LMFDB - Embedded newform 187.4.g.a.86.20

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			86.20
Character	$\chi$	$=$	187.86
Dual form			187.4.g.a.137.20

$q$-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 $\left(\mathbb{Z}/187\mathbb{Z}\right)^\times$.

$n$	$35$	$122$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$

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	−0.263020	−	0.964791i	$-0.584718\pi$
$2$	1.46189	−	4.49925i	0.516857	−	1.59072i	0.779877	−	0.625933i	$-0.215282\pi$
$3$	0.982808	−	0.714052i	0.189141	−	0.137419i	−0.489185	−	0.872180i	$-0.662706\pi$
$3$	0.982808	−	0.714052i	0.189141	−	0.137419i	0.678326	+	0.734761i	$0.262706\pi$
$4$	−11.6339	−	8.45255i	−1.45424	−	1.05657i
$5$	−4.66803	−	14.3667i	−0.417521	−	1.28500i	−0.909976	−	0.414660i	$-0.863901\pi$
$5$	−4.66803	−	14.3667i	−0.417521	−	1.28500i	0.492455	−	0.870338i	$-0.336099\pi$
$6$	−1.77593	−	5.46576i	−0.120837	−	0.371898i
$7$	−7.58718	−	5.51241i	−0.409669	−	0.297642i	0.363799	−	0.931478i	$-0.381480\pi$
$7$	−7.58718	−	5.51241i	−0.409669	−	0.297642i	−0.773468	+	0.633836i	$0.781480\pi$
$8$	−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	−0.333849	−	0.942627i	$-0.608347\pi$
$13$	22.9815	−	70.7299i	0.490303	−	1.50900i	0.824151	−	0.566370i	$-0.191653\pi$
$14$	−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	−0.572747	−	0.819732i	$-0.694122\pi$
$19$	2.47428	−	1.79767i	0.0298757	−	0.0217060i	0.602623	+	0.798026i	$0.294122\pi$
$20$	−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	0.131736	−	0.991285i	$-0.457945\pi$
$29$	−120.301	−	87.4039i	−0.770323	−	0.559673i	−0.902059	+	0.431612i	$0.857945\pi$
$30$	−70.2349	+	51.0286i	−0.427436	+	0.310550i
$31$	−4.77558	+	14.6977i	−0.0276683	+	0.0851544i	−0.963937	−	0.266130i	$-0.914255\pi$
$31$	−4.77558	+	14.6977i	−0.0276683	+	0.0851544i	0.936269	+	0.351284i	$0.114255\pi$
$32$	−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	0.622756	−	0.782416i	$-0.286013\pi$
$37$	15.9967	+	11.6223i	0.0710767	+	0.0516402i	−0.551680	+	0.834056i	$0.686013\pi$
$38$	−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	−0.120636	−	0.992697i	$-0.538494\pi$
$41$	206.398	−	149.957i	0.786195	−	0.571204i	0.906832	+	0.421492i	$0.138494\pi$
$42$	−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	−0.384551	−	0.923104i	$-0.625644\pi$
$47$	120.683	−	87.6813i	0.374541	−	0.272120i	0.759091	+	0.650984i	$0.225644\pi$
$48$	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	−0.813675	−	0.581320i	$-0.802537\pi$
$53$	71.8803	−	221.225i	0.186293	−	0.573351i	0.999968	+	0.00796898i	$0.00253663\pi$
$54$	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	0.849036	−	0.528335i	$-0.177184\pi$
$59$	275.958	+	200.495i	0.608926	+	0.442410i	−0.240110	+	0.970746i	$0.577184\pi$
$60$	81.5480	+	250.979i	0.175463	+	0.540021i
$61$	−217.245	−	668.611i	−0.455990	−	1.40339i	−0.869969	−	0.493106i	$-0.835862\pi$
$61$	−217.245	−	668.611i	−0.455990	−	1.40339i	0.413980	−	0.910286i	$-0.364138\pi$
$62$	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	−0.967159	−	0.254171i	$-0.918197\pi$
$71$	−199.883	−	615.176i	−0.334109	−	1.02828i	0.633050	−	0.774111i	$-0.281803\pi$
$72$	−238.074	−	732.716i	−0.389685	−	1.19933i
