LMFDB - Embedded newform 25.14.a.d.1.1

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			1.1
Root			$-133.966$ 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)

$f(q)$	$=$	$q-117.966 q^{2} -235.672 q^{3} +5724.04 q^{4} +27801.3 q^{6} +227749. q^{7} +291136. q^{8} -1.53878e6 q^{9} +O(q^{10})$	\(q-117.966 q^{2} -235.672 q^{3} +5724.04 q^{4} +27801.3 q^{6} +227749. q^{7} +291136. q^{8} -1.53878e6 q^{9} -768386. q^{11} -1.34899e6 q^{12} +8.24256e6 q^{13} -2.68667e7 q^{14} -8.12356e7 q^{16} -1.56072e8 q^{17} +1.81524e8 q^{18} -2.90939e8 q^{19} -5.36739e7 q^{21} +9.06436e7 q^{22} +7.93768e8 q^{23} -6.86126e7 q^{24} -9.72343e8 q^{26} +7.38384e8 q^{27} +1.30364e9 q^{28} +5.40204e9 q^{29} -1.83768e9 q^{31} +7.19807e9 q^{32} +1.81087e8 q^{33} +1.84112e10 q^{34} -8.80804e9 q^{36} +1.16816e10 q^{37} +3.43210e10 q^{38} -1.94254e9 q^{39} -6.75942e9 q^{41} +6.33171e9 q^{42} +5.43871e10 q^{43} -4.39827e9 q^{44} -9.36378e10 q^{46} -8.65161e10 q^{47} +1.91449e10 q^{48} -4.50196e10 q^{49} +3.67817e10 q^{51} +4.71807e10 q^{52} +7.13568e10 q^{53} -8.71044e10 q^{54} +6.63059e10 q^{56} +6.85661e10 q^{57} -6.37258e11 q^{58} +2.96038e11 q^{59} +6.88737e11 q^{61} +2.16784e11 q^{62} -3.50455e11 q^{63} -1.83647e11 q^{64} -2.13621e10 q^{66} -7.65782e11 q^{67} -8.93360e11 q^{68} -1.87068e11 q^{69} +4.74355e11 q^{71} -4.47995e11 q^{72} +4.21723e11 q^{73} -1.37803e12 q^{74} -1.66535e12 q^{76} -1.74999e11 q^{77} +2.29154e11 q^{78} -1.91617e12 q^{79} +2.27930e12 q^{81} +7.97383e11 q^{82} +5.01649e12 q^{83} -3.07231e11 q^{84} -6.41584e12 q^{86} -1.27311e12 q^{87} -2.23705e11 q^{88} +8.23537e12 q^{89} +1.87723e12 q^{91} +4.54355e12 q^{92} +4.33088e11 q^{93} +1.02060e13 q^{94} -1.69638e12 q^{96} +9.34285e12 q^{97} +5.31079e12 q^{98} +1.18238e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−117.966	−1.30336	−0.651678	−	0.758496i	$-0.725934\pi$
$2$	−117.966	−1.30336	−0.651678	+	0.758496i	$0.725934\pi$
$3$	−235.672	−0.186646	−0.0933231	−	0.995636i	$-0.529749\pi$
$3$	−235.672	−0.186646	−0.0933231	+	0.995636i	$0.529749\pi$
$4$	5724.04	0.698735
$5$	0	0
$5$	0	0
$6$	27801.3	0.243266
$7$	227749.	0.731676	0.365838	−	0.930679i	$-0.380783\pi$
$7$	227749.	0.731676	0.365838	+	0.930679i	$0.380783\pi$
$8$	291136.	0.392655
$9$	−1.53878e6	−0.965163
$10$	0	0
$11$	−768386.	−0.130776	−0.0653878	−	0.997860i	$-0.520828\pi$
$11$	−768386.	−0.130776	−0.0653878	+	0.997860i	$0.520828\pi$
$12$	−1.34899e6	−0.130416
$13$	8.24256e6	0.473620	0.236810	−	0.971556i	$-0.423898\pi$
$13$	8.24256e6	0.473620	0.236810	+	0.971556i	$0.423898\pi$
$14$	−2.68667e7	−0.953633
$15$	0	0
$16$	−8.12356e7	−1.21050
$17$	−1.56072e8	−1.56822	−0.784108	−	0.620624i	$-0.786879\pi$
$17$	−1.56072e8	−1.56822	−0.784108	+	0.620624i	$0.786879\pi$
$18$	1.81524e8	1.25795
$19$	−2.90939e8	−1.41874	−0.709372	−	0.704834i	$-0.751021\pi$
$19$	−2.90939e8	−1.41874	−0.709372	+	0.704834i	$0.751021\pi$
$20$	0	0
$21$	−5.36739e7	−0.136564
$22$	9.06436e7	0.170447
$23$	7.93768e8	1.11805	0.559026	−	0.829150i	$-0.311175\pi$
$23$	7.93768e8	1.11805	0.559026	+	0.829150i	$0.311175\pi$
$24$	−6.86126e7	−0.0732876
$25$	0	0
$26$	−9.72343e8	−0.617295
$27$	7.38384e8	0.366790
$28$	1.30364e9	0.511247
$29$	5.40204e9	1.68644	0.843219	−	0.537570i	$-0.180657\pi$
$29$	5.40204e9	1.68644	0.843219	+	0.537570i	$0.180657\pi$
$30$	0	0
$31$	−1.83768e9	−0.371893	−0.185947	−	0.982560i	$-0.559535\pi$
$31$	−1.83768e9	−0.371893	−0.185947	+	0.982560i	$0.559535\pi$
$32$	7.19807e9	1.18506
$33$	1.81087e8	0.0244088
$34$	1.84112e10	2.04394
$35$	0	0
$36$	−8.80804e9	−0.674393
$37$	1.16816e10	0.748497	0.374248	−	0.927329i	$-0.377901\pi$
$37$	1.16816e10	0.748497	0.374248	+	0.927329i	$0.377901\pi$
$38$	3.43210e10	1.84913
$39$	−1.94254e9	−0.0883994
$40$	0	0
$41$	−6.75942e9	−0.222236	−0.111118	−	0.993807i	$-0.535443\pi$
$41$	−6.75942e9	−0.222236	−0.111118	+	0.993807i	$0.535443\pi$
$42$	6.33171e9	0.177992
$43$	5.43871e10	1.31205	0.656026	−	0.754738i	$-0.272236\pi$
$43$	5.43871e10	1.31205	0.656026	+	0.754738i	$0.272236\pi$
$44$	−4.39827e9	−0.0913775
$45$	0	0
$46$	−9.36378e10	−1.45722
$47$	−8.65161e10	−1.17074	−0.585370	−	0.810766i	$-0.699051\pi$
$47$	−8.65161e10	−1.17074	−0.585370	+	0.810766i	$0.699051\pi$
$48$	1.91449e10	0.225936
$49$	−4.50196e10	−0.464651
$50$	0	0
$51$	3.67817e10	0.292702
$52$	4.71807e10	0.330935
$53$	7.13568e10	0.442224	0.221112	−	0.975248i	$-0.429031\pi$
$53$	7.13568e10	0.442224	0.221112	+	0.975248i	$0.429031\pi$
$54$	−8.71044e10	−0.478058
$55$	0	0
$56$	6.63059e10	0.287296
$57$	6.85661e10	0.264803
$58$	−6.37258e11	−2.19803
$59$	2.96038e11	0.913712	0.456856	−	0.889541i	$-0.348976\pi$
$59$	2.96038e11	0.913712	0.456856	+	0.889541i	$0.348976\pi$
$60$	0	0
$61$	6.88737e11	1.71163	0.855814	−	0.517283i	$-0.173057\pi$
$61$	6.88737e11	1.71163	0.855814	+	0.517283i	$0.173057\pi$
$62$	2.16784e11	0.484709
$63$	−3.50455e11	−0.706186
$64$	−1.83647e11	−0.334052
$65$	0	0
$66$	−2.13621e10	−0.0318133
$67$	−7.65782e11	−1.03423	−0.517117	−	0.855914i	$-0.672995\pi$
$67$	−7.65782e11	−1.03423	−0.517117	+	0.855914i	$0.672995\pi$
$68$	−8.93360e11	−1.09577
$69$	−1.87068e11	−0.208680
$70$	0	0
$71$	4.74355e11	0.439465	0.219733	−	0.975560i	$-0.429482\pi$
$71$	4.74355e11	0.439465	0.219733	+	0.975560i	$0.429482\pi$
$72$	−4.47995e11	−0.378977
$73$	4.21723e11	0.326159	0.163079	−	0.986613i	$-0.447857\pi$
$73$	4.21723e11	0.326159	0.163079	+	0.986613i	$0.447857\pi$
$74$	−1.37803e12	−0.975557
$75$	0	0
$76$	−1.66535e12	−0.991326
$77$	−1.74999e11	−0.0956853
$78$	2.29154e11	0.115216
$79$	−1.91617e12	−0.886868	−0.443434	−	0.896307i	$-0.646240\pi$
