LMFDB - Embedded newform 126.15.n.b.19.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,15,Mod(19,126)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(126, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

N = Newforms(chi, 15, names="a")

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

chi := DirichletCharacter("126.19");

S:= CuspForms(chi, 15);

N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 15 $
Character orbit:	$[\chi]$	$=$	126.n (of order $6$, degree $2$, 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:	$156.654499871$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{19} - 6266655317 x^{18} - 51228207045822 x^{17} + \cdots + 97\!\cdots\!27 $ x^20 - 2x^19 - 6266655317x^18 - 51228207045822x^17 + 15632174634638073641x^16 + 254684633517032380938004x^15 - 18641412845359139776075675486x^14 - 477571169127028120036866596045468x^13 + 9165819466821413838771093559300017421x^12 + 405947286923110068087058118780824806772658x^11 + 739448089551189640637703741877466343356995985x^10 - 139710060599142303599962415929172512032084308797226x^9 - 2013088304155230296127352983299598764263193749426936637x^8 + 4043211648141552501115466515019863014112084248309070599140x^7 + 384627125543671604951529479147020465473199052634689044122397718x^6 + 4648063003246363071142340187413632060339504250286006491643548492900x^5 + 28664306626536517066296806161594580124740253706715570013576539220920315x^4 + 101846372911136032165079965835731746818439645517822594346228424596885073774x^3 + 207779418028766989097691535431559021517211719670480006243871545588781049518351x^2 + 223799219441154401220423912429803564272981178757848425527517642795531527123311570*x + 97951911868488203191999217059221108691676799666671130108921761896633024062553583527
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{76}\cdot 3^{22}\cdot 7^{14} $
Twist minimal:	no (minimal twist has level 14)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.2
Root			$-12795.2 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	126.19
Dual form			126.15.n.b.73.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-45.2548 + 78.3837i) q^{2} +(-4096.00 - 7094.48i) q^{4} +(-38553.6 - 22259.0i) q^{5} +(725749. - 389245. i) q^{7} +741455. q^{8} +O(q^{10})$	\(q+(-45.2548 + 78.3837i) q^{2} +(-4096.00 - 7094.48i) q^{4} +(-38553.6 - 22259.0i) q^{5} +(725749. - 389245. i) q^{7} +741455. q^{8} +(3.48948e6 - 2.01465e6i) q^{10} +(-2.67149e6 - 4.62715e6i) q^{11} +7.96385e7i q^{13} +(-2.33322e6 + 7.45021e7i) q^{14} +(-3.35544e7 + 5.81180e7i) q^{16} +(-1.07709e8 + 6.21860e7i) q^{17} +(-1.05852e9 - 6.11137e8i) q^{19} +3.64691e8i q^{20} +4.83591e8 q^{22} +(1.96995e9 - 3.41205e9i) q^{23} +(-2.06084e9 - 3.56947e9i) q^{25} +(-6.24236e9 - 3.60403e9i) q^{26} +(-5.73416e9 - 3.55447e9i) q^{28} +9.13120e9 q^{29} +(2.41487e10 - 1.39423e10i) q^{31} +(-3.03700e9 - 5.26024e9i) q^{32} -1.12569e10i q^{34} +(-3.66444e10 - 1.14762e9i) q^{35} +(-8.71230e10 + 1.50902e11i) q^{37} +(9.58063e10 - 5.53138e10i) q^{38} +(-2.85858e10 - 1.65040e10i) q^{40} -1.93428e11i q^{41} +2.74771e11 q^{43} +(-2.18848e10 + 3.79056e10i) q^{44} +(1.78299e11 + 3.08824e11i) q^{46} +(6.24524e11 + 3.60569e11i) q^{47} +(3.75200e11 - 5.64988e11i) q^{49} +3.73051e11 q^{50} +(5.64994e11 - 3.26199e11i) q^{52} +(-8.95694e11 - 1.55139e12i) q^{53} +2.37858e11i q^{55} +(5.38110e11 - 2.88607e11i) q^{56} +(-4.13231e11 + 7.15737e11i) q^{58} +(-3.83391e12 + 2.21351e12i) q^{59} +(3.55754e12 + 2.05395e12i) q^{61} +2.52382e12i q^{62} +5.49756e11 q^{64} +(1.77267e12 - 3.07035e12i) q^{65} +(-4.21267e11 - 7.29656e11i) q^{67} +(8.82354e11 + 5.09427e11i) q^{68} +(1.74829e12 - 2.82039e12i) q^{70} -6.19751e12 q^{71} +(-8.71841e12 + 5.03358e12i) q^{73} +(-7.88548e12 - 1.36580e13i) q^{74} +1.00129e13i q^{76} +(-3.73993e12 - 2.31829e12i) q^{77} +(-1.88187e12 + 3.25949e12i) q^{79} +(2.58729e12 - 1.49377e12i) q^{80} +(1.51616e13 + 8.75354e12i) q^{82} -7.24696e12i q^{83} +5.53678e12 q^{85} +(-1.24347e13 + 2.15375e13i) q^{86} +(-1.98079e12 - 3.43083e12i) q^{88} +(1.74616e13 + 1.00814e13i) q^{89} +(3.09988e13 + 5.77975e13i) q^{91} -3.22756e13 q^{92} +(-5.65255e13 + 3.26350e13i) q^{94} +(2.72065e13 + 4.71231e13i) q^{95} +4.36526e12i q^{97} +(2.73062e13 + 5.49780e13i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 81920 q^{4} - 3354 q^{5} + 1455616 q^{7}+O(q^{10}) $ 20 * q - 81920 * q^4 - 3354 * q^5 + 1455616 * q^7	\( 20 q - 81920 q^{4} - 3354 q^{5} + 1455616 q^{7} - 3933696 q^{10} - 8400426 q^{11} + 114693888 q^{14} - 671088640 q^{16} - 2180481042 q^{17} - 3919727442 q^{19} + 5394565632 q^{22} + 6905098386 q^{23} + 14165082644 q^{25} - 12652202496 q^{26} - 17334943744 q^{28} - 27884908704 q^{29} + 45638710782 q^{31} + 18274367202 q^{35} - 27026027926 q^{37} + 354043974912 q^{38} + 32224837632 q^{40} + 726682953656 q^{43} - 68816289792 q^{44} - 286664984832 q^{46} + 2044625353338 q^{47} + 2939974016204 q^{49} - 1161106642944 q^{50} + 1314350333952 q^{52} - 1546271487546 q^{53} - 1720927125504 q^{56} - 2365863040512 q^{58} + 6798944731566 q^{59} - 2214453865554 q^{61} + 10995116277760 q^{64} - 7516703932836 q^{65} - 4655820763226 q^{67} + 17862500696064 q^{68} + 20497461621504 q^{70} - 96606137494152 q^{71} - 65348368908666 q^{73} + 566532483072 q^{74} - 77525241691422 q^{77} - 60517474082978 q^{79} + 225083129856 q^{80} - 43979002397184 q^{82} + 416326699526124 q^{85} - 2363335174656 q^{86} - 22096140828672 q^{88} + 237147002561826 q^{89} + 203506111374408 q^{91} - 113133131956224 q^{92} - 221058962902272 q^{94} - 25202514515490 q^{95} - 165606984015360 q^{98}+O(q^{100}) \) 20 * q - 81920 * q^4 - 3354 * q^5 + 1455616 * q^7 - 3933696 * q^10 - 8400426 * q^11 + 114693888 * q^14 - 671088640 * q^16 - 2180481042 * q^17 - 3919727442 * q^19 + 5394565632 * q^22 + 6905098386 * q^23 + 14165082644 * q^25 - 12652202496 * q^26 - 17334943744 * q^28 - 27884908704 * q^29 + 45638710782 * q^31 + 18274367202 * q^35 - 27026027926 * q^37 + 354043974912 * q^38 + 32224837632 * q^40 + 726682953656 * q^43 - 68816289792 * q^44 - 286664984832 * q^46 + 2044625353338 * q^47 + 2939974016204 * q^49 - 1161106642944 * q^50 + 1314350333952 * q^52 - 1546271487546 * q^53 - 1720927125504 * q^56 - 2365863040512 * q^58 + 6798944731566 * q^59 - 2214453865554 * q^61 + 10995116277760 * q^64 - 7516703932836 * q^65 - 4655820763226 * q^67 + 17862500696064 * q^68 + 20497461621504 * q^70 - 96606137494152 * q^71 - 65348368908666 * q^73 + 566532483072 * q^74 - 77525241691422 * q^77 - 60517474082978 * q^79 + 225083129856 * q^80 - 43979002397184 * q^82 + 416326699526124 * q^85 - 2363335174656 * q^86 - 22096140828672 * q^88 + 237147002561826 * q^89 + 203506111374408 * q^91 - 113133131956224 * q^92 - 221058962902272 * q^94 - 25202514515490 * q^95 - 165606984015360 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−45.2548	+	78.3837i	−0.353553	+	0.612372i
$2$	−45.2548	+	78.3837i	−0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−4096.00	−	7094.48i	−0.250000	−	0.433013i
$5$	−38553.6	−	22259.0i	−0.493487	−	0.284915i	0.232533	−	0.972588i	$-0.425299\pi$
$5$	−38553.6	−	22259.0i	−0.493487	−	0.284915i	−0.726020	+	0.687674i	$0.758632\pi$
$6$		0			0
$7$	725749.	−	389245.i	0.881252	−	0.472646i
$7$	725749.	−	389245.i	0.881252	−	0.472646i
$8$	741455.			0.353553
$9$		0			0
$10$	3.48948e6	−	2.01465e6i	0.348948	−	0.201465i
$11$	−2.67149e6	−	4.62715e6i	−0.137090	−	0.237446i	0.789304	−	0.614002i	$-0.210441\pi$
$11$	−2.67149e6	−	4.62715e6i	−0.137090	−	0.237446i	−0.926394	+	0.376556i	$0.877108\pi$
$12$		0			0
$13$			7.96385e7i			1.26917i	0.772854	+	0.634584i	$0.218829\pi$
$13$			7.96385e7i			1.26917i	−0.772854	+	0.634584i	$0.781171\pi$
$14$	−2.33322e6	+	7.45021e7i	−0.0221340	+	0.706760i
$15$		0			0
$16$	−3.35544e7	+	5.81180e7i	−0.125000	+	0.216506i
$17$	−1.07709e8	+	6.21860e7i	−0.262489	+	0.151548i	−0.625469	−	0.780249i	$-0.715092\pi$
$17$	−1.07709e8	+	6.21860e7i	−0.262489	+	0.151548i	0.362981	+	0.931797i	$0.381759\pi$
$18$		0			0
$19$	−1.05852e9	−	6.11137e8i	−1.18420	−	0.683696i	−0.227215	−	0.973845i	$-0.572962\pi$
$19$	−1.05852e9	−	6.11137e8i	−1.18420	−	0.683696i	−0.956982	+	0.290148i	$0.906295\pi$
$20$			3.64691e8i			0.284915i
$21$		0			0
$22$	4.83591e8			0.193874
$23$	1.96995e9	−	3.41205e9i	0.578575	−	1.00212i	−0.417068	−	0.908875i	$-0.636942\pi$
$23$	1.96995e9	−	3.41205e9i	0.578575	−	1.00212i	0.995643	−	0.0932466i	$-0.0297245\pi$
$24$		0			0
$25$	−2.06084e9	−	3.56947e9i	−0.337647	−	0.584822i
$26$	−6.24236e9	−	3.60403e9i	−0.777204	−	0.448719i
