LMFDB - Embedded newform 245.10.a.n.1.11

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:	$1$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 6 x^{17} - 6671 x^{16} + 28472 x^{15} + 18323094 x^{14} - 49525664 x^{13} + \cdots + 24\!\cdots\!76 $ x^18 - 6x^17 - 6671x^16 + 28472x^15 + 18323094x^14 - 49525664x^13 - 26727434016x^12 + 35963326896x^11 + 22243420534040x^10 - 5616028552544x^9 - 10532182760701856x^8 - 5183005906043136x^7 + 2659690061237093664x^6 + 2008343572364565760x^5 - 306799367113693922304x^4 - 73406894211465090304x^3 + 11518524304617146364800x^2 - 25540525208247540535296*x + 244834460756100997376
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{18}\cdot 3^{4}\cdot 5^{4}\cdot 7^{16} $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Root			$-11.6331$ 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)

$f(q)$	$=$	\(q+14.2189 q^{2} -145.482 q^{3} -309.823 q^{4} -625.000 q^{5} -2068.59 q^{6} -11685.4 q^{8} +1481.93 q^{9} -8886.81 q^{10} +3047.19 q^{11} +45073.6 q^{12} +67030.4 q^{13} +90926.1 q^{15} -7524.42 q^{16} -262538. q^{17} +21071.4 q^{18} -51205.4 q^{19} +193639. q^{20} +43327.7 q^{22} -829244. q^{23} +1.70001e6 q^{24} +390625. q^{25} +953099. q^{26} +2.64792e6 q^{27} +7.28765e6 q^{29} +1.29287e6 q^{30} -235560. q^{31} +5.87594e6 q^{32} -443310. q^{33} -3.73300e6 q^{34} -459136. q^{36} +1.69409e7 q^{37} -728084. q^{38} -9.75170e6 q^{39} +7.30339e6 q^{40} -4.53695e6 q^{41} +3.23590e6 q^{43} -944089. q^{44} -926206. q^{45} -1.17909e7 q^{46} +6.45012e6 q^{47} +1.09467e6 q^{48} +5.55426e6 q^{50} +3.81945e7 q^{51} -2.07676e7 q^{52} +1.88525e7 q^{53} +3.76505e7 q^{54} -1.90449e6 q^{55} +7.44944e6 q^{57} +1.03622e8 q^{58} -1.73163e8 q^{59} -2.81710e7 q^{60} +9.62902e7 q^{61} -3.34940e6 q^{62} +8.74020e7 q^{64} -4.18940e7 q^{65} -6.30338e6 q^{66} -830384. q^{67} +8.13402e7 q^{68} +1.20640e8 q^{69} +9.97328e7 q^{71} -1.73170e7 q^{72} -2.22774e8 q^{73} +2.40880e8 q^{74} -5.68288e7 q^{75} +1.58646e7 q^{76} -1.38658e8 q^{78} -1.53648e7 q^{79} +4.70276e6 q^{80} -4.14393e8 q^{81} -6.45105e7 q^{82} -2.19006e8 q^{83} +1.64086e8 q^{85} +4.60109e7 q^{86} -1.06022e9 q^{87} -3.56077e7 q^{88} -7.71811e6 q^{89} -1.31696e7 q^{90} +2.56919e8 q^{92} +3.42697e7 q^{93} +9.17137e7 q^{94} +3.20034e7 q^{95} -8.54842e8 q^{96} -4.13160e7 q^{97} +4.51572e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 66 q^{2} - 112 q^{3} + 4438 q^{4} - 11250 q^{5} - 5184 q^{6} + 58542 q^{8} + 117250 q^{9} - 41250 q^{10} - 50448 q^{11} + 51200 q^{12} - 265416 q^{13} + 70000 q^{15} + 275354 q^{16} - 742108 q^{17}+ \cdots - 3327698948 q^{99}+O(q^{100}) $ 18 * q + 66 * q^2 - 112 * q^3 + 4438 * q^4 - 11250 * q^5 - 5184 * q^6 + 58542 * q^8 + 117250 * q^9 - 41250 * q^10 - 50448 * q^11 + 51200 * q^12 - 265416 * q^13 + 70000 * q^15 + 275354 * q^16 - 742108 * q^17 + 31422 * q^18 - 2003052 * q^19 - 2773750 * q^20 - 898372 * q^22 + 5864112 * q^23 - 7257292 * q^24 + 7031250 * q^25 - 4213696 * q^26 - 12641932 * q^27 + 6575952 * q^29 + 3240000 * q^30 - 15704952 * q^31 + 24442110 * q^32 - 23661356 * q^33 + 7374732 * q^34 + 49561790 * q^36 + 8711420 * q^37 - 8938900 * q^38 + 48598700 * q^39 - 36588750 * q^40 + 5319344 * q^41 + 52311916 * q^43 - 35094960 * q^44 - 73281250 * q^45 + 98407276 * q^46 - 113473964 * q^47 + 50036228 * q^48 + 25781250 * q^50 + 108467832 * q^51 - 193287600 * q^52 + 31548852 * q^53 - 116650276 * q^54 + 31530000 * q^55 + 68889076 * q^57 - 65260756 * q^58 - 267674844 * q^59 - 32000000 * q^60 - 321756900 * q^61 - 651435868 * q^62 - 585550558 * q^64 + 165885000 * q^65 - 865081780 * q^66 - 234918184 * q^67 - 844088700 * q^68 - 380592968 * q^69 - 795896592 * q^71 + 70394666 * q^72 - 617344800 * q^73 - 1029168024 * q^74 - 43750000 * q^75 - 1200935100 * q^76 - 1277509816 * q^78 - 63002188 * q^79 - 172096250 * q^80 + 306235886 * q^81 + 1719855588 * q^82 - 534295300 * q^83 + 463817500 * q^85 + 65726340 * q^86 + 1504843540 * q^87 - 1698935556 * q^88 - 100440944 * q^89 - 19638750 * q^90 + 3229447776 * q^92 - 414903656 * q^93 + 1013675148 * q^94 + 1251907500 * q^95 + 1575858100 * q^96 - 1852351908 * q^97 - 3327698948 * 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 $

$2$	14.2189	0.628392	0.314196	−	0.949358i	$-0.398265\pi$
$2$	14.2189	0.628392	0.314196	+	0.949358i	$0.398265\pi$
$3$	−145.482	−1.03696	−0.518481	−	0.855089i	$-0.673502\pi$
$3$	−145.482	−1.03696	−0.518481	+	0.855089i	$0.673502\pi$
$4$	−309.823	−0.605123
$5$	−625.000	−0.447214
$5$	−625.000	−0.447214
$6$	−2068.59	−0.651619
$7$	0	0
$7$	0	0
$8$	−11685.4	−1.00865
$9$	1481.93	0.0752898
$10$	−8886.81	−0.281026
$11$	3047.19	0.0627527	0.0313763	−	0.999508i	$-0.490011\pi$
$11$	3047.19	0.0627527	0.0313763	+	0.999508i	$0.490011\pi$
$12$	45073.6	0.627489
$13$	67030.4	0.650919	0.325460	−	0.945556i	$-0.394481\pi$
$13$	67030.4	0.650919	0.325460	+	0.945556i	$0.394481\pi$
$14$	0	0
$15$	90926.1	0.463743
$16$	−7524.42	−0.0287034
$17$	−262538.	−0.762380	−0.381190	−	0.924497i	$-0.624486\pi$
$17$	−262538.	−0.762380	−0.381190	+	0.924497i	$0.624486\pi$
$18$	21071.4	0.0473116
$19$	−51205.4	−0.0901414	−0.0450707	−	0.998984i	$-0.514351\pi$
$19$	−51205.4	−0.0901414	−0.0450707	+	0.998984i	$0.514351\pi$
$20$	193639.	0.270619
$21$	0	0
$22$	43327.7	0.0394333
$23$	−829244.	−0.617884	−0.308942	−	0.951081i	$-0.599975\pi$
$23$	−829244.	−0.617884	−0.308942	+	0.951081i	$0.599975\pi$
$24$	1.70001e6	1.04593
$25$	390625.	0.200000
$26$	953099.	0.409033
$27$	2.64792e6	0.958889
$28$	0	0
$29$	7.28765e6	1.91336	0.956680	−	0.291143i	$-0.0940356\pi$
$29$	7.28765e6	1.91336	0.956680	+	0.291143i	$0.0940356\pi$
$30$	1.29287e6	0.291413
$31$	−235560.	−0.0458114	−0.0229057	−	0.999738i	$-0.507292\pi$
$31$	−235560.	−0.0458114	−0.0229057	+	0.999738i	$0.507292\pi$
$32$	5.87594e6	0.990610
$33$	−443310.	−0.0650721
$34$	−3.73300e6	−0.479074
$35$	0	0
$36$	−459136.	−0.0455596
$37$	1.69409e7	1.48603	0.743015	−	0.669275i	$-0.233395\pi$
$37$	1.69409e7	1.48603	0.743015	+	0.669275i	$0.233395\pi$
$38$	−728084.	−0.0566442
$39$	−9.75170e6	−0.674978
$40$	7.30339e6	0.451081
$41$	−4.53695e6	−0.250748	−0.125374	−	0.992110i	$-0.540013\pi$
$41$	−4.53695e6	−0.250748	−0.125374	+	0.992110i	$0.540013\pi$
