LMFDB - Embedded newform 138.4.d.a.137.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [138,4,Mod(137,138)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(138, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("138.137");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 138 = 2 \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	138.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$8.14226358079$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			137.10
Character	$\chi$	$=$	138.137
Dual form			138.4.d.a.137.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00000i q^{2} +(4.33582 - 2.86368i) q^{3} -4.00000 q^{4} +13.9937 q^{5} +(-5.72736 - 8.67164i) q^{6} +0.843170i q^{7} +8.00000i q^{8} +(10.5987 - 24.8328i) q^{9} +O(q^{10})$	\(q-2.00000i q^{2} +(4.33582 - 2.86368i) q^{3} -4.00000 q^{4} +13.9937 q^{5} +(-5.72736 - 8.67164i) q^{6} +0.843170i q^{7} +8.00000i q^{8} +(10.5987 - 24.8328i) q^{9} -27.9874i q^{10} +54.5358 q^{11} +(-17.3433 + 11.4547i) q^{12} -40.5013 q^{13} +1.68634 q^{14} +(60.6742 - 40.0735i) q^{15} +16.0000 q^{16} -3.33711 q^{17} +(-49.6656 - 21.1974i) q^{18} +20.4910i q^{19} -55.9749 q^{20} +(2.41457 + 3.65584i) q^{21} -109.072i q^{22} +(-95.1032 - 55.8782i) q^{23} +(22.9094 + 34.6866i) q^{24} +70.8240 q^{25} +81.0026i q^{26} +(-25.1591 - 138.022i) q^{27} -3.37268i q^{28} +35.1595i q^{29} +(-80.1470 - 121.348i) q^{30} -138.815 q^{31} -32.0000i q^{32} +(236.458 - 156.173i) q^{33} +6.67421i q^{34} +11.7991i q^{35} +(-42.3948 + 99.3312i) q^{36} -55.4505i q^{37} +40.9820 q^{38} +(-175.606 + 115.983i) q^{39} +111.950i q^{40} +98.3424i q^{41} +(7.31167 - 4.82914i) q^{42} +457.253i q^{43} -218.143 q^{44} +(148.315 - 347.503i) q^{45} +(-111.756 + 190.206i) q^{46} -256.443i q^{47} +(69.3731 - 45.8189i) q^{48} +342.289 q^{49} -141.648i q^{50} +(-14.4691 + 9.55640i) q^{51} +162.005 q^{52} +158.393 q^{53} +(-276.044 + 50.3182i) q^{54} +763.158 q^{55} -6.74536 q^{56} +(58.6796 + 88.8452i) q^{57} +70.3189 q^{58} -102.687i q^{59} +(-242.697 + 160.294i) q^{60} +650.311i q^{61} +277.631i q^{62} +(20.9383 + 8.93650i) q^{63} -64.0000 q^{64} -566.764 q^{65} +(-312.346 - 472.915i) q^{66} +1059.34i q^{67} +13.3484 q^{68} +(-572.368 + 30.0673i) q^{69} +23.5982 q^{70} +1038.38i q^{71} +(198.662 + 84.7895i) q^{72} +56.9648 q^{73} -110.901 q^{74} +(307.080 - 202.817i) q^{75} -81.9639i q^{76} +45.9830i q^{77} +(231.965 + 351.213i) q^{78} -266.480i q^{79} +223.899 q^{80} +(-504.335 - 526.390i) q^{81} +196.685 q^{82} -321.577 q^{83} +(-9.65827 - 14.6233i) q^{84} -46.6985 q^{85} +914.506 q^{86} +(100.685 + 152.445i) q^{87} +436.286i q^{88} +1048.71 q^{89} +(-695.006 - 296.630i) q^{90} -34.1495i q^{91} +(380.413 + 223.513i) q^{92} +(-601.879 + 397.523i) q^{93} -512.886 q^{94} +286.745i q^{95} +(-91.6377 - 138.746i) q^{96} +773.312i q^{97} -684.578i q^{98} +(578.008 - 1354.28i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8 q^{3} - 96 q^{4} + 8 q^{6} + 36 q^{9}+O(q^{10}) $ 24 * q + 8 * q^3 - 96 * q^4 + 8 * q^6 + 36 * q^9	$ 24 q + 8 q^{3} - 96 q^{4} + 8 q^{6} + 36 q^{9} - 32 q^{12} + 96 q^{13} + 384 q^{16} + 128 q^{18} - 32 q^{24} + 144 q^{25} + 188 q^{27} + 72 q^{31} - 144 q^{36} - 660 q^{39} - 96 q^{46} + 128 q^{48} - 504 q^{49} - 384 q^{52} + 88 q^{54} - 672 q^{55} + 816 q^{58} - 1536 q^{64} + 352 q^{69} + 624 q^{70} - 512 q^{72} - 2688 q^{73} - 1072 q^{75} + 80 q^{78} - 2356 q^{81} + 1344 q^{82} + 4872 q^{85} + 3748 q^{87} - 2924 q^{93} - 1296 q^{94} + 128 q^{96}+O(q^{100}) $ 24 * q + 8 * q^3 - 96 * q^4 + 8 * q^6 + 36 * q^9 - 32 * q^12 + 96 * q^13 + 384 * q^16 + 128 * q^18 - 32 * q^24 + 144 * q^25 + 188 * q^27 + 72 * q^31 - 144 * q^36 - 660 * q^39 - 96 * q^46 + 128 * q^48 - 504 * q^49 - 384 * q^52 + 88 * q^54 - 672 * q^55 + 816 * q^58 - 1536 * q^64 + 352 * q^69 + 624 * q^70 - 512 * q^72 - 2688 * q^73 - 1072 * q^75 + 80 * q^78 - 2356 * q^81 + 1344 * q^82 + 4872 * q^85 + 3748 * q^87 - 2924 * q^93 - 1296 * q^94 + 128 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/138\mathbb{Z}\right)^\times$.

$n$	$47$	$97$
$\chi(n)$	$-1$	$-1$

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 $

$2$		−	2.00000i		−	0.707107i
$2$		−	2.00000i		−	0.707107i
$3$	4.33582	−	2.86368i	0.834429	−	0.551115i
$3$	4.33582	−	2.86368i	0.834429	−	0.551115i
$4$	−4.00000			−0.500000
$5$	13.9937			1.25164			0.625818	−	0.779969i	$-0.284765\pi$
$5$	13.9937			1.25164			0.625818	+	0.779969i	$0.284765\pi$
$6$	−5.72736	−	8.67164i	−0.389697	−	0.590031i
$7$			0.843170i			0.0455269i	0.999741	+	0.0227635i	$0.00724646\pi$
$7$			0.843170i			0.0455269i	−0.999741	+	0.0227635i	$0.992754\pi$
$8$			8.00000i			0.353553i
$9$	10.5987	−	24.8328i	0.392544	−	0.919733i
$10$		−	27.9874i		−	0.885040i
$11$	54.5358			1.49483			0.747417	−	0.664356i	$-0.231294\pi$
$11$	54.5358			1.49483			0.747417	+	0.664356i	$0.231294\pi$
$12$	−17.3433	+	11.4547i	−0.417215	+	0.275558i
$13$	−40.5013			−0.864080			−0.432040	−	0.901854i	$-0.642206\pi$
$13$	−40.5013			−0.864080			−0.432040	+	0.901854i	$0.642206\pi$
$14$	1.68634			0.0321924
$15$	60.6742	−	40.0735i	1.04440	−	0.689795i
$16$	16.0000			0.250000
$17$	−3.33711			−0.0476098			−0.0238049	−	0.999717i	$-0.507578\pi$
$17$	−3.33711			−0.0476098			−0.0238049	+	0.999717i	$0.507578\pi$
$18$	−49.6656	−	21.1974i	−0.650350	−	0.277571i
$19$			20.4910i			0.247419i	0.992319	+	0.123709i	$0.0394790\pi$
$19$			20.4910i			0.247419i	−0.992319	+	0.123709i	$0.960521\pi$
$20$	−55.9749			−0.625818
$21$	2.41457	+	3.65584i	0.0250906	+	0.0379890i
$22$		−	109.072i		−	1.05701i
$23$	−95.1032	−	55.8782i	−0.862191	−	0.506583i
$23$	−95.1032	−	55.8782i	−0.862191	−	0.506583i
$24$	22.9094	+	34.6866i	0.194849	+	0.295015i
$25$	70.8240			0.566592
$26$			81.0026i			0.610997i
$27$	−25.1591	−	138.022i	−0.179329	−	0.983789i
$28$		−	3.37268i		−	0.0227635i
$29$			35.1595i			0.225136i	0.993644	+	0.112568i	$0.0359076\pi$
$29$			35.1595i			0.225136i	−0.993644	+	0.112568i	$0.964092\pi$
$30$	−80.1470	−	121.348i	−0.487759	−	0.738503i
$31$	−138.815			−0.804258			−0.402129	−	0.915583i	$-0.631730\pi$
$31$	−138.815			−0.804258			−0.402129	+	0.915583i	$0.631730\pi$
$32$		−	32.0000i		−	0.176777i
$33$	236.458	−	156.173i	1.24733	−	0.823825i
$34$			6.67421i			0.0336652i
$35$			11.7991i			0.0569831i
$36$	−42.3948	+	99.3312i	−0.196272	+	0.459867i
$37$		−	55.4505i		−	0.246379i	−0.992383	−	0.123189i	$-0.960688\pi$
$37$		−	55.4505i		−	0.246379i	0.992383	−	0.123189i	$-0.0393122\pi$
$38$	40.9820			0.174951
$39$	−175.606	+	115.983i	−0.721013	+	0.476207i
$40$			111.950i			0.442520i
$41$			98.3424i			0.374598i	0.982303	+	0.187299i	$0.0599733\pi$
$41$			98.3424i			0.374598i	−0.982303	+	0.187299i	$0.940027\pi$
$42$	7.31167	−	4.82914i	0.0268623	−	0.0177417i
$43$			457.253i			1.62164i	0.585297	+	0.810819i	$0.300978\pi$
$43$			457.253i			1.62164i	−0.585297	+	0.810819i	$0.699022\pi$
$44$	−218.143			−0.747417
$45$	148.315	−	347.503i	0.491322	−	1.15117i
$46$	−111.756	+	190.206i	−0.358208	+	0.609661i
$47$		−	256.443i		−	0.795873i	−0.917413	−	0.397937i	$-0.869726\pi$
$47$		−	256.443i		−	0.795873i	0.917413	−	0.397937i	$-0.130274\pi$
$48$	69.3731	−	45.8189i	0.208607	−	0.137779i
$49$	342.289			0.997927
$50$		−	141.648i		−	0.400641i
$51$	−14.4691	+	9.55640i	−0.0397270	+	0.0262385i
$52$	162.005			0.432040
$53$	158.393			0.410507			0.205254	−	0.978709i	$-0.434198\pi$
$53$	158.393			0.410507			0.205254	+	0.978709i	$0.434198\pi$
$54$	−276.044	+	50.3182i	−0.695644	+	0.126804i
$55$	763.158			1.87099
$56$	−6.74536			−0.0160962
$57$	58.6796	+	88.8452i	0.136356	+	0.206453i
$58$	70.3189			0.159195
