LMFDB - Embedded newform 245.6.a.l.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("245.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$39.2940358542$
Analytic rank:	$1$
Dimension:	$10$
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			1.7
Root			$-4.37629$ 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)

$f(q)$	$=$	$q+5.37629 q^{2} +16.5213 q^{3} -3.09546 q^{4} -25.0000 q^{5} +88.8236 q^{6} -188.684 q^{8} +29.9545 q^{9} +O(q^{10})$	\(q+5.37629 q^{2} +16.5213 q^{3} -3.09546 q^{4} -25.0000 q^{5} +88.8236 q^{6} -188.684 q^{8} +29.9545 q^{9} -134.407 q^{10} -11.0558 q^{11} -51.1411 q^{12} +367.295 q^{13} -413.033 q^{15} -915.363 q^{16} -1173.52 q^{17} +161.044 q^{18} -342.504 q^{19} +77.3865 q^{20} -59.4393 q^{22} -2072.14 q^{23} -3117.30 q^{24} +625.000 q^{25} +1974.69 q^{26} -3519.80 q^{27} -2627.73 q^{29} -2220.59 q^{30} -8264.94 q^{31} +1116.61 q^{32} -182.657 q^{33} -6309.19 q^{34} -92.7229 q^{36} +4807.69 q^{37} -1841.40 q^{38} +6068.21 q^{39} +4717.09 q^{40} -2909.16 q^{41} -10245.5 q^{43} +34.2228 q^{44} -748.862 q^{45} -11140.4 q^{46} -19728.5 q^{47} -15123.0 q^{48} +3360.18 q^{50} -19388.1 q^{51} -1136.95 q^{52} +39395.2 q^{53} -18923.5 q^{54} +276.395 q^{55} -5658.63 q^{57} -14127.4 q^{58} +8056.38 q^{59} +1278.53 q^{60} -46149.3 q^{61} -44434.7 q^{62} +35294.9 q^{64} -9182.38 q^{65} -982.016 q^{66} +39912.1 q^{67} +3632.58 q^{68} -34234.5 q^{69} +60453.6 q^{71} -5651.92 q^{72} +46818.8 q^{73} +25847.6 q^{74} +10325.8 q^{75} +1060.21 q^{76} +32624.5 q^{78} -12641.1 q^{79} +22884.1 q^{80} -65430.7 q^{81} -15640.5 q^{82} +4899.74 q^{83} +29338.0 q^{85} -55082.8 q^{86} -43413.5 q^{87} +2086.05 q^{88} +69297.5 q^{89} -4026.10 q^{90} +6414.22 q^{92} -136548. q^{93} -106066. q^{94} +8562.61 q^{95} +18447.9 q^{96} -14604.2 q^{97} -331.171 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	5.37629	0.950404	0.475202	−	0.879877i	$-0.342375\pi$
$2$	5.37629	0.950404	0.475202	+	0.879877i	$0.342375\pi$
$3$	16.5213	1.05984	0.529922	−	0.848046i	$-0.322221\pi$
$3$	16.5213	1.05984	0.529922	+	0.848046i	$0.322221\pi$
$4$	−3.09546	−0.0967331
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	88.8236	1.00728
$7$	0	0
$7$	0	0
$8$	−188.684	−1.04234
$9$	29.9545	0.123269
$10$	−134.407	−0.425033
$11$	−11.0558	−0.0275492	−0.0137746	−	0.999905i	$-0.504385\pi$
$11$	−11.0558	−0.0275492	−0.0137746	+	0.999905i	$0.504385\pi$
$12$	−51.1411	−0.102522
$13$	367.295	0.602777	0.301389	−	0.953501i	$-0.402550\pi$
$13$	367.295	0.602777	0.301389	+	0.953501i	$0.402550\pi$
$14$	0	0
$15$	−413.033	−0.473977
$16$	−915.363	−0.893910
$17$	−1173.52	−0.984846	−0.492423	−	0.870356i	$-0.663889\pi$
$17$	−1173.52	−0.984846	−0.492423	+	0.870356i	$0.663889\pi$
$18$	161.044	0.117156
$19$	−342.504	−0.217662	−0.108831	−	0.994060i	$-0.534711\pi$
$19$	−342.504	−0.217662	−0.108831	+	0.994060i	$0.534711\pi$
$20$	77.3865	0.0432604
$21$	0	0
$22$	−59.4393	−0.0261828
$23$	−2072.14	−0.816769	−0.408384	−	0.912810i	$-0.633908\pi$
$23$	−2072.14	−0.816769	−0.408384	+	0.912810i	$0.633908\pi$
$24$	−3117.30	−1.10472
$25$	625.000	0.200000
$26$	1974.69	0.572882
$27$	−3519.80	−0.929198
$28$	0	0
$29$	−2627.73	−0.580210	−0.290105	−	0.956995i	$-0.593690\pi$
$29$	−2627.73	−0.580210	−0.290105	+	0.956995i	$0.593690\pi$
$30$	−2220.59	−0.450469
$31$	−8264.94	−1.54467	−0.772335	−	0.635216i	$-0.780911\pi$
$31$	−8264.94	−1.54467	−0.772335	+	0.635216i	$0.780911\pi$
$32$	1116.61	0.192764
$33$	−182.657	−0.0291978
$34$	−6309.19	−0.936001
$35$	0	0
$36$	−92.7229	−0.0119242
$37$	4807.69	0.577341	0.288670	−	0.957429i	$-0.406787\pi$
$37$	4807.69	0.577341	0.288670	+	0.957429i	$0.406787\pi$
$38$	−1841.40	−0.206866
$39$	6068.21	0.638850
$40$	4717.09	0.466148
$41$	−2909.16	−0.270276	−0.135138	−	0.990827i	$-0.543148\pi$
$41$	−2909.16	−0.270276	−0.135138	+	0.990827i	$0.543148\pi$
$42$	0	0
$43$	−10245.5	−0.845011	−0.422505	−	0.906360i	$-0.638849\pi$
$43$	−10245.5	−0.845011	−0.422505	+	0.906360i	$0.638849\pi$
$44$	34.2228	0.00266492
$45$	−748.862	−0.0551278
$46$	−11140.4	−0.776260
$47$	−19728.5	−1.30271	−0.651357	−	0.758771i	$-0.725800\pi$
$47$	−19728.5	−1.30271	−0.651357	+	0.758771i	$0.725800\pi$
$48$	−15123.0	−0.947405
$49$	0	0
$50$	3360.18	0.190081
$51$	−19388.1	−1.04378
$52$	−1136.95	−0.0583085
$53$	39395.2	1.92643	0.963217	−	0.268725i	$-0.0866024\pi$
$53$	39395.2	1.92643	0.963217	+	0.268725i	$0.0866024\pi$
$54$	−18923.5	−0.883113
$55$	276.395	0.0123204
$56$	0	0
$57$	−5658.63	−0.230687
$58$	−14127.4	−0.551433
$59$	8056.38	0.301308	0.150654	−	0.988587i	$-0.451862\pi$
$59$	8056.38	0.301308	0.150654	+	0.988587i	$0.451862\pi$
$60$	1278.53	0.0458492
$61$	−46149.3	−1.58796	−0.793982	−	0.607941i	$-0.791996\pi$
$61$	−46149.3	−1.58796	−0.793982	+	0.607941i	$0.791996\pi$
$62$	−44434.7	−1.46806
$63$	0	0
$64$	35294.9	1.07711
$65$	−9182.38	−0.269570
$66$	−982.016	−0.0277497
$67$	39912.1	1.08622	0.543110	−	0.839662i	$-0.317247\pi$
$67$	39912.1	1.08622	0.543110	+	0.839662i	$0.317247\pi$
$68$	3632.58	0.0952672
$69$	−34234.5	−0.865647
$70$	0	0
$71$	60453.6	1.42323	0.711617	−	0.702567i	$-0.247963\pi$
$71$	60453.6	1.42323	0.711617	+	0.702567i	$0.247963\pi$
$72$	−5651.92	−0.128489
$73$	46818.8	1.02828	0.514142	−	0.857705i	$-0.328110\pi$
$73$	46818.8	1.02828	0.514142	+	0.857705i	$0.328110\pi$
$74$	25847.6	0.548706
$75$	10325.8	0.211969
$76$	1060.21	0.0210551
$77$	0	0
$78$	32624.5	0.607165
$79$	−12641.1	−0.227885	−0.113943	−	0.993487i	$-0.536348\pi$
