LMFDB - Embedded newform 76.5.b.a.39.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,5,Mod(39,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("76.39");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	76.b (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:	$7.85611719437$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			39.6
Character	$\chi$	$=$	76.39
Dual form			76.5.b.a.39.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.24361 + 2.34072i) q^{2} +7.00580i q^{3} +(5.04202 - 15.1848i) q^{4} +9.28704 q^{5} +(-16.3986 - 22.7241i) q^{6} +54.2259i q^{7} +(19.1890 + 61.0556i) q^{8} +31.9187 q^{9} +O(q^{10})$	\(q+(-3.24361 + 2.34072i) q^{2} +7.00580i q^{3} +(5.04202 - 15.1848i) q^{4} +9.28704 q^{5} +(-16.3986 - 22.7241i) q^{6} +54.2259i q^{7} +(19.1890 + 61.0556i) q^{8} +31.9187 q^{9} +(-30.1236 + 21.7384i) q^{10} +65.2388i q^{11} +(106.382 + 35.3234i) q^{12} -57.2879 q^{13} +(-126.928 - 175.888i) q^{14} +65.0632i q^{15} +(-205.156 - 153.124i) q^{16} -431.897 q^{17} +(-103.532 + 74.7130i) q^{18} -82.8191i q^{19} +(46.8255 - 141.022i) q^{20} -379.896 q^{21} +(-152.706 - 211.609i) q^{22} +458.678i q^{23} +(-427.743 + 134.435i) q^{24} -538.751 q^{25} +(185.820 - 134.095i) q^{26} +791.086i q^{27} +(823.410 + 273.408i) q^{28} +231.951 q^{29} +(-152.295 - 211.040i) q^{30} -195.452i q^{31} +(1023.87 + 16.4618i) q^{32} -457.050 q^{33} +(1400.90 - 1010.95i) q^{34} +503.599i q^{35} +(160.935 - 484.679i) q^{36} -1290.44 q^{37} +(193.857 + 268.633i) q^{38} -401.348i q^{39} +(178.210 + 567.026i) q^{40} +2130.04 q^{41} +(1232.24 - 889.232i) q^{42} +1227.02i q^{43} +(990.638 + 328.936i) q^{44} +296.431 q^{45} +(-1073.64 - 1487.77i) q^{46} +1368.32i q^{47} +(1072.76 - 1437.28i) q^{48} -539.453 q^{49} +(1747.50 - 1261.07i) q^{50} -3025.78i q^{51} +(-288.847 + 869.905i) q^{52} +5213.59 q^{53} +(-1851.71 - 2565.98i) q^{54} +605.876i q^{55} +(-3310.79 + 1040.54i) q^{56} +580.214 q^{57} +(-752.359 + 542.933i) q^{58} +1376.46i q^{59} +(987.971 + 328.050i) q^{60} -2239.87 q^{61} +(457.500 + 633.971i) q^{62} +1730.82i q^{63} +(-3359.56 + 2343.20i) q^{64} -532.035 q^{65} +(1482.49 - 1069.83i) q^{66} +1622.09i q^{67} +(-2177.63 + 6558.26i) q^{68} -3213.41 q^{69} +(-1178.79 - 1633.48i) q^{70} +175.649i q^{71} +(612.490 + 1948.82i) q^{72} -2130.61 q^{73} +(4185.68 - 3020.56i) q^{74} -3774.38i q^{75} +(-1257.59 - 417.576i) q^{76} -3537.64 q^{77} +(939.444 + 1301.82i) q^{78} -12054.6i q^{79} +(-1905.29 - 1422.07i) q^{80} -2956.78 q^{81} +(-6909.01 + 4985.83i) q^{82} -3298.59i q^{83} +(-1915.45 + 5768.65i) q^{84} -4011.04 q^{85} +(-2872.12 - 3979.98i) q^{86} +1625.00i q^{87} +(-3983.19 + 1251.87i) q^{88} +14798.3 q^{89} +(-961.506 + 693.862i) q^{90} -3106.49i q^{91} +(6964.93 + 2312.67i) q^{92} +1369.30 q^{93} +(-3202.87 - 4438.31i) q^{94} -769.144i q^{95} +(-115.328 + 7173.01i) q^{96} +10626.1 q^{97} +(1749.78 - 1262.71i) q^{98} +2082.34i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 6 q^{2} - 6 q^{4} + 24 q^{5} + 66 q^{6} + 216 q^{8} - 972 q^{9}+O(q^{10}) $ 36 * q + 6 * q^2 - 6 * q^4 + 24 * q^5 + 66 * q^6 + 216 * q^8 - 972 * q^9	$ 36 q + 6 q^{2} - 6 q^{4} + 24 q^{5} + 66 q^{6} + 216 q^{8} - 972 q^{9} + 152 q^{10} + 160 q^{12} + 120 q^{13} - 60 q^{14} - 38 q^{16} - 600 q^{17} + 286 q^{18} - 600 q^{20} + 608 q^{21} + 1080 q^{22} + 958 q^{24} + 4604 q^{25} - 2766 q^{26} - 2250 q^{28} - 168 q^{29} - 1380 q^{30} + 3576 q^{32} + 1440 q^{33} + 908 q^{34} - 5836 q^{36} - 2248 q^{37} - 1716 q^{40} + 1800 q^{41} - 5006 q^{42} - 2520 q^{44} + 88 q^{45} + 6404 q^{46} + 1064 q^{48} - 12188 q^{49} + 3354 q^{50} + 15492 q^{52} - 6600 q^{53} + 1654 q^{54} + 12924 q^{56} + 5450 q^{58} - 11188 q^{60} + 2200 q^{61} - 9972 q^{62} + 12570 q^{64} - 15792 q^{65} + 10500 q^{66} - 22614 q^{68} + 19904 q^{69} + 900 q^{70} - 11376 q^{72} + 11560 q^{73} + 17304 q^{74} + 1680 q^{77} - 24740 q^{78} + 12900 q^{80} + 13604 q^{81} - 18420 q^{82} + 5644 q^{84} - 11552 q^{85} + 24564 q^{86} - 15304 q^{88} + 13800 q^{89} - 60212 q^{90} - 2142 q^{92} + 34592 q^{93} - 23096 q^{94} - 35770 q^{96} + 8200 q^{97} + 25566 q^{98}+O(q^{100}) $ 36 * q + 6 * q^2 - 6 * q^4 + 24 * q^5 + 66 * q^6 + 216 * q^8 - 972 * q^9 + 152 * q^10 + 160 * q^12 + 120 * q^13 - 60 * q^14 - 38 * q^16 - 600 * q^17 + 286 * q^18 - 600 * q^20 + 608 * q^21 + 1080 * q^22 + 958 * q^24 + 4604 * q^25 - 2766 * q^26 - 2250 * q^28 - 168 * q^29 - 1380 * q^30 + 3576 * q^32 + 1440 * q^33 + 908 * q^34 - 5836 * q^36 - 2248 * q^37 - 1716 * q^40 + 1800 * q^41 - 5006 * q^42 - 2520 * q^44 + 88 * q^45 + 6404 * q^46 + 1064 * q^48 - 12188 * q^49 + 3354 * q^50 + 15492 * q^52 - 6600 * q^53 + 1654 * q^54 + 12924 * q^56 + 5450 * q^58 - 11188 * q^60 + 2200 * q^61 - 9972 * q^62 + 12570 * q^64 - 15792 * q^65 + 10500 * q^66 - 22614 * q^68 + 19904 * q^69 + 900 * q^70 - 11376 * q^72 + 11560 * q^73 + 17304 * q^74 + 1680 * q^77 - 24740 * q^78 + 12900 * q^80 + 13604 * q^81 - 18420 * q^82 + 5644 * q^84 - 11552 * q^85 + 24564 * q^86 - 15304 * q^88 + 13800 * q^89 - 60212 * q^90 - 2142 * q^92 + 34592 * q^93 - 23096 * q^94 - 35770 * q^96 + 8200 * q^97 + 25566 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$1$	$-1$

Coefficient data

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

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

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

$2$	−3.24361	+	2.34072i	−0.810903	+	0.585181i
$2$	−3.24361	+	2.34072i	−0.810903	+	0.585181i
$3$			7.00580i			0.778422i	0.921149	+	0.389211i	$0.127252\pi$
$3$			7.00580i			0.778422i	−0.921149	+	0.389211i	$0.872748\pi$
$4$	5.04202	−	15.1848i	0.315126	−	0.949050i
$5$	9.28704			0.371482			0.185741	−	0.982599i	$-0.440532\pi$
$5$	9.28704			0.371482			0.185741	+	0.982599i	$0.440532\pi$
$6$	−16.3986	−	22.7241i	−0.455518	−	0.631225i
$7$			54.2259i			1.10665i	0.832965	+	0.553326i	$0.186642\pi$
$7$			54.2259i			1.10665i	−0.832965	+	0.553326i	$0.813358\pi$
$8$	19.1890	+	61.0556i	0.299829	+	0.953993i
$9$	31.9187			0.394058
$10$	−30.1236	+	21.7384i	−0.301236	+	0.217384i
$11$			65.2388i			0.539164i	0.962977	+	0.269582i	$0.0868855\pi$
$11$			65.2388i			0.539164i	−0.962977	+	0.269582i	$0.913114\pi$
$12$	106.382	+	35.3234i	0.738762	+	0.245302i
$13$	−57.2879			−0.338982			−0.169491	−	0.985532i	$-0.554212\pi$
$13$	−57.2879			−0.338982			−0.169491	+	0.985532i	$0.554212\pi$
$14$	−126.928	−	175.888i	−0.647592	−	0.897387i
$15$			65.0632i			0.289170i
$16$	−205.156	−	153.124i	−0.801391	−	0.598141i
$17$	−431.897			−1.49445			−0.747226	−	0.664570i	$-0.768615\pi$
$17$	−431.897			−1.49445			−0.747226	+	0.664570i	$0.768615\pi$
$18$	−103.532	+	74.7130i	−0.319543	+	0.230596i
$19$		−	82.8191i		−	0.229416i
$19$		−	82.8191i		−	0.229416i
$20$	46.8255	−	141.022i	0.117064	−	0.352555i
$21$	−379.896			−0.861443
$22$	−152.706	−	211.609i	−0.315508	−	0.437209i
$23$			458.678i			0.867066i	0.901138	+	0.433533i	$0.142733\pi$
$23$			458.678i			0.867066i	−0.901138	+	0.433533i	$0.857267\pi$
$24$	−427.743	+	134.435i	−0.742610	+	0.233394i
$25$	−538.751			−0.862001
$26$	185.820	−	134.095i	0.274881	−	0.198366i
$27$			791.086i			1.08517i
$28$	823.410	+	273.408i	1.05027	+	0.348735i
$29$	231.951			0.275804			0.137902	−	0.990446i	$-0.455964\pi$
$29$	231.951			0.275804			0.137902	+	0.990446i	$0.455964\pi$
$30$	−152.295	−	211.040i	−0.169217	−	0.234488i
$31$		−	195.452i		−	0.203384i	−0.994816	−	0.101692i	$-0.967574\pi$
$31$		−	195.452i		−	0.203384i	0.994816	−	0.101692i	$-0.0324256\pi$
$32$	1023.87	+	16.4618i	0.999871	+	0.0160759i
$33$	−457.050			−0.419697
$34$	1400.90	−	1010.95i	1.21186	−	0.874525i
$35$			503.599i			0.411101i
$36$	160.935	−	484.679i	0.124178	−	0.373981i
$37$	−1290.44			−0.942614			−0.471307	−	0.881969i	$-0.656218\pi$
$37$	−1290.44			−0.942614			−0.471307	+	0.881969i	$0.656218\pi$
$38$	193.857	+	268.633i	0.134250	+	0.186034i
$39$		−	401.348i		−	0.263871i
$40$	178.210	+	567.026i	0.111381	+	0.354391i
$41$	2130.04			1.26712			0.633562	−	0.773692i	$-0.281592\pi$
$41$	2130.04			1.26712			0.633562	+	0.773692i	$0.281592\pi$
$42$	1232.24	−	889.232i	0.698546	−	0.504100i
$43$			1227.02i			0.663614i	0.943347	+	0.331807i	$0.107658\pi$
$43$			1227.02i			0.663614i	−0.943347	+	0.331807i	$0.892342\pi$
