LMFDB - Embedded newform 25.12.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,12,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, 12, names="a")

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

chi := DirichletCharacter("25.1");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 12 $
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:	$19.2085795140$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{151}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 151 $ x^2 - 151
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 5)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-12.2882$ 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)

$f(q)$	$=$	$q-63.7292 q^{2} -283.223 q^{3} +2013.42 q^{4} +18049.6 q^{6} -41926.3 q^{7} +2204.06 q^{8} -96932.0 q^{9} +O(q^{10})$	\(q-63.7292 q^{2} -283.223 q^{3} +2013.42 q^{4} +18049.6 q^{6} -41926.3 q^{7} +2204.06 q^{8} -96932.0 q^{9} -957905. q^{11} -570245. q^{12} -1.39098e6 q^{13} +2.67193e6 q^{14} -4.26394e6 q^{16} -3.76857e6 q^{17} +6.17740e6 q^{18} +9.41036e6 q^{19} +1.18745e7 q^{21} +6.10466e7 q^{22} -3.02942e7 q^{23} -624238. q^{24} +8.86460e7 q^{26} +7.76254e7 q^{27} -8.44151e7 q^{28} +1.03553e8 q^{29} -5.48554e7 q^{31} +2.67224e8 q^{32} +2.71300e8 q^{33} +2.40168e8 q^{34} -1.95164e8 q^{36} -4.78282e8 q^{37} -5.99715e8 q^{38} +3.93957e8 q^{39} -9.29557e8 q^{41} -7.56752e8 q^{42} +2.68608e7 q^{43} -1.92866e9 q^{44} +1.93063e9 q^{46} +1.20497e9 q^{47} +1.20764e9 q^{48} -2.19508e8 q^{49} +1.06735e9 q^{51} -2.80062e9 q^{52} +4.02058e9 q^{53} -4.94700e9 q^{54} -9.24080e7 q^{56} -2.66523e9 q^{57} -6.59933e9 q^{58} +7.97972e9 q^{59} -2.07472e9 q^{61} +3.49589e9 q^{62} +4.06400e9 q^{63} -8.29741e9 q^{64} -1.72898e10 q^{66} -5.61370e9 q^{67} -7.58770e9 q^{68} +8.58000e9 q^{69} +1.51224e10 q^{71} -2.13643e8 q^{72} +6.64484e9 q^{73} +3.04806e10 q^{74} +1.89470e10 q^{76} +4.01615e10 q^{77} -2.51066e10 q^{78} -1.57985e10 q^{79} -4.81405e9 q^{81} +5.92399e10 q^{82} +2.04046e10 q^{83} +2.39083e10 q^{84} -1.71182e9 q^{86} -2.93285e10 q^{87} -2.11128e9 q^{88} -4.21030e10 q^{89} +5.83187e10 q^{91} -6.09948e10 q^{92} +1.55363e10 q^{93} -7.67919e10 q^{94} -7.56837e10 q^{96} -1.10181e11 q^{97} +1.39891e10 q^{98} +9.28516e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 20 q^{2} + 220 q^{3} + 6976 q^{4} + 60184 q^{6} - 57900 q^{7} + 246240 q^{8} - 20846 q^{9}+O(q^{10}) $ 2 * q + 20 * q^2 + 220 * q^3 + 6976 * q^4 + 60184 * q^6 - 57900 * q^7 + 246240 * q^8 - 20846 * q^9	\( 2 q + 20 q^{2} + 220 q^{3} + 6976 q^{4} + 60184 q^{6} - 57900 q^{7} + 246240 q^{8} - 20846 q^{9} - 618176 q^{11} + 1927040 q^{12} - 3414260 q^{13} + 1334472 q^{14} + 6005632 q^{16} - 1317940 q^{17} + 12548020 q^{18} + 5325320 q^{19} + 3836184 q^{21} + 89491840 q^{22} - 58943940 q^{23} + 122180160 q^{24} - 80761736 q^{26} + 26769160 q^{27} - 163685760 q^{28} + 94140380 q^{29} + 244543464 q^{31} + 627301120 q^{32} + 442259840 q^{33} + 445358072 q^{34} + 182418752 q^{36} - 21003220 q^{37} - 941752240 q^{38} - 624203992 q^{39} - 745743316 q^{41} - 1429793040 q^{42} - 629950100 q^{43} - 242725888 q^{44} - 468194856 q^{46} + 1402061540 q^{47} + 6375522560 q^{48} - 1941677414 q^{49} + 2300559784 q^{51} - 12841321600 q^{52} - 1138320580 q^{53} - 9205154480 q^{54} - 3990553920 q^{56} - 4720910480 q^{57} - 7387417960 q^{58} + 7317515560 q^{59} - 1516425676 q^{61} + 28564327440 q^{62} + 2848632180 q^{63} + 819531776 q^{64} - 2975464192 q^{66} - 15734290140 q^{67} + 4573774720 q^{68} - 5837195832 q^{69} + 32938471544 q^{71} + 18354067680 q^{72} + 29982848860 q^{73} + 68768198072 q^{74} - 1325392640 q^{76} + 34734748800 q^{77} - 110356370800 q^{78} - 3302823120 q^{79} - 43884431798 q^{81} + 74630515640 q^{82} - 13299102420 q^{83} - 15982487808 q^{84} - 56706093896 q^{86} - 34064940920 q^{87} + 80794874880 q^{88} - 12674770860 q^{89} + 90637859064 q^{91} - 203171571840 q^{92} + 166200542640 q^{93} - 60289765528 q^{94} + 105515416064 q^{96} + 3080703740 q^{97} - 130206802940 q^{98} + 118700272448 q^{99}+O(q^{100}) \) 2 * q + 20 * q^2 + 220 * q^3 + 6976 * q^4 + 60184 * q^6 - 57900 * q^7 + 246240 * q^8 - 20846 * q^9 - 618176 * q^11 + 1927040 * q^12 - 3414260 * q^13 + 1334472 * q^14 + 6005632 * q^16 - 1317940 * q^17 + 12548020 * q^18 + 5325320 * q^19 + 3836184 * q^21 + 89491840 * q^22 - 58943940 * q^23 + 122180160 * q^24 - 80761736 * q^26 + 26769160 * q^27 - 163685760 * q^28 + 94140380 * q^29 + 244543464 * q^31 + 627301120 * q^32 + 442259840 * q^33 + 445358072 * q^34 + 182418752 * q^36 - 21003220 * q^37 - 941752240 * q^38 - 624203992 * q^39 - 745743316 * q^41 - 1429793040 * q^42 - 629950100 * q^43 - 242725888 * q^44 - 468194856 * q^46 + 1402061540 * q^47 + 6375522560 * q^48 - 1941677414 * q^49 + 2300559784 * q^51 - 12841321600 * q^52 - 1138320580 * q^53 - 9205154480 * q^54 - 3990553920 * q^56 - 4720910480 * q^57 - 7387417960 * q^58 + 7317515560 * q^59 - 1516425676 * q^61 + 28564327440 * q^62 + 2848632180 * q^63 + 819531776 * q^64 - 2975464192 * q^66 - 15734290140 * q^67 + 4573774720 * q^68 - 5837195832 * q^69 + 32938471544 * q^71 + 18354067680 * q^72 + 29982848860 * q^73 + 68768198072 * q^74 - 1325392640 * q^76 + 34734748800 * q^77 - 110356370800 * q^78 - 3302823120 * q^79 - 43884431798 * q^81 + 74630515640 * q^82 - 13299102420 * q^83 - 15982487808 * q^84 - 56706093896 * q^86 - 34064940920 * q^87 + 80794874880 * q^88 - 12674770860 * q^89 + 90637859064 * q^91 - 203171571840 * q^92 + 166200542640 * q^93 - 60289765528 * q^94 + 105515416064 * q^96 + 3080703740 * q^97 - 130206802940 * q^98 + 118700272448 * 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 $

$2$	−63.7292	−1.40823	−0.704115	−	0.710086i	$-0.748656\pi$
$2$	−63.7292	−1.40823	−0.704115	+	0.710086i	$0.748656\pi$
$3$	−283.223	−0.672916	−0.336458	−	0.941698i	$-0.609229\pi$
$3$	−283.223	−0.672916	−0.336458	+	0.941698i	$0.609229\pi$
$4$	2013.42	0.983113
$5$	0	0
$5$	0	0
$6$	18049.6	0.947621
$7$	−41926.3	−0.942861	−0.471431	−	0.881903i	$-0.656262\pi$
$7$	−41926.3	−0.942861	−0.471431	+	0.881903i	$0.656262\pi$
$8$	2204.06	0.0237809
$9$	−96932.0	−0.547184
$10$	0	0
$11$	−957905.	−1.79334	−0.896670	−	0.442699i	$-0.854021\pi$
$11$	−957905.	−1.79334	−0.896670	+	0.442699i	$0.854021\pi$
$12$	−570245.	−0.661553
$13$	−1.39098e6	−1.03904	−0.519520	−	0.854458i	$-0.673889\pi$
$13$	−1.39098e6	−1.03904	−0.519520	+	0.854458i	$0.673889\pi$
$14$	2.67193e6	1.32777
$15$	0	0
$16$	−4.26394e6	−1.01660