$79$	−12641.1	−0.227885	−0.113943	+	0.993487i	$0.536348\pi$
$80$	22884.1	0.399769
$81$	−65430.7	−1.10807
$82$	−15640.5	−0.256872
$83$	4899.74	0.0780689	0.0390344	−	0.999238i	$-0.487572\pi$
$83$	4899.74	0.0780689	0.0390344	+	0.999238i	$0.487572\pi$
$84$	0	0
$85$	29338.0	0.440436
$86$	−55082.8	−0.803101
$87$	−43413.5	−0.614932
$88$	2086.05	0.0287156
$89$	69297.5	0.927348	0.463674	−	0.886006i	$-0.346531\pi$
$89$	69297.5	0.927348	0.463674	+	0.886006i	$0.346531\pi$
$90$	−4026.10	−0.0523936
$91$	0	0
$92$	6414.22	0.0790086
$93$	−136548.	−1.63711
$94$	−106066.	−1.23810
$95$	8562.61	0.0973413
$96$	18447.9	0.204300
$97$	−14604.2	−0.157597	−0.0787984	−	0.996891i	$-0.525108\pi$
$97$	−14604.2	−0.157597	−0.0787984	+	0.996891i	$0.525108\pi$
$98$	0	0
$99$	−331.171	−0.00339597
$100$	−1934.66	−0.0193466
$101$	153606.	1.49832	0.749160	−	0.662389i	$-0.230457\pi$
$101$	153606.	1.49832	0.749160	+	0.662389i	$0.230457\pi$
$102$	−104236.	−0.992015
$103$	−131855.	−1.22463	−0.612315	−	0.790614i	$-0.709762\pi$
$103$	−131855.	−1.22463	−0.612315	+	0.790614i	$0.709762\pi$
$104$	−69302.5	−0.628298
$105$	0	0
$106$	211800.	1.83089
$107$	−169892.	−1.43454	−0.717270	−	0.696795i	$-0.754609\pi$
$107$	−169892.	−1.43454	−0.717270	+	0.696795i	$0.754609\pi$
$108$	10895.4	0.0898842
$109$	21967.1	0.177095	0.0885477	−	0.996072i	$-0.471777\pi$
$109$	21967.1	0.177095	0.0885477	+	0.996072i	$0.471777\pi$
$110$	1485.98	0.0117093
$111$	79429.4	0.611891
$112$	0	0
$113$	−135136.	−0.995575	−0.497787	−	0.867299i	$-0.665854\pi$
$113$	−135136.	−0.995575	−0.497787	+	0.867299i	$0.665854\pi$
$114$	−30422.4	−0.219246
$115$	51803.4	0.365270
$116$	8134.02	0.0561255
$117$	11002.1	0.0743040
$118$	43313.5	0.286364
$119$	0	0
$120$	77932.6	0.494044
$121$	−160929.	−0.999241
$122$	−248112.	−1.50921
$123$	−48063.2	−0.286451
$124$	25583.8	0.149421
$125$	−15625.0	−0.0894427
$126$	0	0
$127$	−286149.	−1.57429	−0.787143	−	0.616771i	$-0.788440\pi$
$127$	−286149.	−1.57429	−0.787143	+	0.616771i	$0.788440\pi$
$128$	154024.	0.830928
$129$	−169269.	−0.895579
$130$	−49367.2	−0.256200
$131$	39360.5	0.200393	0.100196	−	0.994968i	$-0.468053\pi$
$131$	39360.5	0.200393	0.100196	+	0.994968i	$0.468053\pi$
$132$	565.406	0.00282440
$133$	0	0
$134$	214579.	1.03235
$135$	87994.9	0.415550
$136$	221424.	1.02654
$137$	256567.	1.16788	0.583942	−	0.811796i	$-0.301510\pi$
$137$	256567.	1.16788	0.583942	+	0.811796i	$0.301510\pi$
$138$	−184055.	−0.822714
$139$	−51525.4	−0.226196	−0.113098	−	0.993584i	$-0.536077\pi$
$139$	−51525.4	−0.226196	−0.113098	+	0.993584i	$0.536077\pi$
$140$	0	0
$141$	−325941.	−1.38067
$142$	325017.	1.35265
$143$	−4060.74	−0.0166060
$144$	−27419.2	−0.110192
$145$	65693.2	0.259478
$146$	251712.	0.977286
$147$	0	0
$148$	−14882.0	−0.0558480
$149$	420194.	1.55055	0.775273	−	0.631627i	$-0.217612\pi$
$149$	420194.	1.55055	0.775273	+	0.631627i	$0.217612\pi$
$150$	55514.7	0.201456
$151$	79551.5	0.283926	0.141963	−	0.989872i	$-0.454659\pi$
$151$	79551.5	0.283926	0.141963	+	0.989872i	$0.454659\pi$
$152$	64624.9	0.226877
$153$	−35152.2	−0.121401
$154$	0	0
$155$	206623.	0.690797
$156$	−18783.9	−0.0617979
$157$	−143038.	−0.463131	−0.231565	−	0.972819i	$-0.574385\pi$
$157$	−143038.	−0.463131	−0.231565	+	0.972819i	$0.574385\pi$
$158$	−67962.1	−0.216583
$159$	650862.	2.04172
$160$	−27915.2	−0.0862068
$161$	0	0
$162$	−351775.	−1.05312
$163$	528116.	1.55690	0.778449	−	0.627708i	$-0.216007\pi$
$163$	528116.	1.55690	0.778449	+	0.627708i	$0.216007\pi$
$164$	9005.19	0.0261447
$165$	4566.42	0.0130577
$166$	26342.4	0.0741969
$167$	−181743.	−0.504274	−0.252137	−	0.967692i	$-0.581133\pi$
$167$	−181743.	−0.504274	−0.252137	+	0.967692i	$0.581133\pi$
$168$	0	0
$169$	−236387.	−0.636660
$170$	157730.	0.418592
$171$	−10259.5	−0.0268310
$172$	31714.5	0.0817405
$173$	−640689.	−1.62754	−0.813771	−	0.581186i	$-0.802589\pi$
$173$	−640689.	−1.62754	−0.813771	+	0.581186i	$0.802589\pi$
$174$	−233404.	−0.584434
$175$	0	0
$176$	10120.1	0.0246265
$177$	133102.	0.319339
$178$	372564.	0.881354
$179$	565927.	1.32016	0.660082	−	0.751193i	$-0.270521\pi$
$179$	565927.	1.32016	0.660082	+	0.751193i	$0.270521\pi$
$180$	2318.07	0.00533268
$181$	461950.	1.04809	0.524045	−	0.851690i	$-0.324422\pi$
$181$	461950.	1.04809	0.524045	+	0.851690i	$0.324422\pi$
$182$	0	0
$183$	−762448.	−1.68299
$184$	390978.	0.851350
$185$	−120192.	−0.258195
$186$	−734121.	−1.55591
$187$	12974.2	0.0271317
$188$	61068.8	0.126016
$189$	0	0
$190$	46035.1	0.0925135
$191$	−372488.	−0.738804	−0.369402	−	0.929270i	$-0.620437\pi$
$191$	−372488.	−0.738804	−0.369402	+	0.929270i	$0.620437\pi$
$192$	583118.	1.14157
$193$	19371.9	0.0374351	0.0187176	−	0.999825i	$-0.494042\pi$
$193$	19371.9	0.0374351	0.0187176	+	0.999825i	$0.494042\pi$
$194$	−78516.3	−0.149781
$195$	−151705.	−0.285702
$196$	0	0
$197$	−129308.	−0.237388	−0.118694	−	0.992931i	$-0.537871\pi$
$197$	−129308.	−0.237388	−0.118694	+	0.992931i	$0.537871\pi$
$198$	−1780.47	−0.00322754
$199$	−439258.	−0.786298	−0.393149	−	0.919475i	$-0.628614\pi$
$199$	−439258.	−0.786298	−0.393149	+	0.919475i	$0.628614\pi$
$200$	−117927.	−0.208468
$201$	659402.	1.15122
$202$	825831.	1.42401
$203$	0	0
$204$	60015.1	0.100968
$205$	72729.0	0.120871
$206$	−708894.	−1.16389
$207$	−62069.8	−0.100683
$208$	−336208.	−0.538828
$209$	3786.66	0.00599640
$210$	0	0
$211$	−275198.	−0.425540	−0.212770	−	0.977102i	$-0.568248\pi$
$211$	−275198.	−0.425540	−0.212770	+	0.977102i	$0.568248\pi$
