LMFDB - Embedded newform 145.6.a.c.1.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [145,6,Mod(1,145)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("145.1"); S:= CuspForms(chi, 6); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(145, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 6, names="a")

Level:	$ N $	$=$	$ 145 = 5 \cdot 29 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	145.a (trivial)

Newform invariants

comment:select newform

sage:traces = [13,7] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	yes
Analytic conductor:	$23.2556538729$
Analytic rank:	$0$
Dimension:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 6 x^{12} - 296 x^{11} + 1238 x^{10} + 33250 x^{9} - 78360 x^{8} - 1708024 x^{7} + \cdots + 251513192 $ x^13 - 6x^12 - 296x^11 + 1238x^10 + 33250x^9 - 78360x^8 - 1708024x^7 + 1285720x^6 + 37751885x^5 + 19686342x^4 - 252219704x^3 - 352125886x^2 + 108510888x + 251513192
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Root			$-7.41417$ of defining polynomial
Character	$\chi$	$=$	145.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+8.41417 q^{2} -17.8297 q^{3} +38.7982 q^{4} -25.0000 q^{5} -150.022 q^{6} +108.201 q^{7} +57.2014 q^{8} +74.8998 q^{9} -210.354 q^{10} +122.859 q^{11} -691.763 q^{12} +1014.99 q^{13} +910.419 q^{14} +445.744 q^{15} -760.241 q^{16} +228.049 q^{17} +630.220 q^{18} +2696.36 q^{19} -969.956 q^{20} -1929.19 q^{21} +1033.76 q^{22} +1930.09 q^{23} -1019.89 q^{24} +625.000 q^{25} +8540.30 q^{26} +2997.18 q^{27} +4198.00 q^{28} +841.000 q^{29} +3750.56 q^{30} -7530.99 q^{31} -8227.24 q^{32} -2190.55 q^{33} +1918.84 q^{34} -2705.02 q^{35} +2905.98 q^{36} +9306.92 q^{37} +22687.6 q^{38} -18097.0 q^{39} -1430.04 q^{40} +20600.9 q^{41} -16232.5 q^{42} +7544.51 q^{43} +4766.72 q^{44} -1872.50 q^{45} +16240.1 q^{46} -18537.6 q^{47} +13554.9 q^{48} -5099.60 q^{49} +5258.86 q^{50} -4066.05 q^{51} +39379.8 q^{52} +22911.7 q^{53} +25218.8 q^{54} -3071.48 q^{55} +6189.24 q^{56} -48075.4 q^{57} +7076.32 q^{58} -12387.2 q^{59} +17294.1 q^{60} -32734.1 q^{61} -63367.1 q^{62} +8104.22 q^{63} -44897.7 q^{64} -25374.8 q^{65} -18431.6 q^{66} -62626.5 q^{67} +8847.88 q^{68} -34413.0 q^{69} -22760.5 q^{70} +78352.0 q^{71} +4284.38 q^{72} -78052.2 q^{73} +78310.0 q^{74} -11143.6 q^{75} +104614. q^{76} +13293.5 q^{77} -152271. q^{78} +24900.3 q^{79} +19006.0 q^{80} -71639.7 q^{81} +173340. q^{82} +19395.6 q^{83} -74849.2 q^{84} -5701.21 q^{85} +63480.8 q^{86} -14994.8 q^{87} +7027.72 q^{88} +56003.7 q^{89} -15755.5 q^{90} +109823. q^{91} +74884.1 q^{92} +134276. q^{93} -155979. q^{94} -67409.0 q^{95} +146690. q^{96} -114410. q^{97} -42908.9 q^{98} +9202.13 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q + 7 q^{2} + 2 q^{3} + 213 q^{4} - 325 q^{5} - 3 q^{6} - 18 q^{7} - 399 q^{8} + 1155 q^{9} - 175 q^{10} + 844 q^{11} + 167 q^{12} - 704 q^{13} + 4425 q^{14} - 50 q^{15} + 5805 q^{16} - 210 q^{17} + 7378 q^{18}+ \cdots - 3872 q^{99}+O(q^{100}) $ 13 * q + 7 * q^2 + 2 * q^3 + 213 * q^4 - 325 * q^5 - 3 * q^6 - 18 * q^7 - 399 * q^8 + 1155 * q^9 - 175 * q^10 + 844 * q^11 + 167 * q^12 - 704 * q^13 + 4425 * q^14 - 50 * q^15 + 5805 * q^16 - 210 * q^17 + 7378 * q^18 + 2524 * q^19 - 5325 * q^20 + 7088 * q^21 - 3772 * q^22 + 10806 * q^23 + 11131 * q^24 + 8125 * q^25 + 15003 * q^26 - 2872 * q^27 + 6007 * q^28 + 10933 * q^29 + 75 * q^30 + 6820 * q^31 - 9761 * q^32 + 9416 * q^33 + 18557 * q^34 + 450 * q^35 + 28284 * q^36 - 7784 * q^37 + 43872 * q^38 + 30524 * q^39 + 9975 * q^40 + 17950 * q^41 + 104284 * q^42 + 24570 * q^43 + 101386 * q^44 - 28875 * q^45 + 71703 * q^46 + 26242 * q^47 + 96475 * q^48 + 45423 * q^49 + 4375 * q^50 - 5632 * q^51 - 2925 * q^52 + 50580 * q^53 + 61352 * q^54 - 21100 * q^55 + 172651 * q^56 + 71600 * q^57 + 5887 * q^58 + 50712 * q^59 - 4175 * q^60 - 24104 * q^61 + 82941 * q^62 - 1298 * q^63 + 75673 * q^64 + 17600 * q^65 - 7632 * q^66 - 93110 * q^67 - 113909 * q^68 + 116878 * q^69 - 110625 * q^70 + 253344 * q^71 - 206562 * q^72 - 11006 * q^73 - 171316 * q^74 + 1250 * q^75 - 275002 * q^76 + 106744 * q^77 - 84017 * q^78 - 23792 * q^79 - 145125 * q^80 + 229097 * q^81 - 461156 * q^82 + 115802 * q^83 - 224096 * q^84 + 5250 * q^85 + 31283 * q^86 + 1682 * q^87 - 635028 * q^88 + 87446 * q^89 - 184450 * q^90 - 33904 * q^91 + 197053 * q^92 - 168912 * q^93 - 464496 * q^94 - 63100 * q^95 - 186929 * q^96 + 27766 * q^97 - 166558 * q^98 - 3872 * 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 $

$2$	8.41417	1.48743	0.743714	−	0.668497i	$-0.233062\pi$
$2$	8.41417	1.48743	0.743714	+	0.668497i	$0.233062\pi$
$3$	−17.8297	−1.14378	−0.571889	−	0.820331i	$-0.693789\pi$
$3$	−17.8297	−1.14378	−0.571889	+	0.820331i	$0.693789\pi$
$4$	38.7982	1.21244
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	−150.022	−1.70129
$7$	108.201	0.834613	0.417306	−	0.908766i	$-0.362974\pi$
$7$	108.201	0.834613	0.417306	+	0.908766i	$0.362974\pi$
$8$	57.2014	0.315996
$9$	74.8998	0.308230
$10$	−210.354	−0.665198
$11$	122.859	0.306144	0.153072	−	0.988215i	$-0.451083\pi$
$11$	122.859	0.306144	0.153072	+	0.988215i	$0.451083\pi$
$12$	−691.763	−1.38677
$13$	1014.99	1.66573	0.832863	−	0.553479i	$-0.186700\pi$
$13$	1014.99	1.66573	0.832863	+	0.553479i	$0.186700\pi$
$14$	910.419	1.24143
$15$	445.744	0.511513
$16$	−760.241	−0.742423
$17$	228.049	0.191384	0.0956919	−	0.995411i	$-0.469494\pi$
$17$	228.049	0.191384	0.0956919	+	0.995411i	$0.469494\pi$
$18$	630.220	0.458470
$19$	2696.36	1.71354	0.856769	−	0.515700i	$-0.172468\pi$
$19$	2696.36	1.71354	0.856769	+	0.515700i	$0.172468\pi$
$20$	−969.956	−0.542222
$21$	−1929.19	−0.954613
$22$	1033.76	0.455368
$23$	1930.09	0.760779	0.380389	−	0.924826i	$-0.375790\pi$
$23$	1930.09	0.760779	0.380389	+	0.924826i	$0.375790\pi$
$24$	−1019.89	−0.361430
$25$	625.000	0.200000
$26$	8540.30	2.47765
$27$	2997.18	0.791232
$28$	4198.00	1.01192
$29$	841.000	0.185695
$29$	841.000	0.185695
$30$	3750.56	0.760840
$31$	−7530.99	−1.40750	−0.703750	−	0.710448i	$-0.748492\pi$
$31$	−7530.99	−1.40750	−0.703750	+	0.710448i	$0.748492\pi$
$32$	−8227.24	−1.42030
$33$	−2190.55	−0.350161
$34$	1918.84	0.284670
$35$	−2705.02	−0.373250
$36$	2905.98	0.373712
$37$	9306.92	1.11764	0.558820	−	0.829289i	$-0.311254\pi$
