LMFDB - Embedded newform 110.4.k.a.7.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

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

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

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

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

Newform invariants

comment:select newform

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

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

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

Embedding invariants

Embedding label			7.14
Character	$\chi$	$=$	110.7
Dual form			110.4.k.a.63.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.97538 - 0.312869i) q^{2} +(0.0345940 + 0.0678945i) q^{3} +(3.80423 - 1.23607i) q^{4} +(-9.05578 - 6.55690i) q^{5} +(0.0895782 + 0.123294i) q^{6} +(26.9536 + 13.7335i) q^{7} +(7.12805 - 3.63192i) q^{8} +(15.8668 - 21.8388i) q^{9} +(-19.9400 - 10.1191i) q^{10} +(36.4816 - 0.303590i) q^{11} +(0.215525 + 0.215525i) q^{12} +(-12.8946 - 81.4136i) q^{13} +(57.5403 + 18.6960i) q^{14} +(0.131902 - 0.841666i) q^{15} +(12.9443 - 9.40456i) q^{16} +(-0.499816 + 3.15571i) q^{17} +(24.5102 - 48.1040i) q^{18} +(-37.1855 + 114.445i) q^{19} +(-42.5550 - 13.7504i) q^{20} +2.30510i q^{21} +(71.9699 - 12.0137i) q^{22} +(-61.1089 + 61.1089i) q^{23} +(0.493175 + 0.358313i) q^{24} +(39.0142 + 118.756i) q^{25} +(-50.9436 - 156.788i) q^{26} +(4.06369 + 0.643625i) q^{27} +(119.513 + 18.9290i) q^{28} +(-45.3832 - 139.675i) q^{29} +(-0.00277566 - 1.70388i) q^{30} +(60.1821 + 43.7248i) q^{31} +(22.6274 - 22.6274i) q^{32} +(1.28266 + 2.46640i) q^{33} +6.39010i q^{34} +(-154.036 - 301.100i) q^{35} +(33.3667 - 102.692i) q^{36} +(-134.769 + 264.498i) q^{37} +(-37.6490 + 237.706i) q^{38} +(5.08145 - 3.69189i) q^{39} +(-88.3642 - 13.8480i) q^{40} +(-166.393 - 54.0642i) q^{41} +(0.721193 + 4.55344i) q^{42} +(163.048 + 163.048i) q^{43} +(138.409 - 46.2487i) q^{44} +(-286.881 + 93.7301i) q^{45} +(-101.594 + 139.832i) q^{46} +(-291.596 + 148.576i) q^{47} +(1.08631 + 0.553503i) q^{48} +(336.276 + 462.844i) q^{49} +(114.223 + 222.381i) q^{50} +(-0.231546 + 0.0752339i) q^{51} +(-149.687 - 293.777i) q^{52} +(204.013 - 32.3125i) q^{53} +8.22869 q^{54} +(-332.360 - 236.457i) q^{55} +242.006 q^{56} +(-9.05658 + 1.43442i) q^{57} +(-133.349 - 261.712i) q^{58} +(127.738 - 41.5046i) q^{59} +(-0.538573 - 3.36493i) q^{60} +(-359.896 - 495.355i) q^{61} +(132.562 + 67.5439i) q^{62} +(727.591 - 370.726i) q^{63} +(37.6183 - 51.7771i) q^{64} +(-417.049 + 821.812i) q^{65} +(3.30539 + 4.47076i) q^{66} +(-296.485 - 296.485i) q^{67} +(1.99926 + 12.6229i) q^{68} +(-6.26295 - 2.03496i) q^{69} +(-398.485 - 546.592i) q^{70} +(-21.8441 + 15.8707i) q^{71} +(33.7826 - 213.295i) q^{72} +(-444.473 + 872.327i) q^{73} +(-183.465 + 564.649i) q^{74} +(-6.71319 + 6.75708i) q^{75} +481.339i q^{76} +(987.480 + 492.839i) q^{77} +(8.88271 - 8.88271i) q^{78} +(689.704 + 501.100i) q^{79} +(-178.885 + 0.291409i) q^{80} +(-225.128 - 692.873i) q^{81} +(-345.603 - 54.7381i) q^{82} +(-978.558 - 154.988i) q^{83} +(2.84926 + 8.76911i) q^{84} +(25.2179 - 25.3002i) q^{85} +(373.094 + 271.069i) q^{86} +(7.91319 - 7.91319i) q^{87} +(258.940 - 134.662i) q^{88} -818.439i q^{89} +(-537.372 + 274.908i) q^{90} +(770.540 - 2371.48i) q^{91} +(-156.937 + 308.007i) q^{92} +(-0.886738 + 5.59864i) q^{93} +(-529.527 + 384.724i) q^{94} +(1087.15 - 792.568i) q^{95} +(2.31905 + 0.753504i) q^{96} +(126.418 + 798.169i) q^{97} +(809.081 + 809.081i) q^{98} +(572.216 - 801.530i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 8 q^{3} + 32 q^{5} - 40 q^{7} - 44 q^{11} + 128 q^{12} - 256 q^{15} + 576 q^{16} - 640 q^{17} - 64 q^{20} + 312 q^{22} - 984 q^{23} - 520 q^{25} + 304 q^{26} - 364 q^{27} + 240 q^{28} - 432 q^{31}+ \cdots + 7044 q^{97}+O(q^{100}) $ 144 * q + 8 * q^3 + 32 * q^5 - 40 * q^7 - 44 * q^11 + 128 * q^12 - 256 * q^15 + 576 * q^16 - 640 * q^17 - 64 * q^20 + 312 * q^22 - 984 * q^23 - 520 * q^25 + 304 * q^26 - 364 * q^27 + 240 * q^28 - 432 * q^31 + 2368 * q^33 + 1808 * q^36 - 960 * q^37 + 72 * q^38 + 740 * q^41 + 2440 * q^42 + 2656 * q^45 + 720 * q^46 - 1980 * q^47 - 128 * q^48 - 1360 * q^50 - 3880 * q^51 - 1920 * q^52 - 3060 * q^53 - 3044 * q^55 - 64 * q^56 - 4400 * q^57 - 2016 * q^58 - 1120 * q^60 - 960 * q^61 + 80 * q^62 + 1800 * q^63 + 1552 * q^66 + 10160 * q^67 + 2560 * q^68 + 2304 * q^70 + 1312 * q^71 - 2460 * q^73 + 8644 * q^75 - 1272 * q^77 - 5312 * q^78 + 768 * q^80 + 2116 * q^81 + 1280 * q^82 + 320 * q^85 - 5488 * q^86 + 1248 * q^88 - 8480 * q^90 + 11796 * q^91 - 704 * q^92 + 688 * q^93 - 1280 * q^95 + 7044 * q^97