$27$		0			0
$28$	−5.73416e9	−	3.55447e9i	−0.424975	−	0.263432i
$29$	9.13120e9			0.529349			0.264674	−	0.964338i	$-0.414736\pi$
$29$	9.13120e9			0.529349			0.264674	+	0.964338i	$0.414736\pi$
$30$		0			0
$31$	2.41487e10	−	1.39423e10i	0.877732	−	0.506759i	0.00782184	−	0.999969i	$-0.497510\pi$
$31$	2.41487e10	−	1.39423e10i	0.877732	−	0.506759i	0.869910	+	0.493211i	$0.164177\pi$
$32$	−3.03700e9	−	5.26024e9i	−0.0883883	−	0.153093i
$33$		0			0
$34$		−	1.12569e10i		−	0.214321i
$35$	−3.66444e10	−	1.14762e9i	−0.569550	−	0.0178369i
$36$		0			0
$37$	−8.71230e10	+	1.50902e11i	−0.917743	+	1.58958i	−0.114907	+	0.993376i	$0.536657\pi$
$37$	−8.71230e10	+	1.50902e11i	−0.917743	+	1.58958i	−0.802835	+	0.596201i	$0.796676\pi$
$38$	9.58063e10	−	5.53138e10i	0.837354	−	0.483446i
$39$		0			0
$40$	−2.85858e10	−	1.65040e10i	−0.174474	−	0.100733i
$41$		−	1.93428e11i		−	0.993189i	−0.867983	−	0.496595i	$-0.834584\pi$
$41$		−	1.93428e11i		−	0.993189i	0.867983	−	0.496595i	$-0.165416\pi$
$42$		0			0
$43$	2.74771e11			1.01086			0.505430	−	0.862867i	$-0.331334\pi$
$43$	2.74771e11			1.01086			0.505430	+	0.862867i	$0.331334\pi$
$44$	−2.18848e10	+	3.79056e10i	−0.0685448	+	0.118723i
$45$		0			0
$46$	1.78299e11	+	3.08824e11i	0.409115	+	0.708607i
$47$	6.24524e11	+	3.60569e11i	1.23272	+	0.711711i	0.967596	−	0.252504i	$-0.0812540\pi$
$47$	6.24524e11	+	3.60569e11i	1.23272	+	0.711711i	0.265123	+	0.964215i	$0.414587\pi$
$48$		0			0
$49$	3.75200e11	−	5.64988e11i	0.553211	−	0.833041i
$50$	3.73051e11			0.477505
$51$		0			0
$52$	5.64994e11	−	3.26199e11i	0.549566	−	0.317292i
$53$	−8.95694e11	−	1.55139e12i	−0.762480	−	1.32065i	−0.941569	−	0.336821i	$-0.890648\pi$
$53$	−8.95694e11	−	1.55139e12i	−0.762480	−	1.32065i	0.179089	−	0.983833i	$-0.442685\pi$
$54$		0			0
$55$			2.37858e11i			0.156235i
$56$	5.38110e11	−	2.88607e11i	0.311570	−	0.167106i
$57$		0			0
$58$	−4.13231e11	+	7.15737e11i	−0.187153	+	0.324159i
$59$	−3.83391e12	+	2.21351e12i	−1.54056	+	0.889441i	−0.541753	+	0.840538i	$0.682239\pi$
$59$	−3.83391e12	+	2.21351e12i	−1.54056	+	0.889441i	−0.998804	+	0.0489034i	$0.984427\pi$
$60$		0			0
$61$	3.55754e12	+	2.05395e12i	1.13199	+	0.653553i	0.944434	−	0.328702i	$-0.106611\pi$
$61$	3.55754e12	+	2.05395e12i	1.13199	+	0.653553i	0.187553	+	0.982254i	$0.439944\pi$
$62$			2.52382e12i			0.716665i
$63$		0			0
$64$	5.49756e11			0.125000
$65$	1.77267e12	−	3.07035e12i	0.361605	−	0.626318i
$66$		0			0
$67$	−4.21267e11	−	7.29656e11i	−0.0695078	−	0.120391i	0.829177	−	0.558986i	$-0.188810\pi$
$67$	−4.21267e11	−	7.29656e11i	−0.0695078	−	0.120391i	−0.898685	+	0.438595i	$0.855476\pi$
$68$	8.82354e11	+	5.09427e11i	0.131244	+	0.0757740i
$69$		0			0
$70$	1.74829e12	−	2.82039e12i	0.212289	−	0.342470i
$71$	−6.19751e12			−0.681410			−0.340705	−	0.940170i	$-0.610666\pi$
$71$	−6.19751e12			−0.681410			−0.340705	+	0.940170i	$0.610666\pi$
$72$		0			0
$73$	−8.71841e12	+	5.03358e12i	−0.789182	+	0.455635i	−0.839675	−	0.543090i	$-0.817254\pi$
$73$	−8.71841e12	+	5.03358e12i	−0.789182	+	0.455635i	0.0504924	+	0.998724i	$0.483921\pi$
$74$	−7.88548e12	−	1.36580e13i	−0.648942	−	1.12400i
$75$		0			0
$76$			1.00129e13i			0.683696i
$77$	−3.73993e12	−	2.31829e12i	−0.233039	−	0.144455i
$78$		0			0
$79$	−1.88187e12	+	3.25949e12i	−0.0979939	+	0.169730i	−0.910854	−	0.412728i	$-0.864576\pi$
$79$	−1.88187e12	+	3.25949e12i	−0.0979939	+	0.169730i	0.812860	+	0.582459i	$0.197909\pi$
$80$	2.58729e12	−	1.49377e12i	0.123372	−	0.0712286i
$81$		0			0
$82$	1.51616e13	+	8.75354e12i	0.608202	+	0.351145i
$83$		−	7.24696e12i		−	0.267060i	−0.991045	−	0.133530i	$-0.957369\pi$
$83$		−	7.24696e12i		−	0.267060i	0.991045	−	0.133530i	$-0.0426313\pi$
$84$		0			0
$85$	5.53678e12			0.172713
$86$	−1.24347e13	+	2.15375e13i	−0.357393	+	0.619023i
$87$		0			0
$88$	−1.98079e12	−	3.43083e12i	−0.0484685	−	0.0839499i
$89$	1.74616e13	+	1.00814e13i	0.394778	+	0.227925i	0.684228	−	0.729268i	$-0.260139\pi$
$89$	1.74616e13	+	1.00814e13i	0.394778	+	0.227925i	−0.289450	+	0.957193i	$0.593472\pi$
$90$		0			0
$91$	3.09988e13	+	5.77975e13i	0.599868	+	1.11846i
$92$	−3.22756e13			−0.578575
$93$		0			0
$94$	−5.65255e13	+	3.26350e13i	−0.871664	+	0.503256i
$95$	2.72065e13	+	4.71231e13i	0.389590	+	0.674790i
$96$		0			0
$97$			4.36526e12i			0.0540266i	0.999635	+	0.0270133i	$0.00859964\pi$
$97$			4.36526e12i			0.0540266i	−0.999635	+	0.0270133i	$0.991400\pi$
$98$	2.73062e13	+	5.49780e13i	0.314542	+	0.633296i
$99$		0			0
$100$	−1.68824e13	+	2.92411e13i	−0.168824	+	0.292411i
$101$	6.26219e13	−	3.61548e13i	0.584085	−	0.337222i	−0.178670	−	0.983909i	$-0.557179\pi$
$101$	6.26219e13	−	3.61548e13i	0.584085	−	0.337222i	0.762755	+	0.646687i	$0.223846\pi$
$102$		0			0
$103$	−5.63391e13	−	3.25274e13i	−0.458088	−	0.264477i	0.253152	−	0.967427i	$-0.418533\pi$
$103$	−5.63391e13	−	3.25274e13i	−0.458088	−	0.264477i	−0.711240	+	0.702949i	$0.751866\pi$
$104$			5.90484e13i			0.448719i
$105$		0			0
$106$	1.62138e14			1.07831
$107$	−9.17359e13	+	1.58891e14i	−0.571285	+	0.989494i	0.425150	+	0.905123i	$0.360221\pi$
$107$	−9.17359e13	+	1.58891e14i	−0.571285	+	0.989494i	−0.996434	+	0.0843712i	$0.973112\pi$
$108$		0			0
$109$	−6.68227e13	−	1.15740e14i	−0.365543	−	0.633140i	0.623320	−	0.781967i	$-0.285783\pi$
$109$	−6.68227e13	−	1.15740e14i	−0.365543	−	0.633140i	−0.988863	+	0.148827i	$0.952450\pi$
$110$	−1.86442e13	−	1.07642e13i	−0.0956742	−	0.0552375i
$111$		0			0
$112$	−1.72998e12	+	5.52400e13i	−0.00782556	+	0.249877i
$113$	3.46999e14			1.47496			0.737478	−	0.675371i	$-0.236017\pi$
$113$	3.46999e14			1.47496			0.737478	+	0.675371i	$0.236017\pi$
$114$		0			0
$115$	−1.51897e14	+	8.76980e13i	−0.571038	+	0.329689i
$116$	−3.74014e13	−	6.47811e13i	−0.132337	−	0.229215i
$117$		0			0
$118$		−	4.00688e14i		−	1.25786i
$119$	−5.39643e13	+	8.70567e13i	−0.159690	+	0.257616i
$120$		0			0
$121$	1.75601e14	−	3.04150e14i	0.462413	−	0.800923i
$122$	−3.21992e14	+	1.85902e14i	−0.800436	+	0.462132i
$123$		0			0
$124$	−1.97826e14	−	1.14215e14i	−0.438866	−	0.253379i
$125$			4.55204e14i			0.954632i
$126$		0			0
$127$	−3.65726e14			−0.686325			−0.343162	−	0.939276i	$-0.611498\pi$
$127$	−3.65726e14			−0.686325			−0.343162	+	0.939276i	$0.611498\pi$
$128$	−2.48791e13	+	4.30919e13i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	1.60444e14	+	2.77897e14i	0.255693	+	0.442874i
$131$	4.12238e14	+	2.38006e14i	0.622657	+	0.359491i	0.777903	−	0.628385i	$-0.216284\pi$
$131$	4.12238e14	+	2.38006e14i	0.622657	+	0.359491i	−0.155246	+	0.987876i	$0.549617\pi$
$132$		0			0
$133$	−1.00610e15	−	3.15087e13i	−1.36672	−	0.0428025i
$134$	7.62574e13			0.0982989
$135$		0			0
$136$	−7.98616e13	+	4.61081e13i	−0.0928038	+	0.0535803i
$137$	−2.49725e14	−	4.32537e14i	−0.275688	−	0.477506i	0.694620	−	0.719377i	$-0.255572\pi$
$137$	−2.49725e14	−	4.32537e14i	−0.275688	−	0.477506i	−0.970309	+	0.241871i	$0.922239\pi$
$138$		0			0
$139$			8.98704e14i			0.896423i	0.893928	+	0.448212i	$0.147939\pi$
$139$			8.98704e14i			0.896423i	−0.893928	+	0.448212i	$0.852061\pi$
$140$	1.41954e14	+	2.64674e14i	0.134664	+	0.251082i
$141$		0			0
$142$	2.80467e14	−	4.85783e14i	0.240915	−	0.417277i
$143$	3.68499e14	−	2.12753e14i	0.301359	−	0.173990i
$144$		0			0
$145$	−3.52041e14	−	2.03251e14i	−0.261226	−	0.150819i
$146$		−	9.11175e14i		−	0.644365i
$147$		0			0
$148$	1.42742e15			0.917743
$149$	−3.71458e14	+	6.43383e14i	−0.227827	+	0.394608i	−0.957164	−	0.289547i	$-0.906495\pi$
$149$	−3.71458e14	+	6.43383e14i	−0.227827	+	0.394608i	0.729337	+	0.684155i	$0.239829\pi$
$150$		0			0
$151$	−6.40987e14	−	1.11022e15i	−0.358105	−	0.620256i	0.629539	−	0.776969i	$-0.283244\pi$
$151$	−6.40987e14	−	1.11022e15i	−0.358105	−	0.620256i	−0.987644	+	0.156712i	$0.949910\pi$
$152$	−7.84845e14	−	4.53131e14i	−0.418677	−	0.241723i
$153$		0			0
$154$	3.50966e14	−	1.88235e14i	0.170852	−	0.0916339i
$155$	−1.24136e15			−0.577532
$156$		0			0
$157$	−1.78177e15	+	1.02870e15i	−0.757798	+	0.437515i	−0.828504	−	0.559982i	$-0.810808\pi$
$157$	−1.78177e15	+	1.02870e15i	−0.757798	+	0.437515i	0.0707068	+	0.997497i	$0.477475\pi$
$158$	−1.70327e14	−	2.95015e14i	−0.0692921	−	0.120018i
$159$		0			0
$160$			2.70402e14i			0.100733i
$161$	1.01566e14	−	3.24308e15i	0.0362214	−	1.15658i
$162$		0			0
$163$	−1.05994e15	+	1.83587e15i	−0.346711	+	0.600521i	−0.985663	−	0.168726i	$-0.946035\pi$
$163$	−1.05994e15	+	1.83587e15i	−0.346711	+	0.600521i	0.638952	+	0.769246i	$0.279368\pi$
$164$	−1.37227e15	+	7.92280e14i	−0.430064	+	0.248297i
$165$		0			0
$166$	5.68043e14	+	3.27960e14i	0.163540	+	0.0944200i
$167$		−	1.07353e15i		−	0.296345i	−0.988962	−	0.148173i	$-0.952661\pi$
