LMFDB - Embedded newform 130.6.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [130,6,Mod(1,130)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(130, 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("130.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 130 = 2 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	130.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:	$20.8498965757$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{145}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 36 $ x^2 - x - 36
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-5.52080$ of defining polynomial
Character	$\chi$	$=$	130.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-4.00000 q^{2} -9.04159 q^{3} +16.0000 q^{4} -25.0000 q^{5} +36.1664 q^{6} +77.0416 q^{7} -64.0000 q^{8} -161.250 q^{9} +100.000 q^{10} +463.248 q^{11} -144.666 q^{12} -169.000 q^{13} -308.166 q^{14} +226.040 q^{15} +256.000 q^{16} +1869.15 q^{17} +644.998 q^{18} -618.329 q^{19} -400.000 q^{20} -696.579 q^{21} -1852.99 q^{22} -1711.36 q^{23} +578.662 q^{24} +625.000 q^{25} +676.000 q^{26} +3655.06 q^{27} +1232.67 q^{28} -5862.49 q^{29} -904.159 q^{30} -545.331 q^{31} -1024.00 q^{32} -4188.50 q^{33} -7476.62 q^{34} -1926.04 q^{35} -2579.99 q^{36} -12321.6 q^{37} +2473.32 q^{38} +1528.03 q^{39} +1600.00 q^{40} -17708.6 q^{41} +2786.32 q^{42} +12622.2 q^{43} +7411.97 q^{44} +4031.24 q^{45} +6845.46 q^{46} -15968.1 q^{47} -2314.65 q^{48} -10871.6 q^{49} -2500.00 q^{50} -16900.1 q^{51} -2704.00 q^{52} -27930.3 q^{53} -14620.2 q^{54} -11581.2 q^{55} -4930.66 q^{56} +5590.68 q^{57} +23449.9 q^{58} -22214.9 q^{59} +3616.64 q^{60} +5542.43 q^{61} +2181.32 q^{62} -12422.9 q^{63} +4096.00 q^{64} +4225.00 q^{65} +16754.0 q^{66} +59646.7 q^{67} +29906.5 q^{68} +15473.5 q^{69} +7704.16 q^{70} -67225.5 q^{71} +10320.0 q^{72} +67383.3 q^{73} +49286.5 q^{74} -5651.00 q^{75} -9893.27 q^{76} +35689.4 q^{77} -6112.12 q^{78} -49060.5 q^{79} -6400.00 q^{80} +6136.07 q^{81} +70834.3 q^{82} +12542.6 q^{83} -11145.3 q^{84} -46728.9 q^{85} -50488.9 q^{86} +53006.2 q^{87} -29647.9 q^{88} -1361.03 q^{89} -16125.0 q^{90} -13020.0 q^{91} -27381.8 q^{92} +4930.66 q^{93} +63872.4 q^{94} +15458.2 q^{95} +9258.59 q^{96} +58030.7 q^{97} +43486.4 q^{98} -74698.5 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 8 q^{2} + 6 q^{3} + 32 q^{4} - 50 q^{5} - 24 q^{6} + 130 q^{7} - 128 q^{8} - 178 q^{9} + 200 q^{10} + 204 q^{11} + 96 q^{12} - 338 q^{13} - 520 q^{14} - 150 q^{15} + 512 q^{16} - 404 q^{17} + 712 q^{18}+ \cdots - 70356 q^{99}+O(q^{100}) $ 2 * q - 8 * q^2 + 6 * q^3 + 32 * q^4 - 50 * q^5 - 24 * q^6 + 130 * q^7 - 128 * q^8 - 178 * q^9 + 200 * q^10 + 204 * q^11 + 96 * q^12 - 338 * q^13 - 520 * q^14 - 150 * q^15 + 512 * q^16 - 404 * q^17 + 712 * q^18 + 112 * q^19 - 800 * q^20 + 100 * q^21 - 816 * q^22 + 262 * q^23 - 384 * q^24 + 1250 * q^25 + 1352 * q^26 - 252 * q^27 + 2080 * q^28 - 6812 * q^29 + 600 * q^30 - 320 * q^31 - 2048 * q^32 - 8088 * q^33 + 1616 * q^34 - 3250 * q^35 - 2848 * q^36 - 13276 * q^37 - 448 * q^38 - 1014 * q^39 + 3200 * q^40 - 35080 * q^41 - 400 * q^42 + 2534 * q^43 + 3264 * q^44 + 4450 * q^45 - 1048 * q^46 - 22038 * q^47 + 1536 * q^48 - 24874 * q^49 - 5000 * q^50 - 51092 * q^51 - 5408 * q^52 - 44108 * q^53 + 1008 * q^54 - 5100 * q^55 - 8320 * q^56 + 16576 * q^57 + 27248 * q^58 - 21888 * q^59 - 2400 * q^60 - 41272 * q^61 + 1280 * q^62 - 13310 * q^63 + 8192 * q^64 + 8450 * q^65 + 32352 * q^66 + 103230 * q^67 - 6464 * q^68 + 45156 * q^69 + 13000 * q^70 - 15480 * q^71 + 11392 * q^72 + 54088 * q^73 + 53104 * q^74 + 3750 * q^75 + 1792 * q^76 + 21960 * q^77 + 4056 * q^78 + 27208 * q^79 - 12800 * q^80 - 48562 * q^81 + 140320 * q^82 + 42690 * q^83 + 1600 * q^84 + 10100 * q^85 - 10136 * q^86 + 38724 * q^87 - 13056 * q^88 - 68132 * q^89 - 17800 * q^90 - 21970 * q^91 + 4192 * q^92 + 8320 * q^93 + 88152 * q^94 - 2800 * q^95 - 6144 * q^96 + 209456 * q^97 + 99496 * q^98 - 70356 * 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
$3$	−9.04159	−0.580019	−0.290009	−	0.957024i	$-0.593658\pi$
$3$	−9.04159	−0.580019	−0.290009	+	0.957024i	$0.593658\pi$
$4$	16.0000	0.500000
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	36.1664	0.410135
$7$	77.0416	0.594265	0.297133	−	0.954836i	$-0.403970\pi$
$7$	77.0416	0.594265	0.297133	+	0.954836i	$0.403970\pi$
$8$	−64.0000	−0.353553
$9$	−161.250	−0.663578
$10$	100.000	0.316228
$11$	463.248	1.15433	0.577167	−	0.816626i	$-0.304158\pi$
$11$	463.248	1.15433	0.577167	+	0.816626i	$0.304158\pi$
$12$	−144.666	−0.290009
$13$	−169.000	−0.277350
$13$	−169.000	−0.277350
$14$	−308.166	−0.420209
$15$	226.040	0.259392
$16$	256.000	0.250000
$17$	1869.15	1.56864	0.784319	−	0.620357i	$-0.213012\pi$
$17$	1869.15	1.56864	0.784319	+	0.620357i	$0.213012\pi$
$18$	644.998	0.469221
$19$	−618.329	−0.392949	−0.196474	−	0.980509i	$-0.562949\pi$
$19$	−618.329	−0.392949	−0.196474	+	0.980509i	$0.562949\pi$
$20$	−400.000	−0.223607
$21$	−696.579	−0.344685
$22$	−1852.99	−0.816238
$23$	−1711.36	−0.674563	−0.337282	−	0.941404i	$-0.609507\pi$
$23$	−1711.36	−0.674563	−0.337282	+	0.941404i	$0.609507\pi$
$24$	578.662	0.205068
$25$	625.000	0.200000
$26$	676.000	0.196116
$27$	3655.06	0.964906
$28$	1232.67	0.297133
$29$	−5862.49	−1.29445	−0.647227	−	0.762297i	$-0.724072\pi$
$29$	−5862.49	−1.29445	−0.647227	+	0.762297i	$0.724072\pi$
$30$	−904.159	−0.183418
$31$	−545.331	−0.101919	−0.0509596	−	0.998701i	$-0.516228\pi$
$31$	−545.331	−0.101919	−0.0509596	+	0.998701i	$0.516228\pi$
$32$	−1024.00	−0.176777
$33$	−4188.50	−0.669535
$34$	−7476.62	−1.10919
$35$	−1926.04	−0.265763
$36$	−2579.99	−0.331789
$37$	−12321.6	−1.47967	−0.739833	−	0.672790i	$-0.765096\pi$
$37$	−12321.6	−1.47967	−0.739833	+	0.672790i	$0.765096\pi$
$38$	2473.32	0.277857
$39$	1528.03	0.160868
$40$	1600.00	0.158114
$41$	−17708.6	−1.64522	−0.822610	−	0.568606i	$-0.807483\pi$
$41$	−17708.6	−1.64522	−0.822610	+	0.568606i	$0.807483\pi$
$42$	2786.32	0.243729
$43$	12622.2	1.04103	0.520517	−	0.853851i	$-0.325739\pi$
$43$	12622.2	1.04103	0.520517	+	0.853851i	$0.325739\pi$
$44$	7411.97	0.577167
$45$	4031.24	0.296761
$46$	6845.46	0.476988
$47$	−15968.1	−1.05441	−0.527204	−	0.849739i	$-0.676760\pi$
