LMFDB - Embedded newform 175.4.x.a.3.37

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,4,Mod(3,175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([21, 10]))

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

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

chi := DirichletCharacter("175.3");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	175.x (of order $60$, degree $16$, 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:	$10.3253342510$
Analytic rank:	$0$
Dimension:	$928$
Relative dimension:	$58$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			3.37
Character	$\chi$	$=$	175.3
Dual form			175.4.x.a.117.37

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.871966 - 1.34271i) q^{2} +(2.34287 - 6.10339i) q^{3} +(2.21135 + 4.96677i) q^{4} +(-0.438918 + 11.1717i) q^{5} +(-6.15218 - 8.46775i) q^{6} +(-11.5650 + 14.4655i) q^{7} +(21.2474 + 3.36526i) q^{8} +(-11.6974 - 10.5324i) q^{9} +(14.6177 + 10.3307i) q^{10} +(38.8777 + 43.1780i) q^{11} +(35.4951 - 1.86022i) q^{12} +(10.5262 + 5.36337i) q^{13} +(9.33865 + 28.1419i) q^{14} +(67.1571 + 28.8528i) q^{15} +(-6.05787 + 6.72794i) q^{16} +(13.0862 - 16.1601i) q^{17} +(-24.3417 + 6.52235i) q^{18} +(-75.3928 - 33.5671i) q^{19} +(-56.4580 + 22.5246i) q^{20} +(61.1932 + 104.477i) q^{21} +(91.8755 - 14.5516i) q^{22} +(-14.1926 - 9.21678i) q^{23} +(70.3196 - 121.797i) q^{24} +(-124.615 - 9.80694i) q^{25} +(16.3799 - 9.45696i) q^{26} +(65.5876 - 33.4185i) q^{27} +(-97.4211 - 25.4526i) q^{28} +(93.2324 - 128.323i) q^{29} +(97.2996 - 65.0138i) q^{30} +(6.51795 - 0.685064i) q^{31} +(48.2937 + 180.235i) q^{32} +(354.618 - 136.125i) q^{33} +(-10.2876 - 31.6620i) q^{34} +(-156.528 - 135.550i) q^{35} +(26.4450 - 81.3893i) q^{36} +(-13.1233 - 250.407i) q^{37} +(-110.811 + 71.9613i) q^{38} +(57.3963 - 51.6798i) q^{39} +(-46.9217 + 235.893i) q^{40} +(-262.447 + 85.2743i) q^{41} +(193.640 + 8.93538i) q^{42} +(313.362 + 313.362i) q^{43} +(-128.483 + 288.578i) q^{44} +(122.799 - 126.058i) q^{45} +(-24.7509 + 11.0198i) q^{46} +(254.098 - 205.765i) q^{47} +(26.8705 + 52.7363i) q^{48} +(-75.5007 - 334.587i) q^{49} +(-121.828 + 158.770i) q^{50} +(-67.9721 - 117.731i) q^{51} +(-3.36151 + 64.1415i) q^{52} +(446.643 + 171.450i) q^{53} +(12.3187 - 117.205i) q^{54} +(-499.437 + 415.379i) q^{55} +(-294.407 + 268.435i) q^{56} +(-381.509 + 381.509i) q^{57} +(-91.0056 - 237.078i) q^{58} +(-550.672 - 117.049i) q^{59} +(5.20240 + 397.357i) q^{60} +(-9.03578 - 42.5100i) q^{61} +(4.76358 - 9.34906i) q^{62} +(287.638 - 47.4015i) q^{63} +(215.231 + 69.9329i) q^{64} +(-64.5382 + 115.242i) q^{65} +(126.438 - 594.845i) q^{66} +(133.726 + 108.289i) q^{67} +(109.202 + 29.2605i) q^{68} +(-89.5051 + 65.0293i) q^{69} +(-318.492 + 91.9768i) q^{70} +(-212.013 - 154.036i) q^{71} +(-213.096 - 263.152i) q^{72} +(609.595 + 31.9475i) q^{73} +(-347.666 - 200.725i) q^{74} +(-351.812 + 737.596i) q^{75} -448.687i q^{76} +(-1074.21 + 63.0298i) q^{77} +(-19.3434 - 122.130i) q^{78} +(258.305 + 27.1490i) q^{79} +(-72.5038 - 70.6298i) q^{80} +(-94.7269 - 901.266i) q^{81} +(-114.346 + 426.747i) q^{82} +(200.723 - 1267.31i) q^{83} +(-383.592 + 534.967i) q^{84} +(174.792 + 153.288i) q^{85} +(693.995 - 147.513i) q^{86} +(-564.777 - 869.680i) q^{87} +(680.745 + 1048.26i) q^{88} +(-908.236 + 193.051i) q^{89} +(-62.1818 - 274.802i) q^{90} +(-199.319 + 90.2392i) q^{91} +(14.3929 - 90.8729i) q^{92} +(11.0895 - 41.3866i) q^{93} +(-54.7172 - 520.600i) q^{94} +(408.093 - 827.535i) q^{95} +(1213.19 + 127.511i) q^{96} +(160.176 + 1011.31i) q^{97} +(-515.087 - 190.373i) q^{98} -914.548i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 928 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 24 q^{7} + 84 q^{8} - 10 q^{9} - 96 q^{10} - 6 q^{11} - 72 q^{12} - 20 q^{14} - 368 q^{15} - 1670 q^{16} + 120 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} - 880 q^{22}+ \cdots - 19478 q^{98}+O(q^{100}) $ 928 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 24 * q^7 + 84 * q^8 - 10 * q^9 - 96 * q^10 - 6 * q^11 - 72 * q^12 - 20 * q^14 - 368 * q^15 - 1670 * q^16 + 120 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 - 880 * q^22 + 296 * q^23 + 32 * q^25 - 48 * q^26 + 226 * q^28 - 200 * q^29 - 38 * q^30 - 18 * q^31 - 964 * q^32 - 1092 * q^33 + 288 * q^35 + 7400 * q^36 - 392 * q^37 + 5424 * q^38 + 2430 * q^39 + 2172 * q^40 - 2098 * q^42 + 1560 * q^43 - 10 * q^44 - 4224 * q^45 - 6 * q^46 + 96 * q^47 + 6232 * q^50 - 16 * q^51 - 8928 * q^52 - 2384 * q^53 - 30 * q^54 + 244 * q^56 + 1556 * q^57 + 640 * q^58 + 4890 * q^59 + 3676 * q^60 - 18 * q^61 + 224 * q^63 - 9700 * q^64 - 1116 * q^65 - 2610 * q^66 - 2404 * q^67 - 13614 * q^68 - 1700 * q^70 - 24 * q^71 - 518 * q^72 - 4200 * q^73 - 16104 * q^75 - 722 * q^77 - 356 * q^78 - 10 * q^79 + 6414 * q^80 - 6810 * q^81 + 1692 * q^82 + 20620 * q^84 + 2712 * q^85 - 6 * q^86 + 9102 * q^87 + 1650 * q^88 + 20370 * q^89 - 12 * q^91 + 1612 * q^92 - 4604 * q^93 - 30 * q^94 + 1652 * q^95 - 2610 * q^96 - 19478 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{20}\right)$

Coefficient data

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

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

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

$2$	0.871966	−	1.34271i	0.308286	−	0.474719i	−0.650238	−	0.759731i	$-0.725331\pi$
$2$	0.871966	−	1.34271i	0.308286	−	0.474719i	0.958524	+	0.285011i	$0.0919974\pi$
$3$	2.34287	−	6.10339i	0.450886	−	1.17460i	−0.500265	−	0.865872i	$-0.666764\pi$
$3$	2.34287	−	6.10339i	0.450886	−	1.17460i	0.951151	−	0.308726i	$-0.0999026\pi$
$4$	2.21135	+	4.96677i	0.276419	+	0.620846i
$5$	−0.438918	+	11.1717i	−0.0392580	+	0.999229i
$5$	−0.438918	+	11.1717i	−0.0392580	+	0.999229i
$6$	−6.15218	−	8.46775i	−0.418603	−	0.576157i
$7$	−11.5650	+	14.4655i	−0.624452	+	0.781063i
$7$	−11.5650	+	14.4655i	−0.624452	+	0.781063i
$8$	21.2474	+	3.36526i	0.939013	+	0.148725i
$9$	−11.6974	−	10.5324i	−0.433238	−	0.390089i
$10$	14.6177	+	10.3307i	0.462251	+	0.326685i
$11$	38.8777	+	43.1780i	1.06564	+	1.18351i	0.982362	+	0.186988i	$0.0598727\pi$
$11$	38.8777	+	43.1780i	1.06564	+	1.18351i	0.0832792	+	0.996526i	$0.473461\pi$
$12$	35.4951	−	1.86022i	0.853878	−	0.0447499i
$13$	10.5262	+	5.36337i	0.224573	+	0.114425i	0.562657	−	0.826690i	$-0.309779\pi$
$13$	10.5262	+	5.36337i	0.224573	+	0.114425i	−0.338085	+	0.941116i	$0.609779\pi$
$14$	9.33865	+	28.1419i	0.178276	+	0.537231i
$15$	67.1571	+	28.8528i	1.15599	+	0.496651i
$16$	−6.05787	+	6.72794i	−0.0946542	+	0.105124i
$17$	13.0862	−	16.1601i	0.186698	−	0.230553i	−0.675200	−	0.737635i	$-0.735943\pi$
$17$	13.0862	−	16.1601i	0.186698	−	0.230553i	0.861898	+	0.507082i	$0.169276\pi$
$18$	−24.3417	+	6.52235i	−0.318745	+	0.0854073i
$19$	−75.3928	−	33.5671i	−0.910332	−	0.405306i	−0.102510	−	0.994732i	$-0.532687\pi$
$19$	−75.3928	−	33.5671i	−0.910332	−	0.405306i	−0.807822	+	0.589426i	$0.799354\pi$
$20$	−56.4580	+	22.5246i	−0.631219	+	0.251832i
$21$	61.1932	+	104.477i	0.635878	+	1.08565i
$22$	91.8755	−	14.5516i	0.890360	−	0.141019i
$23$	−14.1926	−	9.21678i	−0.128668	−	0.0835579i	0.478700	−	0.877978i	$-0.341108\pi$
$23$	−14.1926	−	9.21678i	−0.128668	−	0.0835579i	−0.607368	+	0.794420i	$0.707775\pi$
$24$	70.3196	−	121.797i	0.598080	−	1.03591i
$25$	−124.615	−	9.80694i	−0.996918	−	0.0784555i
$26$	16.3799	−	9.45696i	0.123553	−	0.0713331i
$27$	65.5876	−	33.4185i	0.467494	−	0.238200i
$28$	−97.4211	−	25.4526i	−0.657530	−	0.171789i
$29$	93.2324	−	128.323i	0.596994	−	0.821692i	−0.398435	−	0.917197i	$-0.630447\pi$
$29$	93.2324	−	128.323i	0.596994	−	0.821692i	0.995429	+	0.0955048i	$0.0304465\pi$
$30$	97.2996	−	65.0138i	0.592146	−	0.395661i
$31$	6.51795	−	0.685064i	0.0377631	−	0.00396907i	−0.0856280	−	0.996327i	$-0.527290\pi$
