LMFDB - Embedded newform 110.4.f.a.87.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [110,4,Mod(43,110)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("110.43"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(110, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([3, 2])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 110 = 2 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	110.f (of order $4$, degree $2$, 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:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			87.1
Character	$\chi$	$=$	110.87
Dual form			110.4.f.a.43.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.41421 + 1.41421i) q^{2} +(-6.61133 + 6.61133i) q^{3} -4.00000i q^{4} +(-10.1738 + 4.63605i) q^{5} -18.6997i q^{6} +(-17.6781 + 17.6781i) q^{7} +(5.65685 + 5.65685i) q^{8} -60.4193i q^{9} +(7.83162 - 20.9443i) q^{10} +(12.9224 + 34.1176i) q^{11} +(26.4453 + 26.4453i) q^{12} +(1.73946 + 1.73946i) q^{13} -50.0012i q^{14} +(36.6121 - 97.9130i) q^{15} -16.0000 q^{16} +(-32.3286 + 32.3286i) q^{17} +(85.4457 + 85.4457i) q^{18} +137.358 q^{19} +(18.5442 + 40.6954i) q^{20} -233.751i q^{21} +(-66.5246 - 29.9746i) q^{22} +(32.6221 - 32.6221i) q^{23} -74.7986 q^{24} +(82.0141 - 94.3329i) q^{25} -4.91994 q^{26} +(220.946 + 220.946i) q^{27} +(70.7124 + 70.7124i) q^{28} -91.6133 q^{29} +(86.6925 + 190.247i) q^{30} -319.604 q^{31} +(22.6274 - 22.6274i) q^{32} +(-310.997 - 140.129i) q^{33} -91.4390i q^{34} +(97.8976 - 261.811i) q^{35} -241.677 q^{36} +(-166.423 - 166.423i) q^{37} +(-194.254 + 194.254i) q^{38} -23.0003 q^{39} +(-83.7774 - 31.3265i) q^{40} +464.662i q^{41} +(330.574 + 330.574i) q^{42} +(-60.7244 - 60.7244i) q^{43} +(136.471 - 51.6895i) q^{44} +(280.107 + 614.696i) q^{45} +92.2694i q^{46} +(126.964 + 126.964i) q^{47} +(105.781 - 105.781i) q^{48} -282.031i q^{49} +(17.4214 + 249.392i) q^{50} -427.469i q^{51} +(6.95784 - 6.95784i) q^{52} +(263.158 - 263.158i) q^{53} -624.929 q^{54} +(-289.641 - 287.199i) q^{55} -200.005 q^{56} +(-908.119 + 908.119i) q^{57} +(129.561 - 129.561i) q^{58} +24.4393i q^{59} +(-391.652 - 146.449i) q^{60} -402.074i q^{61} +(451.988 - 451.988i) q^{62} +(1068.10 + 1068.10i) q^{63} +64.0000i q^{64} +(-25.7612 - 9.63277i) q^{65} +(637.988 - 241.644i) q^{66} +(-132.763 - 132.763i) q^{67} +(129.314 + 129.314i) q^{68} +431.351i q^{69} +(231.808 + 508.705i) q^{70} -188.757 q^{71} +(341.783 - 341.783i) q^{72} +(-601.348 - 601.348i) q^{73} +470.716 q^{74} +(81.4436 + 1165.89i) q^{75} -549.432i q^{76} +(-831.578 - 374.692i) q^{77} +(32.5273 - 32.5273i) q^{78} +852.029 q^{79} +(162.781 - 74.1768i) q^{80} -1290.17 q^{81} +(-657.132 - 657.132i) q^{82} +(418.886 + 418.886i) q^{83} -935.006 q^{84} +(179.029 - 478.782i) q^{85} +171.755 q^{86} +(605.686 - 605.686i) q^{87} +(-119.899 + 266.098i) q^{88} +111.352i q^{89} +(-1265.44 - 473.181i) q^{90} -61.5007 q^{91} +(-130.489 - 130.489i) q^{92} +(2113.00 - 2113.00i) q^{93} -359.110 q^{94} +(-1397.46 + 636.799i) q^{95} +299.194i q^{96} +(-94.0732 - 94.0732i) q^{97} +(398.852 + 398.852i) q^{98} +(2061.36 - 780.760i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 8 q^{3} - 32 q^{5} + 44 q^{11} + 32 q^{12} - 164 q^{15} - 576 q^{16} + 64 q^{20} - 312 q^{22} - 176 q^{23} + 880 q^{25} - 304 q^{26} + 364 q^{27} + 432 q^{31} + 832 q^{33} - 1808 q^{36} + 960 q^{37}+ \cdots - 4224 q^{97}+O(q^{100}) $ 36 * q - 8 * q^3 - 32 * q^5 + 44 * q^11 + 32 * q^12 - 164 * q^15 - 576 * q^16 + 64 * q^20 - 312 * q^22 - 176 * q^23 + 880 * q^25 - 304 * q^26 + 364 * q^27 + 432 * q^31 + 832 * q^33 - 1808 * q^36 + 960 * q^37 + 48 * q^38 - 400 * q^42 - 496 * q^45 + 2100 * q^47 + 128 * q^48 - 60 * q^53 - 1276 * q^55 + 64 * q^56 - 1344 * q^58 + 160 * q^60 + 1568 * q^66 + 1000 * q^67 + 3456 * q^70 - 1312 * q^71 + 3196 * q^75 - 4088 * q^77 + 5312 * q^78 + 512 * q^80 - 10436 * q^81 - 1280 * q^82 - 1472 * q^86 - 1248 * q^88 - 2096 * q^91 + 704 * q^92 + 11372 * q^93 - 4224 * q^97

Character values

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

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

Coefficient data

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

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

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

$2$	−1.41421	+	1.41421i	−0.500000	+	0.500000i
$2$	−1.41421	+	1.41421i	−0.500000	+	0.500000i
$3$	−6.61133	+	6.61133i	−1.27235	+	1.27235i	−0.327499	+	0.944852i	$0.606206\pi$
$3$	−6.61133	+	6.61133i	−1.27235	+	1.27235i	−0.944852	+	0.327499i	$0.893794\pi$
$4$		−	4.00000i		−	0.500000i
$5$	−10.1738	+	4.63605i	−0.909976	+	0.414661i
$5$	−10.1738	+	4.63605i	−0.909976	+	0.414661i
$6$		−	18.6997i		−	1.27235i
$7$	−17.6781	+	17.6781i	−0.954528	+	0.954528i	−0.999010	−	0.0444823i	$-0.985836\pi$
$7$	−17.6781	+	17.6781i	−0.954528	+	0.954528i	0.0444823	+	0.999010i	$0.485836\pi$
$8$	5.65685	+	5.65685i	0.250000	+	0.250000i
$9$		−	60.4193i		−	2.23775i
$10$	7.83162	−	20.9443i	0.247658	−	0.662318i
$11$	12.9224	+	34.1176i	0.354204	+	0.935168i
$11$	12.9224	+	34.1176i	0.354204	+	0.935168i
$12$	26.4453	+	26.4453i	0.636175	+	0.636175i
$13$	1.73946	+	1.73946i	0.0371107	+	0.0371107i	0.725419	−	0.688308i	$-0.241646\pi$
$13$	1.73946	+	1.73946i	0.0371107	+	0.0371107i	−0.688308	+	0.725419i	$0.741646\pi$
$14$		−	50.0012i		−	0.954528i
$15$	36.6121	−	97.9130i	0.630214	−	1.68540i
$16$	−16.0000			−0.250000
$17$	−32.3286	+	32.3286i	−0.461225	+	0.461225i	−0.899057	−	0.437832i	$-0.855747\pi$
$17$	−32.3286	+	32.3286i	−0.461225	+	0.461225i	0.437832	+	0.899057i	$0.355747\pi$
$18$	85.4457	+	85.4457i	1.11888	+	1.11888i
$19$	137.358			1.65853			0.829265	−	0.558855i	$-0.188759\pi$
$19$	137.358			1.65853			0.829265	+	0.558855i	$0.188759\pi$
$20$	18.5442	+	40.6954i	0.207330	+	0.454988i
$21$		−	233.751i		−	2.42899i
$22$	−66.5246	−	29.9746i	−0.644686	−	0.290482i
$23$	32.6221	−	32.6221i	0.295747	−	0.295747i	−0.543598	−	0.839346i	$-0.682938\pi$
$23$	32.6221	−	32.6221i	0.295747	−	0.295747i	0.839346	+	0.543598i	$0.182938\pi$
$24$	−74.7986			−0.636175
$25$	82.0141	−	94.3329i	0.656113	−	0.754663i
$26$	−4.91994			−0.0371107
$27$	220.946	+	220.946i	1.57485	+	1.57485i
$28$	70.7124	+	70.7124i	0.477264	+	0.477264i
$29$	−91.6133			−0.586627			−0.293313	−	0.956016i	$-0.594758\pi$
$29$	−91.6133			−0.586627			−0.293313	+	0.956016i	$0.594758\pi$
$30$	86.6925	+	190.247i	0.527594	+	1.15781i
$31$	−319.604			−1.85169			−0.925847	−	0.377899i	$-0.876647\pi$
$31$	−319.604			−1.85169			−0.925847	+	0.377899i	$0.876647\pi$
$32$	22.6274	−	22.6274i	0.125000	−	0.125000i
$33$	−310.997	−	140.129i	−1.64053	−	0.739191i
$34$		−	91.4390i		−	0.461225i
$35$	97.8976	−	261.811i	0.472792	−	1.26440i
$36$	−241.677			−1.11888
$37$	−166.423	−	166.423i	−0.739455	−	0.739455i	0.233018	−	0.972473i	$-0.425140\pi$
$37$	−166.423	−	166.423i	−0.739455	−	0.739455i	−0.972473	+	0.233018i	$0.925140\pi$
$38$	−194.254	+	194.254i	−0.829265	+	0.829265i
$39$	−23.0003			−0.0944357
$40$	−83.7774	−	31.3265i	−0.331159	−	0.123829i
$41$			464.662i			1.76995i	0.465636	+	0.884976i	$0.345826\pi$
$41$			464.662i			1.76995i	−0.465636	+	0.884976i	$0.654174\pi$
$42$	330.574	+	330.574i	1.21449	+	1.21449i
$43$	−60.7244	−	60.7244i	−0.215358	−	0.215358i	0.591181	−	0.806539i	$-0.298662\pi$
$43$	−60.7244	−	60.7244i	−0.215358	−	0.215358i	−0.806539	+	0.591181i	$0.798662\pi$
$44$	136.471	−	51.6895i	0.467584	−	0.177102i
$45$	280.107	+	614.696i	0.927908	+	2.03630i
$46$			92.2694i			0.295747i
$47$	126.964	+	126.964i	0.394036	+	0.394036i	0.876123	−	0.482088i	$-0.160121\pi$
$47$	126.964	+	126.964i	0.394036	+	0.394036i	−0.482088	+	0.876123i	$0.660121\pi$
$48$	105.781	−	105.781i	0.318088	−	0.318088i
$49$		−	282.031i		−	0.822247i
$50$	17.4214	+	249.392i	0.0492752	+	0.705388i
$51$		−	427.469i		−	1.17368i
$52$	6.95784	−	6.95784i	0.0185554	−	0.0185554i
$53$	263.158	−	263.158i	0.682028	−	0.682028i	−0.278429	−	0.960457i	$-0.589814\pi$
$53$	263.158	−	263.158i	0.682028	−	0.682028i	0.960457	+	0.278429i	$0.0898136\pi$
$54$	−624.929			−1.57485
$55$	−289.641	−	287.199i	−0.710095	−	0.704106i
$56$	−200.005			−0.477264
$57$	−908.119	+	908.119i	−2.11023	+	2.11023i
$58$	129.561	−	129.561i	0.293313	−	0.293313i
$59$			24.4393i			0.0539275i	0.999636	+	0.0269638i	$0.00858387\pi$
$59$			24.4393i			0.0539275i	−0.999636	+	0.0269638i	$0.991416\pi$
$60$	−391.652	−	146.449i	−0.842701	−	0.315107i
$61$		−	402.074i		−	0.843940i	−0.906610	−	0.421970i	$-0.861339\pi$
