LMFDB - Embedded newform 64.24.e.a.17.20

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			17.20
Character	$\chi$	$=$	64.17
Dual form			64.24.e.a.49.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-68436.9 - 68436.9i) q^{3} +(-2.70386e6 + 2.70386e6i) q^{5} +2.28175e9i q^{7} -8.47760e10i q^{9} +O(q^{10})$	\(q+(-68436.9 - 68436.9i) q^{3} +(-2.70386e6 + 2.70386e6i) q^{5} +2.28175e9i q^{7} -8.47760e10i q^{9} +(4.33062e11 - 4.33062e11i) q^{11} +(-3.60366e12 - 3.60366e12i) q^{13} +3.70087e11 q^{15} -2.43286e14 q^{17} +(9.90492e12 + 9.90492e12i) q^{19} +(1.56156e14 - 1.56156e14i) q^{21} +3.84151e15i q^{23} +1.19063e16i q^{25} +(-1.22447e16 + 1.22447e16i) q^{27} +(-4.39280e16 - 4.39280e16i) q^{29} +1.06817e17 q^{31} -5.92748e16 q^{33} +(-6.16953e15 - 6.16953e15i) q^{35} +(1.78754e17 - 1.78754e17i) q^{37} +4.93247e17i q^{39} -1.48960e18i q^{41} +(4.74540e18 - 4.74540e18i) q^{43} +(2.29222e17 + 2.29222e17i) q^{45} -1.55862e19 q^{47} +2.21624e19 q^{49} +(1.66497e19 + 1.66497e19i) q^{51} +(-2.36779e19 + 2.36779e19i) q^{53} +2.34187e18i q^{55} -1.35572e18i q^{57} +(-1.81978e20 + 1.81978e20i) q^{59} +(-4.63677e20 - 4.63677e20i) q^{61} +1.93438e20 q^{63} +1.94876e19 q^{65} +(9.87931e20 + 9.87931e20i) q^{67} +(2.62901e20 - 2.62901e20i) q^{69} +3.79930e20i q^{71} -2.17823e21i q^{73} +(8.14830e20 - 8.14830e20i) q^{75} +(9.88140e20 + 9.88140e20i) q^{77} -4.95268e21 q^{79} -6.30511e21 q^{81} +(-6.24068e21 - 6.24068e21i) q^{83} +(6.57809e20 - 6.57809e20i) q^{85} +6.01259e21i q^{87} +3.61816e22i q^{89} +(8.22267e21 - 8.22267e21i) q^{91} +(-7.31022e21 - 7.31022e21i) q^{93} -5.35629e19 q^{95} +1.92581e21 q^{97} +(-3.67132e22 - 3.67132e22i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−68436.9	−	68436.9i	−0.223047	−	0.223047i	0.586733	−	0.809780i	$-0.300414\pi$
$3$	−68436.9	−	68436.9i	−0.223047	−	0.223047i	−0.809780	+	0.586733i	$0.800414\pi$
$4$		0			0
$5$	−2.70386e6	+	2.70386e6i	−0.0247644	+	0.0247644i	−0.719381	−	0.694616i	$-0.755574\pi$
$5$	−2.70386e6	+	2.70386e6i	−0.0247644	+	0.0247644i	0.694616	+	0.719381i	$0.255574\pi$
$6$		0			0
$7$			2.28175e9i			0.436155i	0.975931	+	0.218078i	$0.0699786\pi$
$7$			2.28175e9i			0.436155i	−0.975931	+	0.218078i	$0.930021\pi$
$8$		0			0
$9$		−	8.47760e10i		−	0.900500i
$10$		0			0
$11$	4.33062e11	−	4.33062e11i	0.457651	−	0.457651i	−0.440233	−	0.897884i	$-0.645104\pi$
$11$	4.33062e11	−	4.33062e11i	0.457651	−	0.457651i	0.897884	+	0.440233i	$0.145104\pi$
$12$		0			0
$13$	−3.60366e12	−	3.60366e12i	−0.557694	−	0.557694i	0.370957	−	0.928650i	$-0.379030\pi$
$13$	−3.60366e12	−	3.60366e12i	−0.557694	−	0.557694i	−0.928650	+	0.370957i	$0.879030\pi$
$14$		0			0
$15$	3.70087e11			0.0110472
$16$		0			0
$17$	−2.43286e14			−1.72169			−0.860843	−	0.508871i	$-0.830063\pi$
$17$	−2.43286e14			−1.72169			−0.860843	+	0.508871i	$0.830063\pi$
$18$		0			0
$19$	9.90492e12	+	9.90492e12i	0.0195067	+	0.0195067i	0.716793	−	0.697286i	$-0.245609\pi$
$19$	9.90492e12	+	9.90492e12i	0.0195067	+	0.0195067i	−0.697286	+	0.716793i	$0.745609\pi$
$20$		0			0
$21$	1.56156e14	−	1.56156e14i	0.0972829	−	0.0972829i
$22$		0			0
$23$			3.84151e15i			0.840681i	0.907366	+	0.420341i	$0.138089\pi$
$23$			3.84151e15i			0.840681i	−0.907366	+	0.420341i	$0.861911\pi$
$24$		0			0
$25$			1.19063e16i			0.998773i
$26$		0			0
$27$	−1.22447e16	+	1.22447e16i	−0.423900	+	0.423900i
$28$		0			0
$29$	−4.39280e16	−	4.39280e16i	−0.668597	−	0.668597i	0.288795	−	0.957391i	$-0.406746\pi$
$29$	−4.39280e16	−	4.39280e16i	−0.668597	−	0.668597i	−0.957391	+	0.288795i	$0.906746\pi$
$30$		0			0
$31$	1.06817e17			0.755059			0.377529	−	0.925998i	$-0.376774\pi$
$31$	1.06817e17			0.755059			0.377529	+	0.925998i	$0.376774\pi$
$32$		0			0
$33$	−5.92748e16			−0.204155
$34$		0			0
$35$	−6.16953e15	−	6.16953e15i	−0.0108011	−	0.0108011i
$36$		0			0
$37$	1.78754e17	−	1.78754e17i	0.165171	−	0.165171i	−0.619682	−	0.784853i	$-0.712738\pi$
$37$	1.78754e17	−	1.78754e17i	0.165171	−	0.165171i	0.784853	+	0.619682i	$0.212738\pi$
$38$		0			0
$39$			4.93247e17i			0.248783i
$40$		0			0
$41$		−	1.48960e18i		−	0.422723i	−0.977408	−	0.211361i	$-0.932210\pi$
$41$		−	1.48960e18i		−	0.422723i	0.977408	−	0.211361i	$-0.0677897\pi$
$42$		0			0
$43$	4.74540e18	−	4.74540e18i	0.778727	−	0.778727i	−0.200887	−	0.979614i	$-0.564382\pi$
$43$	4.74540e18	−	4.74540e18i	0.778727	−	0.778727i	0.979614	+	0.200887i	$0.0643825\pi$
$44$		0			0
$45$	2.29222e17	+	2.29222e17i	0.0223004	+	0.0223004i
$46$		0			0
$47$	−1.55862e19			−0.919631			−0.459816	−	0.888014i	$-0.652085\pi$
$47$	−1.55862e19			−0.919631			−0.459816	+	0.888014i	$0.652085\pi$
$48$		0			0
$49$	2.21624e19			0.809769
$50$		0			0
$51$	1.66497e19	+	1.66497e19i	0.384016	+	0.384016i
$52$		0			0
$53$	−2.36779e19	+	2.36779e19i	−0.350889	+	0.350889i	−0.860440	−	0.509551i	$-0.829811\pi$
$53$	−2.36779e19	+	2.36779e19i	−0.350889	+	0.350889i	0.509551	+	0.860440i	$0.329811\pi$
$54$		0			0
$55$			2.34187e18i			0.0226669i
$56$		0			0
$57$		−	1.35572e18i		−	0.00870182i
$58$		0			0
$59$	−1.81978e20	+	1.81978e20i	−0.785634	+	0.785634i	−0.980775	−	0.195141i	$-0.937483\pi$
$59$	−1.81978e20	+	1.81978e20i	−0.785634	+	0.785634i	0.195141	+	0.980775i	$0.437483\pi$
$60$		0			0
$61$	−4.63677e20	−	4.63677e20i	−1.36434	−	1.36434i	−0.868300	−	0.496039i	$-0.834787\pi$
$61$	−4.63677e20	−	4.63677e20i	−1.36434	−	1.36434i	−0.496039	−	0.868300i	$-0.665213\pi$
$62$		0			0
$63$	1.93438e20			0.392758
$64$		0			0
$65$	1.94876e19			0.0276219
$66$		0			0
$67$	9.87931e20	+	9.87931e20i	0.988249	+	0.988249i	0.999932	−	0.0116825i	$-0.00371873\pi$
$67$	9.87931e20	+	9.87931e20i	0.988249	+	0.988249i	−0.0116825	+	0.999932i	$0.503719\pi$
$68$		0			0
$69$	2.62901e20	−	2.62901e20i	0.187511	−	0.187511i
$70$		0			0
$71$			3.79930e20i			0.195089i	0.995231	+	0.0975444i	$0.0310988\pi$
$71$			3.79930e20i			0.195089i	−0.995231	+	0.0975444i	$0.968901\pi$
$72$		0			0
$73$		−	2.17823e21i		−	0.812628i	−0.913734	−	0.406314i	$-0.866814\pi$
$73$		−	2.17823e21i		−	0.812628i	0.913734	−	0.406314i	$-0.133186\pi$
$74$		0			0
$75$	8.14830e20	−	8.14830e20i	0.222773	−	0.222773i
$76$		0			0
$77$	9.88140e20	+	9.88140e20i	0.199607	+	0.199607i
$78$		0			0
$79$	−4.95268e21			−0.744953			−0.372476	−	0.928042i	$-0.621491\pi$
$79$	−4.95268e21			−0.744953			−0.372476	+	0.928042i	$0.621491\pi$
$80$		0			0
$81$	−6.30511e21			−0.711401
$82$		0			0
$83$	−6.24068e21	−	6.24068e21i	−0.531905	−	0.531905i	0.389234	−	0.921139i	$-0.372740\pi$
