LMFDB - Embedded newform 245.6.a.h.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("245.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$39.2940358542$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 109x^{4} + 41x^{3} + 2208x^{2} - 3204x + 560 $ x^6 - x^5 - 109x^4 + 41x^3 + 2208x^2 - 3204x + 560
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 35)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-8.17253$ 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)

$f(q)$	$=$	$q-9.17253 q^{2} -14.3258 q^{3} +52.1353 q^{4} +25.0000 q^{5} +131.404 q^{6} -184.691 q^{8} -37.7723 q^{9} +O(q^{10})$	\(q-9.17253 q^{2} -14.3258 q^{3} +52.1353 q^{4} +25.0000 q^{5} +131.404 q^{6} -184.691 q^{8} -37.7723 q^{9} -229.313 q^{10} +215.386 q^{11} -746.878 q^{12} -132.696 q^{13} -358.144 q^{15} +25.7572 q^{16} -441.638 q^{17} +346.467 q^{18} -519.002 q^{19} +1303.38 q^{20} -1975.63 q^{22} -4389.66 q^{23} +2645.84 q^{24} +625.000 q^{25} +1217.16 q^{26} +4022.28 q^{27} +7114.31 q^{29} +3285.09 q^{30} +10304.7 q^{31} +5673.86 q^{32} -3085.56 q^{33} +4050.94 q^{34} -1969.27 q^{36} +5568.08 q^{37} +4760.56 q^{38} +1900.98 q^{39} -4617.28 q^{40} -7246.54 q^{41} -184.308 q^{43} +11229.2 q^{44} -944.307 q^{45} +40264.3 q^{46} -16174.2 q^{47} -368.991 q^{48} -5732.83 q^{50} +6326.81 q^{51} -6918.16 q^{52} +7275.69 q^{53} -36894.5 q^{54} +5384.64 q^{55} +7435.11 q^{57} -65256.2 q^{58} +45301.7 q^{59} -18671.9 q^{60} +7369.70 q^{61} -94520.4 q^{62} -52867.9 q^{64} -3317.41 q^{65} +28302.4 q^{66} -64443.0 q^{67} -23024.9 q^{68} +62885.2 q^{69} -343.451 q^{71} +6976.21 q^{72} -45357.4 q^{73} -51073.4 q^{74} -8953.61 q^{75} -27058.3 q^{76} -17436.8 q^{78} -74587.6 q^{79} +643.929 q^{80} -48443.6 q^{81} +66469.1 q^{82} +54772.9 q^{83} -11041.0 q^{85} +1690.57 q^{86} -101918. q^{87} -39779.8 q^{88} +106839. q^{89} +8661.68 q^{90} -228856. q^{92} -147623. q^{93} +148358. q^{94} -12975.1 q^{95} -81282.4 q^{96} -19313.9 q^{97} -8135.60 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 5 q^{2} - 20 q^{3} + 31 q^{4} + 150 q^{5} - 96 q^{6} - 135 q^{8} + 378 q^{9}+O(q^{10}) $ 6 * q - 5 * q^2 - 20 * q^3 + 31 * q^4 + 150 * q^5 - 96 * q^6 - 135 * q^8 + 378 * q^9	\( 6 q - 5 q^{2} - 20 q^{3} + 31 q^{4} + 150 q^{5} - 96 q^{6} - 135 q^{8} + 378 q^{9} - 125 q^{10} - 924 q^{11} - 370 q^{12} + 150 q^{13} - 500 q^{15} + 435 q^{16} - 1540 q^{17} + 195 q^{18} - 92 q^{19} + 775 q^{20} - 6855 q^{22} - 3920 q^{23} + 7200 q^{24} + 3750 q^{25} - 2635 q^{26} - 2060 q^{27} + 1264 q^{29} - 2400 q^{30} + 7160 q^{31} + 9105 q^{32} - 4460 q^{33} - 2166 q^{34} - 26375 q^{36} - 14170 q^{37} + 46215 q^{38} - 15376 q^{39} - 3375 q^{40} - 4098 q^{41} - 24460 q^{43} - 27873 q^{44} + 9450 q^{45} + 6815 q^{46} - 42940 q^{47} - 11610 q^{48} - 3125 q^{50} - 42008 q^{51} + 36115 q^{52} - 2450 q^{53} - 19566 q^{54} - 23100 q^{55} - 97100 q^{57} - 36110 q^{58} + 64600 q^{59} - 9250 q^{60} - 73620 q^{61} - 111440 q^{62} - 157997 q^{64} + 3750 q^{65} + 139138 q^{66} - 142620 q^{67} - 124330 q^{68} - 17344 q^{69} - 154256 q^{71} - 117495 q^{72} + 5120 q^{73} + 2785 q^{74} - 12500 q^{75} - 7775 q^{76} - 214090 q^{78} - 222504 q^{79} + 10875 q^{80} - 43986 q^{81} - 31665 q^{82} - 179580 q^{83} - 38500 q^{85} - 207160 q^{86} + 209300 q^{87} - 45145 q^{88} - 41648 q^{89} + 4875 q^{90} - 292185 q^{92} - 198520 q^{93} + 333699 q^{94} - 2300 q^{95} - 61824 q^{96} + 73980 q^{97} - 190772 q^{99}+O(q^{100}) \) 6 * q - 5 * q^2 - 20 * q^3 + 31 * q^4 + 150 * q^5 - 96 * q^6 - 135 * q^8 + 378 * q^9 - 125 * q^10 - 924 * q^11 - 370 * q^12 + 150 * q^13 - 500 * q^15 + 435 * q^16 - 1540 * q^17 + 195 * q^18 - 92 * q^19 + 775 * q^20 - 6855 * q^22 - 3920 * q^23 + 7200 * q^24 + 3750 * q^25 - 2635 * q^26 - 2060 * q^27 + 1264 * q^29 - 2400 * q^30 + 7160 * q^31 + 9105 * q^32 - 4460 * q^33 - 2166 * q^34 - 26375 * q^36 - 14170 * q^37 + 46215 * q^38 - 15376 * q^39 - 3375 * q^40 - 4098 * q^41 - 24460 * q^43 - 27873 * q^44 + 9450 * q^45 + 6815 * q^46 - 42940 * q^47 - 11610 * q^48 - 3125 * q^50 - 42008 * q^51 + 36115 * q^52 - 2450 * q^53 - 19566 * q^54 - 23100 * q^55 - 97100 * q^57 - 36110 * q^58 + 64600 * q^59 - 9250 * q^60 - 73620 * q^61 - 111440 * q^62 - 157997 * q^64 + 3750 * q^65 + 139138 * q^66 - 142620 * q^67 - 124330 * q^68 - 17344 * q^69 - 154256 * q^71 - 117495 * q^72 + 5120 * q^73 + 2785 * q^74 - 12500 * q^75 - 7775 * q^76 - 214090 * q^78 - 222504 * q^79 + 10875 * q^80 - 43986 * q^81 - 31665 * q^82 - 179580 * q^83 - 38500 * q^85 - 207160 * q^86 + 209300 * q^87 - 45145 * q^88 - 41648 * q^89 + 4875 * q^90 - 292185 * q^92 - 198520 * q^93 + 333699 * q^94 - 2300 * q^95 - 61824 * q^96 + 73980 * q^97 - 190772 * 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 $

$2$	−9.17253	−1.62149	−0.810745	−	0.585400i	$-0.800937\pi$
$2$	−9.17253	−1.62149	−0.810745	+	0.585400i	$0.800937\pi$
$3$	−14.3258	−0.918999	−0.459499	−	0.888178i	$-0.651971\pi$
$3$	−14.3258	−0.918999	−0.459499	+	0.888178i	$0.651971\pi$
$4$	52.1353	1.62923
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	131.404	1.49015
$7$	0	0
$7$	0	0
$8$	−184.691	−1.02028
$9$	−37.7723	−0.155441
$10$	−229.313	−0.725152
$11$	215.386	0.536704	0.268352	−	0.963321i	$-0.413521\pi$
$11$	215.386	0.536704	0.268352	+	0.963321i	$0.413521\pi$
$12$	−746.878	−1.49726
$13$	−132.696	−0.217771	−0.108886	−	0.994054i	$-0.534728\pi$
$13$	−132.696	−0.217771	−0.108886	+	0.994054i	$0.534728\pi$
$14$	0	0
$15$	−358.144	−0.410989
$16$	25.7572	0.0251535
$17$	−441.638	−0.370633	−0.185317	−	0.982679i	$-0.559331\pi$
$17$	−441.638	−0.370633	−0.185317	+	0.982679i	$0.559331\pi$
$18$	346.467	0.252047
$19$	−519.002	−0.329826	−0.164913	−	0.986308i	$-0.552734\pi$
$19$	−519.002	−0.329826	−0.164913	+	0.986308i	$0.552734\pi$
$20$	1303.38	0.728612
$21$	0	0
$22$	−1975.63	−0.870260
$23$	−4389.66	−1.73026	−0.865129	−	0.501549i	$-0.832764\pi$
$23$	−4389.66	−1.73026	−0.865129	+	0.501549i	$0.832764\pi$
$24$	2645.84	0.937640
$25$	625.000	0.200000
$26$	1217.16	0.353114
$27$	4022.28	1.06185
$28$	0	0
$29$	7114.31	1.57086	0.785430	−	0.618950i	$-0.212442\pi$
$29$	7114.31	1.57086	0.785430	+	0.618950i	$0.212442\pi$
