LMFDB - Embedded newform 245.6.a.e.1.1

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:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 82x^{2} + 58x + 1168 $ x^4 - x^3 - 82x^2 + 58x + 1168
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 35)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$8.05190$ 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)

$f(q)$	$=$	$q-6.05190 q^{2} -15.9755 q^{3} +4.62555 q^{4} -25.0000 q^{5} +96.6824 q^{6} +165.668 q^{8} +12.2177 q^{9} +O(q^{10})$	\(q-6.05190 q^{2} -15.9755 q^{3} +4.62555 q^{4} -25.0000 q^{5} +96.6824 q^{6} +165.668 q^{8} +12.2177 q^{9} +151.298 q^{10} +708.632 q^{11} -73.8957 q^{12} -1125.20 q^{13} +399.388 q^{15} -1150.62 q^{16} +393.382 q^{17} -73.9406 q^{18} -1790.32 q^{19} -115.639 q^{20} -4288.57 q^{22} -3577.80 q^{23} -2646.63 q^{24} +625.000 q^{25} +6809.59 q^{26} +3686.87 q^{27} -2.14905 q^{29} -2417.06 q^{30} -8773.75 q^{31} +1662.09 q^{32} -11320.8 q^{33} -2380.71 q^{34} +56.5138 q^{36} -4361.88 q^{37} +10834.8 q^{38} +17975.6 q^{39} -4141.69 q^{40} +8413.22 q^{41} -18110.5 q^{43} +3277.81 q^{44} -305.443 q^{45} +21652.5 q^{46} -8209.65 q^{47} +18381.8 q^{48} -3782.44 q^{50} -6284.49 q^{51} -5204.66 q^{52} -14352.5 q^{53} -22312.6 q^{54} -17715.8 q^{55} +28601.3 q^{57} +13.0059 q^{58} +10197.8 q^{59} +1847.39 q^{60} +2878.09 q^{61} +53097.9 q^{62} +26761.1 q^{64} +28130.0 q^{65} +68512.2 q^{66} +37314.1 q^{67} +1819.61 q^{68} +57157.3 q^{69} -3259.60 q^{71} +2024.08 q^{72} -6122.54 q^{73} +26397.7 q^{74} -9984.71 q^{75} -8281.20 q^{76} -108787. q^{78} +7549.78 q^{79} +28765.5 q^{80} -61868.6 q^{81} -50916.0 q^{82} -1977.20 q^{83} -9834.55 q^{85} +109603. q^{86} +34.3323 q^{87} +117397. q^{88} +46820.1 q^{89} +1848.51 q^{90} -16549.3 q^{92} +140165. q^{93} +49684.0 q^{94} +44757.9 q^{95} -26552.8 q^{96} -19767.0 q^{97} +8657.88 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 7 q^{2} - 14 q^{3} + 49 q^{4} - 100 q^{5} - 136 q^{6} + 489 q^{8} + 774 q^{9}+O(q^{10}) $ 4 * q + 7 * q^2 - 14 * q^3 + 49 * q^4 - 100 * q^5 - 136 * q^6 + 489 * q^8 + 774 * q^9	\( 4 q + 7 q^{2} - 14 q^{3} + 49 q^{4} - 100 q^{5} - 136 q^{6} + 489 q^{8} + 774 q^{9} - 175 q^{10} + 770 q^{11} - 840 q^{12} - 58 q^{13} + 350 q^{15} - 615 q^{16} - 2006 q^{17} - 1409 q^{18} - 564 q^{19} - 1225 q^{20} - 1736 q^{22} - 6340 q^{23} + 6244 q^{24} + 2500 q^{25} + 8730 q^{26} + 7438 q^{27} + 8066 q^{29} + 3400 q^{30} + 5856 q^{31} - 3495 q^{32} + 8130 q^{33} - 3402 q^{34} - 28759 q^{36} + 29544 q^{37} + 36860 q^{38} + 57466 q^{39} - 12225 q^{40} - 13156 q^{41} - 5692 q^{43} + 44952 q^{44} - 19350 q^{45} + 30928 q^{46} - 39926 q^{47} + 57156 q^{48} + 4375 q^{50} + 9830 q^{51} + 23398 q^{52} + 20300 q^{53} - 77292 q^{54} - 19250 q^{55} - 50876 q^{57} - 22234 q^{58} - 8432 q^{59} + 21000 q^{60} - 30540 q^{61} + 137568 q^{62} + 37121 q^{64} + 1450 q^{65} + 166756 q^{66} + 32792 q^{67} + 72554 q^{68} + 36540 q^{69} - 83920 q^{71} - 71795 q^{72} + 75424 q^{73} + 168762 q^{74} - 8750 q^{75} + 125092 q^{76} - 89204 q^{78} + 129486 q^{79} + 15375 q^{80} + 146308 q^{81} - 247230 q^{82} + 187520 q^{83} + 50150 q^{85} + 36156 q^{86} + 238670 q^{87} + 475556 q^{88} + 30324 q^{89} + 35225 q^{90} + 124464 q^{92} + 8256 q^{93} - 245756 q^{94} + 14100 q^{95} - 172340 q^{96} - 180270 q^{97} - 420668 q^{99}+O(q^{100}) \) 4 * q + 7 * q^2 - 14 * q^3 + 49 * q^4 - 100 * q^5 - 136 * q^6 + 489 * q^8 + 774 * q^9 - 175 * q^10 + 770 * q^11 - 840 * q^12 - 58 * q^13 + 350 * q^15 - 615 * q^16 - 2006 * q^17 - 1409 * q^18 - 564 * q^19 - 1225 * q^20 - 1736 * q^22 - 6340 * q^23 + 6244 * q^24 + 2500 * q^25 + 8730 * q^26 + 7438 * q^27 + 8066 * q^29 + 3400 * q^30 + 5856 * q^31 - 3495 * q^32 + 8130 * q^33 - 3402 * q^34 - 28759 * q^36 + 29544 * q^37 + 36860 * q^38 + 57466 * q^39 - 12225 * q^40 - 13156 * q^41 - 5692 * q^43 + 44952 * q^44 - 19350 * q^45 + 30928 * q^46 - 39926 * q^47 + 57156 * q^48 + 4375 * q^50 + 9830 * q^51 + 23398 * q^52 + 20300 * q^53 - 77292 * q^54 - 19250 * q^55 - 50876 * q^57 - 22234 * q^58 - 8432 * q^59 + 21000 * q^60 - 30540 * q^61 + 137568 * q^62 + 37121 * q^64 + 1450 * q^65 + 166756 * q^66 + 32792 * q^67 + 72554 * q^68 + 36540 * q^69 - 83920 * q^71 - 71795 * q^72 + 75424 * q^73 + 168762 * q^74 - 8750 * q^75 + 125092 * q^76 - 89204 * q^78 + 129486 * q^79 + 15375 * q^80 + 146308 * q^81 - 247230 * q^82 + 187520 * q^83 + 50150 * q^85 + 36156 * q^86 + 238670 * q^87 + 475556 * q^88 + 30324 * q^89 + 35225 * q^90 + 124464 * q^92 + 8256 * q^93 - 245756 * q^94 + 14100 * q^95 - 172340 * q^96 - 180270 * q^97 - 420668 * 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 $

$2$	−6.05190	−1.06984	−0.534918	−	0.844904i	$-0.679657\pi$
$2$	−6.05190	−1.06984	−0.534918	+	0.844904i	$0.679657\pi$
$3$	−15.9755	−1.02483	−0.512416	−	0.858738i	$-0.671249\pi$
$3$	−15.9755	−1.02483	−0.512416	+	0.858738i	$0.671249\pi$
$4$	4.62555	0.144548
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	96.6824	1.09640
$7$	0	0
$7$	0	0
$8$	165.668	0.915193
$9$	12.2177	0.0502788
$10$	151.298	0.478445
$11$	708.632	1.76579	0.882894	−	0.469572i	$-0.155592\pi$
$11$	708.632	1.76579	0.882894	+	0.469572i	$0.155592\pi$
$12$	−73.8957	−0.148138
$13$	−1125.20	−1.84659	−0.923295	−	0.384091i	$-0.874515\pi$
$13$	−1125.20	−1.84659	−0.923295	+	0.384091i	$0.874515\pi$
$14$	0	0
$15$	399.388	0.458318
$16$	−1150.62	−1.12365
$17$	393.382	0.330135	0.165068	−	0.986282i	$-0.447216\pi$
$17$	393.382	0.330135	0.165068	+	0.986282i	$0.447216\pi$
$18$	−73.9406	−0.0537900
$19$	−1790.32	−1.13775	−0.568874	−	0.822425i	$-0.692621\pi$
$19$	−1790.32	−1.13775	−0.568874	+	0.822425i	$0.692621\pi$
$20$	−115.639	−0.0646441
$21$	0	0
$22$	−4288.57	−1.88910
$23$	−3577.80	−1.41025	−0.705126	−	0.709082i	$-0.749110\pi$
$23$	−3577.80	−1.41025	−0.705126	+	0.709082i	$0.749110\pi$
$24$	−2646.63	−0.937918
$25$	625.000	0.200000
$26$	6809.59	1.97555
$27$	3686.87	0.973304
$28$	0	0
$29$	−2.14905	−0.000474518 0	−0.000237259	−	1.00000i	$-0.500076\pi$
$29$	−2.14905	−0.000474518 0	−0.000237259		1.00000i	$0.500076\pi$
$30$	−2417.06	−0.490325
$31$	−8773.75	−1.63976	−0.819881	−	0.572534i	$-0.805960\pi$