$83$	−6.24068e21	−	6.24068e21i	−0.531905	−	0.531905i	−0.921139	+	0.389234i	$0.872740\pi$
$84$		0			0
$85$	6.57809e20	−	6.57809e20i	0.0426366	−	0.0426366i
$86$		0			0
$87$			6.01259e21i			0.298256i
$88$		0			0
$89$			3.61816e22i			1.38198i	0.722863	+	0.690991i	$0.242826\pi$
$89$			3.61816e22i			1.38198i	−0.722863	+	0.690991i	$0.757174\pi$
$90$		0			0
$91$	8.22267e21	−	8.22267e21i	0.243241	−	0.243241i
$92$		0			0
$93$	−7.31022e21	−	7.31022e21i	−0.168413	−	0.168413i
$94$		0			0
$95$	−5.35629e19			−0.000966146
$96$		0			0
$97$	1.92581e21			0.0273362			0.0136681	−	0.999907i	$-0.495649\pi$
$97$	1.92581e21			0.0273362			0.0136681	+	0.999907i	$0.495649\pi$
$98$		0			0
$99$	−3.67132e22	−	3.67132e22i	−0.412114	−	0.412114i
$100$		0			0
$101$	−5.96413e22	+	5.96413e22i	−0.531926	+	0.531926i	−0.921145	−	0.389219i	$-0.872745\pi$
$101$	−5.96413e22	+	5.96413e22i	−0.531926	+	0.531926i	0.389219	+	0.921145i	$0.372745\pi$
$102$		0			0
$103$		−	1.61780e23i		−	1.15158i	−0.817596	−	0.575792i	$-0.804694\pi$
$103$		−	1.61780e23i		−	1.15158i	0.817596	−	0.575792i	$-0.195306\pi$
$104$		0			0
$105$			8.44446e20i			0.00481831i
$106$		0			0
$107$	6.95585e22	−	6.95585e22i	0.319475	−	0.319475i	−0.529091	−	0.848565i	$-0.677467\pi$
$107$	6.95585e22	−	6.95585e22i	0.319475	−	0.319475i	0.848565	+	0.529091i	$0.177467\pi$
$108$		0			0
$109$	1.85387e23	+	1.85387e23i	0.688136	+	0.688136i	0.961820	−	0.273684i	$-0.0882422\pi$
$109$	1.85387e23	+	1.85387e23i	0.688136	+	0.688136i	−0.273684	+	0.961820i	$0.588242\pi$
$110$		0			0
$111$	−2.44667e22			−0.0736818
$112$		0			0
$113$	9.48676e21			0.0232657			0.0116328	−	0.999932i	$-0.496297\pi$
$113$	9.48676e21			0.0232657			0.0116328	+	0.999932i	$0.496297\pi$
$114$		0			0
$115$	−1.03869e22	−	1.03869e22i	−0.0208190	−	0.0208190i
$116$		0			0
$117$	−3.05504e23	+	3.05504e23i	−0.502203	+	0.502203i
$118$		0			0
$119$		−	5.55118e23i		−	0.750922i
$120$		0			0
$121$			5.20345e23i			0.581112i
$122$		0			0
$123$	−1.01944e23	+	1.01944e23i	−0.0942869	+	0.0942869i
$124$		0			0
$125$	−6.44254e22	−	6.44254e22i	−0.0494985	−	0.0494985i
$126$		0			0
$127$	1.32613e24			0.848876			0.424438	−	0.905457i	$-0.360472\pi$
$127$	1.32613e24			0.848876			0.424438	+	0.905457i	$0.360472\pi$
$128$		0			0
$129$	−6.49520e23			−0.347385
$130$		0			0
$131$	2.99604e23	+	2.99604e23i	0.134254	+	0.134254i	0.771040	−	0.636786i	$-0.219737\pi$
$131$	2.99604e23	+	2.99604e23i	0.134254	+	0.134254i	−0.636786	+	0.771040i	$0.719737\pi$
$132$		0			0
$133$	−2.26006e22	+	2.26006e22i	−0.00850796	+	0.00850796i
$134$		0			0
$135$		−	6.62156e22i		−	0.0209953i
$136$		0			0
$137$			1.88401e24i			0.504426i	0.967672	+	0.252213i	$0.0811584\pi$
$137$			1.88401e24i			0.504426i	−0.967672	+	0.252213i	$0.918842\pi$
$138$		0			0
$139$	4.95522e24	−	4.95522e24i	1.12303	−	1.12303i	0.131750	−	0.991283i	$-0.457940\pi$
$139$	4.95522e24	−	4.95522e24i	1.12303	−	1.12303i	0.991283	−	0.131750i	$-0.0420596\pi$
$140$		0			0
$141$	1.06667e24	+	1.06667e24i	0.205121	+	0.205121i
$142$		0			0
$143$	−3.12122e24			−0.510458
$144$		0			0
$145$	2.37550e23			0.0331148
$146$		0			0
$147$	−1.51672e24	−	1.51672e24i	−0.180616	−	0.180616i
$148$		0			0
$149$	−1.05958e24	+	1.05958e24i	−0.108017	+	0.108017i	−0.759050	−	0.651033i	$-0.774336\pi$
$149$	−1.05958e24	+	1.05958e24i	−0.108017	+	0.108017i	0.651033	+	0.759050i	$0.274336\pi$
$150$		0			0
$151$		−	7.92542e24i		−	0.693086i	−0.938034	−	0.346543i	$-0.887355\pi$
$151$		−	7.92542e24i		−	0.693086i	0.938034	−	0.346543i	$-0.112645\pi$
$152$		0			0
$153$			2.06248e25i			1.55038i
$154$		0			0
$155$	−2.88818e23	+	2.88818e23i	−0.0186986	+	0.0186986i
$156$		0			0
$157$	7.25837e24	+	7.25837e24i	0.405502	+	0.405502i	0.880167	−	0.474664i	$-0.157431\pi$
$157$	7.25837e24	+	7.25837e24i	0.405502	+	0.405502i	−0.474664	+	0.880167i	$0.657431\pi$
$158$		0			0
$159$	3.24088e24			0.156529
$160$		0			0
$161$	−8.76536e24			−0.366667
$162$		0			0
$163$	−3.79614e24	−	3.79614e24i	−0.137779	−	0.137779i	0.634853	−	0.772633i	$-0.281061\pi$
$163$	−3.79614e24	−	3.79614e24i	−0.137779	−	0.137779i	−0.772633	+	0.634853i	$0.781061\pi$
$164$		0			0
$165$	1.60270e23	−	1.60270e23i	0.00505578	−	0.00505578i
$166$		0			0
$167$		−	2.05747e25i		−	0.565058i	−0.959259	−	0.282529i	$-0.908827\pi$
$167$		−	2.05747e25i		−	0.565058i	0.959259	−	0.282529i	$-0.0911734\pi$
$168$		0			0
$169$		−	1.57811e25i		−	0.377956i
$170$		0			0
$171$	8.39699e23	−	8.39699e23i	0.0175658	−	0.0175658i
$172$		0			0
$173$	−3.53264e24	−	3.53264e24i	−0.0646501	−	0.0646501i	0.674042	−	0.738693i	$-0.264556\pi$
$173$	−3.53264e24	−	3.53264e24i	−0.0646501	−	0.0646501i	−0.738693	+	0.674042i	$0.764556\pi$
$174$		0			0
$175$	−2.71672e25			−0.435620
$176$		0			0
$177$	2.49080e25			0.350466
$178$		0			0
$179$	7.61050e25	+	7.61050e25i	0.941030	+	0.941030i	0.998356	−	0.0573258i	$-0.0182574\pi$
$179$	7.61050e25	+	7.61050e25i	0.941030	+	0.941030i	−0.0573258	+	0.998356i	$0.518257\pi$
$180$		0			0
$181$	−1.05625e25	+	1.05625e25i	−0.114938	+	0.114938i	−0.762237	−	0.647298i	$-0.775899\pi$
$181$	−1.05625e25	+	1.05625e25i	−0.114938	+	0.114938i	0.647298	+	0.762237i	$0.275899\pi$
$182$		0			0
$183$			6.34652e25i			0.608623i
$184$		0			0
$185$			9.66648e23i			0.00818075i
$186$		0			0
$187$	−1.05358e26	+	1.05358e26i	−0.787930	+	0.787930i
$188$		0			0
$189$	−2.79393e25	−	2.79393e25i	−0.184886	−	0.184886i
$190$		0			0
$191$	1.90005e25			0.111399			0.0556995	−	0.998448i	$-0.482261\pi$
$191$	1.90005e25			0.111399			0.0556995	+	0.998448i	$0.482261\pi$
$192$		0			0
$193$	1.31797e25			0.0685483			0.0342741	−	0.999412i	$-0.489088\pi$
$193$	1.31797e25			0.0685483			0.0342741	+	0.999412i	$0.489088\pi$
$194$		0			0
$195$	−1.33367e24	−	1.33367e24i	−0.00616098	−	0.00616098i
$196$		0			0
$197$	2.93717e26	−	2.93717e26i	1.20661	−	1.20661i	0.234495	−	0.972117i	$-0.424656\pi$
$197$	2.93717e26	−	2.93717e26i	1.20661	−	1.20661i	0.972117	−	0.234495i	$-0.0753436\pi$
$198$		0			0
$199$			4.24559e26i			1.55284i	0.630214	+	0.776421i	$0.282967\pi$
$199$			4.24559e26i			1.55284i	−0.630214	+	0.776421i	$0.717033\pi$
$200$		0			0
$201$		−	1.35222e26i		−	0.440851i
$202$		0			0
$203$	1.00233e26	−	1.00233e26i	0.291612	−	0.291612i
$204$		0			0
$205$	4.02767e24	+	4.02767e24i	0.0104685	+	0.0104685i
$206$		0			0
$207$	3.25667e26			0.757034
$208$		0			0
$209$	8.57888e24			0.0178545
$210$		0			0
$211$	6.56659e26	+	6.56659e26i	1.22488	+	1.22488i	0.965878	+	0.258997i	$0.0833920\pi$
