LMFDB - Embedded newform 187.4.g.a.137.20

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [187,4,Mod(69,187)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("187.69"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(187, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([8, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 187 = 11 \cdot 17 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	187.g (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [88] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$11.0333571711$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			137.20
Character	$\chi$	$=$	187.137
Dual form			187.4.g.a.86.20

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.46189 + 4.49925i) q^{2} +(0.982808 + 0.714052i) q^{3} +(-11.6339 + 8.45255i) q^{4} +(-4.66803 + 14.3667i) q^{5} +(-1.77593 + 5.46576i) q^{6} +(-7.58718 + 5.51241i) q^{7} +(-24.4194 - 17.7417i) q^{8} +(-7.88742 - 24.2750i) q^{9} -71.4635 q^{10} +(2.64405 - 36.3869i) q^{11} -17.4695 q^{12} +(22.9815 + 70.7299i) q^{13} +(-35.8933 - 26.0780i) q^{14} +(-14.8463 + 10.7865i) q^{15} +(8.57567 - 26.3932i) q^{16} +(5.25329 - 16.1680i) q^{17} +(97.6885 - 70.9748i) q^{18} +(2.47428 + 1.79767i) q^{19} +(-67.1278 - 206.598i) q^{20} -11.3929 q^{21} +(167.579 - 41.2976i) q^{22} -16.3508 q^{23} +(-11.3311 - 34.8734i) q^{24} +(-83.4847 - 60.6552i) q^{25} +(-284.635 + 206.799i) q^{26} +(19.7176 - 60.6844i) q^{27} +(41.6749 - 128.262i) q^{28} +(-120.301 + 87.4039i) q^{29} +(-70.2349 - 51.0286i) q^{30} +(-4.77558 - 14.6977i) q^{31} -110.186 q^{32} +(28.5807 - 33.8734i) q^{33} +80.4234 q^{34} +(-43.7780 - 134.735i) q^{35} +(296.947 + 215.745i) q^{36} +(15.9967 - 11.6223i) q^{37} +(-4.47102 + 13.7604i) q^{38} +(-27.9184 + 85.9240i) q^{39} +(368.881 - 268.007i) q^{40} +(206.398 + 149.957i) q^{41} +(-16.6552 - 51.2594i) q^{42} -277.874 q^{43} +(276.802 + 445.672i) q^{44} +385.570 q^{45} +(-23.9031 - 73.5661i) q^{46} +(120.683 + 87.6813i) q^{47} +(27.2744 - 19.8160i) q^{48} +(-78.8142 + 242.565i) q^{49} +(150.857 - 464.290i) q^{50} +(16.7077 - 12.1389i) q^{51} +(-865.214 - 628.615i) q^{52} +(71.8803 + 221.225i) q^{53} +301.859 q^{54} +(510.418 + 207.841i) q^{55} +283.074 q^{56} +(1.14811 + 3.53353i) q^{57} +(-569.119 - 413.489i) q^{58} +(275.958 - 200.495i) q^{59} +(81.5480 - 250.979i) q^{60} +(-217.245 + 668.611i) q^{61} +(59.1472 - 42.9730i) q^{62} +(193.657 + 140.700i) q^{63} +(-229.686 - 706.899i) q^{64} -1123.43 q^{65} +(194.187 + 79.0725i) q^{66} -115.186 q^{67} +(75.5441 + 232.501i) q^{68} +(-16.0697 - 11.6753i) q^{69} +(542.206 - 393.936i) q^{70} +(-199.883 + 615.176i) q^{71} +(-238.074 + 732.716i) q^{72} +(223.920 - 162.687i) q^{73} +(75.6769 + 54.9825i) q^{74} +(-38.7385 - 119.225i) q^{75} -43.9805 q^{76} +(180.519 + 290.649i) q^{77} -427.407 q^{78} +(-224.806 - 691.880i) q^{79} +(339.152 + 246.408i) q^{80} +(-494.827 + 359.513i) q^{81} +(-372.962 + 1147.86i) q^{82} +(-403.425 + 1241.61i) q^{83} +(132.544 - 96.2989i) q^{84} +(207.758 + 150.945i) q^{85} +(-406.223 - 1250.22i) q^{86} -180.644 q^{87} +(-710.133 + 841.637i) q^{88} +1062.02 q^{89} +(563.662 + 1734.77i) q^{90} +(-564.257 - 409.957i) q^{91} +(190.224 - 138.206i) q^{92} +(5.80145 - 17.8550i) q^{93} +(-218.074 + 671.163i) q^{94} +(-37.3766 + 27.1557i) q^{95} +(-108.292 - 78.6785i) q^{96} +(-455.880 - 1403.05i) q^{97} -1206.58 q^{98} +(-904.147 + 222.815i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 2 q^{2} + 14 q^{3} - 82 q^{4} + 42 q^{5} + 12 q^{6} + 16 q^{7} + 104 q^{8} - 178 q^{9} - 130 q^{10} - 20 q^{11} - 674 q^{12} + 24 q^{13} + 173 q^{14} + 280 q^{15} + 242 q^{16} - 374 q^{17} - 265 q^{18}+ \cdots + 5224 q^{99}+O(q^{100}) $ 88 * q + 2 * q^2 + 14 * q^3 - 82 * q^4 + 42 * q^5 + 12 * q^6 + 16 * q^7 + 104 * q^8 - 178 * q^9 - 130 * q^10 - 20 * q^11 - 674 * q^12 + 24 * q^13 + 173 * q^14 + 280 * q^15 + 242 * q^16 - 374 * q^17 - 265 * q^18 - 92 * q^19 + 347 * q^20 - 480 * q^21 - 248 * q^22 - 1312 * q^23 + 512 * q^24 + 146 * q^25 + 1045 * q^26 + 314 * q^27 + 51 * q^28 - 526 * q^29 - 712 * q^30 + 1424 * q^31 - 166 * q^32 - 1036 * q^33 + 34 * q^34 - 446 * q^35 - 260 * q^36 + 1344 * q^37 - 1006 * q^38 - 92 * q^39 - 272 * q^40 - 1002 * q^41 + 649 * q^42 + 764 * q^43 + 1894 * q^44 - 2452 * q^45 + 1154 * q^46 + 462 * q^47 + 1399 * q^48 - 1872 * q^49 - 2336 * q^50 + 238 * q^51 - 2266 * q^52 + 1606 * q^53 + 4800 * q^54 + 3492 * q^55 + 54 * q^56 + 2012 * q^57 + 603 * q^58 + 286 * q^59 - 5684 * q^60 - 1348 * q^61 + 508 * q^62 - 2936 * q^63 - 1576 * q^64 - 304 * q^65 + 6572 * q^66 - 6884 * q^67 - 969 * q^68 - 878 * q^69 + 1370 * q^70 - 1432 * q^71 + 753 * q^72 + 3480 * q^73 - 6737 * q^74 - 694 * q^75 + 2522 * q^76 + 3870 * q^77 + 2240 * q^78 + 2118 * q^79 + 1640 * q^80 - 1950 * q^81 - 3285 * q^82 + 5758 * q^83 + 7968 * q^84 - 306 * q^85 - 5066 * q^86 + 3936 * q^87 - 97 * q^88 - 5984 * q^89 + 1819 * q^90 + 2240 * q^91 + 2111 * q^92 - 4076 * q^93 - 1788 * q^94 + 10810 * q^95 - 15349 * q^96 + 3358 * q^97 + 4604 * q^98 + 5224 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/187\mathbb{Z}\right)^\times$.

$n$	$35$	$122$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	1.46189	+	4.49925i	0.516857	+	1.59072i	0.779877	+	0.625933i	$0.215282\pi$
$2$	1.46189	+	4.49925i	0.516857	+	1.59072i	−0.263020	+	0.964791i	$0.584718\pi$
$3$	0.982808	+	0.714052i	0.189141	+	0.137419i	0.678326	−	0.734761i	$-0.262706\pi$
$3$	0.982808	+	0.714052i	0.189141	+	0.137419i	−0.489185	+	0.872180i	$0.662706\pi$
$4$	−11.6339	+	8.45255i	−1.45424	+	1.05657i
$5$	−4.66803	+	14.3667i	−0.417521	+	1.28500i	0.492455	+	0.870338i	$0.336099\pi$
$5$	−4.66803	+	14.3667i	−0.417521	+	1.28500i	−0.909976	+	0.414660i	$0.863901\pi$
$6$	−1.77593	+	5.46576i	−0.120837	+	0.371898i
$7$	−7.58718	+	5.51241i	−0.409669	+	0.297642i	−0.773468	−	0.633836i	$-0.781480\pi$
$7$	−7.58718	+	5.51241i	−0.409669	+	0.297642i	0.363799	+	0.931478i	$0.381480\pi$
$8$	−24.4194	−	17.7417i	−1.07919	−	0.784081i
$9$	−7.88742	−	24.2750i	−0.292127	−	0.899073i
$10$	−71.4635			−2.25987
$11$	2.64405	−	36.3869i	0.0724737	−	0.997370i
$11$	2.64405	−	36.3869i	0.0724737	−	0.997370i
$12$	−17.4695			−0.420251
$13$	22.9815	+	70.7299i	0.490303	+	1.50900i	0.824151	+	0.566370i	$0.191653\pi$
$13$	22.9815	+	70.7299i	0.490303	+	1.50900i	−0.333849	+	0.942627i	$0.608347\pi$
$14$	−35.8933	−	26.0780i	−0.685207	−	0.497832i
$15$	−14.8463	+	10.7865i	−0.255554	+	0.185671i
$16$	8.57567	−	26.3932i	0.133995	−	0.412394i
$17$	5.25329	−	16.1680i	0.0749476	−	0.230665i
$17$	5.25329	−	16.1680i	0.0749476	−	0.230665i
$18$	97.6885	−	70.9748i	1.27919	−	0.929385i
$19$	2.47428	+	1.79767i	0.0298757	+	0.0217060i	0.602623	−	0.798026i	$-0.294122\pi$
$19$	2.47428	+	1.79767i	0.0298757	+	0.0217060i	−0.572747	+	0.819732i	$0.694122\pi$
$20$	−67.1278	−	206.598i	−0.750512	−	2.30984i
$21$	−11.3929			−0.118387
$22$	167.579	−	41.2976i	1.62400	−	0.400213i
$23$	−16.3508			−0.148234			−0.0741168	−	0.997250i	$-0.523614\pi$
$23$	−16.3508			−0.148234			−0.0741168	+	0.997250i	$0.523614\pi$
$24$	−11.3311	−	34.8734i	−0.0963726	−	0.296604i
$25$	−83.4847	−	60.6552i	−0.667878	−	0.485242i
$26$	−284.635	+	206.799i	−2.14698	+	1.55987i
$27$	19.7176	−	60.6844i	0.140542	−	0.432545i
$28$	41.6749	−	128.262i	0.281279	−	0.865687i
$29$	−120.301	+	87.4039i	−0.770323	+	0.559673i	−0.902059	−	0.431612i	$-0.857945\pi$
$29$	−120.301	+	87.4039i	−0.770323	+	0.559673i	0.131736	+	0.991285i	$0.457945\pi$
$30$	−70.2349	−	51.0286i	−0.427436	−	0.310550i
$31$	−4.77558	−	14.6977i	−0.0276683	−	0.0851544i	0.936269	−	0.351284i	$-0.114255\pi$
$31$	−4.77558	−	14.6977i	−0.0276683	−	0.0851544i	−0.963937	+	0.266130i	$0.914255\pi$
$32$	−110.186			−0.608697
$33$	28.5807	−	33.8734i	0.150766	−	0.178685i
$34$	80.4234			0.405662
$35$	−43.7780	−	134.735i	−0.211424	−	0.650696i
$36$	296.947	+	215.745i	1.37476	+	0.998818i
$37$	15.9967	−	11.6223i	0.0710767	−	0.0516402i	−0.551680	−	0.834056i	$-0.686013\pi$
$37$	15.9967	−	11.6223i	0.0710767	−	0.0516402i	0.622756	+	0.782416i	$0.286013\pi$
$38$	−4.47102	+	13.7604i	−0.0190867	+	0.0587429i
$39$	−27.9184	+	85.9240i	−0.114629	+	0.352791i
$40$	368.881	−	268.007i	1.45813	−	1.05939i
$41$	206.398	+	149.957i	0.786195	+	0.571204i	0.906832	−	0.421492i	$-0.138494\pi$
$41$	206.398	+	149.957i	0.786195	+	0.571204i	−0.120636	+	0.992697i	$0.538494\pi$
$42$	−16.6552	−	51.2594i	−0.0611893	−	0.188321i
$43$	−277.874			−0.985475			−0.492738	−	0.870178i	$-0.664004\pi$
$43$	−277.874			−0.985475			−0.492738	+	0.870178i	$0.664004\pi$
$44$	276.802	+	445.672i	0.948396	+	1.52699i
$45$	385.570			1.27728
$46$	−23.9031	−	73.5661i	−0.0766156	−	0.235799i
$47$	120.683	+	87.6813i	0.374541	+	0.272120i	0.759091	−	0.650984i	$-0.225644\pi$
$47$	120.683	+	87.6813i	0.374541	+	0.272120i	−0.384551	+	0.923104i	$0.625644\pi$
$48$	27.2744	−	19.8160i	0.0820149	−	0.0595873i
$49$	−78.8142	+	242.565i	−0.229779	+	0.707187i
$50$	150.857	−	464.290i	0.426688	−	1.31321i
$51$	16.7077	−	12.1389i	0.0458735	−	0.0333291i
$52$	−865.214	−	628.615i	−2.30738	−	1.67641i
$53$	71.8803	+	221.225i	0.186293	+	0.573351i	0.999968	−	0.00796898i	$-0.00253663\pi$
$53$	71.8803	+	221.225i	0.186293	+	0.573351i	−0.813675	+	0.581320i	$0.802537\pi$
