LMFDB - Embedded newform 72.22.f.a.35.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [72,22,Mod(35,72)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(72, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 22, names="a")

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

chi := DirichletCharacter("72.35");

S:= CuspForms(chi, 22);

N := Newforms(S);

Level:	$ N $	$=$	$ 72 = 2^{3} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 22 $
Character orbit:	$[\chi]$	$=$	72.f (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:	$201.223687887$
Analytic rank:	$0$
Dimension:	$84$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			35.5
Character	$\chi$	$=$	72.35
Dual form			72.22.f.a.35.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1420.72 - 280.555i) q^{2} +(1.93973e6 + 797180. i) q^{4} +1.26307e7 q^{5} -2.88458e8i q^{7} +(-2.53216e9 - 1.67677e9i) q^{8} +O(q^{10})$	\(q+(-1420.72 - 280.555i) q^{2} +(1.93973e6 + 797180. i) q^{4} +1.26307e7 q^{5} -2.88458e8i q^{7} +(-2.53216e9 - 1.67677e9i) q^{8} +(-1.79447e10 - 3.54361e9i) q^{10} -3.92167e10i q^{11} -3.88488e11i q^{13} +(-8.09283e10 + 4.09817e11i) q^{14} +(3.12706e12 + 3.09263e12i) q^{16} -1.32533e12i q^{17} -2.57362e13 q^{19} +(2.45001e13 + 1.00689e13i) q^{20} +(-1.10024e13 + 5.57158e13i) q^{22} -2.48502e14 q^{23} -3.17303e14 q^{25} +(-1.08992e14 + 5.51932e14i) q^{26} +(2.29953e14 - 5.59530e14i) q^{28} -9.85080e14 q^{29} +3.59520e15i q^{31} +(-3.57501e15 - 5.27106e15i) q^{32} +(-3.71829e14 + 1.88293e15i) q^{34} -3.64342e15i q^{35} +1.71550e16i q^{37} +(3.65639e16 + 7.22042e15i) q^{38} +(-3.19829e16 - 2.11788e16i) q^{40} +9.67643e16i q^{41} -5.44106e15 q^{43} +(3.12627e16 - 7.60697e16i) q^{44} +(3.53052e17 + 6.97186e16i) q^{46} -1.91059e16 q^{47} +4.75338e17 q^{49} +(4.50798e17 + 8.90209e16i) q^{50} +(3.09695e17 - 7.53562e17i) q^{52} +1.08346e18 q^{53} -4.95334e17i q^{55} +(-4.83677e17 + 7.30420e17i) q^{56} +(1.39952e18 + 2.76369e17i) q^{58} -1.60073e18i q^{59} +6.20372e18i q^{61} +(1.00865e18 - 5.10777e18i) q^{62} +(3.60027e18 + 8.49168e18i) q^{64} -4.90688e18i q^{65} +2.15887e19 q^{67} +(1.05653e18 - 2.57079e18i) q^{68} +(-1.02218e18 + 5.17628e18i) q^{70} -7.99384e18 q^{71} -1.40042e19 q^{73} +(4.81291e18 - 2.43724e19i) q^{74} +(-4.99213e19 - 2.05164e19i) q^{76} -1.13124e19 q^{77} +1.09023e20i q^{79} +(3.94969e19 + 3.90620e19i) q^{80} +(2.71477e19 - 1.37475e20i) q^{82} -1.01596e20i q^{83} -1.67399e19i q^{85} +(7.73021e18 + 1.52652e18i) q^{86} +(-6.57573e19 + 9.93028e19i) q^{88} +1.04361e20i q^{89} -1.12062e20 q^{91} +(-4.82027e20 - 1.98101e20i) q^{92} +(2.71441e19 + 5.36025e18i) q^{94} -3.25066e20 q^{95} -3.48553e20 q^{97} +(-6.75321e20 - 1.33358e20i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q + 2424084 q^{4}+O(q^{10}) $ 84 * q + 2424084 * q^4	$ 84 q + 2424084 q^{4} + 17057181612 q^{10} - 4099708064904 q^{16} + 92015527242864 q^{19} - 236011369239528 q^{22} + 80\!\cdots\!00 q^{25}+ \cdots - 16\!\cdots\!12 q^{97}+O(q^{100}) $ 84 * q + 2424084 * q^4 + 17057181612 * q^10 - 4099708064904 * q^16 + 92015527242864 * q^19 - 236011369239528 * q^22 + 8010864257812500 * q^25 - 3042238700022024 * q^28 + 74414158327329924 * q^34 + 75018327243317184 * q^40 + 707788847336454432 * q^43 - 162639476543943288 * q^46 - 5423745715136249124 * q^49 - 70566629446202808 * q^52 - 14491558288019904108 * q^58 - 28749968749508108064 * q^64 - 13653811098426494352 * q^67 + 140256684870035374392 * q^70 - 71781309378863778384 * q^73 + 376055720386305092400 * q^76 - 368362114062816367548 * q^82 - 592572120184082106720 * q^88 - 522206955652189957200 * q^91 - 528772551789914644488 * q^94 - 1686050813935078492512 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/72\mathbb{Z}\right)^\times$.

$n$	$37$	$55$	$65$
$\chi(n)$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1420.72	−	280.555i	−0.981054	−	0.193733i
$2$	−1420.72	−	280.555i	−0.981054	−	0.193733i
$3$		0			0
$3$		0			0
$4$	1.93973e6	+	797180.i	0.924935	+	0.380125i
$5$	1.26307e7			0.578419			0.289209	−	0.957266i	$-0.406608\pi$
$5$	1.26307e7			0.578419			0.289209	+	0.957266i	$0.406608\pi$
$6$		0			0
$7$		−	2.88458e8i		−	0.385969i	−0.981202	−	0.192985i	$-0.938183\pi$
$7$		−	2.88458e8i		−	0.385969i	0.981202	−	0.192985i	$-0.0618168\pi$
$8$	−2.53216e9	−	1.67677e9i	−0.833769	−	0.552113i
$9$		0			0
$10$	−1.79447e10	−	3.54361e9i	−0.567460	−	0.112059i
$11$		−	3.92167e10i		−	0.455877i	−0.973676	−	0.227938i	$-0.926802\pi$
$11$		−	3.92167e10i		−	0.455877i	0.973676	−	0.227938i	$-0.0731985\pi$
$12$		0			0
$13$		−	3.88488e11i		−	0.781578i	−0.920480	−	0.390789i	$-0.872202\pi$
$13$		−	3.88488e11i		−	0.781578i	0.920480	−	0.390789i	$-0.127798\pi$
$14$	−8.09283e10	+	4.09817e11i	−0.0747749	+	0.378657i
$15$		0			0
$16$	3.12706e12	+	3.09263e12i	0.711010	+	0.703182i
$17$		−	1.32533e12i		−	0.159445i	−0.996817	−	0.0797226i	$-0.974597\pi$
$17$		−	1.32533e12i		−	0.159445i	0.996817	−	0.0797226i	$-0.0254035\pi$
$18$		0			0
$19$	−2.57362e13			−0.963011			−0.481506	−	0.876443i	$-0.659910\pi$
$19$	−2.57362e13			−0.963011			−0.481506	+	0.876443i	$0.659910\pi$
$20$	2.45001e13	+	1.00689e13i	0.535000	+	0.219871i
$21$		0			0
$22$	−1.10024e13	+	5.57158e13i	−0.0883183	+	0.447240i
$23$	−2.48502e14			−1.25080			−0.625400	−	0.780304i	$-0.715064\pi$
$23$	−2.48502e14			−1.25080			−0.625400	+	0.780304i	$0.715064\pi$
$24$		0			0
$25$	−3.17303e14			−0.665432
$26$	−1.08992e14	+	5.51932e14i	−0.151417	+	0.766771i
$27$		0			0
$28$	2.29953e14	−	5.59530e14i	0.146717	−	0.356997i
$29$	−9.85080e14			−0.434803			−0.217401	−	0.976082i	$-0.569758\pi$
$29$	−9.85080e14			−0.434803			−0.217401	+	0.976082i	$0.569758\pi$
$30$		0			0
$31$			3.59520e15i			0.787817i	0.919150	+	0.393908i	$0.128877\pi$
$31$			3.59520e15i			0.787817i	−0.919150	+	0.393908i	$0.871123\pi$
$32$	−3.57501e15	−	5.27106e15i	−0.561310	−	0.827605i
$33$		0			0
$34$	−3.71829e14	+	1.88293e15i	−0.0308898	+	0.156424i
$35$		−	3.64342e15i		−	0.223252i
$36$		0			0
$37$			1.71550e16i			0.586505i	0.956035	+	0.293252i	$0.0947376\pi$
$37$			1.71550e16i			0.586505i	−0.956035	+	0.293252i	$0.905262\pi$
$38$	3.65639e16	+	7.22042e15i	0.944767	+	0.186567i
$39$		0			0
$40$	−3.19829e16	−	2.11788e16i	−0.482268	−	0.319353i
$41$			9.67643e16i			1.12586i	0.826504	+	0.562930i	$0.190326\pi$
$41$			9.67643e16i			1.12586i	−0.826504	+	0.562930i	$0.809674\pi$
$42$		0			0
$43$	−5.44106e15			−0.0383941			−0.0191971	−	0.999816i	$-0.506111\pi$
$43$	−5.44106e15			−0.0383941			−0.0191971	+	0.999816i	$0.506111\pi$
$44$	3.12627e16	−	7.60697e16i	0.173290	−	0.421657i
$45$		0			0
$46$	3.53052e17	+	6.97186e16i	1.22710	+	0.242321i
$47$	−1.91059e16			−0.0529834			−0.0264917	−	0.999649i	$-0.508434\pi$
$47$	−1.91059e16			−0.0529834			−0.0264917	+	0.999649i	$0.508434\pi$
$48$		0			0
$49$	4.75338e17			0.851028
$50$	4.50798e17	+	8.90209e16i	0.652825	+	0.128916i
$51$		0			0
$52$	3.09695e17	−	7.53562e17i	0.297097	−	0.722909i
$53$	1.08346e18			0.850970			0.425485	−	0.904965i	$-0.360104\pi$
$53$	1.08346e18			0.850970			0.425485	+	0.904965i	$0.360104\pi$
$54$		0			0
$55$		−	4.95334e17i		−	0.263688i
$56$	−4.83677e17	+	7.30420e17i	−0.213099	+	0.321809i
$57$		0			0
$58$	1.39952e18	+	2.76369e17i	0.426565	+	0.0842356i