$211$	6.56659e26	+	6.56659e26i	1.22488	+	1.22488i	0.258997	+	0.965878i	$0.416608\pi$
$212$		0			0
$213$	2.60012e25	−	2.60012e25i	0.0435139	−	0.0435139i
$214$		0			0
$215$			2.56617e25i			0.0385695i
$216$		0			0
$217$			2.43730e26i			0.329323i
$218$		0			0
$219$	−1.49072e26	+	1.49072e26i	−0.181254	+	0.181254i
$220$		0			0
$221$	8.76720e26	+	8.76720e26i	0.960173	+	0.960173i
$222$		0			0
$223$	−9.73866e26			−0.961598			−0.480799	−	0.876831i	$-0.659653\pi$
$223$	−9.73866e26			−0.961598			−0.480799	+	0.876831i	$0.659653\pi$
$224$		0			0
$225$	1.00937e27			0.899396
$226$		0			0
$227$	−2.68208e26	−	2.68208e26i	−0.215861	−	0.215861i	0.590891	−	0.806752i	$-0.298776\pi$
$227$	−2.68208e26	−	2.68208e26i	−0.215861	−	0.215861i	−0.806752	+	0.590891i	$0.798776\pi$
$228$		0			0
$229$	−6.76460e26	+	6.76460e26i	−0.492192	+	0.492192i	−0.908996	−	0.416805i	$-0.863150\pi$
$229$	−6.76460e26	+	6.76460e26i	−0.492192	+	0.492192i	0.416805	+	0.908996i	$0.363150\pi$
$230$		0			0
$231$		−	1.35250e26i		−	0.0890432i
$232$		0			0
$233$			2.28819e27i			1.36427i	0.731228	+	0.682133i	$0.238948\pi$
$233$			2.28819e27i			1.36427i	−0.731228	+	0.682133i	$0.761052\pi$
$234$		0			0
$235$	4.21427e25	−	4.21427e25i	0.0227742	−	0.0227742i
$236$		0			0
$237$	3.38946e26	+	3.38946e26i	0.166159	+	0.166159i
$238$		0			0
$239$	4.04691e27			1.80114			0.900571	−	0.434708i	$-0.143149\pi$
$239$	4.04691e27			1.80114			0.900571	+	0.434708i	$0.143149\pi$
$240$		0			0
$241$	2.54732e27			1.03012			0.515059	−	0.857155i	$-0.327770\pi$
$241$	2.54732e27			1.03012			0.515059	+	0.857155i	$0.327770\pi$
$242$		0			0
$243$	1.58425e27	+	1.58425e27i	0.582576	+	0.582576i
$244$		0			0
$245$	−5.99238e25	+	5.99238e25i	−0.0200535	+	0.0200535i
$246$		0			0
$247$		−	7.13880e25i		−	0.0217576i
$248$		0			0
$249$			8.54186e26i			0.237279i
$250$		0			0
$251$	1.00714e27	−	1.00714e27i	0.255176	−	0.255176i	−0.567913	−	0.823089i	$-0.692249\pi$
$251$	1.00714e27	−	1.00714e27i	0.255176	−	0.255176i	0.823089	+	0.567913i	$0.192249\pi$
$252$		0			0
$253$	1.66361e27	+	1.66361e27i	0.384738	+	0.384738i
$254$		0			0
$255$	−9.00368e25			−0.0190199
$256$		0			0
$257$	−2.70031e27			−0.521415			−0.260707	−	0.965418i	$-0.583956\pi$
$257$	−2.70031e27			−0.521415			−0.260707	+	0.965418i	$0.583956\pi$
$258$		0			0
$259$	4.07871e26	+	4.07871e26i	0.0720403	+	0.0720403i
$260$		0			0
$261$	−3.72404e27	+	3.72404e27i	−0.602071	+	0.602071i
$262$		0			0
$263$			1.25204e28i			1.85408i	0.374965	+	0.927039i	$0.377655\pi$
$263$			1.25204e28i			1.85408i	−0.374965	+	0.927039i	$0.622345\pi$
$264$		0			0
$265$		−	1.28043e26i		−	0.0173791i
$266$		0			0
$267$	2.47615e27	−	2.47615e27i	0.308246	−	0.308246i
$268$		0			0
$269$	1.21009e28	+	1.21009e28i	1.38251	+	1.38251i	0.840144	+	0.542363i	$0.182470\pi$
$269$	1.21009e28	+	1.21009e28i	1.38251	+	1.38251i	0.542363	+	0.840144i	$0.317530\pi$
$270$		0			0
$271$	1.11928e28			1.17434			0.587170	−	0.809464i	$-0.300242\pi$
$271$	1.11928e28			1.17434			0.587170	+	0.809464i	$0.300242\pi$
$272$		0			0
$273$	−1.12547e27			−0.108508
$274$		0			0
$275$	5.15617e27	+	5.15617e27i	0.457089	+	0.457089i
$276$		0			0
$277$	−1.78189e27	+	1.78189e27i	−0.145333	+	0.145333i	−0.776029	−	0.630697i	$-0.782769\pi$
$277$	−1.78189e27	+	1.78189e27i	−0.145333	+	0.145333i	0.630697	+	0.776029i	$0.282769\pi$
$278$		0			0
$279$		−	9.05551e27i		−	0.679931i
$280$		0			0
$281$			1.76036e28i			1.21753i	0.793351	+	0.608765i	$0.208335\pi$
$281$			1.76036e28i			1.21753i	−0.793351	+	0.608765i	$0.791665\pi$
$282$		0			0
$283$	−7.38446e27	+	7.38446e27i	−0.470733	+	0.470733i	−0.902152	−	0.431419i	$-0.858013\pi$
$283$	−7.38446e27	+	7.38446e27i	−0.470733	+	0.470733i	0.431419	+	0.902152i	$0.358013\pi$
$284$		0			0
$285$	3.66568e24	+	3.66568e24i	0.000215496	+	0.000215496i
$286$		0			0
$287$	3.39890e27			0.184373
$288$		0			0
$289$	3.92204e28			1.96420
$290$		0			0
$291$	−1.31796e26	−	1.31796e26i	−0.00609724	−	0.00609724i
$292$		0			0
$293$	6.06832e27	−	6.06832e27i	0.259472	−	0.259472i	−0.565367	−	0.824839i	$-0.691266\pi$
$293$	6.06832e27	−	6.06832e27i	0.259472	−	0.259472i	0.824839	+	0.565367i	$0.191266\pi$
$294$		0			0
$295$		−	9.84083e26i		−	0.0389116i
$296$		0			0
$297$			1.06054e28i			0.387996i
$298$		0			0
$299$	1.38435e28	−	1.38435e28i	0.468843	−	0.468843i
$300$		0			0
$301$	1.08278e28	+	1.08278e28i	0.339646	+	0.339646i
$302$		0			0
$303$	8.16333e27			0.237289
$304$		0			0
$305$	2.50743e27			0.0675742
$306$		0			0
$307$	5.12216e28	+	5.12216e28i	1.28045	+	1.28045i	0.940413	+	0.340035i	$0.110439\pi$
$307$	5.12216e28	+	5.12216e28i	1.28045	+	1.28045i	0.340035	+	0.940413i	$0.389561\pi$
$308$		0			0
$309$	−1.10717e28	+	1.10717e28i	−0.256857	+	0.256857i
$310$		0			0
$311$			8.07359e28i			1.73909i	0.493853	+	0.869545i	$0.335588\pi$
$311$			8.07359e28i			1.73909i	−0.493853	+	0.869545i	$0.664412\pi$
$312$		0			0
$313$		−	3.38833e28i		−	0.677993i	−0.940788	−	0.338997i	$-0.889912\pi$
$313$		−	3.38833e28i		−	0.677993i	0.940788	−	0.338997i	$-0.110088\pi$
$314$		0			0
$315$	−5.23028e26	+	5.23028e26i	−0.00972643	+	0.00972643i
$316$		0			0
$317$	1.32405e28	+	1.32405e28i	0.228941	+	0.228941i	0.812250	−	0.583309i	$-0.198243\pi$
$317$	1.32405e28	+	1.32405e28i	0.228941	+	0.228941i	−0.583309	+	0.812250i	$0.698243\pi$
$318$		0			0
$319$	−3.80470e28			−0.611967
$320$		0			0
$321$	−9.52072e27			−0.142516
$322$		0			0
$323$	−2.40972e27	−	2.40972e27i	−0.0335845	−	0.0335845i
$324$		0			0
$325$	4.29063e28	−	4.29063e28i	0.557010	−	0.557010i
$326$		0			0
$327$		−	2.53746e28i		−	0.306973i
$328$		0			0
$329$		−	3.55638e28i		−	0.401102i
$330$		0			0
$331$	−6.86205e28	+	6.86205e28i	−0.721825	+	0.721825i	−0.968977	−	0.247152i	$-0.920505\pi$
$331$	−6.86205e28	+	6.86205e28i	−0.721825	+	0.721825i	0.247152	+	0.968977i	$0.420505\pi$
$332$		0			0
$333$	−1.51540e28	−	1.51540e28i	−0.148737	−	0.148737i
$334$		0			0
$335$	−5.34245e27			−0.0489469
$336$		0			0
$337$	−3.73593e28			−0.319635			−0.159818	−	0.987147i	$-0.551091\pi$
$337$	−3.73593e28			−0.319635			−0.159818	+	0.987147i	$0.551091\pi$
$338$		0			0
$339$	−6.49244e26	−	6.49244e26i	−0.00518933	−	0.00518933i
$340$		0			0
$341$	4.62583e28	−	4.62583e28i	0.345553	−	0.345553i
$342$		0			0
$343$			1.13018e29i			0.789340i
$344$		0			0
$345$			1.42169e27i			0.00928722i
$346$		0			0
$347$	4.81760e28	−	4.81760e28i	0.294470	−	0.294470i	−0.544373	−	0.838843i	$-0.683232\pi$
$347$	4.81760e28	−	4.81760e28i	0.294470	−	0.294470i	0.838843	+	0.544373i	$0.183232\pi$