$59$		−	102.687i		−	0.226589i	−0.993561	−	0.113294i	$-0.963860\pi$
$59$		−	102.687i		−	0.226589i	0.993561	−	0.113294i	$-0.0361403\pi$
$60$	−242.697	+	160.294i	−0.522201	+	0.344898i
$61$			650.311i			1.36498i	0.730894	+	0.682491i	$0.239103\pi$
$61$			650.311i			1.36498i	−0.730894	+	0.682491i	$0.760897\pi$
$62$			277.631i			0.568696i
$63$	20.9383	+	8.93650i	0.0418726	+	0.0178713i
$64$	−64.0000			−0.125000
$65$	−566.764			−1.08151
$66$	−312.346	−	472.915i	−0.582532	−	0.881997i
$67$			1059.34i			1.93162i	0.259252	+	0.965810i	$0.416524\pi$
$67$			1059.34i			1.93162i	−0.259252	+	0.965810i	$0.583476\pi$
$68$	13.3484			0.0238049
$69$	−572.368	+	30.0673i	−0.998623	+	0.0524590i
$70$	23.5982			0.0402932
$71$			1038.38i			1.73568i	0.496840	+	0.867842i	$0.334493\pi$
$71$			1038.38i			1.73568i	−0.496840	+	0.867842i	$0.665507\pi$
$72$	198.662	+	84.7895i	0.325175	+	0.138785i
$73$	56.9648			0.0913318			0.0456659	−	0.998957i	$-0.485459\pi$
$73$	56.9648			0.0913318			0.0456659	+	0.998957i	$0.485459\pi$
$74$	−110.901			−0.174216
$75$	307.080	−	202.817i	0.472781	−	0.312258i
$76$		−	81.9639i		−	0.123709i
$77$			45.9830i			0.0680551i
$78$	231.965	+	351.213i	0.336730	+	0.509833i
$79$		−	266.480i		−	0.379511i	−0.981831	−	0.189755i	$-0.939230\pi$
$79$		−	266.480i		−	0.379511i	0.981831	−	0.189755i	$-0.0607695\pi$
$80$	223.899			0.312909
$81$	−504.335	−	526.390i	−0.691818	−	0.722072i
$82$	196.685			0.264881
$83$	−321.577			−0.425273			−0.212637	−	0.977131i	$-0.568205\pi$
$83$	−321.577			−0.425273			−0.212637	+	0.977131i	$0.568205\pi$
$84$	−9.65827	−	14.6233i	−0.0125453	−	0.0189945i
$85$	−46.6985			−0.0595902
$86$	914.506			1.14667
$87$	100.685	+	152.445i	0.124076	+	0.187860i
$88$			436.286i			0.528503i
$89$	1048.71			1.24903			0.624514	−	0.781014i	$-0.285297\pi$
$89$	1048.71			1.24903			0.624514	+	0.781014i	$0.285297\pi$
$90$	−695.006	−	296.630i	−0.814001	−	0.347417i
$91$		−	34.1495i		−	0.0393389i
$92$	380.413	+	223.513i	0.431096	+	0.253291i
$93$	−601.879	+	397.523i	−0.671096	+	0.443239i
$94$	−512.886			−0.562767
$95$			286.745i			0.309678i
$96$	−91.6377	−	138.746i	−0.0974243	−	0.147508i
$97$			773.312i			0.809463i	0.914436	+	0.404732i	$0.132635\pi$
$97$			773.312i			0.809463i	−0.914436	+	0.404732i	$0.867365\pi$
$98$		−	684.578i		−	0.705641i
$99$	578.008	−	1354.28i	0.586788	−	1.37485i
$100$	−283.296			−0.283296
$101$		−	1419.41i		−	1.39838i	−0.714934	−	0.699192i	$-0.753543\pi$
$101$		−	1419.41i		−	1.39838i	0.714934	−	0.699192i	$-0.246457\pi$
$102$	19.1128	+	28.9382i	0.0185534	+	0.0280912i
$103$		−	1963.42i		−	1.87826i	−0.343557	−	0.939132i	$-0.611632\pi$
$103$		−	1963.42i		−	1.87826i	0.343557	−	0.939132i	$-0.388368\pi$
$104$		−	324.010i		−	0.305498i
$105$	33.7888	+	51.1587i	0.0314043	+	0.0475484i
$106$		−	316.785i		−	0.290273i
$107$	−1758.99			−1.58924			−0.794618	−	0.607110i	$-0.792329\pi$
$107$	−1758.99			−1.58924			−0.794618	+	0.607110i	$0.792329\pi$
$108$	100.636	+	552.087i	0.0896643	+	0.491895i
$109$		−	1533.96i		−	1.34795i	−0.738755	−	0.673974i	$-0.764586\pi$
$109$		−	1533.96i		−	1.34795i	0.738755	−	0.673974i	$-0.235414\pi$
$110$		−	1526.32i		−	1.32299i
$111$	−158.792	−	240.423i	−0.135783	−	0.205585i
$112$			13.4907i			0.0113817i
$113$	182.732			0.152124			0.0760618	−	0.997103i	$-0.475765\pi$
$113$	182.732			0.152124			0.0760618	+	0.997103i	$0.475765\pi$
$114$	177.690	−	117.359i	0.145985	−	0.0964183i
$115$	−1330.85	−	781.943i	−1.07915	−	0.634057i
$116$		−	140.638i		−	0.112568i
$117$	−429.261	+	1005.76i	−0.339190	+	0.794723i
$118$	−205.375			−0.160223
$119$		−	2.81375i		−	0.00216753i
$120$	320.588	+	485.394i	0.243880	+	0.369252i
$121$	1643.15			1.23453
$122$	1300.62			0.965187
$123$	281.621	+	426.395i	0.206446	+	0.312575i
$124$	555.262			0.402129
$125$	−758.123			−0.542469
$126$	17.8730	−	41.8766i	0.0126369	−	0.0296084i
$127$	−1327.66			−0.927646			−0.463823	−	0.885928i	$-0.653523\pi$
$127$	−1327.66			−0.927646			−0.463823	+	0.885928i	$0.653523\pi$
$128$			128.000i			0.0883883i
$129$	1309.43	+	1982.57i	0.893710	+	1.35314i
$130$			1133.53i			0.764745i
$131$			1717.50i			1.14549i	0.819735	+	0.572743i	$0.194121\pi$
$131$			1717.50i			1.14549i	−0.819735	+	0.572743i	$0.805879\pi$
$132$	−945.830	+	624.692i	−0.623666	+	0.411913i
$133$	−17.2774			−0.0112642
$134$	2118.67			1.36586
$135$	−352.069	−	1931.44i	−0.224454	−	1.23135i
$136$		−	26.6968i		−	0.0168326i
$137$	512.662			0.319705			0.159853	−	0.987141i	$-0.448898\pi$
$137$	512.662			0.319705			0.159853	+	0.987141i	$0.448898\pi$
$138$	60.1345	+	1144.74i	0.0370941	+	0.706133i
$139$	−2529.40			−1.54346			−0.771730	−	0.635950i	$-0.780608\pi$
$139$	−2529.40			−1.54346			−0.771730	+	0.635950i	$0.780608\pi$
$140$		−	47.1963i		−	0.0284916i
$141$	−734.370	−	1111.89i	−0.438618	−	0.664100i
$142$	2076.77			1.22731
$143$	−2208.77			−1.29166
$144$	169.579	−	397.325i	0.0981361	−	0.229933i
$145$			492.012i			0.281789i
$146$		−	113.930i		−	0.0645814i
$147$	1484.10	−	980.206i	0.832700	−	0.549973i
$148$			221.802i			0.123189i
$149$	2329.37			1.28073			0.640367	−	0.768069i	$-0.278782\pi$
$149$	2329.37			1.28073			0.640367	+	0.768069i	$0.278782\pi$
$150$	−405.635	−	614.161i	−0.220799	−	0.334307i
$151$	1852.30			0.998267			0.499134	−	0.866525i	$-0.333652\pi$
$151$	1852.30			0.998267			0.499134	+	0.866525i	$0.333652\pi$
$152$	−163.928			−0.0874757
$153$	−35.3690	+	82.8696i	−0.0186890	+	0.0437883i
$154$	91.9660			0.0481223
$155$	−1942.54			−1.00664
$156$	702.425	−	463.931i	0.360507	−	0.238104i
$157$		−	1221.44i		−	0.620904i	−0.950589	−	0.310452i	$-0.899520\pi$
$157$		−	1221.44i		−	0.620904i	0.950589	−	0.310452i	$-0.100480\pi$
$158$	−532.960			−0.268355
$159$	686.762	−	453.585i	0.342539	−	0.226237i
$160$		−	447.799i		−	0.221260i
$161$	47.1148	−	80.1882i	0.0230632	−	0.0392529i
$162$	−1052.78	+	1008.67i	−0.510582	+	0.489189i
$163$	−3484.80			−1.67454			−0.837272	−	0.546787i	$-0.815851\pi$
$163$	−3484.80			−1.67454			−0.837272	+	0.546787i	$0.815851\pi$
$164$		−	393.370i		−	0.187299i
$165$	3308.92	−	2185.44i	1.56121	−	1.03113i
$166$			643.155i			0.300714i
$167$			2758.90i			1.27838i	0.769047	+	0.639192i	$0.220731\pi$
$167$			2758.90i			1.27838i	−0.769047	+	0.639192i	$0.779269\pi$
$168$	−29.2467	+	19.3165i	−0.0134311	+	0.00887086i
$169$	−556.645			−0.253366
$170$			93.3970i			0.0421366i
$171$	508.848	+	217.178i	0.227559	+	0.0971227i
$172$		−	1829.01i		−	0.810819i
$173$			383.388i			0.168488i	0.996445	+	0.0842441i	$0.0268475\pi$
$173$			383.388i			0.168488i	−0.996445	+	0.0842441i	$0.973152\pi$
$174$	304.890	−	201.371i	0.132837	−	0.0877350i
$175$			59.7167i			0.0257952i
$176$	872.573			0.373708
$177$	−294.063	−	445.234i	−0.124877	−	0.189072i
$178$		−	2097.43i		−	0.883196i
$179$		−	2503.09i		−	1.04519i	−0.852580	−	0.522597i	$-0.824963\pi$
$179$		−	2503.09i		−	1.04519i	0.852580	−	0.522597i	$-0.175037\pi$
$180$	−593.260	+	1390.01i	−0.245661	+	0.575585i
$181$			2359.26i			0.968852i	0.874832	+	0.484426i	$0.160972\pi$
$181$			2359.26i			0.968852i	−0.874832	+	0.484426i	$0.839028\pi$
$182$	−68.2990			−0.0278168
$183$	1862.28	+	2819.63i	0.752262	+	1.13898i
$184$	447.026	−	760.826i	0.179104	−	0.304831i
$185$		−	775.959i		−	0.308376i
$186$	795.046	+	1203.76i	0.313417	+	0.474537i
$187$	−181.992			−0.0711687
$188$			1025.77i			0.397937i
$189$	116.376	−	21.2134i	0.0447889	−	0.00816427i
$190$	573.490			0.218975
$191$	−4054.72			−1.53607			−0.768035	−	0.640407i	$-0.778765\pi$
$191$	−4054.72			−1.53607			−0.768035	+	0.640407i	$0.778765\pi$
$192$	−277.493	+	183.275i	−0.104304	+	0.0688894i
$193$	3385.33			1.26260			0.631299	−	0.775539i	$-0.282522\pi$
$193$	3385.33			1.26260			0.631299	+	0.775539i	$0.282522\pi$