$59$		−	1.60073e18i		−	0.407729i	−0.978999	−	0.203865i	$-0.934650\pi$
$59$		−	1.60073e18i		−	0.407729i	0.978999	−	0.203865i	$-0.0653502\pi$
$60$		0			0
$61$			6.20372e18i			1.11350i	0.830681	+	0.556748i	$0.187951\pi$
$61$			6.20372e18i			1.11350i	−0.830681	+	0.556748i	$0.812049\pi$
$62$	1.00865e18	−	5.10777e18i	0.152626	−	0.772891i
$63$		0			0
$64$	3.60027e18	+	8.49168e18i	0.390342	+	0.920670i
$65$		−	4.90688e18i		−	0.452079i
$66$		0			0
$67$	2.15887e19			1.44691			0.723453	−	0.690374i	$-0.242554\pi$
$67$	2.15887e19			1.44691			0.723453	+	0.690374i	$0.242554\pi$
$68$	1.05653e18	−	2.57079e18i	0.0606091	−	0.147477i
$69$		0			0
$70$	−1.02218e18	+	5.17628e18i	−0.0432512	+	0.219022i
$71$	−7.99384e18			−0.291436			−0.145718	−	0.989326i	$-0.546549\pi$
$71$	−7.99384e18			−0.291436			−0.145718	+	0.989326i	$0.546549\pi$
$72$		0			0
$73$	−1.40042e19			−0.381389			−0.190694	−	0.981649i	$-0.561074\pi$
$73$	−1.40042e19			−0.381389			−0.190694	+	0.981649i	$0.561074\pi$
$74$	4.81291e18	−	2.43724e19i	0.113625	−	0.575393i
$75$		0			0
$76$	−4.99213e19	−	2.05164e19i	−0.890723	−	0.366065i
$77$	−1.13124e19			−0.175955
$78$		0			0
$79$			1.09023e20i			1.29548i	0.761859	+	0.647742i	$0.224287\pi$
$79$			1.09023e20i			1.29548i	−0.761859	+	0.647742i	$0.775713\pi$
$80$	3.94969e19	+	3.90620e19i	0.411262	+	0.406733i
$81$		0			0
$82$	2.71477e19	−	1.37475e20i	0.218116	−	1.10453i
$83$		−	1.01596e20i		−	0.718716i	−0.933200	−	0.359358i	$-0.882996\pi$
$83$		−	1.01596e20i		−	0.718716i	0.933200	−	0.359358i	$-0.117004\pi$
$84$		0			0
$85$		−	1.67399e19i		−	0.0922261i
$86$	7.73021e18	+	1.52652e18i	0.0376667	+	0.00743820i
$87$		0			0
$88$	−6.57573e19	+	9.93028e19i	−0.251696	+	0.380096i
$89$			1.04361e20i			0.354767i	0.984142	+	0.177384i	$0.0567633\pi$
$89$			1.04361e20i			0.354767i	−0.984142	+	0.177384i	$0.943237\pi$
$90$		0			0
$91$	−1.12062e20			−0.301665
$92$	−4.82027e20	−	1.98101e20i	−1.15691	−	0.475460i
$93$		0			0
$94$	2.71441e19	+	5.36025e18i	0.0519796	+	0.0102646i
$95$	−3.25066e20			−0.557024
$96$		0			0
$97$	−3.48553e20			−0.479917			−0.239958	−	0.970783i	$-0.577134\pi$
$97$	−3.48553e20			−0.479917			−0.239958	+	0.970783i	$0.577134\pi$
$98$	−6.75321e20	−	1.33358e20i	−0.834904	−	0.164872i
$99$		0			0
$100$	−6.15481e20	−	2.52947e20i	−0.615481	−	0.252947i
$101$	6.66650e20			0.600515			0.300257	−	0.953858i	$-0.402927\pi$
$101$	6.66650e20			0.600515			0.300257	+	0.953858i	$0.402927\pi$
$102$		0			0
$103$			2.59809e20i			0.190486i	0.995454	+	0.0952430i	$0.0303628\pi$
$103$			2.59809e20i			0.190486i	−0.995454	+	0.0952430i	$0.969637\pi$
$104$	−6.51405e20	+	9.83713e20i	−0.431520	+	0.651656i
$105$		0			0
$106$	−1.53928e21	−	3.03969e20i	−0.834848	−	0.164861i
$107$			2.98809e20i			0.146847i	0.997301	+	0.0734234i	$0.0233925\pi$
$107$			2.98809e20i			0.146847i	−0.997301	+	0.0734234i	$0.976608\pi$
$108$		0			0
$109$			1.74224e21i			0.704905i	0.935830	+	0.352453i	$0.114652\pi$
$109$			1.74224e21i			0.704905i	−0.935830	+	0.352453i	$0.885348\pi$
$110$	−1.38968e20	+	7.03730e20i	−0.0510850	+	0.258692i
$111$		0			0
$112$	8.92092e20	−	9.02024e20i	0.271407	−	0.274428i
$113$		−	5.46109e21i		−	1.51341i	−0.653758	−	0.756704i	$-0.726808\pi$
$113$		−	5.46109e21i		−	1.51341i	0.653758	−	0.756704i	$-0.273192\pi$
$114$		0			0
$115$	−3.13876e21			−0.723486
$116$	−1.91079e21	−	7.85286e20i	−0.402165	−	0.165279i
$117$		0			0
$118$	−4.49093e20	+	2.27419e21i	−0.0789905	+	0.400004i
$119$	−3.82303e20			−0.0615410
$120$		0			0
$121$	5.86230e21			0.792176
$122$	1.74048e21	−	8.81374e21i	0.215721	−	1.09240i
$123$		0			0
$124$	−2.86602e21	+	6.97372e21i	−0.299469	+	0.728680i
$125$	−1.00305e22			−0.963317
$126$		0			0
$127$			1.48468e22i			1.20696i	0.797376	+	0.603482i	$0.206221\pi$
$127$			1.48468e22i			1.20696i	−0.797376	+	0.603482i	$0.793779\pi$
$128$	−2.73258e21	−	1.30744e22i	−0.204582	−	0.978849i
$129$		0			0
$130$	−1.37665e21	+	6.97129e21i	−0.0875826	+	0.443514i
$131$		−	2.00791e22i		−	1.17868i	−0.807885	−	0.589340i	$-0.799388\pi$
$131$		−	2.00791e22i		−	1.17868i	0.807885	−	0.589340i	$-0.200612\pi$
$132$		0			0
$133$			7.42380e21i			0.371693i
$134$	−3.06714e22	−	6.05681e21i	−1.41949	−	0.280313i
$135$		0			0
$136$	−2.22228e21	+	3.35595e21i	−0.0880319	+	0.132941i
$137$		−	7.69109e21i		−	0.282112i	−0.990002	−	0.141056i	$-0.954950\pi$
$137$		−	7.69109e21i		−	0.282112i	0.990002	−	0.141056i	$-0.0450498\pi$
$138$		0			0
$139$	−2.65844e22			−0.837474			−0.418737	−	0.908107i	$-0.637527\pi$
$139$	−2.65844e22			−0.837474			−0.418737	+	0.908107i	$0.637527\pi$
$140$	2.90446e21	−	7.06726e21i	0.0848636	−	0.206494i
$141$		0			0
$142$	1.13570e22	+	2.24271e21i	0.285914	+	0.0564607i
$143$	−1.52352e22			−0.356303
$144$		0			0
$145$	−1.24422e22			−0.251498
$146$	1.98960e22	+	3.92895e21i	0.374163	+	0.0738876i
$147$		0			0
$148$	−1.36756e22	+	3.32760e22i	−0.222945	+	0.542479i
$149$	−3.32465e22			−0.504999			−0.252500	−	0.967597i	$-0.581253\pi$
$149$	−3.32465e22			−0.504999			−0.252500	+	0.967597i	$0.581253\pi$
$150$		0			0
$151$		−	4.33781e22i		−	0.572812i	−0.958108	−	0.286406i	$-0.907539\pi$
$151$		−	4.33781e22i		−	0.572812i	0.958108	−	0.286406i	$-0.0924607\pi$
$152$	6.51681e22	+	4.31536e22i	0.802929	+	0.531692i
$153$		0			0
$154$	1.60717e22	+	3.17374e21i	0.172621	+	0.0340882i
$155$			4.54099e22i			0.455688i
$156$		0			0
$157$		−	6.76188e20i		−	0.00593091i	−0.999996	−	0.00296545i	$-0.999056\pi$
$157$		−	6.76188e20i		−	0.00593091i	0.999996	−	0.00296545i	$-0.000943935\pi$
$158$	3.05869e22	−	1.54890e23i	0.250978	−	1.27094i
$159$		0			0
$160$	−4.51549e22	−	6.65772e22i	−0.324672	−	0.478702i
$161$			7.16824e22i			0.482771i
$162$		0			0
$163$	−1.38444e22			−0.0819037			−0.0409518	−	0.999161i	$-0.513039\pi$
$163$	−1.38444e22			−0.0819037			−0.0409518	+	0.999161i	$0.513039\pi$
$164$	−7.71385e22	+	1.87697e23i	−0.427968	+	1.04135i
$165$		0			0
$166$	−2.85033e22	+	1.44340e23i	−0.139239	+	0.705099i
$167$	−8.06883e22			−0.370073			−0.185037	−	0.982732i	$-0.559240\pi$
$167$	−8.06883e22			−0.370073			−0.185037	+	0.982732i	$0.559240\pi$
$168$		0			0
$169$	9.61416e22			0.389135
$170$	−4.69646e21	+	2.37827e22i	−0.0178672	+	0.0904788i
$171$		0			0
$172$	−1.05542e22	−	4.33750e21i	−0.0355121	−	0.0145946i
$173$	1.74367e23			0.552051			0.276026	−	0.961150i	$-0.410983\pi$
$173$	1.74367e23			0.552051			0.276026	+	0.961150i	$0.410983\pi$
$174$		0			0
$175$			9.15284e22i			0.256836i
$176$	1.21282e23	−	1.22633e23i	0.320564	−	0.324133i
$177$		0			0
$178$	2.92790e22	−	1.48268e23i	0.0687300	−	0.348046i
$179$		−	4.16072e23i		−	0.920897i	−0.887686	−	0.460449i	$-0.847689\pi$
$179$		−	4.16072e23i		−	0.920897i	0.887686	−	0.460449i	$-0.152311\pi$
$180$		0			0
$181$		−	1.54507e23i		−	0.304314i	−0.988356	−	0.152157i	$-0.951378\pi$
$181$		−	1.54507e23i		−	0.304314i	0.988356	−	0.152157i	$-0.0486220\pi$
$182$	1.59209e23	+	3.14397e22i	0.295950	+	0.0584425i
$183$		0			0
$184$	6.29247e23	+	4.16681e23i	1.04288	+	0.690584i
$185$			2.16679e23i			0.339245i
$186$		0			0
$187$	−5.19752e22			−0.0726874
$188$	−3.70602e22	−	1.52308e22i	−0.0490062	−	0.0201403i
$189$		0			0
$190$	4.61827e23	+	9.11989e22i	0.546471	+	0.107914i
$191$	1.25425e24			1.40454			0.702268	−	0.711913i	$-0.252171\pi$
$191$	1.25425e24			1.40454			0.702268	+	0.711913i	$0.252171\pi$
$192$		0			0
