LMFDB - Embedded newform 650.6.a.f.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [650,6,Mod(1,650)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(650, 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("650.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 650 = 2 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	650.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:	$104.249482878$
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:	no (minimal twist has level 130)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-5.52080$ of defining polynomial
Character	$\chi$	$=$	650.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	4.00000	0.707107
$2$	4.00000	0.707107
$3$	9.04159	0.580019	0.290009	−	0.957024i	$-0.406342\pi$
$3$	9.04159	0.580019	0.290009	+	0.957024i	$0.406342\pi$
$4$	16.0000	0.500000
$5$	0	0
$5$	0	0
$6$	36.1664	0.410135
$7$	−77.0416	−0.594265	−0.297133	−	0.954836i	$-0.596030\pi$
$7$	−77.0416	−0.594265	−0.297133	+	0.954836i	$0.596030\pi$
$8$	64.0000	0.353553
$9$	−161.250	−0.663578
$10$	0	0
$11$	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
$15$	0	0
$16$	256.000	0.250000
$17$	−1869.15	−1.56864	−0.784319	−	0.620357i	$-0.786988\pi$
$17$	−1869.15	−1.56864	−0.784319	+	0.620357i	$0.786988\pi$
$18$	−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	$0.562949\pi$
$20$	0	0
$21$	−696.579	−0.344685
$22$	1852.99	0.816238
$23$	1711.36	0.674563	0.337282	−	0.941404i	$-0.390493\pi$
$23$	1711.36	0.674563	0.337282	+	0.941404i	$0.390493\pi$
$24$	578.662	0.205068
$25$	0	0
$26$	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	$0.724072\pi$
$30$	0	0
$31$	−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
$35$	0	0
$36$	−2579.99	−0.331789
$37$	12321.6	1.47967	0.739833	−	0.672790i	$-0.234904\pi$
$37$	12321.6	1.47967	0.739833	+	0.672790i	$0.234904\pi$
$38$	−2473.32	−0.277857
$39$	1528.03	0.160868
$40$	0	0
$41$	−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	$-0.674261\pi$
$43$	−12622.2	−1.04103	−0.520517	+	0.853851i	$0.674261\pi$
$44$	7411.97	0.577167
$45$	0	0
$46$	6845.46	0.476988
$47$	15968.1	1.05441	0.527204	−	0.849739i	$-0.323240\pi$
$47$	15968.1	1.05441	0.527204	+	0.849739i	$0.323240\pi$
$48$	2314.65	0.145005
$49$	−10871.6	−0.646849
$50$	0	0
$51$	−16900.1	−0.909839
$52$	2704.00	0.138675
$53$	27930.3	1.36580	0.682898	−	0.730514i	$-0.260719\pi$
$53$	27930.3	1.36580	0.682898	+	0.730514i	$0.260719\pi$
$54$	−14620.2	−0.682292
$55$	0	0
$56$	−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	$0.636365\pi$
$60$	0	0
$61$	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
$65$	0	0
$66$	16754.0	0.473433
$67$	−59646.7	−1.62330	−0.811652	−	0.584142i	$-0.801431\pi$
$67$	−59646.7	−1.62330	−0.811652	+	0.584142i	$0.801431\pi$
$68$	−29906.5	−0.784319
$69$	15473.5	0.391259
$70$	0	0
$71$	−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	$-0.765161\pi$
$73$	−67383.3	−1.47994	−0.739972	+	0.672637i	$0.765161\pi$
$74$	49286.5	1.04628
$75$	0	0
$76$	−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	$0.645807\pi$
$80$	0	0
$81$	6136.07	0.103915
$82$	−70834.3	−1.16335
$83$	−12542.6	−0.199844	−0.0999222	−	0.994995i	$-0.531859\pi$
$83$	−12542.6	−0.199844	−0.0999222	+	0.994995i	$0.531859\pi$
$84$	−11145.3	−0.172342
$85$	0	0
$86$	−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	$0.502899\pi$
$90$	0	0
$91$	−13020.0	−0.164819
$92$	27381.8	0.337282
$93$	−4930.66	−0.0591150
$94$	63872.4	0.745579
$95$	0	0
$96$	9258.59	0.102534
$97$	−58030.7	−0.626222	−0.313111	−	0.949717i	$-0.601371\pi$
$97$	−58030.7	−0.626222	−0.313111	+	0.949717i	$0.601371\pi$
$98$	−43486.4	−0.457391
$99$	−74698.5	−0.765992
$100$	0	0
$101$	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	$-0.310644\pi$
$103$	120678.	1.12082	0.560408	+	0.828216i	$0.310644\pi$
$104$	10816.0	0.0980581
