LMFDB - Embedded newform 33.8.d.b.32.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [33,8,Mod(32,33)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(33, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1])) N = Newforms(chi, 8, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("33.32"); S:= CuspForms(chi, 8); N := Newforms(S);

Level:	$ N $	$=$	$ 33 = 3 \cdot 11 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	33.d (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$10.3087058410$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			32.7
Character	$\chi$	$=$	33.32
Dual form			33.8.d.b.32.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-10.8692 q^{2} +(-0.0827838 - 46.7653i) q^{3} -9.86124 q^{4} -348.238i q^{5} +(0.899791 + 508.300i) q^{6} -1046.71i q^{7} +1498.44 q^{8} +(-2186.99 + 7.74282i) q^{9} +3785.06i q^{10} +(2415.65 - 3694.83i) q^{11} +(0.816351 + 461.164i) q^{12} +2640.65i q^{13} +11376.8i q^{14} +(-16285.5 + 28.8285i) q^{15} -15024.5 q^{16} -30339.8 q^{17} +(23770.7 - 84.1580i) q^{18} +36863.5i q^{19} +3434.06i q^{20} +(-48949.6 + 86.6504i) q^{21} +(-26256.1 + 40159.8i) q^{22} -47795.0i q^{23} +(-124.046 - 70074.8i) q^{24} -43144.7 q^{25} -28701.6i q^{26} +(543.142 + 102274. i) q^{27} +10321.8i q^{28} +189050. q^{29} +(177009. - 313.341i) q^{30} +269812. q^{31} -28495.9 q^{32} +(-172990. - 112663. i) q^{33} +329768. q^{34} -364503. q^{35} +(21566.4 - 76.3538i) q^{36} -90561.6 q^{37} -400675. i q^{38} +(123491. - 218.603i) q^{39} -521813. i q^{40} -478887. q^{41} +(532041. - 941.818i) q^{42} -167164. i q^{43} +(-23821.3 + 36435.7i) q^{44} +(2696.34 + 761592. i) q^{45} +519492. i q^{46} -150168. i q^{47} +(1243.79 + 702626. i) q^{48} -272053. q^{49} +468947. q^{50} +(2511.64 + 1.41885e6i) q^{51} -26040.1i q^{52} +8104.59i q^{53} +(-5903.50 - 1.11164e6i) q^{54} +(-1.28668e6 - 841222. i) q^{55} -1.56842e6i q^{56} +(1.72393e6 - 3051.70i) q^{57} -2.05481e6 q^{58} -1.25309e6i q^{59} +(160595. - 284.285i) q^{60} +2.29402e6i q^{61} -2.93263e6 q^{62} +(8104.47 + 2.28913e6i) q^{63} +2.23287e6 q^{64} +919574. q^{65} +(1.88026e6 + 1.22455e6i) q^{66} -3.88969e6 q^{67} +299188. q^{68} +(-2.23515e6 + 3956.65i) q^{69} +3.96185e6 q^{70} +605145. i q^{71} +(-3.27706e6 + 11602.1i) q^{72} -6.02139e6i q^{73} +984329. q^{74} +(3571.68 + 2.01767e6i) q^{75} -363520. i q^{76} +(-3.86741e6 - 2.52848e6i) q^{77} +(-1.34224e6 + 2376.03i) q^{78} +1.99704e6i q^{79} +5.23211e6i q^{80} +(4.78285e6 - 33866.9i) q^{81} +5.20510e6 q^{82} +2.68553e6 q^{83} +(482704. - 854.481i) q^{84} +1.05655e7i q^{85} +1.81693e6i q^{86} +(-15650.2 - 8.84096e6i) q^{87} +(3.61970e6 - 5.53647e6i) q^{88} -3.70801e6i q^{89} +(-29307.0 - 8.27787e6i) q^{90} +2.76398e6 q^{91} +471318. i q^{92} +(-22336.0 - 1.26178e7i) q^{93} +1.63220e6i q^{94} +1.28373e7 q^{95} +(2359.00 + 1.33262e6i) q^{96} -4.64760e6 q^{97} +2.95699e6 q^{98} +(-5.25439e6 + 8.09925e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 120 q^{3} + 1788 q^{4} - 5940 q^{9} - 6936 q^{12} + 23160 q^{15} + 5844 q^{16} - 17556 q^{22} - 34704 q^{25} + 7560 q^{27} + 131328 q^{31} + 28644 q^{33} - 436080 q^{34} - 302832 q^{36} + 1072488 q^{37}+ \cdots + 53650080 q^{99}+O(q^{100}) $ 24 * q + 120 * q^3 + 1788 * q^4 - 5940 * q^9 - 6936 * q^12 + 23160 * q^15 + 5844 * q^16 - 17556 * q^22 - 34704 * q^25 + 7560 * q^27 + 131328 * q^31 + 28644 * q^33 - 436080 * q^34 - 302832 * q^36 + 1072488 * q^37 - 100296 * q^42 - 1854252 * q^45 + 3172548 * q^48 - 1169304 * q^49 - 4401936 * q^55 - 2920440 * q^58 + 1981452 * q^60 + 14578596 * q^64 + 2895156 * q^66 + 7729200 * q^67 - 4614108 * q^69 - 6924504 * q^70 - 4375800 * q^75 - 26237448 * q^78 + 22367340 * q^81 - 23600232 * q^82 - 25179660 * q^88 + 9380640 * q^91 + 25396908 * q^93 + 72948360 * q^97 + 53650080 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/33\mathbb{Z}\right)^\times$.

$n$	$13$	$23$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−10.8692			−0.960708			−0.480354	−	0.877075i	$-0.659492\pi$
$2$	−10.8692			−0.960708			−0.480354	+	0.877075i	$0.659492\pi$
$3$	−0.0827838	−	46.7653i	−0.00177019	−	0.999998i
$3$	−0.0827838	−	46.7653i	−0.00177019	−	0.999998i
$4$	−9.86124			−0.0770410
$5$		−	348.238i		−	1.24589i	−0.782264	−	0.622947i	$-0.785935\pi$
$5$		−	348.238i		−	1.24589i	0.782264	−	0.622947i	$-0.214065\pi$
$6$	0.899791	+	508.300i	0.00170064	+	0.960706i
$7$		−	1046.71i		−	1.15341i	−0.816954	−	0.576703i	$-0.804339\pi$
$7$		−	1046.71i		−	1.15341i	0.816954	−	0.576703i	$-0.195661\pi$
$8$	1498.44			1.03472
$9$	−2186.99	+	7.74282i	−0.999994	+	0.00354038i
$10$			3785.06i			1.19694i
$11$	2415.65	−	3694.83i	0.547217	−	0.836990i
$11$	2415.65	−	3694.83i	0.547217	−	0.836990i
$12$	0.816351	+	461.164i	0.000136377	+	0.0770408i
$13$			2640.65i			0.333356i	0.986011	+	0.166678i	$0.0533041\pi$
$13$			2640.65i			0.333356i	−0.986011	+	0.166678i	$0.946696\pi$
$14$			11376.8i			1.10809i
$15$	−16285.5	+	28.8285i	−1.24589	+	0.00220547i
$16$	−15024.5			−0.917024
$17$	−30339.8			−1.49776			−0.748879	−	0.662707i	$-0.769407\pi$
$17$	−30339.8			−1.49776			−0.748879	+	0.662707i	$0.769407\pi$
$18$	23770.7	−	84.1580i	0.960702	−	0.00340127i
$19$			36863.5i			1.23299i	0.787360	+	0.616494i	$0.211447\pi$
$19$			36863.5i			1.23299i	−0.787360	+	0.616494i	$0.788553\pi$
$20$			3434.06i			0.0959849i
$21$	−48949.6	+	86.6504i	−1.15340	+	0.00204175i
$22$	−26256.1	+	40159.8i	−0.525716	+	0.804103i
$23$		−	47795.0i		−	0.819097i	−0.912288	−	0.409548i	$-0.865686\pi$
$23$		−	47795.0i		−	0.819097i	0.912288	−	0.409548i	$-0.134314\pi$
$24$	−124.046	−	70074.8i	−0.00183166	−	1.03472i
$25$	−43144.7			−0.552252
$26$		−	28701.6i		−	0.320258i
$27$	543.142	+	102274.i	0.00531056	+	0.999986i
$28$			10321.8i			0.0888595i
$29$	189050.			1.43940			0.719702	−	0.694283i	$-0.244278\pi$
$29$	189050.			1.43940			0.719702	+	0.694283i	$0.244278\pi$
$30$	177009.	−	313.341i	1.19694	−	0.00211882i
$31$	269812.			1.62665			0.813326	−	0.581808i	$-0.197654\pi$
$31$	269812.			1.62665			0.813326	+	0.581808i	$0.197654\pi$
$32$	−28495.9			−0.153730
$33$	−172990.	−	112663.i	−0.837958	−	0.545735i
$34$	329768.			1.43891
$35$	−364503.			−1.43702
$36$	21566.4	−	76.3538i	0.0770405	−	0.000272755i
$37$	−90561.6			−0.293926			−0.146963	−	0.989142i	$-0.546950\pi$
$37$	−90561.6			−0.293926			−0.146963	+	0.989142i	$0.546950\pi$
$38$		−	400675.i		−	1.18454i
$39$	123491.	−	218.603i	0.333356	−	0.000590106i
$40$		−	521813.i		−	1.28915i
$41$	−478887.			−1.08515			−0.542575	−	0.840007i	$-0.682551\pi$
$41$	−478887.			−1.08515			−0.542575	+	0.840007i	$0.682551\pi$
$42$	532041.	−	941.818i	1.10808	−	0.00196153i
$43$		−	167164.i		−	0.320629i	−0.987066	−	0.160314i	$-0.948749\pi$
$43$		−	167164.i		−	0.320629i	0.987066	−	0.160314i	$-0.0512508\pi$
$44$	−23821.3	+	36435.7i	−0.0421582	+	0.0644826i
$45$	2696.34	+	761592.i	0.00441094	+	1.24589i
$46$			519492.i			0.786912i
$47$		−	150168.i		−	0.210977i	−0.994421	−	0.105488i	$-0.966359\pi$
$47$		−	150168.i		−	0.210977i	0.994421	−	0.105488i	$-0.0336406\pi$
$48$	1243.79	+	702626.i	0.00162331	+	0.917022i
$49$	−272053.			−0.330345
$50$	468947.			0.530553
$51$	2511.64	+	1.41885e6i	0.00265132	+	1.49775i
$52$		−	26040.1i		−	0.0256821i
$53$			8104.59i			0.00747766i	0.999993	+	0.00373883i	$0.00119011\pi$
$53$			8104.59i			0.00747766i	−0.999993	+	0.00373883i	$0.998810\pi$
$54$	−5903.50	−	1.11164e6i	−0.00510190	−	0.960694i
$55$	−1.28668e6	−	841222.i	−1.04280	−	0.681775i
$56$		−	1.56842e6i		−	1.19345i
$57$	1.72393e6	−	3051.70i	1.23299	−	0.00218263i
$58$	−2.05481e6			−1.38285
$59$		−	1.25309e6i		−	0.794330i	−0.917747	−	0.397165i	$-0.869994\pi$
$59$		−	1.25309e6i		−	0.794330i	0.917747	−	0.397165i	$-0.130006\pi$
$60$	160595.	−	284.285i	0.0959847	−	0.000169912i
$61$			2.29402e6i			1.29403i	0.762478	+	0.647014i	$0.223982\pi$
$61$			2.29402e6i			1.29403i	−0.762478	+	0.647014i	$0.776018\pi$
$62$	−2.93263e6			−1.56274
$63$	8104.47	+	2.28913e6i	0.00408350	+	1.15340i
$64$	2.23287e6			1.06471
$65$	919574.			0.415327
$66$	1.88026e6	+	1.22455e6i	0.805032	+	0.524292i
