LMFDB - Embedded newform 175.10.a.d.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,10,Mod(1,175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, 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("175.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	175.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:	$90.1312713287$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	$\mathbb{Q}[x]/(x^{3} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 426x + 2016 $ x^3 - x^2 - 426*x + 2016
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2\cdot 3 $
Twist minimal:	no (minimal twist has level 7)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$18.2745$ of defining polynomial
Character	$\chi$	$=$	175.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+34.1627 q^{2} +79.6469 q^{3} +655.088 q^{4} +2720.95 q^{6} -2401.00 q^{7} +4888.28 q^{8} -13339.4 q^{9} +69354.4 q^{11} +52175.7 q^{12} -105959. q^{13} -82024.6 q^{14} -168409. q^{16} -568267. q^{17} -455709. q^{18} -396405. q^{19} -191232. q^{21} +2.36933e6 q^{22} +620765. q^{23} +389336. q^{24} -3.61984e6 q^{26} -2.63013e6 q^{27} -1.57287e6 q^{28} +4.87652e6 q^{29} -1.42482e6 q^{31} -8.25609e6 q^{32} +5.52386e6 q^{33} -1.94135e7 q^{34} -8.73846e6 q^{36} -1.31092e7 q^{37} -1.35423e7 q^{38} -8.43931e6 q^{39} -2.03049e7 q^{41} -6.53300e6 q^{42} +1.11768e7 q^{43} +4.54332e7 q^{44} +2.12070e7 q^{46} +1.99352e7 q^{47} -1.34132e7 q^{48} +5.76480e6 q^{49} -4.52607e7 q^{51} -6.94125e7 q^{52} -5.65007e7 q^{53} -8.98523e7 q^{54} -1.17367e7 q^{56} -3.15725e7 q^{57} +1.66595e8 q^{58} -1.09340e8 q^{59} +3.20008e7 q^{61} -4.86755e7 q^{62} +3.20278e7 q^{63} -1.95825e8 q^{64} +1.88710e8 q^{66} -8.02869e7 q^{67} -3.72265e8 q^{68} +4.94420e7 q^{69} +2.07893e8 q^{71} -6.52065e7 q^{72} +2.70274e8 q^{73} -4.47844e8 q^{74} -2.59680e8 q^{76} -1.66520e8 q^{77} -2.88309e8 q^{78} -5.16196e8 q^{79} +5.30772e7 q^{81} -6.93671e8 q^{82} +6.82693e8 q^{83} -1.25274e8 q^{84} +3.81830e8 q^{86} +3.88400e8 q^{87} +3.39023e8 q^{88} -1.47150e8 q^{89} +2.54408e8 q^{91} +4.06656e8 q^{92} -1.13482e8 q^{93} +6.81040e8 q^{94} -6.57572e8 q^{96} -1.09643e9 q^{97} +1.96941e8 q^{98} -9.25144e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 21 q^{2} - 84 q^{3} + 1557 q^{4} + 4914 q^{6} - 7203 q^{7} - 14055 q^{8} - 26001 q^{9} - 3444 q^{11} + 106386 q^{12} + 19782 q^{13} + 50421 q^{14} + 482961 q^{16} - 1016694 q^{17} + 273267 q^{18}+ \cdots - 1900979172 q^{99}+O(q^{100}) $ 3 * q - 21 * q^2 - 84 * q^3 + 1557 * q^4 + 4914 * q^6 - 7203 * q^7 - 14055 * q^8 - 26001 * q^9 - 3444 * q^11 + 106386 * q^12 + 19782 * q^13 + 50421 * q^14 + 482961 * q^16 - 1016694 * q^17 + 273267 * q^18 + 222852 * q^19 + 201684 * q^21 + 2847048 * q^22 - 1885632 * q^23 - 1449630 * q^24 - 8785056 * q^26 - 551880 * q^27 - 3738357 * q^28 + 4081818 * q^29 + 2869440 * q^31 - 25221951 * q^32 + 20259792 * q^33 - 3981642 * q^34 - 35396379 * q^36 - 1395618 * q^37 - 43479870 * q^38 - 8990688 * q^39 - 14420658 * q^41 - 11798514 * q^42 + 61631172 * q^43 + 97011984 * q^44 + 89747664 * q^46 + 10368960 * q^47 - 16798782 * q^48 + 17294403 * q^49 - 26146728 * q^51 + 80908044 * q^52 - 67502610 * q^53 - 117879300 * q^54 + 33746055 * q^56 - 8471112 * q^57 + 159163830 * q^58 - 42590100 * q^59 + 191746842 * q^61 + 46983468 * q^62 + 62428401 * q^63 + 7852161 * q^64 - 8057952 * q^66 + 255175788 * q^67 - 743485806 * q^68 + 257903856 * q^69 + 296514504 * q^71 + 609314265 * q^72 - 344213310 * q^73 - 690696462 * q^74 + 728839986 * q^76 + 8269044 * q^77 - 280132776 * q^78 - 960412656 * q^79 - 35827677 * q^81 - 562675302 * q^82 + 1100517180 * q^83 - 255432786 * q^84 - 880982256 * q^86 + 621821592 * q^87 - 1206124800 * q^88 + 506816478 * q^89 - 47496582 * q^91 - 691123488 * q^92 - 1693258512 * q^93 + 1388004828 * q^94 + 333385794 * q^96 + 647498250 * q^97 - 121060821 * q^98 - 1900979172 * 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 $

$2$	34.1627	1.50979	0.754896	−	0.655845i	$-0.227688\pi$
$2$	34.1627	1.50979	0.754896	+	0.655845i	$0.227688\pi$
$3$	79.6469	0.567706	0.283853	−	0.958868i	$-0.408387\pi$
$3$	79.6469	0.567706	0.283853	+	0.958868i	$0.408387\pi$
$4$	655.088	1.27947
$5$	0	0
$5$	0	0
$6$	2720.95	0.857117
$7$	−2401.00	−0.377964
$7$	−2401.00	−0.377964
$8$	4888.28	0.421940
$9$	−13339.4	−0.677710
$10$	0	0
$11$	69354.4	1.42826	0.714129	−	0.700014i	$-0.246823\pi$
$11$	69354.4	1.42826	0.714129	+	0.700014i	$0.246823\pi$
$12$	52175.7	0.726362
$13$	−105959.	−1.02895	−0.514473	−	0.857506i	$-0.672013\pi$
$13$	−105959.	−1.02895	−0.514473	+	0.857506i	$0.672013\pi$
$14$	−82024.6	−0.570647
$15$	0	0
$16$	−168409.	−0.642428
$17$	−568267.	−1.65018	−0.825092	−	0.564998i	$-0.808877\pi$
$17$	−568267.	−1.65018	−0.825092	+	0.564998i	$0.808877\pi$
$18$	−455709.	−1.02320
$19$	−396405.	−0.697828	−0.348914	−	0.937155i	$-0.613449\pi$
$19$	−396405.	−0.697828	−0.348914	+	0.937155i	$0.613449\pi$
$20$	0	0
$21$	−191232.	−0.214573
$22$	2.36933e6	2.15637
$23$	620765.	0.462543	0.231271	−	0.972889i	$-0.425712\pi$
$23$	620765.	0.462543	0.231271	+	0.972889i	$0.425712\pi$
$24$	389336.	0.239538
$25$	0	0
$26$	−3.61984e6	−1.55349
$27$	−2.63013e6	−0.952446
$28$	−1.57287e6	−0.483594
$29$	4.87652e6	1.28032	0.640161	−	0.768241i	$-0.278868\pi$
$29$	4.87652e6	1.28032	0.640161	+	0.768241i	$0.278868\pi$
$30$	0	0
$31$	−1.42482e6	−0.277096	−0.138548	−	0.990356i	$-0.544244\pi$
$31$	−1.42482e6	−0.277096	−0.138548	+	0.990356i	$0.544244\pi$
$32$	−8.25609e6	−1.39187
$33$	5.52386e6	0.810830
$34$	−1.94135e7	−2.49143
$35$	0	0
$36$	−8.73846e6	−0.867109
$37$	−1.31092e7	−1.14992	−0.574960	−	0.818182i	$-0.694982\pi$
$37$	−1.31092e7	−1.14992	−0.574960	+	0.818182i	$0.694982\pi$
$38$	−1.35423e7	−1.05357
$39$	−8.43931e6	−0.584139
$40$	0	0
$41$	−2.03049e7	−1.12221	−0.561105	−	0.827744i	$-0.689624\pi$
$41$	−2.03049e7	−1.12221	−0.561105	+	0.827744i	$0.689624\pi$
$42$	−6.53300e6	−0.323960
$43$	1.11768e7	0.498551	0.249276	−	0.968433i	$-0.419807\pi$
$43$	1.11768e7	0.498551	0.249276	+	0.968433i	$0.419807\pi$