$105$	0	0
$106$	111721.	0.965764
$107$	29154.6	0.246177	0.123089	−	0.992396i	$-0.460720\pi$
$107$	29154.6	0.246177	0.123089	+	0.992396i	$0.460720\pi$
$108$	−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	$0.454020\pi$
$110$	0	0
$111$	111407.	0.858234
$112$	−19722.6	−0.148566
$113$	194071.	1.42976	0.714882	−	0.699245i	$-0.246481\pi$
$113$	194071.	1.42976	0.714882	+	0.699245i	$0.246481\pi$
$114$	−22362.7	−0.161162
$115$	0	0
$116$	−93799.8	−0.647227
$117$	−27251.2	−0.184044
$118$	−88859.7	−0.587489
$119$	144003.	0.932187
$120$	0	0
$121$	53547.6	0.332488
$122$	22169.7	0.134853
$123$	−160114.	−0.954259
$124$	−8725.30	−0.0509596
$125$	0	0
$126$	49691.7	0.278842
$127$	−113031.	−0.621855	−0.310927	−	0.950434i	$-0.600640\pi$
$127$	−113031.	−0.621855	−0.310927	+	0.950434i	$0.600640\pi$
$128$	16384.0	0.0883883
$129$	−114125.	−0.603819
$130$	0	0
$131$	−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
$135$	0	0
$136$	−119626.	−0.554597
$137$	−389881.	−1.77473	−0.887363	−	0.461072i	$-0.847465\pi$
$137$	−389881.	−1.77473	−0.887363	+	0.461072i	$0.847465\pi$
$138$	61893.8	0.276662
$139$	−143094.	−0.628179	−0.314090	−	0.949393i	$-0.601699\pi$
$139$	−143094.	−0.628179	−0.314090	+	0.949393i	$0.601699\pi$
$140$	0	0
$141$	144377.	0.611576
$142$	−268902.	−1.11911
$143$	78288.9	0.320155
$144$	−41279.9	−0.165895
$145$	0	0
$146$	−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	$0.466163\pi$
$150$	0	0
$151$	−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
$155$	0	0
$156$	24448.5	0.0804341
$157$	175379.	0.567844	0.283922	−	0.958847i	$-0.408364\pi$
$157$	175379.	0.567844	0.283922	+	0.958847i	$0.408364\pi$
$158$	−196242.	−0.625387
$159$	252534.	0.792187
$160$	0	0
$161$	−131846.	−0.400869
$162$	24544.3	0.0734789
$163$	631372.	1.86130	0.930650	−	0.365909i	$-0.119242\pi$
$163$	631372.	1.86130	0.930650	+	0.365909i	$0.119242\pi$
$164$	−283337.	−0.822610
$165$	0	0
$166$	−50170.4	−0.141311
$167$	261161.	0.724631	0.362315	−	0.932056i	$-0.381986\pi$
$167$	261161.	0.724631	0.362315	+	0.932056i	$0.381986\pi$
$168$	−44581.0	−0.121864
$169$	28561.0	0.0769231
$170$	0	0
$171$	99705.3	0.260752
$172$	−201956.	−0.520517
$173$	333245.	0.846541	0.423270	−	0.906003i	$-0.360882\pi$
$173$	333245.	0.846541	0.423270	+	0.906003i	$0.360882\pi$
$174$	−212025.	−0.530901
$175$	0	0
$176$	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	$0.750432\pi$
$180$	0	0
$181$	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
$185$	0	0
$186$	−19722.6	−0.0418006
$187$	−865882.	−1.81073
$188$	255490.	0.527204
$189$	281592.	0.573410
$190$	0	0
$191$	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	$-0.666787\pi$
$193$	−517817.	−1.00065	−0.500326	+	0.865837i	$0.666787\pi$
$194$	−232123.	−0.442806
$195$	0	0
$196$	−173945.	−0.323425
$197$	−244368.	−0.448619	−0.224310	−	0.974518i	$-0.572013\pi$
$197$	−244368.	−0.448619	−0.224310	+	0.974518i	$0.572013\pi$
$198$	−298794.	−0.541638
$199$	238178.	0.426354	0.213177	−	0.977014i	$-0.431619\pi$
$199$	238178.	0.426354	0.213177	+	0.977014i	$0.431619\pi$
$200$	0	0
$201$	−539302.	−0.941546
$202$	476170.	0.821076
$203$	451655.	0.769249
$204$	−270402.	−0.454920
$205$	0	0
$206$	482712.	0.792537
$207$	−275957.	−0.447626
$208$	43264.0	0.0693375
$209$	−286440.	−0.453594
$210$	0	0
$211$	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
$215$	0	0
$216$	−233924.	−0.341146
$217$	42013.2	0.0605670
$218$	142843.	0.203573
$219$	−609253.	−0.858395
$220$	0	0
$221$	−315887.	−0.435062
$222$	445629.	0.606863
$223$	86442.8	0.116404	0.0582018	−	0.998305i	$-0.481463\pi$
$223$	86442.8	0.116404	0.0582018	+	0.998305i	$0.481463\pi$
$224$	−78890.6	−0.105052
$225$	0	0
$226$	776283.	1.01100
$227$	−622295.	−0.801552	−0.400776	−	0.916176i	$-0.631259\pi$
$227$	−622295.	−0.801552	−0.400776	+	0.916176i	$0.631259\pi$