$67$	−3.88969e6			−1.57999			−0.789993	−	0.613115i	$-0.789916\pi$
$67$	−3.88969e6			−1.57999			−0.789993	+	0.613115i	$0.789916\pi$
$68$	299188.			0.115389
$69$	−2.23515e6	+	3956.65i	−0.819095	+	0.00144996i
$70$	3.96185e6			1.38056
$71$			605145.i			0.200657i	0.994954	+	0.100329i	$0.0319894\pi$
$71$			605145.i			0.200657i	−0.994954	+	0.100329i	$0.968011\pi$
$72$	−3.27706e6	+	11602.1i	−1.03471	+	0.00366331i
$73$		−	6.02139e6i		−	1.81162i	−0.423687	−	0.905809i	$-0.639264\pi$
$73$		−	6.02139e6i		−	1.81162i	0.423687	−	0.905809i	$-0.360736\pi$
$74$	984329.			0.282377
$75$	3571.68	+	2.01767e6i	0.000977594	+	0.552251i
$76$		−	363520.i		−	0.0949905i
$77$	−3.86741e6	−	2.52848e6i	−0.965390	−	0.631164i
$78$	−1.34224e6	+	2376.03i	−0.320257	+	0.000566919i
$79$			1.99704e6i			0.455713i	0.973695	+	0.227857i	$0.0731718\pi$
$79$			1.99704e6i			0.455713i	−0.973695	+	0.227857i	$0.926828\pi$
$80$			5.23211e6i			1.14251i
$81$	4.78285e6	−	33866.9i	0.999975	−	0.00708072i
$82$	5.20510e6			1.04251
$83$	2.68553e6			0.515533			0.257767	−	0.966207i	$-0.417013\pi$
$83$	2.68553e6			0.515533			0.257767	+	0.966207i	$0.417013\pi$
$84$	482704.	−	854.481i	0.0888594	−	0.000157299i
$85$			1.05655e7i			1.86605i
$86$			1.81693e6i			0.308031i
$87$	−15650.2	−	8.84096e6i	−0.00254803	−	1.43940i
$88$	3.61970e6	−	5.53647e6i	0.566218	−	0.866052i
$89$		−	3.70801e6i		−	0.557540i	−0.960358	−	0.278770i	$-0.910073\pi$
$89$		−	3.70801e6i		−	0.557540i	0.960358	−	0.278770i	$-0.0899267\pi$
$90$	−29307.0	−	8.27787e6i	−0.00423763	−	1.19693i
$91$	2.76398e6			0.384495
$92$			471318.i			0.0631040i
$93$	−22336.0	−	1.26178e7i	−0.00287949	−	1.62665i
$94$			1.63220e6i			0.202687i
$95$	1.28373e7			1.53617
$96$	2359.00	+	1.33262e6i	0.000272132	+	0.153730i
$97$	−4.64760e6			−0.517044			−0.258522	−	0.966005i	$-0.583235\pi$
$97$	−4.64760e6			−0.517044			−0.258522	+	0.966005i	$0.583235\pi$
$98$	2.95699e6			0.317365
$99$	−5.25439e6	+	8.09925e6i	−0.544251	+	0.838923i
$100$	425460.			0.0425460
$101$	−1.34603e7			−1.29996			−0.649979	−	0.759953i	$-0.725222\pi$
$101$	−1.34603e7			−1.29996			−0.649979	+	0.759953i	$0.725222\pi$
$102$	−27299.5	−	1.54217e7i	−0.00254714	−	1.43890i
$103$	−94229.8			−0.00849685			−0.00424842	−	0.999991i	$-0.501352\pi$
$103$	−94229.8			−0.00849685			−0.00424842	+	0.999991i	$0.501352\pi$
$104$			3.95684e6i			0.344931i
$105$	30175.0	+	1.70461e7i	0.00254381	+	1.43702i
$106$		−	88090.1i		−	0.00718384i
$107$	1.29347e6			0.102074			0.0510369	−	0.998697i	$-0.483747\pi$
$107$	1.29347e6			0.102074			0.0510369	+	0.998697i	$0.483747\pi$
$108$	−5356.06	−	1.00855e6i	−0.000409131	−	0.0770399i
$109$		−	1.26898e7i		−	0.938563i	−0.883049	−	0.469281i	$-0.844513\pi$
$109$		−	1.26898e7i		−	0.938563i	0.883049	−	0.469281i	$-0.155487\pi$
$110$	1.39852e7	+	9.14338e6i	1.00183	+	0.654986i
$111$	7497.04	+	4.23514e6i	0.000520306	+	0.293926i
$112$			1.57263e7i			1.05770i
$113$			1.82126e7i			1.18740i	0.804685	+	0.593702i	$0.202334\pi$
$113$			1.82126e7i			1.18740i	−0.804685	+	0.593702i	$0.797666\pi$
$114$	−1.87377e7	+	33169.4i	−1.18454	+	0.00209687i
$115$	−1.66440e7			−1.02051
$116$	−1.86426e6			−0.110893
$117$	−20446.1	−	5.77506e6i	−0.00118021	−	0.333354i
$118$			1.36201e7i			0.763119i
$119$			3.17569e7i			1.72752i
$120$	−2.44027e7	+	43197.6i	−1.28915	+	0.00228205i
$121$	−7.81642e6	−	1.78509e7i	−0.401106	−	0.916032i
$122$		−	2.49341e7i		−	1.24318i
$123$	39644.1	+	2.23953e7i	0.00192093	+	1.08515i
$124$	−2.66068e6			−0.125319
$125$		−	1.21815e7i		−	0.557847i
$126$	−88088.8	−	2.48810e7i	−0.00392305	−	1.10808i
$127$		−	1.91701e6i		−	0.0830444i	−0.999138	−	0.0415222i	$-0.986779\pi$
$127$		−	1.91701e6i		−	0.0830444i	0.999138	−	0.0415222i	$-0.0132207\pi$
$128$	−2.06219e7			−0.869148
$129$	−7.81746e6	+	13838.5i	−0.320628	+	0.000567575i
$130$	−9.99500e6			−0.399007
$131$	−2.35503e6			−0.0915264			−0.0457632	−	0.998952i	$-0.514572\pi$
$131$	−2.35503e6			−0.0915264			−0.0457632	+	0.998952i	$0.514572\pi$
$132$	1.70590e6	+	1.11100e6i	0.0645571	+	0.0420440i
$133$	3.85853e7			1.42213
$134$	4.22777e7			1.51791
$135$	3.56158e7	−	189143.i	1.24588	−	0.00661640i
$136$	−4.54623e7			−1.54976
$137$		−	3.66251e7i		−	1.21690i	−0.793591	−	0.608452i	$-0.791791\pi$
$137$		−	3.66251e7i		−	1.21690i	0.793591	−	0.608452i	$-0.208209\pi$
$138$	2.42942e7	−	43005.5i	0.786911	−	0.00139299i
$139$			1.41470e7i			0.446800i	0.974727	+	0.223400i	$0.0717157\pi$
$139$			1.41470e7i			0.446800i	−0.974727	+	0.223400i	$0.928284\pi$
$140$	3.59446e6			0.110710
$141$	−7.02264e6	+	12431.5i	−0.210976	+	0.000373470i
$142$		−	6.57742e6i		−	0.192773i
$143$	9.75675e6	+	6.37888e6i	0.279016	+	0.182418i
$144$	3.28584e7	−	116332.i	0.917018	−	0.00324662i
$145$		−	6.58343e7i		−	1.79335i
$146$			6.54474e7i			1.74043i
$147$	22521.6	+	1.27227e7i	0.000584775	+	0.330344i
$148$	893050.			0.0226444
$149$	−2.01010e7			−0.497811			−0.248906	−	0.968528i	$-0.580071\pi$
$149$	−2.01010e7			−0.497811			−0.248906	+	0.968528i	$0.580071\pi$
$150$	−38821.2	−	2.19304e7i	−0.000939181	−	0.530552i
$151$		−	8.52532e6i		−	0.201507i	−0.994911	−	0.100754i	$-0.967875\pi$
$151$		−	8.52532e6i		−	0.201507i	0.994911	−	0.100754i	$-0.0321254\pi$
$152$			5.52376e7i			1.27580i
$153$	6.63527e7	−	234916.i	1.49775	−	0.00530263i
$154$	4.20355e7	+	2.74825e7i	0.927457	+	0.606364i
$155$		−	9.39587e7i		−	2.02664i
$156$	−1.21777e6	+	2155.70i	−0.0256821	+	4.54623e-5i
$157$	8.15598e7			1.68201			0.841003	−	0.541031i	$-0.181966\pi$
$157$	8.15598e7			1.68201			0.841003	+	0.541031i	$0.181966\pi$
$158$		−	2.17062e7i		−	0.437807i
$159$	379014.	−	670.929i	0.00747765	−	1.32369e-5i
$160$			9.92337e6i			0.191531i
$161$	−5.00274e7			−0.944751
$162$	−5.19856e7	+	368105.i	−0.960683	+	0.00680250i
$163$	−2.43347e7			−0.440119			−0.220059	−	0.975487i	$-0.570625\pi$
$163$	−2.43347e7			−0.440119			−0.220059	+	0.975487i	$0.570625\pi$
$164$	4.72242e6			0.0836010
$165$	−3.92335e7	+	6.02417e7i	−0.679928	+	1.04401i
$166$	−2.91895e7			−0.495277
$167$	−7.75661e7			−1.28874			−0.644369	−	0.764715i	$-0.722880\pi$
$167$	−7.75661e7			−1.28874			−0.644369	+	0.764715i	$0.722880\pi$
$168$	−7.33478e7	+	129840.i	−1.19345	+	0.00211265i
$169$	5.57755e7			0.888874
$170$		−	1.14838e8i		−	1.79273i
$171$	−285427.	−	8.06199e7i	−0.00436525	−	1.23298i
$172$			1.64844e6i			0.0247016i
$173$	8.86937e7			1.30236			0.651181	−	0.758923i	$-0.274274\pi$
$173$	8.86937e7			1.30236			0.651181	+	0.758923i	$0.274274\pi$
$174$	170105.	+	9.60939e7i	0.00244791	+	1.38284i
$175$			4.51599e7i			0.636971i
$176$	−3.62940e7	+	5.55131e7i	−0.501811	+	0.767540i
$177$	−5.86012e7	+	103736.i	−0.794328	+	0.00140612i
$178$			4.03030e7i			0.535633i
$179$		−	4.73183e7i		−	0.616657i	−0.951280	−	0.308329i	$-0.900230\pi$
$179$		−	4.73183e7i		−	0.616657i	0.951280	−	0.308329i	$-0.0997696\pi$
$180$	−26589.3	−	7.51024e6i	−0.000339823	−	0.0959843i
$181$	3.16949e7			0.397296			0.198648	−	0.980071i	$-0.436345\pi$
$181$	3.16949e7			0.397296			0.198648	+	0.980071i	$0.436345\pi$
$182$	−3.00422e7			−0.369387
$183$	1.07281e8	−	189908.i	1.29403	−	0.00229068i
$184$		−	7.16178e7i		−	0.847537i
$185$			3.15370e7i			0.366201i
$186$	242774.	+	1.37145e8i	0.00276635	+	1.56274i
$187$	−7.32904e7	+	1.12100e8i	−0.819599	+	1.25361i
$188$			1.48084e6i			0.0162538i
$189$	1.07051e8	−	568511.i	1.15339	−	0.00612523i
$190$	−1.39530e8			−1.47581
$191$		−	1.31366e7i		−	0.136417i	−0.997671	−	0.0682084i	$-0.978272\pi$
$191$		−	1.31366e7i		−	0.136417i	0.997671	−	0.0682084i	$-0.0217283\pi$
$192$	−184845.	−	1.04421e8i	−0.00188475	−	1.06471i
$193$			6.48665e6i			0.0649486i	0.999473	+	0.0324743i	$0.0103387\pi$
$193$			6.48665e6i			0.0649486i	−0.999473	+	0.0324743i	$0.989661\pi$
$194$	5.05155e7			0.496728
$195$	−76125.8	−	4.30041e7i	−0.000735209	−	0.415326i
$196$	2.68278e6			0.0254501
$197$	−4.70505e7			−0.438463			−0.219231	−	0.975673i	$-0.570355\pi$
$197$	−4.70505e7			−0.438463			−0.219231	+	0.975673i	$0.570355\pi$
$198$	5.71108e7	−	8.80321e7i	0.522866	−	0.805959i
$199$	−1.84450e8			−1.65917			−0.829587	−	0.558377i	$-0.811424\pi$