$193$	1.58700e24			1.59303			0.796516	−	0.604618i	$-0.206674\pi$
$193$	1.58700e24			1.59303			0.796516	+	0.604618i	$0.206674\pi$
$194$	4.95196e23	+	9.77884e22i	0.470825	+	0.0929757i
$195$		0			0
$196$	9.22027e23	+	3.78930e23i	0.787145	+	0.323497i
$197$	1.89785e24			1.53592			0.767958	−	0.640500i	$-0.221273\pi$
$197$	1.89785e24			1.53592			0.767958	+	0.640500i	$0.221273\pi$
$198$		0			0
$199$			1.38349e24i			1.00698i	0.864001	+	0.503489i	$0.167951\pi$
$199$			1.38349e24i			1.00698i	−0.864001	+	0.503489i	$0.832049\pi$
$200$	8.03460e23	+	5.32043e23i	0.554816	+	0.367394i
$201$		0			0
$202$	−9.47123e23	−	1.87032e23i	−0.589138	−	0.116339i
$203$			2.84154e23i			0.167821i
$204$		0			0
$205$			1.22220e24i			0.651219i
$206$	7.28907e22	−	3.69115e23i	0.0369034	−	0.186877i
$207$		0			0
$208$	1.20145e24	−	1.21482e24i	0.549592	−	0.555710i
$209$			1.00929e24i			0.439015i
$210$		0			0
$211$	2.22690e24			0.876467			0.438234	−	0.898861i	$-0.355604\pi$
$211$	2.22690e24			0.876467			0.438234	+	0.898861i	$0.355604\pi$
$212$	2.10161e24	+	8.63708e23i	0.787092	+	0.323475i
$213$		0			0
$214$	8.38325e22	−	4.24524e23i	0.0284491	−	0.144065i
$215$	−6.87244e22			−0.0222079
$216$		0			0
$217$	1.03706e24			0.304073
$218$	4.88795e23	−	2.47524e24i	0.136563	−	0.691550i
$219$		0			0
$220$	3.94870e23	−	9.60814e23i	0.100234	−	0.243894i
$221$	−5.14876e23			−0.124619
$222$		0			0
$223$			5.62076e23i			0.123764i	0.998083	+	0.0618820i	$0.0197102\pi$
$223$			5.62076e23i			0.123764i	−0.998083	+	0.0618820i	$0.980290\pi$
$224$	−1.52048e24	+	1.03124e24i	−0.319430	+	0.216649i
$225$		0			0
$226$	−1.53214e24	+	7.75868e24i	−0.293197	+	1.48474i
$227$		−	7.15428e24i		−	1.30706i	−0.756902	−	0.653528i	$-0.773288\pi$
$227$		−	7.15428e24i		−	1.30706i	0.756902	−	0.653528i	$-0.226712\pi$
$228$		0			0
$229$			5.68123e24i			0.946607i	0.880899	+	0.473304i	$0.156939\pi$
$229$			5.68123e24i			0.946607i	−0.880899	+	0.473304i	$0.843061\pi$
$230$	4.45929e24	+	8.80594e23i	0.709780	+	0.140163i
$231$		0			0
$232$	2.49438e24	+	1.65175e24i	0.362525	+	0.240061i
$233$			3.26495e24i			0.453565i	0.973945	+	0.226782i	$0.0728206\pi$
$233$			3.26495e24i			0.453565i	−0.973945	+	0.226782i	$0.927179\pi$
$234$		0			0
$235$	−2.41321e23			−0.0306466
$236$	1.27607e24	−	3.10498e24i	0.154988	−	0.377123i
$237$		0			0
$238$	5.43145e23	+	1.07257e23i	0.0603751	+	0.0119225i
$239$	3.04072e24			0.323443			0.161722	−	0.986836i	$-0.448295\pi$
$239$	3.04072e24			0.323443			0.161722	+	0.986836i	$0.448295\pi$
$240$		0			0
$241$	−1.22649e24			−0.119532			−0.0597662	−	0.998212i	$-0.519036\pi$
$241$	−1.22649e24			−0.119532			−0.0597662	+	0.998212i	$0.519036\pi$
$242$	−8.32868e24	−	1.64470e24i	−0.777168	−	0.153471i
$243$		0			0
$244$	−4.94548e24	+	1.20335e25i	−0.423268	+	1.02991i
$245$	6.00385e24			0.492250
$246$		0			0
$247$			9.99820e24i			0.752669i
$248$	6.02832e24	−	9.10361e24i	0.434964	−	0.656857i
$249$		0			0
$250$	1.42506e25	+	2.81412e24i	0.945066	+	0.186626i
$251$		−	1.39356e25i		−	0.886241i	−0.896462	−	0.443120i	$-0.853871\pi$
$251$		−	1.39356e25i		−	0.886241i	0.896462	−	0.443120i	$-0.146129\pi$
$252$		0			0
$253$			9.74543e24i			0.570211i
$254$	4.16535e24	−	2.10932e25i	0.233829	−	1.18410i
$255$		0			0
$256$	2.14146e23	+	1.93416e25i	0.0110711	+	0.999939i
$257$		−	1.72167e25i		−	0.854384i	−0.904161	−	0.427192i	$-0.859503\pi$
$257$		−	1.72167e25i		−	0.854384i	0.904161	−	0.427192i	$-0.140497\pi$
$258$		0			0
$259$	4.94848e24			0.226373
$260$	3.91166e24	−	9.51801e24i	0.171847	−	0.418144i
$261$		0			0
$262$	−5.63330e24	+	2.85268e25i	−0.228349	+	1.15635i
$263$	5.12014e24			0.199410			0.0997049	−	0.995017i	$-0.468210\pi$
$263$	5.12014e24			0.199410			0.0997049	+	0.995017i	$0.468210\pi$
$264$		0			0
$265$	1.36848e25			0.492217
$266$	2.08279e24	−	1.05471e25i	0.0720091	−	0.364651i
$267$		0			0
$268$	4.18762e25	+	1.72100e25i	1.33829	+	0.550005i
$269$	−1.05897e25			−0.325451			−0.162725	−	0.986671i	$-0.552028\pi$
$269$	−1.05897e25			−0.325451			−0.162725	+	0.986671i	$0.552028\pi$
$270$		0			0
$271$			4.39486e25i			1.24959i	0.780789	+	0.624795i	$0.214817\pi$
$271$			4.39486e25i			1.24959i	−0.780789	+	0.624795i	$0.785183\pi$
$272$	4.09876e24	−	4.14439e24i	0.112119	−	0.113367i
$273$		0			0
$274$	−2.15777e24	+	1.09269e25i	−0.0546544	+	0.276767i
$275$			1.24436e25i			0.303355i
$276$		0			0
$277$			2.71712e25i			0.613863i	0.951732	+	0.306931i	$0.0993022\pi$
$277$			2.71712e25i			0.613863i	−0.951732	+	0.306931i	$0.900698\pi$
$278$	3.77689e25	+	7.45839e24i	0.821608	+	0.162246i
$279$		0			0
$280$	−6.10918e24	+	9.22572e24i	−0.123260	+	0.186141i
$281$		−	6.15193e25i		−	1.19562i	−0.801636	−	0.597812i	$-0.796037\pi$
$281$		−	6.15193e25i		−	1.19562i	0.801636	−	0.597812i	$-0.203963\pi$
$282$		0			0
$283$	4.30974e25			0.777488			0.388744	−	0.921346i	$-0.372909\pi$
$283$	4.30974e25			0.777488			0.388744	+	0.921346i	$0.372909\pi$
$284$	−1.55059e25	−	6.37253e24i	−0.269559	−	0.110782i
$285$		0			0
$286$	2.16449e25	+	4.27432e24i	0.349553	+	0.0690277i
$287$	2.79124e25			0.434548
$288$		0			0
$289$	6.73354e25			0.974577
$290$	1.76769e25	+	3.49074e24i	0.246733	+	0.0487234i
$291$		0			0
$292$	−2.71644e25	−	1.11639e25i	−0.352760	−	0.144975i
$293$	1.21717e26			1.52489			0.762447	−	0.647051i	$-0.223998\pi$
$293$	1.21717e26			1.52489			0.762447	+	0.647051i	$0.223998\pi$
$294$		0			0
$295$		−	2.02183e25i		−	0.235838i
$296$	2.87649e25	−	4.34390e25i	0.323817	−	0.489009i
$297$		0			0
$298$	4.72340e25	+	9.32749e24i	0.495432	+	0.0978349i
$299$			9.65402e25i			0.977599i
$300$		0			0
$301$			1.56952e24i			0.0148190i
$302$	−1.21699e25	+	6.16280e25i	−0.110973	+	0.561960i
$303$		0			0
$304$	−8.04785e25	−	7.95924e25i	−0.684711	−	0.677172i
$305$			7.83573e25i			0.644067i
$306$		0			0
$307$	−4.84747e25			−0.372016			−0.186008	−	0.982548i	$-0.559555\pi$
$307$	−4.84747e25			−0.372016			−0.186008	+	0.982548i	$0.559555\pi$
$308$	−2.19429e25	−	9.01798e24i	−0.162747	−	0.0668847i
$309$		0			0
$310$	1.27400e25	−	6.45147e25i	0.0882817	−	0.447055i
$311$	6.07657e25			0.407075			0.203537	−	0.979067i	$-0.434756\pi$
$311$	6.07657e25			0.407075			0.203537	+	0.979067i	$0.434756\pi$
$312$		0			0
$313$	−5.97751e25			−0.374373			−0.187187	−	0.982324i	$-0.559937\pi$
$313$	−5.97751e25			−0.374373			−0.187187	+	0.982324i	$0.559937\pi$
$314$	−1.89708e23	+	9.60673e23i	−0.00114901	+	0.00581854i
$315$		0			0
$316$	−8.69106e25	+	2.11474e26i	−0.492446	+	1.19824i
$317$	−1.16509e26			−0.638611			−0.319306	−	0.947652i	$-0.603450\pi$
$317$	−1.16509e26			−0.638611			−0.319306	+	0.947652i	$0.603450\pi$
$318$		0			0
$319$			3.86316e25i			0.198217i
$320$	4.54739e25	+	1.07256e26i	0.225781	+	0.532533i
$321$		0			0
$322$	2.01109e25	−	1.01841e26i	0.0935285	−	0.473624i
$323$			3.41090e25i			0.153548i
$324$		0			0
$325$			1.23268e26i			0.520087i
$326$	1.96690e25	+	3.88411e24i	0.0803519	+	0.0158674i
$327$		0			0
$328$	1.62251e26	−	2.45022e26i	0.621603	−	0.938708i
$329$			5.51124e24i			0.0204500i
$330$		0			0
$331$	4.92930e26			1.71629			0.858147	−	0.513405i	$-0.171616\pi$
$331$	4.92930e26			1.71629			0.858147	+	0.513405i	$0.171616\pi$
$332$	8.09904e25	−	1.97069e26i	0.273202	−	0.664766i
$333$		0			0
$334$	1.14635e26	+	2.26375e25i	0.363062	+	0.0716954i
$335$	2.72680e26			0.836918
$336$		0			0