$348$		0			0
$349$	−2.69398e28	−	2.69398e28i	−0.154135	−	0.154135i	0.625827	−	0.779962i	$-0.284762\pi$
$349$	−2.69398e28	−	2.69398e28i	−0.154135	−	0.154135i	−0.779962	+	0.625827i	$0.784762\pi$
$350$		0			0
$351$	8.82513e28			0.472813
$352$		0			0
$353$	−8.82625e28			−0.442963			−0.221481	−	0.975165i	$-0.571089\pi$
$353$	−8.82625e28			−0.442963			−0.221481	+	0.975165i	$0.571089\pi$
$354$		0			0
$355$	−1.02728e27	−	1.02728e27i	−0.00483126	−	0.00483126i
$356$		0			0
$357$	−3.79905e28	+	3.79905e28i	−0.167491	+	0.167491i
$358$		0			0
$359$		−	3.63691e29i		−	1.50365i	−0.659362	−	0.751825i	$-0.729174\pi$
$359$		−	3.63691e29i		−	1.50365i	0.659362	−	0.751825i	$-0.270826\pi$
$360$		0			0
$361$		−	2.57633e29i		−	0.999239i
$362$		0			0
$363$	3.56108e28	−	3.56108e28i	0.129615	−	0.129615i
$364$		0			0
$365$	5.88963e27	+	5.88963e27i	0.0201243	+	0.0201243i
$366$		0			0
$367$	−5.52615e29			−1.77322			−0.886611	−	0.462517i	$-0.846947\pi$
$367$	−5.52615e29			−1.77322			−0.886611	+	0.462517i	$0.846947\pi$
$368$		0			0
$369$	−1.26282e29			−0.380662
$370$		0			0
$371$	−5.40270e28	−	5.40270e28i	−0.153042	−	0.153042i
$372$		0			0
$373$	−3.80423e29	+	3.80423e29i	−1.01301	+	1.01301i	−0.0130985	+	0.999914i	$0.504169\pi$
$373$	−3.80423e29	+	3.80423e29i	−1.01301	+	1.01301i	−0.999914	+	0.0130985i	$0.995831\pi$
$374$		0			0
$375$			8.81815e27i			0.0220809i
$376$		0			0
$377$			3.16603e29i			0.745744i
$378$		0			0
$379$	4.85474e29	−	4.85474e29i	1.07601	−	1.07601i	0.0791431	−	0.996863i	$-0.474782\pi$
$379$	4.85474e29	−	4.85474e29i	1.07601	−	1.07601i	0.996863	−	0.0791431i	$-0.0252184\pi$
$380$		0			0
$381$	−9.07563e28	−	9.07563e28i	−0.189339	−	0.189339i
$382$		0			0
$383$	−3.70406e29			−0.727600			−0.363800	−	0.931477i	$-0.618521\pi$
$383$	−3.70406e29			−0.727600			−0.363800	+	0.931477i	$0.618521\pi$
$384$		0			0
$385$	−5.34357e27			−0.00988629
$386$		0			0
$387$	−4.02296e29	−	4.02296e29i	−0.701244	−	0.701244i
$388$		0			0
$389$	7.10088e28	−	7.10088e28i	0.116652	−	0.116652i	−0.646371	−	0.763023i	$-0.723714\pi$
$389$	7.10088e28	−	7.10088e28i	0.116652	−	0.116652i	0.763023	+	0.646371i	$0.223714\pi$
$390$		0			0
$391$		−	9.34583e29i		−	1.44739i
$392$		0			0
$393$		−	4.10079e28i		−	0.0598899i
$394$		0			0
$395$	1.33913e28	−	1.33913e28i	0.0184483	−	0.0184483i
$396$		0			0
$397$	2.31054e29	+	2.31054e29i	0.300347	+	0.300347i	0.841150	−	0.540802i	$-0.181879\pi$
$397$	2.31054e29	+	2.31054e29i	0.300347	+	0.300347i	−0.540802	+	0.841150i	$0.681879\pi$
$398$		0			0
$399$	3.09342e27			0.00379534
$400$		0			0
$401$	−3.86636e29			−0.447860			−0.223930	−	0.974605i	$-0.571889\pi$
$401$	−3.86636e29			−0.447860			−0.223930	+	0.974605i	$0.571889\pi$
$402$		0			0
$403$	−3.84932e29	−	3.84932e29i	−0.421092	−	0.421092i
$404$		0			0
$405$	1.70481e28	−	1.70481e28i	0.0176175	−	0.0176175i
$406$		0			0
$407$		−	1.54823e29i		−	0.151182i
$408$		0			0
$409$		−	1.56209e30i		−	1.44175i	−0.693067	−	0.720873i	$-0.743741\pi$
$409$		−	1.56209e30i		−	1.44175i	0.693067	−	0.720873i	$-0.256259\pi$
$410$		0			0
$411$	1.28936e29	−	1.28936e29i	0.112511	−	0.112511i
$412$		0			0
$413$	−4.15228e29	−	4.15228e29i	−0.342658	−	0.342658i
$414$		0			0
$415$	3.37478e28			0.0263447
$416$		0			0
$417$	−6.78239e29			−0.500978
$418$		0			0
$419$	5.04126e29	+	5.04126e29i	0.352434	+	0.352434i	0.861014	−	0.508580i	$-0.169830\pi$
$419$	5.04126e29	+	5.04126e29i	0.352434	+	0.352434i	−0.508580	+	0.861014i	$0.669830\pi$
$420$		0			0
$421$	−6.72017e29	+	6.72017e29i	−0.444771	+	0.444771i	−0.893612	−	0.448841i	$-0.851837\pi$
$421$	−6.72017e29	+	6.72017e29i	−0.444771	+	0.444771i	0.448841	+	0.893612i	$0.351837\pi$
$422$		0			0
$423$			1.32133e30i			0.828128i
$424$		0			0
$425$		−	2.89663e30i		−	1.71957i
$426$		0			0
$427$	1.05800e30	−	1.05800e30i	0.595064	−	0.595064i
$428$		0			0
$429$	2.13606e29	+	2.13606e29i	0.113856	+	0.113856i
$430$		0			0
$431$	−3.50880e30			−1.77284			−0.886421	−	0.462880i	$-0.846816\pi$
$431$	−3.50880e30			−1.77284			−0.886421	+	0.462880i	$0.846816\pi$
$432$		0			0
$433$	−2.02655e30			−0.970838			−0.485419	−	0.874282i	$-0.661333\pi$
$433$	−2.02655e30			−0.970838			−0.485419	+	0.874282i	$0.661333\pi$
$434$		0			0
$435$	−1.62572e28	−	1.62572e28i	−0.00738615	−	0.00738615i
$436$		0			0
$437$	−3.80498e28	+	3.80498e28i	−0.0163989	+	0.0163989i
$438$		0			0
$439$			1.22115e30i			0.499374i	0.968327	+	0.249687i	$0.0803278\pi$
$439$			1.22115e30i			0.499374i	−0.968327	+	0.249687i	$0.919672\pi$
$440$		0			0
$441$		−	1.87884e30i		−	0.729197i
$442$		0			0
$443$	−1.97149e30	+	1.97149e30i	−0.726358	+	0.726358i	−0.969892	−	0.243534i	$-0.921693\pi$
$443$	−1.97149e30	+	1.97149e30i	−0.726358	+	0.726358i	0.243534	+	0.969892i	$0.421693\pi$
$444$		0			0
$445$	−9.78298e28	−	9.78298e28i	−0.0342240	−	0.0342240i
$446$		0			0
$447$	1.45029e29			0.0481857
$448$		0			0
$449$	3.59401e30			1.13435			0.567174	−	0.823598i	$-0.308037\pi$
$449$	3.59401e30			1.13435			0.567174	+	0.823598i	$0.308037\pi$
$450$		0			0
$451$	−6.45089e29	−	6.45089e29i	−0.193459	−	0.193459i
$452$		0			0
$453$	−5.42391e29	+	5.42391e29i	−0.154591	+	0.154591i
$454$		0			0
$455$			4.44658e28i			0.0120474i
$456$		0			0
$457$		−	1.42395e30i		−	0.366825i	−0.983036	−	0.183412i	$-0.941286\pi$
$457$		−	1.42395e30i		−	0.366825i	0.983036	−	0.183412i	$-0.0587143\pi$
$458$		0			0
$459$	2.97895e30	−	2.97895e30i	0.729823	−	0.729823i
$460$		0			0
$461$	2.32754e30	+	2.32754e30i	0.542420	+	0.542420i	0.924238	−	0.381818i	$-0.124702\pi$
$461$	2.32754e30	+	2.32754e30i	0.542420	+	0.542420i	−0.381818	+	0.924238i	$0.624702\pi$
$462$		0			0
$463$	−3.09111e30			−0.685383			−0.342691	−	0.939448i	$-0.611338\pi$
$463$	−3.09111e30			−0.685383			−0.342691	+	0.939448i	$0.611338\pi$
$464$		0			0
$465$	3.95316e28			0.00834132
$466$		0			0
$467$	5.22361e30	+	5.22361e30i	1.04912	+	1.04912i	0.998729	+	0.0503932i	$0.0160475\pi$
$467$	5.22361e30	+	5.22361e30i	1.04912	+	1.04912i	0.0503932	+	0.998729i	$0.483953\pi$
$468$		0			0
$469$	−2.25421e30	+	2.25421e30i	−0.431030	+	0.431030i
$470$		0			0
$471$		−	9.93481e29i		−	0.180892i
$472$		0			0
$473$		−	4.11010e30i		−	0.712770i
$474$		0			0
$475$	−1.17931e29	+	1.17931e29i	−0.0194828	+	0.0194828i
$476$		0			0
$477$	2.00731e30	+	2.00731e30i	0.315976	+	0.315976i
$478$		0			0
$479$	−7.93318e30			−1.19011			−0.595057	−	0.803683i	$-0.702871\pi$
$479$	−7.93318e30			−1.19011			−0.595057	+	0.803683i	$0.702871\pi$