$42$	0	0
$43$	3.23590e6	0.144340	0.0721700	−	0.997392i	$-0.477008\pi$
$43$	3.23590e6	0.144340	0.0721700	+	0.997392i	$0.477008\pi$
$44$	−944089.	−0.0379731
$45$	−926206.	−0.0336706
$46$	−1.17909e7	−0.388274
$47$	6.45012e6	0.192809	0.0964046	−	0.995342i	$-0.469266\pi$
$47$	6.45012e6	0.192809	0.0964046	+	0.995342i	$0.469266\pi$
$48$	1.09467e6	0.0297643
$49$	0	0
$50$	5.55426e6	0.125678
$51$	3.81945e7	0.790559
$52$	−2.07676e7	−0.393886
$53$	1.88525e7	0.328192	0.164096	−	0.986444i	$-0.447529\pi$
$53$	1.88525e7	0.328192	0.164096	+	0.986444i	$0.447529\pi$
$54$	3.76505e7	0.602559
$55$	−1.90449e6	−0.0280638
$56$	0	0
$57$	7.44944e6	0.0934732
$58$	1.03622e8	1.20234
$59$	−1.73163e8	−1.86046	−0.930229	−	0.366978i	$-0.880392\pi$
$59$	−1.73163e8	−1.86046	−0.930229	+	0.366978i	$0.880392\pi$
$60$	−2.81710e7	−0.280622
$61$	9.62902e7	0.890426	0.445213	−	0.895425i	$-0.353128\pi$
$61$	9.62902e7	0.890426	0.445213	+	0.895425i	$0.353128\pi$
$62$	−3.34940e6	−0.0287875
$63$	0	0
$64$	8.74020e7	0.651195
$65$	−4.18940e7	−0.291100
$66$	−6.30338e6	−0.0408908
$67$	−830384.	−0.00503434	−0.00251717	−	0.999997i	$-0.500801\pi$
$67$	−830384.	−0.00503434	−0.00251717	+	0.999997i	$0.500801\pi$
$68$	8.13402e7	0.461334
$69$	1.20640e8	0.640722
$70$	0	0
$71$	9.97328e7	0.465774	0.232887	−	0.972504i	$-0.425183\pi$
$71$	9.97328e7	0.465774	0.232887	+	0.972504i	$0.425183\pi$
$72$	−1.73170e7	−0.0759409
$73$	−2.22774e8	−0.918144	−0.459072	−	0.888399i	$-0.651818\pi$
$73$	−2.22774e8	−0.918144	−0.459072	+	0.888399i	$0.651818\pi$
$74$	2.40880e8	0.933810
$75$	−5.68288e7	−0.207392
$76$	1.58646e7	0.0545466
$77$	0	0
$78$	−1.38658e8	−0.424151
$79$	−1.53648e7	−0.0443817	−0.0221909	−	0.999754i	$-0.507064\pi$
$79$	−1.53648e7	−0.0443817	−0.0221909	+	0.999754i	$0.507064\pi$
$80$	4.70276e6	0.0128365
$81$	−4.14393e8	−1.06962
$82$	−6.45105e7	−0.157568
$83$	−2.19006e8	−0.506529	−0.253265	−	0.967397i	$-0.581504\pi$
$83$	−2.19006e8	−0.506529	−0.253265	+	0.967397i	$0.581504\pi$
$84$	0	0
$85$	1.64086e8	0.340947
$86$	4.60109e7	0.0907021
$87$	−1.06022e9	−1.98408
$88$	−3.56077e7	−0.0632953
$89$	−7.71811e6	−0.0130393	−0.00651967	−	0.999979i	$-0.502075\pi$
$89$	−7.71811e6	−0.0130393	−0.00651967	+	0.999979i	$0.502075\pi$
$90$	−1.31696e7	−0.0211584
$91$	0	0
$92$	2.56919e8	0.373896
$93$	3.42697e7	0.0475047
$94$	9.17137e7	0.121160
$95$	3.20034e7	0.0403125
$96$	−8.54842e8	−1.02722
$97$	−4.13160e7	−0.0473855	−0.0236928	−	0.999719i	$-0.507542\pi$
$97$	−4.13160e7	−0.0473855	−0.0236928	+	0.999719i	$0.507542\pi$
$98$	0	0
$99$	4.51572e6	0.00472464
$100$	−1.21025e8	−0.121025
$101$	5.26293e8	0.503247	0.251624	−	0.967825i	$-0.419035\pi$
$101$	5.26293e8	0.503247	0.251624	+	0.967825i	$0.419035\pi$
$102$	5.43083e8	0.496782
$103$	−1.75013e9	−1.53215	−0.766076	−	0.642750i	$-0.777793\pi$
$103$	−1.75013e9	−1.53215	−0.766076	+	0.642750i	$0.777793\pi$
$104$	−7.83279e8	−0.656548
$105$	0	0
$106$	2.68062e8	0.206234
$107$	1.65470e9	1.22037	0.610186	−	0.792258i	$-0.291095\pi$
$107$	1.65470e9	1.22037	0.610186	+	0.792258i	$0.291095\pi$
$108$	−8.20387e8	−0.580246
$109$	−7.40263e8	−0.502304	−0.251152	−	0.967948i	$-0.580809\pi$
$109$	−7.40263e8	−0.502304	−0.251152	+	0.967948i	$0.580809\pi$
$110$	−2.70798e7	−0.0176351
$111$	−2.46458e9	−1.54096
$112$	0	0
$113$	9.31208e8	0.537272	0.268636	−	0.963242i	$-0.413427\pi$
$113$	9.31208e8	0.537272	0.268636	+	0.963242i	$0.413427\pi$
$114$	1.05923e8	0.0587378
$115$	5.18278e8	0.276326
$116$	−2.25788e9	−1.15782
$117$	9.93344e7	0.0490076
$118$	−2.46218e9	−1.16910
$119$	0	0
$120$	−1.06251e9	−0.467753
$121$	−2.34866e9	−0.996062
$122$	1.36914e9	0.559537
$123$	6.60044e8	0.260016
$124$	7.29818e7	0.0277215
$125$	−2.44141e8	−0.0894427
$126$	0	0
$127$	−7.34546e8	−0.250555	−0.125277	−	0.992122i	$-0.539982\pi$
$127$	−7.34546e8	−0.250555	−0.125277	+	0.992122i	$0.539982\pi$
$128$	−1.76572e9	−0.581404
$129$	−4.70764e8	−0.149675
$130$	−5.95687e8	−0.182925
$131$	−2.85858e8	−0.0848065	−0.0424032	−	0.999101i	$-0.513501\pi$
$131$	−2.85858e8	−0.0848065	−0.0424032	+	0.999101i	$0.513501\pi$
$132$	1.37348e8	0.0393766
$133$	0	0
$134$	−1.18071e7	−0.00316354
$135$	−1.65495e9	−0.428828
$136$	3.06786e9	0.768973
$137$	−5.84226e9	−1.41690	−0.708449	−	0.705762i	$-0.750605\pi$
$137$	−5.84226e9	−1.41690	−0.708449	+	0.705762i	$0.750605\pi$
$138$	1.71537e9	0.402625
$139$	−1.69854e9	−0.385930	−0.192965	−	0.981206i	$-0.561810\pi$
$139$	−1.69854e9	−0.385930	−0.192965	+	0.981206i	$0.561810\pi$
$140$	0	0
$141$	−9.38375e8	−0.199936
$142$	1.41809e9	0.292689
$143$	2.04254e8	0.0408469
$144$	−1.11507e7	−0.00216107
$145$	−4.55478e9	−0.855680
$146$	−3.16760e9	−0.576955
$147$	0	0
$148$	−5.24867e9	−0.899231
$149$	1.01068e10	1.67986	0.839931	−	0.542693i	$-0.182595\pi$
$149$	1.01068e10	1.67986	0.839931	+	0.542693i	$0.182595\pi$
$150$	−8.08043e8	−0.130324
$151$	−5.93766e9	−0.929435	−0.464717	−	0.885459i	$-0.653844\pi$
$151$	−5.93766e9	−0.929435	−0.464717	+	0.885459i	$0.653844\pi$
$152$	5.98356e8	0.0909209
$153$	−3.89063e8	−0.0573995
$154$	0	0
$155$	1.47225e8	0.0204875
$156$	3.02130e9	0.408445
$157$	−1.12508e9	−0.147786	−0.0738932	−	0.997266i	$-0.523542\pi$
$157$	−1.12508e9	−0.147786	−0.0738932	+	0.997266i	$0.523542\pi$
$158$	−2.18470e8	−0.0278891
$159$	−2.74270e9	−0.340323
$160$	−3.67247e9	−0.443014
$161$	0	0
$162$	−5.89221e9	−0.672142
$163$	1.08202e10	1.20058	0.600289	−	0.799783i	$-0.295052\pi$
$163$	1.08202e10	1.20058	0.600289	+	0.799783i	$0.295052\pi$
$164$	1.40565e9	0.151733
$165$	2.77069e8	0.0291011
$166$	−3.11402e9	−0.318299
$167$	2.15266e9	0.214166	0.107083	−	0.994250i	$-0.465849\pi$
$167$	2.15266e9	0.214166	0.107083	+	0.994250i	$0.465849\pi$
$168$	0	0
$169$	−6.11142e9	−0.576304
$170$	2.33312e9	0.214248
$171$	−7.58828e7	−0.00678673
$172$	−1.00255e9	−0.0873434
$173$	−1.33205e10	−1.13061	−0.565304	−	0.824883i	$-0.691241\pi$
$173$	−1.33205e10	−1.13061	−0.565304	+	0.824883i	$0.691241\pi$
$174$	−1.50752e10	−1.24678
$175$	0	0
$176$	−2.29283e7	−0.00180121
$177$	2.51920e10	1.92922
$178$	−1.09743e8	−0.00819383
$179$	−1.87917e9	−0.136813	−0.0684063	−	0.997658i	$-0.521791\pi$
$179$	−1.87917e9	−0.136813	−0.0684063	+	0.997658i	$0.521791\pi$
$180$	2.86960e8	0.0203749