$73$	223.920	+	162.687i	0.359012	+	0.260837i	0.752640	−	0.658432i	$-0.228780\pi$
$73$	223.920	+	162.687i	0.359012	+	0.260837i	−0.393628	+	0.919270i	$0.628780\pi$
$74$	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	0.653419	+	0.756996i	$0.273334\pi$
$79$	−224.806	+	691.880i	−0.320159	+	0.985349i	−0.973578	+	0.228353i	$0.926666\pi$
$80$	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	−0.746840	−	0.665004i	$-0.768430\pi$
$83$	−403.425	−	1241.61i	−0.533513	−	1.64198i	0.213327	−	0.976981i	$-0.431570\pi$
$84$	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	0.365787	+	0.930699i	$0.380800\pi$
$97$	−455.880	+	1403.05i	−0.477192	+	1.46865i	−0.842979	+	0.537947i	$0.819200\pi$
$98$	−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	−0.468765	−	0.883323i	$-0.655301\pi$
$101$	436.139	−	1342.30i	0.429678	−	1.32241i	0.898443	−	0.439090i	$-0.144699\pi$
$102$	79.0407	−	57.4265i	0.0767274	−	0.0557457i
$103$	78.8199	+	57.2660i	0.0754015	+	0.0547824i	0.624847	−	0.780747i	$-0.285161\pi$
$103$	78.8199	+	57.2660i	0.0754015	+	0.0547824i	−0.549446	+	0.835529i	$0.685161\pi$
$104$	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	−0.273145	−	0.961973i	$-0.588064\pi$
$107$	616.872	−	448.184i	0.557339	−	0.404930i	0.830484	+	0.557042i	$0.188064\pi$
$108$	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	−0.303885	−	0.952709i	$-0.598284\pi$
$113$	610.560	−	443.598i	0.508289	−	0.369293i	0.812174	+	0.583415i	$0.198284\pi$
$114$	−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	0.832086	+	0.554646i	$0.187146\pi$
$127$	694.036	+	2136.02i	0.484927	+	1.49245i	−0.347159	+	0.937806i	$0.612854\pi$
$128$	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	0.869148	+	0.494552i	$0.164668\pi$
$137$	732.311	+	2253.82i	0.456683	+	1.40553i	−0.412465	+	0.910973i	$0.635332\pi$
$138$	29.0379	+	89.3694i	0.0179121	+	0.0551277i
$139$	2003.21	+	1455.42i	1.22238	+	0.888108i	0.996295	−	0.0860004i	$-0.0274086\pi$
$139$	2003.21	+	1455.42i	1.22238	+	0.888108i	0.226081	+	0.974109i	$0.427409\pi$
$140$	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	−0.885371	−	0.464886i	$-0.846095\pi$
$149$	−804.524	−	2476.07i	−0.442344	−	1.36139i	0.443027	−	0.896508i	$-0.353905\pi$
$150$	479.790	+	348.588i	0.261165	+	0.189747i
$151$	2427.53	−	1763.71i	1.30828	−	0.950519i	0.308278	−	0.951296i	$-0.400247\pi$
$151$	2427.53	−	1763.71i	1.30828	−	0.950519i	1.00000		0.000777286i	$0.000247418\pi$
$152$	−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	0.0217491	−	0.999763i	$-0.493076\pi$
$157$	1926.49	−	1399.67i	0.979302	−	0.711504i	0.957552	+	0.288259i	$0.0930765\pi$
$158$	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	−0.958712	−	0.284378i	$-0.908213\pi$
$163$	−33.1819	+	102.123i	−0.0159448	+	0.0490731i	0.942768	+	0.333451i	$0.108213\pi$
$164$	−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	0.756157	+	0.654390i	$0.227075\pi$
$167$	−518.439	+	1595.59i	−0.240228	+	0.739345i	−0.996385	+	0.0849550i	$0.972925\pi$
$168$	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	−0.713210	−	0.700950i	$-0.752759\pi$
$173$	−607.458	+	441.344i	−0.266961	+	0.193958i	0.446249	+	0.894909i	$0.352759\pi$
$174$	−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	−0.560606	−	0.828083i	$-0.689432\pi$
