LMFDB - Embedded newform 64.24.e.a.17.45

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [64,24,Mod(17,64)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(64, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3]))

N = Newforms(chi, 24, names="a")

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

chi := DirichletCharacter("64.17");

S:= CuspForms(chi, 24);

N := Newforms(S);

Level:	$ N $	$=$	$ 64 = 2^{6} $
Weight:	$ k $	$=$	$ 24 $
Character orbit:	$[\chi]$	$=$	64.e (of order $4$, degree $2$, not 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:	$214.530583901$
Analytic rank:	$0$
Dimension:	$90$
Relative dimension:	$45$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 16)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			17.45
Character	$\chi$	$=$	64.17
Dual form			64.24.e.a.49.45

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(413460. + 413460. i) q^{3} +(-3.88787e6 + 3.88787e6i) q^{5} +7.12996e9i q^{7} +2.47755e11i q^{9} +O(q^{10})$	\(q+(413460. + 413460. i) q^{3} +(-3.88787e6 + 3.88787e6i) q^{5} +7.12996e9i q^{7} +2.47755e11i q^{9} +(-5.30508e11 + 5.30508e11i) q^{11} +(2.16422e12 + 2.16422e12i) q^{13} -3.21496e12 q^{15} +1.09838e14 q^{17} +(-5.54544e14 - 5.54544e14i) q^{19} +(-2.94795e15 + 2.94795e15i) q^{21} -3.03696e15i q^{23} +1.18907e16i q^{25} +(-6.35126e16 + 6.35126e16i) q^{27} +(-3.21568e16 - 3.21568e16i) q^{29} -1.25797e17 q^{31} -4.38688e17 q^{33} +(-2.77204e16 - 2.77204e16i) q^{35} +(-1.16722e18 + 1.16722e18i) q^{37} +1.78964e18i q^{39} -2.75070e18i q^{41} +(6.78659e18 - 6.78659e18i) q^{43} +(-9.63242e17 - 9.63242e17i) q^{45} +8.15595e18 q^{47} -2.34675e19 q^{49} +(4.54138e19 + 4.54138e19i) q^{51} +(-5.87678e19 + 5.87678e19i) q^{53} -4.12510e18i q^{55} -4.58564e20i q^{57} +(-2.38468e19 + 2.38468e19i) q^{59} +(3.83019e20 + 3.83019e20i) q^{61} -1.76649e21 q^{63} -1.68284e19 q^{65} +(5.83073e20 + 5.83073e20i) q^{67} +(1.25566e21 - 1.25566e21i) q^{69} -1.63662e21i q^{71} -1.55178e21i q^{73} +(-4.91633e21 + 4.91633e21i) q^{75} +(-3.78250e21 - 3.78250e21i) q^{77} -1.07753e21 q^{79} -2.91954e22 q^{81} +(-1.13427e22 - 1.13427e22i) q^{83} +(-4.27038e20 + 4.27038e20i) q^{85} -2.65911e22i q^{87} +2.95437e22i q^{89} +(-1.54308e22 + 1.54308e22i) q^{91} +(-5.20122e22 - 5.20122e22i) q^{93} +4.31200e21 q^{95} +4.92555e22 q^{97} +(-1.31436e23 - 1.31436e23i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 90 q + 2 q^{3} - 2 q^{5}+O(q^{10}) $ 90 * q + 2 * q^3 - 2 * q^5	$ 90 q + 2 q^{3} - 2 q^{5} - 975574266674 q^{11} - 2 q^{13} + 69198046875004 q^{15} - 4 q^{17} - 33497748322214 q^{19} + 188286357652 q^{21} + 68\!\cdots\!12 q^{27}+ \cdots - 15\!\cdots\!18 q^{99}+O(q^{100}) $ 90 * q + 2 * q^3 - 2 * q^5 - 975574266674 * q^11 - 2 * q^13 + 69198046875004 * q^15 - 4 * q^17 - 33497748322214 * q^19 + 188286357652 * q^21 + 68199758786330312 * q^27 + 40182344820854166 * q^29 - 304901722756857968 * q^31 - 4 * q^33 + 71740198139629924 * q^35 - 1247331607738910506 * q^37 + 9188667298883114726 * q^43 + 23841669623798594 * q^45 + 49443184301680246064 * q^47 - 304966041789473067826 * q^49 + 174534019299729287580 * q^51 + 13640530997232145574 * q^53 - 601560376862930647818 * q^59 - 689547400664843490610 * q^61 - 1350487157131380135108 * q^63 + 677755821971313699508 * q^65 + 78203218176043282218 * q^67 - 1740473287260991535900 * q^69 + 4337902598314368797354 * q^75 - 5419518588555145686572 * q^77 - 7302797173814966423104 * q^79 - 72873046761587231233198 * q^81 + 32909130597108510028802 * q^83 - 25986931398852441406252 * q^85 - 85476927041001397522436 * q^91 + 79297851703427311011376 * q^93 - 418206809033540036489460 * q^95 - 4 * q^97 - 153989708813859231365918 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/64\mathbb{Z}\right)^\times$.

$n$	$5$	$63$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	413460.	+	413460.i	1.34753	+	1.34753i	0.888333	+	0.459199i	$0.151864\pi$
$3$	413460.	+	413460.i	1.34753	+	1.34753i	0.459199	+	0.888333i	$0.348136\pi$
$4$		0			0
$5$	−3.88787e6	+	3.88787e6i	−0.0356088	+	0.0356088i	−0.724687	−	0.689078i	$-0.758016\pi$
$5$	−3.88787e6	+	3.88787e6i	−0.0356088	+	0.0356088i	0.689078	+	0.724687i	$0.258016\pi$
$6$		0			0
$7$			7.12996e9i			1.36289i	0.731871	+	0.681443i	$0.238647\pi$
$7$			7.12996e9i			1.36289i	−0.731871	+	0.681443i	$0.761353\pi$
$8$		0			0
$9$			2.47755e11i			2.63169i
$10$		0			0
$11$	−5.30508e11	+	5.30508e11i	−0.560630	+	0.560630i	−0.929486	−	0.368857i	$-0.879749\pi$
$11$	−5.30508e11	+	5.30508e11i	−0.560630	+	0.560630i	0.368857	+	0.929486i	$0.379749\pi$
$12$		0			0
$13$	2.16422e12	+	2.16422e12i	0.334929	+	0.334929i	0.854455	−	0.519526i	$-0.173891\pi$
$13$	2.16422e12	+	2.16422e12i	0.334929	+	0.334929i	−0.519526	+	0.854455i	$0.673891\pi$
$14$		0			0
$15$	−3.21496e12			−0.0959680
$16$		0			0
$17$	1.09838e14			0.777305			0.388653	−	0.921384i	$-0.372941\pi$
$17$	1.09838e14			0.777305			0.388653	+	0.921384i	$0.372941\pi$
$18$		0			0
$19$	−5.54544e14	−	5.54544e14i	−1.09212	−	1.09212i	−0.995302	−	0.0968162i	$-0.969134\pi$
$19$	−5.54544e14	−	5.54544e14i	−1.09212	−	1.09212i	−0.0968162	−	0.995302i	$-0.530866\pi$
$20$		0			0
$21$	−2.94795e15	+	2.94795e15i	−1.83653	+	1.83653i
$22$		0			0
$23$		−	3.03696e15i		−	0.664613i	−0.943171	−	0.332307i	$-0.892173\pi$
$23$		−	3.03696e15i		−	0.664613i	0.943171	−	0.332307i	$-0.107827\pi$
$24$		0			0
$25$			1.18907e16i			0.997464i
$26$		0			0
$27$	−6.35126e16	+	6.35126e16i	−2.19875	+	2.19875i
$28$		0			0
$29$	−3.21568e16	−	3.21568e16i	−0.489435	−	0.489435i	0.418693	−	0.908128i	$-0.362488\pi$
$29$	−3.21568e16	−	3.21568e16i	−0.489435	−	0.489435i	−0.908128	+	0.418693i	$0.862488\pi$
$30$		0			0
$31$	−1.25797e17			−0.889225			−0.444613	−	0.895723i	$-0.646659\pi$
$31$	−1.25797e17			−0.889225			−0.444613	+	0.895723i	$0.646659\pi$
$32$		0			0
$33$	−4.38688e17			−1.51093
$34$		0			0
$35$	−2.77204e16	−	2.77204e16i	−0.0485307	−	0.0485307i
$36$		0			0
$37$	−1.16722e18	+	1.16722e18i	−1.07853	+	1.07853i	−0.0818857	+	0.996642i	$0.526094\pi$
$37$	−1.16722e18	+	1.16722e18i	−1.07853	+	1.07853i	−0.996642	+	0.0818857i	$0.973906\pi$
$38$		0			0
$39$			1.78964e18i			0.902655i
$40$		0			0
$41$		−	2.75070e18i		−	0.780601i	−0.920688	−	0.390300i	$-0.872371\pi$
$41$		−	2.75070e18i		−	0.780601i	0.920688	−	0.390300i	$-0.127629\pi$
$42$		0			0
$43$	6.78659e18	−	6.78659e18i	1.11369	−	1.11369i	0.121042	−	0.992647i	$-0.461376\pi$
$43$	6.78659e18	−	6.78659e18i	1.11369	−	1.11369i	0.992647	−	0.121042i	$-0.0386236\pi$
$44$		0			0
$45$	−9.63242e17	−	9.63242e17i	−0.0937112	−	0.0937112i
$46$		0			0
$47$	8.15595e18			0.481226			0.240613	−	0.970621i	$-0.422652\pi$
$47$	8.15595e18			0.481226			0.240613	+	0.970621i	$0.422652\pi$
$48$		0			0
$49$	−2.34675e19			−0.857457
$50$		0			0
$51$	4.54138e19	+	4.54138e19i	1.04744	+	1.04744i
$52$		0			0