$199$	−1.84450e8			−1.65917			−0.829587	+	0.558377i	$0.811424\pi$
$200$	−6.46496e7			−0.571427
$201$	322004.	+	1.81903e8i	0.00279688	+	1.57998i
$202$	1.46302e8			1.24888
$203$		−	1.97880e8i		−	1.66022i
$204$	−24767.9	−	1.39916e7i	−0.000204260	−	0.115388i
$205$			1.66767e8i			1.35198i
$206$	1.02420e6			0.00816299
$207$	370068.	+	1.04527e8i	0.00289992	+	0.819091i
$208$		−	3.96745e7i		−	0.305696i
$209$	1.36204e8	+	8.90493e7i	1.03200	+	0.674712i
$210$	−327977.	−	1.85277e8i	−0.00244386	−	1.38056i
$211$			2.44770e7i			0.179378i	0.995970	+	0.0896890i	$0.0285873\pi$
$211$			2.44770e7i			0.179378i	−0.995970	+	0.0896890i	$0.971413\pi$
$212$		−	79921.3i		−	0.000576086i
$213$	2.82998e7	−	50096.2i	0.200657	−	0.000355203i
$214$	−1.40590e7			−0.0980631
$215$	−5.82128e7			−0.399470
$216$	813864.	+	1.53252e8i	0.00549495	+	1.03471i
$217$		−	2.82414e8i		−	1.87619i
$218$			1.37928e8i			0.901684i
$219$	−2.81592e8	+	498473.i	−1.81161	+	0.00320691i
$220$	1.26883e7	+	8.29549e6i	0.0803384	+	0.0525246i
$221$		−	8.01167e7i		−	0.499287i
$222$	−81486.5	−	4.60325e7i	−0.000499862	−	0.282377i
$223$	1.66161e6			0.0100337			0.00501686	−	0.999987i	$-0.498403\pi$
$223$	1.66161e6			0.0100337			0.00501686	+	0.999987i	$0.498403\pi$
$224$			2.98269e7i			0.177313i
$225$	9.43568e7	−	334062.i	0.552249	−	0.00195518i
$226$		−	1.97956e8i		−	1.14075i
$227$	−1.54743e8			−0.878054			−0.439027	−	0.898474i	$-0.644677\pi$
$227$	−1.54743e8			−0.878054			−0.439027	+	0.898474i	$0.644677\pi$
$228$	−1.70001e7	+	30093.5i	−0.0949904	+	0.000168152i
$229$	1.90996e8			1.05099			0.525497	−	0.850796i	$-0.323880\pi$
$229$	1.90996e8			1.05099			0.525497	+	0.850796i	$0.323880\pi$
$230$	1.80907e8			0.980409
$231$	−1.17925e8	+	1.81070e8i	−0.629454	+	0.966505i
$232$	2.83279e8			1.48938
$233$	−1.30980e8			−0.678359			−0.339179	−	0.940722i	$-0.610149\pi$
$233$	−1.30980e8			−0.678359			−0.339179	+	0.940722i	$0.610149\pi$
$234$	222232.	+	6.27701e7i	0.00113384	+	0.320256i
$235$	−5.22941e7			−0.262854
$236$			1.23570e7i			0.0611959i
$237$	9.33921e7	−	165323.i	0.455713	−	0.000806701i
$238$		−	3.45171e8i		−	1.65964i
$239$	−7.59556e7			−0.359888			−0.179944	−	0.983677i	$-0.557592\pi$
$239$	−7.59556e7			−0.359888			−0.179944	+	0.983677i	$0.557592\pi$
$240$	2.44681e8	−	433134.i	1.14251	−	0.00202247i
$241$			1.64421e8i			0.756655i	0.925672	+	0.378327i	$0.123501\pi$
$241$			1.64421e8i			0.756655i	−0.925672	+	0.378327i	$0.876499\pi$
$242$	8.49580e7	+	1.94024e8i	0.385346	+	0.880039i
$243$	−1.97974e6	−	2.23669e8i	−0.00885086	−	0.999961i
$244$		−	2.26219e7i		−	0.0996932i
$245$			9.47393e7i			0.411575i
$246$	−430898.	−	2.43418e8i	−0.00184545	−	1.04251i
$247$	−9.73434e7			−0.411024
$248$	4.04296e8			1.68313
$249$	−222318.	−	1.25590e8i	−0.000912594	−	0.515532i
$250$			1.32402e8i			0.535927i
$251$			3.01031e8i			1.20158i	0.799407	+	0.600791i	$0.205147\pi$
$251$			3.01031e8i			1.20158i	−0.799407	+	0.600791i	$0.794853\pi$
$252$	−79920.1	−	2.25737e7i	−0.000314597	−	0.0888589i
$253$	−1.76595e8	−	1.15456e8i	−0.685576	−	0.448224i
$254$			2.08362e7i			0.0797814i
$255$	4.94097e8	−	874650.i	1.86604	−	0.00330327i
$256$	−6.16639e7			−0.229716
$257$		−	4.99179e7i		−	0.183438i	−0.995785	−	0.0917192i	$-0.970764\pi$
$257$		−	4.99179e7i		−	0.183438i	0.995785	−	0.0917192i	$-0.0292362\pi$
$258$	8.49693e7	−	150412.i	0.308030	−	0.000545274i
$259$			9.47915e7i			0.339016i
$260$	−9.06814e6			−0.0319972
$261$	−4.13449e8	+	1.46378e6i	−1.43940	+	0.00509604i
$262$	2.55972e7			0.0879301
$263$	3.52864e8			1.19609			0.598043	−	0.801464i	$-0.295945\pi$
$263$	3.52864e8			1.19609			0.598043	+	0.801464i	$0.295945\pi$
$264$	−2.59215e8	−	1.68818e8i	−0.867053	−	0.564684i
$265$	2.82233e6			0.00931637
$266$	−4.19390e8			−1.36626
$267$	−1.73406e8	+	306963.i	−0.557539	+	0.000986955i
$268$	3.83572e7			0.121724
$269$		−	5.56088e8i		−	1.74185i	−0.491416	−	0.870925i	$-0.663520\pi$
$269$		−	5.56088e8i		−	1.74185i	0.491416	−	0.870925i	$-0.336480\pi$
$270$	−3.87114e8	+	2.05582e6i	−1.19692	+	0.00635642i
$271$			4.26918e8i			1.30302i	0.758638	+	0.651512i	$0.225865\pi$
$271$			4.26918e8i			1.30302i	−0.758638	+	0.651512i	$0.774135\pi$
$272$	4.55841e8			1.37348
$273$	−228813.	−	1.29259e8i	−0.000680631	−	0.384494i
$274$			3.98084e8i			1.16909i
$275$	−1.04223e8	+	1.59412e8i	−0.302202	+	0.462230i
$276$	2.20413e7	−	39017.5i	0.0631039	−	0.000111706i
$277$		−	2.91367e8i		−	0.823685i	−0.911255	−	0.411842i	$-0.864885\pi$
$277$		−	2.91367e8i		−	0.823685i	0.911255	−	0.411842i	$-0.135115\pi$
$278$		−	1.53766e8i		−	0.429244i
$279$	−5.90075e8	+	2.08910e6i	−1.62664	+	0.00575897i
$280$	−5.46185e8			−1.48692
$281$	−1.38541e8			−0.372483			−0.186241	−	0.982504i	$-0.559631\pi$
$281$	−1.38541e8			−0.372483			−0.186241	+	0.982504i	$0.559631\pi$
$282$	7.63302e7	−	135120.i	0.202686	−	0.000358795i
$283$			6.73305e8i			1.76587i	0.469493	+	0.882936i	$0.344437\pi$
$283$			6.73305e8i			1.76587i	−0.469493	+	0.882936i	$0.655563\pi$
$284$		−	5.96748e6i		−	0.0154588i
$285$	−1.06272e6	−	6.00338e8i	−0.00271932	−	1.53617i
$286$	−1.06048e8	−	6.93332e7i	−0.268053	−	0.175251i
$287$			5.01255e8i			1.25162i
$288$	6.23202e7	−	220639.i	0.153729	−	0.000544262i
$289$	5.10164e8			1.24328
$290$			7.15564e8i			1.72288i
$291$	384746.	+	2.17346e8i	0.000915269	+	0.517043i
$292$			5.93783e7i			0.139569i
$293$	−4.54303e8			−1.05514			−0.527569	−	0.849512i	$-0.676896\pi$
$293$	−4.54303e8			−1.05514			−0.527569	+	0.849512i	$0.676896\pi$
$294$	−244791.	−	1.38285e8i	−0.000561797	−	0.317364i
$295$	−4.36374e8			−0.989651
$296$	−1.35701e8			−0.304132
$297$	3.79199e8	+	2.45053e8i	0.839885	+	0.542765i
$298$	2.18481e8			0.478251
$299$	1.26210e8			0.273051
$300$	−35221.2	−	1.98968e7i	−7.53147e−5	−	0.0425460i
$301$	−1.74972e8			−0.369815
$302$			9.26631e7i			0.193590i
$303$	1.11429e6	+	6.29474e8i	0.00230118	+	1.29995i
$304$		−	5.53856e8i		−	1.13068i
$305$	7.98866e8			1.61222
$306$	−7.21199e8	+	2.55334e6i	−1.43890	+	0.00509428i
$307$		−	7.72881e8i		−	1.52450i	−0.647281	−	0.762252i	$-0.724094\pi$
$307$		−	7.72881e8i		−	1.52450i	0.647281	−	0.762252i	$-0.275906\pi$
$308$	3.81375e7	+	2.49340e7i	0.0743745	+	0.0486255i
$309$	7800.70	+	4.40668e6i	1.50411e−5	+	0.00849684i
$310$			1.02125e9i			1.94701i
$311$		−	6.00287e7i		−	0.113161i	−0.998398	−	0.0565806i	$-0.981980\pi$
$311$		−	6.00287e7i		−	0.113161i	0.998398	−	0.0565806i	$-0.0180198\pi$
$312$	1.85043e8	−	327563.i	0.344930	−	0.000610595i
$313$	8.72612e8			1.60848			0.804240	−	0.594304i	$-0.202572\pi$
$313$	8.72612e8			1.60848			0.804240	+	0.594304i	$0.202572\pi$
$314$	−8.86487e8			−1.61592
$315$	7.97164e8	−	2.82228e6i	1.43701	−	0.00508761i
$316$		−	1.96933e7i		−	0.0351086i
$317$		−	5.10125e8i		−	0.899434i	−0.893171	−	0.449717i	$-0.851525\pi$
$317$		−	5.10125e8i		−	0.899434i	0.893171	−	0.449717i	$-0.148475\pi$
$318$	−4.11956e6	+	7292.44i	−0.00718383	+	1.27168e-5i
$319$	4.56678e8	−	6.98507e8i	0.787667	−	1.20477i
$320$		−	7.77568e8i		−	1.32652i
$321$	−107079.	−	6.04897e7i	−0.000180691	−	0.102074i
$322$	5.43756e8			0.907629
$323$		−	1.11843e9i		−	1.84672i
$324$	−4.71648e7	+	333970.i	−0.0770390	+	0.000545506i
$325$		−	1.13930e8i		−	0.184097i
$326$	2.64498e8			0.422825
$327$	−5.93444e8	+	1.05051e6i	−0.938561	+	0.00166144i
$328$	−7.17582e8			−1.12283
$329$	−1.57182e8			−0.243342
$330$	4.26435e8	−	6.54777e8i	0.653212	−	1.00299i
$331$	−5.05329e8			−0.765907			−0.382953	−	0.923768i	$-0.625093\pi$
$331$	−5.05329e8			−0.765907			−0.382953	+	0.923768i	$0.625093\pi$
$332$	−2.64827e7			−0.0397172
$333$	1.98057e8	−	701202.i	0.293924	−	0.00104061i
$334$	8.43079e8			1.23810
$335$			1.35454e9i			1.96850i
$336$	7.35444e8	−	1.30188e6i	1.05770	−	0.00187234i
$337$		−	1.44876e8i		−	0.206201i	−0.994671	−	0.103101i	$-0.967124\pi$
$337$		−	1.44876e8i		−	0.206201i	0.994671	−	0.103101i	$-0.0328764\pi$
$338$	−6.06233e8			−0.853948
$339$	8.51720e8	−	1.50771e6i	1.18740	−	0.00210194i
$340$		−	1.04189e8i		−	0.143762i
$341$	6.51771e8	−	9.96909e8i	0.890133	−	1.36149i
$342$	3.10235e6	+	8.76271e8i	0.00419373	+	1.18453i
$343$		−	5.77248e8i		−	0.772384i
$344$		−	2.50484e8i		−	0.331762i
