LMFDB - Embedded newform 245.10.a.i.1.3

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:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - x^{8} - 3242 x^{7} - 1690 x^{6} + 3235604 x^{5} + 4945456 x^{4} - 1138644128 x^{3} + \cdots + 183792896000 $ x^9 - x^8 - 3242x^7 - 1690x^6 + 3235604x^5 + 4945456x^4 - 1138644128x^3 - 1388068480x^2 + 115392832000*x + 183792896000
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{7}\cdot 3^{4}\cdot 5^{2}\cdot 7^{3} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-24.3613$ 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)

$f(q)$	$=$	\(q-24.3613 q^{2} +124.658 q^{3} +81.4729 q^{4} -625.000 q^{5} -3036.83 q^{6} +10488.2 q^{8} -4143.41 q^{9} +15225.8 q^{10} -79166.7 q^{11} +10156.2 q^{12} -158587. q^{13} -77911.2 q^{15} -297220. q^{16} -486441. q^{17} +100939. q^{18} +209259. q^{19} -50920.6 q^{20} +1.92860e6 q^{22} -1.31142e6 q^{23} +1.30744e6 q^{24} +390625. q^{25} +3.86338e6 q^{26} -2.97015e6 q^{27} -5.04449e6 q^{29} +1.89802e6 q^{30} +6.50959e6 q^{31} +1.87071e6 q^{32} -9.86875e6 q^{33} +1.18503e7 q^{34} -337576. q^{36} -1.80931e7 q^{37} -5.09783e6 q^{38} -1.97691e7 q^{39} -6.55512e6 q^{40} -3.96418e6 q^{41} +2.68166e7 q^{43} -6.44994e6 q^{44} +2.58963e6 q^{45} +3.19479e7 q^{46} -1.26974e7 q^{47} -3.70509e7 q^{48} -9.51613e6 q^{50} -6.06387e7 q^{51} -1.29205e7 q^{52} +1.02048e8 q^{53} +7.23567e7 q^{54} +4.94792e7 q^{55} +2.60858e7 q^{57} +1.22890e8 q^{58} -8.22604e7 q^{59} -6.34765e6 q^{60} -2.00447e8 q^{61} -1.58582e8 q^{62} +1.06604e8 q^{64} +9.91166e7 q^{65} +2.40416e8 q^{66} +1.30451e8 q^{67} -3.96318e7 q^{68} -1.63479e8 q^{69} -1.63519e8 q^{71} -4.34569e7 q^{72} +4.12000e8 q^{73} +4.40772e8 q^{74} +4.86945e7 q^{75} +1.70490e7 q^{76} +4.81600e8 q^{78} -1.90331e8 q^{79} +1.85763e8 q^{80} -2.88698e8 q^{81} +9.65725e7 q^{82} -4.76606e8 q^{83} +3.04026e8 q^{85} -6.53288e8 q^{86} -6.28835e8 q^{87} -8.30316e8 q^{88} -6.55910e8 q^{89} -6.30868e7 q^{90} -1.06845e8 q^{92} +8.11472e8 q^{93} +3.09325e8 q^{94} -1.30787e8 q^{95} +2.33199e8 q^{96} -1.18467e9 q^{97} +3.28020e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + q^{2} + 268 q^{3} + 1877 q^{4} - 5625 q^{5} + 7624 q^{6} + 13773 q^{8} + 17015 q^{9} - 625 q^{10} - 69434 q^{11} + 64966 q^{12} + 153108 q^{13} - 167500 q^{15} + 496777 q^{16} - 380338 q^{17} + 1151915 q^{18}+ \cdots - 2283620136 q^{99}+O(q^{100}) $ 9 * q + q^2 + 268 * q^3 + 1877 * q^4 - 5625 * q^5 + 7624 * q^6 + 13773 * q^8 + 17015 * q^9 - 625 * q^10 - 69434 * q^11 + 64966 * q^12 + 153108 * q^13 - 167500 * q^15 + 496777 * q^16 - 380338 * q^17 + 1151915 * q^18 + 1123026 * q^19 - 1173125 * q^20 - 2442882 * q^22 - 1413844 * q^23 + 2929050 * q^24 + 3515625 * q^25 - 1328856 * q^26 + 3396094 * q^27 - 4065424 * q^29 - 4765000 * q^30 + 10302576 * q^31 + 9549257 * q^32 - 4263462 * q^33 + 22417266 * q^34 - 48189067 * q^36 - 7627054 * q^37 + 49081118 * q^38 + 45214262 * q^39 - 8608125 * q^40 + 25366416 * q^41 - 14266432 * q^43 - 38019508 * q^44 - 10634375 * q^45 + 114958668 * q^46 - 117568854 * q^47 + 28333158 * q^48 + 390625 * q^50 - 79080682 * q^51 + 152491446 * q^52 - 83561830 * q^53 + 58066342 * q^54 + 43396250 * q^55 + 193586512 * q^57 - 115563884 * q^58 + 204491434 * q^59 - 40603750 * q^60 + 46790550 * q^61 + 241308368 * q^62 + 423301633 * q^64 - 95692500 * q^65 + 164532334 * q^66 + 109844000 * q^67 + 275411544 * q^68 + 193803448 * q^69 - 61313132 * q^71 - 10635039 * q^72 + 138674496 * q^73 + 93214602 * q^74 + 104687500 * q^75 - 758320338 * q^76 + 1759315878 * q^78 + 697968218 * q^79 - 310485625 * q^80 - 114074299 * q^81 + 1406591088 * q^82 - 1322818198 * q^83 + 237711250 * q^85 + 408387840 * q^86 + 450465942 * q^87 + 718451872 * q^88 + 136822392 * q^89 - 719946875 * q^90 - 283388084 * q^92 + 1717412492 * q^93 - 242355222 * q^94 - 701891250 * q^95 + 3205386294 * q^96 - 1926148290 * q^97 - 2283620136 * 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 $

$2$	−24.3613	−1.07663	−0.538314	−	0.842745i	$-0.680938\pi$
$2$	−24.3613	−1.07663	−0.538314	+	0.842745i	$0.680938\pi$
$3$	124.658	0.888534	0.444267	−	0.895894i	$-0.353464\pi$
$3$	124.658	0.888534	0.444267	+	0.895894i	$0.353464\pi$
$4$	81.4729	0.159127
$5$	−625.000	−0.447214
$5$	−625.000	−0.447214
$6$	−3036.83	−0.956620
$7$	0	0
$7$	0	0
$8$	10488.2	0.905307
$9$	−4143.41	−0.210507
$10$	15225.8	0.481482
$11$	−79166.7	−1.63033	−0.815165	−	0.579229i	$-0.803354\pi$
$11$	−79166.7	−1.63033	−0.815165	+	0.579229i	$0.803354\pi$
$12$	10156.2	0.141390
$13$	−158587.	−1.54000	−0.770001	−	0.638042i	$-0.779745\pi$
$13$	−158587.	−1.54000	−0.770001	+	0.638042i	$0.779745\pi$
$14$	0	0
$15$	−77911.2	−0.397365
$16$	−297220.	−1.13381
$17$	−486441.	−1.41257	−0.706285	−	0.707927i	$-0.749630\pi$
$17$	−486441.	−1.41257	−0.706285	+	0.707927i	$0.749630\pi$
$18$	100939.	0.226638
$19$	209259.	0.368378	0.184189	−	0.982891i	$-0.441034\pi$
$19$	209259.	0.368378	0.184189	+	0.982891i	$0.441034\pi$
$20$	−50920.6	−0.0711636
$21$	0	0
$22$	1.92860e6	1.75526
$23$	−1.31142e6	−0.977163	−0.488582	−	0.872518i	$-0.662486\pi$
$23$	−1.31142e6	−0.977163	−0.488582	+	0.872518i	$0.662486\pi$
$24$	1.30744e6	0.804396
$25$	390625.	0.200000
$26$	3.86338e6	1.65801
$27$	−2.97015e6	−1.07558
$28$	0	0
$29$	−5.04449e6	−1.32442	−0.662211	−	0.749318i	$-0.730382\pi$
$29$	−5.04449e6	−1.32442	−0.662211	+	0.749318i	$0.730382\pi$
$30$	1.89802e6	0.427814
$31$	6.50959e6	1.26598	0.632989	−	0.774161i	$-0.281828\pi$
$31$	6.50959e6	1.26598	0.632989	+	0.774161i	$0.281828\pi$
$32$	1.87071e6	0.315379
$33$	−9.86875e6	−1.44860
$34$	1.18503e7	1.52081
$35$	0	0
$36$	−337576.	−0.0334973
$37$	−1.80931e7	−1.58710	−0.793552	−	0.608502i	$-0.791771\pi$
$37$	−1.80931e7	−1.58710	−0.793552	+	0.608502i	$0.791771\pi$
$38$	−5.09783e6	−0.396606
$39$	−1.97691e7	−1.36834
$40$	−6.55512e6	−0.404866
$41$	−3.96418e6	−0.219092	−0.109546	−	0.993982i	$-0.534940\pi$
$41$	−3.96418e6	−0.219092	−0.109546	+	0.993982i	$0.534940\pi$
$42$	0	0
$43$	2.68166e7	1.19618	0.598090	−	0.801429i	$-0.295927\pi$
$43$	2.68166e7	1.19618	0.598090	+	0.801429i	$0.295927\pi$
$44$	−6.44994e6	−0.259429
