LMFDB - Embedded newform 245.6.a.g.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [245,6,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, 6, names="a")

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

chi := DirichletCharacter("245.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 245 = 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 6 $
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:	$39.2940358542$
Analytic rank:	$0$
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} - 128x^{3} + 288x^{2} + 3551x - 6510 $ x^5 - 2x^4 - 128x^3 + 288x^2 + 3551x - 6510
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$8.59300$ 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)

$f(q)$	$=$	$q+7.59300 q^{2} +26.8345 q^{3} +25.6536 q^{4} -25.0000 q^{5} +203.754 q^{6} -48.1883 q^{8} +477.089 q^{9} +O(q^{10})$	\(q+7.59300 q^{2} +26.8345 q^{3} +25.6536 q^{4} -25.0000 q^{5} +203.754 q^{6} -48.1883 q^{8} +477.089 q^{9} -189.825 q^{10} +698.100 q^{11} +688.401 q^{12} +469.049 q^{13} -670.862 q^{15} -1186.81 q^{16} +1372.06 q^{17} +3622.54 q^{18} -1617.81 q^{19} -641.340 q^{20} +5300.67 q^{22} -467.734 q^{23} -1293.11 q^{24} +625.000 q^{25} +3561.48 q^{26} +6281.67 q^{27} +2616.48 q^{29} -5093.85 q^{30} +5570.78 q^{31} -7469.41 q^{32} +18733.2 q^{33} +10418.1 q^{34} +12239.1 q^{36} -15243.6 q^{37} -12284.0 q^{38} +12586.7 q^{39} +1204.71 q^{40} +9377.27 q^{41} -19993.4 q^{43} +17908.8 q^{44} -11927.2 q^{45} -3551.50 q^{46} +19951.9 q^{47} -31847.4 q^{48} +4745.62 q^{50} +36818.6 q^{51} +12032.8 q^{52} -3336.99 q^{53} +47696.7 q^{54} -17452.5 q^{55} -43413.1 q^{57} +19866.9 q^{58} +13863.4 q^{59} -17210.0 q^{60} -33380.1 q^{61} +42298.9 q^{62} -18737.3 q^{64} -11726.2 q^{65} +142241. q^{66} -7254.09 q^{67} +35198.3 q^{68} -12551.4 q^{69} -47104.2 q^{71} -22990.1 q^{72} -86597.2 q^{73} -115744. q^{74} +16771.6 q^{75} -41502.7 q^{76} +95570.6 q^{78} -34748.5 q^{79} +29670.2 q^{80} +52632.6 q^{81} +71201.6 q^{82} -85800.6 q^{83} -34301.5 q^{85} -151810. q^{86} +70211.8 q^{87} -33640.3 q^{88} +11833.8 q^{89} -90563.4 q^{90} -11999.1 q^{92} +149489. q^{93} +151495. q^{94} +40445.3 q^{95} -200438. q^{96} +16500.6 q^{97} +333056. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 3 q^{2} + 7 q^{3} + 101 q^{4} - 125 q^{5} + 304 q^{6} - 675 q^{8} + 284 q^{9}+O(q^{10}) $ 5 * q - 3 * q^2 + 7 * q^3 + 101 * q^4 - 125 * q^5 + 304 * q^6 - 675 * q^8 + 284 * q^9	\( 5 q - 3 q^{2} + 7 q^{3} + 101 q^{4} - 125 q^{5} + 304 q^{6} - 675 q^{8} + 284 q^{9} + 75 q^{10} + 1033 q^{11} - 1226 q^{12} + 1117 q^{13} - 175 q^{15} + 297 q^{16} + 3403 q^{17} + 887 q^{18} + 2846 q^{19} - 2525 q^{20} - 1858 q^{22} - 2756 q^{23} + 13290 q^{24} + 3125 q^{25} + 2544 q^{26} + 3661 q^{27} + 485 q^{29} - 7600 q^{30} + 10726 q^{31} - 17383 q^{32} + 12597 q^{33} - 16414 q^{34} + 38165 q^{36} - 2660 q^{37} - 14378 q^{38} - 13171 q^{39} + 16875 q^{40} - 8334 q^{41} - 17294 q^{43} + 42876 q^{44} - 7100 q^{45} + 45724 q^{46} + 59799 q^{47} - 94218 q^{48} - 1875 q^{50} - 12049 q^{51} + 87974 q^{52} - 9250 q^{53} + 106342 q^{54} - 25825 q^{55} - 121778 q^{57} + 35868 q^{58} + 52994 q^{59} + 30650 q^{60} + 81540 q^{61} - 74048 q^{62} + 39745 q^{64} - 27925 q^{65} + 311614 q^{66} - 726 q^{67} + 276216 q^{68} + 21388 q^{69} + 3760 q^{71} - 154815 q^{72} + 90634 q^{73} - 57342 q^{74} + 4375 q^{75} + 43902 q^{76} + 152598 q^{78} + 68243 q^{79} - 7425 q^{80} + 17645 q^{81} + 191552 q^{82} - 133292 q^{83} - 85075 q^{85} - 88352 q^{86} + 216813 q^{87} - 273040 q^{88} + 102852 q^{89} - 22175 q^{90} - 140852 q^{92} + 184862 q^{93} + 332618 q^{94} - 71150 q^{95} + 245574 q^{96} + 186175 q^{97} + 454710 q^{99}+O(q^{100}) \) 5 * q - 3 * q^2 + 7 * q^3 + 101 * q^4 - 125 * q^5 + 304 * q^6 - 675 * q^8 + 284 * q^9 + 75 * q^10 + 1033 * q^11 - 1226 * q^12 + 1117 * q^13 - 175 * q^15 + 297 * q^16 + 3403 * q^17 + 887 * q^18 + 2846 * q^19 - 2525 * q^20 - 1858 * q^22 - 2756 * q^23 + 13290 * q^24 + 3125 * q^25 + 2544 * q^26 + 3661 * q^27 + 485 * q^29 - 7600 * q^30 + 10726 * q^31 - 17383 * q^32 + 12597 * q^33 - 16414 * q^34 + 38165 * q^36 - 2660 * q^37 - 14378 * q^38 - 13171 * q^39 + 16875 * q^40 - 8334 * q^41 - 17294 * q^43 + 42876 * q^44 - 7100 * q^45 + 45724 * q^46 + 59799 * q^47 - 94218 * q^48 - 1875 * q^50 - 12049 * q^51 + 87974 * q^52 - 9250 * q^53 + 106342 * q^54 - 25825 * q^55 - 121778 * q^57 + 35868 * q^58 + 52994 * q^59 + 30650 * q^60 + 81540 * q^61 - 74048 * q^62 + 39745 * q^64 - 27925 * q^65 + 311614 * q^66 - 726 * q^67 + 276216 * q^68 + 21388 * q^69 + 3760 * q^71 - 154815 * q^72 + 90634 * q^73 - 57342 * q^74 + 4375 * q^75 + 43902 * q^76 + 152598 * q^78 + 68243 * q^79 - 7425 * q^80 + 17645 * q^81 + 191552 * q^82 - 133292 * q^83 - 85075 * q^85 - 88352 * q^86 + 216813 * q^87 - 273040 * q^88 + 102852 * q^89 - 22175 * q^90 - 140852 * q^92 + 184862 * q^93 + 332618 * q^94 - 71150 * q^95 + 245574 * q^96 + 186175 * q^97 + 454710 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	7.59300	1.34226	0.671132	−	0.741338i	$-0.265808\pi$
$2$	7.59300	1.34226	0.671132	+	0.741338i	$0.265808\pi$
$3$	26.8345	1.72143	0.860716	−	0.509085i	$-0.170016\pi$
$3$	26.8345	1.72143	0.860716	+	0.509085i	$0.170016\pi$
$4$	25.6536	0.801675
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	203.754	2.31062
$7$	0	0
$7$	0	0
$8$	−48.1883	−0.266205
$9$	477.089	1.96333
$10$	−189.825	−0.600279
$11$	698.100	1.73955	0.869773	−	0.493452i	$-0.164265\pi$
$11$	698.100	1.73955	0.869773	+	0.493452i	$0.164265\pi$
$12$	688.401	1.38003
$13$	469.049	0.769767	0.384884	−	0.922965i	$-0.374242\pi$
$13$	469.049	0.769767	0.384884	+	0.922965i	$0.374242\pi$
$14$	0	0
$15$	−670.862	−0.769848
$16$	−1186.81	−1.15899
$17$	1372.06	1.15147	0.575733	−	0.817638i	$-0.304717\pi$
$17$	1372.06	1.15147	0.575733	+	0.817638i	$0.304717\pi$
$18$	3622.54	2.63531
$19$	−1617.81	−1.02812	−0.514060	−	0.857754i	$-0.671859\pi$
$19$	−1617.81	−1.02812	−0.514060	+	0.857754i	$0.671859\pi$
$20$	−641.340	−0.358520
$21$	0	0
$22$	5300.67	2.33493
$23$	−467.734	−0.184365	−0.0921827	−	0.995742i	$-0.529384\pi$
$23$	−467.734	−0.184365	−0.0921827	+	0.995742i	$0.529384\pi$