$17$	−3.76857e6	−0.643736	−0.321868	−	0.946785i	$-0.604311\pi$
$17$	−3.76857e6	−0.643736	−0.321868	+	0.946785i	$0.604311\pi$
$18$	6.17740e6	0.770561
$19$	9.41036e6	0.871889	0.435945	−	0.899973i	$-0.356414\pi$
$19$	9.41036e6	0.871889	0.435945	+	0.899973i	$0.356414\pi$
$20$	0	0
$21$	1.18745e7	0.634467
$22$	6.10466e7	2.52544
$23$	−3.02942e7	−0.981423	−0.490712	−	0.871322i	$-0.663263\pi$
$23$	−3.02942e7	−0.981423	−0.490712	+	0.871322i	$0.663263\pi$
$24$	−624238.	−0.0160025
$25$	0	0
$26$	8.86460e7	1.46321
$27$	7.76254e7	1.04113
$28$	−8.44151e7	−0.926939
$29$	1.03553e8	0.937502	0.468751	−	0.883330i	$-0.344704\pi$
$29$	1.03553e8	0.937502	0.468751	+	0.883330i	$0.344704\pi$
$30$	0	0
$31$	−5.48554e7	−0.344136	−0.172068	−	0.985085i	$-0.555045\pi$
$31$	−5.48554e7	−0.344136	−0.172068	+	0.985085i	$0.555045\pi$
$32$	2.67224e8	1.40783
$33$	2.71300e8	1.20677
$34$	2.40168e8	0.906529
$35$	0	0
$36$	−1.95164e8	−0.537943
$37$	−4.78282e8	−1.13390	−0.566950	−	0.823752i	$-0.691877\pi$
$37$	−4.78282e8	−1.13390	−0.566950	+	0.823752i	$0.691877\pi$
$38$	−5.99715e8	−1.22782
$39$	3.93957e8	0.699187
$40$	0	0
$41$	−9.29557e8	−1.25304	−0.626520	−	0.779406i	$-0.715521\pi$
$41$	−9.29557e8	−1.25304	−0.626520	+	0.779406i	$0.715521\pi$
$42$	−7.56752e8	−0.893475
$43$	2.68608e7	0.0278639	0.0139320	−	0.999903i	$-0.495565\pi$
$43$	2.68608e7	0.0278639	0.0139320	+	0.999903i	$0.495565\pi$
$44$	−1.92866e9	−1.76306
$45$	0	0
$46$	1.93063e9	1.38207
$47$	1.20497e9	0.766370	0.383185	−	0.923672i	$-0.374827\pi$
$47$	1.20497e9	0.766370	0.383185	+	0.923672i	$0.374827\pi$
$48$	1.20764e9	0.684088
$49$	−2.19508e8	−0.111013
$50$	0	0
$51$	1.06735e9	0.433181
$52$	−2.80062e9	−1.02149
$53$	4.02058e9	1.32060	0.660301	−	0.751001i	$-0.270429\pi$
$53$	4.02058e9	1.32060	0.660301	+	0.751001i	$0.270429\pi$
$54$	−4.94700e9	−1.46614
$55$	0	0
$56$	−9.24080e7	−0.0224221
$57$	−2.66523e9	−0.586709
$58$	−6.59933e9	−1.32022
$59$	7.97972e9	1.45312	0.726560	−	0.687103i	$-0.241118\pi$
$59$	7.97972e9	1.45312	0.726560	+	0.687103i	$0.241118\pi$
$60$	0	0
$61$	−2.07472e9	−0.314518	−0.157259	−	0.987557i	$-0.550266\pi$
$61$	−2.07472e9	−0.314518	−0.157259	+	0.987557i	$0.550266\pi$
$62$	3.49589e9	0.484623
$63$	4.06400e9	0.515918
$64$	−8.29741e9	−0.965946
$65$	0	0
$66$	−1.72898e10	−1.69941
$67$	−5.61370e9	−0.507969	−0.253985	−	0.967208i	$-0.581741\pi$
$67$	−5.61370e9	−0.507969	−0.253985	+	0.967208i	$0.581741\pi$
$68$	−7.58770e9	−0.632865
$69$	8.58000e9	0.660416
$70$	0	0
$71$	1.51224e10	0.994714	0.497357	−	0.867546i	$-0.334304\pi$
$71$	1.51224e10	0.994714	0.497357	+	0.867546i	$0.334304\pi$
$72$	−2.13643e8	−0.0130125
$73$	6.64484e9	0.375153	0.187577	−	0.982250i	$-0.439937\pi$
$73$	6.64484e9	0.375153	0.187577	+	0.982250i	$0.439937\pi$
$74$	3.04806e10	1.59679
$75$	0	0
$76$	1.89470e10	0.857166
$77$	4.01615e10	1.69087
$78$	−2.51066e10	−0.984616
$79$	−1.57985e10	−0.577652	−0.288826	−	0.957382i	$-0.593265\pi$
$79$	−1.57985e10	−0.577652	−0.288826	+	0.957382i	$0.593265\pi$
$80$	0	0
$81$	−4.81405e9	−0.153406
$82$	5.92399e10	1.76457
$83$	2.04046e10	0.568589	0.284295	−	0.958737i	$-0.408241\pi$
$83$	2.04046e10	0.568589	0.284295	+	0.958737i	$0.408241\pi$
$84$	2.39083e10	0.623752
$85$	0	0
$86$	−1.71182e9	−0.0392389
$87$	−2.93285e10	−0.630861
$88$	−2.11128e9	−0.0426472
$89$	−4.21030e10	−0.799223	−0.399611	−	0.916685i	$-0.630855\pi$
$89$	−4.21030e10	−0.799223	−0.399611	+	0.916685i	$0.630855\pi$
$90$	0	0
$91$	5.83187e10	0.979670
$92$	−6.09948e10	−0.964850
$93$	1.55363e10	0.231575
$94$	−7.67919e10	−1.07923
$95$	0	0
$96$	−7.56837e10	−0.947351
$97$	−1.10181e11	−1.30275	−0.651376	−	0.758755i	$-0.725808\pi$
$97$	−1.10181e11	−1.30275	−0.651376	+	0.758755i	$0.725808\pi$
$98$	1.39891e10	0.156331
$99$	9.28516e10	0.981287
$100$	0	0
$101$	−3.33271e10	−0.315522	−0.157761	−	0.987477i	$-0.550428\pi$
$101$	−3.33271e10	−0.315522	−0.157761	+	0.987477i	$0.550428\pi$
$102$	−6.80211e10	−0.610018
$103$	−8.49419e10	−0.721966	−0.360983	−	0.932572i	$-0.617559\pi$
$103$	−8.49419e10	−0.721966	−0.360983	+	0.932572i	$0.617559\pi$
$104$	−3.06580e9	−0.0247093
$105$	0	0
$106$	−2.56229e11	−1.85971
$107$	−1.43774e11	−0.990989	−0.495494	−	0.868611i	$-0.665013\pi$
$107$	−1.43774e11	−0.990989	−0.495494	+	0.868611i	$0.665013\pi$
$108$	1.56292e11	1.02354
$109$	−3.01296e11	−1.87563	−0.937816	−	0.347134i	$-0.887155\pi$
$109$	−3.01296e11	−1.87563	−0.937816	+	0.347134i	$0.887155\pi$
$110$	0	0
$111$	1.35460e11	0.763020
$112$	1.78771e11	0.958515
$113$	2.22891e11	1.13805	0.569026	−	0.822320i	$-0.307320\pi$
$113$	2.22891e11	1.13805	0.569026	+	0.822320i	$0.307320\pi$
$114$	1.69853e11	0.826221
$115$	0	0
$116$	2.08495e11	0.921671
$117$	1.34830e11	0.568546
$118$	−5.08541e11	−2.04633
$119$	1.58003e11	0.606954
$120$	0	0
$121$	6.32271e11	2.21607
$122$	1.32220e11	0.442914
$123$	2.63271e11	0.843191
$124$	−1.10447e11	−0.338324
$125$	0	0
$126$	−2.58996e11	−0.726532
$127$	1.79939e11	0.483287	0.241644	−	0.970365i	$-0.422313\pi$
$127$	1.79939e11	0.483287	0.241644	+	0.970365i	$0.422313\pi$
$128$	−1.84863e10	−0.0475549
$129$	−7.60759e9	−0.0187501
$130$	0	0
$131$	−5.65153e11	−1.27989	−0.639946	−	0.768420i	$-0.721043\pi$
$131$	−5.65153e11	−1.27989	−0.639946	+	0.768420i	$0.721043\pi$
$132$	5.46240e11	1.18639
$133$	−3.94542e11	−0.822071
$134$	3.57757e11	0.715338
$135$	0	0
$136$	−8.30615e9	−0.0153086
$137$	−1.24499e9	−0.00220396	−0.00110198	−	0.999999i	$-0.500351\pi$
$137$	−1.24499e9	−0.00220396	−0.00110198	+	0.999999i	$0.500351\pi$
$138$	−5.46797e11	−0.930017
$139$	4.68084e11	0.765142	0.382571	−	0.923926i	$-0.375039\pi$
$139$	4.68084e11	0.765142	0.382571	+	0.923926i	$0.375039\pi$
$140$	0	0
$141$	−3.41275e11	−0.515703
$142$	−9.63736e11	−1.40079
$143$	1.33243e12	1.86335
$144$	4.13312e11	0.556268
$145$	0	0
$146$	−4.23470e11	−0.528302
$147$	6.21697e10	0.0747022
$148$	−9.62981e11	−1.11475
$149$	1.05439e12	1.17619	0.588096	−	0.808791i	$-0.299878\pi$
$149$	1.05439e12	1.17619	0.588096	+	0.808791i	$0.299878\pi$
$150$	0	0
$151$	4.91301e11	0.509301	0.254651	−	0.967033i	$-0.418040\pi$
$151$	4.91301e11	0.509301	0.254651	+	0.967033i	$0.418040\pi$
$152$	2.07410e10	0.0207343
$153$	3.65295e11	0.352242
$154$	−2.55946e12	−2.38114
$155$	0	0
$156$	7.93198e11	0.687379
$157$	−6.17375e11	−0.516536	−0.258268	−	0.966073i	$-0.583152\pi$
$157$	−6.17375e11	−0.516536	−0.258268	+	0.966073i	$0.583152\pi$
$158$	1.00683e12	0.813467
$159$	−1.13872e12	−0.888654
$160$	0	0
$161$	1.27013e12	0.925346
$162$	3.06795e11	0.216031