$47$	−15968.1	−1.05441	−0.527204	+	0.849739i	$0.676760\pi$
$48$	−2314.65	−0.145005
$49$	−10871.6	−0.646849
$50$	−2500.00	−0.141421
$51$	−16900.1	−0.909839
$52$	−2704.00	−0.138675
$53$	−27930.3	−1.36580	−0.682898	−	0.730514i	$-0.739281\pi$
$53$	−27930.3	−1.36580	−0.682898	+	0.730514i	$0.739281\pi$
$54$	−14620.2	−0.682292
$55$	−11581.2	−0.516234
$56$	−4930.66	−0.210104
$57$	5590.68	0.227918
$58$	23449.9	0.915318
$59$	−22214.9	−0.830835	−0.415418	−	0.909631i	$-0.636365\pi$
$59$	−22214.9	−0.830835	−0.415418	+	0.909631i	$0.636365\pi$
$60$	3616.64	0.129696
$61$	5542.43	0.190711	0.0953554	−	0.995443i	$-0.469601\pi$
$61$	5542.43	0.190711	0.0953554	+	0.995443i	$0.469601\pi$
$62$	2181.32	0.0720678
$63$	−12422.9	−0.394341
$64$	4096.00	0.125000
$65$	4225.00	0.124035
$66$	16754.0	0.473433
$67$	59646.7	1.62330	0.811652	−	0.584142i	$-0.198569\pi$
$67$	59646.7	1.62330	0.811652	+	0.584142i	$0.198569\pi$
$68$	29906.5	0.784319
$69$	15473.5	0.391259
$70$	7704.16	0.187923
$71$	−67225.5	−1.58266	−0.791331	−	0.611388i	$-0.790611\pi$
$71$	−67225.5	−1.58266	−0.791331	+	0.611388i	$0.790611\pi$
$72$	10320.0	0.234610
$73$	67383.3	1.47994	0.739972	−	0.672637i	$-0.234839\pi$
$73$	67383.3	1.47994	0.739972	+	0.672637i	$0.234839\pi$
$74$	49286.5	1.04628
$75$	−5651.00	−0.116004
$76$	−9893.27	−0.196474
$77$	35689.4	0.685981
$78$	−6112.12	−0.113751
$79$	−49060.5	−0.884431	−0.442215	−	0.896909i	$-0.645807\pi$
$79$	−49060.5	−0.884431	−0.442215	+	0.896909i	$0.645807\pi$
$80$	−6400.00	−0.111803
$81$	6136.07	0.103915
$82$	70834.3	1.16335
$83$	12542.6	0.199844	0.0999222	−	0.994995i	$-0.468141\pi$
$83$	12542.6	0.199844	0.0999222	+	0.994995i	$0.468141\pi$
$84$	−11145.3	−0.172342
$85$	−46728.9	−0.701516
$86$	−50488.9	−0.736122
$87$	53006.2	0.750808
$88$	−29647.9	−0.408119
$89$	−1361.03	−0.0182135	−0.00910673	−	0.999959i	$-0.502899\pi$
$89$	−1361.03	−0.0182135	−0.00910673	+	0.999959i	$0.502899\pi$
$90$	−16125.0	−0.209842
$91$	−13020.0	−0.164819
$92$	−27381.8	−0.337282
$93$	4930.66	0.0591150
$94$	63872.4	0.745579
$95$	15458.2	0.175732
$96$	9258.59	0.102534
$97$	58030.7	0.626222	0.313111	−	0.949717i	$-0.398629\pi$
$97$	58030.7	0.626222	0.313111	+	0.949717i	$0.398629\pi$
$98$	43486.4	0.457391
$99$	−74698.5	−0.765992
$100$	10000.0	0.100000
$101$	119042.	1.16118	0.580588	−	0.814197i	$-0.302823\pi$
$101$	119042.	1.16118	0.580588	+	0.814197i	$0.302823\pi$
$102$	67600.5	0.643354
$103$	−120678.	−1.12082	−0.560408	−	0.828216i	$-0.689356\pi$
$103$	−120678.	−1.12082	−0.560408	+	0.828216i	$0.689356\pi$
$104$	10816.0	0.0980581
$105$	17414.5	0.154148
$106$	111721.	0.965764
$107$	−29154.6	−0.246177	−0.123089	−	0.992396i	$-0.539280\pi$
$107$	−29154.6	−0.246177	−0.123089	+	0.992396i	$0.539280\pi$
$108$	58481.0	0.482453
$109$	35710.9	0.287895	0.143948	−	0.989585i	$-0.454020\pi$
$109$	35710.9	0.287895	0.143948	+	0.989585i	$0.454020\pi$
$110$	46324.8	0.365033
$111$	111407.	0.858234
$112$	19722.6	0.148566
$113$	−194071.	−1.42976	−0.714882	−	0.699245i	$-0.753519\pi$
$113$	−194071.	−1.42976	−0.714882	+	0.699245i	$0.753519\pi$
$114$	−22362.7	−0.161162
$115$	42784.1	0.301674
$116$	−93799.8	−0.647227
$117$	27251.2	0.184044
$118$	88859.7	0.587489
$119$	144003.	0.932187
$120$	−14466.6	−0.0917090
$121$	53547.6	0.332488
$122$	−22169.7	−0.134853
$123$	160114.	0.954259
$124$	−8725.30	−0.0509596
$125$	−15625.0	−0.0894427
$126$	49691.7	0.278842
$127$	113031.	0.621855	0.310927	−	0.950434i	$-0.399360\pi$
$127$	113031.	0.621855	0.310927	+	0.950434i	$0.399360\pi$
$128$	−16384.0	−0.0883883
$129$	−114125.	−0.603819
$130$	−16900.0	−0.0877058
$131$	−358787.	−1.82666	−0.913331	−	0.407217i	$-0.866499\pi$
$131$	−358787.	−1.82666	−0.913331	+	0.407217i	$0.866499\pi$
$132$	−67016.0	−0.334768
$133$	−47637.1	−0.233516
$134$	−238587.	−1.14785
$135$	−91376.5	−0.431519
$136$	−119626.	−0.554597
$137$	389881.	1.77473	0.887363	−	0.461072i	$-0.152535\pi$
$137$	389881.	1.77473	0.887363	+	0.461072i	$0.152535\pi$
$138$	−61893.8	−0.276662
$139$	−143094.	−0.628179	−0.314090	−	0.949393i	$-0.601699\pi$
$139$	−143094.	−0.628179	−0.314090	+	0.949393i	$0.601699\pi$
$140$	−30816.6	−0.132882
$141$	144377.	0.611576
$142$	268902.	1.11911
$143$	−78288.9	−0.320155
$144$	−41279.9	−0.165895
$145$	146562.	0.578898
$146$	−269533.	−1.04648
$147$	98296.5	0.375184
$148$	−197146.	−0.739833
$149$	57507.0	0.212205	0.106102	−	0.994355i	$-0.466163\pi$
$149$	57507.0	0.212205	0.106102	+	0.994355i	$0.466163\pi$
$150$	22604.0	0.0820270
$151$	−382788.	−1.36621	−0.683103	−	0.730322i	$-0.739370\pi$
$151$	−382788.	−1.36621	−0.683103	+	0.730322i	$0.739370\pi$
$152$	39573.1	0.138928
$153$	−301400.	−1.04091
$154$	−142757.	−0.485062
$155$	13633.3	0.0455796
$156$	24448.5	0.0804341
$157$	−175379.	−0.567844	−0.283922	−	0.958847i	$-0.591636\pi$
$157$	−175379.	−0.567844	−0.283922	+	0.958847i	$0.591636\pi$
$158$	196242.	0.625387
$159$	252534.	0.792187
$160$	25600.0	0.0790569
$161$	−131846.	−0.400869
$162$	−24544.3	−0.0734789
$163$	−631372.	−1.86130	−0.930650	−	0.365909i	$-0.880758\pi$
$163$	−631372.	−1.86130	−0.930650	+	0.365909i	$0.880758\pi$
$164$	−283337.	−0.822610
$165$	104712.	0.299425
$166$	−50170.4	−0.141311
$167$	−261161.	−0.724631	−0.362315	−	0.932056i	$-0.618014\pi$
$167$	−261161.	−0.724631	−0.362315	+	0.932056i	$0.618014\pi$
$168$	44581.0	0.121864
$169$	28561.0	0.0769231
$170$	186915.	0.496047
$171$	99705.3	0.260752
$172$	201956.	0.520517
$173$	−333245.	−0.846541	−0.423270	−	0.906003i	$-0.639118\pi$
$173$	−333245.	−0.846541	−0.423270	+	0.906003i	$0.639118\pi$
$174$	−212025.	−0.530901
$175$	48151.0	0.118853
$176$	118591.	0.288584
$177$	200858.	0.481900
$178$	5444.12	0.0128789
$179$	−607067.	−1.41613	−0.708066	−	0.706146i	$-0.750432\pi$
$179$	−607067.	−1.41613	−0.708066	+	0.706146i	$0.750432\pi$
$180$	64499.8	0.148381
$181$	145547.	0.330222	0.165111	−	0.986275i	$-0.447202\pi$
$181$	145547.	0.330222	0.165111	+	0.986275i	$0.447202\pi$
$182$	52080.1	0.116545
$183$	−50112.4	−0.110616
$184$	109527.	0.238494
$185$	308041.	0.661727
$186$	−19722.6	−0.0418006
$187$	865882.	1.81073
$188$	−255490.	−0.527204
$189$	281592.	0.573410
$190$	−61832.9	−0.124261
$191$	16804.6	0.0333308	0.0166654	−	0.999861i	$-0.494695\pi$
