LMFDB - Embedded newform 245.6.a.g.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("245.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$39.2940358542$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 128x^{3} + 288x^{2} + 3551x - 6510 $ x^5 - 2x^4 - 128x^3 + 288x^2 + 3551x - 6510
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			1.3
Root			$1.78024$ of defining polynomial
Character	$\chi$	$=$	245.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.780243 q^{2} +4.65090 q^{3} -31.3912 q^{4} -25.0000 q^{5} +3.62883 q^{6} -49.4606 q^{8} -221.369 q^{9} +O(q^{10})$	\(q+0.780243 q^{2} +4.65090 q^{3} -31.3912 q^{4} -25.0000 q^{5} +3.62883 q^{6} -49.4606 q^{8} -221.369 q^{9} -19.5061 q^{10} +379.295 q^{11} -145.997 q^{12} -801.101 q^{13} -116.273 q^{15} +965.928 q^{16} -1714.67 q^{17} -172.722 q^{18} +2883.66 q^{19} +784.781 q^{20} +295.942 q^{22} -3554.38 q^{23} -230.036 q^{24} +625.000 q^{25} -625.054 q^{26} -2159.73 q^{27} +504.522 q^{29} -90.7208 q^{30} +6364.10 q^{31} +2336.40 q^{32} +1764.06 q^{33} -1337.86 q^{34} +6949.05 q^{36} +14308.8 q^{37} +2249.95 q^{38} -3725.84 q^{39} +1236.51 q^{40} +3903.48 q^{41} -9495.34 q^{43} -11906.5 q^{44} +5534.23 q^{45} -2773.28 q^{46} +21545.8 q^{47} +4492.43 q^{48} +487.652 q^{50} -7974.78 q^{51} +25147.6 q^{52} +3534.20 q^{53} -1685.12 q^{54} -9482.37 q^{55} +13411.6 q^{57} +393.650 q^{58} +26443.0 q^{59} +3649.94 q^{60} +33912.2 q^{61} +4965.54 q^{62} -29086.7 q^{64} +20027.5 q^{65} +1376.40 q^{66} -28795.7 q^{67} +53825.7 q^{68} -16531.1 q^{69} -26401.7 q^{71} +10949.0 q^{72} +34658.0 q^{73} +11164.3 q^{74} +2906.81 q^{75} -90521.5 q^{76} -2907.06 q^{78} -38398.0 q^{79} -24148.2 q^{80} +43748.0 q^{81} +3045.67 q^{82} -61438.9 q^{83} +42866.9 q^{85} -7408.67 q^{86} +2346.48 q^{87} -18760.1 q^{88} +143992. q^{89} +4318.04 q^{90} +111576. q^{92} +29598.8 q^{93} +16811.0 q^{94} -72091.4 q^{95} +10866.3 q^{96} -1499.07 q^{97} -83964.1 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 3 q^{2} + 7 q^{3} + 101 q^{4} - 125 q^{5} + 304 q^{6} - 675 q^{8} + 284 q^{9}+O(q^{10}) $ 5 * q - 3 * q^2 + 7 * q^3 + 101 * q^4 - 125 * q^5 + 304 * q^6 - 675 * q^8 + 284 * q^9	\( 5 q - 3 q^{2} + 7 q^{3} + 101 q^{4} - 125 q^{5} + 304 q^{6} - 675 q^{8} + 284 q^{9} + 75 q^{10} + 1033 q^{11} - 1226 q^{12} + 1117 q^{13} - 175 q^{15} + 297 q^{16} + 3403 q^{17} + 887 q^{18} + 2846 q^{19} - 2525 q^{20} - 1858 q^{22} - 2756 q^{23} + 13290 q^{24} + 3125 q^{25} + 2544 q^{26} + 3661 q^{27} + 485 q^{29} - 7600 q^{30} + 10726 q^{31} - 17383 q^{32} + 12597 q^{33} - 16414 q^{34} + 38165 q^{36} - 2660 q^{37} - 14378 q^{38} - 13171 q^{39} + 16875 q^{40} - 8334 q^{41} - 17294 q^{43} + 42876 q^{44} - 7100 q^{45} + 45724 q^{46} + 59799 q^{47} - 94218 q^{48} - 1875 q^{50} - 12049 q^{51} + 87974 q^{52} - 9250 q^{53} + 106342 q^{54} - 25825 q^{55} - 121778 q^{57} + 35868 q^{58} + 52994 q^{59} + 30650 q^{60} + 81540 q^{61} - 74048 q^{62} + 39745 q^{64} - 27925 q^{65} + 311614 q^{66} - 726 q^{67} + 276216 q^{68} + 21388 q^{69} + 3760 q^{71} - 154815 q^{72} + 90634 q^{73} - 57342 q^{74} + 4375 q^{75} + 43902 q^{76} + 152598 q^{78} + 68243 q^{79} - 7425 q^{80} + 17645 q^{81} + 191552 q^{82} - 133292 q^{83} - 85075 q^{85} - 88352 q^{86} + 216813 q^{87} - 273040 q^{88} + 102852 q^{89} - 22175 q^{90} - 140852 q^{92} + 184862 q^{93} + 332618 q^{94} - 71150 q^{95} + 245574 q^{96} + 186175 q^{97} + 454710 q^{99}+O(q^{100}) \) 5 * q - 3 * q^2 + 7 * q^3 + 101 * q^4 - 125 * q^5 + 304 * q^6 - 675 * q^8 + 284 * q^9 + 75 * q^10 + 1033 * q^11 - 1226 * q^12 + 1117 * q^13 - 175 * q^15 + 297 * q^16 + 3403 * q^17 + 887 * q^18 + 2846 * q^19 - 2525 * q^20 - 1858 * q^22 - 2756 * q^23 + 13290 * q^24 + 3125 * q^25 + 2544 * q^26 + 3661 * q^27 + 485 * q^29 - 7600 * q^30 + 10726 * q^31 - 17383 * q^32 + 12597 * q^33 - 16414 * q^34 + 38165 * q^36 - 2660 * q^37 - 14378 * q^38 - 13171 * q^39 + 16875 * q^40 - 8334 * q^41 - 17294 * q^43 + 42876 * q^44 - 7100 * q^45 + 45724 * q^46 + 59799 * q^47 - 94218 * q^48 - 1875 * q^50 - 12049 * q^51 + 87974 * q^52 - 9250 * q^53 + 106342 * q^54 - 25825 * q^55 - 121778 * q^57 + 35868 * q^58 + 52994 * q^59 + 30650 * q^60 + 81540 * q^61 - 74048 * q^62 + 39745 * q^64 - 27925 * q^65 + 311614 * q^66 - 726 * q^67 + 276216 * q^68 + 21388 * q^69 + 3760 * q^71 - 154815 * q^72 + 90634 * q^73 - 57342 * q^74 + 4375 * q^75 + 43902 * q^76 + 152598 * q^78 + 68243 * q^79 - 7425 * q^80 + 17645 * q^81 + 191552 * q^82 - 133292 * q^83 - 85075 * q^85 - 88352 * q^86 + 216813 * q^87 - 273040 * q^88 + 102852 * q^89 - 22175 * q^90 - 140852 * q^92 + 184862 * q^93 + 332618 * q^94 - 71150 * q^95 + 245574 * q^96 + 186175 * q^97 + 454710 * 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 $

$2$	0.780243	0.137929	0.0689644	−	0.997619i	$-0.478031\pi$
$2$	0.780243	0.137929	0.0689644	+	0.997619i	$0.478031\pi$
$3$	4.65090	0.298355	0.149178	−	0.988810i	$-0.452337\pi$
$3$	4.65090	0.298355	0.149178	+	0.988810i	$0.452337\pi$
$4$	−31.3912	−0.980976
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	3.62883	0.0411518
$7$	0	0
$7$	0	0
$8$	−49.4606	−0.273234
$9$	−221.369	−0.910984
$10$	−19.5061	−0.0616836
$11$	379.295	0.945138	0.472569	−	0.881294i	$-0.343327\pi$
$11$	379.295	0.945138	0.472569	+	0.881294i	$0.343327\pi$
$12$	−145.997	−0.292679
$13$	−801.101	−1.31471	−0.657354	−	0.753582i	$-0.728324\pi$
$13$	−801.101	−1.31471	−0.657354	+	0.753582i	$0.728324\pi$
$14$	0	0
$15$	−116.273	−0.133429
$16$	965.928	0.943289
$17$	−1714.67	−1.43900	−0.719498	−	0.694495i	$-0.755628\pi$
$17$	−1714.67	−1.43900	−0.719498	+	0.694495i	$0.755628\pi$
$18$	−172.722	−0.125651
$19$	2883.66	1.83257	0.916283	−	0.400533i	$-0.131175\pi$
$19$	2883.66	1.83257	0.916283	+	0.400533i	$0.131175\pi$
$20$	784.781	0.438706
$21$	0	0
$22$	295.942	0.130362
$23$	−3554.38	−1.40102	−0.700510	−	0.713643i	$-0.747044\pi$
$23$	−3554.38	−1.40102	−0.700510	+	0.713643i	$0.747044\pi$
$24$	−230.036	−0.0815207
$25$	625.000	0.200000
$26$	−625.054	−0.181336
$27$	−2159.73	−0.570152
$28$	0	0
$29$	504.522	0.111400	0.0557000	−	0.998448i	$-0.482261\pi$
