LMFDB - Embedded newform 33.8.d.b.32.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [33,8,Mod(32,33)]

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

lf = mfeigenbasis(mf)

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")

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

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

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

Embedding invariants

Embedding label			32.15
Character	$\chi$	$=$	33.32
Dual form			33.8.d.b.32.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+10.1755 q^{2} +(-20.0376 - 42.2551i) q^{3} -24.4601 q^{4} +419.841i q^{5} +(-203.892 - 429.965i) q^{6} +43.4849i q^{7} -1551.35 q^{8} +(-1383.99 + 1693.38i) q^{9} +O(q^{10})$	\(q+10.1755 q^{2} +(-20.0376 - 42.2551i) q^{3} -24.4601 q^{4} +419.841i q^{5} +(-203.892 - 429.965i) q^{6} +43.4849i q^{7} -1551.35 q^{8} +(-1383.99 + 1693.38i) q^{9} +4272.07i q^{10} +(4376.59 + 576.740i) q^{11} +(490.122 + 1033.56i) q^{12} +13074.7i q^{13} +442.478i q^{14} +(17740.4 - 8412.62i) q^{15} -12654.8 q^{16} -33396.4 q^{17} +(-14082.7 + 17231.0i) q^{18} -667.043i q^{19} -10269.3i q^{20} +(1837.46 - 871.333i) q^{21} +(44533.8 + 5868.59i) q^{22} -55628.7i q^{23} +(31085.4 + 65552.5i) q^{24} -98141.4 q^{25} +133041. i q^{26} +(99285.9 + 24549.1i) q^{27} -1063.64i q^{28} -93142.9 q^{29} +(180517. - 85602.2i) q^{30} -111204. q^{31} +69804.3 q^{32} +(-63326.3 - 196490. i) q^{33} -339823. q^{34} -18256.7 q^{35} +(33852.4 - 41420.3i) q^{36} +487443. q^{37} -6787.47i q^{38} +(552472. - 261985. i) q^{39} -651321. i q^{40} -351121. q^{41} +(18697.0 - 8866.22i) q^{42} +535628. i q^{43} +(-107052. - 14107.1i) q^{44} +(-710952. - 581054. i) q^{45} -566047. i q^{46} -736397. i q^{47} +(253573. + 534731. i) q^{48} +821652. q^{49} -998633. q^{50} +(669184. + 1.41117e6i) q^{51} -319807. i q^{52} +1.13657e6i q^{53} +(1.01028e6 + 249798. i) q^{54} +(-242139. + 1.83747e6i) q^{55} -67460.3i q^{56} +(-28186.0 + 13366.0i) q^{57} -947771. q^{58} +1.44995e6i q^{59} +(-433932. + 205773. i) q^{60} +361505. i q^{61} -1.13155e6 q^{62} +(-73636.6 - 60182.5i) q^{63} +2.33011e6 q^{64} -5.48928e6 q^{65} +(-644374. - 1.99937e6i) q^{66} +803411. q^{67} +816877. q^{68} +(-2.35060e6 + 1.11467e6i) q^{69} -185770. q^{70} -2.35617e6i q^{71} +(2.14705e6 - 2.62703e6i) q^{72} +2.26424e6i q^{73} +4.95996e6 q^{74} +(1.96652e6 + 4.14697e6i) q^{75} +16315.9i q^{76} +(-25079.5 + 190315. i) q^{77} +(5.62165e6 - 2.66582e6i) q^{78} +2.50489e6i q^{79} -5.31301e6i q^{80} +(-952130. - 4.68724e6i) q^{81} -3.57282e6 q^{82} +2.38713e6 q^{83} +(-44944.3 + 21312.9i) q^{84} -1.40212e7i q^{85} +5.45026e6i q^{86} +(1.86636e6 + 3.93576e6i) q^{87} +(-6.78963e6 - 894726. i) q^{88} +4.69732e6i q^{89} +(-7.23426e6 - 5.91249e6i) q^{90} -568550. q^{91} +1.36068e6i q^{92} +(2.22826e6 + 4.69893e6i) q^{93} -7.49317e6i q^{94} +280052. q^{95} +(-1.39871e6 - 2.94959e6i) q^{96} -1.19483e6 q^{97} +8.36069e6 q^{98} +(-7.03379e6 + 6.61305e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 120 q^{3} + 1788 q^{4} - 5940 q^{9}+O(q^{10}) $ 24 * q + 120 * q^3 + 1788 * q^4 - 5940 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

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 $

$2$	10.1755			0.899392			0.449696	−	0.893182i	$-0.351532\pi$
$2$	10.1755			0.899392			0.449696	+	0.893182i	$0.351532\pi$
$3$	−20.0376	−	42.2551i	−0.428472	−	0.903555i
$3$	−20.0376	−	42.2551i	−0.428472	−	0.903555i
$4$	−24.4601			−0.191094
$5$			419.841i			1.50207i	0.660263	+	0.751034i	$0.270445\pi$
$5$			419.841i			1.50207i	−0.660263	+	0.751034i	$0.729555\pi$
$6$	−203.892	−	429.965i	−0.385364	−	0.812650i
$7$			43.4849i			0.0479176i	0.999713	+	0.0239588i	$0.00762705\pi$
$7$			43.4849i			0.0479176i	−0.999713	+	0.0239588i	$0.992373\pi$
$8$	−1551.35			−1.07126
$9$	−1383.99	+	1693.38i	−0.632824	+	0.774295i
$10$			4272.07i			1.35095i
$11$	4376.59	+	576.740i	0.991429	+	0.130649i
$11$	4376.59	+	576.740i	0.991429	+	0.130649i
$12$	490.122	+	1033.56i	0.0818784	+	0.172664i
$13$			13074.7i			1.65055i	0.564730	+	0.825276i	$0.308980\pi$
$13$			13074.7i			1.65055i	−0.564730	+	0.825276i	$0.691020\pi$
$14$			442.478i			0.0430967i
$15$	17740.4	−	8412.62i	1.35720	−	0.643594i
$16$	−12654.8			−0.772389
$17$	−33396.4			−1.64865			−0.824324	−	0.566118i	$-0.808445\pi$
$17$	−33396.4			−1.64865			−0.824324	+	0.566118i	$0.808445\pi$
$18$	−14082.7	+	17231.0i	−0.569157	+	0.696395i
$19$		−	667.043i		−	0.0223109i	−0.999938	−	0.0111554i	$-0.996449\pi$
$19$		−	667.043i		−	0.0223109i	0.999938	−	0.0111554i	$-0.00355096\pi$
$20$		−	10269.3i		−	0.287037i
$21$	1837.46	−	871.333i	0.0432962	−	0.0205313i
$22$	44533.8	+	5868.59i	0.891683	+	0.117505i
$23$		−	55628.7i		−	0.953348i	−0.879080	−	0.476674i	$-0.841842\pi$
$23$		−	55628.7i		−	0.953348i	0.879080	−	0.476674i	$-0.158158\pi$
$24$	31085.4	+	65552.5i	0.459005	+	0.967943i
$25$	−98141.4			−1.25621
$26$			133041.i			1.48449i
$27$	99285.9	+	24549.1i	0.970766	+	0.240028i
$28$		−	1063.64i		−	0.00915677i
$29$	−93142.9			−0.709180			−0.354590	−	0.935022i	$-0.615380\pi$
$29$	−93142.9			−0.709180			−0.354590	+	0.935022i	$0.615380\pi$
$30$	180517.	−	85602.2i	1.22066	−	0.578843i
$31$	−111204.			−0.670430			−0.335215	−	0.942142i	$-0.608809\pi$
$31$	−111204.			−0.670430			−0.335215	+	0.942142i	$0.608809\pi$
$32$	69804.3			0.376580
$33$	−63326.3	−	196490.i	−0.306750	−	0.951790i
$34$	−339823.			−1.48278
$35$	−18256.7			−0.0719755
$36$	33852.4	−	41420.3i	0.120929	−	0.147963i
$37$	487443.			1.58204			0.791021	−	0.611789i	$-0.209550\pi$
$37$	487443.			1.58204			0.791021	+	0.611789i	$0.209550\pi$
$38$		−	6787.47i		−	0.0200662i
$39$	552472.	−	261985.i	1.49136	−	0.707214i
$40$		−	651321.i		−	1.60911i
$41$	−351121.			−0.795635			−0.397817	−	0.917465i	$-0.630232\pi$
$41$	−351121.			−0.795635			−0.397817	+	0.917465i	$0.630232\pi$
$42$	18697.0	−	8866.22i	0.0389402	−	0.0184657i
$43$			535628.i			1.02736i	0.857981	+	0.513682i	$0.171719\pi$
$43$			535628.i			1.02736i	−0.857981	+	0.513682i	$0.828281\pi$
$44$	−107052.	−	14107.1i	−0.189456	−	0.0249662i
$45$	−710952.	−	581054.i	−1.16304	−	0.950545i
$46$		−	566047.i		−	0.857433i
$47$		−	736397.i		−	1.03459i	−0.855806	−	0.517296i	$-0.826939\pi$
$47$		−	736397.i		−	1.03459i	0.855806	−	0.517296i	$-0.173061\pi$
$48$	253573.	+	534731.i	0.330947	+	0.697896i
$49$	821652.			0.997704
$50$	−998633.			−1.12982
$51$	669184.	+	1.41117e6i	0.706399	+	1.48964i
$52$		−	319807.i		−	0.315411i
$53$			1.13657e6i			1.04865i	0.851519	+	0.524323i	$0.175682\pi$
$53$			1.13657e6i			1.04865i	−0.851519	+	0.524323i	$0.824318\pi$
$54$	1.01028e6	+	249798.i	0.873099	+	0.215879i
$55$	−242139.	+	1.83747e6i	−0.196244	+	1.48919i
$56$		−	67460.3i		−	0.0513322i
$57$	−28186.0	+	13366.0i	−0.0201591	+	0.00955957i
$58$	−947771.			−0.637831
$59$			1.44995e6i			0.919114i	0.888148	+	0.459557i	$0.151992\pi$
$59$			1.44995e6i			0.919114i	−0.888148	+	0.459557i	$0.848008\pi$
$60$	−433932.	+	205773.i	−0.259353	+	0.122987i
$61$			361505.i			0.203920i	0.994788	+	0.101960i	$0.0325114\pi$
$61$			361505.i			0.203920i	−0.994788	+	0.101960i	$0.967489\pi$
$62$	−1.13155e6			−0.602979
$63$	−73636.6	−	60182.5i	−0.0371024	−	0.0303234i
$64$	2.33011e6			1.11108
$65$	−5.48928e6			−2.47924
$66$	−644374.	−	1.99937e6i	−0.275889	−	0.856032i
$67$	803411.			0.326344			0.163172	−	0.986598i	$-0.447827\pi$
$67$	803411.			0.326344			0.163172	+	0.986598i	$0.447827\pi$
$68$	816877.			0.315047
$69$	−2.35060e6	+	1.11467e6i	−0.861403	+	0.408482i
$70$	−185770.			−0.0647342
$71$		−	2.35617e6i		−	0.781271i	−0.920545	−	0.390635i	$-0.872255\pi$
$71$		−	2.35617e6i		−	0.781271i	0.920545	−	0.390635i	$-0.127745\pi$
$72$	2.14705e6	−	2.62703e6i	0.677920	−	0.829472i
$73$			2.26424e6i			0.681229i	0.940203	+	0.340615i	$0.110635\pi$
$73$			2.26424e6i			0.681229i	−0.940203	+	0.340615i	$0.889365\pi$
$74$	4.95996e6			1.42288
$75$	1.96652e6	+	4.14697e6i	0.538250	+	1.13505i