$163$	−2.97234e11	−0.202333	−0.101166	−	0.994870i	$-0.532257\pi$
$163$	−2.97234e11	−0.202333	−0.101166	+	0.994870i	$0.532257\pi$
$164$	−1.87158e12	−1.23188
$165$	0	0
$166$	−1.30037e12	−0.800705
$167$	2.53524e11	0.151035	0.0755177	−	0.997144i	$-0.475939\pi$
$167$	2.53524e11	0.151035	0.0755177	+	0.997144i	$0.475939\pi$
$168$	2.61720e10	0.0150882
$169$	1.42662e11	0.0796035
$170$	0	0
$171$	−9.12165e11	−0.477084
$172$	5.40820e10	0.0273934
$173$	−1.80555e12	−0.885843	−0.442922	−	0.896560i	$-0.646058\pi$
$173$	−1.80555e12	−0.885843	−0.442922	+	0.896560i	$0.646058\pi$
$174$	1.86908e12	0.888397
$175$	0	0
$176$	4.08445e12	1.82311
$177$	−2.26004e12	−0.977828
$178$	2.68319e12	1.12549
$179$	1.63020e12	0.663054	0.331527	−	0.943446i	$-0.392436\pi$
$179$	1.63020e12	0.663054	0.331527	+	0.943446i	$0.392436\pi$
$180$	0	0
$181$	−4.16028e12	−1.59181	−0.795904	−	0.605423i	$-0.793004\pi$
$181$	−4.16028e12	−1.59181	−0.795904	+	0.605423i	$0.793004\pi$
$182$	−3.71660e12	−1.37960
$183$	5.87608e11	0.211644
$184$	−6.67701e10	−0.0233391
$185$	0	0
$186$	−9.90115e11	−0.326110
$187$	3.60994e12	1.15444
$188$	2.42611e12	0.753429
$189$	−3.25455e12	−0.981636
$190$	0	0
$191$	−3.03600e12	−0.864208	−0.432104	−	0.901824i	$-0.642229\pi$
$191$	−3.03600e12	−0.864208	−0.432104	+	0.901824i	$0.642229\pi$
$192$	2.35001e12	0.650000
$193$	−3.77397e12	−1.01445	−0.507227	−	0.861812i	$-0.669330\pi$
$193$	−3.77397e12	−1.01445	−0.507227	+	0.861812i	$0.669330\pi$
$194$	7.02174e12	1.83457
$195$	0	0
$196$	−4.41961e11	−0.109138
$197$	1.03079e12	0.247518	0.123759	−	0.992312i	$-0.460505\pi$
$197$	1.03079e12	0.247518	0.123759	+	0.992312i	$0.460505\pi$
$198$	−5.91736e12	−1.38188
$199$	1.14293e12	0.259614	0.129807	−	0.991539i	$-0.458564\pi$
$199$	1.14293e12	0.259614	0.129807	+	0.991539i	$0.458564\pi$
$200$	0	0
$201$	1.58993e12	0.341821
$202$	2.12391e12	0.444328
$203$	−4.34159e12	−0.883935
$204$	2.14901e12	0.425865
$205$	0	0
$206$	5.41328e12	1.01670
$207$	2.93648e12	0.537019
$208$	5.93105e12	1.05629
$209$	−9.01423e12	−1.56359
$210$	0	0
$211$	6.96492e12	1.14647	0.573235	−	0.819391i	$-0.305688\pi$
$211$	6.96492e12	1.14647	0.573235	+	0.819391i	$0.305688\pi$
$212$	8.09510e12	1.29830
$213$	−4.28299e12	−0.669359
$214$	9.16259e12	1.39554
$215$	0	0
$216$	1.71091e11	0.0247589
$217$	2.29989e12	0.324472
$218$	1.92014e13	2.64132
$219$	−1.88197e12	−0.252447
$220$	0	0
$221$	5.24201e12	0.668868
$222$	−8.63279e12	−1.07451
$223$	−6.80403e12	−0.826208	−0.413104	−	0.910684i	$-0.635555\pi$
$223$	−6.80403e12	−0.826208	−0.413104	+	0.910684i	$0.635555\pi$
$224$	−1.12037e13	−1.32739
$225$	0	0
$226$	−1.42047e13	−1.60264
$227$	−8.00368e12	−0.881348	−0.440674	−	0.897667i	$-0.645261\pi$
$227$	−8.00368e12	−0.881348	−0.440674	+	0.897667i	$0.645261\pi$
$228$	−5.36621e12	−0.576801
$229$	1.20624e13	1.26572	0.632862	−	0.774265i	$-0.281880\pi$
$229$	1.20624e13	1.26572	0.632862	+	0.774265i	$0.281880\pi$
$230$	0	0
$231$	−1.13746e13	−1.13781
$232$	2.28236e11	0.0222946
$233$	1.05744e13	1.00878	0.504390	−	0.863476i	$-0.331717\pi$
$233$	1.05744e13	1.00878	0.504390	+	0.863476i	$0.331717\pi$
$234$	−8.59263e12	−0.800643
$235$	0	0
$236$	1.60665e13	1.42858
$237$	4.47449e12	0.388711
$238$	−1.00694e13	−0.854731
$239$	−4.81329e12	−0.399258	−0.199629	−	0.979872i	$-0.563974\pi$
$239$	−4.81329e12	−0.399258	−0.199629	+	0.979872i	$0.563974\pi$
$240$	0	0
$241$	−1.29674e13	−1.02745	−0.513724	−	0.857956i	$-0.671734\pi$
$241$	−1.29674e13	−1.02745	−0.513724	+	0.857956i	$0.671734\pi$
$242$	−4.02941e13	−3.12074
$243$	−1.23877e13	−0.937896
$244$	−4.17728e12	−0.309207
$245$	0	0
$246$	−1.67781e13	−1.18741
$247$	−1.30896e13	−0.905928
$248$	−1.20904e11	−0.00818385
$249$	−5.77905e12	−0.382613
$250$	0	0
$251$	5.10147e12	0.323214	0.161607	−	0.986855i	$-0.448332\pi$
$251$	5.10147e12	0.323214	0.161607	+	0.986855i	$0.448332\pi$
$252$	8.18253e12	0.507206
$253$	2.90190e13	1.76003
$254$	−1.14674e13	−0.680580
$255$	0	0
$256$	1.81712e13	1.03291
$257$	1.20976e13	0.673079	0.336539	−	0.941669i	$-0.390744\pi$
$257$	1.20976e13	0.673079	0.336539	+	0.941669i	$0.390744\pi$
$258$	4.84826e11	0.0264045
$259$	2.00526e13	1.06911
$260$	0	0
$261$	−1.00376e13	−0.512986
$262$	3.60167e13	1.80238
$263$	1.09431e13	0.536271	0.268135	−	0.963381i	$-0.413593\pi$
$263$	1.09431e13	0.536271	0.268135	+	0.963381i	$0.413593\pi$
$264$	5.97961e11	0.0286980
$265$	0	0
$266$	2.51439e13	1.15767
$267$	1.19245e13	0.537810
$268$	−1.13027e13	−0.499391
$269$	1.23621e13	0.535125	0.267562	−	0.963541i	$-0.413782\pi$
$269$	1.23621e13	0.535125	0.267562	+	0.963541i	$0.413782\pi$
$270$	0	0
$271$	1.34683e13	0.559734	0.279867	−	0.960039i	$-0.409710\pi$
$271$	1.34683e13	0.559734	0.279867	+	0.960039i	$0.409710\pi$
$272$	1.60690e13	0.654424
$273$	−1.65172e13	−0.659236
$274$	7.93424e10	0.00310368
$275$	0	0
$276$	1.72751e13	0.649263
$277$	−2.20976e13	−0.814153	−0.407077	−	0.913394i	$-0.633452\pi$
$277$	−2.20976e13	−0.814153	−0.407077	+	0.913394i	$0.633452\pi$
$278$	−2.98306e13	−1.07750
$279$	5.31724e12	0.188306
$280$	0	0
$281$	7.15247e12	0.243541	0.121770	−	0.992558i	$-0.461143\pi$
$281$	7.15247e12	0.243541	0.121770	+	0.992558i	$0.461143\pi$
$282$	2.17492e13	0.726229
$283$	9.90996e12	0.324524	0.162262	−	0.986748i	$-0.448121\pi$
$283$	9.90996e12	0.324524	0.162262	+	0.986748i	$0.448121\pi$
$284$	3.04476e13	0.977917
$285$	0	0
$286$	−8.49145e13	−2.62403
$287$	3.89729e13	1.18144
$288$	−2.59025e13	−0.770341
$289$	−2.00697e13	−0.585604
$290$	0	0
$291$	3.12057e13	0.876642
$292$	1.33788e13	0.368818
$293$	6.76585e13	1.83042	0.915209	−	0.402980i	$-0.132026\pi$
$293$	6.76585e13	1.83042	0.915209	+	0.402980i	$0.132026\pi$
$294$	−3.96203e12	−0.105198
$295$	0	0
$296$	−1.05416e12	−0.0269651
$297$	−7.43577e13	−1.86709
$298$	−6.71957e13	−1.65635
$299$	4.21386e13	1.01974
$300$	0	0
$301$	−1.12618e12	−0.0262718
$302$	−3.13103e13	−0.717213
$303$	9.43898e12	0.212320
$304$	−4.01252e13	−0.886364
$305$	0	0
$306$	−2.32800e13	−0.496038
$307$	2.76335e13	0.578328	0.289164	−	0.957280i	$-0.406623\pi$
$307$	2.76335e13	0.578328	0.289164	+	0.957280i	$0.406623\pi$
$308$	8.08617e13	1.66232
$309$	2.40575e13	0.485823
$310$	0	0
$311$	−1.21728e13	−0.237251	−0.118626	−	0.992939i	$-0.537849\pi$
$311$	−1.21728e13	−0.237251	−0.118626	+	0.992939i	$0.537849\pi$
$312$	8.68302e11	0.0166273
$313$	−8.17271e13	−1.53770	−0.768851	−	0.639428i	$-0.779171\pi$
$313$	−8.17271e13	−1.53770	−0.768851	+	0.639428i	$0.779171\pi$
$314$	3.93448e13	0.727402
$315$	0	0
$316$	−3.18089e13	−0.567897
$317$	−7.61714e13	−1.33649	−0.668246	−	0.743941i	$-0.732955\pi$
