LMFDB - Embedded newform 105.4.g.b.104.7

Newspace parameters

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

Newform invariants

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			104.7
Character	$\chi$	$=$	105.104
Dual form			105.4.g.b.104.8

$q$-expansion

$f(q)$	$=$	$q-4.45958 q^{2} +(5.00290 - 1.40393i) q^{3} +11.8879 q^{4} +(0.892950 - 11.1446i) q^{5} +(-22.3108 + 6.26096i) q^{6} +(-12.5955 - 13.5777i) q^{7} -17.3382 q^{8} +(23.0579 - 14.0475i) q^{9} +O(q^{10})$	\(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} +(-82.0763 - 50.2443i) 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} +(-162.565 + 128.248i) 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} +(366.026 + 224.068i) 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} +(-481.159 - 136.137i) 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} +(724.972 - 571.933i) 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} +(-975.710 - 597.297i) 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})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40q + 184q^{4} + 4q^{9} + O(q^{10}) $	$ 40q + 184q^{4} + 4q^{9} - 188q^{15} + 184q^{16} + 148q^{21} + 712q^{25} - 336q^{30} - 1520q^{36} + 644q^{39} - 1488q^{46} - 1496q^{49} - 220q^{51} + 1984q^{60} + 40q^{64} - 3000q^{70} - 1192q^{79} + 4636q^{81} - 2192q^{84} + 4808q^{85} - 4408q^{91} + 5276q^{99} + O(q^{100}) $