$54$	301.859			0.760700
$55$	510.418	+	207.841i	1.25136	+	0.509552i
$56$	283.074			0.675488
$57$	1.14811	+	3.53353i	0.00266792	+	0.00821100i
$58$	−569.119	−	413.489i	−1.28843	−	0.936100i
$59$	275.958	−	200.495i	0.608926	−	0.442410i	−0.240110	−	0.970746i	$-0.577184\pi$
$59$	275.958	−	200.495i	0.608926	−	0.442410i	0.849036	+	0.528335i	$0.177184\pi$
$60$	81.5480	−	250.979i	0.175463	−	0.540021i
$61$	−217.245	+	668.611i	−0.455990	+	1.40339i	0.413980	+	0.910286i	$0.364138\pi$
$61$	−217.245	+	668.611i	−0.455990	+	1.40339i	−0.869969	+	0.493106i	$0.835862\pi$
$62$	59.1472	−	42.9730i	0.121157	−	0.0880254i
$63$	193.657	+	140.700i	0.387277	+	0.281373i
$64$	−229.686	−	706.899i	−0.448605	−	1.38066i
$65$	−1123.43			−2.14377
$66$	194.187	+	79.0725i	0.362162	+	0.147472i
$67$	−115.186			−0.210034			−0.105017	−	0.994470i	$-0.533490\pi$
$67$	−115.186			−0.210034			−0.105017	+	0.994470i	$0.533490\pi$
$68$	75.5441	+	232.501i	0.134722	+	0.414630i
$69$	−16.0697	−	11.6753i	−0.0280371	−	0.0203701i
$70$	542.206	−	393.936i	0.925801	−	0.672634i
$71$	−199.883	+	615.176i	−0.334109	+	1.02828i	0.633050	+	0.774111i	$0.281803\pi$
$71$	−199.883	+	615.176i	−0.334109	+	1.02828i	−0.967159	+	0.254171i	$0.918197\pi$
$72$	−238.074	+	732.716i	−0.389685	+	1.19933i
$73$	223.920	−	162.687i	0.359012	−	0.260837i	−0.393628	−	0.919270i	$-0.628780\pi$
$73$	223.920	−	162.687i	0.359012	−	0.260837i	0.752640	+	0.658432i	$0.228780\pi$
$74$	75.6769	+	54.9825i	0.118882	+	0.0863727i
$75$	−38.7385	−	119.225i	−0.0596418	−	0.183559i
$76$	−43.9805			−0.0663804
$77$	180.519	+	290.649i	0.267169	+	0.430163i
$78$	−427.407			−0.620439
$79$	−224.806	−	691.880i	−0.320159	−	0.985349i	−0.973578	−	0.228353i	$-0.926666\pi$
$79$	−224.806	−	691.880i	−0.320159	−	0.985349i	0.653419	−	0.756996i	$-0.273334\pi$
$80$	339.152	+	246.408i	0.473979	+	0.344366i
$81$	−494.827	+	359.513i	−0.678775	+	0.493159i
$82$	−372.962	+	1147.86i	−0.502277	+	1.54585i
$83$	−403.425	+	1241.61i	−0.533513	+	1.64198i	0.213327	+	0.976981i	$0.431570\pi$
$83$	−403.425	+	1241.61i	−0.533513	+	1.64198i	−0.746840	+	0.665004i	$0.768430\pi$
$84$	132.544	−	96.2989i	0.172164	−	0.125084i
$85$	207.758	+	150.945i	0.265112	+	0.192615i
$86$	−406.223	−	1250.22i	−0.509350	−	1.56762i
$87$	−180.644			−0.222610
$88$	−710.133	+	841.637i	−0.860232	+	1.01953i
$89$	1062.02			1.26488			0.632438	−	0.774611i	$-0.282054\pi$
$89$	1062.02			1.26488			0.632438	+	0.774611i	$0.282054\pi$
$90$	563.662	+	1734.77i	0.660169	+	2.03179i
$91$	−564.257	−	409.957i	−0.650003	−	0.472255i
$92$	190.224	−	138.206i	0.215567	−	0.156619i
$93$	5.80145	−	17.8550i	0.00646863	−	0.0199084i
$94$	−218.074	+	671.163i	−0.239283	+	0.736438i
$95$	−37.3766	+	27.1557i	−0.0403659	+	0.0293275i
$96$	−108.292	−	78.6785i	−0.115130	−	0.0836468i
$97$	−455.880	−	1403.05i	−0.477192	−	1.46865i	−0.842979	−	0.537947i	$-0.819200\pi$
$97$	−455.880	−	1403.05i	−0.477192	−	1.46865i	0.365787	−	0.930699i	$-0.380800\pi$
$98$	−1206.58			−1.24370
$99$	−904.147	+	222.815i	−0.917880	+	0.226199i
$100$	1483.95			1.48395
$101$	436.139	+	1342.30i	0.429678	+	1.32241i	0.898443	+	0.439090i	$0.144699\pi$
$101$	436.139	+	1342.30i	0.429678	+	1.32241i	−0.468765	+	0.883323i	$0.655301\pi$
$102$	79.0407	+	57.4265i	0.0767274	+	0.0557457i
$103$	78.8199	−	57.2660i	0.0754015	−	0.0547824i	−0.549446	−	0.835529i	$-0.685161\pi$
$103$	78.8199	−	57.2660i	0.0754015	−	0.0547824i	0.624847	+	0.780747i	$0.285161\pi$
$104$	693.676	−	2134.91i	0.654043	−	2.01294i
$105$	53.1823	−	163.678i	0.0494291	−	0.152127i
$106$	−890.264	+	646.815i	−0.815755	+	0.592681i
$107$	616.872	+	448.184i	0.557339	+	0.404930i	0.830484	−	0.557042i	$-0.188064\pi$
$107$	616.872	+	448.184i	0.557339	+	0.404930i	−0.273145	+	0.961973i	$0.588064\pi$
$108$	283.545	+	872.662i	0.252631	+	0.777518i
$109$	1551.22			1.36312			0.681558	−	0.731764i	$-0.261303\pi$
$109$	1551.22			1.36312			0.681558	+	0.731764i	$0.261303\pi$
$110$	−188.953	+	2600.34i	−0.163782	+	2.25393i
$111$	24.0206			0.0205399
$112$	80.4250	+	247.523i	0.0678522	+	0.208828i
$113$	610.560	+	443.598i	0.508289	+	0.369293i	0.812174	−	0.583415i	$-0.198284\pi$
$113$	610.560	+	443.598i	0.508289	+	0.369293i	−0.303885	+	0.952709i	$0.598284\pi$
$114$	−14.2198	+	10.3313i	−0.0116825	+	0.00848784i
$115$	76.3258	−	234.907i	0.0618906	−	0.190480i
$116$	660.791	−	2033.70i	0.528904	−	1.62780i
$117$	1535.70	−	1115.75i	1.21347	−	0.881636i
$118$	1305.50	+	948.498i	1.01848	+	0.739969i
$119$	49.2668	+	151.627i	0.0379519	+	0.116804i
$120$	553.910			0.421374
$121$	−1317.02	−	192.418i	−0.989495	−	0.144566i
$122$	−3325.84			−2.46809
$123$	95.7728	+	294.758i	0.0702076	+	0.216077i
$124$	179.792	+	130.626i	0.130208	+	0.0946017i
$125$	−266.507	+	193.629i	−0.190697	+	0.138549i
$126$	−349.938	+	1077.00i	−0.247420	+	0.761481i
$127$	694.036	−	2136.02i	0.484927	−	1.49245i	−0.347159	−	0.937806i	$-0.612854\pi$
$127$	694.036	−	2136.02i	0.484927	−	1.49245i	0.832086	−	0.554646i	$-0.187146\pi$
$128$	2131.60	−	1548.70i	1.47194	−	1.06943i
$129$	−273.097	−	198.417i	−0.186394	−	0.135423i
$130$	−1642.34	−	5054.61i	−1.10802	−	3.41014i
$131$	−181.227			−0.120869			−0.0604346	−	0.998172i	$-0.519249\pi$
$131$	−181.227			−0.120869			−0.0604346	+	0.998172i	$0.519249\pi$
$132$	−46.1902	+	635.661i	−0.0304571	+	0.419145i
$133$	−28.6823			−0.0186998
$134$	−168.390	−	518.252i	−0.108557	−	0.334105i
$135$	779.793	+	566.553i	0.497140	+	0.361193i
$136$	−415.130	+	301.609i	−0.261743	+	0.190168i
$137$	732.311	−	2253.82i	0.456683	−	1.40553i	−0.412465	−	0.910973i	$-0.635332\pi$
$137$	732.311	−	2253.82i	0.456683	−	1.40553i	0.869148	−	0.494552i	$-0.164668\pi$
$138$	29.0379	−	89.3694i	0.0179121	−	0.0551277i
$139$	2003.21	−	1455.42i	1.22238	−	0.888108i	0.226081	−	0.974109i	$-0.427409\pi$
$139$	2003.21	−	1455.42i	1.22238	−	0.888108i	0.996295	+	0.0860004i	$0.0274086\pi$
$140$	1648.16	+	1197.46i	0.994966	+	0.722885i
$141$	55.9992	+	172.348i	0.0334467	+	0.102938i
$142$	−3060.04			−1.80840
$143$	2634.41	−	649.215i	1.54056	−	0.379651i
$144$	−708.334			−0.409916
$145$	−694.138	−	2136.34i	−0.397552	−	1.22354i
$146$	1059.32	+	769.640i	0.600478	+	0.436273i
$147$	−250.663	+	182.118i	−0.140642	+	0.102182i
$148$	−87.8666	+	270.426i	−0.0488013	+	0.150195i
$149$	−804.524	+	2476.07i	−0.442344	+	1.36139i	0.443027	+	0.896508i	$0.353905\pi$
$149$	−804.524	+	2476.07i	−0.442344	+	1.36139i	−0.885371	+	0.464886i	$0.846095\pi$
$150$	479.790	−	348.588i	0.261165	−	0.189747i
$151$	2427.53	+	1763.71i	1.30828	+	0.950519i	1.00000		0.000777286i	$-0.000247418\pi$
$151$	2427.53	+	1763.71i	1.30828	+	0.950519i	0.308278	+	0.951296i	$0.400247\pi$
$152$	−28.5266	−	87.7960i	−0.0152225	−	0.0468500i
$153$	−433.912			−0.229279
$154$	−1043.80	+	1237.10i	−0.546182	+	0.647325i
$155$	233.450			0.120975
$156$	−401.476	−	1235.62i	−0.206050	−	0.634157i
$157$	1926.49	+	1399.67i	0.979302	+	0.711504i	0.957552	−	0.288259i	$-0.0930765\pi$
$157$	1926.49	+	1399.67i	0.979302	+	0.711504i	0.0217491	+	0.999763i	$0.493076\pi$
$158$	2784.30	−	2022.91i	1.40194	−	1.01857i
$159$	−87.3215	+	268.748i	−0.0435537	+	0.134045i
$160$	514.351	−	1583.01i	0.254144	−	0.782174i
$161$	124.056	−	90.1321i	0.0607267	−	0.0441205i
$162$	−2340.92	−	1700.78i	−1.13531	−	0.824850i
$163$	−33.1819	−	102.123i	−0.0159448	−	0.0490731i	0.942768	−	0.333451i	$-0.108213\pi$
$163$	−33.1819	−	102.123i	−0.0159448	−	0.0490731i	−0.958712	+	0.284378i	$0.908213\pi$
$164$	−3668.75			−1.74684
$165$	353.233	+	568.733i	0.166662	+	0.268338i
$166$	−6176.08			−2.88769
$167$	−518.439	−	1595.59i	−0.240228	−	0.739345i	−0.996385	−	0.0849550i	$-0.972925\pi$
$167$	−518.439	−	1595.59i	−0.240228	−	0.739345i	0.756157	−	0.654390i	$-0.227075\pi$
$168$	278.207	+	202.129i	0.127763	+	0.0928251i
$169$	−2697.16	+	1959.60i	−1.22766	+	0.891945i
$170$	−375.418	+	1155.42i	−0.169372	+	0.521274i
$171$	24.1227	−	74.2421i	0.0107878	−	0.0332014i
$172$	3232.77	−	2348.75i	1.43312	−	1.04122i
$173$	−607.458	−	441.344i	−0.266961	−	0.193958i	0.446249	−	0.894909i	$-0.352759\pi$
$173$	−607.458	−	441.344i	−0.266961	−	0.193958i	−0.713210	+	0.700950i	$0.752759\pi$
$174$	−264.082	−	812.761i	−0.115058	−	0.354111i
$175$	967.770			0.418037
$176$	−937.693	−	381.827i	−0.401598	−	0.163530i
$177$	414.377			0.175969
$178$	1552.56	+	4778.29i	0.653760	+	2.01207i
$179$	128.629	+	93.4542i	0.0537104	+	0.0390229i	0.614317	−	0.789060i	$-0.289432\pi$
$179$	128.629	+	93.4542i	0.0537104	+	0.0390229i	−0.560606	+	0.828083i	$0.689432\pi$
$180$	−4485.70	+	3259.05i	−1.85747	+	1.34953i
$181$	−544.258	+	1675.05i	−0.223505	+	0.687877i	0.774935	+	0.632041i	$0.217783\pi$
$181$	−544.258	+	1675.05i	−0.223505	+	0.687877i	−0.998440	+	0.0558364i	$0.982217\pi$
$182$	1019.61	−	3138.05i	0.415268	−	1.27806i
$183$	−690.933	+	501.992i	−0.279100	+	0.202778i
$184$	399.276	+	290.091i	0.159973	+	0.116227i
$185$	92.3008	+	284.073i	0.0366816	+	0.112894i
$186$	88.8153			0.0350121
$187$	−574.413	−	233.900i	−0.224627	−	0.0914677i
$188$	−2145.15			−0.832186
$189$	184.916	+	569.114i	0.0711677	+	0.219032i
$190$	−176.821	−	128.468i	−0.0675154	−	0.0490528i
$191$	−2990.43	+	2172.68i	−1.13288	+	0.823085i	−0.986111	−	0.166085i	$-0.946887\pi$
$191$	−2990.43	+	2172.68i	−1.13288	+	0.823085i	−0.146769	+	0.989171i	$0.546887\pi$