$37$	9306.92	1.11764	0.558820	+	0.829289i	$0.311254\pi$
$38$	22687.6	2.54877
$39$	−18097.0	−1.90522
$40$	−1430.04	−0.141318
$41$	20600.9	1.91393	0.956966	−	0.290199i	$-0.0937214\pi$
$41$	20600.9	1.91393	0.956966	+	0.290199i	$0.0937214\pi$
$42$	−16232.5	−1.41992
$43$	7544.51	0.622243	0.311121	−	0.950370i	$-0.399295\pi$
$43$	7544.51	0.622243	0.311121	+	0.950370i	$0.399295\pi$
$44$	4766.72	0.371183
$45$	−1872.50	−0.137845
$46$	16240.1	1.13160
$47$	−18537.6	−1.22408	−0.612040	−	0.790827i	$-0.709651\pi$
$47$	−18537.6	−1.22408	−0.612040	+	0.790827i	$0.709651\pi$
$48$	13554.9	0.849167
$49$	−5099.60	−0.303421
$50$	5258.86	0.297486
$51$	−4066.05	−0.218901
$52$	39379.8	2.01960
$53$	22911.7	1.12038	0.560192	−	0.828363i	$-0.310727\pi$
$53$	22911.7	1.12038	0.560192	+	0.828363i	$0.310727\pi$
$54$	25218.8	1.17690
$55$	−3071.48	−0.136912
$56$	6189.24	0.263735
$57$	−48075.4	−1.95991
$58$	7076.32	0.276209
$59$	−12387.2	−0.463278	−0.231639	−	0.972802i	$-0.574409\pi$
$59$	−12387.2	−0.463278	−0.231639	+	0.972802i	$0.574409\pi$
$60$	17294.1	0.620182
$61$	−32734.1	−1.12636	−0.563179	−	0.826335i	$-0.690422\pi$
$61$	−32734.1	−1.12636	−0.563179	+	0.826335i	$0.690422\pi$
$62$	−63367.1	−2.09355
$63$	8104.22	0.257253
$64$	−44897.7	−1.37017
$65$	−25374.8	−0.744935
$66$	−18431.6	−0.520840
$67$	−62626.5	−1.70440	−0.852199	−	0.523218i	$-0.824731\pi$
$67$	−62626.5	−1.70440	−0.852199	+	0.523218i	$0.824731\pi$
$68$	8847.88	0.232042
$69$	−34413.0	−0.870162
$70$	−22760.5	−0.555183
$71$	78352.0	1.84461	0.922304	−	0.386465i	$-0.126304\pi$
$71$	78352.0	1.84461	0.922304	+	0.386465i	$0.126304\pi$
$72$	4284.38	0.0973995
$73$	−78052.2	−1.71427	−0.857133	−	0.515095i	$-0.827757\pi$
$73$	−78052.2	−1.71427	−0.857133	+	0.515095i	$0.827757\pi$
$74$	78310.0	1.66241
$75$	−11143.6	−0.228756
$76$	104614.	2.07757
$77$	13293.5	0.255512
$78$	−152271.	−2.83388
$79$	24900.3	0.448887	0.224444	−	0.974487i	$-0.427944\pi$
$79$	24900.3	0.448887	0.224444	+	0.974487i	$0.427944\pi$
$80$	19006.0	0.332022
$81$	−71639.7	−1.21322
$82$	173340.	2.84684
$83$	19395.6	0.309035	0.154517	−	0.987990i	$-0.450618\pi$
$83$	19395.6	0.309035	0.154517	+	0.987990i	$0.450618\pi$
$84$	−74849.2	−1.15741
$85$	−5701.21	−0.0855894
$86$	63480.8	0.925542
$87$	−14994.8	−0.212394
$88$	7027.72	0.0967404
$89$	56003.7	0.749449	0.374724	−	0.927136i	$-0.377737\pi$
$89$	56003.7	0.749449	0.374724	+	0.927136i	$0.377737\pi$
$90$	−15755.5	−0.205034
$91$	109823.	1.39024
$92$	74884.1	0.922402
$93$	134276.	1.60987
$94$	−155979.	−1.82073
$95$	−67409.0	−0.766318
$96$	146690.	1.62451
$97$	−114410.	−1.23463	−0.617313	−	0.786718i	$-0.711779\pi$
$97$	−114410.	−1.23463	−0.617313	+	0.786718i	$0.711779\pi$
$98$	−42908.9	−0.451317
$99$	9202.13	0.0943628
$100$	24248.9	0.242489
$101$	87850.7	0.856923	0.428461	−	0.903560i	$-0.359056\pi$
$101$	87850.7	0.856923	0.428461	+	0.903560i	$0.359056\pi$
$102$	−34212.4	−0.325599
$103$	68366.4	0.634964	0.317482	−	0.948264i	$-0.397163\pi$
$103$	68366.4	0.634964	0.317482	+	0.948264i	$0.397163\pi$
$104$	58058.9	0.526363
$105$	48229.8	0.426916
$106$	192783.	1.66649
$107$	84195.6	0.710935	0.355468	−	0.934689i	$-0.384322\pi$
$107$	84195.6	0.710935	0.355468	+	0.934689i	$0.384322\pi$
$108$	116285.	0.959325
$109$	−5615.91	−0.0452745	−0.0226373	−	0.999744i	$-0.507206\pi$
$109$	−5615.91	−0.0452745	−0.0226373	+	0.999744i	$0.507206\pi$
$110$	−25843.9	−0.203647
$111$	−165940.	−1.27833
$112$	−82258.6	−0.619636
$113$	102393.	0.754351	0.377176	−	0.926142i	$-0.376895\pi$
$113$	102393.	0.754351	0.377176	+	0.926142i	$0.376895\pi$
$114$	−404515.	−2.91522
$115$	−48252.3	−0.340230
$116$	32629.3	0.225145
$117$	76022.6	0.513427
$118$	−104228.	−0.689093
$119$	24675.0	0.159731
$120$	25497.2	0.161636
$121$	−145957.	−0.906276
$122$	−275431.	−1.67538
$123$	−367309.	−2.18912
$124$	−292189.	−1.70651
$125$	−15625.0	−0.0894427
$126$	68190.3	0.382645
$127$	134335.	0.739060	0.369530	−	0.929219i	$-0.379519\pi$
$127$	134335.	0.739060	0.369530	+	0.929219i	$0.379519\pi$
$128$	−114505.	−0.617731
$129$	−134517.	−0.711708
$130$	−213508.	−1.10804
$131$	20061.6	0.102138	0.0510691	−	0.998695i	$-0.483737\pi$
$131$	20061.6	0.102138	0.0510691	+	0.998695i	$0.483737\pi$
$132$	−84989.4	−0.424551
$133$	291748.	1.43014
$134$	−526950.	−2.53517
$135$	−74929.6	−0.353850
$136$	13044.7	0.0604765
$137$	217421.	0.989691	0.494845	−	0.868981i	$-0.335225\pi$
$137$	217421.	0.989691	0.494845	+	0.868981i	$0.335225\pi$
$138$	−289557.	−1.29430
$139$	−94235.2	−0.413691	−0.206846	−	0.978374i	$-0.566320\pi$
$139$	−94235.2	−0.413691	−0.206846	+	0.978374i	$0.566320\pi$
$140$	−104950.	−0.452545
$141$	330521.	1.40008
$142$	659267.	2.74372
$143$	124701.	0.509952
$144$	−56941.9	−0.228837
$145$	−21025.0	−0.0830455
$146$	−656745.	−2.54985
$147$	90924.6	0.347047
$148$	361092.	1.35508
$149$	−175608.	−0.648005	−0.324003	−	0.946056i	$-0.605029\pi$
$149$	−175608.	−0.648005	−0.324003	+	0.946056i	$0.605029\pi$
$150$	−93764.1	−0.340258
$151$	45146.7	0.161133	0.0805664	−	0.996749i	$-0.474327\pi$
$151$	45146.7	0.161133	0.0805664	+	0.996749i	$0.474327\pi$
$152$	154236.	0.541472
$153$	17080.8	0.0589902
$154$	111853.	0.380056
$155$	188275.	0.629453
$156$	−702132.	−2.30998
$157$	−234893.	−0.760537	−0.380268	−	0.924876i	$-0.624168\pi$
$157$	−234893.	−0.760537	−0.380268	+	0.924876i	$0.624168\pi$
$158$	209516.	0.667688
$159$	−408509.	−1.28147
$160$	205681.	0.635176
$161$	208837.	0.634956
$162$	−602788.	−1.80458
$163$	−142374.	−0.419722	−0.209861	−	0.977731i	$-0.567301\pi$
$163$	−142374.	−0.419722	−0.209861	+	0.977731i	$0.567301\pi$
$164$	799279.	2.32054
$165$	54763.7	0.156597
$166$	163198.	0.459667
$167$	123976.	0.343992	0.171996	−	0.985098i	$-0.444978\pi$
$167$	123976.	0.343992	0.171996	+	0.985098i	$0.444978\pi$
$168$	−110353.	−0.301654
$169$	658913.	1.77464
$170$	−47971.0	−0.127308
$171$	201957.	0.528164
$172$	292714.	0.754435
$173$	−590149.	−1.49915	−0.749577	−	0.661917i	$-0.769743\pi$
$173$	−590149.	−1.49915	−0.749577	+	0.661917i	$0.769743\pi$
$174$	−126169.	−0.315922
$175$	67625.5	0.166923
$176$	−93402.6	−0.227288
$177$	220860.	0.529888
$178$	471225.	1.11475
$179$	838457.	1.95591	0.977954	−	0.208822i	$-0.0669631\pi$
$179$	838457.	1.95591	0.977954	+	0.208822i	$0.0669631\pi$