$61$		−	402.074i		−	0.843940i	0.906610	−	0.421970i	$-0.138661\pi$
$62$	451.988	−	451.988i	0.925847	−	0.925847i
$63$	1068.10	+	1068.10i	2.13600	+	2.13600i
$64$			64.0000i			0.125000i
$65$	−25.7612	−	9.63277i	−0.0491583	−	0.0183815i
$66$	637.988	−	241.644i	1.18986	−	0.450671i
$67$	−132.763	−	132.763i	−0.242083	−	0.242083i	0.575628	−	0.817712i	$-0.304758\pi$
$67$	−132.763	−	132.763i	−0.242083	−	0.242083i	−0.817712	+	0.575628i	$0.804758\pi$
$68$	129.314	+	129.314i	0.230613	+	0.230613i
$69$			431.351i			0.752588i
$70$	231.808	+	508.705i	0.395805	+	0.868597i
$71$	−188.757			−0.315511			−0.157756	−	0.987478i	$-0.550426\pi$
$71$	−188.757			−0.315511			−0.157756	+	0.987478i	$0.550426\pi$
$72$	341.783	−	341.783i	0.559438	−	0.559438i
$73$	−601.348	−	601.348i	−0.964143	−	0.964143i	0.0352363	−	0.999379i	$-0.488782\pi$
$73$	−601.348	−	601.348i	−0.964143	−	0.964143i	−0.999379	+	0.0352363i	$0.988782\pi$
$74$	470.716			0.739455
$75$	81.4436	+	1165.89i	0.125391	+	1.79500i
$76$		−	549.432i		−	0.829265i
$77$	−831.578	−	374.692i	−1.23074	−	0.554547i
$78$	32.5273	−	32.5273i	0.0472179	−	0.0472179i
$79$	852.029			1.21343			0.606714	−	0.794921i	$-0.292488\pi$
$79$	852.029			1.21343			0.606714	+	0.794921i	$0.292488\pi$
$80$	162.781	−	74.1768i	0.227494	−	0.103665i
$81$	−1290.17			−1.76978
$82$	−657.132	−	657.132i	−0.884976	−	0.884976i
$83$	418.886	+	418.886i	0.553960	+	0.553960i	0.927581	−	0.373621i	$-0.121884\pi$
$83$	418.886	+	418.886i	0.553960	+	0.553960i	−0.373621	+	0.927581i	$0.621884\pi$
$84$	−935.006			−1.21449
$85$	179.029	−	478.782i	0.228452	−	0.610956i
$86$	171.755			0.215358
$87$	605.686	−	605.686i	0.746395	−	0.746395i
$88$	−119.899	+	266.098i	−0.145241	+	0.322343i
$89$			111.352i			0.132621i	0.997799	+	0.0663106i	$0.0211228\pi$
$89$			111.352i			0.132621i	−0.997799	+	0.0663106i	$0.978877\pi$
$90$	−1265.44	−	473.181i	−1.48210	−	0.554196i
$91$	−61.5007			−0.0708465
$92$	−130.489	−	130.489i	−0.147874	−	0.147874i
$93$	2113.00	−	2113.00i	2.35600	−	2.35600i
$94$	−359.110			−0.394036
$95$	−1397.46	+	636.799i	−1.50922	+	0.687728i
$96$			299.194i			0.318088i
$97$	−94.0732	−	94.0732i	−0.0984710	−	0.0984710i	0.656155	−	0.754626i	$-0.272182\pi$
$97$	−94.0732	−	94.0732i	−0.0984710	−	0.0984710i	−0.754626	+	0.656155i	$0.772182\pi$
$98$	398.852	+	398.852i	0.411123	+	0.411123i
$99$	2061.36	−	780.760i	2.09267	−	0.792619i
$100$	−377.331	−	328.056i	−0.377331	−	0.328056i
$101$			64.4911i			0.0635357i	0.999495	+	0.0317678i	$0.0101137\pi$
$101$			64.4911i			0.0635357i	−0.999495	+	0.0317678i	$0.989886\pi$
$102$	604.533	+	604.533i	0.586840	+	0.586840i
$103$	461.559	−	461.559i	0.441541	−	0.441541i	−0.450988	−	0.892530i	$-0.648928\pi$
$103$	461.559	−	461.559i	0.441541	−	0.441541i	0.892530	+	0.450988i	$0.148928\pi$
$104$			19.6798i			0.0185554i
$105$	1083.68	+	2378.15i	1.00721	+	2.21032i
$106$			744.323i			0.682028i
$107$	547.171	−	547.171i	0.494364	−	0.494364i	−0.415314	−	0.909678i	$-0.636328\pi$
$107$	547.171	−	547.171i	0.494364	−	0.494364i	0.909678	+	0.415314i	$0.136328\pi$
$108$	883.782	−	883.782i	0.787426	−	0.787426i
$109$	−412.769			−0.362716			−0.181358	−	0.983417i	$-0.558049\pi$
$109$	−412.769			−0.362716			−0.181358	+	0.983417i	$0.558049\pi$
$110$	815.775	−	3.45425i	0.707100	−	0.00299409i
$111$	2200.56			1.88169
$112$	282.850	−	282.850i	0.238632	−	0.238632i
$113$	−12.9184	+	12.9184i	−0.0107545	+	0.0107545i	−0.712464	−	0.701709i	$-0.752421\pi$
$113$	−12.9184	+	12.9184i	−0.0107545	+	0.0107545i	0.701709	+	0.712464i	$0.252421\pi$
$114$		−	2568.55i		−	2.11023i
$115$	−180.655	+	483.130i	−0.146488	+	0.391758i
$116$			366.453i			0.293313i
$117$	105.097	−	105.097i	0.0830446	−	0.0830446i
$118$	−34.5624	−	34.5624i	−0.0269638	−	0.0269638i
$119$		−	1143.02i		−	0.880505i
$120$	760.989	−	346.770i	0.578904	−	0.263797i
$121$	−997.025	+	881.761i	−0.749080	+	0.662480i
$122$	568.619	+	568.619i	0.421970	+	0.421970i
$123$	−3072.03	−	3072.03i	−2.25200	−	2.25200i
$124$			1278.41i			0.925847i
$125$	−397.066	+	1339.95i	−0.284118	+	0.958789i
$126$	−3021.04			−2.13600
$127$	−784.701	+	784.701i	−0.548275	+	0.548275i	−0.925942	−	0.377666i	$-0.876727\pi$
$127$	−784.701	+	784.701i	−0.548275	+	0.548275i	0.377666	+	0.925942i	$0.376727\pi$
$128$	−90.5097	−	90.5097i	−0.0625000	−	0.0625000i
$129$	802.938			0.548021
$130$	50.0547	−	22.8091i	0.0337699	−	0.0153884i
$131$		−	23.4365i		−	0.0156310i	−0.999969	−	0.00781549i	$-0.997512\pi$
$131$		−	23.4365i		−	0.0156310i	0.999969	−	0.00781549i	$-0.00248777\pi$
$132$	−560.515	+	1243.99i	−0.369595	+	0.820266i
$133$	−2428.23	+	2428.23i	−1.58311	+	1.58311i
$134$	375.510			0.242083
$135$	−3272.18	−	1223.55i	−2.08611	−	0.780048i
$136$	−365.756			−0.230613
$137$	1471.18	+	1471.18i	0.917458	+	0.917458i	0.996844	−	0.0793855i	$-0.0252958\pi$
$137$	1471.18	+	1471.18i	0.917458	+	0.917458i	−0.0793855	+	0.996844i	$0.525296\pi$
$138$	−610.023	−	610.023i	−0.376294	−	0.376294i
$139$	−764.896			−0.466746			−0.233373	−	0.972387i	$-0.574976\pi$
$139$	−764.896			−0.466746			−0.233373	+	0.972387i	$0.574976\pi$
$140$	−1047.24	−	391.591i	−0.632201	−	0.236396i
$141$	−1678.81			−1.00270
$142$	266.942	−	266.942i	0.157756	−	0.157756i
$143$	−36.8683	+	81.8242i	−0.0215600	+	0.0478495i
$144$			966.708i			0.559438i
$145$	932.060	−	424.724i	0.533816	−	0.243251i
$146$	1700.87			0.964143
$147$	1864.60	+	1864.60i	1.04619	+	1.04619i
$148$	−665.693	+	665.693i	−0.369727	+	0.369727i
$149$	−1758.31			−0.966752			−0.483376	−	0.875413i	$-0.660590\pi$
$149$	−1758.31			−0.966752			−0.483376	+	0.875413i	$0.660590\pi$
$150$	−1763.99	−	1533.63i	−0.960196	−	0.834805i
$151$		−	721.585i		−	0.388886i	−0.980914	−	0.194443i	$-0.937710\pi$
$151$		−	721.585i		−	0.388886i	0.980914	−	0.194443i	$-0.0622899\pi$
$152$	777.014	+	777.014i	0.414633	+	0.414633i
$153$	1953.27	+	1953.27i	1.03211	+	1.03211i
$154$	1705.92	−	646.134i	0.892644	−	0.338097i
$155$	3251.60	−	1481.70i	1.68500	−	0.767825i
$156$			92.0011i			0.0472179i
$157$	−562.342	−	562.342i	−0.285858	−	0.285858i	0.549582	−	0.835440i	$-0.314787\pi$
$157$	−562.342	−	562.342i	−0.285858	−	0.285858i	−0.835440	+	0.549582i	$0.814787\pi$
$158$	−1204.95	+	1204.95i	−0.606714	+	0.606714i
$159$			3479.64i			1.73556i
$160$	−125.306	+	335.110i	−0.0619144	+	0.165580i
$161$			1153.40i			0.564598i
$162$	1824.57	−	1824.57i	0.884888	−	0.884888i
$163$	−1690.57	+	1690.57i	−0.812368	+	0.812368i	−0.984988	−	0.172620i	$-0.944777\pi$
$163$	−1690.57	+	1690.57i	−0.812368	+	0.812368i	0.172620	+	0.984988i	$0.444777\pi$
$164$	1858.65			0.884976
$165$	3813.68	−	16.1483i	1.79936	−	0.00761905i
$166$	−1184.79			−0.553960
$167$	−2153.99	+	2153.99i	−0.998089	+	0.998089i	−0.999998	−	0.00190956i	$-0.999392\pi$
$167$	−2153.99	+	2153.99i	−0.998089	+	0.998089i	0.00190956	+	0.999998i	$0.499392\pi$
$168$	1322.30	−	1322.30i	0.607247	−	0.607247i
$169$		−	2190.95i		−	0.997246i
$170$	423.916	+	930.286i	0.191252	+	0.419704i
$171$		−	8299.07i		−	3.71138i
$172$	−242.898	+	242.898i	−0.107679	+	0.107679i
$173$	−941.093	−	941.093i	−0.413584	−	0.413584i	0.469401	−	0.882985i	$-0.344470\pi$
$173$	−941.093	−	941.093i	−0.413584	−	0.413584i	−0.882985	+	0.469401i	$0.844470\pi$
$174$			1713.14i			0.746395i
$175$	217.773	+	3117.48i	0.0940690	+	1.34662i
$176$	−206.758	−	545.882i	−0.0885509	−	0.233792i
$177$	−161.576	−	161.576i	−0.0686147	−	0.0686147i
$178$	−157.476	−	157.476i	−0.0663106	−	0.0663106i
$179$			132.346i			0.0552628i	0.999618	+	0.0276314i	$0.00879647\pi$
$179$			132.346i			0.0552628i	−0.999618	+	0.0276314i	$0.991204\pi$
$180$	2458.78	−	1120.43i	1.01815	−	0.463954i
$181$	3441.52			1.41329			0.706647	−	0.707566i	$-0.250207\pi$
$181$	3441.52			1.41329			0.706647	+	0.707566i	$0.250207\pi$
$182$	86.9752	−	86.9752i	0.0354232	−	0.0354232i
$183$	2658.24	+	2658.24i	1.07379	+	1.07379i
$184$	369.077			0.147874
$185$	2464.71	+	921.618i	0.979509	+	0.366263i
$186$			5976.48i			2.35600i
$187$	−1520.74	−	685.212i	−0.594691	−	0.267956i
$188$	507.858	−	507.858i	0.197018	−	0.197018i
$189$	−7811.80			−3.00648
$190$	1075.74	−	2876.87i	0.410748	−	1.09848i
$191$	−2860.27			−1.08357			−0.541784	−	0.840518i	$-0.682251\pi$
$191$	−2860.27			−1.08357			−0.541784	+	0.840518i	$0.682251\pi$
$192$	−423.125	−	423.125i	−0.159044	−	0.159044i
$193$	−2715.95	−	2715.95i	−1.01294	−	1.01294i	−0.999915	−	0.0130296i	$-0.995852\pi$
$193$	−2715.95	−	2715.95i	−1.01294	−	1.01294i	−0.0130296	−	0.999915i	$-0.504148\pi$
$194$	266.079			0.0984710
$195$	234.001	−	106.630i	0.0859342	−	0.0391588i