$53$	−5.87678e19	+	5.87678e19i	−0.870897	+	0.870897i	−0.992570	−	0.121673i	$-0.961174\pi$
$53$	−5.87678e19	+	5.87678e19i	−0.870897	+	0.870897i	0.121673	+	0.992570i	$0.461174\pi$
$54$		0			0
$55$		−	4.12510e18i		−	0.0399267i
$56$		0			0
$57$		−	4.58564e20i		−	2.94333i
$58$		0			0
$59$	−2.38468e19	+	2.38468e19i	−0.102951	+	0.102951i	−0.756706	−	0.653755i	$-0.773193\pi$
$59$	−2.38468e19	+	2.38468e19i	−0.102951	+	0.102951i	0.653755	+	0.756706i	$0.273193\pi$
$60$		0			0
$61$	3.83019e20	+	3.83019e20i	1.12701	+	1.12701i	0.990661	+	0.136349i	$0.0435369\pi$
$61$	3.83019e20	+	3.83019e20i	1.12701	+	1.12701i	0.136349	+	0.990661i	$0.456463\pi$
$62$		0			0
$63$	−1.76649e21			−3.58669
$64$		0			0
$65$	−1.68284e19			−0.0238528
$66$		0			0
$67$	5.83073e20	+	5.83073e20i	0.583261	+	0.583261i	0.935798	−	0.352537i	$-0.114681\pi$
$67$	5.83073e20	+	5.83073e20i	0.583261	+	0.583261i	−0.352537	+	0.935798i	$0.614681\pi$
$68$		0			0
$69$	1.25566e21	−	1.25566e21i	0.895588	−	0.895588i
$70$		0			0
$71$		−	1.63662e21i		−	0.840384i	−0.907435	−	0.420192i	$-0.861963\pi$
$71$		−	1.63662e21i		−	0.840384i	0.907435	−	0.420192i	$-0.138037\pi$
$72$		0			0
$73$		−	1.55178e21i		−	0.578918i	−0.957190	−	0.289459i	$-0.906525\pi$
$73$		−	1.55178e21i		−	0.578918i	0.957190	−	0.289459i	$-0.0934754\pi$
$74$		0			0
$75$	−4.91633e21	+	4.91633e21i	−1.34412	+	1.34412i
$76$		0			0
$77$	−3.78250e21	−	3.78250e21i	−0.764074	−	0.764074i
$78$		0			0
$79$	−1.07753e21			−0.162076			−0.0810381	−	0.996711i	$-0.525824\pi$
$79$	−1.07753e21			−0.162076			−0.0810381	+	0.996711i	$0.525824\pi$
$80$		0			0
$81$	−2.91954e22			−3.29409
$82$		0			0
$83$	−1.13427e22	−	1.13427e22i	−0.966762	−	0.966762i	0.0327035	−	0.999465i	$-0.489588\pi$
$83$	−1.13427e22	−	1.13427e22i	−0.966762	−	0.966762i	−0.999465	+	0.0327035i	$0.989588\pi$
$84$		0			0
$85$	−4.27038e20	+	4.27038e20i	−0.0276789	+	0.0276789i
$86$		0			0
$87$		−	2.65911e22i		−	1.31906i
$88$		0			0
$89$			2.95437e22i			1.12844i	0.825624	+	0.564221i	$0.190823\pi$
$89$			2.95437e22i			1.12844i	−0.825624	+	0.564221i	$0.809177\pi$
$90$		0			0
$91$	−1.54308e22	+	1.54308e22i	−0.456470	+	0.456470i
$92$		0			0
$93$	−5.20122e22	−	5.20122e22i	−1.19826	−	1.19826i
$94$		0			0
$95$	4.31200e21			0.0777780
$96$		0			0
$97$	4.92555e22			0.699164			0.349582	−	0.936906i	$-0.386324\pi$
$97$	4.92555e22			0.699164			0.349582	+	0.936906i	$0.386324\pi$
$98$		0			0
$99$	−1.31436e23	−	1.31436e23i	−1.47540	−	1.47540i
$100$		0			0
$101$	−4.44883e22	+	4.44883e22i	−0.396780	+	0.396780i	−0.877096	−	0.480315i	$-0.840522\pi$
$101$	−4.44883e22	+	4.44883e22i	−0.396780	+	0.396780i	0.480315	+	0.877096i	$0.340522\pi$
$102$		0			0
$103$		−	5.67866e22i		−	0.404220i	−0.979363	−	0.202110i	$-0.935220\pi$
$103$		−	5.67866e22i		−	0.404220i	0.979363	−	0.202110i	$-0.0647799\pi$
$104$		0			0
$105$		−	2.29225e22i		−	0.130793i
$106$		0			0
$107$	1.07572e23	−	1.07572e23i	0.494066	−	0.494066i	−0.415518	−	0.909585i	$-0.636400\pi$
$107$	1.07572e23	−	1.07572e23i	0.494066	−	0.494066i	0.909585	+	0.415518i	$0.136400\pi$
$108$		0			0
$109$	2.12098e23	+	2.12098e23i	0.787286	+	0.787286i	0.981049	−	0.193762i	$-0.0620690\pi$
$109$	2.12098e23	+	2.12098e23i	0.787286	+	0.787286i	−0.193762	+	0.981049i	$0.562069\pi$
$110$		0			0
$111$	−9.65194e23			−2.90670
$112$		0			0
$113$	1.40518e23			0.344611			0.172306	−	0.985044i	$-0.444878\pi$
$113$	1.40518e23			0.344611			0.172306	+	0.985044i	$0.444878\pi$
$114$		0			0
$115$	1.18073e22	+	1.18073e22i	0.0236661	+	0.0236661i
$116$		0			0
$117$	−5.36197e23	+	5.36197e23i	−0.881428	+	0.881428i
$118$		0			0
$119$			7.83143e23i			1.05938i
$120$		0			0
$121$			3.32553e23i			0.371389i
$122$		0			0
$123$	1.13730e24	−	1.13730e24i	1.05188	−	1.05188i
$124$		0			0
$125$	−9.25766e22	−	9.25766e22i	−0.0711273	−	0.0711273i
$126$		0			0
$127$	1.98723e24			1.27205			0.636027	−	0.771667i	$-0.280577\pi$
$127$	1.98723e24			1.27205			0.636027	+	0.771667i	$0.280577\pi$
$128$		0			0
$129$	5.61197e24			3.00147
$130$		0			0
$131$	1.09241e24	+	1.09241e24i	0.489516	+	0.489516i	0.908153	−	0.418638i	$-0.137492\pi$
$131$	1.09241e24	+	1.09241e24i	0.489516	+	0.489516i	−0.418638	+	0.908153i	$0.637492\pi$
$132$		0			0
$133$	3.95388e24	−	3.95388e24i	1.48843	−	1.48843i
$134$		0			0
$135$		−	4.93858e23i		−	0.156590i
$136$		0			0
$137$			5.63782e24i			1.50947i	0.656029	+	0.754735i	$0.272235\pi$
$137$			5.63782e24i			1.50947i	−0.656029	+	0.754735i	$0.727765\pi$
$138$		0			0
$139$	2.80248e23	−	2.80248e23i	0.0635145	−	0.0635145i	−0.674636	−	0.738151i	$-0.735699\pi$
$139$	2.80248e23	−	2.80248e23i	0.0635145	−	0.0635145i	0.738151	+	0.674636i	$0.235699\pi$
$140$		0			0
$141$	3.37216e24	+	3.37216e24i	0.648468	+	0.648468i
$142$		0			0
$143$	−2.29627e24			−0.375542
$144$		0			0
$145$	2.50043e23			0.0348564
$146$		0			0
$147$	−9.70289e24	−	9.70289e24i	−1.15545	−	1.15545i
$148$		0			0
$149$	−2.46325e24	+	2.46325e24i	−0.251111	+	0.251111i	−0.821426	−	0.570315i	$-0.806821\pi$
$149$	−2.46325e24	+	2.46325e24i	−0.251111	+	0.251111i	0.570315	+	0.821426i	$0.306821\pi$
$150$		0			0
$151$			4.64216e24i			0.405962i	0.979183	+	0.202981i	$0.0650629\pi$
$151$			4.64216e24i			0.405962i	−0.979183	+	0.202981i	$0.934937\pi$
$152$		0			0
$153$			2.72131e25i			2.04563i
$154$		0			0
$155$	4.89084e23	−	4.89084e23i	0.0316642	−	0.0316642i
$156$		0			0
$157$	−2.23932e25	−	2.23932e25i	−1.25104	−	1.25104i	−0.955255	−	0.295784i	$-0.904419\pi$
$157$	−2.23932e25	−	2.23932e25i	−1.25104	−	1.25104i	−0.295784	−	0.955255i	$-0.595581\pi$
$158$		0			0
$159$	−4.85963e25			−2.34712
$160$		0			0
$161$	2.16534e25			0.905792
$162$		0			0
$163$	8.79549e24	+	8.79549e24i	0.319229	+	0.319229i	0.848471	−	0.529242i	$-0.177524\pi$
$163$	8.79549e24	+	8.79549e24i	0.319229	+	0.319229i	−0.529242	+	0.848471i	$0.677524\pi$
$164$		0			0
$165$	1.70556e24	−	1.70556e24i	0.0538025	−	0.0538025i
$166$		0			0
$167$		−	2.44337e25i		−	0.671042i	−0.942033	−	0.335521i	$-0.891088\pi$
$167$		−	2.44337e25i		−	0.671042i	0.942033	−	0.335521i	$-0.108912\pi$
$168$		0			0
$169$		−	3.23862e25i		−	0.775645i
$170$		0			0
$171$	1.37391e26	−	1.37391e26i	2.87412	−	2.87412i
$172$		0			0
$173$	−4.63426e25	−	4.63426e25i	−0.848107	−	0.848107i	0.141790	−	0.989897i	$-0.454714\pi$
$173$	−4.63426e25	−	4.63426e25i	−0.848107	−	0.848107i	−0.989897	+	0.141790i	$0.954714\pi$
$174$		0			0
$175$	−8.47801e25			−1.35943
$176$		0			0
$177$	−1.97194e25			−0.277461
$178$		0			0
$179$	−5.10789e25	−	5.10789e25i	−0.631584	−	0.631584i	0.316881	−	0.948465i	$-0.397364\pi$
$179$	−5.10789e25	−	5.10789e25i	−0.631584	−	0.631584i	−0.948465	+	0.316881i	$0.897364\pi$
$180$		0			0
$181$	−1.20766e26	+	1.20766e26i	−1.31414	+	1.31414i	−0.395808	+	0.918333i	$0.629535\pi$
$181$	−1.20766e26	+	1.20766e26i	−1.31414	+	1.31414i	−0.918333	+	0.395808i	$0.870465\pi$
$182$		0			0
$183$			3.16727e26i			3.03737i