$76$			16315.9i			0.00426348i
$77$	−25079.5	+	190315.i	−0.00626038	+	0.0475069i
$78$	5.62165e6	−	2.66582e6i	1.34132	−	0.636063i
$79$			2.50489e6i			0.571603i	0.958289	+	0.285802i	$0.0922598\pi$
$79$			2.50489e6i			0.571603i	−0.958289	+	0.285802i	$0.907740\pi$
$80$		−	5.31301e6i		−	1.16018i
$81$	−952130.	−	4.68724e6i	−0.199067	−	0.979986i
$82$	−3.57282e6			−0.715587
$83$	2.38713e6			0.458251			0.229125	−	0.973397i	$-0.426413\pi$
$83$	2.38713e6			0.458251			0.229125	+	0.973397i	$0.426413\pi$
$84$	−44944.3	+	21312.9i	−0.00827365	+	0.00392342i
$85$		−	1.40212e7i		−	2.47638i
$86$			5.45026e6i			0.924002i
$87$	1.86636e6	+	3.93576e6i	0.303863	+	0.640783i
$88$	−6.78963e6	−	894726.i	−1.06208	−	0.139959i
$89$			4.69732e6i			0.706293i	0.935568	+	0.353146i	$0.114888\pi$
$89$			4.69732e6i			0.706293i	−0.935568	+	0.353146i	$0.885112\pi$
$90$	−7.23426e6	−	5.91249e6i	−1.04603	−	0.854913i
$91$	−568550.			−0.0790904
$92$			1.36068e6i			0.182179i
$93$	2.22826e6	+	4.69893e6i	0.287260	+	0.605771i
$94$		−	7.49317e6i		−	0.930504i
$95$	280052.			0.0335124
$96$	−1.39871e6	−	2.94959e6i	−0.161354	−	0.340261i
$97$	−1.19483e6			−0.132925			−0.0664623	−	0.997789i	$-0.521171\pi$
$97$	−1.19483e6			−0.132925			−0.0664623	+	0.997789i	$0.521171\pi$
$98$	8.36069e6			0.897327
$99$	−7.03379e6	+	6.61305e6i	−0.728561	+	0.684981i
$100$	2.40054e6			0.240054
$101$	9.09713e6			0.878576			0.439288	−	0.898346i	$-0.355231\pi$
$101$	9.09713e6			0.878576			0.439288	+	0.898346i	$0.355231\pi$
$102$	6.80925e6	+	1.43593e7i	0.635329	+	1.33977i
$103$	−5.06322e6			−0.456559			−0.228279	−	0.973596i	$-0.573310\pi$
$103$	−5.06322e6			−0.456559			−0.228279	+	0.973596i	$0.573310\pi$
$104$		−	2.02834e7i		−	1.76817i
$105$	365821.	+	771439.i	0.0308394	+	0.0650338i
$106$			1.15651e7i			0.943144i
$107$	−1.07577e6			−0.0848935			−0.0424468	−	0.999099i	$-0.513515\pi$
$107$	−1.07577e6			−0.0848935			−0.0424468	+	0.999099i	$0.513515\pi$
$108$	−2.42854e6	−	600472.i	−0.185508	−	0.0458680i
$109$			2.33710e7i			1.72856i	0.503008	+	0.864282i	$0.332227\pi$
$109$			2.33710e7i			1.72856i	−0.503008	+	0.864282i	$0.667773\pi$
$110$	−2.46388e6	+	1.86971e7i	−0.176500	+	1.33937i
$111$	−9.76721e6	−	2.05970e7i	−0.677860	−	1.42946i
$112$		−	550293.i		−	0.0370110i
$113$		−	5.96167e6i		−	0.388681i	−0.980934	−	0.194341i	$-0.937743\pi$
$113$		−	5.96167e6i		−	0.388681i	0.980934	−	0.194341i	$-0.0622567\pi$
$114$	−286805.	+	136005.i	−0.0181309	+	0.00859780i
$115$	2.33552e7			1.43199
$116$	2.27828e6			0.135520
$117$	−2.21404e7	−	1.80952e7i	−1.27801	−	1.04451i
$118$			1.47539e7i			0.826644i
$119$		−	1.45224e6i		−	0.0789992i
$120$	−2.75216e7	+	1.30509e7i	−1.45392	+	0.689456i
$121$	1.88219e7	+	5.04831e6i	0.965862	+	0.259058i
$122$			3.67848e6i			0.183404i
$123$	7.03564e6	+	1.48367e7i	0.340907	+	0.718900i
$124$	2.72005e6			0.128115
$125$		−	8.40370e6i		−	0.384844i
$126$	−749286.	−	612384.i	−0.0333696	−	0.0272726i
$127$		−	2.31414e7i		−	1.00248i	−0.865308	−	0.501240i	$-0.832877\pi$
$127$		−	2.31414e7i		−	1.00248i	0.865308	−	0.501240i	$-0.167123\pi$
$128$	1.47750e7			0.622718
$129$	2.26330e7	−	1.07327e7i	0.928279	−	0.440196i
$130$	−5.58560e7			−2.22981
$131$	−9.34470e6			−0.363175			−0.181587	−	0.983375i	$-0.558124\pi$
$131$	−9.34470e6			−0.363175			−0.181587	+	0.983375i	$0.558124\pi$
$132$	1.54896e6	+	4.80615e6i	0.0586182	+	0.181882i
$133$	29006.3			0.00106908
$134$	8.17507e6			0.293511
$135$	−1.03067e7	+	4.16843e7i	−0.360539	+	1.45816i
$136$	5.18095e7			1.76613
$137$		−	3.18024e7i		−	1.05666i	−0.849038	−	0.528332i	$-0.822817\pi$
$137$		−	3.18024e7i		−	1.05666i	0.849038	−	0.528332i	$-0.177183\pi$
$138$	−2.39184e7	+	1.13422e7i	−0.774739	+	0.367386i
$139$		−	3.39708e6i		−	0.107289i	−0.998560	−	0.0536443i	$-0.982916\pi$
$139$		−	3.39708e6i		−	0.107289i	0.998560	−	0.0536443i	$-0.0170837\pi$
$140$	446560.			0.0137541
$141$	−3.11165e7	+	1.47556e7i	−0.934811	+	0.443293i
$142$		−	2.39751e7i		−	0.702669i
$143$	−7.54069e6	+	5.72225e7i	−0.215643	+	1.63640i
$144$	1.75141e7	−	2.14295e7i	0.488786	−	0.598057i
$145$		−	3.91052e7i		−	1.06524i
$146$			2.30397e7i			0.612692i
$147$	−1.64640e7	−	3.47190e7i	−0.427488	−	0.901481i
$148$	−1.19229e7			−0.302319
$149$	3.47046e7			0.859477			0.429739	−	0.902953i	$-0.358606\pi$
$149$	3.47046e7			0.859477			0.429739	+	0.902953i	$0.358606\pi$
$150$	2.00102e7	+	4.21974e7i	0.484098	+	1.02086i
$151$		−	1.17103e7i		−	0.276790i	−0.990377	−	0.138395i	$-0.955806\pi$
$151$		−	1.17103e7i		−	0.276790i	0.990377	−	0.138395i	$-0.0441943\pi$
$152$			1.03482e6i			0.0239007i
$153$	4.62201e7	−	5.65529e7i	1.04330	−	1.27654i
$154$	−255195.	+	1.93655e6i	−0.00563053	+	0.0427273i
$155$		−	4.66879e7i		−	1.00703i
$156$	−1.35135e7	+	6.40818e6i	−0.284991	+	0.135145i
$157$	−6.19057e6			−0.127668			−0.0638339	−	0.997961i	$-0.520333\pi$
$157$	−6.19057e6			−0.127668			−0.0638339	+	0.997961i	$0.520333\pi$
$158$			2.54885e7i			0.514095i
$159$	4.80257e7	−	2.27741e7i	0.947510	−	0.449315i
$160$			2.93067e7i			0.565649i
$161$	2.41901e6			0.0456821
$162$	−9.68836e6	−	4.76948e7i	−0.179039	−	0.881391i
$163$	6.60700e6			0.119494			0.0597472	−	0.998214i	$-0.480971\pi$
$163$	6.60700e6			0.119494			0.0597472	+	0.998214i	$0.480971\pi$
$164$	8.58845e6			0.152041
$165$	8.24944e7	−	2.65870e7i	1.42965	−	0.460760i
$166$	2.42902e7			0.412147
$167$	−7.30755e7			−1.21413			−0.607064	−	0.794653i	$-0.707653\pi$
$167$	−7.30755e7			−1.21413			−0.607064	+	0.794653i	$0.707653\pi$
$168$	−2.85054e6	+	1.35174e6i	−0.0463815	+	0.0219944i
$169$	−1.08199e8			−1.72432
$170$		−	1.42672e8i		−	2.22724i
$171$	1.12956e6	+	923179.i	0.0172752	+	0.0141189i
$172$		−	1.31015e7i		−	0.196323i
$173$	−9.59488e7			−1.40889			−0.704447	−	0.709757i	$-0.748805\pi$
$173$	−9.59488e7			−1.40889			−0.704447	+	0.709757i	$0.748805\pi$
$174$	1.89911e7	+	4.00482e7i	0.273292	+	0.576315i
$175$		−	4.26766e6i		−	0.0601945i
$176$	−5.53850e7	−	7.29854e6i	−0.765768	−	0.100912i
$177$	6.12676e7	−	2.90535e7i	0.830471	−	0.393814i
$178$			4.77974e7i			0.635234i
$179$			7.33801e7i			0.956297i	0.878279	+	0.478148i	$0.158692\pi$
$179$			7.33801e7i			0.956297i	−0.878279	+	0.478148i	$0.841308\pi$
$180$	1.73899e7	+	1.42126e7i	0.222251	+	0.181644i
$181$	9.22345e7			1.15616			0.578080	−	0.815980i	$-0.303802\pi$
$181$	9.22345e7			1.15616			0.578080	+	0.815980i	$0.303802\pi$
$182$	−5.78526e6			−0.0711333
$183$	1.52754e7	−	7.24371e6i	0.184253	−	0.0873740i
$184$			8.62996e7i			1.02128i
$185$			2.04649e8i			2.37634i
$186$	2.26736e7	+	4.78137e7i	0.258360	+	0.544825i
$187$	−1.46162e8	−	1.92610e7i	−1.63452	−	0.215394i
$188$			1.80123e7i			0.197705i
$189$	−1.06751e6	+	4.31743e6i	−0.0115016	+	0.0465168i
$190$	2.84966e6			0.0301408
$191$		−	8.80213e7i		−	0.914052i	−0.889453	−	0.457026i	$-0.848915\pi$
$191$		−	8.80213e7i		−	0.914052i	0.889453	−	0.457026i	$-0.151085\pi$
$192$	−4.66898e7	−	9.84589e7i	−0.476067	−	1.00392i
$193$			1.41386e8i			1.41565i	0.706389	+	0.707824i	$0.250323\pi$
$193$			1.41386e8i			1.41565i	−0.706389	+	0.707824i	$0.749677\pi$
$194$	−1.21579e7			−0.119551
$195$	1.09992e8	+	2.31950e8i	1.06228	+	2.24013i
$196$	−2.00977e7			−0.190655
$197$	−1.01091e8			−0.942063			−0.471032	−	0.882116i	$-0.656118\pi$
$197$	−1.01091e8			−0.942063			−0.471032	+	0.882116i	$0.656118\pi$
$198$	−7.15720e7	+	6.72908e7i	−0.655262	+	0.616066i
$199$	6.84186e7			0.615444			0.307722	−	0.951476i	$-0.400433\pi$
$199$	6.84186e7			0.615444			0.307722	+	0.951476i	$0.400433\pi$
$200$	1.52252e8			1.34573
$201$	−1.60984e7	−	3.39482e7i	−0.139829	−	0.294870i
$202$	9.25674e7			0.790184
$203$		−	4.05030e6i		−	0.0339822i
$204$	−1.63683e7	−	3.45172e7i	−0.134989	−	0.284663i
$205$		−	1.47415e8i		−	1.19510i
$206$	−5.15206e7			−0.410625
$207$	9.42007e7	+	7.69894e7i	0.738173	+	0.603302i
$208$		−	1.65458e8i		−	1.27487i
$209$	384711.	−	2.91937e6i	0.00291489	−	0.0221196i
$210$	3.72240e6	+	7.84975e6i	0.0277367	+	0.0584909i
$211$			1.09648e8i			0.803550i	0.915738	+	0.401775i	$0.131607\pi$