$212$	−121946.	−0.186350
$213$	998775.	1.50841
$214$	−913388.	−1.36339
$215$	256138.	0.377900
$216$	664128.	0.968539
$217$	0	0
$218$	118102.	0.168312
$219$	773510.	1.08982
$220$	−855.570	−0.00119179
$221$	−431028.	−0.593642
$222$	427036.	0.581543
$223$	1.10303e6	1.48534	0.742672	−	0.669655i	$-0.233558\pi$
$223$	1.10303e6	1.48534	0.742672	+	0.669655i	$0.233558\pi$
$224$	0	0
$225$	18721.5	0.0246539
$226$	−726529.	−0.946198
$227$	−773342.	−0.996110	−0.498055	−	0.867145i	$-0.665952\pi$
$227$	−773342.	−0.996110	−0.498055	+	0.867145i	$0.665952\pi$
$228$	17516.1	0.0223151
$229$	1.43998e6	1.81454	0.907271	−	0.420547i	$-0.138162\pi$
$229$	1.43998e6	1.81454	0.907271	+	0.420547i	$0.138162\pi$
$230$	278511.	0.347154
$231$	0	0
$232$	495809.	0.604775
$233$	−5656.54	−0.00682592	−0.00341296	−	0.999994i	$-0.501086\pi$
$233$	−5656.54	−0.00682592	−0.00341296	+	0.999994i	$0.501086\pi$
$234$	59150.7	0.0706188
$235$	493212.	0.582592
$236$	−24938.2	−0.0291464
$237$	−208847.	−0.241523
$238$	0	0
$239$	1.62686e6	1.84227	0.921137	−	0.389238i	$-0.127262\pi$
$239$	1.62686e6	1.84227	0.921137	+	0.389238i	$0.127262\pi$
$240$	378076.	0.423692
$241$	−1.38641e6	−1.53762	−0.768810	−	0.639478i	$-0.779151\pi$
$241$	−1.38641e6	−1.53762	−0.768810	+	0.639478i	$0.779151\pi$
$242$	−865200.	−0.949682
$243$	−225691.	−0.245188
$244$	142853.	0.153609
$245$	0	0
$246$	−258402.	−0.272244
$247$	−125800.	−0.131201
$248$	1.55946e6	1.61007
$249$	80950.2	0.0827408
$250$	−84004.6	−0.0850067
$251$	−398018.	−0.398766	−0.199383	−	0.979922i	$-0.563894\pi$
$251$	−398018.	−0.398766	−0.199383	+	0.979922i	$0.563894\pi$
$252$	0	0
$253$	22909.2	0.0225013
$254$	−1.53842e6	−1.49621
$255$	484703.	0.466794
$256$	−301357.	−0.287396
$257$	−510302.	−0.481942	−0.240971	−	0.970532i	$-0.577466\pi$
$257$	−510302.	−0.481942	−0.240971	+	0.970532i	$0.577466\pi$
$258$	−910042.	−0.851162
$259$	0	0
$260$	28423.7	0.0260764
$261$	−78712.2	−0.0715222
$262$	211614.	0.190454
$263$	1.37462e6	1.22544	0.612722	−	0.790298i	$-0.290074\pi$
$263$	1.37462e6	1.22544	0.612722	+	0.790298i	$0.290074\pi$
$264$	34464.3	0.0304340
$265$	−984881.	−0.861527
$266$	0	0
$267$	1.14489e6	0.982844
$268$	−123546.	−0.105073
$269$	263149.	0.221728	0.110864	−	0.993836i	$-0.464638\pi$
$269$	263149.	0.221728	0.110864	+	0.993836i	$0.464638\pi$
$270$	473087.	0.394940
$271$	−1.25268e6	−1.03614	−0.518069	−	0.855339i	$-0.673349\pi$
$271$	−1.25268e6	−1.03614	−0.518069	+	0.855339i	$0.673349\pi$
$272$	1.07420e6	0.880363
$273$	0	0
$274$	1.37938e6	1.10996
$275$	−6909.88	−0.00550984
$276$	105971.	0.0837368
$277$	−980534.	−0.767827	−0.383914	−	0.923369i	$-0.625424\pi$
$277$	−980534.	−0.767827	−0.383914	+	0.923369i	$0.625424\pi$
$278$	−277016.	−0.214977
$279$	−247572.	−0.190411
$280$	0	0
$281$	−1.52611e6	−1.15298	−0.576489	−	0.817105i	$-0.695578\pi$
$281$	−1.52611e6	−1.15298	−0.576489	+	0.817105i	$0.695578\pi$
$282$	−1.75236e6	−1.31220
$283$	260267.	0.193176	0.0965881	−	0.995324i	$-0.469207\pi$
$283$	260267.	0.193176	0.0965881	+	0.995324i	$0.469207\pi$
$284$	−187132.	−0.137674
$285$	141466.	0.103167
$286$	−21831.8	−0.0157824
$287$	0	0
$288$	33447.5	0.0237619
$289$	−42707.6	−0.0300788
$290$	353186.	0.246609
$291$	−241280.	−0.167028
$292$	−144926.	−0.0994692
$293$	−2.44271e6	−1.66228	−0.831138	−	0.556067i	$-0.812310\pi$
$293$	−2.44271e6	−1.66228	−0.831138	+	0.556067i	$0.812310\pi$
$294$	0	0
$295$	−201410.	−0.134749
$296$	−907132.	−0.601785
$297$	38914.2	0.0255986
$298$	2.25909e6	1.47364
$299$	−761086.	−0.492329
$300$	−31963.2	−0.0205044
$301$	0	0
$302$	427692.	0.269845
$303$	2.53778e6	1.58799
$304$	313516.	0.194570
$305$	1.15373e6	0.710159
$306$	−188988.	−0.115380
$307$	−179892.	−0.108934	−0.0544672	−	0.998516i	$-0.517346\pi$
$307$	−179892.	−0.108934	−0.0544672	+	0.998516i	$0.517346\pi$
$308$	0	0
$309$	−2.17843e6	−1.29792
$310$	1.11087e6	0.656536
$311$	−2.64551e6	−1.55099	−0.775494	−	0.631355i	$-0.782499\pi$
$311$	−2.64551e6	−1.55099	−0.775494	+	0.631355i	$0.782499\pi$
$312$	−1.14497e6	−0.665898
$313$	−2.02011e6	−1.16550	−0.582752	−	0.812650i	$-0.698024\pi$
$313$	−2.02011e6	−1.16550	−0.582752	+	0.812650i	$0.698024\pi$
$314$	−769016.	−0.440161
$315$	0	0
$316$	39129.9	0.0220441
$317$	−2.88723e6	−1.61374	−0.806868	−	0.590731i	$-0.798839\pi$
$317$	−2.88723e6	−1.61374	−0.806868	+	0.590731i	$0.798839\pi$
$318$	3.49922e6	1.94046
$319$	29051.6	0.0159843
$320$	−882371.	−0.481700
$321$	−2.80684e6	−1.52039
$322$	0	0
$323$	401936.	0.214363
$324$	202538.	0.107187
$325$	229559.	0.120555
$326$	2.83931e6	1.47968
$327$	362927.	0.187694
$328$	548910.	0.281719
$329$	0	0
$330$	24550.4	0.0124101
$331$	1.44013e6	0.722492	0.361246	−	0.932471i	$-0.382351\pi$
$331$	1.44013e6	0.722492	0.361246	+	0.932471i	$0.382351\pi$
$332$	−15167.0	−0.00755185
$333$	144012.	0.0711685
$334$	−977104.	−0.479264
$335$	−997803.	−0.485772
$336$	0	0
$337$	401552.	0.192605	0.0963024	−	0.995352i	$-0.469298\pi$
$337$	401552.	0.192605	0.0963024	+	0.995352i	$0.469298\pi$
$338$	−1.27089e6	−0.605084
$339$	−2.23262e6	−1.05515
$340$	−90814.6	−0.0426048
$341$	91375.6	0.0425544
$342$	−55158.3	−0.0255003
$343$	0	0
$344$	1.93316e6	0.880788
$345$	855862.	0.387129
$346$	−3.44453e6	−1.54682
$347$	2.48643e6	1.10854	0.554272	−	0.832336i	$-0.312997\pi$
$347$	2.48643e6	1.10854	0.554272	+	0.832336i	$0.312997\pi$
$348$	134385.	0.0594843
$349$	−760055.	−0.334027	−0.167013	−	0.985955i	$-0.553412\pi$
$349$	−760055.	−0.334027	−0.167013	+	0.985955i	$0.553412\pi$