$345$	1.37786e6	+	7.78363e8i	0.00180650	+	1.02051i
$346$	−9.64027e8			−1.25119
$347$	6.59572e8			0.847440			0.423720	−	0.905793i	$-0.360724\pi$
$347$	6.59572e8			0.847440			0.423720	+	0.905793i	$0.360724\pi$
$348$	154331.	+	8.71829e7i	0.000196302	+	0.110893i
$349$			3.52913e8i			0.444405i	0.975001	+	0.222202i	$0.0713245\pi$
$349$			3.52913e8i			0.444405i	−0.975001	+	0.222202i	$0.928675\pi$
$350$		−	4.90850e8i		−	0.611943i
$351$	−2.70071e8	+	1.43425e6i	−0.333352	+	0.00177031i
$352$	−6.88363e7	+	1.05288e8i	−0.0841236	+	0.128670i
$353$			8.35795e8i			1.01132i	0.862733	+	0.505660i	$0.168751\pi$
$353$			8.35795e8i			1.01132i	−0.862733	+	0.505660i	$0.831249\pi$
$354$	6.36946e8	−	1.12752e6i	0.763117	−	0.00135087i
$355$	2.10734e8			0.249998
$356$			3.65656e7i			0.0429534i
$357$	1.48512e9	−	2.62896e6i	1.72752	−	0.00305805i
$358$			5.14311e8i			0.592427i
$359$	−7.94097e8			−0.905823			−0.452911	−	0.891556i	$-0.649615\pi$
$359$	−7.94097e8			−0.905823			−0.452911	+	0.891556i	$0.649615\pi$
$360$	4.04030e6	+	1.14120e9i	0.00456410	+	1.28915i
$361$	−4.65043e8			−0.520257
$362$	−3.44497e8			−0.381685
$363$	−8.34154e8	+	3.67015e8i	−0.915320	+	0.402727i
$364$	−2.72563e7			−0.0296219
$365$	−2.09688e9			−2.25708
$366$	−1.16605e9	+	2.06414e6i	−1.24318	+	0.00220067i
$367$	2.54522e8			0.268778			0.134389	−	0.990929i	$-0.457093\pi$
$367$	2.54522e8			0.268778			0.134389	+	0.990929i	$0.457093\pi$
$368$			7.18097e8i			0.751131i
$369$	1.04732e9	−	3.70794e6i	1.08514	−	0.00384185i
$370$		−	3.42781e8i		−	0.351812i
$371$	8.48313e6			0.00862477
$372$	220261.	+	1.24427e8i	0.000221839	+	0.125319i
$373$		−	1.78663e9i		−	1.78260i	−0.453418	−	0.891298i	$-0.649796\pi$
$373$		−	1.78663e9i		−	1.78260i	0.453418	−	0.891298i	$-0.350204\pi$
$374$	7.96605e8	−	1.21844e9i	0.787395	−	1.20435i
$375$	−5.69670e8	+	1.00843e6i	−0.557846	+	0.000987497i
$376$		−	2.25017e8i		−	0.218302i
$377$			4.99213e8i			0.479835i
$378$	−1.16356e9	+	6.17924e6i	−1.10807	+	0.00588456i
$379$	−1.31813e9			−1.24371			−0.621856	−	0.783131i	$-0.713621\pi$
$379$	−1.31813e9			−1.24371			−0.621856	+	0.783131i	$0.713621\pi$
$380$	−1.26591e8			−0.118348
$381$	−8.96493e7	+	158697.i	−0.0830443	+	0.000147005i
$382$			1.42784e8i			0.131057i
$383$		−	1.97076e9i		−	1.79241i	−0.443637	−	0.896206i	$-0.646312\pi$
$383$		−	1.97076e9i		−	1.79241i	0.443637	−	0.896206i	$-0.353688\pi$
$384$	1.70716e6	+	9.64389e8i	0.00153856	+	0.869147i
$385$	−8.80513e8	+	1.34678e9i	−0.786363	+	1.20277i
$386$		−	7.05045e7i		−	0.0623966i
$387$	1.29432e6	+	3.65585e8i	0.00113515	+	0.320627i
$388$	4.58311e7			0.0398336
$389$			7.80717e8i			0.672466i	0.941779	+	0.336233i	$0.109153\pi$
$389$			7.80717e8i			0.672466i	−0.941779	+	0.336233i	$0.890847\pi$
$390$	827424.	+	4.67419e8i	0.000706321	+	0.399007i
$391$			1.45009e9i			1.22681i
$392$	−4.07655e8			−0.341815
$393$	194958.	+	1.10134e8i	0.000162019	+	0.0915262i
$394$	5.11400e8			0.421234
$395$	6.95445e8			0.567771
$396$	5.18148e7	−	7.98687e7i	0.0419296	−	0.0646314i
$397$	9.83480e8			0.788858			0.394429	−	0.918926i	$-0.370942\pi$
$397$	9.83480e8			0.788858			0.394429	+	0.918926i	$0.370942\pi$
$398$	2.00481e9			1.59398
$399$	−3.19423e6	−	1.80445e9i	−0.00251745	−	1.42213i
$400$	6.48228e8			0.506428
$401$			1.07636e9i			0.833592i	0.909000	+	0.416796i	$0.136847\pi$
$401$			1.07636e9i			0.833592i	−0.909000	+	0.416796i	$0.863153\pi$
$402$	−3.49991e6	−	1.97713e9i	−0.00268699	−	1.51790i
$403$			7.12478e8i			0.542255i
$404$	1.32735e8			0.100150
$405$	−1.17937e7	−	1.66557e9i	−0.00882183	−	1.24586i
$406$			2.15079e9i			1.59498i
$407$	−2.18765e8	+	3.34610e8i	−0.160842	+	0.246013i
$408$	3.76354e6	+	2.12606e9i	0.00274338	+	1.54976i
$409$		−	5.15625e8i		−	0.372651i	−0.982488	−	0.186326i	$-0.940342\pi$
$409$		−	5.15625e8i		−	0.372651i	0.982488	−	0.186326i	$-0.0596579\pi$
$410$		−	1.81261e9i		−	1.29886i
$411$	−1.71278e9	+	3.03196e6i	−1.21690	+	0.00215416i
$412$	929223.			0.000654605
$413$	−1.31162e9			−0.916184
$414$	−4.02233e6	−	1.13612e9i	−0.00278597	−	0.786907i
$415$		−	9.35204e8i		−	0.642300i
$416$		−	7.52477e7i		−	0.0512468i
$417$	6.61590e8	−	1.17114e6i	0.446800	−	0.000790923i
$418$	−1.48043e9	−	9.67891e8i	−0.991449	−	0.648201i
$419$			1.11146e9i			0.738153i	0.929399	+	0.369076i	$0.120326\pi$
$419$			1.11146e9i			0.738153i	−0.929399	+	0.369076i	$0.879674\pi$
$420$	−297563.	−	1.68096e8i	−0.000195977	−	0.110709i
$421$	−1.11875e9			−0.730711			−0.365356	−	0.930868i	$-0.619053\pi$
$421$	−1.11875e9			−0.730711			−0.365356	+	0.930868i	$0.619053\pi$
$422$		−	2.66044e8i		−	0.172330i
$423$	1.16272e6	+	3.28415e8i	0.000746938	+	0.210975i
$424$			1.21442e7i			0.00773729i
$425$	1.30900e9			0.827139
$426$	−3.07595e8	+	544504.i	−0.192773	+	0.000341246i
$427$	2.40117e9			1.49254
$428$	−1.27553e7			−0.00786387
$429$	2.97503e8	−	4.56806e8i	0.181924	−	0.279339i
$430$	6.32724e8			0.383773
$431$	1.25877e9			0.757311			0.378656	−	0.925538i	$-0.376386\pi$
$431$	1.25877e9			0.757311			0.378656	+	0.925538i	$0.376386\pi$
$432$	−8.16045e6	−	1.53662e9i	−0.00486991	−	0.917011i
$433$	2.01330e9			1.19179			0.595897	−	0.803061i	$-0.296797\pi$
$433$	2.01330e9			1.19179			0.595897	+	0.803061i	$0.296797\pi$
$434$			3.06960e9i			1.80247i
$435$	−3.07876e9	+	5.45001e6i	−1.79334	+	0.00317457i
$436$			1.25138e8i			0.0723078i
$437$	1.76189e9			1.00994
$438$	3.06067e9	−	5.41799e6i	1.74043	−	0.00308091i
$439$			2.14252e8i			0.120865i	0.998172	+	0.0604324i	$0.0192480\pi$
$439$			2.14252e8i			0.120865i	−0.998172	+	0.0604324i	$0.980752\pi$
$440$	−1.92801e9	−	1.26052e9i	−1.07901	−	0.705447i
$441$	5.94977e8	−	2.10646e6i	0.330343	−	0.00116955i
$442$			8.70802e8i			0.479669i
$443$			2.96139e9i			1.61839i	0.587542	+	0.809193i	$0.300096\pi$
$443$			2.96139e9i			1.61839i	−0.587542	+	0.809193i	$0.699904\pi$
$444$	−73930.1	−	4.17638e7i	−4.00849e−5	−	0.0226443i
$445$	−1.29127e9			−0.694636
$446$	−1.80603e7			−0.00963946
$447$	1.66403e6	+	9.40027e8i	0.000881223	+	0.497811i
$448$		−	2.33716e9i		−	1.22805i
$449$			8.63951e8i			0.450430i	0.974309	+	0.225215i	$0.0723084\pi$
$449$			8.63951e8i			0.450430i	−0.974309	+	0.225215i	$0.927692\pi$
$450$	−1.02558e9	+	3.63097e6i	−0.530549	+	0.00187836i
$451$	−1.15682e9	+	1.76941e9i	−0.593813	+	0.908260i
$452$		−	1.79599e8i		−	0.0914787i
$453$	−3.98689e8	+	705758.i	−0.201507	+	0.000356707i
$454$	1.68193e9			0.843553
$455$		−	9.62525e8i		−	0.479040i
$456$	2.58320e9	−	4.57278e6i	1.27580	−	0.00225841i
$457$		−	3.24917e9i		−	1.59245i	−0.605002	−	0.796224i	$-0.706828\pi$
$457$		−	3.24917e9i		−	1.59245i	0.605002	−	0.796224i	$-0.293172\pi$
$458$	−2.07597e9			−1.00970
$459$	−1.64788e7	−	3.10298e9i	−0.00795393	−	1.49774i
$460$	1.64131e8			0.0786209
$461$	1.26720e9			0.602410			0.301205	−	0.953559i	$-0.402611\pi$
$461$	1.26720e9			0.602410			0.301205	+	0.953559i	$0.402611\pi$
$462$	1.28175e9	−	1.96808e9i	0.604721	−	0.928529i
$463$	8.55808e6			0.00400722			0.00200361	−	0.999998i	$-0.499362\pi$
$463$	8.55808e6			0.00400722			0.00200361	+	0.999998i	$0.499362\pi$
$464$	−2.84038e9			−1.31997
$465$	−4.39401e9	+	7.77826e6i	−2.02663	+	0.00358754i
$466$	1.42364e9			0.651704
$467$			1.19556e8i			0.0543204i	0.999631	+	0.0271602i	$0.00864643\pi$
$467$			1.19556e8i			0.0543204i	−0.999631	+	0.0271602i	$0.991354\pi$
$468$	201624.	+	5.69493e7i	9.09245e−5	+	0.0256819i
$469$			4.07137e9i			1.82237i
$470$	5.68393e8			0.252526
$471$	−6.75183e6	−	3.81417e9i	−0.00297748	−	1.68200i
$472$		−	1.87768e9i		−	0.821910i
$473$	−6.17642e8	−	4.03810e8i	−0.268363	−	0.175454i
$474$	−1.01509e9	+	1.79692e6i	−0.437807	+	0.000775004i
$475$		−	1.59046e9i		−	0.680920i
$476$		−	3.13162e8i		−	0.133090i
$477$	−62752.4	−	1.77246e7i	−2.64738e−5	−	0.00747761i
$478$	8.25574e8			0.345747
$479$	3.84497e9			1.59852			0.799262	−	0.600983i	$-0.205224\pi$
$479$	3.84497e9			1.59852			0.799262	+	0.600983i	$0.205224\pi$
$480$	4.64069e8	−	821494.i	0.191531	−	0.000339047i
$481$		−	2.39141e8i		−	0.0979821i
$482$		−	1.78712e9i		−	0.726924i
$483$	4.14146e6	+	2.33955e9i	0.00167239	+	0.944749i
$484$	7.70796e7	+	1.76032e8i	0.0309016	+	0.0705720i
