LMFDB - Embedded newform 75.22.a.m.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,22,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, 22, names="a")

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

chi := DirichletCharacter("75.1");

S:= CuspForms(chi, 22);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 22 $
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:	$209.608008215$
Analytic rank:	$1$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 5 x^{9} - 15486550 x^{8} - 930225020 x^{7} + 80619202368510 x^{6} + \cdots + 47\!\cdots\!18 $ x^10 - 5x^9 - 15486550x^8 - 930225020x^7 + 80619202368510x^6 + 14206919536731394x^5 - 159833300365521427920x^4 - 53427455410418539963580x^3 + 93639331506281672292832825x^2 + 44269185428005803484908321595*x + 4729332062567824907768533377518
Coefficient ring:	$\Z[a_1, \ldots, a_{23}]$
Coefficient ring index:	$ 2^{24}\cdot 3^{14}\cdot 5^{24}\cdot 7^{2} $
Twist minimal:	no (minimal twist has level 15)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$2452.58$ 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)

$f(q)$	$=$	$q+2387.58 q^{2} +59049.0 q^{3} +3.60339e6 q^{4} +1.40984e8 q^{6} +8.76258e8 q^{7} +3.59626e9 q^{8} +3.48678e9 q^{9} +O(q^{10})$	\(q+2387.58 q^{2} +59049.0 q^{3} +3.60339e6 q^{4} +1.40984e8 q^{6} +8.76258e8 q^{7} +3.59626e9 q^{8} +3.48678e9 q^{9} -1.10419e11 q^{11} +2.12776e11 q^{12} -6.22087e11 q^{13} +2.09214e12 q^{14} +1.02950e12 q^{16} -6.51559e12 q^{17} +8.32498e12 q^{18} -4.44912e13 q^{19} +5.17421e13 q^{21} -2.63633e14 q^{22} +2.65057e14 q^{23} +2.12355e14 q^{24} -1.48528e15 q^{26} +2.05891e14 q^{27} +3.15750e15 q^{28} -1.28018e15 q^{29} -5.90644e15 q^{31} -5.08388e15 q^{32} -6.52010e15 q^{33} -1.55565e16 q^{34} +1.25642e16 q^{36} -3.24650e16 q^{37} -1.06226e17 q^{38} -3.67336e16 q^{39} -4.85384e16 q^{41} +1.23539e17 q^{42} +5.89988e16 q^{43} -3.97881e17 q^{44} +6.32845e17 q^{46} -3.80793e17 q^{47} +6.07910e16 q^{48} +2.09282e17 q^{49} -3.84739e17 q^{51} -2.24162e18 q^{52} +7.98759e17 q^{53} +4.91582e17 q^{54} +3.15125e18 q^{56} -2.62716e18 q^{57} -3.05653e18 q^{58} +3.84138e17 q^{59} +3.61141e18 q^{61} -1.41021e19 q^{62} +3.05532e18 q^{63} -1.42972e19 q^{64} -1.55673e19 q^{66} +9.40156e18 q^{67} -2.34782e19 q^{68} +1.56514e19 q^{69} +8.73489e18 q^{71} +1.25394e19 q^{72} +4.81680e19 q^{73} -7.75127e19 q^{74} -1.60319e20 q^{76} -9.67551e19 q^{77} -8.77045e19 q^{78} +8.49792e19 q^{79} +1.21577e19 q^{81} -1.15889e20 q^{82} +1.25162e20 q^{83} +1.86447e20 q^{84} +1.40864e20 q^{86} -7.55933e19 q^{87} -3.97093e20 q^{88} -1.17871e20 q^{89} -5.45109e20 q^{91} +9.55103e20 q^{92} -3.48770e20 q^{93} -9.09175e20 q^{94} -3.00198e20 q^{96} +1.21305e21 q^{97} +4.99677e20 q^{98} -3.85006e20 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 645 q^{2} + 590490 q^{3} + 10043205 q^{4} - 38086605 q^{6} - 115357290 q^{7} - 314142735 q^{8} + 34867844010 q^{9}+O(q^{10}) $ 10 * q - 645 * q^2 + 590490 * q^3 + 10043205 * q^4 - 38086605 * q^6 - 115357290 * q^7 - 314142735 * q^8 + 34867844010 * q^9	$ 10 q - 645 q^{2} + 590490 q^{3} + 10043205 q^{4} - 38086605 q^{6} - 115357290 q^{7} - 314142735 q^{8} + 34867844010 q^{9} + 5976221790 q^{11} + 593041212045 q^{12} - 842570747430 q^{13} + 1605059874570 q^{14} + 6061861547825 q^{16} - 12910340404230 q^{17} - 2248975938645 q^{18} - 76155422176280 q^{19} - 6811732617210 q^{21} - 461780887241010 q^{22} - 82640920915920 q^{23} - 18549814359015 q^{24} + 286555331159670 q^{26} + 20\!\cdots\!90 q^{27}+ \cdots + 20\!\cdots\!90 q^{99}+O(q^{100}) $ 10 * q - 645 * q^2 + 590490 * q^3 + 10043205 * q^4 - 38086605 * q^6 - 115357290 * q^7 - 314142735 * q^8 + 34867844010 * q^9 + 5976221790 * q^11 + 593041212045 * q^12 - 842570747430 * q^13 + 1605059874570 * q^14 + 6061861547825 * q^16 - 12910340404230 * q^17 - 2248975938645 * q^18 - 76155422176280 * q^19 - 6811732617210 * q^21 - 461780887241010 * q^22 - 82640920915920 * q^23 - 18549814359015 * q^24 + 286555331159670 * q^26 + 2058911320946490 * q^27 - 1520428218531930 * q^28 - 2553653160731010 * q^29 - 5579671364724940 * q^31 - 29255856594217815 * q^32 + 352889920477710 * q^33 + 36285968426431010 * q^34 + 35018490530045205 * q^36 - 1797908431222890 * q^37 - 10684960744876320 * q^38 - 49752960064994070 * q^39 - 157319729506021440 * q^41 + 94777180533483930 * q^42 + 148924853700743400 * q^43 + 49118820773767290 * q^44 - 238453286038259540 * q^46 + 43171138083158100 * q^47 + 357946862537518425 * q^48 + 453692886452454950 * q^49 - 762342690529377270 * q^51 - 5077473324432504030 * q^52 - 1835165786666252970 * q^53 - 132799780201048605 * q^54 - 5146515624013530450 * q^56 - 4496901524087157720 * q^57 - 3684042125074285440 * q^58 + 4936135121536323630 * q^59 - 4443080871007408300 * q^61 - 39366851097921260280 * q^62 - 402225999313633290 * q^63 - 14877283608188093455 * q^64 - 27267699610694399490 * q^66 - 33664559574358232580 * q^67 - 44791395195934111290 * q^68 - 4879863739164160080 * q^69 - 74662724971386630180 * q^71 - 1095347988085476735 * q^72 - 16062862692682477620 * q^73 - 130249023546610518030 * q^74 - 258736483662380220720 * q^76 - 56216747719240740180 * q^77 + 16920805749647353830 * q^78 - 49130708010799643300 * q^79 + 121576654590569288010 * q^81 - 117185080045656261930 * q^82 - 118408383608453695560 * q^83 - 89779765876091934570 * q^84 - 1007271272794707382260 * q^86 - 150790665488005409490 * q^87 - 41803519849182967710 * q^88 - 572103976713991581780 * q^89 - 1669810835257196575140 * q^91 + 1206545757146297440260 * q^92 - 329474014415642982060 * q^93 - 1671319720124696594920 * q^94 - 1727529076031967757935 * q^96 + 1299275526640742173920 * q^97 + 2683959884079093505455 * q^98 + 20837796914288297790 * 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 $

$2$	2387.58	1.64871	0.824353	−	0.566077i	$-0.191539\pi$
$2$	2387.58	1.64871	0.824353	+	0.566077i	$0.191539\pi$
$3$	59049.0	0.577350
$3$	59049.0	0.577350
$4$	3.60339e6	1.71823
$5$	0	0
$5$	0	0
$6$	1.40984e8	0.951880
$7$	8.76258e8	1.17247	0.586236	−	0.810140i	$-0.300609\pi$
$7$	8.76258e8	1.17247	0.586236	+	0.810140i	$0.300609\pi$
$8$	3.59626e9	1.18415
$9$	3.48678e9	0.333333
$10$	0	0
$11$	−1.10419e11	−1.28357	−0.641784	−	0.766886i	$-0.721805\pi$
$11$	−1.10419e11	−1.28357	−0.641784	+	0.766886i	$0.721805\pi$
$12$	2.12776e11	0.992020
$13$	−6.22087e11	−1.25154	−0.625772	−	0.780006i	$-0.715216\pi$
