LMFDB - Embedded newform 105.4.g.b.104.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,4,Mod(104,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("105.104");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	105.g (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.19520055060$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			104.6
Character	$\chi$	$=$	105.104
Dual form			105.4.g.b.104.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.45958 q^{2} +(-5.00290 + 1.40393i) q^{3} +11.8879 q^{4} +(-0.892950 + 11.1446i) q^{5} +(22.3108 - 6.26096i) q^{6} +(12.5955 - 13.5777i) q^{7} -17.3382 q^{8} +(23.0579 - 14.0475i) q^{9} +O(q^{10})$	\(q-4.45958 q^{2} +(-5.00290 + 1.40393i) q^{3} +11.8879 q^{4} +(-0.892950 + 11.1446i) q^{5} +(22.3108 - 6.26096i) q^{6} +(12.5955 - 13.5777i) q^{7} -17.3382 q^{8} +(23.0579 - 14.0475i) q^{9} +(3.98218 - 49.7003i) q^{10} +30.2834i q^{11} +(-59.4737 + 16.6898i) q^{12} +18.9551 q^{13} +(-56.1708 + 60.5506i) q^{14} +(-11.1790 - 57.0090i) q^{15} -17.7818 q^{16} +4.59392i q^{17} +(-102.829 + 62.6458i) q^{18} +119.595i q^{19} +(-10.6153 + 132.486i) q^{20} +(-43.9520 + 85.6109i) q^{21} -135.051i q^{22} -134.577 q^{23} +(86.7411 - 24.3417i) q^{24} +(-123.405 - 19.9032i) q^{25} -84.5318 q^{26} +(-95.6347 + 102.650i) q^{27} +(149.734 - 161.409i) q^{28} -203.146i q^{29} +(49.8536 + 254.236i) q^{30} +61.4983i q^{31} +218.005 q^{32} +(-42.5159 - 151.505i) q^{33} -20.4870i q^{34} +(140.071 + 152.497i) q^{35} +(274.109 - 166.994i) q^{36} +337.592i q^{37} -533.342i q^{38} +(-94.8304 + 26.6117i) q^{39} +(15.4821 - 193.227i) q^{40} -135.603 q^{41} +(196.007 - 381.789i) q^{42} -270.630i q^{43} +360.004i q^{44} +(135.964 + 269.516i) q^{45} +600.156 q^{46} +273.318i q^{47} +(88.9606 - 24.9645i) q^{48} +(-25.7052 - 342.035i) q^{49} +(550.336 + 88.7598i) q^{50} +(-6.44957 - 22.9829i) q^{51} +225.335 q^{52} -222.861 q^{53} +(426.491 - 457.775i) q^{54} +(-337.497 - 27.0415i) q^{55} +(-218.384 + 235.412i) q^{56} +(-167.903 - 598.319i) q^{57} +905.947i q^{58} -735.026 q^{59} +(-132.894 - 677.715i) q^{60} +312.240i q^{61} -274.257i q^{62} +(99.6952 - 490.008i) q^{63} -829.955 q^{64} +(-16.9260 + 211.247i) q^{65} +(189.603 + 675.646i) q^{66} +751.739i q^{67} +54.6119i q^{68} +(673.274 - 188.937i) q^{69} +(-624.656 - 680.071i) q^{70} +640.823i q^{71} +(-399.783 + 243.558i) q^{72} -469.117 q^{73} -1505.52i q^{74} +(645.327 - 73.6793i) q^{75} +1421.72i q^{76} +(411.177 + 381.435i) q^{77} +(422.904 - 118.677i) q^{78} +126.493 q^{79} +(15.8783 - 198.172i) q^{80} +(334.337 - 647.812i) q^{81} +604.734 q^{82} +299.265i q^{83} +(-522.495 + 1017.73i) q^{84} +(-51.1976 - 4.10215i) q^{85} +1206.90i q^{86} +(285.204 + 1016.32i) q^{87} -525.058i q^{88} -425.893 q^{89} +(-606.343 - 1201.93i) q^{90} +(238.750 - 257.366i) q^{91} -1599.83 q^{92} +(-86.3396 - 307.670i) q^{93} -1218.88i q^{94} +(-1332.84 - 106.792i) q^{95} +(-1090.66 + 306.064i) q^{96} -561.656 q^{97} +(114.635 + 1525.33i) q^{98} +(425.405 + 698.272i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 184 q^{4} + 4 q^{9}+O(q^{10}) $ 40 * q + 184 * q^4 + 4 * q^9	$ 40 q + 184 q^{4} + 4 q^{9} - 188 q^{15} + 184 q^{16} + 148 q^{21} + 712 q^{25} - 336 q^{30} - 1520 q^{36} + 644 q^{39} - 1488 q^{46} - 1496 q^{49} - 220 q^{51} + 1984 q^{60} + 40 q^{64} - 3000 q^{70} - 1192 q^{79} + 4636 q^{81} - 2192 q^{84} + 4808 q^{85} - 4408 q^{91} + 5276 q^{99}+O(q^{100}) $ 40 * q + 184 * q^4 + 4 * q^9 - 188 * q^15 + 184 * q^16 + 148 * q^21 + 712 * q^25 - 336 * q^30 - 1520 * q^36 + 644 * q^39 - 1488 * q^46 - 1496 * q^49 - 220 * q^51 + 1984 * q^60 + 40 * q^64 - 3000 * q^70 - 1192 * q^79 + 4636 * q^81 - 2192 * q^84 + 4808 * q^85 - 4408 * q^91 + 5276 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−4.45958			−1.57670			−0.788350	−	0.615227i	$-0.789064\pi$
$2$	−4.45958			−1.57670			−0.788350	+	0.615227i	$0.789064\pi$
$3$	−5.00290	+	1.40393i	−0.962808	+	0.270187i
$3$	−5.00290	+	1.40393i	−0.962808	+	0.270187i
$4$	11.8879			1.48598
$5$	−0.892950	+	11.1446i	−0.0798679	+	0.996805i
$5$	−0.892950	+	11.1446i	−0.0798679	+	0.996805i
$6$	22.3108	−	6.26096i	1.51806	−	0.426004i
$7$	12.5955	−	13.5777i	0.680095	−	0.733124i
$7$	12.5955	−	13.5777i	0.680095	−	0.733124i
$8$	−17.3382			−0.766247
$9$	23.0579	−	14.0475i	0.853998	−	0.520277i
$10$	3.98218	−	49.7003i	0.125928	−	1.57166i
$11$			30.2834i			0.830071i	0.909805	+	0.415035i	$0.136231\pi$
$11$			30.2834i			0.830071i	−0.909805	+	0.415035i	$0.863769\pi$
$12$	−59.4737	+	16.6898i	−1.43071	+	0.401493i
$13$	18.9551			0.404400			0.202200	−	0.979344i	$-0.435191\pi$
$13$	18.9551			0.404400			0.202200	+	0.979344i	$0.435191\pi$
$14$	−56.1708	+	60.5506i	−1.07230	+	1.15592i
$15$	−11.1790	−	57.0090i	−0.192427	−	0.981311i
$16$	−17.7818			−0.277841
$17$			4.59392i			0.0655406i	0.999463	+	0.0327703i	$0.0104330\pi$
$17$			4.59392i			0.0655406i	−0.999463	+	0.0327703i	$0.989567\pi$
$18$	−102.829	+	62.6458i	−1.34650	+	0.820320i
$19$			119.595i			1.44405i	0.691869	+	0.722023i	$0.256788\pi$
$19$			119.595i			1.44405i	−0.691869	+	0.722023i	$0.743212\pi$
$20$	−10.6153	+	132.486i	−0.118682	+	1.48123i
$21$	−43.9520	+	85.6109i	−0.456720	+	0.889611i
$22$		−	135.051i		−	1.30877i
$23$	−134.577			−1.22005			−0.610026	−	0.792381i	$-0.708841\pi$
$23$	−134.577			−1.22005			−0.610026	+	0.792381i	$0.708841\pi$
$24$	86.7411	−	24.3417i	0.737748	−	0.207030i
$25$	−123.405	−	19.9032i	−0.987242	−	0.159225i
$26$	−84.5318			−0.637617
$27$	−95.6347	+	102.650i	−0.681663	+	0.731666i
$28$	149.734	−	161.409i	1.01061	−	1.08941i
$29$		−	203.146i		−	1.30080i	−0.759590	−	0.650402i	$-0.774600\pi$
$29$		−	203.146i		−	1.30080i	0.759590	−	0.650402i	$-0.225400\pi$
$30$	49.8536	+	254.236i	0.303399	+	1.54723i
$31$			61.4983i			0.356304i	0.984003	+	0.178152i	$0.0570119\pi$
$31$			61.4983i			0.356304i	−0.984003	+	0.178152i	$0.942988\pi$
$32$	218.005			1.20432
$33$	−42.5159	−	151.505i	−0.224275	−	0.799198i
$34$		−	20.4870i		−	0.103338i
$35$	140.071	+	152.497i	0.676465	+	0.736475i
$36$	274.109	−	166.994i	1.26902	−	0.773122i
$37$			337.592i			1.49999i	0.661441	+	0.749997i	$0.269945\pi$
$37$			337.592i			1.49999i	−0.661441	+	0.749997i	$0.730055\pi$
$38$		−	533.342i		−	2.27683i
$39$	−94.8304	+	26.6117i	−0.389359	+	0.109264i
$40$	15.4821	−	193.227i	0.0611985	−	0.763799i
$41$	−135.603			−0.516529			−0.258264	−	0.966074i	$-0.583151\pi$
$41$	−135.603			−0.516529			−0.258264	+	0.966074i	$0.583151\pi$
$42$	196.007	−	381.789i	0.720110	−	1.40265i
$43$		−	270.630i		−	0.959785i	−0.877327	−	0.479893i	$-0.840676\pi$
$43$		−	270.630i		−	0.959785i	0.877327	−	0.479893i	$-0.159324\pi$
$44$			360.004i			1.23347i
$45$	135.964	+	269.516i	0.450408	+	0.892823i
$46$	600.156			1.92366
$47$			273.318i			0.848245i	0.905605	+	0.424123i	$0.139417\pi$
$47$			273.318i			0.848245i	−0.905605	+	0.424123i	$0.860583\pi$
$48$	88.9606	−	24.9645i	0.267507	−	0.0750691i
$49$	−25.7052	−	342.035i	−0.0749424	−	0.997188i
$50$	550.336	+	88.7598i	1.55658	+	0.251051i
$51$	−6.44957	−	22.9829i	−0.0177082	−	0.0631030i
$52$	225.335			0.600931
$53$	−222.861			−0.577591			−0.288796	−	0.957391i	$-0.593255\pi$
$53$	−222.861			−0.577591			−0.288796	+	0.957391i	$0.593255\pi$
$54$	426.491	−	457.775i	1.07478	−	1.15362i
$55$	−337.497	−	27.0415i	−0.827419	−	0.0662960i
$56$	−218.384	+	235.412i	−0.521120	+	0.561754i
$57$	−167.903	−	598.319i	−0.390163	−	1.39034i
$58$			905.947i			2.05098i
$59$	−735.026			−1.62190			−0.810951	−	0.585114i	$-0.801050\pi$
$59$	−735.026			−1.62190			−0.810951	+	0.585114i	$0.801050\pi$
$60$	−132.894	−	677.715i	−0.285943	−	1.45821i
$61$			312.240i			0.655381i	0.944785	+	0.327691i	$0.106270\pi$
$61$			312.240i			0.655381i	−0.944785	+	0.327691i	$0.893730\pi$
$62$		−	274.257i		−	0.561784i
$63$	99.6952	−	490.008i	0.199372	−	0.979924i
$64$	−829.955			−1.62101
$65$	−16.9260	+	211.247i	−0.0322986	+	0.403108i
$66$	189.603	+	675.646i	0.353614	+	1.26010i
$67$			751.739i			1.37074i	0.728195	+	0.685370i	$0.240359\pi$