$485$			1.61847e9i			0.644182i
$486$	2.15181e7	+	2.43109e9i	0.00850309	+	0.960670i
$487$	2.47960e9			0.972815			0.486408	−	0.873732i	$-0.338307\pi$
$487$	2.47960e9			0.972815			0.486408	+	0.873732i	$0.338307\pi$
$488$			3.43745e9i			1.33896i
$489$	2.01452e6	+	1.13802e9i	0.000779095	+	0.440118i
$490$		−	1.02974e9i		−	0.395403i
$491$	4.35884e9			1.66183			0.830914	−	0.556401i	$-0.187818\pi$
$491$	4.35884e9			1.66183			0.830914	+	0.556401i	$0.187818\pi$
$492$	−390940.	−	2.20846e8i	−0.000147990	−	0.0836009i
$493$	−5.73573e9			−2.15588
$494$	1.05804e9			0.394874
$495$	2.82047e9	+	1.82978e9i	1.04521	+	0.678079i
$496$	−4.05379e9			−1.49168
$497$	6.33410e8			0.231439
$498$	2.41642e6	+	1.36505e9i	0.000876736	+	0.495276i
$499$	3.11108e9			1.12088			0.560440	−	0.828195i	$-0.310632\pi$
$499$	3.11108e9			1.12088			0.560440	+	0.828195i	$0.310632\pi$
$500$			1.20124e8i			0.0429770i
$501$	6.42122e6	+	3.62740e9i	0.00228132	+	1.28874i
$502$		−	3.27195e9i		−	1.15437i
$503$	−3.88319e9			−1.36051			−0.680254	−	0.732977i	$-0.738130\pi$
$503$	−3.88319e9			−1.36051			−0.680254	+	0.732977i	$0.738130\pi$
$504$	1.21440e7	+	3.43012e9i	0.00422528	+	1.19345i
$505$			4.68738e9i			1.61961i
$506$	1.91944e9	+	1.25491e9i	0.658638	+	0.430612i
$507$	−4.61731e6	−	2.60836e9i	−0.00157348	−	0.888872i
$508$			1.89041e7i			0.00639782i
$509$		−	2.37980e9i		−	0.799885i	−0.916540	−	0.399942i	$-0.869030\pi$
$509$		−	2.37980e9i		−	0.799885i	0.916540	−	0.399942i	$-0.130970\pi$
$510$	−5.37042e9	+	9.50671e6i	−1.79272	+	0.00317347i
$511$	−6.30263e9			−2.08953
$512$	3.30984e9			1.08984
$513$	−3.77019e9	+	2.00221e7i	−1.23297	+	0.00654785i
$514$			5.42566e8i			0.176231i
$515$			3.28144e7i			0.0105862i
$516$	7.70899e7	−	136464.i	0.0247015	−	4.37266e-5i
$517$	−5.54845e8	−	3.62753e8i	−0.176585	−	0.115450i
$518$		−	1.03030e9i		−	0.325695i
$519$	−7.34240e6	−	4.14779e9i	−0.00230543	−	1.30236i
$520$	1.37792e9			0.429747
$521$		−	3.31948e9i		−	1.02834i	−0.857687	−	0.514172i	$-0.828099\pi$
$521$		−	3.31948e9i		−	1.02834i	0.857687	−	0.514172i	$-0.171901\pi$
$522$	4.49385e9	−	1.59100e7i	1.38284	−	0.00489581i
$523$		−	3.26086e9i		−	0.996728i	−0.866968	−	0.498364i	$-0.833934\pi$
$523$		−	3.26086e9i		−	0.996728i	0.866968	−	0.498364i	$-0.166066\pi$
$524$	2.32235e7			0.00705128
$525$	2.11191e9	−	3.73851e6i	0.636970	−	0.00112756i
$526$	−3.83534e9			−1.14909
$527$	−8.18603e9			−2.43633
$528$	2.59909e9	+	1.69270e9i	0.768427	+	0.500452i
$529$	1.12046e9			0.329081
$530$	−3.06763e7			−0.00895031
$531$	9.70246e6	+	2.74049e9i	0.00281223	+	0.794325i
$532$	−3.80499e8			−0.109563
$533$		−	1.26457e9i		−	0.361742i
$534$	1.88478e9	−	3.33644e6i	0.535632	−	0.000948175i
$535$		−	4.50437e8i		−	0.127173i
$536$	−5.82846e9			−1.63485
$537$	−2.21286e9	+	3.91719e6i	−0.616656	+	0.00109160i
$538$			6.04422e9i			1.67341i
$539$	−6.57186e8	+	1.00519e9i	−0.180771	+	0.276496i
$540$	−3.51216e8	+	1.86518e6i	−0.0959835	+	0.000509734i
$541$			2.72552e9i			0.740046i	0.929023	+	0.370023i	$0.120650\pi$
$541$			2.72552e9i			0.740046i	−0.929023	+	0.370023i	$0.879350\pi$
$542$		−	4.64025e9i		−	1.25183i
$543$	−2.62382e6	−	1.48222e9i	−0.000703291	−	0.397295i
$544$	8.64561e8			0.230250
$545$	−4.41908e9			−1.16935
$546$	2.48701e6	+	1.40493e9i	0.000653887	+	0.369387i
$547$			2.17750e9i			0.568856i	0.958697	+	0.284428i	$0.0918036\pi$
$547$			2.17750e9i			0.568856i	−0.958697	+	0.284428i	$0.908196\pi$
$548$			3.61169e8i			0.0937515i
$549$	−1.77622e7	−	5.01700e9i	−0.00458135	−	1.29402i
$550$	1.13281e9	−	1.73268e9i	0.290328	−	0.444068i
$551$			6.96902e9i			1.77477i
$552$	−3.34923e9	+	5.92879e6i	−0.847535	+	0.00150030i
$553$	2.09032e9			0.525622
$554$			3.16691e9i			0.791320i
$555$	1.47484e9	−	2.61075e6i	0.366200	−	0.000648247i
$556$		−	1.39507e8i		−	0.0344219i
$557$	−1.97313e9			−0.483796			−0.241898	−	0.970302i	$-0.577770\pi$
$557$	−1.97313e9			−0.483796			−0.241898	+	0.970302i	$0.577770\pi$
$558$	6.41362e9	−	2.27068e7i	1.56273	−	0.00553269i
$559$	4.41421e8			0.106884
$560$	5.47649e9			1.31778
$561$	5.24848e9	+	3.41817e9i	1.25506	+	0.817378i
$562$	1.50582e9			0.357847
$563$	7.12172e9			1.68192			0.840960	−	0.541098i	$-0.181991\pi$
$563$	7.12172e9			1.68192			0.840960	+	0.541098i	$0.181991\pi$
$564$	6.92520e7	−	122590.i	0.0162538	−	2.87725e-5i
$565$	6.34233e9			1.47938
$566$		−	7.31826e9i		−	1.69649i
$567$	−3.54487e7	−	5.00624e9i	−0.00816695	−	1.15338i
$568$			9.06771e8i			0.207625i
$569$	1.11338e9			0.253367			0.126684	−	0.991943i	$-0.459567\pi$
$569$	1.11338e9			0.253367			0.126684	+	0.991943i	$0.459567\pi$
$570$	1.15508e7	+	6.52517e9i	0.00261247	+	1.47581i
$571$		−	7.76269e9i		−	1.74496i	−0.488648	−	0.872481i	$-0.662510\pi$
$571$		−	7.76269e9i		−	1.74496i	0.488648	−	0.872481i	$-0.337490\pi$
$572$	−9.62137e7	−	6.29037e7i	−0.0214957	−	0.0140537i
$573$	−6.14339e8	+	1.08750e6i	−0.136416	+	0.000241484i
$574$		−	5.44822e9i		−	1.20244i
$575$			2.06210e9i			0.452348i
$576$	−4.88325e9	+	1.72887e7i	−1.06471	+	0.00376949i
$577$	−1.81821e8			−0.0394029			−0.0197014	−	0.999806i	$-0.506272\pi$
$577$	−1.81821e8			−0.0394029			−0.0197014	+	0.999806i	$0.506272\pi$
$578$	−5.54506e9			−1.19442
$579$	3.03350e8	−	536990.i	0.0649485	−	0.000114972i
$580$			6.49208e8i			0.138161i
$581$		−	2.81096e9i		−	0.594619i
$582$	−4.18187e6	−	2.36237e9i	−0.000879305	−	0.496727i
$583$	2.99451e7	+	1.95779e7i	0.00625873	+	0.00409190i
$584$		−	9.02266e9i		−	1.87452i
$585$	−2.01110e9	+	7.12009e6i	−0.415324	+	0.00147042i
$586$	4.93790e9			1.01368
$587$		−	1.01363e9i		−	0.206846i	−0.994637	−	0.103423i	$-0.967020\pi$
$587$		−	1.01363e9i		−	0.206846i	0.994637	−	0.103423i	$-0.0329796\pi$
$588$	−222091.	−	1.25461e8i	−4.50516e−5	−	0.0254500i
$589$			9.94619e9i			2.00564i
$590$	4.74302e9			0.950765
$591$	3.89502e6	+	2.20033e9i	0.000776164	+	0.438462i
$592$	1.36064e9			0.269537
$593$	2.01779e9			0.397361			0.198681	−	0.980064i	$-0.436334\pi$
$593$	2.01779e9			0.397361			0.198681	+	0.980064i	$0.436334\pi$
$594$	−4.12158e9	−	2.66352e9i	−0.806884	−	0.521438i
$595$	1.10590e10			2.15231
$596$	1.98220e8			0.0383519
$597$	1.52694e7	+	8.62584e9i	0.00293706	+	1.65917i
$598$	−1.37179e9			−0.262322
$599$		−	7.03119e9i		−	1.33670i	−0.743845	−	0.668352i	$-0.767000\pi$
$599$		−	7.03119e9i		−	1.33670i	0.743845	−	0.668352i	$-0.233000\pi$
$600$	5.35194e6	+	3.02336e9i	0.00101154	+	0.571426i
$601$		−	7.33153e9i		−	1.37763i	−0.724935	−	0.688817i	$-0.758130\pi$
$601$		−	7.33153e9i		−	1.37763i	0.724935	−	0.688817i	$-0.241870\pi$
$602$	1.90179e9			0.355284
$603$	8.50671e9	−	3.01172e7i	1.57998	−	0.00559376i
$604$			8.40702e7i			0.0155243i
$605$	−6.21635e9	+	2.72198e9i	−1.14128	+	0.499736i
$606$	−1.21114e7	−	6.84185e9i	−0.00221076	−	1.24888i
$607$			8.71379e9i			1.58142i	0.612193	+	0.790709i	$0.290288\pi$
$607$			8.71379e9i			1.58142i	−0.612193	+	0.790709i	$0.709712\pi$
$608$		−	1.05046e9i		−	0.189547i
$609$	−9.25390e9	+	1.63812e7i	−1.66021	+	0.00293891i
$610$	−8.68301e9			−1.54887
$611$	3.96540e8			0.0703304
$612$	−6.54320e8	+	2.31656e6i	−0.115388	+	0.000408520i
$613$		−	6.11858e9i		−	1.07285i	−0.843948	−	0.536425i	$-0.819774\pi$
$613$		−	6.11858e9i		−	1.07285i	0.843948	−	0.536425i	$-0.180226\pi$
$614$			8.40057e9i			1.46460i
$615$	7.79890e9	−	1.38056e7i	1.35198	−	0.00239327i
$616$	−5.79507e9	−	3.78877e9i	−0.998909	−	0.653079i
$617$		−	3.41971e9i		−	0.586126i	−0.956093	−	0.293063i	$-0.905325\pi$
$617$		−	3.41971e9i		−	0.586126i	0.956093	−	0.293063i	$-0.0946747\pi$
$618$	−84787.1	−	4.78970e7i	−1.44501e−5	−	0.00816297i
$619$	5.39566e9			0.914381			0.457191	−	0.889369i	$-0.348856\pi$
$619$	5.39566e9			0.914381			0.457191	+	0.889369i	$0.348856\pi$
$620$			9.26549e8i			0.156134i
$621$	4.88821e9	−	2.59595e7i	0.819085	−	0.00434986i
$622$			6.52461e8i			0.108715i
$623$	−3.88120e9			−0.643070
$624$	−1.85539e9	+	3.28440e6i	−0.305695	+	0.000541141i
$625$	−7.61273e9			−1.24727
$626$	−9.48456e9			−1.54528
$627$	4.15314e9	−	6.37701e9i	0.672884	−	1.03319i
$628$	−8.04281e8			−0.129583
$629$	2.74762e9			0.440230
$630$	−8.66450e9	+	3.06759e7i	−1.38055	+	0.00488770i
