LMFDB - Embedded newform 25.14.a.d.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,14,Mod(1,25)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(25, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 14, names="a")

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

chi := DirichletCharacter("25.1");

S:= CuspForms(chi, 14);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 14 $
Character orbit:	$[\chi]$	$=$	25.a (trivial)

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:	yes
Analytic conductor:	$26.8077322380$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 17722x^{2} + 125608x + 10385664 $ x^4 - x^3 - 17722x^2 + 125608x + 10385664
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2}\cdot 5^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$28.7600$ of defining polynomial
Character	$\chi$	$=$	25.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+44.7600 q^{2} -1474.96 q^{3} -6188.54 q^{4} -66019.0 q^{6} -143529. q^{7} -643673. q^{8} +581170. q^{9} +O(q^{10})$	\(q+44.7600 q^{2} -1474.96 q^{3} -6188.54 q^{4} -66019.0 q^{6} -143529. q^{7} -643673. q^{8} +581170. q^{9} -1.01625e7 q^{11} +9.12783e6 q^{12} -1.62266e7 q^{13} -6.42437e6 q^{14} +2.18858e7 q^{16} +9.93899e7 q^{17} +2.60132e7 q^{18} +2.26709e8 q^{19} +2.11699e8 q^{21} -4.54875e8 q^{22} +6.54093e8 q^{23} +9.49389e8 q^{24} -7.26304e8 q^{26} +1.49436e9 q^{27} +8.88237e8 q^{28} -1.51280e9 q^{29} -9.32148e9 q^{31} +6.25257e9 q^{32} +1.49893e10 q^{33} +4.44869e9 q^{34} -3.59660e9 q^{36} -8.08518e9 q^{37} +1.01475e10 q^{38} +2.39336e10 q^{39} -1.29290e10 q^{41} +9.47565e9 q^{42} +7.32164e10 q^{43} +6.28914e10 q^{44} +2.92772e10 q^{46} +5.98209e10 q^{47} -3.22805e10 q^{48} -7.62884e10 q^{49} -1.46596e11 q^{51} +1.00419e11 q^{52} -1.64873e11 q^{53} +6.68873e10 q^{54} +9.23859e10 q^{56} -3.34386e11 q^{57} -6.77127e10 q^{58} -4.56737e11 q^{59} +3.34922e11 q^{61} -4.17229e11 q^{62} -8.34149e10 q^{63} +1.00577e11 q^{64} +6.70921e11 q^{66} +2.08461e11 q^{67} -6.15079e11 q^{68} -9.64758e11 q^{69} +6.65261e11 q^{71} -3.74083e11 q^{72} -1.54439e12 q^{73} -3.61893e11 q^{74} -1.40300e12 q^{76} +1.45862e12 q^{77} +1.07127e12 q^{78} +3.16141e12 q^{79} -3.13068e12 q^{81} -5.78700e11 q^{82} -1.52521e12 q^{83} -1.31011e12 q^{84} +3.27716e12 q^{86} +2.23131e12 q^{87} +6.54135e12 q^{88} +3.22541e12 q^{89} +2.32900e12 q^{91} -4.04788e12 q^{92} +1.37488e13 q^{93} +2.67758e12 q^{94} -9.22227e12 q^{96} +7.73130e12 q^{97} -3.41467e12 q^{98} -5.90616e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 65 q^{2} + 860 q^{3} + 3733 q^{4} + 40333 q^{6} + 102800 q^{7} + 329895 q^{8} + 47872 q^{9}+O(q^{10}) $ 4 * q + 65 * q^2 + 860 * q^3 + 3733 * q^4 + 40333 * q^6 + 102800 * q^7 + 329895 * q^8 + 47872 * q^9	\( 4 q + 65 q^{2} + 860 q^{3} + 3733 q^{4} + 40333 q^{6} + 102800 q^{7} + 329895 q^{8} + 47872 q^{9} + 6675428 q^{11} - 520595 q^{12} + 4926920 q^{13} + 37103466 q^{14} - 8440751 q^{16} + 50416220 q^{17} + 22302110 q^{18} + 282648860 q^{19} - 438887472 q^{21} + 969439305 q^{22} + 1208437080 q^{23} + 1415344455 q^{24} - 3267454372 q^{26} + 1714727420 q^{27} + 11782380170 q^{28} + 7630648840 q^{29} - 12716039032 q^{31} + 5288310415 q^{32} + 36748956820 q^{33} + 23123205021 q^{34} - 45497926906 q^{36} + 38137910960 q^{37} + 99584060705 q^{38} + 60691943624 q^{39} - 81254933612 q^{41} + 62466915570 q^{42} + 97224763400 q^{43} + 111616918681 q^{44} - 77938796802 q^{46} + 69940090280 q^{47} + 107001227905 q^{48} + 118071253428 q^{49} + 91953947668 q^{51} - 165428401300 q^{52} - 179518658440 q^{53} - 275242827665 q^{54} + 403963457310 q^{56} - 99736967860 q^{57} - 810275460480 q^{58} - 858015815320 q^{59} + 589205515328 q^{61} - 942802276470 q^{62} - 2020360823760 q^{63} - 1516614058847 q^{64} + 1418821712381 q^{66} - 685669480180 q^{67} - 2270111055215 q^{68} - 1486209750216 q^{69} + 949682379448 q^{71} - 1359611223390 q^{72} - 1688808513820 q^{73} + 1003330480306 q^{74} + 1964117678945 q^{76} + 2180313451200 q^{77} + 171961033900 q^{78} - 355815036160 q^{79} - 1150994540276 q^{81} - 224361325395 q^{82} + 8420327909340 q^{83} + 9279336345306 q^{84} - 11016868246612 q^{86} + 9035391325160 q^{87} + 12729770641515 q^{88} + 2506082642820 q^{89} - 11092233838352 q^{91} + 403195163070 q^{92} + 17882711708520 q^{93} + 15051571815036 q^{94} - 17345568428737 q^{96} + 12121501720280 q^{97} + 19722093248605 q^{98} + 1425639838304 q^{99}+O(q^{100}) \) 4 * q + 65 * q^2 + 860 * q^3 + 3733 * q^4 + 40333 * q^6 + 102800 * q^7 + 329895 * q^8 + 47872 * q^9 + 6675428 * q^11 - 520595 * q^12 + 4926920 * q^13 + 37103466 * q^14 - 8440751 * q^16 + 50416220 * q^17 + 22302110 * q^18 + 282648860 * q^19 - 438887472 * q^21 + 969439305 * q^22 + 1208437080 * q^23 + 1415344455 * q^24 - 3267454372 * q^26 + 1714727420 * q^27 + 11782380170 * q^28 + 7630648840 * q^29 - 12716039032 * q^31 + 5288310415 * q^32 + 36748956820 * q^33 + 23123205021 * q^34 - 45497926906 * q^36 + 38137910960 * q^37 + 99584060705 * q^38 + 60691943624 * q^39 - 81254933612 * q^41 + 62466915570 * q^42 + 97224763400 * q^43 + 111616918681 * q^44 - 77938796802 * q^46 + 69940090280 * q^47 + 107001227905 * q^48 + 118071253428 * q^49 + 91953947668 * q^51 - 165428401300 * q^52 - 179518658440 * q^53 - 275242827665 * q^54 + 403963457310 * q^56 - 99736967860 * q^57 - 810275460480 * q^58 - 858015815320 * q^59 + 589205515328 * q^61 - 942802276470 * q^62 - 2020360823760 * q^63 - 1516614058847 * q^64 + 1418821712381 * q^66 - 685669480180 * q^67 - 2270111055215 * q^68 - 1486209750216 * q^69 + 949682379448 * q^71 - 1359611223390 * q^72 - 1688808513820 * q^73 + 1003330480306 * q^74 + 1964117678945 * q^76 + 2180313451200 * q^77 + 171961033900 * q^78 - 355815036160 * q^79 - 1150994540276 * q^81 - 224361325395 * q^82 + 8420327909340 * q^83 + 9279336345306 * q^84 - 11016868246612 * q^86 + 9035391325160 * q^87 + 12729770641515 * q^88 + 2506082642820 * q^89 - 11092233838352 * q^91 + 403195163070 * q^92 + 17882711708520 * q^93 + 15051571815036 * q^94 - 17345568428737 * q^96 + 12121501720280 * q^97 + 19722093248605 * q^98 + 1425639838304 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	44.7600	0.494533	0.247266	−	0.968948i	$-0.420468\pi$
$2$	44.7600	0.494533	0.247266	+	0.968948i	$0.420468\pi$
$3$	−1474.96	−1.16813	−0.584064	−	0.811707i	$-0.698538\pi$
$3$	−1474.96	−1.16813	−0.584064	+	0.811707i	$0.698538\pi$
$4$	−6188.54	−0.755438
$5$	0	0
$5$	0	0
$6$	−66019.0	−0.577678
$7$	−143529.	−0.461109	−0.230554	−	0.973059i	$-0.574054\pi$