$31$	−8773.75	−1.63976	−0.819881	+	0.572534i	$0.805960\pi$
$32$	1662.09	0.286933
$33$	−11320.8	−1.80964
$34$	−2380.71	−0.353191
$35$	0	0
$36$	56.5138	0.00726772
$37$	−4361.88	−0.523804	−0.261902	−	0.965094i	$-0.584350\pi$
$37$	−4361.88	−0.523804	−0.261902	+	0.965094i	$0.584350\pi$
$38$	10834.8	1.21720
$39$	17975.6	1.89244
$40$	−4141.69	−0.409287
$41$	8413.22	0.781633	0.390816	−	0.920469i	$-0.372193\pi$
$41$	8413.22	0.781633	0.390816	+	0.920469i	$0.372193\pi$
$42$	0	0
$43$	−18110.5	−1.49368	−0.746842	−	0.665002i	$-0.768431\pi$
$43$	−18110.5	−1.49368	−0.746842	+	0.665002i	$0.768431\pi$
$44$	3277.81	0.255242
$45$	−305.443	−0.0224853
$46$	21652.5	1.50874
$47$	−8209.65	−0.542101	−0.271050	−	0.962565i	$-0.587371\pi$
$47$	−8209.65	−0.542101	−0.271050	+	0.962565i	$0.587371\pi$
$48$	18381.8	1.15156
$49$	0	0
$50$	−3782.44	−0.213967
$51$	−6284.49	−0.338333
$52$	−5204.66	−0.266922
$53$	−14352.5	−0.701837	−0.350919	−	0.936406i	$-0.614131\pi$
$53$	−14352.5	−0.701837	−0.350919	+	0.936406i	$0.614131\pi$
$54$	−22312.6	−1.04128
$55$	−17715.8	−0.789685
$56$	0	0
$57$	28601.3	1.16600
$58$	13.0059	0.000507656 0
$59$	10197.8	0.381398	0.190699	−	0.981649i	$-0.438925\pi$
$59$	10197.8	0.381398	0.190699	+	0.981649i	$0.438925\pi$
$60$	1847.39	0.0662492
$61$	2878.09	0.0990331	0.0495165	−	0.998773i	$-0.484232\pi$
$61$	2878.09	0.0990331	0.0495165	+	0.998773i	$0.484232\pi$
$62$	53097.9	1.75428
$63$	0	0
$64$	26761.1	0.816683
$65$	28130.0	0.825821
$66$	68512.2	1.93601
$67$	37314.1	1.01551	0.507757	−	0.861500i	$-0.330475\pi$
$67$	37314.1	1.01551	0.507757	+	0.861500i	$0.330475\pi$
$68$	1819.61	0.0477206
$69$	57157.3	1.44527
$70$	0	0
$71$	−3259.60	−0.0767393	−0.0383697	−	0.999264i	$-0.512216\pi$
$71$	−3259.60	−0.0767393	−0.0383697	+	0.999264i	$0.512216\pi$
$72$	2024.08	0.0460148
$73$	−6122.54	−0.134470	−0.0672348	−	0.997737i	$-0.521418\pi$
$73$	−6122.54	−0.134470	−0.0672348	+	0.997737i	$0.521418\pi$
$74$	26397.7	0.560385
$75$	−9984.71	−0.204966
$76$	−8281.20	−0.164460
$77$	0	0
$78$	−108787.	−2.02460
$79$	7549.78	0.136103	0.0680514	−	0.997682i	$-0.478322\pi$
$79$	7549.78	0.136103	0.0680514	+	0.997682i	$0.478322\pi$
$80$	28765.5	0.502513
$81$	−61868.6	−1.04775
$82$	−50916.0	−0.836219
$83$	−1977.20	−0.0315032	−0.0157516	−	0.999876i	$-0.505014\pi$
$83$	−1977.20	−0.0315032	−0.0157516	+	0.999876i	$0.505014\pi$
$84$	0	0
$85$	−9834.55	−0.147641
$86$	109603.	1.59800
$87$	34.3323	0.000486301 0
$88$	117397.	1.61604
$89$	46820.1	0.626553	0.313276	−	0.949662i	$-0.398573\pi$
$89$	46820.1	0.626553	0.313276	+	0.949662i	$0.398573\pi$
$90$	1848.51	0.0240556
$91$	0	0
$92$	−16549.3	−0.203850
$93$	140165.	1.68048
$94$	49684.0	0.579959
$95$	44757.9	0.508816
$96$	−26552.8	−0.294058
$97$	−19767.0	−0.213310	−0.106655	−	0.994296i	$-0.534014\pi$
$97$	−19767.0	−0.213310	−0.106655	+	0.994296i	$0.534014\pi$
$98$	0	0
$99$	8657.88	0.0887817
$100$	2890.97	0.0289097
$101$	−30849.4	−0.300915	−0.150458	−	0.988616i	$-0.548075\pi$
$101$	−30849.4	−0.300915	−0.150458	+	0.988616i	$0.548075\pi$
$102$	38033.1	0.361961
$103$	61864.8	0.574580	0.287290	−	0.957844i	$-0.407246\pi$
$103$	61864.8	0.574580	0.287290	+	0.957844i	$0.407246\pi$
$104$	−186409.	−1.68999
$105$	0	0
$106$	86859.7	0.750851
$107$	−172017.	−1.45249	−0.726244	−	0.687437i	$-0.758736\pi$
$107$	−172017.	−1.45249	−0.726244	+	0.687437i	$0.758736\pi$
$108$	17053.8	0.140690
$109$	155361.	1.25249	0.626246	−	0.779625i	$-0.284590\pi$
$109$	155361.	1.25249	0.626246	+	0.779625i	$0.284590\pi$
$110$	107214.	0.844833
$111$	69683.3	0.536811
$112$	0	0
$113$	83885.7	0.618005	0.309002	−	0.951061i	$-0.400005\pi$
$113$	83885.7	0.618005	0.309002	+	0.951061i	$0.400005\pi$
$114$	−173092.	−1.24743
$115$	89445.1	0.630684
$116$	−9.94056	−6.85908e−5 0
$117$	−13747.4	−0.0928443
$118$	−61716.4	−0.408033
$119$	0	0
$120$	66165.7	0.419450
$121$	341108.	2.11801
$122$	−17417.9	−0.105949
$123$	−134406.	−0.801042
$124$	−40583.4	−0.237025
$125$	−15625.0	−0.0894427
$126$	0	0
$127$	−340623.	−1.87398	−0.936988	−	0.349361i	$-0.886399\pi$
$127$	−340623.	−1.87398	−0.936988	+	0.349361i	$0.886399\pi$
$128$	−215142.	−1.16065
$129$	289325.	1.53077
$130$	−170240.	−0.883492
$131$	145084.	0.738652	0.369326	−	0.929300i	$-0.379589\pi$
$131$	145084.	0.738652	0.369326	+	0.929300i	$0.379589\pi$
$132$	−52364.8	−0.261580
$133$	0	0
$134$	−225821.	−1.08643
$135$	−92171.8	−0.435275
$136$	65170.6	0.302137
$137$	−56539.2	−0.257364	−0.128682	−	0.991686i	$-0.541075\pi$
$137$	−56539.2	−0.257364	−0.128682	+	0.991686i	$0.541075\pi$
$138$	−345911.	−1.54620
$139$	285472.	1.25322	0.626610	−	0.779333i	$-0.284442\pi$
$139$	285472.	1.25322	0.626610	+	0.779333i	$0.284442\pi$
$140$	0	0
$141$	131154.	0.555562
$142$	19726.8	0.0820985
$143$	−797351.	−3.26069
$144$	−14058.0	−0.0564959
$145$	53.7264	0.000212211 0
$146$	37053.0	0.143860
$147$	0	0
$148$	−20176.1	−0.0757152
$149$	−216259.	−0.798012	−0.399006	−	0.916948i	$-0.630645\pi$
$149$	−216259.	−0.798012	−0.399006	+	0.916948i	$0.630645\pi$
$150$	60426.5	0.219280
$151$	−153200.	−0.546784	−0.273392	−	0.961903i	$-0.588146\pi$
$151$	−153200.	−0.546784	−0.273392	+	0.961903i	$0.588146\pi$
$152$	−296597.	−1.04126
$153$	4806.24	0.0165988
$154$	0	0
$155$	219344.	0.733324
$156$	83147.3	0.273550
$157$	−375178.	−1.21475	−0.607377	−	0.794413i	$-0.707778\pi$
$157$	−375178.	−1.21475	−0.607377	+	0.794413i	$0.707778\pi$
$158$	−45690.6	−0.145608
$159$	229288.	0.719265
$160$	−41552.3	−0.128320
$161$	0	0
$162$	374423.	1.12092
$163$	−102281.	−0.301527	−0.150764	−	0.988570i	$-0.548173\pi$
$163$	−102281.	−0.301527	−0.150764	+	0.988570i	$0.548173\pi$
$164$	38915.8	0.112984
$165$	283019.	0.809293
$166$	11965.8	0.0337033
$167$	397953.	1.10418	0.552091	−	0.833784i	$-0.313830\pi$
$167$	397953.	1.10418	0.552091	+	0.833784i	$0.313830\pi$
$168$	0	0
$169$	894778.	2.40990
$170$	59517.7	0.157952
$171$	−21873.6	−0.0572046
$172$	−83770.9	−0.215910
$173$	126162.	0.320488	0.160244	−	0.987077i	$-0.448772\pi$
$173$	126162.	0.320488	0.160244	+	0.987077i	$0.448772\pi$
$174$	−207.776	−0.000520262 0
$175$	0	0
$176$	−815367.	−1.98414
$177$	−162916.	−0.390869
$178$	−283351.	−0.670308
$179$	−399204.	−0.931242	−0.465621	−	0.884984i	$-0.654169\pi$
