LMFDB - Embedded newform 75.12.a.k.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,12,Mod(1,75)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(75, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 12, names="a")

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

chi := DirichletCharacter("75.1");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	75.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:	$57.6257385420$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} - 10212x^{4} - 7696x^{3} + 23447760x^{2} - 17883600x - 4555384000 $ x^6 - 3x^5 - 10212x^4 - 7696x^3 + 23447760x^2 - 17883600*x - 4555384000
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{4}\cdot 5^{6} $
Twist minimal:	no (minimal twist has level 15)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-78.4116$ of defining polynomial
Character	$\chi$	$=$	75.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+80.4116 q^{2} +243.000 q^{3} +4418.02 q^{4} +19540.0 q^{6} -53961.2 q^{7} +190577. q^{8} +59049.0 q^{9} +O(q^{10})$	\(q+80.4116 q^{2} +243.000 q^{3} +4418.02 q^{4} +19540.0 q^{6} -53961.2 q^{7} +190577. q^{8} +59049.0 q^{9} +407363. q^{11} +1.07358e6 q^{12} +1.39099e6 q^{13} -4.33911e6 q^{14} +6.27650e6 q^{16} +5.58145e6 q^{17} +4.74822e6 q^{18} +7.86560e6 q^{19} -1.31126e7 q^{21} +3.27567e7 q^{22} +6.07110e7 q^{23} +4.63102e7 q^{24} +1.11851e8 q^{26} +1.43489e7 q^{27} -2.38402e8 q^{28} +1.28534e8 q^{29} +1.16298e7 q^{31} +1.14401e8 q^{32} +9.89893e7 q^{33} +4.48813e8 q^{34} +2.60880e8 q^{36} -6.65198e8 q^{37} +6.32485e8 q^{38} +3.38010e8 q^{39} -1.25903e9 q^{41} -1.05440e9 q^{42} -8.69795e8 q^{43} +1.79974e9 q^{44} +4.88187e9 q^{46} +1.80829e8 q^{47} +1.52519e9 q^{48} +9.34486e8 q^{49} +1.35629e9 q^{51} +6.14541e9 q^{52} -9.98407e8 q^{53} +1.15382e9 q^{54} -1.02838e10 q^{56} +1.91134e9 q^{57} +1.03356e10 q^{58} -2.77404e9 q^{59} -6.22509e9 q^{61} +9.35170e8 q^{62} -3.18636e9 q^{63} -3.65509e9 q^{64} +7.95988e9 q^{66} +6.07983e9 q^{67} +2.46590e10 q^{68} +1.47528e10 q^{69} -3.98266e9 q^{71} +1.12534e10 q^{72} -1.70412e10 q^{73} -5.34896e10 q^{74} +3.47504e10 q^{76} -2.19818e10 q^{77} +2.71799e10 q^{78} -1.16813e10 q^{79} +3.48678e9 q^{81} -1.01241e11 q^{82} +1.63167e10 q^{83} -5.79316e10 q^{84} -6.99416e10 q^{86} +3.12337e10 q^{87} +7.76341e10 q^{88} +1.50572e10 q^{89} -7.50593e10 q^{91} +2.68222e11 q^{92} +2.82604e9 q^{93} +1.45408e10 q^{94} +2.77995e10 q^{96} -1.83308e10 q^{97} +7.51435e10 q^{98} +2.40544e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 9 q^{2} + 1458 q^{3} + 8157 q^{4} + 2187 q^{6} + 64368 q^{7} - 29277 q^{8} + 354294 q^{9}+O(q^{10}) $ 6 * q + 9 * q^2 + 1458 * q^3 + 8157 * q^4 + 2187 * q^6 + 64368 * q^7 - 29277 * q^8 + 354294 * q^9	\( 6 q + 9 q^{2} + 1458 q^{3} + 8157 q^{4} + 2187 q^{6} + 64368 q^{7} - 29277 q^{8} + 354294 q^{9} - 160776 q^{11} + 1982151 q^{12} + 1777464 q^{13} - 2318022 q^{14} + 14360865 q^{16} + 7789536 q^{17} + 531441 q^{18} + 14306328 q^{19} + 15641424 q^{21} + 99540522 q^{22} + 56578896 q^{23} - 7114311 q^{24} + 156248982 q^{26} + 86093442 q^{27} + 29296674 q^{28} + 229450716 q^{29} + 419037696 q^{31} - 496142397 q^{32} - 39068568 q^{33} + 272636394 q^{34} + 481662693 q^{36} - 441738792 q^{37} + 99095256 q^{38} + 431923752 q^{39} - 1880639244 q^{41} - 563279346 q^{42} + 1081616760 q^{43} - 3162393414 q^{44} - 939739884 q^{46} + 1868657040 q^{47} + 3489690195 q^{48} + 511947750 q^{49} + 1892857248 q^{51} + 9215549766 q^{52} + 10349483256 q^{53} + 129140163 q^{54} - 21606208290 q^{56} + 3476437704 q^{57} + 25240036752 q^{58} - 707714568 q^{59} + 8985508380 q^{61} + 25995031416 q^{62} + 3800866032 q^{63} + 4944042873 q^{64} + 24188346846 q^{66} + 13687306776 q^{67} + 94791079962 q^{68} + 13748671728 q^{69} - 8562874608 q^{71} - 1728777573 q^{72} + 63672451056 q^{73} - 44262217422 q^{74} + 69695921208 q^{76} - 10135567584 q^{77} + 37968502626 q^{78} + 41427333360 q^{79} + 20920706406 q^{81} + 34598023506 q^{82} + 124949795688 q^{83} + 7119091782 q^{84} - 18826696116 q^{86} + 55756523988 q^{87} + 430278178518 q^{88} + 90885005748 q^{89} - 48271166064 q^{91} + 310396941828 q^{92} + 101826160128 q^{93} - 139084157808 q^{94} - 120562602471 q^{96} + 257134073616 q^{97} + 405310493781 q^{98} - 9493662024 q^{99}+O(q^{100}) \) 6 * q + 9 * q^2 + 1458 * q^3 + 8157 * q^4 + 2187 * q^6 + 64368 * q^7 - 29277 * q^8 + 354294 * q^9 - 160776 * q^11 + 1982151 * q^12 + 1777464 * q^13 - 2318022 * q^14 + 14360865 * q^16 + 7789536 * q^17 + 531441 * q^18 + 14306328 * q^19 + 15641424 * q^21 + 99540522 * q^22 + 56578896 * q^23 - 7114311 * q^24 + 156248982 * q^26 + 86093442 * q^27 + 29296674 * q^28 + 229450716 * q^29 + 419037696 * q^31 - 496142397 * q^32 - 39068568 * q^33 + 272636394 * q^34 + 481662693 * q^36 - 441738792 * q^37 + 99095256 * q^38 + 431923752 * q^39 - 1880639244 * q^41 - 563279346 * q^42 + 1081616760 * q^43 - 3162393414 * q^44 - 939739884 * q^46 + 1868657040 * q^47 + 3489690195 * q^48 + 511947750 * q^49 + 1892857248 * q^51 + 9215549766 * q^52 + 10349483256 * q^53 + 129140163 * q^54 - 21606208290 * q^56 + 3476437704 * q^57 + 25240036752 * q^58 - 707714568 * q^59 + 8985508380 * q^61 + 25995031416 * q^62 + 3800866032 * q^63 + 4944042873 * q^64 + 24188346846 * q^66 + 13687306776 * q^67 + 94791079962 * q^68 + 13748671728 * q^69 - 8562874608 * q^71 - 1728777573 * q^72 + 63672451056 * q^73 - 44262217422 * q^74 + 69695921208 * q^76 - 10135567584 * q^77 + 37968502626 * q^78 + 41427333360 * q^79 + 20920706406 * q^81 + 34598023506 * q^82 + 124949795688 * q^83 + 7119091782 * q^84 - 18826696116 * q^86 + 55756523988 * q^87 + 430278178518 * q^88 + 90885005748 * q^89 - 48271166064 * q^91 + 310396941828 * q^92 + 101826160128 * q^93 - 139084157808 * q^94 - 120562602471 * q^96 + 257134073616 * q^97 + 405310493781 * q^98 - 9493662024 * 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 $

$2$	80.4116	1.77686	0.888431	−	0.459011i	$-0.151796\pi$
$2$	80.4116	1.77686	0.888431	+	0.459011i	$0.151796\pi$
$3$	243.000	0.577350
$3$	243.000	0.577350
$4$	4418.02	2.15724
$5$	0	0
$5$	0	0
$6$	19540.0	1.02587
$7$	−53961.2	−1.21351	−0.606754	−	0.794890i	$-0.707529\pi$
$7$	−53961.2	−1.21351	−0.606754	+	0.794890i	$0.707529\pi$
$8$	190577.	2.05625
$9$	59049.0	0.333333
$10$	0	0
$11$	407363.	0.762644	0.381322	−	0.924442i	$-0.375469\pi$
$11$	407363.	0.762644	0.381322	+	0.924442i	$0.375469\pi$
$12$	1.07358e6	1.24548
$13$	1.39099e6	1.03905	0.519523	−	0.854457i	$-0.326110\pi$
