LMFDB - Embedded newform 230.6.a.f.1.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [230,6,Mod(1,230)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("230.1"); S:= CuspForms(chi, 6); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(230, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 6, names="a")

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	230.a (trivial)

Newform invariants

comment:select newform

sage:traces = [5,-20,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	yes
Analytic conductor:	$36.8882785570$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 774x^{3} - 197x^{2} + 66287x + 154128 $ x^5 - x^4 - 774x^3 - 197x^2 + 66287*x + 154128
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-8.46823$ of defining polynomial
Character	$\chi$	$=$	230.1

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-4.00000 q^{2} -8.46823 q^{3} +16.0000 q^{4} +25.0000 q^{5} +33.8729 q^{6} -118.977 q^{7} -64.0000 q^{8} -171.289 q^{9} -100.000 q^{10} +358.711 q^{11} -135.492 q^{12} -515.740 q^{13} +475.909 q^{14} -211.706 q^{15} +256.000 q^{16} +2092.78 q^{17} +685.157 q^{18} -2775.19 q^{19} +400.000 q^{20} +1007.53 q^{21} -1434.84 q^{22} -529.000 q^{23} +541.967 q^{24} +625.000 q^{25} +2062.96 q^{26} +3508.29 q^{27} -1903.63 q^{28} -2344.09 q^{29} +846.823 q^{30} -9787.95 q^{31} -1024.00 q^{32} -3037.64 q^{33} -8371.12 q^{34} -2974.43 q^{35} -2740.63 q^{36} +4816.40 q^{37} +11100.8 q^{38} +4367.40 q^{39} -1600.00 q^{40} -24.0689 q^{41} -4030.10 q^{42} -1068.84 q^{43} +5739.37 q^{44} -4282.23 q^{45} +2116.00 q^{46} +17918.2 q^{47} -2167.87 q^{48} -2651.44 q^{49} -2500.00 q^{50} -17722.1 q^{51} -8251.83 q^{52} +15651.6 q^{53} -14033.2 q^{54} +8967.76 q^{55} +7614.54 q^{56} +23501.0 q^{57} +9376.37 q^{58} +45399.8 q^{59} -3387.29 q^{60} +18440.5 q^{61} +39151.8 q^{62} +20379.5 q^{63} +4096.00 q^{64} -12893.5 q^{65} +12150.6 q^{66} +48487.9 q^{67} +33484.5 q^{68} +4479.69 q^{69} +11897.7 q^{70} +3989.29 q^{71} +10962.5 q^{72} +5579.98 q^{73} -19265.6 q^{74} -5292.64 q^{75} -44403.1 q^{76} -42678.4 q^{77} -17469.6 q^{78} +38453.9 q^{79} +6400.00 q^{80} +11914.2 q^{81} +96.2757 q^{82} -29897.7 q^{83} +16120.4 q^{84} +52319.5 q^{85} +4275.37 q^{86} +19850.3 q^{87} -22957.5 q^{88} +50329.9 q^{89} +17128.9 q^{90} +61361.2 q^{91} -8464.00 q^{92} +82886.6 q^{93} -71672.7 q^{94} -69379.8 q^{95} +8671.46 q^{96} -71867.5 q^{97} +10605.8 q^{98} -61443.2 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 20 q^{2} + q^{3} + 80 q^{4} + 125 q^{5} - 4 q^{6} + 102 q^{7} - 320 q^{8} + 334 q^{9} - 500 q^{10} + 251 q^{11} + 16 q^{12} + 1743 q^{13} - 408 q^{14} + 25 q^{15} + 1280 q^{16} + 1944 q^{17} - 1336 q^{18}+ \cdots + 386925 q^{99}+O(q^{100}) $ 5 * q - 20 * q^2 + q^3 + 80 * q^4 + 125 * q^5 - 4 * q^6 + 102 * q^7 - 320 * q^8 + 334 * q^9 - 500 * q^10 + 251 * q^11 + 16 * q^12 + 1743 * q^13 - 408 * q^14 + 25 * q^15 + 1280 * q^16 + 1944 * q^17 - 1336 * q^18 - 845 * q^19 + 2000 * q^20 + 4682 * q^21 - 1004 * q^22 - 2645 * q^23 - 64 * q^24 + 3125 * q^25 - 6972 * q^26 + 2428 * q^27 + 1632 * q^28 - 4021 * q^29 - 100 * q^30 - 15752 * q^31 - 5120 * q^32 + 2931 * q^33 - 7776 * q^34 + 2550 * q^35 + 5344 * q^36 - 3455 * q^37 + 3380 * q^38 - 16708 * q^39 - 8000 * q^40 - 11898 * q^41 - 18728 * q^42 + 6968 * q^43 + 4016 * q^44 + 8350 * q^45 + 10580 * q^46 + 13412 * q^47 + 256 * q^48 + 91041 * q^49 - 12500 * q^50 - 2115 * q^51 + 27888 * q^52 + 53029 * q^53 - 9712 * q^54 + 6275 * q^55 - 6528 * q^56 - 21730 * q^57 + 16084 * q^58 - 31223 * q^59 + 400 * q^60 + 71477 * q^61 + 63008 * q^62 + 262199 * q^63 + 20480 * q^64 + 43575 * q^65 - 11724 * q^66 + 76003 * q^67 + 31104 * q^68 - 529 * q^69 - 10200 * q^70 + 54418 * q^71 - 21376 * q^72 + 69418 * q^73 + 13820 * q^74 + 625 * q^75 - 13520 * q^76 + 283598 * q^77 + 66832 * q^78 + 105024 * q^79 + 32000 * q^80 + 102913 * q^81 + 47592 * q^82 + 89399 * q^83 + 74912 * q^84 + 48600 * q^85 - 27872 * q^86 + 276726 * q^87 - 16064 * q^88 + 96240 * q^89 - 33400 * q^90 + 59261 * q^91 - 42320 * q^92 + 84434 * q^93 - 53648 * q^94 - 21125 * q^95 - 1024 * q^96 + 216087 * q^97 - 364164 * q^98 + 386925 * q^99

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 $

$2$	−4.00000	−0.707107
$2$	−4.00000	−0.707107
$3$	−8.46823	−0.543237	−0.271619	−	0.962405i	$-0.587559\pi$
$3$	−8.46823	−0.543237	−0.271619	+	0.962405i	$0.587559\pi$
$4$	16.0000	0.500000
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	33.8729	0.384127
$7$	−118.977	−0.917737	−0.458869	−	0.888504i	$-0.651745\pi$
$7$	−118.977	−0.917737	−0.458869	+	0.888504i	$0.651745\pi$
$8$	−64.0000	−0.353553
$9$	−171.289	−0.704894
$10$	−100.000	−0.316228
$11$	358.711	0.893846	0.446923	−	0.894573i	$-0.352520\pi$
$11$	358.711	0.893846	0.446923	+	0.894573i	$0.352520\pi$
$12$	−135.492	−0.271619
$13$	−515.740	−0.846393	−0.423197	−	0.906038i	$-0.639092\pi$
$13$	−515.740	−0.846393	−0.423197	+	0.906038i	$0.639092\pi$
$14$	475.909	0.648938
$15$	−211.706	−0.242943
$16$	256.000	0.250000
$17$	2092.78	1.75631	0.878155	−	0.478376i	$-0.158774\pi$
$17$	2092.78	1.75631	0.878155	+	0.478376i	$0.158774\pi$
$18$	685.157	0.498435
$19$	−2775.19	−1.76364	−0.881818	−	0.471589i	$-0.843680\pi$
$19$	−2775.19	−1.76364	−0.881818	+	0.471589i	$0.843680\pi$
$20$	400.000	0.223607
$21$	1007.53	0.498549
$22$	−1434.84	−0.632044
$23$	−529.000	−0.208514
$23$	−529.000	−0.208514
$24$	541.967	0.192063
$25$	625.000	0.200000
$26$	2062.96	0.598490
$27$	3508.29	0.926161
$28$	−1903.63	−0.458869
$29$	−2344.09	−0.517583	−0.258791	−	0.965933i	$-0.583324\pi$
$29$	−2344.09	−0.517583	−0.258791	+	0.965933i	$0.583324\pi$
$30$	846.823	0.171787
$31$	−9787.95	−1.82931	−0.914655	−	0.404235i	$-0.867538\pi$
$31$	−9787.95	−1.82931	−0.914655	+	0.404235i	$0.867538\pi$
$32$	−1024.00	−0.176777
$33$	−3037.64	−0.485570
$34$	−8371.12	−1.24190
$35$	−2974.43	−0.410425
$36$	−2740.63	−0.352447
$37$	4816.40	0.578387	0.289193	−	0.957271i	$-0.406613\pi$
$37$	4816.40	0.578387	0.289193	+	0.957271i	$0.406613\pi$
$38$	11100.8	1.24708
$39$	4367.40	0.459792
$40$	−1600.00	−0.158114
$41$	−24.0689	−0.00223613	−0.00111806	−	0.999999i	$-0.500356\pi$
$41$	−24.0689	−0.00223613	−0.00111806	+	0.999999i	$0.500356\pi$