$191$	16804.6	0.0333308	0.0166654	+	0.999861i	$0.494695\pi$
$192$	−37034.4	−0.0725023
$193$	517817.	1.00065	0.500326	−	0.865837i	$-0.333213\pi$
$193$	517817.	1.00065	0.500326	+	0.865837i	$0.333213\pi$
$194$	−232123.	−0.442806
$195$	−38200.7	−0.0719424
$196$	−173945.	−0.323425
$197$	244368.	0.448619	0.224310	−	0.974518i	$-0.427987\pi$
$197$	244368.	0.448619	0.224310	+	0.974518i	$0.427987\pi$
$198$	298794.	0.541638
$199$	238178.	0.426354	0.213177	−	0.977014i	$-0.431619\pi$
$199$	238178.	0.426354	0.213177	+	0.977014i	$0.431619\pi$
$200$	−40000.0	−0.0707107
$201$	−539302.	−0.941546
$202$	−476170.	−0.821076
$203$	−451655.	−0.769249
$204$	−270402.	−0.454920
$205$	442715.	0.735765
$206$	482712.	0.792537
$207$	275957.	0.447626
$208$	−43264.0	−0.0693375
$209$	−286440.	−0.453594
$210$	−69657.9	−0.108999
$211$	853217.	1.31933	0.659665	−	0.751560i	$-0.270698\pi$
$211$	853217.	1.31933	0.659665	+	0.751560i	$0.270698\pi$
$212$	−446885.	−0.682898
$213$	607826.	0.917973
$214$	116618.	0.174073
$215$	−315556.	−0.465564
$216$	−233924.	−0.341146
$217$	−42013.2	−0.0605670
$218$	−142843.	−0.203573
$219$	−609253.	−0.858395
$220$	−185299.	−0.258117
$221$	−315887.	−0.435062
$222$	−445629.	−0.606863
$223$	−86442.8	−0.116404	−0.0582018	−	0.998305i	$-0.518537\pi$
$223$	−86442.8	−0.116404	−0.0582018	+	0.998305i	$0.518537\pi$
$224$	−78890.6	−0.105052
$225$	−100781.	−0.132716
$226$	776283.	1.01100
$227$	622295.	0.801552	0.400776	−	0.916176i	$-0.368741\pi$
$227$	622295.	0.801552	0.400776	+	0.916176i	$0.368741\pi$
$228$	89450.9	0.113959
$229$	582324.	0.733797	0.366899	−	0.930261i	$-0.380420\pi$
$229$	582324.	0.733797	0.366899	+	0.930261i	$0.380420\pi$
$230$	−171136.	−0.213316
$231$	−322689.	−0.397881
$232$	375199.	0.457659
$233$	865669.	1.04463	0.522315	−	0.852753i	$-0.325069\pi$
$233$	865669.	1.04463	0.522315	+	0.852753i	$0.325069\pi$
$234$	−109005.	−0.130138
$235$	399202.	0.471545
$236$	−355439.	−0.415418
$237$	443585.	0.512986
$238$	−576011.	−0.659156
$239$	−754782.	−0.854726	−0.427363	−	0.904080i	$-0.640557\pi$
$239$	−754782.	−0.854726	−0.427363	+	0.904080i	$0.640557\pi$
$240$	57866.2	0.0648480
$241$	−211415.	−0.234473	−0.117237	−	0.993104i	$-0.537404\pi$
$241$	−211415.	−0.234473	−0.117237	+	0.993104i	$0.537404\pi$
$242$	−214190.	−0.235105
$243$	−943660.	−1.02518
$244$	88678.8	0.0953554
$245$	271790.	0.289280
$246$	−640455.	−0.674763
$247$	104498.	0.108984
$248$	34901.2	0.0360339
$249$	−113405.	−0.115914
$250$	62500.0	0.0632456
$251$	1.60703e6	1.61005	0.805024	−	0.593243i	$-0.202153\pi$
$251$	1.60703e6	1.61005	0.805024	+	0.593243i	$0.202153\pi$
$252$	−198767.	−0.197171
$253$	−792786.	−0.778672
$254$	−452125.	−0.439718
$255$	422503.	0.406893
$256$	65536.0	0.0625000
$257$	−1.29242e6	−1.22059	−0.610295	−	0.792174i	$-0.708949\pi$
$257$	−1.29242e6	−1.22059	−0.610295	+	0.792174i	$0.708949\pi$
$258$	456500.	0.426964
$259$	−949278.	−0.879314
$260$	67600.0	0.0620174
$261$	945323.	0.858972
$262$	1.43515e6	1.29165
$263$	787600.	0.702128	0.351064	−	0.936351i	$-0.385820\pi$
$263$	787600.	0.702128	0.351064	+	0.936351i	$0.385820\pi$
$264$	268064.	0.236717
$265$	698257.	0.610803
$266$	190548.	0.165120
$267$	12305.9	0.0105641
$268$	954348.	0.811652
$269$	−1.13160e6	−0.953480	−0.476740	−	0.879044i	$-0.658182\pi$
$269$	−1.13160e6	−0.953480	−0.476740	+	0.879044i	$0.658182\pi$
$270$	365506.	0.305130
$271$	1.50590e6	1.24559	0.622794	−	0.782386i	$-0.285998\pi$
$271$	1.50590e6	1.24559	0.622794	+	0.782386i	$0.285998\pi$
$272$	478503.	0.392160
$273$	117722.	0.0955983
$274$	−1.55953e6	−1.25492
$275$	289530.	0.230867
$276$	247575.	0.195630
$277$	789483.	0.618221	0.309110	−	0.951026i	$-0.399969\pi$
$277$	789483.	0.618221	0.309110	+	0.951026i	$0.399969\pi$
$278$	572375.	0.444190
$279$	87934.4	0.0676314
$280$	123267.	0.0939615
$281$	−815478.	−0.616093	−0.308047	−	0.951371i	$-0.599675\pi$
$281$	−815478.	−0.616093	−0.308047	+	0.951371i	$0.599675\pi$
$282$	−577508.	−0.432449
$283$	−326725.	−0.242502	−0.121251	−	0.992622i	$-0.538691\pi$
$283$	−326725.	−0.242502	−0.121251	+	0.992622i	$0.538691\pi$
$284$	−1.07561e6	−0.791331
$285$	−139767.	−0.101928
$286$	313156.	0.226384
$287$	−1.36430e6	−0.977697
$288$	165120.	0.117305
$289$	2.07388e6	1.46063
$290$	−586249.	−0.409342
$291$	−524690.	−0.363220
$292$	1.07813e6	0.739972
$293$	1.32473e6	0.901487	0.450743	−	0.892654i	$-0.351159\pi$
$293$	1.32473e6	0.901487	0.450743	+	0.892654i	$0.351159\pi$
$294$	−393186.	−0.265295
$295$	555373.	0.371561
$296$	788584.	0.523141
$297$	1.69320e6	1.11382
$298$	−230028.	−0.150051
$299$	289221.	0.187090
$300$	−90415.9	−0.0580019
$301$	972436.	0.618650
$302$	1.53115e6	0.966054
$303$	−1.07633e6	−0.673504
$304$	−158292.	−0.0982372
$305$	−138561.	−0.0852885
$306$	1.20560e6	0.736038
$307$	550416.	0.333307	0.166654	−	0.986015i	$-0.446704\pi$
$307$	550416.	0.333307	0.166654	+	0.986015i	$0.446704\pi$
$308$	571030.	0.342990
$309$	1.09112e6	0.650095
$310$	−54533.1	−0.0322297
$311$	−3.35779e6	−1.96858	−0.984290	−	0.176561i	$-0.943503\pi$
$311$	−3.35779e6	−1.96858	−0.984290	+	0.176561i	$0.943503\pi$
$312$	−97793.9	−0.0568755
$313$	−2.61647e6	−1.50957	−0.754787	−	0.655970i	$-0.772260\pi$
$313$	−2.61647e6	−1.50957	−0.754787	+	0.655970i	$0.772260\pi$
$314$	701518.	0.401527
$315$	310573.	0.176355
$316$	−784967.	−0.442215
$317$	1.33414e6	0.745683	0.372841	−	0.927895i	$-0.378384\pi$
$317$	1.33414e6	0.745683	0.372841	+	0.927895i	$0.378384\pi$
$318$	−1.01014e6	−0.560161
$319$	−2.71578e6	−1.49423
$320$	−102400.	−0.0559017
$321$	263604.	0.142787
$322$	527385.	0.283458
$323$	−1.15575e6	−0.616394
$324$	98177.1	0.0519574
$325$	−105625.	−0.0554700
$326$	2.52549e6	1.31614
$327$	−322883.	−0.166984
$328$	1.13335e6	0.581673
$329$	−1.23021e6	−0.626597
$330$	−418850.	−0.211726
$331$	−716034.	−0.359223	−0.179611	−	0.983738i	$-0.557484\pi$
$331$	−716034.	−0.359223	−0.179611	+	0.983738i	$0.557484\pi$
$332$	200682.	0.0999222
$333$	1.98686e6	0.981875
$334$	1.04464e6	0.512391
$335$	−1.49117e6	−0.725963
$336$	−178324.	−0.0861712
$337$	−3.87372e6	−1.85803	−0.929016	−	0.370038i	$-0.879345\pi$
$337$	−3.87372e6	−1.85803	−0.929016	+	0.370038i	$0.879345\pi$
$338$	−114244.	−0.0543928
$339$	1.75471e6	0.829289
$340$	−747662.	−0.350758