$67$			751.739i			1.37074i	−0.728195	+	0.685370i	$0.759641\pi$
$68$			54.6119i			0.0973921i
$69$	673.274	−	188.937i	1.17468	−	0.329643i
$70$	−624.656	−	680.071i	−1.06658	−	1.16120i
$71$			640.823i			1.07115i	0.844487	+	0.535576i	$0.179905\pi$
$71$			640.823i			1.07115i	−0.844487	+	0.535576i	$0.820095\pi$
$72$	−399.783	+	243.558i	−0.654373	+	0.398660i
$73$	−469.117			−0.752137			−0.376069	−	0.926592i	$-0.622724\pi$
$73$	−469.117			−0.752137			−0.376069	+	0.926592i	$0.622724\pi$
$74$		−	1505.52i		−	2.36504i
$75$	645.327	−	73.6793i	0.993545	−	0.113437i
$76$			1421.72i			2.14583i
$77$	411.177	+	381.435i	0.608545	+	0.564527i
$78$	422.904	−	118.677i	0.613903	−	0.172276i
$79$	126.493			0.180147			0.0900733	−	0.995935i	$-0.471290\pi$
$79$	126.493			0.180147			0.0900733	+	0.995935i	$0.471290\pi$
$80$	15.8783	−	198.172i	0.0221906	−	0.276953i
$81$	334.337	−	647.812i	0.458624	−	0.888630i
$82$	604.734			0.814411
$83$			299.265i			0.395766i	0.980226	+	0.197883i	$0.0634066\pi$
$83$			299.265i			0.395766i	−0.980226	+	0.197883i	$0.936593\pi$
$84$	−522.495	+	1017.73i	−0.678677	+	1.32194i
$85$	−51.1976	−	4.10215i	−0.0653312	−	0.00523459i
$86$			1206.90i			1.51329i
$87$	285.204	+	1016.32i	0.351461	+	1.25242i
$88$		−	525.058i		−	0.636039i
$89$	−425.893			−0.507242			−0.253621	−	0.967304i	$-0.581622\pi$
$89$	−425.893			−0.507242			−0.253621	+	0.967304i	$0.581622\pi$
$90$	−606.343	−	1201.93i	−0.710158	−	1.40771i
$91$	238.750	−	257.366i	0.275030	−	0.296475i
$92$	−1599.83			−1.81297
$93$	−86.3396	−	307.670i	−0.0962688	−	0.343052i
$94$		−	1218.88i		−	1.33743i
$95$	−1332.84	−	106.792i	−1.43943	−	0.115333i
$96$	−1090.66	+	306.064i	−1.15953	+	0.325391i
$97$	−561.656			−0.587913			−0.293957	−	0.955819i	$-0.594972\pi$
$97$	−561.656			−0.587913			−0.293957	+	0.955819i	$0.594972\pi$
$98$	114.635	+	1525.33i	0.118162	+	1.57227i
$99$	425.405	+	698.272i	0.431867	+	0.708878i
$100$	−1467.02	−	236.606i	−1.46702	−	0.236606i
$101$	1733.15			1.70747			0.853736	−	0.520706i	$-0.174331\pi$
$101$	1733.15			1.70747			0.853736	+	0.520706i	$0.174331\pi$
$102$	28.7624	+	102.494i	0.0279206	+	0.0994945i
$103$	−1704.95			−1.63101			−0.815504	−	0.578751i	$-0.803540\pi$
$103$	−1704.95			−1.63101			−0.815504	+	0.578751i	$0.803540\pi$
$104$	−328.647			−0.309870
$105$	−914.854	−	566.275i	−0.850292	−	0.526312i
$106$	993.867			0.910688
$107$	−397.788			−0.359399			−0.179699	−	0.983722i	$-0.557512\pi$
$107$	−397.788			−0.359399			−0.179699	+	0.983722i	$0.557512\pi$
$108$	−1136.89	+	1220.29i	−1.01294	+	1.08724i
$109$	1382.72			1.21505			0.607526	−	0.794300i	$-0.292162\pi$
$109$	1382.72			1.21505			0.607526	+	0.794300i	$0.292162\pi$
$110$	1505.09	+	120.594i	1.30459	+	0.104529i
$111$	−473.957	−	1688.94i	−0.405280	−	1.44421i
$112$	−223.971	+	241.435i	−0.188958	+	0.203692i
$113$	1029.11			0.856728			0.428364	−	0.903606i	$-0.359090\pi$
$113$	1029.11			0.856728			0.428364	+	0.903606i	$0.359090\pi$
$114$	748.777	+	2668.25i	0.615170	+	2.19215i
$115$	120.170	−	1499.81i	0.0974430	−	1.21615i
$116$		−	2414.97i		−	1.93297i
$117$	437.066	−	266.271i	0.345357	−	0.210400i
$118$	3277.91			2.55725
$119$	62.3747	+	57.8629i	0.0480494	+	0.0445738i
$120$	193.823	+	988.433i	0.147446	+	0.751926i
$121$	413.918			0.310983
$122$		−	1392.46i		−	1.03334i
$123$	678.409	−	190.378i	0.497318	−	0.139559i
$124$			731.083i			0.529461i
$125$	332.008	−	1357.53i	0.237566	−	0.971371i
$126$	−444.599	+	2185.23i	−0.314349	+	1.54505i
$127$		−	1251.75i		−	0.874602i	−0.899315	−	0.437301i	$-0.855934\pi$
$127$		−	1251.75i		−	0.874602i	0.899315	−	0.437301i	$-0.144066\pi$
$128$	1957.21			1.35152
$129$	379.947	+	1353.94i	0.259322	+	0.924089i
$130$	75.4827	−	942.075i	0.0509251	−	0.635580i
$131$	−1225.39			−0.817274			−0.408637	−	0.912697i	$-0.633996\pi$
$131$	−1225.39			−0.817274			−0.408637	+	0.912697i	$0.633996\pi$
$132$	−505.422	−	1801.06i	−0.333268	−	1.18759i
$133$	1623.81	+	1506.36i	1.05867	+	0.982088i
$134$		−	3352.44i		−	2.16124i
$135$	−1058.60	−	1157.47i	−0.674886	−	0.737922i
$136$		−	79.6503i		−	0.0502203i
$137$	1748.45			1.09037			0.545183	−	0.838317i	$-0.316460\pi$
$137$	1748.45			1.09037			0.545183	+	0.838317i	$0.316460\pi$
$138$	−3002.52	+	842.579i	−1.85211	+	0.519747i
$139$			2075.28i			1.26635i	0.774007	+	0.633177i	$0.218250\pi$
$139$			2075.28i			1.26635i	−0.774007	+	0.633177i	$0.781750\pi$
$140$	1665.14	+	1812.86i	1.00521	+	1.09439i
$141$	−383.720	−	1367.38i	−0.229185	−	0.816697i
$142$		−	2857.80i		−	1.68888i
$143$			574.024i			0.335681i
$144$	−410.012	+	249.790i	−0.237275	+	0.144554i
$145$	2263.99	+	181.399i	1.29665	+	0.103892i
$146$	2092.07			1.18589
$147$	608.796	+	1675.08i	0.341583	+	0.939852i
$148$			4013.25i			2.22896i
$149$		−	192.111i		−	0.105627i	−0.998604	−	0.0528133i	$-0.983181\pi$
$149$		−	192.111i		−	0.105627i	0.998604	−	0.0528133i	$-0.0168188\pi$
$150$	−2877.89	+	328.579i	−1.56652	+	0.178856i
$151$	−2157.41			−1.16270			−0.581350	−	0.813654i	$-0.697475\pi$
$151$	−2157.41			−1.16270			−0.581350	+	0.813654i	$0.697475\pi$
$152$		−	2073.55i		−	1.10650i
$153$	64.5330	+	105.926i	0.0340993	+	0.0559715i
$154$	−1833.68	−	1701.04i	−0.959493	−	0.890089i
$155$	−685.376	−	54.9149i	−0.355166	−	0.0284572i
$156$	−1127.33	+	316.356i	−0.578581	+	0.162364i
$157$	−1016.31			−0.516625			−0.258312	−	0.966061i	$-0.583166\pi$
$157$	−1016.31			−0.516625			−0.258312	+	0.966061i	$0.583166\pi$
$158$	−564.106			−0.284037
$159$	1114.95	−	312.882i	0.556109	−	0.156058i
$160$	−194.667	+	2429.58i	−0.0961863	+	1.20047i
$161$	−1695.07	+	1827.24i	−0.829751	+	0.894450i
$162$	−1491.00	+	2888.97i	−0.723112	+	1.40110i
$163$		−	2851.10i		−	1.37003i	−0.728527	−	0.685017i	$-0.759795\pi$
$163$		−	2851.10i		−	1.37003i	0.728527	−	0.685017i	$-0.240205\pi$
$164$	−1612.03			−0.767552
$165$	1726.43	−	338.537i	0.814558	−	0.159728i
$166$		−	1334.59i		−	0.624004i
$167$			1887.62i			0.874662i	0.899301	+	0.437331i	$0.144076\pi$
$167$			1887.62i			0.874662i	−0.899301	+	0.437331i	$0.855924\pi$
$168$	762.048	−	1484.34i	0.349960	−	0.681661i
$169$	−1837.70			−0.836461
$170$	228.320	+	18.2938i	0.103008	+	0.00825338i
$171$	1680.00	+	2757.60i	0.751304	+	1.23321i
$172$		−	3217.21i		−	1.42622i
$173$		−	3491.67i		−	1.53449i	−0.641353	−	0.767246i	$-0.721627\pi$
$173$		−	3491.67i		−	1.53449i	0.641353	−	0.767246i	$-0.278373\pi$
$174$	−1271.89	−	4532.36i	−0.554148	−	1.97470i
$175$	−1824.59	+	1424.86i	−0.788150	+	0.615483i
$176$		−	538.493i		−	0.230628i
$177$	3677.26	−	1031.93i	1.56158	−	0.438217i
$178$	1899.30			0.799769
$179$			172.498i			0.0720286i	0.999351	+	0.0360143i	$0.0114662\pi$
$179$			172.498i			0.0720286i	−0.999351	+	0.0360143i	$0.988534\pi$
$180$	1616.32	+	3203.96i	0.669298	+	1.32672i
$181$			2106.81i			0.865182i	0.901590	+	0.432591i	$0.142401\pi$
$181$			2106.81i			0.865182i	−0.901590	+	0.432591i	$0.857599\pi$
$182$	−1064.72	+	1147.74i	−0.433640	+	0.467453i
$183$	−438.365	−	1562.10i	−0.177076	−	0.631006i
$184$	2333.32			0.934861
$185$	−3762.34	−	301.453i	−1.49520	−	0.119801i
$186$	385.038	+	1372.08i	0.151787	+	0.540890i
$187$	−139.119			−0.0544033
$188$			3249.16i			1.26048i
$189$	189.174	+	2591.42i	0.0728063	+	0.997346i
$190$	5943.89	+	476.247i	2.26955	+	0.181845i
$191$		−	633.737i		−	0.240082i	−0.992769	−	0.120041i	$-0.961697\pi$
$191$		−	633.737i		−	0.240082i	0.992769	−	0.120041i	$-0.0383026\pi$
$192$	4152.18	−	1165.20i	1.56072	−	0.437975i
$193$			4520.88i			1.68611i	0.537824	+	0.843057i	$0.319246\pi$
$193$			4520.88i			1.68611i	−0.537824	+	0.843057i	$0.680754\pi$
$194$	2504.75			0.926962
$195$	−211.899	−	1080.61i	−0.0778174	−	0.396842i
$196$	−305.580	−	4066.07i	−0.111363	−	1.48180i
$197$	3816.25			1.38018			0.690092	−	0.723722i	$-0.257570\pi$
$197$	3816.25			1.38018			0.690092	+	0.723722i	$0.257570\pi$
$198$	−1897.13	−	3114.00i	−0.680924	−	1.11769i
$199$		−	1340.01i		−	0.477341i	−0.971101	−	0.238670i	$-0.923288\pi$
$199$		−	1340.01i		−	0.477341i	0.971101	−	0.238670i	$-0.0767115\pi$
$200$	2139.62	+	345.085i	0.756471	+	0.122006i