$13$	1.39099e6	1.03905	0.519523	+	0.854457i	$0.326110\pi$
$14$	−4.33911e6	−2.15623
$15$	0	0
$16$	6.27650e6	1.49643
$17$	5.58145e6	0.953406	0.476703	−	0.879064i	$-0.341832\pi$
$17$	5.58145e6	0.953406	0.476703	+	0.879064i	$0.341832\pi$
$18$	4.74822e6	0.592287
$19$	7.86560e6	0.728764	0.364382	−	0.931250i	$-0.381280\pi$
$19$	7.86560e6	0.728764	0.364382	+	0.931250i	$0.381280\pi$
$20$	0	0
$21$	−1.31126e7	−0.700619
$22$	3.27567e7	1.35511
$23$	6.07110e7	1.96682	0.983409	−	0.181403i	$-0.0580638\pi$
$23$	6.07110e7	1.96682	0.983409	+	0.181403i	$0.0580638\pi$
$24$	4.63102e7	1.18718
$25$	0	0
$26$	1.11851e8	1.84624
$27$	1.43489e7	0.192450
$28$	−2.38402e8	−2.61782
$29$	1.28534e8	1.16366	0.581832	−	0.813309i	$-0.302336\pi$
$29$	1.28534e8	1.16366	0.581832	+	0.813309i	$0.302336\pi$
$30$	0	0
$31$	1.16298e7	0.0729596	0.0364798	−	0.999334i	$-0.488386\pi$
$31$	1.16298e7	0.0729596	0.0364798	+	0.999334i	$0.488386\pi$
$32$	1.14401e8	0.602706
$33$	9.89893e7	0.440313
$34$	4.48813e8	1.69407
$35$	0	0
$36$	2.60880e8	0.719079
$37$	−6.65198e8	−1.57703	−0.788517	−	0.615012i	$-0.789151\pi$
$37$	−6.65198e8	−1.57703	−0.788517	+	0.615012i	$0.789151\pi$
$38$	6.32485e8	1.29491
$39$	3.38010e8	0.599893
$40$	0	0
$41$	−1.25903e9	−1.69717	−0.848586	−	0.529058i	$-0.822546\pi$
$41$	−1.25903e9	−1.69717	−0.848586	+	0.529058i	$0.822546\pi$
$42$	−1.05440e9	−1.24490
$43$	−8.69795e8	−0.902278	−0.451139	−	0.892454i	$-0.648982\pi$
$43$	−8.69795e8	−0.902278	−0.451139	+	0.892454i	$0.648982\pi$
$44$	1.79974e9	1.64520
$45$	0	0
$46$	4.88187e9	3.49476
$47$	1.80829e8	0.115009	0.0575044	−	0.998345i	$-0.481686\pi$
$47$	1.80829e8	0.115009	0.0575044	+	0.998345i	$0.481686\pi$
$48$	1.52519e9	0.863966
$49$	9.34486e8	0.472601
$50$	0	0
$51$	1.35629e9	0.550449
$52$	6.14541e9	2.24147
$53$	−9.98407e8	−0.327937	−0.163968	−	0.986466i	$-0.552430\pi$
$53$	−9.98407e8	−0.327937	−0.163968	+	0.986466i	$0.552430\pi$
$54$	1.15382e9	0.341957
$55$	0	0
$56$	−1.02838e10	−2.49527
$57$	1.91134e9	0.420752
$58$	1.03356e10	2.06767
$59$	−2.77404e9	−0.505157	−0.252579	−	0.967576i	$-0.581279\pi$
$59$	−2.77404e9	−0.505157	−0.252579	+	0.967576i	$0.581279\pi$
$60$	0	0
$61$	−6.22509e9	−0.943694	−0.471847	−	0.881680i	$-0.656413\pi$
$61$	−6.22509e9	−0.943694	−0.471847	+	0.881680i	$0.656413\pi$
$62$	9.35170e8	0.129639
$63$	−3.18636e9	−0.404503
$64$	−3.65509e9	−0.425509
$65$	0	0
$66$	7.95988e9	0.782375
$67$	6.07983e9	0.550148	0.275074	−	0.961423i	$-0.411298\pi$
$67$	6.07983e9	0.550148	0.275074	+	0.961423i	$0.411298\pi$
$68$	2.46590e10	2.05672
$69$	1.47528e10	1.13554
$70$	0	0
$71$	−3.98266e9	−0.261971	−0.130985	−	0.991384i	$-0.541814\pi$
$71$	−3.98266e9	−0.261971	−0.130985	+	0.991384i	$0.541814\pi$
$72$	1.12534e10	0.685416
$73$	−1.70412e10	−0.962111	−0.481056	−	0.876690i	$-0.659746\pi$
$73$	−1.70412e10	−0.962111	−0.481056	+	0.876690i	$0.659746\pi$
$74$	−5.34896e10	−2.80217
$75$	0	0
$76$	3.47504e10	1.57212
$77$	−2.19818e10	−0.925475
$78$	2.71799e10	1.06593
$79$	−1.16813e10	−0.427111	−0.213556	−	0.976931i	$-0.568504\pi$
$79$	−1.16813e10	−0.427111	−0.213556	+	0.976931i	$0.568504\pi$
$80$	0	0
$81$	3.48678e9	0.111111
$82$	−1.01241e11	−3.01564
$83$	1.63167e10	0.454676	0.227338	−	0.973816i	$-0.426998\pi$
$83$	1.63167e10	0.454676	0.227338	+	0.973816i	$0.426998\pi$
$84$	−5.79316e10	−1.51140
$85$	0	0
$86$	−6.99416e10	−1.60322
$87$	3.12337e10	0.671842
$88$	7.76341e10	1.56819
$89$	1.50572e10	0.285825	0.142912	−	0.989735i	$-0.454353\pi$
$89$	1.50572e10	0.285825	0.142912	+	0.989735i	$0.454353\pi$
$90$	0	0
$91$	−7.50593e10	−1.26089
$92$	2.68222e11	4.24289
$93$	2.82604e9	0.0421233
$94$	1.45408e10	0.204355
$95$	0	0
$96$	2.77995e10	0.347972
$97$	−1.83308e10	−0.216739	−0.108370	−	0.994111i	$-0.534563\pi$
$97$	−1.83308e10	−0.216739	−0.108370	+	0.994111i	$0.534563\pi$
$98$	7.51435e10	0.839746
$99$	2.40544e10	0.254215
$100$	0	0
$101$	1.64893e11	1.56111	0.780556	−	0.625086i	$-0.214936\pi$
$101$	1.64893e11	1.56111	0.780556	+	0.625086i	$0.214936\pi$
$102$	1.09062e11	0.978072
$103$	4.64555e10	0.394851	0.197425	−	0.980318i	$-0.436742\pi$
$103$	4.64555e10	0.394851	0.197425	+	0.980318i	$0.436742\pi$
$104$	2.65090e11	2.13654
$105$	0	0
$106$	−8.02835e10	−0.582699
$107$	7.27211e10	0.501245	0.250622	−	0.968085i	$-0.419365\pi$
$107$	7.27211e10	0.501245	0.250622	+	0.968085i	$0.419365\pi$
$108$	6.33938e10	0.415160
$109$	1.48205e11	0.922608	0.461304	−	0.887242i	$-0.347382\pi$
$109$	1.48205e11	0.922608	0.461304	+	0.887242i	$0.347382\pi$
$110$	0	0
$111$	−1.61643e11	−0.910502
$112$	−3.38687e11	−1.81593
$113$	2.08519e11	1.06467	0.532335	−	0.846534i	$-0.321315\pi$
$113$	2.08519e11	1.06467	0.532335	+	0.846534i	$0.321315\pi$
$114$	1.53694e11	0.747618
$115$	0	0
$116$	5.67864e11	2.51030
$117$	8.21364e10	0.346349
$118$	−2.23065e11	−0.897595
$119$	−3.01182e11	−1.15697
$120$	0	0
$121$	−1.19367e11	−0.418373
$122$	−5.00569e11	−1.67681
$123$	−3.05945e11	−0.979863
$124$	5.13806e10	0.157391
$125$	0	0
$126$	−2.56220e11	−0.718745
$127$	−4.90810e11	−1.31824	−0.659118	−	0.752040i	$-0.729070\pi$
$127$	−4.90810e11	−1.31824	−0.659118	+	0.752040i	$0.729070\pi$
$128$	−5.28205e11	−1.35878
$129$	−2.11360e11	−0.520930
$130$	0	0
$131$	−4.67254e10	−0.105818	−0.0529091	−	0.998599i	$-0.516849\pi$
$131$	−4.67254e10	−0.105818	−0.0529091	+	0.998599i	$0.516849\pi$
$132$	4.37337e11	0.949859
$133$	−4.24437e11	−0.884360
$134$	4.88889e11	0.977538
$135$	0	0
$136$	1.06370e12	1.96044
$137$	4.73733e11	0.838631	0.419315	−	0.907841i	$-0.362270\pi$
$137$	4.73733e11	0.838631	0.419315	+	0.907841i	$0.362270\pi$
$138$	1.18629e12	2.01770
$139$	−8.01917e10	−0.131084	−0.0655418	−	0.997850i	$-0.520878\pi$
$139$	−8.01917e10	−0.131084	−0.0655418	+	0.997850i	$0.520878\pi$
$140$	0	0
$141$	4.39415e10	0.0664003
$142$	−3.20252e11	−0.465486
$143$	5.66637e11	0.792422
$144$	3.70621e11	0.498811
$145$	0	0
$146$	−1.37031e12	−1.70954
$147$	2.27080e11	0.272856
$148$	−2.93886e12	−3.40204
$149$	−5.19630e11	−0.579655	−0.289828	−	0.957079i	$-0.593598\pi$
$149$	−5.19630e11	−0.579655	−0.289828	+	0.957079i	$0.593598\pi$
$150$	0	0
$151$	−1.48939e12	−1.54396	−0.771981	−	0.635645i	$-0.780734\pi$
$151$	−1.48939e12	−1.54396	−0.771981	+	0.635645i	$0.780734\pi$
$152$	1.49900e12	1.49852
$153$	3.29579e11	0.317802
$154$	−1.76759e12	−1.64444
$155$	0	0
$156$	1.49333e12	1.29411
$157$	−1.26118e12	−1.05519	−0.527595	−	0.849496i	$-0.676906\pi$
$157$	−1.26118e12	−1.05519	−0.527595	+	0.849496i	$0.676906\pi$
$158$	−9.39309e11	−0.758918
$159$	−2.42613e11	−0.189334