$192$	279.026	−	858.754i	0.104880	−	0.322788i
$193$	1151.68	−	3544.50i	0.429532	−	1.32196i	−0.469055	−	0.883169i	$-0.655406\pi$
$193$	1151.68	−	3544.50i	0.429532	−	1.32196i	0.898587	−	0.438795i	$-0.144594\pi$
$194$	5646.24	−	4102.23i	2.08957	−	1.51816i
$195$	−1104.12	−	802.191i	−0.405476	−	0.294595i
$196$	−1133.37	−	3488.17i	−0.413037	−	1.27120i
$197$	3744.19			1.35412			0.677062	−	0.735926i	$-0.263253\pi$
$197$	3744.19			1.35412			0.677062	+	0.735926i	$0.263253\pi$
$198$	−2324.26	−	3742.25i	−0.834234	−	1.34318i
$199$	2175.62			0.775004			0.387502	−	0.921869i	$-0.373338\pi$
$199$	2175.62			0.775004			0.387502	+	0.921869i	$0.373338\pi$
$200$	962.518	+	2962.33i	0.340302	+	1.04734i
$201$	−113.206	−	82.2490i	−0.0397261	−	0.0288627i
$202$	−5401.74	+	3924.60i	−1.88151	+	1.36700i
$203$	430.941	−	1326.30i	0.148996	−	0.458561i
$204$	−91.7723	+	282.446i	−0.0314968	+	0.0969371i
$205$	−3117.86	+	2265.26i	−1.06225	+	0.771769i
$206$	372.880	+	270.913i	0.126115	+	0.0916283i
$207$	128.965	+	396.914i	0.0433029	+	0.133273i
$208$	2063.87			0.687999
$209$	71.9538	−	85.2783i	0.0238141	−	0.0282240i
$210$	814.175			0.267540
$211$	−1432.98	−	4410.27i	−0.467538	−	1.43893i	−0.855762	−	0.517370i	$-0.826911\pi$
$211$	−1432.98	−	4410.27i	−0.467538	−	1.43893i	0.388224	−	0.921565i	$-0.373089\pi$
$212$	−2706.17	−	1966.15i	−0.876699	−	0.636959i
$213$	−635.714	+	461.873i	−0.204500	+	0.148578i
$214$	−1114.69	+	3430.65i	−0.356067	+	1.09586i
$215$	1297.12	−	3992.14i	0.411457	−	1.26633i
$216$	−1558.14	+	1132.05i	−0.490823	+	0.356604i
$217$	117.253	+	85.1892i	0.0366804	+	0.0266499i
$218$	2267.71	+	6979.30i	0.704536	+	2.16834i
$219$	336.238			0.103748
$220$	−7694.96	+	1896.32i	−2.35816	+	0.581136i
$221$	1264.29			0.384820
$222$	35.1155	+	108.074i	0.0106162	+	0.0326733i
$223$	−1694.08	−	1230.82i	−0.508717	−	0.369605i	0.303620	−	0.952793i	$-0.401805\pi$
$223$	−1694.08	−	1230.82i	−0.508717	−	0.369605i	−0.812337	+	0.583189i	$0.801805\pi$
$224$	836.001	−	607.390i	0.249364	−	0.181174i
$225$	−813.925	+	2505.00i	−0.241163	+	0.742223i
$226$	−1103.28	+	3395.55i	−0.324731	+	0.999419i
$227$	3476.57	−	2525.87i	1.01651	−	0.738538i	0.0509455	−	0.998701i	$-0.483777\pi$
$227$	3476.57	−	2525.87i	1.01651	−	0.738538i	0.965565	+	0.260164i	$0.0837765\pi$
$228$	−43.2244	−	31.4044i	−0.0125553	−	0.00912195i
$229$	−705.574	−	2171.53i	−0.203606	−	0.626633i	−0.999768	−	0.0215502i	$-0.993140\pi$
$229$	−705.574	−	2171.53i	−0.203606	−	0.626633i	0.796162	−	0.605083i	$-0.206860\pi$
$230$	1168.48			0.334989
$231$	−30.1234	+	414.552i	−0.00857996	+	0.118076i
$232$	4488.38			1.27016
$233$	−1387.96	−	4271.69i	−0.390249	−	1.20106i	−0.932600	−	0.360911i	$-0.882466\pi$
$233$	−1387.96	−	4271.69i	−0.390249	−	1.20106i	0.542352	−	0.840152i	$-0.317534\pi$
$234$	7265.08	+	5278.39i	2.02963	+	1.47461i
$235$	−1823.04	+	1324.52i	−0.506052	+	0.367668i
$236$	−1515.78	+	4665.09i	−0.418088	+	1.28674i
$237$	273.098	−	840.508i	0.0748506	−	0.230367i
$238$	−610.186	+	443.326i	−0.166187	+	0.120742i
$239$	4273.36	+	3104.78i	1.15657	+	0.840299i	0.989341	−	0.145619i	$-0.0465174\pi$
$239$	4273.36	+	3104.78i	1.15657	+	0.840299i	0.167231	+	0.985918i	$0.446517\pi$
$240$	157.373	+	484.344i	0.0423266	+	0.130268i
$241$	−371.992			−0.0994278			−0.0497139	−	0.998763i	$-0.515831\pi$
$241$	−371.992			−0.0994278			−0.0497139	+	0.998763i	$0.515831\pi$
$242$	−1059.61	−	6206.88i	−0.281463	−	1.64873i
$243$	−2465.83			−0.650959
$244$	−3124.06	−	9614.86i	−0.819661	−	2.52266i
$245$	−3116.96	−	2264.60i	−0.812796	−	0.590531i
$246$	−1186.18	+	861.810i	−0.307431	+	0.223362i
$247$	−70.2863	+	216.319i	−0.0181061	+	0.0557249i
$248$	−144.146	+	443.636i	−0.0369084	+	0.113592i
$249$	−1283.06	+	932.201i	−0.326550	+	0.237252i
$250$	−1260.79	−	916.016i	−0.318957	−	0.231736i
$251$	1792.96	+	5518.15i	0.450878	+	1.38766i	0.875907	+	0.482481i	$0.160264\pi$
$251$	1792.96	+	5518.15i	0.450878	+	1.38766i	−0.425028	+	0.905180i	$0.639736\pi$
$252$	−3442.26			−0.860485
$253$	−43.2322	+	594.954i	−0.0107430	+	0.147844i
$254$	10625.1			2.62472
$255$	96.4036	+	296.700i	0.0236746	+	0.0728630i
$256$	5273.54	+	3831.45i	1.28749	+	0.935414i
$257$	−2028.16	+	1473.55i	−0.492270	+	0.357655i	−0.806057	−	0.591838i	$-0.798402\pi$
$257$	−2028.16	+	1473.55i	−0.492270	+	0.357655i	0.313787	+	0.949494i	$0.398402\pi$
$258$	493.486	−	1518.79i	0.119082	−	0.366496i
$259$	−57.3030	+	176.360i	−0.0137476	+	0.0423108i
$260$	13070.0	−	9495.89i	3.11756	−	2.26504i
$261$	3070.59	+	2230.92i	0.728218	+	0.529082i
$262$	−264.934	−	815.384i	−0.0624721	−	0.192269i
$263$	4285.24			1.00471			0.502356	−	0.864661i	$-0.332467\pi$
$263$	4285.24			1.00471			0.502356	+	0.864661i	$0.332467\pi$
$264$	−1298.90	+	320.095i	−0.302809	+	0.0746232i
$265$	−3513.81			−0.814535
$266$	−41.9305	−	129.049i	−0.00966512	−	0.0297462i
$267$	1043.76	+	758.337i	0.239240	+	0.173818i
$268$	1340.07	−	973.619i	0.305440	−	0.221915i
$269$	588.701	−	1811.83i	0.133434	−	0.410667i	−0.861909	−	0.507063i	$-0.830731\pi$
$269$	588.701	−	1811.83i	0.133434	−	0.410667i	0.995343	+	0.0963953i	$0.0307313\pi$
$270$	−1409.09	+	4336.72i	−0.317608	+	0.977497i
$271$	−2790.33	+	2027.30i	−0.625464	+	0.454426i	−0.854826	−	0.518915i	$-0.826336\pi$
$271$	−2790.33	+	2027.30i	−0.625464	+	0.454426i	0.229362	+	0.973341i	$0.426336\pi$
$272$	−381.674	−	277.302i	−0.0850823	−	0.0618159i
$273$	−261.826	−	805.818i	−0.0580456	−	0.178646i
$274$	11211.1			2.47184
$275$	−2427.79	+	2877.38i	−0.532369	+	0.630954i
$276$	285.640			0.0622952
$277$	471.095	+	1449.88i	0.102185	+	0.314494i	0.989060	−	0.147517i	$-0.0471280\pi$
$277$	471.095	+	1449.88i	0.102185	+	0.314494i	−0.886874	+	0.462011i	$0.847128\pi$
$278$	9476.77	+	6885.28i	2.04453	+	1.48544i
$279$	−319.120	+	231.854i	−0.0684774	+	0.0497517i
$280$	−1321.40	+	4066.84i	−0.282031	+	0.868001i
$281$	−470.158	+	1447.00i	−0.0998124	+	0.307191i	−0.988478	−	0.151365i	$-0.951633\pi$
$281$	−470.158	+	1447.00i	−0.0998124	+	0.307191i	0.888666	+	0.458556i	$0.151633\pi$
$282$	−693.570	+	503.908i	−0.146459	+	0.106409i
$283$	4705.72	+	3418.91i	0.988431	+	0.718137i	0.959577	−	0.281446i	$-0.0908141\pi$
$283$	4705.72	+	3418.91i	0.988431	+	0.718137i	0.0288542	+	0.999584i	$0.490814\pi$
$284$	−2874.38	−	8846.44i	−0.600575	−	1.84838i
$285$	−56.1246			−0.0116650
$286$	6772.20	+	10903.8i	1.40017	+	2.25438i
$287$	−2392.61			−0.492095
$288$	869.083	+	2674.76i	0.177817	+	0.547263i
$289$	−233.806	−	169.870i	−0.0475892	−	0.0345756i
$290$	8597.15	−	6246.19i	1.74083	−	1.26479i
$291$	553.811	−	1704.46i	0.111564	−	0.343357i
$292$	−1229.95	+	3785.39i	−0.246498	+	0.758642i
$293$	−3234.61	+	2350.08i	−0.644941	+	0.468577i	−0.861544	−	0.507683i	$-0.830502\pi$
$293$	−3234.61	+	2350.08i	−0.644941	+	0.468577i	0.216603	+	0.976260i	$0.430502\pi$
$294$	−1185.83	−	861.559i	−0.235236	−	0.170909i
$295$	1592.27	+	4900.52i	0.314257	+	0.967183i
$296$	−596.828			−0.117196
$297$	−2155.98	−	877.914i	−0.421222	−	0.171521i
$298$	−12316.6			−2.39423
$299$	−375.766	−	1156.49i	−0.0726793	−	0.223684i
$300$	1458.44	+	1059.62i	0.280676	+	0.203923i
$301$	2108.28	−	1531.76i	0.403719	−	0.293319i
$302$	−4386.55	+	13500.4i	−0.835820	+	2.57239i
$303$	−529.830	+	1630.65i	−0.100455	+	0.309169i
$304$	68.6649	−	49.8880i	0.0129546	−	0.00941208i
$305$	−8591.64	−	6242.19i	−1.61297	−	1.17189i
$306$	−634.333	−	1952.28i	−0.118505	−	0.364719i
$307$	8679.98			1.61366			0.806829	−	0.590785i	$-0.201182\pi$
$307$	8679.98			1.61366			0.806829	+	0.590785i	$0.201182\pi$
$308$	−4556.87	−	1855.55i	−0.843026	−	0.343279i
$309$	118.356			0.0217897
$310$	341.279	+	1050.35i	0.0625270	+	0.192438i
$311$	−5882.43	−	4273.84i	−1.07255	−	0.779251i	−0.0961783	−	0.995364i	$-0.530662\pi$
$311$	−5882.43	−	4273.84i	−1.07255	−	0.779251i	−0.976368	+	0.216113i	$0.930662\pi$
$312$	2206.19	−	1602.89i	0.400323	−	0.290852i
$313$	−33.0758	+	101.797i	−0.00597302	+	0.0183831i	−0.953999	−	0.299811i	$-0.903076\pi$
$313$	−33.0758	+	101.797i	−0.00597302	+	0.0183831i	0.948026	+	0.318194i	$0.103076\pi$
$314$	−3481.16	+	10713.9i	−0.625647	+	1.92554i
$315$	−2925.39	+	2125.42i	−0.523260	+	0.380171i
$316$	8463.53	+	6149.11i	1.50668	+	1.09467i
$317$	−2428.07	−	7472.84i	−0.430202	−	1.32403i	−0.897924	−	0.440151i	$-0.854925\pi$
$317$	−2428.07	−	7472.84i	−0.430202	−	1.32403i	0.467722	−	0.883876i	$-0.345075\pi$
$318$	−1336.82			−0.235739
$319$	2862.28	+	4608.49i	0.502373	+	0.808859i
$320$	11228.0			1.96145
$321$	286.240	+	880.957i	0.0497706	+	0.153178i
$322$	586.883	+	426.396i	0.101571	+	0.0737954i
$323$	42.0628	−	30.5604i	0.00724593	−	0.00526447i
$324$	2717.99	−	8365.10i	0.466047	−	1.43434i
$325$	2371.53	−	7298.82i	0.404766	−	1.24574i
$326$	410.970	−	298.587i	0.0698206	−	0.0507276i
$327$	1524.55	+	1107.65i	0.257822	+	0.187318i
$328$	−2379.62	−	7323.73i	−0.400588	−	1.23288i
$329$	−1398.98			−0.234432
$330$	−2042.48	+	2420.71i	−0.340712	+	0.403805i
$331$	−4599.42			−0.763767			−0.381883	−	0.924210i	$-0.624724\pi$
$331$	−4599.42			−0.763767			−0.381883	+	0.924210i	$0.624724\pi$
$332$	−5801.38	−	17854.8i	−0.959013	−	2.95154i
$333$	−408.303	−	296.649i	−0.0671918	−	0.0488177i
$334$	6421.06	−	4665.17i	1.05193	−	0.764272i
$335$	537.693	−	1654.85i	0.0876934	−	0.269893i
$336$	−97.7017	+	300.695i	−0.0158633	+	0.0488222i