$13$	−6.22087e11	−1.25154	−0.625772	+	0.780006i	$0.715216\pi$
$14$	2.09214e12	1.93306
$15$	0	0
$16$	1.02950e12	0.234082
$17$	−6.51559e12	−0.783863	−0.391931	−	0.919994i	$-0.628193\pi$
$17$	−6.51559e12	−0.783863	−0.391931	+	0.919994i	$0.628193\pi$
$18$	8.32498e12	0.549568
$19$	−4.44912e13	−1.66480	−0.832399	−	0.554177i	$-0.813033\pi$
$19$	−4.44912e13	−1.66480	−0.832399	+	0.554177i	$0.813033\pi$
$20$	0	0
$21$	5.17421e13	0.676927
$22$	−2.63633e14	−2.11622
$23$	2.65057e14	1.33413	0.667063	−	0.745001i	$-0.267551\pi$
$23$	2.65057e14	1.33413	0.667063	+	0.745001i	$0.267551\pi$
$24$	2.12355e14	0.683668
$25$	0	0
$26$	−1.48528e15	−2.06343
$27$	2.05891e14	0.192450
$28$	3.15750e15	2.01458
$29$	−1.28018e15	−0.565056	−0.282528	−	0.959259i	$-0.591173\pi$
$29$	−1.28018e15	−0.565056	−0.282528	+	0.959259i	$0.591173\pi$
$30$	0	0
$31$	−5.90644e15	−1.29428	−0.647140	−	0.762371i	$-0.724035\pi$
$31$	−5.90644e15	−1.29428	−0.647140	+	0.762371i	$0.724035\pi$
$32$	−5.08388e15	−0.798216
$33$	−6.52010e15	−0.741068
$34$	−1.55565e16	−1.29236
$35$	0	0
$36$	1.25642e16	0.572743
$37$	−3.24650e16	−1.10993	−0.554967	−	0.831872i	$-0.687269\pi$
$37$	−3.24650e16	−1.10993	−0.554967	+	0.831872i	$0.687269\pi$
$38$	−1.06226e17	−2.74476
$39$	−3.67336e16	−0.722579
$40$	0	0
$41$	−4.85384e16	−0.564749	−0.282374	−	0.959304i	$-0.591122\pi$
$41$	−4.85384e16	−0.564749	−0.282374	+	0.959304i	$0.591122\pi$
$42$	1.23539e17	1.11605
$43$	5.89988e16	0.416317	0.208159	−	0.978095i	$-0.433253\pi$
$43$	5.89988e16	0.416317	0.208159	+	0.978095i	$0.433253\pi$
$44$	−3.97881e17	−2.20546
$45$	0	0
$46$	6.32845e17	2.19958
$47$	−3.80793e17	−1.05600	−0.527998	−	0.849246i	$-0.677057\pi$
$47$	−3.80793e17	−1.05600	−0.527998	+	0.849246i	$0.677057\pi$
$48$	6.07910e16	0.135147
$49$	2.09282e17	0.374691
$50$	0	0
$51$	−3.84739e17	−0.452563
$52$	−2.24162e18	−2.15044
$53$	7.98759e17	0.627363	0.313682	−	0.949528i	$-0.398438\pi$
$53$	7.98759e17	0.627363	0.313682	+	0.949528i	$0.398438\pi$
$54$	4.91582e17	0.317293
$55$	0	0
$56$	3.15125e18	1.38838
$57$	−2.62716e18	−0.961171
$58$	−3.05653e18	−0.931611
$59$	3.84138e17	0.0978455	0.0489227	−	0.998803i	$-0.484421\pi$
$59$	3.84138e17	0.0978455	0.0489227	+	0.998803i	$0.484421\pi$
$60$	0	0
$61$	3.61141e18	0.648207	0.324104	−	0.946022i	$-0.394937\pi$
$61$	3.61141e18	0.648207	0.324104	+	0.946022i	$0.394937\pi$
$62$	−1.41021e19	−2.13389
$63$	3.05532e18	0.390824
$64$	−1.42972e19	−1.55010
$65$	0	0
$66$	−1.55673e19	−1.22180
$67$	9.40156e18	0.630107	0.315054	−	0.949074i	$-0.397978\pi$
$67$	9.40156e18	0.630107	0.315054	+	0.949074i	$0.397978\pi$
$68$	−2.34782e19	−1.34686
$69$	1.56514e19	0.770258
$70$	0	0
$71$	8.73489e18	0.318453	0.159226	−	0.987242i	$-0.449100\pi$
$71$	8.73489e18	0.318453	0.159226	+	0.987242i	$0.449100\pi$
$72$	1.25394e19	0.394716
$73$	4.81680e19	1.31180	0.655901	−	0.754847i	$-0.272289\pi$
$73$	4.81680e19	1.31180	0.655901	+	0.754847i	$0.272289\pi$
$74$	−7.75127e19	−1.82995
$75$	0	0
$76$	−1.60319e20	−2.86050
$77$	−9.67551e19	−1.50495
$78$	−8.77045e19	−1.19132
$79$	8.49792e19	1.00978	0.504892	−	0.863183i	$-0.331532\pi$
$79$	8.49792e19	1.00978	0.504892	+	0.863183i	$0.331532\pi$
$80$	0	0
$81$	1.21577e19	0.111111
$82$	−1.15889e20	−0.931104
$83$	1.25162e20	0.885428	0.442714	−	0.896663i	$-0.354016\pi$
$83$	1.25162e20	0.885428	0.442714	+	0.896663i	$0.354016\pi$
$84$	1.86447e20	1.16312
$85$	0	0
$86$	1.40864e20	0.686384
$87$	−7.55933e19	−0.326235
$88$	−3.97093e20	−1.51993
$89$	−1.17871e20	−0.400694	−0.200347	−	0.979725i	$-0.564207\pi$
$89$	−1.17871e20	−0.400694	−0.200347	+	0.979725i	$0.564207\pi$
$90$	0	0
$91$	−5.45109e20	−1.46740
$92$	9.55103e20	2.29233
$93$	−3.48770e20	−0.747253
$94$	−9.09175e20	−1.74102
$95$	0	0
$96$	−3.00198e20	−0.460850
$97$	1.21305e21	1.67023	0.835113	−	0.550078i	$-0.185402\pi$
$97$	1.21305e21	1.67023	0.835113	+	0.550078i	$0.185402\pi$
$98$	4.99677e20	0.617755
$99$	−3.85006e20	−0.427856
$100$	0	0
$101$	−5.76859e20	−0.519632	−0.259816	−	0.965658i	$-0.583662\pi$
$101$	−5.76859e20	−0.519632	−0.259816	+	0.965658i	$0.583662\pi$
$102$	−9.18595e20	−0.746143
$103$	2.55658e21	1.87443	0.937214	−	0.348756i	$-0.113396\pi$
$103$	2.55658e21	1.87443	0.937214	+	0.348756i	$0.113396\pi$
$104$	−2.23719e21	−1.48201
$105$	0	0
$106$	1.90710e21	1.03434
$107$	−7.39775e19	−0.0363555	−0.0181777	−	0.999835i	$-0.505786\pi$
$107$	−7.39775e19	−0.0363555	−0.0181777	+	0.999835i	$0.505786\pi$
$108$	7.41905e20	0.330673
$109$	−6.54607e20	−0.264851	−0.132426	−	0.991193i	$-0.542277\pi$
$109$	−6.54607e20	−0.264851	−0.132426	+	0.991193i	$0.542277\pi$
$110$	0	0
$111$	−1.91702e21	−0.640821
$112$	9.02109e20	0.274454
$113$	1.60631e21	0.445148	0.222574	−	0.974916i	$-0.428554\pi$
$113$	1.60631e21	0.445148	0.222574	+	0.974916i	$0.428554\pi$
$114$	−6.27256e21	−1.58469
$115$	0	0
$116$	−4.61298e21	−0.970896
$117$	−2.16908e21	−0.417181
$118$	9.17159e20	0.161318
$119$	−5.70933e21	−0.919057
$120$	0	0
$121$	4.79200e21	0.647545
$122$	8.62254e21	1.06870
$123$	−2.86615e21	−0.326058
$124$	−2.12832e22	−2.22387
$125$	0	0
$126$	7.29483e21	0.644354
$127$	−1.38046e22	−1.12224	−0.561120	−	0.827735i	$-0.689629\pi$
$127$	−1.38046e22	−1.12224	−0.561120	+	0.827735i	$0.689629\pi$
$128$	−2.34740e22	−1.75745
$129$	3.48382e21	0.240361
$130$	0	0
$131$	−2.97523e22	−1.74652	−0.873258	−	0.487259i	$-0.837997\pi$
$131$	−2.97523e22	−1.74652	−0.873258	+	0.487259i	$0.837997\pi$
$132$	−2.34945e22	−1.27332
$133$	−3.89858e22	−1.95193
$134$	2.24470e22	1.03886
$135$	0	0
$136$	−2.34317e22	−0.928209
$137$	−1.31132e22	−0.480998	−0.240499	−	0.970649i	$-0.577311\pi$
$137$	−1.31132e22	−0.480998	−0.240499	+	0.970649i	$0.577311\pi$
$138$	3.73689e22	1.26993
$139$	−3.83710e22	−1.20878	−0.604391	−	0.796688i	$-0.706583\pi$
$139$	−3.83710e22	−1.20878	−0.604391	+	0.796688i	$0.706583\pi$
$140$	0	0
$141$	−2.24855e22	−0.609679
$142$	2.08552e22	0.525034
$143$	6.86900e22	1.60644
$144$	3.58965e21	0.0780272
$145$	0	0
$146$	1.15005e23	2.16278
$147$	1.23579e22	0.216328
$148$	−1.16984e23	−1.90712
$149$	−1.00244e23	−1.52265	−0.761326	−	0.648369i	$-0.775452\pi$
$149$	−1.00244e23	−1.52265	−0.761326	+	0.648369i	$0.775452\pi$
$150$	0	0
$151$	−1.25747e23	−1.66050	−0.830250	−	0.557391i	$-0.811803\pi$
$151$	−1.25747e23	−1.66050	−0.830250	+	0.557391i	$0.811803\pi$
$152$	−1.60002e23	−1.97137
$153$	−2.27184e22	−0.261288
$154$	−2.31011e23	−2.48121
$155$	0	0
$156$	−1.32366e23	−1.24156
$157$	2.01217e23	1.76489	0.882446	−	0.470413i	$-0.155895\pi$
$157$	2.01217e23	1.76489	0.882446	+	0.470413i	$0.155895\pi$
