485\pi$
$312$	−1987.94	−	6118.25i	−0.360721	−	1.11018i
$313$	−5329.21	+	1132.76i	−0.962379	+	0.204560i	−0.662203	−	0.749324i	$-0.730379\pi$
$313$	−5329.21	+	1132.76i	−0.962379	+	0.204560i	−0.300175	+	0.953884i	$0.597045\pi$
$314$	−3454.79	+	2510.05i	−0.620908	+	0.451116i
$315$	−119.152	+	206.377i	−0.0213125	+	0.0369143i
$316$	−1004.68	−	1740.16i	−0.178854	−	0.309784i
$317$	−2483.35	−	1105.66i	−0.439996	−	0.195899i	0.174768	−	0.984610i	$-0.444082\pi$
$317$	−2483.35	−	1105.66i	−0.439996	−	0.195899i	−0.614765	+	0.788711i	$0.710749\pi$
$318$	3370.78	+	2449.02i	0.594415	+	0.431868i
$319$	1625.17	−	723.573i	0.285242	−	0.126998i
$320$	−1920.40	−	408.194i	−0.335480	−	0.0713085i
$321$	785.752	+	7475.93i	0.136624	+	1.29989i
$322$	97.1389	−	107.884i	0.0168116	−	0.0186712i
$323$	−203.627	−	226.150i	−0.0350777	−	0.0389577i
$324$	−84.1493	+	800.627i	−0.0144289	+	0.137282i
$325$	1985.84	−	6111.78i	0.338937	−	1.04314i
$326$	−154.120	+	474.331i	−0.0261837	+	0.0805852i
$327$	669.833	−	6373.04i	0.113278	−	1.07777i
$328$	2524.25	+	2803.46i	0.424933	+	0.471936i
$329$	349.910	−	388.614i	0.0586357	−	0.0651215i
$330$	73.2693	+	697.110i	0.0122222	+	0.116287i
$331$	−5369.54	−	1141.33i	−0.891651	−	0.189526i	−0.260765	−	0.965402i	$-0.583975\pi$
$331$	−5369.54	−	1141.33i	−0.891651	−	0.189526i	−0.630886	+	0.775876i	$0.717308\pi$
$332$	−6276.08	+	2794.29i	−1.03748	+	0.461917i
$333$	1315.05	+	955.441i	0.216409	+	0.157231i
$334$	−1291.36	−	574.951i	−0.211557	−	0.0941915i
$335$	−2182.03	−	3779.38i	−0.355871	−	0.616387i
$336$	−10.3003	+	17.8406i	−0.00167240	+	0.00289668i
$337$	157.293	−	114.280i	0.0254253	−	0.0184726i	−0.575000	−	0.818153i	$-0.694998\pi$
$337$	157.293	−	114.280i	0.0254253	−	0.0184726i	0.600425	+	0.799681i	$0.294998\pi$
$338$	−6911.02	+	1468.98i	−1.11216	+	0.236397i
$339$	1377.87	+	4240.66i	0.220755	+	0.679413i
$340$	−510.921			−0.0814958
$341$	−1694.27	−	2402.50i	−0.269061	−	0.381533i
$342$	478.558			0.0756651
$343$	540.339	+	1662.99i	0.0850600	+	0.261788i
$344$	−4897.44	+	1040.98i	−0.767594	+	0.163157i
$345$	−640.310	+	465.212i	−0.0999221	+	0.0725976i
$346$	2851.11	−	4938.26i	0.442996	−	0.767291i
$347$	−2160.03	−	3741.28i	−0.334168	−	0.578796i	0.649157	−	0.760655i	$-0.275122\pi$
$347$	−2160.03	−	3741.28i	−0.334168	−	0.578796i	−0.983325	+	0.181859i	$0.941789\pi$
$348$	1747.97	+	778.246i	0.269256	+	0.119880i
$349$	−1785.60	−	1297.31i	−0.273871	−	0.198979i	0.442369	−	0.896833i	$-0.354138\pi$
$349$	−1785.60	−	1297.31i	−0.273871	−	0.198979i	−0.716240	+	0.697854i	$0.754138\pi$
$350$	325.429	−	144.891i	0.0496998	−	0.0221278i
$351$	11509.0	+	2446.31i	1.75016	+	0.372007i
$352$	−325.483	−	3096.77i	−0.0492850	−	0.468916i
$353$	−1072.79	+	1191.46i	−0.161754	+	0.179646i	−0.818573	−	0.574402i	$-0.805235\pi$
$353$	−1072.79	+	1191.46i	−0.161754	+	0.179646i	0.656820	+	0.754048i	$0.271901\pi$
$354$	1751.35	+	1945.07i	0.262946	+	0.292031i
$355$	528.532	−	5028.64i	0.0790185	−	0.751810i
$356$	−383.006	+	1178.77i	−0.0570204	+	0.175491i
$357$	43.6183	−	134.243i	0.00646646	−	0.0199017i
$358$	−567.153	+	5396.10i	−0.0837289	+	0.796627i
$359$	1606.04	+	1783.68i	0.236110	+	0.262226i	0.849542	−	0.527521i	$-0.176878\pi$
$359$	1606.04	+	1783.68i	0.236110	+	0.262226i	−0.613432	+	0.789747i	$0.710212\pi$
$360$	1386.41	−	1539.76i	0.202973	−	0.225424i
$361$	674.893	+	6421.18i	0.0983952	+	0.936168i
$362$	4252.67	+	903.933i	0.617446	+	0.131242i
$363$	3437.82	−	1530.61i	0.497076	−	0.221312i
$364$	838.975	+	609.551i	0.120808	+	0.0877724i
$365$	3202.38	+	1425.79i	0.459234	+	0.204464i
$366$	2079.65	+	3602.05i	0.297008	+	0.514433i
$367$	−4498.29	+	7791.27i	−0.639807	+	1.10818i	0.345668	+	0.938357i	$0.387652\pi$
$367$	−4498.29	+	7791.27i	−0.639807	+	1.10818i	−0.985475	+	0.169821i	$0.945681\pi$
$368$	58.9905	−	42.8591i	0.00835623	−	0.00607115i
$369$	−2296.87	+	488.215i	−0.324039	+	0.0688765i
$370$	410.482	+	1263.33i	0.0576756	+	0.177507i
$371$	−1732.04			−0.242381
$372$	700.965	−	3083.28i	0.0976971	−	0.429733i
$373$	10260.9			1.42437			0.712187	−	0.701990i	$-0.247705\pi$
$373$	10260.9			1.42437			0.712187	+	0.701990i	$0.247705\pi$
$374$	136.732	+	420.817i	0.0189044	+	0.0581816i
$375$	−4837.88	+	1028.32i	−0.666206	+	0.141606i
$376$	−3678.35	+	2672.48i	−0.504511	+	0.366549i
$377$	4152.51	−	7192.36i	0.567282	−	0.982561i
$378$	326.113	+	564.845i	0.0443742	+	0.0768584i
$379$	10893.7	+	4850.19i	1.47644	+	0.657354i	0.977817	−	0.209463i	$-0.0671716\pi$
$379$	10893.7	+	4850.19i	1.47644	+	0.657354i	0.498626	+	0.866818i	$0.333838\pi$
$380$	−546.641	−	397.158i	−0.0737950	−	0.0536152i
$381$	6781.37	−	3019.26i	0.911863	−	0.405988i
$382$	1795.73	+	381.694i	0.240517	+	0.0511235i
$383$	872.675	+	8302.95i	0.116427	+	1.10773i	0.884232	+	0.467047i	$0.154682\pi$
$383$	872.675	+	8302.95i	0.116427	+	1.10773i	−0.767805	+	0.640683i	$0.778651\pi$
$384$	2314.36	−	2570.36i	0.307564	−	0.341584i
$385$	−194.977	−	216.544i	−0.0258103	−	0.0286652i
$386$	193.690	−	1842.83i	0.0255403	−	0.243000i
$387$	963.071	−	2964.03i	0.126500	−	0.389328i
$388$	−1192.62	+	3670.51i	−0.156047	+	0.480262i
$389$	1232.25	−	11724.1i	0.160611	−	1.52811i	−0.556321	−	0.830968i	$-0.687787\pi$
$389$	1232.25	−	11724.1i	0.160611	−	1.52811i	0.716932	−	0.697143i	$-0.245546\pi$
$390$	2189.63	+	2431.83i	0.284298	+	0.315744i
$391$	−334.305	+	371.284i	−0.0432392	+	0.0480220i
$392$	−786.834	−	7486.23i	−0.101380	−	0.964570i
$393$	−4798.57	−	1019.97i	−0.615919	−	0.130918i
$394$	−3072.45	+	1367.94i	−0.392862	+	0.174914i
$395$	2132.41	+	1549.28i	0.271628	+	0.197349i
$396$	1098.28	+	488.984i	0.139370	+	0.0620514i
$397$	−1877.24	−	3251.48i	−0.237320	−	0.411051i	0.722624	−	0.691241i	$-0.242936\pi$
$397$	−1877.24	−	3251.48i	−0.237320	−	0.411051i	−0.959944	+	0.280190i	$0.909602\pi$
$398$	−2830.42	+	4902.43i	−0.356473	+	0.617429i
$399$	151.020	−	109.723i	0.0189485	−	0.0137669i
$400$	175.014	−	37.2004i	0.0218768	−	0.00465005i
$401$	−216.930	−	667.643i	−0.0270149	−	0.0831434i	0.936640	−	0.350293i	$-0.113918\pi$
$401$	−216.930	−	667.643i	−0.0270149	−	0.0831434i	−0.963655	+	0.267150i	$0.913918\pi$
$402$	−4064.97			−0.504335
$403$	−12991.6	−	4424.75i	−1.60584	−	0.546929i
$404$	−6951.03			−0.856007
$405$	−326.326	−	1004.33i	−0.0400377	−	0.123223i