$180$	−72649.5	−0.167129
$181$	−287008.	−0.651175	−0.325588	−	0.945512i	$-0.605562\pi$
$181$	−287008.	−0.651175	−0.325588	+	0.945512i	$0.605562\pi$
$182$	924067.	2.06788
$183$	583641.	1.28830
$184$	110404.	0.240403
$185$	−232673.	−0.499824
$186$	1.12982e6	2.39456
$187$	28017.9	0.0585910
$188$	−719228.	−1.48413
$189$	324297.	0.660373
$190$	−567191.	−1.13984
$191$	−197521.	−0.391769	−0.195885	−	0.980627i	$-0.562758\pi$
$191$	−197521.	−0.391769	−0.195885	+	0.980627i	$0.562758\pi$
$192$	800514.	1.56717
$193$	187394.	0.362128	0.181064	−	0.983471i	$-0.442046\pi$
$193$	187394.	0.362128	0.181064	+	0.983471i	$0.442046\pi$
$194$	−962667.	−1.83642
$195$	452426.	0.852041
$196$	−197855.	−0.367881
$197$	−383890.	−0.704760	−0.352380	−	0.935857i	$-0.614628\pi$
$197$	−383890.	−0.704760	−0.352380	+	0.935857i	$0.614628\pi$
$198$	77428.3	0.140358
$199$	474125.	0.848712	0.424356	−	0.905495i	$-0.360500\pi$
$199$	474125.	0.848712	0.424356	+	0.905495i	$0.360500\pi$
$200$	35750.9	0.0631992
$201$	1.11661e6	1.94945
$202$	739191.	1.27461
$203$	90996.8	0.154984
$204$	−157755.	−0.265405
$205$	−515023.	−0.855937
$206$	575246.	0.944464
$207$	144564.	0.234495
$208$	−771637.	−1.23667
$209$	331273.	0.524590
$210$	405814.	0.635007
$211$	150464.	0.232662	0.116331	−	0.993211i	$-0.462887\pi$
$211$	150464.	0.232662	0.116331	+	0.993211i	$0.462887\pi$
$212$	888932.	1.35840
$213$	−1.39700e6	−2.10982
$214$	708436.	1.05747
$215$	−188613.	−0.278275
$216$	171443.	0.250026
$217$	−814859.	−1.17472
$218$	−47253.2	−0.0673426
$219$	1.39165e6	1.96074
$220$	−119168.	−0.165998
$221$	231467.	0.318793
$222$	−1.39625e6	−1.90143
$223$	364182.	0.490407	0.245203	−	0.969472i	$-0.421145\pi$
$223$	364182.	0.490407	0.245203	+	0.969472i	$0.421145\pi$
$224$	−890193.	−1.18540
$225$	46812.4	0.0616460
$226$	861551.	1.12204
$227$	−612476.	−0.788904	−0.394452	−	0.918917i	$-0.629066\pi$
$227$	−612476.	−0.788904	−0.394452	+	0.918917i	$0.629066\pi$
$228$	−1.86524e6	−2.37628
$229$	1.25481e6	1.58121	0.790604	−	0.612327i	$-0.209767\pi$
$229$	1.25481e6	1.58121	0.790604	+	0.612327i	$0.209767\pi$
$230$	−406003.	−0.506069
$231$	−237019.	−0.292249
$232$	48106.4	0.0586790
$233$	−613531.	−0.740366	−0.370183	−	0.928959i	$-0.620705\pi$
$233$	−613531.	−0.740366	−0.370183	+	0.928959i	$0.620705\pi$
$234$	639667.	0.763685
$235$	463441.	0.547425
$236$	−480600.	−0.561699
$237$	−443966.	−0.513428
$238$	207620.	0.237589
$239$	28774.9	0.0325851	0.0162926	−	0.999867i	$-0.494814\pi$
$239$	28774.9	0.0325851	0.0162926	+	0.999867i	$0.494814\pi$
$240$	−338873.	−0.379759
$241$	507833.	0.563220	0.281610	−	0.959529i	$-0.409132\pi$
$241$	507833.	0.563220	0.281610	+	0.959529i	$0.409132\pi$
$242$	−1.22810e6	−1.34802
$243$	549002.	0.596428
$244$	−1.27003e6	−1.36565
$245$	127490.	0.135694
$246$	−3.09060e6	−3.25615
$247$	2.73678e6	2.85429
$248$	−430784.	−0.444764
$249$	−345818.	−0.353468
$250$	−131471.	−0.133040
$251$	10890.8	0.0109113	0.00545566	−	0.999985i	$-0.498263\pi$
$251$	10890.8	0.0109113	0.00545566	+	0.999985i	$0.498263\pi$
$252$	314429.	0.311905
$253$	237129.	0.232908
$254$	1.13032e6	1.09930
$255$	101651.	0.0978954
$256$	473262.	0.451338
$257$	−2.03342e6	−1.92041	−0.960204	−	0.279299i	$-0.909898\pi$
$257$	−2.03342e6	−1.92041	−0.960204	+	0.279299i	$0.909898\pi$
$258$	−1.13185e6	−1.05861
$259$	1.00702e6	0.932797
$260$	−984496.	−0.903193
$261$	62990.8	0.0572368
$262$	168802.	0.151923
$263$	−52391.6	−0.0467059	−0.0233530	−	0.999727i	$-0.507434\pi$
$263$	−52391.6	−0.0467059	−0.0233530	+	0.999727i	$0.507434\pi$
$264$	−125302.	−0.110650
$265$	−572792.	−0.501051
$266$	2.45482e6	2.12723
$267$	−998532.	−0.857204
$268$	−2.42980e6	−2.06649
$269$	−430994.	−0.363153	−0.181577	−	0.983377i	$-0.558120\pi$
$269$	−430994.	−0.363153	−0.181577	+	0.983377i	$0.558120\pi$
$270$	−630470.	−0.526326
$271$	−1.27010e6	−1.05054	−0.525272	−	0.850935i	$-0.676036\pi$
$271$	−1.27010e6	−1.05054	−0.525272	+	0.850935i	$0.676036\pi$
$272$	−173372.	−0.142088
$273$	−1.95811e6	−1.59012
$274$	1.82941e6	1.47209
$275$	76787.0	0.0612288
$276$	−1.33516e6	−1.05502
$277$	−1.57723e6	−1.23508	−0.617541	−	0.786539i	$-0.711871\pi$
$277$	−1.57723e6	−1.23508	−0.617541	+	0.786539i	$0.711871\pi$
$278$	−792911.	−0.615336
$279$	−564070.	−0.433833
$280$	−154731.	−0.117946
$281$	1.41837e6	1.07158	0.535790	−	0.844351i	$-0.320014\pi$
$281$	1.41837e6	1.07158	0.535790	+	0.844351i	$0.320014\pi$
$282$	2.78106e6	2.08251
$283$	−374114.	−0.277676	−0.138838	−	0.990315i	$-0.544337\pi$
$283$	−374114.	−0.277676	−0.138838	+	0.990315i	$0.544337\pi$
$284$	3.03992e6	2.23649
$285$	1.20189e6	0.876498
$286$	1.04925e6	0.758518
$287$	2.22903e6	1.59739
$288$	−616219.	−0.437778
$289$	−1.36785e6	−0.963372
$290$	−176908.	−0.123524
$291$	2.03990e6	1.41214
$292$	−3.02829e6	−2.07845
$293$	1.16381e6	0.791978	0.395989	−	0.918255i	$-0.370402\pi$
$293$	1.16381e6	0.791978	0.395989	+	0.918255i	$0.370402\pi$
$294$	765055.	0.516207
$295$	309679.	0.207184
$296$	532369.	0.353170
$297$	368231.	0.242231
$298$	−1.47760e6	−0.963862
$299$	1.95902e6	1.26725
$300$	−432352.	−0.277354
$301$	816321.	0.519332
$302$	379872.	0.239673
$303$	−1.56636e6	−0.980130
$304$	−2.04988e6	−1.27217
$305$	818354.	0.503723
$306$	143721.	0.0877437
$307$	−1.62020e6	−0.981123	−0.490561	−	0.871407i	$-0.663208\pi$
$307$	−1.62020e6	−0.981123	−0.490561	+	0.871407i	$0.663208\pi$
$308$	515763.	0.309794
$309$	−1.21895e6	−0.726259
$310$	1.58418e6	0.936266
$311$	−2.60499e6	−1.52723	−0.763615	−	0.645671i	$-0.776578\pi$
$311$	−2.60499e6	−1.52723	−0.763615	+	0.645671i	$0.776578\pi$
$312$	−1.03518e6	−0.602043
$313$	−1.22973e6	−0.709496	−0.354748	−	0.934962i	$-0.615433\pi$
$313$	−1.22973e6	−0.709496	−0.354748	+	0.934962i	$0.615433\pi$
$314$	−1.97643e6	−1.13124
$315$	−202605.	−0.115047
$316$	966088.	0.544251
$317$	−3.25297e6	−1.81816	−0.909080	−	0.416621i	$-0.863214\pi$
$317$	−3.25297e6	−1.81816	−0.909080	+	0.416621i	$0.863214\pi$
$318$	−3.43727e6	−1.90610
$319$	103325.	0.0568495
$320$	1.12244e6	0.612758
$321$	−1.50119e6	−0.813152
$322$	1.75719e6	0.944451
$323$	614901.	0.327943
$324$	−2.77949e6	−1.47097
$325$	634369.	0.333145
$326$	−1.19796e6	−0.624306
$327$	100130.	0.0517840
$328$	1.17840e6	0.604796
$329$	−2.00579e6	−1.02163
$330$	460791.	0.232927