$31$	6.51795	−	0.685064i	0.0377631	−	0.00396907i	0.123391	+	0.992358i	$0.460623\pi$
$32$	48.2937	+	180.235i	0.266788	+	0.995666i
$33$	354.618	−	136.125i	1.87064	−	0.718070i
$34$	−10.2876	−	31.6620i	−0.0518914	−	0.159705i
$35$	−156.528	−	135.550i	−0.755946	−	0.654634i
$36$	26.4450	−	81.3893i	0.122431	−	0.376802i
$37$	−13.1233	−	250.407i	−0.0583095	−	1.11261i	−0.858483	−	0.512842i	$-0.828593\pi$
$37$	−13.1233	−	250.407i	−0.0583095	−	1.11261i	0.800173	−	0.599769i	$-0.204741\pi$
$38$	−110.811	+	71.9613i	−0.473049	+	0.307202i
$39$	57.3963	−	51.6798i	0.235661	−	0.212190i
$40$	−46.9217	+	235.893i	−0.185474	+	0.932451i
$41$	−262.447	+	85.2743i	−0.999693	+	0.324820i	−0.762743	−	0.646702i	$-0.776148\pi$
$41$	−262.447	+	85.2743i	−0.999693	+	0.324820i	−0.236950	+	0.971522i	$0.576148\pi$
$42$	193.640	+	8.93538i	0.711412	+	0.0328276i
$43$	313.362	+	313.362i	1.11133	+	1.11133i	0.992971	+	0.118360i	$0.0377638\pi$
$43$	313.362	+	313.362i	1.11133	+	1.11133i	0.118360	+	0.992971i	$0.462236\pi$
$44$	−128.483	+	288.578i	−0.440218	+	0.988745i
$45$	122.799	−	126.058i	0.406797	−	0.417590i
$46$	−24.7509	+	11.0198i	−0.0793331	+	0.0353214i
$47$	254.098	−	205.765i	0.788596	−	0.638593i	−0.148006	−	0.988986i	$-0.547286\pi$
$47$	254.098	−	205.765i	0.788596	−	0.638593i	0.936603	+	0.350394i	$0.113952\pi$
$48$	26.8705	+	52.7363i	0.0808004	+	0.158580i
$49$	−75.5007	−	334.587i	−0.220119	−	0.975473i
$50$	−121.828	+	158.770i	−0.344581	+	0.449069i
$51$	−67.9721	−	117.731i	−0.186627	−	0.323248i
$52$	−3.36151	+	64.1415i	−0.00896458	+	0.171054i
$53$	446.643	+	171.450i	1.15757	+	0.444349i	0.859971	−	0.510343i	$-0.170482\pi$
$53$	446.643	+	171.450i	1.15757	+	0.444349i	0.297597	+	0.954692i	$0.403815\pi$
$54$	12.3187	−	117.205i	0.0310438	−	0.295362i
$55$	−499.437	+	415.379i	−1.22444	+	1.01836i
$56$	−294.407	+	268.435i	−0.702533	+	0.640557i
$57$	−381.509	+	381.509i	−0.886527	+	0.886527i
$58$	−91.0056	−	237.078i	−0.206028	−	0.536721i
$59$	−550.672	−	117.049i	−1.21511	−	0.258279i	−0.444611	−	0.895724i	$-0.646658\pi$
$59$	−550.672	−	117.049i	−1.21511	−	0.258279i	−0.770496	+	0.637445i	$0.779991\pi$
$60$	5.20240	+	397.357i	0.0111938	+	0.854977i
$61$	−9.03578	−	42.5100i	−0.0189658	−	0.0892271i	0.967647	−	0.252309i	$-0.0811899\pi$
$61$	−9.03578	−	42.5100i	−0.0189658	−	0.0892271i	−0.986613	+	0.163082i	$0.947857\pi$
$62$	4.76358	−	9.34906i	0.00975767	−	0.0191505i
$63$	287.638	−	47.4015i	0.575221	−	0.0947941i
$64$	215.231	+	69.9329i	0.420374	+	0.136588i
$65$	−64.5382	+	115.242i	−0.123153	+	0.219907i
$66$	126.438	−	594.845i	0.235810	−	1.10940i
$67$	133.726	+	108.289i	0.243840	+	0.197458i	0.743448	−	0.668794i	$-0.233189\pi$
$67$	133.726	+	108.289i	0.243840	+	0.197458i	−0.499608	+	0.866252i	$0.666523\pi$
$68$	109.202	+	29.2605i	0.194745	+	0.0521817i
$69$	−89.5051	+	65.0293i	−0.156162	+	0.113458i
$70$	−318.492	+	91.9768i	−0.543815	+	0.157048i
$71$	−212.013	−	154.036i	−0.354384	−	0.257475i	0.396322	−	0.918112i	$-0.370286\pi$
$71$	−212.013	−	154.036i	−0.354384	−	0.257475i	−0.750706	+	0.660637i	$0.770286\pi$
$72$	−213.096	−	263.152i	−0.348800	−	0.430733i
$73$	609.595	+	31.9475i	0.977365	+	0.0512216i	0.534324	−	0.845280i	$-0.320566\pi$
$73$	609.595	+	31.9475i	0.977365	+	0.0512216i	0.443041	+	0.896501i	$0.353900\pi$
$74$	−347.666	−	200.725i	−0.546154	−	0.315322i
$75$	−351.812	+	737.596i	−0.541650	+	1.13560i
$76$		−	448.687i		−	0.677210i
$77$	−1074.21	+	63.0298i	−1.58984	+	0.0932846i
$78$	−19.3434	−	122.130i	−0.0280796	−	0.177288i
$79$	258.305	+	27.1490i	0.367868	+	0.0386645i	0.286659	−	0.958033i	$-0.407455\pi$
$79$	258.305	+	27.1490i	0.367868	+	0.0386645i	0.0812090	+	0.996697i	$0.474122\pi$
$80$	−72.5038	−	70.6298i	−0.101327	−	0.0987082i
$81$	−94.7269	−	901.266i	−0.129941	−	1.23630i
$82$	−114.346	+	426.747i	−0.153993	+	0.574711i
$83$	200.723	−	1267.31i	0.265448	−	1.67597i	−0.390066	−	0.920787i	$-0.627548\pi$
$83$	200.723	−	1267.31i	0.265448	−	1.67597i	0.655513	−	0.755184i	$-0.272452\pi$
$84$	−383.592	+	534.967i	−0.498254	+	0.694877i
$85$	174.792	+	153.288i	0.223046	+	0.195605i
$86$	693.995	−	147.513i	0.870179	−	0.184962i
$87$	−564.777	−	869.680i	−0.695982	−	1.07172i
$88$	680.745	+	1048.26i	0.824633	+	1.26982i
$89$	−908.236	+	193.051i	−1.08172	+	0.229926i	−0.714095	−	0.700049i	$-0.753161\pi$
$89$	−908.236	+	193.051i	−1.08172	+	0.229926i	−0.367622	+	0.929975i	$0.619828\pi$
$90$	−62.1818	−	274.802i	−0.0728282	−	0.321852i
$91$	−199.319	+	90.2392i	−0.229608	+	0.103952i
$92$	14.3929	−	90.8729i	0.0163104	−	0.102980i
$93$	11.0895	−	41.3866i	0.0123648	−	0.0461461i
$94$	−54.7172	−	520.600i	−0.0600388	−	0.571231i
$95$	408.093	−	827.535i	0.440731	−	0.893718i
$96$	1213.19	+	127.511i	1.28980	+	0.135563i
$97$	160.176	+	1011.31i	0.167664	+	1.05859i	0.917724	+	0.397219i	$0.130025\pi$
$97$	160.176	+	1011.31i	0.167664	+	1.05859i	−0.750060	+	0.661370i	$0.769975\pi$
$98$	−515.087	−	190.373i	−0.530936	−	0.196230i
$99$		−	914.548i		−	0.928439i
$100$	−226.858	−	640.619i	−0.226858	−	0.640619i
$101$	1542.76	+	890.715i	1.51991	+	0.877519i	0.999725	+	0.0234640i	$0.00746950\pi$
$101$	1542.76	+	890.715i	1.51991	+	0.877519i	0.520183	+	0.854055i	$0.325864\pi$
$102$	−217.348	−	11.3907i	−0.210987	−	0.0110574i
$103$	−825.203	−	1019.04i	−0.789414	−	0.974846i	0.210582	−	0.977576i	$-0.432464\pi$
$103$	−825.203	−	1019.04i	−0.789414	−	0.974846i	−0.999996	+	0.00273068i	$0.999131\pi$
$104$	205.606	+	149.381i	0.193859	+	0.140847i
$105$	−1194.04	+	637.776i	−1.10978	+	0.592768i
$106$	619.665	−	450.213i	0.567803	−	0.412533i
$107$	−1851.88	−	496.211i	−1.67316	−	0.448323i	−0.707202	−	0.707012i	$-0.750043\pi$
$107$	−1851.88	−	496.211i	−1.67316	−	0.448323i	−0.965961	+	0.258689i	$0.916710\pi$
$108$	311.019	+	251.858i	0.277110	+	0.224399i
$109$	−71.1371	+	334.674i	−0.0625110	+	0.294091i	−0.998287	−	0.0585034i	$-0.981367\pi$
$109$	−71.1371	+	334.674i	−0.0625110	+	0.294091i	0.935776	+	0.352594i	$0.114700\pi$
$110$	122.241	+	1032.79i	0.105957	+	0.895210i
$111$	−1559.08	−	506.575i	−1.33316	−	0.433171i
$112$	−27.2636	−	165.439i	−0.0230015	−	0.139576i
$113$	−941.369	+	1847.54i	−0.783686	+	1.53807i	0.0581311	+	0.998309i	$0.481486\pi$
$113$	−941.369	+	1847.54i	−0.783686	+	1.53807i	−0.841818	+	0.539762i	$0.818514\pi$
$114$	179.593	+	844.918i	0.147547	+	0.694156i
$115$	109.197	−	154.510i	0.0885447	−	0.125288i
$116$	843.523	+	179.296i	0.675165	+	0.143511i
$117$	−66.6403	−	173.604i	−0.0526573	−	0.137177i
$118$	−637.329	+	637.329i	−0.497211	+	0.497211i
$119$	82.4217	+	376.190i	0.0634923	+	0.289792i
$120$	1329.82	+	839.050i	1.01163	+	0.638287i
$121$	−213.741	+	2033.61i	−0.160587	+	1.52788i
$122$	−64.9575	−	24.9348i	−0.0482047	−	0.0185041i
$123$	−94.4182	+	1801.61i	−0.0692147	+	1.32069i
$124$	17.8160	+	30.8582i	0.0129026	+	0.0223480i
$125$	164.256	−	1387.86i	0.117532	−	0.993069i
$126$	187.164	−	427.546i	0.132332	−	0.302292i
$127$	−526.571	−	1033.45i	−0.367918	−	0.722081i	0.630622	−	0.776090i	$-0.282800\pi$
$127$	−526.571	−	1033.45i	−0.367918	−	0.722081i	−0.998540	+	0.0540095i	$0.982800\pi$
$128$	−878.504	+	711.399i	−0.606637	+	0.491245i
$129$	2646.74	−	1178.40i	1.80645	−	0.804284i
$130$	98.4610	+	187.143i	0.0664277	+	0.126258i
$131$	833.090	−	1871.15i	0.555629	−	1.24796i	−0.389428	−	0.921057i	$-0.627327\pi$
$131$	833.090	−	1871.15i	0.555629	−	1.24796i	0.945057	−	0.326906i	$-0.106006\pi$
$132$	1460.29	+	1460.29i	0.962890	+	0.962890i
$133$	1357.48	−	702.391i	0.885028	−	0.457932i
$134$	262.006	−	85.1309i	0.168909	−	0.0548820i
$135$	344.555	+	747.394i	0.219663	+	0.476485i
$136$	332.431	−	299.322i	0.209601	−	0.188725i
$137$	145.579	−	94.5403i	0.0907860	−	0.0589571i	−0.498448	−	0.866920i	$-0.666096\pi$
$137$	145.579	−	94.5403i	0.0907860	−	0.0589571i	0.589234	+	0.807963i	$0.299430\pi$
$138$	9.27002	+	176.883i	0.00571824	+	0.109110i
$139$	574.008	−	1766.62i	0.350264	−	1.07800i	−0.608440	−	0.793600i	$-0.708204\pi$