$45$	2.58963e6	0.0941417
$46$	3.19479e7	1.05204
$47$	−1.26974e7	−0.379555	−0.189777	−	0.981827i	$-0.560777\pi$
$47$	−1.26974e7	−0.379555	−0.189777	+	0.981827i	$0.560777\pi$
$48$	−3.70509e7	−1.00742
$49$	0	0
$50$	−9.51613e6	−0.215325
$51$	−6.06387e7	−1.25512
$52$	−1.29205e7	−0.245056
$53$	1.02048e8	1.77649	0.888246	−	0.459368i	$-0.151924\pi$
$53$	1.02048e8	1.77649	0.888246	+	0.459368i	$0.151924\pi$
$54$	7.23567e7	1.15800
$55$	4.94792e7	0.729106
$56$	0	0
$57$	2.60858e7	0.327317
$58$	1.22890e8	1.42591
$59$	−8.22604e7	−0.883806	−0.441903	−	0.897063i	$-0.645696\pi$
$59$	−8.22604e7	−0.883806	−0.441903	+	0.897063i	$0.645696\pi$
$60$	−6.34765e6	−0.0632313
$61$	−2.00447e8	−1.85359	−0.926797	−	0.375563i	$-0.877449\pi$
$61$	−2.00447e8	−1.85359	−0.926797	+	0.375563i	$0.877449\pi$
$62$	−1.58582e8	−1.36299
$63$	0	0
$64$	1.06604e8	0.794260
$65$	9.91166e7	0.688710
$66$	2.40416e8	1.55961
$67$	1.30451e8	0.790881	0.395440	−	0.918492i	$-0.370592\pi$
$67$	1.30451e8	0.790881	0.395440	+	0.918492i	$0.370592\pi$
$68$	−3.96318e7	−0.224778
$69$	−1.63479e8	−0.868243
$70$	0	0
$71$	−1.63519e8	−0.763671	−0.381835	−	0.924230i	$-0.624708\pi$
$71$	−1.63519e8	−0.763671	−0.381835	+	0.924230i	$0.624708\pi$
$72$	−4.34569e7	−0.190574
$73$	4.12000e8	1.69803	0.849014	−	0.528371i	$-0.177197\pi$
$73$	4.12000e8	1.69803	0.849014	+	0.528371i	$0.177197\pi$
$74$	4.40772e8	1.70872
$75$	4.86945e7	0.177707
$76$	1.70490e7	0.0586188
$77$	0	0
$78$	4.81600e8	1.47320
$79$	−1.90331e8	−0.549779	−0.274889	−	0.961476i	$-0.588641\pi$
$79$	−1.90331e8	−0.549779	−0.274889	+	0.961476i	$0.588641\pi$
$80$	1.85763e8	0.507053
$81$	−2.88698e8	−0.745180
$82$	9.65725e7	0.235880
$83$	−4.76606e8	−1.10232	−0.551161	−	0.834399i	$-0.685815\pi$
$83$	−4.76606e8	−1.10232	−0.551161	+	0.834399i	$0.685815\pi$
$84$	0	0
$85$	3.04026e8	0.631721
$86$	−6.53288e8	−1.28784
$87$	−6.28835e8	−1.17679
$88$	−8.30316e8	−1.47595
$89$	−6.55910e8	−1.10813	−0.554063	−	0.832475i	$-0.686923\pi$
$89$	−6.55910e8	−1.10813	−0.554063	+	0.832475i	$0.686923\pi$
$90$	−6.30868e7	−0.101356
$91$	0	0
$92$	−1.06845e8	−0.155493
$93$	8.11472e8	1.12486
$94$	3.09325e8	0.408639
$95$	−1.30787e8	−0.164744
$96$	2.33199e8	0.280225
$97$	−1.18467e9	−1.35871	−0.679354	−	0.733811i	$-0.737740\pi$
$97$	−1.18467e9	−1.35871	−0.679354	+	0.733811i	$0.737740\pi$
$98$	0	0
$99$	3.28020e8	0.343196
$100$	3.18253e7	0.0318253
$101$	5.36258e8	0.512776	0.256388	−	0.966574i	$-0.417468\pi$
$101$	5.36258e8	0.512776	0.256388	+	0.966574i	$0.417468\pi$
$102$	1.47724e9	1.35129
$103$	−7.35607e8	−0.643989	−0.321994	−	0.946742i	$-0.604353\pi$
$103$	−7.35607e8	−0.643989	−0.321994	+	0.946742i	$0.604353\pi$
$104$	−1.66329e9	−1.39418
$105$	0	0
$106$	−2.48602e9	−1.91262
$107$	−1.09116e9	−0.804752	−0.402376	−	0.915475i	$-0.631815\pi$
$107$	−1.09116e9	−0.804752	−0.402376	+	0.915475i	$0.631815\pi$
$108$	−2.41987e8	−0.171153
$109$	−1.16974e9	−0.793727	−0.396864	−	0.917878i	$-0.629901\pi$
$109$	−1.16974e9	−0.793727	−0.396864	+	0.917878i	$0.629901\pi$
$110$	−1.20538e9	−0.784975
$111$	−2.25545e9	−1.41020
$112$	0	0
$113$	1.06978e9	0.617224	0.308612	−	0.951188i	$-0.400136\pi$
$113$	1.06978e9	0.617224	0.308612	+	0.951188i	$0.400136\pi$
$114$	−6.35485e8	−0.352398
$115$	8.19639e8	0.437001
$116$	−4.10989e8	−0.210751
$117$	6.57090e8	0.324182
$118$	2.00397e9	0.951530
$119$	0	0
$120$	−8.17148e8	−0.359737
$121$	3.90942e9	1.65797
$122$	4.88314e9	1.99563
$123$	−4.94166e8	−0.194670
$124$	5.30355e8	0.201451
$125$	−2.44141e8	−0.0894427
$126$	0	0
$127$	−4.45222e8	−0.151866	−0.0759329	−	0.997113i	$-0.524193\pi$
$127$	−4.45222e8	−0.151866	−0.0759329	+	0.997113i	$0.524193\pi$
$128$	−3.55481e9	−1.17050
$129$	3.34291e9	1.06285
$130$	−2.41461e9	−0.741484
$131$	2.45838e9	0.729338	0.364669	−	0.931137i	$-0.381182\pi$
$131$	2.45838e9	0.729338	0.364669	+	0.931137i	$0.381182\pi$
$132$	−8.04036e8	−0.230512
$133$	0	0
$134$	−3.17796e9	−0.851484
$135$	1.85634e9	0.481013
$136$	−5.10189e9	−1.27881
$137$	−8.20147e8	−0.198907	−0.0994533	−	0.995042i	$-0.531709\pi$
$137$	−8.20147e8	−0.198907	−0.0994533	+	0.995042i	$0.531709\pi$
$138$	3.98256e9	0.934774
$139$	−8.94291e8	−0.203195	−0.101597	−	0.994826i	$-0.532395\pi$
$139$	−8.94291e8	−0.203195	−0.101597	+	0.994826i	$0.532395\pi$
$140$	0	0
$141$	−1.58283e9	−0.337248
$142$	3.98354e9	0.822189
$143$	1.25548e10	2.51071
$144$	1.23151e9	0.238674
$145$	3.15281e9	0.592299
$146$	−1.00369e10	−1.82814
$147$	0	0
$148$	−1.47410e9	−0.252551
$149$	5.85451e9	0.973089	0.486544	−	0.873656i	$-0.338257\pi$
$149$	5.85451e9	0.973089	0.486544	+	0.873656i	$0.338257\pi$
$150$	−1.18626e9	−0.191324
$151$	−4.53652e9	−0.710112	−0.355056	−	0.934845i	$-0.615538\pi$
$151$	−4.53652e9	−0.710112	−0.355056	+	0.934845i	$0.615538\pi$
$152$	2.19475e9	0.333495
$153$	2.01553e9	0.297356
$154$	0	0
$155$	−4.06849e9	−0.566162
$156$	−1.61064e9	−0.217740
$157$	−7.00744e9	−0.920472	−0.460236	−	0.887797i	$-0.652235\pi$
$157$	−7.00744e9	−0.920472	−0.460236	+	0.887797i	$0.652235\pi$
$158$	4.63672e9	0.591907
$159$	1.27211e10	1.57847
$160$	−1.16920e9	−0.141042
$161$	0	0
$162$	7.03305e9	0.802281
$163$	8.57679e8	0.0951657	0.0475828	−	0.998867i	$-0.484848\pi$
$163$	8.57679e8	0.0951657	0.0475828	+	0.998867i	$0.484848\pi$
$164$	−3.22973e8	−0.0348633
$165$	6.16797e9	0.647835
$166$	1.16107e10	1.18679
$167$	1.13646e10	1.13065	0.565326	−	0.824867i	$-0.308750\pi$
$167$	1.13646e10	1.13065	0.565326	+	0.824867i	$0.308750\pi$
$168$	0	0
$169$	1.45452e10	1.37161
$170$	−7.40646e9	−0.680128
$171$	−8.67048e8	−0.0775462
$172$	2.18483e9	0.190344
$173$	−4.64952e9	−0.394640	−0.197320	−	0.980339i	$-0.563224\pi$
$173$	−4.64952e9	−0.394640	−0.197320	+	0.980339i	$0.563224\pi$
$174$	1.53192e10	1.26697
$175$	0	0
$176$	2.35299e10	1.84848
$177$	−1.02544e10	−0.785292
$178$	1.59788e10	1.19304
$179$	3.07079e9	0.223569	0.111784	−	0.993732i	$-0.464343\pi$
$179$	3.07079e9	0.223569	0.111784	+	0.993732i	$0.464343\pi$
$180$	2.10985e8	0.0149805
$181$	−4.51450e9	−0.312648	−0.156324	−	0.987706i	$-0.549964\pi$
$181$	−4.51450e9	−0.312648	−0.156324	+	0.987706i	$0.549964\pi$
$182$	0	0
$183$	−2.49873e10	−1.64698