$201$	−1055.39	−	3760.87i	−0.370356	−	1.31976i
$202$	−7729.11			−2.69217
$203$	−2758.25	−	2558.73i	−0.953651	−	0.884670i
$204$	−76.6715	−	273.218i	−0.0263141	−	0.0937699i
$205$	121.087	−	1511.25i	0.0412541	−	0.514879i
$206$	7603.37			2.57161
$207$	−3103.06	+	1890.46i	−1.04192	+	0.634765i
$208$	−337.056			−0.112359
$209$	−3621.73			−1.19866
$210$	4079.86	+	2525.35i	1.34065	+	0.829836i
$211$	729.169			0.237905			0.118953	−	0.992900i	$-0.462046\pi$
$211$	729.169			0.237905			0.118953	+	0.992900i	$0.462046\pi$
$212$	−2649.34			−0.858290
$213$	−899.674	−	3205.97i	−0.289411	−	1.03131i
$214$	1773.97			0.566664
$215$	3016.07	+	241.660i	0.956719	+	0.0766560i
$216$	1658.13	−	1779.76i	0.522322	−	0.560636i
$217$	835.003	+	774.604i	0.261215	+	0.242320i
$218$	−6166.36			−1.91577
$219$	2346.95	−	658.610i	0.724164	−	0.203218i
$220$	−4012.11	−	321.466i	−1.22953	−	0.0985146i
$221$			87.0783i			0.0265046i
$222$	2113.65	+	7531.96i	0.639004	+	2.27708i
$223$	3259.48			0.978793			0.489396	−	0.872061i	$-0.337217\pi$
$223$	3259.48			0.978793			0.489396	+	0.872061i	$0.337217\pi$
$224$	2745.89	−	2959.99i	0.819050	−	0.882915i
$225$	−3125.06	+	1274.61i	−0.925944	+	0.377661i
$226$	−4589.39			−1.35080
$227$			4188.94i			1.22480i	0.790548	+	0.612401i	$0.209796\pi$
$227$			4188.94i			1.22480i	−0.790548	+	0.612401i	$0.790204\pi$
$228$	−1996.01	−	7112.73i	−0.579775	−	2.06602i
$229$			1996.90i			0.576240i	0.957594	+	0.288120i	$0.0930302\pi$
$229$			1996.90i			0.576240i	−0.957594	+	0.288120i	$0.906970\pi$
$230$	−535.909	+	6688.51i	−0.153638	+	1.91751i
$231$	−2592.59	−	1331.01i	−0.738440	−	0.379110i
$232$			3522.19i			0.996736i
$233$	−141.704			−0.0398425			−0.0199213	−	0.999802i	$-0.506342\pi$
$233$	−141.704			−0.0398425			−0.0199213	+	0.999802i	$0.506342\pi$
$234$	−1949.13	+	1187.46i	−0.544524	+	0.331737i
$235$	−3046.03	−	244.059i	−0.845535	−	0.0677476i
$236$	−8737.88			−2.41012
$237$	−632.832	+	177.588i	−0.173447	+	0.0486733i
$238$	−278.165	−	258.044i	−0.0757595	−	0.0702795i
$239$			2702.30i			0.731369i	0.930739	+	0.365684i	$0.119165\pi$
$239$			2702.30i			0.731369i	−0.930739	+	0.365684i	$0.880835\pi$
$240$	198.783	+	1013.72i	0.0534640	+	0.272648i
$241$		−	4299.54i		−	1.14920i	−0.818434	−	0.574601i	$-0.805157\pi$
$241$		−	4299.54i		−	1.14920i	0.818434	−	0.574601i	$-0.194843\pi$
$242$	−1845.90			−0.490326
$243$	−763.168	+	3710.32i	−0.201470	+	0.979495i
$244$			3711.86i			0.973884i
$245$	3834.81	+	18.9455i	0.999988	+	0.00494033i
$246$	−3025.42	+	849.006i	−0.784121	+	0.220043i
$247$			2266.93i			0.583972i
$248$		−	1066.27i		−	0.273017i
$249$	−420.148	−	1497.19i	−0.106931	−	0.381047i
$250$	−1480.62	+	6054.03i	−0.374570	+	1.53156i
$251$	3307.05			0.831630			0.415815	−	0.909449i	$-0.363496\pi$
$251$	3307.05			0.831630			0.415815	+	0.909449i	$0.363496\pi$
$252$	1185.16	−	5825.14i	0.296263	−	1.45615i
$253$		−	4075.44i		−	1.01273i
$254$			5582.26i			1.37898i
$255$	261.895	−	51.3554i	0.0643157	−	0.0126118i
$256$	−2088.71			−0.509938
$257$		−	3931.01i		−	0.954123i	−0.878870	−	0.477061i	$-0.841702\pi$
$257$		−	3931.01i		−	0.954123i	0.878870	−	0.477061i	$-0.158298\pi$
$258$	−1694.41	−	6037.99i	−0.408872	−	1.45701i
$259$	4583.71	+	4252.15i	1.09968	+	1.02014i
$260$	−201.213	+	2511.28i	−0.0479951	+	0.599011i
$261$	−2853.69	−	4684.13i	−0.676778	−	1.11088i
$262$	5464.73			1.28860
$263$	2083.22			0.488430			0.244215	−	0.969721i	$-0.421470\pi$
$263$	2083.22			0.488430			0.244215	+	0.969721i	$0.421470\pi$
$264$	737.147	+	2626.81i	0.171850	+	0.612383i
$265$	199.004	−	2483.70i	0.0461310	−	0.575746i
$266$	−7241.53	−	6717.72i	−1.66920	−	1.54846i
$267$	2130.70	−	597.926i	0.488377	−	0.137050i
$268$			8936.56i			2.03689i
$269$	−2905.93			−0.658653			−0.329326	−	0.944216i	$-0.606822\pi$
$269$	−2905.93			−0.658653			−0.329326	+	0.944216i	$0.606822\pi$
$270$	4720.90	+	5161.85i	1.06409	+	1.16348i
$271$		−	716.004i		−	0.160495i	−0.996775	−	0.0802475i	$-0.974429\pi$
$271$		−	716.004i		−	0.160495i	0.996775	−	0.0802475i	$-0.0255711\pi$
$272$		−	81.6883i		−	0.0182099i
$273$	−833.115	+	1622.76i	−0.184697	+	0.359759i
$274$	−7797.36			−1.71918
$275$	602.735	−	3737.13i	0.132168	−	0.819481i
$276$	8003.78	−	2246.05i	1.74555	−	0.489843i
$277$		−	101.240i		−	0.0219601i	−0.999940	−	0.0109801i	$-0.996505\pi$
$277$		−	101.240i		−	0.0219601i	0.999940	−	0.0109801i	$-0.00349513\pi$
$278$		−	9254.89i		−	1.99666i
$279$	863.896	+	1418.02i	0.185377	+	0.304283i
$280$	−2428.57	−	2644.01i	−0.518339	−	0.564322i
$281$			7745.33i			1.64430i	0.569272	+	0.822149i	$0.307225\pi$
$281$			7745.33i			1.64430i	−0.569272	+	0.822149i	$0.692775\pi$
$282$	1711.23	+	6097.95i	0.361356	+	1.28769i
$283$	−381.119			−0.0800536			−0.0400268	−	0.999199i	$-0.512744\pi$
$283$	−381.119			−0.0800536			−0.0400268	+	0.999199i	$0.512744\pi$
$284$			7618.01i			1.59171i
$285$	6817.97	−	1336.95i	1.41706	−	0.277873i
$286$		−	2559.91i		−	0.529267i
$287$	−1708.00	+	1841.17i	−0.351288	+	0.378680i
$288$	5026.74	−	3062.42i	1.02848	−	0.626579i
$289$	4891.90			0.995704
$290$	−10096.4	−	808.965i	−2.04442	−	0.163807i
$291$	2809.91	−	788.529i	0.566047	−	0.158847i
$292$	−5576.80			−1.11766
$293$			2325.30i			0.463637i	0.972759	+	0.231818i	$0.0744675\pi$
$293$			2325.30i			0.463637i	−0.972759	+	0.231818i	$0.925532\pi$
$294$	−2714.97	−	7470.15i	−0.538573	−	1.48186i
$295$	656.342	−	8191.59i	0.129538	−	1.61672i
$296$		−	5853.23i		−	1.14937i
$297$	−3108.58	−	2896.14i	−0.607334	−	0.565829i
$298$			856.735i			0.166541i
$299$	−2550.92			−0.493389
$300$	7671.55	−	875.889i	1.47639	−	0.168565i
$301$	−3674.53	−	3408.73i	−0.703642	−	0.652745i
$302$	9621.14			1.83323
$303$	−8670.76	+	2433.23i	−1.64397	+	0.461337i
$304$		−	2126.61i		−	0.401215i
$305$	−3479.80	−	278.815i	−0.653287	−	0.0523439i
$306$	−287.790	−	472.387i	−0.0537643	−	0.0882503i
$307$	3447.89			0.640981			0.320491	−	0.947252i	$-0.396152\pi$
$307$	3447.89			0.640981			0.320491	+	0.947252i	$0.396152\pi$
$308$	4888.01	+	4534.44i	0.904286	+	0.838876i
$309$	8529.70	−	2393.64i	1.57035	−	0.440678i
$310$	3056.49	+	244.897i	0.559990	+	0.0448685i
$311$	7675.73			1.39952			0.699760	−	0.714378i	$-0.253290\pi$
$311$	7675.73			1.39952			0.699760	+	0.714378i	$0.253290\pi$
$312$	1644.19	−	461.399i	0.298345	−	0.0837230i
$313$	9734.46			1.75790			0.878952	−	0.476910i	$-0.158243\pi$
$313$	9734.46			1.75790			0.878952	+	0.476910i	$0.158243\pi$
$314$	4532.30			0.814562
$315$	5371.93	+	1548.62i	0.960870	+	0.276999i
$316$	1503.73			0.267694
$317$	−688.561			−0.121998			−0.0609991	−	0.998138i	$-0.519429\pi$
$317$	−688.561			−0.121998			−0.0609991	+	0.998138i	$0.519429\pi$
$318$	−4972.21	+	1395.32i	−0.876817	+	0.246056i
$319$	6151.95			1.07976
$320$	741.109	−	9249.54i	0.129466	−	1.61583i
$321$	1990.09	−	558.469i	0.346032	−	0.0971050i
$322$	7559.28	−	8148.71i	1.30827	−	1.41028i
$323$	−549.409			−0.0946437
$324$	3974.55	−	7701.09i	0.681507	−	1.32049i
$325$	−2339.16	−	377.267i	−0.399241	−	0.0643908i
$326$			12714.7i			2.16013i
$327$	−6917.61	+	1941.25i	−1.16986	+	0.328292i
$328$	2351.11			0.395788
$329$	3711.02	+	3442.58i	0.621869	+	0.576887i
$330$	−7699.13	+	1509.73i	−1.28431	+	0.251843i
$331$	4447.67			0.738568			0.369284	−	0.929317i	$-0.379603\pi$
$331$	4447.67			0.738568			0.369284	+	0.929317i	$0.379603\pi$
$332$			3557.61i			0.588101i
$333$	4742.32	+	7784.18i	0.780413	+	1.28099i
$334$		−	8418.00i		−	1.37908i
$335$	−8377.85	−	671.265i	−1.36636	−	0.109478i
$336$	781.546	−	1522.32i	0.126895	−	0.247170i
$337$		−	4087.57i		−	0.660724i	−0.943854	−	0.330362i	$-0.892829\pi$
$337$		−	4087.57i		−	0.660724i	0.943854	−	0.330362i	$-0.107171\pi$
$338$	8195.39			1.31885
$339$	−5148.52	+	1444.80i	−0.824864	+	0.231477i
$340$	−608.629	−	48.7657i	−0.0970810	−	0.00777850i
$341$	−1862.38			−0.295757
$342$	−7492.10	−	12297.8i	−1.18458	−	1.94441i
$343$	−4967.81	−	3959.10i	−0.782031	−	0.623240i
$344$			4692.24i			0.735432i
$345$	1504.43	+	7672.09i	0.234771	+	1.19725i
$346$			15571.4i			2.41943i
