LMFDB - Embedded newform 245.10.a.f.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("245.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$126.183779860$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 1694x^{3} + 7420x^{2} + 583584x - 2721600 $ x^5 - 2x^4 - 1694x^3 + 7420x^2 + 583584x - 2721600
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{3}\cdot 5 $
Twist minimal:	no (minimal twist has level 35)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$4.68049$ of defining polynomial
Character	$\chi$	$=$	245.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+4.68049 q^{2} +7.83652 q^{3} -490.093 q^{4} +625.000 q^{5} +36.6787 q^{6} -4690.29 q^{8} -19621.6 q^{9} +2925.31 q^{10} +61293.3 q^{11} -3840.62 q^{12} -127788. q^{13} +4897.82 q^{15} +228975. q^{16} +374440. q^{17} -91838.6 q^{18} -351367. q^{19} -306308. q^{20} +286883. q^{22} +1.55822e6 q^{23} -36755.5 q^{24} +390625. q^{25} -598109. q^{26} -308011. q^{27} +3.12932e6 q^{29} +22924.2 q^{30} -6.54089e6 q^{31} +3.47314e6 q^{32} +480326. q^{33} +1.75256e6 q^{34} +9.61640e6 q^{36} -9.25714e6 q^{37} -1.64457e6 q^{38} -1.00141e6 q^{39} -2.93143e6 q^{40} +8.05013e6 q^{41} +1.58627e7 q^{43} -3.00394e7 q^{44} -1.22635e7 q^{45} +7.29324e6 q^{46} +8.88373e6 q^{47} +1.79436e6 q^{48} +1.82832e6 q^{50} +2.93431e6 q^{51} +6.26278e7 q^{52} -5.68387e7 q^{53} -1.44164e6 q^{54} +3.83083e7 q^{55} -2.75349e6 q^{57} +1.46467e7 q^{58} -8.14197e7 q^{59} -2.40039e6 q^{60} +2.04282e8 q^{61} -3.06146e7 q^{62} -1.00979e8 q^{64} -7.98673e7 q^{65} +2.24816e6 q^{66} +8.88281e7 q^{67} -1.83510e8 q^{68} +1.22110e7 q^{69} +2.24233e8 q^{71} +9.20309e7 q^{72} -1.91441e8 q^{73} -4.33280e7 q^{74} +3.06114e6 q^{75} +1.72203e8 q^{76} -4.68709e6 q^{78} +2.39411e7 q^{79} +1.43109e8 q^{80} +3.83798e8 q^{81} +3.76785e7 q^{82} -4.05879e8 q^{83} +2.34025e8 q^{85} +7.42452e7 q^{86} +2.45229e7 q^{87} -2.87483e8 q^{88} -2.03470e8 q^{89} -5.73992e7 q^{90} -7.63674e8 q^{92} -5.12578e7 q^{93} +4.15802e7 q^{94} -2.19604e8 q^{95} +2.72173e7 q^{96} -9.77776e8 q^{97} -1.20267e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 2 q^{2} - 140 q^{3} + 832 q^{4} + 3125 q^{5} + 144 q^{6} - 14136 q^{8} + 67797 q^{9} + 1250 q^{10} + 10312 q^{11} - 63388 q^{12} - 158638 q^{13} - 87500 q^{15} - 526696 q^{16} - 31614 q^{17} + 1816986 q^{18}+ \cdots + 698312668 q^{99}+O(q^{100}) $ 5 * q + 2 * q^2 - 140 * q^3 + 832 * q^4 + 3125 * q^5 + 144 * q^6 - 14136 * q^8 + 67797 * q^9 + 1250 * q^10 + 10312 * q^11 - 63388 * q^12 - 158638 * q^13 - 87500 * q^15 - 526696 * q^16 - 31614 * q^17 + 1816986 * q^18 - 1655376 * q^19 + 520000 * q^20 + 3659464 * q^22 + 796104 * q^23 - 6504576 * q^24 + 1953125 * q^25 - 10219060 * q^26 - 4190732 * q^27 - 3353726 * q^29 + 90000 * q^30 - 2678120 * q^31 - 130400 * q^32 - 20444132 * q^33 - 21548612 * q^34 + 15390460 * q^36 + 50994846 * q^37 + 34907600 * q^38 - 18124 * q^39 - 8835000 * q^40 - 6330194 * q^41 + 6149468 * q^43 - 71225892 * q^44 + 42373125 * q^45 - 142845472 * q^46 + 6897780 * q^47 + 46423032 * q^48 + 781250 * q^50 - 17970212 * q^51 + 22199468 * q^52 - 70886738 * q^53 + 113279328 * q^54 + 6445000 * q^55 - 355886264 * q^57 - 31955924 * q^58 + 152335168 * q^59 - 39617500 * q^60 - 257015698 * q^61 + 215582768 * q^62 - 193988432 * q^64 - 99148750 * q^65 - 183241664 * q^66 + 133467828 * q^67 + 268709380 * q^68 + 191957336 * q^69 + 522788960 * q^71 + 221927400 * q^72 - 159370858 * q^73 - 244178868 * q^74 - 54687500 * q^75 + 345056616 * q^76 + 1164346496 * q^78 + 464174900 * q^79 - 329185000 * q^80 + 865150989 * q^81 - 308947620 * q^82 - 2207636832 * q^83 - 19758750 * q^85 + 694560616 * q^86 - 2952845788 * q^87 + 930528736 * q^88 + 1106708326 * q^89 + 1135616250 * q^90 + 205160216 * q^92 + 767757392 * q^93 + 3602501744 * q^94 - 1034610000 * q^95 + 2652128640 * q^96 - 1956142254 * q^97 + 698312668 * q^99

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	4.68049	0.206850	0.103425	−	0.994637i	$-0.467020\pi$
$2$	4.68049	0.206850	0.103425	+	0.994637i	$0.467020\pi$
$3$	7.83652	0.0558570	0.0279285	−	0.999610i	$-0.491109\pi$
$3$	7.83652	0.0558570	0.0279285	+	0.999610i	$0.491109\pi$
$4$	−490.093	−0.957213
$5$	625.000	0.447214
$5$	625.000	0.447214
$6$	36.6787	0.0115540
$7$	0	0
$7$	0	0
$8$	−4690.29	−0.404850
$9$	−19621.6	−0.996880
$10$	2925.31	0.0925063
$11$	61293.3	1.26225	0.631126	−	0.775680i	$-0.282593\pi$
$11$	61293.3	1.26225	0.631126	+	0.775680i	$0.282593\pi$
$12$	−3840.62	−0.0534670
$13$	−127788.	−1.24092	−0.620460	−	0.784238i	$-0.713054\pi$
$13$	−127788.	−1.24092	−0.620460	+	0.784238i	$0.713054\pi$
$14$	0	0
$15$	4897.82	0.0249800
$16$	228975.	0.873470
$17$	374440.	1.08733	0.543666	−	0.839302i	$-0.317036\pi$
$17$	374440.	1.08733	0.543666	+	0.839302i	$0.317036\pi$
$18$	−91838.6	−0.206205
$19$	−351367.	−0.618543	−0.309272	−	0.950974i	$-0.600085\pi$
$19$	−351367.	−0.618543	−0.309272	+	0.950974i	$0.600085\pi$
$20$	−306308.	−0.428079
$21$	0	0
$22$	286883.	0.261097
$23$	1.55822e6	1.16106	0.580529	−	0.814239i	$-0.302846\pi$
$23$	1.55822e6	1.16106	0.580529	+	0.814239i	$0.302846\pi$
$24$	−36755.5	−0.0226137
$25$	390625.	0.200000
$26$	−598109.	−0.256685
$27$	−308011.	−0.111540
$28$	0	0
$29$	3.12932e6	0.821597	0.410798	−	0.911726i	$-0.365250\pi$
$29$	3.12932e6	0.821597	0.410798	+	0.911726i	$0.365250\pi$
$30$	22924.2	0.00516712
$31$	−6.54089e6	−1.27206	−0.636032	−	0.771662i	$-0.719426\pi$
$31$	−6.54089e6	−1.27206	−0.636032	+	0.771662i	$0.719426\pi$
$32$	3.47314e6	0.585528
$33$	480326.	0.0705056
$34$	1.75256e6	0.224915
$35$	0	0
$36$	9.61640e6	0.954226
$37$	−9.25714e6	−0.812025	−0.406012	−	0.913868i	$-0.633081\pi$
$37$	−9.25714e6	−0.812025	−0.406012	+	0.913868i	$0.633081\pi$
$38$	−1.64457e6	−0.127946
$39$	−1.00141e6	−0.0693140
$40$	−2.93143e6	−0.181055
$41$	8.05013e6	0.444913	0.222457	−	0.974943i	$-0.428592\pi$
$41$	8.05013e6	0.444913	0.222457	+	0.974943i	$0.428592\pi$
$42$	0	0
$43$	1.58627e7	0.707570	0.353785	−	0.935327i	$-0.384895\pi$
$43$	1.58627e7	0.707570	0.353785	+	0.935327i	$0.384895\pi$
$44$	−3.00394e7	−1.20824
$45$	−1.22635e7	−0.445818
$46$	7.29324e6	0.240165
$47$	8.88373e6	0.265555	0.132778	−	0.991146i	$-0.457610\pi$