$194$	1546.62			0.572377
$195$	−2457.39	+	1623.03i	−0.902446	+	0.596038i
$196$	−1369.16			−0.498964
$197$			2338.06i			0.845584i	0.906227	+	0.422792i	$0.138950\pi$
$197$			2338.06i			0.845584i	−0.906227	+	0.422792i	$0.861050\pi$
$198$	−2708.55	−	1156.02i	−0.972164	−	0.414922i
$199$		−	3014.89i		−	1.07397i	−0.843592	−	0.536984i	$-0.819563\pi$
$199$		−	3014.89i		−	1.07397i	0.843592	−	0.536984i	$-0.180437\pi$
$200$			566.592i			0.200321i
$201$	3033.60	+	4593.09i	1.06454	+	1.61180i
$202$	−2838.83			−0.988807
$203$	−29.6454			−0.0102498
$204$	57.8764	−	38.2256i	0.0198635	−	0.0131192i
$205$			1376.18i			0.468860i
$206$	−3926.83			−1.32813
$207$	−2395.58	+	1769.44i	−0.804369	+	0.594130i
$208$	−648.021			−0.216020
$209$			1117.49i			0.369849i
$210$	102.317	−	67.5776i	0.0336218	−	0.0222062i
$211$	2199.56			0.717651			0.358825	−	0.933405i	$-0.383177\pi$
$211$	2199.56			0.717651			0.358825	+	0.933405i	$0.383177\pi$
$212$	−633.570			−0.205254
$213$	2973.60	+	4502.25i	0.956562	+	1.44831i
$214$			3517.98i			1.12376i
$215$			6398.67i			2.02970i
$216$	1104.17	−	201.273i	0.347822	−	0.0634022i
$217$		−	117.045i		−	0.0366154i
$218$	−3067.91			−0.953143
$219$	246.989	−	163.129i	0.0762099	−	0.0503344i
$220$	−3052.63			−0.935493
$221$	135.157			0.0411387
$222$	−480.847	+	317.585i	−0.145371	+	0.0960130i
$223$	2998.08			0.900296			0.450148	−	0.892954i	$-0.351371\pi$
$223$	2998.08			0.900296			0.450148	+	0.892954i	$0.351371\pi$
$224$	26.9815			0.00804810
$225$	750.642	−	1758.76i	0.222413	−	0.521114i
$226$		−	365.464i		−	0.107568i
$227$	−756.576			−0.221215			−0.110607	−	0.993864i	$-0.535280\pi$
$227$	−756.576			−0.221215			−0.110607	+	0.993864i	$0.535280\pi$
$228$	−234.718	−	355.381i	−0.0681781	−	0.103227i
$229$		−	1924.17i		−	0.555252i	−0.960689	−	0.277626i	$-0.910452\pi$
$229$		−	1924.17i		−	0.555252i	0.960689	−	0.277626i	$-0.0895475\pi$
$230$	−1563.89	+	2661.70i	−0.448346	+	0.763074i
$231$	131.680	+	199.374i	0.0375062	+	0.0567872i
$232$	−281.276			−0.0795977
$233$		−	5099.84i		−	1.43391i	−0.697118	−	0.716957i	$-0.745534\pi$
$233$		−	5099.84i		−	1.43391i	0.697118	−	0.716957i	$-0.254466\pi$
$234$	2011.52	+	858.522i	0.561954	+	0.239843i
$235$		−	3588.59i		−	0.996143i
$236$			410.749i			0.113294i
$237$	−763.114	−	1155.41i	−0.209154	−	0.316675i
$238$	−5.62750			−0.00153267
$239$		−	5362.24i		−	1.45127i	−0.688078	−	0.725637i	$-0.741545\pi$
$239$		−	5362.24i		−	1.45127i	0.688078	−	0.725637i	$-0.258455\pi$
$240$	970.788	−	641.176i	0.261100	−	0.172449i
$241$			6539.89i			1.74801i	0.485913	+	0.874007i	$0.338487\pi$
$241$			6539.89i			1.74801i	−0.485913	+	0.874007i	$0.661513\pi$
$242$		−	3286.31i		−	0.872942i
$243$	−3694.12	−	838.080i	−0.975218	−	0.221246i
$244$		−	2601.25i		−	0.682491i
$245$	4789.90			1.24904
$246$	852.790	−	563.242i	0.221024	−	0.145980i
$247$		−	829.911i		−	0.213789i
$248$		−	1110.52i		−	0.284348i
$249$	−1394.30	+	920.894i	−0.354861	+	0.234375i
$250$			1516.25i			0.383583i
$251$	2414.61			0.607206			0.303603	−	0.952799i	$-0.401810\pi$
$251$	2414.61			0.607206			0.303603	+	0.952799i	$0.401810\pi$
$252$	−83.7531	−	35.7460i	−0.0209363	−	0.00893566i
$253$	−5186.53	−	3047.36i	−1.28883	−	0.757257i
$254$			2655.33i			0.655945i
$255$	−202.476	+	133.729i	−0.0497238	+	0.0328410i
$256$	256.000			0.0625000
$257$		−	5439.66i		−	1.32030i	−0.751134	−	0.660149i	$-0.770493\pi$
$257$		−	5439.66i		−	1.32030i	0.751134	−	0.660149i	$-0.229507\pi$
$258$	3965.14	−	2618.85i	0.956816	−	0.631948i
$259$	46.7542			0.0112169
$260$	2267.05			0.540757
$261$	873.108	+	372.644i	0.207065	+	0.0883759i
$262$	3435.00			0.809981
$263$	−2435.47			−0.571018			−0.285509	−	0.958376i	$-0.592163\pi$
$263$	−2435.47			−0.571018			−0.285509	+	0.958376i	$0.592163\pi$
$264$	1249.38	+	1891.66i	0.291266	+	0.440999i
$265$	2216.50			0.513806
$266$			34.5548i			0.00796500i
$267$	4547.04	−	3003.18i	1.04223	−	0.688358i
$268$		−	4237.34i		−	0.965810i
$269$		−	3891.41i		−	0.882020i	−0.897502	−	0.441010i	$-0.854620\pi$
$269$		−	3891.41i		−	0.882020i	0.897502	−	0.441010i	$-0.145380\pi$
$270$	−3862.88	+	704.138i	−0.870693	+	0.158713i
$271$	−2344.25			−0.525471			−0.262736	−	0.964868i	$-0.584625\pi$
$271$	−2344.25			−0.525471			−0.262736	+	0.964868i	$0.584625\pi$
$272$	−53.3937			−0.0119025
$273$	−97.7932	−	148.066i	−0.0216803	−	0.0328255i
$274$		−	1025.32i		−	0.226066i
$275$	3862.45			0.846961
$276$	2289.47	−	120.269i	0.499312	−	0.0262295i
$277$	−1384.73			−0.300361			−0.150181	−	0.988659i	$-0.547986\pi$
$277$	−1384.73			−0.300361			−0.150181	+	0.988659i	$0.547986\pi$
$278$			5058.80i			1.09139i
$279$	−1471.26	+	3447.18i	−0.315707	+	0.739703i
$280$	−94.3927			−0.0201466
$281$	8837.84			1.87623			0.938116	−	0.346321i	$-0.112569\pi$
$281$	8837.84			1.87623			0.938116	+	0.346321i	$0.112569\pi$
$282$	−2223.78	+	1468.74i	−0.469590	+	0.310150i
$283$			1602.31i			0.336563i	0.985739	+	0.168282i	$0.0538218\pi$
$283$			1602.31i			0.336563i	−0.985739	+	0.168282i	$0.946178\pi$
$284$		−	4153.54i		−	0.867842i
$285$	821.145	+	1243.27i	0.170668	+	0.258404i
$286$			4417.54i			0.913338i
$287$	−82.9194			−0.0170543
$288$	−794.649	−	339.158i	−0.162587	−	0.0693927i
$289$	−4901.86			−0.997733
$290$	984.023			0.199255
$291$	2214.52	+	3352.94i	0.446107	+	0.675440i
$292$	−227.859			−0.0456659
$293$	2505.62			0.499591			0.249795	−	0.968299i	$-0.419637\pi$
$293$	2505.62			0.499591			0.249795	+	0.968299i	$0.419637\pi$
$294$	−1960.41	−	2968.21i	−0.388890	−	0.588808i
$295$		−	1436.98i		−	0.283607i
$296$	443.604			0.0871080
$297$	−1372.07	−	7527.13i	−0.268066	−	1.47060i
$298$		−	4658.74i		−	0.905615i
$299$	3851.80	+	2263.14i	0.745002	+	0.437728i
$300$	−1228.32	+	811.269i	−0.236391	+	0.156129i
$301$	−385.542			−0.0738282
$302$		−	3704.61i		−	0.705881i
$303$	−4064.74	−	6154.32i	−0.770671	−	1.16685i
$304$			327.856i			0.0618546i
$305$			9100.27i			1.70846i
$306$	165.739	+	70.7379i	0.0309630	+	0.0132151i
$307$	6596.78			1.22638			0.613189	−	0.789936i	$-0.289886\pi$
$307$	6596.78			1.22638			0.613189	+	0.789936i	$0.289886\pi$
$308$		−	183.932i		−	0.0340276i
$309$	−5622.59	−	8513.02i	−1.03514	−	1.56728i
$310$			3885.09i			0.711801i
$311$		−	9475.69i		−	1.72771i	−0.503743	−	0.863853i	$-0.668044\pi$
$311$		−	9475.69i		−	1.72771i	0.503743	−	0.863853i	$-0.331956\pi$
$312$	−927.861	−	1404.85i	−0.168365	−	0.254917i
$313$			913.302i			0.164929i	0.996594	+	0.0824647i	$0.0262792\pi$
$313$			913.302i			0.164929i	−0.996594	+	0.0824647i	$0.973721\pi$
$314$	−2442.89			−0.439045
$315$	293.004	+	125.055i	0.0524093	+	0.0223684i
$316$			1065.92i			0.189755i
$317$		−	3835.86i		−	0.679632i	−0.940492	−	0.339816i	$-0.889635\pi$
$317$		−	3835.86i		−	0.679632i	0.940492	−	0.339816i	$-0.110365\pi$
$318$	−907.171	−	1373.52i	−0.159974	−	0.242212i
$319$			1917.45i			0.336541i
$320$	−895.598			−0.156454
$321$	−7626.68	+	5037.19i	−1.32610	+	0.875852i
$322$	−160.376	−	94.2297i	−0.0277560	−	0.0163081i
$323$		−	68.3805i		−	0.0117796i
$324$	2017.34	+	2105.56i	0.345909	+	0.361036i
$325$	−2868.47			−0.489581
$326$			6969.60i			1.18408i
$327$	−4392.75	−	6650.96i	−0.742874	−	1.12477i
$328$	−786.739			−0.132440
$329$	216.225			0.0362337
$330$	−4370.88	−	6617.84i	−0.729118	−	1.10394i
$331$	10057.5			1.67013			0.835064	−	0.550153i	$-0.185430\pi$
$331$	10057.5			1.67013			0.835064	+	0.550153i	$0.185430\pi$
$332$	1286.31			0.212637
$333$	−1376.99	−	587.703i	−0.226603	−	0.0967145i
$334$	5517.80			0.903954
$335$			14824.0i			2.41768i
$336$	38.6331	+	58.4934i	0.00627264	+	0.00949725i
$337$		−	5459.71i		−	0.882521i	−0.897379	−	0.441260i	$-0.854532\pi$
$337$		−	5459.71i		−	0.882521i	0.897379	−	0.441260i	$-0.145468\pi$