$317$	−7.61714e13	−1.33649	−0.668246	+	0.743941i	$0.732955\pi$
$318$	7.25697e13	1.25143
$319$	−9.91937e13	−1.68126
$320$	0	0
$321$	4.07200e13	0.666852
$322$	−8.09441e13	−1.30310
$323$	−3.54636e13	−0.561267
$324$	−9.69267e12	−0.150816
$325$	0	0
$326$	1.89425e13	0.284931
$327$	8.53338e13	1.26214
$328$	−2.04880e12	−0.0297984
$329$	−5.05201e13	−0.722581
$330$	0	0
$331$	8.05093e13	1.11376	0.556881	−	0.830592i	$-0.311998\pi$
$331$	8.05093e13	1.11376	0.556881	+	0.830592i	$0.311998\pi$
$332$	4.10830e13	0.558988
$333$	4.63608e13	0.620452
$334$	−1.61569e13	−0.212693
$335$	0	0
$336$	−5.06321e13	−0.645000
$337$	7.90669e13	0.990901	0.495451	−	0.868636i	$-0.335003\pi$
$337$	7.90669e13	0.990901	0.495451	+	0.868636i	$0.335003\pi$
$338$	−9.09176e12	−0.112100
$339$	−6.31279e13	−0.765813
$340$	0	0
$341$	5.25463e13	0.617153
$342$	5.81316e13	0.671844
$343$	9.21053e13	1.04753
$344$	5.92027e10	0.000662629 0
$345$	0	0
$346$	1.15067e14	1.24747
$347$	−1.40156e14	−1.49554	−0.747772	−	0.663956i	$-0.768876\pi$
$347$	−1.40156e14	−1.49554	−0.747772	+	0.663956i	$0.768876\pi$
$348$	−5.90504e13	−0.620207
$349$	−9.88347e13	−1.02181	−0.510905	−	0.859637i	$-0.670689\pi$
$349$	−9.88347e13	−1.02181	−0.510905	+	0.859637i	$0.670689\pi$
$350$	0	0
$351$	−1.07975e14	−1.08177
$352$	−2.55975e14	−2.52472
$353$	2.74254e13	0.266313	0.133156	−	0.991095i	$-0.457489\pi$
$353$	2.74254e13	0.266313	0.133156	+	0.991095i	$0.457489\pi$
$354$	1.44030e14	1.37701
$355$	0	0
$356$	−8.47708e13	−0.785726
$357$	−4.47499e13	−0.408429
$358$	−1.03891e14	−0.933733
$359$	1.57856e14	1.39715	0.698574	−	0.715538i	$-0.253818\pi$
$359$	1.57856e14	1.39715	0.698574	+	0.715538i	$0.253818\pi$
$360$	0	0
$361$	−2.79354e13	−0.239809
$362$	2.65132e14	2.24163
$363$	−1.79073e14	−1.49123
$364$	1.17420e14	0.963127
$365$	0	0
$366$	−3.74478e13	−0.298044
$367$	1.95534e14	1.53306	0.766529	−	0.642210i	$-0.221982\pi$
$367$	1.95534e14	1.53306	0.766529	+	0.642210i	$0.221982\pi$
$368$	1.29173e14	0.997717
$369$	9.01038e13	0.685643
$370$	0	0
$371$	−1.68568e14	−1.24514
$372$	3.12810e13	0.227664
$373$	−8.35940e13	−0.599482	−0.299741	−	0.954021i	$-0.596900\pi$
$373$	−8.35940e13	−0.599482	−0.299741	+	0.954021i	$0.596900\pi$
$374$	−2.30059e14	−1.62572
$375$	0	0
$376$	2.65583e12	0.0182249
$377$	−1.44040e14	−0.974102
$378$	2.07410e14	1.38237
$379$	2.81905e14	1.85177	0.925887	−	0.377802i	$-0.123320\pi$
$379$	2.81905e14	1.85177	0.925887	+	0.377802i	$0.123320\pi$
$380$	0	0
$381$	−5.09629e13	−0.325212
$382$	1.93482e14	1.21700
$383$	−2.51689e13	−0.156053	−0.0780264	−	0.996951i	$-0.524862\pi$
$383$	−2.51689e13	−0.156053	−0.0780264	+	0.996951i	$0.524862\pi$
$384$	5.23574e12	0.0320005
$385$	0	0
$386$	2.40512e14	1.42859
$387$	−2.60367e12	−0.0152467
$388$	−2.21840e14	−1.28075
$389$	−1.44036e14	−0.819879	−0.409939	−	0.912113i	$-0.634450\pi$
$389$	−1.44036e14	−0.819879	−0.409939	+	0.912113i	$0.634450\pi$
$390$	0	0
$391$	1.14166e14	0.631778
$392$	−4.83809e11	−0.00263998
$393$	1.60064e14	0.861261
$394$	−6.56916e13	−0.348563
$395$	0	0
$396$	1.86949e14	0.964716
$397$	−3.78848e13	−0.192804	−0.0964021	−	0.995342i	$-0.530733\pi$
$397$	−3.78848e13	−0.192804	−0.0964021	+	0.995342i	$0.530733\pi$
$398$	−7.28380e13	−0.365596
$399$	1.11743e14	0.553185
$400$	0	0
$401$	1.24111e13	0.0597747	0.0298874	−	0.999553i	$-0.490485\pi$
$401$	1.24111e13	0.0597747	0.0298874	+	0.999553i	$0.490485\pi$
$402$	−1.01325e14	−0.481363
$403$	7.63027e13	0.357571
$404$	−6.71012e13	−0.310194
$405$	0	0
$406$	2.76686e14	1.24478
$407$	4.58149e14	2.03347
$408$	2.35249e12	0.0103014
$409$	−4.37138e14	−1.88860	−0.944301	−	0.329082i	$-0.893261\pi$
$409$	−4.37138e14	−1.88860	−0.944301	+	0.329082i	$0.893261\pi$
$410$	0	0
$411$	3.52610e11	0.00148308
$412$	−1.71023e14	−0.709775
$413$	−3.34560e14	−1.37009
$414$	−1.87139e14	−0.756246
$415$	0	0
$416$	−3.71702e14	−1.46279
$417$	−1.32572e14	−0.514877
$418$	5.74470e14	2.20190
$419$	5.14822e14	1.94751	0.973755	−	0.227598i	$-0.0730871\pi$
$419$	5.14822e14	1.94751	0.973755	+	0.227598i	$0.0730871\pi$
$420$	0	0
$421$	−3.90682e14	−1.43970	−0.719850	−	0.694130i	$-0.755789\pi$
$421$	−3.90682e14	−1.43970	−0.719850	+	0.694130i	$0.755789\pi$
$422$	−4.43869e14	−1.61449
$423$	−1.16800e14	−0.419345
$424$	8.86159e12	0.0314050
$425$	0	0
$426$	2.72952e14	0.942612
$427$	8.69855e13	0.296547
$428$	−2.89476e14	−0.974254
$429$	−3.77373e14	−1.25388
$430$	0	0
$431$	−3.29050e14	−1.06571	−0.532853	−	0.846208i	$-0.678880\pi$
$431$	−3.29050e14	−1.06571	−0.532853	+	0.846208i	$0.678880\pi$
$432$	−3.30990e14	−1.05841
$433$	5.59793e14	1.76744	0.883718	−	0.468019i	$-0.155032\pi$
$433$	5.59793e14	1.76744	0.883718	+	0.468019i	$0.155032\pi$
$434$	−1.46570e14	−0.456932
$435$	0	0
$436$	−6.06634e14	−1.84396
$437$	−2.85079e14	−0.855693
$438$	1.19936e14	0.355503
$439$	1.25752e14	0.368095	0.184047	−	0.982917i	$-0.441080\pi$
$439$	1.25752e14	0.368095	0.184047	+	0.982917i	$0.441080\pi$
$440$	0	0
$441$	2.12774e13	0.0607443
$442$	−3.34069e14	−0.941920
$443$	−3.33211e14	−0.927894	−0.463947	−	0.885863i	$-0.653567\pi$
$443$	−3.33211e14	−0.927894	−0.463947	+	0.885863i	$0.653567\pi$
$444$	2.72738e14	0.750135
$445$	0	0
$446$	4.33616e14	1.16349
$447$	−2.98628e14	−0.791479
$448$	3.47880e14	0.910753
$449$	−1.08196e14	−0.279804	−0.139902	−	0.990165i	$-0.544679\pi$
$449$	−1.08196e14	−0.279804	−0.139902	+	0.990165i	$0.544679\pi$
$450$	0	0
$451$	8.90427e14	2.24713
$452$	4.48773e14	1.11883
$453$	−1.39148e14	−0.342717
$454$	5.10068e14	1.24114
$455$	0	0
$456$	−5.87431e12	−0.0139524
$457$	1.81057e14	0.424890	0.212445	−	0.977173i	$-0.431857\pi$
$457$	1.81057e14	0.424890	0.212445	+	0.977173i	$0.431857\pi$
$458$	−7.68728e14	−1.78243
$459$	−2.92537e14	−0.670210
$460$	0	0
$461$	−3.74610e14	−0.837962	−0.418981	−	0.907995i	$-0.637613\pi$
$461$	−3.74610e14	−0.837962	−0.418981	+	0.907995i	$0.637613\pi$
$462$	7.24897e14	1.60231
$463$	−2.33341e13	−0.0509678	−0.0254839	−	0.999675i	$-0.508113\pi$
$463$	−2.33341e13	−0.0509678	−0.0254839	+	0.999675i	$0.508113\pi$
$464$	−4.41542e14	−0.953067
$465$	0	0
$466$	−6.73896e14	−1.42060
$467$	7.37382e14	1.53621	0.768103	−	0.640326i	$-0.221201\pi$
$467$	7.37382e14	1.53621	0.768103	+	0.640326i	$0.221201\pi$
$468$	2.71469e14	0.558945
$469$	2.35362e14	0.478945
$470$	0	0
$471$	1.74854e14	0.347586
$472$	1.75877e13	0.0345564
$473$	−2.57301e13	−0.0499695
$474$	−2.85156e14	−0.547395
$475$	0	0
$476$	3.18125e14	0.596704
$477$	−3.89723e14	−0.722612
$478$	3.06747e14	0.562247