$179$	128.629	−	93.4542i	0.0537104	−	0.0390229i	0.614317	+	0.789060i	$0.289432\pi$
$180$	−4485.70	−	3259.05i	−1.85747	−	1.34953i
$181$	−544.258	−	1675.05i	−0.223505	−	0.687877i	−0.998440	−	0.0558364i	$-0.982217\pi$
$181$	−544.258	−	1675.05i	−0.223505	−	0.687877i	0.774935	−	0.632041i	$-0.217783\pi$
$182$	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	−0.146769	−	0.989171i	$-0.546887\pi$
$191$	−2990.43	−	2172.68i	−1.13288	−	0.823085i	−0.986111	+	0.166085i	$0.946887\pi$
$192$	279.026	+	858.754i	0.104880	+	0.322788i
$193$	1151.68	+	3544.50i	0.429532	+	1.32196i	0.898587	+	0.438795i	$0.144594\pi$
$193$	1151.68	+	3544.50i	0.429532	+	1.32196i	−0.469055	+	0.883169i	$0.655406\pi$
$194$	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	0.388224	+	0.921565i	$0.373089\pi$
$211$	−1432.98	+	4410.27i	−0.467538	+	1.43893i	−0.855762	+	0.517370i	$0.826911\pi$
$212$	−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	−0.812337	−	0.583189i	$-0.801805\pi$
$223$	−1694.08	+	1230.82i	−0.508717	+	0.369605i	0.303620	+	0.952793i	$0.401805\pi$
$224$	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	0.965565	−	0.260164i	$-0.0837765\pi$
$227$	3476.57	+	2525.87i	1.01651	+	0.738538i	0.0509455	+	0.998701i	$0.483777\pi$
$228$	−43.2244	+	31.4044i	−0.0125553	+	0.00912195i
$229$	−705.574	+	2171.53i	−0.203606	+	0.626633i	0.796162	+	0.605083i	$0.206860\pi$
$229$	−705.574	+	2171.53i	−0.203606	+	0.626633i	−0.999768	+	0.0215502i	$0.993140\pi$
$230$	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	0.542352	+	0.840152i	$0.317534\pi$
$233$	−1387.96	+	4271.69i	−0.390249	+	1.20106i	−0.932600	+	0.360911i	$0.882466\pi$
$234$	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	0.167231	−	0.985918i	$-0.446517\pi$
$239$	4273.36	−	3104.78i	1.15657	−	0.840299i	0.989341	+	0.145619i	$0.0465174\pi$
$240$	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	−0.425028	−	0.905180i	$-0.639736\pi$
$251$	1792.96	−	5518.15i	0.450878	−	1.38766i	0.875907	−	0.482481i	$-0.160264\pi$
$252$	−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	0.313787	−	0.949494i	$-0.398402\pi$
$257$	−2028.16	−	1473.55i	−0.492270	−	0.357655i	−0.806057	+	0.591838i	$0.798402\pi$
$258$	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	0.995343	−	0.0963953i	$-0.0307313\pi$
$269$	588.701	+	1811.83i	0.133434	+	0.410667i	−0.861909	+	0.507063i	$0.830731\pi$
$270$	−1409.09	−	4336.72i	−0.317608	−	0.977497i
$271$	−2790.33	−	2027.30i	−0.625464	−	0.454426i	0.229362	−	0.973341i	$-0.426336\pi$
$271$	−2790.33	−	2027.30i	−0.625464	−	0.454426i	−0.854826	+	0.518915i	$0.826336\pi$
$272$	−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	−0.886874	−	0.462011i	$-0.847128\pi$
$277$	471.095	−	1449.88i	0.102185	−	0.314494i	0.989060	+	0.147517i	$0.0471280\pi$
$278$	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	0.888666	−	0.458556i	$-0.151633\pi$
$281$	−470.158	−	1447.00i	−0.0998124	−	0.307191i	−0.988478	+	0.151365i	$0.951633\pi$
$282$	−693.570	−	503.908i	−0.146459	−	0.106409i
$283$	4705.72	−	3418.91i	0.988431	−	0.718137i	0.0288542	−	0.999584i	$-0.490814\pi$
$283$	4705.72	−	3418.91i	0.988431	−	0.718137i	0.959577	+	0.281446i	$0.0908141\pi$