$179$	−399204.	−0.931242	−0.465621	+	0.884984i	$0.654169\pi$
$180$	−1412.84	−0.00325022
$181$	−409529.	−0.929156	−0.464578	−	0.885532i	$-0.653794\pi$
$181$	−409529.	−0.929156	−0.464578	+	0.885532i	$0.653794\pi$
$182$	0	0
$183$	−45979.1	−0.101492
$184$	−592726.	−1.29065
$185$	109047.	0.234252
$186$	−848267.	−1.79784
$187$	278763.	0.582949
$188$	−37974.2	−0.0783598
$189$	0	0
$190$	−270871.	−0.544350
$191$	491227.	0.974313	0.487156	−	0.873315i	$-0.338034\pi$
$191$	491227.	0.974313	0.487156	+	0.873315i	$0.338034\pi$
$192$	−427523.	−0.836962
$193$	−479243.	−0.926110	−0.463055	−	0.886330i	$-0.653247\pi$
$193$	−479243.	−0.926110	−0.463055	+	0.886330i	$0.653247\pi$
$194$	119628.	0.228207
$195$	−449391.	−0.846327
$196$	0	0
$197$	364897.	0.669892	0.334946	−	0.942237i	$-0.391282\pi$
$197$	364897.	0.669892	0.334946	+	0.942237i	$0.391282\pi$
$198$	−52396.6	−0.0949818
$199$	556031.	0.995329	0.497664	−	0.867370i	$-0.334191\pi$
$199$	556031.	0.995329	0.497664	+	0.867370i	$0.334191\pi$
$200$	103542.	0.183039
$201$	−596113.	−1.04073
$202$	186698.	0.321930
$203$	0	0
$204$	−29069.2	−0.0489055
$205$	−210331.	−0.349557
$206$	−374400.	−0.614706
$207$	−43712.7	−0.0709058
$208$	1.29468e6	2.07493
$209$	−1.26868e6	−2.00902
$210$	0	0
$211$	550443.	0.851150	0.425575	−	0.904923i	$-0.360072\pi$
$211$	550443.	0.851150	0.425575	+	0.904923i	$0.360072\pi$
$212$	−66388.0	−0.101450
$213$	52073.8	0.0786448
$214$	1.04103e6	1.55392
$215$	452762.	0.667996
$216$	610795.	0.890760
$217$	0	0
$218$	−940229.	−1.33996
$219$	97810.8	0.137809
$220$	−81945.3	−0.114148
$221$	−442633.	−0.609625
$222$	−421717.	−0.574300
$223$	−457765.	−0.616425	−0.308212	−	0.951318i	$-0.599731\pi$
$223$	−457765.	−0.616425	−0.308212	+	0.951318i	$0.599731\pi$
$224$	0	0
$225$	7636.09	0.0100558
$226$	−507668.	−0.661163
$227$	1.26171e6	1.62515	0.812575	−	0.582857i	$-0.198065\pi$
$227$	1.26171e6	1.62515	0.812575	+	0.582857i	$0.198065\pi$
$228$	132297.	0.168543
$229$	37076.2	0.0467204	0.0233602	−	0.999727i	$-0.492564\pi$
$229$	37076.2	0.0467204	0.0233602	+	0.999727i	$0.492564\pi$
$230$	−541313.	−0.674728
$231$	0	0
$232$	−356.029	−0.000434275 0
$233$	−101982.	−0.123065	−0.0615325	−	0.998105i	$-0.519599\pi$
$233$	−101982.	−0.123065	−0.0615325	+	0.998105i	$0.519599\pi$
$234$	83197.8	0.0993282
$235$	205241.	0.242435
$236$	47170.7	0.0551305
$237$	−120612.	−0.139482
$238$	0	0
$239$	1.26398e6	1.43134	0.715672	−	0.698437i	$-0.246121\pi$
$239$	1.26398e6	1.43134	0.715672	+	0.698437i	$0.246121\pi$
$240$	−459545.	−0.514991
$241$	−221950.	−0.246158	−0.123079	−	0.992397i	$-0.539277\pi$
$241$	−221950.	−0.246158	−0.123079	+	0.992397i	$0.539277\pi$
$242$	−2.06435e6	−2.26592
$243$	92475.2	0.100464
$244$	13312.8	0.0143151
$245$	0	0
$246$	813411.	0.856983
$247$	2.01446e6	2.10095
$248$	−1.45353e6	−1.50070
$249$	31586.8	0.0322855
$250$	94561.0	0.0956890
$251$	513389.	0.514354	0.257177	−	0.966364i	$-0.417208\pi$
$251$	513389.	0.514354	0.257177	+	0.966364i	$0.417208\pi$
$252$	0	0
$253$	−2.53534e6	−2.49021
$254$	2.06142e6	2.00485
$255$	157112.	0.151307
$256$	445667.	0.425021
$257$	1.37745e6	1.30090	0.650450	−	0.759549i	$-0.274580\pi$
$257$	1.37745e6	1.30090	0.650450	+	0.759549i	$0.274580\pi$
$258$	−1.75096e6	−1.63768
$259$	0	0
$260$	130117.	0.119371
$261$	−26.2566	−2.38582e−5 0
$262$	−878032.	−0.790236
$263$	112502.	0.100293	0.0501465	−	0.998742i	$-0.484031\pi$
$263$	112502.	0.100293	0.0501465	+	0.998742i	$0.484031\pi$
$264$	−1.87548e6	−1.65616
$265$	358811.	0.313871
$266$	0	0
$267$	−747977.	−0.642111
$268$	172598.	0.146791
$269$	858748.	0.723577	0.361789	−	0.932260i	$-0.382166\pi$
$269$	858748.	0.723577	0.361789	+	0.932260i	$0.382166\pi$
$270$	557815.	0.465672
$271$	312828.	0.258751	0.129376	−	0.991596i	$-0.458703\pi$
$271$	312828.	0.258751	0.129376	+	0.991596i	$0.458703\pi$
$272$	−452634.	−0.370958
$273$	0	0
$274$	342170.	0.275338
$275$	442895.	0.353158
$276$	264384.	0.208912
$277$	1.08259e6	0.847743	0.423871	−	0.905722i	$-0.360671\pi$
$277$	1.08259e6	0.847743	0.423871	+	0.905722i	$0.360671\pi$
$278$	−1.72765e6	−1.34074
$279$	−107195.	−0.0824452
$280$	0	0
$281$	1.82814e6	1.38116	0.690580	−	0.723256i	$-0.257355\pi$
$281$	1.82814e6	1.38116	0.690580	+	0.723256i	$0.257355\pi$
$282$	−793729.	−0.594360
$283$	1.89318e6	1.40516	0.702581	−	0.711604i	$-0.252031\pi$
$283$	1.89318e6	1.40516	0.702581	+	0.711604i	$0.252031\pi$
$284$	−15077.4	−0.0110926
$285$	−715032.	−0.521451
$286$	4.82549e6	3.48840
$287$	0	0
$288$	20307.0	0.0144266
$289$	−1.26511e6	−0.891011
$290$	−325.147	−0.000227031 0
$291$	315788.	0.218607
$292$	−28320.1	−0.0194374
$293$	−1.82034e6	−1.23875	−0.619374	−	0.785096i	$-0.712614\pi$
$293$	−1.82034e6	−1.23875	−0.619374	+	0.785096i	$0.712614\pi$
$294$	0	0
$295$	−254946.	−0.170566
$296$	−722622.	−0.479382
$297$	2.61263e6	1.71865
$298$	1.30878e6	0.853741
$299$	4.02574e6	2.60416
$300$	−46184.8	−0.0296276
$301$	0	0
$302$	927150.	0.584969
$303$	492836.	0.308387
$304$	2.05998e6	1.27844
$305$	−71952.3	−0.0442889
$306$	−29086.9	−0.0177580
$307$	2.24274e6	1.35811	0.679053	−	0.734089i	$-0.262391\pi$
$307$	2.24274e6	1.35811	0.679053	+	0.734089i	$0.262391\pi$
$308$	0	0
$309$	−988323.	−0.588848
$310$	−1.32745e6	−0.784536
$311$	−1.09627e6	−0.642715	−0.321358	−	0.946958i	$-0.604139\pi$
$311$	−1.09627e6	−0.642715	−0.321358	+	0.946958i	$0.604139\pi$
$312$	2.97798e6	1.73195
$313$	−216576.	−0.124954	−0.0624768	−	0.998046i	$-0.519900\pi$
$313$	−216576.	−0.124954	−0.0624768	+	0.998046i	$0.519900\pi$
$314$	2.27054e6	1.29959
$315$	0	0
$316$	34921.9	0.0196734
$317$	2.51114e6	1.40353	0.701767	−	0.712407i	$-0.252395\pi$
$317$	2.51114e6	1.40353	0.701767	+	0.712407i	$0.252395\pi$
$318$	−1.38763e6	−0.769495
$319$	−1522.89	−0.000837898 0
$320$	−669027.	−0.365232
$321$	2.74807e6	1.48855
$322$	0	0
$323$	−704278.	−0.375611
$324$	−286177.	−0.151451
$325$	−703249.	−0.369318
$326$	618996.	0.322585
$327$	−2.48197e6	−1.28359
$328$	1.39380e6	0.715345
$329$	0	0
$330$	−1.71281e6	−0.865811
$331$	3.25575e6	1.63336	0.816678	−	0.577094i	$-0.195813\pi$
$331$	3.25575e6	1.63336	0.816678	+	0.577094i	$0.195813\pi$
$332$	−9145.63	−0.00455374
$333$	−53292.3	−0.0263362