$30$	3285.09	0.666414
$31$	10304.7	1.92589	0.962946	−	0.269693i	$-0.0869222\pi$
$31$	10304.7	1.92589	0.962946	+	0.269693i	$0.0869222\pi$
$32$	5673.86	0.979499
$33$	−3085.56	−0.493230
$34$	4050.94	0.600978
$35$	0	0
$36$	−1969.27	−0.253249
$37$	5568.08	0.668654	0.334327	−	0.942457i	$-0.391491\pi$
$37$	5568.08	0.668654	0.334327	+	0.942457i	$0.391491\pi$
$38$	4760.56	0.534810
$39$	1900.98	0.200132
$40$	−4617.28	−0.456285
$41$	−7246.54	−0.673242	−0.336621	−	0.941640i	$-0.609284\pi$
$41$	−7246.54	−0.673242	−0.336621	+	0.941640i	$0.609284\pi$
$42$	0	0
$43$	−184.308	−0.0152010	−0.00760050	−	0.999971i	$-0.502419\pi$
$43$	−184.308	−0.0152010	−0.00760050	+	0.999971i	$0.502419\pi$
$44$	11229.2	0.874413
$45$	−944.307	−0.0695155
$46$	40264.3	2.80560
$47$	−16174.2	−1.06802	−0.534008	−	0.845480i	$-0.679315\pi$
$47$	−16174.2	−1.06802	−0.534008	+	0.845480i	$0.679315\pi$
$48$	−368.991	−0.0231160
$49$	0	0
$50$	−5732.83	−0.324298
$51$	6326.81	0.340611
$52$	−6918.16	−0.354799
$53$	7275.69	0.355782	0.177891	−	0.984050i	$-0.443072\pi$
$53$	7275.69	0.355782	0.177891	+	0.984050i	$0.443072\pi$
$54$	−36894.5	−1.72178
$55$	5384.64	0.240021
$56$	0	0
$57$	7435.11	0.303110
$58$	−65256.2	−2.54713
$59$	45301.7	1.69428	0.847138	−	0.531373i	$-0.178324\pi$
$59$	45301.7	1.69428	0.847138	+	0.531373i	$0.178324\pi$
$60$	−18671.9	−0.669594
$61$	7369.70	0.253586	0.126793	−	0.991929i	$-0.459532\pi$
$61$	7369.70	0.253586	0.126793	+	0.991929i	$0.459532\pi$
$62$	−94520.4	−3.12281
$63$	0	0
$64$	−52867.9	−1.61340
$65$	−3317.41	−0.0973903
$66$	28302.4	0.799767
$67$	−64443.0	−1.75383	−0.876917	−	0.480641i	$-0.840404\pi$
$67$	−64443.0	−1.75383	−0.876917	+	0.480641i	$0.840404\pi$
$68$	−23024.9	−0.603846
$69$	62885.2	1.59011
$70$	0	0
$71$	−343.451	−0.00808573	−0.00404286	−	0.999992i	$-0.501287\pi$
$71$	−343.451	−0.00808573	−0.00404286	+	0.999992i	$0.501287\pi$
$72$	6976.21	0.158595
$73$	−45357.4	−0.996187	−0.498094	−	0.867123i	$-0.665966\pi$
$73$	−45357.4	−0.996187	−0.498094	+	0.867123i	$0.665966\pi$
$74$	−51073.4	−1.08421
$75$	−8953.61	−0.183800
$76$	−27058.3	−0.537362
$77$	0	0
$78$	−17436.8	−0.324511
$79$	−74587.6	−1.34462	−0.672309	−	0.740271i	$-0.734697\pi$
$79$	−74587.6	−1.34462	−0.672309	+	0.740271i	$0.734697\pi$
$80$	643.929	0.0112490
$81$	−48443.6	−0.820396
$82$	66469.1	1.09165
$83$	54772.9	0.872711	0.436356	−	0.899774i	$-0.356269\pi$
$83$	54772.9	0.872711	0.436356	+	0.899774i	$0.356269\pi$
$84$	0	0
$85$	−11041.0	−0.165752
$86$	1690.57	0.0246483
$87$	−101918.	−1.44362
$88$	−39779.8	−0.547591
$89$	106839.	1.42974	0.714868	−	0.699260i	$-0.246487\pi$
$89$	106839.	1.42974	0.714868	+	0.699260i	$0.246487\pi$
$90$	8661.68	0.112719
$91$	0	0
$92$	−228856.	−2.81898
$93$	−147623.	−1.76989
$94$	148358.	1.73178
$95$	−12975.1	−0.147503
$96$	−81282.4	−0.900158
$97$	−19313.9	−0.208421	−0.104210	−	0.994555i	$-0.533231\pi$
$97$	−19313.9	−0.208421	−0.104210	+	0.994555i	$0.533231\pi$
$98$	0	0
$99$	−8135.60	−0.0834261
$100$	32584.5	0.325845
$101$	24524.6	0.239221	0.119610	−	0.992821i	$-0.461835\pi$
$101$	24524.6	0.239221	0.119610	+	0.992821i	$0.461835\pi$
$102$	−58032.8	−0.552298
$103$	46312.7	0.430137	0.215069	−	0.976599i	$-0.431003\pi$
$103$	46312.7	0.430137	0.215069	+	0.976599i	$0.431003\pi$
$104$	24507.9	0.222189
$105$	0	0
$106$	−66736.4	−0.576897
$107$	157154.	1.32699	0.663495	−	0.748181i	$-0.269073\pi$
$107$	157154.	1.32699	0.663495	+	0.748181i	$0.269073\pi$
$108$	209703.	1.72999
$109$	−141538.	−1.14106	−0.570530	−	0.821277i	$-0.693262\pi$
$109$	−141538.	−1.14106	−0.570530	+	0.821277i	$0.693262\pi$
$110$	−49390.7	−0.389192
$111$	−79767.0	−0.614492
$112$	0	0
$113$	−157706.	−1.16186	−0.580928	−	0.813955i	$-0.697310\pi$
$113$	−157706.	−1.16186	−0.580928	+	0.813955i	$0.697310\pi$
$114$	−68198.7	−0.491489
$115$	−109741.	−0.773795
$116$	370906.	2.55929
$117$	5012.25	0.0338507
$118$	−415531.	−2.74725
$119$	0	0
$120$	66146.1	0.419325
$121$	−114660.	−0.711949
$122$	−67598.8	−0.411187
$123$	103812.	0.618709
$124$	537239.	3.13772
$125$	15625.0	0.0894427
$126$	0	0
$127$	−249665.	−1.37356	−0.686782	−	0.726864i	$-0.740977\pi$
$127$	−249665.	−1.37356	−0.686782	+	0.726864i	$0.740977\pi$
$128$	303369.	1.63661
$129$	2640.35	0.0139697
$130$	30429.0	0.157917
$131$	−216534.	−1.10242	−0.551210	−	0.834366i	$-0.685834\pi$
$131$	−216534.	−1.10242	−0.551210	+	0.834366i	$0.685834\pi$
$132$	−160867.	−0.803584
$133$	0	0
$134$	591105.	2.84382
$135$	100557.	0.474873
$136$	81566.7	0.378151
$137$	−58644.1	−0.266946	−0.133473	−	0.991052i	$-0.542613\pi$
$137$	−58644.1	−0.266946	−0.133473	+	0.991052i	$0.542613\pi$
$138$	−576816.	−2.57834
$139$	353961.	1.55388	0.776941	−	0.629573i	$-0.216770\pi$
$139$	353961.	1.55388	0.776941	+	0.629573i	$0.216770\pi$
$140$	0	0
$141$	231708.	0.981505
$142$	3150.32	0.0131109
$143$	−28580.9	−0.116879
$144$	−972.907	−0.00390989
$145$	177858.	0.702510
$146$	416042.	1.61531
$147$	0	0
$148$	290293.	1.08939
$149$	73724.4	0.272048	0.136024	−	0.990706i	$-0.456568\pi$
$149$	73724.4	0.272048	0.136024	+	0.990706i	$0.456568\pi$
$150$	82127.2	0.298029
$151$	−322597.	−1.15138	−0.575689	−	0.817669i	$-0.695266\pi$
$151$	−322597.	−1.15138	−0.575689	+	0.817669i	$0.695266\pi$
$152$	95855.2	0.336517
$153$	16681.7	0.0576118
$154$	0	0
$155$	257618.	0.861285
$156$	99108.0	0.326060
$157$	−224924.	−0.728261	−0.364131	−	0.931348i	$-0.618634\pi$
$157$	−224924.	−0.728261	−0.364131	+	0.931348i	$0.618634\pi$
$158$	684156.	2.18028
$159$	−104230.	−0.326963
$160$	141847.	0.438045
$161$	0	0
$162$	444350.	1.33026
$163$	−158217.	−0.466427	−0.233214	−	0.972426i	$-0.574924\pi$
$163$	−158217.	−0.466427	−0.233214	+	0.972426i	$0.574924\pi$
$164$	−377800.	−1.09686
$165$	−77139.1	−0.220579
$166$	−502406.	−1.41509
$167$	316938.	0.879392	0.439696	−	0.898147i	$-0.355086\pi$
$167$	316938.	0.879392	0.439696	+	0.898147i	$0.355086\pi$
$168$	0	0
$169$	−353685.	−0.952576
$170$	101273.	0.268765
$171$	19603.9	0.0512687
$172$	−9608.93	−0.0247659
$173$	−360124.	−0.914824	−0.457412	−	0.889255i	$-0.651223\pi$
$173$	−360124.	−0.914824	−0.457412	+	0.889255i	$0.651223\pi$
$174$	934845.	2.34081
$175$	0	0