$24$	−1293.11	−0.458254
$25$	625.000	0.200000
$26$	3561.48	1.03323
$27$	6281.67	1.65831
$28$	0	0
$29$	2616.48	0.577726	0.288863	−	0.957370i	$-0.406723\pi$
$29$	2616.48	0.577726	0.288863	+	0.957370i	$0.406723\pi$
$30$	−5093.85	−1.03334
$31$	5570.78	1.04115	0.520574	−	0.853817i	$-0.325718\pi$
$31$	5570.78	1.04115	0.520574	+	0.853817i	$0.325718\pi$
$32$	−7469.41	−1.28947
$33$	18733.2	2.99451
$34$	10418.1	1.54557
$35$	0	0
$36$	12239.1	1.57395
$37$	−15243.6	−1.83055	−0.915276	−	0.402827i	$-0.868028\pi$
$37$	−15243.6	−1.83055	−0.915276	+	0.402827i	$0.868028\pi$
$38$	−12284.0	−1.38001
$39$	12586.7	1.32510
$40$	1204.71	0.119051
$41$	9377.27	0.871198	0.435599	−	0.900141i	$-0.356537\pi$
$41$	9377.27	0.871198	0.435599	+	0.900141i	$0.356537\pi$
$42$	0	0
$43$	−19993.4	−1.64898	−0.824492	−	0.565874i	$-0.808539\pi$
$43$	−19993.4	−1.64898	−0.824492	+	0.565874i	$0.808539\pi$
$44$	17908.8	1.39455
$45$	−11927.2	−0.878028
$46$	−3551.50	−0.247467
$47$	19951.9	1.31747	0.658734	−	0.752376i	$-0.271092\pi$
$47$	19951.9	1.31747	0.658734	+	0.752376i	$0.271092\pi$
$48$	−31847.4	−1.99513
$49$	0	0
$50$	4745.62	0.268453
$51$	36818.6	1.98217
$52$	12032.8	0.617103
$53$	−3336.99	−0.163179	−0.0815897	−	0.996666i	$-0.526000\pi$
$53$	−3336.99	−0.163179	−0.0815897	+	0.996666i	$0.526000\pi$
$54$	47696.7	2.22589
$55$	−17452.5	−0.777949
$56$	0	0
$57$	−43413.1	−1.76984
$58$	19866.9	0.775461
$59$	13863.4	0.518489	0.259245	−	0.965812i	$-0.416526\pi$
$59$	13863.4	0.518489	0.259245	+	0.965812i	$0.416526\pi$
$60$	−17210.0	−0.617168
$61$	−33380.1	−1.14859	−0.574293	−	0.818650i	$-0.694723\pi$
$61$	−33380.1	−1.14859	−0.574293	+	0.818650i	$0.694723\pi$
$62$	42298.9	1.39749
$63$	0	0
$64$	−18737.3	−0.571817
$65$	−11726.2	−0.344250
$66$	142241.	4.01943
$67$	−7254.09	−0.197422	−0.0987110	−	0.995116i	$-0.531472\pi$
$67$	−7254.09	−0.197422	−0.0987110	+	0.995116i	$0.531472\pi$
$68$	35198.3	0.923101
$69$	−12551.4	−0.317373
$70$	0	0
$71$	−47104.2	−1.10895	−0.554477	−	0.832199i	$-0.687082\pi$
$71$	−47104.2	−1.10895	−0.554477	+	0.832199i	$0.687082\pi$
$72$	−22990.1	−0.522649
$73$	−86597.2	−1.90194	−0.950969	−	0.309286i	$-0.899910\pi$
$73$	−86597.2	−1.90194	−0.950969	+	0.309286i	$0.899910\pi$
$74$	−115744.	−2.45709
$75$	16771.6	0.344287
$76$	−41502.7	−0.824218
$77$	0	0
$78$	95570.6	1.77864
$79$	−34748.5	−0.626424	−0.313212	−	0.949683i	$-0.601405\pi$
$79$	−34748.5	−0.626424	−0.313212	+	0.949683i	$0.601405\pi$
$80$	29670.2	0.518317
$81$	52632.6	0.891337
$82$	71201.6	1.16938
$83$	−85800.6	−1.36708	−0.683542	−	0.729911i	$-0.739561\pi$
$83$	−85800.6	−1.36708	−0.683542	+	0.729911i	$0.739561\pi$
$84$	0	0
$85$	−34301.5	−0.514951
$86$	−151810.	−2.21337
$87$	70211.8	0.994517
$88$	−33640.3	−0.463076
$89$	11833.8	0.158361	0.0791806	−	0.996860i	$-0.474770\pi$
$89$	11833.8	0.158361	0.0791806	+	0.996860i	$0.474770\pi$
$90$	−90563.4	−1.17855
$91$	0	0
$92$	−11999.1	−0.147801
$93$	149489.	1.79226
$94$	151495.	1.76839
$95$	40445.3	0.459789
$96$	−200438.	−2.21974
$97$	16500.6	0.178062	0.0890310	−	0.996029i	$-0.471623\pi$
$97$	16500.6	0.178062	0.0890310	+	0.996029i	$0.471623\pi$
$98$	0	0
$99$	333056.	3.41531
$100$	16033.5	0.160335
$101$	47671.3	0.465000	0.232500	−	0.972596i	$-0.425309\pi$
$101$	47671.3	0.465000	0.232500	+	0.972596i	$0.425309\pi$
$102$	279563.	2.66060
$103$	52269.3	0.485461	0.242730	−	0.970094i	$-0.421957\pi$
$103$	52269.3	0.485461	0.242730	+	0.970094i	$0.421957\pi$
$104$	−22602.6	−0.204916
$105$	0	0
$106$	−25337.7	−0.219030
$107$	128057.	1.08130	0.540648	−	0.841249i	$-0.318179\pi$
$107$	128057.	1.08130	0.540648	+	0.841249i	$0.318179\pi$
$108$	161147.	1.32942
$109$	3019.68	0.0243442	0.0121721	−	0.999926i	$-0.496125\pi$
$109$	3019.68	0.0243442	0.0121721	+	0.999926i	$0.496125\pi$
$110$	−132517.	−1.04421
$111$	−409053.	−3.15117
$112$	0	0
$113$	−140745.	−1.03690	−0.518451	−	0.855107i	$-0.673491\pi$
$113$	−140745.	−1.03690	−0.518451	+	0.855107i	$0.673491\pi$
$114$	−329636.	−2.37559
$115$	11693.4	0.0824507
$116$	67122.0	0.463148
$117$	223778.	1.51131
$118$	105265.	0.695950
$119$	0	0
$120$	32327.7	0.204938
$121$	326293.	2.02602
$122$	−253455.	−1.54171
$123$	251634.	1.49971
$124$	142911.	0.834661
$125$	−15625.0	−0.0894427
$126$	0	0
$127$	−247475.	−1.36151	−0.680757	−	0.732509i	$-0.738349\pi$
$127$	−247475.	−1.36151	−0.680757	+	0.732509i	$0.738349\pi$
$128$	96748.7	0.521940
$129$	−536514.	−2.83861
$130$	−89037.1	−0.462075
$131$	137049.	0.697748	0.348874	−	0.937170i	$-0.386564\pi$
$131$	137049.	0.697748	0.348874	+	0.937170i	$0.386564\pi$
$132$	480573.	2.40062
$133$	0	0
$134$	−55080.2	−0.264993
$135$	−157042.	−0.741618
$136$	−66117.3	−0.306526
$137$	−17294.9	−0.0787257	−0.0393628	−	0.999225i	$-0.512533\pi$
$137$	−17294.9	−0.0787257	−0.0393628	+	0.999225i	$0.512533\pi$
$138$	−95302.8	−0.425998
$139$	391614.	1.71918	0.859590	−	0.510984i	$-0.170719\pi$
$139$	391614.	1.71918	0.859590	+	0.510984i	$0.170719\pi$
$140$	0	0
$141$	535400.	2.26793
$142$	−357662.	−1.48851
$143$	327443.	1.33905
$144$	−566214.	−2.27549
$145$	−65411.9	−0.258367
$146$	−657532.	−2.55290
$147$	0	0
$148$	−391052.	−1.46751
$149$	−135354.	−0.499464	−0.249732	−	0.968315i	$-0.580343\pi$
$149$	−135354.	−0.499464	−0.249732	+	0.968315i	$0.580343\pi$
$150$	127346.	0.462124
$151$	−38867.4	−0.138721	−0.0693606	−	0.997592i	$-0.522096\pi$
$151$	−38867.4	−0.138721	−0.0693606	+	0.997592i	$0.522096\pi$
$152$	77959.5	0.273691
$153$	654596.	2.26071
$154$	0	0
$155$	−139270.	−0.465615
$156$	322893.	1.06230
$157$	−447775.	−1.44981	−0.724904	−	0.688850i	$-0.758116\pi$
$157$	−447775.	−1.44981	−0.724904	+	0.688850i	$0.758116\pi$
$158$	−263845.	−0.840827
$159$	−89546.4	−0.280902
$160$	186735.	0.576668
$161$	0	0
$162$	399639.	1.19641
$163$	94068.8	0.277317	0.138659	−	0.990340i	$-0.455721\pi$
$163$	94068.8	0.277317	0.138659	+	0.990340i	$0.455721\pi$
$164$	240561.	0.698417
$165$	−468329.	−1.33919
$166$	−651484.	−1.83499
$167$	29692.0	0.0823850	0.0411925	−	0.999151i	$-0.486884\pi$
$167$	29692.0	0.0823850	0.0411925	+	0.999151i	$0.486884\pi$
$168$	0	0
$169$	−151286.	−0.407458
$170$	−260451.	−0.691201
$171$	−771840.	−2.01854
$172$	−512903.	−1.32195