$184$		0			0
$185$		−	9.07597e24i		−	0.0768101i
$186$		0			0
$187$	−5.82702e25	+	5.82702e25i	−0.435780	+	0.435780i
$188$		0			0
$189$	−4.52842e26	−	4.52842e26i	−2.99665	−	2.99665i
$190$		0			0
$191$	−1.75233e26			−1.02738			−0.513692	−	0.857975i	$-0.671723\pi$
$191$	−1.75233e26			−1.02738			−0.513692	+	0.857975i	$0.671723\pi$
$192$		0			0
$193$	2.30198e26			1.19727			0.598635	−	0.801022i	$-0.295710\pi$
$193$	2.30198e26			1.19727			0.598635	+	0.801022i	$0.295710\pi$
$194$		0			0
$195$	−6.95788e24	−	6.95788e24i	−0.0321424	−	0.0321424i
$196$		0			0
$197$	2.73927e26	−	2.73927e26i	1.12531	−	1.12531i	0.134382	−	0.990930i	$-0.457095\pi$
$197$	2.73927e26	−	2.73927e26i	1.12531	−	1.12531i	0.990930	−	0.134382i	$-0.0429051\pi$
$198$		0			0
$199$			1.70318e25i			0.0622946i	0.999515	+	0.0311473i	$0.00991610\pi$
$199$			1.70318e25i			0.0622946i	−0.999515	+	0.0311473i	$0.990084\pi$
$200$		0			0
$201$			4.82155e26i			1.57193i
$202$		0			0
$203$	2.29276e26	−	2.29276e26i	0.667044	−	0.667044i
$204$		0			0
$205$	1.06944e25	+	1.06944e25i	0.0277962	+	0.0277962i
$206$		0			0
$207$	7.52424e26			1.74905
$208$		0			0
$209$	5.88380e26			1.22455
$210$		0			0
$211$	9.66989e25	+	9.66989e25i	0.180374	+	0.180374i	0.791519	−	0.611145i	$-0.209291\pi$
$211$	9.66989e25	+	9.66989e25i	0.180374	+	0.180374i	−0.611145	+	0.791519i	$0.709291\pi$
$212$		0			0
$213$	6.76679e26	−	6.76679e26i	1.13245	−	1.13245i
$214$		0			0
$215$			5.27708e25i			0.0793143i
$216$		0			0
$217$		−	8.96929e26i		−	1.21191i
$218$		0			0
$219$	6.41599e26	−	6.41599e26i	0.780111	−	0.780111i
$220$		0			0
$221$	2.37714e26	+	2.37714e26i	0.260342	+	0.260342i
$222$		0			0
$223$	−4.41282e26			−0.435723			−0.217862	−	0.975980i	$-0.569908\pi$
$223$	−4.41282e26			−0.435723			−0.217862	+	0.975980i	$0.569908\pi$
$224$		0			0
$225$	−2.94599e27			−2.62501
$226$		0			0
$227$	1.62600e27	+	1.62600e27i	1.30865	+	1.30865i	0.922392	+	0.386256i	$0.126232\pi$
$227$	1.62600e27	+	1.62600e27i	1.30865	+	1.30865i	0.386256	+	0.922392i	$0.373768\pi$
$228$		0			0
$229$	−1.75095e27	+	1.75095e27i	−1.27399	+	1.27399i	−0.330014	+	0.943976i	$0.607053\pi$
$229$	−1.75095e27	+	1.75095e27i	−1.27399	+	1.27399i	−0.943976	+	0.330014i	$0.892947\pi$
$230$		0			0
$231$		−	3.12783e27i		−	2.05923i
$232$		0			0
$233$		−	2.92833e26i		−	0.174593i	−0.996182	−	0.0872965i	$-0.972177\pi$
$233$		−	2.92833e26i		−	0.174593i	0.996182	−	0.0872965i	$-0.0278227\pi$
$234$		0			0
$235$	−3.17093e25	+	3.17093e25i	−0.0171359	+	0.0171359i
$236$		0			0
$237$	−4.45517e26	−	4.45517e26i	−0.218403	−	0.218403i
$238$		0			0
$239$	−2.46769e27			−1.09829			−0.549143	−	0.835728i	$-0.685046\pi$
$239$	−2.46769e27			−1.09829			−0.549143	+	0.835728i	$0.685046\pi$
$240$		0			0
$241$	2.28956e27			0.925883			0.462942	−	0.886389i	$-0.346794\pi$
$241$	2.28956e27			0.925883			0.462942	+	0.886389i	$0.346794\pi$
$242$		0			0
$243$	−6.09184e27	−	6.09184e27i	−2.24015	−	2.24015i
$244$		0			0
$245$	9.12388e25	−	9.12388e25i	0.0305330	−	0.0305330i
$246$		0			0
$247$		−	2.40031e27i		−	0.731564i
$248$		0			0
$249$		−	9.37953e27i		−	2.60549i
$250$		0			0
$251$	−3.04026e27	+	3.04026e27i	−0.770306	+	0.770306i	−0.978160	−	0.207854i	$-0.933352\pi$
$251$	−3.04026e27	+	3.04026e27i	−0.770306	+	0.770306i	0.207854	+	0.978160i	$0.433352\pi$
$252$		0			0
$253$	1.61113e27	+	1.61113e27i	0.372602	+	0.372602i
$254$		0			0
$255$	−3.53126e26			−0.0745964
$256$		0			0
$257$	−5.09902e27			−0.984591			−0.492296	−	0.870428i	$-0.663842\pi$
$257$	−5.09902e27			−0.984591			−0.492296	+	0.870428i	$0.663842\pi$
$258$		0			0
$259$	−8.32219e27	−	8.32219e27i	−1.46991	−	1.46991i
$260$		0			0
$261$	7.96701e27	−	7.96701e27i	1.28804	−	1.28804i
$262$		0			0
$263$		−	7.26287e27i		−	1.07552i	−0.843099	−	0.537758i	$-0.819271\pi$
$263$		−	7.26287e27i		−	1.07552i	0.843099	−	0.537758i	$-0.180729\pi$
$264$		0			0
$265$		−	4.56963e26i		−	0.0620232i
$266$		0			0
$267$	−1.22151e28	+	1.22151e28i	−1.52061	+	1.52061i
$268$		0			0
$269$	−5.75395e27	−	5.75395e27i	−0.657377	−	0.657377i	0.297382	−	0.954759i	$-0.403887\pi$
$269$	−5.75395e27	−	5.75395e27i	−0.657377	−	0.657377i	−0.954759	+	0.297382i	$0.903887\pi$
$270$		0			0
$271$	3.18370e27			0.334030			0.167015	−	0.985954i	$-0.446587\pi$
$271$	3.18370e27			0.334030			0.167015	+	0.985954i	$0.446587\pi$
$272$		0			0
$273$	−1.27600e28			−1.23022
$274$		0			0
$275$	−6.30811e27	−	6.30811e27i	−0.559208	−	0.559208i
$276$		0			0
$277$	−6.93363e27	+	6.93363e27i	−0.565514	+	0.565514i	−0.930868	−	0.365355i	$-0.880948\pi$
$277$	−6.93363e27	+	6.93363e27i	−0.565514	+	0.565514i	0.365355	+	0.930868i	$0.380948\pi$
$278$		0			0
$279$		−	3.11670e28i		−	2.34016i
$280$		0			0
$281$		−	3.31290e27i		−	0.229132i	−0.993416	−	0.114566i	$-0.963452\pi$
$281$		−	3.31290e27i		−	0.229132i	0.993416	−	0.114566i	$-0.0365477\pi$
$282$		0			0
$283$	1.09607e28	−	1.09607e28i	0.698706	−	0.698706i	−0.265425	−	0.964131i	$-0.585512\pi$
$283$	1.09607e28	−	1.09607e28i	0.698706	−	0.698706i	0.964131	+	0.265425i	$0.0855124\pi$
$284$		0			0
$285$	1.78284e27	+	1.78284e27i	0.104808	+	0.104808i
$286$		0			0
$287$	1.96124e28			1.06387
$288$		0			0
$289$	−7.90309e27			−0.395796
$290$		0			0
$291$	2.03652e28	+	2.03652e28i	0.942147	+	0.942147i
$292$		0			0
$293$	5.77690e26	−	5.77690e26i	0.0247012	−	0.0247012i	−0.694648	−	0.719349i	$-0.744440\pi$
$293$	5.77690e26	−	5.77690e26i	0.0247012	−	0.0247012i	0.719349	+	0.694648i	$0.244440\pi$
$294$		0			0
$295$		−	1.85427e26i		−	0.00733196i
$296$		0			0
$297$		−	6.73879e28i		−	2.46537i
$298$		0			0
$299$	6.57264e27	−	6.57264e27i	0.222598	−	0.222598i
$300$		0			0
$301$	4.83881e28	+	4.83881e28i	1.51783	+	1.51783i
$302$		0			0
$303$	−3.67883e28			−1.06935
$304$		0			0
$305$	−2.97826e27			−0.0802629
$306$		0			0
$307$	2.02178e28	+	2.02178e28i	0.505409	+	0.505409i	0.913114	−	0.407705i	$-0.133671\pi$
$307$	2.02178e28	+	2.02178e28i	0.505409	+	0.505409i	−0.407705	+	0.913114i	$0.633671\pi$
$308$		0			0
$309$	2.34790e28	−	2.34790e28i	0.544700	−	0.544700i
$310$		0			0
$311$		−	4.08054e28i		−	0.878968i	−0.898250	−	0.439484i	$-0.855161\pi$
$311$		−	4.08054e28i		−	0.878968i	0.898250	−	0.439484i	$-0.144839\pi$
$312$		0			0
$313$			4.04282e28i			0.808955i	0.914548	+	0.404477i	$0.132547\pi$
$313$			4.04282e28i			0.808955i	−0.914548	+	0.404477i	$0.867453\pi$
$314$		0			0
$315$	6.86788e27	−	6.86788e27i	0.127718	−	0.127718i
$316$		0			0
$317$	−6.36363e28	−	6.36363e28i	−1.10033	−	1.10033i	−0.994370	−	0.105961i	$-0.966208\pi$
$317$	−6.36363e28	−	6.36363e28i	−1.10033	−	1.10033i	−0.105961	−	0.994370i	$-0.533792\pi$
$318$		0			0
$319$	3.41188e28			0.548784
$320$		0			0
$321$	8.89534e28			1.33154
$322$		0			0
$323$	−6.09103e28	−	6.09103e28i	−0.848909	−	0.848909i
$324$		0			0
$325$	−2.57341e28	+	2.57341e28i	−0.334079	+	0.334079i
$326$		0			0
$327$			1.75389e29i			2.12179i
$328$		0			0