$211$			1.09648e8i			0.803550i	−0.915738	+	0.401775i	$0.868393\pi$
$212$		−	2.78005e7i		−	0.200390i
$213$	−9.95600e7	+	4.72120e7i	−0.705921	+	0.334752i
$214$	−1.09464e7			−0.0763526
$215$	−2.24879e8			−1.54317
$216$	−1.54027e8	−	3.80843e7i	−1.03994	−	0.257133i
$217$		−	4.83568e6i		−	0.0321254i
$218$			2.37811e8i			1.55466i
$219$	9.56759e7	−	4.53701e7i	0.615528	−	0.291887i
$220$	5.92274e6	−	4.49447e7i	0.0375010	−	0.284576i
$221$		−	4.36647e8i		−	2.72118i
$222$	−9.93858e7	−	2.09584e8i	−0.609662	−	1.28565i
$223$	−1.15499e8			−0.697450			−0.348725	−	0.937225i	$-0.613385\pi$
$223$	−1.15499e8			−0.697450			−0.348725	+	0.937225i	$0.613385\pi$
$224$			3.03543e6i			0.0180448i
$225$	1.35826e8	−	1.66191e8i	0.794960	−	0.972677i
$226$		−	6.06627e7i		−	0.349577i
$227$	2.18987e8			1.24259			0.621295	−	0.783577i	$-0.286607\pi$
$227$	2.18987e8			1.24259			0.621295	+	0.783577i	$0.286607\pi$
$228$	689430.	−	326932.i	0.00385229	−	0.00182678i
$229$	−1.76352e7			−0.0970414			−0.0485207	−	0.998822i	$-0.515451\pi$
$229$	−1.76352e7			−0.0970414			−0.0485207	+	0.998822i	$0.515451\pi$
$230$	2.37650e8			1.28792
$231$	8.54433e6	−	2.75373e6i	0.0456075	−	0.0146987i
$232$	1.44497e8			0.759717
$233$	2.70653e8			1.40174			0.700869	−	0.713290i	$-0.252796\pi$
$233$	2.70653e8			1.40174			0.700869	+	0.713290i	$0.252796\pi$
$234$	−2.25289e8	−	1.84127e8i	−1.14944	−	0.939423i
$235$	3.09169e8			1.55403
$236$		−	3.54657e7i		−	0.175637i
$237$	1.05845e8	−	5.01922e7i	0.516475	−	0.244916i
$238$		−	1.47772e7i		−	0.0710513i
$239$	−3.02503e8			−1.43330			−0.716650	−	0.697433i	$-0.754326\pi$
$239$	−3.02503e8			−1.43330			−0.716650	+	0.697433i	$0.754326\pi$
$240$	−2.24502e8	+	1.06460e8i	−1.04829	+	0.497104i
$241$			1.28674e8i			0.592148i	0.955165	+	0.296074i	$0.0956775\pi$
$241$			1.28674e8i			0.592148i	−0.955165	+	0.296074i	$0.904323\pi$
$242$	1.91522e8	+	5.13689e7i	0.868688	+	0.232995i
$243$	−1.78981e8	+	1.34154e8i	−0.800177	+	0.599764i
$244$		−	8.84244e6i		−	0.0389680i
$245$			3.44963e8i			1.49862i
$246$	7.15908e7	+	1.50970e8i	0.306609	+	0.646573i
$247$	8.72137e6			0.0368252
$248$	1.72516e8			0.718205
$249$	−4.78325e7	−	1.00868e8i	−0.196347	−	0.414055i
$250$		−	8.55114e7i		−	0.346126i
$251$		−	4.23148e7i		−	0.168902i	−0.996428	−	0.0844509i	$-0.973086\pi$
$251$		−	4.23148e7i		−	0.168902i	0.996428	−	0.0844509i	$-0.0269136\pi$
$252$	1.80115e6	+	1.47207e6i	0.00709005	+	0.00579463i
$253$	3.20833e7	−	2.43464e8i	0.124554	−	0.945177i
$254$		−	2.35474e8i		−	0.901623i
$255$	−5.92466e8	+	2.80951e8i	−2.23755	+	1.06106i
$256$	−1.47912e8			−0.551015
$257$			9.23038e7i			0.339198i	0.985513	+	0.169599i	$0.0542473\pi$
$257$			9.23038e7i			0.339198i	−0.985513	+	0.169599i	$0.945753\pi$
$258$	2.30301e8	−	1.09210e8i	0.834887	−	0.395909i
$259$			2.11964e7i			0.0758076i
$260$	1.34268e8			0.473769
$261$	1.28908e8	−	1.57727e8i	0.448786	−	0.549115i
$262$	−9.50866e7			−0.326636
$263$	−1.99628e8			−0.676669			−0.338334	−	0.941026i	$-0.609863\pi$
$263$	−1.99628e8			−0.676669			−0.338334	+	0.941026i	$0.609863\pi$
$264$	9.82413e7	+	3.04825e8i	0.328610	+	1.01961i
$265$	−4.77177e8			−1.57514
$266$	295152.			0.000961524
$267$	1.98486e8	−	9.41231e7i	0.638175	−	0.302626i
$268$	−1.96515e7			−0.0623625
$269$			6.14700e7i			0.192544i	0.995355	+	0.0962721i	$0.0306919\pi$
$269$			6.14700e7i			0.192544i	−0.995355	+	0.0962721i	$0.969308\pi$
$270$	−1.04876e8	+	4.24157e8i	−0.324266	+	1.31145i
$271$			5.33082e8i			1.62705i	0.581527	+	0.813527i	$0.302455\pi$
$271$			5.33082e8i			1.62705i	−0.581527	+	0.813527i	$0.697545\pi$
$272$	4.22625e8			1.27340
$273$	1.13924e7	+	2.40241e7i	0.0338880	+	0.0714626i
$274$		−	3.23604e8i		−	0.950356i
$275$	−4.29525e8	−	5.66021e7i	−1.24544	−	0.164122i
$276$	5.74957e7	−	2.72648e7i	0.164609	−	0.0780586i
$277$		−	1.98315e8i		−	0.560631i	−0.959908	−	0.280315i	$-0.909561\pi$
$277$		−	1.98315e8i		−	0.560631i	0.959908	−	0.280315i	$-0.0904391\pi$
$278$		−	3.45668e7i		−	0.0964945i
$279$	1.53905e8	−	1.88311e8i	0.424264	−	0.519111i
$280$	2.83226e7			0.0771045
$281$	2.28811e8			0.615183			0.307591	−	0.951519i	$-0.400477\pi$
$281$	2.28811e8			0.615183			0.307591	+	0.951519i	$0.400477\pi$
$282$	−3.16625e8	+	1.50145e8i	−0.840762	+	0.398694i
$283$			2.82492e8i			0.740889i	0.928855	+	0.370445i	$0.120795\pi$
$283$			2.82492e8i			0.740889i	−0.928855	+	0.370445i	$0.879205\pi$
$284$			5.76319e7i			0.149296i
$285$	−5.61158e6	−	1.18336e7i	−0.0143591	−	0.0302803i
$286$	−7.67300e7	+	5.82265e8i	−0.193947	+	1.47177i
$287$		−	1.52685e7i		−	0.0381249i
$288$	−9.66083e7	+	1.18206e8i	−0.238309	+	0.291584i
$289$	7.04979e8			1.71804
$290$		−	3.97913e8i		−	0.958066i
$291$	2.39416e7	+	5.04877e7i	0.0569544	+	0.120105i
$292$		−	5.53835e7i		−	0.130179i
$293$	7.68838e7			0.178566			0.0892829	−	0.996006i	$-0.471542\pi$
$293$	7.68838e7			0.178566			0.0892829	+	0.996006i	$0.471542\pi$
$294$	−1.67528e8	−	3.53282e8i	−0.384479	−	0.810784i
$295$	−6.08746e8			−1.38057
$296$	−7.56196e8			−1.69478
$297$	4.20375e8	+	1.64703e8i	0.931086	+	0.364800i
$298$	3.53135e8			0.773007
$299$	7.27327e8			1.57355
$300$	−4.81012e7	−	1.01435e8i	−0.102856	−	0.216902i
$301$	−2.32917e7			−0.0492287
$302$		−	1.19158e8i		−	0.248943i
$303$	−1.82285e8	−	3.84400e8i	−0.376445	−	0.793842i
$304$			8.44131e6i			0.0172327i
$305$	−1.51775e8			−0.306302
$306$	4.70311e8	−	5.75451e8i	0.938340	−	1.14811i
$307$			9.53334e8i			1.88044i	0.340561	+	0.940222i	$0.389383\pi$
$307$			9.53334e8i			1.88044i	−0.340561	+	0.940222i	$0.610617\pi$
$308$	613445.	−	4.65512e6i	0.00119632	−	0.00907829i
$309$	1.01455e8	+	2.13947e8i	0.195622	+	0.412526i
$310$		−	4.75071e8i		−	0.905716i
$311$			5.74036e8i			1.08213i	0.840982	+	0.541063i	$0.181978\pi$
$311$			5.74036e8i			1.08213i	−0.840982	+	0.541063i	$0.818022\pi$
$312$	−8.57077e8	+	4.06431e8i	−1.59764	+	0.757611i
$313$	−4.19142e8			−0.772602			−0.386301	−	0.922373i	$-0.626247\pi$
$313$	−4.19142e8			−0.772602			−0.386301	+	0.922373i	$0.626247\pi$
$314$	−6.29918e7			−0.114823
$315$	2.52671e7	−	3.09156e7i	0.0455478	−	0.0557303i
$316$		−	6.12699e7i		−	0.109230i
$317$		−	7.30945e8i		−	1.28878i	−0.764699	−	0.644388i	$-0.777112\pi$
$317$		−	7.30945e8i		−	1.28878i	0.764699	−	0.644388i	$-0.222888\pi$
$318$	4.88683e8	−	2.31737e8i	0.852183	−	0.404110i
$319$	−4.07648e8	−	5.37192e7i	−0.703102	−	0.0926536i
$320$			9.78275e8i			1.66892i
$321$	2.15558e7	+	4.54566e7i	0.0363745	+	0.0767060i
$322$	2.46145e7			0.0410861
$323$			2.22768e7i			0.0367828i
$324$	2.32892e7	+	1.14650e8i	0.0380405	+	0.187270i
$325$		−	1.28317e9i		−	2.07344i
$326$	6.72293e7			0.107472
$327$	9.87546e8	−	4.68300e8i	1.56185	−	0.740640i
$328$	5.44712e8			0.852332
$329$	3.20221e7			0.0495752
$330$	8.39419e8	−	2.70535e8i	1.28582	−	0.414404i
$331$	8.53690e8			1.29390			0.646952	−	0.762531i	$-0.276043\pi$
$331$	8.53690e8			1.29390			0.646952	+	0.762531i	$0.276043\pi$
$332$	−5.83894e7			−0.0875690
$333$	−6.74615e8	+	8.25429e8i	−1.00115	+	1.22497i
$334$	−7.43577e8			−1.09198
$335$			3.37305e8i			0.490191i
$336$	−2.32527e7	+	1.10266e7i	−0.0334415	+	0.0158582i
$337$		−	1.16107e9i		−	1.65255i	−0.563267	−	0.826275i	$-0.690456\pi$
$337$		−	1.16107e9i		−	1.65255i	0.563267	−	0.826275i	$-0.309544\pi$
$338$	−1.10097e9			−1.55084
$339$	−2.51911e8	+	1.19458e8i	−0.351195	+	0.166539i
$340$			3.42958e8i			0.473222i
$341$	−4.86693e8	−	6.41357e7i	−0.664684	−	0.0875910i
$342$	1.14938e7	+	9.39377e6i	0.0155372	+	0.0126984i
$343$			7.15411e7i			0.0957251i
$344$		−	8.30947e8i		−	1.10057i
$345$	−4.67983e8	−	9.86876e8i	−0.613569	−	1.29389i
$346$	−9.76323e8			−1.26715
$347$	3.90757e8			0.502058			0.251029	−	0.967980i	$-0.419231\pi$
$347$	3.90757e8			0.502058			0.251029	+	0.967980i	$0.419231\pi$
$348$	−4.56513e7	−	9.62689e7i	−0.0580665	−	0.122450i
$349$		−	1.15476e9i		−	1.45413i	−0.686567	−	0.727067i	$-0.740883\pi$
$349$		−	1.15476e9i		−	1.45413i	0.686567	−	0.727067i	$-0.259117\pi$
$350$		−	4.34254e7i		−	0.0541385i