$79$	−1.91617e12	−0.886868	−0.443434	+	0.896307i	$0.646240\pi$
$80$	0	0
$81$	2.27930e12	0.896703
$82$	7.97383e11	0.289652
$83$	5.01649e12	1.68420	0.842098	−	0.539325i	$-0.181321\pi$
$83$	5.01649e12	1.68420	0.842098	+	0.539325i	$0.181321\pi$
$84$	−3.07231e11	−0.0954223
$85$	0	0
$86$	−6.41584e12	−1.71007
$87$	−1.27311e12	−0.314767
$88$	−2.23705e11	−0.0513498
$89$	8.23537e12	1.75650	0.878250	−	0.478201i	$-0.158711\pi$
$89$	8.23537e12	1.75650	0.878250	+	0.478201i	$0.158711\pi$
$90$	0	0
$91$	1.87723e12	0.346536
$92$	4.54355e12	0.781223
$93$	4.33088e11	0.0694124
$94$	1.02060e13	1.52589
$95$	0	0
$96$	−1.69638e12	−0.221187
$97$	9.34285e12	1.13884	0.569421	−	0.822046i	$-0.307168\pi$
$97$	9.34285e12	1.13884	0.569421	+	0.822046i	$0.307168\pi$
$98$	5.31079e12	0.605605
$99$	1.18238e12	0.126220
$100$	0	0
$101$	3.63276e12	0.340524	0.170262	−	0.985399i	$-0.445539\pi$
$101$	3.63276e12	0.340524	0.170262	+	0.985399i	$0.445539\pi$
$102$	−4.33899e12	−0.381494
$103$	−2.93241e12	−0.241982	−0.120991	−	0.992654i	$-0.538607\pi$
$103$	−2.93241e12	−0.241982	−0.120991	+	0.992654i	$0.538607\pi$
$104$	2.39971e12	0.185969
$105$	0	0
$106$	−8.41770e12	−0.576375
$107$	7.04353e12	0.453729	0.226864	−	0.973926i	$-0.427153\pi$
$107$	7.04353e12	0.453729	0.226864	+	0.973926i	$0.427153\pi$
$108$	4.22654e12	0.256289
$109$	−2.39209e13	−1.36617	−0.683087	−	0.730337i	$-0.739363\pi$
$109$	−2.39209e13	−1.36617	−0.683087	+	0.730337i	$0.739363\pi$
$110$	0	0
$111$	−2.75301e12	−0.139704
$112$	−1.85013e13	−0.885696
$113$	2.65599e12	0.120010	0.0600050	−	0.998198i	$-0.480888\pi$
$113$	2.65599e12	0.120010	0.0600050	+	0.998198i	$0.480888\pi$
$114$	−8.08849e12	−0.345132
$115$	0	0
$116$	3.09215e13	1.17837
$117$	−1.26835e13	−0.457121
$118$	−3.49225e13	−1.19089
$119$	−3.55451e13	−1.14743
$120$	0	0
$121$	−3.39323e13	−0.982898
$122$	−8.12477e13	−2.23086
$123$	1.59300e12	0.0414795
$124$	−1.05189e13	−0.259855
$125$	0	0
$126$	4.13419e13	0.920412
$127$	8.92923e13	1.88838	0.944191	−	0.329400i	$-0.106846\pi$
$127$	8.92923e13	1.88838	0.944191	+	0.329400i	$0.106846\pi$
$128$	−3.73024e13	−0.749673
$129$	−1.28175e13	−0.244889
$130$	0	0
$131$	7.68614e13	1.32876	0.664378	−	0.747397i	$-0.268697\pi$
$131$	7.68614e13	1.32876	0.664378	+	0.747397i	$0.268697\pi$
$132$	1.03655e12	0.0170553
$133$	−6.62610e13	−1.03806
$134$	9.03365e13	1.34798
$135$	0	0
$136$	−4.54381e13	−0.615769
$137$	8.40133e13	1.08559	0.542793	−	0.839866i	$-0.317367\pi$
$137$	8.40133e13	1.08559	0.542793	+	0.839866i	$0.317367\pi$
$138$	2.20678e13	0.271985
$139$	−9.62699e11	−0.0113213	−0.00566063	−	0.999984i	$-0.501802\pi$
$139$	−9.62699e11	−0.0113213	−0.00566063	+	0.999984i	$0.501802\pi$
$140$	0	0
$141$	2.03894e13	0.218514
$142$	−5.59579e13	−0.572779
$143$	−6.33346e12	−0.0619379
$144$	1.25004e14	1.16833
$145$	0	0
$146$	−4.97491e13	−0.425101
$147$	1.06098e13	0.0867253
$148$	6.68657e13	0.523001
$149$	−9.10986e13	−0.682026	−0.341013	−	0.940059i	$-0.610770\pi$
$149$	−9.10986e13	−0.682026	−0.341013	+	0.940059i	$0.610770\pi$
$150$	0	0
$151$	−2.08621e14	−1.43221	−0.716107	−	0.697991i	$-0.754078\pi$
$151$	−2.08621e14	−1.43221	−0.716107	+	0.697991i	$0.754078\pi$
$152$	−8.47030e13	−0.557077
$153$	2.40160e14	1.51359
$154$	2.06439e13	0.124712
$155$	0	0
$156$	−1.11191e13	−0.0617677
$157$	2.18257e14	1.16311	0.581554	−	0.813508i	$-0.302445\pi$
$157$	2.18257e14	1.16311	0.581554	+	0.813508i	$0.302445\pi$
$158$	2.26044e14	1.15590
$159$	−1.68168e13	−0.0825394
$160$	0	0
$161$	1.80779e14	0.818052
$162$	−2.68880e14	−1.16872
$163$	1.16801e14	0.487785	0.243893	−	0.969802i	$-0.421576\pi$
$163$	1.16801e14	0.487785	0.243893	+	0.969802i	$0.421576\pi$
$164$	−3.86912e13	−0.155284
$165$	0	0
$166$	−5.91777e14	−2.19511
$167$	3.48636e13	0.124370	0.0621850	−	0.998065i	$-0.480193\pi$
$167$	3.48636e13	0.124370	0.0621850	+	0.998065i	$0.480193\pi$
$168$	−1.56264e13	−0.0536228
$169$	−2.34935e14	−0.775684
$170$	0	0
$171$	4.47692e14	1.36932
$172$	3.11314e14	0.916776
$173$	1.35285e14	0.383662	0.191831	−	0.981428i	$-0.438557\pi$
$173$	1.35285e14	0.383662	0.191831	+	0.981428i	$0.438557\pi$
$174$	1.50184e14	0.410254
$175$	0	0
$176$	6.24202e13	0.158304
$177$	−6.97677e13	−0.170541
$178$	−9.71496e14	−2.28934
$179$	4.68031e14	1.06348	0.531741	−	0.846907i	$-0.321538\pi$
$179$	4.68031e14	1.06348	0.531741	+	0.846907i	$0.321538\pi$
$180$	0	0
$181$	1.41251e14	0.298595	0.149297	−	0.988792i	$-0.452299\pi$
$181$	1.41251e14	0.298595	0.149297	+	0.988792i	$0.452299\pi$
$182$	−2.21450e14	−0.451660
$183$	−1.62316e14	−0.319469
$184$	2.31095e14	0.439010
$185$	0	0
$186$	−5.10898e13	−0.0904691
$187$	1.19923e14	0.205084
$188$	−4.95221e14	−0.818038
$189$	1.68166e14	0.268371
$190$	0	0
$191$	1.16270e15	1.73281	0.866407	−	0.499339i	$-0.166424\pi$
$191$	1.16270e15	1.73281	0.866407	+	0.499339i	$0.166424\pi$
$192$	4.32804e13	0.0623496
$193$	−4.87236e14	−0.678605	−0.339302	−	0.940677i	$-0.610191\pi$
$193$	−4.87236e14	−0.678605	−0.339302	+	0.940677i	$0.610191\pi$
$194$	−1.10214e15	−1.48431
$195$	0	0
$196$	−2.57694e14	−0.324668
$197$	1.18599e13	0.0144561	0.00722807	−	0.999974i	$-0.497699\pi$
$197$	1.18599e13	0.0144561	0.00722807	+	0.999974i	$0.497699\pi$
$198$	−1.39481e14	−0.164509
$199$	−1.24539e15	−1.42155	−0.710774	−	0.703420i	$-0.751655\pi$
$199$	−1.24539e15	−1.42155	−0.710774	+	0.703420i	$0.751655\pi$
$200$	0	0
$201$	1.80473e14	0.193036
$202$	−4.28543e14	−0.443824
$203$	1.23031e15	1.23393
$204$	2.10540e14	0.204521
$205$	0	0
$206$	3.45925e14	0.315388
$207$	−1.22144e15	−1.07910
$208$	−6.69589e14	−0.573319
$209$	2.23554e14	0.185537
$210$	0	0