$7$	−143529.	−0.461109	−0.230554	+	0.973059i	$0.574054\pi$
$8$	−643673.	−0.868121
$9$	581170.	0.364525
$10$	0	0
$11$	−1.01625e7	−1.72962	−0.864809	−	0.502102i	$-0.832560\pi$
$11$	−1.01625e7	−1.72962	−0.864809	+	0.502102i	$0.832560\pi$
$12$	9.12783e6	0.882448
$13$	−1.62266e7	−0.932388	−0.466194	−	0.884683i	$-0.654375\pi$
$13$	−1.62266e7	−0.932388	−0.466194	+	0.884683i	$0.654375\pi$
$14$	−6.42437e6	−0.228033
$15$	0	0
$16$	2.18858e7	0.326123
$17$	9.93899e7	0.998675	0.499338	−	0.866408i	$-0.333577\pi$
$17$	9.93899e7	0.998675	0.499338	+	0.866408i	$0.333577\pi$
$18$	2.60132e7	0.180269
$19$	2.26709e8	1.10553	0.552765	−	0.833337i	$-0.313573\pi$
$19$	2.26709e8	1.10553	0.552765	+	0.833337i	$0.313573\pi$
$20$	0	0
$21$	2.11699e8	0.538634
$22$	−4.54875e8	−0.855352
$23$	6.54093e8	0.921316	0.460658	−	0.887578i	$-0.347613\pi$
$23$	6.54093e8	0.921316	0.460658	+	0.887578i	$0.347613\pi$
$24$	9.49389e8	1.01408
$25$	0	0
$26$	−7.26304e8	−0.461096
$27$	1.49436e9	0.742317
$28$	8.88237e8	0.348339
$29$	−1.51280e9	−0.472273	−0.236137	−	0.971720i	$-0.575881\pi$
$29$	−1.51280e9	−0.472273	−0.236137	+	0.971720i	$0.575881\pi$
$30$	0	0
$31$	−9.32148e9	−1.88640	−0.943201	−	0.332224i	$-0.892201\pi$
$31$	−9.32148e9	−1.88640	−0.943201	+	0.332224i	$0.892201\pi$
$32$	6.25257e9	1.02940
$33$	1.49893e10	2.02042
$34$	4.44869e9	0.493877
$35$	0	0
$36$	−3.59660e9	−0.275375
$37$	−8.08518e9	−0.518058	−0.259029	−	0.965869i	$-0.583403\pi$
$37$	−8.08518e9	−0.518058	−0.259029	+	0.965869i	$0.583403\pi$
$38$	1.01475e10	0.546721
$39$	2.39336e10	1.08915
$40$	0	0
$41$	−1.29290e10	−0.425078	−0.212539	−	0.977153i	$-0.568173\pi$
$41$	−1.29290e10	−0.425078	−0.212539	+	0.977153i	$0.568173\pi$
$42$	9.47565e9	0.266372
$43$	7.32164e10	1.76630	0.883148	−	0.469095i	$-0.155420\pi$
$43$	7.32164e10	1.76630	0.883148	+	0.469095i	$0.155420\pi$
$44$	6.28914e10	1.30662
$45$	0	0
$46$	2.92772e10	0.455621
$47$	5.98209e10	0.809500	0.404750	−	0.914427i	$-0.367359\pi$
$47$	5.98209e10	0.809500	0.404750	+	0.914427i	$0.367359\pi$
$48$	−3.22805e10	−0.380954
$49$	−7.62884e10	−0.787379
$50$	0	0
$51$	−1.46596e11	−1.16658
$52$	1.00419e11	0.704361
$53$	−1.64873e11	−1.02178	−0.510889	−	0.859647i	$-0.670684\pi$
$53$	−1.64873e11	−1.02178	−0.510889	+	0.859647i	$0.670684\pi$
$54$	6.68873e10	0.367100
$55$	0	0
$56$	9.23859e10	0.400298
$57$	−3.34386e11	−1.29140
$58$	−6.77127e10	−0.233554
$59$	−4.56737e11	−1.40971	−0.704853	−	0.709354i	$-0.748987\pi$
$59$	−4.56737e11	−1.40971	−0.704853	+	0.709354i	$0.748987\pi$
$60$	0	0
$61$	3.34922e11	0.832339	0.416169	−	0.909287i	$-0.363372\pi$
$61$	3.34922e11	0.832339	0.416169	+	0.909287i	$0.363372\pi$
$62$	−4.17229e11	−0.932887
$63$	−8.34149e10	−0.168085
$64$	1.00577e11	0.182948
$65$	0	0
$66$	6.70921e11	0.999161
$67$	2.08461e11	0.281539	0.140770	−	0.990042i	$-0.455042\pi$
$67$	2.08461e11	0.281539	0.140770	+	0.990042i	$0.455042\pi$
$68$	−6.15079e11	−0.754437
$69$	−9.64758e11	−1.07622
$70$	0	0
$71$	6.65261e11	0.616329	0.308165	−	0.951333i	$-0.400285\pi$
$71$	6.65261e11	0.616329	0.308165	+	0.951333i	$0.400285\pi$
$72$	−3.74083e11	−0.316451
$73$	−1.54439e12	−1.19442	−0.597212	−	0.802084i	$-0.703725\pi$
$73$	−1.54439e12	−1.19442	−0.597212	+	0.802084i	$0.703725\pi$
$74$	−3.61893e11	−0.256197
$75$	0	0
$76$	−1.40300e12	−0.835159
$77$	1.45862e12	0.797541
$78$	1.07127e12	0.538620
$79$	3.16141e12	1.46320	0.731601	−	0.681733i	$-0.238773\pi$
$79$	3.16141e12	1.46320	0.731601	+	0.681733i	$0.238773\pi$
$80$	0	0
$81$	−3.13068e12	−1.23165
$82$	−5.78700e11	−0.210215
$83$	−1.52521e12	−0.512061	−0.256031	−	0.966669i	$-0.582415\pi$
$83$	−1.52521e12	−0.512061	−0.256031	+	0.966669i	$0.582415\pi$
$84$	−1.31011e12	−0.406904
$85$	0	0
$86$	3.27716e12	0.873491
$87$	2.23131e12	0.551676
$88$	6.54135e12	1.50152
$89$	3.22541e12	0.687939	0.343969	−	0.938981i	$-0.388228\pi$
$89$	3.22541e12	0.687939	0.343969	+	0.938981i	$0.388228\pi$
$90$	0	0
$91$	2.32900e12	0.429932
$92$	−4.04788e12	−0.695997
$93$	1.37488e13	2.20356
$94$	2.67758e12	0.400324
$95$	0	0
$96$	−9.22227e12	−1.20247
$97$	7.73130e12	0.942402	0.471201	−	0.882026i	$-0.343821\pi$
$97$	7.73130e12	0.942402	0.471201	+	0.882026i	$0.343821\pi$
$98$	−3.41467e12	−0.389385
$99$	−5.90616e12	−0.630488
$100$	0	0
$101$	−6.29728e12	−0.590289	−0.295144	−	0.955453i	$-0.595368\pi$
$101$	−6.29728e12	−0.590289	−0.295144	+	0.955453i	$0.595368\pi$
$102$	−6.56162e12	−0.576912
$103$	−9.31797e11	−0.0768917	−0.0384458	−	0.999261i	$-0.512241\pi$
$103$	−9.31797e11	−0.0768917	−0.0384458	+	0.999261i	$0.512241\pi$
$104$	1.04446e13	0.809425
$105$	0	0
$106$	−7.37971e12	−0.505302
$107$	8.96038e12	0.577207	0.288604	−	0.957449i	$-0.406809\pi$
$107$	8.96038e12	0.577207	0.288604	+	0.957449i	$0.406809\pi$
$108$	−9.24788e12	−0.560774
$109$	−4.02858e12	−0.230080	−0.115040	−	0.993361i	$-0.536700\pi$
$109$	−4.02858e12	−0.230080	−0.115040	+	0.993361i	$0.536700\pi$
$110$	0	0
$111$	1.19253e13	0.605159
$112$	−3.14125e12	−0.150378
$113$	−1.77402e13	−0.801583	−0.400792	−	0.916169i	$-0.631265\pi$
$113$	−1.77402e13	−0.801583	−0.400792	+	0.916169i	$0.631265\pi$
$114$	−1.49671e13	−0.638640
$115$	0	0
$116$	9.36200e12	0.356773
$117$	−9.43043e12	−0.339878
$118$	−2.04436e13	−0.697145
$119$	−1.42654e13	−0.460498
$120$	0	0
$121$	6.87546e13	1.99158
$122$	1.49911e13	0.411619
$123$	1.90696e13	0.496545
$124$	5.76864e13	1.42506
$125$	0	0
$126$	−3.73365e12	−0.0831237
$127$	−4.19421e13	−0.887004	−0.443502	−	0.896273i	$-0.646264\pi$
$127$	−4.19421e13	−0.887004	−0.443502	+	0.896273i	$0.646264\pi$
$128$	−4.67193e13	−0.938926
$129$	−1.07991e14	−2.06326
$130$	0	0
$131$	5.99944e12	0.103716	0.0518582	−	0.998654i	$-0.483486\pi$
$131$	5.99944e12	0.103716	0.0518582	+	0.998654i	$0.483486\pi$
$132$	−9.27619e13	−1.52630
$133$	−3.25394e13	−0.509770
$134$	9.33071e12	0.139230
$135$	0	0
$136$	−6.39746e13	−0.866971
$137$	1.06248e14	1.37289	0.686444	−	0.727182i	$-0.259171\pi$
$137$	1.06248e14	1.37289	0.686444	+	0.727182i	$0.259171\pi$
$138$	−4.31826e13	−0.532224
$139$	−2.39140e13	−0.281227	−0.140613	−	0.990065i	$-0.544907\pi$
$139$	−2.39140e13	−0.281227	−0.140613	+	0.990065i	$0.544907\pi$
$140$	0	0
$141$	−8.82331e13	−0.945600
$142$	2.97771e13	0.304795
$143$	1.64904e14	1.61267
$144$	1.27193e13	0.118880
$145$	0	0
$146$	−6.91268e13	−0.590681
$147$	1.12522e14	0.919760
$148$	5.00355e13	0.391361
$149$	9.59256e13	0.718164	0.359082	−	0.933306i	$-0.383090\pi$
$149$	9.59256e13	0.718164	0.359082	+	0.933306i	$0.383090\pi$
$150$	0	0
$151$	2.60912e14	1.79120	0.895599	−	0.444863i	$-0.146748\pi$
$151$	2.60912e14	1.79120	0.895599	+	0.444863i	$0.146748\pi$
$152$	−1.45927e14	−0.959734