$350$	0	0
$351$	−1.29280e6	−0.560099
$352$	−12345.0	−0.00531050
$353$	322965.	0.137949	0.0689746	−	0.997618i	$-0.478027\pi$
$353$	322965.	0.137949	0.0689746	+	0.997618i	$0.478027\pi$
$354$	715596.	0.303501
$355$	−1.51134e6	−0.636490
$356$	−214508.	−0.0897052
$357$	0	0
$358$	3.04259e6	1.25469
$359$	−3.78096e6	−1.54834	−0.774170	−	0.632978i	$-0.781833\pi$
$359$	−3.78096e6	−1.54834	−0.774170	+	0.632978i	$0.781833\pi$
$360$	141298.	0.0574618
$361$	−2.35879e6	−0.952623
$362$	2.48358e6	0.996109
$363$	−2.65876e6	−1.05904
$364$	0	0
$365$	−1.17047e6	−0.459863
$366$	−4.09915e6	−1.59952
$367$	−4.30592e6	−1.66879	−0.834393	−	0.551170i	$-0.814182\pi$
$367$	−4.30592e6	−1.66879	−0.834393	+	0.551170i	$0.814182\pi$
$368$	1.89676e6	0.730117
$369$	−87142.4	−0.0333168
$370$	−646189.	−0.245389
$371$	0	0
$372$	422678.	0.158363
$373$	4.33886e6	1.61474	0.807371	−	0.590044i	$-0.200890\pi$
$373$	4.33886e6	1.61474	0.807371	+	0.590044i	$0.200890\pi$
$374$	69753.2	0.0257861
$375$	−258146.	−0.0947953
$376$	3.72244e6	1.35787
$377$	−965151.	−0.349737
$378$	0	0
$379$	−3.27628e6	−1.17161	−0.585805	−	0.810452i	$-0.699222\pi$
$379$	−3.27628e6	−1.17161	−0.585805	+	0.810452i	$0.699222\pi$
$380$	−26505.2	−0.00941612
$381$	−4.72757e6	−1.66850
$382$	−2.00261e6	−0.702162
$383$	−3.60923e6	−1.25724	−0.628619	−	0.777713i	$-0.716380\pi$
$383$	−3.60923e6	−1.25724	−0.628619	+	0.777713i	$0.716380\pi$
$384$	2.54468e6	0.880654
$385$	0	0
$386$	104149.	0.0355785
$387$	−306899.	−0.104164
$388$	45206.6	0.0152448
$389$	1.60910e6	0.539148	0.269574	−	0.962980i	$-0.413117\pi$
$389$	1.60910e6	0.539148	0.269574	+	0.962980i	$0.413117\pi$
$390$	−815611.	−0.271532
$391$	2.43170e6	0.804391
$392$	0	0
$393$	650288.	0.212385
$394$	−695197.	−0.225615
$395$	316027.	0.101913
$396$	1025.13	0.000328503 0
$397$	−121454.	−0.0386755	−0.0193377	−	0.999813i	$-0.506156\pi$
$397$	−121454.	−0.0386755	−0.0193377	+	0.999813i	$0.506156\pi$
$398$	−2.36158e6	−0.747300
$399$	0	0
$400$	−572102.	−0.178782
$401$	−5.11280e6	−1.58781	−0.793904	−	0.608043i	$-0.791955\pi$
$401$	−5.11280e6	−1.58781	−0.793904	+	0.608043i	$0.791955\pi$
$402$	3.54514e6	1.09413
$403$	−3.03567e6	−0.931091
$404$	−475481.	−0.144937
$405$	1.63577e6	0.495546
$406$	0	0
$407$	−53152.9	−0.0159053
$408$	3.65822e6	1.08798
$409$	4.66827e6	1.37990	0.689950	−	0.723857i	$-0.257632\pi$
$409$	4.66827e6	1.37990	0.689950	+	0.723857i	$0.257632\pi$
$410$	391012.	0.114876
$411$	4.23883e6	1.23777
$412$	408153.	0.118462
$413$	0	0
$414$	−333706.	−0.0956891
$415$	−122494.	−0.0349135
$416$	410125.	0.116194
$417$	−851268.	−0.239732
$418$	20358.2	0.00569900
$419$	5.36826e6	1.49382	0.746910	−	0.664925i	$-0.231537\pi$
$419$	5.36826e6	1.49382	0.746910	+	0.664925i	$0.231537\pi$
$420$	0	0
$421$	−1.72529e6	−0.474413	−0.237206	−	0.971459i	$-0.576232\pi$
$421$	−1.72529e6	−0.474413	−0.237206	+	0.971459i	$0.576232\pi$
$422$	−1.47955e6	−0.404434
$423$	−590957.	−0.160585
$424$	−7.43323e6	−2.00800
$425$	−733450.	−0.196969
$426$	5.36971e6	1.43360
$427$	0	0
$428$	525893.	0.138768
$429$	−67088.9	−0.0175998
$430$	1.37707e6	0.359158
$431$	−3.97363e6	−1.03037	−0.515186	−	0.857078i	$-0.672277\pi$
$431$	−3.97363e6	−1.03037	−0.515186	+	0.857078i	$0.672277\pi$
$432$	3.22189e6	0.830619
$433$	−1.75813e6	−0.450642	−0.225321	−	0.974285i	$-0.572343\pi$
$433$	−1.75813e6	−0.450642	−0.225321	+	0.974285i	$0.572343\pi$
$434$	0	0
$435$	1.08534e6	0.275006
$436$	−67998.4	−0.0171310
$437$	709716.	0.177779
$438$	4.15862e6	1.03577
$439$	−5.12207e6	−1.26848	−0.634241	−	0.773135i	$-0.718687\pi$
$439$	−5.12207e6	−1.26848	−0.634241	+	0.773135i	$0.718687\pi$
$440$	−52151.2	−0.0128420
$441$	0	0
$442$	−2.31733e6	−0.564200
$443$	6.51360e6	1.57693	0.788464	−	0.615081i	$-0.210877\pi$
$443$	6.51360e6	1.57693	0.788464	+	0.615081i	$0.210877\pi$
$444$	−245871.	−0.0591901
$445$	−1.73244e6	−0.414722
$446$	5.93024e6	1.41168
$447$	6.94217e6	1.64334
$448$	0	0
$449$	−3.84667e6	−0.900469	−0.450234	−	0.892910i	$-0.648660\pi$
$449$	−3.84667e6	−0.900469	−0.450234	+	0.892910i	$0.648660\pi$
$450$	100653.	0.0234311
$451$	32163.1	0.00744589
$452$	418307.	0.0963051
$453$	1.31430e6	0.300918
$454$	−4.15772e6	−0.946706
$455$	0	0
$456$	1.06769e6	0.240455
$457$	4.07431e6	0.912564	0.456282	−	0.889835i	$-0.349181\pi$
$457$	4.07431e6	0.912564	0.456282	+	0.889835i	$0.349181\pi$
$458$	7.74174e6	1.72455
$459$	4.13055e6	0.915116
$460$	−160355.	−0.0353337
$461$	−863488.	−0.189236	−0.0946180	−	0.995514i	$-0.530163\pi$
$461$	−863488.	−0.189236	−0.0946180	+	0.995514i	$0.530163\pi$
$462$	0	0
$463$	7.54412e6	1.63552	0.817761	−	0.575559i	$-0.195215\pi$
$463$	7.54412e6	1.63552	0.817761	+	0.575559i	$0.195215\pi$
$464$	2.40532e6	0.518655
$465$	3.41370e6	0.732137
$466$	−30411.2	−0.00648738
$467$	−2.75815e6	−0.585229	−0.292614	−	0.956231i	$-0.594525\pi$
$467$	−2.75815e6	−0.585229	−0.292614	+	0.956231i	$0.594525\pi$
$468$	−34056.7	−0.00718766
$469$	0	0
$470$	2.65166e6	0.553697
$471$	−2.36318e6	−0.490846
$472$	−1.52011e6	−0.314065
$473$	113272.	0.0232793
$474$	−1.12282e6	−0.229544
$475$	−214065.	−0.0435323
$476$	0	0
$477$	1.18006e6	0.237470
$478$	8.74646e6	1.75090
$479$	3.00065e6	0.597553	0.298776	−	0.954323i	$-0.403422\pi$
$479$	3.00065e6	0.597553	0.298776	+	0.954323i	$0.403422\pi$
$480$	−461197.	−0.0913657
$481$	1.76584e6	0.348008
$482$	−7.45375e6	−1.46136
$483$	0	0
$484$	498149.	0.0966597
$485$	365104.	0.0704794
$486$	−1.21338e6	−0.233028