$44$	4.54332e7	1.82741
$45$	0	0
$46$	2.12070e7	0.698343
$47$	1.99352e7	0.595909	0.297955	−	0.954580i	$-0.403696\pi$
$47$	1.99352e7	0.595909	0.297955	+	0.954580i	$0.403696\pi$
$48$	−1.34132e7	−0.364710
$49$	5.76480e6	0.142857
$50$	0	0
$51$	−4.52607e7	−0.936819
$52$	−6.94125e7	−1.31651
$53$	−5.65007e7	−0.983586	−0.491793	−	0.870712i	$-0.663658\pi$
$53$	−5.65007e7	−0.983586	−0.491793	+	0.870712i	$0.663658\pi$
$54$	−8.98523e7	−1.43799
$55$	0	0
$56$	−1.17367e7	−0.159478
$57$	−3.15725e7	−0.396161
$58$	1.66595e8	1.93302
$59$	−1.09340e8	−1.17475	−0.587375	−	0.809315i	$-0.699839\pi$
$59$	−1.09340e8	−1.17475	−0.587375	+	0.809315i	$0.699839\pi$
$60$	0	0
$61$	3.20008e7	0.295921	0.147961	−	0.988993i	$-0.452729\pi$
$61$	3.20008e7	0.295921	0.147961	+	0.988993i	$0.452729\pi$
$62$	−4.86755e7	−0.418358
$63$	3.20278e7	0.256150
$64$	−1.95825e8	−1.45901
$65$	0	0
$66$	1.88710e8	1.22418
$67$	−8.02869e7	−0.486752	−0.243376	−	0.969932i	$-0.578255\pi$
$67$	−8.02869e7	−0.486752	−0.243376	+	0.969932i	$0.578255\pi$
$68$	−3.72265e8	−2.11136
$69$	4.94420e7	0.262588
$70$	0	0
$71$	2.07893e8	0.970906	0.485453	−	0.874263i	$-0.338655\pi$
$71$	2.07893e8	0.970906	0.485453	+	0.874263i	$0.338655\pi$
$72$	−6.52065e7	−0.285953
$73$	2.70274e8	1.11391	0.556957	−	0.830541i	$-0.311969\pi$
$73$	2.70274e8	1.11391	0.556957	+	0.830541i	$0.311969\pi$
$74$	−4.47844e8	−1.73614
$75$	0	0
$76$	−2.59680e8	−0.892849
$77$	−1.66520e8	−0.539831
$78$	−2.88309e8	−0.881928
$79$	−5.16196e8	−1.49105	−0.745526	−	0.666477i	$-0.767802\pi$
$79$	−5.16196e8	−1.49105	−0.745526	+	0.666477i	$0.767802\pi$
$80$	0	0
$81$	5.30772e7	0.137002
$82$	−6.93671e8	−1.69430
$83$	6.82693e8	1.57897	0.789486	−	0.613769i	$-0.210347\pi$
$83$	6.82693e8	1.57897	0.789486	+	0.613769i	$0.210347\pi$
$84$	−1.25274e8	−0.274539
$85$	0	0
$86$	3.81830e8	0.752708
$87$	3.88400e8	0.726846
$88$	3.39023e8	0.602639
$89$	−1.47150e8	−0.248602	−0.124301	−	0.992245i	$-0.539669\pi$
$89$	−1.47150e8	−0.248602	−0.124301	+	0.992245i	$0.539669\pi$
$90$	0	0
$91$	2.54408e8	0.388905
$92$	4.06656e8	0.591809
$93$	−1.13482e8	−0.157309
$94$	6.81040e8	0.899699
$95$	0	0
$96$	−6.57572e8	−0.790174
$97$	−1.09643e9	−1.25750	−0.628750	−	0.777608i	$-0.716433\pi$
$97$	−1.09643e9	−1.25750	−0.628750	+	0.777608i	$0.716433\pi$
$98$	1.96941e8	0.215684
$99$	−9.25144e8	−0.967945
$100$	0	0
$101$	2.08683e8	0.199545	0.0997727	−	0.995010i	$-0.468188\pi$
$101$	2.08683e8	0.199545	0.0997727	+	0.995010i	$0.468188\pi$
$102$	−1.54623e9	−1.41440
$103$	−6.78194e8	−0.593727	−0.296863	−	0.954920i	$-0.595941\pi$
$103$	−6.78194e8	−0.593727	−0.296863	+	0.954920i	$0.595941\pi$
$104$	−5.17957e8	−0.434154
$105$	0	0
$106$	−1.93021e9	−1.48501
$107$	4.59542e8	0.338921	0.169461	−	0.985537i	$-0.445797\pi$
$107$	4.59542e8	0.338921	0.169461	+	0.985537i	$0.445797\pi$
$108$	−1.72297e9	−1.21862
$109$	5.21086e8	0.353582	0.176791	−	0.984248i	$-0.443428\pi$
$109$	5.21086e8	0.353582	0.176791	+	0.984248i	$0.443428\pi$
$110$	0	0
$111$	−1.04410e9	−0.652816
$112$	4.04349e8	0.242815
$113$	−4.45612e8	−0.257101	−0.128551	−	0.991703i	$-0.541032\pi$
$113$	−4.45612e8	−0.257101	−0.128551	+	0.991703i	$0.541032\pi$
$114$	−1.07860e9	−0.598120
$115$	0	0
$116$	3.19455e9	1.63813
$117$	1.41343e9	0.697328
$118$	−3.73535e9	−1.77363
$119$	1.36441e9	0.623711
$120$	0	0
$121$	2.45208e9	1.03992
$122$	1.09323e9	0.446779
$123$	−1.61723e9	−0.637086
$124$	−9.33380e8	−0.354536
$125$	0	0
$126$	1.09416e9	0.386734
$127$	−9.28626e8	−0.316755	−0.158378	−	0.987379i	$-0.550626\pi$
$127$	−9.28626e8	−0.316755	−0.158378	+	0.987379i	$0.550626\pi$
$128$	−2.46278e9	−0.810925
$129$	8.90198e8	0.283030
$130$	0	0
$131$	2.57694e9	0.764509	0.382255	−	0.924057i	$-0.375148\pi$
$131$	2.57694e9	0.764509	0.382255	+	0.924057i	$0.375148\pi$
$132$	3.61862e9	1.03743
$133$	9.51769e8	0.263754
$134$	−2.74281e9	−0.734894
$135$	0	0
$136$	−2.77785e9	−0.696279
$137$	4.44116e9	1.07710	0.538548	−	0.842595i	$-0.318973\pi$
$137$	4.44116e9	1.07710	0.538548	+	0.842595i	$0.318973\pi$
$138$	1.68907e9	0.396453
$139$	−7.28389e9	−1.65499	−0.827497	−	0.561470i	$-0.810236\pi$
$139$	−7.28389e9	−1.65499	−0.827497	+	0.561470i	$0.810236\pi$
$140$	0	0
$141$	1.58778e9	0.338301
$142$	7.10218e9	1.46587
$143$	−7.34872e9	−1.46960
$144$	2.24647e9	0.435380
$145$	0	0
$146$	9.23328e9	1.68178
$147$	4.59149e8	0.0811008
$148$	−8.58766e9	−1.47129
$149$	4.87355e9	0.810042	0.405021	−	0.914307i	$-0.367264\pi$
$149$	4.87355e9	0.810042	0.405021	+	0.914307i	$0.367264\pi$
$150$	0	0
$151$	−8.63776e9	−1.35209	−0.676044	−	0.736861i	$-0.736307\pi$
$151$	−8.63776e9	−1.35209	−0.676044	+	0.736861i	$0.736307\pi$
$152$	−1.93774e9	−0.294442
$153$	7.58033e9	1.11835
$154$	−5.68876e9	−0.815032
$155$	0	0
$156$	−5.52849e9	−0.747388
$157$	9.34170e9	1.22709	0.613546	−	0.789659i	$-0.289742\pi$
$157$	9.34170e9	1.22709	0.613546	+	0.789659i	$0.289742\pi$
$158$	−1.76346e10	−2.25118
$159$	−4.50010e9	−0.558387
$160$	0	0
$161$	−1.49046e9	−0.174825
$162$	1.81326e9	0.206844
$163$	2.10680e9	0.233765	0.116883	−	0.993146i	$-0.462710\pi$
$163$	2.10680e9	0.233765	0.116883	+	0.993146i	$0.462710\pi$
$164$	−1.33015e10	−1.43583
$165$	0	0
$166$	2.33226e10	2.38392
$167$	−1.39800e10	−1.39086	−0.695431	−	0.718593i	$-0.744787\pi$
$167$	−1.39800e10	−1.39086	−0.695431	+	0.718593i	$0.744787\pi$
$168$	−9.34796e8	−0.0905367
$169$	6.22820e8	0.0587316
$170$	0	0
$171$	5.28780e9	0.472925
$172$	7.32180e9	0.637881
$173$	1.24435e10	1.05618	0.528088	−	0.849190i	$-0.322909\pi$
$173$	1.24435e10	1.05618	0.528088	+	0.849190i	$0.322909\pi$
$174$	1.32688e10	1.09739
$175$	0	0
$176$	−1.16799e10	−0.917553
$177$	−8.70861e9	−0.666913
$178$	−5.02704e9	−0.375338
$179$	7.30178e9	0.531606	0.265803	−	0.964027i	$-0.414363\pi$
$179$	7.30178e9	0.531606	0.265803	+	0.964027i	$0.414363\pi$
$180$	0	0
$181$	−1.27074e10	−0.880038	−0.440019	−	0.897988i	$-0.645028\pi$
$181$	−1.27074e10	−0.880038	−0.440019	+	0.897988i	$0.645028\pi$
$182$	8.69125e9	0.587166
$183$	2.54876e9	0.167996
$184$	3.03447e9	0.195165
$185$	0	0