$211$	−1.89875e15	−1.48126	−0.740632	−	0.671911i	$-0.765474\pi$
$211$	−1.89875e15	−1.48126	−0.740632	+	0.671911i	$0.765474\pi$
$212$	4.08449e14	0.308997
$213$	−1.11792e14	−0.0820245
$214$	−8.30899e14	−0.591369
$215$	0	0
$216$	2.14970e14	0.144022
$217$	−4.18529e14	−0.272105
$218$	2.82186e15	1.78061
$219$	−9.93882e13	−0.0608763
$220$	0	0
$221$	−1.28643e15	−0.742739
$222$	3.24763e14	0.182084
$223$	−6.81265e13	−0.0370966	−0.0185483	−	0.999828i	$-0.505904\pi$
$223$	−6.81265e13	−0.0370966	−0.0185483	+	0.999828i	$0.505904\pi$
$224$	1.63935e15	0.867081
$225$	0	0
$226$	−3.13318e14	−0.156416
$227$	1.93924e15	0.940725	0.470362	−	0.882473i	$-0.344123\pi$
$227$	1.93924e15	0.940725	0.470362	+	0.882473i	$0.344123\pi$
$228$	3.92475e14	0.185027
$229$	2.44273e15	1.11930	0.559648	−	0.828730i	$-0.310936\pi$
$229$	2.44273e15	1.11930	0.559648	+	0.828730i	$0.310936\pi$
$230$	0	0
$231$	4.12422e13	0.0178593
$232$	1.57273e15	0.662189
$233$	−1.43882e15	−0.589104	−0.294552	−	0.955636i	$-0.595170\pi$
$233$	−1.43882e15	−0.589104	−0.294552	+	0.955636i	$0.595170\pi$
$234$	1.49622e15	0.595791
$235$	0	0
$236$	1.69453e15	0.638442
$237$	4.51588e14	0.165530
$238$	4.19312e15	1.49550
$239$	1.65255e15	0.573547	0.286774	−	0.957998i	$-0.407417\pi$
$239$	1.65255e15	0.573547	0.286774	+	0.957998i	$0.407417\pi$
$240$	0	0
$241$	−3.43472e13	−0.0112922	−0.00564612	−	0.999984i	$-0.501797\pi$
$241$	−3.43472e13	−0.0112922	−0.00564612	+	0.999984i	$0.501797\pi$
$242$	4.00287e15	1.28106
$243$	−1.71439e15	−0.534156
$244$	3.94236e15	1.19597
$245$	0	0
$246$	−1.87921e14	−0.0540625
$247$	−2.39808e15	−0.671945
$248$	−5.35015e14	−0.146026
$249$	−1.18224e15	−0.314349
$250$	0	0
$251$	−4.16269e15	−1.05074	−0.525369	−	0.850875i	$-0.676073\pi$
$251$	−4.16269e15	−1.05074	−0.525369	+	0.850875i	$0.676073\pi$
$252$	−2.00602e15	−0.493437
$253$	−6.09919e14	−0.146214
$254$	−1.05335e16	−2.46123
$255$	0	0
$256$	5.90486e15	1.31114
$257$	−1.79987e15	−0.389652	−0.194826	−	0.980838i	$-0.562414\pi$
$257$	−1.79987e15	−0.389652	−0.194826	+	0.980838i	$0.562414\pi$
$258$	1.51203e15	0.319178
$259$	2.66046e15	0.547657
$260$	0	0
$261$	−8.31256e15	−1.62769
$262$	−9.06706e15	−1.73184
$263$	−3.19867e15	−0.596015	−0.298008	−	0.954564i	$-0.596322\pi$
$263$	−3.19867e15	−0.596015	−0.298008	+	0.954564i	$0.596322\pi$
$264$	5.27209e13	0.00958423
$265$	0	0
$266$	7.81656e15	1.35296
$267$	−1.94084e15	−0.327844
$268$	−4.38337e15	−0.722656
$269$	−1.00334e16	−1.61458	−0.807289	−	0.590157i	$-0.799066\pi$
$269$	−1.00334e16	−1.61458	−0.807289	+	0.590157i	$0.799066\pi$
$270$	0	0
$271$	2.47312e15	0.379266	0.189633	−	0.981855i	$-0.439270\pi$
$271$	2.47312e15	0.379266	0.189633	+	0.981855i	$0.439270\pi$
$272$	1.26786e16	1.89833
$273$	−4.42410e14	−0.0646796
$274$	−9.91074e15	−1.41490
$275$	0	0
$276$	−1.07079e15	−0.145812
$277$	−6.35728e15	−0.845577	−0.422788	−	0.906228i	$-0.638949\pi$
$277$	−6.35728e15	−0.845577	−0.422788	+	0.906228i	$0.638949\pi$
$278$	1.13566e14	0.0147556
$279$	2.82778e15	0.358938
$280$	0	0
$281$	6.68334e15	0.809846	0.404923	−	0.914351i	$-0.367298\pi$
$281$	6.68334e15	0.809846	0.404923	+	0.914351i	$0.367298\pi$
$282$	−2.40526e15	−0.284802
$283$	−9.86747e14	−0.114181	−0.0570905	−	0.998369i	$-0.518182\pi$
$283$	−9.86747e14	−0.114181	−0.0570905	+	0.998369i	$0.518182\pi$
$284$	2.71523e15	0.307070
$285$	0	0
$286$	7.47135e14	0.0807271
$287$	−1.53945e15	−0.162605
$288$	−1.10763e16	−1.14378
$289$	1.44538e16	1.45930
$290$	0	0
$291$	−2.20184e15	−0.212560
$292$	2.41396e15	0.227899
$293$	−7.96792e15	−0.735708	−0.367854	−	0.929884i	$-0.619907\pi$
$293$	−7.96792e15	−0.735708	−0.367854	+	0.929884i	$0.619907\pi$
$294$	−1.25160e15	−0.113034
$295$	0	0
$296$	3.40093e15	0.293901
$297$	−5.67363e14	−0.0479672
$298$	1.07466e16	0.888922
$299$	6.54267e15	0.529532
$300$	0	0
$301$	1.23866e16	0.959996
$302$	2.46102e16	1.86668
$303$	−8.56139e14	−0.0635575
$304$	2.36346e16	1.71740
$305$	0	0
$306$	−2.83308e16	−1.97274
$307$	−1.05416e16	−0.718630	−0.359315	−	0.933216i	$-0.616990\pi$
$307$	−1.05416e16	−0.718630	−0.359315	+	0.933216i	$0.616990\pi$
$308$	−1.00170e15	−0.0668587
$309$	6.91086e14	0.0451650
$310$	0	0
$311$	8.18766e14	0.0513118	0.0256559	−	0.999671i	$-0.491833\pi$
$311$	8.18766e14	0.0513118	0.0256559	+	0.999671i	$0.491833\pi$
$312$	−5.65543e14	−0.0347105
$313$	2.78968e16	1.67694	0.838469	−	0.544950i	$-0.183451\pi$
$313$	2.78968e16	1.67694	0.838469	+	0.544950i	$0.183451\pi$
$314$	−2.57469e16	−1.51594
$315$	0	0
$316$	−1.09682e16	−0.619685
$317$	1.17593e16	0.650872	0.325436	−	0.945564i	$-0.394489\pi$
$317$	1.17593e16	0.650872	0.325436	+	0.945564i	$0.394489\pi$
$318$	1.98381e15	0.107578
$319$	−4.15085e15	−0.220545
$320$	0	0
$321$	−1.65996e15	−0.0846867
$322$	−2.13259e16	−1.06621
$323$	4.54074e16	2.22490
$324$	1.30468e16	0.626558
$325$	0	0
$326$	−1.37786e16	−0.635757
$327$	5.63749e15	0.254991
$328$	−1.96791e15	−0.0872622
$329$	−1.97039e16	−0.856602
$330$	0	0
$331$	9.53106e14	0.0398345	0.0199172	−	0.999802i	$-0.493660\pi$
$331$	9.53106e14	0.0398345	0.0199172	+	0.999802i	$0.493660\pi$
$332$	2.87146e16	1.17681
$333$	−1.79754e16	−0.722421
$334$	−4.11273e15	−0.162098
$335$	0	0
$336$	4.36023e15	0.165312
$337$	−3.30722e16	−1.22990	−0.614949	−	0.788567i	$-0.710823\pi$
$337$	−3.30722e16	−1.22990	−0.614949	+	0.788567i	$0.710823\pi$
$338$	2.77144e16	1.01099
$339$	−6.25942e14	−0.0223994
$340$	0	0
$341$	1.41204e15	0.0486346
$342$	−5.28126e16	−1.78471
$343$	−3.23195e16	−1.07165
$344$	1.58341e16	0.515184
$345$	0	0
$346$	−1.59590e16	−0.500048
$347$	5.38052e16	1.65456	0.827280	−	0.561789i	$-0.189887\pi$