$44$	990.638	+	328.936i	0.511693	+	0.169905i
$45$	296.431			0.146386
$46$	−1073.64	−	1487.77i	−0.507391	−	0.703106i
$47$			1368.32i			0.619432i	0.950829	+	0.309716i	$0.100234\pi$
$47$			1368.32i			0.619432i	−0.950829	+	0.309716i	$0.899766\pi$
$48$	1072.76	−	1437.28i	0.465607	−	0.623820i
$49$	−539.453			−0.224678
$50$	1747.50	−	1261.07i	0.698999	−	0.504427i
$51$		−	3025.78i		−	1.16332i
$52$	−288.847	+	869.905i	−0.106822	+	0.321710i
$53$	5213.59			1.85603			0.928015	−	0.372543i	$-0.121514\pi$
$53$	5213.59			1.85603			0.928015	+	0.372543i	$0.121514\pi$
$54$	−1851.71	−	2565.98i	−0.635019	−	0.879964i
$55$			605.876i			0.200290i
$56$	−3310.79	+	1040.54i	−1.05574	+	0.331806i
$57$	580.214			0.178582
$58$	−752.359	+	542.933i	−0.223650	+	0.161395i
$59$			1376.46i			0.395420i	0.980261	+	0.197710i	$0.0633504\pi$
$59$			1376.46i			0.395420i	−0.980261	+	0.197710i	$0.936650\pi$
$60$	987.971	+	328.050i	0.274436	+	0.0911250i
$61$	−2239.87			−0.601953			−0.300976	−	0.953632i	$-0.597313\pi$
$61$	−2239.87			−0.601953			−0.300976	+	0.953632i	$0.597313\pi$
$62$	457.500	+	633.971i	0.119017	+	0.164925i
$63$			1730.82i			0.436086i
$64$	−3359.56	+	2343.20i	−0.820205	+	0.572069i
$65$	−532.035			−0.125925
$66$	1482.49	−	1069.83i	0.340334	−	0.245599i
$67$			1622.09i			0.361347i	0.983543	+	0.180674i	$0.0578278\pi$
$67$			1622.09i			0.361347i	−0.983543	+	0.180674i	$0.942172\pi$
$68$	−2177.63	+	6558.26i	−0.470941	+	1.41831i
$69$	−3213.41			−0.674944
$70$	−1178.79	−	1633.48i	−0.240568	−	0.333363i
$71$			175.649i			0.0348441i	0.999848	+	0.0174221i	$0.00554590\pi$
$71$			175.649i			0.0348441i	−0.999848	+	0.0174221i	$0.994454\pi$
$72$	612.490	+	1948.82i	0.118150	+	0.375929i
$73$	−2130.61			−0.399814			−0.199907	−	0.979815i	$-0.564064\pi$
$73$	−2130.61			−0.399814			−0.199907	+	0.979815i	$0.564064\pi$
$74$	4185.68	−	3020.56i	0.764368	−	0.551600i
$75$		−	3774.38i		−	0.671001i
$76$	−1257.59	−	417.576i	−0.217727	−	0.0722950i
$77$	−3537.64			−0.596667
$78$	939.444	+	1301.82i	0.154412	+	0.213974i
$79$		−	12054.6i		−	1.93152i	−0.259446	−	0.965758i	$-0.583540\pi$
$79$		−	12054.6i		−	1.93152i	0.259446	−	0.965758i	$-0.416460\pi$
$80$	−1905.29	−	1422.07i	−0.297702	−	0.222199i
$81$	−2956.78			−0.450659
$82$	−6909.01	+	4985.83i	−1.02752	+	0.741497i
$83$		−	3298.59i		−	0.478819i	−0.970919	−	0.239410i	$-0.923046\pi$
$83$		−	3298.59i		−	0.478819i	0.970919	−	0.239410i	$-0.0769539\pi$
$84$	−1915.45	+	5768.65i	−0.271463	+	0.817552i
$85$	−4011.04			−0.555162
$86$	−2872.12	−	3979.98i	−0.388334	−	0.538126i
$87$			1625.00i			0.214692i
$88$	−3983.19	+	1251.87i	−0.514359	+	0.161657i
$89$	14798.3			1.86824			0.934118	−	0.356965i	$-0.116188\pi$
$89$	14798.3			1.86824			0.934118	+	0.356965i	$0.116188\pi$
$90$	−961.506	+	693.862i	−0.118704	+	0.0856620i
$91$		−	3106.49i		−	0.375135i
$92$	6964.93	+	2312.67i	0.822889	+	0.273236i
$93$	1369.30			0.158319
$94$	−3202.87	−	4438.31i	−0.362480	−	0.502299i
$95$		−	769.144i		−	0.0852237i
$96$	−115.328	+	7173.01i	−0.0125139	+	0.778322i
$97$	10626.1			1.12935			0.564676	−	0.825312i	$-0.309001\pi$
$97$	10626.1			1.12935			0.564676	+	0.825312i	$0.309001\pi$
$98$	1749.78	−	1262.71i	0.182192	−	0.131478i
$99$			2082.34i			0.212462i
$100$	−2716.39	+	8180.82i	−0.271639	+	0.818082i
$101$	−3350.81			−0.328479			−0.164240	−	0.986420i	$-0.552517\pi$
$101$	−3350.81			−0.328479			−0.164240	+	0.986420i	$0.552517\pi$
$102$	7082.52	+	9814.46i	0.680750	+	0.943335i
$103$			13446.7i			1.26748i	0.773545	+	0.633742i	$0.218482\pi$
$103$			13446.7i			1.26748i	−0.773545	+	0.633742i	$0.781518\pi$
$104$	−1099.30	−	3497.74i	−0.101636	−	0.323386i
$105$	−3528.11			−0.320010
$106$	−16910.8	+	12203.6i	−1.50506	+	1.08611i
$107$		−	5654.93i		−	0.493923i	−0.969025	−	0.246962i	$-0.920568\pi$
$107$		−	5654.93i		−	0.493923i	0.969025	−	0.246962i	$-0.0794322\pi$
$108$	12012.5	+	3988.68i	1.02988	+	0.341965i
$109$	−982.651			−0.0827078			−0.0413539	−	0.999145i	$-0.513167\pi$
$109$	−982.651			−0.0827078			−0.0413539	+	0.999145i	$0.513167\pi$
$110$	−1418.19	−	1965.23i	−0.117206	−	0.162415i
$111$		−	9040.55i		−	0.733752i
$112$	8303.30	−	11124.8i	0.661934	−	0.886860i
$113$	13371.2			1.04716			0.523579	−	0.851977i	$-0.324597\pi$
$113$	13371.2			1.04716			0.523579	+	0.851977i	$0.324597\pi$
$114$	−1881.99	+	1358.12i	−0.144813	+	0.104503i
$115$			4259.76i			0.322099i
$116$	1169.50	−	3522.13i	0.0869131	−	0.261752i
$117$	−1828.56			−0.133579
$118$	−3221.90	−	4464.69i	−0.231392	−	0.320647i
$119$		−	23420.0i		−	1.65384i
$120$	−3972.47	+	1248.50i	−0.275866	+	0.0867014i
$121$	10384.9			0.709302
$122$	7265.26	−	5242.91i	0.488125	−	0.352251i
$123$			14922.6i			0.986358i
$124$	−2967.90	−	985.475i	−0.193022	−	0.0640917i
$125$	−10807.8			−0.691699
$126$	−4051.38	−	5614.12i	−0.255189	−	0.353623i
$127$		−	22279.7i		−	1.38134i	−0.723168	−	0.690672i	$-0.757315\pi$
$127$		−	22279.7i		−	1.38134i	0.723168	−	0.690672i	$-0.242685\pi$
$128$	5412.33	−	15464.2i	0.330343	−	0.943861i
$129$	−8596.27			−0.516572
$130$	1725.71	−	1245.35i	0.102113	−	0.0736892i
$131$			14060.1i			0.819303i	0.912242	+	0.409651i	$0.134350\pi$
$131$			14060.1i			0.819303i	−0.912242	+	0.409651i	$0.865650\pi$
$132$	−2304.46	+	6940.22i	−0.132258	+	0.398314i
$133$	4490.94			0.253883
$134$	−3796.86	−	5261.42i	−0.211454	−	0.293018i
$135$			7346.85i			0.403119i
$136$	−8287.69	−	26369.7i	−0.448080	−	1.42570i
$137$	11224.5			0.598031			0.299016	−	0.954248i	$-0.403342\pi$
$137$	11224.5			0.598031			0.299016	+	0.954248i	$0.403342\pi$
$138$	10423.0	−	7521.70i	0.547314	−	0.394964i
$139$			30773.8i			1.59276i	0.604794	+	0.796382i	$0.293255\pi$
$139$			30773.8i			1.59276i	−0.604794	+	0.796382i	$0.706745\pi$
$140$	7647.04	+	2539.16i	0.390155	+	0.129549i
$141$	−9586.21			−0.482180
$142$	−411.147	−	569.738i	−0.0203901	−	0.0282552i
$143$		−	3737.39i		−	0.182767i
$144$	−6548.32	−	4887.53i	−0.315795	−	0.235703i
$145$	2154.14			0.102456
$146$	6910.87	−	4987.17i	0.324210	−	0.233964i
$147$		−	3779.30i		−	0.174895i
$148$	−6506.42	+	19595.0i	−0.297043	+	0.894587i
$149$	25084.9			1.12990			0.564950	−	0.825125i	$-0.308895\pi$
$149$	25084.9			1.12990			0.564950	+	0.825125i	$0.308895\pi$
$150$	8834.79	+	12242.6i	0.392657	+	0.544117i
$151$		−	12143.6i		−	0.532590i	−0.963892	−	0.266295i	$-0.914200\pi$
$151$		−	12143.6i		−	0.532590i	0.963892	−	0.266295i	$-0.0857996\pi$
$152$	5056.56	−	1589.22i	0.218861	−	0.0687855i
$153$	−13785.6			−0.588902
$154$	11474.7	−	8280.63i	0.483839	−	0.349158i
$155$		−	1815.17i		−	0.0755535i
$156$	−6094.38	−	2023.60i	−0.250427	−	0.0831527i
$157$	4700.03			0.190678			0.0953392	−	0.995445i	$-0.469606\pi$
$157$	4700.03			0.190678			0.0953392	+	0.995445i	$0.469606\pi$
$158$	28216.5	+	39100.4i	1.13029	+	1.56627i
$159$			36525.4i			1.44478i
$160$	9508.70	+	152.881i	0.371434	+	0.00597192i
$161$	−24872.3			−0.959541
$162$	9590.63	−	6921.00i	0.365441	−	0.263717i
$163$			10879.5i			0.409481i	0.978816	+	0.204740i	$0.0656350\pi$
$163$			10879.5i			0.409481i	−0.978816	+	0.204740i	$0.934365\pi$
$164$	10739.7	−	32344.2i	0.399305	−	1.20256i
$165$	−4244.65			−0.155910
$166$	7721.08	+	10699.3i	0.280196	+	0.388276i
$167$			12640.0i			0.453225i	0.973985	+	0.226612i	$0.0727650\pi$
$167$			12640.0i			0.453225i	−0.973985	+	0.226612i	$0.927235\pi$
$168$	−7289.85	−	23194.8i	−0.258285	−	0.821810i
$169$	−25279.1			−0.885092
$170$	13010.3	−	9388.74i	0.450182	−	0.324870i
$171$		−	2643.48i		−	0.0904032i
$172$	18632.1	+	6186.67i	0.629803	+	0.209122i
$173$	−27070.1			−0.904479			−0.452239	−	0.891897i	$-0.649375\pi$
$173$	−27070.1			−0.904479			−0.452239	+	0.891897i	$0.649375\pi$
$174$	−3803.68	−	5270.88i	−0.125634	−	0.174094i
$175$		−	29214.3i		−	0.953935i
$176$	9989.64	−	13384.1i	0.322496	−	0.432081i
$177$	−9643.17			−0.307803
$178$	−47999.9	+	34638.7i	−1.51496	+	1.09326i
$179$			55214.1i			1.72323i	0.507560	+	0.861617i	$0.330548\pi$
$179$			55214.1i			1.72323i	−0.507560	+	0.861617i	$0.669452\pi$
$180$	1494.61	−	4501.24i	0.0461300	−	0.138927i
$181$	17201.1			0.525047			0.262524	−	0.964926i	$-0.415445\pi$
$181$	17201.1			0.525047			0.262524	+	0.964926i	$0.415445\pi$
$182$	7271.43	+	10076.2i	0.219522	+	0.304198i
$183$		−	15692.1i		−	0.468574i
$184$	−28004.8	+	8801.60i	−0.827175	+	0.259972i
$185$	−11984.4			−0.350164
