LMFDB - Embedded newform 245.10.a.g.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [245,10,Mod(1,245)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(245, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("245.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 245 = 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	245.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:	$126.183779860$
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} - 3018x^{4} + 3368x^{3} + 2066979x^{2} - 6329061x - 14714266 $ x^6 - 3x^5 - 3018x^4 + 3368x^3 + 2066979x^2 - 6329061*x - 14714266
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{3}\cdot 3^{2}\cdot 5 $
Twist minimal:	no (minimal twist has level 35)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-1.54749$ of defining polynomial
Character	$\chi$	$=$	245.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+4.54749 q^{2} +98.1335 q^{3} -491.320 q^{4} -625.000 q^{5} +446.261 q^{6} -4562.59 q^{8} -10052.8 q^{9} -2842.18 q^{10} -44050.6 q^{11} -48215.0 q^{12} -142358. q^{13} -61333.4 q^{15} +230808. q^{16} -286886. q^{17} -45715.1 q^{18} -673158. q^{19} +307075. q^{20} -200320. q^{22} -555018. q^{23} -447743. q^{24} +390625. q^{25} -647373. q^{26} -2.91808e6 q^{27} +3.26629e6 q^{29} -278913. q^{30} +4.39550e6 q^{31} +3.38564e6 q^{32} -4.32284e6 q^{33} -1.30461e6 q^{34} +4.93916e6 q^{36} +9.35091e6 q^{37} -3.06118e6 q^{38} -1.39701e7 q^{39} +2.85162e6 q^{40} -2.67199e6 q^{41} -3.17095e7 q^{43} +2.16430e7 q^{44} +6.28302e6 q^{45} -2.52394e6 q^{46} -5.04786e7 q^{47} +2.26500e7 q^{48} +1.77636e6 q^{50} -2.81531e7 q^{51} +6.99436e7 q^{52} -7.41121e7 q^{53} -1.32699e7 q^{54} +2.75316e7 q^{55} -6.60593e7 q^{57} +1.48534e7 q^{58} +7.38382e7 q^{59} +3.01344e7 q^{60} -1.44849e7 q^{61} +1.99885e7 q^{62} -1.02777e8 q^{64} +8.89740e7 q^{65} -1.96581e7 q^{66} +2.27218e7 q^{67} +1.40953e8 q^{68} -5.44658e7 q^{69} +4.15967e8 q^{71} +4.58669e7 q^{72} -2.17283e8 q^{73} +4.25232e7 q^{74} +3.83334e7 q^{75} +3.30736e8 q^{76} -6.35290e7 q^{78} +3.66004e8 q^{79} -1.44255e8 q^{80} -8.84914e7 q^{81} -1.21509e7 q^{82} +2.12240e8 q^{83} +1.79304e8 q^{85} -1.44199e8 q^{86} +3.20532e8 q^{87} +2.00985e8 q^{88} -6.42964e8 q^{89} +2.85720e7 q^{90} +2.72692e8 q^{92} +4.31345e8 q^{93} -2.29551e8 q^{94} +4.20724e8 q^{95} +3.32245e8 q^{96} -9.38511e8 q^{97} +4.42833e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 15 q^{2} + 124 q^{3} + 3009 q^{4} - 3750 q^{5} - 4888 q^{6} + 22041 q^{8} + 111090 q^{9} - 9375 q^{10} - 47796 q^{11} + 541656 q^{12} - 102168 q^{13} - 77500 q^{15} + 2371065 q^{16} + 38472 q^{17}+ \cdots + 3571968784 q^{99}+O(q^{100}) $ 6 * q + 15 * q^2 + 124 * q^3 + 3009 * q^4 - 3750 * q^5 - 4888 * q^6 + 22041 * q^8 + 111090 * q^9 - 9375 * q^10 - 47796 * q^11 + 541656 * q^12 - 102168 * q^13 - 77500 * q^15 + 2371065 * q^16 + 38472 * q^17 + 1837015 * q^18 - 361056 * q^19 - 1880625 * q^20 + 2068680 * q^22 + 697032 * q^23 - 4828076 * q^24 + 2343750 * q^25 - 10847622 * q^26 - 1653188 * q^27 + 16028184 * q^29 + 3055000 * q^30 - 1362912 * q^31 - 1148823 * q^32 - 14059020 * q^33 + 9216294 * q^34 + 92319641 * q^36 - 3912924 * q^37 - 39877140 * q^38 - 20341868 * q^39 - 13775625 * q^40 - 22452756 * q^41 - 29998992 * q^43 - 94378728 * q^44 - 69431250 * q^45 + 49589520 * q^46 + 121271508 * q^47 + 327116052 * q^48 + 5859375 * q^50 - 281338180 * q^51 + 44528550 * q^52 - 20308596 * q^53 + 290104308 * q^54 + 29872500 * q^55 + 186940744 * q^57 + 256759494 * q^58 - 120280392 * q^59 - 338535000 * q^60 + 87693540 * q^61 + 344802528 * q^62 + 640647105 * q^64 + 63855000 * q^65 + 1393970692 * q^66 + 495050664 * q^67 + 141443706 * q^68 - 1031633640 * q^69 + 253762512 * q^71 + 856452205 * q^72 - 187195308 * q^73 - 418806054 * q^74 + 48437500 * q^75 + 584719476 * q^76 - 1728062324 * q^78 + 831079500 * q^79 - 1481915625 * q^80 + 1869314710 * q^81 - 2286848814 * q^82 + 767650536 * q^83 - 24045000 * q^85 + 566199948 * q^86 - 1303216852 * q^87 + 2952495444 * q^88 - 582579684 * q^89 - 1148134375 * q^90 - 4259382384 * q^92 + 15388800 * q^93 + 1115946660 * q^94 + 225660000 * q^95 - 989345252 * q^96 + 1184506872 * q^97 + 3571968784 * q^99

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 $

$2$	4.54749	0.200973	0.100486	−	0.994938i	$-0.467960\pi$
$2$	4.54749	0.200973	0.100486	+	0.994938i	$0.467960\pi$
$3$	98.1335	0.699474	0.349737	−	0.936848i	$-0.386271\pi$
$3$	98.1335	0.699474	0.349737	+	0.936848i	$0.386271\pi$
$4$	−491.320	−0.959610
$5$	−625.000	−0.447214
$5$	−625.000	−0.447214
$6$	446.261	0.140575
$7$	0	0
$7$	0	0
$8$	−4562.59	−0.393828
$9$	−10052.8	−0.510736
$10$	−2842.18	−0.0898777
$11$	−44050.6	−0.907163	−0.453581	−	0.891215i	$-0.649854\pi$
$11$	−44050.6	−0.907163	−0.453581	+	0.891215i	$0.649854\pi$
$12$	−48215.0	−0.671222
$13$	−142358.	−1.38241	−0.691207	−	0.722657i	$-0.742921\pi$
$13$	−142358.	−1.38241	−0.691207	+	0.722657i	$0.742921\pi$
$14$	0	0
$15$	−61333.4	−0.312814
$16$	230808.	0.880461
$17$	−286886.	−0.833084	−0.416542	−	0.909116i	$-0.636758\pi$
$17$	−286886.	−0.833084	−0.416542	+	0.909116i	$0.636758\pi$
$18$	−45715.1	−0.102644
$19$	−673158.	−1.18502	−0.592510	−	0.805563i	$-0.701863\pi$
$19$	−673158.	−1.18502	−0.592510	+	0.805563i	$0.701863\pi$
$20$	307075.	0.429151
$21$	0	0
$22$	−200320.	−0.182315
$23$	−555018.	−0.413554	−0.206777	−	0.978388i	$-0.566297\pi$
$23$	−555018.	−0.413554	−0.206777	+	0.978388i	$0.566297\pi$
$24$	−447743.	−0.275472
$25$	390625.	0.200000
$26$	−647373.	−0.277827
$27$	−2.91808e6	−1.05672
$28$	0	0
$29$	3.26629e6	0.857558	0.428779	−	0.903409i	$-0.358944\pi$
$29$	3.26629e6	0.857558	0.428779	+	0.903409i	$0.358944\pi$
$30$	−278913.	−0.0628671
$31$	4.39550e6	0.854831	0.427416	−	0.904055i	$-0.359424\pi$
$31$	4.39550e6	0.854831	0.427416	+	0.904055i	$0.359424\pi$
$32$	3.38564e6	0.570777
$33$	−4.32284e6	−0.634536
$34$	−1.30461e6	−0.167427
$35$	0	0
$36$	4.93916e6	0.490108
$37$	9.35091e6	0.820249	0.410125	−	0.912029i	$-0.365485\pi$
$37$	9.35091e6	0.820249	0.410125	+	0.912029i	$0.365485\pi$
$38$	−3.06118e6	−0.238156
$39$	−1.39701e7	−0.966962
$40$	2.85162e6	0.176125
$41$	−2.67199e6	−0.147675	−0.0738377	−	0.997270i	$-0.523525\pi$