$158$	2.02895e23	1.66483
$159$	4.71659e22	0.362208
$160$	0	0
$161$	2.32258e23	1.56423
$162$	2.90274e22	0.183189
$163$	−4.19267e22	−0.248039	−0.124020	−	0.992280i	$-0.539579\pi$
$163$	−4.19267e22	−0.248039	−0.124020	+	0.992280i	$0.539579\pi$
$164$	−1.74903e23	−0.970368
$165$	0	0
$166$	2.98835e23	1.45981
$167$	3.15517e23	1.44710	0.723552	−	0.690270i	$-0.242508\pi$
$167$	3.15517e23	1.44710	0.723552	+	0.690270i	$0.242508\pi$
$168$	1.86078e23	0.801582
$169$	1.39928e23	0.566363
$170$	0	0
$171$	−1.55131e23	−0.554932
$172$	2.12596e23	0.715328
$173$	−1.49085e23	−0.472008	−0.236004	−	0.971752i	$-0.575838\pi$
$173$	−1.49085e23	−0.472008	−0.236004	+	0.971752i	$0.575838\pi$
$174$	−1.80485e23	−0.537866
$175$	0	0
$176$	−1.13676e23	−0.300459
$177$	2.26829e22	0.0564911
$178$	−2.81427e23	−0.660626
$179$	5.40567e23	1.19644	0.598222	−	0.801330i	$-0.295874\pi$
$179$	5.40567e23	1.19644	0.598222	+	0.801330i	$0.295874\pi$
$180$	0	0
$181$	−6.19144e23	−1.21946	−0.609729	−	0.792610i	$-0.708722\pi$
$181$	−6.19144e23	−1.21946	−0.609729	+	0.792610i	$0.708722\pi$
$182$	−1.30149e24	−2.41931
$183$	2.13250e23	0.374243
$184$	9.53213e23	1.57980
$185$	0	0
$186$	−8.32715e23	−1.23200
$187$	7.19441e23	1.00614
$188$	−1.37215e24	−1.81444
$189$	1.80414e23	0.225642
$190$	0	0
$191$	2.44367e23	0.273648	0.136824	−	0.990595i	$-0.456310\pi$
$191$	2.44367e23	0.273648	0.136824	+	0.990595i	$0.456310\pi$
$192$	−8.44235e23	−0.894953
$193$	−4.25935e23	−0.427555	−0.213777	−	0.976882i	$-0.568577\pi$
$193$	−4.25935e23	−0.427555	−0.213777	+	0.976882i	$0.568577\pi$
$194$	2.89625e24	2.75371
$195$	0	0
$196$	7.54124e23	0.643804
$197$	−7.93527e23	−0.642194	−0.321097	−	0.947046i	$-0.604052\pi$
$197$	−7.93527e23	−0.642194	−0.321097	+	0.947046i	$0.604052\pi$
$198$	−9.19232e23	−0.705408
$199$	−9.08298e23	−0.661106	−0.330553	−	0.943787i	$-0.607235\pi$
$199$	−9.08298e23	−0.661106	−0.330553	+	0.943787i	$0.607235\pi$
$200$	0	0
$201$	5.55153e23	0.363793
$202$	−1.37730e24	−0.856719
$203$	−1.12177e24	−0.662513
$204$	−1.38636e24	−0.777607
$205$	0	0
$206$	6.10404e24	3.09038
$207$	9.24197e23	0.444709
$208$	−6.40440e23	−0.292963
$209$	4.91265e24	2.13688
$210$	0	0
$211$	−3.95450e24	−1.55642	−0.778208	−	0.628006i	$-0.783871\pi$
$211$	−3.95450e24	−1.55642	−0.778208	+	0.628006i	$0.783871\pi$
$212$	2.87824e24	1.07795
$213$	5.15787e23	0.183859
$214$	−1.76627e23	−0.0599395
$215$	0	0
$216$	7.40437e23	0.227889
$217$	−5.17557e24	−1.51751
$218$	−1.56293e24	−0.436662
$219$	2.84427e24	0.757369
$220$	0	0
$221$	4.05326e24	0.981039
$222$	−4.57705e24	−1.05652
$223$	4.82026e24	1.06138	0.530688	−	0.847567i	$-0.321933\pi$
$223$	4.82026e24	1.06138	0.530688	+	0.847567i	$0.321933\pi$
$224$	−4.45479e24	−0.935886
$225$	0	0
$226$	3.83519e24	0.733918
$227$	4.54756e23	0.0830820	0.0415410	−	0.999137i	$-0.486773\pi$
$227$	4.54756e23	0.0830820	0.0415410	+	0.999137i	$0.486773\pi$
$228$	−9.46668e24	−1.65151
$229$	3.15414e24	0.525543	0.262772	−	0.964858i	$-0.415363\pi$
$229$	3.15414e24	0.525543	0.262772	+	0.964858i	$0.415363\pi$
$230$	0	0
$231$	−5.71329e24	−0.868881
$232$	−4.60385e24	−0.669110
$233$	2.56872e24	0.356845	0.178422	−	0.983954i	$-0.442901\pi$
$233$	2.56872e24	0.356845	0.178422	+	0.983954i	$0.442901\pi$
$234$	−5.17886e24	−0.687809
$235$	0	0
$236$	1.38420e24	0.168121
$237$	5.01794e24	0.582999
$238$	−1.36315e25	−1.51525
$239$	−2.06378e24	−0.219525	−0.109763	−	0.993958i	$-0.535009\pi$
$239$	−2.06378e24	−0.219525	−0.109763	+	0.993958i	$0.535009\pi$
$240$	0	0
$241$	−2.79054e24	−0.271963	−0.135982	−	0.990711i	$-0.543419\pi$
$241$	−2.79054e24	−0.271963	−0.135982	+	0.990711i	$0.543419\pi$
$242$	1.14413e25	1.06761
$243$	7.17898e23	0.0641500
$244$	1.30133e25	1.11377
$245$	0	0
$246$	−6.84315e24	−0.537573
$247$	2.76774e25	2.08357
$248$	−2.12411e25	−1.53262
$249$	7.39070e24	0.511202
$250$	0	0
$251$	2.77647e25	1.76571	0.882854	−	0.469648i	$-0.155619\pi$
$251$	2.77647e25	1.76571	0.882854	+	0.469648i	$0.155619\pi$
$252$	1.10095e25	0.671525
$253$	−2.92672e25	−1.71244
$254$	−3.29596e25	−1.85024
$255$	0	0
$256$	−2.60627e25	−1.34741
$257$	−3.62323e25	−1.79804	−0.899019	−	0.437910i	$-0.855719\pi$
$257$	−3.62323e25	−1.79804	−0.899019	+	0.437910i	$0.855719\pi$
$258$	8.31790e24	0.396284
$259$	−2.84477e25	−1.30137
$260$	0	0
$261$	−4.46371e24	−0.188352
$262$	−7.10361e25	−2.87949
$263$	−3.27196e25	−1.27430	−0.637151	−	0.770739i	$-0.719887\pi$
$263$	−3.27196e25	−1.27430	−0.637151	+	0.770739i	$0.719887\pi$
$264$	−2.34480e25	−0.877534
$265$	0	0
$266$	−9.30817e25	−3.21815
$267$	−6.96018e24	−0.231341
$268$	3.38775e25	1.08267
$269$	−1.90716e25	−0.586121	−0.293061	−	0.956094i	$-0.594674\pi$
$269$	−1.90716e25	−0.586121	−0.293061	+	0.956094i	$0.594674\pi$
$270$	0	0
$271$	−5.72060e25	−1.62654	−0.813268	−	0.581889i	$-0.802314\pi$
$271$	−5.72060e25	−1.62654	−0.813268	+	0.581889i	$0.802314\pi$
$272$	−6.70781e24	−0.183488
$273$	−3.21881e25	−0.847204
$274$	−3.13089e25	−0.793024
$275$	0	0
$276$	5.63979e25	1.32348
$277$	−1.19508e25	−0.269998	−0.134999	−	0.990846i	$-0.543103\pi$
$277$	−1.19508e25	−0.269998	−0.134999	+	0.990846i	$0.543103\pi$
$278$	−9.16138e25	−1.99292
$279$	−2.05945e25	−0.431427
$280$	0	0
$281$	−2.63635e25	−0.512374	−0.256187	−	0.966627i	$-0.582466\pi$
$281$	−2.63635e25	−0.512374	−0.256187	+	0.966627i	$0.582466\pi$
$282$	−5.36859e25	−1.00518
$283$	7.88642e24	0.142273	0.0711365	−	0.997467i	$-0.477337\pi$
$283$	7.88642e24	0.142273	0.0711365	+	0.997467i	$0.477337\pi$
$284$	3.14752e25	0.547174
$285$	0	0
$286$	1.64003e26	2.64855
$287$	−4.25322e25	−0.662152
$288$	−1.77264e25	−0.266072
$289$	−2.66391e25	−0.385560
$290$	0	0
$291$	7.16294e25	0.964306
$292$	1.73568e26	2.25398
$293$	8.38525e25	1.05052	0.525262	−	0.850941i	$-0.323967\pi$
$293$	8.38525e25	1.05052	0.525262	+	0.850941i	$0.323967\pi$
$294$	2.95055e25	0.356661
$295$	0	0
$296$	−1.16752e26	−1.31433
$297$	−2.27342e25	−0.247023
$298$	−2.39340e26	−2.51041
$299$	−1.64889e26	−1.66972
$300$	0	0
$301$	5.16982e25	0.488120
$302$	−3.00231e26	−2.73768
$303$	−3.40630e25	−0.300009
$304$	−4.58038e25	−0.389698
$305$	0	0
$306$	−5.42421e25	−0.430786
$307$	1.09880e26	0.843269	0.421634	−	0.906766i	$-0.361457\pi$
$307$	1.09880e26	0.843269	0.421634	+	0.906766i	$0.361457\pi$
$308$	−3.48646e26	−2.58584
$309$	1.50964e26	1.08220
$310$	0	0
$311$	−3.92080e25	−0.262658	−0.131329	−	0.991339i	$-0.541924\pi$
$311$	−3.92080e25	−0.262658	−0.131329	+	0.991339i	$0.541924\pi$
$312$	−1.32104e26	−0.855641