$186$	−3.87685e9	−0.237504
$187$	−3.94118e10	−2.35689
$188$	1.30593e10	0.762448
$189$	6.31494e9	0.359991
$190$	0	0
$191$	1.61547e10	0.878311	0.439155	−	0.898411i	$-0.355278\pi$
$191$	1.61547e10	0.878311	0.439155	+	0.898411i	$0.355278\pi$
$192$	−1.55968e10	−0.828287
$193$	1.52841e10	0.792924	0.396462	−	0.918051i	$-0.370238\pi$
$193$	1.52841e10	0.792924	0.396462	+	0.918051i	$0.370238\pi$
$194$	−3.74570e10	−1.89856
$195$	0	0
$196$	3.77645e9	0.182781
$197$	−2.33886e10	−1.10639	−0.553193	−	0.833053i	$-0.686591\pi$
$197$	−2.33886e10	−1.10639	−0.553193	+	0.833053i	$0.686591\pi$
$198$	−3.16054e10	−1.46139
$199$	−2.53610e10	−1.14638	−0.573189	−	0.819423i	$-0.694294\pi$
$199$	−2.53610e10	−1.14638	−0.573189	+	0.819423i	$0.694294\pi$
$200$	0	0
$201$	−6.39460e9	−0.276332
$202$	7.12918e9	0.301272
$203$	−1.17085e10	−0.483916
$204$	−2.96498e10	−1.19863
$205$	0	0
$206$	−2.31689e10	−0.896403
$207$	−8.28061e9	−0.313470
$208$	1.78444e10	0.661024
$209$	−2.74924e10	−0.996678
$210$	0	0
$211$	−9.23757e8	−0.0320838	−0.0160419	−	0.999871i	$-0.505107\pi$
$211$	−9.23757e8	−0.0320838	−0.0160419	+	0.999871i	$0.505107\pi$
$212$	−3.70129e10	−1.25847
$213$	1.65580e10	0.551189
$214$	1.56992e10	0.511700
$215$	0	0
$216$	−1.28568e10	−0.401875
$217$	3.42098e9	0.104733
$218$	1.78017e10	0.533835
$219$	2.15265e10	0.632375
$220$	0	0
$221$	6.02130e10	1.69795
$222$	−3.56694e10	−0.985615
$223$	−6.68635e9	−0.181058	−0.0905290	−	0.995894i	$-0.528856\pi$
$223$	−6.68635e9	−0.181058	−0.0905290	+	0.995894i	$0.528856\pi$
$224$	1.98229e10	0.526078
$225$	0	0
$226$	−1.52233e10	−0.388169
$227$	4.82876e10	1.20703	0.603516	−	0.797351i	$-0.293766\pi$
$227$	4.82876e10	1.20703	0.603516	+	0.797351i	$0.293766\pi$
$228$	−2.06827e10	−0.506876
$229$	−2.34264e10	−0.562918	−0.281459	−	0.959573i	$-0.590818\pi$
$229$	−2.34264e10	−0.562918	−0.281459	+	0.959573i	$0.590818\pi$
$230$	0	0
$231$	−1.32628e10	−0.306465
$232$	2.38378e10	0.540219
$233$	3.29140e10	0.731609	0.365805	−	0.930692i	$-0.380794\pi$
$233$	3.29140e10	0.731609	0.365805	+	0.930692i	$0.380794\pi$
$234$	4.82864e10	1.05282
$235$	0	0
$236$	−7.16275e10	−1.50306
$237$	−4.11134e10	−0.846479
$238$	4.66119e10	0.941673
$239$	2.51973e10	0.499533	0.249766	−	0.968306i	$-0.419646\pi$
$239$	2.51973e10	0.499533	0.249766	+	0.968306i	$0.419646\pi$
$240$	0	0
$241$	7.00815e10	1.33822	0.669109	−	0.743165i	$-0.266676\pi$
$241$	7.00815e10	1.33822	0.669109	+	0.743165i	$0.266676\pi$
$242$	8.37696e10	1.57006
$243$	5.59963e10	1.03022
$244$	2.09633e10	0.378622
$245$	0	0
$246$	−5.52488e10	−0.961866
$247$	4.20027e10	0.718028
$248$	−6.96489e9	−0.116918
$249$	5.43744e10	0.896391
$250$	0	0
$251$	4.19681e10	0.667401	0.333701	−	0.942679i	$-0.391703\pi$
$251$	4.19681e10	0.667401	0.333701	+	0.942679i	$0.391703\pi$
$252$	2.09811e10	0.327737
$253$	4.30527e10	0.660630
$254$	−3.17243e10	−0.478235
$255$	0	0
$256$	1.61271e10	0.234680
$257$	−8.37595e10	−1.19766	−0.598832	−	0.800875i	$-0.704368\pi$
$257$	−8.37595e10	−1.19766	−0.598832	+	0.800875i	$0.704368\pi$
$258$	3.04116e10	0.427317
$259$	3.14751e10	0.434629
$260$	0	0
$261$	−6.50497e10	−0.867687
$262$	8.80350e10	1.15425
$263$	2.34604e9	0.0302367	0.0151184	−	0.999886i	$-0.495187\pi$
$263$	2.34604e9	0.0302367	0.0151184	+	0.999886i	$0.495187\pi$
$264$	2.70021e10	0.342122
$265$	0	0
$266$	3.25150e10	0.398214
$267$	−1.17200e10	−0.141133
$268$	−5.25950e10	−0.622784
$269$	−6.44659e10	−0.750663	−0.375332	−	0.926891i	$-0.622471\pi$
$269$	−6.44659e10	−0.750663	−0.375332	+	0.926891i	$0.622471\pi$
$270$	0	0
$271$	−1.40530e10	−0.158273	−0.0791365	−	0.996864i	$-0.525216\pi$
$271$	−1.40530e10	−0.158273	−0.0791365	+	0.996864i	$0.525216\pi$
$272$	9.57011e10	1.06012
$273$	2.02628e10	0.220784
$274$	1.51722e11	1.62619
$275$	0	0
$276$	3.23889e10	0.335973
$277$	7.52768e10	0.768249	0.384124	−	0.923281i	$-0.374503\pi$
$277$	7.52768e10	0.768249	0.384124	+	0.923281i	$0.374503\pi$
$278$	−2.48837e11	−2.49870
$279$	1.90061e10	0.187791
$280$	0	0
$281$	9.56085e10	0.914783	0.457391	−	0.889266i	$-0.348784\pi$
$281$	9.56085e10	0.914783	0.457391	+	0.889266i	$0.348784\pi$
$282$	5.42427e10	0.510764
$283$	−4.82806e10	−0.447439	−0.223719	−	0.974654i	$-0.571820\pi$
$283$	−4.82806e10	−0.447439	−0.223719	+	0.974654i	$0.571820\pi$
$284$	1.36188e11	1.24224
$285$	0	0
$286$	−2.51052e11	−2.21879
$287$	4.87522e10	0.424156
$288$	1.10131e11	0.943286
$289$	2.04340e11	1.72311
$290$	0	0
$291$	−8.73272e10	−0.713890
$292$	1.77053e11	1.42522
$293$	7.07439e10	0.560770	0.280385	−	0.959888i	$-0.409538\pi$
$293$	7.07439e10	0.560770	0.280385	+	0.959888i	$0.409538\pi$
$294$	1.56857e10	0.122445
$295$	0	0
$296$	−6.40812e10	−0.485197
$297$	−1.82411e11	−1.36034
$298$	1.66494e11	1.22299
$299$	−6.57756e10	−0.475932
$300$	0	0
$301$	−2.68355e10	−0.188435
$302$	−2.95089e11	−2.04137
$303$	1.66210e10	0.113283
$304$	6.67581e10	0.448304
$305$	0	0
$306$	2.58964e11	1.68847
$307$	−1.30493e11	−0.838429	−0.419214	−	0.907887i	$-0.637694\pi$
$307$	−1.30493e11	−0.838429	−0.419214	+	0.907887i	$0.637694\pi$
$308$	−1.09085e11	−0.690697
$309$	−5.40161e10	−0.337062
$310$	0	0
$311$	8.51715e10	0.516265	0.258132	−	0.966110i	$-0.416893\pi$
$311$	8.51715e10	0.516265	0.258132	+	0.966110i	$0.416893\pi$
$312$	−4.12537e10	−0.246472
$313$	1.21745e11	0.716969	0.358484	−	0.933536i	$-0.383294\pi$
$313$	1.21745e11	0.716969	0.358484	+	0.933536i	$0.383294\pi$
$314$	3.19137e11	1.85265
$315$	0	0
$316$	−3.38154e11	−1.90775
$317$	2.14595e11	1.19358	0.596791	−	0.802397i	$-0.296442\pi$
$317$	2.14595e11	1.19358	0.596791	+	0.802397i	$0.296442\pi$
$318$	−1.53736e11	−0.843048
$319$	3.38208e11	1.82863
$320$	0	0
$321$	3.66011e10	0.192407
$322$	−5.09180e10	−0.263949
$323$	2.25264e11	1.15154
$324$	3.47703e10	0.175289
$325$	0	0
$326$	7.19740e10	0.352936
$327$	4.15029e10	0.200731
$328$	−9.92562e10	−0.473506
$329$	−4.78644e10	−0.225233
$330$	0	0
$331$	−5.48000e10	−0.250931	−0.125466	−	0.992098i	$-0.540042\pi$
$331$	−5.48000e10	−0.250931	−0.125466	+	0.992098i	$0.540042\pi$
$332$	4.47224e11	2.02025
$333$	1.74868e11	0.779312