$153$	5.77624e13	0.364042
$154$	6.52879e13	0.394410
$155$	0	0
$156$	−1.48114e14	−0.822784
$157$	1.53366e14	0.817299	0.408649	−	0.912691i	$-0.366000\pi$
$157$	1.53366e14	0.817299	0.408649	+	0.912691i	$0.366000\pi$
$158$	1.41505e14	0.723601
$159$	2.43180e14	1.19357
$160$	0	0
$161$	−9.38815e13	−0.424827
$162$	−1.40129e14	−0.609089
$163$	1.84180e14	0.769172	0.384586	−	0.923089i	$-0.374344\pi$
$163$	1.84180e14	0.769172	0.384586	+	0.923089i	$0.374344\pi$
$164$	8.00114e13	0.321120
$165$	0	0
$166$	−6.82684e13	−0.253231
$167$	2.54879e14	0.909237	0.454619	−	0.890686i	$-0.349776\pi$
$167$	2.54879e14	0.909237	0.454619	+	0.890686i	$0.349776\pi$
$168$	−1.36265e14	−0.467600
$169$	−3.95716e13	−0.130653
$170$	0	0
$171$	1.31757e14	0.402993
$172$	−4.53103e14	−1.33433
$173$	−2.24275e14	−0.636035	−0.318017	−	0.948085i	$-0.603017\pi$
$173$	−2.24275e14	−0.636035	−0.318017	+	0.948085i	$0.603017\pi$
$174$	9.98732e13	0.272822
$175$	0	0
$176$	−2.22415e14	−0.564069
$177$	6.73667e14	1.64672
$178$	1.44369e14	0.340208
$179$	−8.20363e14	−1.86407	−0.932033	−	0.362374i	$-0.881966\pi$
$179$	−8.20363e14	−1.86407	−0.932033	+	0.362374i	$0.881966\pi$
$180$	0	0
$181$	−3.55987e14	−0.752529	−0.376265	−	0.926512i	$-0.622792\pi$
$181$	−3.55987e14	−0.752529	−0.376265	+	0.926512i	$0.622792\pi$
$182$	1.04246e14	0.212615
$183$	−4.93995e14	−0.972279
$184$	−4.21022e14	−0.799814
$185$	0	0
$186$	6.15395e14	1.08973
$187$	−1.01005e15	−1.72733
$188$	−3.70204e14	−0.611527
$189$	−2.14484e14	−0.342289
$190$	0	0
$191$	8.43154e14	1.25658	0.628290	−	0.777979i	$-0.283755\pi$
$191$	8.43154e14	1.25658	0.628290	+	0.777979i	$0.283755\pi$
$192$	−1.48346e14	−0.213707
$193$	−1.01323e14	−0.141119	−0.0705597	−	0.997508i	$-0.522479\pi$
$193$	−1.01323e14	−0.141119	−0.0705597	+	0.997508i	$0.522479\pi$
$194$	3.46053e14	0.466049
$195$	0	0
$196$	4.72114e14	0.594816
$197$	−4.38917e14	−0.534997	−0.267499	−	0.963558i	$-0.586197\pi$
$197$	−4.38917e14	−0.534997	−0.267499	+	0.963558i	$0.586197\pi$
$198$	−2.64360e14	−0.311797
$199$	4.59625e14	0.524637	0.262318	−	0.964981i	$-0.415513\pi$
$199$	4.59625e14	0.524637	0.262318	+	0.964981i	$0.415513\pi$
$200$	0	0
$201$	−3.07471e14	−0.328874
$202$	−2.81866e14	−0.291917
$203$	2.17130e14	0.217769
$204$	9.07214e14	0.881279
$205$	0	0
$206$	−4.17072e13	−0.0380254
$207$	3.80139e14	0.335842
$208$	−3.55132e14	−0.304073
$209$	−2.30394e15	−1.91214
$210$	0	0
$211$	5.75680e14	0.449102	0.224551	−	0.974462i	$-0.427908\pi$
$211$	5.75680e14	0.449102	0.224551	+	0.974462i	$0.427908\pi$
$212$	1.02032e15	0.771889
$213$	−9.81230e14	−0.719952
$214$	4.01066e14	0.285448
$215$	0	0
$216$	−9.61876e14	−0.644421
$217$	1.33791e15	0.869836
$218$	−1.80319e14	−0.113782
$219$	2.27791e15	1.39524
$220$	0	0
$221$	−1.61276e15	−0.931152
$222$	5.33776e14	0.299271
$223$	3.15658e15	1.71884	0.859421	−	0.511269i	$-0.170824\pi$
$223$	3.15658e15	1.71884	0.859421	+	0.511269i	$0.170824\pi$
$224$	−8.97428e14	−0.474665
$225$	0	0
$226$	−7.94051e14	−0.396409
$227$	−6.38311e14	−0.309645	−0.154823	−	0.987942i	$-0.549481\pi$
$227$	−6.38311e14	−0.309645	−0.154823	+	0.987942i	$0.549481\pi$
$228$	2.06936e15	0.975573
$229$	1.38242e15	0.633444	0.316722	−	0.948518i	$-0.397418\pi$
$229$	1.38242e15	0.633444	0.316722	+	0.948518i	$0.397418\pi$
$230$	0	0
$231$	−2.15140e15	−0.931631
$232$	9.73745e14	0.409990
$233$	9.23461e14	0.378099	0.189049	−	0.981968i	$-0.439459\pi$
$233$	9.23461e14	0.378099	0.189049	+	0.981968i	$0.439459\pi$
$234$	−4.22106e14	−0.168081
$235$	0	0
$236$	2.82654e15	1.06494
$237$	−4.66293e15	−1.70921
$238$	−6.38517e14	−0.227731
$239$	2.20312e15	0.764630	0.382315	−	0.924032i	$-0.375127\pi$
$239$	2.20312e15	0.764630	0.382315	+	0.924032i	$0.375127\pi$
$240$	0	0
$241$	−2.23875e15	−0.736028	−0.368014	−	0.929820i	$-0.619962\pi$
$241$	−2.23875e15	−0.736028	−0.368014	+	0.929820i	$0.619962\pi$
$242$	3.07746e15	0.984899
$243$	2.23513e15	0.696404
$244$	−2.07268e15	−0.628780
$245$	0	0
$246$	8.53556e14	0.245558
$247$	−3.67873e15	−1.03078
$248$	5.99999e15	1.63762
$249$	2.24962e15	0.598154
$250$	0	0
$251$	5.48372e15	1.38419	0.692095	−	0.721806i	$-0.256688\pi$
$251$	5.48372e15	1.38419	0.692095	+	0.721806i	$0.256688\pi$
$252$	5.16217e14	0.126978
$253$	−6.64725e15	−1.59352
$254$	−1.87733e15	−0.438653
$255$	0	0
$256$	−2.91508e15	−0.647278
$257$	8.54843e15	1.85064	0.925318	−	0.379192i	$-0.123798\pi$
$257$	8.54843e15	1.85064	0.925318	+	0.379192i	$0.123798\pi$
$258$	−4.83367e15	−1.02035
$259$	1.16046e15	0.238881
$260$	0	0
$261$	−8.79191e14	−0.172155
$262$	2.68535e14	0.0512911
$263$	−6.11543e15	−1.13950	−0.569750	−	0.821818i	$-0.692960\pi$
$263$	−6.11543e15	−1.13950	−0.569750	+	0.821818i	$0.692960\pi$
$264$	−9.64821e15	−1.75397
$265$	0	0
$266$	−1.45646e15	−0.252098
$267$	−4.75733e15	−0.803601
$268$	−1.29007e15	−0.212685
$269$	3.37552e15	0.543189	0.271594	−	0.962412i	$-0.412449\pi$
$269$	3.37552e15	0.543189	0.271594	+	0.962412i	$0.412449\pi$
$270$	0	0
$271$	−1.02304e15	−0.156889	−0.0784443	−	0.996918i	$-0.524995\pi$
$271$	−1.02304e15	−0.156889	−0.0784443	+	0.996918i	$0.524995\pi$
$272$	2.17522e15	0.325691
$273$	−3.43517e15	−0.502216
$274$	4.75564e15	0.678938
$275$	0	0
$276$	5.97045e15	0.813014
$277$	−1.16276e16	−1.54658	−0.773289	−	0.634054i	$-0.781390\pi$
$277$	−1.16276e16	−1.54658	−0.773289	+	0.634054i	$0.781390\pi$
$278$	−1.07039e15	−0.139076
$279$	−5.41737e15	−0.687640
$280$	0	0
$281$	9.90333e15	1.20002	0.600012	−	0.799991i	$-0.295162\pi$
$281$	9.90333e15	1.20002	0.600012	+	0.799991i	$0.295162\pi$
$282$	−3.94931e15	−0.467630
$283$	−1.15277e16	−1.33392	−0.666960	−	0.745094i	$-0.732405\pi$
$283$	−1.15277e16	−1.33392	−0.666960	+	0.745094i	$0.732405\pi$
$284$	−4.11700e15	−0.465598
$285$	0	0
$286$	7.38109e15	0.797520
$287$	1.85568e15	0.196007
$288$	3.63381e15	0.375241
$289$	−2.62278e13	−0.00264804
$290$	0	0
$291$	−1.14033e16	−1.10085
$292$	9.55752e15	0.902312
$293$	2.12402e16	1.96118	0.980592	−	0.196060i	$-0.0628148\pi$
$293$	2.12402e16	1.96118	0.980592	+	0.196060i	$0.0628148\pi$
$294$	5.03648e15	0.454851
$295$	0	0
$296$	5.20421e15	0.449737
$297$	−1.51865e16	−1.28392
$298$	4.29363e15	0.355156
$299$	−1.06137e16	−0.859024
$300$	0	0
$301$	−1.05087e16	−0.814454
$302$	1.16784e16	0.885805
$303$	9.28821e15	0.689533
$304$	4.96170e15	0.360539
$305$	0	0
$306$	2.58544e15	0.180030
$307$	1.15836e16	0.789670	0.394835	−	0.918752i	$-0.370802\pi$
$307$	1.15836e16	0.789670	0.394835	+	0.918752i	$0.370802\pi$
$308$	−9.02675e15	−0.602493
$309$	1.37436e15	0.0898194
$310$	0	0
$311$	−1.20392e16	−0.754491	−0.377245	−	0.926113i	$-0.623129\pi$
