LMFDB - Embedded newform 126.15.n.b.19.4

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			19.4
Root			$22558.5 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	126.19
Dual form			126.15.n.b.73.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-45.2548 + 78.3837i) q^{2} +(-4096.00 - 7094.48i) q^{4} +(67507.4 + 38975.4i) q^{5} +(-346065. + 747303. i) q^{7} +741455. q^{8} +O(q^{10})$	\(q+(-45.2548 + 78.3837i) q^{2} +(-4096.00 - 7094.48i) q^{4} +(67507.4 + 38975.4i) q^{5} +(-346065. + 747303. i) q^{7} +741455. q^{8} +(-6.11007e6 + 3.52765e6i) q^{10} +(4.94890e6 + 8.57174e6i) q^{11} -1.06948e7i q^{13} +(-4.29153e7 - 6.09449e7i) q^{14} +(-3.35544e7 + 5.81180e7i) q^{16} +(2.56175e8 - 1.47903e8i) q^{17} +(3.85399e8 + 2.22510e8i) q^{19} -6.38573e8i q^{20} -8.95846e8 q^{22} +(1.70339e9 - 2.95036e9i) q^{23} +(-1.35959e7 - 2.35488e7i) q^{25} +(8.38298e8 + 4.83992e8i) q^{26} +(6.71921e9 - 6.05806e8i) q^{28} +2.75528e10 q^{29} +(-5.44700e9 + 3.14483e9i) q^{31} +(-3.03700e9 - 5.26024e9i) q^{32} +2.67733e10i q^{34} +(-5.24883e10 + 3.69605e10i) q^{35} +(9.12395e10 - 1.58031e11i) q^{37} +(-3.48824e10 + 2.01393e10i) q^{38} +(5.00537e10 + 2.88985e10i) q^{40} +1.84110e11i q^{41} -1.16902e11 q^{43} +(4.05414e10 - 7.02197e10i) q^{44} +(1.54174e11 + 2.67036e11i) q^{46} +(6.76112e11 + 3.90353e11i) q^{47} +(-4.38702e11 - 5.17231e11i) q^{49} +2.46112e9 q^{50} +(-7.58741e10 + 4.38059e10i) q^{52} +(-6.00003e11 - 1.03923e12i) q^{53} +7.71541e11i q^{55} +(-2.56591e11 + 5.54092e11i) q^{56} +(-1.24690e12 + 2.15969e12i) q^{58} +(3.90985e11 - 2.25735e11i) q^{59} +(-2.34687e12 - 1.35497e12i) q^{61} -5.69275e11i q^{62} +5.49756e11 q^{64} +(4.16834e11 - 7.21978e11i) q^{65} +(-7.27991e11 - 1.26092e12i) q^{67} +(-2.09859e12 - 1.21162e12i) q^{68} +(-5.21746e11 - 5.78687e12i) q^{70} -3.35864e12 q^{71} +(9.10071e12 - 5.25430e12i) q^{73} +(8.25805e12 + 1.43034e13i) q^{74} -3.64561e12i q^{76} +(-8.11833e12 + 7.31951e11i) q^{77} +(1.16407e13 - 2.01623e13i) q^{79} +(-4.53034e12 + 2.61559e12i) q^{80} +(-1.44312e13 - 8.33188e12i) q^{82} -5.19742e13i q^{83} +2.30583e13 q^{85} +(5.29038e12 - 9.16321e12i) q^{86} +(3.66939e12 + 6.35556e12i) q^{88} +(2.25113e13 + 1.29969e13i) q^{89} +(7.99227e12 + 3.70109e12i) q^{91} -2.79084e13 q^{92} +(-6.11947e13 + 3.53308e13i) q^{94} +(1.73449e13 + 3.00422e13i) q^{95} +5.20028e13i q^{97} +(6.03958e13 - 1.09799e13i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	67507.4	+	38975.4i	0.864094	+	0.498885i	0.865381	−	0.501114i	$-0.167076\pi$
$5$	67507.4	+	38975.4i	0.864094	+	0.498885i	−0.00128703	+	0.999999i	$0.500410\pi$
$6$		0			0
$7$	−346065.	+	747303.i	−0.420214	+	0.907425i
$7$	−346065.	+	747303.i	−0.420214	+	0.907425i
$8$	741455.			0.353553
$9$		0			0
$10$	−6.11007e6	+	3.52765e6i	−0.611007	+	0.352765i
$11$	4.94890e6	+	8.57174e6i	0.253957	+	0.439866i	0.964612	−	0.263675i	$-0.0849346\pi$
$11$	4.94890e6	+	8.57174e6i	0.253957	+	0.439866i	−0.710655	+	0.703541i	$0.751601\pi$
$12$		0			0
$13$		−	1.06948e7i		−	0.170439i	−0.996362	−	0.0852196i	$-0.972841\pi$
$13$		−	1.06948e7i		−	0.170439i	0.996362	−	0.0852196i	$-0.0271592\pi$
$14$	−4.29153e7	−	6.09449e7i	−0.407114	−	0.578151i
$15$		0			0
$16$	−3.35544e7	+	5.81180e7i	−0.125000	+	0.216506i
$17$	2.56175e8	−	1.47903e8i	0.624302	−	0.360441i	−0.154240	−	0.988033i	$-0.549293\pi$
$17$	2.56175e8	−	1.47903e8i	0.624302	−	0.360441i	0.778542	+	0.627593i	$0.215960\pi$
$18$		0			0
$19$	3.85399e8	+	2.22510e8i	0.431157	+	0.248929i	0.699839	−	0.714300i	$-0.253255\pi$
$19$	3.85399e8	+	2.22510e8i	0.431157	+	0.248929i	−0.268682	+	0.963229i	$0.586588\pi$
$20$		−	6.38573e8i		−	0.498885i
$21$		0			0
$22$	−8.95846e8			−0.359149
$23$	1.70339e9	−	2.95036e9i	0.500288	−	0.866524i	−0.499712	−	0.866192i	$-0.666561\pi$
$23$	1.70339e9	−	2.95036e9i	0.500288	−	0.866524i	1.00000		0.000332535i	$-0.000105849\pi$
$24$		0			0
$25$	−1.35959e7	−	2.35488e7i	−0.00222755	−	0.00385823i
$26$	8.38298e8	+	4.83992e8i	0.104372	+	0.0602594i
$27$		0			0
$28$	6.71921e9	−	6.05806e8i	0.497980	−	0.0448980i
$29$	2.75528e10			1.59727			0.798636	−	0.601814i	$-0.205555\pi$
$29$	2.75528e10			1.59727			0.798636	+	0.601814i	$0.205555\pi$
$30$		0			0
$31$	−5.44700e9	+	3.14483e9i	−0.197982	+	0.114305i	−0.595714	−	0.803197i	$-0.703131\pi$
$31$	−5.44700e9	+	3.14483e9i	−0.197982	+	0.114305i	0.397732	+	0.917502i	$0.369797\pi$
$32$	−3.03700e9	−	5.26024e9i	−0.0883883	−	0.153093i
$33$		0			0
$34$			2.67733e10i			0.509740i
$35$	−5.24883e10	+	3.69605e10i	−0.815805	+	0.574462i
$36$		0			0
$37$	9.12395e10	−	1.58031e11i	0.961105	−	1.66468i	0.241370	−	0.970433i	$-0.422403\pi$
$37$	9.12395e10	−	1.58031e11i	0.961105	−	1.66468i	0.719735	−	0.694249i	$-0.244263\pi$
$38$	−3.48824e10	+	2.01393e10i	−0.304874	+	0.176019i
$39$		0			0
$40$	5.00537e10	+	2.88985e10i	0.305503	+	0.176382i
$41$			1.84110e11i			0.945347i	0.881238	+	0.472673i	$0.156711\pi$
$41$			1.84110e11i			0.945347i	−0.881238	+	0.472673i	$0.843289\pi$
$42$		0			0
$43$	−1.16902e11			−0.430074			−0.215037	−	0.976606i	$-0.568987\pi$
$43$	−1.16902e11			−0.430074			−0.215037	+	0.976606i	$0.568987\pi$
$44$	4.05414e10	−	7.02197e10i	0.126978	−	0.219933i
$45$		0			0
$46$	1.54174e11	+	2.67036e11i	0.353757	+	0.612725i
$47$	6.76112e11	+	3.90353e11i	1.33455	+	0.770501i	0.985993	−	0.166788i	$-0.0533397\pi$
$47$	6.76112e11	+	3.90353e11i	1.33455	+	0.770501i	0.348553	+	0.937289i	$0.386673\pi$
$48$		0			0
$49$	−4.38702e11	−	5.17231e11i	−0.646840	−	0.762626i
$50$	2.46112e9			0.00315023
$51$		0			0
$52$	−7.58741e10	+	4.38059e10i	−0.0738023	+	0.0426098i
$53$	−6.00003e11	−	1.03923e12i	−0.510766	−	0.884673i	−0.999922	−	0.0124765i	$-0.996029\pi$
$53$	−6.00003e11	−	1.03923e12i	−0.510766	−	0.884673i	0.489156	−	0.872196i	$-0.337305\pi$
$54$		0			0
$55$			7.71541e11i			0.506781i
$56$	−2.56591e11	+	5.54092e11i	−0.148568	+	0.320823i
$57$		0			0
$58$	−1.24690e12	+	2.15969e12i	−0.564721	+	0.978126i
$59$	3.90985e11	−	2.25735e11i	0.157107	−	0.0907058i	−0.419385	−	0.907808i	$-0.637754\pi$
$59$	3.90985e11	−	2.25735e11i	0.157107	−	0.0907058i	0.576492	+	0.817103i	$0.304421\pi$
$60$		0			0
$61$	−2.34687e12	−	1.35497e12i	−0.746758	−	0.431141i	0.0777631	−	0.996972i	$-0.475222\pi$
$61$	−2.34687e12	−	1.35497e12i	−0.746758	−	0.431141i	−0.824521	+	0.565831i	$0.808556\pi$
$62$		−	5.69275e11i		−	0.161652i
$63$		0			0
$64$	5.49756e11			0.125000
$65$	4.16834e11	−	7.21978e11i	0.0850296	−	0.147276i
$66$		0			0
$67$	−7.27991e11	−	1.26092e12i	−0.120116	−	0.208048i	0.799697	−	0.600404i	$-0.204993\pi$
$67$	−7.27991e11	−	1.26092e12i	−0.120116	−	0.208048i	−0.919813	+	0.392356i	$0.871660\pi$
$68$	−2.09859e12	−	1.21162e12i	−0.312151	−	0.180220i
$69$		0			0
$70$	−5.21746e11	−	5.78687e12i	−0.0633538	−	0.702680i
$71$	−3.35864e12			−0.369279			−0.184640	−	0.982806i	$-0.559112\pi$
$71$	−3.35864e12			−0.369279			−0.184640	+	0.982806i	$0.559112\pi$
$72$		0			0
$73$	9.10071e12	−	5.25430e12i	0.823787	−	0.475614i	−0.0279334	−	0.999610i	$-0.508893\pi$
$73$	9.10071e12	−	5.25430e12i	0.823787	−	0.475614i	0.851721	+	0.523996i	$0.175559\pi$
$74$	8.25805e12	+	1.43034e13i	0.679604	+	1.17711i
$75$		0			0
$76$		−	3.64561e12i		−	0.248929i
$77$	−8.11833e12	+	7.31951e11i	−0.505862	+	0.0456086i
$78$		0			0
$79$	1.16407e13	−	2.01623e13i	0.606162	−	1.04990i	−0.385705	−	0.922622i	$-0.626042\pi$
$79$	1.16407e13	−	2.01623e13i	0.606162	−	1.04990i	0.991867	−	0.127281i	$-0.0406251\pi$
$80$	−4.53034e12	+	2.61559e12i	−0.216024	+	0.124721i
$81$		0			0
$82$	−1.44312e13	−	8.33188e12i	−0.578904	−	0.334231i
$83$		−	5.19742e13i		−	1.91532i	−0.287900	−	0.957660i	$-0.592957\pi$
$83$		−	5.19742e13i		−	1.91532i	0.287900	−	0.957660i	$-0.407043\pi$
$84$		0			0
$85$	2.30583e13			0.719274