$284$	−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	0.216603	−	0.976260i	$-0.430502\pi$
$293$	−3234.61	−	2350.08i	−0.644941	−	0.468577i	−0.861544	+	0.507683i	$0.830502\pi$
$294$	−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	−0.976368	−	0.216113i	$-0.930662\pi$
$311$	−5882.43	+	4273.84i	−1.07255	+	0.779251i	−0.0961783	+	0.995364i	$0.530662\pi$
$312$	2206.19	+	1602.89i	0.400323	+	0.290852i
$313$	−33.0758	−	101.797i	−0.00597302	−	0.0183831i	0.948026	−	0.318194i	$-0.103076\pi$
$313$	−33.0758	−	101.797i	−0.00597302	−	0.0183831i	−0.953999	+	0.299811i	$0.903076\pi$
$314$	−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	0.467722	+	0.883876i	$0.345075\pi$
$317$	−2428.07	+	7472.84i	−0.430202	+	1.32403i	−0.897924	+	0.440151i	$0.854925\pi$
$318$	−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	−0.307926	−	0.951410i	$-0.599635\pi$
$337$	−8091.47	−	5878.80i	−1.30792	−	0.950263i	−0.999999	+	0.00114744i	$0.999635\pi$
$338$	−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	−0.897398	−	0.441222i	$-0.854545\pi$
$347$	−2784.20	−	8568.90i	−0.430732	−	1.32566i	0.466666	−	0.884434i	$-0.345455\pi$
$348$	2101.60	+	1526.90i	0.323729	+	0.235203i
$349$	−3092.48	+	2246.82i	−0.474318	+	0.344612i	−0.799122	−	0.601169i	$-0.794702\pi$
$349$	−3092.48	+	2246.82i	−0.474318	+	0.344612i	0.324804	+	0.945781i	$0.394702\pi$
$350$	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	0.760154	−	0.649743i	$-0.225123\pi$
$359$	2565.15	+	1863.69i	0.377113	+	0.273988i	−0.383041	+	0.923731i	$0.625123\pi$
$360$	−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	0.844538	−	0.535496i	$-0.179875\pi$
$367$	4191.90	+	3045.60i	0.596228	+	0.433185i	−0.248310	+	0.968681i	$0.579875\pi$
$368$	−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	−0.995361	−	0.0962079i	$-0.969329\pi$
$379$	−1819.84	−	5600.90i	−0.246647	−	0.759100i	0.748715	−	0.662893i	$-0.230671\pi$
$380$	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	−0.734718	−	0.678373i	$-0.762686\pi$
$383$	1936.97	−	5961.37i	0.258419	−	0.795331i	0.993137	−	0.116958i	$-0.0373144\pi$
$384$	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	−0.0635492	−	0.997979i	$-0.520242\pi$
$389$	−7920.26	−	5754.40i	−1.03232	−	0.750025i	−0.968772	+	0.247953i	$0.920242\pi$
$390$	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	−0.979946	−	0.199265i	$-0.936145\pi$
$401$	−2443.36	−	7519.88i	−0.304278	−	0.936471i	0.675668	−	0.737206i	$-0.263855\pi$
$402$	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	−0.740571	−	0.671978i	$-0.765445\pi$
$409$	2097.18	−	6454.44i	0.253542	−	0.780322i	0.994113	−	0.108344i	$-0.0345549\pi$
$410$	−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	−0.275065	−	0.961426i	$-0.588699\pi$
$421$	4788.20	−	3478.83i	0.554305	−	0.402726i	0.829370	+	0.558699i	$0.188699\pi$
$422$	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	−0.622912	−	0.782292i	$-0.714050\pi$
$431$	3049.89	−	9386.60i	0.340854	−	1.04904i	0.963766	−	0.266749i	$-0.0859495\pi$
$432$	−1432.56	+	1040.82i	−0.159547	+	0.115918i
$433$	−3800.01	−	2760.87i	−0.421748	−	0.306418i	0.356593	−	0.934260i	$-0.383938\pi$
$433$	−3800.01	−	2760.87i	−0.421748	−	0.306418i	−0.778341	+	0.627842i	$0.783938\pi$