$42$	−4030.10	−0.352527
$43$	−1068.84	−0.0881541	−0.0440770	−	0.999028i	$-0.514035\pi$
$43$	−1068.84	−0.0881541	−0.0440770	+	0.999028i	$0.514035\pi$
$44$	5739.37	0.446923
$45$	−4282.23	−0.315238
$46$	2116.00	0.147442
$47$	17918.2	1.18317	0.591587	−	0.806241i	$-0.298501\pi$
$47$	17918.2	1.18317	0.591587	+	0.806241i	$0.298501\pi$
$48$	−2167.87	−0.135809
$49$	−2651.44	−0.157758
$50$	−2500.00	−0.141421
$51$	−17722.1	−0.954093
$52$	−8251.83	−0.423197
$53$	15651.6	0.765365	0.382682	−	0.923880i	$-0.375000\pi$
$53$	15651.6	0.765365	0.382682	+	0.923880i	$0.375000\pi$
$54$	−14033.2	−0.654895
$55$	8967.76	0.399740
$56$	7614.54	0.324469
$57$	23501.0	0.958073
$58$	9376.37	0.365986
$59$	45399.8	1.69795	0.848973	−	0.528436i	$-0.177221\pi$
$59$	45399.8	1.69795	0.848973	+	0.528436i	$0.177221\pi$
$60$	−3387.29	−0.121471
$61$	18440.5	0.634525	0.317263	−	0.948338i	$-0.397236\pi$
$61$	18440.5	0.634525	0.317263	+	0.948338i	$0.397236\pi$
$62$	39151.8	1.29352
$63$	20379.5	0.646907
$64$	4096.00	0.125000
$65$	−12893.5	−0.378519
$66$	12150.6	0.343350
$67$	48487.9	1.31961	0.659806	−	0.751436i	$-0.270639\pi$
$67$	48487.9	1.31961	0.659806	+	0.751436i	$0.270639\pi$
$68$	33484.5	0.878155
$69$	4479.69	0.113273
$70$	11897.7	0.290214
$71$	3989.29	0.0939182	0.0469591	−	0.998897i	$-0.485047\pi$
$71$	3989.29	0.0939182	0.0469591	+	0.998897i	$0.485047\pi$
$72$	10962.5	0.249218
$73$	5579.98	0.122553	0.0612767	−	0.998121i	$-0.480483\pi$
$73$	5579.98	0.122553	0.0612767	+	0.998121i	$0.480483\pi$
$74$	−19265.6	−0.408981
$75$	−5292.64	−0.108647
$76$	−44403.1	−0.881818
$77$	−42678.4	−0.820316
$78$	−17469.6	−0.325122
$79$	38453.9	0.693222	0.346611	−	0.938009i	$-0.387332\pi$
$79$	38453.9	0.693222	0.346611	+	0.938009i	$0.387332\pi$
$80$	6400.00	0.111803
$81$	11914.2	0.201768
$82$	96.2757	0.00158118
$83$	−29897.7	−0.476368	−0.238184	−	0.971220i	$-0.576552\pi$
$83$	−29897.7	−0.476368	−0.238184	+	0.971220i	$0.576552\pi$
$84$	16120.4	0.249274
$85$	52319.5	0.785446
$86$	4275.37	0.0623343
$87$	19850.3	0.281170
$88$	−22957.5	−0.316022
$89$	50329.9	0.673521	0.336760	−	0.941590i	$-0.390669\pi$
$89$	50329.9	0.673521	0.336760	+	0.941590i	$0.390669\pi$
$90$	17128.9	0.222907
$91$	61361.2	0.776767
$92$	−8464.00	−0.104257
$93$	82886.6	0.993749
$94$	−71672.7	−0.836631
$95$	−69379.8	−0.788722
$96$	8671.46	0.0960316
$97$	−71867.5	−0.775538	−0.387769	−	0.921757i	$-0.626754\pi$
$97$	−71867.5	−0.775538	−0.387769	+	0.921757i	$0.626754\pi$
$98$	10605.8	0.111552
$99$	−61443.2	−0.630066
$100$	10000.0	0.100000
$101$	61080.4	0.595798	0.297899	−	0.954597i	$-0.403714\pi$
$101$	61080.4	0.595798	0.297899	+	0.954597i	$0.403714\pi$
$102$	70888.5	0.674645
$103$	181954.	1.68993	0.844964	−	0.534823i	$-0.179622\pi$
$103$	181954.	1.68993	0.844964	+	0.534823i	$0.179622\pi$
$104$	33007.3	0.299245
$105$	25188.1	0.222958
$106$	−62606.3	−0.541195
$107$	−99429.8	−0.839571	−0.419785	−	0.907623i	$-0.637895\pi$
$107$	−99429.8	−0.839571	−0.419785	+	0.907623i	$0.637895\pi$
$108$	56132.7	0.463081
$109$	157698.	1.27134	0.635668	−	0.771963i	$-0.280725\pi$
$109$	157698.	1.27134	0.635668	+	0.771963i	$0.280725\pi$
$110$	−35871.1	−0.282659
$111$	−40786.4	−0.314201
$112$	−30458.2	−0.229434
$113$	178966.	1.31848	0.659242	−	0.751931i	$-0.270877\pi$
$113$	178966.	1.31848	0.659242	+	0.751931i	$0.270877\pi$
$114$	−94003.8	−0.677460
$115$	−13225.0	−0.0932505
$116$	−37505.5	−0.258791
$117$	88340.6	0.596617
$118$	−181599.	−1.20063
$119$	−248993.	−1.61183
$120$	13549.2	0.0858933
$121$	−32377.7	−0.201040
$122$	−73762.2	−0.448677
$123$	203.821	0.00121475
$124$	−156607.	−0.914655
$125$	15625.0	0.0894427
$126$	−81518.0	−0.457432
$127$	161206.	0.886896	0.443448	−	0.896300i	$-0.353755\pi$
$127$	161206.	0.886896	0.443448	+	0.896300i	$0.353755\pi$
$128$	−16384.0	−0.0883883
$129$	9051.19	0.0478885
$130$	51574.0	0.267653
$131$	−137424.	−0.699654	−0.349827	−	0.936814i	$-0.613760\pi$
$131$	−137424.	−0.699654	−0.349827	+	0.936814i	$0.613760\pi$
$132$	−48602.3	−0.242785
$133$	330184.	1.61856
$134$	−193951.	−0.933106
$135$	87707.4	0.414192
$136$	−133938.	−0.620949
$137$	305275.	1.38960	0.694800	−	0.719203i	$-0.255493\pi$
$137$	305275.	1.38960	0.694800	+	0.719203i	$0.255493\pi$
$138$	−17918.8	−0.0800959
$139$	−143928.	−0.631840	−0.315920	−	0.948786i	$-0.602313\pi$
$139$	−143928.	−0.631840	−0.315920	+	0.948786i	$0.602313\pi$
$140$	−47590.9	−0.205212
$141$	−151735.	−0.642744
$142$	−15957.2	−0.0664102
$143$	−185001.	−0.756545
$144$	−43850.0	−0.176223
$145$	−58602.3	−0.231470
$146$	−22319.9	−0.0866583
$147$	22453.0	0.0856999
$148$	77062.4	0.289193
$149$	355454.	1.31165	0.655824	−	0.754913i	$-0.272321\pi$
$149$	355454.	1.31165	0.655824	+	0.754913i	$0.272321\pi$
$150$	21170.6	0.0768253
$151$	−225364.	−0.804344	−0.402172	−	0.915564i	$-0.631745\pi$
$151$	−225364.	−0.804344	−0.402172	+	0.915564i	$0.631745\pi$
$152$	177612.	0.623540
$153$	−358470.	−1.23801
$154$	170713.	0.580051
$155$	−244699.	−0.818092
$156$	69878.4	0.229896
$157$	279940.	0.906391	0.453195	−	0.891411i	$-0.350284\pi$
$157$	279940.	0.906391	0.453195	+	0.891411i	$0.350284\pi$
$158$	−153816.	−0.490182
$159$	−132541.	−0.415775
$160$	−25600.0	−0.0790569
$161$	62938.9	0.191361
$162$	−47656.9	−0.142672
$163$	−642292.	−1.89349	−0.946747	−	0.321980i	$-0.895652\pi$
$163$	−642292.	−1.89349	−0.946747	+	0.321980i	$0.895652\pi$
$164$	−385.103	−0.00111806
$165$	−75941.1	−0.217153
$166$	119591.	0.336843
$167$	−61147.1	−0.169662	−0.0848310	−	0.996395i	$-0.527035\pi$
$167$	−61147.1	−0.169662	−0.0848310	+	0.996395i	$0.527035\pi$
$168$	−64481.6	−0.176264
$169$	−105306.	−0.283619
$170$	−209278.	−0.555394
$171$	475360.	1.24318
$172$	−17101.5	−0.0440770
$173$	−270177.	−0.686331	−0.343165	−	0.939275i	$-0.611499\pi$
$173$	−270177.	−0.686331	−0.343165	+	0.939275i	$0.611499\pi$
$174$	−79401.2	−0.198817
$175$	−74360.7	−0.183547
$176$	91829.9	0.223461
$177$	−384456.	−0.922387
$178$	−201320.	−0.476251
$179$	−222698.	−0.519499	−0.259749	−	0.965676i	$-0.583640\pi$
$179$	−222698.	−0.519499	−0.259749	+	0.965676i	$0.583640\pi$
$180$	−68515.7	−0.157619
$181$	−277646.	−0.629934	−0.314967	−	0.949103i	$-0.601994\pi$
$181$	−277646.	−0.629934	−0.314967	+	0.949103i	$0.601994\pi$
$182$	−245445.	−0.549257