$351$	−3.20971e8	+	1.29813e9i	−0.396179	+	1.60230i
$352$	3.05505e8	+	4.02590e7i	0.373352	+	0.0491998i
$353$			3.75350e8i			0.454177i	0.973874	+	0.227089i	$0.0729207\pi$
$353$			3.75350e8i			0.454177i	−0.973874	+	0.227089i	$0.927079\pi$
$354$	6.23426e8	−	2.95632e8i	0.746919	−	0.354193i
$355$	9.89215e8			1.17352
$356$		−	1.14897e8i		−	0.134968i
$357$	−6.13644e7	+	2.90994e7i	−0.0713802	+	0.0338489i
$358$			7.46676e8i			0.860086i
$359$	1.52942e8			0.174460			0.0872300	−	0.996188i	$-0.472199\pi$
$359$	1.52942e8			0.174460			0.0872300	+	0.996188i	$0.472199\pi$
$360$	1.10294e9	+	9.01419e8i	1.24592	+	1.01828i
$361$	8.93427e8			0.999502
$362$	9.38528e8			1.03984
$363$	−1.63830e8	−	8.96478e8i	−0.179771	−	0.983709i
$364$	1.39068e7			0.0151137
$365$	−9.50622e8			−1.02325
$366$	1.55435e8	−	7.37081e7i	0.165716	−	0.0785835i
$367$	1.40250e9			1.48106			0.740530	−	0.672023i	$-0.234574\pi$
$367$	1.40250e9			1.48106			0.740530	+	0.672023i	$0.234574\pi$
$368$			7.03971e8i			0.736355i
$369$	4.85947e8	−	5.94583e8i	0.503497	−	0.616056i
$370$			2.08239e9i			2.13726i
$371$	−4.94234e7			−0.0502486
$372$	−5.45034e7	−	1.14936e8i	−0.0548938	−	0.115759i
$373$		−	5.52640e8i		−	0.551393i	−0.961245	−	0.275696i	$-0.911092\pi$
$373$		−	5.52640e8i		−	0.551393i	0.961245	−	0.275696i	$-0.0889084\pi$
$374$	−1.48727e9	−	1.95990e8i	−1.47007	−	0.193724i
$375$	−3.55099e8	+	1.68390e8i	−0.347728	+	0.164895i
$376$			1.14241e9i			1.10832i
$377$		−	1.21781e9i		−	1.17054i
$378$	−1.08624e7	+	4.39319e7i	−0.0103444	+	0.0418368i
$379$	−1.25619e9			−1.18528			−0.592638	−	0.805469i	$-0.701914\pi$
$379$	−1.25619e9			−1.18528			−0.592638	+	0.805469i	$0.701914\pi$
$380$	−6.85009e6			−0.00640403
$381$	−9.77841e8	+	4.63698e8i	−0.905796	+	0.429534i
$382$		−	8.95657e8i		−	0.822091i
$383$		−	1.98068e9i		−	1.80144i	−0.434401	−	0.900719i	$-0.643040\pi$
$383$		−	1.98068e9i		−	1.80144i	0.434401	−	0.900719i	$-0.356960\pi$
$384$	−2.96055e8	−	6.24317e8i	−0.266817	−	0.562660i
$385$	−7.99022e7	−	1.05294e7i	−0.0713586	−	0.00940352i
$386$			1.43867e9i			1.27322i
$387$	−9.07024e8	−	7.41302e8i	−0.795482	−	0.650140i
$388$	2.92256e7			0.0254011
$389$			1.54614e9i			1.33176i	0.746061	+	0.665878i	$0.231943\pi$
$389$			1.54614e9i			1.33176i	−0.746061	+	0.665878i	$0.768057\pi$
$390$	1.11922e9	+	2.36020e9i	0.955410	+	2.01476i
$391$			1.85780e9i			1.57174i
$392$	−1.27467e9			−1.06880
$393$	1.87246e8	+	3.94861e8i	0.155610	+	0.328148i
$394$	−1.02865e9			−0.847284
$395$	−1.05166e9			−0.858587
$396$	1.72047e8	−	1.61756e8i	0.139224	−	0.130896i
$397$	−1.86958e9			−1.49961			−0.749803	−	0.661661i	$-0.769852\pi$
$397$	−1.86958e9			−1.49961			−0.749803	+	0.661661i	$0.769852\pi$
$398$	6.96191e8			0.553526
$399$	−581217.	−	1.22566e6i	−0.000458071	−	0.000965975i
$400$	1.24196e9			0.970282
$401$			6.95968e8i			0.538994i	0.963001	+	0.269497i	$0.0868574\pi$
$401$			6.95968e8i			0.538994i	−0.963001	+	0.269497i	$0.913143\pi$
$402$	−1.63809e8	−	3.45438e8i	−0.125761	−	0.265204i
$403$		−	1.45395e9i		−	1.10658i
$404$	−2.22516e8			−0.167891
$405$	1.96790e9	−	3.99743e8i	1.47201	−	0.299012i
$406$		−	4.12137e7i		−	0.0305633i
$407$	2.13334e9	+	2.81128e8i	1.56848	+	0.206692i
$408$	−1.03814e9	−	2.18922e9i	−0.756737	−	1.59580i
$409$			2.01563e9i			1.45673i	0.685190	+	0.728364i	$0.259719\pi$
$409$			2.01563e9i			1.45673i	−0.685190	+	0.728364i	$0.740281\pi$
$410$		−	1.50002e9i		−	1.07486i
$411$	−1.34381e9	+	6.37244e8i	−0.954755	+	0.452751i
$412$	1.23847e8			0.0872457
$413$	−6.30506e7			−0.0440417
$414$	9.58536e8	+	7.83402e8i	0.663907	+	0.542605i
$415$			1.00222e9i			0.688324i
$416$			9.12669e8i			0.621565i
$417$	−1.43544e8	+	6.80694e7i	−0.0969412	+	0.0459701i
$418$	3.91461e6	−	2.97060e7i	0.00262163	−	0.0198942i
$419$			8.99916e8i			0.597658i	0.954307	+	0.298829i	$0.0965961\pi$
$419$			8.99916e8i			0.597658i	−0.954307	+	0.298829i	$0.903404\pi$
$420$	−8.94801e6	−	1.88695e7i	−0.00589324	−	0.0124276i
$421$	−3.37910e8			−0.220706			−0.110353	−	0.993892i	$-0.535198\pi$
$421$	−3.37910e8			−0.220706			−0.110353	+	0.993892i	$0.535198\pi$
$422$			1.11572e9i			0.722706i
$423$	1.24700e9	+	1.01916e9i	0.801080	+	0.654715i
$424$		−	1.76321e9i		−	1.12337i
$425$	3.27757e9			2.07105
$426$	−1.01307e9	+	4.80403e8i	−0.634900	+	0.301073i
$427$	−1.57200e7			−0.00977136
$428$	2.63133e7			0.0162227
$429$	2.56904e9	−	8.27970e8i	1.57098	−	0.506307i
$430$	−2.28824e9			−1.38791
$431$	6.51513e8			0.391970			0.195985	−	0.980607i	$-0.437210\pi$
$431$	6.51513e8			0.391970			0.195985	+	0.980607i	$0.437210\pi$
$432$	−1.25645e9	−	3.10664e8i	−0.749809	−	0.185395i
$433$	1.98562e9			1.17540			0.587702	−	0.809077i	$-0.300033\pi$
$433$	1.98562e9			1.17540			0.587702	+	0.809077i	$0.300033\pi$
$434$		−	4.92052e7i		−	0.0288933i
$435$	−1.65239e9	+	7.83575e8i	−0.962501	+	0.456424i
$436$		−	5.71657e8i		−	0.330319i
$437$	−3.71067e7			−0.0212700
$438$	9.73546e8	−	4.61661e8i	0.553601	−	0.262521i
$439$		−	1.28056e9i		−	0.722392i	−0.932490	−	0.361196i	$-0.882369\pi$
$439$		−	1.28056e9i		−	0.722392i	0.932490	−	0.361196i	$-0.117631\pi$
$440$	3.75643e8	−	2.85056e9i	0.210228	−	1.59531i
$441$	−1.13716e9	+	1.39137e9i	−0.631371	+	0.772518i
$442$		−	4.44308e9i		−	2.44741i
$443$		−	2.54447e9i		−	1.39054i	−0.718748	−	0.695271i	$-0.755284\pi$
$443$		−	2.54447e9i		−	1.39054i	0.718748	−	0.695271i	$-0.244716\pi$
$444$	2.38907e8	+	5.03803e8i	0.129535	+	0.273162i
$445$	−1.97213e9			−1.06090
$446$	−1.17526e9			−0.627281
$447$	−6.95397e8	−	1.46644e9i	−0.368262	−	0.776585i
$448$			1.01324e8i			0.0532404i
$449$		−	1.83957e9i		−	0.959079i	−0.877520	−	0.479540i	$-0.840804\pi$
$449$		−	1.83957e9i		−	0.959079i	0.877520	−	0.479540i	$-0.159196\pi$
$450$	1.38210e9	−	1.69107e9i	0.714981	−	0.874818i
$451$	−1.53671e9	−	2.02506e8i	−0.788815	−	0.103949i
$452$			1.45823e8i			0.0742747i
$453$	−4.94822e8	+	2.34648e8i	−0.250095	+	0.118597i
$454$	2.22829e9			1.11758
$455$		−	2.38701e8i		−	0.118799i
$456$	4.37263e7	−	2.07353e7i	0.0215956	−	0.0102408i
$457$			3.80384e8i			0.186430i	0.995646	+	0.0932150i	$0.0297144\pi$
$457$			3.80384e8i			0.186430i	−0.995646	+	0.0932150i	$0.970286\pi$
$458$	−1.79447e8			−0.0872782
$459$	−3.31579e9	−	8.19851e8i	−1.60045	−	0.395722i
$460$	−5.71270e8			−0.273646
$461$	6.06432e8			0.288289			0.144145	−	0.989557i	$-0.453957\pi$
$461$	6.06432e8			0.288289			0.144145	+	0.989557i	$0.453957\pi$
$462$	8.69425e7	−	2.80205e7i	0.0410190	−	0.0132199i
$463$	2.20208e9			1.03110			0.515548	−	0.856861i	$-0.327588\pi$
$463$	2.20208e9			1.03110			0.515548	+	0.856861i	$0.327588\pi$
$464$	1.17871e9			0.547763
$465$	−1.97280e9	+	9.35515e8i	−0.909909	+	0.431484i
$466$	2.75402e9			1.26071
$467$			3.42410e9i			1.55574i	0.628425	+	0.777870i	$0.283700\pi$
$467$			3.42410e9i			1.55574i	−0.628425	+	0.777870i	$0.716300\pi$
$468$	5.41556e8	+	4.42609e8i	0.244221	+	0.199600i
$469$			3.49362e7i			0.0156376i
$470$	3.14594e9			1.39768
$471$	1.24044e8	+	2.61583e8i	0.0547020	+	0.115355i
$472$		−	2.24937e9i		−	0.984611i
$473$	−3.08918e8	+	2.34423e9i	−0.134224	+	1.01856i
$474$	1.07702e9	−	5.10728e8i	0.464514	−	0.220275i
$475$			6.54645e7i			0.0280271i
$476$			3.55218e7i			0.0150963i
$477$	−1.92464e9	−	1.57299e9i	−0.811962	−	0.663609i
$478$	−3.07811e9			−1.28910
$479$	3.33647e9			1.38712			0.693559	−	0.720400i	$-0.256042\pi$
$479$	3.33647e9			1.38712			0.693559	+	0.720400i	$0.256042\pi$
$480$	1.23836e9	−	5.87237e8i	0.511095	−	0.242365i
$481$			6.37316e9i			2.61124i
$482$			1.30931e9i			0.532573i
$483$	−4.84711e7	−	1.02215e8i	−0.0195735	−	0.0412763i
$484$	−4.60385e8	−	1.23482e8i	−0.184571	−	0.0495045i
$485$		−	5.01639e8i		−	0.199662i
$486$	−1.82122e9	+	1.36507e9i	−0.719673	+	0.539423i
$487$	−1.60319e9			−0.628977			−0.314489	−	0.949261i	$-0.601833\pi$
$487$	−1.60319e9			−0.628977			−0.314489	+	0.949261i	$0.601833\pi$
$488$		−	5.60822e8i		−	0.218452i
$489$	−1.32389e8	−	2.79179e8i	−0.0512000	−	0.107970i
$490$			3.51016e9i			1.34785i
