LMFDB - Embedded newform 64.13.f.a.47.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [64,13,Mod(15,64)]

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([2, 1]))

N = Newforms(chi, 13, names="a")

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

chi := DirichletCharacter("64.15");

S:= CuspForms(chi, 13);

N := Newforms(S);

Level:	$ N $	$=$	$ 64 = 2^{6} $
Weight:	$ k $	$=$	$ 13 $
Character orbit:	$[\chi]$	$=$	64.f (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:	$58.4956043057$
Analytic rank:	$0$
Dimension:	$46$
Relative dimension:	$23$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 16)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			47.17
Character	$\chi$	$=$	64.47
Dual form			64.13.f.a.15.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(435.597 - 435.597i) q^{3} +(17337.6 - 17337.6i) q^{5} -102408. q^{7} +151952. i q^{9} +O(q^{10})$	\(q+(435.597 - 435.597i) q^{3} +(17337.6 - 17337.6i) q^{5} -102408. q^{7} +151952. i q^{9} +(1.38379e6 + 1.38379e6i) q^{11} +(-5.77232e6 - 5.77232e6i) q^{13} -1.51044e7i q^{15} -3.78167e7 q^{17} +(-2.52129e7 + 2.52129e7i) q^{19} +(-4.46085e7 + 4.46085e7i) q^{21} -1.57577e8 q^{23} -3.57046e8i q^{25} +(2.97684e8 + 2.97684e8i) q^{27} +(5.46743e7 + 5.46743e7i) q^{29} -6.13795e8i q^{31} +1.20555e9 q^{33} +(-1.77551e9 + 1.77551e9i) q^{35} +(-5.91379e8 + 5.91379e8i) q^{37} -5.02881e9 q^{39} -6.47790e9i q^{41} +(6.63091e8 + 6.63091e8i) q^{43} +(2.63449e9 + 2.63449e9i) q^{45} +6.80100e9i q^{47} -3.35394e9 q^{49} +(-1.64728e10 + 1.64728e10i) q^{51} +(1.10020e10 - 1.10020e10i) q^{53} +4.79832e10 q^{55} +2.19653e10i q^{57} +(-1.35652e10 - 1.35652e10i) q^{59} +(2.49781e10 + 2.49781e10i) q^{61} -1.55611e10i q^{63} -2.00157e11 q^{65} +(-6.49828e10 + 6.49828e10i) q^{67} +(-6.86401e10 + 6.86401e10i) q^{69} -2.09515e11 q^{71} +9.47375e10i q^{73} +(-1.55528e11 - 1.55528e11i) q^{75} +(-1.41711e11 - 1.41711e11i) q^{77} -6.54519e10i q^{79} +1.78586e11 q^{81} +(-5.21790e10 + 5.21790e10i) q^{83} +(-6.55652e11 + 6.55652e11i) q^{85} +4.76319e10 q^{87} +1.94016e11i q^{89} +(5.91131e11 + 5.91131e11i) q^{91} +(-2.67367e11 - 2.67367e11i) q^{93} +8.74265e11i q^{95} -3.18157e11 q^{97} +(-2.10270e11 + 2.10270e11i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 46 q + 2 q^{3} - 2 q^{5} + 4 q^{7}+O(q^{10}) $ 46 * q + 2 * q^3 - 2 * q^5 + 4 * q^7	$ 46 q + 2 q^{3} - 2 q^{5} + 4 q^{7} - 2668318 q^{11} - 2 q^{13} - 4 q^{17} - 51868606 q^{19} - 1062884 q^{21} - 298270076 q^{23} - 970053760 q^{27} + 704570398 q^{29} - 4 q^{33} + 3815032900 q^{35} + 364298398 q^{37} - 15553507196 q^{39} - 363863518 q^{43} + 489344130 q^{45} + 67229109258 q^{49} - 33806024892 q^{51} - 11168756642 q^{53} + 74491808260 q^{55} - 104334793054 q^{59} - 106371743810 q^{61} - 75186419620 q^{65} + 43778233922 q^{67} - 214340079908 q^{69} + 188251854340 q^{71} - 308961520610 q^{75} - 341607754084 q^{77} - 941431788274 q^{81} + 1025936323202 q^{83} + 436332718748 q^{85} - 2368412421756 q^{87} + 2028231531652 q^{91} + 1534541270080 q^{93} - 4 q^{97} - 4950023059646 q^{99}+O(q^{100}) $ 46 * q + 2 * q^3 - 2 * q^5 + 4 * q^7 - 2668318 * q^11 - 2 * q^13 - 4 * q^17 - 51868606 * q^19 - 1062884 * q^21 - 298270076 * q^23 - 970053760 * q^27 + 704570398 * q^29 - 4 * q^33 + 3815032900 * q^35 + 364298398 * q^37 - 15553507196 * q^39 - 363863518 * q^43 + 489344130 * q^45 + 67229109258 * q^49 - 33806024892 * q^51 - 11168756642 * q^53 + 74491808260 * q^55 - 104334793054 * q^59 - 106371743810 * q^61 - 75186419620 * q^65 + 43778233922 * q^67 - 214340079908 * q^69 + 188251854340 * q^71 - 308961520610 * q^75 - 341607754084 * q^77 - 941431788274 * q^81 + 1025936323202 * q^83 + 436332718748 * q^85 - 2368412421756 * q^87 + 2028231531652 * q^91 + 1534541270080 * q^93 - 4 * q^97 - 4950023059646 * 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
$3$	435.597	−	435.597i	0.597526	−	0.597526i	−0.342127	−	0.939654i	$-0.611147\pi$
$3$	435.597	−	435.597i	0.597526	−	0.597526i	0.939654	+	0.342127i	$0.111147\pi$
$4$		0			0
$5$	17337.6	−	17337.6i	1.10961	−	1.10961i	0.116406	−	0.993202i	$-0.462862\pi$
$5$	17337.6	−	17337.6i	1.10961	−	1.10961i	0.993202	−	0.116406i	$-0.0371375\pi$
$6$		0			0
$7$	−102408.			−0.870452			−0.435226	−	0.900321i	$-0.643331\pi$
$7$	−102408.			−0.870452			−0.435226	+	0.900321i	$0.643331\pi$
$8$		0			0
$9$			151952.i			0.285925i
$10$		0			0
$11$	1.38379e6	+	1.38379e6i	0.781112	+	0.781112i	0.980018	−	0.198907i	$-0.0637390\pi$
$11$	1.38379e6	+	1.38379e6i	0.781112	+	0.781112i	−0.198907	+	0.980018i	$0.563739\pi$
$12$		0			0
$13$	−5.77232e6	−	5.77232e6i	−1.19589	−	1.19589i	−0.975387	−	0.220502i	$-0.929231\pi$
$13$	−5.77232e6	−	5.77232e6i	−1.19589	−	1.19589i	−0.220502	−	0.975387i	$-0.570769\pi$
$14$		0			0
$15$		−	1.51044e7i		−	1.32604i
$16$		0			0
$17$	−3.78167e7			−1.56672			−0.783358	−	0.621571i	$-0.786495\pi$
$17$	−3.78167e7			−1.56672			−0.783358	+	0.621571i	$0.786495\pi$
$18$		0			0
$19$	−2.52129e7	+	2.52129e7i	−0.535922	+	0.535922i	−0.922329	−	0.386406i	$-0.873716\pi$
$19$	−2.52129e7	+	2.52129e7i	−0.535922	+	0.535922i	0.386406	+	0.922329i	$0.373716\pi$
$20$		0			0
$21$	−4.46085e7	+	4.46085e7i	−0.520118	+	0.520118i
$22$		0			0
$23$	−1.57577e8			−1.06445			−0.532227	−	0.846602i	$-0.678645\pi$
$23$	−1.57577e8			−1.06445			−0.532227	+	0.846602i	$0.678645\pi$
$24$		0			0
$25$		−	3.57046e8i		−	1.46246i
$26$		0			0
$27$	2.97684e8	+	2.97684e8i	0.768374	+	0.768374i
$28$		0			0
$29$	5.46743e7	+	5.46743e7i	0.0919168	+	0.0919168i	0.751570	−	0.659653i	$-0.229297\pi$
$29$	5.46743e7	+	5.46743e7i	0.0919168	+	0.0919168i	−0.659653	+	0.751570i	$0.729297\pi$
$30$		0			0
$31$		−	6.13795e8i		−	0.691597i	−0.938309	−	0.345799i	$-0.887608\pi$
$31$		−	6.13795e8i		−	0.691597i	0.938309	−	0.345799i	$-0.112392\pi$
$32$		0			0
$33$	1.20555e9			0.933470
$34$		0			0
$35$	−1.77551e9	+	1.77551e9i	−0.965860	+	0.965860i
$36$		0			0
$37$	−5.91379e8	+	5.91379e8i	−0.230492	+	0.230492i	−0.812898	−	0.582406i	$-0.802111\pi$
$37$	−5.91379e8	+	5.91379e8i	−0.230492	+	0.230492i	0.582406	+	0.812898i	$0.302111\pi$
$38$		0			0
$39$	−5.02881e9			−1.42915
$40$		0			0
$41$		−	6.47790e9i		−	1.36374i	−0.731474	−	0.681870i	$-0.761167\pi$
$41$		−	6.47790e9i		−	1.36374i	0.731474	−	0.681870i	$-0.238833\pi$
$42$		0			0
$43$	6.63091e8	+	6.63091e8i	0.104897	+	0.104897i	0.757607	−	0.652711i	$-0.226368\pi$
$43$	6.63091e8	+	6.63091e8i	0.104897	+	0.104897i	−0.652711	+	0.757607i	$0.726368\pi$
$44$		0			0
$45$	2.63449e9	+	2.63449e9i	0.317265	+	0.317265i
$46$		0			0
$47$			6.80100e9i			0.630937i	0.948936	+	0.315468i	$0.102162\pi$
$47$			6.80100e9i			0.630937i	−0.948936	+	0.315468i	$0.897838\pi$
$48$		0			0
$49$	−3.35394e9			−0.242314
$50$		0			0
$51$	−1.64728e10	+	1.64728e10i	−0.936154	+	0.936154i
$52$		0			0
$53$	1.10020e10	−	1.10020e10i	0.496382	−	0.496382i	−0.413928	−	0.910310i	$-0.635843\pi$