$173$	−297366.	−0.755398	−0.377699	−	0.925928i	$-0.623285\pi$
$173$	−297366.	−0.755398	−0.377699	+	0.925928i	$0.623285\pi$
$174$	533118.	1.33490
$175$	0	0
$176$	−828511.	−2.01612
$177$	372017.	0.892544
$178$	89853.9	0.212563
$179$	−276952.	−0.646058	−0.323029	−	0.946389i	$-0.604701\pi$
$179$	−276952.	−0.646058	−0.323029	+	0.946389i	$0.604701\pi$
$180$	−305976.	−0.703893
$181$	564752.	1.28133	0.640666	−	0.767820i	$-0.278658\pi$
$181$	564752.	1.28133	0.640666	+	0.767820i	$0.278658\pi$
$182$	0	0
$183$	−895739.	−1.97721
$184$	22539.3	0.0490790
$185$	381089.	0.818648
$186$	1.13507e6	2.40569
$187$	957836.	2.00303
$188$	511838.	1.05618
$189$	0	0
$190$	307101.	0.617159
$191$	−334962.	−0.664374	−0.332187	−	0.943214i	$-0.607787\pi$
$191$	−334962.	−0.664374	−0.332187	+	0.943214i	$0.607787\pi$
$192$	−502806.	−0.984345
$193$	928808.	1.79487	0.897434	−	0.441149i	$-0.145429\pi$
$193$	928808.	1.79487	0.897434	+	0.441149i	$0.145429\pi$
$194$	125289.	0.239006
$195$	−314667.	−0.592604
$196$	0	0
$197$	745289.	1.36823	0.684115	−	0.729374i	$-0.260189\pi$
$197$	745289.	1.36823	0.684115	+	0.729374i	$0.260189\pi$
$198$	2.52889e6	4.58424
$199$	−892226.	−1.59714	−0.798569	−	0.601904i	$-0.794409\pi$
$199$	−892226.	−1.59714	−0.798569	+	0.601904i	$0.794409\pi$
$200$	−30117.7	−0.0532410
$201$	−194660.	−0.339849
$202$	361968.	0.624154
$203$	0	0
$204$	944528.	1.58906
$205$	−234432.	−0.389612
$206$	396881.	0.651617
$207$	−223151.	−0.361970
$208$	−556671.	−0.892155
$209$	−1.12939e6	−1.78846
$210$	0	0
$211$	132089.	0.204249	0.102124	−	0.994772i	$-0.467436\pi$
$211$	132089.	0.204249	0.102124	+	0.994772i	$0.467436\pi$
$212$	−85605.7	−0.130817
$213$	−1.26402e6	−1.90899
$214$	972338.	1.45139
$215$	499836.	0.737448
$216$	−302703.	−0.441451
$217$	0	0
$218$	22928.4	0.0326763
$219$	−2.32379e6	−3.27406
$220$	−447719.	−0.623662
$221$	643564.	0.886361
$222$	−3.10594e6	−4.22971
$223$	−346910.	−0.467148	−0.233574	−	0.972339i	$-0.575042\pi$
$223$	−346910.	−0.467148	−0.233574	+	0.972339i	$0.575042\pi$
$224$	0	0
$225$	298181.	0.392666
$226$	−1.06868e6	−1.39180
$227$	698825.	0.900127	0.450064	−	0.892996i	$-0.351401\pi$
$227$	698825.	0.900127	0.450064	+	0.892996i	$0.351401\pi$
$228$	−1.11370e6	−1.41884
$229$	−501406.	−0.631831	−0.315916	−	0.948787i	$-0.602312\pi$
$229$	−501406.	−0.631831	−0.315916	+	0.948787i	$0.602312\pi$
$230$	88787.6	0.110671
$231$	0	0
$232$	−126084.	−0.153794
$233$	−465877.	−0.562188	−0.281094	−	0.959680i	$-0.590697\pi$
$233$	−465877.	−0.562188	−0.281094	+	0.959680i	$0.590697\pi$
$234$	1.69915e6	2.02858
$235$	−498798.	−0.589190
$236$	355646.	0.415660
$237$	−932459.	−1.07835
$238$	0	0
$239$	−556724.	−0.630442	−0.315221	−	0.949018i	$-0.602079\pi$
$239$	−556724.	−0.630442	−0.315221	+	0.949018i	$0.602079\pi$
$240$	796185.	0.892248
$241$	814454.	0.903283	0.451642	−	0.892199i	$-0.350839\pi$
$241$	814454.	0.903283	0.451642	+	0.892199i	$0.350839\pi$
$242$	2.47754e6	2.71946
$243$	−114078.	−0.123932
$244$	−856320.	−0.920792
$245$	0	0
$246$	1.91066e6	2.01301
$247$	−758832.	−0.791413
$248$	−268447.	−0.277159
$249$	−2.30242e6	−2.35334
$250$	−118641.	−0.120056
$251$	1.43550e6	1.43820	0.719099	−	0.694907i	$-0.244555\pi$
$251$	1.43550e6	1.43820	0.719099	+	0.694907i	$0.244555\pi$
$252$	0	0
$253$	−326525.	−0.320712
$254$	−1.87908e6	−1.82751
$255$	−920464.	−0.886454
$256$	1.33421e6	1.27240
$257$	1.47265e6	1.39081	0.695403	−	0.718620i	$-0.255226\pi$
$257$	1.47265e6	1.39081	0.695403	+	0.718620i	$0.255226\pi$
$258$	−4.07375e6	−3.81017
$259$	0	0
$260$	−300819.	−0.275977
$261$	1.24829e6	1.13427
$262$	1.04061e6	0.936562
$263$	−343306.	−0.306050	−0.153025	−	0.988222i	$-0.548902\pi$
$263$	−343306.	−0.306050	−0.153025	+	0.988222i	$0.548902\pi$
$264$	−902719.	−0.797155
$265$	83424.7	0.0729760
$266$	0	0
$267$	317554.	0.272608
$268$	−186093.	−0.158268
$269$	−556577.	−0.468970	−0.234485	−	0.972120i	$-0.575340\pi$
$269$	−556577.	−0.468970	−0.234485	+	0.972120i	$0.575340\pi$
$270$	−1.19242e6	−0.995448
$271$	−535326.	−0.442788	−0.221394	−	0.975184i	$-0.571061\pi$
$271$	−535326.	−0.442788	−0.221394	+	0.975184i	$0.571061\pi$
$272$	−1.62837e6	−1.33454
$273$	0	0
$274$	−131320.	−0.105671
$275$	436313.	0.347909
$276$	−321989.	−0.254430
$277$	273417.	0.214105	0.107052	−	0.994253i	$-0.465859\pi$
$277$	273417.	0.214105	0.107052	+	0.994253i	$0.465859\pi$
$278$	2.97353e6	2.30760
$279$	2.65776e6	2.04412
$280$	0	0
$281$	414223.	0.312945	0.156473	−	0.987682i	$-0.449988\pi$
$281$	414223.	0.312945	0.156473	+	0.987682i	$0.449988\pi$
$282$	4.06529e6	3.04417
$283$	156284.	0.115997	0.0579987	−	0.998317i	$-0.481528\pi$
$283$	156284.	0.115997	0.0579987	+	0.998317i	$0.481528\pi$
$284$	−1.20839e6	−0.889020
$285$	1.08533e6	0.791496
$286$	2.48627e6	1.79735
$287$	0	0
$288$	−3.56357e6	−2.53166
$289$	462696.	0.325875
$290$	−496673.	−0.346797
$291$	442786.	0.306522
$292$	−2.22153e6	−1.52474
$293$	361437.	0.245960	0.122980	−	0.992409i	$-0.460755\pi$
$293$	361437.	0.245960	0.122980	+	0.992409i	$0.460755\pi$
$294$	0	0
$295$	−346585.	−0.231875
$296$	734561.	0.487303
$297$	4.38523e6	2.88471
$298$	−1.02774e6	−0.670414
$299$	−219390.	−0.141919
$300$	430250.	0.276006
$301$	0	0
$302$	−295120.	−0.186201
$303$	1.27923e6	0.800467
$304$	1.92003e6	1.19158
$305$	834504.	0.513663
$306$	4.97034e6	3.03447
$307$	1.13284e6	0.685997	0.342998	−	0.939336i	$-0.388557\pi$
$307$	1.13284e6	0.685997	0.342998	+	0.939336i	$0.388557\pi$
$308$	0	0
$309$	1.40262e6	0.835688
$310$	−1.05747e6	−0.624979
$311$	2.54545e6	1.49233	0.746163	−	0.665763i	$-0.231894\pi$
$311$	2.54545e6	1.49233	0.746163	+	0.665763i	$0.231894\pi$
$312$	−606530.	−0.352749
$313$	−534678.	−0.308483	−0.154242	−	0.988033i	$-0.549293\pi$
$313$	−534678.	−0.308483	−0.154242	+	0.988033i	$0.549293\pi$
$314$	−3.39995e6	−1.94603
$315$	0	0
$316$	−891424.	−0.502188
$317$	6730.34	0.00376174	0.00188087	−	0.999998i	$-0.499401\pi$
$317$	6730.34	0.00376174	0.00188087	+	0.999998i	$0.499401\pi$
$318$	−679925.	−0.377045
$319$	1.82656e6	1.00498
$320$	468432.	0.255724
$321$	3.43635e6	1.86138
$322$	0	0
$323$	−2.21974e6	−1.18385
$324$	1.35021e6	0.714562
$325$	293155.	0.153953
$326$	714264.	0.372233