$313$	2.47324e26	1.54900	0.774498	−	0.632577i	$-0.218003\pi$
$313$	2.47324e26	1.54900	0.774498	+	0.632577i	$0.218003\pi$
$314$	4.80422e26	2.90979
$315$	0	0
$316$	3.06213e26	1.73504
$317$	7.89343e25	0.432657	0.216328	−	0.976321i	$-0.430592\pi$
$317$	7.89343e25	0.432657	0.216328	+	0.976321i	$0.430592\pi$
$318$	1.12612e26	0.597175
$319$	1.41355e26	0.725288
$320$	0	0
$321$	−4.36830e24	−0.0209898
$322$	5.54535e26	2.57895
$323$	2.89886e26	1.30497
$324$	4.38088e25	0.190914
$325$	0	0
$326$	−1.00103e26	−0.408944
$327$	−3.86539e25	−0.152912
$328$	−1.74557e26	−0.668746
$329$	−3.33673e26	−1.23812
$330$	0	0
$331$	−2.32921e26	−0.810988	−0.405494	−	0.914098i	$-0.632900\pi$
$331$	−2.32921e26	−0.810988	−0.405494	+	0.914098i	$0.632900\pi$
$332$	4.51008e26	1.52137
$333$	−1.13198e26	−0.369978
$334$	7.53322e26	2.38585
$335$	0	0
$336$	5.32686e25	0.158456
$337$	−1.21446e24	−0.00350161	−0.00175081	−	0.999998i	$-0.500557\pi$
$337$	−1.21446e24	−0.00350161	−0.00175081	+	0.999998i	$0.500557\pi$
$338$	3.34090e26	0.933765
$339$	9.48508e25	0.257007
$340$	0	0
$341$	6.52181e26	1.66130
$342$	−3.70388e26	−0.914920
$343$	−3.06045e26	−0.733158
$344$	2.12175e26	0.492981
$345$	0	0
$346$	−3.55952e26	−0.778203
$347$	−7.09460e26	−1.50476	−0.752382	−	0.658727i	$-0.771095\pi$
$347$	−7.09460e26	−1.50476	−0.752382	+	0.658727i	$0.771095\pi$
$348$	−2.72392e26	−0.560547
$349$	5.40523e26	1.07931	0.539656	−	0.841886i	$-0.318554\pi$
$349$	5.40523e26	1.07931	0.539656	+	0.841886i	$0.318554\pi$
$350$	0	0
$351$	−1.28082e26	−0.240860
$352$	5.61354e26	1.02456
$353$	−4.72052e26	−0.836287	−0.418144	−	0.908381i	$-0.637319\pi$
$353$	−4.72052e26	−0.836287	−0.418144	+	0.908381i	$0.637319\pi$
$354$	5.41573e25	0.0931372
$355$	0	0
$356$	−4.24736e26	−0.688484
$357$	−3.37131e26	−0.530618
$358$	1.29065e27	1.97258
$359$	−3.20233e26	−0.475307	−0.237653	−	0.971350i	$-0.576378\pi$
$359$	−3.20233e26	−0.475307	−0.237653	+	0.971350i	$0.576378\pi$
$360$	0	0
$361$	1.26526e27	1.77155
$362$	−1.47826e27	−2.01053
$363$	2.82963e26	0.373860
$364$	−1.96424e27	−2.52133
$365$	0	0
$366$	5.09152e26	0.617016
$367$	5.97709e26	0.703876	0.351938	−	0.936023i	$-0.385523\pi$
$367$	5.97709e26	0.703876	0.351938	+	0.936023i	$0.385523\pi$
$368$	2.72877e26	0.312294
$369$	−1.69243e26	−0.188250
$370$	0	0
$371$	6.99919e26	0.735566
$372$	−1.25675e27	−1.28395
$373$	−1.06103e27	−1.05386	−0.526932	−	0.849908i	$-0.676658\pi$
$373$	−1.06103e27	−1.05386	−0.526932	+	0.849908i	$0.676658\pi$
$374$	1.71772e27	1.65883
$375$	0	0
$376$	−1.36943e27	−1.25045
$377$	7.96383e26	0.707193
$378$	4.30752e26	0.372018
$379$	−2.28626e26	−0.192050	−0.0960248	−	0.995379i	$-0.530613\pi$
$379$	−2.28626e26	−0.192050	−0.0960248	+	0.995379i	$0.530613\pi$
$380$	0	0
$381$	−8.15149e26	−0.647925
$382$	5.83446e26	0.451165
$383$	1.31136e27	0.986587	0.493293	−	0.869863i	$-0.335793\pi$
$383$	1.31136e27	0.986587	0.493293	+	0.869863i	$0.335793\pi$
$384$	−1.38612e27	−1.01466
$385$	0	0
$386$	−1.01695e27	−0.704911
$387$	2.05716e26	0.138772
$388$	4.37109e27	2.86983
$389$	−1.54163e27	−0.985164	−0.492582	−	0.870266i	$-0.663947\pi$
$389$	−1.54163e27	−0.985164	−0.492582	+	0.870266i	$0.663947\pi$
$390$	0	0
$391$	−1.72700e27	−1.04577
$392$	7.52632e26	0.443689
$393$	−1.75685e27	−1.00835
$394$	−1.89461e27	−1.05879
$395$	0	0
$396$	−1.38732e27	−0.735154
$397$	2.00697e27	1.03572	0.517858	−	0.855467i	$-0.326730\pi$
$397$	2.00697e27	1.03572	0.517858	+	0.855467i	$0.326730\pi$
$398$	−2.16863e27	−1.08997
$399$	−2.30207e27	−1.12695
$400$	0	0
$401$	1.45786e27	0.677174	0.338587	−	0.940935i	$-0.390051\pi$
$401$	1.45786e27	0.677174	0.338587	+	0.940935i	$0.390051\pi$
$402$	1.32547e27	0.599787
$403$	3.67432e27	1.61985
$404$	−2.07865e27	−0.892846
$405$	0	0
$406$	−2.67831e27	−1.09229
$407$	3.58473e27	1.42467
$408$	−1.38362e27	−0.535902
$409$	−4.07184e26	−0.153708	−0.0768539	−	0.997042i	$-0.524487\pi$
$409$	−4.07184e26	−0.153708	−0.0768539	+	0.997042i	$0.524487\pi$
$410$	0	0
$411$	−7.74323e26	−0.277705
$412$	9.21235e27	3.22069
$413$	3.36604e26	0.114721
$414$	2.20659e27	0.733194
$415$	0	0
$416$	3.16262e27	0.999003
$417$	−2.26577e27	−0.697890
$418$	1.17294e28	3.52308
$419$	6.24808e27	1.83020	0.915102	−	0.403222i	$-0.132110\pi$
$419$	6.24808e27	1.83020	0.915102	+	0.403222i	$0.132110\pi$
$420$	0	0
$421$	−2.35871e26	−0.0657222	−0.0328611	−	0.999460i	$-0.510462\pi$
$421$	−2.35871e26	−0.0657222	−0.0328611	+	0.999460i	$0.510462\pi$
$422$	−9.44169e27	−2.56607
$423$	−1.32774e27	−0.351998
$424$	2.87254e27	0.742891
$425$	0	0
$426$	1.23148e27	0.303129
$427$	3.16453e27	0.760005
$428$	−2.66569e26	−0.0624670
$429$	4.05607e27	0.927479
$430$	0	0
$431$	4.15650e27	0.905142	0.452571	−	0.891728i	$-0.350507\pi$
$431$	4.15650e27	0.905142	0.452571	+	0.891728i	$0.350507\pi$
$432$	2.11965e26	0.0450490
$433$	5.57069e26	0.115554	0.0577771	−	0.998330i	$-0.481599\pi$
$433$	5.57069e26	0.115554	0.0577771	+	0.998330i	$0.481599\pi$
$434$	−1.23571e28	−2.50192
$435$	0	0
$436$	−2.35880e27	−0.455075
$437$	−1.17927e28	−2.22105
$438$	6.79093e27	1.24868
$439$	−2.53634e27	−0.455333	−0.227667	−	0.973739i	$-0.573110\pi$
$439$	−2.53634e27	−0.455333	−0.227667	+	0.973739i	$0.573110\pi$
$440$	0	0
$441$	7.29721e26	0.124897
$442$	9.67749e27	1.61744
$443$	2.56725e27	0.419014	0.209507	−	0.977807i	$-0.432814\pi$
$443$	2.56725e27	0.419014	0.209507	+	0.977807i	$0.432814\pi$
$444$	−6.90778e27	−1.10108
$445$	0	0
$446$	1.15088e28	1.74990
$447$	−5.91929e27	−0.879104
$448$	−1.25280e28	−1.81745
$449$	7.06573e27	1.00131	0.500657	−	0.865646i	$-0.333092\pi$
$449$	7.06573e27	1.00131	0.500657	+	0.865646i	$0.333092\pi$
$450$	0	0
$451$	5.35954e27	0.724893
$452$	5.78814e27	0.764867
$453$	−7.42522e27	−0.958690
$454$	1.08577e27	0.136978
$455$	0	0
$456$	−9.44795e27	−1.13817
$457$	−6.21874e27	−0.732120	−0.366060	−	0.930591i	$-0.619293\pi$
$457$	−6.21874e27	−0.732120	−0.366060	+	0.930591i	$0.619293\pi$
$458$	7.53076e27	0.866466
$459$	−1.34150e27	−0.150854
$460$	0	0
$461$	−1.49683e28	−1.60810	−0.804051	−	0.594560i	$-0.797326\pi$
$461$	−1.49683e28	−1.60810	−0.804051	+	0.594560i	$0.797326\pi$
$462$	−1.36409e28	−1.43253
$463$	−3.94663e27	−0.405159	−0.202580	−	0.979266i	$-0.564933\pi$
$463$	−3.94663e27	−0.405159	−0.202580	+	0.979266i	$0.564933\pi$
$464$	−1.31795e27	−0.132269
$465$	0	0
$466$	6.13302e27	0.588331
$467$	8.85697e27	0.830726	0.415363	−	0.909656i	$-0.363655\pi$
$467$	8.85697e27	0.830726	0.415363	+	0.909656i	$0.363655\pi$
$468$	−7.81605e27	−0.716813