$167$		−	1.07353e15i		−	0.296345i	0.988962	−	0.148173i	$-0.0473391\pi$
$168$		0			0
$169$	−2.40491e15			−0.610790
$170$	−2.50566e14	+	4.33993e14i	−0.0610632	+	0.105765i
$171$		0			0
$172$	−1.12546e15	−	1.94936e15i	−0.252715	−	0.437716i
$173$	−5.18857e15	−	2.99562e15i	−1.11873	−	0.645899i	−0.177653	−	0.984093i	$-0.556850\pi$
$173$	−5.18857e15	−	2.99562e15i	−1.11873	−	0.645899i	−0.941076	+	0.338195i	$0.890184\pi$
$174$		0			0
$175$	−2.88505e15	−	1.78837e15i	−0.573967	−	0.355788i
$176$	3.58561e14			0.0685448
$177$		0			0
$178$	−1.58044e15	+	9.12468e14i	−0.279150	+	0.161168i
$179$	−9.34762e14	−	1.61906e15i	−0.158756	−	0.274973i	0.775664	−	0.631146i	$-0.217415\pi$
$179$	−9.34762e14	−	1.61906e15i	−0.158756	−	0.274973i	−0.934420	+	0.356172i	$0.884082\pi$
$180$		0			0
$181$		−	6.49718e15i		−	1.02088i	−0.859913	−	0.510441i	$-0.829482\pi$
$181$		−	6.49718e15i		−	1.02088i	0.859913	−	0.510441i	$-0.170518\pi$
$182$	−5.93323e15	−	1.85814e14i	−0.896998	−	0.0280918i
$183$		0			0
$184$	1.46063e15	−	2.52988e15i	0.204557	−	0.354304i
$185$	6.71782e15	−	3.87854e15i	0.905787	−	0.522957i
$186$		0			0
$187$	5.75488e14	+	3.32258e14i	0.0719689	+	0.0415513i
$188$		−	5.90756e15i		−	0.711711i
$189$		0			0
$190$	−4.92491e15			−0.550964
$191$	3.46574e14	−	6.00284e14i	0.0373734	−	0.0647327i	−0.846734	−	0.532017i	$-0.821434\pi$
$191$	3.46574e14	−	6.00284e14i	0.0373734	−	0.0647327i	0.884107	+	0.467284i	$0.154768\pi$
$192$		0			0
$193$	−4.38683e15	−	7.59821e15i	−0.439794	−	0.761746i	0.557879	−	0.829922i	$-0.311615\pi$
$193$	−4.38683e15	−	7.59821e15i	−0.439794	−	0.761746i	−0.997673	+	0.0681763i	$0.978282\pi$
$194$	−3.42165e14	−	1.97549e14i	−0.0330844	−	0.0191013i
$195$		0			0
$196$	−5.54512e15	−	3.47660e14i	−0.499020	−	0.0312869i
$197$	−1.82865e16			−1.58806			−0.794032	−	0.607876i	$-0.792022\pi$
$197$	−1.82865e16			−1.58806			−0.794032	+	0.607876i	$0.792022\pi$
$198$		0			0
$199$	−1.02883e15	+	5.93997e14i	−0.0832479	+	0.0480632i	−0.541046	−	0.840993i	$-0.681972\pi$
$199$	−1.02883e15	+	5.93997e14i	−0.0832479	+	0.0480632i	0.457798	+	0.889056i	$0.348638\pi$
$200$	−1.52802e15	−	2.64660e15i	−0.119376	−	0.206766i
$201$		0			0
$202$			6.54471e15i			0.476904i
$203$	6.62696e15	−	3.55427e15i	0.466490	−	0.250195i
$204$		0			0
$205$	−4.30550e15	+	7.45735e15i	−0.282974	+	0.490125i
$206$	5.09923e15	−	2.94404e15i	0.323917	−	0.187014i
$207$		0			0
$208$	−4.62843e15	−	2.67222e15i	−0.274783	−	0.158646i
$209$			6.53058e15i			0.374911i
$210$		0			0
$211$	−2.72476e16			−1.46336			−0.731680	−	0.681648i	$-0.761264\pi$
$211$	−2.72476e16			−1.46336			−0.731680	+	0.681648i	$0.761264\pi$
$212$	−7.33752e15	+	1.27090e16i	−0.381240	+	0.660327i
$213$		0			0
$214$	−8.30298e15	−	1.43812e16i	−0.403959	−	0.699678i
$215$	−1.05934e16	−	6.11611e15i	−0.498846	−	0.288009i
$216$		0			0
$217$	1.20989e16	−	1.95183e16i	0.533985	−	0.861439i
$218$	1.20962e16			0.516956
$219$		0			0
$220$	1.68748e15	−	9.74267e14i	0.0676519	−	0.0390588i
$221$	−4.95240e15	−	8.57780e15i	−0.192340	−	0.333142i
$222$		0			0
$223$		−	8.06396e15i		−	0.294045i	−0.989133	−	0.147023i	$-0.953031\pi$
$223$		−	8.06396e15i		−	0.294045i	0.989133	−	0.147023i	$-0.0469690\pi$
$224$	−4.25162e15	−	2.63548e15i	−0.150251	−	0.0931372i
$225$		0			0
$226$	−1.57034e16	+	2.71991e16i	−0.521476	+	0.903223i
$227$	−6.15886e14	+	3.55582e14i	−0.0198299	+	0.0114488i	−0.509882	−	0.860244i	$-0.670311\pi$
$227$	−6.15886e14	+	3.55582e14i	−0.0198299	+	0.0114488i	0.490052	+	0.871693i	$0.336978\pi$
$228$		0			0
$229$	−4.57486e16	−	2.64130e16i	−1.38525	−	0.799776i	−0.392478	−	0.919762i	$-0.628382\pi$
$229$	−4.57486e16	−	2.64130e16i	−1.38525	−	0.799776i	−0.992776	+	0.119985i	$0.961715\pi$
$230$		−	1.58750e16i		−	0.466251i
$231$		0			0
$232$	6.77038e15			0.187153
$233$	−1.61306e16	+	2.79389e16i	−0.432671	+	0.749408i	−0.997102	−	0.0760717i	$-0.975762\pi$
$233$	−1.61306e16	+	2.79389e16i	−0.432671	+	0.749408i	0.564431	+	0.825480i	$0.309096\pi$
$234$		0			0
$235$	−1.60518e16	−	2.78025e16i	−0.405554	−	0.702439i
$236$	3.14074e16	+	1.81331e16i	0.770278	+	0.444720i
$237$		0			0
$238$	−4.38167e15	−	8.16966e15i	−0.101298	−	0.188871i
$239$	−2.47318e16			−0.555227			−0.277613	−	0.960693i	$-0.589543\pi$
$239$	−2.47318e16			−0.555227			−0.277613	+	0.960693i	$0.589543\pi$
$240$		0			0
$241$	−5.48108e16	+	3.16450e16i	−1.16077	+	0.670172i	−0.951489	−	0.307683i	$-0.900446\pi$
$241$	−5.48108e16	+	3.16450e16i	−1.16077	+	0.670172i	−0.209283	+	0.977855i	$0.567113\pi$
$242$	1.58936e16	+	2.75285e16i	0.326975	+	0.566338i
$243$		0			0
$244$		−	3.36519e16i		−	0.653553i
$245$	−2.70414e16	+	1.34308e16i	−0.510348	+	0.253477i
$246$		0			0
$247$	4.86700e16	−	8.42989e16i	0.867726	−	1.50295i
$248$	1.79052e16	−	1.03376e16i	0.310325	−	0.179166i
$249$		0			0
$250$	−3.56806e16	−	2.06002e16i	−0.584590	−	0.337513i
$251$			9.04032e16i			1.44035i	0.693793	+	0.720175i	$0.255938\pi$
$251$			9.04032e16i			1.44035i	−0.693793	+	0.720175i	$0.744062\pi$
$252$		0			0
$253$	−2.10508e16			−0.317267
$254$	1.65509e16	−	2.86669e16i	0.242652	−	0.420286i
$255$		0			0
$256$	−2.25180e15	−	3.90023e15i	−0.0312500	−	0.0541266i
$257$	−1.39819e16	−	8.07248e15i	−0.188815	−	0.109012i	0.402613	−	0.915370i	$-0.368102\pi$
$257$	−1.39819e16	−	8.07248e15i	−0.188815	−	0.109012i	−0.591428	+	0.806358i	$0.701435\pi$
$258$		0			0
$259$	−4.49184e15	+	1.43429e17i	−0.0574548	+	1.83459i
$260$	−2.90434e16			−0.361605
$261$		0			0
$262$	−3.73115e16	+	2.15418e16i	−0.440285	+	0.254199i
$263$	−6.07368e15	−	1.05199e16i	−0.0697849	−	0.120871i	0.829022	−	0.559217i	$-0.188898\pi$
$263$	−6.07368e15	−	1.05199e16i	−0.0697849	−	0.120871i	−0.898807	+	0.438346i	$0.855565\pi$
$264$		0			0
$265$			7.97488e16i			0.868967i
$266$	4.80007e16	−	7.74360e16i	0.509421	−	0.821810i
$267$		0			0
$268$	−3.45102e15	+	5.97734e15i	−0.0347539	+	0.0601955i
$269$	−8.14901e16	+	4.70483e16i	−0.799538	+	0.461613i	−0.843309	−	0.537428i	$-0.819396\pi$
$269$	−8.14901e16	+	4.70483e16i	−0.799538	+	0.461613i	0.0437718	+	0.999042i	$0.486063\pi$
$270$		0			0
$271$	1.13271e17	+	6.53972e16i	1.05520	+	0.609220i	0.924101	−	0.382149i	$-0.124816\pi$
$271$	1.13271e17	+	6.53972e16i	1.05520	+	0.609220i	0.131100	+	0.991369i	$0.458149\pi$
$272$		−	8.34646e15i		−	0.0757740i
$273$		0			0
$274$	4.52051e16			0.389882
$275$	−1.10110e16	+	1.90716e16i	−0.0925759	+	0.160346i
$276$		0			0
$277$	−5.90475e16	−	1.02273e17i	−0.471893	−	0.817342i	0.527590	−	0.849499i	$-0.323096\pi$
$277$	−5.90475e16	−	1.02273e17i	−0.471893	−	0.817342i	−0.999483	+	0.0321569i	$0.989762\pi$
$278$	−7.04437e16	−	4.06707e16i	−0.548945	−	0.316933i
$279$		0			0
$280$	−2.71702e16	−	8.50905e14i	−0.201366	−	0.00630631i
$281$	−7.38675e16			−0.533961			−0.266980	−	0.963702i	$-0.586026\pi$
$281$	−7.38675e16			−0.533961			−0.266980	+	0.963702i	$0.586026\pi$
$282$		0			0
$283$	−1.24777e17	+	7.20402e16i	−0.858283	+	0.495530i	−0.863437	−	0.504457i	$-0.831693\pi$
$283$	−1.24777e17	+	7.20402e16i	−0.858283	+	0.495530i	0.00515374	+	0.999987i	$0.498360\pi$
$284$	2.53850e16	+	4.39681e16i	0.170352	+	0.295059i
$285$		0			0
$286$			3.85125e16i			0.246059i
$287$	−7.52908e16	−	1.40380e17i	−0.469427	−	0.875250i
$288$		0			0
$289$	−7.64547e16	+	1.32423e17i	−0.454066	+	0.786466i
$290$	3.18631e16	−	1.83962e16i	0.184715	−	0.106645i
$291$		0			0
$292$	7.14212e16	+	4.12351e16i	0.394591	+	0.227817i
$293$		−	1.95449e17i		−	1.05429i	−0.849775	−	0.527146i	$-0.823262\pi$
$293$		−	1.95449e17i		−	1.05429i	0.849775	−	0.527146i	$-0.176738\pi$
$294$		0			0
$295$	1.97082e17			1.01366
$296$	−6.45978e16	+	1.11887e17i	−0.324471	+	0.562000i
$297$		0			0
$298$	−3.36205e16	−	5.82324e16i	−0.161098	−	0.279030i
$299$	2.71731e17	+	1.56884e17i	1.27186	+	0.734310i
$300$		0			0
$301$	1.99415e17	−	1.06953e17i	0.890823	−	0.477780i
$302$	1.16031e17			0.506437
$303$		0			0
$304$	7.10361e16	−	4.10127e16i	0.296049	−	0.170924i
$305$	−9.14375e16	−	1.58374e17i	−0.372414	−	0.645039i
$306$		0			0
$307$			5.43740e16i			0.211555i	0.994390	+	0.105777i	$0.0337331\pi$
$307$			5.43740e16i			0.211555i	−0.994390	+	0.105777i	$0.966267\pi$
$308$	−1.12833e15	+	3.60285e16i	−0.00429121	+	0.137022i
$309$		0			0
$310$	5.61775e16	−	9.73023e16i	0.204188	−	0.353664i
$311$	−1.24757e17	+	7.20284e16i	−0.443345	+	0.255965i	−0.705015	−	0.709192i	$-0.749060\pi$
$311$	−1.24757e17	+	7.20284e16i	−0.443345	+	0.255965i	0.261671	+	0.965157i	$0.415727\pi$
$312$		0			0
$313$	−2.82041e17	−	1.62837e17i	−0.958302	−	0.553276i	−0.0626520	−	0.998035i	$-0.519956\pi$
$313$	−2.82041e17	−	1.62837e17i	−0.958302	−	0.553276i	−0.895650	+	0.444760i	$0.853289\pi$