Character values

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

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

Coefficient data

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

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

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

$2$	1.97538	−	0.312869i	0.698401	−	0.110616i
$2$	1.97538	−	0.312869i	0.698401	−	0.110616i
$3$	0.0345940	+	0.0678945i	0.00665761	+	0.0130663i	0.894311	−	0.447445i	$-0.147666\pi$
$3$	0.0345940	+	0.0678945i	0.00665761	+	0.0130663i	−0.887654	+	0.460511i	$0.847666\pi$
$4$	3.80423	−	1.23607i	0.475528	−	0.154508i
$5$	−9.05578	−	6.55690i	−0.809973	−	0.586467i
$5$	−9.05578	−	6.55690i	−0.809973	−	0.586467i
$6$	0.0895782	+	0.123294i	0.00609502	+	0.00838908i
$7$	26.9536	+	13.7335i	1.45536	+	0.741542i	0.989664	−	0.143404i	$-0.0458049\pi$
$7$	26.9536	+	13.7335i	1.45536	+	0.741542i	0.465693	+	0.884946i	$0.345805\pi$
$8$	7.12805	−	3.63192i	0.315018	−	0.160510i
$9$	15.8668	−	21.8388i	0.587659	−	0.808843i
$10$	−19.9400	−	10.1191i	−0.630559	−	0.319993i
$11$	36.4816	−	0.303590i	0.999965	−	0.00832145i
$11$	36.4816	−	0.303590i	0.999965	−	0.00832145i
$12$	0.215525	+	0.215525i	0.00518474	+	0.00518474i
$13$	−12.8946	−	81.4136i	−0.275102	−	1.73693i	−0.607975	−	0.793956i	$-0.708018\pi$
$13$	−12.8946	−	81.4136i	−0.275102	−	1.73693i	0.332873	−	0.942972i	$-0.391982\pi$
$14$	57.5403	+	18.6960i	1.09845	+	0.356908i
$15$	0.131902	−	0.841666i	0.00227046	−	0.0144878i
$16$	12.9443	−	9.40456i	0.202254	−	0.146946i
$17$	−0.499816	+	3.15571i	−0.00713077	+	0.0450219i	−0.990997	−	0.133883i	$-0.957255\pi$
$17$	−0.499816	+	3.15571i	−0.00713077	+	0.0450219i	0.983866	+	0.178905i	$0.0572554\pi$
$18$	24.5102	−	48.1040i	0.320951	−	0.629901i
$19$	−37.1855	+	114.445i	−0.448996	+	1.38187i	0.429045	+	0.903283i	$0.358850\pi$
$19$	−37.1855	+	114.445i	−0.448996	+	1.38187i	−0.878041	+	0.478585i	$0.841150\pi$
$20$	−42.5550	−	13.7504i	−0.475779	−	0.153734i
$21$			2.30510i			0.0239530i
$22$	71.9699	−	12.0137i	0.697456	−	0.116424i
$23$	−61.1089	+	61.1089i	−0.554004	+	0.554004i	−0.927594	−	0.373590i	$-0.878127\pi$
$23$	−61.1089	+	61.1089i	−0.554004	+	0.554004i	0.373590	+	0.927594i	$0.378127\pi$
$24$	0.493175	+	0.358313i	0.00419454	+	0.00304751i
$25$	39.0142	+	118.756i	0.312114	+	0.950045i
$26$	−50.9436	−	156.788i	−0.384264	−	1.18264i
$27$	4.06369	+	0.643625i	0.0289651	+	0.00458762i
$28$	119.513	+	18.9290i	0.806638	+	0.127759i
$29$	−45.3832	−	139.675i	−0.290602	−	0.894380i	−0.984663	−	0.174465i	$-0.944180\pi$
$29$	−45.3832	−	139.675i	−0.290602	−	0.894380i	0.694062	−	0.719916i	$-0.255820\pi$
$30$	−0.00277566	−	1.70388i	−1.68921e−5	−	0.0103695i
$31$	60.1821	+	43.7248i	0.348678	+	0.253329i	0.748314	−	0.663344i	$-0.230864\pi$
$31$	60.1821	+	43.7248i	0.348678	+	0.253329i	−0.399636	+	0.916674i	$0.630864\pi$
$32$	22.6274	−	22.6274i	0.125000	−	0.125000i
$33$	1.28266	+	2.46640i	0.00676611	+	0.0130104i
$34$			6.39010i			0.0322321i
$35$	−154.036	−	301.100i	−0.743912	−	1.45415i
$36$	33.3667	−	102.692i	0.154475	−	0.475426i
$37$	−134.769	+	264.498i	−0.598806	+	1.17522i	0.370377	+	0.928881i	$0.379228\pi$
$37$	−134.769	+	264.498i	−0.598806	+	1.17522i	−0.969183	+	0.246341i	$0.920772\pi$
$38$	−37.6490	+	237.706i	−0.160723	+	1.01476i
$39$	5.08145	−	3.69189i	0.0208637	−	0.0151584i
$40$	−88.3642	−	13.8480i	−0.349290	−	0.0547390i
$41$	−166.393	−	54.0642i	−0.633808	−	0.205937i	−0.0255470	−	0.999674i	$-0.508133\pi$
$41$	−166.393	−	54.0642i	−0.633808	−	0.205937i	−0.608261	+	0.793737i	$0.708133\pi$
$42$	0.721193	+	4.55344i	0.00264959	+	0.0167288i
$43$	163.048	+	163.048i	0.578247	+	0.578247i	0.934420	−	0.356173i	$-0.115919\pi$
$43$	163.048	+	163.048i	0.578247	+	0.578247i	−0.356173	+	0.934420i	$0.615919\pi$
$44$	138.409	−	46.2487i	0.474226	−	0.158460i
$45$	−286.881	+	93.7301i	−0.950347	+	0.310499i
$46$	−101.594	+	139.832i	−0.325635	+	0.448198i
$47$	−291.596	+	148.576i	−0.904971	+	0.461106i	−0.843577	−	0.537008i	$-0.819555\pi$
$47$	−291.596	+	148.576i	−0.904971	+	0.461106i	−0.0613940	+	0.998114i	$0.519555\pi$
$48$	1.08631	+	0.553503i	0.00326657	+	0.00166440i
$49$	336.276	+	462.844i	0.980396	+	1.34940i
$50$	114.223	+	222.381i	0.323071	+	0.628988i
$51$	−0.231546	+	0.0752339i	−0.000635744	+	0.000206566i
$52$	−149.687	−	293.777i	−0.399189	−	0.783453i
$53$	204.013	−	32.3125i	0.528743	−	0.0837446i	0.113645	−	0.993521i	$-0.463747\pi$
$53$	204.013	−	32.3125i	0.528743	−	0.0837446i	0.415098	+	0.909777i	$0.363747\pi$
$54$	8.22869			0.0207367
$55$	−332.360	−	236.457i	−0.814826	−	0.579706i
$56$	242.006			0.577489
$57$	−9.05658	+	1.43442i	−0.0210451	+	0.00333322i
$58$	−133.349	−	261.712i	−0.301889	−	0.592491i
$59$	127.738	−	41.5046i	0.281866	−	0.0915837i	−0.164672	−	0.986348i	$-0.552657\pi$
$59$	127.738	−	41.5046i	0.281866	−	0.0915837i	0.446538	+	0.894765i	$0.352657\pi$
$60$	−0.538573	−	3.36493i	−0.00115882	−	0.00724017i
$61$	−359.896	−	495.355i	−0.755410	−	1.03973i	−0.997582	−	0.0694996i	$-0.977860\pi$
$61$	−359.896	−	495.355i	−0.755410	−	1.03973i	0.242172	−	0.970233i	$-0.422140\pi$
$62$	132.562	+	67.5439i	0.271539	+	0.138356i
$63$	727.591	−	370.726i	1.45504	−	0.741382i
$64$	37.6183	−	51.7771i	0.0734732	−	0.101127i
$65$	−417.049	+	821.812i	−0.795825	+	1.56820i
$66$	3.30539	+	4.47076i	0.00616462	+	0.00833807i
$67$	−296.485	−	296.485i	−0.540618	−	0.540618i	0.383092	−	0.923710i	$-0.374859\pi$
$67$	−296.485	−	296.485i	−0.540618	−	0.540618i	−0.923710	+	0.383092i	$0.874859\pi$
$68$	1.99926	+	12.6229i	0.00356539	+	0.0225110i
$69$	−6.26295	−	2.03496i	−0.0109271	−	0.00355044i
$70$	−398.485	−	546.592i	−0.680400	−	0.933290i
$71$	−21.8441	+	15.8707i	−0.0365130	+	0.0265282i	−0.605892	−	0.795547i	$-0.707184\pi$
$71$	−21.8441	+	15.8707i	−0.0365130	+	0.0265282i	0.569379	+	0.822075i	$0.307184\pi$
$72$	33.7826	−	213.295i	0.0552960	−	0.349125i
$73$	−444.473	+	872.327i	−0.712625	+	1.39861i	0.195836	+	0.980637i	$0.437258\pi$
$73$	−444.473	+	872.327i	−0.712625	+	1.39861i	−0.908461	+	0.417969i	$0.862742\pi$
$74$	−183.465	+	564.649i	−0.288208	+	0.887014i
$75$	−6.71319	+	6.75708i	−0.0103356	+	0.0104032i
$76$			481.339i			0.726491i
$77$	987.480	+	492.839i	1.46148	+	0.729405i
$78$	8.88271	−	8.88271i	0.0128945	−	0.0128945i
$79$	689.704	+	501.100i	0.982251	+	0.713647i	0.958210	−	0.286064i	$-0.0923470\pi$
$79$	689.704	+	501.100i	0.982251	+	0.713647i	0.0240403	+	0.999711i	$0.492347\pi$
$80$	−178.885	+	0.291409i	−0.250000	+	0.000407256i
$81$	−225.128	−	692.873i	−0.308818	−	0.950443i
$82$	−345.603	−	54.7381i	−0.465432	−	0.0737172i
$83$	−978.558	−	154.988i	−1.29410	−	0.204966i	−0.528862	−	0.848708i	$-0.677381\pi$
$83$	−978.558	−	154.988i	−1.29410	−	0.204966i	−0.765243	+	0.643742i	$0.777381\pi$
$84$	2.84926	+	8.76911i	0.00370095	+	0.0113903i
$85$	25.2179	−	25.3002i	0.0321796	−	0.0322846i
$86$	373.094	+	271.069i	0.467811	+	0.339885i
$87$	7.91319	−	7.91319i	0.00975152	−	0.00975152i
$88$	258.940	−	134.662i	0.313672	−	0.163126i
$89$		−	818.439i		−	0.974768i	−0.873188	−	0.487384i	$-0.837951\pi$
$89$		−	818.439i		−	0.974768i	0.873188	−	0.487384i	$-0.162049\pi$
$90$	−537.372	+	274.908i	−0.629378	+	0.321976i
$91$	770.540	−	2371.48i	0.887632	−	2.73185i
$92$	−156.937	+	308.007i	−0.177846	+	0.349043i
$93$	−0.886738	+	5.59864i	−0.000988714	+	0.00624250i
$94$	−529.527	+	384.724i	−0.581027	+	0.422141i
$95$	1087.15	−	792.568i	1.17409	−	0.855956i
$96$	2.31905	+	0.753504i	0.00246549	+	0.000801086i
$97$	126.418	+	798.169i	0.132327	+	0.835483i	0.961161	+	0.275988i	$0.0890049\pi$
$97$	126.418	+	798.169i	0.132327	+	0.835483i	−0.828834	+	0.559495i	$0.810995\pi$
$98$	809.081	+	809.081i	0.833975	+	0.833975i
$99$	572.216	−	801.530i	0.580908	−	0.813705i
$100$	295.209	+	403.549i	0.295209	+	0.403549i
$101$	483.912	−	666.048i	0.476743	−	0.656181i	−0.501132	−	0.865371i	$-0.667083\pi$
$101$	483.912	−	666.048i	0.476743	−	0.656181i	0.977875	+	0.209190i	$0.0670827\pi$
$102$	−0.433852	+	0.221059i	−0.000421155	+	0.000214589i
$103$	725.051	+	369.432i	0.693606	+	0.353410i	0.764993	−	0.644039i	$-0.222743\pi$
$103$	725.051	+	369.432i	0.693606	+	0.353410i	−0.0713870	+	0.997449i	$0.522743\pi$
$104$	−387.602	−	533.488i	−0.365456	−	0.503008i
$105$	15.1143	−	20.8745i	0.0140476	−	0.0194013i
$106$	392.893	−	127.659i	0.360011	−	0.116975i
$107$	−117.357	−	230.326i	−0.106031	−	0.208098i	0.831895	−	0.554933i	$-0.187256\pi$
$107$	−117.357	−	230.326i	−0.106031	−	0.208098i	−0.937926	+	0.346835i	$0.887256\pi$
$108$	16.2548	−	2.57450i	0.0144825	−	0.00229381i
$109$	872.557			0.766750			0.383375	−	0.923593i	$-0.374762\pi$
$109$	872.557			0.766750			0.383375	+	0.923593i	$0.374762\pi$
$110$	−730.516	−	363.106i	−0.633200	−	0.314735i
$111$	−22.6201			−0.0193424
$112$	478.053	−	75.7161i	0.403319	−	0.0638795i
$113$	533.870	+	1047.78i	0.444445	+	0.872273i	0.999190	+	0.0402520i	$0.0128161\pi$
$113$	533.870	+	1047.78i	0.444445	+	0.872273i	−0.554744	+	0.832021i	$0.687184\pi$
$114$	−17.4414	+	5.66705i	−0.0143292	+	0.00465585i
$115$	954.073	−	152.704i	0.773633	−	0.123824i
$116$	−345.296	−	475.259i	−0.276379	−	0.380403i
$117$	−1982.57	−	1010.17i	−1.56657	−	0.798207i
$118$	239.345	−	121.953i	0.186725	−	0.0951410i
$119$	−56.8110	+	78.1936i	−0.0437635	+	0.0602352i
$120$	−2.11667	−	6.47850i	−0.00161020	−	0.00492836i
$121$	1330.82	−	22.1509i	0.999862	−	0.0166423i
$122$	−865.912	−	865.912i	−0.642590	−	0.642590i
$123$	−2.08552	−	13.1674i	−0.00152882	−	0.00965257i
$124$	282.993	+	91.9500i	0.204948	+	0.0665916i
$125$	425.364	−	1331.24i	0.304365	−	0.952555i
$126$	1321.28	−	959.964i	0.934196	−	0.678733i
$127$	−339.519	+	2143.64i	−0.237224	+	1.49777i	0.525358	+	0.850882i	$0.323932\pi$
$127$	−339.519	+	2143.64i	−0.237224	+	1.49777i	−0.762582	+	0.646892i	$0.776068\pi$
$128$	58.1108	−	114.049i	0.0401275	−	0.0787546i
$129$	−5.42958	+	16.7105i	−0.00370580	+	0.0114053i
$130$	−566.710	+	1753.87i	−0.382337	+	1.18327i
$131$			2136.33i			1.42483i	0.701761	+	0.712413i	$0.252398\pi$
$131$			2136.33i			1.42483i	−0.701761	+	0.712413i	$0.747602\pi$
$132$	7.92814	+	7.79728i	0.00522770	+	0.00514141i
$133$	−2574.02	+	2574.02i	−1.67816	+	1.67816i
$134$	−678.430	−	492.908i	−0.437369	−	0.317767i
$135$	−32.5797	−	32.4737i	−0.0207705	−	0.0207029i
$136$	7.89860	+	24.3094i	0.00498014	+	0.0153273i
$137$	−207.922	−	32.9316i	−0.129664	−	0.0205367i	0.0912652	−	0.995827i	$-0.470909\pi$