$338$			1113.29i			0.179157i
$339$	792.293	−	523.285i	0.126936	−	0.0838376i
$340$	186.794			0.0297951
$341$	−7570.41			−1.20223
$342$	434.355	−	1017.70i	0.0686761	−	0.160909i
$343$			577.815i			0.0909595i
$344$	−3658.03			−0.573336
$345$	−8009.55	+	420.753i	−1.24991	+	0.0656596i
$346$	766.776			0.119139
$347$		−	1686.18i		−	0.260861i	−0.991457	−	0.130431i	$-0.958364\pi$
$347$		−	1686.18i		−	0.260861i	0.991457	−	0.130431i	$-0.0416360\pi$
$348$	−402.742	−	609.781i	−0.0620380	−	0.0939301i
$349$	−7194.39			−1.10346			−0.551729	−	0.834024i	$-0.686032\pi$
$349$	−7194.39			−1.10346			−0.551729	+	0.834024i	$0.686032\pi$
$350$	119.433			0.0182400
$351$	1018.98	+	5590.06i	0.154954	+	0.850072i
$352$		−	1745.15i		−	0.264252i
$353$		−	2246.05i		−	0.338654i	−0.985560	−	0.169327i	$-0.945841\pi$
$353$		−	2246.05i		−	0.338654i	0.985560	−	0.169327i	$-0.0541594\pi$
$354$	−890.467	+	588.127i	−0.133694	+	0.0883011i
$355$			14530.9i			2.17244i
$356$	−4194.86			−0.624514
$357$	−8.05767	−	12.1999i	−0.00119456	−	0.00180865i
$358$	−5006.18			−0.739064
$359$	−2458.84			−0.361484			−0.180742	−	0.983531i	$-0.557850\pi$
$359$	−2458.84			−0.361484			−0.180742	+	0.983531i	$0.557850\pi$
$360$	2780.02	+	1186.52i	0.407000	+	0.173709i
$361$	6439.12			0.938784
$362$	4718.52			0.685082
$363$	7124.42	−	4705.46i	1.03012	−	0.680366i
$364$			136.598i			0.0196694i
$365$	797.149			0.114314
$366$	5639.27	−	3724.57i	0.805381	−	0.531929i
$367$			3862.99i			0.549446i	0.961523	+	0.274723i	$0.0885861\pi$
$367$			3862.99i			0.549446i	−0.961523	+	0.274723i	$0.911414\pi$
$368$	−1521.65	−	894.051i	−0.215548	−	0.126646i
$369$	2442.12	+	1042.30i	0.344530	+	0.147046i
$370$	−1551.92			−0.218055
$371$			133.552i			0.0186891i
$372$	2407.52	−	1590.09i	0.335548	−	0.221619i
$373$			8099.32i			1.12431i	0.827033	+	0.562154i	$0.190027\pi$
$373$			8099.32i			1.12431i	−0.827033	+	0.562154i	$0.809973\pi$
$374$			363.983i			0.0503239i
$375$	−3287.09	+	2171.02i	−0.452652	+	0.298963i
$376$	2051.54			0.281384
$377$		−	1424.00i		−	0.194536i
$378$	−42.4268	−	232.752i	−0.00577301	−	0.0316705i
$379$		−	3591.10i		−	0.486709i	−0.969937	−	0.243354i	$-0.921752\pi$
$379$		−	3591.10i		−	0.486709i	0.969937	−	0.243354i	$-0.0782478\pi$
$380$		−	1146.98i		−	0.154839i
$381$	−5756.51	+	3802.00i	−0.774055	+	0.511240i
$382$			8109.45i			1.08617i
$383$	−540.739			−0.0721422			−0.0360711	−	0.999349i	$-0.511484\pi$
$383$	−540.739			−0.0721422			−0.0360711	+	0.999349i	$0.511484\pi$
$384$	366.551	+	554.985i	0.0487122	+	0.0737538i
$385$			643.473i			0.0851803i
$386$		−	6770.66i		−	0.892792i
$387$	11354.9	+	4846.29i	1.49147	+	0.636565i
$388$		−	3093.25i		−	0.404732i
$389$	102.798			0.0133986			0.00669931	−	0.999978i	$-0.497868\pi$
$389$	102.798			0.0133986			0.00669931	+	0.999978i	$0.497868\pi$
$390$	3246.06	+	4914.77i	0.421463	+	0.638126i
$391$	317.370	+	186.471i	0.0410488	+	0.0241183i
$392$			2738.31i			0.352821i
$393$	4918.37	+	7446.78i	0.631295	+	0.955828i
$394$	4676.13			0.597918
$395$		−	3729.05i		−	0.475010i
$396$	−2312.03	+	5417.11i	−0.293394	+	0.687424i
$397$	−11202.2			−1.41617			−0.708086	−	0.706127i	$-0.750441\pi$
$397$	−11202.2			−1.41617			−0.708086	+	0.706127i	$0.750441\pi$
$398$	−6029.78			−0.759410
$399$	−74.9117	+	49.4769i	−0.00939918	+	0.00620787i
$400$	1133.18			0.141648
$401$	244.695			0.0304725			0.0152363	−	0.999884i	$-0.495150\pi$
$401$	244.695			0.0304725			0.0152363	+	0.999884i	$0.495150\pi$
$402$	9186.18	−	6067.19i	1.13971	−	0.752747i
$403$	5622.21			0.694943
$404$			5677.65i			0.699192i
$405$	−7057.53	−	7366.16i	−0.865904	−	0.903771i
$406$			59.2908i			0.00724767i
$407$		−	3024.04i		−	0.368295i
$408$	−76.4512	−	115.753i	−0.00927671	−	0.0140456i
$409$	12935.8			1.56390			0.781948	−	0.623344i	$-0.214226\pi$
$409$	12935.8			1.56390			0.781948	+	0.623344i	$0.214226\pi$
$410$	2752.35			0.331534
$411$	2222.81	−	1468.10i	0.266772	−	0.176194i
$412$			7853.67i			0.939132i
$413$	86.5829			0.0103159
$414$	3538.89	+	4791.16i	0.420113	+	0.568775i
$415$	−4500.06			−0.532287
$416$			1296.04i			0.152749i
$417$	−10967.0	+	7243.39i	−1.28791	+	0.850624i
$418$	2234.98			0.261523
$419$	−7216.30			−0.841383			−0.420691	−	0.907204i	$-0.638212\pi$
$419$	−7216.30			−0.841383			−0.420691	+	0.907204i	$0.638212\pi$
$420$	−135.155	−	204.635i	−0.0157021	−	0.0237742i
$421$			6609.28i			0.765122i	0.923930	+	0.382561i	$0.124958\pi$
$421$			6609.28i			0.765122i	−0.923930	+	0.382561i	$0.875042\pi$
$422$		−	4399.13i		−	0.507456i
$423$	−6368.19	−	2717.96i	−0.731991	−	0.312415i
$424$			1267.14i			0.145136i
$425$	−236.347			−0.0269754
$426$	9004.50	−	5947.20i	1.02411	−	0.676391i
$427$	−548.323			−0.0621434
$428$	7035.97			0.794618
$429$	−9576.83	+	6325.21i	−1.07779	+	0.711851i
$430$	12797.3			1.43522
$431$	−15368.8			−1.71761			−0.858805	−	0.512303i	$-0.828793\pi$
$431$	−15368.8			−1.71761			−0.858805	+	0.512303i	$0.828793\pi$
$432$	−402.545	−	2208.35i	−0.0448321	−	0.245947i
$433$		−	8992.52i		−	0.998044i	−0.866589	−	0.499022i	$-0.833693\pi$
$433$		−	8992.52i		−	0.998044i	0.866589	−	0.499022i	$-0.166307\pi$
$434$	−234.090			−0.0258910
$435$	1408.96	+	2133.27i	0.155298	+	0.235133i
$436$			6135.82i			0.673974i
$437$	1145.00	−	1948.76i	0.125338	−	0.213322i
$438$	−326.258	−	493.978i	−0.0355918	−	0.0538886i
$439$	−3107.72			−0.337866			−0.168933	−	0.985627i	$-0.554032\pi$
$439$	−3107.72			−0.337866			−0.168933	+	0.985627i	$0.554032\pi$
$440$			6105.27i			0.661494i
$441$	3627.82	−	8499.99i	0.391731	−	0.917827i
$442$		−	270.314i		−	0.0290894i
$443$			6531.21i			0.700467i	0.936662	+	0.350234i	$0.113898\pi$
$443$			6531.21i			0.700467i	−0.936662	+	0.350234i	$0.886102\pi$
$444$	635.170	+	961.694i	0.0678915	+	0.102793i
$445$	14675.4			1.56333
$446$		−	5996.15i		−	0.636606i
$447$	10099.7	−	6670.56i	1.06868	−	0.705832i
$448$		−	53.9629i		−	0.00569087i
$449$		−	7159.09i		−	0.752469i	−0.926525	−	0.376234i	$-0.877219\pi$
$449$		−	7159.09i		−	0.752469i	0.926525	−	0.376234i	$-0.122781\pi$
$450$	−3517.52	−	1501.28i	−0.368483	−	0.157269i
$451$			5363.18i			0.559961i
$452$	−730.927			−0.0760618
$453$	8031.26	−	5304.40i	0.832983	−	0.550160i
$454$			1513.15i			0.156422i
$455$		−	477.878i		−	0.0492380i
$456$	−710.762	+	469.437i	−0.0729923	+	0.0482092i
$457$		−	6701.97i		−	0.686006i	−0.939334	−	0.343003i	$-0.888556\pi$
$457$		−	6701.97i		−	0.686006i	0.939334	−	0.343003i	$-0.111444\pi$
$458$	−3848.34			−0.392622
$459$	83.9585	+	460.593i	0.00853780	+	0.0468380i
$460$	5323.39	+	3127.77i	0.539575	+	0.317029i
$461$		−	5057.48i		−	0.510955i	−0.966815	−	0.255478i	$-0.917767\pi$
$461$		−	5057.48i		−	0.510955i	0.966815	−	0.255478i	$-0.0822327\pi$
$462$	398.748	−	263.361i	0.0401546	−	0.0265209i
$463$	−10776.2			−1.08167			−0.540835	−	0.841128i	$-0.681892\pi$
$463$	−10776.2			−1.08167			−0.540835	+	0.841128i	$0.681892\pi$
$464$			562.552i			0.0562841i
$465$	−8422.52	+	5562.82i	−0.839968	+	0.554773i
$466$	−10199.7			−1.01393
$467$	11995.6			1.18863			0.594313	−	0.804234i	$-0.297424\pi$
$467$	11995.6			1.18863			0.594313	+	0.804234i	$0.297424\pi$
$468$	1717.04	−	4023.04i	0.169595	−	0.397361i
$469$	−893.201			−0.0879407
$470$	−7177.18			−0.704380
$471$	−3497.82	−	5295.96i	−0.342189	−	0.518100i
$472$	821.498			0.0801113
$473$			24936.7i			2.42408i
$474$	−2310.82	+	1526.23i	−0.223923	+	0.147894i
$475$			1451.25i			0.140185i
$476$			11.2550i			0.00108376i
$477$	1678.75	−	3933.33i	0.161142	−	0.377557i
$478$	−10724.5			−1.02621
$479$	9172.29			0.874932			0.437466	−	0.899235i	$-0.355876\pi$
$479$	9172.29			0.874932			0.437466	+	0.899235i	$0.355876\pi$