$196$	−1128.12			−0.411123
$197$	−1216.07	+	1216.07i	−0.439802	+	0.439802i	−0.891945	−	0.452143i	$-0.850660\pi$
$197$	−1216.07	+	1216.07i	−0.439802	+	0.439802i	0.452143	+	0.891945i	$0.350660\pi$
$198$	−1811.04	+	4019.37i	−0.650027	+	1.44265i
$199$		−	1110.55i		−	0.395602i	−0.980242	−	0.197801i	$-0.936620\pi$
$199$		−	1110.55i		−	0.395602i	0.980242	−	0.197801i	$-0.0633800\pi$
$200$	997.569	−	69.6856i	0.352694	−	0.0246376i
$201$	1755.48			0.616029
$202$	−91.2041	−	91.2041i	−0.0317678	−	0.0317678i
$203$	1619.55	−	1619.55i	0.559951	−	0.559951i
$204$	−1709.88			−0.586840
$205$	−2154.20	−	4727.40i	−0.733930	−	1.61061i
$206$			1305.49i			0.441541i
$207$	−1971.01	−	1971.01i	−0.661809	−	0.661809i
$208$	−27.8314	−	27.8314i	−0.00927769	−	0.00927769i
$209$	1774.99	+	4686.33i	0.587458	+	1.55101i
$210$	−4895.77	−	1830.65i	−1.60876	−	0.601557i
$211$		−	1934.18i		−	0.631065i	−0.948915	−	0.315532i	$-0.897817\pi$
$211$		−	1934.18i		−	0.631065i	0.948915	−	0.315532i	$-0.102183\pi$
$212$	−1052.63	−	1052.63i	−0.341014	−	0.341014i
$213$	1247.93	−	1247.93i	0.401441	−	0.401441i
$214$			1547.63i			0.494364i
$215$	899.322	+	336.279i	0.285271	+	0.106670i
$216$			2499.71i			0.787426i
$217$	5649.99	−	5649.99i	1.76749	−	1.76749i
$218$	583.743	−	583.743i	0.181358	−	0.181358i
$219$	7951.41			2.45345
$220$	−1148.79	+	1158.56i	−0.352053	+	0.355047i
$221$	−112.469			−0.0342328
$222$	−3112.06	+	3112.06i	−0.940846	+	0.940846i
$223$	−3112.99	+	3112.99i	−0.934803	+	0.934803i	−0.998001	−	0.0631978i	$-0.979870\pi$
$223$	−3112.99	+	3112.99i	−0.934803	+	0.934803i	0.0631978	+	0.998001i	$0.479870\pi$
$224$			800.020i			0.238632i
$225$	−5699.52	−	4955.23i	−1.68875	−	1.46822i
$226$		−	36.5388i		−	0.0107545i
$227$	1409.67	−	1409.67i	0.412173	−	0.412173i	−0.470322	−	0.882495i	$-0.655862\pi$
$227$	1409.67	−	1409.67i	0.412173	−	0.412173i	0.882495	+	0.470322i	$0.155862\pi$
$228$	3632.47	+	3632.47i	1.05512	+	1.05512i
$229$		−	6357.92i		−	1.83469i	−0.398097	−	0.917343i	$-0.630329\pi$
$229$		−	6357.92i		−	1.83469i	0.398097	−	0.917343i	$-0.369671\pi$
$230$	−427.765	−	938.734i	−0.122635	−	0.269123i
$231$	7975.04	−	3020.62i	2.27151	−	0.860356i
$232$	−518.243	−	518.243i	−0.146657	−	0.146657i
$233$	−2445.62	−	2445.62i	−0.687629	−	0.687629i	0.274078	−	0.961707i	$-0.411627\pi$
$233$	−2445.62	−	2445.62i	−0.687629	−	0.687629i	−0.961707	+	0.274078i	$0.911627\pi$
$234$			297.259i			0.0830446i
$235$	−1880.33	−	703.103i	−0.521954	−	0.195172i
$236$	97.7571			0.0269638
$237$	−5633.04	+	5633.04i	−1.54390	+	1.54390i
$238$	1616.47	+	1616.47i	0.440252	+	0.440252i
$239$	−2414.36			−0.653440			−0.326720	−	0.945121i	$-0.605943\pi$
$239$	−2414.36			−0.653440			−0.326720	+	0.945121i	$0.605943\pi$
$240$	−585.794	+	1566.61i	−0.157554	+	0.421351i
$241$			4798.61i			1.28260i	0.767292	+	0.641298i	$0.221604\pi$
$241$			4798.61i			1.28260i	−0.767292	+	0.641298i	$0.778396\pi$
$242$	163.008	−	2657.00i	0.0432998	−	0.705780i
$243$	2564.18	−	2564.18i	0.676923	−	0.676923i
$244$	−1608.30			−0.421970
$245$	1307.51	+	2869.34i	0.340954	+	0.748225i
$246$	8689.02			2.25200
$247$	238.929	+	238.929i	0.0615493	+	0.0615493i
$248$	−1807.95	−	1807.95i	−0.462923	−	0.462923i
$249$	−5538.78			−1.40966
$250$	−1333.44	−	2456.51i	−0.337336	−	0.621453i
$251$	4205.46			1.05755			0.528777	−	0.848761i	$-0.322651\pi$
$251$	4205.46			1.05755			0.528777	+	0.848761i	$0.322651\pi$
$252$	4272.39	−	4272.39i	1.06800	−	1.06800i
$253$	1534.55	+	691.435i	0.381328	+	0.171819i
$254$		−	2219.47i		−	0.548275i
$255$	1981.77	+	4349.00i	0.486679	+	1.06802i
$256$	256.000			0.0625000
$257$	−4024.38	−	4024.38i	−0.976785	−	0.976785i	0.0229518	−	0.999737i	$-0.492694\pi$
$257$	−4024.38	−	4024.38i	−0.976785	−	0.976785i	−0.999737	+	0.0229518i	$0.992694\pi$
$258$	−1135.53	+	1135.53i	−0.274011	+	0.274011i
$259$	5884.10			1.41166
$260$	−38.5311	+	103.045i	−0.00919076	+	0.0245791i
$261$			5535.21i			1.31272i
$262$	33.1443	+	33.1443i	0.00781549	+	0.00781549i
$263$	−4232.12	−	4232.12i	−0.992258	−	0.992258i	0.00771216	−	0.999970i	$-0.497545\pi$
$263$	−4232.12	−	4232.12i	−0.992258	−	0.992258i	−0.999970	+	0.00771216i	$0.997545\pi$
$264$	−966.575	−	2551.95i	−0.225336	−	0.594931i
$265$	−1457.31	+	3897.34i	−0.337819	+	0.903440i
$266$		−	6868.07i		−	1.58311i
$267$	−736.185	−	736.185i	−0.168741	−	0.168741i
$268$	−531.052	+	531.052i	−0.121042	+	0.121042i
$269$		−	6379.75i		−	1.44602i	−0.690836	−	0.723012i	$-0.742757\pi$
$269$		−	6379.75i		−	1.44602i	0.690836	−	0.723012i	$-0.257243\pi$
$270$	6357.92	−	2897.20i	1.43308	−	0.653030i
$271$			7223.78i			1.61924i	0.586955	+	0.809619i	$0.300326\pi$
$271$			7223.78i			1.61924i	−0.586955	+	0.809619i	$0.699674\pi$
$272$	517.257	−	517.257i	0.115306	−	0.115306i
$273$	406.601	−	406.601i	0.0901415	−	0.0901415i
$274$	−4161.14			−0.917458
$275$	4278.23	+	1579.12i	0.938134	+	0.346271i
$276$	1725.41			0.376294
$277$	4661.37	−	4661.37i	1.01110	−	1.01110i	0.0111612	−	0.999938i	$-0.496447\pi$
$277$	4661.37	−	4661.37i	1.01110	−	1.01110i	0.999938	−	0.0111612i	$-0.00355279\pi$
$278$	1081.73	−	1081.73i	0.233373	−	0.233373i
$279$			19310.2i			4.14363i
$280$	2034.82	−	927.233i	0.434299	−	0.197903i
$281$			399.230i			0.0847546i	0.999102	+	0.0423773i	$0.0134932\pi$
$281$			399.230i			0.0847546i	−0.999102	+	0.0423773i	$0.986507\pi$
$282$	2374.19	−	2374.19i	0.501351	−	0.501351i
$283$	5990.23	+	5990.23i	1.25824	+	1.25824i	0.951932	+	0.306309i	$0.0990940\pi$
$283$	5990.23	+	5990.23i	1.25824	+	1.25824i	0.306309	+	0.951932i	$0.400906\pi$
$284$			755.027i			0.157756i
$285$	5028.97	−	13449.1i	1.04523	−	2.79529i
$286$	−63.5772	−	167.857i	−0.0131448	−	0.0347048i
$287$	−8214.35	−	8214.35i	−1.68947	−	1.68947i
$288$	−1367.13	−	1367.13i	−0.279719	−	0.279719i
$289$			2822.73i			0.574543i
$290$	−717.481	+	1918.78i	−0.145283	+	0.388534i
$291$	1243.90			0.250579
$292$	−2405.39	+	2405.39i	−0.482071	+	0.482071i
$293$	2563.94	+	2563.94i	0.511218	+	0.511218i	0.914900	−	0.403681i	$-0.132270\pi$
$293$	2563.94	+	2563.94i	0.511218	+	0.511218i	−0.403681	+	0.914900i	$0.632270\pi$
$294$	−5273.88			−1.04619
$295$	−113.302	−	248.641i	−0.0223616	−	0.0490727i
$296$		−	1882.87i		−	0.369727i
$297$	−4683.00	+	10393.3i	−0.914933	+	2.03057i
$298$	2486.62	−	2486.62i	0.483376	−	0.483376i
$299$	113.490			0.0219508
$300$	4663.55	−	325.774i	0.897500	−	0.0626953i
$301$	2146.99			0.411130
$302$	1020.47	+	1020.47i	0.194443	+	0.194443i
$303$	−426.371	−	426.371i	−0.0808396	−	0.0808396i
$304$	−2197.73			−0.414633
$305$	1864.04	+	4090.64i	0.349949	+	0.767965i
$306$	−5524.67			−1.03211
$307$	−1415.31	+	1415.31i	−0.263115	+	0.263115i	−0.826318	−	0.563204i	$-0.809569\pi$
$307$	−1415.31	+	1415.31i	−0.263115	+	0.263115i	0.563204	+	0.826318i	$0.309569\pi$
$308$	−1498.77	+	3326.31i	−0.277274	+	0.615371i
$309$			6103.03i			1.12359i
$310$	−2503.01	+	6693.89i	−0.458586	+	1.22641i
$311$	785.642			0.143247			0.0716233	−	0.997432i	$-0.477182\pi$
$311$	785.642			0.143247			0.0716233	+	0.997432i	$0.477182\pi$
$312$	−130.109	−	130.109i	−0.0236089	−	0.0236089i
$313$	−1698.83	+	1698.83i	−0.306784	+	0.306784i	−0.843661	−	0.536877i	$-0.819604\pi$
$313$	−1698.83	+	1698.83i	−0.306784	+	0.306784i	0.536877	+	0.843661i	$0.319604\pi$
$314$	1590.54			0.285858
$315$	−15818.4	−	5914.90i	−2.82942	−	1.05799i
$316$		−	3408.12i		−	0.606714i
$317$	−387.258	−	387.258i	−0.0686138	−	0.0686138i	0.671967	−	0.740581i	$-0.265450\pi$
$317$	−387.258	−	387.258i	−0.0686138	−	0.0686138i	−0.740581	+	0.671967i	$0.765450\pi$
$318$	−4920.96	−	4920.96i	−0.867779	−	0.867779i
$319$	−1183.86	−	3125.63i	−0.207785	−	0.548595i
$320$	−296.707	−	651.126i	−0.0518326	−	0.113747i
$321$			7235.05i			1.25801i
$322$	−1631.15	−	1631.15i	−0.282299	−	0.282299i
$323$	−4440.59	+	4440.59i	−0.764956	+	0.764956i
$324$			5160.67i			0.884888i
$325$	306.749	−	21.4281i	0.0523549	−	0.00365728i
$326$		−	4781.67i		−	0.812368i
$327$	2728.95	−	2728.95i	0.461502	−	0.461502i
$328$	−2628.53	+	2628.53i	−0.442488	+	0.442488i
$329$	−4488.98			−0.752236
$330$	−5370.51	+	5416.19i	−0.895870	+	0.903489i
$331$	−8741.02			−1.45151			−0.725755	−	0.687953i	$-0.758509\pi$
$331$	−8741.02			−1.45151			−0.725755	+	0.687953i	$0.758509\pi$
$332$	1675.54	−	1675.54i	0.276980	−	0.276980i
$333$	−10055.2	+	10055.2i	−1.65472	+	1.65472i
$334$		−	6092.41i		−	0.998089i
$335$	1966.21	+	735.214i	0.320672	+	0.119908i
$336$			3740.02i			0.607247i
$337$	4889.80	−	4889.80i	0.790399	−	0.790399i	−0.191160	−	0.981559i	$-0.561225\pi$