$176$	5547.72	0.0135000
$177$	−648981.	−1.55704
$178$	−979986.	−2.31830
$179$	−440948.	−1.02862	−0.514310	−	0.857604i	$-0.671952\pi$
$179$	−440948.	−1.02862	−0.514310	+	0.857604i	$0.671952\pi$
$180$	−49231.7	−0.113257
$181$	−19489.0	−0.0442175	−0.0221087	−	0.999756i	$-0.507038\pi$
$181$	−19489.0	−0.0442175	−0.0221087	+	0.999756i	$0.507038\pi$
$182$	0	0
$183$	−105577.	−0.233045
$184$	810731.	1.76536
$185$	139202.	0.299031
$186$	1.35408e6	2.86986
$187$	−95122.5	−0.198920
$188$	−843245.	−1.74004
$189$	0	0
$190$	119014.	0.239174
$191$	−418719.	−0.830499	−0.415250	−	0.909708i	$-0.636306\pi$
$191$	−418719.	−0.830499	−0.415250	+	0.909708i	$0.636306\pi$
$192$	757373.	1.48271
$193$	4008.29	0.00774578	0.00387289	−	0.999993i	$-0.498767\pi$
$193$	4008.29	0.00774578	0.00387289	+	0.999993i	$0.498767\pi$
$194$	177157.	0.337952
$195$	47524.5	0.0895016
$196$	0	0
$197$	1.02060e6	1.87366	0.936830	−	0.349786i	$-0.113746\pi$
$197$	1.02060e6	1.87366	0.936830	+	0.349786i	$0.113746\pi$
$198$	74624.0	0.135274
$199$	157196.	0.281391	0.140695	−	0.990053i	$-0.455066\pi$
$199$	157196.	0.281391	0.140695	+	0.990053i	$0.455066\pi$
$200$	−115432.	−0.204057
$201$	923195.	1.61177
$202$	−224953.	−0.387894
$203$	0	0
$204$	329850.	0.554933
$205$	−181164.	−0.301083
$206$	−424804.	−0.697463
$207$	165807.	0.268954
$208$	−3417.88	−0.00547771
$209$	−111786.	−0.177019
$210$	0	0
$211$	−797769.	−1.23359	−0.616795	−	0.787124i	$-0.711569\pi$
$211$	−797769.	−1.23359	−0.616795	+	0.787124i	$0.711569\pi$
$212$	379320.	0.579650
$213$	4920.20	0.00743077
$214$	−1.44150e6	−2.15170
$215$	−4607.69	−0.00679810
$216$	−742880.	−1.08339
$217$	0	0
$218$	1.29827e6	1.85022
$219$	649780.	0.915495
$220$	280730.	0.391049
$221$	58603.8	0.0807133
$222$	731665.	0.996392
$223$	−1.17028e6	−1.57590	−0.787951	−	0.615739i	$-0.788858\pi$
$223$	−1.17028e6	−1.57590	−0.787951	+	0.615739i	$0.788858\pi$
$224$	0	0
$225$	−23607.7	−0.0310883
$226$	1.44656e6	1.88394
$227$	−419223.	−0.539983	−0.269991	−	0.962863i	$-0.587021\pi$
$227$	−419223.	−0.539983	−0.269991	+	0.962863i	$0.587021\pi$
$228$	387631.	0.493835
$229$	457265.	0.576208	0.288104	−	0.957599i	$-0.406975\pi$
$229$	457265.	0.576208	0.288104	+	0.957599i	$0.406975\pi$
$230$	1.00661e6	1.25470
$231$	0	0
$232$	−1.31395e6	−1.60273
$233$	−669972.	−0.808475	−0.404237	−	0.914654i	$-0.632463\pi$
$233$	−669972.	−0.808475	−0.404237	+	0.914654i	$0.632463\pi$
$234$	−45975.0	−0.0548886
$235$	−404354.	−0.477631
$236$	2.36181e6	2.76036
$237$	1.06852e6	1.23570
$238$	0	0
$239$	−550244.	−0.623104	−0.311552	−	0.950229i	$-0.600849\pi$
$239$	−550244.	−0.623104	−0.311552	+	0.950229i	$0.600849\pi$
$240$	−9224.78	−0.0103378
$241$	−163023.	−0.180804	−0.0904018	−	0.995905i	$-0.528815\pi$
$241$	−163023.	−0.180804	−0.0904018	+	0.995905i	$0.528815\pi$
$242$	1.05172e6	1.15442
$243$	−283422.	−0.307906
$244$	384221.	0.413149
$245$	0	0
$246$	−952221.	−1.00323
$247$	68869.8	0.0718267
$248$	−1.90319e6	−1.96496
$249$	−784664.	−0.802020
$250$	−143321.	−0.145030
$251$	−1.31883e6	−1.32131	−0.660654	−	0.750690i	$-0.729721\pi$
$251$	−1.31883e6	−1.32131	−0.660654	+	0.750690i	$0.729721\pi$
$252$	0	0
$253$	−945469.	−0.928637
$254$	2.29006e6	2.22722
$255$	158170.	0.152326
$256$	−1.09088e6	−1.04035
$257$	832987.	0.786693	0.393347	−	0.919390i	$-0.371317\pi$
$257$	832987.	0.786693	0.393347	+	0.919390i	$0.371317\pi$
$258$	−24218.7	−0.0226517
$259$	0	0
$260$	−172954.	−0.158671
$261$	−268724.	−0.244177
$262$	1.98616e6	1.78756
$263$	−1.64512e6	−1.46659	−0.733296	−	0.679910i	$-0.762019\pi$
$263$	−1.64512e6	−1.46659	−0.733296	+	0.679910i	$0.762019\pi$
$264$	569877.	0.503235
$265$	181892.	0.159111
$266$	0	0
$267$	−1.53055e6	−1.31392
$268$	−3.35975e6	−2.85739
$269$	−454521.	−0.382978	−0.191489	−	0.981495i	$-0.561332\pi$
$269$	−454521.	−0.382978	−0.191489	+	0.981495i	$0.561332\pi$
$270$	−922362.	−0.770002
$271$	−831066.	−0.687405	−0.343702	−	0.939079i	$-0.611681\pi$
$271$	−831066.	−0.687405	−0.343702	+	0.939079i	$0.611681\pi$
$272$	−11375.3	−0.00932272
$273$	0	0
$274$	537915.	0.432850
$275$	134616.	0.107341
$276$	3.27854e6	2.59064
$277$	1.30960e6	1.02551	0.512756	−	0.858534i	$-0.328625\pi$
$277$	1.30960e6	1.02551	0.512756	+	0.858534i	$0.328625\pi$
$278$	−3.24671e6	−2.51960
$279$	−389233.	−0.299364
$280$	0	0
$281$	175721.	0.132757	0.0663784	−	0.997795i	$-0.478856\pi$
$281$	175721.	0.132757	0.0663784	+	0.997795i	$0.478856\pi$
$282$	−2.12534e6	−1.59150
$283$	−953011.	−0.707346	−0.353673	−	0.935369i	$-0.615067\pi$
$283$	−953011.	−0.707346	−0.353673	+	0.935369i	$0.615067\pi$
$284$	−17905.9	−0.0131735
$285$	185878.	0.135555
$286$	262159.	0.189518
$287$	0	0
$288$	−214315.	−0.152255
$289$	−1.22481e6	−0.862631
$290$	−1.63140e6	−1.13911
$291$	276686.	0.191538
$292$	−2.36472e6	−1.62302
$293$	−275025.	−0.187156	−0.0935778	−	0.995612i	$-0.529830\pi$
$293$	−275025.	−0.187156	−0.0935778	+	0.995612i	$0.529830\pi$
$294$	0	0
$295$	1.13254e6	0.757703
$296$	−1.02838e6	−0.682217
$297$	866341.	0.569899
$298$	−676239.	−0.441123
$299$	582492.	0.376801
$300$	−466799.	−0.299451
$301$	0	0
$302$	2.95903e6	1.86695
$303$	−351334.	−0.219843
$304$	−13368.0	−0.00829628
$305$	184242.	0.113407
$306$	−153013.	−0.0934169
$307$	−473977.	−0.287019	−0.143510	−	0.989649i	$-0.545839\pi$
$307$	−473977.	−0.287019	−0.143510	+	0.989649i	$0.545839\pi$
$308$	0	0
$309$	−663465.	−0.395295
$310$	−2.36301e6	−1.39656
$311$	−3.10860e6	−1.82248	−0.911241	−	0.411873i	$-0.864875\pi$
$311$	−3.10860e6	−1.82248	−0.911241	+	0.411873i	$0.864875\pi$
$312$	−351094.	−0.204191
$313$	−1.51927e6	−0.876544	−0.438272	−	0.898842i	$-0.644409\pi$
$313$	−1.51927e6	−0.876544	−0.438272	+	0.898842i	$0.644409\pi$
$314$	2.06312e6	1.18087
$315$	0	0
$316$	−3.88864e6	−2.19069
$317$	2.53235e6	1.41539	0.707695	−	0.706518i	$-0.249735\pi$
$317$	2.53235e6	1.41539	0.707695	+	0.706518i	$0.249735\pi$
$318$	956051.	0.530168
$319$	1.53232e6	0.843087
$320$	−1.32170e6	−0.721534
$321$	−2.25136e6	−1.21950
$322$	0	0
$323$	229211.	0.122245
$324$	−2.52562e6	−1.33661
$325$	−82935.3	−0.0435543
$326$	1.45125e6	0.756307
$327$	2.02765e6	1.04863
$328$	1.33837e6	0.686899
$329$	0	0
$330$	707560.	0.357667