$480$	−1282.35	−	1941.58i	−0.121940	−	0.184626i
$481$			2245.82i			0.212891i
$482$	13079.8			1.23603
$483$	−25.3518	−	482.604i	−0.00238830	−	0.0454642i
$484$	−6572.62			−0.617263
$485$			10821.5i			1.01315i
$486$	−1676.16	+	7388.24i	−0.156445	+	0.689583i
$487$	−6236.13			−0.580259			−0.290129	−	0.956987i	$-0.593698\pi$
$487$	−6236.13			−0.580259			−0.290129	+	0.956987i	$0.593698\pi$
$488$	−5202.49			−0.482594
$489$	−15109.5	+	9979.35i	−1.39729	+	0.922867i
$490$		−	9579.79i		−	0.883206i
$491$			11424.6i			1.05007i	0.851081	+	0.525035i	$0.175948\pi$
$491$			11424.6i			1.05007i	−0.851081	+	0.525035i	$0.824052\pi$
$492$	−1126.48	−	1705.58i	−0.103223	−	0.156288i
$493$		−	117.331i		−	0.0107187i
$494$	−1659.82			−0.151172
$495$	8088.48	−	18951.4i	0.734445	−	1.72081i
$496$	−2221.05			−0.201064
$497$	−875.535			−0.0790203
$498$	1841.79	+	2788.60i	0.165728	+	0.250924i
$499$	2241.86			0.201121			0.100561	−	0.994931i	$-0.467936\pi$
$499$	2241.86			0.201121			0.100561	+	0.994931i	$0.467936\pi$
$500$	3032.49			0.271234
$501$	7900.61	+	11962.1i	0.704537	+	1.06672i
$502$		−	4829.22i		−	0.429360i
$503$	−10382.3			−0.920322			−0.460161	−	0.887835i	$-0.652208\pi$
$503$	−10382.3			−0.920322			−0.460161	+	0.887835i	$0.652208\pi$
$504$	−71.4920	+	167.506i	−0.00631847	+	0.0148042i
$505$		−	19862.9i		−	1.75027i
$506$	−6094.72	+	10373.1i	−0.535462	+	0.911342i
$507$	−2413.51	+	1594.05i	−0.211416	+	0.139634i
$508$	5310.65			0.463823
$509$			1867.59i			0.162632i	0.996688	+	0.0813158i	$0.0259122\pi$
$509$			1867.59i			0.162632i	−0.996688	+	0.0813158i	$0.974088\pi$
$510$	267.459	+	404.953i	0.0232221	+	0.0351600i
$511$			48.0310i			0.00415806i
$512$		−	512.000i		−	0.0441942i
$513$	2828.20	−	515.534i	0.243408	−	0.0443692i
$514$	−10879.3			−0.933592
$515$		−	27475.5i		−	2.35090i
$516$	−5237.70	−	7930.27i	−0.446855	−	0.676571i
$517$		−	13985.3i		−	1.18970i
$518$		−	93.5084i		−	0.00793152i
$519$	1097.90	+	1662.30i	0.0928564	+	0.140591i
$520$		−	4534.11i		−	0.382373i
$521$	−2035.02			−0.171125			−0.0855624	−	0.996333i	$-0.527269\pi$
$521$	−2035.02			−0.171125			−0.0855624	+	0.996333i	$0.527269\pi$
$522$	745.289	−	1746.22i	0.0624912	−	0.146417i
$523$		−	13839.6i		−	1.15710i	−0.815648	−	0.578549i	$-0.803619\pi$
$523$		−	13839.6i		−	1.15710i	0.815648	−	0.578549i	$-0.196381\pi$
$524$		−	6870.00i		−	0.572743i
$525$	171.010	+	258.921i	0.0142161	+	0.0215243i
$526$			4870.94i			0.403770i
$527$	463.242			0.0382906
$528$	3783.32	−	2498.77i	0.311833	−	0.205956i
$529$	5922.26	+	10628.4i	0.486747	+	0.873543i
$530$		−	4433.00i		−	0.363316i
$531$	−2550.01	−	1088.35i	−0.208401	−	0.0889461i
$532$	69.1095			0.00563210
$533$		−	3982.99i		−	0.323682i
$534$	−6006.36	−	9094.08i	−0.486743	−	0.736965i
$535$	−24614.8			−1.98914
$536$	−8474.69			−0.682931
$537$	−7168.05	−	10853.0i	−0.576023	−	0.872141i
$538$	−7782.82			−0.623683
$539$	18667.0			1.49173
$540$	1408.28	+	7725.75i	0.112227	+	0.615673i
$541$	10928.3			0.868476			0.434238	−	0.900798i	$-0.357018\pi$
$541$	10928.3			0.868476			0.434238	+	0.900798i	$0.357018\pi$
$542$			4688.49i			0.371564i
$543$	6756.16	+	10229.3i	0.533949	+	0.808439i
$544$			106.787i			0.00841631i
$545$		−	21465.7i		−	1.68714i
$546$	−296.132	+	195.586i	−0.0232111	+	0.0153303i
$547$	5907.81			0.461791			0.230895	−	0.972979i	$-0.425834\pi$
$547$	5907.81			0.461791			0.230895	+	0.972979i	$0.425834\pi$
$548$	−2050.65			−0.159853
$549$	16149.1	+	6892.45i	1.25542	+	0.535815i
$550$		−	7724.89i		−	0.598892i
$551$	−720.452			−0.0557029
$552$	−240.538	−	4578.94i	−0.0185471	−	0.353067i
$553$	224.688			0.0172780
$554$			2769.45i			0.212388i
$555$	−2222.10	−	3364.42i	−0.169951	−	0.257318i
$556$	10117.6			0.771730
$557$	17483.5			1.32998			0.664989	−	0.746853i	$-0.268436\pi$
$557$	17483.5			1.32998			0.664989	+	0.746853i	$0.268436\pi$
$558$	6894.35	+	2942.53i	0.523049	+	0.223238i
$559$		−	18519.3i		−	1.40123i
$560$			188.785i			0.0142458i
$561$	−789.084	+	521.166i	−0.0593853	+	0.0392222i
$562$		−	17675.7i		−	1.32670i
$563$	14765.8			1.10534			0.552669	−	0.833401i	$-0.313610\pi$
$563$	14765.8			1.10534			0.552669	+	0.833401i	$0.313610\pi$
$564$	2937.48	+	4447.56i	0.219309	+	0.332050i
$565$	2557.10			0.190403
$566$	3204.62			0.237986
$567$	443.837	−	425.241i	0.0328737	−	0.0314963i
$568$	−8307.08			−0.613657
$569$	8919.94			0.657194			0.328597	−	0.944470i	$-0.393424\pi$
$569$	8919.94			0.657194			0.328597	+	0.944470i	$0.393424\pi$
$570$	2486.55	−	1642.29i	0.182719	−	0.120681i
$571$			24832.1i			1.81995i	0.414667	+	0.909973i	$0.363898\pi$
$571$			24832.1i			1.81995i	−0.414667	+	0.909973i	$0.636102\pi$
$572$	8835.08			0.645828
$573$	−17580.6	+	11611.4i	−1.28174	+	0.846552i
$574$			165.839i			0.0120592i
$575$	−6735.60	−	3957.52i	−0.488511	−	0.287026i
$576$	−678.316	+	1589.30i	−0.0490680	+	0.114967i
$577$	−19376.7			−1.39803			−0.699015	−	0.715107i	$-0.746378\pi$
$577$	−19376.7			−1.39803			−0.699015	+	0.715107i	$0.746378\pi$
$578$			9803.73i			0.705504i
$579$	14678.2	−	9694.50i	1.05355	−	0.695837i
$580$		−	1968.05i		−	0.140894i
$581$		−	271.144i		−	0.0193614i
$582$	6705.88	−	4429.03i	0.477608	−	0.315446i
$583$	8638.07			0.613640
$584$			455.718i			0.0322907i
$585$	−6006.95	+	14074.3i	−0.424542	+	0.994704i
$586$		−	5011.25i		−	0.353264i
$587$		−	12303.2i		−	0.865091i	−0.901612	−	0.432545i	$-0.857616\pi$
$587$		−	12303.2i		−	0.865091i	0.901612	−	0.432545i	$-0.142384\pi$
$588$	−5936.42	+	3920.82i	−0.416350	+	0.274986i
$589$		−	2844.46i		−	0.198988i
$590$	−2873.95			−0.200540
$591$	6695.46	+	10137.4i	0.466014	+	0.705580i
$592$		−	887.208i		−	0.0615946i
$593$		−	13717.3i		−	0.949919i	−0.880008	−	0.474960i	$-0.842463\pi$
$593$		−	13717.3i		−	0.949919i	0.880008	−	0.474960i	$-0.157537\pi$
$594$	−15054.3	+	2744.14i	−1.03987	+	0.189551i
$595$		−	39.3748i		−	0.00271296i
$596$	−9317.47			−0.640367
$597$	−8633.67	−	13072.0i	−0.591880	−	0.896151i
$598$	4526.28	−	7703.61i	0.309521	−	0.526796i
$599$			13552.2i			0.924421i	0.886770	+	0.462210i	$0.152944\pi$
$599$			13552.2i			0.924421i	−0.886770	+	0.462210i	$0.847056\pi$
$600$	1622.54	+	2456.64i	0.110400	+	0.167153i
$601$	−5455.34			−0.370263			−0.185131	−	0.982714i	$-0.559271\pi$
$601$	−5455.34			−0.370263			−0.185131	+	0.982714i	$0.559271\pi$
$602$			771.085i			0.0522044i
$603$	26306.3	+	11227.6i	1.77657	+	0.758246i
$604$	−7409.21			−0.499134
$605$	22993.8			1.54518
$606$	−12308.6	+	8129.48i	−0.825090	+	0.544947i
$607$	16359.4			1.09392			0.546958	−	0.837160i	$-0.315786\pi$
$607$	16359.4			1.09392			0.546958	+	0.837160i	$0.315786\pi$
$608$	655.711			0.0437378
$609$	−128.537	+	84.8950i	−0.00855270	+	0.00564880i
$610$	18200.5			1.20806
$611$			10386.3i			0.687698i
$612$	141.476	−	331.479i	0.00934448	−	0.0218942i
$613$			3441.65i			0.226765i	0.993551	+	0.113382i	$0.0361685\pi$
$613$			3441.65i			0.226765i	−0.993551	+	0.113382i	$0.963831\pi$
$614$		−	13193.6i		−	0.867180i
$615$	3940.92	+	5966.85i	0.258396	+	0.391230i
$616$	−367.864			−0.0240611
$617$	−22139.9			−1.44460			−0.722302	−	0.691578i	$-0.756916\pi$
$617$	−22139.9			−1.44460			−0.722302	+	0.691578i	$0.756916\pi$
$618$	−17026.0	+	11245.2i	−1.10823	+	0.731954i
$619$			11536.4i			0.749088i	0.927209	+	0.374544i	$0.122201\pi$
$619$			11536.4i			0.749088i	−0.927209	+	0.374544i	$0.877799\pi$
$620$	7770.18			0.503319
$621$	−5319.70	+	14532.2i	−0.343755	+	0.939059i
$622$	−18951.4			−1.22167
$623$			884.245i			0.0568644i
$624$	−2809.70	+	1855.72i	−0.180253	+	0.119052i
$625$	−19462.0			−1.24557
$626$	1826.60			0.116623
$627$	3200.14	+	4845.25i	0.203830	+	0.308613i
$628$			4885.78i			0.310452i
$629$			185.044i			0.0117300i