$314$		−	1.86215e17i		−	0.618739i
$315$		0			0
$316$	3.08325e16			0.0979939
$317$	−1.48518e17	+	2.57241e17i	−0.461705	+	0.799696i	−0.999046	−	0.0436690i	$-0.986095\pi$
$317$	−1.48518e17	+	2.57241e17i	−0.461705	+	0.799696i	0.537341	+	0.843365i	$0.319429\pi$
$318$		0			0
$319$	−2.43939e16	−	4.22515e16i	−0.0725682	−	0.125692i
$320$	−2.11951e16	−	1.22370e16i	−0.0616858	−	0.0356143i
$321$		0			0
$322$	2.49609e17	+	1.54726e17i	0.695454	+	0.431095i
$323$	1.52017e17			0.414451
$324$		0			0
$325$	2.84267e17	−	1.64122e17i	0.742238	−	0.428532i
$326$	−9.59347e16	−	1.66164e17i	−0.245162	−	0.424632i
$327$		0			0
$328$		−	1.43418e17i		−	0.351145i
$329$	5.93597e17	+	1.85900e16i	1.42272	+	0.0445563i
$330$		0			0
$331$	1.88604e16	−	3.26672e16i	0.0433267	−	0.0750440i	−0.843549	−	0.537052i	$-0.819538\pi$
$331$	1.88604e16	−	3.26672e16i	0.0433267	−	0.0750440i	0.886876	+	0.462008i	$0.152871\pi$
$332$	−5.14134e16	+	2.96835e16i	−0.115640	+	0.0667650i
$333$		0			0
$334$	8.41470e16	+	4.85823e16i	0.181474	+	0.104774i
$335$			3.75078e16i			0.0792152i
$336$		0			0
$337$	−2.49681e17			−0.505796			−0.252898	−	0.967493i	$-0.581384\pi$
$337$	−2.49681e17			−0.505796			−0.252898	+	0.967493i	$0.581384\pi$
$338$	1.08834e17	−	1.88506e17i	0.215947	−	0.374031i
$339$		0			0
$340$	−2.26786e16	−	3.92806e16i	−0.0431782	−	0.0747869i
$341$	−1.29026e17	−	7.44932e16i	−0.240656	−	0.138943i
$342$		0			0
$343$	5.23827e16	−	5.56084e17i	0.0937840	−	0.995593i
$344$	2.03730e17			0.357393
$345$		0			0
$346$	4.69616e17	−	2.71133e17i	0.791061	−	0.456719i
$347$	3.25398e17	+	5.63605e17i	0.537166	+	0.930398i	0.999055	+	0.0434606i	$0.0138383\pi$
$347$	3.25398e17	+	5.63605e17i	0.537166	+	0.930398i	−0.461890	+	0.886937i	$0.652828\pi$
$348$		0			0
$349$			6.27518e17i			0.995057i	0.867448	+	0.497528i	$0.165759\pi$
$349$			6.27518e17i			0.995057i	−0.867448	+	0.497528i	$0.834241\pi$
$350$	2.70742e17	−	1.45208e17i	0.420803	−	0.225691i
$351$		0			0
$352$	−1.62266e16	+	2.81053e16i	−0.0242342	+	0.0419750i
$353$	3.86571e17	−	2.23187e17i	0.565987	−	0.326773i	−0.189558	−	0.981870i	$-0.560705\pi$
$353$	3.86571e17	−	2.23187e17i	0.565987	−	0.326773i	0.755545	+	0.655097i	$0.227372\pi$
$354$		0			0
$355$	2.38936e17	+	1.37950e17i	0.336267	+	0.194144i
$356$		−	1.65174e17i		−	0.227925i
$357$		0			0
$358$	1.69210e17			0.224515
$359$	−2.55847e17	+	4.43140e17i	−0.332904	+	0.576607i	−0.983080	−	0.183177i	$-0.941362\pi$
$359$	−2.55847e17	+	4.43140e17i	−0.332904	+	0.576607i	0.650176	+	0.759784i	$0.274695\pi$
$360$		0			0
$361$	3.47473e17	+	6.01841e17i	0.434882	+	0.753237i
$362$	5.09273e17	+	2.94029e17i	0.625159	+	0.360936i
$363$		0			0
$364$	2.83072e17	−	4.56659e17i	0.334339	−	0.539365i
$365$	4.48169e17			0.519268
$366$		0			0
$367$	−6.76573e17	+	3.90620e17i	−0.754488	+	0.435604i	−0.827313	−	0.561741i	$-0.810132\pi$
$367$	−6.76573e17	+	3.90620e17i	−0.754488	+	0.435604i	0.0728252	+	0.997345i	$0.476798\pi$
$368$	1.32201e17	+	2.28979e17i	0.144644	+	0.250531i
$369$		0			0
$370$			7.02090e17i			0.739572i
$371$	−1.25392e18	−	7.77274e17i	−1.29614	−	0.803446i
$372$		0			0
$373$	−1.82687e17	+	3.16422e17i	−0.181863	+	0.314996i	−0.942515	−	0.334164i	$-0.891546\pi$
$373$	−1.82687e17	+	3.16422e17i	−0.181863	+	0.314996i	0.760652	+	0.649160i	$0.224879\pi$
$374$	−5.20872e16	+	3.00726e16i	−0.0508897	+	0.0293812i
$375$		0			0
$376$	4.63057e17	+	2.67346e17i	0.435832	+	0.251628i
$377$			7.27195e17i			0.671833i
$378$		0			0
$379$	8.66799e17			0.771692			0.385846	−	0.922563i	$-0.373910\pi$
$379$	8.66799e17			0.771692			0.385846	+	0.922563i	$0.373910\pi$
$380$	2.22876e17	−	3.86032e17i	0.194795	−	0.337395i
$381$		0			0
$382$	3.13683e16	+	5.43315e16i	0.0264270	+	0.0457729i
$383$	−3.55044e17	−	2.04985e17i	−0.293691	−	0.169562i	0.345914	−	0.938266i	$-0.387569\pi$
$383$	−3.55044e17	−	2.04985e17i	−0.293691	−	0.169562i	−0.639605	+	0.768704i	$0.720902\pi$
$384$		0			0
$385$	9.25850e16	+	1.72625e17i	0.0738441	+	0.137683i
$386$	7.94101e17			0.621963
$387$		0			0
$388$	3.09692e16	−	1.78801e16i	0.0233942	−	0.0135066i
$389$	2.78940e17	+	4.83138e17i	0.206949	+	0.358446i	0.950752	−	0.309953i	$-0.100313\pi$
$389$	2.78940e17	+	4.83138e17i	0.206949	+	0.358446i	−0.743803	+	0.668399i	$0.766980\pi$
$390$		0			0
$391$			4.90013e17i			0.350728i
$392$	2.78194e17	−	4.18913e17i	0.195590	−	0.294525i
$393$		0			0
$394$	8.27554e17	−	1.43337e18i	0.561465	−	0.972486i
$395$	1.45106e17	−	8.37767e16i	0.0967173	−	0.0558398i
$396$		0			0
$397$	−6.39071e17	−	3.68968e17i	−0.411165	−	0.237386i	0.280125	−	0.959963i	$-0.409624\pi$
$397$	−6.39071e17	−	3.68968e17i	−0.411165	−	0.237386i	−0.691290	+	0.722577i	$0.742957\pi$
$398$		−	1.07525e17i		−	0.0679716i
$399$		0			0
$400$	2.76601e17			0.168824
$401$	−1.10884e18	+	1.92057e18i	−0.665055	+	1.15191i	0.314215	+	0.949352i	$0.398259\pi$
$401$	−1.10884e18	+	1.92057e18i	−0.665055	+	1.15191i	−0.979270	+	0.202558i	$0.935075\pi$
$402$		0			0
$403$	1.11034e18	+	1.92316e18i	0.643162	+	1.11399i
$404$	−5.12998e17	−	2.96180e17i	−0.292043	−	0.168611i
$405$		0			0
$406$	−2.13051e16	+	6.80293e17i	−0.0117166	+	0.374123i
$407$	9.30993e17			0.503252
$408$		0			0
$409$	2.21511e18	−	1.27889e18i	1.15699	−	0.667991i	0.206412	−	0.978465i	$-0.433821\pi$
$409$	2.21511e18	−	1.27889e18i	1.15699	−	0.667991i	0.950582	+	0.310474i	$0.100488\pi$
$410$	−3.89689e17	−	6.74962e17i	−0.200093	−	0.346571i
$411$		0			0
$412$			5.32929e17i			0.264477i
$413$	−1.92086e18	+	3.09878e18i	−0.937228	+	1.51196i
$414$		0			0
$415$	−1.61310e17	+	2.79397e17i	−0.0760893	+	0.131791i
$416$	4.18917e17	−	2.41862e17i	0.194301	−	0.112180i
$417$		0			0
$418$	−5.11891e17	−	2.95540e17i	−0.229585	−	0.132551i
$419$		−	3.54851e18i		−	1.56512i	−0.622574	−	0.782561i	$-0.713913\pi$
$419$		−	3.54851e18i		−	1.56512i	0.622574	−	0.782561i	$-0.286087\pi$
$420$		0			0
$421$	−2.35456e18			−1.00446			−0.502232	−	0.864733i	$-0.667488\pi$
$421$	−2.35456e18			−1.00446			−0.502232	+	0.864733i	$0.667488\pi$
$422$	1.23309e18	−	2.13577e18i	0.517376	−	0.896122i
$423$		0			0
$424$	−6.64117e17	−	1.15028e18i	−0.269577	−	0.466922i
$425$	4.43942e17	+	2.56310e17i	0.177257	+	0.102340i
$426$		0			0
$427$	3.38137e18	+	1.05896e17i	1.30647	+	0.0409153i
$428$	1.50300e18			0.571285
$429$		0			0
$430$	9.58806e17	−	5.53567e17i	0.352738	−	0.203653i
$431$	−3.39210e17	−	5.87529e17i	−0.122780	−	0.212661i	0.798083	−	0.602548i	$-0.205848\pi$
$431$	−3.39210e17	−	5.87529e17i	−0.122780	−	0.212661i	−0.920863	+	0.389886i	$0.872514\pi$
$432$		0			0
$433$			3.54821e18i			1.24335i	0.783275	+	0.621675i	$0.213548\pi$
$433$			3.54821e18i			1.24335i	−0.783275	+	0.621675i	$0.786452\pi$
$434$	9.82383e17	+	1.83166e18i	0.338729	+	0.631562i
$435$		0			0
$436$	−5.47412e17	+	9.48145e17i	−0.182772	+	0.316570i
$437$	−4.17046e18	+	2.40782e18i	−1.37029	+	0.791140i
$438$		0			0
$439$	2.53109e18	+	1.46133e18i	0.805484	+	0.465046i	0.845385	−	0.534157i	$-0.179371\pi$
$439$	2.53109e18	+	1.46133e18i	0.805484	+	0.465046i	−0.0399014	+	0.999204i	$0.512704\pi$
$440$			1.76361e17i			0.0552375i
$441$		0			0
$442$	8.96479e17			0.272010
$443$	−2.85984e18	+	4.95338e18i	−0.854113	+	1.47937i	0.0233533	+	0.999727i	$0.492566\pi$
$443$	−2.85984e18	+	4.95338e18i	−0.854113	+	1.47937i	−0.877466	+	0.479639i	$0.840768\pi$
$444$		0			0
$445$	−4.48805e17	−	7.77352e17i	−0.129878	−	0.224956i
$446$	6.32083e17	+	3.64933e17i	0.180065	+	0.103961i
$447$		0			0
$448$	3.98985e17	−	2.13990e17i	0.110157	−	0.0590808i
$449$	6.27750e18			1.70633			0.853163	−	0.521644i	$-0.174681\pi$
$449$	6.27750e18			1.70633			0.853163	+	0.521644i	$0.174681\pi$
$450$		0			0
$451$	−8.95020e17	+	5.16740e17i	−0.235829	+	0.136156i
$452$	−1.42131e18	−	2.46178e18i	−0.368739	−	0.638675i
$453$		0			0
$454$		−	6.43672e16i		−	0.0161910i
$455$	9.13943e16	−	2.91831e18i	0.0226381	−	0.722855i
$456$		0			0
$457$	7.70753e17	−	1.33498e18i	0.185141	−	0.320673i	−0.758483	−	0.651692i	$-0.774059\pi$
$457$	7.70753e17	−	1.33498e18i	0.185141	−	0.320673i	0.943624	+	0.331020i	$0.107393\pi$
$458$	4.14069e18	−	2.39063e18i	0.979522	−	0.565527i
$459$		0			0
$460$	1.24434e18	+	7.18422e17i	0.285519	+	0.164845i
$461$			2.82419e18i			0.638245i	0.947713	+	0.319123i	$0.103388\pi$
$461$			2.82419e18i			0.638245i	−0.947713	+	0.319123i	$0.896612\pi$
$462$		0			0
$463$	−5.56867e18			−1.22091			−0.610457	−	0.792050i	$-0.709014\pi$
$463$	−5.56867e18			−1.22091			−0.610457	+	0.792050i	$0.709014\pi$
$464$	−3.06392e17	+	5.30687e17i	−0.0661686	+	0.114607i
$465$		0			0
$466$	−1.45997e18	−	2.52874e18i	−0.305945	−	0.529912i
$467$	−1.39975e18	−	8.08148e17i	−0.288957	−	0.166830i	0.348514	−	0.937303i	$-0.386686\pi$