$29$	504.522	0.111400	0.0557000	+	0.998448i	$0.482261\pi$
$30$	−90.7208	−0.0184036
$31$	6364.10	1.18941	0.594706	−	0.803943i	$-0.297268\pi$
$31$	6364.10	1.18941	0.594706	+	0.803943i	$0.297268\pi$
$32$	2336.40	0.403340
$33$	1764.06	0.281987
$34$	−1337.86	−0.198479
$35$	0	0
$36$	6949.05	0.893653
$37$	14308.8	1.71829	0.859147	−	0.511729i	$-0.170995\pi$
$37$	14308.8	1.71829	0.859147	+	0.511729i	$0.170995\pi$
$38$	2249.95	0.252763
$39$	−3725.84	−0.392250
$40$	1236.51	0.122194
$41$	3903.48	0.362654	0.181327	−	0.983423i	$-0.441961\pi$
$41$	3903.48	0.362654	0.181327	+	0.983423i	$0.441961\pi$
$42$	0	0
$43$	−9495.34	−0.783140	−0.391570	−	0.920148i	$-0.628068\pi$
$43$	−9495.34	−0.783140	−0.391570	+	0.920148i	$0.628068\pi$
$44$	−11906.5	−0.927157
$45$	5534.23	0.407404
$46$	−2773.28	−0.193241
$47$	21545.8	1.42272	0.711358	−	0.702830i	$-0.248080\pi$
$47$	21545.8	1.42272	0.711358	+	0.702830i	$0.248080\pi$
$48$	4492.43	0.281435
$49$	0	0
$50$	487.652	0.0275858
$51$	−7974.78	−0.429332
$52$	25147.6	1.28970
$53$	3534.20	0.172823	0.0864114	−	0.996260i	$-0.472460\pi$
$53$	3534.20	0.172823	0.0864114	+	0.996260i	$0.472460\pi$
$54$	−1685.12	−0.0786404
$55$	−9482.37	−0.422678
$56$	0	0
$57$	13411.6	0.546756
$58$	393.650	0.0153653
$59$	26443.0	0.988966	0.494483	−	0.869187i	$-0.335357\pi$
$59$	26443.0	0.988966	0.494483	+	0.869187i	$0.335357\pi$
$60$	3649.94	0.130890
$61$	33912.2	1.16689	0.583447	−	0.812151i	$-0.301704\pi$
$61$	33912.2	1.16689	0.583447	+	0.812151i	$0.301704\pi$
$62$	4965.54	0.164054
$63$	0	0
$64$	−29086.7	−0.887657
$65$	20027.5	0.587955
$66$	1376.40	0.0388941
$67$	−28795.7	−0.783683	−0.391842	−	0.920033i	$-0.628162\pi$
$67$	−28795.7	−0.783683	−0.391842	+	0.920033i	$0.628162\pi$
$68$	53825.7	1.41162
$69$	−16531.1	−0.418002
$70$	0	0
$71$	−26401.7	−0.621564	−0.310782	−	0.950481i	$-0.600591\pi$
$71$	−26401.7	−0.621564	−0.310782	+	0.950481i	$0.600591\pi$
$72$	10949.0	0.248911
$73$	34658.0	0.761195	0.380597	−	0.924741i	$-0.375718\pi$
$73$	34658.0	0.761195	0.380597	+	0.924741i	$0.375718\pi$
$74$	11164.3	0.237002
$75$	2906.81	0.0596711
$76$	−90521.5	−1.79770
$77$	0	0
$78$	−2907.06	−0.0541026
$79$	−38398.0	−0.692215	−0.346107	−	0.938195i	$-0.612497\pi$
$79$	−38398.0	−0.692215	−0.346107	+	0.938195i	$0.612497\pi$
$80$	−24148.2	−0.421852
$81$	43748.0	0.740876
$82$	3045.67	0.0500205
$83$	−61438.9	−0.978923	−0.489461	−	0.872025i	$-0.662807\pi$
$83$	−61438.9	−0.978923	−0.489461	+	0.872025i	$0.662807\pi$
$84$	0	0
$85$	42866.9	0.643538
$86$	−7408.67	−0.108018
$87$	2346.48	0.0332368
$88$	−18760.1	−0.258243
$89$	143992.	1.92692	0.963460	−	0.267852i	$-0.0863139\pi$
$89$	143992.	1.92692	0.963460	+	0.267852i	$0.0863139\pi$
$90$	4318.04	0.0561928
$91$	0	0
$92$	111576.	1.37437
$93$	29598.8	0.354868
$94$	16811.0	0.196234
$95$	−72091.4	−0.819548
$96$	10866.3	0.120339
$97$	−1499.07	−0.0161768	−0.00808840	−	0.999967i	$-0.502575\pi$
$97$	−1499.07	−0.0161768	−0.00808840	+	0.999967i	$0.502575\pi$
$98$	0	0
$99$	−83964.1	−0.861005
$100$	−19619.5	−0.196195
$101$	101617.	0.991207	0.495604	−	0.868549i	$-0.334947\pi$
$101$	101617.	0.991207	0.495604	+	0.868549i	$0.334947\pi$
$102$	−6222.27	−0.0592172
$103$	−18394.3	−0.170840	−0.0854199	−	0.996345i	$-0.527223\pi$
$103$	−18394.3	−0.170840	−0.0854199	+	0.996345i	$0.527223\pi$
$104$	39622.9	0.359222
$105$	0	0
$106$	2757.53	0.0238372
$107$	50886.1	0.429675	0.214837	−	0.976650i	$-0.431078\pi$
$107$	50886.1	0.429675	0.214837	+	0.976650i	$0.431078\pi$
$108$	67796.7	0.559306
$109$	156189.	1.25917	0.629586	−	0.776931i	$-0.283225\pi$
$109$	156189.	1.25917	0.629586	+	0.776931i	$0.283225\pi$
$110$	−7398.55	−0.0582995
$111$	66548.6	0.512662
$112$	0	0
$113$	−53756.8	−0.396039	−0.198019	−	0.980198i	$-0.563451\pi$
$113$	−53756.8	−0.396039	−0.198019	+	0.980198i	$0.563451\pi$
$114$	10464.3	0.0754133
$115$	88859.5	0.626555
$116$	−15837.6	−0.109281
$117$	177339.	1.19768
$118$	20632.0	0.136407
$119$	0	0
$120$	5750.90	0.0364572
$121$	−17186.5	−0.106715
$122$	26459.7	0.160948
$123$	18154.7	0.108200
$124$	−199777.	−1.16678
$125$	−15625.0	−0.0894427
$126$	0	0
$127$	147989.	0.814179	0.407089	−	0.913388i	$-0.366544\pi$
$127$	147989.	0.814179	0.407089	+	0.913388i	$0.366544\pi$
$128$	−97459.4	−0.525774
$129$	−44161.9	−0.233654
$130$	15626.3	0.0810959
$131$	−183982.	−0.936691	−0.468346	−	0.883545i	$-0.655150\pi$
$131$	−183982.	−0.936691	−0.468346	+	0.883545i	$0.655150\pi$
$132$	−55376.1	−0.276622
$133$	0	0
$134$	−22467.6	−0.108092
$135$	53993.4	0.254980
$136$	84808.7	0.393182
$137$	−75377.2	−0.343114	−0.171557	−	0.985174i	$-0.554880\pi$
$137$	−75377.2	−0.343114	−0.171557	+	0.985174i	$0.554880\pi$
$138$	−12898.2	−0.0576545
$139$	−52490.9	−0.230434	−0.115217	−	0.993340i	$-0.536756\pi$
$139$	−52490.9	−0.230434	−0.115217	+	0.993340i	$0.536756\pi$
$140$	0	0
$141$	100207.	0.424475
$142$	−20599.7	−0.0857316
$143$	−303854.	−1.24258
$144$	−213827.	−0.859321
$145$	−12613.1	−0.0498196
$146$	27041.6	0.104991
$147$	0	0
$148$	−449169.	−1.68560
$149$	−277053.	−1.02235	−0.511173	−	0.859478i	$-0.670789\pi$
$149$	−277053.	−1.02235	−0.511173	+	0.859478i	$0.670789\pi$
$150$	2268.02	0.00823036
$151$	177712.	0.634271	0.317136	−	0.948380i	$-0.397279\pi$
$151$	177712.	0.634271	0.317136	+	0.948380i	$0.397279\pi$
$152$	−142627.	−0.500718
$153$	379576.	1.31090
$154$	0	0
$155$	−159102.	−0.531921
$156$	116959.	0.384788
$157$	−315695.	−1.02216	−0.511080	−	0.859533i	$-0.670755\pi$
$157$	−315695.	−1.02216	−0.511080	+	0.859533i	$0.670755\pi$
$158$	−29959.8	−0.0954763
$159$	16437.2	0.0515626
$160$	−58409.9	−0.180379
$161$	0	0
$162$	34134.1	0.102188
$163$	345956.	1.01989	0.509943	−	0.860208i	$-0.329667\pi$
$163$	345956.	1.01989	0.509943	+	0.860208i	$0.329667\pi$
$164$	−122535.	−0.355755
$165$	−44101.6	−0.126108
$166$	−47937.3	−0.135022
$167$	435351.	1.20795	0.603974	−	0.797004i	$-0.293583\pi$
$167$	435351.	1.20795	0.603974	+	0.797004i	$0.293583\pi$
$168$	0	0
$169$	270471.	0.728456
$170$	33446.6	0.0887624
$171$	−638352.	−1.66944
$172$	298070.	0.768241
$173$	−101962.	−0.259015	−0.129507	−	0.991578i	$-0.541340\pi$
$173$	−101962.	−0.259015	−0.129507	+	0.991578i	$0.541340\pi$