$311$	−1.20392e16	−0.754491	−0.377245	+	0.926113i	$0.623129\pi$
$312$	−1.54054e16	−0.945513
$313$	−1.29879e16	−0.780727	−0.390364	−	0.920661i	$-0.627651\pi$
$313$	−1.29879e16	−0.780727	−0.390364	+	0.920661i	$0.627651\pi$
$314$	6.86465e15	0.404181
$315$	0	0
$316$	−1.95645e16	−1.10536
$317$	2.78161e16	1.53961	0.769806	−	0.638278i	$-0.220353\pi$
$317$	2.78161e16	1.53961	0.769806	+	0.638278i	$0.220353\pi$
$318$	1.08847e16	0.590258
$319$	1.53739e16	0.816852
$320$	0	0
$321$	−1.32162e16	−0.674252
$322$	−4.20214e15	−0.210091
$323$	2.25326e16	1.10407
$324$	1.93744e16	0.930432
$325$	0	0
$326$	8.24390e15	0.380381
$327$	5.94197e15	0.268763
$328$	8.32202e15	0.369019
$329$	−8.58605e15	−0.373267
$330$	0	0
$331$	−1.54824e16	−0.647079	−0.323539	−	0.946215i	$-0.604873\pi$
$331$	−1.54824e16	−0.647079	−0.323539	+	0.946215i	$0.604873\pi$
$332$	9.43883e15	0.386830
$333$	−4.69886e15	−0.188845
$334$	1.14084e16	0.449647
$335$	0	0
$336$	4.63320e15	0.175661
$337$	−3.41506e16	−1.27000	−0.635000	−	0.772512i	$-0.719000\pi$
$337$	−3.41506e16	−1.27000	−0.635000	+	0.772512i	$0.719000\pi$
$338$	−1.77122e15	−0.0646123
$339$	2.61660e16	0.936353
$340$	0	0
$341$	9.47300e16	3.26275
$342$	5.89742e15	0.199293
$343$	2.48560e16	0.824176
$344$	−4.71274e16	−1.53336
$345$	0	0
$346$	−1.00385e16	−0.314540
$347$	3.56378e16	1.09590	0.547948	−	0.836512i	$-0.315409\pi$
$347$	3.56378e16	1.09590	0.547948	+	0.836512i	$0.315409\pi$
$348$	−1.38085e16	−0.416757
$349$	−2.42667e16	−0.718862	−0.359431	−	0.933172i	$-0.617029\pi$
$349$	−2.42667e16	−0.718862	−0.359431	+	0.933172i	$0.617029\pi$
$350$	0	0
$351$	−2.42484e16	−0.692127
$352$	−6.35421e16	−1.78047
$353$	−5.54359e15	−0.152495	−0.0762475	−	0.997089i	$-0.524294\pi$
$353$	−5.54359e15	−0.152495	−0.0762475	+	0.997089i	$0.524294\pi$
$354$	3.01533e16	0.814356
$355$	0	0
$356$	−1.99606e16	−0.519695
$357$	2.10408e16	0.537921
$358$	−3.67194e16	−0.921841
$359$	−5.69346e16	−1.40366	−0.701830	−	0.712344i	$-0.747634\pi$
$359$	−5.69346e16	−1.40366	−0.701830	+	0.712344i	$0.747634\pi$
$360$	0	0
$361$	9.34407e15	0.222197
$362$	−1.59340e16	−0.372150
$363$	−1.01410e17	−2.32642
$364$	−1.44131e16	−0.324787
$365$	0	0
$366$	−2.21112e16	−0.480824
$367$	1.55048e16	0.331235	0.165617	−	0.986190i	$-0.447038\pi$
$367$	1.55048e16	0.331235	0.165617	+	0.986190i	$0.447038\pi$
$368$	1.43153e16	0.300463
$369$	−7.51392e15	−0.154951
$370$	0	0
$371$	2.36641e16	0.471150
$372$	−8.50849e16	−1.66465
$373$	2.60390e16	0.500630	0.250315	−	0.968165i	$-0.419466\pi$
$373$	2.60390e16	0.500630	0.250315	+	0.968165i	$0.419466\pi$
$374$	−4.52100e16	−0.854219
$375$	0	0
$376$	−3.85051e16	−0.702744
$377$	2.45476e16	0.440342
$378$	−9.60029e15	−0.169273
$379$	−4.97661e14	−0.00862539	−0.00431269	−	0.999991i	$-0.501373\pi$
$379$	−4.97661e14	−0.00862539	−0.00431269	+	0.999991i	$0.501373\pi$
$380$	0	0
$381$	6.18627e16	1.03614
$382$	3.77396e16	0.621420
$383$	−1.17220e15	−0.0189762	−0.00948809	−	0.999955i	$-0.503020\pi$
$383$	−1.17220e15	−0.0189762	−0.00948809	+	0.999955i	$0.503020\pi$
$384$	6.89088e16	1.09679
$385$	0	0
$386$	−4.53523e15	−0.0697881
$387$	4.25512e16	0.643858
$388$	−4.78455e16	−0.711926
$389$	−6.18130e15	−0.0904498	−0.0452249	−	0.998977i	$-0.514400\pi$
$389$	−6.18130e15	−0.0904498	−0.0452249	+	0.998977i	$0.514400\pi$
$390$	0	0
$391$	6.50102e16	0.920096
$392$	4.91047e16	0.683540
$393$	−8.84891e15	−0.121154
$394$	−1.96459e16	−0.264574
$395$	0	0
$396$	3.65506e16	0.476294
$397$	−1.18749e17	−1.52227	−0.761135	−	0.648593i	$-0.775358\pi$
$397$	−1.18749e17	−1.52227	−0.761135	+	0.648593i	$0.775358\pi$
$398$	2.05728e16	0.259450
$399$	4.79942e16	0.595476
$400$	0	0
$401$	4.73984e14	0.00569280	0.00284640	−	0.999996i	$-0.499094\pi$
$401$	4.73984e14	0.00569280	0.00284640	+	0.999996i	$0.499094\pi$
$402$	−1.37624e16	−0.162639
$403$	1.51256e17	1.75886
$404$	3.89710e16	0.445926
$405$	0	0
$406$	9.71876e15	0.107694
$407$	8.21660e16	0.896043
$408$	9.43596e16	1.01273
$409$	1.17064e17	1.23658	0.618290	−	0.785950i	$-0.287826\pi$
$409$	1.17064e17	1.23658	0.618290	+	0.785950i	$0.287826\pi$
$410$	0	0
$411$	−1.56710e17	−1.60371
$412$	5.76647e15	0.0580869
$413$	6.55552e16	0.650027
$414$	1.70150e16	0.166085
$415$	0	0
$416$	−1.01458e17	−0.959800
$417$	3.52721e16	0.328509
$418$	−1.03124e17	−0.945618
$419$	−5.68253e16	−0.513039	−0.256520	−	0.966539i	$-0.582576\pi$
$419$	−5.68253e16	−0.513039	−0.256520	+	0.966539i	$0.582576\pi$
$420$	0	0
$421$	−5.95226e16	−0.521013	−0.260506	−	0.965472i	$-0.583890\pi$
$421$	−5.95226e16	−0.521013	−0.260506	+	0.965472i	$0.583890\pi$
$422$	2.57674e16	0.222096
$423$	3.47661e16	0.295083
$424$	1.06124e17	0.887026
$425$	0	0
$426$	−4.39198e16	−0.356040
$427$	−4.80712e16	−0.383799
$428$	−5.54517e16	−0.436044
$429$	−2.43226e17	−1.88381
$430$	0	0
$431$	−5.18459e16	−0.389594	−0.194797	−	0.980844i	$-0.562405\pi$
$431$	−5.18459e16	−0.389594	−0.194797	+	0.980844i	$0.562405\pi$
$432$	3.27051e16	0.242087
$433$	−2.89118e16	−0.210816	−0.105408	−	0.994429i	$-0.533615\pi$
$433$	−2.89118e16	−0.210816	−0.105408	+	0.994429i	$0.533615\pi$
$434$	5.98846e16	0.430162
$435$	0	0
$436$	2.49310e16	0.173811
$437$	1.48289e17	1.01854
$438$	1.01959e17	0.689992
$439$	3.17865e16	0.211945	0.105973	−	0.994369i	$-0.466204\pi$
$439$	3.17865e16	0.211945	0.105973	+	0.994369i	$0.466204\pi$
$440$	0	0
$441$	−4.43365e16	−0.287019
$442$	−7.21872e16	−0.460485
$443$	2.95209e17	1.85569	0.927844	−	0.372968i	$-0.121660\pi$
$443$	2.95209e17	1.85569	0.927844	+	0.372968i	$0.121660\pi$
$444$	−7.38001e16	−0.457160
$445$	0	0
$446$	1.41289e17	0.850023
$447$	−1.41486e17	−0.838908
$448$	−1.44357e16	−0.0843591
$449$	−1.03940e16	−0.0598659	−0.0299330	−	0.999552i	$-0.509529\pi$
$449$	−1.03940e16	−0.0598659	−0.0299330	+	0.999552i	$0.509529\pi$
$450$	0	0
$451$	1.31391e17	0.735222
$452$	1.09786e17	0.605546
$453$	−3.84833e17	−2.09235
$454$	−2.85708e16	−0.153130
$455$	0	0
$456$	2.15235e17	1.12109
$457$	−1.32509e17	−0.680441	−0.340220	−	0.940346i	$-0.610502\pi$
$457$	−1.32509e17	−0.680441	−0.340220	+	0.940346i	$0.610502\pi$
$458$	6.18770e16	0.313259
$459$	1.48524e17	0.741334
$460$	0	0
$461$	7.59869e16	0.368708	0.184354	−	0.982860i	$-0.440981\pi$
$461$	7.59869e16	0.368708	0.184354	+	0.982860i	$0.440981\pi$
$462$	−9.62968e16	−0.460722
$463$	−1.18447e17	−0.558789	−0.279394	−	0.960176i	$-0.590134\pi$
$463$	−1.18447e17	−0.558789	−0.279394	+	0.960176i	$0.590134\pi$
$464$	−3.31087e16	−0.154019
$465$	0	0
$466$	4.13341e16	0.186982
$467$	−2.60144e17	−1.16052	−0.580261	−	0.814431i	$-0.697049\pi$
$467$	−2.60144e17	−1.16052	−0.580261	+	0.814431i	$0.697049\pi$
$468$	5.83606e16	0.256757
