LMFDB - Embedded newform 105.4.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,4,Mod(1,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("105.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	105.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:	$6.19520055060$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{17}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 4 $ x^2 - x - 4
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.56155$ of defining polynomial
Character	$\chi$	$=$	105.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.56155 q^{2} -3.00000 q^{3} +22.9309 q^{4} -5.00000 q^{5} +16.6847 q^{6} -7.00000 q^{7} -83.0388 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-5.56155 q^{2} -3.00000 q^{3} +22.9309 q^{4} -5.00000 q^{5} +16.6847 q^{6} -7.00000 q^{7} -83.0388 q^{8} +9.00000 q^{9} +27.8078 q^{10} -33.6155 q^{11} -68.7926 q^{12} -38.3542 q^{13} +38.9309 q^{14} +15.0000 q^{15} +278.378 q^{16} +65.7235 q^{17} -50.0540 q^{18} +33.3996 q^{19} -114.654 q^{20} +21.0000 q^{21} +186.955 q^{22} +207.447 q^{23} +249.116 q^{24} +25.0000 q^{25} +213.309 q^{26} -27.0000 q^{27} -160.516 q^{28} -189.170 q^{29} -83.4233 q^{30} +202.108 q^{31} -883.902 q^{32} +100.847 q^{33} -365.525 q^{34} +35.0000 q^{35} +206.378 q^{36} -16.5227 q^{37} -185.754 q^{38} +115.062 q^{39} +415.194 q^{40} +388.617 q^{41} -116.793 q^{42} +41.8144 q^{43} -770.833 q^{44} -45.0000 q^{45} -1153.73 q^{46} +368.648 q^{47} -835.133 q^{48} +49.0000 q^{49} -139.039 q^{50} -197.170 q^{51} -879.494 q^{52} +458.172 q^{53} +150.162 q^{54} +168.078 q^{55} +581.272 q^{56} -100.199 q^{57} +1052.08 q^{58} +256.216 q^{59} +343.963 q^{60} -123.511 q^{61} -1124.03 q^{62} -63.0000 q^{63} +2688.85 q^{64} +191.771 q^{65} -560.864 q^{66} -336.277 q^{67} +1507.10 q^{68} -622.341 q^{69} -194.654 q^{70} -453.312 q^{71} -747.349 q^{72} +22.0436 q^{73} +91.8920 q^{74} -75.0000 q^{75} +765.882 q^{76} +235.309 q^{77} -639.926 q^{78} +385.417 q^{79} -1391.89 q^{80} +81.0000 q^{81} -2161.32 q^{82} +23.7501 q^{83} +481.548 q^{84} -328.617 q^{85} -232.553 q^{86} +567.511 q^{87} +2791.39 q^{88} -1482.81 q^{89} +250.270 q^{90} +268.479 q^{91} +4756.94 q^{92} -606.324 q^{93} -2050.25 q^{94} -166.998 q^{95} +2651.71 q^{96} +51.9867 q^{97} -272.516 q^{98} -302.540 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 7 q^{2} - 6 q^{3} + 17 q^{4} - 10 q^{5} + 21 q^{6} - 14 q^{7} - 63 q^{8} + 18 q^{9}+O(q^{10}) $ 2 * q - 7 * q^2 - 6 * q^3 + 17 * q^4 - 10 * q^5 + 21 * q^6 - 14 * q^7 - 63 * q^8 + 18 * q^9	\( 2 q - 7 q^{2} - 6 q^{3} + 17 q^{4} - 10 q^{5} + 21 q^{6} - 14 q^{7} - 63 q^{8} + 18 q^{9} + 35 q^{10} - 26 q^{11} - 51 q^{12} + 14 q^{13} + 49 q^{14} + 30 q^{15} + 297 q^{16} + 16 q^{17} - 63 q^{18} + 174 q^{19} - 85 q^{20} + 42 q^{21} + 176 q^{22} + 184 q^{23} + 189 q^{24} + 50 q^{25} + 138 q^{26} - 54 q^{27} - 119 q^{28} - 32 q^{29} - 105 q^{30} + 330 q^{31} - 1071 q^{32} + 78 q^{33} - 294 q^{34} + 70 q^{35} + 153 q^{36} - 132 q^{37} - 388 q^{38} - 42 q^{39} + 315 q^{40} + 200 q^{41} - 147 q^{42} + 364 q^{43} - 816 q^{44} - 90 q^{45} - 1120 q^{46} + 292 q^{47} - 891 q^{48} + 98 q^{49} - 175 q^{50} - 48 q^{51} - 1190 q^{52} + 34 q^{53} + 189 q^{54} + 130 q^{55} + 441 q^{56} - 522 q^{57} + 826 q^{58} + 364 q^{59} + 255 q^{60} + 792 q^{61} - 1308 q^{62} - 126 q^{63} + 2809 q^{64} - 70 q^{65} - 528 q^{66} - 788 q^{67} + 1802 q^{68} - 552 q^{69} - 245 q^{70} + 454 q^{71} - 567 q^{72} + 778 q^{73} + 258 q^{74} - 150 q^{75} - 68 q^{76} + 182 q^{77} - 