$334$	−4.77595e11	−2.09991
$335$	0	0
$336$	3.22051e10	0.137847
$337$	2.34297e11	0.989538	0.494769	−	0.869025i	$-0.335253\pi$
$337$	2.34297e11	0.989538	0.494769	+	0.869025i	$0.335253\pi$
$338$	2.12772e10	0.0886725
$339$	−3.54916e10	−0.145958
$340$	0	0
$341$	−9.88172e10	−0.395765
$342$	1.80645e11	0.714018
$343$	−1.38413e10	−0.0539949
$344$	5.46353e10	0.210359
$345$	0	0
$346$	4.25104e11	1.59460
$347$	−3.43449e10	−0.127169	−0.0635843	−	0.997976i	$-0.520253\pi$
$347$	−3.43449e10	−0.127169	−0.0635843	+	0.997976i	$0.520253\pi$
$348$	2.54436e11	0.929977
$349$	−2.13485e11	−0.770288	−0.385144	−	0.922856i	$-0.625848\pi$
$349$	−2.13485e11	−0.770288	−0.385144	+	0.922856i	$0.625848\pi$
$350$	0	0
$351$	2.78686e11	0.980016
$352$	−5.72595e11	−1.98795
$353$	−2.75882e11	−0.945664	−0.472832	−	0.881153i	$-0.656768\pi$
$353$	−2.75882e11	−0.945664	−0.472832	+	0.881153i	$0.656768\pi$
$354$	−2.97509e11	−1.00690
$355$	0	0
$356$	−9.63962e10	−0.318079
$357$	1.08671e11	0.354084
$358$	2.49448e11	0.802614
$359$	−3.46238e11	−1.10015	−0.550073	−	0.835117i	$-0.685400\pi$
$359$	−3.46238e11	−1.10015	−0.550073	+	0.835117i	$0.685400\pi$
$360$	0	0
$361$	−1.65550e11	−0.513036
$362$	−4.34117e11	−1.32867
$363$	1.95300e11	0.590369
$364$	1.66659e11	0.497592
$365$	0	0
$366$	8.70725e10	0.253639
$367$	−3.56842e11	−1.02678	−0.513391	−	0.858155i	$-0.671611\pi$
$367$	−3.56842e11	−1.02678	−0.513391	+	0.858155i	$0.671611\pi$
$368$	−1.04542e11	−0.297150
$369$	2.70855e11	0.760534
$370$	0	0
$371$	1.35658e11	0.371760
$372$	−7.43408e10	−0.201272
$373$	−6.73833e11	−1.80245	−0.901224	−	0.433354i	$-0.857330\pi$
$373$	−6.73833e11	−1.80245	−0.901224	+	0.433354i	$0.857330\pi$
$374$	−1.34641e12	−3.55841
$375$	0	0
$376$	9.74487e10	0.251438
$377$	−5.16711e11	−1.31738
$378$	2.15735e11	0.543511
$379$	5.90163e11	1.46925	0.734625	−	0.678473i	$-0.237358\pi$
$379$	5.90163e11	1.46925	0.734625	+	0.678473i	$0.237358\pi$
$380$	0	0
$381$	−7.39622e10	−0.179824
$382$	5.51887e11	1.32607
$383$	1.58931e11	0.377412	0.188706	−	0.982034i	$-0.439571\pi$
$383$	1.58931e11	0.377412	0.188706	+	0.982034i	$0.439571\pi$
$384$	−1.96153e11	−0.460367
$385$	0	0
$386$	5.22145e11	1.19715
$387$	−1.49092e11	−0.337873
$388$	−7.18258e11	−1.60893
$389$	−3.75434e11	−0.831304	−0.415652	−	0.909524i	$-0.636447\pi$
$389$	−3.75434e11	−0.831304	−0.415652	+	0.909524i	$0.636447\pi$
$390$	0	0
$391$	−3.52760e11	−0.763280
$392$	2.81799e10	0.0602771
$393$	2.05245e11	0.434016
$394$	−7.99018e11	−1.67041
$395$	0	0
$396$	−6.06051e11	−1.23846
$397$	4.33507e11	0.875869	0.437935	−	0.899007i	$-0.355710\pi$
$397$	4.33507e11	0.875869	0.437935	+	0.899007i	$0.355710\pi$
$398$	−8.66400e11	−1.73079
$399$	7.58055e10	0.149735
$400$	0	0
$401$	−1.77805e11	−0.343395	−0.171698	−	0.985150i	$-0.554925\pi$
$401$	−1.77805e11	−0.343395	−0.171698	+	0.985150i	$0.554925\pi$
$402$	−2.18457e11	−0.417203
$403$	1.50972e11	0.285118
$404$	1.36706e11	0.255312
$405$	0	0
$406$	−3.99994e11	−0.730612
$407$	−9.09178e11	−1.64238
$408$	−2.21247e11	−0.395281
$409$	−7.67870e11	−1.35685	−0.678427	−	0.734668i	$-0.737338\pi$
$409$	−7.67870e11	−1.35685	−0.678427	+	0.734668i	$0.737338\pi$
$410$	0	0
$411$	3.53725e11	0.611473
$412$	−4.44277e11	−0.759655
$413$	2.62526e11	0.444014
$414$	−2.82888e11	−0.473274
$415$	0	0
$416$	8.74807e11	1.43216
$417$	−5.80139e11	−0.939550
$418$	−9.39215e11	−1.50478
$419$	4.96552e11	0.787048	0.393524	−	0.919314i	$-0.371256\pi$
$419$	4.96552e11	0.787048	0.393524	+	0.919314i	$0.371256\pi$
$420$	0	0
$421$	−4.48514e11	−0.695835	−0.347917	−	0.937525i	$-0.613111\pi$
$421$	−4.48514e11	−0.695835	−0.347917	+	0.937525i	$0.613111\pi$
$422$	−3.15580e10	−0.0484399
$423$	−2.65923e11	−0.403854
$424$	−2.76191e11	−0.415014
$425$	0	0
$426$	5.65667e11	0.832180
$427$	−7.68338e10	−0.111848
$428$	3.01041e11	0.433639
$429$	−5.85303e11	−0.834301
$430$	0	0
$431$	−1.65940e11	−0.231635	−0.115817	−	0.993271i	$-0.536949\pi$
$431$	−1.65940e11	−0.231635	−0.115817	+	0.993271i	$0.536949\pi$
$432$	4.42936e11	0.611878
$433$	4.10674e11	0.561438	0.280719	−	0.959790i	$-0.409427\pi$
$433$	4.10674e11	0.561438	0.280719	+	0.959790i	$0.409427\pi$
$434$	1.16870e11	0.158124
$435$	0	0
$436$	3.41358e11	0.452398
$437$	−2.46074e11	−0.322775
$438$	7.35402e11	0.954754
$439$	−3.29593e11	−0.423534	−0.211767	−	0.977320i	$-0.567922\pi$
$439$	−3.29593e11	−0.423534	−0.211767	+	0.977320i	$0.567922\pi$
$440$	0	0
$441$	−7.68988e10	−0.0968158
$442$	2.05704e12	2.56355
$443$	−5.09091e11	−0.628027	−0.314014	−	0.949418i	$-0.601674\pi$
$443$	−5.09091e11	−0.628027	−0.314014	+	0.949418i	$0.601674\pi$
$444$	−6.83981e11	−0.835258
$445$	0	0
$446$	−2.28424e11	−0.273360
$447$	3.88163e11	0.459865
$448$	4.70175e11	0.551453
$449$	1.49596e12	1.73705	0.868525	−	0.495646i	$-0.165069\pi$
$449$	1.49596e12	1.73705	0.868525	+	0.495646i	$0.165069\pi$
$450$	0	0
$451$	−1.40824e12	−1.60281
$452$	−2.91915e11	−0.328953
$453$	−6.87971e11	−0.767588
$454$	1.64963e12	1.82237
$455$	0	0
$456$	−1.54335e11	−0.167156
$457$	−1.43920e12	−1.54347	−0.771735	−	0.635944i	$-0.780611\pi$
$457$	−1.43920e12	−1.54347	−0.771735	+	0.635944i	$0.780611\pi$
$458$	−8.00307e11	−0.849889
$459$	1.49462e12	1.57171
$460$	0	0
$461$	−1.37741e12	−1.42039	−0.710195	−	0.704005i	$-0.751393\pi$
$461$	−1.37741e12	−1.42039	−0.710195	+	0.704005i	$0.751393\pi$
$462$	−4.53092e11	−0.462698
$463$	−1.76612e12	−1.78610	−0.893049	−	0.449960i	$-0.851438\pi$
$463$	−1.76612e12	−1.78610	−0.893049	+	0.449960i	$0.851438\pi$
$464$	−8.21248e11	−0.822514
$465$	0	0
$466$	1.12443e12	1.10458
$467$	1.17323e12	1.14145	0.570727	−	0.821140i	$-0.306661\pi$
$467$	1.17323e12	1.14145	0.570727	+	0.821140i	$0.306661\pi$
$468$	9.25919e11	0.892209
$469$	1.92769e11	0.183975
$470$	0	0
$471$	7.44037e11	0.696627
$472$	−5.34485e11	−0.495674
$473$	7.75161e11	0.712060
$474$	−1.40454e12	−1.27801
$475$	0	0
$476$	8.93808e11	0.798019
$477$	7.53683e11	0.666586
$478$	8.60808e11	0.754190
$479$	−1.98723e12	−1.72480	−0.862401	−	0.506225i	$-0.831040\pi$
$479$	−1.98723e12	−1.72480	−0.862401	+	0.506225i	$0.831040\pi$