$228$	−89450.9	−0.113959
$229$	582324.	0.733797	0.366899	−	0.930261i	$-0.380420\pi$
$229$	582324.	0.733797	0.366899	+	0.930261i	$0.380420\pi$
$230$	0	0
$231$	−322689.	−0.397881
$232$	−375199.	−0.457659
$233$	−865669.	−1.04463	−0.522315	−	0.852753i	$-0.674931\pi$
$233$	−865669.	−1.04463	−0.522315	+	0.852753i	$0.674931\pi$
$234$	−109005.	−0.130138
$235$	0	0
$236$	−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	$0.640557\pi$
$240$	0	0
$241$	−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
$245$	0	0
$246$	−640455.	−0.674763
$247$	−104498.	−0.108984
$248$	−34901.2	−0.0360339
$249$	−113405.	−0.115914
$250$	0	0
$251$	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
$255$	0	0
$256$	65536.0	0.0625000
$257$	1.29242e6	1.22059	0.610295	−	0.792174i	$-0.291051\pi$
$257$	1.29242e6	1.22059	0.610295	+	0.792174i	$0.291051\pi$
$258$	−456500.	−0.426964
$259$	−949278.	−0.879314
$260$	0	0
$261$	945323.	0.858972
$262$	−1.43515e6	−1.29165
$263$	−787600.	−0.702128	−0.351064	−	0.936351i	$-0.614180\pi$
$263$	−787600.	−0.702128	−0.351064	+	0.936351i	$0.614180\pi$
$264$	268064.	0.236717
$265$	0	0
$266$	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	$0.658182\pi$
$270$	0	0
$271$	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
$275$	0	0
$276$	247575.	0.195630
$277$	−789483.	−0.618221	−0.309110	−	0.951026i	$-0.600031\pi$
$277$	−789483.	−0.618221	−0.309110	+	0.951026i	$0.600031\pi$
$278$	−572375.	−0.444190
$279$	87934.4	0.0676314
$280$	0	0
$281$	−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	$-0.461309\pi$
$283$	326725.	0.242502	0.121251	+	0.992622i	$0.461309\pi$
$284$	−1.07561e6	−0.791331
$285$	0	0
$286$	313156.	0.226384
$287$	1.36430e6	0.977697
$288$	−165120.	−0.117305
$289$	2.07388e6	1.46063
$290$	0	0
$291$	−524690.	−0.363220
$292$	−1.07813e6	−0.739972
$293$	−1.32473e6	−0.901487	−0.450743	−	0.892654i	$-0.648841\pi$
$293$	−1.32473e6	−0.901487	−0.450743	+	0.892654i	$0.648841\pi$
$294$	−393186.	−0.265295
$295$	0	0
$296$	788584.	0.523141
$297$	−1.69320e6	−1.11382
$298$	230028.	0.150051
$299$	289221.	0.187090
$300$	0	0
$301$	972436.	0.618650
$302$	−1.53115e6	−0.966054
$303$	1.07633e6	0.673504
$304$	−158292.	−0.0982372
$305$	0	0
$306$	1.20560e6	0.736038
$307$	−550416.	−0.333307	−0.166654	−	0.986015i	$-0.553296\pi$
$307$	−550416.	−0.333307	−0.166654	+	0.986015i	$0.553296\pi$
$308$	−571030.	−0.342990
$309$	1.09112e6	0.650095
$310$	0	0
$311$	−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	$-0.227740\pi$
$313$	2.61647e6	1.50957	0.754787	+	0.655970i	$0.227740\pi$
$314$	701518.	0.401527
$315$	0	0
$316$	−784967.	−0.442215
$317$	−1.33414e6	−0.745683	−0.372841	−	0.927895i	$-0.621616\pi$
$317$	−1.33414e6	−0.745683	−0.372841	+	0.927895i	$0.621616\pi$
$318$	1.01014e6	0.560161
$319$	−2.71578e6	−1.49423
$320$	0	0
$321$	263604.	0.142787
$322$	−527385.	−0.283458
$323$	1.15575e6	0.616394
$324$	98177.1	0.0519574
$325$	0	0
$326$	2.52549e6	1.31614
$327$	322883.	0.166984
$328$	−1.13335e6	−0.581673
$329$	−1.23021e6	−0.626597
$330$	0	0
$331$	−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
$335$	0	0
$336$	−178324.	−0.0861712
$337$	3.87372e6	1.85803	0.929016	−	0.370038i	$-0.120655\pi$
$337$	3.87372e6	1.85803	0.929016	+	0.370038i	$0.120655\pi$
$338$	114244.	0.0543928
$339$	1.75471e6	0.829289
$340$	0	0
$341$	−252623.	−0.117649
$342$	398821.	0.184380
$343$	2.13240e6	0.978665
$344$	−807822.	−0.368061
$345$	0	0
$346$	1.33298e6	0.598595
$347$	−41926.2	−0.0186923	−0.00934613	−	0.999956i	$-0.502975\pi$
$347$	−41926.2	−0.0186923	−0.00934613	+	0.999956i	$0.502975\pi$
$348$	−848099.	−0.375404
$349$	2.08136e6	0.914711	0.457356	−	0.889284i	$-0.348797\pi$
$349$	2.08136e6	0.914711	0.457356	+	0.889284i	$0.348797\pi$
$350$	0	0
$351$	−617705.	−0.267617
$352$	474366.	0.204059