414 q^{78} + 408 q^{79} - 1485 q^{80} + 162 q^{81} - 1890 q^{82} + 1136 q^{83} + 357 q^{84} - 80 q^{85} - 696 q^{86} + 96 q^{87} + 2944 q^{88} + 36 q^{89} + 315 q^{90} - 98 q^{91} + 4896 q^{92} - 990 q^{93} - 1940 q^{94} - 870 q^{95} + 3213 q^{96} - 498 q^{97} - 343 q^{98} - 234 q^{99}+O(q^{100}) \) 2 * q - 7 * q^2 - 6 * q^3 + 17 * q^4 - 10 * q^5 + 21 * q^6 - 14 * q^7 - 63 * q^8 + 18 * q^9 + 35 * q^10 - 26 * q^11 - 51 * q^12 + 14 * q^13 + 49 * q^14 + 30 * q^15 + 297 * q^16 + 16 * q^17 - 63 * q^18 + 174 * q^19 - 85 * q^20 + 42 * q^21 + 176 * q^22 + 184 * q^23 + 189 * q^24 + 50 * q^25 + 138 * q^26 - 54 * q^27 - 119 * q^28 - 32 * q^29 - 105 * q^30 + 330 * q^31 - 1071 * q^32 + 78 * q^33 - 294 * q^34 + 70 * q^35 + 153 * q^36 - 132 * q^37 - 388 * q^38 - 42 * q^39 + 315 * q^40 + 200 * q^41 - 147 * q^42 + 364 * q^43 - 816 * q^44 - 90 * q^45 - 1120 * q^46 + 292 * q^47 - 891 * q^48 + 98 * q^49 - 175 * q^50 - 48 * q^51 - 1190 * q^52 + 34 * q^53 + 189 * q^54 + 130 * q^55 + 441 * q^56 - 522 * q^57 + 826 * q^58 + 364 * q^59 + 255 * q^60 + 792 * q^61 - 1308 * q^62 - 126 * q^63 + 2809 * q^64 - 70 * q^65 - 528 * q^66 - 788 * q^67 + 1802 * q^68 - 552 * q^69 - 245 * q^70 + 454 * q^71 - 567 * q^72 + 778 * q^73 + 258 * q^74 - 150 * q^75 - 68 * q^76 + 182 * q^77 - 414 * q^78 + 408 * q^79 - 1485 * q^80 + 162 * q^81 - 1890 * q^82 + 1136 * q^83 + 357 * q^84 - 80 * q^85 - 696 * q^86 + 96 * q^87 + 2944 * q^88 + 36 * q^89 + 315 * q^90 - 98 * q^91 + 4896 * q^92 - 990 * q^93 - 1940 * q^94 - 870 * q^95 + 3213 * q^96 - 498 * q^97 - 343 * q^98 - 234 * 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 $

$2$	−5.56155	−1.96631	−0.983153	−	0.182785i	$-0.941489\pi$
$2$	−5.56155	−1.96631	−0.983153	+	0.182785i	$0.941489\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	22.9309	2.86636
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	16.6847	1.13525
$7$	−7.00000	−0.377964
$7$	−7.00000	−0.377964
$8$	−83.0388	−3.66983
$9$	9.00000	0.333333
$10$	27.8078	0.879359
$11$	−33.6155	−0.921406	−0.460703	−	0.887554i	$-0.652403\pi$
$11$	−33.6155	−0.921406	−0.460703	+	0.887554i	$0.652403\pi$
$12$	−68.7926	−1.65489
$13$	−38.3542	−0.818272	−0.409136	−	0.912474i	$-0.634170\pi$
$13$	−38.3542	−0.818272	−0.409136	+	0.912474i	$0.634170\pi$
$14$	38.9309	0.743194
$15$	15.0000	0.258199
$16$	278.378	4.34965
$17$	65.7235	0.937664	0.468832	−	0.883287i	$-0.344675\pi$
$17$	65.7235	0.937664	0.468832	+	0.883287i	$0.344675\pi$
$18$	−50.0540	−0.655435
$19$	33.3996	0.403284	0.201642	−	0.979459i	$-0.435372\pi$
$19$	33.3996	0.403284	0.201642	+	0.979459i	$0.435372\pi$
$20$	−114.654	−1.28187
$21$	21.0000	0.218218
$22$	186.955	1.81177
$23$	207.447	1.88068	0.940341	−	0.340234i	$-0.110506\pi$
$23$	207.447	1.88068	0.940341	+	0.340234i	$0.110506\pi$
$24$	249.116	2.11878
$25$	25.0000	0.200000
$26$	213.309	1.60897
$27$	−27.0000	−0.192450
$28$	−160.516	−1.08338
$29$	−189.170	−1.21131	−0.605656	−	0.795726i	$-0.707089\pi$
$29$	−189.170	−1.21131	−0.605656	+	0.795726i	$0.707089\pi$
$30$	−83.4233	−0.507698
$31$	202.108	1.17096	0.585478	−	0.810688i	$-0.300907\pi$
$31$	202.108	1.17096	0.585478	+	0.810688i	$0.300907\pi$
$32$	−883.902	−4.88292
$33$	100.847	0.531974
$34$	−365.525	−1.84373
$35$	35.0000	0.169031
$36$	206.378	0.955453
$37$	−16.5227	−0.0734141	−0.0367070	−	0.999326i	$-0.511687\pi$
$37$	−16.5227	−0.0734141	−0.0367070	+	0.999326i	$0.511687\pi$
$38$	−185.754	−0.792980
$39$	115.062	0.472429
$40$	415.194	1.64120
$41$	388.617	1.48029	0.740144	−	0.672448i	$-0.234757\pi$