$630$	250.110	−	586.009i	0.0158168	−	0.0370590i
$631$		−	20198.9i		−	1.27433i	−0.770726	−	0.637166i	$-0.780106\pi$
$631$		−	20198.9i		−	1.27433i	0.770726	−	0.637166i	$-0.219894\pi$
$632$	2131.84			0.134177
$633$	9536.92	−	6298.85i	0.598829	−	0.395508i
$634$	−7671.72			−0.480572
$635$	−18578.9			−1.16107
$636$	−2747.05	+	1814.34i	−0.171270	+	0.113118i
$637$	−13863.1			−0.862289
$638$	3834.90			0.237970
$639$	25786.0	+	11005.5i	1.59637	+	0.681333i
$640$			1791.20i			0.110630i
$641$	−18534.8			−1.14209			−0.571044	−	0.820919i	$-0.693462\pi$
$641$	−18534.8			−1.14209			−0.571044	+	0.820919i	$0.693462\pi$
$642$	10074.4	+	15253.4i	0.619321	+	0.937698i
$643$		−	11674.7i		−	0.716024i	−0.933717	−	0.358012i	$-0.883455\pi$
$643$		−	11674.7i		−	0.716024i	0.933717	−	0.358012i	$-0.116545\pi$
$644$	−188.459	+	320.753i	−0.0115316	+	0.0196265i
$645$	18323.7	+	27743.5i	1.11860	+	1.69364i
$646$	−136.761			−0.00832940
$647$			4418.42i			0.268479i	0.990949	+	0.134240i	$0.0428591\pi$
$647$			4418.42i			0.268479i	−0.990949	+	0.134240i	$0.957141\pi$
$648$	4211.12	−	4034.68i	0.255291	−	0.244595i
$649$		−	5600.13i		−	0.338713i
$650$			5736.93i			0.346186i
$651$	−335.179	−	507.487i	−0.0201793	−	0.0305529i
$652$	13939.2			0.837272
$653$		−	12129.5i		−	0.726895i	−0.931615	−	0.363447i	$-0.881600\pi$
$653$		−	12129.5i		−	0.726895i	0.931615	−	0.363447i	$-0.118400\pi$
$654$	−13301.9	+	8785.51i	−0.795330	+	0.525291i
$655$			24034.2i			1.43373i
$656$			1573.48i			0.0936494i
$657$	603.752	−	1414.59i	0.0358518	−	0.0840009i
$658$		−	432.450i		−	0.0256211i
$659$	6468.72			0.382376			0.191188	−	0.981553i	$-0.438766\pi$
$659$	6468.72			0.382376			0.191188	+	0.981553i	$0.438766\pi$
$660$	−13235.7	+	8741.76i	−0.780603	+	0.515565i
$661$			21005.0i			1.23601i	0.786176	+	0.618003i	$0.212058\pi$
$661$			21005.0i			1.23601i	−0.786176	+	0.618003i	$0.787942\pi$
$662$		−	20115.1i		−	1.18096i
$663$	586.017	−	387.046i	0.0343273	−	0.0226721i
$664$		−	2572.62i		−	0.150357i
$665$	−241.775			−0.0140987
$666$	−1175.41	+	2753.98i	−0.0683875	+	0.160232i
$667$	1964.65	−	3343.78i	0.114050	−	0.194110i
$668$		−	11035.6i		−	0.639192i
$669$	12999.1	−	8585.53i	0.751233	−	0.496167i
$670$	29648.1			1.70956
$671$			35465.3i			2.04042i
$672$	116.987	−	77.2662i	0.00671557	−	0.00443543i
$673$	−5882.66			−0.336939			−0.168469	−	0.985707i	$-0.553882\pi$
$673$	−5882.66			−0.336939			−0.168469	+	0.985707i	$0.553882\pi$
$674$	−10919.4			−0.624036
$675$	−1781.87	−	9775.26i	−0.101606	−	0.557407i
$676$	2226.58			0.126683
$677$	−1290.90			−0.0732843			−0.0366421	−	0.999328i	$-0.511666\pi$
$677$	−1290.90			−0.0732843			−0.0366421	+	0.999328i	$0.511666\pi$
$678$	−1046.57	−	1584.59i	−0.0592821	−	0.0897576i
$679$	−652.034			−0.0368524
$680$		−	373.588i		−	0.0210683i
$681$	−3280.38	+	2166.59i	−0.184588	+	0.121915i
$682$			15140.8i			0.850106i
$683$		−	3694.16i		−	0.206959i	−0.994632	−	0.103479i	$-0.967002\pi$
$683$		−	3694.16i		−	0.206959i	0.994632	−	0.103479i	$-0.0329976\pi$
$684$	−2035.39	−	868.710i	−0.113780	−	0.0485614i
$685$	7174.04			0.400155
$686$	1155.63			0.0643181
$687$	−5510.20	−	8342.85i	−0.306008	−	0.463318i
$688$			7316.05i			0.405410i
$689$	−6415.10			−0.354711
$690$	841.505	+	16019.1i	0.0464284	+	0.883822i
$691$	27141.2			1.49421			0.747105	−	0.664706i	$-0.231443\pi$
$691$	27141.2			1.49421			0.747105	+	0.664706i	$0.231443\pi$
$692$		−	1533.55i		−	0.0842441i
$693$	1141.89	+	487.359i	0.0625926	+	0.0267147i
$694$	−3372.36			−0.184457
$695$	−35395.7			−1.93185
$696$	−1219.56	+	805.483i	−0.0664186	+	0.0438675i
$697$		−	328.179i		−	0.0178345i
$698$			14388.8i			0.780262i
$699$	−14604.3	−	22112.0i	−0.790251	−	1.19650i
$700$		−	238.867i		−	0.0128976i
$701$	−16850.4			−0.907889			−0.453944	−	0.891030i	$-0.649984\pi$
$701$	−16850.4			−0.907889			−0.453944	+	0.891030i	$0.649984\pi$
$702$	11180.1	−	2037.95i	0.601092	−	0.109569i
$703$	1136.24			0.0609586
$704$	−3490.29			−0.186854
$705$	−10276.6	−	15559.5i	−0.548990	−	0.831211i
$706$	−4492.09			−0.239465
$707$	1196.81			0.0636641
$708$	1176.25	+	1780.93i	0.0624383	+	0.0945362i
$709$		−	7068.87i		−	0.374439i	−0.982318	−	0.187219i	$-0.940052\pi$
$709$		−	7068.87i		−	0.374439i	0.982318	−	0.187219i	$-0.0599475\pi$
$710$	29061.7			1.53615
$711$	−6617.45	−	2824.34i	−0.349049	−	0.148975i
$712$			8389.71i			0.441598i
$713$	13201.8	+	7756.76i	0.693424	+	0.407423i
$714$	−24.3998	+	16.1153i	−0.00127891	+	0.000844680i
$715$	−30908.9			−1.61668
$716$			10012.4i			0.522597i
$717$	−15355.7	−	23249.7i	−0.799819	−	1.21098i
$718$			4917.68i			0.255608i
$719$		−	10657.4i		−	0.552787i	−0.961044	−	0.276394i	$-0.910861\pi$
$719$		−	10657.4i		−	0.552787i	0.961044	−	0.276394i	$-0.0891394\pi$
$720$	2373.04	−	5560.05i	0.122831	−	0.287793i
$721$	1655.49			0.0855116
$722$		−	12878.2i		−	0.663821i
$723$	18728.2	+	28355.8i	0.963357	+	1.45859i
$724$		−	9437.03i		−	0.484426i
$725$			2490.14i			0.127560i
$726$	−9410.93	−	14248.8i	−0.481091	−	0.728408i
$727$		−	23547.6i		−	1.20128i	−0.799518	−	0.600642i	$-0.794912\pi$
$727$		−	23547.6i		−	1.20128i	0.799518	−	0.600642i	$-0.205088\pi$
$728$	273.196			0.0139084
$729$	−18417.0	+	6945.01i	−0.935683	+	0.352843i
$730$		−	1594.30i		−	0.0808323i
$731$		−	1525.90i		−	0.0772059i
$732$	−7449.13	−	11278.5i	−0.376131	−	0.569490i
$733$			12775.8i			0.643773i	0.946778	+	0.321887i	$0.104317\pi$
$733$			12775.8i			0.643773i	−0.946778	+	0.321887i	$0.895683\pi$
$734$	7725.99			0.388517
$735$	20768.1	−	13716.7i	1.04224	−	0.688366i
$736$	−1788.10	+	3043.30i	−0.0895521	+	0.152415i
$737$			57771.7i			2.88745i
$738$	2084.60	−	4884.23i	0.103977	−	0.243619i
$739$	−4647.87			−0.231359			−0.115680	−	0.993287i	$-0.536905\pi$
$739$	−4647.87			−0.231359			−0.115680	+	0.993287i	$0.536905\pi$
$740$			3103.83i			0.154188i
$741$	−2376.60	−	3598.35i	−0.117823	−	0.178392i
$742$	267.104			0.0132152
$743$	−27932.5			−1.37920			−0.689600	−	0.724190i	$-0.742214\pi$
$743$	−27932.5			−1.37920			−0.689600	+	0.724190i	$0.742214\pi$
$744$	−3180.18	−	4815.03i	−0.156709	−	0.237268i
$745$	32596.5			1.60301
$746$	16198.6			0.795006
$747$	−3408.30	+	7985.66i	−0.166939	+	0.391138i
$748$	727.967			0.0355844
$749$		−	1483.13i		−	0.0723530i
$750$	4342.04	+	6574.17i	0.211399	+	0.320073i
$751$			29983.5i			1.45688i	0.685111	+	0.728439i	$0.259754\pi$
$751$			29983.5i			1.45688i	−0.685111	+	0.728439i	$0.740246\pi$
$752$		−	4103.09i		−	0.198968i
$753$	10469.3	−	6914.66i	0.506671	−	0.334641i
$754$	−2848.01			−0.137557
$755$	25920.6			1.24947
$756$	−465.504	+	84.8536i	−0.0223944	+	0.00408214i
$757$		−	40712.1i		−	1.95470i	−0.211632	−	0.977350i	$-0.567878\pi$
$757$		−	40712.1i		−	1.95470i	0.211632	−	0.977350i	$-0.432122\pi$
$758$	−7182.21			−0.344155
$759$	−31214.5	+	1639.74i	−1.49277	+	0.0784175i
$760$	−2293.96			−0.109488
$761$			15847.5i			0.754890i	0.926032	+	0.377445i	$0.123197\pi$
$761$			15847.5i			0.754890i	−0.926032	+	0.377445i	$0.876803\pi$
$762$	7604.00	+	11513.0i	0.361501	+	0.547339i
$763$	1293.39			0.0613679
$764$	16218.9			0.768035
$765$	−494.943	+	1159.65i	−0.0233918	+	0.0548070i
$766$			1081.48i			0.0510122i
$767$			4158.97i			0.195791i
$768$	1109.97	−	733.102i	0.0521518	−	0.0344447i
$769$		−	19495.4i		−	0.914204i	−0.889414	−	0.457102i	$-0.848887\pi$
$769$		−	19495.4i		−	0.914204i	0.889414	−	0.457102i	$-0.151113\pi$
$770$	1286.95			0.0602315
$771$	−15577.4	−	23585.4i	−0.727637	−	1.10170i
$772$	−13541.3			−0.631299
$773$	5309.35			0.247043			0.123521	−	0.992342i	$-0.460581\pi$
$773$	5309.35			0.247043			0.123521	+	0.992342i	$0.460581\pi$
$774$	9692.57	−	22709.7i	0.450119	−	1.05463i
$775$	−9831.47			−0.455686