$186$	−4441.47	+	3205.15i	−0.128381	+	0.0926451i
$187$		−	28176.4i		−	0.805755i
$188$	20777.7	+	6899.13i	0.587872	+	0.195199i
$189$	−42897.4			−1.20090
$190$	1800.35	+	2494.80i	0.0498713	+	0.0691082i
$191$			50118.9i			1.37384i	0.726735	+	0.686918i	$0.241037\pi$
$191$			50118.9i			1.37384i	−0.726735	+	0.686918i	$0.758963\pi$
$192$	−16416.0	−	23536.4i	−0.445312	−	0.638466i
$193$	−39940.4			−1.07225			−0.536127	−	0.844138i	$-0.680113\pi$
$193$	−39940.4			−1.07225			−0.536127	+	0.844138i	$0.680113\pi$
$194$	−34466.9	+	24872.7i	−0.915795	+	0.660876i
$195$		−	3727.33i		−	0.0980232i
$196$	−2719.94	+	8191.48i	−0.0708021	+	0.213231i
$197$	18965.7			0.488694			0.244347	−	0.969688i	$-0.421426\pi$
$197$	18965.7			0.488694			0.244347	+	0.969688i	$0.421426\pi$
$198$	−4874.19	−	6754.30i	−0.124329	−	0.172286i
$199$		−	56483.6i		−	1.42632i	−0.701003	−	0.713158i	$-0.747264\pi$
$199$		−	56483.6i		−	1.42632i	0.701003	−	0.713158i	$-0.252736\pi$
$200$	−10338.1	−	32893.7i	−0.258453	−	0.822343i
$201$	−11364.0			−0.281281
$202$	10868.7	−	7843.33i	0.266365	−	0.192220i
$203$			12577.8i			0.305219i
$204$	−45945.9	−	15256.1i	−1.10404	−	0.366591i
$205$	19781.7			0.470714
$206$	−31475.1	−	43616.0i	−0.741707	−	1.02781i
$207$			14640.4i			0.341675i
$208$	11753.0	+	8772.16i	0.271657	+	0.202759i
$209$	5403.02			0.123693
$210$	11443.8	−	8258.34i	0.259497	−	0.187264i
$211$			75536.8i			1.69666i	0.529471	+	0.848328i	$0.322390\pi$
$211$			75536.8i			1.69666i	−0.529471	+	0.848328i	$0.677610\pi$
$212$	26287.0	−	79167.2i	0.584884	−	1.76146i
$213$	−1230.56			−0.0271235
$214$	13236.6	+	18342.4i	0.289035	+	0.400524i
$215$			11395.4i			0.246520i
$216$	−48300.2	+	15180.2i	−1.03524	+	0.325364i
$217$	10598.6			0.225075
$218$	3187.34	−	2300.11i	0.0670680	−	0.0483990i
$219$		−	14926.6i		−	0.311224i
$220$	9200.10	+	3054.84i	0.190085	+	0.0631165i
$221$	24742.4			0.506592
$222$	21161.4	+	29324.0i	0.429378	+	0.595001i
$223$		−	62091.5i		−	1.24860i	−0.781186	−	0.624299i	$-0.785385\pi$
$223$		−	62091.5i		−	1.24860i	0.781186	−	0.624299i	$-0.214615\pi$
$224$	−892.655	+	55520.2i	−0.0177905	+	1.10651i
$225$	−17196.2			−0.339679
$226$	−43370.8	+	31298.2i	−0.849143	+	0.612777i
$227$		−	17045.7i		−	0.330798i	−0.986227	−	0.165399i	$-0.947109\pi$
$227$		−	17045.7i		−	0.330798i	0.986227	−	0.165399i	$-0.0528912\pi$
$228$	2925.45	−	8810.43i	0.0562760	−	0.169484i
$229$	95090.5			1.81329			0.906643	−	0.421899i	$-0.138636\pi$
$229$	95090.5			1.81329			0.906643	+	0.421899i	$0.138636\pi$
$230$	−9970.93	−	13817.0i	−0.188486	−	0.261191i
$231$		−	24784.0i		−	0.464459i
$232$	4450.92	+	14161.9i	0.0826940	+	0.263115i
$233$	21580.1			0.397504			0.198752	−	0.980050i	$-0.436311\pi$
$233$	21580.1			0.397504			0.198752	+	0.980050i	$0.436311\pi$
$234$	5931.13	−	4280.15i	0.108319	−	0.0781676i
$235$			12707.7i			0.230108i
$236$	20901.2	+	6940.12i	0.375273	+	0.124607i
$237$	84452.0			1.50353
$238$	54819.8	+	75965.4i	0.967795	+	1.34110i
$239$		−	70168.3i		−	1.22842i	−0.789144	−	0.614208i	$-0.789476\pi$
$239$		−	70168.3i		−	1.22842i	0.789144	−	0.614208i	$-0.210524\pi$
$240$	9962.75	−	13348.1i	0.172964	−	0.231738i
$241$	−45263.7			−0.779321			−0.389661	−	0.920959i	$-0.627408\pi$
$241$	−45263.7			−0.779321			−0.389661	+	0.920959i	$0.627408\pi$
$242$	−33684.6	+	24308.2i	−0.575175	+	0.415070i
$243$			43363.4i			0.734363i
$244$	−11293.5	+	34011.9i	−0.189691	+	0.571283i
$245$	−5009.92			−0.0834639
$246$	−34929.7	−	48403.2i	−0.577198	−	0.799841i
$247$			4744.53i			0.0777677i
$248$	11933.4	−	3750.54i	0.194027	−	0.0609804i
$249$	23109.2			0.372724
$250$	35056.3	−	25298.1i	0.560901	−	0.404769i
$251$		−	27444.5i		−	0.435619i	−0.975991	−	0.217810i	$-0.930109\pi$
$251$		−	27444.5i		−	0.435619i	0.975991	−	0.217810i	$-0.0698912\pi$
$252$	26282.2	+	8726.85i	0.413867	+	0.137422i
$253$	−29923.6			−0.467491
$254$	52150.6	+	72266.6i	0.808336	+	1.12014i
$255$		−	28100.6i		−	0.432150i
$256$	18642.0	+	62828.7i	0.284454	+	0.958690i
$257$	117041.			1.77203			0.886017	−	0.463652i	$-0.153461\pi$
$257$	117041.			1.77203			0.886017	+	0.463652i	$0.153461\pi$
$258$	27883.0	−	20121.5i	0.418890	−	0.302288i
$259$		−	69975.2i		−	1.04315i
$260$	−2682.53	+	8078.84i	−0.0396824	+	0.119509i
$261$	7403.59			0.108683
$262$	−32910.7	−	45605.4i	−0.479441	−	0.664375i
$263$		−	111901.i		−	1.61780i	−0.587950	−	0.808898i	$-0.700065\pi$
$263$		−	111901.i		−	1.61780i	0.587950	−	0.808898i	$-0.299935\pi$
$264$	−8770.36	−	27905.5i	−0.125837	−	0.400388i
$265$	48418.8			0.689481
$266$	−14566.9	+	10512.1i	−0.205875	+	0.148568i
$267$			103674.i			1.45428i
$268$	24631.1	+	8178.61i	0.342937	+	0.113870i
$269$	−100294.			−1.38602			−0.693012	−	0.720926i	$-0.743717\pi$
$269$	−100294.			−1.38602			−0.693012	+	0.720926i	$0.743717\pi$
$270$	−17197.0	−	23830.3i	−0.235898	−	0.326891i
$271$		−	85286.1i		−	1.16129i	−0.814158	−	0.580643i	$-0.802801\pi$
$271$		−	85286.1i		−	1.16129i	0.814158	−	0.580643i	$-0.197199\pi$
$272$	88606.2	+	66133.8i	1.19764	+	0.893894i
$273$	21763.4			0.292013
$274$	−36407.8	+	26273.3i	−0.484945	+	0.349957i
$275$		−	35147.5i		−	0.464760i
$276$	−16202.1	+	48794.9i	−0.212693	+	0.640555i
$277$	126023.			1.64244			0.821221	−	0.570610i	$-0.193293\pi$
$277$	126023.			1.64244			0.821221	+	0.570610i	$0.193293\pi$
$278$	−72032.9	−	99818.2i	−0.932055	−	1.29158i
$279$		−	6238.59i		−	0.0801453i
$280$	−30747.5	+	9663.58i	−0.392187	+	0.123260i
$281$	−58903.3			−0.745979			−0.372990	−	0.927836i	$-0.621667\pi$
$281$	−58903.3			−0.745979			−0.372990	+	0.927836i	$0.621667\pi$
$282$	31093.9	−	22438.7i	0.391001	−	0.282162i
$283$		−	9474.47i		−	0.118299i	−0.998249	−	0.0591497i	$-0.981161\pi$
$283$		−	9474.47i		−	0.118299i	0.998249	−	0.0591497i	$-0.0188389\pi$
$284$	2667.20	+	885.628i	0.0330688	+	0.0109803i
$285$	5388.47			0.0663401
$286$	8748.21	+	12122.7i	0.106952	+	0.148206i
$287$			115503.i			1.40227i
$288$	32680.6	+	525.439i	0.394008	+	0.00633486i
$289$	103014.			1.23339
$290$	−6987.19	+	5042.25i	−0.0830819	+	0.0599554i
$291$			74444.2i			0.879114i
$292$	−10742.6	+	32352.9i	−0.125992	+	0.379443i
$293$	−111767.			−1.30190			−0.650948	−	0.759122i	$-0.725629\pi$
$293$	−111767.			−1.30190			−0.650948	+	0.759122i	$0.725629\pi$
$294$	8846.30	+	12258.6i	0.102345	+	0.141823i
$295$			12783.2i			0.146891i
$296$	−24762.3	−	78788.4i	−0.282623	−	0.899247i
$297$	−51609.5			−0.585083
$298$	−81365.7	+	58716.8i	−0.916239	+	0.661196i
$299$		−	26276.7i		−	0.293919i
$300$	−57313.2	−	19030.5i	−0.636813	−	0.211450i
$301$	−66536.4			−0.734390
$302$	28424.8	+	39389.1i	0.311662	+	0.431879i
$303$		−	23475.1i		−	0.255695i
$304$	−12681.6	+	16990.8i	−0.137223	+	0.183852i
$305$	−20801.7			−0.223614
$306$	44715.1	−	32268.3i	0.477542	−	0.344614i
$307$		−	102343.i		−	1.08588i	−0.839771	−	0.542941i	$-0.817311\pi$
$307$		−	102343.i		−	1.08588i	0.839771	−	0.542941i	$-0.182689\pi$
$308$	−17836.9	+	53718.3i	−0.188025	+	0.566266i
$309$	−94205.2			−0.986638
$310$	4248.82	+	5887.71i	0.0442125	+	0.0612665i
$311$		−	40563.4i		−	0.419386i	−0.977767	−	0.209693i	$-0.932754\pi$
$311$		−	40563.4i		−	0.419386i	0.977767	−	0.209693i	$-0.0672464\pi$
$312$	24504.5	−	7701.48i	0.251731	−	0.0791161i
$313$	−155893.			−1.59124			−0.795622	−	0.605794i	$-0.792856\pi$
$313$	−155893.			−1.59124			−0.795622	+	0.605794i	$0.792856\pi$
$314$	−15245.1	+	11001.5i	−0.154622	+	0.111581i
$315$			16074.2i			0.161998i
$316$	−183046.	−	60779.5i	−1.83310	−	0.608672i
$317$	−10787.5			−0.107350			−0.0536750	−	0.998558i	$-0.517094\pi$
$317$	−10787.5			−0.107350			−0.0536750	+	0.998558i	$0.517094\pi$
$318$	−85495.8	−	118474.i	−0.845455	−	1.17157i
$319$			15132.2i			0.148704i
$320$	−31200.4	+	21761.4i	−0.304691	+	0.212513i
$321$	39617.3			0.384481
$322$	80675.9	−	58219.1i	0.778094	−	0.561505i
$323$			35769.3i			0.342851i
$324$	−14908.1	+	44898.0i	−0.142015	+	0.427698i
$325$	30863.9			0.292203
$326$	−25465.9	−	35288.8i	−0.239620	−	0.332049i
$327$		−	6884.26i		−	0.0643816i
$328$	40873.4	+	130051.i	0.379921	+	1.20883i
$329$	−74198.7			−0.685495
$330$	13768.0	−	9935.54i	0.126428	−	0.0912355i
$331$			44440.4i			0.405623i	0.979218	+	0.202811i	$0.0650078\pi$
$331$			44440.4i			0.405623i	−0.979218	+	0.202811i	$0.934992\pi$
$332$	−50088.4	−	16631.6i	−0.454423	−	0.150889i