$184$	−1.37545e10	−0.884633
$185$	1.13082e10	0.709775
$186$	−1.97685e10	−1.21106
$187$	3.85099e10	2.30296
$188$	−1.03449e9	−0.0603973
$189$	0	0
$190$	3.18614e9	0.177368
$191$	8.68597e8	0.0472246	0.0236123	−	0.999721i	$-0.492483\pi$
$191$	8.68597e8	0.0472246	0.0236123	+	0.999721i	$0.492483\pi$
$192$	1.32890e10	0.705727
$193$	3.04967e9	0.158214	0.0791070	−	0.996866i	$-0.474793\pi$
$193$	3.04967e9	0.158214	0.0791070	+	0.996866i	$0.474793\pi$
$194$	2.88602e10	1.46282
$195$	1.23557e10	0.611942
$196$	0	0
$197$	5.98881e9	0.283297	0.141649	−	0.989917i	$-0.454760\pi$
$197$	5.98881e9	0.283297	0.141649	+	0.989917i	$0.454760\pi$
$198$	−7.99100e9	−0.369494
$199$	7.93408e9	0.358639	0.179320	−	0.983791i	$-0.442610\pi$
$199$	7.93408e9	0.358639	0.179320	+	0.983791i	$0.442610\pi$
$200$	4.09695e9	0.181061
$201$	1.62618e10	0.702724
$202$	−1.30639e10	−0.552068
$203$	0	0
$204$	−4.94041e9	−0.199723
$205$	2.47761e9	0.0979808
$206$	1.79203e10	0.693336
$207$	5.43376e9	0.205700
$208$	4.71352e10	1.74606
$209$	−1.65664e10	−0.600578
$210$	0	0
$211$	−3.81245e9	−0.132414	−0.0662068	−	0.997806i	$-0.521090\pi$
$211$	−3.81245e9	−0.132414	−0.0662068	+	0.997806i	$0.521090\pi$
$212$	8.31415e9	0.282687
$213$	−2.03839e10	−0.678547
$214$	2.65821e10	0.866418
$215$	−1.67604e10	−0.534948
$216$	−3.11515e10	−0.973728
$217$	0	0
$218$	2.84965e10	0.854549
$219$	5.13591e10	1.50876
$220$	4.03121e9	0.116020
$221$	7.71431e10	2.17536
$222$	5.49457e10	1.51826
$223$	5.45190e10	1.47631	0.738153	−	0.674634i	$-0.235698\pi$
$223$	5.45190e10	1.47631	0.738153	+	0.674634i	$0.235698\pi$
$224$	0	0
$225$	−1.61852e9	−0.0421014
$226$	−2.60613e10	−0.664520
$227$	−2.21379e10	−0.553375	−0.276687	−	0.960960i	$-0.589237\pi$
$227$	−2.21379e10	−0.553375	−0.276687	+	0.960960i	$0.589237\pi$
$228$	2.12529e9	0.0520848
$229$	3.40542e10	0.818298	0.409149	−	0.912468i	$-0.365826\pi$
$229$	3.40542e10	0.818298	0.409149	+	0.912468i	$0.365826\pi$
$230$	−1.99675e10	−0.470487
$231$	0	0
$232$	−5.29076e10	−1.19901
$233$	−1.02878e10	−0.228677	−0.114338	−	0.993442i	$-0.536475\pi$
$233$	−1.02878e10	−0.228677	−0.114338	+	0.993442i	$0.536475\pi$
$234$	−1.60076e10	−0.349023
$235$	7.93588e9	0.169742
$236$	−6.70199e9	−0.140637
$237$	−2.37263e10	−0.488497
$238$	0	0
$239$	−5.67300e10	−1.12466	−0.562331	−	0.826912i	$-0.690095\pi$
$239$	−5.67300e10	−1.12466	−0.562331	+	0.826912i	$0.690095\pi$
$240$	2.31568e10	0.450534
$241$	1.03319e11	1.97289	0.986445	−	0.164091i	$-0.0524692\pi$
$241$	1.03319e11	1.97289	0.986445	+	0.164091i	$0.0524692\pi$
$242$	−9.52385e10	−1.78502
$243$	2.24730e10	0.413459
$244$	−1.63310e10	−0.294956
$245$	0	0
$246$	1.20385e10	0.209587
$247$	−3.31857e10	−0.567303
$248$	6.82739e10	1.14610
$249$	−5.94127e10	−0.979450
$250$	5.94758e9	0.0962965
$251$	5.15148e10	0.819219	0.409610	−	0.912261i	$-0.365665\pi$
$251$	5.15148e10	0.819219	0.409610	+	0.912261i	$0.365665\pi$
$252$	0	0
$253$	1.03821e11	1.59310
$254$	1.08462e10	0.163503
$255$	3.78992e10	0.561305
$256$	3.20187e10	0.465933
$257$	−1.68591e10	−0.241065	−0.120533	−	0.992709i	$-0.538460\pi$
$257$	−1.68591e10	−0.241065	−0.120533	+	0.992709i	$0.538460\pi$
$258$	−8.14375e10	−1.14429
$259$	0	0
$260$	8.07532e9	0.109592
$261$	2.09014e10	0.278800
$262$	−5.98894e10	−0.785225
$263$	−1.37831e11	−1.77643	−0.888213	−	0.459432i	$-0.848053\pi$
$263$	−1.37831e11	−1.77643	−0.888213	+	0.459432i	$0.848053\pi$
$264$	−1.03505e11	−1.31143
$265$	−6.37800e10	−0.794471
$266$	0	0
$267$	−8.17643e10	−0.984607
$268$	1.06282e10	0.125850
$269$	6.99545e10	0.814573	0.407287	−	0.913300i	$-0.366475\pi$
$269$	6.99545e10	0.814573	0.407287	+	0.913300i	$0.366475\pi$
$270$	−4.52229e10	−0.517871
$271$	−1.53385e11	−1.72752	−0.863758	−	0.503907i	$-0.831895\pi$
$271$	−1.53385e11	−1.72752	−0.863758	+	0.503907i	$0.831895\pi$
$272$	1.44580e11	1.60158
$273$	0	0
$274$	1.99798e10	0.214148
$275$	−3.09245e10	−0.326066
$276$	−1.33191e10	−0.138161
$277$	1.64129e11	1.67505	0.837523	−	0.546402i	$-0.184003\pi$
$277$	1.64129e11	1.67505	0.837523	+	0.546402i	$0.184003\pi$
$278$	2.17861e10	0.218765
$279$	−2.69719e10	−0.266497
$280$	0	0
$281$	−8.61945e10	−0.824710	−0.412355	−	0.911023i	$-0.635294\pi$
$281$	−8.61945e10	−0.824710	−0.412355	+	0.911023i	$0.635294\pi$
$282$	3.85598e10	0.363090
$283$	−2.45226e10	−0.227263	−0.113631	−	0.993523i	$-0.536248\pi$
$283$	−2.45226e10	−0.227263	−0.113631	+	0.993523i	$0.536248\pi$
$284$	−1.33224e10	−0.121520
$285$	−1.63036e10	−0.146380
$286$	−3.05851e11	−2.70310
$287$	0	0
$288$	−7.75114e9	−0.0663895
$289$	1.18037e11	0.995356
$290$	−7.68064e10	−0.637686
$291$	−1.47679e11	−1.20726
$292$	3.35669e10	0.270202
$293$	−1.77933e11	−1.41043	−0.705216	−	0.708993i	$-0.749150\pi$
$293$	−1.77933e11	−1.41043	−0.705216	+	0.708993i	$0.749150\pi$
$294$	0	0
$295$	5.14128e10	0.395250
$296$	−1.89764e11	−1.43682
$297$	2.35137e11	1.75354
$298$	−1.42624e11	−1.04765
$299$	2.07974e11	1.50483
$300$	3.96728e9	0.0282779
$301$	0	0
$302$	1.10516e11	0.764526
$303$	6.68487e10	0.455619
$304$	−6.21961e10	−0.417669
$305$	1.25279e11	0.828952
$306$	−4.91008e10	−0.320142
$307$	1.29389e11	0.831331	0.415665	−	0.909518i	$-0.363549\pi$
$307$	1.29389e11	0.831331	0.415665	+	0.909518i	$0.363549\pi$
$308$	0	0
$309$	−9.16992e10	−0.572206
$310$	9.91138e10	0.609546
$311$	5.63041e10	0.341286	0.170643	−	0.985333i	$-0.445416\pi$
$311$	5.63041e10	0.341286	0.170643	+	0.985333i	$0.445416\pi$
$312$	−2.07342e11	−1.23877
$313$	−1.95176e11	−1.14942	−0.574709	−	0.818358i	$-0.694885\pi$
$313$	−1.95176e11	−1.14942	−0.574709	+	0.818358i	$0.694885\pi$
$314$	1.70710e11	0.991006
$315$	0	0
$316$	−1.55068e10	−0.0874845
$317$	−2.93551e10	−0.163274	−0.0816369	−	0.996662i	$-0.526015\pi$
$317$	−2.93551e10	−0.163274	−0.0816369	+	0.996662i	$0.526015\pi$
$318$	−3.09902e11	−1.69943
$319$	3.99355e11	2.15924
$320$	−6.66274e10	−0.355204
$321$	−1.36022e11	−0.715049
$322$	0	0
$323$	−1.01792e11	−0.520360
$324$	−2.35210e10	−0.118578
$325$	−6.19479e10	−0.308001
$326$	−2.08942e10	−0.102458
$327$	−1.45818e11	−0.705254
$328$	−4.15771e10	−0.198345
$329$	0	0
$330$	−1.50260e11	−0.697477
$331$	−8.93928e10	−0.409333	−0.204666	−	0.978832i	$-0.565611\pi$