$329$			5.81516e28i			0.655856i
$330$		0			0
$331$	3.76430e28	−	3.76430e28i	0.395970	−	0.395970i	−0.480839	−	0.876809i	$-0.659668\pi$
$331$	3.76430e28	−	3.76430e28i	0.395970	−	0.395970i	0.876809	+	0.480839i	$0.159668\pi$
$332$		0			0
$333$	−2.89184e29	−	2.89184e29i	−2.83835	−	2.83835i
$334$		0			0
$335$	−4.53383e27			−0.0415384
$336$		0			0
$337$	−4.33695e28			−0.371057			−0.185528	−	0.982639i	$-0.559400\pi$
$337$	−4.33695e28			−0.371057			−0.185528	+	0.982639i	$0.559400\pi$
$338$		0			0
$339$	5.80985e28	+	5.80985e28i	0.464375	+	0.464375i
$340$		0			0
$341$	6.67365e28	−	6.67365e28i	0.498526	−	0.498526i
$342$		0			0
$343$			2.78156e28i			0.194270i
$344$		0			0
$345$			9.76371e27i			0.0637816i
$346$		0			0
$347$	1.04551e29	−	1.04551e29i	0.639054	−	0.639054i	−0.311268	−	0.950322i	$-0.600754\pi$
$347$	1.04551e29	−	1.04551e29i	0.639054	−	0.639054i	0.950322	+	0.311268i	$0.100754\pi$
$348$		0			0
$349$	−5.01381e28	−	5.01381e28i	−0.286864	−	0.286864i	0.548975	−	0.835839i	$-0.315018\pi$
$349$	−5.01381e28	−	5.01381e28i	−0.286864	−	0.286864i	−0.835839	+	0.548975i	$0.815018\pi$
$350$		0			0
$351$	−2.74910e29			−1.47285
$352$		0			0
$353$	3.69372e28			0.185376			0.0926882	−	0.995695i	$-0.470454\pi$
$353$	3.69372e28			0.185376			0.0926882	+	0.995695i	$0.470454\pi$
$354$		0			0
$355$	6.36299e27	+	6.36299e27i	0.0299251	+	0.0299251i
$356$		0			0
$357$	−3.23798e29	+	3.23798e29i	−1.42755	+	1.42755i
$358$		0			0
$359$			9.60781e28i			0.397227i	0.980078	+	0.198613i	$0.0636438\pi$
$359$			9.60781e28i			0.397227i	−0.980078	+	0.198613i	$0.936356\pi$
$360$		0			0
$361$			3.57209e29i			1.38545i
$362$		0			0
$363$	−1.37497e29	+	1.37497e29i	−0.500459	+	0.500459i
$364$		0			0
$365$	6.03313e27	+	6.03313e27i	0.0206146	+	0.0206146i
$366$		0			0
$367$	−1.53567e29			−0.492762			−0.246381	−	0.969173i	$-0.579241\pi$
$367$	−1.53567e29			−0.492762			−0.246381	+	0.969173i	$0.579241\pi$
$368$		0			0
$369$	6.81501e29			2.05430
$370$		0			0
$371$	−4.19012e29	−	4.19012e29i	−1.18693	−	1.18693i
$372$		0			0
$373$	7.58794e28	−	7.58794e28i	0.202056	−	0.202056i	−0.598824	−	0.800881i	$-0.704365\pi$
$373$	7.58794e28	−	7.58794e28i	0.202056	−	0.202056i	0.800881	+	0.598824i	$0.204365\pi$
$374$		0			0
$375$		−	7.65535e28i		−	0.191693i
$376$		0			0
$377$		−	1.39188e29i		−	0.327852i
$378$		0			0
$379$	2.12000e29	−	2.12000e29i	0.469878	−	0.469878i	−0.431997	−	0.901875i	$-0.642191\pi$
$379$	2.12000e29	−	2.12000e29i	0.469878	−	0.469878i	0.901875	+	0.431997i	$0.142191\pi$
$380$		0			0
$381$	8.21641e29	+	8.21641e29i	1.71413	+	1.71413i
$382$		0			0
$383$	−7.91961e29			−1.55567			−0.777836	−	0.628467i	$-0.783683\pi$
$383$	−7.91961e29			−1.55567			−0.777836	+	0.628467i	$0.783683\pi$
$384$		0			0
$385$	2.94118e28			0.0544155
$386$		0			0
$387$	1.68141e30	+	1.68141e30i	2.93088	+	2.93088i
$388$		0			0
$389$	−1.37999e29	+	1.37999e29i	−0.226702	+	0.226702i	−0.811313	−	0.584612i	$-0.801247\pi$
$389$	−1.37999e29	+	1.37999e29i	−0.226702	+	0.226702i	0.584612	+	0.811313i	$0.301247\pi$
$390$		0			0
$391$		−	3.33575e29i		−	0.516607i
$392$		0			0
$393$			9.03338e29i			1.31928i
$394$		0			0
$395$	4.18932e27	−	4.18932e27i	0.00577134	−	0.00577134i
$396$		0			0
$397$	9.14687e29	+	9.14687e29i	1.18900	+	1.18900i	0.977344	+	0.211655i	$0.0678854\pi$
$397$	9.14687e29	+	9.14687e29i	1.18900	+	1.18900i	0.211655	+	0.977344i	$0.432115\pi$
$398$		0			0
$399$	3.26954e30			4.01142
$400$		0			0
$401$	6.13962e29			0.711183			0.355592	−	0.934641i	$-0.384279\pi$
$401$	6.13962e29			0.711183			0.355592	+	0.934641i	$0.384279\pi$
$402$		0			0
$403$	−2.72253e29	−	2.72253e29i	−0.297827	−	0.297827i
$404$		0			0
$405$	1.13508e29	−	1.13508e29i	0.117299	−	0.117299i
$406$		0			0
$407$		−	1.23843e30i		−	1.20931i
$408$		0			0
$409$			7.58802e28i			0.0700342i	0.999387	+	0.0350171i	$0.0111486\pi$
$409$			7.58802e28i			0.0700342i	−0.999387	+	0.0350171i	$0.988851\pi$
$410$		0			0
$411$	−2.33101e30	+	2.33101e30i	−2.03406	+	2.03406i
$412$		0			0
$413$	−1.70027e29	−	1.70027e29i	−0.140311	−	0.140311i
$414$		0			0
$415$	8.81982e28			0.0688504
$416$		0			0
$417$	2.31743e29			0.171176
$418$		0			0
$419$	6.29670e29	+	6.29670e29i	0.440201	+	0.440201i	0.892080	−	0.451878i	$-0.149246\pi$
$419$	6.29670e29	+	6.29670e29i	0.440201	+	0.440201i	−0.451878	+	0.892080i	$0.649246\pi$
$420$		0			0
$421$	−2.48107e29	+	2.48107e29i	−0.164208	+	0.164208i	−0.784428	−	0.620220i	$-0.787043\pi$
$421$	−2.48107e29	+	2.48107e29i	−0.164208	+	0.164208i	0.620220	+	0.784428i	$0.287043\pi$
$422$		0			0
$423$			2.02068e30i			1.26644i
$424$		0			0
$425$			1.30606e30i			0.775334i
$426$		0			0
$427$	−2.73091e30	+	2.73091e30i	−1.53599	+	1.53599i
$428$		0			0
$429$	−9.49416e29	−	9.49416e29i	−0.506055	−	0.506055i
$430$		0			0
$431$	7.39038e29			0.373403			0.186702	−	0.982417i	$-0.440220\pi$
$431$	7.39038e29			0.373403			0.186702	+	0.982417i	$0.440220\pi$
$432$		0			0
$433$	−6.70039e29			−0.320988			−0.160494	−	0.987037i	$-0.551309\pi$
$433$	−6.70039e29			−0.320988			−0.160494	+	0.987037i	$0.551309\pi$
$434$		0			0
$435$	1.03383e29	+	1.03383e29i	0.0469701	+	0.0469701i
$436$		0			0
$437$	−1.68413e30	+	1.68413e30i	−0.725836	+	0.725836i
$438$		0			0
$439$		−	2.81983e30i		−	1.15314i	−0.817048	−	0.576569i	$-0.804391\pi$
$439$		−	2.81983e30i		−	1.15314i	0.817048	−	0.576569i	$-0.195609\pi$
$440$		0			0
$441$		−	5.81421e30i		−	2.25656i
$442$		0			0
$443$	3.35646e30	−	3.35646e30i	1.23663	−	1.23663i	0.275256	−	0.961371i	$-0.411237\pi$
$443$	3.35646e30	−	3.35646e30i	1.23663	−	1.23663i	0.961371	−	0.275256i	$-0.0887625\pi$
$444$		0			0
$445$	−1.14862e29	−	1.14862e29i	−0.0401825	−	0.0401825i
$446$		0			0
$447$	−2.03691e30			−0.676760
$448$		0			0
$449$	1.31342e30			0.414543			0.207271	−	0.978283i	$-0.433542\pi$
$449$	1.31342e30			0.414543			0.207271	+	0.978283i	$0.433542\pi$
$450$		0			0
$451$	1.45927e30	+	1.45927e30i	0.437628	+	0.437628i
$452$		0			0
$453$	−1.91935e30	+	1.91935e30i	−0.547047	+	0.547047i
$454$		0			0
$455$		−	1.19986e29i		−	0.0325087i
$456$		0			0
$457$		−	6.10645e30i		−	1.57309i	−0.617536	−	0.786543i	$-0.711869\pi$
$457$		−	6.10645e30i		−	1.57309i	0.617536	−	0.786543i	$-0.288131\pi$
$458$		0			0
$459$	−6.97612e30	+	6.97612e30i	−1.70910	+	1.70910i
$460$		0			0
$461$	2.64152e30	+	2.64152e30i	0.615593	+	0.615593i	0.944398	−	0.328805i	$-0.106646\pi$
$461$	2.64152e30	+	2.64152e30i	0.615593	+	0.615593i	−0.328805	+	0.944398i	$0.606646\pi$
$462$		0			0
$463$	2.83079e30			0.627663			0.313832	−	0.949479i	$-0.398387\pi$
$463$	2.83079e30			0.627663			0.313832	+	0.949479i	$0.398387\pi$
$464$		0			0
$465$	4.04434e29			0.0853372
$466$		0			0
$467$	8.04608e29	+	8.04608e29i	0.161600	+	0.161600i	0.783275	−	0.621675i	$-0.213548\pi$
$467$	8.04608e29	+	8.04608e29i	0.161600	+	0.161600i	−0.621675	+	0.783275i	$0.713548\pi$
$468$		0			0
$469$	−4.15728e30	+	4.15728e30i	−0.794918	+	0.794918i