$47$	8.88373e6	0.265555	0.132778	+	0.991146i	$0.457610\pi$
$48$	1.79436e6	0.0487894
$49$	0	0
$50$	1.82832e6	0.0413701
$51$	2.93431e6	0.0607351
$52$	6.26278e7	1.18782
$53$	−5.68387e7	−0.989471	−0.494735	−	0.869044i	$-0.664735\pi$
$53$	−5.68387e7	−0.989471	−0.494735	+	0.869044i	$0.664735\pi$
$54$	−1.44164e6	−0.0230720
$55$	3.83083e7	0.564496
$56$	0	0
$57$	−2.75349e6	−0.0345499
$58$	1.46467e7	0.169948
$59$	−8.14197e7	−0.874773	−0.437387	−	0.899274i	$-0.644096\pi$
$59$	−8.14197e7	−0.874773	−0.437387	+	0.899274i	$0.644096\pi$
$60$	−2.40039e6	−0.0239112
$61$	2.04282e8	1.88906	0.944531	−	0.328421i	$-0.106517\pi$
$61$	2.04282e8	1.88906	0.944531	+	0.328421i	$0.106517\pi$
$62$	−3.06146e7	−0.263127
$63$	0	0
$64$	−1.00979e8	−0.752353
$65$	−7.98673e7	−0.554956
$66$	2.24816e6	0.0145841
$67$	8.88281e7	0.538535	0.269267	−	0.963065i	$-0.413218\pi$
$67$	8.88281e7	0.538535	0.269267	+	0.963065i	$0.413218\pi$
$68$	−1.83510e8	−1.04081
$69$	1.22110e7	0.0648532
$70$	0	0
$71$	2.24233e8	1.04722	0.523609	−	0.851959i	$-0.324585\pi$
$71$	2.24233e8	1.04722	0.523609	+	0.851959i	$0.324585\pi$
$72$	9.20309e7	0.403587
$73$	−1.91441e8	−0.789010	−0.394505	−	0.918894i	$-0.629084\pi$
$73$	−1.91441e8	−0.789010	−0.394505	+	0.918894i	$0.629084\pi$
$74$	−4.33280e7	−0.167968
$75$	3.06114e6	0.0111714
$76$	1.72203e8	0.592077
$77$	0	0
$78$	−4.68709e6	−0.0143376
$79$	2.39411e7	0.0691549	0.0345774	−	0.999402i	$-0.488991\pi$
$79$	2.39411e7	0.0691549	0.0345774	+	0.999402i	$0.488991\pi$
$80$	1.43109e8	0.390627
$81$	3.83798e8	0.990650
$82$	3.76785e7	0.0920305
$83$	−4.05879e8	−0.938741	−0.469370	−	0.883001i	$-0.655519\pi$
$83$	−4.05879e8	−0.938741	−0.469370	+	0.883001i	$0.655519\pi$
$84$	0	0
$85$	2.34025e8	0.486270
$86$	7.42452e7	0.146361
$87$	2.45229e7	0.0458919
$88$	−2.87483e8	−0.511023
$89$	−2.03470e8	−0.343752	−0.171876	−	0.985119i	$-0.554983\pi$
$89$	−2.03470e8	−0.343752	−0.171876	+	0.985119i	$0.554983\pi$
$90$	−5.73992e7	−0.0922177
$91$	0	0
$92$	−7.63674e8	−1.11138
$93$	−5.12578e7	−0.0710537
$94$	4.15802e7	0.0549302
$95$	−2.19604e8	−0.276621
$96$	2.72173e7	0.0327058
$97$	−9.77776e8	−1.12142	−0.560708	−	0.828014i	$-0.689471\pi$
$97$	−9.77776e8	−1.12142	−0.560708	+	0.828014i	$0.689471\pi$
$98$	0	0
$99$	−1.20267e9	−1.25831
$100$	−1.91443e8	−0.191443
$101$	−1.21059e9	−1.15758	−0.578792	−	0.815475i	$-0.696476\pi$
$101$	−1.21059e9	−1.15758	−0.578792	+	0.815475i	$0.696476\pi$
$102$	1.37340e7	0.0125631
$103$	−1.67608e9	−1.46733	−0.733666	−	0.679511i	$-0.762192\pi$
$103$	−1.67608e9	−1.46733	−0.733666	+	0.679511i	$0.762192\pi$
$104$	5.99361e8	0.502387
$105$	0	0
$106$	−2.66033e8	−0.204672
$107$	−1.18347e9	−0.872831	−0.436416	−	0.899745i	$-0.643752\pi$
$107$	−1.18347e9	−0.872831	−0.436416	+	0.899745i	$0.643752\pi$
$108$	1.50954e8	0.106767
$109$	−2.42544e9	−1.64578	−0.822888	−	0.568203i	$-0.807639\pi$
$109$	−2.42544e9	−1.64578	−0.822888	+	0.568203i	$0.807639\pi$
$110$	1.79302e8	0.116766
$111$	−7.25438e7	−0.0453572
$112$	0	0
$113$	1.29095e9	0.744828	0.372414	−	0.928067i	$-0.378530\pi$
$113$	1.29095e9	0.744828	0.372414	+	0.928067i	$0.378530\pi$
$114$	−1.28877e7	−0.00714667
$115$	9.73889e8	0.519241
$116$	−1.53366e9	−0.786443
$117$	2.50740e9	1.23705
$118$	−3.81084e8	−0.180947
$119$	0	0
$120$	−2.29722e7	−0.0101132
$121$	1.39892e9	0.593280
$122$	9.56141e8	0.390753
$123$	6.30850e7	0.0248515
$124$	3.20564e9	1.21764
$125$	2.44141e8	0.0894427
$126$	0	0
$127$	4.57285e9	1.55980	0.779902	−	0.625902i	$-0.215269\pi$
$127$	4.57285e9	1.55980	0.779902	+	0.625902i	$0.215269\pi$
$128$	−2.25088e9	−0.741152
$129$	1.24308e8	0.0395227
$130$	−3.73818e8	−0.114793
$131$	−1.97356e9	−0.585504	−0.292752	−	0.956188i	$-0.594571\pi$
$131$	−1.97356e9	−0.585504	−0.292752	+	0.956188i	$0.594571\pi$
$132$	−2.35404e8	−0.0674888
$133$	0	0
$134$	4.15759e8	0.111396
$135$	−1.92507e8	−0.0498821
$136$	−1.75623e9	−0.440207
$137$	2.91623e9	0.707260	0.353630	−	0.935385i	$-0.384947\pi$
$137$	2.91623e9	0.707260	0.353630	+	0.935385i	$0.384947\pi$
$138$	5.71536e7	0.0134149
$139$	−1.68574e8	−0.0383023	−0.0191512	−	0.999817i	$-0.506096\pi$
$139$	−1.68574e8	−0.0383023	−0.0191512	+	0.999817i	$0.506096\pi$
$140$	0	0
$141$	6.96175e7	0.0148331
$142$	1.04952e9	0.216617
$143$	−7.83253e9	−1.56635
$144$	−4.49285e9	−0.870744
$145$	1.95582e9	0.367429
$146$	−8.96039e8	−0.163207
$147$	0	0
$148$	4.53686e9	0.777281
$149$	−1.03146e10	−1.71440	−0.857202	−	0.514980i	$-0.827799\pi$
$149$	−1.03146e10	−1.71440	−0.857202	+	0.514980i	$0.827799\pi$
$150$	1.43276e7	0.00231081
$151$	−6.51350e9	−1.01957	−0.509786	−	0.860301i	$-0.670276\pi$
$151$	−6.51350e9	−1.01957	−0.509786	+	0.860301i	$0.670276\pi$
$152$	1.64801e9	0.250417
$153$	−7.34711e9	−1.08394
$154$	0	0
$155$	−4.08806e9	−0.568885
$156$	4.90784e8	0.0663483
$157$	−1.06861e10	−1.40369	−0.701843	−	0.712332i	$-0.747639\pi$
$157$	−1.06861e10	−1.40369	−0.701843	+	0.712332i	$0.747639\pi$
$158$	1.12056e8	0.0143047
$159$	−4.45418e8	−0.0552688
$160$	2.17071e9	0.261856
$161$	0	0
$162$	1.79636e9	0.204916
$163$	1.42299e10	1.57891	0.789457	−	0.613806i	$-0.210362\pi$
$163$	1.42299e10	1.57891	0.789457	+	0.613806i	$0.210362\pi$
$164$	−3.94531e9	−0.425877
$165$	3.00204e8	0.0315311
$166$	−1.89971e9	−0.194179
$167$	−2.78646e9	−0.277223	−0.138611	−	0.990347i	$-0.544264\pi$
$167$	−2.78646e9	−0.277223	−0.138611	+	0.990347i	$0.544264\pi$
$168$	0	0
$169$	5.72518e9	0.539882
$170$	1.09535e9	0.100585
$171$	6.89438e9	0.616613
$172$	−7.77420e9	−0.677295
$173$	1.71904e10	1.45908	0.729540	−	0.683938i	$-0.239734\pi$
$173$	1.71904e10	1.45908	0.729540	+	0.683938i	$0.239734\pi$
$174$	1.14779e8	0.00949276
$175$	0	0
$176$	1.40346e10	1.10254
$177$	−6.38047e8	−0.0488622
$178$	−9.52340e8	−0.0711053
$179$	−2.31226e10	−1.68344	−0.841719	−	0.539915i	$-0.818456\pi$
$179$	−2.31226e10	−1.68344	−0.841719	+	0.539915i	$0.818456\pi$
$180$	6.01025e9	0.426743
$181$	−2.28943e10	−1.58553	−0.792763	−	0.609531i	$-0.791358\pi$
$181$	−2.28943e10	−1.58553	−0.792763	+	0.609531i	$0.791358\pi$
$182$	0	0
$183$	1.60086e9	0.105517
$184$	−7.30851e9	−0.470055
$185$	−5.78572e9	−0.363149
$186$	−2.39912e8	−0.0146975
$187$	2.29507e10	1.37249
$188$	−4.35386e9	−0.254193
$189$	0	0