$174$	1830.83	0.00458431
$175$	0	0
$176$	366371.	0.891538
$177$	122984.	0.295063
$178$	112349.	0.265778
$179$	−181238.	−0.422783	−0.211392	−	0.977401i	$-0.567800\pi$
$179$	−181238.	−0.422783	−0.211392	+	0.977401i	$0.567800\pi$
$180$	−173726.	−0.399654
$181$	−294673.	−0.668564	−0.334282	−	0.942473i	$-0.608494\pi$
$181$	−294673.	−0.668564	−0.334282	+	0.942473i	$0.608494\pi$
$182$	0	0
$183$	157722.	0.348149
$184$	175802.	0.382805
$185$	−357719.	−0.768444
$186$	23094.2	0.0489465
$187$	−650367.	−1.36005
$188$	−676349.	−1.39565
$189$	0	0
$190$	−56248.8	−0.113039
$191$	−488987.	−0.969870	−0.484935	−	0.874550i	$-0.661157\pi$
$191$	−488987.	−0.969870	−0.484935	+	0.874550i	$0.661157\pi$
$192$	−135280.	−0.264837
$193$	−950371.	−1.83654	−0.918269	−	0.395958i	$-0.870412\pi$
$193$	−950371.	−1.83654	−0.918269	+	0.395958i	$0.870412\pi$
$194$	−1169.64	−0.00223125
$195$	93146.1	0.175420
$196$	0	0
$197$	−825260.	−1.51504	−0.757522	−	0.652810i	$-0.773590\pi$
$197$	−825260.	−1.51504	−0.757522	+	0.652810i	$0.773590\pi$
$198$	−65512.4	−0.118757
$199$	−274724.	−0.491772	−0.245886	−	0.969299i	$-0.579079\pi$
$199$	−274724.	−0.491772	−0.245886	+	0.969299i	$0.579079\pi$
$200$	−30912.8	−0.0546467
$201$	−133926.	−0.233816
$202$	79286.2	0.136716
$203$	0	0
$204$	250338.	0.421164
$205$	−97587.1	−0.162184
$206$	−14352.0	−0.0235637
$207$	786830.	1.27631
$208$	−773806.	−1.24015
$209$	1.09376e6	1.73203
$210$	0	0
$211$	201376.	0.311388	0.155694	−	0.987805i	$-0.450239\pi$
$211$	201376.	0.311388	0.155694	+	0.987805i	$0.450239\pi$
$212$	−110943.	−0.169535
$213$	−122792.	−0.185447
$214$	39703.5	0.0592645
$215$	237383.	0.350231
$216$	106822.	0.155785
$217$	0	0
$218$	121866.	0.173676
$219$	161191.	0.227107
$220$	297663.	0.414637
$221$	1.37363e6	1.89186
$222$	51924.1	0.0707109
$223$	820756.	1.10523	0.552614	−	0.833437i	$-0.313630\pi$
$223$	820756.	1.10523	0.552614	+	0.833437i	$0.313630\pi$
$224$	0	0
$225$	−138356.	−0.182197
$226$	−41943.4	−0.0546251
$227$	490987.	0.632420	0.316210	−	0.948689i	$-0.397590\pi$
$227$	490987.	0.632420	0.316210	+	0.948689i	$0.397590\pi$
$228$	−421006.	−0.536354
$229$	−866371.	−1.09173	−0.545865	−	0.837873i	$-0.683799\pi$
$229$	−866371.	−1.09173	−0.545865	+	0.837873i	$0.683799\pi$
$230$	69332.0	0.0864199
$231$	0	0
$232$	−24954.0	−0.0304382
$233$	1.22483e6	1.47803	0.739017	−	0.673686i	$-0.235290\pi$
$233$	1.22483e6	1.47803	0.739017	+	0.673686i	$0.235290\pi$
$234$	138368.	0.165194
$235$	−538645.	−0.636258
$236$	−830079.	−0.970152
$237$	−178585.	−0.206526
$238$	0	0
$239$	827824.	0.937439	0.468720	−	0.883347i	$-0.344715\pi$
$239$	827824.	0.937439	0.468720	+	0.883347i	$0.344715\pi$
$240$	−112311.	−0.125862
$241$	487218.	0.540357	0.270179	−	0.962810i	$-0.412917\pi$
$241$	487218.	0.540357	0.270179	+	0.962810i	$0.412917\pi$
$242$	−13409.6	−0.0147190
$243$	728283.	0.791197
$244$	−1.06454e6	−1.14469
$245$	0	0
$246$	14165.1	0.0149239
$247$	−2.31010e6	−2.40929
$248$	−314772.	−0.324987
$249$	−285746.	−0.292067
$250$	−12191.3	−0.0123367
$251$	1.04778e6	1.04975	0.524875	−	0.851179i	$-0.324112\pi$
$251$	1.04778e6	1.04975	0.524875	+	0.851179i	$0.324112\pi$
$252$	0	0
$253$	−1.34816e6	−1.32416
$254$	115467.	0.112299
$255$	199369.	0.192003
$256$	854733.	0.815137
$257$	1.24414e6	1.17499	0.587496	−	0.809227i	$-0.300114\pi$
$257$	1.24414e6	1.17499	0.587496	+	0.809227i	$0.300114\pi$
$258$	−34457.0	−0.0322276
$259$	0	0
$260$	−628689.	−0.576770
$261$	−111686.	−0.101484
$262$	−143550.	−0.129197
$263$	−1.44773e6	−1.29062	−0.645312	−	0.763919i	$-0.723273\pi$
$263$	−1.44773e6	−1.29062	−0.645312	+	0.763919i	$0.723273\pi$
$264$	−87251.5	−0.0770483
$265$	−88354.9	−0.0772887
$266$	0	0
$267$	669693.	0.574907
$268$	903932.	0.768774
$269$	−576663.	−0.485893	−0.242947	−	0.970040i	$-0.578114\pi$
$269$	−576663.	−0.485893	−0.242947	+	0.970040i	$0.578114\pi$
$270$	42127.9	0.0351691
$271$	1.78478e6	1.47626	0.738129	−	0.674659i	$-0.235710\pi$
$271$	1.78478e6	1.47626	0.738129	+	0.674659i	$0.235710\pi$
$272$	−1.65625e6	−1.35739
$273$	0	0
$274$	−58812.5	−0.0473253
$275$	237059.	0.189028
$276$	518930.	0.410049
$277$	249175.	0.195121	0.0975606	−	0.995230i	$-0.468896\pi$
$277$	249175.	0.195121	0.0975606	+	0.995230i	$0.468896\pi$
$278$	−40955.7	−0.0317835
$279$	−1.40881e6	−1.08354
$280$	0	0
$281$	2.09862e6	1.58551	0.792753	−	0.609543i	$-0.208647\pi$
$281$	2.09862e6	1.58551	0.792753	+	0.609543i	$0.208647\pi$
$282$	78186.2	0.0585473
$283$	642157.	0.476623	0.238312	−	0.971189i	$-0.423406\pi$
$283$	642157.	0.476623	0.238312	+	0.971189i	$0.423406\pi$
$284$	828782.	0.609740
$285$	−335290.	−0.244517
$286$	−237080.	−0.171388
$287$	0	0
$288$	−517206.	−0.367437
$289$	1.52025e6	1.07071
$290$	−9841.25	−0.00687156
$291$	−6972.03	−0.00482644
$292$	−1.08796e6	−0.746714
$293$	−1.18881e6	−0.808992	−0.404496	−	0.914540i	$-0.632553\pi$
$293$	−1.18881e6	−0.808992	−0.404496	+	0.914540i	$0.632553\pi$
$294$	0	0
$295$	−661076.	−0.442279
$296$	−707719.	−0.469496
$297$	−819176.	−0.538873
$298$	−216169.	−0.141011
$299$	2.84742e6	1.84193
$300$	−91248.4	−0.0585359
$301$	0	0
$302$	138659.	0.0874843
$303$	472612.	0.295732
$304$	2.78540e6	1.72864
$305$	−847805.	−0.521851
$306$	296161.	0.180811
$307$	1.05005e6	0.635864	0.317932	−	0.948114i	$-0.397012\pi$
$307$	1.05005e6	0.635864	0.317932	+	0.948114i	$0.397012\pi$
$308$	0	0
$309$	−85549.8	−0.0509710
$310$	−124139.	−0.0733673
$311$	−274856.	−0.161140	−0.0805702	−	0.996749i	$-0.525674\pi$
$311$	−274856.	−0.161140	−0.0805702	+	0.996749i	$0.525674\pi$
$312$	184282.	0.107176
$313$	1.95827e6	1.12983	0.564913	−	0.825151i	$-0.308910\pi$
$313$	1.95827e6	1.12983	0.564913	+	0.825151i	$0.308910\pi$
$314$	−246319.	−0.140985
$315$	0	0
$316$	1.20536e6	0.679046
$317$	646275.	0.361218	0.180609	−	0.983555i	$-0.442193\pi$
$317$	646275.	0.361218	0.180609	+	0.983555i	$0.442193\pi$
$318$	12825.0	0.00711197
$319$	191363.	0.105288
$320$	727168.	0.396972
$321$	236666.	0.128196
$322$	0	0
$323$	−4.94453e6	−2.63705
$324$	−1.37330e6	−0.726781
$325$	−500688.	−0.262942
$326$	269929.	0.140672
$327$	726421.	0.375681
$328$	−193069.	−0.0990893
$329$	0	0
$330$	−34409.9	−0.0173940