$86$	5.29038e12	−	9.16321e12i	0.152054	−	0.263365i
$87$		0			0
$88$	3.66939e12	+	6.35556e12i	0.0897873	+	0.155516i
$89$	2.25113e13	+	1.29969e13i	0.508945	+	0.293839i	0.732400	−	0.680875i	$-0.238400\pi$
$89$	2.25113e13	+	1.29969e13i	0.508945	+	0.293839i	−0.223455	+	0.974714i	$0.571734\pi$
$90$		0			0
$91$	7.99227e12	+	3.70109e12i	0.154661	+	0.0716210i
$92$	−2.79084e13			−0.500288
$93$		0			0
$94$	−6.11947e13	+	3.53308e13i	−0.943667	+	0.544826i
$95$	1.73449e13	+	3.00422e13i	0.248374	+	0.430196i
$96$		0			0
$97$			5.20028e13i			0.643613i	0.946805	+	0.321807i	$0.104290\pi$
$97$			5.20028e13i			0.643613i	−0.946805	+	0.321807i	$0.895710\pi$
$98$	6.03958e13	−	1.09799e13i	0.695704	−	0.126478i
$99$		0			0
$100$	−1.11378e11	+	1.92912e11i	−0.00111378	+	0.00192912i
$101$	1.56899e14	−	9.05856e13i	1.46342	−	0.844908i	0.464256	−	0.885701i	$-0.346322\pi$
$101$	1.56899e14	−	9.05856e13i	1.46342	−	0.844908i	0.999168	+	0.0407932i	$0.0129885\pi$
$102$		0			0
$103$	9.44788e13	+	5.45473e13i	0.768199	+	0.443520i	0.832232	−	0.554428i	$-0.187063\pi$
$103$	9.44788e13	+	5.45473e13i	0.768199	+	0.443520i	−0.0640328	+	0.997948i	$0.520396\pi$
$104$		−	7.92972e12i		−	0.0602594i
$105$		0			0
$106$	1.08612e14			0.722332
$107$	−4.11220e13	+	7.12255e13i	−0.256087	+	0.443556i	−0.965190	−	0.261549i	$-0.915767\pi$
$107$	−4.11220e13	+	7.12255e13i	−0.256087	+	0.443556i	0.709103	+	0.705105i	$0.249100\pi$
$108$		0			0
$109$	−3.29414e13	−	5.70562e13i	−0.180201	−	0.312117i	0.761748	−	0.647873i	$-0.224341\pi$
$109$	−3.29414e13	−	5.70562e13i	−0.180201	−	0.312117i	−0.941949	+	0.335757i	$0.891008\pi$
$110$	−6.04762e13	−	3.49160e13i	−0.310339	−	0.179174i
$111$		0			0
$112$	−3.18198e13	−	4.51879e13i	−0.143936	−	0.204407i
$113$	1.48098e14			0.629506			0.314753	−	0.949174i	$-0.398078\pi$
$113$	1.48098e14			0.629506			0.314753	+	0.949174i	$0.398078\pi$
$114$		0			0
$115$	2.29983e14	−	1.32781e14i	0.864592	−	0.499172i
$116$	−1.12856e14	−	1.95473e14i	−0.399318	−	0.691639i
$117$		0			0
$118$			4.08624e13i			0.128277i
$119$	2.18751e13	+	2.42624e14i	0.0647323	+	0.717969i
$120$		0			0
$121$	1.40892e14	−	2.44032e14i	0.371012	−	0.642612i
$122$	2.12414e14	−	1.22637e14i	0.528038	−	0.304863i
$123$		0			0
$124$	4.46219e13	+	2.57624e13i	0.0989910	+	0.0571525i
$125$		−	4.77893e14i		−	1.00222i
$126$		0			0
$127$	−8.03620e14			−1.50808			−0.754041	−	0.656827i	$-0.771898\pi$
$127$	−8.03620e14			−1.50808			−0.754041	+	0.656827i	$0.771898\pi$
$128$	−2.48791e13	+	4.30919e13i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	3.77275e13	+	6.53460e13i	0.0601250	+	0.104140i
$131$	−5.53433e14	−	3.19525e14i	−0.835922	−	0.482620i	0.0199539	−	0.999801i	$-0.493648\pi$
$131$	−5.53433e14	−	3.19525e14i	−0.835922	−	0.482620i	−0.855876	+	0.517181i	$0.826981\pi$
$132$		0			0
$133$	−2.99656e14	+	2.11007e14i	−0.407063	+	0.286639i
$134$	1.31780e14			0.169870
$135$		0			0
$136$	1.89942e14	−	1.09663e14i	0.220724	−	0.127435i
$137$	−5.13837e14	−	8.89992e14i	−0.567259	−	0.982521i	−0.996836	−	0.0794909i	$-0.974671\pi$
$137$	−5.13837e14	−	8.89992e14i	−0.567259	−	0.982521i	0.429577	−	0.903030i	$-0.358663\pi$
$138$		0			0
$139$			1.22498e15i			1.22187i	0.791681	+	0.610935i	$0.209206\pi$
$139$			1.22498e15i			1.22187i	−0.791681	+	0.610935i	$0.790794\pi$
$140$	4.77208e14	+	2.20987e14i	0.452701	+	0.209639i
$141$		0			0
$142$	1.51995e14	−	2.63263e14i	0.130560	−	0.226136i
$143$	9.16732e13	−	5.29275e13i	0.0749704	−	0.0432842i
$144$		0			0
$145$	1.86001e15	+	1.07388e15i	1.38019	+	0.796855i
$146$			9.51129e14i			0.672620i
$147$		0			0
$148$	−1.49487e15			−0.961105
$149$	−4.16513e14	+	7.21422e14i	−0.255461	+	0.442472i	−0.965021	−	0.262174i	$-0.915561\pi$
$149$	−4.16513e14	+	7.21422e14i	−0.255461	+	0.442472i	0.709560	+	0.704645i	$0.248894\pi$
$150$		0			0
$151$	9.62670e14	+	1.66739e15i	0.537822	+	0.931535i	0.999021	+	0.0442386i	$0.0140862\pi$
$151$	9.62670e14	+	1.66739e15i	0.537822	+	0.931535i	−0.461199	+	0.887297i	$0.652580\pi$
$152$	2.85756e14	+	1.64981e14i	0.152437	+	0.0880096i
$153$		0			0
$154$	3.10021e14	−	6.69469e14i	0.150920	−	0.325901i
$155$	−4.90284e14			−0.228100
$156$		0			0
$157$	−3.17325e15	+	1.83208e15i	−1.34961	+	0.779195i	−0.988194	−	0.153211i	$-0.951039\pi$
$157$	−3.17325e15	+	1.83208e15i	−1.34961	+	0.779195i	−0.361412	+	0.932406i	$0.617705\pi$
$158$	1.05359e15	+	1.82488e15i	0.428621	+	0.742394i
$159$		0			0
$160$		−	4.73473e14i		−	0.176382i
$161$	1.61533e15	+	2.29397e15i	0.576077	+	0.818100i
$162$		0			0
$163$	2.88932e15	−	5.00445e15i	0.945111	−	1.63698i	0.189581	−	0.981865i	$-0.439287\pi$
$163$	2.88932e15	−	5.00445e15i	0.945111	−	1.63698i	0.755529	−	0.655115i	$-0.227380\pi$
$164$	1.30617e15	−	7.54116e14i	0.409347	−	0.236337i
$165$		0			0
$166$	4.07393e15	+	2.35209e15i	1.17289	+	0.677168i
$167$			5.18360e15i			1.43092i	0.698652	+	0.715461i	$0.253783\pi$
$167$			5.18360e15i			1.43092i	−0.698652	+	0.715461i	$0.746217\pi$
$168$		0			0
$169$	3.82300e15			0.970950
$170$	−1.04350e15	+	1.80739e15i	−0.254302	+	0.440463i
$171$		0			0
$172$	4.78831e14	+	8.29359e14i	0.107518	+	0.186227i
$173$	−1.89953e15	−	1.09669e15i	−0.409565	−	0.236462i	0.281038	−	0.959697i	$-0.409321\pi$
$173$	−1.89953e15	−	1.09669e15i	−0.409565	−	0.236462i	−0.690603	+	0.723234i	$0.742655\pi$
$174$		0			0
$175$	2.23031e13	−	2.01086e12i	0.00443710	−	0.000400051i
$176$	−6.64230e14			−0.126978
$177$		0			0
$178$	−2.03749e15	+	1.17635e15i	−0.359878	+	0.207776i
$179$	2.78595e15	+	4.82541e15i	0.473154	+	0.819527i	0.999528	−	0.0307266i	$-0.00978212\pi$
$179$	2.78595e15	+	4.82541e15i	0.473154	+	0.819527i	−0.526374	+	0.850253i	$0.676449\pi$
$180$		0			0
$181$			1.15526e16i			1.81523i	0.419807	+	0.907613i	$0.362098\pi$
$181$			1.15526e16i			1.81523i	−0.419807	+	0.907613i	$0.637902\pi$
$182$	−6.51794e14	+	4.58971e14i	−0.0985396	+	0.0693881i
$183$		0			0
$184$	1.26299e15	−	2.18756e15i	0.176879	−	0.306363i
$185$	1.23187e16	−	7.11219e15i	1.66097	−	0.958961i
$186$		0			0
$187$	2.53557e15	+	1.46391e15i	0.317091	+	0.183073i
$188$		−	6.39555e15i		−	0.770501i
$189$		0			0
$190$	−3.13975e15			−0.351253
$191$	−7.14355e15	+	1.23730e16i	−0.770337	+	1.33426i	0.167041	+	0.985950i	$0.446579\pi$
$191$	−7.14355e15	+	1.23730e16i	−0.770337	+	1.33426i	−0.937378	+	0.348313i	$0.886755\pi$
$192$		0			0
$193$	4.06583e15	+	7.04222e15i	0.407613	+	0.706006i	0.994622	−	0.103574i	$-0.0330280\pi$
$193$	4.06583e15	+	7.04222e15i	0.407613	+	0.706006i	−0.587009	+	0.809580i	$0.699695\pi$
$194$	−4.07617e15	−	2.35338e15i	−0.394131	−	0.227552i
$195$		0			0
$196$	−1.87256e15	+	5.23094e15i	−0.168517	+	0.470746i
$197$	6.50117e15			0.564583			0.282291	−	0.959329i	$-0.408906\pi$
$197$	6.50117e15			0.564583			0.282291	+	0.959329i	$0.408906\pi$
$198$		0			0
$199$	−2.52113e15	+	1.45558e15i	−0.203997	+	0.117778i	−0.598519	−	0.801109i	$-0.704244\pi$
$199$	−2.52113e15	+	1.45558e15i	−0.203997	+	0.117778i	0.394521	+	0.918887i	$0.370910\pi$
$200$	−1.00807e13	−	1.74604e13i	−0.000787558	−	0.00136409i
$201$		0			0
$202$			1.63977e16i			1.19488i
$203$	−9.53504e15	+	2.05903e16i	−0.671197	+	1.44941i
$204$		0			0
$205$	−7.17577e15	+	1.24288e16i	−0.471619	+	0.816869i
$206$	−8.55124e15	+	4.93706e15i	−0.543199	+	0.313616i
$207$		0			0
$208$	6.21561e14	+	3.58858e14i	0.0369012	+	0.0213049i
$209$			4.40472e15i			0.252869i
$210$		0			0
$211$	2.34044e16			1.25696			0.628479	−	0.777826i	$-0.283678\pi$
$211$	2.34044e16			1.25696			0.628479	+	0.777826i	$0.283678\pi$
$212$	−4.91522e15	+	8.51341e15i	−0.255383	+	0.442336i
$213$		0			0
$214$	−3.72194e15	−	6.44659e15i	−0.181081	−	0.313642i
$215$	−7.89175e15	−	4.55630e15i	−0.371624	−	0.214557i
$216$		0			0
$217$	−4.65126e14	−	5.15888e15i	−0.0205283	−	0.227686i