$337$	−8091.47	+	5878.80i	−1.30792	+	0.950263i	−0.999999	−	0.00114744i	$-0.999635\pi$
$337$	−8091.47	+	5878.80i	−1.30792	+	0.950263i	−0.307926	+	0.951410i	$0.599635\pi$
$338$	−12759.7	−	9270.46i	−2.05336	−	1.49185i
$339$	283.311	+	871.943i	0.0453904	+	0.139697i
$340$	−3692.91			−0.589048
$341$	−547.432	+	134.907i	−0.0869357	+	0.0214241i
$342$	369.298			0.0583899
$343$	−1733.17	−	5334.15i	−0.272835	−	0.839700i
$344$	6785.52	+	4929.97i	1.06352	+	0.772692i
$345$	242.749	−	176.368i	0.0378817	−	0.0275226i
$346$	1097.68	−	3378.30i	0.170553	−	0.524909i
$347$	−2784.20	+	8568.90i	−0.430732	+	1.32566i	0.466666	+	0.884434i	$0.345455\pi$
$347$	−2784.20	+	8568.90i	−0.430732	+	1.32566i	−0.897398	+	0.441222i	$0.854545\pi$
$348$	2101.60	−	1526.90i	0.323729	−	0.235203i
$349$	−3092.48	−	2246.82i	−0.474318	−	0.344612i	0.324804	−	0.945781i	$-0.394702\pi$
$349$	−3092.48	−	2246.82i	−0.474318	−	0.344612i	−0.799122	+	0.601169i	$0.794702\pi$
$350$	1414.78	+	4354.23i	0.216066	+	0.664982i
$351$	4745.34			0.721617
$352$	−291.337	+	4009.33i	−0.0441146	+	0.607097i
$353$	−6424.02			−0.968601			−0.484301	−	0.874902i	$-0.660926\pi$
$353$	−6424.02			−0.968601			−0.484301	+	0.874902i	$0.660926\pi$
$354$	605.775	+	1864.38i	0.0909508	+	0.279918i
$355$	−7905.00	−	5743.32i	−1.18184	−	0.858658i
$356$	−12355.5	+	8976.78i	−1.83944	+	1.33643i
$357$	−59.8501	+	184.200i	−0.00887284	+	0.0273078i
$358$	−232.432	+	715.352i	−0.0343140	+	0.105608i
$359$	2565.15	−	1863.69i	0.377113	−	0.273988i	−0.383041	−	0.923731i	$-0.625123\pi$
$359$	2565.15	−	1863.69i	0.377113	−	0.273988i	0.760154	+	0.649743i	$0.225123\pi$
$360$	−9415.39	−	6840.68i	−1.37843	−	1.00149i
$361$	−2116.66	−	6514.40i	−0.308596	−	0.949760i
$362$	−8332.13			−1.20974
$363$	−1156.98	−	1129.53i	−0.167288	−	0.163319i
$364$	10029.7			1.44423
$365$	1292.02	+	3976.42i	0.185280	+	0.570234i
$366$	−3268.66	−	2374.82i	−0.466818	−	0.339163i
$367$	4191.90	−	3045.60i	0.596228	−	0.433185i	−0.248310	−	0.968681i	$-0.579875\pi$
$367$	4191.90	−	3045.60i	0.596228	−	0.433185i	0.844538	+	0.535496i	$0.179875\pi$
$368$	−140.219	+	431.549i	−0.0198625	+	0.0611306i
$369$	2012.26	−	6193.09i	0.283886	−	0.873711i
$370$	−1143.18	+	830.568i	−0.160624	+	0.116700i
$371$	−1764.85	−	1282.24i	−0.246972	−	0.179435i
$372$	83.4269	+	256.762i	0.0116276	+	0.0357862i
$373$	552.488			0.0766936			0.0383468	−	0.999264i	$-0.487791\pi$
$373$	552.488			0.0766936			0.0383468	+	0.999264i	$0.487791\pi$
$374$	212.643	−	2926.36i	0.0293998	−	0.404595i
$375$	−400.186			−0.0551080
$376$	−1391.39	−	4282.25i	−0.190838	−	0.587340i
$377$	−8946.78	−	6500.22i	−1.22224	−	0.888006i
$378$	−2290.26	+	1663.97i	−0.311635	+	0.226416i
$379$	−1819.84	+	5600.90i	−0.246647	+	0.759100i	0.748715	+	0.662893i	$0.230671\pi$
$379$	−1819.84	+	5600.90i	−0.246647	+	0.759100i	−0.995361	+	0.0962079i	$0.969329\pi$
$380$	205.302	−	631.855i	0.0277152	−	0.0852987i
$381$	2207.34	−	1603.72i	0.296812	−	0.215646i
$382$	−14147.1	−	10278.5i	−1.89484	−	1.37668i
$383$	1936.97	+	5961.37i	0.258419	+	0.795331i	0.993137	+	0.116958i	$0.0373144\pi$
$383$	1936.97	+	5961.37i	0.258419	+	0.795331i	−0.734718	+	0.678373i	$0.762686\pi$
$384$	3200.80			0.425365
$385$	−5018.34	+	1236.70i	−0.664307	+	0.163710i
$386$	17631.2			2.32488
$387$	2191.71	+	6745.39i	0.287883	+	0.886014i
$388$	17163.1	+	12469.7i	2.24568	+	1.63158i
$389$	−7920.26	+	5754.40i	−1.03232	+	0.750025i	−0.968772	−	0.247953i	$-0.920242\pi$
$389$	−7920.26	+	5754.40i	−1.03232	+	0.750025i	−0.0635492	+	0.997979i	$0.520242\pi$
$390$	1995.15	−	6140.43i	0.259046	−	0.797263i
$391$	−85.8953	+	264.359i	−0.0111097	+	0.0341923i
$392$	6228.12	−	4524.99i	0.802468	−	0.583027i
$393$	−178.111	−	129.405i	−0.0228614	−	0.0166098i
$394$	5473.60	+	16846.0i	0.699889	+	2.15404i
$395$	10989.4			1.39984
$396$	8635.43	−	10234.6i	1.09583	−	1.29875i
$397$	−12072.6			−1.52621			−0.763103	−	0.646276i	$-0.776325\pi$
$397$	−12072.6			−1.52621			−0.763103	+	0.646276i	$0.776325\pi$
$398$	3180.53	+	9788.67i	0.400567	+	1.23282i
$399$	−28.1892	−	20.4806i	−0.00353690	−	0.00256971i
$400$	−2316.82	+	1683.27i	−0.289603	+	0.210409i
$401$	−2443.36	+	7519.88i	−0.304278	+	0.936471i	0.675668	+	0.737206i	$0.263855\pi$
$401$	−2443.36	+	7519.88i	−0.304278	+	0.936471i	−0.979946	+	0.199265i	$0.936145\pi$
$402$	204.563	−	629.581i	0.0253798	−	0.0781111i
$403$	929.818	−	675.552i	0.114932	−	0.0835029i
$404$	−16419.9	−	11929.7i	−2.02208	−	1.46913i
$405$	−2855.15	−	8787.25i	−0.350305	−	1.07813i
$406$	6597.33			0.806453
$407$	−380.603	−	612.800i	−0.0463533	−	0.0746324i
$408$	−623.357			−0.0756392
$409$	2097.18	+	6454.44i	0.253542	+	0.780322i	0.994113	+	0.108344i	$0.0345549\pi$
$409$	2097.18	+	6454.44i	0.253542	+	0.780322i	−0.740571	+	0.671978i	$0.765445\pi$
$410$	−14750.0	−	10716.5i	−1.77670	−	1.29085i
$411$	2329.07	−	1692.17i	0.279524	−	0.203086i
$412$	−432.942	+	1332.46i	−0.0517707	+	0.159334i
$413$	−988.529	+	3042.38i	−0.117778	+	0.362484i
$414$	−1597.28	+	1160.49i	−0.189619	+	0.137766i
$415$	−15954.7	−	11591.8i	−1.88719	−	1.37113i
$416$	−2532.24	−	7793.45i	−0.298446	−	0.918522i
$417$	3008.02			0.353245
$418$	488.877	+	199.070i	0.0572052	+	0.0232939i
$419$	−8453.14			−0.985592			−0.492796	−	0.870145i	$-0.664025\pi$
$419$	−8453.14			−0.985592			−0.492796	+	0.870145i	$0.664025\pi$
$420$	764.779	+	2353.75i	0.0888510	+	0.273455i
$421$	4788.20	+	3478.83i	0.554305	+	0.402726i	0.829370	−	0.558699i	$-0.188699\pi$
$421$	4788.20	+	3478.83i	0.554305	+	0.402726i	−0.275065	+	0.961426i	$0.588699\pi$
$422$	17748.0	−	12894.7i	2.04730	−	1.48745i
$423$	1176.58	−	3621.15i	0.135242	−	0.416233i
$424$	2169.64	−	6677.46i	0.248507	−	0.764826i
$425$	−1419.24	+	1031.14i	−0.161984	+	0.117688i
$426$	−3007.43	−	2185.02i	−0.342043	−	0.248509i
$427$	−2037.38	−	6270.42i	−0.230904	−	0.710648i
$428$	−10964.9			−1.23834
$429$	3052.69	+	1243.05i	0.343556	+	0.139895i
$430$	19857.9			2.22705
$431$	3049.89	+	9386.60i	0.340854	+	1.04904i	0.963766	+	0.266749i	$0.0859495\pi$
$431$	3049.89	+	9386.60i	0.340854	+	1.04904i	−0.622912	+	0.782292i	$0.714050\pi$
$432$	−1432.56	−	1040.82i	−0.159547	−	0.115918i
$433$	−3800.01	+	2760.87i	−0.421748	+	0.306418i	−0.778341	−	0.627842i	$-0.783938\pi$
$433$	−3800.01	+	2760.87i	−0.421748	+	0.306418i	0.356593	+	0.934260i	$0.383938\pi$
$434$	−211.876	+	652.087i	−0.0234340	+	0.0721226i
$435$	843.251	−	2595.26i	0.0929443	−	0.286053i
$436$	−18046.8	+	13111.7i	−1.98230	+	1.44023i
$437$	−40.4564	−	29.3933i	−0.00442858	−	0.00321755i
$438$	491.544	+	1512.82i	0.0536230	+	0.165035i
$439$	11226.2			1.22049			0.610246	−	0.792212i	$-0.291071\pi$
$439$	11226.2			1.22049			0.610246	+	0.792212i	$0.291071\pi$
$440$	−8776.63	−	14131.1i	−0.950930	−	1.53107i
$441$	6509.90			0.702937
$442$	1848.25	+	5688.34i	0.198897	+	0.612142i
$443$	14701.5	+	10681.2i	1.57672	+	1.14556i	0.920335	+	0.391130i	$0.127916\pi$
$443$	14701.5	+	10681.2i	1.57672	+	1.14556i	0.656386	+	0.754425i	$0.272084\pi$
$444$	−279.454	+	203.035i	−0.0298700	+	0.0217018i
$445$	−4957.54	+	15257.7i	−0.528112	+	1.62536i
$446$	3061.20	−	9421.40i	0.325005	−	1.00026i
$447$	−2558.74	+	1859.03i	−0.270747	+	0.196709i
$448$	5639.38	+	4097.25i	0.594723	+	0.432091i
$449$	333.309	+	1025.82i	0.0350330	+	0.107821i	0.967044	−	0.254610i	$-0.0819470\pi$
$449$	333.309	+	1025.82i	0.0350330	+	0.107821i	−0.932011	+	0.362430i	$0.881947\pi$
$450$	−12460.5			−1.30532
$451$	6002.21	−	7113.71i	0.626681	−	0.742731i
$452$	−10852.7			−1.12936
$453$	1126.42	+	3466.77i	0.116830	+	0.359565i
$454$	16446.9	+	11949.4i	1.70020	+	1.23527i
$455$	8523.70	−	6192.83i	0.878236	−	0.638076i
$456$	34.6547	−	106.656i	0.00355889	−	0.0109531i
$457$	−2203.59	+	6781.95i	−0.225557	+	0.694193i	0.772678	+	0.634799i	$0.218917\pi$
$457$	−2203.59	+	6781.95i	−0.225557	+	0.694193i	−0.998235	+	0.0593944i	$0.981083\pi$
$458$	8738.79	−	6349.10i	0.891565	−	0.647760i
$459$	−877.561	−	637.585i	−0.0892397	−	0.0648364i
$460$	1097.59	+	3378.04i	0.111251	+	0.342395i
$461$	4180.76			0.422380			0.211190	−	0.977445i	$-0.432266\pi$
$461$	4180.76			0.422380			0.211190	+	0.977445i	$0.432266\pi$
$462$	−1909.21	+	470.499i	−0.192261	+	0.0473800i
$463$	14236.4			1.42899			0.714495	−	0.699641i	$-0.246657\pi$
$463$	14236.4			1.42899			0.714495	+	0.699641i	$0.246657\pi$
$464$	1275.21	+	3924.68i	0.127586	+	0.392670i
$465$	229.437	+	166.696i	0.0228815	+	0.0166243i
$466$	17190.3	−	12489.5i	1.70886	−	1.24156i
$467$	508.730	−	1565.71i	0.0504095	−	0.155145i	−0.922683	−	0.385560i	$-0.874008\pi$
$467$	508.730	−	1565.71i	0.0504095	−	0.155145i	0.973092	+	0.230415i	$0.0740084\pi$
$468$	−8435.31	+	25961.2i	−0.833167	+	2.56422i
$469$	873.939	−	634.954i	0.0860443	−	0.0625148i
$470$	−8624.43	−	6266.01i	−0.846415	−	0.614957i
$471$	893.926	+	2751.22i	0.0874521	+	0.269150i
$472$	−10295.8			−1.00403
$473$	−734.714	+	10111.0i	−0.0714211	+	0.982884i
$474$	4180.89			0.405137
$475$	−97.5266	−	300.156i	−0.00942069	−	0.0289939i
$476$	−1854.81	−	1347.60i	−0.178603	−	0.129762i
$477$	4803.28	−	3489.79i	0.461063	−	0.334982i
$478$	−7721.96	+	23765.7i	−0.738900	+	2.27410i
$479$	2736.69	−	8422.66i	0.261049	−	0.803427i	−0.731528	−	0.681811i	$-0.761193\pi$
$479$	2736.69	−	8422.66i	0.261049	−	0.803427i	0.992577	−	0.121615i	$-0.0388074\pi$