$347$	−5812.08			−0.899161			−0.449580	−	0.893240i	$-0.648427\pi$
$347$	−5812.08			−0.899161			−0.449580	+	0.893240i	$0.648427\pi$
$348$	3390.46	+	12081.9i	0.522264	+	1.86108i
$349$		−	2804.01i		−	0.430073i	−0.976606	−	0.215036i	$-0.931013\pi$
$349$		−	2804.01i		−	0.430073i	0.976606	−	0.215036i	$-0.0689870\pi$
$350$	8136.92	−	6354.29i	1.24268	−	0.970431i
$351$	−1812.77	+	1945.74i	−0.275665	+	0.295886i
$352$			6601.92i			0.999669i
$353$			1183.07i			0.178381i	0.996015	+	0.0891907i	$0.0284281\pi$
$353$			1183.07i			0.178381i	−0.996015	+	0.0891907i	$0.971572\pi$
$354$	−16399.0	+	4601.97i	−2.46214	+	0.690937i
$355$	−7141.74	−	572.223i	−1.06773	−	0.0855506i
$356$	−5062.95			−0.753753
$357$	−393.290	−	201.912i	−0.0583056	−	0.0299337i
$358$		−	769.269i		−	0.113567i
$359$		−	8708.99i		−	1.28034i	−0.768232	−	0.640171i	$-0.778863\pi$
$359$		−	8708.99i		−	1.28034i	0.768232	−	0.640171i	$-0.221137\pi$
$360$	−2357.37	−	4672.91i	−0.345123	−	0.684122i
$361$	−7443.86			−1.08527
$362$		−	9395.49i		−	1.36413i
$363$	−2070.79	+	581.114i	−0.299417	+	0.0840236i
$364$	2838.22	−	3059.53i	0.408690	−	0.440557i
$365$	418.898	−	5228.14i	0.0600716	−	0.749735i
$366$	1954.92	+	6966.33i	0.279195	+	0.994907i
$367$	7352.20			1.04573			0.522864	−	0.852416i	$-0.324864\pi$
$367$	7352.20			1.04573			0.522864	+	0.852416i	$0.324864\pi$
$368$	2393.02			0.338980
$369$	−3126.73	+	1904.88i	−0.441114	+	0.268738i
$370$	16778.4	+	1344.35i	2.35749	+	0.188891i
$371$	−2807.05	+	3025.93i	−0.392817	+	0.423446i
$372$	−1026.39	−	3657.53i	−0.143054	−	0.509769i
$373$			1319.56i			0.183174i	0.995797	+	0.0915872i	$0.0291940\pi$
$373$			1319.56i			0.183174i	−0.995797	+	0.0915872i	$0.970806\pi$
$374$	620.414			0.0857777
$375$	244.884	+	7257.71i	0.0337220	+	0.999431i
$376$		−	4738.84i		−	0.649965i
$377$		−	3850.66i		−	0.526045i
$378$	−843.637	−	11556.7i	−0.114794	−	1.57252i
$379$	−10334.2			−1.40062			−0.700309	−	0.713839i	$-0.746955\pi$
$379$	−10334.2			−1.40062			−0.700309	+	0.713839i	$0.746955\pi$
$380$	−15844.6	−	1269.53i	−2.13897	−	0.171383i
$381$	1757.37	+	6262.35i	0.236306	+	0.842074i
$382$			2826.20i			0.378537i
$383$			13328.0i			1.77815i	0.457763	+	0.889074i	$0.348651\pi$
$383$			13328.0i			1.77815i	−0.457763	+	0.889074i	$0.651349\pi$
$384$	−9791.74	+	2747.80i	−1.30126	+	0.365164i
$385$	−4618.11	+	4241.81i	−0.611326	+	0.561513i
$386$		−	20161.2i		−	2.65850i
$387$	−3801.67	−	6240.18i	−0.499354	−	0.819654i
$388$	−6676.89			−0.873628
$389$			6183.45i			0.805947i	0.915212	+	0.402973i	$0.132023\pi$
$389$			6183.45i			0.805947i	−0.915212	+	0.402973i	$0.867977\pi$
$390$	944.979	+	4819.08i	0.122695	+	0.625701i
$391$		−	618.236i		−	0.0799630i
$392$	445.682	+	5930.27i	0.0574243	+	0.764092i
$393$	6130.50	−	1720.37i	0.786878	−	0.220817i
$394$	−17018.8			−2.17614
$395$	−112.952	+	1409.72i	−0.0143879	+	0.179571i
$396$	5057.15	+	8300.95i	0.641746	+	1.05338i
$397$	−2722.53			−0.344181			−0.172091	−	0.985081i	$-0.555052\pi$
$397$	−2722.53			−0.344181			−0.172091	+	0.985081i	$0.555052\pi$
$398$			5975.88i			0.752623i
$399$	−10238.6	−	5256.42i	−1.28464	−	0.659524i
$400$	2194.37	+	353.915i	0.274296	+	0.0442393i
$401$		−	6359.86i		−	0.792011i	−0.918248	−	0.396005i	$-0.870396\pi$
$401$		−	6359.86i		−	0.792011i	0.918248	−	0.396005i	$-0.129604\pi$
$402$	4706.60	+	16771.9i	0.583941	+	2.08086i
$403$			1165.71i			0.144089i
$404$	20603.4			2.53727
$405$	6921.07	+	4304.52i	0.849162	+	0.528132i
$406$	12300.6	+	11410.9i	1.50362	+	1.39486i
$407$	−10223.4			−1.24510
$408$	111.824	+	398.482i	0.0135689	+	0.0483525i
$409$			2243.08i			0.271181i	0.990765	+	0.135591i	$0.0432932\pi$
$409$			2243.08i			0.271181i	−0.990765	+	0.135591i	$0.956707\pi$
$410$	−539.997	+	6739.53i	−0.0650453	+	0.811809i
$411$	−8747.32	+	2454.71i	−1.04981	+	0.294603i
$412$	−20268.2			−2.42365
$413$	−9258.04	+	9979.93i	−1.10305	+	1.18906i
$414$	13838.4	−	8430.67i	1.64280	−	1.00083i
$415$	−3335.19	−	267.229i	−0.394502	−	0.0316090i
$416$	4132.30			0.487026
$417$	−2913.56	−	10382.4i	−0.342153	−	1.21926i
$418$	16151.4			1.88993
$419$	12565.4			1.46505			0.732527	−	0.680738i	$-0.238341\pi$
$419$	12565.4			1.46505			0.732527	+	0.680738i	$0.238341\pi$
$420$	−10875.6	−	6731.79i	−1.26352	−	0.782090i
$421$	3903.57			0.451896			0.225948	−	0.974139i	$-0.427452\pi$
$421$	3903.57			0.451896			0.225948	+	0.974139i	$0.427452\pi$
$422$	−3251.79			−0.375105
$423$	3839.43	+	6302.15i	0.441322	+	0.724399i
$424$	3864.01			0.442577
$425$	91.4337	−	566.915i	0.0104357	−	0.0647045i
$426$	4012.17	+	14297.3i	0.456315	+	1.62607i
$427$	4239.49	+	3932.83i	0.480476	+	0.445721i
$428$	−4728.85			−0.534060
$429$	−805.892	−	2871.78i	−0.0906966	−	0.323196i
$430$	−13450.4	−	1077.70i	−1.50846	−	0.120864i
$431$		−	5029.93i		−	0.562142i	−0.959687	−	0.281071i	$-0.909310\pi$
$431$		−	5029.93i		−	0.562142i	0.959687	−	0.281071i	$-0.0906897\pi$
$432$	1700.56	−	1825.30i	0.189394	−	0.203287i
$433$	−14864.3			−1.64972			−0.824862	−	0.565334i	$-0.808747\pi$
$433$	−14864.3			−1.64972			−0.824862	+	0.565334i	$0.808747\pi$
$434$	−3723.76	−	3454.41i	−0.411858	−	0.382066i
$435$	−11581.2	+	2270.97i	−1.27649	+	0.250309i
$436$	16437.6			1.80555
$437$		−	16094.7i		−	1.76181i
$438$	−10466.4	+	2937.12i	−1.14179	+	0.320414i
$439$			11284.2i			1.22680i	0.789771	+	0.613402i	$0.210199\pi$
$439$			11284.2i			1.22680i	−0.789771	+	0.613402i	$0.789801\pi$
$440$	5851.58	+	468.851i	0.634007	+	0.0507991i
$441$	−5397.44	−	7525.54i	−0.582814	−	0.812605i
$442$		−	388.333i		−	0.0417898i
$443$	6406.23			0.687064			0.343532	−	0.939141i	$-0.388377\pi$
$443$	6406.23			0.687064			0.343532	+	0.939141i	$0.388377\pi$
$444$	−5634.33	−	20077.8i	−0.602238	−	2.14606i
$445$	380.301	−	4746.42i	0.0405124	−	0.505622i
$446$	−14535.9			−1.54326
$447$	269.712	+	961.113i	0.0285390	+	0.101698i
$448$	−10453.7	+	11268.8i	−1.10244	+	1.18840i
$449$			5647.45i			0.593585i	0.954942	+	0.296792i	$0.0959169\pi$
$449$			5647.45i			0.593585i	−0.954942	+	0.296792i	$0.904083\pi$
$450$	13936.5	−	5684.21i	1.45994	−	0.595458i
$451$		−	4106.52i		−	0.428755i
$452$	12233.9			1.27308
$453$	10793.3	−	3028.86i	1.11946	−	0.314147i
$454$		−	18680.9i		−	1.93114i
$455$	2655.05	+	2890.59i	0.273562	+	0.297831i
$456$	2911.13	+	10373.8i	0.298961	+	1.06534i
$457$		−	4027.42i		−	0.412243i	−0.978526	−	0.206121i	$-0.933916\pi$
$457$		−	4027.42i		−	0.412243i	0.978526	−	0.206121i	$-0.0660842\pi$
$458$		−	8905.34i		−	0.908558i
$459$	−471.566	−	439.339i	−0.0479538	−	0.0446766i
$460$	1428.57	−	17829.5i	0.144798	−	1.80718i
$461$	4322.13			0.436663			0.218332	−	0.975875i	$-0.429939\pi$
$461$	4322.13			0.436663			0.218332	+	0.975875i	$0.429939\pi$
$462$	11561.8	+	5935.76i	1.16430	+	0.597742i
$463$			13087.8i			1.31370i	0.754021	+	0.656850i	$0.228111\pi$
$463$			13087.8i			1.31370i	−0.754021	+	0.656850i	$0.771889\pi$
$464$			3612.31i			0.361416i
$465$	3505.96	−	687.489i	0.349645	−	0.0685624i
$466$	631.938			0.0628197
$467$		−	2525.04i		−	0.250203i	−0.992144	−	0.125102i	$-0.960074\pi$
$467$		−	2525.04i		−	0.250203i	0.992144	−	0.125102i	$-0.0399257\pi$
$468$	5195.77	−	3165.39i	0.513193	−	0.312650i
$469$	10206.8	+	9468.55i	1.00492	+	0.932232i
$470$	13584.0	+	1088.40i	1.33316	+	0.106818i
$471$	5084.47	−	1426.83i	0.497410	−	0.139585i
$472$	12744.0			1.24278
$473$	8195.60			0.796689
$474$	2822.16	−	791.968i	0.273473	−	0.0767432i
$475$	2380.31	−	14758.6i	0.229929	−	1.42562i
$476$	741.501	+	687.866i	0.0714005	+	0.0662359i
$477$	−5138.72	+	3130.64i	−0.493262	+	0.300507i
$478$		−	12051.1i		−	1.15315i
$479$	−3175.55			−0.302911			−0.151456	−	0.988464i	$-0.548396\pi$
$479$	−3175.55			−0.302911			−0.151456	+	0.988464i	$0.548396\pi$
$480$	−2437.07	−	12428.2i	−0.231743	−	1.18181i
$481$			6399.09i			0.606598i
$482$			19174.1i			1.81195i
$483$	5914.92	−	11521.2i	0.557222	−	1.08537i
$484$	4920.59			0.462114
$485$	501.531	−	6259.45i	0.0469554	−	0.586035i
$486$	3403.41	−	16546.5i	0.317658	−	1.54437i
$487$			3971.81i			0.369569i	0.982779	+	0.184785i	$0.0591587\pi$