$41$	388.617	1.48029	0.740144	+	0.672448i	$0.234757\pi$
$42$	−116.793	−0.429083
$43$	41.8144	0.148294	0.0741469	−	0.997247i	$-0.476377\pi$
$43$	41.8144	0.148294	0.0741469	+	0.997247i	$0.476377\pi$
$44$	−770.833	−2.64108
$45$	−45.0000	−0.149071
$46$	−1153.73	−3.69800
$47$	368.648	1.14410	0.572051	−	0.820218i	$-0.306148\pi$
$47$	368.648	1.14410	0.572051	+	0.820218i	$0.306148\pi$
$48$	−835.133	−2.51127
$49$	49.0000	0.142857
$50$	−139.039	−0.393261
$51$	−197.170	−0.541360
$52$	−879.494	−2.34546
$53$	458.172	1.18745	0.593725	−	0.804668i	$-0.297657\pi$
$53$	458.172	1.18745	0.593725	+	0.804668i	$0.297657\pi$
$54$	150.162	0.378416
$55$	168.078	0.412065
$56$	581.272	1.38707
$57$	−100.199	−0.232836
$58$	1052.08	2.38181
$59$	256.216	0.565364	0.282682	−	0.959214i	$-0.408776\pi$
$59$	256.216	0.565364	0.282682	+	0.959214i	$0.408776\pi$
$60$	343.963	0.740091
$61$	−123.511	−0.259246	−0.129623	−	0.991563i	$-0.541377\pi$
$61$	−123.511	−0.259246	−0.129623	+	0.991563i	$0.541377\pi$
$62$	−1124.03	−2.30246
$63$	−63.0000	−0.125988
$64$	2688.85	5.25166
$65$	191.771	0.365942
$66$	−560.864	−1.04602
$67$	−336.277	−0.613175	−0.306587	−	0.951843i	$-0.599187\pi$
$67$	−336.277	−0.613175	−0.306587	+	0.951843i	$0.599187\pi$
$68$	1507.10	2.68768
$69$	−622.341	−1.08581
$70$	−194.654	−0.332366
$71$	−453.312	−0.757722	−0.378861	−	0.925454i	$-0.623684\pi$
$71$	−453.312	−0.757722	−0.378861	+	0.925454i	$0.623684\pi$
$72$	−747.349	−1.22328
$73$	22.0436	0.0353426	0.0176713	−	0.999844i	$-0.494375\pi$
$73$	22.0436	0.0353426	0.0176713	+	0.999844i	$0.494375\pi$
$74$	91.8920	0.144355
$75$	−75.0000	−0.115470
$76$	765.882	1.15596
$77$	235.309	0.348259
$78$	−639.926	−0.928941
$79$	385.417	0.548896	0.274448	−	0.961602i	$-0.411505\pi$
$79$	385.417	0.548896	0.274448	+	0.961602i	$0.411505\pi$
$80$	−1391.89	−1.94522
$81$	81.0000	0.111111
$82$	−2161.32	−2.91070
$83$	23.7501	0.0314085	0.0157043	−	0.999877i	$-0.495001\pi$
$83$	23.7501	0.0314085	0.0157043	+	0.999877i	$0.495001\pi$
$84$	481.548	0.625491
$85$	−328.617	−0.419336
$86$	−232.553	−0.291591
$87$	567.511	0.699352
$88$	2791.39	3.38140
$89$	−1482.81	−1.76604	−0.883020	−	0.469335i	$-0.844494\pi$
$89$	−1482.81	−1.76604	−0.883020	+	0.469335i	$0.844494\pi$
$90$	250.270	0.293120
$91$	268.479	0.309278
$92$	4756.94	5.39071
$93$	−606.324	−0.676052
$94$	−2050.25	−2.24965
$95$	−166.998	−0.180354
$96$	2651.71	2.81915
$97$	51.9867	0.0544170	0.0272085	−	0.999630i	$-0.491338\pi$
$97$	51.9867	0.0544170	0.0272085	+	0.999630i	$0.491338\pi$
$98$	−272.516	−0.280901
$99$	−302.540	−0.307135
$100$	573.272	0.573272
$101$	1429.30	1.40812	0.704062	−	0.710138i	$-0.251368\pi$
$101$	1429.30	1.40812	0.704062	+	0.710138i	$0.251368\pi$
$102$	1096.57	1.06448
$103$	434.212	0.415381	0.207690	−	0.978195i	$-0.433405\pi$
$103$	434.212	0.415381	0.207690	+	0.978195i	$0.433405\pi$
$104$	3184.88	3.00292
$105$	−105.000	−0.0975900
$106$	−2548.15	−2.33489
$107$	666.307	0.602003	0.301001	−	0.953624i	$-0.402679\pi$
$107$	666.307	0.602003	0.301001	+	0.953624i	$0.402679\pi$
$108$	−619.133	−0.551631
$109$	−1199.51	−1.05406	−0.527029	−	0.849847i	$-0.676694\pi$
$109$	−1199.51	−1.05406	−0.527029	+	0.849847i	$0.676694\pi$
$110$	−934.773	−0.810246
$111$	49.5682	0.0423856
$112$	−1948.64	−1.64401
$113$	−81.5171	−0.0678627	−0.0339314	−	0.999424i	$-0.510803\pi$
$113$	−81.5171	−0.0678627	−0.0339314	+	0.999424i	$0.510803\pi$
$114$	557.261	0.457827
$115$	−1037.23	−0.841066
$116$	−4337.84	−3.47206
$117$	−345.187	−0.272757
$118$	−1424.96	−1.11168
$119$	−460.064	−0.354404
$120$	−1245.58	−0.947547