$470$		0			0
$471$		−	1.85174e31i		−	3.37163i
$472$		0			0
$473$			7.20068e30i			1.24873i
$474$		0			0
$475$	6.59392e30	−	6.59392e30i	1.08935	−	1.08935i
$476$		0			0
$477$	−1.45600e31	−	1.45600e31i	−2.29193	−	2.29193i
$478$		0			0
$479$	−8.62313e30			−1.29362			−0.646810	−	0.762651i	$-0.723897\pi$
$479$	−8.62313e30			−1.29362			−0.646810	+	0.762651i	$0.723897\pi$
$480$		0			0
$481$	−5.05222e30			−0.722460
$482$		0			0
$483$	8.95282e30	+	8.95282e30i	1.22058	+	1.22058i
$484$		0			0
$485$	−1.91499e29	+	1.91499e29i	−0.0248964	+	0.0248964i
$486$		0			0
$487$			8.64386e30i			1.07183i	0.844273	+	0.535913i	$0.180033\pi$
$487$			8.64386e30i			1.07183i	−0.844273	+	0.535913i	$0.819967\pi$
$488$		0			0
$489$			7.27317e30i			0.860344i
$490$		0			0
$491$	−8.42191e30	+	8.42191e30i	−0.950546	+	0.950546i	−0.998833	−	0.0482871i	$-0.984624\pi$
$491$	−8.42191e30	+	8.42191e30i	−0.950546	+	0.950546i	0.0482871	+	0.998833i	$0.484624\pi$
$492$		0			0
$493$	−3.53205e30	−	3.53205e30i	−0.380441	−	0.380441i
$494$		0			0
$495$	1.02202e30			0.105075
$496$		0			0
$497$	1.16691e31			1.14535
$498$		0			0
$499$	−7.24291e30	−	7.24291e30i	−0.678824	−	0.678824i	0.280910	−	0.959734i	$-0.409364\pi$
$499$	−7.24291e30	−	7.24291e30i	−0.678824	−	0.678824i	−0.959734	+	0.280910i	$0.909364\pi$
$500$		0			0
$501$	1.01024e31	−	1.01024e31i	0.904251	−	0.904251i
$502$		0			0
$503$		−	3.76960e29i		−	0.0322302i	−0.999870	−	0.0161151i	$-0.994870\pi$
$503$		−	3.76960e29i		−	0.0322302i	0.999870	−	0.0161151i	$-0.00512982\pi$
$504$		0			0
$505$		−	3.45930e29i		−	0.0282577i
$506$		0			0
$507$	1.33904e31	−	1.33904e31i	1.04521	−	1.04521i
$508$		0			0
$509$	−2.75535e29	−	2.75535e29i	−0.0205552	−	0.0205552i	0.696754	−	0.717310i	$-0.254627\pi$
$509$	−2.75535e29	−	2.75535e29i	−0.0205552	−	0.0205552i	−0.717310	+	0.696754i	$0.754627\pi$
$510$		0			0
$511$	1.10641e31			0.788999
$512$		0			0
$513$	7.04411e31			4.80260
$514$		0			0
$515$	2.20779e29	+	2.20779e29i	0.0143938	+	0.0143938i
$516$		0			0
$517$	−4.32680e30	+	4.32680e30i	−0.269790	+	0.269790i
$518$		0			0
$519$		−	3.83217e31i		−	2.28570i
$520$		0			0
$521$			1.81840e31i			1.03766i	0.854878	+	0.518830i	$0.173632\pi$
$521$			1.81840e31i			1.03766i	−0.854878	+	0.518830i	$0.826368\pi$
$522$		0			0
$523$	−7.60811e30	+	7.60811e30i	−0.415439	+	0.415439i	−0.883628	−	0.468189i	$-0.844907\pi$
$523$	−7.60811e30	+	7.60811e30i	−0.415439	+	0.415439i	0.468189	+	0.883628i	$0.344907\pi$
$524$		0			0
$525$	−3.50532e31	−	3.50532e31i	−1.83188	−	1.83188i
$526$		0			0
$527$	−1.38174e31			−0.691199
$528$		0			0
$529$	1.16573e31			0.558289
$530$		0			0
$531$	−5.90819e30	−	5.90819e30i	−0.270936	−	0.270936i
$532$		0			0
$533$	5.95311e30	−	5.95311e30i	0.261446	−	0.261446i
$534$		0			0
$535$			8.36452e29i			0.0351862i
$536$		0			0
$537$		−	4.22382e31i		−	1.70216i
$538$		0			0
$539$	1.24497e31	−	1.24497e31i	0.480716	−	0.480716i
$540$		0			0
$541$	−1.33778e31	−	1.33778e31i	−0.495014	−	0.495014i	0.414868	−	0.909882i	$-0.363828\pi$
$541$	−1.33778e31	−	1.33778e31i	−0.495014	−	0.495014i	−0.909882	+	0.414868i	$0.863828\pi$
$542$		0			0
$543$	−9.98641e31			−3.54170
$544$		0			0
$545$	−1.64922e30			−0.0560686
$546$		0			0
$547$	4.09839e30	+	4.09839e30i	0.133585	+	0.133585i	0.770738	−	0.637153i	$-0.219888\pi$
$547$	4.09839e30	+	4.09839e30i	0.133585	+	0.133585i	−0.637153	+	0.770738i	$0.719888\pi$
$548$		0			0
$549$	−9.48952e31	+	9.48952e31i	−2.96594	+	2.96594i
$550$		0			0
$551$			3.56647e31i			1.06904i
$552$		0			0
$553$		−	7.68277e30i		−	0.220891i
$554$		0			0
$555$	3.75255e30	−	3.75255e30i	0.103504	−	0.103504i
$556$		0			0
$557$	6.75875e30	+	6.75875e30i	0.178868	+	0.178868i	0.790862	−	0.611994i	$-0.209633\pi$
$557$	6.75875e30	+	6.75875e30i	0.178868	+	0.178868i	−0.611994	+	0.790862i	$0.709633\pi$
$558$		0			0
$559$	2.93753e31			0.746013
$560$		0			0
$561$	−4.81848e31			−1.17446
$562$		0			0
$563$	−1.29263e31	−	1.29263e31i	−0.302431	−	0.302431i	0.539533	−	0.841964i	$-0.318601\pi$
$563$	−1.29263e31	−	1.29263e31i	−0.302431	−	0.302431i	−0.841964	+	0.539533i	$0.818601\pi$
$564$		0			0
$565$	−5.46316e29	+	5.46316e29i	−0.0122712	+	0.0122712i
$566$		0			0
$567$		−	2.08162e32i		−	4.48947i
$568$		0			0
$569$			1.86683e30i			0.0386646i	0.999813	+	0.0193323i	$0.00615405\pi$
$569$			1.86683e30i			0.0386646i	−0.999813	+	0.0193323i	$0.993846\pi$
$570$		0			0
$571$	−5.64962e31	+	5.64962e31i	−1.12384	+	1.12384i	−0.132679	+	0.991159i	$0.542358\pi$
$571$	−5.64962e31	+	5.64962e31i	−1.12384	+	1.12384i	−0.991159	+	0.132679i	$0.957642\pi$
$572$		0			0
$573$	−7.24520e31	−	7.24520e31i	−1.38443	−	1.38443i
$574$		0			0
$575$	3.61116e31			0.662928
$576$		0			0
$577$	3.06780e28			0.000541134			0.000270567	−	1.00000i	$-0.499914\pi$
$577$	3.06780e28			0.000541134			0.000270567		1.00000i	$0.499914\pi$
$578$		0			0
$579$	9.51776e31	+	9.51776e31i	1.61336	+	1.61336i
$580$		0			0
$581$	8.08731e31	−	8.08731e31i	1.31759	−	1.31759i
$582$		0			0
$583$		−	6.23535e31i		−	0.976501i
$584$		0			0
$585$		−	4.16933e30i		−	0.0627732i
$586$		0			0
$587$	−8.34622e31	+	8.34622e31i	−1.20824	+	1.20824i	−0.236638	+	0.971598i	$0.576046\pi$
$587$	−8.34622e31	+	8.34622e31i	−1.20824	+	1.20824i	−0.971598	+	0.236638i	$0.923954\pi$
$588$		0			0
$589$	6.97601e31	+	6.97601e31i	0.971139	+	0.971139i
$590$		0			0
$591$	2.26516e32			3.03279
$592$		0			0
$593$	−1.38215e31			−0.178003			−0.0890015	−	0.996031i	$-0.528368\pi$
$593$	−1.38215e31			−0.178003			−0.0890015	+	0.996031i	$0.528368\pi$
$594$		0			0
$595$	−3.04476e30	−	3.04476e30i	−0.0377232	−	0.0377232i
$596$		0			0
$597$	−7.04197e30	+	7.04197e30i	−0.0839440	+	0.0839440i
$598$		0			0
$599$			8.68323e31i			0.996031i	0.867168	+	0.498016i	$0.165938\pi$
$599$			8.68323e31i			0.996031i	−0.867168	+	0.498016i	$0.834062\pi$
$600$		0			0
$601$		−	4.78480e31i		−	0.528211i	−0.964494	−	0.264106i	$-0.914923\pi$
$601$		−	4.78480e31i		−	0.528211i	0.964494	−	0.264106i	$-0.0850768\pi$
$602$		0			0
$603$	−1.44460e32	+	1.44460e32i	−1.53496	+	1.53496i
$604$		0			0
$605$	−1.29292e30	−	1.29292e30i	−0.0132247	−	0.0132247i
$606$		0			0
$607$	2.43435e31			0.239725			0.119863	−	0.992790i	$-0.461755\pi$
$607$	2.43435e31			0.239725			0.119863	+	0.992790i	$0.461755\pi$
$608$		0			0
$609$	1.89593e32			1.79773
$610$		0			0
$611$	1.76513e31	+	1.76513e31i	0.161176	+	0.161176i
$612$		0			0
$613$	−5.69111e31	+	5.69111e31i	−0.500497	+	0.500497i	−0.911592	−	0.411095i	$-0.865146\pi$
$613$	−5.69111e31	+	5.69111e31i	−0.500497	+	0.500497i	0.411095	+	0.911592i	$0.365146\pi$
$614$		0			0
$615$			8.84340e30i			0.0749127i
$616$		0			0
$617$		−	2.91058e31i		−	0.237520i	−0.992923	−	0.118760i	$-0.962108\pi$
$617$		−	2.91058e31i		−	0.237520i	0.992923	−	0.118760i	$-0.0378919\pi$
$618$		0			0
$619$	−2.20195e31	+	2.20195e31i	−0.173127	+	0.173127i	−0.788352	−	0.615225i	$-0.789065\pi$