$479$	−3.39424e14	−0.615030	−0.307515	−	0.951543i	$-0.599497\pi$
$479$	−3.39424e14	−0.615030	−0.307515	+	0.951543i	$0.599497\pi$
$480$	0	0
$481$	6.65281e14	1.17817
$482$	8.26404e14	1.44688
$483$	−3.59728e14	−0.622680
$484$	1.27302e15	2.17865
$485$	0	0
$486$	7.89456e14	1.32077
$487$	3.27468e14	0.541700	0.270850	−	0.962622i	$-0.412695\pi$
$487$	3.27468e14	0.541700	0.270850	+	0.962622i	$0.412695\pi$
$488$	−4.57280e12	−0.00747952
$489$	8.41833e13	0.136153
$490$	0	0
$491$	−3.28187e14	−0.519006	−0.259503	−	0.965742i	$-0.583559\pi$
$491$	−3.28187e14	−0.519006	−0.259503	+	0.965742i	$0.583559\pi$
$492$	5.30075e14	0.828952
$493$	−3.90246e14	−0.603504
$494$	8.34191e14	1.27576
$495$	0	0
$496$	2.33900e14	0.349849
$497$	−6.34025e14	−0.937878
$498$	3.68294e14	0.538807
$499$	2.84812e14	0.412103	0.206052	−	0.978541i	$-0.433939\pi$
$499$	2.84812e14	0.412103	0.206052	+	0.978541i	$0.433939\pi$
$500$	0	0
$501$	−7.18038e13	−0.101634
$502$	−3.25112e14	−0.455159
$503$	2.01563e13	0.0279117	0.0139559	−	0.999903i	$-0.495558\pi$
$503$	2.01563e13	0.0279117	0.0139559	+	0.999903i	$0.495558\pi$
$504$	8.95729e12	0.0122690
$505$	0	0
$506$	−1.84936e15	−2.47852
$507$	−4.04052e13	−0.0535665
$508$	3.62292e14	0.475126
$509$	−6.91697e14	−0.897362	−0.448681	−	0.893692i	$-0.648106\pi$
$509$	−6.91697e14	−0.897362	−0.448681	+	0.893692i	$0.648106\pi$
$510$	0	0
$511$	−2.78594e14	−0.353717
$512$	−1.12018e15	−1.40703
$513$	7.30482e14	0.907746
$514$	−7.70969e14	−0.947850
$515$	0	0
$516$	−1.53172e13	−0.0184335
$517$	−1.15425e15	−1.37436
$518$	−1.27794e15	−1.50555
$519$	5.11374e14	0.596098
$520$	0	0
$521$	5.00013e14	0.570656	0.285328	−	0.958430i	$-0.407898\pi$
$521$	5.00013e14	0.570656	0.285328	+	0.958430i	$0.407898\pi$
$522$	6.39686e14	0.722403
$523$	2.89272e14	0.323256	0.161628	−	0.986852i	$-0.448326\pi$
$523$	2.89272e14	0.323256	0.161628	+	0.986852i	$0.448326\pi$
$524$	−1.13789e15	−1.25828
$525$	0	0
$526$	−6.97396e14	−0.755193
$527$	2.06727e14	0.221533
$528$	−1.15681e15	−1.22680
$529$	−3.50713e13	−0.0368083
$530$	0	0
$531$	−7.73490e14	−0.795123
$532$	−7.94377e14	−0.808188
$533$	1.29299e15	1.30196
$534$	−7.59940e14	−0.757360
$535$	0	0
$536$	−1.23729e13	−0.0120800
$537$	−4.61709e14	−0.446180
$538$	−7.87828e14	−0.753579
$539$	2.10268e14	0.199084
$540$	0	0
$541$	1.20798e15	1.12066	0.560331	−	0.828269i	$-0.310674\pi$
$541$	1.20798e15	1.12066	0.560331	+	0.828269i	$0.310674\pi$
$542$	−8.58325e14	−0.788235
$543$	1.17829e15	1.07115
$544$	−1.00705e15	−0.906271
$545$	0	0
$546$	1.05263e15	0.928356
$547$	1.74686e15	1.52521	0.762603	−	0.646867i	$-0.223921\pi$
$547$	1.74686e15	1.52521	0.762603	+	0.646867i	$0.223921\pi$
$548$	−2.50668e12	−0.00216674
$549$	2.01107e14	0.172099
$550$	0	0
$551$	9.74468e14	0.817398
$552$	1.89108e13	0.0157053
$553$	6.62373e14	0.544646
$554$	1.40826e15	1.14652
$555$	0	0
$556$	9.42447e14	0.752221
$557$	−8.14516e14	−0.643719	−0.321859	−	0.946787i	$-0.604308\pi$
$557$	−8.14516e14	−0.643719	−0.321859	+	0.946787i	$0.604308\pi$
$558$	−3.38864e14	−0.265178
$559$	−3.73628e13	−0.0289517
$560$	0	0
$561$	−1.02242e15	−0.776840
$562$	−4.55821e14	−0.342961
$563$	8.94179e14	0.666237	0.333118	−	0.942885i	$-0.391899\pi$
$563$	8.94179e14	0.666237	0.333118	+	0.942885i	$0.391899\pi$
$564$	−6.87129e14	−0.506994
$565$	0	0
$566$	−6.31554e14	−0.457004
$567$	2.01835e14	0.144641
$568$	3.33305e13	0.0236552
$569$	5.58478e14	0.392544	0.196272	−	0.980549i	$-0.437116\pi$
$569$	5.58478e14	0.392544	0.196272	+	0.980549i	$0.437116\pi$
$570$	0	0
$571$	1.19826e15	0.826136	0.413068	−	0.910700i	$-0.364457\pi$
$571$	1.19826e15	0.826136	0.413068	+	0.910700i	$0.364457\pi$
$572$	2.68273e15	1.83189
$573$	8.59863e14	0.581539
$574$	−2.48371e15	−1.66374
$575$	0	0
$576$	8.04284e14	0.528550
$577$	1.70453e15	1.10953	0.554764	−	0.832008i	$-0.312808\pi$
$577$	1.70453e15	1.10953	0.554764	+	0.832008i	$0.312808\pi$
$578$	1.27903e15	0.824665
$579$	1.06887e15	0.682643
$580$	0	0
$581$	−8.55491e14	−0.536101
$582$	−1.98872e15	−1.23451
$583$	−3.85134e15	−2.36829
$584$	1.46456e13	0.00892147
$585$	0	0
$586$	−4.31182e15	−2.57765
$587$	−8.77553e14	−0.519713	−0.259857	−	0.965647i	$-0.583675\pi$
$587$	−8.77553e14	−0.519713	−0.259857	+	0.965647i	$0.583675\pi$
$588$	1.25173e14	0.0734407
$589$	−5.16209e14	−0.300048
$590$	0	0
$591$	−2.91944e14	−0.166559
$592$	2.03937e15	1.15273
$593$	−3.16216e15	−1.77086	−0.885428	−	0.464776i	$-0.846135\pi$
$593$	−3.16216e15	−1.77086	−0.885428	+	0.464776i	$0.846135\pi$
$594$	4.73876e15	2.62930
$595$	0	0
$596$	2.12293e15	1.15633
$597$	−3.23704e14	−0.174698
$598$	−2.68546e15	−1.43603
$599$	1.86633e15	0.988873	0.494437	−	0.869214i	$-0.335374\pi$
$599$	1.86633e15	0.988873	0.494437	+	0.869214i	$0.335374\pi$
$600$	0	0
$601$	8.57728e14	0.446211	0.223105	−	0.974794i	$-0.428381\pi$
$601$	8.57728e14	0.446211	0.223105	+	0.974794i	$0.428381\pi$
$602$	7.17703e13	0.0369968
$603$	5.44147e14	0.277953
$604$	9.89193e14	0.500701
$605$	0	0
$606$	−6.01539e14	−0.298995
$607$	−2.90938e15	−1.43306	−0.716528	−	0.697558i	$-0.754270\pi$
$607$	−2.90938e15	−1.43306	−0.716528	+	0.697558i	$0.754270\pi$
$608$	2.51467e15	1.22747
$609$	1.22964e15	0.594814
$610$	0	0
$611$	−1.67609e15	−0.796289
$612$	7.35491e14	0.346294
$613$	3.95415e15	1.84510	0.922551	−	0.385875i	$-0.126100\pi$
$613$	3.95415e15	1.84510	0.922551	+	0.385875i	$0.126100\pi$
$614$	−1.76106e15	−0.814419
$615$	0	0
$616$	8.85181e13	0.0402104
$617$	1.44545e15	0.650778	0.325389	−	0.945580i	$-0.394505\pi$
$617$	1.44545e15	0.650778	0.325389	+	0.945580i	$0.394505\pi$
$618$	−1.53316e15	−0.684151
$619$	−4.27132e15	−1.88914	−0.944569	−	0.328314i	$-0.893519\pi$
$619$	−4.27132e15	−1.88914	−0.944569	+	0.328314i	$0.893519\pi$
$620$	0	0
$621$	−2.35160e15	−1.02178
$622$	7.75764e14	0.334105
$623$	1.76522e15	0.753556
$624$	−1.67981e15	−0.710794
$625$	0	0
$626$	5.20840e15	2.16544
$627$	2.55303e15	1.05217
$628$	−1.24303e15	−0.507813
$629$	1.80244e15	0.729933
$630$	0	0
$631$	2.19799e15	0.874711	0.437355	−	0.899289i	$-0.355915\pi$
$631$	2.19799e15	0.874711	0.437355	+	0.899289i	$0.355915\pi$
$632$	−3.48207e13	−0.0137371
$633$	−1.97262e15	−0.771478
$634$	4.85435e15	1.88209
$635$	0	0
$636$	−2.29272e15	−0.873647
$637$	3.05331e14	0.115347
$638$	6.32154e15	2.36760
$639$	−1.46584e15	−0.544292
$640$	0	0
$641$	−6.69744e14	−0.244450	−0.122225	−	0.992502i	$-0.539003\pi$
$641$	−6.69744e14	−0.244450	−0.122225	+	0.992502i	$0.539003\pi$
$642$	−2.59505e15	−0.939082
$643$	−3.43086e15	−1.23096	−0.615478	−	0.788154i	$-0.711037\pi$