$331$	−825772.	−0.414277	−0.207138	−	0.978312i	$-0.566415\pi$
$331$	−825772.	−0.414277	−0.207138	+	0.978312i	$0.566415\pi$
$332$	1.92864e6	0.960299
$333$	−3.16752e6	−1.56534
$334$	339679.	0.166611
$335$	719892.	0.350474
$336$	0	0
$337$	3.06676e6	1.47097	0.735487	−	0.677539i	$-0.236954\pi$
$337$	3.06676e6	1.47097	0.735487	+	0.677539i	$0.236954\pi$
$338$	211033.	0.100475
$339$	−250018.	−0.118160
$340$	−1.34564e6	−0.631295
$341$	2.41387e6	1.12416
$342$	−498070.	−0.230263
$343$	0	0
$344$	469645.	0.213980
$345$	413277.	0.186936
$346$	−79555.4	−0.0357256
$347$	3.02368e6	1.34807	0.674035	−	0.738699i	$-0.264560\pi$
$347$	3.02368e6	1.34807	0.674035	+	0.738699i	$0.264560\pi$
$348$	−73659.0	−0.0326045
$349$	3.15070e6	1.38466	0.692330	−	0.721581i	$-0.256584\pi$
$349$	3.15070e6	1.38466	0.692330	+	0.721581i	$0.256584\pi$
$350$	0	0
$351$	1.73017e6	0.749584
$352$	886183.	0.381212
$353$	2.82997e6	1.20877	0.604386	−	0.796691i	$-0.293418\pi$
$353$	2.82997e6	1.20877	0.604386	+	0.796691i	$0.293418\pi$
$354$	95957.4	0.0406977
$355$	660043.	0.277972
$356$	−4.52009e6	−1.89026
$357$	0	0
$358$	−141410.	−0.0583140
$359$	−2.65902e6	−1.08889	−0.544446	−	0.838796i	$-0.683260\pi$
$359$	−2.65902e6	−1.08889	−0.544446	+	0.838796i	$0.683260\pi$
$360$	−273726.	−0.111317
$361$	5.83937e6	2.35829
$362$	−229916.	−0.0922143
$363$	−79932.7	−0.0318389
$364$	0	0
$365$	−866449.	−0.340417
$366$	123062.	0.0480198
$367$	4.01238e6	1.55502	0.777511	−	0.628869i	$-0.216482\pi$
$367$	4.01238e6	1.55502	0.777511	+	0.628869i	$0.216482\pi$
$368$	−3.43327e6	−1.32157
$369$	−864111.	−0.330372
$370$	−279108.	−0.105991
$371$	0	0
$372$	−929142.	−0.348117
$373$	−1.10404e6	−0.410876	−0.205438	−	0.978670i	$-0.565862\pi$
$373$	−1.10404e6	−0.410876	−0.205438	+	0.978670i	$0.565862\pi$
$374$	−507444.	−0.187590
$375$	−72670.3	−0.0266857
$376$	−1.06567e6	−0.388734
$377$	−404174.	−0.146458
$378$	0	0
$379$	−2.68499e6	−0.960164	−0.480082	−	0.877224i	$-0.659393\pi$
$379$	−2.68499e6	−0.960164	−0.480082	+	0.877224i	$0.659393\pi$
$380$	2.26304e6	0.803957
$381$	688281.	0.242915
$382$	−381529.	−0.133773
$383$	−1.82910e6	−0.637149	−0.318575	−	0.947898i	$-0.603204\pi$
$383$	−1.82910e6	−0.637149	−0.318575	+	0.947898i	$0.603204\pi$
$384$	−453274.	−0.156867
$385$	0	0
$386$	−741520.	−0.253311
$387$	2.10197e6	0.713428
$388$	47057.7	0.0158691
$389$	1.35020e6	0.452402	0.226201	−	0.974081i	$-0.427369\pi$
$389$	1.35020e6	0.452402	0.226201	+	0.974081i	$0.427369\pi$
$390$	72676.6	0.0241954
$391$	6.09460e6	2.01606
$392$	0	0
$393$	−855681.	−0.279467
$394$	−643903.	−0.208968
$395$	959950.	0.309568
$396$	2.63574e6	0.844625
$397$	3.31628e6	1.05603	0.528013	−	0.849236i	$-0.322937\pi$
$397$	3.31628e6	1.05603	0.528013	+	0.849236i	$0.322937\pi$
$398$	−214351.	−0.0678295
$399$	0	0
$400$	603705.	0.188658
$401$	−2.45150e6	−0.761328	−0.380664	−	0.924714i	$-0.624304\pi$
$401$	−2.45150e6	−0.761328	−0.380664	+	0.924714i	$0.624304\pi$
$402$	−104495.	−0.0322500
$403$	−5.09829e6	−1.56373
$404$	−3.18989e6	−0.972350
$405$	−1.09370e6	−0.331330
$406$	0	0
$407$	5.42723e6	1.62402
$408$	394437.	0.117308
$409$	−651359.	−0.192536	−0.0962681	−	0.995355i	$-0.530691\pi$
$409$	−651359.	−0.192536	−0.0962681	+	0.995355i	$0.530691\pi$
$410$	−76141.7	−0.0223698
$411$	−350572.	−0.102370
$412$	577418.	0.167590
$413$	0	0
$414$	613918.	0.176039
$415$	1.53597e6	0.437788
$416$	−1.87169e6	−0.530274
$417$	−244130.	−0.0687513
$418$	853395.	0.238896
$419$	−4.05323e6	−1.12789	−0.563945	−	0.825812i	$-0.690717\pi$
$419$	−4.05323e6	−1.12789	−0.563945	+	0.825812i	$0.690717\pi$
$420$	0	0
$421$	4.65432e6	1.27983	0.639914	−	0.768447i	$-0.278970\pi$
$421$	4.65432e6	1.27983	0.639914	+	0.768447i	$0.278970\pi$
$422$	157122.	0.0429494
$423$	−4.76958e6	−1.29607
$424$	−174803.	−0.0472210
$425$	−1.07167e6	−0.287799
$426$	−95807.4	−0.0255785
$427$	0	0
$428$	−1.59738e6	−0.421500
$429$	−1.41319e6	−0.370730
$430$	185217.	0.0483069
$431$	1.92116e6	0.498162	0.249081	−	0.968483i	$-0.419871\pi$
$431$	1.92116e6	0.498162	0.249081	+	0.968483i	$0.419871\pi$
$432$	−2.08615e6	−0.537818
$433$	4.55873e6	1.16849	0.584244	−	0.811578i	$-0.301391\pi$
$433$	4.55873e6	1.16849	0.584244	+	0.811578i	$0.301391\pi$
$434$	0	0
$435$	−58662.1	−0.0148640
$436$	−4.90297e6	−1.23522
$437$	−1.02496e7	−2.56746
$438$	125768.	0.0313245
$439$	884808.	0.219123	0.109561	−	0.993980i	$-0.465055\pi$
$439$	884808.	0.219123	0.109561	+	0.993980i	$0.465055\pi$
$440$	469003.	0.115490
$441$	0	0
$442$	1.07176e6	0.260942
$443$	7.52827e6	1.82258	0.911288	−	0.411769i	$-0.135089\pi$
$443$	7.52827e6	1.82258	0.911288	+	0.411769i	$0.135089\pi$
$444$	−2.08904e6	−0.502909
$445$	−3.59980e6	−0.861745
$446$	640389.	0.152443
$447$	−1.28855e6	−0.305022
$448$	0	0
$449$	−2.66640e6	−0.624180	−0.312090	−	0.950053i	$-0.601029\pi$
$449$	−2.66640e6	−0.624180	−0.312090	+	0.950053i	$0.601029\pi$
$450$	−107951.	−0.0251302
$451$	1.48057e6	0.342758
$452$	1.68749e6	0.388504
$453$	826522.	0.189238
$454$	383089.	0.0872289
$455$	0	0
$456$	−663345.	−0.149392
$457$	−276297.	−0.0618850	−0.0309425	−	0.999521i	$-0.509851\pi$
$457$	−276297.	−0.0618850	−0.0309425	+	0.999521i	$0.509851\pi$
$458$	−675980.	−0.150581
$459$	3.70324e6	0.820447
$460$	−2.78941e6	−0.614635
$461$	−3.94989e6	−0.865631	−0.432815	−	0.901483i	$-0.642480\pi$
$461$	−3.94989e6	−0.865631	−0.432815	+	0.901483i	$0.642480\pi$
$462$	0	0
$463$	−9.01968e6	−1.95541	−0.977707	−	0.209972i	$-0.932663\pi$
$463$	−9.01968e6	−1.95541	−0.977707	+	0.209972i	$0.932663\pi$
$464$	487332.	0.105082
$465$	−739969.	−0.158702
$466$	955662.	0.203864
$467$	−6.92104e6	−1.46852	−0.734259	−	0.678869i	$-0.762470\pi$
$467$	−6.92104e6	−1.46852	−0.734259	+	0.678869i	$0.762470\pi$
$468$	−5.56689e6	−1.17489
$469$	0	0
$470$	−420274.	−0.0877583
$471$	−1.46827e6	−0.304967
$472$	−1.30789e6	−0.270219
$473$	−3.60153e6	−0.740175
$474$	−139340.	−0.0284859
$475$	1.80228e6	0.366513
$476$	0	0
$477$	−782362.	−0.157439
$478$	645904.	0.129300
$479$	121277.	0.0241512	0.0120756	−	0.999927i	$-0.496156\pi$
$479$	121277.	0.0241512	0.0120756	+	0.999927i	$0.496156\pi$
$480$	−271659.	−0.0538171
$481$	−1.14628e7	−2.25905
$482$	380149.	0.0745308