$353$	4.19749e6	1.79289	0.896443	−	0.443160i	$-0.146143\pi$
$353$	4.19749e6	1.79289	0.896443	+	0.443160i	$0.146143\pi$
$354$	−803434.	−0.340755
$355$	0	0
$356$	−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	$0.394774\pi$
$360$	0	0
$361$	−2.09377e6	−0.845591
$362$	582187.	0.233502
$363$	484155.	0.192849
$364$	−208320.	−0.0824097
$365$	0	0
$366$	200449.	0.0782172
$367$	693454.	0.268752	0.134376	−	0.990930i	$-0.457097\pi$
$367$	693454.	0.268752	0.134376	+	0.990930i	$0.457097\pi$
$368$	438109.	0.168641
$369$	2.85550e6	1.09173
$370$	0	0
$371$	−2.15179e6	−0.811645
$372$	−78890.6	−0.0295575
$373$	−3.74196e6	−1.39260	−0.696300	−	0.717751i	$-0.745172\pi$
$373$	−3.74196e6	−1.39260	−0.696300	+	0.717751i	$0.745172\pi$
$374$	−3.46353e6	−1.28038
$375$	0	0
$376$	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	$0.498145\pi$
$380$	0	0
$381$	−1.02198e6	−0.360687
$382$	67218.5	0.0235684
$383$	4.99326e6	1.73935	0.869676	−	0.493624i	$-0.164328\pi$
$383$	4.99326e6	1.73935	0.869676	+	0.493624i	$0.164328\pi$
$384$	148137.	0.0512669
$385$	0	0
$386$	−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	$0.679964\pi$
$390$	0	0
$391$	−3.19880e6	−1.05815
$392$	−695782.	−0.228696
$393$	−3.24401e6	−1.05950
$394$	−977470.	−0.317222
$395$	0	0
$396$	−1.19518e6	−0.382996
$397$	1.12978e6	0.359764	0.179882	−	0.983688i	$-0.442428\pi$
$397$	1.12978e6	0.359764	0.179882	+	0.983688i	$0.442428\pi$
$398$	952714.	0.301477
$399$	430715.	0.135443
$400$	0	0
$401$	−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
$405$	0	0
$406$	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	$0.238520\pi$
$410$	0	0
$411$	−3.52515e6	−1.02937
$412$	1.93085e6	0.560408
$413$	1.71147e6	0.493736
$414$	−1.10383e6	−0.316519
$415$	0	0
$416$	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	$0.324705\pi$
$420$	0	0
$421$	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
$425$	0	0
$426$	−2.43130e6	−0.649105
$427$	−426997.	−0.113333
$428$	466473.	0.123089
$429$	707856.	0.185696
$430$	0	0
$431$	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	$-0.468456\pi$
$433$	771976.	0.197872	0.0989360	+	0.995094i	$0.468456\pi$
$434$	168053.	0.0428273
$435$	0	0
$436$	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	$0.655572\pi$
$440$	0	0
$441$	1.75304e6	0.429235
$442$	−1.26355e6	−0.307635
$443$	−153363.	−0.0371289	−0.0185644	−	0.999828i	$-0.505910\pi$
$443$	−153363.	−0.0371289	−0.0185644	+	0.999828i	$0.505910\pi$
$444$	1.78252e6	0.429117
$445$	0	0
$446$	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	$0.207116\pi$
$450$	0	0
$451$	−8.20346e6	−1.89914
$452$	3.10513e6	0.714882
$453$	−3.46102e6	−0.792425
$454$	−2.48918e6	−0.566783
$455$	0	0
$456$	−357804.	−0.0805810
$457$	−5.30770e6	−1.18882	−0.594409	−	0.804163i	$-0.702614\pi$
$457$	−5.30770e6	−1.18882	−0.594409	+	0.804163i	$0.702614\pi$
$458$	2.32930e6	0.518873
$459$	6.83187e6	1.51359
$460$	0	0
$461$	−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	$-0.710919\pi$
$463$	−5.67529e6	−1.23037	−0.615185	+	0.788383i	$0.710919\pi$
$464$	−1.50080e6	−0.323614
$465$	0	0
$466$	−3.46268e6	−0.738664
$467$	1.97672e6	0.419425	0.209712	−	0.977763i	$-0.432747\pi$
$467$	1.97672e6	0.419425	0.209712	+	0.977763i	$0.432747\pi$
$468$	−436019.	−0.0920218
$469$	4.59528e6	0.964672
$470$	0	0
$471$	1.58571e6	0.329360
$472$	−1.42176e6	−0.293745
$473$	−5.84722e6	−1.20170
$474$	−1.77434e6	−0.362736
$475$	0	0
$476$	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	$0.230463\pi$
$480$	0	0
$481$	2.08236e6	0.410386
$482$	−845661.	−0.165798
$483$	−1.19210e6	−0.232512
$484$	856761.	0.166244
$485$	0	0
$486$	3.77464e6	0.724911
$487$	4.51302e6	0.862274	0.431137	−	0.902287i	$-0.358113\pi$
$487$	4.51302e6	0.862274	0.431137	+	0.902287i	$0.358113\pi$
$488$	354715.	0.0674265
$489$	5.70861e6	1.07959
$490$	0	0