$121$	−200.996	−0.151011
$122$	686.915	0.509757
$123$	−1165.85	−0.854645
$124$	4634.51	3.35638
$125$	−125.000	−0.0894427
$126$	350.378	0.247731
$127$	−336.985	−0.235453	−0.117727	−	0.993046i	$-0.537561\pi$
$127$	−336.985	−0.235453	−0.117727	+	0.993046i	$0.537561\pi$
$128$	−7882.95	−5.44344
$129$	−125.443	−0.0856175
$130$	−1066.54	−0.719554
$131$	2931.15	1.95493	0.977465	−	0.211097i	$-0.0677035\pi$
$131$	2931.15	1.95493	0.977465	+	0.211097i	$0.0677035\pi$
$132$	2312.50	1.52483
$133$	−233.797	−0.152427
$134$	1870.22	1.20569
$135$	135.000	0.0860663
$136$	−5457.60	−3.44107
$137$	−1585.07	−0.988477	−0.494238	−	0.869326i	$-0.664553\pi$
$137$	−1585.07	−0.988477	−0.494238	+	0.869326i	$0.664553\pi$
$138$	3461.18	2.13504
$139$	−1298.85	−0.792569	−0.396284	−	0.918128i	$-0.629701\pi$
$139$	−1298.85	−0.792569	−0.396284	+	0.918128i	$0.629701\pi$
$140$	802.580	0.484503
$141$	−1105.94	−0.660548
$142$	2521.12	1.48991
$143$	1289.30	0.753960
$144$	2505.40	1.44988
$145$	945.852	0.541716
$146$	−122.597	−0.0694943
$147$	−147.000	−0.0824786
$148$	−378.881	−0.210431
$149$	−2003.29	−1.10145	−0.550724	−	0.834687i	$-0.685648\pi$
$149$	−2003.29	−1.10145	−0.550724	+	0.834687i	$0.685648\pi$
$150$	417.116	0.227049
$151$	2740.96	1.47719	0.738596	−	0.674148i	$-0.235489\pi$
$151$	2740.96	1.47719	0.738596	+	0.674148i	$0.235489\pi$
$152$	−2773.47	−1.47999
$153$	591.511	0.312555
$154$	−1308.68	−0.684783
$155$	−1010.54	−0.523668
$156$	2638.48	1.35415
$157$	3644.22	1.85249	0.926243	−	0.376928i	$-0.123019\pi$
$157$	3644.22	1.85249	0.926243	+	0.376928i	$0.123019\pi$
$158$	−2143.52	−1.07930
$159$	−1374.52	−0.685574
$160$	4419.51	2.18371
$161$	−1452.13	−0.710831
$162$	−450.486	−0.218478
$163$	2774.27	1.33311	0.666557	−	0.745454i	$-0.267767\pi$
$163$	2774.27	1.33311	0.666557	+	0.745454i	$0.267767\pi$
$164$	8911.33	4.24304
$165$	−504.233	−0.237906
$166$	−132.087	−0.0617588
$167$	1154.91	0.535149	0.267574	−	0.963537i	$-0.413778\pi$
$167$	1154.91	0.535149	0.267574	+	0.963537i	$0.413778\pi$
$168$	−1743.82	−0.800823
$169$	−725.958	−0.330432
$170$	1827.62	0.824543
$171$	300.597	0.134428
$172$	958.841	0.425064
$173$	−3387.46	−1.48869	−0.744346	−	0.667794i	$-0.767239\pi$
$173$	−3387.46	−1.48869	−0.744346	+	0.667794i	$0.767239\pi$
$174$	−3156.24	−1.37514
$175$	−175.000	−0.0755929
$176$	−9357.82	−4.00780
$177$	−768.648	−0.326413
$178$	8246.73	3.47258
$179$	1603.32	0.669486	0.334743	−	0.942309i	$-0.391350\pi$
$179$	1603.32	0.669486	0.334743	+	0.942309i	$0.391350\pi$
$180$	−1031.89	−0.427292
$181$	544.220	0.223489	0.111745	−	0.993737i	$-0.464356\pi$
$181$	544.220	0.223489	0.111745	+	0.993737i	$0.464356\pi$
$182$	−1493.16	−0.608134
$183$	370.534	0.149676
$184$	−17226.2	−6.90179
$185$	82.6137	0.0328318
$186$	3372.10	1.32933
$187$	−2209.33	−0.863969
$188$	8453.41	3.27941
$189$	189.000	0.0727393
$190$	928.769	0.354631
$191$	2993.44	1.13402	0.567010	−	0.823711i	$-0.308100\pi$
$191$	2993.44	1.13402	0.567010	+	0.823711i	$0.308100\pi$
$192$	−8066.54	−3.03204
$193$	1309.32	0.488325	0.244163	−	0.969734i	$-0.421487\pi$
$193$	1309.32	0.488325	0.244163	+	0.969734i	$0.421487\pi$
$194$	−289.127	−0.107001
$195$	−575.312	−0.211277
$196$	1123.61	0.409480
$197$	−1141.38	−0.412790	−0.206395	−	0.978469i	$-0.566173\pi$
$197$	−1141.38	−0.412790	−0.206395	+	0.978469i	$0.566173\pi$
$198$	1682.59	0.603922
$199$	2370.23	0.844327	0.422164	−	0.906520i	$-0.361271\pi$
$199$	2370.23	0.844327	0.422164	+	0.906520i	$0.361271\pi$
$200$	−2075.97	−0.733966
$201$	1008.83	0.354017
$202$	−7949.12	−2.76880