$183$	−156159.	−0.344698
$184$	33856.0	0.0737210
$185$	120410.	0.258662
$186$	−331546.	−0.702687
$187$	750702.	1.56987
$188$	286691.	0.591587
$189$	−417407.	−0.849973
$190$	277519.	0.557711
$191$	541372.	1.07377	0.536886	−	0.843655i	$-0.319600\pi$
$191$	541372.	1.07377	0.536886	+	0.843655i	$0.319600\pi$
$192$	−34685.9	−0.0679046
$193$	−33487.9	−0.0647136	−0.0323568	−	0.999476i	$-0.510301\pi$
$193$	−33487.9	−0.0647136	−0.0323568	+	0.999476i	$0.510301\pi$
$194$	287470.	0.548388
$195$	109185.	0.205625
$196$	−42423.0	−0.0788790
$197$	−149329.	−0.274144	−0.137072	−	0.990561i	$-0.543769\pi$
$197$	−149329.	−0.274144	−0.137072	+	0.990561i	$0.543769\pi$
$198$	245773.	0.445524
$199$	274716.	0.491759	0.245879	−	0.969300i	$-0.420923\pi$
$199$	274716.	0.491759	0.245879	+	0.969300i	$0.420923\pi$
$200$	−40000.0	−0.0707107
$201$	−410606.	−0.716862
$202$	−244322.	−0.421292
$203$	278893.	0.475005
$204$	−283554.	−0.477046
$205$	−601.723	−0.00100003
$206$	−727816.	−1.19496
$207$	90611.9	0.146980
$208$	−132029.	−0.211598
$209$	−995491.	−1.57642
$210$	−100753.	−0.157655
$211$	353497.	0.546612	0.273306	−	0.961927i	$-0.411883\pi$
$211$	353497.	0.546612	0.273306	+	0.961927i	$0.411883\pi$
$212$	250425.	0.382682
$213$	−33782.2	−0.0510198
$214$	397719.	0.593666
$215$	−26721.0	−0.0394237
$216$	−224531.	−0.327447
$217$	1.16454e6	1.67883
$218$	−630792.	−0.898970
$219$	−47252.5	−0.0665755
$220$	143484.	0.199870
$221$	−1.07933e6	−1.48653
$222$	163146.	0.222174
$223$	−602989.	−0.811984	−0.405992	−	0.913877i	$-0.633074\pi$
$223$	−602989.	−0.811984	−0.405992	+	0.913877i	$0.633074\pi$
$224$	121833.	0.162235
$225$	−107056.	−0.140979
$226$	−715865.	−0.932309
$227$	543612.	0.700204	0.350102	−	0.936712i	$-0.386147\pi$
$227$	543612.	0.700204	0.350102	+	0.936712i	$0.386147\pi$
$228$	376015.	0.479036
$229$	890736.	1.12243	0.561216	−	0.827669i	$-0.310334\pi$
$229$	890736.	1.12243	0.561216	+	0.827669i	$0.310334\pi$
$230$	52900.0	0.0659380
$231$	361410.	0.445626
$232$	150022.	0.182993
$233$	1.05640e6	1.27478	0.637392	−	0.770539i	$-0.280013\pi$
$233$	1.05640e6	1.27478	0.637392	+	0.770539i	$0.280013\pi$
$234$	−353362.	−0.421872
$235$	447954.	0.529132
$236$	726397.	0.848973
$237$	−325636.	−0.376584
$238$	995972.	1.13974
$239$	−805507.	−0.912167	−0.456084	−	0.889937i	$-0.650748\pi$
$239$	−805507.	−0.912167	−0.456084	+	0.889937i	$0.650748\pi$
$240$	−54196.7	−0.0607357
$241$	−848758.	−0.941328	−0.470664	−	0.882312i	$-0.655986\pi$
$241$	−848758.	−0.941328	−0.470664	+	0.882312i	$0.655986\pi$
$242$	129511.	0.142157
$243$	−953408.	−1.03577
$244$	295049.	0.317263
$245$	−66285.9	−0.0705515
$246$	−815.284	−0.000858957 0
$247$	1.43128e6	1.49273
$248$	626429.	0.646759
$249$	253180.	0.258781
$250$	−62500.0	−0.0632456
$251$	−1.61847e6	−1.62151	−0.810755	−	0.585386i	$-0.800943\pi$
$251$	−1.61847e6	−1.62151	−0.810755	+	0.585386i	$0.800943\pi$
$252$	326072.	0.323454
$253$	−189758.	−0.186380
$254$	−644825.	−0.627130
$255$	−443053.	−0.426683
$256$	65536.0	0.0625000
$257$	1.31624e6	1.24309	0.621544	−	0.783379i	$-0.286506\pi$
$257$	1.31624e6	1.24309	0.621544	+	0.783379i	$0.286506\pi$
$258$	−36204.8	−0.0338623
$259$	−573042.	−0.530807
$260$	−206296.	−0.189259
$261$	401518.	0.364841
$262$	549695.	0.494730
$263$	−605771.	−0.540032	−0.270016	−	0.962856i	$-0.587029\pi$
$263$	−605771.	−0.540032	−0.270016	+	0.962856i	$0.587029\pi$
$264$	194409.	0.171675
$265$	391290.	0.342282
$266$	−1.32074e6	−1.14449
$267$	−426205.	−0.365881
$268$	775806.	0.659806
$269$	11040.1	0.00930233	0.00465116	−	0.999989i	$-0.498519\pi$
$269$	11040.1	0.00930233	0.00465116	+	0.999989i	$0.498519\pi$
$270$	−350829.	−0.292878
$271$	1.30158e6	1.07658	0.538291	−	0.842759i	$-0.319070\pi$
$271$	1.30158e6	1.07658	0.538291	+	0.842759i	$0.319070\pi$
$272$	535752.	0.439078
$273$	−519621.	−0.421968
$274$	−1.22110e6	−0.982596
$275$	224194.	0.178769
$276$	71675.1	0.0566364
$277$	2.07170e6	1.62229	0.811143	−	0.584848i	$-0.198846\pi$
$277$	2.07170e6	1.62229	0.811143	+	0.584848i	$0.198846\pi$
$278$	575710.	0.446778
$279$	1.67657e6	1.28947
$280$	190363.	0.145107
$281$	705629.	0.533102	0.266551	−	0.963821i	$-0.414116\pi$
$281$	705629.	0.533102	0.266551	+	0.963821i	$0.414116\pi$
$282$	606940.	0.454489
$283$	−1.85265e6	−1.37508	−0.687538	−	0.726148i	$-0.741309\pi$
$283$	−1.85265e6	−1.37508	−0.687538	+	0.726148i	$0.741309\pi$
$284$	63828.6	0.0469591
$285$	587524.	0.428463
$286$	740005.	0.534958
$287$	2863.65	0.00205218
$288$	175400.	0.124609
$289$	2.95987e6	2.08462
$290$	234409.	0.163674
$291$	608590.	0.421301
$292$	89279.6	0.0612767
$293$	1.06802e6	0.726790	0.363395	−	0.931635i	$-0.381618\pi$
$293$	1.06802e6	0.726790	0.363395	+	0.931635i	$0.381618\pi$
$294$	−89811.9	−0.0605990
$295$	1.13500e6	0.759345
$296$	−308250.	−0.204491
$297$	1.25846e6	0.827845
$298$	−1.42182e6	−0.927476
$299$	272826.	0.176485
$300$	−84682.3	−0.0543237
$301$	127168.	0.0809023
$302$	901455.	0.568757
$303$	−517243.	−0.323659
$304$	−710449.	−0.440909
$305$	461013.	0.283768
$306$	1.43388e6	0.875406
$307$	−34869.7	−0.0211156	−0.0105578	−	0.999944i	$-0.503361\pi$
$307$	−34869.7	−0.0211156	−0.0105578	+	0.999944i	$0.503361\pi$
$308$	−682854.	−0.410158
$309$	−1.54083e6	−0.918032
$310$	978795.	0.578479
$311$	2.27802e6	1.33554	0.667770	−	0.744368i	$-0.267249\pi$
$311$	2.27802e6	1.33554	0.667770	+	0.744368i	$0.267249\pi$
$312$	−279514.	−0.162561
$313$	−1.31658e6	−0.759600	−0.379800	−	0.925069i	$-0.624007\pi$
$313$	−1.31658e6	−0.759600	−0.379800	+	0.925069i	$0.624007\pi$
$314$	−1.11976e6	−0.640915
$315$	509487.	0.289306
$316$	615262.	0.346611
$317$	−1.15067e6	−0.643135	−0.321568	−	0.946887i	$-0.604210\pi$
$317$	−1.15067e6	−0.643135	−0.321568	+	0.946887i	$0.604210\pi$
$318$	530165.	0.293997
$319$	−840851.	−0.462639
$320$	102400.	0.0559017
$321$	841995.	0.456086
$322$	−251756.	−0.135313
$323$	−5.80787e6	−3.09749
$324$	190628.	0.100884
$325$	−322337.	−0.169279
$326$	2.56917e6	1.33890
$327$	−1.33542e6	−0.690637
$328$	1540.41	0.000790591 0
$329$	−2.13185e6	−1.08584
$330$	303764.	0.153551
$331$	−3.62446e6	−1.81833	−0.909166	−	0.416434i	$-0.863280\pi$
$331$	−3.62446e6	−1.81833	−0.909166	+	0.416434i	$0.863280\pi$
$332$	−478363.	−0.238184
$333$	−824997.	−0.407701