$41$	−2.67199e6	−0.147675	−0.0738377	+	0.997270i	$0.523525\pi$
$42$	0	0
$43$	−3.17095e7	−1.41443	−0.707214	−	0.706999i	$-0.750048\pi$
$43$	−3.17095e7	−1.41443	−0.707214	+	0.706999i	$0.750048\pi$
$44$	2.16430e7	0.870522
$45$	6.28302e6	0.228408
$46$	−2.52394e6	−0.0831129
$47$	−5.04786e7	−1.50892	−0.754462	−	0.656344i	$-0.772102\pi$
$47$	−5.04786e7	−1.50892	−0.754462	+	0.656344i	$0.772102\pi$
$48$	2.26500e7	0.615860
$49$	0	0
$50$	1.77636e6	0.0401945
$51$	−2.81531e7	−0.582720
$52$	6.99436e7	1.32658
$53$	−7.41121e7	−1.29017	−0.645086	−	0.764110i	$-0.723178\pi$
$53$	−7.41121e7	−1.29017	−0.645086	+	0.764110i	$0.723178\pi$
$54$	−1.32699e7	−0.212372
$55$	2.75316e7	0.405695
$56$	0	0
$57$	−6.60593e7	−0.828890
$58$	1.48534e7	0.172346
$59$	7.38382e7	0.793317	0.396659	−	0.917966i	$-0.370170\pi$
$59$	7.38382e7	0.793317	0.396659	+	0.917966i	$0.370170\pi$
$60$	3.01344e7	0.300180
$61$	−1.44849e7	−0.133946	−0.0669731	−	0.997755i	$-0.521334\pi$
$61$	−1.44849e7	−0.133946	−0.0669731	+	0.997755i	$0.521334\pi$
$62$	1.99885e7	0.171798
$63$	0	0
$64$	−1.02777e8	−0.765751
$65$	8.89740e7	0.618234
$66$	−1.96581e7	−0.127524
$67$	2.27218e7	0.137755	0.0688773	−	0.997625i	$-0.478058\pi$
$67$	2.27218e7	0.137755	0.0688773	+	0.997625i	$0.478058\pi$
$68$	1.40953e8	0.799436
$69$	−5.44658e7	−0.289270
$70$	0	0
$71$	4.15967e8	1.94266	0.971328	−	0.237742i	$-0.0764074\pi$
$71$	4.15967e8	1.94266	0.971328	+	0.237742i	$0.0764074\pi$
$72$	4.58669e7	0.201142
$73$	−2.17283e8	−0.895516	−0.447758	−	0.894155i	$-0.647777\pi$
$73$	−2.17283e8	−0.895516	−0.447758	+	0.894155i	$0.647777\pi$
$74$	4.25232e7	0.164848
$75$	3.83334e7	0.139895
$76$	3.30736e8	1.13716
$77$	0	0
$78$	−6.35290e7	−0.194333
$79$	3.66004e8	1.05722	0.528608	−	0.848866i	$-0.322714\pi$
$79$	3.66004e8	1.05722	0.528608	+	0.848866i	$0.322714\pi$
$80$	−1.44255e8	−0.393754
$81$	−8.84914e7	−0.228412
$82$	−1.21509e7	−0.0296787
$83$	2.12240e8	0.490880	0.245440	−	0.969412i	$-0.421068\pi$
$83$	2.12240e8	0.490880	0.245440	+	0.969412i	$0.421068\pi$
$84$	0	0
$85$	1.79304e8	0.372566
$86$	−1.44199e8	−0.284261
$87$	3.20532e8	0.599839
$88$	2.00985e8	0.357266
$89$	−6.42964e8	−1.08625	−0.543127	−	0.839650i	$-0.682760\pi$
$89$	−6.42964e8	−1.08625	−0.543127	+	0.839650i	$0.682760\pi$
$90$	2.85720e7	0.0459038
$91$	0	0
$92$	2.72692e8	0.396850
$93$	4.31345e8	0.597932
$94$	−2.29551e8	−0.303252
$95$	4.20724e8	0.529957
$96$	3.32245e8	0.399243
$97$	−9.38511e8	−1.07638	−0.538191	−	0.842823i	$-0.680892\pi$
$97$	−9.38511e8	−1.07638	−0.538191	+	0.842823i	$0.680892\pi$
$98$	0	0
$99$	4.42833e8	0.463321
$100$	−1.91922e8	−0.191922
$101$	4.67360e8	0.446895	0.223447	−	0.974716i	$-0.428269\pi$
$101$	4.67360e8	0.446895	0.223447	+	0.974716i	$0.428269\pi$
$102$	−1.28026e8	−0.117111
$103$	9.04818e8	0.792125	0.396062	−	0.918224i	$-0.370376\pi$
$103$	9.04818e8	0.792125	0.396062	+	0.918224i	$0.370376\pi$
$104$	6.49523e8	0.544433
$105$	0	0
$106$	−3.37024e8	−0.259289
$107$	−6.17787e8	−0.455629	−0.227815	−	0.973705i	$-0.573158\pi$
$107$	−6.17787e8	−0.455629	−0.227815	+	0.973705i	$0.573158\pi$
$108$	1.43371e9	1.01404
$109$	2.54838e9	1.72920	0.864599	−	0.502463i	$-0.167573\pi$
$109$	2.54838e9	1.72920	0.864599	+	0.502463i	$0.167573\pi$
$110$	1.25200e8	0.0815337
$111$	9.17637e8	0.573743
$112$	0	0
$113$	−1.26981e9	−0.732631	−0.366315	−	0.930491i	$-0.619381\pi$
$113$	−1.26981e9	−0.732631	−0.366315	+	0.930491i	$0.619381\pi$
$114$	−3.00404e8	−0.166584
$115$	3.46886e8	0.184947
$116$	−1.60479e9	−0.822921
$117$	1.43110e9	0.706049
$118$	3.35778e8	0.159435
$119$	0	0
$120$	2.79839e8	0.123195
$121$	−4.17489e8	−0.177056
$122$	−6.58698e7	−0.0269195
$123$	−2.62212e8	−0.103295
$124$	−2.15960e9	−0.820305
$125$	−2.44141e8	−0.0894427
$126$	0	0
$127$	−1.76485e9	−0.601991	−0.300996	−	0.953626i	$-0.597319\pi$
$127$	−1.76485e9	−0.601991	−0.300996	+	0.953626i	$0.597319\pi$
$128$	−2.20083e9	−0.724671
$129$	−3.11176e9	−0.989356
$130$	4.04608e8	0.124248
$131$	−3.86727e9	−1.14732	−0.573659	−	0.819094i	$-0.694477\pi$
$131$	−3.86727e9	−1.14732	−0.573659	+	0.819094i	$0.694477\pi$
$132$	2.12390e9	0.608907
$133$	0	0
$134$	1.03327e8	0.0276849
$135$	1.82380e9	0.472580
$136$	1.30894e9	0.328092
$137$	5.95463e9	1.44415	0.722075	−	0.691815i	$-0.243189\pi$
$137$	5.95463e9	1.44415	0.722075	+	0.691815i	$0.243189\pi$
$138$	−2.47683e8	−0.0581353
$139$	−6.51557e9	−1.48042	−0.740211	−	0.672374i	$-0.765275\pi$
$139$	−6.51557e9	−1.48042	−0.740211	+	0.672374i	$0.765275\pi$
$140$	0	0
$141$	−4.95364e9	−1.05545
$142$	1.89160e9	0.390421
$143$	6.27098e9	1.25407
$144$	−2.32027e9	−0.449684
$145$	−2.04143e9	−0.383512
$146$	−9.88093e8	−0.179974
$147$	0	0
$148$	−4.59429e9	−0.787120
$149$	5.08275e9	0.844814	0.422407	−	0.906406i	$-0.361185\pi$
$149$	5.08275e9	0.844814	0.422407	+	0.906406i	$0.361185\pi$
$150$	1.74321e8	0.0281150
$151$	1.05147e10	1.64589	0.822945	−	0.568120i	$-0.192329\pi$
$151$	1.05147e10	1.64589	0.822945	+	0.568120i	$0.192329\pi$
$152$	3.07134e9	0.466694
$153$	2.88401e9	0.425486
$154$	0	0
$155$	−2.74719e9	−0.382292
$156$	6.86380e9	0.927906
$157$	5.28495e9	0.694212	0.347106	−	0.937826i	$-0.387164\pi$
$157$	5.28495e9	0.694212	0.347106	+	0.937826i	$0.387164\pi$
$158$	1.66440e9	0.212471
$159$	−7.27287e9	−0.902441
$160$	−2.11603e9	−0.255259
$161$	0	0
$162$	−4.02414e8	−0.0459045
$163$	−4.40792e9	−0.489091	−0.244545	−	0.969638i	$-0.578639\pi$
$163$	−4.40792e9	−0.489091	−0.244545	+	0.969638i	$0.578639\pi$
$164$	1.31280e9	0.141711
$165$	2.70178e9	0.283773
$166$	9.65159e8	0.0986535
$167$	1.04618e10	1.04083	0.520416	−	0.853913i	$-0.325777\pi$
$167$	1.04618e10	1.04083	0.520416	+	0.853913i	$0.325777\pi$
$168$	0	0
$169$	9.66141e9	0.911067
$170$	8.15381e8	0.0748756
$171$	6.76714e9	0.605233
$172$	1.55795e10	1.35730
$173$	−1.44477e10	−1.22628	−0.613141	−	0.789973i	$-0.710094\pi$
$173$	−1.44477e10	−1.22628	−0.613141	+	0.789973i	$0.710094\pi$
$174$	1.45762e9	0.120551
$175$	0	0
$176$	−1.01672e10	−0.798722
$177$	7.24599e9	0.554905
$178$	−2.92387e9	−0.218307
$179$	1.38421e10	1.00777	0.503887	−	0.863769i	$-0.331903\pi$
$179$	1.38421e10	1.00777	0.503887	+	0.863769i	$0.331903\pi$
$180$	−3.08697e9	−0.219183
$181$	2.58030e10	1.78697	0.893484	−	0.449095i	$-0.148254\pi$