$203$	1324.19	0.457833
$204$	−4521.29	−1.55173
$205$	−1943.09	−0.662005
$206$	−2414.89	−0.816765
$207$	1867.02	0.626894
$208$	−10676.9	−3.55920
$209$	−1122.75	−0.371588
$210$	583.963	0.191892
$211$	−687.159	−0.224199	−0.112099	−	0.993697i	$-0.535758\pi$
$211$	−687.159	−0.224199	−0.112099	+	0.993697i	$0.535758\pi$
$212$	10506.3	3.40366
$213$	1359.94	0.437471
$214$	−3705.70	−1.18372
$215$	−209.072	−0.0663190
$216$	2242.05	0.706260
$217$	−1414.76	−0.442580
$218$	6671.15	2.07260
$219$	−66.1308	−0.0204050
$220$	3854.17	1.18113
$221$	−2520.77	−0.767264
$222$	−275.676	−0.0833431
$223$	990.496	0.297437	0.148719	−	0.988880i	$-0.452485\pi$
$223$	990.496	0.297437	0.148719	+	0.988880i	$0.452485\pi$
$224$	6187.32	1.84557
$225$	225.000	0.0666667
$226$	453.362	0.133439
$227$	1479.25	0.432517	0.216258	−	0.976336i	$-0.430615\pi$
$227$	1479.25	0.432517	0.216258	+	0.976336i	$0.430615\pi$
$228$	−2297.65	−0.667392
$229$	6704.47	1.93469	0.967345	−	0.253463i	$-0.0815696\pi$
$229$	6704.47	1.93469	0.967345	+	0.253463i	$0.0815696\pi$
$230$	5768.64	1.65379
$231$	−705.926	−0.201067
$232$	15708.5	4.44531
$233$	−1749.09	−0.491789	−0.245895	−	0.969297i	$-0.579082\pi$
$233$	−1749.09	−0.491789	−0.245895	+	0.969297i	$0.579082\pi$
$234$	1919.78	0.536324
$235$	−1843.24	−0.511658
$236$	5875.25	1.62054
$237$	−1156.25	−0.316905
$238$	2558.67	0.696866
$239$	−6320.89	−1.71073	−0.855365	−	0.518027i	$-0.826667\pi$
$239$	−6320.89	−1.71073	−0.855365	+	0.518027i	$0.826667\pi$
$240$	4175.67	1.12308
$241$	3359.62	0.897975	0.448988	−	0.893538i	$-0.351785\pi$
$241$	3359.62	0.897975	0.448988	+	0.893538i	$0.351785\pi$
$242$	1117.85	0.296935
$243$	−243.000	−0.0641500
$244$	−2832.22	−0.743092
$245$	−245.000	−0.0638877
$246$	6483.95	1.68049
$247$	−1281.01	−0.329996
$248$	−16782.8	−4.29721
$249$	−71.2502	−0.0181337
$250$	695.194	0.175872
$251$	−1330.50	−0.334582	−0.167291	−	0.985908i	$-0.553502\pi$
$251$	−1330.50	−0.334582	−0.167291	+	0.985908i	$0.553502\pi$
$252$	−1444.64	−0.361127
$253$	−6973.44	−1.73287
$254$	1874.16	0.462973
$255$	985.852	0.242104
$256$	22330.6	5.45182
$257$	−2476.95	−0.601197	−0.300599	−	0.953751i	$-0.597186\pi$
$257$	−2476.95	−0.601197	−0.300599	+	0.953751i	$0.597186\pi$
$258$	697.659	0.168350
$259$	115.659	0.0277479
$260$	4397.47	1.04892
$261$	−1702.53	−0.403771
$262$	−16301.8	−3.84399
$263$	−5152.56	−1.20806	−0.604032	−	0.796960i	$-0.706440\pi$
$263$	−5152.56	−1.20806	−0.604032	+	0.796960i	$0.706440\pi$
$264$	−8374.18	−1.95225
$265$	−2290.86	−0.531043
$266$	1300.28	0.299718
$267$	4448.43	1.01962
$268$	−7711.11	−1.75758
$269$	−1150.97	−0.260876	−0.130438	−	0.991456i	$-0.541638\pi$
$269$	−1150.97	−0.260876	−0.130438	+	0.991456i	$0.541638\pi$
$270$	−750.810	−0.169233
$271$	1838.32	0.412067	0.206034	−	0.978545i	$-0.433944\pi$
$271$	1838.32	0.412067	0.206034	+	0.978545i	$0.433944\pi$
$272$	18296.0	4.07851
$273$	−805.437	−0.178561
$274$	8815.43	1.94365
$275$	−840.388	−0.184281
$276$	−14270.8	−3.11233
$277$	568.447	0.123302	0.0616510	−	0.998098i	$-0.480363\pi$
$277$	568.447	0.123302	0.0616510	+	0.998098i	$0.480363\pi$
$278$	7223.62	1.55843
$279$	1818.97	0.390319
$280$	−2906.36	−0.620315
$281$	6015.00	1.27696	0.638479	−	0.769640i	$-0.279564\pi$
$281$	6015.00	1.27696	0.638479	+	0.769640i	$0.279564\pi$
$282$	6150.76	1.29884
$283$	3985.75	0.837202	0.418601	−	0.908170i	$-0.362521\pi$
$283$	3985.75	0.837202	0.418601	+	0.908170i	$0.362521\pi$
$284$	−10394.8	−2.17190
$285$	500.994	0.104128
$286$	−7170.48	−1.48252
$287$	−2720.32	−0.559497
$288$	−7955.12	−1.62764