$334$	244588.	0.119969
$335$	1.21220e6	0.590148
$336$	257927.	0.124637
$337$	308341.	0.147896	0.0739481	−	0.997262i	$-0.476440\pi$
$337$	308341.	0.147896	0.0739481	+	0.997262i	$0.476440\pi$
$338$	421222.	0.200549
$339$	−1.51553e6	−0.716249
$340$	837112.	0.392723
$341$	−3.51104e6	−1.63512
$342$	−1.90144e6	−0.879058
$343$	2.31511e6	1.06252
$344$	68405.9	0.0311672
$345$	111992.	0.0506571
$346$	1.08071e6	0.485309
$347$	−850011.	−0.378967	−0.189483	−	0.981884i	$-0.560681\pi$
$347$	−850011.	−0.378967	−0.189483	+	0.981884i	$0.560681\pi$
$348$	317605.	0.140585
$349$	−2.96385e6	−1.30255	−0.651273	−	0.758844i	$-0.725765\pi$
$349$	−2.96385e6	−1.30255	−0.651273	+	0.758844i	$0.725765\pi$
$350$	297443.	0.129788
$351$	−1.80937e6	−0.783897
$352$	−367320.	−0.158011
$353$	2.14490e6	0.916157	0.458078	−	0.888912i	$-0.348538\pi$
$353$	2.14490e6	0.916157	0.458078	+	0.888912i	$0.348538\pi$
$354$	1.53782e6	0.652226
$355$	99732.2	0.0420015
$356$	805278.	0.336760
$357$	2.10853e6	0.875607
$358$	890793.	0.367341
$359$	−438888.	−0.179729	−0.0898643	−	0.995954i	$-0.528643\pi$
$359$	−438888.	−0.179729	−0.0898643	+	0.995954i	$0.528643\pi$
$360$	274063.	0.111453
$361$	5.22559e6	2.11041
$362$	1.11058e6	0.445431
$363$	274182.	0.109212
$364$	981780.	0.388383
$365$	139499.	0.0548075
$366$	624635.	0.243738
$367$	1.38893e6	0.538289	0.269144	−	0.963100i	$-0.413259\pi$
$367$	1.38893e6	0.538289	0.269144	+	0.963100i	$0.413259\pi$
$368$	−135424.	−0.0521286
$369$	4122.74	0.00157623
$370$	−481640.	−0.182902
$371$	−1.86218e6	−0.702404
$372$	1.32618e6	0.496875
$373$	2.14429e6	0.798017	0.399009	−	0.916947i	$-0.369354\pi$
$373$	2.14429e6	0.798017	0.399009	+	0.916947i	$0.369354\pi$
$374$	−3.00281e6	−1.11007
$375$	−132316.	−0.0485886
$376$	−1.14676e6	−0.418316
$377$	1.20894e6	0.438078
$378$	1.66963e6	0.601022
$379$	2.55976e6	0.915378	0.457689	−	0.889112i	$-0.348677\pi$
$379$	2.55976e6	0.915378	0.457689	+	0.889112i	$0.348677\pi$
$380$	−1.11008e6	−0.394361
$381$	−1.36513e6	−0.481795
$382$	−2.16549e6	−0.759272
$383$	−2.89975e6	−1.01010	−0.505049	−	0.863091i	$-0.668526\pi$
$383$	−2.89975e6	−1.01010	−0.505049	+	0.863091i	$0.668526\pi$
$384$	138743.	0.0480158
$385$	−1.06696e6	−0.366856
$386$	133952.	0.0457594
$387$	183081.	0.0621392
$388$	−1.14988e6	−0.387769
$389$	1.47101e6	0.492882	0.246441	−	0.969158i	$-0.420739\pi$
$389$	1.47101e6	0.492882	0.246441	+	0.969158i	$0.420739\pi$
$390$	−436740.	−0.145399
$391$	−1.10708e6	−0.366216
$392$	169692.	0.0557759
$393$	1.16374e6	0.380078
$394$	597316.	0.193849
$395$	961347.	0.310018
$396$	−983092.	−0.315033
$397$	−4.88528e6	−1.55565	−0.777827	−	0.628479i	$-0.783678\pi$
$397$	−4.88528e6	−1.55565	−0.777827	+	0.628479i	$0.783678\pi$
$398$	−1.09887e6	−0.347726
$399$	−2.79608e6	−0.879259
$400$	160000.	0.0500000
$401$	−4.03714e6	−1.25376	−0.626878	−	0.779117i	$-0.715668\pi$
$401$	−4.03714e6	−1.25376	−0.626878	+	0.779117i	$0.715668\pi$
$402$	1.64243e6	0.506898
$403$	5.04803e6	1.54832
$404$	977287.	0.297899
$405$	297856.	0.0902336
$406$	−1.11557e6	−0.335879
$407$	1.72769e6	0.516989
$408$	1.13422e6	0.337323
$409$	−4.13883e6	−1.22340	−0.611702	−	0.791088i	$-0.709515\pi$
$409$	−4.13883e6	−1.22340	−0.611702	+	0.791088i	$0.709515\pi$
$410$	2406.89	0.000707126 0
$411$	−2.58514e6	−0.754882
$412$	2.91126e6	0.844964
$413$	−5.40154e6	−1.55827
$414$	−362448.	−0.103931
$415$	−747442.	−0.213038
$416$	528117.	0.149623
$417$	1.21881e6	0.343239
$418$	3.98196e6	1.11470
$419$	536280.	0.149230	0.0746150	−	0.997212i	$-0.476227\pi$
$419$	536280.	0.149230	0.0746150	+	0.997212i	$0.476227\pi$
$420$	403010.	0.111479
$421$	6.59556e6	1.81362	0.906810	−	0.421539i	$-0.138510\pi$
$421$	6.59556e6	1.81362	0.906810	+	0.421539i	$0.138510\pi$
$422$	−1.41399e6	−0.386513
$423$	−3.06919e6	−0.834012
$424$	−1.00170e6	−0.270597
$425$	1.30799e6	0.351262
$426$	135129.	0.0360765
$427$	−2.19400e6	−0.582328
$428$	−1.59088e6	−0.419785
$429$	1.56663e6	0.410983
$430$	106884.	0.0278768
$431$	3.65012e6	0.946486	0.473243	−	0.880932i	$-0.343083\pi$
$431$	3.65012e6	0.946486	0.473243	+	0.880932i	$0.343083\pi$
$432$	898123.	0.231540
$433$	5.50340e6	1.41062	0.705311	−	0.708898i	$-0.250807\pi$
$433$	5.50340e6	1.41062	0.705311	+	0.708898i	$0.250807\pi$
$434$	−4.65817e6	−1.18711
$435$	496258.	0.125743
$436$	2.52317e6	0.635668
$437$	1.46808e6	0.367744
$438$	189010.	0.0470760
$439$	−4.23173e6	−1.04799	−0.523994	−	0.851722i	$-0.675559\pi$
$439$	−4.23173e6	−1.04799	−0.523994	+	0.851722i	$0.675559\pi$
$440$	−573937.	−0.141329
$441$	454162.	0.111203
$442$	4.31732e6	1.05113
$443$	−4.22418e6	−1.02266	−0.511332	−	0.859383i	$-0.670848\pi$
$443$	−4.22418e6	−1.02266	−0.511332	+	0.859383i	$0.670848\pi$
$444$	−652582.	−0.157101
$445$	1.25825e6	0.301208
$446$	2.41196e6	0.574159
$447$	−3.01006e6	−0.712536
$448$	−487330.	−0.114717
$449$	−6.45197e6	−1.51035	−0.755173	−	0.655526i	$-0.772447\pi$
$449$	−6.45197e6	−1.51035	−0.755173	+	0.655526i	$0.772447\pi$
$450$	428223.	0.0996870
$451$	−8633.78	−0.00199875
$452$	2.86346e6	0.659242
$453$	1.90843e6	0.436949
$454$	−2.17445e6	−0.495119
$455$	1.53403e6	0.347381
$456$	−1.50406e6	−0.338730
$457$	1.98425e6	0.444432	0.222216	−	0.974997i	$-0.428671\pi$
$457$	1.98425e6	0.444432	0.222216	+	0.974997i	$0.428671\pi$
$458$	−3.56294e6	−0.793679
$459$	7.34209e6	1.62663
$460$	−211600.	−0.0466252
$461$	5.78438e6	1.26767	0.633833	−	0.773470i	$-0.281481\pi$
$461$	5.78438e6	1.26767	0.633833	+	0.773470i	$0.281481\pi$
$462$	−1.44564e6	−0.315105
$463$	−7.76227e6	−1.68281	−0.841407	−	0.540402i	$-0.818272\pi$
$463$	−7.76227e6	−1.68281	−0.841407	+	0.540402i	$0.818272\pi$
$464$	−600088.	−0.129396
$465$	2.07216e6	0.444418
$466$	−4.22558e6	−0.901409
$467$	7.51036e6	1.59356	0.796780	−	0.604269i	$-0.206535\pi$
$467$	7.51036e6	1.59356	0.796780	+	0.604269i	$0.206535\pi$
$468$	1.41345e6	0.298309
$469$	−5.76895e6	−1.21106
$470$	−1.79182e6	−0.374153
$471$	−2.37059e6	−0.492385
$472$	−2.90559e6	−0.600315
$473$	−383405.	−0.0787961
$474$	1.30255e6	0.266285
$475$	−1.73450e6	−0.352727
$476$	−3.98389e6	−0.805916
$477$	−2.68095e6	−0.539501
$478$	3.22203e6	0.645000
$479$	−7.38377e6	−1.47041	−0.735207	−	0.677843i	$-0.762915\pi$
$479$	−7.38377e6	−1.47041	−0.735207	+	0.677843i	$0.762915\pi$