$218$	5.96303e15			0.254842
$219$		0			0
$220$	5.47368e15	−	3.16023e15i	0.219443	−	0.126695i
$221$	−1.58179e15	−	2.73974e15i	−0.0614332	−	0.106405i
$222$		0			0
$223$			5.99930e15i			0.218759i	0.994000	+	0.109380i	$0.0348864\pi$
$223$			5.99930e15i			0.218759i	−0.994000	+	0.109380i	$0.965114\pi$
$224$	4.98199e15	−	4.49178e14i	0.176063	−	0.0158738i
$225$		0			0
$226$	−6.70215e15	+	1.16085e16i	−0.222564	+	0.385492i
$227$	4.94190e15	−	2.85320e15i	0.159116	−	0.0918654i	−0.418328	−	0.908296i	$-0.637384\pi$
$227$	4.94190e15	−	2.85320e15i	0.159116	−	0.0918654i	0.577443	+	0.816431i	$0.304050\pi$
$228$		0			0
$229$	1.67924e16	+	9.69509e15i	0.508469	+	0.293564i	0.732204	−	0.681085i	$-0.238492\pi$
$229$	1.67924e16	+	9.69509e15i	0.508469	+	0.293564i	−0.223735	+	0.974650i	$0.571825\pi$
$230$			2.40359e16i			0.705936i
$231$		0			0
$232$	2.04291e16			0.564721
$233$	2.37422e16	−	4.11226e16i	0.636837	−	1.10303i	−0.349285	−	0.937016i	$-0.613576\pi$
$233$	2.37422e16	−	4.11226e16i	0.636837	−	1.10303i	0.986123	−	0.166018i	$-0.0530911\pi$
$234$		0			0
$235$	3.04283e16	+	5.27034e16i	0.768782	+	1.33157i
$236$	−3.20295e15	−	1.84922e15i	−0.0785535	−	0.0453529i
$237$		0			0
$238$	−2.00077e16	−	9.26528e15i	−0.462551	−	0.214200i
$239$	5.97167e16			1.34063			0.670317	−	0.742074i	$-0.266158\pi$
$239$	5.97167e16			1.34063			0.670317	+	0.742074i	$0.266158\pi$
$240$		0			0
$241$	−1.71508e16	+	9.90203e15i	−0.363216	+	0.209703i	−0.670491	−	0.741918i	$-0.733916\pi$
$241$	−1.71508e16	+	9.90203e15i	−0.363216	+	0.209703i	0.307274	+	0.951621i	$0.400583\pi$
$242$	1.27521e16	+	2.20872e16i	0.262345	+	0.454395i
$243$		0			0
$244$			2.21998e16i			0.431141i
$245$	−9.45632e15	−	5.20154e16i	−0.178468	−	0.981679i
$246$		0			0
$247$	2.37971e15	−	4.12177e15i	0.0424272	−	0.0734861i
$248$	−4.03871e15	+	2.33175e15i	−0.0699972	+	0.0404129i
$249$		0			0
$250$	3.74590e16	+	2.16270e16i	0.613729	+	0.354337i
$251$			4.39475e15i			0.0700194i	0.999387	+	0.0350097i	$0.0111462\pi$
$251$			4.39475e15i			0.0700194i	−0.999387	+	0.0350097i	$0.988854\pi$
$252$		0			0
$253$	3.37197e16			0.508206
$254$	3.63677e16	−	6.29907e16i	0.533187	−	0.923508i
$255$		0			0
$256$	−2.25180e15	−	3.90023e15i	−0.0312500	−	0.0541266i
$257$	5.01427e16	+	2.89499e16i	0.677135	+	0.390944i	0.798775	−	0.601630i	$-0.205482\pi$
$257$	5.01427e16	+	2.89499e16i	0.677135	+	0.390944i	−0.121639	+	0.992574i	$0.538815\pi$
$258$		0			0
$259$	8.65226e16	+	1.22873e17i	1.10670	+	1.57165i
$260$	−6.82941e15			−0.0850296
$261$		0			0
$262$	5.00910e16	−	2.89201e16i	0.591086	−	0.341264i
$263$	7.61427e16	+	1.31883e17i	0.874859	+	1.51530i	0.856913	+	0.515462i	$0.172380\pi$
$263$	7.61427e16	+	1.31883e17i	0.874859	+	1.51530i	0.0179466	+	0.999839i	$0.494287\pi$
$264$		0			0
$265$		−	9.35413e16i		−	1.01925i
$266$	−2.97864e15	−	3.30372e16i	−0.0316116	−	0.350616i
$267$		0			0
$268$	−5.96370e15	+	1.03294e16i	−0.0600582	+	0.104024i
$269$	−6.59727e15	+	3.80894e15i	−0.0647290	+	0.0373713i	−0.532015	−	0.846735i	$-0.678565\pi$
$269$	−6.59727e15	+	3.80894e15i	−0.0647290	+	0.0373713i	0.467286	+	0.884106i	$0.345232\pi$
$270$		0			0
$271$	−1.32983e17	−	7.67780e16i	−1.23883	−	0.715240i	−0.269977	−	0.962867i	$-0.587016\pi$
$271$	−1.32983e17	−	7.67780e16i	−1.23883	−	0.715240i	−0.968855	+	0.247627i	$0.920349\pi$
$272$			1.98512e16i			0.180220i
$273$		0			0
$274$	9.30144e16			0.802225
$275$	1.34569e14	−	2.33081e14i	0.00113140	−	0.00195965i
$276$		0			0
$277$	−1.78804e16	−	3.09697e16i	−0.142895	−	0.247502i	0.785690	−	0.618620i	$-0.212308\pi$
$277$	−1.78804e16	−	3.09697e16i	−0.142895	−	0.247502i	−0.928586	+	0.371118i	$0.878975\pi$
$278$	−9.60184e16	−	5.54362e16i	−0.748240	−	0.431996i
$279$		0			0
$280$	−3.89178e16	+	2.74045e16i	−0.288431	+	0.203103i
$281$	2.57762e16			0.186327			0.0931634	−	0.995651i	$-0.470302\pi$
$281$	2.57762e16			0.186327			0.0931634	+	0.995651i	$0.470302\pi$
$282$		0			0
$283$	5.83377e16	−	3.36813e16i	0.401277	−	0.231677i	−0.285758	−	0.958302i	$-0.592245\pi$
$283$	5.83377e16	−	3.36813e16i	0.401277	−	0.231677i	0.687035	+	0.726624i	$0.258912\pi$
$284$	1.37570e16	+	2.38278e16i	0.0923198	+	0.159903i
$285$		0			0
$286$			9.58090e15i			0.0612131i
$287$	−1.37586e17	−	6.37141e16i	−0.857831	−	0.397248i
$288$		0			0
$289$	−4.04385e16	+	7.00415e16i	−0.240165	+	0.415978i
$290$	−1.68349e17	+	9.71965e16i	−0.975945	+	0.563462i
$291$		0			0
$292$	−7.45530e16	−	4.30432e16i	−0.411894	−	0.237807i
$293$			3.06340e17i			1.65246i	0.563334	+	0.826229i	$0.309518\pi$
$293$			3.06340e17i			1.65246i	−0.563334	+	0.826229i	$0.690482\pi$
$294$		0			0
$295$	3.51925e16			0.181007
$296$	6.76500e16	−	1.17173e17i	0.339802	−	0.588554i
$297$		0			0
$298$	−3.76985e16	−	6.52957e16i	−0.180638	−	0.312875i
$299$	−3.15536e16	−	1.82175e16i	−0.147690	−	0.0852687i
$300$		0			0
$301$	4.04557e16	−	8.73613e16i	0.180723	−	0.390260i
$302$	−1.74262e17			−0.760596
$303$		0			0
$304$	−2.58637e16	+	1.49324e16i	−0.107789	+	0.0622322i
$305$	−1.05621e17	−	1.82940e17i	−0.430180	−	0.745093i
$306$		0			0
$307$			1.36311e17i			0.530348i	0.964201	+	0.265174i	$0.0854294\pi$
$307$			1.36311e17i			0.530348i	−0.964201	+	0.265174i	$0.914571\pi$
$308$	3.84455e16	+	5.45973e16i	0.146215	+	0.207642i
$309$		0			0
$310$	2.21877e16	−	3.84302e16i	0.0806456	−	0.139682i
$311$	3.57294e17	−	2.06284e17i	1.26971	−	0.733065i	0.294774	−	0.955567i	$-0.404756\pi$
$311$	3.57294e17	−	2.06284e17i	1.26971	−	0.733065i	0.974932	+	0.222502i	$0.0714224\pi$
$312$		0			0
$313$	−3.36075e17	−	1.94033e17i	−1.14189	−	0.659273i	−0.194995	−	0.980804i	$-0.562469\pi$
$313$	−3.36075e17	−	1.94033e17i	−1.14189	−	0.659273i	−0.946899	+	0.321532i	$0.895802\pi$
$314$		−	3.31642e17i		−	1.10195i
$315$		0			0
$316$	−1.90721e17			−0.606162
$317$	2.02786e17	−	3.51235e17i	0.630409	−	1.09190i	−0.357059	−	0.934082i	$-0.616220\pi$
$317$	2.02786e17	−	3.51235e17i	0.630409	−	1.09190i	0.987468	−	0.157819i	$-0.0504462\pi$
$318$		0			0
$319$	1.36356e17	+	2.36175e17i	0.405638	+	0.702586i
$320$	3.71126e16	+	2.14269e16i	0.108012	+	0.0623606i
$321$		0			0
$322$	−2.52911e17	+	2.28025e16i	−0.704656	+	0.0635320i
$323$	1.31640e17			0.358896
$324$		0			0
$325$	−2.51850e14	+	1.45405e14i	−0.000657594	+	0.000379662i
$326$	2.61512e17	+	4.52951e17i	0.668294	+	1.15752i
$327$		0			0
$328$			1.36510e17i			0.334231i
$329$	−5.25691e17	+	3.70173e17i	−1.25997	+	0.887225i
$330$		0			0
$331$	9.82038e16	−	1.70094e17i	0.225596	−	0.390744i	−0.730902	−	0.682483i	$-0.760900\pi$
$331$	9.82038e16	−	1.70094e17i	0.225596	−	0.390744i	0.956498	+	0.291738i	$0.0942336\pi$
$332$	−3.68730e17	+	2.12887e17i	−0.829358	+	0.478830i
$333$		0			0
$334$	−4.06310e17	−	2.34583e17i	−0.876258	−	0.505908i
$335$		−	1.13495e17i		−	0.239697i
$336$		0			0
$337$	3.36134e17			0.680931			0.340465	−	0.940257i	$-0.389415\pi$
$337$	3.36134e17			0.680931			0.340465	+	0.940257i	$0.389415\pi$
$338$	−1.73009e17	+	2.99661e17i	−0.343283	+	0.594583i
$339$		0			0
$340$	−9.44467e16	−	1.63586e17i	−0.179818	−	0.311455i
$341$	−5.39134e16	−	3.11269e16i	−0.100558	−	0.0580571i
$342$		0			0
$343$	5.38347e17	−	1.48848e17i	0.963837	−	0.266492i
$344$	−8.66776e16			−0.152054
$345$		0			0
$346$	1.71926e17	−	9.92613e16i	0.289606	−	0.167204i
$347$	−4.92888e15	−	8.53708e15i	−0.00813659	−	0.0140930i	0.861928	−	0.507030i	$-0.169257\pi$
$347$	−4.92888e15	−	8.53708e15i	−0.00813659	−	0.0140930i	−0.870065	+	0.492937i	$0.835923\pi$
$348$		0			0
$349$		−	3.37354e17i		−	0.534944i	−0.963566	−	0.267472i	$-0.913812\pi$
$349$		−	3.37354e17i		−	0.534944i	0.963566	−	0.267472i	$-0.0861883\pi$
$350$	−8.51706e14	+	1.83920e15i	−0.00132377	+	0.00285860i
$351$		0			0
$352$	3.00596e16	−	5.20648e16i	0.0448936	−	0.0777581i