$337$	2.49650e24			0.00719808			0.00359904	−	0.999994i	$-0.498854\pi$
$337$	2.49650e24			0.00719808			0.00359904	+	0.999994i	$0.498854\pi$
$338$	−1.36590e26	−	2.69730e25i	−0.381763	−	0.0753883i
$339$		0			0
$340$	1.33447e25	−	3.24709e25i	0.0350574	−	0.0853032i
$341$	1.40992e26			0.359148
$342$		0			0
$343$		−	2.98232e26i		−	0.714440i
$344$	1.37776e25	+	9.12340e24i	0.0320118	+	0.0211979i
$345$		0			0
$346$	−2.47726e26	−	4.89195e25i	−0.541592	−	0.106950i
$347$			4.25076e26i			0.901586i	0.892628	+	0.450793i	$0.148859\pi$
$347$			4.25076e26i			0.901586i	−0.892628	+	0.450793i	$0.851141\pi$
$348$		0			0
$349$		−	7.53504e26i		−	1.50459i	−0.658826	−	0.752295i	$-0.728947\pi$
$349$		−	7.53504e26i		−	1.50459i	0.658826	−	0.752295i	$-0.271053\pi$
$350$	2.56788e25	−	1.30036e26i	0.0497576	−	0.251970i
$351$		0			0
$352$	−2.06713e26	+	1.40200e26i	−0.377286	+	0.255888i
$353$			3.73358e26i			0.661441i	0.943729	+	0.330720i	$0.107292\pi$
$353$			3.73358e26i			0.661441i	−0.943729	+	0.330720i	$0.892708\pi$
$354$		0			0
$355$	−1.00968e26			−0.168572
$356$	−8.31945e25	+	2.02432e26i	−0.134856	+	0.328137i
$357$		0			0
$358$	−1.16731e26	+	5.91121e26i	−0.178408	+	0.903450i
$359$	−3.26249e26			−0.484237			−0.242119	−	0.970247i	$-0.577842\pi$
$359$	−3.26249e26			−0.484237			−0.242119	+	0.970247i	$0.577842\pi$
$360$		0			0
$361$	−5.18580e25			−0.0726090
$362$	−4.33476e25	+	2.19511e26i	−0.0589557	+	0.298549i
$363$		0			0
$364$	−2.17371e26	−	8.93339e25i	−0.279021	−	0.114670i
$365$	−1.76883e26			−0.220603
$366$		0			0
$367$		−	8.68923e26i		−	1.02326i	−0.859205	−	0.511632i	$-0.829041\pi$
$367$		−	8.68923e26i		−	1.02326i	0.859205	−	0.511632i	$-0.170959\pi$
$368$	−7.77081e26	−	7.68525e26i	−0.889332	−	0.879540i
$369$		0			0
$370$	6.07904e25	−	3.07840e26i	0.0657229	−	0.332818i
$371$		−	3.12531e26i		−	0.328448i
$372$		0			0
$373$			4.31159e26i			0.428247i	0.976807	+	0.214124i	$0.0686895\pi$
$373$			4.31159e26i			0.428247i	−0.976807	+	0.214124i	$0.931310\pi$
$374$	7.38421e25	+	1.45819e25i	0.0713103	+	0.0140819i
$375$		0			0
$376$	4.83791e25	+	3.20361e25i	0.0441759	+	0.0292528i
$377$			3.82692e26i			0.339833i
$378$		0			0
$379$	−1.85931e27			−1.56186			−0.780928	−	0.624621i	$-0.785254\pi$
$379$	−1.85931e27			−1.56186			−0.780928	+	0.624621i	$0.785254\pi$
$380$	−6.30540e26	−	2.59136e26i	−0.515211	−	0.211739i
$381$		0			0
$382$	−1.78193e27	−	3.51885e26i	−1.37793	−	0.272105i
$383$	−2.15760e27			−1.62324			−0.811621	−	0.584184i	$-0.801415\pi$
$383$	−2.15760e27			−1.62324			−0.811621	+	0.584184i	$0.801415\pi$
$384$		0			0
$385$	−1.42883e26			−0.101775
$386$	−2.25468e27	−	4.45240e26i	−1.56285	−	0.308623i
$387$		0			0
$388$	−6.76099e26	−	2.77860e26i	−0.443892	−	0.182428i
$389$	−1.11177e27			−0.710464			−0.355232	−	0.934778i	$-0.615598\pi$
$389$	−1.11177e27			−0.710464			−0.355232	+	0.934778i	$0.615598\pi$
$390$		0			0
$391$			3.29348e26i			0.199434i
$392$	−1.20363e27	−	7.97032e26i	−0.709560	−	0.469864i
$393$		0			0
$394$	−2.69632e27	−	5.32453e26i	−1.50682	−	0.297557i
$395$			1.37703e27i			0.749333i
$396$		0			0
$397$		−	2.82207e27i		−	1.45636i	−0.685388	−	0.728178i	$-0.740367\pi$
$397$		−	2.82207e27i		−	1.45636i	0.685388	−	0.728178i	$-0.259633\pi$
$398$	3.88147e26	−	1.96556e27i	0.195085	−	0.987901i
$399$		0			0
$400$	−9.92223e26	−	9.81298e26i	−0.473129	−	0.467919i
$401$			3.27950e27i			1.52332i	0.647975	+	0.761662i	$0.275616\pi$
$401$			3.27950e27i			1.52332i	−0.647975	+	0.761662i	$0.724384\pi$
$402$		0			0
$403$	1.39669e27			0.615741
$404$	1.29312e27	+	5.31440e26i	0.555437	+	0.228271i
$405$		0			0
$406$	7.97208e25	−	4.03703e26i	0.0325124	−	0.164641i
$407$	6.72760e26			0.267374
$408$		0			0
$409$	−9.04414e26			−0.341407			−0.170703	−	0.985322i	$-0.554604\pi$
$409$	−9.04414e26			−0.341407			−0.170703	+	0.985322i	$0.554604\pi$
$410$	3.42895e26	−	1.73640e27i	0.126162	−	0.638881i
$411$		0			0
$412$	−2.07114e26	+	5.03959e26i	−0.0724085	+	0.176187i
$413$	−4.61743e26			−0.157371
$414$		0			0
$415$		−	1.28323e27i		−	0.415719i
$416$	−2.04774e27	+	1.38885e27i	−0.646838	+	0.438708i
$417$		0			0
$418$	2.83161e26	−	1.43391e27i	0.0850515	−	0.430697i
$419$			1.74108e27i			0.510003i	0.966941	+	0.255001i	$0.0820760\pi$
$419$			1.74108e27i			0.510003i	−0.966941	+	0.255001i	$0.917924\pi$
$420$		0			0
$421$			8.10879e25i			0.0225940i	0.999936	+	0.0112970i	$0.00359603\pi$
$421$			8.10879e25i			0.0225940i	−0.999936	+	0.0112970i	$0.996404\pi$
$422$	−3.16380e27	−	6.24769e26i	−0.859862	−	0.169800i
$423$		0			0
$424$	−2.74348e27	−	1.81670e27i	−0.709513	−	0.469832i
$425$			4.20532e26i			0.106100i
$426$		0			0
$427$	1.78951e27			0.429776
$428$	−2.38205e26	+	5.79610e26i	−0.0558201	+	0.135824i
$429$		0			0
$430$	9.76380e25	+	1.92810e25i	0.0217871	+	0.00430239i
$431$	5.77021e27			1.25655			0.628276	−	0.777991i	$-0.283761\pi$
$431$	5.77021e27			1.25655			0.628276	+	0.777991i	$0.283761\pi$
$432$		0			0
$433$	8.70274e27			1.80523			0.902617	−	0.430446i	$-0.141644\pi$
$433$	8.70274e27			1.80523			0.902617	+	0.430446i	$0.141644\pi$
$434$	−1.47338e27	−	2.90953e26i	−0.298312	−	0.0589090i
$435$		0			0
$436$	−1.38888e27	+	3.37948e27i	−0.267952	+	0.651991i
$437$	6.39550e27			1.20454
$438$		0			0
$439$		−	2.00137e27i		−	0.359294i	−0.983731	−	0.179647i	$-0.942504\pi$
$439$		−	2.00137e27i		−	0.359294i	0.983731	−	0.179647i	$-0.0574956\pi$
$440$	−8.30560e26	+	1.25426e27i	−0.145585	+	0.219855i
$441$		0			0
$442$	7.31494e26	+	1.44451e26i	0.122258	+	0.0241428i
$443$			8.50340e26i			0.138789i	0.997589	+	0.0693943i	$0.0221067\pi$
$443$			8.50340e26i			0.138789i	−0.997589	+	0.0693943i	$0.977893\pi$
$444$		0			0
$445$			1.31815e27i			0.205204i
$446$	1.57693e26	−	7.98552e26i	0.0239771	−	0.121419i
$447$		0			0
$448$	2.44949e27	−	1.03852e27i	0.355350	−	0.150660i
$449$			1.28689e28i			1.82371i	0.410514	+	0.911854i	$0.365349\pi$
$449$			1.28689e28i			1.82371i	−0.410514	+	0.911854i	$0.634651\pi$
$450$		0			0
$451$	3.79477e27			0.513254
$452$	4.35347e27	−	1.05930e28i	0.575284	−	1.39980i
$453$		0			0
$454$	−2.00717e27	+	1.01642e28i	−0.253220	+	1.28229i
$455$	−1.41543e27			−0.174489
$456$		0			0
$457$	5.83702e27			0.687181			0.343590	−	0.939120i	$-0.388357\pi$
$457$	5.83702e27			0.687181			0.343590	+	0.939120i	$0.388357\pi$
$458$	1.59390e27	−	8.07143e27i	0.183389	−	0.928673i
$459$		0			0
$460$	−6.08834e27	−	2.50215e27i	−0.669178	−	0.275015i
$461$	6.86810e27			0.737865			0.368933	−	0.929456i	$-0.379723\pi$
$461$	6.86810e27			0.737865			0.368933	+	0.929456i	$0.379723\pi$
$462$		0			0
$463$		−	7.14213e27i		−	0.733208i	−0.930377	−	0.366604i	$-0.880520\pi$
$463$		−	7.14213e27i		−	0.733208i	0.930377	−	0.366604i	$-0.119480\pi$
$464$	−3.08040e27	−	3.04648e27i	−0.309149	−	0.305745i
$465$		0			0
$466$	9.15998e26	−	4.63857e27i	0.0878703	−	0.444972i
$467$			1.84942e28i			1.73463i	0.497757	+	0.867317i	$0.334157\pi$
$467$			1.84942e28i			1.73463i	−0.497757	+	0.867317i	$0.665843\pi$
$468$		0			0
$469$		−	6.22742e27i		−	0.558462i
$470$	3.42849e26	+	6.77037e25i	0.0300659	+	0.00593724i
$471$		0			0
$472$	−2.68405e27	+	4.05330e27i	−0.225113	+	0.339952i
$473$			2.13380e26i			0.0175030i
$474$		0			0
$475$	8.16616e27			0.640819
$476$	−7.41564e26	−	3.04764e26i	−0.0569214	−	0.0233933i
$477$		0			0
$478$	−4.32000e27	−	8.53088e26i	−0.317315	−	0.0626615i