$469$	8.23819e27	0.738783
$470$	0	0
$471$	1.18817e28	1.01896
$472$	1.38146e27	0.115863
$473$	−6.51456e27	−0.534371
$474$	1.19807e28	0.961193
$475$	0	0
$476$	−2.05729e28	−1.57915
$477$	2.78510e27	0.209121
$478$	−4.92743e27	−0.361933
$479$	1.14619e28	0.823631	0.411816	−	0.911267i	$-0.364895\pi$
$479$	1.14619e28	0.823631	0.411816	+	0.911267i	$0.364895\pi$
$480$	0	0
$481$	2.01961e28	1.38913
$482$	−6.66265e27	−0.448387
$483$	1.37146e28	0.903106
$484$	1.72674e28	1.11263
$485$	0	0
$486$	1.71404e27	0.105764
$487$	−1.56047e28	−0.942326	−0.471163	−	0.882046i	$-0.656166\pi$
$487$	−1.56047e28	−0.942326	−0.471163	+	0.882046i	$0.656166\pi$
$488$	1.29876e28	0.767573
$489$	−2.47573e27	−0.143206
$490$	0	0
$491$	−6.12854e27	−0.339626	−0.169813	−	0.985476i	$-0.554316\pi$
$491$	−6.12854e27	−0.339626	−0.169813	+	0.985476i	$0.554316\pi$
$492$	−1.03278e28	−0.560242
$493$	8.34112e27	0.442927
$494$	6.60821e28	3.43519
$495$	0	0
$496$	−6.08069e27	−0.302967
$497$	7.65402e27	0.373377
$498$	1.76459e28	0.842821
$499$	3.53336e27	0.165247	0.0826233	−	0.996581i	$-0.473670\pi$
$499$	3.53336e27	0.165247	0.0826233	+	0.996581i	$0.473670\pi$
$500$	0	0
$501$	1.86310e28	0.835486
$502$	6.62904e28	2.91113
$503$	−1.55458e28	−0.668575	−0.334287	−	0.942471i	$-0.608496\pi$
$503$	−1.55458e28	−0.668575	−0.334287	+	0.942471i	$0.608496\pi$
$504$	1.09877e28	0.462793
$505$	0	0
$506$	−6.98778e28	−2.82331
$507$	8.26262e27	0.326990
$508$	−4.97434e28	−1.92826
$509$	−2.47938e27	−0.0941469	−0.0470735	−	0.998891i	$-0.514989\pi$
$509$	−2.47938e27	−0.0941469	−0.0470735	+	0.998891i	$0.514989\pi$
$510$	0	0
$511$	4.22076e28	1.53805
$512$	−1.29983e28	−0.464035
$513$	−9.16035e27	−0.320390
$514$	−8.65076e28	−2.96443
$515$	0	0
$516$	1.25536e28	0.412995
$517$	4.20466e28	1.35544
$518$	−6.79211e28	−2.14557
$519$	−8.80332e27	−0.272514
$520$	0	0
$521$	5.55830e28	1.65252	0.826258	−	0.563292i	$-0.190465\pi$
$521$	5.55830e28	1.65252	0.826258	+	0.563292i	$0.190465\pi$
$522$	−1.06575e28	−0.310537
$523$	1.46478e27	0.0418315	0.0209158	−	0.999781i	$-0.493342\pi$
$523$	1.46478e27	0.0418315	0.0209158	+	0.999781i	$0.493342\pi$
$524$	−1.07209e29	−3.00091
$525$	0	0
$526$	−7.81207e28	−2.10095
$527$	3.84839e28	1.01454
$528$	−6.71245e27	−0.173470
$529$	3.07836e28	0.779893
$530$	0	0
$531$	1.33940e27	0.0326152
$532$	−1.40481e29	−3.35386
$533$	3.01952e28	0.706808
$534$	−1.66180e28	−0.381413
$535$	0	0
$536$	3.38104e28	0.746140
$537$	3.19199e28	0.690767
$538$	−4.55349e28	−0.966341
$539$	−2.31086e28	−0.480941
$540$	0	0
$541$	6.62234e28	1.32569	0.662843	−	0.748759i	$-0.269350\pi$
$541$	6.62234e28	1.32569	0.662843	+	0.748759i	$0.269350\pi$
$542$	−1.36584e29	−2.68168
$543$	−3.65598e28	−0.704054
$544$	3.31245e28	0.625692
$545$	0	0
$546$	−7.68518e28	−1.39679
$547$	−8.00185e28	−1.42667	−0.713335	−	0.700823i	$-0.752816\pi$
$547$	−8.00185e28	−1.42667	−0.713335	+	0.700823i	$0.752816\pi$
$548$	−4.72520e28	−0.826465
$549$	1.25922e28	0.216069
$550$	0	0
$551$	5.69567e28	0.940704
$552$	5.62863e28	0.912100
$553$	7.44637e28	1.18394
$554$	−2.85335e28	−0.445146
$555$	0	0
$556$	−1.38266e29	−2.07696
$557$	−5.93633e28	−0.875062	−0.437531	−	0.899203i	$-0.644147\pi$
$557$	−5.93633e28	−0.875062	−0.437531	+	0.899203i	$0.644147\pi$
$558$	−4.91710e28	−0.711295
$559$	−3.67024e28	−0.521039
$560$	0	0
$561$	4.24823e28	0.580895
$562$	−6.29450e28	−0.844753
$563$	−2.16875e28	−0.285674	−0.142837	−	0.989746i	$-0.545623\pi$
$563$	−2.16875e28	−0.285674	−0.142837	+	0.989746i	$0.545623\pi$
$564$	−8.10238e28	−1.04757
$565$	0	0
$566$	1.88295e28	0.234566
$567$	1.06532e28	0.130275
$568$	3.14129e28	0.377095
$569$	−1.70076e28	−0.200431	−0.100215	−	0.994966i	$-0.531953\pi$
$569$	−1.70076e28	−0.200431	−0.100215	+	0.994966i	$0.531953\pi$
$570$	0	0
$571$	−4.09152e28	−0.464736	−0.232368	−	0.972628i	$-0.574647\pi$
$571$	−4.09152e28	−0.464736	−0.232368	+	0.972628i	$0.574647\pi$
$572$	2.47516e29	2.76023
$573$	1.44296e28	0.157991
$574$	−1.01549e29	−1.09169
$575$	0	0
$576$	−4.98512e28	−0.516702
$577$	−1.54135e29	−1.56876	−0.784380	−	0.620281i	$-0.787019\pi$
$577$	−1.54135e29	−1.56876	−0.784380	+	0.620281i	$0.787019\pi$
$578$	−6.36029e28	−0.635674
$579$	−2.51510e28	−0.246849
$580$	0	0
$581$	1.09674e29	1.03814
$582$	1.71021e29	1.58986
$583$	−8.81977e28	−0.805263
$584$	1.73224e29	1.55337
$585$	0	0
$586$	2.00204e29	1.73200
$587$	4.81480e28	0.409146	0.204573	−	0.978851i	$-0.434419\pi$
$587$	4.81480e28	0.409146	0.204573	+	0.978851i	$0.434419\pi$
$588$	4.45303e28	0.371701
$589$	2.62785e29	2.15471
$590$	0	0
$591$	−4.68570e28	−0.370771
$592$	−3.34227e28	−0.259815
$593$	7.07719e28	0.540489	0.270244	−	0.962792i	$-0.412895\pi$
$593$	7.07719e28	0.540489	0.270244	+	0.962792i	$0.412895\pi$
$594$	−5.42797e28	−0.407268
$595$	0	0
$596$	−3.61217e29	−2.61627
$597$	−5.36341e28	−0.381690
$598$	−3.93685e29	−2.75287
$599$	1.82931e29	1.25692	0.628458	−	0.777844i	$-0.283687\pi$
$599$	1.82931e29	1.25692	0.628458	+	0.777844i	$0.283687\pi$
$600$	0	0
$601$	−1.82502e29	−1.21084	−0.605419	−	0.795907i	$-0.706994\pi$
$601$	−1.82502e29	−1.21084	−0.605419	+	0.795907i	$0.706994\pi$
$602$	1.23434e29	0.804767
$603$	3.27812e28	0.210036
$604$	−4.53114e29	−2.85312
$605$	0	0
$606$	−8.13281e28	−0.494627
$607$	−1.98079e29	−1.18401	−0.592007	−	0.805933i	$-0.701664\pi$
$607$	−1.98079e29	−1.18401	−0.592007	+	0.805933i	$0.701664\pi$
$608$	2.26188e29	1.32887
$609$	−6.62392e28	−0.382502
$610$	0	0
$611$	2.36887e29	1.32162
$612$	−8.18634e28	−0.448952
$613$	1.05402e29	0.568215	0.284108	−	0.958792i	$-0.408303\pi$
$613$	1.05402e29	0.568215	0.284108	+	0.958792i	$0.408303\pi$
$614$	2.62348e29	1.39030
$615$	0	0
$616$	−3.47956e29	−1.78208
$617$	2.71351e29	1.36627	0.683136	−	0.730291i	$-0.260616\pi$
$617$	2.71351e29	1.36627	0.683136	+	0.730291i	$0.260616\pi$
$618$	3.60437e29	1.78423
$619$	−1.34723e29	−0.655677	−0.327839	−	0.944734i	$-0.606320\pi$
$619$	−1.34723e29	−0.655677	−0.327839	+	0.944734i	$0.606320\pi$
$620$	0	0
$621$	5.45729e28	0.256753
$622$	−9.36124e28	−0.433046
$623$	−1.03286e29	−0.469803
$624$	−3.78173e28	−0.169142
$625$	0	0
$626$	5.90505e29	2.55384
$627$	2.90087e29	1.23373
$628$	7.25063e29	3.03249
$629$	2.11528e29	0.870035
$630$	0	0
$631$	−2.19411e29	−0.872870	−0.436435	−	0.899736i	$-0.643759\pi$
$631$	−2.19411e29	−0.872870	−0.436435	+	0.899736i	$0.643759\pi$
$632$	3.05607e29	1.19573
$633$	−2.33509e29	−0.898597
$634$	1.88462e29	0.713323
$635$	0	0
$636$	1.69957e29	0.622357
$637$	−1.30192e29	−0.468942