$331$	−8.93928e10	−0.409333	−0.204666	+	0.978832i	$0.565611\pi$
$332$	−3.88305e10	−0.175409
$333$	7.49672e10	0.334097
$334$	−2.76856e11	−1.21729
$335$	−8.15319e10	−0.353693
$336$	0	0
$337$	4.98453e10	0.210518	0.105259	−	0.994445i	$-0.466433\pi$
$337$	4.98453e10	0.210518	0.105259	+	0.994445i	$0.466433\pi$
$338$	−3.54341e11	−1.47671
$339$	1.33357e11	0.548424
$340$	2.47699e10	0.100524
$341$	−5.15343e11	−2.06396
$342$	2.11224e10	0.0834884
$343$	0	0
$344$	2.81258e11	1.08291
$345$	1.02174e11	0.388290
$346$	1.13268e11	0.424880
$347$	3.68855e11	1.36576	0.682878	−	0.730532i	$-0.260728\pi$
$347$	3.68855e11	1.36576	0.682878	+	0.730532i	$0.260728\pi$
$348$	−5.12330e10	−0.187259
$349$	4.87434e11	1.75874	0.879369	−	0.476141i	$-0.157965\pi$
$349$	4.87434e11	1.75874	0.879369	+	0.476141i	$0.157965\pi$
$350$	0	0
$351$	4.71026e11	1.65639
$352$	−1.48098e11	−0.514171
$353$	−1.93933e11	−0.664760	−0.332380	−	0.943146i	$-0.607852\pi$
$353$	−1.93933e11	−0.664760	−0.332380	+	0.943146i	$0.607852\pi$
$354$	2.49811e11	0.845466
$355$	1.02199e11	0.341524
$356$	−5.34389e10	−0.176332
$357$	0	0
$358$	−7.48084e10	−0.240701
$359$	4.93636e11	1.56849	0.784246	−	0.620450i	$-0.213050\pi$
$359$	4.93636e11	1.56849	0.784246	+	0.620450i	$0.213050\pi$
$360$	2.71606e10	0.0852271
$361$	−2.78898e11	−0.864298
$362$	1.09979e11	0.336606
$363$	4.87340e11	1.47317
$364$	0	0
$365$	−2.57500e11	−0.759381
$366$	6.08722e11	1.77319
$367$	−6.61094e11	−1.90224	−0.951122	−	0.308816i	$-0.900067\pi$
$367$	−6.61094e11	−1.90224	−0.951122	+	0.308816i	$0.900067\pi$
$368$	3.89781e11	1.10791
$369$	1.64252e10	0.0461204
$370$	−2.75482e11	−0.764163
$371$	0	0
$372$	6.61129e10	0.178996
$373$	−4.84240e11	−1.29530	−0.647651	−	0.761937i	$-0.724248\pi$
$373$	−4.84240e11	−1.29530	−0.647651	+	0.761937i	$0.724248\pi$
$374$	−9.38152e11	−2.47943
$375$	−3.04341e10	−0.0794729
$376$	−1.33173e11	−0.343614
$377$	7.99988e11	2.03961
$378$	0	0
$379$	−4.77257e11	−1.18816	−0.594081	−	0.804405i	$-0.702484\pi$
$379$	−4.77257e11	−1.18816	−0.594081	+	0.804405i	$0.702484\pi$
$380$	−1.06556e10	−0.0262151
$381$	−5.55005e10	−0.134938
$382$	−2.11601e10	−0.0508433
$383$	1.14195e11	0.271177	0.135588	−	0.990765i	$-0.456708\pi$
$383$	1.14195e11	0.271177	0.135588	+	0.990765i	$0.456708\pi$
$384$	−4.43135e11	−1.04003
$385$	0	0
$386$	−7.42939e10	−0.170338
$387$	−1.11112e11	−0.251804
$388$	−9.65189e10	−0.216207
$389$	−3.00810e11	−0.666069	−0.333035	−	0.942915i	$-0.608073\pi$
$389$	−3.00810e11	−0.666069	−0.333035	+	0.942915i	$0.608073\pi$
$390$	−3.01000e11	−0.658834
$391$	6.37930e11	1.38031
$392$	0	0
$393$	3.06457e11	0.648041
$394$	−1.45895e11	−0.305006
$395$	1.18957e11	0.245869
$396$	2.67248e10	0.0546117
$397$	3.29112e10	0.0664946	0.0332473	−	0.999447i	$-0.489415\pi$
$397$	3.29112e10	0.0664946	0.0332473	+	0.999447i	$0.489415\pi$
$398$	−1.93285e11	−0.386121
$399$	0	0
$400$	−1.16102e11	−0.226761
$401$	−6.83225e11	−1.31951	−0.659757	−	0.751479i	$-0.729341\pi$
$401$	−6.83225e11	−1.31951	−0.659757	+	0.751479i	$0.729341\pi$
$402$	−3.96157e11	−0.756572
$403$	−1.03233e12	−1.94961
$404$	4.36905e10	0.0815963
$405$	1.80436e11	0.333254
$406$	0	0
$407$	1.43237e12	2.58750
$408$	−6.35991e11	−1.13627
$409$	2.63701e11	0.465969	0.232985	−	0.972480i	$-0.425151\pi$
$409$	2.63701e11	0.465969	0.232985	+	0.972480i	$0.425151\pi$
$410$	−6.03578e10	−0.105489
$411$	−1.02238e11	−0.176735
$412$	−5.99320e10	−0.102476
$413$	0	0
$414$	−1.32374e11	−0.221462
$415$	2.97879e11	0.492973
$416$	−2.96670e11	−0.485684
$417$	−1.11480e11	−0.180545
$418$	4.03578e11	0.646599
$419$	2.26328e11	0.358737	0.179368	−	0.983782i	$-0.442595\pi$
$419$	2.26328e11	0.358737	0.179368	+	0.983782i	$0.442595\pi$
$420$	0	0
$421$	1.57840e11	0.244877	0.122439	−	0.992476i	$-0.460929\pi$
$421$	1.57840e11	0.244877	0.122439	+	0.992476i	$0.460929\pi$
$422$	9.28762e10	0.142560
$423$	5.26106e10	0.0798990
$424$	1.07030e12	1.60827
$425$	−1.90016e11	−0.282514
$426$	4.96579e11	0.730543
$427$	0	0
$428$	−8.89000e10	−0.128057
$429$	1.56505e12	2.23085
$430$	4.08305e11	0.575939
$431$	−3.53941e11	−0.494064	−0.247032	−	0.969007i	$-0.579455\pi$
$431$	−3.53941e11	−0.494064	−0.247032	+	0.969007i	$0.579455\pi$
$432$	8.82789e11	1.21949
$433$	1.22396e12	1.67329	0.836646	−	0.547743i	$-0.184513\pi$
$433$	1.22396e12	1.67329	0.836646	+	0.547743i	$0.184513\pi$
$434$	0	0
$435$	3.93022e11	0.526278
$436$	−9.53024e10	−0.126303
$437$	−2.74427e11	−0.359966
$438$	−1.25117e12	−1.62437
$439$	−4.33788e11	−0.557426	−0.278713	−	0.960374i	$-0.589908\pi$
$439$	−4.33788e11	−0.557426	−0.278713	+	0.960374i	$0.589908\pi$
$440$	5.18948e11	0.660065
$441$	0	0
$442$	−1.87931e12	−2.34206
$443$	−7.04265e11	−0.868799	−0.434399	−	0.900720i	$-0.643039\pi$
$443$	−7.04265e11	−0.868799	−0.434399	+	0.900720i	$0.643039\pi$
$444$	−1.83758e11	−0.224400
$445$	4.09944e11	0.495569
$446$	−1.32815e12	−1.58943
$447$	7.29811e11	0.864623
$448$	0	0
$449$	−1.18089e12	−1.37120	−0.685600	−	0.727978i	$-0.740460\pi$
$449$	−1.18089e12	−1.37120	−0.685600	+	0.727978i	$0.740460\pi$
$450$	3.94293e10	0.0453276
$451$	3.13831e11	0.357192
$452$	8.71583e10	0.0982168
$453$	−5.65513e11	−0.630958
$454$	5.39307e11	0.595778
$455$	0	0
$456$	2.73593e11	0.296322
$457$	3.84366e11	0.412213	0.206107	−	0.978530i	$-0.433921\pi$
$457$	3.84366e11	0.412213	0.206107	+	0.978530i	$0.433921\pi$
$458$	−8.29605e11	−0.881002
$459$	1.44480e12	1.51933
$460$	6.67783e10	0.0695385
$461$	−1.52014e12	−1.56758	−0.783789	−	0.621027i	$-0.786716\pi$
$461$	−1.52014e12	−1.56758	−0.783789	+	0.621027i	$0.786716\pi$
$462$	0	0
$463$	−2.20397e11	−0.222891	−0.111445	−	0.993771i	$-0.535548\pi$
$463$	−2.20397e11	−0.222891	−0.111445	+	0.993771i	$0.535548\pi$
$464$	1.49932e12	1.50164
$465$	−5.07170e11	−0.503055
$466$	2.50625e11	0.246200
$467$	−5.89397e11	−0.573432	−0.286716	−	0.958016i	$-0.592564\pi$
$467$	−5.89397e11	−0.573432	−0.286716	+	0.958016i	$0.592564\pi$
$468$	5.35350e10	0.0515860
$469$	0	0
$470$	−1.93328e11	−0.182749
$471$	−8.73532e11	−0.817871
$472$	−8.62764e11	−0.800116
$473$	−2.12299e12	−1.95017
$474$	5.78003e11	0.525930
$475$	8.17420e10	0.0736756
$476$	0	0