$467$	−1.39975e18	−	8.08148e17i	−0.288957	−	0.166830i	−0.637471	+	0.770474i	$0.720020\pi$
$468$		0			0
$469$	−5.89749e17	−	3.65571e17i	−0.118156	−	0.0732423i
$470$	2.90568e18			0.573539
$471$		0			0
$472$	−2.84267e18	+	1.64122e18i	−0.544669	+	0.314465i
$473$	−7.34047e17	−	1.27141e18i	−0.138579	−	0.240025i
$474$		0			0
$475$			5.03781e18i			0.923393i
$476$	8.38660e17	+	2.62648e16i	0.151474	+	0.00474379i
$477$		0			0
$478$	1.11923e18	−	1.93857e18i	0.196302	−	0.340005i
$479$	−7.34016e18	+	4.23784e18i	−1.26869	+	0.732481i	−0.974741	−	0.223339i	$-0.928304\pi$
$479$	−7.34016e18	+	4.23784e18i	−1.26869	+	0.732481i	−0.293953	+	0.955820i	$0.594971\pi$
$480$		0			0
$481$	−1.20176e19	−	6.93835e18i	−2.01744	−	1.16477i
$482$		−	5.72836e18i		−	0.947767i
$483$		0			0
$484$	−2.87705e18			−0.462413
$485$	9.71660e16	−	1.68296e17i	0.0153930	−	0.0266614i
$486$		0			0
$487$	−6.25813e18	−	1.08394e19i	−0.963257	−	1.66841i	−0.714227	−	0.699914i	$-0.753222\pi$
$487$	−6.25813e18	−	1.08394e19i	−0.963257	−	1.66841i	−0.249030	−	0.968496i	$-0.580112\pi$
$488$	2.63776e18	+	1.52291e18i	0.400218	+	0.231066i
$489$		0			0
$490$	1.70999e17	−	2.72741e18i	0.0252129	−	0.402140i
$491$	−1.12919e19			−1.64134			−0.820669	−	0.571405i	$-0.806399\pi$
$491$	−1.12919e19			−1.64134			−0.820669	+	0.571405i	$0.806399\pi$
$492$		0			0
$493$	−9.83515e17	+	5.67832e17i	−0.138948	+	0.0802217i
$494$	4.40511e18	+	7.62987e18i	0.613575	+	1.06274i
$495$		0			0
$496$			1.87130e18i			0.253379i
$497$	−4.49783e18	+	2.41235e18i	−0.600494	+	0.322066i
$498$		0			0
$499$	1.65033e18	−	2.85846e18i	0.214224	−	0.371047i	−0.738808	−	0.673916i	$-0.764611\pi$
$499$	1.65033e18	−	2.85846e18i	0.214224	−	0.371047i	0.953032	+	0.302869i	$0.0979444\pi$
$500$	3.22944e18	−	1.86452e18i	0.413368	−	0.238658i
$501$		0			0
$502$	−7.08614e18	−	4.09118e18i	−0.882030	−	0.509241i
$503$		−	7.11585e18i		−	0.873475i	−0.899589	−	0.436738i	$-0.856134\pi$
$503$		−	7.11585e18i		−	0.873475i	0.899589	−	0.436738i	$-0.143866\pi$
$504$		0			0
$505$	−3.21907e18			−0.384318
$506$	9.52650e17	−	1.65004e18i	0.112171	−	0.194285i
$507$		0			0
$508$	1.49801e18	+	2.59463e18i	0.171581	+	0.297187i
$509$	−7.75832e18	−	4.47927e18i	−0.876483	−	0.506038i	−0.00698572	−	0.999976i	$-0.502224\pi$
$509$	−7.75832e18	−	4.47927e18i	−0.876483	−	0.506038i	−0.869497	+	0.493938i	$0.835557\pi$
$510$		0			0
$511$	−4.36808e18	+	7.04671e18i	−0.480114	+	0.774533i
$512$	4.07619e17			0.0441942
$513$		0			0
$514$	1.26550e18	−	7.30638e17i	0.133512	−	0.0770833i
$515$	1.44805e18	+	2.50810e18i	0.150707	+	0.261032i
$516$		0			0
$517$		−	3.85303e18i		−	0.390273i
$518$	−1.10392e19	−	6.84293e18i	−1.10314	−	0.683808i
$519$		0			0
$520$	1.31435e18	−	2.27653e18i	0.127847	−	0.221437i
$521$	3.55444e18	−	2.05216e18i	0.341120	−	0.196946i	−0.319647	−	0.947537i	$-0.603564\pi$
$521$	3.55444e18	−	2.05216e18i	0.341120	−	0.196946i	0.660767	+	0.750591i	$0.270231\pi$
$522$		0			0
$523$	−6.77270e18	−	3.91022e18i	−0.632776	−	0.365333i	0.149050	−	0.988830i	$-0.452378\pi$
$523$	−6.77270e18	−	3.91022e18i	−0.632776	−	0.365333i	−0.781826	+	0.623496i	$0.785712\pi$
$524$		−	3.89948e18i		−	0.359491i
$525$		0			0
$526$	1.09945e18			0.0986907
$527$	−1.73403e18	+	3.00342e18i	−0.153596	+	0.266037i
$528$		0			0
$529$	−1.96498e18	−	3.40344e18i	−0.169499	−	0.293581i
$530$	−6.25101e18	−	3.60902e18i	−0.532131	−	0.307226i
$531$		0			0
$532$	3.89746e18	+	7.26683e18i	0.323147	+	0.602509i
$533$	1.54043e19			1.26052
$534$		0			0
$535$	7.07350e18	−	4.08389e18i	0.563843	−	0.325535i
$536$	−3.12350e17	−	5.41007e17i	−0.0245747	−	0.0425647i
$537$		0			0
$538$		−	8.51666e18i		−	0.652820i
$539$	−3.61663e18	−	2.26751e17i	−0.273642	−	0.0171564i
$540$		0			0
$541$	1.89449e18	−	3.28135e18i	0.139673	−	0.241920i	−0.787700	−	0.616059i	$-0.788728\pi$
$541$	1.89449e18	−	3.28135e18i	0.139673	−	0.241920i	0.927373	+	0.374139i	$0.122062\pi$
$542$	−1.02521e19	+	5.91908e18i	−0.746139	+	0.430784i
$543$		0			0
$544$	6.54226e17	+	3.77718e17i	0.0464019	+	0.0267901i
$545$			5.94962e18i			0.416594i
$546$		0			0
$547$	−1.39588e19			−0.952658			−0.476329	−	0.879267i	$-0.658033\pi$
$547$	−1.39588e19			−0.952658			−0.476329	+	0.879267i	$0.658033\pi$
$548$	−2.04575e18	+	3.54334e18i	−0.137844	+	0.238753i
$549$		0			0
$550$	−9.96602e17	−	1.72617e18i	−0.0654610	−	0.113382i
$551$	−9.66556e18	−	5.58041e18i	−0.626853	−	0.361914i
$552$		0			0
$553$	−9.70242e16	+	3.09808e18i	−0.00613486	+	0.195892i
$554$	1.06887e19			0.667357
$555$		0			0
$556$	6.37584e18	−	3.68109e18i	0.388163	−	0.224106i
$557$	−6.88069e17	−	1.19177e18i	−0.0413662	−	0.0716484i	0.844601	−	0.535396i	$-0.179838\pi$
$557$	−6.88069e17	−	1.19177e18i	−0.0413662	−	0.0716484i	−0.885967	+	0.463748i	$0.846504\pi$
$558$		0			0
$559$			2.18823e19i			1.28295i
$560$	1.29628e18	−	2.09119e18i	0.0750555	−	0.121082i
$561$		0			0
$562$	3.34286e18	−	5.79001e18i	0.188784	−	0.326983i
$563$	2.93601e19	−	1.69510e19i	1.63756	−	0.945448i	0.655895	−	0.754852i	$-0.272291\pi$
$563$	2.93601e19	−	1.69510e19i	1.63756	−	0.945448i	0.981669	−	0.190596i	$-0.0610419\pi$
$564$		0			0
$565$	−1.33781e19	−	7.72383e18i	−0.727871	−	0.420237i
$566$		−	1.30407e19i		−	0.700785i
$567$		0			0
$568$	−4.59517e18			−0.240915
$569$	1.85744e18	−	3.21718e18i	0.0961897	−	0.166605i	−0.813915	−	0.580984i	$-0.802668\pi$
$569$	1.85744e18	−	3.21718e18i	0.0961897	−	0.166605i	0.910105	+	0.414379i	$0.136001\pi$
$570$		0			0
$571$	1.48754e19	+	2.57649e19i	0.751650	+	1.30190i	0.947022	+	0.321167i	$0.104075\pi$
$571$	1.48754e19	+	2.57649e19i	0.751650	+	1.30190i	−0.195372	+	0.980729i	$0.562591\pi$
$572$	−3.01875e18	−	1.74287e18i	−0.150680	−	0.0869949i
$573$		0			0
$574$	1.44108e19	+	4.51311e17i	0.701947	+	0.0219833i
$575$	−1.62390e19			−0.781418
$576$		0			0
$577$	2.05080e19	−	1.18403e19i	0.963146	−	0.556073i	0.0660064	−	0.997819i	$-0.478974\pi$
$577$	2.05080e19	−	1.18403e19i	0.963146	−	0.556073i	0.897140	+	0.441746i	$0.145641\pi$
$578$	−6.91989e18	−	1.19856e19i	−0.321073	−	0.556116i
$579$		0			0
$580$			3.33006e18i			0.150819i
$581$	−2.82084e18	−	5.25947e18i	−0.126225	−	0.235347i
$582$		0			0
$583$	−4.78567e18	+	8.28903e18i	−0.209056	+	0.362096i
$584$	−6.46431e18	+	3.73217e18i	−0.279018	+	0.161091i
$585$		0			0
$586$	1.53200e19	+	8.84503e18i	0.645620	+	0.372749i
$587$		−	2.85495e19i		−	1.18886i	−0.804146	−	0.594432i	$-0.797377\pi$
$587$		−	2.85495e19i		−	1.18886i	0.804146	−	0.594432i	$-0.202623\pi$
$588$		0			0
$589$	−3.40825e19			−1.38588
$590$	−8.91889e18	+	1.54480e19i	−0.358382	+	0.620737i
$591$		0			0
$592$	−5.84673e18	−	1.01268e19i	−0.229436	−	0.397394i
$593$	−5.03486e18	−	2.90688e18i	−0.195256	−	0.112731i	0.399185	−	0.916871i	$-0.369293\pi$
$593$	−5.03486e18	−	2.90688e18i	−0.195256	−	0.112731i	−0.594441	+	0.804139i	$0.702627\pi$
$594$		0			0
$595$	4.01831e18	−	2.15516e18i	0.152204	−	0.0816321i
$596$	6.08596e18			0.227827
$597$		0			0
$598$	−2.45942e19	+	1.41995e19i	−0.899342	+	0.519236i
$599$	1.58214e19	+	2.74036e19i	0.571819	+	0.990419i	0.996379	+	0.0850197i	$0.0270953\pi$
$599$	1.58214e19	+	2.74036e19i	0.571819	+	0.990419i	−0.424560	+	0.905400i	$0.639571\pi$
$600$		0			0
$601$		−	1.11746e19i		−	0.394556i	−0.980348	−	0.197278i	$-0.936790\pi$
$601$		−	1.11746e19i		−	0.394556i	0.980348	−	0.197278i	$-0.0632102\pi$
$602$	−6.41102e17	+	2.04710e19i	−0.0223744	+	0.714436i
$603$		0			0
$604$	−5.25097e18	+	9.09494e18i	−0.179053	+	0.310128i
$605$	−1.35401e19	+	7.81740e18i	−0.456389	+	0.263496i
$606$		0			0
$607$	1.72270e19	+	9.94600e18i	0.567398	+	0.327588i	0.756110	−	0.654445i	$-0.227098\pi$
$607$	1.72270e19	+	9.94600e18i	0.567398	+	0.327588i	−0.188711	+	0.982033i	$0.560431\pi$
$608$			7.42409e18i			0.241723i
$609$		0			0
$610$	1.65520e19			0.526672
$611$	−2.87152e19	+	4.97361e19i	−0.903281	+	1.56453i
$612$		0			0
$613$	−7.93642e18	−	1.37463e19i	−0.244006	−	0.422631i	0.717845	−	0.696203i	$-0.245128\pi$
$613$	−7.93642e18	−	1.37463e19i	−0.244006	−	0.422631i	−0.961852	+	0.273571i	$0.911795\pi$
$614$	−4.26203e18	−	2.46069e18i	−0.129550	−	0.0747958i
$615$		0			0
$616$	−2.77299e18	−	1.71891e18i	−0.0823916	−	0.0510726i
$617$	1.84386e19			0.541666			0.270833	−	0.962626i	$-0.412701\pi$
$617$	1.84386e19			0.541666			0.270833	+	0.962626i	$0.412701\pi$
$618$		0			0
$619$	−2.03486e19	+	1.17482e19i	−0.584385	+	0.337395i	−0.762874	−	0.646547i	$-0.776212\pi$
$619$	−2.03486e19	+	1.17482e19i	−0.584385	+	0.337395i	0.178489	+	0.983942i	$0.442879\pi$
$620$	5.08461e18	+	8.80680e18i	0.144383	+	0.250079i
$621$		0			0
$622$		−	1.30385e19i		−	0.361990i
$623$	1.65969e19	+	5.19774e17i	0.455627	+	0.0142691i