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	$-0.564809\pi$
$13$	−18.9551			−0.404400			−0.202200	+	0.979344i	$0.564809\pi$
$14$	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	$-0.989567\pi$
$17$		−	4.59392i		−	0.0655406i	0.999463	−	0.0327703i	$-0.0104330\pi$
$18$	−102.829	+	62.6458i	−1.34650	+	0.820320i
$19$		−	119.595i		−	1.44405i	−0.691869	−	0.722023i	$-0.743212\pi$
$19$		−	119.595i		−	1.44405i	0.691869	−	0.722023i	$-0.256788\pi$
$20$	10.6153	−	132.486i	0.118682	−	1.48123i
$21$	−82.0763	−	50.2443i	−0.852881	−	0.522105i
$22$		−	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	$-0.942988\pi$
$31$		−	61.4983i		−	0.356304i	0.984003	−	0.178152i	$-0.0570119\pi$
$32$	218.005			1.20432
$33$	42.5159	+	151.505i	0.224275	+	0.799198i
$34$			20.4870i			0.103338i
$35$	−162.565	+	128.248i	−0.785100	+	0.619369i
$36$	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	$-0.416849\pi$
$41$	135.603			0.516529			0.258264	+	0.966074i	$0.416849\pi$
$42$	366.026	+	224.068i	1.34474	+	0.823202i
$43$		−	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	$-0.860583\pi$
$47$		−	273.318i		−	0.848245i	0.905605	−	0.424123i	$-0.139417\pi$
$48$	−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	$-0.198950\pi$
$59$	735.026			1.62190			0.810951	+	0.585114i	$0.198950\pi$
$60$	−132.894	−	677.715i	−0.285943	−	1.45821i
$61$		−	312.240i		−	0.655381i	−0.944785	−	0.327691i	$-0.893730\pi$
$61$		−	312.240i		−	0.655381i	0.944785	−	0.327691i	$-0.106270\pi$
$62$			274.257i			0.561784i
$63$	−481.159	−	136.137i	−0.962227	−	0.272249i
$64$	−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
$70$	724.972	−	571.933i	1.23787	−	0.976559i
$71$			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	$-0.377276\pi$
$73$	469.117			0.752137			0.376069	+	0.926592i	$0.377276\pi$
$74$		−	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	$-0.936593\pi$
$83$		−	299.265i		−	0.395766i	0.980226	−	0.197883i	$-0.0634066\pi$
$84$	−975.710	−	597.297i	−1.26737	−	0.775838i
$85$	−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	$-0.418378\pi$
$89$	425.893			0.507242			0.253621	+	0.967304i	$0.418378\pi$
$90$	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	$-0.405028\pi$
$97$	561.656			0.587913			0.293957	+	0.955819i	$0.405028\pi$
$98$	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	$-0.825669\pi$
$101$	−1733.15			−1.70747			−0.853736	+	0.520706i	$0.825669\pi$
$102$	28.7624	+	102.494i	0.0279206	+	0.0994945i
$103$	1704.95			1.63101			0.815504	−	0.578751i	$-0.196460\pi$
$103$	1704.95			1.63101			0.815504	+	0.578751i	$0.196460\pi$
$104$	328.647			0.309870
$105$	−633.244	+	869.843i	−0.588555	+	0.808457i
$106$	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
$126$	2145.77	+	607.115i	1.51714	+	0.429255i
$127$		−	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	$-0.366004\pi$
$131$	1225.39			0.817274			0.408637	+	0.912697i	$0.366004\pi$
$132$	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	$-0.781750\pi$
$139$		−	2075.28i		−	1.26635i	0.774007	−	0.633177i	$-0.218250\pi$
$140$	−1932.55	+	1524.60i	−1.16664	+	0.920371i
$141$	−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
$147$	351.595	+	1747.26i	0.197272	+	0.980349i
$148$			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	$-0.416834\pi$
$157$	1016.31			0.516625			0.258312	+	0.966061i	$0.416834\pi$
$158$	−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	$-0.855924\pi$
$167$		−	1887.62i		−	0.874662i	0.899301	−	0.437331i	$-0.144076\pi$
$168$	1423.05	+	871.144i	0.653517	+	0.400061i
$169$	−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	$0.278373\pi$
$173$			3491.67i			1.53449i	−0.641353	+	0.767246i	$0.721627\pi$
$174$	1271.89	+	4532.36i	0.554148	+	1.97470i
$175$	1284.12	+	1926.25i	0.554686	+	0.832060i
$176$		−	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	$-0.857599\pi$
$181$		−	2106.81i		−	0.865182i	0.901590	−	0.432591i	$-0.142401\pi$
$182$	−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
$189$	−2598.31	−	5.56529i	−0.999998	−	0.00214188i