$491$	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
$495$	0	0
$496$	−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	$0.595113\pi$
$500$	0	0
$501$	2.36131e6	0.420299
$502$	6.42810e6	1.13848
$503$	3.30838e6	0.583037	0.291518	−	0.956565i	$-0.405840\pi$
$503$	3.30838e6	0.583037	0.291518	+	0.956565i	$0.405840\pi$
$504$	795067.	0.139421
$505$	0	0
$506$	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	$0.309461\pi$
$510$	0	0
$511$	5.19132e6	0.879479
$512$	262144.	0.0441942
$513$	2.26003e6	0.379159
$514$	5.16967e6	0.863087
$515$	0	0
$516$	−1.82600e6	−0.301909
$517$	7.39719e6	1.21714
$518$	−3.79711e6	−0.621769
$519$	3.01306e6	0.491009
$520$	0	0
$521$	−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	$-0.527407\pi$
$523$	−1.07586e6	−0.171990	−0.0859950	+	0.996296i	$0.527407\pi$
$524$	−5.74059e6	−0.913331
$525$	0	0
$526$	−3.15040e6	−0.496480
$527$	1.01931e6	0.159874
$528$	1.07226e6	0.167384
$529$	−3.50758e6	−0.544964
$530$	0	0
$531$	3.58215e6	0.551324
$532$	762193.	0.116758
$533$	−2.99275e6	−0.456302
$534$	−49223.5	−0.00746998
$535$	0	0
$536$	−3.81739e6	−0.573924
$537$	−5.48885e6	−0.821383
$538$	−4.52639e6	−0.674212
$539$	−5.03624e6	−0.746680
$540$	0	0
$541$	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
$545$	0	0
$546$	−470887.	−0.0675982
$547$	−8.04405e6	−1.14949	−0.574747	−	0.818331i	$-0.694899\pi$
$547$	−8.04405e6	−1.14949	−0.574747	+	0.818331i	$0.694899\pi$
$548$	−6.23810e6	−0.887363
$549$	−893714.	−0.126552
$550$	0	0
$551$	3.62495e6	0.508654
$552$	990301.	0.138331
$553$	3.77970e6	0.525586
$554$	−3.15793e6	−0.437148
$555$	0	0
$556$	−2.28950e6	−0.314090
$557$	1.90075e6	0.259590	0.129795	−	0.991541i	$-0.458568\pi$
$557$	1.90075e6	0.259590	0.129795	+	0.991541i	$0.458568\pi$
$558$	351738.	0.0478226
$559$	−2.13316e6	−0.288731
$560$	0	0
$561$	−7.82895e6	−1.05026
$562$	−3.26191e6	−0.435644
$563$	−6.26708e6	−0.833286	−0.416643	−	0.909070i	$-0.636793\pi$
$563$	−6.26708e6	−0.833286	−0.416643	+	0.909070i	$0.636793\pi$
$564$	2.31003e6	0.305788
$565$	0	0
$566$	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	$0.352157\pi$
$570$	0	0
$571$	−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
$575$	0	0
$576$	−660478.	−0.0829473
$577$	1.23874e7	1.54896	0.774481	−	0.632597i	$-0.218011\pi$
$577$	1.23874e7	1.54896	0.774481	+	0.632597i	$0.218011\pi$
$578$	8.29552e6	1.03282
$579$	−4.68189e6	−0.580397
$580$	0	0
$581$	966301.	0.118761
$582$	−2.09876e6	−0.256836
$583$	1.29387e7	1.57659
$584$	−4.31253e6	−0.523239
$585$	0	0
$586$	−5.29893e6	−0.637447
$587$	−3.70271e6	−0.443531	−0.221766	−	0.975100i	$-0.571182\pi$
$587$	−3.70271e6	−0.443531	−0.221766	+	0.975100i	$0.571182\pi$
$588$	−1.57274e6	−0.187592
$589$	337194.	0.0400490
$590$	0	0
$591$	−2.20947e6	−0.260208
$592$	3.15434e6	0.369917
$593$	−4.98645e6	−0.582310	−0.291155	−	0.956676i	$-0.594040\pi$
$593$	−4.98645e6	−0.582310	−0.291155	+	0.956676i	$0.594040\pi$
$594$	−6.77280e6	−0.787593
$595$	0	0
$596$	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	$0.560298\pi$
$600$	0	0
$601$	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
$605$	0	0
$606$	4.30533e6	0.476239
$607$	−4.57734e6	−0.504245	−0.252123	−	0.967695i	$-0.581129\pi$
$607$	−4.57734e6	−0.504245	−0.252123	+	0.967695i	$0.581129\pi$
$608$	−633169.	−0.0694642
$609$	4.08368e6	0.446179
$610$	0	0
$611$	2.69861e6	0.292440
$612$	4.82241e6	0.520457
$613$	−5.04824e6	−0.542611	−0.271306	−	0.962493i	$-0.587455\pi$
$613$	−5.04824e6	−0.542611	−0.271306	+	0.962493i	$0.587455\pi$
$614$	−2.20166e6	−0.235684
$615$	0	0
$616$	−2.28412e6	−0.242531
$617$	1.31376e7	1.38932	0.694662	−	0.719336i	$-0.255554\pi$
$617$	1.31376e7	1.38932	0.694662	+	0.719336i	$0.255554\pi$
$618$	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	$0.299536\pi$
$620$	0	0
$621$	−6.25514e6	−0.650891
$622$	−1.34312e7	−1.39200