$487$	−855280.	−0.163413	−0.0817064	−	0.996656i	$-0.526037\pi$
$487$	−855280.	−0.163413	−0.0817064	+	0.996656i	$0.526037\pi$
$488$	8.70761e6	1.65520
$489$	8.72518e6	1.65007
$490$	0	0
$491$	6.37895e6	1.19411	0.597056	−	0.802199i	$-0.296337\pi$
$491$	6.37895e6	1.19411	0.597056	+	0.802199i	$0.296337\pi$
$492$	148778.	0.0277093
$493$	3.08369e6	0.571417
$494$	−676339.	−0.124694
$495$	8279.27	0.00151873
$496$	7.56542e6	1.38079
$497$	0	0
$498$	435212.	0.0786372
$499$	−1.75331e6	−0.315216	−0.157608	−	0.987502i	$-0.550378\pi$
$499$	−1.75331e6	−0.315216	−0.157608	+	0.987502i	$0.550378\pi$
$500$	48366.6	0.00865207
$501$	−3.00264e6	−0.534452
$502$	−2.13986e6	−0.378989
$503$	−261372.	−0.0460617	−0.0230308	−	0.999735i	$-0.507332\pi$
$503$	−261372.	−0.0460617	−0.0230308	+	0.999735i	$0.507332\pi$
$504$	0	0
$505$	−3.84015e6	−0.670069
$506$	123166.	0.0213853
$507$	−3.90543e6	−0.674760
$508$	885764.	0.152286
$509$	32421.3	0.00554672	0.00277336	−	0.999996i	$-0.499117\pi$
$509$	32421.3	0.00554672	0.00277336	+	0.999996i	$0.499117\pi$
$510$	2.60591e6	0.443643
$511$	0	0
$512$	−6.54895e6	−1.10407
$513$	1.20555e6	0.202251
$514$	−2.74353e6	−0.458039
$515$	3.29639e6	0.547671
$516$	523967.	0.0866322
$517$	218114.	0.0358887
$518$	0	0
$519$	−1.05850e7	−1.72494
$520$	1.73256e6	0.280983
$521$	5.56412e6	0.898053	0.449027	−	0.893518i	$-0.351771\pi$
$521$	5.56412e6	0.898053	0.449027	+	0.893518i	$0.351771\pi$
$522$	−423180.	−0.0679749
$523$	−3.94058e6	−0.629950	−0.314975	−	0.949100i	$-0.601996\pi$
$523$	−3.94058e6	−0.629950	−0.314975	+	0.949100i	$0.601996\pi$
$524$	−121839.	−0.0193846
$525$	0	0
$526$	7.39037e6	1.16467
$527$	9.69907e6	1.52126
$528$	167197.	0.0261002
$529$	−2.14259e6	−0.332889
$530$	−5.29501e6	−0.818799
$531$	241325.	0.0371420
$532$	0	0
$533$	−1.06852e6	−0.162916
$534$	6.15525e6	0.934098
$535$	4.24729e6	0.641546
$536$	−7.53076e6	−1.13221
$537$	9.34988e6	1.39917
$538$	1.41476e6	0.210731
$539$	0	0
$540$	−272385.	−0.0401974
$541$	7.33948e6	1.07813	0.539066	−	0.842263i	$-0.318777\pi$
$541$	7.33948e6	1.07813	0.539066	+	0.842263i	$0.318777\pi$
$542$	−6.73479e6	−0.984750
$543$	7.63204e6	1.11081
$544$	−1.31036e6	−0.189843
$545$	−549179.	−0.0791995
$546$	0	0
$547$	−5.92706e6	−0.846976	−0.423488	−	0.905902i	$-0.639194\pi$
$547$	−5.92706e6	−0.846976	−0.423488	+	0.905902i	$0.639194\pi$
$548$	−794193.	−0.112973
$549$	−1.38238e6	−0.195747
$550$	−37149.5	−0.00523657
$551$	900007.	0.126289
$552$	6.45948e6	0.902298
$553$	0	0
$554$	−5.27164e6	−0.729746
$555$	−1.98574e6	−0.273646
$556$	159495.	0.0218806
$557$	3.87133e6	0.528715	0.264358	−	0.964425i	$-0.414840\pi$
$557$	3.87133e6	0.528715	0.264358	+	0.964425i	$0.414840\pi$
$558$	−1.33102e6	−0.180967
$559$	−3.76312e6	−0.509353
$560$	0	0
$561$	214351.	0.0287554
$562$	−8.20484e6	−1.09579
$563$	1.25365e6	0.166688	0.0833442	−	0.996521i	$-0.473440\pi$
$563$	1.25365e6	0.166688	0.0833442	+	0.996521i	$0.473440\pi$
$564$	1.00894e6	0.133557
$565$	3.37839e6	0.445235
$566$	1.39927e6	0.183595
$567$	0	0
$568$	−1.14066e7	−1.48349
$569$	−1.00618e7	−1.30285	−0.651425	−	0.758713i	$-0.725829\pi$
$569$	−1.00618e7	−1.30285	−0.651425	+	0.758713i	$0.725829\pi$
$570$	760561.	0.0980499
$571$	−1.20255e7	−1.54352	−0.771759	−	0.635915i	$-0.780623\pi$
$571$	−1.20255e7	−1.54352	−0.771759	+	0.635915i	$0.780623\pi$
$572$	12569.9	0.00160635
$573$	−6.15400e6	−0.783017
$574$	0	0
$575$	−1.29509e6	−0.163354
$576$	1.05724e6	0.132775
$577$	−1.46566e7	−1.83271	−0.916355	−	0.400366i	$-0.868883\pi$
$577$	−1.46566e7	−1.83271	−0.916355	+	0.400366i	$0.868883\pi$
$578$	−229609.	−0.0285870
$579$	320050.	0.0396754
$580$	−203351.	−0.0251001
$581$	0	0
$582$	−1.29719e6	−0.158744
$583$	−435546.	−0.0530717
$584$	−8.83394e6	−1.07182
$585$	−275053.	−0.0332298
$586$	−1.31327e7	−1.57983
$587$	−610951.	−0.0731832	−0.0365916	−	0.999330i	$-0.511650\pi$
$587$	−610951.	−0.0731832	−0.0365916	+	0.999330i	$0.511650\pi$
$588$	0	0
$589$	2.83078e6	0.336215
$590$	−1.08284e6	−0.128066
$591$	−2.13634e6	−0.251595
$592$	−4.40078e6	−0.516090
$593$	8.89186e6	1.03838	0.519190	−	0.854659i	$-0.326234\pi$
$593$	8.89186e6	1.03838	0.519190	+	0.854659i	$0.326234\pi$
$594$	209214.	0.0243290
$595$	0	0
$596$	−1.30069e6	−0.149989
$597$	−7.25713e6	−0.833353
$598$	−4.09182e6	−0.467912
$599$	5.57297e6	0.634629	0.317314	−	0.948320i	$-0.397219\pi$
$599$	5.57297e6	0.634629	0.317314	+	0.948320i	$0.397219\pi$
$600$	−1.94831e6	−0.220943
$601$	−9.30873e6	−1.05125	−0.525623	−	0.850718i	$-0.676168\pi$
$601$	−9.30873e6	−1.05125	−0.525623	+	0.850718i	$0.676168\pi$
$602$	0	0
$603$	1.19555e6	0.133898
$604$	−246248.	−0.0274651
$605$	4.02322e6	0.446874
$606$	1.36438e7	1.50923
$607$	−626627.	−0.0690300	−0.0345150	−	0.999404i	$-0.510989\pi$
$607$	−626627.	−0.0690300	−0.0345150	+	0.999404i	$0.510989\pi$
$608$	−382444.	−0.0419574
$609$	0	0
$610$	6.20281e6	0.674938
$611$	−7.24618e6	−0.785247
$612$	108812.	0.0117435
$613$	2.98473e6	0.320814	0.160407	−	0.987051i	$-0.448719\pi$
$613$	2.98473e6	0.320814	0.160407	+	0.987051i	$0.448719\pi$
$614$	−967151.	−0.103532
$615$	1.20158e6	0.128105
$616$	0	0
$617$	345728.	0.0365613	0.0182806	−	0.999833i	$-0.494181\pi$
$617$	345728.	0.0365613	0.0182806	+	0.999833i	$0.494181\pi$
$618$	−1.17119e7	−1.23355
$619$	−2.73766e6	−0.287179	−0.143589	−	0.989637i	$-0.545864\pi$
$619$	−2.73766e6	−0.287179	−0.143589	+	0.989637i	$0.545864\pi$
$620$	−639595.	−0.0668230
$621$	7.29350e6	0.758939
$622$	−1.42230e7	−1.47406
$623$	0	0
$624$	−5.55461e6	−0.571074