$139$	574.008	−	1766.62i	0.350264	−	1.07800i	0.958705	−	0.284403i	$-0.0917955\pi$
$140$	327.109	−	1077.19i	0.197470	−	0.650279i
$141$	−660.543	−	2032.94i	−0.394523	−	1.21422i
$142$	−391.694	+	150.357i	−0.231480	+	0.0888570i
$143$	177.655	+	663.016i	0.103890	+	0.387721i
$144$	141.723	−	14.8957i	0.0820156	−	0.00862019i
$145$	1392.67	+	1097.89i	0.797622	+	0.628792i
$146$	574.442	−	790.652i	0.325624	−	0.448183i
$147$	−2219.01	−	323.085i	−1.24504	−	0.181276i
$148$	1214.69	−	618.917i	0.674643	−	0.343748i
$149$	−1221.32	+	705.128i	−0.671505	+	0.387694i	−0.796647	−	0.604445i	$-0.793395\pi$
$149$	−1221.32	+	705.128i	−0.671505	+	0.387694i	0.125142	+	0.992139i	$0.460061\pi$
$150$	683.609	+	1115.54i	0.372110	+	0.607223i
$151$	500.718	−	867.269i	0.269853	−	0.467400i	−0.698970	−	0.715151i	$-0.746358\pi$
$151$	500.718	−	867.269i	0.269853	−	0.467400i	0.968824	+	0.247751i	$0.0796914\pi$
$152$	−1488.94	−	966.931i	−0.794534	−	0.515977i
$153$	−323.280	+	51.2025i	−0.170821	+	0.0270554i
$154$	−852.045	+	1497.31i	−0.445843	+	0.783487i
$155$	4.79250	+	73.1174i	0.00248350	+	0.0378899i
$156$	383.605	+	170.792i	0.196878	+	0.0876558i
$157$	2968.18	−	795.322i	1.50883	−	0.404291i	0.592785	−	0.805360i	$-0.298028\pi$
$157$	2968.18	−	795.322i	1.50883	−	0.404291i	0.916047	+	0.401070i	$0.131362\pi$
$158$	261.686	−	323.156i	0.131764	−	0.162715i
$159$	2092.85	−	2324.35i	1.04386	−	1.15933i
$160$	−2034.73	+	460.416i	−1.00537	+	0.227494i
$161$	297.463	−	98.7106i	0.145611	−	0.0483198i
$162$	−1292.74	−	658.682i	−0.626957	−	0.319450i
$163$	2844.37	−	149.067i	1.36680	−	0.0716309i	0.645238	−	0.763982i	$-0.276758\pi$
$163$	2844.37	−	149.067i	1.36680	−	0.0716309i	0.721561	+	0.692351i	$0.243425\pi$
$164$	−1003.90	−	1114.94i	−0.477997	−	0.530869i
$165$	1365.10	+	4021.44i	0.644079	+	1.89739i
$166$	−1526.61	−	1374.56i	−0.713782	−	0.642692i
$167$	−2060.93	−	326.420i	−0.954968	−	0.151252i	−0.340545	−	0.940228i	$-0.610611\pi$
$167$	−2060.93	−	326.420i	−0.954968	−	0.151252i	−0.614424	+	0.788976i	$0.710611\pi$
$168$	948.607	+	2425.79i	0.435635	+	1.11401i
$169$	−1209.33	−	1664.50i	−0.550446	−	0.757623i
$170$	358.234	−	101.033i	0.161619	−	0.0455817i
$171$	528.361	+	1186.72i	0.236285	+	0.530705i
$172$	−863.444	+	2249.35i	−0.382773	+	0.997158i
$173$	1651.06	−	2542.41i	0.725594	−	1.11732i	−0.262719	−	0.964873i	$-0.584619\pi$
$173$	1651.06	−	2542.41i	0.725594	−	1.11732i	0.988312	−	0.152444i	$-0.0487143\pi$
$174$	−1660.19			−0.723327
$175$	1583.03	−	1689.20i	0.683806	−	0.729664i
$176$	−526.015			−0.225283
$177$	−2004.55	+	3086.73i	−0.851249	+	1.31081i
$178$	−532.738	+	1387.83i	−0.224328	+	0.584395i
$179$	828.659	+	1861.20i	0.346016	+	0.777165i	0.999790	+	0.0204751i	$0.00651789\pi$
$179$	828.659	+	1861.20i	0.346016	+	0.777165i	−0.653774	+	0.756690i	$0.726815\pi$
$180$	897.652	+	331.159i	0.371706	+	0.137129i
$181$	361.179	+	497.120i	0.148322	+	0.204147i	0.876713	−	0.481014i	$-0.159732\pi$
$181$	361.179	+	497.120i	0.148322	+	0.204147i	−0.728391	+	0.685162i	$0.759732\pi$
$182$	−52.6347	+	346.314i	−0.0214370	+	0.141047i
$183$	−280.625	−	44.4466i	−0.113357	−	0.0179540i
$184$	−270.540	−	243.595i	−0.108394	−	0.0975981i
$185$	2803.23	−	36.7013i	1.11404	−	0.0145856i
$186$	−45.9005	−	50.9777i	−0.0180946	−	0.0200960i
$187$	1206.52	−	63.2311i	0.471816	−	0.0247268i
$188$	1583.89	+	807.030i	0.614451	+	0.313078i
$189$	−275.106	+	1335.24i	−0.105878	+	0.513887i
$190$	−755.295	−	1269.53i	−0.288394	−	0.484745i
$191$	1330.68	−	1477.87i	0.504108	−	0.559868i	−0.436351	−	0.899777i	$-0.643729\pi$
$191$	1330.68	−	1477.87i	0.504108	−	0.559868i	0.940459	+	0.339908i	$0.110396\pi$
$192$	931.088	−	1149.80i	0.349976	−	0.432185i
$193$	11.5331	−	3.09030i	0.00430142	−	0.00115256i	−0.256668	−	0.966500i	$-0.582625\pi$
$193$	11.5331	−	3.09030i	0.00430142	−	0.00115256i	0.260969	+	0.965347i	$0.415958\pi$
$194$	1497.57	+	666.759i	0.554221	+	0.246755i
$195$	552.161	+	663.899i	0.202775	+	0.243809i
$196$	1494.86	−	1114.88i	0.544774	−	0.406299i
$197$	−568.813	+	90.0912i	−0.205717	+	0.0325824i	−0.258442	−	0.966027i	$-0.583209\pi$
$197$	−568.813	+	90.0912i	−0.205717	+	0.0325824i	0.0527253	+	0.998609i	$0.483209\pi$
$198$	−1227.97	−	797.454i	−0.440748	−	0.286225i
$199$	448.040	−	776.028i	0.159602	−	0.276438i	−0.775123	−	0.631810i	$-0.782312\pi$
$199$	448.040	−	776.028i	0.159602	−	0.276438i	0.934725	+	0.355372i	$0.115646\pi$
$200$	−2614.74	−	627.734i	−0.924450	−	0.221937i
$201$	974.236	−	562.475i	0.341877	−	0.197383i
$202$	2541.21	−	1294.81i	0.885142	−	0.451002i
$203$	778.026	+	2832.72i	0.268999	+	0.979397i
$204$	434.434	−	597.947i	0.149100	−	0.205219i
$205$	−837.468	−	2969.42i	−0.285323	−	1.01167i
$206$	−2087.82	+	219.439i	−0.706144	+	0.0742187i
$207$	68.9420	+	257.295i	0.0231488	+	0.0863925i
$208$	−99.8508	+	38.3291i	−0.0332856	+	0.0127771i
$209$	−1481.74	−	4560.32i	−0.490402	−	1.50930i
$210$	−184.816	+	2159.37i	−0.0607310	+	0.709575i
$211$	−716.387	+	2204.81i	−0.233735	+	0.719363i	0.763551	+	0.645747i	$0.223454\pi$
$211$	−716.387	+	2204.81i	−0.233735	+	0.719363i	−0.997287	+	0.0736160i	$0.976546\pi$
$212$	136.130	+	2597.51i	0.0441010	+	0.841498i
$213$	−1436.86	+	933.109i	−0.462217	+	0.300167i
$214$	−2281.05	+	2053.86i	−0.728641	+	0.656071i
$215$	−3638.33	+	3363.25i	−1.15410	+	1.06685i
$216$	1506.03	−	489.339i	0.474409	−	0.154145i
$217$	−65.4704	+	102.208i	−0.0204812	+	0.0319739i
$218$	387.340	+	387.340i	0.120339	+	0.120339i
$219$	1623.19	−	3645.75i	0.500845	−	1.12492i
$220$	−3167.52	−	1562.04i	−0.970701	−	0.478694i
$221$	224.420	−	99.9184i	0.0683083	−	0.0304128i
$222$	−2039.64	+	1651.67i	−0.616630	+	0.499337i
$223$	−1072.80	−	2105.49i	−0.322153	−	0.632262i	0.671962	−	0.740585i	$-0.265452\pi$
$223$	−1072.80	−	2105.49i	−0.322153	−	0.632262i	−0.994116	+	0.108324i	$0.965452\pi$
$224$	−3165.70	−	1385.83i	−0.944274	−	0.413368i
$225$	1354.38	+	1427.21i	0.401298	+	0.422877i
$226$	1659.87	+	2874.98i	0.488552	+	0.846198i
$227$	35.4681	−	676.771i	0.0103705	−	0.197881i	−0.988531	−	0.151019i	$-0.951745\pi$
$227$	35.4681	−	676.771i	0.0103705	−	0.197881i	0.998901	−	0.0468618i	$-0.0149220\pi$
$228$	−2738.52	−	1051.22i	−0.795450	−	0.305345i
$229$	−220.305	+	2096.07i	−0.0635729	+	0.604855i	0.915637	+	0.402006i	$0.131687\pi$
$229$	−220.305	+	2096.07i	−0.0635729	+	0.604855i	−0.979210	+	0.202850i	$0.934980\pi$
$230$	−112.247	−	281.347i	−0.0321797	−	0.0806586i
$231$	−2132.05	+	6704.01i	−0.607266	+	1.90949i
$232$	2412.79	−	2412.79i	0.682791	−	0.682791i
$233$	−1466.39	−	3820.08i	−0.412302	−	1.07408i	−0.969799	−	0.243905i	$-0.921572\pi$
$233$	−1466.39	−	3820.08i	−0.412302	−	1.07408i	0.557497	−	0.830179i	$-0.311762\pi$
$234$	−291.208	−	61.8981i	−0.0813540	−	0.0172923i
$235$	2187.22	+	2929.03i	0.607142	+	0.813058i
$236$	−636.372	−	2993.90i	−0.175527	−	0.825788i
$237$	770.877	−	1512.93i	0.211282	−	0.414664i
$238$	576.982	+	217.356i	0.157144	+	0.0591980i
$239$	−3409.00	−	1107.65i	−0.922636	−	0.299782i	−0.191088	−	0.981573i	$-0.561202\pi$
$239$	−3409.00	−	1107.65i	−0.922636	−	0.299782i	−0.731548	+	0.681790i	$0.761202\pi$
$240$	−600.949	+	277.042i	−0.161629	+	0.0745125i
$241$	−893.091	+	4201.66i	−0.238710	+	1.12304i	0.681562	+	0.731761i	$0.261301\pi$
$241$	−893.091	+	4201.66i	−0.238710	+	1.12304i	−0.920272	+	0.391280i	$0.872032\pi$
$242$	2544.17	+	2060.23i	0.675809	+	0.547259i
$243$	−3802.95	−	1019.00i	−1.00395	−	0.269007i
$244$	191.156	−	138.883i	0.0501538	−	0.0364389i
$245$	3771.05	−	696.616i	0.983363	−	0.181654i
$246$	2336.70	+	1697.72i	0.605621	+	0.440010i
$247$	−613.568	−	757.693i	−0.158058	−	0.195186i
$248$	140.795	+	7.37876i	0.0360504	+	0.00188932i
$249$	−7264.63	−	4194.24i	−1.84891	−	1.06747i
$250$	−1720.26	−	1430.71i	−0.435196	−	0.361944i
$251$		−	1721.08i		−	0.432803i	−0.976304	−	0.216402i	$-0.930568\pi$