$181$	−1.86256e9	−0.128990	−0.0644950	−	0.997918i	$-0.520544\pi$
$181$	−1.86256e9	−0.128990	−0.0644950	+	0.997918i	$0.520544\pi$
$182$	0	0
$183$	−1.40085e10	−0.923337
$184$	9.69006e9	0.623227
$185$	−1.05880e10	−0.664573
$186$	4.87277e8	0.0298516
$187$	−8.00002e8	−0.0478414
$188$	−1.99840e9	−0.116673
$189$	0	0
$190$	4.55052e8	0.0253320
$191$	2.95507e10	1.60664	0.803319	−	0.595548i	$-0.203065\pi$
$191$	2.95507e10	1.60664	0.803319	+	0.595548i	$0.203065\pi$
$192$	−1.27154e10	−0.675265
$193$	2.56834e10	1.33243	0.666216	−	0.745759i	$-0.267913\pi$
$193$	2.56834e10	1.33243	0.666216	+	0.745759i	$0.267913\pi$
$194$	−5.87469e8	−0.0297767
$195$	6.09481e9	0.301859
$196$	0	0
$197$	−2.49541e10	−1.18044	−0.590221	−	0.807242i	$-0.700959\pi$
$197$	−2.49541e10	−1.18044	−0.590221	+	0.807242i	$0.700959\pi$
$198$	6.42086e7	0.00296893
$199$	1.43726e10	0.649677	0.324839	−	0.945769i	$-0.394690\pi$
$199$	1.43726e10	0.649677	0.324839	+	0.945769i	$0.394690\pi$
$200$	−4.56462e9	−0.201729
$201$	1.20806e8	0.00522041
$202$	7.48331e9	0.316237
$203$	0	0
$204$	−1.18335e10	−0.478386
$205$	2.83560e9	0.112138
$206$	−2.48849e10	−0.962792
$207$	−1.22888e9	−0.0465204
$208$	−5.04365e8	−0.0186836
$209$	−1.56032e8	−0.00565661
$210$	0	0
$211$	1.40852e10	0.489208	0.244604	−	0.969623i	$-0.421342\pi$
$211$	1.40852e10	0.489208	0.244604	+	0.969623i	$0.421342\pi$
$212$	−5.84095e9	−0.198597
$213$	−1.45093e10	−0.482990
$214$	2.35280e10	0.766872
$215$	−2.02244e9	−0.0645508
$216$	−3.09421e10	−0.967181
$217$	0	0
$218$	−1.05257e10	−0.315644
$219$	3.24095e10	0.952081
$220$	5.90056e8	0.0169821
$221$	−1.75980e10	−0.496248
$222$	−3.50437e10	−0.968325
$223$	−6.09969e10	−1.65172	−0.825859	−	0.563877i	$-0.809309\pi$
$223$	−6.09969e10	−1.65172	−0.825859	+	0.563877i	$0.809309\pi$
$224$	0	0
$225$	5.78879e8	0.0150580
$226$	1.32408e10	0.337617
$227$	7.12988e10	1.78224	0.891119	−	0.453769i	$-0.149921\pi$
$227$	7.12988e10	1.78224	0.891119	+	0.453769i	$0.149921\pi$
$228$	−2.30801e9	−0.0565628
$229$	−2.21068e10	−0.531210	−0.265605	−	0.964082i	$-0.585572\pi$
$229$	−2.21068e10	−0.531210	−0.265605	+	0.964082i	$0.585572\pi$
$230$	7.36934e9	0.173641
$231$	0	0
$232$	−8.51592e10	−1.92990
$233$	4.27030e10	0.949198	0.474599	−	0.880202i	$-0.342593\pi$
$233$	4.27030e10	0.949198	0.474599	+	0.880202i	$0.342593\pi$
$234$	1.41243e9	0.0307960
$235$	−4.03133e9	−0.0862269
$236$	5.36497e10	1.12581
$237$	2.23529e9	0.0460222
$238$	0	0
$239$	2.61844e10	0.519101	0.259551	−	0.965730i	$-0.416426\pi$
$239$	2.61844e10	0.519101	0.259551	+	0.965730i	$0.416426\pi$
$240$	−6.84166e8	−0.0133110
$241$	−7.37691e10	−1.40863	−0.704317	−	0.709886i	$-0.748746\pi$
$241$	−7.37691e10	−1.40863	−0.704317	+	0.709886i	$0.748746\pi$
$242$	−3.33954e10	−0.625918
$243$	8.16757e9	0.150267
$244$	−2.98329e10	−0.538817
$245$	0	0
$246$	9.38509e9	0.163392
$247$	−3.43232e9	−0.0586747
$248$	2.75262e9	0.0462076
$249$	3.18614e10	0.525251
$250$	−3.47141e9	−0.0562051
$251$	−5.66878e10	−0.901484	−0.450742	−	0.892654i	$-0.648841\pi$
$251$	−5.66878e10	−0.901484	−0.450742	+	0.892654i	$0.648841\pi$
$252$	0	0
$253$	−2.52686e9	−0.0387739
$254$	−1.04444e10	−0.157447
$255$	−2.38715e10	−0.353549
$256$	−6.98565e10	−1.01655
$257$	−6.06404e10	−0.867088	−0.433544	−	0.901132i	$-0.642737\pi$
$257$	−6.06404e10	−0.867088	−0.433544	+	0.901132i	$0.642737\pi$
$258$	−6.69374e9	−0.0940547
$259$	0	0
$260$	1.29797e10	0.176151
$261$	1.07998e10	0.144056
$262$	−4.06458e9	−0.0532918
$263$	−1.39622e11	−1.79951	−0.899754	−	0.436397i	$-0.856254\pi$
$263$	−1.39622e11	−1.79951	−0.899754	+	0.436397i	$0.856254\pi$
$264$	5.18026e9	0.0656348
$265$	−1.17828e10	−0.146772
$266$	0	0
$267$	1.12284e9	0.0135213
$268$	2.57272e8	0.00304639
$269$	1.55947e11	1.81590	0.907950	−	0.419079i	$-0.137647\pi$
$269$	1.55947e11	1.81590	0.907950	+	0.419079i	$0.137647\pi$
$270$	−2.35316e10	−0.269472
$271$	−1.37528e11	−1.54892	−0.774458	−	0.632625i	$-0.781978\pi$
$271$	−1.37528e11	−1.54892	−0.774458	+	0.632625i	$0.781978\pi$
$272$	1.97544e9	0.0218829
$273$	0	0
$274$	−8.30705e10	−0.890368
$275$	1.19031e9	0.0125505
$276$	−3.73770e10	−0.387716
$277$	−7.55822e10	−0.771366	−0.385683	−	0.922631i	$-0.626034\pi$
$277$	−7.55822e10	−0.771366	−0.385683	+	0.922631i	$0.626034\pi$
$278$	−2.41513e10	−0.242516
$279$	−3.49083e8	−0.00344913
$280$	0	0
$281$	1.70202e11	1.62850	0.814249	−	0.580515i	$-0.197149\pi$
$281$	1.70202e11	1.62850	0.814249	+	0.580515i	$0.197149\pi$
$282$	−1.33427e10	−0.125638
$283$	9.81251e10	0.909371	0.454686	−	0.890652i	$-0.349752\pi$
$283$	9.81251e10	0.909371	0.454686	+	0.890652i	$0.349752\pi$
$284$	−3.08995e10	−0.281851
$285$	−4.65590e9	−0.0418025
$286$	2.90427e9	0.0256679
$287$	0	0
$288$	8.70774e9	0.0745829
$289$	−4.96618e10	−0.418776
$290$	−6.47640e10	−0.537703
$291$	6.01073e9	0.0491370
$292$	6.90204e10	0.555590
$293$	−1.77981e10	−0.141082	−0.0705408	−	0.997509i	$-0.522472\pi$
$293$	−1.77981e10	−0.141082	−0.0705408	+	0.997509i	$0.522472\pi$
$294$	0	0
$295$	1.08227e11	0.832023
$296$	−1.97961e11	−1.49888
$297$	8.06872e9	0.0601729
$298$	1.43707e11	1.05561
$299$	−5.55846e10	−0.402193
$300$	1.76069e10	0.125498
$301$	0	0
$302$	−8.44270e10	−0.584050
$303$	−7.65660e10	−0.521848
$304$	3.85290e8	0.00258736
$305$	−6.01813e10	−0.398210
$306$	−5.53204e9	−0.0360694
$307$	2.52234e11	1.62062	0.810308	−	0.586004i	$-0.199300\pi$
$307$	2.52234e11	1.62062	0.810308	+	0.586004i	$0.199300\pi$
$308$	0	0
$309$	2.54611e11	1.58878
$310$	2.09338e9	0.0128742
$311$	−1.71829e11	−1.04154	−0.520770	−	0.853697i	$-0.674355\pi$
$311$	−1.71829e11	−1.04154	−0.520770	+	0.853697i	$0.674355\pi$
$312$	1.13953e11	0.680815
$313$	2.71094e11	1.59651	0.798253	−	0.602322i	$-0.205758\pi$
$313$	2.71094e11	1.59651	0.798253	+	0.602322i	$0.205758\pi$
$314$	−1.59974e10	−0.0928678
$315$	0	0
$316$	4.76036e9	0.0268564
$317$	4.34647e10	0.241752	0.120876	−	0.992668i	$-0.461430\pi$
$317$	4.34647e10	0.241752	0.120876	+	0.992668i	$0.461430\pi$
$318$	−3.89982e10	−0.213856
$319$	2.22068e10	0.120068
$320$	−5.46262e10	−0.291223
$321$	−2.40728e11	−1.26548
$322$	0	0
$323$	1.34433e10	0.0687220
$324$	1.28389e11	0.647252
$325$	2.61838e10	0.130184
$326$	1.53851e11	0.754434
$327$	1.07695e11	0.520870
