LMFDB - Embedded newform 245.6.a.m.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [245,6,Mod(1,245)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("245.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$39.2940358542$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 246 x^{8} - 192 x^{7} + 20336 x^{6} + 25380 x^{5} - 639206 x^{4} - 722920 x^{3} + \cdots - 22888100 $ x^10 - 246x^8 - 192x^7 + 20336x^6 + 25380x^5 - 639206x^4 - 722920x^3 + 7583055x^2 + 5935300x - 22888100
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{3}\cdot 7^{5} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$1.63335$ 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)

$f(q)$	$=$	$q-0.633352 q^{2} +19.5171 q^{3} -31.5989 q^{4} +25.0000 q^{5} -12.3612 q^{6} +40.2804 q^{8} +137.918 q^{9} +O(q^{10})$	\(q-0.633352 q^{2} +19.5171 q^{3} -31.5989 q^{4} +25.0000 q^{5} -12.3612 q^{6} +40.2804 q^{8} +137.918 q^{9} -15.8338 q^{10} +76.2344 q^{11} -616.719 q^{12} +266.495 q^{13} +487.928 q^{15} +985.652 q^{16} +267.518 q^{17} -87.3504 q^{18} -1763.32 q^{19} -789.972 q^{20} -48.2831 q^{22} +4413.22 q^{23} +786.158 q^{24} +625.000 q^{25} -168.785 q^{26} -2050.90 q^{27} +129.019 q^{29} -309.030 q^{30} +5981.45 q^{31} -1913.24 q^{32} +1487.87 q^{33} -169.433 q^{34} -4358.04 q^{36} +8909.64 q^{37} +1116.80 q^{38} +5201.22 q^{39} +1007.01 q^{40} +9262.01 q^{41} -6782.24 q^{43} -2408.92 q^{44} +3447.94 q^{45} -2795.12 q^{46} +25145.7 q^{47} +19237.1 q^{48} -395.845 q^{50} +5221.19 q^{51} -8420.94 q^{52} -3066.58 q^{53} +1298.94 q^{54} +1905.86 q^{55} -34415.0 q^{57} -81.7146 q^{58} -23669.3 q^{59} -15418.0 q^{60} +32287.4 q^{61} -3788.36 q^{62} -30329.1 q^{64} +6662.38 q^{65} -942.348 q^{66} -31965.8 q^{67} -8453.28 q^{68} +86133.2 q^{69} +59587.9 q^{71} +5555.39 q^{72} -24102.7 q^{73} -5642.93 q^{74} +12198.2 q^{75} +55719.0 q^{76} -3294.20 q^{78} +107001. q^{79} +24641.3 q^{80} -73541.7 q^{81} -5866.11 q^{82} +5517.40 q^{83} +6687.96 q^{85} +4295.54 q^{86} +2518.08 q^{87} +3070.75 q^{88} +39714.8 q^{89} -2183.76 q^{90} -139453. q^{92} +116741. q^{93} -15926.0 q^{94} -44083.0 q^{95} -37340.9 q^{96} -131282. q^{97} +10514.1 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 10 q^{2} + 58 q^{3} + 182 q^{4} + 250 q^{5} + 144 q^{6} + 270 q^{8} + 700 q^{9}+O(q^{10}) $ 10 * q + 10 * q^2 + 58 * q^3 + 182 * q^4 + 250 * q^5 + 144 * q^6 + 270 * q^8 + 700 * q^9	\( 10 q + 10 q^{2} + 58 q^{3} + 182 q^{4} + 250 q^{5} + 144 q^{6} + 270 q^{8} + 700 q^{9} + 250 q^{10} + 794 q^{11} + 2560 q^{12} + 474 q^{13} + 1450 q^{15} + 2394 q^{16} + 802 q^{17} + 3702 q^{18} + 7292 q^{19} + 4550 q^{20} + 3948 q^{22} + 3708 q^{23} + 2092 q^{24} + 6250 q^{25} + 6576 q^{26} + 11818 q^{27} - 8866 q^{29} + 3600 q^{30} + 13292 q^{31} + 2590 q^{32} + 9854 q^{33} + 44468 q^{34} - 10690 q^{36} + 16124 q^{37} + 2180 q^{38} - 24982 q^{39} + 6750 q^{40} + 34836 q^{41} - 28604 q^{43} - 31120 q^{44} + 17500 q^{45} - 39732 q^{46} + 18106 q^{47} + 101788 q^{48} + 6250 q^{50} + 31602 q^{51} - 22480 q^{52} + 36440 q^{53} + 80836 q^{54} + 19850 q^{55} + 126988 q^{57} - 100356 q^{58} + 18644 q^{59} + 64000 q^{60} + 68120 q^{61} + 181052 q^{62} - 59358 q^{64} + 11850 q^{65} + 157780 q^{66} + 92328 q^{67} + 288540 q^{68} + 170888 q^{69} + 5044 q^{71} - 61654 q^{72} + 170160 q^{73} - 216584 q^{74} + 36250 q^{75} + 505180 q^{76} - 158008 q^{78} + 26442 q^{79} + 59850 q^{80} - 56314 q^{81} + 353948 q^{82} + 353360 q^{83} + 20050 q^{85} - 52940 q^{86} - 3190 q^{87} - 114916 q^{88} + 90704 q^{89} + 92550 q^{90} + 183520 q^{92} + 188560 q^{93} - 121388 q^{94} + 182300 q^{95} + 442220 q^{96} + 236382 q^{97} + 109024 q^{99}+O(q^{100}) \) 10 * q + 10 * q^2 + 58 * q^3 + 182 * q^4 + 250 * q^5 + 144 * q^6 + 270 * q^8 + 700 * q^9 + 250 * q^10 + 794 * q^11 + 2560 * q^12 + 474 * q^13 + 1450 * q^15 + 2394 * q^16 + 802 * q^17 + 3702 * q^18 + 7292 * q^19 + 4550 * q^20 + 3948 * q^22 + 3708 * q^23 + 2092 * q^24 + 6250 * q^25 + 6576 * q^26 + 11818 * q^27 - 8866 * q^29 + 3600 * q^30 + 13292 * q^31 + 2590 * q^32 + 9854 * q^33 + 44468 * q^34 - 10690 * q^36 + 16124 * q^37 + 2180 * q^38 - 24982 * q^39 + 6750 * q^40 + 34836 * q^41 - 28604 * q^43 - 31120 * q^44 + 17500 * q^45 - 39732 * q^46 + 18106 * q^47 + 101788 * q^48 + 6250 * q^50 + 31602 * q^51 - 22480 * q^52 + 36440 * q^53 + 80836 * q^54 + 19850 * q^55 + 126988 * q^57 - 100356 * q^58 + 18644 * q^59 + 64000 * q^60 + 68120 * q^61 + 181052 * q^62 - 59358 * q^64 + 11850 * q^65 + 157780 * q^66 + 92328 * q^67 + 288540 * q^68 + 170888 * q^69 + 5044 * q^71 - 61654 * q^72 + 170160 * q^73 - 216584 * q^74 + 36250 * q^75 + 505180 * q^76 - 158008 * q^78 + 26442 * q^79 + 59850 * q^80 - 56314 * q^81 + 353948 * q^82 + 353360 * q^83 + 20050 * q^85 - 52940 * q^86 - 3190 * q^87 - 114916 * q^88 + 90704 * q^89 + 92550 * q^90 + 183520 * q^92 + 188560 * q^93 - 121388 * q^94 + 182300 * q^95 + 442220 * q^96 + 236382 * q^97 + 109024 * 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 $

$2$	−0.633352	−0.111962	−0.0559809	−	0.998432i	$-0.517829\pi$
$2$	−0.633352	−0.111962	−0.0559809	+	0.998432i	$0.517829\pi$
$3$	19.5171	1.25202	0.626012	−	0.779814i	$-0.284686\pi$
$3$	19.5171	1.25202	0.626012	+	0.779814i	$0.284686\pi$
$4$	−31.5989	−0.987465
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	−12.3612	−0.140179
$7$	0	0
$7$	0	0
$8$	40.2804	0.222520
$9$	137.918	0.567563
$10$	−15.8338	−0.0500708
$11$	76.2344	0.189963	0.0949815	−	0.995479i	$-0.469721\pi$
$11$	76.2344	0.189963	0.0949815	+	0.995479i	$0.469721\pi$
$12$	−616.719	−1.23633
$13$	266.495	0.437352	0.218676	−	0.975798i	$-0.429826\pi$
$13$	266.495	0.437352	0.218676	+	0.975798i	$0.429826\pi$
$14$	0	0
$15$	487.928	0.559922
$16$	985.652	0.962551
$17$	267.518	0.224508	0.112254	−	0.993680i	$-0.464193\pi$
$17$	267.518	0.224508	0.112254	+	0.993680i	$0.464193\pi$
$18$	−87.3504	−0.0635453
$19$	−1763.32	−1.12059	−0.560296	−	0.828292i	$-0.689313\pi$
$19$	−1763.32	−1.12059	−0.560296	+	0.828292i	$0.689313\pi$
$20$	−789.972	−0.441608
$21$	0	0
$22$	−48.2831	−0.0212686
$23$	4413.22	1.73954	0.869772	−	0.493453i	$-0.164266\pi$
$23$	4413.22	1.73954	0.869772	+	0.493453i	$0.164266\pi$