$477$	−4.22827e11	−0.373964
$478$	1.38202e12	1.21084
$479$	−9.01785e10	−0.0782696	−0.0391348	−	0.999234i	$-0.512460\pi$
$479$	−9.01785e10	−0.0782696	−0.0391348	+	0.999234i	$0.512460\pi$
$480$	−1.45750e11	−0.125320
$481$	2.86933e12	2.44415
$482$	−2.51698e12	−2.12407
$483$	0	0
$484$	3.18512e11	0.263828
$485$	7.40422e11	0.607633
$486$	−5.47472e11	−0.445142
$487$	−1.21268e12	−0.976933	−0.488467	−	0.872583i	$-0.662444\pi$
$487$	−1.21268e12	−0.976933	−0.488467	+	0.872583i	$0.662444\pi$
$488$	−2.10232e12	−1.67807
$489$	1.06916e11	0.0845580
$490$	0	0
$491$	−1.91290e12	−1.48534	−0.742671	−	0.669657i	$-0.766441\pi$
$491$	−1.91290e12	−1.48534	−0.742671	+	0.669657i	$0.766441\pi$
$492$	−4.02611e10	−0.0309773
$493$	2.45385e12	1.87084
$494$	8.08448e11	0.610774
$495$	−2.05013e11	−0.153482
$496$	−1.93478e12	−1.43537
$497$	0	0
$498$	1.44737e12	1.05450
$499$	−1.06963e12	−0.772291	−0.386146	−	0.922438i	$-0.626194\pi$
$499$	−1.06963e12	−0.772291	−0.386146	+	0.922438i	$0.626194\pi$
$500$	−1.98908e10	−0.0142327
$501$	1.41668e12	1.00462
$502$	−1.25497e12	−0.881994
$503$	−8.23356e11	−0.573498	−0.286749	−	0.958006i	$-0.592575\pi$
$503$	−8.23356e11	−0.573498	−0.286749	+	0.958006i	$0.592575\pi$
$504$	0	0
$505$	−3.35161e11	−0.229320
$506$	−2.52921e12	−1.71517
$507$	1.81318e12	1.21872
$508$	−3.62735e10	−0.0241659
$509$	7.68795e11	0.507669	0.253834	−	0.967248i	$-0.418308\pi$
$509$	7.68795e11	0.507669	0.253834	+	0.967248i	$0.418308\pi$
$510$	−9.23274e11	−0.604317
$511$	0	0
$512$	1.04005e12	0.668864
$513$	−6.21532e11	−0.396219
$514$	4.10709e11	0.259537
$515$	4.59754e11	0.288001
$516$	2.72356e11	0.169127
$517$	1.00521e12	0.618800
$518$	0	0
$519$	−5.79599e11	−0.350651
$520$	1.03956e12	0.623494
$521$	−1.92808e12	−1.14645	−0.573224	−	0.819398i	$-0.694308\pi$
$521$	−1.92808e12	−1.14645	−0.573224	+	0.819398i	$0.694308\pi$
$522$	−5.09185e11	−0.300164
$523$	1.48683e12	0.868970	0.434485	−	0.900679i	$-0.356930\pi$
$523$	1.48683e12	0.868970	0.434485	+	0.900679i	$0.356930\pi$
$524$	2.00291e11	0.116057
$525$	0	0
$526$	3.35775e12	1.91255
$527$	−3.16653e12	−1.78828
$528$	2.93319e12	1.64243
$529$	−8.13248e10	−0.0451515
$530$	1.55376e12	0.855350
$531$	3.40839e11	0.186047
$532$	0	0
$533$	6.28666e11	0.337402
$534$	1.99188e12	1.06006
$535$	6.81976e11	0.359896
$536$	1.36820e12	0.715990
$537$	3.82798e11	0.198649
$538$	−1.70418e12	−0.876992
$539$	0	0
$540$	1.51242e11	0.0765420
$541$	−1.51765e12	−0.761700	−0.380850	−	0.924637i	$-0.624368\pi$
$541$	−1.51765e12	−0.761700	−0.380850	+	0.924637i	$0.624368\pi$
$542$	3.73666e12	1.85989
$543$	−5.62768e11	−0.277799
$544$	−9.09992e11	−0.445495
$545$	7.31090e11	0.354966
$546$	0	0
$547$	5.39040e11	0.257441	0.128721	−	0.991681i	$-0.458913\pi$
$547$	5.39040e11	0.257441	0.128721	+	0.991681i	$0.458913\pi$
$548$	−6.68197e10	−0.0316513
$549$	8.30533e11	0.390195
$550$	7.53361e11	0.351052
$551$	−1.05561e12	−0.487888
$552$	−1.71460e12	−0.786027
$553$	0	0
$554$	−3.99840e12	−1.80340
$555$	1.40966e12	0.630659
$556$	−7.28605e10	−0.0323337
$557$	2.33957e11	0.102988	0.0514941	−	0.998673i	$-0.483602\pi$
$557$	2.33957e11	0.102988	0.0514941	+	0.998673i	$0.483602\pi$
$558$	6.57071e11	0.286918
$559$	−4.25276e12	−1.84212
$560$	0	0
$561$	4.80057e12	2.04625
$562$	2.09981e12	0.887905
$563$	1.04620e12	0.438861	0.219431	−	0.975628i	$-0.429580\pi$
$563$	1.04620e12	0.438861	0.219431	+	0.975628i	$0.429580\pi$
$564$	−1.28958e11	−0.0536651
$565$	−6.68614e11	−0.276031
$566$	5.97403e11	0.244677
$567$	0	0
$568$	−1.71502e12	−0.691356
$569$	4.42842e12	1.77110	0.885550	−	0.464544i	$-0.153782\pi$
$569$	4.42842e12	1.77110	0.885550	+	0.464544i	$0.153782\pi$
$570$	3.97178e11	0.157597
$571$	7.70937e10	0.0303498	0.0151749	−	0.999885i	$-0.495169\pi$
$571$	7.70937e10	0.0303498	0.0151749	+	0.999885i	$0.495169\pi$
$572$	1.02287e12	0.399521
$573$	1.08277e11	0.0419606
$574$	0	0
$575$	−5.12274e11	−0.195433
$576$	−4.41703e11	−0.167197
$577$	2.85527e11	0.107240	0.0536200	−	0.998561i	$-0.482924\pi$
$577$	2.85527e11	0.107240	0.0536200	+	0.998561i	$0.482924\pi$
$578$	−2.87554e12	−1.07163
$579$	3.80166e11	0.140579
$580$	2.56868e11	0.0942506
$581$	0	0
$582$	3.59765e12	1.29977
$583$	−8.07881e12	−2.89627
$584$	4.32114e12	1.53724
$585$	−4.10681e11	−0.144978
$586$	4.33468e12	1.51851
$587$	−3.11740e12	−1.08373	−0.541866	−	0.840465i	$-0.682282\pi$
$587$	−3.11740e12	−1.08373	−0.541866	+	0.840465i	$0.682282\pi$
$588$	0	0
$589$	1.36219e12	0.466358
$590$	−1.25248e12	−0.425537
$591$	7.46552e11	0.251719
$592$	5.37764e12	1.79947
$593$	2.45088e12	0.813910	0.406955	−	0.913448i	$-0.366591\pi$
$593$	2.45088e12	0.813910	0.406955	+	0.913448i	$0.366591\pi$
$594$	−5.72824e12	−1.88791
$595$	0	0
$596$	4.76984e11	0.154844
$597$	9.89046e11	0.318663
$598$	−5.06652e12	−1.62015
$599$	5.75249e12	1.82572	0.912861	−	0.408270i	$-0.133868\pi$
$599$	5.75249e12	1.82572	0.912861	+	0.408270i	$0.133868\pi$
$600$	5.10717e11	0.160879
$601$	3.35853e12	1.05006	0.525029	−	0.851084i	$-0.324054\pi$
$601$	3.35853e12	1.05006	0.525029	+	0.851084i	$0.324054\pi$
$602$	0	0
$603$	−5.40513e11	−0.166486
$604$	−3.69603e11	−0.112998
$605$	−2.44339e12	−0.741469
$606$	−1.62852e12	−0.490531
$607$	−1.55525e12	−0.464998	−0.232499	−	0.972597i	$-0.574690\pi$
$607$	−1.55525e12	−0.464998	−0.232499	+	0.972597i	$0.574690\pi$
$608$	3.91465e11	0.116179
$609$	0	0
$610$	−3.05196e12	−0.892473
$611$	2.01364e12	0.584516
$612$	1.64211e11	0.0473173
$613$	−4.17629e12	−1.19459	−0.597294	−	0.802022i	$-0.703758\pi$
$613$	−4.17629e12	−1.19459	−0.597294	+	0.802022i	$0.703758\pi$
$614$	−3.15208e12	−0.895034
$615$	3.08854e11	0.0870592
$616$	0	0
$617$	−2.41875e12	−0.671906	−0.335953	−	0.941879i	$-0.609058\pi$
$617$	−2.41875e12	−0.671906	−0.335953	+	0.941879i	$0.609058\pi$
$618$	2.23391e12	0.616053
$619$	8.00006e11	0.219021	0.109510	−	0.993986i	$-0.465072\pi$
$619$	8.00006e11	0.219021	0.109510	+	0.993986i	$0.465072\pi$
$620$	−3.31472e11	−0.0900916
$621$	3.89512e12	1.05101
$622$	−1.37164e12	−0.367438
$623$	0	0
$624$	5.87577e12	1.55144
$625$	1.52588e11	0.0400000
$626$	4.75475e12	1.23749
$627$	−2.06513e12	−0.533634
$628$	−5.70916e11	−0.146472
$629$	8.80123e12	2.24190