$483$	0	0
$484$	539505.	0.104684
$485$	37476.8	0.00723449
$486$	568238.	0.109129
$487$	−1.29579e6	−0.247578	−0.123789	−	0.992309i	$-0.539505\pi$
$487$	−1.29579e6	−0.247578	−0.123789	+	0.992309i	$0.539505\pi$
$488$	−1.67732e6	−0.318834
$489$	1.60901e6	0.304288
$490$	0	0
$491$	8.01759e6	1.50086	0.750430	−	0.660950i	$-0.229846\pi$
$491$	8.01759e6	1.50086	0.750430	+	0.660950i	$0.229846\pi$
$492$	−569899.	−0.106141
$493$	−865091.	−0.160304
$494$	−1.80244e6	−0.332310
$495$	2.09910e6	0.385053
$496$	6.14726e6	1.12196
$497$	0	0
$498$	−222952.	−0.0402844
$499$	5.68594e6	1.02223	0.511117	−	0.859511i	$-0.329232\pi$
$499$	5.68594e6	1.02223	0.511117	+	0.859511i	$0.329232\pi$
$500$	490488.	0.0877411
$501$	2.02477e6	0.360398
$502$	817523.	0.144791
$503$	4.83989e6	0.852934	0.426467	−	0.904503i	$-0.359758\pi$
$503$	4.83989e6	0.852934	0.426467	+	0.904503i	$0.359758\pi$
$504$	0	0
$505$	−2.54043e6	−0.443281
$506$	−1.05189e6	−0.182639
$507$	1.25793e6	0.217339
$508$	−4.64555e6	−0.798689
$509$	1.43840e6	0.246085	0.123043	−	0.992401i	$-0.460735\pi$
$509$	1.43840e6	0.246085	0.123043	+	0.992401i	$0.460735\pi$
$510$	155557.	0.0264828
$511$	0	0
$512$	3.78560e6	0.638205
$513$	−6.22793e6	−1.04484
$514$	970728.	0.162065
$515$	459856.	0.0764019
$516$	1.38630e6	0.229209
$517$	8.17222e6	1.34466
$518$	0	0
$519$	−474217.	−0.0772785
$520$	−990573.	−0.160649
$521$	−5.43249e6	−0.876808	−0.438404	−	0.898778i	$-0.644456\pi$
$521$	−5.43249e6	−0.876808	−0.438404	+	0.898778i	$0.644456\pi$
$522$	−87142.0	−0.0139975
$523$	−1.11777e7	−1.78690	−0.893449	−	0.449165i	$-0.851722\pi$
$523$	−1.11777e7	−1.78690	−0.893449	+	0.449165i	$0.851722\pi$
$524$	5.77541e6	0.918871
$525$	0	0
$526$	−1.12958e6	−0.178014
$527$	−1.09124e7	−1.71156
$528$	1.70396e6	0.265995
$529$	6.19726e6	0.962855
$530$	−68938.3	−0.0106603
$531$	−5.85367e6	−0.900932
$532$	0	0
$533$	−3.12709e6	−0.476784
$534$	522523.	0.0792962
$535$	−1.27215e6	−0.192156
$536$	1.42425e6	0.214129
$537$	−842922.	−0.126140
$538$	−449937.	−0.0670187
$539$	0	0
$540$	−1.69492e6	−0.250129
$541$	9.70389e6	1.42545	0.712726	−	0.701442i	$-0.247460\pi$
$541$	9.70389e6	1.42545	0.712726	+	0.701442i	$0.247460\pi$
$542$	1.39256e6	0.203618
$543$	−1.37049e6	−0.199470
$544$	−4.00616e6	−0.580405
$545$	−3.90473e6	−0.563119
$546$	0	0
$547$	−1.94622e6	−0.278114	−0.139057	−	0.990284i	$-0.544407\pi$
$547$	−1.94622e6	−0.278114	−0.139057	+	0.990284i	$0.544407\pi$
$548$	2.36618e6	0.336587
$549$	−7.50711e6	−1.06302
$550$	184964.	0.0260723
$551$	1.45487e6	0.204148
$552$	817635.	0.114212
$553$	0	0
$554$	194417.	0.0269128
$555$	−1.66371e6	−0.229270
$556$	1.64775e6	0.226050
$557$	−1.77835e6	−0.242873	−0.121437	−	0.992599i	$-0.538750\pi$
$557$	−1.77835e6	−0.242873	−0.121437	+	0.992599i	$0.538750\pi$
$558$	−1.09922e6	−0.149451
$559$	7.60673e6	1.02960
$560$	0	0
$561$	−3.02479e6	−0.405778
$562$	1.63743e6	0.218687
$563$	−2.23711e6	−0.297452	−0.148726	−	0.988878i	$-0.547517\pi$
$563$	−2.23711e6	−0.297452	−0.148726	+	0.988878i	$0.547517\pi$
$564$	−3.14563e6	−0.416400
$565$	1.34392e6	0.177114
$566$	501039.	0.0657401
$567$	0	0
$568$	1.30584e6	0.169832
$569$	4.70849e6	0.609679	0.304839	−	0.952404i	$-0.401397\pi$
$569$	4.70849e6	0.609679	0.304839	+	0.952404i	$0.401397\pi$
$570$	−261608.	−0.0337259
$571$	4.09684e6	0.525847	0.262923	−	0.964817i	$-0.415313\pi$
$571$	4.09684e6	0.525847	0.262923	+	0.964817i	$0.415313\pi$
$572$	9.53833e6	1.21894
$573$	−2.27423e6	−0.289366
$574$	0	0
$575$	−2.22149e6	−0.280204
$576$	6.43890e6	0.808641
$577$	1.40471e7	1.75649	0.878245	−	0.478211i	$-0.158715\pi$
$577$	1.40471e7	1.75649	0.878245	+	0.478211i	$0.158715\pi$
$578$	1.18617e6	0.147681
$579$	−4.42008e6	−0.547941
$580$	395939.	0.0488718
$581$	0	0
$582$	−5439.88	−0.000665705 0
$583$	1.34050e6	0.163341
$584$	−1.71420e6	−0.207984
$585$	−4.43348e6	−0.535618
$586$	−927563.	−0.111583
$587$	−1.94475e6	−0.232953	−0.116476	−	0.993193i	$-0.537160\pi$
$587$	−1.94475e6	−0.232953	−0.116476	+	0.993193i	$0.537160\pi$
$588$	0	0
$589$	1.83519e7	2.17968
$590$	−515800.	−0.0610030
$591$	−3.83820e6	−0.452022
$592$	1.38212e7	1.62085
$593$	1.13830e7	1.32929	0.664645	−	0.747160i	$-0.268583\pi$
$593$	1.13830e7	1.32929	0.664645	+	0.747160i	$0.268583\pi$
$594$	−639156.	−0.0743260
$595$	0	0
$596$	8.69705e6	1.00290
$597$	−1.27771e6	−0.146723
$598$	2.22168e6	0.254055
$599$	−8.61360e6	−0.980884	−0.490442	−	0.871474i	$-0.663165\pi$
$599$	−8.61360e6	−0.980884	−0.490442	+	0.871474i	$0.663165\pi$
$600$	−143773.	−0.0163041
$601$	−8.45317e6	−0.954626	−0.477313	−	0.878733i	$-0.658389\pi$
$601$	−8.45317e6	−0.954626	−0.477313	+	0.878733i	$0.658389\pi$
$602$	0	0
$603$	6.37448e6	0.713923
$604$	−5.57861e6	−0.622205
$605$	429663.	0.0477242
$606$	368752.	0.0407900
$607$	−3.19212e6	−0.351647	−0.175824	−	0.984422i	$-0.556259\pi$
$607$	−3.19212e6	−0.351647	−0.175824	+	0.984422i	$0.556259\pi$
$608$	6.73736e6	0.739147
$609$	0	0
$610$	−661494.	−0.0719782
$611$	−1.72604e7	−1.87046
$612$	−1.19154e7	−1.28596
$613$	−5.59500e6	−0.601380	−0.300690	−	0.953722i	$-0.597217\pi$
$613$	−5.59500e6	−0.601380	−0.300690	+	0.953722i	$0.597217\pi$
$614$	819294.	0.0877039
$615$	−453868.	−0.0483884
$616$	0	0
$617$	−1.22656e7	−1.29711	−0.648553	−	0.761170i	$-0.724626\pi$
$617$	−1.22656e7	−1.29711	−0.648553	+	0.761170i	$0.724626\pi$
$618$	−66749.7	−0.00703036
$619$	1.46717e7	1.53905	0.769526	−	0.638616i	$-0.220493\pi$
$619$	1.46717e7	1.53905	0.769526	+	0.638616i	$0.220493\pi$
$620$	4.99442e6	0.521802
$621$	7.67651e6	0.798794
$622$	−214454.	−0.0222259
$623$	0	0
$624$	−3.59890e6	−0.370005
$625$	390625.	0.0400000
$626$	1.52793e6	0.155835
$627$	5.08695e6	0.516759
$628$	9.91006e6	1.00271
$629$	−2.45349e7	−2.47262
$630$	0	0
$631$	−5.64473e6	−0.564378	−0.282189	−	0.959359i	$-0.591060\pi$
$631$	−5.64473e6	−0.564378	−0.282189	+	0.959359i	$0.591060\pi$
$632$	1.89919e6	0.189136
$633$	936581.	0.0929043
$634$	504251.	0.0498223
$635$	−3.69972e6	−0.364112
$636$	−515984.	−0.0505817
$637$	0	0
$638$	149309.	0.0145223
$639$	5.84452e6	0.566235
$640$	2.43648e6	0.235133
$641$	−1.04615e7	−1.00566	−0.502830	−	0.864386i	$-0.667708\pi$