$337$	4889.80	−	4889.80i	0.790399	−	0.790399i	0.981559	+	0.191160i	$0.0612249\pi$
$338$	3098.47	+	3098.47i	0.498623	+	0.498623i
$339$		−	170.816i		−	0.0273670i
$340$	−1915.13	−	716.115i	−0.305478	−	0.114226i
$341$	−4130.03	−	10904.1i	−0.655877	−	1.73165i
$342$	11736.7	+	11736.7i	1.85569	+	1.85569i
$343$	−1077.82	−	1077.82i	−0.169670	−	0.169670i
$344$		−	687.019i		−	0.107679i
$345$	−1999.77	−	4388.50i	−0.312069	−	0.684837i
$346$	2661.81			0.413584
$347$	−8226.73	+	8226.73i	−1.27272	+	1.27272i	−0.328066	+	0.944655i	$0.606397\pi$
$347$	−8226.73	+	8226.73i	−1.27272	+	1.27272i	−0.944655	+	0.328066i	$0.893603\pi$
$348$	−2422.74	−	2422.74i	−0.373197	−	0.373197i
$349$	−2663.90			−0.408583			−0.204292	−	0.978910i	$-0.565489\pi$
$349$	−2663.90			−0.408583			−0.204292	+	0.978910i	$0.565489\pi$
$350$	−4716.76	−	4100.80i	−0.720347	−	0.626278i
$351$			768.652i			0.116888i
$352$	1064.39	+	479.594i	0.161171	+	0.0726206i
$353$	3299.95	−	3299.95i	0.497559	−	0.497559i	−0.413118	−	0.910677i	$-0.635560\pi$
$353$	3299.95	−	3299.95i	0.497559	−	0.497559i	0.910677	+	0.413118i	$0.135560\pi$
$354$	457.006			0.0686147
$355$	1920.38	−	875.086i	0.287108	−	0.130830i
$356$	445.408			0.0663106
$357$	7556.85	+	7556.85i	1.12031	+	1.12031i
$358$	−187.166	−	187.166i	−0.0276314	−	0.0276314i
$359$	2081.19			0.305963			0.152982	−	0.988229i	$-0.451112\pi$
$359$	2081.19			0.305963			0.152982	+	0.988229i	$0.451112\pi$
$360$	−1892.72	+	5061.77i	−0.277098	+	0.741052i
$361$	12008.2			1.75072
$362$	−4867.05	+	4867.05i	−0.706647	+	0.706647i
$363$	762.049	−	12421.3i	0.110185	−	1.79600i
$364$			246.003i			0.0354232i
$365$	8905.89	+	3330.14i	1.27714	+	0.477554i
$366$	−7518.65			−1.07379
$367$	8617.56	+	8617.56i	1.22570	+	1.22570i	0.965574	+	0.260129i	$0.0837651\pi$
$367$	8617.56	+	8617.56i	1.22570	+	1.22570i	0.260129	+	0.965574i	$0.416235\pi$
$368$	−521.954	+	521.954i	−0.0739368	+	0.0739368i
$369$	28074.5			3.96071
$370$	−4788.99	+	2182.26i	−0.672886	+	0.306623i
$371$			9304.26i			1.30203i
$372$	−8452.02	−	8452.02i	−1.17800	−	1.17800i
$373$	449.635	+	449.635i	0.0624161	+	0.0624161i	0.737626	−	0.675210i	$-0.235947\pi$
$373$	449.635	+	449.635i	0.0624161	+	0.0624161i	−0.675210	+	0.737626i	$0.735947\pi$
$374$	3119.68	−	1181.61i	0.431323	−	0.163368i
$375$	−6233.70	−	11484.0i	−0.858419	−	1.58141i
$376$			1436.44i			0.197018i
$377$	−159.358	−	159.358i	−0.0217701	−	0.0217701i
$378$	11047.6	−	11047.6i	1.50324	−	1.50324i
$379$			704.849i			0.0955295i	0.998859	+	0.0477648i	$0.0152098\pi$
$379$			704.849i			0.0955295i	−0.998859	+	0.0477648i	$0.984790\pi$
$380$	2547.19	+	5589.83i	0.343864	+	0.754612i
$381$		−	10375.8i		−	1.39520i
$382$	4045.03	−	4045.03i	0.541784	−	0.541784i
$383$	−6833.40	+	6833.40i	−0.911671	+	0.911671i	−0.996404	−	0.0847323i	$-0.972997\pi$
$383$	−6833.40	+	6833.40i	−0.911671	+	0.911671i	0.0847323	+	0.996404i	$0.472997\pi$
$384$	1196.78			0.159044
$385$	10197.4	−	43.1791i	1.34989	−	0.00571588i
$386$	7681.87			1.01294
$387$	−3668.93	+	3668.93i	−0.481917	+	0.481917i
$388$	−376.293	+	376.293i	−0.0492355	+	0.0492355i
$389$		−	3215.25i		−	0.419074i	−0.977801	−	0.209537i	$-0.932804\pi$
$389$		−	3215.25i		−	0.419074i	0.977801	−	0.209537i	$-0.0671957\pi$
$390$	−180.129	+	481.726i	−0.0233877	+	0.0625465i
$391$			2109.25i			0.272812i
$392$	1595.41	−	1595.41i	0.205562	−	0.205562i
$393$	154.947	+	154.947i	0.0198881	+	0.0198881i
$394$		−	3439.55i		−	0.439802i
$395$	−8668.41	+	3950.05i	−1.10419	+	0.503161i
$396$	−3123.04	−	8245.45i	−0.396310	−	1.04634i
$397$	2304.98	+	2304.98i	0.291394	+	0.291394i	0.837631	−	0.546237i	$-0.183940\pi$
$397$	2304.98	+	2304.98i	0.291394	+	0.291394i	−0.546237	+	0.837631i	$0.683940\pi$
$398$	1570.56	+	1570.56i	0.197801	+	0.197801i
$399$		−	32107.6i		−	4.02855i
$400$	−1312.23	+	1509.33i	−0.164028	+	0.188666i
$401$	−13780.0			−1.71606			−0.858030	−	0.513600i	$-0.828312\pi$
$401$	−13780.0			−1.71606			−0.858030	+	0.513600i	$0.828312\pi$
$402$	−2482.62	+	2482.62i	−0.308015	+	0.308015i
$403$	−555.938	−	555.938i	−0.0687177	−	0.0687177i
$404$	257.964			0.0317678
$405$	13126.0	−	5981.28i	1.61045	−	0.733857i
$406$			4580.78i			0.559951i
$407$	3527.39	−	7828.55i	0.429597	−	0.953432i
$408$	2418.13	−	2418.13i	0.293420	−	0.293420i
$409$	−168.809			−0.0204084			−0.0102042	−	0.999948i	$-0.503248\pi$
$409$	−168.809			−0.0204084			−0.0102042	+	0.999948i	$0.503248\pi$
$410$	9732.05	+	3639.06i	1.17227	+	0.438342i
$411$	−19453.0			−2.33466
$412$	−1846.24	−	1846.24i	−0.220771	−	0.220771i
$413$	−432.040	−	432.040i	−0.0514753	−	0.0514753i
$414$	5574.85			0.661809
$415$	−6203.65	−	2319.70i	−0.733796	−	0.274385i
$416$	78.7190			0.00927769
$417$	5056.98	−	5056.98i	0.593864	−	0.593864i
$418$	−9137.69	−	4117.26i	−1.06923	−	0.481774i
$419$			15565.0i			1.81479i	0.420276	+	0.907396i	$0.361933\pi$
$419$			15565.0i			1.81479i	−0.420276	+	0.907396i	$0.638067\pi$
$420$	9512.60	−	4334.73i	1.10516	−	0.503603i
$421$	8710.58			1.00838			0.504190	−	0.863593i	$-0.331791\pi$
$421$	8710.58			1.00838			0.504190	+	0.863593i	$0.331791\pi$
$422$	2735.35	+	2735.35i	0.315532	+	0.315532i
$423$	7671.10	−	7671.10i	0.881753	−	0.881753i
$424$	2977.29			0.341014
$425$	398.249	+	5701.04i	0.0454539	+	0.650685i
$426$			3529.69i			0.401441i
$427$	7107.91	+	7107.91i	0.805564	+	0.805564i
$428$	−2188.68	−	2188.68i	−0.247182	−	0.247182i
$429$	−297.218	−	784.715i	−0.0334495	−	0.0883133i
$430$	−1747.40	+	796.263i	−0.195971	+	0.0893005i
$431$		−	3118.85i		−	0.348561i	−0.984696	−	0.174280i	$-0.944240\pi$
$431$		−	3118.85i		−	0.348561i	0.984696	−	0.174280i	$-0.0557599\pi$
$432$	−3535.13	−	3535.13i	−0.393713	−	0.393713i
$433$	2779.24	−	2779.24i	0.308456	−	0.308456i	−0.535854	−	0.844311i	$-0.680010\pi$
$433$	2779.24	−	2779.24i	0.308456	−	0.308456i	0.844311	+	0.535854i	$0.180010\pi$
$434$			15980.6i			1.76749i
$435$	−3354.16	+	8970.14i	−0.369700	+	0.988702i
$436$			1651.07i			0.181358i
$437$	4480.91	−	4480.91i	0.490506	−	0.490506i
$438$	−11245.0	+	11245.0i	−1.22673	+	1.22673i
$439$	−12206.0			−1.32701			−0.663507	−	0.748170i	$-0.730933\pi$
$439$	−12206.0			−1.32701			−0.663507	+	0.748170i	$0.730933\pi$
$440$	−13.8170	−	3263.10i	−0.00149704	−	0.353550i
$441$	−17040.1			−1.83998
$442$	159.055	−	159.055i	0.0171164	−	0.0171164i
$443$	10911.4	−	10911.4i	1.17024	−	1.17024i	0.188083	−	0.982153i	$-0.439773\pi$
$443$	10911.4	−	10911.4i	1.17024	−	1.17024i	0.982153	−	0.188083i	$-0.0602274\pi$
$444$		−	8802.23i		−	0.940846i
$445$	−516.234	−	1132.88i	−0.0549929	−	0.120682i
$446$		−	8804.86i		−	0.934803i
$447$	11624.7	−	11624.7i	1.23005	−	1.23005i
$448$	−1131.40	−	1131.40i	−0.119316	−	0.119316i
$449$			2168.45i			0.227918i	0.993485	+	0.113959i	$0.0363533\pi$
$449$			2168.45i			0.227918i	−0.993485	+	0.113959i	$0.963647\pi$
$450$	15068.1	−	1052.59i	1.57848	−	0.110266i
$451$	−15853.2	+	6004.54i	−1.65520	+	0.626924i
$452$	51.6736	+	51.6736i	0.00537726	+	0.00537726i
$453$	4770.63	+	4770.63i	0.494799	+	0.494799i
$454$			3987.15i			0.412173i
$455$	625.699	−	285.121i	0.0644686	−	0.0293773i
$456$	−10274.2			−1.05512
$457$	−5548.13	+	5548.13i	−0.567900	+	0.567900i	−0.931540	−	0.363640i	$-0.881534\pi$
$457$	−5548.13	+	5548.13i	−0.567900	+	0.567900i	0.363640	+	0.931540i	$0.381534\pi$
$458$	8991.46	+	8991.46i	0.917343	+	0.917343i
$459$	−14285.7			−1.45272
$460$	1932.52	+	722.619i	0.195879	+	0.0732441i
$461$			5307.52i			0.536216i	0.963389	+	0.268108i	$0.0863985\pi$
$461$			5307.52i			0.536216i	−0.963389	+	0.268108i	$0.913602\pi$
$462$	−7006.61	+	15550.2i	−0.705578	+	1.56593i
$463$	7920.96	−	7920.96i	0.795072	−	0.795072i	−0.187242	−	0.982314i	$-0.559955\pi$
$463$	7920.96	−	7920.96i	0.795072	−	0.795072i	0.982314	+	0.187242i	$0.0599548\pi$
$464$	1465.81			0.146657
$465$	−11701.4	+	31293.4i	−1.16696	+	3.12085i
$466$	6917.25			0.687629
$467$	−3515.79	−	3515.79i	−0.348375	−	0.348375i	0.511129	−	0.859504i	$-0.329227\pi$
$467$	−3515.79	−	3515.79i	−0.348375	−	0.348375i	−0.859504	+	0.511129i	$0.829227\pi$
$468$	−420.388	−	420.388i	−0.0415223	−	0.0415223i
$469$	4694.00			0.462150
$470$	3653.53	−	1664.85i	0.358563	−	0.163391i
$471$	7435.65			0.727424
$472$	−138.249	+	138.249i	−0.0134819	+	0.0134819i
$473$	1287.07	−	2856.48i	0.125115	−	0.277676i
$474$		−	15932.6i		−	1.54390i
$475$	11265.3	−	12957.4i	1.08818	−	1.25163i
$476$	−4572.06			−0.440252
$477$	−15899.8	−	15899.8i	−1.52621	−	1.52621i
$478$	3414.42	−	3414.42i	0.326720	−	0.326720i
$479$	−19230.3			−1.83435			−0.917175	−	0.398484i	$-0.869537\pi$