$630$	0	0
$631$	−5.19659e11	−0.130493	−0.0652464	−	0.997869i	$-0.520783\pi$
$631$	−5.19659e11	−0.130493	−0.0652464	+	0.997869i	$0.520783\pi$
$632$	−1.99623e12	−0.497719
$633$	−4.75252e11	−0.117654
$634$	7.15128e11	0.175785
$635$	2.78264e11	0.0679165
$636$	1.03642e12	0.251177
$637$	0	0
$638$	−9.72882e12	−2.32470
$639$	6.77527e11	0.160758
$640$	2.22176e12	0.523464
$641$	2.87136e11	0.0671780	0.0335890	−	0.999436i	$-0.489306\pi$
$641$	2.87136e11	0.0671780	0.0335890	+	0.999436i	$0.489306\pi$
$642$	3.31367e12	0.769842
$643$	3.19225e11	0.0736457	0.0368228	−	0.999322i	$-0.488276\pi$
$643$	3.19225e11	0.0736457	0.0368228	+	0.999322i	$0.488276\pi$
$644$	0	0
$645$	−2.08932e12	−0.475319
$646$	2.47980e12	0.560234
$647$	−6.28890e12	−1.41093	−0.705464	−	0.708745i	$-0.749262\pi$
$647$	−6.28890e12	−1.41093	−0.705464	+	0.708745i	$0.749262\pi$
$648$	−3.02792e12	−0.674616
$649$	6.51228e12	1.44089
$650$	1.50913e12	0.331602
$651$	0	0
$652$	6.98776e10	0.0151434
$653$	3.67037e12	0.789952	0.394976	−	0.918691i	$-0.370753\pi$
$653$	3.67037e12	0.789952	0.394976	+	0.918691i	$0.370753\pi$
$654$	3.55231e12	0.759296
$655$	−1.53649e12	−0.326170
$656$	1.17823e12	0.248407
$657$	−1.70709e12	−0.357447
$658$	0	0
$659$	−9.30220e11	−0.192133	−0.0960664	−	0.995375i	$-0.530626\pi$
$659$	−9.30220e11	−0.192133	−0.0960664	+	0.995375i	$0.530626\pi$
$660$	5.02522e11	0.103088
$661$	8.29301e12	1.68968	0.844842	−	0.535016i	$-0.179694\pi$
$661$	8.29301e12	1.68968	0.844842	+	0.535016i	$0.179694\pi$
$662$	2.17772e12	0.440699
$663$	9.61649e12	1.93288
$664$	−4.99874e12	−0.997940
$665$	0	0
$666$	−1.82630e12	−0.359698
$667$	6.61545e12	1.29418
$668$	9.25905e11	0.179917
$669$	6.79623e12	1.31175
$670$	1.98622e12	0.380795
$671$	1.58687e13	3.02197
$672$	0	0
$673$	−2.69943e11	−0.0507230	−0.0253615	−	0.999678i	$-0.508074\pi$
$673$	−2.69943e11	−0.0507230	−0.0253615	+	0.999678i	$0.508074\pi$
$674$	−1.21430e12	−0.226649
$675$	−1.16021e12	−0.215115
$676$	1.18504e12	0.218260
$677$	−1.28604e12	−0.235292	−0.117646	−	0.993056i	$-0.537535\pi$
$677$	−1.28604e12	−0.235292	−0.117646	+	0.993056i	$0.537535\pi$
$678$	−3.24875e12	−0.590449
$679$	0	0
$680$	3.18868e12	0.571901
$681$	−2.75966e12	−0.491692
$682$	1.25544e13	2.22212
$683$	−6.71947e12	−1.18152	−0.590761	−	0.806846i	$-0.701172\pi$
$683$	−6.71947e12	−1.18152	−0.590761	+	0.806846i	$0.701172\pi$
$684$	−7.06409e10	−0.0123397
$685$	5.12592e11	0.0889537
$686$	0	0
$687$	4.24513e12	0.727085
$688$	−7.97045e12	−1.35623
$689$	−1.61835e13	−2.73580
$690$	−2.48910e12	−0.418044
$691$	5.58524e12	0.931946	0.465973	−	0.884799i	$-0.345704\pi$
$691$	5.58524e12	0.931946	0.465973	+	0.884799i	$0.345704\pi$
$692$	−3.78810e11	−0.0627977
$693$	0	0
$694$	−8.98579e12	−1.47041
$695$	5.58932e11	0.0908714
$696$	−6.59535e12	−1.06536
$697$	1.92834e12	0.309482
$698$	−1.18745e13	−1.89351
$699$	−1.28246e12	−0.203187
$700$	0	0
$701$	6.83154e12	1.06853	0.534266	−	0.845316i	$-0.320588\pi$
$701$	6.83154e12	1.06853	0.534266	+	0.845316i	$0.320588\pi$
$702$	−1.14748e13	−1.78332
$703$	−3.78615e12	−0.584655
$704$	−8.43947e12	−1.29491
$705$	9.89270e11	0.150822
$706$	4.72445e12	0.715699
$707$	0	0
$708$	−8.35456e11	−0.124961
$709$	−1.75544e12	−0.260903	−0.130451	−	0.991455i	$-0.541643\pi$
$709$	−1.75544e12	−0.260903	−0.130451	+	0.991455i	$0.541643\pi$
$710$	−2.48971e12	−0.367694
$711$	7.88621e11	0.115732
$712$	−6.87931e12	−1.00319
$713$	−8.53682e12	−1.23707
$714$	0	0
$715$	−7.84674e12	−1.12282
$716$	2.50186e11	0.0355758
$717$	−7.07184e12	−0.999301
$718$	−1.20256e13	−1.68868
$719$	1.02389e13	1.42881	0.714406	−	0.699732i	$-0.246697\pi$
$719$	1.02389e13	1.42881	0.714406	+	0.699732i	$0.246697\pi$
$720$	−7.69691e11	−0.106738
$721$	0	0
$722$	6.79432e12	0.930527
$723$	1.28795e13	1.75298
$724$	−3.67809e11	−0.0497507
$725$	−1.97050e12	−0.264884
$726$	−1.18722e13	−1.58605
$727$	3.88957e12	0.516412	0.258206	−	0.966090i	$-0.416869\pi$
$727$	3.88957e12	0.516412	0.258206	+	0.966090i	$0.416869\pi$
$728$	0	0
$729$	8.48388e12	1.11255
$730$	6.27304e12	0.817570
$731$	−1.30447e13	−1.68969
$732$	−2.03578e12	−0.262079
$733$	7.82721e12	1.00147	0.500736	−	0.865600i	$-0.333063\pi$
$733$	7.82721e12	1.00147	0.500736	+	0.865600i	$0.333063\pi$
$734$	1.61051e13	2.04801
$735$	0	0
$736$	−2.45330e12	−0.308177
$737$	−1.03274e13	−1.28940
$738$	−4.00140e11	−0.0496545
$739$	−9.38922e12	−1.15806	−0.579028	−	0.815308i	$-0.696568\pi$
$739$	−9.38922e12	−1.15806	−0.579028	+	0.815308i	$0.696568\pi$
$740$	9.21311e11	0.112944
$741$	−4.13687e12	−0.504068
$742$	0	0
$743$	−1.79429e12	−0.215994	−0.107997	−	0.994151i	$-0.534444\pi$
$743$	−1.79429e12	−0.215994	−0.107997	+	0.994151i	$0.534444\pi$
$744$	8.51088e12	1.01835
$745$	−3.65907e12	−0.435179
$746$	1.17967e13	1.39456
$747$	1.97478e12	0.232047
$748$	3.13752e12	0.366462
$749$	0	0
$750$	7.41413e11	0.0855627
$751$	−1.48690e13	−1.70570	−0.852851	−	0.522155i	$-0.825128\pi$
$751$	−1.48690e13	−1.70570	−0.852851	+	0.522155i	$0.825128\pi$
$752$	3.77393e12	0.430341
$753$	6.42172e12	0.727904
$754$	−1.94888e13	−2.19590
$755$	2.83533e12	0.317572
$756$	0	0
$757$	−5.27048e12	−0.583336	−0.291668	−	0.956520i	$-0.594210\pi$
$757$	−5.27048e12	−0.583336	−0.291668	+	0.956520i	$0.594210\pi$
$758$	1.16266e13	1.27921
$759$	1.29421e13	1.41552
$760$	−1.37172e12	−0.149144
$761$	−3.97216e12	−0.429334	−0.214667	−	0.976687i	$-0.568867\pi$
$761$	−3.97216e12	−0.429334	−0.214667	+	0.976687i	$0.568867\pi$
$762$	1.35206e12	0.145278
$763$	0	0
$764$	7.07671e10	0.00751469
$765$	−1.25970e12	−0.132982
$766$	−2.78194e12	−0.291957
$767$	1.30454e13	1.36106
$768$	3.99138e12	0.413998
$769$	−5.20785e12	−0.537019	−0.268510	−	0.963277i	$-0.586531\pi$
$769$	−5.20785e12	−0.537019	−0.268510	+	0.963277i	$0.586531\pi$
$770$	0	0
$771$	−2.10162e12	−0.214195
$772$	2.48465e11	0.0251761
$773$	−8.29538e12	−0.835658	−0.417829	−	0.908526i	$-0.637209\pi$
$773$	−8.29538e12	−0.835658	−0.417829	+	0.908526i	$0.637209\pi$
$774$	2.70684e12	0.271100
$775$	2.54281e12	0.253196
$776$	−1.24251e13	−1.23005
$777$	0	0
$778$	7.32813e12	0.717108
$779$	−8.29542e11	−0.0807086
$780$	1.00665e12	0.0973764