$480$	216787.	0.0429467
$481$	−2.48401e6	−0.489543
$482$	3.39503e6	0.665620
$483$	−532981.	−0.103955
$484$	−518043.	−0.100520
$485$	−1.79669e6	−0.346831
$486$	3.81363e6	0.732400
$487$	−9.26947e6	−1.77106	−0.885528	−	0.464586i	$-0.846203\pi$
$487$	−9.26947e6	−1.77106	−0.885528	+	0.464586i	$0.846203\pi$
$488$	−1.18019e6	−0.224339
$489$	5.43908e6	1.02862
$490$	265144.	0.0498874
$491$	−3.61323e6	−0.676381	−0.338190	−	0.941078i	$-0.609815\pi$
$491$	−3.61323e6	−0.676381	−0.338190	+	0.941078i	$0.609815\pi$
$492$	3261.14	0.000607374 0
$493$	−4.90567e6	−0.909036
$494$	−5.72511e6	−1.05552
$495$	−1.53608e6	−0.281774
$496$	−2.50571e6	−0.457328
$497$	−474634.	−0.0861922
$498$	−1.01272e6	−0.182986
$499$	6.40637e6	1.15176	0.575878	−	0.817535i	$-0.304660\pi$
$499$	6.40637e6	1.15176	0.575878	+	0.817535i	$0.304660\pi$
$500$	250000.	0.0447214
$501$	517808.	0.0921667
$502$	6.47387e6	1.14658
$503$	1.04304e7	1.83815	0.919074	−	0.394086i	$-0.128939\pi$
$503$	1.04304e7	1.83815	0.919074	+	0.394086i	$0.128939\pi$
$504$	−1.30429e6	−0.228716
$505$	1.52701e6	0.266449
$506$	759032.	0.131790
$507$	891752.	0.154072
$508$	2.57930e6	0.443448
$509$	44659.2	0.00764040	0.00382020	−	0.999993i	$-0.498784\pi$
$509$	44659.2	0.00764040	0.00382020	+	0.999993i	$0.498784\pi$
$510$	1.77221e6	0.301711
$511$	−663890.	−0.112472
$512$	−262144.	−0.0441942
$513$	−9.73619e6	−1.63341
$514$	−5.26496e6	−0.878997
$515$	4.54885e6	0.755759
$516$	144819.	0.0239443
$517$	6.42744e6	1.05758
$518$	2.29217e6	0.375337
$519$	2.28792e6	0.372840
$520$	825183.	0.133827
$521$	6.03155e6	0.973497	0.486749	−	0.873542i	$-0.338183\pi$
$521$	6.03155e6	0.973497	0.486749	+	0.873542i	$0.338183\pi$
$522$	−1.60607e6	−0.257981
$523$	1.12464e6	0.179788	0.0898939	−	0.995951i	$-0.471347\pi$
$523$	1.12464e6	0.179788	0.0898939	+	0.995951i	$0.471347\pi$
$524$	−2.19878e6	−0.349827
$525$	629703.	0.0997098
$526$	2.42309e6	0.381860
$527$	−2.04840e7	−3.21284
$528$	−777637.	−0.121392
$529$	279841.	0.0434783
$530$	−1.56516e6	−0.242030
$531$	−7.77649e6	−1.19687
$532$	5.28295e6	0.809278
$533$	12413.3	0.00189264
$534$	1.70482e6	0.258717
$535$	−2.48575e6	−0.375467
$536$	−3.10322e6	−0.466553
$537$	1.88586e6	0.282211
$538$	−44160.3	−0.00657774
$539$	−951099.	−0.141011
$540$	1.40332e6	0.207096
$541$	−8.07492e6	−1.18617	−0.593083	−	0.805142i	$-0.702089\pi$
$541$	−8.07492e6	−1.18617	−0.593083	+	0.805142i	$0.702089\pi$
$542$	−5.20631e6	−0.761258
$543$	2.35117e6	0.342204
$544$	−2.14301e6	−0.310475
$545$	3.94245e6	0.568559
$546$	2.07848e6	0.298377
$547$	5.64519e6	0.806697	0.403348	−	0.915047i	$-0.367846\pi$
$547$	5.64519e6	0.806697	0.403348	+	0.915047i	$0.367846\pi$
$548$	4.88440e6	0.694800
$549$	−3.15866e6	−0.447273
$550$	−896776.	−0.126409
$551$	6.50531e6	0.912828
$552$	−286700.	−0.0400480
$553$	−4.57513e6	−0.636196
$554$	−8.28680e6	−1.14713
$555$	−1.01966e6	−0.140515
$556$	−2.30284e6	−0.315920
$557$	1.00532e7	1.37299	0.686496	−	0.727134i	$-0.259148\pi$
$557$	1.00532e7	1.37299	0.686496	+	0.727134i	$0.259148\pi$
$558$	−6.70628e6	−0.911792
$559$	551244.	0.0746130
$560$	−761454.	−0.102606
$561$	−6.35712e6	−0.852811
$562$	−2.82251e6	−0.376960
$563$	−7.02958e6	−0.934670	−0.467335	−	0.884080i	$-0.654786\pi$
$563$	−7.02958e6	−0.934670	−0.467335	+	0.884080i	$0.654786\pi$
$564$	−2.42776e6	−0.321372
$565$	4.47415e6	0.589644
$566$	7.41059e6	0.972326
$567$	−1.41752e6	−0.185170
$568$	−255315.	−0.0332051
$569$	−6.22757e6	−0.806377	−0.403188	−	0.915117i	$-0.632098\pi$
$569$	−6.22757e6	−0.806377	−0.403188	+	0.915117i	$0.632098\pi$
$570$	−2.35010e6	−0.302969
$571$	1.08461e7	1.39215	0.696074	−	0.717970i	$-0.254929\pi$
$571$	1.08461e7	1.39215	0.696074	+	0.717970i	$0.254929\pi$
$572$	−2.96002e6	−0.378272
$573$	−4.58446e6	−0.583313
$574$	−11454.6	−0.00145111
$575$	−330625.	−0.0417029
$576$	−701600.	−0.0881117
$577$	1.08904e6	0.136178	0.0680889	−	0.997679i	$-0.478310\pi$
$577$	1.08904e6	0.136178	0.0680889	+	0.997679i	$0.478310\pi$
$578$	−1.18395e7	−1.47405
$579$	283584.	0.0351548
$580$	−937637.	−0.115735
$581$	3.55714e6	0.437181
$582$	−2.43436e6	−0.297905
$583$	5.61439e6	0.684118
$584$	−357118.	−0.0433292
$585$	2.20851e6	0.266815
$586$	−4.27207e6	−0.513918
$587$	1.40443e7	1.68230	0.841150	−	0.540801i	$-0.181879\pi$
$587$	1.40443e7	1.68230	0.841150	+	0.540801i	$0.181879\pi$
$588$	359248.	0.0428500
$589$	2.71634e7	3.22624
$590$	−4.53998e6	−0.536938
$591$	1.26455e6	0.148925
$592$	1.23300e6	0.144597
$593$	1.43036e7	1.67036	0.835180	−	0.549977i	$-0.185363\pi$
$593$	1.43036e7	1.67036	0.835180	+	0.549977i	$0.185363\pi$
$594$	−5.03385e6	−0.585375
$595$	−6.22482e6	−0.720833
$596$	5.68726e6	0.655824
$597$	−2.32636e6	−0.267141
$598$	−1.09131e6	−0.124794
$599$	−4.51234e6	−0.513848	−0.256924	−	0.966432i	$-0.582709\pi$
$599$	−4.51234e6	−0.513848	−0.256924	+	0.966432i	$0.582709\pi$
$600$	338729.	0.0384127
$601$	1.00918e7	1.13968	0.569838	−	0.821757i	$-0.307006\pi$
$601$	1.00918e7	1.13968	0.569838	+	0.821757i	$0.307006\pi$
$602$	−508671.	−0.0572065
$603$	−8.30544e6	−0.930186
$604$	−3.60582e6	−0.402172
$605$	−809443.	−0.0899079
$606$	2.06897e6	0.228862
$607$	8.46363e6	0.932363	0.466182	−	0.884689i	$-0.345629\pi$
$607$	8.46363e6	0.932363	0.466182	+	0.884689i	$0.345629\pi$
$608$	2.84180e6	0.311770
$609$	−2.36173e6	−0.258040
$610$	−1.84405e6	−0.200655
$611$	−9.24111e6	−1.00143
$612$	−5.73553e6	−0.619006
$613$	453516.	0.0487463	0.0243732	−	0.999703i	$-0.492241\pi$
$613$	453516.	0.0487463	0.0243732	+	0.999703i	$0.492241\pi$
$614$	139479.	0.0149310
$615$	5095.53	0.000543252 0
$616$	2.73142e6	0.290025
$617$	6.89013e6	0.728643	0.364321	−	0.931273i	$-0.381301\pi$
$617$	6.89013e6	0.728643	0.364321	+	0.931273i	$0.381301\pi$
$618$	6.16331e6	0.649147
$619$	2.03233e6	0.213190	0.106595	−	0.994303i	$-0.466005\pi$
$619$	2.03233e6	0.213190	0.106595	+	0.994303i	$0.466005\pi$
$620$	−3.91518e6	−0.409046
$621$	−1.85589e6	−0.193118
$622$	−9.11208e6	−0.944369
$623$	−5.98811e6	−0.618115
$624$	1.11805e6	0.114948
$625$	390625.	0.0400000
$626$	5.26630e6	0.537118
$627$	8.43004e6	0.856369
$628$	4.47904e6	0.453195
$629$	1.00797e7	1.01583
$630$	−2.03795e6	−0.204570
$631$	1.36301e7	1.36278	0.681392	−	0.731919i	$-0.261375\pi$