$491$	−3.30925e9			−1.26167			−0.630833	−	0.775919i	$-0.717287\pi$
$491$	−3.30925e9			−1.26167			−0.630833	+	0.775919i	$0.717287\pi$
$492$	−1.72092e8	−	3.62906e8i	−0.0651453	−	0.137378i
$493$	3.11063e9			1.16919
$494$	8.87439e7			0.0331203
$495$	−2.77643e9	−	2.95307e9i	−1.02889	−	1.09435i
$496$	1.40726e9			0.517833
$497$	1.02458e8			0.0374366
$498$	−4.86717e8	−	1.02638e9i	−0.176593	−	0.372398i
$499$	−1.20716e9			−0.434923			−0.217461	−	0.976069i	$-0.569778\pi$
$499$	−1.20716e9			−0.434923			−0.217461	+	0.976069i	$0.569778\pi$
$500$			2.05555e8i			0.0735415i
$501$	1.46426e9	+	3.08781e9i	0.520219	+	1.09703i
$502$		−	4.30572e8i		−	0.151909i
$503$	−1.44191e9			−0.505184			−0.252592	−	0.967573i	$-0.581283\pi$
$503$	−1.44191e9			−0.505184			−0.252592	+	0.967573i	$0.581283\pi$
$504$	1.14236e8	+	9.33641e7i	0.0397463	+	0.0324843i
$505$			3.81935e9i			1.31968i
$506$	3.26462e8	−	2.47736e9i	0.112023	−	0.850084i
$507$	2.16804e9	+	4.57194e9i	0.738822	+	1.55802i
$508$			5.66039e8i			0.191568i
$509$			3.03795e9i			1.02110i	0.859848	+	0.510549i	$0.170558\pi$
$509$			3.03795e9i			1.02110i	−0.859848	+	0.510549i	$0.829442\pi$
$510$	−6.02861e9	+	2.85880e9i	−2.01243	+	0.954308i
$511$	−9.84603e7			−0.0326429
$512$	−3.39627e9			−1.11830
$513$	1.63753e7	−	6.62280e7i	0.00535524	−	0.0216586i
$514$			9.39233e8i			0.305072i
$515$		−	2.12575e9i		−	0.685783i
$516$	−5.53605e8	+	2.62523e8i	−0.177389	+	0.0841189i
$517$	4.24709e8	−	3.22291e9i	0.135168	−	1.02572i
$518$			2.15683e8i			0.0681808i
$519$	1.92259e9	+	4.05433e9i	0.603671	+	1.27301i
$520$	8.51580e9			2.65591
$521$		−	1.53227e9i		−	0.474681i	−0.971426	−	0.237341i	$-0.923724\pi$
$521$		−	1.53227e9i		−	0.474681i	0.971426	−	0.237341i	$-0.0762757\pi$
$522$	1.31170e9	−	1.60494e9i	0.403635	−	0.493870i
$523$		−	4.63092e9i		−	1.41550i	−0.706461	−	0.707752i	$-0.749709\pi$
$523$		−	4.63092e9i		−	1.41550i	0.706461	−	0.707752i	$-0.250291\pi$
$524$	2.28572e8			0.0694006
$525$	−1.80331e8	+	8.55139e7i	−0.0543891	+	0.0257916i
$526$	−2.03131e9			−0.608590
$527$	3.71380e9			1.10530
$528$	8.01383e8	+	2.48654e9i	0.236931	+	0.735152i
$529$	3.10274e8			0.0911276
$530$	−4.85549e9			−1.41667
$531$	−2.45531e9	−	2.00670e9i	−0.711666	−	0.581638i
$532$	−709495.			−0.000204295
$533$		−	4.59080e9i		−	1.31324i
$534$	2.01968e9	−	9.57746e8i	0.573969	−	0.272180i
$535$		−	4.51651e8i		−	0.127516i
$536$	−1.24637e9			−0.349600
$537$	3.10068e9	−	1.47036e9i	0.864067	−	0.409746i
$538$			6.25486e8i			0.173173i
$539$	3.59603e9	+	4.73880e8i	0.989152	+	0.130349i
$540$	2.52103e8	−	1.01960e9i	0.0688969	−	0.278645i
$541$			3.36982e9i			0.914991i	0.889212	+	0.457496i	$0.151253\pi$
$541$			3.36982e9i			0.914991i	−0.889212	+	0.457496i	$0.848747\pi$
$542$			5.42436e9i			1.46336i
$543$	−1.84816e9	−	3.89738e9i	−0.495382	−	1.04466i
$544$	−2.33121e9			−0.620848
$545$	−9.81212e9			−2.59642
$546$	1.15923e8	+	2.44457e8i	0.0304786	+	0.0642729i
$547$		−	5.87543e9i		−	1.53491i	−0.641101	−	0.767457i	$-0.721522\pi$
$547$		−	5.87543e9i		−	1.53491i	0.641101	−	0.767457i	$-0.278478\pi$
$548$			7.77887e8i			0.201923i
$549$	−6.12167e8	−	5.00319e8i	−0.157895	−	0.129046i
$550$	−4.37061e9	−	5.75952e8i	−1.12014	−	0.147610i
$551$			6.21303e7i			0.0158224i
$552$	3.64660e9	−	1.72924e9i	0.922787	−	0.437591i
$553$	−1.08925e8			−0.0273898
$554$		−	2.01795e9i		−	0.504227i
$555$	8.64745e9	−	4.10067e9i	2.14715	−	1.01819i
$556$			8.30927e7i			0.0205022i
$557$	2.74035e8			0.0671913			0.0335956	−	0.999436i	$-0.489304\pi$
$557$	2.74035e8			0.0671913			0.0335956	+	0.999436i	$0.489304\pi$
$558$	1.56605e9	−	1.91615e9i	0.381580	−	0.466884i
$559$	−7.00316e9			−1.69572
$560$	2.31035e8			0.0555931
$561$	2.11487e9	+	6.56204e9i	0.505724	+	1.56917i
$562$	2.32825e9			0.553290
$563$	−8.96945e8			−0.211829			−0.105915	−	0.994375i	$-0.533777\pi$
$563$	−8.96945e8			−0.211829			−0.105915	+	0.994375i	$0.533777\pi$
$564$	7.61112e8	−	3.60924e8i	0.178637	−	0.0847108i
$565$	2.50295e9			0.583826
$566$			2.87448e9i			0.666350i
$567$	2.03824e8	−	4.14032e7i	0.0469586	−	0.00953880i
$568$			3.65524e9i			0.836945i
$569$	2.19164e9			0.498743			0.249372	−	0.968408i	$-0.419776\pi$
$569$	2.19164e9			0.498743			0.249372	+	0.968408i	$0.419776\pi$
$570$	−5.71004e7	−	1.20413e8i	−0.0129145	−	0.0272339i
$571$		−	6.35050e9i		−	1.42752i	−0.700391	−	0.713759i	$-0.746991\pi$
$571$		−	6.35050e9i		−	1.42752i	0.700391	−	0.713759i	$-0.253009\pi$
$572$	1.84446e8	−	1.39967e9i	0.0412081	−	0.312707i
$573$	−3.71935e9	+	1.76374e9i	−0.825897	+	0.391645i
$574$		−	1.55364e8i		−	0.0342892i
$575$			5.45948e9i			1.19760i
$576$	−3.22484e9	+	3.94577e9i	−0.703120	+	0.860306i
$577$	−3.58606e9			−0.777144			−0.388572	−	0.921418i	$-0.627032\pi$
$577$	−3.58606e9			−0.777144			−0.388572	+	0.921418i	$0.627032\pi$
$578$	7.17348e9			1.54519
$579$	5.97427e9	−	2.83304e9i	1.27912	−	0.606565i
$580$			9.56515e8i			0.203561i
$581$			1.03804e8i			0.0219583i
$582$	2.43616e8	+	5.13735e8i	0.0512243	+	0.108021i
$583$	−6.55503e8	+	4.97428e9i	−0.137004	+	1.03966i
$584$		−	3.51264e9i		−	0.729774i
$585$	7.59709e9	−	9.29546e9i	1.56892	−	1.91967i
$586$	7.82328e8			0.160601
$587$		−	3.73609e9i		−	0.762402i	−0.924492	−	0.381201i	$-0.875511\pi$
$587$		−	3.73609e9i		−	0.762402i	0.924492	−	0.381201i	$-0.124489\pi$
$588$	4.02709e8	+	8.49228e8i	0.0816904	+	0.172268i
$589$			7.41777e7i			0.0149579i
$590$	−6.19427e9			−1.24168
$591$	2.02562e9	+	4.27160e9i	0.403647	+	0.851206i
$592$	−6.16851e9			−1.22195
$593$	−4.26979e9			−0.840843			−0.420422	−	0.907329i	$-0.638118\pi$
$593$	−4.26979e9			−0.840843			−0.420422	+	0.907329i	$0.638118\pi$
$594$	4.27751e9	+	1.67593e9i	0.837411	+	0.328098i
$595$	6.09708e8			0.118662
$596$	−8.48875e8			−0.164241
$597$	−1.37095e9	−	2.89104e9i	−0.263700	−	0.556088i
$598$	7.40089e9			1.41524
$599$		−	2.38915e9i		−	0.454203i	−0.973871	−	0.227101i	$-0.927075\pi$
$599$		−	2.38915e9i		−	0.454203i	0.973871	−	0.227101i	$-0.0729249\pi$
$600$	−3.05076e9	−	6.43341e9i	−0.576606	−	1.21594i
$601$			2.00116e9i			0.376029i	0.982166	+	0.188015i	$0.0602052\pi$
$601$			2.00116e9i			0.376029i	−0.982166	+	0.188015i	$0.939795\pi$
$602$	−2.37004e8			−0.0442759
$603$	−1.11191e9	+	1.36048e9i	−0.206518	+	0.252687i
$604$			2.86436e8i			0.0528930i
$605$	−2.11949e9	+	7.90221e9i	−0.389123	+	1.45079i
$606$	−1.85483e9	−	3.91145e9i	−0.338572	−	0.713975i
$607$		−	5.05497e9i		−	0.917398i	−0.888592	−	0.458699i	$-0.848316\pi$
$607$		−	5.05497e9i		−	0.917398i	0.888592	−	0.458699i	$-0.151684\pi$
$608$		−	4.65625e7i		−	0.00840183i
$609$	−1.71146e8	+	8.11585e7i	−0.0307048	+	0.0145604i
$610$	−1.54438e9			−0.275486
$611$	9.62814e9			1.70765
$612$	−1.13055e9	+	1.38329e9i	−0.199369	+	0.243940i
$613$		−	9.69280e9i		−	1.69956i	−0.527134	−	0.849782i	$-0.676734\pi$
$613$		−	9.69280e9i		−	1.69956i	0.527134	−	0.849782i	$-0.323266\pi$
$614$			9.70061e9i			1.69126i
$615$	−6.22904e9	+	2.95385e9i	−1.07984	+	0.512065i
$616$	3.89070e7	−	2.95246e8i	0.00670650	−	0.0508922i
$617$		−	9.99516e9i		−	1.71314i	−0.516034	−	0.856568i	$-0.672592\pi$
$617$		−	9.99516e9i		−	1.71314i	0.516034	−	0.856568i	$-0.327408\pi$
$618$	1.03235e9	+	2.17701e9i	0.175941	+	0.371023i
$619$	−3.56766e9			−0.604598			−0.302299	−	0.953213i	$-0.597754\pi$
$619$	−3.56766e9			−0.604598			−0.302299	+	0.953213i	$0.597754\pi$
$620$			1.14199e9i			0.192438i
$621$	1.36563e9	−	5.52315e9i	0.228830	−	0.925478i
$622$			5.84108e9i			0.973255i
$623$	−2.04262e8			−0.0338438
$624$	−6.99143e9	+	3.31538e9i	−1.15191	+	0.546244i
$625$	−4.13908e9			−0.678147
$626$	−4.26496e9			−0.694872
$627$	−1.31067e8	+	4.22414e7i	−0.0212353	+	0.00684387i
$628$	1.51422e8			0.0243966
$629$	−1.62788e10			−2.60823
$630$	2.57104e8	−	3.14581e8i	0.0409654	−	0.0501234i
$631$	1.16758e10			1.85005			0.925026	−	0.379904i	$-0.124043\pi$
$631$	1.16758e10			1.85005			0.925026	+	0.379904i	$0.124043\pi$
$632$		−	3.88597e9i		−	0.612336i
$633$	4.63319e9	−	2.19709e9i	0.726052	−	0.344298i
$634$		−	7.43770e9i		−	1.15911i
$635$	9.71569e9			1.50579