$341$	−252623.	−0.117649
$342$	−398821.	−0.184380
$343$	−2.13240e6	−0.978665
$344$	−807822.	−0.368061
$345$	−386836.	−0.174976
$346$	1.33298e6	0.598595
$347$	41926.2	0.0186923	0.00934613	−	0.999956i	$-0.497025\pi$
$347$	41926.2	0.0186923	0.00934613	+	0.999956i	$0.497025\pi$
$348$	848099.	0.375404
$349$	2.08136e6	0.914711	0.457356	−	0.889284i	$-0.348797\pi$
$349$	2.08136e6	0.914711	0.457356	+	0.889284i	$0.348797\pi$
$350$	−192604.	−0.0840418
$351$	−617705.	−0.267617
$352$	−474366.	−0.204059
$353$	−4.19749e6	−1.79289	−0.896443	−	0.443160i	$-0.853857\pi$
$353$	−4.19749e6	−1.79289	−0.896443	+	0.443160i	$0.853857\pi$
$354$	−803434.	−0.340755
$355$	1.68064e6	0.707788
$356$	−21776.5	−0.00910673
$357$	−1.30201e6	−0.540686
$358$	2.42827e6	1.00136
$359$	1.58526e6	0.649179	0.324590	−	0.945855i	$-0.394774\pi$
$359$	1.58526e6	0.649179	0.324590	+	0.945855i	$0.394774\pi$
$360$	−257999.	−0.104921
$361$	−2.09377e6	−0.845591
$362$	−582187.	−0.233502
$363$	−484155.	−0.192849
$364$	−208320.	−0.0824097
$365$	−1.68458e6	−0.661851
$366$	200449.	0.0782172
$367$	−693454.	−0.268752	−0.134376	−	0.990930i	$-0.542903\pi$
$367$	−693454.	−0.268752	−0.134376	+	0.990930i	$0.542903\pi$
$368$	−438109.	−0.168641
$369$	2.85550e6	1.09173
$370$	−1.23216e6	−0.467912
$371$	−2.15179e6	−0.811645
$372$	78890.6	0.0295575
$373$	3.74196e6	1.39260	0.696300	−	0.717751i	$-0.254828\pi$
$373$	3.74196e6	1.39260	0.696300	+	0.717751i	$0.254828\pi$
$374$	−3.46353e6	−1.28038
$375$	141275.	0.0518784
$376$	1.02196e6	0.372789
$377$	990760.	0.359017
$378$	−1.12637e6	−0.405462
$379$	32595.4	0.0116562	0.00582812	−	0.999983i	$-0.498145\pi$
$379$	32595.4	0.0116562	0.00582812	+	0.999983i	$0.498145\pi$
$380$	247332.	0.0878660
$381$	−1.02198e6	−0.360687
$382$	−67218.5	−0.0235684
$383$	−4.99326e6	−1.73935	−0.869676	−	0.493624i	$-0.835672\pi$
$383$	−4.99326e6	−1.73935	−0.869676	+	0.493624i	$0.835672\pi$
$384$	148137.	0.0512669
$385$	−892234.	−0.306780
$386$	−2.07127e6	−0.707568
$387$	−2.03533e6	−0.690807
$388$	928491.	0.313111
$389$	−3.19780e6	−1.07146	−0.535732	−	0.844388i	$-0.679964\pi$
$389$	−3.19780e6	−1.07146	−0.535732	+	0.844388i	$0.679964\pi$
$390$	152803.	0.0508710
$391$	−3.19880e6	−1.05815
$392$	695782.	0.228696
$393$	3.24401e6	1.05950
$394$	−977470.	−0.317222
$395$	1.22651e6	0.395529
$396$	−1.19518e6	−0.382996
$397$	−1.12978e6	−0.359764	−0.179882	−	0.983688i	$-0.557572\pi$
$397$	−1.12978e6	−0.359764	−0.179882	+	0.983688i	$0.557572\pi$
$398$	−952714.	−0.301477
$399$	430715.	0.135443
$400$	160000.	0.0500000
$401$	−560089.	−0.173939	−0.0869693	−	0.996211i	$-0.527718\pi$
$401$	−560089.	−0.173939	−0.0869693	+	0.996211i	$0.527718\pi$
$402$	2.15721e6	0.665774
$403$	92160.9	0.0282673
$404$	1.90468e6	0.580588
$405$	−153402.	−0.0464721
$406$	1.80662e6	0.543941
$407$	−5.70797e6	−1.70803
$408$	1.08161e6	0.321677
$409$	4.95376e6	1.46429	0.732144	−	0.681150i	$-0.238520\pi$
$409$	4.95376e6	1.46429	0.732144	+	0.681150i	$0.238520\pi$
$410$	−1.77086e6	−0.520264
$411$	−3.52515e6	−1.02937
$412$	−1.93085e6	−0.560408
$413$	−1.71147e6	−0.493736
$414$	−1.10383e6	−0.316519
$415$	−313565.	−0.0893732
$416$	173056.	0.0490290
$417$	1.29379e6	0.364355
$418$	1.14576e6	0.320740
$419$	3.76102e6	1.04658	0.523288	−	0.852156i	$-0.324705\pi$
$419$	3.76102e6	1.04658	0.523288	+	0.852156i	$0.324705\pi$
$420$	278632.	0.0770739
$421$	1.47722e6	0.406199	0.203099	−	0.979158i	$-0.434899\pi$
$421$	1.47722e6	0.406199	0.203099	+	0.979158i	$0.434899\pi$
$422$	−3.41287e6	−0.932907
$423$	2.57485e6	0.699682
$424$	1.78754e6	0.482882
$425$	1.16822e6	0.313728
$426$	−2.43130e6	−0.649105
$427$	426997.	0.113333
$428$	−466473.	−0.123089
$429$	707856.	0.185696
$430$	1.26222e6	0.329204
$431$	7.00591e6	1.81665	0.908326	−	0.418264i	$-0.137361\pi$
$431$	7.00591e6	1.81665	0.908326	+	0.418264i	$0.137361\pi$
$432$	935696.	0.241227
$433$	−771976.	−0.197872	−0.0989360	−	0.995094i	$-0.531544\pi$
$433$	−771976.	−0.197872	−0.0989360	+	0.995094i	$0.531544\pi$
$434$	168053.	0.0428273
$435$	−1.32516e6	−0.335771
$436$	571374.	0.143948
$437$	1.05819e6	0.265069
$438$	2.43701e6	0.606977
$439$	−3.79177e6	−0.939032	−0.469516	−	0.882924i	$-0.655572\pi$
$439$	−3.79177e6	−0.939032	−0.469516	+	0.882924i	$0.655572\pi$
$440$	741197.	0.182516
$441$	1.75304e6	0.429235
$442$	1.26355e6	0.307635
$443$	153363.	0.0371289	0.0185644	−	0.999828i	$-0.494090\pi$
$443$	153363.	0.0371289	0.0185644	+	0.999828i	$0.494090\pi$
$444$	1.78252e6	0.429117
$445$	34025.7	0.00814531
$446$	345771.	0.0823098
$447$	−519955.	−0.123083
$448$	315562.	0.0742831
$449$	6.79802e6	1.59135	0.795676	−	0.605722i	$-0.207116\pi$
$449$	6.79802e6	1.59135	0.795676	+	0.605722i	$0.207116\pi$
$450$	403124.	0.0938442
$451$	−8.20346e6	−1.89914
$452$	−3.10513e6	−0.714882
$453$	3.46102e6	0.792425
$454$	−2.48918e6	−0.566783
$455$	325501.	0.0737095
$456$	−357804.	−0.0805810
$457$	5.30770e6	1.18882	0.594409	−	0.804163i	$-0.297386\pi$
$457$	5.30770e6	1.18882	0.594409	+	0.804163i	$0.297386\pi$
$458$	−2.32930e6	−0.518873
$459$	6.83187e6	1.51359
$460$	684546.	0.150837
$461$	−2.92325e6	−0.640640	−0.320320	−	0.947309i	$-0.603790\pi$
$461$	−2.92325e6	−0.640640	−0.320320	+	0.947309i	$0.603790\pi$
$462$	1.29075e6	0.281345
$463$	5.67529e6	1.23037	0.615185	−	0.788383i	$-0.289081\pi$
$463$	5.67529e6	1.23037	0.615185	+	0.788383i	$0.289081\pi$
$464$	−1.50080e6	−0.323614
$465$	−123267.	−0.0264370
$466$	−3.46268e6	−0.738664
$467$	−1.97672e6	−0.419425	−0.209712	−	0.977763i	$-0.567253\pi$
$467$	−1.97672e6	−0.419425	−0.209712	+	0.977763i	$0.567253\pi$
$468$	436019.	0.0920218
$469$	4.59528e6	0.964672
$470$	−1.59681e6	−0.333433
$471$	1.58571e6	0.329360
$472$	1.42176e6	0.293745
$473$	5.84722e6	1.20170
$474$	−1.77434e6	−0.362736
$475$	−386456.	−0.0785897
$476$	2.30404e6	0.466093
$477$	4.50375e6	0.906313
$478$	3.01913e6	0.604383
$479$	7.52380e6	1.49830	0.749149	−	0.662401i	$-0.230463\pi$
$479$	7.52380e6	1.49830	0.749149	+	0.662401i	$0.230463\pi$
$480$	−231465.	−0.0458545
$481$	2.08236e6	0.410386
$482$	845661.	0.165798
$483$	1.19210e6	0.232512
$484$	856761.	0.166244
$485$	−1.45077e6	−0.280055
$486$	3.77464e6	0.724911
$487$	−4.51302e6	−0.862274	−0.431137	−	0.902287i	$-0.641887\pi$
$487$	−4.51302e6	−0.862274	−0.431137	+	0.902287i	$0.641887\pi$