$434$	−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	0.656386	−	0.754425i	$-0.272084\pi$
$443$	14701.5	−	10681.2i	1.57672	−	1.14556i	0.920335	−	0.391130i	$-0.127916\pi$
$444$	−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	−0.932011	−	0.362430i	$-0.881947\pi$
$449$	333.309	−	1025.82i	0.0350330	−	0.107821i	0.967044	+	0.254610i	$0.0819470\pi$
$450$	−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	−0.998235	−	0.0593944i	$-0.981083\pi$
$457$	−2203.59	−	6781.95i	−0.225557	−	0.694193i	0.772678	−	0.634799i	$-0.218917\pi$
$458$	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	0.973092	−	0.230415i	$-0.0740084\pi$
$467$	508.730	+	1565.71i	0.0504095	+	0.155145i	−0.922683	+	0.385560i	$0.874008\pi$
$468$	−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	0.992577	+	0.121615i	$0.0388074\pi$
$479$	2736.69	+	8422.66i	0.261049	+	0.803427i	−0.731528	+	0.681811i	$0.761193\pi$
$480$	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	−0.735649	−	0.677362i	$-0.763123\pi$
$487$	−3425.84	+	2489.02i	−0.318768	+	0.231598i	0.416882	+	0.908961i	$0.363123\pi$
$488$	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	0.981294	−	0.192515i	$-0.0616644\pi$
$491$	11983.5	+	8706.49i	1.10144	+	0.800242i	0.120144	+	0.992756i	$0.461664\pi$
$492$	−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	0.871721	−	0.490003i	$-0.163004\pi$
$499$	7524.95	+	5467.20i	0.675076	+	0.490471i	−0.196644	+	0.980475i	$0.563004\pi$
$500$	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	−0.989171	−	0.146764i	$-0.953114\pi$
$503$	−13032.6	+	9468.76i	−1.15526	+	0.839346i	−0.166090	+	0.986111i	$0.553114\pi$
$504$	−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	−0.927249	−	0.374445i	$-0.877833\pi$
$509$	−9849.07	+	7155.77i	−0.857666	+	0.623131i	0.0695826	+	0.997576i	$0.477833\pi$
$510$	−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	0.989709	−	0.143091i	$-0.0457043\pi$
$521$	13788.3	+	10017.8i	1.15946	+	0.842396i	0.169749	+	0.985487i	$0.445704\pi$
$522$	−5548.56	−	17076.7i	−0.465238	−	1.43185i
$523$	6642.80	+	20444.4i	0.555391	+	1.70932i	0.694908	+	0.719098i	$0.255445\pi$
$523$	6642.80	+	20444.4i	0.555391	+	1.70932i	−0.139517	+	0.990220i	$0.544555\pi$
$524$	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	0.405851	+	0.913939i	$0.366975\pi$
$541$	−5784.43	+	17802.6i	−0.459689	+	1.41478i	−0.865540	+	0.500839i	$0.833025\pi$
$542$	−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	0.0182455	−	0.999834i	$-0.494192\pi$
$547$	12470.6	−	9060.44i	0.974782	−	0.708221i	0.956536	+	0.291613i	$0.0941919\pi$
$548$	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	0.346058	−	0.938213i	$-0.387520\pi$
$557$	−5774.88	−	4195.69i	−0.439299	−	0.319169i	−0.785356	+	0.619044i	$0.787520\pi$
$558$	−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	−0.846003	−	0.533178i	$-0.820998\pi$
$563$	2028.14	−	6241.96i	0.151822	−	0.467260i	0.997825	+	0.0659180i	$0.0209976\pi$
$564$	−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	0.0484117	−	0.998827i	$-0.484584\pi$
$569$	13753.5	−	9992.48i	1.01331	−	0.736215i	0.964901	+	0.262612i	$0.0845841\pi$
$570$	−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	−0.859008	−	0.511962i	$-0.828919\pi$