$137$	−207.922	−	32.9316i	−0.129664	−	0.0205367i	−0.220929	+	0.975290i	$0.570909\pi$
$138$	−13.0084	−	2.06032i	−0.00802424	−	0.00127092i
$139$	−206.933	−	636.874i	−0.126272	−	0.388626i	0.867859	−	0.496811i	$-0.165496\pi$
$139$	−206.933	−	636.874i	−0.126272	−	0.388626i	−0.994131	+	0.108186i	$0.965496\pi$
$140$	−958.169	−	955.053i	−0.578429	−	0.576548i
$141$	−20.1749	−	14.6579i	−0.0120499	−	0.00875476i
$142$	−38.1849	+	38.1849i	−0.0225662	+	0.0225662i
$143$	−495.134	−	2966.18i	−0.289547	−	1.73458i
$144$		−	431.907i		−	0.249946i
$145$	−504.855	+	1562.44i	−0.289144	+	0.894853i
$146$	−605.078	+	1862.24i	−0.342990	+	1.05562i
$147$	−19.7914	+	38.8429i	−0.0111046	+	0.0217939i
$148$	−185.752	+	1172.79i	−0.103167	+	0.651372i
$149$	960.895	−	698.131i	0.528319	−	0.383846i	−0.291409	−	0.956598i	$-0.594124\pi$
$149$	960.895	−	698.131i	0.528319	−	0.383846i	0.819729	+	0.572752i	$0.194124\pi$
$150$	−11.1470	+	15.4481i	−0.00606766	+	0.00840889i
$151$	−2604.33	−	846.197i	−1.40356	−	0.456043i	−0.493217	−	0.869906i	$-0.664179\pi$
$151$	−2604.33	−	846.197i	−1.40356	−	0.456043i	−0.910339	+	0.413863i	$0.864179\pi$
$152$	150.596	+	950.825i	0.0803615	+	0.507382i
$153$	60.9864	+	60.9864i	0.0322252	+	0.0322252i
$154$	2104.84	+	664.591i	1.10138	+	0.347755i
$155$	−258.296	−	790.570i	−0.133851	−	0.409678i
$156$	14.7676	−	20.3258i	0.00757918	−	0.0104318i
$157$	1001.96	−	510.522i	0.509330	−	0.259517i	−0.180387	−	0.983596i	$-0.557735\pi$
$157$	1001.96	−	510.522i	0.509330	−	0.259517i	0.689717	+	0.724079i	$0.257735\pi$
$158$	1519.20	+	774.073i	0.764946	+	0.389759i
$159$	9.25146	+	12.7335i	0.00461440	+	0.00635117i
$160$	−353.274	+	56.5433i	−0.174555	+	0.0279384i
$161$	−2486.35	+	807.863i	−1.21709	+	0.395457i
$162$	−661.491	−	1298.25i	−0.320813	−	0.629630i
$163$	−437.594	+	69.3081i	−0.210276	+	0.0333045i	−0.260684	−	0.965424i	$-0.583948\pi$
$163$	−437.594	+	69.3081i	−0.210276	+	0.0333045i	0.0504075	+	0.998729i	$0.483948\pi$
$164$	−699.822			−0.333213
$165$	4.55646	−	30.7454i	0.00214982	−	0.0145062i
$166$	−1981.51			−0.926476
$167$	1028.37	−	162.878i	0.476515	−	0.0754725i	0.0864426	−	0.996257i	$-0.472450\pi$
$167$	1028.37	−	162.878i	0.476515	−	0.0754725i	0.390072	+	0.920784i	$0.372450\pi$
$168$	8.37194	+	16.4309i	0.00384470	+	0.00754564i
$169$	−4372.43	+	1420.69i	−1.99018	+	0.646649i
$170$	41.8992	−	57.8673i	0.0189031	−	0.0261072i
$171$	1909.33	+	2627.96i	0.853858	+	1.17523i
$172$	821.810	+	418.733i	0.364317	+	0.185629i
$173$	−1465.12	+	746.518i	−0.643880	+	0.328073i	−0.745260	−	0.666774i	$-0.767674\pi$
$173$	−1465.12	+	746.518i	−0.643880	+	0.328073i	0.101379	+	0.994848i	$0.467674\pi$
$174$	13.1557	−	18.1073i	0.00573180	−	0.00788915i
$175$	−579.361	+	3736.69i	−0.250260	+	1.61410i
$176$	469.373	−	347.023i	0.201024	−	0.148624i
$177$	7.23690	+	7.23690i	0.00307321	+	0.00307321i
$178$	−256.064	−	1616.73i	−0.107825	−	0.680779i
$179$	419.625	+	136.345i	0.175219	+	0.0569322i	0.395313	−	0.918547i	$-0.370636\pi$
$179$	419.625	+	136.345i	0.175219	+	0.0569322i	−0.220093	+	0.975479i	$0.570636\pi$
$180$	−975.502	+	711.174i	−0.403942	+	0.294488i
$181$	−803.497	+	583.775i	−0.329964	+	0.239733i	−0.740415	−	0.672150i	$-0.765371\pi$
$181$	−803.497	+	583.775i	−0.329964	+	0.239733i	0.410451	+	0.911882i	$0.365371\pi$
$182$	780.145	−	4925.64i	0.317737	−	2.00611i
$183$	21.1816	−	41.5713i	0.00855623	−	0.0167925i
$184$	−213.645	+	657.530i	−0.0855983	+	0.263444i
$185$	2954.72	−	1511.57i	1.17425	−	0.600720i
$186$			11.3369i			0.00446913i
$187$	−17.2760	+	115.277i	−0.00675588	+	0.0450797i
$188$	−925.648	+	925.648i	−0.359095	+	0.359095i
$189$	100.692	+	73.1569i	0.0387526	+	0.0281554i
$190$	1899.56	−	1905.76i	0.725307	−	0.727674i
$191$	−1254.68	−	3861.51i	−0.475316	−	1.46287i	−0.845531	−	0.533927i	$-0.820716\pi$
$191$	−1254.68	−	3861.51i	−0.475316	−	1.46287i	0.370215	−	0.928946i	$-0.379284\pi$
$192$	4.81674	+	0.762897i	0.00181051	+	0.000286757i
$193$	2538.77	+	402.102i	0.946864	+	0.149969i	0.610724	−	0.791843i	$-0.290878\pi$
$193$	2538.77	+	402.102i	0.946864	+	0.149969i	0.336140	+	0.941812i	$0.390878\pi$
$194$	499.445	+	1537.13i	0.184835	+	0.568864i
$195$	−70.2239	+	0.114397i	−0.0257889	+	4.20108e-5i
$196$	1851.38	+	1345.10i	0.674700	+	0.490198i
$197$	−3084.40	+	3084.40i	−1.11551	+	1.11551i	−0.123113	+	0.992393i	$0.539288\pi$
$197$	−3084.40	+	3084.40i	−1.11551	+	1.11551i	−0.992393	+	0.123113i	$0.960712\pi$
$198$	879.568	−	1762.35i	0.315698	−	0.632550i
$199$		−	1439.73i		−	0.512864i	−0.966562	−	0.256432i	$-0.917453\pi$
$199$		−	1439.73i		−	0.512864i	0.966562	−	0.256432i	$-0.0825470\pi$
$200$	709.407	+	704.799i	0.250813	+	0.249184i
$201$	9.87310	−	30.3863i	0.00346465	−	0.0106631i
$202$	747.523	−	1467.10i	0.260374	−	0.511013i
$203$	694.994	−	4388.02i	0.240291	−	1.51714i
$204$	−0.787859	+	0.572413i	−0.000270398	+	0.000196456i
$205$	1152.32	+	1580.61i	0.392593	+	0.538511i
$206$	1547.83	+	502.921i	0.523508	+	0.170098i
$207$	364.941	+	2304.14i	0.122537	+	0.773667i
$208$	−932.571	−	932.571i	−0.310876	−	0.310876i
$209$	−1321.84	+	4186.43i	−0.437482	+	1.38556i
$210$	23.3254	−	45.9637i	0.00766480	−	0.0151038i
$211$	−57.4189	+	79.0303i	−0.0187340	+	0.0257852i	−0.818281	−	0.574818i	$-0.805073\pi$
$211$	−57.4189	+	79.0303i	−0.0187340	+	0.0257852i	0.799547	+	0.600603i	$0.205073\pi$
$212$	736.172	−	375.098i	0.238493	−	0.121518i
$213$	−1.83321	−	0.934065i	−0.000589714	−	0.000300475i
$214$	−303.887	−	418.264i	−0.0970713	−	0.133607i
$215$	−407.438	−	2545.62i	−0.129242	−	0.807487i
$216$	31.3038	−	10.1712i	0.00986089	−	0.00320400i
$217$	1021.63	+	2005.05i	0.319597	+	0.627244i
$218$	1723.63	−	272.996i	0.535499	−	0.0848147i
$219$	−74.6023			−0.0230190
$220$	−1556.65	−	488.716i	−0.477042	−	0.149769i
$221$	263.363			0.0801615
$222$	−44.6833	+	7.07714i	−0.0135088	+	0.00213958i
$223$	−981.329	−	1925.97i	−0.294685	−	0.578351i	0.695433	−	0.718591i	$-0.255213\pi$
$223$	−981.329	−	1925.97i	−0.294685	−	0.578351i	−0.990118	+	0.140240i	$0.955213\pi$
$224$	920.645	−	299.136i	0.274612	−	0.0892270i
$225$	3212.51	+	1032.25i	0.951854	+	0.305851i
$226$	1382.41	+	1902.73i	0.406888	+	0.560034i
$227$	−1778.24	−	906.056i	−0.519937	−	0.264921i	0.174268	−	0.984698i	$-0.444244\pi$
$227$	−1778.24	−	906.056i	−0.519937	−	0.264921i	−0.694205	+	0.719777i	$0.744244\pi$
$228$	−32.6802	+	16.6514i	−0.00949255	+	0.00483670i
$229$	3041.94	−	4186.87i	0.877804	−	1.20819i	−0.0992209	−	0.995065i	$-0.531635\pi$
$229$	3041.94	−	4186.87i	0.877804	−	1.20819i	0.977024	−	0.213127i	$-0.0683650\pi$
$230$	1836.88	−	600.148i	0.526609	−	0.172055i
$231$	0.699806	+	84.0937i	0.000199324	+	0.0239522i
$232$	−830.784	−	830.784i	−0.235102	−	0.235102i
$233$	−616.858	−	3894.69i	−0.173441	−	1.09506i	−0.908753	−	0.417334i	$-0.862964\pi$
$233$	−616.858	−	3894.69i	−0.173441	−	1.09506i	0.735312	−	0.677729i	$-0.237036\pi$
$234$	−4232.37	−	1375.18i	−1.18239	−	0.384181i
$235$	3614.82	+	566.497i	1.00343	+	0.157252i
$236$	434.642	−	315.786i	0.119885	−	0.0871013i
$237$	−10.1623	+	64.1621i	−0.00278528	+	0.0175856i
$238$	−87.7587	+	172.236i	−0.0239015	+	0.0469093i
$239$	1237.26	−	3807.91i	0.334862	−	1.03060i	−0.631929	−	0.775027i	$-0.717736\pi$
$239$	1237.26	−	3807.91i	0.334862	−	1.03060i	0.966790	−	0.255571i	$-0.0822636\pi$
$240$	−6.20813	−	12.1352i	−0.00166972	−	0.00326386i
$241$			2357.74i			0.630189i	0.949060	+	0.315094i	$0.102036\pi$
$241$			2357.74i			0.630189i	−0.949060	+	0.315094i	$0.897964\pi$
$242$	2621.93	−	460.127i	0.696463	−	0.122224i
$243$	117.805	−	117.805i	0.0310995	−	0.0310995i
$244$	−1981.42	−	1439.59i	−0.519866	−	0.377705i
$245$	−10.4198	−	6396.34i	−0.00271713	−	1.66795i
$246$	−8.23936	−	25.3581i	−0.00213546	−	0.00657226i
$247$	9796.88	+	1551.67i	2.52373	+	0.399719i
$248$	587.786	+	93.0962i	0.150502	+	0.0238371i
$249$	−23.3293	−	71.8003i	−0.00593750	−	0.0182737i
$250$	423.751	−	2762.78i	0.107201	−	0.698933i
$251$	4469.38	+	3247.20i	1.12392	+	0.816579i	0.984799	−	0.173696i	$-0.0555711\pi$
$251$	4469.38	+	3247.20i	1.12392	+	0.816579i	0.139125	+	0.990275i	$0.455571\pi$
$252$	2309.68	−	2309.68i	0.577365	−	0.577365i
$253$	−2210.80	+	2247.90i	−0.549374	+	0.558595i
$254$			4340.72i			1.07229i
$255$	2.59013	+	0.836922i	0.000636079	+	0.000205530i
$256$	79.1084	−	243.470i	0.0193136	−	0.0594410i
$257$	971.180	−	1906.05i	0.235722	−	0.462631i	−0.742596	−	0.669740i	$-0.766406\pi$
$257$	971.180	−	1906.05i	0.235722	−	0.462631i	0.978318	+	0.207109i	$0.0664056\pi$
$258$	−5.49726	+	34.7084i	−0.00132653	+	0.00837538i
$259$	−7265.00	+	5278.33i	−1.74295	+	1.26633i
$260$	−570.734	+	3641.86i	−0.136136	+	0.868687i
$261$	−3770.42	−	1225.08i	−0.894188	−	0.290539i
$262$	668.392	+	4220.06i	0.157608	+	0.995100i
$263$	−972.053	−	972.053i	−0.227906	−	0.227906i	0.583911	−	0.811818i	$-0.301522\pi$
$263$	−972.053	−	972.053i	−0.227906	−	0.227906i	−0.811818	+	0.583911i	$0.801522\pi$
$264$	18.1006	+	12.9221i	0.00421975	+	0.00301250i
$265$	−2059.37	−	1045.08i	−0.477381	−	0.242259i
$266$	−4279.33	+	5889.99i	−0.986400	+	1.35766i
$267$	55.5675	−	28.3131i	0.0127366	−	0.00648963i
$268$	−1494.37	−	761.420i	−0.340609	−	0.173549i
$269$	−1498.83	−	2062.96i	−0.339722	−	0.467587i	0.604638	−	0.796500i	$-0.293318\pi$
$269$	−1498.83	−	2062.96i	−0.339722	−	0.467587i	−0.944360	+	0.328913i	$0.893318\pi$
$270$	−74.5172	−	53.9546i	−0.0167962	−	0.0121614i
$271$	−5795.11	+	1882.95i	−1.29900	+	0.422069i	−0.875232	−	0.483703i	$-0.839291\pi$
$271$	−5795.11	+	1882.95i	−1.29900	+	0.422069i	−0.423764	+	0.905773i	$0.639291\pi$
$272$	23.2084	+	45.5490i	0.00517358	+	0.0101537i
$273$	187.666	−	29.7234i	0.0416047	−	0.00658953i
$274$	−421.027			−0.0928291
$275$	1459.36	+	4320.55i	0.320009	+	0.947415i
$276$	−26.3410			−0.00574472
$277$	492.343	−	77.9794i	0.106794	−	0.0169145i	−0.102809	−	0.994701i	$-0.532783\pi$
$277$	492.343	−	77.9794i	0.106794	−	0.0169145i	0.209603	+	0.977787i	$0.432783\pi$
$278$	−608.029	−	1193.32i	−0.131177	−	0.257449i
$279$	1909.79	−	620.529i	0.409807	−	0.133154i
$280$	−2191.55	−	1586.81i	−0.467751	−	0.338678i
$281$	−146.083	−	201.067i	−0.0310128	−	0.0426855i	0.793229	−	0.608923i	$-0.208398\pi$
$281$	−146.083	−	201.067i	−0.0310128	−	0.0426855i	−0.824242	+	0.566238i	$0.808398\pi$
$282$	−44.4391	−	22.6428i	−0.00938407	−	0.00478142i