$781$	1.29453e13	1.24503
$782$	−1.55408e13	−1.48608
$783$	1.49829e13	1.42452
$784$	0	0
$785$	4.37965e12	0.411648
$786$	−7.46568e12	−0.697699
$787$	−1.99659e12	−0.185525	−0.0927625	−	0.995688i	$-0.529570\pi$
$787$	−1.99659e12	−0.185525	−0.0927625	+	0.995688i	$0.529570\pi$
$788$	4.87926e11	0.0450802
$789$	−1.71818e13	−1.57842
$790$	−2.89795e12	−0.264709
$791$	0	0
$792$	3.44034e12	0.310698
$793$	3.17882e13	2.85454
$794$	−8.01759e11	−0.0715899
$795$	−7.95068e12	−0.705915
$796$	6.46413e11	0.0570691
$797$	1.15788e13	1.01648	0.508242	−	0.861214i	$-0.330295\pi$
$797$	1.15788e13	1.01648	0.508242	+	0.861214i	$0.330295\pi$
$798$	0	0
$799$	6.17654e12	0.536148
$800$	7.30748e11	0.0630758
$801$	2.71770e12	0.233268
$802$	1.66443e13	1.42063
$803$	−3.26167e13	−2.76834
$804$	1.32489e12	0.111822
$805$	0	0
$806$	2.51490e13	2.09900
$807$	8.72037e12	0.723776
$808$	5.62438e12	0.464219
$809$	1.18509e13	0.972707	0.486354	−	0.873762i	$-0.338327\pi$
$809$	1.18509e13	0.972707	0.486354	+	0.873762i	$0.338327\pi$
$810$	−4.39566e12	−0.358791
$811$	−6.58925e12	−0.534863	−0.267431	−	0.963577i	$-0.586175\pi$
$811$	−6.58925e12	−0.534863	−0.267431	+	0.963577i	$0.586175\pi$
$812$	0	0
$813$	−1.91207e13	−1.53496
$814$	−3.48944e13	−2.78578
$815$	−5.36049e11	−0.0425594
$816$	1.80231e13	1.42306
$817$	5.61164e12	0.440646
$818$	−6.42410e12	−0.501675
$819$	0	0
$820$	2.01858e11	0.0155914
$821$	4.77380e12	0.366707	0.183354	−	0.983047i	$-0.441305\pi$
$821$	4.77380e12	0.366707	0.183354	+	0.983047i	$0.441305\pi$
$822$	2.49064e12	0.190278
$823$	−7.00298e12	−0.532088	−0.266044	−	0.963961i	$-0.585717\pi$
$823$	−7.00298e12	−0.532088	−0.266044	+	0.963961i	$0.585717\pi$
$824$	−7.71519e12	−0.583008
$825$	−3.85498e12	−0.289721
$826$	0	0
$827$	−1.60647e13	−1.19426	−0.597128	−	0.802146i	$-0.703692\pi$
$827$	−1.60647e13	−1.19426	−0.597128	+	0.802146i	$0.703692\pi$
$828$	4.42704e11	0.0327324
$829$	5.58641e11	0.0410806	0.0205403	−	0.999789i	$-0.493461\pi$
$829$	5.58641e11	0.0410806	0.0205403	+	0.999789i	$0.493461\pi$
$830$	−7.25672e12	−0.530749
$831$	2.04600e13	1.48834
$832$	−1.69059e13	−1.22316
$833$	0	0
$834$	2.71581e12	0.194380
$835$	−7.10286e12	−0.505643
$836$	−1.34971e12	−0.0955680
$837$	−1.93345e13	−1.36166
$838$	−5.51365e12	−0.386226
$839$	−2.37598e13	−1.65544	−0.827720	−	0.561142i	$-0.810362\pi$
$839$	−2.37598e13	−1.65544	−0.827720	+	0.561142i	$0.810362\pi$
$840$	0	0
$841$	1.09397e13	0.754091
$842$	−3.84520e12	−0.263642
$843$	−1.07448e13	−0.732783
$844$	−3.10611e11	−0.0210706
$845$	−9.09076e12	−0.613402
$846$	−1.28166e12	−0.0860215
$847$	0	0
$848$	−3.03308e13	−2.01420
$849$	−3.05694e12	−0.201931
$850$	4.62904e12	0.304162
$851$	2.37277e13	1.55086
$852$	−1.66074e12	−0.107975
$853$	2.09014e13	1.35177	0.675887	−	0.737006i	$-0.263761\pi$
$853$	2.09014e13	1.35177	0.675887	+	0.737006i	$0.263761\pi$
$854$	0	0
$855$	5.41905e11	0.0346797
$856$	−1.14443e13	−0.728547
$857$	−2.45387e13	−1.55395	−0.776976	−	0.629530i	$-0.783248\pi$
$857$	−2.45387e13	−1.55395	−0.776976	+	0.629530i	$0.783248\pi$
$858$	−3.81267e13	−2.40180
$859$	2.18164e13	1.36715	0.683573	−	0.729882i	$-0.260425\pi$
$859$	2.18164e13	1.36715	0.683573	+	0.729882i	$0.260425\pi$
$860$	−1.36552e12	−0.0851245
$861$	0	0
$862$	8.62246e12	0.531923
$863$	−2.23249e13	−1.37006	−0.685031	−	0.728514i	$-0.740212\pi$
$863$	−2.23249e13	−1.37006	−0.685031	+	0.728514i	$0.740212\pi$
$864$	−5.55630e12	−0.339214
$865$	2.90595e12	0.176488
$866$	−2.98173e13	−1.80151
$867$	1.47143e13	0.884408
$868$	0	0
$869$	1.50679e13	0.896321
$870$	−9.57453e12	−0.566605
$871$	−2.06878e13	−1.21796
$872$	−1.22685e13	−0.718567
$873$	4.90860e12	0.286018
$874$	6.68541e12	0.387549
$875$	0	0
$876$	4.18437e12	0.240083
$877$	1.78843e13	1.02088	0.510439	−	0.859914i	$-0.329483\pi$
$877$	1.78843e13	1.02088	0.510439	+	0.859914i	$0.329483\pi$
$878$	1.05676e13	0.600140
$879$	−2.21807e13	−1.25322
$880$	−1.47062e13	−0.826664
$881$	−1.09498e13	−0.612371	−0.306186	−	0.951972i	$-0.599053\pi$
$881$	−1.09498e13	−0.612371	−0.306186	+	0.951972i	$0.599053\pi$
$882$	0	0
$883$	−1.51202e13	−0.837016	−0.418508	−	0.908213i	$-0.637447\pi$
$883$	−1.51202e13	−0.837016	−0.418508	+	0.908213i	$0.637447\pi$
$884$	6.28507e12	0.346158
$885$	6.40901e12	0.351193
$886$	1.71568e13	0.935373
$887$	−3.10713e13	−1.68540	−0.842700	−	0.538383i	$-0.819035\pi$
$887$	−3.10713e13	−1.68540	−0.842700	+	0.538383i	$0.819035\pi$
$888$	−2.36556e13	−1.27666
$889$	0	0
$890$	−9.98676e12	−0.533543
$891$	2.28553e13	1.21489
$892$	4.44182e12	0.234920
$893$	−2.65705e12	−0.139820
$894$	−1.77791e13	−0.930876
$895$	−1.91924e12	−0.0999831
$896$	0	0
$897$	2.59256e13	1.33710
$898$	2.87680e13	1.47627
$899$	−3.28375e13	−1.67669
$900$	−1.31866e11	−0.00669946
$901$	−4.96404e13	−2.50942
$902$	−7.64533e12	−0.384562
$903$	0	0
$904$	1.12201e13	0.558777
$905$	2.82156e12	0.139821
$906$	1.37766e13	0.679307
$907$	3.34433e13	1.64088	0.820439	−	0.571733i	$-0.193729\pi$
$907$	3.34433e13	1.64088	0.820439	+	0.571733i	$0.193729\pi$
$908$	−1.80364e12	−0.0880567
$909$	−2.22194e12	−0.107943
$910$	0	0
$911$	−8.97982e10	−0.00431951	−0.00215976	−	0.999998i	$-0.500687\pi$
$911$	−8.97982e10	−0.00431951	−0.00215976	+	0.999998i	$0.500687\pi$
$912$	−7.75324e12	−0.371113
$913$	3.77313e13	1.79715
$914$	−9.36365e12	−0.443800
$915$	1.56170e13	0.736552
$916$	2.77450e12	0.130213
$917$	0	0
$918$	−3.51973e13	−1.63575
$919$	−3.75591e13	−1.73698	−0.868492	−	0.495704i	$-0.834910\pi$
$919$	−3.75591e13	−1.73698	−0.868492	+	0.495704i	$0.834910\pi$
$920$	8.59654e12	0.395620
$921$	1.61293e13	0.738666
$922$	3.70326e13	1.68770
$923$	2.59320e13	1.17605
$924$	0	0
$925$	−7.06762e12	−0.317421
$926$	5.36916e12	0.239970
$927$	3.04792e12	0.135564
$928$	−9.43679e12	−0.417694
$929$	2.20434e13	0.970976	0.485488	−	0.874243i	$-0.338642\pi$
$929$	2.20434e13	0.970976	0.485488	+	0.874243i	$0.338642\pi$
$930$	1.23553e13	0.541602
$931$	0	0
$932$	−8.38179e11	−0.0363886
$933$	7.01875e12	0.303244
$934$	1.43585e13	0.617373
$935$	−2.40687e13	−1.02991
$936$	6.89169e12	0.293484
$937$	−1.69037e11	−0.00716398	−0.00358199	−	0.999994i	$-0.501140\pi$
$937$	−1.69037e11	−0.00716398	−0.00358199	+	0.999994i	$0.501140\pi$