$251$		−	1721.08i		−	0.432803i	0.976304	−	0.216402i	$-0.0694321\pi$
$252$	871.499	+	1323.81i	0.217854	+	0.330921i
$253$	−153.813	−	971.135i	−0.0382218	−	0.241323i
$254$	−1846.78	−	194.104i	−0.456210	−	0.0479496i
$255$	1345.09	−	707.691i	0.330326	−	0.173793i
$256$	378.421	+	3600.43i	0.0923879	+	0.879012i
$257$	−3.80556	+	14.2025i	−0.000923674	+	0.00344720i	−0.966386	−	0.257095i	$-0.917235\pi$
$257$	−3.80556	+	14.2025i	−0.000923674	+	0.00344720i	0.965462	+	0.260542i	$0.0839013\pi$
$258$	725.611	−	4581.33i	0.175095	−	1.10551i
$259$	3774.03	+	2706.12i	0.905431	+	0.649229i
$260$	−715.096	−	65.7068i	−0.170571	−	0.0156729i
$261$	−2442.14	+	519.092i	−0.579174	+	0.123107i
$262$	−1785.98	−	2750.18i	−0.421139	−	0.648498i
$263$	−401.185	−	617.771i	−0.0940613	−	0.144842i	0.788507	−	0.615025i	$-0.210854\pi$
$263$	−401.185	−	617.771i	−0.0940613	−	0.144842i	−0.882569	+	0.470184i	$0.844188\pi$
$264$	7992.82	−	1698.93i	1.86335	−	0.396067i
$265$	−2111.43	+	4914.52i	−0.489450	+	1.13923i
$266$	240.572	−	2435.17i	0.0554528	−	0.561314i
$267$	−949.612	+	5995.61i	−0.217660	+	1.37425i
$268$	−242.133	+	903.653i	−0.0551889	+	0.205968i
$269$	−304.133	−	2893.63i	−0.0689343	−	0.655866i	−0.973367	−	0.229251i	$-0.926372\pi$
$269$	−304.133	−	2893.63i	−0.0689343	−	0.655866i	0.904433	−	0.426615i	$-0.140294\pi$
$270$	1303.97	+	189.065i	0.293916	+	0.0426152i
$271$	−6820.09	−	716.821i	−1.52875	−	0.160678i	−0.697503	−	0.716582i	$-0.745706\pi$
$271$	−6820.09	−	716.821i	−1.52875	−	0.160678i	−0.831247	+	0.555904i	$0.812372\pi$
$272$	29.4498	+	185.939i	0.00656492	+	0.0414492i
$273$	83.7851	+	1427.94i	0.0185748	+	0.316568i
$274$		−	277.907i		−	0.0612736i
$275$	−4421.28	−	5761.89i	−0.969503	−	1.26347i
$276$	−520.912	−	300.749i	−0.113606	−	0.0655904i
$277$	−387.577	−	20.3121i	−0.0840696	−	0.00440590i	0.0102548	−	0.999947i	$-0.496736\pi$
$277$	−387.577	−	20.3121i	−0.0840696	−	0.00440590i	−0.0943244	+	0.995542i	$0.530069\pi$
$278$	−1871.54	−	2311.16i	−0.403767	−	0.498611i
$279$	−83.4586	−	60.6362i	−0.0179087	−	0.0130115i
$280$	−2869.66	−	3406.86i	−0.612483	−	0.727138i
$281$	1842.94	−	1338.97i	0.391248	−	0.284258i	−0.374719	−	0.927138i	$-0.622261\pi$
$281$	1842.94	−	1338.97i	0.391248	−	0.284258i	0.765967	+	0.642880i	$0.222261\pi$
$282$	−3305.62	−	885.738i	−0.698038	−	0.187039i
$283$	4340.20	+	3514.62i	0.911654	+	0.738243i	0.965526	−	0.260305i	$-0.0838232\pi$
$283$	4340.20	+	3514.62i	0.911654	+	0.738243i	−0.0538728	+	0.998548i	$0.517157\pi$
$284$	296.229	−	1393.65i	0.0618941	−	0.291189i
$285$	−4094.66	−	4429.56i	−0.851041	−	0.920647i
$286$	1045.15	+	339.588i	0.216087	+	0.0702108i
$287$	1801.67	−	4782.63i	0.370556	−	0.983657i
$288$	1333.39	−	2616.93i	0.272816	−	0.535432i
$289$	931.570	+	4382.69i	0.189613	+	0.892060i
$290$	2688.51	−	912.631i	0.544396	−	0.184798i
$291$	6547.70	+	1391.76i	1.31901	+	0.280365i
$292$	1189.35	+	3098.37i	0.238361	+	0.620952i
$293$	−3119.86	+	3119.86i	−0.622062	+	0.622062i	−0.946058	−	0.323996i	$-0.894974\pi$
$293$	−3119.86	+	3119.86i	−0.622062	+	0.622062i	0.323996	+	0.946058i	$0.394974\pi$
$294$	−2368.71	+	2697.76i	−0.469883	+	0.535159i
$295$	1549.34	−	6100.57i	0.305783	−	1.20403i
$296$	563.849	−	5364.67i	0.110720	−	1.05343i
$297$	3992.84	+	1532.71i	0.780094	+	0.299450i
$298$	−118.165	+	2254.72i	−0.0229702	+	0.438297i
$299$	−99.9612	−	173.138i	−0.0193341	−	0.0334877i
$300$	−4441.45	−	116.288i	−0.854757	−	0.0223796i
$301$	−8156.97	+	908.897i	−1.56199	+	0.174046i
$302$	−727.882	−	1428.55i	−0.138692	−	0.272198i
$303$	9050.88	−	7329.26i	1.71604	−	1.38962i
$304$	682.557	−	303.894i	0.128774	−	0.0573339i
$305$	478.876	−	82.2868i	0.0899028	−	0.0154483i
$306$	−213.139	+	478.717i	−0.0398181	+	0.0894328i
$307$	−1516.00	−	1516.00i	−0.281834	−	0.281834i	0.552006	−	0.833840i	$-0.313862\pi$
$307$	−1516.00	−	1516.00i	−0.281834	−	0.281834i	−0.833840	+	0.552006i	$0.813862\pi$
$308$	−2688.51	−	5195.98i	−0.497377	−	0.961262i
$309$	−8152.95	+	2649.05i	−1.50099	+	0.487701i
$310$	102.354	+	57.3209i	0.0187527	+	0.0105020i
$311$	−961.116	+	865.393i	−0.175241	+	0.157788i	−0.752084	−	0.659068i	$-0.770951\pi$
$311$	−961.116	+	865.393i	−0.175241	+	0.157788i	0.576843	+	0.816855i	$0.304284\pi$
$312$	1393.44	−	904.911i	0.252846	−	0.164200i
$313$	131.677	+	2512.55i	0.0237790	+	0.453731i	0.984408	+	0.175898i	$0.0562828\pi$
$313$	131.677	+	2512.55i	0.0237790	+	0.453731i	−0.960629	+	0.277833i	$0.910384\pi$
$314$	1520.27	−	4678.90i	0.273228	−	0.840909i
$315$	403.307	+	3234.21i	0.0721390	+	0.578499i
$316$	436.360	+	1342.98i	0.0776809	+	0.239077i
$317$	−4012.42	+	1540.22i	−0.710914	+	0.272895i	−0.686833	−	0.726815i	$-0.741000\pi$
$317$	−4012.42	+	1540.22i	−0.710914	+	0.272895i	−0.0240817	+	0.999710i	$0.507666\pi$
$318$	−1296.03	−	4836.85i	−0.228546	−	0.852946i
$319$	9165.41	−	963.323i	1.60867	−	0.169078i
$320$	−875.740	+	2373.81i	−0.152986	+	0.414688i
$321$	−7367.30	+	10140.2i	−1.28100	+	1.76315i
$322$	126.838	−	485.479i	0.0219515	−	0.0840207i
$323$	−1529.05	+	779.090i	−0.263401	+	0.134210i
$324$	4266.91	−	2463.50i	0.731637	−	0.422411i
$325$	−1259.12	−	771.584i	−0.214903	−	0.131692i
$326$	2280.04	−	3949.14i	0.387361	−	0.670929i
$327$	1875.98	+	1218.28i	0.317254	+	0.206027i
$328$	−5863.31	+	928.657i	−0.987033	+	0.156331i
$329$	37.8361	+	6055.33i	0.00634033	+	1.01471i
$330$	6589.95	+	1673.62i	1.09929	+	0.279181i
$331$	8893.61	+	3959.69i	1.47685	+	0.657535i	0.977896	−	0.209094i	$-0.0670513\pi$
$331$	8893.61	+	3959.69i	1.47685	+	0.657535i	0.498953	+	0.866629i	$0.333718\pi$
$332$	6738.32	−	1805.53i	1.11389	−	0.298467i
$333$	−2483.88	+	3067.34i	−0.408756	+	0.504772i
$334$	−2235.35	+	2482.61i	−0.366206	+	0.406713i
$335$	−1268.47	+	1446.42i	−0.206878	+	0.235900i
$336$	−1073.61	−	221.201i	−0.174317	−	0.0359152i
$337$	8673.94	+	4419.60i	1.40208	+	0.714394i	0.981249	−	0.192747i	$-0.0617395\pi$
$337$	8673.94	+	4419.60i	1.40208	+	0.714394i	0.420828	+	0.907140i	$0.361740\pi$
$338$	−3289.43	+	172.392i	−0.529353	+	0.0277422i
$339$	9070.76	+	10074.1i	1.45326	+	1.61401i
$340$	−374.820	+	1207.13i	−0.0597867	+	0.192546i
$341$	282.982	+	254.798i	0.0449394	+	0.0404636i
$342$	2054.13	+	325.342i	0.324779	+	0.0514400i
$343$	5713.14	+	2777.35i	0.899360	+	0.437210i
$344$	5603.59	+	7712.68i	0.878272	+	1.20884i
$345$	−687.203	−	1028.47i	−0.107240	−	0.160495i
$346$	−1974.05	−	4433.78i	−0.306721	−	0.688907i
$347$	850.728	−	2216.22i	0.131612	−	0.342862i	−0.851900	−	0.523705i	$-0.824549\pi$
$347$	850.728	−	2216.22i	0.131612	−	0.342862i	0.983512	+	0.180843i	$0.0578827\pi$
$348$	3070.58	−	4728.28i	0.472990	−	0.728340i
$349$	−7509.60			−1.15180			−0.575902	−	0.817519i	$-0.695349\pi$
$349$	−7509.60			−1.15180			−0.575902	+	0.817519i	$0.695349\pi$
$350$	−887.747	−	3598.47i	−0.135577	−	0.549561i
$351$	869.624			0.132242
$352$	−5904.63	+	9092.33i	−0.894085	+	1.37677i
$353$	−2790.25	+	7268.85i	−0.420708	+	1.09598i	0.545475	+	0.838127i	$0.316349\pi$
$353$	−2790.25	+	7268.85i	−0.420708	+	1.09598i	−0.966183	+	0.257856i	$0.916984\pi$
$354$	2396.69	+	5383.05i	0.359838	+	0.808209i
$355$	1813.91	−	2300.94i	0.271189	−	0.344003i
$356$	−2967.27	−	4084.09i	−0.441755	−	0.608024i
$357$	2489.14	+	378.313i	0.369017	+	0.0560853i
$358$	3221.61	+	510.253i	0.475607	+	0.0753288i
$359$	6538.19	+	5887.01i	0.961204	+	0.865472i	0.990970	−	0.134084i	$-0.0428094\pi$
$359$	6538.19	+	5887.01i	0.961204	+	0.865472i	−0.0297654	+	0.999557i	$0.509476\pi$
$360$	3033.39	−	2265.15i	0.444094	−	0.331622i
$361$	−32.2341	−	35.7996i	−0.00469953	−	0.00521936i
$362$	982.424	−	51.4866i	0.142638	−	0.00747535i
$363$	11911.2	+	6069.04i	1.72224	+	0.877526i
$364$	−888.962	−	790.424i	−0.128006	−	0.113817i
$365$	−624.471	+	6796.20i	−0.0895515	+	0.974601i
$366$	−304.374	+	338.042i	−0.0434697	+	0.0482780i
$367$	1700.07	−	2099.41i	0.241806	−	0.298605i	−0.641767	−	0.766900i	$-0.721798\pi$