$479$	−19230.3			−1.83435			−0.917175	+	0.398484i	$0.869537\pi$
$480$	−1387.08	−	3043.96i	−0.131898	−	0.289452i
$481$		−	578.974i		−	0.0548834i
$482$	−6786.26	−	6786.26i	−0.641298	−	0.641298i
$483$	−7625.47	−	7625.47i	−0.718367	−	0.718367i
$484$	3527.04	+	3988.10i	0.331240	+	0.374540i
$485$	1393.21	+	520.958i	0.130438	+	0.0487742i
$486$			7252.60i			0.676923i
$487$	7204.85	+	7204.85i	0.670396	+	0.670396i	0.957807	−	0.287411i	$-0.0927947\pi$
$487$	7204.85	+	7204.85i	0.670396	+	0.670396i	−0.287411	+	0.957807i	$0.592795\pi$
$488$	2274.48	−	2274.48i	0.210985	−	0.210985i
$489$		−	22353.9i		−	2.06723i
$490$	−5906.95	−	2208.76i	−0.544589	−	0.203636i
$491$			11028.4i			1.01365i	0.862048	+	0.506826i	$0.169181\pi$
$491$			11028.4i			1.01365i	−0.862048	+	0.506826i	$0.830819\pi$
$492$	−12288.1	+	12288.1i	−1.12600	+	1.12600i
$493$	2961.73	−	2961.73i	0.270567	−	0.270567i
$494$	−675.793			−0.0615493
$495$	−17352.3	+	17499.9i	−1.57561	+	1.58901i
$496$	5113.66			0.462923
$497$	3336.86	−	3336.86i	0.301164	−	0.301164i
$498$	7833.02	−	7833.02i	0.704831	−	0.704831i
$499$		−	14005.1i		−	1.25642i	−0.778044	−	0.628209i	$-0.783788\pi$
$499$		−	14005.1i		−	1.25642i	0.778044	−	0.628209i	$-0.216212\pi$
$500$	5359.80	+	1588.27i	0.479395	+	0.142059i
$501$		−	28481.5i		−	2.53984i
$502$	−5947.41	+	5947.41i	−0.528777	+	0.528777i
$503$	−6100.23	−	6100.23i	−0.540747	−	0.540747i	0.383001	−	0.923748i	$-0.374891\pi$
$503$	−6100.23	−	6100.23i	−0.540747	−	0.540747i	−0.923748	+	0.383001i	$0.874891\pi$
$504$			12084.1i			1.06800i
$505$	−298.984	−	656.122i	−0.0263458	−	0.0578159i
$506$	−3148.01	+	1192.34i	−0.276574	+	0.104755i
$507$	14485.1	+	14485.1i	1.26885	+	1.26885i
$508$	3138.80	+	3138.80i	0.274138	+	0.274138i
$509$			10775.6i			0.938349i	0.883105	+	0.469175i	$0.155448\pi$
$509$			10775.6i			0.938349i	−0.883105	+	0.469175i	$0.844552\pi$
$510$	−8953.07	−	3347.78i	−0.777350	−	0.290671i
$511$	21261.4			1.84060
$512$	−362.039	+	362.039i	−0.0312500	+	0.0312500i
$513$	30348.6	+	30348.6i	2.61194	+	2.61194i
$514$	11382.7			0.976785
$515$	−2556.02	+	6835.64i	−0.218702	+	0.584882i
$516$		−	3211.75i		−	0.274011i
$517$	−2691.05	+	5972.41i	−0.228921	+	0.508058i
$518$	−8321.37	+	8321.37i	−0.705830	+	0.705830i
$519$	12443.7			1.05245
$520$	−91.2363	−	200.219i	−0.00769419	−	0.0168849i
$521$	11837.4			0.995407			0.497704	−	0.867347i	$-0.334177\pi$
$521$	11837.4			0.995407			0.497704	+	0.867347i	$0.334177\pi$
$522$	−7827.97	−	7827.97i	−0.656362	−	0.656362i
$523$	4965.34	+	4965.34i	0.415141	+	0.415141i	0.883525	−	0.468384i	$-0.155164\pi$
$523$	4965.34	+	4965.34i	0.415141	+	0.415141i	−0.468384	+	0.883525i	$0.655164\pi$
$524$	−93.7461			−0.00781549
$525$	−22050.4	−	19170.9i	−1.83307	−	1.59369i
$526$	11970.3			0.992258
$527$	10332.3	−	10332.3i	0.854048	−	0.854048i
$528$	4975.95	+	2242.06i	0.410133	+	0.184798i
$529$			10038.6i			0.825067i
$530$	−3450.72	−	7572.62i	−0.282810	−	0.620629i
$531$	1476.60			0.120676
$532$	9712.92	+	9712.92i	0.791557	+	0.791557i
$533$	−808.262	+	808.262i	−0.0656843	+	0.0656843i
$534$	2082.24			0.168741
$535$	−3030.12	+	8103.54i	−0.244866	+	0.654853i
$536$		−	1502.04i		−	0.121042i
$537$	−874.986	−	874.986i	−0.0703136	−	0.0703136i
$538$	9022.33	+	9022.33i	0.723012	+	0.723012i
$539$	9622.22	−	3644.50i	0.768939	−	0.291243i
$540$	−4894.20	+	13088.7i	−0.390024	+	1.04305i
$541$		−	7649.60i		−	0.607915i	−0.952686	−	0.303957i	$-0.901692\pi$
$541$		−	7649.60i		−	0.607915i	0.952686	−	0.303957i	$-0.0983081\pi$
$542$	−10216.0	−	10216.0i	−0.809619	−	0.809619i
$543$	−22753.0	+	22753.0i	−1.79821	+	1.79821i
$544$			1463.02i			0.115306i
$545$	4199.44	−	1913.62i	0.330063	−	0.150404i
$546$			1150.04i			0.0901415i
$547$	1264.68	−	1264.68i	0.0988552	−	0.0988552i	−0.655950	−	0.754805i	$-0.727732\pi$
$547$	1264.68	−	1264.68i	0.0988552	−	0.0988552i	0.754805	+	0.655950i	$0.227732\pi$
$548$	5884.74	−	5884.74i	0.458729	−	0.458729i
$549$	−24293.0			−1.88853
$550$	−8283.55	+	3817.11i	−0.642203	+	0.295931i
$551$	−12583.8			−0.972938
$552$	−2440.09	+	2440.09i	−0.188147	+	0.188147i
$553$	−15062.3	+	15062.3i	−1.15825	+	1.15825i
$554$			13184.3i			1.01110i
$555$	−22388.1	+	10201.9i	−1.71229	+	0.780264i
$556$			3059.58i			0.233373i
$557$	−10202.3	+	10202.3i	−0.776099	+	0.776099i	−0.979165	−	0.203066i	$-0.934909\pi$
$557$	−10202.3	+	10202.3i	−0.776099	+	0.776099i	0.203066	+	0.979165i	$0.434909\pi$
$558$	−27308.8	−	27308.8i	−2.07181	−	2.07181i
$559$		−	211.256i		−	0.0159842i
$560$	−1566.36	+	4188.97i	−0.118198	+	0.316101i
$561$	14584.2	−	5523.91i	1.09759	−	0.415722i
$562$	−564.596	−	564.596i	−0.0423773	−	0.0423773i
$563$	−7557.58	−	7557.58i	−0.565744	−	0.565744i	0.365189	−	0.930933i	$-0.381004\pi$
$563$	−7557.58	−	7557.58i	−0.565744	−	0.565744i	−0.930933	+	0.365189i	$0.881004\pi$
$564$			6715.23i			0.501351i
$565$	71.5394	−	191.320i	0.00532688	−	0.0142458i
$566$	−16942.9			−1.25824
$567$	22807.7	−	22807.7i	1.68930	−	1.68930i
$568$	−1067.77	−	1067.77i	−0.0788779	−	0.0788779i
$569$	−9932.21			−0.731775			−0.365887	−	0.930659i	$-0.619234\pi$
$569$	−9932.21			−0.731775			−0.365887	+	0.930659i	$0.619234\pi$
$570$	11907.9	+	26132.0i	0.875031	+	1.92026i
$571$			20888.2i			1.53090i	0.643497	+	0.765448i	$0.277483\pi$
$571$			20888.2i			1.53090i	−0.643497	+	0.765448i	$0.722517\pi$
$572$	327.297	+	147.473i	0.0239248	+	0.0107800i
$573$	18910.1	−	18910.1i	1.37868	−	1.37868i
$574$	23233.7			1.68947
$575$	−401.865	−	5752.82i	−0.0291460	−	0.417233i
$576$	3866.83			0.279719
$577$	−4880.53	−	4880.53i	−0.352130	−	0.352130i	0.508772	−	0.860902i	$-0.330100\pi$
$577$	−4880.53	−	4880.53i	−0.352130	−	0.352130i	−0.860902	+	0.508772i	$0.830100\pi$
$578$	−3991.94	−	3991.94i	−0.287271	−	0.287271i
$579$	35912.1			2.57764
$580$	−1698.90	−	3728.24i	−0.121626	−	0.266908i
$581$	−14810.2			−1.05754
$582$	−1759.14	+	1759.14i	−0.125290	+	0.125290i
$583$	12378.9	+	5577.70i	0.879388	+	0.396234i
$584$		−	6803.47i		−	0.482071i
$585$	−582.005	+	1556.47i	−0.0411332	+	0.110004i
$586$	−7251.92			−0.511218
$587$	1085.01	+	1085.01i	0.0762913	+	0.0762913i	0.744223	−	0.667931i	$-0.232820\pi$
$587$	1085.01	+	1085.01i	0.0762913	+	0.0762913i	−0.667931	+	0.744223i	$0.732820\pi$
$588$	7458.39	−	7458.39i	0.523093	−	0.523093i
$589$	−43900.1			−3.07109
$590$	511.865	+	191.399i	0.0357172	+	0.0133556i
$591$		−	16079.6i		−	1.11917i
$592$	2662.77	+	2662.77i	0.184864	+	0.184864i
$593$	11338.7	+	11338.7i	0.785203	+	0.785203i	0.980704	−	0.195501i	$-0.0626333\pi$
$593$	11338.7	+	11338.7i	0.785203	+	0.785203i	−0.195501	+	0.980704i	$0.562633\pi$
$594$	−8075.55	−	21321.1i	−0.557818	−	1.47275i
$595$	5299.08	+	11628.9i	0.365111	+	0.801238i
$596$			7033.23i			0.483376i
$597$	7342.21	+	7342.21i	0.503344	+	0.503344i
$598$	−160.499	+	160.499i	−0.0109754	+	0.0109754i
$599$			8931.33i			0.609223i	0.952477	+	0.304611i	$0.0985266\pi$
$599$			8931.33i			0.609223i	−0.952477	+	0.304611i	$0.901473\pi$
$600$	−6134.54	+	7055.97i	−0.417403	+	0.480098i
$601$		−	18769.1i		−	1.27389i	−0.770910	−	0.636944i	$-0.780198\pi$
$601$		−	18769.1i		−	1.27389i	0.770910	−	0.636944i	$-0.219802\pi$
$602$	−3036.30	+	3036.30i	−0.205565	+	0.205565i
$603$	−8021.44	+	8021.44i	−0.541722	+	0.541722i
$604$	−2886.34			−0.194443
$605$	6055.69	−	13593.2i	0.406940	−	0.913455i
$606$	1205.96			0.0808396
$607$	−536.005	+	536.005i	−0.0358415	+	0.0358415i	−0.724800	−	0.688959i	$-0.758068\pi$
$607$	−536.005	+	536.005i	−0.0358415	+	0.0358415i	0.688959	+	0.724800i	$0.258068\pi$
$608$	3108.06	−	3108.06i	0.207316	−	0.207316i
$609$			21414.7i			1.42491i
$610$	−8421.18	−	3148.89i	−0.558957	−	0.209008i
$611$			441.699i			0.0292459i
$612$	7813.07	−	7813.07i	0.516053	−	0.516053i
$613$	−1653.44	−	1653.44i	−0.108943	−	0.108943i	0.650534	−	0.759477i	$-0.274545\pi$
$613$	−1653.44	−	1653.44i	−0.108943	−	0.108943i	−0.759477	+	0.650534i	$0.774545\pi$
$614$		−	4003.11i		−	0.263115i
$615$	45496.5	+	17012.3i	2.98308	+	1.11545i
$616$	−2584.54	−	6823.69i	−0.169049	−	0.446322i
$617$	6551.75	+	6551.75i	0.427494	+	0.427494i	0.887774	−	0.460280i	$-0.152251\pi$
$617$	6551.75	+	6551.75i	0.427494	+	0.427494i	−0.460280	+	0.887774i	$0.652251\pi$
$618$	−8630.99	−	8630.99i	−0.561795	−	0.561795i
$619$		−	15622.4i		−	1.01441i	−0.861827	−	0.507203i	$-0.830679\pi$
$619$		−	15622.4i		−	1.01441i	0.861827	−	0.507203i	$-0.169321\pi$
$620$	−5926.79	−	13006.4i	−0.383913	−	0.842499i
$621$	14415.4			0.931516
$622$	−1111.07	+	1111.07i	−0.0716233	+	0.0716233i
$623$	−1968.49	−	1968.49i	−0.126591	−	0.126591i