$283$	−6525.69	+	3325.01i	−1.37071	+	0.698414i	−0.975464	−	0.220160i	$-0.929342\pi$
$283$	−6525.69	+	3325.01i	−1.37071	+	0.698414i	−0.395250	+	0.918574i	$0.629342\pi$
$284$	−63.4827	+	87.3765i	−0.0132641	+	0.0182565i
$285$	91.4197	+	46.3933i	0.0190008	+	0.00964245i
$286$	−1906.10	−	5704.42i	−0.394092	−	1.17940i
$287$	−3742.38	−	3742.38i	−0.769707	−	0.769707i
$288$	−135.130	−	853.179i	−0.0276480	−	0.174563i
$289$	4662.83	+	1515.05i	0.949080	+	0.308375i
$290$	−508.440	+	3244.36i	−0.102954	+	0.656950i
$291$	−49.8180	+	36.1949i	−0.0100357	+	0.00729135i
$292$	−612.620	+	3867.93i	−0.122777	+	0.775183i
$293$	3304.30	−	6485.05i	0.658837	−	1.29304i	−0.283692	−	0.958916i	$-0.591559\pi$
$293$	3304.30	−	6485.05i	0.658837	−	1.29304i	0.942529	−	0.334125i	$-0.108441\pi$
$294$	−26.9428	+	82.9215i	−0.00534468	+	0.0164492i
$295$	−1428.91	−	461.709i	−0.282015	−	0.0911245i
$296$			2374.83i			0.466331i
$297$	148.445	+	22.2468i	0.0290023	+	0.00434643i
$298$	1679.71	−	1679.71i	0.326519	−	0.326519i
$299$	5763.07	+	4187.12i	1.11467	+	0.809857i
$300$	−17.1863	+	34.0034i	−0.00330750	+	0.00654396i
$301$	2155.50	+	6633.96i	0.412762	+	1.27035i
$302$	−5409.27	−	856.745i	−1.03069	−	0.163245i
$303$	61.9614	+	9.81373i	0.0117478	+	0.00186067i
$304$	594.967	+	1831.12i	0.112249	+	0.345467i
$305$	11.1517	+	6845.63i	0.00209359	+	1.28518i
$306$	139.552	+	101.390i	0.0260707	+	0.0189415i
$307$	1355.10	−	1355.10i	0.251921	−	0.251921i	−0.569837	−	0.821758i	$-0.692994\pi$
$307$	1355.10	−	1355.10i	0.251921	−	0.251921i	0.821758	+	0.569837i	$0.192994\pi$
$308$	4365.78	+	654.278i	0.807673	+	0.121042i
$309$			62.0071i			0.0114157i
$310$	−757.577	−	1480.86i	−0.138798	−	0.271314i
$311$	13.9394	−	42.9011i	0.00254158	−	0.00782219i	−0.949778	−	0.312925i	$-0.898691\pi$
$311$	13.9394	−	42.9011i	0.00254158	−	0.00782219i	0.952319	+	0.305103i	$0.0986910\pi$
$312$	22.8122	−	44.7715i	0.00413938	−	0.00812399i
$313$	1277.87	−	8068.16i	0.230765	−	1.45700i	−0.551565	−	0.834132i	$-0.685969\pi$
$313$	1277.87	−	8068.16i	0.230765	−	1.45700i	0.782331	−	0.622863i	$-0.214031\pi$
$314$	1819.51	−	1321.95i	0.327010	−	0.237587i
$315$	−9019.71	−	1413.52i	−1.61334	−	0.252835i
$316$	3243.18	+	1053.77i	0.577353	+	0.187593i
$317$	−1313.38	−	8292.37i	−0.232703	−	1.46923i	−0.776555	−	0.630049i	$-0.783035\pi$
$317$	−1313.38	−	8292.37i	−0.232703	−	1.46923i	0.543852	−	0.839181i	$-0.316965\pi$
$318$	22.2591	+	22.2591i	0.00392524	+	0.00392524i
$319$	−1698.06	−	5081.80i	−0.298034	−	0.891931i
$320$	−680.160	+	222.223i	−0.118819	+	0.0388207i
$321$	11.5780	−	15.9358i	0.00201316	−	0.00277087i
$322$	−4658.72	+	2373.73i	−0.806273	+	0.410817i
$323$	−342.570	−	174.548i	−0.0590127	−	0.0300685i
$324$	−1712.88	−	2357.57i	−0.293703	−	0.404248i
$325$	9165.24	−	4707.60i	1.56430	−	0.803479i
$326$	−842.729	+	273.819i	−0.143173	+	0.0465198i
$327$	30.1852	+	59.2418i	0.00510472	+	0.0100186i
$328$	−1382.41	+	218.952i	−0.232716	+	0.0368586i
$329$	−9900.03			−1.65899
$330$	−0.618541	−	62.1593i	−0.000103180	−	0.0103690i
$331$	189.047			0.0313927			0.0156963	−	0.999877i	$-0.495003\pi$
$331$	189.047			0.0313927			0.0156963	+	0.999877i	$0.495003\pi$
$332$	−3914.23	+	619.953i	−0.647052	+	0.102483i
$333$	3637.97	+	7139.92i	0.598677	+	1.17497i
$334$	1980.47	−	643.492i	0.324450	−	0.105420i
$335$	740.881	+	4628.92i	0.120832	+	0.754940i
$336$	21.6784	+	29.8378i	0.00351981	+	0.00484460i
$337$	4622.93	+	2355.50i	0.747262	+	0.380749i	0.785778	−	0.618509i	$-0.212263\pi$
$337$	4622.93	+	2355.50i	0.747262	+	0.380749i	−0.0385159	+	0.999258i	$0.512263\pi$
$338$	−8192.70	+	4174.39i	−1.31842	+	0.671766i
$339$	−52.6698	+	72.4937i	−0.00843843	+	0.0116145i
$340$	64.6618	−	127.419i	0.0103141	−	0.0203243i
$341$	2208.81	+	1576.88i	0.350774	+	0.250419i
$342$	4593.84	+	4593.84i	0.726335	+	0.726335i
$343$	1084.19	+	6845.32i	0.170673	+	1.07759i
$344$	1754.39	+	570.037i	0.274973	+	0.0893440i
$345$	43.3729	+	59.4936i	0.00676846	+	0.00928415i
$346$	−2660.61	+	1933.05i	−0.413397	+	0.300350i
$347$	210.944	−	1331.85i	0.0326342	−	0.206044i	−0.965984	−	0.258603i	$-0.916738\pi$
$347$	210.944	−	1331.85i	0.0326342	−	0.206044i	0.998618	+	0.0525590i	$0.0167378\pi$
$348$	20.3223	−	39.8848i	0.00313043	−	0.00614382i
$349$	1508.29	−	4642.05i	0.231339	−	0.711987i	−0.766247	−	0.642546i	$-0.777878\pi$
$349$	1508.29	−	4642.05i	0.231339	−	0.711987i	0.997586	−	0.0694414i	$-0.0221217\pi$
$350$	24.6396	+	7562.64i	0.00376297	+	1.15497i
$351$		−	339.139i		−	0.0515723i
$352$	818.615	−	832.354i	0.123955	−	0.126036i
$353$	−3529.19	+	3529.19i	−0.532124	+	0.532124i	−0.921204	−	0.389080i	$-0.872793\pi$
$353$	−3529.19	+	3529.19i	−0.532124	+	0.532124i	0.389080	+	0.921204i	$0.372793\pi$
$354$	16.5598	+	12.0314i	0.00248628	+	0.00180639i
$355$	301.878	−	0.491767i	0.0451324	−	7.35220e-5i
$356$	−1011.65	−	3113.53i	−0.150610	−	0.463530i
$357$	−7.27423	−	1.15212i	−0.00107841	−	0.000170804i
$358$	871.576	+	138.044i	0.128671	+	0.0203795i
$359$	1351.70	+	4160.12i	0.198719	+	0.611595i	0.999913	+	0.0131899i	$0.00419860\pi$
$359$	1351.70	+	4160.12i	0.198719	+	0.611595i	−0.801194	+	0.598405i	$0.795801\pi$
$360$	−1704.48	+	1710.04i	−0.249539	+	0.250353i
$361$	−6165.87	−	4479.77i	−0.898947	−	0.653123i
$362$	−1404.56	+	1404.56i	−0.203929	+	0.203929i
$363$	47.5421	+	89.5887i	0.00687414	+	0.0129537i
$364$		−	9974.08i		−	1.43622i
$365$	9744.81	−	4985.24i	1.39744	−	0.714903i
$366$	28.8353	−	88.7460i	0.00411816	−	0.0126744i
$367$	−235.688	+	462.564i	−0.0335226	+	0.0657919i	−0.907160	−	0.420785i	$-0.861755\pi$
$367$	−235.688	+	462.564i	−0.0335226	+	0.0657919i	0.873638	+	0.486577i	$0.161755\pi$
$368$	−216.308	+	1365.71i	−0.0306408	+	0.193458i
$369$	−3820.81	+	2775.98i	−0.539034	+	0.391631i
$370$	5363.76	−	3910.37i	0.753646	−	0.549434i
$371$	5942.66	+	1930.89i	0.831610	+	0.270206i
$372$	3.54695	+	22.3946i	0.000494357	+	0.00312125i
$373$	2211.19	+	2211.19i	0.306946	+	0.306946i	0.843724	−	0.536777i	$-0.180359\pi$
$373$	2211.19	+	2211.19i	0.306946	+	0.306946i	−0.536777	+	0.843724i	$0.680359\pi$
$374$	1.93997	+	233.121i	0.000268218	+	0.0322310i
$375$	105.099	−	17.1729i	0.0144727	−	0.00236481i
$376$	−1538.90	+	2118.11i	−0.211071	+	0.290514i
$377$	−10786.3	+	5495.87i	−1.47353	+	0.750801i
$378$	221.793	+	113.009i	0.0301793	+	0.0153771i
$379$	−3701.05	−	5094.05i	−0.501610	−	0.690406i	0.480867	−	0.876794i	$-0.340322\pi$
$379$	−3701.05	−	5094.05i	−0.501610	−	0.690406i	−0.982476	+	0.186387i	$0.940322\pi$
$380$	3156.09	−	4358.90i	0.426063	−	0.588439i
$381$	−157.287	+	51.1055i	−0.0211497	+	0.00687195i
$382$	−3686.61	−	7235.38i	−0.493778	−	0.969095i
$383$	−3057.75	+	484.300i	−0.407947	+	0.0646125i	−0.357036	−	0.934091i	$-0.616213\pi$
$383$	−3057.75	+	484.300i	−0.407947	+	0.0646125i	−0.0509115	+	0.998703i	$0.516213\pi$
$384$	9.75357			0.00129618
$385$	−5710.91	−	10937.8i	−0.755986	−	1.44791i
$386$	5140.84			0.677880
$387$	6147.82	−	973.719i	0.807522	−	0.127899i
$388$	1467.51	+	2880.16i	0.192015	+	0.376850i
$389$	6466.06	−	2100.95i	0.842782	−	0.273837i	0.144362	−	0.989525i	$-0.453887\pi$
$389$	6466.06	−	2100.95i	0.842782	−	0.273837i	0.698420	+	0.715688i	$0.253887\pi$
$390$	−138.683	+	22.1968i	−0.0180064	+	0.00288200i
$391$	−162.299	−	223.385i	−0.0209918	−	0.0288928i
$392$	4078.01	+	2077.85i	0.525435	+	0.267722i
$393$	−145.045	+	73.9042i	−0.0186172	+	0.00948593i
$394$	−5127.84	+	7057.87i	−0.655678	+	0.902463i
$395$	−2960.15	−	9060.17i	−0.377067	−	1.15409i
$396$	1186.09	−	3756.50i	0.150514	−	0.476695i
$397$	−2414.44	−	2414.44i	−0.305233	−	0.305233i	0.537824	−	0.843057i	$-0.319246\pi$
$397$	−2414.44	−	2414.44i	−0.305233	−	0.305233i	−0.843057	+	0.537824i	$0.819246\pi$
$398$	−450.448	−	2844.02i	−0.0567309	−	0.358185i
$399$	−263.807	−	85.7161i	−0.0330999	−	0.0107548i
$400$	1621.86	+	1170.29i	0.202732	+	0.146287i
$401$	2713.15	−	1971.22i	0.337876	−	0.245481i	−0.405889	−	0.913922i	$-0.633038\pi$
$401$	2713.15	−	1971.22i	0.337876	−	0.245481i	0.743765	+	0.668441i	$0.233038\pi$
$402$	9.99616	−	63.1133i	0.00124021	−	0.00783036i
$403$	2783.77	−	5463.45i	0.344093	−	0.675320i
$404$	1017.63	−	3131.95i	0.125319	−	0.385694i
$405$	−2504.39	+	7750.64i	−0.307269	+	0.950945i
$406$		−	8885.44i		−	1.08615i
$407$	−4836.28	+	9690.24i	−0.589006	+	1.18017i
$408$	−1.37723	+	1.37723i	−0.000167115	+	0.000167115i
$409$	−3135.45	−	2278.04i	−0.379066	−	0.275407i	0.381894	−	0.924206i	$-0.375272\pi$
$409$	−3135.45	−	2278.04i	−0.379066	−	0.275407i	−0.760960	+	0.648799i	$0.775272\pi$
$410$	2770.79	+	2761.78i	0.333755	+	0.332670i
$411$	−4.95696	−	15.2560i	−0.000594912	−	0.00183095i
$412$	3214.90	+	509.190i	0.384434	+	0.0608884i
$413$	4013.01	+	635.598i	0.478129	+	0.0757281i
$414$	1441.79	+	4437.37i	0.171160	+	0.526775i
$415$	7845.36	+	7819.84i	0.927984	+	0.924966i
$416$	−2133.95	−	1550.41i	−0.251504	−	0.182728i
$417$	36.0816	−	36.0816i	0.00423723	−	0.00423723i
$418$	−1301.33	+	8683.34i	−0.152273	+	1.01607i
$419$			16395.5i			1.91162i	0.293977	+	0.955812i	$0.405021\pi$
$419$			16395.5i			1.91162i	−0.293977	+	0.955812i	$0.594979\pi$
$420$	31.6959	−	98.0934i	0.00368239	−	0.0113964i
$421$	5180.35	−	15943.5i	0.599703	−	1.84569i	0.0699360	−	0.997551i	$-0.477720\pi$
$421$	5180.35	−	15943.5i	0.599703	−	1.84569i	0.529767	−	0.848143i	$-0.322280\pi$
$422$	−88.6978	+	174.079i	−0.0102316	+	0.0200807i
$423$	−1381.99	+	8725.51i	−0.158852	+	1.00295i
$424$	1336.86	−	971.286i	0.153122	−	0.111250i
$425$	−394.258	+	63.7618i	−0.0449985	+	0.00727742i
$426$	−3.91351	−	1.27158i	−0.000445095	−	0.000144620i
$427$	−2897.53	−	18294.3i	−0.328387	−	2.07335i
$428$	−731.152	−	731.152i	−0.0825738	−	0.0825738i
$429$	184.259	−	136.229i	0.0207368	−	0.0153314i
$430$	−1601.29	−	4901.08i	−0.179584	−	0.549653i
$431$	679.460	−	935.197i	0.0759361	−	0.104517i	−0.769359	−	0.638816i	$-0.779424\pi$
$431$	679.460	−	935.197i	0.0759361	−	0.104517i	0.845295	+	0.534299i	$0.179424\pi$
$432$	58.6545	−	29.8860i	0.00653244	−	0.00332845i
$433$	−351.104	−	178.897i	−0.0389676	−	0.0198550i	0.434398	−	0.900721i	$-0.356961\pi$
$433$	−351.104	−	178.897i	−0.0389676	−	0.0198550i	−0.473366	+	0.880866i	$0.656961\pi$
$434$	2645.42	+	3641.10i	0.292590	+	0.402716i
$435$	−123.546	+	19.7741i	−0.0136174	+	0.00217953i
$436$	3319.40	−	1078.54i	0.364611	−	0.118469i
$437$	−4721.25	−	9265.98i	−0.516815	−	1.01431i
$438$	−147.368	+	23.3407i	−0.0160765	+	0.00254626i