$333$	−41189.2			−0.371445
$334$	−29586.7	−	40999.2i	−0.265218	−	0.367521i
$335$			15064.4i			0.134234i
$336$	77938.0	+	58171.3i	0.690352	+	0.515265i
$337$	178698.			1.57347			0.786736	−	0.617289i	$-0.211769\pi$
$337$	178698.			1.57347			0.786736	+	0.617289i	$0.211769\pi$
$338$	81995.6	−	59171.4i	0.717723	−	0.517939i
$339$			93675.7i			0.815131i
$340$	−20223.8	+	60906.9i	−0.174946	+	0.526876i
$341$	12751.1			0.109657
$342$	6187.66	+	8574.42i	0.0529022	+	0.0733082i
$343$			100944.i			0.858011i
$344$	−74916.5	+	23545.4i	−0.633083	+	0.198971i
$345$	−29843.1			−0.250729
$346$	87805.0	−	63363.7i	0.733444	−	0.529284i
$347$			185822.i			1.54326i	0.636073	+	0.771629i	$0.280558\pi$
$347$			185822.i			1.54326i	−0.636073	+	0.771629i	$0.719442\pi$
$348$	24675.3	+	8193.31i	0.203753	+	0.0676551i
$349$	21510.5			0.176604			0.0883020	−	0.996094i	$-0.471856\pi$
$349$	21510.5			0.176604			0.0883020	+	0.996094i	$0.471856\pi$
$350$	68382.5	+	94759.7i	0.558225	+	0.773549i
$351$		−	45319.7i		−	0.367851i
$352$	−1073.95	+	66795.9i	−0.00866757	+	0.539094i
$353$	−141598.			−1.13634			−0.568168	−	0.822912i	$-0.692348\pi$
$353$	−141598.			−1.13634			−0.568168	+	0.822912i	$0.692348\pi$
$354$	31278.7	−	22572.0i	0.249599	−	0.180121i
$355$			1631.26i			0.0129440i
$356$	74613.4	−	224709.i	0.588731	−	1.77305i
$357$	164076.			1.28738
$358$	−129241.	−	179093.i	−1.00840	−	1.39737i
$359$			141834.i			1.10051i	0.834998	+	0.550253i	$0.185469\pi$
$359$			141834.i			1.10051i	−0.834998	+	0.550253i	$0.814531\pi$
$360$	5688.22	+	18098.7i	0.0438906	+	0.139651i
$361$	−6859.00			−0.0526316
$362$	−55793.6	+	40263.0i	−0.425762	+	0.307248i
$363$			72754.5i			0.552137i
$364$	−47171.4	−	15663.0i	−0.356021	−	0.118215i
$365$	−19787.1			−0.148524
$366$	36730.8	+	50898.9i	0.274200	+	0.379968i
$367$		−	137772.i		−	1.02289i	−0.859316	−	0.511445i	$-0.829110\pi$
$367$		−	137772.i		−	1.02289i	0.859316	−	0.511445i	$-0.170890\pi$
$368$	70234.7	−	94100.6i	0.518628	−	0.694859i
$369$	67988.1			0.499321
$370$	38872.6	−	28052.1i	0.283949	−	0.204909i
$371$			282712.i			2.05398i
$372$	6904.04	−	20792.5i	0.0498904	−	0.150252i
$373$	−27182.6			−0.195377			−0.0976883	−	0.995217i	$-0.531145\pi$
$373$	−27182.6			−0.195377			−0.0976883	+	0.995217i	$0.531145\pi$
$374$	65953.2	+	91393.4i	0.471512	+	0.653389i
$375$		−	75717.3i		−	0.538434i
$376$	−83543.8	+	26256.9i	−0.590934	+	0.185724i
$377$	−13288.0			−0.0934924
$378$	139142.	−	100411.i	0.973814	−	0.702745i
$379$		−	73961.1i		−	0.514902i	−0.966291	−	0.257451i	$-0.917117\pi$
$379$		−	73961.1i		−	0.514902i	0.966291	−	0.257451i	$-0.0828826\pi$
$380$	−11679.3	−	3878.04i	−0.0808816	−	0.0268563i
$381$	156087.			1.07527
$382$	−117315.	−	162566.i	−0.803943	−	1.11405i
$383$		−	84818.9i		−	0.578222i	−0.957296	−	0.289111i	$-0.906640\pi$
$383$		−	84818.9i		−	0.578222i	0.957296	−	0.289111i	$-0.0933597\pi$
$384$	108339.	+	37917.7i	0.734723	+	0.257146i
$385$	−32854.2			−0.221651
$386$	129551.	−	93489.3i	0.869493	−	0.627462i
$387$			39165.0i			0.261503i
$388$	53577.0	−	161355.i	0.355889	−	1.07181i
$389$	−282901.			−1.86954			−0.934771	−	0.355251i	$-0.884396\pi$
$389$	−282901.			−1.86954			−0.934771	+	0.355251i	$0.884396\pi$
$390$	8724.65	+	12090.0i	0.0573613	+	0.0794873i
$391$		−	198102.i		−	1.29579i
$392$	−10351.6	−	32936.6i	−0.0673651	−	0.214342i
$393$	−98502.0			−0.637764
$394$	−61517.5	+	44393.6i	−0.396284	+	0.285975i
$395$		−	111951.i		−	0.717522i
$396$	31619.9	+	10499.2i	0.201637	+	0.0669524i
$397$	−5600.84			−0.0355363			−0.0177682	−	0.999842i	$-0.505656\pi$
$397$	−5600.84			−0.0355363			−0.0177682	+	0.999842i	$0.505656\pi$
$398$	132212.	+	183211.i	0.834654	+	1.15660i
$399$			31462.7i			0.197629i
$400$	110528.	+	82495.8i	0.690800	+	0.515599i
$401$	187182.			1.16406			0.582031	−	0.813167i	$-0.302258\pi$
$401$	187182.			1.16406			0.582031	+	0.813167i	$0.302258\pi$
$402$	36860.5	−	26600.1i	0.228092	−	0.164600i
$403$			11197.0i			0.0689435i
$404$	−16894.9	+	50881.4i	−0.103512	+	0.311743i
$405$	−27459.7			−0.167412
$406$	−29441.1	−	40797.4i	−0.178608	−	0.247503i
$407$		−	84186.7i		−	0.508223i
$408$	184741.	−	58061.9i	1.10979	−	0.348795i
$409$	−185228.			−1.10728			−0.553642	−	0.832754i	$-0.686763\pi$
$409$	−185228.			−1.10728			−0.553642	+	0.832754i	$0.686763\pi$
$410$	−64164.3	+	46303.6i	−0.381703	+	0.275453i
$411$			78636.3i			0.465521i
$412$	204186.	+	67798.8i	1.20291	+	0.399418i
$413$	−74639.6			−0.437592
$414$	−34269.2	−	47487.8i	−0.199942	−	0.277065i
$415$		−	30634.1i		−	0.177873i
$416$	−58655.2	−	943.059i	−0.338938	−	0.00544945i
$417$	−215595.			−1.23984
$418$	−17525.3	+	12647.0i	−0.100303	+	0.0723826i
$419$			274896.i			1.56581i	0.622139	+	0.782907i	$0.286264\pi$
$419$			274896.i			1.56581i	−0.622139	+	0.782907i	$0.713736\pi$
$420$	−17788.8	+	53573.7i	−0.100844	+	0.303706i
$421$	791.303			0.00446456			0.00223228	−	0.999998i	$-0.499289\pi$
$421$	791.303			0.00446456			0.00223228	+	0.999998i	$0.499289\pi$
$422$	−176811.	−	245012.i	−0.992851	−	1.37582i
$423$			43675.2i			0.244092i
$424$	100044.	+	318318.i	0.556491	+	1.77064i
$425$	232685.			1.28822
$426$	3991.47	−	2880.41i	0.0219945	−	0.0158721i
$427$		−	121459.i		−	0.666152i
$428$	−85868.9	−	28512.3i	−0.468758	−	0.155648i
$429$	26183.4			0.142270
$430$	−26673.5	−	36962.3i	−0.144259	−	0.199904i
$431$			6040.74i			0.0325189i	0.999868	+	0.0162594i	$0.00517577\pi$
$431$			6040.74i			0.0325189i	−0.999868	+	0.0162594i	$0.994824\pi$
$432$	121134.	−	162296.i	0.649083	−	0.869642i
$433$	84459.4			0.450476			0.225238	−	0.974304i	$-0.427684\pi$
$433$	84459.4			0.450476			0.225238	+	0.974304i	$0.427684\pi$
$434$	−34377.7	+	24808.3i	−0.182514	+	0.131710i
$435$			15091.5i			0.0797541i
$436$	−4954.55	+	14921.4i	−0.0260634	+	0.0784938i
$437$	37987.3			0.198919
$438$	34939.1	+	48416.2i	0.182122	+	0.252373i
$439$		−	144855.i		−	0.751633i	−0.926694	−	0.375816i	$-0.877362\pi$
$439$		−	144855.i		−	0.751633i	0.926694	−	0.375816i	$-0.122638\pi$
$440$	−36992.1	+	11626.2i	−0.191075	+	0.0600526i
$441$	−17218.7			−0.0885365
$442$	−80254.9	+	57915.2i	−0.410797	+	0.296448i
$443$		−	238301.i		−	1.21428i	−0.794596	−	0.607139i	$-0.792317\pi$
$443$		−	238301.i		−	1.21428i	0.794596	−	0.607139i	$-0.207683\pi$
$444$	−137279.	−	45582.7i	−0.696367	−	0.231225i
$445$	137432.			0.694015
$446$	145339.	+	201401.i	0.730655	+	1.01249i
$447$			175740.i			0.879540i
$448$	−127062.	−	182175.i	−0.633082	−	0.907682i
$449$	196543.			0.974909			0.487455	−	0.873148i	$-0.337925\pi$
$449$	196543.			0.974909			0.487455	+	0.873148i	$0.337925\pi$
$450$	55777.9	−	40251.7i	0.275447	−	0.198774i
$451$			138961.i			0.683188i
$452$	67417.7	−	203038.i	0.329987	−	0.993805i
$453$	85075.6			0.414580
$454$	39899.3	+	55289.6i	0.193577	+	0.268245i
$455$		−	28850.1i		−	0.139356i
$456$	11133.8	+	35425.3i	0.0535441	+	0.170366i
$457$	316770.			1.51674			0.758372	−	0.651822i	$-0.225995\pi$
$457$	316770.			1.51674			0.758372	+	0.651822i	$0.225995\pi$
$458$	−308437.	+	222581.i	−1.47040	+	1.06110i
$459$		−	341668.i		−	1.62173i
$460$	64683.6	+	21477.8i	0.305688	+	0.101502i
$461$	−254791.			−1.19890			−0.599450	−	0.800412i	$-0.704614\pi$
$461$	−254791.			−1.19890			−0.599450	+	0.800412i	$0.704614\pi$
$462$	58012.5	+	80389.6i	0.271792	+	0.376631i
$463$			222613.i			1.03846i	0.854635	+	0.519229i	$0.173781\pi$
$463$			222613.i			1.03846i	−0.854635	+	0.519229i	$0.826219\pi$
$464$	−47586.2	−	35517.3i	−0.221027	−	0.164970i
$465$	12716.7			0.0588125
$466$	−69997.5	+	50513.1i	−0.322337	+	0.232612i
$467$		−	177875.i		−	0.815606i	−0.913070	−	0.407803i	$-0.866295\pi$
$467$		−	177875.i		−	0.815606i	0.913070	−	0.407803i	$-0.133705\pi$
$468$	−9219.63	+	27766.3i	−0.0420941	+	0.126773i
$469$	−87959.3			−0.399886
$470$	−29745.2	−	41218.8i	−0.134655	−	0.186595i
$471$			32927.5i			0.148428i
$472$	−84040.2	+	26412.9i	−0.377227	+	0.118558i
$473$	−80049.5			−0.357797
$474$	−273930.	+	197679.i	−1.21922	+	0.879840i
$475$			44618.8i			0.197757i
$476$	−355628.	−	118084.i	−1.56957	−	0.521168i
$477$	166411.			0.731384
$478$	164245.	+	227599.i	0.718845	+	0.996126i
$479$			341477.i			1.48830i	0.668012	+	0.744150i	$0.267145\pi$
$479$			341477.i			1.48830i	−0.668012	+	0.744150i	$0.732855\pi$
$480$	−1071.05	+	66616.1i	−0.00464867	+	0.289132i