$160$	0	0
$161$	−3.27604e12	−2.38675
$162$	2.80378e11	0.197429
$163$	1.03561e12	0.704961	0.352481	−	0.935819i	$-0.385338\pi$
$163$	1.03561e12	0.704961	0.352481	+	0.935819i	$0.385338\pi$
$164$	−5.56243e12	−3.66120
$165$	0	0
$166$	1.31205e12	0.807897
$167$	5.24371e11	0.312391	0.156195	−	0.987726i	$-0.450077\pi$
$167$	5.24371e11	0.312391	0.156195	+	0.987726i	$0.450077\pi$
$168$	−2.49896e12	−1.44065
$169$	1.42684e11	0.0796158
$170$	0	0
$171$	4.64456e11	0.242921
$172$	−3.84277e12	−1.94643
$173$	−9.08960e11	−0.445955	−0.222978	−	0.974824i	$-0.571578\pi$
$173$	−9.08960e11	−0.445955	−0.222978	+	0.974824i	$0.571578\pi$
$174$	2.51155e12	1.19377
$175$	0	0
$176$	2.55681e12	1.14125
$177$	−6.74092e11	−0.291653
$178$	1.21078e12	0.507871
$179$	1.12298e12	0.456753	0.228376	−	0.973573i	$-0.426658\pi$
$179$	1.12298e12	0.456753	0.228376	+	0.973573i	$0.426658\pi$
$180$	0	0
$181$	1.20890e12	0.462549	0.231274	−	0.972889i	$-0.425711\pi$
$181$	1.20890e12	0.462549	0.231274	+	0.972889i	$0.425711\pi$
$182$	−6.03564e12	−2.24043
$183$	−1.51270e12	−0.544842
$184$	1.15701e13	4.04427
$185$	0	0
$186$	2.27246e11	0.0748472
$187$	2.27368e12	0.727110
$188$	7.98908e11	0.248101
$189$	−7.74284e11	−0.233540
$190$	0	0
$191$	−4.10117e12	−1.16741	−0.583706	−	0.811965i	$-0.698398\pi$
$191$	−4.10117e12	−1.16741	−0.583706	+	0.811965i	$0.698398\pi$
$192$	−8.88188e11	−0.245668
$193$	2.87485e12	0.772770	0.386385	−	0.922338i	$-0.373724\pi$
$193$	2.87485e12	0.772770	0.386385	+	0.922338i	$0.373724\pi$
$194$	−1.47401e12	−0.385116
$195$	0	0
$196$	4.12858e12	1.01951
$197$	6.29125e12	1.51068	0.755341	−	0.655332i	$-0.227471\pi$
$197$	6.29125e12	1.51068	0.755341	+	0.655332i	$0.227471\pi$
$198$	1.93425e12	0.451705
$199$	−3.01537e12	−0.684934	−0.342467	−	0.939530i	$-0.611263\pi$
$199$	−3.01537e12	−0.684934	−0.342467	+	0.939530i	$0.611263\pi$
$200$	0	0
$201$	1.47740e12	0.317628
$202$	1.32593e13	2.77388
$203$	−6.93583e12	−1.41211
$204$	5.99213e12	1.18745
$205$	0	0
$206$	3.73556e12	0.701595
$207$	3.58492e12	0.655606
$208$	8.73053e12	1.55486
$209$	3.20415e12	0.555788
$210$	0	0
$211$	−1.18554e13	−1.95147	−0.975734	−	0.218959i	$-0.929734\pi$
$211$	−1.18554e13	−1.95147	−0.975734	+	0.218959i	$0.929734\pi$
$212$	−4.41098e12	−0.707438
$213$	−9.67787e11	−0.151249
$214$	5.84762e12	0.890643
$215$	0	0
$216$	2.73457e12	0.395725
$217$	−6.27558e11	−0.0885370
$218$	1.19174e13	1.63935
$219$	−4.14102e12	−0.555475
$220$	0	0
$221$	7.76372e12	0.990632
$222$	−1.29980e13	−1.61784
$223$	5.86559e12	0.712254	0.356127	−	0.934438i	$-0.384097\pi$
$223$	5.86559e12	0.712254	0.356127	+	0.934438i	$0.384097\pi$
$224$	−6.17322e12	−0.731388
$225$	0	0
$226$	1.67674e13	1.89177
$227$	−3.26667e12	−0.359719	−0.179859	−	0.983692i	$-0.557564\pi$
$227$	−3.26667e12	−0.359719	−0.179859	+	0.983692i	$0.557564\pi$
$228$	8.44434e12	0.907662
$229$	−7.54585e12	−0.791796	−0.395898	−	0.918294i	$-0.629567\pi$
$229$	−7.54585e12	−0.791796	−0.395898	+	0.918294i	$0.629567\pi$
$230$	0	0
$231$	−5.34158e12	−0.534323
$232$	2.44956e13	2.39278
$233$	1.33760e13	1.27605	0.638026	−	0.770015i	$-0.279751\pi$
$233$	1.33760e13	1.27605	0.638026	+	0.770015i	$0.279751\pi$
$234$	6.60472e12	0.615413
$235$	0	0
$236$	−1.22558e13	−1.08974
$237$	−2.83855e12	−0.246593
$238$	−2.42185e13	−2.05577
$239$	−1.38673e13	−1.15028	−0.575141	−	0.818055i	$-0.695053\pi$
$239$	−1.38673e13	−1.15028	−0.575141	+	0.818055i	$0.695053\pi$
$240$	0	0
$241$	−6.50128e12	−0.515116	−0.257558	−	0.966263i	$-0.582918\pi$
$241$	−6.50128e12	−0.515116	−0.257558	+	0.966263i	$0.582918\pi$
$242$	−9.59847e12	−0.743392
$243$	8.47289e11	0.0641500
$244$	−2.75026e13	−2.03577
$245$	0	0
$246$	−2.46015e13	−1.74108
$247$	1.09409e13	0.757219
$248$	2.21637e12	0.150023
$249$	3.96495e12	0.262508
$250$	0	0
$251$	1.02135e13	0.647094	0.323547	−	0.946212i	$-0.395125\pi$
$251$	1.02135e13	0.647094	0.323547	+	0.946212i	$0.395125\pi$
$252$	−1.40774e13	−0.872608
$253$	2.47314e13	1.49998
$254$	−3.94668e13	−2.34232
$255$	0	0
$256$	−3.49882e13	−1.98885
$257$	−2.71999e13	−1.51333	−0.756667	−	0.653800i	$-0.773174\pi$
$257$	−2.71999e13	−1.51333	−0.756667	+	0.653800i	$0.773174\pi$
$258$	−1.69958e13	−0.925621
$259$	3.58949e13	1.91374
$260$	0	0
$261$	7.58978e12	0.387888
$262$	−3.75726e12	−0.188024
$263$	−2.89468e13	−1.41855	−0.709273	−	0.704934i	$-0.750977\pi$
$263$	−2.89468e13	−1.41855	−0.709273	+	0.704934i	$0.750977\pi$
$264$	1.88651e13	0.905393
$265$	0	0
$266$	−3.41297e13	−1.57139
$267$	3.65891e12	0.165021
$268$	2.68608e13	1.18680
$269$	−2.37805e13	−1.02940	−0.514698	−	0.857371i	$-0.672096\pi$
$269$	−2.37805e13	−1.02940	−0.514698	+	0.857371i	$0.672096\pi$
$270$	0	0
$271$	3.41537e13	1.41941	0.709703	−	0.704501i	$-0.248829\pi$
$271$	3.41537e13	1.41941	0.709703	+	0.704501i	$0.248829\pi$
$272$	3.50320e13	1.42671
$273$	−1.82394e13	−0.727975
$274$	3.80936e13	1.49013
$275$	0	0
$276$	6.51780e13	2.44963
$277$	2.68879e13	0.990646	0.495323	−	0.868709i	$-0.335050\pi$
$277$	2.68879e13	0.990646	0.495323	+	0.868709i	$0.335050\pi$
$278$	−6.44834e12	−0.232917
$279$	6.86727e11	0.0243199
$280$	0	0
$281$	3.80106e13	1.29426	0.647128	−	0.762381i	$-0.275970\pi$
$281$	3.80106e13	1.29426	0.647128	+	0.762381i	$0.275970\pi$
$282$	3.53341e12	0.117984
$283$	−4.51272e12	−0.147779	−0.0738896	−	0.997266i	$-0.523541\pi$
$283$	−4.51272e12	−0.147779	−0.0738896	+	0.997266i	$0.523541\pi$
$284$	−1.75955e13	−0.565133
$285$	0	0
$286$	4.55642e13	1.40802
$287$	6.79389e13	2.05953
$288$	6.75527e12	0.200902
$289$	−3.11932e12	−0.0910169
$290$	0	0
$291$	−4.45439e12	−0.125135
$292$	−7.52885e13	−2.07550
$293$	1.27666e13	0.345384	0.172692	−	0.984976i	$-0.444754\pi$
$293$	1.27666e13	0.345384	0.172692	+	0.984976i	$0.444754\pi$
$294$	1.82599e13	0.484827
$295$	0	0
$296$	−1.26771e14	−3.24278
$297$	5.84522e12	0.146771
$298$	−4.17843e13	−1.02997
$299$	8.44482e13	2.04361
$300$	0	0
$301$	4.69352e13	1.09492
$302$	−1.19765e14	−2.74341
$303$	4.00689e13	0.901308
$304$	4.93684e13	1.09055
$305$	0	0
$306$	2.65020e13	0.564690
$307$	2.88748e12	0.0604308	0.0302154	−	0.999543i	$-0.490381\pi$
$307$	2.88748e12	0.0604308	0.0302154	+	0.999543i	$0.490381\pi$
$308$	−9.71161e13	−1.99647
$309$	1.12887e13	0.227967
$310$	0	0
$311$	−3.04131e13	−0.592760	−0.296380	−	0.955070i	$-0.595779\pi$
$311$	−3.04131e13	−0.592760	−0.296380	+	0.955070i	$0.595779\pi$
$312$	6.44169e13	1.23353
$313$	−8.83600e12	−0.166250	−0.0831250	−	0.996539i	$-0.526490\pi$
$313$	−8.83600e12	−0.166250	−0.0831250	+	0.996539i	$0.526490\pi$
$314$	−1.01414e14	−1.87492
$315$	0	0