$353$	−1.19183e17	+	6.88102e16i	−0.174498	+	0.100746i	−0.584705	−	0.811246i	$-0.698790\pi$
$353$	−1.19183e17	+	6.88102e16i	−0.174498	+	0.100746i	0.410207	+	0.911992i	$0.365456\pi$
$354$		0			0
$355$	−2.26733e17	−	1.30904e17i	−0.319092	−	0.184228i
$356$		−	2.12941e17i		−	0.293839i
$357$		0			0
$358$	−5.04311e17			−0.669141
$359$	−5.44235e16	+	9.42643e16i	−0.0708150	+	0.122655i	−0.899259	−	0.437417i	$-0.855893\pi$
$359$	−5.44235e16	+	9.42643e16i	−0.0708150	+	0.122655i	0.828444	+	0.560072i	$0.189227\pi$
$360$		0			0
$361$	−3.00482e17	−	5.20449e17i	−0.376069	−	0.651371i
$362$	−9.05538e17	−	5.22812e17i	−1.11159	−	0.641780i
$363$		0			0
$364$	−6.47898e15	−	7.18607e16i	−0.00765238	−	0.0848753i
$365$	8.19153e17			0.949106
$366$		0			0
$367$	−1.30597e18	+	7.54003e17i	−1.45637	+	0.840835i	−0.998830	−	0.0483544i	$-0.984602\pi$
$367$	−1.30597e18	+	7.54003e17i	−1.45637	+	0.840835i	−0.457539	+	0.889190i	$0.651269\pi$
$368$	1.14313e17	+	1.97996e17i	0.125072	+	0.216631i
$369$		0			0
$370$			1.28744e18i			1.35618i
$371$	9.84263e17	−	8.87415e16i	1.01741	−	0.0917295i
$372$		0			0
$373$	6.58177e17	−	1.14000e18i	0.655210	−	1.13486i	−0.326631	−	0.945152i	$-0.605913\pi$
$373$	6.58177e17	−	1.14000e18i	0.655210	−	1.13486i	0.981841	−	0.189706i	$-0.0607534\pi$
$374$	−2.29493e17	+	1.32498e17i	−0.224217	+	0.129452i
$375$		0			0
$376$	5.01307e17	+	2.89430e17i	0.471833	+	0.272413i
$377$		−	2.94671e17i		−	0.272238i
$378$		0			0
$379$	1.12046e17			0.0997522			0.0498761	−	0.998755i	$-0.484117\pi$
$379$	1.12046e17			0.0997522			0.0498761	+	0.998755i	$0.484117\pi$
$380$	1.42089e17	−	2.46105e17i	0.124187	−	0.215098i
$381$		0			0
$382$	−6.46561e17	−	1.11988e18i	−0.544711	−	0.943466i
$383$	−1.09263e18	−	6.30830e17i	−0.903819	−	0.521820i	−0.0253820	−	0.999678i	$-0.508080\pi$
$383$	−1.09263e18	−	6.30830e17i	−0.903819	−	0.521820i	−0.878437	+	0.477857i	$0.841414\pi$
$384$		0			0
$385$	−5.76575e17	−	2.67003e17i	−0.459866	−	0.212957i
$386$	−7.35994e17			−0.576452
$387$		0			0
$388$	3.68933e17	−	2.13004e17i	0.278693	−	0.160903i
$389$	−6.57817e17	−	1.13937e18i	−0.488043	−	0.845314i	0.511863	−	0.859067i	$-0.328956\pi$
$389$	−6.57817e17	−	1.13937e18i	−0.488043	−	0.845314i	−0.999905	+	0.0137527i	$0.995622\pi$
$390$		0			0
$391$		−	1.00775e18i		−	0.721296i
$392$	−3.25278e17	−	3.83503e17i	−0.228692	−	0.269629i
$393$		0			0
$394$	−2.94209e17	+	5.09585e17i	−0.199610	+	0.345735i
$395$	1.57166e18	−	9.07400e17i	1.04756	−	0.604810i
$396$		0			0
$397$	−1.05783e17	−	6.10740e16i	−0.0680587	−	0.0392937i	0.465585	−	0.885003i	$-0.345844\pi$
$397$	−1.05783e17	−	6.10740e16i	−0.0680587	−	0.0392937i	−0.533643	+	0.845710i	$0.679177\pi$
$398$		−	2.63488e17i		−	0.166563i
$399$		0			0
$400$	1.82481e15			0.00111378
$401$	−4.00051e17	+	6.92909e17i	−0.239941	+	0.415590i	−0.960697	−	0.277599i	$-0.910461\pi$
$401$	−4.00051e17	+	6.92909e17i	−0.239941	+	0.415590i	0.720756	+	0.693189i	$0.243795\pi$
$402$		0			0
$403$	3.36333e16	+	5.82547e16i	0.0194821	+	0.0337439i
$404$	−1.28531e18	−	7.42077e17i	−0.731712	−	0.422454i
$405$		0			0
$406$	−1.18243e18	−	1.67920e18i	−0.650272	−	0.923465i
$407$	1.80614e18			0.976316
$408$		0			0
$409$	6.74457e17	−	3.89398e17i	0.352282	−	0.203390i	−0.313408	−	0.949619i	$-0.601471\pi$
$409$	6.74457e17	−	3.89398e17i	0.352282	−	0.203390i	0.665690	+	0.746228i	$0.268137\pi$
$410$	−6.49477e17	−	1.12493e18i	−0.333485	−	0.577613i
$411$		0			0
$412$		−	8.93704e17i		−	0.443520i
$413$	3.33866e16	+	3.70303e17i	0.0162900	+	0.180679i
$414$		0			0
$415$	2.02572e18	−	3.50864e18i	0.955525	−	1.65502i
$416$	−5.62572e16	+	3.24801e16i	−0.0260931	+	0.0150648i
$417$		0			0
$418$	−3.45258e17	−	1.99335e17i	−0.154850	−	0.0894025i
$419$			1.10427e18i			0.487054i	0.969894	+	0.243527i	$0.0783044\pi$
$419$			1.10427e18i			0.487054i	−0.969894	+	0.243527i	$0.921696\pi$
$420$		0			0
$421$	−4.05832e18			−1.73130			−0.865649	−	0.500651i	$-0.833094\pi$
$421$	−4.05832e18			−1.73130			−0.865649	+	0.500651i	$0.833094\pi$
$422$	−1.05916e18	+	1.83452e18i	−0.444402	+	0.769727i
$423$		0			0
$424$	−4.44875e17	−	7.70546e17i	−0.180583	−	0.312779i
$425$	−6.96586e15	−	4.02174e15i	−0.00278133	−	0.00160580i
$426$		0			0
$427$	1.82474e18	−	1.28492e18i	0.705027	−	0.496455i
$428$	6.73743e17			0.256087
$429$		0			0
$430$	7.14279e17	−	4.12389e17i	0.262778	−	0.151715i
$431$	2.03737e17	+	3.52883e17i	0.0737445	+	0.127729i	0.900540	−	0.434774i	$-0.143172\pi$
$431$	2.03737e17	+	3.52883e17i	0.0737445	+	0.127729i	−0.826795	+	0.562503i	$0.809838\pi$
$432$		0			0
$433$			4.58610e18i			1.60705i	0.595274	+	0.803523i	$0.297044\pi$
$433$			4.58610e18i			1.60705i	−0.595274	+	0.803523i	$0.702956\pi$
$434$	4.25421e17	+	1.97006e17i	0.146687	+	0.0679284i
$435$		0			0
$436$	−2.69856e17	+	4.67404e17i	−0.0901003	+	0.156058i
$437$	1.31297e18	−	7.58045e17i	0.431405	−	0.249072i
$438$		0			0
$439$	1.52050e18	+	8.77860e17i	0.483876	+	0.279366i	0.722030	−	0.691861i	$-0.243209\pi$
$439$	1.52050e18	+	8.77860e17i	0.483876	+	0.279366i	−0.238154	+	0.971227i	$0.576542\pi$
$440$			5.72063e17i			0.179174i
$441$		0			0
$442$	2.86335e17			0.0868797
$443$	−2.07751e17	+	3.59836e17i	−0.0620465	+	0.107468i	−0.895380	−	0.445303i	$-0.853096\pi$
$443$	−2.07751e17	+	3.59836e17i	−0.0620465	+	0.107468i	0.833334	+	0.552770i	$0.186429\pi$
$444$		0			0
$445$	1.01312e18	+	1.75477e18i	0.293184	+	0.507810i
$446$	−4.70247e17	−	2.71498e17i	−0.133962	−	0.0773431i
$447$		0			0
$448$	−1.90251e17	+	4.10834e17i	−0.0525268	+	0.113428i
$449$	6.86642e18			1.86641			0.933203	−	0.359350i	$-0.117001\pi$
$449$	6.86642e18			1.86641			0.933203	+	0.359350i	$0.117001\pi$
$450$		0			0
$451$	−1.57815e18	+	9.11143e17i	−0.415826	+	0.240077i
$452$	−6.06610e17	−	1.05068e18i	−0.157377	−	0.272584i
$453$		0			0
$454$			5.16485e17i			0.129917i
$455$	3.95285e17	+	5.61353e17i	0.0979108	+	0.139045i
$456$		0			0
$457$	−2.71084e18	+	4.69531e18i	−0.651164	+	1.12785i	0.331677	+	0.943393i	$0.392385\pi$
$457$	−2.71084e18	+	4.69531e18i	−0.651164	+	1.12785i	−0.982841	+	0.184456i	$0.940948\pi$
$458$	−1.51987e18	+	8.77499e17i	−0.359542	+	0.207581i
$459$		0			0
$460$	−1.88402e18	−	1.08774e18i	−0.432296	−	0.249586i
$461$		−	5.61041e18i		−	1.26791i	−0.773370	−	0.633955i	$-0.781430\pi$
$461$		−	5.61041e18i		−	1.26791i	0.773370	−	0.633955i	$-0.218570\pi$
$462$		0			0
$463$	8.48778e18			1.86092			0.930459	−	0.366396i	$-0.119408\pi$
$463$	8.48778e18			1.86092			0.930459	+	0.366396i	$0.119408\pi$
$464$	−9.24517e17	+	1.60131e18i	−0.199659	+	0.345820i
$465$		0			0
$466$	2.14889e18	+	3.72199e18i	0.450312	+	0.779963i
$467$	5.56099e18	+	3.21064e18i	1.14798	+	0.662786i	0.948394	−	0.317095i	$-0.102707\pi$
$467$	5.56099e18	+	3.21064e18i	1.14798	+	0.662786i	0.199585	+	0.979881i	$0.436041\pi$
$468$		0			0
$469$	1.19422e18	−	1.07671e17i	0.239262	−	0.0215720i
$470$	−5.50812e18			−1.08722
$471$		0			0
$472$	2.89898e17	−	1.67373e17i	0.0555457	−	0.0320693i
$473$	−5.78536e17	−	1.00205e18i	−0.109220	−	0.189175i
$474$		0			0
$475$		−	1.21009e16i		−	0.00221801i
$476$	1.63169e18	−	1.14898e18i	0.294707	−	0.207522i
$477$		0			0
$478$	−2.70247e18	+	4.68081e18i	−0.473986	+	0.820968i
$479$	3.52204e17	−	2.03345e17i	0.0608759	−	0.0351467i	−0.469253	−	0.883064i	$-0.655477\pi$
$479$	3.52204e17	−	2.03345e17i	0.0608759	−	0.0351467i	0.530129	+	0.847917i	$0.322143\pi$
$480$		0			0
$481$	−1.69012e18	−	9.75789e17i	−0.283727	−	0.163810i
$482$		−	1.79246e18i		−	0.296565i
$483$		0			0
$484$	−2.30837e18			−0.371012
$485$	−2.02683e18	+	3.51057e18i	−0.321089	+	0.556142i
$486$		0			0
$487$	−3.65518e18	−	6.33096e18i	−0.562609	−	0.974467i	−0.997268	−	0.0738715i	$-0.976465\pi$
$487$	−3.65518e18	−	6.33096e18i	−0.562609	−	0.974467i	0.434659	−	0.900595i	$-0.356869\pi$