$480$	0	0
$481$	1.38903e12	1.18321
$482$	2.39417e12	2.02043
$483$	−1.18710e11	−0.0992489
$484$	1.60633e12	1.33055
$485$	0	0
$486$	1.91298e12	1.55542
$487$	1.23240e12	0.992825	0.496413	−	0.868087i	$-0.334650\pi$
$487$	1.23240e12	0.992825	0.496413	+	0.868087i	$0.334650\pi$
$488$	1.56428e11	0.124861
$489$	1.67800e11	0.132710
$490$	0	0
$491$	−2.03763e12	−1.58219	−0.791095	−	0.611693i	$-0.790489\pi$
$491$	−2.03763e12	−1.58219	−0.791095	+	0.611693i	$0.790489\pi$
$492$	−1.05943e12	−0.815131
$493$	−2.77117e12	−2.11277
$494$	1.43493e12	1.08407
$495$	0	0
$496$	2.39951e11	0.178014
$497$	−4.99151e11	−0.366968
$498$	1.85758e12	1.35336
$499$	−3.26299e11	−0.235594	−0.117797	−	0.993038i	$-0.537583\pi$
$499$	−3.26299e11	−0.235594	−0.117797	+	0.993038i	$0.537583\pi$
$500$	0	0
$501$	−1.11347e12	−0.789601
$502$	1.43374e12	1.00764
$503$	4.46869e11	0.311261	0.155630	−	0.987815i	$-0.450259\pi$
$503$	4.46869e11	0.311261	0.155630	+	0.987815i	$0.450259\pi$
$504$	1.56561e11	0.108080
$505$	0	0
$506$	1.47080e12	0.997413
$507$	4.96056e10	0.0333423
$508$	−6.08332e11	−0.405279
$509$	1.34100e12	0.885523	0.442761	−	0.896639i	$-0.353999\pi$
$509$	1.34100e12	0.885523	0.442761	+	0.896639i	$0.353999\pi$
$510$	0	0
$511$	−6.48928e11	−0.421020
$512$	1.81189e12	1.16524
$513$	1.04260e12	0.664643
$514$	−2.86145e12	−1.80822
$515$	0	0
$516$	5.83158e11	0.362129
$517$	1.38259e12	0.851112
$518$	1.07527e12	0.656199
$519$	9.91089e11	0.599597
$520$	0	0
$521$	2.98523e12	1.77504	0.887520	−	0.460769i	$-0.152426\pi$
$521$	2.98523e12	1.77504	0.887520	+	0.460769i	$0.152426\pi$
$522$	−2.22227e12	−1.31003
$523$	−1.64651e12	−0.962289	−0.481145	−	0.876641i	$-0.659779\pi$
$523$	−1.64651e12	−0.962289	−0.481145	+	0.876641i	$0.659779\pi$
$524$	1.68812e12	0.978166
$525$	0	0
$526$	8.01470e10	0.0456511
$527$	8.09676e11	0.457260
$528$	−9.30265e11	−0.520900
$529$	−1.41580e12	−0.786054
$530$	0	0
$531$	1.45853e12	0.796141
$532$	6.23493e11	0.337465
$533$	2.15149e12	1.15470
$534$	−4.00388e11	−0.213081
$535$	0	0
$536$	−3.92464e11	−0.205380
$537$	5.81564e11	0.301796
$538$	−2.20233e12	−1.13334
$539$	3.99814e11	0.204037
$540$	0	0
$541$	−4.57968e11	−0.229852	−0.114926	−	0.993374i	$-0.536663\pi$
$541$	−4.57968e11	−0.229852	−0.114926	+	0.993374i	$0.536663\pi$
$542$	−4.80087e11	−0.238959
$543$	−1.01210e12	−0.499603
$544$	4.69166e12	2.29684
$545$	0	0
$546$	6.92231e11	0.333337
$547$	−2.39624e12	−1.14443	−0.572213	−	0.820105i	$-0.693915\pi$
$547$	−2.39624e12	−1.14443	−0.572213	+	0.820105i	$0.693915\pi$
$548$	2.90935e12	1.37811
$549$	−4.26870e11	−0.200549
$550$	0	0
$551$	−1.93308e12	−0.893444
$552$	2.41686e11	0.110796
$553$	1.23939e12	0.563565
$554$	2.57166e12	1.15990
$555$	0	0
$556$	−4.77159e12	−2.11751
$557$	−1.07863e12	−0.474814	−0.237407	−	0.971410i	$-0.576298\pi$
$557$	−1.07863e12	−0.474814	−0.237407	+	0.971410i	$0.576298\pi$
$558$	6.49301e11	0.283525
$559$	−1.18428e12	−0.512983
$560$	0	0
$561$	−3.13903e12	−1.33802
$562$	3.26624e12	1.38113
$563$	−2.33140e11	−0.0977976	−0.0488988	−	0.998804i	$-0.515571\pi$
$563$	−2.33140e11	−0.0977976	−0.0488988	+	0.998804i	$0.515571\pi$
$564$	1.04013e12	0.432846
$565$	0	0
$566$	−1.64939e12	−0.675539
$567$	−1.27438e11	−0.0517817
$568$	1.01624e12	0.409664
$569$	4.50535e11	0.180187	0.0900934	−	0.995933i	$-0.471283\pi$
$569$	4.50535e11	0.180187	0.0900934	+	0.995933i	$0.471283\pi$
$570$	0	0
$571$	−4.38839e12	−1.72760	−0.863800	−	0.503835i	$-0.831922\pi$
$571$	−4.38839e12	−1.72760	−0.863800	+	0.503835i	$0.831922\pi$
$572$	−4.81406e12	−1.88031
$573$	1.28667e12	0.498622
$574$	1.66550e12	0.640387
$575$	0	0
$576$	2.61218e12	0.988785
$577$	−3.13994e12	−1.17932	−0.589658	−	0.807653i	$-0.700737\pi$
$577$	−3.13994e12	−1.17932	−0.589658	+	0.807653i	$0.700737\pi$
$578$	6.98079e12	2.60153
$579$	1.21733e12	0.450148
$580$	0	0
$581$	−1.63915e12	−0.596795
$582$	−2.98333e12	−1.07782
$583$	−3.91857e12	−1.40481
$584$	1.32117e12	0.470005
$585$	0	0
$586$	2.41680e12	0.846645
$587$	−2.52512e12	−0.877829	−0.438915	−	0.898529i	$-0.644637\pi$
$587$	−2.52512e12	−0.877829	−0.438915	+	0.898529i	$0.644637\pi$
$588$	3.00783e11	0.103766
$589$	5.64805e11	0.193366
$590$	0	0
$591$	−1.86283e12	−0.628102
$592$	2.20770e12	0.738740
$593$	9.35417e11	0.310641	0.155321	−	0.987864i	$-0.450359\pi$
$593$	9.35417e11	0.310641	0.155321	+	0.987864i	$0.450359\pi$
$594$	−6.23165e12	−2.05383
$595$	0	0
$596$	3.19261e12	1.03642
$597$	−2.01993e12	−0.650805
$598$	−2.24707e12	−0.718557
$599$	4.73586e12	1.50307	0.751534	−	0.659694i	$-0.229314\pi$
$599$	4.73586e12	1.50307	0.751534	+	0.659694i	$0.229314\pi$
$600$	0	0
$601$	−5.99855e12	−1.87548	−0.937738	−	0.347344i	$-0.887084\pi$
$601$	−5.99855e12	−1.87548	−0.937738	+	0.347344i	$0.887084\pi$
$602$	−9.16773e11	−0.284497
$603$	1.07098e12	0.329877
$604$	−5.65850e12	−1.72995
$605$	0	0
$606$	5.67817e11	0.171034
$607$	−3.43715e12	−1.02766	−0.513830	−	0.857892i	$-0.671774\pi$
$607$	−3.43715e12	−1.02766	−0.513830	+	0.857892i	$0.671774\pi$
$608$	3.27276e12	0.971287
$609$	−9.32548e11	−0.274722
$610$	0	0
$611$	−2.11231e12	−0.613159
$612$	4.96578e12	1.43089
$613$	−4.15273e12	−1.18785	−0.593925	−	0.804520i	$-0.702423\pi$
$613$	−4.15273e12	−1.18785	−0.593925	+	0.804520i	$0.702423\pi$
$614$	−4.45801e12	−1.26585
$615$	0	0
$616$	−8.13995e11	−0.227776
$617$	1.12196e12	0.311669	0.155834	−	0.987783i	$-0.450193\pi$
$617$	1.12196e12	0.311669	0.155834	+	0.987783i	$0.450193\pi$
$618$	−1.84533e12	−0.508893
$619$	−5.98940e12	−1.63974	−0.819871	−	0.572549i	$-0.805955\pi$
$619$	−5.98940e12	−1.63974	−0.819871	+	0.572549i	$0.805955\pi$
$620$	0	0
$621$	−1.63269e12	−0.440547
$622$	2.90969e12	0.779452
$623$	3.53307e11	0.0939628
$624$	1.42125e12	0.375267
$625$	0	0
$626$	4.15912e12	1.08247
$627$	−2.18969e12	−0.565820
$628$	6.11963e12	1.57003
$629$	7.44951e12	1.89758
$630$	0	0
$631$	4.97135e12	1.24837	0.624184	−	0.781277i	$-0.285432\pi$
$631$	4.97135e12	1.24837	0.624184	+	0.781277i	$0.285432\pi$
$632$	−2.52331e12	−0.629134
$633$	−7.35743e10	−0.0182142
$634$	7.33113e12	1.80206