$53$	1.10020e10	−	1.10020e10i	0.496382	−	0.496382i	0.910310	+	0.413928i	$0.135843\pi$
$54$		0			0
$55$	4.79832e10			1.73346
$56$		0			0
$57$			2.19653e10i			0.640455i
$58$		0			0
$59$	−1.35652e10	−	1.35652e10i	−0.321599	−	0.321599i	0.527781	−	0.849380i	$-0.323024\pi$
$59$	−1.35652e10	−	1.35652e10i	−0.321599	−	0.321599i	−0.849380	+	0.527781i	$0.823024\pi$
$60$		0			0
$61$	2.49781e10	+	2.49781e10i	0.484819	+	0.484819i	0.906667	−	0.421848i	$-0.138618\pi$
$61$	2.49781e10	+	2.49781e10i	0.484819	+	0.484819i	−0.421848	+	0.906667i	$0.638618\pi$
$62$		0			0
$63$		−	1.55611e10i		−	0.248884i
$64$		0			0
$65$	−2.00157e11			−2.65393
$66$		0			0
$67$	−6.49828e10	+	6.49828e10i	−0.718372	+	0.718372i	−0.968272	−	0.249899i	$-0.919602\pi$
$67$	−6.49828e10	+	6.49828e10i	−0.718372	+	0.718372i	0.249899	+	0.968272i	$0.419602\pi$
$68$		0			0
$69$	−6.86401e10	+	6.86401e10i	−0.636039	+	0.636039i
$70$		0			0
$71$	−2.09515e11			−1.63555			−0.817776	−	0.575537i	$-0.804793\pi$
$71$	−2.09515e11			−1.63555			−0.817776	+	0.575537i	$0.804793\pi$
$72$		0			0
$73$			9.47375e10i			0.626015i	0.949751	+	0.313008i	$0.101337\pi$
$73$			9.47375e10i			0.626015i	−0.949751	+	0.313008i	$0.898663\pi$
$74$		0			0
$75$	−1.55528e11	−	1.55528e11i	−0.873858	−	0.873858i
$76$		0			0
$77$	−1.41711e11	−	1.41711e11i	−0.679920	−	0.679920i
$78$		0			0
$79$		−	6.54519e10i		−	0.269252i	−0.990896	−	0.134626i	$-0.957017\pi$
$79$		−	6.54519e10i		−	0.269252i	0.990896	−	0.134626i	$-0.0429834\pi$
$80$		0			0
$81$	1.78586e11			0.632322
$82$		0			0
$83$	−5.21790e10	+	5.21790e10i	−0.159598	+	0.159598i	−0.782389	−	0.622791i	$-0.785999\pi$
$83$	−5.21790e10	+	5.21790e10i	−0.159598	+	0.159598i	0.622791	+	0.782389i	$0.285999\pi$
$84$		0			0
$85$	−6.55652e11	+	6.55652e11i	−1.73844	+	1.73844i
$86$		0			0
$87$	4.76319e10			0.109845
$88$		0			0
$89$			1.94016e11i			0.390390i	0.980764	+	0.195195i	$0.0625339\pi$
$89$			1.94016e11i			0.390390i	−0.980764	+	0.195195i	$0.937466\pi$
$90$		0			0
$91$	5.91131e11	+	5.91131e11i	1.04096	+	1.04096i
$92$		0			0
$93$	−2.67367e11	−	2.67367e11i	−0.413248	−	0.413248i
$94$		0			0
$95$			8.74265e11i			1.18933i
$96$		0			0
$97$	−3.18157e11			−0.381954			−0.190977	−	0.981595i	$-0.561166\pi$
$97$	−3.18157e11			−0.381954			−0.190977	+	0.981595i	$0.561166\pi$
$98$		0			0
$99$	−2.10270e11	+	2.10270e11i	−0.223339	+	0.223339i
$100$		0			0
$101$	1.38439e12	−	1.38439e12i	1.30416	−	1.30416i	0.378594	−	0.925563i	$-0.376408\pi$
$101$	1.38439e12	−	1.38439e12i	1.30416	−	1.30416i	0.925563	−	0.378594i	$-0.123592\pi$
$102$		0			0
$103$	−1.28474e12			−1.07595			−0.537975	−	0.842961i	$-0.680811\pi$
$103$	−1.28474e12			−1.07595			−0.537975	+	0.842961i	$0.680811\pi$
$104$		0			0
$105$			1.54681e12i			1.15425i
$106$		0			0
$107$	−1.79747e12	−	1.79747e12i	−1.19773	−	1.19773i	−0.974844	−	0.222888i	$-0.928452\pi$
$107$	−1.79747e12	−	1.79747e12i	−1.19773	−	1.19773i	−0.222888	−	0.974844i	$-0.571548\pi$
$108$		0			0
$109$	−7.75931e11	−	7.75931e11i	−0.462662	−	0.462662i	0.436865	−	0.899527i	$-0.356089\pi$
$109$	−7.75931e11	−	7.75931e11i	−0.462662	−	0.462662i	−0.899527	+	0.436865i	$0.856089\pi$
$110$		0			0
$111$			5.15205e11i			0.275450i
$112$		0			0
$113$	8.78084e10			0.0421760			0.0210880	−	0.999778i	$-0.493287\pi$
$113$	8.78084e10			0.0421760			0.0210880	+	0.999778i	$0.493287\pi$
$114$		0			0
$115$	−2.73202e12	+	2.73202e12i	−1.18113	+	1.18113i
$116$		0			0
$117$	8.77118e11	−	8.77118e11i	0.341934	−	0.341934i
$118$		0			0
$119$	3.87273e12			1.36375
$120$		0			0
$121$			6.91307e11i			0.220272i
$122$		0			0
$123$	−2.82175e12	−	2.82175e12i	−0.814870	−	0.814870i
$124$		0			0
$125$	−1.95751e12	−	1.95751e12i	−0.513149	−	0.513149i
$126$		0			0
$127$			6.95890e11i			0.165851i	0.996556	+	0.0829255i	$0.0264264\pi$
$127$			6.95890e11i			0.165851i	−0.996556	+	0.0829255i	$0.973574\pi$
$128$		0			0
$129$	5.77680e11			0.125357
$130$		0			0
$131$	3.48750e12	−	3.48750e12i	0.690060	−	0.690060i	−0.272185	−	0.962245i	$-0.587746\pi$
$131$	3.48750e12	−	3.48750e12i	0.690060	−	0.690060i	0.962245	+	0.272185i	$0.0877463\pi$
$132$		0			0
$133$	2.58200e12	−	2.58200e12i	0.466495	−	0.466495i
$134$		0			0
$135$	1.03223e13			1.70519
$136$		0			0
$137$			5.46598e12i			0.826693i	0.910574	+	0.413347i	$0.135640\pi$
$137$			5.46598e12i			0.826693i	−0.910574	+	0.413347i	$0.864360\pi$
$138$		0			0
$139$	6.77872e12	+	6.77872e12i	0.939851	+	0.939851i	0.998291	−	0.0584397i	$-0.0186125\pi$
$139$	6.77872e12	+	6.77872e12i	0.939851	+	0.939851i	−0.0584397	+	0.998291i	$0.518613\pi$
$140$		0			0
$141$	2.96249e12	+	2.96249e12i	0.377001	+	0.377001i
$142$		0			0
$143$		−	1.59753e13i		−	1.86825i
$144$		0			0
$145$	1.89584e12			0.203983
$146$		0			0
$147$	−1.46096e12	+	1.46096e12i	−0.144789	+	0.144789i
$148$		0			0
$149$	1.51238e12	−	1.51238e12i	0.138212	−	0.138212i	−0.634616	−	0.772828i	$-0.718842\pi$
$149$	1.51238e12	−	1.51238e12i	0.138212	−	0.138212i	0.772828	+	0.634616i	$0.218842\pi$
$150$		0			0
$151$	1.84488e13			1.55635			0.778174	−	0.628049i	$-0.216146\pi$
$151$	1.84488e13			1.55635			0.778174	+	0.628049i	$0.216146\pi$
$152$		0			0
$153$		−	5.74634e12i		−	0.447963i
$154$		0			0
$155$	−1.06418e13	−	1.06418e13i	−0.767402	−	0.767402i
$156$		0			0
$157$	−2.08644e12	−	2.08644e12i	−0.139319	−	0.139319i	0.634008	−	0.773327i	$-0.281409\pi$
$157$	−2.08644e12	−	2.08644e12i	−0.139319	−	0.139319i	−0.773327	+	0.634008i	$0.781409\pi$
$158$		0			0
$159$		−	9.58486e12i		−	0.593202i
$160$		0			0
$161$	1.61371e13			0.926555
$162$		0			0
$163$	−1.86481e13	+	1.86481e13i	−0.994279	+	0.994279i	−0.999984	−	0.00570509i	$-0.998184\pi$
$163$	−1.86481e13	+	1.86481e13i	−0.994279	+	0.994279i	0.00570509	+	0.999984i	$0.498184\pi$
$164$		0			0
$165$	2.09013e13	−	2.09013e13i	1.03579	−	1.03579i
$166$		0			0
$167$	1.86916e13			0.861684			0.430842	−	0.902427i	$-0.358217\pi$
$167$	1.86916e13			0.861684			0.430842	+	0.902427i	$0.358217\pi$
$168$		0			0
$169$			4.33414e13i			1.86030i
$170$		0			0
$171$	−3.83116e12	−	3.83116e12i	−0.153234	−	0.153234i
$172$		0			0
$173$	−1.96126e13	−	1.96126e13i	−0.731573	−	0.731573i	0.239358	−	0.970931i	$-0.423063\pi$
$173$	−1.96126e13	−	1.96126e13i	−0.731573	−	0.731573i	−0.970931	+	0.239358i	$0.923063\pi$
$174$		0			0
$175$			3.65643e13i			1.27300i
$176$		0			0
$177$	−1.18179e13			−0.384328
$178$		0			0
$179$	2.08631e13	−	2.08631e13i	0.634251	−	0.634251i	−0.314880	−	0.949131i	$-0.601964\pi$
$179$	2.08631e13	−	2.08631e13i	0.634251	−	0.634251i	0.949131	+	0.314880i	$0.101964\pi$
$180$		0			0
$181$	3.60364e13	−	3.60364e13i	1.02487	−	1.02487i	0.0251913	−	0.999683i	$-0.491981\pi$
$181$	3.60364e13	−	3.60364e13i	1.02487	−	1.02487i	0.999683	−	0.0251913i	$-0.00801950\pi$
$182$		0			0
$183$	2.17607e13			0.579384
$184$		0			0
$185$			2.05062e13i			0.511511i
$186$		0			0
$187$	−5.23303e13	−	5.23303e13i	−1.22378	−	1.22378i
$188$		0			0
$189$	−3.04851e13	−	3.04851e13i	−0.668832	−	0.668832i