$480$	1635.86	−	1188.52i	0.155555	−	0.113017i
$481$	1189.67	+	864.346i	0.112774	+	0.0819351i
$482$	−543.813	−	1673.68i	−0.0513900	−	0.158162i
$483$	186.282			0.0175489
$484$	16948.5	−	8893.59i	1.59171	−	0.835235i
$485$	22285.3			2.08644
$486$	−3604.78	−	11094.4i	−0.336453	−	1.03550i
$487$	−3425.84	−	2489.02i	−0.318768	−	0.231598i	0.416882	−	0.908961i	$-0.363123\pi$
$487$	−3425.84	−	2489.02i	−0.318768	−	0.231598i	−0.735649	+	0.677362i	$0.763123\pi$
$488$	17167.3	−	12472.8i	1.59247	−	1.15700i
$489$	40.3099	−	124.061i	0.00372777	−	0.0114729i
$490$	5632.34	−	17334.6i	0.519272	−	1.59815i
$491$	11983.5	−	8706.49i	1.10144	−	0.800242i	0.120144	−	0.992756i	$-0.461664\pi$
$491$	11983.5	−	8706.49i	1.10144	−	0.800242i	0.981294	+	0.192515i	$0.0616644\pi$
$492$	−3605.67	−	2619.68i	−0.330399	−	0.240049i
$493$	781.167	+	2404.18i	0.0713630	+	0.219633i
$494$	−1076.02			−0.0980011
$495$	1019.47	−	14029.7i	0.0925689	−	1.27392i
$496$	−428.874			−0.0388246
$497$	−1874.56	−	5769.29i	−0.169186	−	0.520700i
$498$	−6069.91	−	4410.04i	−0.546183	−	0.396825i
$499$	7524.95	−	5467.20i	0.675076	−	0.490471i	−0.196644	−	0.980475i	$-0.563004\pi$
$499$	7524.95	−	5467.20i	0.675076	−	0.490471i	0.871721	+	0.490003i	$0.163004\pi$
$500$	1463.87	−	4505.33i	0.130932	−	0.402969i
$501$	629.809	−	1938.35i	0.0561633	−	0.172853i
$502$	−22206.4	+	16133.9i	−1.97434	+	1.43445i
$503$	−13032.6	−	9468.76i	−1.15526	−	0.839346i	−0.166090	−	0.986111i	$-0.553114\pi$
$503$	−13032.6	−	9468.76i	−1.15526	−	0.839346i	−0.989171	+	0.146764i	$0.953114\pi$
$504$	−2232.72	−	6871.61i	−0.197328	−	0.607313i
$505$	−21320.3			−1.87870
$506$	−2740.05	+	675.247i	−0.240731	+	0.0593249i
$507$	−4050.05			−0.354771
$508$	9980.48	+	30716.7i	0.871677	+	2.68275i
$509$	−9849.07	−	7155.77i	−0.857666	−	0.623131i	0.0695826	−	0.997576i	$-0.477833\pi$
$509$	−9849.07	−	7155.77i	−0.857666	−	0.623131i	−0.927249	+	0.374445i	$0.877833\pi$
$510$	−1193.99	+	867.487i	−0.103668	+	0.0753195i
$511$	−802.122	+	2468.68i	−0.0694399	+	0.213714i
$512$	−3015.71	+	9281.39i	−0.260306	+	0.801139i
$513$	157.877	−	114.705i	0.0135876	−	0.00987199i
$514$	−9594.81	−	6971.04i	−0.823364	−	0.598209i
$515$	454.791	+	1399.70i	0.0389135	+	0.119764i
$516$	4854.32			0.414146
$517$	3509.54	−	4159.45i	0.298549	−	0.353834i
$518$	−877.260			−0.0744104
$519$	−281.872	−	867.513i	−0.0238397	−	0.0733711i
$520$	27433.6	+	19931.7i	2.31354	+	1.68089i
$521$	13788.3	−	10017.8i	1.15946	−	0.842396i	0.169749	−	0.985487i	$-0.445704\pi$
$521$	13788.3	−	10017.8i	1.15946	−	0.842396i	0.989709	+	0.143091i	$0.0457043\pi$
$522$	−5548.56	+	17076.7i	−0.465238	+	1.43185i
$523$	6642.80	−	20444.4i	0.555391	−	1.70932i	−0.139517	−	0.990220i	$-0.544555\pi$
$523$	6642.80	−	20444.4i	0.555391	−	1.70932i	0.694908	−	0.719098i	$-0.255445\pi$
$524$	2108.38	−	1531.83i	0.175773	−	0.127707i
$525$	951.132	+	691.038i	0.0790682	+	0.0574464i
$526$	6264.56	+	19280.3i	0.519293	+	1.59822i
$527$	−262.720			−0.0217158
$528$	−648.928	−	1044.82i	−0.0534867	−	0.0861177i
$529$	−11899.7			−0.978027
$530$	−5136.82	−	15809.5i	−0.420999	−	1.29570i
$531$	−7043.60	−	5117.47i	−0.575643	−	0.418229i
$532$	333.688	−	242.439i	0.0271940	−	0.0197576i
$533$	−5863.11	+	18044.8i	−0.476472	+	1.46643i
$534$	−1886.08	+	5804.75i	−0.152844	+	0.470405i
$535$	−9318.50	+	6770.28i	−0.753035	+	0.547112i
$536$	2812.78	+	2043.60i	0.226667	+	0.164683i
$537$	59.6861	+	183.695i	0.00479636	+	0.0147617i
$538$	9012.51			0.722224
$539$	8617.81	+	3509.16i	0.688674	+	0.280427i
$540$	−13860.9			−1.10459
$541$	−5784.43	−	17802.6i	−0.459689	−	1.41478i	−0.865540	−	0.500839i	$-0.833025\pi$
$541$	−5784.43	−	17802.6i	−0.459689	−	1.41478i	0.405851	−	0.913939i	$-0.366975\pi$
$542$	−13200.5	−	9590.70i	−1.04614	−	0.760066i
$543$	−1730.98	+	1257.63i	−0.136802	+	0.0993922i
$544$	−578.839	+	1781.48i	−0.0456204	+	0.140405i
$545$	−7241.12	+	22285.9i	−0.569129	+	1.75160i
$546$	3242.81	−	2356.04i	0.254175	−	0.184669i
$547$	12470.6	+	9060.44i	0.974782	+	0.708221i	0.956536	−	0.291613i	$-0.0941919\pi$
$547$	12470.6	+	9060.44i	0.974782	+	0.708221i	0.0182455	+	0.999834i	$0.494192\pi$
$548$	10530.9	+	32410.7i	0.820907	+	2.52649i
$549$	17944.0			1.39496
$550$	−16495.2	−	6716.82i	−1.27883	−	0.520739i
$551$	−454.782			−0.0351622
$552$	185.272	+	570.207i	0.0142857	+	0.0439667i
$553$	5519.57	+	4010.20i	0.424441	+	0.308374i
$554$	−5834.68	+	4239.14i	−0.447458	+	0.325097i
$555$	−112.129	+	345.096i	−0.00857585	+	0.0263937i
$556$	−11003.2	+	33864.5i	−0.839284	+	2.58305i
$557$	−5774.88	+	4195.69i	−0.439299	+	0.319169i	−0.785356	−	0.619044i	$-0.787520\pi$
$557$	−5774.88	+	4195.69i	−0.439299	+	0.319169i	0.346058	+	0.938213i	$0.387520\pi$
$558$	−1509.69	−	1096.85i	−0.114534	−	0.0832140i
$559$	−6385.98	−	19654.0i	−0.483181	−	1.48708i
$560$	−3931.51			−0.296673
$561$	−397.521	−	640.039i	−0.0299168	−	0.0481684i
$562$	−7197.72			−0.540245
$563$	2028.14	+	6241.96i	0.151822	+	0.467260i	0.997825	−	0.0659180i	$-0.0209976\pi$
$563$	2028.14	+	6241.96i	0.151822	+	0.467260i	−0.846003	+	0.533178i	$0.820998\pi$
$564$	−2108.27	−	1531.75i	−0.157401	−	0.114358i
$565$	−9223.15	+	6701.01i	−0.686763	+	0.498962i
$566$	−8503.23	+	26170.3i	−0.631480	+	1.94350i
$567$	1772.56	−	5455.38i	0.131288	−	0.404064i
$568$	15795.3	−	11476.0i	1.16682	−	0.847748i
$569$	13753.5	+	9992.48i	1.01331	+	0.736215i	0.964901	−	0.262612i	$-0.0845841\pi$
$569$	13753.5	+	9992.48i	1.01331	+	0.736215i	0.0484117	+	0.998827i	$0.484584\pi$
$570$	−82.0482	−	252.518i	−0.00602916	−	0.0185558i
$571$	5317.38			0.389712			0.194856	−	0.980832i	$-0.437576\pi$
$571$	5317.38			0.389712			0.194856	+	0.980832i	$0.437576\pi$
$572$	−25161.0	+	29820.4i	−1.83922	+	2.17981i
$573$	−4490.42			−0.327382
$574$	−3497.74	−	10764.9i	−0.254343	−	0.782786i
$575$	1365.04	+	991.759i	0.0990019	+	0.0719291i
$576$	−15348.3	+	11151.2i	−1.11027	+	0.806657i
$577$	−6444.63	+	19834.5i	−0.464980	+	1.43106i	0.394028	+	0.919098i	$0.371081\pi$
$577$	−6444.63	+	19834.5i	−0.464980	+	1.43106i	−0.859008	+	0.511962i	$0.828919\pi$
$578$	422.487	−	1300.28i	0.0304034	−	0.0935720i
$579$	3662.84	−	2661.21i	0.262906	−	0.191012i
$580$	26133.1	+	18986.8i	1.87089	+	1.35928i
$581$	−3783.42	−	11644.2i	−0.270160	−	0.831466i
$582$	8478.37			0.603849
$583$	8239.75	−	2030.58i	0.585344	−	0.144250i
$584$	−8354.35			−0.591961
$585$	8861.00	+	27271.4i	0.626252	+	1.92740i
$586$	−15302.2	−	11117.7i	−1.07872	−	0.783735i
$587$	−9796.54	+	7117.60i	−0.688836	+	0.500468i	−0.876277	−	0.481807i	$-0.839981\pi$
$587$	−9796.54	+	7117.60i	−0.688836	+	0.500468i	0.187441	+	0.982276i	$0.439981\pi$
$588$	1376.84	−	4237.49i	0.0965647	−	0.297196i
$589$	14.6055	−	44.9512i	0.00102175	−	0.00314462i
$590$	−19720.9	+	14328.1i	−1.37610	+	0.999792i
$591$	3679.82	+	2673.54i	0.256121	+	0.186083i
$592$	−169.567	−	521.872i	−0.0117722	−	0.0362311i
$593$	18341.2			1.27012			0.635060	−	0.772463i	$-0.280975\pi$
$593$	18341.2			1.27012			0.635060	+	0.772463i	$0.280975\pi$
$594$	798.130	−	10983.7i	0.0551308	−	0.758699i
$595$	−2408.37			−0.165938
$596$	−11569.3	−	35606.7i	−0.795131	−	2.44716i
$597$	2138.22	+	1553.51i	0.146585	+	0.106501i
$598$	4654.00	−	3381.33i	0.318254	−	0.231225i
$599$	3700.00	−	11387.4i	0.252384	−	0.776758i	−0.741950	−	0.670455i	$-0.766099\pi$
$599$	3700.00	−	11387.4i	0.252384	−	0.776758i	0.994334	−	0.106303i	$-0.0339012\pi$
$600$	−1169.28	+	3598.69i	−0.0795597	+	0.244860i
$601$	−3491.88	+	2537.00i	−0.237000	+	0.172190i	−0.699945	−	0.714196i	$-0.746792\pi$
$601$	−3491.88	+	2537.00i	−0.237000	+	0.172190i	0.462946	+	0.886387i	$0.346792\pi$
$602$	9973.83	+	7246.41i	0.675254	+	0.490601i
$603$	908.523	+	2796.15i	0.0613564	+	0.188836i
$604$	−43149.6			−2.90684
$605$	8912.29	−	18023.0i	0.598902	−	1.21114i
$606$	−8111.24			−0.543724
$607$	−7349.76	−	22620.2i	−0.491462	−	1.51257i	−0.822398	−	0.568912i	$-0.807364\pi$
$607$	−7349.76	−	22620.2i	−0.491462	−	1.51257i	0.330936	−	0.943653i	$-0.392636\pi$
$608$	−272.631	−	198.078i	−0.0181853	−	0.0132124i
$609$	1370.58	−	995.783i	0.0911964	−	0.0662581i
$610$	15525.1	−	47781.3i	1.03048	−	3.17149i
$611$	−3428.21	+	10550.9i	−0.226989	+	0.698602i
$612$	5048.10	−	3667.66i	0.333427	−	0.242249i
$613$	−16319.7	−	11856.9i	−1.07528	−	0.781236i	−0.0984251	−	0.995144i	$-0.531380\pi$
$613$	−16319.7	−	11856.9i	−1.07528	−	0.781236i	−0.976854	+	0.213909i	$0.931380\pi$
$614$	12689.2	+	39053.4i	0.834031	+	2.56688i
$615$	−4681.78			−0.306971
$616$	748.462	−	10300.2i	0.0489552	−	0.673712i
$617$	27515.2			1.79533			0.897667	−	0.440674i	$-0.145261\pi$
$617$	27515.2			1.79533			0.897667	+	0.440674i	$0.145261\pi$
$618$	173.023	+	532.511i	0.0112622	+	0.0346614i
$619$	−13336.1	−	9689.25i	−0.865951	−	0.629150i	0.0635467	−	0.997979i	$-0.479759\pi$
$619$	−13336.1	−	9689.25i	−0.865951	−	0.629150i	−0.929497	+	0.368829i	$0.879759\pi$
$620$	−2715.95	+	1973.25i	−0.175927	+	0.127819i
$621$	−322.397	+	992.236i	−0.0208331	+	0.0641177i
$622$	10629.5	−	32714.4i	0.685219	−	2.10889i
$623$	−8057.74	+	5854.29i	−0.518180	+	0.376480i
$624$	2028.39	+	1473.71i	0.130129	+	0.0945444i
$625$	−5523.79	−	17000.5i	−0.353522	−	1.08803i
$626$	−506.362			−0.0323296
$627$	131.610	−	32.4335i	0.00838277	−	0.00206582i
$628$	−34243.4			−2.17590
$629$	−103.873	−	319.689i	−0.00658457	−	0.0202652i