$481$	73926.5			0.319529
$482$	146818.	−	105950.i	0.631954	−	0.456044i
$483$		−	174250.i		−	0.746928i
$484$	52360.9	−	157692.i	0.223520	−	0.673163i
$485$	98684.9			0.419534
$486$	−101502.	−	140654.i	−0.429735	−	0.595497i
$487$		−	167256.i		−	0.705219i	−0.935771	−	0.352610i	$-0.885294\pi$
$487$		−	167256.i		−	0.705219i	0.935771	−	0.352610i	$-0.114706\pi$
$488$	−42980.9	−	136756.i	−0.180483	−	0.574259i
$489$	−76219.6			−0.318749
$490$	16250.2	−	11726.8i	0.0676811	−	0.0488415i
$491$			34068.5i			0.141316i	0.997501	+	0.0706579i	$0.0225099\pi$
$491$			34068.5i			0.141316i	−0.997501	+	0.0706579i	$0.977490\pi$
$492$	226597.	+	75240.2i	0.936103	+	0.310828i
$493$	−100179.			−0.412176
$494$	−11105.6	−	15389.4i	−0.0455082	−	0.0630620i
$495$			19338.8i			0.0789258i
$496$	−29928.5	+	40098.2i	−0.121652	+	0.162990i
$497$	−9524.75			−0.0385603
$498$	−74957.4	+	54092.4i	−0.302243	+	0.218111i
$499$		−	307058.i		−	1.23316i	−0.787292	−	0.616581i	$-0.788517\pi$
$499$		−	307058.i		−	1.23316i	0.787292	−	0.616581i	$-0.211483\pi$
$500$	−54493.2	+	164114.i	−0.217973	+	0.656457i
$501$	−88553.2			−0.352800
$502$	64239.9	+	89019.1i	0.254916	+	0.353245i
$503$		−	62356.5i		−	0.246460i	−0.992378	−	0.123230i	$-0.960675\pi$
$503$		−	62356.5i		−	0.246460i	0.992378	−	0.123230i	$-0.0393253\pi$
$504$	−105676.	+	33212.9i	−0.416023	+	0.130751i
$505$	−31119.2			−0.122024
$506$	97060.6	−	70042.9i	0.379090	−	0.273567i
$507$		−	177100.i		−	0.688975i
$508$	−338313.	−	112335.i	−1.31096	−	0.435298i
$509$	218212.			0.842253			0.421127	−	0.907002i	$-0.361635\pi$
$509$	218212.			0.842253			0.421127	+	0.907002i	$0.361635\pi$
$510$	65775.7	+	91147.3i	0.252886	+	0.350432i
$511$		−	115534.i		−	0.442455i
$512$	−207532.	−	160156.i	−0.791671	−	0.610947i
$513$	65517.0			0.248954
$514$	−379636.	+	273961.i	−1.43695	+	1.03696i
$515$			124880.i			0.470847i
$516$	−43342.6	+	130533.i	−0.162786	+	0.490252i
$517$	−89267.9			−0.333975
$518$	163793.	+	226972.i	0.610429	+	0.845889i
$519$		−	189648.i		−	0.704067i
$520$	−10209.2	−	32483.7i	−0.0377561	−	0.120132i
$521$	−199683.			−0.735642			−0.367821	−	0.929897i	$-0.619896\pi$
$521$	−199683.			−0.735642			−0.367821	+	0.929897i	$0.619896\pi$
$522$	−24014.4	+	17329.8i	−0.0881312	+	0.0635992i
$523$			431293.i			1.57677i	0.615181	+	0.788386i	$0.289083\pi$
$523$			431293.i			1.57677i	−0.615181	+	0.788386i	$0.710917\pi$
$524$	213499.	+	70891.1i	0.777559	+	0.258184i
$525$	204669.			0.742565
$526$	261930.	+	362964.i	0.946703	+	1.31187i
$527$			84415.1i			0.303948i
$528$	93766.6	+	69985.5i	0.336341	+	0.251038i
$529$	69455.4			0.248196
$530$	−157052.	+	113335.i	−0.559102	+	0.403471i
$531$			43934.7i			0.155818i
$532$	22643.4	−	68194.0i	0.0800054	−	0.240948i
$533$	−122025.			−0.429532
$534$	−242672.	−	336278.i	−0.851015	−	1.17928i
$535$		−	52517.6i		−	0.183483i
$536$	−99037.5	+	31126.3i	−0.344723	+	0.108342i
$537$	−386819.			−1.34140
$538$	325315.	−	234761.i	1.12393	−	0.811075i
$539$		−	35193.3i		−	0.121139i
$540$	111560.	+	37043.0i	0.382580	+	0.127034i
$541$	−12646.4			−0.0432087			−0.0216044	−	0.999767i	$-0.506877\pi$
$541$	−12646.4			−0.0432087			−0.0216044	+	0.999767i	$0.506877\pi$
$542$	199631.	+	276635.i	0.679563	+	0.941691i
$543$			120507.i			0.408709i
$544$	−442205.	−	7109.78i	−1.49426	−	0.0240247i
$545$	−9125.92			−0.0307244
$546$	−70592.2	+	50942.2i	−0.236794	+	0.170881i
$547$		−	130015.i		−	0.434530i	−0.976113	−	0.217265i	$-0.930286\pi$
$547$		−	130015.i		−	0.434530i	0.976113	−	0.217265i	$-0.0697135\pi$
$548$	56594.0	−	170441.i	0.188456	−	0.567562i
$549$	−71493.7			−0.237205
$550$	82270.5	+	114005.i	0.271969	+	0.376875i
$551$		−	19210.0i		−	0.0632738i
$552$	−61662.2	−	196196.i	−0.202368	−	0.643892i
$553$	653671.			2.13751
$554$	−408770.	+	294985.i	−1.33186	+	0.961126i
$555$		−	83960.0i		−	0.272575i
$556$	467294.	+	155162.i	1.51161	+	0.501922i
$557$	−585623.			−1.88759			−0.943794	−	0.330533i	$-0.892772\pi$
$557$	−585623.			−1.88759			−0.943794	+	0.330533i	$0.892772\pi$
$558$	14602.8	+	20235.5i	0.0468995	+	0.0649900i
$559$		−	70293.5i		−	0.224953i
$560$	77113.1	−	103316.i	0.245896	−	0.329452i
$561$	197399.			0.627217
$562$	191059.	−	137876.i	0.604916	−	0.436533i
$563$			419511.i			1.32351i	0.749721	+	0.661754i	$0.230188\pi$
$563$			419511.i			1.32351i	−0.749721	+	0.661754i	$0.769812\pi$
$564$	−48333.9	+	145565.i	−0.151948	+	0.457612i
$565$	124179.			0.389000
$566$	22177.1	+	30731.5i	0.0692265	+	0.0959292i
$567$		−	160334.i		−	0.498723i
$568$	−10724.4	+	3370.54i	−0.0332411	+	0.0104473i
$569$	138356.			0.427340			0.213670	−	0.976906i	$-0.431458\pi$
$569$	138356.			0.427340			0.213670	+	0.976906i	$0.431458\pi$
$570$	−17478.1	+	12612.9i	−0.0537953	+	0.0388210i
$571$		−	185798.i		−	0.569861i	−0.958548	−	0.284931i	$-0.908029\pi$
$571$		−	185798.i		−	0.569861i	0.958548	−	0.284931i	$-0.0919706\pi$
$572$	−56751.6	−	18844.0i	−0.173455	−	0.0575946i
$573$	−351123.			−1.06943
$574$	−270361.	−	374648.i	−0.820579	−	1.13710i
$575$		−	247113.i		−	0.747412i
$576$	−107233.	+	74791.9i	−0.323209	+	0.225429i
$577$	−286148.			−0.859485			−0.429743	−	0.902951i	$-0.641396\pi$
$577$	−286148.			−0.859485			−0.429743	+	0.902951i	$0.641396\pi$
$578$	−334136.	+	241127.i	−1.00016	+	0.721755i
$579$		−	279814.i		−	0.834666i
$580$	10861.2	−	32710.2i	0.0322866	−	0.0972359i
$581$	178869.			0.529886
$582$	−174253.	−	241468.i	−0.514441	−	0.712876i
$583$			340128.i			1.00070i
$584$	−40884.4	−	130086.i	−0.119876	−	0.381420i
$585$	−16981.9			−0.0496220
$586$	362527.	−	261615.i	1.05571	−	0.761845i
$587$		−	476683.i		−	1.38342i	−0.722176	−	0.691709i	$-0.756858\pi$
$587$		−	476683.i		−	1.38342i	0.722176	−	0.691709i	$-0.243142\pi$
$588$	−57387.9	−	19055.3i	−0.165984	−	0.0551140i
$589$	−16187.2			−0.0466595
$590$	−29921.9	−	41463.7i	−0.0859579	−	0.119114i
$591$			132870.i			0.380411i
$592$	264741.	+	197597.i	0.755402	+	0.563816i
$593$	−279771.			−0.795599			−0.397799	−	0.917472i	$-0.630226\pi$
$593$	−279771.			−0.795599			−0.397799	+	0.917472i	$0.630226\pi$
$594$	167401.	−	120804.i	0.474445	−	0.342379i
$595$		−	217503.i		−	0.614371i
$596$	126479.	−	380909.i	0.356061	−	1.07233i
$597$	395713.			1.11028
$598$	61506.5	+	85231.4i	0.171996	+	0.238340i
$599$		−	582238.i		−	1.62273i	−0.584538	−	0.811366i	$-0.698724\pi$
$599$		−	582238.i		−	1.62273i	0.584538	−	0.811366i	$-0.301276\pi$
$600$	230447.	−	72426.8i	0.640130	−	0.201186i
$601$	354668.			0.981913			0.490956	−	0.871184i	$-0.336647\pi$
$601$	354668.			0.981913			0.490956	+	0.871184i	$0.336647\pi$
$602$	215818.	−	155743.i	0.595519	−	0.429751i
$603$			51775.0i			0.142392i
$604$	−184398.	−	61228.3i	−0.505455	−	0.167833i
$605$	96445.0			0.263493
$606$	54948.8	+	76144.2i	0.149628	+	0.207344i
$607$			374690.i			1.01694i	0.861080	+	0.508470i	$0.169789\pi$
$607$			374690.i			1.01694i	−0.861080	+	0.508470i	$0.830211\pi$
$608$	1363.35	−	84795.8i	0.00368807	−	0.229386i
$609$	−88117.4			−0.237589
$610$	67472.7	−	48691.1i	0.181330	−	0.130855i
$611$		−	78388.4i		−	0.209976i
$612$	−69507.3	+	209331.i	−0.185578	+	0.558897i
$613$	−16488.8			−0.0438800			−0.0219400	−	0.999759i	$-0.506984\pi$
$613$	−16488.8			−0.0438800			−0.0219400	+	0.999759i	$0.506984\pi$
$614$	239557.	+	331962.i	0.635437	+	0.880545i
$615$			138587.i			0.366414i
$616$	−67883.9	−	215992.i	−0.178898	−	0.569216i
$617$	−35065.7			−0.0921111			−0.0460555	−	0.998939i	$-0.514665\pi$
$617$	−35065.7			−0.0921111			−0.0460555	+	0.998939i	$0.514665\pi$
$618$	305565.	−	220508.i	0.800067	−	0.577362i
$619$			381682.i			0.996140i	0.867137	+	0.498070i	$0.165958\pi$
$619$			381682.i			0.996140i	−0.867137	+	0.498070i	$0.834042\pi$
$620$	−27563.0	−	9152.14i	−0.0717040	−	0.0238089i
$621$	−362854.			−0.940911
$622$	94947.7	+	131572.i	0.245416	+	0.340081i
$623$			802452.i			2.06749i
$624$	−61456.0	+	82338.9i	−0.157832	+	0.211464i
$625$	236347.			0.605048
$626$	505655.	−	364901.i	1.29034	−	0.931165i
$627$			37852.5i			0.0962852i
$628$	23697.7	−	71369.0i	0.0600878	−	0.180963i
$629$	557336.			1.40869
$630$	−37625.3	−	52138.6i	−0.0947980	−	0.131364i
$631$			522005.i			1.31104i	0.755178	+	0.655520i	$0.227551\pi$
$631$			522005.i			1.31104i	−0.755178	+	0.655520i	$0.772449\pi$
$632$	735999.	−	231316.i	1.84265	−	0.579124i