$24$	786.158	0.278600
$25$	625.000	0.200000
$26$	−168.785	−0.0489667
$27$	−2050.90	−0.541422
$28$	0	0
$29$	129.019	0.0284879	0.0142439	−	0.999899i	$-0.495466\pi$
$29$	129.019	0.0284879	0.0142439	+	0.999899i	$0.495466\pi$
$30$	−309.030	−0.0626899
$31$	5981.45	1.11790	0.558949	−	0.829202i	$-0.311205\pi$
$31$	5981.45	1.11790	0.558949	+	0.829202i	$0.311205\pi$
$32$	−1913.24	−0.330289
$33$	1487.87	0.237838
$34$	−169.433	−0.0251363
$35$	0	0
$36$	−4358.04	−0.560448
$37$	8909.64	1.06993	0.534966	−	0.844874i	$-0.320325\pi$
$37$	8909.64	1.06993	0.534966	+	0.844874i	$0.320325\pi$
$38$	1116.80	0.125464
$39$	5201.22	0.547575
$40$	1007.01	0.0995140
$41$	9262.01	0.860490	0.430245	−	0.902712i	$-0.358427\pi$
$41$	9262.01	0.860490	0.430245	+	0.902712i	$0.358427\pi$
$42$	0	0
$43$	−6782.24	−0.559374	−0.279687	−	0.960091i	$-0.590231\pi$
$43$	−6782.24	−0.559374	−0.279687	+	0.960091i	$0.590231\pi$
$44$	−2408.92	−0.187582
$45$	3447.94	0.253822
$46$	−2795.12	−0.194763
$47$	25145.7	1.66042	0.830211	−	0.557450i	$-0.188220\pi$
$47$	25145.7	1.66042	0.830211	+	0.557450i	$0.188220\pi$
$48$	19237.1	1.20514
$49$	0	0
$50$	−395.845	−0.0223924
$51$	5221.19	0.281089
$52$	−8420.94	−0.431869
$53$	−3066.58	−0.149956	−0.0749782	−	0.997185i	$-0.523889\pi$
$53$	−3066.58	−0.149956	−0.0749782	+	0.997185i	$0.523889\pi$
$54$	1298.94	0.0606185
$55$	1905.86	0.0849540
$56$	0	0
$57$	−34415.0	−1.40301
$58$	−81.7146	−0.00318955
$59$	−23669.3	−0.885230	−0.442615	−	0.896712i	$-0.645949\pi$
$59$	−23669.3	−0.885230	−0.442615	+	0.896712i	$0.645949\pi$
$60$	−15418.0	−0.552903
$61$	32287.4	1.11099	0.555493	−	0.831521i	$-0.312529\pi$
$61$	32287.4	1.11099	0.555493	+	0.831521i	$0.312529\pi$
$62$	−3788.36	−0.125162
$63$	0	0
$64$	−30329.1	−0.925571
$65$	6662.38	0.195590
$66$	−942.348	−0.0266288
$67$	−31965.8	−0.869960	−0.434980	−	0.900440i	$-0.643245\pi$
$67$	−31965.8	−0.869960	−0.434980	+	0.900440i	$0.643245\pi$
$68$	−8453.28	−0.221693
$69$	86133.2	2.17795
$70$	0	0
$71$	59587.9	1.40285	0.701426	−	0.712742i	$-0.252547\pi$
$71$	59587.9	1.40285	0.701426	+	0.712742i	$0.252547\pi$
$72$	5555.39	0.126294
$73$	−24102.7	−0.529370	−0.264685	−	0.964335i	$-0.585268\pi$
$73$	−24102.7	−0.529370	−0.264685	+	0.964335i	$0.585268\pi$
$74$	−5642.93	−0.119791
$75$	12198.2	0.250405
$76$	55719.0	1.10655
$77$	0	0
$78$	−3294.20	−0.0613074
$79$	107001.	1.92895	0.964474	−	0.264178i	$-0.0851007\pi$
$79$	107001.	1.92895	0.964474	+	0.264178i	$0.0851007\pi$
$80$	24641.3	0.430466
$81$	−73541.7	−1.24544
$82$	−5866.11	−0.0963420
$83$	5517.40	0.0879101	0.0439551	−	0.999034i	$-0.486004\pi$
$83$	5517.40	0.0879101	0.0439551	+	0.999034i	$0.486004\pi$
$84$	0	0
$85$	6687.96	0.100403
$86$	4295.54	0.0626285
$87$	2518.08	0.0356675
$88$	3070.75	0.0422706
$89$	39714.8	0.531469	0.265734	−	0.964046i	$-0.414386\pi$
$89$	39714.8	0.531469	0.265734	+	0.964046i	$0.414386\pi$
$90$	−2183.76	−0.0284183
$91$	0	0
$92$	−139453.	−1.71774
$93$	116741.	1.39963
$94$	−15926.0	−0.185904
$95$	−44083.0	−0.501144
$96$	−37340.9	−0.413530
$97$	−131282.	−1.41670	−0.708348	−	0.705864i	$-0.750559\pi$
$97$	−131282.	−1.41670	−0.708348	+	0.705864i	$0.750559\pi$
$98$	0	0
$99$	10514.1	0.107816
$100$	−19749.3	−0.197493
$101$	170783.	1.66587	0.832935	−	0.553371i	$-0.186659\pi$
$101$	170783.	1.66587	0.832935	+	0.553371i	$0.186659\pi$
$102$	−3306.85	−0.0314712
$103$	41960.6	0.389716	0.194858	−	0.980831i	$-0.437575\pi$
$103$	41960.6	0.389716	0.194858	+	0.980831i	$0.437575\pi$
$104$	10734.5	0.0973196
$105$	0	0
$106$	1942.22	0.0167894
$107$	126667.	1.06956	0.534779	−	0.844992i	$-0.320395\pi$
$107$	126667.	1.06956	0.534779	+	0.844992i	$0.320395\pi$
$108$	64806.2	0.534635
$109$	149620.	1.20621	0.603107	−	0.797661i	$-0.293929\pi$
$109$	149620.	1.20621	0.603107	+	0.797661i	$0.293929\pi$
$110$	−1207.08	−0.00951161
$111$	173890.	1.33958
$112$	0	0
$113$	84809.5	0.624810	0.312405	−	0.949949i	$-0.398865\pi$
$113$	84809.5	0.624810	0.312405	+	0.949949i	$0.398865\pi$
$114$	21796.8	0.157083
$115$	110330.	0.777948
$116$	−4076.86	−0.0281307
$117$	36754.4	0.248225
$118$	14991.0	0.0991120
$119$	0	0
$120$	19653.9	0.124594
$121$	−155239.	−0.963914
$122$	−20449.3	−0.124388
$123$	180768.	1.07735
$124$	−189007.	−1.10388
$125$	15625.0	0.0894427
$126$	0	0
$127$	−248125.	−1.36509	−0.682545	−	0.730844i	$-0.739127\pi$
$127$	−248125.	−1.36509	−0.682545	+	0.730844i	$0.739127\pi$
$128$	80432.6	0.433918
$129$	−132370.	−0.700349
$130$	−4219.63	−0.0218986
$131$	261050.	1.32906	0.664532	−	0.747260i	$-0.268631\pi$
$131$	261050.	1.32906	0.664532	+	0.747260i	$0.268631\pi$
$132$	−47015.1	−0.234857
$133$	0	0
$134$	20245.6	0.0974022
$135$	−51272.6	−0.242131
$136$	10775.8	0.0499575
$137$	−16931.3	−0.0770706	−0.0385353	−	0.999257i	$-0.512269\pi$
$137$	−16931.3	−0.0770706	−0.0385353	+	0.999257i	$0.512269\pi$
$138$	−54552.6	−0.243847
$139$	−179252.	−0.786914	−0.393457	−	0.919343i	$-0.628721\pi$
$139$	−179252.	−0.786914	−0.393457	+	0.919343i	$0.628721\pi$
$140$	0	0
$141$	490771.	2.07889
$142$	−37740.1	−0.157066
$143$	20316.1	0.0830806
$144$	135939.	0.546308
$145$	3225.48	0.0127402
$146$	15265.5	0.0592692
$147$	0	0
$148$	−281535.	−1.05652
$149$	−376763.	−1.39028	−0.695140	−	0.718875i	$-0.744658\pi$
$149$	−376763.	−1.39028	−0.695140	+	0.718875i	$0.744658\pi$
$150$	−7725.75	−0.0280358
$151$	−355503.	−1.26882	−0.634412	−	0.772995i	$-0.718758\pi$
$151$	−355503.	−1.26882	−0.634412	+	0.772995i	$0.718758\pi$
$152$	−71027.4	−0.249354
$153$	36895.5	0.127422
$154$	0	0
$155$	149536.	0.499939
$156$	−164353.	−0.540711
$157$	−491459.	−1.59125	−0.795624	−	0.605791i	$-0.792857\pi$
$157$	−491459.	−1.59125	−0.795624	+	0.605791i	$0.792857\pi$
$158$	−67769.3	−0.215968
$159$	−59850.8	−0.187749
$160$	−47831.0	−0.147710
$161$	0	0
$162$	46577.8	0.139441
$163$	−143009.	−0.421593	−0.210796	−	0.977530i	$-0.567606\pi$
$163$	−143009.	−0.421593	−0.210796	+	0.977530i	$0.567606\pi$
$164$	−292669.	−0.849703
$165$	37196.9	0.106364
$166$	−3494.45	−0.00984258
$167$	−313947.	−0.871094	−0.435547	−	0.900166i	$-0.643445\pi$
$167$	−313947.	−0.871094	−0.435547	+	0.900166i	$0.643445\pi$
$168$	0	0
$169$	−300273.	−0.808723
$170$	−4235.83	−0.0112413