$487$			3971.81i			0.369569i	−0.982779	+	0.184785i	$0.940841\pi$
$488$		−	5413.67i		−	0.502183i
$489$	4002.76	+	14263.8i	0.370166	+	1.31908i
$490$	−17101.6	−	84.4888i	−1.57668	−	0.00778941i
$491$			10854.4i			0.997665i	0.866698	+	0.498833i	$0.166238\pi$
$491$			10854.4i			0.997665i	−0.866698	+	0.498833i	$0.833762\pi$
$492$	8064.83	−	2263.19i	0.739005	−	0.207383i
$493$	933.239			0.0852555
$494$		−	10109.5i		−	0.920749i
$495$	−8161.84	+	4117.45i	−0.741106	+	0.373870i
$496$		−	1093.55i		−	0.0989958i
$497$	8700.88	+	8071.51i	0.785287	+	0.728484i
$498$	1873.68	+	6676.84i	0.168598	+	0.600796i
$499$	−4802.55			−0.430845			−0.215423	−	0.976521i	$-0.569113\pi$
$499$	−4802.55			−0.430845			−0.215423	+	0.976521i	$0.569113\pi$
$500$	3946.87	−	16138.1i	0.353018	−	1.44344i
$501$	−2650.10	−	9443.57i	−0.236323	−	0.842131i
$502$	−14748.1			−1.31123
$503$		−	13959.0i		−	1.23738i	−0.785636	−	0.618689i	$-0.787664\pi$
$503$		−	13959.0i		−	1.23738i	0.785636	−	0.618689i	$-0.212336\pi$
$504$	−1728.53	+	8495.85i	−0.152768	+	0.750863i
$505$	−1547.61	+	19315.3i	−0.136372	+	1.70202i
$506$			18174.7i			1.59677i
$507$	9193.84	−	2580.02i	0.805351	−	0.226001i
$508$		−	14880.6i		−	1.29964i
$509$	−13117.5			−1.14228			−0.571141	−	0.820852i	$-0.693499\pi$
$509$	−13117.5			−1.14228			−0.571141	+	0.820852i	$0.693499\pi$
$510$	−1167.94	+	229.024i	−0.101407	+	0.0198850i
$511$	−5908.78	+	6369.51i	−0.511525	+	0.551410i
$512$	−6342.96			−0.547503
$513$	−12276.4	−	11437.4i	−1.05656	−	0.984354i
$514$			17530.6i			1.50436i
$515$	1522.44	−	19001.0i	0.130265	−	1.62580i
$516$	4516.76	+	16095.4i	0.385347	+	1.37318i
$517$	−8276.99			−0.704103
$518$	−20441.4	−	18962.8i	−1.73387	−	1.60845i
$519$	4902.08	+	17468.5i	0.414600	+	1.47742i
$520$	293.465	−	3662.65i	0.0247487	−	0.308880i
$521$	3567.96			0.300029			0.150015	−	0.988684i	$-0.452068\pi$
$521$	3567.96			0.300029			0.150015	+	0.988684i	$0.452068\pi$
$522$	12726.3	+	20889.3i	1.06708	+	1.75153i
$523$	−6801.37			−0.568648			−0.284324	−	0.958728i	$-0.591769\pi$
$523$	−6801.37			−0.568648			−0.284324	+	0.958728i	$0.591769\pi$
$524$	−14567.3			−1.21445
$525$	7127.84	−	9690.05i	0.592542	−	0.805540i
$526$	−9290.30			−0.770107
$527$	−282.519			−0.0233524
$528$	756.009	+	2694.02i	0.0623126	+	0.222050i
$529$	5943.91			0.488527
$530$	−887.474	+	11076.3i	−0.0727347	+	0.907779i
$531$	−16948.2	+	10325.3i	−1.38510	+	0.843838i
$532$	19303.7	+	17907.3i	1.57316	+	1.45936i
$533$	−2570.37			−0.208884
$534$	−9502.02	+	2666.50i	−0.770024	+	0.216087i
$535$	355.205	−	4433.20i	0.0287044	−	0.358251i
$536$		−	13033.8i		−	1.05032i
$537$	−242.176	−	862.991i	−0.0194612	−	0.0693497i
$538$	12959.2			1.03850
$539$	10358.0	−	778.441i	0.827736	−	0.0622075i
$540$	−12584.4	−	13759.9i	−1.00287	−	1.09654i
$541$	2446.78			0.194446			0.0972229	−	0.995263i	$-0.469004\pi$
$541$	2446.78			0.194446			0.0972229	+	0.995263i	$0.469004\pi$
$542$			3193.07i			0.253052i
$543$	−2957.82	−	10540.2i	−0.233761	−	0.833004i
$544$			1001.50i			0.0789317i
$545$	−1234.70	+	15409.9i	−0.0970437	+	1.21117i
$546$	3715.34	−	7236.84i	0.291212	−	0.567231i
$547$			11784.9i			0.921179i	0.887613	+	0.460590i	$0.152362\pi$
$547$			11784.9i			0.921179i	−0.887613	+	0.460590i	$0.847638\pi$
$548$	20785.3			1.62026
$549$	4386.18	+	7199.61i	0.340980	+	0.559694i
$550$	−2687.95	+	16666.0i	−0.208390	+	1.29208i
$551$	24295.2			1.87842
$552$	−11673.3	+	3275.82i	−0.900091	+	0.252587i
$553$	1593.25	−	1717.48i	0.122517	−	0.132070i
$554$			451.490i			0.0346245i
$555$	19245.8	−	3773.94i	1.47196	−	0.288639i
$556$			24670.7i			1.88178i
$557$	−1115.57			−0.0848618			−0.0424309	−	0.999099i	$-0.513510\pi$
$557$	−1115.57			−0.0848618			−0.0424309	+	0.999099i	$0.513510\pi$
$558$	−3852.61	−	6323.79i	−0.292283	−	0.479762i
$559$		−	5129.83i		−	0.388137i
$560$	−2490.71	−	2711.67i	−0.187949	−	0.204623i
$561$	696.000	−	195.315i	0.0523800	−	0.0146991i
$562$		−	34540.9i		−	2.59256i
$563$		−	16595.3i		−	1.24229i	−0.783696	−	0.621145i	$-0.786668\pi$
$563$		−	16595.3i		−	1.24229i	0.783696	−	0.621145i	$-0.213332\pi$
$564$	−4561.61	−	16255.2i	−0.340565	−	1.21360i
$565$	−918.941	+	11469.0i	−0.0684251	+	0.853991i
$566$	1699.63			0.126220
$567$	−4584.61	−	12699.0i	−0.339569	−	0.940581i
$568$		−	11110.7i		−	0.820766i
$569$		−	15891.3i		−	1.17082i	−0.810736	−	0.585412i	$-0.800933\pi$
$569$		−	15891.3i		−	1.17082i	0.810736	−	0.585412i	$-0.199067\pi$
$570$	−30405.3	+	5962.22i	−2.23428	+	0.438122i
$571$	1303.38			0.0955252			0.0477626	−	0.998859i	$-0.484791\pi$
$571$	1303.38			0.0955252			0.0477626	+	0.998859i	$0.484791\pi$
$572$			6823.91i			0.498815i
$573$	889.725	+	3170.52i	0.0648670	+	0.231153i
$574$	7616.94	−	8210.86i	0.553876	−	0.597064i
$575$	16607.5	+	2678.51i	1.20449	+	0.194263i
$576$	−19137.1	+	11658.8i	−1.38434	+	0.843372i
$577$	8256.36			0.595696			0.297848	−	0.954613i	$-0.403731\pi$
$577$	8256.36			0.595696			0.297848	+	0.954613i	$0.403731\pi$
$578$	−21815.8			−1.56993
$579$	−6347.02	−	22617.5i	−0.455567	−	1.62340i
$580$	26914.0	+	2156.45i	1.92680	+	0.154382i
$581$	4063.31	+	3769.40i	0.290146	+	0.269158i
$582$	−12531.0	+	3516.51i	−0.892487	+	0.250453i
$583$		−	6748.99i		−	0.479442i
$584$	8133.64			0.576323
$585$	2577.22	+	5108.70i	0.182145	+	0.361058i
$586$		−	10369.9i		−	0.731016i
$587$		−	22031.8i		−	1.54915i	−0.632484	−	0.774573i	$-0.717965\pi$
$587$		−	22031.8i		−	1.54915i	0.632484	−	0.774573i	$-0.282035\pi$
$588$	7237.27	+	19913.1i	0.507585	+	1.39660i
$589$	−7354.86			−0.514519
$590$	−2927.01	+	36531.0i	−0.204242	+	2.54908i
$591$	−19092.3	+	5357.76i	−1.32885	+	0.372908i
$592$		−	6003.00i		−	0.416760i
$593$		−	11710.2i		−	0.810929i	−0.914111	−	0.405465i	$-0.867110\pi$
$593$		−	11710.2i		−	0.810929i	0.914111	−	0.405465i	$-0.132890\pi$
$594$	13863.0	+	12915.6i	0.957584	+	0.892142i
$595$	−700.558	+	643.474i	−0.0482690	+	0.0443359i
$596$		−	2283.79i		−	0.156959i
$597$	1881.29	+	6703.93i	0.128971	+	0.459587i
$598$	11376.0			0.777926
$599$		−	14539.0i		−	0.991729i	−0.868400	−	0.495865i	$-0.834851\pi$
$599$		−	14539.0i		−	0.991729i	0.868400	−	0.495865i	$-0.165149\pi$
$600$	−11188.8	+	1277.47i	−0.761301	+	0.0869205i
$601$		−	20293.0i		−	1.37732i	−0.725083	−	0.688661i	$-0.758199\pi$
$601$		−	20293.0i		−	1.37732i	0.725083	−	0.688661i	$-0.241801\pi$
$602$	16386.8	+	15201.5i	1.10943	+	1.02918i
$603$	10560.0	+	17333.5i	0.713164	+	1.17061i
$604$	−25647.0			−1.72775
$605$	−369.608	+	4612.96i	−0.0248375	+	0.309989i
$606$	38667.9	−	10851.2i	2.59204	−	0.727390i
$607$	4143.51			0.277068			0.138534	−	0.990358i	$-0.455761\pi$
$607$	4143.51			0.277068			0.138534	+	0.990358i	$0.455761\pi$
$608$			26072.2i			1.73909i
$609$	17391.5	+	8928.68i	1.15721	+	0.594103i
$610$	15518.4	+	1243.40i	1.03004	+	0.0825306i
$611$			5180.77i			0.343030i
$612$	767.159	+	1259.24i	0.0506709	+	0.0831727i
$613$		−	13166.7i		−	0.867534i	−0.901025	−	0.433767i	$-0.857184\pi$
$613$		−	13166.7i		−	0.867534i	0.901025	−	0.433767i	$-0.142816\pi$
$614$	−15376.1			−1.01063
$615$	1515.91	+	7730.61i	0.0993939	+	0.506875i
$616$	−7129.06	−	6613.39i	−0.466295	−	0.432567i
$617$	−8241.67			−0.537759			−0.268880	−	0.963174i	$-0.586653\pi$
$617$	−8241.67			−0.537759			−0.268880	+	0.963174i	$0.586653\pi$
$618$	−38038.9	+	10674.6i	−2.47597	+	0.694816i
$619$		−	12892.7i		−	0.837162i	−0.908180	−	0.418581i	$-0.862528\pi$
$619$		−	12892.7i		−	0.837162i	0.908180	−	0.418581i	$-0.137472\pi$
$620$	−8147.64	−	652.820i	−0.527770	−	0.0422869i
$621$	12870.2	−	13814.3i	0.831665	−	0.892671i
$622$	−34230.5			−2.20662
$623$	−5364.35	+	5782.63i	−0.344973	+	0.371872i
$624$	1686.26	−	473.205i	0.108180	−	0.0303579i
$625$	14832.7	+	4912.32i	0.949294	+	0.314388i
$626$	−43411.6			−2.77169
$627$	18119.1	−	5084.67i	1.15408	−	0.323863i
$628$	−12081.7			−0.767695
$629$	−1550.87			−0.0983106
$630$	−23956.6	−	6906.19i	−1.51500	−	0.436745i
$631$	26758.6			1.68818			0.844092	−	0.536198i	$-0.180140\pi$
$631$	26758.6			1.68818			0.844092	+	0.536198i	$0.180140\pi$
$632$	−2193.16			−0.138037