$643$	−3.43086e15	−1.23096	−0.615478	+	0.788154i	$0.711037\pi$
$644$	2.55729e15	0.909720
$645$	0	0
$646$	2.26007e15	0.790393
$647$	2.12502e15	0.736869	0.368435	−	0.929654i	$-0.379894\pi$
$647$	2.12502e15	0.736869	0.368435	+	0.929654i	$0.379894\pi$
$648$	−1.06104e13	−0.00364813
$649$	−7.64381e15	−2.60594
$650$	0	0
$651$	−6.51380e14	−0.218343
$652$	−5.98455e14	−0.198916
$653$	−4.76025e15	−1.56894	−0.784471	−	0.620166i	$-0.787065\pi$
$653$	−4.76025e15	−1.56894	−0.784471	+	0.620166i	$0.787065\pi$
$654$	−5.43826e15	−1.77739
$655$	0	0
$656$	3.96357e15	1.27384
$657$	−6.44097e14	−0.205278
$658$	3.21961e15	1.01756
$659$	1.31734e15	0.412886	0.206443	−	0.978459i	$-0.433811\pi$
$659$	1.31734e15	0.412886	0.206443	+	0.978459i	$0.433811\pi$
$660$	0	0
$661$	−2.45528e15	−0.756822	−0.378411	−	0.925638i	$-0.623529\pi$
$661$	−2.45528e15	−0.756822	−0.378411	+	0.925638i	$0.623529\pi$
$662$	−5.13080e15	−1.56843
$663$	−1.48465e15	−0.450092
$664$	4.49729e13	0.0135215
$665$	0	0
$666$	−2.95454e15	−0.873739
$667$	−3.13705e15	−0.920087
$668$	5.10449e14	0.148485
$669$	1.92706e15	0.555969
$670$	0	0
$671$	1.98739e15	0.564038
$672$	3.17314e15	0.893220
$673$	8.60705e14	0.240310	0.120155	−	0.992755i	$-0.461661\pi$
$673$	8.60705e14	0.240310	0.120155	+	0.992755i	$0.461661\pi$
$674$	−5.03888e15	−1.39542
$675$	0	0
$676$	2.87238e14	0.0782593
$677$	−1.90003e15	−0.513479	−0.256739	−	0.966481i	$-0.582648\pi$
$677$	−1.90003e15	−0.513479	−0.256739	+	0.966481i	$0.582648\pi$
$678$	4.02309e15	1.07844
$679$	4.61948e15	1.22831
$680$	0	0
$681$	2.26682e15	0.593073
$682$	−3.34873e15	−0.869093
$683$	2.35084e15	0.605214	0.302607	−	0.953115i	$-0.402143\pi$
$683$	2.35084e15	0.605214	0.302607	+	0.953115i	$0.402143\pi$
$684$	−1.83657e15	−0.469027
$685$	0	0
$686$	−5.86980e15	−1.47516
$687$	−3.41635e15	−0.851726
$688$	−1.14533e14	−0.0283265
$689$	−5.59255e15	−1.37216
$690$	0	0
$691$	−6.60668e15	−1.59534	−0.797672	−	0.603092i	$-0.793935\pi$
$691$	−6.60668e15	−1.59534	−0.797672	+	0.603092i	$0.793935\pi$
$692$	−3.63533e15	−0.870884
$693$	−3.89293e15	−0.925217
$694$	8.93203e15	2.10607
$695$	0	0
$696$	−6.46416e13	−0.0150024
$697$	3.50310e15	0.806627
$698$	6.29866e15	1.43894
$699$	−2.99490e15	−0.678825
$700$	0	0
$701$	−8.01300e14	−0.178791	−0.0893956	−	0.995996i	$-0.528494\pi$
$701$	−8.01300e14	−0.178791	−0.0893956	+	0.995996i	$0.528494\pi$
$702$	6.88118e15	1.52338
$703$	−4.50081e15	−0.988636
$704$	7.94813e15	1.73227
$705$	0	0
$706$	−1.74780e15	−0.375030
$707$	1.39728e15	0.297493
$708$	−4.55039e15	−0.961315
$709$	4.10789e15	0.861121	0.430560	−	0.902562i	$-0.358316\pi$
$709$	4.10789e15	0.861121	0.430560	+	0.902562i	$0.358316\pi$
$710$	0	0
$711$	1.53138e15	0.316082
$712$	−9.27973e13	−0.0190062
$713$	1.66180e15	0.337743
$714$	2.85188e15	0.575162
$715$	0	0
$716$	3.28227e15	0.651857
$717$	1.36323e15	0.268667
$718$	−1.00601e16	−1.96751
$719$	2.12875e15	0.413157	0.206578	−	0.978430i	$-0.433767\pi$
$719$	2.12875e15	0.413157	0.206578	+	0.978430i	$0.433767\pi$
$720$	0	0
$721$	3.56130e15	0.680714
$722$	1.78030e15	0.337706
$723$	3.67267e15	0.691386
$724$	−8.37637e15	−1.56493
$725$	0	0
$726$	1.14122e16	2.10000
$727$	4.60450e15	0.840898	0.420449	−	0.907316i	$-0.361873\pi$
$727$	4.60450e15	0.840898	0.420449	+	0.907316i	$0.361873\pi$
$728$	1.28538e14	0.0232974
$729$	4.36126e15	0.784531
$730$	0	0
$731$	−1.01227e14	−0.0179370
$732$	1.18310e15	0.208070
$733$	3.94830e15	0.689190	0.344595	−	0.938752i	$-0.388016\pi$
$733$	3.94830e15	0.689190	0.344595	+	0.938752i	$0.388016\pi$
$734$	−1.24612e16	−2.15890
$735$	0	0
$736$	−8.09532e15	−1.38168
$737$	5.37739e15	0.910962
$738$	−5.74224e15	−0.965543
$739$	2.01640e15	0.336537	0.168269	−	0.985741i	$-0.446182\pi$
$739$	2.01640e15	0.336537	0.168269	+	0.985741i	$0.446182\pi$
$740$	0	0
$741$	3.70727e15	0.609613
$742$	1.07427e16	1.75345
$743$	7.15627e15	1.15944	0.579720	−	0.814816i	$-0.303162\pi$
$743$	7.15627e15	1.15944	0.579720	+	0.814816i	$0.303162\pi$
$744$	3.42428e13	0.00550704
$745$	0	0
$746$	5.32738e15	0.844209
$747$	−1.97786e15	−0.311123
$748$	7.26830e15	1.13494
$749$	6.02791e15	0.934365
$750$	0	0
$751$	−2.55257e14	−0.0389904	−0.0194952	−	0.999810i	$-0.506206\pi$
$751$	−2.55257e14	−0.0389904	−0.0194952	+	0.999810i	$0.506206\pi$
$752$	−5.13792e15	−0.779094
$753$	−1.44485e15	−0.217496
$754$	9.17953e15	1.37176
$755$	0	0
$756$	−6.55276e15	−0.965059
$757$	5.67357e15	0.829524	0.414762	−	0.909930i	$-0.363865\pi$
$757$	5.67357e15	0.829524	0.414762	+	0.909930i	$0.363865\pi$
$758$	−1.79656e16	−2.60772
$759$	−8.21883e15	−1.18435
$760$	0	0
$761$	8.59220e15	1.22036	0.610181	−	0.792262i	$-0.291097\pi$
$761$	8.59220e15	1.22036	0.610181	+	0.792262i	$0.291097\pi$
$762$	3.24782e15	0.457973
$763$	1.26322e16	1.76846
$764$	−6.11273e15	−0.849614
$765$	0	0
$766$	1.60400e15	0.219758
$767$	−1.10996e16	−1.50985
$768$	−5.14650e15	−0.695064
$769$	1.23682e16	1.65849	0.829243	−	0.558888i	$-0.188772\pi$
$769$	1.23682e16	1.65849	0.829243	+	0.558888i	$0.188772\pi$
$770$	0	0
$771$	−3.42630e15	−0.452925
$772$	−7.59856e15	−0.997324
$773$	−8.62674e15	−1.12424	−0.562120	−	0.827055i	$-0.690014\pi$
$773$	−8.62674e15	−1.12424	−0.562120	+	0.827055i	$0.690014\pi$
$774$	1.65930e14	0.0214709
$775$	0	0
$776$	−2.42845e14	−0.0309806
$777$	−5.67936e15	−0.719422
$778$	9.17933e15	1.15458
$779$	−8.74746e15	−1.09251
$780$	0	0
$781$	−1.44858e16	−1.78386
$782$	−7.27571e15	−0.889689
$783$	8.03831e15	0.976057
$784$	9.35970e14	0.112856
$785$	0	0
$786$	−1.02008e16	−1.21285
$787$	−1.18931e16	−1.40421	−0.702106	−	0.712073i	$-0.747757\pi$
$787$	−1.18931e16	−1.40421	−0.702106	+	0.712073i	$0.747757\pi$
$788$	2.07541e15	0.243338
$789$	−3.09933e15	−0.360865
$790$	0	0
$791$	−9.34502e15	−1.07302
$792$	2.04650e14	0.0233359
$793$	2.88589e15	0.326797
$794$	2.41437e15	0.271513
$795$	0	0
$796$	2.30119e15	0.255230
$797$	6.33100e15	0.697351	0.348676	−	0.937243i	$-0.386631\pi$
$797$	6.33100e15	0.697351	0.348676	+	0.937243i	$0.386631\pi$
$798$	−7.12131e15	−0.779012
$799$	−4.54103e15	−0.493340
$800$	0	0
$801$	4.08112e15	0.437322
$802$	−7.90952e14	−0.0841766
$803$	−6.36512e15	−0.672777
$804$	3.20118e15	0.336049
$805$	0	0
$806$	−4.86271e15	−0.503542
$807$	−3.50123e15	−0.360094
$808$	−7.34547e13	−0.00750339
$809$	1.06496e16	1.08048	0.540238	−	0.841512i	$-0.318334\pi$
$809$	1.06496e16	1.08048	0.540238	+	0.841512i	$0.318334\pi$
$810$	0	0
$811$	6.79444e15	0.680047	0.340024	−	0.940417i	$-0.389565\pi$
$811$	6.79444e15	0.680047	0.340024	+	0.940417i	$0.389565\pi$