$633$	−529196.			−1.32072
$634$	34990.5	−	25250.6i	0.0870505	−	0.0628192i
$635$		−	206912.i		−	0.513144i
$636$	554630.	+	184162.i	1.37116	+	0.455287i
$637$	30904.1			0.0761619
$638$	−35420.3	−	49083.0i	−0.0870185	−	0.120584i
$639$			5606.51i			0.0137306i
$640$	50264.6	−	143617.i	0.122716	−	0.350627i
$641$	260928.			0.635045			0.317523	−	0.948251i	$-0.397149\pi$
$641$	260928.			0.635045			0.317523	+	0.948251i	$0.397149\pi$
$642$	−128503.	+	92733.2i	−0.311777	+	0.224991i
$643$			537090.i			1.29905i	0.760341	+	0.649524i	$0.225032\pi$
$643$			537090.i			1.29905i	−0.760341	+	0.649524i	$0.774968\pi$
$644$	−125406.	+	377680.i	−0.302377	+	0.910652i
$645$	−79834.0			−0.191897
$646$	−83726.0	−	116022.i	−0.200630	−	0.278019i
$647$			241047.i			0.575828i	0.957656	+	0.287914i	$0.0929618\pi$
$647$			241047.i			0.575828i	−0.957656	+	0.287914i	$0.907038\pi$
$648$	−56737.7	−	180528.i	−0.135121	−	0.429926i
$649$	−89798.3			−0.213196
$650$	−100110.	+	72243.8i	−0.236948	+	0.170991i
$651$			74251.5i			0.175204i
$652$	165203.	+	54854.7i	0.388618	+	0.129038i
$653$	687386.			1.61203			0.806017	−	0.591892i	$-0.201619\pi$
$653$	687386.			1.61203			0.806017	+	0.591892i	$0.201619\pi$
$654$	16114.1	+	22329.9i	0.0376749	+	0.0522072i
$655$			130576.i			0.304356i
$656$	−436990.	−	326160.i	−1.01546	−	0.757920i
$657$	−68006.4			−0.157550
$658$	240672.	−	173679.i	0.555870	−	0.401139i
$659$		−	532754.i		−	1.22675i	−0.789792	−	0.613375i	$-0.789812\pi$
$659$		−	532754.i		−	1.22675i	0.789792	−	0.613375i	$-0.210188\pi$
$660$	−21401.6	+	64454.1i	−0.0491313	+	0.147966i
$661$	−486735.			−1.11401			−0.557006	−	0.830509i	$-0.688050\pi$
$661$	−486735.			−1.11401			−0.557006	+	0.830509i	$0.688050\pi$
$662$	−104023.	−	144147.i	−0.237363	−	0.328921i
$663$			173341.i			0.394342i
$664$	201397.	−	63296.7i	0.456790	−	0.143564i
$665$	41707.6			0.0943130
$666$	133602.	−	96412.4i	0.301206	−	0.217362i
$667$			106391.i			0.239140i
$668$	191935.	+	63731.1i	0.430133	+	0.142823i
$669$	435001.			0.971936
$670$	−35261.6	−	48863.1i	−0.0785512	−	0.108851i
$671$		−	146126.i		−	0.324551i
$672$	−388963.	−	6253.76i	−0.861331	−	0.0138485i
$673$	−209752.			−0.463102			−0.231551	−	0.972823i	$-0.574380\pi$
$673$	−209752.			−0.463102			−0.231551	+	0.972823i	$0.574380\pi$
$674$	−579626.	+	418282.i	−1.27593	+	0.920766i
$675$		−	426198.i		−	0.935415i
$676$	−127458.	+	383858.i	−0.278916	+	0.839996i
$677$	94093.7			0.205297			0.102649	−	0.994718i	$-0.467268\pi$
$677$	94093.7			0.205297			0.102649	+	0.994718i	$0.467268\pi$
$678$	−219269.	−	303847.i	−0.476999	−	0.660992i
$679$			576209.i			1.24980i
$680$	−76968.1	−	244896.i	−0.166453	−	0.529620i
$681$	119419.			0.257501
$682$	−41359.5	+	29846.7i	−0.0889215	+	0.0641694i
$683$		−	438548.i		−	0.940103i	−0.882639	−	0.470052i	$-0.844235\pi$
$683$		−	438548.i		−	0.940103i	0.882639	−	0.470052i	$-0.155765\pi$
$684$	−40140.7	−	13328.5i	−0.0857971	−	0.0284884i
$685$	104242.			0.222158
$686$	−236282.	−	327424.i	−0.502092	−	0.695763i
$687$			666185.i			1.41150i
$688$	187887.	−	251731.i	0.396935	−	0.531814i
$689$	−298675.			−0.629160
$690$	96799.3	−	69854.3i	0.203317	−	0.146722i
$691$			549329.i			1.15047i	0.817987	+	0.575236i	$0.195090\pi$
$691$			549329.i			1.15047i	−0.817987	+	0.575236i	$0.804910\pi$
$692$	−136488.	+	411055.i	−0.285025	+	0.858395i
$693$	−112917.			−0.235122
$694$	−434958.	−	602735.i	−0.903085	−	1.25143i
$695$			285797.i			0.591682i
$696$	−99215.5	+	31182.3i	−0.204815	+	0.0643709i
$697$	−919956.			−1.89366
$698$	−69771.8	+	50350.2i	−0.143209	+	0.103345i
$699$			151186.i			0.309426i
$700$	−443613.	−	147299.i	−0.905332	−	0.300610i
$701$	−633965.			−1.29012			−0.645058	−	0.764133i	$-0.723167\pi$
$701$	−633965.			−1.29012			−0.645058	+	0.764133i	$0.723167\pi$
$702$	106081.	+	146999.i	0.215260	+	0.298292i
$703$			106873.i			0.216250i
$704$	−152867.	−	219174.i	−0.308439	−	0.442225i
$705$	−89027.6			−0.179121
$706$	459288.	−	331441.i	0.921458	−	0.664962i
$707$		−	181701.i		−	0.363512i
$708$	−48621.1	+	146430.i	−0.0969970	+	0.292121i
$709$	−170276.			−0.338735			−0.169367	−	0.985553i	$-0.554172\pi$
$709$	−170276.			−0.338735			−0.169367	+	0.985553i	$0.554172\pi$
$710$	−3818.34	−	5291.18i	−0.00757456	−	0.0104963i
$711$		−	384767.i		−	0.761130i
$712$	283965.	+	903518.i	0.560151	+	1.78228i
$713$	89649.6			0.176348
$714$	−532198.	+	384056.i	−1.04394	+	0.753353i
$715$		−	34709.3i		−	0.0678944i
$716$	838415.	+	278391.i	1.63543	+	0.543036i
$717$	491585.			0.956226
$718$	−331995.	−	460055.i	−0.643995	−	0.892403i
$719$			67445.2i			0.130465i	0.997870	+	0.0652324i	$0.0207789\pi$
$719$			67445.2i			0.130465i	−0.997870	+	0.0652324i	$0.979221\pi$
$720$	−60814.5	−	45390.7i	−0.117312	−	0.0875592i
$721$	−729162.			−1.40266
$722$	22247.9	−	16055.0i	0.0426791	−	0.0307990i
$723$		−	317109.i		−	0.606641i
$724$	86728.2	−	261195.i	0.165456	−	0.498296i
$725$	−124964.			−0.237743
$726$	−170298.	−	235987.i	−0.323100	−	0.447729i
$727$		−	835867.i		−	1.58150i	−0.612141	−	0.790749i	$-0.709692\pi$
$727$		−	835867.i		−	1.58150i	0.612141	−	0.790749i	$-0.290308\pi$
$728$	189668.	−	59610.6i	0.357876	−	0.112476i
$729$	−543294.			−1.02230
$730$	64181.5	−	46316.0i	0.120438	−	0.0869132i
$731$		−	529947.i		−	0.991739i
$732$	−238281.	−	79119.7i	−0.444700	−	0.147660i
$733$	−846256.			−1.57505			−0.787524	−	0.616284i	$-0.788637\pi$
$733$	−846256.			−1.57505			−0.787524	+	0.616284i	$0.788637\pi$
$734$	322487.	+	446879.i	0.598576	+	0.829465i
$735$		−	35098.5i		−	0.0649702i
$736$	−7550.65	+	469626.i	−0.0139389	+	0.866954i
$737$	−105823.			−0.194826
$738$	−220527.	+	159141.i	−0.404901	+	0.292193i
$739$		−	881595.i		−	1.61428i	−0.590357	−	0.807142i	$-0.701013\pi$
$739$		−	881595.i		−	1.61428i	0.590357	−	0.807142i	$-0.298987\pi$
$740$	−60425.4	+	181980.i	−0.110346	+	0.332323i
$741$	−33239.2			−0.0605361
$742$	−661750.	−	917007.i	−1.20195	−	1.66558i
$743$			462837.i			0.838399i	0.907894	+	0.419199i	$0.137689\pi$
$743$			462837.i			0.838399i	−0.907894	+	0.419199i	$0.862311\pi$
$744$	26275.6	+	83603.3i	0.0474685	+	0.151035i
$745$	232965.			0.419737
$746$	88169.7	−	63626.9i	0.158431	−	0.114331i
$747$		−	105287.i		−	0.188683i
$748$	−427853.	−	142066.i	−0.764701	−	0.253915i
$749$	306644.			0.546601
$750$	177233.	+	245598.i	0.315082	+	0.436618i
$751$			30861.7i			0.0547192i	0.999626	+	0.0273596i	$0.00870992\pi$
$751$			30861.7i			0.0547192i	−0.999626	+	0.0273596i	$0.991290\pi$
$752$	209524.	−	280720.i	0.370508	−	0.496407i
$753$	192270.			0.339096
$754$	43101.1	−	31103.5i	0.0758133	−	0.0547100i
$755$		−	112778.i		−	0.197848i
$756$	−216290.	+	651388.i	−0.378436	+	1.13972i
$757$	181464.			0.316665			0.158332	−	0.987386i	$-0.449388\pi$
$757$	181464.			0.316665			0.158332	+	0.987386i	$0.449388\pi$
$758$	173122.	+	239901.i	0.301311	+	0.417536i
$759$		−	209639.i		−	0.363905i
$760$	46960.5	−	14759.1i	0.0813029	−	0.0255525i
$761$	799903.			1.38124			0.690618	−	0.723220i	$-0.257339\pi$
$761$	799903.			1.38124			0.690618	+	0.723220i	$0.257339\pi$
$762$	−506286.	+	365357.i	−0.871938	+	0.629227i
$763$		−	53285.2i		−	0.0915287i
$764$	761046.	+	252701.i	1.30384	+	0.432932i
$765$	−128027.			−0.218766
$766$	198538.	+	275119.i	0.338365	+	0.468882i
$767$		−	78854.2i		−	0.134040i
$768$	−440165.	+	130602.i	−0.746266	+	0.221425i
$769$	−994747.			−1.68213			−0.841066	−	0.540933i	$-0.818071\pi$
$769$	−994747.			−1.68213			−0.841066	+	0.540933i	$0.818071\pi$
$770$	106566.	−	76902.6i	0.179737	−	0.129706i
$771$			819967.i			1.37939i
$772$	−201380.	+	606486.i	−0.337895	+	1.01762i
$773$	−272744.			−0.456453			−0.228226	−	0.973608i	$-0.573293\pi$
$773$	−272744.			−0.456453			−0.228226	+	0.973608i	$0.573293\pi$
$774$	−91674.4	−	127036.i	−0.153026	−	0.212053i
$775$			105300.i			0.175317i
$776$	203904.	+	648781.i	0.338613	+	1.07739i
$777$	490233.			0.812008
$778$	917621.	−	662193.i	1.51602	−	1.09402i
$779$		−	176408.i		−	0.290698i
$780$	−56598.8	−	18793.3i	−0.0930289	−	0.0308897i
$781$	−11459.2			−0.0187867
$782$	463701.	+	642564.i	0.758271	+	1.05076i
$783$			183493.i			0.299293i
$784$	110672.	+	82603.3i	0.180055	+	0.134390i
$785$	43649.4			0.0708336
$786$	319502.	−	230566.i	0.517164	−	0.373207i
$787$			1.10455e6i			1.78335i	0.452677	+	0.891674i	$0.350469\pi$