$631$	1.36301e7	1.36278	0.681392	+	0.731919i	$0.261375\pi$
$632$	−2.46105e6	−0.245091
$633$	−2.99349e6	−0.296940
$634$	4.60268e6	0.454765
$635$	4.03016e6	0.396632
$636$	−2.12066e6	−0.207887
$637$	1.36745e6	0.133525
$638$	3.36340e6	0.327135
$639$	−683322.	−0.0662023
$640$	−409600.	−0.0395285
$641$	−1.27425e7	−1.22492	−0.612462	−	0.790500i	$-0.709821\pi$
$641$	−1.27425e7	−1.22492	−0.612462	+	0.790500i	$0.709821\pi$
$642$	−3.36798e6	−0.322501
$643$	1.23274e7	1.17583	0.587913	−	0.808924i	$-0.299950\pi$
$643$	1.23274e7	1.17583	0.587913	+	0.808924i	$0.299950\pi$
$644$	1.00702e6	0.0956807
$645$	226280.	0.0214164
$646$	2.32315e7	2.19026
$647$	−1.16678e7	−1.09579	−0.547894	−	0.836548i	$-0.684570\pi$
$647$	−1.16678e7	−1.09579	−0.547894	+	0.836548i	$0.684570\pi$
$648$	−762510.	−0.0713359
$649$	1.62854e7	1.51770
$650$	1.28935e6	0.119698
$651$	−9.86161e6	−0.912001
$652$	−1.02767e7	−0.946747
$653$	1.07123e7	0.983108	0.491554	−	0.870847i	$-0.336429\pi$
$653$	1.07123e7	0.983108	0.491554	+	0.870847i	$0.336429\pi$
$654$	5.34169e6	0.488354
$655$	−3.43559e6	−0.312895
$656$	−6161.64	−0.000559032 0
$657$	−955789.	−0.0863871
$658$	8.52741e6	0.767808
$659$	1.03868e7	0.931686	0.465843	−	0.884867i	$-0.345751\pi$
$659$	1.03868e7	0.931686	0.465843	+	0.884867i	$0.345751\pi$
$660$	−1.21506e6	−0.108577
$661$	1.32825e7	1.18243	0.591215	−	0.806514i	$-0.298649\pi$
$661$	1.32825e7	1.18243	0.591215	+	0.806514i	$0.298649\pi$
$662$	1.44978e7	1.28576
$663$	9.14001e6	0.807538
$664$	1.91345e6	0.168421
$665$	8.25461e6	0.723840
$666$	3.29999e6	0.288288
$667$	1.24002e6	0.107923
$668$	−978354.	−0.0848310
$669$	5.10625e6	0.441100
$670$	−4.84879e6	−0.417298
$671$	6.61482e6	0.567168
$672$	−1.03171e6	−0.0881318
$673$	−1.21571e7	−1.03465	−0.517323	−	0.855790i	$-0.673071\pi$
$673$	−1.21571e7	−1.03465	−0.517323	+	0.855790i	$0.673071\pi$
$674$	−1.23336e6	−0.104578
$675$	2.19268e6	0.185232
$676$	−1.68489e6	−0.141809
$677$	−1.63957e7	−1.37486	−0.687431	−	0.726250i	$-0.741262\pi$
$677$	−1.63957e7	−1.37486	−0.687431	+	0.726250i	$0.741262\pi$
$678$	6.06210e6	0.506465
$679$	8.55059e6	0.711740
$680$	−3.34845e6	−0.277697
$681$	−4.60343e6	−0.380377
$682$	1.40442e7	1.15621
$683$	−5.50399e6	−0.451467	−0.225733	−	0.974189i	$-0.572478\pi$
$683$	−5.50399e6	−0.451467	−0.225733	+	0.974189i	$0.572478\pi$
$684$	7.60576e6	0.621588
$685$	7.63188e6	0.621448
$686$	−9.26044e6	−0.751314
$687$	−7.54295e6	−0.609747
$688$	−273623.	−0.0220385
$689$	−8.07214e6	−0.647800
$690$	−447969.	−0.0358200
$691$	8.81682e6	0.702452	0.351226	−	0.936291i	$-0.385765\pi$
$691$	8.81682e6	0.702452	0.351226	+	0.936291i	$0.385765\pi$
$692$	−4.32284e6	−0.343165
$693$	7.31034e6	0.578235
$694$	3.40004e6	0.267970
$695$	−3.59819e6	−0.282567
$696$	−1.27042e6	−0.0994086
$697$	−50370.9	−0.00392734
$698$	1.18554e7	0.921039
$699$	−8.94580e6	−0.692510
$700$	−1.18977e6	−0.0917737
$701$	9.94017e6	0.764010	0.382005	−	0.924160i	$-0.375234\pi$
$701$	9.94017e6	0.764010	0.382005	+	0.924160i	$0.375234\pi$
$702$	7.23747e6	0.554299
$703$	−1.33664e7	−1.02006
$704$	1.46928e6	0.111731
$705$	−3.79338e6	−0.287444
$706$	−8.57959e6	−0.647821
$707$	−7.26718e6	−0.546786
$708$	−6.15129e6	−0.461194
$709$	2.13658e7	1.59626	0.798128	−	0.602488i	$-0.205824\pi$
$709$	2.13658e7	1.59626	0.798128	+	0.602488i	$0.205824\pi$
$710$	−398929.	−0.0296995
$711$	−6.58673e6	−0.488648
$712$	−3.22111e6	−0.238126
$713$	5.17782e6	0.381438
$714$	−8.43412e6	−0.619147
$715$	−4.62503e6	−0.338337
$716$	−3.56317e6	−0.259749
$717$	6.82121e6	0.495523
$718$	1.75555e6	0.127087
$719$	2.21914e6	0.160089	0.0800445	−	0.996791i	$-0.474494\pi$
$719$	2.21914e6	0.160089	0.0800445	+	0.996791i	$0.474494\pi$
$720$	−1.09625e6	−0.0788095
$721$	−2.16484e7	−1.55091
$722$	−2.09024e7	−1.49229
$723$	7.18747e6	0.511364
$724$	−4.44234e6	−0.314967
$725$	−1.46506e6	−0.103517
$726$	−1.09673e6	−0.0772249
$727$	1.66600e7	1.16906	0.584532	−	0.811371i	$-0.301278\pi$
$727$	1.66600e7	1.16906	0.584532	+	0.811371i	$0.301278\pi$
$728$	−3.92712e6	−0.274629
$729$	5.17852e6	0.360900
$730$	−557998.	−0.0387548
$731$	−2.23685e6	−0.154826
$732$	−2.49854e6	−0.172349
$733$	6.84915e6	0.470844	0.235422	−	0.971893i	$-0.424353\pi$
$733$	6.84915e6	0.470844	0.235422	+	0.971893i	$0.424353\pi$
$734$	−5.55572e6	−0.380627
$735$	561324.	0.0383262
$736$	541696.	0.0368605
$737$	1.73931e7	1.17953
$738$	−16491.0	−0.00111457
$739$	4.66486e6	0.314216	0.157108	−	0.987581i	$-0.449783\pi$
$739$	4.66486e6	0.314216	0.157108	+	0.987581i	$0.449783\pi$
$740$	1.92656e6	0.129331
$741$	−1.21204e7	−0.810906
$742$	7.44872e6	0.496675
$743$	−7.85896e6	−0.522268	−0.261134	−	0.965303i	$-0.584096\pi$
$743$	−7.85896e6	−0.522268	−0.261134	+	0.965303i	$0.584096\pi$
$744$	−5.30474e6	−0.351343
$745$	8.88635e6	0.586587
$746$	−8.57718e6	−0.564284
$747$	5.12115e6	0.335789
$748$	1.20112e7	0.784935
$749$	1.18299e7	0.770506
$750$	529264.	0.0343573
$751$	−1.85421e7	−1.19966	−0.599830	−	0.800128i	$-0.704765\pi$
$751$	−1.85421e7	−1.19966	−0.599830	+	0.800128i	$0.704765\pi$
$752$	4.58705e6	0.295794
$753$	1.37055e7	0.880864
$754$	−4.83577e6	−0.309768
$755$	−5.63409e6	−0.359714
$756$	−6.67851e6	−0.424986
$757$	−1.07470e7	−0.681629	−0.340815	−	0.940130i	$-0.610703\pi$
$757$	−1.07470e7	−0.681629	−0.340815	+	0.940130i	$0.610703\pi$
$758$	−1.02390e7	−0.647270
$759$	1.60691e6	0.101248
$760$	4.44031e6	0.278855
$761$	−6.27486e6	−0.392774	−0.196387	−	0.980526i	$-0.562921\pi$
$761$	−6.27486e6	−0.392774	−0.196387	+	0.980526i	$0.562921\pi$
$762$	5.46053e6	0.340680
$763$	−1.87625e7	−1.16675
$764$	8.66195e6	0.536886
$765$	−8.96176e6	−0.553656
$766$	1.15990e7	0.714247
$767$	−2.34145e7	−1.43713
$768$	−554974.	−0.0339523
$769$	−3.06263e7	−1.86758	−0.933788	−	0.357827i	$-0.883518\pi$
$769$	−3.06263e7	−1.86758	−0.933788	+	0.357827i	$0.883518\pi$
$770$	4.26784e6	0.259407
$771$	−1.11462e7	−0.675292
$772$	−535807.	−0.0323568
$773$	2.73276e7	1.64495	0.822474	−	0.568803i	$-0.192593\pi$
$773$	2.73276e7	1.64495	0.822474	+	0.568803i	$0.192593\pi$
$774$	−732324.	−0.0439391
$775$	−6.11747e6	−0.365862
$776$	4.59952e6	0.274194
$777$	4.85265e6	0.288354
$778$	−5.88406e6	−0.348520
$779$	66795.9	0.00394372
$780$	1.74696e6	0.102813
$781$	1.43100e6	0.0839483
$782$	4.42832e6	0.258954
$783$	−8.22377e6	−0.479365