$641$	−1.04615e7	−1.00566	−0.502830	+	0.864386i	$0.667708\pi$
$642$	184657.	0.0176819
$643$	−5.52421e6	−0.526918	−0.263459	−	0.964671i	$-0.584863\pi$
$643$	−5.52421e6	−0.526918	−0.263459	+	0.964671i	$0.584863\pi$
$644$	0	0
$645$	1.10405e6	0.104493
$646$	−3.85794e6	−0.363725
$647$	−5.62091e6	−0.527893	−0.263946	−	0.964537i	$-0.585024\pi$
$647$	−5.62091e6	−0.527893	−0.263946	+	0.964537i	$0.585024\pi$
$648$	−2.16380e6	−0.202432
$649$	1.00297e7	0.934709
$650$	−390659.	−0.0362672
$651$	0	0
$652$	−1.08600e7	−1.00048
$653$	1.27629e7	1.17129	0.585646	−	0.810567i	$-0.300841\pi$
$653$	1.27629e7	1.17129	0.585646	+	0.810567i	$0.300841\pi$
$654$	566785.	0.0518172
$655$	4.59954e6	0.418901
$656$	3.77048e6	0.342088
$657$	−7.67220e6	−0.693436
$658$	0	0
$659$	−1.54453e6	−0.138543	−0.0692713	−	0.997598i	$-0.522067\pi$
$659$	−1.54453e6	−0.138543	−0.0692713	+	0.997598i	$0.522067\pi$
$660$	1.38440e6	0.123709
$661$	1.56476e7	1.39298	0.696491	−	0.717566i	$-0.254744\pi$
$661$	1.56476e7	1.39298	0.696491	+	0.717566i	$0.254744\pi$
$662$	−644303.	−0.0571407
$663$	6.38861e6	0.564446
$664$	3.03880e6	0.267475
$665$	0	0
$666$	−2.47143e6	−0.215905
$667$	−1.79326e6	−0.156074
$668$	−1.36662e7	−1.18497
$669$	3.81725e6	0.329751
$670$	561691.	0.0483404
$671$	1.28627e7	1.10287
$672$	0	0
$673$	1.65914e7	1.41203	0.706017	−	0.708195i	$-0.250490\pi$
$673$	1.65914e7	1.41203	0.706017	+	0.708195i	$0.250490\pi$
$674$	2.39282e6	0.202890
$675$	−1.34983e6	−0.114030
$676$	−8.49040e6	−0.714598
$677$	1.02816e7	0.862160	0.431080	−	0.902314i	$-0.358133\pi$
$677$	1.02816e7	0.862160	0.431080	+	0.902314i	$0.358133\pi$
$678$	−195075.	−0.0162977
$679$	0	0
$680$	−2.12022e6	−0.175836
$681$	2.28353e6	0.188686
$682$	1.88340e6	0.155054
$683$	1.85658e7	1.52287	0.761435	−	0.648241i	$-0.224495\pi$
$683$	1.85658e7	1.52287	0.761435	+	0.648241i	$0.224495\pi$
$684$	2.00387e7	1.63768
$685$	1.88443e6	0.153445
$686$	0	0
$687$	−4.02940e6	−0.325723
$688$	−9.17181e6	−0.738727
$689$	−2.83125e6	−0.227212
$690$	322456.	0.0257839
$691$	1.70135e6	0.135550	0.0677750	−	0.997701i	$-0.478410\pi$
$691$	1.70135e6	0.135550	0.0677750	+	0.997701i	$0.478410\pi$
$692$	3.20072e6	0.254087
$693$	0	0
$694$	2.35921e6	0.185938
$695$	1.31227e6	0.103053
$696$	−116058.	−0.00908141
$697$	−6.69320e6	−0.521858
$698$	2.45831e6	0.190985
$699$	5.69655e6	0.440980
$700$	0	0
$701$	−9.75235e6	−0.749574	−0.374787	−	0.927111i	$-0.622284\pi$
$701$	−9.75235e6	−0.749574	−0.374787	+	0.927111i	$0.622284\pi$
$702$	1.34995e6	0.103389
$703$	4.12615e7	3.14889
$704$	−1.10324e7	−0.838958
$705$	−2.50519e6	−0.189831
$706$	2.20806e6	0.166724
$707$	0	0
$708$	−3.86062e6	−0.289450
$709$	−1.45512e7	−1.08713	−0.543567	−	0.839366i	$-0.682926\pi$
$709$	−1.45512e7	−1.08713	−0.543567	+	0.839366i	$0.682926\pi$
$710$	514994.	0.0383403
$711$	8.50013e6	0.630597
$712$	−7.12193e6	−0.526499
$713$	−2.26204e7	−1.66639
$714$	0	0
$715$	7.59634e6	0.555699
$716$	5.68930e6	0.414740
$717$	3.85013e6	0.279690
$718$	−2.07468e6	−0.150189
$719$	−9.28338e6	−0.669705	−0.334853	−	0.942271i	$-0.608687\pi$
$719$	−9.28338e6	−0.669705	−0.334853	+	0.942271i	$0.608687\pi$
$720$	5.34566e6	0.384300
$721$	0	0
$722$	4.55613e6	0.325277
$723$	2.26600e6	0.161219
$724$	9.25013e6	0.655845
$725$	315326.	0.0222800
$726$	−62366.9	−0.00439150
$727$	−1.09540e7	−0.768662	−0.384331	−	0.923195i	$-0.625568\pi$
$727$	−1.09540e7	−0.768662	−0.384331	+	0.923195i	$0.625568\pi$
$728$	0	0
$729$	−7.24359e6	−0.504818
$730$	−676041.	−0.0469533
$731$	1.62814e7	1.12693
$732$	−4.95109e6	−0.341526
$733$	−2.49754e7	−1.71693	−0.858465	−	0.512871i	$-0.828582\pi$
$733$	−2.49754e7	−1.71693	−0.858465	+	0.512871i	$0.828582\pi$
$734$	3.13063e6	0.214482
$735$	0	0
$736$	−8.30444e6	−0.565087
$737$	−1.09221e7	−0.740689
$738$	−674216.	−0.0455678
$739$	−9.22124e6	−0.621124	−0.310562	−	0.950553i	$-0.600517\pi$
$739$	−9.22124e6	−0.621124	−0.310562	+	0.950553i	$0.600517\pi$
$740$	1.12292e7	0.753825
$741$	−1.07440e7	−0.718824
$742$	0	0
$743$	3.86796e6	0.257045	0.128523	−	0.991707i	$-0.458977\pi$
$743$	3.86796e6	0.257045	0.128523	+	0.991707i	$0.458977\pi$
$744$	−1.46397e6	−0.0969618
$745$	6.92634e6	0.457207
$746$	−861416.	−0.0566717
$747$	1.36007e7	0.891783
$748$	2.04158e7	1.33417
$749$	0	0
$750$	−56700.5	−0.00368073
$751$	2.30393e7	1.49063	0.745316	−	0.666712i	$-0.232299\pi$
$751$	2.30393e7	1.49063	0.745316	+	0.666712i	$0.232299\pi$
$752$	2.08117e7	1.34203
$753$	4.87312e6	0.313199
$754$	−315354.	−0.0202008
$755$	−4.44281e6	−0.283655
$756$	0	0
$757$	3.43239e6	0.217699	0.108850	−	0.994058i	$-0.465283\pi$
$757$	3.43239e6	0.217699	0.108850	+	0.994058i	$0.465283\pi$
$758$	−2.09495e6	−0.132434
$759$	−6.27014e6	−0.395069
$760$	3.56568e6	0.223928
$761$	−1.58931e6	−0.0994826	−0.0497413	−	0.998762i	$-0.515840\pi$
$761$	−1.58931e6	−0.0994826	−0.0497413	+	0.998762i	$0.515840\pi$
$762$	537027.	0.0335049
$763$	0	0
$764$	1.53499e7	0.951419
$765$	−9.48940e6	−0.586253
$766$	−1.42714e6	−0.0878812
$767$	−2.11836e7	−1.30020
$768$	3.97528e6	0.243201
$769$	877265.	0.0534952	0.0267476	−	0.999642i	$-0.491485\pi$
$769$	877265.	0.0534952	0.0267476	+	0.999642i	$0.491485\pi$
$770$	0	0
$771$	5.78635e6	0.350565
$772$	2.98333e7	1.80160
$773$	−2.77626e7	−1.67113	−0.835567	−	0.549388i	$-0.814861\pi$
$773$	−2.77626e7	−1.67113	−0.835567	+	0.549388i	$0.814861\pi$
$774$	1.64005e6	0.0984022
$775$	3.97756e6	0.237883
$776$	74144.9	0.00442005
$777$	0	0
$778$	1.05349e6	0.0623993
$779$	1.12563e7	0.664588
$780$	−2.92397e6	−0.172082
$781$	−1.00140e7	−0.587464
$782$	4.75527e6	0.278073
$783$	−1.08963e6	−0.0635150
$784$	0	0
$785$	7.89239e6	0.457124
$786$	−667639.	−0.0385465
$787$	6.35578e6	0.365790	0.182895	−	0.983132i	$-0.441453\pi$
$787$	6.35578e6	0.365790	0.182895	+	0.983132i	$0.441453\pi$
$788$	2.59059e7	1.48622
$789$	−6.73327e6	−0.385064
$790$	748994.	0.0426983
$791$	0	0
$792$	4.15291e6	0.235256
$793$	−2.71671e7	−1.53412
$794$	2.58750e6	0.145656
$795$	−410930.	−0.0230595
$796$	8.62392e6	0.482417
$797$	−1.32562e7	−0.739220	−0.369610	−	0.929187i	$-0.620509\pi$
$797$	−1.32562e7	−0.739220	−0.369610	+	0.929187i	$0.620509\pi$
$798$	0	0
$799$	−3.69441e7	−2.04728
$800$	1.46025e6	0.0806680