$331$	−1.31245e6	−0.658435	−0.329218	−	0.944254i	$-0.606785\pi$
$331$	−1.31245e6	−0.658435	−0.329218	+	0.944254i	$0.606785\pi$
$332$	752514.	0.374688
$333$	697087.	0.344490
$334$	1.04316e6	0.511663
$335$	1.56566e6	0.762230
$336$	1.46665e6	0.708726
$337$	3.13373e6	1.50309	0.751547	−	0.659679i	$-0.229308\pi$
$337$	3.13373e6	1.50309	0.751547	+	0.659679i	$0.229308\pi$
$338$	5.54420e6	2.63966
$339$	−1.82564e6	−0.862811
$340$	−221197.	−0.103772
$341$	−925252.	−0.430898
$342$	1.69930e6	0.785606
$343$	−2.37031e6	−1.08785
$344$	431557.	0.196626
$345$	860326.	0.389148
$346$	−4.96561e6	−2.22988
$347$	−1.35263e6	−0.603054	−0.301527	−	0.953458i	$-0.597496\pi$
$347$	−1.35263e6	−0.603054	−0.301527	+	0.953458i	$0.597496\pi$
$348$	−581772.	−0.257516
$349$	−4.06262e6	−1.78543	−0.892715	−	0.450622i	$-0.851202\pi$
$349$	−4.06262e6	−1.78543	−0.892715	+	0.450622i	$0.851202\pi$
$350$	569012.	0.248285
$351$	3.04211e6	1.31798
$352$	−1.01079e6	−0.434816
$353$	593560.	0.253529	0.126765	−	0.991933i	$-0.459541\pi$
$353$	593560.	0.253529	0.126765	+	0.991933i	$0.459541\pi$
$354$	1.85835e6	0.788170
$355$	−1.95880e6	−0.824934
$356$	2.17285e6	0.908665
$357$	−439949.	−0.182697
$358$	7.05492e6	2.90927
$359$	657659.	0.269317	0.134659	−	0.990892i	$-0.457006\pi$
$359$	657659.	0.269317	0.134659	+	0.990892i	$0.457006\pi$
$360$	−107109.	−0.0435584
$361$	4.79426e6	1.93621
$362$	−2.41493e6	−0.968577
$363$	2.60237e6	1.03658
$364$	4.26093e6	1.68559
$365$	1.95131e6	0.766643
$366$	4.91086e6	1.91626
$367$	−1.91160e6	−0.740852	−0.370426	−	0.928862i	$-0.620788\pi$
$367$	−1.91160e6	−0.740852	−0.370426	+	0.928862i	$0.620788\pi$
$368$	−1.46733e6	−0.564819
$369$	1.54300e6	0.589931
$370$	−1.95775e6	−0.743452
$371$	2.47906e6	0.935088
$372$	5.20966e6	1.95188
$373$	−2.72571e6	−1.01439	−0.507197	−	0.861830i	$-0.669319\pi$
$373$	−2.72571e6	−1.01439	−0.507197	+	0.861830i	$0.669319\pi$
$374$	235747.	0.0871500
$375$	278590.	0.102303
$376$	−1.06038e6	−0.386805
$377$	853607.	0.309318
$378$	2.72869e6	0.982257
$379$	4.36078e6	1.55943	0.779716	−	0.626133i	$-0.215363\pi$
$379$	4.36078e6	1.55943	0.779716	+	0.626133i	$0.215363\pi$
$380$	−2.61535e6	−0.929118
$381$	−2.39516e6	−0.845321
$382$	−1.66198e6	−0.582729
$383$	1.86081e6	0.648194	0.324097	−	0.946024i	$-0.394940\pi$
$383$	1.86081e6	0.648194	0.324097	+	0.946024i	$0.394940\pi$
$384$	2.04159e6	0.706547
$385$	−332336.	−0.114268
$386$	1.57676e6	0.538639
$387$	565083.	0.191794
$388$	−4.43891e6	−1.49692
$389$	−2.90623e6	−0.973770	−0.486885	−	0.873466i	$-0.661867\pi$
$389$	−2.90623e6	−0.973770	−0.486885	+	0.873466i	$0.661867\pi$
$390$	3.80679e6	1.26735
$391$	440155.	0.145601
$392$	−291704.	−0.0958799
$393$	−357694.	−0.116824
$394$	−3.23012e6	−1.04828
$395$	−622508.	−0.200748
$396$	357027.	0.114410
$397$	−5.49890e6	−1.75106	−0.875528	−	0.483168i	$-0.839486\pi$
$397$	−5.49890e6	−1.75106	−0.875528	+	0.483168i	$0.839486\pi$
$398$	3.98937e6	1.26240
$399$	−5.20180e6	−1.63577
$400$	−475151.	−0.148485
$401$	−2.31594e6	−0.719228	−0.359614	−	0.933101i	$-0.617092\pi$
$401$	−2.31594e6	−0.719228	−0.359614	+	0.933101i	$0.617092\pi$
$402$	9.39538e6	2.89967
$403$	−7.64389e6	−2.34451
$404$	3.40845e6	1.03897
$405$	1.79099e6	0.542570
$406$	765663.	0.230527
$407$	1.14344e6	0.342159
$408$	−232584.	−0.0691718
$409$	3.95053e6	1.16774	0.583871	−	0.811846i	$-0.301537\pi$
$409$	3.95053e6	1.16774	0.583871	+	0.811846i	$0.301537\pi$
$410$	−4.33349e6	−1.27315
$411$	−3.87656e6	−1.13199
$412$	2.65249e6	0.769859
$413$	−1.34030e6	−0.386658
$414$	1.21638e6	0.348794
$415$	−484890.	−0.138205
$416$	−8.35057e6	−2.36583
$417$	1.68019e6	0.473171
$418$	2.78738e6	0.780290
$419$	909937.	0.253207	0.126604	−	0.991953i	$-0.459592\pi$
$419$	909937.	0.253207	0.126604	+	0.991953i	$0.459592\pi$
$420$	1.87123e6	0.517612
$421$	2.60594e6	0.716570	0.358285	−	0.933612i	$-0.383362\pi$
$421$	2.60594e6	0.716570	0.358285	+	0.933612i	$0.383362\pi$
$422$	1.26603e6	0.346068
$423$	−1.38847e6	−0.377298
$424$	1.31058e6	0.354037
$425$	142530.	0.0382767
$426$	−1.17546e7	−3.13821
$427$	−3.54186e6	−0.940073
$428$	3.26664e6	0.861969
$429$	−2.22339e6	−0.583273
$430$	−1.58702e6	−0.413915
$431$	6.43510e6	1.66864	0.834319	−	0.551282i	$-0.185861\pi$
$431$	6.43510e6	1.66864	0.834319	+	0.551282i	$0.185861\pi$
$432$	−2.27858e6	−0.587429
$433$	−7.13239e6	−1.82816	−0.914082	−	0.405530i	$-0.867087\pi$
$433$	−7.13239e6	−1.82816	−0.914082	+	0.405530i	$0.867087\pi$
$434$	−6.85636e6	−1.74731
$435$	374870.	0.0949857
$436$	−217887.	−0.0548929
$437$	5.20422e6	1.30362
$438$	1.17096e7	2.91646
$439$	3.93283e6	0.973967	0.486983	−	0.873411i	$-0.338097\pi$
$439$	3.93283e6	0.973967	0.486983	+	0.873411i	$0.338097\pi$
$440$	−175693.	−0.0432636
$441$	−381959.	−0.0935234
$442$	1.94760e6	0.474182
$443$	6.12456e6	1.48274	0.741371	−	0.671096i	$-0.234176\pi$
$443$	6.12456e6	1.48274	0.741371	+	0.671096i	$0.234176\pi$
$444$	−6.43818e6	−1.54991
$445$	−1.40009e6	−0.335164
$446$	3.06429e6	0.729446
$447$	3.13105e6	0.741175
$448$	−4.85796e6	−1.14356
$449$	478620.	0.112041	0.0560203	−	0.998430i	$-0.482159\pi$
$449$	478620.	0.112041	0.0560203	+	0.998430i	$0.482159\pi$
$450$	393887.	0.0916940
$451$	2.53101e6	0.585939
$452$	3.97266e6	0.914609
$453$	−804955.	−0.184300
$454$	−5.15347e6	−1.17344
$455$	−2.74557e6	−0.621733
$456$	−2.74998e6	−0.619324
$457$	−8.49339e6	−1.90235	−0.951175	−	0.308651i	$-0.900123\pi$
$457$	−8.49339e6	−1.90235	−0.951175	+	0.308651i	$0.900123\pi$
$458$	1.05582e7	2.35194
$459$	683503.	0.151429
$460$	−1.87210e6	−0.412511
$461$	−3.69429e6	−0.809616	−0.404808	−	0.914402i	$-0.632662\pi$
$461$	−3.69429e6	−0.809616	−0.404808	+	0.914402i	$0.632662\pi$
$462$	−1.99432e6	−0.434700
$463$	−1.57989e6	−0.342511	−0.171256	−	0.985227i	$-0.554782\pi$
$463$	−1.57989e6	−0.342511	−0.171256	+	0.985227i	$0.554782\pi$
$464$	−639363.	−0.137864
$465$	−3.35689e6	−0.719955
$466$	−5.16235e6	−1.10124
$467$	1.47606e6	0.313192	0.156596	−	0.987663i	$-0.449948\pi$
$467$	1.47606e6	0.313192	0.156596	+	0.987663i	$0.449948\pi$
$468$	2.94954e6	0.622501
$469$	−6.77623e6	−1.42251
$470$	3.89947e6	0.814256
$471$	4.18808e6	0.869886
$472$	−708563.	−0.146394
$473$	926912.	0.190496
$474$	−3.73561e6	−0.763687
$475$	1.68522e6	0.342708
$476$	957347.	0.193665
$477$	1.71608e6	0.345336
$478$	242117.	0.0484681