$784$	−678768.	−0.0394395
$785$	6.99850e6	0.405350
$786$	−4.65494e6	−0.268756
$787$	−1.25785e7	−0.723925	−0.361963	−	0.932193i	$-0.617893\pi$
$787$	−1.25785e7	−0.723925	−0.361963	+	0.932193i	$0.617893\pi$
$788$	−2.38927e6	−0.137072
$789$	5.12981e6	0.293365
$790$	−3.84539e6	−0.219216
$791$	−2.12929e7	−1.21002
$792$	3.93237e6	0.222762
$793$	−9.51052e6	−0.537058
$794$	1.95411e7	1.10001
$795$	−3.31353e6	−0.185940
$796$	4.39546e6	0.245879
$797$	−2.82459e7	−1.57511	−0.787554	−	0.616246i	$-0.788653\pi$
$797$	−2.82459e7	−1.57511	−0.787554	+	0.616246i	$0.788653\pi$
$798$	1.11843e7	0.621730
$799$	3.74988e7	2.07802
$800$	−640000.	−0.0353553
$801$	−8.62096e6	−0.474760
$802$	1.61486e7	0.886540
$803$	2.00160e6	0.109544
$804$	−6.56970e6	−0.358431
$805$	1.57347e6	0.0855795
$806$	−2.01921e7	−1.09482
$807$	−93489.9	−0.00505337
$808$	−3.90915e6	−0.210646
$809$	3.02669e7	1.62591	0.812956	−	0.582325i	$-0.197857\pi$
$809$	3.02669e7	1.62591	0.812956	+	0.582325i	$0.197857\pi$
$810$	−1.19142e6	−0.0638048
$811$	−2.24011e7	−1.19596	−0.597981	−	0.801510i	$-0.704030\pi$
$811$	−2.24011e7	−1.19596	−0.597981	+	0.801510i	$0.704030\pi$
$812$	4.46229e6	0.237503
$813$	−1.10221e7	−0.584839
$814$	−6.91078e6	−0.365566
$815$	−1.60573e7	−0.846796
$816$	−4.53687e6	−0.238523
$817$	2.96624e6	0.155472
$818$	1.65553e7	0.865077
$819$	−1.05105e7	−0.547538
$820$	−9627.57	−0.000500014 0
$821$	2.07746e7	1.07566	0.537830	−	0.843053i	$-0.319244\pi$
$821$	2.07746e7	1.07566	0.537830	+	0.843053i	$0.319244\pi$
$822$	1.03406e7	0.533782
$823$	−1.77559e7	−0.913784	−0.456892	−	0.889522i	$-0.651037\pi$
$823$	−1.77559e7	−0.913784	−0.456892	+	0.889522i	$0.651037\pi$
$824$	−1.16451e7	−0.597480
$825$	−1.89853e6	−0.0971140
$826$	2.16062e7	1.10186
$827$	−7.87984e6	−0.400639	−0.200320	−	0.979731i	$-0.564198\pi$
$827$	−7.87984e6	−0.400639	−0.200320	+	0.979731i	$0.564198\pi$
$828$	1.44979e6	0.0734902
$829$	2.16609e7	1.09469	0.547345	−	0.836907i	$-0.315639\pi$
$829$	2.16609e7	1.09469	0.547345	+	0.836907i	$0.315639\pi$
$830$	2.98977e6	0.150641
$831$	−1.75436e7	−0.881286
$832$	−2.11247e6	−0.105799
$833$	−5.54887e6	−0.277072
$834$	−4.87525e6	−0.242707
$835$	−1.52868e6	−0.0758752
$836$	−1.59279e7	−0.788209
$837$	−3.43390e7	−1.69424
$838$	−2.14512e6	−0.105522
$839$	2.69565e7	1.32208	0.661041	−	0.750350i	$-0.270115\pi$
$839$	2.69565e7	1.32208	0.661041	+	0.750350i	$0.270115\pi$
$840$	−1.61204e6	−0.0788275
$841$	−1.50164e7	−0.732108
$842$	−2.63822e7	−1.28242
$843$	−5.97542e6	−0.289601
$844$	5.65594e6	0.273306
$845$	−2.63264e6	−0.126838
$846$	1.22767e7	0.589736
$847$	3.85221e6	0.184502
$848$	4.00680e6	0.191341
$849$	1.56886e7	0.746993
$850$	−5.23195e6	−0.248380
$851$	−2.54788e6	−0.120602
$852$	−540515.	−0.0255099
$853$	−3.01511e7	−1.41883	−0.709415	−	0.704791i	$-0.751041\pi$
$853$	−3.01511e7	−1.41883	−0.709415	+	0.704791i	$0.751041\pi$
$854$	8.77601e6	0.411768
$855$	1.18840e7	0.555965
$856$	6.36351e6	0.296833
$857$	9.17229e6	0.426605	0.213302	−	0.976986i	$-0.431578\pi$
$857$	9.17229e6	0.426605	0.213302	+	0.976986i	$0.431578\pi$
$858$	−6.26653e6	−0.290609
$859$	−9.12169e6	−0.421786	−0.210893	−	0.977509i	$-0.567637\pi$
$859$	−9.12169e6	−0.421786	−0.210893	+	0.977509i	$0.567637\pi$
$860$	−427537.	−0.0197118
$861$	−24250.1	−0.00111482
$862$	−1.46005e7	−0.669267
$863$	1.54060e7	0.704145	0.352072	−	0.935973i	$-0.385477\pi$
$863$	1.54060e7	0.704145	0.352072	+	0.935973i	$0.385477\pi$
$864$	−3.59249e6	−0.163724
$865$	−6.75443e6	−0.306937
$866$	−2.20136e7	−0.997461
$867$	−2.50648e7	−1.13245
$868$	1.86327e7	0.839413
$869$	1.37938e7	0.619634
$870$	−1.98503e6	−0.0889138
$871$	−2.50071e7	−1.11691
$872$	−1.00927e7	−0.449485
$873$	1.23101e7	0.546672
$874$	−5.87231e6	−0.260034
$875$	−1.85902e6	−0.0820849
$876$	−756040.	−0.0332878
$877$	−1.74936e7	−0.768032	−0.384016	−	0.923326i	$-0.625459\pi$
$877$	−1.74936e7	−0.768032	−0.384016	+	0.923326i	$0.625459\pi$
$878$	1.69269e7	0.741040
$879$	−9.04421e6	−0.394819
$880$	2.29575e6	0.0999350
$881$	−1.82811e7	−0.793527	−0.396763	−	0.917921i	$-0.629867\pi$
$881$	−1.82811e7	−0.793527	−0.396763	+	0.917921i	$0.629867\pi$
$882$	−1.81665e6	−0.0786321
$883$	1.89568e7	0.818206	0.409103	−	0.912488i	$-0.365842\pi$
$883$	1.89568e7	0.818206	0.409103	+	0.912488i	$0.365842\pi$
$884$	−1.72693e7	−0.743264
$885$	−9.61140e6	−0.412504
$886$	1.68967e7	0.723133
$887$	4.61134e6	0.196797	0.0983985	−	0.995147i	$-0.468628\pi$
$887$	4.61134e6	0.196797	0.0983985	+	0.995147i	$0.468628\pi$
$888$	2.61033e6	0.111087
$889$	−1.91799e7	−0.813938
$890$	−5.03299e6	−0.212986
$891$	4.27376e6	0.180350
$892$	−9.64782e6	−0.405992
$893$	−4.97264e7	−2.08669
$894$	1.20403e7	0.503839
$895$	−5.56746e6	−0.232327
$896$	1.94932e6	0.0811173
$897$	−2.31035e6	−0.0958733
$898$	2.58079e7	1.06798
$899$	2.29439e7	0.946819
$900$	−1.71289e6	−0.0704894
$901$	3.27553e7	1.34422
$902$	34535.1	0.00141333
$903$	−1.07689e6	−0.0439491
$904$	−1.14538e7	−0.466154
$905$	−6.94116e6	−0.281715
$906$	−7.63373e6	−0.308970
$907$	−1.05722e7	−0.426726	−0.213363	−	0.976973i	$-0.568442\pi$
$907$	−1.05722e7	−0.426726	−0.213363	+	0.976973i	$0.568442\pi$
$908$	8.69780e6	0.350102
$909$	−1.04624e7	−0.419974
$910$	−6.13612e6	−0.245635
$911$	1.06672e7	0.425849	0.212925	−	0.977069i	$-0.431701\pi$
$911$	1.06672e7	0.425849	0.212925	+	0.977069i	$0.431701\pi$
$912$	6.01625e6	0.239518
$913$	−1.07246e7	−0.425799
$914$	−7.93699e6	−0.314261
$915$	−3.90397e6	−0.154153
$916$	1.42518e7	0.561216
$917$	1.63503e7	0.642099
$918$	−2.93683e7	−1.15020
$919$	6018.39	0.000235067 0	0.000117534	−	1.00000i	$-0.499963\pi$
$919$	6018.39	0.000235067 0	0.000117534		1.00000i	$0.499963\pi$
$920$	846400.	0.0329690
$921$	295285.	0.0114708
$922$	−2.31375e7	−0.896375
$923$	−2.05743e6	−0.0794917
$924$	5.78256e6	0.222813
$925$	3.01025e6	0.115677
$926$	3.10491e7	1.18993
$927$	−3.11667e7	−1.19122
$928$	2.40035e6	0.0914966
$929$	−4.69368e7	−1.78432	−0.892162	−	0.451715i	$-0.850812\pi$
$929$	−4.69368e7	−1.78432	−0.892162	+	0.451715i	$0.850812\pi$
$930$	−8.28866e6	−0.314251
$931$	7.35825e6	0.278228
$932$	1.69023e7	0.637392
$933$	−1.92908e7	−0.725514
$934$	−3.00414e7	−1.12682
$935$	1.87676e7	0.702067
$936$	−5.65380e6	−0.210936
$937$	−4.09932e7	−1.52533	−0.762664	−	0.646795i	$-0.776109\pi$