$625$	390625.	0.0400000
$626$	−1.08607e7	−1.10770
$627$	62560.7	0.00635525
$628$	442770.	0.0448001
$629$	−5.64192e6	−0.568591
$630$	0	0
$631$	4.80556e6	0.480474	0.240237	−	0.970714i	$-0.422775\pi$
$631$	4.80556e6	0.480474	0.240237	+	0.970714i	$0.422775\pi$
$632$	2.38516e6	0.237534
$633$	−4.54665e6	−0.451006
$634$	−1.55226e7	−1.53370
$635$	7.15373e6	0.704042
$636$	−2.01472e6	−0.197502
$637$	0	0
$638$	156190.	0.0151915
$639$	1.81086e6	0.175441
$640$	−3.85060e6	−0.371602
$641$	3.79928e6	0.365221	0.182611	−	0.983185i	$-0.441545\pi$
$641$	3.79928e6	0.365221	0.182611	+	0.983185i	$0.441545\pi$
$642$	−1.50904e7	−1.44498
$643$	2.46468e6	0.235089	0.117545	−	0.993068i	$-0.462498\pi$
$643$	2.46468e6	0.235089	0.117545	+	0.993068i	$0.462498\pi$
$644$	0	0
$645$	4.23173e6	0.400515
$646$	2.16092e6	0.203732
$647$	5.72708e6	0.537865	0.268932	−	0.963159i	$-0.413329\pi$
$647$	5.72708e6	0.537865	0.268932	+	0.963159i	$0.413329\pi$
$648$	1.23457e7	1.15499
$649$	−89069.8	−0.00830078
$650$	1.23418e6	0.114576
$651$	0	0
$652$	−1.63476e6	−0.150604
$653$	−2.62713e6	−0.241101	−0.120550	−	0.992707i	$-0.538466\pi$
$653$	−2.62713e6	−0.241101	−0.120550	+	0.992707i	$0.538466\pi$
$654$	1.95120e6	0.178385
$655$	−984012.	−0.0896184
$656$	2.66294e6	0.241603
$657$	1.40243e6	0.126756
$658$	0	0
$659$	1.46417e7	1.31334	0.656671	−	0.754177i	$-0.271964\pi$
$659$	1.46417e7	1.31334	0.656671	+	0.754177i	$0.271964\pi$
$660$	−14135.2	−0.00126311
$661$	1.34296e7	1.19553	0.597763	−	0.801673i	$-0.296056\pi$
$661$	1.34296e7	1.19553	0.597763	+	0.801673i	$0.296056\pi$
$662$	7.74259e6	0.686659
$663$	−7.12116e6	−0.629168
$664$	−924500.	−0.0813742
$665$	0	0
$666$	774250.	0.0676387
$667$	5.44501e6	0.473897
$668$	562579.	0.0487800
$669$	1.82236e7	1.57423
$670$	−5.36448e6	−0.461680
$671$	510218.	0.0437471
$672$	0	0
$673$	8.25651e6	0.702682	0.351341	−	0.936248i	$-0.385726\pi$
$673$	8.25651e6	0.702682	0.351341	+	0.936248i	$0.385726\pi$
$674$	2.15886e6	0.183052
$675$	−2.19987e6	−0.185840
$676$	731727.	0.0615861
$677$	4.92012e6	0.412576	0.206288	−	0.978491i	$-0.433862\pi$
$677$	4.92012e6	0.412576	0.206288	+	0.978491i	$0.433862\pi$
$678$	−1.20032e7	−1.00282
$679$	0	0
$680$	−5.53560e6	−0.459084
$681$	−1.27766e7	−1.05572
$682$	491262.	0.0404438
$683$	−1.47407e7	−1.20911	−0.604556	−	0.796563i	$-0.706649\pi$
$683$	−1.47407e7	−1.20911	−0.604556	+	0.796563i	$0.706649\pi$
$684$	31758.0	0.00259545
$685$	−6.41418e6	−0.522293
$686$	0	0
$687$	2.37903e7	1.92313
$688$	9.37836e6	0.755363
$689$	1.44697e7	1.16121
$690$	4.60137e6	0.367929
$691$	−1.37360e7	−1.09437	−0.547185	−	0.837012i	$-0.684301\pi$
$691$	−1.37360e7	−1.09437	−0.547185	+	0.837012i	$0.684301\pi$
$692$	1.98323e6	0.157437
$693$	0	0
$694$	1.33678e7	1.05356
$695$	1.28813e6	0.101158
$696$	8.19142e6	0.640968
$697$	3.41396e6	0.266180
$698$	−4.08628e6	−0.317460
$699$	−93453.6	−0.00723441
$700$	0	0
$701$	−9.23895e6	−0.710113	−0.355057	−	0.934845i	$-0.615538\pi$
$701$	−9.23895e6	−0.710113	−0.355057	+	0.934845i	$0.615538\pi$
$702$	−6.95049e6	−0.532320
$703$	−1.64665e6	−0.125665
$704$	−390213.	−0.0296736
$705$	8.14853e6	0.617457
$706$	1.73636e6	0.131107
$707$	0	0
$708$	−412012.	−0.0308907
$709$	−1.56718e7	−1.17086	−0.585428	−	0.810724i	$-0.699074\pi$
$709$	−1.56718e7	−1.17086	−0.585428	+	0.810724i	$0.699074\pi$
$710$	−8.12541e6	−0.604922
$711$	−378657.	−0.0280913
$712$	−1.30753e7	−0.966611
$713$	1.71261e7	1.26164
$714$	0	0
$715$	101519.	0.00742644
$716$	−1.75181e6	−0.127704
$717$	2.68778e7	1.95252
$718$	−2.03276e7	−1.47155
$719$	7.77979e6	0.561236	0.280618	−	0.959819i	$-0.409461\pi$
$719$	7.77979e6	0.561236	0.280618	+	0.959819i	$0.409461\pi$
$720$	685481.	0.0492792
$721$	0	0
$722$	−1.26815e7	−0.905377
$723$	−2.29053e7	−1.62964
$724$	−1.42995e6	−0.101385
$725$	−1.64233e6	−0.116042
$726$	−1.42943e7	−1.00652
$727$	3.18266e6	0.223334	0.111667	−	0.993746i	$-0.464381\pi$
$727$	3.18266e6	0.223334	0.111667	+	0.993746i	$0.464381\pi$
$728$	0	0
$729$	1.21709e7	0.848213
$730$	−6.29280e6	−0.437055
$731$	1.20233e7	0.832205
$732$	2.36013e6	0.162801
$733$	−2.33890e7	−1.60787	−0.803935	−	0.594717i	$-0.797264\pi$
$733$	−2.33890e7	−1.60787	−0.803935	+	0.594717i	$0.797264\pi$
$734$	−2.31499e7	−1.58602
$735$	0	0
$736$	−2.31377e6	−0.157444
$737$	−441261.	−0.0299245
$738$	−468503.	−0.0316644
$739$	2.22717e6	0.150017	0.0750087	−	0.997183i	$-0.476102\pi$
$739$	2.22717e6	0.150017	0.0750087	+	0.997183i	$0.476102\pi$
$740$	372050.	0.0249760
$741$	−2.07839e6	−0.139053
$742$	0	0
$743$	−936803.	−0.0622553	−0.0311276	−	0.999515i	$-0.509910\pi$
$743$	−936803.	−0.0622553	−0.0311276	+	0.999515i	$0.509910\pi$
$744$	2.57643e7	1.70642
$745$	−1.05049e7	−0.693425
$746$	2.33270e7	1.53466
$747$	146769.	0.00962351
$748$	−40161.2	−0.00262453
$749$	0	0
$750$	−1.38787e6	−0.0900938
$751$	−1.70492e6	−0.110307	−0.0551536	−	0.998478i	$-0.517565\pi$
$751$	−1.70492e6	−0.110307	−0.0551536	+	0.998478i	$0.517565\pi$
$752$	1.80587e7	1.16451
$753$	−6.57579e6	−0.422630
$754$	−5.18894e6	−0.332391
$755$	−1.98879e6	−0.126976
$756$	0	0
$757$	2.53663e7	1.60886	0.804428	−	0.594051i	$-0.202472\pi$
$757$	2.53663e7	1.60886	0.804428	+	0.594051i	$0.202472\pi$
$758$	−1.76143e7	−1.11350
$759$	378490.	0.0238479
$760$	−1.61562e6	−0.101463
$761$	1.83989e7	1.15167	0.575837	−	0.817565i	$-0.304676\pi$
$761$	1.83989e7	1.15167	0.575837	+	0.817565i	$0.304676\pi$
$762$	−2.54168e7	−1.58575
$763$	0	0
$764$	1.15302e6	0.0714668
$765$	878805.	0.0542924