$635$	0	0
$636$	−2.94796e12	−0.714439
$637$	−6.10833e11	−0.146992
$638$	1.15541e13	2.76085
$639$	−2.77316e12	−0.657993
$640$	0	0
$641$	−2.41181e12	−0.564263	−0.282131	−	0.959376i	$-0.591041\pi$
$641$	−2.41181e12	−0.564263	−0.282131	+	0.959376i	$0.591041\pi$
$642$	1.25039e12	0.290495
$643$	−6.86804e12	−1.58447	−0.792234	−	0.610217i	$-0.791082\pi$
$643$	−6.86804e12	−1.58447	−0.792234	+	0.610217i	$0.791082\pi$
$644$	−9.76380e11	−0.223683
$645$	0	0
$646$	7.69562e12	1.73859
$647$	1.73394e12	0.389013	0.194506	−	0.980901i	$-0.437690\pi$
$647$	1.73394e12	0.389013	0.194506	+	0.980901i	$0.437690\pi$
$648$	2.59456e11	0.0578064
$649$	−7.58322e12	−1.67785
$650$	0	0
$651$	2.72471e11	0.0594573
$652$	1.38014e12	0.299095
$653$	−2.86440e10	−0.00616488	−0.00308244	−	0.999995i	$-0.500981\pi$
$653$	−2.86440e10	−0.00616488	−0.00308244	+	0.999995i	$0.500981\pi$
$654$	1.41785e12	0.303061
$655$	0	0
$656$	3.41953e12	0.720940
$657$	−3.60529e12	−0.754911
$658$	−1.63518e12	−0.340054
$659$	−6.31728e12	−1.30481	−0.652403	−	0.757872i	$-0.726239\pi$
$659$	−6.31728e12	−1.30481	−0.652403	+	0.757872i	$0.726239\pi$
$660$	0	0
$661$	−3.49558e12	−0.712217	−0.356109	−	0.934445i	$-0.615897\pi$
$661$	−3.49558e12	−0.712217	−0.356109	+	0.934445i	$0.615897\pi$
$662$	−1.87212e12	−0.378854
$663$	4.79578e12	0.963937
$664$	3.33719e12	0.666231
$665$	0	0
$666$	5.97396e12	1.17660
$667$	3.02717e12	0.592203
$668$	−9.15816e12	−1.77957
$669$	−5.32547e11	−0.102788
$670$	0	0
$671$	2.21939e12	0.422652
$672$	1.57883e12	0.298658
$673$	8.02535e12	1.50798	0.753991	−	0.656885i	$-0.228126\pi$
$673$	8.02535e12	1.50798	0.753991	+	0.656885i	$0.228126\pi$
$674$	8.00422e12	1.49400
$675$	0	0
$676$	4.08002e11	0.0751453
$677$	−1.17163e12	−0.214358	−0.107179	−	0.994240i	$-0.534182\pi$
$677$	−1.17163e12	−0.214358	−0.107179	+	0.994240i	$0.534182\pi$
$678$	−1.21249e12	−0.220366
$679$	2.63253e12	0.475290
$680$	0	0
$681$	3.84596e12	0.685239
$682$	−3.37586e12	−0.597523
$683$	−4.69754e12	−0.825995	−0.412997	−	0.910732i	$-0.635518\pi$
$683$	−4.69754e12	−0.825995	−0.412997	+	0.910732i	$0.635518\pi$
$684$	3.46397e12	0.605093
$685$	0	0
$686$	−4.72855e11	−0.0815211
$687$	−1.86584e12	−0.319572
$688$	−1.88227e12	−0.320283
$689$	5.98676e12	1.01206
$690$	0	0
$691$	−7.83193e12	−1.30683	−0.653413	−	0.757001i	$-0.726664\pi$
$691$	−7.83193e12	−1.30683	−0.653413	+	0.757001i	$0.726664\pi$
$692$	8.15161e12	1.35134
$693$	2.22127e12	0.365849
$694$	−1.17332e12	−0.191998
$695$	0	0
$696$	1.89860e12	0.306685
$697$	1.15386e13	1.85185
$698$	−7.29322e12	−1.16297
$699$	2.62150e12	0.415339
$700$	0	0
$701$	7.13243e12	1.11559	0.557797	−	0.829977i	$-0.311647\pi$
$701$	7.13243e12	1.11559	0.557797	+	0.829977i	$0.311647\pi$
$702$	9.52066e12	1.47962
$703$	5.19655e12	0.802446
$704$	−1.35813e13	−2.08384
$705$	0	0
$706$	−9.42486e12	−1.42776
$707$	−5.01049e11	−0.0754211
$708$	−5.70491e12	−0.853294
$709$	8.65274e12	1.28601	0.643007	−	0.765861i	$-0.277687\pi$
$709$	8.65274e12	1.28601	0.643007	+	0.765861i	$0.277687\pi$
$710$	0	0
$711$	6.88573e12	1.01050
$712$	−7.19310e11	−0.104895
$713$	−8.84475e11	−0.128169
$714$	3.71249e12	0.534593
$715$	0	0
$716$	4.78331e12	0.680174
$717$	2.00689e12	0.283588
$718$	−1.18284e13	−1.66099
$719$	4.58446e11	0.0639747	0.0319873	−	0.999488i	$-0.489816\pi$
$719$	4.58446e11	0.0639747	0.0319873	+	0.999488i	$0.489816\pi$
$720$	0	0
$721$	1.62834e12	0.224408
$722$	−5.65565e12	−0.774577
$723$	5.58177e12	0.759713
$724$	−8.32444e12	−1.12598
$725$	0	0
$726$	6.67199e12	0.891334
$727$	2.53850e12	0.337033	0.168517	−	0.985699i	$-0.446102\pi$
$727$	2.53850e12	0.337033	0.168517	+	0.985699i	$0.446102\pi$
$728$	1.24361e12	0.164095
$729$	3.41521e12	0.447861
$730$	0	0
$731$	−6.35141e12	−0.822701
$732$	1.66966e12	0.214946
$733$	−1.09361e13	−1.39925	−0.699624	−	0.714511i	$-0.746649\pi$
$733$	−1.09361e13	−1.39925	−0.699624	+	0.714511i	$0.746649\pi$
$734$	−1.21907e13	−1.55023
$735$	0	0
$736$	−5.12509e12	−0.643800
$737$	−5.56824e12	−0.695208
$738$	9.25314e12	1.14825
$739$	7.34996e12	0.906536	0.453268	−	0.891374i	$-0.350258\pi$
$739$	7.34996e12	0.906536	0.453268	+	0.891374i	$0.350258\pi$
$740$	0	0
$741$	3.34539e12	0.407628
$742$	4.63444e12	0.561281
$743$	1.60813e12	0.193584	0.0967922	−	0.995305i	$-0.469142\pi$
$743$	1.60813e12	0.193584	0.0967922	+	0.995305i	$0.469142\pi$
$744$	−5.54732e11	−0.0663751
$745$	0	0
$746$	−2.30199e13	−2.72132
$747$	−9.10670e12	−1.07009
$748$	−2.58182e13	−3.01557
$749$	−1.10336e12	−0.128100
$750$	0	0
$751$	−2.95903e12	−0.339446	−0.169723	−	0.985492i	$-0.554287\pi$
$751$	−2.95903e12	−0.339446	−0.169723	+	0.985492i	$0.554287\pi$
$752$	−3.35726e12	−0.382829
$753$	3.34263e12	0.378888
$754$	−1.76522e13	−1.98897
$755$	0	0
$756$	4.13684e12	0.460597
$757$	4.83223e12	0.534830	0.267415	−	0.963581i	$-0.413830\pi$
$757$	4.83223e12	0.534830	0.267415	+	0.963581i	$0.413830\pi$
$758$	2.01616e13	2.21826
$759$	3.42902e12	0.375043
$760$	0	0
$761$	3.15213e12	0.340701	0.170350	−	0.985384i	$-0.445510\pi$
$761$	3.15213e12	0.340701	0.170350	+	0.985384i	$0.445510\pi$
$762$	−2.52675e12	−0.271496
$763$	−1.25113e12	−0.133642
$764$	1.05827e13	1.12377
$765$	0	0
$766$	5.42952e12	0.569813
$767$	1.15856e13	1.20876
$768$	1.28447e12	0.133229
$769$	−6.87650e12	−0.709086	−0.354543	−	0.935040i	$-0.615364\pi$
$769$	−6.87650e12	−0.709086	−0.354543	+	0.935040i	$0.615364\pi$
$770$	0	0
$771$	−6.67118e12	−0.679920
$772$	1.00124e13	1.01452
$773$	−1.16083e13	−1.16939	−0.584696	−	0.811253i	$-0.698786\pi$
$773$	−1.16083e13	−1.16939	−0.584696	+	0.811253i	$0.698786\pi$
$774$	−5.09337e12	−0.510118
$775$	0	0
$776$	−5.35965e12	−0.530590
$777$	2.50690e12	0.246741
$778$	−1.28258e13	−1.25510
$779$	8.04899e12	0.783110
$780$	0	0
$781$	1.44183e13	1.38670
$782$	−1.20512e13	−1.15239
$783$	−1.28259e13	−1.21944
$784$	−9.70842e11	−0.0917754
$785$	0	0
$786$	7.01171e12	0.655274
$787$	2.50005e12	0.232307	0.116154	−	0.993231i	$-0.462943\pi$
$787$	2.50005e12	0.232307	0.116154	+	0.993231i	$0.462943\pi$
$788$	−1.53216e13	−1.41559
$789$	1.86855e11	0.0171656