$488$	−354715.	−0.0674265
$489$	5.70861e6	1.07959
$490$	−1.08716e6	−0.204552
$491$	1.48957e6	0.278841	0.139421	−	0.990233i	$-0.455476\pi$
$491$	1.48957e6	0.278841	0.139421	+	0.990233i	$0.455476\pi$
$492$	2.56182e6	0.477129
$493$	−1.09579e7	−2.03053
$494$	−417991.	−0.0770636
$495$	1.86746e6	0.342562
$496$	−139605.	−0.0254798
$497$	−5.17916e6	−0.940520
$498$	453620.	0.0819632
$499$	−3.27484e6	−0.588761	−0.294380	−	0.955688i	$-0.595113\pi$
$499$	−3.27484e6	−0.588761	−0.294380	+	0.955688i	$0.595113\pi$
$500$	−250000.	−0.0447214
$501$	2.36131e6	0.420299
$502$	−6.42810e6	−1.13848
$503$	−3.30838e6	−0.583037	−0.291518	−	0.956565i	$-0.594160\pi$
$503$	−3.30838e6	−0.583037	−0.291518	+	0.956565i	$0.594160\pi$
$504$	795067.	0.139421
$505$	−2.97606e6	−0.519294
$506$	3.17114e6	0.550604
$507$	−258237.	−0.0446168
$508$	1.80850e6	0.310927
$509$	6.58728e6	1.12697	0.563484	−	0.826127i	$-0.309461\pi$
$509$	6.58728e6	1.12697	0.563484	+	0.826127i	$0.309461\pi$
$510$	−1.69001e6	−0.287716
$511$	5.19132e6	0.879479
$512$	−262144.	−0.0441942
$513$	−2.26003e6	−0.379159
$514$	5.16967e6	0.863087
$515$	3.01695e6	0.501245
$516$	−1.82600e6	−0.301909
$517$	−7.39719e6	−1.21714
$518$	3.79711e6	0.621769
$519$	3.01306e6	0.491009
$520$	−270400.	−0.0438529
$521$	−2.79881e6	−0.451731	−0.225865	−	0.974159i	$-0.572521\pi$
$521$	−2.79881e6	−0.451731	−0.225865	+	0.974159i	$0.572521\pi$
$522$	−3.78129e6	−0.607385
$523$	1.07586e6	0.171990	0.0859950	−	0.996296i	$-0.472593\pi$
$523$	1.07586e6	0.171990	0.0859950	+	0.996296i	$0.472593\pi$
$524$	−5.74059e6	−0.913331
$525$	−435362.	−0.0689369
$526$	−3.15040e6	−0.496480
$527$	−1.01931e6	−0.159874
$528$	−1.07226e6	−0.167384
$529$	−3.50758e6	−0.544964
$530$	−2.79303e6	−0.431903
$531$	3.58215e6	0.551324
$532$	−762193.	−0.116758
$533$	2.99275e6	0.456302
$534$	−49223.5	−0.00746998
$535$	728865.	0.110094
$536$	−3.81739e6	−0.573924
$537$	5.48885e6	0.821383
$538$	4.52639e6	0.674212
$539$	−5.03624e6	−0.746680
$540$	−1.46202e6	−0.215760
$541$	7.54330e6	1.10807	0.554037	−	0.832492i	$-0.313087\pi$
$541$	7.54330e6	1.10807	0.554037	+	0.832492i	$0.313087\pi$
$542$	−6.02362e6	−0.880763
$543$	−1.31598e6	−0.191535
$544$	−1.91401e6	−0.277299
$545$	−892772.	−0.128751
$546$	−470887.	−0.0675982
$547$	8.04405e6	1.14949	0.574747	−	0.818331i	$-0.305101\pi$
$547$	8.04405e6	1.14949	0.574747	+	0.818331i	$0.305101\pi$
$548$	6.23810e6	0.887363
$549$	−893714.	−0.126552
$550$	−1.15812e6	−0.163248
$551$	3.62495e6	0.508654
$552$	−990301.	−0.138331
$553$	−3.77970e6	−0.525586
$554$	−3.15793e6	−0.437148
$555$	−2.78518e6	−0.383814
$556$	−2.28950e6	−0.314090
$557$	−1.90075e6	−0.259590	−0.129795	−	0.991541i	$-0.541432\pi$
$557$	−1.90075e6	−0.259590	−0.129795	+	0.991541i	$0.541432\pi$
$558$	−351738.	−0.0478226
$559$	−2.13316e6	−0.288731
$560$	−493066.	−0.0664408
$561$	−7.82895e6	−1.05026
$562$	3.26191e6	0.435644
$563$	6.26708e6	0.833286	0.416643	−	0.909070i	$-0.363207\pi$
$563$	6.26708e6	0.833286	0.416643	+	0.909070i	$0.363207\pi$
$564$	2.31003e6	0.305788
$565$	4.85177e6	0.639410
$566$	1.30690e6	0.171475
$567$	472732.	0.0617530
$568$	4.30243e6	0.559555
$569$	6.91884e6	0.895885	0.447943	−	0.894062i	$-0.352157\pi$
$569$	6.91884e6	0.895885	0.447943	+	0.894062i	$0.352157\pi$
$570$	559068.	0.0720738
$571$	−5.72155e6	−0.734385	−0.367192	−	0.930145i	$-0.619681\pi$
$571$	−5.72155e6	−0.734385	−0.367192	+	0.930145i	$0.619681\pi$
$572$	−1.25262e6	−0.160077
$573$	−151941.	−0.0193325
$574$	5.45719e6	0.691336
$575$	−1.06960e6	−0.134913
$576$	−660478.	−0.0829473
$577$	−1.23874e7	−1.54896	−0.774481	−	0.632597i	$-0.781989\pi$
$577$	−1.23874e7	−1.54896	−0.774481	+	0.632597i	$0.781989\pi$
$578$	−8.29552e6	−1.03282
$579$	−4.68189e6	−0.580397
$580$	2.34499e6	0.289449
$581$	966301.	0.118761
$582$	2.09876e6	0.256836
$583$	−1.29387e7	−1.57659
$584$	−4.31253e6	−0.523239
$585$	−681279.	−0.0823068
$586$	−5.29893e6	−0.637447
$587$	3.70271e6	0.443531	0.221766	−	0.975100i	$-0.428818\pi$
$587$	3.70271e6	0.443531	0.221766	+	0.975100i	$0.428818\pi$
$588$	1.57274e6	0.187592
$589$	337194.	0.0400490
$590$	−2.22149e6	−0.262733
$591$	−2.20947e6	−0.260208
$592$	−3.15434e6	−0.369917
$593$	4.98645e6	0.582310	0.291155	−	0.956676i	$-0.405960\pi$
$593$	4.98645e6	0.582310	0.291155	+	0.956676i	$0.405960\pi$
$594$	−6.77280e6	−0.787593
$595$	−3.60007e6	−0.416887
$596$	920111.	0.106102
$597$	−2.15351e6	−0.247293
$598$	−1.15688e6	−0.132293
$599$	−3.30712e6	−0.376602	−0.188301	−	0.982111i	$-0.560298\pi$
$599$	−3.30712e6	−0.376602	−0.188301	+	0.982111i	$0.560298\pi$
$600$	361664.	0.0410135
$601$	5.21917e6	0.589407	0.294703	−	0.955589i	$-0.404779\pi$
$601$	5.21917e6	0.589407	0.294703	+	0.955589i	$0.404779\pi$
$602$	−3.88974e6	−0.437451
$603$	−9.61801e6	−1.07719
$604$	−6.12462e6	−0.683103
$605$	−1.33869e6	−0.148693
$606$	4.30533e6	0.476239
$607$	4.57734e6	0.504245	0.252123	−	0.967695i	$-0.418871\pi$
$607$	4.57734e6	0.504245	0.252123	+	0.967695i	$0.418871\pi$
$608$	633169.	0.0694642
$609$	4.08368e6	0.446179
$610$	554243.	0.0603081
$611$	2.69861e6	0.292440
$612$	−4.82241e6	−0.520457
$613$	5.04824e6	0.542611	0.271306	−	0.962493i	$-0.412545\pi$
$613$	5.04824e6	0.542611	0.271306	+	0.962493i	$0.412545\pi$
$614$	−2.20166e6	−0.235684
$615$	−4.00285e6	−0.426757
$616$	−2.28412e6	−0.242531
$617$	−1.31376e7	−1.38932	−0.694662	−	0.719336i	$-0.744446\pi$
$617$	−1.31376e7	−1.38932	−0.694662	+	0.719336i	$0.744446\pi$
$618$	−4.36448e6	−0.459686
$619$	1.12291e7	1.17793	0.588964	−	0.808159i	$-0.299536\pi$
$619$	1.12291e7	1.17793	0.588964	+	0.808159i	$0.299536\pi$
$620$	218132.	0.0227898
$621$	−6.25514e6	−0.650891
$622$	1.34312e7	1.39200
$623$	−104856.	−0.0108236
$624$	391176.	0.0402171
$625$	390625.	0.0400000
$626$	1.04659e7	1.06743
$627$	2.58987e6	0.263093
$628$	−2.80607e6	−0.283922
$629$	−2.30310e7	−2.32106
$630$	−1.24229e6	−0.124702
$631$	5.42646e6	0.542554	0.271277	−	0.962501i	$-0.412554\pi$
$631$	5.42646e6	0.542554	0.271277	+	0.962501i	$0.412554\pi$
$632$	3.13987e6	0.312694
$633$	−7.71444e6	−0.765236
$634$	−5.33657e6	−0.527277
$635$	−2.82578e6	−0.278102
$636$	4.04055e6	0.396094
$637$	1.83730e6	0.179404
$638$	1.08631e7	1.05658
$639$	1.08401e7	1.05022
$640$	409600.	0.0395285