$328$	5.30162e10	0.252916
$329$	0	0
$330$	3.93961e9	0.0182869
$331$	−3.32864e11	−1.52420	−0.762098	−	0.647461i	$-0.775831\pi$
$331$	−3.32864e11	−1.52420	−0.762098	+	0.647461i	$0.775831\pi$
$332$	6.78531e10	0.306512
$333$	2.51052e10	0.111883
$334$	3.06084e10	0.134580
$335$	5.18990e8	0.00225142
$336$	0	0
$337$	−2.14358e11	−0.905327	−0.452663	−	0.891681i	$-0.649526\pi$
$337$	−2.14358e11	−0.905327	−0.452663	+	0.891681i	$0.649526\pi$
$338$	−8.68977e10	−0.362145
$339$	−1.35474e11	−0.557130
$340$	−5.08377e10	−0.206315
$341$	−7.17795e8	−0.00287479
$342$	−1.07897e9	−0.00426473
$343$	0	0
$344$	−3.78128e10	−0.145588
$345$	−7.53999e10	−0.286540
$346$	−1.89402e11	−0.710466
$347$	3.24293e11	1.20075	0.600377	−	0.799717i	$-0.295017\pi$
$347$	3.24293e11	1.20075	0.600377	+	0.799717i	$0.295017\pi$
$348$	3.28480e11	1.20061
$349$	3.22203e11	1.16256	0.581279	−	0.813704i	$-0.302552\pi$
$349$	3.22203e11	1.16256	0.581279	+	0.813704i	$0.302552\pi$
$350$	0	0
$351$	1.77491e11	0.624159
$352$	1.79051e10	0.0621634
$353$	−2.14305e11	−0.734591	−0.367296	−	0.930104i	$-0.619716\pi$
$353$	−2.14305e11	−0.734591	−0.367296	+	0.930104i	$0.619716\pi$
$354$	3.58202e11	1.21231
$355$	−6.23330e10	−0.208301
$356$	2.39125e9	0.00789041
$357$	0	0
$358$	−2.67197e10	−0.0859721
$359$	2.99291e11	0.950973	0.475487	−	0.879723i	$-0.342272\pi$
$359$	2.99291e11	0.950973	0.475487	+	0.879723i	$0.342272\pi$
$360$	1.08231e10	0.0339618
$361$	−3.20066e11	−0.991875
$362$	−2.64835e10	−0.0810563
$363$	3.41687e11	1.03288
$364$	0	0
$365$	1.39234e11	0.410607
$366$	−1.99185e11	−0.580218
$367$	2.26354e11	0.651313	0.325657	−	0.945488i	$-0.394415\pi$
$367$	2.26354e11	0.651313	0.325657	+	0.945488i	$0.394415\pi$
$368$	6.23958e9	0.0177354
$369$	−6.72345e9	−0.0188788
$370$	−1.50550e11	−0.417613
$371$	0	0
$372$	−1.06175e10	−0.0287462
$373$	1.49101e11	0.398834	0.199417	−	0.979915i	$-0.436095\pi$
$373$	1.49101e11	0.398834	0.199417	+	0.979915i	$0.436095\pi$
$374$	−1.13752e10	−0.0300632
$375$	3.55180e10	0.0927487
$376$	−7.53724e10	−0.194476
$377$	4.88494e11	1.24544
$378$	0	0
$379$	−1.37752e8	−0.000342943 0	−0.000171472	−	1.00000i	$-0.500055\pi$
$379$	−1.37752e8	−0.000342943 0	−0.000171472		1.00000i	$0.500055\pi$
$380$	−9.91537e9	−0.0243940
$381$	1.06863e11	0.259816
$382$	4.20179e11	1.00960
$383$	1.86906e11	0.443842	0.221921	−	0.975065i	$-0.428767\pi$
$383$	1.86906e11	0.443842	0.221921	+	0.975065i	$0.428767\pi$
$384$	2.56881e11	0.602894
$385$	0	0
$386$	3.65190e11	0.837290
$387$	4.79537e9	0.0108673
$388$	1.28007e10	0.0286741
$389$	3.59779e11	0.796640	0.398320	−	0.917246i	$-0.369593\pi$
$389$	3.59779e11	0.796640	0.398320	+	0.917246i	$0.369593\pi$
$390$	8.66615e10	0.189686
$391$	2.17708e11	0.471063
$392$	0	0
$393$	4.15871e10	0.0879411
$394$	−3.54821e11	−0.741781
$395$	9.60298e9	0.0198481
$396$	−1.39907e9	−0.00285899
$397$	6.18525e11	1.24968	0.624842	−	0.780751i	$-0.285163\pi$
$397$	6.18525e11	1.24968	0.624842	+	0.780751i	$0.285163\pi$
$398$	2.04363e11	0.408252
$399$	0	0
$400$	−2.93923e9	−0.00574067
$401$	−7.66178e11	−1.47972	−0.739861	−	0.672760i	$-0.765109\pi$
$401$	−7.66178e11	−1.47972	−0.739861	+	0.672760i	$0.765109\pi$
$402$	1.71772e9	0.00328047
$403$	−1.57897e10	−0.0298195
$404$	−1.63058e11	−0.304526
$405$	2.58996e11	0.478349
$406$	0	0
$407$	5.16220e10	0.0932524
$408$	−4.46318e11	−0.797396
$409$	9.59126e11	1.69481	0.847404	−	0.530948i	$-0.178164\pi$
$409$	9.59126e11	1.69481	0.847404	+	0.530948i	$0.178164\pi$
$410$	4.03190e10	0.0704665
$411$	8.49942e11	1.46927
$412$	5.42229e11	0.927140
$413$	0	0
$414$	−1.74733e10	−0.0292331
$415$	1.36879e11	0.226527
$416$	3.93867e11	0.644807
$417$	2.47106e11	0.400195
$418$	−2.21861e9	−0.00355457
$419$	1.06964e12	1.69541	0.847707	−	0.530464i	$-0.177982\pi$
$419$	1.06964e12	1.69541	0.847707	+	0.530464i	$0.177982\pi$
$420$	0	0
$421$	1.13045e10	0.0175380	0.00876900	−	0.999962i	$-0.497209\pi$
$421$	1.13045e10	0.0175380	0.00876900	+	0.999962i	$0.497209\pi$
$422$	2.00277e11	0.307415
$423$	9.55863e9	0.0145166
$424$	−2.20300e11	−0.331030
$425$	−1.02554e11	−0.152476
$426$	−2.06306e11	−0.303507
$427$	0	0
$428$	−5.12664e11	−0.738475
$429$	−2.97153e10	−0.0423567
$430$	−2.87568e10	−0.0405632
$431$	−1.07684e12	−1.50315	−0.751576	−	0.659647i	$-0.770706\pi$
$431$	−1.07684e12	−1.50315	−0.751576	+	0.659647i	$0.770706\pi$
$432$	−1.99241e10	−0.0275234
$433$	−3.64149e11	−0.497832	−0.248916	−	0.968525i	$-0.580074\pi$
$433$	−3.64149e11	−0.497832	−0.248916	+	0.968525i	$0.580074\pi$
$434$	0	0
$435$	6.62637e11	0.887308
$436$	2.29350e11	0.303956
$437$	4.24617e10	0.0556969
$438$	4.60827e11	0.598280
$439$	−6.94204e11	−0.892066	−0.446033	−	0.895017i	$-0.647164\pi$
$439$	−6.94204e11	−0.892066	−0.446033	+	0.895017i	$0.647164\pi$
$440$	2.22548e10	0.0283065
$441$	0	0
$442$	−2.50225e11	−0.311838
$443$	−5.15843e11	−0.636357	−0.318178	−	0.948031i	$-0.603071\pi$
$443$	−5.15843e11	−0.636357	−0.318178	+	0.948031i	$0.603071\pi$
$444$	7.63585e11	0.932468
$445$	4.82382e9	0.00583137
$446$	−8.67309e11	−1.03793
$447$	−1.47035e12	−1.74195
$448$	0	0
$449$	3.19581e11	0.371084	0.185542	−	0.982636i	$-0.440596\pi$
$449$	3.19581e11	0.371084	0.185542	+	0.982636i	$0.440596\pi$
$450$	8.23102e9	0.00946231
$451$	−1.38249e10	−0.0157351
$452$	−2.88510e11	−0.325115
$453$	8.63821e11	0.963788
$454$	1.01379e12	1.11995
$455$	0	0
$456$	−8.70499e10	−0.0942815
$457$	−1.15689e12	−1.24071	−0.620354	−	0.784322i	$-0.713011\pi$
$457$	−1.15689e12	−1.24071	−0.620354	+	0.784322i	$0.713011\pi$
$458$	−3.14334e11	−0.333808
$459$	−6.95180e11	−0.731038
$460$	−1.60574e11	−0.167211
$461$	−3.60114e11	−0.371352	−0.185676	−	0.982611i	$-0.559447\pi$
$461$	−3.60114e11	−0.371352	−0.185676	+	0.982611i	$0.559447\pi$
$462$	0	0
$463$	−1.37722e12	−1.39280	−0.696402	−	0.717652i	$-0.745217\pi$
$463$	−1.37722e12	−1.39280	−0.696402	+	0.717652i	$0.745217\pi$
$464$	−5.48353e10	−0.0549199
$465$	−2.14185e10	−0.0212447
$466$	6.07189e11	0.596469
$467$	7.87091e10	0.0765772	0.0382886	−	0.999267i	$-0.487809\pi$
$467$	7.87091e10	0.0765772	0.0382886	+	0.999267i	$0.487809\pi$
$468$	−3.07761e10	−0.0296556
$469$	0	0
$470$	−5.73210e10	−0.0541843
$471$	1.63678e11	0.153249
$472$	2.02348e12	1.87655
$473$	9.86039e9	0.00905772