$190$	−1.02786e9	−0.0572191
$191$	−1.66664e10	−0.906131	−0.453065	−	0.891477i	$-0.649670\pi$
$191$	−1.66664e10	−0.906131	−0.453065	+	0.891477i	$0.649670\pi$
$192$	−7.91324e8	−0.0420242
$193$	−2.30952e10	−1.19816	−0.599079	−	0.800690i	$-0.704466\pi$
$193$	−2.30952e10	−1.19816	−0.599079	+	0.800690i	$0.704466\pi$
$194$	−4.57647e9	−0.231965
$195$	−6.25881e8	−0.0309982
$196$	0	0
$197$	−2.42166e10	−1.14555	−0.572776	−	0.819712i	$-0.694134\pi$
$197$	−2.42166e10	−1.14555	−0.572776	+	0.819712i	$0.694134\pi$
$198$	−5.62910e9	−0.260283
$199$	2.18408e10	0.987257	0.493628	−	0.869673i	$-0.335670\pi$
$199$	2.18408e10	0.987257	0.493628	+	0.869673i	$0.335670\pi$
$200$	−1.83214e9	−0.0809700
$201$	6.96103e8	0.0300809
$202$	−5.66617e9	−0.239447
$203$	0	0
$204$	−1.43808e9	−0.0581364
$205$	5.03133e9	0.198971
$206$	−7.84489e9	−0.303518
$207$	−3.05748e10	−1.15744
$208$	−2.92601e10	−1.08391
$209$	−2.15365e10	−0.780757
$210$	0	0
$211$	7.72507e9	0.268307	0.134153	−	0.990961i	$-0.457169\pi$
$211$	7.72507e9	0.268307	0.134153	+	0.990961i	$0.457169\pi$
$212$	2.78563e10	0.947134
$213$	1.75720e9	0.0584944
$214$	−5.53922e9	−0.180545
$215$	9.91419e9	0.316435
$216$	1.44466e9	0.0451569
$217$	0	0
$218$	−1.13522e10	−0.340429
$219$	−1.50023e9	−0.0440717
$220$	−1.87746e10	−0.540343
$221$	−4.78488e10	−1.34929
$222$	−3.39540e8	−0.00938216
$223$	−2.17022e10	−0.587668	−0.293834	−	0.955856i	$-0.594931\pi$
$223$	−2.17022e10	−0.587668	−0.293834	+	0.955856i	$0.594931\pi$
$224$	0	0
$225$	−7.66468e9	−0.199376
$226$	6.04227e9	0.154068
$227$	−4.79669e10	−1.19902	−0.599508	−	0.800369i	$-0.704637\pi$
$227$	−4.79669e10	−1.19902	−0.599508	+	0.800369i	$0.704637\pi$
$228$	1.34947e9	0.0330716
$229$	−4.12350e10	−0.990846	−0.495423	−	0.868652i	$-0.664987\pi$
$229$	−4.12350e10	−0.990846	−0.495423	+	0.868652i	$0.664987\pi$
$230$	4.55828e9	0.107405
$231$	0	0
$232$	−1.46774e10	−0.332624
$233$	−7.25284e10	−1.61215	−0.806077	−	0.591811i	$-0.798413\pi$
$233$	−7.25284e10	−1.61215	−0.806077	+	0.591811i	$0.798413\pi$
$234$	1.17358e10	0.255884
$235$	5.55233e9	0.118760
$236$	3.99032e10	0.837344
$237$	1.87615e8	0.00386278
$238$	0	0
$239$	8.27096e10	1.63970	0.819852	−	0.572576i	$-0.194056\pi$
$239$	8.27096e10	1.63970	0.819852	+	0.572576i	$0.194056\pi$
$240$	1.12148e9	0.0218193
$241$	−5.66304e10	−1.08137	−0.540683	−	0.841226i	$-0.681834\pi$
$241$	−5.66304e10	−1.08137	−0.540683	+	0.841226i	$0.681834\pi$
$242$	6.54765e9	0.122720
$243$	9.07022e9	0.166874
$244$	−1.00117e11	−1.80824
$245$	0	0
$246$	2.95269e8	0.00514054
$247$	4.49004e10	0.767562
$248$	3.06786e10	0.514996
$249$	−3.18068e9	−0.0524352
$250$	1.14270e9	0.0185013
$251$	4.37000e10	0.694944	0.347472	−	0.937690i	$-0.387040\pi$
$251$	4.37000e10	0.694944	0.347472	+	0.937690i	$0.387040\pi$
$252$	0	0
$253$	9.55086e10	1.46555
$254$	2.14032e10	0.322646
$255$	1.83394e9	0.0271615
$256$	4.11661e10	0.599045
$257$	1.04178e11	1.48963	0.744815	−	0.667271i	$-0.232538\pi$
$257$	1.04178e11	1.48963	0.744815	+	0.667271i	$0.232538\pi$
$258$	5.81824e8	0.00817529
$259$	0	0
$260$	3.91424e10	0.531211
$261$	−6.14022e10	−0.819033
$262$	−9.23723e9	−0.121112
$263$	−1.04346e11	−1.34485	−0.672424	−	0.740166i	$-0.734747\pi$
$263$	−1.04346e11	−1.34485	−0.672424	+	0.740166i	$0.734747\pi$
$264$	−2.25287e9	−0.0285442
$265$	−3.55242e10	−0.442505
$266$	0	0
$267$	−1.59450e9	−0.0192010
$268$	−4.35340e10	−0.515493
$269$	−9.25092e10	−1.07721	−0.538604	−	0.842559i	$-0.681048\pi$
$269$	−9.25092e10	−1.07721	−0.538604	+	0.842559i	$0.681048\pi$
$270$	−9.01027e8	−0.0103181
$271$	5.41823e10	0.610233	0.305117	−	0.952315i	$-0.401305\pi$
$271$	5.41823e10	0.610233	0.305117	+	0.952315i	$0.401305\pi$
$272$	8.57373e10	0.949751
$273$	0	0
$274$	1.36494e10	0.146297
$275$	2.39427e10	0.252450
$276$	−5.98454e9	−0.0620783
$277$	1.18973e11	1.21420	0.607099	−	0.794627i	$-0.292333\pi$
$277$	1.18973e11	1.21420	0.607099	+	0.794627i	$0.292333\pi$
$278$	−7.89011e8	−0.00792285
$279$	1.28343e11	1.26810
$280$	0	0
$281$	−7.86550e10	−0.752572	−0.376286	−	0.926504i	$-0.622799\pi$
$281$	−7.86550e10	−0.752572	−0.376286	+	0.926504i	$0.622799\pi$
$282$	3.25844e8	0.00306824
$283$	8.35155e10	0.773977	0.386989	−	0.922085i	$-0.373515\pi$
$283$	8.35155e10	0.773977	0.386989	+	0.922085i	$0.373515\pi$
$284$	−1.09895e11	−1.00241
$285$	−1.72093e9	−0.0154512
$286$	−3.66601e10	−0.324001
$287$	0	0
$288$	−6.81485e10	−0.583701
$289$	2.16174e10	0.182290
$290$	9.15421e9	0.0760029
$291$	−7.66236e9	−0.0626389
$292$	9.38240e10	0.755251
$293$	6.91745e10	0.548330	0.274165	−	0.961683i	$-0.411599\pi$
$293$	6.91745e10	0.548330	0.274165	+	0.961683i	$0.411599\pi$
$294$	0	0
$295$	−5.08873e10	−0.391210
$296$	4.34187e10	0.328748
$297$	−1.88790e10	−0.140791
$298$	−4.82773e10	−0.354625
$299$	−1.99122e11	−1.44078
$300$	−1.50024e9	−0.0106934
$301$	0	0
$302$	−3.04864e10	−0.210899
$303$	−9.48684e9	−0.0646591
$304$	−8.04542e10	−0.540278
$305$	1.27676e11	0.844814
$306$	−3.43881e10	−0.224213
$307$	−1.72821e10	−0.111039	−0.0555194	−	0.998458i	$-0.517681\pi$
$307$	−1.72821e10	−0.111039	−0.0555194	+	0.998458i	$0.517681\pi$
$308$	0	0
$309$	−1.31347e10	−0.0819607
$310$	−1.91341e10	−0.117674
$311$	2.24570e11	1.36123	0.680614	−	0.732642i	$-0.261713\pi$
$311$	2.24570e11	1.36123	0.680614	+	0.732642i	$0.261713\pi$
$312$	4.69690e9	0.0280618
$313$	−6.15640e10	−0.362558	−0.181279	−	0.983432i	$-0.558024\pi$
$313$	−6.15640e10	−0.362558	−0.181279	+	0.983432i	$0.558024\pi$
$314$	−5.00161e10	−0.290353
$315$	0	0
$316$	−1.17334e10	−0.0661959
$317$	−1.03866e11	−0.577705	−0.288853	−	0.957374i	$-0.593274\pi$
$317$	−1.03866e11	−0.577705	−0.288853	+	0.957374i	$0.593274\pi$
$318$	−2.08477e9	−0.0114324
$319$	1.91806e11	1.03706
$320$	−6.31119e10	−0.336462
$321$	−9.27428e9	−0.0487537
$322$	0	0
$323$	−1.31566e11	−0.672561
$324$	−1.88097e11	−0.948263
$325$	−4.99170e10	−0.248184
$326$	6.66030e10	0.326599
$327$	−1.90070e10	−0.0919281
$328$	−3.77574e10	−0.180123
$329$	0	0
$330$	1.40510e9	0.00652221
$331$	1.19600e11	0.547651	0.273826	−	0.961779i	$-0.411711\pi$
$331$	1.19600e11	0.547651	0.273826	+	0.961779i	$0.411711\pi$
$332$	1.98919e11	0.898575
$333$	1.81640e11	0.809491
$334$	−1.30420e10	−0.0573436
$335$	5.55176e10	0.240840