$633$	−3647.95	+	1023.70i	−0.229057	+	0.0642790i
$634$	3070.69			0.192355
$635$	13950.2	+	1117.75i	0.871808	+	0.0698526i
$636$	13254.4	−	3719.50i	0.826368	−	0.231899i
$637$	−487.245	−	6483.32i	−0.0303067	−	0.403263i
$638$	−27435.1			−1.70246
$639$	9001.95	+	14776.1i	0.557295	+	0.914761i
$640$	−1747.69	+	21812.4i	−0.107943	+	1.34721i
$641$			12483.3i			0.769204i	0.923082	+	0.384602i	$0.125661\pi$
$641$			12483.3i			0.769204i	−0.923082	+	0.384602i	$0.874339\pi$
$642$	−8874.98	+	2490.54i	−0.545588	+	0.153105i
$643$	15859.5			0.972689			0.486345	−	0.873767i	$-0.338330\pi$
$643$	15859.5			0.972689			0.486345	+	0.873767i	$0.338330\pi$
$644$	−20150.7	+	21721.9i	−1.23299	+	1.32914i
$645$	−15428.4	+	3025.37i	−0.941848	+	0.184688i
$646$	2450.13			0.149225
$647$			26235.0i			1.59413i	0.603893	+	0.797066i	$0.293616\pi$
$647$			26235.0i			1.59413i	−0.603893	+	0.797066i	$0.706384\pi$
$648$	−5796.79	+	11231.9i	−0.351419	+	0.680910i
$649$		−	22259.1i		−	1.34629i
$650$	10431.7	+	1682.45i	0.629483	+	0.101525i
$651$	−5264.92	−	2702.97i	−0.316972	−	0.162731i
$652$		−	33893.5i		−	2.03584i
$653$	11488.0			0.688451			0.344226	−	0.938887i	$-0.388142\pi$
$653$	11488.0			0.688451			0.344226	+	0.938887i	$0.388142\pi$
$654$	30849.6	−	8657.16i	1.84452	−	0.517617i
$655$	1094.21	−	13656.5i	0.0652740	−	0.814663i
$656$	2411.27			0.143513
$657$	−10816.9	+	6589.91i	−0.642324	+	0.391320i
$658$	−16549.6	−	15352.5i	−0.980501	−	0.909578i
$659$		−	13746.7i		−	0.812588i	−0.913743	−	0.406294i	$-0.866821\pi$
$659$		−	13746.7i		−	0.812588i	0.913743	−	0.406294i	$-0.133179\pi$
$660$	20523.5	−	4024.48i	1.21042	−	0.237353i
$661$		−	18205.0i		−	1.07124i	−0.844458	−	0.535621i	$-0.820077\pi$
$661$		−	18205.0i		−	1.07124i	0.844458	−	0.535621i	$-0.179923\pi$
$662$	−19834.7			−1.16450
$663$	−122.252	−	435.644i	−0.00716121	−	0.0255189i
$664$		−	5188.71i		−	0.303254i
$665$	−18237.8	+	16751.7i	−1.06350	+	0.976846i
$666$	−21148.7	−	34714.2i	−1.23048	−	2.01974i
$667$			27338.8i			1.58705i
$668$			22439.8i			1.29973i
$669$	−16306.8	+	4576.09i	−0.942389	+	0.264457i
$670$	37361.7	+	2993.56i	2.15434	+	0.172614i
$671$	−9455.68			−0.544013
$672$	−9581.75	+	18663.6i	−0.550036	+	1.07137i
$673$		−	2132.80i		−	0.122160i	−0.998133	−	0.0610799i	$-0.980546\pi$
$673$		−	2132.80i		−	0.122160i	0.998133	−	0.0610799i	$-0.0194544\pi$
$674$			18228.8i			1.04176i
$675$	13844.9	−	10764.1i	0.789467	−	0.613793i
$676$	−21846.4			−1.24296
$677$			995.751i			0.0565285i	0.999600	+	0.0282643i	$0.00899799\pi$
$677$			995.751i			0.0565285i	−0.999600	+	0.0282643i	$0.991002\pi$
$678$	22960.2	−	6443.20i	1.30056	−	0.364970i
$679$	−7074.36	+	7625.98i	−0.399837	+	0.431013i
$680$	887.673	+	71.1237i	0.0500598	+	0.00401099i
$681$	−5881.00	−	20956.8i	−0.330926	−	1.17925i
$682$	8305.41			0.466321
$683$	24097.2			1.35000			0.675002	−	0.737816i	$-0.264143\pi$
$683$	24097.2			1.35000			0.675002	+	0.737816i	$0.264143\pi$
$684$	19971.6	+	32782.0i	1.11642	+	1.83253i
$685$	−1561.28	+	19485.8i	−0.0870853	+	1.08688i
$686$	22154.3	+	17655.9i	1.23303	+	0.982662i
$687$	−2803.52	−	9990.29i	−0.155693	−	0.554809i
$688$			4812.30i			0.266667i
$689$	−4224.36			−0.233578
$690$	−6709.13	−	34214.3i	−0.370163	−	1.88771i
$691$			18883.3i			1.03959i	0.854291	+	0.519794i	$0.173991\pi$
$691$			18883.3i			1.03959i	−0.854291	+	0.519794i	$0.826009\pi$
$692$		−	41508.5i		−	2.28023i
$693$	14839.1	+	3019.11i	0.813406	+	0.165493i
$694$	25919.4			1.41771
$695$	−23128.3	−	1853.12i	−1.26231	−	0.101141i
$696$	−4944.92	−	17621.1i	−0.269306	−	0.959666i
$697$		−	622.951i		−	0.0338536i
$698$			12504.7i			0.678095i
$699$	708.928	−	198.942i	0.0383607	−	0.0107649i
$700$	−21690.5	+	16938.6i	−1.17118	+	0.914596i
$701$		−	6421.10i		−	0.345965i	−0.984925	−	0.172983i	$-0.944660\pi$
$701$		−	6421.10i		−	0.345965i	0.984925	−	0.172983i	$-0.0553404\pi$
$702$	8084.17	−	8677.18i	0.434640	−	0.466523i
$703$	−40374.2			−2.16606
$704$		−	25133.8i		−	1.34555i
$705$	15581.6	−	3055.42i	0.832393	−	0.163225i
$706$		−	5276.01i		−	0.281254i
$707$	21829.9	−	23532.1i	1.16124	−	1.25179i
$708$	43714.7	−	12267.4i	2.32048	−	0.651183i
$709$	−5206.72			−0.275800			−0.137900	−	0.990446i	$-0.544035\pi$
$709$	−5206.72			−0.275800			−0.137900	+	0.990446i	$0.544035\pi$
$710$	31849.1	+	2551.88i	1.68349	+	0.134888i
$711$	2916.67	−	1776.91i	0.153845	−	0.0937261i
$712$	7384.21			0.388673
$713$		−	8276.24i		−	0.434709i
$714$	1753.91	+	900.443i	0.0919305	+	0.0471964i
$715$	−6397.28	−	512.575i	−0.334608	−	0.0268101i
$716$			2050.63i			0.107033i
$717$	−3793.85	−	13519.3i	−0.197607	−	0.704168i
$718$			38838.4i			2.01872i
$719$	−26323.4			−1.36537			−0.682683	−	0.730715i	$-0.739187\pi$
$719$	−26323.4			−1.36537			−0.682683	+	0.730715i	$0.739187\pi$
$720$	−2417.69	−	4792.48i	−0.125142	−	0.248063i
$721$	−21474.8	+	23149.2i	−1.10924	+	1.19573i
$722$	33196.5			1.71114
$723$	6036.27	+	21510.2i	0.310500	+	1.10646i
$724$			25045.5i			1.28565i
$725$	−4043.26	+	25069.3i	−0.207121	+	1.28421i
$726$	9234.85	−	2591.52i	0.472090	−	0.132480i
$727$	653.079			0.0333169			0.0166584	−	0.999861i	$-0.494697\pi$
$727$	653.079			0.0333169			0.0166584	+	0.999861i	$0.494697\pi$
$728$	−4139.48	+	4462.25i	−0.210741	+	0.227173i
$729$	−1391.00	−	19633.8i	−0.0706700	−	0.997500i
$730$	−1868.11	+	23315.3i	−0.0947149	+	1.18211i
$731$	1243.26			0.0629049
$732$	−5211.21	−	18570.1i	−0.263131	−	0.937663i
$733$	−19283.5			−0.971696			−0.485848	−	0.874043i	$-0.661489\pi$
$733$	−19283.5			−0.971696			−0.485848	+	0.874043i	$0.661489\pi$
$734$	−32787.7			−1.64880
$735$	−19211.8	+	5289.04i	−0.964131	+	0.265427i
$736$	−29338.4			−1.46933
$737$	−22765.2			−1.13781
$738$	13943.9	−	8494.98i	0.695505	−	0.423719i
$739$	11829.3			0.588832			0.294416	−	0.955677i	$-0.404875\pi$
$739$	11829.3			0.588832			0.294416	+	0.955677i	$0.404875\pi$
$740$	−44726.1	−	3583.63i	−2.22184	−	0.178023i
$741$	−3182.62	−	11341.2i	−0.157782	−	0.562253i
$742$	12518.3	−	13494.4i	0.619354	−	0.667647i
$743$	−15784.6			−0.779380			−0.389690	−	0.920946i	$-0.627418\pi$
$743$	−15784.6			−0.779380			−0.389690	+	0.920946i	$0.627418\pi$
$744$	1496.97	+	5334.43i	0.0737656	+	0.262863i
$745$	2141.01	+	171.546i	0.105289	+	0.00843618i
$746$		−	5884.67i		−	0.288811i
$747$	4203.91	+	6900.43i	0.205908	+	0.337983i
$748$	−1653.83			−0.0808423
$749$	−5010.36	+	5401.03i	−0.244425	+	0.263484i
$750$	−1092.08	−	32366.4i	−0.0531695	−	1.57580i
$751$	−719.429			−0.0349565			−0.0174782	−	0.999847i	$-0.505564\pi$
$751$	−719.429			−0.0349565			−0.0174782	+	0.999847i	$0.505564\pi$
$752$		−	4860.09i		−	0.235677i
$753$	−16544.8	+	4642.88i	−0.800700	+	0.224696i
$754$			17172.3i			0.829415i
$755$	1926.46	−	24043.5i	0.0928623	−	1.15899i
$756$	2248.87	+	30806.5i	0.108189	+	1.48204i
$757$			23060.3i			1.10719i	0.832787	+	0.553593i	$0.186744\pi$
$757$			23060.3i			1.10719i	−0.832787	+	0.553593i	$0.813256\pi$
$758$	46086.4			2.20835
$759$	5721.65	+	20389.0i	0.273627	+	0.975064i
$760$	23109.0	+	1851.58i	1.10296	+	0.0883735i
$761$	19804.3			0.943371			0.471686	−	0.881767i	$-0.343646\pi$
$761$	19804.3			0.943371			0.471686	+	0.881767i	$0.343646\pi$
$762$	−7837.13	−	27927.5i	−0.372584	−	1.32770i
$763$	17416.1	−	18774.1i	0.826351	−	0.890784i
$764$		−	7533.77i		−	0.356757i
$765$	−1238.14	+	624.609i	−0.0585162	+	0.0295200i
$766$		−	59437.4i		−	2.80361i
$767$	−13932.5			−0.655897
$768$	10449.6	−	2932.41i	0.490972	−	0.137779i
$769$			14623.5i			0.685746i	0.939382	+	0.342873i	$0.111400\pi$
$769$			14623.5i			0.685746i	−0.939382	+	0.342873i	$0.888600\pi$
$770$	20594.8	−	18916.7i	0.963878	−	0.885338i
$771$	5518.88	+	19666.4i	0.257792	+	0.918637i
$772$			53743.5i			2.50553i
$773$			40353.9i			1.87766i	0.344384	+	0.938829i	$0.388088\pi$
$773$			40353.9i			1.87766i	−0.344384	+	0.938829i	$0.611912\pi$
$774$	16953.9	+	27828.6i	0.787331	+	1.29235i
$775$	1224.01	−	7589.22i	0.0567327	−	0.351758i
$776$	9738.10			0.450486
$777$	−28901.6	−	14837.8i	−1.33441	−	0.685077i
$778$		−	27575.6i		−	1.27074i
$779$		−	16217.4i		−	0.745891i