$367$	1700.07	−	2099.41i	0.241806	−	0.298605i	0.883572	+	0.468295i	$0.155132\pi$
$368$	147.987	−	39.6530i	0.0209629	−	0.00561699i
$369$	3968.11	+	1766.71i	0.559814	+	0.249245i
$370$	2395.04	−	3795.93i	0.336520	−	0.533354i
$371$	−7645.54	+	4478.08i	−1.06991	+	0.626659i
$372$	230.081	−	36.4412i	0.0320675	−	0.00507900i
$373$	3164.40	+	2054.99i	0.439267	+	0.285263i	0.745264	−	0.666769i	$-0.232323\pi$
$373$	3164.40	+	2054.99i	0.439267	+	0.285263i	−0.305997	+	0.952032i	$0.598990\pi$
$374$	967.144	−	1675.14i	0.133716	−	0.231603i
$375$	−8085.80	−	4254.09i	−1.11346	−	0.585814i
$376$	6091.39	−	3516.86i	0.835477	−	0.482363i
$377$	1669.63	−	850.719i	0.228091	−	0.116218i
$378$	1552.96	+	1533.67i	0.211311	+	0.208687i
$379$	−6672.84	+	9184.37i	−0.904381	+	1.24477i	0.0646680	+	0.997907i	$0.479401\pi$
$379$	−6672.84	+	9184.37i	−0.904381	+	1.24477i	−0.969049	+	0.246867i	$0.920599\pi$
$380$	5012.61	+	196.937i	0.676688	+	0.0265859i
$381$	−7541.27	+	792.619i	−1.01404	+	0.106580i
$382$	−824.042	−	3075.37i	−0.110371	−	0.411910i
$383$	−9186.21	+	3526.25i	−1.22557	+	0.470452i	−0.883148	−	0.469094i	$-0.844581\pi$
$383$	−9186.21	+	3526.25i	−1.22557	+	0.470452i	−0.342422	+	0.939546i	$0.611247\pi$
$384$	2283.72	+	7028.57i	0.303491	+	0.934050i
$385$	−232.660	−	12028.5i	−0.0307986	−	1.59228i
$386$	5.90714	−	18.1803i	0.000778926	−	0.00239729i
$387$	−365.072	−	6965.99i	−0.0479526	−	0.914990i
$388$	−4668.75	+	3031.92i	−0.610876	+	0.396707i
$389$	5533.60	−	4982.47i	0.721245	−	0.649412i	−0.224443	−	0.974487i	$-0.572056\pi$
$389$	5533.60	−	4982.47i	0.721245	−	0.649412i	0.945688	+	0.325075i	$0.105390\pi$
$390$	1372.89	−	162.494i	0.178254	−	0.0210980i
$391$	−334.671	+	108.741i	−0.0432866	+	0.0140647i
$392$	−478.222	−	7363.20i	−0.0616170	−	0.948719i
$393$	−9468.54	−	9468.54i	−1.21533	−	1.21533i
$394$	−375.019	+	842.307i	−0.0479523	+	0.107703i
$395$	−416.676	+	2873.80i	−0.0530765	+	0.366067i
$396$	4542.35	−	2022.38i	0.576418	−	0.256638i
$397$	5249.30	−	4250.80i	0.663614	−	0.537384i	−0.237270	−	0.971444i	$-0.576253\pi$
$397$	5249.30	−	4250.80i	0.663614	−	0.537384i	0.900884	+	0.434060i	$0.142919\pi$
$398$	−651.305	−	1278.26i	−0.0820275	−	0.160988i
$399$	−1106.55	−	9930.87i	−0.138840	−	1.24603i
$400$	820.880	−	778.991i	0.102610	−	0.0973739i
$401$	−2975.74	−	5154.14i	−0.370577	−	0.641859i	0.619077	−	0.785330i	$-0.287507\pi$
$401$	−2975.74	−	5154.14i	−0.370577	−	0.641859i	−0.989654	+	0.143471i	$0.954174\pi$
$402$	94.2593	−	1798.58i	0.0116946	−	0.223146i
$403$	72.2835	+	27.7470i	0.00893473	+	0.00342972i
$404$	−1012.39	+	9632.23i	−0.124674	+	1.18619i
$405$	10110.3	−	662.680i	1.24045	−	0.0813058i
$406$	4481.93	+	1425.37i	0.547868	+	0.174236i
$407$	10301.9	−	10301.9i	1.25465	−	1.25465i
$408$	−1048.04	−	2730.23i	−0.127170	−	0.331290i
$409$	−10402.5	−	2211.12i	−1.25763	−	0.267317i	−0.469558	−	0.882902i	$-0.655587\pi$
$409$	−10402.5	−	2211.12i	−1.25763	−	0.267317i	−0.788071	+	0.615585i	$0.788920\pi$
$410$	−4717.31	−	1464.75i	−0.568223	−	0.176437i
$411$	−235.943	−	1110.02i	−0.0283168	−	0.133220i
$412$	3236.53	−	6352.05i	0.387020	−	0.759570i
$413$	8061.70	−	6612.06i	0.960509	−	0.787792i
$414$	405.588	+	131.783i	0.0481486	+	0.0156444i
$415$	14070.0	+	2798.66i	1.66426	+	0.331038i
$416$	−458.315	+	2156.20i	−0.0540162	+	0.254126i
$417$	−9437.52	−	7642.36i	−1.10829	−	0.897477i
$418$	−7415.21	−	1986.90i	−0.867679	−	0.232494i
$419$	−7296.77	+	5301.41i	−0.850765	+	0.618117i	−0.925357	−	0.379097i	$-0.876235\pi$
$419$	−7296.77	+	5301.41i	−0.850765	+	0.618117i	0.0745919	+	0.997214i	$0.476235\pi$
$420$	−5808.13	−	4520.19i	−0.674781	−	0.525149i
$421$	10111.3	+	7346.28i	1.17053	+	0.850441i	0.991073	−	0.133324i	$-0.0425650\pi$
$421$	10111.3	+	7346.28i	1.17053	+	0.850441i	0.179460	+	0.983765i	$0.442565\pi$
$422$	2335.76	+	2884.42i	0.269438	+	0.332728i
$423$	−5139.50	−	269.350i	−0.590758	−	0.0309603i
$424$	8913.04	+	5145.95i	1.02089	+	0.589409i
$425$	−1789.21	+	1885.45i	−0.204211	+	0.215195i
$426$			2742.93i			0.311961i
$427$	719.427	+	360.922i	0.0815352	+	0.0409046i
$428$	−1630.60	−	10295.2i	−0.184154	−	1.16270i
$429$	4462.87	+	469.066i	0.502259	+	0.0527896i
$430$	1343.37	+	7817.86i	0.150658	+	0.876769i
$431$	−1549.54	−	14742.9i	−0.173176	−	1.64766i	−0.643705	−	0.765273i	$-0.722604\pi$
$431$	−1549.54	−	14742.9i	−0.173176	−	1.64766i	0.470530	−	0.882384i	$-0.344063\pi$
$432$	−172.483	+	643.714i	−0.0192097	+	0.0716915i
$433$	−880.875	+	5561.63i	−0.0977648	+	0.617263i	0.889347	+	0.457232i	$0.151159\pi$
$433$	−880.875	+	5561.63i	−0.0977648	+	0.617263i	−0.987112	+	0.160030i	$0.948841\pi$
$434$	80.1478	+	177.030i	0.00886455	+	0.0195799i
$435$	9963.71	−	5927.81i	1.09821	−	0.653372i
$436$	−1819.56	+	386.759i	−0.199865	+	0.0424825i
$437$	760.640	+	1171.28i	0.0832640	+	0.128215i
$438$	−3479.81	−	5358.44i	−0.379616	−	0.584558i
$439$	10411.8	−	2213.09i	1.13195	−	0.240603i	0.396403	−	0.918077i	$-0.370258\pi$
$439$	10411.8	−	2213.09i	1.13195	−	0.240603i	0.735547	+	0.677473i	$0.236925\pi$
$440$	−12009.6	+	7145.00i	−1.30122	+	0.774146i
$441$	−2640.85	+	4709.02i	−0.285158	+	0.508478i
$442$	61.5255	−	388.457i	0.00662097	−	0.0418032i
$443$	−937.861	+	3500.15i	−0.100585	+	0.375388i	−0.997807	−	0.0661917i	$-0.978915\pi$
$443$	−937.861	+	3500.15i	−0.100585	+	0.375388i	0.897222	+	0.441580i	$0.145582\pi$
$444$	−931.622	−	8863.79i	−0.0995784	−	0.947425i
$445$	−1758.08	−	10231.3i	−0.187283	−	1.08991i
$446$	−3762.51	−	395.456i	−0.399462	−	0.0419852i
$447$	1442.28	+	9106.21i	0.152612	+	0.963555i
$448$	−3500.77	+	2304.65i	−0.369187	+	0.243046i
$449$			12149.7i			1.27702i	0.769614	+	0.638509i	$0.220449\pi$
$449$			12149.7i			1.27702i	−0.769614	+	0.638509i	$0.779551\pi$
$450$	3097.30	−	574.062i	0.324463	−	0.0601368i
$451$	−13885.3	−	8016.69i	−1.44974	−	0.837010i
$452$	−11258.0	−	590.007i	−1.17153	−	0.0613974i
$453$	−4120.17	−	5087.98i	−0.427334	−	0.527713i
$454$	−877.780	−	637.744i	−0.0907406	−	0.0659269i
$455$	−920.642	−	2266.35i	−0.0948580	−	0.233512i
$456$	−9389.96	+	6822.21i	−0.964310	+	0.700612i
$457$	−4265.23	−	1142.86i	−0.436584	−	0.116982i	0.0338312	−	0.999428i	$-0.489229\pi$
$457$	−4265.23	−	1142.86i	−0.436584	−	0.116982i	−0.470415	+	0.882445i	$0.655896\pi$
$458$	2622.31	+	2123.50i	0.267538	+	0.216648i
$459$	318.244	−	1497.22i	0.0323625	−	0.152253i
$460$	1008.89	+	200.679i	0.102260	+	0.0203406i
$461$	3281.50	+	1066.22i	0.331528	+	0.107720i	0.470051	−	0.882639i	$-0.344235\pi$
$461$	3281.50	+	1066.22i	0.331528	+	0.107720i	−0.138523	+	0.990359i	$0.544235\pi$
$462$	7142.46	+	8708.38i	0.719258	+	0.876949i
$463$	324.120	−	636.121i	0.0325337	−	0.0638511i	−0.874168	−	0.485625i	$-0.838592\pi$
$463$	324.120	−	636.121i	0.0325337	−	0.0638511i	0.906701	+	0.421773i	$0.138592\pi$
$464$	298.563	+	1404.63i	0.0298716	+	0.140535i
$465$	457.492	+	142.054i	0.0456251	+	0.0141669i
$466$	−6407.89	−	1362.04i	−0.636995	−	0.135398i
$467$	5362.18	+	13968.9i	0.531332	+	1.38417i	0.892238	+	0.451565i	$0.149134\pi$
$467$	5362.18	+	13968.9i	0.531332	+	1.38417i	−0.360906	+	0.932602i	$0.617533\pi$
$468$	714.886	−	714.886i	0.0706103	−	0.0706103i
$469$	−3113.01	+	682.047i	−0.306493	+	0.0671514i
$470$	5840.01	−	382.785i	0.573148	−	0.0375671i
$471$	2099.91	−	19979.3i	0.205433	−	1.95456i
$472$	−11306.5	−	4340.14i	−1.10259	−	0.423244i
$473$	−1347.57	+	25713.1i	−0.130996	+	2.49956i
$474$	−1359.25	−	2354.29i	−0.131714	−	0.228135i
$475$	9065.87	+	4922.32i	0.875727	+	0.475477i
$476$	−1686.19	+	1241.26i	−0.162366	+	0.119523i
$477$	−3418.79	−	6709.75i	−0.328167	−	0.644064i
$478$	−4459.78	+	3611.46i	−0.426749	+	0.345574i
$479$	−556.927	+	247.960i	−0.0531245	+	0.0236526i	−0.433127	−	0.901333i	$-0.642590\pi$
$479$	−556.927	+	247.960i	−0.0531245	+	0.0236526i	0.380002	+	0.924985i	$0.375923\pi$
$480$	−1957.01	+	13497.4i	−0.186094	+	1.28348i
$481$	1204.89	−	2706.22i	0.114216	−	0.256534i