$641$	1.64890e7	1.58507	0.792536	−	0.609826i	$-0.208761\pi$
$641$	1.64890e7	1.58507	0.792536	+	0.609826i	$0.208761\pi$
$642$	−1.05442e6	−0.100966
$643$	3.20604e6	0.305803	0.152901	−	0.988241i	$-0.451138\pi$
$643$	3.20604e6	0.305803	0.152901	+	0.988241i	$0.451138\pi$
$644$	−2.10954e6	−0.200435
$645$	2.85313e6	0.270036
$646$	4.62301e6	0.435857
$647$	−1.26054e7	−1.18385	−0.591923	−	0.805994i	$-0.701631\pi$
$647$	−1.26054e7	−1.18385	−0.591923	+	0.805994i	$0.701631\pi$
$648$	−392708.	−0.0367394
$649$	−1.02910e7	−0.959062
$650$	422500.	0.0392232
$651$	379866.	0.0351300
$652$	−1.01020e7	−0.930650
$653$	1.20010e7	1.10137	0.550685	−	0.834713i	$-0.314366\pi$
$653$	1.20010e7	1.10137	0.550685	+	0.834713i	$0.314366\pi$
$654$	1.29153e6	0.118076
$655$	8.96967e6	0.816909
$656$	−4.53340e6	−0.411305
$657$	−1.08655e7	−0.982059
$658$	4.92083e6	0.443071
$659$	−5.28381e6	−0.473951	−0.236976	−	0.971516i	$-0.576156\pi$
$659$	−5.28381e6	−0.473951	−0.236976	+	0.971516i	$0.576156\pi$
$660$	1.67540e6	0.149713
$661$	866979.	0.0771801	0.0385900	−	0.999255i	$-0.487713\pi$
$661$	866979.	0.0771801	0.0385900	+	0.999255i	$0.487713\pi$
$662$	2.86414e6	0.254009
$663$	2.85612e6	0.252344
$664$	−802726.	−0.0706557
$665$	1.19093e6	0.104431
$666$	−7.94743e6	−0.694291
$667$	1.00328e7	0.873192
$668$	−4.17857e6	−0.362315
$669$	781581.	0.0675163
$670$	5.96467e6	0.513334
$671$	2.56752e6	0.220144
$672$	713297.	0.0609322
$673$	−1.14870e7	−0.977620	−0.488810	−	0.872390i	$-0.662569\pi$
$673$	−1.14870e7	−0.977620	−0.488810	+	0.872390i	$0.662569\pi$
$674$	1.54949e7	1.31383
$675$	2.28441e6	0.192981
$676$	456976.	0.0384615
$677$	−4.22852e6	−0.354582	−0.177291	−	0.984158i	$-0.556733\pi$
$677$	−4.22852e6	−0.354582	−0.177291	+	0.984158i	$0.556733\pi$
$678$	−7.01884e6	−0.586396
$679$	4.47078e6	0.372142
$680$	2.99065e6	0.248024
$681$	−5.62654e6	−0.464915
$682$	1.01049e6	0.0831903
$683$	7.70437e6	0.631954	0.315977	−	0.948767i	$-0.397668\pi$
$683$	7.70437e6	0.631954	0.315977	+	0.948767i	$0.397668\pi$
$684$	1.59529e6	0.130376
$685$	−9.74704e6	−0.793681
$686$	8.52961e6	0.692021
$687$	−5.26514e6	−0.425616
$688$	3.23129e6	0.260258
$689$	4.72022e6	0.378804
$690$	1.54735e6	0.123727
$691$	−1.44971e6	−0.115501	−0.0577504	−	0.998331i	$-0.518393\pi$
$691$	−1.44971e6	−0.115501	−0.0577504	+	0.998331i	$0.518393\pi$
$692$	−5.33191e6	−0.423270
$693$	−5.75489e6	−0.455202
$694$	−167705.	−0.0132174
$695$	3.57734e6	0.280930
$696$	−3.39240e6	−0.265451
$697$	−3.31001e7	−2.58076
$698$	−8.32545e6	−0.646798
$699$	−7.82703e6	−0.605904
$700$	770416.	0.0594265
$701$	−3.04812e6	−0.234281	−0.117140	−	0.993115i	$-0.537373\pi$
$701$	−3.04812e6	−0.234281	−0.117140	+	0.993115i	$0.537373\pi$
$702$	2.47082e6	0.189234
$703$	7.61883e6	0.581433
$704$	1.89746e6	0.144292
$705$	−3.60943e6	−0.273505
$706$	1.67899e7	1.26776
$707$	9.17121e6	0.690046
$708$	3.21373e6	0.240950
$709$	−7.81300e6	−0.583717	−0.291858	−	0.956462i	$-0.594274\pi$
$709$	−7.81300e6	−0.583717	−0.291858	+	0.956462i	$0.594274\pi$
$710$	−6.72255e6	−0.500481
$711$	7.91098e6	0.586889
$712$	87105.9	0.00643943
$713$	933260.	0.0687510
$714$	5.20805e6	0.382323
$715$	1.95722e6	0.143178
$716$	−9.71307e6	−0.708066
$717$	6.82443e6	0.495757
$718$	−6.34104e6	−0.459039
$719$	−1.82691e7	−1.31794	−0.658969	−	0.752170i	$-0.729007\pi$
$719$	−1.82691e7	−1.31794	−0.658969	+	0.752170i	$0.729007\pi$
$720$	1.03200e6	0.0741903
$721$	−9.29722e6	−0.666062
$722$	8.37507e6	0.597923
$723$	1.91153e6	0.135999
$724$	2.32875e6	0.165111
$725$	−3.66405e6	−0.258891
$726$	1.93662e6	0.136365
$727$	2.73815e6	0.192142	0.0960708	−	0.995374i	$-0.469372\pi$
$727$	2.73815e6	0.192142	0.0960708	+	0.995374i	$0.469372\pi$
$728$	833282.	0.0582725
$729$	7.04112e6	0.490708
$730$	6.73833e6	0.468000
$731$	2.35929e7	1.63301
$732$	−801798.	−0.0553079
$733$	−1.19371e6	−0.0820614	−0.0410307	−	0.999158i	$-0.513064\pi$
$733$	−1.19371e6	−0.0820614	−0.0410307	+	0.999158i	$0.513064\pi$
$734$	2.77381e6	0.190037
$735$	−2.45741e6	−0.167788
$736$	1.75244e6	0.119247
$737$	2.76312e7	1.87384
$738$	−1.14220e7	−0.771972
$739$	−6.31824e6	−0.425584	−0.212792	−	0.977098i	$-0.568256\pi$
$739$	−6.31824e6	−0.425584	−0.212792	+	0.977098i	$0.568256\pi$
$740$	4.92865e6	0.330864
$741$	−944825.	−0.0632129
$742$	8.60718e6	0.573920
$743$	−268541.	−0.0178459	−0.00892296	−	0.999960i	$-0.502840\pi$
$743$	−268541.	−0.0178459	−0.00892296	+	0.999960i	$0.502840\pi$
$744$	−315562.	−0.0209003
$745$	−1.43767e6	−0.0949008
$746$	−1.49678e7	−0.984717
$747$	−2.02249e6	−0.132612
$748$	1.38541e7	0.905367
$749$	−2.24612e6	−0.146294
$750$	−565100.	−0.0366836
$751$	−604825.	−0.0391318	−0.0195659	−	0.999809i	$-0.506228\pi$
$751$	−604825.	−0.0391318	−0.0195659	+	0.999809i	$0.506228\pi$
$752$	−4.08783e6	−0.263602
$753$	−1.45301e7	−0.933857
$754$	−3.96304e6	−0.253863
$755$	9.56971e6	0.610986
$756$	4.50547e6	0.286705
$757$	2.65907e7	1.68651	0.843256	−	0.537512i	$-0.180636\pi$
$757$	2.65907e7	1.68651	0.843256	+	0.537512i	$0.180636\pi$
$758$	−130382.	−0.00824221
$759$	7.16805e6	0.451644
$760$	−989327.	−0.0621306
$761$	−2.32242e7	−1.45371	−0.726856	−	0.686789i	$-0.759019\pi$
$761$	−2.32242e7	−1.45371	−0.726856	+	0.686789i	$0.759019\pi$
$762$	4.08793e6	0.255044
$763$	2.75122e6	0.171086
$764$	268874.	0.0166654
$765$	7.53501e6	0.465511
$766$	1.99730e7	1.22991
$767$	3.75432e6	0.230432
$768$	−592550.	−0.0362512
$769$	1.05706e7	0.644590	0.322295	−	0.946639i	$-0.395546\pi$
$769$	1.05706e7	0.644590	0.322295	+	0.946639i	$0.395546\pi$
$770$	3.56894e6	0.216926
$771$	1.16855e7	0.707965
$772$	8.28508e6	0.500326
$773$	1.87286e6	0.112734	0.0563671	−	0.998410i	$-0.482048\pi$
$773$	1.87286e6	0.112734	0.0563671	+	0.998410i	$0.482048\pi$
$774$	8.14131e6	0.488475
$775$	−340832.	−0.0203838
$776$	−3.71396e6	−0.221403
$777$	8.58299e6	0.510019
$778$	1.27912e7	0.757640
$779$	1.09497e7	0.646487
$780$	−611212.	−0.0359712
$781$	−3.11421e7	−1.82692
$782$	1.27952e7	0.748222
$783$	−2.14277e7	−1.24903
$784$	−2.78313e6	−0.161712
$785$	4.38448e6	0.253948
$786$	−1.29760e7	−0.749179
$787$	−1.36103e6	−0.0783303	−0.0391651	−	0.999233i	$-0.512470\pi$
$787$	−1.36103e6	−0.0783303	−0.0391651	+	0.999233i	$0.512470\pi$
$788$	3.90988e6	0.224310
$789$	−7.12116e6	−0.407247