$631$	−1.09274e9			−0.173147			−0.0865734	−	0.996245i	$-0.527592\pi$
$631$	−1.09274e9			−0.173147			−0.0865734	+	0.996245i	$0.527592\pi$
$632$			2.99244e9i			0.471536i
$633$	1.14467e9	−	2.02630e6i	0.179378	−	0.000317534i
$634$			5.54463e9i			0.864093i
$635$	−6.67574e8			−0.103465
$636$	−3.73755e6	+	6616.19i	−0.000576085	+	1.01978e-6i
$637$		−	7.18397e8i		−	0.110123i
$638$	−4.96371e9	+	7.59219e9i	−0.756718	+	1.15743i
$639$	−4.68553e6	−	1.32344e9i	−0.000710404	−	0.200656i
$640$			7.18133e9i			1.08287i
$641$			4.97779e9i			0.746506i	0.927730	+	0.373253i	$0.121758\pi$
$641$			4.97779e9i			0.746506i	−0.927730	+	0.373253i	$0.878242\pi$
$642$	1.16386e6	+	6.57473e8i	0.000173591	+	0.0980630i
$643$	−8.00751e9			−1.18784			−0.593922	−	0.804523i	$-0.702421\pi$
$643$	−8.00751e9			−1.18784			−0.593922	+	0.804523i	$0.702421\pi$
$644$	4.93332e8			0.0727845
$645$	4.81908e6	+	2.72234e9i	0.000707139	+	0.399469i
$646$			1.21564e10i			1.77415i
$647$			7.57131e9i			1.09902i	0.835487	+	0.549510i	$0.185186\pi$
$647$			7.57131e9i			1.09902i	−0.835487	+	0.549510i	$0.814814\pi$
$648$	7.16680e9	−	5.07474e7i	1.03470	−	0.00732658i
$649$	−4.62997e9	−	3.02703e9i	−0.664846	−	0.434671i
$650$			1.23832e9i			0.176863i
$651$	−1.32072e10	+	2.33793e7i	−1.87619	+	0.00332122i
$652$	2.39971e8			0.0339072
$653$		−	1.10367e10i		−	1.55111i	−0.631280	−	0.775555i	$-0.717470\pi$
$653$		−	1.10367e10i		−	1.55111i	0.631280	−	0.775555i	$-0.282530\pi$
$654$	6.45024e9	−	1.14182e7i	0.901683	−	0.00159616i
$655$			8.20110e8i			0.114032i
$656$	7.19505e9			0.995108
$657$	4.66225e7	+	1.31687e10i	0.00641382	+	1.81161i
$658$	1.70843e9			0.233780
$659$	−4.27744e8			−0.0582217			−0.0291108	−	0.999576i	$-0.509268\pi$
$659$	−4.27744e8			−0.0582217			−0.0291108	+	0.999576i	$0.509268\pi$
$660$	3.86891e8	−	5.94058e8i	0.0523823	−	0.0804313i
$661$	−6.06091e9			−0.816268			−0.408134	−	0.912922i	$-0.633820\pi$
$661$	−6.06091e9			−0.816268			−0.408134	+	0.912922i	$0.633820\pi$
$662$	5.49250e9			0.735812
$663$	−3.74668e9	+	6.63236e6i	−0.499286	+	0.000883835i
$664$	4.02410e9			0.533433
$665$		−	1.34369e10i		−	1.77183i
$666$	−2.15271e9	+	7.62148e6i	−0.282375	+	0.000999723i
$667$		−	9.03563e9i		−	1.17901i
$668$	7.64898e8			0.0992856
$669$	−137554.	−	7.77056e7i	−1.77616e−5	−	0.0100337i
$670$		−	1.47227e10i		−	1.89115i
$671$	8.47604e9	+	5.54156e9i	1.08309	+	0.708115i
$672$	1.39486e9	−	2.46918e6i	0.177313	−	0.000313878i
$673$		−	9.96057e9i		−	1.25960i	−0.776759	−	0.629798i	$-0.783137\pi$
$673$		−	9.96057e9i		−	1.25960i	0.776759	−	0.629798i	$-0.216863\pi$
$674$			1.57468e9i			0.198099i
$675$	−2.34337e7	−	4.41260e9i	−0.00293277	−	0.552244i
$676$	−5.50016e8			−0.0684797
$677$	9.03655e9			1.11929			0.559645	−	0.828733i	$-0.310938\pi$
$677$	9.03655e9			1.11929			0.559645	+	0.828733i	$0.310938\pi$
$678$	−9.25748e9	+	1.63876e7i	−1.14075	+	0.00201935i
$679$			4.86468e9i			0.596362i
$680$			1.58317e10i			1.93084i
$681$	1.28102e7	+	7.23662e9i	0.00155433	+	0.878053i
$682$	−7.08421e9	+	1.08356e10i	−0.855157	+	1.30800i
$683$		−	9.81205e9i		−	1.17839i	−0.807992	−	0.589193i	$-0.799446\pi$
$683$		−	9.81205e9i		−	1.17839i	0.807992	−	0.589193i	$-0.200554\pi$
$684$	2.81467e6	+	7.95012e8i	0.000336303	+	0.0949899i
$685$	−1.27542e10			−1.51613
$686$			6.27421e9i			0.742035i
$687$	−1.58114e7	−	8.93198e9i	−0.00186046	−	1.05099i
$688$			2.51156e9i			0.294024i
$689$	−2.14014e7			−0.00249272
$690$	−1.49762e7	−	8.46016e9i	−0.00173552	−	0.980408i
$691$	1.48559e10			1.71287			0.856435	−	0.516255i	$-0.172674\pi$
$691$	1.48559e10			1.71287			0.856435	+	0.516255i	$0.172674\pi$
$692$	−8.74630e8			−0.100335
$693$	8.47755e9	+	5.49981e9i	0.967618	+	0.627742i
$694$	−7.16900e9			−0.814142
$695$	4.92653e9			0.556666
$696$	−2.34509e7	−	1.32476e10i	−0.00263650	−	1.48938i
$697$	1.45293e10			1.62529
$698$		−	3.83587e9i		−	0.426943i
$699$	1.08430e7	+	6.12532e9i	0.00120083	+	0.678358i
$700$		−	4.45332e8i		−	0.0490728i
$701$	−1.04249e10			−1.14303			−0.571517	−	0.820590i	$-0.693645\pi$
$701$	−1.04249e10			−1.14303			−0.571517	+	0.820590i	$0.693645\pi$
$702$	2.93544e9	−	1.55891e7i	0.320253	−	0.00170075i
$703$		−	3.33841e9i		−	0.362407i
$704$	5.39383e9	−	8.25007e9i	0.582630	−	0.891155i
$705$	4.32911e6	+	2.44555e9i	0.000465303	+	0.262854i
$706$		−	9.08440e9i		−	0.971583i
$707$			1.40890e10i			1.49938i
$708$	5.77881e8	−	1.02296e6i	0.0611958	−	0.000108329i
$709$	9.80256e9			1.03295			0.516473	−	0.856303i	$-0.327245\pi$
$709$	9.80256e9			1.03295			0.516473	+	0.856303i	$0.327245\pi$
$710$	−2.29051e9			−0.240175
$711$	−1.54627e7	−	4.36750e9i	−0.00161340	−	0.455711i
$712$		−	5.55622e9i		−	0.576899i
$713$		−	1.28957e10i		−	1.33239i
$714$	−1.61420e10	+	2.85746e7i	−1.65964	+	0.00293789i
$715$	2.22137e9	−	3.39767e9i	0.227274	−	0.347624i
$716$			4.66618e8i			0.0475079i
$717$	6.28789e6	+	3.55209e9i	0.000637072	+	0.359887i
$718$	8.63118e9			0.870231
$719$			8.94483e9i			0.897472i	0.893664	+	0.448736i	$0.148126\pi$
$719$			8.94483e9i			0.897472i	−0.893664	+	0.448736i	$0.851874\pi$
$720$	−4.05113e7	−	1.14425e10i	−0.00404494	−	1.14251i
$721$			9.86310e7i			0.00980031i
$722$	5.05463e9			0.499815
$723$	7.68920e9	−	1.36114e7i	0.756654	−	0.00133943i
$724$	−3.12551e8			−0.0306081
$725$	−8.15649e9			−0.794914
$726$	9.06656e9	−	3.98915e9i	0.879355	−	0.386903i
$727$	−1.03291e10			−0.996989			−0.498495	−	0.866893i	$-0.666114\pi$
$727$	−1.03291e10			−0.996989			−0.498495	+	0.866893i	$0.666114\pi$
$728$	4.14166e9			0.397845
$729$	−1.04598e10	+	1.11099e8i	−0.999944	+	0.0106210i
$730$	2.27913e10			2.16840
$731$			5.07171e9i			0.480224i
$732$	−1.05792e9	+	1.87273e6i	−0.0996930	+	0.000176476i
$733$			6.23025e9i			0.584307i	0.956371	+	0.292154i	$0.0943719\pi$
$733$			6.23025e9i			0.584307i	−0.956371	+	0.292154i	$0.905628\pi$
$734$	−2.76644e9			−0.258217
$735$	4.43051e9	−	7.84288e6i	0.411574	−	0.000728567i
$736$			1.36196e9i			0.125920i
$737$	−9.39614e9	+	1.43718e10i	−0.864597	+	1.32243i
$738$	−1.13835e10	+	4.03022e7i	−1.04251	+	0.00369089i
$739$		−	2.69049e9i		−	0.245231i	−0.992454	−	0.122616i	$-0.960872\pi$
$739$		−	2.69049e9i		−	0.245231i	0.992454	−	0.122616i	$-0.0391282\pi$
$740$		−	3.10994e8i		−	0.0282125i
$741$	8.05846e6	+	4.55229e9i	0.000727592	+	0.411023i
$742$	−9.22046e7			−0.00828588
$743$	5.08802e9			0.455080			0.227540	−	0.973769i	$-0.426932\pi$
$743$	5.08802e9			0.455080			0.227540	+	0.973769i	$0.426932\pi$
$744$	−3.34691e7	−	1.89070e10i	−0.00297947	−	1.68313i
$745$			6.99992e9i			0.620220i
$746$			1.94191e10i			1.71255i
$747$	−5.87322e9	+	2.07936e7i	−0.515530	+	0.00182519i
$748$	7.22734e8	−	1.10545e9i	0.0631427	−	0.0965792i
$749$		−	1.35389e9i		−	0.117733i
$750$	6.19184e9	−	1.09608e7i	0.535927	−	0.000948696i
$751$	3.13996e9			0.270511			0.135255	−	0.990811i	$-0.456815\pi$
$751$	3.13996e9			0.270511			0.135255	+	0.990811i	$0.456815\pi$
$752$			2.25620e9i			0.193471i
$753$	1.40778e10	−	2.49205e7i	1.20158	−	0.00212703i
$754$		−	5.42603e9i		−	0.460981i
$755$	−2.96884e9			−0.251057
$756$	−1.05566e9	+	5.60623e6i	−0.0888582	+	0.000471894i
$757$	−2.02487e10			−1.69653			−0.848264	−	0.529574i	$-0.822352\pi$
$757$	−2.02487e10			−1.69653			−0.848264	+	0.529574i	$0.822352\pi$
$758$	1.43269e10			1.19484
$759$	−5.38472e9	+	8.26806e9i	−0.447010	+	0.686368i
$760$	1.92358e10			1.58951
$761$	−1.25541e10			−1.03262			−0.516311	−	0.856401i	$-0.672695\pi$
$761$	−1.25541e10			−1.03262			−0.516311	+	0.856401i	$0.672695\pi$
$762$	9.74413e8	−	1.72490e6i	0.0797812	−	0.000141229i
$763$	−1.32825e10			−1.08254
$764$			1.29544e8i			0.0105097i
$765$	−8.18065e7	−	2.31065e10i	−0.00660652	−	1.86603i
$766$			2.14205e10i			1.72198i
$767$	3.30897e9			0.264795
$768$	5.10477e6	+	2.88373e9i	0.000406642	+	0.229716i
$769$			2.12827e10i			1.68765i	0.536615	+	0.843827i	$0.319703\pi$
$769$			2.12827e10i			1.68765i	−0.536615	+	0.843827i	$0.680297\pi$
$770$	9.57044e9	−	1.46384e10i	0.755465	−	1.15551i
$771$	−2.33443e9	+	4.13239e6i	−0.183438	+	0.000324722i
$772$		−	6.39665e7i		−	0.00500371i
$773$			8.66823e9i			0.674998i	0.941326	+	0.337499i	$0.109581\pi$