$406$	450.309	−	95.7162i	0.0550455	−	0.0117003i
$407$	−1608.00	+	1168.28i	−0.195837	+	0.142284i
$408$	−613.630	+	1062.84i	−0.0744589	+	0.128967i
$409$	1190.01	+	2061.16i	0.143869	+	0.249188i	0.928950	−	0.370204i	$-0.120712\pi$
$409$	1190.01	+	2061.16i	0.143869	+	0.249188i	−0.785081	+	0.619393i	$0.787379\pi$
$410$	−1753.03	−	780.499i	−0.211161	−	0.0940148i
$411$	2845.19	+	2067.15i	0.341467	+	0.248090i
$412$	−2229.67	+	992.712i	−0.266621	+	0.118707i
$413$	−1064.27	−	226.217i	−0.126802	−	0.0269526i
$414$	−82.1255	−	781.372i	−0.00974939	−	0.0927593i
$415$	6030.07	−	6697.07i	0.713264	−	0.792160i
$416$	−9726.96	−	10802.9i	−1.14640	−	1.27321i
$417$	1027.67	−	9777.59i	0.120684	−	1.14823i
$418$	−180.826	+	556.524i	−0.0211590	+	0.0651208i
$419$	−4576.12	+	14083.8i	−0.533551	+	1.64210i	0.213207	+	0.977007i	$0.431609\pi$
$419$	−4576.12	+	14083.8i	−0.533551	+	1.64210i	−0.746759	+	0.665095i	$0.768391\pi$
$420$	32.7599	−	311.689i	0.00380599	−	0.0362116i
$421$	5969.45	+	6629.74i	0.691052	+	0.767491i	0.981925	−	0.189270i	$-0.0606123\pi$
$421$	5969.45	+	6629.74i	0.691052	+	0.767491i	−0.290873	+	0.956762i	$0.593946\pi$
$422$	−983.795	+	1092.61i	−0.113484	+	0.126037i
$423$	−295.829	−	2814.63i	−0.0340040	−	0.323527i
$424$	14730.4	+	3131.04i	1.68719	+	0.358624i
$425$	−1119.97	+	498.644i	−0.127827	+	0.0569124i
$426$	−3810.32	−	2768.36i	−0.433359	−	0.314854i
$427$	−1579.56	−	703.265i	−0.179017	−	0.0797034i
$428$	5267.95	+	9124.36i	0.594944	+	1.03047i
$429$	−2448.19	+	4240.39i	−0.275524	+	0.477221i
$430$	2060.44	−	1497.00i	0.231078	−	0.167888i
$431$	−15022.9	+	3193.22i	−1.67895	+	0.356872i	−0.946190	−	0.323612i	$-0.895103\pi$
$431$	−15022.9	+	3193.22i	−1.67895	+	0.356872i	−0.732763	+	0.680484i	$0.761769\pi$
$432$	101.233	+	311.564i	0.0112745	+	0.0346994i
$433$	−5903.99			−0.655260			−0.327630	−	0.944806i	$-0.606250\pi$
$433$	−5903.99			−0.655260			−0.327630	+	0.944806i	$0.606250\pi$
$434$	−299.603	−	699.302i	−0.0331369	−	0.0773446i
$435$	−2509.90			−0.276645
$436$	−2775.46	−	8541.99i	−0.304864	−	0.938274i
$437$	−646.290	+	137.373i	−0.0707466	+	0.0150376i
$438$	2641.61	−	1919.24i	0.288176	−	0.209372i
$439$	−5502.99	+	9531.46i	−0.598277	+	1.03625i	0.394799	+	0.918768i	$0.370814\pi$
$439$	−5502.99	+	9531.46i	−0.598277	+	1.03625i	−0.993075	+	0.117478i	$0.962519\pi$
$440$	1266.76	+	2194.09i	0.137251	+	0.237725i
$441$	4280.46	+	1905.78i	0.462202	+	0.205786i
$442$	1671.15	+	1214.17i	0.179839	+	0.130661i
$443$	−2955.83	+	1316.02i	−0.317010	+	0.141142i	−0.559073	−	0.829119i	$-0.688843\pi$
$443$	−2955.83	+	1316.02i	−0.317010	+	0.141142i	0.242063	+	0.970261i	$0.422176\pi$
$444$	−2091.06	−	444.469i	−0.223508	−	0.0475080i
$445$	−169.946	−	1616.93i	−0.0181038	−	0.172247i
$446$	5146.76	−	5716.06i	0.546427	−	0.606869i
$447$	−6557.33	−	7282.65i	−0.693850	−	0.770599i
$448$	79.4650	−	756.059i	0.00838028	−	0.0797331i
$449$	3972.55	−	12226.2i	0.417542	−	1.28506i	−0.492416	−	0.870360i	$-0.663886\pi$
$449$	3972.55	−	12226.2i	0.417542	−	1.28506i	0.909958	−	0.414701i	$-0.136114\pi$
$450$	595.759	−	1833.56i	0.0624097	−	0.192077i
$451$	300.130	−	2855.55i	0.0313361	−	0.298143i
$452$	4181.76	+	4644.31i	0.435162	+	0.483297i
$453$	−2795.07	+	3104.24i	−0.289899	+	0.321965i
$454$	−341.828	−	3252.28i	−0.0353365	−	0.336204i
$455$	−1330.61	−	282.829i	−0.137098	−	0.0291412i
$456$	−1482.72	+	660.147i	−0.152269	+	0.0677944i
$457$	4594.77	+	3338.29i	0.470315	+	0.341704i	0.797564	−	0.603234i	$-0.206122\pi$
$457$	4594.77	+	3338.29i	0.470315	+	0.341704i	−0.327249	+	0.944938i	$0.606122\pi$
$458$	−2089.35	−	930.237i	−0.213163	−	0.0949064i
$459$	−1122.33	−	1943.93i	−0.114130	−	0.197679i
$460$	−554.656	+	960.692i	−0.0562195	+	0.0973750i
$461$	10032.7	−	7289.18i	1.01360	−	0.736423i	0.0486379	−	0.998816i	$-0.484512\pi$
$461$	10032.7	−	7289.18i	1.01360	−	0.736423i	0.964961	+	0.262394i	$0.0845120\pi$
$462$	−265.488	+	56.4313i	−0.0267351	+	0.00568273i
$463$	−2230.83	−	6865.79i	−0.223921	−	0.689159i	−0.998399	−	0.0565580i	$-0.981987\pi$
$463$	−2230.83	−	6865.79i	−0.223921	−	0.689159i	0.774478	−	0.632601i	$-0.218013\pi$
$464$	231.232			0.0231351
$465$	805.051	+	4068.84i	0.0802867	+	0.405780i
$466$	−1753.15			−0.174277
$467$	695.061	+	2139.18i	0.0688728	+	0.211969i	0.979569	−	0.201108i	$-0.0644542\pi$
$467$	695.061	+	2139.18i	0.0688728	+	0.211969i	−0.910696	+	0.413077i	$0.864454\pi$
$468$	5489.81	−	1166.90i	0.542236	−	0.115256i
$469$	1367.10	−	993.259i	0.134599	−	0.0977919i
$470$	1156.39	−	2002.92i	0.113490	−	0.196570i
$471$	4507.52	+	7807.26i	0.440967	+	0.763778i
$472$	8642.26	+	3847.78i	0.842780	+	0.375230i
$473$	3083.02	+	2239.95i	0.299699	+	0.217744i
$474$	2242.90	−	998.604i	0.217342	−	0.0967667i
$475$	−1585.89	−	337.091i	−0.153190	−	0.0325616i
$476$	−20.6796	−	196.753i	−0.00199128	−	0.0189457i
$477$	−6272.36	+	6966.17i	−0.602079	+	0.668677i
$478$	−2510.95	−	2788.69i	−0.240268	−	0.266845i
$479$	−90.4397	+	860.476i	−0.00862692	+	0.0820796i	−0.997988	−	0.0633996i	$-0.979806\pi$
$479$	−90.4397	+	860.476i	−0.00862692	+	0.0820796i	0.989361	+	0.145479i	$0.0464724\pi$
$480$	−1357.58	+	4178.19i	−0.129093	+	0.397307i
$481$	−2867.36	+	8824.83i	−0.271810	+	0.836544i
$482$	486.074	−	4624.69i	0.0459338	−	0.437031i
$483$	−205.068	−	227.751i	−0.0193186	−	0.0214555i
$484$	3529.27	−	3919.65i	0.331449	−	0.368111i
$485$	−529.185	−	5034.86i	−0.0495444	−	0.471384i
$486$	5730.42	+	1218.04i	0.534850	+	0.113686i
$487$	2267.35	−	1009.49i	0.210972	−	0.0939309i	−0.298530	−	0.954400i	$-0.596496\pi$
$487$	2267.35	−	1009.49i	0.210972	−	0.0939309i	0.509502	+	0.860469i	$0.329830\pi$
$488$	12162.2	+	8836.38i	1.12819	+	0.819681i
$489$	961.855	+	428.245i	0.0889501	+	0.0396031i
$490$	1914.51	+	3316.02i	0.176507	+	0.305720i
$491$	−2815.28	+	4876.20i	−0.258761	+	0.448187i	−0.965910	−	0.258877i	$-0.916648\pi$
$491$	−2815.28	+	4876.20i	−0.258761	+	0.448187i	0.707149	+	0.707064i	$0.249981\pi$
$492$	2498.43	−	1815.22i	0.228939	−	0.166334i
$493$	−1549.75	+	329.409i	−0.141576	+	0.0300930i
$494$	844.174	+	2598.10i	0.0768850	+	0.236628i
$495$	−1577.01			−0.143195
$496$	−74.1677	−	374.854i	−0.00671417	−	0.0339344i
$497$	1957.90			0.176708
$498$	−2593.95	−	7983.36i	−0.233409	−	0.718359i
$499$	−16803.0	+	3571.60i	−1.50743	+	0.320414i	−0.886233	−	0.463240i	$-0.846687\pi$