$623$	104856.	0.0108236
$624$	391176.	0.0402171
$625$	0	0
$626$	1.04659e7	1.06743
$627$	−2.58987e6	−0.263093
$628$	2.80607e6	0.283922
$629$	−2.30310e7	−2.32106
$630$	0	0
$631$	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
$635$	0	0
$636$	4.04055e6	0.396094
$637$	−1.83730e6	−0.179404
$638$	−1.08631e7	−1.05658
$639$	1.08401e7	1.05022
$640$	0	0
$641$	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	$-0.548862\pi$
$643$	−3.20604e6	−0.305803	−0.152901	+	0.988241i	$0.548862\pi$
$644$	−2.10954e6	−0.200435
$645$	0	0
$646$	4.62301e6	0.435857
$647$	1.26054e7	1.18385	0.591923	−	0.805994i	$-0.298369\pi$
$647$	1.26054e7	1.18385	0.591923	+	0.805994i	$0.298369\pi$
$648$	392708.	0.0367394
$649$	−1.02910e7	−0.959062
$650$	0	0
$651$	379866.	0.0351300
$652$	1.01020e7	0.930650
$653$	−1.20010e7	−1.10137	−0.550685	−	0.834713i	$-0.685634\pi$
$653$	−1.20010e7	−1.10137	−0.550685	+	0.834713i	$0.685634\pi$
$654$	1.29153e6	0.118076
$655$	0	0
$656$	−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	$0.576156\pi$
$660$	0	0
$661$	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
$665$	0	0
$666$	−7.94743e6	−0.694291
$667$	−1.00328e7	−0.873192
$668$	4.17857e6	0.362315
$669$	781581.	0.0675163
$670$	0	0
$671$	2.56752e6	0.220144
$672$	−713297.	−0.0609322
$673$	1.14870e7	0.977620	0.488810	−	0.872390i	$-0.337431\pi$
$673$	1.14870e7	0.977620	0.488810	+	0.872390i	$0.337431\pi$
$674$	1.54949e7	1.31383
$675$	0	0
$676$	456976.	0.0384615
$677$	4.22852e6	0.354582	0.177291	−	0.984158i	$-0.443267\pi$
$677$	4.22852e6	0.354582	0.177291	+	0.984158i	$0.443267\pi$
$678$	7.01884e6	0.586396
$679$	4.47078e6	0.372142
$680$	0	0
$681$	−5.62654e6	−0.464915
$682$	−1.01049e6	−0.0831903
$683$	−7.70437e6	−0.631954	−0.315977	−	0.948767i	$-0.602332\pi$
$683$	−7.70437e6	−0.631954	−0.315977	+	0.948767i	$0.602332\pi$
$684$	1.59529e6	0.130376
$685$	0	0
$686$	8.52961e6	0.692021
$687$	5.26514e6	0.425616
$688$	−3.23129e6	−0.260258
$689$	4.72022e6	0.378804
$690$	0	0
$691$	−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
$695$	0	0
$696$	−3.39240e6	−0.265451
$697$	3.31001e7	2.58076
$698$	8.32545e6	0.646798
$699$	−7.82703e6	−0.605904
$700$	0	0
$701$	−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
$705$	0	0
$706$	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	$0.594274\pi$
$710$	0	0
$711$	7.91098e6	0.586889
$712$	−87105.9	−0.00643943
$713$	−933260.	−0.0687510
$714$	5.20805e6	0.382323
$715$	0	0
$716$	−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	$0.729007\pi$
$720$	0	0
$721$	−9.29722e6	−0.666062
$722$	−8.37507e6	−0.597923
$723$	−1.91153e6	−0.135999
$724$	2.32875e6	0.165111
$725$	0	0
$726$	1.93662e6	0.136365
$727$	−2.73815e6	−0.192142	−0.0960708	−	0.995374i	$-0.530628\pi$
$727$	−2.73815e6	−0.192142	−0.0960708	+	0.995374i	$0.530628\pi$
$728$	−833282.	−0.0582725
$729$	7.04112e6	0.490708
$730$	0	0
$731$	2.35929e7	1.63301
$732$	801798.	0.0553079
$733$	1.19371e6	0.0820614	0.0410307	−	0.999158i	$-0.486936\pi$
$733$	1.19371e6	0.0820614	0.0410307	+	0.999158i	$0.486936\pi$
$734$	2.77381e6	0.190037
$735$	0	0
$736$	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	$0.568256\pi$
$740$	0	0
$741$	−944825.	−0.0632129
$742$	−8.60718e6	−0.573920
$743$	268541.	0.0178459	0.00892296	−	0.999960i	$-0.497160\pi$
$743$	268541.	0.0178459	0.00892296	+	0.999960i	$0.497160\pi$
$744$	−315562.	−0.0209003
$745$	0	0
$746$	−1.49678e7	−0.984717
$747$	2.02249e6	0.132612
$748$	−1.38541e7	−0.905367
$749$	−2.24612e6	−0.146294
$750$	0	0
$751$	−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
$755$	0	0
$756$	4.50547e6	0.286705
$757$	−2.65907e7	−1.68651	−0.843256	−	0.537512i	$-0.819364\pi$
$757$	−2.65907e7	−1.68651	−0.843256	+	0.537512i	$0.819364\pi$
$758$	130382.	0.00824221
$759$	7.16805e6	0.451644
$760$	0	0