$488$	−1.74010e18	−	1.00465e18i	−0.264019	−	0.152431i
$489$		0			0
$490$	4.50510e18	+	1.61273e18i	0.664251	+	0.237787i
$491$	−3.97545e18			−0.577851			−0.288925	−	0.957352i	$-0.593298\pi$
$491$	−3.97545e18			−0.577851			−0.288925	+	0.957352i	$0.593298\pi$
$492$		0			0
$493$	7.05833e18	−	4.07513e18i	0.997180	−	0.575722i
$494$	2.15386e17	+	3.73060e17i	0.0300006	+	0.0519625i
$495$		0			0
$496$		−	4.22092e17i		−	0.0571525i
$497$	1.16231e18	−	2.50992e18i	0.155177	−	0.335093i
$498$		0			0
$499$	−3.27595e17	+	5.67412e17i	−0.0425240	+	0.0736537i	−0.886504	−	0.462721i	$-0.846873\pi$
$499$	−3.27595e17	+	5.67412e17i	−0.0425240	+	0.0736537i	0.843980	+	0.536375i	$0.180207\pi$
$500$	−3.39041e18	+	1.95745e18i	−0.433972	+	0.250554i
$501$		0			0
$502$	−3.44477e17	−	1.98884e17i	−0.0428779	−	0.0247556i
$503$			2.50022e18i			0.306903i	0.988156	+	0.153452i	$0.0490390\pi$
$503$			2.50022e18i			0.306903i	−0.988156	+	0.153452i	$0.950961\pi$
$504$		0			0
$505$	1.41224e19			1.68605
$506$	−1.52598e18	+	2.64307e18i	−0.179678	+	0.311211i
$507$		0			0
$508$	3.29163e18	+	5.70127e18i	0.377020	+	0.653019i
$509$	1.24044e19	+	7.16168e18i	1.40136	+	0.809078i	0.994533	−	0.104425i	$-0.0333003\pi$
$509$	1.24044e19	+	7.16168e18i	1.40136	+	0.809078i	0.406831	+	0.913503i	$0.366634\pi$
$510$		0			0
$511$	7.77120e17	+	8.61932e18i	0.0854165	+	0.947385i
$512$	4.07619e17			0.0441942
$513$		0			0
$514$	−4.53840e18	+	2.62024e18i	−0.478807	+	0.276439i
$515$	4.25201e18	+	7.36469e18i	0.442531	+	0.766486i
$516$		0			0
$517$			7.72728e18i			0.782695i
$518$	−1.35468e19	+	1.22138e18i	−1.35372	+	0.122051i
$519$		0			0
$520$	3.09064e17	−	5.35314e17i	0.0300625	−	0.0520698i
$521$	−5.69400e18	+	3.28743e18i	−0.546454	+	0.315495i	−0.747691	−	0.664047i	$-0.768837\pi$
$521$	−5.69400e18	+	3.28743e18i	−0.546454	+	0.315495i	0.201237	+	0.979543i	$0.435504\pi$
$522$		0			0
$523$	9.39499e18	+	5.42420e18i	0.877778	+	0.506785i	0.869925	−	0.493184i	$-0.164167\pi$
$523$	9.39499e18	+	5.42420e18i	0.877778	+	0.506785i	0.00785283	+	0.999969i	$0.497500\pi$
$524$			5.23509e18i			0.482620i
$525$		0			0
$526$	−1.37833e19			−1.23724
$527$	−9.30258e17	+	1.61125e18i	−0.0824003	+	0.142722i
$528$		0			0
$529$	−6.67837e15	−	1.15673e16i	−0.000576078	−	0.000997796i
$530$	7.33211e18	+	4.23320e18i	0.624163	+	0.360361i
$531$		0			0
$532$	2.72438e18	+	1.26162e18i	0.225884	+	0.104603i
$533$	1.96902e18			0.161124
$534$		0			0
$535$	−5.55208e18	+	3.20549e18i	−0.442567	+	0.255516i
$536$	−5.39773e17	−	9.34914e17i	−0.0424676	−	0.0735560i
$537$		0			0
$538$		−	6.89491e17i		−	0.0528510i
$539$	2.26248e18	−	6.32016e18i	0.171184	−	0.478197i
$540$		0			0
$541$	−1.24416e19	+	2.15495e19i	−0.917265	+	1.58875i	−0.113715	+	0.993513i	$0.536275\pi$
$541$	−1.24416e19	+	2.15495e19i	−0.917265	+	1.58875i	−0.803551	+	0.595236i	$0.797058\pi$
$542$	1.20363e19	−	6.94915e18i	0.875987	−	0.505751i
$543$		0			0
$544$	−1.55601e18	−	8.98361e17i	−0.110362	−	0.0637175i
$545$		−	5.13561e18i		−	0.359598i
$546$		0			0
$547$	−1.32156e19			−0.901937			−0.450968	−	0.892540i	$-0.648921\pi$
$547$	−1.32156e19			−0.901937			−0.450968	+	0.892540i	$0.648921\pi$
$548$	−4.20935e18	+	7.29081e18i	−0.283629	+	0.491261i
$549$		0			0
$550$	1.21798e16	+	2.10961e16i	0.000800023	+	0.00138568i
$551$	1.06188e19	+	6.13077e18i	0.688676	+	0.397607i
$552$		0			0
$553$	1.10389e19	+	1.56766e19i	0.697990	+	0.991231i
$554$	3.23669e18			0.202085
$555$		0			0
$556$	8.69059e18	−	5.01752e18i	0.529085	−	0.305468i
$557$	−1.21140e18	−	2.09821e18i	−0.0728286	−	0.126143i	0.827311	−	0.561744i	$-0.189869\pi$
$557$	−1.21140e18	−	2.09821e18i	−0.0728286	−	0.126143i	−0.900140	+	0.435601i	$0.856536\pi$
$558$		0			0
$559$			1.25024e18i			0.0733014i
$560$	−3.86851e17	−	4.29070e18i	−0.0223989	−	0.248435i
$561$		0			0
$562$	−1.16650e18	+	2.02044e18i	−0.0658765	+	0.114101i
$563$	−2.37837e19	+	1.37316e19i	−1.32654	+	0.765880i	−0.984763	−	0.173900i	$-0.944363\pi$
$563$	−2.37837e19	+	1.37316e19i	−1.32654	+	0.765880i	−0.341780	+	0.939780i	$0.611030\pi$
$564$		0			0
$565$	9.99771e18	+	5.77218e18i	0.543953	+	0.314051i
$566$			6.09696e18i			0.327641i
$567$		0			0
$568$	−2.49028e18			−0.130560
$569$	−6.36025e18	+	1.10163e19i	−0.329373	+	0.570491i	−0.982388	−	0.186855i	$-0.940171\pi$
$569$	−6.36025e18	+	1.10163e19i	−0.329373	+	0.570491i	0.653015	+	0.757345i	$0.273504\pi$
$570$		0			0
$571$	−4.13724e18	−	7.16590e18i	−0.209054	−	0.362091i	0.742363	−	0.669998i	$-0.233705\pi$
$571$	−4.13724e18	−	7.16590e18i	−0.209054	−	0.362091i	−0.951417	+	0.307906i	$0.900372\pi$
$572$	−7.50986e17	−	4.33582e17i	−0.0374852	−	0.0216421i
$573$		0			0
$574$	1.12206e19	−	7.90115e18i	0.546553	−	0.384864i
$575$	−9.26366e16			−0.00445767
$576$		0			0
$577$	2.97960e19	−	1.72028e19i	1.39936	−	0.807918i	0.405030	−	0.914303i	$-0.367261\pi$
$577$	2.97960e19	−	1.72028e19i	1.39936	−	0.807918i	0.994325	+	0.106385i	$0.0339277\pi$
$578$	−3.66007e18	−	6.33943e18i	−0.169822	−	0.294141i
$579$		0			0
$580$		−	1.75944e19i		−	0.796855i
$581$	3.88405e19	+	1.79864e19i	1.73801	+	0.804845i
$582$		0			0
$583$	5.93870e18	−	1.02861e19i	0.259425	−	0.449337i
$584$	6.74777e18	−	3.89583e18i	0.291253	−	0.168155i
$585$		0			0
$586$	−2.40121e19	−	1.38634e19i	−1.01192	−	0.584232i
$587$		−	1.72472e19i		−	0.718213i	−0.933297	−	0.359106i	$-0.883082\pi$
$587$		−	1.72472e19i		−	0.718213i	0.933297	−	0.359106i	$-0.116918\pi$
$588$		0			0
$589$	−2.79903e18			−0.113815
$590$	−1.59263e18	+	2.75851e18i	−0.0639957	+	0.110844i
$591$		0			0
$592$	6.12298e18	+	1.06053e19i	0.240276	+	0.416171i
$593$	−3.97886e19	−	2.29719e19i	−1.54303	−	0.890871i	−0.998645	−	0.0520383i	$-0.983428\pi$
$593$	−3.97886e19	−	2.29719e19i	−1.54303	−	0.890871i	−0.544389	−	0.838833i	$-0.683238\pi$
$594$		0			0
$595$	−7.97965e18	+	1.72315e19i	−0.302249	+	0.652687i
$596$	6.82415e18			0.255461
$597$		0			0
$598$	2.85590e18	−	1.64886e18i	0.104432	−	0.0602941i
$599$	5.37158e18	+	9.30385e18i	0.194140	+	0.336260i	0.946618	−	0.322357i	$-0.104475\pi$
$599$	5.37158e18	+	9.30385e18i	0.194140	+	0.336260i	−0.752479	+	0.658617i	$0.771142\pi$
$600$		0			0
$601$		−	2.74940e19i		−	0.970772i	−0.874300	−	0.485386i	$-0.838679\pi$
$601$		−	2.74940e19i		−	0.970772i	0.874300	−	0.485386i	$-0.161321\pi$
$602$	5.01688e18	+	7.12458e18i	0.175089	+	0.248647i
$603$		0			0
$604$	7.88619e18	−	1.36593e19i	0.268911	−	0.465768i
$605$	1.90225e19	−	1.09826e19i	0.641178	−	0.370185i
$606$		0			0
$607$	−8.27907e18	−	4.77992e18i	−0.272685	−	0.157435i	0.357422	−	0.933943i	$-0.383656\pi$
$607$	−8.27907e18	−	4.77992e18i	−0.272685	−	0.157435i	−0.630107	+	0.776508i	$0.716989\pi$
$608$		−	2.70306e18i		−	0.0880096i
$609$		0			0
$610$	1.91194e19			0.608366
$611$	4.17475e18	−	7.23089e18i	0.131323	−	0.227459i
$612$		0			0
$613$	−2.43865e19	−	4.22386e19i	−0.749766	−	1.29863i	−0.947935	−	0.318465i	$-0.896833\pi$
$613$	−2.43865e19	−	4.22386e19i	−0.749766	−	1.29863i	0.198168	−	0.980168i	$-0.436501\pi$
$614$	−1.06845e19	−	6.16871e18i	−0.324771	−	0.187506i
$615$		0			0
$616$	−6.01938e18	+	5.42709e17i	−0.178849	+	0.0161251i
$617$	−6.60776e18			−0.194114			−0.0970572	−	0.995279i	$-0.530943\pi$
$617$	−6.60776e18			−0.194114			−0.0970572	+	0.995279i	$0.530943\pi$
$618$		0			0
$619$	−7.83336e18	+	4.52259e18i	−0.224964	+	0.129883i	−0.608247	−	0.793748i	$-0.708127\pi$
$619$	−7.83336e18	+	4.52259e18i	−0.224964	+	0.129883i	0.383283	+	0.923631i	$0.374794\pi$
$620$	2.00820e18	+	3.47831e18i	0.0570251	+	0.0987703i
$621$		0			0
$622$			3.73414e19i			1.03671i
$623$	−1.75030e19	+	1.23250e19i	−0.480503	+	0.338354i
$624$		0			0
$625$	1.85431e19	−	3.21176e19i	0.497763	−	0.862150i
$626$	3.04180e19	−	1.75619e19i	0.807441	−	0.466176i
$627$		0			0