$812$	−8.74141e15	−0.869008
$813$	−3.81453e15	−0.376654
$814$	−2.91975e16	−2.86359
$815$	0	0
$816$	−4.55109e15	−0.440372
$817$	2.52770e14	0.0242943
$818$	2.78585e16	2.65959
$819$	−5.65294e15	−0.536060
$820$	0	0
$821$	2.03099e16	1.90029	0.950145	−	0.311807i	$-0.100934\pi$
$821$	2.03099e16	1.90029	0.950145	+	0.311807i	$0.100934\pi$
$822$	−2.24715e13	−0.00208852
$823$	1.88821e15	0.174322	0.0871609	−	0.996194i	$-0.472221\pi$
$823$	1.88821e15	0.174322	0.0871609	+	0.996194i	$0.472221\pi$
$824$	−1.87217e14	−0.0171690
$825$	0	0
$826$	2.13213e16	1.92940
$827$	1.10204e16	0.990644	0.495322	−	0.868710i	$-0.335050\pi$
$827$	1.10204e16	0.990644	0.495322	+	0.868710i	$0.335050\pi$
$828$	5.91235e15	0.527950
$829$	−8.45180e15	−0.749720	−0.374860	−	0.927081i	$-0.622309\pi$
$829$	−8.45180e15	−0.749720	−0.374860	+	0.927081i	$0.622309\pi$
$830$	0	0
$831$	6.25854e15	0.547857
$832$	1.15415e16	1.00366
$833$	8.27233e14	0.0714629
$834$	8.44870e15	0.725065
$835$	0	0
$836$	−1.81494e16	−1.53719
$837$	−4.25817e15	−0.358288
$838$	−3.28092e16	−2.74254
$839$	5.30367e15	0.440439	0.220219	−	0.975450i	$-0.429323\pi$
$839$	5.30367e15	0.440439	0.220219	+	0.975450i	$0.429323\pi$
$840$	0	0
$841$	−1.47735e15	−0.121089
$842$	2.48979e16	2.02743
$843$	−2.02574e15	−0.163882
$844$	1.40233e16	1.12711
$845$	0	0
$846$	7.44359e15	0.590535
$847$	−2.65088e16	−2.08945
$848$	−1.71435e16	−1.34253
$849$	−2.80672e15	−0.218377
$850$	0	0
$851$	1.44892e16	1.11284
$852$	−8.62344e15	−0.658056
$853$	4.43767e15	0.336462	0.168231	−	0.985748i	$-0.446195\pi$
$853$	4.43767e15	0.336462	0.168231	+	0.985748i	$0.446195\pi$
$854$	−5.54352e15	−0.417607
$855$	0	0
$856$	−3.16885e14	−0.0235666
$857$	2.12803e16	1.57247	0.786236	−	0.617926i	$-0.212027\pi$
$857$	2.12803e16	1.57247	0.786236	+	0.617926i	$0.212027\pi$
$858$	2.40497e16	1.76575
$859$	−4.61602e15	−0.336748	−0.168374	−	0.985723i	$-0.553852\pi$
$859$	−4.61602e15	−0.336748	−0.168374	+	0.985723i	$0.553852\pi$
$860$	0	0
$861$	−1.10380e16	−0.795012
$862$	2.09701e16	1.50076
$863$	−6.10081e15	−0.433839	−0.216919	−	0.976190i	$-0.569601\pi$
$863$	−6.10081e15	−0.433839	−0.216919	+	0.976190i	$0.569601\pi$
$864$	2.07433e16	1.46573
$865$	0	0
$866$	−3.56752e16	−2.48896
$867$	5.68420e15	0.394062
$868$	4.63062e15	0.318993
$869$	1.51334e16	1.03593
$870$	0	0
$871$	7.80854e15	0.527800
$872$	−6.64073e14	−0.0446041
$873$	1.06800e16	0.712844
$874$	1.81679e16	1.20501
$875$	0	0
$876$	−3.78918e15	−0.248184
$877$	−9.32501e14	−0.0606948	−0.0303474	−	0.999539i	$-0.509661\pi$
$877$	−9.32501e14	−0.0606948	−0.0303474	+	0.999539i	$0.509661\pi$
$878$	−8.01407e15	−0.518362
$879$	−1.91624e16	−1.23172
$880$	0	0
$881$	−1.26049e16	−0.800150	−0.400075	−	0.916482i	$-0.631016\pi$
$881$	−1.26049e16	−0.800150	−0.400075	+	0.916482i	$0.631016\pi$
$882$	−1.35599e15	−0.0855420
$883$	−2.18236e16	−1.36818	−0.684090	−	0.729397i	$-0.739801\pi$
$883$	−2.18236e16	−1.36818	−0.684090	+	0.729397i	$0.739801\pi$
$884$	1.05543e16	0.657572
$885$	0	0
$886$	2.12353e16	1.30669
$887$	2.71175e16	1.65832	0.829162	−	0.559008i	$-0.188818\pi$
$887$	2.71175e16	1.65832	0.829162	+	0.559008i	$0.188818\pi$
$888$	2.98562e14	0.0181453
$889$	−7.54420e15	−0.455673
$890$	0	0
$891$	4.61140e15	0.275109
$892$	−1.36993e16	−0.812256
$893$	1.13392e16	0.668190
$894$	1.90313e16	1.11458
$895$	0	0
$896$	7.75064e14	0.0448377
$897$	−1.19346e16	−0.686198
$898$	6.89522e15	0.394029
$899$	−5.68042e15	−0.322628
$900$	0	0
$901$	−1.51519e16	−0.850119
$902$	−5.67463e16	−3.16447
$903$	3.18958e14	0.0176787
$904$	4.91265e14	0.0270638
$905$	0	0
$906$	8.86777e15	0.482624
$907$	−2.41689e16	−1.30742	−0.653712	−	0.756744i	$-0.726789\pi$
$907$	−2.41689e16	−1.30742	−0.653712	+	0.756744i	$0.726789\pi$
$908$	−1.61147e16	−0.866465
$909$	3.23046e15	0.172649
$910$	0	0
$911$	−2.08024e16	−1.09841	−0.549203	−	0.835689i	$-0.685069\pi$
$911$	−2.08024e16	−1.09841	−0.549203	+	0.835689i	$0.685069\pi$
$912$	1.13644e16	0.596449
$913$	−1.95457e16	−1.01967
$914$	−1.15386e16	−0.598342
$915$	0	0
$916$	2.42866e16	1.24435
$917$	2.36948e16	1.20676
$918$	1.86432e16	0.943810
$919$	−1.27606e16	−0.642151	−0.321076	−	0.947054i	$-0.604044\pi$
$919$	−1.27606e16	−0.642151	−0.321076	+	0.947054i	$0.604044\pi$
$920$	0	0
$921$	−7.82642e15	−0.389166
$922$	2.38736e16	1.18004
$923$	−2.10349e16	−1.03355
$924$	−2.29019e16	−1.11860
$925$	0	0
$926$	1.48707e15	0.0717744
$927$	8.23358e15	0.395048
$928$	2.76717e16	1.31984
$929$	2.66057e16	1.26150	0.630751	−	0.775985i	$-0.282747\pi$
$929$	2.66057e16	1.26150	0.630751	+	0.775985i	$0.282747\pi$
$930$	0	0
$931$	−2.06565e15	−0.0967908
$932$	2.12906e16	0.991745
$933$	3.44761e15	0.159650
$934$	−4.69928e16	−2.16333
$935$	0	0
$936$	2.97174e14	0.0135205
$937$	1.35312e16	0.612023	0.306012	−	0.952028i	$-0.401005\pi$
$937$	1.35312e16	0.612023	0.306012	+	0.952028i	$0.401005\pi$
$938$	−1.49994e16	−0.674465
$939$	2.31470e16	1.03474
$940$	0	0
$941$	2.75735e16	1.21829	0.609143	−	0.793061i	$-0.291514\pi$
$941$	2.75735e16	1.21829	0.609143	+	0.793061i	$0.291514\pi$
$942$	−1.11433e16	−0.489481
$943$	2.81602e16	1.22976
$944$	−3.40250e16	−1.47724
$945$	0	0
$946$	1.63976e15	0.0703686
$947$	−4.64018e16	−1.97975	−0.989873	−	0.141955i	$-0.954661\pi$
$947$	−4.64018e16	−1.97975	−0.989873	+	0.141955i	$0.954661\pi$
$948$	9.00900e15	0.382147
$949$	−9.24283e15	−0.389799
$950$	0	0
$951$	2.15735e16	0.899347
$952$	3.48246e14	0.0144339
$953$	−5.27189e15	−0.217248	−0.108624	−	0.994083i	$-0.534644\pi$
$953$	−5.27189e15	−0.217248	−0.108624	+	0.994083i	$0.534644\pi$
$954$	2.48367e16	1.01760
$955$	0	0
$956$	−9.69115e15	−0.392516
$957$	2.80939e16	1.13135
$958$	2.16312e16	0.866105
$959$	5.21979e13	0.00207803
$960$	0	0
$961$	−2.23994e16	−0.881571
$962$	−4.23978e16	−1.65913
$963$	1.39363e16	0.542253
$964$	−2.61088e16	−1.01010
$965$	0	0
$966$	2.29252e16	0.876877
$967$	−3.13722e16	−1.19316	−0.596581	−	0.802553i	$-0.703474\pi$
$967$	−3.13722e16	−1.19316	−0.596581	+	0.802553i	$0.703474\pi$
$968$	1.39356e15	0.0527001
$969$	1.00441e16	0.377686
$970$	0	0
$971$	−4.02261e16	−1.49555	−0.747776	−	0.663951i	$-0.768878\pi$
$971$	−4.02261e16	−1.49555	−0.747776	+	0.663951i	$0.768878\pi$
$972$	−2.49415e16	−0.922057
$973$	−1.96250e16	−0.721423
$974$	−2.08693e16	−0.762839
$975$	0	0
$976$	8.84648e15	0.319740
$977$	1.61108e16	0.579025	0.289513	−	0.957174i	$-0.406507\pi$
$977$	1.61108e16	0.579025	0.289513	+	0.957174i	$0.406507\pi$
$978$	−5.36494e15	−0.191735
$979$	4.03307e16	1.43328
$980$	0	0
$981$	2.92052e16	1.02631
$982$	2.09151e16	0.730880