$336$	0	0
$337$	1.78854e11	0.755379	0.377690	−	0.925932i	$-0.376719\pi$
$337$	1.78854e11	0.755379	0.377690	+	0.925932i	$0.376719\pi$
$338$	2.67967e10	0.111675
$339$	1.01165e10	0.0416038
$340$	−1.14694e11	−0.465464
$341$	−4.00913e11	−1.60567
$342$	3.22691e10	0.127547
$343$	0	0
$344$	−7.44006e10	−0.286460
$345$	7.63189e9	0.0290032
$346$	8.04596e10	0.301811
$347$	2.90904e11	1.07713	0.538563	−	0.842585i	$-0.318967\pi$
$347$	2.90904e11	1.07713	0.538563	+	0.842585i	$0.318967\pi$
$348$	−1.20185e10	−0.0439283
$349$	1.20156e11	0.433543	0.216772	−	0.976222i	$-0.430447\pi$
$349$	1.20156e11	0.433543	0.216772	+	0.976222i	$0.430447\pi$
$350$	0	0
$351$	3.93600e10	0.138412
$352$	2.12880e11	0.739084
$353$	−2.68637e11	−0.920831	−0.460415	−	0.887704i	$-0.652300\pi$
$353$	−2.68637e11	−0.920831	−0.460415	+	0.887704i	$0.652300\pi$
$354$	−2.98637e9	−0.0101072
$355$	1.40146e11	0.468330
$356$	9.97193e10	0.329044
$357$	0	0
$358$	−1.08225e11	−0.348220
$359$	4.23529e11	1.34573	0.672865	−	0.739765i	$-0.265063\pi$
$359$	4.23529e11	1.34573	0.672865	+	0.739765i	$0.265063\pi$
$360$	5.75193e10	0.180490
$361$	−1.99229e11	−0.617405
$362$	−1.07156e11	−0.327966
$363$	1.09627e10	0.0331388
$364$	0	0
$365$	−1.19651e11	−0.352856
$366$	7.49281e9	0.0218263
$367$	3.14338e11	0.904480	0.452240	−	0.891896i	$-0.350625\pi$
$367$	3.14338e11	0.904480	0.452240	+	0.891896i	$0.350625\pi$
$368$	3.56794e11	1.01415
$369$	−1.57956e11	−0.443525
$370$	−2.70800e10	−0.0751174
$371$	0	0
$372$	2.51211e10	0.0680135
$373$	4.22978e11	1.13143	0.565715	−	0.824601i	$-0.308600\pi$
$373$	4.22978e11	1.13143	0.565715	+	0.824601i	$0.308600\pi$
$374$	1.07420e11	0.283899
$375$	1.91321e9	0.00499600
$376$	−4.16673e10	−0.107510
$377$	−3.99888e11	−1.01954
$378$	0	0
$379$	−4.54590e11	−1.13173	−0.565866	−	0.824497i	$-0.691458\pi$
$379$	−4.54590e11	−1.13173	−0.565866	+	0.824497i	$0.691458\pi$
$380$	1.07627e11	0.264785
$381$	3.58352e10	0.0871259
$382$	−7.80068e10	−0.187433
$383$	2.56165e11	0.608311	0.304155	−	0.952622i	$-0.401626\pi$
$383$	2.56165e11	0.608311	0.304155	+	0.952622i	$0.401626\pi$
$384$	−1.76391e10	−0.0413985
$385$	0	0
$386$	−1.08097e11	−0.247839
$387$	−3.11252e11	−0.705362
$388$	4.79201e11	1.07343
$389$	4.07620e9	0.00902572	0.00451286	−	0.999990i	$-0.498564\pi$
$389$	4.07620e9	0.00902572	0.00451286	+	0.999990i	$0.498564\pi$
$390$	−2.92943e9	−0.00641198
$391$	5.83461e11	1.26246
$392$	0	0
$393$	−1.54658e10	−0.0327045
$394$	−1.13346e11	−0.236958
$395$	1.49632e10	0.0309270
$396$	5.89421e11	1.20447
$397$	−5.25740e11	−1.06222	−0.531109	−	0.847303i	$-0.678225\pi$
$397$	−5.25740e11	−1.06222	−0.531109	+	0.847303i	$0.678225\pi$
$398$	1.02226e11	0.204214
$399$	0	0
$400$	8.94433e10	0.174694
$401$	−4.96583e11	−0.959051	−0.479526	−	0.877528i	$-0.659191\pi$
$401$	−4.96583e11	−0.959051	−0.479526	+	0.877528i	$0.659191\pi$
$402$	3.25810e9	0.00622225
$403$	8.35845e11	1.57853
$404$	5.93304e11	1.10805
$405$	2.39874e11	0.443032
$406$	0	0
$407$	−5.67401e11	−1.02498
$408$	−1.37627e10	−0.0245886
$409$	6.22845e11	1.10059	0.550294	−	0.834971i	$-0.314516\pi$
$409$	6.22845e11	1.10059	0.550294	+	0.834971i	$0.314516\pi$
$410$	2.35491e10	0.0411573
$411$	2.28531e10	0.0395054
$412$	8.21437e11	1.40455
$413$	0	0
$414$	−1.43105e11	−0.239416
$415$	−2.53675e11	−0.419818
$416$	−4.43824e11	−0.726593
$417$	−1.32104e9	−0.00213945
$418$	−1.00801e11	−0.161500
$419$	9.02432e11	1.43038	0.715190	−	0.698930i	$-0.246340\pi$
$419$	9.02432e11	1.43038	0.715190	+	0.698930i	$0.246340\pi$
$420$	0	0
$421$	1.13768e12	1.76502	0.882509	−	0.470296i	$-0.155853\pi$
$421$	1.13768e12	1.76502	0.882509	+	0.470296i	$0.155853\pi$
$422$	3.61571e10	0.0554993
$423$	−1.74313e11	−0.264727
$424$	2.66590e11	0.400587
$425$	1.46266e11	0.217466
$426$	8.22458e9	0.0120996
$427$	0	0
$428$	5.80010e11	0.835485
$429$	−6.13797e10	−0.0874918
$430$	4.64033e10	0.0654547
$431$	4.68899e11	0.654533	0.327266	−	0.944932i	$-0.393873\pi$
$431$	4.68899e11	0.654533	0.327266	+	0.944932i	$0.393873\pi$
$432$	−7.05268e10	−0.0974265
$433$	−3.39136e11	−0.463638	−0.231819	−	0.972759i	$-0.574468\pi$
$433$	−3.39136e11	−0.463638	−0.231819	+	0.972759i	$0.574468\pi$
$434$	0	0
$435$	1.53268e10	0.0205235
$436$	1.18869e12	1.57536
$437$	−5.47508e11	−0.718165
$438$	−7.02182e9	−0.00911625
$439$	8.34074e11	1.07180	0.535901	−	0.844281i	$-0.319972\pi$
$439$	8.34074e11	1.07180	0.535901	+	0.844281i	$0.319972\pi$
$440$	−1.79677e11	−0.228536
$441$	0	0
$442$	−2.23956e11	−0.279101
$443$	−8.87244e11	−1.09453	−0.547263	−	0.836961i	$-0.684330\pi$
$443$	−8.87244e11	−1.09453	−0.547263	+	0.836961i	$0.684330\pi$
$444$	3.55532e10	0.0434165
$445$	−1.27169e11	−0.153731
$446$	−1.01577e11	−0.121559
$447$	−8.08304e10	−0.0957615
$448$	0	0
$449$	−2.68409e9	−0.00311665	−0.00155832	−	0.999999i	$-0.500496\pi$
$449$	−2.68409e9	−0.00311665	−0.00155832	+	0.999999i	$0.500496\pi$
$450$	−3.58745e10	−0.0412410
$451$	4.93419e11	0.561593
$452$	−6.32685e11	−0.712959
$453$	−5.10431e10	−0.0569502
$454$	−2.24509e11	−0.248017
$455$	0	0
$456$	1.29147e10	0.0139875
$457$	9.37032e11	1.00492	0.502460	−	0.864600i	$-0.332428\pi$
$457$	9.37032e11	1.00492	0.502460	+	0.864600i	$0.332428\pi$
$458$	−1.93000e11	−0.204957
$459$	−1.15332e11	−0.121281
$460$	−4.77296e11	−0.497024
$461$	2.76095e11	0.284711	0.142356	−	0.989816i	$-0.454532\pi$
$461$	2.76095e11	0.284711	0.142356	+	0.989816i	$0.454532\pi$
$462$	0	0
$463$	−1.47542e11	−0.149211	−0.0746055	−	0.997213i	$-0.523770\pi$
$463$	−1.47542e11	−0.149211	−0.0746055	+	0.997213i	$0.523770\pi$
$464$	7.16535e11	0.717640
$465$	−3.20361e10	−0.0317762
$466$	−3.39468e11	−0.333475
$467$	−1.62968e12	−1.58554	−0.792770	−	0.609521i	$-0.791362\pi$
$467$	−1.62968e12	−1.58554	−0.792770	+	0.609521i	$0.791362\pi$
$468$	−1.22886e12	−1.18412
$469$	0	0
$470$	2.59876e10	0.0245656
$471$	−8.37416e10	−0.0784056
$472$	3.81882e11	0.354152
$473$	9.72278e11	0.893131
$474$	8.78130e8	0.000799018 0
$475$	−1.37253e11	−0.123709
$476$	0	0
$477$	1.11527e12	0.986383
$478$	3.87121e11	0.339173
$479$	−1.04475e12	−0.906779	−0.453389	−	0.891313i	$-0.649785\pi$
$479$	−1.04475e12	−0.906779	−0.453389	+	0.891313i	$0.649785\pi$
$480$	1.70108e10	0.0146265
$481$	1.18295e12	1.00766