$619$	−2.20195e31	+	2.20195e31i	−0.173127	+	0.173127i	0.615225	+	0.788352i	$0.289065\pi$
$620$		0			0
$621$	1.92885e32	+	1.92885e32i	1.46132	+	1.46132i
$622$		0			0
$623$	−2.10645e32			−1.53794
$624$		0			0
$625$	−1.41028e32			−0.992399
$626$		0			0
$627$	2.43272e32	+	2.43272e32i	1.65012	+	1.65012i
$628$		0			0
$629$	−1.28205e32	+	1.28205e32i	−0.838345	+	0.838345i
$630$		0			0
$631$			1.80137e32i			1.13570i	0.823130	+	0.567852i	$0.192226\pi$
$631$			1.80137e32i			1.13570i	−0.823130	+	0.567852i	$0.807774\pi$
$632$		0			0
$633$			7.99623e31i			0.486119i
$634$		0			0
$635$	−7.72611e30	+	7.72611e30i	−0.0452963	+	0.0452963i
$636$		0			0
$637$	−5.07888e31	−	5.07888e31i	−0.287187	−	0.287187i
$638$		0			0
$639$	4.05483e32			2.21163
$640$		0			0
$641$	2.46958e32			1.29944			0.649720	−	0.760173i	$-0.274886\pi$
$641$	2.46958e32			1.29944			0.649720	+	0.760173i	$0.274886\pi$
$642$		0			0
$643$	1.26113e32	+	1.26113e32i	0.640224	+	0.640224i	0.950611	−	0.310386i	$-0.100458\pi$
$643$	1.26113e32	+	1.26113e32i	0.640224	+	0.640224i	−0.310386	+	0.950611i	$0.600458\pi$
$644$		0			0
$645$	−2.18186e31	+	2.18186e31i	−0.106879	+	0.106879i
$646$		0			0
$647$		−	3.33543e32i		−	1.57671i	−0.615218	−	0.788357i	$-0.710932\pi$
$647$		−	3.33543e32i		−	1.57671i	0.615218	−	0.788357i	$-0.289068\pi$
$648$		0			0
$649$		−	2.53019e31i		−	0.115435i
$650$		0			0
$651$	3.70844e32	−	3.70844e32i	1.63309	−	1.63309i
$652$		0			0
$653$	1.09727e32	+	1.09727e32i	0.466459	+	0.466459i	0.900765	−	0.434307i	$-0.143007\pi$
$653$	1.09727e32	+	1.09727e32i	0.466459	+	0.466459i	−0.434307	+	0.900765i	$0.643007\pi$
$654$		0			0
$655$	−8.49432e30			−0.0348621
$656$		0			0
$657$	3.84462e32			1.52353
$658$		0			0
$659$	1.20437e32	+	1.20437e32i	0.460868	+	0.460868i	0.898940	−	0.438072i	$-0.144339\pi$
$659$	1.20437e32	+	1.20437e32i	0.460868	+	0.460868i	−0.438072	+	0.898940i	$0.644339\pi$
$660$		0			0
$661$	−1.64234e32	+	1.64234e32i	−0.606941	+	0.606941i	−0.942145	−	0.335205i	$-0.891195\pi$
$661$	−1.64234e32	+	1.64234e32i	−0.606941	+	0.606941i	0.335205	+	0.942145i	$0.391195\pi$
$662$		0			0
$663$			1.96571e32i			0.701638i
$664$		0			0
$665$			3.07443e31i			0.106003i
$666$		0			0
$667$	−9.76588e31	+	9.76588e31i	−0.325285	+	0.325285i
$668$		0			0
$669$	−1.82453e32	−	1.82453e32i	−0.587151	−	0.587151i
$670$		0			0
$671$	−4.06390e32			−1.26367
$672$		0			0
$673$	−1.43606e32			−0.431520			−0.215760	−	0.976446i	$-0.569223\pi$
$673$	−1.43606e32			−0.431520			−0.215760	+	0.976446i	$0.569223\pi$
$674$		0			0
$675$	−7.55209e32	−	7.55209e32i	−2.19318	−	2.19318i
$676$		0			0
$677$	−7.47612e31	+	7.47612e31i	−0.209849	+	0.209849i	−0.804203	−	0.594354i	$-0.797408\pi$
$677$	−7.47612e31	+	7.47612e31i	−0.209849	+	0.209849i	0.594354	+	0.804203i	$0.297408\pi$
$678$		0			0
$679$			3.51189e32i			0.952881i
$680$		0			0
$681$			1.34457e33i			3.52689i
$682$		0			0
$683$	−2.03984e32	+	2.03984e32i	−0.517318	+	0.517318i	−0.916759	−	0.399441i	$-0.869204\pi$
$683$	−2.03984e32	+	2.03984e32i	−0.517318	+	0.517318i	0.399441	+	0.916759i	$0.369204\pi$
$684$		0			0
$685$	−2.19191e31	−	2.19191e31i	−0.0537504	−	0.0537504i
$686$		0			0
$687$	−1.44790e33			−3.43349
$688$		0			0
$689$	−2.54373e32			−0.583377
$690$		0			0
$691$	−1.79869e32	−	1.79869e32i	−0.398987	−	0.398987i	0.478889	−	0.877875i	$-0.341040\pi$
$691$	−1.79869e32	−	1.79869e32i	−0.398987	−	0.398987i	−0.877875	+	0.478889i	$0.841040\pi$
$692$		0			0
$693$	9.37135e32	−	9.37135e32i	2.01080	−	2.01080i
$694$		0			0
$695$			2.17914e30i			0.00452335i
$696$		0			0
$697$		−	3.02132e32i		−	0.606765i
$698$		0			0
$699$	1.21075e32	−	1.21075e32i	0.235270	−	0.235270i
$700$		0			0
$701$	−2.11377e32	−	2.11377e32i	−0.397466	−	0.397466i	0.479872	−	0.877338i	$-0.340683\pi$
$701$	−2.11377e32	−	2.11377e32i	−0.397466	−	0.397466i	−0.877338	+	0.479872i	$0.840683\pi$
$702$		0			0
$703$	1.29455e33			2.35576
$704$		0			0
$705$	−2.62211e31			−0.0461823
$706$		0			0
$707$	−3.17200e32	−	3.17200e32i	−0.540766	−	0.540766i
$708$		0			0
$709$	−7.71195e32	+	7.71195e32i	−1.27272	+	1.27272i	−0.328064	+	0.944656i	$0.606396\pi$
$709$	−7.71195e32	+	7.71195e32i	−1.27272	+	1.27272i	−0.944656	+	0.328064i	$0.893604\pi$
$710$		0			0
$711$		−	2.66965e32i		−	0.426534i
$712$		0			0
$713$			3.82041e32i			0.590991i
$714$		0			0
$715$	8.92761e30	−	8.92761e30i	0.0133726	−	0.0133726i
$716$		0			0
$717$	−1.02029e33	−	1.02029e33i	−1.47998	−	1.47998i
$718$		0			0
$719$	−1.98038e32			−0.278206			−0.139103	−	0.990278i	$-0.544422\pi$
$719$	−1.98038e32			−0.278206			−0.139103	+	0.990278i	$0.544422\pi$
$720$		0			0
$721$	4.04886e32			0.550906
$722$		0			0
$723$	9.46642e32	+	9.46642e32i	1.24766	+	1.24766i
$724$		0			0
$725$	3.82366e32	−	3.82366e32i	0.488194	−	0.488194i
$726$		0			0
$727$			1.06311e33i			1.31502i	0.753447	+	0.657509i	$0.228390\pi$
$727$			1.06311e33i			1.31502i	−0.753447	+	0.657509i	$0.771610\pi$
$728$		0			0
$729$		−	2.28892e33i		−	2.74325i
$730$		0			0
$731$	7.45428e32	−	7.45428e32i	0.865677	−	0.865677i
$732$		0			0
$733$	9.33473e32	+	9.33473e32i	1.05052	+	1.05052i	0.998654	+	0.0518702i	$0.0165182\pi$
$733$	9.33473e32	+	9.33473e32i	1.05052	+	1.05052i	0.0518702	+	0.998654i	$0.483482\pi$
$734$		0			0
$735$	7.54472e31			0.0822884
$736$		0			0
$737$	−6.18650e32			−0.653986
$738$		0			0
$739$	2.05364e32	+	2.05364e32i	0.210433	+	0.210433i	0.804451	−	0.594019i	$-0.202459\pi$
$739$	2.05364e32	+	2.05364e32i	0.210433	+	0.210433i	−0.594019	+	0.804451i	$0.702459\pi$
$740$		0			0
$741$	9.92432e32	−	9.92432e32i	0.985806	−	0.985806i
$742$		0			0
$743$			5.38126e32i			0.518218i	0.965848	+	0.259109i	$0.0834288\pi$
$743$			5.38126e32i			0.518218i	−0.965848	+	0.259109i	$0.916571\pi$
$744$		0			0
$745$		−	1.91536e31i		−	0.0178835i
$746$		0			0
$747$	2.81022e33	−	2.81022e33i	2.54422	−	2.54422i
$748$		0			0
$749$	7.66983e32	+	7.66983e32i	0.673356	+	0.673356i
$750$		0			0
$751$	−6.79917e32			−0.578891			−0.289445	−	0.957195i	$-0.593471\pi$
$751$	−6.79917e32			−0.578891			−0.289445	+	0.957195i	$0.593471\pi$
$752$		0			0
$753$	−2.51406e33			−2.07603
$754$		0			0
$755$	−1.80481e31	−	1.80481e31i	−0.0144558	−	0.0144558i
$756$		0			0
$757$	−4.56844e32	+	4.56844e32i	−0.354948	+	0.354948i	−0.861947	−	0.506999i	$-0.830755\pi$
$757$	−4.56844e32	+	4.56844e32i	−0.354948	+	0.354948i	0.506999	+	0.861947i	$0.330755\pi$
$758$		0			0
$759$			1.33228e33i			1.00419i
$760$		0			0
$761$			2.31413e33i			1.69225i	0.532987	+	0.846124i	$0.321070\pi$
$761$			2.31413e33i			1.69225i	−0.532987	+	0.846124i	$0.678930\pi$
$762$		0			0
$763$	−1.51225e33	+	1.51225e33i	−1.07298	+	1.07298i
$764$		0			0
$765$	−1.05801e32	−	1.05801e32i	−0.0728422	−	0.0728422i
$766$		0			0
$767$	−1.03220e32			−0.0689628
$768$		0			0
$769$	9.56779e32			0.620381			0.310191	−	0.950674i	$-0.399607\pi$
$769$	9.56779e32			0.620381			0.310191	+	0.950674i	$0.399607\pi$