$334$	−2.40837e6	−1.18129
$335$	−932852.	−0.454152
$336$	0	0
$337$	1.94506e6	0.932951	0.466475	−	0.884534i	$-0.345524\pi$
$337$	1.94506e6	0.932951	0.466475	+	0.884534i	$0.345524\pi$
$338$	−5.41511e6	−2.57819
$339$	−1.34012e6	−0.633350
$340$	−45490.2	−0.0213413
$341$	−6.21735e6	−2.89547
$342$	132377.	0.0611995
$343$	0	0
$344$	−3.00032e6	−1.36701
$345$	−1.42893e6	−0.646345
$346$	−763518.	−0.342870
$347$	−474653.	−0.211618	−0.105809	−	0.994386i	$-0.533743\pi$
$347$	−474653.	−0.211618	−0.105809	+	0.994386i	$0.533743\pi$
$348$	158.806	7.02940e−5 0
$349$	−137677.	−0.0605059	−0.0302530	−	0.999542i	$-0.509631\pi$
$349$	−137677.	−0.0605059	−0.0302530	+	0.999542i	$0.509631\pi$
$350$	0	0
$351$	−4.14846e6	−1.79729
$352$	1.17781e6	0.506663
$353$	406419.	0.173595	0.0867975	−	0.996226i	$-0.472337\pi$
$353$	406419.	0.173595	0.0867975	+	0.996226i	$0.472337\pi$
$354$	985952.	0.418165
$355$	81489.9	0.0343189
$356$	216569.	0.0905672
$357$	0	0
$358$	2.41594e6	0.996275
$359$	95290.6	0.0390224	0.0195112	−	0.999810i	$-0.493789\pi$
$359$	95290.6	0.0390224	0.0195112	+	0.999810i	$0.493789\pi$
$360$	−50602.1	−0.0205784
$361$	729137.	0.294470
$362$	2.47843e6	0.994044
$363$	−5.44938e6	−2.17060
$364$	0	0
$365$	153063.	0.0601366
$366$	278261.	0.108580
$367$	−3.53302e6	−1.36924	−0.684622	−	0.728898i	$-0.740033\pi$
$367$	−3.53302e6	−1.36924	−0.684622	+	0.728898i	$0.740033\pi$
$368$	4.11670e6	1.58464
$369$	102791.	0.0392995
$370$	−659942.	−0.250612
$371$	0	0
$372$	648342.	0.242911
$373$	−367500.	−0.136768	−0.0683842	−	0.997659i	$-0.521784\pi$
$373$	−367500.	−0.136768	−0.0683842	+	0.997659i	$0.521784\pi$
$374$	−1.68705e6	−0.623660
$375$	249618.	0.0916637
$376$	−1.36007e6	−0.496127
$377$	2418.11	0.000876240 0
$378$	0	0
$379$	601916.	0.215247	0.107624	−	0.994192i	$-0.465676\pi$
$379$	601916.	0.215247	0.107624	+	0.994192i	$0.465676\pi$
$380$	207030.	0.0735486
$381$	5.44163e6	1.92051
$382$	−2.97286e6	−1.04235
$383$	3.09685e6	1.07875	0.539377	−	0.842064i	$-0.318660\pi$
$383$	3.09685e6	1.07875	0.539377	+	0.842064i	$0.318660\pi$
$384$	3.43702e6	1.18947
$385$	0	0
$386$	2.90033e6	0.990786
$387$	−221269.	−0.0751006
$388$	−91433.2	−0.0308336
$389$	−3.34374e6	−1.12036	−0.560181	−	0.828370i	$-0.689269\pi$
$389$	−3.34374e6	−1.12036	−0.560181	+	0.828370i	$0.689269\pi$
$390$	2.71967e6	0.905430
$391$	−1.40744e6	−0.465574
$392$	0	0
$393$	−2.31779e6	−0.756994
$394$	−2.20832e6	−0.716674
$395$	−188745.	−0.0608670
$396$	40047.5	0.0128333
$397$	−1.30101e6	−0.414291	−0.207146	−	0.978310i	$-0.566417\pi$
$397$	−1.30101e6	−0.414291	−0.207146	+	0.978310i	$0.566417\pi$
$398$	−3.36505e6	−1.06484
$399$	0	0
$400$	−719139.	−0.224731
$401$	−3.95826e6	−1.22926	−0.614630	−	0.788816i	$-0.710695\pi$
$401$	−3.95826e6	−1.22926	−0.614630	+	0.788816i	$0.710695\pi$
$402$	3.60762e6	1.11341
$403$	9.87220e6	3.02797
$404$	−142696.	−0.0434968
$405$	1.54672e6	0.468568
$406$	0	0
$407$	−3.09096e6	−0.924928
$408$	−1.04114e6	−0.309640
$409$	−2.57625e6	−0.761516	−0.380758	−	0.924675i	$-0.624337\pi$
$409$	−2.57625e6	−0.761516	−0.380758	+	0.924675i	$0.624337\pi$
$410$	1.27290e6	0.373968
$411$	903245.	0.263755
$412$	286159.	0.0830547
$413$	0	0
$414$	264545.	0.0758575
$415$	49430.0	0.0140887
$416$	−1.87018e6	−0.529848
$417$	−4.56058e6	−1.28434
$418$	7.67790e6	2.14932
$419$	1.45659e6	0.405324	0.202662	−	0.979249i	$-0.435041\pi$
$419$	1.45659e6	0.405324	0.202662	+	0.979249i	$0.435041\pi$
$420$	0	0
$421$	1.97451e6	0.542944	0.271472	−	0.962446i	$-0.412490\pi$
$421$	1.97451e6	0.542944	0.271472	+	0.962446i	$0.412490\pi$
$422$	−3.33123e6	−0.910591
$423$	−100303.	−0.0272562
$424$	−2.37774e6	−0.642316
$425$	245864.	0.0660271
$426$	−315146.	−0.0841370
$427$	0	0
$428$	−795674.	−0.209955
$429$	1.27381e7	3.34166
$430$	−2.74007e6	−0.714646
$431$	−7.36508e6	−1.90978	−0.954892	−	0.296955i	$-0.904029\pi$
$431$	−7.36508e6	−1.90978	−0.954892	+	0.296955i	$0.904029\pi$
$432$	−4.24219e6	−1.09366
$433$	−3.17734e6	−0.814411	−0.407205	−	0.913337i	$-0.633497\pi$
$433$	−3.17734e6	−0.814411	−0.407205	+	0.913337i	$0.633497\pi$
$434$	0	0
$435$	−858.308	−0.000217480 0
$436$	718630.	0.181046
$437$	6.40540e6	1.60451
$438$	−591942.	−0.147433
$439$	−2.27765e6	−0.564061	−0.282030	−	0.959405i	$-0.591008\pi$
$439$	−2.27765e6	−0.564061	−0.282030	+	0.959405i	$0.591008\pi$
$440$	−2.93493e6	−0.722714
$441$	0	0
$442$	2.67877e6	0.652199
$443$	201316.	0.0487380	0.0243690	−	0.999703i	$-0.492242\pi$
$443$	201316.	0.0487380	0.0243690	+	0.999703i	$0.492242\pi$
$444$	322324.	0.0775952
$445$	−1.17050e6	−0.280203
$446$	2.77035e6	0.659473
$447$	3.45486e6	0.817827
$448$	0	0
$449$	−1.93977e6	−0.454082	−0.227041	−	0.973885i	$-0.572905\pi$
$449$	−1.93977e6	−0.454082	−0.227041	+	0.973885i	$0.572905\pi$
$450$	−46212.9	−0.0107580
$451$	5.96188e6	1.38020
$452$	388018.	0.0893316
$453$	2.44745e6	0.560361
$454$	−7.63572e6	−1.73864
$455$	0	0
$456$	4.73830e6	1.06711
$457$	5.78748e6	1.29628	0.648140	−	0.761521i	$-0.275547\pi$
$457$	5.78748e6	1.29628	0.648140	+	0.761521i	$0.275547\pi$
$458$	−224382.	−0.0499832
$459$	1.45035e6	0.321322
$460$	413733.	0.0911644
$461$	−1.96920e6	−0.431556	−0.215778	−	0.976442i	$-0.569229\pi$
$461$	−1.96920e6	−0.431556	−0.215778	+	0.976442i	$0.569229\pi$
$462$	0	0
$463$	5.43903e6	1.17915	0.589575	−	0.807713i	$-0.299295\pi$
$463$	5.43903e6	1.17915	0.589575	+	0.807713i	$0.299295\pi$
$464$	2472.75	0.000533194 0
$465$	−3.50413e6	−0.751533
$466$	617187.	0.131659
$467$	1.77123e6	0.375823	0.187911	−	0.982186i	$-0.439828\pi$
$467$	1.77123e6	0.375823	0.187911	+	0.982186i	$0.439828\pi$
$468$	−63589.2	−0.0134205
$469$	0	0
$470$	−1.24210e6	−0.259365
$471$	5.99367e6	1.24492
$472$	1.68945e6	0.349053
$473$	−1.28337e7	−2.63753
$474$	729931.	0.149223
$475$	−1.11895e6	−0.227550
$476$	0	0
$477$	−175355.	−0.0352875
$478$	−7.64946e6	−1.53130
$479$	−9.35974e6	−1.86391	−0.931955	−	0.362575i	$-0.881898\pi$
$479$	−9.35974e6	−1.86391	−0.931955	+	0.362575i	$0.881898\pi$
$480$	663821.	0.131507
$481$	4.90798e6	0.967253
$482$	1.34322e6	0.263348
$483$	0	0
$484$	1.57781e6	0.306155
$485$	494175.	0.0953951
$486$	−559651.	−0.107480
$487$	801260.	0.153091	0.0765457	−	0.997066i	$-0.475611\pi$