$482$	−2.65058e11	−0.223681
$483$	0	0
$484$	−6.85603e11	−0.567895
$485$	−6.11110e11	−0.501512
$486$	4.24531e10	0.0345180
$487$	−6.55197e11	−0.527827	−0.263913	−	0.964546i	$-0.585013\pi$
$487$	−6.55197e11	−0.527827	−0.263913	+	0.964546i	$0.585013\pi$
$488$	−9.58142e11	−0.764787
$489$	1.11513e11	0.0881933
$490$	0	0
$491$	−1.69481e12	−1.31600	−0.657998	−	0.753019i	$-0.728597\pi$
$491$	−1.69481e12	−1.31600	−0.657998	+	0.753019i	$0.728597\pi$
$492$	−3.09175e10	−0.0237882
$493$	1.17174e12	0.893348
$494$	2.10156e11	0.158771
$495$	−7.51670e11	−0.562735
$496$	−1.49770e12	−1.11111
$497$	0	0
$498$	−1.48871e10	−0.0108462
$499$	−9.93558e11	−0.717366	−0.358683	−	0.933459i	$-0.616774\pi$
$499$	−9.93558e11	−0.717366	−0.358683	+	0.933459i	$0.616774\pi$
$500$	−1.19652e11	−0.0856157
$501$	−2.18362e10	−0.0154848
$502$	2.04537e11	0.143749
$503$	−2.36079e11	−0.164438	−0.0822188	−	0.996614i	$-0.526201\pi$
$503$	−2.36079e11	−0.164438	−0.0822188	+	0.996614i	$0.526201\pi$
$504$	0	0
$505$	−7.56621e11	−0.517687
$506$	4.47027e11	0.303149
$507$	4.48655e10	0.0301562
$508$	−2.24112e12	−1.49306
$509$	−6.12223e11	−0.404277	−0.202139	−	0.979357i	$-0.564789\pi$
$509$	−6.12223e11	−0.404277	−0.202139	+	0.979357i	$0.564789\pi$
$510$	8.58374e9	0.00561838
$511$	0	0
$512$	1.34513e12	0.865065
$513$	1.08225e11	0.0689921
$514$	4.87605e11	0.308130
$515$	−1.04755e12	−0.656211
$516$	−6.09227e10	−0.0378316
$517$	5.44514e11	0.335198
$518$	0	0
$519$	1.34713e11	0.0814998
$520$	3.74600e11	0.224674
$521$	3.50205e11	0.208235	0.104117	−	0.994565i	$-0.466798\pi$
$521$	3.50205e11	0.208235	0.104117	+	0.994565i	$0.466798\pi$
$522$	−2.87392e11	−0.169417
$523$	2.61442e12	1.52798	0.763989	−	0.645229i	$-0.223238\pi$
$523$	2.61442e12	1.52798	0.763989	+	0.645229i	$0.223238\pi$
$524$	9.67229e11	0.560452
$525$	0	0
$526$	−4.88388e11	−0.278182
$527$	−2.44917e12	−1.38316
$528$	1.09983e11	0.0615845
$529$	6.26903e11	0.348057
$530$	−1.66271e11	−0.0915323
$531$	1.59758e12	0.872044
$532$	0	0
$533$	−1.02871e12	−0.552102
$534$	−7.46303e9	−0.00397173
$535$	−7.39669e11	−0.390342
$536$	−4.16629e11	−0.218026
$537$	−1.81200e11	−0.0940318
$538$	−4.32988e11	−0.222821
$539$	0	0
$540$	9.43463e10	0.0477477
$541$	−1.47804e12	−0.741821	−0.370911	−	0.928669i	$-0.620954\pi$
$541$	−1.47804e12	−0.741821	−0.370911	+	0.928669i	$0.620954\pi$
$542$	2.53600e11	0.126227
$543$	−1.79411e11	−0.0885626
$544$	1.30048e12	0.636663
$545$	−1.51590e12	−0.736014
$546$	0	0
$547$	7.35485e11	0.351262	0.175631	−	0.984456i	$-0.443804\pi$
$547$	7.35485e11	0.351262	0.175631	+	0.984456i	$0.443804\pi$
$548$	−1.42922e12	−0.676999
$549$	−4.00834e12	−1.88317
$550$	1.12064e11	0.0522195
$551$	−1.09954e12	−0.508193
$552$	−5.72732e10	−0.0262558
$553$	0	0
$554$	5.56852e11	0.251157
$555$	−4.53399e10	−0.0202844
$556$	8.26172e10	0.0366635
$557$	−9.41535e11	−0.414465	−0.207233	−	0.978292i	$-0.566446\pi$
$557$	−9.41535e11	−0.414465	−0.207233	+	0.978292i	$0.566446\pi$
$558$	6.00706e11	0.262306
$559$	−2.02706e12	−0.878037
$560$	0	0
$561$	1.79853e11	0.0766630
$562$	−3.68144e11	−0.155670
$563$	−3.00632e12	−1.26110	−0.630548	−	0.776151i	$-0.717170\pi$
$563$	−3.00632e12	−1.26110	−0.630548	+	0.776151i	$0.717170\pi$
$564$	−3.41191e10	−0.0141985
$565$	8.06843e11	0.333097
$566$	3.90893e11	0.160097
$567$	0	0
$568$	−1.05172e12	−0.423966
$569$	3.42996e12	1.37178	0.685889	−	0.727706i	$-0.259413\pi$
$569$	3.42996e12	1.37178	0.685889	+	0.727706i	$0.259413\pi$
$570$	−8.05481e9	−0.00319609
$571$	−3.90075e12	−1.53563	−0.767814	−	0.640673i	$-0.778656\pi$
$571$	−3.90075e12	−1.53563	−0.767814	+	0.640673i	$0.778656\pi$
$572$	3.83867e12	1.49933
$573$	−1.30606e11	−0.0506137
$574$	0	0
$575$	6.08680e11	0.232212
$576$	1.98137e12	0.750006
$577$	−6.26050e11	−0.235135	−0.117568	−	0.993065i	$-0.537510\pi$
$577$	−6.26050e11	−0.235135	−0.117568	+	0.993065i	$0.537510\pi$
$578$	1.01180e11	0.0377069
$579$	−1.80986e11	−0.0669254
$580$	−9.58535e11	−0.351708
$581$	0	0
$582$	−3.58636e10	−0.0129569
$583$	−3.48383e12	−1.24896
$584$	8.97914e11	0.319431
$585$	1.56712e12	0.553225
$586$	3.23771e11	0.113422
$587$	−1.68145e12	−0.584538	−0.292269	−	0.956336i	$-0.594410\pi$
$587$	−1.68145e12	−0.584538	−0.292269	+	0.956336i	$0.594410\pi$
$588$	0	0
$589$	2.29825e12	0.786827
$590$	−2.38177e11	−0.0809220
$591$	−1.89774e11	−0.0639871
$592$	−2.11965e12	−0.709279
$593$	1.58522e12	0.526434	0.263217	−	0.964737i	$-0.415217\pi$
$593$	1.58522e12	0.526434	0.263217	+	0.964737i	$0.415217\pi$
$594$	−8.83631e10	−0.0291227
$595$	0	0
$596$	5.05510e12	1.64105
$597$	1.71156e11	0.0551452
$598$	−9.31986e11	−0.298026
$599$	−4.78087e12	−1.51735	−0.758675	−	0.651469i	$-0.774153\pi$
$599$	−4.78087e12	−1.51735	−0.758675	+	0.651469i	$0.774153\pi$
$600$	−1.43576e10	−0.00452274
$601$	−2.13180e10	−0.00666516	−0.00333258	−	0.999994i	$-0.501061\pi$
$601$	−2.13180e10	−0.00666516	−0.00333258	+	0.999994i	$0.501061\pi$
$602$	0	0
$603$	−1.74295e12	−0.536855
$604$	3.19222e12	0.975948
$605$	8.74327e11	0.265323
$606$	−4.44030e10	−0.0133748
$607$	−3.71643e12	−1.11116	−0.555580	−	0.831463i	$-0.687504\pi$
$607$	−3.71643e12	−1.11116	−0.555580	+	0.831463i	$0.687504\pi$
$608$	−1.22035e12	−0.362174
$609$	0	0
$610$	5.97588e11	0.174750
$611$	−1.13523e12	−0.329533
$612$	3.60077e12	1.03756
$613$	2.28399e12	0.653315	0.326657	−	0.945143i	$-0.394078\pi$
$613$	2.28399e12	0.653315	0.326657	+	0.945143i	$0.394078\pi$
$614$	−8.08889e10	−0.0229684
$615$	3.94281e10	0.0111139
$616$	0	0
$617$	4.11730e12	1.14374	0.571872	−	0.820343i	$-0.306217\pi$
$617$	4.11730e12	1.14374	0.571872	+	0.820343i	$0.306217\pi$
$618$	−6.14766e10	−0.0169536
$619$	−5.99191e12	−1.64043	−0.820214	−	0.572057i	$-0.806146\pi$
$619$	−5.99191e12	−1.64043	−0.820214	+	0.572057i	$0.806146\pi$
$620$	2.00353e12	0.544544
$621$	−4.79950e11	−0.129504
$622$	1.05110e12	0.281571
$623$	0	0
$624$	−2.29298e11	−0.0605437
$625$	1.52588e11	0.0400000
$626$	−2.88150e11	−0.0749952
$627$	−1.68771e11	−0.0436107
$628$	5.23717e12	1.34363
$629$	−3.46625e12	−0.882940
$630$	0	0
$631$	4.14396e12	1.04060	0.520300	−	0.853984i	$-0.325820\pi$
$631$	4.14396e12	1.04060	0.520300	+	0.853984i	$0.325820\pi$
$632$	−1.12291e11	−0.0279974