$469$	−2.99203e16	−0.129820
$470$	0	0
$471$	−2.26208e17	−0.954710
$472$	2.93989e17	1.22380
$473$	−7.44065e17	−3.05502
$474$	−2.08713e17	−0.845259
$475$	0	0
$476$	8.82818e16	0.347877
$477$	−9.58192e16	−0.372463
$478$	9.86115e16	0.378134
$479$	4.38913e17	1.66034	0.830171	−	0.557509i	$-0.188243\pi$
$479$	4.38913e17	1.66034	0.830171	+	0.557509i	$0.188243\pi$
$480$	0	0
$481$	1.31195e17	0.483031
$482$	−1.00206e17	−0.363990
$483$	1.38471e17	0.496252
$484$	−4.25491e17	−1.50451
$485$	0	0
$486$	1.00044e17	0.344395
$487$	3.80917e17	1.29387	0.646937	−	0.762543i	$-0.276050\pi$
$487$	3.80917e17	1.29387	0.646937	+	0.762543i	$0.276050\pi$
$488$	−2.15580e17	−0.722571
$489$	−2.71657e17	−0.898492
$490$	0	0
$491$	1.21613e16	0.0391697	0.0195849	−	0.999808i	$-0.493766\pi$
$491$	1.21613e16	0.0391697	0.0195849	+	0.999808i	$0.493766\pi$
$492$	−1.18013e17	−0.375109
$493$	−1.50357e17	−0.471647
$494$	−1.64660e17	−0.509756
$495$	0	0
$496$	−2.04008e17	−0.615199
$497$	−9.54844e16	−0.284195
$498$	1.00693e17	0.295807
$499$	1.31200e17	0.380436	0.190218	−	0.981742i	$-0.439080\pi$
$499$	1.31200e17	0.380436	0.190218	+	0.981742i	$0.439080\pi$
$500$	0	0
$501$	−3.75935e17	−1.06211
$502$	2.45451e17	0.684527
$503$	3.44739e17	0.949070	0.474535	−	0.880237i	$-0.342616\pi$
$503$	3.44739e17	0.949070	0.474535	+	0.880237i	$0.342616\pi$
$504$	5.36919e16	0.145918
$505$	0	0
$506$	−2.97531e17	−0.788050
$507$	5.83664e16	0.152620
$508$	2.59560e17	0.670076
$509$	−1.91920e16	−0.0489164	−0.0244582	−	0.999701i	$-0.507786\pi$
$509$	−1.91920e16	−0.0489164	−0.0244582	+	0.999701i	$0.507786\pi$
$510$	0	0
$511$	2.21665e17	0.550759
$512$	2.52245e17	0.618826
$513$	3.38784e17	0.820654
$514$	3.82628e17	0.915200
$515$	0	0
$516$	6.68306e17	1.55866
$517$	−6.07933e17	−1.40013
$518$	5.19422e16	0.118135
$519$	3.30795e17	0.742970
$520$	0	0
$521$	−8.02478e15	−0.0175788	−0.00878938	−	0.999961i	$-0.502798\pi$
$521$	−8.02478e15	−0.0175788	−0.00878938	+	0.999961i	$0.502798\pi$
$522$	−3.93526e16	−0.0851363
$523$	1.95967e17	0.418719	0.209359	−	0.977839i	$-0.432862\pi$
$523$	1.95967e17	0.418719	0.209359	+	0.977839i	$0.432862\pi$
$524$	−3.71278e16	−0.0783512
$525$	0	0
$526$	−2.73727e17	−0.563520
$527$	−9.26461e17	−1.88390
$528$	3.28052e17	0.658905
$529$	−7.61985e16	−0.151177
$530$	0	0
$531$	−2.65442e17	−0.513872
$532$	2.01372e17	0.385099
$533$	2.09793e17	0.396337
$534$	−2.12938e17	−0.397407
$535$	0	0
$536$	−1.34181e17	−0.244410
$537$	1.21000e18	2.17747
$538$	1.51088e17	0.268624
$539$	7.75284e17	1.36186
$540$	0	0
$541$	−6.10417e17	−1.04675	−0.523377	−	0.852101i	$-0.675328\pi$
$541$	−6.10417e17	−1.04675	−0.523377	+	0.852101i	$0.675328\pi$
$542$	−4.57912e16	−0.0775866
$543$	5.25065e17	0.879051
$544$	6.21443e17	1.02804
$545$	0	0
$546$	−1.53758e17	−0.248362
$547$	7.47440e17	1.19305	0.596525	−	0.802594i	$-0.296548\pi$
$547$	7.47440e17	1.19305	0.596525	+	0.802594i	$0.296548\pi$
$548$	−6.57518e17	−1.03713
$549$	1.94647e17	0.303408
$550$	0	0
$551$	−3.42965e17	−0.522112
$552$	6.20989e17	0.934286
$553$	−4.53754e17	−0.674695
$554$	−5.20451e17	−0.764833
$555$	0	0
$556$	1.47993e17	0.212449
$557$	−9.26749e17	−1.31493	−0.657466	−	0.753484i	$-0.728372\pi$
$557$	−9.26749e17	−1.31493	−0.657466	+	0.753484i	$0.728372\pi$
$558$	−2.42481e17	−0.340060
$559$	−1.18806e18	−1.64687
$560$	0	0
$561$	1.48978e18	2.01774
$562$	4.43273e17	0.593451
$563$	2.79039e17	0.369284	0.184642	−	0.982806i	$-0.440888\pi$
$563$	2.79039e17	0.369284	0.184642	+	0.982806i	$0.440888\pi$
$564$	5.46035e17	0.714342
$565$	0	0
$566$	−5.15978e17	−0.659667
$567$	4.49344e17	0.567923
$568$	−4.28210e17	−0.535048
$569$	−5.36843e17	−0.663158	−0.331579	−	0.943427i	$-0.607581\pi$
$569$	−5.36843e17	−0.663158	−0.331579	+	0.943427i	$0.607581\pi$
$570$	0	0
$571$	−2.77022e17	−0.334487	−0.167244	−	0.985916i	$-0.553487\pi$
$571$	−2.77022e17	−0.334487	−0.167244	+	0.985916i	$0.553487\pi$
$572$	−1.02051e18	−1.21827
$573$	−1.24361e18	−1.46785
$574$	8.30603e16	0.0969318
$575$	0	0
$576$	5.84523e16	0.0666892
$577$	−5.56513e17	−0.627816	−0.313908	−	0.949453i	$-0.601638\pi$
$577$	−5.56513e17	−0.627816	−0.313908	+	0.949453i	$0.601638\pi$
$578$	−1.17395e15	−0.00130954
$579$	1.49447e17	0.164846
$580$	0	0
$581$	2.18912e17	0.236116
$582$	−5.10412e17	−0.544405
$583$	1.67553e18	1.76728
$584$	9.94082e17	1.03690
$585$	0	0
$586$	9.50709e17	0.969869
$587$	−7.11206e17	−0.717543	−0.358771	−	0.933425i	$-0.616804\pi$
$587$	−7.11206e17	−0.717543	−0.358771	+	0.933425i	$0.616804\pi$
$588$	−6.96347e17	−0.694821
$589$	−2.11327e18	−2.08547
$590$	0	0
$591$	6.47383e17	0.624946
$592$	−1.76950e17	−0.168951
$593$	−1.41645e18	−1.33766	−0.668830	−	0.743416i	$-0.733204\pi$
$593$	−1.41645e18	−1.33766	−0.668830	+	0.743416i	$0.733204\pi$
$594$	−6.79745e17	−0.634943
$595$	0	0
$596$	−5.93640e17	−0.542528
$597$	−6.77927e17	−0.612843
$598$	−4.75070e17	−0.424815
$599$	1.59052e18	1.40690	0.703452	−	0.710743i	$-0.251641\pi$
$599$	1.59052e18	1.40690	0.703452	+	0.710743i	$0.251641\pi$
$600$	0	0
$601$	1.58347e18	1.37064	0.685322	−	0.728240i	$-0.259661\pi$
$601$	1.58347e18	1.37064	0.685322	+	0.728240i	$0.259661\pi$
$602$	−4.70369e17	−0.402774
$603$	1.21151e17	0.102628
$604$	−1.61466e18	−1.35314
$605$	0	0
$606$	4.15740e17	0.340997
$607$	1.59884e18	1.29742	0.648708	−	0.761037i	$-0.275310\pi$
$607$	1.59884e18	1.29742	0.648708	+	0.761037i	$0.275310\pi$
$608$	1.41752e18	1.13803
$609$	−3.20258e17	−0.254382
$610$	0	0
$611$	−9.70691e17	−0.754768
$612$	−3.57465e17	−0.275011
$613$	−7.75812e17	−0.590559	−0.295280	−	0.955411i	$-0.595413\pi$
$613$	−7.75812e17	−0.590559	−0.295280	+	0.955411i	$0.595413\pi$
$614$	5.18484e17	0.390518
$615$	0	0
$616$	−9.38876e17	−0.692363
$617$	6.34915e17	0.463300	0.231650	−	0.972799i	$-0.425588\pi$
$617$	6.34915e17	0.463300	0.231650	+	0.972799i	$0.425588\pi$
$618$	6.15163e16	0.0444186
$619$	−6.95828e17	−0.497179	−0.248589	−	0.968609i	$-0.579967\pi$
$619$	−6.95828e17	−0.497179	−0.248589	+	0.968609i	$0.579967\pi$
$620$	0	0
$621$	9.77448e17	0.683909
$622$	−5.38873e17	−0.373120
$623$	−4.62941e17	−0.317214
$624$	5.23804e17	0.355197
$625$	0	0
$626$	−5.81336e17	−0.386095
$627$	3.39821e18	2.23363
$628$	−9.49111e17	−0.617418
$629$	−8.03586e17	−0.517372
$630$	0	0
$631$	−2.32559e18	−1.46670	−0.733352	−	0.679850i	$-0.762045\pi$
$631$	−2.32559e18	−1.46670	−0.733352	+	0.679850i	$0.762045\pi$
$632$	−2.03491e18	−1.27024
$633$	−8.49102e17	−0.524609
$634$	1.24505e18	0.761388
$635$	0	0
$636$	−1.50493e18	−0.901665
$637$	1.23790e18	0.734142
$638$	6.88133e17	0.403960
$639$	3.86630e17	0.224667
$640$	0	0