$479$	−3.76734e6	−0.750233	−0.375116	−	0.926978i	$-0.622397\pi$
$479$	−3.76734e6	−0.750233	−0.375116	+	0.926978i	$0.622397\pi$
$480$	−3.66724e6	−0.726501
$481$	9.44644e6	1.86168
$482$	4.27299e6	0.837750
$483$	−3.72352e6	−0.726249
$484$	−5.66286e6	−1.09881
$485$	2.86026e6	0.552142
$486$	4.61939e6	0.887144
$487$	−3.49960e6	−0.668646	−0.334323	−	0.942459i	$-0.608508\pi$
$487$	−3.49960e6	−0.668646	−0.334323	+	0.942459i	$0.608508\pi$
$488$	−1.87244e6	−0.355925
$489$	2.53849e6	0.480069
$490$	1.07272e6	0.201835
$491$	4004.99	0.000749718 0	0.000374859	−	1.00000i	$-0.499881\pi$
$491$	4004.99	0.000749718 0	0.000374859		1.00000i	$0.499881\pi$
$492$	−1.42509e7	−2.65418
$493$	191789.	0.0355391
$494$	2.30277e7	4.24555
$495$	−230053.	−0.0422003
$496$	5.72537e6	1.04496
$497$	8.47774e6	1.53953
$498$	−2.90977e6	−0.525758
$499$	2.48693e6	0.447108	0.223554	−	0.974692i	$-0.428234\pi$
$499$	2.48693e6	0.447108	0.223554	+	0.974692i	$0.428234\pi$
$500$	−606222.	−0.108444
$501$	−2.21047e6	−0.393450
$502$	91637.3	0.0162298
$503$	2.40169e6	0.423251	0.211625	−	0.977351i	$-0.432124\pi$
$503$	2.40169e6	0.423251	0.211625	+	0.977351i	$0.432124\pi$
$504$	463573.	0.0812909
$505$	−2.19627e6	−0.383228
$506$	1.99525e6	0.346434
$507$	−1.17483e7	−2.02980
$508$	5.21195e6	0.896069
$509$	−7.25461e6	−1.24114	−0.620569	−	0.784152i	$-0.713098\pi$
$509$	−7.25461e6	−1.24114	−0.620569	+	0.784152i	$0.713098\pi$
$510$	855310.	0.145612
$511$	−8.44531e6	−1.43075
$512$	7.64626e6	1.28906
$513$	8.08148e6	1.35581
$514$	−1.71095e7	−2.85647
$515$	−1.70916e6	−0.283965
$516$	−5.21901e6	−0.862906
$517$	−2.27752e6	−0.374745
$518$	8.47320e6	1.38747
$519$	1.05222e7	1.71470
$520$	−1.45147e6	−0.235397
$521$	−3.23090e6	−0.521471	−0.260735	−	0.965410i	$-0.583965\pi$
$521$	−3.23090e6	−0.521471	−0.260735	+	0.965410i	$0.583965\pi$
$522$	530015.	0.0851357
$523$	4.69228e6	0.750118	0.375059	−	0.927001i	$-0.377622\pi$
$523$	4.69228e6	0.750118	0.375059	+	0.927001i	$0.377622\pi$
$524$	778356.	0.123837
$525$	−1.20574e6	−0.190923
$526$	−440831.	−0.0694717
$527$	−1.71743e6	−0.269372
$528$	1.66534e6	0.259968
$529$	−2.71109e6	−0.421216
$530$	−4.81957e6	−0.745278
$531$	−927796.	−0.142796
$532$	1.13193e7	1.73397
$533$	2.09097e7	3.18809
$534$	−8.40182e6	−1.27503
$535$	−2.10489e6	−0.317940
$536$	−3.58232e6	−0.538583
$537$	−1.49495e7	−2.23713
$538$	−3.62645e6	−0.540165
$539$	−626533.	−0.0928906
$540$	−2.90713e6	−0.429023
$541$	−2.16755e6	−0.318402	−0.159201	−	0.987246i	$-0.550892\pi$
$541$	−2.16755e6	−0.318402	−0.159201	+	0.987246i	$0.550892\pi$
$542$	−1.06868e7	−1.56261
$543$	5.11728e6	0.744800
$544$	−1.87621e6	−0.271822
$545$	140398.	0.0202474
$546$	−1.64759e7	−2.36520
$547$	−1.09034e7	−1.55809	−0.779046	−	0.626967i	$-0.784296\pi$
$547$	−1.09034e7	−1.55809	−0.779046	+	0.626967i	$0.784296\pi$
$548$	8.43554e6	1.19994
$549$	−2.45178e6	−0.347177
$550$	646099.	0.0910735
$551$	2.26764e6	0.318196
$552$	−1.96847e6	−0.274968
$553$	2.69423e6	0.374647
$554$	−1.32711e7	−1.83710
$555$	4.14850e6	0.571688
$556$	−3.65616e6	−0.501578
$557$	−5.86844e6	−0.801465	−0.400732	−	0.916195i	$-0.631244\pi$
$557$	−5.86844e6	−0.801465	−0.400732	+	0.916195i	$0.631244\pi$
$558$	−4.74618e6	−0.645296
$559$	7.65760e6	1.03649
$560$	2.05647e6	0.277109
$561$	−499551.	−0.0670152
$562$	1.19344e7	1.59390
$563$	−4.66713e6	−0.620553	−0.310276	−	0.950646i	$-0.600422\pi$
$563$	−4.66713e6	−0.620553	−0.310276	+	0.950646i	$0.600422\pi$
$564$	1.28236e7	1.69752
$565$	−2.55982e6	−0.337356
$566$	−3.14786e6	−0.413023
$567$	−7.75147e6	−1.01257
$568$	4.48184e6	0.582889
$569$	8.64171e6	1.11897	0.559486	−	0.828840i	$-0.310999\pi$
$569$	8.64171e6	1.11897	0.559486	+	0.828840i	$0.310999\pi$
$570$	1.01129e7	1.30373
$571$	−9.35750e6	−1.20107	−0.600537	−	0.799597i	$-0.705046\pi$
$571$	−9.35750e6	−1.20107	−0.600537	+	0.799597i	$0.705046\pi$
$572$	4.83817e6	0.618289
$573$	3.52175e6	0.448097
$574$	1.87555e7	2.37601
$575$	1.20631e6	0.152156
$576$	−3.36283e6	−0.422327
$577$	6.84399e6	0.855796	0.427898	−	0.903827i	$-0.359254\pi$
$577$	6.84399e6	0.855796	0.427898	+	0.903827i	$0.359254\pi$
$578$	−1.15093e7	−1.43295
$579$	−3.34118e6	−0.414194
$580$	−815733.	−0.100688
$581$	2.09862e6	0.257925
$582$	1.71641e7	2.10046
$583$	2.81491e6	0.342999
$584$	−4.46470e6	−0.541702
$585$	−1.90057e6	−0.229611
$586$	9.79250e6	1.17801
$587$	3.03476e6	0.363520	0.181760	−	0.983343i	$-0.441821\pi$
$587$	3.03476e6	0.363520	0.181760	+	0.983343i	$0.441821\pi$
$588$	3.52771e6	0.420775
$589$	−2.03063e7	−2.41180
$590$	2.60569e6	0.308172
$591$	6.84466e6	0.806090
$592$	−7.07550e6	−0.829761
$593$	5.46963e6	0.638736	0.319368	−	0.947631i	$-0.396529\pi$
$593$	5.46963e6	0.638736	0.319368	+	0.947631i	$0.396529\pi$
$594$	3.09836e6	0.360301
$595$	−616876.	−0.0714340
$596$	−6.81328e6	−0.785671
$597$	−8.45354e6	−0.970739
$598$	1.64836e7	1.88494
$599$	4.70553e6	0.535847	0.267924	−	0.963440i	$-0.413662\pi$
$599$	4.70553e6	0.535847	0.267924	+	0.963440i	$0.413662\pi$
$600$	−637429.	−0.0722859
$601$	1.05357e6	0.118981	0.0594904	−	0.998229i	$-0.481052\pi$
$601$	1.05357e6	0.118981	0.0594904	+	0.998229i	$0.481052\pi$
$602$	6.86867e6	0.772469
$603$	−4.69071e6	−0.525346
$604$	1.75161e6	0.195365
$605$	3.64892e6	0.405299
$606$	−1.31796e7	−1.45787
$607$	1.06562e7	1.17390	0.586951	−	0.809622i	$-0.300328\pi$
$607$	1.06562e7	1.17390	0.586951	+	0.809622i	$0.300328\pi$
$608$	−2.21836e7	−2.43373
$609$	−1.62245e6	−0.177267
$610$	6.88576e6	0.749251
$611$	−1.88155e7	−2.03898
$612$	662705.	0.0715223
$613$	7.67755e6	0.825224	0.412612	−	0.910907i	$-0.364617\pi$
$613$	7.67755e6	0.825224	0.412612	+	0.910907i	$0.364617\pi$
$614$	−1.36327e7	−1.45935
$615$	9.18272e6	0.979002
$616$	760405.	0.0807408
$617$	−3.74926e6	−0.396491	−0.198245	−	0.980152i	$-0.563524\pi$
$617$	−3.74926e6	−0.396491	−0.198245	+	0.980152i	$0.563524\pi$
$618$	−1.02565e7	−1.08026
$619$	549073.	0.0575974	0.0287987	−	0.999585i	$-0.490832\pi$
$619$	549073.	0.0575974	0.0287987	+	0.999585i	$0.490832\pi$
$620$	7.30473e6	0.763177
$621$	5.78484e6	0.601952
$622$	−2.19188e7	−2.27165
$623$	6.05965e6	0.625500
$624$	1.37581e7	1.41448
$625$	390625.	0.0400000
$626$	−1.03472e7	−1.05533
$627$	−5.90651e6	−0.600015
$628$	−9.11342e6	−0.922109
$629$	2.12243e6	0.213898
$630$	−1.70476e6	−0.171124