$439$	15213.7			1.65401			0.827004	−	0.562197i	$-0.190044\pi$
$439$	15213.7			1.65401			0.827004	+	0.562197i	$0.190044\pi$
$440$	−3227.87	−	478.371i	−0.349734	−	0.0518305i
$441$	15443.6			1.66759
$442$	520.241	−	82.3980i	0.0559849	−	0.00886714i
$443$	4093.18	+	8033.31i	0.438990	+	0.861567i	0.999443	+	0.0333804i	$0.0106273\pi$
$443$	4093.18	+	8033.31i	0.438990	+	0.861567i	−0.560452	+	0.828187i	$0.689373\pi$
$444$	−86.0521	+	27.9600i	−0.00919787	+	0.00298857i
$445$	−5366.42	+	7411.60i	−0.571669	+	0.789537i
$446$	−2541.07	−	3497.48i	−0.269783	−	0.371324i
$447$	80.6404	+	41.0883i	0.00853280	+	0.00434768i
$448$	1725.03	−	878.947i	0.181920	−	0.0926927i
$449$	724.497	−	997.185i	0.0761495	−	0.104811i	−0.769243	−	0.638956i	$-0.779366\pi$
$449$	724.497	−	997.185i	0.0761495	−	0.104811i	0.845393	+	0.534145i	$0.179366\pi$
$450$	6668.87	+	1033.98i	0.698608	+	0.108317i
$451$	−6086.68	−	1921.83i	−0.635500	−	0.200656i
$452$	3326.09	+	3326.09i	0.346120	+	0.346120i
$453$	−32.6419	−	206.093i	−0.00338554	−	0.0213754i
$454$	−3796.16	−	1233.45i	−0.392429	−	0.127508i
$455$	−22527.4	+	16423.2i	−2.32110	+	1.69216i
$456$	−59.3461	+	43.1174i	−0.00609459	+	0.00442798i
$457$	−2541.50	+	16046.4i	−0.260145	+	1.64249i	0.418639	+	0.908153i	$0.362507\pi$
$457$	−2541.50	+	16046.4i	−0.260145	+	1.64249i	−0.678784	+	0.734338i	$0.737493\pi$
$458$	4699.03	−	9222.37i	0.479414	−	0.940902i
$459$	−4.06219	+	12.5021i	−0.000413087	+	0.00127135i
$460$	3440.76	−	1760.22i	0.348752	−	0.178414i
$461$		−	11632.9i		−	1.17527i	−0.809126	−	0.587636i	$-0.800059\pi$
$461$		−	11632.9i		−	1.17527i	0.809126	−	0.587636i	$-0.199941\pi$
$462$	27.6927	+	165.898i	0.00278870	+	0.0167062i
$463$	7018.26	−	7018.26i	0.704462	−	0.704462i	−0.260903	−	0.965365i	$-0.584020\pi$
$463$	7018.26	−	7018.26i	0.704462	−	0.704462i	0.965365	+	0.260903i	$0.0840202\pi$
$464$	−1901.04	−	1381.18i	−0.190201	−	0.138189i
$465$	44.7398	−	44.8858i	0.00446185	−	0.00447641i
$466$	−2437.06	−	7500.48i	−0.242263	−	0.745608i
$467$	8107.17	+	1284.05i	0.803330	+	0.127235i	0.544580	−	0.838709i	$-0.316689\pi$
$467$	8107.17	+	1284.05i	0.803330	+	0.127235i	0.258751	+	0.965944i	$0.416689\pi$
$468$	−8790.78	−	1392.32i	−0.868277	−	0.137522i
$469$	−3919.55	−	12063.1i	−0.385902	−	1.18768i
$470$	7317.88	−	11.9210i	0.718188	−	0.00116995i
$471$	69.3233	+	50.3663i	0.00678184	+	0.00492730i
$472$	759.782	−	759.782i	0.0740928	−	0.0740928i
$473$	5997.76	+	5898.76i	0.583038	+	0.573415i
$474$			129.924i			0.0125899i
$475$	−15041.8	+	49.0070i	−1.45298	+	0.00473389i
$476$	−119.469	+	367.688i	−0.0115039	+	0.0354054i
$477$	2531.37	−	4968.09i	0.242984	−	0.476883i
$478$	1252.69	−	7909.15i	0.119867	−	0.756812i
$479$	−8376.41	+	6085.82i	−0.799015	+	0.580518i	−0.910625	−	0.413234i	$-0.864399\pi$
$479$	−8376.41	+	6085.82i	−0.799015	+	0.580518i	0.111610	+	0.993752i	$0.464399\pi$
$480$	−16.0601	−	22.0293i	−0.00152717	−	0.00209478i
$481$	23271.5	+	7561.38i	2.20601	+	0.716776i
$482$	737.664	+	4657.43i	0.0697089	+	0.440125i
$483$	−140.862	−	140.862i	−0.0132701	−	0.0132701i
$484$	5035.34	−	1729.25i	0.472891	−	0.162401i
$485$	4088.70	−	8056.95i	0.382801	−	0.754324i
$486$	195.851	−	269.566i	0.0182798	−	0.0251600i
$487$	−338.796	+	172.625i	−0.0315243	+	0.0160624i	−0.469682	−	0.882836i	$-0.655631\pi$
$487$	−338.796	+	172.625i	−0.0315243	+	0.0160624i	0.438157	+	0.898898i	$0.355631\pi$
$488$	−4364.45	−	2223.80i	−0.404856	−	0.206284i
$489$	−19.8438	−	27.3126i	−0.00183510	−	0.00252580i
$490$	−2021.80	−	12631.9i	−0.186399	−	1.16460i
$491$	−14540.4	+	4724.45i	−1.33645	+	0.434239i	−0.888113	−	0.459625i	$-0.847984\pi$
$491$	−14540.4	+	4724.45i	−1.33645	+	0.434239i	−0.448337	+	0.893864i	$0.647984\pi$
$492$	−24.2096	−	47.5140i	−0.00221840	−	0.00435386i
$493$	463.458	−	73.4045i	0.0423389	−	0.00670583i
$494$	19838.0			1.80679
$495$	−10437.4	+	3506.52i	−0.947731	+	0.318397i
$496$	1190.23			0.107747
$497$	−806.738	+	127.775i	−0.0728112	+	0.0115322i
$498$	−68.5483	−	134.534i	−0.00616812	−	0.0121056i
$499$	7105.30	−	2308.65i	0.637429	−	0.207113i	0.0275657	−	0.999620i	$-0.491224\pi$
$499$	7105.30	−	2308.65i	0.637429	−	0.207113i	0.609863	+	0.792507i	$0.291224\pi$
$500$	−27.3195	−	5590.10i	−0.00244353	−	0.499994i
$501$	46.6341	+	64.1863i	0.00415860	+	0.00572382i
$502$	9844.66	+	5016.11i	0.875276	+	0.445976i
$503$	13152.3	−	6701.45i	1.16587	−	0.594041i	0.239590	−	0.970874i	$-0.422987\pi$
$503$	13152.3	−	6701.45i	1.16587	−	0.594041i	0.926281	+	0.376833i	$0.122987\pi$
$504$	3839.86	−	5285.11i	0.339367	−	0.467098i
$505$	−8749.41	+	2858.62i	−0.770978	+	0.251895i
$506$	−3663.86	+	5132.14i	−0.321894	+	0.450893i
$507$	−247.716	−	247.716i	−0.0216992	−	0.0216992i
$508$	1358.08	+	8574.56i	0.118612	+	0.748887i
$509$	−1826.87	−	593.587i	−0.159086	−	0.0516901i	0.228391	−	0.973569i	$-0.426653\pi$
$509$	−1826.87	−	593.587i	−0.159086	−	0.0516901i	−0.387477	+	0.921879i	$0.626653\pi$
$510$	5.37833	+	0.842865i	0.000466973	+	7.31817e-5i
$511$	−23960.3	+	17408.2i	−2.07425	+	1.50703i
$512$	80.0944	−	505.696i	0.00691349	−	0.0436501i
$513$	−224.770	+	441.136i	−0.0193447	+	0.0379661i
$514$	1322.10	−	4069.02i	0.113454	−	0.349176i
$515$	−4143.57	−	8099.58i	−0.354539	−	0.693029i
$516$			70.2820i			0.00599611i
$517$	−10592.8	+	5508.80i	−0.901103	+	0.468621i
$518$	−12699.7	+	12699.7i	−1.07720	+	1.07720i
$519$	−101.369	−	73.6488i	−0.00857341	−	0.00622895i
$520$	12.0102	+	7372.61i	0.00101285	+	0.621751i
$521$	−149.879	−	461.279i	−0.0126033	−	0.0387889i	0.944557	−	0.328347i	$-0.106492\pi$
$521$	−149.879	−	461.279i	−0.0126033	−	0.0387889i	−0.957160	+	0.289558i	$0.906492\pi$
$522$	−7831.29	−	1240.35i	−0.656640	−	0.104002i
$523$	−10960.4	−	1735.95i	−0.916373	−	0.145139i	−0.319603	−	0.947552i	$-0.603549\pi$
$523$	−10960.4	−	1735.95i	−0.916373	−	0.145139i	−0.596770	+	0.802412i	$0.703549\pi$
$524$	2640.65	+	8127.09i	0.220148	+	0.677545i
$525$	−273.743	+	89.9316i	−0.0227564	+	0.00747607i
$526$	−2224.30	−	1616.05i	−0.184380	−	0.133960i
$527$	−168.063	+	168.063i	−0.0138917	+	0.0138917i
$528$	39.7984	+	19.8629i	0.00328031	+	0.00163716i
$529$			4698.41i			0.386160i
$530$	−4395.00	−	1420.11i	−0.360201	−	0.116388i
$531$	1120.38	−	3448.19i	0.0915641	−	0.281805i
$532$	−6610.49	+	12973.8i	−0.538724	+	1.05730i
$533$	−2255.99	+	14243.7i	−0.183335	+	1.15753i
$534$	100.908	−	73.3143i	0.00817741	−	0.00594123i
$535$	−447.466	+	2855.28i	−0.0361601	+	0.230738i
$536$	−3190.17	−	1036.55i	−0.257079	−	0.0835300i
$537$	5.25946	+	33.2069i	0.000422649	+	0.00266850i
$538$	−3606.19	−	3606.19i	−0.288985	−	0.288985i
$539$	12408.4	+	16783.2i	0.991591	+	1.34119i
$540$	−164.080	−	83.2666i	−0.0130757	−	0.00663560i
$541$	3706.22	−	5101.18i	0.294534	−	0.405391i	−0.635946	−	0.771733i	$-0.719390\pi$
$541$	3706.22	−	5101.18i	0.294534	−	0.405391i	0.930480	+	0.366342i	$0.119390\pi$
$542$	−10858.4	+	5532.64i	−0.860533	+	0.438463i
$543$	−67.4312	−	34.3579i	−0.00532919	−	0.00271536i
$544$	60.0961	+	82.7152i	0.00473639	+	0.00651909i
$545$	−7901.68	−	5721.26i	−0.621047	−	0.449673i
$546$	361.412	−	117.430i	0.0283279	−	0.00920428i
$547$	47.2601	+	92.7531i	0.00369414	+	0.00725016i	0.892846	−	0.450362i	$-0.148705\pi$
$547$	47.2601	+	92.7531i	0.00369414	+	0.00725016i	−0.889152	+	0.457612i	$0.848705\pi$
$548$	−831.687	+	131.726i	−0.0648319	+	0.0102684i
$549$	−16528.3			−1.28490
$550$	4234.54	+	8078.13i	0.328294	+	0.626277i
$551$	17672.7			1.36640
$552$	−52.0335	+	8.24129i	−0.00401212	+	0.000635458i
$553$	11708.1	+	22978.5i	0.900327	+	1.76699i
$554$	948.165	−	308.078i	0.0727142	−	0.0236263i
$555$	204.843	+	148.318i	0.0156669	+	0.0113437i
$556$	−1574.44	−	2167.03i	−0.120092	−	0.165292i
$557$	6057.43	+	3086.42i	0.460793	+	0.234786i	0.668947	−	0.743310i	$-0.266745\pi$
$557$	6057.43	+	3086.42i	0.460793	+	0.234786i	−0.208154	+	0.978096i	$0.566745\pi$
$558$	3578.41	−	1823.29i	0.271481	−	0.138326i
$559$	11171.9	−	15376.8i	0.845296	−	1.16345i
$560$	−4825.60	−	2448.87i	−0.364141	−	0.184792i
$561$	−8.42433	+	2.81495i	−0.000634003	+	0.000211849i
$562$	−351.477	−	351.477i	−0.0263811	−	0.0263811i
$563$	−3120.54	−	19702.3i	−0.233597	−	1.47487i	−0.773849	−	0.633370i	$-0.781671\pi$
$563$	−3120.54	−	19702.3i	−0.233597	−	1.47487i	0.540252	−	0.841503i	$-0.318329\pi$
$564$	−94.8682	−	30.8245i	−0.00708275	−	0.00230132i
$565$	2035.57	−	12989.0i	0.151570	−	0.967170i
$566$	−11850.4	+	8609.82i	−0.880053	+	0.639396i
$567$	3447.59	−	21767.2i	0.255353	−	1.61224i
$568$	−98.0649	+	192.463i	−0.00724421	+	0.0142176i
$569$	−330.409	+	1016.89i	−0.0243435	+	0.0749216i	−0.962490	−	0.271316i	$-0.912541\pi$
$569$	−330.409	+	1016.89i	−0.0243435	+	0.0749216i	0.938147	+	0.346238i	$0.112541\pi$
$570$	195.103	+	63.0417i	0.0143368	+	0.00463251i
$571$			1864.20i			0.136628i	0.997664	+	0.0683138i	$0.0217619\pi$
$571$			1864.20i			0.136628i	−0.997664	+	0.0683138i	$0.978238\pi$
$572$	−5550.01	−	10672.0i	−0.405695	−	0.780104i
$573$	218.771	−	218.771i	0.0159499	−	0.0159499i
$574$	−8563.49	−	6221.74i	−0.622706	−	0.452423i
$575$	−9641.14	−	4872.90i	−0.699240	−	0.353416i
$576$	−533.867	−	1643.07i	−0.0386188	−	0.118856i
$577$	−19813.5	−	3138.14i	−1.42954	−	0.226417i	−0.606809	−	0.794848i	$-0.707551\pi$
$577$	−19813.5	−	3138.14i	−1.42954	−	0.226417i	−0.822731	+	0.568431i	$0.807551\pi$
$578$	9684.86	+	1533.93i	0.696950	+	0.110386i
$579$	60.5257	+	186.279i	0.00434432	+	0.0133704i
$580$	10.6993	+	6567.91i	0.000765974	+	0.470203i
$581$	−24247.1	−	17616.6i	−1.73139	−	1.25793i
$582$	−87.0850	+	87.0850i	−0.00620239	+	0.00620239i
$583$	7432.92	−	1240.75i	0.528028	−	0.0881416i
$584$			7832.29i			0.554970i
$585$	11330.1	+	22147.4i	0.800757	+	1.56527i
$586$	4498.27	−	13844.2i	0.317102	−	0.975939i
$587$	−6886.00	+	13514.5i	−0.484184	+	0.950264i	0.511660	+	0.859188i	$0.329031\pi$
$587$	−6886.00	+	13514.5i	−0.484184	+	0.950264i	−0.995844	+	0.0910761i	$0.970969\pi$
$588$	−27.2787	+	172.231i	−0.00191319	+	0.0120794i
$589$	−7241.99	+	5261.61i	−0.506623	+	0.368083i
$590$	−2967.09	−	464.987i	−0.207039	−	0.0324461i
$591$	−316.115	−	102.712i	−0.0220021	−	0.00714892i
$592$	743.010	+	4691.18i	0.0515836	+	0.325686i
$593$	6769.45	+	6769.45i	0.468783	+	0.468783i	0.901520	−	0.432737i	$-0.142452\pi$
$593$	6769.45	+	6769.45i	0.468783	+	0.468783i	−0.432737	+	0.901520i	$0.642452\pi$
$594$	300.196	−	2.49815i	0.0207360	−	0.000172560i