$630$	−13839.4	−	10054.9i	−0.875198	−	0.635868i
$631$	1929.84	−	1402.11i	0.121752	−	0.0884583i	−0.525243	−	0.850953i	$-0.676025\pi$
$631$	1929.84	−	1402.11i	0.121752	−	0.0884583i	0.646995	+	0.762494i	$0.276025\pi$
$632$	−6785.54	+	20883.7i	−0.427079	+	1.31441i
$633$	1740.81	−	5357.67i	0.109307	−	0.336411i
$634$	30072.6	−	21849.0i	1.88381	−	1.36867i
$635$	27447.9	+	19942.0i	1.71533	+	1.24626i
$636$	−1255.71	−	3864.69i	−0.0782897	−	0.240951i
$637$	−18967.9			−1.17980
$638$	−16550.4	+	19615.2i	−1.02702	+	1.21720i
$639$	16509.9			1.02210
$640$	12299.3	+	37853.4i	0.759646	+	2.33795i
$641$	2457.03	+	1785.13i	0.151399	+	0.109998i	0.660906	−	0.750469i	$-0.270172\pi$
$641$	2457.03	+	1785.13i	0.151399	+	0.109998i	−0.509507	+	0.860467i	$0.670172\pi$
$642$	−3545.19	+	2575.73i	−0.217940	+	0.158343i
$643$	7955.97	−	24486.0i	0.487952	−	1.50176i	−0.339709	−	0.940531i	$-0.610328\pi$
$643$	7955.97	−	24486.0i	0.487952	−	1.50176i	0.827660	−	0.561230i	$-0.189672\pi$
$644$	−681.416	+	2097.18i	−0.0416950	+	0.128324i
$645$	4125.42	−	2997.29i	0.251842	−	0.182974i
$646$	198.990	+	144.575i	0.0121194	+	0.00880528i
$647$	2788.13	+	8580.98i	0.169417	+	0.521411i	0.999335	−	0.0364744i	$-0.0116127\pi$
$647$	2788.13	+	8580.98i	0.169417	+	0.521411i	−0.829918	+	0.557886i	$0.811613\pi$
$648$	18461.7			1.11921
$649$	−6565.75	−	10571.4i	−0.397116	−	0.639387i
$650$	36306.1			2.19083
$651$	54.4076	+	167.449i	0.00327558	+	0.0100812i
$652$	1249.24	+	907.625i	0.0750368	+	0.0545174i
$653$	−3689.66	+	2680.69i	−0.221114	+	0.160649i	−0.692828	−	0.721103i	$-0.743635\pi$
$653$	−3689.66	+	2680.69i	−0.221114	+	0.160649i	0.471714	+	0.881752i	$0.343635\pi$
$654$	−2754.86	+	8478.58i	−0.164715	+	0.506940i
$655$	845.972	−	2603.63i	0.0504654	−	0.155317i
$656$	5727.86	−	4161.53i	0.340907	−	0.247684i
$657$	−5715.39	−	4152.47i	−0.339389	−	0.246580i
$658$	−2045.16	−	6294.34i	−0.121168	−	0.372917i
$659$	6296.60			0.372201			0.186101	−	0.982531i	$-0.440415\pi$
$659$	6296.60			0.372201			0.186101	+	0.982531i	$0.440415\pi$
$660$	−8916.74	−	3630.88i	−0.525884	−	0.214139i
$661$	17023.8			1.00174			0.500870	−	0.865522i	$-0.333013\pi$
$661$	17023.8			1.00174			0.500870	+	0.865522i	$0.333013\pi$
$662$	−6723.86	−	20693.9i	−0.394759	−	1.21494i
$663$	1242.55	+	902.767i	0.0727854	+	0.0528817i
$664$	31879.7	−	23162.0i	1.86321	−	1.35370i
$665$	133.890	−	412.070i	0.00780755	−	0.0240292i
$666$	737.803	−	2270.72i	0.0429269	−	0.132115i
$667$	1967.02	−	1429.12i	0.114188	−	0.0829622i
$668$	19518.3	+	14180.9i	1.13052	+	0.821370i
$669$	−786.085	−	2419.32i	−0.0454287	−	0.139815i
$670$	8231.62			0.474650
$671$	23754.3	+	9672.72i	1.36665	+	0.556500i
$672$	1255.34			0.0720620
$673$	−5797.17	−	17841.8i	−0.332042	−	1.02192i	−0.968161	−	0.250329i	$-0.919461\pi$
$673$	−5797.17	−	17841.8i	−0.332042	−	1.02192i	0.636118	−	0.771591i	$-0.280539\pi$
$674$	−38279.0	−	27811.3i	−2.18762	−	1.58940i
$675$	−5326.94	+	3870.25i	−0.303754	+	0.220690i
$676$	14815.0	−	45595.8i	0.842909	−	2.59421i
$677$	5397.79	−	16612.7i	0.306431	−	0.943098i	−0.672708	−	0.739908i	$-0.734869\pi$
$677$	5397.79	−	16612.7i	0.306431	−	0.943098i	0.979139	−	0.203190i	$-0.0651309\pi$
$678$	−3508.91	+	2549.37i	−0.198760	+	0.144407i
$679$	11193.1	+	8132.23i	0.632621	+	0.459626i
$680$	−2395.30	−	7371.97i	−0.135082	−	0.415738i
$681$	5220.40			0.293754
$682$	−1407.27	−	2265.81i	−0.0790132	−	0.127217i
$683$	−13898.3			−0.778630			−0.389315	−	0.921105i	$-0.627288\pi$
$683$	−13898.3			−0.778630			−0.389315	+	0.921105i	$0.627288\pi$
$684$	346.893	+	1067.63i	0.0193915	+	0.0596809i
$685$	28961.5	+	21041.8i	1.61542	+	1.17367i
$686$	21465.9	−	15595.9i	1.19471	−	0.868010i
$687$	857.144	−	2638.02i	0.0476013	−	0.146502i
$688$	−2382.96	+	7333.99i	−0.132049	+	0.406404i
$689$	−13995.3	+	10168.2i	−0.773844	+	0.562231i
$690$	1148.39	+	834.357i	0.0633603	+	0.0460340i
$691$	6505.61	+	20022.2i	0.358155	+	1.10229i	0.954157	+	0.299305i	$0.0967549\pi$
$691$	6505.61	+	20022.2i	0.358155	+	1.10229i	−0.596002	+	0.802983i	$0.703245\pi$
$692$	10797.6			0.593156
$693$	5631.68	−	6674.56i	0.308701	−	0.365867i
$694$	−42623.8			−2.33138
$695$	11558.5	+	35573.5i	0.630849	+	1.94155i
$696$	4411.21	+	3204.93i	0.240239	+	0.174544i
$697$	3508.77	−	2549.27i	0.190680	−	0.138537i
$698$	5588.12	−	17198.5i	0.303028	−	0.932624i
$699$	1686.11	−	5189.32i	0.0912370	−	0.280798i
$700$	−11259.0	+	8180.12i	−0.607928	+	0.441685i
$701$	1529.55	+	1111.29i	0.0824115	+	0.0598754i	0.628228	−	0.778029i	$-0.283780\pi$
$701$	1529.55	+	1111.29i	0.0824115	+	0.0598754i	−0.545817	+	0.837905i	$0.683780\pi$
$702$	6937.18	+	21350.5i	0.372973	+	1.14789i
$703$	60.4733			0.00324437
$704$	−26329.2	+	6488.48i	−1.40954	+	0.347363i
$705$	−2737.48			−0.146240
$706$	−9391.24	−	28903.3i	−0.500629	−	1.54078i
$707$	−10708.4	−	7780.09i	−0.569632	−	0.413862i
$708$	−4820.84	+	3502.54i	−0.255901	+	0.185923i
$709$	−3426.33	+	10545.2i	−0.181493	+	0.558578i	−0.999870	−	0.0161035i	$-0.994874\pi$
$709$	−3426.33	+	10545.2i	−0.181493	+	0.558578i	0.818377	+	0.574681i	$0.194874\pi$
$710$	14284.3	−	43962.7i	0.755044	−	2.32379i
$711$	−15022.2	+	10914.3i	−0.792374	+	0.575694i
$712$	−25933.9	−	18842.1i	−1.36505	−	0.991765i
$713$	78.0843	+	240.319i	0.00410138	+	0.0126227i
$714$	−916.254			−0.0480251
$715$	−2970.42	+	40878.3i	−0.155367	+	2.13813i
$716$	−2286.38			−0.119338
$717$	1982.92	+	6102.80i	0.103282	+	0.317871i
$718$	12135.2	+	8816.72i	0.630753	+	0.458269i
$719$	−14452.4	+	10500.3i	−0.749628	+	0.544637i	−0.895712	−	0.444635i	$-0.853333\pi$
$719$	−14452.4	+	10500.3i	−0.749628	+	0.544637i	0.146083	+	0.989272i	$0.453333\pi$
$720$	3306.52	−	10176.4i	0.171148	−	0.526741i
$721$	−282.347	+	868.975i	−0.0145841	+	0.0448853i
$722$	26215.6	−	19046.7i	1.35130	−	0.981780i
$723$	−365.597	−	265.622i	−0.0188059	−	0.0136633i
$724$	−7826.62	−	24087.8i	−0.401760	−	1.23649i
$725$	15344.8			0.786058
$726$	3390.65	−	6856.79i	0.173332	−	0.350522i
$727$	−31914.5			−1.62812			−0.814060	−	0.580781i	$-0.802747\pi$
$727$	−31914.5			−1.62812			−0.814060	+	0.580781i	$0.802747\pi$
$728$	6505.48	+	20021.8i	0.331194	+	1.01931i
$729$	10936.9	+	7946.12i	0.555652	+	0.403704i
$730$	−16002.1	+	11626.2i	−0.811322	+	0.589460i
$731$	−1459.75	+	4492.66i	−0.0738590	+	0.227315i
$732$	3795.16	−	11680.3i	0.191630	−	0.589776i
$733$	6591.34	−	4788.89i	0.332137	−	0.241312i	−0.409200	−	0.912445i	$-0.634192\pi$
$733$	6591.34	−	4788.89i	0.332137	−	0.241312i	0.741337	+	0.671133i	$0.234192\pi$
$734$	19831.0	+	14408.1i	0.997242	+	0.724539i
$735$	−1446.33	−	4451.34i	−0.0725831	−	0.223388i
$736$	1801.63			0.0902293
$737$	−304.558	+	4191.28i	−0.0152219	+	0.209481i
$738$	30805.9			1.53656
$739$	−11137.6	−	34278.0i	−0.554402	−	1.70627i	−0.697518	−	0.716567i	$-0.745712\pi$
$739$	−11137.6	−	34278.0i	−0.554402	−	1.70627i	0.143117	−	0.989706i	$-0.454288\pi$
$740$	−3474.96	−	2524.71i	−0.172624	−	0.125419i
$741$	−223.541	+	162.412i	−0.0110823	+	0.00805175i
$742$	3189.09	−	9814.99i	0.157783	−	0.485606i
$743$	−7198.98	+	22156.2i	−0.355457	+	1.09399i	0.600286	+	0.799785i	$0.295053\pi$
$743$	−7198.98	+	22156.2i	−0.355457	+	1.09399i	−0.955744	+	0.294200i	$0.904947\pi$
$744$	−458.447	+	333.081i	−0.0225907	+	0.0164131i
$745$	−31817.5	−	23116.7i	−1.56470	−	1.13682i
$746$	807.678	+	2485.78i	0.0396397	+	0.121998i
$747$	33322.1			1.63212
$748$	8659.73	−	2134.07i	0.423304	−	0.104317i
$749$	−7150.89			−0.348849
$750$	−585.029	−	1800.53i	−0.0284830	−	0.0876616i
$751$	17013.2	+	12360.8i	0.826659	+	0.600603i	0.918612	−	0.395160i	$-0.129311\pi$
$751$	17013.2	+	12360.8i	0.826659	+	0.600603i	−0.0919532	+	0.995763i	$0.529311\pi$
$752$	3349.13	−	2433.28i	0.162407	−	0.117996i
$753$	−2178.12	+	6703.55i	−0.105412	+	0.324424i
$754$	16166.8	−	49756.4i	0.780851	−	2.40321i
$755$	−36670.4	+	26642.6i	−1.76765	+	1.28427i
$756$	−6961.78	−	5058.03i	−0.334917	−	0.243332i
$757$	4236.05	+	13037.2i	0.203384	+	0.625952i	0.999776	+	0.0211709i	$0.00673940\pi$
$757$	4236.05	+	13037.2i	0.203384	+	0.625952i	−0.796392	+	0.604781i	$0.793261\pi$
$758$	−27860.3			−1.33500
$759$	−467.317	+	553.856i	−0.0223485	+	0.0264871i
$760$	1394.50			0.0665578
$761$	615.600	+	1894.62i	0.0293239	+	0.0902497i	0.964647	−	0.263544i	$-0.0848915\pi$
$761$	615.600	+	1894.62i	0.0293239	+	0.0902497i	−0.935323	+	0.353794i	$0.884891\pi$
$762$	10442.4	+	7586.87i	0.496443	+	0.360687i
$763$	−11769.4	+	8550.94i	−0.558426	+	0.405720i
$764$	16425.8	−	50553.6i	0.777836	−	2.39393i
$765$	2025.51	−	6233.88i	0.0957288	−	0.294623i
$766$	−23990.0	+	17429.8i	−1.13159	+	0.822145i
$767$	20522.9	+	14910.8i	0.966153	+	0.701952i
$768$	2447.02	+	7531.17i	0.114973	+	0.353851i
$769$	−29040.4			−1.36180			−0.680899	−	0.732377i	$-0.738411\pi$
$769$	−29040.4			−1.36180			−0.680899	+	0.732377i	$0.738411\pi$
$770$	−12900.5	−	20770.8i	−0.603769	−	0.972115i
$771$	−3045.48			−0.142257
$772$	16561.5	+	50971.2i	0.772102	+	2.37629i
$773$	−26880.1	−	19529.5i	−1.25072	−	0.908705i	−0.252461	−	0.967607i	$-0.581240\pi$
$773$	−26880.1	−	19529.5i	−1.25072	−	0.908705i	−0.998264	+	0.0589022i	$0.981240\pi$
$774$	−27145.1	+	19722.1i	−1.26061	+	0.915886i
$775$	−492.805	+	1516.70i	−0.0228414	+	0.0702986i
$776$	−13760.3	+	42349.8i	−0.636554	+	1.95911i
$777$	−182.248	+	132.411i	−0.00841457	+	0.00611354i