$327$	81031.6	0.0419069
$328$	−451875.	−0.231917
$329$	0	0
$330$	−3.55602e6	−1.79754
$331$	−1.43037e6	−0.717594	−0.358797	−	0.933416i	$-0.616813\pi$
$331$	−1.43037e6	−0.717594	−0.358797	+	0.933416i	$0.616813\pi$
$332$	−2.20109e6	−1.09596
$333$	−7.27254e6	−3.59398
$334$	225451.	0.110583
$335$	181352.	0.0882898
$336$	0	0
$337$	2.72804e6	1.30850	0.654252	−	0.756276i	$-0.272983\pi$
$337$	2.72804e6	1.30850	0.654252	+	0.756276i	$0.272983\pi$
$338$	−1.14872e6	−0.546917
$339$	−3.77683e6	−1.78496
$340$	−879958.	−0.412824
$341$	3.88897e6	1.81112
$342$	−5.86058e6	−2.70941
$343$	0	0
$344$	963450.	0.438968
$345$	313785.	0.141933
$346$	−2.25790e6	−1.01394
$347$	947097.	0.422251	0.211125	−	0.977459i	$-0.432287\pi$
$347$	947097.	0.422251	0.211125	+	0.977459i	$0.432287\pi$
$348$	1.80118e6	0.797279
$349$	−2.35300e6	−1.03409	−0.517045	−	0.855958i	$-0.672968\pi$
$349$	−2.35300e6	−1.03409	−0.517045	+	0.855958i	$0.672968\pi$
$350$	0	0
$351$	2.94641e6	1.27651
$352$	−5.21439e6	−2.24309
$353$	2.21454e6	0.945905	0.472952	−	0.881088i	$-0.343188\pi$
$353$	2.21454e6	0.945905	0.472952	+	0.881088i	$0.343188\pi$
$354$	2.82472e6	1.19803
$355$	1.17760e6	0.495939
$356$	303579.	0.126954
$357$	0	0
$358$	−2.10289e6	−0.867181
$359$	2.15088e6	0.880806	0.440403	−	0.897800i	$-0.354836\pi$
$359$	2.15088e6	0.880806	0.440403	+	0.897800i	$0.354836\pi$
$360$	574753.	0.233736
$361$	141213.	0.0570305
$362$	4.28816e6	1.71989
$363$	8.75590e6	3.48766
$364$	0	0
$365$	2.16493e6	0.850573
$366$	−6.80134e6	−2.65394
$367$	−1.95284e6	−0.756834	−0.378417	−	0.925635i	$-0.623532\pi$
$367$	−1.95284e6	−0.756834	−0.378417	+	0.925635i	$0.623532\pi$
$368$	555111.	0.213678
$369$	4.47380e6	1.71045
$370$	2.89361e6	1.09884
$371$	0	0
$372$	3.83493e6	1.43681
$373$	4.61421e6	1.71722	0.858609	−	0.512632i	$-0.171329\pi$
$373$	4.61421e6	1.71722	0.858609	+	0.512632i	$0.171329\pi$
$374$	7.27285e6	2.68860
$375$	−419289.	−0.153970
$376$	−961449.	−0.350717
$377$	1.22725e6	0.444715
$378$	0	0
$379$	−1.73321e6	−0.619802	−0.309901	−	0.950769i	$-0.600296\pi$
$379$	−1.73321e6	−0.619802	−0.309901	+	0.950769i	$0.600296\pi$
$380$	1.03757e6	0.368601
$381$	−6.64087e6	−2.34376
$382$	−2.54337e6	−0.891766
$383$	−1.32941e6	−0.463087	−0.231543	−	0.972825i	$-0.574378\pi$
$383$	−1.32941e6	−0.463087	−0.231543	+	0.972825i	$0.574378\pi$
$384$	2.59620e6	0.898484
$385$	0	0
$386$	7.05243e6	2.40919
$387$	−9.53866e6	−3.23750
$388$	423300.	0.142748
$389$	4.21937e6	1.41375	0.706877	−	0.707337i	$-0.250104\pi$
$389$	4.21937e6	1.41375	0.706877	+	0.707337i	$0.250104\pi$
$390$	−2.38926e6	−0.795431
$391$	−641760.	−0.212291
$392$	0	0
$393$	3.67765e6	1.20113
$394$	5.65897e6	1.83653
$395$	868713.	0.280145
$396$	8.54409e6	2.73796
$397$	−2.01357e6	−0.641195	−0.320597	−	0.947216i	$-0.603884\pi$
$397$	−2.01357e6	−0.641195	−0.320597	+	0.947216i	$0.603884\pi$
$398$	−6.77467e6	−2.14378
$399$	0	0
$400$	−741755.	−0.231798
$401$	2.81365e6	0.873794	0.436897	−	0.899512i	$-0.356077\pi$
$401$	2.81365e6	0.873794	0.436897	+	0.899512i	$0.356077\pi$
$402$	−1.47805e6	−0.456167
$403$	2.61297e6	0.801441
$404$	1.22294e6	0.372779
$405$	−1.31581e6	−0.398618
$406$	0	0
$407$	−1.06415e7	−3.18433
$408$	−1.77422e6	−0.527664
$409$	189571.	0.0560356	0.0280178	−	0.999607i	$-0.491080\pi$
$409$	189571.	0.0560356	0.0280178	+	0.999607i	$0.491080\pi$
$410$	−1.78004e6	−0.522962
$411$	−464099.	−0.135521
$412$	1.34090e6	0.389181
$413$	0	0
$414$	−1.69439e6	−0.485860
$415$	2.14502e6	0.611379
$416$	−3.50351e6	−0.992591
$417$	1.05088e7	2.95945
$418$	−8.57549e6	−2.40059
$419$	−3.22872e6	−0.898452	−0.449226	−	0.893418i	$-0.648300\pi$
$419$	−3.22872e6	−0.898452	−0.449226	+	0.893418i	$0.648300\pi$
$420$	0	0
$421$	−275253.	−0.0756881	−0.0378440	−	0.999284i	$-0.512049\pi$
$421$	−275253.	−0.0756881	−0.0378440	+	0.999284i	$0.512049\pi$
$422$	1.00295e6	0.274156
$423$	9.51885e6	2.58663
$424$	160804.	0.0434392
$425$	857538.	0.230293
$426$	−9.59767e6	−2.56237
$427$	0	0
$428$	3.28513e6	0.866848
$429$	8.78676e6	2.30508
$430$	3.79525e6	0.989850
$431$	684294.	0.177439	0.0887196	−	0.996057i	$-0.471723\pi$
$431$	684294.	0.177439	0.0887196	+	0.996057i	$0.471723\pi$
$432$	−7.45513e6	−1.92197
$433$	4.93269e6	1.26434	0.632170	−	0.774830i	$-0.282164\pi$
$433$	4.93269e6	1.26434	0.632170	+	0.774830i	$0.282164\pi$
$434$	0	0
$435$	−1.75530e6	−0.444761
$436$	77465.7	0.0195161
$437$	756706.	0.189550
$438$	−1.76445e7	−4.39465
$439$	−6.59042e6	−1.63212	−0.816060	−	0.577968i	$-0.803846\pi$
$439$	−6.59042e6	−1.63212	−0.816060	+	0.577968i	$0.803846\pi$
$440$	841006.	0.207094
$441$	0	0
$442$	4.88658e6	1.18973
$443$	−323829.	−0.0783983	−0.0391992	−	0.999231i	$-0.512481\pi$
$443$	−323829.	−0.0783983	−0.0391992	+	0.999231i	$0.512481\pi$
$444$	−1.04937e7	−2.52622
$445$	−295845.	−0.0708213
$446$	−2.63408e6	−0.627036
$447$	−3.63215e6	−0.859794
$448$	0	0
$449$	−2.95442e6	−0.691602	−0.345801	−	0.938308i	$-0.612393\pi$
$449$	−2.95442e6	−0.691602	−0.345801	+	0.938308i	$0.612393\pi$
$450$	2.26409e6	0.527062
$451$	6.54627e6	1.51549
$452$	−3.61062e6	−0.831259
$453$	−1.04299e6	−0.238799
$454$	5.30618e6	1.20821
$455$	0	0
$456$	2.09200e6	0.471140
$457$	2.35062e6	0.526492	0.263246	−	0.964729i	$-0.415207\pi$
$457$	2.35062e6	0.526492	0.263246	+	0.964729i	$0.415207\pi$
$458$	−3.80718e6	−0.848085
$459$	8.61883e6	1.90949
$460$	299977.	0.0660987
$461$	−3.88566e6	−0.851554	−0.425777	−	0.904828i	$-0.639999\pi$
$461$	−3.88566e6	−0.851554	−0.425777	+	0.904828i	$0.639999\pi$
$462$	0	0
$463$	−714348.	−0.154867	−0.0774333	−	0.996998i	$-0.524672\pi$
$463$	−714348.	−0.154867	−0.0774333	+	0.996998i	$0.524672\pi$
$464$	−3.10526e6	−0.669580
$465$	−3.73723e6	−0.801525
$466$	−3.53740e6	−0.754605
$467$	4.32118e6	0.916875	0.458438	−	0.888727i	$-0.348409\pi$
$467$	4.32118e6	0.916875	0.458438	+	0.888727i	$0.348409\pi$
$468$	5.74071e6	1.21158
$469$	0	0
$470$	−3.78737e6	−0.790849
$471$	−1.20158e7	−2.49575
$472$	−668053.	−0.138024
$473$	−1.39574e7	−2.86848
$474$	−7.08015e6	−1.44743
$475$	−1.01113e6	−0.205624
$476$	0	0
$477$	−1.59204e6	−0.320375
$478$	−4.22720e6	−0.846220
$479$	−3.50208e6	−0.697409	−0.348705	−	0.937233i	$-0.613378\pi$