$190$	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	$0.0767115\pi$
$199$			1340.01i			0.477341i	−0.971101	+	0.238670i	$0.923288\pi$
$200$	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
$210$	2824.00	−	3879.14i	0.927974	−	1.27469i
$211$	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	$-0.662783\pi$
$223$	−3259.48			−0.978793			−0.489396	+	0.872061i	$0.662783\pi$
$224$	−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	$-0.790204\pi$
$227$		−	4188.94i		−	1.22480i	0.790548	−	0.612401i	$-0.209796\pi$
$228$	−1996.01	−	7112.73i	−0.579775	−	2.06602i
$229$		−	1996.90i		−	0.576240i	−0.957594	−	0.288120i	$-0.906970\pi$
$229$		−	1996.90i		−	0.576240i	0.957594	−	0.288120i	$-0.0930302\pi$
$230$	535.909	−	6688.51i	0.153638	−	1.91751i
$231$	1521.57	−	2485.55i	0.433384	−	0.707952i
$232$			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	$0.194843\pi$
$241$			4299.54i			1.14920i	−0.818434	+	0.574601i	$0.805157\pi$
$242$	−1845.90			−0.490326
$243$	763.168	−	3710.32i	0.201470	−	0.979495i
$244$		−	3711.86i		−	0.973884i
$245$	3788.90	+	591.896i	0.988017	+	0.154346i
$246$	−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	$-0.636504\pi$
$251$	−3307.05			−0.831630			−0.415815	+	0.909449i	$0.636504\pi$
$252$	−5719.94	−	1618.38i	−1.42985	−	0.404557i
$253$		−	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	$0.158298\pi$
$257$			3931.01i			0.954123i	−0.878870	+	0.477061i	$0.841702\pi$
$258$	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	$-0.393178\pi$
$269$	2905.93			0.658653			0.329326	+	0.944216i	$0.393178\pi$
$270$	4720.90	+	5161.85i	1.06409	+	1.16348i
$271$			716.004i			0.160495i	0.996775	+	0.0802475i	$0.0255711\pi$
$271$			716.004i			0.160495i	−0.996775	+	0.0802475i	$0.974429\pi$
$272$			81.6883i			0.0182099i
$273$	1555.76	+	952.385i	0.344905	+	0.211139i
$274$	−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
$280$	2818.58	−	2223.59i	0.601580	−	0.474589i
$281$			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	$-0.487256\pi$
$283$	381.119			0.0800536			0.0400268	+	0.999199i	$0.487256\pi$
$284$			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	$-0.925532\pi$
$293$		−	2325.30i		−	0.463637i	0.972759	−	0.231818i	$-0.0744675\pi$
$294$	−1567.96	−	7792.03i	−0.311039	−	1.54572i
$295$	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	$-0.603848\pi$
$307$	−3447.89			−0.640981			−0.320491	+	0.947252i	$0.603848\pi$
$308$	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	$-0.746710\pi$
$311$	−7675.73			−1.39952			−0.699760	+	0.714378i	$0.746710\pi$
$312$	1644.19	−	461.399i	0.298345	−	0.0837230i
$313$	−9734.46			−1.75790			−0.878952	−	0.476910i	$-0.841757\pi$
$313$	−9734.46			−1.75790			−0.878952	+	0.476910i	$0.841757\pi$
$314$	−4532.30			−0.814562
$315$	−1946.85	+	5240.77i	−0.348230	+	0.937409i
$316$	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
$336$	1459.46	+	893.434i	0.236965	+	0.145062i
$337$		−	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	$0.0689870\pi$
$349$			2804.01i			0.430073i	−0.976606	+	0.215036i	$0.931013\pi$
$350$	−5726.62	−	8590.24i	−0.874573	−	1.31191i
$351$	−1812.77	+	1945.74i	−0.275665	+	0.295886i
$352$			6601.92i			0.999669i
$353$		−	1183.07i		−	0.178381i	−0.996015	−	0.0891907i	$-0.971572\pi$
$353$		−	1183.07i		−	0.178381i	0.996015	−	0.0891907i	$-0.0284281\pi$
$354$	−16399.0	+	4601.97i	−2.46214	+	0.690937i
$355$	7141.74	+	572.223i	1.06773	+	0.0855506i
$356$	5062.95			0.753753
$357$	−230.818	+	377.052i	−0.0342191	+	0.0558984i
$358$		−	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	$-0.675136\pi$
$367$	−7352.20			−1.04573			−0.522864	+	0.852416i	$0.675136\pi$
$368$	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
$378$	11587.4	+	24.8188i	1.57670	+	0.00337710i
$379$	−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	$-0.651349\pi$
$383$		−	13328.0i		−	1.77815i	0.457763	−	0.889074i	$-0.348651\pi$
$384$	9791.74	−	2747.80i	1.30126	−	0.365164i
$385$	−3883.79	−	4923.01i	−0.514120	−	0.651688i