$171$	−243193.	−0.636006
$172$	214311.	0.552362
$173$	−437124.	−1.11043	−0.555213	−	0.831708i	$-0.687363\pi$
$173$	−437124.	−1.11043	−0.555213	+	0.831708i	$0.687363\pi$
$174$	−1594.83	−0.00399339
$175$	0	0
$176$	75140.5	0.182849
$177$	−461957.	−1.10833
$178$	−25153.5	−0.0595042
$179$	−391475.	−0.913211	−0.456605	−	0.889669i	$-0.650935\pi$
$179$	−391475.	−0.913211	−0.456605	+	0.889669i	$0.650935\pi$
$180$	−108951.	−0.250640
$181$	−82459.5	−0.187087	−0.0935437	−	0.995615i	$-0.529819\pi$
$181$	−82459.5	−0.187087	−0.0935437	+	0.995615i	$0.529819\pi$
$182$	0	0
$183$	630157.	1.39098
$184$	177766.	0.387084
$185$	222741.	0.478488
$186$	−73937.9	−0.156706
$187$	20394.1	0.0426482
$188$	−794574.	−1.63961
$189$	0	0
$190$	27920.1	0.0561090
$191$	−849381.	−1.68469	−0.842343	−	0.538942i	$-0.818824\pi$
$191$	−849381.	−1.68469	−0.842343	+	0.538942i	$0.818824\pi$
$192$	−591937.	−1.15884
$193$	284540.	0.549857	0.274928	−	0.961465i	$-0.411346\pi$
$193$	284540.	0.549857	0.274928	+	0.961465i	$0.411346\pi$
$194$	83147.8	0.158616
$195$	130030.	0.244883
$196$	0	0
$197$	554266.	1.01754	0.508772	−	0.860902i	$-0.330100\pi$
$197$	554266.	1.01754	0.508772	+	0.860902i	$0.330100\pi$
$198$	−6659.10	−0.0120713
$199$	635373.	1.13735	0.568677	−	0.822561i	$-0.307455\pi$
$199$	635373.	1.13735	0.568677	+	0.822561i	$0.307455\pi$
$200$	25175.3	0.0445040
$201$	−623881.	−1.08921
$202$	−108166.	−0.186514
$203$	0	0
$204$	−164984.	−0.277565
$205$	231550.	0.384823
$206$	−26575.8	−0.0436333
$207$	608661.	0.987301
$208$	262671.	0.420973
$209$	−134426.	−0.212871
$210$	0	0
$211$	−280331.	−0.433476	−0.216738	−	0.976230i	$-0.569542\pi$
$211$	−280331.	−0.433476	−0.216738	+	0.976230i	$0.569542\pi$
$212$	96900.5	0.148077
$213$	1.16298e6	1.75640
$214$	−80224.8	−0.119750
$215$	−169556.	−0.250160
$216$	−82611.3	−0.120477
$217$	0	0
$218$	−94762.2	−0.135050
$219$	−470416.	−0.662783
$220$	−60223.0	−0.0838891
$221$	71292.3	0.0981888
$222$	−110134.	−0.149982
$223$	−970109.	−1.30635	−0.653173	−	0.757208i	$-0.726563\pi$
$223$	−970109.	−1.30635	−0.653173	+	0.757208i	$0.726563\pi$
$224$	0	0
$225$	86198.6	0.113513
$226$	−53714.2	−0.0699549
$227$	569413.	0.733437	0.366719	−	0.930332i	$-0.380481\pi$
$227$	569413.	0.733437	0.366719	+	0.930332i	$0.380481\pi$
$228$	1.08747e6	1.38542
$229$	77988.6	0.0982748	0.0491374	−	0.998792i	$-0.484353\pi$
$229$	77988.6	0.0982748	0.0491374	+	0.998792i	$0.484353\pi$
$230$	−69877.9	−0.0871005
$231$	0	0
$232$	5196.95	0.00633912
$233$	829373.	1.00083	0.500415	−	0.865786i	$-0.333181\pi$
$233$	829373.	1.00083	0.500415	+	0.865786i	$0.333181\pi$
$234$	−23278.5	−0.0277917
$235$	628641.	0.742563
$236$	747924.	0.874133
$237$	2.08835e6	2.41509
$238$	0	0
$239$	252273.	0.285678	0.142839	−	0.989746i	$-0.454377\pi$
$239$	252273.	0.285678	0.142839	+	0.989746i	$0.454377\pi$
$240$	480927.	0.538953
$241$	−535968.	−0.594424	−0.297212	−	0.954812i	$-0.596057\pi$
$241$	−535968.	−0.594424	−0.297212	+	0.954812i	$0.596057\pi$
$242$	98321.1	0.107922
$243$	−936953.	−1.01789
$244$	−1.02025e6	−1.09706
$245$	0	0
$246$	−114490.	−0.120622
$247$	−469917.	−0.490093
$248$	240935.	0.248755
$249$	107684.	0.110066
$250$	−9896.12	−0.0100142
$251$	−52953.6	−0.0530531	−0.0265266	−	0.999648i	$-0.508445\pi$
$251$	−52953.6	−0.0530531	−0.0265266	+	0.999648i	$0.508445\pi$
$252$	0	0
$253$	336439.	0.330449
$254$	157150.	0.152838
$255$	130530.	0.125707
$256$	919589.	0.876989
$257$	−527109.	−0.497814	−0.248907	−	0.968527i	$-0.580071\pi$
$257$	−527109.	−0.497814	−0.248907	+	0.968527i	$0.580071\pi$
$258$	83836.6	0.0784123
$259$	0	0
$260$	−210524.	−0.193138
$261$	17794.1	0.0161686
$262$	−165337.	−0.148804
$263$	−1.26966e6	−1.13187	−0.565935	−	0.824450i	$-0.691485\pi$
$263$	−1.26966e6	−1.13187	−0.565935	+	0.824450i	$0.691485\pi$
$264$	59932.2	0.0529238
$265$	−76664.6	−0.0670625
$266$	0	0
$267$	775119.	0.665412
$268$	1.01008e6	0.859054
$269$	863268.	0.727386	0.363693	−	0.931519i	$-0.381516\pi$
$269$	863268.	0.727386	0.363693	+	0.931519i	$0.381516\pi$
$270$	32473.6	0.0271094
$271$	1.82397e6	1.50867	0.754335	−	0.656490i	$-0.227960\pi$
$271$	1.82397e6	1.50867	0.754335	+	0.656490i	$0.227960\pi$
$272$	263680.	0.216100
$273$	0	0
$274$	10723.5	0.00862896
$275$	47646.5	0.0379926
$276$	−2.72171e6	−2.15065
$277$	−2.09940e6	−1.64398	−0.821990	−	0.569503i	$-0.807136\pi$
$277$	−2.09940e6	−1.64398	−0.821990	+	0.569503i	$0.807136\pi$
$278$	113530.	0.0881042
$279$	824948.	0.634477
$280$	0	0
$281$	−1.72140e6	−1.30052	−0.650260	−	0.759712i	$-0.725340\pi$
$281$	−1.72140e6	−1.30052	−0.650260	+	0.759712i	$0.725340\pi$
$282$	−310830.	−0.232756
$283$	2.53726e6	1.88321	0.941606	−	0.336716i	$-0.109316\pi$
$283$	2.53726e6	1.88321	0.941606	+	0.336716i	$0.109316\pi$
$284$	−1.88291e6	−1.38527
$285$	−860374.	−0.627444
$286$	−12867.2	−0.00930186
$287$	0	0
$288$	−263869.	−0.187460
$289$	−1.34829e6	−0.949596
$290$	−2042.86	−0.00142641
$291$	−2.56225e6	−1.77374
$292$	761619.	0.522734
$293$	1.14064e6	0.776213	0.388106	−	0.921615i	$-0.373129\pi$
$293$	1.14064e6	0.776213	0.388106	+	0.921615i	$0.373129\pi$
$294$	0	0
$295$	−591734.	−0.395887
$296$	358884.	0.238081
$297$	−156349.	−0.102850
$298$	238623.	0.155658
$299$	1.17610e6	0.760793
$300$	−385449.	−0.247266
$301$	0	0
$302$	225158.	0.142060
$303$	3.33319e6	2.08571
$304$	−1.73802e6	−1.07863
$305$	807186.	0.496848
$306$	−23367.8	−0.0142664
$307$	1.50913e6	0.913861	0.456931	−	0.889502i	$-0.348949\pi$
$307$	1.50913e6	0.913861	0.456931	+	0.889502i	$0.348949\pi$
$308$	0	0
$309$	818950.	0.487934
$310$	−94709.0	−0.0559741
$311$	−3.37087e6	−1.97625	−0.988124	−	0.153660i	$-0.950894\pi$
$311$	−3.37087e6	−1.97625	−0.988124	+	0.153660i	$0.950894\pi$
$312$	209507.	0.121846
$313$	−427067.	−0.246397	−0.123198	−	0.992382i	$-0.539315\pi$
$313$	−427067.	−0.246397	−0.123198	+	0.992382i	$0.539315\pi$
$314$	311266.	0.178159
$315$	0	0
$316$	−3.38111e6	−1.90477
$317$	−868486.	−0.485417	−0.242708	−	0.970099i	$-0.578036\pi$
$317$	−868486.	−0.485417	−0.242708	+	0.970099i	$0.578036\pi$
$318$	37906.6	0.0210207
$319$	9835.70	0.00541164
$320$	−758228.	−0.413928
$321$	2.47218e6	1.33911
$322$	0	0
$323$	−471721.	−0.251582