$190$		0			0
$191$			4.71683e13i			0.971515i	0.874094	+	0.485758i	$0.161456\pi$
$191$			4.71683e13i			0.971515i	−0.874094	+	0.485758i	$0.838544\pi$
$192$		0			0
$193$	1.03913e13			0.201061			0.100530	−	0.994934i	$-0.467946\pi$
$193$	1.03913e13			0.201061			0.100530	+	0.994934i	$0.467946\pi$
$194$		0			0
$195$	−8.71876e13	+	8.71876e13i	−1.58580	+	1.58580i
$196$		0			0
$197$	−1.34100e13	+	1.34100e13i	−0.229421	+	0.229421i	−0.812451	−	0.583030i	$-0.801867\pi$
$197$	−1.34100e13	+	1.34100e13i	−0.229421	+	0.229421i	0.583030	+	0.812451i	$0.301867\pi$
$198$		0			0
$199$	−4.13297e13			−0.665494			−0.332747	−	0.943016i	$-0.607975\pi$
$199$	−4.13297e13			−0.665494			−0.332747	+	0.943016i	$0.607975\pi$
$200$		0			0
$201$			5.66126e13i			0.858493i
$202$		0			0
$203$	−5.59907e12	−	5.59907e12i	−0.0800092	−	0.0800092i
$204$		0			0
$205$	−1.12311e14	−	1.12311e14i	−1.51322	−	1.51322i
$206$		0			0
$207$		−	2.39442e13i		−	0.304354i
$208$		0			0
$209$	−6.97787e13			−0.837231
$210$		0			0
$211$	2.81308e13	−	2.81308e13i	0.318777	−	0.318777i	−0.529520	−	0.848297i	$-0.677628\pi$
$211$	2.81308e13	−	2.81308e13i	0.318777	−	0.318777i	0.848297	+	0.529520i	$0.177628\pi$
$212$		0			0
$213$	−9.12639e13	+	9.12639e13i	−0.977285	+	0.977285i
$214$		0			0
$215$	2.29928e13			0.232789
$216$		0			0
$217$			6.28574e13i			0.602002i
$218$		0			0
$219$	4.12673e13	+	4.12673e13i	0.374061	+	0.374061i
$220$		0			0
$221$	2.18290e14	+	2.18290e14i	1.87362	+	1.87362i
$222$		0			0
$223$		−	6.30099e13i		−	0.512365i	−0.966628	−	0.256182i	$-0.917535\pi$
$223$		−	6.30099e13i		−	0.512365i	0.966628	−	0.256182i	$-0.0824648\pi$
$224$		0			0
$225$	5.42539e13			0.418154
$226$		0			0
$227$	−2.01564e13	+	2.01564e13i	−0.147319	+	0.147319i	−0.776919	−	0.629600i	$-0.783219\pi$
$227$	−2.01564e13	+	2.01564e13i	−0.147319	+	0.147319i	0.629600	+	0.776919i	$0.283219\pi$
$228$		0			0
$229$	−1.16531e13	+	1.16531e13i	−0.0808032	+	0.0808032i	−0.746353	−	0.665550i	$-0.768197\pi$
$229$	−1.16531e13	+	1.16531e13i	−0.0808032	+	0.0808032i	0.665550	+	0.746353i	$0.268197\pi$
$230$		0			0
$231$	−1.23457e14			−0.812540
$232$		0			0
$233$		−	1.09329e14i		−	0.683283i	−0.939830	−	0.341642i	$-0.889017\pi$
$233$		−	1.09329e14i		−	0.683283i	0.939830	−	0.341642i	$-0.110983\pi$
$234$		0			0
$235$	1.17913e14	+	1.17913e14i	0.700092	+	0.700092i
$236$		0			0
$237$	−2.85106e13	−	2.85106e13i	−0.160885	−	0.160885i
$238$		0			0
$239$		−	2.20844e14i		−	1.18494i	−0.805591	−	0.592472i	$-0.798152\pi$
$239$		−	2.20844e14i		−	1.18494i	0.805591	−	0.592472i	$-0.201848\pi$
$240$		0			0
$241$	−1.06439e14			−0.543248			−0.271624	−	0.962403i	$-0.587561\pi$
$241$	−1.06439e14			−0.543248			−0.271624	+	0.962403i	$0.587561\pi$
$242$		0			0
$243$	−8.04097e13	+	8.04097e13i	−0.390545	+	0.390545i
$244$		0			0
$245$	−5.81493e13	+	5.81493e13i	−0.268874	+	0.268874i
$246$		0			0
$247$	2.91075e14			1.28181
$248$		0			0
$249$			4.54580e13i			0.190728i
$250$		0			0
$251$	−2.99032e14	−	2.99032e14i	−1.19585	−	1.19585i	−0.975399	−	0.220448i	$-0.929248\pi$
$251$	−2.99032e14	−	2.99032e14i	−1.19585	−	1.19585i	−0.220448	−	0.975399i	$-0.570752\pi$
$252$		0			0
$253$	−2.18053e14	−	2.18053e14i	−0.831457	−	0.831457i
$254$		0			0
$255$			5.71200e14i			2.07753i
$256$		0			0
$257$	−4.04863e14			−1.40511			−0.702553	−	0.711632i	$-0.747957\pi$
$257$	−4.04863e14			−1.40511			−0.702553	+	0.711632i	$0.747957\pi$
$258$		0			0
$259$	6.05618e13	−	6.05618e13i	0.200632	−	0.200632i
$260$		0			0
$261$	−8.30788e12	+	8.30788e12i	−0.0262813	+	0.0262813i
$262$		0			0
$263$	−4.24956e14			−1.28413			−0.642066	−	0.766649i	$-0.721923\pi$
$263$	−4.24956e14			−1.28413			−0.642066	+	0.766649i	$0.721923\pi$
$264$		0			0
$265$		−	3.81497e14i		−	1.10158i
$266$		0			0
$267$	8.45129e13	+	8.45129e13i	0.233268	+	0.233268i
$268$		0			0
$269$	4.55382e14	+	4.55382e14i	1.20188	+	1.20188i	0.973593	+	0.228291i	$0.0733138\pi$
$269$	4.55382e14	+	4.55382e14i	1.20188	+	1.20188i	0.228291	+	0.973593i	$0.426686\pi$
$270$		0			0
$271$		−	5.17694e14i		−	1.30694i	−0.756951	−	0.653472i	$-0.773312\pi$
$271$		−	5.17694e14i		−	1.30694i	0.756951	−	0.653472i	$-0.226688\pi$
$272$		0			0
$273$	5.14989e14			1.24400
$274$		0			0
$275$	4.94076e14	−	4.94076e14i	1.14234	−	1.14234i
$276$		0			0
$277$	4.54799e14	−	4.54799e14i	1.00679	−	1.00679i	0.00681762	−	0.999977i	$-0.497830\pi$
$277$	4.54799e14	−	4.54799e14i	1.00679	−	1.00679i	0.999977	−	0.00681762i	$-0.00217013\pi$
$278$		0			0
$279$	9.32676e13			0.197745
$280$		0			0
$281$		−	9.19632e14i		−	1.86800i	−0.357278	−	0.933998i	$-0.616295\pi$
$281$		−	9.19632e14i		−	1.86800i	0.357278	−	0.933998i	$-0.383705\pi$
$282$		0			0
$283$	4.78608e14	+	4.78608e14i	0.931669	+	0.931669i	0.997810	−	0.0661413i	$-0.0210688\pi$
$283$	4.78608e14	+	4.78608e14i	0.931669	+	0.931669i	−0.0661413	+	0.997810i	$0.521069\pi$
$284$		0			0
$285$	3.80827e14	+	3.80827e14i	0.710654	+	0.710654i
$286$		0			0
$287$			6.63388e14i			1.18707i
$288$		0			0
$289$	8.47482e14			1.45460
$290$		0			0
$291$	−1.38588e14	+	1.38588e14i	−0.228227	+	0.228227i
$292$		0			0
$293$	−1.21041e13	+	1.21041e13i	−0.0191305	+	0.0191305i	−0.716607	−	0.697477i	$-0.754306\pi$
$293$	−1.21041e13	+	1.21041e13i	−0.0191305	+	0.0191305i	0.697477	+	0.716607i	$0.254306\pi$
$294$		0			0
$295$	−4.70377e14			−0.713698
$296$		0			0
$297$			8.23862e14i			1.20037i
$298$		0			0
$299$	9.09587e14	+	9.09587e14i	1.27297	+	1.27297i
$300$		0			0
$301$	−6.79057e13	−	6.79057e13i	−0.0913076	−	0.0913076i
$302$		0			0
$303$		−	1.20607e15i		−	1.55854i
$304$		0			0
$305$	8.66121e14			1.07592
$306$		0			0
$307$	1.10114e15	−	1.10114e15i	1.31527	−	1.31527i	0.397792	−	0.917476i	$-0.369777\pi$
$307$	1.10114e15	−	1.10114e15i	1.31527	−	1.31527i	0.917476	−	0.397792i	$-0.130223\pi$
$308$		0			0
$309$	−5.59629e14	+	5.59629e14i	−0.642909	+	0.642909i
$310$		0			0
$311$	−8.83075e14			−0.975968			−0.487984	−	0.872853i	$-0.662268\pi$
$311$	−8.83075e14			−0.975968			−0.487984	+	0.872853i	$0.662268\pi$
$312$		0			0
$313$		−	1.63760e15i		−	1.74158i	−0.491659	−	0.870788i	$-0.663609\pi$
$313$		−	1.63760e15i		−	1.74158i	0.491659	−	0.870788i	$-0.336391\pi$
$314$		0			0
$315$	−2.69792e14	−	2.69792e14i	−0.276164	−	0.276164i
$316$		0			0
$317$	−7.51370e13	−	7.51370e13i	−0.0740454	−	0.0740454i	0.669114	−	0.743160i	$-0.266674\pi$
$317$	−7.51370e13	−	7.51370e13i	−0.0740454	−	0.0740454i	−0.743160	+	0.669114i	$0.766674\pi$
$318$		0			0
$319$			1.51315e14i			0.143595i
$320$		0			0
$321$	−1.56595e15			−1.43135
$322$		0			0
$323$	9.53471e14	−	9.53471e14i	0.839638	−	0.839638i
$324$		0			0
$325$	−2.06098e15	+	2.06098e15i	−1.74894	+	1.74894i
$326$		0			0
$327$	−6.75986e14			−0.552906
$328$		0			0
$329$		−	6.96475e14i		−	0.549200i
$330$		0			0
$331$	−9.42251e13	−	9.42251e13i	−0.0716471	−	0.0716471i	0.670375	−	0.742022i	$-0.266133\pi$
$331$	−9.42251e13	−	9.42251e13i	−0.0716471	−	0.0716471i	−0.742022	+	0.670375i	$0.766133\pi$