$331$	557600.	0.279739	0.139869	−	0.990170i	$-0.455332\pi$
$331$	557600.	0.279739	0.139869	+	0.990170i	$0.455332\pi$
$332$	2.85560e6	1.42184
$333$	−210319.	−0.103937
$334$	−2.90712e6	−1.42592
$335$	−1.61107e6	−0.784339
$336$	0	0
$337$	501783.	0.240681	0.120340	−	0.992733i	$-0.461601\pi$
$337$	501783.	0.240681	0.120340	+	0.992733i	$0.461601\pi$
$338$	3.24418e6	1.54459
$339$	2.25926e6	1.06774
$340$	−575623.	−0.270048
$341$	2.21949e6	1.03363
$342$	−179817.	−0.0831316
$343$	0	0
$344$	34040.0	0.0155094
$345$	1.57213e6	0.711117
$346$	3.30325e6	1.48338
$347$	283359.	0.126332	0.0631661	−	0.998003i	$-0.479880\pi$
$347$	283359.	0.126332	0.0631661	+	0.998003i	$0.479880\pi$
$348$	−5.31352e6	−2.35198
$349$	−569924.	−0.250469	−0.125234	−	0.992127i	$-0.539968\pi$
$349$	−569924.	−0.250469	−0.125234	+	0.992127i	$0.539968\pi$
$350$	0	0
$351$	−533742.	−0.231240
$352$	1.22207e6	0.525701
$353$	1.74073e6	0.743522	0.371761	−	0.928328i	$-0.378754\pi$
$353$	1.74073e6	0.743522	0.371761	+	0.928328i	$0.378754\pi$
$354$	5.95280e6	2.52472
$355$	−8586.28	−0.00361605
$356$	5.57009e6	2.32936
$357$	0	0
$358$	4.04461e6	1.66790
$359$	933824.	0.382410	0.191205	−	0.981550i	$-0.438761\pi$
$359$	933824.	0.382410	0.191205	+	0.981550i	$0.438761\pi$
$360$	174405.	0.0709256
$361$	−2.20674e6	−0.891215
$362$	178764.	0.0716982
$363$	1.64259e6	0.654280
$364$	0	0
$365$	−1.13394e6	−0.445509
$366$	968404.	0.377880
$367$	−1.52484e6	−0.590962	−0.295481	−	0.955349i	$-0.595480\pi$
$367$	−1.52484e6	−0.590962	−0.295481	+	0.955349i	$0.595480\pi$
$368$	−113065.	−0.0435220
$369$	273719.	0.104650
$370$	−1.27683e6	−0.484875
$371$	0	0
$372$	−7.69637e6	−2.88356
$373$	2.28822e6	0.851579	0.425789	−	0.904822i	$-0.359996\pi$
$373$	2.28822e6	0.851579	0.425789	+	0.904822i	$0.359996\pi$
$374$	872514.	0.322547
$375$	−223840.	−0.0821977
$376$	2.98723e6	1.08968
$377$	−944044.	−0.342089
$378$	0	0
$379$	−210030.	−0.0751074	−0.0375537	−	0.999295i	$-0.511957\pi$
$379$	−210030.	−0.0751074	−0.0375537	+	0.999295i	$0.511957\pi$
$380$	−676458.	−0.240316
$381$	3.57665e6	1.26230
$382$	3.84071e6	1.34665
$383$	3.37503e6	1.17566	0.587828	−	0.808986i	$-0.299983\pi$
$383$	3.37503e6	1.17566	0.587828	+	0.808986i	$0.299983\pi$
$384$	−4.34599e6	−1.50404
$385$	0	0
$386$	−36766.1	−0.0125597
$387$	6961.72	0.00236287
$388$	−1.00693e6	−0.339564
$389$	1.98548e6	0.665259	0.332630	−	0.943058i	$-0.392064\pi$
$389$	1.98548e6	0.665259	0.332630	+	0.943058i	$0.392064\pi$
$390$	−435920.	−0.145126
$391$	1.93864e6	0.641291
$392$	0	0
$393$	3.10201e6	1.01312
$394$	−9.36150e6	−3.03812
$395$	−1.86469e6	−0.601331
$396$	−424152.	−0.135920
$397$	−2.53409e6	−0.806948	−0.403474	−	0.914991i	$-0.632197\pi$
$397$	−2.53409e6	−0.806948	−0.403474	+	0.914991i	$0.632197\pi$
$398$	−1.44189e6	−0.456272
$399$	0	0
$400$	16098.2	0.00503070
$401$	3.79055e6	1.17717	0.588587	−	0.808434i	$-0.299684\pi$
$401$	3.79055e6	1.17717	0.588587	+	0.808434i	$0.299684\pi$
$402$	−8.46804e6	−2.61347
$403$	−1.36740e6	−0.419404
$404$	1.27860e6	0.389745
$405$	−1.21109e6	−0.366892
$406$	0	0
$407$	1.19928e6	0.358869
$408$	−1.16851e6	−0.347521
$409$	5.10159e6	1.50798	0.753992	−	0.656883i	$-0.228126\pi$
$409$	5.10159e6	1.50798	0.753992	+	0.656883i	$0.228126\pi$
$410$	1.66173e6	0.488203
$411$	840122.	0.245323
$412$	2.41452e6	0.700791
$413$	0	0
$414$	−1.52087e6	−0.436106
$415$	1.36932e6	0.390288
$416$	−752901.	−0.213307
$417$	−5.07076e6	−1.42802
$418$	1.02536e6	0.287035
$419$	−6.31053e6	−1.75603	−0.878013	−	0.478637i	$-0.841131\pi$
$419$	−6.31053e6	−1.75603	−0.878013	+	0.478637i	$0.841131\pi$
$420$	0	0
$421$	−3.26642e6	−0.898186	−0.449093	−	0.893485i	$-0.648253\pi$
$421$	−3.26642e6	−0.898186	−0.449093	+	0.893485i	$0.648253\pi$
$422$	7.31756e6	2.00025
$423$	610935.	0.166014
$424$	−1.34376e6	−0.362999
$425$	−276024.	−0.0741267
$426$	−45130.7	−0.0120489
$427$	0	0
$428$	8.19329e6	2.16197
$429$	409443.	0.107411
$430$	42264.2	0.0110230
$431$	−2.31016e6	−0.599031	−0.299516	−	0.954091i	$-0.596825\pi$
$431$	−2.31016e6	−0.599031	−0.299516	+	0.954091i	$0.596825\pi$
$432$	103603.	0.0267092
$433$	3.81574e6	0.978044	0.489022	−	0.872271i	$-0.337354\pi$
$433$	3.81574e6	0.978044	0.489022	+	0.872271i	$0.337354\pi$
$434$	0	0
$435$	−2.54795e6	−0.645606
$436$	−7.37915e6	−1.85905
$437$	2.27824e6	0.570685
$438$	−5.96012e6	−1.48446
$439$	673888.	0.166889	0.0834443	−	0.996512i	$-0.473408\pi$
$439$	673888.	0.166889	0.0834443	+	0.996512i	$0.473408\pi$
$440$	−994496.	−0.244890
$441$	0	0
$442$	−537545.	−0.130876
$443$	−4.84599e6	−1.17320	−0.586602	−	0.809875i	$-0.699535\pi$
$443$	−4.84599e6	−1.17320	−0.586602	+	0.809875i	$0.699535\pi$
$444$	−4.15868e6	−1.00115
$445$	2.67098e6	0.639397
$446$	1.07345e7	2.55531
$447$	−1.05616e6	−0.250012
$448$	0	0
$449$	3.09732e6	0.725055	0.362527	−	0.931973i	$-0.381914\pi$
$449$	3.09732e6	0.725055	0.362527	+	0.931973i	$0.381914\pi$
$450$	216542.	0.0504093
$451$	−1.56080e6	−0.361332
$452$	−8.22204e6	−1.89293
$453$	4.62145e6	1.05812
$454$	3.84533e6	0.875577
$455$	0	0
$456$	−1.37320e6	−0.309258
$457$	−6.58726e6	−1.47542	−0.737708	−	0.675120i	$-0.764092\pi$
$457$	−6.58726e6	−1.47542	−0.737708	+	0.675120i	$0.764092\pi$
$458$	−4.19428e6	−0.934315
$459$	−1.77639e6	−0.393557
$460$	−5.72140e6	−1.26069
$461$	5.26481e6	1.15380	0.576900	−	0.816815i	$-0.304262\pi$
$461$	5.26481e6	1.15380	0.576900	+	0.816815i	$0.304262\pi$
$462$	0	0
$463$	−2.79127e6	−0.605131	−0.302565	−	0.953129i	$-0.597843\pi$
$463$	−2.79127e6	−0.605131	−0.302565	+	0.953129i	$0.597843\pi$
$464$	183244.	0.0395126
$465$	−3.69058e6	−0.791520
$466$	6.14533e6	1.31093
$467$	3.23304e6	0.685992	0.342996	−	0.939337i	$-0.388558\pi$
$467$	3.23304e6	0.685992	0.342996	+	0.939337i	$0.388558\pi$
$468$	261315.	0.0551505
$469$	0	0
$470$	3.70895e6	0.774473
$471$	3.22221e6	0.669271
$472$	−8.36682e6	−1.72864
$473$	−39697.2	−0.00815844
$474$	−9.80107e6	−2.00368
$475$	−324376.	−0.0659653
$476$	0	0
$477$	−274819.	−0.0553033
$478$	5.04713e6	1.01036
$479$	−3.97758e6	−0.792100	−0.396050	−	0.918229i	$-0.629619\pi$
$479$	−3.97758e6	−0.792100	−0.396050	+	0.918229i	$0.629619\pi$
$480$	−2.03206e6	−0.402563
$481$	−738864.	−0.145614