$487$	801260.	0.153091	0.0765457	+	0.997066i	$0.475611\pi$
$488$	476807.	0.0906344
$489$	1.63400e6	0.309014
$490$	0	0
$491$	7.25783e6	1.35864	0.679318	−	0.733844i	$-0.262276\pi$
$491$	7.25783e6	1.35864	0.679318	+	0.733844i	$0.262276\pi$
$492$	−621701.	−0.115789
$493$	−845.399	−0.000156655 0
$494$	−1.21913e7	−2.24768
$495$	−216447.	−0.0397044
$496$	1.00953e7	1.84253
$497$	0	0
$498$	−191160.	−0.0345402
$499$	−6.82872e6	−1.22769	−0.613844	−	0.789427i	$-0.710378\pi$
$499$	−6.82872e6	−1.22769	−0.613844	+	0.789427i	$0.710378\pi$
$500$	−72274.2	−0.0129288
$501$	−6.35751e6	−1.13160
$502$	−3.10698e6	−0.550274
$503$	−5.24113e6	−0.923644	−0.461822	−	0.886973i	$-0.652804\pi$
$503$	−5.24113e6	−0.923644	−0.461822	+	0.886973i	$0.652804\pi$
$504$	0	0
$505$	771236.	0.134573
$506$	1.53437e7	2.66411
$507$	−1.42946e7	−2.46974
$508$	−1.57557e6	−0.270881
$509$	−5.13517e6	−0.878538	−0.439269	−	0.898356i	$-0.644763\pi$
$509$	−5.13517e6	−0.878538	−0.439269	+	0.898356i	$0.644763\pi$
$510$	−950828.	−0.161874
$511$	0	0
$512$	4.18742e6	0.705947
$513$	−6.60067e6	−1.10737
$514$	−8.33621e6	−1.39175
$515$	−1.54662e6	−0.256960
$516$	1.33829e6	0.221271
$517$	−5.81762e6	−0.957235
$518$	0	0
$519$	−2.01550e6	−0.328446
$520$	4.66022e6	0.755785
$521$	5.75165e6	0.928320	0.464160	−	0.885751i	$-0.346356\pi$
$521$	5.75165e6	0.928320	0.464160	+	0.885751i	$0.346356\pi$
$522$	158.902	2.55243e−5 0
$523$	−3.17862e6	−0.508142	−0.254071	−	0.967186i	$-0.581770\pi$
$523$	−3.17862e6	−0.508142	−0.254071	+	0.967186i	$0.581770\pi$
$524$	671092.	0.106771
$525$	0	0
$526$	−680852.	−0.107297
$527$	−3.45143e6	−0.541343
$528$	1.30259e7	2.03340
$529$	6.36433e6	0.988812
$530$	−2.17149e6	−0.335791
$531$	124595.	0.0191762
$532$	0	0
$533$	−9.46654e6	−1.44336
$534$	4.52668e6	0.686953
$535$	4.30043e6	0.649572
$536$	6.18173e6	0.929391
$537$	6.37750e6	0.954365
$538$	−5.19706e6	−0.774109
$539$	0	0
$540$	−426345.	−0.0629183
$541$	−9.67662e6	−1.42145	−0.710724	−	0.703471i	$-0.751632\pi$
$541$	−9.67662e6	−1.42145	−0.710724	+	0.703471i	$0.751632\pi$
$542$	−1.89320e6	−0.276821
$543$	6.54245e6	0.952228
$544$	653837.	0.0947267
$545$	−3.88402e6	−0.560132
$546$	0	0
$547$	3.14094e6	0.448840	0.224420	−	0.974493i	$-0.427951\pi$
$547$	3.14094e6	0.448840	0.224420	+	0.974493i	$0.427951\pi$
$548$	−261525.	−0.0372016
$549$	35163.8	0.00497926
$550$	−2.68036e6	−0.377821
$551$	3847.49	0.000539882 0
$552$	9.46911e6	1.32270
$553$	0	0
$554$	−6.55172e6	−0.906945
$555$	−1.74208e6	−0.240069
$556$	1.32047e6	0.181151
$557$	−532897.	−0.0727788	−0.0363894	−	0.999338i	$-0.511586\pi$
$557$	−532897.	−0.0727788	−0.0363894	+	0.999338i	$0.511586\pi$
$558$	648736.	0.0882028
$559$	2.03779e7	2.75822
$560$	0	0
$561$	−4.45339e6	−0.597425
$562$	−1.10637e7	−1.47762
$563$	1.24343e7	1.65329	0.826645	−	0.562724i	$-0.190247\pi$
$563$	1.24343e7	1.65329	0.826645	+	0.562724i	$0.190247\pi$
$564$	606658.	0.0803056
$565$	−2.09714e6	−0.276380
$566$	−1.14574e7	−1.50329
$567$	0	0
$568$	−540009.	−0.0702312
$569$	−8.82869e6	−1.14318	−0.571591	−	0.820538i	$-0.693674\pi$
$569$	−8.82869e6	−1.14318	−0.571591	+	0.820538i	$0.693674\pi$
$570$	4.32730e6	0.557867
$571$	−9.42799e6	−1.21012	−0.605060	−	0.796180i	$-0.706851\pi$
$571$	−9.42799e6	−1.21012	−0.605060	+	0.796180i	$0.706851\pi$
$572$	−3.68819e6	−0.471328
$573$	−7.84761e6	−0.998506
$574$	0	0
$575$	−2.23613e6	−0.282050
$576$	326960.	0.0410618
$577$	−6.92633e6	−0.866091	−0.433046	−	0.901372i	$-0.642561\pi$
$577$	−6.92633e6	−0.866091	−0.433046	+	0.901372i	$0.642561\pi$
$578$	7.65631e6	0.953235
$579$	7.65617e6	0.949106
$580$	248.514	3.06748e−5 0
$581$	0	0
$582$	−1.91112e6	−0.233873
$583$	−1.01706e7	−1.23930
$584$	−1.01431e6	−0.123066
$585$	343684.	0.0415212
$586$	1.10165e7	1.32526
$587$	−3.94161e6	−0.472148	−0.236074	−	0.971735i	$-0.575861\pi$
$587$	−3.94161e6	−0.472148	−0.236074	+	0.971735i	$0.575861\pi$
$588$	0	0
$589$	1.57078e7	1.86564
$590$	1.54291e6	0.182478
$591$	−5.82942e6	−0.686526
$592$	5.01887e6	0.588575
$593$	−1.13618e7	−1.32681	−0.663405	−	0.748260i	$-0.730889\pi$
$593$	−1.13618e7	−1.32681	−0.663405	+	0.748260i	$0.730889\pi$
$594$	−1.58114e7	−1.83867
$595$	0	0
$596$	−1.00032e6	−0.115351
$597$	−8.88290e6	−1.02004
$598$	−2.43634e7	−2.78602
$599$	9.73442e6	1.10852	0.554260	−	0.832344i	$-0.313002\pi$
$599$	9.73442e6	1.10852	0.554260	+	0.832344i	$0.313002\pi$
$600$	−1.65414e6	−0.187584
$601$	1.24040e7	1.40080	0.700400	−	0.713750i	$-0.253005\pi$
$601$	1.24040e7	1.40080	0.700400	+	0.713750i	$0.253005\pi$
$602$	0	0
$603$	455894.	0.0510588
$604$	−708633.	−0.0790368
$605$	−8.52769e6	−0.947203
$606$	−2.98260e6	−0.329924
$607$	1.36871e7	1.50779	0.753893	−	0.656997i	$-0.228174\pi$
$607$	1.36871e7	1.50779	0.753893	+	0.656997i	$0.228174\pi$
$608$	−2.97567e6	−0.326457
$609$	0	0
$610$	435449.	0.0473819
$611$	9.23748e6	1.00104
$612$	22231.5	0.00239933
$613$	1.10357e7	1.18617	0.593087	−	0.805138i	$-0.297909\pi$
$613$	1.10357e7	1.18617	0.593087	+	0.805138i	$0.297909\pi$
$614$	−1.35729e7	−1.45295
$615$	3.36014e6	0.358237
$616$	0	0
$617$	−9.49061e6	−1.00365	−0.501824	−	0.864970i	$-0.667337\pi$
$617$	−9.49061e6	−1.00365	−0.501824	+	0.864970i	$0.667337\pi$
$618$	5.98124e6	0.629970
$619$	−950326.	−0.0996887	−0.0498444	−	0.998757i	$-0.515873\pi$
$619$	−950326.	−0.0996887	−0.0498444	+	0.998757i	$0.515873\pi$
$620$	1.01459e6	0.106001
$621$	−1.31909e7	−1.37260
$622$	6.63455e6	0.687600
$623$	0	0
$624$	−2.06832e7	−2.12645
$625$	390625.	0.0400000
$626$	1.31070e6	0.133680
$627$	2.02678e7	2.05891
$628$	−1.73541e6	−0.175591
$629$	−1.71588e6	−0.172926
$630$	0	0
$631$	1.60839e7	1.60812	0.804061	−	0.594547i	$-0.202668\pi$
$631$	1.60839e7	1.60812	0.804061	+	0.594547i	$0.202668\pi$
$632$	1.25075e6	0.124560
$633$	−8.79362e6	−0.872285
$634$	−1.51972e7	−1.50155
$635$	8.51557e6	0.838068
$636$	1.06058e6	0.103969
$637$	0	0
$638$	9216.37	0.000896413 0
$639$	−39824.9	−0.00385836
$640$	5.37856e6	0.519058
$641$	1.90411e7	1.83041	0.915204	−	0.402991i	$-0.132029\pi$
$641$	1.90411e7	1.83041	0.915204	+	0.402991i	$0.132029\pi$
$642$	−1.66310e7	−1.59251
$643$	1.03943e7	0.991439	0.495720	−	0.868483i	$-0.334904\pi$
$643$	1.03943e7	0.991439	0.495720	+	0.868483i	$0.334904\pi$