$479$	1.64383e28			1.18123			0.590615	−	0.806954i	$-0.298885\pi$
$479$	1.64383e28			1.18123			0.590615	+	0.806954i	$0.298885\pi$
$480$		0			0
$481$	6.66450e27			0.458399
$482$	1.74250e27	+	3.44098e26i	0.117268	+	0.0231573i
$483$		0			0
$484$	1.13713e28	+	4.67331e27i	0.732712	+	0.301126i
$485$	−4.40247e27			−0.277593
$486$		0			0
$487$			1.01367e28i			0.612128i	0.952011	+	0.306064i	$0.0990121\pi$
$487$			1.01367e28i			0.612128i	−0.952011	+	0.306064i	$0.900988\pi$
$488$	1.04022e28	−	1.57088e28i	0.614776	−	0.928399i
$489$		0			0
$490$	−8.52978e27	−	1.68441e27i	−0.482924	−	0.0953650i
$491$			2.34662e28i			1.30043i	0.759750	+	0.650216i	$0.225321\pi$
$491$			2.34662e28i			1.30043i	−0.759750	+	0.650216i	$0.774679\pi$
$492$		0			0
$493$			1.30556e27i			0.0693273i
$494$	2.80505e27	−	1.42046e28i	0.145817	−	0.738409i
$495$		0			0
$496$	−1.11186e28	+	1.12424e28i	−0.553978	+	0.560146i
$497$			2.30589e27i			0.112485i
$498$		0			0
$499$	2.03408e28			0.951286			0.475643	−	0.879638i	$-0.342215\pi$
$499$	2.03408e28			0.951286			0.475643	+	0.879638i	$0.342215\pi$
$500$	−1.94565e28	−	7.99614e27i	−0.891006	−	0.366181i
$501$		0			0
$502$	−3.90970e27	+	1.97986e28i	−0.171694	+	0.869450i
$503$	1.95226e27			0.0839601			0.0419801	−	0.999118i	$-0.486633\pi$
$503$	1.95226e27			0.0839601			0.0419801	+	0.999118i	$0.486633\pi$
$504$		0			0
$505$	8.42026e27			0.347349
$506$	2.73413e27	−	1.38455e28i	0.110469	−	0.559408i
$507$		0			0
$508$	−1.18356e28	+	2.87988e28i	−0.458797	+	1.11636i
$509$	2.01801e28			0.766277			0.383138	−	0.923691i	$-0.374843\pi$
$509$	2.01801e28			0.766277			0.383138	+	0.923691i	$0.374843\pi$
$510$		0			0
$511$			4.03962e27i			0.147204i
$512$	5.12215e27	−	2.75391e28i	0.182860	−	0.983139i
$513$		0			0
$514$	−4.83025e27	+	2.44602e28i	−0.165522	+	0.838198i
$515$			3.28157e27i			0.110181i
$516$		0			0
$517$			7.49269e26i			0.0241539i
$518$	−7.03040e27	−	1.38832e27i	−0.222084	−	0.0438558i
$519$		0			0
$520$	−8.22769e27	+	1.24250e28i	−0.249599	+	0.376930i
$521$			2.27717e28i			0.677016i	0.940964	+	0.338508i	$0.109922\pi$
$521$			2.27717e28i			0.677016i	−0.940964	+	0.338508i	$0.890078\pi$
$522$		0			0
$523$	4.85211e28			1.38568			0.692840	−	0.721091i	$-0.256359\pi$
$523$	4.85211e28			1.38568			0.692840	+	0.721091i	$0.256359\pi$
$524$	1.60067e28	−	3.89481e28i	0.448046	−	1.09020i
$525$		0			0
$526$	−7.27428e27	−	1.43648e27i	−0.195632	−	0.0386322i
$527$	4.76484e27			0.125614
$528$		0			0
$529$	2.22818e28			0.564502
$530$	−1.94422e28	−	3.83934e27i	−0.482892	−	0.0953586i
$531$		0			0
$532$	−5.91811e27	+	1.44002e28i	−0.141290	+	0.343792i
$533$	3.75918e28			0.879948
$534$		0			0
$535$			3.77417e27i			0.0849390i
$536$	−5.46659e28	−	3.61992e28i	−1.20639	−	0.798856i
$537$		0			0
$538$	1.50450e28	+	2.97100e27i	0.319285	+	0.0630505i
$539$		−	1.86412e28i		−	0.387964i
$540$		0			0
$541$			9.83271e28i			1.96835i	0.177206	+	0.984174i	$0.443294\pi$
$541$			9.83271e28i			1.96835i	−0.177206	+	0.984174i	$0.556706\pi$
$542$	1.23300e28	−	6.24386e28i	0.242086	−	1.22592i
$543$		0			0
$544$	−6.98592e27	+	4.73809e27i	−0.131958	+	0.0894983i
$545$			2.20057e28i			0.407730i
$546$		0			0
$547$	5.53513e28			0.986872			0.493436	−	0.869782i	$-0.335741\pi$
$547$	5.53513e28			0.986872			0.493436	+	0.869782i	$0.335741\pi$
$548$	6.13118e27	−	1.49186e28i	0.107238	−	0.260936i
$549$		0			0
$550$	3.49110e27	−	1.76788e28i	0.0587698	−	0.297608i
$551$	2.53522e28			0.418720
$552$		0			0
$553$	3.14484e28			0.500017
$554$	7.62302e27	−	3.86026e28i	0.118925	−	0.602233i
$555$		0			0
$556$	−5.15666e28	−	2.11925e28i	−0.774609	−	0.318345i
$557$	1.75916e28			0.259314			0.129657	−	0.991559i	$-0.458612\pi$
$557$	1.75916e28			0.259314			0.129657	+	0.991559i	$0.458612\pi$
$558$		0			0
$559$			2.11379e27i			0.0300080i
$560$	1.12677e28	−	1.13932e28i	0.156987	−	0.158734i
$561$		0			0
$562$	−1.72595e28	+	8.74015e28i	−0.231632	+	1.17297i
$563$			7.72492e28i			1.01755i	0.860900	+	0.508775i	$0.169902\pi$
$563$			7.72492e28i			1.01755i	−0.860900	+	0.508775i	$0.830098\pi$
$564$		0			0
$565$		−	6.89774e28i		−	0.875383i
$566$	−6.12293e28	−	1.20912e28i	−0.762758	−	0.150625i
$567$		0			0
$568$	2.02417e28	+	1.34038e28i	0.242990	+	0.160906i
$569$		−	1.70073e28i		−	0.200427i	−0.994966	−	0.100213i	$-0.968047\pi$
$569$		−	1.70073e28i		−	0.200427i	0.994966	−	0.100213i	$-0.0319525\pi$
$570$		0			0
$571$	−4.06815e28			−0.462081			−0.231041	−	0.972944i	$-0.574213\pi$
$571$	−4.06815e28			−0.462081			−0.231041	+	0.972944i	$0.574213\pi$
$572$	−2.95522e28	−	1.21452e28i	−0.329558	−	0.135440i
$573$		0			0
$574$	−3.96557e28	−	7.83097e27i	−0.426315	−	0.0841862i
$575$	7.88504e28			0.832323
$576$		0			0
$577$	−1.33998e28			−0.136380			−0.0681902	−	0.997672i	$-0.521722\pi$
$577$	−1.33998e28			−0.136380			−0.0681902	+	0.997672i	$0.521722\pi$
$578$	−9.56647e28	−	1.88913e28i	−0.956113	−	0.188808i
$579$		0			0
$580$	−2.41346e28	−	9.91870e27i	−0.232619	−	0.0956007i
$581$	−2.93062e28			−0.277402
$582$		0			0
$583$		−	4.24895e28i		−	0.387938i
$584$	3.54608e28	+	2.34818e28i	0.317990	+	0.210570i
$585$		0			0
$586$	−1.72925e29	−	3.41482e28i	−1.49600	−	0.295422i
$587$			1.35443e29i			1.15095i	0.817820	+	0.575474i	$0.195182\pi$
$587$			1.35443e29i			1.15095i	−0.817820	+	0.575474i	$0.804818\pi$
$588$		0			0
$589$		−	9.25268e28i		−	0.758677i
$590$	−5.67235e27	+	2.87245e28i	−0.0456896	+	0.231370i
$591$		0			0
$592$	−5.30539e28	+	5.36445e28i	−0.412419	+	0.417011i
$593$			1.98032e29i			1.51238i	0.654354	+	0.756189i	$0.272941\pi$
$593$			1.98032e29i			1.51238i	−0.654354	+	0.756189i	$0.727059\pi$
$594$		0			0
$595$	−4.82875e27			−0.0355965
$596$	−6.44893e28	−	2.65035e28i	−0.467092	−	0.191963i
$597$		0			0
$598$	2.70848e28	−	1.37156e29i	0.189393	−	0.959077i
$599$	−9.63667e28			−0.662133			−0.331067	−	0.943607i	$-0.607408\pi$
$599$	−9.63667e28			−0.662133			−0.331067	+	0.943607i	$0.607408\pi$
$600$		0			0
$601$	2.25757e29			1.49782			0.748909	−	0.662672i	$-0.230578\pi$
$601$	2.25757e29			1.49782			0.748909	+	0.662672i	$0.230578\pi$
$602$	4.40336e26	−	2.22984e27i	0.00287092	−	0.0145382i
$603$		0			0
$604$	3.45801e28	−	8.41418e28i	0.217740	−	0.529814i
$605$	7.40450e28			0.458210
$606$		0			0
$607$		−	2.32358e29i		−	1.38892i	−0.719532	−	0.694460i	$-0.755643\pi$
$607$		−	2.32358e29i		−	1.38892i	0.719532	−	0.694460i	$-0.244357\pi$
$608$	9.20072e28	+	1.35657e29i	0.540548	+	0.796993i
$609$		0			0
$610$	2.19835e28	−	1.11324e29i	0.124777	−	0.631865i
$611$			7.42241e27i			0.0414106i
$612$		0			0
$613$		−	7.79578e28i		−	0.420266i	−0.977673	−	0.210133i	$-0.932610\pi$
$613$		−	7.79578e28i		−	0.420266i	0.977673	−	0.210133i	$-0.0673897\pi$
$614$	6.88689e28	+	1.35998e28i	0.364968	+	0.0720718i
$615$		0			0
$616$	2.86447e28	+	1.89682e28i	0.146705	+	0.0971468i
$617$			2.85401e29i			1.43702i	0.695518	+	0.718509i	$0.255175\pi$
$617$			2.85401e29i			1.43702i	−0.695518	+	0.718509i	$0.744825\pi$
$618$		0			0
$619$	−1.14885e29			−0.559130			−0.279565	−	0.960127i	$-0.590190\pi$
$619$	−1.14885e29			−0.559130			−0.279565	+	0.960127i	$0.590190\pi$
$620$	−3.61998e28	+	8.80829e28i	−0.173218	+	0.421482i
$621$		0			0
$622$	−8.63309e28	−	1.70481e28i	−0.399363	−	0.0788638i
$623$	3.01038e28			0.136929
$624$		0			0
$625$	2.46090e28			0.108231