$181$	2.58030e10	1.78697	0.893484	+	0.449095i	$0.148254\pi$
$182$	0	0
$183$	−1.42145e9	−0.0936919
$184$	2.53232e9	0.162869
$185$	−5.84432e9	−0.366827
$186$	1.96154e9	0.120168
$187$	1.26375e10	0.755743
$188$	2.48012e10	1.44798
$189$	0	0
$190$	1.91324e9	0.106507
$191$	−2.65408e10	−1.44299	−0.721495	−	0.692419i	$-0.756545\pi$
$191$	−2.65408e10	−1.44299	−0.721495	+	0.692419i	$0.756545\pi$
$192$	−1.00859e10	−0.535623
$193$	1.62976e9	0.0845505	0.0422753	−	0.999106i	$-0.486539\pi$
$193$	1.62976e9	0.0845505	0.0422753	+	0.999106i	$0.486539\pi$
$194$	−4.26787e9	−0.216323
$195$	8.73132e9	0.432439
$196$	0	0
$197$	−1.73941e10	−0.822819	−0.411410	−	0.911451i	$-0.634963\pi$
$197$	−1.73941e10	−0.822819	−0.411410	+	0.911451i	$0.634963\pi$
$198$	2.01378e9	0.0931148
$199$	3.31064e10	1.49649	0.748243	−	0.663424i	$-0.230897\pi$
$199$	3.31064e10	1.49649	0.748243	+	0.663424i	$0.230897\pi$
$200$	−1.78226e9	−0.0787656
$201$	2.22977e9	0.0963557
$202$	2.12532e9	0.0898136
$203$	0	0
$204$	1.38322e10	0.559184
$205$	1.67000e9	0.0660424
$206$	4.11465e9	0.159195
$207$	5.57950e9	0.211217
$208$	−3.28574e10	−1.21716
$209$	2.96530e10	1.07501
$210$	0	0
$211$	3.21024e10	1.11498	0.557490	−	0.830184i	$-0.311765\pi$
$211$	3.21024e10	1.11498	0.557490	+	0.830184i	$0.311765\pi$
$212$	3.64128e10	1.23806
$213$	4.08202e10	1.35884
$214$	−2.80938e9	−0.0915690
$215$	1.98184e10	0.632552
$216$	1.33140e10	0.416166
$217$	0	0
$218$	1.15887e10	0.347521
$219$	−2.13227e10	−0.626390
$220$	−1.35269e10	−0.389309
$221$	4.08406e10	1.15167
$222$	4.17294e9	0.115307
$223$	−3.79801e10	−1.02845	−0.514226	−	0.857655i	$-0.671921\pi$
$223$	−3.79801e10	−1.02845	−0.514226	+	0.857655i	$0.671921\pi$
$224$	0	0
$225$	−3.92688e9	−0.102147
$226$	−5.77444e9	−0.147239
$227$	1.71268e10	0.428113	0.214057	−	0.976821i	$-0.431332\pi$
$227$	1.71268e10	0.428113	0.214057	+	0.976821i	$0.431332\pi$
$228$	3.24563e10	0.795411
$229$	−7.66667e10	−1.84224	−0.921122	−	0.389274i	$-0.872726\pi$
$229$	−7.66667e10	−1.84224	−0.921122	+	0.389274i	$0.872726\pi$
$230$	1.57746e9	0.0371692
$231$	0	0
$232$	−1.49027e10	−0.337730
$233$	2.18072e10	0.484729	0.242364	−	0.970185i	$-0.422077\pi$
$233$	2.18072e10	0.484729	0.242364	+	0.970185i	$0.422077\pi$
$234$	6.50793e9	0.141896
$235$	3.15491e10	0.674811
$236$	−3.62782e10	−0.761275
$237$	3.59172e10	0.739495
$238$	0	0
$239$	−7.61451e10	−1.50956	−0.754782	−	0.655976i	$-0.772257\pi$
$239$	−7.61451e10	−1.50956	−0.754782	+	0.655976i	$0.772257\pi$
$240$	−1.41562e10	−0.275421
$241$	−6.28307e10	−1.19976	−0.599881	−	0.800089i	$-0.704786\pi$
$241$	−6.28307e10	−1.19976	−0.599881	+	0.800089i	$0.704786\pi$
$242$	−1.89853e9	−0.0355834
$243$	4.87526e10	0.896952
$244$	7.11671e9	0.128536
$245$	0	0
$246$	−1.19241e9	−0.0207595
$247$	9.58296e10	1.63819
$248$	−2.00548e10	−0.336656
$249$	2.08278e10	0.343358
$250$	−1.11023e9	−0.0179755
$251$	−4.82160e10	−0.766760	−0.383380	−	0.923591i	$-0.625240\pi$
$251$	−4.82160e10	−0.766760	−0.383380	+	0.923591i	$0.625240\pi$
$252$	0	0
$253$	2.44489e10	0.375160
$254$	−8.02562e9	−0.120984
$255$	1.75957e10	0.260600
$256$	4.26138e10	0.620112
$257$	4.02899e10	0.576099	0.288049	−	0.957616i	$-0.406993\pi$
$257$	4.02899e10	0.576099	0.288049	+	0.957616i	$0.406993\pi$
$258$	−1.41507e10	−0.198833
$259$	0	0
$260$	−4.37147e10	−0.593264
$261$	−3.28354e10	−0.437986
$262$	−1.75864e10	−0.230580
$263$	1.91897e10	0.247325	0.123662	−	0.992324i	$-0.460536\pi$
$263$	1.91897e10	0.247325	0.123662	+	0.992324i	$0.460536\pi$
$264$	1.97234e10	0.249898
$265$	4.63200e10	0.576982
$266$	0	0
$267$	−6.30963e10	−0.759806
$268$	−1.11637e10	−0.132191
$269$	1.55364e11	1.80911	0.904554	−	0.426359i	$-0.140204\pi$
$269$	1.55364e11	1.80911	0.904554	+	0.426359i	$0.140204\pi$
$270$	8.29371e9	0.0949756
$271$	−1.07856e11	−1.21474	−0.607370	−	0.794419i	$-0.707776\pi$
$271$	−1.07856e11	−1.21474	−0.607370	+	0.794419i	$0.707776\pi$
$272$	−6.62154e10	−0.733498
$273$	0	0
$274$	2.70786e10	0.290234
$275$	−1.72073e10	−0.181433
$276$	2.67602e10	0.277586
$277$	1.00953e11	1.03030	0.515148	−	0.857101i	$-0.327737\pi$
$277$	1.00953e11	1.03030	0.515148	+	0.857101i	$0.327737\pi$
$278$	−2.96295e10	−0.297524
$279$	−4.41872e10	−0.436593
$280$	0	0
$281$	−5.97756e10	−0.571934	−0.285967	−	0.958239i	$-0.592315\pi$
$281$	−5.97756e10	−0.571934	−0.285967	+	0.958239i	$0.592315\pi$
$282$	−2.25266e10	−0.212117
$283$	−2.37771e10	−0.220353	−0.110177	−	0.993912i	$-0.535142\pi$
$283$	−2.37771e10	−0.220353	−0.110177	+	0.993912i	$0.535142\pi$
$284$	−2.04373e11	−1.86419
$285$	4.12871e10	0.370691
$286$	2.85172e10	0.252034
$287$	0	0
$288$	−3.40353e10	−0.291516
$289$	−3.62845e10	−0.305971
$290$	−9.28338e9	−0.0770753
$291$	−9.20993e10	−0.752901
$292$	1.06756e11	0.859346
$293$	−8.15841e10	−0.646698	−0.323349	−	0.946280i	$-0.604809\pi$
$293$	−8.15841e10	−0.646698	−0.323349	+	0.946280i	$0.604809\pi$
$294$	0	0
$295$	−4.61489e10	−0.354782
$296$	−4.26643e10	−0.323037
$297$	1.28543e11	0.958617
$298$	2.31138e10	0.169784
$299$	7.90114e10	0.571702
$300$	−1.88340e10	−0.134244
$301$	0	0
$302$	4.78155e10	0.330779
$303$	4.58636e10	0.312591
$304$	−1.55370e11	−1.04336
$305$	9.05305e9	0.0599026
$306$	1.31150e10	0.0855111
$307$	3.31601e9	0.0213056	0.0106528	−	0.999943i	$-0.496609\pi$
$307$	3.31601e9	0.0213056	0.0106528	+	0.999943i	$0.496609\pi$
$308$	0	0
$309$	8.87929e10	0.554071
$310$	−1.24928e10	−0.0768302
$311$	−2.69649e10	−0.163447	−0.0817234	−	0.996655i	$-0.526042\pi$
$311$	−2.69649e10	−0.163447	−0.0817234	+	0.996655i	$0.526042\pi$
$312$	6.37399e10	0.380817
$313$	−6.20886e10	−0.365648	−0.182824	−	0.983146i	$-0.558524\pi$
$313$	−6.20886e10	−0.365648	−0.182824	+	0.983146i	$0.558524\pi$
$314$	2.40333e10	0.139518
$315$	0	0
$316$	−1.79825e11	−1.01452
$317$	1.67449e11	0.931359	0.465679	−	0.884954i	$-0.345810\pi$
$317$	1.67449e11	0.931359	0.465679	+	0.884954i	$0.345810\pi$
$318$	−3.30733e10	−0.181366
$319$	−1.43882e11	−0.777944
$320$	6.42358e10	0.342454
$321$	−6.06256e10	−0.318701
$322$	0	0
$323$	1.93119e11	0.987221
$324$	4.34776e10	0.219186
$325$	−5.56087e10	−0.276483
$326$	−2.00450e10	−0.0982938
$327$	2.50081e11	1.20953
$328$	1.21912e10	0.0581587
$329$	0	0
$330$	1.22863e10	0.0570307
$331$	−2.01516e11	−0.922750	−0.461375	−	0.887205i	$-0.652644\pi$