$577$	−6444.63	−	19834.5i	−0.464980	−	1.43106i	0.394028	−	0.919098i	$-0.371081\pi$
$578$	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	0.187441	−	0.982276i	$-0.439981\pi$
$587$	−9796.54	−	7117.60i	−0.688836	−	0.500468i	−0.876277	+	0.481807i	$0.839981\pi$
$588$	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	0.994334	+	0.106303i	$0.0339012\pi$
$599$	3700.00	+	11387.4i	0.252384	+	0.776758i	−0.741950	+	0.670455i	$0.766099\pi$
$600$	−1169.28	−	3598.69i	−0.0795597	−	0.244860i
$601$	−3491.88	−	2537.00i	−0.237000	−	0.172190i	0.462946	−	0.886387i	$-0.346792\pi$
$601$	−3491.88	−	2537.00i	−0.237000	−	0.172190i	−0.699945	+	0.714196i	$0.746792\pi$
$602$	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	0.330936	+	0.943653i	$0.392636\pi$
$607$	−7349.76	+	22620.2i	−0.491462	+	1.51257i	−0.822398	+	0.568912i	$0.807364\pi$
$608$	−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	−0.976854	−	0.213909i	$-0.931380\pi$
$613$	−16319.7	+	11856.9i	−1.07528	+	0.781236i	−0.0984251	+	0.995144i	$0.531380\pi$
$614$	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	−0.929497	−	0.368829i	$-0.879759\pi$
$619$	−13336.1	+	9689.25i	−0.865951	+	0.629150i	0.0635467	+	0.997979i	$0.479759\pi$
$620$	−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	0.646995	−	0.762494i	$-0.276025\pi$
$631$	1929.84	+	1402.11i	0.121752	+	0.0884583i	−0.525243	+	0.850953i	$0.676025\pi$
$632$	−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	−0.509507	−	0.860467i	$-0.670172\pi$
$641$	2457.03	−	1785.13i	0.151399	−	0.109998i	0.660906	+	0.750469i	$0.270172\pi$
$642$	−3545.19	−	2575.73i	−0.217940	−	0.158343i
$643$	7955.97	+	24486.0i	0.487952	+	1.50176i	0.827660	+	0.561230i	$0.189672\pi$
$643$	7955.97	+	24486.0i	0.487952	+	1.50176i	−0.339709	+	0.940531i	$0.610328\pi$
$644$	−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	−0.829918	−	0.557886i	$-0.811613\pi$
$647$	2788.13	−	8580.98i	0.169417	−	0.521411i	0.999335	+	0.0364744i	$0.0116127\pi$
$648$	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	0.471714	−	0.881752i	$-0.343635\pi$
$653$	−3689.66	−	2680.69i	−0.221114	−	0.160649i	−0.692828	+	0.721103i	$0.743635\pi$
$654$	−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	0.636118	+	0.771591i	$0.280539\pi$
$673$	−5797.17	+	17841.8i	−0.332042	+	1.02192i	−0.968161	+	0.250329i	$0.919461\pi$
$674$	−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	0.979139	+	0.203190i	$0.0651309\pi$
$677$	5397.79	+	16612.7i	0.306431	+	0.943098i	−0.672708	+	0.739908i	$0.734869\pi$
$678$	−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	−0.596002	−	0.802983i	$-0.703245\pi$
$691$	6505.61	−	20022.2i	0.358155	−	1.10229i	0.954157	−	0.299305i	$-0.0967549\pi$
$692$	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	−0.545817	−	0.837905i	$-0.683780\pi$
$701$	1529.55	−	1111.29i	0.0824115	−	0.0598754i	0.628228	+	0.778029i	$0.283780\pi$
$702$	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	0.818377	−	0.574681i	$-0.194874\pi$
$709$	−3426.33	−	10545.2i	−0.181493	−	0.558578i	−0.999870	+	0.0161035i	$0.994874\pi$
$710$	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	0.146083	−	0.989272i	$-0.453333\pi$
$719$	−14452.4	−	10500.3i	−0.749628	−	0.544637i	−0.895712	+	0.444635i	$0.853333\pi$