$595$	1027.17	−	335.600i	0.0707732	−	0.0231231i
$596$	2792.52	−	3843.58i	0.191923	−	0.264160i
$597$	97.7499	−	49.8061i	0.00670123	−	0.00341445i
$598$	12694.3	+	6468.05i	0.868071	+	0.442304i
$599$	11817.9	+	16265.9i	0.806118	+	1.10953i	0.991911	+	0.126937i	$0.0405146\pi$
$599$	11817.9	+	16265.9i	0.806118	+	1.10953i	−0.185793	+	0.982589i	$0.559485\pi$
$600$	−23.3108	+	72.5466i	−0.00158610	+	0.00493617i
$601$	11145.0	−	3621.24i	0.756430	−	0.245779i	0.0946845	−	0.995507i	$-0.469816\pi$
$601$	11145.0	−	3621.24i	0.756430	−	0.245779i	0.661746	+	0.749728i	$0.269816\pi$
$602$	6333.49	+	12430.2i	0.428794	+	0.841556i
$603$	−11179.1	+	1770.60i	−0.754974	+	0.119576i
$604$	−10953.4			−0.737893
$605$	−12196.8	−	8525.43i	−0.819621	−	0.572905i
$606$	125.468			0.00841051
$607$	11690.2	−	1851.55i	0.781699	−	0.123809i	0.247185	−	0.968968i	$-0.420495\pi$
$607$	11690.2	−	1851.55i	0.781699	−	0.123809i	0.534514	+	0.845160i	$0.320495\pi$
$608$	1748.19	+	3431.01i	0.116609	+	0.228858i
$609$	321.965	−	104.613i	0.0214231	−	0.00696079i
$610$	2163.81	+	13519.2i	0.143623	+	0.897339i
$611$	15856.1	+	21824.0i	1.04987	+	1.44502i
$612$	307.389	+	156.623i	0.0203031	+	0.0103449i
$613$	−18446.4	+	9398.92i	−1.21541	+	0.619280i	−0.939713	−	0.341965i	$-0.888908\pi$
$613$	−18446.4	+	9398.92i	−1.21541	+	0.619280i	−0.275694	+	0.961246i	$0.588908\pi$
$614$	2252.87	−	3100.81i	0.148076	−	0.203808i
$615$	−67.4515	+	132.916i	−0.00442261	+	0.00871493i
$616$	8828.76	−	73.4707i	0.577469	−	0.00480555i
$617$	−1702.75	−	1702.75i	−0.111102	−	0.111102i	0.649370	−	0.760472i	$-0.275033\pi$
$617$	−1702.75	−	1702.75i	−0.111102	−	0.111102i	−0.760472	+	0.649370i	$0.775033\pi$
$618$	19.4001	+	122.487i	0.00126276	+	0.00797275i
$619$	−9739.65	−	3164.60i	−0.632423	−	0.205487i	−0.0247747	−	0.999693i	$-0.507887\pi$
$619$	−9739.65	−	3164.60i	−0.632423	−	0.205487i	−0.607648	+	0.794206i	$0.707887\pi$
$620$	−1959.82	−	2688.23i	−0.126949	−	0.174132i
$621$	−287.659	+	208.996i	−0.0185883	+	0.0135052i
$622$	14.1132	−	89.1071i	0.000909786	−	0.00574416i
$623$	11240.1	−	22059.9i	0.722831	−	1.41864i
$624$	31.0551	−	95.5777i	0.00199231	−	0.00613168i
$625$	−12580.8	+	9266.32i	−0.805170	+	0.593044i
$626$		−	16337.5i		−	1.04309i
$627$	−329.963	+	55.0795i	−0.0210167	+	0.00350823i
$628$	3180.63	−	3180.63i	0.202103	−	0.202103i
$629$	−767.321	−	557.491i	−0.0486409	−	0.0353396i
$630$	−18259.6	+	29.7454i	−1.15473	+	0.00188108i
$631$	−3968.15	−	12212.7i	−0.250348	−	0.770492i	−0.994711	−	0.102717i	$-0.967247\pi$
$631$	−3968.15	−	12212.7i	−0.250348	−	0.770492i	0.744363	−	0.667776i	$-0.232753\pi$
$632$	6736.20	+	1066.91i	0.423974	+	0.0671510i
$633$	−7.35207	−	1.16445i	−0.000461640	−	7.31167e-5i
$634$	−5188.85	−	15969.6i	−0.325040	−	1.00037i
$635$	17130.2	−	17186.1i	1.07054	−	1.07403i
$636$	50.9342	+	37.0059i	0.00317559	+	0.00230720i
$637$	33345.6	−	33345.6i	2.07410	−	2.07410i
$638$	−4944.24	−	9507.19i	−0.306809	−	0.589958i
$639$			728.865i			0.0451228i
$640$	−1274.04	+	651.775i	−0.0786891	+	0.0402557i
$641$	−8205.85	+	25255.0i	−0.505634	+	1.55618i	0.294067	+	0.955785i	$0.404991\pi$
$641$	−8205.85	+	25255.0i	−0.505634	+	1.55618i	−0.799701	+	0.600398i	$0.795009\pi$
$642$	17.8852	−	35.1016i	0.00109949	−	0.00215787i
$643$	3569.91	−	22539.5i	0.218948	−	1.38238i	−0.596063	−	0.802938i	$-0.703269\pi$
$643$	3569.91	−	22539.5i	0.218948	−	1.38238i	0.815011	−	0.579446i	$-0.196731\pi$
$644$	−8460.05	+	6146.59i	−0.517659	+	0.376102i
$645$	158.738	−	115.726i	0.00969042	−	0.00706465i
$646$	−731.315	−	237.619i	−0.0445406	−	0.0144721i
$647$	640.094	+	4041.39i	0.0388944	+	0.245570i	0.999474	−	0.0324362i	$-0.0103266\pi$
$647$	640.094	+	4041.39i	0.0388944	+	0.245570i	−0.960579	+	0.278006i	$0.910327\pi$
$648$	−4121.19	−	4121.19i	−0.249839	−	0.249839i
$649$	4647.49	−	1552.94i	0.281094	−	0.0939261i
$650$	16631.9	−	12166.8i	1.00363	−	0.734187i
$651$	−100.790	+	138.726i	−0.00606801	+	0.00835189i
$652$	−1579.04	+	804.560i	−0.0948465	+	0.0483267i
$653$	12333.3	+	6284.11i	0.739109	+	0.376595i	0.782654	−	0.622457i	$-0.213865\pi$
$653$	12333.3	+	6284.11i	0.739109	+	0.376595i	−0.0435455	+	0.999051i	$0.513865\pi$
$654$	78.1620	+	107.581i	0.00467336	+	0.00643233i
$655$	14007.7	−	19346.1i	0.835613	−	1.15407i
$656$	−2662.28	+	865.027i	−0.158452	+	0.0514842i
$657$	11998.2	+	23547.8i	0.712472	+	1.39830i
$658$	−19556.3	+	3097.41i	−1.15864	+	0.183510i
$659$	13610.3			0.804526			0.402263	−	0.915524i	$-0.368224\pi$
$659$	13610.3			0.804526			0.402263	+	0.915524i	$0.368224\pi$
$660$	−20.6696	−	122.594i	−0.00121903	−	0.00723028i
$661$	19181.2			1.12869			0.564345	−	0.825539i	$-0.309129\pi$
$661$	19181.2			1.12869			0.564345	+	0.825539i	$0.309129\pi$
$662$	373.439	−	59.1470i	0.0219247	−	0.00347253i
$663$	9.11076	+	17.8809i	0.000533684	+	0.00104741i
$664$	−7538.12	+	2449.28i	−0.440566	+	0.143148i
$665$	40187.3	−	6432.17i	2.34345	−	0.375081i
$666$	9420.22	+	12965.8i	0.548087	+	0.754377i
$667$	11308.7	+	5762.08i	0.656484	+	0.334496i
$668$	3710.84	−	1890.77i	0.214935	−	0.109515i
$669$	96.8145	−	133.254i	0.00559501	−	0.00770087i
$670$	2911.76	+	8912.06i	0.167897	+	0.513885i
$671$	−13280.0	−	17962.1i	−0.764036	−	1.03341i
$672$	52.1584	+	52.1584i	0.00299413	+	0.00299413i
$673$	−2616.91	−	16522.5i	−0.149888	−	0.946354i	−0.941911	−	0.335863i	$-0.890972\pi$
$673$	−2616.91	−	16522.5i	−0.149888	−	0.946354i	0.792023	−	0.610491i	$-0.209028\pi$
$674$	9869.00	+	3206.63i	0.564005	+	0.183256i
$675$	82.1077	+	507.696i	0.00468196	+	0.0289500i
$676$	−14877.6	+	10809.2i	−0.846475	+	0.615000i
$677$	2939.79	−	18561.1i	0.166891	−	1.05371i	−0.751989	−	0.659175i	$-0.770906\pi$
$677$	2939.79	−	18561.1i	0.166891	−	1.05371i	0.918881	−	0.394535i	$-0.129094\pi$
$678$	−81.3616	+	159.681i	−0.00460866	+	0.00904501i
$679$	−7554.28	+	23249.7i	−0.426961	+	1.31405i
$680$	87.8661	−	271.931i	0.00495516	−	0.0153354i
$681$		−	152.076i		−	0.00855739i
$682$	4856.59	+	2423.87i	0.272681	+	0.136092i
$683$	1111.95	−	1111.95i	0.0622953	−	0.0622953i	−0.675273	−	0.737568i	$-0.735974\pi$
$683$	1111.95	−	1111.95i	0.0622953	−	0.0622953i	0.737568	+	0.675273i	$0.235974\pi$
$684$	10511.8	+	7637.30i	0.587617	+	0.426929i
$685$	1666.96	+	1661.54i	0.0929802	+	0.0926777i
$686$	4283.38	+	13182.9i	0.238397	+	0.733709i
$687$	389.498	+	61.6904i	0.0216307	+	0.00342596i
$688$	3643.94	+	577.143i	0.201924	+	0.0319816i
$689$	−5261.36	−	16192.8i	−0.290917	−	0.895350i
$690$	104.292	+	103.952i	0.00575408	+	0.00573536i
$691$	4984.39	+	3621.37i	0.274407	+	0.199368i	0.716474	−	0.697614i	$-0.245755\pi$
$691$	4984.39	+	3621.37i	0.274407	+	0.199368i	−0.442067	+	0.896982i	$0.645755\pi$
$692$	−4650.92	+	4650.92i	−0.255493	+	0.255493i
$693$	26431.1	−	13745.6i	1.44882	−	0.753465i
$694$		−	2696.90i		−	0.147511i
$695$	−2301.98	+	7124.23i	−0.125639	+	0.388831i
$696$	27.6655	−	85.1457i	0.00150669	−	0.00463713i
$697$	253.777	−	498.065i	0.0137912	−	0.0270668i
$698$	1527.10	−	9641.70i	0.0828101	−	0.522842i
$699$	243.088	−	176.614i	0.0131537	−	0.00955673i
$700$	2414.79	+	14931.4i	0.130386	+	0.806218i
$701$	−33945.8	−	11029.7i	−1.82898	−	0.594272i	−0.999353	−	0.0359574i	$-0.988552\pi$
$701$	−33945.8	−	11029.7i	−1.82898	−	0.594272i	−0.829629	−	0.558315i	$-0.811448\pi$
$702$	−106.106	−	669.927i	−0.00570472	−	0.0360182i
$703$	−25259.1	−	25259.1i	−1.35514	−	1.35514i
$704$	1356.66	−	1900.33i	0.0726291	−	0.101735i
$705$	86.5890	+	265.024i	0.00462572	+	0.0141580i
$706$	−5867.30	+	8075.65i	−0.312774	+	0.430497i
$707$	22190.4	−	11306.6i	1.18042	−	0.601453i
$708$	36.4761	+	18.5855i	0.00193624	+	0.000986562i
$709$	−2634.78	−	3626.46i	−0.139564	−	0.192094i	0.733513	−	0.679675i	$-0.237879\pi$
$709$	−2634.78	−	3626.46i	−0.139564	−	0.192094i	−0.873078	+	0.487581i	$0.837879\pi$
$710$	596.169	−	95.4196i	0.0315124	−	0.00504371i
$711$	21886.8	−	7111.45i	1.15446	−	0.375106i
$712$	−2972.51	−	5833.88i	−0.156460	−	0.307070i
$713$	−6349.63	+	1005.68i	−0.333514	+	0.0528235i
$714$	−14.7298			−0.000772057
$715$	−14965.1	+	30107.6i	−0.782747	+	1.57477i
$716$	1764.88			0.0921183
$717$	301.338	−	47.7272i	0.0156955	−	0.00248592i
$718$	3971.70	+	7794.89i	0.206438	+	0.405157i
$719$	−393.003	+	127.694i	−0.0203846	+	0.00662336i	−0.319192	−	0.947690i	$-0.603411\pi$
$719$	−393.003	+	127.694i	−0.0203846	+	0.00662336i	0.298807	+	0.954314i	$0.403411\pi$
$720$	−2831.97	+	3911.25i	−0.146585	+	0.202450i
$721$	14469.1	+	19915.0i	0.747376	+	1.02868i
$722$	−13581.5	−	6920.12i	−0.700071	−	0.356704i
$723$	−160.078	+	81.5636i	−0.00823424	+	0.00419555i
$724$	−2335.10	+	3213.99i	−0.119866	+	0.164982i
$725$	14816.6	−	10838.8i	0.759000	−	0.555233i
$726$	121.943	+	162.097i	0.00623379	+	0.00828648i
$727$	−15408.2	−	15408.2i	−0.786052	−	0.786052i	0.194792	−	0.980845i	$-0.437597\pi$
$727$	−15408.2	−	15408.2i	−0.786052	−	0.786052i	−0.980845	+	0.194792i	$0.937597\pi$
$728$	−3120.58	−	19702.6i	−0.158869	−	1.00306i
$729$	−18695.5	−	6074.53i	−0.949830	−	0.308618i
$730$	17689.9	−	12896.6i	0.896896	−	0.653868i
$731$	−596.027	+	433.039i	−0.0301571	+	0.0219104i
$732$	29.1948	−	184.328i	0.00147414	−	0.00930734i
$733$	−9935.99	+	19500.5i	−0.500674	+	0.982629i	0.492968	+	0.870047i	$0.335912\pi$
$733$	−9935.99	+	19500.5i	−0.500674	+	0.982629i	−0.993643	+	0.112581i	$0.964088\pi$
$734$	−320.851	+	987.477i	−0.0161346	+	0.0496573i
$735$	433.916	−	221.982i	0.0217758	−	0.0111400i
$736$			2765.47i			0.138501i
$737$	−10906.3	−	10726.2i	−0.545098	−	0.536100i
$738$	−6679.02	+	6679.02i	−0.333141	+	0.333141i
$739$	2628.91	+	1910.01i	0.130860	+	0.0950757i	0.651290	−	0.758829i	$-0.274228\pi$
$739$	2628.91	+	1910.01i	0.130860	+	0.0950757i	−0.520430	+	0.853905i	$0.674228\pi$
$740$	9372.02	−	9402.61i	0.465571	−	0.467090i
$741$	233.563	+	718.832i	0.0115791	+	0.0356369i
$742$	12343.1	+	1954.95i	0.610686	+	0.0967232i
$743$	−37326.9	−	5912.00i	−1.84306	−	0.291912i	−0.865238	−	0.501361i	$-0.832833\pi$
$743$	−37326.9	−	5912.00i	−1.84306	−	0.291912i	−0.977820	+	0.209449i	$0.932833\pi$
$744$	14.0131	+	43.1280i	0.000690519	+	0.00212520i
$745$	−13279.2	+	21.6322i	−0.653038	+	0.00106382i
$746$	5059.74	+	3676.12i	0.248325	+	0.180419i
$747$	−18911.3	+	18911.3i	−0.926277	+	0.926277i
$748$	76.7685	+	459.895i	0.00375259	+	0.0224805i
$749$		−	7819.86i		−	0.381484i
$750$	202.236	−	66.8050i	0.00984617	−	0.00325250i
$751$	4138.92	−	12738.3i	0.201107	−	0.618944i	−0.798744	−	0.601671i	$-0.794502\pi$