$776$	−6186.49			−0.286188
$777$	202.718	−	133.889i	0.00935967	−	0.00618178i
$778$		−	205.596i		−	0.00947425i
$779$	−2015.13			−0.0926824
$780$	9829.54	−	6492.11i	0.451223	−	0.298019i
$781$			56629.1i			2.59456i
$782$	372.943	−	634.739i	0.0170542	−	0.0290259i
$783$	4852.77	−	884.580i	0.221487	−	0.0403733i
$784$	5476.63			0.249482
$785$		−	17092.5i		−	0.777145i
$786$	14893.6	−	9836.74i	0.675872	−	0.446393i
$787$			1148.70i			0.0520290i	0.999662	+	0.0260145i	$0.00828161\pi$
$787$			1148.70i			0.0520290i	−0.999662	+	0.0260145i	$0.991718\pi$
$788$		−	9352.25i		−	0.422792i
$789$	−10559.8	+	6974.41i	−0.476474	+	0.314696i
$790$	−7458.10			−0.335882
$791$			154.074i			0.00692572i
$792$	10834.2	+	4624.07i	0.486082	+	0.207461i
$793$		−	26338.5i		−	1.17945i
$794$			22404.3i			1.00138i
$795$	9610.35	−	6347.34i	0.428735	−	0.283166i
$796$			12059.6i			0.536984i
$797$	6667.44			0.296327			0.148164	−	0.988963i	$-0.452664\pi$
$797$	6667.44			0.296327			0.148164	+	0.988963i	$0.452664\pi$
$798$	98.9538	+	149.823i	0.00438963	+	0.00664623i
$799$			855.777i			0.0378914i
$800$		−	2266.37i		−	0.100160i
$801$	11115.0	−	26042.5i	0.490299	−	1.14877i
$802$		−	489.390i		−	0.0215473i
$803$	3106.62			0.136526
$804$	−12134.4	−	18372.4i	−0.532272	−	0.805900i
$805$	659.312	−	1122.13i	0.0288667	−	0.0491304i
$806$		−	11244.4i		−	0.491399i
$807$	−11143.7	−	16872.5i	−0.486095	−	0.735984i
$808$	11355.3			0.494404
$809$		−	21561.8i		−	0.937049i	−0.883450	−	0.468525i	$-0.844786\pi$
$809$		−	21561.8i		−	0.937049i	0.883450	−	0.468525i	$-0.155214\pi$
$810$	−14732.3	+	14115.1i	−0.639063	+	0.612287i
$811$	2608.29			0.112934			0.0564669	−	0.998404i	$-0.482016\pi$
$811$	2608.29			0.112934			0.0564669	+	0.998404i	$0.482016\pi$
$812$	118.582			0.00512488
$813$	−10164.2	+	6713.16i	−0.438469	+	0.289595i
$814$	−6048.08			−0.260424
$815$	−48765.3			−2.09592
$816$	−231.505	+	152.902i	−0.00993176	+	0.00655962i
$817$	−9369.56			−0.401223
$818$		−	25871.6i		−	1.10584i
$819$	−848.027	−	361.940i	−0.0361813	−	0.0154423i
$820$		−	5504.70i		−	0.234430i
$821$		−	20601.2i		−	0.875746i	−0.899037	−	0.437873i	$-0.855732\pi$
$821$		−	20601.2i		−	0.875746i	0.899037	−	0.437873i	$-0.144268\pi$
$822$	−2936.20	−	4445.62i	−0.124588	−	0.188636i
$823$	28511.1			1.20757			0.603787	−	0.797146i	$-0.293658\pi$
$823$	28511.1			1.20757			0.603787	+	0.797146i	$0.293658\pi$
$824$	15707.3			0.664067
$825$	16746.9	−	11060.8i	0.706729	−	0.466773i
$826$		−	173.166i		−	0.00729444i
$827$	−43427.5			−1.82602			−0.913012	−	0.407933i	$-0.866250\pi$
$827$	−43427.5			−1.82602			−0.913012	+	0.407933i	$0.866250\pi$
$828$	9582.33	−	7077.77i	0.402185	−	0.297065i
$829$	16019.3			0.671136			0.335568	−	0.942016i	$-0.391072\pi$
$829$	16019.3			0.671136			0.335568	+	0.942016i	$0.391072\pi$
$830$			9000.12i			0.376384i
$831$	−6003.93	+	3965.41i	−0.250630	+	0.165534i
$832$	2592.08			0.108010
$833$	−1142.25			−0.0475111
$834$	14486.8	+	21934.1i	0.601482	+	0.910689i
$835$			38607.3i			1.60007i
$836$		−	4469.97i		−	0.184925i
$837$	3492.47	+	19159.6i	0.144226	+	0.791220i
$838$			14432.6i			0.594947i
$839$	33998.4			1.39899			0.699496	−	0.714637i	$-0.253408\pi$
$839$	33998.4			1.39899			0.699496	+	0.714637i	$0.253408\pi$
$840$	−409.270	+	270.310i	−0.0168109	+	0.0111031i
$841$	23152.8			0.949314
$842$	13218.6			0.541023
$843$	38319.3	−	25308.7i	1.56558	−	1.03402i
$844$	−8798.26			−0.358825
$845$	−7789.54			−0.317122
$846$	−5435.92	+	12736.4i	−0.220911	+	0.517596i
$847$			1385.46i			0.0562042i
$848$	2534.28			0.102627
$849$	4588.50	+	6947.33i	0.185485	+	0.280838i
$850$			472.695i			0.0190745i
$851$	−3098.47	+	5273.52i	−0.124811	+	0.212425i
$852$	−11894.4	−	18009.0i	−0.478281	−	0.724153i
$853$	−35523.5			−1.42591			−0.712955	−	0.701209i	$-0.752644\pi$
$853$	−35523.5			−1.42591			−0.712955	+	0.701209i	$0.752644\pi$
$854$			1096.65i			0.0439420i
$855$	7120.68	+	3039.12i	0.284821	+	0.121562i
$856$		−	14071.9i		−	0.561880i
$857$		−	29813.3i		−	1.18833i	−0.804342	−	0.594167i	$-0.797482\pi$
$857$		−	29813.3i		−	1.18833i	0.804342	−	0.594167i	$-0.202518\pi$
$858$	12650.4	+	19153.7i	0.503354	+	0.762116i
$859$	−26460.5			−1.05101			−0.525506	−	0.850790i	$-0.676124\pi$
$859$	−26460.5			−1.05101			−0.525506	+	0.850790i	$0.676124\pi$
$860$		−	25594.7i		−	1.01485i
$861$	−359.524	+	237.454i	−0.0142306	+	0.00939887i
$862$			30737.6i			1.21453i
$863$			14045.2i			0.554001i	0.960870	+	0.277001i	$0.0893404\pi$
$863$			14045.2i			0.554001i	−0.960870	+	0.277001i	$0.910660\pi$
$864$	−4416.70	+	805.091i	−0.173911	+	0.0317011i
$865$			5365.02i			0.210886i
$866$	−17985.0			−0.705723
$867$	−21253.6	+	14037.4i	−0.832538	+	0.549866i
$868$			468.180i			0.0183077i
$869$		−	14532.7i		−	0.567305i
$870$	4266.55	−	2817.93i	0.166264	−	0.109812i
$871$		−	42904.5i		−	1.66907i
$872$	12271.6			0.476571
$873$	19203.5	+	8196.10i	0.744490	+	0.317750i
$874$	−3897.52	−	2290.00i	−0.150842	−	0.0886274i
$875$		−	639.227i		−	0.0246969i
$876$	−987.956	+	652.515i	−0.0381050	+	0.0251672i
$877$	26850.2			1.03383			0.516914	−	0.856037i	$-0.327081\pi$
$877$	26850.2			1.03383			0.516914	+	0.856037i	$0.327081\pi$
$878$			6215.44i			0.238908i
$879$	10863.9	−	7175.30i	0.416873	−	0.275332i
$880$	12210.5			0.467747
$881$	21869.7			0.836331			0.418165	−	0.908371i	$-0.362673\pi$
$881$	21869.7			0.836331			0.418165	+	0.908371i	$0.362673\pi$
$882$	−17000.0	−	7255.63i	−0.649002	−	0.276995i
$883$	15541.6			0.592319			0.296159	−	0.955139i	$-0.404294\pi$
$883$	15541.6			0.592319			0.296159	+	0.955139i	$0.404294\pi$
$884$	−540.628			−0.0205693
$885$	−4115.04	−	6230.47i	−0.156300	−	0.236650i
$886$	13062.4			0.495305
$887$			40054.3i			1.51623i	0.652123	+	0.758113i	$0.273879\pi$
$887$			40054.3i			1.51623i	−0.652123	+	0.758113i	$0.726121\pi$
$888$	1923.39	−	1270.34i	0.0726854	−	0.0480065i
$889$		−	1119.45i		−	0.0422329i
$890$		−	29350.8i		−	1.10544i
$891$	−27504.3	−	28707.1i	−1.03415	−	1.07938i
$892$	−11992.3			−0.450148
$893$	5254.77			0.196914
$894$	−13341.1	−	20199.5i	−0.499098	−	0.755672i
$895$		−	35027.6i		−	1.30820i
$896$	−107.926			−0.00402405
$897$	23181.6	−	1217.76i	0.862890	−	0.0453288i
$898$	−14318.2			−0.532076
$899$		−	4880.68i		−	0.181068i
$900$	−3002.57	+	7035.04i	−0.111206	+	0.260557i
$901$	−528.573			−0.0195442
$902$	10726.4			0.395952
$903$	−1671.64	+	1104.07i	−0.0616044	+	0.0406878i
$904$			1461.85i			0.0537838i
$905$			33014.8i			1.21265i
$906$	−10608.8	−	16062.5i	−0.389022	−	0.589008i
$907$		−	5981.20i		−	0.218966i	−0.993989	−	0.109483i	$-0.965080\pi$
$907$		−	5981.20i		−	0.218966i	0.993989	−	0.109483i	$-0.0349196\pi$
$908$	3026.31			0.110607
$909$	−35248.0	−	15043.9i	−1.28614	−	0.548928i
$910$	−955.756			−0.0348165
$911$	8787.70			0.319593			0.159797	−	0.987150i	$-0.448916\pi$
$911$	8787.70			0.319593			0.159797	+	0.987150i	$0.448916\pi$
$912$	938.873	+	1421.52i	0.0340890	+	0.0516133i
$913$	−17537.5			−0.635713
$914$	−13403.9			−0.485080
$915$	26060.3	+	39457.2i	0.941558	+	1.42559i
$916$			7696.67i			0.277626i
$917$	−1448.15			−0.0521505
$918$	921.187	−	167.917i	0.0331195	−	0.00603713i
$919$			40445.8i			1.45178i	0.687812	+	0.725888i	$0.258571\pi$
$919$			40445.8i			1.45178i	−0.687812	+	0.725888i	$0.741429\pi$
$920$	6255.55	−	10646.8i	0.224173	−	0.381537i
$921$	28602.4	−	18891.0i	1.02333	−	0.675875i
$922$	−10115.0			−0.361300
$923$		−	42055.9i		−	1.49977i
$924$	−526.722	−	797.496i	−0.0187531	−	0.0283936i
$925$		−	3927.23i		−	0.139596i
$926$			21552.4i			0.764857i
$927$	−48757.1	−	20809.6i	−1.72750	−	0.737302i
$928$	1125.10			0.0397988
$929$			23872.8i			0.843102i	0.906805	+	0.421551i	$0.138514\pi$