$331$	−2.01516e11	−0.922750	−0.461375	+	0.887205i	$0.652644\pi$
$332$	−1.04278e11	−0.471054
$333$	−9.40030e10	−0.418931
$334$	4.75748e10	0.209179
$335$	−1.42011e10	−0.0616057
$336$	0	0
$337$	4.50890e11	1.90430	0.952151	−	0.305629i	$-0.0988669\pi$
$337$	4.50890e11	1.90430	0.952151	+	0.305629i	$0.0988669\pi$
$338$	4.39352e10	0.183099
$339$	−1.24611e11	−0.512456
$340$	−8.80955e10	−0.357519
$341$	−1.93624e11	−0.775471
$342$	3.07735e10	0.121635
$343$	0	0
$344$	1.44677e11	0.557041
$345$	3.40411e10	0.129365
$346$	−6.57007e10	−0.246449
$347$	−4.50544e11	−1.66823	−0.834113	−	0.551594i	$-0.814020\pi$
$347$	−4.50544e11	−1.66823	−0.834113	+	0.551594i	$0.814020\pi$
$348$	−1.57484e11	−0.575612
$349$	−7.01952e10	−0.253275	−0.126638	−	0.991949i	$-0.540419\pi$
$349$	−7.01952e10	−0.253275	−0.126638	+	0.991949i	$0.540419\pi$
$350$	0	0
$351$	4.15413e11	1.46082
$352$	−1.49140e11	−0.517787
$353$	−2.25165e11	−0.771819	−0.385910	−	0.922537i	$-0.626112\pi$
$353$	−2.25165e11	−0.771819	−0.385910	+	0.922537i	$0.626112\pi$
$354$	3.29511e10	0.111521
$355$	−2.59979e11	−0.868782
$356$	3.15901e11	1.04238
$357$	0	0
$358$	6.29468e10	0.202535
$359$	1.97594e11	0.627841	0.313920	−	0.949449i	$-0.398357\pi$
$359$	1.97594e11	0.627841	0.313920	+	0.949449i	$0.398357\pi$
$360$	−2.86668e10	−0.0899536
$361$	1.30454e11	0.404272
$362$	1.17339e11	0.359132
$363$	−4.09697e10	−0.123846
$364$	0	0
$365$	1.35802e11	0.400487
$366$	−6.46404e9	−0.0188295
$367$	3.92725e10	0.113003	0.0565016	−	0.998403i	$-0.482005\pi$
$367$	3.92725e10	0.113003	0.0565016	+	0.998403i	$0.482005\pi$
$368$	−1.28102e11	−0.364118
$369$	2.68611e10	0.0754232
$370$	−2.65770e10	−0.0737221
$371$	0	0
$372$	−2.11929e11	−0.573782
$373$	−5.28306e11	−1.41317	−0.706587	−	0.707627i	$-0.749766\pi$
$373$	−5.28306e11	−1.41317	−0.706587	+	0.707627i	$0.749766\pi$
$374$	5.74689e10	0.151884
$375$	−2.39584e10	−0.0625628
$376$	2.30313e11	0.594256
$377$	−4.64983e11	−1.18550
$378$	0	0
$379$	−2.47671e11	−0.616594	−0.308297	−	0.951290i	$-0.599759\pi$
$379$	−2.47671e11	−0.616594	−0.308297	+	0.951290i	$0.599759\pi$
$380$	−2.06710e11	−0.508552
$381$	−1.73191e11	−0.421077
$382$	−1.20694e11	−0.290002
$383$	6.30255e11	1.49666	0.748328	−	0.663329i	$-0.230857\pi$
$383$	6.30255e11	1.49666	0.748328	+	0.663329i	$0.230857\pi$
$384$	−2.15975e11	−0.506889
$385$	0	0
$386$	7.41133e9	0.0169923
$387$	3.18770e11	0.722400
$388$	4.61109e11	1.03291
$389$	−3.11450e11	−0.689628	−0.344814	−	0.938671i	$-0.612058\pi$
$389$	−3.11450e11	−0.689628	−0.344814	+	0.938671i	$0.612058\pi$
$390$	3.97056e10	0.0869083
$391$	1.59227e11	0.344525
$392$	0	0
$393$	−3.79509e11	−0.802519
$394$	−7.90996e10	−0.165364
$395$	−2.28752e11	−0.472801
$396$	−2.17573e11	−0.444607
$397$	−9.31030e10	−0.188108	−0.0940538	−	0.995567i	$-0.529983\pi$
$397$	−9.31030e10	−0.188108	−0.0940538	+	0.995567i	$0.529983\pi$
$398$	1.50551e11	0.300753
$399$	0	0
$400$	9.01592e10	0.176092
$401$	1.67787e11	0.324048	0.162024	−	0.986787i	$-0.448198\pi$
$401$	1.67787e11	0.324048	0.162024	+	0.986787i	$0.448198\pi$
$402$	1.01398e10	0.0193649
$403$	−6.25736e11	−1.18173
$404$	−2.29623e11	−0.428845
$405$	5.53071e10	0.102149
$406$	0	0
$407$	−4.11913e11	−0.744100
$408$	1.28451e11	0.229492
$409$	−6.66489e11	−1.17771	−0.588855	−	0.808239i	$-0.700421\pi$
$409$	−6.66489e11	−1.17771	−0.588855	+	0.808239i	$0.700421\pi$
$410$	7.59429e9	0.0132727
$411$	5.84348e11	1.01014
$412$	−4.44555e11	−0.760131
$413$	0	0
$414$	2.53727e10	0.0424488
$415$	−1.32650e11	−0.219528
$416$	−4.81974e11	−0.789049
$417$	−6.39395e11	−1.03552
$418$	1.34847e11	0.216047
$419$	−3.35339e11	−0.531522	−0.265761	−	0.964039i	$-0.585623\pi$
$419$	−3.35339e11	−0.531522	−0.265761	+	0.964039i	$0.585623\pi$
$420$	0	0
$421$	−1.58071e11	−0.245235	−0.122617	−	0.992454i	$-0.539129\pi$
$421$	−1.58071e11	−0.245235	−0.122617	+	0.992454i	$0.539129\pi$
$422$	1.45986e11	0.224080
$423$	5.07453e11	0.770662
$424$	3.38143e11	0.508106
$425$	−1.12065e11	−0.166617
$426$	1.85630e11	0.273089
$427$	0	0
$428$	3.03531e11	0.437227
$429$	6.15393e11	0.877192
$430$	9.01241e10	0.127126
$431$	−7.97845e11	−1.11371	−0.556853	−	0.830611i	$-0.687991\pi$
$431$	−7.97845e11	−1.11371	−0.556853	+	0.830611i	$0.687991\pi$
$432$	−6.73515e11	−0.930402
$433$	−1.13662e12	−1.55389	−0.776944	−	0.629570i	$-0.783231\pi$
$433$	−1.13662e12	−1.55389	−0.776944	+	0.629570i	$0.783231\pi$
$434$	0	0
$435$	−2.00333e11	−0.268256
$436$	−1.25207e12	−1.65935
$437$	3.73615e11	0.490069
$438$	−9.69650e10	−0.125887
$439$	5.03443e11	0.646934	0.323467	−	0.946239i	$-0.395151\pi$
$439$	5.03443e11	0.646934	0.323467	+	0.946239i	$0.395151\pi$
$440$	−1.25616e11	−0.159774
$441$	0	0
$442$	1.85722e11	0.231453
$443$	−5.69695e11	−0.702790	−0.351395	−	0.936227i	$-0.614293\pi$
$443$	−5.69695e11	−0.702790	−0.351395	+	0.936227i	$0.614293\pi$
$444$	−4.50854e11	−0.550569
$445$	4.01852e11	0.485788
$446$	−1.72714e11	−0.206691
$447$	4.98788e11	0.590925
$448$	0	0
$449$	1.67088e11	0.194015	0.0970076	−	0.995284i	$-0.469073\pi$
$449$	1.67088e11	0.194015	0.0970076	+	0.995284i	$0.469073\pi$
$450$	−1.78575e10	−0.0205288
$451$	1.17703e11	0.133966
$452$	6.23882e11	0.703040
$453$	1.03184e12	1.15126
$454$	7.78838e10	0.0860391
$455$	0	0
$456$	3.01401e11	0.326440
$457$	−8.65375e11	−0.928071	−0.464036	−	0.885817i	$-0.653599\pi$
$457$	−8.65375e11	−0.928071	−0.464036	+	0.885817i	$0.653599\pi$
$458$	−3.48641e11	−0.370241
$459$	8.37155e11	0.880337
$460$	−1.70432e11	−0.177477
$461$	−5.61050e11	−0.578559	−0.289279	−	0.957245i	$-0.593416\pi$
$461$	−5.61050e11	−0.578559	−0.289279	+	0.957245i	$0.593416\pi$
$462$	0	0
$463$	−1.04005e12	−1.05182	−0.525908	−	0.850542i	$-0.676274\pi$
$463$	−1.04005e12	−1.05182	−0.525908	+	0.850542i	$0.676274\pi$
$464$	7.53884e11	0.755047
$465$	−2.69591e11	−0.267403
$466$	9.91682e10	0.0974172
$467$	−1.18851e12	−1.15632	−0.578158	−	0.815925i	$-0.696228\pi$
$467$	−1.18851e12	−1.15632	−0.578158	+	0.815925i	$0.696228\pi$
$468$	−7.03130e11	−0.677532
$469$	0	0
$470$	1.43469e11	0.135619
$471$	5.18630e11	0.485583
$472$	−3.36893e11	−0.312430
$473$	1.39682e12	1.28312
$474$	1.63333e11	0.148618
$475$	−2.62952e11	−0.237004
$476$	0	0
$477$	7.45036e11	0.658938