$499$	−16803.0	+	3571.60i	−1.50743	+	0.320414i	−0.621197	+	0.783654i	$0.713353\pi$
$500$	−5608.28	+	4074.65i	−0.501619	+	0.364448i
$501$	−1492.08	+	2584.36i	−0.133056	+	0.230460i
$502$	1816.29	+	3145.90i	0.161484	+	0.279698i
$503$	13396.8	+	5964.66i	1.18755	+	0.528729i	0.902878	−	0.429897i	$-0.141450\pi$
$503$	13396.8	+	5964.66i	1.18755	+	0.528729i	0.284668	+	0.958626i	$0.408117\pi$
$504$	649.070	+	471.577i	0.0573648	+	0.0416780i
$505$	8329.77	−	3708.65i	0.734000	−	0.326798i
$506$	939.704	+	199.740i	0.0825592	+	0.0175485i
$507$	1559.11	+	14833.9i	0.136573	+	1.29940i
$508$	6961.76	−	7731.81i	0.608028	−	0.675283i
$509$	4224.78	+	4692.09i	0.367898	+	0.408592i	0.898461	−	0.439054i	$-0.144686\pi$
$509$	4224.78	+	4692.09i	0.367898	+	0.408592i	−0.530563	+	0.847645i	$0.678019\pi$
$510$	65.2544	−	620.854i	0.00566571	−	0.0539056i
$511$	−419.449	+	1290.93i	−0.0363118	+	0.111756i
$512$	247.548	−	761.874i	0.0213675	−	0.0657625i
$513$	310.295	−	2952.26i	0.0267053	−	0.254084i
$514$	−801.856	−	890.551i	−0.0688100	−	0.0764212i
$515$	2142.27	−	2379.23i	0.183300	−	0.203576i
$516$	428.438	+	4076.32i	0.0365522	+	0.347771i
$517$	3384.96	+	719.496i	0.287951	+	0.0612058i
$518$	−469.890	+	209.208i	−0.0398567	+	0.0177453i
$519$	−9738.80	−	7075.65i	−0.823672	−	0.598433i
$520$	10805.0	+	4810.70i	0.911214	+	0.405699i
$521$	−8254.79	−	14297.7i	−0.694144	−	1.20229i	−0.970468	−	0.241228i	$-0.922450\pi$
$521$	−8254.79	−	14297.7i	−0.694144	−	1.20229i	0.276325	−	0.961064i	$-0.410883\pi$
$522$	1245.77	−	2157.74i	0.104456	−	0.180923i
$523$	−3936.19	+	2859.81i	−0.329097	+	0.239103i	−0.740047	−	0.672555i	$-0.765197\pi$
$523$	−3936.19	+	2859.81i	−0.329097	+	0.239103i	0.410951	+	0.911658i	$0.365197\pi$
$524$	−6725.63	+	1429.58i	−0.560707	+	0.119182i
$525$	−232.388	−	715.216i	−0.0193185	−	0.0594563i
$526$	−8943.95			−0.741397
$527$	1031.09	+	2406.66i	0.0852278	+	0.198929i
$528$	−136.327			−0.0112365
$529$	−3424.60	−	10539.8i	−0.281466	−	0.866265i
$530$	−7492.93	+	1592.67i	−0.614098	+	0.130531i
$531$	−4763.94	+	3461.20i	−0.389336	+	0.282869i
$532$	130.818	−	226.584i	0.0106611	−	0.0184655i
$533$	−6702.19	−	11608.5i	−0.544661	−	0.943380i
$534$	−1383.48	−	615.967i	−0.112115	−	0.0499166i
$535$	−11181.1	−	8123.51i	−0.903550	−	0.656467i
$536$	−13422.2	+	5975.95i	−1.08163	+	0.481571i
$537$	11204.0	+	2381.49i	0.900352	+	0.191376i
$538$	576.879	+	5488.63i	0.0462286	+	0.439836i
$539$	−3833.66	+	4257.71i	−0.306359	+	0.340246i
$540$	−3334.89	−	3703.77i	−0.265760	−	0.295157i
$541$	1063.66	−	10120.1i	0.0845294	−	0.804243i	−0.867335	−	0.497724i	$-0.834169\pi$
$541$	1063.66	−	10120.1i	0.0845294	−	0.804243i	0.951865	−	0.306519i	$-0.0991642\pi$
$542$	−113.764	+	350.130i	−0.00901584	+	0.0277479i
$543$	2836.24	−	8729.06i	0.224153	−	0.689871i
$544$	−289.879	+	2758.01i	−0.0228464	+	0.217369i
$545$	7883.47	+	8755.48i	0.619616	+	0.688153i
$546$	−847.859	+	941.643i	−0.0664561	+	0.0738070i
$547$	−1469.33	−	13979.7i	−0.114852	−	1.09274i	−0.888421	−	0.459029i	$-0.848197\pi$
$547$	−1469.33	−	13979.7i	−0.114852	−	1.09274i	0.773569	−	0.633712i	$-0.218469\pi$
$548$	4821.46	+	1024.83i	0.375844	+	0.0798882i
$549$	−8548.64	+	3806.10i	−0.664567	+	0.295884i
$550$	1907.17	+	1385.64i	0.147858	+	0.107425i
$551$	−1914.16	−	852.238i	−0.147996	−	0.0658921i
$552$	1332.31	+	2307.63i	0.102730	+	0.177934i
$553$	−510.312	+	883.887i	−0.0392417	+	0.0679687i
$554$	7503.35	−	5451.50i	0.575427	−	0.418072i
$555$	2742.97	−	583.035i	0.209788	−	0.0445918i
$556$	−4258.15	−	13105.2i	−0.324795	−	0.999615i
$557$	−287.931			−0.0219031			−0.0109515	−	0.999940i	$-0.503486\pi$
$557$	−287.931			−0.0219031			−0.0109515	+	0.999940i	$0.503486\pi$
$558$	−3897.52	−	1327.44i	−0.295690	−	0.100708i
$559$	17790.6			1.34609
$560$	−11.7040	−	36.0213i	−0.000883188	−	0.00271817i
$561$	913.683	−	194.209i	0.0687624	−	0.0146159i
$562$	−8601.97	+	6249.70i	−0.645645	+	0.469088i
$563$	9516.93	−	16483.8i	0.712417	−	1.23394i	−0.251531	−	0.967849i	$-0.580934\pi$
$563$	9516.93	−	16483.8i	0.712417	−	1.23394i	0.963947	−	0.266093i	$-0.0857327\pi$
$564$	1861.03	+	3223.40i	0.138943	+	0.240656i
$565$	−7489.13	−	3334.38i	−0.557646	−	0.248280i
$566$	−1441.23	−	1047.11i	−0.107031	−	0.0777623i
$567$	373.554	−	166.317i	0.0276680	−	0.0123186i
$568$	−16651.2	−	3539.32i	−1.23005	−	0.261455i
$569$	496.161	+	4720.65i	0.0365556	+	0.347803i	0.997477	+	0.0709836i	$0.0226138\pi$
$569$	496.161	+	4720.65i	0.0365556	+	0.347803i	−0.960922	+	0.276820i	$0.910720\pi$
$570$	552.429	−	613.535i	0.0405942	−	0.0450845i
$571$	12860.3	+	14282.8i	0.942536	+	1.04679i	0.998829	+	0.0483777i	$0.0154051\pi$
$571$	12860.3	+	14282.8i	0.942536	+	1.04679i	−0.0562933	+	0.998414i	$0.517928\pi$
$572$	−717.349	+	6825.12i	−0.0524369	+	0.498903i
$573$	1197.63	−	3685.93i	0.0873155	−	0.268730i
$574$	229.612	−	706.674i	0.0166966	−	0.0513867i
$575$	−278.235	+	2647.23i	−0.0201795	+	0.191995i
$576$	−2753.05	−	3057.57i	−0.199150	−	0.221178i
$577$	−8502.34	+	9442.80i	−0.613444	+	0.681298i	−0.967193	−	0.254042i	$-0.918240\pi$
$577$	−8502.34	+	9442.80i	−0.613444	+	0.681298i	0.353750	+	0.935340i	$0.384907\pi$
$578$	838.283	+	7975.73i	0.0603252	+	0.573956i
$579$	−3826.31	−	813.308i	−0.274639	−	0.0583764i
$580$	−3213.72	+	1430.84i	−0.230073	+	0.102435i
$581$	2823.08	+	2051.09i	0.201585	+	0.146460i
$582$	−4307.95	−	1918.02i	−0.306822	−	0.136606i
$583$	−5731.04	−	9926.45i	−0.407128	−	0.705166i
$584$	5900.88	−	10220.6i	0.418117	−	0.724199i
$585$	−5956.13	+	4327.38i	−0.420950	+	0.305838i
$586$	11654.8	−	2477.31i	0.821597	−	0.174636i
$587$	4124.72	+	12694.6i	0.290026	+	0.892609i	0.984847	+	0.173426i	$0.0554838\pi$
$587$	4124.72	+	12694.6i	0.290026	+	0.892609i	−0.694820	+	0.719183i	$0.744516\pi$
$588$	−6162.23			−0.432187
$589$	−767.609	+	3376.42i	−0.0536991	+	0.236202i
$590$	−4812.11			−0.335782
$591$	2194.02	+	6752.50i	0.152707	+	0.469984i
$592$	−252.704	+	53.7139i	−0.0175440	+	0.00372910i
$593$	20371.8	−	14801.0i	1.41074	−	1.02496i	0.417525	−	0.908666i	$-0.362898\pi$
$593$	20371.8	−	14801.0i	1.41074	−	1.02496i	0.993215	−	0.116296i	$-0.0371023\pi$
$594$	−2158.11	+	3737.95i	−0.149071	+	0.258199i
$595$	129.757	+	224.746i	0.00894037	+	0.0154852i
$596$	−12547.8	−	5586.64i	−0.862378	−	0.383956i
$597$	9668.13	+	7024.31i	0.662798	+	0.481551i