$761$	−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
$765$	0	0
$766$	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	$0.395546\pi$
$770$	0	0
$771$	1.16855e7	0.707965
$772$	−8.28508e6	−0.500326
$773$	−1.87286e6	−0.112734	−0.0563671	−	0.998410i	$-0.517952\pi$
$773$	−1.87286e6	−0.112734	−0.0563671	+	0.998410i	$0.517952\pi$
$774$	8.14131e6	0.488475
$775$	0	0
$776$	−3.71396e6	−0.221403
$777$	−8.58299e6	−0.510019
$778$	−1.27912e7	−0.757640
$779$	1.09497e7	0.646487
$780$	0	0
$781$	−3.11421e7	−1.82692
$782$	−1.27952e7	−0.748222
$783$	2.14277e7	1.24903
$784$	−2.78313e6	−0.161712
$785$	0	0
$786$	−1.29760e7	−0.749179
$787$	1.36103e6	0.0783303	0.0391651	−	0.999233i	$-0.487530\pi$
$787$	1.36103e6	0.0783303	0.0391651	+	0.999233i	$0.487530\pi$
$788$	−3.90988e6	−0.224310
$789$	−7.12116e6	−0.407247
$790$	0	0
$791$	−1.49515e7	−0.849658
$792$	−4.78070e6	−0.270819
$793$	936670.	0.0528937
$794$	4.51912e6	0.254391
$795$	0	0
$796$	3.81086e6	0.213177
$797$	−1.70704e7	−0.951917	−0.475958	−	0.879468i	$-0.657899\pi$
$797$	−1.70704e7	−0.951917	−0.475958	+	0.879468i	$0.657899\pi$
$798$	1.72286e6	0.0957730
$799$	−2.98468e7	−1.65398
$800$	0	0
$801$	219465.	0.0120861
$802$	−2.24036e6	−0.122993
$803$	−3.12152e7	−1.70835
$804$	−8.62883e6	−0.470773
$805$	0	0
$806$	−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	$0.746344\pi$
$810$	0	0
$811$	−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
$815$	0	0
$816$	−4.32643e6	−0.227460
$817$	7.80469e6	0.409073
$818$	1.98150e7	1.03541
$819$	2.09947e6	0.109371
$820$	0	0
$821$	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	$-0.642307\pi$
$823$	−1.68012e7	−0.864650	−0.432325	+	0.901718i	$0.642307\pi$
$824$	7.72339e6	0.396269
$825$	0	0
$826$	6.84590e6	0.349124
$827$	−2.18393e7	−1.11039	−0.555195	−	0.831720i	$-0.687356\pi$
$827$	−2.18393e7	−1.11039	−0.555195	+	0.831720i	$0.687356\pi$
$828$	−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	$0.369136\pi$
$830$	0	0
$831$	−7.13819e6	−0.358579
$832$	692224.	0.0346688
$833$	2.03207e7	1.01467
$834$	−5.17518e6	−0.257638
$835$	0	0
$836$	−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	$0.749717\pi$
$840$	0	0
$841$	1.38576e7	0.675612
$842$	5.90886e6	0.287226
$843$	−7.37322e6	−0.357346
$844$	1.36515e7	0.659665
$845$	0	0
$846$	−1.02994e7	−0.494750
$847$	−4.12539e6	−0.197586
$848$	7.15016e6	0.341449
$849$	2.95411e6	0.140656
$850$	0	0
$851$	2.10868e7	0.998129
$852$	−9.72521e6	−0.458987
$853$	−1.92928e7	−0.907867	−0.453933	−	0.891036i	$-0.649980\pi$
$853$	−1.92928e7	−0.907867	−0.453933	+	0.891036i	$0.649980\pi$
$854$	−1.70799e6	−0.0801384
$855$	0	0
$856$	1.86589e6	0.0870367
$857$	−3.80802e7	−1.77112	−0.885559	−	0.464528i	$-0.846224\pi$
$857$	−3.80802e7	−1.77112	−0.885559	+	0.464528i	$0.846224\pi$
$858$	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	$0.520151\pi$
$860$	0	0
$861$	1.23354e7	0.567082
$862$	2.80237e7	1.28457
$863$	−1.00854e7	−0.460962	−0.230481	−	0.973077i	$-0.574030\pi$
$863$	−1.00854e7	−0.460962	−0.230481	+	0.973077i	$0.574030\pi$
$864$	−3.74278e6	−0.170573
$865$	0	0
$866$	3.08790e6	0.139917
$867$	1.87512e7	0.847190
$868$	672211.	0.0302835
$869$	−2.27272e7	−1.02093
$870$	0	0
$871$	−1.00803e7	−0.450223
$872$	2.28550e6	0.101786
$873$	9.35742e6	0.415548
$874$	−4.23275e6	−0.187432
$875$	0	0
$876$	−9.74805e6	−0.429198
$877$	−1.31876e7	−0.578984	−0.289492	−	0.957180i	$-0.593486\pi$
$877$	−1.31876e7	−0.578984	−0.289492	+	0.957180i	$0.593486\pi$
$878$	−1.51671e7	−0.663996
$879$	−1.19777e7	−0.522879
$880$	0	0
$881$	−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	$-0.379770\pi$
$883$	1.70890e7	0.737591	0.368795	+	0.929511i	$0.379770\pi$
$884$	−5.05419e6	−0.217531
$885$	0	0
$886$	−613452.	−0.0262541
$887$	−3.63465e6	−0.155115	−0.0775574	−	0.996988i	$-0.524712\pi$
$887$	−3.63465e6	−0.155115	−0.0775574	+	0.996988i	$0.524712\pi$