$347$	5.38052e16	1.65456	0.827280	+	0.561789i	$0.189887\pi$
$348$	−7.28731e15	−0.219939
$349$	1.36838e16	0.405361	0.202681	−	0.979245i	$-0.435035\pi$
$349$	1.36838e16	0.405361	0.202681	+	0.979245i	$0.435035\pi$
$350$	0	0
$351$	6.08617e15	0.173719
$352$	−5.53089e15	−0.154977
$353$	−2.10736e16	−0.579700	−0.289850	−	0.957072i	$-0.593605\pi$
$353$	−2.10736e16	−0.579700	−0.289850	+	0.957072i	$0.593605\pi$
$354$	8.23023e15	0.222275
$355$	0	0
$356$	4.71396e16	1.22733
$357$	8.37697e15	0.214163
$358$	−5.52119e16	−1.38609
$359$	−3.04883e16	−0.751656	−0.375828	−	0.926689i	$-0.622642\pi$
$359$	−3.04883e16	−0.751656	−0.375828	+	0.926689i	$0.622642\pi$
$360$	0	0
$361$	4.25927e16	1.01283
$362$	−1.66629e16	−0.389175
$363$	7.99688e15	0.183454
$364$	1.07453e16	0.242137
$365$	0	0
$366$	1.91478e16	0.416381
$367$	5.87957e16	1.25608	0.628038	−	0.778183i	$-0.283858\pi$
$367$	5.87957e16	1.25608	0.628038	+	0.778183i	$0.283858\pi$
$368$	−6.44822e16	−1.35341
$369$	1.04013e16	0.214494
$370$	0	0
$371$	1.62514e16	0.323565
$372$	2.47901e15	0.0485009
$373$	−3.88656e16	−0.747236	−0.373618	−	0.927583i	$-0.621883\pi$
$373$	−3.88656e16	−0.747236	−0.373618	+	0.927583i	$0.621883\pi$
$374$	−1.41469e16	−0.267298
$375$	0	0
$376$	−2.51880e16	−0.459698
$377$	4.45266e16	0.798731
$378$	−1.98379e16	−0.349783
$379$	−2.79124e16	−0.483774	−0.241887	−	0.970304i	$-0.577766\pi$
$379$	−2.79124e16	−0.483774	−0.241887	+	0.970304i	$0.577766\pi$
$380$	0	0
$381$	−2.10437e16	−0.352459
$382$	−1.37160e17	−2.25847
$383$	5.36788e16	0.868982	0.434491	−	0.900676i	$-0.356928\pi$
$383$	5.36788e16	0.868982	0.434491	+	0.900676i	$0.356928\pi$
$384$	8.79112e15	0.139924
$385$	0	0
$386$	5.74774e16	0.884463
$387$	−8.36899e16	−1.26634
$388$	5.34788e16	0.795748
$389$	−9.12421e16	−1.33513	−0.667564	−	0.744553i	$-0.732663\pi$
$389$	−9.12421e16	−1.33513	−0.667564	+	0.744553i	$0.732663\pi$
$390$	0	0
$391$	−1.23885e17	−1.75335
$392$	−1.31068e16	−0.182448
$393$	−1.81141e16	−0.248007
$394$	−1.39907e15	−0.0188415
$395$	0	0
$396$	6.76797e15	0.0881942
$397$	1.14440e17	1.46703	0.733515	−	0.679673i	$-0.237878\pi$
$397$	1.14440e17	1.46703	0.733515	+	0.679673i	$0.237878\pi$
$398$	1.46914e17	1.85278
$399$	1.56158e16	0.193750
$400$	0	0
$401$	7.17723e16	0.862023	0.431011	−	0.902346i	$-0.358157\pi$
$401$	7.17723e16	0.862023	0.431011	+	0.902346i	$0.358157\pi$
$402$	−2.12897e16	−0.251594
$403$	−1.51472e16	−0.176136
$404$	2.07941e16	0.237936
$405$	0	0
$406$	−1.45135e17	−1.60824
$407$	−8.97595e15	−0.0978851
$408$	1.07085e16	0.114931
$409$	−6.60514e16	−0.697719	−0.348859	−	0.937175i	$-0.613431\pi$
$409$	−6.60514e16	−0.697719	−0.348859	+	0.937175i	$0.613431\pi$
$410$	0	0
$411$	−1.97996e16	−0.202621
$412$	−1.67852e16	−0.169081
$413$	6.74222e16	0.668540
$414$	1.44088e17	1.40646
$415$	0	0
$416$	5.93305e16	0.561269
$417$	2.26881e14	0.00211307
$418$	−2.63718e16	−0.241821
$419$	8.43204e16	0.761275	0.380637	−	0.924724i	$-0.375705\pi$
$419$	8.43204e16	0.761275	0.380637	+	0.924724i	$0.375705\pi$
$420$	0	0
$421$	−6.44030e16	−0.563732	−0.281866	−	0.959454i	$-0.590953\pi$
$421$	−6.44030e16	−0.563732	−0.281866	+	0.959454i	$0.590953\pi$
$422$	2.23989e17	1.93061
$423$	1.33129e17	1.12996
$424$	2.07746e16	0.173642
$425$	0	0
$426$	1.31877e16	0.106907
$427$	1.56859e17	1.25236
$428$	4.03174e16	0.317036
$429$	1.49262e15	0.0115605
$430$	0	0
$431$	7.32807e16	0.550665	0.275332	−	0.961349i	$-0.411212\pi$
$431$	7.32807e16	0.550665	0.275332	+	0.961349i	$0.411212\pi$
$432$	−5.99830e16	−0.444001
$433$	−1.52550e17	−1.11235	−0.556175	−	0.831065i	$-0.687732\pi$
$433$	−1.52550e17	−1.11235	−0.556175	+	0.831065i	$0.687732\pi$
$434$	4.93722e16	0.354650
$435$	0	0
$436$	−1.36924e17	−0.954593
$437$	−2.30938e17	−1.58623
$438$	1.17245e16	0.0793434
$439$	2.76223e17	1.84179	0.920895	−	0.389811i	$-0.127460\pi$
$439$	2.76223e17	1.84179	0.920895	+	0.389811i	$0.127460\pi$
$440$	0	0
$441$	6.92753e16	0.448464
$442$	1.51755e17	0.968053
$443$	−1.27522e17	−0.801607	−0.400804	−	0.916164i	$-0.631269\pi$
$443$	−1.27522e17	−0.801607	−0.400804	+	0.916164i	$0.631269\pi$
$444$	−1.57583e16	−0.0976161
$445$	0	0
$446$	8.03662e15	0.0483501
$447$	2.14694e16	0.127298
$448$	−4.18254e16	−0.244418
$449$	2.29866e16	0.132396	0.0661979	−	0.997807i	$-0.478913\pi$
$449$	2.29866e16	0.132396	0.0661979	+	0.997807i	$0.478913\pi$
$450$	0	0
$451$	5.19384e15	0.0290630
$452$	1.52030e16	0.0838551
$453$	4.91660e16	0.267317
$454$	−2.28764e17	−1.22610
$455$	0	0
$456$	1.99621e16	0.103976
$457$	−3.04529e17	−1.56377	−0.781887	−	0.623421i	$-0.785742\pi$
$457$	−3.04529e17	−1.56377	−0.781887	+	0.623421i	$0.785742\pi$
$458$	−2.88160e17	−1.45884
$459$	−1.15241e17	−0.575206
$460$	0	0
$461$	1.58779e17	0.770438	0.385219	−	0.922825i	$-0.374126\pi$
$461$	1.58779e17	0.770438	0.385219	+	0.922825i	$0.374126\pi$
$462$	−4.86519e15	−0.0232770
$463$	3.66537e17	1.72919	0.864593	−	0.502472i	$-0.167576\pi$
$463$	3.66537e17	1.72919	0.864593	+	0.502472i	$0.167576\pi$
$464$	−4.38838e17	−2.04144
$465$	0	0
$466$	1.69732e17	0.767811
$467$	−1.03579e17	−0.462073	−0.231037	−	0.972945i	$-0.574212\pi$
$467$	−1.03579e17	−0.462073	−0.231037	+	0.972945i	$0.574212\pi$
$468$	−7.26008e16	−0.319406
$469$	−1.74406e17	−0.756724
$470$	0	0
$471$	−5.14369e16	−0.217090
$472$	8.61874e16	0.358774
$473$	−4.17903e16	−0.171584
$474$	−5.32721e16	−0.215745
$475$	0	0
$476$	−2.03462e17	−0.801746
$477$	−1.09803e17	−0.426818
$478$	−1.94946e17	−0.747536
$479$	4.18688e16	0.158384	0.0791918	−	0.996859i	$-0.474766\pi$
$479$	4.18688e16	0.158384	0.0791918	+	0.996859i	$0.474766\pi$
$480$	0	0
$481$	9.62860e16	0.354503
$482$	4.05181e15	0.0147178