$790$	−4.90605e6	−0.279682
$791$	−1.49515e7	−0.849658
$792$	4.78070e6	0.270819
$793$	−936670.	−0.0528937
$794$	4.51912e6	0.254391
$795$	−6.31336e6	−0.354277
$796$	3.81086e6	0.213177
$797$	1.70704e7	0.951917	0.475958	−	0.879468i	$-0.342101\pi$
$797$	1.70704e7	0.951917	0.475958	+	0.879468i	$0.342101\pi$
$798$	−1.72286e6	−0.0957730
$799$	−2.98468e7	−1.65398
$800$	−640000.	−0.0353553
$801$	219465.	0.0120861
$802$	2.24036e6	0.122993
$803$	3.12152e7	1.70835
$804$	−8.62883e6	−0.470773
$805$	3.29616e6	0.179274
$806$	−368644.	−0.0199880
$807$	1.02315e7	0.553036
$808$	−7.61871e6	−0.410538
$809$	−2.60220e7	−1.39788	−0.698938	−	0.715182i	$-0.746344\pi$
$809$	−2.60220e7	−1.39788	−0.698938	+	0.715182i	$0.746344\pi$
$810$	613607.	0.0328608
$811$	−2.10104e7	−1.12171	−0.560857	−	0.827913i	$-0.689528\pi$
$811$	−2.10104e7	−1.12171	−0.560857	+	0.827913i	$0.689528\pi$
$812$	−7.22648e6	−0.384624
$813$	−1.36158e7	−0.722464
$814$	2.28319e7	1.20776
$815$	1.57843e7	0.832399
$816$	−4.32643e6	−0.227460
$817$	−7.80469e6	−0.409073
$818$	−1.98150e7	−1.03541
$819$	2.09947e6	0.109371
$820$	7.08343e6	0.367883
$821$	8.52765e6	0.441542	0.220771	−	0.975326i	$-0.429143\pi$
$821$	8.52765e6	0.441542	0.220771	+	0.975326i	$0.429143\pi$
$822$	1.41006e7	0.727877
$823$	1.68012e7	0.864650	0.432325	−	0.901718i	$-0.357693\pi$
$823$	1.68012e7	0.864650	0.432325	+	0.901718i	$0.357693\pi$
$824$	7.72339e6	0.396269
$825$	−2.61781e6	−0.133907
$826$	6.84590e6	0.349124
$827$	2.18393e7	1.11039	0.555195	−	0.831720i	$-0.312644\pi$
$827$	2.18393e7	1.11039	0.555195	+	0.831720i	$0.312644\pi$
$828$	4.41531e6	0.223813
$829$	1.58155e7	0.799277	0.399639	−	0.916673i	$-0.369136\pi$
$829$	1.58155e7	0.799277	0.399639	+	0.916673i	$0.369136\pi$
$830$	1.25426e6	0.0631964
$831$	−7.13819e6	−0.358579
$832$	−692224.	−0.0346688
$833$	−2.03207e7	−1.01467
$834$	−5.17518e6	−0.257638
$835$	6.52902e6	0.324065
$836$	−4.58304e6	−0.226797
$837$	−1.99322e6	−0.0983425
$838$	−1.50441e7	−0.740041
$839$	−2.88093e7	−1.41295	−0.706477	−	0.707736i	$-0.749717\pi$
$839$	−2.88093e7	−1.41295	−0.706477	+	0.707736i	$0.749717\pi$
$840$	−1.11453e6	−0.0544994
$841$	1.38576e7	0.675612
$842$	−5.90886e6	−0.287226
$843$	7.37322e6	0.357346
$844$	1.36515e7	0.659665
$845$	−714025.	−0.0344010
$846$	−1.02994e7	−0.494750
$847$	4.12539e6	0.197586
$848$	−7.15016e6	−0.341449
$849$	2.95411e6	0.140656
$850$	−4.67289e6	−0.221839
$851$	2.10868e7	0.998129
$852$	9.72521e6	0.458987
$853$	1.92928e7	0.907867	0.453933	−	0.891036i	$-0.350020\pi$
$853$	1.92928e7	0.907867	0.453933	+	0.891036i	$0.350020\pi$
$854$	−1.70799e6	−0.0801384
$855$	−2.49263e6	−0.116612
$856$	1.86589e6	0.0870367
$857$	3.80802e7	1.77112	0.885559	−	0.464528i	$-0.153776\pi$
$857$	3.80802e7	1.77112	0.885559	+	0.464528i	$0.153776\pi$
$858$	−2.83143e6	−0.131307
$859$	−2.73638e6	−0.126530	−0.0632651	−	0.997997i	$-0.520151\pi$
$859$	−2.73638e6	−0.126530	−0.0632651	+	0.997997i	$0.520151\pi$
$860$	−5.04889e6	−0.232782
$861$	1.23354e7	0.567082
$862$	−2.80237e7	−1.28457
$863$	1.00854e7	0.460962	0.230481	−	0.973077i	$-0.425970\pi$
$863$	1.00854e7	0.460962	0.230481	+	0.973077i	$0.425970\pi$
$864$	−3.74278e6	−0.170573
$865$	8.33112e6	0.378585
$866$	3.08790e6	0.139917
$867$	−1.87512e7	−0.847190
$868$	−672211.	−0.0302835
$869$	−2.27272e7	−1.02093
$870$	5.30062e6	0.237426
$871$	−1.00803e7	−0.450223
$872$	−2.28550e6	−0.101786
$873$	−9.35742e6	−0.415548
$874$	−4.23275e6	−0.187432
$875$	−1.20377e6	−0.0531527
$876$	−9.74805e6	−0.429198
$877$	1.31876e7	0.578984	0.289492	−	0.957180i	$-0.406514\pi$
$877$	1.31876e7	0.578984	0.289492	+	0.957180i	$0.406514\pi$
$878$	1.51671e7	0.663996
$879$	−1.19777e7	−0.522879
$880$	−2.96479e6	−0.129059
$881$	−1.21216e7	−0.526163	−0.263082	−	0.964774i	$-0.584739\pi$
$881$	−1.21216e7	−0.526163	−0.263082	+	0.964774i	$0.584739\pi$
$882$	−7.01216e6	−0.303515
$883$	−1.70890e7	−0.737591	−0.368795	−	0.929511i	$-0.620230\pi$
$883$	−1.70890e7	−0.737591	−0.368795	+	0.929511i	$0.620230\pi$
$884$	−5.05419e6	−0.217531
$885$	−5.02146e6	−0.215512
$886$	−613452.	−0.0262541
$887$	3.63465e6	0.155115	0.0775574	−	0.996988i	$-0.475288\pi$
$887$	3.63465e6	0.155115	0.0775574	+	0.996988i	$0.475288\pi$
$888$	−7.13006e6	−0.303432
$889$	8.70810e6	0.369547
$890$	−136103.	−0.00575960
$891$	2.84252e6	0.119952
$892$	−1.38308e6	−0.0582018
$893$	9.87354e6	0.414328
$894$	2.07982e6	0.0870325
$895$	1.51767e7	0.633314
$896$	−1.26225e6	−0.0525261
$897$	−2.61501e6	−0.108516
$898$	−2.71921e7	−1.12526
$899$	3.19700e6	0.131930
$900$	−1.61250e6	−0.0663578
$901$	−5.22060e7	−2.14244
$902$	3.28138e7	1.34289
$903$	−8.79237e6	−0.358828
$904$	1.24205e7	0.505498
$905$	−3.63867e6	−0.147680
$906$	−1.38441e7	−0.560329
$907$	−2.76573e6	−0.111633	−0.0558163	−	0.998441i	$-0.517776\pi$
$907$	−2.76573e6	−0.111633	−0.0558163	+	0.998441i	$0.517776\pi$
$908$	9.95672e6	0.400776
$909$	−1.91955e7	−0.770532
$910$	−1.30200e6	−0.0521205
$911$	3.42270e7	1.36639	0.683193	−	0.730238i	$-0.260591\pi$
$911$	3.42270e7	1.36639	0.683193	+	0.730238i	$0.260591\pi$
$912$	1.43121e6	0.0569794
$913$	5.81033e6	0.230687
$914$	−2.12308e7	−0.840622
$915$	1.25281e6	0.0494689
$916$	9.31719e6	0.366899
$917$	−2.76415e7	−1.08552
$918$	−2.73275e7	−1.07027
$919$	−1.47495e7	−0.576086	−0.288043	−	0.957618i	$-0.593005\pi$
$919$	−1.47495e7	−0.576086	−0.288043	+	0.957618i	$0.593005\pi$
$920$	−2.73818e6	−0.106658
$921$	−4.97664e6	−0.193324
$922$	1.16930e7	0.453001
$923$	1.13611e7	0.438951
$924$	−5.16302e6	−0.198941
$925$	−7.70102e6	−0.295933
$926$	−2.27012e7	−0.870003
$927$	1.94593e7	0.743750
$928$	6.00318e6	0.228829
$929$	2.35885e7	0.896729	0.448365	−	0.893851i	$-0.352007\pi$
$929$	2.35885e7	0.896729	0.448365	+	0.893851i	$0.352007\pi$
$930$	493066.	0.0186938
$931$	6.72222e6	0.254178
$932$	1.38507e7	0.522315
$933$	3.03598e7	1.14181
$934$	7.90690e6	0.296578
$935$	−2.16470e7	−0.809785
$936$	−1.74408e6	−0.0650692
$937$	5.87866e6	0.218741	0.109370	−	0.994001i	$-0.465117\pi$
$937$	5.87866e6	0.218741	0.109370	+	0.994001i	$0.465117\pi$
$938$	−1.83811e7	−0.682126
$939$	2.36570e7	0.875581
$940$	6.38724e6	0.235773
$941$	1.78458e7	0.656996	0.328498	−	0.944505i	$-0.393458\pi$
$941$	1.78458e7	0.656996	0.328498	+	0.944505i	$0.393458\pi$
$942$	−6.34284e6	−0.232893