$479$	−3.50208e6	−0.697409	−0.348705	+	0.937233i	$0.613378\pi$
$480$	5.01094e6	0.992696
$481$	−7.14997e6	−1.40910
$482$	6.18415e6	1.21245
$483$	0	0
$484$	8.37058e6	1.62421
$485$	−412516.	−0.0796318
$486$	−866190.	−0.166350
$487$	−4.90842e6	−0.937820	−0.468910	−	0.883246i	$-0.655353\pi$
$487$	−4.90842e6	−0.937820	−0.468910	+	0.883246i	$0.655353\pi$
$488$	1.60853e6	0.305760
$489$	2.52429e6	0.477383
$490$	0	0
$491$	−2.36454e6	−0.442633	−0.221317	−	0.975202i	$-0.571035\pi$
$491$	−2.36454e6	−0.442633	−0.221317	+	0.975202i	$0.571035\pi$
$492$	6.45532e6	1.20228
$493$	3.58997e6	0.665232
$494$	−5.76181e6	−1.06229
$495$	−8.32641e6	−1.52737
$496$	−6.61145e6	−1.20668
$497$	0	0
$498$	−1.74822e7	−3.15881
$499$	623899.	0.112166	0.0560832	−	0.998426i	$-0.482139\pi$
$499$	623899.	0.112166	0.0560832	+	0.998426i	$0.482139\pi$
$500$	−400837.	−0.0717040
$501$	796769.	0.141820
$502$	1.08997e7	1.93044
$503$	−7.58820e6	−1.33727	−0.668634	−	0.743591i	$-0.733121\pi$
$503$	−7.58820e6	−1.33727	−0.668634	+	0.743591i	$0.733121\pi$
$504$	0	0
$505$	−1.19178e6	−0.207954
$506$	−2.47931e6	−0.430481
$507$	−4.05969e6	−0.701412
$508$	−6.34863e6	−1.09149
$509$	5.82660e6	0.996829	0.498414	−	0.866939i	$-0.333916\pi$
$509$	5.82660e6	0.996829	0.498414	+	0.866939i	$0.333916\pi$
$510$	−6.98908e6	−1.18986
$511$	0	0
$512$	7.03466e6	1.18596
$513$	−1.01626e7	−1.70494
$514$	1.11818e7	1.86683
$515$	−1.30673e6	−0.217105
$516$	−1.37635e7	−2.27565
$517$	1.39284e7	2.29180
$518$	0	0
$519$	−7.97966e6	−1.30037
$520$	565066.	0.0916412
$521$	2.50715e6	0.404655	0.202328	−	0.979318i	$-0.435149\pi$
$521$	2.50715e6	0.404655	0.202328	+	0.979318i	$0.435149\pi$
$522$	9.47829e6	1.52249
$523$	521695.	0.0833992	0.0416996	−	0.999130i	$-0.486723\pi$
$523$	521695.	0.0833992	0.0416996	+	0.999130i	$0.486723\pi$
$524$	3.51581e6	0.559367
$525$	0	0
$526$	−2.60672e6	−0.410800
$527$	7.64346e6	1.19885
$528$	−2.22327e7	−3.47062
$529$	−6.21757e6	−0.966009
$530$	633444.	0.0979531
$531$	6.61408e6	1.01797
$532$	0	0
$533$	4.39840e6	0.670620
$534$	2.41118e6	0.365912
$535$	−3.20143e6	−0.483570
$536$	349562.	0.0525548
$537$	−7.43186e6	−1.11215
$538$	−4.22609e6	−0.629481
$539$	0	0
$540$	−4.02868e6	−0.594537
$541$	1.08613e7	1.59548	0.797738	−	0.603004i	$-0.206030\pi$
$541$	1.08613e7	1.59548	0.797738	+	0.603004i	$0.206030\pi$
$542$	−4.06473e6	−0.594338
$543$	1.51548e7	2.20573
$544$	−1.02485e7	−1.48478
$545$	−75492.1	−0.0108870
$546$	0	0
$547$	−673442.	−0.0962347	−0.0481174	−	0.998842i	$-0.515322\pi$
$547$	−673442.	−0.0962347	−0.0481174	+	0.998842i	$0.515322\pi$
$548$	−443676.	−0.0631124
$549$	−1.59253e7	−2.25505
$550$	3.31292e6	0.466986
$551$	−4.23297e6	−0.593972
$552$	604831.	0.0844863
$553$	0	0
$554$	2.07606e6	0.287385
$555$	1.02263e7	1.40925
$556$	1.00463e7	1.37822
$557$	−2.59342e6	−0.354189	−0.177095	−	0.984194i	$-0.556670\pi$
$557$	−2.59342e6	−0.354189	−0.177095	+	0.984194i	$0.556670\pi$
$558$	2.01804e7	2.74374
$559$	−9.37790e6	−1.26933
$560$	0	0
$561$	2.57030e7	3.44808
$562$	3.14519e6	0.420055
$563$	−9.11377e6	−1.21179	−0.605895	−	0.795545i	$-0.707185\pi$
$563$	−9.11377e6	−1.21179	−0.605895	+	0.795545i	$0.707185\pi$
$564$	1.37349e7	1.81814
$565$	3.51863e6	0.463717
$566$	1.18666e6	0.155699
$567$	0	0
$568$	2.26987e6	0.295209
$569$	3.18251e6	0.412087	0.206043	−	0.978543i	$-0.433941\pi$
$569$	3.18251e6	0.412087	0.206043	+	0.978543i	$0.433941\pi$
$570$	8.24089e6	1.06240
$571$	−5.41091e6	−0.694512	−0.347256	−	0.937770i	$-0.612887\pi$
$571$	−5.41091e6	−0.694512	−0.347256	+	0.937770i	$0.612887\pi$
$572$	8.40009e6	1.07348
$573$	−8.98854e6	−1.14368
$574$	0	0
$575$	−292334.	−0.0368731
$576$	−8.93937e6	−1.12267
$577$	−1.08325e7	−1.35454	−0.677268	−	0.735736i	$-0.736836\pi$
$577$	−1.08325e7	−1.35454	−0.677268	+	0.735736i	$0.736836\pi$
$578$	3.51325e6	0.437411
$579$	2.49241e7	3.08974
$580$	−1.67805e6	−0.207126
$581$	0	0
$582$	3.36207e6	0.411433
$583$	−2.32955e6	−0.283858
$584$	4.17297e6	0.506306
$585$	−5.59445e6	−0.675877
$586$	2.74439e6	0.330143
$587$	1.52994e7	1.83265	0.916325	−	0.400435i	$-0.131141\pi$
$587$	1.52994e7	1.83265	0.916325	+	0.400435i	$0.131141\pi$
$588$	0	0
$589$	−9.01247e6	−1.07042
$590$	−2.63162e6	−0.311238
$591$	1.99994e7	2.35531
$592$	1.80912e7	2.12160
$593$	−4.88972e6	−0.571015	−0.285507	−	0.958377i	$-0.592162\pi$
$593$	−4.88972e6	−0.571015	−0.285507	+	0.958377i	$0.592162\pi$
$594$	3.32971e7	3.87204
$595$	0	0
$596$	−3.47231e6	−0.400408
$597$	−2.39424e7	−2.74936
$598$	−1.66583e6	−0.190492
$599$	1.39938e7	1.59356	0.796779	−	0.604271i	$-0.206535\pi$
$599$	1.39938e7	1.59356	0.796779	+	0.604271i	$0.206535\pi$
$600$	−808192.	−0.0916509
$601$	6.13403e6	0.692723	0.346362	−	0.938101i	$-0.387417\pi$
$601$	6.13403e6	0.692723	0.346362	+	0.938101i	$0.387417\pi$
$602$	0	0
$603$	−3.46085e6	−0.387605
$604$	−997088.	−0.111209
$605$	−8.15732e6	−0.906065
$606$	9.71322e6	1.07444
$607$	−6.38921e6	−0.703843	−0.351921	−	0.936030i	$-0.614472\pi$
$607$	−6.38921e6	−0.703843	−0.351921	+	0.936030i	$0.614472\pi$
$608$	1.20841e7	1.32573
$609$	0	0
$610$	6.33638e6	0.689472
$611$	9.35842e6	1.01414
$612$	1.67927e7	1.81235
$613$	−2.61958e6	−0.281567	−0.140783	−	0.990040i	$-0.544962\pi$
$613$	−2.61958e6	−0.281567	−0.140783	+	0.990040i	$0.544962\pi$
$614$	8.60164e6	0.920789
$615$	−6.29085e6	−0.670690
$616$	0	0
$617$	1.35499e7	1.43293	0.716463	−	0.697625i	$-0.245760\pi$
$617$	1.35499e7	1.43293	0.716463	+	0.697625i	$0.245760\pi$
$618$	1.06501e7	1.12171
$619$	1.19780e7	1.25649	0.628244	−	0.778017i	$-0.283774\pi$
$619$	1.19780e7	1.25649	0.628244	+	0.778017i	$0.283774\pi$
$620$	−3.57276e6	−0.373272
$621$	−2.93815e6	−0.305735
$622$	1.93276e7	2.00310
$623$	0	0
$624$	−1.49380e7	−1.53578
$625$	390625.	0.0400000
$626$	−4.05981e6	−0.414066
$627$	−3.03067e7	−3.07872
$628$	−1.14870e7	−1.16227
$629$	−2.09151e7	−2.10782
$630$	0	0
$631$	1.13690e7	1.13671	0.568355	−	0.822783i	$-0.307580\pi$
$631$	1.13690e7	1.13671	0.568355	+	0.822783i	$0.307580\pi$
$632$	1.67447e6	0.166757
$633$	3.54453e6	0.351601
$634$	51103.4	0.00504925
$635$	6.18688e6	0.608888
$636$	−2.29719e6	−0.225192
$637$	0	0
$638$	1.38691e7	1.34895
$639$	−2.24729e7	−2.17724
$640$	−2.41872e6	−0.233419