$770$		0			0
$771$	−2.10824e33	−	2.10824e33i	−1.32677	−	1.32677i
$772$		0			0
$773$	−7.78234e31	+	7.78234e31i	−0.0475385	+	0.0475385i	−0.730476	−	0.682938i	$-0.760702\pi$
$773$	−7.78234e31	+	7.78234e31i	−0.0475385	+	0.0475385i	0.682938	+	0.730476i	$0.260702\pi$
$774$		0			0
$775$		−	1.49582e33i		−	0.886970i
$776$		0			0
$777$		−	6.88179e33i		−	3.96150i
$778$		0			0
$779$	−1.52538e33	+	1.52538e33i	−0.852508	+	0.852508i
$780$		0			0
$781$	8.68242e32	+	8.68242e32i	0.471144	+	0.471144i
$782$		0			0
$783$	4.08472e33			2.15229
$784$		0			0
$785$	1.74124e32			0.0890960
$786$		0			0
$787$	−2.59201e33	−	2.59201e33i	−1.28803	−	1.28803i	−0.935980	−	0.352053i	$-0.885484\pi$
$787$	−2.59201e33	−	2.59201e33i	−1.28803	−	1.28803i	−0.352053	−	0.935980i	$-0.614516\pi$
$788$		0			0
$789$	3.00291e33	−	3.00291e33i	1.44929	−	1.44929i
$790$		0			0
$791$			1.00189e33i			0.469665i
$792$		0			0
$793$			1.65788e33i			0.754936i
$794$		0			0
$795$	1.88936e32	−	1.88936e32i	0.0835782	−	0.0835782i
$796$		0			0
$797$	−3.28553e32	−	3.28553e32i	−0.141200	−	0.141200i	0.632973	−	0.774174i	$-0.281834\pi$
$797$	−3.28553e32	−	3.28553e32i	−0.141200	−	0.141200i	−0.774174	+	0.632973i	$0.781834\pi$
$798$		0			0
$799$	8.95836e32			0.374060
$800$		0			0
$801$	−7.31960e33			−2.96971
$802$		0			0
$803$	8.23232e32	+	8.23232e32i	0.324559	+	0.324559i
$804$		0			0
$805$	−8.41857e31	+	8.41857e31i	−0.0322541	+	0.0322541i
$806$		0			0
$807$		−	4.75806e33i		−	1.77167i
$808$		0			0
$809$			3.77070e33i			1.36463i	0.731059	+	0.682314i	$0.239026\pi$
$809$			3.77070e33i			1.36463i	−0.731059	+	0.682314i	$0.760974\pi$
$810$		0			0
$811$	−6.69185e32	+	6.69185e32i	−0.235400	+	0.235400i	−0.814942	−	0.579542i	$-0.803231\pi$
$811$	−6.69185e32	+	6.69185e32i	−0.235400	+	0.235400i	0.579542	+	0.814942i	$0.303231\pi$
$812$		0			0
$813$	1.31634e33	+	1.31634e33i	0.450117	+	0.450117i
$814$		0			0
$815$	−6.83916e31			−0.0227347
$816$		0			0
$817$	−7.52692e33			−2.43256
$818$		0			0
$819$	−3.82306e33	−	3.82306e33i	−1.20129	−	1.20129i
$820$		0			0
$821$	−2.91011e33	+	2.91011e33i	−0.889125	+	0.889125i	−0.994439	−	0.105314i	$-0.966415\pi$
$821$	−2.91011e33	+	2.91011e33i	−0.889125	+	0.889125i	0.105314	+	0.994439i	$0.466415\pi$
$822$		0			0
$823$		−	1.12876e33i		−	0.335355i	−0.985842	−	0.167678i	$-0.946373\pi$
$823$		−	1.12876e33i		−	0.335355i	0.985842	−	0.167678i	$-0.0536268\pi$
$824$		0			0
$825$		−	5.21630e33i		−	1.50710i
$826$		0			0
$827$	−8.55227e32	+	8.55227e32i	−0.240308	+	0.240308i	−0.816977	−	0.576670i	$-0.804352\pi$
$827$	−8.55227e32	+	8.55227e32i	−0.240308	+	0.240308i	0.576670	+	0.816977i	$0.304352\pi$
$828$		0			0
$829$	1.79886e33	+	1.79886e33i	0.491610	+	0.491610i	0.908813	−	0.417203i	$-0.136990\pi$
$829$	1.79886e33	+	1.79886e33i	0.491610	+	0.491610i	−0.417203	+	0.908813i	$0.636990\pi$
$830$		0			0
$831$	−5.73356e33			−1.52410
$832$		0			0
$833$	−2.57764e33			−0.666506
$834$		0			0
$835$	9.49951e31	+	9.49951e31i	0.0238950	+	0.0238950i
$836$		0			0
$837$	7.98971e33	−	7.98971e33i	1.95519	−	1.95519i
$838$		0			0
$839$			7.84419e33i			1.86761i	0.357787	+	0.933803i	$0.383532\pi$
$839$			7.84419e33i			1.86761i	−0.357787	+	0.933803i	$0.616468\pi$
$840$		0			0
$841$		−	2.24861e33i		−	0.520906i
$842$		0			0
$843$	1.36975e33	−	1.36975e33i	0.308763	−	0.308763i
$844$		0			0
$845$	1.25914e32	+	1.25914e32i	0.0276198	+	0.0276198i
$846$		0			0
$847$	−2.37109e33			−0.506161
$848$		0			0
$849$	9.06363e33			1.88306
$850$		0			0
$851$	3.54479e33	+	3.54479e33i	0.716804	+	0.716804i
$852$		0			0
$853$	−3.45092e33	+	3.45092e33i	−0.679237	+	0.679237i	−0.959827	−	0.280591i	$-0.909470\pi$
$853$	−3.45092e33	+	3.45092e33i	−0.679237	+	0.679237i	0.280591	+	0.959827i	$0.409470\pi$
$854$		0			0
$855$			1.06832e33i			0.204688i
$856$		0			0
$857$		−	3.59169e32i		−	0.0669914i	−0.999439	−	0.0334957i	$-0.989336\pi$
$857$		−	3.59169e32i		−	0.0669914i	0.999439	−	0.0334957i	$-0.0106640\pi$
$858$		0			0
$859$	2.50352e33	−	2.50352e33i	0.454599	−	0.454599i	−0.442278	−	0.896878i	$-0.645830\pi$
$859$	2.50352e33	−	2.50352e33i	0.454599	−	0.454599i	0.896878	+	0.442278i	$0.145830\pi$
$860$		0			0
$861$	8.10893e33	+	8.10893e33i	1.43360	+	1.43360i
$862$		0			0
$863$	−1.96771e33			−0.338716			−0.169358	−	0.985555i	$-0.554169\pi$
$863$	−1.96771e33			−0.338716			−0.169358	+	0.985555i	$0.554169\pi$
$864$		0			0
$865$	3.60349e32			0.0604001
$866$		0			0
$867$	−3.26761e33	−	3.26761e33i	−0.533349	−	0.533349i
$868$		0			0
$869$	5.71640e32	−	5.71640e32i	0.0908648	−	0.0908648i
$870$		0			0
$871$			2.52379e33i			0.390702i
$872$		0			0
$873$			1.22033e34i			1.83998i
$874$		0			0
$875$	6.60067e32	−	6.60067e32i	0.0969383	−	0.0969383i
$876$		0			0
$877$	2.66848e33	+	2.66848e33i	0.381740	+	0.381740i	0.871729	−	0.489989i	$-0.162999\pi$
$877$	2.66848e33	+	2.66848e33i	0.381740	+	0.381740i	−0.489989	+	0.871729i	$0.662999\pi$
$878$		0			0
$879$	4.77704e32			0.0665712
$880$		0			0
$881$	1.22905e34			1.66858			0.834288	−	0.551329i	$-0.185879\pi$
$881$	1.22905e34			1.66858			0.834288	+	0.551329i	$0.185879\pi$
$882$		0			0
$883$	2.73943e33	+	2.73943e33i	0.362336	+	0.362336i	0.864672	−	0.502336i	$-0.167526\pi$
$883$	2.73943e33	+	2.73943e33i	0.362336	+	0.362336i	−0.502336	+	0.864672i	$0.667526\pi$
$884$		0			0
$885$	7.66667e31	−	7.66667e31i	0.00988005	−	0.00988005i
$886$		0			0
$887$			4.48329e33i			0.562957i	0.959567	+	0.281479i	$0.0908249\pi$
$887$			4.48329e33i			0.562957i	−0.959567	+	0.281479i	$0.909175\pi$
$888$		0			0
$889$			1.41689e34i			1.73366i
$890$		0			0
$891$	1.54884e34	−	1.54884e34i	1.84677	−	1.84677i
$892$		0			0
$893$	−4.52283e33	−	4.52283e33i	−0.525556	−	0.525556i
$894$		0			0
$895$	3.97176e32			0.0449799
$896$		0			0
$897$	5.43505e33			0.599916
$898$		0			0
$899$	4.04523e33	+	4.04523e33i	0.435218	+	0.435218i
$900$		0			0
$901$	−6.45496e33	+	6.45496e33i	−0.676953	+	0.676953i
$902$		0			0
$903$			4.00131e34i			4.09065i
$904$		0			0
$905$		−	9.39048e32i		−	0.0935899i
$906$		0			0
$907$	−2.37928e33	+	2.37928e33i	−0.231186	+	0.231186i	−0.813188	−	0.582001i	$-0.802270\pi$
$907$	−2.37928e33	+	2.37928e33i	−0.231186	+	0.231186i	0.582001	+	0.813188i	$0.302270\pi$
$908$		0			0
$909$	−1.10222e34	−	1.10222e34i	−1.04420	−	1.04420i
$910$		0			0
$911$	1.71172e34			1.58114			0.790572	−	0.612370i	$-0.209784\pi$
$911$	1.71172e34			1.58114			0.790572	+	0.612370i	$0.209784\pi$
$912$		0			0
$913$	1.20348e34			1.08399
$914$		0			0
$915$	−1.23139e33	−	1.23139e33i	−0.108157	−	0.108157i
$916$		0			0
$917$	−7.78885e33	+	7.78885e33i	−0.667154	+	0.667154i
$918$		0			0
$919$		−	1.04227e34i		−	0.870669i	−0.900269	−	0.435334i	$-0.856630\pi$
$919$		−	1.04227e34i		−	0.870669i	0.900269	−	0.435334i	$-0.143370\pi$
$920$		0			0
$921$			1.67185e34i			1.36211i
$922$		0			0
$923$	3.54201e33	−	3.54201e33i	0.281469	−	0.281469i
$924$		0			0