$626$	8.49236e28	+	1.67702e28i	0.367280	+	0.0725284i
$627$		0			0
$628$	5.39043e26	−	1.31162e27i	0.00225449	−	0.00548571i
$629$	2.27360e28			0.0935154
$630$		0			0
$631$		−	6.05866e28i		−	0.241028i	−0.992712	−	0.120514i	$-0.961546\pi$
$631$		−	6.05866e28i		−	0.241028i	0.992712	−	0.120514i	$-0.0384543\pi$
$632$	1.82806e29	−	2.76062e29i	0.715254	−	1.08014i
$633$		0			0
$634$	1.65526e29	+	3.26871e28i	0.626512	+	0.123720i
$635$			1.87526e29i			0.698131i
$636$		0			0
$637$		−	1.84663e29i		−	0.665145i
$638$	1.08383e28	−	5.48846e28i	0.0384011	−	0.194461i
$639$		0			0
$640$	−3.45144e28	−	1.65138e29i	−0.118334	−	0.566185i
$641$		−	2.32482e29i		−	0.784115i	−0.919941	−	0.392058i	$-0.871763\pi$
$641$		−	2.32482e29i		−	0.784115i	0.919941	−	0.392058i	$-0.128237\pi$
$642$		0			0
$643$	−1.15244e29			−0.376186			−0.188093	−	0.982151i	$-0.560231\pi$
$643$	−1.15244e29			−0.376186			−0.188093	+	0.982151i	$0.560231\pi$
$644$	−5.71438e28	+	1.39045e29i	−0.183513	+	0.446532i
$645$		0			0
$646$	9.56947e27	−	4.84593e28i	0.0297472	−	0.150639i
$647$	−5.52470e29			−1.68971			−0.844857	−	0.534992i	$-0.820315\pi$
$647$	−5.52470e29			−1.68971			−0.844857	+	0.534992i	$0.820315\pi$
$648$		0			0
$649$	−6.27753e28			−0.185874
$650$	3.45835e28	−	1.75130e29i	0.100758	−	0.510234i
$651$		0			0
$652$	−2.68543e28	−	1.10364e28i	−0.0757556	−	0.0311336i
$653$	−1.24212e28			−0.0344805			−0.0172402	−	0.999851i	$-0.505488\pi$
$653$	−1.24212e28			−0.0344805			−0.0172402	+	0.999851i	$0.505488\pi$
$654$		0			0
$655$		−	2.53613e29i		−	0.681771i
$656$	−2.99256e29	+	3.02587e29i	−0.791685	+	0.800499i
$657$		0			0
$658$	1.54621e27	−	7.82992e27i	0.00396183	−	0.0200625i
$659$		−	2.13249e29i		−	0.537763i	−0.963173	−	0.268881i	$-0.913346\pi$
$659$		−	2.13249e29i		−	0.537763i	0.963173	−	0.268881i	$-0.0866539\pi$
$660$		0			0
$661$			3.64733e29i			0.890963i	0.895291	+	0.445481i	$0.146967\pi$
$661$			3.64733e29i			0.890963i	−0.895291	+	0.445481i	$0.853033\pi$
$662$	−7.00315e29	−	1.38294e29i	−1.68378	−	0.332502i
$663$		0			0
$664$	−1.70353e29	+	2.57257e29i	−0.396813	+	0.599243i
$665$			9.37678e28i			0.214994i
$666$		0			0
$667$	2.44795e29			0.543852
$668$	−1.56514e29	−	6.43231e28i	−0.342294	−	0.140674i
$669$		0			0
$670$	−3.87401e29	−	7.65017e28i	−0.821062	−	0.162138i
$671$	2.43289e29			0.507617
$672$		0			0
$673$	−8.71986e29			−1.76340			−0.881701	−	0.471809i	$-0.843601\pi$
$673$	−8.71986e29			−1.76340			−0.881701	+	0.471809i	$0.843601\pi$
$674$	−3.54682e27	−	7.00404e26i	−0.00706171	−	0.00139450i
$675$		0			0
$676$	1.86489e29	+	7.66421e28i	0.359925	+	0.147920i
$677$	−3.37073e28			−0.0640535			−0.0320268	−	0.999487i	$-0.510196\pi$
$677$	−3.37073e28			−0.0640535			−0.0320268	+	0.999487i	$0.510196\pi$
$678$		0			0
$679$			1.00543e29i			0.185233i
$680$	−2.80689e28	+	4.23880e28i	−0.0509193	+	0.0768953i
$681$		0			0
$682$	−2.00310e29	−	3.95560e28i	−0.352343	−	0.0695787i
$683$		−	5.16670e29i		−	0.894943i	−0.894298	−	0.447472i	$-0.852325\pi$
$683$		−	5.16670e29i		−	0.894943i	0.894298	−	0.447472i	$-0.147675\pi$
$684$		0			0
$685$		−	9.71438e28i		−	0.163179i
$686$	−8.36705e28	+	4.23703e29i	−0.138410	+	0.700904i
$687$		0			0
$688$	−1.70145e28	−	1.68272e28i	−0.0272986	−	0.0269980i
$689$		−	4.20909e29i		−	0.665100i
$690$		0			0
$691$	−6.54018e29			−1.00247			−0.501233	−	0.865312i	$-0.667120\pi$
$691$	−6.54018e29			−1.00247			−0.501233	+	0.865312i	$0.667120\pi$
$692$	3.38224e29	+	1.39002e29i	0.510612	+	0.209848i
$693$		0			0
$694$	1.19257e29	−	6.03914e29i	0.174667	−	0.884505i
$695$	−3.35780e29			−0.484411
$696$		0			0
$697$	1.28245e29			0.179513
$698$	−2.11399e29	+	1.07052e30i	−0.291489	+	1.47609i
$699$		0			0
$700$	−7.29646e28	+	1.77540e29i	−0.0976299	+	0.237557i
$701$	−4.61494e29			−0.608312			−0.304156	−	0.952622i	$-0.598374\pi$
$701$	−4.61494e29			−0.608312			−0.304156	+	0.952622i	$0.598374\pi$
$702$		0			0
$703$		−	4.41503e29i		−	0.564811i
$704$	3.33016e29	−	1.41190e29i	0.419712	−	0.177948i
$705$		0			0
$706$	1.04747e29	−	5.30437e29i	0.128143	−	0.648909i
$707$		−	1.92301e29i		−	0.231780i
$708$		0			0
$709$			9.25637e29i			1.08307i	0.840679	+	0.541533i	$0.182156\pi$
$709$			9.25637e29i			1.08307i	−0.840679	+	0.541533i	$0.817844\pi$
$710$	1.43447e29	+	2.83270e28i	0.165378	+	0.0326579i
$711$		0			0
$712$	1.74989e29	−	2.64258e29i	0.195872	−	0.295794i
$713$		−	8.93416e29i		−	0.985402i
$714$		0			0
$715$	−1.92431e29			−0.206093
$716$	3.31684e29	−	8.07066e29i	0.350056	−	0.851770i
$717$		0			0
$718$	4.63509e29	+	9.15309e28i	0.475063	+	0.0938126i
$719$	−8.05335e29			−0.813435			−0.406718	−	0.913554i	$-0.633327\pi$
$719$	−8.05335e29			−0.813435			−0.406718	+	0.913554i	$0.633327\pi$
$720$		0			0
$721$	7.49439e28			0.0735218
$722$	7.36756e28	+	1.45490e28i	0.0712333	+	0.0140667i
$723$		0			0
$724$	1.23170e29	−	2.99701e29i	0.115677	−	0.281471i
$725$	3.12568e29			0.289332
$726$		0			0
$727$			7.04103e29i			0.633177i	0.948563	+	0.316588i	$0.102537\pi$
$727$			7.04103e29i			0.633177i	−0.948563	+	0.316588i	$0.897463\pi$
$728$	2.83760e29	+	1.87903e29i	0.251519	+	0.166553i
$729$		0			0
$730$	2.51301e29	+	4.96254e28i	0.216423	+	0.0427379i
$731$			7.21122e27i			0.00612176i
$732$		0			0
$733$			1.59242e30i			1.31361i	0.754061	+	0.656804i	$0.228092\pi$
$733$			1.59242e30i			1.31361i	−0.754061	+	0.656804i	$0.771908\pi$
$734$	−2.43781e29	+	1.23450e30i	−0.198240	+	1.00388i
$735$		0			0
$736$	8.88399e29	+	1.30987e30i	0.702087	+	1.03517i
$737$		−	8.46636e29i		−	0.659611i
$738$		0			0
$739$	−2.85144e29			−0.215923			−0.107961	−	0.994155i	$-0.534432\pi$
$739$	−2.85144e29			−0.215923			−0.107961	+	0.994155i	$0.534432\pi$
$740$	−1.72732e29	+	4.20299e29i	−0.128956	+	0.313780i
$741$		0			0
$742$	−8.76822e28	+	4.44019e29i	−0.0636312	+	0.322226i
$743$	3.45973e29			0.247548			0.123774	−	0.992310i	$-0.460500\pi$
$743$	3.45973e29			0.247548			0.123774	+	0.992310i	$0.460500\pi$
$744$		0			0
$745$	−4.19927e29			−0.292101
$746$	1.20964e29	−	6.12555e29i	0.0829655	−	0.420134i
$747$		0			0
$748$	−1.00818e29	−	4.14335e28i	−0.0672311	−	0.0276303i
$749$	8.61939e28			0.0566784
$750$		0			0
$751$		−	1.33112e29i		−	0.0851131i	−0.999094	−	0.0425565i	$-0.986450\pi$
$751$		−	1.33112e29i		−	0.0851131i	0.999094	−	0.0425565i	$-0.0135503\pi$
$752$	−5.97451e28	−	5.90873e28i	−0.0376717	−	0.0372569i
$753$		0			0
$754$	1.07366e29	−	5.43697e29i	0.0658367	−	0.333394i
$755$		−	5.47895e29i		−	0.331325i
$756$		0			0
$757$			1.79693e30i			1.05688i	0.848972	+	0.528438i	$0.177222\pi$
$757$			1.79693e30i			1.05688i	−0.848972	+	0.528438i	$0.822778\pi$
$758$	2.64156e30	+	5.21640e29i	1.53227	+	0.302583i
$759$		0			0
$760$	8.23118e29	+	5.45061e29i	0.464429	+	0.307540i
$761$		−	3.39198e30i		−	1.88762i	−0.330493	−	0.943809i	$-0.607215\pi$
$761$		−	3.39198e30i		−	1.88762i	0.330493	−	0.943809i	$-0.392785\pi$
$762$		0			0
$763$	5.02564e29			0.272072
$764$	2.43290e30	+	9.99860e29i	1.29910	+	0.533899i
$765$		0			0
$766$	3.06534e30	+	6.05325e29i	1.59249	+	0.314475i
$767$	−6.21864e29			−0.318672
$768$		0			0
$769$	−1.06042e30			−0.528749			−0.264374	−	0.964420i	$-0.585165\pi$
$769$	−1.06042e30			−0.528749			−0.264374	+	0.964420i	$0.585165\pi$
$770$	2.02996e29	+	4.00865e28i	0.0998472	+	0.0197172i
$771$		0			0
$772$	3.07835e30	+	1.26512e30i	1.47345	+	0.605551i