$386$		−	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	$-0.444948\pi$
$397$	2722.53			0.344181			0.172091	+	0.985081i	$0.444948\pi$
$398$		−	5975.88i		−	0.752623i
$399$	−6008.94	+	9815.88i	−0.753944	+	1.23160i
$400$	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	$-0.956707\pi$
$409$		−	2243.08i		−	0.271181i	0.990765	−	0.135591i	$-0.0432932\pi$
$410$	−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	$-0.761659\pi$
$419$	−12565.4			−1.46505			−0.732527	+	0.680738i	$0.761659\pi$
$420$	−7527.91	+	10340.6i	−0.874581	+	1.20135i
$421$	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	$-0.191253\pi$
$433$	14864.3			1.64972			0.824862	+	0.565334i	$0.191253\pi$
$434$	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	$-0.789801\pi$
$439$		−	11284.2i		−	1.22680i	0.789771	−	0.613402i	$-0.210199\pi$
$440$	−5851.58	−	468.851i	−0.634007	−	0.0507991i
$441$	4212.02	+	8247.73i	0.454813	+	0.890587i
$442$		−	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
$455$	3081.44	−	2430.96i	0.317494	−	0.250473i
$456$	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	$-0.570061\pi$
$461$	−4322.13			−0.436663			−0.218332	+	0.975875i	$0.570061\pi$
$462$	−6785.54	+	11084.5i	−0.683316	+	1.11623i
$463$			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	$0.0399257\pi$
$467$			2525.04i			0.250203i	−0.992144	+	0.125102i	$0.960074\pi$
$468$	−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	$-0.451604\pi$
$479$	3175.55			0.302911			0.151456	+	0.988464i	$0.451604\pi$
$480$	−2437.07	−	12428.2i	−0.231743	−	1.18181i
$481$		−	6399.09i		−	0.606598i
$482$		−	19174.1i		−	1.81195i
$483$	11045.6	+	6761.71i	1.04056	+	0.636995i
$484$	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
$490$	−16896.9	−	2639.61i	−1.55781	−	0.243358i
$491$			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	$0.212336\pi$
$503$			13959.0i			1.23738i	−0.785636	+	0.618689i	$0.787664\pi$
$504$	8342.42	+	2360.37i	0.737303	+	0.208610i
$505$	−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	$-0.306501\pi$
$509$	13117.5			1.14228			0.571141	+	0.820852i	$0.306501\pi$
$510$	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	$-0.547932\pi$
$521$	−3567.96			−0.300029			−0.150015	+	0.988684i	$0.547932\pi$
$522$	12726.3	+	20889.3i	1.06708	+	1.75153i
$523$	6801.37			0.568648			0.284324	−	0.958728i	$-0.408231\pi$
$523$	6801.37			0.568648			0.284324	+	0.958728i	$0.408231\pi$
$524$	14567.3			1.21445
$525$	9128.62	+	7833.99i	0.758868	+	0.651244i
$526$	−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
$546$	−6938.05	−	4247.24i	−0.543812	−	0.332903i
$547$			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
$560$	2890.70	−	2280.49i	0.218133	−	0.172086i
$561$	696.000	−	195.315i	0.0523800	−	0.0146991i
$562$		−	34540.9i		−	2.59256i
$563$			16595.3i			1.24229i	0.783696	+	0.621145i	$0.213332\pi$
$563$			16595.3i			1.24229i	−0.783696	+	0.621145i	$0.786668\pi$
$564$	−4561.61	−	16255.2i	−0.340565	−	1.21360i
$565$	918.941	−	11469.0i	0.0684251	−	0.853991i
$566$	−1699.63			−0.126220
$567$	−13006.9	+	3620.02i	−0.963384	+	0.268124i
$568$		−	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	$-0.596269\pi$
$577$	−8256.36			−0.595696			−0.297848	+	0.954613i	$0.596269\pi$
$578$	−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	$0.282035\pi$
$587$			22031.8i			1.54915i	−0.632484	+	0.774573i	$0.717965\pi$
$588$	4179.71	+	20771.1i	0.293143	+	1.45678i
$589$	−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	$0.132890\pi$
$593$			11710.2i			0.810929i	−0.914111	+	0.405465i	$0.867110\pi$
$594$	−13863.0	−	12915.6i	−0.957584	−	0.892142i
$595$	589.163	+	746.811i	0.0405938	+	0.0514559i
$596$		−	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	$0.241801\pi$
$601$			20293.0i			1.37732i	−0.725083	+	0.688661i	$0.758199\pi$
$602$	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	$-0.544239\pi$
$607$	−4143.51			−0.277068			−0.138534	+	0.990358i	$0.544239\pi$
$608$		−	26072.2i		−	1.73909i
$609$	−10206.9	+	16673.5i	−0.679156	+	1.10943i