$925$	−1.38790e34	−	1.38790e34i	−1.07579	−	1.07579i
$926$		0			0
$927$	1.40692e34			1.06378
$928$		0			0
$929$	−2.07870e34			−1.53324			−0.766622	−	0.642099i	$-0.778064\pi$
$929$	−2.07870e34			−1.53324			−0.766622	+	0.642099i	$0.778064\pi$
$930$		0			0
$931$	1.30138e34	+	1.30138e34i	0.936445	+	0.936445i
$932$		0			0
$933$	1.68714e34	−	1.68714e34i	1.18444	−	1.18444i
$934$		0			0
$935$		−	4.53094e32i		−	0.0310352i
$936$		0			0
$937$			1.07866e34i			0.720906i	0.932777	+	0.360453i	$0.117378\pi$
$937$			1.07866e34i			0.720906i	−0.932777	+	0.360453i	$0.882622\pi$
$938$		0			0
$939$	−1.67154e34	+	1.67154e34i	−1.09009	+	1.09009i
$940$		0			0
$941$	3.78205e33	+	3.78205e33i	0.240684	+	0.240684i	0.817133	−	0.576449i	$-0.195562\pi$
$941$	3.78205e33	+	3.78205e33i	0.240684	+	0.240684i	−0.576449	+	0.817133i	$0.695562\pi$
$942$		0			0
$943$	−8.35377e33			−0.518797
$944$		0			0
$945$	3.52118e33			0.213414
$946$		0			0
$947$	−3.91394e33	−	3.91394e33i	−0.231520	−	0.231520i	0.581807	−	0.813327i	$-0.302346\pi$
$947$	−3.91394e33	−	3.91394e33i	−0.231520	−	0.231520i	−0.813327	+	0.581807i	$0.802346\pi$
$948$		0			0
$949$	3.35839e33	−	3.35839e33i	0.193896	−	0.193896i
$950$		0			0
$951$		−	5.26222e34i		−	2.96546i
$952$		0			0
$953$		−	2.86566e34i		−	1.57637i	−0.615441	−	0.788183i	$-0.711022\pi$
$953$		−	2.86566e34i		−	1.57637i	0.615441	−	0.788183i	$-0.288978\pi$
$954$		0			0
$955$	6.81285e32	−	6.81285e32i	0.0365839	−	0.0365839i
$956$		0			0
$957$	1.41068e34	+	1.41068e34i	0.739504	+	0.739504i
$958$		0			0
$959$	−4.01974e34			−2.05724
$960$		0			0
$961$	−4.18836e33			−0.209279
$962$		0			0
$963$	2.66515e34	+	2.66515e34i	1.30023	+	1.30023i
$964$		0			0
$965$	−8.94980e32	+	8.94980e32i	−0.0426333	+	0.0426333i
$966$		0			0
$967$			2.95827e34i			1.37605i	0.725687	+	0.688025i	$0.241522\pi$
$967$			2.95827e34i			1.37605i	−0.725687	+	0.688025i	$0.758478\pi$
$968$		0			0
$969$		−	5.03679e34i		−	2.28787i
$970$		0			0
$971$	−1.76308e34	+	1.76308e34i	−0.782078	+	0.782078i	−0.980181	−	0.198103i	$-0.936522\pi$
$971$	−1.76308e34	+	1.76308e34i	−0.782078	+	0.782078i	0.198103	+	0.980181i	$0.436522\pi$
$972$		0			0
$973$	1.99816e33	+	1.99816e33i	0.0865629	+	0.0865629i
$974$		0			0
$975$	−2.12800e34			−0.900366
$976$		0			0
$977$	−2.50377e34			−1.03468			−0.517341	−	0.855779i	$-0.673078\pi$
$977$	−2.50377e34			−1.03468			−0.517341	+	0.855779i	$0.673078\pi$
$978$		0			0
$979$	−1.56731e34	−	1.56731e34i	−0.632638	−	0.632638i
$980$		0			0
$981$	−5.25486e34	+	5.25486e34i	−2.07189	+	2.07189i
$982$		0			0
$983$			2.46494e34i			0.949383i	0.880152	+	0.474691i	$0.157440\pi$
$983$			2.46494e34i			0.949383i	−0.880152	+	0.474691i	$0.842560\pi$
$984$		0			0
$985$			2.12999e33i			0.0801420i
$986$		0			0
$987$	−2.40434e34	+	2.40434e34i	−0.883787	+	0.883787i
$988$		0			0
$989$	−2.06106e34	−	2.06106e34i	−0.740173	−	0.740173i
$990$		0			0
$991$	−7.64245e33			−0.268155			−0.134077	−	0.990971i	$-0.542807\pi$
$991$	−7.64245e33			−0.268155			−0.134077	+	0.990971i	$0.542807\pi$
$992$		0			0
$993$	3.11278e34			1.06717
$994$		0			0
$995$	−6.62175e31	−	6.62175e31i	−0.00221823	−	0.00221823i
$996$		0			0
$997$	5.50250e33	−	5.50250e33i	0.180122	−	0.180122i	−0.611287	−	0.791409i	$-0.709348\pi$
$997$	5.50250e33	−	5.50250e33i	0.180122	−	0.180122i	0.791409	+	0.611287i	$0.209348\pi$
$998$		0			0
$999$		−	1.48266e35i		−	4.74283i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	64.24.e.a.17.45		90
4.3	odd	2		16.24.e.a.13.30	yes	90
16.5	even	4	inner	64.24.e.a.49.45		90
16.11	odd	4		16.24.e.a.5.30	✓	90

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.24.e.a.5.30	✓	90	16.11	odd	4
16.24.e.a.13.30	yes	90	4.3	odd	2
64.24.e.a.17.45		90	1.1	even	1	trivial
64.24.e.a.49.45		90	16.5	even	4	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:	\( N \)	\(=\)	\( 64 = 2^{6} \)
Weight:	\( k \)	\(=\)	\( 24 \)
Character orbit:	\([\chi]\)	\(=\)	64.e (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(413460. + 413460. i) q^{3} +(-3.88787e6 + 3.88787e6i) q^{5} +7.12996e9i q^{7} +2.47755e11i q^{9} +O(q^{10})\)	\(q+(413460. + 413460. i) q^{3} +(-3.88787e6 + 3.88787e6i) q^{5} +7.12996e9i q^{7} +2.47755e11i q^{9} +(-5.30508e11 + 5.30508e11i) q^{11} +(2.16422e12 + 2.16422e12i) q^{13} -3.21496e12 q^{15} +1.09838e14 q^{17} +(-5.54544e14 - 5.54544e14i) q^{19} +(-2.94795e15 + 2.94795e15i) q^{21} -3.03696e15i q^{23} +1.18907e16i q^{25} +(-6.35126e16 + 6.35126e16i) q^{27} +(-3.21568e16 - 3.21568e16i) q^{29} -1.25797e17 q^{31} -4.38688e17 q^{33} +(-2.77204e16 - 2.77204e16i) q^{35} +(-1.16722e18 + 1.16722e18i) q^{37} +1.78964e18i q^{39} -2.75070e18i q^{41} +(6.78659e18 - 6.78659e18i) q^{43} +(-9.63242e17 - 9.63242e17i) q^{45} +8.15595e18 q^{47} -2.34675e19 q^{49} +(4.54138e19 + 4.54138e19i) q^{51} +(-5.87678e19 + 5.87678e19i) q^{53} -4.12510e18i q^{55} -4.58564e20i q^{57} +(-2.38468e19 + 2.38468e19i) q^{59} +(3.83019e20 + 3.83019e20i) q^{61} -1.76649e21 q^{63} -1.68284e19 q^{65} +(5.83073e20 + 5.83073e20i) q^{67} +(1.25566e21 - 1.25566e21i) q^{69} -1.63662e21i q^{71} -1.55178e21i q^{73} +(-4.91633e21 + 4.91633e21i) q^{75} +(-3.78250e21 - 3.78250e21i) q^{77} -1.07753e21 q^{79} -2.91954e22 q^{81} +(-1.13427e22 - 1.13427e22i) q^{83} +(-4.27038e20 + 4.27038e20i) q^{85} -2.65911e22i q^{87} +2.95437e22i q^{89} +(-1.54308e22 + 1.54308e22i) q^{91} +(-5.20122e22 - 5.20122e22i) q^{93} +4.31200e21 q^{95} +4.92555e22 q^{97} +(-1.31436e23 - 1.31436e23i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 90 q + 2 q^{3} - 2 q^{5}+O(q^{10}) \) 90 * q + 2 * q^3 - 2 * q^5	\( 90 q + 2 q^{3} - 2 q^{5} - 975574266674 q^{11} - 2 q^{13} + 69198046875004 q^{15} - 4 q^{17} - 33497748322214 q^{19} + 188286357652 q^{21} + 68\!\cdots\!12 q^{27}+ \cdots - 15\!\cdots\!18 q^{99}+O(q^{100}) \) 90 * q + 2 * q^3 - 2 * q^5 - 975574266674 * q^11 - 2 * q^13 + 69198046875004 * q^15 - 4 * q^17 - 33497748322214 * q^19 + 188286357652 * q^21 + 68199758786330312 * q^27 + 40182344820854166 * q^29 - 304901722756857968 * q^31 - 4 * q^33 + 71740198139629924 * q^35 - 1247331607738910506 * q^37 + 9188667298883114726 * q^43 + 23841669623798594 * q^45 + 49443184301680246064 * q^47 - 304966041789473067826 * q^49 + 174534019299729287580 * q^51 + 13640530997232145574 * q^53 - 601560376862930647818 * q^59 - 689547400664843490610 * q^61 - 1350487157131380135108 * q^63 + 677755821971313699508 * q^65 + 78203218176043282218 * q^67 - 1740473287260991535900 * q^69 + 4337902598314368797354 * q^75 - 5419518588555145686572 * q^77 - 7302797173814966423104 * q^79 - 72873046761587231233198 * q^81 + 32909130597108510028802 * q^83 - 25986931398852441406252 * q^85 - 85476927041001397522436 * q^91 + 79297851703427311011376 * q^93 - 418206809033540036489460 * q^95 - 4 * q^97 - 153989708813859231365918 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more