$478$	−3.46269e11	−0.303381
$479$	2.60913e11	0.226457	0.113228	−	0.993569i	$-0.463881\pi$
$479$	2.60913e11	0.226457	0.113228	+	0.993569i	$0.463881\pi$
$480$	−2.07653e11	−0.178547
$481$	−1.33118e12	−1.13392
$482$	−2.85722e11	−0.241119
$483$	0	0
$484$	2.05121e11	0.169905
$485$	5.86569e11	0.481373
$486$	2.21702e11	0.180263
$487$	−2.15539e12	−1.73638	−0.868190	−	0.496231i	$-0.834717\pi$
$487$	−2.15539e12	−1.73638	−0.868190	+	0.496231i	$0.834717\pi$
$488$	6.60886e10	0.0527518
$489$	−4.32564e11	−0.342106
$490$	0	0
$491$	5.31182e10	0.0412455	0.0206227	−	0.999787i	$-0.493435\pi$
$491$	5.31182e10	0.0412455	0.0206227	+	0.999787i	$0.493435\pi$
$492$	1.28830e11	0.0991230
$493$	−9.37051e11	−0.714418
$494$	4.35784e11	0.329231
$495$	−2.76771e11	−0.207203
$496$	1.01451e12	0.752646
$497$	0	0
$498$	9.47144e10	0.0690055
$499$	−5.97480e11	−0.431391	−0.215695	−	0.976461i	$-0.569202\pi$
$499$	−5.97480e11	−0.431391	−0.215695	+	0.976461i	$0.569202\pi$
$500$	1.19951e11	0.0858301
$501$	1.02665e12	0.728035
$502$	−2.19262e11	−0.154098
$503$	1.30692e12	0.910321	0.455160	−	0.890410i	$-0.349582\pi$
$503$	1.30692e12	0.910321	0.455160	+	0.890410i	$0.349582\pi$
$504$	0	0
$505$	−2.92100e11	−0.199857
$506$	1.11181e11	0.0753969
$507$	9.48107e11	0.637267
$508$	8.67105e11	0.577677
$509$	1.42204e12	0.939035	0.469518	−	0.882923i	$-0.344428\pi$
$509$	1.42204e12	0.939035	0.469518	+	0.882923i	$0.344428\pi$
$510$	8.00162e10	0.0523736
$511$	0	0
$512$	1.32061e12	0.849297
$513$	1.96433e12	1.25223
$514$	1.83218e11	0.115780
$515$	−5.65511e11	−0.354249
$516$	1.52887e12	0.949396
$517$	2.22362e12	1.36884
$518$	0	0
$519$	−1.41780e12	−0.857753
$520$	−4.05952e11	−0.243478
$521$	1.61928e12	0.962834	0.481417	−	0.876492i	$-0.340122\pi$
$521$	1.61928e12	0.962834	0.481417	+	0.876492i	$0.340122\pi$
$522$	−1.49319e11	−0.0880232
$523$	2.92425e11	0.170906	0.0854529	−	0.996342i	$-0.472766\pi$
$523$	2.92425e11	0.170906	0.0854529	+	0.996342i	$0.472766\pi$
$524$	1.90007e12	1.10098
$525$	0	0
$526$	8.72650e10	0.0497055
$527$	−1.26101e12	−0.712146
$528$	−9.97745e11	−0.558685
$529$	−1.49311e12	−0.828973
$530$	2.10640e11	0.115958
$531$	−7.42282e11	−0.405176
$532$	0	0
$533$	3.80381e11	0.204148
$534$	−2.86930e11	−0.152700
$535$	3.86117e11	0.203764
$536$	−1.03670e11	−0.0542516
$537$	1.35837e12	0.704912
$538$	7.06515e11	0.363581
$539$	0	0
$540$	−8.96070e11	−0.453492
$541$	2.64098e12	1.32549	0.662747	−	0.748844i	$-0.269391\pi$
$541$	2.64098e12	1.32549	0.662747	+	0.748844i	$0.269391\pi$
$542$	−4.90475e11	−0.244130
$543$	2.53214e12	1.24994
$544$	−9.71292e11	−0.475505
$545$	−1.59274e12	−0.773320
$546$	0	0
$547$	1.57238e12	0.750954	0.375477	−	0.926832i	$-0.377479\pi$
$547$	1.57238e12	0.750954	0.375477	+	0.926832i	$0.377479\pi$
$548$	−2.92563e12	−1.38582
$549$	1.45614e11	0.0684112
$550$	−7.82499e10	−0.0364630
$551$	−2.19873e12	−1.01622
$552$	2.48505e11	0.113923
$553$	0	0
$554$	4.59085e11	0.207061
$555$	−5.73523e11	−0.256586
$556$	3.20123e12	1.42063
$557$	2.92127e12	1.28595	0.642974	−	0.765888i	$-0.277700\pi$
$557$	2.92127e12	1.28595	0.642974	+	0.765888i	$0.277700\pi$
$558$	−2.00941e11	−0.0877433
$559$	4.51411e12	1.95533
$560$	0	0
$561$	1.24016e12	0.528622
$562$	−2.71829e11	−0.114943
$563$	2.29076e12	0.960932	0.480466	−	0.877013i	$-0.340468\pi$
$563$	2.29076e12	0.960932	0.480466	+	0.877013i	$0.340468\pi$
$564$	2.43382e12	1.01282
$565$	7.93630e11	0.327642
$566$	−1.08126e11	−0.0442850
$567$	0	0
$568$	−1.89789e12	−0.765072
$569$	3.78939e12	1.51553	0.757764	−	0.652528i	$-0.226292\pi$
$569$	3.78939e12	1.51553	0.757764	+	0.652528i	$0.226292\pi$
$570$	1.87752e11	0.0744987
$571$	8.33507e11	0.328131	0.164065	−	0.986449i	$-0.447539\pi$
$571$	8.33507e11	0.328131	0.164065	+	0.986449i	$0.447539\pi$
$572$	−3.08106e12	−1.20342
$573$	−2.60454e12	−1.00933
$574$	0	0
$575$	−2.16804e11	−0.0827107
$576$	1.03320e12	0.391097
$577$	1.53253e12	0.575595	0.287797	−	0.957691i	$-0.407077\pi$
$577$	1.53253e12	0.575595	0.287797	+	0.957691i	$0.407077\pi$
$578$	−1.65003e11	−0.0614918
$579$	1.59934e11	0.0591409
$580$	1.00300e12	0.368022
$581$	0	0
$582$	−4.18821e11	−0.151312
$583$	3.26468e12	1.17040
$584$	9.91374e11	0.352679
$585$	−8.94440e11	−0.315755
$586$	−3.71003e11	−0.129969
$587$	1.16935e12	0.406510	0.203255	−	0.979126i	$-0.434848\pi$
$587$	1.16935e12	0.406510	0.203255	+	0.979126i	$0.434848\pi$
$588$	0	0
$589$	−2.95886e12	−1.01299
$590$	−2.09861e11	−0.0713015
$591$	−1.70695e12	−0.575541
$592$	2.15826e12	0.722198
$593$	−2.99104e12	−0.993290	−0.496645	−	0.867954i	$-0.665435\pi$
$593$	−2.99104e12	−0.993290	−0.496645	+	0.867954i	$0.665435\pi$
$594$	5.84549e11	0.192656
$595$	0	0
$596$	−2.49726e12	−0.810692
$597$	3.24884e12	1.04675
$598$	3.59304e11	0.114896
$599$	−2.53486e12	−0.804513	−0.402256	−	0.915527i	$-0.631774\pi$
$599$	−2.53486e12	−0.804513	−0.402256	+	0.915527i	$0.631774\pi$
$600$	−1.74899e11	−0.0550945
$601$	4.31006e12	1.34756	0.673781	−	0.738931i	$-0.264669\pi$
$601$	4.31006e12	1.34756	0.673781	+	0.738931i	$0.264669\pi$
$602$	0	0
$603$	−2.28418e11	−0.0703563
$604$	−5.16609e12	−1.57941
$605$	2.60931e11	0.0791819
$606$	2.08565e11	0.0628223
$607$	−3.99341e12	−1.19397	−0.596986	−	0.802252i	$-0.703635\pi$
$607$	−3.99341e12	−1.19397	−0.596986	+	0.802252i	$0.703635\pi$
$608$	−2.27907e12	−0.676381
$609$	0	0
$610$	4.11687e10	0.0120388
$611$	7.18605e12	2.08596
$612$	−1.41697e12	−0.408301
$613$	4.02942e12	1.15258	0.576289	−	0.817246i	$-0.304500\pi$
$613$	4.02942e12	1.15258	0.576289	+	0.817246i	$0.304500\pi$
$614$	1.50795e10	0.00428184
$615$	1.63883e11	0.0461950
$616$	0	0
$617$	−5.94209e12	−1.65065	−0.825326	−	0.564656i	$-0.809009\pi$
$617$	−5.94209e12	−1.65065	−0.825326	+	0.564656i	$0.809009\pi$
$618$	4.03785e11	0.111353
$619$	−3.62900e12	−0.993526	−0.496763	−	0.867886i	$-0.665478\pi$
$619$	−3.62900e12	−0.993526	−0.496763	+	0.867886i	$0.665478\pi$
$620$	1.34975e12	0.366851
$621$	1.61959e12	0.437010
$622$	−1.22622e11	−0.0328483
$623$	0	0
$624$	−3.22441e12	−0.851373
$625$	1.52588e11	0.0400000
$626$	−2.82348e11	−0.0734851
$627$	2.90995e12	0.751938
$628$	−2.59660e12	−0.666173
$629$	−2.68264e12	−0.683337
$630$	0	0
$631$	5.56207e12	1.39670	0.698352	−	0.715755i	$-0.253917\pi$