$888$	7.13006e6	0.303432
$889$	8.70810e6	0.369547
$890$	0	0
$891$	2.84252e6	0.119952
$892$	1.38308e6	0.0582018
$893$	−9.87354e6	−0.414328
$894$	2.07982e6	0.0870325
$895$	0	0
$896$	−1.26225e6	−0.0525261
$897$	2.61501e6	0.108516
$898$	2.71921e7	1.12526
$899$	3.19700e6	0.131930
$900$	0	0
$901$	−5.22060e7	−2.14244
$902$	−3.28138e7	−1.34289
$903$	8.79237e6	0.358828
$904$	1.24205e7	0.505498
$905$	0	0
$906$	−1.38441e7	−0.560329
$907$	2.76573e6	0.111633	0.0558163	−	0.998441i	$-0.482224\pi$
$907$	2.76573e6	0.111633	0.0558163	+	0.998441i	$0.482224\pi$
$908$	−9.95672e6	−0.400776
$909$	−1.91955e7	−0.770532
$910$	0	0
$911$	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
$915$	0	0
$916$	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	$0.593005\pi$
$920$	0	0
$921$	−4.97664e6	−0.193324
$922$	−1.16930e7	−0.453001
$923$	−1.13611e7	−0.438951
$924$	−5.16302e6	−0.198941
$925$	0	0
$926$	−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	$0.352007\pi$
$930$	0	0
$931$	6.72222e6	0.254178
$932$	−1.38507e7	−0.522315
$933$	−3.03598e7	−1.14181
$934$	7.90690e6	0.296578
$935$	0	0
$936$	−1.74408e6	−0.0650692
$937$	−5.87866e6	−0.218741	−0.109370	−	0.994001i	$-0.534883\pi$
$937$	−5.87866e6	−0.218741	−0.109370	+	0.994001i	$0.534883\pi$
$938$	1.83811e7	0.682126
$939$	2.36570e7	0.875581
$940$	0	0
$941$	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
$945$	0	0
$946$	−2.33889e7	−0.849731
$947$	8.73411e6	0.316478	0.158239	−	0.987401i	$-0.449418\pi$
$947$	8.73411e6	0.316478	0.158239	+	0.987401i	$0.449418\pi$
$948$	−7.09736e6	−0.256493
$949$	−1.13878e7	−0.410463
$950$	0	0
$951$	−1.20628e7	−0.432510
$952$	9.21617e6	0.329578
$953$	2.03640e6	0.0726323	0.0363162	−	0.999340i	$-0.488438\pi$
$953$	2.03640e6	0.0726323	0.0363162	+	0.999340i	$0.488438\pi$
$954$	−1.80150e7	−0.640860
$955$	0	0
$956$	−1.20765e7	−0.427363
$957$	−2.45550e7	−0.866683
$958$	3.00952e7	1.05946
$959$	3.00371e7	1.05466
$960$	0	0
$961$	−2.83318e7	−0.989612
$962$	8.32942e6	0.290187
$963$	−4.70117e6	−0.163358
$964$	−3.38264e6	−0.117237
$965$	0	0
$966$	−4.76840e6	−0.164411
$967$	2.25922e7	0.776948	0.388474	−	0.921460i	$-0.373002\pi$
$967$	2.25922e7	0.776948	0.388474	+	0.921460i	$0.373002\pi$
$968$	3.42704e6	0.117552
$969$	1.04498e7	0.357520
$970$	0	0
$971$	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
$975$	0	0
$976$	1.41886e6	0.0476777
$977$	−3.59351e7	−1.20443	−0.602217	−	0.798333i	$-0.705716\pi$
$977$	−3.59351e7	−1.20443	−0.602217	+	0.798333i	$0.705716\pi$
$978$	2.28345e7	0.763385
$979$	−630494.	−0.0210244
$980$	0	0
$981$	−5.75836e6	−0.191041
$982$	5.95828e6	0.197171
$983$	3.51635e7	1.16067	0.580335	−	0.814378i	$-0.302922\pi$
$983$	3.51635e7	1.16067	0.580335	+	0.814378i	$0.302922\pi$
$984$	−1.02473e7	−0.337381
$985$	0	0
$986$	4.38316e7	1.43580
$987$	−1.11230e7	−0.363438
$988$	−1.67196e6	−0.0544922
$989$	−2.16012e7	−0.702243
$990$	0	0
$991$	−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
$995$	0	0
$996$	−1.81448e6	−0.0579568
$997$	868537.	0.0276726	0.0138363	−	0.999904i	$-0.495596\pi$
$997$	868537.	0.0276726	0.0138363	+	0.999904i	$0.495596\pi$
$998$	−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	650.6.a.f.1.2		2
5.2	odd	4		650.6.b.f.599.3		4
5.3	odd	4		650.6.b.f.599.2		4
5.4	even	2		130.6.a.c.1.1	✓	2
20.19	odd	2		1040.6.a.c.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.6.a.c.1.1	✓	2	5.4	even	2
650.6.a.f.1.2		2	1.1	even	1	trivial
650.6.b.f.599.2		4	5.3	odd	4
650.6.b.f.599.3		4	5.2	odd	4
1040.6.a.c.1.2		2	20.19	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:	\( N \)	\(=\)	\( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	650.a (trivial)

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

Introduction

L-functions

Modular forms

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