$332$		0			0
$333$	−8.98614e13	−	8.98614e13i	−0.0659034	−	0.0659034i
$334$		0			0
$335$			2.25330e15i			1.59422i
$336$		0			0
$337$	−6.64120e14			−0.453385			−0.226693	−	0.973966i	$-0.572791\pi$
$337$	−6.64120e14			−0.453385			−0.226693	+	0.973966i	$0.572791\pi$
$338$		0			0
$339$	3.82490e13	−	3.82490e13i	0.0252013	−	0.0252013i
$340$		0			0
$341$	8.49362e14	−	8.49362e14i	0.540215	−	0.540215i
$342$		0			0
$343$	1.76092e15			1.08137
$344$		0			0
$345$			2.38011e15i			1.41151i
$346$		0			0
$347$	−1.09203e15	−	1.09203e15i	−0.625542	−	0.625542i	0.321401	−	0.946943i	$-0.395846\pi$
$347$	−1.09203e15	−	1.09203e15i	−0.625542	−	0.625542i	−0.946943	+	0.321401i	$0.895846\pi$
$348$		0			0
$349$	−3.23097e13	−	3.23097e13i	−0.0178805	−	0.0178805i	0.698110	−	0.715991i	$-0.254025\pi$
$349$	−3.23097e13	−	3.23097e13i	−0.0178805	−	0.0178805i	−0.715991	+	0.698110i	$0.754025\pi$
$350$		0			0
$351$		−	3.43665e15i		−	1.83778i
$352$		0			0
$353$	−1.45631e15			−0.752671			−0.376335	−	0.926484i	$-0.622816\pi$
$353$	−1.45631e15			−0.752671			−0.376335	+	0.926484i	$0.622816\pi$
$354$		0			0
$355$	−3.63249e15	+	3.63249e15i	−1.81482	+	1.81482i
$356$		0			0
$357$	1.68695e15	−	1.68695e15i	0.814877	−	0.814877i
$358$		0			0
$359$	−1.70859e15			−0.798127			−0.399063	−	0.916923i	$-0.630665\pi$
$359$	−1.70859e15			−0.798127			−0.399063	+	0.916923i	$0.630665\pi$
$360$		0			0
$361$			9.41930e14i			0.425574i
$362$		0			0
$363$	3.01131e14	+	3.01131e14i	0.131618	+	0.131618i
$364$		0			0
$365$	1.64252e15	+	1.64252e15i	0.694632	+	0.694632i
$366$		0			0
$367$			2.45710e15i			1.00560i	0.864402	+	0.502801i	$0.167697\pi$
$367$			2.45710e15i			1.00560i	−0.864402	+	0.502801i	$0.832303\pi$
$368$		0			0
$369$	9.84332e14			0.389927
$370$		0			0
$371$	−1.12669e15	+	1.12669e15i	−0.432076	+	0.432076i
$372$		0			0
$373$	−3.87777e13	+	3.87777e13i	−0.0143989	+	0.0143989i	−0.714270	−	0.699871i	$-0.753241\pi$
$373$	−3.87777e13	+	3.87777e13i	−0.0143989	+	0.0143989i	0.699871	+	0.714270i	$0.253241\pi$
$374$		0			0
$375$	−1.70537e15			−0.613240
$376$		0			0
$377$		−	6.31195e14i		−	0.219845i
$378$		0			0
$379$	−4.50036e14	−	4.50036e14i	−0.151849	−	0.151849i	0.627094	−	0.778943i	$-0.284244\pi$
$379$	−4.50036e14	−	4.50036e14i	−0.151849	−	0.151849i	−0.778943	+	0.627094i	$0.784244\pi$
$380$		0			0
$381$	3.03127e14	+	3.03127e14i	0.0991004	+	0.0991004i
$382$		0			0
$383$			1.78654e15i			0.566004i	0.959119	+	0.283002i	$0.0913303\pi$
$383$			1.78654e15i			0.566004i	−0.959119	+	0.283002i	$0.908670\pi$
$384$		0			0
$385$	−4.91385e15			−1.50889
$386$		0			0
$387$	−1.00758e14	+	1.00758e14i	−0.0299926	+	0.0299926i
$388$		0			0
$389$	−2.59487e15	+	2.59487e15i	−0.748890	+	0.748890i	−0.974271	−	0.225381i	$-0.927637\pi$
$389$	−2.59487e15	+	2.59487e15i	−0.748890	+	0.748890i	0.225381	+	0.974271i	$0.427637\pi$
$390$		0			0
$391$	5.95906e15			1.66770
$392$		0			0
$393$		−	3.03829e15i		−	0.824658i
$394$		0			0
$395$	−1.13478e15	−	1.13478e15i	−0.298765	−	0.298765i
$396$		0			0
$397$	−5.38599e15	−	5.38599e15i	−1.37570	−	1.37570i	−0.851752	−	0.523945i	$-0.824460\pi$
$397$	−5.38599e15	−	5.38599e15i	−1.37570	−	1.37570i	−0.523945	−	0.851752i	$-0.675540\pi$
$398$		0			0
$399$		−	2.24942e15i		−	0.557485i
$400$		0			0
$401$	4.63060e15			1.11371			0.556854	−	0.830610i	$-0.312008\pi$
$401$	4.63060e15			1.11371			0.556854	+	0.830610i	$0.312008\pi$
$402$		0			0
$403$	−3.54303e15	+	3.54303e15i	−0.827073	+	0.827073i
$404$		0			0
$405$	3.09626e15	−	3.09626e15i	0.701629	−	0.701629i
$406$		0			0
$407$	−1.63669e15			−0.360080
$408$		0			0
$409$			2.72387e15i			0.581897i	0.956739	+	0.290949i	$0.0939709\pi$
$409$			2.72387e15i			0.581897i	−0.956739	+	0.290949i	$0.906029\pi$
$410$		0			0
$411$	2.38096e15	+	2.38096e15i	0.493971	+	0.493971i
$412$		0			0
$413$	1.38918e15	+	1.38918e15i	0.279936	+	0.279936i
$414$		0			0
$415$			1.80932e15i			0.354182i
$416$		0			0
$417$	5.90558e15			1.12317
$418$		0			0
$419$	3.32809e15	−	3.32809e15i	0.615051	−	0.615051i	−0.329207	−	0.944258i	$-0.606781\pi$
$419$	3.32809e15	−	3.32809e15i	0.615051	−	0.615051i	0.944258	+	0.329207i	$0.106781\pi$
$420$		0			0
$421$	−1.67770e15	+	1.67770e15i	−0.301315	+	0.301315i	−0.841528	−	0.540213i	$-0.818344\pi$
$421$	−1.67770e15	+	1.67770e15i	−0.301315	+	0.301315i	0.540213	+	0.841528i	$0.318344\pi$
$422$		0			0
$423$	−1.03343e15			−0.180401
$424$		0			0
$425$			1.35023e16i			2.29126i
$426$		0			0
$427$	−2.55795e15	−	2.55795e15i	−0.422012	−	0.422012i
$428$		0			0
$429$	−6.95880e15	−	6.95880e15i	−1.11633	−	1.11633i
$430$		0			0
$431$		−	5.38391e15i		−	0.839913i	−0.907544	−	0.419957i	$-0.862045\pi$
$431$		−	5.38391e15i		−	0.839913i	0.907544	−	0.419957i	$-0.137955\pi$
$432$		0			0
$433$	2.57674e14			0.0390970			0.0195485	−	0.999809i	$-0.493777\pi$
$433$	2.57674e14			0.0390970			0.0195485	+	0.999809i	$0.493777\pi$
$434$		0			0
$435$	8.25823e14	−	8.25823e14i	0.121885	−	0.121885i
$436$		0			0
$437$	3.97299e15	−	3.97299e15i	0.570464	−	0.570464i
$438$		0			0
$439$	7.62921e15			1.06584			0.532920	−	0.846165i	$-0.321095\pi$
$439$	7.62921e15			1.06584			0.532920	+	0.846165i	$0.321095\pi$
$440$		0			0
$441$		−	5.09639e14i		−	0.0692837i
$442$		0			0
$443$	−3.27823e15	−	3.27823e15i	−0.433727	−	0.433727i	0.456167	−	0.889894i	$-0.349222\pi$
$443$	−3.27823e15	−	3.27823e15i	−0.433727	−	0.433727i	−0.889894	+	0.456167i	$0.849222\pi$
$444$		0			0
$445$	3.36378e15	+	3.36378e15i	0.433180	+	0.433180i
$446$		0			0
$447$		−	1.31758e15i		−	0.165170i
$448$		0			0
$449$	−3.42092e14			−0.0417508			−0.0208754	−	0.999782i	$-0.506645\pi$
$449$	−3.42092e14			−0.0417508			−0.0208754	+	0.999782i	$0.506645\pi$
$450$		0			0
$451$	8.96404e15	−	8.96404e15i	1.06523	−	1.06523i
$452$		0			0
$453$	8.03624e15	−	8.03624e15i	0.929959	−	0.929959i
$454$		0			0
$455$	2.04976e16			2.31012
$456$		0			0
$457$			1.86967e15i			0.205243i	0.994720	+	0.102621i	$0.0327230\pi$
$457$			1.86967e15i			0.205243i	−0.994720	+	0.102621i	$0.967277\pi$
$458$		0			0
$459$	−1.12574e16	−	1.12574e16i	−1.20382	−	1.20382i
$460$		0			0
$461$	−2.51007e15	−	2.51007e15i	−0.261505	−	0.261505i	0.564160	−	0.825665i	$-0.309200\pi$
$461$	−2.51007e15	−	2.51007e15i	−0.261505	−	0.261505i	−0.825665	+	0.564160i	$0.809200\pi$
$462$		0			0
$463$			9.59534e15i			0.974034i	0.873392	+	0.487017i	$0.161915\pi$
$463$			9.59534e15i			0.974034i	−0.873392	+	0.487017i	$0.838085\pi$
$464$		0			0
$465$	−9.27102e15			−0.917086
$466$		0			0
$467$	−1.20140e16	+	1.20140e16i	−1.15820	+	1.15820i	−0.173342	+	0.984862i	$0.555457\pi$
$467$	−1.20140e16	+	1.20140e16i	−1.15820	+	1.15820i	−0.984862	+	0.173342i	$0.944543\pi$
$468$		0			0
$469$	6.65474e15	−	6.65474e15i	0.625308	−	0.625308i
$470$		0			0
$471$	−1.81770e15			−0.166493
$472$		0			0
$473$			1.83515e15i			0.163872i
$474$		0			0
$475$	9.00218e15	+	9.00218e15i	0.783765	+	0.783765i
$476$		0			0