$631$	8.27453e6	0.827313	0.413657	−	0.910433i	$-0.364251\pi$
$631$	8.27453e6	0.827313	0.413657	+	0.910433i	$0.364251\pi$
$632$	1.42433e6	0.141847
$633$	−2.68273e6	−0.266114
$634$	−2.73711e7	−2.70438
$635$	−3.35837e6	−0.330518
$636$	−1.58494e7	−1.55371
$637$	−5.17605e6	−0.505417
$638$	869390.	0.0845596
$639$	5.86855e6	0.568563
$640$	2.86262e6	0.276258
$641$	1.04022e7	0.999954	0.499977	−	0.866039i	$-0.333342\pi$
$641$	1.04022e7	0.999954	0.499977	+	0.866039i	$0.333342\pi$
$642$	−1.26312e7	−1.20951
$643$	7.34934e6	0.701004	0.350502	−	0.936562i	$-0.386011\pi$
$643$	7.34934e6	0.701004	0.350502	+	0.936562i	$0.386011\pi$
$644$	8.10252e6	0.769849
$645$	3.36292e6	0.318285
$646$	5.17388e6	0.487792
$647$	1.69436e7	1.59128	0.795639	−	0.605771i	$-0.207135\pi$
$647$	1.69436e7	1.59128	0.795639	+	0.605771i	$0.207135\pi$
$648$	−4.09789e6	−0.383374
$649$	−1.52188e6	−0.141830
$650$	5.33769e6	0.495530
$651$	1.45287e7	1.34362
$652$	−5.52385e6	−0.508889
$653$	−1.68999e7	−1.55096	−0.775481	−	0.631371i	$-0.782492\pi$
$653$	−1.68999e7	−1.55096	−0.775481	+	0.631371i	$0.782492\pi$
$654$	842513.	0.0770251
$655$	−501541.	−0.0456776
$656$	−1.56617e7	−1.42095
$657$	−5.84610e6	−0.528388
$658$	−1.68770e7	−1.51961
$659$	1.24291e6	0.111488	0.0557438	−	0.998445i	$-0.482247\pi$
$659$	1.24291e6	0.111488	0.0557438	+	0.998445i	$0.482247\pi$
$660$	2.12473e6	0.189865
$661$	5.22902e6	0.465497	0.232748	−	0.972537i	$-0.425228\pi$
$661$	5.22902e6	0.465497	0.232748	+	0.972537i	$0.425228\pi$
$662$	−1.10432e7	−0.979376
$663$	−4.12700e6	−0.364629
$664$	1.10945e6	0.0976539
$665$	−7.29370e6	−0.639579
$666$	5.86541e6	0.512404
$667$	1.62321e6	0.141273
$668$	4.81006e6	0.417071
$669$	−6.49328e6	−0.560917
$670$	1.31737e7	1.13376
$671$	−4.02169e6	−0.344828
$672$	1.58719e7	1.35583
$673$	1.38184e7	1.17603	0.588016	−	0.808849i	$-0.299909\pi$
$673$	1.38184e7	1.17603	0.588016	+	0.808849i	$0.299909\pi$
$674$	2.63677e7	2.23575
$675$	1.87324e6	0.158246
$676$	2.55647e7	2.15166
$677$	1.33744e7	1.12151	0.560755	−	0.827982i	$-0.310511\pi$
$677$	1.33744e7	1.12151	0.560755	+	0.827982i	$0.310511\pi$
$678$	−1.53612e7	−1.28337
$679$	−1.23793e7	−1.03043
$680$	−326118.	−0.0270459
$681$	1.09203e7	0.902332
$682$	−7.78523e6	−0.640929
$683$	491792.	0.0403394	0.0201697	−	0.999797i	$-0.493579\pi$
$683$	491792.	0.0403394	0.0201697	+	0.999797i	$0.493579\pi$
$684$	7.83557e6	0.640369
$685$	−5.43552e6	−0.442603
$686$	−1.99442e7	−1.61810
$687$	−2.23729e7	−1.80855
$688$	−5.73564e6	−0.461967
$689$	2.32551e7	1.86625
$690$	7.23893e6	0.578831
$691$	7.64609e6	0.609178	0.304589	−	0.952484i	$-0.401481\pi$
$691$	7.64609e6	0.609178	0.304589	+	0.952484i	$0.401481\pi$
$692$	−2.28967e7	−1.81764
$693$	995678.	0.0787564
$694$	−1.13813e7	−0.896999
$695$	2.35588e6	0.185008
$696$	−857725.	−0.0671158
$697$	4.69801e6	0.366296
$698$	−3.41836e7	−2.65570
$699$	1.09391e7	0.846815
$700$	2.62375e6	0.202384
$701$	1.47009e7	1.12992	0.564961	−	0.825118i	$-0.308891\pi$
$701$	1.47009e7	1.12992	0.564961	+	0.825118i	$0.308891\pi$
$702$	2.55968e7	1.96040
$703$	2.50948e7	1.91512
$704$	−5.51609e6	−0.419469
$705$	−8.26304e6	−0.626133
$706$	4.99431e6	0.377107
$707$	9.50551e6	0.715199
$708$	8.56897e6	0.642459
$709$	1.79168e7	1.33858	0.669291	−	0.743000i	$-0.266598\pi$
$709$	1.79168e7	1.33858	0.669291	+	0.743000i	$0.266598\pi$
$710$	−1.64817e7	−1.22703
$711$	1.86503e6	0.138360
$712$	3.20349e6	0.236823
$713$	−1.45355e7	−1.07080
$714$	−3.70181e6	−0.271749
$715$	−3.11752e6	−0.228058
$716$	3.25306e7	2.37143
$717$	−513049.	−0.0372702
$718$	5.53365e6	0.400590
$719$	1.35890e6	0.0980313	0.0490157	−	0.998798i	$-0.484392\pi$
$719$	1.35890e6	0.0980313	0.0490157	+	0.998798i	$0.484392\pi$
$720$	1.42355e6	0.102339
$721$	7.39729e6	0.529950
$722$	4.03397e7	2.87998
$723$	−9.05453e6	−0.644199
$724$	−1.11354e7	−0.789514
$725$	525625.	0.0371391
$726$	2.18968e7	1.54184
$727$	490288.	0.0344045	0.0172023	−	0.999852i	$-0.494524\pi$
$727$	490288.	0.0344045	0.0172023	+	0.999852i	$0.494524\pi$
$728$	6.28202e6	0.439310
$729$	7.61988e6	0.531042
$730$	1.64186e7	1.14033
$731$	1.72051e6	0.119087
$732$	2.26443e7	1.56200
$733$	−2.50427e6	−0.172155	−0.0860777	−	0.996288i	$-0.527433\pi$
$733$	−2.50427e6	−0.172155	−0.0860777	+	0.996288i	$0.527433\pi$
$734$	−1.60845e7	−1.10197
$735$	−2.27311e6	−0.155204
$736$	−1.58793e7	−1.08053
$737$	−7.69424e6	−0.521791
$738$	1.29831e7	0.877481
$739$	−1.77705e7	−1.19699	−0.598493	−	0.801128i	$-0.704234\pi$
$739$	−1.77705e7	−1.19699	−0.598493	+	0.801128i	$0.704234\pi$
$740$	−9.02730e6	−0.606008
$741$	−4.87961e7	−3.26467
$742$	2.08592e7	1.39088
$743$	−5.64219e6	−0.374952	−0.187476	−	0.982269i	$-0.560031\pi$
$743$	−5.64219e6	−0.374952	−0.187476	+	0.982269i	$0.560031\pi$
$744$	7.68076e6	0.508712
$745$	4.39020e6	0.289797
$746$	−2.29346e7	−1.50884
$747$	1.45273e6	0.0952538
$748$	1.08704e6	0.0710384
$749$	9.11003e6	0.593356
$750$	2.34410e6	0.152168
$751$	2.20425e7	1.42614	0.713069	−	0.701094i	$-0.247305\pi$
$751$	2.20425e7	1.42614	0.713069	+	0.701094i	$0.247305\pi$
$752$	1.40931e7	0.908785
$753$	−194181.	−0.0124801
$754$	7.18239e6	0.460088
$755$	−1.12867e6	−0.0720608
$756$	1.25822e7	0.800665
$757$	−1.62573e7	−1.03112	−0.515561	−	0.856853i	$-0.672416\pi$
$757$	−1.62573e7	−1.03112	−0.515561	+	0.856853i	$0.672416\pi$
$758$	3.66924e7	2.31954
$759$	−4.22796e6	−0.266395
$760$	−3.85589e6	−0.242153
$761$	−1.10995e7	−0.694771	−0.347385	−	0.937722i	$-0.612930\pi$
$761$	−1.10995e7	−0.694771	−0.347385	+	0.937722i	$0.612930\pi$
$762$	−2.01533e7	−1.25735
$763$	−607646.	−0.0377867
$764$	−7.66348e6	−0.474999
$765$	−427020.	−0.0263812
$766$	1.56572e7	0.964142
$767$	−1.25728e7	−0.771694
$768$	−8.43814e6	−0.516231
$769$	1.95216e7	1.19042	0.595210	−	0.803570i	$-0.297069\pi$
$769$	1.95216e7	1.19042	0.595210	+	0.803570i	$0.297069\pi$
$770$	−2.79633e6	−0.169966
$771$	3.62553e7	2.19652
$772$	7.27055e6	0.439060
$773$	−4.61524e6	−0.277809	−0.138904	−	0.990306i	$-0.544358\pi$
$773$	−4.61524e6	−0.277809	−0.138904	+	0.990306i	$0.544358\pi$
$774$	4.75470e6	0.285280
$775$	−4.70687e6	−0.281500
$776$	−6.54443e6	−0.390137
$777$	−1.79548e7	−1.06691
$778$	−2.44535e7	−1.44841
$779$	5.55475e7	3.27960
$780$	1.75533e7	1.03305
$781$	9.62626e6	0.564716
$782$	3.70353e6	0.216571
$783$	2.52063e6	0.146928