$633$	6.05377e10	0.0149868
$634$	−4.86143e11	−0.119498
$635$	2.85803e12	0.697565
$636$	2.18296e11	0.0529040
$637$	0	0
$638$	8.97747e11	0.214517
$639$	−4.39981e12	−1.04395
$640$	−1.40680e12	−0.331453
$641$	−3.87177e12	−0.905833	−0.452917	−	0.891553i	$-0.649617\pi$
$641$	−3.87177e12	−0.905833	−0.452917	+	0.891553i	$0.649617\pi$
$642$	−4.34082e10	−0.0100847
$643$	−6.81081e12	−1.57127	−0.785633	−	0.618693i	$-0.787662\pi$
$643$	−6.81081e12	−1.57127	−0.785633	+	0.618693i	$0.787662\pi$
$644$	0	0
$645$	7.76927e10	0.0176751
$646$	−6.15793e11	−0.139120
$647$	−2.40797e12	−0.540233	−0.270117	−	0.962828i	$-0.587062\pi$
$647$	−2.40797e12	−0.540233	−0.270117	+	0.962828i	$0.587062\pi$
$648$	−1.80012e12	−0.401065
$649$	−4.99048e12	−1.10418
$650$	−2.33636e11	−0.0513370
$651$	0	0
$652$	−6.97399e12	−1.51136
$653$	−4.90892e12	−1.05652	−0.528259	−	0.849083i	$-0.677155\pi$
$653$	−4.90892e12	−1.05652	−0.528259	+	0.849083i	$0.677155\pi$
$654$	−8.89620e10	−0.0190154
$655$	−1.23348e12	−0.261845
$656$	1.84328e12	0.388618
$657$	3.75638e12	0.786549
$658$	0	0
$659$	−3.36518e11	−0.0695062	−0.0347531	−	0.999396i	$-0.511064\pi$
$659$	−3.36518e11	−0.0695062	−0.0347531	+	0.999396i	$0.511064\pi$
$660$	−1.47128e11	−0.0301819
$661$	5.58058e11	0.113703	0.0568516	−	0.998383i	$-0.481894\pi$
$661$	5.58058e11	0.113703	0.0568516	+	0.998383i	$0.481894\pi$
$662$	5.59785e11	0.113282
$663$	−3.74968e11	−0.0753674
$664$	1.90369e12	0.380049
$665$	0	0
$666$	8.50164e11	0.167444
$667$	4.87617e12	0.953922
$668$	1.36563e12	0.265361
$669$	−1.70070e11	−0.0328254
$670$	2.59849e11	0.0498179
$671$	1.25211e13	2.38447
$672$	0	0
$673$	−3.26341e12	−0.613202	−0.306601	−	0.951838i	$-0.599192\pi$
$673$	−3.26341e12	−0.613202	−0.306601	+	0.951838i	$0.599192\pi$
$674$	8.37126e11	0.156250
$675$	−1.20317e11	−0.0223079
$676$	−2.80587e12	−0.516782
$677$	2.71325e12	0.496410	0.248205	−	0.968708i	$-0.420159\pi$
$677$	2.71325e12	0.496410	0.248205	+	0.968708i	$0.420159\pi$
$678$	4.73503e10	0.00860577
$679$	0	0
$680$	−1.09764e12	−0.196866
$681$	−3.75893e11	−0.0669734
$682$	−1.87647e12	−0.332133
$683$	2.42887e12	0.427082	0.213541	−	0.976934i	$-0.431500\pi$
$683$	2.42887e12	0.427082	0.213541	+	0.976934i	$0.431500\pi$
$684$	−3.37889e12	−0.590230
$685$	1.82264e12	0.316296
$686$	0	0
$687$	−3.23139e11	−0.0553457
$688$	3.63216e12	0.618041
$689$	7.26329e12	1.22785
$690$	3.57210e10	0.00599933
$691$	−5.97125e12	−0.996355	−0.498178	−	0.867075i	$-0.665997\pi$
$691$	−5.97125e12	−0.996355	−0.498178	+	0.867075i	$0.665997\pi$
$692$	−8.42491e12	−1.39665
$693$	0	0
$694$	1.36157e12	0.222804
$695$	−1.05359e11	−0.0171293
$696$	−1.15020e11	−0.0185793
$697$	3.01429e12	0.483768
$698$	5.62391e11	0.0896786
$699$	−5.68370e11	−0.0900500
$700$	0	0
$701$	−4.18398e12	−0.654423	−0.327212	−	0.944951i	$-0.606109\pi$
$701$	−4.18398e12	−0.654423	−0.327212	+	0.944951i	$0.606109\pi$
$702$	1.84224e11	0.0286305
$703$	3.25266e12	0.502272
$704$	−6.18934e12	−0.949659
$705$	4.35110e10	0.00663357
$706$	−1.25735e12	−0.190474
$707$	0	0
$708$	3.12702e11	0.0467715
$709$	−8.83893e12	−1.31369	−0.656843	−	0.754027i	$-0.728109\pi$
$709$	−8.83893e12	−1.31369	−0.656843	+	0.754027i	$0.728109\pi$
$710$	6.55950e11	0.0968742
$711$	−4.69763e11	−0.0689391
$712$	9.54333e11	0.139168
$713$	−1.01922e13	−1.47694
$714$	0	0
$715$	−4.89533e12	−0.700495
$716$	1.13322e13	1.61141
$717$	6.48155e11	0.0915889
$718$	1.98232e12	0.278365
$719$	2.92264e12	0.407845	0.203922	−	0.978987i	$-0.434631\pi$
$719$	2.92264e12	0.407845	0.203922	+	0.978987i	$0.434631\pi$
$720$	−2.80803e12	−0.389409
$721$	0	0
$722$	−9.32489e11	−0.127710
$723$	−4.43785e11	−0.0604019
$724$	1.12203e13	1.51769
$725$	1.22239e12	0.164319
$726$	5.13107e10	0.00685478
$727$	1.21723e13	1.61610	0.808048	−	0.589117i	$-0.200524\pi$
$727$	1.21723e13	1.61610	0.808048	+	0.589117i	$0.200524\pi$
$728$	0	0
$729$	−7.48322e12	−0.981329
$730$	−5.60024e11	−0.0729884
$731$	5.93963e12	0.769363
$732$	−7.84571e11	−0.101003
$733$	−1.08103e13	−1.38315	−0.691574	−	0.722305i	$-0.743082\pi$
$733$	−1.08103e13	−1.38315	−0.691574	+	0.722305i	$0.743082\pi$
$734$	1.47125e12	0.187092
$735$	0	0
$736$	5.41192e12	0.679832
$737$	5.44457e12	0.679767
$738$	−7.39313e11	−0.0917434
$739$	9.83935e12	1.21357	0.606787	−	0.794864i	$-0.292458\pi$
$739$	9.83935e12	1.21357	0.606787	+	0.794864i	$0.292458\pi$
$740$	2.83554e12	0.347610
$741$	3.51863e11	0.0428737
$742$	0	0
$743$	−1.84462e12	−0.222053	−0.111027	−	0.993817i	$-0.535414\pi$
$743$	−1.84462e12	−0.222053	−0.111027	+	0.993817i	$0.535414\pi$
$744$	2.40414e11	0.0287661
$745$	−6.44661e12	−0.766705
$746$	1.97974e12	0.234037
$747$	7.96400e12	0.935812
$748$	−1.12480e13	−1.31376
$749$	0	0
$750$	8.95477e9	0.00103342
$751$	1.55156e13	1.77987	0.889936	−	0.456085i	$-0.150749\pi$
$751$	1.55156e13	1.77987	0.889936	+	0.456085i	$0.150749\pi$
$752$	2.03415e12	0.231955
$753$	3.42456e11	0.0388174
$754$	−1.87167e12	−0.210891
$755$	−4.07094e12	−0.455967
$756$	0	0
$757$	−1.10594e12	−0.122406	−0.0612029	−	0.998125i	$-0.519494\pi$
$757$	−1.10594e12	−0.122406	−0.0612029	+	0.998125i	$0.519494\pi$
$758$	−2.12770e12	−0.234099
$759$	7.48455e11	0.0818611
$760$	1.03001e12	0.111990
$761$	−1.94850e12	−0.210606	−0.105303	−	0.994440i	$-0.533581\pi$
$761$	−1.94850e12	−0.210606	−0.105303	+	0.994440i	$0.533581\pi$
$762$	1.67726e11	0.0180220
$763$	0	0
$764$	8.16807e12	0.867360
$765$	−4.59194e12	−0.484752
$766$	1.19898e12	0.125829
$767$	1.04044e13	1.08552
$768$	3.22599e11	0.0334609
$769$	1.56599e13	1.61481	0.807405	−	0.589998i	$-0.200871\pi$
$769$	1.56599e13	1.61481	0.807405	+	0.589998i	$0.200871\pi$
$770$	0	0
$771$	8.16395e11	0.0832062
$772$	1.13188e13	1.14689
$773$	−1.42340e13	−1.43390	−0.716949	−	0.697126i	$-0.754462\pi$
$773$	−1.42340e13	−1.43390	−0.716949	+	0.697126i	$0.754462\pi$
$774$	−1.45681e12	−0.145904
$775$	−2.55504e12	−0.254413
$776$	4.58605e12	0.454005
$777$	0	0
$778$	1.90786e10	0.00186697
$779$	−2.82855e12	−0.275198
$780$	3.06740e11	0.0296719
$781$	1.37440e13	1.32185
$782$	2.73088e12	0.261139
$783$	−9.63864e11	−0.0916406
$784$	0	0
$785$	−6.67880e12	−0.627747
$786$	−7.23877e10	−0.00676493
$787$	−1.81218e13	−1.68390	−0.841949	−	0.539556i	$-0.818592\pi$