$636$	−1.17471e9	+	5.57055e8i	−0.181064	+	0.0858615i
$637$			1.07428e10i			1.64676i
$638$	−4.14801e9	−	5.46618e8i	−0.632364	−	0.0833319i
$639$	3.98989e9	+	3.26090e9i	0.604934	+	0.494407i
$640$			6.20313e9i			0.935365i
$641$			5.72931e9i			0.859210i	0.903017	+	0.429605i	$0.141347\pi$
$641$			5.72931e9i			0.859210i	−0.903017	+	0.429605i	$0.858653\pi$
$642$	2.19340e8	+	4.62542e8i	0.0327149	+	0.0689888i
$643$	5.96239e9			0.884468			0.442234	−	0.896900i	$-0.354186\pi$
$643$	5.96239e9			0.884468			0.442234	+	0.896900i	$0.354186\pi$
$644$	−5.91690e7			−0.00872959
$645$	4.50604e9	+	9.50227e9i	0.661204	+	1.39434i
$646$			2.26677e8i			0.0330821i
$647$		−	6.43364e9i		−	0.933882i	−0.884289	−	0.466941i	$-0.845356\pi$
$647$		−	6.43364e9i		−	0.933882i	0.884289	−	0.466941i	$-0.154644\pi$
$648$	1.47709e9	+	7.27156e9i	0.213252	+	1.04982i
$649$	−8.36241e8	+	6.34582e9i	−0.120081	+	0.911236i
$650$		−	1.30568e10i		−	1.86483i
$651$	−2.04332e8	+	9.68955e7i	−0.0290271	+	0.0137648i
$652$	−1.61608e8			−0.0228347
$653$			4.39211e9i			0.617273i	0.951180	+	0.308636i	$0.0998726\pi$
$653$			4.39211e9i			0.617273i	−0.951180	+	0.308636i	$0.900127\pi$
$654$	1.00487e10	−	4.76517e9i	1.40472	−	0.666126i
$655$		−	3.92329e9i		−	0.545513i
$656$	4.44338e9			0.614539
$657$	−3.83423e9	−	3.13368e9i	−0.527473	−	0.431098i
$658$	3.25839e8			0.0445875
$659$	9.06711e9			1.23416			0.617078	−	0.786902i	$-0.288316\pi$
$659$	9.06711e9			1.23416			0.617078	+	0.786902i	$0.288316\pi$
$660$	−2.01782e9	+	6.50319e8i	−0.273199	+	0.0880486i
$661$	−3.42062e9			−0.460681			−0.230340	−	0.973110i	$-0.573984\pi$
$661$	−3.42062e9			−0.460681			−0.230340	+	0.973110i	$0.573984\pi$
$662$	8.68668e9			1.16373
$663$	−1.84505e10	+	8.74936e9i	−2.45874	+	1.16595i
$664$	−3.70328e9			−0.490906
$665$			1.21780e7i			0.00160583i
$666$	−6.86452e9	+	8.39912e9i	−0.900431	+	1.10173i
$667$			5.18142e9i			0.676095i
$668$	1.78743e9			0.232013
$669$	2.31434e9	+	4.88044e9i	0.298837	+	0.630184i
$670$			3.43223e9i			0.440874i
$671$	−2.08495e8	+	1.58216e9i	−0.0266420	+	0.202172i
$672$	1.28262e8	−	6.08229e7i	0.0163045	−	0.00773169i
$673$		−	3.47247e9i		−	0.439122i	−0.975599	−	0.219561i	$-0.929537\pi$
$673$		−	3.47247e9i		−	0.439122i	0.975599	−	0.219561i	$-0.0704625\pi$
$674$		−	1.18144e10i		−	1.48629i
$675$	−9.74406e9	−	2.40928e9i	−1.21949	−	0.301526i
$676$	2.64654e9			0.329508
$677$	−4.61302e9			−0.571379			−0.285690	−	0.958322i	$-0.592223\pi$
$677$	−4.61302e9			−0.571379			−0.285690	+	0.958322i	$0.592223\pi$
$678$	−2.56331e9	+	1.21554e9i	−0.315862	+	0.149784i
$679$		−	5.19570e7i		−	0.00636942i
$680$			2.17517e10i			2.65285i
$681$	−4.38798e9	−	9.25332e9i	−0.532415	−	1.12275i
$682$	−4.95233e9	−	6.52610e8i	−0.597811	−	0.0787786i
$683$			1.31126e10i			1.57477i	0.616465	+	0.787383i	$0.288564\pi$
$683$			1.31126e10i			1.57477i	−0.616465	+	0.787383i	$0.711436\pi$
$684$	−2.76291e7	−	2.25810e7i	−0.00330119	−	0.00269803i
$685$	1.33519e10			1.58718
$686$			7.27963e8i			0.0860944i
$687$	3.53368e8	+	7.45178e8i	0.0415795	+	0.0876823i
$688$		−	6.77828e9i		−	0.793524i
$689$	−1.48602e10			−1.73084
$690$	−4.76194e9	−	1.00419e10i	−0.551839	−	1.16371i
$691$	7.67665e9			0.885113			0.442557	−	0.896741i	$-0.354072\pi$
$691$	7.67665e9			0.885113			0.442557	+	0.896741i	$0.354072\pi$
$692$	2.34691e9			0.269231
$693$	−2.87567e8	−	3.05863e8i	−0.0328226	−	0.0349109i
$694$	3.97614e9			0.451547
$695$	1.42623e9			0.161155
$696$	−2.89538e9	−	6.10575e9i	−0.325517	−	0.686446i
$697$	1.17262e10			1.31172
$698$		−	1.17503e10i		−	1.30784i
$699$	−5.42324e9	−	1.14365e10i	−0.600605	−	1.26655i
$700$			1.04387e8i			0.0115028i
$701$	3.37340e9			0.369874			0.184937	−	0.982750i	$-0.440792\pi$
$701$	3.37340e9			0.369874			0.184937	+	0.982750i	$0.440792\pi$
$702$	−3.26603e9	+	1.32091e10i	−0.356320	+	1.44109i
$703$		−	3.25146e8i		−	0.0352967i
$704$	1.01979e10	+	1.34387e9i	1.10156	+	0.145162i
$705$	−6.19502e9	−	1.30640e10i	−0.665857	−	1.40415i
$706$			3.81936e9i			0.408483i
$707$			3.95587e8i			0.0420993i
$708$	−1.49861e9	+	7.10649e8i	−0.158698	+	0.0752556i
$709$	−1.70961e10			−1.80151			−0.900754	−	0.434330i	$-0.856985\pi$
$709$	−1.70961e10			−1.80151			−0.900754	+	0.434330i	$0.856985\pi$
$710$	1.00657e10			1.05546
$711$	−4.24175e9	−	3.46674e9i	−0.442590	−	0.361724i
$712$		−	7.28719e9i		−	0.756624i
$713$			6.18612e9i			0.639153i
$714$	−6.24411e8	+	2.96099e8i	−0.0641988	+	0.0304434i
$715$	−2.40243e10	−	3.16589e9i	−2.45799	−	0.323910i
$716$		−	1.79488e9i		−	0.182743i
$717$	6.06145e9	+	1.27823e10i	0.614128	+	1.29507i
$718$	1.55625e9			0.156908
$719$		−	6.47538e9i		−	0.649702i	−0.945765	−	0.324851i	$-0.894686\pi$
$719$		−	6.47538e9i		−	0.649702i	0.945765	−	0.324851i	$-0.105314\pi$
$720$	8.99697e9	+	7.35314e9i	0.898323	+	0.734191i
$721$		−	2.20173e8i		−	0.0218772i
$722$	9.09103e9			0.898944
$723$	5.43712e9	−	2.57832e9i	0.535038	−	0.253718i
$724$	−2.25606e9			−0.220936
$725$	9.14117e9			0.890879
$726$	−1.66704e9	−	9.12207e9i	−0.161685	−	0.884739i
$727$	1.63870e10			1.58172			0.790861	−	0.611996i	$-0.209633\pi$
$727$	1.63870e10			1.58172			0.790861	+	0.611996i	$0.209633\pi$
$728$	8.82021e8			0.0847265
$729$	9.25504e9	+	4.87476e9i	0.884773	+	0.466022i
$730$	−9.67302e9			−0.920305
$731$		−	1.78880e10i		−	1.69376i
$732$	−3.73638e8	+	1.77182e8i	−0.0352097	+	0.0166967i
$733$			4.63181e8i			0.0434397i	0.999764	+	0.0217199i	$0.00691419\pi$
$733$			4.63181e8i			0.0434397i	−0.999764	+	0.0217199i	$0.993086\pi$
$734$	1.42711e10			1.33205
$735$	1.45765e10	−	6.91224e9i	1.35409	−	0.642116i
$736$		−	3.88312e9i		−	0.359012i
$737$	3.51620e9	+	4.63359e8i	0.323547	+	0.0426365i
$738$	4.94474e9	−	6.05016e9i	0.452841	−	0.554076i
$739$		−	9.26961e9i		−	0.844902i	−0.906386	−	0.422451i	$-0.861170\pi$
$739$		−	9.26961e9i		−	0.844902i	0.906386	−	0.422451i	$-0.138830\pi$
$740$		−	5.00572e9i		−	0.454104i
$741$	−1.74756e8	−	3.68522e8i	−0.0157786	−	0.0332736i
$742$	−5.02906e8			−0.0451932
$743$	−1.68716e10			−1.50902			−0.754509	−	0.656289i	$-0.772125\pi$
$743$	−1.68716e10			−1.50902			−0.754509	+	0.656289i	$0.772125\pi$
$744$	−3.45681e9	−	7.28968e9i	−0.307731	−	0.648938i
$745$			1.45704e10i			1.29099i
$746$		−	5.62336e9i		−	0.495918i
$747$	−3.30376e9	+	4.04233e9i	−0.289992	+	0.354821i
$748$	3.57514e9	+	4.71126e8i	0.312347	+	0.0411606i
$749$		−	4.67795e7i		−	0.00406789i
$750$	−3.61329e9	+	1.71345e9i	−0.312744	+	0.148305i
$751$	−8.52556e9			−0.734485			−0.367243	−	0.930125i	$-0.619698\pi$
$751$	−8.52556e9			−0.734485			−0.367243	+	0.930125i	$0.619698\pi$
$752$			9.31896e9i			0.799108i
$753$	−1.78802e9	+	8.47888e8i	−0.152612	+	0.0723696i
$754$		−	1.23918e10i		−	1.05277i
$755$	4.91648e9			0.415757
$756$	2.61114e7	−	1.05605e8i	0.00219788	−	0.00888908i
$757$	2.93575e9			0.245971			0.122985	−	0.992408i	$-0.460753\pi$
$757$	2.93575e9			0.245971			0.122985	+	0.992408i	$0.460753\pi$
$758$	−1.27824e10			−1.06603
$759$	−1.09305e10	+	3.52276e9i	−0.907387	+	0.292440i
$760$	−4.34459e8			−0.0359006
$761$	1.13618e10			0.934550			0.467275	−	0.884112i	$-0.345236\pi$
$761$	1.13618e10			0.934550			0.467275	+	0.884112i	$0.345236\pi$
$762$	−9.94998e9	+	4.71834e9i	−0.814666	+	0.386320i
$763$	−1.01629e9			−0.0828286
$764$			2.15301e9i			0.174670i
$765$	2.37432e10	+	1.94051e10i	1.91745	+	1.56712i
$766$		−	2.01544e10i		−	1.62020i
$767$	−1.89576e10			−1.51705
$768$	2.96380e9	+	6.25003e9i	0.236094	+	0.497872i
$769$		−	1.82751e9i		−	0.144917i	−0.997371	−	0.0724583i	$-0.976916\pi$
$769$		−	1.82751e9i		−	0.144917i	0.997371	−	0.0724583i	$-0.0230844\pi$
$770$	−8.13041e8	−	1.07141e8i	−0.0641793	−	0.00845745i
$771$	3.90031e9	−	1.84955e9i	0.306484	−	0.145337i
$772$		−	3.45831e9i		−	0.270522i
$773$			2.01967e9i			0.157272i	0.996903	+	0.0786360i	$0.0250565\pi$
$773$			2.01967e9i			0.157272i	−0.996903	+	0.0786360i	$0.974944\pi$
$774$	−9.22939e9	−	7.54309e9i	−0.715450	−	0.584731i
$775$	1.09137e10			0.842201
$776$	1.85360e9			0.142397