$784$	3.87692e6	0.225267
$785$	5.87232e6	0.340122
$786$	−3.00970e6	−0.173767
$787$	2.19270e7	1.26195	0.630976	−	0.775802i	$-0.282655\pi$
$787$	2.19270e7	1.26195	0.630976	+	0.775802i	$0.282655\pi$
$788$	−1.48943e7	−0.854483
$789$	934128.	0.0534212
$790$	−5.23789e6	−0.298599
$791$	1.10790e7	0.629591
$792$	526375.	0.0298183
$793$	−3.32248e7	−1.87620
$794$	−4.62687e7	−2.60457
$795$	1.02127e7	0.573092
$796$	1.83952e7	1.02902
$797$	−2.88511e6	−0.160886	−0.0804428	−	0.996759i	$-0.525633\pi$
$797$	−2.88511e6	−0.160886	−0.0804428	+	0.996759i	$0.525633\pi$
$798$	−4.37688e7	−2.43308
$799$	−4.22748e6	−0.234269
$800$	−5.14203e6	−0.284059
$801$	4.19467e6	0.231002
$802$	−1.94867e7	−1.06980
$803$	−9.58944e6	−0.524812
$804$	4.33226e7	2.36360
$805$	−5.22093e6	−0.283961
$806$	−6.43170e7	−3.48729
$807$	7.68451e6	0.415367
$808$	5.02519e6	0.270784
$809$	−3.37982e7	−1.81561	−0.907803	−	0.419396i	$-0.862242\pi$
$809$	−3.37982e7	−1.81561	−0.907803	+	0.419396i	$0.862242\pi$
$810$	1.50697e7	0.807035
$811$	−3.64110e7	−1.94393	−0.971964	−	0.235130i	$-0.924448\pi$
$811$	−3.64110e7	−1.94393	−0.971964	+	0.235130i	$0.924448\pi$
$812$	3.53052e6	0.187909
$813$	2.26455e7	1.20159
$814$	9.62110e6	0.508937
$815$	3.55935e6	0.187705
$816$	3.09118e6	0.162517
$817$	2.03427e7	1.06624
$818$	3.32404e7	1.73693
$819$	8.22571e6	0.428512
$820$	−1.99820e7	−1.03778
$821$	−2.29723e7	−1.18945	−0.594724	−	0.803930i	$-0.702739\pi$
$821$	−2.29723e7	−1.18945	−0.594724	+	0.803930i	$0.702739\pi$
$822$	−3.26180e7	−1.68375
$823$	1.70994e7	0.879998	0.439999	−	0.897998i	$-0.354979\pi$
$823$	1.70994e7	0.879998	0.439999	+	0.897998i	$0.354979\pi$
$824$	3.91065e6	0.200646
$825$	−1.36909e6	−0.0700322
$826$	−1.12775e7	−0.575126
$827$	1.66022e7	0.844115	0.422058	−	0.906569i	$-0.361308\pi$
$827$	1.66022e7	0.844115	0.422058	+	0.906569i	$0.361308\pi$
$828$	5.60881e6	0.284312
$829$	1.29179e7	0.652839	0.326419	−	0.945225i	$-0.394158\pi$
$829$	1.29179e7	0.652839	0.326419	+	0.945225i	$0.394158\pi$
$830$	−4.07994e6	−0.205570
$831$	2.81216e7	1.41266
$832$	−4.55707e7	−2.28233
$833$	−1.16296e6	−0.0580699
$834$	1.41374e7	0.703809
$835$	−3.09941e6	−0.153838
$836$	1.28528e7	0.636036
$837$	−2.25718e7	−1.11366
$838$	7.65636e6	0.376628
$839$	−2.99519e7	−1.46899	−0.734496	−	0.678614i	$-0.762581\pi$
$839$	−2.99519e7	−1.46899	−0.734496	+	0.678614i	$0.762581\pi$
$840$	2.75881e6	0.134904
$841$	707281.	0.0344828
$842$	2.19268e7	1.06585
$843$	−2.52892e7	−1.22565
$844$	5.83772e6	0.282090
$845$	−1.64728e7	−0.793645
$846$	−1.16828e7	−0.561204
$847$	−1.57926e7	−0.756390
$848$	−1.74184e7	−0.831799
$849$	6.67036e6	0.317599
$850$	1.19927e6	0.0569339
$851$	1.79632e7	0.850276
$852$	−5.42010e7	−2.55804
$853$	2.98009e6	0.140235	0.0701176	−	0.997539i	$-0.477663\pi$
$853$	2.98009e6	0.140235	0.0701176	+	0.997539i	$0.477663\pi$
$854$	−2.98018e7	−1.39829
$855$	−5.04892e6	−0.236202
$856$	4.81611e6	0.224653
$857$	−1.83307e7	−0.852565	−0.426282	−	0.904590i	$-0.640177\pi$
$857$	−1.83307e7	−0.852565	−0.426282	+	0.904590i	$0.640177\pi$
$858$	−1.87079e7	−0.867577
$859$	1.43925e7	0.665508	0.332754	−	0.943014i	$-0.392022\pi$
$859$	1.43925e7	0.665508	0.332754	+	0.943014i	$0.392022\pi$
$860$	−7.31784e6	−0.337393
$861$	−3.97431e7	−1.82706
$862$	5.41460e7	2.48198
$863$	2.37456e7	1.08532	0.542658	−	0.839954i	$-0.317418\pi$
$863$	2.37456e7	1.08532	0.542658	+	0.839954i	$0.317418\pi$
$864$	−2.46585e7	−1.12378
$865$	1.47537e7	0.670442
$866$	−6.00131e7	−2.71926
$867$	2.43884e7	1.10188
$868$	−3.16151e7	−1.42428
$869$	3.05923e6	0.137424
$870$	3.15422e6	0.141284
$871$	−6.35653e7	−2.83906
$872$	−321238.	−0.0143066
$873$	−8.56931e6	−0.380549
$874$	4.37892e7	1.93905
$875$	−1.69064e6	−0.0746501
$876$	5.39936e7	2.37729
$877$	−2.36568e7	−1.03862	−0.519311	−	0.854585i	$-0.673811\pi$
$877$	−2.36568e7	−1.03862	−0.519311	+	0.854585i	$0.673811\pi$
$878$	3.30915e7	1.44871
$879$	−2.07504e7	−0.905848
$880$	2.33506e6	0.101646
$881$	−1.13263e7	−0.491639	−0.245820	−	0.969316i	$-0.579057\pi$
$881$	−1.13263e7	−0.491639	−0.245820	+	0.969316i	$0.579057\pi$
$882$	−3.21387e6	−0.139109
$883$	−1.95391e7	−0.843341	−0.421671	−	0.906749i	$-0.638556\pi$
$883$	−1.95391e7	−0.843341	−0.421671	+	0.906749i	$0.638556\pi$
$884$	8.98052e6	0.386519
$885$	−5.52150e6	−0.236973
$886$	5.15331e7	2.20547
$887$	−2.63343e7	−1.12386	−0.561931	−	0.827184i	$-0.689941\pi$
$887$	−2.63343e7	−1.12386	−0.561931	+	0.827184i	$0.689941\pi$
$888$	−9.49201e6	−0.403948
$889$	1.45351e7	0.616829
$890$	−1.17806e7	−0.498532
$891$	−8.80159e6	−0.371421
$892$	1.41296e7	0.594591
$893$	−4.99841e7	−2.09751
$894$	2.63451e7	1.10244
$895$	−2.09614e7	−0.874708
$896$	−1.23895e7	−0.515566
$897$	−3.49289e7	−1.44945
$898$	4.02719e6	0.166652
$899$	−6.33357e6	−0.261366
$900$	1.81624e6	0.0747423
$901$	5.22498e6	0.214423
$902$	2.12964e7	0.871543
$903$	−1.45548e7	−0.594001
$904$	5.85702e6	0.238372
$905$	7.17520e6	0.291214
$906$	−6.77302e6	−0.274133
$907$	−3.82413e7	−1.54353	−0.771765	−	0.635908i	$-0.780626\pi$
$907$	−3.82413e7	−1.54353	−0.771765	+	0.635908i	$0.780626\pi$
$908$	−2.37630e7	−0.956502
$909$	6.58000e6	0.264129
$910$	−2.31017e7	−0.924783
$911$	−4.36962e7	−1.74441	−0.872203	−	0.489144i	$-0.837309\pi$
$911$	−4.36962e7	−1.74441	−0.872203	+	0.489144i	$0.837309\pi$
$912$	3.65489e7	1.45508
$913$	2.38293e6	0.0946092
$914$	−7.14648e7	−2.82961
$915$	−1.45910e7	−0.576147
$916$	4.86844e7	1.91713
$917$	2.17069e6	0.0852459
$918$	5.75111e6	0.225240
$919$	−2.29974e6	−0.0898234	−0.0449117	−	0.998991i	$-0.514301\pi$
$919$	−2.29974e6	−0.0898234	−0.0449117	+	0.998991i	$0.514301\pi$
$920$	−2.76010e6	−0.107512
$921$	2.88878e7	1.12219
$922$	−3.10844e7	−1.20425
$923$	7.95265e7	3.07261
$924$	−9.19591e6	−0.354336
$925$	5.81683e6	0.223528
$926$	−1.32935e7	−0.509461
$927$	5.12063e6	0.195715
$928$	−6.91911e6	−0.263743
$929$	−3.74465e7	−1.42355	−0.711773	−	0.702409i	$-0.752108\pi$
$929$	−3.74465e7	−1.42355	−0.711773	+	0.702409i	$0.752108\pi$
$930$	−2.82455e7	−1.07088
$931$	−1.37504e7	−0.519924
$932$	−2.38039e7	−0.897653
$933$	4.64463e7	1.74681
$934$	1.24198e7	0.465851
$935$	−700447.	−0.0262027
$936$	4.34860e6	0.162241
$937$	−2.96887e6	−0.110469	−0.0552347	−	0.998473i	$-0.517591\pi$
$937$	−2.96887e6	−0.110469	−0.0552347	+	0.998473i	$0.517591\pi$
$938$	−5.70163e7	−2.11589