$787$	−1.81218e13	−1.68390	−0.841949	+	0.539556i	$0.818592\pi$
$788$	1.18684e13	1.09654
$789$	−8.17706e11	−0.0751191
$790$	7.00351e10	0.00639726
$791$	0	0
$792$	5.64088e12	0.509429
$793$	−2.61047e13	−2.34418
$794$	−2.46072e12	−0.219720
$795$	−2.78386e11	−0.0247170
$796$	−1.07040e13	−0.945015
$797$	2.21087e13	1.94089	0.970446	−	0.241319i	$-0.0775799\pi$
$797$	2.21087e13	1.94089	0.970446	+	0.241319i	$0.0775799\pi$
$798$	0	0
$799$	3.32643e12	0.288747
$800$	1.35670e12	0.117106
$801$	3.99241e12	0.342680
$802$	−2.32425e12	−0.198380
$803$	−1.17341e13	−0.995930
$804$	−3.41155e11	−0.0287939
$805$	0	0
$806$	3.91216e12	0.326520
$807$	−7.24950e11	−0.0601696
$808$	5.67803e12	0.468648
$809$	1.80822e12	0.148417	0.0742084	−	0.997243i	$-0.476357\pi$
$809$	1.80822e12	0.148417	0.0742084	+	0.997243i	$0.476357\pi$
$810$	1.12273e12	0.0916413
$811$	1.59062e13	1.29113	0.645567	−	0.763703i	$-0.276621\pi$
$811$	1.59062e13	1.29113	0.645567	+	0.763703i	$0.276621\pi$
$812$	0	0
$813$	4.24601e11	0.0340858
$814$	−2.65572e12	−0.212017
$815$	8.89370e12	0.706112
$816$	6.71882e11	0.0530502
$817$	−5.57363e12	−0.437662
$818$	2.91522e12	0.227657
$819$	0	0
$820$	−2.46582e12	−0.190458
$821$	−1.49953e13	−1.15189	−0.575945	−	0.817489i	$-0.695366\pi$
$821$	−1.49953e13	−1.15189	−0.575945	+	0.817489i	$0.695366\pi$
$822$	1.06964e11	0.00817171
$823$	2.41121e13	1.83204	0.916020	−	0.401132i	$-0.131383\pi$
$823$	2.41121e13	1.83204	0.916020	+	0.401132i	$0.131383\pi$
$824$	7.86131e12	0.594049
$825$	1.87627e11	0.0141011
$826$	0	0
$827$	−3.51697e12	−0.261453	−0.130727	−	0.991418i	$-0.541731\pi$
$827$	−3.51697e12	−0.261453	−0.130727	+	0.991418i	$0.541731\pi$
$828$	1.49845e13	1.10791
$829$	2.21258e13	1.62706	0.813531	−	0.581522i	$-0.197543\pi$
$829$	2.21258e13	1.62706	0.813531	+	0.581522i	$0.197543\pi$
$830$	−1.18732e12	−0.0868394
$831$	9.32333e11	0.0678214
$832$	1.29039e13	0.933610
$833$	0	0
$834$	−6.18310e9	−0.000442546 0
$835$	−1.74154e12	−0.123978
$836$	1.05549e13	0.747351
$837$	2.01467e12	0.141886
$838$	4.22382e12	0.295875
$839$	−4.84005e12	−0.337226	−0.168613	−	0.985682i	$-0.553929\pi$
$839$	−4.84005e12	−0.337226	−0.168613	+	0.985682i	$0.553929\pi$
$840$	0	0
$841$	−4.71452e12	−0.324979
$842$	5.32488e12	0.365095
$843$	−6.16381e11	−0.0420364
$844$	−3.78600e12	−0.256827
$845$	3.57824e12	0.241443
$846$	−8.15870e11	−0.0547589
$847$	0	0
$848$	−1.30146e13	−0.864272
$849$	6.54471e11	0.0432320
$850$	6.84595e11	0.0449830
$851$	−1.44247e13	−0.942808
$852$	−8.61194e11	−0.0559916
$853$	−2.65572e13	−1.71756	−0.858779	−	0.512345i	$-0.828777\pi$
$853$	−2.65572e13	−1.71756	−0.858779	+	0.512345i	$0.828777\pi$
$854$	0	0
$855$	4.30899e12	0.275758
$856$	5.55081e12	0.353366
$857$	1.86512e13	1.18112	0.590560	−	0.806994i	$-0.298907\pi$
$857$	1.86512e13	1.18112	0.590560	+	0.806994i	$0.298907\pi$
$858$	−2.87287e11	−0.0180977
$859$	−1.19252e13	−0.747305	−0.373652	−	0.927569i	$-0.621895\pi$
$859$	−1.19252e13	−0.747305	−0.373652	+	0.927569i	$0.621895\pi$
$860$	−4.85888e12	−0.302895
$861$	0	0
$862$	2.19468e12	0.135390
$863$	−1.97885e13	−1.21441	−0.607205	−	0.794545i	$-0.707709\pi$
$863$	−1.97885e13	−1.21441	−0.607205	+	0.794545i	$0.707709\pi$
$864$	−1.06977e12	−0.0653096
$865$	1.07440e13	0.652521
$866$	−1.58732e12	−0.0959037
$867$	1.69405e11	0.0101822
$868$	0	0
$869$	1.46743e12	0.0872909
$870$	7.17371e10	0.00424529
$871$	−1.13511e13	−0.668279
$872$	1.13760e13	0.666293
$873$	1.91855e13	1.11792
$874$	−2.56261e12	−0.148553
$875$	0	0
$876$	7.35254e11	0.0421860
$877$	−3.21002e12	−0.183235	−0.0916177	−	0.995794i	$-0.529204\pi$
$877$	−3.21002e12	−0.183235	−0.0916177	+	0.995794i	$0.529204\pi$
$878$	3.90387e12	0.221702
$879$	5.42087e11	0.0306281
$880$	8.77164e12	0.493070
$881$	3.43067e13	1.91862	0.959308	−	0.282363i	$-0.0911182\pi$
$881$	3.43067e13	1.91862	0.959308	+	0.282363i	$0.0911182\pi$
$882$	0	0
$883$	−2.27401e13	−1.25884	−0.629418	−	0.777067i	$-0.716707\pi$
$883$	−2.27401e13	−1.25884	−0.629418	+	0.777067i	$0.716707\pi$
$884$	2.34504e13	1.29156
$885$	−3.98779e11	−0.0218518
$886$	−4.15274e12	−0.226403
$887$	−3.40833e13	−1.84878	−0.924390	−	0.381448i	$-0.875426\pi$
$887$	−3.40833e13	−1.84878	−0.924390	+	0.381448i	$0.875426\pi$
$888$	3.40251e11	0.0183629
$889$	0	0
$890$	−5.95212e11	−0.0317993
$891$	2.35243e13	1.25045
$892$	1.06361e13	0.562524
$893$	−3.12145e12	−0.164257
$894$	−3.78326e11	−0.0198083
$895$	−1.44516e13	−0.752857
$896$	0	0
$897$	−1.56042e12	−0.0804776
$898$	−1.25628e10	−0.000644680 0
$899$	−2.04685e13	−1.04512
$900$	3.75641e12	0.190845
$901$	−2.12827e13	−1.07588
$902$	2.30944e12	0.116166
$903$	0	0
$904$	−6.05492e12	−0.301544
$905$	−1.43089e13	−0.709068
$906$	−2.38907e11	−0.0117802
$907$	−2.39990e13	−1.17750	−0.588750	−	0.808315i	$-0.700380\pi$
$907$	−2.39990e13	−1.17750	−0.588750	+	0.808315i	$0.700380\pi$
$908$	2.35082e13	1.14771
$909$	2.37538e13	1.15397
$910$	0	0
$911$	1.81078e13	0.871029	0.435515	−	0.900182i	$-0.356566\pi$
$911$	1.81078e13	0.871029	0.435515	+	0.900182i	$0.356566\pi$
$912$	−6.30481e11	−0.0301783
$913$	−2.48777e13	−1.18493
$914$	4.38577e12	0.207868
$915$	1.00054e12	0.0471888
$916$	2.02090e13	0.948451
$917$	0	0
$918$	−5.39809e11	−0.0250869
$919$	−1.93468e12	−0.0894724	−0.0447362	−	0.998999i	$-0.514245\pi$
$919$	−1.93468e12	−0.0894724	−0.0447362	+	0.998999i	$0.514245\pi$
$920$	−4.56782e12	−0.210215
$921$	−1.35432e11	−0.00620229
$922$	1.29226e12	0.0588926
$923$	−2.86542e13	−1.29951
$924$	0	0
$925$	−3.61607e12	−0.162405
$926$	−6.90568e11	−0.0308644
$927$	3.28874e13	1.46275
$928$	1.08686e13	0.481068
$929$	−2.56977e13	−1.13194	−0.565971	−	0.824425i	$-0.691499\pi$
$929$	−2.56977e13	−1.13194	−0.565971	+	0.824425i	$0.691499\pi$
$930$	−1.49945e11	−0.00657291
$931$	0	0
$932$	3.55457e13	1.54317
$933$	1.75985e12	0.0760341
$934$	−7.62771e12	−0.327969
$935$	1.43442e13	0.613795
$936$	−1.17604e13	−0.500819
$937$	−2.26453e13	−0.959731	−0.479865	−	0.877342i	$-0.659314\pi$
$937$	−2.26453e13	−0.959731	−0.479865	+	0.877342i	$0.659314\pi$
$938$	0	0
$939$	−4.82447e11	−0.0202514
$940$	−2.72116e12	−0.113679
$941$	−2.28097e13	−0.948345	−0.474173	−	0.880432i	$-0.657253\pi$
$941$	−2.28097e13	−0.948345	−0.474173	+	0.880432i	$0.657253\pi$