$638$	3.37498e29	1.19579
$639$	3.04567e28	0.106151
$640$	0	0
$641$	4.79415e29	1.61697	0.808486	−	0.588516i	$-0.200287\pi$
$641$	4.79415e29	1.61697	0.808486	+	0.588516i	$0.200287\pi$
$642$	−1.04297e28	−0.0346061
$643$	−3.40654e29	−1.11198	−0.555991	−	0.831188i	$-0.687661\pi$
$643$	−3.40654e29	−1.11198	−0.555991	+	0.831188i	$0.687661\pi$
$644$	8.36916e29	2.68770
$645$	0	0
$646$	6.92127e29	2.15151
$647$	1.79416e29	0.548740	0.274370	−	0.961624i	$-0.411531\pi$
$647$	1.79416e29	0.548740	0.274370	+	0.961624i	$0.411531\pi$
$648$	4.37221e28	0.131572
$649$	−4.24159e28	−0.125591
$650$	0	0
$651$	−3.05612e29	−0.876133
$652$	−1.51078e29	−0.426188
$653$	1.03635e29	0.287686	0.143843	−	0.989601i	$-0.454054\pi$
$653$	1.03635e29	0.287686	0.143843	+	0.989601i	$0.454054\pi$
$654$	−9.22892e28	−0.252107
$655$	0	0
$656$	−4.99704e28	−0.132197
$657$	1.67951e29	0.437267
$658$	−7.96671e29	−2.04130
$659$	−4.66342e29	−1.17600	−0.588000	−	0.808861i	$-0.700085\pi$
$659$	−4.66342e29	−1.17600	−0.588000	+	0.808861i	$0.700085\pi$
$660$	0	0
$661$	3.43345e29	0.838717	0.419359	−	0.907821i	$-0.362255\pi$
$661$	3.43345e29	0.838717	0.419359	+	0.907821i	$0.362255\pi$
$662$	−5.56117e29	−1.33708
$663$	2.39341e29	0.566403
$664$	4.50115e29	1.04848
$665$	0	0
$666$	−2.70270e29	−0.609984
$667$	−3.39320e29	−0.753857
$668$	1.13693e30	2.48646
$669$	2.84632e29	0.612786
$670$	0	0
$671$	−3.98767e29	−0.832018
$672$	−2.63051e29	−0.540334
$673$	3.52314e29	0.712478	0.356239	−	0.934395i	$-0.384059\pi$
$673$	3.52314e29	0.712478	0.356239	+	0.934395i	$0.384059\pi$
$674$	−2.89961e27	−0.00577312
$675$	0	0
$676$	5.04215e29	0.973141
$677$	−4.66819e29	−0.887090	−0.443545	−	0.896252i	$-0.646279\pi$
$677$	−4.66819e29	−0.887090	−0.443545	+	0.896252i	$0.646279\pi$
$678$	2.26464e29	0.423728
$679$	1.06294e30	1.95829
$680$	0	0
$681$	2.68529e28	0.0479674
$682$	1.55713e30	2.73899
$683$	−6.85211e29	−1.18688	−0.593440	−	0.804878i	$-0.702231\pi$
$683$	−6.85211e29	−1.18688	−0.593440	+	0.804878i	$0.702231\pi$
$684$	−5.58998e29	−0.953501
$685$	0	0
$686$	−7.30708e29	−1.20876
$687$	1.86249e29	0.303422
$688$	6.07394e28	0.0974522
$689$	−4.96898e29	−0.785173
$690$	0	0
$691$	−8.35817e29	−1.28113	−0.640563	−	0.767906i	$-0.721299\pi$
$691$	−8.35817e29	−1.28113	−0.640563	+	0.767906i	$0.721299\pi$
$692$	−5.37211e29	−0.811019
$693$	−3.37364e29	−0.501649
$694$	−1.69389e30	−2.48091
$695$	0	0
$696$	−2.71853e29	−0.386311
$697$	3.16256e29	0.442685
$698$	1.29054e30	1.77947
$699$	1.51680e29	0.206024
$700$	0	0
$701$	−1.07923e30	−1.42258	−0.711288	−	0.702901i	$-0.751888\pi$
$701$	−1.07923e30	−1.42258	−0.711288	+	0.702901i	$0.751888\pi$
$702$	−3.05807e29	−0.397107
$703$	1.44441e30	1.84781
$704$	1.57867e30	1.98966
$705$	0	0
$706$	−1.12706e30	−1.37879
$707$	−5.05478e29	−0.609253
$708$	8.17354e28	0.0970646
$709$	−1.13039e30	−1.32264	−0.661322	−	0.750102i	$-0.730004\pi$
$709$	−1.13039e30	−1.32264	−0.661322	+	0.750102i	$0.730004\pi$
$710$	0	0
$711$	2.96304e29	0.336594
$712$	−4.23895e29	−0.474481
$713$	−1.56554e30	−1.72673
$714$	−8.04926e29	−0.874832
$715$	0	0
$716$	1.94787e30	2.05576
$717$	−1.21864e29	−0.126743
$718$	−7.64581e29	−0.783640
$719$	−8.61924e29	−0.870594	−0.435297	−	0.900287i	$-0.643357\pi$
$719$	−8.61924e29	−0.870594	−0.435297	+	0.900287i	$0.643357\pi$
$720$	0	0
$721$	2.24022e30	2.19771
$722$	3.02091e30	2.92076
$723$	−1.64779e29	−0.157018
$724$	−2.23102e30	−2.09531
$725$	0	0
$726$	6.75596e29	0.616385
$727$	1.05467e29	0.0948434	0.0474217	−	0.998875i	$-0.484900\pi$
$727$	1.05467e29	0.0948434	0.0474217	+	0.998875i	$0.484900\pi$
$728$	−1.96035e30	−1.73762
$729$	4.23912e28	0.0370370
$730$	0	0
$731$	−3.84412e29	−0.326336
$732$	7.68423e29	0.643034
$733$	8.43407e29	0.695738	0.347869	−	0.937543i	$-0.386905\pi$
$733$	8.43407e29	0.695738	0.347869	+	0.937543i	$0.386905\pi$
$734$	1.42708e30	1.16048
$735$	0	0
$736$	−1.34752e30	−1.06492
$737$	−1.03811e30	−0.808785
$738$	−4.04081e29	−0.310368
$739$	−1.05159e30	−0.796307	−0.398154	−	0.917319i	$-0.630349\pi$
$739$	−1.05159e30	−0.796307	−0.398154	+	0.917319i	$0.630349\pi$
$740$	0	0
$741$	1.63432e30	1.20295
$742$	1.67111e30	1.21273
$743$	1.23200e30	0.881509	0.440755	−	0.897628i	$-0.354711\pi$
$743$	1.23200e30	0.881509	0.440755	+	0.897628i	$0.354711\pi$
$744$	−1.25426e30	−0.884858
$745$	0	0
$746$	−2.53329e30	−1.73751
$747$	4.36413e29	0.295143
$748$	2.59243e30	1.72878
$749$	−6.48233e28	−0.0426258
$750$	0	0
$751$	−2.93994e30	−1.87983	−0.939915	−	0.341408i	$-0.889096\pi$
$751$	−2.93994e30	−1.87983	−0.939915	+	0.341408i	$0.889096\pi$
$752$	−3.92027e29	−0.247189
$753$	1.63948e30	1.01943
$754$	1.90143e30	1.16595
$755$	0	0
$756$	6.50100e29	0.387705
$757$	−1.01914e30	−0.599414	−0.299707	−	0.954031i	$-0.596889\pi$
$757$	−1.01914e30	−0.599414	−0.299707	+	0.954031i	$0.596889\pi$
$758$	−5.45862e29	−0.316633
$759$	−1.72820e30	−0.988678
$760$	0	0
$761$	−1.85986e30	−1.03500	−0.517500	−	0.855683i	$-0.673137\pi$
$761$	−1.85986e30	−1.03500	−0.517500	+	0.855683i	$0.673137\pi$
$762$	−1.94623e30	−1.06824
$763$	−5.73604e29	−0.310531
$764$	8.80550e29	0.470190
$765$	0	0
$766$	3.13098e30	1.62659
$767$	−2.38967e29	−0.122458
$768$	−1.53898e30	−0.777928
$769$	−2.17566e30	−1.08484	−0.542418	−	0.840109i	$-0.682491\pi$
$769$	−2.17566e30	−1.08484	−0.542418	+	0.840109i	$0.682491\pi$
$770$	0	0
$771$	−2.13948e30	−1.03810
$772$	−1.53481e30	−0.734636
$773$	1.69040e30	0.798189	0.399094	−	0.916910i	$-0.369325\pi$
$773$	1.69040e30	0.798189	0.399094	+	0.916910i	$0.369325\pi$
$774$	4.91164e29	0.228795
$775$	0	0
$776$	4.36244e30	1.97779
$777$	−1.67981e30	−0.751344
$778$	−3.68076e30	−1.62425
$779$	2.15953e30	0.940192
$780$	0	0
$781$	−9.64493e29	−0.408755
$782$	−4.12336e30	−1.72417
$783$	−2.63578e29	−0.108745
$784$	2.15456e29	0.0877082
$785$	0	0
$786$	−4.19461e30	−1.66247
$787$	1.29849e30	0.507813	0.253906	−	0.967229i	$-0.418285\pi$
$787$	1.29849e30	0.507813	0.253906	+	0.967229i	$0.418285\pi$
$788$	−2.85939e30	−1.10344
$789$	−1.93206e30	−0.735719
$790$	0	0
$791$	1.40754e30	0.521924
$792$	−1.38458e30	−0.506644
$793$	−2.24661e30	−0.811260
$794$	4.79180e30	1.70759
$795$	0	0
$796$	−3.27295e30	−1.13593
$797$	4.07673e30	1.39637	0.698184	−	0.715918i	$-0.253992\pi$
$797$	4.07673e30	1.39637	0.698184	+	0.715918i	$0.253992\pi$
$798$	−5.49638e30	−1.85800
$799$	2.48109e30	0.827755
$800$	0	0
$801$	−4.10992e29	−0.133565
$802$	3.48076e30	1.11646
$803$	−5.31864e30	−1.68379
$804$	2.00043e30	0.625079
$805$	0	0
$806$	8.77274e30	2.67065