$787$			1.10455e6i			1.78335i	−0.452677	+	0.891674i	$0.649531\pi$
$788$	95625.7	−	287991.i	0.154001	−	0.463795i
$789$	783958.			1.25933
$790$	262047.	+	363127.i	0.419880	+	0.581841i
$791$			725064.i			1.15884i
$792$	−127138.	+	39958.1i	−0.202687	+	0.0637023i
$793$	128317.			0.204051
$794$	18167.0	−	13110.0i	0.0288165	−	0.0207952i
$795$			339213.i			0.536707i
$796$	−857692.	−	284792.i	−1.35365	−	0.449470i
$797$	764048.			1.20283			0.601415	−	0.798937i	$-0.294604\pi$
$797$	764048.			1.20283			0.601415	+	0.798937i	$0.294604\pi$
$798$	−73645.4	−	102053.i	−0.115648	−	0.160257i
$799$		−	590975.i		−	0.925711i
$800$	−551610.	−	8868.79i	−0.861890	−	0.0138575i
$801$	472343.			0.736194
$802$	−607146.	+	438142.i	−0.943941	+	0.681187i
$803$		−	138998.i		−	0.215565i
$804$	−57297.7	+	172561.i	−0.0886391	+	0.266950i
$805$	−230990.			−0.356452
$806$	−26209.2	−	36318.8i	−0.0403444	−	0.0559065i
$807$		−	702640.i		−	1.07891i
$808$	−64298.9	−	204586.i	−0.0984875	−	0.313367i
$809$	1.01243e6			1.54692			0.773461	−	0.633844i	$-0.218524\pi$
$809$	1.01243e6			1.54692			0.773461	+	0.633844i	$0.218524\pi$
$810$	89068.6	−	64275.6i	0.135755	−	0.0979662i
$811$		−	1.08114e6i		−	1.64377i	−0.569652	−	0.821886i	$-0.692922\pi$
$811$		−	1.08114e6i		−	1.64377i	0.569652	−	0.821886i	$-0.307078\pi$
$812$	190991.	+	63417.4i	0.289668	+	0.0961826i
$813$	597497.			0.903972
$814$	197058.	+	273069.i	0.297403	+	0.412120i
$815$			101038.i			0.152115i
$816$	−463320.	+	620757.i	−0.695827	+	0.932270i
$817$	101621.			0.152243
$818$	600807.	−	433567.i	0.897900	−	0.647962i
$819$		−	99155.2i		−	0.147825i
$820$	99740.0	−	300382.i	0.148334	−	0.446731i
$821$	1.26350e6			1.87451			0.937254	−	0.348646i	$-0.113359\pi$
$821$	1.26350e6			1.87451			0.937254	+	0.348646i	$0.113359\pi$
$822$	−184066.	−	255066.i	−0.272414	−	0.377492i
$823$		−	628392.i		−	0.927750i	−0.885901	−	0.463875i	$-0.846459\pi$
$823$		−	628392.i		−	0.927750i	0.885901	−	0.463875i	$-0.153541\pi$
$824$	−820998.	+	258030.i	−1.20917	+	0.380028i
$825$	246236.			0.361780
$826$	242102.	−	174711.i	0.354844	−	0.256070i
$827$		−	1.16065e6i		−	1.69704i	−0.529165	−	0.848519i	$-0.677495\pi$
$827$		−	1.16065e6i		−	1.69704i	0.529165	−	0.848519i	$-0.322505\pi$
$828$	222312.	+	73817.4i	0.324266	+	0.107671i
$829$	396401.			0.576801			0.288401	−	0.957510i	$-0.406877\pi$
$829$	396401.			0.576801			0.288401	+	0.957510i	$0.406877\pi$
$830$	71706.0	+	99365.1i	0.104088	+	0.144237i
$831$			882892.i			1.27851i
$832$	192462.	−	134237.i	0.278034	−	0.193921i
$833$	232988.			0.335771
$834$	699306.	−	504648.i	1.00539	−	0.725532i
$835$			117388.i			0.168365i
$836$	27242.2	−	82043.8i	0.0389788	−	0.117391i
$837$	154620.			0.220706
$838$	−643455.	−	891655.i	−0.916284	−	1.26972i
$839$		−	502265.i		−	0.713524i	−0.934195	−	0.356762i	$-0.883881\pi$
$839$		−	502265.i		−	0.713524i	0.934195	−	0.356762i	$-0.116119\pi$
$840$	−67701.1	−	215411.i	−0.0959483	−	0.305287i
$841$	−653480.			−0.923932
$842$	−2566.68	+	1852.22i	−0.00362033	+	0.00261258i
$843$		−	412665.i		−	0.580687i
$844$	1.14701e6	+	380858.i	1.61021	+	0.534661i
$845$	−234768.			−0.328795
$846$	−102232.	−	141665.i	−0.142838	−	0.197935i
$847$			563131.i			0.784951i
$848$	−1.06960e6	−	798326.i	−1.48740	−	1.11017i
$849$	66376.3			0.0920868
$850$	−754739.	+	544651.i	−1.04462	+	0.753842i
$851$		−	591896.i		−	0.817309i
$852$	−6204.54	+	18685.9i	−0.00854732	+	0.0257415i
$853$	−143054.			−0.196608			−0.0983041	−	0.995156i	$-0.531342\pi$
$853$	−143054.			−0.196608			−0.0983041	+	0.995156i	$0.531342\pi$
$854$	284302.	+	393965.i	0.389820	+	0.540185i
$855$		−	24550.1i		−	0.0335831i
$856$	345265.	−	108513.i	0.471199	−	0.148092i
$857$	−650012.			−0.885034			−0.442517	−	0.896760i	$-0.645914\pi$
$857$	−650012.			−0.885034			−0.442517	+	0.896760i	$0.645914\pi$
$858$	−84928.9	+	61288.2i	−0.115367	+	0.0832535i
$859$		−	1.12052e6i		−	1.51856i	−0.650762	−	0.759282i	$-0.725550\pi$
$859$		−	1.12052e6i		−	1.51856i	0.650762	−	0.759282i	$-0.274450\pi$
$860$	173037.	+	57455.9i	0.233960	+	0.0776851i
$861$	−809193.			−1.09156
$862$	−14139.7	−	19593.8i	−0.0190294	−	0.0263697i
$863$			500249.i			0.671684i	0.941918	+	0.335842i	$0.109021\pi$
$863$			500249.i			0.671684i	−0.941918	+	0.335842i	$0.890979\pi$
$864$	−13022.7	+	809968.i	−0.0174451	+	1.08503i
$865$	−251402.			−0.335997
$866$	−273953.	+	197696.i	−0.365293	+	0.263610i
$867$			721694.i			0.960096i
$868$	53438.3	−	160937.i	0.0709272	−	0.213608i
$869$	786427.			1.04140
$870$	−35325.0	−	48950.9i	−0.0466706	−	0.0646728i
$871$		−	92926.0i		−	0.122490i
$872$	−18856.1	−	59996.3i	−0.0247982	−	0.0789026i
$873$	339171.			0.445031
$874$	−123216.	+	88917.8i	−0.161304	+	0.116403i
$875$		−	586063.i		−	0.765471i
$876$	−226658.	−	75260.4i	−0.295367	−	0.0980750i
$877$	157601.			0.204908			0.102454	−	0.994738i	$-0.467331\pi$
$877$	157601.			0.204908			0.102454	+	0.994738i	$0.467331\pi$
$878$	339067.	+	469855.i	0.439841	+	0.609501i
$879$		−	783014.i		−	1.01343i
$880$	92774.2	−	124299.i	0.119801	−	0.160510i
$881$	122993.			0.158463			0.0792313	−	0.996856i	$-0.474753\pi$
$881$	122993.			0.158463			0.0792313	+	0.996856i	$0.474753\pi$
$882$	55850.6	−	40304.1i	0.0717945	−	0.0518099i
$883$			1.22265e6i			1.56813i	0.620681	+	0.784063i	$0.286856\pi$
$883$			1.22265e6i			1.56813i	−0.620681	+	0.784063i	$0.713144\pi$
$884$	124752.	−	375709.i	0.159640	−	0.480781i
$885$	−89556.6			−0.114343
$886$	557796.	+	772955.i	0.710572	+	0.984661i
$887$		−	420137.i		−	0.534003i	−0.963696	−	0.267001i	$-0.913967\pi$
$887$		−	420137.i		−	0.534003i	0.963696	−	0.267001i	$-0.0860329\pi$
$888$	551976.	−	173480.i	0.699994	−	0.220000i
$889$	1.20814e6			1.52867
$890$	−445777.	+	321691.i	−0.562779	+	0.406125i
$891$		−	192897.i		−	0.242979i
$892$	−942847.	−	313067.i	−1.18498	−	0.393466i
$893$	113323.			0.142107
$894$	−411359.	−	570032.i	−0.514690	−	0.713221i
$895$			512776.i			0.640150i
$896$	838562.	+	293489.i	1.04453	+	0.365574i
$897$	184089.			0.228794
$898$	−637508.	+	460052.i	−0.790557	+	0.570498i
$899$		−	45335.4i		−	0.0560942i
$900$	−86703.9	+	261121.i	−0.107042	+	0.322372i
$901$	−2.25173e6			−2.77375
$902$	−325270.	−	450736.i	−0.399789	−	0.553999i
$903$		−	466141.i		−	0.571665i
$904$	256580.	+	816383.i	0.313968	+	0.998981i
$905$	159747.			0.195045
$906$	−275952.	+	199139.i	−0.336184	+	0.242605i
$907$			1.05252e6i			1.27942i	0.768615	+	0.639711i	$0.220946\pi$
$907$			1.05252e6i			1.27942i	−0.768615	+	0.639711i	$0.779054\pi$
$908$	−258835.	−	85944.8i	−0.313944	−	0.104243i
$909$	−106954.			−0.129440
$910$	67530.1	+	93578.5i	0.0815483	+	0.113004i
$911$			177415.i			0.213774i	0.994271	+	0.106887i	$0.0340883\pi$
$911$			177415.i			0.213774i	−0.994271	+	0.106887i	$0.965912\pi$
$912$	−119034.	−	88844.8i	−0.143114	−	0.106817i
$913$	215196.			0.258162
$914$	−1.02748e6	+	741472.i	−1.22993	+	0.887569i
$915$		−	145733.i		−	0.174067i
$916$	479449.	−	1.44393e6i	0.571414	−	1.72090i
$917$	−762420.			−0.906683
$918$	799749.	+	1.10824e6i	0.949005	+	1.31506i
$919$		−	375597.i		−	0.444724i	−0.974964	−	0.222362i	$-0.928623\pi$
$919$		−	375597.i		−	0.444724i	0.974964	−	0.222362i	$-0.0713767\pi$
$920$	−260082.	+	81740.8i	−0.307280	+	0.0965747i
$921$	716997.			0.845275
$922$	826444.	−	596396.i	0.972191	−	0.701573i
$923$		−	10062.6i		−	0.0118115i
$924$	−376340.	−	124961.i	−0.440794	−	0.146363i
$925$	695225.			0.812534
$926$	−521076.	−	722071.i	−0.607686	−	0.842089i
$927$			429203.i			0.499463i
$928$	237487.	+	3818.32i	0.275768	+	0.00443381i
$929$	−488394.			−0.565899			−0.282950	−	0.959135i	$-0.591313\pi$
$929$	−488394.			−0.565899			−0.282950	+	0.959135i	$0.591313\pi$
$930$	−41248.2	+	29766.4i	−0.0476912	+	0.0344160i
$931$			44677.0i			0.0515448i
$932$	108807.	−	327689.i	0.125264	−	0.377251i
$933$	284179.			0.326459
$934$	416355.	+	576956.i	0.477277	+	0.661377i
$935$		−	261676.i		−	0.299323i
$936$	−35088.3	−	111644.i	−0.0400507	−	0.127433i
$937$	−967842.			−1.10236			−0.551182	−	0.834385i	$-0.685823\pi$
$937$	−967842.			−1.10236			−0.551182	+	0.834385i	$0.685823\pi$
$938$	285306.	−	205888.i	0.324269	−	0.234006i
$939$		−	1.09215e6i		−	1.23866i
$940$	192964.	+	64072.5i	0.218384	+	0.0725130i
$941$	−1.25331e6			−1.41540			−0.707702	−	0.706512i	$-0.750268\pi$