$942$	−3.91952e11	−0.0162182
$943$	1.25439e13	0.516570
$944$	−1.86431e13	−0.764088
$945$	0	0
$946$	4.55074e12	0.184745
$947$	3.24218e12	0.130997	0.0654987	−	0.997853i	$-0.479136\pi$
$947$	3.24218e12	0.130997	0.0654987	+	0.997853i	$0.479136\pi$
$948$	−9.19488e10	−0.00369750
$949$	2.44638e13	0.979099
$950$	−6.42410e11	−0.0255892
$951$	−8.13946e11	−0.0322689
$952$	0	0
$953$	−4.96092e13	−1.94825	−0.974124	−	0.226014i	$-0.927430\pi$
$953$	−4.96092e13	−1.94825	−0.974124	+	0.226014i	$0.927430\pi$
$954$	5.21999e12	0.204034
$955$	−1.04165e13	−0.405234
$956$	−4.05354e13	−1.56955
$957$	1.50309e12	0.0579271
$958$	−4.88993e12	−0.187567
$959$	0	0
$960$	−4.94578e11	−0.0187938
$961$	1.63436e13	0.618149
$962$	5.53678e12	0.208434
$963$	2.32216e13	0.870108
$964$	2.77542e13	1.03510
$965$	−1.44345e13	−0.535832
$966$	0	0
$967$	−2.45015e13	−0.901100	−0.450550	−	0.892751i	$-0.648772\pi$
$967$	−2.45015e13	−0.901100	−0.450550	+	0.892751i	$0.648772\pi$
$968$	−6.56135e12	−0.240190
$969$	−1.03102e12	−0.0375672
$970$	−2.86029e12	−0.103738
$971$	1.85016e13	0.667917	0.333958	−	0.942588i	$-0.391616\pi$
$971$	1.85016e13	0.667917	0.333958	+	0.942588i	$0.391616\pi$
$972$	−4.44525e12	−0.159734
$973$	0	0
$974$	−3.06664e12	−0.109181
$975$	−3.91176e11	−0.0138628
$976$	4.67755e13	1.65004
$977$	−2.19913e13	−0.772193	−0.386096	−	0.922458i	$-0.626177\pi$
$977$	−2.19913e13	−0.772193	−0.386096	+	0.922458i	$0.626177\pi$
$978$	5.21936e11	0.0182428
$979$	−1.24714e13	−0.433902
$980$	0	0
$981$	4.75909e13	1.64064
$982$	−7.93255e12	−0.272214
$983$	−1.25865e12	−0.0429946	−0.0214973	−	0.999769i	$-0.506843\pi$
$983$	−1.25865e12	−0.0429946	−0.0214973	+	0.999769i	$0.506843\pi$
$984$	−2.95887e11	−0.0100611
$985$	−1.51354e13	−0.512307
$986$	5.48432e12	0.184789
$987$	0	0
$988$	−2.20054e13	−0.734721
$989$	2.47176e13	0.821530
$990$	−3.51818e12	−0.116402
$991$	−5.19617e12	−0.171140	−0.0855701	−	0.996332i	$-0.527271\pi$
$991$	−5.19617e12	−0.171140	−0.0855701	+	0.996332i	$0.527271\pi$
$992$	−2.27174e13	−0.744829
$993$	9.37245e11	0.0305901
$994$	0	0
$995$	1.36505e13	0.441515
$996$	1.55883e12	0.0501917
$997$	−5.63563e12	−0.180640	−0.0903200	−	0.995913i	$-0.528789\pi$
$997$	−5.63563e12	−0.180640	−0.0903200	+	0.995913i	$0.528789\pi$
$998$	−4.65034e12	−0.148387
$999$	2.85130e12	0.0905730

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.10.a.f.1.3		5
7.6	odd	2		35.10.a.d.1.3	✓	5
21.20	even	2		315.10.a.j.1.3		5
35.13	even	4		175.10.b.f.99.5		10
35.27	even	4		175.10.b.f.99.6		10
35.34	odd	2		175.10.a.f.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.10.a.d.1.3	✓	5	7.6	odd	2
175.10.a.f.1.3		5	35.34	odd	2
175.10.b.f.99.5		10	35.13	even	4
175.10.b.f.99.6		10	35.27	even	4
245.10.a.f.1.3		5	1.1	even	1	trivial
315.10.a.j.1.3		5	21.20	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+4.68049 q^{2} +7.83652 q^{3} -490.093 q^{4} +625.000 q^{5} +36.6787 q^{6} -4690.29 q^{8} -19621.6 q^{9} +2925.31 q^{10} +61293.3 q^{11} -3840.62 q^{12} -127788. q^{13} +4897.82 q^{15} +228975. q^{16} +374440. q^{17} -91838.6 q^{18} -351367. q^{19} -306308. q^{20} +286883. q^{22} +1.55822e6 q^{23} -36755.5 q^{24} +390625. q^{25} -598109. q^{26} -308011. q^{27} +3.12932e6 q^{29} +22924.2 q^{30} -6.54089e6 q^{31} +3.47314e6 q^{32} +480326. q^{33} +1.75256e6 q^{34} +9.61640e6 q^{36} -9.25714e6 q^{37} -1.64457e6 q^{38} -1.00141e6 q^{39} -2.93143e6 q^{40} +8.05013e6 q^{41} +1.58627e7 q^{43} -3.00394e7 q^{44} -1.22635e7 q^{45} +7.29324e6 q^{46} +8.88373e6 q^{47} +1.79436e6 q^{48} +1.82832e6 q^{50} +2.93431e6 q^{51} +6.26278e7 q^{52} -5.68387e7 q^{53} -1.44164e6 q^{54} +3.83083e7 q^{55} -2.75349e6 q^{57} +1.46467e7 q^{58} -8.14197e7 q^{59} -2.40039e6 q^{60} +2.04282e8 q^{61} -3.06146e7 q^{62} -1.00979e8 q^{64} -7.98673e7 q^{65} +2.24816e6 q^{66} +8.88281e7 q^{67} -1.83510e8 q^{68} +1.22110e7 q^{69} +2.24233e8 q^{71} +9.20309e7 q^{72} -1.91441e8 q^{73} -4.33280e7 q^{74} +3.06114e6 q^{75} +1.72203e8 q^{76} -4.68709e6 q^{78} +2.39411e7 q^{79} +1.43109e8 q^{80} +3.83798e8 q^{81} +3.76785e7 q^{82} -4.05879e8 q^{83} +2.34025e8 q^{85} +7.42452e7 q^{86} +2.45229e7 q^{87} -2.87483e8 q^{88} -2.03470e8 q^{89} -5.73992e7 q^{90} -7.63674e8 q^{92} -5.12578e7 q^{93} +4.15802e7 q^{94} -2.19604e8 q^{95} +2.72173e7 q^{96} -9.77776e8 q^{97} -1.20267e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 2 q^{2} - 140 q^{3} + 832 q^{4} + 3125 q^{5} + 144 q^{6} - 14136 q^{8} + 67797 q^{9} + 1250 q^{10} + 10312 q^{11} - 63388 q^{12} - 158638 q^{13} - 87500 q^{15} - 526696 q^{16} - 31614 q^{17} + 1816986 q^{18}+ \cdots + 698312668 q^{99}+O(q^{100}) \) 5 * q + 2 * q^2 - 140 * q^3 + 832 * q^4 + 3125 * q^5 + 144 * q^6 - 14136 * q^8 + 67797 * q^9 + 1250 * q^10 + 10312 * q^11 - 63388 * q^12 - 158638 * q^13 - 87500 * q^15 - 526696 * q^16 - 31614 * q^17 + 1816986 * q^18 - 1655376 * q^19 + 520000 * q^20 + 3659464 * q^22 + 796104 * q^23 - 6504576 * q^24 + 1953125 * q^25 - 10219060 * q^26 - 4190732 * q^27 - 3353726 * q^29 + 90000 * q^30 - 2678120 * q^31 - 130400 * q^32 - 20444132 * q^33 - 21548612 * q^34 + 15390460 * q^36 + 50994846 * q^37 + 34907600 * q^38 - 18124 * q^39 - 8835000 * q^40 - 6330194 * q^41 + 6149468 * q^43 - 71225892 * q^44 + 42373125 * q^45 - 142845472 * q^46 + 6897780 * q^47 + 46423032 * q^48 + 781250 * q^50 - 17970212 * q^51 + 22199468 * q^52 - 70886738 * q^53 + 113279328 * q^54 + 6445000 * q^55 - 355886264 * q^57 - 31955924 * q^58 + 152335168 * q^59 - 39617500 * q^60 - 257015698 * q^61 + 215582768 * q^62 - 193988432 * q^64 - 99148750 * q^65 - 183241664 * q^66 + 133467828 * q^67 + 268709380 * q^68 + 191957336 * q^69 + 522788960 * q^71 + 221927400 * q^72 - 159370858 * q^73 - 244178868 * q^74 - 54687500 * q^75 + 345056616 * q^76 + 1164346496 * q^78 + 464174900 * q^79 - 329185000 * q^80 + 865150989 * q^81 - 308947620 * q^82 - 2207636832 * q^83 - 19758750 * q^85 + 694560616 * q^86 - 2952845788 * q^87 + 930528736 * q^88 + 1106708326 * q^89 + 1135616250 * q^90 + 205160216 * q^92 + 767757392 * q^93 + 3602501744 * q^94 - 1034610000 * q^95 + 2652128640 * q^96 - 1956142254 * q^97 + 698312668 * q^99

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