$624$	368.005			0.0236089
$625$	−2172.38	−	15473.2i	−0.139032	−	0.990288i
$626$		−	4805.01i		−	0.306784i
$627$	−42717.9	−	19247.8i	−2.72087	−	1.22597i
$628$	−2249.37	+	2249.37i	−0.142929	+	0.142929i
$629$	10760.5			0.682110
$630$	30735.6	−	14005.7i	1.94370	−	0.885714i
$631$	−10156.8			−0.640783			−0.320392	−	0.947285i	$-0.603814\pi$
$631$	−10156.8			−0.640783			−0.320392	+	0.947285i	$0.603814\pi$
$632$	4819.80	+	4819.80i	0.303357	+	0.303357i
$633$	12787.5	+	12787.5i	0.802936	+	0.802936i
$634$	1095.33			0.0686138
$635$	4345.51	−	11621.3i	0.271569	−	0.726266i
$636$	13918.6			0.867779
$637$	490.581	−	490.581i	0.0305142	−	0.0305142i
$638$	6094.54	+	2746.08i	0.378190	+	0.170405i
$639$			11404.5i			0.706036i
$640$	1340.44	+	501.224i	0.0827898	+	0.0309572i
$641$	−18400.6			−1.13382			−0.566910	−	0.823780i	$-0.691861\pi$
$641$	−18400.6			−1.13382			−0.566910	+	0.823780i	$0.691861\pi$
$642$	−10231.9	−	10231.9i	−0.629005	−	0.629005i
$643$	8998.23	−	8998.23i	0.551875	−	0.551875i	−0.375107	−	0.926982i	$-0.622394\pi$
$643$	8998.23	−	8998.23i	0.551875	−	0.551875i	0.926982	+	0.375107i	$0.122394\pi$
$644$	4613.58			0.282299
$645$	−8168.96	+	3722.46i	−0.498686	+	0.227243i
$646$		−	12559.9i		−	0.764956i
$647$	−8167.91	−	8167.91i	−0.496312	−	0.496312i	0.413976	−	0.910288i	$-0.364140\pi$
$647$	−8167.91	−	8167.91i	−0.496312	−	0.496312i	−0.910288	+	0.413976i	$0.864140\pi$
$648$	−7298.29	−	7298.29i	−0.442444	−	0.442444i
$649$	−833.810	+	315.813i	−0.0504313	+	0.0191013i
$650$	−403.504	+	464.112i	−0.0243488	+	0.0280061i
$651$			74707.8i			4.49774i
$652$	6762.30	+	6762.30i	0.406184	+	0.406184i
$653$	10277.8	−	10277.8i	0.615927	−	0.615927i	−0.328557	−	0.944484i	$-0.606562\pi$
$653$	10277.8	−	10277.8i	0.615927	−	0.615927i	0.944484	+	0.328557i	$0.106562\pi$
$654$			7718.63i			0.461502i
$655$	108.653	+	238.439i	0.00648156	+	0.0142238i
$656$		−	7434.60i		−	0.442488i
$657$	−36333.0	+	36333.0i	−2.15751	+	2.15751i
$658$	6348.38	−	6348.38i	0.376118	−	0.376118i
$659$	−21002.0			−1.24146			−0.620731	−	0.784024i	$-0.713164\pi$
$659$	−21002.0			−1.24146			−0.620731	+	0.784024i	$0.713164\pi$
$660$	−64.5932	−	15254.7i	−0.00380953	−	0.899679i
$661$	−265.345			−0.0156138			−0.00780691	−	0.999970i	$-0.502485\pi$
$661$	−265.345			−0.0156138			−0.00780691	+	0.999970i	$0.502485\pi$
$662$	12361.7	−	12361.7i	0.725755	−	0.725755i
$663$	743.566	−	743.566i	0.0435561	−	0.0435561i
$664$			4739.15i			0.276980i
$665$	13447.0	−	35961.8i	0.784140	−	2.09705i
$666$		−	28440.3i		−	1.65472i
$667$	−2988.62	+	2988.62i	−0.173493	+	0.173493i
$668$	8615.96	+	8615.96i	0.499044	+	0.499044i
$669$		−	41162.0i		−	2.37879i
$670$	−3820.38	+	1740.89i	−0.220290	+	0.100382i
$671$	13717.8	−	5195.75i	0.789226	−	0.298927i
$672$	−5289.19	−	5289.19i	−0.303623	−	0.303623i
$673$	12840.2	+	12840.2i	0.735443	+	0.735443i	0.971693	−	0.236249i	$-0.0759181\pi$
$673$	12840.2	+	12840.2i	0.735443	+	0.735443i	−0.236249	+	0.971693i	$0.575918\pi$
$674$			13830.5i			0.790399i
$675$	38963.1	−	2721.78i	2.22176	−	0.155202i
$676$	−8763.79			−0.498623
$677$	15755.0	−	15755.0i	0.894408	−	0.894408i	−0.100527	−	0.994934i	$-0.532053\pi$
$677$	15755.0	−	15755.0i	0.894408	−	0.894408i	0.994934	+	0.100527i	$0.0320528\pi$
$678$	241.570	+	241.570i	0.0136835	+	0.0136835i
$679$	3326.07			0.187987
$680$	3721.14	−	1695.66i	0.209852	−	0.0956260i
$681$			18639.6i			1.04886i
$682$	21261.5	+	9580.00i	1.19376	+	0.537884i
$683$	3285.11	−	3285.11i	0.184043	−	0.184043i	−0.609072	−	0.793115i	$-0.708458\pi$
$683$	3285.11	−	3285.11i	0.184043	−	0.184043i	0.793115	+	0.609072i	$0.208458\pi$
$684$	−33196.3			−1.85569
$685$	−21788.1	−	8147.11i	−1.21530	−	0.454431i
$686$	3048.54			0.169670
$687$	42034.3	+	42034.3i	2.33436	+	2.33436i
$688$	971.591	+	971.591i	0.0538395	+	0.0538395i
$689$	915.505			0.0506211
$690$	9034.37	+	3378.18i	0.498453	+	0.186384i
$691$	−17160.3			−0.944728			−0.472364	−	0.881404i	$-0.656599\pi$
$691$	−17160.3			−0.944728			−0.472364	+	0.881404i	$0.656599\pi$
$692$	−3764.37	+	3764.37i	−0.206792	+	0.206792i
$693$	−22638.6	+	50243.3i	−1.24094	+	2.75409i
$694$		−	23268.7i		−	1.27272i
$695$	7781.93	−	3546.10i	0.424727	−	0.193541i
$696$	6852.55			0.373197
$697$	−15021.9	−	15021.9i	−0.816347	−	0.816347i
$698$	3767.33	−	3767.33i	0.204292	−	0.204292i
$699$	32337.5			1.74981
$700$	12469.9	−	871.092i	0.673312	−	0.0470345i
$701$			13280.6i			0.715549i	0.933808	+	0.357775i	$0.116464\pi$
$701$			13280.6i			0.715549i	−0.933808	+	0.357775i	$0.883536\pi$
$702$	−1087.04	−	1087.04i	−0.0584439	−	0.0584439i
$703$	−22859.6	−	22859.6i	−1.22641	−	1.22641i
$704$	−2183.53	+	827.031i	−0.116896	+	0.0442754i
$705$	17079.9	−	7783.03i	0.912435	−	0.415781i
$706$			9333.65i			0.497559i
$707$	−1140.08	−	1140.08i	−0.0606466	−	0.0606466i
$708$	−646.304	+	646.304i	−0.0343073	+	0.0343073i
$709$			5208.16i			0.275876i	0.990441	+	0.137938i	$0.0440475\pi$
$709$			5208.16i			0.275876i	−0.990441	+	0.137938i	$0.955952\pi$
$710$	−1478.27	+	3953.39i	−0.0781388	+	0.208969i
$711$		−	51479.0i		−	2.71535i
$712$	−629.902	+	629.902i	−0.0331553	+	0.0331553i
$713$	−10426.2	+	10426.2i	−0.547634	+	0.547634i
$714$	−21374.0			−1.12031
$715$	−4.24867	−	1003.39i	−0.000222226	−	0.0524820i
$716$	529.386			0.0276314
$717$	15962.1	−	15962.1i	0.831404	−	0.831404i
$718$	−2943.24	+	2943.24i	−0.152982	+	0.152982i
$719$		−	14747.4i		−	0.764929i	−0.923970	−	0.382464i	$-0.875076\pi$
$719$		−	14747.4i		−	0.764929i	0.923970	−	0.382464i	$-0.124924\pi$
$720$	−4481.71	−	9835.13i	−0.231977	−	0.509075i
$721$			16319.0i			0.842927i
$722$	−16982.2	+	16982.2i	−0.875362	+	0.875362i
$723$	−31725.2	−	31725.2i	−1.63191	−	1.63191i
$724$		−	13766.1i		−	0.706647i
$725$	−7513.58	+	8642.15i	−0.384893	+	0.442705i
$726$	16488.6	+	18644.0i	0.842907	+	0.953092i
$727$	−11296.2	−	11296.2i	−0.576274	−	0.576274i	0.357601	−	0.933875i	$-0.383595\pi$
$727$	−11296.2	−	11296.2i	−0.576274	−	0.576274i	−0.933875	+	0.357601i	$0.883595\pi$
$728$	−347.901	−	347.901i	−0.0177116	−	0.0177116i
$729$		−	929.225i		−	0.0472095i
$730$	−17304.4	+	7885.31i	−0.877347	+	0.399792i
$731$	3926.27			0.198657
$732$	10633.0	−	10633.0i	0.536894	−	0.536894i
$733$	−13560.7	−	13560.7i	−0.683323	−	0.683323i	0.277424	−	0.960747i	$-0.410519\pi$
$733$	−13560.7	−	13560.7i	−0.683323	−	0.683323i	−0.960747	+	0.277424i	$0.910519\pi$
$734$	−24374.1			−1.22570
$735$	−27614.5	−	10325.7i	−1.38582	−	0.518192i
$736$		−	1476.31i		−	0.0739368i
$737$	2813.95	−	6245.17i	0.140642	−	0.312135i
$738$	−39703.4	+	39703.4i	−1.98036	+	1.98036i
$739$	29879.6			1.48734			0.743668	−	0.668550i	$-0.233085\pi$
$739$	29879.6			1.48734			0.743668	+	0.668550i	$0.233085\pi$
$740$	3686.47	−	9858.85i	0.183132	−	0.489755i
$741$	−3159.27			−0.156625
$742$	−13158.2	−	13158.2i	−0.651015	−	0.651015i
$743$	−2883.92	−	2883.92i	−0.142397	−	0.142397i	0.632315	−	0.774712i	$-0.282105\pi$
$743$	−2883.92	−	2883.92i	−0.142397	−	0.142397i	−0.774712	+	0.632315i	$0.782105\pi$
$744$	23905.9			1.17800
$745$	17888.7	−	8151.60i	0.879721	−	0.400874i
$746$	−1271.76			−0.0624161
$747$	25308.8	−	25308.8i	1.23962	−	1.23962i
$748$	−2740.85	+	6082.94i	−0.133978	+	0.297345i
$749$			19345.9i			0.943769i
$750$	25056.6	+	7425.00i	1.21992	+	0.361497i
$751$	−13494.7			−0.655697			−0.327848	−	0.944730i	$-0.606324\pi$
$751$	−13494.7			−0.655697			−0.327848	+	0.944730i	$0.606324\pi$
$752$	−2031.43	−	2031.43i	−0.0985089	−	0.0985089i
$753$	−27803.6	+	27803.6i	−1.34558	+	1.34558i
$754$	450.732			0.0217701
$755$	3345.30	+	7341.29i	0.161256	+	0.353877i
$756$			31247.2i			1.50324i
$757$	28460.4	+	28460.4i	1.36646	+	1.36646i	0.865432	+	0.501027i	$0.167044\pi$
$757$	28460.4	+	28460.4i	1.36646	+	1.36646i	0.501027	+	0.865432i	$0.332956\pi$
$758$	−996.808	−	996.808i	−0.0477648	−	0.0477648i
$759$	−14716.7	+	5574.08i	−0.703797	+	0.266569i
$760$	−11507.5	−	4302.94i	−0.549238	−	0.205374i
$761$		−	23961.3i		−	1.14139i	−0.821163	−	0.570693i	$-0.806674\pi$
$761$		−	23961.3i		−	1.14139i	0.821163	−	0.570693i	$-0.193326\pi$
$762$	14673.6	+	14673.6i	0.697598	+	0.697598i
$763$	7296.97	−	7296.97i	0.346223	−	0.346223i
$764$			11441.1i			0.541784i
$765$	−28927.7	−	10816.8i	−1.36717	−	0.511218i
$766$		−	19327.8i		−	0.911671i
$767$	−42.5112	+	42.5112i	−0.00200129	+	0.00200129i
$768$	−1692.50	+	1692.50i	−0.0795219	+	0.0795219i
$769$	20530.1			0.962723			0.481362	−	0.876522i	$-0.340142\pi$
$769$	20530.1			0.962723			0.481362	+	0.876522i	$0.340142\pi$
$770$	−14360.3	+	14482.4i	−0.672089	+	0.677805i