$780$	−2519.02	−	12846.2i	−0.115635	−	0.589700i
$781$	−19406.3			−0.889131
$782$			2757.07i			0.126078i
$783$	20852.9	+	19427.8i	0.951754	+	0.886710i
$784$	457.086	+	6082.01i	0.0208220	+	0.277059i
$785$	907.511	−	11326.4i	0.0412617	−	0.514974i
$786$	−27339.5	+	7672.12i	−1.24067	+	0.348162i
$787$	9011.80			0.408178			0.204089	−	0.978952i	$-0.434577\pi$
$787$	9011.80			0.408178			0.204089	+	0.978952i	$0.434577\pi$
$788$	45367.0			2.05093
$789$	−10422.1	+	2924.71i	−0.470264	+	0.131968i
$790$	503.718	−	6286.75i	0.0226854	−	0.283130i
$791$	12962.2	−	13972.9i	0.582656	−	0.628088i
$792$	−7375.74	−	12106.8i	−0.330916	−	0.543176i
$793$			5918.54i			0.265036i
$794$	12141.3			0.542670
$795$	2491.36	+	12705.1i	0.111144	+	0.566797i
$796$		−	15929.8i		−	0.709319i
$797$			23157.4i			1.02921i	0.857428	+	0.514604i	$0.172061\pi$
$797$			23157.4i			1.02921i	−0.857428	+	0.514604i	$0.827939\pi$
$798$	45659.8	+	23441.4i	2.02549	+	1.03987i
$799$	−1255.60			−0.0555945
$800$	−26902.9	−	4338.99i	−1.18895	−	0.191758i
$801$	−9820.22	+	5982.72i	−0.433184	+	0.263907i
$802$			28362.3i			1.24876i
$803$		−	14206.4i		−	0.624327i
$804$	−12546.3	−	44708.7i	−0.550342	−	1.96114i
$805$	−18850.3	−	20522.5i	−0.825322	−	0.898538i
$806$		−	5198.56i		−	0.227186i
$807$	14538.1	−	4079.73i	0.634156	−	0.177960i
$808$	−30049.6			−1.30834
$809$		−	612.672i		−	0.0266259i	−0.999911	−	0.0133130i	$-0.995762\pi$
$809$		−	612.672i		−	0.0266259i	0.999911	−	0.0133130i	$-0.00423778\pi$
$810$	−30865.1	−	19196.4i	−1.33887	−	0.832705i
$811$			20636.7i			0.893529i	0.894652	+	0.446764i	$0.147424\pi$
$811$			20636.7i			0.893529i	−0.894652	+	0.446764i	$0.852576\pi$
$812$	−32789.7	−	30417.9i	−1.41711	−	1.31460i
$813$	1005.22	+	3582.09i	0.0433637	+	0.154526i
$814$	45592.2			1.96315
$815$	31774.4	+	2545.89i	1.36566	+	0.109422i
$816$	114.685	+	408.678i	0.00492007	+	0.0175326i
$817$	32365.9			1.38597
$818$		−	10003.2i		−	0.427571i
$819$	1889.73	−	9288.15i	0.0806259	−	0.396281i
$820$	1439.46	−	17965.5i	0.0613028	−	0.765100i
$821$			29514.0i			1.25462i	0.778768	+	0.627312i	$0.215845\pi$
$821$			29514.0i			1.25462i	−0.778768	+	0.627312i	$0.784155\pi$
$822$	39009.4	−	10947.0i	1.65524	−	0.464501i
$823$		−	8964.57i		−	0.379690i	−0.981814	−	0.189845i	$-0.939201\pi$
$823$		−	8964.57i		−	0.379690i	0.981814	−	0.189845i	$-0.0607986\pi$
$824$	29560.8			1.24975
$825$	2231.26	+	19542.7i	0.0941605	+	0.824713i
$826$	41287.0	−	44506.3i	1.73917	−	1.87478i
$827$	36886.7			1.55100			0.775500	−	0.631348i	$-0.217498\pi$
$827$	36886.7			1.55100			0.775500	+	0.631348i	$0.217498\pi$
$828$	−36888.7	+	22473.6i	−1.54828	+	0.943249i
$829$		−	29077.8i		−	1.21823i	−0.793081	−	0.609116i	$-0.791525\pi$
$829$		−	29077.8i		−	1.21823i	0.793081	−	0.609116i	$-0.208475\pi$
$830$	14873.6	+	1191.73i	0.622011	+	0.0498379i
$831$	142.135	+	506.495i	0.00593334	+	0.0211434i
$832$	−15731.9			−0.655535
$833$	1571.29	−	118.088i	0.0653563	−	0.00491177i
$834$	12993.3	+	46301.3i	0.539472	+	1.92240i
$835$	−21036.8	−	1685.55i	−0.871868	−	0.0698574i
$836$	−43054.5			−1.78119
$837$	−6312.79	−	5881.37i	−0.260695	−	0.242879i
$838$	−56036.2			−2.30995
$839$	32262.6			1.32757			0.663784	−	0.747924i	$-0.268949\pi$
$839$	32262.6			1.32757			0.663784	+	0.747924i	$0.268949\pi$
$840$	15861.9	+	9818.17i	0.651533	+	0.403285i
$841$	−16879.4			−0.692091
$842$	−17408.3			−0.712505
$843$	−10873.9	−	38749.1i	−0.444268	−	1.58314i
$844$	8668.25			0.353523
$845$	1640.98	−	20480.5i	0.0668063	−	0.833789i
$846$	−17122.2	−	28104.9i	−0.695833	−	1.14216i
$847$	5213.52	−	5620.03i	0.211498	−	0.227989i
$848$	3962.88			0.160478
$849$	1906.70	−	535.066i	0.0770762	−	0.0216295i
$850$	−407.756	+	2528.20i	−0.0164540	+	0.102019i
$851$		−	45432.1i		−	1.83007i
$852$	−10695.2	−	38112.1i	−0.430060	−	1.53251i
$853$	14995.9			0.601935			0.300968	−	0.953634i	$-0.402690\pi$
$853$	14995.9			0.601935			0.300968	+	0.953634i	$0.402690\pi$
$854$	−18906.3	−	17538.8i	−0.757566	−	0.702768i
$855$	−32232.6	+	16260.6i	−1.28928	+	0.650410i
$856$	6896.93			0.275388
$857$			36795.5i			1.46664i	0.679884	+	0.733319i	$0.262030\pi$
$857$			36795.5i			1.46664i	−0.679884	+	0.733319i	$0.737970\pi$
$858$	3593.94	+	12806.9i	0.143001	+	0.509583i
$859$			6908.88i			0.274421i	0.990542	+	0.137211i	$0.0438137\pi$
$859$			6908.88i			0.274421i	−0.990542	+	0.137211i	$0.956186\pi$
$860$	35854.6	+	2872.81i	1.42167	+	0.113909i
$861$	5960.04	−	11609.1i	0.235909	−	0.459509i
$862$			22431.4i			0.886330i
$863$	4307.42			0.169903			0.0849515	−	0.996385i	$-0.472926\pi$
$863$	4307.42			0.169903			0.0849515	+	0.996385i	$0.472926\pi$
$864$	−20848.8	+	22378.2i	−0.820940	+	0.881158i
$865$	38913.4	+	3117.89i	1.52959	+	0.122557i
$866$	66288.3			2.60112
$867$	−24473.6	+	6867.90i	−0.958672	+	0.269027i
$868$	9926.39	+	9208.37i	0.388161	+	0.360084i
$869$			3830.64i			0.149534i
$870$	51647.2	−	10127.6i	2.01265	−	0.394663i
$871$			14249.3i			0.554327i
$872$	−23973.9			−0.931030
$873$	−12950.6	+	7889.85i	−0.502076	+	0.305878i
$874$			71775.4i			2.77785i
$875$	−14250.3	−	21606.7i	−0.550569	−	0.834790i
$876$	27900.1	−	7829.46i	1.07609	−	0.301978i
$877$		−	1580.51i		−	0.0608552i	−0.999537	−	0.0304276i	$-0.990313\pi$
$877$		−	1580.51i		−	0.0608552i	0.999537	−	0.0304276i	$-0.00968690\pi$
$878$		−	50322.9i		−	1.93430i
$879$	−3264.57	−	11633.2i	−0.125269	−	0.446393i
$880$	6001.30	+	480.847i	0.229891	+	0.0184197i
$881$	−29644.9			−1.13367			−0.566834	−	0.823832i	$-0.691832\pi$
$881$	−29644.9			−1.13367			−0.566834	+	0.823832i	$0.691832\pi$
$882$	24070.3	+	33560.7i	0.918923	+	1.28123i
$883$		−	16316.4i		−	0.621847i	−0.950435	−	0.310923i	$-0.899362\pi$
$883$		−	16316.4i		−	0.621847i	0.950435	−	0.310923i	$-0.100638\pi$
$884$			1035.17i			0.0393854i
$885$	8216.85	+	41903.1i	0.312097	+	1.59159i
$886$	−28569.1			−1.08329
$887$			16452.1i			0.622783i	0.950282	+	0.311392i	$0.100795\pi$
$887$			16452.1i			0.622783i	−0.950282	+	0.311392i	$0.899205\pi$
$888$	8217.56	+	29283.1i	0.310544	+	1.10662i
$889$	−16995.8	−	15766.4i	−0.641192	−	0.594812i
$890$	−1695.98	+	21167.0i	−0.0638759	+	0.797214i
$891$	19617.9	+	10124.8i	0.737626	+	0.380690i
$892$	38748.2			1.45447
$893$	−32687.4			−1.22491
$894$	−1202.80	−	4286.16i	−0.0449974	−	0.160347i
$895$	−1922.43	−	154.032i	−0.0717985	−	0.00575277i
$896$	24652.1	−	26574.4i	0.919163	−	0.990834i
$897$	12762.0	−	3581.32i	0.475039	−	0.133307i
$898$		−	25185.2i		−	0.935905i
$899$	12493.2			0.463482
$900$	−37150.3	+	15152.3i	−1.37594	+	0.561197i
$901$		−	1023.81i		−	0.0378557i
$902$			18313.4i			0.676018i
$903$	23168.9	+	11894.8i	0.853835	+	0.438353i
$904$	−17842.8			−0.656465
$905$	−23479.6	−	1881.28i	−0.862419	−	0.0691003i
$906$	−48133.6	+	13507.5i	−1.76505	+	0.495315i
$907$		−	15972.5i		−	0.584737i	−0.956306	−	0.292369i	$-0.905557\pi$
$907$		−	15972.5i		−	0.584737i	0.956306	−	0.292369i	$-0.0944434\pi$
$908$			49797.5i			1.82003i
$909$	39962.8	−	24346.3i	1.45818	−	0.888358i
$910$	−11840.4	−	12890.8i	−0.431325	−	0.469589i
$911$			47647.5i			1.73285i	0.499303	+	0.866427i	$0.333589\pi$
$911$			47647.5i			1.73285i	−0.499303	+	0.866427i	$0.666411\pi$
$912$	2985.62	+	10639.2i	0.108403	+	0.386293i
$913$	−9062.74			−0.328514
$914$			17960.6i			0.649983i
$915$	17800.5	−	3490.53i	0.643133	−	0.126113i
$916$			23738.9i			0.856282i
$917$	−15434.4	+	16637.9i	−0.555824	+	0.599163i
$918$	2102.99	+	1959.27i	0.0756088	+	0.0704416i
$919$	−40628.7			−1.45834			−0.729171	−	0.684331i	$-0.760094\pi$
$919$	−40628.7			−1.45834			−0.729171	+	0.684331i	$0.760094\pi$
$920$	−2083.54	+	26003.9i	−0.0746654	+	0.931874i
$921$	−17249.4	+	4840.60i	−0.617142	+	0.173185i
$922$	−19274.9			−0.688487
$923$			12146.9i			0.433174i
$924$	−30820.3	−	15822.9i	−1.09731	−	0.563350i
$925$	6719.16	−	41660.7i	0.238837	−	1.48086i
$926$		−	58366.2i		−	2.07131i
$927$	−39312.7	+	23950.3i	−1.39288	+	0.848576i
$928$		−	44286.9i		−	1.56658i
$929$	−42333.4			−1.49506			−0.747532	−	0.664226i	$-0.768761\pi$
$929$	−42333.4			−1.49506			−0.747532	+	0.664226i	$0.768761\pi$