$480$		0			0
$481$	−1.28834e30			−0.184230
$482$		0			0
$483$	5.99874e29	+	5.99874e29i	0.0817839	+	0.0817839i
$484$		0			0
$485$	−5.20710e27	+	5.20710e27i	−0.000676965	+	0.000676965i
$486$		0			0
$487$			3.66980e30i			0.455050i	0.973772	+	0.227525i	$0.0730633\pi$
$487$			3.66980e30i			0.455050i	−0.973772	+	0.227525i	$0.926937\pi$
$488$		0			0
$489$			5.19591e29i			0.0614625i
$490$		0			0
$491$	1.06971e31	−	1.06971e31i	1.20734	−	1.20734i	0.235455	−	0.971885i	$-0.424342\pi$
$491$	1.06971e31	−	1.06971e31i	1.20734	−	1.20734i	0.971885	−	0.235455i	$-0.0756580\pi$
$492$		0			0
$493$	1.06870e31	+	1.06870e31i	1.15111	+	1.15111i
$494$		0			0
$495$	1.98535e29			0.0204116
$496$		0			0
$497$	−8.66905e29			−0.0850890
$498$		0			0
$499$	1.32952e31	+	1.32952e31i	1.24606	+	1.24606i	0.957444	+	0.288618i	$0.0931957\pi$
$499$	1.32952e31	+	1.32952e31i	1.24606	+	1.24606i	0.288618	+	0.957444i	$0.406804\pi$
$500$		0			0
$501$	−1.40807e30	+	1.40807e30i	−0.126034	+	0.126034i
$502$		0			0
$503$			1.06967e31i			0.914572i	0.889320	+	0.457286i	$0.151178\pi$
$503$			1.06967e31i			0.914572i	−0.889320	+	0.457286i	$0.848822\pi$
$504$		0			0
$505$		−	3.22523e29i		−	0.0263457i
$506$		0			0
$507$	−1.08001e30	+	1.08001e30i	−0.0843017	+	0.0843017i
$508$		0			0
$509$	1.42726e31	+	1.42726e31i	1.06475	+	1.06475i	0.997753	+	0.0669984i	$0.0213422\pi$
$509$	1.42726e31	+	1.42726e31i	1.06475	+	1.06475i	0.0669984	+	0.997753i	$0.478658\pi$
$510$		0			0
$511$	4.97019e30			0.354432
$512$		0			0
$513$	−2.42565e29			−0.0165378
$514$		0			0
$515$	4.37429e29	+	4.37429e29i	0.0285183	+	0.0285183i
$516$		0			0
$517$	−6.74977e30	+	6.74977e30i	−0.420870	+	0.420870i
$518$		0			0
$519$			4.83526e29i			0.0288400i
$520$		0			0
$521$		−	3.99024e30i		−	0.227701i	−0.993498	−	0.113851i	$-0.963681\pi$
$521$		−	3.99024e30i		−	0.227701i	0.993498	−	0.113851i	$-0.0363186\pi$
$522$		0			0
$523$	2.12113e31	−	2.12113e31i	1.15824	−	1.15824i	0.173382	−	0.984855i	$-0.444531\pi$
$523$	2.12113e31	−	2.12113e31i	1.15824	−	1.15824i	0.984855	−	0.173382i	$-0.0554694\pi$
$524$		0			0
$525$	1.85924e30	+	1.85924e30i	0.0971636	+	0.0971636i
$526$		0			0
$527$	−2.59870e31			−1.29997
$528$		0			0
$529$	6.12330e30			0.293255
$530$		0			0
$531$	1.54273e31	+	1.54273e31i	0.707463	+	0.707463i
$532$		0			0
$533$	−5.36802e30	+	5.36802e30i	−0.235750	+	0.235750i
$534$		0			0
$535$			3.76152e29i			0.0158232i
$536$		0			0
$537$		−	1.04168e31i		−	0.419787i
$538$		0			0
$539$	9.59767e30	−	9.59767e30i	0.370591	−	0.370591i
$540$		0			0
$541$	2.53694e31	+	2.53694e31i	0.938732	+	0.938732i	0.998229	−	0.0594965i	$-0.0189495\pi$
$541$	2.53694e31	+	2.53694e31i	0.938732	+	0.938732i	−0.0594965	+	0.998229i	$0.518950\pi$
$542$		0			0
$543$	1.44574e30			0.0512732
$544$		0			0
$545$	−1.00252e30			−0.0340826
$546$		0			0
$547$	3.08318e31	+	3.08318e31i	1.00495	+	1.00495i	0.999988	+	0.00496212i	$0.00157950\pi$
$547$	3.08318e31	+	3.08318e31i	1.00495	+	1.00495i	0.00496212	+	0.999988i	$0.498421\pi$
$548$		0			0
$549$	−3.93087e31	+	3.93087e31i	−1.22859	+	1.22859i
$550$		0			0
$551$		−	8.70206e29i		−	0.0260843i
$552$		0			0
$553$		−	1.13008e31i		−	0.324915i
$554$		0			0
$555$	6.61543e28	−	6.61543e28i	0.00182469	−	0.00182469i
$556$		0			0
$557$	3.50560e31	+	3.50560e31i	0.927742	+	0.927742i	0.997560	−	0.0698175i	$-0.0222417\pi$
$557$	3.50560e31	+	3.50560e31i	0.927742	+	0.927742i	−0.0698175	+	0.997560i	$0.522242\pi$
$558$		0			0
$559$	−3.42016e31			−0.868582
$560$		0			0
$561$	1.44207e31			0.351491
$562$		0			0
$563$	−1.50636e31	−	1.50636e31i	−0.352437	−	0.352437i	0.508578	−	0.861016i	$-0.330171\pi$
$563$	−1.50636e31	−	1.50636e31i	−0.352437	−	0.352437i	−0.861016	+	0.508578i	$0.830171\pi$
$564$		0			0
$565$	−2.56508e28	+	2.56508e28i	−0.000576161	+	0.000576161i
$566$		0			0
$567$		−	1.43867e31i		−	0.310281i
$568$		0			0
$569$		−	5.00594e31i		−	1.03680i	−0.855138	−	0.518400i	$-0.826528\pi$
$569$		−	5.00594e31i		−	1.03680i	0.855138	−	0.518400i	$-0.173472\pi$
$570$		0			0
$571$	2.14479e31	−	2.14479e31i	0.426649	−	0.426649i	−0.460836	−	0.887485i	$-0.652451\pi$
$571$	2.14479e31	−	2.14479e31i	0.426649	−	0.426649i	0.887485	+	0.460836i	$0.152451\pi$
$572$		0			0
$573$	−1.30033e30	−	1.30033e30i	−0.0248472	−	0.0248472i
$574$		0			0
$575$	−4.57382e31			−0.839650
$576$		0			0
$577$	−2.72871e31			−0.481321			−0.240660	−	0.970609i	$-0.577364\pi$
$577$	−2.72871e31			−0.481321			−0.240660	+	0.970609i	$0.577364\pi$
$578$		0			0
$579$	−9.01977e29	−	9.01977e29i	−0.0152895	−	0.0152895i
$580$		0			0
$581$	1.42397e31	−	1.42397e31i	0.231993	−	0.231993i
$582$		0			0
$583$			2.05079e31i			0.321169i
$584$		0			0
$585$		−	1.65208e30i		−	0.0248736i
$586$		0			0
$587$	−5.18378e30	+	5.18378e30i	−0.0750427	+	0.0750427i	−0.743632	−	0.668589i	$-0.766898\pi$
$587$	−5.18378e30	+	5.18378e30i	−0.0750427	+	0.0750427i	0.668589	+	0.743632i	$0.266898\pi$
$588$		0			0
$589$	1.05801e30	+	1.05801e30i	0.0147287	+	0.0147287i
$590$		0			0
$591$	−4.02022e31			−0.538262
$592$		0			0
$593$	−1.82913e31			−0.235567			−0.117784	−	0.993039i	$-0.537579\pi$
$593$	−1.82913e31			−0.235567			−0.117784	+	0.993039i	$0.537579\pi$
$594$		0			0
$595$	1.50096e30	+	1.50096e30i	0.0185962	+	0.0185962i
$596$		0			0
$597$	2.90555e31	−	2.90555e31i	0.346356	−	0.346356i
$598$		0			0
$599$			1.55422e32i			1.78281i	0.453211	+	0.891404i	$0.350279\pi$
$599$			1.55422e32i			1.78281i	−0.453211	+	0.891404i	$0.649721\pi$
$600$		0			0
$601$		−	1.69132e32i		−	1.86711i	−0.358431	−	0.933556i	$-0.616688\pi$
$601$		−	1.69132e32i		−	1.86711i	0.358431	−	0.933556i	$-0.383312\pi$
$602$		0			0
$603$	8.37528e31	−	8.37528e31i	0.889919	−	0.889919i
$604$		0			0
$605$	−1.40694e30	−	1.40694e30i	−0.0143909	−	0.0143909i
$606$		0			0
$607$	−7.52678e31			−0.741207			−0.370603	−	0.928791i	$-0.620849\pi$
$607$	−7.52678e31			−0.741207			−0.370603	+	0.928791i	$0.620849\pi$
$608$		0			0
$609$	−1.37192e31			−0.130086
$610$		0			0
$611$	5.61673e31	+	5.61673e31i	0.512873	+	0.512873i
$612$		0			0
$613$	−5.67210e31	+	5.67210e31i	−0.498826	+	0.498826i	−0.911072	−	0.412247i	$-0.864744\pi$
$613$	−5.67210e31	+	5.67210e31i	−0.498826	+	0.498826i	0.412247	+	0.911072i	$0.364744\pi$
$614$		0			0
$615$		−	5.51282e29i		−	0.00466992i
$616$		0			0
$617$		−	1.80563e32i		−	1.47350i	−0.676165	−	0.736750i	$-0.736360\pi$
$617$		−	1.80563e32i		−	1.47350i	0.676165	−	0.736750i	$-0.263640\pi$
$618$		0			0
$619$	−4.82794e31	+	4.82794e31i	−0.379594	+	0.379594i	−0.870956	−	0.491362i	$-0.836499\pi$