$771$	53212.9			2.48562
$772$	−10863.8	+	10863.8i	−0.506472	+	0.506472i
$773$	15220.6	−	15220.6i	0.708209	−	0.708209i	−0.257949	−	0.966158i	$-0.583047\pi$
$773$	15220.6	−	15220.6i	0.708209	−	0.708209i	0.966158	+	0.257949i	$0.0830468\pi$
$774$		−	10377.3i		−	0.481917i
$775$	−26212.0	+	30149.1i	−1.21492	+	1.39740i
$776$		−	1064.32i		−	0.0492355i
$777$	−38901.7	+	38901.7i	−1.79613	+	1.79613i
$778$	4547.05	+	4547.05i	0.209537	+	0.209537i
$779$			63825.1i			2.93552i
$780$	−426.522	−	936.005i	−0.0195794	−	0.0429671i
$781$	−2439.18	−	6439.94i	−0.111755	−	0.295056i
$782$	−2982.94	−	2982.94i	−0.136406	−	0.136406i
$783$	−20241.6	−	20241.6i	−0.923850	−	0.923850i
$784$			4512.49i			0.205562i
$785$	8328.22	+	3114.13i	0.378658	+	0.141590i
$786$	−438.255			−0.0198881
$787$	−21119.1	+	21119.1i	−0.956564	+	0.956564i	−0.999095	−	0.0425316i	$-0.986458\pi$
$787$	−21119.1	+	21119.1i	−0.956564	+	0.956564i	0.0425316	+	0.999095i	$0.486458\pi$
$788$	4864.26	+	4864.26i	0.219901	+	0.219901i
$789$	55959.9			2.52500
$790$	6672.77	−	17845.2i	0.300514	−	0.803675i
$791$		−	456.746i		−	0.0205310i
$792$	16077.5	+	7244.18i	0.721323	+	0.325014i
$793$	699.393	−	699.393i	0.0313192	−	0.0313192i
$794$	−6519.45			−0.291394
$795$	−16131.8	−	35401.3i	−0.719668	−	1.57932i
$796$	−4442.20			−0.197801
$797$	428.686	+	428.686i	0.0190525	+	0.0190525i	0.716569	−	0.697516i	$-0.245712\pi$
$797$	428.686	+	428.686i	0.0190525	+	0.0190525i	−0.697516	+	0.716569i	$0.745712\pi$
$798$	45407.0	+	45407.0i	2.01428	+	2.01428i
$799$	−8209.16			−0.363478
$800$	−278.742	−	3990.28i	−0.0123188	−	0.176347i
$801$	6727.81			0.296773
$802$	19487.9	−	19487.9i	0.858030	−	0.858030i
$803$	12745.7	−	28287.4i	0.560133	−	1.24314i
$804$		−	7021.91i		−	0.308015i
$805$	−5347.20	−	11734.5i	−0.234117	−	0.513771i
$806$	1572.43			0.0687177
$807$	42178.6	+	42178.6i	1.83985	+	1.83985i
$808$	−364.817	+	364.817i	−0.0158839	+	0.0158839i
$809$	10410.8			0.452442			0.226221	−	0.974076i	$-0.427363\pi$
$809$	10410.8			0.452442			0.226221	+	0.974076i	$0.427363\pi$
$810$	−10104.1	+	27021.7i	−0.438298	+	1.17216i
$811$		−	621.358i		−	0.0269036i	−0.999910	−	0.0134518i	$-0.995718\pi$
$811$		−	621.358i		−	0.0269036i	0.999910	−	0.0134518i	$-0.00428197\pi$
$812$	−6478.20	−	6478.20i	−0.279976	−	0.279976i
$813$	−47758.8	−	47758.8i	−2.06024	−	2.06024i
$814$	6082.77	+	16059.7i	0.261918	+	0.691515i
$815$	9362.05	−	25037.2i	0.402378	−	1.07609i
$816$			6839.51i			0.293420i
$817$	−8340.99	−	8340.99i	−0.357178	−	0.357178i
$818$	238.731	−	238.731i	0.0102042	−	0.0102042i
$819$			3715.83i			0.158537i
$820$	−18909.6	+	8616.79i	−0.805307	+	0.366965i
$821$		−	4269.72i		−	0.181504i	−0.995874	−	0.0907518i	$-0.971073\pi$
$821$		−	4269.72i		−	0.181504i	0.995874	−	0.0907518i	$-0.0289270\pi$
$822$	27510.6	−	27510.6i	1.16733	−	1.16733i
$823$	9436.72	−	9436.72i	0.399688	−	0.399688i	−0.478435	−	0.878123i	$-0.658796\pi$
$823$	9436.72	−	9436.72i	0.399688	−	0.399688i	0.878123	+	0.478435i	$0.158796\pi$
$824$	5221.94			0.220771
$825$	−38724.9	+	17844.7i	−1.63421	+	0.753057i
$826$	1221.99			0.0514753
$827$	26058.8	−	26058.8i	1.09571	−	1.09571i	0.100804	−	0.994906i	$-0.467858\pi$
$827$	26058.8	−	26058.8i	1.09571	−	1.09571i	0.994906	−	0.100804i	$-0.0321416\pi$
$828$	−7884.02	+	7884.02i	−0.330904	+	0.330904i
$829$		−	4867.34i		−	0.203920i	−0.994789	−	0.101960i	$-0.967489\pi$
$829$		−	4867.34i		−	0.203920i	0.994789	−	0.101960i	$-0.0325114\pi$
$830$	12053.8	−	5492.74i	0.504091	−	0.229706i
$831$			61635.6i			2.57294i
$832$	−111.325	+	111.325i	−0.00463884	+	0.00463884i
$833$	9117.65	+	9117.65i	0.379241	+	0.379241i
$834$			14303.3i			0.593864i
$835$	11928.3	−	31900.4i	0.494368	−	1.32211i
$836$	18745.3	−	7099.96i	0.775503	−	0.293729i
$837$	−70615.0	−	70615.0i	−2.91614	−	2.91614i
$838$	−22012.2	−	22012.2i	−0.907396	−	0.907396i
$839$			16964.5i			0.698070i	0.937110	+	0.349035i	$0.113491\pi$
$839$			16964.5i			0.698070i	−0.937110	+	0.349035i	$0.886509\pi$
$840$	−7322.61	+	19583.1i	−0.300779	+	0.804382i
$841$	−15996.0			−0.655869
$842$	−12318.6	+	12318.6i	−0.504190	+	0.504190i
$843$	−2639.44	−	2639.44i	−0.107838	−	0.107838i
$844$	−7736.73			−0.315532
$845$	10157.3	+	22290.4i	0.413519	+	0.907470i
$846$			21697.1i			0.881753i
$847$	2037.65	−	33213.4i	0.0826618	−	1.34737i
$848$	−4210.52	+	4210.52i	−0.170507	+	0.170507i
$849$	−79206.7			−3.20185
$850$	−8625.70	−	7499.28i	−0.348070	−	0.302616i
$851$	−10858.2			−0.437384
$852$	−4991.73	−	4991.73i	−0.200721	−	0.200721i
$853$	20973.0	+	20973.0i	0.841855	+	0.841855i	0.989100	−	0.147245i	$-0.0470406\pi$
$853$	20973.0	+	20973.0i	0.841855	+	0.841855i	−0.147245	+	0.989100i	$0.547041\pi$
$854$	−20104.2			−0.805564
$855$	38474.9	+	84433.4i	1.53896	+	3.37726i
$856$	6190.53			0.247182
$857$	−9933.30	+	9933.30i	−0.395934	+	0.395934i	−0.876796	−	0.480862i	$-0.840324\pi$
$857$	−9933.30	+	9933.30i	−0.395934	+	0.395934i	0.480862	+	0.876796i	$0.340324\pi$
$858$	1530.08	+	689.425i	0.0608814	+	0.0274319i
$859$			27193.4i			1.08012i	0.841625	+	0.540062i	$0.181599\pi$
$859$			27193.4i			1.08012i	−0.841625	+	0.540062i	$0.818401\pi$
$860$	1345.12	−	3597.29i	0.0533350	−	0.142636i
$861$	108615.			4.29919
$862$	4410.72	+	4410.72i	0.174280	+	0.174280i
$863$	27588.7	−	27588.7i	1.08822	−	1.08822i	0.0925030	−	0.995712i	$-0.470513\pi$
$863$	27588.7	−	27588.7i	1.08822	−	1.08822i	0.995712	−	0.0925030i	$-0.0294868\pi$
$864$	9998.86			0.393713
$865$	13937.5	+	5211.58i	0.547848	+	0.204854i
$866$			7860.87i			0.308456i
$867$	−18662.0	−	18662.0i	−0.731020	−	0.731020i
$868$	−22599.9	−	22599.9i	−0.883747	−	0.883747i
$869$	11010.2	+	29069.2i	0.429800	+	1.13476i
$870$	−7942.19	−	17429.2i	−0.309501	−	0.679201i
$871$		−	461.872i		−	0.0179678i
$872$	−2334.97	−	2334.97i	−0.0906791	−	0.0906791i
$873$	−5683.83	+	5683.83i	−0.220353	+	0.220353i
$874$			12673.9i			0.490506i
$875$	−16668.4	−	30707.1i	−0.643993	−	1.18639i
$876$		−	31805.6i		−	1.22673i
$877$	−17091.2	+	17091.2i	−0.658071	+	0.658071i	−0.954923	−	0.296852i	$-0.904063\pi$
$877$	−17091.2	+	17091.2i	−0.658071	+	0.658071i	0.296852	+	0.954923i	$0.404063\pi$
$878$	17261.8	−	17261.8i	0.663507	−	0.663507i
$879$	−33902.1			−1.30090
$880$	4634.26	+	4595.18i	0.177524	+	0.176027i
$881$	−3221.66			−0.123201			−0.0616007	−	0.998101i	$-0.519621\pi$
$881$	−3221.66			−0.123201			−0.0616007	+	0.998101i	$0.519621\pi$
$882$	24098.3	−	24098.3i	0.919992	−	0.919992i
$883$	−30291.2	+	30291.2i	−1.15445	+	1.15445i	−0.168801	+	0.985650i	$0.553990\pi$
$883$	−30291.2	+	30291.2i	−1.15445	+	1.15445i	−0.985650	+	0.168801i	$0.946010\pi$
$884$			449.874i			0.0171164i
$885$	2392.92	+	894.774i	0.0908896	+	0.0339859i
$886$			30862.0i			1.17024i
$887$	−23297.7	+	23297.7i	−0.881915	+	0.881915i	−0.993729	−	0.111814i	$-0.964334\pi$
$887$	−23297.7	+	23297.7i	−0.881915	+	0.881915i	0.111814	+	0.993729i	$0.464334\pi$
$888$	12448.2	+	12448.2i	0.470423	+	0.470423i
$889$		−	27744.1i		−	1.04669i
$890$	2332.20	+	872.067i	0.0878375	+	0.0328447i
$891$	−16672.0	−	44017.4i	−0.626861	−	1.65504i
$892$	12452.0	+	12452.0i	0.467402	+	0.467402i
$893$	17439.6	+	17439.6i	0.653520	+	0.653520i
$894$			32879.7i			1.23005i
$895$	−613.565	−	1346.47i	−0.0229153	−	0.0502878i
$896$	3200.08			0.119316
$897$	−750.319	+	750.319i	−0.0279291	+	0.0279291i
$898$	−3066.65	−	3066.65i	−0.113959	−	0.113959i
$899$	29280.0			1.08625
$900$	−19820.9	+	22798.1i	−0.734108	+	0.844374i
$901$			17015.0i			0.629137i
$902$	13928.1	−	30911.5i	0.514140	−	1.14106i
$903$	−14194.4	+	14194.4i	−0.523102	+	0.523102i
$904$	−146.155			−0.00537726
$905$	−35013.5	+	15955.1i	−1.28606	+	0.586038i
$906$	−13493.4			−0.494799
$907$	−19467.5	−	19467.5i	−0.712688	−	0.712688i	0.254409	−	0.967097i	$-0.418119\pi$
$907$	−19467.5	−	19467.5i	−0.712688	−	0.712688i	−0.967097	+	0.254409i	$0.918119\pi$
$908$	−5638.69	−	5638.69i	−0.206086	−	0.206086i
$909$	3896.50			0.142177
$910$	−481.650	+	1288.09i	−0.0175457	+	0.0469229i
$911$	−33677.9			−1.22481			−0.612403	−	0.790545i	$-0.709797\pi$
$911$	−33677.9			−1.22481			−0.612403	+	0.790545i	$0.709797\pi$
$912$	14529.9	−	14529.9i	0.527558	−	0.527558i
$913$	−8878.40	+	19704.4i	−0.321831	+	0.714261i
$914$		−	15692.5i		−	0.567900i
$915$	−39368.3	−	14720.8i	−1.42238	−	0.531863i
$916$	−25431.7			−0.917343
$917$	414.313	+	414.313i	0.0149202	+	0.0149202i
$918$	20203.0	−	20203.0i	0.726361	−	0.726361i
$919$	18532.9			0.665228			0.332614	−	0.943063i	$-0.392069\pi$
$919$	18532.9			0.665228			0.332614	+	0.943063i	$0.392069\pi$