$720$	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	0.741337	−	0.671133i	$-0.234192\pi$
$733$	6591.34	+	4788.89i	0.332137	+	0.241312i	−0.409200	+	0.912445i	$0.634192\pi$
$734$	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	0.143117	+	0.989706i	$0.454288\pi$
$739$	−11137.6	+	34278.0i	−0.554402	+	1.70627i	−0.697518	+	0.716567i	$0.745712\pi$
$740$	−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	−0.955744	−	0.294200i	$-0.904947\pi$
$743$	−7198.98	−	22156.2i	−0.355457	−	1.09399i	0.600286	−	0.799785i	$-0.295053\pi$
$744$	−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	−0.0919532	−	0.995763i	$-0.529311\pi$
$751$	17013.2	−	12360.8i	0.826659	−	0.600603i	0.918612	+	0.395160i	$0.129311\pi$
$752$	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	−0.796392	−	0.604781i	$-0.793261\pi$
$757$	4236.05	−	13037.2i	0.203384	−	0.625952i	0.999776	−	0.0211709i	$-0.00673940\pi$
$758$	−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	−0.935323	−	0.353794i	$-0.884891\pi$
$761$	615.600	−	1894.62i	0.0293239	−	0.0902497i	0.964647	+	0.263544i	$0.0848915\pi$
$762$	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	−0.998264	−	0.0589022i	$-0.981240\pi$
$773$	−26880.1	+	19529.5i	−1.25072	+	0.908705i	−0.252461	+	0.967607i	$0.581240\pi$
$774$	−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	0.990531	−	0.137291i	$-0.0438396\pi$
$787$	2394.96	+	7370.94i	0.108477	+	0.333857i	−0.882054	+	0.471148i	$0.843840\pi$
$788$	−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	0.931575	−	0.363550i	$-0.118435\pi$
$797$	−804.931	−	2477.32i	−0.0357743	−	0.110102i	−0.967349	+	0.253448i	$0.918435\pi$
$798$	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	0.976664	−	0.214772i	$-0.0689008\pi$
$809$	1387.21	+	4269.40i	0.0602866	+	0.185543i	−0.916378	+	0.400315i	$0.868901\pi$
$810$	35362.1	+	25692.0i	1.53395	+	1.11448i
$811$	19598.9	−	14239.4i	0.848594	−	0.616539i	−0.0761643	−	0.997095i	$-0.524267\pi$
$811$	19598.9	−	14239.4i	0.848594	−	0.616539i	0.924758	+	0.380556i	$0.124267\pi$
$812$	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	0.261402	−	0.965230i	$-0.415815\pi$
$821$	−13545.4	−	9841.35i	−0.575809	−	0.418350i	−0.837211	+	0.546880i	$0.815815\pi$
$822$	11018.3	−	8005.27i	0.467528	−	0.339679i
$823$	−6678.21	+	20553.4i	−0.282853	+	0.870531i	0.704181	+	0.710020i	$0.251314\pi$
$823$	−6678.21	+	20553.4i	−0.282853	+	0.870531i	−0.987034	+	0.160511i	$0.948686\pi$
$824$	−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	−0.978824	−	0.204704i	$-0.934377\pi$
$827$	−1584.31	+	4876.01i	−0.0666166	+	0.205025i	0.912207	+	0.409729i	$0.134377\pi$
$828$	−4855.31	+	3527.59i	−0.203785	+	0.148058i
$829$	13451.0	+	9772.72i	0.563537	+	0.409434i	0.832752	−	0.553646i	$-0.186764\pi$
$829$	13451.0	+	9772.72i	0.563537	+	0.409434i	−0.269215	+	0.963080i	$0.586764\pi$
$830$	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	−0.642542	−	0.766251i	$-0.722120\pi$
$839$	−2730.34	+	1983.71i	−0.112350	+	0.0816272i	0.530191	+	0.847878i	$0.322120\pi$
$840$	−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	0.989469	−	0.144744i	$-0.0462358\pi$
$853$	2588.28	+	7965.92i	0.103894	+	0.319751i	−0.885576	+	0.464495i	$0.846236\pi$