$598$	4097.22	−	1824.20i	0.280180	−	0.124744i
$599$	21901.5	+	4655.31i	1.49394	+	0.317547i	0.881203	−	0.472739i	$-0.156735\pi$
$599$	21901.5	+	4655.31i	1.49394	+	0.317547i	0.612738	+	0.790286i	$0.290068\pi$
$600$	683.464	+	6502.72i	0.0465038	+	0.442454i
$601$	−17766.0	+	19731.1i	−1.20580	+	1.33918i	−0.280548	+	0.959840i	$0.590516\pi$
$601$	−17766.0	+	19731.1i	−1.20580	+	1.33918i	−0.925257	+	0.379342i	$0.876150\pi$
$602$	659.884	+	732.875i	0.0446758	+	0.0496175i
$603$	955.960	−	9095.35i	0.0645600	−	0.614248i
$604$	−1809.20	+	5568.13i	−0.121879	+	0.375106i
$605$	−2138.01	+	6580.11i	−0.143673	+	0.442181i
$606$	887.780	−	8446.66i	0.0595109	−	0.566208i
$607$	−6436.64	−	7148.62i	−0.430404	−	0.478012i	0.488460	−	0.872586i	$-0.337559\pi$
$607$	−6436.64	−	7148.62i	−0.430404	−	0.478012i	−0.918864	+	0.394574i	$0.870892\pi$
$608$	−2454.05	+	2725.50i	−0.163692	+	0.181799i
$609$	−101.589	−	966.551i	−0.00675957	−	0.0643130i
$610$	−7479.94	−	1589.91i	−0.496482	−	0.105531i
$611$	14758.8	−	6571.05i	0.977214	−	0.435084i
$612$	−866.217	−	629.343i	−0.0572136	−	0.0415681i
$613$	−10857.2	−	4833.92i	−0.715361	−	0.318499i	0.0165844	−	0.999862i	$-0.494721\pi$
$613$	−10857.2	−	4833.92i	−0.715361	−	0.318499i	−0.731945	+	0.681363i	$0.761387\pi$
$614$	5116.10	+	8861.34i	0.336269	+	0.582434i
$615$	−2025.50	+	3508.27i	−0.132807	+	0.230028i
$616$	−793.660	+	576.628i	−0.0519115	+	0.0377159i
$617$	8297.79	−	1763.75i	0.541420	−	0.115082i	0.0709196	−	0.997482i	$-0.477407\pi$
$617$	8297.79	−	1763.75i	0.541420	−	0.115082i	0.470501	+	0.882400i	$0.344073\pi$
$618$	−921.538	−	2836.20i	−0.0599833	−	0.184610i
$619$	25393.8			1.64889			0.824445	−	0.565942i	$-0.191487\pi$
$619$	25393.8			1.64889			0.824445	+	0.565942i	$0.191487\pi$
$620$	3350.35	+	4750.86i	0.217022	+	0.307741i
$621$	−4873.58			−0.314928
$622$	2756.74	+	8484.39i	0.177710	+	0.546934i
$623$	615.792	−	130.891i	0.0396006	−	0.00841737i
$624$	−514.888	+	374.088i	−0.0330321	+	0.0239992i
$625$	−504.466	+	873.761i	−0.0322858	+	0.0559207i
$626$	−4665.20	−	8080.36i	−0.297858	−	0.515905i
$627$	1128.53	+	502.453i	0.0718804	+	0.0320032i
$628$	10222.2	+	7426.90i	0.649542	+	0.471920i
$629$	1617.13	−	719.995i	0.102511	−	0.0456408i
$630$	−399.187	−	84.8498i	−0.0252444	−	0.00536587i
$631$	−1389.46	−	13219.9i	−0.0876604	−	0.834033i	−0.946698	−	0.322121i	$-0.895604\pi$
$631$	−1389.46	−	13219.9i	−0.0876604	−	0.834033i	0.859038	−	0.511912i	$-0.171063\pi$
$632$	5937.82	−	6594.62i	0.373724	−	0.415063i
$633$	2076.87	+	2306.59i	0.130408	+	0.144832i
$634$	486.614	−	4629.82i	0.0304825	−	0.290022i
$635$	−4217.39	+	12979.8i	−0.263562	+	0.811161i
$636$	3809.61	−	11724.8i	0.237517	−	0.731002i
$637$	−2795.82	+	26600.5i	−0.173900	+	1.65455i
$638$	2038.55	+	2264.04i	0.126500	+	0.140493i
$639$	7090.27	−	7874.54i	0.438946	−	0.487499i
$640$	664.706	+	6324.26i	0.0410544	+	0.390606i
$641$	3859.09	+	820.274i	0.237792	+	0.0505443i	0.325266	−	0.945623i	$-0.394546\pi$
$641$	3859.09	+	820.274i	0.237792	+	0.0505443i	−0.0874740	+	0.996167i	$0.527879\pi$
$642$	−11760.4	+	5236.08i	−0.722970	+	0.321887i
$643$	−6358.83	−	4619.96i	−0.389997	−	0.283349i	0.375457	−	0.926840i	$-0.377486\pi$
$643$	−6358.83	−	4619.96i	−0.389997	−	0.283349i	−0.765454	+	0.643490i	$0.777486\pi$
$644$	−392.407	−	174.711i	−0.0240109	−	0.0106903i
$645$	−2688.30	−	4656.26i	−0.164111	−	0.284248i
$646$	260.577	−	451.332i	0.0158704	−	0.0274883i
$647$	4339.95	−	3153.16i	0.263711	−	0.191597i	−0.448070	−	0.893998i	$-0.647889\pi$
$647$	4339.95	−	3153.16i	0.263711	−	0.191597i	0.711782	+	0.702401i	$0.247889\pi$
$648$	−3477.58	+	739.183i	−0.210822	+	0.0448115i
$649$	−2225.02	−	6847.91i	−0.134576	−	0.414181i
$650$	11005.3			0.664100
$651$	−1534.31	+	474.708i	−0.0923720	+	0.0285795i
$652$	1475.71			0.0886398
$653$	7113.54	+	21893.2i	0.426301	+	1.31202i	0.901743	+	0.432272i	$0.142288\pi$
$653$	7113.54	+	21893.2i	0.426301	+	1.31202i	−0.475443	+	0.879747i	$0.657712\pi$
$654$	10734.4	−	2281.67i	0.641818	−	0.136423i
$655$	7296.92	−	5301.53i	0.435289	−	0.316256i
$656$	186.606	−	323.210i	0.0111063	−	0.0192367i
$657$	3673.06	+	6361.93i	0.218112	+	0.377781i
$658$	818.120	+	364.251i	0.0484706	+	0.0215805i
$659$	1722.54	+	1251.50i	0.101822	+	0.0739782i	0.637531	−	0.770424i	$-0.279956\pi$
$659$	1722.54	+	1251.50i	0.101822	+	0.0739782i	−0.535709	+	0.844403i	$0.679956\pi$
$660$	1894.71	−	843.578i	0.111745	−	0.0497519i
$661$	−7448.84	−	1583.30i	−0.438315	−	0.0931668i	−0.0165318	−	0.999863i	$-0.505262\pi$
$661$	−7448.84	−	1583.30i	−0.438315	−	0.0931668i	−0.421784	+	0.906697i	$0.638596\pi$
$662$	−982.673	−	9349.51i	−0.0576929	−	0.548911i
$663$	2917.92	−	3240.68i	0.170924	−	0.189831i
$664$	−20301.4	−	22547.0i	−1.18652	−	1.31776i
$665$	−35.8745	+	341.323i	−0.00209196	+	0.0199037i
$666$	−860.220	+	2647.48i	−0.0500493	+	0.154036i
$667$	−1063.01	+	3271.62i	−0.0617092	+	0.189921i
$668$	−437.197	+	4159.65i	−0.0253229	+	0.240931i
$669$	−10865.2	−	12067.0i	−0.627913	−	0.697368i
$670$	5000.84	−	5554.00i	0.288357	−	0.320253i
$671$	−1196.04	−	11379.5i	−0.0688115	−	0.654697i
$672$	−1663.95	−	353.683i	−0.0955182	−	0.0203030i
$673$	912.682	−	406.352i	0.0522753	−	0.0232745i	−0.380432	−	0.924809i	$-0.624225\pi$
$673$	912.682	−	406.352i	0.0522753	−	0.0232745i	0.432708	+	0.901534i	$0.357558\pi$
$674$	269.372	+	195.710i	0.0153944	+	0.0111847i
$675$	−10925.0	−	4864.14i	−0.622971	−	0.277364i
$676$	10452.8	+	18104.8i	0.594720	+	1.03008i
$677$	684.239	−	1185.14i	0.0388441	−	0.0672799i	−0.845950	−	0.533263i	$-0.820966\pi$
$677$	684.239	−	1185.14i	0.0388441	−	0.0672799i	0.884794	+	0.465983i	$0.154299\pi$
$678$	−6177.70	+	4488.36i	−0.349931	+	0.254240i
$679$	1917.48	−	407.573i	0.108374	−	0.0230357i
$680$	−697.258	−	2145.94i	−0.0393215	−	0.121019i
$681$	−6903.62			−0.388469
$682$	3016.41	−	4030.92i	0.169361	−	0.226322i
$683$	−17980.7			−1.00734			−0.503669	−	0.863897i	$-0.668017\pi$
$683$	−17980.7			−1.00734			−0.503669	+	0.863897i	$0.668017\pi$
$684$	−437.565	−	1346.69i	−0.0244601	−	0.0752804i
$685$	−6324.59	+	1344.33i	−0.352774	+	0.0749844i
$686$	−2422.61	+	1760.13i	−0.134833	+	0.0979622i
$687$	−2414.09	+	4181.33i	−0.134066	+	0.232209i
$688$	247.667	+	428.972i	0.0137242	+	0.0237710i
$689$	−48883.9	−	21764.5i	−2.70294	−	1.20343i