$482$	1.49534e6	0.293171
$483$	0	0
$484$	−5.97783e6	−1.15993
$485$	−482847.	−0.0932085
$486$	2.59970e6	0.499266
$487$	517375.	0.0988515	0.0494257	−	0.998778i	$-0.484261\pi$
$487$	517375.	0.0988515	0.0494257	+	0.998778i	$0.484261\pi$
$488$	−1.36112e6	−0.258730
$489$	2.26658e6	0.428646
$490$	0	0
$491$	−992388.	−0.185771	−0.0928854	−	0.995677i	$-0.529609\pi$
$491$	−992388.	−0.185771	−0.0928854	+	0.995677i	$0.529609\pi$
$492$	5.41228e6	1.00802
$493$	−3.14195e6	−0.582213
$494$	−631710.	−0.116466
$495$	−203390.	−0.0373093
$496$	265420.	0.0484429
$497$	0	0
$498$	7.19735e6	1.30047
$499$	2.95997e6	0.532153	0.266076	−	0.963952i	$-0.414273\pi$
$499$	2.95997e6	0.532153	0.266076	+	0.963952i	$0.414273\pi$
$500$	814613.	0.145722
$501$	−4.54038e6	−0.808160
$502$	1.20970e7	2.14249
$503$	2.55586e6	0.450419	0.225210	−	0.974310i	$-0.427693\pi$
$503$	2.55586e6	0.450419	0.225210	+	0.974310i	$0.427693\pi$
$504$	0	0
$505$	613115.	0.106983
$506$	8.67234e6	1.50577
$507$	5.06681e6	0.875416
$508$	−1.30164e7	−2.23785
$509$	571600.	0.0977907	0.0488953	−	0.998804i	$-0.484430\pi$
$509$	571600.	0.0977907	0.0488953	+	0.998804i	$0.484430\pi$
$510$	−1.45082e6	−0.246995
$511$	0	0
$512$	298370.	0.0503015
$513$	−2.08757e6	−0.350226
$514$	−7.64060e6	−1.27561
$515$	1.15782e6	0.192363
$516$	137655.	0.0227598
$517$	−3.48368e6	−0.573208
$518$	0	0
$519$	5.15906e6	0.840722
$520$	612697.	0.0993659
$521$	−3.84947e6	−0.621307	−0.310653	−	0.950523i	$-0.600548\pi$
$521$	−3.84947e6	−0.621307	−0.310653	+	0.950523i	$0.600548\pi$
$522$	2.46488e6	0.395930
$523$	−3.34856e6	−0.535308	−0.267654	−	0.963515i	$-0.586248\pi$
$523$	−3.34856e6	−0.535308	−0.267654	+	0.963515i	$0.586248\pi$
$524$	−1.12890e7	−1.79609
$525$	0	0
$526$	1.50899e7	2.37806
$527$	−4.55096e6	−0.713800
$528$	−79475.4	−0.0124065
$529$	1.28327e7	1.99379
$530$	−1.66841e6	−0.257996
$531$	−1.71115e6	−0.263361
$532$	0	0
$533$	961591.	0.146613
$534$	1.40391e7	2.13052
$535$	3.92886e6	0.593448
$536$	1.19021e7	1.78941
$537$	6.31692e6	0.945301
$538$	4.16911e6	0.620994
$539$	0	0
$540$	5.24256e6	0.773677
$541$	3.28206e6	0.482117	0.241059	−	0.970511i	$-0.422505\pi$
$541$	3.28206e6	0.482117	0.241059	+	0.970511i	$0.422505\pi$
$542$	7.62298e6	1.11462
$543$	279196.	0.0406358
$544$	−2.50579e6	−0.363035
$545$	−3.53846e6	−0.510297
$546$	0	0
$547$	7.92785e6	1.13289	0.566444	−	0.824100i	$-0.308319\pi$
$547$	7.92785e6	1.13289	0.566444	+	0.824100i	$0.308319\pi$
$548$	−3.05743e6	−0.434915
$549$	−278370.	−0.0394178
$550$	−1.23477e6	−0.174052
$551$	−3.69234e6	−0.518111
$552$	−1.16144e7	−1.62236
$553$	0	0
$554$	−1.20124e7	−1.66286
$555$	−1.99418e6	−0.274809
$556$	1.84538e7	2.53163
$557$	9.22341e6	1.25966	0.629830	−	0.776733i	$-0.283124\pi$
$557$	9.22341e6	1.25966	0.629830	+	0.776733i	$0.283124\pi$
$558$	3.57025e6	0.485415
$559$	24457.0	0.00331035
$560$	0	0
$561$	1.36270e6	0.182808
$562$	−1.61180e6	−0.215264
$563$	−1.16920e7	−1.55460	−0.777298	−	0.629132i	$-0.783410\pi$
$563$	−1.16920e7	−1.55460	−0.777298	+	0.629132i	$0.783410\pi$
$564$	1.20801e7	1.59909
$565$	−3.94265e6	−0.519598
$566$	8.74152e6	1.14695
$567$	0	0
$568$	63432.4	0.00824974
$569$	252494.	0.0326941	0.0163471	−	0.999866i	$-0.494796\pi$
$569$	252494.	0.0326941	0.0163471	+	0.999866i	$0.494796\pi$
$570$	−1.70497e6	−0.219801
$571$	4.62266e6	0.593337	0.296669	−	0.954981i	$-0.404124\pi$
$571$	4.62266e6	0.593337	0.296669	+	0.954981i	$0.404124\pi$
$572$	−1.49007e6	−0.190422
$573$	5.99847e6	0.763228
$574$	0	0
$575$	−2.74354e6	−0.346052
$576$	1.99694e6	0.250789
$577$	1.36752e7	1.71000	0.854999	−	0.518630i	$-0.173558\pi$
$577$	1.36752e7	1.71000	0.854999	+	0.518630i	$0.173558\pi$
$578$	1.12346e7	1.39875
$579$	−57421.8	−0.00711836
$580$	9.27266e6	1.14455
$581$	0	0
$582$	−2.53791e6	−0.310577
$583$	1.56708e6	0.190950
$584$	8.37712e6	1.01639
$585$	125306.	0.0151385
$586$	2.52267e6	0.303471
$587$	1.08136e7	1.29532	0.647659	−	0.761930i	$-0.275748\pi$
$587$	1.08136e7	1.29532	0.647659	+	0.761930i	$0.275748\pi$
$588$	0	0
$589$	−5.34817e6	−0.635210
$590$	−1.03883e7	−1.22861
$591$	−1.46209e7	−1.72189
$592$	143418.	0.0168190
$593$	−5.20786e6	−0.608166	−0.304083	−	0.952645i	$-0.598350\pi$
$593$	−5.20786e6	−0.608166	−0.304083	+	0.952645i	$0.598350\pi$
$594$	−7.94654e6	−0.924085
$595$	0	0
$596$	3.84364e6	0.443228
$597$	−2.25196e6	−0.258598
$598$	−5.34292e6	−0.610979
$599$	−1.43236e7	−1.63112	−0.815561	−	0.578671i	$-0.803572\pi$
$599$	−1.43236e7	−1.63112	−0.815561	+	0.578671i	$0.803572\pi$
$600$	1.65365e6	0.187528
$601$	−5.68832e6	−0.642389	−0.321194	−	0.947013i	$-0.604084\pi$
$601$	−5.68832e6	−0.642389	−0.321194	+	0.947013i	$0.604084\pi$
$602$	0	0
$603$	2.43416e6	0.272619
$604$	−1.68187e7	−1.87586
$605$	−2.86650e6	−0.318393
$606$	3.22262e6	0.356474
$607$	−1.54940e7	−1.70683	−0.853417	−	0.521228i	$-0.825474\pi$
$607$	−1.54940e7	−1.70683	−0.853417	+	0.521228i	$0.825474\pi$
$608$	−2.94475e6	−0.323064
$609$	0	0
$610$	−1.68997e6	−0.183888
$611$	2.14626e6	0.232583
$612$	869704.	0.0938627
$613$	−1.68053e7	−1.80632	−0.903161	−	0.429303i	$-0.858759\pi$
$613$	−1.68053e7	−1.80632	−0.903161	+	0.429303i	$0.858759\pi$
$614$	4.34756e6	0.465399
$615$	2.59531e6	0.276695
$616$	0	0
$617$	−4.82924e6	−0.510700	−0.255350	−	0.966849i	$-0.582191\pi$
$617$	−4.82924e6	−0.510700	−0.255350	+	0.966849i	$0.582191\pi$
$618$	6.08565e6	0.640967
$619$	2.06396e6	0.216508	0.108254	−	0.994123i	$-0.465474\pi$
$619$	2.06396e6	0.216508	0.108254	+	0.994123i	$0.465474\pi$
$620$	1.34310e7	1.40323
$621$	−1.76564e7	−1.83727
$622$	2.85137e7	2.95514
$623$	0	0
$624$	48963.8	0.00503401
$625$	390625.	0.0400000
$626$	1.39355e7	1.42131
$627$	1.60141e6	0.162680
$628$	−1.17265e7	−1.18650
$629$	−2.45908e6	−0.247825
$630$	0	0
$631$	−1.37020e7	−1.36997	−0.684986	−	0.728556i	$-0.740192\pi$
$631$	−1.37020e7	−1.36997	−0.684986	+	0.728556i	$0.740192\pi$
$632$	1.37757e7	1.37189
$633$	1.14287e7	1.13367
$634$	−2.32281e7	−2.29504
$635$	−6.24163e6	−0.614276
$636$	−5.43405e6	−0.532698
$637$	0	0
$638$	−1.40552e7	−1.36706
$639$	12972.9	0.00125686
$640$	7.58421e6	0.731915
$641$	1.70359e6	0.163764	0.0818821	−	0.996642i	$-0.473907\pi$