$641$	5.17376e6	0.497349	0.248675	−	0.968587i	$-0.420005\pi$
$641$	5.17376e6	0.497349	0.248675	+	0.968587i	$0.420005\pi$
$642$	2.60922e7	2.49846
$643$	9.66270e6	0.921660	0.460830	−	0.887488i	$-0.347552\pi$
$643$	9.66270e6	0.921660	0.460830	+	0.887488i	$0.347552\pi$
$644$	0	0
$645$	1.34128e7	1.26947
$646$	−1.68544e7	−1.58903
$647$	−1.10865e6	−0.104120	−0.0520599	−	0.998644i	$-0.516579\pi$
$647$	−1.10865e6	−0.104120	−0.0520599	+	0.998644i	$0.516579\pi$
$648$	−2.53627e6	−0.237279
$649$	9.67804e6	0.901936
$650$	2.22593e6	0.206646
$651$	0	0
$652$	2.41320e6	0.222318
$653$	−8.03223e6	−0.737145	−0.368573	−	0.929599i	$-0.620153\pi$
$653$	−8.03223e6	−0.737145	−0.368573	+	0.929599i	$0.620153\pi$
$654$	615273.	0.0562501
$655$	−3.42623e6	−0.312042
$656$	−1.11290e7	−1.00971
$657$	−4.13146e7	−3.73413
$658$	0	0
$659$	1.96081e7	1.75882	0.879411	−	0.476062i	$-0.157936\pi$
$659$	1.96081e7	1.75882	0.879411	+	0.476062i	$0.157936\pi$
$660$	−1.20143e7	−1.07359
$661$	−4.65533e6	−0.414426	−0.207213	−	0.978296i	$-0.566439\pi$
$661$	−4.65533e6	−0.414426	−0.207213	+	0.978296i	$0.566439\pi$
$662$	−1.08608e7	−0.963201
$663$	1.72697e7	1.52581
$664$	4.13459e6	0.363925
$665$	0	0
$666$	−5.52204e7	−4.82407
$667$	−1.22382e6	−0.106513
$668$	761706.	0.0660460
$669$	−9.30914e6	−0.804163
$670$	1.37701e6	0.118508
$671$	−2.33027e7	−1.99802
$672$	0	0
$673$	−1.26377e7	−1.07555	−0.537774	−	0.843089i	$-0.680735\pi$
$673$	−1.26377e7	−1.07555	−0.537774	+	0.843089i	$0.680735\pi$
$674$	2.07140e7	1.75636
$675$	3.92604e6	0.331662
$676$	−3.88104e6	−0.326649
$677$	−4.41154e6	−0.369929	−0.184965	−	0.982745i	$-0.559217\pi$
$677$	−4.41154e6	−0.369929	−0.184965	+	0.982745i	$0.559217\pi$
$678$	−2.86775e7	−2.39589
$679$	0	0
$680$	1.65293e6	0.137083
$681$	1.87526e7	1.54951
$682$	2.95289e7	2.43101
$683$	−2.81517e6	−0.230915	−0.115458	−	0.993312i	$-0.536833\pi$
$683$	−2.81517e6	−0.230915	−0.115458	+	0.993312i	$0.536833\pi$
$684$	−1.98005e7	−1.61821
$685$	432372.	0.0352072
$686$	0	0
$687$	−1.34550e7	−1.08766
$688$	2.37284e7	1.91116
$689$	−1.56521e6	−0.125610
$690$	2.38257e6	0.190512
$691$	1.33377e7	1.06264	0.531321	−	0.847170i	$-0.321696\pi$
$691$	1.33377e7	1.06264	0.531321	+	0.847170i	$0.321696\pi$
$692$	−7.62850e6	−0.605583
$693$	0	0
$694$	7.19130e6	0.566773
$695$	−9.79036e6	−0.768841
$696$	−3.38339e6	−0.264745
$697$	1.28662e7	1.00316
$698$	−1.78663e7	−1.38802
$699$	−1.25016e7	−0.967769
$700$	0	0
$701$	−1.97623e7	−1.51895	−0.759475	−	0.650536i	$-0.774544\pi$
$701$	−1.97623e7	−1.51895	−0.759475	+	0.650536i	$0.774544\pi$
$702$	2.23721e7	1.71342
$703$	2.46612e7	1.88203
$704$	−1.30805e7	−0.994702
$705$	−1.33850e7	−1.01425
$706$	1.68150e7	1.26965
$707$	0	0
$708$	9.54357e6	0.715530
$709$	−6.80579e6	−0.508468	−0.254234	−	0.967143i	$-0.581823\pi$
$709$	−6.80579e6	−0.508468	−0.254234	+	0.967143i	$0.581823\pi$
$710$	8.94155e6	0.665682
$711$	−1.65782e7	−1.22988
$712$	−570250.	−0.0421566
$713$	−2.60565e6	−0.191952
$714$	0	0
$715$	−8.18607e6	−0.598840
$716$	−7.10481e6	−0.517928
$717$	−1.49394e7	−1.08526
$718$	1.63316e7	1.18227
$719$	−2.27287e7	−1.63966	−0.819828	−	0.572611i	$-0.805931\pi$
$719$	−2.27287e7	−1.63966	−0.819828	+	0.572611i	$0.805931\pi$
$720$	1.41553e7	1.01763
$721$	0	0
$722$	1.07223e6	0.0765500
$723$	2.18555e7	1.55494
$724$	1.44879e7	1.02721
$725$	1.63530e6	0.115545
$726$	6.64835e7	4.68136
$727$	1.31854e7	0.925244	0.462622	−	0.886556i	$-0.346909\pi$
$727$	1.31854e7	0.925244	0.462622	+	0.886556i	$0.346909\pi$
$728$	0	0
$729$	−1.58509e7	−1.10468
$730$	1.64383e7	1.14169
$731$	−2.74322e7	−1.89875
$732$	−2.29789e7	−1.58508
$733$	6.83544e6	0.469901	0.234950	−	0.972007i	$-0.424507\pi$
$733$	6.83544e6	0.469901	0.234950	+	0.972007i	$0.424507\pi$
$734$	−1.48279e7	−1.01587
$735$	0	0
$736$	3.49370e6	0.237734
$737$	−5.06408e6	−0.343425
$738$	3.39695e7	2.29588
$739$	5.26046e6	0.354334	0.177167	−	0.984181i	$-0.443307\pi$
$739$	5.26046e6	0.354334	0.177167	+	0.984181i	$0.443307\pi$
$740$	9.77630e6	0.656289
$741$	−2.03629e7	−1.36236
$742$	0	0
$743$	−1.48927e7	−0.989692	−0.494846	−	0.868981i	$-0.664776\pi$
$743$	−1.48927e7	−0.989692	−0.494846	+	0.868981i	$0.664776\pi$
$744$	−7.20362e6	−0.477110
$745$	3.38384e6	0.223367
$746$	3.50357e7	2.30496
$747$	−4.09346e7	−2.68404
$748$	2.45719e7	1.60578
$749$	0	0
$750$	−3.18366e6	−0.206668
$751$	1.04426e7	0.675627	0.337813	−	0.941213i	$-0.390313\pi$
$751$	1.04426e7	0.675627	0.337813	+	0.941213i	$0.390313\pi$
$752$	−2.36791e7	−1.52694
$753$	3.85209e7	2.47576
$754$	9.31854e6	0.596925
$755$	971685.	0.0620380
$756$	0	0
$757$	−7.41183e6	−0.470095	−0.235048	−	0.971984i	$-0.575525\pi$
$757$	−7.41183e6	−0.470095	−0.235048	+	0.971984i	$0.575525\pi$
$758$	−1.31602e7	−0.831938
$759$	−8.76214e6	−0.552085
$760$	−1.94899e6	−0.122398
$761$	−2.15041e6	−0.134605	−0.0673023	−	0.997733i	$-0.521439\pi$
$761$	−2.15041e6	−0.134605	−0.0673023	+	0.997733i	$0.521439\pi$
$762$	−5.04241e7	−3.14594
$763$	0	0
$764$	−8.59299e6	−0.532612
$765$	−1.63649e7	−1.01102
$766$	−1.00942e7	−0.621585
$767$	6.50261e6	0.399116
$768$	3.58027e7	2.19035
$769$	−2.13316e7	−1.30079	−0.650397	−	0.759594i	$-0.725397\pi$
$769$	−2.13316e7	−1.30079	−0.650397	+	0.759594i	$0.725397\pi$
$770$	0	0
$771$	3.95178e7	2.39418
$772$	2.38272e7	1.43890
$773$	1.34827e7	0.811573	0.405787	−	0.913968i	$-0.366998\pi$
$773$	1.34827e7	0.811573	0.405787	+	0.913968i	$0.366998\pi$
$774$	−7.24270e7	−4.34558
$775$	3.48174e6	0.208229
$776$	−795137.	−0.0474010
$777$	0	0
$778$	3.20377e7	1.89763
$779$	−1.51707e7	−0.895696
$780$	−8.07234e6	−0.475076
$781$	−3.28834e7	−1.92908
$782$	−4.87288e6	−0.284950
$783$	1.64358e7	0.958048
$784$	0	0
$785$	1.11944e7	0.648374
$786$	2.79244e7	1.61223
$787$	2.29002e7	1.31796	0.658980	−	0.752160i	$-0.270988\pi$
$787$	2.29002e7	1.31796	0.658980	+	0.752160i	$0.270988\pi$
$788$	1.91193e7	1.09687
$789$	−9.21245e6	−0.526845
$790$	6.59613e6	0.376029
$791$	0	0
$792$	−1.60494e7	−0.909172
$793$	−1.56569e7	−0.884144
$794$	−1.52890e7	−0.860653
$795$	2.23866e6	0.125623
$796$	−2.28888e7	−1.28038
$797$	−2.39100e7	−1.33332	−0.666660	−	0.745362i	$-0.732277\pi$
$797$	−2.39100e7	−1.33332	−0.666660	+	0.745362i	$0.732277\pi$
$798$	0	0