$930$	−15635.1	+	3065.91i	−0.551285	+	0.108102i
$931$	40905.6	−	3074.21i	1.43999	−	0.108220i
$932$	−1684.55			−0.0592052
$933$	−38400.9	+	10776.2i	−1.34747	+	0.378132i
$934$			11260.6i			0.394495i
$935$	124.227	−	1550.43i	0.00434508	−	0.0542295i
$936$	−7577.92	+	4616.66i	−0.264628	+	0.161218i
$937$	14777.6			0.515224			0.257612	−	0.966248i	$-0.417064\pi$
$937$	14777.6			0.515224			0.257612	+	0.966248i	$0.417064\pi$
$938$	−45518.3	−	42225.8i	−1.58446	−	1.46985i
$939$	−48700.5	+	13666.5i	−1.69252	+	0.474963i
$940$	−36210.7	−	2901.34i	−1.25645	−	0.100672i
$941$	−37729.8			−1.30707			−0.653537	−	0.756894i	$-0.726716\pi$
$941$	−37729.8			−1.30707			−0.653537	+	0.756894i	$0.726716\pi$
$942$	−22674.6	+	6363.05i	−0.784266	+	0.220084i
$943$	18249.1			0.630192
$944$	13070.1			0.450631
$945$	−29049.4	−	205.738i	−0.999975	−	0.00708217i
$946$	−36548.9			−1.25614
$947$	13860.2			0.475602			0.237801	−	0.971314i	$-0.423573\pi$
$947$	13860.2			0.475602			0.237801	+	0.971314i	$0.423573\pi$
$948$	−7523.01	+	2111.14i	−0.257738	+	0.0723276i
$949$	−8892.17			−0.304164
$950$	−10615.2	+	65817.2i	−0.362529	+	2.24778i
$951$	3444.80	−	966.695i	0.117461	−	0.0329624i
$952$	−1081.46	−	1003.24i	−0.0368177	−	0.0341545i
$953$	−54882.6			−1.86550			−0.932750	−	0.360523i	$-0.882598\pi$
$953$	−54882.6			−1.86550			−0.932750	+	0.360523i	$0.882598\pi$
$954$	22916.5	−	13961.3i	0.777725	−	0.473810i
$955$	7062.76	+	565.896i	0.239315	+	0.0191748i
$956$			32124.5i			1.08680i
$957$	−30777.6	+	8636.94i	−1.03960	+	0.291737i
$958$	14161.6			0.477600
$959$	22022.7	−	23739.9i	0.741553	−	0.799374i
$960$	9278.06	+	47315.0i	0.311925	+	1.59071i
$961$	26009.0			0.873048
$962$		−	28537.3i		−	0.956423i
$963$	−9172.18	+	5587.92i	−0.306926	+	0.186987i
$964$		−	51112.3i		−	1.70769i
$965$	−50383.5	−	4036.92i	−1.68073	−	0.134666i
$966$	−26378.1	+	51379.9i	−0.878571	+	1.71130i
$967$			21656.2i			0.720183i	0.932917	+	0.360092i	$0.117255\pi$
$967$			21656.2i			0.720183i	−0.932917	+	0.360092i	$0.882745\pi$
$968$	−7176.58			−0.238289
$969$	2748.63	−	771.333i	0.0911237	−	0.0255715i
$970$	−2236.62	+	27914.5i	−0.0740345	+	0.924001i
$971$	4409.47			0.145733			0.0728664	−	0.997342i	$-0.476785\pi$
$971$	4409.47			0.145733			0.0728664	+	0.997342i	$0.476785\pi$
$972$	−9072.43	+	44107.7i	−0.299381	+	1.45551i
$973$	28177.5	+	26139.3i	0.928395	+	0.861241i
$974$		−	17712.6i		−	0.582699i
$975$	12232.2	−	1396.60i	0.401790	−	0.0458738i
$976$		−	5552.19i		−	0.182092i
$977$	36452.4			1.19367			0.596834	−	0.802364i	$-0.296425\pi$
$977$	36452.4			1.19367			0.596834	+	0.802364i	$0.296425\pi$
$978$	−17850.6	−	63610.4i	−0.583640	−	2.07979i
$979$		−	12897.5i		−	0.421047i
$980$	45587.6	+	225.221i	1.48596	+	0.00734124i
$981$	31882.7	−	19423.7i	1.03765	−	0.632164i
$982$		−	48406.2i		−	1.57302i
$983$			2111.09i			0.0684979i	0.999413	+	0.0342489i	$0.0109039\pi$
$983$			2111.09i			0.0684979i	−0.999413	+	0.0342489i	$0.989096\pi$
$984$	−11762.4	+	3300.81i	−0.381068	+	0.106937i
$985$	−3407.72	+	42530.6i	−0.110232	+	1.37577i
$986$	−4161.85			−0.134422
$987$	−23399.0	−	12012.9i	−0.754608	−	0.387410i
$988$			26948.9i			0.867772i
$989$			36420.6i			1.17099i
$990$	36398.4	−	18362.1i	1.16850	−	0.589481i
$991$	5791.29			0.185637			0.0928186	−	0.995683i	$-0.470412\pi$
$991$	5791.29			0.185637			0.0928186	+	0.995683i	$0.470412\pi$
$992$			13406.9i			0.429103i
$993$	−22251.2	+	6244.24i	−0.711099	+	0.199552i
$994$	−38802.3	−	35995.5i	−1.23816	−	1.14860i
$995$	14933.9	+	1196.56i	0.475816	+	0.0381242i
$996$	−4994.66	−	17798.4i	−0.158897	−	0.566228i
$997$	15024.7			0.477269			0.238635	−	0.971109i	$-0.423300\pi$
$997$	15024.7			0.477269			0.238635	+	0.971109i	$0.423300\pi$
$998$	21417.4			0.679314
$999$	−34653.8	−	32285.5i	−1.09750	−	1.02249i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.4.g.b.104.6	yes	40
3.2	odd	2	inner	105.4.g.b.104.33	yes	40
5.4	even	2	inner	105.4.g.b.104.35	yes	40
7.6	odd	2	inner	105.4.g.b.104.7	yes	40
15.14	odd	2	inner	105.4.g.b.104.8	yes	40
21.20	even	2	inner	105.4.g.b.104.36	yes	40
35.34	odd	2	inner	105.4.g.b.104.34	yes	40
105.104	even	2	inner	105.4.g.b.104.5	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.4.g.b.104.5	✓	40	105.104	even	2	inner
105.4.g.b.104.6	yes	40	1.1	even	1	trivial
105.4.g.b.104.7	yes	40	7.6	odd	2	inner
105.4.g.b.104.8	yes	40	15.14	odd	2	inner
105.4.g.b.104.33	yes	40	3.2	odd	2	inner
105.4.g.b.104.34	yes	40	35.34	odd	2	inner
105.4.g.b.104.35	yes	40	5.4	even	2	inner
105.4.g.b.104.36	yes	40	21.20	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	105.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-4.45958 q^{2} +(-5.00290 + 1.40393i) q^{3} +11.8879 q^{4} +(-0.892950 + 11.1446i) q^{5} +(22.3108 - 6.26096i) q^{6} +(12.5955 - 13.5777i) q^{7} -17.3382 q^{8} +(23.0579 - 14.0475i) q^{9} +O(q^{10})\)	\(q-4.45958 q^{2} +(-5.00290 + 1.40393i) q^{3} +11.8879 q^{4} +(-0.892950 + 11.1446i) q^{5} +(22.3108 - 6.26096i) q^{6} +(12.5955 - 13.5777i) q^{7} -17.3382 q^{8} +(23.0579 - 14.0475i) q^{9} +(3.98218 - 49.7003i) q^{10} +30.2834i q^{11} +(-59.4737 + 16.6898i) q^{12} +18.9551 q^{13} +(-56.1708 + 60.5506i) q^{14} +(-11.1790 - 57.0090i) q^{15} -17.7818 q^{16} +4.59392i q^{17} +(-102.829 + 62.6458i) q^{18} +119.595i q^{19} +(-10.6153 + 132.486i) q^{20} +(-43.9520 + 85.6109i) q^{21} -135.051i q^{22} -134.577 q^{23} +(86.7411 - 24.3417i) q^{24} +(-123.405 - 19.9032i) q^{25} -84.5318 q^{26} +(-95.6347 + 102.650i) q^{27} +(149.734 - 161.409i) q^{28} -203.146i q^{29} +(49.8536 + 254.236i) q^{30} +61.4983i q^{31} +218.005 q^{32} +(-42.5159 - 151.505i) q^{33} -20.4870i q^{34} +(140.071 + 152.497i) q^{35} +(274.109 - 166.994i) q^{36} +337.592i q^{37} -533.342i q^{38} +(-94.8304 + 26.6117i) q^{39} +(15.4821 - 193.227i) q^{40} -135.603 q^{41} +(196.007 - 381.789i) q^{42} -270.630i q^{43} +360.004i q^{44} +(135.964 + 269.516i) q^{45} +600.156 q^{46} +273.318i q^{47} +(88.9606 - 24.9645i) q^{48} +(-25.7052 - 342.035i) q^{49} +(550.336 + 88.7598i) q^{50} +(-6.44957 - 22.9829i) q^{51} +225.335 q^{52} -222.861 q^{53} +(426.491 - 457.775i) q^{54} +(-337.497 - 27.0415i) q^{55} +(-218.384 + 235.412i) q^{56} +(-167.903 - 598.319i) q^{57} +905.947i q^{58} -735.026 q^{59} +(-132.894 - 677.715i) q^{60} +312.240i q^{61} -274.257i q^{62} +(99.6952 - 490.008i) q^{63} -829.955 q^{64} +(-16.9260 + 211.247i) q^{65} +(189.603 + 675.646i) q^{66} +751.739i q^{67} +54.6119i q^{68} +(673.274 - 188.937i) q^{69} +(-624.656 - 680.071i) q^{70} +640.823i q^{71} +(-399.783 + 243.558i) q^{72} -469.117 q^{73} -1505.52i q^{74} +(645.327 - 73.6793i) q^{75} +1421.72i q^{76} +(411.177 + 381.435i) q^{77} +(422.904 - 118.677i) q^{78} +126.493 q^{79} +(15.8783 - 198.172i) q^{80} +(334.337 - 647.812i) q^{81} +604.734 q^{82} +299.265i q^{83} +(-522.495 + 1017.73i) q^{84} +(-51.1976 - 4.10215i) q^{85} +1206.90i q^{86} +(285.204 + 1016.32i) q^{87} -525.058i q^{88} -425.893 q^{89} +(-606.343 - 1201.93i) q^{90} +(238.750 - 257.366i) q^{91} -1599.83 q^{92} +(-86.3396 - 307.670i) q^{93} -1218.88i q^{94} +(-1332.84 - 106.792i) q^{95} +(-1090.66 + 306.064i) q^{96} -561.656 q^{97} +(114.635 + 1525.33i) q^{98} +(425.405 + 698.272i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 184 q^{4} + 4 q^{9}+O(q^{10}) \) 40 * q + 184 * q^4 + 4 * q^9	\( 40 q + 184 q^{4} + 4 q^{9} - 188 q^{15} + 184 q^{16} + 148 q^{21} + 712 q^{25} - 336 q^{30} - 1520 q^{36} + 644 q^{39} - 1488 q^{46} - 1496 q^{49} - 220 q^{51} + 1984 q^{60} + 40 q^{64} - 3000 q^{70} - 1192 q^{79} + 4636 q^{81} - 2192 q^{84} + 4808 q^{85} - 4408 q^{91} + 5276 q^{99}+O(q^{100}) \) 40 * q + 184 * q^4 + 4 * q^9 - 188 * q^15 + 184 * q^16 + 148 * q^21 + 712 * q^25 - 336 * q^30 - 1520 * q^36 + 644 * q^39 - 1488 * q^46 - 1496 * q^49 - 220 * q^51 + 1984 * q^60 + 40 * q^64 - 3000 * q^70 - 1192 * q^79 + 4636 * q^81 - 2192 * q^84 + 4808 * q^85 - 4408 * q^91 + 5276 * q^99

Introduction

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