$690$	−1096.56	−	796.697i	−0.0605004	−	0.0439561i
$691$	8220.87	−	3660.17i	0.452585	−	0.201504i	−0.167768	−	0.985827i	$-0.553656\pi$
$691$	8220.87	−	3660.17i	0.452585	−	0.201504i	0.620353	+	0.784323i	$0.286989\pi$
$692$	−16503.4	−	3507.90i	−0.906596	−	0.192703i
$693$	−63.8297	−	607.299i	−0.00349883	−	0.0332891i
$694$	4950.42	−	5498.00i	0.270771	−	0.300722i
$695$	12094.9	+	13432.8i	0.660124	+	0.733142i
$696$	−883.274	+	8403.79i	−0.0481040	+	0.457679i
$697$	−790.215	+	2432.03i	−0.0429434	+	0.132166i
$698$	1168.02	−	3594.80i	0.0633385	−	0.194936i
$699$	−386.862	+	3680.75i	−0.0209334	+	0.199168i
$700$	−705.282	−	783.295i	−0.0380816	−	0.0422939i
$701$	8098.33	−	8994.10i	0.436333	−	0.484597i	−0.484369	−	0.874864i	$-0.660951\pi$
$701$	8098.33	−	8994.10i	0.436333	−	0.484597i	0.920702	+	0.390267i	$0.127617\pi$
$702$	2106.25	+	20039.6i	0.113241	+	1.07742i
$703$	2289.87	+	486.727i	0.122851	+	0.0261128i
$704$	4595.96	−	2046.25i	0.246046	−	0.109547i
$705$	−3949.98	−	2869.83i	−0.211014	−	0.153311i
$706$	−2508.29	−	1116.76i	−0.133712	−	0.0595325i
$707$	1765.33	+	3057.64i	0.0939068	+	0.162651i
$708$	3872.18	−	6706.82i	0.205545	−	0.356014i
$709$	−19445.2	+	14127.7i	−1.03001	+	0.748347i	−0.968311	−	0.249747i	$-0.919652\pi$
$709$	−19445.2	+	14127.7i	−1.03001	+	0.748347i	−0.0617007	+	0.998095i	$0.519652\pi$
$710$	8469.99	−	1800.35i	0.447709	−	0.0951634i
$711$	1706.91	+	5253.32i	0.0900338	+	0.277095i
$712$	−5473.69			−0.288111
$713$	5644.63	+	673.895i	0.296484	+	0.0353963i
$714$	241.729			0.0126701
$715$	−2781.84	−	8561.62i	−0.145503	−	0.447813i
$716$	15703.4	−	3337.87i	0.819644	−	0.174221i
$717$	−6408.98	+	4656.40i	−0.333818	+	0.242533i
$718$	−2055.21	+	3559.73i	−0.106824	+	0.185025i
$719$	−13297.5	−	23031.9i	−0.689725	−	1.19464i	−0.971927	−	0.235284i	$-0.924398\pi$
$719$	−13297.5	−	23031.9i	−0.689725	−	1.19464i	0.282201	−	0.959355i	$-0.408935\pi$
$720$	−187.260	−	83.3734i	−0.00969272	−	0.00431548i
$721$	1002.94	+	728.678i	0.0518050	+	0.0376385i
$722$	−10101.2	+	4497.34i	−0.520675	+	0.231820i
$723$	−9602.33	−	2041.04i	−0.493934	−	0.104989i
$724$	−1344.67	−	12793.7i	−0.0690254	−	0.656733i
$725$	−5648.23	+	6272.99i	−0.289338	+	0.321342i
$726$	4312.27	+	4789.26i	0.220445	+	0.244829i
$727$	−2995.90	+	28504.1i	−0.152836	+	1.45414i	0.602143	+	0.798388i	$0.294314\pi$
$727$	−2995.90	+	28504.1i	−0.152836	+	1.45414i	−0.754979	+	0.655749i	$0.772353\pi$
$728$	−1415.24	+	4355.67i	−0.0720500	+	0.221747i
$729$	5147.35	−	15841.9i	0.261513	−	0.804853i
$730$	−627.508	+	5970.34i	−0.0318152	+	0.302702i
$731$	−2271.00	−	2522.20i	−0.114906	−	0.127616i
$732$	8234.85	−	9145.72i	0.415804	−	0.461797i
$733$	2390.70	+	22746.0i	0.120468	+	1.14617i	0.873035	+	0.487657i	$0.162148\pi$
$733$	2390.70	+	22746.0i	0.120468	+	1.14617i	−0.752568	+	0.658515i	$0.771185\pi$
$734$	−15070.4	−	3203.31i	−0.757845	−	0.161085i
$735$	7384.50	−	3287.79i	0.370587	−	0.164996i
$736$	4871.24	+	3539.16i	0.243962	+	0.177249i
$737$	10215.9	+	4548.43i	0.510596	+	0.227332i
$738$	−2010.68	−	3482.61i	−0.100290	−	0.173708i
$739$	18056.1	−	31274.2i	0.898790	−	1.55675i	0.0697476	−	0.997565i	$-0.477781\pi$
$739$	18056.1	−	31274.2i	0.898790	−	1.55675i	0.829043	−	0.559186i	$-0.188886\pi$
$740$	3179.76	−	2310.23i	0.157960	−	0.114765i
$741$	5641.03	−	1199.04i	0.279660	−	0.0594436i
$742$	−916.607	−	2821.03i	−0.0453500	−	0.139573i
$743$	−2297.84			−0.113458			−0.0567292	−	0.998390i	$-0.518067\pi$
$743$	−2297.84			−0.113458			−0.0567292	+	0.998390i	$0.518067\pi$
$744$	13906.8	−	1263.63i	0.685280	−	0.0622671i
$745$	18017.3			0.886045
$746$	5430.15	+	16712.3i	0.266504	+	0.820215i
$747$	18472.7	−	3926.50i	0.904795	−	0.192320i
$748$	1059.18	−	769.539i	0.0517747	−	0.0376165i
$749$	2675.77	−	4634.57i	0.130535	−	0.226093i
$750$	−4235.09	−	7335.40i	−0.206192	−	0.357134i
$751$	9973.68	+	4440.57i	0.484613	+	0.215764i	0.634475	−	0.772943i	$-0.281216\pi$
$751$	9973.68	+	4440.57i	0.484613	+	0.215764i	−0.149862	+	0.988707i	$0.547883\pi$
$752$	363.904	+	264.392i	0.0176466	+	0.0128210i
$753$	7005.66	−	3119.12i	0.339044	−	0.150952i
$754$	13911.9	+	2957.07i	0.671940	+	0.142825i
$755$	−802.770	−	7637.85i	−0.0386964	−	0.368172i
$756$	1291.32	−	1434.16i	0.0621229	−	0.0689945i
$757$	17216.8	+	19121.2i	0.826626	+	0.918061i	0.997740	−	0.0671904i	$-0.0214035\pi$
$757$	17216.8	+	19121.2i	0.826626	+	0.918061i	−0.171115	+	0.985251i	$0.554737\pi$
$758$	−2134.63	+	20309.6i	−0.102286	+	0.973190i
$759$	626.719	−	1928.84i	0.0299716	−	0.0922432i
$760$	922.113	−	2837.97i	0.0440113	−	0.135453i
$761$	−286.534	+	2726.19i	−0.0136489	+	0.129861i	−0.999225	−	0.0393750i	$-0.987463\pi$
$761$	−286.534	+	2726.19i	−0.0136489	+	0.129861i	0.985576	+	0.169236i	$0.0541300\pi$
$762$	8506.29	+	9447.19i	0.404397	+	0.449128i
$763$	−3052.61	+	3390.26i	−0.144839	+	0.160859i
$764$	−567.801	−	5402.27i	−0.0268879	−	0.255821i
$765$	1373.81	+	292.012i	0.0649284	+	0.0138010i
$766$	−13061.4	+	5815.32i	−0.616094	+	0.274303i
$767$	−27194.5	−	19758.0i	−1.28023	−	0.930141i
$768$	13215.5	+	5883.91i	0.620928	+	0.276455i
$769$	1187.49	+	2056.80i	0.0556854	+	0.0964499i	0.892524	−	0.450999i	$-0.148932\pi$
$769$	1187.49	+	2056.80i	0.0556854	+	0.0964499i	−0.836839	+	0.547449i	$0.815599\pi$
$770$	249.508	−	432.161i	0.0116775	−	0.0202260i
$771$	−2046.67	+	1486.99i	−0.0956016	+	0.0694587i
$772$	−5362.92	+	1139.92i	−0.250020	+	0.0531435i
$773$	7561.22	+	23271.0i	0.351822	+	1.08280i	0.957830	+	0.287337i	$0.0927700\pi$
$773$	7561.22	+	23271.0i	0.351822	+	1.08280i	−0.606008	+	0.795459i	$0.707230\pi$
$774$	5337.26			0.247860
$775$	11980.9	+	7144.35i	0.555311	+	0.331139i
$776$	−17044.2			−0.788468
$777$	335.546	+	1032.70i	0.0154925	+	0.0476809i
$778$	19747.5	−	4197.45i	0.910001	−	0.193427i
$779$	−2735.97	+	1987.80i	−0.125836	+	0.0914252i
$780$	4841.21	−	8385.23i	0.222235	−	0.384922i
$781$	6478.35	+	11220.8i	0.296817	+	0.514101i
$782$	−781.636	−	348.007i	−0.0357433	−	0.0159139i
$783$	−12503.5	−	9084.31i	−0.570674	−	0.414619i
$784$	−680.319	+	302.898i	−0.0309912	+	0.0137982i
$785$	−16212.4	−	3446.05i	−0.737127	−	0.156681i
$786$	−878.182	−	8355.34i	−0.0398521	−	0.379167i
$787$	−2066.22	+	2294.77i	−0.0935869	+	0.103939i	−0.788119	−	0.615523i	$-0.788945\pi$