$799$	2.73753e7	1.51702
$800$	−4.66838e6	−0.257894
$801$	5.64577e6	0.310915
$802$	2.13640e7	1.17286
$803$	−6.04535e7	−3.30851
$804$	−4.99372e6	−0.272448
$805$	0	0
$806$	1.98403e7	1.07575
$807$	−1.49355e7	−0.807300
$808$	−2.29720e6	−0.123785
$809$	−9.70802e6	−0.521506	−0.260753	−	0.965406i	$-0.583971\pi$
$809$	−9.70802e6	−0.521506	−0.260753	+	0.965406i	$0.583971\pi$
$810$	−9.99097e6	−0.535051
$811$	2.22841e7	1.18971	0.594856	−	0.803832i	$-0.297209\pi$
$811$	2.22841e7	1.18971	0.594856	+	0.803832i	$0.297209\pi$
$812$	0	0
$813$	−1.43652e7	−0.762229
$814$	−8.08011e7	−4.27422
$815$	−2.35172e6	−0.124020
$816$	−4.36966e7	−2.29732
$817$	3.23456e7	1.69535
$818$	1.43941e6	0.0752146
$819$	0	0
$820$	−6.01402e6	−0.312342
$821$	1.65227e7	0.855505	0.427753	−	0.903896i	$-0.359305\pi$
$821$	1.65227e7	0.855505	0.427753	+	0.903896i	$0.359305\pi$
$822$	−3.52391e6	−0.181905
$823$	2.19532e7	1.12979	0.564895	−	0.825163i	$-0.308917\pi$
$823$	2.19532e7	1.12979	0.564895	+	0.825163i	$0.308917\pi$
$824$	−2.51877e6	−0.129232
$825$	1.17082e7	0.598903
$826$	0	0
$827$	−3.43008e7	−1.74397	−0.871987	−	0.489529i	$-0.837169\pi$
$827$	−3.43008e7	−1.74397	−0.871987	+	0.489529i	$0.837169\pi$
$828$	−5.72463e6	−0.290183
$829$	3.52088e7	1.77936	0.889682	−	0.456581i	$-0.150926\pi$
$829$	3.52088e7	1.77936	0.889682	+	0.456581i	$0.150926\pi$
$830$	1.62871e7	0.820632
$831$	7.33701e6	0.368567
$832$	−8.78870e6	−0.440166
$833$	0	0
$834$	7.97930e7	3.97237
$835$	−742300.	−0.0368437
$836$	−2.89730e7	−1.43376
$837$	3.49938e7	1.72654
$838$	−2.45156e7	−1.20596
$839$	2.51326e7	1.23263	0.616314	−	0.787500i	$-0.288625\pi$
$839$	2.51326e7	1.23263	0.616314	+	0.787500i	$0.288625\pi$
$840$	0	0
$841$	−1.36652e7	−0.666233
$842$	−2.09000e6	−0.101593
$843$	1.11155e7	0.538714
$844$	3.38855e6	0.163741
$845$	3.78216e6	0.182221
$846$	7.22766e7	3.47194
$847$	0	0
$848$	3.96037e6	0.189124
$849$	4.19380e6	0.199682
$850$	6.51129e6	0.309115
$851$	7.12994e6	0.337491
$852$	−3.24266e7	−1.53039
$853$	−7.18129e6	−0.337933	−0.168966	−	0.985622i	$-0.554043\pi$
$853$	−7.18129e6	−0.337933	−0.168966	+	0.985622i	$0.554043\pi$
$854$	0	0
$855$	1.92960e7	0.902718
$856$	−6.17086e6	−0.287847
$857$	2.87502e6	0.133718	0.0668588	−	0.997762i	$-0.478702\pi$
$857$	2.87502e6	0.133718	0.0668588	+	0.997762i	$0.478702\pi$
$858$	6.67178e7	3.09402
$859$	2.90535e7	1.34343	0.671715	−	0.740810i	$-0.265558\pi$
$859$	2.90535e7	1.34343	0.671715	+	0.740810i	$0.265558\pi$
$860$	1.28226e7	0.591193
$861$	0	0
$862$	5.19584e6	0.238170
$863$	1.31697e7	0.601933	0.300967	−	0.953635i	$-0.402691\pi$
$863$	1.31697e7	0.601933	0.300967	+	0.953635i	$0.402691\pi$
$864$	−4.69203e7	−2.13834
$865$	7.43415e6	0.337824
$866$	3.74539e7	1.69708
$867$	1.24162e7	0.560972
$868$	0	0
$869$	−2.42580e7	−1.08969
$870$	−1.33279e7	−0.596987
$871$	−3.40252e6	−0.151969
$872$	−145513.	−0.00648055
$873$	7.87228e6	0.349595
$874$	5.74566e6	0.254426
$875$	0	0
$876$	−5.96135e7	−2.62473
$877$	−1.31462e7	−0.577165	−0.288583	−	0.957455i	$-0.593184\pi$
$877$	−1.31462e7	−0.577165	−0.288583	+	0.957455i	$0.593184\pi$
$878$	−5.00410e7	−2.19074
$879$	9.69898e6	0.423403
$880$	2.07128e7	0.901637
$881$	2.72039e7	1.18084	0.590421	−	0.807096i	$-0.298962\pi$
$881$	2.72039e7	1.18084	0.590421	+	0.807096i	$0.298962\pi$
$882$	0	0
$883$	1.22906e6	0.0530481	0.0265240	−	0.999648i	$-0.491556\pi$
$883$	1.22906e6	0.0530481	0.0265240	+	0.999648i	$0.491556\pi$
$884$	1.65097e7	0.710573
$885$	−9.30043e6	−0.399158
$886$	−2.45884e6	−0.105231
$887$	−2.33373e7	−0.995959	−0.497980	−	0.867189i	$-0.665925\pi$
$887$	−2.33373e7	−0.995959	−0.497980	+	0.867189i	$0.665925\pi$
$888$	1.97116e7	0.838859
$889$	0	0
$890$	−2.24635e6	−0.0950609
$891$	3.67428e7	1.55052
$892$	−8.89947e6	−0.374500
$893$	−3.22784e7	−1.35452
$894$	−2.75789e7	−1.15407
$895$	6.92379e6	0.288926
$896$	0	0
$897$	−5.88722e6	−0.244303
$898$	−2.24329e7	−0.928313
$899$	1.45758e7	0.601498
$900$	7.64941e6	0.314791
$901$	−4.57855e6	−0.187896
$902$	4.97058e7	2.03419
$903$	0	0
$904$	6.78228e6	0.276029
$905$	−1.41188e7	−0.573029
$906$	−7.91939e6	−0.320532
$907$	−3.66815e6	−0.148057	−0.0740284	−	0.997256i	$-0.523586\pi$
$907$	−3.66815e6	−0.148057	−0.0740284	+	0.997256i	$0.523586\pi$
$908$	1.79274e7	0.721609
$909$	2.27435e7	0.912949
$910$	0	0
$911$	4.50022e6	0.179654	0.0898272	−	0.995957i	$-0.471369\pi$
$911$	4.50022e6	0.179654	0.0898272	+	0.995957i	$0.471369\pi$
$912$	5.15230e7	2.05123
$913$	−5.98975e7	−2.37811
$914$	1.78482e7	0.706691
$915$	2.23935e7	0.884237
$916$	−1.28629e7	−0.506523
$917$	0	0
$918$	6.54428e7	2.56304
$919$	4.79190e7	1.87162	0.935812	−	0.352500i	$-0.114668\pi$
$919$	4.79190e7	1.87162	0.935812	+	0.352500i	$0.114668\pi$
$920$	−563483.	−0.0219488
$921$	3.03991e7	1.18090
$922$	−2.95038e7	−1.14301
$923$	−2.20942e7	−0.853637
$924$	0	0
$925$	−9.52723e6	−0.366111
$926$	−5.42404e6	−0.207872
$927$	2.49371e7	0.953120
$928$	−1.95435e7	−0.744960
$929$	−1.08765e7	−0.413476	−0.206738	−	0.978396i	$-0.566285\pi$
$929$	−1.08765e7	−0.413476	−0.206738	+	0.978396i	$0.566285\pi$
$930$	−2.83768e7	−1.07586
$931$	0	0
$932$	−1.19514e7	−0.450692
$933$	6.83059e7	2.56894
$934$	3.28107e7	1.23069
$935$	−2.39459e7	−0.895782
$936$	−1.07835e7	−0.402318
$937$	−1.93338e6	−0.0719398	−0.0359699	−	0.999353i	$-0.511452\pi$
$937$	−1.93338e6	−0.0719398	−0.0359699	+	0.999353i	$0.511452\pi$
$938$	0	0
$939$	−1.43478e7	−0.531033
$940$	−1.27960e7	−0.472338
$941$	−1.50149e7	−0.552776	−0.276388	−	0.961046i	$-0.589137\pi$
$941$	−1.50149e7	−0.552776	−0.276388	+	0.961046i	$0.589137\pi$
$942$	−9.12359e7	−3.34995
$943$	−4.38607e6	−0.160619
$944$	−1.64532e7	−0.600925
$945$	0	0
$946$	−1.05979e8	−3.85027
$947$	−2.11167e7	−0.765159	−0.382580	−	0.923923i	$-0.624964\pi$
$947$	−2.11167e7	−0.765159	−0.382580	+	0.923923i	$0.624964\pi$
$948$	−2.39209e7	−0.864484
$949$	−4.06183e7	−1.46405
$950$	−7.67752e6	−0.276002
$951$	180605.	0.00647558
$952$	0	0
$953$	1.84024e7	0.656360	0.328180	−	0.944615i	$-0.393565\pi$
$953$	1.84024e7	0.656360	0.328180	+	0.944615i	$0.393565\pi$
$954$	−1.20884e7	−0.430028
$955$	8.37406e6	0.297117
$956$	−1.42820e7	−0.505409
$957$	4.90149e7	1.73001
$958$	−2.65913e7	−0.936108
$959$	0	0