$316$	−5.16081e13	−0.921380
$317$	3.59874e13	0.631429	0.315715	−	0.948854i	$-0.397756\pi$
$317$	3.59874e13	0.631429	0.315715	+	0.948854i	$0.397756\pi$
$318$	−1.95089e13	−0.336421
$319$	5.23599e13	0.887462
$320$	0	0
$321$	1.76712e13	0.289394
$322$	−2.63431e14	−4.24092
$323$	4.39014e13	0.694808
$324$	1.54047e13	0.239693
$325$	0	0
$326$	8.32752e13	1.25262
$327$	3.60138e13	0.532668
$328$	−2.39943e14	−3.48981
$329$	−9.75777e12	−0.139564
$330$	0	0
$331$	−5.78829e12	−0.0800749	−0.0400375	−	0.999198i	$-0.512748\pi$
$331$	−5.78829e12	−0.0800749	−0.0400375	+	0.999198i	$0.512748\pi$
$332$	7.20874e13	0.980845
$333$	−3.92793e13	−0.525678
$334$	4.21655e13	0.555075
$335$	0	0
$336$	−8.23010e13	−1.04843
$337$	5.21768e13	0.653902	0.326951	−	0.945041i	$-0.393979\pi$
$337$	5.21768e13	0.653902	0.326951	+	0.945041i	$0.393979\pi$
$338$	1.14735e13	0.141466
$339$	5.06702e13	0.614688
$340$	0	0
$341$	4.73755e12	0.0556422
$342$	3.73476e13	0.431637
$343$	5.62730e13	0.640003
$344$	−1.65763e14	−1.85531
$345$	0	0
$346$	−7.30909e13	−0.792401
$347$	−3.49233e13	−0.372652	−0.186326	−	0.982488i	$-0.559658\pi$
$347$	−3.49233e13	−0.372652	−0.186326	+	0.982488i	$0.559658\pi$
$348$	1.37991e14	1.44932
$349$	−1.31202e14	−1.35644	−0.678220	−	0.734859i	$-0.737248\pi$
$349$	−1.31202e14	−1.35644	−0.678220	+	0.734859i	$0.737248\pi$
$350$	0	0
$351$	1.99591e13	0.199964
$352$	4.66028e13	0.459650
$353$	1.79171e13	0.173983	0.0869913	−	0.996209i	$-0.472275\pi$
$353$	1.79171e13	0.173983	0.0869913	+	0.996209i	$0.472275\pi$
$354$	−5.42048e13	−0.518227
$355$	0	0
$356$	6.65231e13	0.616592
$357$	−7.31872e13	−0.667974
$358$	9.03007e13	0.811586
$359$	8.82889e13	0.781424	0.390712	−	0.920513i	$-0.372229\pi$
$359$	8.82889e13	0.781424	0.390712	+	0.920513i	$0.372229\pi$
$360$	0	0
$361$	−5.46227e13	−0.468903
$362$	9.72093e13	0.821885
$363$	−2.90061e13	−0.241548
$364$	−3.31614e14	−2.72004
$365$	0	0
$366$	−1.21638e14	−0.968109
$367$	2.21257e14	1.73474	0.867369	−	0.497666i	$-0.165810\pi$
$367$	2.21257e14	1.73474	0.867369	+	0.497666i	$0.165810\pi$
$368$	3.81052e14	2.94321
$369$	−7.43446e13	−0.565724
$370$	0	0
$371$	5.38753e13	0.397954
$372$	1.24855e13	0.0908698
$373$	1.62826e14	1.16768	0.583842	−	0.811867i	$-0.301549\pi$
$373$	1.62826e14	1.16768	0.583842	+	0.811867i	$0.301549\pi$
$374$	1.82830e14	1.29197
$375$	0	0
$376$	3.44619e13	0.236487
$377$	1.78789e14	1.20910
$378$	−6.22614e13	−0.414968
$379$	−1.44303e14	−0.947897	−0.473948	−	0.880553i	$-0.657172\pi$
$379$	−1.44303e14	−0.947897	−0.473948	+	0.880553i	$0.657172\pi$
$380$	0	0
$381$	−1.19267e14	−0.761084
$382$	−3.29782e14	−2.07433
$383$	−1.85455e14	−1.14986	−0.574929	−	0.818203i	$-0.694970\pi$
$383$	−1.85455e14	−1.14986	−0.574929	+	0.818203i	$0.694970\pi$
$384$	−1.28354e14	−0.784490
$385$	0	0
$386$	2.31171e14	1.37310
$387$	−5.13605e13	−0.300759
$388$	−8.09860e13	−0.467558
$389$	8.72399e12	0.0496583	0.0248292	−	0.999692i	$-0.492096\pi$
$389$	8.72399e12	0.0496583	0.0248292	+	0.999692i	$0.492096\pi$
$390$	0	0
$391$	3.38855e14	1.87518
$392$	1.78092e14	0.971785
$393$	−1.13543e13	−0.0610942
$394$	5.05890e14	2.68427
$395$	0	0
$396$	1.06273e14	0.548402
$397$	−1.10441e14	−0.562061	−0.281031	−	0.959699i	$-0.590676\pi$
$397$	−1.10441e14	−0.562061	−0.281031	+	0.959699i	$0.590676\pi$
$398$	−2.42471e14	−1.21703
$399$	−1.03138e14	−0.510586
$400$	0	0
$401$	−2.63717e14	−1.27012	−0.635060	−	0.772463i	$-0.719025\pi$
$401$	−2.63717e14	−1.27012	−0.635060	+	0.772463i	$0.719025\pi$
$402$	1.18800e14	0.564382
$403$	1.61769e13	0.0758084
$404$	7.28499e14	3.36769
$405$	0	0
$406$	−5.57721e14	−2.50913
$407$	−2.70977e14	−1.20272
$408$	2.58478e14	1.13186
$409$	−4.23351e13	−0.182904	−0.0914519	−	0.995809i	$-0.529151\pi$
$409$	−4.23351e13	−0.182904	−0.0914519	+	0.995809i	$0.529151\pi$
$410$	0	0
$411$	1.15117e14	0.484184
$412$	2.05242e14	0.851786
$413$	1.49691e14	0.613012
$414$	2.88269e14	1.16492
$415$	0	0
$416$	1.59130e14	0.626239
$417$	−1.94866e13	−0.0756811
$418$	2.57651e14	0.987558
$419$	−3.77425e14	−1.42776	−0.713878	−	0.700270i	$-0.753063\pi$
$419$	−3.77425e14	−1.42776	−0.713878	+	0.700270i	$0.753063\pi$
$420$	0	0
$421$	−1.97871e14	−0.729172	−0.364586	−	0.931170i	$-0.618789\pi$
$421$	−1.97871e14	−0.729172	−0.364586	+	0.931170i	$0.618789\pi$
$422$	−9.53309e14	−3.46749
$423$	1.06778e13	0.0383362
$424$	−1.90274e14	−0.674320
$425$	0	0
$426$	−7.78213e13	−0.268748
$427$	3.35913e14	1.14518
$428$	3.21284e14	1.08130
$429$	1.37693e14	0.457505
$430$	0	0
$431$	7.10530e13	0.230121	0.115061	−	0.993358i	$-0.463294\pi$
$431$	7.10530e13	0.230121	0.115061	+	0.993358i	$0.463294\pi$
$432$	9.00609e13	0.287989
$433$	1.67508e12	0.00528874	0.00264437	−	0.999997i	$-0.499158\pi$
$433$	1.67508e12	0.00528874	0.00264437	+	0.999997i	$0.499158\pi$
$434$	−5.04629e13	−0.157318
$435$	0	0
$436$	6.54773e14	1.99028
$437$	4.77528e14	1.43335
$438$	−3.32986e14	−0.987002
$439$	5.87778e14	1.72051	0.860257	−	0.509860i	$-0.170303\pi$
$439$	5.87778e14	1.72051	0.860257	+	0.509860i	$0.170303\pi$
$440$	0	0
$441$	5.51805e13	0.157534
$442$	6.24293e14	1.76022
$443$	1.82664e14	0.508667	0.254333	−	0.967117i	$-0.418144\pi$
$443$	1.82664e14	0.508667	0.254333	+	0.967117i	$0.418144\pi$
$444$	−7.14142e14	−1.96417
$445$	0	0
$446$	4.71661e14	1.26558
$447$	−1.26270e14	−0.334664
$448$	1.97233e14	0.516358
$449$	9.01894e13	0.233239	0.116619	−	0.993177i	$-0.462794\pi$
$449$	9.01894e13	0.233239	0.116619	+	0.993177i	$0.462794\pi$
$450$	0	0
$451$	−5.12884e14	−1.29434
$452$	9.21243e14	2.29675
$453$	−3.61923e14	−0.891407
$454$	−2.62678e14	−0.639170
$455$	0	0
$456$	3.64258e14	0.865171
$457$	1.03357e14	0.242549	0.121275	−	0.992619i	$-0.461302\pi$
$457$	1.03357e14	0.242549	0.121275	+	0.992619i	$0.461302\pi$
$458$	−6.06774e14	−1.40691
$459$	8.00877e13	0.183483
$460$	0	0
$461$	−5.89021e14	−1.31758	−0.658788	−	0.752328i	$-0.728931\pi$
$461$	−5.89021e14	−1.31758	−0.658788	+	0.752328i	$0.728931\pi$
$462$	−4.29525e14	−0.949418
$463$	7.22784e14	1.57875	0.789375	−	0.613912i	$-0.210405\pi$
$463$	7.22784e14	1.57875	0.789375	+	0.613912i	$0.210405\pi$
$464$	8.06741e14	1.74135
$465$	0	0
$466$	1.07558e15	2.26737
$467$	−8.68233e14	−1.80881	−0.904406	−	0.426674i	$-0.859685\pi$
$467$	−8.68233e14	−1.80881	−0.904406	+	0.426674i	$0.859685\pi$
$468$	3.62880e14	0.747156
$469$	−3.28075e14	−0.667609
$470$	0	0
$471$	−3.06468e14	−0.609214
$472$	−5.28669e14	−1.03873
$473$	−3.54322e14	−0.688117
$474$	−2.28252e14	−0.438161
$475$	0	0
$476$	−1.33063e15	−2.49585
$477$	−5.89549e13	−0.109312