$787$	−2066.22	+	2294.77i	−0.0935869	+	0.103939i	0.694532	+	0.719462i	$0.255611\pi$
$788$	6658.71	+	7395.25i	0.301024	+	0.334321i
$789$	−1973.64	+	18777.9i	−0.0890538	+	0.847290i
$790$	−1394.88	+	4293.00i	−0.0628197	+	0.193339i
$791$	980.929	−	3018.99i	0.0440933	−	0.135705i
$792$	−554.974	+	5280.23i	−0.0248992	+	0.236900i
$793$	−35743.2	−	39696.8i	−1.60060	−	1.77765i
$794$	4302.33	−	4778.22i	0.192297	−	0.213568i
$795$	1690.39	+	16083.0i	0.0754111	+	0.717489i
$796$	16383.6	+	3482.45i	0.729526	+	0.155066i
$797$	8658.36	−	3854.95i	0.384812	−	0.171329i	−0.205207	−	0.978719i	$-0.565787\pi$
$797$	8658.36	−	3854.95i	0.384812	−	0.171329i	0.590019	+	0.807389i	$0.299120\pi$
$798$	258.629	+	187.905i	0.0114729	+	0.00833554i
$799$	−2815.58	−	1253.58i	−0.124666	−	0.0555048i
$800$	7387.48	+	12795.5i	0.326484	+	0.565486i
$801$	1703.57	−	2950.68i	0.0751471	−	0.130159i
$802$	972.608	−	706.641i	0.0428229	−	0.0311127i
$803$	−8786.29	+	1867.58i	−0.386129	+	0.0820742i
$804$	3716.77	+	11439.0i	0.163035	+	0.501770i
$805$	563.456			0.0246699
$806$	331.503	−	23501.3i	0.0144872	−	1.02704i
$807$	11650.7			0.508210
$808$	−9486.13	−	29195.3i	−0.413021	−	1.27115i
$809$	−21660.3	+	4604.04i	−0.941330	+	0.200086i	−0.652925	−	0.757423i	$-0.726458\pi$
$809$	−21660.3	+	4604.04i	−0.941330	+	0.200086i	−0.288405	+	0.957509i	$0.593125\pi$
$810$	1463.08	−	1062.99i	0.0634661	−	0.0461108i
$811$	−10230.4	+	17719.5i	−0.442956	+	0.767223i	−0.997907	−	0.0646604i	$-0.979404\pi$
$811$	−10230.4	+	17719.5i	−0.442956	+	0.767223i	0.554951	+	0.831883i	$0.312737\pi$
$812$	−681.085	−	1179.67i	−0.0294352	−	0.0509833i
$813$	709.998	+	316.111i	0.0306282	+	0.0136365i
$814$	−2753.77	−	2000.73i	−0.118574	−	0.0861494i
$815$	−1768.41	+	787.348i	−0.0760059	+	0.0338400i
$816$	118.761	+	25.2435i	0.00509495	+	0.00108297i
$817$	−469.172	−	4463.87i	−0.0200909	−	0.191152i
$818$	−2727.31	+	3028.99i	−0.116575	+	0.129470i
$819$	−1907.53	−	2118.52i	−0.0813851	−	0.0903874i
$820$	−593.497	+	5646.75i	−0.0252754	+	0.240479i
$821$	783.681	−	2411.92i	0.0333138	−	0.102529i	−0.933017	−	0.359832i	$-0.882834\pi$
$821$	783.681	−	2411.92i	0.0333138	−	0.102529i	0.966331	+	0.257303i	$0.0828339\pi$
$822$	−1861.14	+	5727.99i	−0.0789715	+	0.243049i
$823$	149.826	−	1425.50i	0.00634580	−	0.0603763i	−0.990891	−	0.134668i	$-0.957003\pi$
$823$	149.826	−	1425.50i	0.00634580	−	0.0603763i	0.997237	+	0.0742922i	$0.0236697\pi$
$824$	−7212.37	−	8010.15i	−0.304921	−	0.338649i
$825$	3330.02	−	3698.36i	0.140529	−	0.156073i
$826$	−194.771	−	1853.12i	−0.00820452	−	0.0780608i
$827$	−43867.9	−	9324.40i	−1.84454	−	0.392069i	−0.853005	−	0.521902i	$-0.825222\pi$
$827$	−43867.9	−	9324.40i	−1.84454	−	0.392069i	−0.991536	+	0.129833i	$0.958556\pi$
$828$	−2123.73	+	945.544i	−0.0891360	+	0.0396859i
$829$	5014.83	+	3643.49i	0.210099	+	0.152646i	0.687859	−	0.725845i	$-0.258551\pi$
$829$	5014.83	+	3643.49i	0.210099	+	0.152646i	−0.477759	+	0.878491i	$0.658551\pi$
$830$	14098.8	+	6277.21i	0.589612	+	0.262512i
$831$	−9789.74	−	16956.3i	−0.408667	−	0.707832i
$832$	11743.2	−	20339.9i	0.489331	−	0.847546i
$833$	4128.08	−	2999.23i	0.171704	−	0.124750i
$834$	16468.9	−	3500.57i	0.683778	−	0.145341i
$835$	−1695.42	−	5217.98i	−0.0702666	−	0.216258i
$836$	1731.42			0.0716297
$837$	−10716.2	+	23183.3i	−0.442540	+	0.957388i
$838$	−25360.4			−1.04542
$839$	11345.7	+	34918.4i	0.466861	+	1.43685i	0.856627	+	0.515936i	$0.172556\pi$
$839$	11345.7	+	34918.4i	0.466861	+	1.43685i	−0.389767	+	0.920914i	$0.627444\pi$
$840$	1353.85	−	287.769i	0.0556097	−	0.0118202i
$841$	10905.6	−	7923.40i	0.447154	−	0.324876i
$842$	−7638.98	+	13231.1i	−0.312656	+	0.541537i
$843$	11223.1	+	19439.1i	0.458536	+	0.794207i
$844$	3974.19	+	1769.42i	0.162082	+	0.0721636i
$845$	−22185.7	−	16118.9i	−0.903209	−	0.656220i
$846$	4427.70	−	1971.34i	0.179938	−	0.0801136i
$847$	−2620.50	−	557.005i	−0.106306	−	0.0225961i
$848$	−155.732	−	1481.69i	−0.00630644	−	0.0600017i
$849$	−2516.46	+	2794.81i	−0.101725	+	0.112977i
$850$	−1404.85	−	1560.24i	−0.0566894	−	0.0629599i
$851$	401.745	−	3822.34i	0.0161829	−	0.153970i
$852$	−4306.37	+	13253.7i	−0.173162	+	0.532937i
$853$	9106.53	−	28027.0i	0.365535	−	1.12500i	−0.584110	−	0.811675i	$-0.698556\pi$
$853$	9106.53	−	28027.0i	0.365535	−	1.12500i	0.949645	−	0.313328i	$-0.101444\pi$
$854$	309.515	−	2944.84i	0.0124021	−	0.117998i
$855$	1242.87	+	1380.34i	0.0497136	+	0.0552125i
$856$	−31134.3	+	34578.2i	−1.24317	+	1.38068i
$857$	−3478.57	−	33096.4i	−0.138653	−	1.31920i	−0.813641	−	0.581368i	$-0.802518\pi$
$857$	−3478.57	−	33096.4i	−0.138653	−	1.31920i	0.674987	−	0.737829i	$-0.264149\pi$
$858$	−8202.04	−	1743.40i	−0.326355	−	0.0693690i
$859$	27794.9	−	12375.1i	1.10402	−	0.491540i	0.227922	−	0.973679i	$-0.426807\pi$
$859$	27794.9	−	12375.1i	1.10402	−	0.491540i	0.876094	+	0.482140i	$0.160140\pi$
$860$	−6096.57	−	4429.42i	−0.241734	−	0.175630i
$861$	−1433.00	−	638.013i	−0.0567207	−	0.0252537i
$862$	−13151.1	−	22778.4i	−0.519638	−	0.900040i
$863$	−22414.2	+	38822.5i	−0.884110	+	1.53132i	−0.0373807	+	0.999301i	$0.511901\pi$
$863$	−22414.2	+	38822.5i	−0.884110	+	1.53132i	−0.846730	+	0.532023i	$0.821432\pi$
$864$	−21885.5	+	15900.7i	−0.861758	+	0.626104i
$865$	21648.4	−	4601.52i	0.850946	−	0.180874i
$866$	−3124.42	−	9615.99i	−0.122601	−	0.377326i
$867$	16930.1			0.663180
$868$	−1693.93	+	1482.50i	−0.0662393	+	0.0579715i
$869$	−6754.15			−0.263658
$870$	−1328.26	−	4087.95i	−0.0517610	−	0.159304i
$871$	51065.1	−	10854.2i	1.98654	−	0.422252i
$872$	32089.9	−	23314.6i	1.24622	−	0.905428i
$873$	5304.67	−	9187.95i	0.205654	−	0.356203i
$874$	−565.764	−	979.932i	−0.0218962	−	0.0379253i
$875$	3216.69	+	1432.16i	0.124279	+	0.0553325i
$876$	−7816.16	−	5678.77i	−0.301465	−	0.219027i
$877$	−15478.8	+	6891.59i	−0.595987	+	0.265351i	−0.682483	−	0.730902i	$-0.739100\pi$
$877$	−15478.8	+	6891.59i	−0.595987	+	0.265351i	0.0864957	+	0.996252i	$0.472433\pi$
$878$	−18436.4	−	3918.77i	−0.708653	−	0.150629i
$879$	−2629.30	−	25016.1i	−0.100892	−	0.959922i
$880$	167.714	−	186.265i	0.00642457	−	0.00713521i
$881$	13914.9	+	15454.0i	0.532127	+	0.590986i	0.947934	−	0.318466i	$-0.103168\pi$
$881$	13914.9	+	15454.0i	0.532127	+	0.590986i	−0.415808	+	0.909453i	$0.636501\pi$
$882$	−838.758	+	7980.25i	−0.0320209	+	0.304659i