$619$	−4.82794e31	+	4.82794e31i	−0.379594	+	0.379594i	0.491362	+	0.870956i	$0.336499\pi$
$620$		0			0
$621$	−4.70380e31	−	4.70380e31i	−0.356365	−	0.356365i
$622$		0			0
$623$	−8.25574e31			−0.602759
$624$		0			0
$625$	−1.41586e32			−0.996322
$626$		0			0
$627$	−5.87112e29	−	5.87112e29i	−0.00398239	−	0.00398239i
$628$		0			0
$629$	−4.34882e31	+	4.34882e31i	−0.284373	+	0.284373i
$630$		0			0
$631$		−	1.19165e32i		−	0.751293i	−0.926763	−	0.375647i	$-0.877421\pi$
$631$		−	1.19165e32i		−	0.751293i	0.926763	−	0.375647i	$-0.122579\pi$
$632$		0			0
$633$		−	8.98794e31i		−	0.546409i
$634$		0			0
$635$	−3.58567e30	+	3.58567e30i	−0.0210219	+	0.0210219i
$636$		0			0
$637$	−7.98657e31	−	7.98657e31i	−0.451603	−	0.451603i
$638$		0			0
$639$	3.22089e31			0.175677
$640$		0			0
$641$	2.66682e32			1.40322			0.701612	−	0.712559i	$-0.252464\pi$
$641$	2.66682e32			1.40322			0.701612	+	0.712559i	$0.252464\pi$
$642$		0			0
$643$	−1.15184e32	−	1.15184e32i	−0.584746	−	0.584746i	0.351458	−	0.936204i	$-0.385686\pi$
$643$	−1.15184e32	−	1.15184e32i	−0.584746	−	0.584746i	−0.936204	+	0.351458i	$0.885686\pi$
$644$		0			0
$645$	1.75621e30	−	1.75621e30i	0.00860279	−	0.00860279i
$646$		0			0
$647$		−	3.25068e32i		−	1.53665i	−0.640061	−	0.768324i	$-0.721091\pi$
$647$		−	3.25068e32i		−	1.53665i	0.640061	−	0.768324i	$-0.278909\pi$
$648$		0			0
$649$			1.57615e32i			0.719091i
$650$		0			0
$651$	1.66801e31	−	1.66801e31i	0.0734543	−	0.0734543i
$652$		0			0
$653$	1.11435e32	+	1.11435e32i	0.473720	+	0.473720i	0.903116	−	0.429396i	$-0.141274\pi$
$653$	1.11435e32	+	1.11435e32i	0.473720	+	0.473720i	−0.429396	+	0.903116i	$0.641274\pi$
$654$		0			0
$655$	−1.62017e30			−0.00664946
$656$		0			0
$657$	−1.84662e32			−0.731772
$658$		0			0
$659$	−1.71594e32	−	1.71594e32i	−0.656628	−	0.656628i	0.297953	−	0.954581i	$-0.403696\pi$
$659$	−1.71594e32	−	1.71594e32i	−0.656628	−	0.656628i	−0.954581	+	0.297953i	$0.903696\pi$
$660$		0			0
$661$	2.90855e30	−	2.90855e30i	0.0107488	−	0.0107488i	−0.701712	−	0.712461i	$-0.747581\pi$
$661$	2.90855e30	−	2.90855e30i	0.0107488	−	0.0107488i	0.712461	+	0.701712i	$0.247581\pi$
$662$		0			0
$663$		−	1.20000e32i		−	0.428327i
$664$		0			0
$665$		−	1.22217e29i		−	0.000421390i
$666$		0			0
$667$	1.68750e32	−	1.68750e32i	0.562077	−	0.562077i
$668$		0			0
$669$	6.66484e31	+	6.66484e31i	0.214481	+	0.214481i
$670$		0			0
$671$	−4.01601e32			−1.24878
$672$		0			0
$673$	−5.16475e32			−1.55194			−0.775972	−	0.630768i	$-0.782740\pi$
$673$	−5.16475e32			−1.55194			−0.775972	+	0.630768i	$0.782740\pi$
$674$		0			0
$675$	−1.45789e32	−	1.45789e32i	−0.423380	−	0.423380i
$676$		0			0
$677$	−2.63610e32	+	2.63610e32i	−0.739931	+	0.739931i	−0.972565	−	0.232633i	$-0.925266\pi$
$677$	−2.63610e32	+	2.63610e32i	−0.739931	+	0.739931i	0.232633	+	0.972565i	$0.425266\pi$
$678$		0			0
$679$			4.39421e30i			0.0119228i
$680$		0			0
$681$			3.67106e31i			0.0962942i
$682$		0			0
$683$	−1.41336e31	+	1.41336e31i	−0.0358438	+	0.0358438i	−0.724802	−	0.688958i	$-0.758069\pi$
$683$	−1.41336e31	+	1.41336e31i	−0.0358438	+	0.0358438i	0.688958	+	0.724802i	$0.258069\pi$
$684$		0			0
$685$	−5.09410e30	−	5.09410e30i	−0.0124918	−	0.0124918i
$686$		0			0
$687$	9.25896e31			0.219563
$688$		0			0
$689$	1.70654e32			0.391377
$690$		0			0
$691$	2.69076e32	+	2.69076e32i	0.596868	+	0.596868i	0.939478	−	0.342610i	$-0.111311\pi$
$691$	2.69076e32	+	2.69076e32i	0.596868	+	0.596868i	−0.342610	+	0.939478i	$0.611311\pi$
$692$		0			0
$693$	8.37705e31	−	8.37705e31i	0.179746	−	0.179746i
$694$		0			0
$695$			2.67964e31i			0.0556226i
$696$		0			0
$697$			3.62399e32i			0.727796i
$698$		0			0
$699$	1.56597e32	−	1.56597e32i	0.304295	−	0.304295i
$700$		0			0
$701$	−3.96233e32	−	3.96233e32i	−0.745063	−	0.745063i	0.228485	−	0.973548i	$-0.426623\pi$
$701$	−3.96233e32	−	3.96233e32i	−0.745063	−	0.745063i	−0.973548	+	0.228485i	$0.926623\pi$
$702$		0			0
$703$	3.54108e30			0.00644391
$704$		0			0
$705$	−5.76823e30			−0.0101594
$706$		0			0
$707$	−1.36087e32	−	1.36087e32i	−0.232002	−	0.232002i
$708$		0			0
$709$	4.30226e32	−	4.30226e32i	0.710012	−	0.710012i	−0.256526	−	0.966537i	$-0.582578\pi$
$709$	4.30226e32	−	4.30226e32i	0.710012	−	0.710012i	0.966537	+	0.256526i	$0.0825779\pi$
$710$		0			0
$711$			4.19868e32i			0.670830i
$712$		0			0
$713$			4.10338e32i			0.634764i
$714$		0			0
$715$	8.43932e30	−	8.43932e30i	0.0126412	−	0.0126412i
$716$		0			0
$717$	−2.76958e32	−	2.76958e32i	−0.401739	−	0.401739i
$718$		0			0
$719$	1.07968e33			1.51674			0.758370	−	0.651825i	$-0.225996\pi$
$719$	1.07968e33			1.51674			0.758370	+	0.651825i	$0.225996\pi$
$720$		0			0
$721$	3.69141e32			0.502269
$722$		0			0
$723$	−1.74331e32	−	1.74331e32i	−0.229765	−	0.229765i
$724$		0			0
$725$	5.23020e32	−	5.23020e32i	0.667777	−	0.667777i
$726$		0			0
$727$		−	9.89982e32i		−	1.22456i	−0.790640	−	0.612282i	$-0.790252\pi$
$727$		−	9.89982e32i		−	1.22456i	0.790640	−	0.612282i	$-0.209748\pi$
$728$		0			0
$729$			3.76740e32i			0.451518i
$730$		0			0
$731$	−1.15449e33	+	1.15449e33i	−1.34072	+	1.34072i
$732$		0			0
$733$	1.95319e32	+	1.95319e32i	0.219811	+	0.219811i	0.808419	−	0.588608i	$-0.200324\pi$
$733$	1.95319e32	+	1.95319e32i	0.219811	+	0.219811i	−0.588608	+	0.808419i	$0.700324\pi$
$734$		0			0
$735$	8.20200e30			0.00894572
$736$		0			0
$737$	8.55671e32			0.904546
$738$		0			0
$739$	9.62503e32	+	9.62503e32i	0.986260	+	0.986260i	0.999907	−	0.0136472i	$-0.00434419\pi$
$739$	9.62503e32	+	9.62503e32i	0.986260	+	0.986260i	−0.0136472	+	0.999907i	$0.504344\pi$
$740$		0			0
$741$	−4.88557e30	+	4.88557e30i	−0.00485295	+	0.00485295i
$742$		0			0
$743$			1.78863e33i			1.72246i	0.508216	+	0.861230i	$0.330305\pi$
$743$			1.78863e33i			1.72246i	−0.508216	+	0.861230i	$0.669695\pi$
$744$		0			0
$745$		−	5.72991e30i		−	0.00534996i
$746$		0			0
$747$	−5.29060e32	+	5.29060e32i	−0.478981	+	0.478981i
$748$		0			0
$749$	1.58715e32	+	1.58715e32i	0.139341	+	0.139341i
$750$		0			0
$751$	1.07182e33			0.912565			0.456282	−	0.889835i	$-0.349181\pi$
$751$	1.07182e33			0.912565			0.456282	+	0.889835i	$0.349181\pi$
$752$		0			0
$753$	−1.37850e32			−0.113832
$754$		0			0
$755$	2.14292e31	+	2.14292e31i	0.0171639	+	0.0171639i
$756$		0			0
$757$	−8.43262e32	+	8.43262e32i	−0.655179	+	0.655179i	−0.954235	−	0.299056i	$-0.903328\pi$
$757$	−8.43262e32	+	8.43262e32i	−0.655179	+	0.655179i	0.299056	+	0.954235i	$0.403328\pi$
$758$		0			0