$478$	−1.11509e15	−2.04389
$479$	−5.56924e14	−1.00914	−0.504569	−	0.863371i	$-0.668349\pi$
$479$	−5.56924e14	−1.00914	−0.504569	+	0.863371i	$0.668349\pi$
$480$	0	0
$481$	−9.25281e14	−1.63861
$482$	−5.22778e14	−0.915290
$483$	−7.96077e14	−1.37799
$484$	−5.27365e14	−0.902531
$485$	0	0
$486$	6.81318e13	0.113986
$487$	7.83719e14	1.29644	0.648218	−	0.761455i	$-0.275515\pi$
$487$	7.83719e14	1.29644	0.648218	+	0.761455i	$0.275515\pi$
$488$	−1.18636e15	−1.94047
$489$	2.51654e14	0.407010
$490$	0	0
$491$	−3.79538e14	−0.600215	−0.300108	−	0.953905i	$-0.597023\pi$
$491$	−3.79538e14	−0.600215	−0.300108	+	0.953905i	$0.597023\pi$
$492$	−1.35167e15	−2.11380
$493$	7.17404e14	1.10944
$494$	8.79778e14	1.34547
$495$	0	0
$496$	7.29943e13	0.109179
$497$	2.14909e14	0.317903
$498$	3.18828e14	0.466440
$499$	−1.13606e15	−1.64379	−0.821895	−	0.569639i	$-0.807083\pi$
$499$	−1.13606e15	−1.64379	−0.821895	+	0.569639i	$0.807083\pi$
$500$	0	0
$501$	1.27422e14	0.180359
$502$	8.21281e14	1.14980
$503$	−8.32928e14	−1.15341	−0.576705	−	0.816952i	$-0.695662\pi$
$503$	−8.32928e14	−1.15341	−0.576705	+	0.816952i	$0.695662\pi$
$504$	−6.07246e14	−0.831758
$505$	0	0
$506$	1.98869e15	2.66526
$507$	3.46723e13	0.0459662
$508$	−2.16841e15	−2.84375
$509$	3.87858e13	0.0503182	0.0251591	−	0.999683i	$-0.491991\pi$
$509$	3.87858e13	0.0503182	0.0251591	+	0.999683i	$0.491991\pi$
$510$	0	0
$511$	9.19565e14	1.16753
$512$	−1.73169e15	−2.17513
$513$	1.12863e14	0.140251
$514$	−2.18719e15	−2.68899
$515$	0	0
$516$	−9.33793e14	−1.12377
$517$	7.36633e13	0.0877108
$518$	2.88636e15	3.40046
$519$	−2.20877e14	−0.257472
$520$	0	0
$521$	9.99928e14	1.14120	0.570599	−	0.821229i	$-0.306711\pi$
$521$	9.99928e14	1.14120	0.570599	+	0.821229i	$0.306711\pi$
$522$	6.10306e14	0.689223
$523$	1.34636e15	1.50453	0.752265	−	0.658861i	$-0.228961\pi$
$523$	1.34636e15	1.50453	0.752265	+	0.658861i	$0.228961\pi$
$524$	−2.06434e14	−0.228275
$525$	0	0
$526$	−2.32765e15	−2.52056
$527$	6.49111e13	0.0695601
$528$	6.21306e14	0.658899
$529$	2.73301e15	2.86837
$530$	0	0
$531$	−1.63804e14	−0.168386
$532$	−1.87517e15	−1.90777
$533$	−1.75130e15	−1.76344
$534$	2.94218e14	0.293220
$535$	0	0
$536$	1.15868e15	1.13124
$537$	2.72885e14	0.263706
$538$	−1.91222e15	−1.82910
$539$	3.80675e14	0.360426
$540$	0	0
$541$	−2.30463e14	−0.213804	−0.106902	−	0.994270i	$-0.534093\pi$
$541$	−2.30463e14	−0.213804	−0.106902	+	0.994270i	$0.534093\pi$
$542$	2.74635e15	2.52209
$543$	2.93762e14	0.267053
$544$	6.38524e14	0.574623
$545$	0	0
$546$	−1.46666e15	−1.29351
$547$	−9.99552e14	−0.872721	−0.436360	−	0.899772i	$-0.643733\pi$
$547$	−9.99552e14	−0.872721	−0.436360	+	0.899772i	$0.643733\pi$
$548$	2.09296e15	1.80912
$549$	−3.67585e14	−0.314565
$550$	0	0
$551$	1.01099e15	0.848036
$552$	2.81154e15	2.33496
$553$	6.30336e14	0.518303
$554$	2.16210e15	1.76024
$555$	0	0
$556$	−3.54289e14	−0.282778
$557$	−1.31319e15	−1.03783	−0.518914	−	0.854827i	$-0.673663\pi$
$557$	−1.31319e15	−1.03783	−0.518914	+	0.854827i	$0.673663\pi$
$558$	5.52208e13	0.0432130
$559$	−1.20987e15	−0.937508
$560$	0	0
$561$	5.52504e14	0.419797
$562$	3.05650e15	2.29972
$563$	2.25902e14	0.168315	0.0841576	−	0.996452i	$-0.473180\pi$
$563$	2.25902e14	0.168315	0.0841576	+	0.996452i	$0.473180\pi$
$564$	1.94135e14	0.143241
$565$	0	0
$566$	−3.62875e14	−0.262583
$567$	−1.88151e14	−0.134834
$568$	−7.59004e14	−0.538677
$569$	7.59211e14	0.533636	0.266818	−	0.963747i	$-0.414028\pi$
$569$	7.59211e14	0.533636	0.266818	+	0.963747i	$0.414028\pi$
$570$	0	0
$571$	1.77852e15	1.22619	0.613097	−	0.790008i	$-0.289923\pi$
$571$	1.77852e15	1.22619	0.613097	+	0.790008i	$0.289923\pi$
$572$	2.50341e15	1.70944
$573$	−9.96584e14	−0.674006
$574$	5.46308e15	3.65950
$575$	0	0
$576$	−2.15830e14	−0.141836
$577$	−2.68413e15	−1.74718	−0.873589	−	0.486665i	$-0.838213\pi$
$577$	−2.68413e15	−1.74718	−0.873589	+	0.486665i	$0.838213\pi$
$578$	−2.50829e14	−0.161724
$579$	6.98589e14	0.446159
$580$	0	0
$581$	−8.80468e14	−0.551753
$582$	−3.58185e14	−0.222347
$583$	−4.06714e14	−0.250099
$584$	−3.24767e15	−1.97834
$585$	0	0
$586$	1.02658e15	0.613699
$587$	−2.00659e15	−1.18836	−0.594182	−	0.804331i	$-0.702524\pi$
$587$	−2.00659e15	−1.18836	−0.594182	+	0.804331i	$0.702524\pi$
$588$	1.00324e15	0.588615
$589$	9.14752e13	0.0531703
$590$	0	0
$591$	1.52877e15	0.872192
$592$	−4.17511e15	−2.35993
$593$	−1.05793e15	−0.592456	−0.296228	−	0.955117i	$-0.595729\pi$
$593$	−1.05793e15	−0.592456	−0.296228	+	0.955117i	$0.595729\pi$
$594$	4.70023e14	0.260792
$595$	0	0
$596$	−2.29574e15	−1.25045
$597$	−7.32735e14	−0.395447
$598$	6.79061e15	3.63122
$599$	1.55942e15	0.826257	0.413129	−	0.910673i	$-0.364436\pi$
$599$	1.55942e15	0.826257	0.413129	+	0.910673i	$0.364436\pi$
$600$	0	0
$601$	9.08336e14	0.472538	0.236269	−	0.971688i	$-0.424075\pi$
$601$	9.08336e14	0.472538	0.236269	+	0.971688i	$0.424075\pi$
$602$	3.77413e15	1.94552
$603$	3.59008e14	0.183383
$604$	−6.58018e15	−3.33069
$605$	0	0
$606$	3.22201e15	1.60150
$607$	−2.36128e15	−1.16308	−0.581539	−	0.813518i	$-0.697549\pi$
$607$	−2.36128e15	−1.16308	−0.581539	+	0.813518i	$0.697549\pi$
$608$	8.99833e14	0.439230
$609$	−1.68541e15	−0.815285
$610$	0	0
$611$	2.51531e14	0.119499
$612$	1.45609e15	0.685574
$613$	3.99150e15	1.86253	0.931264	−	0.364344i	$-0.118707\pi$
$613$	3.99150e15	1.86253	0.931264	+	0.364344i	$0.118707\pi$
$614$	2.32187e14	0.107377
$615$	0	0
$616$	−4.18923e15	−1.90301
$617$	3.07280e15	1.38346	0.691730	−	0.722156i	$-0.256849\pi$
$617$	3.07280e15	1.38346	0.691730	+	0.722156i	$0.256849\pi$
$618$	9.07742e14	0.405066
$619$	1.21134e15	0.535756	0.267878	−	0.963453i	$-0.413678\pi$
$619$	1.21134e15	0.535756	0.267878	+	0.963453i	$0.413678\pi$
$620$	0	0
$621$	8.71136e14	0.378514
$622$	−2.44557e15	−1.05325
$623$	−8.12506e14	−0.346851
$624$	2.12152e15	0.897700
$625$	0	0
$626$	−7.10516e14	−0.295403
$627$	7.78610e14	0.320884
$628$	−5.57194e15	−2.27629
$629$	−3.71277e15	−1.50355
$630$	0	0
$631$	1.08899e15	0.433374	0.216687	−	0.976241i	$-0.430475\pi$
$631$	1.08899e15	0.433374	0.216687	+	0.976241i	$0.430475\pi$
$632$	−2.22618e15	−0.878247
$633$	−2.88085e15	−1.12668
$634$	2.89380e15	1.12196
$635$	0	0
$636$	−1.07187e15	−0.408439
$637$	1.29986e15	0.491054
$638$	4.21034e15	1.57690
$639$	−2.35172e14	−0.0873236
$640$	0	0
$641$	−3.06660e15	−1.11928	−0.559639	−	0.828736i	$-0.689060\pi$
$641$	−3.06660e15	−1.11928	−0.559639	+	0.828736i	$0.689060\pi$
$642$	1.42097e15	0.514213
$643$	−4.72581e15	−1.69557	−0.847786	−	0.530339i	$-0.822065\pi$