$801$	−3.18754e7	−1.75539
$802$	−1.91277e6	−0.105009
$803$	1.31456e7	0.719434
$804$	4.20410e6	0.229368
$805$	0	0
$806$	−3.97790e6	−0.215683
$807$	−2.68200e6	−0.144969
$808$	−5.02605e6	−0.270831
$809$	3.36780e7	1.80915	0.904577	−	0.426311i	$-0.140187\pi$
$809$	3.36780e7	1.80915	0.904577	+	0.426311i	$0.140187\pi$
$810$	−853351.	−0.0456999
$811$	1.97559e6	0.105474	0.0527368	−	0.998608i	$-0.483206\pi$
$811$	1.97559e6	0.105474	0.0527368	+	0.998608i	$0.483206\pi$
$812$	0	0
$813$	8.30085e6	0.440450
$814$	4.23456e6	0.224000
$815$	−8.64889e6	−0.456107
$816$	−7.70306e6	−0.404984
$817$	−2.73813e7	−1.43515
$818$	−508219.	−0.0265563
$819$	0	0
$820$	3.06338e6	0.159098
$821$	2.04969e6	0.106128	0.0530641	−	0.998591i	$-0.483101\pi$
$821$	2.04969e6	0.106128	0.0530641	+	0.998591i	$0.483101\pi$
$822$	−273531.	−0.0141198
$823$	2.90679e7	1.49594	0.747970	−	0.663732i	$-0.231028\pi$
$823$	2.90679e7	1.49594	0.747970	+	0.663732i	$0.231028\pi$
$824$	909790.	0.0466792
$825$	1.10254e6	0.0563974
$826$	0	0
$827$	1.95711e7	0.995064	0.497532	−	0.867446i	$-0.334240\pi$
$827$	1.95711e7	0.995064	0.497532	+	0.867446i	$0.334240\pi$
$828$	−2.46995e7	−1.25203
$829$	−3.41027e6	−0.172346	−0.0861732	−	0.996280i	$-0.527464\pi$
$829$	−3.41027e6	−0.172346	−0.0861732	+	0.996280i	$0.527464\pi$
$830$	1.19843e6	0.0603835
$831$	1.15889e6	0.0582155
$832$	2.33014e7	1.16701
$833$	0	0
$834$	−190481.	−0.00948278
$835$	−1.08838e7	−0.540211
$836$	−3.43343e7	−1.69908
$837$	−1.37448e7	−0.678146
$838$	−3.16251e6	−0.155568
$839$	−5.78503e6	−0.283727	−0.141864	−	0.989886i	$-0.545309\pi$
$839$	−5.78503e6	−0.283727	−0.141864	+	0.989886i	$0.545309\pi$
$840$	0	0
$841$	−2.02566e7	−0.987590
$842$	3.63150e6	0.176525
$843$	9.76047e6	0.473044
$844$	−6.32144e6	−0.305464
$845$	−6.76177e6	−0.325775
$846$	−3.72143e6	−0.178766
$847$	0	0
$848$	3.41378e6	0.163022
$849$	2.98661e6	0.142203
$850$	−836164.	−0.0396958
$851$	−5.08587e7	−2.40736
$852$	3.85458e6	0.181919
$853$	4.20141e6	0.197707	0.0988535	−	0.995102i	$-0.468482\pi$
$853$	4.20141e6	0.197707	0.0988535	+	0.995102i	$0.468482\pi$
$854$	0	0
$855$	1.59588e7	0.746595
$856$	−2.51686e6	−0.117402
$857$	−2.50742e7	−1.16621	−0.583104	−	0.812398i	$-0.698162\pi$
$857$	−2.50742e7	−1.16621	−0.583104	+	0.812398i	$0.698162\pi$
$858$	−1.10263e6	−0.0511344
$859$	−3.30203e7	−1.52686	−0.763429	−	0.645892i	$-0.776486\pi$
$859$	−3.30203e7	−1.52686	−0.763429	+	0.645892i	$0.776486\pi$
$860$	−7.45176e6	−0.343568
$861$	0	0
$862$	1.49897e6	0.0687109
$863$	1.79270e7	0.819370	0.409685	−	0.912227i	$-0.365639\pi$
$863$	1.79270e7	0.819370	0.409685	+	0.912227i	$0.365639\pi$
$864$	−5.04600e6	−0.229965
$865$	2.54906e6	0.115835
$866$	3.55692e6	0.161168
$867$	7.07054e6	0.319451
$868$	0	0
$869$	−1.45642e7	−0.654238
$870$	−45770.7	−0.00205017
$871$	2.30683e7	1.03031
$872$	−7.72521e6	−0.344048
$873$	331848.	0.0147368
$874$	−7.99718e6	−0.354126
$875$	0	0
$876$	−5.05997e6	−0.222786
$877$	1.34831e7	0.591956	0.295978	−	0.955195i	$-0.404354\pi$
$877$	1.34831e7	0.591956	0.295978	+	0.955195i	$0.404354\pi$
$878$	690365.	0.0302234
$879$	−5.52905e6	−0.241367
$880$	−9.15928e6	−0.398708
$881$	1.30003e7	0.564304	0.282152	−	0.959370i	$-0.408952\pi$
$881$	1.30003e7	0.564304	0.282152	+	0.959370i	$0.408952\pi$
$882$	0	0
$883$	1.30021e7	0.561194	0.280597	−	0.959826i	$-0.409468\pi$
$883$	1.30021e7	0.561194	0.280597	+	0.959826i	$0.409468\pi$
$884$	−4.31199e7	−1.85587
$885$	−3.07460e6	−0.131956
$886$	5.87388e6	0.251386
$887$	−3.48525e7	−1.48739	−0.743694	−	0.668520i	$-0.766928\pi$
$887$	−3.48525e7	−1.48739	−0.743694	+	0.668520i	$0.766928\pi$
$888$	−3.29153e6	−0.140077
$889$	0	0
$890$	−2.80872e6	−0.118859
$891$	1.65934e7	0.700230
$892$	−2.57645e7	−1.08420
$893$	6.21307e7	2.60722
$894$	−1.00538e6	−0.0420714
$895$	4.53096e6	0.189074
$896$	0	0
$897$	1.32431e7	0.549550
$898$	−2.08044e6	−0.0860924
$899$	3.21083e6	0.132501
$900$	4.34315e6	0.178731
$901$	−6.06000e6	−0.248691
$902$	1.15521e6	0.0472762
$903$	0	0
$904$	2.65884e6	0.108211
$905$	7.36681e6	0.298991
$906$	644888.	0.0261014
$907$	−3.79566e6	−0.153204	−0.0766018	−	0.997062i	$-0.524407\pi$
$907$	−3.79566e6	−0.153204	−0.0766018	+	0.997062i	$0.524407\pi$
$908$	−1.54127e7	−0.620389
$909$	−2.24949e7	−0.902974
$910$	0	0
$911$	−3.28696e7	−1.31219	−0.656097	−	0.754677i	$-0.727794\pi$
$911$	−3.28696e7	−1.31219	−0.656097	+	0.754677i	$0.727794\pi$
$912$	1.29546e7	0.515749
$913$	−2.33035e7	−0.925217
$914$	−215579.	−0.00853572
$915$	−3.94305e6	−0.155697
$916$	2.71964e7	1.07096
$917$	0	0
$918$	2.88943e6	0.113163
$919$	−6.61639e6	−0.258424	−0.129212	−	0.991617i	$-0.541245\pi$
$919$	−6.61639e6	−0.258424	−0.129212	+	0.991617i	$0.541245\pi$
$920$	−4.39504e6	−0.171196
$921$	4.88368e6	0.189713
$922$	−3.08187e6	−0.119395
$923$	2.11504e7	0.817176
$924$	0	0
$925$	8.94297e6	0.343659
$926$	−7.03755e6	−0.269708
$927$	4.07192e6	0.155632
$928$	1.17876e6	0.0449321
$929$	2.66354e7	1.01256	0.506279	−	0.862370i	$-0.331021\pi$
$929$	2.66354e7	1.01256	0.506279	+	0.862370i	$0.331021\pi$
$930$	−577356.	−0.0218895
$931$	0	0
$932$	−3.84488e7	−1.44992
$933$	−1.27833e6	−0.0480771
$934$	−5.40010e6	−0.202551
$935$	1.62592e7	0.608232
$936$	−8.77129e6	−0.327246
$937$	1.20665e6	0.0448986	0.0224493	−	0.999748i	$-0.492854\pi$
$937$	1.20665e6	0.0448986	0.0224493	+	0.999748i	$0.492854\pi$
$938$	0	0
$939$	9.10771e6	0.337090
$940$	1.69087e7	0.624154
$941$	−8.71612e6	−0.320885	−0.160442	−	0.987045i	$-0.551292\pi$
$941$	−8.71612e6	−0.320885	−0.160442	+	0.987045i	$0.551292\pi$
$942$	−1.14561e6	−0.0420637
$943$	−1.38745e7	−0.508086
$944$	2.55421e7	0.932881
$945$	0	0
$946$	−2.81007e6	−0.102091
$947$	−1.13077e7	−0.409730	−0.204865	−	0.978790i	$-0.565676\pi$
$947$	−1.13077e7	−0.409730	−0.204865	+	0.978790i	$0.565676\pi$
$948$	5.60601e6	0.202597
$949$	−2.77645e7	−1.00075
$950$	1.40622e6	0.0505527
$951$	3.00576e6	0.107771
$952$	0	0
$953$	1.75327e7	0.625340	0.312670	−	0.949862i	$-0.398777\pi$
$953$	1.75327e7	0.625340	0.312670	+	0.949862i	$0.398777\pi$
$954$	−610433.	−0.0217153
$955$	1.22247e7	0.433739
$956$	−2.59864e7	−0.919605
$957$	890009.	0.0314134
$958$	94625.4	0.00333115