$631$	5.56207e12	1.39670	0.698352	+	0.715755i	$0.253917\pi$
$632$	−1.66993e12	−0.416361
$633$	3.15032e12	0.779899
$634$	7.61475e11	0.187178
$635$	1.10303e12	0.269219
$636$	3.57331e12	0.865992
$637$	0	0
$638$	−6.54302e11	−0.156345
$639$	−4.18164e12	−0.992185
$640$	1.37552e12	0.324083
$641$	4.70928e11	0.110178	0.0550888	−	0.998481i	$-0.482456\pi$
$641$	4.70928e11	0.110178	0.0550888	+	0.998481i	$0.482456\pi$
$642$	−2.75694e11	−0.0640501
$643$	−6.13138e12	−1.41452	−0.707260	−	0.706954i	$-0.750069\pi$
$643$	−6.13138e12	−1.41452	−0.707260	+	0.706954i	$0.750069\pi$
$644$	0	0
$645$	1.94485e12	0.442453
$646$	8.78208e11	0.198404
$647$	2.95457e12	0.662864	0.331432	−	0.943479i	$-0.392468\pi$
$647$	2.95457e12	0.662864	0.331432	+	0.943479i	$0.392468\pi$
$648$	4.03750e11	0.0899550
$649$	−3.25262e12	−0.719668
$650$	−2.52880e11	−0.0555654
$651$	0	0
$652$	2.16570e12	0.469336
$653$	−7.91440e12	−1.70337	−0.851685	−	0.524055i	$-0.824419\pi$
$653$	−7.91440e12	−1.70337	−0.851685	+	0.524055i	$0.824419\pi$
$654$	1.13724e12	0.243082
$655$	2.41705e12	0.513096
$656$	−6.16717e11	−0.130022
$657$	2.18431e12	0.457372
$658$	0	0
$659$	3.06617e12	0.633304	0.316652	−	0.948542i	$-0.397441\pi$
$659$	3.06617e12	0.633304	0.316652	+	0.948542i	$0.397441\pi$
$660$	−1.32744e12	−0.272312
$661$	2.69526e12	0.549153	0.274577	−	0.961565i	$-0.411462\pi$
$661$	2.69526e12	0.549153	0.274577	+	0.961565i	$0.411462\pi$
$662$	−9.16393e11	−0.185447
$663$	4.00783e12	0.805560
$664$	−9.68364e11	−0.193322
$665$	0	0
$666$	−4.27478e11	−0.0841937
$667$	−1.81285e12	−0.354646
$668$	−5.14008e12	−0.998793
$669$	−3.72712e12	−0.719375
$670$	−6.45794e10	−0.0123811
$671$	6.38068e11	0.121511
$672$	0	0
$673$	2.97220e12	0.558483	0.279241	−	0.960221i	$-0.409917\pi$
$673$	2.97220e12	0.558483	0.279241	+	0.960221i	$0.409917\pi$
$674$	2.05042e12	0.382712
$675$	−1.13987e12	−0.211344
$676$	−4.74685e12	−0.874269
$677$	8.14226e12	1.48969	0.744845	−	0.667237i	$-0.232523\pi$
$677$	8.14226e12	1.48969	0.744845	+	0.667237i	$0.232523\pi$
$678$	−5.66666e11	−0.102990
$679$	0	0
$680$	−8.18089e11	−0.146727
$681$	1.68071e12	0.299454
$682$	−8.80505e11	−0.155848
$683$	3.46018e11	0.0608423	0.0304211	−	0.999537i	$-0.490315\pi$
$683$	3.46018e11	0.0608423	0.0304211	+	0.999537i	$0.490315\pi$
$684$	−3.32483e12	−0.580787
$685$	−3.72164e12	−0.645843
$686$	0	0
$687$	−7.52357e12	−1.28860
$688$	−7.31879e12	−1.24535
$689$	1.05505e13	1.78355
$690$	1.54802e11	0.0259989
$691$	3.34581e12	0.558277	0.279139	−	0.960251i	$-0.409951\pi$
$691$	3.34581e12	0.558277	0.279139	+	0.960251i	$0.409951\pi$
$692$	7.09844e12	1.17675
$693$	0	0
$694$	−2.04885e12	−0.335268
$695$	4.07223e12	0.662065
$696$	−1.46246e12	−0.236233
$697$	7.66557e11	0.123026
$698$	−3.19212e11	−0.0509014
$699$	2.14002e12	0.339055
$700$	0	0
$701$	8.95269e12	1.40030	0.700152	−	0.713994i	$-0.253116\pi$
$701$	8.95269e12	1.40030	0.700152	+	0.713994i	$0.253116\pi$
$702$	1.88909e12	0.293586
$703$	−6.29463e12	−0.972012
$704$	4.52741e12	0.694661
$705$	3.09603e12	0.472013
$706$	−1.02394e12	−0.155115
$707$	0	0
$708$	−3.56010e12	−0.532492
$709$	3.19448e12	0.474779	0.237390	−	0.971415i	$-0.423708\pi$
$709$	3.19448e12	0.474779	0.237390	+	0.971415i	$0.423708\pi$
$710$	−1.18225e12	−0.174601
$711$	−3.67937e12	−0.539959
$712$	2.93358e12	0.427797
$713$	−2.43958e12	−0.353518
$714$	0	0
$715$	−3.91936e12	−0.560839
$716$	−6.80091e12	−0.967070
$717$	−7.47238e12	−1.05590
$718$	8.98559e11	0.126179
$719$	−6.25538e12	−0.872918	−0.436459	−	0.899724i	$-0.643768\pi$
$719$	−6.25538e12	−0.872918	−0.436459	+	0.899724i	$0.643768\pi$
$720$	1.45017e12	0.201105
$721$	0	0
$722$	5.93236e11	0.0812475
$723$	−6.16579e12	−0.839202
$724$	−1.26775e13	−1.71479
$725$	1.27589e12	0.171512
$726$	−1.86309e11	−0.0248897
$727$	−3.88891e12	−0.516325	−0.258162	−	0.966102i	$-0.583117\pi$
$727$	−3.88891e12	−0.516325	−0.258162	+	0.966102i	$0.583117\pi$
$728$	0	0
$729$	6.52604e12	0.855807
$730$	6.17558e11	0.0804869
$731$	9.09700e12	1.17834
$732$	6.98388e11	0.0899077
$733$	9.29539e12	1.18932	0.594662	−	0.803976i	$-0.297286\pi$
$733$	9.29539e12	1.18932	0.594662	+	0.803976i	$0.297286\pi$
$734$	1.78591e11	0.0227106
$735$	0	0
$736$	−1.87909e12	−0.236047
$737$	−1.00091e12	−0.124966
$738$	1.22151e11	0.0151580
$739$	3.81274e12	0.470259	0.235130	−	0.971964i	$-0.424449\pi$
$739$	3.81274e12	0.470259	0.235130	+	0.971964i	$0.424449\pi$
$740$	2.87143e12	0.352011
$741$	9.40409e12	1.14587
$742$	0	0
$743$	−9.68333e12	−1.16567	−0.582834	−	0.812591i	$-0.698056\pi$
$743$	−9.68333e12	−1.16567	−0.582834	+	0.812591i	$0.698056\pi$
$744$	−1.96805e12	−0.235482
$745$	−3.17672e12	−0.377812
$746$	−2.40246e12	−0.284009
$747$	−2.13361e12	−0.250710
$748$	−6.20906e12	−0.725218
$749$	0	0
$750$	−1.08950e11	−0.0125734
$751$	1.35639e13	1.55598	0.777991	−	0.628275i	$-0.216239\pi$
$751$	1.35639e13	1.55598	0.777991	+	0.628275i	$0.216239\pi$
$752$	−1.16509e13	−1.32855
$753$	−4.73160e12	−0.536328
$754$	−2.11451e12	−0.238253
$755$	−6.57169e12	−0.736065
$756$	0	0
$757$	1.46852e13	1.62535	0.812676	−	0.582716i	$-0.198010\pi$
$757$	1.46852e13	1.62535	0.812676	+	0.582716i	$0.198010\pi$
$758$	−1.12628e12	−0.123919
$759$	2.39925e12	0.262415
$760$	−1.91959e12	−0.208712
$761$	−7.82013e12	−0.845246	−0.422623	−	0.906306i	$-0.638891\pi$
$761$	−7.82013e12	−0.845246	−0.422623	+	0.906306i	$0.638891\pi$
$762$	−7.87582e11	−0.0846250
$763$	0	0
$764$	1.30400e13	1.38471
$765$	−1.80251e12	−0.190283
$766$	2.86608e12	0.300787
$767$	−1.05115e13	−1.09669
$768$	4.18184e12	0.433752
$769$	−9.67364e12	−0.997519	−0.498760	−	0.866740i	$-0.666211\pi$
$769$	−9.67364e12	−0.997519	−0.498760	+	0.866740i	$0.666211\pi$
$770$	0	0
$771$	3.95379e12	0.402966
$772$	−8.00735e11	−0.0811355
$773$	3.41240e12	0.343758	0.171879	−	0.985118i	$-0.445016\pi$
$773$	3.41240e12	0.343758	0.171879	+	0.985118i	$0.445016\pi$
$774$	1.44960e12	0.145183
$775$	1.71699e12	0.170966
$776$	4.28204e12	0.423909
$777$	0	0
$778$	−1.41632e12	−0.138596
$779$	1.79867e12	0.174998
$780$	−4.28988e12	−0.414972
$781$	−1.83236e13	−1.76231
$782$	7.24082e11	0.0692400
$783$	−9.53129e12	−0.906199
$784$	0	0
$785$	−3.30309e12	−0.310461
$786$	−1.72581e12	−0.161284
$787$	4.15741e12	0.386311	0.193155	−	0.981168i	$-0.438128\pi$