$777$	8.95656e8	−	4.24726e8i	0.0684964	−	0.0324814i
$778$			1.57327e10i			1.19777i
$779$			2.34213e8i			0.0177513i
$780$	−2.69042e9	−	5.67351e9i	−0.202996	−	0.428076i
$781$	1.35890e9	−	1.03120e10i	0.102072	−	0.774574i
$782$			1.89039e10i			1.41361i
$783$	−9.24778e9	−	2.28657e9i	−0.688448	−	0.170223i
$784$	−1.03979e10			−0.770615
$785$		−	2.59905e9i		−	0.191766i
$786$	1.90531e9	+	4.01789e9i	0.139954	+	0.295134i
$787$			2.11316e10i			1.54532i	0.634817	+	0.772662i	$0.281075\pi$
$787$			2.11316e10i			1.54532i	−0.634817	+	0.772662i	$0.718925\pi$
$788$	2.47269e9			0.180023
$789$	4.00007e9	+	8.43530e9i	0.289933	+	0.611408i
$790$	−1.07011e10			−0.772206
$791$	2.59242e8			0.0186247
$792$	1.09119e10	−	1.02592e10i	0.780479	−	0.733793i
$793$	−4.72656e9			−0.336581
$794$	−1.90238e10			−1.34873
$795$	9.56149e9	+	2.01632e10i	0.674902	+	1.42322i
$796$	−1.67352e9			−0.117608
$797$		−	3.21685e9i		−	0.225075i	−0.993647	−	0.112537i	$-0.964102\pi$
$797$		−	3.21685e9i		−	0.225075i	0.993647	−	0.112537i	$-0.0358978\pi$
$798$	−5.91415e6	−	1.24717e7i	−0.000411986	−	0.000868790i
$799$			2.45930e10i			1.70568i
$800$	−6.85069e9			−0.473064
$801$	−7.95436e9	−	6.50103e9i	−0.546879	−	0.446959i
$802$			7.08179e9i			0.484767i
$803$	−1.30588e9	+	9.90967e9i	−0.0890018	+	0.675390i
$804$	3.93769e8	+	8.30375e8i	0.0267205	+	0.0563479i
$805$			1.01560e9i			0.0686177i
$806$		−	1.47946e10i		−	0.995249i
$807$	2.59742e9	−	1.23171e9i	0.173974	−	0.0824997i
$808$	−1.41128e10			−0.941184
$809$	−1.05082e10			−0.697765			−0.348883	−	0.937166i	$-0.613439\pi$
$809$	−1.05082e10			−0.697765			−0.348883	+	0.937166i	$0.613439\pi$
$810$	2.00242e10	−	4.06757e9i	1.32391	−	0.268929i
$811$			5.25933e9i			0.346224i	0.984902	+	0.173112i	$0.0553823\pi$
$811$			5.25933e9i			0.346224i	−0.984902	+	0.173112i	$0.944618\pi$
$812$			9.90707e7i			0.00649380i
$813$	2.25255e10	−	1.06817e10i	1.47013	−	0.697146i
$814$	2.17077e10	+	2.86061e9i	1.41068	+	0.185897i
$815$			2.77389e9i			0.179489i
$816$	−8.46840e9	−	1.78581e10i	−0.545615	−	1.15059i
$817$	3.57287e8			0.0229214
$818$			2.05099e10i			1.31017i
$819$	7.86866e8	−	9.62774e8i	0.0500503	−	0.0612394i
$820$			3.60578e9i			0.228376i
$821$	−9.53317e9			−0.601224			−0.300612	−	0.953746i	$-0.597191\pi$
$821$	−9.53317e9			−0.601224			−0.300612	+	0.953746i	$0.597191\pi$
$822$	−1.36739e10	+	6.48425e9i	−0.858699	+	0.407200i
$823$	−1.11314e10			−0.696067			−0.348033	−	0.937482i	$-0.613150\pi$
$823$	−1.11314e10			−0.696067			−0.348033	+	0.937482i	$0.613150\pi$
$824$	7.85483e9			0.489093
$825$	6.21493e9	+	1.92838e10i	0.385343	+	1.19565i
$826$	−6.41569e8			−0.0396108
$827$	8.78607e9			0.540164			0.270082	−	0.962837i	$-0.412949\pi$
$827$	8.78607e9			0.540164			0.270082	+	0.962837i	$0.412949\pi$
$828$	−2.30416e9	−	1.88316e9i	−0.141061	−	0.115287i
$829$	2.63008e10			1.60335			0.801675	−	0.597760i	$-0.203943\pi$
$829$	2.63008e10			1.60335			0.801675	+	0.597760i	$0.203943\pi$
$830$			1.01980e10i			0.619073i
$831$	−8.37983e9	+	3.97377e9i	−0.506561	+	0.240214i
$832$			3.04654e10i			1.83390i
$833$	−2.74402e10			−1.64486
$834$	−1.46062e9	+	6.92637e8i	−0.0871882	+	0.0413452i
$835$		−	3.06801e10i		−	1.82370i
$836$	−9.41004e6	+	7.14081e7i	−0.000557018	+	0.00422693i
$837$	−1.10410e10	−	2.72995e9i	−0.650831	−	0.160922i
$838$			9.15706e9i			0.537529i
$839$			1.76026e10i			1.02899i	0.857494	+	0.514495i	$0.172020\pi$
$839$			1.76026e10i			1.02899i	−0.857494	+	0.514495i	$0.827980\pi$
$840$	−5.67517e8	−	1.19677e9i	−0.0330371	−	0.0696682i
$841$	−8.57428e9			−0.497064
$842$	−3.43839e9			−0.198501
$843$	−4.58482e9	−	9.66842e9i	−0.263588	−	0.555852i
$844$		−	2.68200e9i		−	0.153554i
$845$		−	4.54262e10i		−	2.59005i
$846$	1.26888e10	+	1.03705e10i	0.720485	+	0.588846i
$847$	−2.19525e8	+	8.18468e8i	−0.0124134	+	0.0462818i
$848$		−	1.43830e10i		−	0.809963i
$849$	1.19367e10	−	5.66047e9i	0.669435	−	0.317450i
$850$	3.33507e10			1.86268
$851$		−	2.71158e10i		−	1.50824i
$852$	2.43524e9	−	1.15481e9i	0.134897	−	0.0639692i
$853$			1.30824e10i			0.721717i	0.932621	+	0.360858i	$0.117516\pi$
$853$			1.30824e10i			0.721717i	−0.932621	+	0.360858i	$0.882484\pi$
$854$	−1.59958e8			−0.00878829
$855$	−3.87588e8	+	4.74236e8i	−0.0212075	+	0.0259485i
$856$	1.66889e9			0.0909431
$857$	−2.27893e10			−1.23680			−0.618398	−	0.785865i	$-0.712218\pi$
$857$	−2.27893e10			−1.23680			−0.618398	+	0.785865i	$0.712218\pi$
$858$	2.61412e10	−	8.42498e9i	1.41293	−	0.455369i
$859$	−1.48776e10			−0.800859			−0.400430	−	0.916328i	$-0.631139\pi$
$859$	−1.48776e10			−0.800859			−0.400430	+	0.916328i	$0.631139\pi$
$860$	5.50054e9			0.294891
$861$	−6.45170e8	+	3.05944e8i	−0.0344479	+	0.0163354i
$862$	6.62944e9			0.352534
$863$			3.26206e10i			1.72764i	0.503797	+	0.863822i	$0.331936\pi$
$863$			3.26206e10i			1.72764i	−0.503797	+	0.863822i	$0.668064\pi$
$864$	6.93059e9	+	1.71363e9i	0.365571	+	0.0903899i
$865$		−	4.02832e10i		−	2.11625i
$866$	2.02045e10			1.05715
$867$	−1.41261e10	−	2.97890e10i	−0.736132	−	1.55235i
$868$			1.18281e8i			0.00613897i
$869$	−1.44467e9	+	1.09629e10i	−0.0746793	+	0.566704i
$870$	−1.68139e10	+	7.97324e9i	−0.865665	+	0.410504i
$871$			1.05043e10i			0.538648i
$872$		−	3.62567e10i		−	1.85174i
$873$	1.65363e9	−	2.02331e9i	0.0841179	−	0.102923i
$874$	−3.77578e8			−0.0191301
$875$	3.65433e8			0.0184408
$876$	−2.34024e9	+	1.10975e9i	−0.117624	+	0.0557780i
$877$		−	1.98201e10i		−	0.992220i	−0.868260	−	0.496110i	$-0.834761\pi$
$877$		−	1.98201e10i		−	0.992220i	0.868260	−	0.496110i	$-0.165239\pi$
$878$		−	1.30303e10i		−	0.649714i
$879$	−1.54057e9	−	3.24873e9i	−0.0765103	−	0.161344i
$880$	3.06423e9	−	2.32529e10i	0.151576	−	1.15024i
$881$			2.57438e10i			1.26840i	0.773169	+	0.634200i	$0.218671\pi$
$881$			2.57438e10i			1.26840i	−0.773169	+	0.634200i	$0.781329\pi$
$882$	−1.15711e10	+	1.41579e10i	−0.567850	+	0.694796i
$883$	1.79024e10			0.875083			0.437541	−	0.899198i	$-0.355849\pi$
$883$	1.79024e10			0.875083			0.437541	+	0.899198i	$0.355849\pi$
$884$			1.06804e10i			0.520002i
$885$	1.21978e10	+	2.57226e10i	0.591536	+	1.24742i
$886$		−	2.58911e10i		−	1.25064i
$887$	2.75072e10			1.32347			0.661734	−	0.749738i	$-0.269821\pi$
$887$	2.75072e10			1.32347			0.661734	+	0.749738i	$0.269821\pi$
$888$	1.51524e10	+	3.19531e10i	0.726165	+	1.53133i
$889$	1.00630e9			0.0480364
$890$	−2.00673e10			−0.954165
$891$	−1.46376e9	−	2.10633e10i	−0.0693265	−	0.997594i
$892$	2.82512e9			0.133279
$893$	−4.91208e8			−0.0230826
$894$	−7.07598e9	−	1.49217e10i	−0.331212	−	0.698455i
$895$	−3.08080e10			−1.43642
$896$			6.42487e8i			0.0298391i
$897$	−1.45739e10	−	3.07333e10i	−0.674221	−	1.42179i
$898$		−	1.87185e10i		−	0.862588i
$899$	1.03578e10			0.475456
$900$	−3.32232e9	+	4.06504e9i	−0.151912	+	0.185873i
$901$		−	3.79572e10i		−	1.72885i
$902$	−1.56368e10	−	2.06059e9i	−0.709454	−	0.0934907i
$903$	4.66711e8	+	9.84194e8i	0.0210931	+	0.0444809i
$904$			9.24865e9i			0.416379i
$905$			3.87238e10i			1.73663i
$906$	−5.03504e9	+	2.38765e9i	−0.224933	+	0.106665i
$907$	1.38067e10			0.614420			0.307210	−	0.951642i	$-0.400605\pi$
$907$	1.38067e10			0.614420			0.307210	+	0.951642i	$0.400605\pi$
$908$	−5.35644e9			−0.237452
$909$	−1.25903e10	+	1.54049e10i	−0.555984	+	0.680278i
$910$		−	2.42889e9i		−	0.106847i
$911$			1.73114e10i			0.758608i	0.925272	+	0.379304i	$0.123837\pi$
$911$			1.73114e10i			0.758608i	−0.925272	+	0.379304i	$0.876163\pi$
$912$	3.56688e8	−	1.69144e8i	0.0155707	−	0.00738370i
$913$	1.04475e10	+	1.37675e9i	0.454323	+	0.0598699i
$914$			3.87058e9i			0.167674i
$915$	3.04121e9	+	6.41326e9i	0.131242	+	0.276761i
$916$	4.31359e8			0.0185440
$917$		−	4.06353e8i		−	0.0174025i
$918$	−3.37397e10	−	8.34236e9i	−1.43943	−	0.355909i
$919$			3.81101e10i			1.61971i	0.586634	+	0.809853i	$0.300453\pi$
$919$			3.81101e10i			1.61971i	−0.586634	+	0.809853i	$0.699547\pi$
$920$	−3.62321e10			−1.53404
$921$	4.02832e10	−	1.91025e10i	1.69909	−	0.805717i
$922$	6.17072e9			0.259285
$923$	3.08061e10			1.28953