$482$	4862.87	+	4862.87i	0.459538	+	0.459538i
$483$	94.4481	−	2046.80i	0.00889759	−	0.192821i
$484$	−10573.1	+	3435.42i	−0.992969	+	0.322635i
$485$	−11368.4	+	1345.56i	−1.06436	+	0.125977i
$486$	−4684.26	+	4217.72i	−0.437206	+	0.393662i
$487$	9636.94	−	6258.30i	0.896697	−	0.582322i	−0.0119306	−	0.999929i	$-0.503798\pi$
$487$	9636.94	−	6258.30i	0.896697	−	0.582322i	0.908628	+	0.417607i	$0.137131\pi$
$488$	−48.9298	−	933.637i	−0.00453883	−	0.0866061i
$489$	5754.18	−	17709.6i	0.532133	−	1.63774i
$490$	2352.88	−	5670.86i	0.216923	−	0.522823i
$491$	−4291.00	−	13206.3i	−0.394400	−	1.21384i	−0.929428	−	0.369003i	$-0.879699\pi$
$491$	−4291.00	−	13206.3i	−0.394400	−	1.21384i	0.535029	−	0.844834i	$-0.320301\pi$
$492$	−9156.96	+	3515.03i	−0.839080	+	0.322093i
$493$	−853.662	−	3185.91i	−0.0779858	−	0.291047i
$494$	−1552.37	+	163.161i	−0.141386	+	0.0148602i
$495$	10217.1	+	401.412i	0.927724	+	0.0364487i
$496$	−34.8758	+	48.0024i	−0.00315719	+	0.00434551i
$497$	4680.14	−	1285.44i	0.422400	−	0.116015i
$498$	−11966.2	+	6097.06i	−1.07674	+	0.548626i
$499$	−13730.2	+	7927.13i	−1.23176	+	0.711157i	−0.967397	−	0.253267i	$-0.918495\pi$
$499$	−13730.2	+	7927.13i	−1.23176	+	0.711157i	−0.264363	+	0.964423i	$0.585162\pi$
$500$	7256.39	−	2253.21i	0.649031	−	0.201533i
$501$	−6820.77	+	11813.9i	−0.608243	+	1.05351i
$502$	−2310.91	−	1500.72i	−0.205460	−	0.133427i
$503$	5927.34	−	938.799i	0.525422	−	0.0832186i	0.111912	−	0.993718i	$-0.464303\pi$
$503$	5927.34	−	938.799i	0.525422	−	0.0832186i	0.413510	+	0.910500i	$0.364303\pi$
$504$	6271.08	−	39.1842i	0.554238	−	0.00346310i
$505$	−10628.0	+	16844.4i	−0.936511	+	1.48429i
$506$	−1438.07	−	640.271i	−0.126344	−	0.0562520i
$507$	−12992.4	+	3481.30i	−1.13809	+	0.304951i
$508$	3968.50	−	4900.69i	0.346602	−	0.428017i
$509$	−10324.8	+	11466.9i	−0.899098	+	0.998550i	0.100895	+	0.994897i	$0.467829\pi$
$509$	−10324.8	+	11466.9i	−0.899098	+	0.998550i	−0.999993	+	0.00365252i	$0.998837\pi$
$510$	222.652	−	2423.15i	0.0193318	−	0.210390i
$511$	−7512.11	+	8448.61i	−0.650325	+	0.731399i
$512$	−2893.41	−	1474.27i	−0.249750	−	0.127254i
$513$	−6066.59	+	317.937i	−0.522118	+	0.0273631i
$514$	15.7516	+	17.4939i	0.00135170	+	0.00150121i
$515$	11746.6	−	8771.66i	1.00508	−	0.750535i
$516$	11705.7	+	10539.9i	0.998674	+	0.899210i
$517$	18763.3	+	2971.81i	1.59614	+	0.252804i
$518$	6924.36	−	2707.77i	0.587334	−	0.229677i
$519$	−11649.1	−	16033.6i	−0.985238	−	1.35606i
$520$	−1759.09	+	2231.40i	−0.148348	+	0.188180i
$521$	5902.90	+	13258.1i	0.496374	+	1.11487i	0.971947	+	0.235198i	$0.0755739\pi$
$521$	5902.90	+	13258.1i	0.496374	+	1.11487i	−0.475574	+	0.879676i	$0.657759\pi$
$522$	−1432.47	+	3731.71i	−0.120110	+	0.312897i
$523$	4659.72	−	7175.34i	0.389589	−	0.599915i	−0.588400	−	0.808570i	$-0.700242\pi$
$523$	4659.72	−	7175.34i	0.389589	−	0.599915i	0.977989	+	0.208655i	$0.0669086\pi$
$524$	11135.8			0.928379
$525$	−6600.97	−	13619.4i	−0.548743	−	1.13219i
$526$	−1179.31			−0.0977570
$527$	74.2243	−	114.295i	0.00613522	−	0.00944742i
$528$	−1232.39	+	3210.48i	−0.101577	+	0.264617i
$529$	−4832.28	−	10853.5i	−0.397163	−	0.892043i
$530$	4757.67	+	7120.33i	0.389924	+	0.583561i
$531$	5208.64	+	7169.07i	0.425679	+	0.585897i
$532$	6490.48	+	5189.08i	0.528944	+	0.422885i
$533$	−3219.93	−	509.987i	−0.261671	−	0.0414446i
$534$	7222.34	+	6503.02i	0.585283	+	0.526991i
$535$	6356.36	−	20470.9i	0.513662	−	1.65427i
$536$	2476.92	+	2750.90i	0.199602	+	0.221680i
$537$	13301.1	−	697.079i	1.06887	−	0.0560171i
$538$	−4150.50	−	2114.79i	−0.332604	−	0.169470i
$539$	11511.5	−	16267.9i	0.919919	−	1.30002i
$540$	−2950.20	+	3364.07i	−0.235105	+	0.268086i
$541$	606.068	−	673.106i	0.0481643	−	0.0534919i	−0.718581	−	0.695443i	$-0.755208\pi$
$541$	606.068	−	673.106i	0.0481643	−	0.0534919i	0.766746	+	0.641951i	$0.221875\pi$
$542$	−6909.37	+	8532.36i	−0.547570	+	0.676192i
$543$	3880.32	−	1039.73i	0.306667	−	0.0821712i
$544$	3544.59	+	1578.15i	0.279362	+	0.124380i
$545$	−3707.66	−	941.618i	−0.291410	−	0.0740082i
$546$	1990.37	+	1132.62i	0.156007	+	0.0887758i
$547$	−17456.2	+	2764.80i	−1.36449	+	0.216114i	−0.795361	−	0.606136i	$-0.792719\pi$
$547$	−17456.2	+	2764.80i	−1.36449	+	0.216114i	−0.569127	+	0.822250i	$0.692719\pi$
$548$	791.487	+	513.998i	0.0616983	+	0.0400673i
$549$	−342.038	+	592.427i	−0.0265898	+	0.0460549i
$550$	−11591.7	+	912.332i	−0.898679	+	0.0707308i
$551$	−11336.5	+	6545.13i	−0.876499	+	0.506047i
$552$	−2120.59	+	1080.50i	−0.163512	+	0.0833134i
$553$	−3380.03	+	3422.53i	−0.259916	+	0.263184i
$554$	−365.227	+	502.692i	−0.0280091	+	0.0385512i
$555$	6343.62	−	17195.2i	0.485174	−	1.31513i
$556$	10043.7	−	1055.64i	0.766094	−	0.0805197i
$557$	−1499.55	−	5596.40i	−0.114072	−	0.425722i	0.885144	−	0.465317i	$-0.154060\pi$
$557$	−1499.55	−	5596.40i	−0.114072	−	0.425722i	−0.999216	+	0.0395956i	$0.987393\pi$
$558$	−154.190	+	59.1879i	−0.0116978	+	0.00449037i
$559$	1617.84	+	4979.18i	0.122410	+	0.376739i
$560$	1860.20	−	231.968i	0.140371	−	0.0175043i
$561$	2440.80	−	7512.01i	0.183691	−	0.565343i
$562$	−190.873	−	3642.07i	−0.0143265	−	0.273366i
$563$	−12692.7	+	8242.75i	−0.950150	+	0.617034i	−0.923905	−	0.382621i	$-0.875021\pi$
$563$	−12692.7	+	8242.75i	−0.950150	+	0.617034i	−0.0262442	+	0.999656i	$0.508355\pi$
$564$	8636.46	−	7776.31i	0.644788	−	0.580570i
$565$	−20227.0	−	11327.6i	−1.50612	−	0.843464i
$566$	8503.62	−	2762.99i	0.631508	−	0.205190i
$567$	14132.8	+	9052.89i	1.04677	+	0.670521i
$568$	−3986.35	−	3986.35i	−0.294478	−	0.294478i
$569$	−7690.60	+	17273.4i	−0.566620	+	1.27265i	0.372172	+	0.928164i	$0.378613\pi$
$569$	−7690.60	+	17273.4i	−0.566620	+	1.27265i	−0.938792	+	0.344486i	$0.888053\pi$
$570$	−9518.01	+	1635.51i	−0.699413	+	0.120182i
$571$	−6473.67	+	2882.26i	−0.474457	+	0.211242i	−0.630012	−	0.776585i	$-0.716950\pi$
$571$	−6473.67	+	2882.26i	−0.474457	+	0.211242i	0.155555	+	0.987827i	$0.450283\pi$
$572$	−2900.19	+	2348.53i	−0.211998	+	0.171673i
$573$	−5902.40	−	11584.1i	−0.430325	−	0.844561i
$574$	−4850.68	−	6589.41i	−0.352724	−	0.479158i
$575$	1678.22	+	1287.73i	0.121716	+	0.0933951i
$576$	−1781.09	−	3084.94i	−0.128841	−	0.223158i
$577$	614.012	−	11716.0i	0.0443009	−	0.845312i	−0.882627	−	0.470073i	$-0.844227\pi$
$577$	614.012	−	11716.0i	0.0443009	−	0.845312i	0.926928	−	0.375239i	$-0.122439\pi$
$578$	6696.98	+	2570.73i	0.481933	+	0.184997i
$579$	8.15940	−	77.6315i	0.000585653	−	0.00557212i
$580$	−2373.29	+	9344.90i	−0.169906	+	0.669010i
$581$	16010.9	+	17560.0i	1.14328	+	1.25390i
$582$	7578.10	−	7578.10i	0.539729	−	0.539729i
$583$	9961.55	+	25950.7i	0.707659	+	1.84351i
$584$	12844.8	+	2730.25i	0.910141	+	0.193456i
$585$	1968.70	−	668.289i	0.139138	−	0.0472314i
$586$	1468.66	+	6909.48i	0.103532	+	0.487079i
$587$	−918.769	+	1803.19i	−0.0646025	+	0.126790i	−0.921050	−	0.389445i	$-0.872667\pi$
$587$	−918.769	+	1803.19i	−0.0646025	+	0.126790i	0.856447	+	0.516235i	$0.172667\pi$
$588$	−3302.31	−	11735.7i	−0.231607	−	0.823085i
$589$	−514.402	−	167.139i	−0.0359857	−	0.0116925i
$590$	−6840.33	−	7399.80i	−0.477308	−	0.516347i
$591$	−782.795	+	3682.76i	−0.0544838	+	0.256326i
$592$	1764.22	+	1428.64i	0.122481	+	0.0991836i
$593$	6684.51	+	1791.11i	0.462900	+	0.124034i	0.482729	−	0.875770i	$-0.339645\pi$
$593$	6684.51	+	1791.11i	0.462900	+	0.124034i	−0.0198289	+	0.999803i	$0.506312\pi$
$594$	5539.60	−	4024.75i	0.382647	−	0.278009i
$595$	−4238.86	+	755.675i	−0.292061	+	0.0520667i
$596$	−6202.97	−	4506.72i	−0.426315	−	0.309736i
$597$	−3686.70	−	4552.70i	−0.252742	−	0.312110i
$598$	−319.637	−	16.7514i	−0.0218577	−	0.00114551i
$599$	−21991.4	−	12696.8i	−1.50008	−	0.866069i	−1.00000		8.76916e-5i	$-0.999972\pi$
$599$	−21991.4	−	12696.8i	−1.50008	−	0.866069i	−0.500076	−	0.865982i	$-0.666695\pi$
$600$	−9957.31	+	14488.1i	−0.677509	+	0.985789i