$787$	4.15741e12	0.386311	0.193155	+	0.981168i	$0.438128\pi$
$788$	8.54609e12	0.789586
$789$	1.88315e12	0.172997
$790$	−1.04025e12	−0.0950201
$791$	0	0
$792$	−2.02047e12	−0.182469
$793$	2.06204e12	0.185169
$794$	−4.23385e11	−0.0378045
$795$	4.54555e12	0.403584
$796$	−1.62658e13	−1.43604
$797$	9.55824e12	0.839103	0.419552	−	0.907732i	$-0.362187\pi$
$797$	9.55824e12	0.839103	0.419552	+	0.907732i	$0.362187\pi$
$798$	0	0
$799$	1.44816e13	1.25706
$800$	1.32252e12	0.114155
$801$	6.46360e12	0.554790
$802$	7.63010e11	0.0651247
$803$	9.57146e12	0.812378
$804$	−1.09553e12	−0.0924639
$805$	0	0
$806$	−2.84553e12	−0.237495
$807$	1.52464e13	1.26542
$808$	−2.13237e12	−0.176000
$809$	−1.61537e13	−1.32588	−0.662941	−	0.748672i	$-0.730692\pi$
$809$	−1.61537e13	−1.32588	−0.662941	+	0.748672i	$0.730692\pi$
$810$	2.51509e11	0.0205291
$811$	−7.59785e12	−0.616733	−0.308366	−	0.951268i	$-0.599782\pi$
$811$	−7.59785e12	−0.616733	−0.308366	+	0.951268i	$0.599782\pi$
$812$	0	0
$813$	−1.05843e13	−0.849679
$814$	−1.87317e12	−0.149544
$815$	2.75495e12	0.218728
$816$	−6.49795e12	−0.513063
$817$	2.13455e13	1.67613
$818$	−3.03085e12	−0.236687
$819$	0	0
$820$	−8.20503e11	−0.0633750
$821$	5.50773e12	0.423086	0.211543	−	0.977369i	$-0.432151\pi$
$821$	5.50773e12	0.423086	0.211543	+	0.977369i	$0.432151\pi$
$822$	2.65732e12	0.203011
$823$	−2.31393e13	−1.75813	−0.879064	−	0.476703i	$-0.841832\pi$
$823$	−2.31393e13	−1.75813	−0.879064	+	0.476703i	$0.841832\pi$
$824$	−4.12831e12	−0.311961
$825$	−1.68861e12	−0.126907
$826$	0	0
$827$	7.41789e12	0.551449	0.275725	−	0.961237i	$-0.411082\pi$
$827$	7.41789e12	0.551449	0.275725	+	0.961237i	$0.411082\pi$
$828$	−2.74132e12	−0.202686
$829$	5.62762e11	0.0413837	0.0206919	−	0.999786i	$-0.493413\pi$
$829$	5.62762e11	0.0413837	0.0206919	+	0.999786i	$0.493413\pi$
$830$	−6.03224e11	−0.0441192
$831$	9.90691e12	0.720666
$832$	1.46312e13	1.05858
$833$	0	0
$834$	−2.90764e12	−0.208111
$835$	−6.53860e12	−0.465474
$836$	−1.45691e13	−1.03159
$837$	−1.28264e13	−0.903318
$838$	−1.52495e12	−0.106821
$839$	−4.54982e12	−0.317004	−0.158502	−	0.987359i	$-0.550666\pi$
$839$	−4.54982e12	−0.317004	−0.158502	+	0.987359i	$0.550666\pi$
$840$	0	0
$841$	−3.83851e12	−0.264595
$842$	−7.18826e11	−0.0492855
$843$	−5.86599e12	−0.400053
$844$	−1.57726e13	−1.06995
$845$	−6.03838e12	−0.407441
$846$	2.30764e12	0.154882
$847$	0	0
$848$	−1.71056e13	−1.13595
$849$	−2.33333e12	−0.154131
$850$	−5.09613e11	−0.0334854
$851$	−5.18992e12	−0.339217
$852$	−2.00558e13	−1.30395
$853$	−2.58407e13	−1.67122	−0.835609	−	0.549324i	$-0.814885\pi$
$853$	−2.58407e13	−1.67122	−0.835609	+	0.549324i	$0.814885\pi$
$854$	0	0
$855$	−4.22946e12	−0.270668
$856$	2.81871e12	0.179440
$857$	7.97451e12	0.504999	0.252499	−	0.967597i	$-0.418747\pi$
$857$	7.97451e12	0.504999	0.252499	+	0.967597i	$0.418747\pi$
$858$	2.79849e12	0.176291
$859$	3.92748e12	0.246119	0.123059	−	0.992399i	$-0.460729\pi$
$859$	3.92748e12	0.246119	0.123059	+	0.992399i	$0.460729\pi$
$860$	−9.73719e12	−0.607003
$861$	0	0
$862$	−3.62819e12	−0.223825
$863$	−2.87231e13	−1.76272	−0.881359	−	0.472448i	$-0.843371\pi$
$863$	−2.87231e13	−1.76272	−0.881359	+	0.472448i	$0.843371\pi$
$864$	−9.87957e12	−0.603151
$865$	9.02980e12	0.548410
$866$	−5.16877e12	−0.312289
$867$	−3.56072e12	−0.214019
$868$	0	0
$869$	−1.61227e13	−0.959067
$870$	−9.11010e11	−0.0539122
$871$	−3.23464e12	−0.190434
$872$	−1.16272e13	−0.681006
$873$	9.43469e12	0.549748
$874$	1.69901e12	0.0984905
$875$	0	0
$876$	1.04763e13	0.601090
$877$	2.44180e13	1.39384	0.696918	−	0.717151i	$-0.254554\pi$
$877$	2.44180e13	1.39384	0.696918	+	0.717151i	$0.254554\pi$
$878$	2.28940e12	0.130016
$879$	−8.00613e12	−0.452348
$880$	6.35452e12	0.357199
$881$	3.03025e13	1.69468	0.847339	−	0.531052i	$-0.178203\pi$
$881$	3.03025e13	1.69468	0.847339	+	0.531052i	$0.178203\pi$
$882$	0	0
$883$	2.36415e13	1.30874	0.654368	−	0.756176i	$-0.272935\pi$
$883$	2.36415e13	1.30874	0.654368	+	0.756176i	$0.272935\pi$
$884$	−2.00658e13	−1.10515
$885$	−4.52875e12	−0.248161
$886$	−2.59068e12	−0.141242
$887$	−2.21901e12	−0.120366	−0.0601828	−	0.998187i	$-0.519168\pi$
$887$	−2.21901e12	−0.120366	−0.0601828	+	0.998187i	$0.519168\pi$
$888$	−4.18680e12	−0.225956
$889$	0	0
$890$	1.82742e12	0.0976300
$891$	3.89810e12	0.207207
$892$	1.86604e13	0.986913
$893$	3.39801e13	1.78810
$894$	2.26823e12	0.118760
$895$	−8.65131e12	−0.450690
$896$	0	0
$897$	7.75367e12	0.399890
$898$	7.59829e11	0.0389917
$899$	1.43570e13	0.733067
$900$	1.92936e12	0.0980216
$901$	2.12617e13	1.07482
$902$	5.35253e11	0.0269234
$903$	0	0
$904$	5.79361e12	0.288530
$905$	−1.61269e13	−0.799156
$906$	4.69230e12	0.231371
$907$	1.01297e13	0.497007	0.248504	−	0.968631i	$-0.420061\pi$
$907$	1.01297e13	0.497007	0.248504	+	0.968631i	$0.420061\pi$
$908$	−8.41472e12	−0.410822
$909$	−4.69829e12	−0.228245
$910$	0	0
$911$	3.67990e13	1.77012	0.885062	−	0.465474i	$-0.154116\pi$
$911$	3.67990e13	1.77012	0.885062	+	0.465474i	$0.154116\pi$
$912$	−1.52470e13	−0.729806
$913$	−9.34930e12	−0.445308
$914$	−3.93528e12	−0.186517
$915$	8.88407e11	0.0419003
$916$	3.76679e13	1.76784
$917$	0	0
$918$	3.80696e12	0.176924
$919$	4.04334e13	1.86991	0.934955	−	0.354768i	$-0.115440\pi$
$919$	4.04334e13	1.86991	0.934955	+	0.354768i	$0.115440\pi$
$920$	−1.58270e12	−0.0728372
$921$	3.25412e11	0.0149027
$922$	−2.55137e12	−0.116274
$923$	−5.92163e13	−2.68555
$924$	0	0
$925$	3.65270e12	0.164050
$926$	−4.72962e12	−0.211386
$927$	−9.09598e12	−0.404567
$928$	1.10585e13	0.489474
$929$	2.99476e13	1.31914	0.659571	−	0.751642i	$-0.270738\pi$
$929$	2.99476e13	1.31914	0.659571	+	0.751642i	$0.270738\pi$
$930$	−1.22596e12	−0.0537407
$931$	0	0
$932$	−1.07143e13	−0.465151
$933$	−2.64615e12	−0.114327
$934$	−5.40473e12	−0.232388
$935$	−7.89844e12	−0.337978
$936$	−6.52954e12	−0.278062
$937$	−1.77154e13	−0.750796	−0.375398	−	0.926864i	$-0.622494\pi$
$937$	−1.77154e13	−0.750796	−0.375398	+	0.926864i	$0.622494\pi$
$938$	0	0
$939$	−6.09297e12	−0.255761
$940$	−1.55007e13	−0.647555
$941$	−4.44968e13	−1.85002	−0.925008	−	0.379947i	$-0.875942\pi$
$941$	−4.44968e13	−1.85002	−0.925008	+	0.379947i	$0.875942\pi$
$942$	2.35847e12	0.0975889
$943$	1.48300e12	0.0610717