$766$	−1.94043e7	−1.19488
$767$	2.95907e6	0.181621
$768$	−4.97882e6	−0.304595
$769$	619294.	0.0377643	0.0188821	−	0.999822i	$-0.493989\pi$
$769$	619294.	0.0377643	0.0188821	+	0.999822i	$0.493989\pi$
$770$	0	0
$771$	−8.43087e6	−0.510783
$772$	−59965.0	−0.00362122
$773$	1.09079e7	0.656588	0.328294	−	0.944576i	$-0.393526\pi$
$773$	1.09079e7	0.656588	0.328294	+	0.944576i	$0.393526\pi$
$774$	−1.64998e6	−0.0989978
$775$	−5.16559e6	−0.308934
$776$	2.75557e6	0.164269
$777$	0	0
$778$	8.65098e6	0.512408
$779$	996400.	0.0588288
$780$	469597.	0.0276369
$781$	−668364.	−0.0392090
$782$	1.30735e7	0.764496
$783$	9.24906e6	0.539130
$784$	0	0
$785$	3.57596e6	0.207118
$786$	3.49614e6	0.201852
$787$	184858.	0.0106390	0.00531951	−	0.999986i	$-0.498307\pi$
$787$	184858.	0.0106390	0.00531951	+	0.999986i	$0.498307\pi$
$788$	400267.	0.0229633
$789$	2.27106e7	1.29878
$790$	1.69905e6	0.0968588
$791$	0	0
$792$	62486.5	0.00353975
$793$	−1.69504e7	−0.957188
$794$	−652972.	−0.0367573
$795$	−1.62715e7	−0.913085
$796$	1.35971e6	0.0760611
$797$	3.23367e7	1.80323	0.901613	−	0.432543i	$-0.142384\pi$
$797$	3.23367e7	1.80323	0.901613	+	0.432543i	$0.142384\pi$
$798$	0	0
$799$	2.31518e7	1.28297
$800$	697881.	0.0385528
$801$	2.07577e6	0.114314
$802$	−2.74879e7	−1.50906
$803$	−517620.	−0.0283284
$804$	−2.04115e6	−0.111362
$805$	0	0
$806$	−1.63207e7	−0.884912
$807$	4.34757e6	0.234997
$808$	−2.89829e7	−1.56176
$809$	9.09846e6	0.488761	0.244381	−	0.969679i	$-0.421415\pi$
$809$	9.09846e6	0.488761	0.244381	+	0.969679i	$0.421415\pi$
$810$	8.79436e6	0.470968
$811$	−3.70294e7	−1.97695	−0.988473	−	0.151396i	$-0.951623\pi$
$811$	−3.70294e7	−1.97695	−0.988473	+	0.151396i	$0.951623\pi$
$812$	0	0
$813$	−2.06960e7	−1.09815
$814$	−285765.	−0.0151164
$815$	−1.32029e7	−0.696266
$816$	1.77472e7	0.933048
$817$	3.50913e6	0.183926
$818$	2.50980e7	1.31146
$819$	0	0
$820$	−225130.	−0.0116923
$821$	3.14038e7	1.62601	0.813007	−	0.582254i	$-0.197829\pi$
$821$	3.14038e7	1.62601	0.813007	+	0.582254i	$0.197829\pi$
$822$	2.27892e7	1.17639
$823$	−3.33574e7	−1.71669	−0.858346	−	0.513072i	$-0.828507\pi$
$823$	−3.33574e7	−1.71669	−0.858346	+	0.513072i	$0.828507\pi$
$824$	2.48789e7	1.27648
$825$	−114160.	−0.00583957
$826$	0	0
$827$	6.34159e6	0.322429	0.161215	−	0.986919i	$-0.448459\pi$
$827$	6.34159e6	0.322429	0.161215	+	0.986919i	$0.448459\pi$
$828$	192135.	0.00973934
$829$	−1.57969e7	−0.798334	−0.399167	−	0.916878i	$-0.630701\pi$
$829$	−1.57969e7	−0.798334	−0.399167	+	0.916878i	$0.630701\pi$
$830$	−658561.	−0.0331819
$831$	−1.61997e7	−0.813777
$832$	1.29636e7	0.649259
$833$	0	0
$834$	−4.57667e6	−0.227842
$835$	4.54358e6	0.225518
$836$	−11721.5	−0.000580051 0
$837$	2.90909e7	1.43530
$838$	2.88613e7	1.41973
$839$	1.88579e7	0.924888	0.462444	−	0.886649i	$-0.346973\pi$
$839$	1.88579e7	0.924888	0.462444	+	0.886649i	$0.346973\pi$
$840$	0	0
$841$	−1.36062e7	−0.663357
$842$	−9.27565e6	−0.450883
$843$	−2.52134e7	−1.22198
$844$	851866.	0.0411638
$845$	5.90968e6	0.284723
$846$	−3.17716e6	−0.152621
$847$	0	0
$848$	−3.60610e7	−1.72206
$849$	4.29996e6	0.204737
$850$	−3.94324e6	−0.187200
$851$	−9.96219e6	−0.471554
$852$	−3.09167e6	−0.145913
$853$	1.96760e7	0.925898	0.462949	−	0.886385i	$-0.346791\pi$
$853$	1.96760e7	0.925898	0.462949	+	0.886385i	$0.346791\pi$
$854$	0	0
$855$	256488.	0.0119992
$856$	3.20558e7	1.49528
$857$	−1.15028e7	−0.534997	−0.267499	−	0.963558i	$-0.586197\pi$
$857$	−1.15028e7	−0.534997	−0.267499	+	0.963558i	$0.586197\pi$
$858$	−360690.	−0.0167269
$859$	−9.91985e6	−0.458693	−0.229347	−	0.973345i	$-0.573659\pi$
$859$	−9.91985e6	−0.458693	−0.229347	+	0.973345i	$0.573659\pi$
$860$	−792864.	−0.0365555
$861$	0	0
$862$	−2.13634e7	−0.979269
$863$	6.99312e6	0.319628	0.159814	−	0.987147i	$-0.448911\pi$
$863$	6.99312e6	0.319628	0.159814	+	0.987147i	$0.448911\pi$
$864$	−3.93024e6	−0.179116
$865$	1.60172e7	0.727859
$866$	−9.45224e6	−0.428292
$867$	−705587.	−0.0318788
$868$	0	0
$869$	139757.	0.00627805
$870$	5.83510e6	0.261367
$871$	1.46595e7	0.654749
$872$	−4.14484e6	−0.184594
$873$	−437460.	−0.0194269
$874$	3.81564e6	0.168962
$875$	0	0
$876$	−2.39437e6	−0.105422
$877$	4.60833e6	0.202323	0.101161	−	0.994870i	$-0.467744\pi$
$877$	4.60833e6	0.202323	0.101161	+	0.994870i	$0.467744\pi$
$878$	−2.75378e7	−1.20557
$879$	−4.03568e7	−1.76175
$880$	−253002.	−0.0110133
$881$	3.09916e7	1.34525	0.672627	−	0.739982i	$-0.265166\pi$
$881$	3.09916e7	1.34525	0.672627	+	0.739982i	$0.265166\pi$
$882$	0	0
$883$	−2.62829e7	−1.13441	−0.567207	−	0.823575i	$-0.691976\pi$
$883$	−2.62829e7	−1.13441	−0.567207	+	0.823575i	$0.691976\pi$
$884$	1.33423e6	0.0574249
$885$	−3.32755e6	−0.142813
$886$	3.50190e7	1.49872
$887$	−1.77899e6	−0.0759215	−0.0379607	−	0.999279i	$-0.512086\pi$
$887$	−1.77899e6	−0.0759215	−0.0379607	+	0.999279i	$0.512086\pi$
$888$	−1.49870e7	−0.637798
$889$	0	0
$890$	−9.31409e6	−0.394154
$891$	723389.	0.0305265
$892$	−3.41440e6	−0.143682
$893$	6.75709e6	0.283551
$894$	3.73232e7	1.56183
$895$	−1.41482e7	−0.590396
$896$	0	0
$897$	−1.25742e7	−0.521792
$898$	−2.06808e7	−0.855809
$899$	2.17180e7	0.896232
$900$	−57951.8	−0.00238485
$901$	−4.62311e7	−1.89724
$902$	172918.	0.00707660
$903$	0	0
$904$	2.54979e7	1.03773
$905$	−1.15488e7	−0.468720
$906$	7.06604e6	0.285993
$907$	−2.60166e7	−1.05010	−0.525051	−	0.851071i	$-0.675954\pi$
$907$	−2.60166e7	−1.05010	−0.525051	+	0.851071i	$0.675954\pi$
$908$	2.39385e6	0.0963568
$909$	4.60119e6	0.184697