$759$		−	2.27704e32i		−	0.171629i
$760$		0			0
$761$			7.15783e32i			0.523429i	0.965145	+	0.261715i	$0.0842879\pi$
$761$			7.15783e32i			0.523429i	−0.965145	+	0.261715i	$0.915712\pi$
$762$		0			0
$763$	−4.23007e32	+	4.23007e32i	−0.300134	+	0.300134i
$764$		0			0
$765$	−5.57664e31	−	5.57664e31i	−0.0383943	−	0.0383943i
$766$		0			0
$767$	1.31157e33			0.876286
$768$		0			0
$769$	9.69790e32			0.628818			0.314409	−	0.949288i	$-0.398194\pi$
$769$	9.69790e32			0.628818			0.314409	+	0.949288i	$0.398194\pi$
$770$		0			0
$771$	1.84801e32	+	1.84801e32i	0.116300	+	0.116300i
$772$		0			0
$773$	1.74983e33	−	1.74983e33i	1.06888	−	1.06888i	0.0714400	−	0.997445i	$-0.477241\pi$
$773$	1.74983e33	−	1.74983e33i	1.06888	−	1.06888i	0.997445	−	0.0714400i	$-0.0227594\pi$
$774$		0			0
$775$			1.27180e33i			0.754133i
$776$		0			0
$777$		−	5.58269e31i		−	0.0321367i
$778$		0			0
$779$	1.47544e31	−	1.47544e31i	0.00824594	−	0.00824594i
$780$		0			0
$781$	1.64533e32	+	1.64533e32i	0.0892825	+	0.0892825i
$782$		0			0
$783$	1.07577e33			0.566836
$784$		0			0
$785$	−3.92512e31			−0.0200841
$786$		0			0
$787$	−1.26268e33	−	1.26268e33i	−0.627459	−	0.627459i	0.319969	−	0.947428i	$-0.396327\pi$
$787$	−1.26268e33	−	1.26268e33i	−0.627459	−	0.627459i	−0.947428	+	0.319969i	$0.896327\pi$
$788$		0			0
$789$	8.56859e32	−	8.56859e32i	0.413546	−	0.413546i
$790$		0			0
$791$			2.16464e31i			0.0101474i
$792$		0			0
$793$			3.34187e33i			1.52177i
$794$		0			0
$795$	−8.76286e30	+	8.76286e30i	−0.00387636	+	0.00387636i
$796$		0			0
$797$	−7.99479e32	−	7.99479e32i	−0.343587	−	0.343587i	0.514127	−	0.857714i	$-0.328116\pi$
$797$	−7.99479e32	−	7.99479e32i	−0.343587	−	0.343587i	−0.857714	+	0.514127i	$0.828116\pi$
$798$		0			0
$799$	3.79189e33			1.58332
$800$		0			0
$801$	3.06733e33			1.24448
$802$		0			0
$803$	−9.43310e32	−	9.43310e32i	−0.371900	−	0.371900i
$804$		0			0
$805$	2.37003e31	−	2.37003e31i	0.00908031	−	0.00908031i
$806$		0			0
$807$		−	1.65630e33i		−	0.616727i
$808$		0			0
$809$			4.63412e33i			1.67710i	0.544824	+	0.838550i	$0.316596\pi$
$809$			4.63412e33i			1.67710i	−0.544824	+	0.838550i	$0.683404\pi$
$810$		0			0
$811$	−3.27295e33	+	3.27295e33i	−1.15133	+	1.15133i	−0.165044	+	0.986286i	$0.552777\pi$
$811$	−3.27295e33	+	3.27295e33i	−1.15133	+	1.15133i	−0.986286	+	0.165044i	$0.947223\pi$
$812$		0			0
$813$	−7.66003e32	−	7.66003e32i	−0.261932	−	0.261932i
$814$		0			0
$815$	2.05284e31			0.00682406
$816$		0			0
$817$	9.40056e31			0.0303808
$818$		0			0
$819$	−6.97085e32	−	6.97085e32i	−0.219039	−	0.219039i
$820$		0			0
$821$	−1.12850e33	+	1.12850e33i	−0.344792	+	0.344792i	−0.858165	−	0.513374i	$-0.828396\pi$
$821$	−1.12850e33	+	1.12850e33i	−0.344792	+	0.344792i	0.513374	+	0.858165i	$0.328396\pi$
$822$		0			0
$823$			2.51312e33i			0.746646i	0.927701	+	0.373323i	$0.121782\pi$
$823$			2.51312e33i			0.746646i	−0.927701	+	0.373323i	$0.878218\pi$
$824$		0			0
$825$		−	7.05744e32i		−	0.203904i
$826$		0			0
$827$	9.13578e32	−	9.13578e32i	0.256704	−	0.256704i	−0.567008	−	0.823712i	$-0.691899\pi$
$827$	9.13578e32	−	9.13578e32i	0.256704	−	0.256704i	0.823712	+	0.567008i	$0.191899\pi$
$828$		0			0
$829$	−1.66953e33	−	1.66953e33i	−0.456264	−	0.456264i	0.441163	−	0.897427i	$-0.354566\pi$
$829$	−1.66953e33	−	1.66953e33i	−0.456264	−	0.456264i	−0.897427	+	0.441163i	$0.854566\pi$
$830$		0			0
$831$	2.43894e32			0.0648320
$832$		0			0
$833$	−5.39178e33			−1.39417
$834$		0			0
$835$	5.56309e31	+	5.56309e31i	0.0139934	+	0.0139934i
$836$		0			0
$837$	−1.30794e33	+	1.30794e33i	−0.320070	+	0.320070i
$838$		0			0
$839$		−	4.09255e33i		−	0.974386i	−0.873294	−	0.487193i	$-0.838021\pi$
$839$		−	4.09255e33i		−	0.974386i	0.873294	−	0.487193i	$-0.161979\pi$
$840$		0			0
$841$		−	4.57388e32i		−	0.105957i
$842$		0			0
$843$	1.20474e33	−	1.20474e33i	0.271566	−	0.271566i
$844$		0			0
$845$	4.26699e31	+	4.26699e31i	0.00935986	+	0.00935986i
$846$		0			0
$847$	−1.18730e33			−0.253455
$848$		0			0
$849$	1.01074e33			0.209991
$850$		0			0
$851$	6.86683e32	+	6.86683e32i	0.138856	+	0.138856i
$852$		0			0
$853$	3.93702e33	−	3.93702e33i	0.774915	−	0.774915i	−0.204046	−	0.978961i	$-0.565409\pi$
$853$	3.93702e33	−	3.93702e33i	0.774915	−	0.774915i	0.978961	+	0.204046i	$0.0654092\pi$
$854$		0			0
$855$			4.54085e30i			0.000870015i
$856$		0			0
$857$			2.06911e33i			0.385925i	0.981206	+	0.192963i	$0.0618097\pi$
$857$			2.06911e33i			0.385925i	−0.981206	+	0.192963i	$0.938190\pi$
$858$		0			0
$859$	−2.03107e33	+	2.03107e33i	−0.368811	+	0.368811i	−0.867043	−	0.498233i	$-0.833983\pi$
$859$	−2.03107e33	+	2.03107e33i	−0.368811	+	0.368811i	0.498233	+	0.867043i	$0.333983\pi$
$860$		0			0
$861$	−2.32610e32	−	2.32610e32i	−0.0411237	−	0.0411237i
$862$		0			0
$863$	6.37071e33			1.09664			0.548319	−	0.836269i	$-0.315268\pi$
$863$	6.37071e33			1.09664			0.548319	+	0.836269i	$0.315268\pi$
$864$		0			0
$865$	1.91035e31			0.00320205
$866$		0			0
$867$	−2.68412e33	−	2.68412e33i	−0.438109	−	0.438109i
$868$		0			0
$869$	−2.14482e33	+	2.14482e33i	−0.340928	+	0.340928i
$870$		0			0
$871$		−	7.12034e33i		−	1.10228i
$872$		0			0
$873$		−	1.63262e32i		−	0.0246162i
$874$		0			0
$875$	1.47003e32	−	1.47003e32i	0.0215890	−	0.0215890i
$876$		0			0
$877$	−8.39692e33	−	8.39692e33i	−1.20123	−	1.20123i	−0.973794	−	0.227431i	$-0.926967\pi$
$877$	−8.39692e33	−	8.39692e33i	−1.20123	−	1.20123i	−0.227431	−	0.973794i	$-0.573033\pi$
$878$		0			0
$879$	−8.30593e32			−0.115749
$880$		0			0
$881$	2.27930e33			0.309442			0.154721	−	0.987958i	$-0.450552\pi$
$881$	2.27930e33			0.309442			0.154721	+	0.987958i	$0.450552\pi$
$882$		0			0
$883$	−4.78321e33	−	4.78321e33i	−0.632661	−	0.632661i	0.316073	−	0.948735i	$-0.397635\pi$
$883$	−4.78321e33	−	4.78321e33i	−0.632661	−	0.632661i	−0.948735	+	0.316073i	$0.897635\pi$
$884$		0			0
$885$	−6.73476e31	+	6.73476e31i	−0.00867909	+	0.00867909i
$886$		0			0
$887$		−	4.90254e33i		−	0.615601i	−0.951451	−	0.307801i	$-0.900407\pi$
$887$		−	4.90254e33i		−	0.615601i	0.951451	−	0.307801i	$-0.0995930\pi$
$888$		0			0
$889$			3.02591e33i			0.370241i
$890$		0			0
$891$	−2.73050e33	+	2.73050e33i	−0.325573	+	0.325573i
$892$		0			0
$893$	−1.54380e32	−	1.54380e32i	−0.0179390	−	0.0179390i
$894$		0			0
$895$	−4.11554e32			−0.0466081
$896$		0			0
$897$	−1.89481e33			−0.209148
$898$		0			0
$899$	−4.69225e33	−	4.69225e33i	−0.504830	−	0.504830i
$900$		0			0
$901$	5.76048e33	−	5.76048e33i	0.604121	−	0.604121i
$902$		0			0
$903$		−	1.48204e33i		−	0.151514i