$610$	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	$0.137472\pi$
$619$			12892.7i			0.837162i	−0.908180	+	0.418581i	$0.862528\pi$
$620$	−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
$630$	8682.13	−	23371.6i	0.549054	−	1.47801i
$631$	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	$-0.661670\pi$
$643$	−15859.5			−0.972689			−0.486345	+	0.873767i	$0.661670\pi$
$644$	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	$-0.706384\pi$
$647$		−	26235.0i		−	1.59413i	0.603893	−	0.797066i	$-0.293616\pi$
$648$	−5796.79	+	11231.9i	−0.351419	+	0.680910i
$649$			22259.1i			1.34629i
$650$	−10431.7	−	1682.45i	−0.629483	−	0.101525i
$651$	−3089.94	+	5047.55i	−0.186028	+	0.303885i
$652$		−	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	$0.179923\pi$
$661$			18205.0i			1.07124i	−0.844458	+	0.535621i	$0.820077\pi$
$662$	−19834.7			−1.16450
$663$	122.252	+	435.644i	0.00716121	+	0.0255189i
$664$			5188.71i			0.303254i
$665$	15337.8	+	19441.9i	0.894398	+	1.13372i
$666$	−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
$672$	−17893.0	−	10953.5i	−1.02714	−	0.628780i
$673$		−	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	$-0.991002\pi$
$677$		−	995.751i		−	0.0565285i	0.999600	−	0.0282643i	$-0.00899799\pi$
$678$	−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	$-0.826009\pi$
$691$		−	18883.3i		−	1.03959i	0.854291	−	0.519794i	$-0.173991\pi$
$692$			41508.5i			2.28023i
$693$	4122.69	−	14571.1i	0.225986	−	0.798716i
$694$	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
$700$	15265.4	+	22898.9i	0.824253	+	1.23643i
$701$		−	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
$714$	1029.35	−	1681.49i	0.0539532	−	0.0881349i
$715$	−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	$-0.260813\pi$
$719$	26323.4			1.36537			0.682683	+	0.730715i	$0.260813\pi$
$720$	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	$-0.505303\pi$
$727$	−653.079			−0.0333169			−0.0166584	+	0.999861i	$0.505303\pi$
$728$	−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	$-0.338511\pi$
$733$	19283.5			0.971696			0.485848	+	0.874043i	$0.338511\pi$
$734$	32787.7			1.64880
$735$	19786.5	−	2358.18i	0.992973	−	0.118344i
$736$	−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
$756$	−30888.4	−	66.1593i	−1.48598	−	0.00318279i
$757$			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	$-0.656354\pi$
$761$	−19804.3			−0.943371			−0.471686	+	0.881767i	$0.656354\pi$
$762$	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	$-0.888600\pi$
$769$		−	14623.5i		−	0.685746i	0.939382	−	0.342873i	$-0.111400\pi$
$770$	17320.1	+	21954.6i	0.810613	+	1.02752i
$771$	5518.88	+	19666.4i	0.257792	+	0.918637i
$772$			53743.5i			2.50553i
$773$		−	40353.9i		−	1.87766i	−0.344384	−	0.938829i	$-0.611912\pi$
$773$		−	40353.9i		−	1.87766i	0.344384	−	0.938829i	$-0.388088\pi$
$774$	16953.9	+	27828.6i	0.787331	+	1.29235i
$775$	−1224.01	+	7589.22i	−0.0567327	+	0.351758i
$776$	−9738.10			−0.450486
$777$	16962.1	−	27708.3i	0.783155	−	1.27932i
$778$		−	27575.6i		−	1.27074i
$779$		−

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} +(-82.0763 - 50.2443i) 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} +(-162.565 + 128.248i) 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} +(366.026 + 224.068i) 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} +(-481.159 - 136.137i) 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} +(724.972 - 571.933i) 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} +(-975.710 - 597.297i) 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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40q + 184q^{4} + 4q^{9} + O(q^{10}) \)	\( 40q + 184q^{4} + 4q^{9} - 188q^{15} + 184q^{16} + 148q^{21} + 712q^{25} - 336q^{30} - 1520q^{36} + 644q^{39} - 1488q^{46} - 1496q^{49} - 220q^{51} + 1984q^{60} + 40q^{64} - 3000q^{70} - 1192q^{79} + 4636q^{81} - 2192q^{84} + 4808q^{85} - 4408q^{91} + 5276q^{99} + O(q^{100}) \)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

Related objects

Downloads

Learn more about