$483$	−4.26046e16	−0.152686
$484$	−1.94230e17	−0.686785
$485$	0	0
$486$	2.02240e17	0.696196
$487$	−2.73471e17	−0.928910	−0.464455	−	0.885597i	$-0.653750\pi$
$487$	−2.73471e17	−0.928910	−0.464455	+	0.885597i	$0.653750\pi$
$488$	2.00516e17	0.672080
$489$	−2.75268e16	−0.0910432
$490$	0	0
$491$	−2.67740e17	−0.862351	−0.431176	−	0.902268i	$-0.641901\pi$
$491$	−2.67740e17	−0.862351	−0.431176	+	0.902268i	$0.641901\pi$
$492$	9.11841e15	0.0289832
$493$	−8.43105e17	−2.64470
$494$	2.82893e17	0.875784
$495$	0	0
$496$	1.49285e17	0.450178
$497$	1.08034e17	0.321546
$498$	1.39465e17	0.409708
$499$	4.27754e17	1.24034	0.620169	−	0.784468i	$-0.287064\pi$
$499$	4.27754e17	1.24034	0.620169	+	0.784468i	$0.287064\pi$
$500$	0	0
$501$	−8.21637e15	−0.0232132
$502$	4.91056e17	1.36948
$503$	2.05745e17	0.566419	0.283209	−	0.959058i	$-0.408601\pi$
$503$	2.05745e17	0.566419	0.283209	+	0.959058i	$0.408601\pi$
$504$	−1.02030e17	−0.277288
$505$	0	0
$506$	7.19499e16	0.190569
$507$	5.53676e16	0.144778
$508$	5.11112e17	1.31948
$509$	3.75464e17	0.956980	0.478490	−	0.878093i	$-0.341184\pi$
$509$	3.75464e17	0.956980	0.478490	+	0.878093i	$0.341184\pi$
$510$	0	0
$511$	9.60469e16	0.238642
$512$	−3.90993e17	−0.959211
$513$	−2.14825e17	−0.520381
$514$	2.12324e17	0.507854
$515$	0	0
$516$	−7.33678e16	−0.171113
$517$	6.64777e16	0.153104
$518$	−3.13845e17	−0.713791
$519$	−3.18827e16	−0.0716090
$520$	0	0
$521$	−4.89914e17	−1.07319	−0.536593	−	0.843841i	$-0.680289\pi$
$521$	−4.89914e17	−1.07319	−0.536593	+	0.843841i	$0.680289\pi$
$522$	9.80601e17	2.12146
$523$	7.85669e17	1.67872	0.839361	−	0.543574i	$-0.182929\pi$
$523$	7.85669e17	1.67872	0.839361	+	0.543574i	$0.182929\pi$
$524$	4.39958e17	0.928448
$525$	0	0
$526$	3.77335e17	0.776819
$527$	2.86809e17	0.583209
$528$	−1.47107e16	−0.0295469
$529$	1.26030e17	0.250042
$530$	0	0
$531$	−4.55538e17	−0.881881
$532$	−3.79281e17	−0.725329
$533$	−5.57149e16	−0.105255
$534$	2.28954e17	0.427297
$535$	0	0
$536$	−2.22947e17	−0.406098
$537$	−1.10302e17	−0.198495
$538$	1.18360e18	2.10437
$539$	3.45924e16	0.0607650
$540$	0	0
$541$	5.13270e17	0.880163	0.440082	−	0.897958i	$-0.354949\pi$
$541$	5.13270e17	0.880163	0.440082	+	0.897958i	$0.354949\pi$
$542$	−2.91744e17	−0.494319
$543$	−3.32889e16	−0.0557315
$544$	−1.12341e18	−1.85843
$545$	0	0
$546$	5.21894e16	0.0843006
$547$	5.65456e16	0.0902571	0.0451285	−	0.998981i	$-0.485630\pi$
$547$	5.65456e16	0.0902571	0.0451285	+	0.998981i	$0.485630\pi$
$548$	4.80895e17	0.758537
$549$	−1.05982e18	−1.65200
$550$	0	0
$551$	−1.57166e18	−2.39262
$552$	−5.44624e16	−0.0819395
$553$	−4.36406e17	−0.648899
$554$	7.49945e17	1.10209
$555$	0	0
$556$	−5.51053e15	−0.00791055
$557$	−9.16588e17	−1.30051	−0.650257	−	0.759714i	$-0.725339\pi$
$557$	−9.16588e17	−1.30051	−0.650257	+	0.759714i	$0.725339\pi$
$558$	−3.33583e17	−0.467823
$559$	4.48289e17	0.621414
$560$	0	0
$561$	−2.82625e16	−0.0382782
$562$	−7.88409e17	−1.05552
$563$	2.33848e17	0.309478	0.154739	−	0.987955i	$-0.450546\pi$
$563$	2.33848e17	0.309478	0.154739	+	0.987955i	$0.450546\pi$
$564$	1.16710e17	0.152684
$565$	0	0
$566$	1.16403e17	0.148818
$567$	5.19107e17	0.656096
$568$	1.38102e17	0.172558
$569$	−1.40011e18	−1.72955	−0.864774	−	0.502162i	$-0.832538\pi$
$569$	−1.40011e18	−1.72955	−0.864774	+	0.502162i	$0.832538\pi$
$570$	0	0
$571$	7.39303e17	0.892663	0.446332	−	0.894868i	$-0.352730\pi$
$571$	7.39303e17	0.892663	0.446332	+	0.894868i	$0.352730\pi$
$572$	−3.62530e16	−0.0432782
$573$	−2.74016e17	−0.323423
$574$	1.81603e17	0.211932
$575$	0	0
$576$	2.82593e17	0.322415
$577$	1.40170e18	1.58130	0.790649	−	0.612270i	$-0.209743\pi$
$577$	1.40170e18	1.58130	0.790649	+	0.612270i	$0.209743\pi$
$578$	−1.70506e18	−1.90199
$579$	1.14828e17	0.126659
$580$	0	0
$581$	1.14250e18	1.23228
$582$	2.59743e17	0.277042
$583$	−5.48296e16	−0.0578321
$584$	1.22779e17	0.128068
$585$	0	0
$586$	9.39945e17	0.958888
$587$	−6.47482e15	−0.00653251	−0.00326625	−	0.999995i	$-0.501040\pi$
$587$	−6.47482e15	−0.00653251	−0.00326625	+	0.999995i	$0.501040\pi$
$588$	6.07311e16	0.0605980
$589$	5.34653e17	0.527621
$590$	0	0
$591$	−2.79505e15	−0.00269818
$592$	−9.48959e17	−0.906059
$593$	−1.60602e18	−1.51669	−0.758344	−	0.651855i	$-0.773991\pi$
$593$	−1.60602e18	−1.51669	−0.758344	+	0.651855i	$0.773991\pi$
$594$	6.69297e16	0.0625183
$595$	0	0
$596$	−5.21452e17	−0.476556
$597$	2.93504e17	0.265327
$598$	−7.71815e17	−0.690169
$599$	5.98360e17	0.529284	0.264642	−	0.964347i	$-0.414746\pi$
$599$	5.98360e17	0.529284	0.264642	+	0.964347i	$0.414746\pi$
$600$	0	0
$601$	1.16250e18	1.00625	0.503126	−	0.864213i	$-0.332183\pi$
$601$	1.16250e18	1.00625	0.503126	+	0.864213i	$0.332183\pi$
$602$	−1.46120e18	−1.25122
$603$	1.17837e18	0.998205
$604$	−1.19415e18	−1.00074
$605$	0	0
$606$	1.00995e17	0.0828381
$607$	1.19478e18	0.969533	0.484766	−	0.874644i	$-0.338905\pi$
$607$	1.19478e18	0.969533	0.484766	+	0.874644i	$0.338905\pi$
$608$	−2.09420e18	−1.68130
$609$	−2.89948e17	−0.230308
$610$	0	0
$611$	−7.13114e17	−0.554486
$612$	1.37469e18	1.05759
$613$	−2.38137e16	−0.0181273	−0.00906366	−	0.999959i	$-0.502885\pi$
$613$	−2.38137e16	−0.0181273	−0.00906366	+	0.999959i	$0.502885\pi$
$614$	1.24355e18	0.936631
$615$	0	0
$616$	−5.09485e16	−0.0375714
$617$	−1.58237e18	−1.15466	−0.577330	−	0.816511i	$-0.695905\pi$
$617$	−1.58237e18	−1.15466	−0.577330	+	0.816511i	$0.695905\pi$
$618$	−8.15248e16	−0.0588660
$619$	6.94179e17	0.496001	0.248000	−	0.968760i	$-0.420227\pi$
$619$	6.94179e17	0.496001	0.248000	+	0.968760i	$0.420227\pi$
$620$	0	0
$621$	5.86105e17	0.410091
$622$	−9.65868e16	−0.0668775