$920$	−3754.94	+	1711.06i	−0.134561	+	0.0613174i
$921$		−	18714.2i		−	0.669548i
$922$	−7505.97	−	7505.97i	−0.268108	−	0.268108i
$923$	−328.335	−	328.335i	−0.0117089	−	0.0117089i
$924$	−12082.5	−	31900.2i	−0.430178	−	1.13576i
$925$	−29348.3	+	2050.13i	−1.04320	+	0.0728735i
$926$			22403.9i			0.795072i
$927$	−27887.0	−	27887.0i	−0.988059	−	0.988059i
$928$	−2072.97	+	2072.97i	−0.0733283	+	0.0733283i
$929$		−	173.636i		−	0.00613219i	−0.999995	−	0.00306609i	$-0.999024\pi$
$929$		−	173.636i		−	0.00613219i	0.999995	−	0.00306609i	$-0.000975970\pi$
$930$	−27707.2	−	60803.7i	−0.976942	−	2.14391i
$931$		−	38739.2i		−	1.36372i
$932$	−9782.46	+	9782.46i	−0.343815	+	0.343815i
$933$	−5194.14	+	5194.14i	−0.182260	+	0.182260i
$934$	9944.14			0.348375
$935$	18648.4	−	78.9632i	0.652265	−	0.00276190i
$936$	1189.04			0.0415223
$937$	−19506.4	+	19506.4i	−0.680093	+	0.680093i	−0.960021	−	0.279928i	$-0.909689\pi$
$937$	−19506.4	+	19506.4i	−0.680093	+	0.680093i	0.279928	+	0.960021i	$0.409689\pi$
$938$	−6638.31	+	6638.31i	−0.231075	+	0.231075i
$939$		−	22463.0i		−	0.780674i
$940$	−2812.41	+	7521.32i	−0.0975859	+	0.260977i
$941$			15426.8i			0.534430i	0.963637	+	0.267215i	$0.0861034\pi$
$941$			15426.8i			0.534430i	−0.963637	+	0.267215i	$0.913897\pi$
$942$	−10515.6	+	10515.6i	−0.363712	+	0.363712i
$943$	15158.3	+	15158.3i	0.523459	+	0.523459i
$944$		−	391.029i		−	0.0134819i
$945$	79476.0	−	36215.9i	2.73582	−	1.24667i
$946$	2219.48	+	5859.86i	0.0762805	+	0.201396i
$947$	16506.8	+	16506.8i	0.566420	+	0.566420i	0.931124	−	0.364703i	$-0.118830\pi$
$947$	16506.8	+	16506.8i	0.566420	+	0.566420i	−0.364703	+	0.931124i	$0.618830\pi$
$948$	22532.2	+	22532.2i	0.771952	+	0.771952i
$949$		−	2092.04i		−	0.0715601i
$950$	2392.97	+	34256.0i	0.0817244	+	1.16991i
$951$	5120.57			0.174601
$952$	6465.87	−	6465.87i	0.220126	−	0.220126i
$953$	425.100	+	425.100i	0.0144495	+	0.0144495i	0.714295	−	0.699845i	$-0.246748\pi$
$953$	425.100	+	425.100i	0.0144495	+	0.0144495i	−0.699845	+	0.714295i	$0.746748\pi$
$954$	44971.4			1.52621
$955$	29099.9	−	13260.3i	0.986021	−	0.449313i
$956$			9657.45i			0.326720i
$957$	28491.5	+	12837.7i	0.962380	+	0.433629i
$958$	27195.7	−	27195.7i	0.917175	−	0.917175i
$959$	−52015.5			−1.75148
$960$	6266.43	+	2343.18i	0.210675	+	0.0787768i
$961$	72355.5			2.42877
$962$	818.793	+	818.793i	0.0274417	+	0.0274417i
$963$	−33059.7	−	33059.7i	−1.10626	−	1.10626i
$964$	19194.4			0.641298
$965$	40222.9	+	15040.4i	1.34178	+	0.501727i
$966$	21568.1			0.718367
$967$	−27286.1	+	27286.1i	−0.907407	+	0.907407i	−0.996062	−	0.0886555i	$-0.971743\pi$
$967$	−27286.1	+	27286.1i	−0.907407	+	0.907407i	0.0886555	+	0.996062i	$0.471743\pi$
$968$	−10628.0	−	652.033i	−0.352890	−	0.0216499i
$969$		−	58716.3i		−	1.94658i
$970$	−2707.05	+	1233.56i	−0.0896062	+	0.0408321i
$971$	34162.7			1.12908			0.564538	−	0.825407i	$-0.309054\pi$
$971$	34162.7			1.12908			0.564538	+	0.825407i	$0.309054\pi$
$972$	−10256.7	−	10256.7i	−0.338462	−	0.338462i
$973$	13521.9	−	13521.9i	0.445522	−	0.445522i
$974$	−20378.4			−0.670396
$975$	−1886.35	+	2169.68i	−0.0619605	+	0.0712671i
$976$			6433.19i			0.210985i
$977$	1413.02	+	1413.02i	0.0462707	+	0.0462707i	0.729864	−	0.683593i	$-0.239584\pi$
$977$	1413.02	+	1413.02i	0.0462707	+	0.0462707i	−0.683593	+	0.729864i	$0.739584\pi$
$978$	31613.2	+	31613.2i	1.03362	+	1.03362i
$979$	−3799.07	+	1438.93i	−0.124023	+	0.0469749i
$980$	11477.3	−	5230.03i	0.374112	−	0.170477i
$981$			24939.2i			0.811668i
$982$	−15596.5	−	15596.5i	−0.506826	−	0.506826i
$983$	2375.11	−	2375.11i	0.0770644	−	0.0770644i	−0.667524	−	0.744588i	$-0.732646\pi$
$983$	2375.11	−	2375.11i	0.0770644	−	0.0770644i	0.744588	+	0.667524i	$0.232646\pi$
$984$		−	34756.1i		−	1.12600i
$985$	6734.32	−	18009.8i	0.217841	−	0.582579i
$986$			8377.03i			0.270567i
$987$	29678.1	−	29678.1i	0.957107	−	0.957107i
$988$	955.716	−	955.716i	0.0307747	−	0.0307747i
$989$	−3961.92			−0.127383
$990$	−208.703	−	49288.5i	−0.00670002	−	1.58231i
$991$	20236.5			0.648672			0.324336	−	0.945942i	$-0.394859\pi$
$991$	20236.5			0.648672			0.324336	+	0.945942i	$0.394859\pi$
$992$	−7231.81	+	7231.81i	−0.231462	+	0.231462i
$993$	57789.7	−	57789.7i	1.84683	−	1.84683i
$994$			9438.07i			0.301164i
$995$	5148.57	+	11298.6i	0.164041	+	0.359988i
$996$			22155.1i			0.704831i
$997$	18718.0	−	18718.0i	0.594589	−	0.594589i	−0.344278	−	0.938868i	$-0.611876\pi$
$997$	18718.0	−	18718.0i	0.594589	−	0.594589i	0.938868	+	0.344278i	$0.111876\pi$
$998$	19806.2	+	19806.2i	0.628209	+	0.628209i
$999$		−	73541.0i		−	2.32906i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	110.4.f.a.87.1	yes	36
5.3	odd	4	inner	110.4.f.a.43.10	yes	36
11.10	odd	2	inner	110.4.f.a.87.10	yes	36
55.43	even	4	inner	110.4.f.a.43.1	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.4.f.a.43.1	✓	36	55.43	even	4	inner
110.4.f.a.43.10	yes	36	5.3	odd	4	inner
110.4.f.a.87.1	yes	36	1.1	even	1	trivial
110.4.f.a.87.10	yes	36	11.10	odd	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(-1.41421 + 1.41421i) q^{2} +(-6.61133 + 6.61133i) q^{3} -4.00000i q^{4} +(-10.1738 + 4.63605i) q^{5} -18.6997i q^{6} +(-17.6781 + 17.6781i) q^{7} +(5.65685 + 5.65685i) q^{8} -60.4193i q^{9} +(7.83162 - 20.9443i) q^{10} +(12.9224 + 34.1176i) q^{11} +(26.4453 + 26.4453i) q^{12} +(1.73946 + 1.73946i) q^{13} -50.0012i q^{14} +(36.6121 - 97.9130i) q^{15} -16.0000 q^{16} +(-32.3286 + 32.3286i) q^{17} +(85.4457 + 85.4457i) q^{18} +137.358 q^{19} +(18.5442 + 40.6954i) q^{20} -233.751i q^{21} +(-66.5246 - 29.9746i) q^{22} +(32.6221 - 32.6221i) q^{23} -74.7986 q^{24} +(82.0141 - 94.3329i) q^{25} -4.91994 q^{26} +(220.946 + 220.946i) q^{27} +(70.7124 + 70.7124i) q^{28} -91.6133 q^{29} +(86.6925 + 190.247i) q^{30} -319.604 q^{31} +(22.6274 - 22.6274i) q^{32} +(-310.997 - 140.129i) q^{33} -91.4390i q^{34} +(97.8976 - 261.811i) q^{35} -241.677 q^{36} +(-166.423 - 166.423i) q^{37} +(-194.254 + 194.254i) q^{38} -23.0003 q^{39} +(-83.7774 - 31.3265i) q^{40} +464.662i q^{41} +(330.574 + 330.574i) q^{42} +(-60.7244 - 60.7244i) q^{43} +(136.471 - 51.6895i) q^{44} +(280.107 + 614.696i) q^{45} +92.2694i q^{46} +(126.964 + 126.964i) q^{47} +(105.781 - 105.781i) q^{48} -282.031i q^{49} +(17.4214 + 249.392i) q^{50} -427.469i q^{51} +(6.95784 - 6.95784i) q^{52} +(263.158 - 263.158i) q^{53} -624.929 q^{54} +(-289.641 - 287.199i) q^{55} -200.005 q^{56} +(-908.119 + 908.119i) q^{57} +(129.561 - 129.561i) q^{58} +24.4393i q^{59} +(-391.652 - 146.449i) q^{60} -402.074i q^{61} +(451.988 - 451.988i) q^{62} +(1068.10 + 1068.10i) q^{63} +64.0000i q^{64} +(-25.7612 - 9.63277i) q^{65} +(637.988 - 241.644i) q^{66} +(-132.763 - 132.763i) q^{67} +(129.314 + 129.314i) q^{68} +431.351i q^{69} +(231.808 + 508.705i) q^{70} -188.757 q^{71} +(341.783 - 341.783i) q^{72} +(-601.348 - 601.348i) q^{73} +470.716 q^{74} +(81.4436 + 1165.89i) q^{75} -549.432i q^{76} +(-831.578 - 374.692i) q^{77} +(32.5273 - 32.5273i) q^{78} +852.029 q^{79} +(162.781 - 74.1768i) q^{80} -1290.17 q^{81} +(-657.132 - 657.132i) q^{82} +(418.886 + 418.886i) q^{83} -935.006 q^{84} +(179.029 - 478.782i) q^{85} +171.755 q^{86} +(605.686 - 605.686i) q^{87} +(-119.899 + 266.098i) q^{88} +111.352i q^{89} +(-1265.44 - 473.181i) q^{90} -61.5007 q^{91} +(-130.489 - 130.489i) q^{92} +(2113.00 - 2113.00i) q^{93} -359.110 q^{94} +(-1397.46 + 636.799i) q^{95} +299.194i q^{96} +(-94.0732 - 94.0732i) q^{97} +(398.852 + 398.852i) q^{98} +(2061.36 - 780.760i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 8 q^{3} - 32 q^{5} + 44 q^{11} + 32 q^{12} - 164 q^{15} - 576 q^{16} + 64 q^{20} - 312 q^{22} - 176 q^{23} + 880 q^{25} - 304 q^{26} + 364 q^{27} + 432 q^{31} + 832 q^{33} - 1808 q^{36} + 960 q^{37}+ \cdots - 4224 q^{97}+O(q^{100}) \) 36 * q - 8 * q^3 - 32 * q^5 + 44 * q^11 + 32 * q^12 - 164 * q^15 - 576 * q^16 + 64 * q^20 - 312 * q^22 - 176 * q^23 + 880 * q^25 - 304 * q^26 + 364 * q^27 + 432 * q^31 + 832 * q^33 - 1808 * q^36 + 960 * q^37 + 48 * q^38 - 400 * q^42 - 496 * q^45 + 2100 * q^47 + 128 * q^48 - 60 * q^53 - 1276 * q^55 + 64 * q^56 - 1344 * q^58 + 160 * q^60 + 1568 * q^66 + 1000 * q^67 + 3456 * q^70 - 1312 * q^71 + 3196 * q^75 - 4088 * q^77 + 5312 * q^78 + 512 * q^80 - 10436 * q^81 - 1280 * q^82 - 1472 * q^86 - 1248 * q^88 - 2096 * q^91 + 704 * q^92 + 11372 * q^93 - 4224 * q^97

Introduction

L-functions

Modular forms

Varieties

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