$807$	−1.12616e30	−0.338397
$808$	−2.07453e30	−0.615320
$809$	−4.20285e29	−0.123051	−0.0615254	−	0.998106i	$-0.519597\pi$
$809$	−4.20285e29	−0.123051	−0.0615254	+	0.998106i	$0.519597\pi$
$810$	0	0
$811$	1.58234e30	0.451420	0.225710	−	0.974194i	$-0.427530\pi$
$811$	1.58234e30	0.451420	0.225710	+	0.974194i	$0.427530\pi$
$812$	−4.04216e30	−1.13835
$813$	−3.37795e30	−0.939081
$814$	8.55884e30	2.34887
$815$	0	0
$816$	−3.96089e29	−0.105937
$817$	−2.62493e30	−0.693084
$818$	−9.72184e29	−0.253419
$819$	−1.90068e30	−0.489133
$820$	0	0
$821$	8.65746e29	0.217164	0.108582	−	0.994088i	$-0.465369\pi$
$821$	8.65746e29	0.217164	0.108582	+	0.994088i	$0.465369\pi$
$822$	−1.84876e30	−0.457853
$823$	6.70681e29	0.163990	0.0819951	−	0.996633i	$-0.473871\pi$
$823$	6.70681e29	0.163990	0.0819951	+	0.996633i	$0.473871\pi$
$824$	9.19412e30	2.21960
$825$	0	0
$826$	8.03668e29	0.189141
$827$	−6.75355e30	−1.56937	−0.784684	−	0.619897i	$-0.787175\pi$
$827$	−6.75355e30	−1.56937	−0.784684	+	0.619897i	$0.787175\pi$
$828$	3.33024e30	0.764112
$829$	−2.45186e29	−0.0555486	−0.0277743	−	0.999614i	$-0.508842\pi$
$829$	−2.45186e29	−0.0555486	−0.0277743	+	0.999614i	$0.508842\pi$
$830$	0	0
$831$	−7.05683e29	−0.155883
$832$	8.89410e30	1.94002
$833$	−1.36359e30	−0.293706
$834$	−5.40971e30	−1.15062
$835$	0	0
$836$	1.77022e31	3.67165
$837$	−1.21608e30	−0.249084
$838$	1.49178e31	3.01747
$839$	9.50527e30	1.89873	0.949366	−	0.314172i	$-0.101727\pi$
$839$	9.50527e30	1.89873	0.949366	+	0.314172i	$0.101727\pi$
$840$	0	0
$841$	−3.49398e30	−0.680711
$842$	−5.63161e29	−0.108357
$843$	−1.55674e30	−0.295819
$844$	−1.42496e31	−2.67428
$845$	0	0
$846$	−3.17010e30	−0.580341
$847$	4.19902e30	0.759229
$848$	8.22323e29	0.146854
$849$	4.65685e29	0.0821413
$850$	0	0
$851$	−8.60507e30	−1.48079
$852$	1.85858e30	0.315911
$853$	7.37170e29	0.123766	0.0618832	−	0.998083i	$-0.480289\pi$
$853$	7.37170e29	0.123766	0.0618832	+	0.998083i	$0.480289\pi$
$854$	7.55557e30	1.25302
$855$	0	0
$856$	−2.66042e29	−0.0430502
$857$	−6.21542e30	−0.993510	−0.496755	−	0.867891i	$-0.665475\pi$
$857$	−6.21542e30	−0.993510	−0.496755	+	0.867891i	$0.665475\pi$
$858$	9.68420e30	1.52914
$859$	1.78321e30	0.278147	0.139073	−	0.990282i	$-0.455588\pi$
$859$	1.78321e30	0.278147	0.139073	+	0.990282i	$0.455588\pi$
$860$	0	0
$861$	−2.51148e30	−0.382294
$862$	9.92398e30	1.49231
$863$	−1.16050e30	−0.172399	−0.0861993	−	0.996278i	$-0.527472\pi$
$863$	−1.16050e30	−0.172399	−0.0861993	+	0.996278i	$0.527472\pi$
$864$	−1.04673e30	−0.153617
$865$	0	0
$866$	1.33005e30	0.190515
$867$	−1.57301e30	−0.222603
$868$	−1.86496e31	−2.60742
$869$	−9.38327e30	−1.29612
$870$	0	0
$871$	−5.84859e30	−0.788607
$872$	−2.35413e30	−0.313623
$873$	4.22964e30	0.556742
$874$	−2.81560e31	−3.66186
$875$	0	0
$876$	1.02490e31	1.30133
$877$	3.61643e29	0.0453717	0.0226858	−	0.999743i	$-0.492778\pi$
$877$	3.61643e29	0.0453717	0.0226858	+	0.999743i	$0.492778\pi$
$878$	−6.05571e30	−0.750711
$879$	4.95140e30	0.606520
$880$	0	0
$881$	−4.75866e30	−0.569164	−0.284582	−	0.958652i	$-0.591855\pi$
$881$	−4.75866e30	−0.569164	−0.284582	+	0.958652i	$0.591855\pi$
$882$	1.74227e30	0.205918
$883$	−3.94770e30	−0.461059	−0.230530	−	0.973065i	$-0.574046\pi$
$883$	−3.94770e30	−0.461059	−0.230530	+	0.973065i	$0.574046\pi$
$884$	1.46055e31	1.68565
$885$	0	0
$886$	6.12951e30	0.690831
$887$	1.28571e31	1.43201	0.716005	−	0.698095i	$-0.245969\pi$
$887$	1.28571e31	1.43201	0.716005	+	0.698095i	$0.245969\pi$
$888$	−6.89411e30	−0.758826
$889$	−1.20964e31	−1.31579
$890$	0	0
$891$	−1.34243e30	−0.142619
$892$	1.73693e31	1.82369
$893$	1.69420e31	1.75802
$894$	−1.41328e31	−1.44938
$895$	0	0
$896$	−2.05693e31	−2.06056
$897$	−9.73651e30	−0.964012
$898$	1.68700e31	1.65087
$899$	7.56131e30	0.731341
$900$	0	0
$901$	−5.20438e30	−0.491766
$902$	1.27963e31	1.19514
$903$	3.05272e30	0.281816
$904$	5.77669e30	0.527121
$905$	0	0
$906$	−1.77283e31	−1.58060
$907$	−1.43790e31	−1.26722	−0.633609	−	0.773654i	$-0.718427\pi$
$907$	−1.43790e31	−1.26722	−0.633609	+	0.773654i	$0.718427\pi$
$908$	1.63866e30	0.142754
$909$	−2.01138e30	−0.173211
$910$	0	0
$911$	1.28284e30	0.107952	0.0539758	−	0.998542i	$-0.482811\pi$
$911$	1.28284e30	0.107952	0.0539758	+	0.998542i	$0.482811\pi$
$912$	−2.70467e30	−0.224992
$913$	−1.38202e31	−1.13651
$914$	−1.48477e31	−1.20705
$915$	0	0
$916$	1.13656e31	0.903003
$917$	−2.60707e31	−2.04774
$918$	−3.20294e30	−0.248714
$919$	1.98254e31	1.52198	0.760988	−	0.648765i	$-0.224714\pi$
$919$	1.98254e31	1.52198	0.760988	+	0.648765i	$0.224714\pi$
$920$	0	0
$921$	6.48831e30	0.486862
$922$	−3.57381e31	−2.65129
$923$	−5.43386e30	−0.398557
$924$	−2.05872e31	−1.49294
$925$	0	0
$926$	−9.42289e30	−0.667988
$927$	8.91424e30	0.624809
$928$	6.50828e30	0.451037
$929$	−9.64247e30	−0.660729	−0.330364	−	0.943853i	$-0.607172\pi$
$929$	−9.64247e30	−0.660729	−0.330364	+	0.943853i	$0.607172\pi$
$930$	0	0
$931$	−9.31121e30	−0.623784
$932$	9.25608e30	0.613141
$933$	−2.31520e30	−0.151646
$934$	2.11467e31	1.36962
$935$	0	0
$936$	−7.80058e30	−0.494004
$937$	−1.51040e31	−0.945861	−0.472930	−	0.881100i	$-0.656804\pi$
$937$	−1.51040e31	−0.945861	−0.472930	+	0.881100i	$0.656804\pi$
$938$	1.96693e31	1.21804
$939$	1.46042e31	0.894313
$940$	0	0
$941$	2.80176e31	1.67780	0.838899	−	0.544288i	$-0.183200\pi$
$941$	2.80176e31	1.67780	0.838899	+	0.544288i	$0.183200\pi$
$942$	2.83684e31	1.67997
$943$	−1.28655e31	−0.753446
$944$	3.95470e29	0.0229038
$945$	0	0
$946$	−1.55540e31	−0.881021
$947$	7.64271e29	0.0428127	0.0214064	−	0.999771i	$-0.493186\pi$
$947$	7.64271e29	0.0428127	0.0214064	+	0.999771i	$0.493186\pi$
$948$	1.80816e31	1.00172
$949$	−2.99647e31	−1.64178
$950$	0	0
$951$	4.66099e30	0.249794
$952$	−2.05322e31	−1.08830
$953$	2.10283e31	1.10237	0.551187	−	0.834382i	$-0.314175\pi$
$953$	2.10283e31	1.10237	0.551187	+	0.834382i	$0.314175\pi$
$954$	6.64965e30	0.344779
$955$	0	0
$956$	−7.43659e30	−0.377195
$957$	8.34690e30	0.418745
$958$	2.73661e31	1.35792
$959$	−1.14906e31	−0.563957
$960$	0	0
$961$	1.40606e31	0.675161
$962$	4.82197e31	2.29027
$963$	−2.57943e29	−0.0121185
$964$	−1.00554e31	−0.467295
$965$	0	0
$966$	3.27448e31	1.48896
$967$	2.07417e31	0.932967	0.466483	−	0.884530i	$-0.345521\pi$
$967$	2.07417e31	0.932967	0.466483	+	0.884530i	$0.345521\pi$
$968$	1.72332e31	0.766789
$969$	1.71175e31	0.753426
$970$	0	0
$971$	−2.53741e31	−1.09292	−0.546460	−	0.837485i	$-0.684025\pi$
$971$	−2.53741e31	−1.09292	−0.546460	+	0.837485i	$0.684025\pi$