$324$	2.32383e6	1.22982
$325$	166559.	0.0874703
$326$	90574.7	0.0472023
$327$	2.92016e6	1.51021
$328$	373078.	0.191476
$329$	0	0
$330$	−23558.7	−0.0119088
$331$	−1.48917e6	−0.747092	−0.373546	−	0.927612i	$-0.621858\pi$
$331$	−1.48917e6	−0.747092	−0.373546	+	0.927612i	$0.621858\pi$
$332$	−174343.	−0.0868082
$333$	1.22880e6	0.607253
$334$	198839.	0.0975293
$335$	−799146.	−0.389058
$336$	0	0
$337$	1.73365e6	0.831547	0.415773	−	0.909468i	$-0.363511\pi$
$337$	1.73365e6	0.831547	0.415773	+	0.909468i	$0.363511\pi$
$338$	190179.	0.0905461
$339$	1.65524e6	0.782277
$340$	−211332.	−0.0991443
$341$	455992.	0.212359
$342$	154027.	0.0712084
$343$	0	0
$344$	−273192.	−0.124472
$345$	2.15333e6	0.974009
$346$	276853.	0.124325
$347$	−3.26650e6	−1.45633	−0.728164	−	0.685403i	$-0.759626\pi$
$347$	−3.26650e6	−1.45633	−0.728164	+	0.685403i	$0.759626\pi$
$348$	−79568.6	−0.0352204
$349$	4.01741e6	1.76556	0.882779	−	0.469788i	$-0.155670\pi$
$349$	4.01741e6	1.76556	0.882779	+	0.469788i	$0.155670\pi$
$350$	0	0
$351$	−546555.	−0.236792
$352$	−145854.	−0.0627427
$353$	2.44907e6	1.04608	0.523040	−	0.852308i	$-0.324798\pi$
$353$	2.44907e6	1.04608	0.523040	+	0.852308i	$0.324798\pi$
$354$	292581.	0.124090
$355$	1.48970e6	0.627375
$356$	−1.25494e6	−0.524807
$357$	0	0
$358$	247941.	0.102245
$359$	−177274.	−0.0725954	−0.0362977	−	0.999341i	$-0.511556\pi$
$359$	−177274.	−0.0725954	−0.0362977	+	0.999341i	$0.511556\pi$
$360$	138885.	0.0564804
$361$	633205.	0.255727
$362$	52225.9	0.0209466
$363$	−3.02982e6	−1.20684
$364$	0	0
$365$	−602568.	−0.236741
$366$	−399111.	−0.155737
$367$	3.26871e6	1.26681	0.633405	−	0.773820i	$-0.281657\pi$
$367$	3.26871e6	1.26681	0.633405	+	0.773820i	$0.281657\pi$
$368$	4.34990e6	1.67440
$369$	1.27740e6	0.488382
$370$	−141073.	−0.0535724
$371$	0	0
$372$	−3.68887e6	−1.38209
$373$	3.59046e6	1.33622	0.668110	−	0.744062i	$-0.267104\pi$
$373$	3.59046e6	1.33622	0.668110	+	0.744062i	$0.267104\pi$
$374$	−12916.6	−0.00477496
$375$	304955.	0.111984
$376$	1.01288e6	0.369477
$377$	34383.0	0.0124592
$378$	0	0
$379$	−444241.	−0.158862	−0.0794312	−	0.996840i	$-0.525310\pi$
$379$	−444241.	−0.158862	−0.0794312	+	0.996840i	$0.525310\pi$
$380$	1.39297e6	0.494862
$381$	−4.84268e6	−1.70912
$382$	537957.	0.188621
$383$	−4.56035e6	−1.58855	−0.794275	−	0.607558i	$-0.792149\pi$
$383$	−4.56035e6	−1.58855	−0.794275	+	0.607558i	$0.792149\pi$
$384$	1.56981e6	0.543275
$385$	0	0
$386$	−180214.	−0.0615629
$387$	−935391.	−0.317480
$388$	4.14837e6	1.39894
$389$	2.50465e6	0.839215	0.419608	−	0.907706i	$-0.362168\pi$
$389$	2.50465e6	0.839215	0.419608	+	0.907706i	$0.362168\pi$
$390$	−82354.9	−0.0274175
$391$	1.18062e6	0.390541
$392$	0	0
$393$	5.09495e6	1.66402
$394$	−351045.	−0.113926
$395$	2.67503e6	0.862652
$396$	−332233.	−0.106464
$397$	2.38913e6	0.760787	0.380394	−	0.924825i	$-0.375789\pi$
$397$	2.38913e6	0.760787	0.380394	+	0.924825i	$0.375789\pi$
$398$	−402414.	−0.127340
$399$	0	0
$400$	616033.	0.192510
$401$	62929.2	0.0195430	0.00977150	−	0.999952i	$-0.496890\pi$
$401$	62929.2	0.0195430	0.00977150	+	0.999952i	$0.496890\pi$
$402$	395136.	0.121950
$403$	1.59403e6	0.488915
$404$	−5.39655e6	−1.64499
$405$	−1.83854e6	−0.556976
$406$	0	0
$407$	679221.	0.203247
$408$	210312.	0.0625479
$409$	404988.	0.119711	0.0598555	−	0.998207i	$-0.480936\pi$
$409$	404988.	0.119711	0.0598555	+	0.998207i	$0.480936\pi$
$410$	−146653.	−0.0430855
$411$	−330450.	−0.0964942
$412$	−1.32591e6	−0.384831
$413$	0	0
$414$	−385496.	−0.110540
$415$	137935.	0.0393146
$416$	−509869.	−0.144452
$417$	−3.49848e6	−0.985234
$418$	85138.7	0.0238334
$419$	−1.73727e6	−0.483429	−0.241714	−	0.970347i	$-0.577710\pi$
$419$	−1.73727e6	−0.483429	−0.241714	+	0.970347i	$0.577710\pi$
$420$	0	0
$421$	3.09244e6	0.850347	0.425174	−	0.905112i	$-0.360213\pi$
$421$	3.09244e6	0.850347	0.425174	+	0.905112i	$0.360213\pi$
$422$	177548.	0.0485328
$423$	3.46803e6	0.942393
$424$	−123523.	−0.0333683
$425$	167199.	0.0449015
$426$	−736577.	−0.196650
$427$	0	0
$428$	−4.00254e6	−1.05615
$429$	396511.	0.104019
$430$	107389.	0.0280083
$431$	−3.04862e6	−0.790515	−0.395258	−	0.918570i	$-0.629345\pi$
$431$	−3.04862e6	−0.790515	−0.395258	+	0.918570i	$0.629345\pi$
$432$	−2.02148e6	−0.521146
$433$	−986108.	−0.252758	−0.126379	−	0.991982i	$-0.540336\pi$
$433$	−986108.	−0.252758	−0.126379	+	0.991982i	$0.540336\pi$
$434$	0	0
$435$	62952.1	0.0159510
$436$	−4.72783e6	−1.19109
$437$	−7.78192e6	−1.94932
$438$	297939.	0.0742064
$439$	3.69313e6	0.914603	0.457302	−	0.889312i	$-0.348816\pi$
$439$	3.69313e6	0.914603	0.457302	+	0.889312i	$0.348816\pi$
$440$	76768.8	0.0189040
$441$	0	0
$442$	−45153.1	−0.0109934
$443$	1.92890e6	0.466983	0.233492	−	0.972359i	$-0.424985\pi$
$443$	1.92890e6	0.466983	0.233492	+	0.972359i	$0.424985\pi$
$444$	−5.49474e6	−1.32279
$445$	992871.	0.237680
$446$	614420.	0.146261
$447$	−7.35332e6	−1.74066
$448$	0	0
$449$	4.12359e6	0.965295	0.482647	−	0.875815i	$-0.339675\pi$
$449$	4.12359e6	0.965295	0.482647	+	0.875815i	$0.339675\pi$
$450$	−54594.0	−0.0127091
$451$	706084.	0.163461
$452$	−2.67988e6	−0.616978
$453$	−6.93840e6	−1.58860
$454$	−360639.	−0.0821170
$455$	0	0
$456$	−1.38625e6	−0.312197
$457$	−3.96950e6	−0.889089	−0.444544	−	0.895757i	$-0.646634\pi$
$457$	−3.96950e6	−0.889089	−0.444544	+	0.895757i	$0.646634\pi$
$458$	−49394.2	−0.0110030
$459$	−548654.	−0.121553
$460$	−3.48632e6	−0.768196
$461$	3.39581e6	0.744202	0.372101	−	0.928192i	$-0.378638\pi$
$461$	3.39581e6	0.744202	0.372101	+	0.928192i	$0.378638\pi$
$462$	0	0
$463$	1.05461e6	0.228633	0.114317	−	0.993444i	$-0.463532\pi$
$463$	1.05461e6	0.228633	0.114317	+	0.993444i	$0.463532\pi$
$464$	127168.	0.0274210
$465$	2.91852e6	0.625936
$466$	−525285.	−0.112055
$467$	984239.	0.208837	0.104419	−	0.994533i	$-0.466702\pi$
$467$	984239.	0.208837	0.104419	+	0.994533i	$0.466702\pi$
$468$	−1.16140e6	−0.245113
$469$	0	0
$470$	−398151.	−0.0831387
$471$	−9.59186e6	−1.99228
$472$	−953412.	−0.196982
$473$	−517040.	−0.106260
$474$	−1.32266e6	−0.270398
$475$	−1.10208e6	−0.224118
$476$	0	0
$477$	−422936.	−0.0851097
$478$	−159778.	−0.0319850
$479$	−5.10476e6	−1.01657	−0.508284	−	0.861189i	$-0.669720\pi$