$773$	3.18532e30			1.50407			0.752034	−	0.659124i	$-0.229073\pi$
$773$	3.18532e30			1.50407			0.752034	+	0.659124i	$0.229073\pi$
$774$		0			0
$775$		−	1.14077e30i		−	0.524239i
$776$	8.82592e29	+	5.84443e29i	0.400140	+	0.264969i
$777$		0			0
$778$	1.57951e30	+	3.11911e29i	0.697004	+	0.137640i
$779$		−	2.49034e30i		−	1.08422i
$780$		0			0
$781$			3.13492e29i			0.132859i
$782$	9.24004e28	−	4.67911e29i	0.0386370	−	0.195656i
$783$		0			0
$784$	1.48641e30	+	1.47004e30i	0.605089	+	0.598427i
$785$		−	8.54073e27i		−	0.00343055i
$786$		0			0
$787$	3.70851e29			0.145032			0.0725162	−	0.997367i	$-0.476897\pi$
$787$	3.70851e29			0.145032			0.0725162	+	0.997367i	$0.476897\pi$
$788$	3.68133e30	+	1.51293e30i	1.42062	+	0.583840i
$789$		0			0
$790$	3.86333e29	−	1.95637e30i	0.145170	−	0.735136i
$791$	−1.57530e30			−0.584129
$792$		0			0
$793$	2.41007e30			0.870285
$794$	−7.91746e29	+	4.00937e30i	−0.282144	+	1.42876i
$795$		0			0
$796$	−1.10289e30	+	2.68361e30i	−0.382778	+	0.931390i
$797$	1.07896e30			0.369568			0.184784	−	0.982779i	$-0.440842\pi$
$797$	1.07896e30			0.369568			0.184784	+	0.982779i	$0.440842\pi$
$798$		0			0
$799$			2.53217e28i			0.00844794i
$800$	1.13436e30	+	1.67252e30i	0.373514	+	0.550715i
$801$		0			0
$802$	9.20081e29	−	4.65925e30i	0.295118	−	1.49446i
$803$			5.49198e29i			0.173866i
$804$		0			0
$805$			9.05399e29i			0.279244i
$806$	−1.98431e30	−	3.91849e29i	−0.604075	−	0.119289i
$807$		0			0
$808$	−1.68806e30	−	1.11782e30i	−0.500691	−	0.331552i
$809$			2.83812e29i			0.0830944i	0.999137	+	0.0415472i	$0.0132287\pi$
$809$			2.83812e29i			0.0830944i	−0.999137	+	0.0415472i	$0.986771\pi$
$810$		0			0
$811$	−4.46506e30			−1.27382			−0.636910	−	0.770938i	$-0.719788\pi$
$811$	−4.46506e30			−1.27382			−0.636910	+	0.770938i	$0.719788\pi$
$812$	−2.26522e29	+	5.51182e29i	−0.0637928	+	0.155223i
$813$		0			0
$814$	−9.55803e29	−	1.88746e29i	−0.262308	−	0.0517991i
$815$	−1.74864e29			−0.0473746
$816$		0			0
$817$	1.40032e29			0.0369740
$818$	1.28492e30	+	2.53738e29i	0.334939	+	0.0661417i
$819$		0			0
$820$	−9.74313e29	+	2.37074e30i	−0.247544	+	0.602335i
$821$	−9.72752e29			−0.244005			−0.122003	−	0.992530i	$-0.538932\pi$
$821$	−9.72752e29			−0.244005			−0.122003	+	0.992530i	$0.538932\pi$
$822$		0			0
$823$		−	2.50469e30i		−	0.612430i	−0.951962	−	0.306215i	$-0.900937\pi$
$823$		−	2.50469e30i		−	0.612430i	0.951962	−	0.306215i	$-0.0990626\pi$
$824$	4.35639e29	−	6.57877e29i	0.105170	−	0.158821i
$825$		0			0
$826$	6.56007e29	+	1.29544e29i	0.154389	+	0.0304879i
$827$		−	3.09889e30i		−	0.720110i	−0.932931	−	0.360055i	$-0.882758\pi$
$827$		−	3.09889e30i		−	0.720110i	0.932931	−	0.360055i	$-0.117242\pi$
$828$		0			0
$829$			6.77675e30i			1.53532i	0.640857	+	0.767660i	$0.278579\pi$
$829$			6.77675e30i			1.53532i	−0.640857	+	0.767660i	$0.721421\pi$
$830$	−3.60017e29	+	1.82311e30i	−0.0805383	+	0.407843i
$831$		0			0
$832$	3.29892e30	−	1.39866e30i	0.719576	−	0.305083i
$833$		−	6.29981e29i		−	0.135692i
$834$		0			0
$835$	−1.01915e30			−0.214057
$836$	−8.04584e29	+	1.95775e30i	−0.166880	+	0.406060i
$837$		0			0
$838$	4.88470e29	−	2.47359e30i	0.0988043	−	0.500341i
$839$	−4.72269e30			−0.943385			−0.471693	−	0.881763i	$-0.656357\pi$
$839$	−4.72269e30			−0.943385			−0.471693	+	0.881763i	$0.656357\pi$
$840$		0			0
$841$	−4.16246e30			−0.810946
$842$	2.27496e28	−	1.15203e29i	0.00437721	−	0.0221660i
$843$		0			0
$844$	4.31959e30	+	1.77524e30i	0.810675	+	0.333167i
$845$	1.21433e30			0.225083
$846$		0			0
$847$		−	1.69103e30i		−	0.305756i
$848$	3.38803e30	+	3.35072e30i	0.605048	+	0.598387i
$849$		0			0
$850$	1.17982e29	−	5.97457e29i	0.0205550	−	0.104090i
$851$		−	4.26305e30i		−	0.733600i
$852$		0			0
$853$			1.99566e30i			0.335059i	0.985867	+	0.167530i	$0.0535790\pi$
$853$			1.99566e30i			0.335059i	−0.985867	+	0.167530i	$0.946421\pi$
$854$	−2.54239e30	−	5.02056e29i	−0.421633	−	0.0832616i
$855$		0			0
$856$	5.01034e29	−	7.56632e29i	0.0810761	−	0.122436i
$857$		−	6.68470e30i		−	1.06852i	−0.845320	−	0.534261i	$-0.820590\pi$
$857$		−	6.68470e30i		−	1.06852i	0.845320	−	0.534261i	$-0.179410\pi$
$858$		0			0
$859$	−8.11717e30			−1.26612			−0.633062	−	0.774101i	$-0.718202\pi$
$859$	−8.11717e30			−1.26612			−0.633062	+	0.774101i	$0.718202\pi$
$860$	−1.33307e29	−	5.47857e28i	−0.0205408	−	0.00844176i
$861$		0			0
$862$	−8.19784e30	−	1.61886e30i	−1.23274	−	0.243435i
$863$	−5.82775e30			−0.865741			−0.432870	−	0.901456i	$-0.642499\pi$
$863$	−5.82775e30			−0.865741			−0.432870	+	0.901456i	$0.642499\pi$
$864$		0			0
$865$	2.20237e30			0.319317
$866$	−1.23641e31	−	2.44160e30i	−1.77103	−	0.349733i
$867$		0			0
$868$	2.01162e30	+	8.26726e29i	0.281248	+	0.115586i
$869$	4.27551e30			0.590581
$870$		0			0
$871$		−	8.38694e30i		−	1.13087i
$872$	2.92134e30	−	4.41163e30i	0.389188	−	0.587728i
$873$		0			0
$874$	−9.08621e30	−	1.79429e30i	−1.18171	−	0.233358i
$875$			2.89339e30i			0.371811i
$876$		0			0
$877$			1.49736e31i			1.87858i	0.343126	+	0.939289i	$0.388514\pi$
$877$			1.49736e31i			1.87858i	−0.343126	+	0.939289i	$0.611486\pi$
$878$	−5.61495e29	+	2.84338e30i	−0.0696071	+	0.352487i
$879$		0			0
$880$	1.53188e30	−	1.54894e30i	0.185420	−	0.187485i
$881$			1.75535e30i			0.209951i	0.994475	+	0.104975i	$0.0334764\pi$
$881$			1.75535e30i			0.209951i	−0.994475	+	0.104975i	$0.966524\pi$
$882$		0			0
$883$	−1.66963e30			−0.195000			−0.0974999	−	0.995236i	$-0.531085\pi$
$883$	−1.66963e30			−0.195000			−0.0974999	+	0.995236i	$0.531085\pi$
$884$	−9.98721e29	−	4.10449e29i	−0.115264	−	0.0473708i
$885$		0			0
$886$	2.38567e29	−	1.20809e30i	0.0268879	−	0.136159i
$887$	−5.21045e30			−0.580333			−0.290167	−	0.956976i	$-0.593711\pi$
$887$	−5.21045e30			−0.580333			−0.290167	+	0.956976i	$0.593711\pi$
$888$		0			0
$889$	4.28268e30			0.465851
$890$	3.69814e29	−	1.87272e30i	0.0397547	−	0.201316i
$891$		0			0
$892$	−4.48076e29	+	1.09028e30i	−0.0470457	+	0.114474i
$893$	4.91712e29			0.0510236
$894$		0			0
$895$		−	5.25527e30i		−	0.532664i
$896$	−3.77140e30	+	7.88234e29i	−0.377806	+	0.0789625i
$897$		0			0
$898$	3.61044e30	−	1.82831e31i	0.353312	−	1.78916i
$899$		−	3.54156e30i		−	0.342545i
$900$		0			0
$901$		−	1.43594e30i		−	0.135683i
$902$	−5.39131e30	−	1.06464e30i	−0.503530	−	0.0994341i
$903$		0			0
$904$	−9.15699e30	+	1.38283e31i	−0.835573	+	1.26183i
$905$		−	1.95153e30i		−	0.176021i
$906$		0			0
$907$	6.99978e30			0.616890			0.308445	−	0.951242i	$-0.400191\pi$
$907$	6.99978e30			0.616890			0.308445	+	0.951242i	$0.400191\pi$
$908$	5.70324e30	−	1.38774e31i	0.496845	−	1.20894i
$909$		0			0
$910$	2.01092e30	+	3.97105e29i	0.171183	+	0.0338042i
$911$	−2.09804e31			−1.76551			−0.882755	−	0.469833i	$-0.844314\pi$
$911$	−2.09804e31			−1.76551			−0.882755	+	0.469833i	$0.844314\pi$
$912$		0			0
$913$	−3.98426e30			−0.327646
$914$	−8.29276e30	−	1.63761e30i	−0.674162	−	0.133129i
$915$		0			0
$916$	−4.52896e30	+	1.10200e31i	−0.359829	+	0.875550i
$917$	−5.79198e30			−0.454935
$918$		0			0
$919$		−	1.93321e31i		−	1.48411i	−0.670341	−	0.742053i	$-0.733852\pi$
$919$		−	1.93321e31i		−	1.48411i	0.670341	−	0.742053i	$-0.266148\pi$
$920$	7.94783e30	+	5.26297e30i	0.603221	+	0.399447i
$921$		0			0
$922$	−9.75764e30	−	1.92688e30i	−0.723886	−	0.142949i
$923$			3.10551e30i			0.227780i