$624$		0			0
$625$	−2.44598e18	+	4.23657e18i	−0.0656588	+	0.113724i
$626$	2.55275e19	−	1.47383e19i	0.677622	−	0.391225i
$627$		0			0
$628$	1.45962e19	+	8.42714e18i	0.378899	+	0.218757i
$629$		−	2.16713e19i		−	0.556328i
$630$		0			0
$631$	4.50708e19			1.13159			0.565796	−	0.824545i	$-0.308569\pi$
$631$	4.50708e19			1.13159			0.565796	+	0.824545i	$0.308569\pi$
$632$	−1.39532e18	+	2.41676e18i	−0.0346461	+	0.0600088i
$633$		0			0
$634$	−1.34423e19	−	2.32828e19i	−0.326474	−	0.565470i
$635$	1.41001e19	+	8.14067e18i	0.338692	+	0.195544i
$636$		0			0
$637$	4.49948e19	+	2.98804e19i	1.05727	+	0.702118i
$638$	4.41577e18			0.102627
$639$		0			0
$640$	1.91836e18	−	1.10757e18i	0.0436185	−	0.0251831i
$641$	3.71351e19	+	6.43200e19i	0.835178	+	1.44657i	0.893886	+	0.448295i	$0.147969\pi$
$641$	3.71351e19	+	6.43200e19i	0.835178	+	1.44657i	−0.0587079	+	0.998275i	$0.518698\pi$
$642$		0			0
$643$		−	1.53471e19i		−	0.337715i	−0.985641	−	0.168857i	$-0.945992\pi$
$643$		−	1.53471e19i		−	0.337715i	0.985641	−	0.168857i	$-0.0540077\pi$
$644$	−2.34240e19	+	1.25631e19i	−0.509871	+	0.273462i
$645$		0			0
$646$	−6.87948e18	+	1.19156e19i	−0.146531	+	0.253798i
$647$	1.41075e19	−	8.14499e18i	0.297250	−	0.171617i	−0.343957	−	0.938985i	$-0.611767\pi$
$647$	1.41075e19	−	8.14499e18i	0.297250	−	0.171617i	0.641207	+	0.767368i	$0.278434\pi$
$648$		0			0
$649$	2.04845e19	+	1.18267e19i	0.422389	+	0.243866i
$650$			2.97092e19i			0.606035i
$651$		0			0
$652$	1.73660e19			0.346711
$653$	−2.70795e19	+	4.69030e19i	−0.534869	+	0.926421i	0.464300	+	0.885678i	$0.346306\pi$
$653$	−2.70795e19	+	4.69030e19i	−0.534869	+	0.926421i	−0.999170	+	0.0407430i	$0.987028\pi$
$654$		0			0
$655$	−1.05955e19	−	1.83520e19i	−0.204848	−	0.354808i
$656$	1.12416e19	+	6.49036e18i	0.215032	+	0.124149i
$657$		0			0
$658$	−2.83203e19	+	4.56871e19i	−0.530294	+	0.855484i
$659$	1.49061e19			0.276163			0.138081	−	0.990421i	$-0.455906\pi$
$659$	1.49061e19			0.276163			0.138081	+	0.990421i	$0.455906\pi$
$660$		0			0
$661$	−1.30899e18	+	7.55746e17i	−0.0237425	+	0.0137077i	−0.511824	−	0.859090i	$-0.671030\pi$
$661$	−1.30899e18	+	7.55746e17i	−0.0237425	+	0.0137077i	0.488082	+	0.872798i	$0.337697\pi$
$662$	1.70705e18	+	2.95670e18i	0.0306366	+	0.0530641i
$663$		0			0
$664$		−	5.37329e18i		−	0.0944200i
$665$	3.80875e19	+	2.36095e19i	0.662264	+	0.410522i
$666$		0			0
$667$	1.79880e19	−	3.11561e19i	0.306268	−	0.530472i
$668$	−7.61612e18	+	4.39717e18i	−0.128321	+	0.0740863i
$669$		0			0
$670$	−2.94000e18	−	1.69741e18i	−0.0485092	−	0.0280068i
$671$		−	2.19484e19i		−	0.358381i
$672$		0			0
$673$	4.17784e19			0.668107			0.334054	−	0.942554i	$-0.391583\pi$
$673$	4.17784e19			0.668107			0.334054	+	0.942554i	$0.391583\pi$
$674$	1.12993e19	−	1.95709e19i	0.178826	−	0.309736i
$675$		0			0
$676$	9.85051e18	+	1.70616e19i	0.152697	+	0.264480i
$677$	4.84118e19	+	2.79506e19i	0.742730	+	0.428815i	0.823061	−	0.567953i	$-0.192264\pi$
$677$	4.84118e19	+	2.79506e19i	0.742730	+	0.428815i	−0.0803311	+	0.996768i	$0.525598\pi$
$678$		0			0
$679$	1.69915e18	+	3.16808e18i	0.0255355	+	0.0476110i
$680$	4.10527e18			0.0610632
$681$		0			0
$682$	1.16781e19	−	6.74235e18i	0.170169	−	0.0982473i
$683$	−6.33178e19	−	1.09670e20i	−0.913232	−	1.58176i	−0.809469	−	0.587163i	$-0.800245\pi$
$683$	−6.33178e19	−	1.09670e20i	−0.913232	−	1.58176i	−0.103763	−	0.994602i	$-0.533088\pi$
$684$		0			0
$685$			2.22345e19i			0.314190i
$686$	4.12173e19	+	2.92714e19i	0.576516	+	0.409426i
$687$		0			0
$688$	−9.21978e18	+	1.59691e19i	−0.126358	+	0.218858i
$689$	1.23550e20	−	7.13317e19i	1.67613	−	0.967716i
$690$		0			0
$691$	6.65969e19	+	3.84497e19i	0.885335	+	0.511148i	0.872414	−	0.488768i	$-0.162554\pi$
$691$	6.65969e19	+	3.84497e19i	0.885335	+	0.511148i	0.0129211	+	0.999917i	$0.495887\pi$
$692$			4.90803e19i			0.645899i
$693$		0			0
$694$	−5.89033e19			−0.759667
$695$	2.00042e19	−	3.46483e19i	0.255404	−	0.442373i
$696$		0			0
$697$	1.20285e19	+	2.08340e19i	0.150516	+	0.260701i
$698$	−4.91871e19	−	2.83982e19i	−0.609345	−	0.351806i
$699$		0			0
$700$	−8.70412e17	+	2.77931e19i	−0.0105691	+	0.337482i
$701$	−1.80979e19			−0.217571			−0.108786	−	0.994065i	$-0.534696\pi$
$701$	−1.80979e19			−0.217571			−0.108786	+	0.994065i	$0.534696\pi$
$702$		0			0
$703$	1.84443e20	−	1.06488e20i	2.17358	−	1.25491i
$704$	−1.46867e18	−	2.54381e18i	−0.0171362	−	0.0296808i
$705$		0			0
$706$			4.04012e19i			0.462127i
$707$	3.13747e19	−	5.06145e19i	0.355340	−	0.573243i
$708$		0			0
$709$	7.13792e19	−	1.23632e20i	0.792589	−	1.37280i	−0.131770	−	0.991280i	$-0.542066\pi$
$709$	7.13792e19	−	1.23632e20i	0.792589	−	1.37280i	0.924359	−	0.381524i	$-0.124601\pi$
$710$	−2.16261e19	+	1.24858e19i	−0.237776	+	0.137280i
$711$		0			0
$712$	1.29470e19	+	7.47494e18i	0.139575	+	0.0805838i
$713$		−	1.09862e20i		−	1.17279i
$714$		0			0
$715$	−1.89427e19			−0.198289
$716$	−7.65757e18	+	1.32633e19i	−0.0793780	+	0.137487i
$717$		0			0
$718$	−2.31566e19	−	4.01084e19i	−0.235399	−	0.407722i
$719$	−9.32773e18	−	5.38537e18i	−0.0939018	−	0.0542142i	0.452314	−	0.891859i	$-0.350599\pi$
$719$	−9.32773e18	−	5.38537e18i	−0.0939018	−	0.0542142i	−0.546216	+	0.837645i	$0.683932\pi$
$720$		0			0
$721$	−5.35492e19	−	1.67703e18i	−0.528696	−	0.0165575i
$722$	−6.28994e19			−0.615015
$723$		0			0
$724$	−4.60941e19	+	2.66125e19i	−0.442055	+	0.255220i
$725$	−1.88179e19	−	3.25936e19i	−0.178733	−	0.309575i
$726$		0			0
$727$			3.78756e19i			0.352873i	0.984312	+	0.176436i	$0.0564570\pi$
$727$			3.78756e19i			0.352873i	−0.984312	+	0.176436i	$0.943543\pi$
$728$	2.29843e19	+	4.28543e19i	0.212085	+	0.395435i
$729$		0			0
$730$	−2.02818e19	+	3.51291e19i	−0.183589	+	0.317985i
$731$	−2.95954e19	+	1.70869e19i	−0.265340	+	0.153194i
$732$		0			0
$733$	−4.43918e19	−	2.56296e19i	−0.390459	−	0.225432i	0.291900	−	0.956449i	$-0.405713\pi$
$733$	−4.43918e19	−	2.56296e19i	−0.390459	−	0.225432i	−0.682359	+	0.731017i	$0.739046\pi$
$734$		−	7.07097e19i		−	0.616037i
$735$		0			0
$736$	−2.39309e19			−0.204557
$737$	−2.25082e18	+	3.89853e18i	−0.0190576	+	0.0330087i
$738$		0			0
$739$	8.81253e19	+	1.52637e20i	0.732132	+	1.26809i	0.955970	+	0.293464i	$0.0948079\pi$
$739$	8.81253e19	+	1.52637e20i	0.732132	+	1.26809i	−0.223838	+	0.974626i	$0.571859\pi$
$740$	−5.50324e19	−	3.17730e19i	−0.452894	−	0.261478i
$741$		0			0
$742$	1.17671e20	−	6.31113e19i	0.950263	−	0.509659i
$743$	6.26592e19			0.501260			0.250630	−	0.968083i	$-0.419362\pi$
$743$	6.26592e19			0.501260			0.250630	+	0.968083i	$0.419362\pi$
$744$		0			0
$745$	2.86421e19	−	1.65365e19i	0.224859	−	0.129823i
$746$	−1.65349e19	−	2.86393e19i	−0.128597	−	0.222736i
$747$		0			0
$748$		−	5.44372e18i		−	0.0415513i
$749$	−4.72967e18	+	1.51023e20i	−0.0357650	+	1.14201i
$750$		0			0
$751$	−1.21616e20	+	2.10644e20i	−0.902629	+	1.56340i	−0.0785611	+	0.996909i	$0.525033\pi$
$751$	−1.21616e20	+	2.10644e20i	−0.902629	+	1.56340i	−0.824068	+	0.566491i	$0.808301\pi$
$752$	−4.19111e19	+	2.41974e19i	−0.308180	+	0.177928i
$753$		0			0
$754$	−5.70002e19	−	3.29091e19i	−0.411412	−	0.237529i
$755$			5.70708e19i			0.408118i
$756$		0			0
$757$	2.19935e20			1.54391			0.771956	−	0.635676i	$-0.219279\pi$
$757$	2.19935e20			1.54391			0.771956	+	0.635676i	$0.219279\pi$
$758$	−3.92268e19	+	6.79429e19i	−0.272834	+	0.472563i
$759$		0			0
$760$	2.01724e19	+	3.49397e19i	0.137741	+	0.238574i
$761$	−8.60729e19	−	4.96942e19i	−0.582336	−	0.336212i	0.179725	−	0.983717i	$-0.442479\pi$
$761$	−8.60729e19	−	4.96942e19i	−0.582336	−	0.336212i	−0.762061	+	0.647505i	$0.775812\pi$
$762$		0			0
$763$	−9.35479e19	−	5.79881e19i	−0.621387	−	0.385183i
$764$	−5.67827e18			−0.0373734
$765$		0			0
$766$	3.21349e19	−	1.85531e19i	0.207671	−	0.119899i
$767$	−1.76280e20	−	3.05327e20i	−1.12885	−	1.95523i
$768$		0			0
$769$		−	2.45034e20i		−	1.54078i	−0.637570	−	0.770392i	$-0.720060\pi$
$769$		−	2.45034e20i		−	1.54078i	0.637570	−	0.770392i	$-0.279940\pi$
$770$	−1.77209e19	−	5.54977e17i	−0.110421	−	0.00345812i
$771$		0			0
$772$	−3.59369e19	+	6.22445e19i	−0.219897	+	0.380873i
$773$	1.27651e20	−	7.36995e19i	0.774050	−	0.446898i	−0.0602677	−	0.998182i	$-0.519195\pi$
$773$	1.27651e20	−	7.36995e19i	0.774050	−	0.446898i	0.834317	+	0.551284i	$0.185862\pi$
$774$		0			0
$775$	−9.95330e19	−	5.74654e19i	−0.592728	−	0.342211i
$776$			3.23664e18i			0.0191013i
$777$		0			0
$778$	−5.04935e19			−0.292670
$779$	−1.18211e20	+	2.04747e20i	−0.679040	+	1.17613i
$780$		0			0
$781$	1.65566e19	+	2.86768e19i	0.0934142	+	0.161798i
$782$	−3.84090e19	−	2.21754e19i	−0.214776	−	0.124001i
$783$		0			0