$910$	0	0
$911$	−2.82785e7	−1.12891	−0.564457	−	0.825463i	$-0.690914\pi$
$911$	−2.82785e7	−1.12891	−0.564457	+	0.825463i	$0.690914\pi$
$912$	5.17970e6	0.206214
$913$	−54170.6	−0.00215073
$914$	2.19047e7	0.867304
$915$	1.90612e7	0.752658
$916$	−4.45739e6	−0.175526
$917$	0	0
$918$	2.22071e7	0.869730
$919$	3.48158e7	1.35984	0.679920	−	0.733286i	$-0.262014\pi$
$919$	3.48158e7	1.35984	0.679920	+	0.733286i	$0.262014\pi$
$920$	−9.77446e6	−0.380735
$921$	−2.97205e6	−0.115454
$922$	−4.64236e6	−0.179851
$923$	2.22043e7	0.857893
$924$	0	0
$925$	3.00481e6	0.115468
$926$	4.05594e7	1.55440
$927$	−3.94966e6	−0.150960
$928$	−2.93414e6	−0.111844
$929$	−2.23517e7	−0.849710	−0.424855	−	0.905261i	$-0.639675\pi$
$929$	−2.23517e7	−0.849710	−0.424855	+	0.905261i	$0.639675\pi$
$930$	1.83530e7	0.695826
$931$	0	0
$932$	17509.6	0.000660292 0
$933$	−4.37074e7	−1.64381
$934$	−1.48286e7	−0.556203
$935$	−324355.	−0.0121337
$936$	−2.07592e6	−0.0774500
$937$	−6.87782e6	−0.255919	−0.127959	−	0.991779i	$-0.540843\pi$
$937$	−6.87782e6	−0.255919	−0.127959	+	0.991779i	$0.540843\pi$
$938$	0	0
$939$	−3.33749e7	−1.23525
$940$	−1.52672e6	−0.0563559
$941$	3.65000e7	1.34375	0.671875	−	0.740664i	$-0.265489\pi$
$941$	3.65000e7	1.34375	0.671875	+	0.740664i	$0.265489\pi$
$942$	−1.27052e7	−0.466502
$943$	6.02818e6	0.220753
$944$	−7.37452e6	−0.269342
$945$	0	0
$946$	608985.	0.0221248
$947$	3.53650e7	1.28144	0.640721	−	0.767773i	$-0.278635\pi$
$947$	3.53650e7	1.28144	0.640721	+	0.767773i	$0.278635\pi$
$948$	646479.	0.0233633
$949$	1.71963e7	0.619827
$950$	−1.15088e6	−0.0413733
$951$	−4.77008e7	−1.71031
$952$	0	0
$953$	−8.09150e6	−0.288600	−0.144300	−	0.989534i	$-0.546093\pi$
$953$	−8.09150e6	−0.288600	−0.144300	+	0.989534i	$0.546093\pi$
$954$	6.34437e6	0.225693
$955$	9.31221e6	0.330403
$956$	−5.03587e6	−0.178209
$957$	479972.	0.0169409
$958$	1.61324e7	0.567916
$959$	0	0
$960$	−1.45780e7	−0.510527
$961$	3.96801e7	1.38600
$962$	9.49368e6	0.330748
$963$	−5.08902e6	−0.176835
$964$	4.29158e6	0.148739
$965$	−484298.	−0.0167415
$966$	0	0
$967$	1.82499e7	0.627617	0.313808	−	0.949486i	$-0.398395\pi$
$967$	1.82499e7	0.627617	0.313808	+	0.949486i	$0.398395\pi$
$968$	3.03646e7	1.04155
$969$	6.64051e6	0.227192
$970$	1.96291e6	0.0669839
$971$	−1.53154e7	−0.521292	−0.260646	−	0.965434i	$-0.583935\pi$
$971$	−1.53154e7	−0.521292	−0.260646	+	0.965434i	$0.583935\pi$
$972$	698619.	0.0237178
$973$	0	0
$974$	−4.59824e6	−0.155308
$975$	3.79263e6	0.127770
$976$	4.22434e7	1.41950
$977$	1.80410e7	0.604679	0.302339	−	0.953200i	$-0.402232\pi$
$977$	1.80410e7	0.604679	0.302339	+	0.953200i	$0.402232\pi$
$978$	4.69091e7	1.56823
$979$	−766140.	−0.0255477
$980$	0	0
$981$	658014.	0.0218305
$982$	3.42951e7	1.13489
$983$	1.41126e7	0.465824	0.232912	−	0.972498i	$-0.425175\pi$
$983$	1.41126e7	0.465824	0.232912	+	0.972498i	$0.425175\pi$
$984$	9.06873e6	0.298579
$985$	3.23270e6	0.106163
$986$	1.65788e7	0.543077
$987$	0	0
$988$	389409.	0.0126915
$989$	2.12301e7	0.690178
$990$	44511.8	0.00144340
$991$	−5.56339e6	−0.179952	−0.0899758	−	0.995944i	$-0.528679\pi$
$991$	−5.56339e6	−0.179952	−0.0899758	+	0.995944i	$0.528679\pi$
$992$	−9.22871e6	−0.297757
$993$	2.37929e7	0.765729
$994$	0	0
$995$	1.09815e7	0.351643
$996$	−250578.	−0.00800378
$997$	−2.71962e6	−0.0866503	−0.0433252	−	0.999061i	$-0.513795\pi$
$997$	−2.71962e6	−0.0866503	−0.0433252	+	0.999061i	$0.513795\pi$
$998$	−9.42632e6	−0.299582
$999$	−1.69221e7	−0.536463

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.6.a.l.1.7	✓	10
7.6	odd	2		245.6.a.m.1.7	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
245.6.a.l.1.7	✓	10	1.1	even	1	trivial
245.6.a.m.1.7	yes	10	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+5.37629 q^{2} +16.5213 q^{3} -3.09546 q^{4} -25.0000 q^{5} +88.8236 q^{6} -188.684 q^{8} +29.9545 q^{9} +O(q^{10})\)	\(q+5.37629 q^{2} +16.5213 q^{3} -3.09546 q^{4} -25.0000 q^{5} +88.8236 q^{6} -188.684 q^{8} +29.9545 q^{9} -134.407 q^{10} -11.0558 q^{11} -51.1411 q^{12} +367.295 q^{13} -413.033 q^{15} -915.363 q^{16} -1173.52 q^{17} +161.044 q^{18} -342.504 q^{19} +77.3865 q^{20} -59.4393 q^{22} -2072.14 q^{23} -3117.30 q^{24} +625.000 q^{25} +1974.69 q^{26} -3519.80 q^{27} -2627.73 q^{29} -2220.59 q^{30} -8264.94 q^{31} +1116.61 q^{32} -182.657 q^{33} -6309.19 q^{34} -92.7229 q^{36} +4807.69 q^{37} -1841.40 q^{38} +6068.21 q^{39} +4717.09 q^{40} -2909.16 q^{41} -10245.5 q^{43} +34.2228 q^{44} -748.862 q^{45} -11140.4 q^{46} -19728.5 q^{47} -15123.0 q^{48} +3360.18 q^{50} -19388.1 q^{51} -1136.95 q^{52} +39395.2 q^{53} -18923.5 q^{54} +276.395 q^{55} -5658.63 q^{57} -14127.4 q^{58} +8056.38 q^{59} +1278.53 q^{60} -46149.3 q^{61} -44434.7 q^{62} +35294.9 q^{64} -9182.38 q^{65} -982.016 q^{66} +39912.1 q^{67} +3632.58 q^{68} -34234.5 q^{69} +60453.6 q^{71} -5651.92 q^{72} +46818.8 q^{73} +25847.6 q^{74} +10325.8 q^{75} +1060.21 q^{76} +32624.5 q^{78} -12641.1 q^{79} +22884.1 q^{80} -65430.7 q^{81} -15640.5 q^{82} +4899.74 q^{83} +29338.0 q^{85} -55082.8 q^{86} -43413.5 q^{87} +2086.05 q^{88} +69297.5 q^{89} -4026.10 q^{90} +6414.22 q^{92} -136548. q^{93} -106066. q^{94} +8562.61 q^{95} +18447.9 q^{96} -14604.2 q^{97} -331.171 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 10 q^{2} - 58 q^{3} + 182 q^{4} - 250 q^{5} - 144 q^{6} + 270 q^{8} + 700 q^{9}+O(q^{10}) \) 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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