$643$	−4.72581e15	−1.69557	−0.847786	+	0.530339i	$0.822065\pi$
$644$	−1.44736e16	−5.14878
$645$	0	0
$646$	3.53018e15	1.23458
$647$	8.05345e14	0.279260	0.139630	−	0.990204i	$-0.455409\pi$
$647$	8.05345e14	0.279260	0.139630	+	0.990204i	$0.455409\pi$
$648$	6.64501e14	0.228472
$649$	−1.13004e15	−0.385256
$650$	0	0
$651$	−1.52496e14	−0.0511169
$652$	4.57536e15	1.52077
$653$	2.41841e15	0.797089	0.398545	−	0.917149i	$-0.369515\pi$
$653$	2.41841e15	0.797089	0.398545	+	0.917149i	$0.369515\pi$
$654$	2.89593e15	0.946477
$655$	0	0
$656$	−7.90232e15	−2.53970
$657$	−1.00627e15	−0.320704
$658$	−7.84638e14	−0.247986
$659$	5.45221e14	0.170885	0.0854423	−	0.996343i	$-0.472770\pi$
$659$	5.45221e14	0.170885	0.0854423	+	0.996343i	$0.472770\pi$
$660$	0	0
$661$	3.83169e15	1.18109	0.590545	−	0.807005i	$-0.298913\pi$
$661$	3.83169e15	1.18109	0.590545	+	0.807005i	$0.298913\pi$
$662$	−4.65446e14	−0.142282
$663$	1.88658e15	0.571942
$664$	3.10959e15	0.934928
$665$	0	0
$666$	−3.15851e15	−0.934058
$667$	7.80340e15	2.28871
$668$	2.31668e15	0.673900
$669$	1.42534e15	0.411220
$670$	0	0
$671$	−2.53587e15	−0.719703
$672$	−1.50009e15	−0.422267
$673$	8.45687e14	0.236117	0.118058	−	0.993007i	$-0.462333\pi$
$673$	8.45687e14	0.236117	0.118058	+	0.993007i	$0.462333\pi$
$674$	4.19562e15	1.16189
$675$	0	0
$676$	6.30382e14	0.171750
$677$	−1.10360e15	−0.298246	−0.149123	−	0.988819i	$-0.547645\pi$
$677$	−1.10360e15	−0.298246	−0.149123	+	0.988819i	$0.547645\pi$
$678$	4.07447e15	1.09221
$679$	9.89154e14	0.263015
$680$	0	0
$681$	−7.93801e14	−0.207684
$682$	3.80954e14	0.0988686
$683$	−1.71703e15	−0.442042	−0.221021	−	0.975269i	$-0.570939\pi$
$683$	−1.71703e15	−0.442042	−0.221021	+	0.975269i	$0.570939\pi$
$684$	2.05197e15	0.524039
$685$	0	0
$686$	4.52500e15	1.13720
$687$	−1.83364e15	−0.457144
$688$	−5.45926e15	−1.35020
$689$	−1.38877e15	−0.340741
$690$	0	0
$691$	−6.23773e15	−1.50625	−0.753125	−	0.657877i	$-0.771455\pi$
$691$	−6.23773e15	−1.50625	−0.753125	+	0.657877i	$0.771455\pi$
$692$	−4.01581e15	−0.962031
$693$	−1.29800e15	−0.308492
$694$	−2.80824e15	−0.662151
$695$	0	0
$696$	5.95242e15	1.38147
$697$	−7.02723e15	−1.61809
$698$	−1.05502e16	−2.41021
$699$	3.25036e15	0.736729
$700$	0	0
$701$	7.00158e15	1.56224	0.781118	−	0.624383i	$-0.214650\pi$
$701$	7.00158e15	1.56224	0.781118	+	0.624383i	$0.214650\pi$
$702$	1.60495e15	0.355309
$703$	−5.23218e15	−1.14929
$704$	−1.48895e15	−0.324512
$705$	0	0
$706$	1.44074e15	0.309143
$707$	−8.89781e15	−1.89442
$708$	−2.97815e15	−0.629164
$709$	1.59675e15	0.334721	0.167360	−	0.985896i	$-0.446476\pi$
$709$	1.59675e15	0.334721	0.167360	+	0.985896i	$0.446476\pi$
$710$	0	0
$711$	−6.89767e14	−0.142370
$712$	2.86956e15	0.587727
$713$	7.06056e14	0.143498
$714$	−5.88510e15	−1.18690
$715$	0	0
$716$	4.96136e15	0.985324
$717$	−3.36976e15	−0.664115
$718$	7.09945e15	1.38848
$719$	6.11364e15	1.18656	0.593282	−	0.804995i	$-0.297832\pi$
$719$	6.11364e15	1.18656	0.593282	+	0.804995i	$0.297832\pi$
$720$	0	0
$721$	−2.50680e15	−0.479154
$722$	−4.39229e15	−0.833176
$723$	−1.57981e15	−0.297402
$724$	5.34093e15	0.997827
$725$	0	0
$726$	−2.33243e15	−0.429197
$727$	1.20859e15	0.220719	0.110359	−	0.993892i	$-0.464800\pi$
$727$	1.20859e15	0.220719	0.110359	+	0.993892i	$0.464800\pi$
$728$	−1.43046e16	−2.59270
$729$	2.05891e14	0.0370370
$730$	0	0
$731$	−4.85472e15	−0.860237
$732$	−6.68312e15	−1.17535
$733$	7.84018e15	1.36853	0.684265	−	0.729234i	$-0.260123\pi$
$733$	7.84018e15	1.36853	0.684265	+	0.729234i	$0.260123\pi$
$734$	1.77916e16	3.08239
$735$	0	0
$736$	6.94540e15	1.18541
$737$	2.47670e15	0.419568
$738$	−5.97817e15	−1.00521
$739$	−3.60946e15	−0.602417	−0.301209	−	0.953558i	$-0.597390\pi$
$739$	−3.60946e15	−0.602417	−0.301209	+	0.953558i	$0.597390\pi$
$740$	0	0
$741$	2.65865e15	0.437180
$742$	4.33219e15	0.707109
$743$	6.18300e15	1.00175	0.500876	−	0.865519i	$-0.333011\pi$
$743$	6.18300e15	1.00175	0.500876	+	0.865519i	$0.333011\pi$
$744$	5.38578e14	0.0866159
$745$	0	0
$746$	1.30931e16	2.07481
$747$	9.63484e14	0.151559
$748$	1.00452e16	1.56855
$749$	−3.92412e15	−0.608264
$750$	0	0
$751$	5.47550e15	0.836381	0.418190	−	0.908359i	$-0.362665\pi$
$751$	5.47550e15	0.836381	0.418190	+	0.908359i	$0.362665\pi$
$752$	1.13498e15	0.172103
$753$	2.48187e15	0.373600
$754$	1.43767e16	2.14840
$755$	0	0
$756$	−3.42080e15	−0.503800
$757$	4.99668e15	0.730557	0.365279	−	0.930898i	$-0.380974\pi$
$757$	4.99668e15	0.730557	0.365279	+	0.930898i	$0.380974\pi$
$758$	−1.16037e16	−1.68428
$759$	6.00974e15	0.866015
$760$	0	0
$761$	4.55305e14	0.0646675	0.0323338	−	0.999477i	$-0.489706\pi$
$761$	4.55305e14	0.0646675	0.0323338	+	0.999477i	$0.489706\pi$
$762$	−9.59043e15	−1.35234
$763$	−7.99732e15	−1.11959
$764$	−1.81191e16	−2.51838
$765$	0	0
$766$	−1.49127e16	−2.04314
$767$	−3.85865e15	−0.524882
$768$	−8.50213e15	−1.14826
$769$	−9.69796e15	−1.30043	−0.650213	−	0.759752i	$-0.725320\pi$
$769$	−9.69796e15	−1.30043	−0.650213	+	0.759752i	$0.725320\pi$
$770$	0	0
$771$	−6.60957e15	−0.873724
$772$	1.27011e16	1.66705
$773$	5.14400e15	0.670369	0.335184	−	0.942153i	$-0.391201\pi$
$773$	5.14400e15	0.670369	0.335184	+	0.942153i	$0.391201\pi$
$774$	−4.12998e15	−0.534408
$775$	0	0
$776$	−3.49344e15	−0.445670
$777$	8.72246e15	1.10490
$778$	7.01509e14	0.0882360
$779$	−9.90304e15	−1.23684
$780$	0	0
$781$	−1.62239e15	−0.199790
$782$	2.72479e16	3.33193
$783$	1.84432e15	0.223947
$784$	5.86530e15	0.707215
$785$	0	0
$786$	−9.13014e14	−0.108556
$787$	8.00900e15	0.945621	0.472811	−	0.881164i	$-0.343239\pi$
$787$	8.00900e15	0.945621	0.472811	+	0.881164i	$0.343239\pi$
$788$	2.77949e16	3.25890
$789$	−7.03406e15	−0.818998
$790$	0	0
$791$	−1.12520e16	−1.29199
$792$	4.58422e15	0.522729
$793$	−8.65901e15	−0.980541
$794$	−8.88076e15	−0.998705
$795$	0	0
$796$	−1.33220e16	−1.47757
$797$	1.27052e15	0.139946	0.0699729	−	0.997549i	$-0.477709\pi$
$797$	1.27052e15	0.139946	0.0699729	+	0.997549i	$0.477709\pi$
$798$	−8.29351e15	−0.907240
$799$	1.00929e15	0.109650
$800$	0	0
$801$	8.89114e14	0.0952749
$802$	−2.12059e16	−2.25683
$803$	−6.94197e15	−0.733749
$804$	6.52718e15	0.685200
$805$	0	0
$806$	1.30081e15	0.134701
$807$	−5.77865e15	−0.594322
$808$	3.14248e16	3.21003
$809$	−1.53605e15	−0.155843	−0.0779216	−	0.996959i	$-0.524828\pi$
$809$	−1.53605e15	−0.155843	−0.0779216	+	0.996959i	$0.524828\pi$
$810$	0	0
$811$	2.96275e15	0.296538	0.148269	−	0.988947i	$-0.452630\pi$
$811$	2.96275e15	0.296538	0.148269	+	0.988947i	$0.452630\pi$
$812$	−3.06426e16	−3.04627
$813$	8.29935e15	0.819495