$641$	1.70359e6	0.163764	0.0818821	+	0.996642i	$0.473907\pi$
$642$	2.06507e7	1.97741
$643$	1.74387e7	1.66336	0.831682	−	0.555252i	$-0.187378\pi$
$643$	1.74387e7	1.66336	0.831682	+	0.555252i	$0.187378\pi$
$644$	0	0
$645$	66008.8	0.00624744
$646$	−2.10245e6	−0.198218
$647$	1.08759e7	1.02142	0.510712	−	0.859752i	$-0.329382\pi$
$647$	1.08759e7	1.02142	0.510712	+	0.859752i	$0.329382\pi$
$648$	8.94711e6	0.837038
$649$	9.75732e6	0.909325
$650$	760726.	0.0706228
$651$	0	0
$652$	−8.24868e6	−0.759916
$653$	−4.27466e6	−0.392300	−0.196150	−	0.980574i	$-0.562844\pi$
$653$	−4.27466e6	−0.392300	−0.196150	+	0.980574i	$0.562844\pi$
$654$	−1.85987e7	−1.70035
$655$	−5.41334e6	−0.493018
$656$	−186650.	−0.0169344
$657$	1.71325e6	0.154849
$658$	0	0
$659$	1.15036e7	1.03186	0.515931	−	0.856630i	$-0.327446\pi$
$659$	1.15036e7	1.03186	0.515931	+	0.856630i	$0.327446\pi$
$660$	−4.02167e6	−0.359374
$661$	−2.11275e7	−1.88081	−0.940403	−	0.340062i	$-0.889552\pi$
$661$	−2.11275e7	−1.88081	−0.940403	+	0.340062i	$0.889552\pi$
$662$	−5.11460e6	−0.453593
$663$	−839545.	−0.0741755
$664$	−1.01161e7	−0.890414
$665$	0	0
$666$	1.92916e6	0.168532
$667$	−3.12294e7	−2.71800
$668$	1.65236e7	1.43273
$669$	1.67652e7	1.44825
$670$	1.47776e7	1.27180
$671$	1.58733e6	0.136101
$672$	0	0
$673$	8.51341e6	0.724546	0.362273	−	0.932072i	$-0.382001\pi$
$673$	8.51341e6	0.724546	0.362273	+	0.932072i	$0.382001\pi$
$674$	−4.60262e6	−0.390261
$675$	2.51392e6	0.212370
$676$	−1.84394e7	−1.55196
$677$	−9.53112e6	−0.799231	−0.399616	−	0.916683i	$-0.630856\pi$
$677$	−9.53112e6	−0.799231	−0.399616	+	0.916683i	$0.630856\pi$
$678$	−2.07231e7	−1.73133
$679$	0	0
$680$	2.03917e6	0.169114
$681$	6.00569e6	0.496244
$682$	−2.03583e7	−1.67603
$683$	2.84219e6	0.233132	0.116566	−	0.993183i	$-0.462811\pi$
$683$	2.84219e6	0.233132	0.116566	+	0.993183i	$0.462811\pi$
$684$	1.02205e6	0.0835283
$685$	−1.46610e6	−0.119382
$686$	0	0
$687$	−6.55067e6	−0.529534
$688$	−4747.24	−0.000382358 0
$689$	−965458.	−0.0774792
$690$	−1.44204e7	−1.15307
$691$	7.23494e6	0.576421	0.288210	−	0.957567i	$-0.406940\pi$
$691$	7.23494e6	0.576421	0.288210	+	0.957567i	$0.406940\pi$
$692$	−1.87752e7	−1.49046
$693$	0	0
$694$	−2.59912e6	−0.204846
$695$	8.84902e6	0.694917
$696$	1.88234e7	1.47290
$697$	3.20035e6	0.249526
$698$	5.22764e6	0.406132
$699$	9.59786e6	0.742987
$700$	0	0
$701$	−3.46129e6	−0.266038	−0.133019	−	0.991114i	$-0.542467\pi$
$701$	−3.46129e6	−0.266038	−0.133019	+	0.991114i	$0.542467\pi$
$702$	4.89576e6	0.374954
$703$	−2.88985e6	−0.220540
$704$	−1.13870e7	−0.865918
$705$	5.79269e6	0.438942
$706$	−1.59669e7	−1.20561
$707$	0	0
$708$	−3.38348e7	−2.53677
$709$	1.40088e6	0.104661	0.0523306	−	0.998630i	$-0.483335\pi$
$709$	1.40088e6	0.104661	0.0523306	+	0.998630i	$0.483335\pi$
$710$	78757.9	0.00586338
$711$	2.81734e6	0.209009
$712$	−1.97323e7	−1.45874
$713$	−4.52342e7	−3.33229
$714$	0	0
$715$	−714522.	−0.0522698
$716$	−2.29890e7	−1.67586
$717$	7.88267e6	0.572631
$718$	−8.56553e6	−0.620073
$719$	−5.86524e6	−0.423120	−0.211560	−	0.977365i	$-0.567854\pi$
$719$	−5.86524e6	−0.423120	−0.211560	+	0.977365i	$0.567854\pi$
$720$	−24322.7	−0.00174856
$721$	0	0
$722$	2.02413e7	1.44509
$723$	2.33543e6	0.166158
$724$	−1.01607e6	−0.0720403
$725$	4.44644e6	0.314172
$726$	−1.50667e7	−1.06091
$727$	−1.11670e7	−0.783609	−0.391804	−	0.920049i	$-0.628149\pi$
$727$	−1.11670e7	−0.783609	−0.391804	+	0.920049i	$0.628149\pi$
$728$	0	0
$729$	1.58320e7	1.10336
$730$	1.04011e7	0.722387
$731$	81397.3	0.00563400
$732$	−5.50426e6	−0.379683
$733$	−6.21665e6	−0.427362	−0.213681	−	0.976903i	$-0.568545\pi$
$733$	−6.21665e6	−0.427362	−0.213681	+	0.976903i	$0.568545\pi$
$734$	1.39866e7	0.958238
$735$	0	0
$736$	−2.49063e7	−1.69479
$737$	−1.38801e7	−0.941290
$738$	−2.51069e6	−0.169688
$739$	−1.07075e7	−0.721236	−0.360618	−	0.932714i	$-0.617434\pi$
$739$	−1.07075e7	−0.721236	−0.360618	+	0.932714i	$0.617434\pi$
$740$	7.25733e6	0.487189
$741$	−986612.	−0.0660087
$742$	0	0
$743$	−7.87985e6	−0.523656	−0.261828	−	0.965115i	$-0.584325\pi$
$743$	−7.87985e6	−0.523656	−0.261828	+	0.965115i	$0.584325\pi$
$744$	2.72647e7	1.80579
$745$	1.84311e6	0.121664
$746$	−2.09887e7	−1.38083
$747$	−2.06890e6	−0.135656
$748$	−4.95924e6	−0.324086
$749$	0	0
$750$	2.05318e6	0.133283
$751$	−9.79080e6	−0.633459	−0.316729	−	0.948516i	$-0.602585\pi$
$751$	−9.79080e6	−0.633459	−0.316729	+	0.948516i	$0.602585\pi$
$752$	−416601.	−0.0268643
$753$	1.88932e7	1.21428
$754$	8.65927e6	0.554693
$755$	−8.06493e6	−0.514912
$756$	0	0
$757$	9.46073e6	0.600047	0.300023	−	0.953932i	$-0.403006\pi$
$757$	9.46073e6	0.600047	0.300023	+	0.953932i	$0.403006\pi$
$758$	1.92650e6	0.121786
$759$	1.35446e7	0.853416
$760$	2.39638e6	0.150495
$761$	1.23890e7	0.775488	0.387744	−	0.921767i	$-0.373255\pi$
$761$	1.23890e7	0.775488	0.387744	+	0.921767i	$0.373255\pi$
$762$	−3.28069e7	−2.04681
$763$	0	0
$764$	−2.18300e7	−1.35307
$765$	417042.	0.0257648
$766$	−3.09575e7	−1.90631
$767$	−6.01137e6	−0.368965
$768$	1.56278e7	0.956078
$769$	2.81052e7	1.71384	0.856921	−	0.515447i	$-0.172374\pi$
$769$	2.81052e7	1.71384	0.856921	+	0.515447i	$0.172374\pi$
$770$	0	0
$771$	−1.19332e7	−0.722970
$772$	208973.	0.0126196
$773$	2.36299e7	1.42237	0.711187	−	0.703003i	$-0.248158\pi$
$773$	2.36299e7	1.42237	0.711187	+	0.703003i	$0.248158\pi$
$774$	−63856.6	−0.00383136
$775$	6.44045e6	0.385179
$776$	3.56711e6	0.212648
$777$	0	0
$778$	−1.82119e7	−1.07871
$779$	3.76097e6	0.222053
$780$	2.47770e6	0.145818
$781$	−73974.4	−0.00433964
$782$	−1.77822e7	−1.03985
$783$	2.86157e7	1.66802
$784$	0	0
$785$	−5.62311e6	−0.325688
$786$	−2.84533e7	−1.64277
$787$	−1.10151e7	−0.633946	−0.316973	−	0.948435i	$-0.602667\pi$
$787$	−1.10151e7	−0.633946	−0.316973	+	0.948435i	$0.602667\pi$
$788$	5.32093e7	3.05262
$789$	2.35677e7	1.34780
$790$	1.71039e7	0.975052
$791$	0	0
$792$	1.50257e6	0.0851183
$793$	−977933.	−0.0552238
$794$	2.32440e7	1.30846
$795$	−2.60575e6	−0.146223
$796$	8.19547e6	0.458449
$797$	1.94131e7	1.08256	0.541278	−	0.840844i	$-0.317941\pi$
$797$	1.94131e7	1.08256	0.541278	+	0.840844i	$0.317941\pi$
$798$	0	0
$799$	7.14313e6	0.395842
$800$	3.54616e6	0.195900
$801$	−4.03556e6	−0.222240