$883$	15030.1	−	46258.0i	0.572824	−	1.76297i	−0.0706463	−	0.997501i	$-0.522506\pi$
$883$	15030.1	−	46258.0i	0.572824	−	1.76297i	0.643471	−	0.765471i	$-0.277494\pi$
$884$	1888.71	−	5812.87i	0.0718601	−	0.221163i
$885$	−1061.88	+	10103.1i	−0.0403329	+	0.383742i
$886$	−3707.67	−	4117.79i	−0.140589	−	0.156140i
$887$	−28378.7	+	31517.8i	−1.07425	+	1.19308i	−0.0939527	+	0.995577i	$0.529950\pi$
$887$	−28378.7	+	31517.8i	−1.07425	+	1.19308i	−0.980302	+	0.197504i	$0.936716\pi$
$888$	−986.858	−	9389.32i	−0.0372937	−	0.354825i
$889$	−5169.15	−	1098.74i	−0.195014	−	0.0414516i
$890$	2543.60	−	1132.48i	0.0957995	−	0.0426527i
$891$	2189.20	+	1590.55i	0.0823130	+	0.0598039i
$892$	−20791.2	−	9256.82i	−0.780425	−	0.347468i
$893$	−2037.97	−	3529.87i	−0.0763697	−	0.132276i
$894$	8391.28	−	14534.1i	0.313922	−	0.543729i
$895$	−17037.3	+	12378.3i	−0.636307	+	0.462304i
$896$	−2408.54	+	511.950i	−0.0898030	+	0.0190882i
$897$	−2925.80	−	9004.69i	−0.108907	−	0.335182i
$898$	22015.5			0.818115
$899$	13225.5	+	12250.4i	0.490651	+	0.454477i
$900$	−5704.44			−0.211276
$901$	3154.52	+	9708.62i	0.116640	+	0.358980i
$902$	4809.74	−	1022.34i	0.177546	−	0.0377386i
$903$	1684.30	−	1223.71i	0.0620707	−	0.0450970i
$904$	−13799.9	+	23902.1i	−0.507718	+	0.879394i
$905$	8437.34	+	14613.9i	0.309908	+	0.536776i
$906$	−6535.14	−	2909.63i	−0.239642	−	0.106695i
$907$	−2430.89	−	1766.14i	−0.0889926	−	0.0646569i	0.542399	−	0.840121i	$-0.317516\pi$
$907$	−2430.89	−	1766.14i	−0.0889926	−	0.0646569i	−0.631392	+	0.775464i	$0.717516\pi$
$908$	−8839.51	+	3935.60i	−0.323072	+	0.143841i
$909$	18690.6	+	3972.80i	0.681987	+	0.144961i
$910$	−243.513	−	2316.87i	−0.00887073	−	0.0843994i
$911$	−3156.51	+	3505.66i	−0.114797	+	0.127495i	−0.797804	−	0.602917i	$-0.794005\pi$
$911$	−3156.51	+	3505.66i	−0.114797	+	0.127495i	0.683007	+	0.730412i	$0.260672\pi$
$912$	107.442	+	119.326i	0.00390104	+	0.00433254i
$913$	−2413.82	+	22965.9i	−0.0874980	+	0.832488i
$914$	−3005.59	+	9250.26i	−0.108770	+	0.334761i
$915$	−4988.62	+	15353.4i	−0.180239	+	0.554718i
$916$	−707.359	+	6730.07i	−0.0255151	+	0.242760i
$917$	2336.94	+	2595.43i	0.0841575	+	0.0934663i
$918$	2572.18	−	2856.70i	0.0924779	−	0.102707i
$919$	888.240	+	8451.04i	0.0318828	+	0.303345i	0.998830	+	0.0483668i	$0.0154016\pi$
$919$	888.240	+	8451.04i	0.0318828	+	0.303345i	−0.966947	+	0.254978i	$0.917932\pi$
$920$	−4791.98	−	1018.57i	−0.171725	−	0.0365013i
$921$	19733.5	−	8785.90i	0.706015	−	0.314338i
$922$	17181.4	+	12483.0i	0.613710	+	0.445886i
$923$	55258.2	+	24602.5i	1.97058	+	0.877359i
$924$	401.546	+	695.499i	0.0142964	+	0.0247622i
$925$	4715.53	−	8167.53i	0.167617	−	0.290321i
$926$	10001.9	−	7266.83i	0.354950	−	0.257887i
$927$	6562.70	−	1394.95i	0.232521	−	0.0494240i
$928$	5900.50	+	18159.9i	0.208721	+	0.642378i
$929$	7959.30			0.281094			0.140547	−	0.990074i	$-0.455114\pi$
$929$	7959.30			0.281094			0.140547	+	0.990074i	$0.455114\pi$
$930$	−6200.99	+	3464.46i	−0.218644	+	0.122155i
$931$	6748.10			0.237551
$932$	1602.97	+	4933.43i	0.0563380	+	0.173390i
$933$	18421.4	−	3915.59i	0.646398	−	0.137396i
$934$	−3116.31	+	2264.13i	−0.109174	+	0.0793197i
$935$	−858.688	+	1487.29i	−0.0300343	+	0.0520210i
$936$	12393.1	+	21465.5i	0.432779	+	0.749596i
$937$	22022.3	+	9804.96i	0.767809	+	0.341851i	0.752983	−	0.658039i	$-0.228614\pi$
$937$	22022.3	+	9804.96i	0.767809	+	0.341851i	0.0148257	+	0.999890i	$0.495281\pi$
$938$	2341.23	+	1701.00i	0.0814965	+	0.0592107i
$939$	−17994.3	+	8011.57i	−0.625369	+	0.278432i
$940$	−6693.64	−	1422.78i	−0.232258	−	0.0493680i
$941$	−1963.97	−	18685.9i	−0.0680377	−	0.647335i	−0.974398	−	0.224830i	$-0.927817\pi$
$941$	−1963.97	−	18685.9i	−0.0680377	−	0.647335i	0.906360	−	0.422506i	$-0.138849\pi$
$942$	−10330.5	+	11473.2i	−0.357309	+	0.396832i
$943$	3715.12	+	4126.06i	0.128294	+	0.142485i
$944$	97.8286	−	930.777i	0.00337293	−	0.0320913i
$945$	−782.275	+	2407.59i	−0.0269285	+	0.0828773i
$946$	−2016.71	+	6206.80i	−0.0693117	+	0.213320i
$947$	5117.10	−	48686.0i	0.175590	−	1.67062i	−0.451952	−	0.892042i	$-0.649272\pi$
$947$	5117.10	−	48686.0i	0.175590	−	1.67062i	0.627542	−	0.778583i	$-0.284061\pi$
$948$	−4860.89	−	5398.57i	−0.166534	−	0.184955i
$949$	−28059.8	+	31163.5i	−0.959809	+	1.06598i
$950$	−290.231	−	2761.37i	−0.00991195	−	0.0943059i
$951$	−9612.99	−	2043.30i	−0.327784	−	0.0696726i
$952$	798.169	−	355.368i	0.0271731	−	0.0120982i
$953$	11261.0	+	8181.63i	0.382771	+	0.278100i	0.762487	−	0.647004i	$-0.223978\pi$
$953$	11261.0	+	8181.63i	0.382771	+	0.278100i	−0.379716	+	0.925103i	$0.623978\pi$
$954$	−14665.4	−	6529.44i	−0.497703	−	0.221592i
$955$	3562.75	+	6170.86i	0.120720	+	0.209094i
$956$	−5551.65	+	9615.74i	−0.187817	+	0.325309i
$957$	5203.23	−	3780.37i	0.175754	−	0.127693i
$958$	−1449.34	+	308.067i	−0.0488790	+	0.0103896i
$959$	−773.685	−	2381.16i	−0.0260517	−	0.0801789i
$960$	−7097.96			−0.238631
$961$	15617.3	−	25369.4i	0.524228	−	0.851578i
$962$	−15890.7			−0.532574
$963$	−8949.99	−	27545.2i	−0.299491	−	0.921737i
$964$	−13458.5	+	2860.70i	−0.449658	+	0.0955777i
$965$	5818.46	−	4227.36i	0.194096	−	0.141019i
$966$	262.421	−	454.526i	0.00874042	−	0.0151389i
$967$	5577.89	+	9661.18i	0.185494	+	0.321285i	0.943743	−	0.330680i	$-0.107278\pi$
$967$	5577.89	+	9661.18i	0.185494	+	0.321285i	−0.758249	+	0.651965i	$0.773945\pi$
$968$	21279.5	+	9474.23i	0.706558	+	0.314580i
$969$	−890.077	−	646.678i	−0.0295081	−	0.0214389i
$970$	7920.37	−	3526.37i	0.262173	−	0.116727i
$971$	−30169.3	−	6412.68i	−0.997095	−	0.211939i	−0.319668	−	0.947529i	$-0.603572\pi$
$971$	−30169.3	−	6412.68i	−0.997095	−	0.211939i	−0.677427	+	0.735590i	$0.736905\pi$
$972$	−1811.93	−	17239.4i	−0.0597919	−	0.568882i
$973$	−4683.35	+	5201.39i	−0.154308	+	0.171376i
$974$	2844.08	+	3158.67i	0.0935628	+	0.103912i
$975$	2428.52	−	23105.8i	0.0797691	−	0.758953i
$976$	459.592	−	1414.48i	0.0150729	−	0.0463897i
$977$	15834.6	−	48733.9i	0.518520	−	1.59584i	−0.258266	−	0.966074i	$-0.583151\pi$
$977$	15834.6	−	48733.9i	0.518520	−	1.59584i	0.776786	−	0.629765i	$-0.216849\pi$
$978$	−188.476	+	1793.23i	−0.00616237	+	0.0586310i
$979$	2787.69	+	3096.05i	0.0910062	+	0.101073i
$980$	7580.94	−	8419.48i	0.247106	−	0.274439i
$981$	2580.81	+	24554.8i	0.0839948	+	0.799157i
$982$	−9431.86	−	2004.80i	−0.306500	−	0.0651485i