$959$	0	0
$960$	3.38199e6	0.118439
$961$	1.18726e7	0.414702
$962$	−8.94374e6	−0.311589
$963$	−1.12646e7	−0.391427
$964$	−1.52944e7	−0.530077
$965$	2.37593e7	0.821324
$966$	0	0
$967$	8.62619e6	0.296656	0.148328	−	0.988938i	$-0.452611\pi$
$967$	8.62619e6	0.296656	0.148328	+	0.988938i	$0.452611\pi$
$968$	850054.	0.0291580
$969$	−2.29965e7	−0.786779
$970$	29241.0	0.000997844 0
$971$	−5.54825e7	−1.88846	−0.944231	−	0.329284i	$-0.893193\pi$
$971$	−5.54825e7	−1.88846	−0.944231	+	0.329284i	$0.893193\pi$
$972$	−2.28617e7	−0.776145
$973$	0	0
$974$	−1.01103e6	−0.0341482
$975$	−2.32865e6	−0.0784500
$976$	3.27567e7	1.10072
$977$	−3.72258e7	−1.24769	−0.623846	−	0.781547i	$-0.714431\pi$
$977$	−3.72258e7	−1.24769	−0.623846	+	0.781547i	$0.714431\pi$
$978$	1.25542e6	0.0419701
$979$	5.46155e7	1.82120
$980$	0	0
$981$	−3.45755e7	−1.14709
$982$	6.25567e6	0.207012
$983$	−300859.	−0.00993068	−0.00496534	−	0.999988i	$-0.501581\pi$
$983$	−300859.	−0.00993068	−0.00496534	+	0.999988i	$0.501581\pi$
$984$	−897942.	−0.0295638
$985$	2.06315e7	0.677548
$986$	−674982.	−0.0221106
$987$	0	0
$988$	7.25169e7	2.36345
$989$	3.37500e7	1.09719
$990$	1.63781e6	0.0531099
$991$	−3.50772e7	−1.13460	−0.567298	−	0.823513i	$-0.692011\pi$
$991$	−3.50772e7	−1.13460	−0.567298	+	0.823513i	$0.692011\pi$
$992$	1.48691e7	0.479738
$993$	−3.84059e6	−0.123602
$994$	0	0
$995$	6.86810e6	0.219927
$996$	8.96993e6	0.286511
$997$	2.27730e7	0.725576	0.362788	−	0.931872i	$-0.381825\pi$
$997$	2.27730e7	0.725576	0.362788	+	0.931872i	$0.381825\pi$
$998$	4.43641e6	0.140996
$999$	−3.09031e7	−0.979690

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.6.a.g.1.3	yes	5
7.6	odd	2		245.6.a.f.1.3	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
245.6.a.f.1.3	✓	5	7.6	odd	2
245.6.a.g.1.3	yes	5	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+0.780243 q^{2} +4.65090 q^{3} -31.3912 q^{4} -25.0000 q^{5} +3.62883 q^{6} -49.4606 q^{8} -221.369 q^{9} +O(q^{10})\)	\(q+0.780243 q^{2} +4.65090 q^{3} -31.3912 q^{4} -25.0000 q^{5} +3.62883 q^{6} -49.4606 q^{8} -221.369 q^{9} -19.5061 q^{10} +379.295 q^{11} -145.997 q^{12} -801.101 q^{13} -116.273 q^{15} +965.928 q^{16} -1714.67 q^{17} -172.722 q^{18} +2883.66 q^{19} +784.781 q^{20} +295.942 q^{22} -3554.38 q^{23} -230.036 q^{24} +625.000 q^{25} -625.054 q^{26} -2159.73 q^{27} +504.522 q^{29} -90.7208 q^{30} +6364.10 q^{31} +2336.40 q^{32} +1764.06 q^{33} -1337.86 q^{34} +6949.05 q^{36} +14308.8 q^{37} +2249.95 q^{38} -3725.84 q^{39} +1236.51 q^{40} +3903.48 q^{41} -9495.34 q^{43} -11906.5 q^{44} +5534.23 q^{45} -2773.28 q^{46} +21545.8 q^{47} +4492.43 q^{48} +487.652 q^{50} -7974.78 q^{51} +25147.6 q^{52} +3534.20 q^{53} -1685.12 q^{54} -9482.37 q^{55} +13411.6 q^{57} +393.650 q^{58} +26443.0 q^{59} +3649.94 q^{60} +33912.2 q^{61} +4965.54 q^{62} -29086.7 q^{64} +20027.5 q^{65} +1376.40 q^{66} -28795.7 q^{67} +53825.7 q^{68} -16531.1 q^{69} -26401.7 q^{71} +10949.0 q^{72} +34658.0 q^{73} +11164.3 q^{74} +2906.81 q^{75} -90521.5 q^{76} -2907.06 q^{78} -38398.0 q^{79} -24148.2 q^{80} +43748.0 q^{81} +3045.67 q^{82} -61438.9 q^{83} +42866.9 q^{85} -7408.67 q^{86} +2346.48 q^{87} -18760.1 q^{88} +143992. q^{89} +4318.04 q^{90} +111576. q^{92} +29598.8 q^{93} +16811.0 q^{94} -72091.4 q^{95} +10866.3 q^{96} -1499.07 q^{97} -83964.1 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 3 q^{2} + 7 q^{3} + 101 q^{4} - 125 q^{5} + 304 q^{6} - 675 q^{8} + 284 q^{9}+O(q^{10}) \) 5 * q - 3 * q^2 + 7 * q^3 + 101 * q^4 - 125 * q^5 + 304 * q^6 - 675 * q^8 + 284 * q^9	\( 5 q - 3 q^{2} + 7 q^{3} + 101 q^{4} - 125 q^{5} + 304 q^{6} - 675 q^{8} + 284 q^{9} + 75 q^{10} + 1033 q^{11} - 1226 q^{12} + 1117 q^{13} - 175 q^{15} + 297 q^{16} + 3403 q^{17} + 887 q^{18} + 2846 q^{19} - 2525 q^{20} - 1858 q^{22} - 2756 q^{23} + 13290 q^{24} + 3125 q^{25} + 2544 q^{26} + 3661 q^{27} + 485 q^{29} - 7600 q^{30} + 10726 q^{31} - 17383 q^{32} + 12597 q^{33} - 16414 q^{34} + 38165 q^{36} - 2660 q^{37} - 14378 q^{38} - 13171 q^{39} + 16875 q^{40} - 8334 q^{41} - 17294 q^{43} + 42876 q^{44} - 7100 q^{45} + 45724 q^{46} + 59799 q^{47} - 94218 q^{48} - 1875 q^{50} - 12049 q^{51} + 87974 q^{52} - 9250 q^{53} + 106342 q^{54} - 25825 q^{55} - 121778 q^{57} + 35868 q^{58} + 52994 q^{59} + 30650 q^{60} + 81540 q^{61} - 74048 q^{62} + 39745 q^{64} - 27925 q^{65} + 311614 q^{66} - 726 q^{67} + 276216 q^{68} + 21388 q^{69} + 3760 q^{71} - 154815 q^{72} + 90634 q^{73} - 57342 q^{74} + 4375 q^{75} + 43902 q^{76} + 152598 q^{78} + 68243 q^{79} - 7425 q^{80} + 17645 q^{81} + 191552 q^{82} - 133292 q^{83} - 85075 q^{85} - 88352 q^{86} + 216813 q^{87} - 273040 q^{88} + 102852 q^{89} - 22175 q^{90} - 140852 q^{92} + 184862 q^{93} + 332618 q^{94} - 71150 q^{95} + 245574 q^{96} + 186175 q^{97} + 454710 q^{99}+O(q^{100}) \) 5 * q - 3 * q^2 + 7 * q^3 + 101 * q^4 - 125 * q^5 + 304 * q^6 - 675 * q^8 + 284 * q^9 + 75 * q^10 + 1033 * q^11 - 1226 * q^12 + 1117 * q^13 - 175 * q^15 + 297 * q^16 + 3403 * q^17 + 887 * q^18 + 2846 * q^19 - 2525 * q^20 - 1858 * q^22 - 2756 * q^23 + 13290 * q^24 + 3125 * q^25 + 2544 * q^26 + 3661 * q^27 + 485 * q^29 - 7600 * q^30 + 10726 * q^31 - 17383 * q^32 + 12597 * q^33 - 16414 * q^34 + 38165 * q^36 - 2660 * q^37 - 14378 * q^38 - 13171 * q^39 + 16875 * q^40 - 8334 * q^41 - 17294 * q^43 + 42876 * q^44 - 7100 * q^45 + 45724 * q^46 + 59799 * q^47 - 94218 * q^48 - 1875 * q^50 - 12049 * q^51 + 87974 * q^52 - 9250 * q^53 + 106342 * q^54 - 25825 * q^55 - 121778 * q^57 + 35868 * q^58 + 52994 * q^59 + 30650 * q^60 + 81540 * q^61 - 74048 * q^62 + 39745 * q^64 - 27925 * q^65 + 311614 * q^66 - 726 * q^67 + 276216 * q^68 + 21388 * q^69 + 3760 * q^71 - 154815 * q^72 + 90634 * q^73 - 57342 * q^74 + 4375 * q^75 + 43902 * q^76 + 152598 * q^78 + 68243 * q^79 - 7425 * q^80 + 17645 * q^81 + 191552 * q^82 - 133292 * q^83 - 85075 * q^85 - 88352 * q^86 + 216813 * q^87 - 273040 * q^88 + 102852 * q^89 - 22175 * q^90 - 140852 * q^92 + 184862 * q^93 + 332618 * q^94 - 71150 * q^95 + 245574 * q^96 + 186175 * q^97 + 454710 * q^99

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