$778$	−37469.0	−	27222.9i	−1.72665	−	1.25448i
$779$	241.114	+	742.072i	0.0110896	+	0.0341303i
$780$	19625.8			0.900920
$781$	21855.9	+	8899.68i	1.00136	+	0.407754i
$782$	−1314.98			−0.0601326
$783$	2932.01	+	9023.80i	0.133821	+	0.411857i
$784$	5726.19	+	4160.32i	0.260850	+	0.189519i
$785$	−29101.6	+	21143.6i	−1.32316	+	0.961332i
$786$	321.847	−	990.543i	0.0146055	−	0.0449510i
$787$	2394.96	−	7370.94i	0.108477	−	0.333857i	−0.882054	−	0.471148i	$-0.843840\pi$
$787$	2394.96	−	7370.94i	0.108477	−	0.333857i	0.990531	+	0.137291i	$0.0438396\pi$
$788$	−43559.6	+	31647.9i	−1.96922	+	1.43072i
$789$	4211.57	+	3059.88i	0.190033	+	0.138067i
$790$	16065.4	+	49444.2i	0.723520	+	2.22677i
$791$	−7077.72			−0.318148
$792$	26031.8	+	10600.1i	1.16793	+	0.475579i
$793$	−52283.5			−2.34129
$794$	−17648.8	−	54317.4i	−0.788831	−	2.42777i
$795$	−3453.40	−	2509.04i	−0.154062	−	0.111933i
$796$	−25311.1	+	18389.6i	−1.12704	+	0.818846i
$797$	−804.931	+	2477.32i	−0.0357743	+	0.110102i	−0.967349	−	0.253448i	$-0.918435\pi$
$797$	−804.931	+	2477.32i	−0.0357743	+	0.110102i	0.931575	+	0.363550i	$0.118435\pi$
$798$	50.9379	−	156.771i	0.00225962	−	0.00695441i
$799$	2051.61	−	1490.58i	0.0908395	−	0.0659987i
$800$	9198.85	+	6683.35i	0.406535	+	0.295365i
$801$	−8376.60	−	25780.5i	−0.369504	−	1.13722i
$802$	−37405.7			−1.64693
$803$	−5327.64	−	8577.92i	−0.234133	−	0.376972i
$804$	2012.25			0.0882667
$805$	715.804	+	2203.02i	0.0313401	+	0.0964549i
$806$	4398.77	+	3195.89i	0.192233	+	0.139666i
$807$	1872.32	−	1360.32i	0.0816715	−	0.0593378i
$808$	13164.4	−	40516.0i	0.573173	−	1.76404i
$809$	1387.21	−	4269.40i	0.0602866	−	0.185543i	−0.916378	−	0.400315i	$-0.868901\pi$
$809$	1387.21	−	4269.40i	0.0602866	−	0.185543i	0.976664	+	0.214772i	$0.0689008\pi$
$810$	35362.1	−	25692.0i	1.53395	−	1.11448i
$811$	19598.9	+	14239.4i	0.848594	+	0.616539i	0.924758	−	0.380556i	$-0.124267\pi$
$811$	19598.9	+	14239.4i	0.848594	+	0.616539i	−0.0761643	+	0.997095i	$0.524267\pi$
$812$	6197.07	+	19072.6i	0.267826	+	0.824283i
$813$	−4189.96			−0.180748
$814$	2200.74	−	2608.27i	0.0947614	−	0.112309i
$815$	1622.07			0.0697161
$816$	−177.104	−	545.070i	−0.00759789	−	0.0233839i
$817$	−687.539	−	499.526i	−0.0294418	−	0.0213907i
$818$	−25974.3	+	18871.4i	−1.11023	+	0.806630i
$819$	−5501.16	+	16930.8i	−0.234708	+	0.722358i
$820$	17125.8	−	52707.8i	0.729341	−	2.24468i
$821$	−13545.4	+	9841.35i	−0.575809	+	0.418350i	−0.837211	−	0.546880i	$-0.815815\pi$
$821$	−13545.4	+	9841.35i	−0.575809	+	0.418350i	0.261402	+	0.965230i	$0.415815\pi$
$822$	11018.3	+	8005.27i	0.467528	+	0.339679i
$823$	−6678.21	−	20553.4i	−0.282853	−	0.870531i	−0.987034	−	0.160511i	$-0.948686\pi$
$823$	−6678.21	−	20553.4i	−0.282853	−	0.870531i	0.704181	−	0.710020i	$-0.251314\pi$
$824$	−2940.73			−0.124327
$825$	−4440.65	+	1094.34i	−0.187398	+	0.0461818i
$826$	−15133.5			−0.637486
$827$	−1584.31	−	4876.01i	−0.0666166	−	0.205025i	0.912207	−	0.409729i	$-0.134377\pi$
$827$	−1584.31	−	4876.01i	−0.0666166	−	0.205025i	−0.978824	+	0.204704i	$0.934377\pi$
$828$	−4855.31	−	3527.59i	−0.203785	−	0.148058i
$829$	13451.0	−	9772.72i	0.563537	−	0.409434i	−0.269215	−	0.963080i	$-0.586764\pi$
$829$	13451.0	−	9772.72i	0.563537	−	0.409434i	0.832752	+	0.553646i	$0.186764\pi$
$830$	28830.1	−	88730.0i	1.20567	−	3.71068i
$831$	−572.294	+	1761.34i	−0.0238901	+	0.0735261i
$832$	44720.4	−	32491.3i	1.86346	−	1.35389i
$833$	3507.75	+	2548.53i	0.145902	+	0.106004i
$834$	4397.40	+	13533.8i	0.182577	+	0.561915i
$835$	25343.5			1.05036
$836$	−116.287	+	1600.32i	−0.00481084	+	0.0662059i
$837$	−986.084			−0.0407217
$838$	−12357.6	−	38032.8i	−0.509411	−	1.56780i
$839$	−2730.34	−	1983.71i	−0.112350	−	0.0816272i	0.530191	−	0.847878i	$-0.322120\pi$
$839$	−2730.34	−	1983.71i	−0.112350	−	0.0816272i	−0.642542	+	0.766251i	$0.722120\pi$
$840$	−4202.61	+	3053.38i	−0.172624	+	0.125418i
$841$	−703.685	+	2165.72i	−0.0288525	+	0.0887990i
$842$	−8652.28	+	26629.0i	−0.354130	+	1.08990i
$843$	−1495.31	+	1086.40i	−0.0610926	+	0.0443864i
$844$	53949.2	+	39196.4i	2.20025	+	1.59857i
$845$	−15562.6	−	47896.8i	−0.633574	−	1.94994i
$846$	18012.5			0.732012
$847$	11053.1	−	5800.03i	0.448395	−	0.235291i
$848$	6455.26			0.261409
$849$	2183.54	+	6720.26i	0.0882674	+	0.271659i
$850$	−6714.12	−	4878.10i	−0.270932	−	0.196844i
$851$	−261.558	+	190.033i	−0.0105359	+	0.00765481i
$852$	3491.85	−	10746.8i	0.140409	−	0.432136i
$853$	2588.28	−	7965.92i	0.103894	−	0.319751i	−0.885576	−	0.464495i	$-0.846236\pi$
$853$	2588.28	−	7965.92i	0.103894	−	0.319751i	0.989469	+	0.144744i	$0.0462358\pi$
$854$	25233.7	−	18333.4i	1.01110	−	0.734607i
$855$	954.009	+	693.128i	0.0381595	+	0.0277245i
$856$	−7112.08	−	21888.7i	−0.283979	−	0.873997i
$857$	44120.2			1.75860			0.879298	−	0.476273i	$-0.158013\pi$
$857$	44120.2			1.75860			0.879298	+	0.476273i	$0.158013\pi$
$858$	−1130.08	+	15552.0i	−0.0449656	+	0.618808i
$859$	16898.3			0.671203			0.335601	−	0.942004i	$-0.391060\pi$
$859$	16898.3			0.671203			0.335601	+	0.942004i	$0.391060\pi$
$860$	18653.1	+	57408.3i	0.739611	+	2.27629i
$861$	−2351.47	−	1708.45i	−0.0930755	−	0.0676233i
$862$	−37774.0	+	27444.4i	−1.49256	+	1.08441i
$863$	1283.34	−	3949.73i	0.0506206	−	0.155794i	−0.922551	−	0.385876i	$-0.873899\pi$
$863$	1283.34	−	3949.73i	0.0506206	−	0.155794i	0.973171	+	0.230082i	$0.0738993\pi$
$864$	−2172.60	+	6686.57i	−0.0855478	+	0.263289i
$865$	9176.29	−	6666.97i	0.360697	−	0.262062i
$866$	−17977.0	−	13061.1i	−0.705409	−	0.512510i
$867$	−108.490	−	333.899i	−0.00424974	−	0.0130794i
$868$	−2084.18			−0.0814996
$869$	−25769.8	+	6350.62i	−1.00596	+	0.247906i
$870$	12909.4			0.503070
$871$	−2647.16	−	8147.12i	−0.102980	−	0.316940i
$872$	−37879.8	−	27521.3i	−1.47107	−	1.06879i
$873$	−30463.4	+	22133.0i	−1.18102	+	0.858061i
$874$	73.1047	−	224.993i	0.00282929	−	0.00870767i
$875$	954.676	−	2938.19i	0.0368845	−	0.113519i
$876$	−3911.77	+	2842.07i	−0.150875	+	0.109617i
$877$	−20855.7	−	15152.6i	−0.803018	−	0.583427i	0.108780	−	0.994066i	$-0.465306\pi$
$877$	−20855.7	−	15152.6i	−0.803018	−	0.583427i	−0.911798	+	0.410639i	$0.865306\pi$
$878$	16411.5	+	50509.3i	0.630820	+	1.94146i
$879$	−4857.08			−0.186377
$880$	9862.78	−	11689.2i	0.377812	−	0.447776i
$881$	41808.9			1.59884			0.799420	−	0.600773i	$-0.205140\pi$
$881$	41808.9			1.59884			0.799420	+	0.600773i	$0.205140\pi$
$882$	9516.78	+	29289.6i	0.363318	+	1.11818i
$883$	5917.83	+	4299.55i	0.225539	+	0.163864i	0.694816	−	0.719187i	$-0.255486\pi$
$883$	5917.83	+	4299.55i	0.225539	+	0.163864i	−0.469278	+	0.883051i	$0.655486\pi$
$884$	−14708.6	+	10686.5i	−0.559621	+	0.406589i
$885$	−1934.32	+	5953.23i	−0.0734707	+	0.226119i
$886$	−26565.5	+	81760.3i	−1.00732	+	3.10022i
$887$	−6316.44	+	4589.16i	−0.239104	+	0.173719i	−0.700884	−	0.713275i	$-0.747211\pi$
$887$	−6316.44	+	4589.16i	−0.239104	+	0.173719i	0.461780	+	0.886995i	$0.347211\pi$
$888$	−586.568	−	426.166i	−0.0221666	−	0.0161050i
$889$	6508.86	+	20032.2i	0.245557	+	0.755746i
$890$	−75895.7			−2.85846
$891$	11773.2	+	18955.8i	0.442669	+	0.712731i
$892$	30112.4			1.13031
$893$	140.981	+	433.896i	0.00528305	+	0.0162596i
$894$	−12104.8	−	8794.68i	−0.452848	−	0.329013i
$895$	−1943.07	+	1411.72i	−0.0725695	+	0.0527248i
$896$	−7635.77	+	23500.5i	−0.284702	+	0.876224i
$897$	456.487	−	1404.92i	0.0169918	−	0.0522954i
$898$	−4128.16	+	2999.28i	−0.153406	+	0.111456i
$899$	1859.15	+	1350.75i	0.0689722	+	0.0501112i
$900$	−11704.5	−	36022.8i	−0.433501	−	1.33418i
$901$	3954.36			0.146214
$902$	40780.9	+	16605.9i	1.50538	+	0.612990i
$903$	3165.79			0.116668
$904$	−7039.31	−	21664.8i	−0.258987	−	0.797079i
$905$	−21524.4	−	15638.4i	−0.790603	−	0.574406i
$906$	−13951.1	+	10136.1i	−0.511584	+	0.371688i
$907$	−4728.43	+	14552.6i	−0.173104	+	0.532758i	−0.999542	−	0.0302695i	$-0.990363\pi$
$907$	−4728.43	+	14552.6i	−0.173104	+	0.532758i	0.826438	+	0.563027i	$0.190363\pi$
$908$	−19096.1	+	58771.7i	−0.697936	+	2.14803i
$909$	29144.3	−	21174.5i	1.06343	−	0.772624i
$910$	40323.8	+	29297.0i	1.46892	+	1.06724i
$911$	−6030.61	−	18560.3i	−0.219323	−	0.675006i	−0.998818	−	0.0485985i	$-0.984525\pi$
$911$	−6030.61	−	18560.3i	−0.219323	−	0.675006i	0.779496	−	0.626408i	$-0.215475\pi$
$912$	103.107			0.00374366
$913$	44111.8	+	17962.3i	1.59900	+	0.651111i
$914$	−33735.1			−1.22085
$915$	−3986.68	−	12269.7i	−0.144039	−	0.443306i
$916$	26563.6	+	19299.6i	0.958173	+	0.696154i
$917$	1375.00	−	998.996i	0.0495164	−	0.0359757i
$918$	1585.75	−	4880.44i	0.0570126	−	0.175467i
$919$	2179.99	−	6709.33i	0.0782495	−	0.240827i	−0.904278	−	0.426944i	$-0.859590\pi$
$919$	2179.99	−	6709.33i	0.0782495	−	0.240827i	0.982528	+	0.186117i	$0.0595902\pi$
$920$	−6031.48	+	4382.13i	−0.216143	+	0.157037i
$921$	8530.76	+	6197.96i	0.305210	+	0.221748i
$922$	6111.82	+	18810.2i	0.218310	+	0.671890i
$923$	−48105.0			−1.71549
$924$	−3153.57	−	5077.49i	−0.112278	−	0.180776i
$925$	−2040.43			−0.0725286
$926$	20812.1	+	64053.1i	0.738584	+	2.27313i
$927$	−2011.82	−	1461.67i	−0.0712802	−	0.0517881i
$928$	13255.5	−	9630.69i	0.468894	−	0.340671i
$929$	−3892.78	+	11980.7i	−0.137479	+	0.423116i	−0.995967	−	0.0897164i	$-0.971404\pi$
$929$	−3892.78	+	11980.7i	−0.137479	+	0.423116i	0.858488	+	0.512833i	$0.171404\pi$