$628$	2.59953e19	+	1.50084e19i	0.674803	+	0.389598i
$629$		−	5.39783e19i		−	1.38568i
$630$		0			0
$631$	−5.48595e19			−1.37736			−0.688678	−	0.725067i	$-0.741809\pi$
$631$	−5.48595e19			−1.37736			−0.688678	+	0.725067i	$0.741809\pi$
$632$	8.63104e18	−	1.49494e19i	0.214311	−	0.371197i
$633$		0			0
$634$	1.83541e19	+	3.17902e19i	0.445767	+	0.772090i
$635$	−5.42503e19	−	3.13214e19i	−1.30312	−	0.752359i
$636$		0			0
$637$	−5.53168e18	+	4.69183e18i	−0.129981	+	0.110247i
$638$	−2.46830e19			−0.573659
$639$		0			0
$640$	−3.35905e18	+	1.93935e18i	−0.0763759	+	0.0440956i
$641$	−4.55332e18	−	7.88659e18i	−0.102405	−	0.177371i	0.810270	−	0.586057i	$-0.199321\pi$
$641$	−4.55332e18	−	7.88659e18i	−0.102405	−	0.177371i	−0.912675	+	0.408686i	$0.865987\pi$
$642$		0			0
$643$			4.79964e19i			1.05617i	0.849193	+	0.528083i	$0.177089\pi$
$643$			4.79964e19i			1.05617i	−0.849193	+	0.528083i	$0.822911\pi$
$644$	9.65811e18	−	2.08560e19i	0.210228	−	0.453974i
$645$		0			0
$646$	−5.95733e18	+	1.03184e19i	−0.126889	+	0.219778i
$647$	5.25281e19	−	3.03271e19i	1.10678	−	0.639001i	0.168788	−	0.985652i	$-0.446015\pi$
$647$	5.25281e19	−	3.03271e19i	1.10678	−	0.639001i	0.937994	+	0.346652i	$0.112681\pi$
$648$		0			0
$649$	3.86989e18	+	2.23428e18i	0.0797968	+	0.0460707i
$650$		−	2.63212e16i		−	0.000536923i
$651$		0			0
$652$	−4.73386e19			−0.945111
$653$	−1.95657e19	+	3.38888e19i	−0.386459	+	0.669367i	−0.991970	−	0.126470i	$-0.959635\pi$
$653$	−1.95657e19	+	3.38888e19i	−0.386459	+	0.669367i	0.605511	+	0.795837i	$0.292969\pi$
$654$		0			0
$655$	−2.49072e19	−	4.31405e19i	−0.481544	−	0.834058i
$656$	−1.07001e19	−	6.17772e18i	−0.204674	−	0.118168i
$657$		0			0
$658$	−5.22548e18	−	5.79577e19i	−0.0978465	−	1.08525i
$659$	2.98014e19			0.552127			0.276064	−	0.961139i	$-0.410970\pi$
$659$	2.98014e19			0.552127			0.276064	+	0.961139i	$0.410970\pi$
$660$		0			0
$661$	−8.37369e19	+	4.83455e19i	−1.51882	+	0.876891i	−0.519066	+	0.854734i	$0.673720\pi$
$661$	−8.37369e19	+	4.83455e19i	−1.51882	+	0.876891i	−0.999754	+	0.0221573i	$0.992947\pi$
$662$	8.88839e18	+	1.53951e19i	0.159521	+	0.276298i
$663$		0			0
$664$		−	3.85366e19i		−	0.677168i
$665$	−2.84531e19	+	2.56533e18i	−0.494740	+	0.0446059i
$666$		0			0
$667$	4.69332e19	−	8.12907e19i	0.799096	−	1.38408i
$668$	3.67750e19	−	2.12320e19i	0.619608	−	0.357731i
$669$		0			0
$670$	8.89615e18	+	5.13619e18i	0.146784	+	0.0847457i
$671$		−	2.68224e19i		−	0.437965i
$672$		0			0
$673$	9.26340e19			1.48137			0.740687	−	0.671850i	$-0.234500\pi$
$673$	9.26340e19			1.48137			0.740687	+	0.671850i	$0.234500\pi$
$674$	−1.52117e19	+	2.63474e19i	−0.240745	+	0.416983i
$675$		0			0
$676$	−1.56590e19	−	2.71222e19i	−0.242738	−	0.420434i
$677$	−1.89152e19	−	1.09207e19i	−0.290195	−	0.167544i	0.347835	−	0.937556i	$-0.386917\pi$
$677$	−1.89152e19	−	1.09207e19i	−0.290195	−	0.167544i	−0.638030	+	0.770012i	$0.720250\pi$
$678$		0			0
$679$	−3.88619e19	−	1.79963e19i	−0.584031	−	0.270456i
$680$	1.70967e19			0.254302
$681$		0			0
$682$	4.87968e18	−	2.81728e18i	0.0711051	−	0.0410525i
$683$	−4.69498e19	−	8.13195e19i	−0.677156	−	1.17287i	−0.975834	−	0.218515i	$-0.929879\pi$
$683$	−4.69498e19	−	8.13195e19i	−0.677156	−	1.17287i	0.298677	−	0.954354i	$-0.403455\pi$
$684$		0			0
$685$		−	8.01080e19i		−	1.13199i
$686$	−1.26956e19	+	4.89337e19i	−0.177576	+	0.684446i
$687$		0			0
$688$	3.92258e18	−	6.79411e18i	0.0537592	−	0.0931137i
$689$	−1.11144e19	+	6.41691e18i	−0.150783	+	0.0870546i
$690$		0			0
$691$	−7.47944e19	−	4.31826e19i	−0.994312	−	0.574066i	−0.0877517	−	0.996142i	$-0.527968\pi$
$691$	−7.47944e19	−	4.31826e19i	−0.994312	−	0.574066i	−0.906560	+	0.422076i	$0.861302\pi$
$692$			1.79682e19i			0.236462i
$693$		0			0
$694$	8.92223e17			0.0115069
$695$	−4.77441e19	+	8.26951e19i	−0.609573	+	1.05581i
$696$		0			0
$697$	2.72304e19	+	4.71645e19i	0.340741	+	0.590181i
$698$	2.64431e19	+	1.52669e19i	0.327585	+	0.189131i
$699$		0			0
$700$	−1.05620e17	−	1.49993e17i	−0.00128250	−	0.00182131i
$701$	1.70829e19			0.205369			0.102684	−	0.994714i	$-0.467257\pi$
$701$	1.70829e19			0.205369			0.102684	+	0.994714i	$0.467257\pi$
$702$		0			0
$703$	7.03272e19	−	4.06034e19i	0.828774	−	0.478493i
$704$	2.72069e18	+	4.71237e18i	0.0317446	+	0.0549833i
$705$		0			0
$706$		−	1.24560e19i		−	0.142477i
$707$	1.33978e19	+	1.48599e20i	0.151739	+	1.68299i
$708$		0			0
$709$	−4.57744e19	+	7.92835e19i	−0.508275	+	0.880358i	0.491679	+	0.870776i	$0.336383\pi$
$709$	−4.57744e19	+	7.92835e19i	−0.508275	+	0.880358i	−0.999954	+	0.00958151i	$0.996950\pi$
$710$	2.05215e19	−	1.18481e19i	0.225632	−	0.130269i
$711$		0			0
$712$	1.66911e19	+	9.63663e18i	0.179939	+	0.103888i
$713$			2.14275e19i			0.228742i
$714$		0			0
$715$	8.25148e18			0.0863753
$716$	2.28225e19	−	3.95298e19i	0.236577	−	0.409763i
$717$		0			0
$718$	−4.92585e18	−	8.53183e18i	−0.0500738	−	0.0867304i
$719$	−1.23257e20	−	7.11622e19i	−1.24082	−	0.716386i	−0.271557	−	0.962422i	$-0.587538\pi$
$719$	−1.23257e20	−	7.11622e19i	−1.24082	−	0.716386i	−0.969261	+	0.246036i	$0.920872\pi$
$720$		0			0
$721$	−7.34592e19	+	5.17274e19i	−0.725269	+	0.510709i
$722$	5.43930e19			0.531842
$723$		0			0
$724$	8.19599e19	−	4.73196e19i	0.786016	−	0.453807i
$725$	−3.74604e17	−	6.48834e17i	−0.00355801	−	0.00616265i
$726$		0			0
$727$		−	6.69549e19i		−	0.623795i	−0.950116	−	0.311897i	$-0.899036\pi$
$727$		−	6.69549e19i		−	0.623795i	0.950116	−	0.311897i	$-0.100964\pi$
$728$	5.92591e18	+	2.74420e18i	0.0546808	+	0.0253219i
$729$		0			0
$730$	−3.70706e19	+	6.42082e19i	−0.335560	+	0.581207i
$731$	−2.99474e19	+	1.72901e19i	−0.268496	+	0.155016i
$732$		0			0
$733$	−1.21753e20	−	7.02942e19i	−1.07091	−	0.618289i	−0.142479	−	0.989798i	$-0.545507\pi$
$733$	−1.21753e20	−	7.02942e19i	−1.07091	−	0.618289i	−0.928429	+	0.371509i	$0.878841\pi$
$734$		−	1.36489e20i		−	1.18912i
$735$		0			0
$736$	−2.06928e19			−0.176879
$737$	7.20551e18	−	1.24803e19i	0.0610087	−	0.105670i
$738$		0			0
$739$	8.48650e18	+	1.46991e19i	0.0705047	+	0.122118i	0.899123	−	0.437697i	$-0.144206\pi$
$739$	8.48650e18	+	1.46991e19i	0.0705047	+	0.122118i	−0.828618	+	0.559815i	$0.810872\pi$
$740$	−1.00915e20	−	5.82630e19i	−0.830485	−	0.479481i
$741$		0			0
$742$	−3.75868e19	+	8.11662e19i	−0.303534	+	0.655462i
$743$	2.94222e19			0.235371			0.117686	−	0.993051i	$-0.462452\pi$
$743$	2.94222e19			0.235371			0.117686	+	0.993051i	$0.462452\pi$
$744$		0			0
$745$	−5.62354e19	+	3.24675e19i	−0.441485	+	0.254891i
$746$	5.95714e19	+	1.03181e20i	0.463304	+	0.802466i
$747$		0			0
$748$		−	2.39847e19i		−	0.183073i
$749$	−3.89961e19	−	5.53792e19i	−0.294882	−	0.418769i
$750$		0			0
$751$	−5.54318e19	+	9.60106e19i	−0.411414	+	0.712590i	−0.995045	−	0.0994292i	$-0.968298\pi$
$751$	−5.54318e19	+	9.60106e19i	−0.411414	+	0.712590i	0.583631	+	0.812019i	$0.301632\pi$
$752$	−4.53731e19	+	2.61962e19i	−0.333637	+	0.192625i
$753$		0			0
$754$	2.30974e19	+	1.33353e19i	0.166711	+	0.0962506i
$755$			1.50082e20i			1.07325i
$756$		0			0
$757$	−1.67563e20			−1.17627			−0.588137	−	0.808762i	$-0.700138\pi$
$757$	−1.67563e20			−1.17627			−0.588137	+	0.808762i	$0.700138\pi$
$758$	−5.07063e18	+	8.78259e18i	−0.0352677	+	0.0610855i
$759$		0			0
$760$	1.28604e19	+	2.22749e19i	0.0878133	+	0.152097i
$761$	−6.92283e19	−	3.99690e19i	−0.468372	−	0.270415i	0.247186	−	0.968968i	$-0.420494\pi$
$761$	−6.92283e19	−	3.99690e19i	−0.468372	−	0.270415i	−0.715558	+	0.698553i	$0.753828\pi$
$762$		0			0
$763$	5.40381e19	−	4.87209e18i	0.358945	−	0.0323626i
$764$	1.17040e20			0.770337
$765$		0			0
$766$	9.88936e19	−	5.70962e19i	0.639097	−	0.368983i
$767$	−2.41419e18	−	4.18151e18i	−0.0154598	−	0.0267772i
$768$		0			0
$769$		−	1.28830e19i		−	0.0810091i	−0.999179	−	0.0405045i	$-0.987103\pi$