$641$	1.13369e18	0.645530	0.322765	−	0.946479i	$-0.395388\pi$
$641$	1.13369e18	0.645530	0.322765	+	0.946479i	$0.395388\pi$
$642$	−5.91555e17	−0.333440
$643$	2.01062e18	1.12191	0.560955	−	0.827847i	$-0.310434\pi$
$643$	2.01062e18	1.12191	0.560955	+	0.827847i	$0.310434\pi$
$644$	5.80990e17	0.320930
$645$	0	0
$646$	1.00856e18	0.545996
$647$	1.76519e18	0.946047	0.473024	−	0.881050i	$-0.343163\pi$
$647$	1.76519e18	0.946047	0.473024	+	0.881050i	$0.343163\pi$
$648$	2.01513e18	1.06922
$649$	4.64161e18	2.43825
$650$	0	0
$651$	−1.97335e18	−1.01608
$652$	−1.13981e18	−0.581061
$653$	2.09466e18	1.05725	0.528624	−	0.848856i	$-0.322708\pi$
$653$	2.09466e18	1.05725	0.528624	+	0.848856i	$0.322708\pi$
$654$	2.65962e17	0.132912
$655$	0	0
$656$	−2.82960e17	−0.138628
$657$	−8.97553e17	−0.435397
$658$	−3.84311e17	−0.184593
$659$	1.27391e18	0.605875	0.302938	−	0.953010i	$-0.402033\pi$
$659$	1.27391e18	0.605875	0.302938	+	0.953010i	$0.402033\pi$
$660$	0	0
$661$	3.92283e18	1.82932	0.914660	−	0.404225i	$-0.132459\pi$
$661$	3.92283e18	1.82932	0.914660	+	0.404225i	$0.132459\pi$
$662$	−6.92993e17	−0.320002
$663$	2.37875e18	1.08771
$664$	9.81736e17	0.444531
$665$	0	0
$666$	−2.10321e17	−0.0933900
$667$	−9.89509e17	−0.435113
$668$	−1.57733e18	−0.686872
$669$	−4.65582e18	−2.00783
$670$	0	0
$671$	−3.40366e18	−1.43963
$672$	1.32367e18	0.554470
$673$	1.20945e18	0.501751	0.250876	−	0.968019i	$-0.419282\pi$
$673$	1.20945e18	0.501751	0.250876	+	0.968019i	$0.419282\pi$
$674$	−1.52858e18	−0.628057
$675$	0	0
$676$	2.44891e17	0.0987004
$677$	−8.20534e17	−0.327544	−0.163772	−	0.986498i	$-0.552366\pi$
$677$	−8.20534e17	−0.327544	−0.163772	+	0.986498i	$0.552366\pi$
$678$	1.17119e18	0.463057
$679$	−1.10967e18	−0.434550
$680$	0	0
$681$	9.41480e17	0.361705
$682$	4.24011e18	1.61354
$683$	−2.73459e18	−1.03076	−0.515380	−	0.856962i	$-0.672349\pi$
$683$	−2.73459e18	−1.03076	−0.515380	+	0.856962i	$0.672349\pi$
$684$	−8.15381e17	−0.304436
$685$	0	0
$686$	1.11256e18	0.407582
$687$	−2.03900e18	−0.739944
$688$	1.60240e18	0.576030
$689$	2.67533e18	0.952692
$690$	0	0
$691$	2.94232e16	0.0102821	0.00514106	−	0.999987i	$-0.498364\pi$
$691$	2.94232e16	0.0102821	0.00514106	+	0.999987i	$0.498364\pi$
$692$	1.38793e18	0.480484
$693$	8.47708e17	0.290723
$694$	1.59515e18	0.541956
$695$	0	0
$696$	−1.43623e18	−0.478921
$697$	−1.28501e18	−0.424514
$698$	−1.08618e18	−0.355501
$699$	−1.36206e18	−0.441668
$700$	0	0
$701$	−3.97824e18	−1.26626	−0.633131	−	0.774045i	$-0.718231\pi$
$701$	−3.97824e18	−1.26626	−0.633131	+	0.774045i	$0.718231\pi$
$702$	−1.08536e18	−0.342280
$703$	−1.83299e18	−0.572729
$704$	−1.02212e18	−0.316431
$705$	0	0
$706$	−2.48131e17	−0.0754137
$707$	9.03845e17	0.272187
$708$	−4.16902e18	−1.24399
$709$	−6.30741e18	−1.86488	−0.932440	−	0.361325i	$-0.882324\pi$
$709$	−6.30741e18	−1.86488	−0.932440	+	0.361325i	$0.882324\pi$
$710$	0	0
$711$	1.83731e18	0.533373
$712$	−2.07611e18	−0.597214
$713$	−6.09712e18	−1.73797
$714$	9.41784e17	0.266019
$715$	0	0
$716$	5.07685e18	1.40818
$717$	−3.24950e18	−0.893186
$718$	−2.54839e18	−0.694156
$719$	−1.29144e18	−0.348606	−0.174303	−	0.984692i	$-0.555767\pi$
$719$	−1.29144e18	−0.348606	−0.174303	+	0.984692i	$0.555767\pi$
$720$	0	0
$721$	1.33740e17	0.0354554
$722$	4.18240e17	0.109884
$723$	3.30205e18	0.859775
$724$	2.20304e18	0.568489
$725$	0	0
$726$	−4.53911e18	−1.15049
$727$	−4.56590e17	−0.114697	−0.0573486	−	0.998354i	$-0.518265\pi$
$727$	−4.56590e17	−0.114697	−0.0573486	+	0.998354i	$0.518265\pi$
$728$	−1.49911e18	−0.373233
$729$	1.69460e18	0.418157
$730$	0	0
$731$	7.27697e18	1.76396
$732$	3.05711e18	0.734496
$733$	−1.69953e18	−0.404719	−0.202359	−	0.979311i	$-0.564861\pi$
$733$	−1.69953e18	−0.404719	−0.202359	+	0.979311i	$0.564861\pi$
$734$	6.93993e17	0.163806
$735$	0	0
$736$	4.08977e18	0.948403
$737$	−2.11849e18	−0.486955
$738$	−3.36323e17	−0.0766284
$739$	5.61563e18	1.26826	0.634131	−	0.773225i	$-0.281358\pi$
$739$	5.61563e18	1.26826	0.634131	+	0.773225i	$0.281358\pi$
$740$	0	0
$741$	5.42596e18	1.20409
$742$	1.05920e18	0.232999
$743$	3.99308e18	0.870725	0.435363	−	0.900255i	$-0.356620\pi$
$743$	3.99308e18	0.870725	0.435363	+	0.900255i	$0.356620\pi$
$744$	−8.84971e18	−1.91296
$745$	0	0
$746$	1.16550e18	0.247578
$747$	−8.86406e17	−0.186659
$748$	6.25077e18	1.30489
$749$	−1.28608e18	−0.266155
$750$	0	0
$751$	−5.06059e18	−1.02930	−0.514650	−	0.857400i	$-0.672078\pi$
$751$	−5.06059e18	−1.02930	−0.514650	+	0.857400i	$0.672078\pi$
$752$	1.30923e18	0.263997
$753$	−8.08824e18	−1.61691
$754$	1.09875e18	0.217763
$755$	0	0
$756$	1.32734e18	0.258578
$757$	−5.40203e18	−1.04336	−0.521680	−	0.853141i	$-0.674694\pi$
$757$	−5.40203e18	−1.04336	−0.521680	+	0.853141i	$0.674694\pi$
$758$	−2.22753e16	−0.00426554
$759$	9.80440e18	1.86144
$760$	0	0
$761$	−1.10559e18	−0.206345	−0.103173	−	0.994663i	$-0.532899\pi$
$761$	−1.10559e18	−0.206345	−0.103173	+	0.994663i	$0.532899\pi$
$762$	2.76897e18	0.512403
$763$	5.78219e17	0.106092
$764$	−5.21790e18	−0.949268
$765$	0	0
$766$	−5.24676e16	−0.00938434
$767$	7.41131e18	1.31439
$768$	4.29961e18	0.756104
$769$	−2.74540e18	−0.478724	−0.239362	−	0.970930i	$-0.576938\pi$
$769$	−2.74540e18	−0.478724	−0.239362	+	0.970930i	$0.576938\pi$
$770$	0	0
$771$	−1.26085e19	−2.16178
$772$	6.27044e17	0.106607
$773$	7.22627e18	1.21828	0.609141	−	0.793062i	$-0.291514\pi$
$773$	7.22627e18	1.21828	0.609141	+	0.793062i	$0.291514\pi$
$774$	1.90459e18	0.318409
$775$	0	0
$776$	−4.97643e18	−0.818119
$777$	−1.71163e18	−0.279044
$778$	−2.76675e17	−0.0447304
$779$	−2.93111e18	−0.469936
$780$	0	0
$781$	−6.76074e18	−1.06601
$782$	2.90986e18	0.455017
$783$	−2.26065e18	−0.350576
$784$	−1.66963e18	−0.256783
$785$	0	0
$786$	−3.96077e17	−0.0599146
$787$	−1.14757e19	−1.72164	−0.860821	−	0.508907i	$-0.830050\pi$
$787$	−1.14757e19	−1.72164	−0.860821	+	0.508907i	$0.830050\pi$
$788$	2.71626e18	0.404157
$789$	9.01998e18	1.33108
$790$	0	0
$791$	2.54624e18	0.369617
$792$	3.80164e18	0.547340
$793$	−5.43466e18	−0.776062
$794$	−5.31520e18	−0.752812
$795$	0	0
$796$	−2.84441e18	−0.396330
$797$	7.97300e18	1.10190	0.550950	−	0.834538i	$-0.314265\pi$
$797$	7.97300e18	1.10190	0.550950	+	0.834538i	$0.314265\pi$
$798$	2.14822e18	0.294483
$799$	5.94559e18	0.808427
$800$	0	0
$801$	1.87451e18	0.250771
$802$	2.12155e16	0.00281527
$803$	1.56949e19	2.06590
$804$	1.90280e18	0.248444
$805$	0	0
$806$	6.77023e18	0.869812
$807$	−4.97874e18	−0.634514
$808$	4.05339e18	0.512442
$809$	3.41268e18	0.427986	0.213993	−	0.976835i	$-0.431353\pi$
$809$	3.41268e18	0.427986	0.213993	+	0.976835i	$0.431353\pi$
$810$	0	0