$623$	1.87560e18	1.28519
$624$	1.57803e17	0.107008
$625$	0	0
$626$	−3.29089e18	−2.18565
$627$	−5.26852e16	−0.0346298
$628$	1.24931e18	0.812704
$629$	−1.82316e18	−1.17381
$630$	0	0
$631$	1.12569e18	0.709948	0.354974	−	0.934876i	$-0.384490\pi$
$631$	1.12569e18	0.709948	0.354974	+	0.934876i	$0.384490\pi$
$632$	−5.57868e17	−0.348233
$633$	4.47482e17	0.276472
$634$	−1.38720e18	−0.848318
$635$	0	0
$636$	−9.62598e16	−0.0576732
$637$	−3.71076e17	−0.220068
$638$	4.89660e17	0.287449
$639$	−7.29929e17	−0.424156
$640$	0	0
$641$	1.88777e18	1.07491	0.537456	−	0.843292i	$-0.319386\pi$
$641$	1.88777e18	1.07491	0.537456	+	0.843292i	$0.319386\pi$
$642$	1.95819e17	0.110377
$643$	2.08824e18	1.16522	0.582612	−	0.812751i	$-0.302031\pi$
$643$	2.08824e18	1.16522	0.582612	+	0.812751i	$0.302031\pi$
$644$	1.03479e18	0.571601
$645$	0	0
$646$	−5.35654e18	−2.89983
$647$	6.09392e17	0.326602	0.163301	−	0.986576i	$-0.447786\pi$
$647$	6.09392e17	0.326602	0.163301	+	0.986576i	$0.447786\pi$
$648$	6.63587e17	0.352095
$649$	−2.27471e17	−0.119491
$650$	0	0
$651$	9.86353e16	0.0507874
$652$	6.68576e17	0.340833
$653$	1.05893e18	0.534478	0.267239	−	0.963630i	$-0.413889\pi$
$653$	1.05893e18	0.534478	0.267239	+	0.963630i	$0.413889\pi$
$654$	−6.65033e17	−0.332344
$655$	0	0
$656$	5.49105e17	0.269018
$657$	−6.48940e17	−0.314796
$658$	2.32440e18	1.11646
$659$	1.29805e18	0.617356	0.308678	−	0.951167i	$-0.400114\pi$
$659$	1.29805e18	0.617356	0.308678	+	0.951167i	$0.400114\pi$
$660$	0	0
$661$	−1.85367e17	−0.0864414	−0.0432207	−	0.999066i	$-0.513762\pi$
$661$	−1.85367e17	−0.0864414	−0.0432207	+	0.999066i	$0.513762\pi$
$662$	−1.12434e17	−0.0519185
$663$	3.03175e17	0.138629
$664$	1.46048e18	0.661309
$665$	0	0
$666$	2.12049e18	0.941572
$667$	4.28796e18	1.88553
$668$	1.99561e17	0.0869016
$669$	1.60555e16	0.00692394
$670$	0	0
$671$	−5.29216e17	−0.223839
$672$	−3.86348e17	−0.161837
$673$	−4.54029e18	−1.88359	−0.941793	−	0.336193i	$-0.890860\pi$
$673$	−4.54029e18	−1.88359	−0.941793	+	0.336193i	$0.890860\pi$
$674$	3.90141e18	1.60299
$675$	0	0
$676$	−1.34478e18	−0.541998
$677$	−1.65009e18	−0.658690	−0.329345	−	0.944210i	$-0.606828\pi$
$677$	−1.65009e18	−0.658690	−0.329345	+	0.944210i	$0.606828\pi$
$678$	7.38401e16	0.0291944
$679$	2.12782e18	0.833262
$680$	0	0
$681$	−4.57023e17	−0.175583
$682$	−1.66574e17	−0.0633881
$683$	2.98250e18	1.12421	0.562103	−	0.827067i	$-0.309992\pi$
$683$	2.98250e18	1.12421	0.562103	+	0.827067i	$0.309992\pi$
$684$	2.56261e18	0.956791
$685$	0	0
$686$	3.81261e18	1.39674
$687$	−5.75682e17	−0.208912
$688$	−4.41817e18	−1.58824
$689$	5.88163e17	0.209446
$690$	0	0
$691$	−3.16901e18	−1.10743	−0.553714	−	0.832707i	$-0.686790\pi$
$691$	−3.16901e18	−1.10743	−0.553714	+	0.832707i	$0.686790\pi$
$692$	7.74374e17	0.268078
$693$	2.69285e17	0.0923519
$694$	−6.34720e18	−2.15648
$695$	0	0
$696$	−3.70648e17	−0.123595
$697$	1.05495e18	0.348514
$698$	−1.61423e18	−0.528330
$699$	3.39088e17	0.109954
$700$	0	0
$701$	1.54527e18	0.491855	0.245927	−	0.969288i	$-0.420908\pi$
$701$	1.54527e18	0.491855	0.245927	+	0.969288i	$0.420908\pi$
$702$	−7.17963e17	−0.226418
$703$	−3.39863e18	−1.06193
$704$	1.41112e17	0.0436859
$705$	0	0
$706$	2.48598e18	0.755555
$707$	8.27357e17	0.249153
$708$	−3.99353e17	−0.119163
$709$	−2.38315e18	−0.704614	−0.352307	−	0.935884i	$-0.614603\pi$
$709$	−2.38315e18	−0.704614	−0.352307	+	0.935884i	$0.614603\pi$
$710$	0	0
$711$	2.94857e18	0.855972
$712$	2.39762e18	0.689700
$713$	−1.45869e18	−0.415796
$714$	−9.88200e17	−0.279130
$715$	0	0
$716$	2.67903e18	0.743092
$717$	−3.89460e17	−0.107050
$718$	3.59659e18	0.979675
$719$	−3.52277e18	−0.950926	−0.475463	−	0.879736i	$-0.657719\pi$
$719$	−3.52277e18	−0.950926	−0.475463	+	0.879736i	$0.657719\pi$
$720$	0	0
$721$	−6.67852e17	−0.177052
$722$	−5.02450e18	−1.32008
$723$	8.09465e15	0.00210765
$724$	8.08528e17	0.208638
$725$	0	0
$726$	−9.43362e17	−0.239106
$727$	−5.08798e18	−1.27812	−0.639061	−	0.769156i	$-0.720677\pi$
$727$	−5.08798e18	−1.27812	−0.639061	+	0.769156i	$0.720677\pi$
$728$	5.46530e17	0.136069
$729$	−3.22991e18	−0.797005
$730$	0	0
$731$	−8.48828e18	−2.05758
$732$	−9.29101e17	−0.223224
$733$	−6.37827e18	−1.51889	−0.759446	−	0.650570i	$-0.774530\pi$
$733$	−6.37827e18	−1.51889	−0.759446	+	0.650570i	$0.774530\pi$
$734$	−6.93591e18	−1.63711
$735$	0	0
$736$	5.71359e18	1.32496
$737$	5.88416e17	0.135253
$738$	−1.22700e18	−0.279562
$739$	2.22439e18	0.502369	0.251185	−	0.967939i	$-0.419180\pi$
$739$	2.22439e18	0.502369	0.251185	+	0.967939i	$0.419180\pi$
$740$	0	0
$741$	5.65160e17	0.125416
$742$	−1.91712e18	−0.421720
$743$	5.29231e18	1.15403	0.577017	−	0.816732i	$-0.304217\pi$
$743$	5.29231e18	1.15403	0.577017	+	0.816732i	$0.304217\pi$
$744$	1.26088e17	0.0272552
$745$	0	0
$746$	4.58482e18	0.973913
$747$	−7.71929e18	−1.62552
$748$	6.86445e17	0.143300
$749$	1.60416e18	0.331982
$750$	0	0
$751$	−7.19787e18	−1.46401	−0.732006	−	0.681299i	$-0.761416\pi$
$751$	−7.19787e18	−1.46401	−0.732006	+	0.681299i	$0.761416\pi$
$752$	7.02818e18	1.41719
$753$	9.81027e17	0.196116
$754$	−5.25264e18	−1.04103
$755$	0	0
$756$	9.62588e17	0.187520
$757$	2.14019e18	0.413360	0.206680	−	0.978409i	$-0.433734\pi$
$757$	2.14019e18	0.413360	0.206680	+	0.978409i	$0.433734\pi$
$758$	3.29272e18	0.630529
$759$	1.43741e17	0.0272903
$760$	0	0
$761$	3.70155e18	0.690850	0.345425	−	0.938446i	$-0.387735\pi$
$761$	3.70155e18	0.690850	0.345425	+	0.938446i	$0.387735\pi$
$762$	2.48244e18	0.459379
$763$	−5.44796e18	−0.999596
$764$	6.65535e18	1.21078
$765$	0	0
$766$	−6.33229e18	−1.13259
$767$	2.44011e18	0.432752
$768$	−1.39161e18	−0.244720
