LMFDB - Embedded newform 245.6.a.f.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:	$1$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 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	$-0.829984\pi$
$3$	−26.8345	−1.72143	−0.860716	+	0.509085i	$0.829984\pi$
$4$	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	$-0.625758\pi$
$13$	−469.049	−0.769767	−0.384884	+	0.922965i	$0.625758\pi$
$14$	0	0
$15$	−670.862	−0.769848
$16$	−1186.81	−1.15899
$17$	−1372.06	−1.15147	−0.575733	−	0.817638i	$-0.695283\pi$
$17$	−1372.06	−1.15147	−0.575733	+	0.817638i	$0.695283\pi$
$18$	3622.54	2.63531
$19$	1617.81	1.02812	0.514060	−	0.857754i	$-0.328141\pi$
$19$	1617.81	1.02812	0.514060	+	0.857754i	$0.328141\pi$
$20$	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	$-0.674282\pi$
$31$	−5570.78	−1.04115	−0.520574	+	0.853817i	$0.674282\pi$
$32$	−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	$-0.643463\pi$
$41$	−9377.27	−0.871198	−0.435599	+	0.900141i	$0.643463\pi$
$42$	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	$-0.728908\pi$
$47$	−19951.9	−1.31747	−0.658734	+	0.752376i	$0.728908\pi$
$48$	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	$-0.583474\pi$
$59$	−13863.4	−0.518489	−0.259245	+	0.965812i	$0.583474\pi$
$60$	−17210.0	−0.617168
$61$	33380.1	1.14859	0.574293	−	0.818650i	$-0.305277\pi$
$61$	33380.1	1.14859	0.574293	+	0.818650i	$0.305277\pi$
$62$	−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	$-0.100090\pi$
$73$	86597.2	1.90194	0.950969	+	0.309286i	$0.100090\pi$
$74$	−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	$-0.260439\pi$
$83$	85800.6	1.36708	0.683542	+	0.729911i	$0.260439\pi$
$84$	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	$-0.525230\pi$
$89$	−11833.8	−0.158361	−0.0791806	+	0.996860i	$0.525230\pi$
$90$	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	$-0.528377\pi$
$97$	−16500.6	−0.178062	−0.0890310	+	0.996029i	$0.528377\pi$
$98$	0	0
$99$	333056.	3.41531
$100$	16033.5	0.160335
$101$	−47671.3	−0.465000	−0.232500	−	0.972596i	$-0.574691\pi$
$101$	−47671.3	−0.465000	−0.232500	+	0.972596i	$0.574691\pi$
$102$	279563.	2.66060
$103$	−52269.3	−0.485461	−0.242730	−	0.970094i	$-0.578043\pi$
$103$	−52269.3	−0.485461	−0.242730	+	0.970094i	$0.578043\pi$
$104$	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	$-0.613436\pi$
$131$	−137049.	−0.697748	−0.348874	+	0.937170i	$0.613436\pi$
$132$	−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	$-0.829281\pi$
$139$	−391614.	−1.71918	−0.859590	+	0.510984i	$0.829281\pi$
$140$	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	$-0.241884\pi$
$157$	447775.	1.44981	0.724904	+	0.688850i	$0.241884\pi$
$158$	−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	$-0.513116\pi$
$167$	−29692.0	−0.0823850	−0.0411925	+	0.999151i	$0.513116\pi$
$168$	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	$-0.376715\pi$
$173$	297366.	0.755398	0.377699	+	0.925928i	$0.376715\pi$
$174$	−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	$-0.721342\pi$
$181$	−564752.	−1.28133	−0.640666	+	0.767820i	$0.721342\pi$
$182$	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	$-0.205591\pi$
$199$	892226.	1.59714	0.798569	+	0.601904i	$0.205591\pi$
$200$	−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	$-0.424958\pi$
$223$	346910.	0.467148	0.233574	+	0.972339i	$0.424958\pi$
$224$	0	0
$225$	298181.	0.392666
$226$	−1.06868e6	−1.39180
$227$	−698825.	−0.900127	−0.450064	−	0.892996i	$-0.648599\pi$
$227$	−698825.	−0.900127	−0.450064	+	0.892996i	$0.648599\pi$
$228$	−1.11370e6	−1.41884
$229$	501406.	0.631831	0.315916	−	0.948787i	$-0.397688\pi$
$229$	501406.	0.631831	0.315916	+	0.948787i	$0.397688\pi$
$230$	−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	$-0.649161\pi$
$241$	−814454.	−0.903283	−0.451642	+	0.892199i	$0.649161\pi$
$242$	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	$-0.755445\pi$
$251$	−1.43550e6	−1.43820	−0.719099	+	0.694907i	$0.755445\pi$
$252$	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	$-0.744774\pi$
$257$	−1.47265e6	−1.39081	−0.695403	+	0.718620i	$0.744774\pi$
$258$	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	$-0.424660\pi$