$802$	−3.47689e7	−1.90878
$803$	−9.76933e6	−0.534658
$804$	4.81310e7	2.62594
$805$	0	0
$806$	1.25425e7	0.680060
$807$	6.51137e6	0.351956
$808$	−4.52948e6	−0.244073
$809$	−1.03581e7	−0.556427	−0.278213	−	0.960519i	$-0.589742\pi$
$809$	−1.03581e7	−0.556427	−0.278213	+	0.960519i	$0.589742\pi$
$810$	1.11088e7	0.594912
$811$	−1.22637e6	−0.0654740	−0.0327370	−	0.999464i	$-0.510422\pi$
$811$	−1.22637e6	−0.0654740	−0.0327370	+	0.999464i	$0.510422\pi$
$812$	0	0
$813$	1.19057e7	0.631724
$814$	−1.10005e7	−0.581902
$815$	−3.95542e6	−0.208593
$816$	162961.	0.00856756
$817$	95656.1	0.00501369
$818$	−4.67944e7	−2.44518
$819$	0	0
$820$	−9.44501e6	−0.490533
$821$	1.50056e7	0.776955	0.388478	−	0.921458i	$-0.373001\pi$
$821$	1.50056e7	0.776955	0.388478	+	0.921458i	$0.373001\pi$
$822$	−7.70604e6	−0.397788
$823$	2.08511e7	1.07307	0.536537	−	0.843877i	$-0.319732\pi$
$823$	2.08511e7	1.07307	0.536537	+	0.843877i	$0.319732\pi$
$824$	−8.55355e6	−0.438862
$825$	−1.92848e6	−0.0986460
$826$	0	0
$827$	−1.11289e7	−0.565833	−0.282917	−	0.959145i	$-0.591302\pi$
$827$	−1.11289e7	−0.565833	−0.282917	+	0.959145i	$0.591302\pi$
$828$	8.64441e6	0.438187
$829$	−1.49680e7	−0.756446	−0.378223	−	0.925714i	$-0.623465\pi$
$829$	−1.49680e7	−0.756446	−0.378223	+	0.925714i	$0.623465\pi$
$830$	−1.25601e7	−0.632848
$831$	−1.87611e7	−0.942444
$832$	7.01538e6	0.351352
$833$	0	0
$834$	4.65117e7	2.31551
$835$	7.92344e6	0.393276
$836$	−5.82797e6	−0.288404
$837$	4.14485e7	2.04501
$838$	5.78835e7	2.84738
$839$	3.53209e7	1.73232	0.866159	−	0.499769i	$-0.166582\pi$
$839$	3.53209e7	1.73232	0.866159	+	0.499769i	$0.166582\pi$
$840$	0	0
$841$	3.01022e7	1.46760
$842$	2.99613e7	1.45640
$843$	−2.51733e6	−0.122003
$844$	−4.15919e7	−2.00980
$845$	−8.84212e6	−0.426005
$846$	−5.60382e6	−0.269190
$847$	0	0
$848$	187401.	0.00894916
$849$	1.36526e7	0.650050
$850$	2.53184e6	0.120196
$851$	−2.44420e7	−1.15694
$852$	256516.	0.0121064
$853$	9.41887e6	0.443227	0.221613	−	0.975135i	$-0.428868\pi$
$853$	9.41887e6	0.443227	0.221613	+	0.975135i	$0.428868\pi$
$854$	0	0
$855$	490098.	0.0229281
$856$	−2.90251e7	−1.35391
$857$	−1.05121e7	−0.488918	−0.244459	−	0.969660i	$-0.578610\pi$
$857$	−1.05121e7	−0.488918	−0.244459	+	0.969660i	$0.578610\pi$
$858$	−3.75563e6	−0.174167
$859$	−3.10282e7	−1.43474	−0.717371	−	0.696692i	$-0.754655\pi$
$859$	−3.10282e7	−1.43474	−0.717371	+	0.696692i	$0.754655\pi$
$860$	−240223.	−0.0110756
$861$	0	0
$862$	2.11900e7	0.971323
$863$	−2.79996e7	−1.27975	−0.639876	−	0.768479i	$-0.721014\pi$
$863$	−2.79996e7	−1.27975	−0.639876	+	0.768479i	$0.721014\pi$
$864$	2.28219e7	1.04008
$865$	−9.00311e6	−0.409122
$866$	−3.49999e7	−1.58589
$867$	1.75464e7	0.792757
$868$	0	0
$869$	−1.60651e7	−0.721661
$870$	2.33711e7	1.04684
$871$	8.55136e6	0.381935
$872$	2.61409e7	1.16421
$873$	729530.	0.0323972
$874$	−2.08972e7	−0.925359
$875$	0	0
$876$	3.38764e7	1.49155
$877$	2.14218e7	0.940497	0.470248	−	0.882534i	$-0.344164\pi$
$877$	2.14218e7	0.940497	0.470248	+	0.882534i	$0.344164\pi$
$878$	−6.18126e6	−0.270608
$879$	3.93994e6	0.171996
$880$	138693.	0.00603737
$881$	−3.42843e7	−1.48818	−0.744090	−	0.668079i	$-0.767117\pi$
$881$	−3.42843e7	−1.48818	−0.744090	+	0.668079i	$0.767117\pi$
$882$	0	0
$883$	1.15229e7	0.497346	0.248673	−	0.968587i	$-0.420006\pi$
$883$	1.15229e7	0.497346	0.248673	+	0.968587i	$0.420006\pi$
$884$	3.05533e6	0.131500
$885$	−1.62245e7	−0.696328
$886$	4.44500e7	1.90234
$887$	4.07371e6	0.173853	0.0869263	−	0.996215i	$-0.472296\pi$
$887$	4.07371e6	0.173853	0.0869263	+	0.996215i	$0.472296\pi$
$888$	1.47323e7	0.626956
$889$	0	0
$890$	−2.44996e7	−1.03678
$891$	−1.04340e7	−0.440310
$892$	−6.10130e7	−2.56750
$893$	8.39443e6	0.352259
$894$	9.68764e6	0.405391
$895$	−1.10237e7	−0.460013
$896$	0	0
$897$	−8.34465e6	−0.346280
$898$	−2.84103e7	−1.17567
$899$	7.33110e7	3.02531
$900$	−1.23079e6	−0.0506499
$901$	−3.21322e6	−0.131865
$902$	1.43165e7	0.585895
$903$	0	0
$904$	2.91269e7	1.18542
$905$	−487226.	−0.0197747
$906$	−4.23904e7	−1.71572
$907$	4.25486e7	1.71738	0.858690	−	0.512495i	$-0.171279\pi$
$907$	4.25486e7	1.71738	0.858690	+	0.512495i	$0.171279\pi$
$908$	−2.18563e7	−0.879755
$909$	−926350.	−0.0371848
$910$	0	0
$911$	2.33369e7	0.931638	0.465819	−	0.884880i	$-0.345760\pi$
$911$	2.33369e7	0.931638	0.465819	+	0.884880i	$0.345760\pi$
$912$	191507.	0.00762427
$913$	1.17973e7	0.468388
$914$	6.04218e7	2.39237
$915$	−2.63941e6	−0.104221
$916$	2.38396e7	0.938773
$917$	0	0
$918$	1.62940e7	0.638148
$919$	−1.46257e7	−0.571251	−0.285626	−	0.958341i	$-0.592201\pi$
$919$	−1.46257e7	−0.571251	−0.285626	+	0.958341i	$0.592201\pi$
$920$	2.02683e7	0.789491
$921$	6.79008e6	0.263770
$922$	−4.82916e7	−1.87087
$923$	45574.7	0.00176084
$924$	0	0
$925$	3.48005e6	0.133731
$926$	2.56030e7	0.981213
$927$	−1.74934e6	−0.0668612
$928$	4.03656e7	1.53866
$929$	3.12828e7	1.18923	0.594616	−	0.804010i	$-0.297304\pi$
$929$	3.12828e7	1.18923	0.594616	+	0.804010i	$0.297304\pi$
$930$	3.38519e7	1.28344
$931$	0	0
$932$	−3.49291e7	−1.31719
$933$	4.45330e7	1.67486
$934$	−2.96552e7	−1.11233
$935$	−2.37806e6	−0.0889599
$936$	−925718.	−0.0345374
$937$	−4.86044e7	−1.80853	−0.904266	−	0.426969i	$-0.859581\pi$
$937$	−4.86044e7	−1.80853	−0.904266	+	0.426969i	$0.859581\pi$
$938$	0	0
$939$	2.17647e7	0.805543
$940$	−2.10811e7	−0.778169
$941$	−2.53759e7	−0.934217	−0.467109	−	0.884200i	$-0.654704\pi$
$941$	−2.53759e7	−0.934217	−0.467109	+	0.884200i	$0.654704\pi$
$942$	−2.95558e7	−1.08522
$943$	3.18098e7	1.16488
$944$	1.16684e6	0.0426169
$945$	0	0
$946$	364124.	0.0132288
$947$	2.04500e7	0.740999	0.370500	−	0.928833i	$-0.379186\pi$
$947$	2.04500e7	0.740999	0.370500	+	0.928833i	$0.379186\pi$
$948$	5.57078e7	2.01324
$949$	6.01877e6	0.216941
$950$	2.97535e6	0.106962
$951$	−3.62779e7	−1.30074
$952$	0	0
$953$	−2.96732e7	−1.05836	−0.529178	−	0.848511i	$-0.677500\pi$
$953$	−2.96732e7	−1.05836	−0.529178	+	0.848511i	$0.677500\pi$
$954$	2.52079e6	0.0896738
$955$	−1.04680e7	−0.371411
$956$	−2.86871e7	−1.01518
$957$	−2.19517e7	−0.774796
$958$	3.64844e7	1.28438
$959$	0	0
$960$	1.89343e7	0.663089
$961$	7.75582e7	2.70906
$962$	6.77725e6	0.236111