$924$		0			0
$925$		−	5.44331e30i		−	0.390279i
$926$	−2.00376e30	+	1.01470e31i	−0.142047	+	0.719317i
$927$		0			0
$928$	3.52167e30	+	5.19242e30i	0.244059	+	0.359845i
$929$			2.03508e31i			1.39449i	0.716831	+	0.697247i	$0.245592\pi$
$929$			2.03508e31i			1.39449i	−0.716831	+	0.697247i	$0.754408\pi$
$930$		0			0
$931$	−1.22334e31			−0.819549
$932$	−2.60275e30	+	6.33312e30i	−0.172411	+	0.419518i
$933$		0			0
$934$	5.18863e30	−	2.62750e31i	0.336055	−	1.70177i
$935$	−6.56483e29			−0.0420437
$936$		0			0
$937$	−1.14056e31			−0.714252			−0.357126	−	0.934056i	$-0.616243\pi$
$937$	−1.14056e31			−0.714252			−0.357126	+	0.934056i	$0.616243\pi$
$938$	−1.74713e30	+	8.84741e30i	−0.108192	+	0.547881i
$939$		0			0
$940$	−4.68097e29	−	1.92376e29i	−0.0283461	−	0.0116495i
$941$	3.14376e31			1.88260			0.941300	−	0.337571i	$-0.109605\pi$
$941$	3.14376e31			1.88260			0.941300	+	0.337571i	$0.109605\pi$
$942$		0			0
$943$		−	2.40462e31i		−	1.40823i
$944$	4.95046e30	−	5.00557e30i	0.286708	−	0.289900i
$945$		0			0
$946$	5.98649e28	−	3.03153e29i	0.00339090	−	0.0171714i
$947$			2.80622e31i			1.57198i	0.618240	+	0.785990i	$0.287846\pi$
$947$			2.80622e31i			1.57198i	−0.618240	+	0.785990i	$0.712154\pi$
$948$		0			0
$949$			5.44046e30i			0.298085i
$950$	−1.16018e31	−	2.29106e30i	−0.628678	−	0.124148i
$951$		0			0
$952$	9.68051e29	+	6.41033e29i	0.0513110	+	0.0339776i
$953$			1.14106e31i			0.598181i	0.954225	+	0.299090i	$0.0966832\pi$
$953$			1.14106e31i			0.598181i	−0.954225	+	0.299090i	$0.903317\pi$
$954$		0			0
$955$	1.58420e31			0.812410
$956$	5.89817e30	+	2.42400e30i	0.299164	+	0.122949i
$957$		0			0
$958$	−2.33542e31	−	4.61185e30i	−1.15885	−	0.228843i
$959$	−2.21855e30			−0.108887
$960$		0			0
$961$	7.90004e30			0.379344
$962$	−9.46837e30	−	1.86976e30i	−0.449715	−	0.0888070i
$963$		0			0
$964$	−2.37906e30	−	9.77733e29i	−0.110560	−	0.0454372i
$965$	2.00449e31			0.921439
$966$		0			0
$967$		−	3.65650e31i		−	1.64470i	−0.568981	−	0.822351i	$-0.692662\pi$
$967$		−	3.65650e31i		−	1.64470i	0.568981	−	0.822351i	$-0.307338\pi$
$968$	−1.48443e31	−	9.82973e30i	−0.660492	−	0.437371i
$969$		0			0
$970$	6.25467e30	+	1.23514e30i	0.272334	+	0.0537789i
$971$			4.32015e31i			1.86079i	0.366562	+	0.930394i	$0.380535\pi$
$971$			4.32015e31i			1.86079i	−0.366562	+	0.930394i	$0.619465\pi$
$972$		0			0
$973$			7.66848e30i			0.323239i
$974$	2.84390e30	−	1.44014e31i	0.118589	−	0.600530i
$975$		0			0
$976$	−1.91858e31	+	1.93994e31i	−0.782990	+	0.791707i
$977$		−	1.19922e31i		−	0.484180i	−0.970254	−	0.242090i	$-0.922167\pi$
$977$		−	1.19922e31i		−	0.484180i	0.970254	−	0.242090i	$-0.0778329\pi$
$978$		0			0
$979$	4.09269e30			0.161730
$980$	1.16458e31	+	4.78615e30i	0.455300	+	0.187117i
$981$		0			0
$982$	6.58357e30	−	3.33389e31i	0.251936	−	1.27579i
$983$	−8.52609e29			−0.0322803			−0.0161402	−	0.999870i	$-0.505138\pi$
$983$	−8.52609e29			−0.0322803			−0.0161402	+	0.999870i	$0.505138\pi$
$984$		0			0
$985$	2.39712e31			0.888403
$986$	3.66281e29	−	1.85483e30i	0.0134310	−	0.0680138i
$987$		0			0
$988$	−7.97036e30	+	1.93938e31i	−0.286108	+	0.696170i
$989$	1.35212e30			0.0480234
$990$		0			0
$991$		−	4.35165e31i		−	1.51315i	−0.653910	−	0.756573i	$-0.726872\pi$
$991$		−	4.35165e31i		−	1.51315i	0.653910	−	0.756573i	$-0.273128\pi$
$992$	1.89505e31	−	1.28529e31i	0.652002	−	0.442210i
$993$		0			0
$994$	6.46928e29	−	3.27601e30i	0.0217921	−	0.110354i
$995$			1.74745e31i			0.582455i
$996$		0			0
$997$			4.74655e31i			1.54910i	0.632514	+	0.774549i	$0.282023\pi$
$997$			4.74655e31i			1.54910i	−0.632514	+	0.774549i	$0.717977\pi$
$998$	−2.88985e31	−	5.70670e30i	−0.933264	−	0.184295i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.22.f.a.35.5	✓	84
3.2	odd	2	inner	72.22.f.a.35.80	yes	84
8.3	odd	2	inner	72.22.f.a.35.79	yes	84
24.11	even	2	inner	72.22.f.a.35.6	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.22.f.a.35.5	✓	84	1.1	even	1	trivial
72.22.f.a.35.6	yes	84	24.11	even	2	inner
72.22.f.a.35.79	yes	84	8.3	odd	2	inner
72.22.f.a.35.80	yes	84	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 72 = 2^{3} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 22 \)
Character orbit:	\([\chi]\)	\(=\)	72.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1420.72 - 280.555i) q^{2} +(1.93973e6 + 797180. i) q^{4} +1.26307e7 q^{5} -2.88458e8i q^{7} +(-2.53216e9 - 1.67677e9i) q^{8} +O(q^{10})\)	\(q+(-1420.72 - 280.555i) q^{2} +(1.93973e6 + 797180. i) q^{4} +1.26307e7 q^{5} -2.88458e8i q^{7} +(-2.53216e9 - 1.67677e9i) q^{8} +(-1.79447e10 - 3.54361e9i) q^{10} -3.92167e10i q^{11} -3.88488e11i q^{13} +(-8.09283e10 + 4.09817e11i) q^{14} +(3.12706e12 + 3.09263e12i) q^{16} -1.32533e12i q^{17} -2.57362e13 q^{19} +(2.45001e13 + 1.00689e13i) q^{20} +(-1.10024e13 + 5.57158e13i) q^{22} -2.48502e14 q^{23} -3.17303e14 q^{25} +(-1.08992e14 + 5.51932e14i) q^{26} +(2.29953e14 - 5.59530e14i) q^{28} -9.85080e14 q^{29} +3.59520e15i q^{31} +(-3.57501e15 - 5.27106e15i) q^{32} +(-3.71829e14 + 1.88293e15i) q^{34} -3.64342e15i q^{35} +1.71550e16i q^{37} +(3.65639e16 + 7.22042e15i) q^{38} +(-3.19829e16 - 2.11788e16i) q^{40} +9.67643e16i q^{41} -5.44106e15 q^{43} +(3.12627e16 - 7.60697e16i) q^{44} +(3.53052e17 + 6.97186e16i) q^{46} -1.91059e16 q^{47} +4.75338e17 q^{49} +(4.50798e17 + 8.90209e16i) q^{50} +(3.09695e17 - 7.53562e17i) q^{52} +1.08346e18 q^{53} -4.95334e17i q^{55} +(-4.83677e17 + 7.30420e17i) q^{56} +(1.39952e18 + 2.76369e17i) q^{58} -1.60073e18i q^{59} +6.20372e18i q^{61} +(1.00865e18 - 5.10777e18i) q^{62} +(3.60027e18 + 8.49168e18i) q^{64} -4.90688e18i q^{65} +2.15887e19 q^{67} +(1.05653e18 - 2.57079e18i) q^{68} +(-1.02218e18 + 5.17628e18i) q^{70} -7.99384e18 q^{71} -1.40042e19 q^{73} +(4.81291e18 - 2.43724e19i) q^{74} +(-4.99213e19 - 2.05164e19i) q^{76} -1.13124e19 q^{77} +1.09023e20i q^{79} +(3.94969e19 + 3.90620e19i) q^{80} +(2.71477e19 - 1.37475e20i) q^{82} -1.01596e20i q^{83} -1.67399e19i q^{85} +(7.73021e18 + 1.52652e18i) q^{86} +(-6.57573e19 + 9.93028e19i) q^{88} +1.04361e20i q^{89} -1.12062e20 q^{91} +(-4.82027e20 - 1.98101e20i) q^{92} +(2.71441e19 + 5.36025e18i) q^{94} -3.25066e20 q^{95} -3.48553e20 q^{97} +(-6.75321e20 - 1.33358e20i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q + 2424084 q^{4}+O(q^{10}) \) 84 * q + 2424084 * q^4	\( 84 q + 2424084 q^{4} + 17057181612 q^{10} - 4099708064904 q^{16} + 92015527242864 q^{19} - 236011369239528 q^{22} + 80\!\cdots\!00 q^{25}+ \cdots - 16\!\cdots\!12 q^{97}+O(q^{100}) \) 84 * q + 2424084 * q^4 + 17057181612 * q^10 - 4099708064904 * q^16 + 92015527242864 * q^19 - 236011369239528 * q^22 + 8010864257812500 * q^25 - 3042238700022024 * q^28 + 74414158327329924 * q^34 + 75018327243317184 * q^40 + 707788847336454432 * q^43 - 162639476543943288 * q^46 - 5423745715136249124 * q^49 - 70566629446202808 * q^52 - 14491558288019904108 * q^58 - 28749968749508108064 * q^64 - 13653811098426494352 * q^67 + 140256684870035374392 * q^70 - 71781309378863778384 * q^73 + 376055720386305092400 * q^76 - 368362114062816367548 * q^82 - 592572120184082106720 * q^88 - 522206955652189957200 * q^91 - 528772551789914644488 * q^94 - 1686050813935078492512 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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