$479$	−5.10476e6	−1.01657	−0.508284	+	0.861189i	$0.669720\pi$
$480$	−933522.	−0.184936
$481$	2.37438e6	0.467936
$482$	339456.	0.0665527
$483$	0	0
$484$	4.90539e6	0.951831
$485$	−3.28206e6	−0.633566
$486$	593420.	0.113965
$487$	6.71429e6	1.28286	0.641428	−	0.767184i	$-0.278342\pi$
$487$	6.71429e6	1.28286	0.641428	+	0.767184i	$0.278342\pi$
$488$	1.30055e6	0.247217
$489$	−2.79111e6	−0.527844
$490$	0	0
$491$	8.62514e6	1.61459	0.807295	−	0.590148i	$-0.200931\pi$
$491$	8.62514e6	1.61459	0.807295	+	0.590148i	$0.200931\pi$
$492$	−5.71206e6	−1.06385
$493$	34515.0	0.00639574
$494$	297622.	0.0548717
$495$	262852.	0.0482167
$496$	5.89563e6	1.07603
$497$	0	0
$498$	−68201.6	−0.0123231
$499$	−9.39508e6	−1.68908	−0.844538	−	0.535496i	$-0.820125\pi$
$499$	−9.39508e6	−1.68908	−0.844538	+	0.535496i	$0.820125\pi$
$500$	−493732.	−0.0883215
$501$	−6.12734e6	−1.09063
$502$	33538.2	0.00593993
$503$	−429394.	−0.0756722	−0.0378361	−	0.999284i	$-0.512046\pi$
$503$	−429394.	−0.0756722	−0.0378361	+	0.999284i	$0.512046\pi$
$504$	0	0
$505$	4.26957e6	0.745000
$506$	−213084.	−0.0369977
$507$	−5.86047e6	−1.01254
$508$	7.84047e6	1.34798
$509$	−248510.	−0.0425157	−0.0212579	−	0.999774i	$-0.506767\pi$
$509$	−248510.	−0.0425157	−0.0212579	+	0.999774i	$0.506767\pi$
$510$	−82671.2	−0.0140744
$511$	0	0
$512$	−3.15627e6	−0.532107
$513$	3.61640e6	0.606713
$514$	333845.	0.0557362
$515$	1.04901e6	0.174286
$516$	4.18273e6	0.691570
$517$	1.91696e6	0.315419
$518$	0	0
$519$	−8.53140e6	−1.39028
$520$	268364.	0.0435226
$521$	−4.77060e6	−0.769979	−0.384990	−	0.922921i	$-0.625795\pi$
$521$	−4.77060e6	−0.769979	−0.384990	+	0.922921i	$0.625795\pi$
$522$	−11269.9	−0.00181027
$523$	2.70325e6	0.432148	0.216074	−	0.976377i	$-0.430675\pi$
$523$	2.70325e6	0.432148	0.216074	+	0.976377i	$0.430675\pi$
$524$	−8.24889e6	−1.31240
$525$	0	0
$526$	804139.	0.126726
$527$	1.60015e6	0.250977
$528$	1.46653e6	0.228931
$529$	1.30401e7	2.02602
$530$	48555.6	0.00750844
$531$	−3.26442e6	−0.502424
$532$	0	0
$533$	2.46828e6	0.376337
$534$	−490923.	−0.0745007
$535$	3.16668e6	0.478321
$536$	−1.28760e6	−0.193584
$537$	−7.64046e6	−1.14336
$538$	−546752.	−0.0814395
$539$	0	0
$540$	1.62015e6	0.239096
$541$	−5.93736e6	−0.872168	−0.436084	−	0.899906i	$-0.643635\pi$
$541$	−5.93736e6	−0.872168	−0.436084	+	0.899906i	$0.643635\pi$
$542$	−1.15521e6	−0.168913
$543$	−1.60937e6	−0.234238
$544$	−511826.	−0.0741524
$545$	3.74051e6	0.539435
$546$	0	0
$547$	−1.27658e7	−1.82422	−0.912112	−	0.409941i	$-0.865549\pi$
$547$	−1.27658e7	−1.82422	−0.912112	+	0.409941i	$0.865549\pi$
$548$	535010.	0.0761045
$549$	4.45301e6	0.630555
$550$	−30177.0	−0.00425372
$551$	−227503.	−0.0319233
$552$	3.46948e6	0.484638
$553$	0	0
$554$	1.32966e6	0.184063
$555$	4.34726e6	0.599078
$556$	5.66416e6	0.777049
$557$	7.25744e6	0.991163	0.495582	−	0.868561i	$-0.334955\pi$
$557$	7.25744e6	0.991163	0.495582	+	0.868561i	$0.334955\pi$
$558$	−522482.	−0.0710372
$559$	−1.80743e6	−0.244643
$560$	0	0
$561$	398034.	0.0533965
$562$	1.09025e6	0.145609
$563$	6.52782e6	0.867955	0.433977	−	0.900924i	$-0.357110\pi$
$563$	6.52782e6	0.867955	0.433977	+	0.900924i	$0.357110\pi$
$564$	−1.55078e7	−2.05283
$565$	2.12024e6	0.279424
$566$	−1.60698e6	−0.210848
$567$	0	0
$568$	2.40023e6	0.312163
$569$	3.51551e6	0.455206	0.227603	−	0.973754i	$-0.426911\pi$
$569$	3.51551e6	0.455206	0.227603	+	0.973754i	$0.426911\pi$
$570$	544919.	0.0702498
$571$	−41320.8	−0.00530370	−0.00265185	−	0.999996i	$-0.500844\pi$
$571$	−41320.8	−0.00530370	−0.00265185	+	0.999996i	$0.500844\pi$
$572$	−641965.	−0.0820392
$573$	−1.65775e7	−2.10927
$574$	0	0
$575$	2.75826e6	0.347909
$576$	−4.18292e6	−0.525320
$577$	−919163.	−0.114935	−0.0574676	−	0.998347i	$-0.518303\pi$
$577$	−919163.	−0.114935	−0.0574676	+	0.998347i	$0.518303\pi$
$578$	853942.	0.106319
$579$	5.55339e6	0.688434
$580$	−101922.	−0.0125805
$581$	0	0
$582$	1.62280e6	0.198591
$583$	−233779.	−0.0284862
$584$	−970869.	−0.117795
$585$	918860.	0.111009
$586$	−722428.	−0.0869062
$587$	−182482.	−0.0218587	−0.0109294	−	0.999940i	$-0.503479\pi$
$587$	−182482.	−0.0218587	−0.0109294	+	0.999940i	$0.503479\pi$
$588$	0	0
$589$	−1.05472e7	−1.25271
$590$	374775.	0.0443242
$591$	1.08177e7	1.27399
$592$	8.78181e6	1.02986
$593$	−1.59052e7	−1.85739	−0.928695	−	0.370846i	$-0.879068\pi$
$593$	−1.59052e7	−1.85739	−0.928695	+	0.370846i	$0.879068\pi$
$594$	99024.0	0.0115153
$595$	0	0
$596$	1.19053e7	1.37285
$597$	1.24006e7	1.42399
$598$	−744885.	−0.0851797
$599$	935648.	0.106548	0.0532740	−	0.998580i	$-0.483034\pi$
$599$	935648.	0.106548	0.0532740	+	0.998580i	$0.483034\pi$
$600$	491349.	0.0557201
$601$	6.79914e6	0.767835	0.383917	−	0.923367i	$-0.374575\pi$
$601$	6.79914e6	0.767835	0.383917	+	0.923367i	$0.374575\pi$
$602$	0	0
$603$	−4.40866e6	−0.493757
$604$	1.12335e7	1.25292
$605$	−3.88098e6	−0.431075
$606$	−2.11108e6	−0.233520
$607$	3.15831e6	0.347923	0.173962	−	0.984752i	$-0.444343\pi$
$607$	3.15831e6	0.347923	0.173962	+	0.984752i	$0.444343\pi$
$608$	3.37366e6	0.370119
$609$	0	0
$610$	−511232.	−0.0556280
$611$	6.70119e6	0.726188
$612$	−1.16586e6	−0.125825
$613$	−2.50952e6	−0.269736	−0.134868	−	0.990864i	$-0.543061\pi$
$613$	−2.50952e6	−0.269736	−0.134868	+	0.990864i	$0.543061\pi$
$614$	−955809.	−0.102318
$615$	4.51919e6	0.481807
$616$	0	0
$617$	1.18777e7	1.25608	0.628042	−	0.778179i	$-0.283857\pi$
$617$	1.18777e7	1.25608	0.628042	+	0.778179i	$0.283857\pi$
$618$	−518683.	−0.0546300
$619$	6.97529e6	0.731705	0.365852	−	0.930673i	$-0.380778\pi$
$619$	6.97529e6	0.731705	0.365852	+	0.930673i	$0.380778\pi$
$620$	−4.72518e6	−0.493672
$621$	−9.05108e6	−0.941827
$622$	2.13495e6	0.221264
$623$	0	0
$624$	5.12659e6	0.527068
$625$	390625.	0.0400000
$626$	270484.	0.0275870
$627$	−2.62360e6	−0.266520
$628$	1.55295e7	1.57130
$629$	2.38349e6	0.240208
$630$	0	0
$631$	−1.05579e7	−1.05561	−0.527807	−	0.849364i	$-0.676986\pi$
$631$	−1.05579e7	−1.05561	−0.527807	+	0.849364i	$0.676986\pi$
$632$	4.31005e6	0.429230
$633$	−5.47126e6	−0.542723
$634$	550057.	0.0543481
$635$	−6.20313e6	−0.610487
$636$	1.89122e6	0.185395
$637$	0	0
$638$	−6229.46	−0.000605897 0
$639$	8.21822e6	0.796207
$640$	2.01082e6	0.194054