$477$	1.67178e15	+	1.67178e15i	0.141928	+	0.141928i
$478$		0			0
$479$		−	1.18327e16i		−	0.979646i	−0.871822	−	0.489823i	$-0.837061\pi$
$479$		−	1.18327e16i		−	0.979646i	0.871822	−	0.489823i	$-0.162939\pi$
$480$		0			0
$481$	6.82726e15			0.551285
$482$		0			0
$483$	7.02928e15	−	7.02928e15i	0.553641	−	0.553641i
$484$		0			0
$485$	−5.51608e15	+	5.51608e15i	−0.423819	+	0.423819i
$486$		0			0
$487$	−3.35801e15			−0.251714			−0.125857	−	0.992048i	$-0.540168\pi$
$487$	−3.35801e15			−0.251714			−0.125857	+	0.992048i	$0.540168\pi$
$488$		0			0
$489$			1.62461e16i			1.18821i
$490$		0			0
$491$	2.81583e15	+	2.81583e15i	0.200964	+	0.200964i	0.800413	−	0.599449i	$-0.204614\pi$
$491$	2.81583e15	+	2.81583e15i	0.200964	+	0.200964i	−0.599449	+	0.800413i	$0.704614\pi$
$492$		0			0
$493$	−2.06760e15	−	2.06760e15i	−0.144008	−	0.144008i
$494$		0			0
$495$			7.29115e15i			0.495638i
$496$		0			0
$497$	2.14559e16			1.42367
$498$		0			0
$499$	1.10251e15	−	1.10251e15i	0.0714131	−	0.0714131i	−0.670498	−	0.741911i	$-0.733920\pi$
$499$	1.10251e15	−	1.10251e15i	0.0714131	−	0.0714131i	0.741911	+	0.670498i	$0.233920\pi$
$500$		0			0
$501$	8.14200e15	−	8.14200e15i	0.514879	−	0.514879i
$502$		0			0
$503$	8.84148e15			0.545905			0.272953	−	0.962027i	$-0.412000\pi$
$503$	8.84148e15			0.545905			0.272953	+	0.962027i	$0.412000\pi$
$504$		0			0
$505$		−	4.80040e16i		−	2.89421i
$506$		0			0
$507$	1.88794e16	+	1.88794e16i	1.11158	+	1.11158i
$508$		0			0
$509$	8.58229e15	+	8.58229e15i	0.493511	+	0.493511i	0.909410	−	0.415900i	$-0.136533\pi$
$509$	8.58229e15	+	8.58229e15i	0.493511	+	0.493511i	−0.415900	+	0.909410i	$0.636533\pi$
$510$		0			0
$511$		−	9.70186e15i		−	0.544916i
$512$		0			0
$513$	−1.50110e16			−0.823578
$514$		0			0
$515$	−2.22744e16	+	2.22744e16i	−1.19388	+	1.19388i
$516$		0			0
$517$	−9.41114e15	+	9.41114e15i	−0.492832	+	0.492832i
$518$		0			0
$519$	−1.70863e16			−0.874268
$520$		0			0
$521$		−	2.71665e15i		−	0.135834i	−0.997691	−	0.0679168i	$-0.978365\pi$
$521$		−	2.71665e15i		−	0.135834i	0.997691	−	0.0679168i	$-0.0216352\pi$
$522$		0			0
$523$	−1.42472e16	−	1.42472e16i	−0.696178	−	0.696178i	0.267406	−	0.963584i	$-0.413834\pi$
$523$	−1.42472e16	−	1.42472e16i	−0.696178	−	0.696178i	−0.963584	+	0.267406i	$0.913834\pi$
$524$		0			0
$525$	1.59273e16	+	1.59273e16i	0.760651	+	0.760651i
$526$		0			0
$527$			2.32117e16i			1.08354i
$528$		0			0
$529$	2.91597e15			0.133060
$530$		0			0
$531$	2.06127e15	−	2.06127e15i	0.0919532	−	0.0919532i
$532$		0			0
$533$	−3.73926e16	+	3.73926e16i	−1.63088	+	1.63088i
$534$		0			0
$535$	−6.23278e16			−2.65803
$536$		0			0
$537$		−	1.81758e16i		−	0.757963i
$538$		0			0
$539$	−4.64114e15	−	4.64114e15i	−0.189274	−	0.189274i
$540$		0			0
$541$	−1.12763e16	−	1.12763e16i	−0.449761	−	0.449761i	0.445514	−	0.895275i	$-0.353021\pi$
$541$	−1.12763e16	−	1.12763e16i	−0.449761	−	0.449761i	−0.895275	+	0.445514i	$0.853021\pi$
$542$		0			0
$543$		−	3.13947e16i		−	1.22478i
$544$		0			0
$545$	−2.69056e16			−1.02675
$546$		0			0
$547$	3.85942e15	−	3.85942e15i	0.144078	−	0.144078i	−0.631388	−	0.775467i	$-0.717515\pi$
$547$	3.85942e15	−	3.85942e15i	0.144078	−	0.144078i	0.775467	+	0.631388i	$0.217515\pi$
$548$		0			0
$549$	−3.79547e15	+	3.79547e15i	−0.138622	+	0.138622i
$550$		0			0
$551$	−2.75700e15			−0.0985206
$552$		0			0
$553$			6.70278e15i			0.234371i
$554$		0			0
$555$	8.93244e15	+	8.93244e15i	0.305641	+	0.305641i
$556$		0			0
$557$	−1.07374e16	−	1.07374e16i	−0.359558	−	0.359558i	0.504092	−	0.863650i	$-0.331827\pi$
$557$	−1.07374e16	−	1.07374e16i	−0.359558	−	0.359558i	−0.863650	+	0.504092i	$0.831827\pi$
$558$		0			0
$559$		−	7.65515e15i		−	0.250890i
$560$		0			0
$561$	−4.55898e16			−1.46248
$562$		0			0
$563$	8.36599e15	−	8.36599e15i	0.262704	−	0.262704i	−0.563448	−	0.826152i	$-0.690525\pi$
$563$	8.36599e15	−	8.36599e15i	0.262704	−	0.262704i	0.826152	+	0.563448i	$0.190525\pi$
$564$		0			0
$565$	1.52239e15	−	1.52239e15i	0.0467988	−	0.0467988i
$566$		0			0
$567$	−1.82886e16			−0.550406
$568$		0			0
$569$			5.49386e16i			1.61884i	0.587230	+	0.809420i	$0.300218\pi$
$569$			5.49386e16i			1.61884i	−0.587230	+	0.809420i	$0.699782\pi$
$570$		0			0
$571$	−1.06761e16	−	1.06761e16i	−0.308032	−	0.308032i	0.536114	−	0.844146i	$-0.319892\pi$
$571$	−1.06761e16	−	1.06761e16i	−0.308032	−	0.308032i	−0.844146	+	0.536114i	$0.819892\pi$
$572$		0			0
$573$	2.05463e16	+	2.05463e16i	0.580506	+	0.580506i
$574$		0			0
$575$			5.62623e16i			1.55672i
$576$		0			0
$577$	−1.09196e16			−0.295904			−0.147952	−	0.988995i	$-0.547268\pi$
$577$	−1.09196e16			−0.295904			−0.147952	+	0.988995i	$0.547268\pi$
$578$		0			0
$579$	4.52643e15	−	4.52643e15i	0.120139	−	0.120139i
$580$		0			0
$581$	5.34354e15	−	5.34354e15i	0.138922	−	0.138922i
$582$		0			0
$583$	3.04488e16			0.775460
$584$		0			0
$585$		−	3.04143e16i		−	0.758826i
$586$		0			0
$587$	4.58233e16	+	4.58233e16i	1.12010	+	1.12010i	0.991726	+	0.128376i	$0.0409765\pi$
$587$	4.58233e16	+	4.58233e16i	1.12010	+	1.12010i	0.128376	+	0.991726i	$0.459024\pi$
$588$		0			0
$589$	1.54756e16	+	1.54756e16i	0.370643	+	0.370643i
$590$		0			0
$591$			1.16827e16i			0.274170i
$592$		0			0
$593$	7.16509e16			1.64776			0.823879	−	0.566766i	$-0.191806\pi$
$593$	7.16509e16			1.64776			0.823879	+	0.566766i	$0.191806\pi$
$594$		0			0
$595$	6.71439e16	−	6.71439e16i	1.51323	−	1.51323i
$596$		0			0
$597$	−1.80031e16	+	1.80031e16i	−0.397650	+	0.397650i
$598$		0			0
$599$	3.39103e16			0.734126			0.367063	−	0.930196i	$-0.380363\pi$
$599$	3.39103e16			0.734126			0.367063	+	0.930196i	$0.380363\pi$
$600$		0			0
$601$		−	7.11102e15i		−	0.150899i	−0.997150	−	0.0754493i	$-0.975961\pi$
$601$		−	7.11102e15i		−	0.150899i	0.997150	−	0.0754493i	$-0.0240391\pi$
$602$		0			0
$603$	−9.87428e15	−	9.87428e15i	−0.205401	−	0.205401i
$604$		0			0
$605$	1.19856e16	+	1.19856e16i	0.244415	+	0.244415i
$606$		0			0
$607$			1.16324e16i			0.232560i	0.993216	+	0.116280i	$0.0370970\pi$
$607$			1.16324e16i			0.232560i	−0.993216	+	0.116280i	$0.962903\pi$
$608$		0			0
$609$	−4.87787e15			−0.0956151
$610$		0			0
$611$	3.92576e16	−	3.92576e16i	0.754530	−	0.754530i
$612$		0			0
$613$	−3.39708e16	+	3.39708e16i	−0.640241	+	0.640241i	−0.950615	−	0.310374i	$-0.899546\pi$
$613$	−3.39708e16	+	3.39708e16i	−0.640241	+	0.640241i	0.310374	+	0.950615i	$0.399546\pi$
$614$		0			0
$615$	−9.78450e16			−1.80837
$616$		0			0
$617$		−	5.22842e16i		−	0.947675i	−0.880612	−	0.473837i	$-0.842868\pi$
$617$		−	5.22842e16i		−	0.947675i	0.880612	−	0.473837i	$-0.157132\pi$
$618$		0			0
$619$	−1.14108e16	−	1.14108e16i	−0.202848	−	0.202848i	0.598371	−	0.801219i	$-0.295815\pi$
$619$	−1.14108e16	−	1.14108e16i	−0.202848	−	0.202848i	−0.801219	+	0.598371i	$0.795815\pi$
$620$		0			0
$621$	−4.69082e16	−	4.69082e16i	−0.817898	−	0.817898i
$622$		0			0
$623$		−	1.98688e16i		−	0.339815i
$624$		0			0
$625$	1.92923e16			0.323671
$626$		0			0