$937$	−4.09932e7	−1.52533	−0.762664	+	0.646795i	$0.776109\pi$
$938$	2.30758e7	0.856347
$939$	1.11491e7	0.412643
$940$	7.16727e6	0.264566
$941$	2.29251e7	0.843988	0.421994	−	0.906599i	$-0.361330\pi$
$941$	2.29251e7	0.843988	0.421994	+	0.906599i	$0.361330\pi$
$942$	9.48238e6	0.348169
$943$	12732.5	0.000466265 0
$944$	1.16223e7	0.424487
$945$	−1.04352e7	−0.380119
$946$	1.53362e6	0.0557173
$947$	−1.17141e6	−0.0424456	−0.0212228	−	0.999775i	$-0.506756\pi$
$947$	−1.17141e6	−0.0424456	−0.0212228	+	0.999775i	$0.506756\pi$
$948$	−5.21018e6	−0.188292
$949$	−2.87781e6	−0.103728
$950$	6.93798e6	0.249416
$951$	9.74413e6	0.349375
$952$	1.59355e7	0.569869
$953$	−1.77064e7	−0.631537	−0.315768	−	0.948836i	$-0.602262\pi$
$953$	−1.77064e7	−0.631537	−0.315768	+	0.948836i	$0.602262\pi$
$954$	1.07238e7	0.381485
$955$	1.35343e7	0.480206
$956$	−1.28881e7	−0.456084
$957$	7.12052e6	0.251323
$958$	2.95351e7	1.03974
$959$	−3.63208e7	−1.27529
$960$	−867146.	−0.0303679
$961$	6.71748e7	2.34638
$962$	9.93604e6	0.346159
$963$	1.70313e7	0.591808
$964$	−1.35801e7	−0.470664
$965$	−837199.	−0.0289408
$966$	2.13192e6	0.0735070
$967$	−2.36387e7	−0.812937	−0.406468	−	0.913665i	$-0.633240\pi$
$967$	−2.36387e7	−0.812937	−0.406468	+	0.913665i	$0.633240\pi$
$968$	2.07217e6	0.0710784
$969$	4.91823e7	1.68267
$970$	7.18675e6	0.245247
$971$	2.33077e7	0.793324	0.396662	−	0.917965i	$-0.370168\pi$
$971$	2.33077e7	0.793324	0.396662	+	0.917965i	$0.370168\pi$
$972$	−1.52545e7	−0.517885
$973$	1.71241e7	0.579863
$974$	3.70779e7	1.25233
$975$	2.72963e6	0.0919584
$976$	4.72078e6	0.158631
$977$	2.37183e7	0.794964	0.397482	−	0.917610i	$-0.369884\pi$
$977$	2.37183e7	0.794964	0.397482	+	0.917610i	$0.369884\pi$
$978$	−2.17563e7	−0.727341
$979$	1.80539e7	0.602024
$980$	−1.06058e6	−0.0352757
$981$	−2.70120e7	−0.896156
$982$	1.44529e7	0.478274
$983$	−2.54913e7	−0.841413	−0.420706	−	0.907197i	$-0.638218\pi$
$983$	−2.54913e7	−0.841413	−0.420706	+	0.907197i	$0.638218\pi$
$984$	−13044.5	−0.000429478 0
$985$	−3.73323e6	−0.122601
$986$	1.96227e7	0.642785
$987$	1.80530e7	0.589871
$988$	2.29004e7	0.746365
$989$	565417.	0.0183814
$990$	6.14432e6	0.199244
$991$	−3.42847e7	−1.10896	−0.554481	−	0.832197i	$-0.687083\pi$
$991$	−3.42847e7	−1.10896	−0.554481	+	0.832197i	$0.687083\pi$
$992$	1.00229e7	0.323379
$993$	3.06927e7	0.987785
$994$	1.89854e6	0.0609471
$995$	6.86791e6	0.219921
$996$	4.05089e6	0.129390
$997$	−2.64620e6	−0.0843111	−0.0421555	−	0.999111i	$-0.513423\pi$
$997$	−2.64620e6	−0.0843111	−0.0421555	+	0.999111i	$0.513423\pi$
$998$	−2.56255e7	−0.814415
$999$	1.68974e7	0.535680

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.6.a.f.1.2	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.6.a.f.1.2	✓	5	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	230.a (trivial)

\(f(q)\)	\(=\)	\(q-4.00000 q^{2} -8.46823 q^{3} +16.0000 q^{4} +25.0000 q^{5} +33.8729 q^{6} -118.977 q^{7} -64.0000 q^{8} -171.289 q^{9} -100.000 q^{10} +358.711 q^{11} -135.492 q^{12} -515.740 q^{13} +475.909 q^{14} -211.706 q^{15} +256.000 q^{16} +2092.78 q^{17} +685.157 q^{18} -2775.19 q^{19} +400.000 q^{20} +1007.53 q^{21} -1434.84 q^{22} -529.000 q^{23} +541.967 q^{24} +625.000 q^{25} +2062.96 q^{26} +3508.29 q^{27} -1903.63 q^{28} -2344.09 q^{29} +846.823 q^{30} -9787.95 q^{31} -1024.00 q^{32} -3037.64 q^{33} -8371.12 q^{34} -2974.43 q^{35} -2740.63 q^{36} +4816.40 q^{37} +11100.8 q^{38} +4367.40 q^{39} -1600.00 q^{40} -24.0689 q^{41} -4030.10 q^{42} -1068.84 q^{43} +5739.37 q^{44} -4282.23 q^{45} +2116.00 q^{46} +17918.2 q^{47} -2167.87 q^{48} -2651.44 q^{49} -2500.00 q^{50} -17722.1 q^{51} -8251.83 q^{52} +15651.6 q^{53} -14033.2 q^{54} +8967.76 q^{55} +7614.54 q^{56} +23501.0 q^{57} +9376.37 q^{58} +45399.8 q^{59} -3387.29 q^{60} +18440.5 q^{61} +39151.8 q^{62} +20379.5 q^{63} +4096.00 q^{64} -12893.5 q^{65} +12150.6 q^{66} +48487.9 q^{67} +33484.5 q^{68} +4479.69 q^{69} +11897.7 q^{70} +3989.29 q^{71} +10962.5 q^{72} +5579.98 q^{73} -19265.6 q^{74} -5292.64 q^{75} -44403.1 q^{76} -42678.4 q^{77} -17469.6 q^{78} +38453.9 q^{79} +6400.00 q^{80} +11914.2 q^{81} +96.2757 q^{82} -29897.7 q^{83} +16120.4 q^{84} +52319.5 q^{85} +4275.37 q^{86} +19850.3 q^{87} -22957.5 q^{88} +50329.9 q^{89} +17128.9 q^{90} +61361.2 q^{91} -8464.00 q^{92} +82886.6 q^{93} -71672.7 q^{94} -69379.8 q^{95} +8671.46 q^{96} -71867.5 q^{97} +10605.8 q^{98} -61443.2 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 20 q^{2} + q^{3} + 80 q^{4} + 125 q^{5} - 4 q^{6} + 102 q^{7} - 320 q^{8} + 334 q^{9} - 500 q^{10} + 251 q^{11} + 16 q^{12} + 1743 q^{13} - 408 q^{14} + 25 q^{15} + 1280 q^{16} + 1944 q^{17} - 1336 q^{18}+ \cdots + 386925 q^{99}+O(q^{100}) \) 5 * q - 20 * q^2 + q^3 + 80 * q^4 + 125 * q^5 - 4 * q^6 + 102 * q^7 - 320 * q^8 + 334 * q^9 - 500 * q^10 + 251 * q^11 + 16 * q^12 + 1743 * q^13 - 408 * q^14 + 25 * q^15 + 1280 * q^16 + 1944 * q^17 - 1336 * q^18 - 845 * q^19 + 2000 * q^20 + 4682 * q^21 - 1004 * q^22 - 2645 * q^23 - 64 * q^24 + 3125 * q^25 - 6972 * q^26 + 2428 * q^27 + 1632 * q^28 - 4021 * q^29 - 100 * q^30 - 15752 * q^31 - 5120 * q^32 + 2931 * q^33 - 7776 * q^34 + 2550 * q^35 + 5344 * q^36 - 3455 * q^37 + 3380 * q^38 - 16708 * q^39 - 8000 * q^40 - 11898 * q^41 - 18728 * q^42 + 6968 * q^43 + 4016 * q^44 + 8350 * q^45 + 10580 * q^46 + 13412 * q^47 + 256 * q^48 + 91041 * q^49 - 12500 * q^50 - 2115 * q^51 + 27888 * q^52 + 53029 * q^53 - 9712 * q^54 + 6275 * q^55 - 6528 * q^56 - 21730 * q^57 + 16084 * q^58 - 31223 * q^59 + 400 * q^60 + 71477 * q^61 + 63008 * q^62 + 262199 * q^63 + 20480 * q^64 + 43575 * q^65 - 11724 * q^66 + 76003 * q^67 + 31104 * q^68 - 529 * q^69 - 10200 * q^70 + 54418 * q^71 - 21376 * q^72 + 69418 * q^73 + 13820 * q^74 + 625 * q^75 - 13520 * q^76 + 283598 * q^77 + 66832 * q^78 + 105024 * q^79 + 32000 * q^80 + 102913 * q^81 + 47592 * q^82 + 89399 * q^83 + 74912 * q^84 + 48600 * q^85 - 27872 * q^86 + 276726 * q^87 - 16064 * q^88 + 96240 * q^89 - 33400 * q^90 + 59261 * q^91 - 42320 * q^92 + 84434 * q^93 - 53648 * q^94 - 21125 * q^95 - 1024 * q^96 + 216087 * q^97 - 364164 * q^98 + 386925 * q^99

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