$474$	3.17834e10	0.0289200
$475$	−2.00021e10	−0.0180283
$476$	0	0
$477$	2.79381e10	0.0247095
$478$	3.72313e11	0.326199
$479$	−1.03512e12	−0.898426	−0.449213	−	0.893425i	$-0.648296\pi$
$479$	−1.03512e12	−0.898426	−0.449213	+	0.893425i	$0.648296\pi$
$480$	5.34277e11	0.459389
$481$	1.13555e12	0.967285
$482$	−1.04892e12	−0.885175
$483$	0	0
$484$	7.27669e11	0.602740
$485$	2.58225e10	0.0211915
$486$	1.16134e11	0.0944268
$487$	−4.54585e11	−0.366214	−0.183107	−	0.983093i	$-0.558615\pi$
$487$	−4.54585e11	−0.366214	−0.183107	+	0.983093i	$0.558615\pi$
$488$	−1.12519e12	−0.898125
$489$	−1.57414e12	−1.24495
$490$	0	0
$491$	−3.19689e11	−0.248234	−0.124117	−	0.992268i	$-0.539610\pi$
$491$	−3.19689e11	−0.248234	−0.124117	+	0.992268i	$0.539610\pi$
$492$	−2.04497e11	−0.157341
$493$	−1.91328e12	−1.45871
$494$	−4.88038e10	−0.0368708
$495$	−2.82232e9	−0.00211292
$496$	1.77245e9	0.00131494
$497$	0	0
$498$	4.53033e11	0.330064
$499$	1.53580e11	0.110887	0.0554435	−	0.998462i	$-0.482343\pi$
$499$	1.53580e11	0.110887	0.0554435	+	0.998462i	$0.482343\pi$
$500$	7.56404e10	0.0541238
$501$	−3.13172e11	−0.222082
$502$	−8.06038e11	−0.566486
$503$	−1.03951e12	−0.724056	−0.362028	−	0.932167i	$-0.617915\pi$
$503$	−1.03951e12	−0.724056	−0.362028	+	0.932167i	$0.617915\pi$
$504$	0	0
$505$	−3.28933e11	−0.225059
$506$	−3.59292e10	−0.0243652
$507$	8.89100e11	0.597606
$508$	2.27579e11	0.151616
$509$	−1.99303e12	−1.31608	−0.658042	−	0.752981i	$-0.728615\pi$
$509$	−1.99303e12	−1.31608	−0.658042	+	0.752981i	$0.728615\pi$
$510$	−3.39427e11	−0.222167
$511$	0	0
$512$	−8.92311e10	−0.0573854
$513$	−1.35588e11	−0.0864356
$514$	−8.62240e11	−0.544872
$515$	1.09383e12	0.685199
$516$	1.45853e11	0.0905718
$517$	1.96547e10	0.0120993
$518$	0	0
$519$	1.93789e12	1.17240
$520$	4.89549e11	0.293617
$521$	−1.23517e12	−0.734444	−0.367222	−	0.930133i	$-0.619691\pi$
$521$	−1.23517e12	−0.734444	−0.367222	+	0.930133i	$0.619691\pi$
$522$	1.53561e11	0.0905240
$523$	1.36296e12	0.796572	0.398286	−	0.917261i	$-0.369605\pi$
$523$	1.36296e12	0.796572	0.398286	+	0.917261i	$0.369605\pi$
$524$	8.85653e10	0.0513183
$525$	0	0
$526$	−1.98528e12	−1.13080
$527$	6.18434e10	0.0349257
$528$	3.33565e9	0.00186779
$529$	−1.11351e12	−0.618219
$530$	−1.67539e11	−0.0922305
$531$	−2.56615e11	−0.140074
$532$	0	0
$533$	−3.04114e11	−0.163216
$534$	1.59656e10	0.00849669
$535$	−1.03419e12	−0.545767
$536$	9.70338e9	0.00507787
$537$	2.73384e11	0.141870
$538$	2.21739e12	1.14110
$539$	0	0
$540$	5.12742e11	0.259494
$541$	1.23521e12	0.619944	0.309972	−	0.950746i	$-0.399680\pi$
$541$	1.23521e12	0.619944	0.309972	+	0.950746i	$0.399680\pi$
$542$	−1.95549e12	−0.973328
$543$	2.70968e11	0.133758
$544$	−1.54266e12	−0.755222
$545$	4.62664e11	0.224637
$546$	0	0
$547$	3.11783e12	1.48905	0.744525	−	0.667594i	$-0.232676\pi$
$547$	3.11783e12	1.48905	0.744525	+	0.667594i	$0.232676\pi$
$548$	1.81007e12	0.857397
$549$	1.42695e11	0.0670400
$550$	1.69249e10	0.00788666
$551$	−3.73167e11	−0.172473
$552$	−1.40973e12	−0.646263
$553$	0	0
$554$	−1.07470e12	−0.484721
$555$	1.54037e12	0.689137
$556$	5.26246e11	0.233535
$557$	−3.07379e12	−1.35309	−0.676544	−	0.736402i	$-0.736523\pi$
$557$	−3.07379e12	−1.35309	−0.676544	+	0.736402i	$0.736523\pi$
$558$	−4.96358e9	−0.00216741
$559$	2.16904e11	0.0939536
$560$	0	0
$561$	1.16386e11	0.0496097
$562$	2.42009e12	1.02334
$563$	−4.57752e12	−1.92018	−0.960092	−	0.279685i	$-0.909770\pi$
$563$	−4.57752e12	−1.92018	−0.960092	+	0.279685i	$0.909770\pi$
$564$	2.90730e11	0.120986
$565$	−5.82005e11	−0.240275
$566$	1.39523e12	0.571442
$567$	0	0
$568$	−1.16542e12	−0.469802
$569$	4.09281e12	1.63688	0.818439	−	0.574593i	$-0.194840\pi$
$569$	4.09281e12	1.63688	0.818439	+	0.574593i	$0.194840\pi$
$570$	−6.62018e10	−0.0262684
$571$	6.05625e11	0.238419	0.119210	−	0.992869i	$-0.461964\pi$
$571$	6.05625e11	0.238419	0.119210	+	0.992869i	$0.461964\pi$
$572$	−6.32827e10	−0.0247174
$573$	−4.29909e12	−1.66602
$574$	0	0
$575$	−3.23923e11	−0.123577
$576$	1.29524e11	0.0490284
$577$	−3.79815e12	−1.42653	−0.713264	−	0.700895i	$-0.752784\pi$
$577$	−3.79815e12	−1.42653	−0.713264	+	0.700895i	$0.752784\pi$
$578$	−7.06135e11	−0.263156
$579$	−3.73647e12	−1.38168
$580$	1.41118e12	0.517792
$581$	0	0
$582$	8.54659e10	0.0308773
$583$	5.74472e10	0.0205949
$584$	2.60320e12	0.926084
$585$	−6.20840e10	−0.0219169
$586$	−2.53070e11	−0.0886546
$587$	−2.98554e12	−1.03789	−0.518946	−	0.854807i	$-0.673675\pi$
$587$	−2.98554e12	−1.03789	−0.518946	+	0.854807i	$0.673675\pi$
$588$	0	0
$589$	1.20619e10	0.00412950
$590$	1.53886e12	0.522837
$591$	3.63037e12	1.22407
$592$	−1.27470e11	−0.0426541
$593$	3.67544e12	1.22057	0.610285	−	0.792182i	$-0.291055\pi$
$593$	3.67544e12	1.22057	0.610285	+	0.792182i	$0.291055\pi$
$594$	1.14728e11	0.0378122
$595$	0	0
$596$	−3.13130e12	−1.01652
$597$	−2.09096e12	−0.673691
$598$	−7.90352e11	−0.252735
$599$	−3.77319e12	−1.19753	−0.598767	−	0.800923i	$-0.704342\pi$
$599$	−3.77319e12	−1.19753	−0.598767	+	0.800923i	$0.704342\pi$
$600$	6.64068e11	0.209186
$601$	−4.65341e12	−1.45491	−0.727455	−	0.686156i	$-0.759297\pi$
$601$	−4.65341e12	−1.45491	−0.727455	+	0.686156i	$0.759297\pi$
$602$	0	0
$603$	−1.23057e9	−0.000379034 0
$604$	1.83962e12	0.562422
$605$	1.46791e12	0.445453
$606$	−1.08868e12	−0.327926
$607$	−1.19001e12	−0.355795	−0.177898	−	0.984049i	$-0.556930\pi$
$607$	−1.19001e12	−0.355795	−0.177898	+	0.984049i	$0.556930\pi$
$608$	−3.00880e11	−0.0892950
$609$	0	0
$610$	−8.55712e11	−0.250232
$611$	4.32355e11	0.125503
$612$	1.20541e11	0.0347338
$613$	−1.22351e12	−0.349974	−0.174987	−	0.984571i	$-0.555988\pi$
$613$	−1.22351e12	−0.349974	−0.174987	+	0.984571i	$0.555988\pi$
$614$	3.58648e12	1.01838
$615$	−4.12527e11	−0.116283
$616$	0	0
$617$	−5.57232e10	−0.0154794	−0.00773968	−	0.999970i	$-0.502464\pi$
$617$	−5.57232e10	−0.0154794	−0.00773968	+	0.999970i	$0.502464\pi$
$618$	3.62029e12	0.998379
$619$	−3.96796e12	−1.08632	−0.543162	−	0.839628i	$-0.682773\pi$
$619$	−3.96796e12	−1.08632	−0.543162	+	0.839628i	$0.682773\pi$
$620$	−4.56137e10	−0.0123974
$621$	−2.19577e12	−0.592482
$622$	−2.44323e12	−0.654496
$623$	0	0
$624$	7.33759e10	0.0193741
$625$	1.52588e11	0.0400000
$626$	3.85466e12	1.00323