$773$			8.66823e9i			0.674998i	−0.941326	+	0.337499i	$0.890419\pi$
$774$	−1.40682e7	−	3.97360e9i	−0.00109055	−	0.308029i
$775$	−1.16409e10			−0.898322
$776$	−6.96413e9			−0.534997
$777$	4.43295e9	−	7.84720e6i	0.339016	−	0.000600124i
$778$		−	8.48574e9i		−	0.646043i
$779$		−	1.76534e10i		−	1.33798i
$780$	750695.	+	4.24074e8i	5.66412e−5	+	0.0319971i
$781$	2.23591e9	+	1.46182e9i	0.167948	+	0.109803i
$782$		−	1.57613e10i		−	1.17860i
$783$	1.02681e8	+	1.93349e10i	0.00764405	+	1.43938i
$784$	4.08747e9			0.302934
$785$		−	2.84022e10i		−	2.09560i
$786$	−2.11903e6	−	1.19706e9i	−0.000155653	−	0.0879299i
$787$		−	2.85264e9i		−	0.208610i	−0.994545	−	0.104305i	$-0.966738\pi$
$787$		−	2.85264e9i		−	0.208610i	0.994545	−	0.104305i	$-0.0332618\pi$
$788$	4.63976e8			0.0337796
$789$	−2.92114e7	−	1.65018e10i	−0.00211731	−	1.19608i
$790$	−7.55891e9			−0.545462
$791$	1.90633e10			1.36956
$792$	−7.87337e9	+	1.21362e10i	−0.563148	+	0.868051i
$793$	−6.05771e9			−0.431372
$794$	−1.06896e10			−0.757862
$795$	−233643.	−	1.31987e8i	−1.64918e−5	−	0.00931635i
$796$	1.81890e9			0.127824
$797$			1.80257e10i			1.26121i	0.776103	+	0.630606i	$0.217194\pi$
$797$			1.80257e10i			1.26121i	−0.776103	+	0.630606i	$0.782806\pi$
$798$	3.47187e7	+	1.96129e10i	0.00241854	+	1.36625i
$799$			4.55606e9i			0.315992i
$800$	1.22945e9			0.0848976
$801$	2.87105e7	+	8.10937e9i	0.00197391	+	0.557537i
$802$		−	1.16992e10i		−	0.800838i
$803$	−2.22480e10	−	1.45456e10i	−1.51631	−	0.991349i
$804$	−3.17536e6	−	1.79379e9i	−0.000215475	−	0.121724i
$805$			1.74214e10i			1.17706i
$806$		−	7.74404e9i		−	0.520948i
$807$	−2.60056e10	+	4.60351e7i	−1.74185	+	0.00308341i
$808$	−2.01694e10			−1.34509
$809$	−2.77447e9			−0.184230			−0.0921149	−	0.995748i	$-0.529363\pi$
$809$	−2.77447e9			−0.184230			−0.0921149	+	0.995748i	$0.529363\pi$
$810$	1.28188e8	+	1.81034e10i	0.00847520	+	1.19691i
$811$		−	1.92521e10i		−	1.26738i	−0.773588	−	0.633689i	$-0.781540\pi$
$811$		−	1.92521e10i		−	1.26738i	0.773588	−	0.633689i	$-0.218460\pi$
$812$			1.95134e9i			0.127905i
$813$	1.99650e10	−	3.53419e7i	1.30302	−	0.00230661i
$814$	2.37780e9	−	3.63693e9i	0.154522	−	0.236347i
$815$			8.47427e9i			0.548341i
$816$	−3.77362e7	−	2.13175e10i	−0.00243132	−	1.37348i
$817$	6.16224e9			0.395331
$818$			5.60442e9i			0.358009i
$819$	−6.04480e9	+	2.14010e7i	−0.384493	+	0.00136126i
$820$		−	1.64453e9i		−	0.104158i
$821$	1.05163e10			0.663227			0.331614	−	0.943415i	$-0.392407\pi$
$821$	1.05163e10			0.663227			0.331614	+	0.943415i	$0.392407\pi$
$822$	1.86165e10	−	3.29549e7i	1.16909	−	0.00206951i
$823$	1.00262e10			0.626956			0.313478	−	0.949595i	$-0.398506\pi$
$823$	1.00262e10			0.626956			0.313478	+	0.949595i	$0.398506\pi$
$824$	−1.41197e8			−0.00879187
$825$	7.46360e9	+	4.86080e9i	0.462764	+	0.301383i
$826$	1.42562e10			0.880185
$827$	−4.87559e9			−0.299749			−0.149875	−	0.988705i	$-0.547887\pi$
$827$	−4.87559e9			−0.299749			−0.149875	+	0.988705i	$0.547887\pi$
$828$	−3.64933e6	−	1.03077e9i	−0.000223412	−	0.0631036i
$829$	−1.13229e10			−0.690267			−0.345133	−	0.938554i	$-0.612166\pi$
$829$	−1.13229e10			−0.690267			−0.345133	+	0.938554i	$0.612166\pi$
$830$			1.01649e10i			0.617062i
$831$	−1.36259e10	+	2.41205e7i	−0.823683	+	0.00145808i
$832$			5.89621e9i			0.354929i
$833$	8.25404e9			0.494776
$834$	−7.19093e9	+	1.27294e7i	−0.429244	+	0.000759846i
$835$			2.70115e10i			1.60563i
$836$	−1.34314e9	−	8.78137e8i	−0.0795061	−	0.0519805i
$837$	1.46546e8	+	2.75948e10i	0.00863844	+	1.62663i
$838$		−	1.20807e10i		−	0.709149i
$839$			6.78505e9i			0.396630i	0.980138	+	0.198315i	$0.0635470\pi$
$839$			6.78505e9i			0.396630i	−0.980138	+	0.198315i	$0.936453\pi$
$840$	4.52153e7	+	2.55425e10i	0.00263213	+	1.48691i
$841$	1.84899e10			1.07189
$842$	1.21599e10			0.702000
$843$	1.14689e7	+	6.47891e9i	0.000659367	+	0.372482i
$844$		−	2.41373e8i		−	0.0138195i
$845$		−	1.94231e10i		−	1.10744i
$846$	−1.26378e7	−	3.56960e9i	−0.000717589	−	0.202686i
$847$	−1.86846e10	+	8.18151e9i	−1.05656	+	0.462638i
$848$		−	1.21768e8i		−	0.00685719i
$849$	3.14873e10	−	5.57387e7i	1.76587	−	0.00312594i
$850$	−1.42277e10			−0.794639
$851$			4.32839e9i			0.240754i
$852$	−2.79071e8	+	494011.i	−0.0154588	+	2.73652e-5i
$853$		−	1.03168e10i		−	0.569148i	−0.958654	−	0.284574i	$-0.908148\pi$
$853$		−	1.03168e10i		−	0.569148i	0.958654	−	0.284574i	$-0.0918522\pi$
$854$	−2.60987e10			−1.43389
$855$	−2.80749e10	+	9.93966e7i	−1.53616	+	0.00543864i
$856$	1.93819e9			0.105618
$857$	−3.39699e10			−1.84358			−0.921788	−	0.387694i	$-0.873272\pi$
$857$	−3.39699e10			−1.84358			−0.921788	+	0.387694i	$0.873272\pi$
$858$	−3.23361e9	+	4.96509e9i	−0.174776	+	0.268363i
$859$	9.58191e9			0.515794			0.257897	−	0.966172i	$-0.416971\pi$
$859$	9.58191e9			0.515794			0.257897	+	0.966172i	$0.416971\pi$
$860$	5.74050e8			0.0307755
$861$	2.34413e10	−	4.14958e7i	1.25162	−	0.00221561i
$862$	−1.36817e10			−0.727555
$863$		−	1.46669e10i		−	0.776784i	−0.921494	−	0.388392i	$-0.873031\pi$
$863$		−	1.46669e10i		−	0.776784i	0.921494	−	0.388392i	$-0.126969\pi$
$864$	−1.54773e7	−	2.91441e9i	−0.000816391	−	0.153728i
$865$		−	3.08865e10i		−	1.62260i
$866$	−2.18829e10			−1.14496
$867$	−4.22333e7	−	2.38580e10i	−0.00220084	−	1.24327i
$868$			2.78495e9i			0.144544i
$869$	7.37873e9	+	4.82415e9i	0.381428	+	0.249374i
$870$	3.34635e10	−	5.92371e7i	1.72288	−	0.00304983i
$871$		−	1.02713e10i		−	0.526699i
$872$		−	1.90149e10i		−	0.971151i
$873$	1.01642e10	−	3.59855e7i	0.517041	−	0.00183053i
$874$	−1.91503e10			−0.970253
$875$	−1.27504e10			−0.643423
$876$	2.77685e9	−	4.91557e6i	0.139569	−	0.000247064i
$877$		−	1.90740e10i		−	0.954870i	−0.878667	−	0.477435i	$-0.841567\pi$
$877$		−	1.90740e10i		−	0.954870i	0.878667	−	0.477435i	$-0.158433\pi$
$878$		−	2.32875e9i		−	0.116116i
$879$	3.76089e7	+	2.12456e10i	0.00186780	+	1.05514i
$880$	1.93318e10	+	1.26390e10i	0.956274	+	0.625204i
$881$		−	1.76902e9i		−	0.0871599i	−0.999050	−	0.0435799i	$-0.986124\pi$
$881$		−	1.76902e9i		−	0.0871599i	0.999050	−	0.0435799i	$-0.0138763\pi$
$882$	−6.46690e9	+	2.28954e7i	−0.317363	+	0.00112359i
$883$	3.28663e10			1.60653			0.803264	−	0.595623i	$-0.203095\pi$
$883$	3.28663e10			1.60653			0.803264	+	0.595623i	$0.203095\pi$
$884$			7.90050e8i			0.0384655i
$885$	3.61247e7	+	2.04072e10i	0.00175187	+	0.989649i
$886$		−	3.21878e10i		−	1.55480i
$887$	−6.93021e9			−0.333437			−0.166719	−	0.986005i	$-0.553317\pi$
$887$	−6.93021e9			−0.333437			−0.166719	+	0.986005i	$0.553317\pi$
$888$	1.12338e7	+	6.34609e9i	0.000538372	+	0.304131i
$889$	−2.00654e9			−0.0957839
$890$	1.40350e10			0.667342
$891$	1.14286e10	−	1.77536e10i	0.541277	−	0.840844i
$892$	−1.63855e7			−0.000773007
$893$	5.53570e9			0.260131
$894$	−1.80867e7	−	1.02173e10i	−0.000846597	−	0.478250i
$895$	−1.64780e10			−0.768289
$896$			2.15851e10i			1.00248i
$897$	−1.04481e7	−	5.90224e9i	−0.000483353	−	0.273051i
$898$		−	9.39043e9i		−	0.432731i
$899$	5.10078e10			2.34141
$900$	−9.30476e8	+	3.29426e6i	−0.0425458	+	0.000150629i
$901$		−	2.45892e8i		−	0.0111997i
$902$	1.25737e10	−	1.92320e10i	0.570481	−	0.872572i
$903$	1.44848e7	+	8.18260e9i	0.000654645	+	0.369815i
$904$			2.72905e10i			1.22863i
$905$		−	1.10374e10i		−	0.494989i
$906$	4.33342e9	−	7.67100e6i	0.193589	−	0.000342692i
$907$	2.22914e10			0.992002			0.496001	−	0.868322i	$-0.334801\pi$
$907$	2.22914e10			0.992002			0.496001	+	0.868322i	$0.334801\pi$
$908$	1.52596e9			0.0676462
$909$	2.94374e10	−	1.04220e8i	1.29995	−	0.00460235i
$910$			1.04618e10i			0.460217i
$911$		−	3.24874e10i		−	1.42364i	−0.702362	−	0.711820i	$-0.747871\pi$
$911$		−	3.24874e10i		−	1.42364i	0.702362	−	0.711820i	$-0.252129\pi$
$912$	−2.59012e10	+	4.58503e7i	−1.13068	+	0.00200152i
$913$	6.48731e9	−	9.92259e9i	0.282109	−	0.431496i
$914$			3.53157e10i			1.52988i
$915$	−6.61332e7	−	3.73592e10i	−0.00285395	−	1.61222i
$916$	−1.88346e9			−0.0809695
$917$			2.46502e9i			0.105567i
$918$	1.79111e8	+	3.37269e10i	0.00764140	+	1.43889i
$919$			2.67382e9i			0.113639i	0.998384	+	0.0568196i	$0.0180960\pi$
$919$			2.67382e9i			0.113639i	−0.998384	+	0.0568196i	$0.981904\pi$