$814$	−2.17897e16	−2.13706
$815$	0	0
$816$	8.51276e15	0.823711
$817$	−6.84145e15	−0.657547
$818$	−3.40423e15	−0.324995
$819$	−4.43218e15	−0.420297
$820$	0	0
$821$	−5.47376e15	−0.512151	−0.256076	−	0.966657i	$-0.582430\pi$
$821$	−5.47376e15	−0.512151	−0.256076	+	0.966657i	$0.582430\pi$
$822$	9.25675e15	0.860327
$823$	−5.77757e15	−0.533391	−0.266696	−	0.963781i	$-0.585932\pi$
$823$	−5.77757e15	−0.533391	−0.266696	+	0.963781i	$0.585932\pi$
$824$	8.85336e15	0.811911
$825$	0	0
$826$	1.20369e16	1.08924
$827$	9.27831e14	0.0834043	0.0417022	−	0.999130i	$-0.486722\pi$
$827$	9.27831e14	0.0834043	0.0417022	+	0.999130i	$0.486722\pi$
$828$	1.58383e16	1.41430
$829$	2.04388e16	1.81303	0.906516	−	0.422171i	$-0.138732\pi$
$829$	2.04388e16	1.81303	0.906516	+	0.422171i	$0.138732\pi$
$830$	0	0
$831$	6.53377e15	0.571950
$832$	−5.08419e15	−0.442123
$833$	5.21579e15	0.450580
$834$	−1.56695e15	−0.134475
$835$	0	0
$836$	1.41560e16	1.19897
$837$	1.66875e14	0.0140411
$838$	−3.03494e16	−2.53692
$839$	1.54581e15	0.128371	0.0641855	−	0.997938i	$-0.479555\pi$
$839$	1.54581e15	0.128371	0.0641855	+	0.997938i	$0.479555\pi$
$840$	0	0
$841$	4.32037e15	0.354114
$842$	−1.59111e16	−1.29564
$843$	9.23659e15	0.747240
$844$	−5.23773e16	−4.20978
$845$	0	0
$846$	8.58618e14	0.0681182
$847$	6.44118e15	0.507699
$848$	−6.26650e15	−0.490736
$849$	−1.09659e15	−0.0853204
$850$	0	0
$851$	−4.03848e16	−3.10174
$852$	−4.27570e15	−0.326280
$853$	−2.26066e15	−0.171402	−0.0857011	−	0.996321i	$-0.527313\pi$
$853$	−2.26066e15	−0.171402	−0.0857011	+	0.996321i	$0.527313\pi$
$854$	2.70113e16	2.03483
$855$	0	0
$856$	1.38590e16	1.03068
$857$	2.36638e16	1.74860	0.874301	−	0.485385i	$-0.161320\pi$
$857$	2.36638e16	1.74860	0.874301	+	0.485385i	$0.161320\pi$
$858$	1.10721e16	0.812924
$859$	−1.57637e16	−1.14999	−0.574997	−	0.818156i	$-0.694997\pi$
$859$	−1.57637e16	−1.14999	−0.574997	+	0.818156i	$0.694997\pi$
$860$	0	0
$861$	1.65092e16	1.18907
$862$	5.71348e15	0.408894
$863$	−5.89289e15	−0.419053	−0.209526	−	0.977803i	$-0.567192\pi$
$863$	−5.89289e15	−0.419053	−0.209526	+	0.977803i	$0.567192\pi$
$864$	1.64153e15	0.115991
$865$	0	0
$866$	1.34696e14	0.00939736
$867$	−7.57995e14	−0.0525486
$868$	−2.77256e15	−0.190995
$869$	−4.75852e15	−0.325734
$870$	0	0
$871$	8.45696e15	0.571629
$872$	2.82445e16	1.89711
$873$	−1.08242e15	−0.0722465
$874$	3.83988e16	2.54686
$875$	0	0
$876$	−1.82951e16	−1.19829
$877$	−2.29572e16	−1.49424	−0.747121	−	0.664688i	$-0.768564\pi$
$877$	−2.29572e16	−1.49424	−0.747121	+	0.664688i	$0.768564\pi$
$878$	4.72642e16	3.05712
$879$	3.10227e15	0.199407
$880$	0	0
$881$	−2.40041e16	−1.52377	−0.761883	−	0.647715i	$-0.775725\pi$
$881$	−2.40041e16	−1.52377	−0.761883	+	0.647715i	$0.775725\pi$
$882$	4.43715e15	0.279915
$883$	2.43844e16	1.52872	0.764359	−	0.644790i	$-0.223055\pi$
$883$	2.43844e16	1.52872	0.764359	+	0.644790i	$0.223055\pi$
$884$	3.43003e16	2.13703
$885$	0	0
$886$	1.46883e16	0.903830
$887$	2.16945e16	1.32669	0.663345	−	0.748313i	$-0.269136\pi$
$887$	2.16945e16	1.32669	0.663345	+	0.748313i	$0.269136\pi$
$888$	−3.08055e16	−1.87222
$889$	2.64847e16	1.59969
$890$	0	0
$891$	1.42039e15	0.0847383
$892$	2.59143e16	1.53650
$893$	1.42233e15	0.0838142
$894$	−1.01536e16	−0.594652
$895$	0	0
$896$	2.85026e16	1.64889
$897$	2.05209e16	1.17988
$898$	7.25227e15	0.414433
$899$	1.49482e15	0.0849005
$900$	0	0
$901$	−5.57256e15	−0.312657
$902$	−4.12418e16	−2.29986
$903$	1.14052e16	0.632153
$904$	3.97390e16	2.18923
$905$	0	0
$906$	−2.91028e16	−1.58391
$907$	5.53795e15	0.299577	0.149789	−	0.988718i	$-0.452141\pi$
$907$	5.53795e15	0.299577	0.149789	+	0.988718i	$0.452141\pi$
$908$	−1.44322e16	−0.775999
$909$	9.73675e15	0.520370
$910$	0	0
$911$	3.49081e16	1.84321	0.921606	−	0.388127i	$-0.126878\pi$
$911$	3.49081e16	1.84321	0.921606	+	0.388127i	$0.126878\pi$
$912$	1.19965e16	0.629627
$913$	6.64682e15	0.346756
$914$	8.31108e15	0.430976
$915$	0	0
$916$	−3.33377e16	−1.70809
$917$	2.52136e15	0.128411
$918$	6.43998e15	0.326024
$919$	−3.16111e15	−0.159076	−0.0795379	−	0.996832i	$-0.525344\pi$
$919$	−3.16111e15	−0.159076	−0.0795379	+	0.996832i	$0.525344\pi$
$920$	0	0
$921$	7.01658e14	0.0348897
$922$	−4.73641e16	−2.34115
$923$	−5.53983e15	−0.272199
$924$	−2.35992e16	−1.15266
$925$	0	0
$926$	5.81202e16	2.80522
$927$	2.74315e15	0.131617
$928$	1.47044e16	0.701347
$929$	3.67556e16	1.74276	0.871380	−	0.490609i	$-0.163226\pi$
$929$	3.67556e16	1.74276	0.871380	+	0.490609i	$0.163226\pi$
$930$	0	0
$931$	7.35029e15	0.344414
$932$	5.90954e16	2.75274
$933$	−7.39039e15	−0.342230
$934$	−6.98159e16	−3.21401
$935$	0	0
$936$	1.56533e16	0.712179
$937$	−2.24894e15	−0.101721	−0.0508604	−	0.998706i	$-0.516196\pi$
$937$	−2.24894e15	−0.101721	−0.0508604	+	0.998706i	$0.516196\pi$
$938$	−2.63810e16	−1.18625
$939$	−2.14715e15	−0.0959845
$940$	0	0
$941$	3.72889e16	1.64754	0.823772	−	0.566921i	$-0.191866\pi$
$941$	3.72889e16	1.64754	0.823772	+	0.566921i	$0.191866\pi$
$942$	−2.46435e16	−1.08249
$943$	−7.64371e16	−3.33803
$944$	−1.74113e16	−0.755935
$945$	0	0
$946$	−2.84916e16	−1.22269
$947$	−2.11920e15	−0.0904164	−0.0452082	−	0.998978i	$-0.514395\pi$
$947$	−2.11920e15	−0.0904164	−0.0452082	+	0.998978i	$0.514395\pi$
$948$	−1.25408e16	−0.531959
$949$	−2.37041e16	−0.999677
$950$	0	0
$951$	8.74494e15	0.364556
$952$	−5.73983e16	−2.37901
$953$	1.98151e16	0.816556	0.408278	−	0.912858i	$-0.366129\pi$
$953$	1.98151e16	0.816556	0.408278	+	0.912858i	$0.366129\pi$
$954$	−4.74066e15	−0.194233
$955$	0	0
$956$	−6.12661e16	−2.48143
$957$	1.27234e16	0.512376
$958$	−4.47831e16	−1.79310
$959$	−2.55632e16	−1.01768
$960$	0	0
$961$	−2.52732e16	−0.994677
$962$	−7.44033e16	−2.91159
$963$	4.29411e15	0.167082
$964$	−2.87228e16	−1.11123
$965$	0	0
$966$	−6.40138e16	−2.44850
$967$	−3.04573e16	−1.15837	−0.579183	−	0.815198i	$-0.696628\pi$
$967$	−3.04573e16	−1.15837	−0.579183	+	0.815198i	$0.696628\pi$
$968$	−2.27486e16	−0.860280
$969$	1.06680e16	0.401147
$970$	0	0
$971$	1.30252e16	0.484260	0.242130	−	0.970244i	$-0.422154\pi$
$971$	1.30252e16	0.484260	0.242130	+	0.970244i	$0.422154\pi$
$972$	3.74334e15	0.138387
$973$	4.32724e15	0.159071
$974$	6.30201e16	2.30359
$975$	0	0
$976$	−3.90717e16	−1.41218
$977$	2.72899e16	0.980802	0.490401	−	0.871497i	$-0.336850\pi$
$977$	2.72899e16	0.980802	0.490401	+	0.871497i	$0.336850\pi$
$978$	2.02359e16	0.723200
$979$	6.13376e15	0.217983
$980$	0	0
$981$	8.75136e15	0.307536
$982$	−3.05192e16	−1.06650
$983$	3.53452e16	1.22825	0.614123	−	0.789210i	$-0.289510\pi$