$269$	556577.	0.468970	0.234485	+	0.972120i	$0.424660\pi$
$270$	−1.19242e6	−0.995448
$271$	535326.	0.442788	0.221394	−	0.975184i	$-0.428939\pi$
$271$	535326.	0.442788	0.221394	+	0.975184i	$0.428939\pi$
$272$	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	$-0.518472\pi$
$283$	−156284.	−0.115997	−0.0579987	+	0.998317i	$0.518472\pi$
$284$	−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	$-0.539245\pi$
$293$	−361437.	−0.245960	−0.122980	+	0.992409i	$0.539245\pi$
$294$	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	$-0.611443\pi$
$307$	−1.13284e6	−0.685997	−0.342998	+	0.939336i	$0.611443\pi$
$308$	0	0
$309$	1.40262e6	0.835688
$310$	−1.05747e6	−0.624979
$311$	−2.54545e6	−1.49233	−0.746163	−	0.665763i	$-0.768106\pi$
$311$	−2.54545e6	−1.49233	−0.746163	+	0.665763i	$0.768106\pi$
$312$	−606530.	−0.352749
$313$	534678.	0.308483	0.154242	−	0.988033i	$-0.450707\pi$
$313$	534678.	0.308483	0.154242	+	0.988033i	$0.450707\pi$
$314$	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	$-0.327032\pi$
$349$	2.35300e6	1.03409	0.517045	+	0.855958i	$0.327032\pi$
$350$	0	0
$351$	2.94641e6	1.27651
$352$	−5.21439e6	−2.24309
$353$	−2.21454e6	−0.945905	−0.472952	−	0.881088i	$-0.656812\pi$
$353$	−2.21454e6	−0.945905	−0.472952	+	0.881088i	$0.656812\pi$
$354$	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	$-0.376468\pi$
$367$	1.95284e6	0.756834	0.378417	+	0.925635i	$0.376468\pi$
$368$	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	$-0.425622\pi$
$383$	1.32941e6	0.463087	0.231543	+	0.972825i	$0.425622\pi$
$384$	−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	$-0.396116\pi$
$397$	2.01357e6	0.641195	0.320597	+	0.947216i	$0.396116\pi$
$398$	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	$-0.508920\pi$
$409$	−189571.	−0.0560356	−0.0280178	+	0.999607i	$0.508920\pi$
$410$	−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	$-0.351700\pi$
$419$	3.22872e6	0.898452	0.449226	+	0.893418i	$0.351700\pi$
$420$	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	$-0.717836\pi$
$433$	−4.93269e6	−1.26434	−0.632170	+	0.774830i	$0.717836\pi$
$434$	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	$-0.196154\pi$
$439$	6.59042e6	1.63212	0.816060	+	0.577968i	$0.196154\pi$
$440$	−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	$-0.360001\pi$
$461$	3.88566e6	0.851554	0.425777	+	0.904828i	$0.360001\pi$
$462$	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	$-0.651591\pi$
$467$	−4.32118e6	−0.916875	−0.458438	+	0.888727i	$0.651591\pi$
$468$	−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	$-0.386622\pi$
$479$	3.50208e6	0.697409	0.348705	+	0.937233i	$0.386622\pi$
$480$	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	$-0.266879\pi$
$503$	7.58820e6	1.33727	0.668634	+	0.743591i	$0.266879\pi$
$504$	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	$-0.666084\pi$
$509$	−5.82660e6	−0.996829	−0.498414	+	0.866939i	$0.666084\pi$
$510$	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	$-0.564851\pi$
$521$	−2.50715e6	−0.404655	−0.202328	+	0.979318i	$0.564851\pi$
$522$	9.47829e6	1.52249
$523$	−521695.	−0.0833992	−0.0416996	−	0.999130i	$-0.513277\pi$
$523$	−521695.	−0.0833992	−0.0416996	+	0.999130i	$0.513277\pi$
$524$	−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	$-0.292815\pi$
$563$	9.11377e6	1.21179	0.605895	+	0.795545i	$0.292815\pi$
$564$	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	$-0.263164\pi$
$577$	1.08325e7	1.35454	0.677268	+	0.735736i	$0.263164\pi$
$578$	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	$-0.868859\pi$
$587$	−1.52994e7	−1.83265	−0.916325	+	0.400435i	$0.868859\pi$
$588$	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	$-0.407838\pi$
$593$	4.88972e6	0.571015	0.285507	+	0.958377i	$0.407838\pi$
$594$	−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	$-0.612583\pi$
$601$	−6.13403e6	−0.692723	−0.346362	+	0.938101i	$0.612583\pi$
$602$	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	$-0.385528\pi$
$607$	6.38921e6	0.703843	0.351921	+	0.936030i	$0.385528\pi$
$608$	−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	$-0.716226\pi$
$619$	−1.19780e7	−1.25649	−0.628244	+	0.778017i	$0.716226\pi$