$784$	2.02463e19	+	4.07637e19i	0.111207	+	0.223904i
$785$	9.15914e19			0.498617
$786$		0			0
$787$	7.71007e19	−	4.45141e19i	0.412321	−	0.238053i	−0.279466	−	0.960156i	$-0.590157\pi$
$787$	7.71007e19	−	4.45141e19i	0.412321	−	0.238053i	0.691786	+	0.722102i	$0.256824\pi$
$788$	7.49017e19	+	1.29733e20i	0.397016	+	0.687652i
$789$		0			0
$790$			1.51652e19i			0.0789694i
$791$	2.51834e20	−	1.35068e20i	1.29981	−	0.697133i
$792$		0			0
$793$	−1.63573e20	+	2.83317e20i	−0.829469	+	1.43668i
$794$	5.78421e19	−	3.33952e19i	0.290737	−	0.167857i
$795$		0			0
$796$	8.42820e18	+	4.86602e18i	0.0416239	+	0.0240316i
$797$			1.70408e20i			0.834225i	0.908855	+	0.417112i	$0.136958\pi$
$797$			1.70408e20i			0.834225i	−0.908855	+	0.417112i	$0.863042\pi$
$798$		0			0
$799$	−8.96894e19			−0.431433
$800$	−1.25175e19	+	2.16810e19i	−0.0596882	+	0.103383i
$801$		0			0
$802$	−1.00361e20	−	1.73830e20i	−0.470265	−	0.814523i
$803$	4.65823e19	+	2.68943e19i	0.216377	+	0.124926i
$804$		0			0
$805$	−7.61034e19	+	1.22772e20i	−0.347402	+	0.560439i
$806$	−2.00993e20			−0.909569
$807$		0			0
$808$	4.64313e19	−	2.68071e19i	0.206505	−	0.119226i
$809$	−1.08746e20	−	1.88354e20i	−0.479484	−	0.830490i	0.520240	−	0.854020i	$-0.325843\pi$
$809$	−1.08746e20	−	1.88354e20i	−0.479484	−	0.830490i	−0.999723	+	0.0235305i	$0.992509\pi$
$810$		0			0
$811$		−	1.24772e20i		−	0.540717i	−0.962760	−	0.270359i	$-0.912858\pi$
$811$		−	1.24772e20i		−	0.540717i	0.962760	−	0.270359i	$-0.0871423\pi$
$812$	−5.23597e19	−	3.24565e19i	−0.224960	−	0.139447i
$813$		0			0
$814$	−4.21319e19	+	7.29746e19i	−0.177926	+	0.308178i
$815$	8.17289e19	−	4.71862e19i	0.342194	−	0.197566i
$816$		0			0
$817$	−2.90850e20	−	1.67923e20i	−1.19706	−	0.691122i
$818$			2.31504e20i			0.944682i
$819$		0			0
$820$	7.05413e19			0.282974
$821$	3.87923e19	−	6.71902e19i	0.154292	−	0.267242i	−0.778509	−	0.627633i	$-0.784024\pi$
$821$	3.87923e19	−	6.71902e19i	0.154292	−	0.267242i	0.932801	+	0.360392i	$0.117357\pi$
$822$		0			0
$823$	−1.96370e20	−	3.40123e20i	−0.767850	−	1.32996i	−0.938727	−	0.344663i	$-0.887993\pi$
$823$	−1.96370e20	−	3.40123e20i	−0.767850	−	1.32996i	0.170877	−	0.985292i	$-0.445340\pi$
$824$	−4.17729e19	−	2.41176e19i	−0.161959	−	0.0935069i
$825$		0			0
$826$	−1.55966e20	−	2.90799e20i	−0.594523	−	1.10849i
$827$	−1.72427e20			−0.651727			−0.325864	−	0.945417i	$-0.605655\pi$
$827$	−1.72427e20			−0.651727			−0.325864	+	0.945417i	$0.605655\pi$
$828$		0			0
$829$	−2.25989e20	+	1.30475e20i	−0.839859	+	0.484893i	−0.857216	−	0.514957i	$-0.827808\pi$
$829$	−2.25989e20	+	1.30475e20i	−0.839859	+	0.484893i	0.0173575	+	0.999849i	$0.494475\pi$
$830$	−1.46001e19	−	2.52881e19i	−0.0538033	−	0.0931900i
$831$		0			0
$832$			4.37817e19i			0.158646i
$833$	−5.27822e18	+	8.41866e19i	−0.0189659	+	0.302502i
$834$		0			0
$835$	−2.38956e19	+	4.13884e19i	−0.0844331	+	0.146242i
$836$	4.63311e19	−	2.67493e19i	0.162341	−	0.0937277i
$837$		0			0
$838$	2.78145e20	+	1.60587e20i	0.958437	+	0.553354i
$839$			2.35212e19i			0.0803758i	0.999192	+	0.0401879i	$0.0127957\pi$
$839$			2.35212e19i			0.0803758i	−0.999192	+	0.0401879i	$0.987204\pi$
$840$		0			0
$841$	−2.14179e20			−0.719790
$842$	1.06555e20	−	1.84559e20i	0.355132	−	0.615106i
$843$		0			0
$844$	1.11606e20	+	1.93308e20i	0.365840	+	0.633654i
$845$	9.27180e19	+	5.35308e19i	0.301417	+	0.174023i
$846$		0			0
$847$	9.05355e18	−	2.89089e20i	0.0289491	−	0.924373i
$848$	1.20218e20			0.381240
$849$		0			0
$850$	−4.01811e19	+	2.31985e19i	−0.125340	+	0.0723650i
$851$	3.43256e20	+	5.94537e20i	1.06197	+	1.83938i
$852$		0			0
$853$			2.15554e19i			0.0656013i	0.999462	+	0.0328007i	$0.0104426\pi$
$853$			2.15554e19i			0.0656013i	−0.999462	+	0.0328007i	$0.989557\pi$
$854$	−1.61324e20	+	2.60252e20i	−0.486961	+	0.785578i
$855$		0			0
$856$	−6.80180e19	+	1.17811e20i	−0.201980	+	0.349839i
$857$	−7.17916e19	+	4.14489e19i	−0.211450	+	0.122081i	−0.601985	−	0.798507i	$-0.705623\pi$
$857$	−7.17916e19	+	4.14489e19i	−0.211450	+	0.122081i	0.390535	+	0.920588i	$0.372290\pi$
$858$		0			0
$859$	−3.05644e20	−	1.76464e20i	−0.885654	−	0.511332i	−0.0131354	−	0.999914i	$-0.504181\pi$
$859$	−3.05644e20	−	1.76464e20i	−0.885654	−	0.511332i	−0.872518	+	0.488581i	$0.837515\pi$
$860$			1.00206e20i			0.288009i
$861$		0			0
$862$	6.14035e19			0.173637
$863$	1.25873e20	−	2.18018e20i	0.353067	−	0.611530i	−0.633718	−	0.773564i	$-0.718472\pi$
$863$	1.25873e20	−	2.18018e20i	0.353067	−	0.611530i	0.986785	+	0.162034i	$0.0518055\pi$
$864$		0			0
$865$	1.33359e20	+	2.30984e20i	0.368052	+	0.637484i
$866$	−2.78121e20	−	1.60573e20i	−0.761394	−	0.439591i
$867$		0			0
$868$	−1.88030e20	−	5.88863e18i	−0.506510	−	0.0158627i
$869$	2.01095e19			0.0537358
$870$		0			0
$871$	5.81087e19	−	3.35490e19i	0.152797	−	0.0882172i
$872$	−4.95461e19	−	8.58163e19i	−0.129239	−	0.223849i
$873$		0			0
$874$		−	4.35861e20i		−	1.11884i
$875$	1.77186e20	+	3.30364e20i	0.451203	+	0.841271i
$876$		0			0
$877$	1.90881e20	−	3.30616e20i	0.478372	−	0.828565i	−0.521320	−	0.853361i	$-0.674560\pi$
$877$	1.90881e20	−	3.30616e20i	0.478372	−	0.828565i	0.999693	+	0.0247962i	$0.00789370\pi$
$878$	−2.29089e20	+	1.32264e20i	−0.569563	+	0.328837i
$879$		0			0
$880$	−1.38238e19	−	7.98120e18i	−0.0338259	−	0.0195294i
$881$			2.65263e20i			0.643941i	0.946750	+	0.321970i	$0.104345\pi$
$881$			2.65263e20i			0.643941i	−0.946750	+	0.321970i	$0.895655\pi$
$882$		0			0
$883$	3.08288e20			0.736601			0.368300	−	0.929707i	$-0.379940\pi$
$883$	3.08288e20			0.736601			0.368300	+	0.929707i	$0.379940\pi$
$884$	−4.05700e19	+	7.02693e19i	−0.0961699	+	0.166571i
$885$		0			0
$886$	−2.58843e20	−	4.48329e20i	−0.603949	−	1.04607i
$887$	−3.38946e20	−	1.95690e20i	−0.784630	−	0.453006i	0.0534389	−	0.998571i	$-0.482982\pi$
$887$	−3.38946e20	−	1.95690e20i	−0.784630	−	0.453006i	−0.838069	+	0.545565i	$0.816315\pi$
$888$		0			0
$889$	−2.65425e20	+	1.42357e20i	−0.604825	+	0.324389i
$890$	8.12423e19			0.183676
$891$		0			0
$892$	−5.72096e19	+	3.30300e19i	−0.127325	+	0.0735114i
$893$	−4.40714e20	−	7.63339e20i	−0.973188	−	1.68561i
$894$		0			0
$895$			8.32273e19i			0.180928i
$896$	−1.28270e18	+	4.09579e19i	−0.00276675	+	0.0883450i
$897$		0			0
$898$	−2.84087e20	+	4.92053e20i	−0.603277	+	1.04491i
$899$	2.20507e20	−	1.27310e20i	0.464626	−	0.268252i
$900$		0			0
$901$	1.92949e20	+	1.11399e20i	0.400285	+	0.231105i
$902$		−	9.35400e19i		−	0.192554i
$903$		0			0
$904$	2.57284e20			0.521476
$905$	−1.44621e20	+	2.50490e20i	−0.290864	+	0.503791i
$906$		0			0
$907$	7.93635e19	+	1.37462e20i	0.157170	+	0.272226i	0.933847	−	0.357673i	$-0.116430\pi$
$907$	7.93635e19	+	1.37462e20i	0.157170	+	0.272226i	−0.776677	+	0.629899i	$0.783096\pi$
$908$	5.04534e18	+	2.91293e18i	0.00991493	+	0.00572439i
$909$		0			0
$910$	2.24612e20	+	1.39231e20i	0.434653	+	0.269431i
$911$	−3.49365e20			−0.670889			−0.335445	−	0.942060i	$-0.608887\pi$
$911$	−3.49365e20			−0.670889			−0.335445	+	0.942060i	$0.608887\pi$
$912$		0			0
$913$	−3.35328e19	+	1.93602e19i	−0.0634124	+	0.0366112i
$914$	6.97606e19	+	1.20829e20i	0.130914	+	0.226750i
$915$		0			0
$916$			4.32750e20i			0.799776i
$917$	3.91824e20	+	1.22710e19i	0.718630	+	0.0225057i
$918$		0			0
$919$	−6.03407e19	+	1.04513e20i	−0.108994	+	0.188783i	−0.915363	−	0.402630i	$-0.868096\pi$
$919$	−6.03407e19	+	1.04513e20i	−0.108994	+	0.188783i	0.806369	+	0.591413i	$0.201430\pi$
$920$	−1.12625e20	+	6.50241e19i	−0.201893	+	0.116563i
$921$		0			0
$922$	−2.21370e20	−	1.27808e20i	−0.390844	−	0.225654i
$923$		−	4.93560e20i		−	0.864824i
$924$		0			0
$925$	7.18185e20			1.23949
$926$	2.52009e20	−	4.36493e20i	0.431658	−	0.747654i
$927$		0			0
$928$	−2.77315e19	−	4.80323e19i	−0.0467883	−	0.0810396i
$929$	−3.15644e20	−	1.82237e20i	−0.528552	−	0.305159i	0.211875	−	0.977297i	$-0.432043\pi$
$929$	−3.15644e20	−	1.82237e20i	−0.528552	−	0.305159i	−0.740426	+	0.672137i	$0.765376\pi$
$930$		0			0
$931$	−7.42442e20	+	3.68752e20i	−1.22466	+	0.608257i
$932$	2.64283e20			0.432671
$933$		0			0
$934$	1.26691e20	−	7.31452e19i	0.204324	−	0.117966i
$935$	−1.47914e19	−	2.56195e19i	−0.0236771	−	0.0410100i
$936$		0			0
$937$			4.84631e20i			0.764248i	0.924111	+	0.382124i	$0.124807\pi$
$937$			4.84631e20i			0.764248i	−0.924111	+	0.382124i	$0.875193\pi$
$938$	5.53438e19	−	2.96828e19i	0.0866261	−	0.0464606i
$939$		0			0
$940$	−1.31496e20	+	2.27758e20i	−0.202777	+	0.351220i
$941$	−2.38054e20	+	1.37440e20i	−0.364374	+	0.210372i	−0.670998	−	0.741459i	$-0.734134\pi$
$941$	−2.38054e20	+	1.37440e20i	−0.364374	+	0.210372i	0.306624	+	0.951831i	$0.400801\pi$
$942$		0			0
$943$	−6.59986e20	−	3.81043e20i	−0.995297	−	0.574635i