$641$	−1.01477e7	−0.975488	−0.487744	−	0.872987i	$-0.662180\pi$
$641$	−1.01477e7	−0.975488	−0.487744	+	0.872987i	$0.662180\pi$
$642$	−1.56576e6	−0.149929
$643$	9.41430e6	0.897968	0.448984	−	0.893540i	$-0.351786\pi$
$643$	9.41430e6	0.897968	0.448984	+	0.893540i	$0.351786\pi$
$644$	0	0
$645$	−3.30924e6	−0.313206
$646$	298765.	0.0281675
$647$	−1.08548e7	−1.01943	−0.509717	−	0.860342i	$-0.670250\pi$
$647$	−1.08548e7	−1.01943	−0.509717	+	0.860342i	$0.670250\pi$
$648$	−2.96229e6	−0.277134
$649$	−1.80442e6	−0.168161
$650$	−105491.	−0.00979334
$651$	0	0
$652$	4.51891e6	0.416308
$653$	7.47330e6	0.685850	0.342925	−	0.939363i	$-0.388582\pi$
$653$	7.47330e6	0.685850	0.342925	+	0.939363i	$0.388582\pi$
$654$	−1.84948e6	−0.169086
$655$	6.52626e6	0.594376
$656$	9.12912e6	0.828265
$657$	−3.32419e6	−0.300451
$658$	0	0
$659$	−1.62806e7	−1.46035	−0.730176	−	0.683259i	$-0.760562\pi$
$659$	−1.62806e7	−1.46035	−0.730176	+	0.683259i	$0.760562\pi$
$660$	−1.17538e6	−0.105031
$661$	−5.36073e6	−0.477222	−0.238611	−	0.971115i	$-0.576692\pi$
$661$	−5.36073e6	−0.477222	−0.238611	+	0.971115i	$0.576692\pi$
$662$	943168.	0.0836458
$663$	1.39142e6	0.122935
$664$	222243.	0.0195618
$665$	0	0
$666$	−778261.	−0.0679891
$667$	569390.	0.0495559
$668$	9.92037e6	0.860175
$669$	−1.89337e7	−1.63558
$670$	506140.	0.0435596
$671$	2.46141e6	0.211046
$672$	0	0
$673$	−1.77331e7	−1.50920	−0.754602	−	0.656183i	$-0.772170\pi$
$673$	−1.77331e7	−1.50920	−0.754602	+	0.656183i	$0.772170\pi$
$674$	−1.09801e6	−0.0931015
$675$	−1.28181e6	−0.108284
$676$	9.48830e6	0.798586
$677$	5.82373e6	0.488348	0.244174	−	0.969731i	$-0.421483\pi$
$677$	5.82373e6	0.488348	0.244174	+	0.969731i	$0.421483\pi$
$678$	−1.04835e6	−0.0875852
$679$	0	0
$680$	269394.	0.0223417
$681$	1.11133e7	0.918281
$682$	−288803.	−0.0237761
$683$	−1.56080e7	−1.28025	−0.640126	−	0.768270i	$-0.721118\pi$
$683$	−1.56080e7	−1.28025	−0.640126	+	0.768270i	$0.721118\pi$
$684$	7.68463e6	0.628034
$685$	−423282.	−0.0344670
$686$	0	0
$687$	1.52211e6	0.123042
$688$	−6.68493e6	−0.538426
$689$	−817229.	−0.0655837
$690$	−1.36382e6	−0.109052
$691$	8.52021e6	0.678821	0.339410	−	0.940638i	$-0.389772\pi$
$691$	8.52021e6	0.678821	0.339410	+	0.940638i	$0.389772\pi$
$692$	1.38126e7	1.09651
$693$	0	0
$694$	2.06884e6	0.163053
$695$	−4.48130e6	−0.351918
$696$	101430.	0.00793673
$697$	2.47776e6	0.193187
$698$	−2.54443e6	−0.197675
$699$	1.61870e7	1.25306
$700$	0	0
$701$	−5.48253e6	−0.421392	−0.210696	−	0.977552i	$-0.567573\pi$
$701$	−5.48253e6	−0.421392	−0.210696	+	0.977552i	$0.567573\pi$
$702$	346162.	0.0265116
$703$	−1.57106e7	−1.19896
$704$	−2.31212e6	−0.175824
$705$	1.22693e7	0.929706
$706$	−1.55112e6	−0.117121
$707$	0	0
$708$	1.45973e7	1.09444
$709$	−1.75446e7	−1.31078	−0.655388	−	0.755292i	$-0.727495\pi$
$709$	−1.75446e7	−1.31078	−0.655388	+	0.755292i	$0.727495\pi$
$710$	−943502.	−0.0702420
$711$	1.47573e7	1.09480
$712$	1.59973e6	0.118263
$713$	2.63974e7	1.94463
$714$	0	0
$715$	507902.	0.0371548
$716$	1.23702e7	0.901763
$717$	4.92365e6	0.357675
$718$	112277.	0.00812791
$719$	2.90492e6	0.209562	0.104781	−	0.994495i	$-0.466586\pi$
$719$	2.90492e6	0.209562	0.104781	+	0.994495i	$0.466586\pi$
$720$	3.39847e6	0.244316
$721$	0	0
$722$	−401042.	−0.0286317
$723$	−1.04605e7	−0.744232
$724$	2.60563e6	0.184742
$725$	80637.1	0.00569757
$726$	1.91894e6	0.135120
$727$	1.58709e7	1.11369	0.556846	−	0.830616i	$-0.312012\pi$
$727$	1.58709e7	1.11369	0.556846	+	0.830616i	$0.312012\pi$
$728$	0	0
$729$	−415975.	−0.0289900
$730$	381638.	0.0265060
$731$	−1.81437e6	−0.125584
$732$	−1.99123e7	−1.37354
$733$	2.22308e7	1.52825	0.764127	−	0.645065i	$-0.223170\pi$
$733$	2.22308e7	1.52825	0.764127	+	0.645065i	$0.223170\pi$
$734$	−2.07025e6	−0.141834
$735$	0	0
$736$	−8.44353e6	−0.574552
$737$	−2.43690e6	−0.165260
$738$	−809041.	−0.0546801
$739$	2.25210e7	1.51697	0.758484	−	0.651691i	$-0.225940\pi$
$739$	2.25210e7	1.51697	0.758484	+	0.651691i	$0.225940\pi$
$740$	−7.03836e6	−0.472490
$741$	−9.17142e6	−0.613608
$742$	0	0
$743$	−1.71099e7	−1.13704	−0.568521	−	0.822669i	$-0.692484\pi$
$743$	−1.71099e7	−1.13704	−0.568521	+	0.822669i	$0.692484\pi$
$744$	4.70236e6	0.311447
$745$	−9.41907e6	−0.621752
$746$	−2.27402e6	−0.149606
$747$	760947.	0.0498945
$748$	−644430.	−0.0421135
$749$	0	0
$750$	−193144.	−0.0125380
$751$	1.52459e7	0.986401	0.493201	−	0.869916i	$-0.335827\pi$
$751$	1.52459e7	0.986401	0.493201	+	0.869916i	$0.335827\pi$
$752$	2.47849e7	1.59824
$753$	−1.03350e6	−0.0664238
$754$	−21776.5	−0.00139496
$755$	−8.88758e6	−0.567435
$756$	0	0
$757$	−1.18251e7	−0.750004	−0.375002	−	0.927024i	$-0.622358\pi$
$757$	−1.18251e7	−0.750004	−0.375002	+	0.927024i	$0.622358\pi$
$758$	281361.	0.0177865
$759$	6.56631e6	0.413730
$760$	−1.77568e6	−0.111515
$761$	−4.31523e6	−0.270111	−0.135056	−	0.990838i	$-0.543121\pi$
$761$	−4.31523e6	−0.270111	−0.135056	+	0.990838i	$0.543121\pi$
$762$	3.06712e6	0.191357
$763$	0	0
$764$	2.68395e7	1.66357
$765$	922388.	0.0569849
$766$	2.88830e6	0.177857
$767$	−6.30776e6	−0.387157
$768$	1.79477e7	1.09801
$769$	−1.74124e7	−1.06180	−0.530900	−	0.847434i	$-0.678146\pi$
$769$	−1.74124e7	−1.06180	−0.530900	+	0.847434i	$0.678146\pi$
$770$	0	0
$771$	−1.02876e7	−0.623275
$772$	−8.99113e6	−0.542964
$773$	−2.39416e7	−1.44113	−0.720566	−	0.693386i	$-0.756118\pi$
$773$	−2.39416e7	−1.44113	−0.720566	+	0.693386i	$0.756118\pi$
$774$	592431.	0.0355456
$775$	3.73841e6	0.223580
$776$	−5.28811e6	−0.315243
$777$	0	0
$778$	−1.58632e6	−0.0939600
$779$	−1.63319e7	−0.964258
$780$	−4.10881e6	−0.241813
$781$	4.54264e6	0.266490
$782$	−747745.	−0.0437257
$783$	−264606.	−0.0154239
$784$	0	0
$785$	−1.22865e7	−0.711628
$786$	−3.22689e6	−0.186307
$787$	3.01391e7	1.73458	0.867288	−	0.497807i	$-0.165861\pi$
$787$	3.01391e7	1.73458	0.867288	+	0.497807i	$0.165861\pi$
$788$	−1.75142e7	−1.00479
$789$	−2.47800e7	−1.41713
$790$	−1.69423e6	−0.0965840
$791$	0	0
$792$	423511.	0.0239912
$793$	8.60444e6	0.485892
$794$	−1.51316e6	−0.0851791
$795$	−1.49627e6	−0.0839639
$796$	−2.00771e7	−1.12310
$797$	−2.19395e7	−1.22344	−0.611718	−	0.791076i	$-0.709521\pi$
$797$	−2.19395e7	−1.22344	−0.611718	+	0.791076i	$0.709521\pi$