$929$			23872.8i			0.843102i	−0.906805	+	0.421551i	$0.861486\pi$
$930$	11125.6	+	16845.0i	0.392284	+	0.593947i
$931$			7013.84i			0.246906i
$932$			20399.4i			0.716957i
$933$	−27135.3	−	41084.9i	−0.952165	−	1.44165i
$934$		−	23991.1i		−	0.840485i
$935$	−2546.74			−0.0890773
$936$	−8046.08	−	3434.09i	−0.280977	−	0.119922i
$937$			24437.0i			0.851998i	0.904724	+	0.425999i	$0.140077\pi$
$937$			24437.0i			0.851998i	−0.904724	+	0.425999i	$0.859923\pi$
$938$			1786.40i			0.0621834i
$939$	2615.40	+	3959.91i	0.0908951	+	0.137622i
$940$			14354.4i			0.498072i
$941$	32243.7			1.11702			0.558509	−	0.829498i	$-0.311373\pi$
$941$	32243.7			1.11702			0.558509	+	0.829498i	$0.311373\pi$
$942$	−10591.9	+	6995.65i	−0.366352	+	0.241964i
$943$	5495.20	−	9352.68i	0.189765	−	0.322975i
$944$		−	1643.00i		−	0.0566472i
$945$	1628.53	−	296.854i	0.0560594	−	0.0102187i
$946$	49873.3			1.71408
$947$			20203.6i			0.693273i	0.938000	+	0.346636i	$0.112676\pi$
$947$			20203.6i			0.693273i	−0.938000	+	0.346636i	$0.887324\pi$
$948$	3052.45	+	4621.64i	0.104577	+	0.158338i
$949$	−2307.15			−0.0789180
$950$	2902.51			0.0991261
$951$	−10984.7	−	16631.6i	−0.374555	−	0.567104i
$952$	22.5100			0.000766337
$953$	−27705.0			−0.941713			−0.470856	−	0.882210i	$-0.656055\pi$
$953$	−27705.0			−0.941713			−0.470856	+	0.882210i	$0.656055\pi$
$954$	−7866.66	−	3357.51i	−0.266973	−	0.113945i
$955$	−56740.6			−1.92260
$956$			21449.0i			0.725637i
$957$	5490.96	+	8313.72i	0.185473	+	0.280820i
$958$		−	18344.6i		−	0.618670i
$959$			432.261i			0.0145552i
$960$	−3883.15	+	2564.70i	−0.130550	+	0.0862244i
$961$	−10521.3			−0.353169
$962$	4491.63			0.150536
$963$	−18643.0	+	43680.7i	−0.623845	+	1.46167i
$964$		−	26159.6i		−	0.874007i
$965$	47373.4			1.58031
$966$	−965.207	+	50.7037i	−0.0321481	+	0.00168878i
$967$	−10332.1			−0.343595			−0.171798	−	0.985132i	$-0.554957\pi$
$967$	−10332.1			−0.343595			−0.171798	+	0.985132i	$0.554957\pi$
$968$			13145.2i			0.436471i
$969$	−195.820	−	296.486i	−0.00649189	−	0.00982920i
$970$	21643.0			0.716407
$971$	−17334.7			−0.572911			−0.286455	−	0.958094i	$-0.592477\pi$
$971$	−17334.7			−0.572911			−0.286455	+	0.958094i	$0.592477\pi$
$972$	14776.5	+	3352.32i	0.487609	+	0.110623i
$973$		−	2132.72i		−	0.0702690i
$974$			12472.3i			0.410305i
$975$	−12437.2	+	8214.36i	−0.408521	+	0.269816i
$976$			10405.0i			0.341245i
$977$	−56623.6			−1.85419			−0.927097	−	0.374820i	$-0.877704\pi$
$977$	−56623.6			−1.85419			−0.927097	+	0.374820i	$0.877704\pi$
$978$	19958.7	+	30219.0i	0.652565	+	0.988032i
$979$	57192.5			1.86709
$980$	−19159.6			−0.624521
$981$	−38092.4	−	16257.9i	−1.23975	−	0.529129i
$982$	22849.2			0.742512
$983$	18752.9			0.608467			0.304234	−	0.952597i	$-0.401600\pi$
$983$	18752.9			0.608467			0.304234	+	0.952597i	$0.401600\pi$
$984$	−3411.16	+	2252.97i	−0.110512	+	0.0729898i
$985$			32718.2i			1.05836i
$986$	−234.662			−0.00757926
$987$	937.513	−	619.199i	0.0302344	−	0.0199689i
$988$			3319.64i			0.106895i
$989$	25550.5	−	43486.3i	0.821494	−	1.39816i
$990$	−37902.7	−	16177.0i	−1.21680	−	0.519331i
$991$	−25268.7			−0.809977			−0.404988	−	0.914322i	$-0.632724\pi$
$991$	−25268.7			−0.809977			−0.404988	+	0.914322i	$0.632724\pi$
$992$			4442.09i			0.142174i
$993$	43607.7	−	28801.6i	1.39360	−	0.920433i
$994$			1751.07i			0.0558758i
$995$		−	42189.5i		−	1.34422i
$996$	5577.21	−	3683.58i	0.177430	−	0.117187i
$997$	42054.7			1.33589			0.667946	−	0.744209i	$-0.267174\pi$
$997$	42054.7			1.33589			0.667946	+	0.744209i	$0.267174\pi$
$998$		−	4483.73i		−	0.142214i
$999$	−7653.38	+	1395.08i	−0.242385	+	0.0441827i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	138.4.d.a.137.10	yes	24
3.2	odd	2	inner	138.4.d.a.137.21	yes	24
23.22	odd	2	inner	138.4.d.a.137.9	✓	24
69.68	even	2	inner	138.4.d.a.137.22	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.4.d.a.137.9	✓	24	23.22	odd	2	inner
138.4.d.a.137.10	yes	24	1.1	even	1	trivial
138.4.d.a.137.21	yes	24	3.2	odd	2	inner
138.4.d.a.137.22	yes	24	69.68	even	2	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 138 = 2 \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	138.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.00000i q^{2} +(4.33582 - 2.86368i) q^{3} -4.00000 q^{4} +13.9937 q^{5} +(-5.72736 - 8.67164i) q^{6} +0.843170i q^{7} +8.00000i q^{8} +(10.5987 - 24.8328i) q^{9} +O(q^{10})\)	\(q-2.00000i q^{2} +(4.33582 - 2.86368i) q^{3} -4.00000 q^{4} +13.9937 q^{5} +(-5.72736 - 8.67164i) q^{6} +0.843170i q^{7} +8.00000i q^{8} +(10.5987 - 24.8328i) q^{9} -27.9874i q^{10} +54.5358 q^{11} +(-17.3433 + 11.4547i) q^{12} -40.5013 q^{13} +1.68634 q^{14} +(60.6742 - 40.0735i) q^{15} +16.0000 q^{16} -3.33711 q^{17} +(-49.6656 - 21.1974i) q^{18} +20.4910i q^{19} -55.9749 q^{20} +(2.41457 + 3.65584i) q^{21} -109.072i q^{22} +(-95.1032 - 55.8782i) q^{23} +(22.9094 + 34.6866i) q^{24} +70.8240 q^{25} +81.0026i q^{26} +(-25.1591 - 138.022i) q^{27} -3.37268i q^{28} +35.1595i q^{29} +(-80.1470 - 121.348i) q^{30} -138.815 q^{31} -32.0000i q^{32} +(236.458 - 156.173i) q^{33} +6.67421i q^{34} +11.7991i q^{35} +(-42.3948 + 99.3312i) q^{36} -55.4505i q^{37} +40.9820 q^{38} +(-175.606 + 115.983i) q^{39} +111.950i q^{40} +98.3424i q^{41} +(7.31167 - 4.82914i) q^{42} +457.253i q^{43} -218.143 q^{44} +(148.315 - 347.503i) q^{45} +(-111.756 + 190.206i) q^{46} -256.443i q^{47} +(69.3731 - 45.8189i) q^{48} +342.289 q^{49} -141.648i q^{50} +(-14.4691 + 9.55640i) q^{51} +162.005 q^{52} +158.393 q^{53} +(-276.044 + 50.3182i) q^{54} +763.158 q^{55} -6.74536 q^{56} +(58.6796 + 88.8452i) q^{57} +70.3189 q^{58} -102.687i q^{59} +(-242.697 + 160.294i) q^{60} +650.311i q^{61} +277.631i q^{62} +(20.9383 + 8.93650i) q^{63} -64.0000 q^{64} -566.764 q^{65} +(-312.346 - 472.915i) q^{66} +1059.34i q^{67} +13.3484 q^{68} +(-572.368 + 30.0673i) q^{69} +23.5982 q^{70} +1038.38i q^{71} +(198.662 + 84.7895i) q^{72} +56.9648 q^{73} -110.901 q^{74} +(307.080 - 202.817i) q^{75} -81.9639i q^{76} +45.9830i q^{77} +(231.965 + 351.213i) q^{78} -266.480i q^{79} +223.899 q^{80} +(-504.335 - 526.390i) q^{81} +196.685 q^{82} -321.577 q^{83} +(-9.65827 - 14.6233i) q^{84} -46.6985 q^{85} +914.506 q^{86} +(100.685 + 152.445i) q^{87} +436.286i q^{88} +1048.71 q^{89} +(-695.006 - 296.630i) q^{90} -34.1495i q^{91} +(380.413 + 223.513i) q^{92} +(-601.879 + 397.523i) q^{93} -512.886 q^{94} +286.745i q^{95} +(-91.6377 - 138.746i) q^{96} +773.312i q^{97} -684.578i q^{98} +(578.008 - 1354.28i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{3} - 96 q^{4} + 8 q^{6} + 36 q^{9}+O(q^{10}) \) 24 * q + 8 * q^3 - 96 * q^4 + 8 * q^6 + 36 * q^9	\( 24 q + 8 q^{3} - 96 q^{4} + 8 q^{6} + 36 q^{9} - 32 q^{12} + 96 q^{13} + 384 q^{16} + 128 q^{18} - 32 q^{24} + 144 q^{25} + 188 q^{27} + 72 q^{31} - 144 q^{36} - 660 q^{39} - 96 q^{46} + 128 q^{48} - 504 q^{49} - 384 q^{52} + 88 q^{54} - 672 q^{55} + 816 q^{58} - 1536 q^{64} + 352 q^{69} + 624 q^{70} - 512 q^{72} - 2688 q^{73} - 1072 q^{75} + 80 q^{78} - 2356 q^{81} + 1344 q^{82} + 4872 q^{85} + 3748 q^{87} - 2924 q^{93} - 1296 q^{94} + 128 q^{96}+O(q^{100}) \) 24 * q + 8 * q^3 - 96 * q^4 + 8 * q^6 + 36 * q^9 - 32 * q^12 + 96 * q^13 + 384 * q^16 + 128 * q^18 - 32 * q^24 + 144 * q^25 + 188 * q^27 + 72 * q^31 - 144 * q^36 - 660 * q^39 - 96 * q^46 + 128 * q^48 - 504 * q^49 - 384 * q^52 + 88 * q^54 - 672 * q^55 + 816 * q^58 - 1536 * q^64 + 352 * q^69 + 624 * q^70 - 512 * q^72 - 2688 * q^73 - 1072 * q^75 + 80 * q^78 - 2356 * q^81 + 1344 * q^82 + 4872 * q^85 + 3748 * q^87 - 2924 * q^93 - 1296 * q^94 + 128 * q^96

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