$983$	3.39027e16	1.17812	0.589060	−	0.808089i	$-0.299498\pi$
$983$	3.39027e16	1.17812	0.589060	+	0.808089i	$0.299498\pi$
$984$	5.80265e14	0.0200518
$985$	0	0
$986$	2.48701e16	0.849873
$987$	1.43084e16	0.486236
$988$	−2.63548e16	−0.890629
$989$	−8.13727e14	−0.0273463
$990$	0	0
$991$	−4.18340e16	−1.39035	−0.695174	−	0.718841i	$-0.744673\pi$
$991$	−4.18340e16	−1.39035	−0.695174	+	0.718841i	$0.744673\pi$
$992$	−1.46586e16	−0.484484
$993$	−2.28021e16	−0.749468
$994$	4.04059e16	1.32075
$995$	0	0
$996$	−1.16356e16	−0.376152
$997$	−3.94947e16	−1.26974	−0.634871	−	0.772618i	$-0.718947\pi$
$997$	−3.94947e16	−1.26974	−0.634871	+	0.772618i	$0.718947\pi$
$998$	−1.81509e16	−0.580336
$999$	−3.71268e16	−1.18053

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.12.a.c.1.1		2
3.2	odd	2		225.12.a.h.1.2		2
5.2	odd	4		25.12.b.c.24.2		4
5.3	odd	4		25.12.b.c.24.3		4
5.4	even	2		5.12.a.b.1.2	✓	2
15.2	even	4		225.12.b.f.199.3		4
15.8	even	4		225.12.b.f.199.2		4
15.14	odd	2		45.12.a.d.1.1		2
20.19	odd	2		80.12.a.j.1.1		2
35.34	odd	2		245.12.a.b.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.12.a.b.1.2	✓	2	5.4	even	2
25.12.a.c.1.1		2	1.1	even	1	trivial
25.12.b.c.24.2		4	5.2	odd	4
25.12.b.c.24.3		4	5.3	odd	4
45.12.a.d.1.1		2	15.14	odd	2
80.12.a.j.1.1		2	20.19	odd	2
225.12.a.h.1.2		2	3.2	odd	2
225.12.b.f.199.2		4	15.8	even	4
225.12.b.f.199.3		4	15.2	even	4
245.12.a.b.1.2		2	35.34	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	25.a (trivial)

\(f(q)\)	\(=\)	\(q-63.7292 q^{2} -283.223 q^{3} +2013.42 q^{4} +18049.6 q^{6} -41926.3 q^{7} +2204.06 q^{8} -96932.0 q^{9} +O(q^{10})\)	\(q-63.7292 q^{2} -283.223 q^{3} +2013.42 q^{4} +18049.6 q^{6} -41926.3 q^{7} +2204.06 q^{8} -96932.0 q^{9} -957905. q^{11} -570245. q^{12} -1.39098e6 q^{13} +2.67193e6 q^{14} -4.26394e6 q^{16} -3.76857e6 q^{17} +6.17740e6 q^{18} +9.41036e6 q^{19} +1.18745e7 q^{21} +6.10466e7 q^{22} -3.02942e7 q^{23} -624238. q^{24} +8.86460e7 q^{26} +7.76254e7 q^{27} -8.44151e7 q^{28} +1.03553e8 q^{29} -5.48554e7 q^{31} +2.67224e8 q^{32} +2.71300e8 q^{33} +2.40168e8 q^{34} -1.95164e8 q^{36} -4.78282e8 q^{37} -5.99715e8 q^{38} +3.93957e8 q^{39} -9.29557e8 q^{41} -7.56752e8 q^{42} +2.68608e7 q^{43} -1.92866e9 q^{44} +1.93063e9 q^{46} +1.20497e9 q^{47} +1.20764e9 q^{48} -2.19508e8 q^{49} +1.06735e9 q^{51} -2.80062e9 q^{52} +4.02058e9 q^{53} -4.94700e9 q^{54} -9.24080e7 q^{56} -2.66523e9 q^{57} -6.59933e9 q^{58} +7.97972e9 q^{59} -2.07472e9 q^{61} +3.49589e9 q^{62} +4.06400e9 q^{63} -8.29741e9 q^{64} -1.72898e10 q^{66} -5.61370e9 q^{67} -7.58770e9 q^{68} +8.58000e9 q^{69} +1.51224e10 q^{71} -2.13643e8 q^{72} +6.64484e9 q^{73} +3.04806e10 q^{74} +1.89470e10 q^{76} +4.01615e10 q^{77} -2.51066e10 q^{78} -1.57985e10 q^{79} -4.81405e9 q^{81} +5.92399e10 q^{82} +2.04046e10 q^{83} +2.39083e10 q^{84} -1.71182e9 q^{86} -2.93285e10 q^{87} -2.11128e9 q^{88} -4.21030e10 q^{89} +5.83187e10 q^{91} -6.09948e10 q^{92} +1.55363e10 q^{93} -7.67919e10 q^{94} -7.56837e10 q^{96} -1.10181e11 q^{97} +1.39891e10 q^{98} +9.28516e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 20 q^{2} + 220 q^{3} + 6976 q^{4} + 60184 q^{6} - 57900 q^{7} + 246240 q^{8} - 20846 q^{9}+O(q^{10}) \) 2 * q + 20 * q^2 + 220 * q^3 + 6976 * q^4 + 60184 * q^6 - 57900 * q^7 + 246240 * q^8 - 20846 * q^9	\( 2 q + 20 q^{2} + 220 q^{3} + 6976 q^{4} + 60184 q^{6} - 57900 q^{7} + 246240 q^{8} - 20846 q^{9} - 618176 q^{11} + 1927040 q^{12} - 3414260 q^{13} + 1334472 q^{14} + 6005632 q^{16} - 1317940 q^{17} + 12548020 q^{18} + 5325320 q^{19} + 3836184 q^{21} + 89491840 q^{22} - 58943940 q^{23} + 122180160 q^{24} - 80761736 q^{26} + 26769160 q^{27} - 163685760 q^{28} + 94140380 q^{29} + 244543464 q^{31} + 627301120 q^{32} + 442259840 q^{33} + 445358072 q^{34} + 182418752 q^{36} - 21003220 q^{37} - 941752240 q^{38} - 624203992 q^{39} - 745743316 q^{41} - 1429793040 q^{42} - 629950100 q^{43} - 242725888 q^{44} - 468194856 q^{46} + 1402061540 q^{47} + 6375522560 q^{48} - 1941677414 q^{49} + 2300559784 q^{51} - 12841321600 q^{52} - 1138320580 q^{53} - 9205154480 q^{54} - 3990553920 q^{56} - 4720910480 q^{57} - 7387417960 q^{58} + 7317515560 q^{59} - 1516425676 q^{61} + 28564327440 q^{62} + 2848632180 q^{63} + 819531776 q^{64} - 2975464192 q^{66} - 15734290140 q^{67} + 4573774720 q^{68} - 5837195832 q^{69} + 32938471544 q^{71} + 18354067680 q^{72} + 29982848860 q^{73} + 68768198072 q^{74} - 1325392640 q^{76} + 34734748800 q^{77} - 110356370800 q^{78} - 3302823120 q^{79} - 43884431798 q^{81} + 74630515640 q^{82} - 13299102420 q^{83} - 15982487808 q^{84} - 56706093896 q^{86} - 34064940920 q^{87} + 80794874880 q^{88} - 12674770860 q^{89} + 90637859064 q^{91} - 203171571840 q^{92} + 166200542640 q^{93} - 60289765528 q^{94} + 105515416064 q^{96} + 3080703740 q^{97} - 130206802940 q^{98} + 118700272448 q^{99}+O(q^{100}) \) 2 * q + 20 * q^2 + 220 * q^3 + 6976 * q^4 + 60184 * q^6 - 57900 * q^7 + 246240 * q^8 - 20846 * q^9 - 618176 * q^11 + 1927040 * q^12 - 3414260 * q^13 + 1334472 * q^14 + 6005632 * q^16 - 1317940 * q^17 + 12548020 * q^18 + 5325320 * q^19 + 3836184 * q^21 + 89491840 * q^22 - 58943940 * q^23 + 122180160 * q^24 - 80761736 * q^26 + 26769160 * q^27 - 163685760 * q^28 + 94140380 * q^29 + 244543464 * q^31 + 627301120 * q^32 + 442259840 * q^33 + 445358072 * q^34 + 182418752 * q^36 - 21003220 * q^37 - 941752240 * q^38 - 624203992 * q^39 - 745743316 * q^41 - 1429793040 * q^42 - 629950100 * q^43 - 242725888 * q^44 - 468194856 * q^46 + 1402061540 * q^47 + 6375522560 * q^48 - 1941677414 * q^49 + 2300559784 * q^51 - 12841321600 * q^52 - 1138320580 * q^53 - 9205154480 * q^54 - 3990553920 * q^56 - 4720910480 * q^57 - 7387417960 * q^58 + 7317515560 * q^59 - 1516425676 * q^61 + 28564327440 * q^62 + 2848632180 * q^63 + 819531776 * q^64 - 2975464192 * q^66 - 15734290140 * q^67 + 4573774720 * q^68 - 5837195832 * q^69 + 32938471544 * q^71 + 18354067680 * q^72 + 29982848860 * q^73 + 68768198072 * q^74 - 1325392640 * q^76 + 34734748800 * q^77 - 110356370800 * q^78 - 3302823120 * q^79 - 43884431798 * q^81 + 74630515640 * q^82 - 13299102420 * q^83 - 15982487808 * q^84 - 56706093896 * q^86 - 34064940920 * q^87 + 80794874880 * q^88 - 12674770860 * q^89 + 90637859064 * q^91 - 203171571840 * q^92 + 166200542640 * q^93 - 60289765528 * q^94 + 105515416064 * q^96 + 3080703740 * q^97 - 130206802940 * q^98 + 118700272448 * q^99

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