$769$	6.24559e18	1.08906	0.544531	−	0.838741i	$-0.316708\pi$
$769$	6.24559e18	1.08906	0.544531	+	0.838741i	$0.316708\pi$
$770$	0	0
$771$	4.24179e17	0.0727270
$772$	−2.78896e18	−0.474165
$773$	−5.49122e18	−0.925768	−0.462884	−	0.886419i	$-0.653185\pi$
$773$	−5.49122e18	−0.925768	−0.462884	+	0.886419i	$0.653185\pi$
$774$	9.87258e18	1.65050
$775$	0	0
$776$	2.72004e18	0.447172
$777$	−6.26995e17	−0.102218
$778$	1.07635e19	1.74015
$779$	1.96658e18	0.315296
$780$	0	0
$781$	−3.64488e17	−0.0574713
$782$	1.46142e19	2.28524
$783$	3.98878e18	0.618569
$784$	3.65719e18	0.562462
$785$	0	0
$786$	2.13685e18	0.323241
$787$	9.41449e18	1.41241	0.706205	−	0.708007i	$-0.250406\pi$
$787$	9.41449e18	1.41241	0.706205	+	0.708007i	$0.250406\pi$
$788$	6.78868e16	0.0101010
$789$	7.53836e17	0.111244
$790$	0	0
$791$	6.04899e17	0.0878083
$792$	3.44233e17	0.0495609
$793$	5.67695e18	0.810662
$794$	−1.35000e19	−1.91206
$795$	0	0
$796$	−7.12868e18	−0.993286
$797$	−4.72248e18	−0.652667	−0.326333	−	0.945255i	$-0.605813\pi$
$797$	−4.72248e18	−0.652667	−0.326333	+	0.945255i	$0.605813\pi$
$798$	−1.84214e18	−0.252525
$799$	1.35027e19	1.83598
$800$	0	0
$801$	−1.26724e19	−1.69531
$802$	−8.46671e18	−1.12352
$803$	−3.24046e17	−0.0426536
$804$	1.03303e18	0.134881
$805$	0	0
$806$	1.78685e18	0.229568
$807$	2.36459e18	0.301355
$808$	1.05763e18	0.133709
$809$	−5.48617e17	−0.0688025	−0.0344012	−	0.999408i	$-0.510952\pi$
$809$	−5.48617e17	−0.0688025	−0.0344012	+	0.999408i	$0.510952\pi$
$810$	0	0
$811$	1.56426e19	1.93051	0.965256	−	0.261306i	$-0.0841530\pi$
$811$	1.56426e19	1.93051	0.965256	+	0.261306i	$0.0841530\pi$
$812$	7.04232e18	0.862187
$813$	−5.82843e17	−0.0707886
$814$	1.05886e18	0.127579
$815$	0	0
$816$	−2.98798e18	−0.354317
$817$	−1.58233e19	−1.86147
$818$	7.79184e18	0.909376
$819$	−2.88865e18	−0.334464
$820$	0	0
$821$	−8.35727e18	−0.952432	−0.476216	−	0.879328i	$-0.657992\pi$
$821$	−8.35727e18	−0.952432	−0.476216	+	0.879328i	$0.657992\pi$
$822$	2.33568e18	0.264087
$823$	6.58521e18	0.738704	0.369352	−	0.929290i	$-0.379580\pi$
$823$	6.58521e18	0.738704	0.369352	+	0.929290i	$0.379580\pi$
$824$	−8.53731e17	−0.0950155
$825$	0	0
$826$	−7.95355e18	−0.871346
$827$	−9.69988e18	−1.05434	−0.527170	−	0.849760i	$-0.676747\pi$
$827$	−9.69988e18	−1.05434	−0.527170	+	0.849760i	$0.676747\pi$
$828$	−6.99154e18	−0.754007
$829$	−9.74971e18	−1.04325	−0.521624	−	0.853176i	$-0.674673\pi$
$829$	−9.74971e18	−1.04325	−0.521624	+	0.853176i	$0.674673\pi$
$830$	0	0
$831$	1.49823e18	0.157824
$832$	−1.51372e18	−0.158214
$833$	7.02628e18	0.728673
$834$	−2.67643e16	−0.00275408
$835$	0	0
$836$	1.27963e18	0.129641
$837$	−1.35691e18	−0.136407
$838$	−9.94696e18	−0.992211
$839$	−7.03714e18	−0.696536	−0.348268	−	0.937395i	$-0.613230\pi$
$839$	−7.03714e18	−0.696536	−0.348268	+	0.937395i	$0.613230\pi$
$840$	0	0
$841$	1.89214e19	1.84408
$842$	7.59738e18	0.734743
$843$	−1.57507e18	−0.151155
$844$	−1.08685e19	−1.03501
$845$	0	0
$846$	−1.57048e19	−1.47273
$847$	−7.72803e18	−0.719162
$848$	−5.79671e18	−0.535314
$849$	2.32548e17	0.0213115
$850$	0	0
$851$	9.27245e18	0.836859
$852$	−6.39902e17	−0.0573134
$853$	4.89051e18	0.434696	0.217348	−	0.976094i	$-0.430259\pi$
$853$	4.89051e18	0.434696	0.217348	+	0.976094i	$0.430259\pi$
$854$	−1.85041e19	−1.63227
$855$	0	0
$856$	2.05063e18	0.178159
$857$	1.67666e19	1.44567	0.722835	−	0.691021i	$-0.242839\pi$
$857$	1.67666e19	1.44567	0.722835	+	0.691021i	$0.242839\pi$
$858$	−1.76078e17	−0.0150674
$859$	−7.61243e17	−0.0646499	−0.0323250	−	0.999477i	$-0.510291\pi$
$859$	−7.61243e17	−0.0646499	−0.0323250	+	0.999477i	$0.510291\pi$
$860$	0	0
$861$	3.62804e17	0.0303495
$862$	−8.64465e18	−0.717712
$863$	−1.21299e19	−0.999512	−0.499756	−	0.866166i	$-0.666577\pi$
$863$	−1.21299e19	−0.999512	−0.499756	+	0.866166i	$0.666577\pi$
$864$	5.31494e18	0.434669
$865$	0	0
$866$	1.79958e19	1.44979
$867$	−3.40635e18	−0.272373
$868$	−2.39567e18	−0.190129
$869$	1.47236e18	0.115981
$870$	0	0
$871$	−6.31200e18	−0.489834
$872$	−6.96426e18	−0.536436
$873$	−1.43766e19	−1.09917
$874$	2.72429e19	2.06742
$875$	0	0
$876$	−5.68902e17	−0.0425364
$877$	3.40358e18	0.252603	0.126301	−	0.991992i	$-0.459689\pi$
$877$	3.40358e18	0.252603	0.126301	+	0.991992i	$0.459689\pi$
$878$	−3.25850e19	−2.40051
$879$	1.87781e18	0.137317
$880$	0	0
$881$	7.36350e18	0.530568	0.265284	−	0.964170i	$-0.414534\pi$
$881$	7.36350e18	0.530568	0.265284	+	0.964170i	$0.414534\pi$
$882$	−8.17215e18	−0.584508
$883$	−3.56118e18	−0.252842	−0.126421	−	0.991977i	$-0.540349\pi$
$883$	−3.56118e18	−0.252842	−0.126421	+	0.991977i	$0.540349\pi$
$884$	−7.36357e18	−0.518978
$885$	0	0
$886$	1.50433e19	1.04478
$887$	2.55596e19	1.76218	0.881091	−	0.472946i	$-0.156810\pi$
$887$	2.55596e19	1.76218	0.881091	+	0.472946i	$0.156810\pi$
$888$	−8.01502e17	−0.0548555
$889$	2.03362e19	1.38168
$890$	0	0
$891$	−1.75138e18	−0.117267
$892$	−3.89958e17	−0.0259207
$893$	2.51709e19	1.66098
$894$	−2.53266e18	−0.165914
$895$	0	0
$896$	−8.49557e18	−0.548518
$897$	−1.54192e18	−0.0988352
$898$	−2.71165e18	−0.172559
$899$	−9.92720e18	−0.627175
$900$	0	0
$901$	−1.11368e19	−0.693503
$902$	−6.12698e17	−0.0378795
$903$	−2.91917e18	−0.179180
$904$	7.73257e17	0.0471226
$905$	0	0
$906$	−5.79993e18	−0.348409
$907$	−7.53136e18	−0.449186	−0.224593	−	0.974453i	$-0.572105\pi$
$907$	−7.53136e18	−0.449186	−0.224593	+	0.974453i	$0.572105\pi$
$908$	1.11003e19	0.657317
$909$	−5.59003e18	−0.328662
$910$	0	0
$911$	4.35308e18	0.252306	0.126153	−	0.992011i	$-0.459737\pi$
$911$	4.35308e18	0.252306	0.126153	+	0.992011i	$0.459737\pi$