$854$	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	0.973171	−	0.230082i	$-0.0738993\pi$
$863$	1283.34	+	3949.73i	0.0506206	+	0.155794i	−0.922551	+	0.385876i	$0.873899\pi$
$864$	−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	−0.911798	−	0.410639i	$-0.865306\pi$
$877$	−20855.7	+	15152.6i	−0.803018	+	0.583427i	0.108780	+	0.994066i	$0.465306\pi$
$878$	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	−0.469278	−	0.883051i	$-0.655486\pi$
$883$	5917.83	−	4299.55i	0.225539	−	0.163864i	0.694816	+	0.719187i	$0.255486\pi$
$884$	−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	0.461780	−	0.886995i	$-0.347211\pi$
$887$	−6316.44	−	4589.16i	−0.239104	−	0.173719i	−0.700884	+	0.713275i	$0.747211\pi$
$888$	−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	0.826438	−	0.563027i	$-0.190363\pi$
$907$	−4728.43	−	14552.6i	−0.173104	−	0.532758i	−0.999542	+	0.0302695i	$0.990363\pi$
$908$	−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	0.779496	+	0.626408i	$0.215475\pi$
$911$	−6030.61	+	18560.3i	−0.219323	+	0.675006i	−0.998818	+	0.0485985i	$0.984525\pi$
$912$	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	0.982528	−	0.186117i	$-0.0595902\pi$
$919$	2179.99	+	6709.33i	0.0782495	+	0.240827i	−0.904278	+	0.426944i	$0.859590\pi$
$920$	−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	0.858488	−	0.512833i	$-0.171404\pi$
$929$	−3892.78	−	11980.7i	−0.137479	−	0.423116i	−0.995967	+	0.0897164i	$0.971404\pi$
$930$	−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	0.796250	+	0.604968i	$0.206814\pi$
$937$	−5837.39	+	17965.7i	−0.203521	+	0.626374i	−0.999771	+	0.0214057i	$0.993186\pi$
$938$	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	−0.965125	−	0.261789i	$-0.915688\pi$
$941$	−9762.38	−	30045.5i	−0.338198	−	1.04087i	0.626927	−	0.779078i	$-0.284312\pi$
$942$	−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	0.920705	−	0.390260i	$-0.127615\pi$
$953$	24537.8	+	17827.8i	0.834059	+	0.605979i	−0.0866461	+	0.996239i	$0.527615\pi$
$954$	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	−0.995683	−	0.0928226i	$-0.970411\pi$
$971$	−36765.1	+	26711.4i	−1.21509	+	0.882812i	−0.219403	+	0.975634i	$0.570411\pi$
$972$	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	0.0170001	+	0.999855i	$0.494588\pi$
$977$	−17848.1	+	54930.8i	−0.584454	+	1.79876i	−0.601454	+	0.798908i	$0.705412\pi$
$978$	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	0.287390	−	0.957814i	$-0.407213\pi$
$983$	−16480.5	−	11973.8i	−0.534737	−	0.388509i	−0.822127	+	0.569304i	$0.807213\pi$
$984$	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	0.487003	−	0.873400i	$-0.338090\pi$
$997$	−6080.71	−	4417.90i	−0.193158	−	0.140337i	−0.680161	+	0.733063i	$0.738090\pi$
$998$	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.86.20	✓	88
11.4	even	5		2057.4.a.t.1.40		44
11.5	even	5	inner	187.4.g.a.137.20	yes	88
11.7	odd	10		2057.4.a.s.1.5		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.4.g.a.86.20	✓	88	1.1	even	1	trivial
187.4.g.a.137.20	yes	88	11.5	even	5	inner
2057.4.a.s.1.5		44	11.7	odd	10
2057.4.a.t.1.40		44	11.4	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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