$972$	2.58686e30	0.110224
$973$	−3.36229e31	−1.41726
$974$	−3.72574e31	−1.55362
$975$	0	0
$976$	3.71795e30	0.151733
$977$	2.63670e31	1.06455	0.532277	−	0.846570i	$-0.321337\pi$
$977$	2.63670e31	1.06455	0.532277	+	0.846570i	$0.321337\pi$
$978$	−5.91100e30	−0.236104
$979$	1.30152e31	0.514318
$980$	0	0
$981$	−2.28247e30	−0.0882838
$982$	−1.46324e31	−0.559944
$983$	−9.74890e30	−0.369100	−0.184550	−	0.982823i	$-0.559083\pi$
$983$	−9.74890e30	−0.369100	−0.184550	+	0.982823i	$0.559083\pi$
$984$	−1.03074e31	−0.386101
$985$	0	0
$986$	1.99151e31	0.730255
$987$	−1.97031e31	−0.714832
$988$	9.97325e31	3.58005
$989$	1.56380e31	0.555420
$990$	0	0
$991$	3.38462e31	1.17689	0.588446	−	0.808537i	$-0.299740\pi$
$991$	3.38462e31	1.17689	0.588446	+	0.808537i	$0.299740\pi$
$992$	3.00276e31	1.03312
$993$	−1.37537e31	−0.468224
$994$	1.82746e31	0.615588
$995$	0	0
$996$	2.66316e31	0.878362
$997$	1.33109e31	0.434417	0.217208	−	0.976125i	$-0.430305\pi$
$997$	1.33109e31	0.434417	0.217208	+	0.976125i	$0.430305\pi$
$998$	8.43619e30	0.272443
$999$	−6.68425e30	−0.213607

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.22.a.m.1.10		10
5.2	odd	4		15.22.b.a.4.19	yes	20
5.3	odd	4		15.22.b.a.4.2	✓	20
5.4	even	2		75.22.a.n.1.1		10
15.2	even	4		45.22.b.d.19.2		20
15.8	even	4		45.22.b.d.19.19		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.22.b.a.4.2	✓	20	5.3	odd	4
15.22.b.a.4.19	yes	20	5.2	odd	4
45.22.b.d.19.2		20	15.2	even	4
45.22.b.d.19.19		20	15.8	even	4
75.22.a.m.1.10		10	1.1	even	1	trivial
75.22.a.n.1.1		10	5.4	even	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:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 22 \)
Character orbit:	\([\chi]\)	\(=\)	75.a (trivial)

\(f(q)\)	\(=\)	\(q+2387.58 q^{2} +59049.0 q^{3} +3.60339e6 q^{4} +1.40984e8 q^{6} +8.76258e8 q^{7} +3.59626e9 q^{8} +3.48678e9 q^{9} +O(q^{10})\)	\(q+2387.58 q^{2} +59049.0 q^{3} +3.60339e6 q^{4} +1.40984e8 q^{6} +8.76258e8 q^{7} +3.59626e9 q^{8} +3.48678e9 q^{9} -1.10419e11 q^{11} +2.12776e11 q^{12} -6.22087e11 q^{13} +2.09214e12 q^{14} +1.02950e12 q^{16} -6.51559e12 q^{17} +8.32498e12 q^{18} -4.44912e13 q^{19} +5.17421e13 q^{21} -2.63633e14 q^{22} +2.65057e14 q^{23} +2.12355e14 q^{24} -1.48528e15 q^{26} +2.05891e14 q^{27} +3.15750e15 q^{28} -1.28018e15 q^{29} -5.90644e15 q^{31} -5.08388e15 q^{32} -6.52010e15 q^{33} -1.55565e16 q^{34} +1.25642e16 q^{36} -3.24650e16 q^{37} -1.06226e17 q^{38} -3.67336e16 q^{39} -4.85384e16 q^{41} +1.23539e17 q^{42} +5.89988e16 q^{43} -3.97881e17 q^{44} +6.32845e17 q^{46} -3.80793e17 q^{47} +6.07910e16 q^{48} +2.09282e17 q^{49} -3.84739e17 q^{51} -2.24162e18 q^{52} +7.98759e17 q^{53} +4.91582e17 q^{54} +3.15125e18 q^{56} -2.62716e18 q^{57} -3.05653e18 q^{58} +3.84138e17 q^{59} +3.61141e18 q^{61} -1.41021e19 q^{62} +3.05532e18 q^{63} -1.42972e19 q^{64} -1.55673e19 q^{66} +9.40156e18 q^{67} -2.34782e19 q^{68} +1.56514e19 q^{69} +8.73489e18 q^{71} +1.25394e19 q^{72} +4.81680e19 q^{73} -7.75127e19 q^{74} -1.60319e20 q^{76} -9.67551e19 q^{77} -8.77045e19 q^{78} +8.49792e19 q^{79} +1.21577e19 q^{81} -1.15889e20 q^{82} +1.25162e20 q^{83} +1.86447e20 q^{84} +1.40864e20 q^{86} -7.55933e19 q^{87} -3.97093e20 q^{88} -1.17871e20 q^{89} -5.45109e20 q^{91} +9.55103e20 q^{92} -3.48770e20 q^{93} -9.09175e20 q^{94} -3.00198e20 q^{96} +1.21305e21 q^{97} +4.99677e20 q^{98} -3.85006e20 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 645 q^{2} + 590490 q^{3} + 10043205 q^{4} - 38086605 q^{6} - 115357290 q^{7} - 314142735 q^{8} + 34867844010 q^{9}+O(q^{10}) \) 10 * q - 645 * q^2 + 590490 * q^3 + 10043205 * q^4 - 38086605 * q^6 - 115357290 * q^7 - 314142735 * q^8 + 34867844010 * q^9	\( 10 q - 645 q^{2} + 590490 q^{3} + 10043205 q^{4} - 38086605 q^{6} - 115357290 q^{7} - 314142735 q^{8} + 34867844010 q^{9} + 5976221790 q^{11} + 593041212045 q^{12} - 842570747430 q^{13} + 1605059874570 q^{14} + 6061861547825 q^{16} - 12910340404230 q^{17} - 2248975938645 q^{18} - 76155422176280 q^{19} - 6811732617210 q^{21} - 461780887241010 q^{22} - 82640920915920 q^{23} - 18549814359015 q^{24} + 286555331159670 q^{26} + 20\!\cdots\!90 q^{27}+ \cdots + 20\!\cdots\!90 q^{99}+O(q^{100}) \) 10 * q - 645 * q^2 + 590490 * q^3 + 10043205 * q^4 - 38086605 * q^6 - 115357290 * q^7 - 314142735 * q^8 + 34867844010 * q^9 + 5976221790 * q^11 + 593041212045 * q^12 - 842570747430 * q^13 + 1605059874570 * q^14 + 6061861547825 * q^16 - 12910340404230 * q^17 - 2248975938645 * q^18 - 76155422176280 * q^19 - 6811732617210 * q^21 - 461780887241010 * q^22 - 82640920915920 * q^23 - 18549814359015 * q^24 + 286555331159670 * q^26 + 2058911320946490 * q^27 - 1520428218531930 * q^28 - 2553653160731010 * q^29 - 5579671364724940 * q^31 - 29255856594217815 * q^32 + 352889920477710 * q^33 + 36285968426431010 * q^34 + 35018490530045205 * q^36 - 1797908431222890 * q^37 - 10684960744876320 * q^38 - 49752960064994070 * q^39 - 157319729506021440 * q^41 + 94777180533483930 * q^42 + 148924853700743400 * q^43 + 49118820773767290 * q^44 - 238453286038259540 * q^46 + 43171138083158100 * q^47 + 357946862537518425 * q^48 + 453692886452454950 * q^49 - 762342690529377270 * q^51 - 5077473324432504030 * q^52 - 1835165786666252970 * q^53 - 132799780201048605 * q^54 - 5146515624013530450 * q^56 - 4496901524087157720 * q^57 - 3684042125074285440 * q^58 + 4936135121536323630 * q^59 - 4443080871007408300 * q^61 - 39366851097921260280 * q^62 - 402225999313633290 * q^63 - 14877283608188093455 * q^64 - 27267699610694399490 * q^66 - 33664559574358232580 * q^67 - 44791395195934111290 * q^68 - 4879863739164160080 * q^69 - 74662724971386630180 * q^71 - 1095347988085476735 * q^72 - 16062862692682477620 * q^73 - 130249023546610518030 * q^74 - 258736483662380220720 * q^76 - 56216747719240740180 * q^77 + 16920805749647353830 * q^78 - 49130708010799643300 * q^79 + 121576654590569288010 * q^81 - 117185080045656261930 * q^82 - 118408383608453695560 * q^83 - 89779765876091934570 * q^84 - 1007271272794707382260 * q^86 - 150790665488005409490 * q^87 - 41803519849182967710 * q^88 - 572103976713991581780 * q^89 - 1669810835257196575140 * q^91 + 1206545757146297440260 * q^92 - 329474014415642982060 * q^93 - 1671319720124696594920 * q^94 - 1727529076031967757935 * q^96 + 1299275526640742173920 * q^97 + 2683959884079093505455 * q^98 + 20837796914288297790 * q^99

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