$289$	−593.424	−0.120787
$290$	−5260.41	−1.06518
$291$	−155.960	−0.0314177
$292$	505.479	0.101305
$293$	−2490.01	−0.496478	−0.248239	−	0.968699i	$-0.579852\pi$
$293$	−2490.01	−0.496478	−0.248239	+	0.968699i	$0.579852\pi$
$294$	817.548	0.162178
$295$	−1281.08	−0.252838
$296$	1372.03	0.269417
$297$	907.619	0.177325
$298$	11141.4	2.16578
$299$	−7956.45	−1.53891
$300$	−1719.82	−0.330979
$301$	−292.701	−0.0560498
$302$	−15244.0	−2.90461
$303$	−4287.90	−0.812981
$304$	9297.72	1.75415
$305$	617.557	0.115938
$306$	−3289.72	−0.614578
$307$	−141.853	−0.0263712	−0.0131856	−	0.999913i	$-0.504197\pi$
$307$	−141.853	−0.0263712	−0.0131856	+	0.999913i	$0.504197\pi$
$308$	5395.83	0.998234
$309$	−1302.64	−0.239820
$310$	5620.17	1.02969
$311$	2091.92	0.381420	0.190710	−	0.981646i	$-0.438921\pi$
$311$	2091.92	0.381420	0.190710	+	0.981646i	$0.438921\pi$
$312$	−9554.65	−1.73374
$313$	5521.44	0.997094	0.498547	−	0.866863i	$-0.333867\pi$
$313$	5521.44	0.997094	0.498547	+	0.866863i	$0.333867\pi$
$314$	−20267.5	−3.64255
$315$	315.000	0.0563436
$316$	8837.94	1.57333
$317$	5351.63	0.948195	0.474097	−	0.880472i	$-0.342774\pi$
$317$	5351.63	0.948195	0.474097	+	0.880472i	$0.342774\pi$
$318$	7644.45	1.34805
$319$	6359.06	1.11611
$320$	−13444.2	−2.34861
$321$	−1998.92	−0.347567
$322$	8076.09	1.39771
$323$	2195.14	0.378145
$324$	1857.40	0.318484
$325$	−958.854	−0.163654
$326$	−15429.2	−2.62131
$327$	3598.53	0.608561
$328$	−32270.3	−5.43241
$329$	−2580.53	−0.432430
$330$	2804.32	0.467796
$331$	−4383.52	−0.727916	−0.363958	−	0.931415i	$-0.618575\pi$
$331$	−4383.52	−0.727916	−0.363958	+	0.931415i	$0.618575\pi$
$332$	544.609	0.0900281
$333$	−148.705	−0.0244714
$334$	−6423.11	−1.05227
$335$	1681.38	0.274220
$336$	5845.93	0.949172
$337$	−7124.57	−1.15163	−0.575817	−	0.817579i	$-0.695316\pi$
$337$	−7124.57	−1.15163	−0.575817	+	0.817579i	$0.695316\pi$
$338$	4037.46	0.649730
$339$	244.551	0.0391806
$340$	−7535.48	−1.20197
$341$	−6793.97	−1.07893
$342$	−1671.78	−0.264327
$343$	−343.000	−0.0539949
$344$	−3472.22	−0.544214
$345$	3111.70	0.485590
$346$	18839.5	2.92722
$347$	507.743	0.0785506	0.0392753	−	0.999228i	$-0.487495\pi$
$347$	507.743	0.0785506	0.0392753	+	0.999228i	$0.487495\pi$
$348$	13013.5	2.00459
$349$	6155.14	0.944060	0.472030	−	0.881582i	$-0.343521\pi$
$349$	6155.14	0.944060	0.472030	+	0.881582i	$0.343521\pi$
$350$	973.272	0.148639
$351$	1035.56	0.157476
$352$	29712.8	4.49915
$353$	−6429.56	−0.969437	−0.484718	−	0.874670i	$-0.661078\pi$
$353$	−6429.56	−0.969437	−0.484718	+	0.874670i	$0.661078\pi$
$354$	4274.87	0.641828
$355$	2266.56	0.338864
$356$	−34002.1	−5.06211
$357$	1380.19	0.204615
$358$	−8916.97	−1.31641
$359$	10075.4	1.48123	0.740614	−	0.671931i	$-0.234535\pi$
$359$	10075.4	1.48123	0.740614	+	0.671931i	$0.234535\pi$
$360$	3736.75	0.547066
$361$	−5743.46	−0.837362
$362$	−3026.71	−0.439448
$363$	602.989	0.0871865
$364$	6156.46	0.886501
$365$	−110.218	−0.0158057
$366$	−2060.74	−0.294308
$367$	816.898	0.116190	0.0580950	−	0.998311i	$-0.481497\pi$
$367$	816.898	0.116190	0.0580950	+	0.998311i	$0.481497\pi$
$368$	57748.6	8.18031
$369$	3497.56	0.493430
$370$	−459.460	−0.0645573
$371$	−3207.21	−0.448814
$372$	−13903.5	−1.93781
$373$	−3737.85	−0.518870	−0.259435	−	0.965761i	$-0.583536\pi$
$373$	−3737.85	−0.518870	−0.259435	+	0.965761i	$0.583536\pi$
$374$	12287.3	1.69883
$375$	375.000	0.0516398
$376$	−30612.1	−4.19866
$377$	7255.47	0.991183
$378$	−1051.13	−0.143028
$379$	1950.47	0.264351	0.132176	−	0.991226i	$-0.457804\pi$