$751$	4138.92	−	12738.3i	0.201107	−	0.618944i	0.999851	−	0.0172727i	$-0.00549833\pi$
$752$	−2377.21	+	4665.54i	−0.115276	+	0.226243i
$753$	−65.8530	+	415.780i	−0.00318701	+	0.0201220i
$754$	−19587.4	+	14231.1i	−0.946064	+	0.687356i
$755$	18035.8	+	24739.3i	0.869389	+	1.19252i
$756$	473.481	+	153.843i	0.0227782	+	0.00740110i
$757$	3759.85	+	23738.7i	0.180520	+	1.13976i	0.896960	+	0.442112i	$0.145771\pi$
$757$	3759.85	+	23738.7i	0.180520	+	1.13976i	−0.716439	+	0.697649i	$0.754229\pi$
$758$	−8904.73	−	8904.73i	−0.426695	−	0.426695i
$759$	−229.100	−	72.3371i	−0.0109563	−	0.00345938i
$760$	4870.70	−	9597.91i	0.232472	−	0.458096i
$761$	−22937.3	+	31570.5i	−1.09261	+	1.50385i	−0.247777	+	0.968817i	$0.579700\pi$
$761$	−22937.3	+	31570.5i	−1.09261	+	1.50385i	−0.844832	+	0.535031i	$0.820300\pi$
$762$	−294.711	+	150.163i	−0.0140108	+	0.00713887i
$763$	23518.5	+	11983.3i	1.11590	+	0.568577i
$764$	−9546.17	−	13139.2i	−0.452053	−	0.622197i
$765$	−152.398	−	952.161i	−0.00720256	−	0.0450006i
$766$	−5888.69	+	1913.35i	−0.277764	+	0.0902509i
$767$	−5026.18	−	9864.43i	−0.236616	−	0.464386i
$768$	19.2670	−	3.05159i	0.000905256	−	0.000143378i
$769$	−5380.62			−0.252315			−0.126157	−	0.992010i	$-0.540264\pi$
$769$	−5380.62			−0.252315			−0.126157	+	0.992010i	$0.540264\pi$
$770$	−14703.3	−	19819.6i	−0.688143	−	0.927596i
$771$	163.007			0.00761421
$772$	10155.1	−	1608.41i	0.473432	−	0.0749843i
$773$	9371.15	+	18391.9i	0.436037	+	0.855771i	0.999560	+	0.0296704i	$0.00944575\pi$
$773$	9371.15	+	18391.9i	0.436037	+	0.855771i	−0.563523	+	0.826101i	$0.690554\pi$
$774$	11839.6	−	3846.92i	0.549827	−	0.178650i
$775$	−2844.61	+	8852.85i	−0.131847	+	0.410327i
$776$	3800.00	+	5230.25i	0.175789	+	0.241952i
$777$	−609.694	−	310.655i	−0.0281501	−	0.0143432i
$778$	12115.6	−	6173.20i	0.558309	−	0.284473i
$779$	12374.8	−	17032.4i	0.569155	−	0.783375i
$780$	−267.006	+	87.2367i	−0.0122569	+	0.00400458i
$781$	−792.090	+	585.620i	−0.0362909	+	0.0268311i
$782$	−390.492	−	390.492i	−0.0178567	−	0.0178567i
$783$	−94.5248	−	596.806i	−0.00431423	−	0.0272390i
$784$	8705.70	+	2828.65i	0.396579	+	0.128856i
$785$	−12420.9	−	1946.55i	−0.564742	−	0.0885035i
$786$	−263.396	+	191.369i	−0.0119530	+	0.00868434i
$787$	−2248.57	+	14196.9i	−0.101846	+	0.643030i	0.882970	+	0.469429i	$0.155540\pi$
$787$	−2248.57	+	14196.9i	−0.101846	+	0.643030i	−0.984816	+	0.173601i	$0.944460\pi$
$788$	−7921.23	+	15546.3i	−0.358099	+	0.702809i
$789$	32.3699	−	99.6242i	0.00146058	−	0.00449520i
$790$	−8682.06	−	16971.1i	−0.391005	−	0.764310i
$791$			35573.4i			1.59904i
$792$	1167.69	−	7791.59i	0.0523889	−	0.349574i
$793$	−35687.9	+	35687.9i	−1.59813	+	1.59813i
$794$	−5524.84	−	4014.03i	−0.246938	−	0.179411i
$795$	−0.286665	−	175.973i	−1.27886e−5	−	0.00785047i
$796$	−1779.61	−	5477.07i	−0.0792419	−	0.243881i
$797$	−27074.9	−	4288.25i	−1.20332	−	0.190587i	−0.477598	−	0.878578i	$-0.658493\pi$
$797$	−27074.9	−	4288.25i	−1.20332	−	0.190587i	−0.725719	+	0.687992i	$0.758493\pi$
$798$	−547.936	−	86.7846i	−0.0243067	−	0.00384980i
$799$	−323.118	−	994.454i	−0.0143067	−	0.0440316i
$800$	3569.92	+	1804.34i	0.157770	+	0.0797413i
$801$	−17873.7	−	12986.0i	−0.788435	−	0.572831i
$802$	4742.76	−	4742.76i	0.208819	−	0.208819i
$803$	−15950.3	+	31958.8i	−0.700962	+	1.40449i
$804$		−	127.800i		−	0.00560592i
$805$	27812.9	+	8986.89i	1.21773	+	0.393473i
$806$	3789.65	−	11663.3i	0.165614	−	0.509706i
$807$	88.2132	−	173.128i	0.00384789	−	0.00755192i
$808$	1030.32	−	6505.16i	0.0448594	−	0.283231i
$809$	4304.06	−	3127.08i	0.187049	−	0.135899i	−0.490320	−	0.871543i	$-0.663120\pi$
$809$	4304.06	−	3127.08i	0.187049	−	0.135899i	0.677369	+	0.735643i	$0.263120\pi$
$810$	−2522.17	+	16094.0i	−0.109407	+	0.698130i
$811$	28717.4	+	9330.84i	1.24341	+	0.404008i	0.855554	−	0.517713i	$-0.173217\pi$
$811$	28717.4	+	9330.84i	1.24341	+	0.404008i	0.387854	+	0.921721i	$0.373217\pi$
$812$	−2779.98	−	17552.1i	−0.120145	−	0.758568i
$813$	−328.317	−	328.317i	−0.0141631	−	0.0141631i
$814$	−6521.69	+	20655.0i	−0.280817	+	0.889382i
$815$	4417.20	+	2241.62i	0.189850	+	0.0963443i
$816$	−2.28965	+	3.15144i	−9.82278e−5	+	0.000135199i
$817$	−24723.1	+	12597.0i	−1.05869	+	0.539430i
$818$	−6906.42	−	3519.00i	−0.295204	−	0.150414i
$819$	−39564.2	−	54455.4i	−1.68801	−	2.32335i
$820$	6337.43	+	4588.66i	0.269894	+	0.195418i
$821$	−34751.9	+	11291.6i	−1.47728	+	0.479999i	−0.933300	−	0.359096i	$-0.883085\pi$
$821$	−34751.9	+	11291.6i	−1.47728	+	0.479999i	−0.543984	+	0.839095i	$0.683085\pi$
$822$	−14.5650	−	28.5854i	−0.000618020	−	0.00121293i
$823$	34023.5	−	5388.80i	1.44105	−	0.228240i	0.613529	−	0.789672i	$-0.289750\pi$
$823$	34023.5	−	5388.80i	1.44105	−	0.228240i	0.827523	+	0.561432i	$0.189750\pi$
$824$	6509.95			0.275224
$825$	−242.857	+	248.547i	−0.0102487	+	0.0104888i
$826$	8126.06			0.342302
$827$	−16875.9	+	2672.88i	−0.709593	+	0.112388i	−0.500789	−	0.865569i	$-0.666957\pi$
$827$	−16875.9	+	2672.88i	−0.709593	+	0.112388i	−0.208803	+	0.977958i	$0.566957\pi$
$828$	4236.40	+	8314.39i	0.177808	+	0.348968i
$829$	−4942.25	+	1605.83i	−0.207058	+	0.0672773i	−0.410710	−	0.911766i	$-0.634719\pi$
$829$	−4942.25	+	1605.83i	−0.207058	+	0.0672773i	0.203651	+	0.979043i	$0.434719\pi$
$830$	17944.1	+	12992.6i	0.750421	+	0.543347i
$831$	22.3265	+	30.7297i	0.000932005	+	0.00128279i
$832$	−4700.43	−	2394.99i	−0.195863	−	0.0997973i
$833$	−1628.68	+	829.854i	−0.0677436	+	0.0345171i
$834$	59.9859	−	82.5635i	0.00249058	−	0.00342799i
$835$	−10380.7	−	5267.95i	−0.430226	−	0.218329i
$836$	146.130	+	17560.0i	0.00604546	+	0.726466i
$837$	216.419	+	216.419i	0.00893731	+	0.00893731i
$838$	5129.63	+	32387.2i	0.211456	+	1.33508i
$839$	−26039.9	−	8460.89i	−1.07151	−	0.348155i	−0.280436	−	0.959873i	$-0.590479\pi$
$839$	−26039.9	−	8460.89i	−1.07151	−	0.348155i	−0.791076	+	0.611718i	$0.790479\pi$
$840$	31.9210	−	203.688i	0.00131116	−	0.00836656i
$841$	2281.60	−	1657.68i	0.0935502	−	0.0679682i
$842$	5244.92	−	33115.1i	0.214670	−	1.35537i
$843$	8.59770	−	16.8739i	0.000351270	−	0.000689406i
$844$	−120.748	+	371.623i	−0.00492453	+	0.0151561i
$845$	48911.0	+	15804.1i	1.99123	+	0.643406i
$846$			17668.6i			0.718035i
$847$	36174.5	+	17679.8i	1.46750	+	0.717219i
$848$	2336.92	−	2336.92i	0.0946345	−	0.0946345i
$849$	−451.499	−	328.033i	−0.0182514	−	0.0132604i
$850$	−758.860	+	249.305i	−0.0306220	+	0.0100601i
$851$	−7927.64	−	24398.8i	−0.319337	−	0.982819i
$852$	−8.12850	−	1.28743i	−0.000326852	−	5.17682e-5i
$853$	−20437.5	−	3236.98i	−0.820358	−	0.129932i	−0.267872	−	0.963454i	$-0.586321\pi$
$853$	−20437.5	−	3236.98i	−0.820358	−	0.129932i	−0.552486	+	0.833522i	$0.686321\pi$
$854$	−11447.4	−	35231.5i	−0.458691	−	1.41171i
$855$	−59.1622	−	36317.5i	−0.00236644	−	1.45267i
$856$	−1673.06	−	1215.55i	−0.0668036	−	0.0485357i
$857$	−2075.06	+	2075.06i	−0.0827104	+	0.0827104i	−0.747252	−	0.664541i	$-0.768627\pi$
$857$	−2075.06	+	2075.06i	−0.0827104	+	0.0827104i	0.664541	+	0.747252i	$0.268627\pi$
$858$	321.359	−	326.752i	0.0127867	−	0.0130013i
$859$		−	644.554i		−	0.0256017i	−0.999918	−	0.0128009i	$-0.995925\pi$
$859$		−	644.554i		−	0.0256017i	0.999918	−	0.0128009i	$-0.00407475\pi$
$860$	−4696.54	−	9180.48i	−0.186222	−	0.364014i
$861$	124.623	−	383.551i	0.00493281	−	0.0151816i
$862$	1049.60	−	2059.95i	0.0414726	−	0.0813946i
$863$	2628.74	−	16597.2i	0.103689	−	0.654665i	−0.880026	−	0.474926i	$-0.842475\pi$
$863$	2628.74	−	16597.2i	0.103689	−	0.654665i	0.983714	−	0.179739i	$-0.0575252\pi$
$864$	106.514	−	77.3872i	0.00419409	−	0.00304718i
$865$	18162.7	+	2846.36i	0.713930	+	0.111884i
$866$	−749.534	−	243.538i	−0.0294113	−	0.00955632i
$867$	58.4426	+	368.992i	0.00228929	+	0.0144540i
$868$	6364.88	+	6364.88i	0.248892	+	0.248892i
$869$	25313.7	+	18071.5i	0.988155	+	0.705448i
$870$	−237.863	+	77.7150i	−0.00926933	+	0.00302849i
$871$	−20314.8	+	27961.0i	−0.790289	+	1.08774i
$872$	6219.63	−	3169.06i	0.241540	−	0.123071i
$873$	19436.9	+	9903.58i	0.753538	+	0.383947i
$874$	−12225.3	−	16826.7i	−0.473142	−	0.651225i
$875$	29747.7	−	30039.9i	1.14932	−	1.16061i
$876$	−283.804	+	92.2135i	−0.0109462	+	0.00355663i
$877$	−1880.36	−	3690.42i	−0.0724006	−	0.142094i	0.851969	−	0.523592i	$-0.175408\pi$
$877$	−1880.36	−	3690.42i	−0.0724006	−	0.142094i	−0.924370	+	0.381498i	$0.875408\pi$
$878$	30052.7	−	4759.89i	1.15516	−	0.182959i
$879$	554.608			0.0212815
$880$	−6525.93	+	64.9389i	−0.249988	+	0.00248760i
$881$	20552.4			0.785959			0.392979	−	0.919547i	$-0.371444\pi$
$881$	20552.4			0.785959			0.392979	+	0.919547i	$0.371444\pi$
$882$	30506.9	−	4831.81i	1.16465	−	0.184462i
$883$	−23175.8	−	45485.0i	−0.883269	−	1.73351i	−0.648094	−	0.761561i	$-0.724433\pi$
$883$	−23175.8	−	45485.0i	−0.883269	−	1.73351i	−0.235176	−	0.971953i	$-0.575567\pi$
$884$	1001.89	−	325.534i	0.0381191	−	0.0123856i
$885$	−18.0842	−	112.987i	−0.000686884	−	0.00429156i
$886$	10598.9	+	14588.2i	0.401894	+	0.553160i
$887$	587.366	+	299.278i	0.0222343	+	0.0113289i	0.465072	−	0.885273i	$-0.346028\pi$
$887$	587.366	+	299.278i	0.0222343	+	0.0113289i	−0.442838	+	0.896602i	$0.646028\pi$
$888$	−161.238	+	82.1547i	−0.00609322	+	0.00310465i
$889$	−38591.0	+	53116.0i	−1.45591	+	2.00388i
$890$	−8281.84	+	16319.7i	−0.311919	+	0.614649i
$891$	−8423.38	−	25208.8i	−0.316716	−	0.947840i
$892$	−6113.83	−	6113.83i	−0.229491	−	0.229491i
$893$	−6160.61	−	38896.6i	−0.230859	−	1.45759i
$894$	172.150	+	55.9351i	0.00644024	+	0.00209256i
$895$	−2906.04	−	3986.15i	−0.108534	−	0.148874i
$896$	3132.59	−	2275.96i	0.116800	−	0.0848599i
$897$	−84.9146	+	536.129i	−0.00316077	+	0.0199563i
$898$	1119.17	−	2196.49i	0.0415892	−	0.0816234i
$899$	3376.02	−	10390.3i	0.125246	−	0.385469i
$900$	13497.0	−	43.9742i	0.499890	−	0.00162867i
$901$			659.957i			0.0244022i
$902$	−12624.8	−	1892.01i	−0.466030	−	0.0698416i
$903$	−375.842	+	375.842i	−0.0138508	+	0.0138508i
$904$	7610.91	+	5529.65i	0.280017	+	0.203444i
$905$	11104.0	−	18.0888i	0.407857	−	0.000664411i
$906$	−128.960	−	396.898i	−0.00472893	−	0.0145541i
$907$	48154.6	+	7626.94i	1.76290	+	0.279216i	0.952028	−	0.306011i	$-0.0989944\pi$
$907$	48154.6	+	7626.94i	1.76290	+	0.279216i	0.810870	+	0.585227i	$0.198994\pi$
$908$	−7884.76	−	1248.82i	−0.288177	−	0.0456428i
$909$	−6867.53	−	21136.1i	−0.250585	−	0.771221i