$798$	0	0
$799$	6.72692e6	0.372777
$800$	−1.19577e6	−0.0660578
$801$	5.47738e6	0.301642
$802$	−39856.3	−0.00218807
$803$	−1.83746e6	−0.100561
$804$	1.97139e7	1.07556
$805$	0	0
$806$	−1.00958e6	−0.0547398
$807$	1.68485e7	0.910705
$808$	6.87921e6	0.370690
$809$	−1.09650e7	−0.589029	−0.294514	−	0.955647i	$-0.595158\pi$
$809$	−1.09650e7	−0.589029	−0.294514	+	0.955647i	$0.595158\pi$
$810$	1.16444e6	0.0623600
$811$	−1.80078e7	−0.961409	−0.480705	−	0.876883i	$-0.659619\pi$
$811$	−1.80078e7	−0.961409	−0.480705	+	0.876883i	$0.659619\pi$
$812$	0	0
$813$	3.55986e7	1.88889
$814$	−430185.	−0.0227559
$815$	−3.57521e6	−0.188542
$816$	5.14627e6	0.270562
$817$	1.19593e7	0.626830
$818$	−256500.	−0.0134030
$819$	0	0
$820$	−7.31673e6	−0.379999
$821$	3.23751e7	1.67630	0.838152	−	0.545437i	$-0.183636\pi$
$821$	3.23751e7	1.67630	0.838152	+	0.545437i	$0.183636\pi$
$822$	209291.	0.0108037
$823$	3.24695e7	1.67100	0.835500	−	0.549491i	$-0.185178\pi$
$823$	3.24695e7	1.67100	0.835500	+	0.549491i	$0.185178\pi$
$824$	1.69019e6	0.0867197
$825$	929922.	0.0475676
$826$	0	0
$827$	3.10708e7	1.57975	0.789876	−	0.613267i	$-0.210145\pi$
$827$	3.10708e7	1.57975	0.789876	+	0.613267i	$0.210145\pi$
$828$	−1.92330e7	−0.974924
$829$	2.82139e6	0.142586	0.0712931	−	0.997455i	$-0.477287\pi$
$829$	2.82139e6	0.142586	0.0712931	+	0.997455i	$0.477287\pi$
$830$	−87361.3	−0.00440173
$831$	−4.09743e7	−2.05830
$832$	−8.08256e6	−0.404800
$833$	0	0
$834$	2.21577e6	0.110309
$835$	−7.84867e6	−0.389565
$836$	4.24770e6	0.210203
$837$	−1.22674e7	−0.605254
$838$	1.10030e6	0.0541255
$839$	2.48604e6	0.121928	0.0609639	−	0.998140i	$-0.480583\pi$
$839$	2.48604e6	0.121928	0.0609639	+	0.998140i	$0.480583\pi$
$840$	0	0
$841$	−2.04945e7	−0.999188
$842$	−1.95860e6	−0.0952064
$843$	−3.35968e7	−1.62828
$844$	8.85815e6	0.428043
$845$	−7.50683e6	−0.361672
$846$	−2.19648e6	−0.105512
$847$	0	0
$848$	−3.02258e6	−0.144341
$849$	4.95201e7	2.35783
$850$	−105896.	−0.00502726
$851$	3.93202e7	1.86119
$852$	−3.67489e7	−1.73439
$853$	−2.80284e6	−0.131894	−0.0659472	−	0.997823i	$-0.521007\pi$
$853$	−2.80284e6	−0.131894	−0.0659472	+	0.997823i	$0.521007\pi$
$854$	0	0
$855$	−6.07983e6	−0.284431
$856$	5.10220e6	0.237998
$857$	8.57829e6	0.398978	0.199489	−	0.979900i	$-0.436072\pi$
$857$	8.57829e6	0.398978	0.199489	+	0.979900i	$0.436072\pi$
$858$	−251131.	−0.0116461
$859$	7.92542e6	0.366471	0.183235	−	0.983069i	$-0.441343\pi$
$859$	7.92542e6	0.366471	0.183235	+	0.983069i	$0.441343\pi$
$860$	5.35778e6	0.247024
$861$	0	0
$862$	1.93085e6	0.0885075
$863$	−3.64157e7	−1.66441	−0.832207	−	0.554466i	$-0.812923\pi$
$863$	−3.64157e7	−1.66441	−0.832207	+	0.554466i	$0.812923\pi$
$864$	3.92387e6	0.178826
$865$	−1.09281e7	−0.496598
$866$	624553.	0.0282992
$867$	−2.63147e7	−1.18892
$868$	0	0
$869$	8.15716e6	0.366429
$870$	−39870.8	−0.00178590
$871$	−8.51874e6	−0.380478
$872$	6.02677e6	0.268407
$873$	−1.81061e7	−0.804064
$874$	4.92869e6	0.218249
$875$	0	0
$876$	1.48646e7	0.654475
$877$	−1.69244e7	−0.743045	−0.371523	−	0.928424i	$-0.621164\pi$
$877$	−1.69244e7	−0.743045	−0.371523	+	0.928424i	$0.621164\pi$
$878$	−2.33905e6	−0.102401
$879$	2.22621e7	0.971837
$880$	1.87851e6	0.0817726
$881$	−4.18273e7	−1.81560	−0.907799	−	0.419405i	$-0.862239\pi$
$881$	−4.18273e7	−1.81560	−0.907799	+	0.419405i	$0.862239\pi$
$882$	0	0
$883$	1.08396e7	0.467857	0.233928	−	0.972254i	$-0.424842\pi$
$883$	1.08396e7	0.467857	0.233928	+	0.972254i	$0.424842\pi$
$884$	−2.25276e6	−0.0969580
$885$	−1.15489e7	−0.495660
$886$	−1.22167e6	−0.0522843
$887$	1.10623e7	0.472104	0.236052	−	0.971740i	$-0.424146\pi$
$887$	1.10623e7	0.472104	0.236052	+	0.971740i	$0.424146\pi$
$888$	7.00438e6	0.298083
$889$	0	0
$890$	−628836.	−0.0266111
$891$	−5.60640e6	−0.236587
$892$	3.06544e7	1.28997
$893$	−4.43399e7	−1.86066
$894$	4.65724e6	0.194888
$895$	−9.78687e6	−0.408400
$896$	0	0
$897$	2.29541e7	0.952530
$898$	−2.61168e6	−0.108076
$899$	771723.	0.0318465
$900$	−2.72378e6	−0.112090
$901$	−820367.	−0.0336664
$902$	−447199.	−0.0183014
$903$	0	0
$904$	3.41616e6	0.139033
$905$	−2.06149e6	−0.0836680
$906$	4.39444e6	0.177862
$907$	9.50001e6	0.383447	0.191724	−	0.981449i	$-0.438592\pi$
$907$	9.50001e6	0.383447	0.191724	+	0.981449i	$0.438592\pi$
$908$	−1.79928e7	−0.724243
$909$	2.35540e7	0.945486
$910$	0	0
$911$	1.64397e7	0.656295	0.328147	−	0.944627i	$-0.393576\pi$
$911$	1.64397e7	0.656295	0.328147	+	0.944627i	$0.393576\pi$
$912$	−3.39212e7	−1.35047
$913$	420615.	0.0166997
$914$	2.51409e6	0.0995440
$915$	1.57539e7	0.622066
$916$	−2.46435e6	−0.0970429
$917$	0	0
$918$	347491.	0.0136093
$919$	−3.69090e7	−1.44160	−0.720799	−	0.693144i	$-0.756225\pi$
$919$	−3.69090e7	−1.44160	−0.720799	+	0.693144i	$0.756225\pi$
$920$	4.44416e6	0.173109
$921$	2.94538e7	1.14418
$922$	−2.15074e6	−0.0833222
$923$	1.58799e7	0.613540
$924$	0	0
$925$	5.56853e6	0.213986
$926$	−667939.	−0.0255982
$927$	5.78711e6	0.221188
$928$	−246845.	−0.00940922
$929$	−3.53275e7	−1.34299	−0.671497	−	0.741007i	$-0.734348\pi$
$929$	−3.53275e7	−1.34299	−0.671497	+	0.741007i	$0.734348\pi$
$930$	−1.84845e6	−0.0700809
$931$	0	0
$932$	−2.62073e7	−0.988284
$933$	−6.57897e7	−2.47431
$934$	−623369.	−0.0233818
$935$	509852.	0.0190728
$936$	1.48048e6	0.0552349
$937$	−4.24339e7	−1.57893	−0.789467	−	0.613793i	$-0.789643\pi$
$937$	−4.24339e7	−1.57893	−0.789467	+	0.613793i	$0.789643\pi$
$938$	0	0
$939$	−8.33512e6	−0.308495
$940$	−1.98644e7	−0.733255
$941$	−3.71877e6	−0.136907	−0.0684534	−	0.997654i	$-0.521806\pi$
$941$	−3.71877e6	−0.136907	−0.0684534	+	0.997654i	$0.521806\pi$
$942$	6.07502e6	0.223059
$943$	4.08753e7	1.49686
$944$	−2.33297e7	−0.852079
$945$	0	0
$946$	327468.	0.0118971
$947$	3.42458e7	1.24089	0.620444	−	0.784250i	$-0.286952\pi$
$947$	3.42458e7	1.24089	0.620444	+	0.784250i	$0.286952\pi$
$948$	−6.59896e7	−2.38481
$949$	−6.42326e6	−0.231521
$950$	698002.	0.0250927
$951$	−1.69503e7	−0.607753
$952$	0	0
$953$	−4.77379e7	−1.70267	−0.851336	−	0.524621i	$-0.824207\pi$
$953$	−4.77379e7	−1.70267	−0.851336	+	0.524621i	$0.824207\pi$
$954$	267867.	0.00952903
$955$	−2.12345e7	−0.753415
$956$	−7.97155e6	−0.282097
$957$	191965.	0.00677550
$958$	3.23311e6	0.113817