$943$	3.03058e7	1.10981
$944$	−5.68702e6	−0.207709
$945$	−7.03979e6	−0.256437
$946$	−2.33889e7	−0.849731
$947$	−8.73411e6	−0.316478	−0.158239	−	0.987401i	$-0.550582\pi$
$947$	−8.73411e6	−0.316478	−0.158239	+	0.987401i	$0.550582\pi$
$948$	7.09736e6	0.256493
$949$	−1.13878e7	−0.410463
$950$	1.54582e6	0.0555713
$951$	−1.20628e7	−0.432510
$952$	−9.21617e6	−0.329578
$953$	−2.03640e6	−0.0726323	−0.0363162	−	0.999340i	$-0.511562\pi$
$953$	−2.03640e6	−0.0726323	−0.0363162	+	0.999340i	$0.511562\pi$
$954$	−1.80150e7	−0.640860
$955$	−420115.	−0.0149060
$956$	−1.20765e7	−0.427363
$957$	2.45550e7	0.866683
$958$	−3.00952e7	−1.05946
$959$	3.00371e7	1.05466
$960$	925859.	0.0324240
$961$	−2.83318e7	−0.989612
$962$	−8.32942e6	−0.290187
$963$	4.70117e6	0.163358
$964$	−3.38264e6	−0.117237
$965$	−1.29454e7	−0.447505
$966$	−4.76840e6	−0.164411
$967$	−2.25922e7	−0.776948	−0.388474	−	0.921460i	$-0.626998\pi$
$967$	−2.25922e7	−0.776948	−0.388474	+	0.921460i	$0.626998\pi$
$968$	−3.42704e6	−0.117552
$969$	1.04498e7	0.357520
$970$	5.80307e6	0.198029
$971$	4.94414e7	1.68284	0.841420	−	0.540382i	$-0.181720\pi$
$971$	4.94414e7	1.68284	0.841420	+	0.540382i	$0.181720\pi$
$972$	−1.50986e7	−0.512589
$973$	−1.10242e7	−0.373305
$974$	1.80521e7	0.609720
$975$	955018.	0.0321736
$976$	1.41886e6	0.0476777
$977$	3.59351e7	1.20443	0.602217	−	0.798333i	$-0.294284\pi$
$977$	3.59351e7	1.20443	0.602217	+	0.798333i	$0.294284\pi$
$978$	−2.28345e7	−0.763385
$979$	−630494.	−0.0210244
$980$	4.34864e6	0.144640
$981$	−5.75836e6	−0.191041
$982$	−5.95828e6	−0.197171
$983$	−3.51635e7	−1.16067	−0.580335	−	0.814378i	$-0.697078\pi$
$983$	−3.51635e7	−1.16067	−0.580335	+	0.814378i	$0.697078\pi$
$984$	−1.02473e7	−0.337381
$985$	−6.10919e6	−0.200629
$986$	4.38316e7	1.43580
$987$	1.11230e7	0.363438
$988$	1.67196e6	0.0544922
$989$	−2.16012e7	−0.702243
$990$	−7.46985e6	−0.242228
$991$	−3.90004e7	−1.26149	−0.630747	−	0.775989i	$-0.717251\pi$
$991$	−3.90004e7	−1.26149	−0.630747	+	0.775989i	$0.717251\pi$
$992$	558419.	0.0180169
$993$	6.47409e6	0.208356
$994$	2.07166e7	0.665048
$995$	−5.95446e6	−0.190671
$996$	−1.81448e6	−0.0579568
$997$	−868537.	−0.0276726	−0.0138363	−	0.999904i	$-0.504404\pi$
$997$	−868537.	−0.0276726	−0.0138363	+	0.999904i	$0.504404\pi$
$998$	1.30994e7	0.416317
$999$	−4.50363e7	−1.42774

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	130.6.a.c.1.1	✓	2
4.3	odd	2		1040.6.a.c.1.2		2
5.2	odd	4		650.6.b.f.599.2		4
5.3	odd	4		650.6.b.f.599.3		4
5.4	even	2		650.6.a.f.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.6.a.c.1.1	✓	2	1.1	even	1	trivial
650.6.a.f.1.2		2	5.4	even	2
650.6.b.f.599.2		4	5.2	odd	4
650.6.b.f.599.3		4	5.3	odd	4
1040.6.a.c.1.2		2	4.3	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:	\( N \)	\(=\)	\( 130 = 2 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	130.a (trivial)

\(f(q)\)	\(=\)	\(q-4.00000 q^{2} -9.04159 q^{3} +16.0000 q^{4} -25.0000 q^{5} +36.1664 q^{6} +77.0416 q^{7} -64.0000 q^{8} -161.250 q^{9} +100.000 q^{10} +463.248 q^{11} -144.666 q^{12} -169.000 q^{13} -308.166 q^{14} +226.040 q^{15} +256.000 q^{16} +1869.15 q^{17} +644.998 q^{18} -618.329 q^{19} -400.000 q^{20} -696.579 q^{21} -1852.99 q^{22} -1711.36 q^{23} +578.662 q^{24} +625.000 q^{25} +676.000 q^{26} +3655.06 q^{27} +1232.67 q^{28} -5862.49 q^{29} -904.159 q^{30} -545.331 q^{31} -1024.00 q^{32} -4188.50 q^{33} -7476.62 q^{34} -1926.04 q^{35} -2579.99 q^{36} -12321.6 q^{37} +2473.32 q^{38} +1528.03 q^{39} +1600.00 q^{40} -17708.6 q^{41} +2786.32 q^{42} +12622.2 q^{43} +7411.97 q^{44} +4031.24 q^{45} +6845.46 q^{46} -15968.1 q^{47} -2314.65 q^{48} -10871.6 q^{49} -2500.00 q^{50} -16900.1 q^{51} -2704.00 q^{52} -27930.3 q^{53} -14620.2 q^{54} -11581.2 q^{55} -4930.66 q^{56} +5590.68 q^{57} +23449.9 q^{58} -22214.9 q^{59} +3616.64 q^{60} +5542.43 q^{61} +2181.32 q^{62} -12422.9 q^{63} +4096.00 q^{64} +4225.00 q^{65} +16754.0 q^{66} +59646.7 q^{67} +29906.5 q^{68} +15473.5 q^{69} +7704.16 q^{70} -67225.5 q^{71} +10320.0 q^{72} +67383.3 q^{73} +49286.5 q^{74} -5651.00 q^{75} -9893.27 q^{76} +35689.4 q^{77} -6112.12 q^{78} -49060.5 q^{79} -6400.00 q^{80} +6136.07 q^{81} +70834.3 q^{82} +12542.6 q^{83} -11145.3 q^{84} -46728.9 q^{85} -50488.9 q^{86} +53006.2 q^{87} -29647.9 q^{88} -1361.03 q^{89} -16125.0 q^{90} -13020.0 q^{91} -27381.8 q^{92} +4930.66 q^{93} +63872.4 q^{94} +15458.2 q^{95} +9258.59 q^{96} +58030.7 q^{97} +43486.4 q^{98} -74698.5 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 8 q^{2} + 6 q^{3} + 32 q^{4} - 50 q^{5} - 24 q^{6} + 130 q^{7} - 128 q^{8} - 178 q^{9} + 200 q^{10} + 204 q^{11} + 96 q^{12} - 338 q^{13} - 520 q^{14} - 150 q^{15} + 512 q^{16} - 404 q^{17} + 712 q^{18}+ \cdots - 70356 q^{99}+O(q^{100}) \) 2 * q - 8 * q^2 + 6 * q^3 + 32 * q^4 - 50 * q^5 - 24 * q^6 + 130 * q^7 - 128 * q^8 - 178 * q^9 + 200 * q^10 + 204 * q^11 + 96 * q^12 - 338 * q^13 - 520 * q^14 - 150 * q^15 + 512 * q^16 - 404 * q^17 + 712 * q^18 + 112 * q^19 - 800 * q^20 + 100 * q^21 - 816 * q^22 + 262 * q^23 - 384 * q^24 + 1250 * q^25 + 1352 * q^26 - 252 * q^27 + 2080 * q^28 - 6812 * q^29 + 600 * q^30 - 320 * q^31 - 2048 * q^32 - 8088 * q^33 + 1616 * q^34 - 3250 * q^35 - 2848 * q^36 - 13276 * q^37 - 448 * q^38 - 1014 * q^39 + 3200 * q^40 - 35080 * q^41 - 400 * q^42 + 2534 * q^43 + 3264 * q^44 + 4450 * q^45 - 1048 * q^46 - 22038 * q^47 + 1536 * q^48 - 24874 * q^49 - 5000 * q^50 - 51092 * q^51 - 5408 * q^52 - 44108 * q^53 + 1008 * q^54 - 5100 * q^55 - 8320 * q^56 + 16576 * q^57 + 27248 * q^58 - 21888 * q^59 - 2400 * q^60 - 41272 * q^61 + 1280 * q^62 - 13310 * q^63 + 8192 * q^64 + 8450 * q^65 + 32352 * q^66 + 103230 * q^67 - 6464 * q^68 + 45156 * q^69 + 13000 * q^70 - 15480 * q^71 + 11392 * q^72 + 54088 * q^73 + 53104 * q^74 + 3750 * q^75 + 1792 * q^76 + 21960 * q^77 + 4056 * q^78 + 27208 * q^79 - 12800 * q^80 - 48562 * q^81 + 140320 * q^82 + 42690 * q^83 + 1600 * q^84 + 10100 * q^85 - 10136 * q^86 + 38724 * q^87 - 13056 * q^88 - 68132 * q^89 - 17800 * q^90 - 21970 * q^91 + 4192 * q^92 + 8320 * q^93 + 88152 * q^94 - 2800 * q^95 - 6144 * q^96 + 209456 * q^97 + 99496 * q^98 - 70356 * q^99

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