$790$	0	0
$791$	1.06991e12	0.0971751
$792$	−4.52236e12	−0.408415
$793$	−3.39077e12	−0.304487
$794$	1.48098e13	1.32238
$795$	0	0
$796$	−1.66137e13	−1.46675
$797$	−2.77023e12	−0.243194	−0.121597	−	0.992580i	$-0.538802\pi$
$797$	−2.77023e12	−0.243194	−0.121597	+	0.992580i	$0.538802\pi$
$798$	2.58972e12	0.226068
$799$	−1.13285e13	−0.983360
$800$	0	0
$801$	1.96289e12	0.168480
$802$	−6.07429e12	−0.518455
$803$	1.87447e13	1.59096
$804$	−4.18903e12	−0.353558
$805$	0	0
$806$	5.15761e12	0.430468
$807$	−5.13451e12	−0.426156
$808$	1.02010e12	0.0841962
$809$	−2.96640e12	−0.243479	−0.121739	−	0.992562i	$-0.538847\pi$
$809$	−2.96640e12	−0.243479	−0.121739	+	0.992562i	$0.538847\pi$
$810$	0	0
$811$	−9.01447e12	−0.731722	−0.365861	−	0.930669i	$-0.619225\pi$
$811$	−9.01447e12	−0.731722	−0.365861	+	0.930669i	$0.619225\pi$
$812$	−7.67012e12	−0.619156
$813$	−1.11928e12	−0.0898524
$814$	−3.10599e13	−2.47965
$815$	0	0
$816$	7.62229e12	0.601838
$817$	−4.43055e12	−0.347903
$818$	−2.62325e13	−2.04857
$819$	−3.39364e12	−0.263565
$820$	0	0
$821$	1.25176e13	0.961563	0.480782	−	0.876840i	$-0.340353\pi$
$821$	1.25176e13	0.961563	0.480782	+	0.876840i	$0.340353\pi$
$822$	1.20842e13	0.923197
$823$	1.50348e13	1.14234	0.571172	−	0.820830i	$-0.306489\pi$
$823$	1.50348e13	1.14234	0.571172	+	0.820830i	$0.306489\pi$
$824$	−3.31520e12	−0.250517
$825$	0	0
$826$	8.96858e12	0.670369
$827$	−2.31522e13	−1.72115	−0.860574	−	0.509325i	$-0.829895\pi$
$827$	−2.31522e13	−1.72115	−0.860574	+	0.509325i	$0.829895\pi$
$828$	−5.42453e12	−0.401075
$829$	4.88071e12	0.358912	0.179456	−	0.983766i	$-0.442566\pi$
$829$	4.88071e12	0.358912	0.179456	+	0.983766i	$0.442566\pi$
$830$	0	0
$831$	5.99556e12	0.436139
$832$	2.07494e13	1.50124
$833$	−3.27595e12	−0.235741
$834$	−1.98191e13	−1.41852
$835$	0	0
$836$	−1.80100e13	−1.27522
$837$	3.74745e12	0.263919
$838$	1.69635e13	1.18828
$839$	−1.18015e13	−0.822258	−0.411129	−	0.911577i	$-0.634865\pi$
$839$	−1.18015e13	−0.822258	−0.411129	+	0.911577i	$0.634865\pi$
$840$	0	0
$841$	9.27330e12	0.639223
$842$	−1.53224e13	−1.05057
$843$	7.61492e12	0.519327
$844$	−6.05142e11	−0.0410503
$845$	0	0
$846$	−9.08464e12	−0.609735
$847$	−5.88744e12	−0.393053
$848$	9.51520e12	0.631883
$849$	−3.84540e12	−0.254014
$850$	0	0
$851$	−8.13771e12	−0.531887
$852$	1.08470e13	0.705229
$853$	2.54707e13	1.64729	0.823646	−	0.567104i	$-0.191936\pi$
$853$	2.54707e13	1.64729	0.823646	+	0.567104i	$0.191936\pi$
$854$	−2.62485e12	−0.168867
$855$	0	0
$856$	2.24637e12	0.143004
$857$	−1.26584e13	−0.801615	−0.400807	−	0.916162i	$-0.631270\pi$
$857$	−1.26584e13	−0.801615	−0.400807	+	0.916162i	$0.631270\pi$
$858$	−1.99955e13	−1.25962
$859$	2.01387e13	1.26201	0.631004	−	0.775779i	$-0.282643\pi$
$859$	2.01387e13	1.26201	0.631004	+	0.775779i	$0.282643\pi$
$860$	0	0
$861$	3.88296e12	0.240796
$862$	−5.66896e12	−0.349720
$863$	1.44977e13	0.889716	0.444858	−	0.895601i	$-0.353254\pi$
$863$	1.44977e13	0.889716	0.444858	+	0.895601i	$0.353254\pi$
$864$	2.17146e13	1.32568
$865$	0	0
$866$	1.40297e13	0.847655
$867$	1.62750e13	0.978217
$868$	2.24104e12	0.134002
$869$	−3.58004e13	−2.12961
$870$	0	0
$871$	8.50712e12	0.500842
$872$	2.54721e12	0.149191
$873$	1.46257e13	0.852221
$874$	−8.40656e12	−0.487323
$875$	0	0
$876$	1.41018e13	0.809104
$877$	−1.83297e13	−1.04630	−0.523150	−	0.852241i	$-0.675243\pi$
$877$	−1.83297e13	−1.04630	−0.523150	+	0.852241i	$0.675243\pi$
$878$	−1.12598e13	−0.639448
$879$	5.63453e12	0.318352
$880$	0	0
$881$	4.57369e12	0.255785	0.127892	−	0.991788i	$-0.459179\pi$
$881$	4.57369e12	0.255785	0.127892	+	0.991788i	$0.459179\pi$
$882$	−2.62707e12	−0.146172
$883$	−3.07854e13	−1.70420	−0.852101	−	0.523377i	$-0.824672\pi$
$883$	−3.07854e13	−1.70420	−0.852101	+	0.523377i	$0.824672\pi$
$884$	3.94448e13	2.17248
$885$	0	0
$886$	−1.73919e13	−0.948190
$887$	2.58803e13	1.40382	0.701911	−	0.712264i	$-0.252330\pi$
$887$	2.58803e13	1.40382	0.701911	+	0.712264i	$0.252330\pi$
$888$	−5.10387e12	−0.275449
$889$	2.22963e12	0.119722
$890$	0	0
$891$	3.68114e12	0.195674
$892$	−4.38015e12	−0.231658
$893$	−7.90242e12	−0.415842
$894$	1.32607e13	0.694301
$895$	0	0
$896$	5.91314e12	0.306501
$897$	−5.23882e12	−0.270189
$898$	5.11061e13	2.62258
$899$	−6.94814e12	−0.354773
$900$	0	0
$901$	3.21075e13	1.62310
$902$	−4.81091e13	−2.41990
$903$	−2.13737e12	−0.106975
$904$	−2.17827e12	−0.108481
$905$	0	0
$906$	−2.35029e13	−1.15890
$907$	−9.64118e12	−0.473040	−0.236520	−	0.971627i	$-0.576007\pi$
$907$	−9.64118e12	−0.473040	−0.236520	+	0.971627i	$0.576007\pi$
$908$	3.16326e13	1.54436
$909$	−2.78371e12	−0.135234
$910$	0	0
$911$	7.28746e12	0.350545	0.175272	−	0.984520i	$-0.443919\pi$
$911$	7.28746e12	0.350545	0.175272	+	0.984520i	$0.443919\pi$
$912$	5.31707e12	0.254505
$913$	4.73478e13	2.25518
$914$	−4.91669e13	−2.33032
$915$	0	0
$916$	−1.53463e13	−0.720236
$917$	−6.18722e12	−0.288957
$918$	5.10601e13	2.37295
$919$	2.73276e13	1.26381	0.631906	−	0.775045i	$-0.282273\pi$
$919$	2.73276e13	1.26381	0.631906	+	0.775045i	$0.282273\pi$
$920$	0	0
$921$	−1.03934e13	−0.475981
$922$	−4.70559e13	−2.14449
$923$	−2.20281e13	−0.999011
$924$	−8.68829e12	−0.392112
$925$	0	0
$926$	−6.03353e13	−2.69663
$927$	9.04668e12	0.402375
$928$	−4.02610e13	−1.78204
$929$	−7.21805e12	−0.317943	−0.158971	−	0.987283i	$-0.550818\pi$
$929$	−7.21805e12	−0.317943	−0.158971	+	0.987283i	$0.550818\pi$
$930$	0	0
$931$	−2.28520e12	−0.0996897
$932$	2.15616e13	0.936071
$933$	6.78365e12	0.293087
$934$	4.00808e13	1.72336
$935$	0	0
$936$	6.90922e12	0.294231
$937$	−1.41988e13	−0.601761	−0.300880	−	0.953662i	$-0.597281\pi$
$937$	−1.41988e13	−0.601761	−0.300880	+	0.953662i	$0.597281\pi$
$938$	6.58550e12	0.277764
$939$	9.69658e12	0.407027
$940$	0	0
$941$	−2.53242e13	−1.05289	−0.526445	−	0.850209i	$-0.676475\pi$
$941$	−2.53242e13	−1.05289	−0.526445	+	0.850209i	$0.676475\pi$
$942$	2.54183e13	1.05176
$943$	−1.26046e13	−0.519070
$944$	1.84138e13	0.754693
$945$	0	0
$946$	2.64816e13	1.07506
$947$	1.37160e13	0.554182	0.277091	−	0.960844i	$-0.410630\pi$