$983$	3.53452e16	1.22825	0.614123	+	0.789210i	$0.289510\pi$
$984$	−5.83061e16	−2.01484
$985$	0	0
$986$	5.76875e16	1.97133
$987$	−2.37114e15	−0.0805773
$988$	4.83373e16	1.63350
$989$	−5.28061e16	−1.77462
$990$	0	0
$991$	2.66757e16	0.886564	0.443282	−	0.896382i	$-0.353814\pi$
$991$	2.66757e16	0.886564	0.443282	+	0.896382i	$0.353814\pi$
$992$	1.33046e15	0.0439732
$993$	−1.40656e15	−0.0462313
$994$	1.72812e16	0.564870
$995$	0	0
$996$	1.75173e16	0.566291
$997$	1.41711e16	0.455597	0.227799	−	0.973708i	$-0.426847\pi$
$997$	1.41711e16	0.455597	0.227799	+	0.973708i	$0.426847\pi$
$998$	−9.13520e16	−2.92079
$999$	−9.54486e15	−0.303501

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.12.a.k.1.6		6
3.2	odd	2		225.12.a.v.1.1		6
5.2	odd	4		15.12.b.a.4.11	yes	12
5.3	odd	4		15.12.b.a.4.2	✓	12
5.4	even	2		75.12.a.j.1.1		6
15.2	even	4		45.12.b.d.19.2		12
15.8	even	4		45.12.b.d.19.11		12
15.14	odd	2		225.12.a.y.1.6		6
20.3	even	4		240.12.f.d.49.2		12
20.7	even	4		240.12.f.d.49.8		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.12.b.a.4.2	✓	12	5.3	odd	4
15.12.b.a.4.11	yes	12	5.2	odd	4
45.12.b.d.19.2		12	15.2	even	4
45.12.b.d.19.11		12	15.8	even	4
75.12.a.j.1.1		6	5.4	even	2
75.12.a.k.1.6		6	1.1	even	1	trivial
225.12.a.v.1.1		6	3.2	odd	2
225.12.a.y.1.6		6	15.14	odd	2
240.12.f.d.49.2		12	20.3	even	4
240.12.f.d.49.8		12	20.7	even	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:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	75.a (trivial)

\(f(q)\)	\(=\)	\(q+80.4116 q^{2} +243.000 q^{3} +4418.02 q^{4} +19540.0 q^{6} -53961.2 q^{7} +190577. q^{8} +59049.0 q^{9} +O(q^{10})\)	\(q+80.4116 q^{2} +243.000 q^{3} +4418.02 q^{4} +19540.0 q^{6} -53961.2 q^{7} +190577. q^{8} +59049.0 q^{9} +407363. q^{11} +1.07358e6 q^{12} +1.39099e6 q^{13} -4.33911e6 q^{14} +6.27650e6 q^{16} +5.58145e6 q^{17} +4.74822e6 q^{18} +7.86560e6 q^{19} -1.31126e7 q^{21} +3.27567e7 q^{22} +6.07110e7 q^{23} +4.63102e7 q^{24} +1.11851e8 q^{26} +1.43489e7 q^{27} -2.38402e8 q^{28} +1.28534e8 q^{29} +1.16298e7 q^{31} +1.14401e8 q^{32} +9.89893e7 q^{33} +4.48813e8 q^{34} +2.60880e8 q^{36} -6.65198e8 q^{37} +6.32485e8 q^{38} +3.38010e8 q^{39} -1.25903e9 q^{41} -1.05440e9 q^{42} -8.69795e8 q^{43} +1.79974e9 q^{44} +4.88187e9 q^{46} +1.80829e8 q^{47} +1.52519e9 q^{48} +9.34486e8 q^{49} +1.35629e9 q^{51} +6.14541e9 q^{52} -9.98407e8 q^{53} +1.15382e9 q^{54} -1.02838e10 q^{56} +1.91134e9 q^{57} +1.03356e10 q^{58} -2.77404e9 q^{59} -6.22509e9 q^{61} +9.35170e8 q^{62} -3.18636e9 q^{63} -3.65509e9 q^{64} +7.95988e9 q^{66} +6.07983e9 q^{67} +2.46590e10 q^{68} +1.47528e10 q^{69} -3.98266e9 q^{71} +1.12534e10 q^{72} -1.70412e10 q^{73} -5.34896e10 q^{74} +3.47504e10 q^{76} -2.19818e10 q^{77} +2.71799e10 q^{78} -1.16813e10 q^{79} +3.48678e9 q^{81} -1.01241e11 q^{82} +1.63167e10 q^{83} -5.79316e10 q^{84} -6.99416e10 q^{86} +3.12337e10 q^{87} +7.76341e10 q^{88} +1.50572e10 q^{89} -7.50593e10 q^{91} +2.68222e11 q^{92} +2.82604e9 q^{93} +1.45408e10 q^{94} +2.77995e10 q^{96} -1.83308e10 q^{97} +7.51435e10 q^{98} +2.40544e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 9 q^{2} + 1458 q^{3} + 8157 q^{4} + 2187 q^{6} + 64368 q^{7} - 29277 q^{8} + 354294 q^{9}+O(q^{10}) \) 6 * q + 9 * q^2 + 1458 * q^3 + 8157 * q^4 + 2187 * q^6 + 64368 * q^7 - 29277 * q^8 + 354294 * q^9	\( 6 q + 9 q^{2} + 1458 q^{3} + 8157 q^{4} + 2187 q^{6} + 64368 q^{7} - 29277 q^{8} + 354294 q^{9} - 160776 q^{11} + 1982151 q^{12} + 1777464 q^{13} - 2318022 q^{14} + 14360865 q^{16} + 7789536 q^{17} + 531441 q^{18} + 14306328 q^{19} + 15641424 q^{21} + 99540522 q^{22} + 56578896 q^{23} - 7114311 q^{24} + 156248982 q^{26} + 86093442 q^{27} + 29296674 q^{28} + 229450716 q^{29} + 419037696 q^{31} - 496142397 q^{32} - 39068568 q^{33} + 272636394 q^{34} + 481662693 q^{36} - 441738792 q^{37} + 99095256 q^{38} + 431923752 q^{39} - 1880639244 q^{41} - 563279346 q^{42} + 1081616760 q^{43} - 3162393414 q^{44} - 939739884 q^{46} + 1868657040 q^{47} + 3489690195 q^{48} + 511947750 q^{49} + 1892857248 q^{51} + 9215549766 q^{52} + 10349483256 q^{53} + 129140163 q^{54} - 21606208290 q^{56} + 3476437704 q^{57} + 25240036752 q^{58} - 707714568 q^{59} + 8985508380 q^{61} + 25995031416 q^{62} + 3800866032 q^{63} + 4944042873 q^{64} + 24188346846 q^{66} + 13687306776 q^{67} + 94791079962 q^{68} + 13748671728 q^{69} - 8562874608 q^{71} - 1728777573 q^{72} + 63672451056 q^{73} - 44262217422 q^{74} + 69695921208 q^{76} - 10135567584 q^{77} + 37968502626 q^{78} + 41427333360 q^{79} + 20920706406 q^{81} + 34598023506 q^{82} + 124949795688 q^{83} + 7119091782 q^{84} - 18826696116 q^{86} + 55756523988 q^{87} + 430278178518 q^{88} + 90885005748 q^{89} - 48271166064 q^{91} + 310396941828 q^{92} + 101826160128 q^{93} - 139084157808 q^{94} - 120562602471 q^{96} + 257134073616 q^{97} + 405310493781 q^{98} - 9493662024 q^{99}+O(q^{100}) \) 6 * q + 9 * q^2 + 1458 * q^3 + 8157 * q^4 + 2187 * q^6 + 64368 * q^7 - 29277 * q^8 + 354294 * q^9 - 160776 * q^11 + 1982151 * q^12 + 1777464 * q^13 - 2318022 * q^14 + 14360865 * q^16 + 7789536 * q^17 + 531441 * q^18 + 14306328 * q^19 + 15641424 * q^21 + 99540522 * q^22 + 56578896 * q^23 - 7114311 * q^24 + 156248982 * q^26 + 86093442 * q^27 + 29296674 * q^28 + 229450716 * q^29 + 419037696 * q^31 - 496142397 * q^32 - 39068568 * q^33 + 272636394 * q^34 + 481662693 * q^36 - 441738792 * q^37 + 99095256 * q^38 + 431923752 * q^39 - 1880639244 * q^41 - 563279346 * q^42 + 1081616760 * q^43 - 3162393414 * q^44 - 939739884 * q^46 + 1868657040 * q^47 + 3489690195 * q^48 + 511947750 * q^49 + 1892857248 * q^51 + 9215549766 * q^52 + 10349483256 * q^53 + 129140163 * q^54 - 21606208290 * q^56 + 3476437704 * q^57 + 25240036752 * q^58 - 707714568 * q^59 + 8985508380 * q^61 + 25995031416 * q^62 + 3800866032 * q^63 + 4944042873 * q^64 + 24188346846 * q^66 + 13687306776 * q^67 + 94791079962 * q^68 + 13748671728 * q^69 - 8562874608 * q^71 - 1728777573 * q^72 + 63672451056 * q^73 - 44262217422 * q^74 + 69695921208 * q^76 - 10135567584 * q^77 + 37968502626 * q^78 + 41427333360 * q^79 + 20920706406 * q^81 + 34598023506 * q^82 + 124949795688 * q^83 + 7119091782 * q^84 - 18826696116 * q^86 + 55756523988 * q^87 + 430278178518 * q^88 + 90885005748 * q^89 - 48271166064 * q^91 + 310396941828 * q^92 + 101826160128 * q^93 - 139084157808 * q^94 - 120562602471 * q^96 + 257134073616 * q^97 + 405310493781 * q^98 - 9493662024 * q^99

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