$644$	0	0
$645$	−7.23311e6	−0.684583
$646$	4.26223e6	0.401842
$647$	3.14502e6	0.295367	0.147684	−	0.989035i	$-0.452818\pi$
$647$	3.14502e6	0.295367	0.147684	+	0.989035i	$0.452818\pi$
$648$	−1.02496e7	−0.958894
$649$	7.22652e6	0.673468
$650$	4.25600e6	0.395110
$651$	0	0
$652$	−473107.	−0.0435853
$653$	1.83320e7	1.68239	0.841196	−	0.540731i	$-0.181852\pi$
$653$	1.83320e7	1.68239	0.841196	+	0.540731i	$0.181852\pi$
$654$	1.50207e7	1.37323
$655$	−3.62709e6	−0.330335
$656$	−9.68044e6	−0.878285
$657$	−74803.5	−0.00676097
$658$	0	0
$659$	2.76429e6	0.247954	0.123977	−	0.992285i	$-0.460435\pi$
$659$	2.76429e6	0.247954	0.123977	+	0.992285i	$0.460435\pi$
$660$	1.30912e6	0.116982
$661$	4.80051e6	0.427350	0.213675	−	0.976905i	$-0.431457\pi$
$661$	4.80051e6	0.427350	0.213675	+	0.976905i	$0.431457\pi$
$662$	−1.97035e7	−1.74742
$663$	7.07129e6	0.624763
$664$	−327558.	−0.0288315
$665$	0	0
$666$	322520.	0.0281755
$667$	7688.90	0.000669190 0
$668$	1.84075e6	0.159608
$669$	7.31304e6	0.631731
$670$	5.64553e6	0.485868
$671$	2.03951e6	0.174872
$672$	0	0
$673$	−3.73117e6	−0.317546	−0.158773	−	0.987315i	$-0.550754\pi$
$673$	−3.73117e6	−0.317546	−0.158773	+	0.987315i	$0.550754\pi$
$674$	−1.17713e7	−0.998104
$675$	2.30429e6	0.194661
$676$	4.13884e6	0.348347
$677$	−1.48375e7	−1.24419	−0.622096	−	0.782941i	$-0.713719\pi$
$677$	−1.48375e7	−1.24419	−0.622096	+	0.782941i	$0.713719\pi$
$678$	8.11027e6	0.677581
$679$	0	0
$680$	−1.62927e6	−0.135120
$681$	−2.01564e7	−1.66550
$682$	3.76268e7	3.09768
$683$	206230.	0.0169161	0.00845804	−	0.999964i	$-0.497308\pi$
$683$	206230.	0.0169161	0.00845804	+	0.999964i	$0.497308\pi$
$684$	−101178.	−0.00826883
$685$	1.41348e6	0.115097
$686$	0	0
$687$	−592312.	−0.0478805
$688$	2.08383e7	1.67838
$689$	1.61494e7	1.29601
$690$	8.64777e6	0.691483
$691$	−1.44687e7	−1.15275	−0.576376	−	0.817185i	$-0.695534\pi$
$691$	−1.44687e7	−1.15275	−0.576376	+	0.817185i	$0.695534\pi$
$692$	583567.	0.0463261
$693$	0	0
$694$	2.87255e6	0.226396
$695$	−7.13681e6	−0.560457
$696$	5687.75	0.000445059 0
$697$	3.30961e6	0.258045
$698$	833208.	0.0647314
$699$	1.62922e6	0.126121
$700$	0	0
$701$	−9.14822e6	−0.703140	−0.351570	−	0.936162i	$-0.614352\pi$
$701$	−9.14822e6	−0.703140	−0.351570	+	0.936162i	$0.614352\pi$
$702$	2.51061e7	1.92281
$703$	7.80915e6	0.595957
$704$	1.89637e7	1.44209
$705$	−3.27884e6	−0.248455
$706$	−2.45961e6	−0.185718
$707$	0	0
$708$	−753577.	−0.0564995
$709$	5.64865e6	0.422016	0.211008	−	0.977484i	$-0.432325\pi$
$709$	5.64865e6	0.422016	0.211008	+	0.977484i	$0.432325\pi$
$710$	−493169.	−0.0367155
$711$	92241.3	0.00684308
$712$	7.75658e6	0.573416
$713$	3.13907e7	2.31248
$714$	0	0
$715$	1.99338e7	1.45822
$716$	−1.84654e6	−0.134610
$717$	−2.01927e7	−1.46689
$718$	−576690.	−0.0417476
$719$	5.23347e6	0.377544	0.188772	−	0.982021i	$-0.439549\pi$
$719$	5.23347e6	0.377544	0.188772	+	0.982021i	$0.439549\pi$
$720$	351450.	0.0252658
$721$	0	0
$722$	−4.41267e6	−0.315034
$723$	3.54578e6	0.252270
$724$	−1.89430e6	−0.134308
$725$	−1343.16	−9.49036e−5 0
$726$	3.29791e7	2.32219
$727$	1.90417e6	0.133619	0.0668097	−	0.997766i	$-0.478718\pi$
$727$	1.90417e6	0.133619	0.0668097	+	0.997766i	$0.478718\pi$
$728$	0	0
$729$	1.35567e7	0.944792
$730$	−926325.	−0.0643363
$731$	−7.12433e6	−0.493118
$732$	−212679.	−0.0146705
$733$	−1.99067e6	−0.136848	−0.0684242	−	0.997656i	$-0.521797\pi$
$733$	−1.99067e6	−0.136848	−0.0684242	+	0.997656i	$0.521797\pi$
$734$	2.13815e7	1.46487
$735$	0	0
$736$	−5.94664e6	−0.404648
$737$	2.64419e7	1.79318
$738$	−622079.	−0.0420440
$739$	−1.12289e7	−0.756357	−0.378178	−	0.925733i	$-0.623449\pi$
$739$	−1.12289e7	−0.756357	−0.378178	+	0.925733i	$0.623449\pi$
$740$	504402.	0.0338608
$741$	−3.21821e7	−2.15312
$742$	0	0
$743$	9.86132e6	0.655335	0.327667	−	0.944793i	$-0.393737\pi$
$743$	9.86132e6	0.655335	0.327667	+	0.944793i	$0.393737\pi$
$744$	2.32208e7	1.53796
$745$	5.40648e6	0.356882
$746$	2.22408e6	0.146320
$747$	−24156.9	−0.00158394
$748$	1.28943e6	0.0842645
$749$	0	0
$750$	−1.51066e6	−0.0980651
$751$	−9.24657e6	−0.598247	−0.299124	−	0.954214i	$-0.596694\pi$
$751$	−9.24657e6	−0.598247	−0.299124	+	0.954214i	$0.596694\pi$
$752$	9.44620e6	0.609134
$753$	−8.20166e6	−0.527126
$754$	−14634.2	−0.000937433 0
$755$	3.82999e6	0.244529
$756$	0	0
$757$	5.85772e6	0.371526	0.185763	−	0.982595i	$-0.440524\pi$
$757$	5.85772e6	0.371526	0.185763	+	0.982595i	$0.440524\pi$
$758$	−3.64274e6	−0.230279
$759$	4.05035e7	2.55204
$760$	7.41494e6	0.465665
$761$	−1.36326e7	−0.853329	−0.426665	−	0.904410i	$-0.640312\pi$
$761$	−1.36326e7	−0.853329	−0.426665	+	0.904410i	$0.640312\pi$
$762$	−3.29322e7	−2.05463
$763$	0	0
$764$	2.27219e6	0.140835
$765$	−120156.	−0.00742321
$766$	−1.87418e7	−1.15409
$767$	−1.14746e7	−0.704286
$768$	−7.11977e6	−0.435575
$769$	−1.95250e7	−1.19062	−0.595312	−	0.803494i	$-0.702972\pi$
$769$	−1.95250e7	−1.19062	−0.595312	+	0.803494i	$0.702972\pi$
$770$	0	0
$771$	−2.20055e7	−1.33320
$772$	−2.21676e6	−0.133868
$773$	−978993.	−0.0589292	−0.0294646	−	0.999566i	$-0.509380\pi$
$773$	−978993.	−0.0589292	−0.0294646	+	0.999566i	$0.509380\pi$
$774$	1.33910e6	0.0803453
$775$	−5.48359e6	−0.327952
$776$	−3.27475e6	−0.195220
$777$	0	0
$778$	2.02360e7	1.19860
$779$	−1.50623e7	−0.889301
$780$	−2.07868e6	−0.122335
$781$	−2.30985e6	−0.135505
$782$	8.51771e6	0.498088
$783$	−7923.29	−0.000461850 0
$784$	0	0
$785$	9.37946e6	0.543255
$786$	1.40270e7	0.809859
$787$	−2.41473e7	−1.38974	−0.694868	−	0.719138i	$-0.744537\pi$
$787$	−2.41473e7	−1.38974	−0.694868	+	0.719138i	$0.744537\pi$
$788$	1.68785e6	0.0968318
$789$	−1.79728e6	−0.102783
$790$	1.14226e6	0.0651177
$791$	0	0
$792$	1.43433e6	0.0812523
$793$	−3.23843e6	−0.182874
$794$	7.87362e6	0.443224
$795$	−5.73220e6	−0.321665
$796$	2.57195e6	0.143873
$797$	2.16881e7	1.20942	0.604708	−	0.796447i	$-0.293290\pi$
$797$	2.16881e7	1.20942	0.604708	+	0.796447i	$0.293290\pi$
$798$	0	0
$799$	−3.22953e6	−0.178967
$800$	1.03881e6	0.0573866
$801$	572036.	0.0315023
$802$	2.39550e7	1.31511
$803$	−4.33862e6	−0.237445
$804$	−2.75735e6	−0.150436
$805$	0	0
$806$	−5.97456e7	−3.23943
$807$	−1.37190e7	−0.741544
$808$	−5.11075e6	−0.275395