$769$		−	1.28830e19i		−	0.0810091i	0.999179	−	0.0405045i	$-0.0128965\pi$
$770$	4.70215e19	−	3.31109e19i	0.292996	−	0.206317i
$771$		0			0
$772$	3.33073e19	−	5.76899e19i	0.203806	−	0.353003i
$773$	1.28249e19	−	7.40446e18i	0.0777674	−	0.0448991i	−0.460612	−	0.887602i	$-0.652370\pi$
$773$	1.28249e19	−	7.40446e18i	0.0777674	−	0.0448991i	0.538379	+	0.842703i	$0.319037\pi$
$774$		0			0
$775$	1.48114e17	+	8.55135e16i	0.000882030	+	0.000509240i
$776$			3.85578e19i			0.227552i
$777$		0			0
$778$	1.19078e20			0.690196
$779$	−4.09664e19	+	7.09560e19i	−0.235324	+	0.407593i
$780$		0			0
$781$	−1.66216e19	−	2.87894e19i	−0.0937810	−	0.162433i
$782$	7.89908e19	+	4.56054e19i	0.441702	+	0.255017i
$783$		0			0
$784$	4.47808e19	−	8.14107e18i	0.245968	−	0.0447166i
$785$	−2.85624e20			−1.55492
$786$		0			0
$787$	1.53142e20	−	8.84166e19i	0.818976	−	0.472836i	−0.0310870	−	0.999517i	$-0.509897\pi$
$787$	1.53142e20	−	8.84166e19i	0.818976	−	0.472836i	0.850063	+	0.526680i	$0.176564\pi$
$788$	−2.66288e19	−	4.61224e19i	−0.141146	−	0.244472i
$789$		0			0
$790$			1.64257e20i			0.855331i
$791$	−5.12515e19	+	1.10674e20i	−0.264528	+	0.571230i
$792$		0			0
$793$	−1.44911e19	+	2.50993e19i	−0.0734834	+	0.127277i
$794$	9.57441e18	−	5.52779e18i	0.0481247	−	0.0277848i
$795$		0			0
$796$	2.06531e19	+	1.19241e19i	0.101999	+	0.0588890i
$797$			1.54278e20i			0.755259i	0.925957	+	0.377629i	$0.123261\pi$
$797$			1.54278e20i			0.755259i	−0.925957	+	0.377629i	$0.876739\pi$
$798$		0			0
$799$	2.30937e20			1.11088
$800$	−8.25815e16	+	1.43035e17i	−0.000393779	+	0.000682045i
$801$		0			0
$802$	−3.62085e19	−	6.27149e19i	−0.169664	−	0.293867i
$803$	9.00770e19	+	5.20060e19i	0.418413	+	0.241571i
$804$		0			0
$805$	1.96385e19	+	2.17818e20i	0.0896474	+	0.994311i
$806$	−6.08829e18			−0.0275518
$807$		0			0
$808$	1.16333e20	−	6.71651e19i	0.517398	−	0.298720i
$809$	−4.14065e19	−	7.17182e19i	−0.182570	−	0.316220i	0.760185	−	0.649707i	$-0.225108\pi$
$809$	−4.14065e19	−	7.17182e19i	−0.182570	−	0.316220i	−0.942755	+	0.333486i	$0.891775\pi$
$810$		0			0
$811$		−	1.22037e20i		−	0.528868i	−0.964404	−	0.264434i	$-0.914815\pi$
$811$		−	1.22037e20i		−	0.528868i	0.964404	−	0.264434i	$-0.0851851\pi$
$812$	1.85133e20	−	1.66916e19i	0.795410	−	0.0717144i
$813$		0			0
$814$	−8.17366e19	+	1.41572e20i	−0.345180	+	0.597869i
$815$	3.90101e20	−	2.25225e20i	1.63333	−	0.943003i
$816$		0			0
$817$	−4.50539e19	−	2.60119e19i	−0.185429	−	0.107058i
$818$			7.04885e19i			0.287637i
$819$		0			0
$820$	1.17568e20			0.471619
$821$	1.04812e20	−	1.81540e20i	0.416879	−	0.722056i	−0.578744	−	0.815509i	$-0.696457\pi$
$821$	1.04812e20	−	1.81540e20i	0.416879	−	0.722056i	0.995624	+	0.0934527i	$0.0297904\pi$
$822$		0			0
$823$	1.46097e20	+	2.53047e20i	0.571271	+	0.989471i	0.996436	+	0.0843549i	$0.0268829\pi$
$823$	1.46097e20	+	2.53047e20i	0.571271	+	0.989471i	−0.425164	+	0.905116i	$0.639784\pi$
$824$	7.00518e19	+	4.04444e19i	0.271599	+	0.156808i
$825$		0			0
$826$	−3.05366e19	−	1.41410e19i	−0.116402	−	0.0539040i
$827$	3.25414e17			0.00122998			0.000614989	−	1.00000i	$-0.499804\pi$
$827$	3.25414e17			0.00122998			0.000614989		1.00000i	$0.499804\pi$
$828$		0			0
$829$	−3.06875e19	+	1.77174e19i	−0.114046	+	0.0658445i	−0.555938	−	0.831224i	$-0.687641\pi$
$829$	−3.06875e19	+	1.77174e19i	−0.114046	+	0.0658445i	0.441892	+	0.897068i	$0.354307\pi$
$830$	1.83347e20	+	3.17566e20i	0.675658	+	1.17027i
$831$		0			0
$832$		−	5.87953e18i		−	0.0213049i
$833$	−1.88884e20	−	6.76164e19i	−0.678704	−	0.242961i
$834$		0			0
$835$	−2.02033e20	+	3.49931e20i	−0.713866	+	1.23645i
$836$	3.12492e19	−	1.80418e19i	0.109495	−	0.0632171i
$837$		0			0
$838$	−8.65567e19	−	4.99735e19i	−0.298258	−	0.172199i
$839$		−	3.67704e19i		−	0.125651i	−0.998025	−	0.0628253i	$-0.979989\pi$
$839$		−	3.67704e19i		−	0.125651i	0.998025	−	0.0628253i	$-0.0200111\pi$
$840$		0			0
$841$	4.61596e20			1.55128
$842$	1.83659e20	−	3.18106e20i	0.612106	−	1.06020i
$843$		0			0
$844$	−9.58645e19	−	1.66042e20i	−0.314240	−	0.544279i
$845$	2.58080e20	+	1.49003e20i	0.838993	+	0.484393i
$846$		0			0
$847$	1.33608e20	+	1.89740e20i	0.427217	+	0.606700i
$848$	8.05310e19			0.255383
$849$		0			0
$850$	6.30477e17	−	3.64006e17i	0.00196670	−	0.00113547i
$851$	−3.10833e20	−	5.38379e20i	−0.961658	−	1.66564i
$852$		0			0
$853$			4.14427e20i			1.26126i	0.776083	+	0.630631i	$0.217204\pi$
$853$			4.14427e20i			1.26126i	−0.776083	+	0.630631i	$0.782796\pi$
$854$	1.81383e19	+	2.01178e20i	0.0547509	+	0.607262i
$855$		0			0
$856$	−3.04901e19	+	5.28105e19i	−0.0905406	+	0.156821i
$857$	−1.60214e20	+	9.24998e19i	−0.471884	+	0.272443i	−0.717028	−	0.697044i	$-0.754498\pi$
$857$	−1.60214e20	+	9.24998e19i	−0.471884	+	0.272443i	0.245144	+	0.969487i	$0.421165\pi$
$858$		0			0
$859$	1.26235e20	+	7.28820e19i	0.365787	+	0.211187i	0.671616	−	0.740899i	$-0.265600\pi$
$859$	1.26235e20	+	7.28820e19i	0.365787	+	0.211187i	−0.305829	+	0.952086i	$0.598934\pi$
$860$			7.46505e19i			0.214557i
$861$		0			0
$862$	−3.68804e19			−0.104290
$863$	−4.09474e19	+	7.09229e19i	−0.114855	+	0.198935i	−0.917722	−	0.397224i	$-0.869974\pi$
$863$	−4.09474e19	+	7.09229e19i	−0.114855	+	0.198935i	0.802867	+	0.596159i	$0.203307\pi$
$864$		0			0
$865$	−8.54880e19	−	1.48070e20i	−0.235935	−	0.408652i
$866$	−3.59475e20	−	2.07543e20i	−0.984110	−	0.568176i
$867$		0			0
$868$	−3.46944e19	+	2.44306e19i	−0.0934591	+	0.0658106i
$869$	2.30434e20			0.615756
$870$		0			0
$871$	−1.34853e19	+	7.78572e18i	−0.0354595	+	0.0204725i
$872$	−2.44246e19	−	4.23046e19i	−0.0637106	−	0.110350i
$873$		0			0
$874$			1.37221e20i			0.352241i
$875$	3.57131e20	+	1.65382e20i	0.909435	+	0.421145i
$876$		0			0
$877$	3.88575e19	−	6.73032e19i	0.0973819	−	0.168670i	−0.813218	−	0.581959i	$-0.802287\pi$
$877$	3.88575e19	−	6.73032e19i	0.0973819	−	0.168670i	0.910600	+	0.413288i	$0.135620\pi$
$878$	−1.37620e20	+	7.94548e19i	−0.342152	+	0.197542i
$879$		0			0
$880$	−4.48404e19	−	2.58886e19i	−0.109721	−	0.0633476i
$881$		−	1.94272e20i		−	0.471606i	−0.971801	−	0.235803i	$-0.924228\pi$
$881$		−	1.94272e20i		−	0.471606i	0.971801	−	0.235803i	$-0.0757720\pi$
$882$		0			0
$883$	−3.31822e20			−0.792830			−0.396415	−	0.918071i	$-0.629746\pi$
$883$	−3.31822e20			−0.792830			−0.396415	+	0.918071i	$0.629746\pi$
$884$	−1.29580e19	+	2.24440e19i	−0.0307166	+	0.0532027i
$885$		0			0
$886$	−1.88035e19	−	3.25686e19i	−0.0438735	−	0.0759911i
$887$	1.92743e20	+	1.11280e20i	0.446184	+	0.257604i	0.706217	−	0.707995i	$-0.250400\pi$
$887$	1.92743e20	+	1.11280e20i	0.446184	+	0.257604i	−0.260033	+	0.965600i	$0.583734\pi$
$888$		0			0
$889$	2.78105e20	−	6.00548e20i	0.633718	−	1.36847i
$890$	−1.83394e20			−0.414625
$891$		0			0
$892$	4.25619e19	−	2.45731e19i	0.0947256	−	0.0546899i
$893$	1.73715e20	+	3.00884e20i	0.383599	+	0.664414i
$894$		0			0
$895$			4.34334e20i			0.944197i
$896$	−2.35929e19	−	3.35048e19i	−0.0508892	−	0.0722689i
$897$		0			0
$898$	−3.10739e20	+	5.38215e20i	−0.659874	+	1.14294i
$899$	−1.50080e20	+	8.66487e19i	−0.316231	+	0.182576i
$900$		0			0
$901$	−3.07411e20	−	1.77484e20i	−0.637744	−	0.368202i
$902$		−	1.64935e20i		−	0.339520i
$903$		0			0
$904$	1.09808e20			0.222564
$905$	−4.50268e20	+	7.79888e20i	−0.905589	+	1.56853i
$906$		0			0
$907$	2.11304e20	+	3.65990e20i	0.418463	+	0.724800i	0.995785	−	0.0917170i	$-0.0292355\pi$
$907$	2.11304e20	+	3.65990e20i	0.418463	+	0.724800i	−0.577322	+	0.816517i	$0.695902\pi$
$908$	−4.04840e19	−	2.33735e19i	−0.0795578	−	0.0459327i
$909$		0			0
$910$	−6.18895e19	+	5.57997e18i	−0.119764	+	0.0107980i
$911$	1.01733e20			0.195359			0.0976793	−	0.995218i	$-0.468858\pi$
$911$	1.01733e20			0.195359			0.0976793	+	0.995218i	$0.468858\pi$