$947$	1.37160e13	0.554182	0.277091	+	0.960844i	$0.410630\pi$
$948$	−2.69329e13	−1.08304
$949$	−2.86380e13	−1.14616
$950$	0	0
$951$	1.70918e13	0.677604
$952$	6.66961e12	0.263169
$953$	−2.44096e13	−0.958610	−0.479305	−	0.877648i	$-0.659111\pi$
$953$	−2.44096e13	−0.958610	−0.479305	+	0.877648i	$0.659111\pi$
$954$	2.57478e13	1.00641
$955$	0	0
$956$	1.65065e13	0.639137
$957$	2.69372e13	1.03812
$958$	−6.78892e13	−2.60409
$959$	−1.06632e13	−0.407104
$960$	0	0
$961$	−2.44095e13	−0.923218
$962$	4.74531e13	1.78639
$963$	−6.13001e12	−0.229690
$964$	4.59096e13	1.71221
$965$	0	0
$966$	−4.05546e12	−0.149845
$967$	4.19850e13	1.54410	0.772049	−	0.635563i	$-0.219232\pi$
$967$	4.19850e13	1.54410	0.772049	+	0.635563i	$0.219232\pi$
$968$	1.19864e13	0.438784
$969$	1.79416e13	0.653738
$970$	0	0
$971$	3.13254e12	0.113086	0.0565432	−	0.998400i	$-0.481992\pi$
$971$	3.13254e12	0.113086	0.0565432	+	0.998400i	$0.481992\pi$
$972$	3.66825e13	1.31814
$973$	1.74886e13	0.625529
$974$	4.21022e13	1.49896
$975$	0	0
$976$	−5.38920e12	−0.190108
$977$	−4.53124e13	−1.59108	−0.795539	−	0.605902i	$-0.792812\pi$
$977$	−4.53124e13	−1.59108	−0.795539	+	0.605902i	$0.792812\pi$
$978$	5.73251e12	0.200364
$979$	−1.02055e13	−0.355068
$980$	0	0
$981$	−6.95097e12	−0.239626
$982$	−6.96109e13	−2.38878
$983$	2.54481e13	0.869290	0.434645	−	0.900602i	$-0.356874\pi$
$983$	2.54481e13	0.869290	0.434645	+	0.900602i	$0.356874\pi$
$984$	−7.90545e12	−0.268812
$985$	0	0
$986$	−9.46704e13	−3.18983
$987$	−3.81225e12	−0.127866
$988$	2.75155e13	0.918694
$989$	6.93817e12	0.230601
$990$	0	0
$991$	−5.41691e13	−1.78410	−0.892052	−	0.451933i	$-0.850734\pi$
$991$	−5.41691e13	−1.78410	−0.892052	+	0.451933i	$0.850734\pi$
$992$	1.17634e13	0.385683
$993$	−4.36465e12	−0.142455
$994$	−1.70523e13	−0.554045
$995$	0	0
$996$	3.56200e13	1.14690
$997$	4.29329e13	1.37614	0.688069	−	0.725646i	$-0.258459\pi$
$997$	4.29329e13	1.37614	0.688069	+	0.725646i	$0.258459\pi$
$998$	−1.11473e13	−0.355697
$999$	3.44788e13	1.09524

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.10.a.d.1.3		3
5.2	odd	4		175.10.b.d.99.5		6
5.3	odd	4		175.10.b.d.99.2		6
5.4	even	2		7.10.a.b.1.1	✓	3
15.14	odd	2		63.10.a.e.1.3		3
20.19	odd	2		112.10.a.h.1.3		3
35.4	even	6		49.10.c.d.30.3		6
35.9	even	6		49.10.c.d.18.3		6
35.19	odd	6		49.10.c.e.18.3		6
35.24	odd	6		49.10.c.e.30.3		6
35.34	odd	2		49.10.a.c.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.10.a.b.1.1	✓	3	5.4	even	2
49.10.a.c.1.1		3	35.34	odd	2
49.10.c.d.18.3		6	35.9	even	6
49.10.c.d.30.3		6	35.4	even	6
49.10.c.e.18.3		6	35.19	odd	6
49.10.c.e.30.3		6	35.24	odd	6
63.10.a.e.1.3		3	15.14	odd	2
112.10.a.h.1.3		3	20.19	odd	2
175.10.a.d.1.3		3	1.1	even	1	trivial
175.10.b.d.99.2		6	5.3	odd	4
175.10.b.d.99.5		6	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	175.a (trivial)

\(f(q)\)	\(=\)	\(q+34.1627 q^{2} +79.6469 q^{3} +655.088 q^{4} +2720.95 q^{6} -2401.00 q^{7} +4888.28 q^{8} -13339.4 q^{9} +69354.4 q^{11} +52175.7 q^{12} -105959. q^{13} -82024.6 q^{14} -168409. q^{16} -568267. q^{17} -455709. q^{18} -396405. q^{19} -191232. q^{21} +2.36933e6 q^{22} +620765. q^{23} +389336. q^{24} -3.61984e6 q^{26} -2.63013e6 q^{27} -1.57287e6 q^{28} +4.87652e6 q^{29} -1.42482e6 q^{31} -8.25609e6 q^{32} +5.52386e6 q^{33} -1.94135e7 q^{34} -8.73846e6 q^{36} -1.31092e7 q^{37} -1.35423e7 q^{38} -8.43931e6 q^{39} -2.03049e7 q^{41} -6.53300e6 q^{42} +1.11768e7 q^{43} +4.54332e7 q^{44} +2.12070e7 q^{46} +1.99352e7 q^{47} -1.34132e7 q^{48} +5.76480e6 q^{49} -4.52607e7 q^{51} -6.94125e7 q^{52} -5.65007e7 q^{53} -8.98523e7 q^{54} -1.17367e7 q^{56} -3.15725e7 q^{57} +1.66595e8 q^{58} -1.09340e8 q^{59} +3.20008e7 q^{61} -4.86755e7 q^{62} +3.20278e7 q^{63} -1.95825e8 q^{64} +1.88710e8 q^{66} -8.02869e7 q^{67} -3.72265e8 q^{68} +4.94420e7 q^{69} +2.07893e8 q^{71} -6.52065e7 q^{72} +2.70274e8 q^{73} -4.47844e8 q^{74} -2.59680e8 q^{76} -1.66520e8 q^{77} -2.88309e8 q^{78} -5.16196e8 q^{79} +5.30772e7 q^{81} -6.93671e8 q^{82} +6.82693e8 q^{83} -1.25274e8 q^{84} +3.81830e8 q^{86} +3.88400e8 q^{87} +3.39023e8 q^{88} -1.47150e8 q^{89} +2.54408e8 q^{91} +4.06656e8 q^{92} -1.13482e8 q^{93} +6.81040e8 q^{94} -6.57572e8 q^{96} -1.09643e9 q^{97} +1.96941e8 q^{98} -9.25144e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 21 q^{2} - 84 q^{3} + 1557 q^{4} + 4914 q^{6} - 7203 q^{7} - 14055 q^{8} - 26001 q^{9} - 3444 q^{11} + 106386 q^{12} + 19782 q^{13} + 50421 q^{14} + 482961 q^{16} - 1016694 q^{17} + 273267 q^{18}+ \cdots - 1900979172 q^{99}+O(q^{100}) \) 3 * q - 21 * q^2 - 84 * q^3 + 1557 * q^4 + 4914 * q^6 - 7203 * q^7 - 14055 * q^8 - 26001 * q^9 - 3444 * q^11 + 106386 * q^12 + 19782 * q^13 + 50421 * q^14 + 482961 * q^16 - 1016694 * q^17 + 273267 * q^18 + 222852 * q^19 + 201684 * q^21 + 2847048 * q^22 - 1885632 * q^23 - 1449630 * q^24 - 8785056 * q^26 - 551880 * q^27 - 3738357 * q^28 + 4081818 * q^29 + 2869440 * q^31 - 25221951 * q^32 + 20259792 * q^33 - 3981642 * q^34 - 35396379 * q^36 - 1395618 * q^37 - 43479870 * q^38 - 8990688 * q^39 - 14420658 * q^41 - 11798514 * q^42 + 61631172 * q^43 + 97011984 * q^44 + 89747664 * q^46 + 10368960 * q^47 - 16798782 * q^48 + 17294403 * q^49 - 26146728 * q^51 + 80908044 * q^52 - 67502610 * q^53 - 117879300 * q^54 + 33746055 * q^56 - 8471112 * q^57 + 159163830 * q^58 - 42590100 * q^59 + 191746842 * q^61 + 46983468 * q^62 + 62428401 * q^63 + 7852161 * q^64 - 8057952 * q^66 + 255175788 * q^67 - 743485806 * q^68 + 257903856 * q^69 + 296514504 * q^71 + 609314265 * q^72 - 344213310 * q^73 - 690696462 * q^74 + 728839986 * q^76 + 8269044 * q^77 - 280132776 * q^78 - 960412656 * q^79 - 35827677 * q^81 - 562675302 * q^82 + 1100517180 * q^83 - 255432786 * q^84 - 880982256 * q^86 + 621821592 * q^87 - 1206124800 * q^88 + 506816478 * q^89 - 47496582 * q^91 - 691123488 * q^92 - 1693258512 * q^93 + 1388004828 * q^94 + 333385794 * q^96 + 647498250 * q^97 - 121060821 * q^98 - 1900979172 * q^99

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