$811$	2.93631e18	0.362382	0.181191	−	0.983448i	$-0.442005\pi$
$811$	2.93631e18	0.362382	0.181191	+	0.983448i	$0.442005\pi$
$812$	−1.34372e18	−0.164511
$813$	1.50894e18	0.183266
$814$	3.67775e18	0.443122
$815$	0	0
$816$	−3.20836e18	−0.380449
$817$	1.65988e19	1.95269
$818$	5.23979e18	0.611530
$819$	1.35354e18	0.156721
$820$	0	0
$821$	−8.24000e18	−0.939067	−0.469534	−	0.882915i	$-0.655578\pi$
$821$	−8.24000e18	−0.939067	−0.469534	+	0.882915i	$0.655578\pi$
$822$	−7.01435e18	−0.793087
$823$	−4.17732e18	−0.468597	−0.234298	−	0.972165i	$-0.575279\pi$
$823$	−4.17732e18	−0.468597	−0.234298	+	0.972165i	$0.575279\pi$
$824$	5.99772e17	0.0667513
$825$	0	0
$826$	2.93425e18	0.321460
$827$	4.86384e18	0.528680	0.264340	−	0.964430i	$-0.414846\pi$
$827$	4.86384e18	0.528680	0.264340	+	0.964430i	$0.414846\pi$
$828$	−2.35251e18	−0.253708
$829$	−1.00807e19	−1.07867	−0.539333	−	0.842093i	$-0.681324\pi$
$829$	−1.00807e19	−1.07867	−0.539333	+	0.842093i	$0.681324\pi$
$830$	0	0
$831$	1.71502e19	1.80660
$832$	−1.63202e18	−0.170579
$833$	−7.58229e18	−0.786336
$834$	1.57878e18	0.162458
$835$	0	0
$836$	1.42580e19	1.44451
$837$	−1.39296e19	−1.40031
$838$	−2.54350e18	−0.253715
$839$	−3.20269e18	−0.317002	−0.158501	−	0.987359i	$-0.550666\pi$
$839$	−3.20269e18	−0.317002	−0.158501	+	0.987359i	$0.550666\pi$
$840$	0	0
$841$	−7.97208e18	−0.776958
$842$	−2.66423e18	−0.257658
$843$	−1.46070e19	−1.40178
$844$	−3.56262e18	−0.339268
$845$	0	0
$846$	1.55613e18	0.145928
$847$	−9.86830e18	−0.918333
$848$	−3.60837e18	−0.333225
$849$	1.70028e19	1.55819
$850$	0	0
$851$	−5.28846e18	−0.477296
$852$	6.07238e18	0.543879
$853$	−2.56558e18	−0.228043	−0.114022	−	0.993478i	$-0.536373\pi$
$853$	−2.56558e18	−0.228043	−0.114022	+	0.993478i	$0.536373\pi$
$854$	−2.15166e18	−0.189801
$855$	0	0
$856$	−5.76755e18	−0.501086
$857$	1.24767e19	1.07578	0.537890	−	0.843015i	$-0.319222\pi$
$857$	1.24767e19	1.07578	0.537890	+	0.843015i	$0.319222\pi$
$858$	−1.08868e19	−0.931606
$859$	−1.24400e19	−1.05649	−0.528244	−	0.849093i	$-0.677149\pi$
$859$	−1.24400e19	−1.05649	−0.528244	+	0.849093i	$0.677149\pi$
$860$	0	0
$861$	−2.73705e18	−0.228961
$862$	−2.32062e18	−0.192667
$863$	−1.45267e18	−0.119701	−0.0598506	−	0.998207i	$-0.519062\pi$
$863$	−1.45267e18	−0.119701	−0.0598506	+	0.998207i	$0.519062\pi$
$864$	9.34357e18	0.764141
$865$	0	0
$866$	−1.29409e18	−0.104256
$867$	3.86848e16	0.00309326
$868$	−8.27969e18	−0.657107
$869$	−3.21279e19	−2.53078
$870$	0	0
$871$	−3.38262e18	−0.262504
$872$	2.59309e18	0.199738
$873$	4.49320e18	0.343529
$874$	6.63741e18	0.503703
$875$	0	0
$876$	−1.40969e19	−1.05402
$877$	−8.05385e18	−0.597731	−0.298866	−	0.954295i	$-0.596608\pi$
$877$	−8.05385e18	−0.597731	−0.298866	+	0.954295i	$0.596608\pi$
$878$	1.42277e18	0.104814
$879$	−3.13283e19	−2.29091
$880$	0	0
$881$	1.03252e19	0.743966	0.371983	−	0.928240i	$-0.378678\pi$
$881$	1.03252e19	0.743966	0.371983	+	0.928240i	$0.378678\pi$
$882$	−1.98450e18	−0.141940
$883$	−5.47741e18	−0.388894	−0.194447	−	0.980913i	$-0.562291\pi$
$883$	−5.47741e18	−0.388894	−0.194447	+	0.980913i	$0.562291\pi$
$884$	9.98065e18	0.703427
$885$	0	0
$886$	1.32135e19	0.917698
$887$	−2.66366e18	−0.183643	−0.0918216	−	0.995775i	$-0.529269\pi$
$887$	−2.66366e18	−0.183643	−0.0918216	+	0.995775i	$0.529269\pi$
$888$	−7.67598e18	−0.525351
$889$	6.01992e18	0.409005
$890$	0	0
$891$	3.18157e19	2.13028
$892$	−1.95347e19	−1.29848
$893$	1.35619e19	0.894927
$894$	−6.33291e18	−0.414868
$895$	0	0
$896$	6.70558e18	0.432947
$897$	1.56548e19	1.00345
$898$	−4.65233e17	−0.0296057
$899$	1.41015e19	0.890897
$900$	0	0
$901$	−1.63867e19	−1.02042
$902$	5.88106e18	0.363591
$903$	1.54999e19	0.951387
$904$	1.14189e19	0.695872
$905$	0	0
$906$	−1.72251e19	−1.03473
$907$	−2.49194e18	−0.148625	−0.0743123	−	0.997235i	$-0.523676\pi$
$907$	−2.49194e18	−0.148625	−0.0743123	+	0.997235i	$0.523676\pi$
$908$	3.95022e18	0.233918
$909$	−3.65979e18	−0.215175
$910$	0	0
$911$	2.79314e19	1.61891	0.809455	−	0.587181i	$-0.199763\pi$
$911$	2.79314e19	1.61891	0.809455	+	0.587181i	$0.199763\pi$
$912$	−7.31829e18	−0.421156
$913$	1.55000e19	0.885670
$914$	−5.93110e18	−0.336500
$915$	0	0
$916$	−8.55515e18	−0.478528
$917$	−8.61095e17	−0.0478245
$918$	6.64792e18	0.366614
$919$	1.35052e19	0.739520	0.369760	−	0.929127i	$-0.379440\pi$
$919$	1.35052e19	0.739520	0.369760	+	0.929127i	$0.379440\pi$
$920$	0	0
$921$	−1.70854e19	−0.922437
$922$	3.40117e18	0.182338
$923$	−1.07949e19	−0.574658
$924$	1.33141e19	0.703789
$925$	0	0
$926$	−5.30169e18	−0.276339
$927$	−5.41532e17	−0.0280289
$928$	−9.45887e18	−0.486158
$929$	2.02304e19	1.03253	0.516264	−	0.856430i	$-0.327322\pi$
$929$	2.02304e19	1.03253	0.516264	+	0.856430i	$0.327322\pi$
$930$	0	0
$931$	−1.72953e19	−0.870471
$932$	−5.71488e18	−0.285630
$933$	1.77572e19	0.881342
$934$	−1.16440e19	−0.573916
$935$	0	0
$936$	6.07011e18	0.295055
$937$	3.47272e19	1.67634	0.838172	−	0.545407i	$-0.183625\pi$
$937$	3.47272e19	1.67634	0.838172	+	0.545407i	$0.183625\pi$
$938$	−1.33923e18	−0.0642003
$939$	1.91565e19	0.911990
$940$	0	0
$941$	5.04834e18	0.237037	0.118518	−	0.992952i	$-0.462186\pi$
$941$	5.04834e18	0.237037	0.118518	+	0.992952i	$0.462186\pi$
$942$	−1.01251e19	−0.472135
$943$	−8.45674e18	−0.391631
$944$	−9.99605e18	−0.459738
$945$	0	0
$946$	−3.33043e19	−1.51080
$947$	3.10611e19	1.39940	0.699700	−	0.714436i	$-0.253317\pi$
$947$	3.10611e19	1.39940	0.699700	+	0.714436i	$0.253317\pi$
$948$	2.88568e19	1.29120
$949$	2.50602e19	1.11367
$950$	0	0
$951$	−4.10275e19	−1.79846
$952$	9.18223e18	0.399768
$953$	−7.59449e17	−0.0328393	−0.0164197	−	0.999865i	$-0.505227\pi$
$953$	−7.59449e17	−0.0328393	−0.0164197	+	0.999865i	$0.505227\pi$
$954$	−4.28886e18	−0.184195
$955$	0	0
$956$	−1.36341e19	−0.577630
$957$	−2.26757e19	−0.954188
$958$	1.96457e19	0.821093
$959$	−1.52496e19	−0.633051
$960$	0	0
$961$	6.24725e19	2.55851
$962$	5.87230e18	0.238875
$963$	5.20750e18	0.210406
$964$	1.38546e19	0.556023
$965$	0	0
$966$	6.19796e18	0.245413
$967$	2.52651e19	0.993687	0.496843	−	0.867840i	$-0.334492\pi$
$967$	2.52651e19	0.993687	0.496843	+	0.867840i	$0.334492\pi$
$968$	−4.42555e19	−1.72893
$969$	−3.32346e19	−1.28969
$970$	0	0
$971$	−5.75184e18	−0.220233	−0.110116	−	0.993919i	$-0.535122\pi$
$971$	−5.75184e18	−0.220233	−0.110116	+	0.993919i	$0.535122\pi$
$972$	−1.38322e19	−0.526090
$973$	3.43237e18	0.129676
$974$	1.70498e19	0.639863
$975$	0	0
$976$	7.33003e18	0.271445
$977$	5.40269e18	0.198745	0.0993724	−	0.995050i	$-0.468316\pi$
$977$	5.40269e18	0.198745	0.0993724	+	0.995050i	$0.468316\pi$
$978$	−1.21594e19	−0.444333