$809$	2.18877e7	1.17579	0.587895	−	0.808938i	$-0.299957\pi$
$809$	2.18877e7	1.17579	0.587895	+	0.808938i	$0.299957\pi$
$810$	−9.36058e6	−0.501291
$811$	1.02862e7	0.549167	0.274583	−	0.961563i	$-0.411460\pi$
$811$	1.02862e7	0.549167	0.274583	+	0.961563i	$0.411460\pi$
$812$	0	0
$813$	−4.99759e6	−0.265176
$814$	1.87062e7	0.989521
$815$	2.55703e6	0.134847
$816$	7.23107e6	0.380169
$817$	3.24235e7	1.69944
$818$	1.55912e7	0.814697
$819$	0	0
$820$	−972895.	−0.0505279
$821$	−1.03817e7	−0.537540	−0.268770	−	0.963204i	$-0.586617\pi$
$821$	−1.03817e7	−0.537540	−0.268770	+	0.963204i	$0.586617\pi$
$822$	−5.46635e6	−0.282175
$823$	−2.02906e7	−1.04423	−0.522115	−	0.852875i	$-0.674857\pi$
$823$	−2.02906e7	−1.04423	−0.522115	+	0.852875i	$0.674857\pi$
$824$	1.02490e7	0.525851
$825$	−7.07548e6	−0.361927
$826$	0	0
$827$	−1.27595e7	−0.648741	−0.324370	−	0.945930i	$-0.605152\pi$
$827$	−1.27595e7	−0.648741	−0.324370	+	0.945930i	$0.605152\pi$
$828$	−202195.	−0.0102493
$829$	−3.54147e7	−1.78977	−0.894885	−	0.446296i	$-0.852743\pi$
$829$	−3.54147e7	−1.78977	−0.894885	+	0.446296i	$0.852743\pi$
$830$	−299145.	−0.0150726
$831$	−1.72949e7	−0.868793
$832$	−3.01115e7	−1.50808
$833$	0	0
$834$	2.76002e7	1.37403
$835$	−9.94882e6	−0.493805
$836$	−5.86832e6	−0.290401
$837$	−3.23477e7	−1.59599
$838$	−8.81515e6	−0.433630
$839$	−3.26655e7	−1.60208	−0.801040	−	0.598611i	$-0.795720\pi$
$839$	−3.26655e7	−1.60208	−0.801040	+	0.598611i	$0.795720\pi$
$840$	0	0
$841$	−2.05111e7	−1.00000
$842$	−1.19496e7	−0.580861
$843$	−2.92056e7	−1.41546
$844$	2.54610e6	0.123032
$845$	−2.23695e7	−1.07774
$846$	607026.	0.0291596
$847$	0	0
$848$	1.65143e7	0.788623
$849$	−3.02446e7	−1.44005
$850$	−1.48794e6	−0.0706381
$851$	1.56059e7	0.738697
$852$	240870.	0.0113680
$853$	3.13879e7	1.47703	0.738516	−	0.674236i	$-0.235527\pi$
$853$	3.13879e7	1.47703	0.738516	+	0.674236i	$0.235527\pi$
$854$	0	0
$855$	546841.	0.0255827
$856$	−2.84977e7	−1.32931
$857$	2.68286e7	1.24780	0.623902	−	0.781502i	$-0.285546\pi$
$857$	2.68286e7	1.24780	0.623902	+	0.781502i	$0.285546\pi$
$858$	−7.70898e7	−3.57502
$859$	3.01479e7	1.39404	0.697019	−	0.717053i	$-0.254509\pi$
$859$	3.01479e7	1.39404	0.697019	+	0.717053i	$0.254509\pi$
$860$	2.09427e6	0.0965578
$861$	0	0
$862$	4.45727e7	2.04315
$863$	6.05947e6	0.276954	0.138477	−	0.990366i	$-0.455779\pi$
$863$	6.05947e6	0.276954	0.138477	+	0.990366i	$0.455779\pi$
$864$	6.12792e6	0.279273
$865$	−3.15404e6	−0.143327
$866$	1.92289e7	0.871285
$867$	2.02108e7	0.913135
$868$	0	0
$869$	5.35001e6	0.240329
$870$	5194.40	0.000232668 0
$871$	−4.19858e7	−1.87524
$872$	2.57382e7	1.14627
$873$	−241508.	−0.0107250
$874$	−3.87649e7	−1.71656
$875$	0	0
$876$	452429.	0.0199200
$877$	−6.94230e6	−0.304792	−0.152396	−	0.988319i	$-0.548699\pi$
$877$	−6.94230e6	−0.304792	−0.152396	+	0.988319i	$0.548699\pi$
$878$	1.37841e7	0.603452
$879$	2.90809e7	1.26951
$880$	2.03842e7	0.887333
$881$	−9.89661e6	−0.429583	−0.214791	−	0.976660i	$-0.568907\pi$
$881$	−9.89661e6	−0.429583	−0.214791	+	0.976660i	$0.568907\pi$
$882$	0	0
$883$	−1.02503e7	−0.442419	−0.221209	−	0.975226i	$-0.571000\pi$
$883$	−1.02503e7	−0.442419	−0.221209	+	0.975226i	$0.571000\pi$
$884$	−2.04742e6	−0.0881204
$885$	4.07290e6	0.174802
$886$	−1.21834e6	−0.0521417
$887$	−8.61386e6	−0.367611	−0.183806	−	0.982963i	$-0.558842\pi$
$887$	−8.61386e6	−0.367611	−0.183806	+	0.982963i	$0.558842\pi$
$888$	1.15443e7	0.491286
$889$	0	0
$890$	7.08377e6	0.299771
$891$	−4.38421e7	−1.85011
$892$	−2.11741e6	−0.0891033
$893$	1.46979e7	0.616774
$894$	−2.09085e7	−0.874941
$895$	9.98010e6	0.416464
$896$	0	0
$897$	−6.43133e7	−2.66882
$898$	1.17393e7	0.485794
$899$	18855.3	0.000778096 0
$900$	35321.1	0.00145354
$901$	−5.64600e6	−0.231701
$902$	−3.60807e7	−1.47659
$903$	0	0
$904$	1.38971e7	0.565593
$905$	1.02382e7	0.415531
$906$	−1.48117e7	−0.599494
$907$	−1.87395e6	−0.0756380	−0.0378190	−	0.999285i	$-0.512041\pi$
$907$	−1.87395e6	−0.0756380	−0.0378190	+	0.999285i	$0.512041\pi$
$908$	5.83608e6	0.234913
$909$	−376911.	−0.0151296
$910$	0	0
$911$	4.93810e7	1.97135	0.985676	−	0.168649i	$-0.0539405\pi$
$911$	4.93810e7	1.97135	0.985676	+	0.168649i	$0.0539405\pi$
$912$	−3.29093e7	−1.31018
$913$	−1.40111e6	−0.0556280
$914$	−3.50253e7	−1.38681
$915$	1.14948e6	0.0453887
$916$	171498.	0.00675336
$917$	0	0
$918$	−8.77737e6	−0.343762
$919$	−3.25462e7	−1.27119	−0.635597	−	0.772021i	$-0.719246\pi$
$919$	−3.25462e7	−1.27119	−0.635597	+	0.772021i	$0.719246\pi$
$920$	1.48181e7	0.577197
$921$	−3.58290e7	−1.39183
$922$	1.19174e7	0.461694
$923$	3.66769e6	0.141706
$924$	0	0
$925$	−2.72617e6	−0.104761
$926$	−3.29165e7	−1.26150
$927$	755848.	0.0288892
$928$	−3571.93	−0.000136155 0
$929$	−1.13881e6	−0.0432923	−0.0216462	−	0.999766i	$-0.506891\pi$
$929$	−1.13881e6	−0.0432923	−0.0216462	+	0.999766i	$0.506891\pi$
$930$	2.12067e7	0.804017
$931$	0	0
$932$	−471724.	−0.0177889
$933$	1.75136e7	0.658674
$934$	−1.07193e7	−0.402068
$935$	−6.96907e6	−0.260703
$936$	−2.27749e6	−0.0849704
$937$	−3.02967e7	−1.12732	−0.563658	−	0.826008i	$-0.690607\pi$
$937$	−3.02967e7	−1.12732	−0.563658	+	0.826008i	$0.690607\pi$
$938$	0	0
$939$	3.45991e6	0.128056
$940$	949354.	0.0350436
$941$	2.34042e7	0.861628	0.430814	−	0.902441i	$-0.358227\pi$
$941$	2.34042e7	0.861628	0.430814	+	0.902441i	$0.358227\pi$
$942$	−3.62731e7	−1.33186
$943$	−3.01009e7	−1.10230
$944$	−1.17339e7	−0.428559
$945$	0	0
$946$	7.76680e7	2.82172
$947$	4.77998e7	1.73201	0.866006	−	0.500034i	$-0.166679\pi$
$947$	4.77998e7	1.73201	0.866006	+	0.500034i	$0.166679\pi$
$948$	−557896.	−0.0201620
$949$	6.88907e6	0.248310
$950$	6.77177e6	0.243441
$951$	−4.01168e7	−1.43838
$952$	0	0
$953$	−5.13376e7	−1.83106	−0.915532	−	0.402246i	$-0.868230\pi$
$953$	−5.13376e7	−1.83106	−0.915532	+	0.402246i	$0.868230\pi$
$954$	1.06123e6	0.0377519
$955$	−1.22807e7	−0.435726
$956$	5.84658e6	0.206899
$957$	24329.0	0.000858704 0
$958$	5.66442e7	1.99408
$959$	0	0
$960$	1.06881e7	0.374301
$961$	4.83495e7	1.68882
$962$	−2.97026e7	−1.03480
$963$	−2.10166e6	−0.0730293
$964$	−1.02664e6	−0.0355817
$965$	1.19811e7	0.414169
$966$	0	0
$967$	1.30795e6	0.0449807	0.0224904	−	0.999747i	$-0.492840\pi$