$627$	2.26999e10	0.00586569
$628$	3.48575e11	0.0894289
$629$	−4.44762e12	−1.13292
$630$	0	0
$631$	−6.59314e12	−1.65562	−0.827809	−	0.561011i	$-0.810413\pi$
$631$	−6.59314e12	−1.65562	−0.827809	+	0.561011i	$0.810413\pi$
$632$	1.79544e11	0.0447655
$633$	−2.04915e12	−0.507290
$634$	6.18019e11	0.151915
$635$	4.59091e11	0.112051
$636$	8.49751e11	0.205937
$637$	0	0
$638$	3.15757e11	0.0754501
$639$	1.47797e11	0.0350681
$640$	1.10358e12	0.260012
$641$	−2.43610e12	−0.569947	−0.284973	−	0.958535i	$-0.591985\pi$
$641$	−2.43610e12	−0.569947	−0.284973	+	0.958535i	$0.591985\pi$
$642$	−3.42289e12	−0.795217
$643$	4.53115e12	1.04534	0.522672	−	0.852534i	$-0.324935\pi$
$643$	4.53115e12	1.04534	0.522672	+	0.852534i	$0.324935\pi$
$644$	0	0
$645$	2.94227e11	0.0669367
$646$	1.91150e11	0.0431844
$647$	−1.94277e10	−0.00435865	−0.00217932	−	0.999998i	$-0.500694\pi$
$647$	−1.94277e10	−0.00435865	−0.00217932	+	0.999998i	$0.500694\pi$
$648$	4.84236e12	1.07887
$649$	−5.27659e11	−0.116749
$650$	3.72304e11	0.0818065
$651$	0	0
$652$	−3.35234e12	−0.726497
$653$	4.89742e12	1.05404	0.527021	−	0.849852i	$-0.323309\pi$
$653$	4.89742e12	1.05404	0.527021	+	0.849852i	$0.323309\pi$
$654$	1.53130e12	0.327311
$655$	1.78661e11	0.0379266
$656$	3.41379e10	0.00719730
$657$	−3.30135e11	−0.0691269
$658$	0	0
$659$	1.90161e12	0.392768	0.196384	−	0.980527i	$-0.437080\pi$
$659$	1.90161e12	0.392768	0.196384	+	0.980527i	$0.437080\pi$
$660$	−8.58423e10	−0.0176098
$661$	8.99572e12	1.83286	0.916430	−	0.400196i	$-0.131058\pi$
$661$	8.99572e12	1.83286	0.916430	+	0.400196i	$0.131058\pi$
$662$	−4.73296e12	−0.957794
$663$	2.56019e12	0.514590
$664$	2.55918e12	0.510909
$665$	0	0
$666$	3.56968e11	0.0703064
$667$	−6.04324e12	−1.18223
$668$	−6.66942e11	−0.129597
$669$	8.87393e12	1.71277
$670$	7.37946e9	0.00141478
$671$	2.93414e11	0.0558766
$672$	0	0
$673$	3.47509e12	0.652977	0.326489	−	0.945201i	$-0.394135\pi$
$673$	3.47509e12	0.652977	0.326489	+	0.945201i	$0.394135\pi$
$674$	−3.04794e12	−0.568901
$675$	1.03434e12	0.191778
$676$	1.89346e12	0.348735
$677$	−3.14898e12	−0.576130	−0.288065	−	0.957611i	$-0.593012\pi$
$677$	−3.14898e12	−0.576130	−0.288065	+	0.957611i	$0.593012\pi$
$678$	−1.92629e12	−0.350096
$679$	0	0
$680$	−1.91742e12	−0.343895
$681$	−1.03727e13	−1.84811
$682$	−1.02063e10	−0.00180650
$683$	−4.88179e12	−0.858392	−0.429196	−	0.903211i	$-0.641203\pi$
$683$	−4.88179e12	−0.858392	−0.429196	+	0.903211i	$0.641203\pi$
$684$	2.35102e10	0.00410681
$685$	3.65141e12	0.633656
$686$	0	0
$687$	3.21613e12	0.550844
$688$	−2.43482e10	−0.00414304
$689$	1.26369e12	0.213627
$690$	−1.07210e12	−0.180059
$691$	−9.58720e12	−1.59971	−0.799854	−	0.600195i	$-0.795090\pi$
$691$	−9.58720e12	−1.59971	−0.799854	+	0.600195i	$0.795090\pi$
$692$	4.12699e12	0.684157
$693$	0	0
$694$	4.61108e12	0.754545
$695$	1.06159e12	0.172593
$696$	1.23891e13	2.00124
$697$	1.19112e12	0.191165
$698$	4.58137e12	0.730543
$699$	−6.21250e12	−0.984282
$700$	0	0
$701$	−8.76308e12	−1.37065	−0.685324	−	0.728238i	$-0.740339\pi$
$701$	−8.76308e12	−1.37065	−0.685324	+	0.728238i	$0.740339\pi$
$702$	2.52373e12	0.392217
$703$	−8.67463e11	−0.133953
$704$	2.66330e11	0.0408642
$705$	5.86484e11	0.0894140
$706$	−3.04718e12	−0.461612
$707$	0	0
$708$	−7.80506e12	−1.16742
$709$	−7.45035e12	−1.10731	−0.553654	−	0.832747i	$-0.686767\pi$
$709$	−7.45035e12	−1.10731	−0.553654	+	0.832747i	$0.686767\pi$
$710$	−8.86307e11	−0.130895
$711$	−2.27695e10	−0.00334149
$712$	9.01893e10	0.0131521
$713$	1.95337e11	0.0283061
$714$	0	0
$715$	−1.27659e11	−0.0182673
$716$	5.82208e11	0.0827885
$717$	−3.80935e12	−0.538288
$718$	4.25558e12	0.597584
$719$	−1.06434e13	−1.48526	−0.742629	−	0.669703i	$-0.766421\pi$
$719$	−1.06434e13	−1.48526	−0.742629	+	0.669703i	$0.766421\pi$
$720$	6.96916e9	0.000966461 0
$721$	0	0
$722$	−4.55098e12	−0.623286
$723$	1.07321e13	1.46070
$724$	5.77063e11	0.0780548
$725$	2.84674e12	0.382672
$726$	4.85842e12	0.649053
$727$	5.23781e12	0.695417	0.347708	−	0.937603i	$-0.386960\pi$
$727$	5.23781e12	0.695417	0.347708	+	0.937603i	$0.386960\pi$
$728$	0	0
$729$	6.96827e12	0.913800
$730$	1.97975e12	0.258022
$731$	−8.49545e11	−0.110042
$732$	4.34014e12	0.558733
$733$	2.02400e11	0.0258966	0.0129483	−	0.999916i	$-0.495878\pi$
$733$	2.02400e11	0.0258966	0.0129483	+	0.999916i	$0.495878\pi$
$734$	3.21850e12	0.409280
$735$	0	0
$736$	−4.87259e12	−0.612082
$737$	−2.53034e9	−0.000315918 0
$738$	−9.56000e10	−0.0118633
$739$	−7.60490e12	−0.937980	−0.468990	−	0.883204i	$-0.655382\pi$
$739$	−7.60490e12	−0.937980	−0.468990	+	0.883204i	$0.655382\pi$
$740$	3.28042e12	0.402148
$741$	4.99339e11	0.0608435
$742$	0	0
$743$	7.81025e12	0.940189	0.470095	−	0.882616i	$-0.344220\pi$
$743$	7.81025e12	0.940189	0.470095	+	0.882616i	$0.344220\pi$
$744$	−4.00455e11	−0.0479155
$745$	−6.31672e12	−0.751257
$746$	2.12006e12	0.250624
$747$	−3.24551e11	−0.0381365
$748$	2.47859e11	0.0289499
$749$	0	0
$750$	5.05027e11	0.0582826
$751$	−1.27518e13	−1.46282	−0.731412	−	0.681936i	$-0.761138\pi$
$751$	−1.27518e13	−1.46282	−0.731412	+	0.681936i	$0.761138\pi$
$752$	−4.85334e10	−0.00553427
$753$	8.24704e12	0.934805
$754$	6.94585e12	0.782626
$755$	3.71104e12	0.415656
$756$	0	0
$757$	8.99962e12	0.996076	0.498038	−	0.867155i	$-0.334054\pi$
$757$	8.99962e12	0.996076	0.498038	+	0.867155i	$0.334054\pi$
$758$	−1.95869e9	−0.000215503 0
$759$	3.67612e11	0.0402070
$760$	−3.73972e11	−0.0406610
$761$	−6.18645e12	−0.668668	−0.334334	−	0.942455i	$-0.608511\pi$
$761$	−6.18645e12	−0.668668	−0.334334	+	0.942455i	$0.608511\pi$
$762$	1.51947e12	0.163266
$763$	0	0
$764$	−9.15550e12	−0.972214
$765$	2.43164e11	0.0256698
$766$	2.65760e12	0.278907
$767$	−1.16072e13	−1.21101
$768$	1.01628e13	1.05412
$769$	4.93796e12	0.509189	0.254594	−	0.967048i	$-0.418058\pi$
$769$	4.93796e12	0.509189	0.254594	+	0.967048i	$0.418058\pi$
$770$	0	0
$771$	8.82208e12	0.899138
$772$	−7.95731e12	−0.806285
$773$	−1.49263e13	−1.50365	−0.751823	−	0.659366i	$-0.770825\pi$
$773$	−1.49263e13	−1.50365	−0.751823	+	0.659366i	$0.770825\pi$
$774$	6.81849e10	0.00682895
$775$	−9.20156e10	−0.00916228
$776$	4.82795e11	0.0477953
$777$	0	0
$778$	5.11566e12	0.500603
$779$	2.32316e11	0.0226027