$627$	−3.03954e16	+	3.03954e16i	−0.500267	+	0.500267i
$628$		0			0
$629$	2.23640e16	−	2.23640e16i	0.361115	−	0.361115i
$630$		0			0
$631$	−4.43491e16			−0.702602			−0.351301	−	0.936263i	$-0.614261\pi$
$631$	−4.43491e16			−0.702602			−0.351301	+	0.936263i	$0.614261\pi$
$632$		0			0
$633$		−	2.45074e16i		−	0.380955i
$634$		0			0
$635$	1.20651e16	+	1.20651e16i	0.184030	+	0.184030i
$636$		0			0
$637$	1.93600e16	+	1.93600e16i	0.289781	+	0.289781i
$638$		0			0
$639$		−	3.18362e16i		−	0.467645i
$640$		0			0
$641$	9.48509e16			1.36739			0.683697	−	0.729766i	$-0.260371\pi$
$641$	9.48509e16			1.36739			0.683697	+	0.729766i	$0.260371\pi$
$642$		0			0
$643$	−8.74171e16	+	8.74171e16i	−1.23689	+	1.23689i	−0.275622	+	0.961266i	$0.588884\pi$
$643$	−8.74171e16	+	8.74171e16i	−1.23689	+	1.23689i	−0.961266	+	0.275622i	$0.911116\pi$
$644$		0			0
$645$	1.00156e16	−	1.00156e16i	0.139097	−	0.139097i
$646$		0			0
$647$	−4.86476e16			−0.663186			−0.331593	−	0.943423i	$-0.607586\pi$
$647$	−4.86476e16			−0.663186			−0.331593	+	0.943423i	$0.607586\pi$
$648$		0			0
$649$		−	3.75428e16i		−	0.502410i
$650$		0			0
$651$	2.73805e16	+	2.73805e16i	0.359712	+	0.359712i
$652$		0			0
$653$	4.49878e16	+	4.49878e16i	0.580251	+	0.580251i	0.934972	−	0.354721i	$-0.115424\pi$
$653$	4.49878e16	+	4.49878e16i	0.580251	+	0.580251i	−0.354721	+	0.934972i	$0.615424\pi$
$654$		0			0
$655$		−	1.20930e17i		−	1.53139i
$656$		0			0
$657$	−1.43956e16			−0.178993
$658$		0			0
$659$	−3.04780e16	+	3.04780e16i	−0.372112	+	0.372112i	−0.868246	−	0.496134i	$-0.834753\pi$
$659$	−3.04780e16	+	3.04780e16i	−0.372112	+	0.372112i	0.496134	+	0.868246i	$0.334753\pi$
$660$		0			0
$661$	9.55765e16	−	9.55765e16i	1.14589	−	1.14589i	0.158535	−	0.987353i	$-0.449323\pi$
$661$	9.55765e16	−	9.55765e16i	1.14589	−	1.14589i	0.987353	−	0.158535i	$-0.0506771\pi$
$662$		0			0
$663$	1.90173e17			2.23907
$664$		0			0
$665$		−	8.95315e16i		−	1.03525i
$666$		0			0
$667$	−8.61542e15	−	8.61542e15i	−0.0978412	−	0.0978412i
$668$		0			0
$669$	−2.74469e16	−	2.74469e16i	−0.306151	−	0.306151i
$670$		0			0
$671$			6.91287e16i			0.757396i
$672$		0			0
$673$	−5.46378e16			−0.588035			−0.294017	−	0.955800i	$-0.594992\pi$
$673$	−5.46378e16			−0.588035			−0.294017	+	0.955800i	$0.594992\pi$
$674$		0			0
$675$	1.06287e17	−	1.06287e17i	1.12372	−	1.12372i
$676$		0			0
$677$	2.78931e16	−	2.78931e16i	0.289710	−	0.289710i	−0.547255	−	0.836966i	$-0.684327\pi$
$677$	2.78931e16	−	2.78931e16i	0.289710	−	0.289710i	0.836966	+	0.547255i	$0.184327\pi$
$678$		0			0
$679$	3.25817e16			0.332472
$680$		0			0
$681$			1.75601e16i			0.176054i
$682$		0			0
$683$	7.97169e16	+	7.97169e16i	0.785283	+	0.785283i	0.980717	−	0.195434i	$-0.0626114\pi$
$683$	7.97169e16	+	7.97169e16i	0.785283	+	0.785283i	−0.195434	+	0.980717i	$0.562611\pi$
$684$		0			0
$685$	9.47671e16	+	9.47671e16i	0.917306	+	0.917306i
$686$		0			0
$687$			1.01521e16i			0.0965641i
$688$		0			0
$689$	−1.27014e17			−1.18723
$690$		0			0
$691$	4.93252e16	−	4.93252e16i	0.453107	−	0.453107i	−0.443278	−	0.896384i	$-0.646184\pi$
$691$	4.93252e16	−	4.93252e16i	0.453107	−	0.453107i	0.896384	+	0.443278i	$0.146184\pi$
$692$		0			0
$693$	2.15332e16	−	2.15332e16i	0.194406	−	0.194406i
$694$		0			0
$695$	2.35054e17			2.08573
$696$		0			0
$697$			2.44973e17i			2.13659i
$698$		0			0
$699$	−4.76234e16	−	4.76234e16i	−0.408280	−	0.408280i
$700$		0			0
$701$	−7.08488e16	−	7.08488e16i	−0.597069	−	0.597069i	0.342463	−	0.939531i	$-0.388739\pi$
$701$	−7.08488e16	−	7.08488e16i	−0.597069	−	0.597069i	−0.939531	+	0.342463i	$0.888739\pi$
$702$		0			0
$703$		−	2.98208e16i		−	0.247052i
$704$		0			0
$705$	1.02725e17			0.836647
$706$		0			0
$707$	−1.41772e17	+	1.41772e17i	−1.13521	+	1.13521i
$708$		0			0
$709$	−5.44097e16	+	5.44097e16i	−0.428351	+	0.428351i	−0.888066	−	0.459716i	$-0.847951\pi$
$709$	−5.44097e16	+	5.44097e16i	−0.428351	+	0.428351i	0.459716	+	0.888066i	$0.347951\pi$
$710$		0			0
$711$	9.94556e15			0.0769860
$712$		0			0
$713$			9.67202e16i			0.736173i
$714$		0			0
$715$	−2.76974e17	−	2.76974e17i	−2.07302	−	2.07302i
$716$		0			0
$717$	−9.61988e16	−	9.61988e16i	−0.708035	−	0.708035i
$718$		0			0
$719$			7.02231e16i			0.508284i	0.967167	+	0.254142i	$0.0817931\pi$
$719$			7.02231e16i			0.508284i	−0.967167	+	0.254142i	$0.918207\pi$
$720$		0			0
$721$	1.31567e17			0.936563
$722$		0			0
$723$	−4.63644e16	+	4.63644e16i	−0.324605	+	0.324605i
$724$		0			0
$725$	1.95212e16	−	1.95212e16i	0.134425	−	0.134425i
$726$		0			0
$727$	1.07723e17			0.729629			0.364814	−	0.931080i	$-0.381132\pi$
$727$	1.07723e17			0.729629			0.364814	+	0.931080i	$0.381132\pi$
$728$		0			0
$729$			1.64961e17i			1.09904i
$730$		0			0
$731$	−2.50759e16	−	2.50759e16i	−0.164344	−	0.164344i
$732$		0			0
$733$	−1.78490e17	−	1.78490e17i	−1.15077	−	1.15077i	−0.986398	−	0.164373i	$-0.947440\pi$
$733$	−1.78490e17	−	1.78490e17i	−1.15077	−	1.15077i	−0.164373	−	0.986398i	$-0.552560\pi$
$734$		0			0
$735$			5.06593e16i			0.321318i
$736$		0			0
$737$	−1.79845e17			−1.12226
$738$		0			0
$739$	−1.69064e17	+	1.69064e17i	−1.03797	+	1.03797i	−0.0387200	+	0.999250i	$0.512328\pi$
$739$	−1.69064e17	+	1.69064e17i	−1.03797	+	1.03797i	−0.999250	+	0.0387200i	$0.987672\pi$
$740$		0			0
$741$	1.26791e17	−	1.26791e17i	0.765913	−	0.765913i
$742$		0			0
$743$	−1.06591e17			−0.633561			−0.316780	−	0.948499i	$-0.602602\pi$
$743$	−1.06591e17			−0.633561			−0.316780	+	0.948499i	$0.602602\pi$
$744$		0			0
$745$		−	5.24423e16i		−	0.306721i
$746$		0			0
$747$	−7.92872e15	−	7.92872e15i	−0.0456331	−	0.0456331i
$748$		0			0
$749$	1.84075e17	+	1.84075e17i	1.04257	+	1.04257i
$750$		0			0
$751$		−	1.28217e17i		−	0.714673i	−0.933976	−	0.357337i	$-0.883685\pi$
$751$		−	1.28217e17i		−	0.714673i	0.933976	−	0.357337i	$-0.116315\pi$
$752$		0			0
$753$	−2.60515e17			−1.42910
$754$		0			0
$755$	3.19859e17	−	3.19859e17i	1.72694	−	1.72694i
$756$		0			0
$757$	−1.88639e17	+	1.88639e17i	−1.00243	+	1.00243i	−0.00243592	+	0.999997i	$0.500775\pi$
$757$	−1.88639e17	+	1.88639e17i	−1.00243	+	1.00243i	−0.999997	+	0.00243592i	$0.999225\pi$
$758$		0			0
$759$	−1.89967e17			−0.993635
$760$		0			0
$761$			2.68331e17i			1.38154i	0.723076	+	0.690769i	$0.242728\pi$
$761$			2.68331e17i			1.38154i	−0.723076	+	0.690769i	$0.757272\pi$
$762$		0			0
$763$	7.94614e16	+	7.94614e16i	0.402725	+	0.402725i
$764$		0			0
$765$	−9.96278e16	−	9.96278e16i	−0.497064	−	0.497064i
$766$		0			0
$767$			1.56606e17i			0.769193i
$768$		0			0
$769$	3.27355e17			1.58293			0.791463	−	0.611217i	$-0.209320\pi$
$769$	3.27355e17			1.58293			0.791463	+	0.611217i	$0.209320\pi$
$770$		0			0
$771$	−1.76357e17	+	1.76357e17i	−0.839587	+	0.839587i
$772$		0			0
$773$	4.98865e15	−	4.98865e15i	0.0233833	−	0.0233833i	−0.695318	−	0.718702i	$-0.744737\pi$
$773$	4.98865e15	−	4.98865e15i	0.0233833	−	0.0233833i	0.718702	+	0.695318i	$0.244737\pi$
$774$		0			0
$775$	−2.19153e17			−1.01143