$379$	1950.47	0.264351	0.132176	+	0.991226i	$0.457804\pi$
$380$	−3829.41	−0.516960
$381$	1010.95	0.135939
$382$	−16648.2	−2.22983
$383$	6762.06	0.902155	0.451077	−	0.892485i	$-0.351040\pi$
$383$	6762.06	0.902155	0.451077	+	0.892485i	$0.351040\pi$
$384$	23648.8	3.14277
$385$	−1176.54	−0.155746
$386$	−7281.84	−0.960197
$387$	376.330	0.0494313
$388$	1192.10	0.155979
$389$	−2551.98	−0.332624	−0.166312	−	0.986073i	$-0.553186\pi$
$389$	−2551.98	−0.332624	−0.166312	+	0.986073i	$0.553186\pi$
$390$	3199.63	0.415435
$391$	13634.1	1.76345
$392$	−4068.90	−0.524262
$393$	−8793.45	−1.12868
$394$	6347.83	0.811672
$395$	−1927.08	−0.245474
$396$	−6937.50	−0.880360
$397$	−4097.93	−0.518058	−0.259029	−	0.965869i	$-0.583403\pi$
$397$	−4097.93	−0.518058	−0.259029	+	0.965869i	$0.583403\pi$
$398$	−13182.2	−1.66021
$399$	701.392	0.0880038
$400$	6959.45	0.869931
$401$	−1046.81	−0.130362	−0.0651811	−	0.997873i	$-0.520762\pi$
$401$	−1046.81	−0.130362	−0.0651811	+	0.997873i	$0.520762\pi$
$402$	−5610.66	−0.696105
$403$	−7751.68	−0.958161
$404$	32775.1	4.03619
$405$	−405.000	−0.0496904
$406$	−7364.57	−0.900240
$407$	555.420	0.0676441
$408$	16372.8	1.98670
$409$	6516.92	0.787876	0.393938	−	0.919137i	$-0.371113\pi$
$409$	6516.92	0.787876	0.393938	+	0.919137i	$0.371113\pi$
$410$	10806.6	1.30170
$411$	4755.20	0.570697
$412$	9956.86	1.19063
$413$	−1793.51	−0.213687
$414$	−10383.5	−1.23267
$415$	−118.750	−0.0140463
$416$	33901.3	3.99555
$417$	3896.55	0.457590
$418$	6244.21	0.730656
$419$	12279.1	1.43168	0.715838	−	0.698267i	$-0.246045\pi$
$419$	12279.1	1.43168	0.715838	+	0.698267i	$0.246045\pi$
$420$	−2407.74	−0.279728
$421$	10146.9	1.17465	0.587325	−	0.809351i	$-0.300181\pi$
$421$	10146.9	1.17465	0.587325	+	0.809351i	$0.300181\pi$
$422$	3821.67	0.440844
$423$	3317.83	0.381367
$424$	−38046.1	−4.35774
$425$	1643.09	0.187533
$426$	−7563.36	−0.860202
$427$	864.579	0.0979858
$428$	15279.0	1.72556
$429$	−3867.89	−0.435299
$430$	1162.77	0.130404
$431$	7059.04	0.788914	0.394457	−	0.918914i	$-0.370933\pi$
$431$	7059.04	0.788914	0.394457	+	0.918914i	$0.370933\pi$
$432$	−7516.20	−0.837091
$433$	6468.98	0.717966	0.358983	−	0.933344i	$-0.383124\pi$
$433$	6468.98	0.717966	0.358983	+	0.933344i	$0.383124\pi$
$434$	7868.24	0.870248
$435$	−2837.56	−0.312760
$436$	−27505.8	−3.02131
$437$	6928.65	0.758449
$438$	367.790	0.0401226
$439$	4767.13	0.518275	0.259137	−	0.965840i	$-0.416562\pi$
$439$	4767.13	0.518275	0.259137	+	0.965840i	$0.416562\pi$
$440$	−13957.0	−1.51221
$441$	441.000	0.0476190
$442$	14019.4	1.50868
$443$	2366.55	0.253810	0.126905	−	0.991915i	$-0.459496\pi$
$443$	2366.55	0.253810	0.126905	+	0.991915i	$0.459496\pi$
$444$	1136.64	0.121492
$445$	7414.05	0.789797
$446$	−5508.70	−0.584853
$447$	6009.86	0.635921
$448$	−18821.9	−1.98494
$449$	1814.17	0.190681	0.0953406	−	0.995445i	$-0.469606\pi$
$449$	1814.17	0.190681	0.0953406	+	0.995445i	$0.469606\pi$
$450$	−1251.35	−0.131087
$451$	−13063.6	−1.36395
$452$	−1869.26	−0.194519
$453$	−8222.87	−0.852857
$454$	−8226.93	−0.850460
$455$	−1342.40	−0.138313
$456$	8320.40	0.854470
$457$	8284.13	0.847955	0.423977	−	0.905673i	$-0.360634\pi$
$457$	8284.13	0.847955	0.423977	+	0.905673i	$0.360634\pi$
$458$	−37287.3	−3.80419
$459$	−1774.53	−0.180453
$460$	−23784.7	−2.41080
$461$	1384.62	0.139888	0.0699439	−	0.997551i	$-0.477718\pi$
$461$	1384.62	0.139888	0.0699439	+	0.997551i	$0.477718\pi$
$462$	3926.05	0.395360
$463$	−13210.3	−1.32599	−0.662994	−	0.748624i	$-0.730715\pi$
$463$	−13210.3	−1.32599	−0.662994	+	0.748624i	$0.730715\pi$
$464$	−52660.9	−5.26879