$780$	−1.88831e12	−0.182662
$781$	3.03905e11	0.0292286
$782$	3.09557e12	0.296012
$783$	1.92971e13	1.83470
$784$	0	0
$785$	7.03174e11	0.0660921
$786$	5.91322e11	0.0552615
$787$	−2.09196e12	−0.194387	−0.0971933	−	0.995266i	$-0.530987\pi$
$787$	−2.09196e12	−0.194387	−0.0971933	+	0.995266i	$0.530987\pi$
$788$	7.73137e12	0.714313
$789$	2.03125e13	1.86602
$790$	1.36544e11	0.0124724
$791$	0	0
$792$	−5.27681e10	−0.00476549
$793$	6.45437e12	0.579595
$794$	8.79475e12	0.785292
$795$	1.71419e12	0.152197
$796$	−4.45297e12	−0.393135
$797$	−5.38220e12	−0.472495	−0.236248	−	0.971693i	$-0.575918\pi$
$797$	−5.38220e12	−0.472495	−0.236248	+	0.971693i	$0.575918\pi$
$798$	0	0
$799$	−1.69340e12	−0.146994
$800$	2.29529e12	0.198122
$801$	−1.14377e10	−0.000981731 0
$802$	−1.08942e13	−0.929846
$803$	−6.78833e11	−0.0576160
$804$	−3.74284e10	−0.00315899
$805$	0	0
$806$	−2.24512e11	−0.0187384
$807$	−2.26874e13	−1.88302
$808$	−6.14995e12	−0.507599
$809$	1.22280e13	1.00366	0.501832	−	0.864965i	$-0.332660\pi$
$809$	1.22280e13	1.00366	0.501832	+	0.864965i	$0.332660\pi$
$810$	3.68263e12	0.300591
$811$	1.20686e13	0.979629	0.489815	−	0.871827i	$-0.337064\pi$
$811$	1.20686e13	0.979629	0.489815	+	0.871827i	$0.337064\pi$
$812$	0	0
$813$	2.00078e13	1.60617
$814$	7.34008e11	0.0585991
$815$	−6.76261e12	−0.536915
$816$	−2.87391e11	−0.0226917
$817$	−1.65695e11	−0.0130110
$818$	1.36377e13	1.06500
$819$	0	0
$820$	−8.78532e11	−0.0678571
$821$	−3.22207e12	−0.247509	−0.123754	−	0.992313i	$-0.539493\pi$
$821$	−3.22207e12	−0.247509	−0.123754	+	0.992313i	$0.539493\pi$
$822$	1.20852e13	0.923277
$823$	1.90497e13	1.44740	0.723702	−	0.690113i	$-0.242439\pi$
$823$	1.90497e13	1.44740	0.723702	+	0.690113i	$0.242439\pi$
$824$	2.04509e13	1.54540
$825$	−1.73168e11	−0.0130144
$826$	0	0
$827$	4.51813e12	0.335880	0.167940	−	0.985797i	$-0.446289\pi$
$827$	4.51813e12	0.335880	0.167940	+	0.985797i	$0.446289\pi$
$828$	3.80736e11	0.0281506
$829$	−1.54856e13	−1.13876	−0.569380	−	0.822074i	$-0.692817\pi$
$829$	−1.54856e13	−1.13876	−0.569380	+	0.822074i	$0.692817\pi$
$830$	1.94626e12	0.142348
$831$	1.09958e13	0.799877
$832$	5.85859e12	0.423875
$833$	0	0
$834$	3.51358e12	0.251479
$835$	−1.34541e12	−0.0957779
$836$	4.83424e10	0.00342295
$837$	−6.23744e11	−0.0439281
$838$	1.52092e13	1.06539
$839$	−1.30090e13	−0.906390	−0.453195	−	0.891411i	$-0.649716\pi$
$839$	−1.30090e13	−0.906390	−0.453195	+	0.891411i	$0.649716\pi$
$840$	0	0
$841$	3.86027e13	2.66094
$842$	1.60737e11	0.0110207
$843$	−2.47613e13	−1.68869
$844$	−4.36393e12	−0.296031
$845$	3.81964e12	0.257731
$846$	1.35913e11	0.00912210
$847$	0	0
$848$	−1.41854e11	−0.00942023
$849$	−1.42754e13	−0.942983
$850$	−1.45820e12	−0.0958148
$851$	−1.40481e13	−0.918195
$852$	4.49531e12	0.292268
$853$	−1.05756e13	−0.683964	−0.341982	−	0.939706i	$-0.611098\pi$
$853$	−1.05756e13	−0.683964	−0.341982	+	0.939706i	$0.611098\pi$
$854$	0	0
$855$	4.74267e10	0.00303512
$856$	−1.93358e13	−1.23092
$857$	2.80237e13	1.77465	0.887323	−	0.461149i	$-0.152563\pi$
$857$	2.80237e13	1.77465	0.887323	+	0.461149i	$0.152563\pi$
$858$	−4.22518e11	−0.0266166
$859$	−1.66570e13	−1.04382	−0.521912	−	0.852999i	$-0.674781\pi$
$859$	−1.66570e13	−1.04382	−0.521912	+	0.852999i	$0.674781\pi$
$860$	6.26597e11	0.0390612
$861$	0	0
$862$	−1.53115e13	−0.944569
$863$	6.58663e12	0.404217	0.202109	−	0.979363i	$-0.435221\pi$
$863$	6.58663e12	0.404217	0.202109	+	0.979363i	$0.435221\pi$
$864$	1.55590e13	0.949885
$865$	8.32529e12	0.505623
$866$	−5.17779e12	−0.312834
$867$	7.22488e12	0.434255
$868$	0	0
$869$	−4.68193e10	−0.00278507
$870$	9.42197e12	0.557577
$871$	−5.56610e10	−0.00327694
$872$	8.65028e12	0.506648
$873$	−6.12275e10	−0.00356765
$874$	6.03759e11	0.0349995
$875$	0	0
$876$	−1.00412e13	−0.576126
$877$	−1.98607e12	−0.113369	−0.0566847	−	0.998392i	$-0.518053\pi$
$877$	−1.98607e12	−0.113369	−0.0566847	+	0.998392i	$0.518053\pi$
$878$	−9.87082e12	−0.560568
$879$	2.58930e12	0.146296
$880$	1.43302e10	0.000805527 0
$881$	−2.94431e13	−1.64662	−0.823308	−	0.567595i	$-0.807874\pi$
$881$	−2.94431e13	−1.64662	−0.823308	+	0.567595i	$0.807874\pi$
$882$	0	0
$883$	2.03034e13	1.12395	0.561973	−	0.827156i	$-0.310043\pi$
$883$	2.03034e13	1.12395	0.561973	+	0.827156i	$0.310043\pi$
$884$	5.45227e12	0.300291
$885$	−1.57450e13	−0.862776
$886$	−7.33472e12	−0.399882
$887$	−1.55384e13	−0.842851	−0.421426	−	0.906863i	$-0.638470\pi$
$887$	−1.55384e13	−0.842851	−0.421426	+	0.906863i	$0.638470\pi$
$888$	2.87997e13	1.55428
$889$	0	0
$890$	6.85894e10	0.00366439
$891$	−1.26273e12	−0.0671216
$892$	1.88982e13	0.999492
$893$	−3.30281e11	−0.0173801
$894$	−2.09067e13	−1.09463
$895$	1.17448e12	0.0611845
$896$	0	0
$897$	8.08654e12	0.417058
$898$	4.54408e12	0.233186
$899$	−1.71668e12	−0.0876537
$900$	−1.79350e11	−0.00911192
$901$	−4.94951e12	−0.250207
$902$	−1.96576e11	−0.00988781
$903$	0	0
$904$	−1.08816e13	−0.541918
$905$	1.16410e12	0.0576860
$906$	1.22826e13	0.605637
$907$	3.47876e12	0.170684	0.0853419	−	0.996352i	$-0.472802\pi$
$907$	3.47876e12	0.170684	0.0853419	+	0.996352i	$0.472802\pi$
$908$	−2.20900e13	−1.07847
$909$	7.79929e11	0.0378894
$910$	0	0
$911$	1.97042e13	0.947820	0.473910	−	0.880573i	$-0.342842\pi$
$911$	1.97042e13	0.947820	0.473910	+	0.880573i	$0.342842\pi$
$912$	−5.60527e10	−0.00268300
$913$	−6.67352e11	−0.0317861
$914$	−1.64497e13	−0.779652
$915$	8.75529e12	0.412929
$916$	6.84919e12	0.321447
$917$	0	0
$918$	−9.88469e12	−0.459379
$919$	−4.10432e13	−1.89811	−0.949055	−	0.315110i	$-0.897959\pi$
$919$	−4.10432e13	−1.89811	−0.949055	+	0.315110i	$0.897959\pi$
$920$	−6.05629e12	−0.278716
$921$	−3.66954e13	−1.68052
$922$	−5.12042e12	−0.233355
$923$	6.68513e12	0.303181
$924$	0	0
$925$	6.61752e12	0.297206
$926$	−1.95826e13	−0.875228
$927$	−2.59356e12	−0.115355
$928$	4.28218e13	1.89539
$929$	2.27448e12	0.100187	0.0500935	−	0.998745i	$-0.484048\pi$
$929$	2.27448e12	0.100187	0.0500935	+	0.998745i	$0.484048\pi$
$930$	−3.04548e11	−0.0133500
$931$	0	0
$932$	−1.32304e13	−0.574381
$933$	2.49980e13	1.08004
$934$	1.11916e12	0.0481205
$935$	5.00001e11	0.0213953
$936$	−1.16076e12	−0.0494314
$937$	−1.56837e13	−0.664693	−0.332346	−	0.943157i	$-0.607840\pi$