$776$		0			0
$777$		−	5.27610e16i		−	0.239766i
$778$		0			0
$779$	1.63327e17	+	1.63327e17i	0.730858	+	0.730858i
$780$		0			0
$781$	−2.89924e17	−	2.89924e17i	−1.27755	−	1.27755i
$782$		0			0
$783$			3.25513e16i			0.141253i
$784$		0			0
$785$	−7.23480e16			−0.309178
$786$		0			0
$787$	−2.12572e17	+	2.12572e17i	−0.894659	+	0.894659i	−0.994957	−	0.100299i	$-0.968020\pi$
$787$	−2.12572e17	+	2.12572e17i	−0.894659	+	0.894659i	0.100299	+	0.994957i	$0.468020\pi$
$788$		0			0
$789$	−1.85109e17	+	1.85109e17i	−0.767303	+	0.767303i
$790$		0			0
$791$	−8.99226e15			−0.0367121
$792$		0			0
$793$		−	2.88363e17i		−	1.15958i
$794$		0			0
$795$	−1.66179e17	−	1.66179e17i	−0.658222	−	0.658222i
$796$		0			0
$797$	1.72760e17	+	1.72760e17i	0.674052	+	0.674052i	0.958648	−	0.284595i	$-0.0918592\pi$
$797$	1.72760e17	+	1.72760e17i	0.674052	+	0.674052i	−0.284595	+	0.958648i	$0.591859\pi$
$798$		0			0
$799$		−	2.57192e17i		−	0.988499i
$800$		0			0
$801$	−2.94812e16			−0.111622
$802$		0			0
$803$	−1.31097e17	+	1.31097e17i	−0.488988	+	0.488988i
$804$		0			0
$805$	2.79780e17	−	2.79780e17i	1.02811	−	1.02811i
$806$		0			0
$807$	3.96726e17			1.43631
$808$		0			0
$809$			4.00331e17i			1.42800i	0.700146	+	0.714000i	$0.253118\pi$
$809$			4.00331e17i			1.42800i	−0.700146	+	0.714000i	$0.746882\pi$
$810$		0			0
$811$	1.38580e17	+	1.38580e17i	0.487054	+	0.487054i	0.907375	−	0.420321i	$-0.138083\pi$
$811$	1.38580e17	+	1.38580e17i	0.487054	+	0.487054i	−0.420321	+	0.907375i	$0.638083\pi$
$812$		0			0
$813$	−2.25506e17	−	2.25506e17i	−0.780933	−	0.780933i
$814$		0			0
$815$			6.46626e17i			2.20652i
$816$		0			0
$817$	−3.34370e16			−0.112433
$818$		0			0
$819$	−8.98237e16	+	8.98237e16i	−0.297637	+	0.297637i
$820$		0			0
$821$	−1.86717e17	+	1.86717e17i	−0.609711	+	0.609711i	−0.942871	−	0.333159i	$-0.891885\pi$
$821$	−1.86717e17	+	1.86717e17i	−0.609711	+	0.609711i	0.333159	+	0.942871i	$0.391885\pi$
$822$		0			0
$823$	−1.28345e17			−0.413028			−0.206514	−	0.978444i	$-0.566212\pi$
$823$	−1.28345e17			−0.413028			−0.206514	+	0.978444i	$0.566212\pi$
$824$		0			0
$825$		−	4.30435e17i		−	1.36516i
$826$		0			0
$827$	−1.19983e17	−	1.19983e17i	−0.375047	−	0.375047i	0.494265	−	0.869312i	$-0.335437\pi$
$827$	−1.19983e17	−	1.19983e17i	−0.375047	−	0.375047i	−0.869312	+	0.494265i	$0.835437\pi$
$828$		0			0
$829$	−5.19028e16	−	5.19028e16i	−0.159906	−	0.159906i	0.622619	−	0.782525i	$-0.286069\pi$
$829$	−5.19028e16	−	5.19028e16i	−0.159906	−	0.159906i	−0.782525	+	0.622619i	$0.786069\pi$
$830$		0			0
$831$		−	3.96218e17i		−	1.20317i
$832$		0			0
$833$	1.26835e17			0.379637
$834$		0			0
$835$	3.24068e17	−	3.24068e17i	0.956131	−	0.956131i
$836$		0			0
$837$	1.82717e17	−	1.82717e17i	0.531405	−	0.531405i
$838$		0			0
$839$	−2.30886e17			−0.661950			−0.330975	−	0.943640i	$-0.607378\pi$
$839$	−2.30886e17			−0.661950			−0.330975	+	0.943640i	$0.607378\pi$
$840$		0			0
$841$		−	3.47836e17i		−	0.983103i
$842$		0			0
$843$	−4.00588e17	−	4.00588e17i	−1.11618	−	1.11618i
$844$		0			0
$845$	7.51436e17	+	7.51436e17i	2.06420	+	2.06420i
$846$		0			0
$847$		−	7.07952e16i		−	0.191736i
$848$		0			0
$849$	4.16960e17			1.11339
$850$		0			0
$851$	9.31879e16	−	9.31879e16i	0.245348	−	0.245348i
$852$		0			0
$853$	2.41607e17	−	2.41607e17i	0.627213	−	0.627213i	−0.320153	−	0.947366i	$-0.603734\pi$
$853$	2.41607e17	−	2.41607e17i	0.627213	−	0.627213i	0.947366	+	0.320153i	$0.103734\pi$
$854$		0			0
$855$	−1.32847e17			−0.340059
$856$		0			0
$857$			4.42667e17i			1.11736i	0.829384	+	0.558679i	$0.188692\pi$
$857$			4.42667e17i			1.11736i	−0.829384	+	0.558679i	$0.811308\pi$
$858$		0			0
$859$	4.40796e17	+	4.40796e17i	1.09718	+	1.09718i	0.994739	+	0.102444i	$0.0326662\pi$
$859$	4.40796e17	+	4.40796e17i	1.09718	+	1.09718i	0.102444	+	0.994739i	$0.467334\pi$
$860$		0			0
$861$	2.88969e17	+	2.88969e17i	0.709305	+	0.709305i
$862$		0			0
$863$			1.23647e17i			0.299309i	0.988738	+	0.149654i	$0.0478161\pi$
$863$			1.23647e17i			0.299309i	−0.988738	+	0.149654i	$0.952184\pi$
$864$		0			0
$865$	−6.80070e17			−1.62352
$866$		0			0
$867$	3.69160e17	−	3.69160e17i	0.869161	−	0.869161i
$868$		0			0
$869$	9.05715e16	−	9.05715e16i	0.210316	−	0.210316i
$870$		0			0
$871$	7.50204e17			1.71819
$872$		0			0
$873$		−	4.83446e16i		−	0.109210i
$874$		0			0
$875$	2.00464e17	+	2.00464e17i	0.446672	+	0.446672i
$876$		0			0
$877$	−7.92222e16	−	7.92222e16i	−0.174120	−	0.174120i	0.614667	−	0.788787i	$-0.289291\pi$
$877$	−7.92222e16	−	7.92222e16i	−0.174120	−	0.174120i	−0.788787	+	0.614667i	$0.789291\pi$
$878$		0			0
$879$			1.05450e16i			0.0228620i
$880$		0			0
$881$	−3.79725e17			−0.812107			−0.406054	−	0.913849i	$-0.633095\pi$
$881$	−3.79725e17			−0.812107			−0.406054	+	0.913849i	$0.633095\pi$
$882$		0			0
$883$	7.71156e16	−	7.71156e16i	0.162696	−	0.162696i	−0.621064	−	0.783760i	$-0.713299\pi$
$883$	7.71156e16	−	7.71156e16i	0.162696	−	0.162696i	0.783760	+	0.621064i	$0.213299\pi$
$884$		0			0
$885$	−2.04895e17	+	2.04895e17i	−0.426453	+	0.426453i
$886$		0			0
$887$	4.26595e17			0.875939			0.437970	−	0.898990i	$-0.355698\pi$
$887$	4.26595e17			0.875939			0.437970	+	0.898990i	$0.355698\pi$
$888$		0			0
$889$		−	7.12645e16i		−	0.144365i
$890$		0			0
$891$	2.47126e17	+	2.47126e17i	0.493914	+	0.493914i
$892$		0			0
$893$	−1.71473e17	−	1.71473e17i	−0.338133	−	0.338133i
$894$		0			0
$895$		−	7.23434e17i		−	1.40754i
$896$		0			0
$897$	7.92426e17			1.52126
$898$		0			0
$899$	3.35588e16	−	3.35588e16i	0.0635695	−	0.0635695i
$900$		0			0
$901$	−4.16059e17	+	4.16059e17i	−0.777690	+	0.777690i
$902$		0			0
$903$	−5.91589e16			−0.109117
$904$		0			0
$905$		−	1.24957e18i		−	2.27442i
$906$		0			0
$907$	−3.68718e17	−	3.68718e17i	−0.662294	−	0.662294i	0.293626	−	0.955920i	$-0.405138\pi$
$907$	−3.68718e17	−	3.68718e17i	−0.662294	−	0.662294i	−0.955920	+	0.293626i	$0.905138\pi$
$908$		0			0
$909$	2.10361e17	+	2.10361e17i	0.372891	+	0.372891i
$910$		0			0
$911$		−	4.36461e17i		−	0.763546i	−0.924256	−	0.381773i	$-0.875314\pi$
$911$		−	4.36461e17i		−	0.763546i	0.924256	−	0.381773i	$-0.124686\pi$
$912$		0			0
$913$	−1.44409e17			−0.249328
$914$		0			0
$915$	3.77279e17	−	3.77279e17i	0.642889	−	0.642889i
$916$		0			0
$917$	−3.57147e17	+	3.57147e17i	−0.600664	+	0.600664i
$918$		0			0
$919$	−8.75854e17			−1.45391			−0.726957	−	0.686683i	$-0.759066\pi$
$919$	−8.75854e17			−1.45391			−0.726957	+	0.686683i	$0.759066\pi$
$920$		0			0
$921$		−	9.59310e17i		−	1.57181i
$922$		0			0
$923$	1.20939e18	+	1.20939e18i	1.95594	+	1.95594i
$924$		0			0
$925$	2.11150e17	+	2.11150e17i	0.337085	+	0.337085i
$926$		0			0
$927$		−	1.95219e17i		−	0.307641i
$928$		0			0
$929$	7.33273e17			1.14070			0.570350	−	0.821402i	$-0.306808\pi$
$929$	7.33273e17			1.14070			0.570350	+	0.821402i	$0.306808\pi$
$930$		0			0
$931$	8.45627e16	−	8.45627e16i	0.129862	−	0.129862i
$932$		0			0
$933$	−3.84665e17	+	3.84665e17i	−0.583166	+	0.583166i