$979$	−3.27784e19	−1.18987
$980$	0	0
$981$	−2.34129e18	−0.0838699
$982$	5.44340e17	0.0193707
$983$	1.41530e19	0.500324	0.250162	−	0.968204i	$-0.419516\pi$
$983$	1.41530e19	0.500324	0.250162	+	0.968204i	$0.419516\pi$
$984$	−1.22746e19	−0.431061
$985$	0	0
$986$	−6.72996e18	−0.233245
$987$	1.26640e19	0.436024
$988$	2.27660e19	0.778692
$989$	4.78903e19	1.62732
$990$	0	0
$991$	3.53143e19	1.18433	0.592164	−	0.805817i	$-0.298274\pi$
$991$	3.53143e19	1.18433	0.592164	+	0.805817i	$0.298274\pi$
$992$	−5.82833e19	−1.94186
$993$	2.28359e19	0.755871
$994$	−4.27388e18	−0.140544
$995$	0	0
$996$	−1.39219e19	−0.451868
$997$	−3.42861e19	−1.10560	−0.552802	−	0.833313i	$-0.686441\pi$
$997$	−3.42861e19	−1.10560	−0.552802	+	0.833313i	$0.686441\pi$
$998$	5.87253e18	0.188138
$999$	−1.20821e19	−0.384564

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.14.a.d.1.3	yes	4
5.2	odd	4		25.14.b.c.24.6		8
5.3	odd	4		25.14.b.c.24.3		8
5.4	even	2		25.14.a.c.1.2	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.14.a.c.1.2	✓	4	5.4	even	2
25.14.a.d.1.3	yes	4	1.1	even	1	trivial
25.14.b.c.24.3		8	5.3	odd	4
25.14.b.c.24.6		8	5.2	odd	4

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:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	25.a (trivial)

\(f(q)\)	\(=\)	\(q+44.7600 q^{2} -1474.96 q^{3} -6188.54 q^{4} -66019.0 q^{6} -143529. q^{7} -643673. q^{8} +581170. q^{9} +O(q^{10})\)	\(q+44.7600 q^{2} -1474.96 q^{3} -6188.54 q^{4} -66019.0 q^{6} -143529. q^{7} -643673. q^{8} +581170. q^{9} -1.01625e7 q^{11} +9.12783e6 q^{12} -1.62266e7 q^{13} -6.42437e6 q^{14} +2.18858e7 q^{16} +9.93899e7 q^{17} +2.60132e7 q^{18} +2.26709e8 q^{19} +2.11699e8 q^{21} -4.54875e8 q^{22} +6.54093e8 q^{23} +9.49389e8 q^{24} -7.26304e8 q^{26} +1.49436e9 q^{27} +8.88237e8 q^{28} -1.51280e9 q^{29} -9.32148e9 q^{31} +6.25257e9 q^{32} +1.49893e10 q^{33} +4.44869e9 q^{34} -3.59660e9 q^{36} -8.08518e9 q^{37} +1.01475e10 q^{38} +2.39336e10 q^{39} -1.29290e10 q^{41} +9.47565e9 q^{42} +7.32164e10 q^{43} +6.28914e10 q^{44} +2.92772e10 q^{46} +5.98209e10 q^{47} -3.22805e10 q^{48} -7.62884e10 q^{49} -1.46596e11 q^{51} +1.00419e11 q^{52} -1.64873e11 q^{53} +6.68873e10 q^{54} +9.23859e10 q^{56} -3.34386e11 q^{57} -6.77127e10 q^{58} -4.56737e11 q^{59} +3.34922e11 q^{61} -4.17229e11 q^{62} -8.34149e10 q^{63} +1.00577e11 q^{64} +6.70921e11 q^{66} +2.08461e11 q^{67} -6.15079e11 q^{68} -9.64758e11 q^{69} +6.65261e11 q^{71} -3.74083e11 q^{72} -1.54439e12 q^{73} -3.61893e11 q^{74} -1.40300e12 q^{76} +1.45862e12 q^{77} +1.07127e12 q^{78} +3.16141e12 q^{79} -3.13068e12 q^{81} -5.78700e11 q^{82} -1.52521e12 q^{83} -1.31011e12 q^{84} +3.27716e12 q^{86} +2.23131e12 q^{87} +6.54135e12 q^{88} +3.22541e12 q^{89} +2.32900e12 q^{91} -4.04788e12 q^{92} +1.37488e13 q^{93} +2.67758e12 q^{94} -9.22227e12 q^{96} +7.73130e12 q^{97} -3.41467e12 q^{98} -5.90616e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 65 q^{2} + 860 q^{3} + 3733 q^{4} + 40333 q^{6} + 102800 q^{7} + 329895 q^{8} + 47872 q^{9}+O(q^{10}) \) 4 * q + 65 * q^2 + 860 * q^3 + 3733 * q^4 + 40333 * q^6 + 102800 * q^7 + 329895 * q^8 + 47872 * q^9	\( 4 q + 65 q^{2} + 860 q^{3} + 3733 q^{4} + 40333 q^{6} + 102800 q^{7} + 329895 q^{8} + 47872 q^{9} + 6675428 q^{11} - 520595 q^{12} + 4926920 q^{13} + 37103466 q^{14} - 8440751 q^{16} + 50416220 q^{17} + 22302110 q^{18} + 282648860 q^{19} - 438887472 q^{21} + 969439305 q^{22} + 1208437080 q^{23} + 1415344455 q^{24} - 3267454372 q^{26} + 1714727420 q^{27} + 11782380170 q^{28} + 7630648840 q^{29} - 12716039032 q^{31} + 5288310415 q^{32} + 36748956820 q^{33} + 23123205021 q^{34} - 45497926906 q^{36} + 38137910960 q^{37} + 99584060705 q^{38} + 60691943624 q^{39} - 81254933612 q^{41} + 62466915570 q^{42} + 97224763400 q^{43} + 111616918681 q^{44} - 77938796802 q^{46} + 69940090280 q^{47} + 107001227905 q^{48} + 118071253428 q^{49} + 91953947668 q^{51} - 165428401300 q^{52} - 179518658440 q^{53} - 275242827665 q^{54} + 403963457310 q^{56} - 99736967860 q^{57} - 810275460480 q^{58} - 858015815320 q^{59} + 589205515328 q^{61} - 942802276470 q^{62} - 2020360823760 q^{63} - 1516614058847 q^{64} + 1418821712381 q^{66} - 685669480180 q^{67} - 2270111055215 q^{68} - 1486209750216 q^{69} + 949682379448 q^{71} - 1359611223390 q^{72} - 1688808513820 q^{73} + 1003330480306 q^{74} + 1964117678945 q^{76} + 2180313451200 q^{77} + 171961033900 q^{78} - 355815036160 q^{79} - 1150994540276 q^{81} - 224361325395 q^{82} + 8420327909340 q^{83} + 9279336345306 q^{84} - 11016868246612 q^{86} + 9035391325160 q^{87} + 12729770641515 q^{88} + 2506082642820 q^{89} - 11092233838352 q^{91} + 403195163070 q^{92} + 17882711708520 q^{93} + 15051571815036 q^{94} - 17345568428737 q^{96} + 12121501720280 q^{97} + 19722093248605 q^{98} + 1425639838304 q^{99}+O(q^{100}) \) 4 * q + 65 * q^2 + 860 * q^3 + 3733 * q^4 + 40333 * q^6 + 102800 * q^7 + 329895 * q^8 + 47872 * q^9 + 6675428 * q^11 - 520595 * q^12 + 4926920 * q^13 + 37103466 * q^14 - 8440751 * q^16 + 50416220 * q^17 + 22302110 * q^18 + 282648860 * q^19 - 438887472 * q^21 + 969439305 * q^22 + 1208437080 * q^23 + 1415344455 * q^24 - 3267454372 * q^26 + 1714727420 * q^27 + 11782380170 * q^28 + 7630648840 * q^29 - 12716039032 * q^31 + 5288310415 * q^32 + 36748956820 * q^33 + 23123205021 * q^34 - 45497926906 * q^36 + 38137910960 * q^37 + 99584060705 * q^38 + 60691943624 * q^39 - 81254933612 * q^41 + 62466915570 * q^42 + 97224763400 * q^43 + 111616918681 * q^44 - 77938796802 * q^46 + 69940090280 * q^47 + 107001227905 * q^48 + 118071253428 * q^49 + 91953947668 * q^51 - 165428401300 * q^52 - 179518658440 * q^53 - 275242827665 * q^54 + 403963457310 * q^56 - 99736967860 * q^57 - 810275460480 * q^58 - 858015815320 * q^59 + 589205515328 * q^61 - 942802276470 * q^62 - 2020360823760 * q^63 - 1516614058847 * q^64 + 1418821712381 * q^66 - 685669480180 * q^67 - 2270111055215 * q^68 - 1486209750216 * q^69 + 949682379448 * q^71 - 1359611223390 * q^72 - 1688808513820 * q^73 + 1003330480306 * q^74 + 1964117678945 * q^76 + 2180313451200 * q^77 + 171961033900 * q^78 - 355815036160 * q^79 - 1150994540276 * q^81 - 224361325395 * q^82 + 8420327909340 * q^83 + 9279336345306 * q^84 - 11016868246612 * q^86 + 9035391325160 * q^87 + 12729770641515 * q^88 + 2506082642820 * q^89 - 11092233838352 * q^91 + 403195163070 * q^92 + 17882711708520 * q^93 + 15051571815036 * q^94 - 17345568428737 * q^96 + 12121501720280 * q^97 + 19722093248605 * q^98 + 1425639838304 * q^99

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