$938$	0	0
$939$	−2.43303e13	−1.02130
$940$	6.46559e11	0.0270105
$941$	−3.28576e12	−0.136610	−0.0683050	−	0.997664i	$-0.521759\pi$
$941$	−3.28576e12	−0.136610	−0.0683050	+	0.997664i	$0.521759\pi$
$942$	2.12804e13	0.880542
$943$	5.19871e12	0.214088
$944$	2.44495e13	1.00206
$945$	0	0
$946$	5.17187e13	2.09960
$947$	−2.48210e13	−1.00287	−0.501434	−	0.865196i	$-0.667194\pi$
$947$	−2.48210e13	−1.00287	−0.501434	+	0.865196i	$0.667194\pi$
$948$	−1.93305e12	−0.0777330
$949$	−6.53378e13	−2.61497
$950$	−1.99134e12	−0.0793212
$951$	−3.65934e12	−0.145074
$952$	0	0
$953$	−4.38622e13	−1.72255	−0.861277	−	0.508136i	$-0.830335\pi$
$953$	−4.38622e13	−1.72255	−0.861277	+	0.508136i	$0.830335\pi$
$954$	1.03006e13	0.402620
$955$	−5.42873e11	−0.0211195
$956$	−4.62196e12	−0.178964
$957$	4.97828e13	1.91856
$958$	2.19687e12	0.0842672
$959$	0	0
$960$	−8.30562e12	−0.315611
$961$	1.59351e13	0.602699
$962$	−6.99005e13	−2.63143
$963$	4.52113e12	0.169406
$964$	8.41769e12	0.313940
$965$	−1.90604e12	−0.0707555
$966$	0	0
$967$	1.91540e13	0.704433	0.352216	−	0.935919i	$-0.385428\pi$
$967$	1.91540e13	0.704433	0.352216	+	0.935919i	$0.385428\pi$
$968$	4.10028e13	1.50098
$969$	−1.26892e13	−0.462358
$970$	−1.80376e13	−0.654194
$971$	1.37443e13	0.496177	0.248088	−	0.968737i	$-0.420198\pi$
$971$	1.37443e13	0.496177	0.248088	+	0.968737i	$0.420198\pi$
$972$	1.83094e12	0.0657925
$973$	0	0
$974$	2.95424e13	1.05179
$975$	−7.72229e12	−0.273669
$976$	5.95768e13	2.10161
$977$	−2.39141e13	−0.839707	−0.419854	−	0.907592i	$-0.637919\pi$
$977$	−2.39141e13	−0.839707	−0.419854	+	0.907592i	$0.637919\pi$
$978$	−2.60462e12	−0.0910374
$979$	5.19262e13	1.80661
$980$	0	0
$981$	4.84673e12	0.167085
$982$	4.66008e13	1.59916
$983$	−2.37709e13	−0.811998	−0.405999	−	0.913873i	$-0.633076\pi$
$983$	−2.37709e13	−0.811998	−0.405999	+	0.913873i	$0.633076\pi$
$984$	−5.18291e12	−0.176237
$985$	−3.74301e12	−0.126694
$986$	−5.97789e13	−2.01420
$987$	0	0
$988$	−2.70374e12	−0.0902731
$989$	−3.51679e13	−1.16886
$990$	4.99438e12	0.165243
$991$	5.49088e13	1.80847	0.904234	−	0.427038i	$-0.140443\pi$
$991$	5.49088e13	1.80847	0.904234	+	0.427038i	$0.140443\pi$
$992$	1.21776e13	0.399262
$993$	−1.11435e13	−0.363706
$994$	0	0
$995$	−4.95880e12	−0.160388
$996$	−4.84053e12	−0.155857
$997$	1.34017e13	0.429568	0.214784	−	0.976662i	$-0.431095\pi$
$997$	1.34017e13	0.429568	0.214784	+	0.976662i	$0.431095\pi$
$998$	2.60576e13	0.831470
$999$	5.37393e13	1.70705

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.10.a.i.1.3	yes	9
7.6	odd	2		245.10.a.h.1.3	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
245.10.a.h.1.3	✓	9	7.6	odd	2
245.10.a.i.1.3	yes	9	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q-24.3613 q^{2} +124.658 q^{3} +81.4729 q^{4} -625.000 q^{5} -3036.83 q^{6} +10488.2 q^{8} -4143.41 q^{9} +15225.8 q^{10} -79166.7 q^{11} +10156.2 q^{12} -158587. q^{13} -77911.2 q^{15} -297220. q^{16} -486441. q^{17} +100939. q^{18} +209259. q^{19} -50920.6 q^{20} +1.92860e6 q^{22} -1.31142e6 q^{23} +1.30744e6 q^{24} +390625. q^{25} +3.86338e6 q^{26} -2.97015e6 q^{27} -5.04449e6 q^{29} +1.89802e6 q^{30} +6.50959e6 q^{31} +1.87071e6 q^{32} -9.86875e6 q^{33} +1.18503e7 q^{34} -337576. q^{36} -1.80931e7 q^{37} -5.09783e6 q^{38} -1.97691e7 q^{39} -6.55512e6 q^{40} -3.96418e6 q^{41} +2.68166e7 q^{43} -6.44994e6 q^{44} +2.58963e6 q^{45} +3.19479e7 q^{46} -1.26974e7 q^{47} -3.70509e7 q^{48} -9.51613e6 q^{50} -6.06387e7 q^{51} -1.29205e7 q^{52} +1.02048e8 q^{53} +7.23567e7 q^{54} +4.94792e7 q^{55} +2.60858e7 q^{57} +1.22890e8 q^{58} -8.22604e7 q^{59} -6.34765e6 q^{60} -2.00447e8 q^{61} -1.58582e8 q^{62} +1.06604e8 q^{64} +9.91166e7 q^{65} +2.40416e8 q^{66} +1.30451e8 q^{67} -3.96318e7 q^{68} -1.63479e8 q^{69} -1.63519e8 q^{71} -4.34569e7 q^{72} +4.12000e8 q^{73} +4.40772e8 q^{74} +4.86945e7 q^{75} +1.70490e7 q^{76} +4.81600e8 q^{78} -1.90331e8 q^{79} +1.85763e8 q^{80} -2.88698e8 q^{81} +9.65725e7 q^{82} -4.76606e8 q^{83} +3.04026e8 q^{85} -6.53288e8 q^{86} -6.28835e8 q^{87} -8.30316e8 q^{88} -6.55910e8 q^{89} -6.30868e7 q^{90} -1.06845e8 q^{92} +8.11472e8 q^{93} +3.09325e8 q^{94} -1.30787e8 q^{95} +2.33199e8 q^{96} -1.18467e9 q^{97} +3.28020e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + q^{2} + 268 q^{3} + 1877 q^{4} - 5625 q^{5} + 7624 q^{6} + 13773 q^{8} + 17015 q^{9} - 625 q^{10} - 69434 q^{11} + 64966 q^{12} + 153108 q^{13} - 167500 q^{15} + 496777 q^{16} - 380338 q^{17} + 1151915 q^{18}+ \cdots - 2283620136 q^{99}+O(q^{100}) \) 9 * q + q^2 + 268 * q^3 + 1877 * q^4 - 5625 * q^5 + 7624 * q^6 + 13773 * q^8 + 17015 * q^9 - 625 * q^10 - 69434 * q^11 + 64966 * q^12 + 153108 * q^13 - 167500 * q^15 + 496777 * q^16 - 380338 * q^17 + 1151915 * q^18 + 1123026 * q^19 - 1173125 * q^20 - 2442882 * q^22 - 1413844 * q^23 + 2929050 * q^24 + 3515625 * q^25 - 1328856 * q^26 + 3396094 * q^27 - 4065424 * q^29 - 4765000 * q^30 + 10302576 * q^31 + 9549257 * q^32 - 4263462 * q^33 + 22417266 * q^34 - 48189067 * q^36 - 7627054 * q^37 + 49081118 * q^38 + 45214262 * q^39 - 8608125 * q^40 + 25366416 * q^41 - 14266432 * q^43 - 38019508 * q^44 - 10634375 * q^45 + 114958668 * q^46 - 117568854 * q^47 + 28333158 * q^48 + 390625 * q^50 - 79080682 * q^51 + 152491446 * q^52 - 83561830 * q^53 + 58066342 * q^54 + 43396250 * q^55 + 193586512 * q^57 - 115563884 * q^58 + 204491434 * q^59 - 40603750 * q^60 + 46790550 * q^61 + 241308368 * q^62 + 423301633 * q^64 - 95692500 * q^65 + 164532334 * q^66 + 109844000 * q^67 + 275411544 * q^68 + 193803448 * q^69 - 61313132 * q^71 - 10635039 * q^72 + 138674496 * q^73 + 93214602 * q^74 + 104687500 * q^75 - 758320338 * q^76 + 1759315878 * q^78 + 697968218 * q^79 - 310485625 * q^80 - 114074299 * q^81 + 1406591088 * q^82 - 1322818198 * q^83 + 237711250 * q^85 + 408387840 * q^86 + 450465942 * q^87 + 718451872 * q^88 + 136822392 * q^89 - 719946875 * q^90 - 283388084 * q^92 + 1717412492 * q^93 - 242355222 * q^94 - 701891250 * q^95 + 3205386294 * q^96 - 1926148290 * q^97 - 2283620136 * q^99

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