$920$	−2.49400e10			−1.05594
$921$	−3.61440e10	+	6.39820e7i	−1.52450	+	0.00269867i
$922$	−1.37734e10			−0.578739
$923$	−1.59797e9			−0.0668904
$924$	1.16289e9	−	1.78557e9i	0.0484937	−	0.0744605i
$925$	3.90725e9			0.162321
$926$	−9.30192e7			−0.00384977
$927$	2.06079e8	−	729604.i	0.00849680	−	3.00821e-5i
$928$	−5.38715e9			−0.221279
$929$			4.20467e9i			0.172059i	0.996293	+	0.0860293i	$0.0274179\pi$
$929$			4.20467e9i			0.172059i	−0.996293	+	0.0860293i	$0.972582\pi$
$930$	4.77592e10	−	8.45432e7i	1.94700	−	0.00344658i
$931$		−	1.00288e10i		−	0.407311i
$932$	1.29163e9			0.0522614
$933$	−2.80726e9	+	4.96940e6i	−0.113161	+	0.000200317i
$934$		−	1.29948e9i		−	0.0521860i
$935$	3.90376e10	+	2.55225e10i	1.56186	+	1.02113i
$936$	−3.06371e7	−	8.65356e9i	−0.00122119	−	0.344929i
$937$			4.34501e9i			0.172545i	0.996272	+	0.0862725i	$0.0274956\pi$
$937$			4.34501e9i			0.172545i	−0.996272	+	0.0862725i	$0.972504\pi$
$938$		−	4.42524e10i		−	1.75076i
$939$	−7.22381e7	−	4.08079e10i	−0.00284732	−	1.60848i
$940$	5.15685e8			0.0202506
$941$	1.18732e10			0.464520			0.232260	−	0.972654i	$-0.425388\pi$
$941$	1.18732e10			0.464520			0.232260	+	0.972654i	$0.425388\pi$
$942$	7.33868e7	+	4.14568e10i	0.00286048	+	1.61591i
$943$			2.28884e10i			0.888843i
$944$			1.88271e10i			0.728419i
$945$	−1.97977e8	−	3.72794e10i	−0.00763139	−	1.43700i
$946$	6.71326e9	+	4.38907e9i	0.257819	+	0.168560i
$947$			2.98586e10i			1.14247i	0.820786	+	0.571236i	$0.193536\pi$
$947$			2.98586e10i			1.14247i	−0.820786	+	0.571236i	$0.806464\pi$
$948$	−9.20963e8	+	1.63029e6i	−0.0351085	+	6.21491e-5i
$949$	1.59004e10			0.603914
$950$			1.72870e10i			0.654165i
$951$	−2.38561e10	+	4.22301e7i	−0.899432	+	0.00159217i
$952$			4.75857e10i			1.78750i
$953$	−4.53039e9			−0.169555			−0.0847776	−	0.996400i	$-0.527018\pi$
$953$	−4.53039e9			−0.169555			−0.0847776	+	0.996400i	$0.527018\pi$
$954$	682066.	+	1.92652e8i	2.54336e−5	+	0.00718380i
$955$	−4.57468e9			−0.169961
$956$	7.49017e8			0.0277261
$957$	−3.27037e10	−	2.12989e10i	−1.20616	−	0.785533i
$958$	−4.17916e10			−1.53571
$959$	−3.83357e10			−1.40358
$960$	−3.63632e10	+	6.43701e7i	−1.32652	+	0.00234820i
$961$	4.52857e10			1.64600
$962$			2.59927e9i			0.0941322i
$963$	−2.82881e9	+	1.00151e7i	−0.102073	+	0.000361381i
$964$		−	1.62140e9i		−	0.0582934i
$965$	2.25890e9			0.0809191
$966$	−4.50142e7	−	2.54289e10i	−0.00160668	−	0.907628i
$967$			2.30257e10i			0.818878i	0.912337	+	0.409439i	$0.134276\pi$
$967$			2.30257e10i			0.818878i	−0.912337	+	0.409439i	$0.865724\pi$
$968$	−1.17124e10	−	2.67484e10i	−0.415033	−	0.947838i
$969$	−5.23037e10	+	9.25879e7i	−1.84671	+	0.00326904i
$970$		−	1.75914e10i		−	0.618871i
$971$			4.49193e10i			1.57458i	0.616580	+	0.787292i	$0.288518\pi$
$971$			4.49193e10i			1.57458i	−0.616580	+	0.787292i	$0.711482\pi$
$972$	1.95227e7	+	2.20565e9i	0.000681879	+	0.0770379i
$973$	1.48078e10			0.515342
$974$	−2.69512e10			−0.934591
$975$	−5.32797e9	+	9.43155e6i	−0.184096	+	0.000325887i
$976$		−	3.44666e10i		−	1.18665i
$977$		−	1.50720e10i		−	0.517059i	−0.966003	−	0.258530i	$-0.916762\pi$
$977$		−	1.50720e10i		−	0.517059i	0.966003	−	0.258530i	$-0.0832380\pi$
$978$	−2.18962e7	−	1.23693e10i	−0.000748483	−	0.422825i
$979$	−1.37005e10	−	8.95727e9i	−0.466656	−	0.305096i
$980$		−	9.34247e8i		−	0.0317081i
$981$	9.82551e7	+	2.77525e10i	0.00332287	+	0.938557i
$982$	−4.73770e10			−1.59653
$983$			1.59581e10i			0.535851i	0.963440	+	0.267925i	$0.0863380\pi$
$983$			1.59581e10i			0.535851i	−0.963440	+	0.267925i	$0.913662\pi$
$984$	5.94042e7	+	3.35579e10i	0.00198762	+	1.12283i
$985$			1.63848e10i			0.546278i
$986$	6.23426e10			2.07117
$987$	1.30121e7	+	7.35065e9i	0.000430762	+	0.243341i
$988$	9.59927e8			0.0316657
$989$	−7.98959e9			−0.262626
$990$	−3.06561e10	−	1.98882e10i	−1.00414	−	0.651435i
$991$	−3.50853e9			−0.114516			−0.0572582	−	0.998359i	$-0.518236\pi$
$991$	−3.50853e9			−0.114516			−0.0572582	+	0.998359i	$0.518236\pi$
$992$	−7.68854e9			−0.250065
$993$	4.18330e7	+	2.36318e10i	0.00135580	+	0.765906i
$994$	−6.88463e9			−0.222346
$995$			6.42324e10i			2.06716i
$996$	2.19234e6	+	1.23847e9i	7.03071e−5	+	0.0397171i
$997$			8.84561e9i			0.282680i	0.989961	+	0.141340i	$0.0451411\pi$
$997$			8.84561e9i			0.282680i	−0.989961	+	0.141340i	$0.954859\pi$
$998$	−3.38148e10			−1.07684
$999$	−4.91878e7	−	9.26214e9i	−0.00156091	−	0.293922i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.8.d.b.32.7	✓	24
3.2	odd	2	inner	33.8.d.b.32.18	yes	24
11.10	odd	2	inner	33.8.d.b.32.17	yes	24
33.32	even	2	inner	33.8.d.b.32.8	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.8.d.b.32.7	✓	24	1.1	even	1	trivial
33.8.d.b.32.8	yes	24	33.32	even	2	inner
33.8.d.b.32.17	yes	24	11.10	odd	2	inner
33.8.d.b.32.18	yes	24	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	33.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-10.8692 q^{2} +(-0.0827838 - 46.7653i) q^{3} -9.86124 q^{4} -348.238i q^{5} +(0.899791 + 508.300i) q^{6} -1046.71i q^{7} +1498.44 q^{8} +(-2186.99 + 7.74282i) q^{9} +3785.06i q^{10} +(2415.65 - 3694.83i) q^{11} +(0.816351 + 461.164i) q^{12} +2640.65i q^{13} +11376.8i q^{14} +(-16285.5 + 28.8285i) q^{15} -15024.5 q^{16} -30339.8 q^{17} +(23770.7 - 84.1580i) q^{18} +36863.5i q^{19} +3434.06i q^{20} +(-48949.6 + 86.6504i) q^{21} +(-26256.1 + 40159.8i) q^{22} -47795.0i q^{23} +(-124.046 - 70074.8i) q^{24} -43144.7 q^{25} -28701.6i q^{26} +(543.142 + 102274. i) q^{27} +10321.8i q^{28} +189050. q^{29} +(177009. - 313.341i) q^{30} +269812. q^{31} -28495.9 q^{32} +(-172990. - 112663. i) q^{33} +329768. q^{34} -364503. q^{35} +(21566.4 - 76.3538i) q^{36} -90561.6 q^{37} -400675. i q^{38} +(123491. - 218.603i) q^{39} -521813. i q^{40} -478887. q^{41} +(532041. - 941.818i) q^{42} -167164. i q^{43} +(-23821.3 + 36435.7i) q^{44} +(2696.34 + 761592. i) q^{45} +519492. i q^{46} -150168. i q^{47} +(1243.79 + 702626. i) q^{48} -272053. q^{49} +468947. q^{50} +(2511.64 + 1.41885e6i) q^{51} -26040.1i q^{52} +8104.59i q^{53} +(-5903.50 - 1.11164e6i) q^{54} +(-1.28668e6 - 841222. i) q^{55} -1.56842e6i q^{56} +(1.72393e6 - 3051.70i) q^{57} -2.05481e6 q^{58} -1.25309e6i q^{59} +(160595. - 284.285i) q^{60} +2.29402e6i q^{61} -2.93263e6 q^{62} +(8104.47 + 2.28913e6i) q^{63} +2.23287e6 q^{64} +919574. q^{65} +(1.88026e6 + 1.22455e6i) q^{66} -3.88969e6 q^{67} +299188. q^{68} +(-2.23515e6 + 3956.65i) q^{69} +3.96185e6 q^{70} +605145. i q^{71} +(-3.27706e6 + 11602.1i) q^{72} -6.02139e6i q^{73} +984329. q^{74} +(3571.68 + 2.01767e6i) q^{75} -363520. i q^{76} +(-3.86741e6 - 2.52848e6i) q^{77} +(-1.34224e6 + 2376.03i) q^{78} +1.99704e6i q^{79} +5.23211e6i q^{80} +(4.78285e6 - 33866.9i) q^{81} +5.20510e6 q^{82} +2.68553e6 q^{83} +(482704. - 854.481i) q^{84} +1.05655e7i q^{85} +1.81693e6i q^{86} +(-15650.2 - 8.84096e6i) q^{87} +(3.61970e6 - 5.53647e6i) q^{88} -3.70801e6i q^{89} +(-29307.0 - 8.27787e6i) q^{90} +2.76398e6 q^{91} +471318. i q^{92} +(-22336.0 - 1.26178e7i) q^{93} +1.63220e6i q^{94} +1.28373e7 q^{95} +(2359.00 + 1.33262e6i) q^{96} -4.64760e6 q^{97} +2.95699e6 q^{98} +(-5.25439e6 + 8.09925e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 120 q^{3} + 1788 q^{4} - 5940 q^{9} - 6936 q^{12} + 23160 q^{15} + 5844 q^{16} - 17556 q^{22} - 34704 q^{25} + 7560 q^{27} + 131328 q^{31} + 28644 q^{33} - 436080 q^{34} - 302832 q^{36} + 1072488 q^{37}+ \cdots + 53650080 q^{99}+O(q^{100}) \) 24 * q + 120 * q^3 + 1788 * q^4 - 5940 * q^9 - 6936 * q^12 + 23160 * q^15 + 5844 * q^16 - 17556 * q^22 - 34704 * q^25 + 7560 * q^27 + 131328 * q^31 + 28644 * q^33 - 436080 * q^34 - 302832 * q^36 + 1072488 * q^37 - 100296 * q^42 - 1854252 * q^45 + 3172548 * q^48 - 1169304 * q^49 - 4401936 * q^55 - 2920440 * q^58 + 1981452 * q^60 + 14578596 * q^64 + 2895156 * q^66 + 7729200 * q^67 - 4614108 * q^69 - 6924504 * q^70 - 4375800 * q^75 - 26237448 * q^78 + 22367340 * q^81 - 23600232 * q^82 - 25179660 * q^88 + 9380640 * q^91 + 25396908 * q^93 + 72948360 * q^97 + 53650080 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more