$934$		0			0
$935$	−1.81457e18			−2.71583
$936$		0			0
$937$			6.44896e17i			0.952910i	0.879199	+	0.476455i	$0.158078\pi$
$937$			6.44896e17i			0.952910i	−0.879199	+	0.476455i	$0.841922\pi$
$938$		0			0
$939$	−7.13334e17	−	7.13334e17i	−1.04064	−	1.04064i
$940$		0			0
$941$	−5.80024e16	−	5.80024e16i	−0.0835427	−	0.0835427i	0.664101	−	0.747643i	$-0.268815\pi$
$941$	−5.80024e16	−	5.80024e16i	−0.0835427	−	0.0835427i	−0.747643	+	0.664101i	$0.768815\pi$
$942$		0			0
$943$			1.02077e18i			1.45164i
$944$		0			0
$945$	−1.05708e18			−1.48428
$946$		0			0
$947$	1.69724e17	−	1.69724e17i	0.235312	−	0.235312i	−0.579594	−	0.814905i	$-0.696789\pi$
$947$	1.69724e17	−	1.69724e17i	0.235312	−	0.235312i	0.814905	+	0.579594i	$0.196789\pi$
$948$		0			0
$949$	5.46856e17	−	5.46856e17i	0.748644	−	0.748644i
$950$		0			0
$951$	−6.54588e16			−0.0884882
$952$		0			0
$953$			4.21955e17i			0.563260i	0.959523	+	0.281630i	$0.0908750\pi$
$953$			4.21955e17i			0.563260i	−0.959523	+	0.281630i	$0.909125\pi$
$954$		0			0
$955$	8.17786e17	+	8.17786e17i	1.07800	+	1.07800i
$956$		0			0
$957$	6.59124e16	+	6.59124e16i	0.0858016	+	0.0858016i
$958$		0			0
$959$		−	5.59759e17i		−	0.719597i
$960$		0			0
$961$	4.10918e17			0.521693
$962$		0			0
$963$	2.73130e17	−	2.73130e17i	0.342461	−	0.342461i
$964$		0			0
$965$	1.80161e17	−	1.80161e17i	0.223099	−	0.223099i
$966$		0			0
$967$	−6.57665e17			−0.804351			−0.402175	−	0.915563i	$-0.631746\pi$
$967$	−6.57665e17			−0.804351			−0.402175	+	0.915563i	$0.631746\pi$
$968$		0			0
$969$		−	8.30657e17i		−	1.00341i
$970$		0			0
$971$	−6.38230e17	−	6.38230e17i	−0.761486	−	0.761486i	0.215105	−	0.976591i	$-0.430991\pi$
$971$	−6.38230e17	−	6.38230e17i	−0.761486	−	0.761486i	−0.976591	+	0.215105i	$0.930991\pi$
$972$		0			0
$973$	−6.94194e17	−	6.94194e17i	−0.818095	−	0.818095i
$974$		0			0
$975$			1.79552e18i			2.09007i
$976$		0			0
$977$	1.50754e18			1.73341			0.866705	−	0.498821i	$-0.166233\pi$
$977$	1.50754e18			1.73341			0.866705	+	0.498821i	$0.166233\pi$
$978$		0			0
$979$	−2.68477e17	+	2.68477e17i	−0.304938	+	0.304938i
$980$		0			0
$981$	1.17905e17	−	1.17905e17i	0.132287	−	0.132287i
$982$		0			0
$983$	1.58461e18			1.75631			0.878153	−	0.478380i	$-0.158776\pi$
$983$	1.58461e18			1.75631			0.878153	+	0.478380i	$0.158776\pi$
$984$		0			0
$985$			4.64997e17i			0.509134i
$986$		0			0
$987$	−3.03382e17	−	3.03382e17i	−0.328161	−	0.328161i
$988$		0			0
$989$	−1.04488e17	−	1.04488e17i	−0.111658	−	0.111658i
$990$		0			0
$991$			5.67558e17i			0.599195i	0.954066	+	0.299598i	$0.0968524\pi$
$991$			5.67558e17i			0.599195i	−0.954066	+	0.299598i	$0.903148\pi$
$992$		0			0
$993$	−8.20883e16			−0.0856221
$994$		0			0
$995$	−7.16559e17	+	7.16559e17i	−0.738437	+	0.738437i
$996$		0			0
$997$	−1.08804e18	+	1.08804e18i	−1.10783	+	1.10783i	−0.114394	+	0.993435i	$0.536493\pi$
$997$	−1.08804e18	+	1.08804e18i	−1.10783	+	1.10783i	−0.993435	+	0.114394i	$0.963507\pi$
$998$		0			0
$999$	−3.52088e17			−0.354208

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	64.13.f.a.47.17		46
4.3	odd	2		16.13.f.a.3.16	✓	46
8.3	odd	2		128.13.f.b.95.17		46
8.5	even	2		128.13.f.a.95.7		46
16.3	odd	4		128.13.f.a.31.7		46
16.5	even	4		16.13.f.a.11.16	yes	46
16.11	odd	4	inner	64.13.f.a.15.17		46
16.13	even	4		128.13.f.b.31.17		46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.13.f.a.3.16	✓	46	4.3	odd	2
16.13.f.a.11.16	yes	46	16.5	even	4
64.13.f.a.15.17		46	16.11	odd	4	inner
64.13.f.a.47.17		46	1.1	even	1	trivial
128.13.f.a.31.7		46	16.3	odd	4
128.13.f.a.95.7		46	8.5	even	2
128.13.f.b.31.17		46	16.13	even	4
128.13.f.b.95.17		46	8.3	odd	2

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:	\( k \)	\(=\)	\( 13 \)
Character orbit:	\([\chi]\)	\(=\)	64.f (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(435.597 - 435.597i) q^{3} +(17337.6 - 17337.6i) q^{5} -102408. q^{7} +151952. i q^{9} +O(q^{10})\)	\(q+(435.597 - 435.597i) q^{3} +(17337.6 - 17337.6i) q^{5} -102408. q^{7} +151952. i q^{9} +(1.38379e6 + 1.38379e6i) q^{11} +(-5.77232e6 - 5.77232e6i) q^{13} -1.51044e7i q^{15} -3.78167e7 q^{17} +(-2.52129e7 + 2.52129e7i) q^{19} +(-4.46085e7 + 4.46085e7i) q^{21} -1.57577e8 q^{23} -3.57046e8i q^{25} +(2.97684e8 + 2.97684e8i) q^{27} +(5.46743e7 + 5.46743e7i) q^{29} -6.13795e8i q^{31} +1.20555e9 q^{33} +(-1.77551e9 + 1.77551e9i) q^{35} +(-5.91379e8 + 5.91379e8i) q^{37} -5.02881e9 q^{39} -6.47790e9i q^{41} +(6.63091e8 + 6.63091e8i) q^{43} +(2.63449e9 + 2.63449e9i) q^{45} +6.80100e9i q^{47} -3.35394e9 q^{49} +(-1.64728e10 + 1.64728e10i) q^{51} +(1.10020e10 - 1.10020e10i) q^{53} +4.79832e10 q^{55} +2.19653e10i q^{57} +(-1.35652e10 - 1.35652e10i) q^{59} +(2.49781e10 + 2.49781e10i) q^{61} -1.55611e10i q^{63} -2.00157e11 q^{65} +(-6.49828e10 + 6.49828e10i) q^{67} +(-6.86401e10 + 6.86401e10i) q^{69} -2.09515e11 q^{71} +9.47375e10i q^{73} +(-1.55528e11 - 1.55528e11i) q^{75} +(-1.41711e11 - 1.41711e11i) q^{77} -6.54519e10i q^{79} +1.78586e11 q^{81} +(-5.21790e10 + 5.21790e10i) q^{83} +(-6.55652e11 + 6.55652e11i) q^{85} +4.76319e10 q^{87} +1.94016e11i q^{89} +(5.91131e11 + 5.91131e11i) q^{91} +(-2.67367e11 - 2.67367e11i) q^{93} +8.74265e11i q^{95} -3.18157e11 q^{97} +(-2.10270e11 + 2.10270e11i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q + 2 q^{3} - 2 q^{5} + 4 q^{7}+O(q^{10}) \) 46 * q + 2 * q^3 - 2 * q^5 + 4 * q^7	\( 46 q + 2 q^{3} - 2 q^{5} + 4 q^{7} - 2668318 q^{11} - 2 q^{13} - 4 q^{17} - 51868606 q^{19} - 1062884 q^{21} - 298270076 q^{23} - 970053760 q^{27} + 704570398 q^{29} - 4 q^{33} + 3815032900 q^{35} + 364298398 q^{37} - 15553507196 q^{39} - 363863518 q^{43} + 489344130 q^{45} + 67229109258 q^{49} - 33806024892 q^{51} - 11168756642 q^{53} + 74491808260 q^{55} - 104334793054 q^{59} - 106371743810 q^{61} - 75186419620 q^{65} + 43778233922 q^{67} - 214340079908 q^{69} + 188251854340 q^{71} - 308961520610 q^{75} - 341607754084 q^{77} - 941431788274 q^{81} + 1025936323202 q^{83} + 436332718748 q^{85} - 2368412421756 q^{87} + 2028231531652 q^{91} + 1534541270080 q^{93} - 4 q^{97} - 4950023059646 q^{99}+O(q^{100}) \) 46 * q + 2 * q^3 - 2 * q^5 + 4 * q^7 - 2668318 * q^11 - 2 * q^13 - 4 * q^17 - 51868606 * q^19 - 1062884 * q^21 - 298270076 * q^23 - 970053760 * q^27 + 704570398 * q^29 - 4 * q^33 + 3815032900 * q^35 + 364298398 * q^37 - 15553507196 * q^39 - 363863518 * q^43 + 489344130 * q^45 + 67229109258 * q^49 - 33806024892 * q^51 - 11168756642 * q^53 + 74491808260 * q^55 - 104334793054 * q^59 - 106371743810 * q^61 - 75186419620 * q^65 + 43778233922 * q^67 - 214340079908 * q^69 + 188251854340 * q^71 - 308961520610 * q^75 - 341607754084 * q^77 - 941431788274 * q^81 + 1025936323202 * q^83 + 436332718748 * q^85 - 2368412421756 * q^87 + 2028231531652 * q^91 + 1534541270080 * q^93 - 4 * q^97 - 4950023059646 * q^99

Introduction

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