$963$	−5.93608e6	−0.206269
$964$	−8.49926e6	−0.294570
$965$	100207.	0.00346402
$966$	0	0
$967$	4.86315e7	1.67245	0.836223	−	0.548390i	$-0.184759\pi$
$967$	4.86315e7	1.67245	0.836223	+	0.548390i	$0.184759\pi$
$968$	2.11767e7	0.726390
$969$	−3.28363e6	−0.112343
$970$	4.42893e6	0.151137
$971$	−8.43394e6	−0.287067	−0.143533	−	0.989645i	$-0.545846\pi$
$971$	−8.43394e6	−0.287067	−0.143533	+	0.989645i	$0.545846\pi$
$972$	−1.47763e7	−0.501649
$973$	0	0
$974$	−4.74564e6	−0.160287
$975$	1.18811e6	0.0400263
$976$	189822.	0.00637857
$977$	−2.01326e7	−0.674781	−0.337391	−	0.941365i	$-0.609544\pi$
$977$	−2.01326e7	−0.674781	−0.337391	+	0.941365i	$0.609544\pi$
$978$	−2.07903e7	−0.695045
$979$	2.30116e7	0.767345
$980$	0	0
$981$	5.34623e6	0.177368
$982$	9.10270e6	0.301225
$983$	−4.21959e7	−1.39279	−0.696396	−	0.717658i	$-0.745214\pi$
$983$	−4.21959e7	−1.39279	−0.696396	+	0.717658i	$0.745214\pi$
$984$	−1.91732e7	−0.631259
$985$	2.55150e7	0.837926
$986$	2.88196e7	0.944053
$987$	0	0
$988$	3.59054e6	0.117022
$989$	809048.	0.0263017
$990$	1.86560e6	0.0604966
$991$	1.35590e6	0.0438574	0.0219287	−	0.999760i	$-0.493019\pi$
$991$	1.35590e6	0.0438574	0.0219287	+	0.999760i	$0.493019\pi$
$992$	5.84676e7	1.88641
$993$	−7.98805e6	−0.257080
$994$	0	0
$995$	3.92991e6	0.125842
$996$	−4.09087e7	−1.30667
$997$	4.39971e7	1.40180	0.700900	−	0.713259i	$-0.252782\pi$
$997$	4.39971e7	1.40180	0.700900	+	0.713259i	$0.252782\pi$
$998$	−2.71504e7	−0.862880
$999$	2.23964e7	0.710009

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.6.a.h.1.1		6
7.3	odd	6		35.6.e.a.16.6	yes	12
7.5	odd	6		35.6.e.a.11.6	✓	12
7.6	odd	2		245.6.a.i.1.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.6.e.a.11.6	✓	12	7.5	odd	6
35.6.e.a.16.6	yes	12	7.3	odd	6
245.6.a.h.1.1		6	1.1	even	1	trivial
245.6.a.i.1.1		6	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)

\(f(q)\)	\(=\)	\(q-9.17253 q^{2} -14.3258 q^{3} +52.1353 q^{4} +25.0000 q^{5} +131.404 q^{6} -184.691 q^{8} -37.7723 q^{9} +O(q^{10})\)	\(q-9.17253 q^{2} -14.3258 q^{3} +52.1353 q^{4} +25.0000 q^{5} +131.404 q^{6} -184.691 q^{8} -37.7723 q^{9} -229.313 q^{10} +215.386 q^{11} -746.878 q^{12} -132.696 q^{13} -358.144 q^{15} +25.7572 q^{16} -441.638 q^{17} +346.467 q^{18} -519.002 q^{19} +1303.38 q^{20} -1975.63 q^{22} -4389.66 q^{23} +2645.84 q^{24} +625.000 q^{25} +1217.16 q^{26} +4022.28 q^{27} +7114.31 q^{29} +3285.09 q^{30} +10304.7 q^{31} +5673.86 q^{32} -3085.56 q^{33} +4050.94 q^{34} -1969.27 q^{36} +5568.08 q^{37} +4760.56 q^{38} +1900.98 q^{39} -4617.28 q^{40} -7246.54 q^{41} -184.308 q^{43} +11229.2 q^{44} -944.307 q^{45} +40264.3 q^{46} -16174.2 q^{47} -368.991 q^{48} -5732.83 q^{50} +6326.81 q^{51} -6918.16 q^{52} +7275.69 q^{53} -36894.5 q^{54} +5384.64 q^{55} +7435.11 q^{57} -65256.2 q^{58} +45301.7 q^{59} -18671.9 q^{60} +7369.70 q^{61} -94520.4 q^{62} -52867.9 q^{64} -3317.41 q^{65} +28302.4 q^{66} -64443.0 q^{67} -23024.9 q^{68} +62885.2 q^{69} -343.451 q^{71} +6976.21 q^{72} -45357.4 q^{73} -51073.4 q^{74} -8953.61 q^{75} -27058.3 q^{76} -17436.8 q^{78} -74587.6 q^{79} +643.929 q^{80} -48443.6 q^{81} +66469.1 q^{82} +54772.9 q^{83} -11041.0 q^{85} +1690.57 q^{86} -101918. q^{87} -39779.8 q^{88} +106839. q^{89} +8661.68 q^{90} -228856. q^{92} -147623. q^{93} +148358. q^{94} -12975.1 q^{95} -81282.4 q^{96} -19313.9 q^{97} -8135.60 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 5 q^{2} - 20 q^{3} + 31 q^{4} + 150 q^{5} - 96 q^{6} - 135 q^{8} + 378 q^{9}+O(q^{10}) \) 6 * q - 5 * q^2 - 20 * q^3 + 31 * q^4 + 150 * q^5 - 96 * q^6 - 135 * q^8 + 378 * q^9	\( 6 q - 5 q^{2} - 20 q^{3} + 31 q^{4} + 150 q^{5} - 96 q^{6} - 135 q^{8} + 378 q^{9} - 125 q^{10} - 924 q^{11} - 370 q^{12} + 150 q^{13} - 500 q^{15} + 435 q^{16} - 1540 q^{17} + 195 q^{18} - 92 q^{19} + 775 q^{20} - 6855 q^{22} - 3920 q^{23} + 7200 q^{24} + 3750 q^{25} - 2635 q^{26} - 2060 q^{27} + 1264 q^{29} - 2400 q^{30} + 7160 q^{31} + 9105 q^{32} - 4460 q^{33} - 2166 q^{34} - 26375 q^{36} - 14170 q^{37} + 46215 q^{38} - 15376 q^{39} - 3375 q^{40} - 4098 q^{41} - 24460 q^{43} - 27873 q^{44} + 9450 q^{45} + 6815 q^{46} - 42940 q^{47} - 11610 q^{48} - 3125 q^{50} - 42008 q^{51} + 36115 q^{52} - 2450 q^{53} - 19566 q^{54} - 23100 q^{55} - 97100 q^{57} - 36110 q^{58} + 64600 q^{59} - 9250 q^{60} - 73620 q^{61} - 111440 q^{62} - 157997 q^{64} + 3750 q^{65} + 139138 q^{66} - 142620 q^{67} - 124330 q^{68} - 17344 q^{69} - 154256 q^{71} - 117495 q^{72} + 5120 q^{73} + 2785 q^{74} - 12500 q^{75} - 7775 q^{76} - 214090 q^{78} - 222504 q^{79} + 10875 q^{80} - 43986 q^{81} - 31665 q^{82} - 179580 q^{83} - 38500 q^{85} - 207160 q^{86} + 209300 q^{87} - 45145 q^{88} - 41648 q^{89} + 4875 q^{90} - 292185 q^{92} - 198520 q^{93} + 333699 q^{94} - 2300 q^{95} - 61824 q^{96} + 73980 q^{97} - 190772 q^{99}+O(q^{100}) \) 6 * q - 5 * q^2 - 20 * q^3 + 31 * q^4 + 150 * q^5 - 96 * q^6 - 135 * q^8 + 378 * q^9 - 125 * q^10 - 924 * q^11 - 370 * q^12 + 150 * q^13 - 500 * q^15 + 435 * q^16 - 1540 * q^17 + 195 * q^18 - 92 * q^19 + 775 * q^20 - 6855 * q^22 - 3920 * q^23 + 7200 * q^24 + 3750 * q^25 - 2635 * q^26 - 2060 * q^27 + 1264 * q^29 - 2400 * q^30 + 7160 * q^31 + 9105 * q^32 - 4460 * q^33 - 2166 * q^34 - 26375 * q^36 - 14170 * q^37 + 46215 * q^38 - 15376 * q^39 - 3375 * q^40 - 4098 * q^41 - 24460 * q^43 - 27873 * q^44 + 9450 * q^45 + 6815 * q^46 - 42940 * q^47 - 11610 * q^48 - 3125 * q^50 - 42008 * q^51 + 36115 * q^52 - 2450 * q^53 - 19566 * q^54 - 23100 * q^55 - 97100 * q^57 - 36110 * q^58 + 64600 * q^59 - 9250 * q^60 - 73620 * q^61 - 111440 * q^62 - 157997 * q^64 + 3750 * q^65 + 139138 * q^66 - 142620 * q^67 - 124330 * q^68 - 17344 * q^69 - 154256 * q^71 - 117495 * q^72 + 5120 * q^73 + 2785 * q^74 - 12500 * q^75 - 7775 * q^76 - 214090 * q^78 - 222504 * q^79 + 10875 * q^80 - 43986 * q^81 - 31665 * q^82 - 179580 * q^83 - 38500 * q^85 - 207160 * q^86 + 209300 * q^87 - 45145 * q^88 - 41648 * q^89 + 4875 * q^90 - 292185 * q^92 - 198520 * q^93 + 333699 * q^94 - 2300 * q^95 - 61824 * q^96 + 73980 * q^97 - 190772 * q^99

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