$910$	−39361.7	+	39490.2i	−1.43388	+	1.43856i
$911$	36513.8	+	26528.8i	1.32794	+	0.964807i	0.999796	+	0.0201802i	$0.00642400\pi$
$911$	36513.8	+	26528.8i	1.32794	+	0.964807i	0.328147	+	0.944627i	$0.393576\pi$
$912$	−103.741	+	103.741i	−0.00376667	+	0.00376667i
$913$	−35746.4	−	5357.14i	−1.29577	−	0.194190i
$914$			32492.8i			1.17589i
$915$	−464.394	+	237.575i	−0.0167786	+	0.00858358i
$916$	6396.97	−	19687.8i	0.230744	−	0.710158i
$917$	−29339.4	+	57581.8i	−1.05657	+	2.07363i
$918$	−4.11283	+	25.9674i	−0.000147869	+	0.000933607i
$919$	10220.5	−	7425.60i	0.366857	−	0.266538i	−0.389049	−	0.921217i	$-0.627196\pi$
$919$	10220.5	−	7425.60i	0.366857	−	0.266538i	0.755907	+	0.654679i	$0.227196\pi$
$920$	6246.07	−	4553.60i	0.223834	−	0.163182i
$921$	138.882	+	45.1256i	0.00496887	+	0.00161448i
$922$	−3639.59	−	22979.4i	−0.130004	−	0.820811i
$923$	1573.76	+	1573.76i	0.0561224	+	0.0561224i
$924$	106.608	+	319.046i	0.00379560	+	0.0113591i
$925$	−36668.5	−	5685.32i	−1.30341	−	0.202089i
$926$	11667.9	−	16059.5i	0.414073	−	0.569922i
$927$	19572.2	−	9972.52i	0.693457	−	0.353334i
$928$	−4187.39	−	2133.58i	−0.148123	−	0.0754723i
$929$	16332.7	+	22480.0i	0.576811	+	0.793912i	0.993341	−	0.115210i	$-0.0367540\pi$
$929$	16332.7	+	22480.0i	0.576811	+	0.793912i	−0.416530	+	0.909122i	$0.636754\pi$
$930$	74.3346	−	102.664i	0.00262100	−	0.00361988i
$931$	−65474.8	+	21274.1i	−2.30489	+	0.748904i
$932$	−7160.77	−	14053.8i	−0.251673	−	0.493935i
$933$	3.39497	−	0.537710i	0.000119128	−	1.88680e-5i
$934$	16416.5			0.575121
$935$	912.309	−	930.648i	0.0319098	−	0.0325513i
$936$	−17800.7			−0.621618
$937$	−15005.3	+	2376.61i	−0.523161	+	0.0828606i	−0.412429	−	0.910990i	$-0.635320\pi$
$937$	−15005.3	+	2376.61i	−0.523161	+	0.0828606i	−0.110732	+	0.993850i	$0.535320\pi$
$938$	−11516.8	−	22602.9i	−0.400891	−	0.786792i
$939$	591.990	−	192.349i	0.0205739	−	0.00668486i
$940$	14451.8	−	2313.09i	0.501454	−	0.0802601i
$941$	29658.1	+	40820.9i	1.02745	+	1.41416i	0.906848	+	0.421457i	$0.138481\pi$
$941$	29658.1	+	40820.9i	1.02745	+	1.41416i	0.120598	+	0.992701i	$0.461519\pi$
$942$	152.698	+	77.8033i	0.00528148	+	0.00269105i
$943$	13471.9	−	6864.26i	0.465222	−	0.237042i
$944$	1263.14	−	1738.57i	0.0435507	−	0.0599423i
$945$	−432.161	−	1322.72i	−0.0148764	−	0.0455323i
$946$	13693.4	+	9775.76i	0.470623	+	0.335980i
$947$	−5128.67	−	5128.67i	−0.175987	−	0.175987i	0.613617	−	0.789604i	$-0.289714\pi$
$947$	−5128.67	−	5128.67i	−0.175987	−	0.175987i	−0.789604	+	0.613617i	$0.789714\pi$
$948$	40.6491	+	256.649i	0.00139264	+	0.00879278i
$949$	76750.6	+	24937.8i	2.62532	+	0.853019i
$950$	−29697.8	+	4802.91i	−1.01424	+	0.164028i
$951$	517.571	−	376.037i	0.0176481	−	0.0128221i
$952$	−120.958	+	763.701i	−0.00411794	+	0.0259997i
$953$	7671.62	−	15056.4i	0.260764	−	0.511778i	−0.723089	−	0.690754i	$-0.757279\pi$
$953$	7671.62	−	15056.4i	0.260764	−	0.511778i	0.983853	+	0.178976i	$0.0572786\pi$
$954$	3446.05	−	10605.8i	0.116950	−	0.359934i
$955$	−13957.4	+	43195.7i	−0.472933	+	1.46365i
$956$		−	16015.5i		−	0.541817i
$957$	286.283	−	291.088i	0.00967004	−	0.00983233i
$958$	−14642.5	+	14642.5i	−0.493818	+	0.493818i
$959$	−5151.97	−	3743.13i	−0.173478	−	0.126039i
$960$	−38.6171	−	38.4915i	−0.00129829	−	0.00129407i
$961$	−7495.91	−	23070.0i	−0.251616	−	0.774396i
$962$	48335.8	+	7655.64i	1.61997	+	0.256578i
$963$	−6892.13	−	1091.61i	−0.230629	−	0.0365280i
$964$	2914.33	+	8969.39i	0.0973696	+	0.299673i
$965$	−20354.0	−	20287.8i	−0.678983	−	0.676775i
$966$	−322.327	−	234.184i	−0.0107357	−	0.00779995i
$967$	3625.50	−	3625.50i	0.120567	−	0.120567i	−0.644249	−	0.764816i	$-0.722830\pi$
$967$	3625.50	−	3625.50i	0.120567	−	0.120567i	0.764816	+	0.644249i	$0.222830\pi$
$968$	9405.67	−	4991.31i	0.312303	−	0.165730i
$969$		−	29.2969i		−	0.000971262i
$970$	5555.96	−	17194.7i	0.183908	−	0.569165i
$971$	7678.13	−	23630.9i	0.253762	−	0.780999i	−0.740309	−	0.672267i	$-0.765321\pi$
$971$	7678.13	−	23630.9i	0.253762	−	0.780999i	0.994071	−	0.108733i	$-0.0346792\pi$
$972$	302.541	−	593.770i	0.00998355	−	0.0195938i
$973$	3168.95	−	20008.0i	0.104411	−	0.659225i
$974$	−615.241	+	446.999i	−0.0202398	+	0.0147051i
$975$	636.682	+	459.415i	0.0209130	+	0.0150903i
$976$	−9317.20	−	3027.34i	−0.305570	−	0.0992857i
$977$	−2189.44	−	13823.6i	−0.0716954	−	0.452667i	−0.997254	−	0.0740619i	$-0.976404\pi$
$977$	−2189.44	−	13823.6i	−0.0716954	−	0.452667i	0.925558	−	0.378605i	$-0.123596\pi$
$978$	−47.7442	−	47.7442i	−0.00156103	−	0.00156103i
$979$	−248.470	−	29858.0i	−0.00811149	−	0.974735i
$980$	−7945.95	−	24320.2i	−0.259004	−	0.792736i
$981$	13844.7	−	19055.6i	0.450588	−	0.620181i
$982$	−27244.5	+	13881.8i	−0.885345	+	0.451106i
$983$	−14005.6	−	7136.18i	−0.454433	−	0.231545i	0.211764	−	0.977321i	$-0.432079\pi$
$983$	−14005.6	−	7136.18i	−0.454433	−	0.231545i	−0.666197	+	0.745776i	$0.732079\pi$
$984$	−62.6887	−	86.2837i	−0.00203094	−	0.00279535i
$985$	48155.8	−	7707.56i	1.55774	−	0.249323i
$986$	892.538	−	290.003i	0.0288278	−	0.00936672i
$987$	−342.481	−	672.157i	−0.0110449	−	0.0216768i
$988$	39187.5	−	6206.69i	1.26186	−	0.199860i
$989$	−19927.4			−0.640701
$990$	−19520.7	+	10192.2i	−0.626676	+	0.327203i
$991$	23055.7			0.739040			0.369520	−	0.929223i	$-0.379522\pi$
$991$	23055.7			0.739040			0.369520	+	0.929223i	$0.379522\pi$
$992$	2351.14	−	372.385i	0.0752509	−	0.0119186i
$993$	6.53989	+	12.8353i	0.000209000	+	0.000410186i
$994$	−1553.64	+	504.807i	−0.0495758	+	0.0161081i
$995$	−9440.18	+	13037.9i	−0.300778	+	0.415406i
$996$	−177.500	−	244.308i	−0.00564689	−	0.00777228i
$997$	37644.0	+	19180.6i	1.19579	+	0.609283i	0.934495	−	0.355977i	$-0.115852\pi$
$997$	37644.0	+	19180.6i	1.19579	+	0.609283i	0.261291	+	0.965260i	$0.415852\pi$
$998$	13313.3	−	6783.48i	0.422271	−	0.215158i
$999$	−717.895	+	988.098i	−0.0227359	+	0.0312933i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	110.4.k.a.7.14	✓	144
5.3	odd	4	inner	110.4.k.a.73.5	yes	144
11.8	odd	10	inner	110.4.k.a.107.5	yes	144
55.8	even	20	inner	110.4.k.a.63.14	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.4.k.a.7.14	✓	144	1.1	even	1	trivial
110.4.k.a.63.14	yes	144	55.8	even	20	inner
110.4.k.a.73.5	yes	144	5.3	odd	4	inner
110.4.k.a.107.5	yes	144	11.8	odd	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.97538 - 0.312869i) q^{2} +(0.0345940 + 0.0678945i) q^{3} +(3.80423 - 1.23607i) q^{4} +(-9.05578 - 6.55690i) q^{5} +(0.0895782 + 0.123294i) q^{6} +(26.9536 + 13.7335i) q^{7} +(7.12805 - 3.63192i) q^{8} +(15.8668 - 21.8388i) q^{9} +(-19.9400 - 10.1191i) q^{10} +(36.4816 - 0.303590i) q^{11} +(0.215525 + 0.215525i) q^{12} +(-12.8946 - 81.4136i) q^{13} +(57.5403 + 18.6960i) q^{14} +(0.131902 - 0.841666i) q^{15} +(12.9443 - 9.40456i) q^{16} +(-0.499816 + 3.15571i) q^{17} +(24.5102 - 48.1040i) q^{18} +(-37.1855 + 114.445i) q^{19} +(-42.5550 - 13.7504i) q^{20} +2.30510i q^{21} +(71.9699 - 12.0137i) q^{22} +(-61.1089 + 61.1089i) q^{23} +(0.493175 + 0.358313i) q^{24} +(39.0142 + 118.756i) q^{25} +(-50.9436 - 156.788i) q^{26} +(4.06369 + 0.643625i) q^{27} +(119.513 + 18.9290i) q^{28} +(-45.3832 - 139.675i) q^{29} +(-0.00277566 - 1.70388i) q^{30} +(60.1821 + 43.7248i) q^{31} +(22.6274 - 22.6274i) q^{32} +(1.28266 + 2.46640i) q^{33} +6.39010i q^{34} +(-154.036 - 301.100i) q^{35} +(33.3667 - 102.692i) q^{36} +(-134.769 + 264.498i) q^{37} +(-37.6490 + 237.706i) q^{38} +(5.08145 - 3.69189i) q^{39} +(-88.3642 - 13.8480i) q^{40} +(-166.393 - 54.0642i) q^{41} +(0.721193 + 4.55344i) q^{42} +(163.048 + 163.048i) q^{43} +(138.409 - 46.2487i) q^{44} +(-286.881 + 93.7301i) q^{45} +(-101.594 + 139.832i) q^{46} +(-291.596 + 148.576i) q^{47} +(1.08631 + 0.553503i) q^{48} +(336.276 + 462.844i) q^{49} +(114.223 + 222.381i) q^{50} +(-0.231546 + 0.0752339i) q^{51} +(-149.687 - 293.777i) q^{52} +(204.013 - 32.3125i) q^{53} +8.22869 q^{54} +(-332.360 - 236.457i) q^{55} +242.006 q^{56} +(-9.05658 + 1.43442i) q^{57} +(-133.349 - 261.712i) q^{58} +(127.738 - 41.5046i) q^{59} +(-0.538573 - 3.36493i) q^{60} +(-359.896 - 495.355i) q^{61} +(132.562 + 67.5439i) q^{62} +(727.591 - 370.726i) q^{63} +(37.6183 - 51.7771i) q^{64} +(-417.049 + 821.812i) q^{65} +(3.30539 + 4.47076i) q^{66} +(-296.485 - 296.485i) q^{67} +(1.99926 + 12.6229i) q^{68} +(-6.26295 - 2.03496i) q^{69} +(-398.485 - 546.592i) q^{70} +(-21.8441 + 15.8707i) q^{71} +(33.7826 - 213.295i) q^{72} +(-444.473 + 872.327i) q^{73} +(-183.465 + 564.649i) q^{74} +(-6.71319 + 6.75708i) q^{75} +481.339i q^{76} +(987.480 + 492.839i) q^{77} +(8.88271 - 8.88271i) q^{78} +(689.704 + 501.100i) q^{79} +(-178.885 + 0.291409i) q^{80} +(-225.128 - 692.873i) q^{81} +(-345.603 - 54.7381i) q^{82} +(-978.558 - 154.988i) q^{83} +(2.84926 + 8.76911i) q^{84} +(25.2179 - 25.3002i) q^{85} +(373.094 + 271.069i) q^{86} +(7.91319 - 7.91319i) q^{87} +(258.940 - 134.662i) q^{88} -818.439i q^{89} +(-537.372 + 274.908i) q^{90} +(770.540 - 2371.48i) q^{91} +(-156.937 + 308.007i) q^{92} +(-0.886738 + 5.59864i) q^{93} +(-529.527 + 384.724i) q^{94} +(1087.15 - 792.568i) q^{95} +(2.31905 + 0.753504i) q^{96} +(126.418 + 798.169i) q^{97} +(809.081 + 809.081i) q^{98} +(572.216 - 801.530i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 8 q^{3} + 32 q^{5} - 40 q^{7} - 44 q^{11} + 128 q^{12} - 256 q^{15} + 576 q^{16} - 640 q^{17} - 64 q^{20} + 312 q^{22} - 984 q^{23} - 520 q^{25} + 304 q^{26} - 364 q^{27} + 240 q^{28} - 432 q^{31}+ \cdots + 7044 q^{97}+O(q^{100}) \) 144 * q + 8 * q^3 + 32 * q^5 - 40 * q^7 - 44 * q^11 + 128 * q^12 - 256 * q^15 + 576 * q^16 - 640 * q^17 - 64 * q^20 + 312 * q^22 - 984 * q^23 - 520 * q^25 + 304 * q^26 - 364 * q^27 + 240 * q^28 - 432 * q^31 + 2368 * q^33 + 1808 * q^36 - 960 * q^37 + 72 * q^38 + 740 * q^41 + 2440 * q^42 + 2656 * q^45 + 720 * q^46 - 1980 * q^47 - 128 * q^48 - 1360 * q^50 - 3880 * q^51 - 1920 * q^52 - 3060 * q^53 - 3044 * q^55 - 64 * q^56 - 4400 * q^57 - 2016 * q^58 - 1120 * q^60 - 960 * q^61 + 80 * q^62 + 1800 * q^63 + 1552 * q^66 + 10160 * q^67 + 2560 * q^68 + 2304 * q^70 + 1312 * q^71 - 2460 * q^73 + 8644 * q^75 - 1272 * q^77 - 5312 * q^78 + 768 * q^80 + 2116 * q^81 + 1280 * q^82 + 320 * q^85 - 5488 * q^86 + 1248 * q^88 - 8480 * q^90 + 11796 * q^91 - 704 * q^92 + 688 * q^93 - 1280 * q^95 + 7044 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more