$944$		−	2.97092e20i		−	0.444720i
$945$		0			0
$946$	1.32877e20			0.195980
$947$	−5.24233e20	+	9.07998e20i	−0.767493	+	1.32934i	0.171426	+	0.985197i	$0.445163\pi$
$947$	−5.24233e20	+	9.07998e20i	−0.767493	+	1.32934i	−0.938918	+	0.344140i	$0.888171\pi$
$948$		0			0
$949$	−4.00866e20	−	6.94321e20i	−0.578277	−	1.00161i
$950$	−3.94882e20	−	2.27985e20i	−0.565461	−	0.326469i
$951$		0			0
$952$	−4.00121e19	+	6.45486e19i	−0.0564590	+	0.0910811i
$953$	−9.35175e20			−1.30991			−0.654957	−	0.755666i	$-0.727313\pi$
$953$	−9.35175e20			−1.30991			−0.654957	+	0.755666i	$0.727313\pi$
$954$		0			0
$955$	−2.67234e19	+	1.54288e19i	−0.0368866	+	0.0212965i
$956$	1.01301e20	+	1.75459e20i	0.138807	+	0.240420i
$957$		0			0
$958$		−	7.67131e20i		−	1.03588i
$959$	−3.49600e20	−	2.16709e20i	−0.468642	−	0.290500i
$960$		0			0
$961$	1.03009e19	−	1.78418e19i	0.0136086	−	0.0235708i
$962$	1.08771e21	−	6.27987e20i	1.42655	−	0.823617i
$963$		0			0
$964$	4.49010e20	+	2.59236e20i	0.580386	+	0.335086i
$965$			3.90585e20i			0.501215i
$966$		0			0
$967$	9.32261e20			1.17910			0.589552	−	0.807730i	$-0.299304\pi$
$967$	9.32261e20			1.17910			0.589552	+	0.807730i	$0.299304\pi$
$968$	1.30200e20	−	2.25514e20i	0.163488	−	0.283169i
$969$		0			0
$970$	8.79446e18	+	1.52325e19i	0.0108845	+	0.0188525i
$971$	−8.85544e20	−	5.11269e20i	−1.08812	−	0.628225i	−0.155042	−	0.987908i	$-0.549551\pi$
$971$	−8.85544e20	−	5.11269e20i	−1.08812	−	0.628225i	−0.933074	+	0.359683i	$0.882885\pi$
$972$		0			0
$973$	3.49816e20	+	6.52233e20i	0.423691	+	0.789975i
$974$	1.13284e21			1.36225
$975$		0			0
$976$	−2.38743e20	+	1.37838e20i	−0.282997	+	0.163388i
$977$	−4.47836e20	−	7.75675e20i	−0.527056	−	0.912888i	−0.999503	−	0.0315289i	$-0.989962\pi$
$977$	−4.47836e20	−	7.75675e20i	−0.527056	−	0.912888i	0.472447	−	0.881359i	$-0.343371\pi$
$978$		0			0
$979$		−	1.07730e20i		−	0.124985i
$980$	2.06046e20	+	1.36832e20i	0.237346	+	0.157618i
$981$		0			0
$982$	5.11014e20	−	8.85103e20i	0.580300	−	1.00511i
$983$	9.46057e20	−	5.46206e20i	1.06670	−	0.615860i	0.139423	−	0.990233i	$-0.455475\pi$
$983$	9.46057e20	−	5.46206e20i	1.06670	−	0.615860i	0.927278	+	0.374373i	$0.122142\pi$
$984$		0			0
$985$	7.05013e20	+	4.07039e20i	0.783688	+	0.452463i
$986$		−	1.02789e20i		−	0.113451i
$987$		0			0
$988$	−7.97409e20			−0.867726
$989$	5.41284e20	−	9.37532e20i	0.584859	−	1.01301i
$990$		0			0
$991$	2.42367e20	+	4.19791e20i	0.258200	+	0.447216i	0.965760	−	0.259437i	$-0.0835372\pi$
$991$	2.42367e20	+	4.19791e20i	0.258200	+	0.447216i	−0.707559	+	0.706654i	$0.750204\pi$
$992$	−1.46679e20	−	8.46853e19i	−0.155163	−	0.0895831i
$993$		0			0
$994$	1.44602e19	−	4.61727e20i	0.0150823	−	0.481593i
$995$	5.28870e19			0.0547756
$996$		0			0
$997$	5.07994e19	−	2.93291e19i	0.0518791	−	0.0299524i	−0.473836	−	0.880613i	$-0.657131\pi$
$997$	5.07994e19	−	2.93291e19i	0.0518791	−	0.0299524i	0.525715	+	0.850661i	$0.323798\pi$
$998$	1.49371e20	+	2.58718e20i	0.151479	+	0.262370i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.15.n.b.19.2		20
3.2	odd	2		14.15.d.a.5.10	yes	20
7.3	odd	6	inner	126.15.n.b.73.2		20
21.2	odd	6		98.15.b.c.97.10		20
21.5	even	6		98.15.b.c.97.1		20
21.11	odd	6		98.15.d.b.31.6		20
21.17	even	6		14.15.d.a.3.10	✓	20
21.20	even	2		98.15.d.b.19.6		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.15.d.a.3.10	✓	20	21.17	even	6
14.15.d.a.5.10	yes	20	3.2	odd	2
98.15.b.c.97.1		20	21.5	even	6
98.15.b.c.97.10		20	21.2	odd	6
98.15.d.b.19.6		20	21.20	even	2
98.15.d.b.31.6		20	21.11	odd	6
126.15.n.b.19.2		20	1.1	even	1	trivial
126.15.n.b.73.2		20	7.3	odd	6	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:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 15 \)
Character orbit:	\([\chi]\)	\(=\)	126.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-45.2548 + 78.3837i) q^{2} +(-4096.00 - 7094.48i) q^{4} +(-38553.6 - 22259.0i) q^{5} +(725749. - 389245. i) q^{7} +741455. q^{8} +O(q^{10})\)	\(q+(-45.2548 + 78.3837i) q^{2} +(-4096.00 - 7094.48i) q^{4} +(-38553.6 - 22259.0i) q^{5} +(725749. - 389245. i) q^{7} +741455. q^{8} +(3.48948e6 - 2.01465e6i) q^{10} +(-2.67149e6 - 4.62715e6i) q^{11} +7.96385e7i q^{13} +(-2.33322e6 + 7.45021e7i) q^{14} +(-3.35544e7 + 5.81180e7i) q^{16} +(-1.07709e8 + 6.21860e7i) q^{17} +(-1.05852e9 - 6.11137e8i) q^{19} +3.64691e8i q^{20} +4.83591e8 q^{22} +(1.96995e9 - 3.41205e9i) q^{23} +(-2.06084e9 - 3.56947e9i) q^{25} +(-6.24236e9 - 3.60403e9i) q^{26} +(-5.73416e9 - 3.55447e9i) q^{28} +9.13120e9 q^{29} +(2.41487e10 - 1.39423e10i) q^{31} +(-3.03700e9 - 5.26024e9i) q^{32} -1.12569e10i q^{34} +(-3.66444e10 - 1.14762e9i) q^{35} +(-8.71230e10 + 1.50902e11i) q^{37} +(9.58063e10 - 5.53138e10i) q^{38} +(-2.85858e10 - 1.65040e10i) q^{40} -1.93428e11i q^{41} +2.74771e11 q^{43} +(-2.18848e10 + 3.79056e10i) q^{44} +(1.78299e11 + 3.08824e11i) q^{46} +(6.24524e11 + 3.60569e11i) q^{47} +(3.75200e11 - 5.64988e11i) q^{49} +3.73051e11 q^{50} +(5.64994e11 - 3.26199e11i) q^{52} +(-8.95694e11 - 1.55139e12i) q^{53} +2.37858e11i q^{55} +(5.38110e11 - 2.88607e11i) q^{56} +(-4.13231e11 + 7.15737e11i) q^{58} +(-3.83391e12 + 2.21351e12i) q^{59} +(3.55754e12 + 2.05395e12i) q^{61} +2.52382e12i q^{62} +5.49756e11 q^{64} +(1.77267e12 - 3.07035e12i) q^{65} +(-4.21267e11 - 7.29656e11i) q^{67} +(8.82354e11 + 5.09427e11i) q^{68} +(1.74829e12 - 2.82039e12i) q^{70} -6.19751e12 q^{71} +(-8.71841e12 + 5.03358e12i) q^{73} +(-7.88548e12 - 1.36580e13i) q^{74} +1.00129e13i q^{76} +(-3.73993e12 - 2.31829e12i) q^{77} +(-1.88187e12 + 3.25949e12i) q^{79} +(2.58729e12 - 1.49377e12i) q^{80} +(1.51616e13 + 8.75354e12i) q^{82} -7.24696e12i q^{83} +5.53678e12 q^{85} +(-1.24347e13 + 2.15375e13i) q^{86} +(-1.98079e12 - 3.43083e12i) q^{88} +(1.74616e13 + 1.00814e13i) q^{89} +(3.09988e13 + 5.77975e13i) q^{91} -3.22756e13 q^{92} +(-5.65255e13 + 3.26350e13i) q^{94} +(2.72065e13 + 4.71231e13i) q^{95} +4.36526e12i q^{97} +(2.73062e13 + 5.49780e13i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 81920 q^{4} - 3354 q^{5} + 1455616 q^{7}+O(q^{10}) \) 20 * q - 81920 * q^4 - 3354 * q^5 + 1455616 * q^7	\( 20 q - 81920 q^{4} - 3354 q^{5} + 1455616 q^{7} - 3933696 q^{10} - 8400426 q^{11} + 114693888 q^{14} - 671088640 q^{16} - 2180481042 q^{17} - 3919727442 q^{19} + 5394565632 q^{22} + 6905098386 q^{23} + 14165082644 q^{25} - 12652202496 q^{26} - 17334943744 q^{28} - 27884908704 q^{29} + 45638710782 q^{31} + 18274367202 q^{35} - 27026027926 q^{37} + 354043974912 q^{38} + 32224837632 q^{40} + 726682953656 q^{43} - 68816289792 q^{44} - 286664984832 q^{46} + 2044625353338 q^{47} + 2939974016204 q^{49} - 1161106642944 q^{50} + 1314350333952 q^{52} - 1546271487546 q^{53} - 1720927125504 q^{56} - 2365863040512 q^{58} + 6798944731566 q^{59} - 2214453865554 q^{61} + 10995116277760 q^{64} - 7516703932836 q^{65} - 4655820763226 q^{67} + 17862500696064 q^{68} + 20497461621504 q^{70} - 96606137494152 q^{71} - 65348368908666 q^{73} + 566532483072 q^{74} - 77525241691422 q^{77} - 60517474082978 q^{79} + 225083129856 q^{80} - 43979002397184 q^{82} + 416326699526124 q^{85} - 2363335174656 q^{86} - 22096140828672 q^{88} + 237147002561826 q^{89} + 203506111374408 q^{91} - 113133131956224 q^{92} - 221058962902272 q^{94} - 25202514515490 q^{95} - 165606984015360 q^{98}+O(q^{100}) \) 20 * q - 81920 * q^4 - 3354 * q^5 + 1455616 * q^7 - 3933696 * q^10 - 8400426 * q^11 + 114693888 * q^14 - 671088640 * q^16 - 2180481042 * q^17 - 3919727442 * q^19 + 5394565632 * q^22 + 6905098386 * q^23 + 14165082644 * q^25 - 12652202496 * q^26 - 17334943744 * q^28 - 27884908704 * q^29 + 45638710782 * q^31 + 18274367202 * q^35 - 27026027926 * q^37 + 354043974912 * q^38 + 32224837632 * q^40 + 726682953656 * q^43 - 68816289792 * q^44 - 286664984832 * q^46 + 2044625353338 * q^47 + 2939974016204 * q^49 - 1161106642944 * q^50 + 1314350333952 * q^52 - 1546271487546 * q^53 - 1720927125504 * q^56 - 2365863040512 * q^58 + 6798944731566 * q^59 - 2214453865554 * q^61 + 10995116277760 * q^64 - 7516703932836 * q^65 - 4655820763226 * q^67 + 17862500696064 * q^68 + 20497461621504 * q^70 - 96606137494152 * q^71 - 65348368908666 * q^73 + 566532483072 * q^74 - 77525241691422 * q^77 - 60517474082978 * q^79 + 225083129856 * q^80 - 43979002397184 * q^82 + 416326699526124 * q^85 - 2363335174656 * q^86 - 22096140828672 * q^88 + 237147002561826 * q^89 + 203506111374408 * q^91 - 113133131956224 * q^92 - 221058962902272 * q^94 - 25202514515490 * q^95 - 165606984015360 * q^98

Introduction

L-functions

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