$967$	1.30795e6	0.0449807	0.0224904	+	0.999747i	$0.492840\pi$
$968$	5.65105e7	1.93839
$969$	1.12512e7	0.384938
$970$	−2.99070e6	−0.102057
$971$	1.92507e7	0.655236	0.327618	−	0.944810i	$-0.393754\pi$
$971$	1.92507e7	0.655236	0.327618	+	0.944810i	$0.393754\pi$
$972$	427749.	0.0145219
$973$	0	0
$974$	−4.84915e6	−0.163783
$975$	1.12348e7	0.378489
$976$	−3.31160e6	−0.111279
$977$	4.79097e6	0.160578	0.0802892	−	0.996772i	$-0.474416\pi$
$977$	4.79097e6	0.160578	0.0802892	+	0.996772i	$0.474416\pi$
$978$	−9.88879e6	−0.330595
$979$	3.31782e7	1.10636
$980$	0	0
$981$	1.89816e6	0.0629738
$982$	−4.39237e7	−1.45352
$983$	−4.02177e7	−1.32750	−0.663748	−	0.747956i	$-0.731035\pi$
$983$	−4.02177e7	−1.32750	−0.663748	+	0.747956i	$0.731035\pi$
$984$	−2.22667e7	−0.733107
$985$	−9.12242e6	−0.299585
$986$	5116.28	0.000167595 0
$987$	0	0
$988$	9.31800e6	0.303690
$989$	6.47957e7	2.10647
$990$	1.30992e6	0.0424772
$991$	7.65202e6	0.247510	0.123755	−	0.992313i	$-0.460506\pi$
$991$	7.65202e6	0.247510	0.123755	+	0.992313i	$0.460506\pi$
$992$	−1.45828e7	−0.470502
$993$	−5.20123e7	−1.67391
$994$	0	0
$995$	−1.39008e7	−0.445125
$996$	146106.	0.00466682
$997$	−3.97848e7	−1.26759	−0.633796	−	0.773500i	$-0.718504\pi$
$997$	−3.97848e7	−1.26759	−0.633796	+	0.773500i	$0.718504\pi$
$998$	4.13268e7	1.31342
$999$	−1.60817e7	−0.509821

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.6.a.e.1.1		4
7.6	odd	2		35.6.a.d.1.1	✓	4
21.20	even	2		315.6.a.l.1.4		4
28.27	even	2		560.6.a.v.1.2		4
35.13	even	4		175.6.b.f.99.7		8
35.27	even	4		175.6.b.f.99.2		8
35.34	odd	2		175.6.a.f.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.6.a.d.1.1	✓	4	7.6	odd	2
175.6.a.f.1.4		4	35.34	odd	2
175.6.b.f.99.2		8	35.27	even	4
175.6.b.f.99.7		8	35.13	even	4
245.6.a.e.1.1		4	1.1	even	1	trivial
315.6.a.l.1.4		4	21.20	even	2
560.6.a.v.1.2		4	28.27	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-6.05190 q^{2} -15.9755 q^{3} +4.62555 q^{4} -25.0000 q^{5} +96.6824 q^{6} +165.668 q^{8} +12.2177 q^{9} +O(q^{10})\)	\(q-6.05190 q^{2} -15.9755 q^{3} +4.62555 q^{4} -25.0000 q^{5} +96.6824 q^{6} +165.668 q^{8} +12.2177 q^{9} +151.298 q^{10} +708.632 q^{11} -73.8957 q^{12} -1125.20 q^{13} +399.388 q^{15} -1150.62 q^{16} +393.382 q^{17} -73.9406 q^{18} -1790.32 q^{19} -115.639 q^{20} -4288.57 q^{22} -3577.80 q^{23} -2646.63 q^{24} +625.000 q^{25} +6809.59 q^{26} +3686.87 q^{27} -2.14905 q^{29} -2417.06 q^{30} -8773.75 q^{31} +1662.09 q^{32} -11320.8 q^{33} -2380.71 q^{34} +56.5138 q^{36} -4361.88 q^{37} +10834.8 q^{38} +17975.6 q^{39} -4141.69 q^{40} +8413.22 q^{41} -18110.5 q^{43} +3277.81 q^{44} -305.443 q^{45} +21652.5 q^{46} -8209.65 q^{47} +18381.8 q^{48} -3782.44 q^{50} -6284.49 q^{51} -5204.66 q^{52} -14352.5 q^{53} -22312.6 q^{54} -17715.8 q^{55} +28601.3 q^{57} +13.0059 q^{58} +10197.8 q^{59} +1847.39 q^{60} +2878.09 q^{61} +53097.9 q^{62} +26761.1 q^{64} +28130.0 q^{65} +68512.2 q^{66} +37314.1 q^{67} +1819.61 q^{68} +57157.3 q^{69} -3259.60 q^{71} +2024.08 q^{72} -6122.54 q^{73} +26397.7 q^{74} -9984.71 q^{75} -8281.20 q^{76} -108787. q^{78} +7549.78 q^{79} +28765.5 q^{80} -61868.6 q^{81} -50916.0 q^{82} -1977.20 q^{83} -9834.55 q^{85} +109603. q^{86} +34.3323 q^{87} +117397. q^{88} +46820.1 q^{89} +1848.51 q^{90} -16549.3 q^{92} +140165. q^{93} +49684.0 q^{94} +44757.9 q^{95} -26552.8 q^{96} -19767.0 q^{97} +8657.88 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 7 q^{2} - 14 q^{3} + 49 q^{4} - 100 q^{5} - 136 q^{6} + 489 q^{8} + 774 q^{9}+O(q^{10}) \) 4 * q + 7 * q^2 - 14 * q^3 + 49 * q^4 - 100 * q^5 - 136 * q^6 + 489 * q^8 + 774 * q^9	\( 4 q + 7 q^{2} - 14 q^{3} + 49 q^{4} - 100 q^{5} - 136 q^{6} + 489 q^{8} + 774 q^{9} - 175 q^{10} + 770 q^{11} - 840 q^{12} - 58 q^{13} + 350 q^{15} - 615 q^{16} - 2006 q^{17} - 1409 q^{18} - 564 q^{19} - 1225 q^{20} - 1736 q^{22} - 6340 q^{23} + 6244 q^{24} + 2500 q^{25} + 8730 q^{26} + 7438 q^{27} + 8066 q^{29} + 3400 q^{30} + 5856 q^{31} - 3495 q^{32} + 8130 q^{33} - 3402 q^{34} - 28759 q^{36} + 29544 q^{37} + 36860 q^{38} + 57466 q^{39} - 12225 q^{40} - 13156 q^{41} - 5692 q^{43} + 44952 q^{44} - 19350 q^{45} + 30928 q^{46} - 39926 q^{47} + 57156 q^{48} + 4375 q^{50} + 9830 q^{51} + 23398 q^{52} + 20300 q^{53} - 77292 q^{54} - 19250 q^{55} - 50876 q^{57} - 22234 q^{58} - 8432 q^{59} + 21000 q^{60} - 30540 q^{61} + 137568 q^{62} + 37121 q^{64} + 1450 q^{65} + 166756 q^{66} + 32792 q^{67} + 72554 q^{68} + 36540 q^{69} - 83920 q^{71} - 71795 q^{72} + 75424 q^{73} + 168762 q^{74} - 8750 q^{75} + 125092 q^{76} - 89204 q^{78} + 129486 q^{79} + 15375 q^{80} + 146308 q^{81} - 247230 q^{82} + 187520 q^{83} + 50150 q^{85} + 36156 q^{86} + 238670 q^{87} + 475556 q^{88} + 30324 q^{89} + 35225 q^{90} + 124464 q^{92} + 8256 q^{93} - 245756 q^{94} + 14100 q^{95} - 172340 q^{96} - 180270 q^{97} - 420668 q^{99}+O(q^{100}) \) 4 * q + 7 * q^2 - 14 * q^3 + 49 * q^4 - 100 * q^5 - 136 * q^6 + 489 * q^8 + 774 * q^9 - 175 * q^10 + 770 * q^11 - 840 * q^12 - 58 * q^13 + 350 * q^15 - 615 * q^16 - 2006 * q^17 - 1409 * q^18 - 564 * q^19 - 1225 * q^20 - 1736 * q^22 - 6340 * q^23 + 6244 * q^24 + 2500 * q^25 + 8730 * q^26 + 7438 * q^27 + 8066 * q^29 + 3400 * q^30 + 5856 * q^31 - 3495 * q^32 + 8130 * q^33 - 3402 * q^34 - 28759 * q^36 + 29544 * q^37 + 36860 * q^38 + 57466 * q^39 - 12225 * q^40 - 13156 * q^41 - 5692 * q^43 + 44952 * q^44 - 19350 * q^45 + 30928 * q^46 - 39926 * q^47 + 57156 * q^48 + 4375 * q^50 + 9830 * q^51 + 23398 * q^52 + 20300 * q^53 - 77292 * q^54 - 19250 * q^55 - 50876 * q^57 - 22234 * q^58 - 8432 * q^59 + 21000 * q^60 - 30540 * q^61 + 137568 * q^62 + 37121 * q^64 + 1450 * q^65 + 166756 * q^66 + 32792 * q^67 + 72554 * q^68 + 36540 * q^69 - 83920 * q^71 - 71795 * q^72 + 75424 * q^73 + 168762 * q^74 - 8750 * q^75 + 125092 * q^76 - 89204 * q^78 + 129486 * q^79 + 15375 * q^80 + 146308 * q^81 - 247230 * q^82 + 187520 * q^83 + 50150 * q^85 + 36156 * q^86 + 238670 * q^87 + 475556 * q^88 + 30324 * q^89 + 35225 * q^90 + 124464 * q^92 + 8256 * q^93 - 245756 * q^94 + 14100 * q^95 - 172340 * q^96 - 180270 * q^97 - 420668 * q^99

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