$912$	−5.57001e18	−0.320545
$913$	−3.85460e18	−0.220252
$914$	3.59242e19	2.03815
$915$	0	0
$916$	1.39823e19	0.782091
$917$	1.75051e19	0.972218
$918$	1.35945e19	0.749698
$919$	−3.19432e19	−1.74915	−0.874575	−	0.484890i	$-0.838860\pi$
$919$	−3.19432e19	−1.74915	−0.874575	+	0.484890i	$0.838860\pi$
$920$	0	0
$921$	2.48435e18	0.134130
$922$	−1.87306e19	−1.00415
$923$	3.90990e18	0.208140
$924$	2.36072e17	0.0124789
$925$	0	0
$926$	−4.32390e19	−2.25374
$927$	4.51234e18	0.233552
$928$	3.88842e19	1.99853
$929$	−1.17430e19	−0.599344	−0.299672	−	0.954042i	$-0.596877\pi$
$929$	−1.17430e19	−0.599344	−0.299672	+	0.954042i	$0.596877\pi$
$930$	0	0
$931$	1.30980e19	0.659221
$932$	−8.23583e18	−0.411627
$933$	−1.92960e17	−0.00957715
$934$	1.22188e19	0.602246
$935$	0	0
$936$	−3.69263e18	−0.179491
$937$	2.23556e19	1.07914	0.539572	−	0.841940i	$-0.318586\pi$
$937$	2.23556e19	1.07914	0.539572	+	0.841940i	$0.318586\pi$
$938$	2.05740e19	0.986281
$939$	−6.57449e18	−0.312994
$940$	0	0
$941$	−2.83714e19	−1.33214	−0.666068	−	0.745891i	$-0.732024\pi$
$941$	−2.83714e19	−1.33214	−0.666068	+	0.745891i	$0.732024\pi$
$942$	6.06782e18	0.282945
$943$	−5.36541e18	−0.248472
$944$	−2.40488e19	−1.10605
$945$	0	0
$946$	4.92984e18	0.223635
$947$	5.53869e18	0.249536	0.124768	−	0.992186i	$-0.460181\pi$
$947$	5.53869e18	0.249536	0.124768	+	0.992186i	$0.460181\pi$
$948$	2.58490e18	0.115662
$949$	3.47608e18	0.154475
$950$	0	0
$951$	−2.77133e18	−0.121483
$952$	−1.03485e19	−0.450543
$953$	3.68310e19	1.59261	0.796306	−	0.604894i	$-0.206785\pi$
$953$	3.68310e19	1.59261	0.796306	+	0.604894i	$0.206785\pi$
$954$	1.29530e19	0.556296
$955$	0	0
$956$	9.45927e18	0.400757
$957$	9.78237e17	0.0411639
$958$	−4.93911e18	−0.206430
$959$	1.91339e19	0.794297
$960$	0	0
$961$	−2.10405e19	−0.861695
$962$	−1.13585e19	−0.462043
$963$	−1.08385e19	−0.437922
$964$	−1.96604e17	−0.00789028
$965$	0	0
$966$	5.02590e18	0.199004
$967$	−1.72654e19	−0.679055	−0.339527	−	0.940596i	$-0.610267\pi$
$967$	−1.72654e19	−0.679055	−0.339527	+	0.940596i	$0.610267\pi$
$968$	−9.87893e18	−0.385940
$969$	−1.07012e19	−0.415269
$970$	0	0
$971$	−2.43618e19	−0.932790	−0.466395	−	0.884577i	$-0.654447\pi$
$971$	−2.43618e19	−0.932790	−0.466395	+	0.884577i	$0.654447\pi$
$972$	−9.81322e18	−0.373234
$973$	−2.19253e17	−0.00828348
$974$	3.22604e19	1.21070
$975$	0	0
$976$	−5.59500e19	−2.07193
$977$	5.71246e18	0.210140	0.105070	−	0.994465i	$-0.466493\pi$
$977$	5.71246e18	0.210140	0.105070	+	0.994465i	$0.466493\pi$
$978$	3.24723e18	0.118662
$979$	−6.32794e18	−0.229707
$980$	0	0
$981$	3.68091e19	1.31858
$982$	3.15843e19	1.12395
$983$	−2.19482e19	−0.775891	−0.387945	−	0.921682i	$-0.626815\pi$
$983$	−2.19482e19	−0.775891	−0.387945	+	0.921682i	$0.626815\pi$
$984$	4.63781e17	0.0162871
$985$	0	0
$986$	9.94579e19	3.44699
$987$	4.64365e18	0.159882
$988$	−1.37267e19	−0.469512
$989$	4.31707e19	1.46694
$990$	0	0
$991$	3.44937e19	1.15681	0.578404	−	0.815751i	$-0.303676\pi$
$991$	3.44937e19	1.15681	0.578404	+	0.815751i	$0.303676\pi$
$992$	−1.32277e19	−0.440716
$993$	−2.24620e17	−0.00743496
$994$	−1.27443e19	−0.419089
$995$	0	0
$996$	−6.76721e18	−0.219646
$997$	5.74384e19	1.85218	0.926091	−	0.377301i	$-0.123148\pi$
$997$	5.74384e19	1.85218	0.926091	+	0.377301i	$0.123148\pi$
$998$	−5.04605e19	−1.61660
$999$	8.62548e18	0.274541

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.14.a.d.1.1	yes	4
5.2	odd	4		25.14.b.c.24.2		8
5.3	odd	4		25.14.b.c.24.7		8
5.4	even	2		25.14.a.c.1.4	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.14.a.c.1.4	✓	4	5.4	even	2
25.14.a.d.1.1	yes	4	1.1	even	1	trivial
25.14.b.c.24.2		8	5.2	odd	4
25.14.b.c.24.7		8	5.3	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)

\(f(q)\)	\(=\)	\(q-117.966 q^{2} -235.672 q^{3} +5724.04 q^{4} +27801.3 q^{6} +227749. q^{7} +291136. q^{8} -1.53878e6 q^{9} +O(q^{10})\)	\(q-117.966 q^{2} -235.672 q^{3} +5724.04 q^{4} +27801.3 q^{6} +227749. q^{7} +291136. q^{8} -1.53878e6 q^{9} -768386. q^{11} -1.34899e6 q^{12} +8.24256e6 q^{13} -2.68667e7 q^{14} -8.12356e7 q^{16} -1.56072e8 q^{17} +1.81524e8 q^{18} -2.90939e8 q^{19} -5.36739e7 q^{21} +9.06436e7 q^{22} +7.93768e8 q^{23} -6.86126e7 q^{24} -9.72343e8 q^{26} +7.38384e8 q^{27} +1.30364e9 q^{28} +5.40204e9 q^{29} -1.83768e9 q^{31} +7.19807e9 q^{32} +1.81087e8 q^{33} +1.84112e10 q^{34} -8.80804e9 q^{36} +1.16816e10 q^{37} +3.43210e10 q^{38} -1.94254e9 q^{39} -6.75942e9 q^{41} +6.33171e9 q^{42} +5.43871e10 q^{43} -4.39827e9 q^{44} -9.36378e10 q^{46} -8.65161e10 q^{47} +1.91449e10 q^{48} -4.50196e10 q^{49} +3.67817e10 q^{51} +4.71807e10 q^{52} +7.13568e10 q^{53} -8.71044e10 q^{54} +6.63059e10 q^{56} +6.85661e10 q^{57} -6.37258e11 q^{58} +2.96038e11 q^{59} +6.88737e11 q^{61} +2.16784e11 q^{62} -3.50455e11 q^{63} -1.83647e11 q^{64} -2.13621e10 q^{66} -7.65782e11 q^{67} -8.93360e11 q^{68} -1.87068e11 q^{69} +4.74355e11 q^{71} -4.47995e11 q^{72} +4.21723e11 q^{73} -1.37803e12 q^{74} -1.66535e12 q^{76} -1.74999e11 q^{77} +2.29154e11 q^{78} -1.91617e12 q^{79} +2.27930e12 q^{81} +7.97383e11 q^{82} +5.01649e12 q^{83} -3.07231e11 q^{84} -6.41584e12 q^{86} -1.27311e12 q^{87} -2.23705e11 q^{88} +8.23537e12 q^{89} +1.87723e12 q^{91} +4.54355e12 q^{92} +4.33088e11 q^{93} +1.02060e13 q^{94} -1.69638e12 q^{96} +9.34285e12 q^{97} +5.31079e12 q^{98} +1.18238e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 65 q^{2} + 860 q^{3} + 3733 q^{4} + 40333 q^{6} + 102800 q^{7} + 329895 q^{8} + 47872 q^{9}+O(q^{10}) \) 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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