$601$			12370.1i			0.839577i	0.907622	+	0.419788i	$0.137896\pi$
$601$			12370.1i			0.839577i	−0.907622	+	0.419788i	$0.862104\pi$
$602$	−5892.21	+	11745.0i	−0.398918	+	0.795164i
$603$	−423.705	−	2675.17i	−0.0286146	−	0.180665i
$604$	5414.79	+	569.117i	0.364776	+	0.0383395i
$605$	−22625.1	−	3280.45i	−1.52040	−	0.220445i
$606$	−1949.01	−	18543.6i	−0.130648	−	1.24304i
$607$	2350.52	−	8772.24i	0.157174	−	0.586580i	−0.841736	−	0.539890i	$-0.818466\pi$
$607$	2350.52	−	8772.24i	0.157174	−	0.586580i	0.998909	−	0.0466905i	$-0.0148675\pi$
$608$	2408.95	−	15209.5i	0.160684	−	1.01452i
$609$	19112.0	+	1888.09i	1.27169	+	0.125631i
$610$	307.076	−	714.743i	0.0203822	−	0.0474411i
$611$	3778.28	−	803.098i	0.250168	−	0.0531749i
$612$	−969.195	−	1492.43i	−0.0640153	−	0.0985750i
$613$	−10974.5	−	16899.2i	−0.723090	−	1.11346i	−0.988777	−	0.149401i	$-0.952265\pi$
$613$	−10974.5	−	16899.2i	−0.723090	−	1.11346i	0.265687	−	0.964059i	$-0.414401\pi$
$614$	−3357.46	+	713.649i	−0.220677	+	0.0469064i
$615$	−20085.6	−	1845.57i	−1.31696	−	0.121009i
$616$	−23036.4	−	2275.78i	−1.50676	−	0.148854i
$617$	3100.38	−	19575.0i	0.202296	−	1.27725i	−0.652304	−	0.757958i	$-0.726197\pi$
$617$	3100.38	−	19575.0i	0.202296	−	1.27725i	0.854599	−	0.519288i	$-0.173803\pi$
$618$	−3552.18	+	13256.9i	−0.231213	+	0.862900i
$619$	1242.74	+	11823.8i	0.0806942	+	0.767755i	0.957796	+	0.287450i	$0.0928074\pi$
$619$	1242.74	+	11823.8i	0.0806942	+	0.767755i	−0.877102	+	0.480305i	$0.840526\pi$
$620$	−352.559	+	185.491i	−0.0228373	+	0.0120153i
$621$	−1238.87	−	130.210i	−0.0800549	−	0.00841411i
$622$	323.911	+	2045.09i	0.0208805	+	0.131834i
$623$	7711.18	−	15370.7i	0.495894	−	0.988467i
$624$			699.229i			0.0448582i
$625$	15432.6	+	2444.18i	0.987689	+	0.156427i
$626$	3488.44	+	2014.05i	0.222725	+	0.128591i
$627$	−31305.0	−	1640.62i	−1.99394	−	0.104498i
$628$	10513.9	+	12983.5i	0.668072	+	0.825000i
$629$	−4218.33	−	3064.80i	−0.267402	−	0.194279i
$630$	4694.28	+	2278.60i	0.296864	+	0.144098i
$631$	6777.69	−	4924.28i	0.427600	−	0.310669i	−0.353089	−	0.935590i	$-0.614869\pi$
$631$	6777.69	−	4924.28i	0.427600	−	0.310669i	0.780688	+	0.624920i	$0.214869\pi$
$632$	5396.96	+	1446.11i	0.339683	+	0.0910178i
$633$	11778.4	+	9537.99i	0.739575	+	0.598896i
$634$	−1430.62	+	6730.53i	−0.0896169	+	0.421615i
$635$	11776.6	−	5429.11i	0.735968	−	0.339287i
$636$	16172.5	+	5254.78i	1.00831	+	0.327619i
$637$	999.779	−	3926.87i	0.0621863	−	0.244252i
$638$	6698.46	−	13146.5i	0.415665	−	0.815789i
$639$	857.631	+	4034.83i	0.0530944	+	0.249790i
$640$	−7561.96	−	10126.6i	−0.467051	−	0.625455i
$641$	20469.9	+	4351.00i	1.26133	+	0.268103i	0.789589	−	0.613636i	$-0.210294\pi$
$641$	20469.9	+	4351.00i	1.26133	+	0.268103i	0.471738	+	0.881739i	$0.343627\pi$
$642$	7191.33	+	18734.1i	0.442086	+	1.15167i
$643$	18582.6	−	18582.6i	1.13970	−	1.13970i	0.151194	−	0.988504i	$-0.451688\pi$
$643$	18582.6	−	18582.6i	1.13970	−	1.13970i	0.988504	−	0.151194i	$-0.0483119\pi$
$644$	1148.07	+	1259.15i	0.0702488	+	0.0770455i
$645$	12003.1	+	30085.8i	0.732746	+	1.83663i
$646$	−287.188	+	2732.41i	−0.0174911	+	0.166417i
$647$	25775.4	+	9894.25i	1.56621	+	0.601211i	0.978204	−	0.207648i	$-0.0665808\pi$
$647$	25775.4	+	9894.25i	1.56621	+	0.601211i	0.588004	+	0.808858i	$0.299914\pi$
$648$	1020.29	−	19468.4i	0.0618533	−	1.18023i
$649$	−16354.9	−	28327.5i	−0.989192	−	1.71333i
$650$	−2133.92	+	1017.84i	−0.128768	+	0.0614199i
$651$	470.427	+	639.052i	0.0283218	+	0.0384738i
$652$	7030.28	+	13797.7i	0.422281	+	0.828772i
$653$	9073.69	−	7347.73i	0.543769	−	0.440335i	−0.317667	−	0.948202i	$-0.602899\pi$
$653$	9073.69	−	7347.73i	0.543769	−	0.440335i	0.861435	+	0.507867i	$0.169566\pi$
$654$	3271.58	−	1456.60i	0.195610	−	0.0870912i
$655$	20538.3	+	10128.3i	1.22519	+	0.604193i
$656$	1016.15	−	2282.31i	0.0604787	−	0.135837i
$657$	−6794.21	−	6794.21i	−0.403451	−	0.403451i
$658$	8163.53	+	5229.23i	0.483659	+	0.309813i
$659$	−4770.63	+	1550.07i	−0.281999	+	0.0916270i	−0.446602	−	0.894733i	$-0.647366\pi$
$659$	−4770.63	+	1550.07i	−0.281999	+	0.0916270i	0.164603	+	0.986360i	$0.447366\pi$
$660$	−16954.8	+	15673.0i	−0.999949	+	0.924347i
$661$	434.581	−	391.299i	0.0255722	−	0.0230253i	−0.656245	−	0.754547i	$-0.727856\pi$
$661$	434.581	−	391.299i	0.0255722	−	0.0230253i	0.681818	+	0.731522i	$0.261190\pi$
$662$	13071.6	−	8488.82i	0.767437	−	0.498380i
$663$	−84.0527	−	1603.82i	−0.00492358	−	0.0939476i
$664$	8529.68	−	26251.7i	0.498518	−	1.53428i
$665$	7251.09	+	15473.7i	0.422835	+	0.902323i
$666$	1952.68	+	6009.74i	0.113611	+	0.349659i
$667$	−2505.94	+	961.940i	−0.145473	+	0.0558418i
$668$	−2936.19	−	10958.0i	−0.170067	−	0.634698i
$669$	−15364.1	+	1614.83i	−0.887908	+	0.0933229i
$670$	836.059	+	2964.42i	0.0482086	+	0.170934i
$671$	1484.21	−	2042.84i	0.0853908	−	0.117530i
$672$	−15875.1	+	16074.7i	−0.911301	+	0.922761i
$673$	20844.9	−	10621.0i	1.19392	−	0.608334i	0.259930	−	0.965627i	$-0.416300\pi$
$673$	20844.9	−	10621.0i	1.19392	−	0.608334i	0.933992	+	0.357293i	$0.116300\pi$
$674$	13497.6	−	7792.85i	0.771378	−	0.445355i
$675$	−8500.91	+	3521.23i	−0.484741	+	0.200788i
$676$	5592.93	−	9687.25i	0.318214	−	0.551163i
$677$	−17092.4	−	11100.0i	−0.970333	−	0.630142i	−0.0409122	−	0.999163i	$-0.513026\pi$
$677$	−17092.4	−	11100.0i	−0.970333	−	0.630142i	−0.929421	+	0.369021i	$0.879693\pi$
$678$	21436.0	−	3395.13i	1.21422	−	0.192314i
$679$	−16481.6	−	9378.81i	−0.931523	−	0.530082i
$680$	3198.03	+	3845.20i	0.180351	+	0.216848i
$681$	−4047.50	−	1802.06i	−0.227754	−	0.101403i
$682$	588.871	−	157.787i	0.0330631	−	0.00885923i
$683$	−11015.3	+	13602.8i	−0.617114	+	0.762072i	−0.985881	−	0.167450i	$-0.946447\pi$
$683$	−11015.3	+	13602.8i	−0.617114	+	0.762072i	0.368767	+	0.929522i	$0.379780\pi$
$684$	−4725.76	+	5248.49i	−0.264173	+	0.293393i
$685$	992.281	+	1667.87i	0.0553476	+	0.0930306i
$686$	8710.84	−	5249.32i	0.484812	−	0.292158i
$687$	12277.0	+	6255.42i	0.681798	+	0.347394i
$688$	−4006.58	+	209.976i	−0.222020	+	0.0116356i
$689$	3781.90	+	4200.23i	0.209113	+	0.232244i
$690$	−1980.15	+	25.9251i	−0.109251	+	0.00143037i
$691$	−1582.84	−	1425.20i	−0.0871405	−	0.0784617i	0.624409	−	0.781097i	$-0.285340\pi$
$691$	−1582.84	−	1425.20i	−0.0871405	−	0.0784617i	−0.711550	+	0.702636i	$0.752006\pi$
$692$	16278.6	+	2578.28i	0.894249	+	0.141635i
$693$	13229.4	+	10576.8i	0.725170	+	0.579766i
$694$	−2233.94	−	3074.75i	−0.122189	−	0.168179i
$695$	19484.2	+	7188.06i	1.06342	+	0.392315i
$696$	−9073.35	−	20379.1i	−0.494145	−	1.10987i
$697$	−2056.39	+	5357.09i	−0.111752	+	0.291125i
$698$	−6548.11	+	10083.2i	−0.355085	+	0.546784i
$699$	−26751.0			−1.44752
$700$	11890.5	+	4127.17i	0.642026	+	0.222846i
$701$	31870.7			1.71717			0.858587	−	0.512667i	$-0.171343\pi$
$701$	31870.7			1.71717			0.858587	+	0.512667i	$0.171343\pi$
$702$	758.282	−	1167.65i	0.0407685	−	0.0627780i
$703$	−7416.02	+	19319.4i	−0.397867	+	1.03648i
$704$	5348.13	+	12012.1i	0.286314	+	0.643072i
$705$	23001.4	−	6487.10i	1.22877	−	0.346551i
$706$	7326.95	+	10084.7i	0.390586	+	0.537595i
$707$	−30726.7	+	12015.7i	−1.63451	+	0.639175i
$708$	−19763.9	−	3130.29i	−1.04911	−	0.166163i
$709$	−15404.1	−	13870.0i	−0.815959	−	0.734692i	0.151299	−	0.988488i	$-0.451654\pi$
$709$	−15404.1	−	13870.0i	−0.815959	−	0.734692i	−0.967258	+	0.253796i	$0.918321\pi$
$710$	−1507.83	−	4441.89i	−0.0797010	−	0.234790i
$711$	−2735.56	−	3038.15i	−0.144292	−	0.160253i
$712$	−19947.4	+	1045.40i	−1.04994	+	0.0550251i
$713$	−98.8207	−	50.3517i	−0.00519055	−	0.00264472i
$714$	2678.41	−	3012.31i	0.140388	−	0.157889i
$715$	−7485.00	+	1693.70i	−0.391501	+	0.0885884i
$716$	−7411.69	+	8231.52i	−0.386855	+	0.429646i
$717$	−14747.3	+	18211.4i	−0.768128	+	0.948559i
$718$	13605.6	−	3645.62i	0.707183	−	0.189489i
$719$	−8261.21	−	3678.13i	−0.428499	−	0.190780i	0.181143	−	0.983457i	$-0.442020\pi$