$959$	0	0
$960$	−1.47984e7	−0.518248
$961$	7.14860e6	0.249696
$962$	−1.50381e6	−0.0523910
$963$	1.74696e7	0.607041
$964$	1.69360e7	0.586972
$965$	7.11349e6	0.245903
$966$	0	0
$967$	4.11582e6	0.141543	0.0707717	−	0.997493i	$-0.477454\pi$
$967$	4.11582e6	0.141543	0.0707717	+	0.997493i	$0.477454\pi$
$968$	−6.25311e6	−0.214490
$969$	−9.20663e6	−0.314986
$970$	2.07869e6	0.0709351
$971$	3.11715e7	1.06099	0.530493	−	0.847689i	$-0.322007\pi$
$971$	3.11715e7	1.06099	0.530493	+	0.847689i	$0.322007\pi$
$972$	2.96066e7	1.00513
$973$	0	0
$974$	−4.25251e6	−0.143631
$975$	3.25076e6	0.109515
$976$	3.18242e7	1.06938
$977$	−1.40483e7	−0.470857	−0.235428	−	0.971892i	$-0.575649\pi$
$977$	−1.40483e7	−0.470857	−0.235428	+	0.971892i	$0.575649\pi$
$978$	1.76776e6	0.0590984
$979$	3.02764e6	0.100959
$980$	0	0
$981$	2.06353e7	0.684602
$982$	−5.46274e6	−0.180772
$983$	−4.87717e6	−0.160985	−0.0804923	−	0.996755i	$-0.525649\pi$
$983$	−4.87717e6	−0.160985	−0.0804923	+	0.996755i	$0.525649\pi$
$984$	7.28141e6	0.239733
$985$	1.38567e7	0.455059
$986$	−21860.1	−0.000716079 0
$987$	0	0
$988$	1.48488e7	0.483949
$989$	−2.99315e7	−0.973056
$990$	−166478.	−0.00539843
$991$	2.73913e7	0.885990	0.442995	−	0.896524i	$-0.353916\pi$
$991$	2.73913e7	0.885990	0.442995	+	0.896524i	$0.353916\pi$
$992$	−1.14439e7	−0.369230
$993$	−2.90643e7	−0.935377
$994$	0	0
$995$	1.58843e7	0.508641
$996$	−3.40268e6	−0.108686
$997$	−3.59221e7	−1.14452	−0.572261	−	0.820072i	$-0.693933\pi$
$997$	−3.59221e7	−1.14452	−0.572261	+	0.820072i	$0.693933\pi$
$998$	5.95039e6	0.189112
$999$	−1.82728e7	−0.579284

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.6.a.m.1.5	yes	10
7.6	odd	2		245.6.a.l.1.5	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
245.6.a.l.1.5	✓	10	7.6	odd	2
245.6.a.m.1.5	yes	10	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-0.633352 q^{2} +19.5171 q^{3} -31.5989 q^{4} +25.0000 q^{5} -12.3612 q^{6} +40.2804 q^{8} +137.918 q^{9} +O(q^{10})\)	\(q-0.633352 q^{2} +19.5171 q^{3} -31.5989 q^{4} +25.0000 q^{5} -12.3612 q^{6} +40.2804 q^{8} +137.918 q^{9} -15.8338 q^{10} +76.2344 q^{11} -616.719 q^{12} +266.495 q^{13} +487.928 q^{15} +985.652 q^{16} +267.518 q^{17} -87.3504 q^{18} -1763.32 q^{19} -789.972 q^{20} -48.2831 q^{22} +4413.22 q^{23} +786.158 q^{24} +625.000 q^{25} -168.785 q^{26} -2050.90 q^{27} +129.019 q^{29} -309.030 q^{30} +5981.45 q^{31} -1913.24 q^{32} +1487.87 q^{33} -169.433 q^{34} -4358.04 q^{36} +8909.64 q^{37} +1116.80 q^{38} +5201.22 q^{39} +1007.01 q^{40} +9262.01 q^{41} -6782.24 q^{43} -2408.92 q^{44} +3447.94 q^{45} -2795.12 q^{46} +25145.7 q^{47} +19237.1 q^{48} -395.845 q^{50} +5221.19 q^{51} -8420.94 q^{52} -3066.58 q^{53} +1298.94 q^{54} +1905.86 q^{55} -34415.0 q^{57} -81.7146 q^{58} -23669.3 q^{59} -15418.0 q^{60} +32287.4 q^{61} -3788.36 q^{62} -30329.1 q^{64} +6662.38 q^{65} -942.348 q^{66} -31965.8 q^{67} -8453.28 q^{68} +86133.2 q^{69} +59587.9 q^{71} +5555.39 q^{72} -24102.7 q^{73} -5642.93 q^{74} +12198.2 q^{75} +55719.0 q^{76} -3294.20 q^{78} +107001. q^{79} +24641.3 q^{80} -73541.7 q^{81} -5866.11 q^{82} +5517.40 q^{83} +6687.96 q^{85} +4295.54 q^{86} +2518.08 q^{87} +3070.75 q^{88} +39714.8 q^{89} -2183.76 q^{90} -139453. q^{92} +116741. q^{93} -15926.0 q^{94} -44083.0 q^{95} -37340.9 q^{96} -131282. q^{97} +10514.1 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 10 q^{2} + 58 q^{3} + 182 q^{4} + 250 q^{5} + 144 q^{6} + 270 q^{8} + 700 q^{9}+O(q^{10}) \) 10 * q + 10 * q^2 + 58 * q^3 + 182 * q^4 + 250 * q^5 + 144 * q^6 + 270 * q^8 + 700 * q^9	\( 10 q + 10 q^{2} + 58 q^{3} + 182 q^{4} + 250 q^{5} + 144 q^{6} + 270 q^{8} + 700 q^{9} + 250 q^{10} + 794 q^{11} + 2560 q^{12} + 474 q^{13} + 1450 q^{15} + 2394 q^{16} + 802 q^{17} + 3702 q^{18} + 7292 q^{19} + 4550 q^{20} + 3948 q^{22} + 3708 q^{23} + 2092 q^{24} + 6250 q^{25} + 6576 q^{26} + 11818 q^{27} - 8866 q^{29} + 3600 q^{30} + 13292 q^{31} + 2590 q^{32} + 9854 q^{33} + 44468 q^{34} - 10690 q^{36} + 16124 q^{37} + 2180 q^{38} - 24982 q^{39} + 6750 q^{40} + 34836 q^{41} - 28604 q^{43} - 31120 q^{44} + 17500 q^{45} - 39732 q^{46} + 18106 q^{47} + 101788 q^{48} + 6250 q^{50} + 31602 q^{51} - 22480 q^{52} + 36440 q^{53} + 80836 q^{54} + 19850 q^{55} + 126988 q^{57} - 100356 q^{58} + 18644 q^{59} + 64000 q^{60} + 68120 q^{61} + 181052 q^{62} - 59358 q^{64} + 11850 q^{65} + 157780 q^{66} + 92328 q^{67} + 288540 q^{68} + 170888 q^{69} + 5044 q^{71} - 61654 q^{72} + 170160 q^{73} - 216584 q^{74} + 36250 q^{75} + 505180 q^{76} - 158008 q^{78} + 26442 q^{79} + 59850 q^{80} - 56314 q^{81} + 353948 q^{82} + 353360 q^{83} + 20050 q^{85} - 52940 q^{86} - 3190 q^{87} - 114916 q^{88} + 90704 q^{89} + 92550 q^{90} + 183520 q^{92} + 188560 q^{93} - 121388 q^{94} + 182300 q^{95} + 442220 q^{96} + 236382 q^{97} + 109024 q^{99}+O(q^{100}) \) 10 * q + 10 * q^2 + 58 * q^3 + 182 * q^4 + 250 * q^5 + 144 * q^6 + 270 * q^8 + 700 * q^9 + 250 * q^10 + 794 * q^11 + 2560 * q^12 + 474 * q^13 + 1450 * q^15 + 2394 * q^16 + 802 * q^17 + 3702 * q^18 + 7292 * q^19 + 4550 * q^20 + 3948 * q^22 + 3708 * q^23 + 2092 * q^24 + 6250 * q^25 + 6576 * q^26 + 11818 * q^27 - 8866 * q^29 + 3600 * q^30 + 13292 * q^31 + 2590 * q^32 + 9854 * q^33 + 44468 * q^34 - 10690 * q^36 + 16124 * q^37 + 2180 * q^38 - 24982 * q^39 + 6750 * q^40 + 34836 * q^41 - 28604 * q^43 - 31120 * q^44 + 17500 * q^45 - 39732 * q^46 + 18106 * q^47 + 101788 * q^48 + 6250 * q^50 + 31602 * q^51 - 22480 * q^52 + 36440 * q^53 + 80836 * q^54 + 19850 * q^55 + 126988 * q^57 - 100356 * q^58 + 18644 * q^59 + 64000 * q^60 + 68120 * q^61 + 181052 * q^62 - 59358 * q^64 + 11850 * q^65 + 157780 * q^66 + 92328 * q^67 + 288540 * q^68 + 170888 * q^69 + 5044 * q^71 - 61654 * q^72 + 170160 * q^73 - 216584 * q^74 + 36250 * q^75 + 505180 * q^76 - 158008 * q^78 + 26442 * q^79 + 59850 * q^80 - 56314 * q^81 + 353948 * q^82 + 353360 * q^83 + 20050 * q^85 - 52940 * q^86 - 3190 * q^87 - 114916 * q^88 + 90704 * q^89 + 92550 * q^90 + 183520 * q^92 + 188560 * q^93 - 121388 * q^94 + 182300 * q^95 + 442220 * q^96 + 236382 * q^97 + 109024 * q^99

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