$937$	−1.56837e13	−0.664693	−0.332346	+	0.943157i	$0.607840\pi$
$938$	0	0
$939$	−3.94392e13	−1.65552
$940$	1.24900e12	0.0521779
$941$	3.08044e13	1.28073	0.640367	−	0.768069i	$-0.278782\pi$
$941$	3.08044e13	1.28073	0.640367	+	0.768069i	$0.278782\pi$
$942$	2.32733e12	0.0963004
$943$	3.76224e12	0.154933
$944$	1.30295e12	0.0534014
$945$	0	0
$946$	1.40204e11	0.00569180
$947$	2.34156e12	0.0946084	0.0473042	−	0.998881i	$-0.484937\pi$
$947$	2.34156e12	0.0946084	0.0473042	+	0.998881i	$0.484937\pi$
$948$	−6.92545e11	−0.0278491
$949$	−1.49326e13	−0.597638
$950$	−2.84408e11	−0.0113288
$951$	−6.32331e12	−0.250687
$952$	0	0
$953$	−1.89037e13	−0.742383	−0.371192	−	0.928556i	$-0.621051\pi$
$953$	−1.89037e13	−0.742383	−0.371192	+	0.928556i	$0.621051\pi$
$954$	3.97250e11	0.0155273
$955$	−1.84692e13	−0.718511
$956$	−8.11253e12	−0.314120
$957$	−3.23069e12	−0.124506
$958$	−1.47183e13	−0.564564
$959$	0	0
$960$	7.94712e12	0.301988
$961$	−2.63841e13	−0.997901
$962$	1.61463e13	0.607835
$963$	2.45215e12	0.0918816
$964$	2.28554e13	0.852396
$965$	−1.60521e13	−0.595882
$966$	0	0
$967$	−2.08781e13	−0.767842	−0.383921	−	0.923366i	$-0.625427\pi$
$967$	−2.08781e13	−0.767842	−0.383921	+	0.923366i	$0.625427\pi$
$968$	2.74451e13	1.00468
$969$	−1.95576e12	−0.0712621
$970$	3.67168e11	0.0133166
$971$	−4.59498e13	−1.65881	−0.829406	−	0.558646i	$-0.811321\pi$
$971$	−4.59498e13	−1.65881	−0.829406	+	0.558646i	$0.811321\pi$
$972$	−2.53050e12	−0.0909302
$973$	0	0
$974$	−6.46369e12	−0.230126
$975$	−3.80926e12	−0.134996
$976$	−7.24527e11	−0.0255582
$977$	2.95507e13	1.03763	0.518814	−	0.854887i	$-0.326374\pi$
$977$	2.95507e13	1.03763	0.518814	+	0.854887i	$0.326374\pi$
$978$	−2.23825e13	−0.782319
$979$	−2.35185e10	−0.000818254 0
$980$	0	0
$981$	−1.09702e12	−0.0378184
$982$	−4.54563e12	−0.155988
$983$	−3.19858e13	−1.09261	−0.546306	−	0.837586i	$-0.683966\pi$
$983$	−3.19858e13	−1.09261	−0.546306	+	0.837586i	$0.683966\pi$
$984$	−7.71288e12	−0.262264
$985$	1.55963e13	0.527910
$986$	−2.72048e13	−0.916641
$987$	0	0
$988$	1.06341e12	0.0355054
$989$	−2.68335e12	−0.0891854
$990$	−4.01303e10	−0.00132774
$991$	−3.48375e13	−1.14740	−0.573700	−	0.819065i	$-0.694493\pi$
$991$	−3.48375e13	−1.14740	−0.573700	+	0.819065i	$0.694493\pi$
$992$	−1.38414e12	−0.0453813
$993$	4.84256e13	1.58053
$994$	0	0
$995$	−8.98290e12	−0.290545
$996$	−9.87138e12	−0.317842
$997$	5.14253e13	1.64835	0.824174	−	0.566336i	$-0.191640\pi$
$997$	5.14253e13	1.64835	0.824174	+	0.566336i	$0.191640\pi$
$998$	2.18373e12	0.0696806
$999$	4.48581e13	1.42494

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.10.a.n.1.11	✓	18
7.6	odd	2		245.10.a.o.1.11	yes	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
245.10.a.n.1.11	✓	18	1.1	even	1	trivial
245.10.a.o.1.11	yes	18	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	245.a (trivial)

\(f(q)\)	\(=\)	\(q+14.2189 q^{2} -145.482 q^{3} -309.823 q^{4} -625.000 q^{5} -2068.59 q^{6} -11685.4 q^{8} +1481.93 q^{9} -8886.81 q^{10} +3047.19 q^{11} +45073.6 q^{12} +67030.4 q^{13} +90926.1 q^{15} -7524.42 q^{16} -262538. q^{17} +21071.4 q^{18} -51205.4 q^{19} +193639. q^{20} +43327.7 q^{22} -829244. q^{23} +1.70001e6 q^{24} +390625. q^{25} +953099. q^{26} +2.64792e6 q^{27} +7.28765e6 q^{29} +1.29287e6 q^{30} -235560. q^{31} +5.87594e6 q^{32} -443310. q^{33} -3.73300e6 q^{34} -459136. q^{36} +1.69409e7 q^{37} -728084. q^{38} -9.75170e6 q^{39} +7.30339e6 q^{40} -4.53695e6 q^{41} +3.23590e6 q^{43} -944089. q^{44} -926206. q^{45} -1.17909e7 q^{46} +6.45012e6 q^{47} +1.09467e6 q^{48} +5.55426e6 q^{50} +3.81945e7 q^{51} -2.07676e7 q^{52} +1.88525e7 q^{53} +3.76505e7 q^{54} -1.90449e6 q^{55} +7.44944e6 q^{57} +1.03622e8 q^{58} -1.73163e8 q^{59} -2.81710e7 q^{60} +9.62902e7 q^{61} -3.34940e6 q^{62} +8.74020e7 q^{64} -4.18940e7 q^{65} -6.30338e6 q^{66} -830384. q^{67} +8.13402e7 q^{68} +1.20640e8 q^{69} +9.97328e7 q^{71} -1.73170e7 q^{72} -2.22774e8 q^{73} +2.40880e8 q^{74} -5.68288e7 q^{75} +1.58646e7 q^{76} -1.38658e8 q^{78} -1.53648e7 q^{79} +4.70276e6 q^{80} -4.14393e8 q^{81} -6.45105e7 q^{82} -2.19006e8 q^{83} +1.64086e8 q^{85} +4.60109e7 q^{86} -1.06022e9 q^{87} -3.56077e7 q^{88} -7.71811e6 q^{89} -1.31696e7 q^{90} +2.56919e8 q^{92} +3.42697e7 q^{93} +9.17137e7 q^{94} +3.20034e7 q^{95} -8.54842e8 q^{96} -4.13160e7 q^{97} +4.51572e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 66 q^{2} - 112 q^{3} + 4438 q^{4} - 11250 q^{5} - 5184 q^{6} + 58542 q^{8} + 117250 q^{9} - 41250 q^{10} - 50448 q^{11} + 51200 q^{12} - 265416 q^{13} + 70000 q^{15} + 275354 q^{16} - 742108 q^{17}+ \cdots - 3327698948 q^{99}+O(q^{100}) \) 18 * q + 66 * q^2 - 112 * q^3 + 4438 * q^4 - 11250 * q^5 - 5184 * q^6 + 58542 * q^8 + 117250 * q^9 - 41250 * q^10 - 50448 * q^11 + 51200 * q^12 - 265416 * q^13 + 70000 * q^15 + 275354 * q^16 - 742108 * q^17 + 31422 * q^18 - 2003052 * q^19 - 2773750 * q^20 - 898372 * q^22 + 5864112 * q^23 - 7257292 * q^24 + 7031250 * q^25 - 4213696 * q^26 - 12641932 * q^27 + 6575952 * q^29 + 3240000 * q^30 - 15704952 * q^31 + 24442110 * q^32 - 23661356 * q^33 + 7374732 * q^34 + 49561790 * q^36 + 8711420 * q^37 - 8938900 * q^38 + 48598700 * q^39 - 36588750 * q^40 + 5319344 * q^41 + 52311916 * q^43 - 35094960 * q^44 - 73281250 * q^45 + 98407276 * q^46 - 113473964 * q^47 + 50036228 * q^48 + 25781250 * q^50 + 108467832 * q^51 - 193287600 * q^52 + 31548852 * q^53 - 116650276 * q^54 + 31530000 * q^55 + 68889076 * q^57 - 65260756 * q^58 - 267674844 * q^59 - 32000000 * q^60 - 321756900 * q^61 - 651435868 * q^62 - 585550558 * q^64 + 165885000 * q^65 - 865081780 * q^66 - 234918184 * q^67 - 844088700 * q^68 - 380592968 * q^69 - 795896592 * q^71 + 70394666 * q^72 - 617344800 * q^73 - 1029168024 * q^74 - 43750000 * q^75 - 1200935100 * q^76 - 1277509816 * q^78 - 63002188 * q^79 - 172096250 * q^80 + 306235886 * q^81 + 1719855588 * q^82 - 534295300 * q^83 + 463817500 * q^85 + 65726340 * q^86 + 1504843540 * q^87 - 1698935556 * q^88 - 100440944 * q^89 - 19638750 * q^90 + 3229447776 * q^92 - 414903656 * q^93 + 1013675148 * q^94 + 1251907500 * q^95 + 1575858100 * q^96 - 1852351908 * q^97 - 3327698948 * q^99

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