$719$	−8261.21	−	3678.13i	−0.428499	−	0.190780i	−0.609642	+	0.792677i	$0.708687\pi$
$720$	104.206	+	1589.83i	0.00539377	+	0.0822908i
$721$	24284.4	−	151.739i	1.25437	−	0.00783778i
$722$	−76.1755	+	12.0650i	−0.00392653	+	0.000621902i
$723$	23552.0	+	15294.8i	1.21149	+	0.786752i
$724$	−1670.39	+	2893.20i	−0.0857452	+	0.148515i
$725$	−12876.6	+	15076.7i	−0.659620	+	0.772322i
$726$	18535.1	−	10701.2i	0.947522	−	0.547052i
$727$	4962.69	−	2528.62i	0.253172	−	0.128998i	−0.322800	−	0.946467i	$-0.604624\pi$
$727$	4962.69	−	2528.62i	0.253172	−	0.128998i	0.575971	+	0.817470i	$0.304624\pi$
$728$	−4538.71	+	1246.59i	−0.231065	+	0.0634639i
$729$	−747.099	+	1028.29i	−0.0379566	+	0.0522427i
$730$	8580.81	+	6764.54i	0.435055	+	0.342968i
$731$	9164.67	−	963.245i	0.463704	−	0.0487372i
$732$	−399.804	−	1492.09i	−0.0201874	−	0.0753403i
$733$	−34285.2	+	13160.9i	−1.72763	+	0.663176i	−0.999746	−	0.0225223i	$-0.992830\pi$
$733$	−34285.2	+	13160.9i	−1.72763	+	0.663176i	−0.727886	+	0.685698i	$0.759497\pi$
$734$	−1336.49	−	4113.30i	−0.0672083	−	0.206846i
$735$	4583.38	−	24648.3i	0.230014	−	1.23696i
$736$	975.770	−	3003.11i	0.0488687	−	0.150402i
$737$	523.243	+	9984.07i	0.0261518	+	0.499007i
$738$	5832.24	−	3787.50i	0.290905	−	0.188916i
$739$	18958.3	−	17070.1i	0.943696	−	0.849708i	−0.0450994	−	0.998983i	$-0.514360\pi$
$739$	18958.3	−	17070.1i	0.943696	−	0.849708i	0.988796	+	0.149274i	$0.0476938\pi$
$740$	6381.22	+	13841.9i	0.316998	+	0.687618i
$741$	−6062.01	+	1969.67i	−0.300531	+	0.0976484i
$742$	−653.886	+	14170.5i	−0.0323516	+	0.701098i
$743$	11098.2	+	11098.2i	0.547985	+	0.547985i	0.925858	−	0.377873i	$-0.123344\pi$
$743$	11098.2	+	11098.2i	0.547985	+	0.547985i	−0.377873	+	0.925858i	$0.623344\pi$
$744$	374.900	−	842.040i	0.0184738	−	0.0414929i
$745$	−7341.44	−	13953.7i	−0.361033	−	0.686208i
$746$	5518.50	−	2457.00i	0.270840	−	0.120586i
$747$	−15695.8	+	12710.2i	−0.768781	+	0.622546i
$748$	2982.09	+	5852.69i	0.145770	+	0.286090i
$749$	28595.0	−	21049.7i	1.39498	−	1.02689i
$750$	−12762.5	+	7147.46i	−0.621363	+	0.347984i
$751$	−11452.3	−	19836.0i	−0.556461	−	0.963818i	−0.997788	−	0.0664719i	$-0.978826\pi$
$751$	−11452.3	−	19836.0i	−0.556461	−	0.963818i	0.441328	−	0.897346i	$-0.354508\pi$
$752$	−154.920	+	2956.05i	−0.00751244	+	0.143346i
$753$	−10504.4	−	4032.27i	−0.508370	−	0.195145i
$754$	313.591	−	2983.62i	0.0151463	−	0.144108i
$755$	9469.12	+	5974.54i	0.456446	+	0.287995i
$756$	−7240.20	+	1586.30i	−0.348311	+	0.0763136i
$757$	3527.14	−	3527.14i	0.169347	−	0.169347i	−0.617345	−	0.786693i	$-0.711792\pi$
$757$	3527.14	−	3527.14i	0.169347	−	0.169347i	0.786693	+	0.617345i	$0.211792\pi$
$758$	6513.46	+	16968.1i	0.312110	+	0.813074i
$759$	−6287.58	−	1336.47i	−0.300691	−	0.0639139i
$760$	11455.8	−	16209.7i	0.546771	−	0.773666i
$761$	−2867.59	−	13490.9i	−0.136597	−	0.642636i	−0.992164	−	0.124945i	$-0.960125\pi$
$761$	−2867.59	−	13490.9i	−0.136597	−	0.642636i	0.855567	−	0.517692i	$-0.173209\pi$
$762$	−5511.47	+	10816.9i	−0.262020	+	0.514244i
$763$	−4018.52	−	4899.54i	−0.190669	−	0.232471i
$764$	10282.8	+	3341.10i	0.486937	+	0.158215i
$765$	−430.126	−	3634.06i	−0.0203284	−	0.171751i
$766$	−3275.32	+	15409.2i	−0.154494	+	0.726836i
$767$	−5168.70	−	4185.53i	−0.243326	−	0.197042i

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:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	175.x (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.871966 - 1.34271i) q^{2} +(2.34287 - 6.10339i) q^{3} +(2.21135 + 4.96677i) q^{4} +(-0.438918 + 11.1717i) q^{5} +(-6.15218 - 8.46775i) q^{6} +(-11.5650 + 14.4655i) q^{7} +(21.2474 + 3.36526i) q^{8} +(-11.6974 - 10.5324i) q^{9} +(14.6177 + 10.3307i) q^{10} +(38.8777 + 43.1780i) q^{11} +(35.4951 - 1.86022i) q^{12} +(10.5262 + 5.36337i) q^{13} +(9.33865 + 28.1419i) q^{14} +(67.1571 + 28.8528i) q^{15} +(-6.05787 + 6.72794i) q^{16} +(13.0862 - 16.1601i) q^{17} +(-24.3417 + 6.52235i) q^{18} +(-75.3928 - 33.5671i) q^{19} +(-56.4580 + 22.5246i) q^{20} +(61.1932 + 104.477i) q^{21} +(91.8755 - 14.5516i) q^{22} +(-14.1926 - 9.21678i) q^{23} +(70.3196 - 121.797i) q^{24} +(-124.615 - 9.80694i) q^{25} +(16.3799 - 9.45696i) q^{26} +(65.5876 - 33.4185i) q^{27} +(-97.4211 - 25.4526i) q^{28} +(93.2324 - 128.323i) q^{29} +(97.2996 - 65.0138i) q^{30} +(6.51795 - 0.685064i) q^{31} +(48.2937 + 180.235i) q^{32} +(354.618 - 136.125i) q^{33} +(-10.2876 - 31.6620i) q^{34} +(-156.528 - 135.550i) q^{35} +(26.4450 - 81.3893i) q^{36} +(-13.1233 - 250.407i) q^{37} +(-110.811 + 71.9613i) q^{38} +(57.3963 - 51.6798i) q^{39} +(-46.9217 + 235.893i) q^{40} +(-262.447 + 85.2743i) q^{41} +(193.640 + 8.93538i) q^{42} +(313.362 + 313.362i) q^{43} +(-128.483 + 288.578i) q^{44} +(122.799 - 126.058i) q^{45} +(-24.7509 + 11.0198i) q^{46} +(254.098 - 205.765i) q^{47} +(26.8705 + 52.7363i) q^{48} +(-75.5007 - 334.587i) q^{49} +(-121.828 + 158.770i) q^{50} +(-67.9721 - 117.731i) q^{51} +(-3.36151 + 64.1415i) q^{52} +(446.643 + 171.450i) q^{53} +(12.3187 - 117.205i) q^{54} +(-499.437 + 415.379i) q^{55} +(-294.407 + 268.435i) q^{56} +(-381.509 + 381.509i) q^{57} +(-91.0056 - 237.078i) q^{58} +(-550.672 - 117.049i) q^{59} +(5.20240 + 397.357i) q^{60} +(-9.03578 - 42.5100i) q^{61} +(4.76358 - 9.34906i) q^{62} +(287.638 - 47.4015i) q^{63} +(215.231 + 69.9329i) q^{64} +(-64.5382 + 115.242i) q^{65} +(126.438 - 594.845i) q^{66} +(133.726 + 108.289i) q^{67} +(109.202 + 29.2605i) q^{68} +(-89.5051 + 65.0293i) q^{69} +(-318.492 + 91.9768i) q^{70} +(-212.013 - 154.036i) q^{71} +(-213.096 - 263.152i) q^{72} +(609.595 + 31.9475i) q^{73} +(-347.666 - 200.725i) q^{74} +(-351.812 + 737.596i) q^{75} -448.687i q^{76} +(-1074.21 + 63.0298i) q^{77} +(-19.3434 - 122.130i) q^{78} +(258.305 + 27.1490i) q^{79} +(-72.5038 - 70.6298i) q^{80} +(-94.7269 - 901.266i) q^{81} +(-114.346 + 426.747i) q^{82} +(200.723 - 1267.31i) q^{83} +(-383.592 + 534.967i) q^{84} +(174.792 + 153.288i) q^{85} +(693.995 - 147.513i) q^{86} +(-564.777 - 869.680i) q^{87} +(680.745 + 1048.26i) q^{88} +(-908.236 + 193.051i) q^{89} +(-62.1818 - 274.802i) q^{90} +(-199.319 + 90.2392i) q^{91} +(14.3929 - 90.8729i) q^{92} +(11.0895 - 41.3866i) q^{93} +(-54.7172 - 520.600i) q^{94} +(408.093 - 827.535i) q^{95} +(1213.19 + 127.511i) q^{96} +(160.176 + 1011.31i) q^{97} +(-515.087 - 190.373i) q^{98} -914.548i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 928 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 24 q^{7} + 84 q^{8} - 10 q^{9} - 96 q^{10} - 6 q^{11} - 72 q^{12} - 20 q^{14} - 368 q^{15} - 1670 q^{16} + 120 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} - 880 q^{22}+ \cdots - 19478 q^{98}+O(q^{100}) \) 928 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 24 * q^7 + 84 * q^8 - 10 * q^9 - 96 * q^10 - 6 * q^11 - 72 * q^12 - 20 * q^14 - 368 * q^15 - 1670 * q^16 + 120 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 - 880 * q^22 + 296 * q^23 + 32 * q^25 - 48 * q^26 + 226 * q^28 - 200 * q^29 - 38 * q^30 - 18 * q^31 - 964 * q^32 - 1092 * q^33 + 288 * q^35 + 7400 * q^36 - 392 * q^37 + 5424 * q^38 + 2430 * q^39 + 2172 * q^40 - 2098 * q^42 + 1560 * q^43 - 10 * q^44 - 4224 * q^45 - 6 * q^46 + 96 * q^47 + 6232 * q^50 - 16 * q^51 - 8928 * q^52 - 2384 * q^53 - 30 * q^54 + 244 * q^56 + 1556 * q^57 + 640 * q^58 + 4890 * q^59 + 3676 * q^60 - 18 * q^61 + 224 * q^63 - 9700 * q^64 - 1116 * q^65 - 2610 * q^66 - 2404 * q^67 - 13614 * q^68 - 1700 * q^70 - 24 * q^71 - 518 * q^72 - 4200 * q^73 - 16104 * q^75 - 722 * q^77 - 356 * q^78 - 10 * q^79 + 6414 * q^80 - 6810 * q^81 + 1692 * q^82 + 20620 * q^84 + 2712 * q^85 - 6 * q^86 + 9102 * q^87 + 1650 * q^88 + 20370 * q^89 - 12 * q^91 + 1612 * q^92 - 4604 * q^93 - 30 * q^94 + 1652 * q^95 - 2610 * q^96 - 19478 * q^98

Introduction

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