$924$	−2.08995e8	+	6.73565e7i	−0.00871532	+	0.00280884i
$925$	−4.78384e10			−1.98738
$926$	2.24072e10			0.927360
$927$	7.00743e9	−	8.57398e9i	0.288921	−	0.353511i
$928$	−6.50178e9			−0.267063
$929$		−	1.25694e10i		−	0.514350i	−0.966365	−	0.257175i	$-0.917208\pi$
$929$		−	1.25694e10i		−	0.514350i	0.966365	−	0.257175i	$-0.0827916\pi$
$930$	−2.00742e10	+	9.51929e9i	−0.818365	+	0.388074i
$931$		−	5.48077e8i		−	0.0222596i
$932$	−6.62019e9			−0.267864
$933$	2.42559e10	−	1.15023e10i	0.977760	−	0.463660i
$934$			3.48418e10i			1.39922i
$935$	8.08657e9	−	6.13649e10i	0.323537	−	2.45516i
$936$	3.43476e10	+	2.80720e10i	1.36909	+	1.11894i
$937$			3.86518e8i			0.0153490i	0.999971	+	0.00767452i	$0.00244290\pi$
$937$			3.86518e8i			0.0153490i	−0.999971	+	0.00767452i	$0.997557\pi$
$938$			3.55492e8i			0.0140643i
$939$	8.39861e9	+	1.77109e10i	0.331038	+	0.698089i
$940$	−7.56230e9			−0.296966
$941$	4.73339e10			1.85186			0.925931	−	0.377694i	$-0.123283\pi$
$941$	4.73339e10			1.85186			0.925931	+	0.377694i	$0.123283\pi$
$942$	1.26221e9	+	2.66173e9i	0.0491986	+	0.103749i
$943$			1.95324e10i			0.758517i
$944$		−	1.83488e10i		−	0.709914i
$945$	−1.81264e9	−	4.48186e8i	−0.0698713	−	0.0172761i
$946$	−3.14339e9	+	2.38536e10i	−0.120720	+	0.916082i
$947$			2.27937e10i			0.872147i	0.899911	+	0.436074i	$0.143631\pi$
$947$			2.27937e10i			0.872147i	−0.899911	+	0.436074i	$0.856369\pi$
$948$	−2.58896e9	+	1.22770e9i	−0.0986954	+	0.0468020i
$949$	−2.96043e10			−1.12440
$950$			6.66132e8i			0.0252074i
$951$	−3.08861e10	+	1.46464e10i	−1.16448	+	0.552203i
$952$			2.25293e9i			0.0846288i
$953$	2.77522e10			1.03866			0.519328	−	0.854575i	$-0.326182\pi$
$953$	2.77522e10			1.03866			0.519328	+	0.854575i	$0.326182\pi$
$954$	−1.95841e10	−	1.60059e10i	−0.730272	−	0.596844i
$955$	3.69549e10			1.37297
$956$	7.39924e9			0.273895
$957$	5.89839e9	+	1.83016e10i	0.217541	+	0.674991i
$958$	3.39501e10			1.24756
$959$	1.38292e9			0.0506328
$960$	4.13371e10	−	1.96023e10i	1.50796	−	0.715085i
$961$	−1.51463e10			−0.550523
$962$			6.48498e10i			2.34853i
$963$	1.48885e9	−	1.82169e9i	0.0537227	−	0.0657327i
$964$		−	3.14737e9i		−	0.113156i
$965$	−5.93596e10			−2.12640
$966$	−4.93216e8	−	1.04009e9i	−0.0176042	−	0.0371236i
$967$			5.06908e10i			1.80276i	0.433034	+	0.901378i	$0.357443\pi$
$967$			5.06908e10i			1.80276i	−0.433034	+	0.901378i	$0.642557\pi$
$968$	−2.91994e10	−	7.83170e9i	−1.03469	−	0.277519i
$969$	9.41309e8	−	4.46375e8i	0.0332353	−	0.0157604i
$970$		−	5.10440e9i		−	0.179574i
$971$		−	1.23613e10i		−	0.433307i	−0.976249	−	0.216654i	$-0.930486\pi$
$971$		−	1.23613e10i		−	0.433307i	0.976249	−	0.216654i	$-0.0695143\pi$
$972$	4.37790e9	−	3.28140e9i	0.152909	−	0.114611i
$973$	1.47721e8			0.00514101
$974$	−1.63132e10			−0.565697
$975$	−5.42203e10	+	2.57116e10i	−1.87347	+	0.888409i
$976$		−	4.57479e9i		−	0.157506i
$977$		−	3.11630e10i		−	1.06907i	−0.845145	−	0.534537i	$-0.820486\pi$
$977$		−	3.11630e10i		−	1.06907i	0.845145	−	0.534537i	$-0.179514\pi$
$978$	−1.34712e9	−	2.84078e9i	−0.0460488	−	0.0971072i
$979$	−2.70913e9	+	2.05582e10i	−0.0922764	+	0.700239i
$980$		−	8.43782e9i		−	0.286377i
$981$	−3.95762e10	−	3.23452e10i	−1.33842	−	1.09388i
$982$	−3.36731e10			−1.13473
$983$		−	4.42906e10i		−	1.48722i	−0.668615	−	0.743609i	$-0.733112\pi$
$983$		−	4.42906e10i		−	1.48722i	0.668615	−	0.743609i	$-0.266888\pi$
$984$	−1.09147e10	−	2.30169e10i	−0.365200	−	0.770129i
$985$		−	4.24421e10i		−	1.41504i
$986$	3.16521e10			1.05156
$987$	−6.41647e8	−	1.35310e9i	−0.0212415	−	0.0447939i
$988$	−2.13325e8			−0.00703709
$989$	2.97963e10			0.979434
$990$	−2.82514e10	−	3.00488e10i	−0.925374	−	0.984248i
$991$	2.72950e10			0.890894			0.445447	−	0.895308i	$-0.353045\pi$
$991$	2.72950e10			0.890894			0.445447	+	0.895308i	$0.353045\pi$
$992$	−7.76250e9			−0.252471
$993$	−1.71059e10	−	3.60727e10i	−0.554401	−	1.16911i
$994$	1.04255e9			0.0336702
$995$			2.87249e10i			0.924439i
$996$	1.16998e9	+	2.46725e9i	0.0375208	+	0.0791235i
$997$			1.44656e10i			0.462279i	0.972921	+	0.231139i	$0.0742454\pi$
$997$			1.44656e10i			0.462279i	−0.972921	+	0.231139i	$0.925755\pi$
$998$	−1.22834e10			−0.391166
$999$	4.83963e10	+	1.19663e10i	1.53579	+	0.379735i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.8.d.b.32.15	yes	24
3.2	odd	2	inner	33.8.d.b.32.10	yes	24
11.10	odd	2	inner	33.8.d.b.32.9	✓	24
33.32	even	2	inner	33.8.d.b.32.16	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.8.d.b.32.9	✓	24	11.10	odd	2	inner
33.8.d.b.32.10	yes	24	3.2	odd	2	inner
33.8.d.b.32.15	yes	24	1.1	even	1	trivial
33.8.d.b.32.16	yes	24	33.32	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+10.1755 q^{2} +(-20.0376 - 42.2551i) q^{3} -24.4601 q^{4} +419.841i q^{5} +(-203.892 - 429.965i) q^{6} +43.4849i q^{7} -1551.35 q^{8} +(-1383.99 + 1693.38i) q^{9} +O(q^{10})\)	\(q+10.1755 q^{2} +(-20.0376 - 42.2551i) q^{3} -24.4601 q^{4} +419.841i q^{5} +(-203.892 - 429.965i) q^{6} +43.4849i q^{7} -1551.35 q^{8} +(-1383.99 + 1693.38i) q^{9} +4272.07i q^{10} +(4376.59 + 576.740i) q^{11} +(490.122 + 1033.56i) q^{12} +13074.7i q^{13} +442.478i q^{14} +(17740.4 - 8412.62i) q^{15} -12654.8 q^{16} -33396.4 q^{17} +(-14082.7 + 17231.0i) q^{18} -667.043i q^{19} -10269.3i q^{20} +(1837.46 - 871.333i) q^{21} +(44533.8 + 5868.59i) q^{22} -55628.7i q^{23} +(31085.4 + 65552.5i) q^{24} -98141.4 q^{25} +133041. i q^{26} +(99285.9 + 24549.1i) q^{27} -1063.64i q^{28} -93142.9 q^{29} +(180517. - 85602.2i) q^{30} -111204. q^{31} +69804.3 q^{32} +(-63326.3 - 196490. i) q^{33} -339823. q^{34} -18256.7 q^{35} +(33852.4 - 41420.3i) q^{36} +487443. q^{37} -6787.47i q^{38} +(552472. - 261985. i) q^{39} -651321. i q^{40} -351121. q^{41} +(18697.0 - 8866.22i) q^{42} +535628. i q^{43} +(-107052. - 14107.1i) q^{44} +(-710952. - 581054. i) q^{45} -566047. i q^{46} -736397. i q^{47} +(253573. + 534731. i) q^{48} +821652. q^{49} -998633. q^{50} +(669184. + 1.41117e6i) q^{51} -319807. i q^{52} +1.13657e6i q^{53} +(1.01028e6 + 249798. i) q^{54} +(-242139. + 1.83747e6i) q^{55} -67460.3i q^{56} +(-28186.0 + 13366.0i) q^{57} -947771. q^{58} +1.44995e6i q^{59} +(-433932. + 205773. i) q^{60} +361505. i q^{61} -1.13155e6 q^{62} +(-73636.6 - 60182.5i) q^{63} +2.33011e6 q^{64} -5.48928e6 q^{65} +(-644374. - 1.99937e6i) q^{66} +803411. q^{67} +816877. q^{68} +(-2.35060e6 + 1.11467e6i) q^{69} -185770. q^{70} -2.35617e6i q^{71} +(2.14705e6 - 2.62703e6i) q^{72} +2.26424e6i q^{73} +4.95996e6 q^{74} +(1.96652e6 + 4.14697e6i) q^{75} +16315.9i q^{76} +(-25079.5 + 190315. i) q^{77} +(5.62165e6 - 2.66582e6i) q^{78} +2.50489e6i q^{79} -5.31301e6i q^{80} +(-952130. - 4.68724e6i) q^{81} -3.57282e6 q^{82} +2.38713e6 q^{83} +(-44944.3 + 21312.9i) q^{84} -1.40212e7i q^{85} +5.45026e6i q^{86} +(1.86636e6 + 3.93576e6i) q^{87} +(-6.78963e6 - 894726. i) q^{88} +4.69732e6i q^{89} +(-7.23426e6 - 5.91249e6i) q^{90} -568550. q^{91} +1.36068e6i q^{92} +(2.22826e6 + 4.69893e6i) q^{93} -7.49317e6i q^{94} +280052. q^{95} +(-1.39871e6 - 2.94959e6i) q^{96} -1.19483e6 q^{97} +8.36069e6 q^{98} +(-7.03379e6 + 6.61305e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 120 q^{3} + 1788 q^{4} - 5940 q^{9}+O(q^{10}) \) 24 * q + 120 * q^3 + 1788 * q^4 - 5940 * q^9	\( 24 q + 120 q^{3} + 1788 q^{4} - 5940 q^{9} - 6936 q^{12} + 23160 q^{15} + 5844 q^{16} - 17556 q^{22} - 34704 q^{25} + 7560 q^{27} + 131328 q^{31} + 28644 q^{33} - 436080 q^{34} - 302832 q^{36} + 1072488 q^{37} - 100296 q^{42} - 1854252 q^{45} + 3172548 q^{48} - 1169304 q^{49} - 4401936 q^{55} - 2920440 q^{58} + 1981452 q^{60} + 14578596 q^{64} + 2895156 q^{66} + 7729200 q^{67} - 4614108 q^{69} - 6924504 q^{70} - 4375800 q^{75} - 26237448 q^{78} + 22367340 q^{81} - 23600232 q^{82} - 25179660 q^{88} + 9380640 q^{91} + 25396908 q^{93} + 72948360 q^{97} + 53650080 q^{99}+O(q^{100}) \) 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

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