$983$	11763.2	−	5237.31i	0.381676	−	0.169933i	−0.206925	−	0.978357i	$-0.566346\pi$
$983$	11763.2	−	5237.31i	0.381676	−	0.169933i	0.588601	+	0.808424i	$0.299679\pi$
$984$	11033.8	+	8016.51i	0.357464	+	0.259712i
$985$	−11925.1	−	5309.41i	−0.385752	−	0.171748i
$986$	−1356.65	−	2349.79i	−0.0438181	−	0.0758952i
$987$	945.281	−	1637.27i	0.0304849	−	0.0528015i
$988$	6539.32	−	4751.09i	0.210570	−	0.152988i
$989$	−7207.93	+	1532.09i	−0.231748	+	0.0492596i
$990$	−834.563	−	2568.52i	−0.0267921	−	0.0824575i
$991$	−47006.0			−1.50676			−0.753379	−	0.657587i	$-0.771577\pi$
$991$	−47006.0			−1.50676			−0.753379	+	0.657587i	$0.771577\pi$
$992$	27546.6	−	15390.1i	0.881659	−	0.492578i
$993$	−19846.3			−0.634242
$994$	1036.13	+	3188.88i	0.0330624	+	0.101756i
$995$	−21491.3	+	4568.13i	−0.684745	+	0.145547i
$996$	−20093.8	+	14599.0i	−0.639253	+	0.464444i
$997$	12617.9	−	21854.9i	0.400816	−	0.694234i	−0.593009	−	0.805196i	$-0.702060\pi$
$997$	12617.9	−	21854.9i	0.400816	−	0.694234i	0.993825	+	0.110962i	$0.0353933\pi$
$998$	−14709.4	−	25477.5i	−0.466552	−	0.808091i
$999$	15774.7	+	7023.37i	0.499590	+	0.222432i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	31.4.g.a.7.5	✓	56
31.3	odd	30		961.4.a.l.1.19		28
31.9	even	15	inner	31.4.g.a.9.5	yes	56
31.28	even	15		961.4.a.m.1.19		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.4.g.a.7.5	✓	56	1.1	even	1	trivial
31.4.g.a.9.5	yes	56	31.9	even	15	inner
961.4.a.l.1.19		28	31.3	odd	30
961.4.a.m.1.19		28	31.28	even	15

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:	\( N \)	\(=\)	\( 31 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	31.g (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.529206 + 1.62873i) q^{2} +(3.53631 - 0.751666i) q^{3} +(4.09944 - 2.97842i) q^{4} +(-3.32346 + 5.75640i) q^{5} +(3.09570 + 5.36190i) q^{6} +(-2.35128 - 1.04686i) q^{7} +(18.1043 + 13.1535i) q^{8} +(-12.7252 + 5.66564i) q^{9} +(-11.1344 - 2.36669i) q^{10} +(-1.78038 - 16.9392i) q^{11} +(12.2581 - 13.6140i) q^{12} +(-53.2061 - 59.0914i) q^{13} +(0.460734 - 4.38360i) q^{14} +(-7.42590 + 22.8546i) q^{15} +(0.684133 - 2.10555i) q^{16} +(-1.58563 + 15.0862i) q^{17} +(-15.9620 - 17.7276i) q^{18} +(-13.4236 + 14.9084i) q^{19} +(3.52064 + 33.4967i) q^{20} +(-9.10174 - 1.93463i) q^{21} +(26.6472 - 11.8641i) q^{22} +(26.6455 + 19.3591i) q^{23} +(73.9095 + 32.9066i) q^{24} +(40.4092 + 69.9908i) q^{25} +(68.0868 - 117.930i) q^{26} +(-119.713 + 86.9764i) q^{27} +(-12.7569 + 2.71156i) q^{28} +(32.2755 + 99.3338i) q^{29} -41.1537 q^{30} +(150.679 - 84.1835i) q^{31} +182.817 q^{32} +(-19.0286 - 58.5640i) q^{33} +(-25.4105 + 5.40116i) q^{34} +(13.8405 - 10.0557i) q^{35} +(-35.2917 + 61.1270i) q^{36} +(-58.3471 - 101.060i) q^{37} +(-31.3855 - 13.9737i) q^{38} +(-232.570 - 168.972i) q^{39} +(-135.886 + 60.5004i) q^{40} +(164.892 + 35.0490i) q^{41} +(-1.66570 - 15.8481i) q^{42} +(-149.710 + 166.270i) q^{43} +(-57.7506 - 64.1385i) q^{44} +(9.67811 - 92.0810i) q^{45} +(-17.4297 + 53.6432i) q^{46} +(-62.7846 + 193.231i) q^{47} +(0.836641 - 7.96010i) q^{48} +(-225.079 - 249.976i) q^{49} +(-92.6112 + 102.855i) q^{50} +(5.73254 + 54.5415i) q^{51} +(-394.114 - 83.7715i) q^{52} +(614.773 - 273.715i) q^{53} +(-205.013 - 148.951i) q^{54} +(103.426 + 46.0482i) q^{55} +(-28.7984 - 49.8803i) q^{56} +(-36.2638 + 62.8107i) q^{57} +(-144.707 + 105.136i) q^{58} +(413.502 - 87.8925i) q^{59} +(37.6284 + 115.808i) q^{60} +671.787 q^{61} +(216.852 + 200.865i) q^{62} +35.8517 q^{63} +(91.2745 + 280.914i) q^{64} +(516.982 - 109.888i) q^{65} +(85.3148 - 61.9848i) q^{66} +(-328.276 + 568.591i) q^{67} +(38.4329 + 66.5678i) q^{68} +(108.778 + 48.4312i) q^{69} +(23.7025 + 17.2209i) q^{70} +(-694.938 + 309.406i) q^{71} +(-304.905 - 64.8095i) q^{72} +(-55.1261 - 524.490i) q^{73} +(133.722 - 148.513i) q^{74} +(195.509 + 217.135i) q^{75} +(-10.6257 + 101.097i) q^{76} +(-13.5467 + 41.6926i) q^{77} +(152.132 - 468.215i) q^{78} +(41.4502 - 394.372i) q^{79} +(9.84667 + 10.9358i) q^{80} +(-106.307 + 118.065i) q^{81} +(30.1768 + 287.113i) q^{82} +(-1326.16 - 281.884i) q^{83} +(-43.0742 + 19.1779i) q^{84} +(-81.5726 - 59.2660i) q^{85} +(-350.036 - 155.846i) q^{86} +(188.802 + 327.015i) q^{87} +(190.578 - 330.091i) q^{88} +(-197.885 + 143.772i) q^{89} +(155.097 - 32.9668i) q^{90} +(63.2422 + 194.639i) q^{91} +166.891 q^{92} +(469.570 - 410.959i) q^{93} -347.947 q^{94} +(-41.2060 - 126.819i) q^{95} +(646.497 - 137.417i) q^{96} +(-616.184 + 447.684i) q^{97} +(288.029 - 498.881i) q^{98} +(118.627 + 205.468i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 6 q^{2} + q^{3} - 42 q^{4} - 53 q^{6} - 71 q^{7} - 7 q^{8} + 4 q^{9} + 48 q^{10} - 25 q^{11} + 319 q^{12} - 45 q^{13} - 50 q^{14} + 217 q^{15} - 322 q^{16} + 61 q^{17} + 285 q^{18} - 143 q^{19}+ \cdots - 6383 q^{99}+O(q^{100}) \) 56 * q - 6 * q^2 + q^3 - 42 * q^4 - 53 * q^6 - 71 * q^7 - 7 * q^8 + 4 * q^9 + 48 * q^10 - 25 * q^11 + 319 * q^12 - 45 * q^13 - 50 * q^14 + 217 * q^15 - 322 * q^16 + 61 * q^17 + 285 * q^18 - 143 * q^19 + 95 * q^20 - 257 * q^21 - 1147 * q^22 - 244 * q^23 - 226 * q^24 - 96 * q^25 - 1019 * q^26 + 124 * q^27 + 1920 * q^28 - 142 * q^29 + 2430 * q^30 + 112 * q^31 + 618 * q^32 + 134 * q^33 + 2488 * q^34 + 813 * q^35 - 857 * q^36 - 866 * q^37 - 1186 * q^38 - 1090 * q^39 - 663 * q^40 - 333 * q^41 - 3347 * q^42 + 703 * q^43 + 1327 * q^44 - 1201 * q^45 - 818 * q^46 + 1886 * q^47 - 3046 * q^48 + 1346 * q^49 - 4015 * q^50 - 3179 * q^51 - 4447 * q^52 - 1613 * q^53 + 1276 * q^54 + 2486 * q^55 + 4558 * q^56 + 104 * q^57 + 415 * q^58 + 863 * q^59 + 9839 * q^60 + 6180 * q^61 + 427 * q^62 + 3128 * q^63 + 2807 * q^64 + 5398 * q^65 + 7976 * q^66 + 1026 * q^67 - 4992 * q^68 - 4882 * q^69 - 7786 * q^70 + 583 * q^71 - 299 * q^72 - 3709 * q^73 - 5029 * q^74 - 5668 * q^75 - 9928 * q^76 - 9614 * q^77 - 4597 * q^78 + 2323 * q^79 - 2582 * q^80 - 1715 * q^81 - 4314 * q^82 - 2399 * q^83 - 1740 * q^84 + 733 * q^85 + 11232 * q^86 + 4919 * q^87 + 3611 * q^88 - 2244 * q^89 + 10029 * q^90 + 9776 * q^91 + 15424 * q^92 - 2975 * q^93 + 988 * q^94 + 5791 * q^95 + 20204 * q^96 + 10170 * q^97 + 2332 * q^98 - 6383 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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