$930$	−414.592	+	1275.98i	−0.0146183	+	0.0449905i
$931$	−631.060	+	458.492i	−0.0222150	+	0.0161401i
$932$	52254.0	+	37964.8i	1.83652	+	1.33431i
$933$	−2729.56	−	8400.72i	−0.0957789	−	0.294777i
$934$	7788.23			0.272847
$935$	6041.75	−	7160.57i	0.211322	−	0.250455i
$936$	−57296.3			−2.00084
$937$	−5837.39	−	17965.7i	−0.203521	−	0.626374i	−0.999771	−	0.0214057i	$-0.993186\pi$
$937$	−5837.39	−	17965.7i	−0.203521	−	0.626374i	0.796250	−	0.604968i	$-0.206814\pi$
$938$	4134.42	+	3003.83i	0.143916	+	0.104561i
$939$	−105.195	+	76.4289i	−0.00365593	+	0.00265619i
$940$	10013.6	−	30818.7i	0.347455	−	1.06936i
$941$	−9762.38	+	30045.5i	−0.338198	+	1.04087i	0.626927	+	0.779078i	$0.284312\pi$
$941$	−9762.38	+	30045.5i	−0.338198	+	1.04087i	−0.965125	+	0.261789i	$0.915688\pi$
$942$	−11071.6	+	8043.99i	−0.382943	+	0.278224i
$943$	−3374.77	−	2451.92i	−0.116541	−	0.0846716i
$944$	−2925.18	−	9002.78i	−0.100854	−	0.310398i
$945$	−9039.50			−0.311169
$946$	−46565.9	+	11475.5i	−1.60041	+	0.394399i
$947$	48580.1			1.66699			0.833495	−	0.552527i	$-0.186336\pi$
$947$	48580.1			1.66699			0.833495	+	0.552527i	$0.186336\pi$
$948$	3927.24	+	12086.8i	0.134547	+	0.414094i
$949$	16652.9	+	12099.0i	0.569627	+	0.413858i
$950$	1207.90	−	877.592i	0.0412521	−	0.0299714i
$951$	2949.66	−	9078.13i	0.100578	−	0.309546i
$952$	1487.07	−	4576.73i	0.0506262	−	0.155812i
$953$	24537.8	−	17827.8i	0.834059	−	0.605979i	−0.0866461	−	0.996239i	$-0.527615\pi$
$953$	24537.8	−	17827.8i	0.834059	−	0.605979i	0.920705	+	0.390260i	$0.127615\pi$
$954$	22723.3	+	16509.4i	0.771167	+	0.560286i
$955$	−17254.8	−	53104.8i	−0.584662	−	1.79940i
$956$	−75959.3			−2.56977
$957$	−477.632	+	6573.08i	−0.0161334	+	0.222025i
$958$	41896.4			1.41295
$959$	6867.81	+	21136.9i	0.231255	+	0.711728i
$960$	11035.0	+	8017.37i	0.370992	+	0.269541i
$961$	23908.2	−	17370.3i	0.802531	−	0.583073i
$962$	−2149.73	+	6616.20i	−0.0720480	+	0.221741i
$963$	6014.12	−	18509.6i	0.201249	−	0.619379i
$964$	4327.73	−	3144.28i	0.144592	−	0.105052i
$965$	45546.8	+	33091.7i	1.51938	+	1.10389i
$966$	272.325	+	838.130i	0.00907030	+	0.0279155i
$967$	3638.39			0.120996			0.0604978	−	0.998168i	$-0.480731\pi$
$967$	3638.39			0.120996			0.0604978	+	0.998168i	$0.480731\pi$
$968$	28747.0	+	28064.9i	0.954506	+	0.931859i
$969$	63.1613			0.00209395
$970$	32578.8	+	100267.i	1.07839	+	3.31895i
$971$	−36765.1	−	26711.4i	−1.21509	−	0.882812i	−0.219403	−	0.975634i	$-0.570411\pi$
$971$	−36765.1	−	26711.4i	−1.21509	−	0.882812i	−0.995683	+	0.0928226i	$0.970411\pi$
$972$	28687.3	−	20842.5i	0.946652	−	0.687783i
$973$	−7175.87	+	22085.0i	−0.236431	+	0.727661i
$974$	6190.50	−	19052.4i	0.203651	−	0.626774i
$975$	7542.49	−	5479.94i	0.247747	−	0.179999i
$976$	15783.8	+	11467.6i	0.517650	+	0.376095i
$977$	−17848.1	−	54930.8i	−0.584454	−	1.79876i	−0.601454	−	0.798908i	$-0.705412\pi$
$977$	−17848.1	−	54930.8i	−0.584454	−	1.79876i	0.0170001	−	0.999855i	$-0.494588\pi$
$978$	617.111			0.0201769
$979$	2808.03	−	38643.7i	0.0916702	−	1.26155i
$980$	55404.1			1.80594
$981$	−12235.1	−	37655.7i	−0.398202	−	1.22554i
$982$	56691.2	+	41188.6i	1.84225	+	1.33847i
$983$	−16480.5	+	11973.8i	−0.534737	+	0.388509i	−0.822127	−	0.569304i	$-0.807213\pi$
$983$	−16480.5	+	11973.8i	−0.534737	+	0.388509i	0.287390	+	0.957814i	$0.407213\pi$
$984$	2890.81	−	8896.99i	0.0936541	−	0.288238i
$985$	−17478.0	+	53791.6i	−0.565375	+	1.74004i
$986$	−9675.03	+	7029.32i	−0.312491	+	0.227038i
$987$	−1374.93	−	998.943i	−0.0443408	−	0.0322155i
$988$	−1010.74	−	3110.74i	−0.0325465	−	0.100168i
$989$	4543.46			0.146080
$990$	64613.5	−	15923.1i	2.07429	−	0.511182i
$991$	−26839.8			−0.860336			−0.430168	−	0.902749i	$-0.641546\pi$
$991$	−26839.8			−0.860336			−0.430168	+	0.902749i	$0.641546\pi$
$992$	526.202	+	1619.48i	0.0168416	+	0.0518333i
$993$	−4520.34	−	3284.22i	−0.144460	−	0.104956i
$994$	23217.0	−	16868.2i	0.740845	−	0.538255i
$995$	−10155.9	+	31256.6i	−0.323581	+	0.995879i
$996$	7047.62	−	21690.3i	0.224209	−	0.690045i
$997$	−6080.71	+	4417.90i	−0.193158	+	0.140337i	−0.680161	−	0.733063i	$-0.738090\pi$
$997$	−6080.71	+	4417.90i	−0.193158	+	0.140337i	0.487003	+	0.873400i	$0.338090\pi$
$998$	35598.9	+	25864.1i	1.12912	+	0.820356i
$999$	−389.875	−	1199.91i	−0.0123474	−	0.0380015i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	187.4.g.a.137.20	yes	88
11.3	even	5		2057.4.a.t.1.40		44
11.8	odd	10		2057.4.a.s.1.5		44
11.9	even	5	inner	187.4.g.a.86.20	✓	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.4.g.a.86.20	✓	88	11.9	even	5	inner
187.4.g.a.137.20	yes	88	1.1	even	1	trivial
2057.4.a.s.1.5		44	11.8	odd	10
2057.4.a.t.1.40		44	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:	\( N \)	\(=\)	\( 187 = 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	187.g (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.46189 + 4.49925i) q^{2} +(0.982808 + 0.714052i) q^{3} +(-11.6339 + 8.45255i) q^{4} +(-4.66803 + 14.3667i) q^{5} +(-1.77593 + 5.46576i) q^{6} +(-7.58718 + 5.51241i) q^{7} +(-24.4194 - 17.7417i) q^{8} +(-7.88742 - 24.2750i) q^{9} -71.4635 q^{10} +(2.64405 - 36.3869i) q^{11} -17.4695 q^{12} +(22.9815 + 70.7299i) q^{13} +(-35.8933 - 26.0780i) q^{14} +(-14.8463 + 10.7865i) q^{15} +(8.57567 - 26.3932i) q^{16} +(5.25329 - 16.1680i) q^{17} +(97.6885 - 70.9748i) q^{18} +(2.47428 + 1.79767i) q^{19} +(-67.1278 - 206.598i) q^{20} -11.3929 q^{21} +(167.579 - 41.2976i) q^{22} -16.3508 q^{23} +(-11.3311 - 34.8734i) q^{24} +(-83.4847 - 60.6552i) q^{25} +(-284.635 + 206.799i) q^{26} +(19.7176 - 60.6844i) q^{27} +(41.6749 - 128.262i) q^{28} +(-120.301 + 87.4039i) q^{29} +(-70.2349 - 51.0286i) q^{30} +(-4.77558 - 14.6977i) q^{31} -110.186 q^{32} +(28.5807 - 33.8734i) q^{33} +80.4234 q^{34} +(-43.7780 - 134.735i) q^{35} +(296.947 + 215.745i) q^{36} +(15.9967 - 11.6223i) q^{37} +(-4.47102 + 13.7604i) q^{38} +(-27.9184 + 85.9240i) q^{39} +(368.881 - 268.007i) q^{40} +(206.398 + 149.957i) q^{41} +(-16.6552 - 51.2594i) q^{42} -277.874 q^{43} +(276.802 + 445.672i) q^{44} +385.570 q^{45} +(-23.9031 - 73.5661i) q^{46} +(120.683 + 87.6813i) q^{47} +(27.2744 - 19.8160i) q^{48} +(-78.8142 + 242.565i) q^{49} +(150.857 - 464.290i) q^{50} +(16.7077 - 12.1389i) q^{51} +(-865.214 - 628.615i) q^{52} +(71.8803 + 221.225i) q^{53} +301.859 q^{54} +(510.418 + 207.841i) q^{55} +283.074 q^{56} +(1.14811 + 3.53353i) q^{57} +(-569.119 - 413.489i) q^{58} +(275.958 - 200.495i) q^{59} +(81.5480 - 250.979i) q^{60} +(-217.245 + 668.611i) q^{61} +(59.1472 - 42.9730i) q^{62} +(193.657 + 140.700i) q^{63} +(-229.686 - 706.899i) q^{64} -1123.43 q^{65} +(194.187 + 79.0725i) q^{66} -115.186 q^{67} +(75.5441 + 232.501i) q^{68} +(-16.0697 - 11.6753i) q^{69} +(542.206 - 393.936i) q^{70} +(-199.883 + 615.176i) q^{71} +(-238.074 + 732.716i) q^{72} +(223.920 - 162.687i) q^{73} +(75.6769 + 54.9825i) q^{74} +(-38.7385 - 119.225i) q^{75} -43.9805 q^{76} +(180.519 + 290.649i) q^{77} -427.407 q^{78} +(-224.806 - 691.880i) q^{79} +(339.152 + 246.408i) q^{80} +(-494.827 + 359.513i) q^{81} +(-372.962 + 1147.86i) q^{82} +(-403.425 + 1241.61i) q^{83} +(132.544 - 96.2989i) q^{84} +(207.758 + 150.945i) q^{85} +(-406.223 - 1250.22i) q^{86} -180.644 q^{87} +(-710.133 + 841.637i) q^{88} +1062.02 q^{89} +(563.662 + 1734.77i) q^{90} +(-564.257 - 409.957i) q^{91} +(190.224 - 138.206i) q^{92} +(5.80145 - 17.8550i) q^{93} +(-218.074 + 671.163i) q^{94} +(-37.3766 + 27.1557i) q^{95} +(-108.292 - 78.6785i) q^{96} +(-455.880 - 1403.05i) q^{97} -1206.58 q^{98} +(-904.147 + 222.815i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 2 q^{2} + 14 q^{3} - 82 q^{4} + 42 q^{5} + 12 q^{6} + 16 q^{7} + 104 q^{8} - 178 q^{9} - 130 q^{10} - 20 q^{11} - 674 q^{12} + 24 q^{13} + 173 q^{14} + 280 q^{15} + 242 q^{16} - 374 q^{17} - 265 q^{18}+ \cdots + 5224 q^{99}+O(q^{100}) \) 88 * q + 2 * q^2 + 14 * q^3 - 82 * q^4 + 42 * q^5 + 12 * q^6 + 16 * q^7 + 104 * q^8 - 178 * q^9 - 130 * q^10 - 20 * q^11 - 674 * q^12 + 24 * q^13 + 173 * q^14 + 280 * q^15 + 242 * q^16 - 374 * q^17 - 265 * q^18 - 92 * q^19 + 347 * q^20 - 480 * q^21 - 248 * q^22 - 1312 * q^23 + 512 * q^24 + 146 * q^25 + 1045 * q^26 + 314 * q^27 + 51 * q^28 - 526 * q^29 - 712 * q^30 + 1424 * q^31 - 166 * q^32 - 1036 * q^33 + 34 * q^34 - 446 * q^35 - 260 * q^36 + 1344 * q^37 - 1006 * q^38 - 92 * q^39 - 272 * q^40 - 1002 * q^41 + 649 * q^42 + 764 * q^43 + 1894 * q^44 - 2452 * q^45 + 1154 * q^46 + 462 * q^47 + 1399 * q^48 - 1872 * q^49 - 2336 * q^50 + 238 * q^51 - 2266 * q^52 + 1606 * q^53 + 4800 * q^54 + 3492 * q^55 + 54 * q^56 + 2012 * q^57 + 603 * q^58 + 286 * q^59 - 5684 * q^60 - 1348 * q^61 + 508 * q^62 - 2936 * q^63 - 1576 * q^64 - 304 * q^65 + 6572 * q^66 - 6884 * q^67 - 969 * q^68 - 878 * q^69 + 1370 * q^70 - 1432 * q^71 + 753 * q^72 + 3480 * q^73 - 6737 * q^74 - 694 * q^75 + 2522 * q^76 + 3870 * q^77 + 2240 * q^78 + 2118 * q^79 + 1640 * q^80 - 1950 * q^81 - 3285 * q^82 + 5758 * q^83 + 7968 * q^84 - 306 * q^85 - 5066 * q^86 + 3936 * q^87 - 97 * q^88 - 5984 * q^89 + 1819 * q^90 + 2240 * q^91 + 2111 * q^92 - 4076 * q^93 - 1788 * q^94 + 10810 * q^95 - 15349 * q^96 + 3358 * q^97 + 4604 * q^98 + 5224 * q^99

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