$941$	−1.25331e6			−1.41540			−0.707702	+	0.706512i	$0.750268\pi$
$942$	−77074.2	−	106804.i	−0.0868575	−	0.120361i
$943$			977001.i			1.09868i
$944$	210769.	−	282388.i	0.236517	−	0.316885i
$945$	−398390.			−0.446113
$946$	259649.	−	187374.i	0.290138	−	0.209376i
$947$			769128.i			0.857627i	0.903393	+	0.428814i	$0.141068\pi$
$947$			769128.i			0.857627i	−0.903393	+	0.428814i	$0.858932\pi$
$948$	425809.	−	1.28239e6i	0.473804	−	1.42693i
$949$	122058.			0.135530
$950$	−104440.	−	144726.i	−0.115723	−	0.160361i
$951$		−	75575.1i		−	0.0835637i
$952$	1.42992e6	−	449408.i	1.57775	−	0.495868i
$953$	−100319.			−0.110458			−0.0552291	−	0.998474i	$-0.517589\pi$
$953$	−100319.			−0.110458			−0.0552291	+	0.998474i	$0.517589\pi$
$954$	−539773.	+	389522.i	−0.593081	+	0.427992i
$955$			465457.i			0.510355i
$956$	−1.06549e6	−	353790.i	−1.16583	−	0.387106i
$957$	−106013.			−0.115754
$958$	−799304.	−	1.10762e6i	−0.870925	−	1.20687i
$959$			608657.i			0.661813i
$960$	−152456.	−	218584.i	−0.165425	−	0.237179i
$961$	885319.			0.958635
$962$	−239789.	+	173041.i	−0.259107	+	0.186982i
$963$		−	180498.i		−	0.194635i
$964$	−228221.	+	687321.i	−0.245585	+	0.739614i
$965$	−370928.			−0.398322
$966$	407871.	+	565199.i	0.437088	+	0.605686i
$967$			576613.i			0.616640i	0.951283	+	0.308320i	$0.0997668\pi$
$967$			576613.i			0.616640i	−0.951283	+	0.308320i	$0.900233\pi$
$968$	199276.	+	634055.i	0.212669	+	0.676669i
$969$	−250593.			−0.266883
$970$	−320095.	+	230994.i	−0.340201	+	0.245503i
$971$			46726.7i			0.0495594i	0.999693	+	0.0247797i	$0.00788844\pi$
$971$			46726.7i			0.0495594i	−0.999693	+	0.0247797i	$0.992112\pi$
$972$	658464.	+	218639.i	0.696947	+	0.231417i
$973$	−1.66874e6			−1.76263
$974$	391500.	+	542514.i	0.412681	+	0.571864i
$975$			216226.i			0.227457i
$976$	459522.	+	342978.i	0.482399	+	0.360053i
$977$	−322899.			−0.338281			−0.169140	−	0.985592i	$-0.554099\pi$
$977$	−322899.			−0.338281			−0.169140	+	0.985592i	$0.554099\pi$
$978$	247227.	−	178409.i	0.258474	−	0.186526i
$979$			965423.i			1.00729i
$980$	−25260.2	+	76074.7i	−0.0263017	+	0.0792114i
$981$	−31365.0			−0.0325917
$982$	−79745.0	−	110505.i	−0.0826953	−	0.114593i
$983$			509974.i			0.527766i	0.964555	+	0.263883i	$0.0850032\pi$
$983$			509974.i			0.527766i	−0.964555	+	0.263883i	$0.914997\pi$
$984$	−911109.	+	286351.i	−0.940979	+	0.295739i
$985$	176136.			0.181541
$986$	324941.	−	234491.i	0.334234	−	0.241197i
$987$		−	519821.i		−	0.533605i
$988$	72044.7	+	23922.0i	0.0738054	+	0.0245067i
$989$	−562808.			−0.575397
$990$	−45266.8	−	62727.5i	−0.0461859	−	0.0640011i
$991$			1.38788e6i			1.41320i	0.707612	+	0.706602i	$0.249773\pi$
$991$			1.38788e6i			1.41320i	−0.707612	+	0.706602i	$0.750227\pi$
$992$	3217.49	−	200117.i	0.00326959	−	0.203358i
$993$	−311341.			−0.315746
$994$	30894.6	−	22294.8i	0.0312687	−	0.0225648i
$995$		−	524565.i		−	0.529851i
$996$	116517.	−	350909.i	0.117455	−	0.353733i
$997$	−1.04517e6			−1.05147			−0.525734	−	0.850649i	$-0.676209\pi$
$997$	−1.04517e6			−1.05147			−0.525734	+	0.850649i	$0.676209\pi$
$998$	718739.	+	995978.i	0.721622	+	0.999974i
$999$		−	1.02085e6i		−	1.02289i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.5.b.a.39.6	yes	36
4.3	odd	2	inner	76.5.b.a.39.5	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.5.b.a.39.5	✓	36	4.3	odd	2	inner
76.5.b.a.39.6	yes	36	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	76.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.24361 + 2.34072i) q^{2} +7.00580i q^{3} +(5.04202 - 15.1848i) q^{4} +9.28704 q^{5} +(-16.3986 - 22.7241i) q^{6} +54.2259i q^{7} +(19.1890 + 61.0556i) q^{8} +31.9187 q^{9} +O(q^{10})\)	\(q+(-3.24361 + 2.34072i) q^{2} +7.00580i q^{3} +(5.04202 - 15.1848i) q^{4} +9.28704 q^{5} +(-16.3986 - 22.7241i) q^{6} +54.2259i q^{7} +(19.1890 + 61.0556i) q^{8} +31.9187 q^{9} +(-30.1236 + 21.7384i) q^{10} +65.2388i q^{11} +(106.382 + 35.3234i) q^{12} -57.2879 q^{13} +(-126.928 - 175.888i) q^{14} +65.0632i q^{15} +(-205.156 - 153.124i) q^{16} -431.897 q^{17} +(-103.532 + 74.7130i) q^{18} -82.8191i q^{19} +(46.8255 - 141.022i) q^{20} -379.896 q^{21} +(-152.706 - 211.609i) q^{22} +458.678i q^{23} +(-427.743 + 134.435i) q^{24} -538.751 q^{25} +(185.820 - 134.095i) q^{26} +791.086i q^{27} +(823.410 + 273.408i) q^{28} +231.951 q^{29} +(-152.295 - 211.040i) q^{30} -195.452i q^{31} +(1023.87 + 16.4618i) q^{32} -457.050 q^{33} +(1400.90 - 1010.95i) q^{34} +503.599i q^{35} +(160.935 - 484.679i) q^{36} -1290.44 q^{37} +(193.857 + 268.633i) q^{38} -401.348i q^{39} +(178.210 + 567.026i) q^{40} +2130.04 q^{41} +(1232.24 - 889.232i) q^{42} +1227.02i q^{43} +(990.638 + 328.936i) q^{44} +296.431 q^{45} +(-1073.64 - 1487.77i) q^{46} +1368.32i q^{47} +(1072.76 - 1437.28i) q^{48} -539.453 q^{49} +(1747.50 - 1261.07i) q^{50} -3025.78i q^{51} +(-288.847 + 869.905i) q^{52} +5213.59 q^{53} +(-1851.71 - 2565.98i) q^{54} +605.876i q^{55} +(-3310.79 + 1040.54i) q^{56} +580.214 q^{57} +(-752.359 + 542.933i) q^{58} +1376.46i q^{59} +(987.971 + 328.050i) q^{60} -2239.87 q^{61} +(457.500 + 633.971i) q^{62} +1730.82i q^{63} +(-3359.56 + 2343.20i) q^{64} -532.035 q^{65} +(1482.49 - 1069.83i) q^{66} +1622.09i q^{67} +(-2177.63 + 6558.26i) q^{68} -3213.41 q^{69} +(-1178.79 - 1633.48i) q^{70} +175.649i q^{71} +(612.490 + 1948.82i) q^{72} -2130.61 q^{73} +(4185.68 - 3020.56i) q^{74} -3774.38i q^{75} +(-1257.59 - 417.576i) q^{76} -3537.64 q^{77} +(939.444 + 1301.82i) q^{78} -12054.6i q^{79} +(-1905.29 - 1422.07i) q^{80} -2956.78 q^{81} +(-6909.01 + 4985.83i) q^{82} -3298.59i q^{83} +(-1915.45 + 5768.65i) q^{84} -4011.04 q^{85} +(-2872.12 - 3979.98i) q^{86} +1625.00i q^{87} +(-3983.19 + 1251.87i) q^{88} +14798.3 q^{89} +(-961.506 + 693.862i) q^{90} -3106.49i q^{91} +(6964.93 + 2312.67i) q^{92} +1369.30 q^{93} +(-3202.87 - 4438.31i) q^{94} -769.144i q^{95} +(-115.328 + 7173.01i) q^{96} +10626.1 q^{97} +(1749.78 - 1262.71i) q^{98} +2082.34i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 6 q^{2} - 6 q^{4} + 24 q^{5} + 66 q^{6} + 216 q^{8} - 972 q^{9}+O(q^{10}) \) 36 * q + 6 * q^2 - 6 * q^4 + 24 * q^5 + 66 * q^6 + 216 * q^8 - 972 * q^9	\( 36 q + 6 q^{2} - 6 q^{4} + 24 q^{5} + 66 q^{6} + 216 q^{8} - 972 q^{9} + 152 q^{10} + 160 q^{12} + 120 q^{13} - 60 q^{14} - 38 q^{16} - 600 q^{17} + 286 q^{18} - 600 q^{20} + 608 q^{21} + 1080 q^{22} + 958 q^{24} + 4604 q^{25} - 2766 q^{26} - 2250 q^{28} - 168 q^{29} - 1380 q^{30} + 3576 q^{32} + 1440 q^{33} + 908 q^{34} - 5836 q^{36} - 2248 q^{37} - 1716 q^{40} + 1800 q^{41} - 5006 q^{42} - 2520 q^{44} + 88 q^{45} + 6404 q^{46} + 1064 q^{48} - 12188 q^{49} + 3354 q^{50} + 15492 q^{52} - 6600 q^{53} + 1654 q^{54} + 12924 q^{56} + 5450 q^{58} - 11188 q^{60} + 2200 q^{61} - 9972 q^{62} + 12570 q^{64} - 15792 q^{65} + 10500 q^{66} - 22614 q^{68} + 19904 q^{69} + 900 q^{70} - 11376 q^{72} + 11560 q^{73} + 17304 q^{74} + 1680 q^{77} - 24740 q^{78} + 12900 q^{80} + 13604 q^{81} - 18420 q^{82} + 5644 q^{84} - 11552 q^{85} + 24564 q^{86} - 15304 q^{88} + 13800 q^{89} - 60212 q^{90} - 2142 q^{92} + 34592 q^{93} - 23096 q^{94} - 35770 q^{96} + 8200 q^{97} + 25566 q^{98}+O(q^{100}) \) 36 * q + 6 * q^2 - 6 * q^4 + 24 * q^5 + 66 * q^6 + 216 * q^8 - 972 * q^9 + 152 * q^10 + 160 * q^12 + 120 * q^13 - 60 * q^14 - 38 * q^16 - 600 * q^17 + 286 * q^18 - 600 * q^20 + 608 * q^21 + 1080 * q^22 + 958 * q^24 + 4604 * q^25 - 2766 * q^26 - 2250 * q^28 - 168 * q^29 - 1380 * q^30 + 3576 * q^32 + 1440 * q^33 + 908 * q^34 - 5836 * q^36 - 2248 * q^37 - 1716 * q^40 + 1800 * q^41 - 5006 * q^42 - 2520 * q^44 + 88 * q^45 + 6404 * q^46 + 1064 * q^48 - 12188 * q^49 + 3354 * q^50 + 15492 * q^52 - 6600 * q^53 + 1654 * q^54 + 12924 * q^56 + 5450 * q^58 - 11188 * q^60 + 2200 * q^61 - 9972 * q^62 + 12570 * q^64 - 15792 * q^65 + 10500 * q^66 - 22614 * q^68 + 19904 * q^69 + 900 * q^70 - 11376 * q^72 + 11560 * q^73 + 17304 * q^74 + 1680 * q^77 - 24740 * q^78 + 12900 * q^80 + 13604 * q^81 - 18420 * q^82 + 5644 * q^84 - 11552 * q^85 + 24564 * q^86 - 15304 * q^88 + 13800 * q^89 - 60212 * q^90 - 2142 * q^92 + 34592 * q^93 - 23096 * q^94 - 35770 * q^96 + 8200 * q^97 + 25566 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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