$912$		0			0
$913$	4.45510e20	−	2.57215e20i	0.842485	−	0.486409i
$914$	−2.45357e20	−	4.24971e20i	−0.460442	−	0.797509i
$915$		0			0
$916$		−	1.58844e20i		−	0.293564i
$917$	4.30305e20	−	3.03006e20i	0.789208	−	0.555733i
$918$		0			0
$919$	2.52902e20	−	4.38039e20i	0.456819	−	0.791233i	−0.541972	−	0.840396i	$-0.682322\pi$
$919$	2.52902e20	−	4.38039e20i	0.456819	−	0.791233i	0.998791	+	0.0491634i	$0.0156555\pi$
$920$	1.70522e20	−	9.84510e19i	0.305679	−	0.176484i
$921$		0			0
$922$	4.39765e20	+	2.53898e20i	0.776433	+	0.448274i
$923$			3.59200e19i			0.0629397i
$924$		0			0
$925$	−4.96193e18			−0.00856364
$926$	−3.84113e20	+	6.65303e20i	−0.657934	+	1.13957i
$927$		0			0
$928$	−8.36777e19	−	1.44934e20i	−0.141180	−	0.244531i
$929$	−2.67492e20	−	1.54436e20i	−0.447920	−	0.258606i	0.259032	−	0.965869i	$-0.416597\pi$
$929$	−2.67492e20	−	1.54436e20i	−0.447920	−	0.258606i	−0.706951	+	0.707262i	$0.749930\pi$
$930$		0			0
$931$	−5.39861e19	−	2.96956e20i	−0.0890500	−	0.489829i
$932$	−3.88991e20			−0.636837
$933$		0			0
$934$	−5.03323e20	+	2.90594e20i	−0.811743	+	0.468660i
$935$	1.14113e20	+	1.97650e20i	0.182664	+	0.316384i
$936$		0			0
$937$		−	5.06993e20i		−	0.799512i	−0.916621	−	0.399756i	$-0.869095\pi$
$937$		−	5.06993e20i		−	0.799512i	0.916621	−	0.399756i	$-0.130905\pi$
$938$	−4.56045e19	+	9.84800e19i	−0.0713819	+	0.154144i
$939$		0			0
$940$	2.49269e20	−	4.31747e20i	0.384391	−	0.665785i
$941$	3.86232e20	−	2.22991e20i	0.591181	−	0.341319i	−0.174383	−	0.984678i	$-0.555793\pi$
$941$	3.86232e20	−	2.22991e20i	0.591181	−	0.341319i	0.765564	+	0.643359i	$0.222460\pi$
$942$		0			0
$943$	5.43192e20	+	3.13612e20i	0.819166	+	0.472946i
$944$			3.02977e19i			0.0453529i
$945$		0			0
$946$	1.04726e20			0.154461
$947$	−3.01223e20	+	5.21734e20i	−0.441000	+	0.763835i	−0.997764	−	0.0668361i	$-0.978710\pi$
$947$	−3.01223e20	+	5.21734e20i	−0.441000	+	0.763835i	0.556764	+	0.830671i	$0.312043\pi$
$948$		0			0
$949$	−5.61937e19	−	9.73303e19i	−0.0810632	−	0.140406i
$950$	9.48513e17	+	5.47624e17i	0.00135825	+	0.000784183i
$951$		0			0
$952$	1.62194e19	+	1.79895e20i	0.0228863	+	0.253840i
$953$	4.32972e20			0.606470			0.303235	−	0.952916i	$-0.401933\pi$
$953$	4.32972e20			0.606470			0.303235	+	0.952916i	$0.401933\pi$
$954$		0			0
$955$	−9.64485e20	+	5.56846e20i	−1.33129	+	0.768619i
$956$	−2.44600e20	−	4.23659e20i	−0.335159	−	0.580512i
$957$		0			0
$958$			3.68094e19i			0.0497050i
$959$	8.42915e20	−	7.59974e19i	1.12993	−	0.101875i
$960$		0			0
$961$	−3.58692e20	+	6.21273e20i	−0.473869	+	0.820765i
$962$	1.52972e20	−	8.83183e19i	0.200625	−	0.115831i
$963$		0			0
$964$	1.40499e20	+	8.11174e19i	0.181608	+	0.104852i
$965$			6.33869e20i			0.813408i
$966$		0			0
$967$	3.06464e20			0.387609			0.193804	−	0.981040i	$-0.437917\pi$
$967$	3.06464e20			0.387609			0.193804	+	0.981040i	$0.437917\pi$
$968$	1.04465e20	−	1.80939e20i	0.131173	−	0.227197i
$969$		0			0
$970$	−1.83448e20	−	3.17741e20i	−0.227044	−	0.393252i
$971$	−8.91234e20	−	5.14554e20i	−1.09511	−	0.632261i	−0.160176	−	0.987088i	$-0.551206\pi$
$971$	−8.91234e20	−	5.14554e20i	−1.09511	−	0.632261i	−0.934932	+	0.354827i	$0.884540\pi$
$972$		0			0
$973$	−9.15431e20	−	4.23922e20i	−1.10876	−	0.513448i
$974$	6.61659e20			0.795649
$975$		0			0
$976$	1.57496e20	−	9.09302e19i	0.186690	−	0.107785i
$977$	−2.44710e20	−	4.23850e20i	−0.287998	−	0.498828i	0.685334	−	0.728229i	$-0.259656\pi$
$977$	−2.44710e20	−	4.23850e20i	−0.287998	−	0.498828i	−0.973332	+	0.229402i	$0.926323\pi$
$978$		0			0
$979$			2.57282e20i			0.298490i
$980$	−3.30289e20	+	2.80143e20i	−0.380463	+	0.322699i
$981$		0			0
$982$	1.79908e20	−	3.11610e20i	0.204301	−	0.353860i
$983$	1.07196e21	−	6.18897e20i	1.20866	−	0.697820i	0.246194	−	0.969221i	$-0.420820\pi$
$983$	1.07196e21	−	6.18897e20i	1.20866	−	0.697820i	0.962467	+	0.271400i	$0.0874867\pi$
$984$		0			0
$985$	4.38876e20	+	2.53385e20i	0.487853	+	0.281662i
$986$			7.37677e20i			0.814194i
$987$		0			0
$988$	−3.89891e19			−0.0424272
$989$	−1.99130e20	+	3.44904e20i	−0.215161	+	0.372669i
$990$		0			0
$991$	−6.13960e20	−	1.06341e21i	−0.654071	−	1.13288i	−0.982126	−	0.188225i	$-0.939727\pi$
$991$	−6.13960e20	−	1.06341e21i	−0.654071	−	1.13288i	0.328055	−	0.944658i	$-0.393607\pi$
$992$	3.30851e19	+	1.91017e19i	0.0349986	+	0.0202065i
$993$		0			0
$994$	1.44137e20	+	2.04692e20i	0.150339	+	0.213499i
$995$	−2.26927e20			−0.235031
$996$		0			0
$997$	1.62396e21	−	9.37592e20i	1.65847	−	0.957520i	0.685053	−	0.728493i	$-0.259779\pi$
$997$	1.62396e21	−	9.37592e20i	1.65847	−	0.957520i	0.973420	−	0.229026i	$-0.0735542\pi$
$998$	−2.96505e19	−	5.13562e19i	−0.0300690	−	0.0520810i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.15.n.b.19.4		20
3.2	odd	2		14.15.d.a.5.9	yes	20
7.3	odd	6	inner	126.15.n.b.73.4		20
21.2	odd	6		98.15.b.c.97.7		20
21.5	even	6		98.15.b.c.97.4		20
21.11	odd	6		98.15.d.b.31.7		20
21.17	even	6		14.15.d.a.3.9	✓	20
21.20	even	2		98.15.d.b.19.7		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.15.d.a.3.9	✓	20	21.17	even	6
14.15.d.a.5.9	yes	20	3.2	odd	2
98.15.b.c.97.4		20	21.5	even	6
98.15.b.c.97.7		20	21.2	odd	6
98.15.d.b.19.7		20	21.20	even	2
98.15.d.b.31.7		20	21.11	odd	6
126.15.n.b.19.4		20	1.1	even	1	trivial
126.15.n.b.73.4		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)

\(f(q)\)	\(=\)	\(q+(-45.2548 + 78.3837i) q^{2} +(-4096.00 - 7094.48i) q^{4} +(67507.4 + 38975.4i) q^{5} +(-346065. + 747303. i) q^{7} +741455. q^{8} +O(q^{10})\)	\(q+(-45.2548 + 78.3837i) q^{2} +(-4096.00 - 7094.48i) q^{4} +(67507.4 + 38975.4i) q^{5} +(-346065. + 747303. i) q^{7} +741455. q^{8} +(-6.11007e6 + 3.52765e6i) q^{10} +(4.94890e6 + 8.57174e6i) q^{11} -1.06948e7i q^{13} +(-4.29153e7 - 6.09449e7i) q^{14} +(-3.35544e7 + 5.81180e7i) q^{16} +(2.56175e8 - 1.47903e8i) q^{17} +(3.85399e8 + 2.22510e8i) q^{19} -6.38573e8i q^{20} -8.95846e8 q^{22} +(1.70339e9 - 2.95036e9i) q^{23} +(-1.35959e7 - 2.35488e7i) q^{25} +(8.38298e8 + 4.83992e8i) q^{26} +(6.71921e9 - 6.05806e8i) q^{28} +2.75528e10 q^{29} +(-5.44700e9 + 3.14483e9i) q^{31} +(-3.03700e9 - 5.26024e9i) q^{32} +2.67733e10i q^{34} +(-5.24883e10 + 3.69605e10i) q^{35} +(9.12395e10 - 1.58031e11i) q^{37} +(-3.48824e10 + 2.01393e10i) q^{38} +(5.00537e10 + 2.88985e10i) q^{40} +1.84110e11i q^{41} -1.16902e11 q^{43} +(4.05414e10 - 7.02197e10i) q^{44} +(1.54174e11 + 2.67036e11i) q^{46} +(6.76112e11 + 3.90353e11i) q^{47} +(-4.38702e11 - 5.17231e11i) q^{49} +2.46112e9 q^{50} +(-7.58741e10 + 4.38059e10i) q^{52} +(-6.00003e11 - 1.03923e12i) q^{53} +7.71541e11i q^{55} +(-2.56591e11 + 5.54092e11i) q^{56} +(-1.24690e12 + 2.15969e12i) q^{58} +(3.90985e11 - 2.25735e11i) q^{59} +(-2.34687e12 - 1.35497e12i) q^{61} -5.69275e11i q^{62} +5.49756e11 q^{64} +(4.16834e11 - 7.21978e11i) q^{65} +(-7.27991e11 - 1.26092e12i) q^{67} +(-2.09859e12 - 1.21162e12i) q^{68} +(-5.21746e11 - 5.78687e12i) q^{70} -3.35864e12 q^{71} +(9.10071e12 - 5.25430e12i) q^{73} +(8.25805e12 + 1.43034e13i) q^{74} -3.64561e12i q^{76} +(-8.11833e12 + 7.31951e11i) q^{77} +(1.16407e13 - 2.01623e13i) q^{79} +(-4.53034e12 + 2.61559e12i) q^{80} +(-1.44312e13 - 8.33188e12i) q^{82} -5.19742e13i q^{83} +2.30583e13 q^{85} +(5.29038e12 - 9.16321e12i) q^{86} +(3.66939e12 + 6.35556e12i) q^{88} +(2.25113e13 + 1.29969e13i) q^{89} +(7.99227e12 + 3.70109e12i) q^{91} -2.79084e13 q^{92} +(-6.11947e13 + 3.53308e13i) q^{94} +(1.73449e13 + 3.00422e13i) q^{95} +5.20028e13i q^{97} +(6.03958e13 - 1.09799e13i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 81920 q^{4} - 3354 q^{5} + 1455616 q^{7}+O(q^{10}) \) 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

Modular forms

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