$960$	1.25701e7	0.440212
$961$	2.40448e6	0.0839872
$962$	−5.42897e7	−1.89138
$963$	6.10947e7	2.12294
$964$	2.08937e7	0.724139
$965$	−2.32202e7	−0.802689
$966$	0	0
$967$	1.76833e7	0.608130	0.304065	−	0.952651i	$-0.401656\pi$
$967$	1.76833e7	0.608130	0.304065	+	0.952651i	$0.401656\pi$
$968$	−1.57235e7	−0.539338
$969$	−5.95655e7	−2.03791
$970$	−3.13223e6	−0.106887
$971$	−5.05405e7	−1.72025	−0.860125	−	0.510083i	$-0.829615\pi$
$971$	−5.05405e7	−1.72025	−0.860125	+	0.510083i	$0.829615\pi$
$972$	−2.92650e6	−0.0993534
$973$	0	0
$974$	−3.72696e7	−1.25880
$975$	7.86667e6	0.265021
$976$	3.96158e7	1.33120
$977$	−1.56204e6	−0.0523547	−0.0261774	−	0.999657i	$-0.508333\pi$
$977$	−1.56204e6	−0.0523547	−0.0261774	+	0.999657i	$0.508333\pi$
$978$	1.91669e7	0.640774
$979$	8.26117e6	0.275477
$980$	0	0
$981$	1.44066e6	0.0477957
$982$	−1.79540e7	−0.594131
$983$	−3.46523e7	−1.14379	−0.571897	−	0.820325i	$-0.693792\pi$
$983$	−3.46523e7	−1.14379	−0.571897	+	0.820325i	$0.693792\pi$
$984$	−1.21258e7	−0.399230
$985$	−1.86322e7	−0.611891
$986$	2.72586e7	0.892918
$987$	0	0
$988$	−1.94668e7	−0.634456
$989$	9.35162e6	0.304016
$990$	−6.32224e7	−2.05014
$991$	−5.06788e7	−1.63924	−0.819620	−	0.572908i	$-0.805815\pi$
$991$	−5.06788e7	−1.63924	−0.819620	+	0.572908i	$0.805815\pi$
$992$	−4.16104e7	−1.34253
$993$	−3.83833e7	−1.23529
$994$	0	0
$995$	2.23057e7	0.714262
$996$	−5.90652e7	−1.88662
$997$	4.24677e7	1.35307	0.676535	−	0.736410i	$-0.263481\pi$
$997$	4.24677e7	1.35307	0.676535	+	0.736410i	$0.263481\pi$
$998$	4.73726e6	0.150557
$999$	−9.57550e7	−3.03562

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.6.a.g.1.5	yes	5
7.6	odd	2		245.6.a.f.1.5	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
245.6.a.f.1.5	✓	5	7.6	odd	2
245.6.a.g.1.5	yes	5	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	245.a (trivial)

\(f(q)\)	\(=\)	\(q+7.59300 q^{2} +26.8345 q^{3} +25.6536 q^{4} -25.0000 q^{5} +203.754 q^{6} -48.1883 q^{8} +477.089 q^{9} +O(q^{10})\)	\(q+7.59300 q^{2} +26.8345 q^{3} +25.6536 q^{4} -25.0000 q^{5} +203.754 q^{6} -48.1883 q^{8} +477.089 q^{9} -189.825 q^{10} +698.100 q^{11} +688.401 q^{12} +469.049 q^{13} -670.862 q^{15} -1186.81 q^{16} +1372.06 q^{17} +3622.54 q^{18} -1617.81 q^{19} -641.340 q^{20} +5300.67 q^{22} -467.734 q^{23} -1293.11 q^{24} +625.000 q^{25} +3561.48 q^{26} +6281.67 q^{27} +2616.48 q^{29} -5093.85 q^{30} +5570.78 q^{31} -7469.41 q^{32} +18733.2 q^{33} +10418.1 q^{34} +12239.1 q^{36} -15243.6 q^{37} -12284.0 q^{38} +12586.7 q^{39} +1204.71 q^{40} +9377.27 q^{41} -19993.4 q^{43} +17908.8 q^{44} -11927.2 q^{45} -3551.50 q^{46} +19951.9 q^{47} -31847.4 q^{48} +4745.62 q^{50} +36818.6 q^{51} +12032.8 q^{52} -3336.99 q^{53} +47696.7 q^{54} -17452.5 q^{55} -43413.1 q^{57} +19866.9 q^{58} +13863.4 q^{59} -17210.0 q^{60} -33380.1 q^{61} +42298.9 q^{62} -18737.3 q^{64} -11726.2 q^{65} +142241. q^{66} -7254.09 q^{67} +35198.3 q^{68} -12551.4 q^{69} -47104.2 q^{71} -22990.1 q^{72} -86597.2 q^{73} -115744. q^{74} +16771.6 q^{75} -41502.7 q^{76} +95570.6 q^{78} -34748.5 q^{79} +29670.2 q^{80} +52632.6 q^{81} +71201.6 q^{82} -85800.6 q^{83} -34301.5 q^{85} -151810. q^{86} +70211.8 q^{87} -33640.3 q^{88} +11833.8 q^{89} -90563.4 q^{90} -11999.1 q^{92} +149489. q^{93} +151495. q^{94} +40445.3 q^{95} -200438. q^{96} +16500.6 q^{97} +333056. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 3 q^{2} + 7 q^{3} + 101 q^{4} - 125 q^{5} + 304 q^{6} - 675 q^{8} + 284 q^{9}+O(q^{10}) \) 5 * q - 3 * q^2 + 7 * q^3 + 101 * q^4 - 125 * q^5 + 304 * q^6 - 675 * q^8 + 284 * q^9	\( 5 q - 3 q^{2} + 7 q^{3} + 101 q^{4} - 125 q^{5} + 304 q^{6} - 675 q^{8} + 284 q^{9} + 75 q^{10} + 1033 q^{11} - 1226 q^{12} + 1117 q^{13} - 175 q^{15} + 297 q^{16} + 3403 q^{17} + 887 q^{18} + 2846 q^{19} - 2525 q^{20} - 1858 q^{22} - 2756 q^{23} + 13290 q^{24} + 3125 q^{25} + 2544 q^{26} + 3661 q^{27} + 485 q^{29} - 7600 q^{30} + 10726 q^{31} - 17383 q^{32} + 12597 q^{33} - 16414 q^{34} + 38165 q^{36} - 2660 q^{37} - 14378 q^{38} - 13171 q^{39} + 16875 q^{40} - 8334 q^{41} - 17294 q^{43} + 42876 q^{44} - 7100 q^{45} + 45724 q^{46} + 59799 q^{47} - 94218 q^{48} - 1875 q^{50} - 12049 q^{51} + 87974 q^{52} - 9250 q^{53} + 106342 q^{54} - 25825 q^{55} - 121778 q^{57} + 35868 q^{58} + 52994 q^{59} + 30650 q^{60} + 81540 q^{61} - 74048 q^{62} + 39745 q^{64} - 27925 q^{65} + 311614 q^{66} - 726 q^{67} + 276216 q^{68} + 21388 q^{69} + 3760 q^{71} - 154815 q^{72} + 90634 q^{73} - 57342 q^{74} + 4375 q^{75} + 43902 q^{76} + 152598 q^{78} + 68243 q^{79} - 7425 q^{80} + 17645 q^{81} + 191552 q^{82} - 133292 q^{83} - 85075 q^{85} - 88352 q^{86} + 216813 q^{87} - 273040 q^{88} + 102852 q^{89} - 22175 q^{90} - 140852 q^{92} + 184862 q^{93} + 332618 q^{94} - 71150 q^{95} + 245574 q^{96} + 186175 q^{97} + 454710 q^{99}+O(q^{100}) \) 5 * q - 3 * q^2 + 7 * q^3 + 101 * q^4 - 125 * q^5 + 304 * q^6 - 675 * q^8 + 284 * q^9 + 75 * q^10 + 1033 * q^11 - 1226 * q^12 + 1117 * q^13 - 175 * q^15 + 297 * q^16 + 3403 * q^17 + 887 * q^18 + 2846 * q^19 - 2525 * q^20 - 1858 * q^22 - 2756 * q^23 + 13290 * q^24 + 3125 * q^25 + 2544 * q^26 + 3661 * q^27 + 485 * q^29 - 7600 * q^30 + 10726 * q^31 - 17383 * q^32 + 12597 * q^33 - 16414 * q^34 + 38165 * q^36 - 2660 * q^37 - 14378 * q^38 - 13171 * q^39 + 16875 * q^40 - 8334 * q^41 - 17294 * q^43 + 42876 * q^44 - 7100 * q^45 + 45724 * q^46 + 59799 * q^47 - 94218 * q^48 - 1875 * q^50 - 12049 * q^51 + 87974 * q^52 - 9250 * q^53 + 106342 * q^54 - 25825 * q^55 - 121778 * q^57 + 35868 * q^58 + 52994 * q^59 + 30650 * q^60 + 81540 * q^61 - 74048 * q^62 + 39745 * q^64 - 27925 * q^65 + 311614 * q^66 - 726 * q^67 + 276216 * q^68 + 21388 * q^69 + 3760 * q^71 - 154815 * q^72 + 90634 * q^73 - 57342 * q^74 + 4375 * q^75 + 43902 * q^76 + 152598 * q^78 + 68243 * q^79 - 7425 * q^80 + 17645 * q^81 + 191552 * q^82 - 133292 * q^83 - 85075 * q^85 - 88352 * q^86 + 216813 * q^87 - 273040 * q^88 + 102852 * q^89 - 22175 * q^90 - 140852 * q^92 + 184862 * q^93 + 332618 * q^94 - 71150 * q^95 + 245574 * q^96 + 186175 * q^97 + 454710 * q^99

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