$904$		0			0
$905$		−	5.71192e31i		−	0.00569277i
$906$		0			0
$907$	2.96393e33	−	2.96393e33i	0.287994	−	0.287994i	−0.548293	−	0.836287i	$-0.684722\pi$
$907$	2.96393e33	−	2.96393e33i	0.287994	−	0.287994i	0.836287	+	0.548293i	$0.184722\pi$
$908$		0			0
$909$	5.05615e33	+	5.05615e33i	0.479000	+	0.479000i
$910$		0			0
$911$	−1.22025e34			−1.12717			−0.563585	−	0.826058i	$-0.690578\pi$
$911$	−1.22025e34			−1.12717			−0.563585	+	0.826058i	$0.690578\pi$
$912$		0			0
$913$	−5.40520e33			−0.486853
$914$		0			0
$915$	−1.71601e32	−	1.71601e32i	−0.0150722	−	0.0150722i
$916$		0			0
$917$	−6.83622e32	+	6.83622e32i	−0.0585557	+	0.0585557i
$918$		0			0
$919$			1.19730e34i			1.00017i	0.865976	+	0.500086i	$0.166698\pi$
$919$			1.19730e34i			1.00017i	−0.865976	+	0.500086i	$0.833302\pi$
$920$		0			0
$921$		−	7.01089e33i		−	0.571199i
$922$		0			0
$923$	1.36914e33	−	1.36914e33i	0.108800	−	0.108800i
$924$		0			0
$925$	2.12829e33	+	2.12829e33i	0.164969	+	0.164969i
$926$		0			0
$927$	−1.37150e34			−1.03700
$928$		0			0
$929$	−1.00657e34			−0.742443			−0.371221	−	0.928544i	$-0.621061\pi$
$929$	−1.00657e34			−0.742443			−0.371221	+	0.928544i	$0.621061\pi$
$930$		0			0
$931$	2.19516e32	+	2.19516e32i	0.0157959	+	0.0157959i
$932$		0			0
$933$	5.52531e33	−	5.52531e33i	0.387898	−	0.387898i
$934$		0			0
$935$		−	5.69744e32i		−	0.0390253i
$936$		0			0
$937$		−	2.06419e34i		−	1.37957i	−0.724014	−	0.689785i	$-0.757705\pi$
$937$		−	2.06419e34i		−	1.37957i	0.724014	−	0.689785i	$-0.242295\pi$
$938$		0			0
$939$	−2.31886e33	+	2.31886e33i	−0.151224	+	0.151224i
$940$		0			0
$941$	−2.03742e34	−	2.03742e34i	−1.29658	−	1.29658i	−0.930636	−	0.365947i	$-0.880745\pi$
$941$	−2.03742e34	−	2.03742e34i	−1.29658	−	1.29658i	−0.365947	−	0.930636i	$-0.619255\pi$
$942$		0			0
$943$	5.72231e33			0.355375
$944$		0			0
$945$	1.51088e32			0.00915721
$946$		0			0
$947$	1.51293e34	+	1.51293e34i	0.894939	+	0.894939i	0.994983	−	0.100044i	$-0.0318983\pi$
$947$	1.51293e34	+	1.51293e34i	0.894939	+	0.894939i	−0.100044	+	0.994983i	$0.531898\pi$
$948$		0			0
$949$	−7.84962e33	+	7.84962e33i	−0.453197	+	0.453197i
$950$		0			0
$951$		−	1.81228e33i		−	0.102129i
$952$		0			0
$953$		−	1.64821e34i		−	0.906660i	−0.891343	−	0.453330i	$-0.850236\pi$
$953$		−	1.64821e34i		−	0.906660i	0.891343	−	0.453330i	$-0.149764\pi$
$954$		0			0
$955$	−5.13746e31	+	5.13746e31i	−0.00275873	+	0.00275873i
$956$		0			0
$957$	2.60382e33	+	2.60382e33i	0.136497	+	0.136497i
$958$		0			0
$959$	−4.29885e33			−0.220008
$960$		0			0
$961$	−8.60344e33			−0.429886
$962$		0			0
$963$	−5.89689e33	−	5.89689e33i	−0.287687	−	0.287687i
$964$		0			0
$965$	−3.56360e31	+	3.56360e31i	−0.00169756	+	0.00169756i
$966$		0			0
$967$			1.20564e34i			0.560807i	0.959882	+	0.280403i	$0.0904683\pi$
$967$			1.20564e34i			0.560807i	−0.959882	+	0.280403i	$0.909532\pi$
$968$		0			0
$969$			3.29828e32i			0.0149818i
$970$		0			0
$971$	−1.73750e33	+	1.73750e33i	−0.0770732	+	0.0770732i	−0.744592	−	0.667519i	$-0.767356\pi$
$971$	−1.73750e33	+	1.73750e33i	−0.0770732	+	0.0770732i	0.667519	+	0.744592i	$0.267356\pi$
$972$		0			0
$973$	1.13066e34	+	1.13066e34i	0.489817	+	0.489817i
$974$		0			0
$975$	−5.87275e33			−0.248478
$976$		0			0
$977$	2.55837e34			1.05725			0.528623	−	0.848857i	$-0.322708\pi$
$977$	2.55837e34			1.05725			0.528623	+	0.848857i	$0.322708\pi$
$978$		0			0
$979$	1.56689e34	+	1.56689e34i	0.632465	+	0.632465i
$980$		0			0
$981$	1.57163e34	−	1.57163e34i	0.619667	−	0.619667i
$982$		0			0
$983$		−	6.91216e33i		−	0.266225i	−0.991101	−	0.133112i	$-0.957503\pi$
$983$		−	6.91216e33i		−	0.266225i	0.991101	−	0.133112i	$-0.0424971\pi$
$984$		0			0
$985$			1.58834e33i			0.0597621i
$986$		0			0
$987$	−2.43387e33	+	2.43387e33i	−0.0894644	+	0.0894644i
$988$		0			0
$989$	1.82295e34	+	1.82295e34i	0.654661	+	0.654661i
$990$		0			0
$991$	−2.37972e34			−0.834987			−0.417493	−	0.908680i	$-0.637091\pi$
$991$	−2.37972e34			−0.834987			−0.417493	+	0.908680i	$0.637091\pi$
$992$		0			0
$993$	9.39235e33			0.322001
$994$		0			0
$995$	−1.14795e33	−	1.14795e33i	−0.0384553	−	0.0384553i
$996$		0			0
$997$	−4.22622e34	+	4.22622e34i	−1.38343	+	1.38343i	−0.544985	+	0.838446i	$0.683464\pi$
$997$	−4.22622e34	+	4.22622e34i	−1.38343	+	1.38343i	−0.838446	+	0.544985i	$0.816536\pi$
$998$		0			0
$999$			4.37755e33i			0.140032i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	64.24.e.a.17.20		90
4.3	odd	2		16.24.e.a.13.37	yes	90
16.5	even	4	inner	64.24.e.a.49.20		90
16.11	odd	4		16.24.e.a.5.37	✓	90

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.24.e.a.5.37	✓	90	16.11	odd	4
16.24.e.a.13.37	yes	90	4.3	odd	2
64.24.e.a.17.20		90	1.1	even	1	trivial
64.24.e.a.49.20		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)

\(f(q)\)	\(=\)	\(q+(-68436.9 - 68436.9i) q^{3} +(-2.70386e6 + 2.70386e6i) q^{5} +2.28175e9i q^{7} -8.47760e10i q^{9} +O(q^{10})\)	\(q+(-68436.9 - 68436.9i) q^{3} +(-2.70386e6 + 2.70386e6i) q^{5} +2.28175e9i q^{7} -8.47760e10i q^{9} +(4.33062e11 - 4.33062e11i) q^{11} +(-3.60366e12 - 3.60366e12i) q^{13} +3.70087e11 q^{15} -2.43286e14 q^{17} +(9.90492e12 + 9.90492e12i) q^{19} +(1.56156e14 - 1.56156e14i) q^{21} +3.84151e15i q^{23} +1.19063e16i q^{25} +(-1.22447e16 + 1.22447e16i) q^{27} +(-4.39280e16 - 4.39280e16i) q^{29} +1.06817e17 q^{31} -5.92748e16 q^{33} +(-6.16953e15 - 6.16953e15i) q^{35} +(1.78754e17 - 1.78754e17i) q^{37} +4.93247e17i q^{39} -1.48960e18i q^{41} +(4.74540e18 - 4.74540e18i) q^{43} +(2.29222e17 + 2.29222e17i) q^{45} -1.55862e19 q^{47} +2.21624e19 q^{49} +(1.66497e19 + 1.66497e19i) q^{51} +(-2.36779e19 + 2.36779e19i) q^{53} +2.34187e18i q^{55} -1.35572e18i q^{57} +(-1.81978e20 + 1.81978e20i) q^{59} +(-4.63677e20 - 4.63677e20i) q^{61} +1.93438e20 q^{63} +1.94876e19 q^{65} +(9.87931e20 + 9.87931e20i) q^{67} +(2.62901e20 - 2.62901e20i) q^{69} +3.79930e20i q^{71} -2.17823e21i q^{73} +(8.14830e20 - 8.14830e20i) q^{75} +(9.88140e20 + 9.88140e20i) q^{77} -4.95268e21 q^{79} -6.30511e21 q^{81} +(-6.24068e21 - 6.24068e21i) q^{83} +(6.57809e20 - 6.57809e20i) q^{85} +6.01259e21i q^{87} +3.61816e22i q^{89} +(8.22267e21 - 8.22267e21i) q^{91} +(-7.31022e21 - 7.31022e21i) q^{93} -5.35629e19 q^{95} +1.92581e21 q^{97} +(-3.67132e22 - 3.67132e22i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 90 q + 2 q^{3} - 2 q^{5}+O(q^{10}) \) 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

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