$939$	2.19258e7	0.811507
$940$	1.79807e7	0.663723
$941$	4.68984e7	1.72657	0.863284	−	0.504719i	$-0.168404\pi$
$941$	4.68984e7	1.72657	0.863284	+	0.504719i	$0.168404\pi$
$942$	3.52392e7	1.29389
$943$	3.97616e7	1.45608
$944$	9.41722e6	0.343948
$945$	−8.10744e6	−0.295328
$946$	7.79919e6	0.283349
$947$	3.51964e7	1.27533	0.637666	−	0.770313i	$-0.279900\pi$
$947$	3.51964e7	1.27533	0.637666	+	0.770313i	$0.279900\pi$
$948$	−1.72251e7	−0.622503
$949$	−7.92223e7	−2.85550
$950$	1.41798e7	0.509753
$951$	5.79997e7	2.07957
$952$	1.41145e6	0.0504745
$953$	2.82281e7	1.00681	0.503407	−	0.864049i	$-0.332080\pi$
$953$	2.82281e7	1.00681	0.503407	+	0.864049i	$0.332080\pi$
$954$	1.44394e7	0.513663
$955$	4.93803e6	0.175205
$956$	1.11642e6	0.0395077
$957$	−1.84225e6	−0.0650233
$958$	−3.16990e7	−1.11592
$959$	2.35251e7	0.826009
$960$	−2.00129e7	−0.700859
$961$	2.80867e7	0.981054
$962$	7.94839e7	2.76912
$963$	6.30624e6	0.219131
$964$	1.97030e7	0.682873
$965$	−4.68484e6	−0.161948
$966$	−3.13303e7	−1.08024
$967$	4.99644e7	1.71828	0.859140	−	0.511740i	$-0.170999\pi$
$967$	4.99644e7	1.71828	0.859140	+	0.511740i	$0.170999\pi$
$968$	−8.34893e6	−0.286380
$969$	−1.09635e7	−0.375095
$970$	2.40667e7	0.821271
$971$	−1.14066e7	−0.388247	−0.194124	−	0.980977i	$-0.562186\pi$
$971$	−1.14066e7	−0.388247	−0.194124	+	0.980977i	$0.562186\pi$
$972$	2.13003e7	0.723136
$973$	−1.01963e7	−0.345272
$974$	−2.94462e7	−0.994563
$975$	−1.13106e7	−0.381044
$976$	2.48858e7	0.836234
$977$	2.53123e7	0.848391	0.424195	−	0.905571i	$-0.360557\pi$
$977$	2.53123e7	0.848391	0.424195	+	0.905571i	$0.360557\pi$
$978$	2.13593e7	0.714068
$979$	6.88057e6	0.229439
$980$	4.94639e6	0.164522
$981$	−420631.	−0.0139550
$982$	33698.7	0.00111515
$983$	−1.58838e7	−0.524287	−0.262144	−	0.965029i	$-0.584429\pi$
$983$	−1.58838e7	−0.524287	−0.262144	+	0.965029i	$0.584429\pi$
$984$	−2.10106e7	−0.691752
$985$	9.59725e6	0.315178
$986$	1.61374e6	0.0528618
$987$	3.57627e7	1.16852
$988$	1.06182e8	3.46066
$989$	1.45616e7	0.473389
$990$	−1.93571e6	−0.0627700
$991$	−3.84143e6	−0.124254	−0.0621268	−	0.998068i	$-0.519788\pi$
$991$	−3.84143e6	−0.124254	−0.0621268	+	0.998068i	$0.519788\pi$
$992$	6.19593e7	1.99907
$993$	2.34007e7	0.753104
$994$	7.13331e7	2.28995
$995$	−1.18531e7	−0.379556
$996$	−1.34171e7	−0.428560
$997$	−2.19239e7	−0.698521	−0.349260	−	0.937026i	$-0.613567\pi$
$997$	−2.19239e7	−0.698521	−0.349260	+	0.937026i	$0.613567\pi$
$998$	2.09254e7	0.665041
$999$	2.78946e7	0.884312

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	145.6.a.c.1.11	✓	13
5.4	even	2		725.6.a.f.1.3		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
145.6.a.c.1.11	✓	13	1.1	even	1	trivial
725.6.a.f.1.3		13	5.4	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 145 = 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	145.a (trivial)

\(f(q)\)	\(=\)	\(q+8.41417 q^{2} -17.8297 q^{3} +38.7982 q^{4} -25.0000 q^{5} -150.022 q^{6} +108.201 q^{7} +57.2014 q^{8} +74.8998 q^{9} -210.354 q^{10} +122.859 q^{11} -691.763 q^{12} +1014.99 q^{13} +910.419 q^{14} +445.744 q^{15} -760.241 q^{16} +228.049 q^{17} +630.220 q^{18} +2696.36 q^{19} -969.956 q^{20} -1929.19 q^{21} +1033.76 q^{22} +1930.09 q^{23} -1019.89 q^{24} +625.000 q^{25} +8540.30 q^{26} +2997.18 q^{27} +4198.00 q^{28} +841.000 q^{29} +3750.56 q^{30} -7530.99 q^{31} -8227.24 q^{32} -2190.55 q^{33} +1918.84 q^{34} -2705.02 q^{35} +2905.98 q^{36} +9306.92 q^{37} +22687.6 q^{38} -18097.0 q^{39} -1430.04 q^{40} +20600.9 q^{41} -16232.5 q^{42} +7544.51 q^{43} +4766.72 q^{44} -1872.50 q^{45} +16240.1 q^{46} -18537.6 q^{47} +13554.9 q^{48} -5099.60 q^{49} +5258.86 q^{50} -4066.05 q^{51} +39379.8 q^{52} +22911.7 q^{53} +25218.8 q^{54} -3071.48 q^{55} +6189.24 q^{56} -48075.4 q^{57} +7076.32 q^{58} -12387.2 q^{59} +17294.1 q^{60} -32734.1 q^{61} -63367.1 q^{62} +8104.22 q^{63} -44897.7 q^{64} -25374.8 q^{65} -18431.6 q^{66} -62626.5 q^{67} +8847.88 q^{68} -34413.0 q^{69} -22760.5 q^{70} +78352.0 q^{71} +4284.38 q^{72} -78052.2 q^{73} +78310.0 q^{74} -11143.6 q^{75} +104614. q^{76} +13293.5 q^{77} -152271. q^{78} +24900.3 q^{79} +19006.0 q^{80} -71639.7 q^{81} +173340. q^{82} +19395.6 q^{83} -74849.2 q^{84} -5701.21 q^{85} +63480.8 q^{86} -14994.8 q^{87} +7027.72 q^{88} +56003.7 q^{89} -15755.5 q^{90} +109823. q^{91} +74884.1 q^{92} +134276. q^{93} -155979. q^{94} -67409.0 q^{95} +146690. q^{96} -114410. q^{97} -42908.9 q^{98} +9202.13 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 7 q^{2} + 2 q^{3} + 213 q^{4} - 325 q^{5} - 3 q^{6} - 18 q^{7} - 399 q^{8} + 1155 q^{9} - 175 q^{10} + 844 q^{11} + 167 q^{12} - 704 q^{13} + 4425 q^{14} - 50 q^{15} + 5805 q^{16} - 210 q^{17} + 7378 q^{18}+ \cdots - 3872 q^{99}+O(q^{100}) \) 13 * q + 7 * q^2 + 2 * q^3 + 213 * q^4 - 325 * q^5 - 3 * q^6 - 18 * q^7 - 399 * q^8 + 1155 * q^9 - 175 * q^10 + 844 * q^11 + 167 * q^12 - 704 * q^13 + 4425 * q^14 - 50 * q^15 + 5805 * q^16 - 210 * q^17 + 7378 * q^18 + 2524 * q^19 - 5325 * q^20 + 7088 * q^21 - 3772 * q^22 + 10806 * q^23 + 11131 * q^24 + 8125 * q^25 + 15003 * q^26 - 2872 * q^27 + 6007 * q^28 + 10933 * q^29 + 75 * q^30 + 6820 * q^31 - 9761 * q^32 + 9416 * q^33 + 18557 * q^34 + 450 * q^35 + 28284 * q^36 - 7784 * q^37 + 43872 * q^38 + 30524 * q^39 + 9975 * q^40 + 17950 * q^41 + 104284 * q^42 + 24570 * q^43 + 101386 * q^44 - 28875 * q^45 + 71703 * q^46 + 26242 * q^47 + 96475 * q^48 + 45423 * q^49 + 4375 * q^50 - 5632 * q^51 - 2925 * q^52 + 50580 * q^53 + 61352 * q^54 - 21100 * q^55 + 172651 * q^56 + 71600 * q^57 + 5887 * q^58 + 50712 * q^59 - 4175 * q^60 - 24104 * q^61 + 82941 * q^62 - 1298 * q^63 + 75673 * q^64 + 17600 * q^65 - 7632 * q^66 - 93110 * q^67 - 113909 * q^68 + 116878 * q^69 - 110625 * q^70 + 253344 * q^71 - 206562 * q^72 - 11006 * q^73 - 171316 * q^74 + 1250 * q^75 - 275002 * q^76 + 106744 * q^77 - 84017 * q^78 - 23792 * q^79 - 145125 * q^80 + 229097 * q^81 - 461156 * q^82 + 115802 * q^83 - 224096 * q^84 + 5250 * q^85 + 31283 * q^86 + 1682 * q^87 - 635028 * q^88 + 87446 * q^89 - 184450 * q^90 - 33904 * q^91 + 197053 * q^92 - 168912 * q^93 - 464496 * q^94 - 63100 * q^95 - 186929 * q^96 + 27766 * q^97 - 166558 * q^98 - 3872 * q^99

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