$620$	−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	$-0.652448\pi$
$643$	−9.66270e6	−0.921660	−0.460830	+	0.887488i	$0.652448\pi$
$644$	0	0
$645$	1.34128e7	1.26947
$646$	−1.68544e7	−1.58903
$647$	1.10865e6	0.104120	0.0520599	−	0.998644i	$-0.483421\pi$
$647$	1.10865e6	0.104120	0.0520599	+	0.998644i	$0.483421\pi$
$648$	−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	$-0.433561\pi$
$661$	4.65533e6	0.414426	0.207213	+	0.978296i	$0.433561\pi$
$662$	−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	$-0.440783\pi$
$677$	4.41154e6	0.369929	0.184965	+	0.982745i	$0.440783\pi$
$678$	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	$-0.678304\pi$
$691$	−1.33377e7	−1.06264	−0.531321	+	0.847170i	$0.678304\pi$
$692$	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	$-0.194069\pi$
$719$	2.27287e7	1.63966	0.819828	+	0.572611i	$0.194069\pi$
$720$	−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	$-0.653091\pi$
$727$	−1.31854e7	−0.925244	−0.462622	+	0.886556i	$0.653091\pi$
$728$	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	$-0.575493\pi$
$733$	−6.83544e6	−0.469901	−0.234950	+	0.972007i	$0.575493\pi$
$734$	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	$-0.478561\pi$
$761$	2.15041e6	0.134605	0.0673023	+	0.997733i	$0.478561\pi$
$762$	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	$-0.274603\pi$
$769$	2.13316e7	1.30079	0.650397	+	0.759594i	$0.274603\pi$
$770$	0	0
$771$	3.95178e7	2.39418
$772$	2.38272e7	1.43890
$773$	−1.34827e7	−0.811573	−0.405787	−	0.913968i	$-0.633002\pi$
$773$	−1.34827e7	−0.811573	−0.405787	+	0.913968i	$0.633002\pi$
$774$	−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	$-0.729012\pi$
$787$	−2.29002e7	−1.31796	−0.658980	+	0.752160i	$0.729012\pi$
$788$	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	$-0.267723\pi$
$797$	2.39100e7	1.33332	0.666660	+	0.745362i	$0.267723\pi$
$798$	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	$-0.702791\pi$
$811$	−2.22841e7	−1.18971	−0.594856	+	0.803832i	$0.702791\pi$
$812$	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	$-0.849074\pi$
$829$	−3.52088e7	−1.77936	−0.889682	+	0.456581i	$0.849074\pi$
$830$	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	$-0.711375\pi$
$839$	−2.51326e7	−1.23263	−0.616314	+	0.787500i	$0.711375\pi$
$840$	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	$-0.445957\pi$
$853$	7.18129e6	0.337933	0.168966	+	0.985622i	$0.445957\pi$
$854$	0	0
$855$	1.92960e7	0.902718
$856$	−6.17086e6	−0.287847
$857$	−2.87502e6	−0.133718	−0.0668588	−	0.997762i	$-0.521298\pi$
$857$	−2.87502e6	−0.133718	−0.0668588	+	0.997762i	$0.521298\pi$
$858$	6.67178e7	3.09402
$859$	−2.90535e7	−1.34343	−0.671715	−	0.740810i	$-0.734442\pi$
$859$	−2.90535e7	−1.34343	−0.671715	+	0.740810i	$0.734442\pi$
$860$	−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	$-0.701038\pi$
$881$	−2.72039e7	−1.18084	−0.590421	+	0.807096i	$0.701038\pi$
$882$	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	$-0.334075\pi$
$887$	2.33373e7	0.995959	0.497980	+	0.867189i	$0.334075\pi$
$888$	−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	$-0.433715\pi$
$929$	1.08765e7	0.413476	0.206738	+	0.978396i	$0.433715\pi$
$930$	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	$-0.488548\pi$
$937$	1.93338e6	0.0719398	0.0359699	+	0.999353i	$0.488548\pi$
$938$	0	0
$939$	−1.43478e7	−0.531033
$940$	−1.27960e7	−0.472338
$941$	1.50149e7	0.552776	0.276388	−	0.961046i	$-0.410863\pi$
$941$	1.50149e7	0.552776	0.276388	+	0.961046i	$0.410863\pi$
$942$	−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	$-0.170385\pi$
$971$	5.05405e7	1.72025	0.860125	+	0.510083i	$0.170385\pi$
$972$	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	$-0.306208\pi$
$983$	3.46523e7	1.14379	0.571897	+	0.820325i	$0.306208\pi$
$984$	−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	$-0.736519\pi$
$997$	−4.24677e7	−1.35307	−0.676535	+	0.736410i	$0.736519\pi$
$998$	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.f.1.5	✓	5
7.6	odd	2		245.6.a.g.1.5	yes	5

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
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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