$944$	1.70424e13	0.698485
$945$	0	0
$946$	6.35204e12	0.257871
$947$	1.35940e13	0.549251	0.274626	−	0.961551i	$-0.411446\pi$
$947$	1.35940e13	0.549251	0.274626	+	0.961551i	$0.411446\pi$
$948$	−1.76469e13	−0.709627
$949$	3.09321e13	1.23797
$950$	−1.19577e12	−0.0476313
$951$	1.64324e13	0.651461
$952$	0	0
$953$	−2.72131e13	−1.06871	−0.534355	−	0.845260i	$-0.679445\pi$
$953$	−2.72131e13	−1.06871	−0.534355	+	0.845260i	$0.679445\pi$
$954$	3.38804e12	0.132428
$955$	1.65880e13	0.645325
$956$	3.74116e13	1.44859
$957$	−1.41196e13	−0.544152
$958$	1.18650e12	0.0455116
$959$	0	0
$960$	6.30369e12	0.239538
$961$	−7.11923e12	−0.269264
$962$	−6.05353e12	−0.227888
$963$	6.21050e12	0.232707
$964$	3.08700e13	1.15130
$965$	−1.01860e12	−0.0378121
$966$	0	0
$967$	4.01406e13	1.47627	0.738133	−	0.674656i	$-0.235708\pi$
$967$	4.01406e13	1.47627	0.738133	+	0.674656i	$0.235708\pi$
$968$	1.90483e12	0.0697297
$969$	1.89515e13	0.690535
$970$	2.66742e12	0.0967427
$971$	−3.63950e13	−1.31388	−0.656939	−	0.753944i	$-0.728149\pi$
$971$	−3.63950e13	−1.31388	−0.656939	+	0.753944i	$0.728149\pi$
$972$	−2.39531e13	−0.860725
$973$	0	0
$974$	−9.80160e12	−0.348965
$975$	−5.45708e12	−0.193392
$976$	−3.34322e12	−0.117935
$977$	−2.79320e13	−0.980790	−0.490395	−	0.871500i	$-0.663147\pi$
$977$	−2.79320e13	−0.980790	−0.490395	+	0.871500i	$0.663147\pi$
$978$	−1.96708e12	−0.0687539
$979$	2.83230e13	0.985409
$980$	0	0
$981$	−2.56184e13	−0.883164
$982$	2.41554e11	0.00828921
$983$	−4.77777e13	−1.63205	−0.816027	−	0.578013i	$-0.803828\pi$
$983$	−4.77777e13	−1.63205	−0.816027	+	0.578013i	$0.803828\pi$
$984$	1.19637e12	0.0406805
$985$	1.08713e13	0.367976
$986$	−4.26123e12	−0.143578
$987$	0	0
$988$	−4.70830e13	−1.57202
$989$	1.75993e13	0.584942
$990$	−1.25861e12	−0.0416422
$991$	−2.06515e13	−0.680174	−0.340087	−	0.940394i	$-0.610457\pi$
$991$	−2.06515e13	−0.680174	−0.340087	+	0.940394i	$0.610457\pi$
$992$	1.48816e13	0.487918
$993$	−1.97755e13	−0.645439
$994$	0	0
$995$	−2.06915e13	−0.669249
$996$	−1.02331e13	−0.329490
$997$	3.80815e13	1.22063	0.610317	−	0.792157i	$-0.291042\pi$
$997$	3.80815e13	1.22063	0.610317	+	0.792157i	$0.291042\pi$
$998$	−2.71703e12	−0.0866977
$999$	−2.72867e13	−0.866774

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.10.a.g.1.4		6
7.6	odd	2		35.10.a.e.1.4	✓	6
21.20	even	2		315.10.a.l.1.3		6
35.13	even	4		175.10.b.g.99.5		12
35.27	even	4		175.10.b.g.99.8		12
35.34	odd	2		175.10.a.g.1.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.10.a.e.1.4	✓	6	7.6	odd	2
175.10.a.g.1.3		6	35.34	odd	2
175.10.b.g.99.5		12	35.13	even	4
175.10.b.g.99.8		12	35.27	even	4
245.10.a.g.1.4		6	1.1	even	1	trivial
315.10.a.l.1.3		6	21.20	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:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	245.a (trivial)

\(f(q)\)	\(=\)	\(q+4.54749 q^{2} +98.1335 q^{3} -491.320 q^{4} -625.000 q^{5} +446.261 q^{6} -4562.59 q^{8} -10052.8 q^{9} -2842.18 q^{10} -44050.6 q^{11} -48215.0 q^{12} -142358. q^{13} -61333.4 q^{15} +230808. q^{16} -286886. q^{17} -45715.1 q^{18} -673158. q^{19} +307075. q^{20} -200320. q^{22} -555018. q^{23} -447743. q^{24} +390625. q^{25} -647373. q^{26} -2.91808e6 q^{27} +3.26629e6 q^{29} -278913. q^{30} +4.39550e6 q^{31} +3.38564e6 q^{32} -4.32284e6 q^{33} -1.30461e6 q^{34} +4.93916e6 q^{36} +9.35091e6 q^{37} -3.06118e6 q^{38} -1.39701e7 q^{39} +2.85162e6 q^{40} -2.67199e6 q^{41} -3.17095e7 q^{43} +2.16430e7 q^{44} +6.28302e6 q^{45} -2.52394e6 q^{46} -5.04786e7 q^{47} +2.26500e7 q^{48} +1.77636e6 q^{50} -2.81531e7 q^{51} +6.99436e7 q^{52} -7.41121e7 q^{53} -1.32699e7 q^{54} +2.75316e7 q^{55} -6.60593e7 q^{57} +1.48534e7 q^{58} +7.38382e7 q^{59} +3.01344e7 q^{60} -1.44849e7 q^{61} +1.99885e7 q^{62} -1.02777e8 q^{64} +8.89740e7 q^{65} -1.96581e7 q^{66} +2.27218e7 q^{67} +1.40953e8 q^{68} -5.44658e7 q^{69} +4.15967e8 q^{71} +4.58669e7 q^{72} -2.17283e8 q^{73} +4.25232e7 q^{74} +3.83334e7 q^{75} +3.30736e8 q^{76} -6.35290e7 q^{78} +3.66004e8 q^{79} -1.44255e8 q^{80} -8.84914e7 q^{81} -1.21509e7 q^{82} +2.12240e8 q^{83} +1.79304e8 q^{85} -1.44199e8 q^{86} +3.20532e8 q^{87} +2.00985e8 q^{88} -6.42964e8 q^{89} +2.85720e7 q^{90} +2.72692e8 q^{92} +4.31345e8 q^{93} -2.29551e8 q^{94} +4.20724e8 q^{95} +3.32245e8 q^{96} -9.38511e8 q^{97} +4.42833e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 15 q^{2} + 124 q^{3} + 3009 q^{4} - 3750 q^{5} - 4888 q^{6} + 22041 q^{8} + 111090 q^{9} - 9375 q^{10} - 47796 q^{11} + 541656 q^{12} - 102168 q^{13} - 77500 q^{15} + 2371065 q^{16} + 38472 q^{17}+ \cdots + 3571968784 q^{99}+O(q^{100}) \) 6 * q + 15 * q^2 + 124 * q^3 + 3009 * q^4 - 3750 * q^5 - 4888 * q^6 + 22041 * q^8 + 111090 * q^9 - 9375 * q^10 - 47796 * q^11 + 541656 * q^12 - 102168 * q^13 - 77500 * q^15 + 2371065 * q^16 + 38472 * q^17 + 1837015 * q^18 - 361056 * q^19 - 1880625 * q^20 + 2068680 * q^22 + 697032 * q^23 - 4828076 * q^24 + 2343750 * q^25 - 10847622 * q^26 - 1653188 * q^27 + 16028184 * q^29 + 3055000 * q^30 - 1362912 * q^31 - 1148823 * q^32 - 14059020 * q^33 + 9216294 * q^34 + 92319641 * q^36 - 3912924 * q^37 - 39877140 * q^38 - 20341868 * q^39 - 13775625 * q^40 - 22452756 * q^41 - 29998992 * q^43 - 94378728 * q^44 - 69431250 * q^45 + 49589520 * q^46 + 121271508 * q^47 + 327116052 * q^48 + 5859375 * q^50 - 281338180 * q^51 + 44528550 * q^52 - 20308596 * q^53 + 290104308 * q^54 + 29872500 * q^55 + 186940744 * q^57 + 256759494 * q^58 - 120280392 * q^59 - 338535000 * q^60 + 87693540 * q^61 + 344802528 * q^62 + 640647105 * q^64 + 63855000 * q^65 + 1393970692 * q^66 + 495050664 * q^67 + 141443706 * q^68 - 1031633640 * q^69 + 253762512 * q^71 + 856452205 * q^72 - 187195308 * q^73 - 418806054 * q^74 + 48437500 * q^75 + 584719476 * q^76 - 1728062324 * q^78 + 831079500 * q^79 - 1481915625 * q^80 + 1869314710 * q^81 - 2286848814 * q^82 + 767650536 * q^83 - 24045000 * q^85 + 566199948 * q^86 - 1303216852 * q^87 + 2952495444 * q^88 - 582579684 * q^89 - 1148134375 * q^90 - 4259382384 * q^92 + 15388800 * q^93 + 1115946660 * q^94 + 225660000 * q^95 - 989345252 * q^96 + 1184506872 * q^97 + 3571968784 * q^99

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