$465$	3031.62	0.302340
$466$	9727.67	0.967008
$467$	−4574.24	−0.453256	−0.226628	−	0.973981i	$-0.572770\pi$
$467$	−4574.24	−0.453256	−0.226628	+	0.973981i	$0.572770\pi$
$468$	−7915.45	−0.781820
$469$	2353.94	0.231758
$470$	10251.3	1.00608
$471$	−10932.7	−1.06953
$472$	−21275.9	−2.07479
$473$	−1405.61	−0.136639
$474$	6430.55	0.623132
$475$	834.991	0.0806568
$476$	−10549.7	−1.01585
$477$	4123.55	0.395816
$478$	35154.0	3.36382
$479$	−11031.8	−1.05231	−0.526154	−	0.850389i	$-0.676366\pi$
$479$	−11031.8	−1.05231	−0.526154	+	0.850389i	$0.676366\pi$
$480$	−13258.5	−1.26076
$481$	633.716	0.0600726
$482$	−18684.7	−1.76569
$483$	4356.39	0.410398
$484$	−4609.02	−0.432853
$485$	−259.934	−0.0243360
$486$	1351.46	0.126139
$487$	−5194.06	−0.483296	−0.241648	−	0.970364i	$-0.577688\pi$
$487$	−5194.06	−0.483296	−0.241648	+	0.970364i	$0.577688\pi$
$488$	10256.2	0.951389
$489$	−8322.81	−0.769673
$490$	1362.58	0.125623
$491$	11954.7	1.09880	0.549398	−	0.835561i	$-0.314857\pi$
$491$	11954.7	1.09880	0.549398	+	0.835561i	$0.314857\pi$
$492$	−26734.0	−2.44972
$493$	−12432.9	−1.13580
$494$	7124.43	0.648873
$495$	1512.70	0.137355
$496$	56262.4	5.09326
$497$	3173.19	0.286392
$498$	396.262	0.0356564
$499$	2566.05	0.230205	0.115102	−	0.993354i	$-0.463280\pi$
$499$	2566.05	0.230205	0.115102	+	0.993354i	$0.463280\pi$
$500$	−2866.36	−0.256375
$501$	−3464.74	−0.308968
$502$	7399.62	0.657891
$503$	21103.5	1.87069	0.935347	−	0.353731i	$-0.115087\pi$
$503$	21103.5	1.87069	0.935347	+	0.353731i	$0.115087\pi$
$504$	5231.45	0.462355
$505$	−7146.50	−0.629732
$506$	38783.1	3.40735
$507$	2177.87	0.190775
$508$	−7727.36	−0.674894
$509$	−781.732	−0.0680740	−0.0340370	−	0.999421i	$-0.510836\pi$
$509$	−781.732	−0.0680740	−0.0340370	+	0.999421i	$0.510836\pi$
$510$	−5482.87	−0.476050
$511$	−154.305	−0.0133582
$512$	−61129.5	−5.27650
$513$	−901.790	−0.0776121
$514$	13775.7	1.18214
$515$	−2171.06	−0.185764
$516$	−2876.52	−0.245411
$517$	−12392.3	−1.05418
$518$	−643.244	−0.0545609
$519$	10162.4	0.859497
$520$	−15924.4	−1.34295
$521$	14013.0	1.17835	0.589176	−	0.808005i	$-0.299453\pi$
$521$	14013.0	1.17835	0.589176	+	0.808005i	$0.299453\pi$
$522$	9468.73	0.793937
$523$	−10310.7	−0.862052	−0.431026	−	0.902339i	$-0.641848\pi$
$523$	−10310.7	−0.862052	−0.431026	+	0.902339i	$0.641848\pi$
$524$	67213.8	5.60353
$525$	525.000	0.0436436
$526$	28656.3	2.37542
$527$	13283.2	1.09796
$528$	28073.5	2.31390
$529$	30867.2	2.53696
$530$	12740.7	1.04419
$531$	2305.94	0.188455
$532$	−5361.18	−0.436911
$533$	−14905.1	−1.21128
$534$	−24740.2	−2.00489
$535$	−3331.53	−0.269224
$536$	27924.0	2.25025
$537$	−4809.97	−0.386528
$538$	6401.16	0.512962
$539$	−1647.16	−0.131629
$540$	3095.67	0.246697
$541$	−17562.9	−1.39572	−0.697862	−	0.716232i	$-0.745865\pi$
$541$	−17562.9	−1.39572	−0.697862	+	0.716232i	$0.745865\pi$
$542$	−10223.9	−0.810250
$543$	−1632.66	−0.129031
$544$	−58093.1	−4.57853
$545$	5997.56	0.471389
$546$	4479.48	0.351107
$547$	−19889.6	−1.55469	−0.777347	−	0.629072i	$-0.783435\pi$
$547$	−19889.6	−1.55469	−0.777347	+	0.629072i	$0.783435\pi$
$548$	−36346.9	−2.83333
$549$	−1111.60	−0.0864153
$550$	4673.86	0.362353
$551$	−6318.22	−0.488503
$552$	51678.5	3.98475
$553$	−2697.92	−0.207463
$554$	−3161.45	−0.242450
$555$	−247.841	−0.0189554
$556$	−29783.8	−2.27179
$557$	5579.54	0.424439	0.212219	−	0.977222i	$-0.431931\pi$
$557$	5579.54	0.424439	0.212219	+	0.977222i	$0.431931\pi$
$558$	−10116.3	−0.767486
$559$	−1603.76	−0.121345
$560$	9743.22	0.735226
$561$	6627.99	0.498813
$562$	−33452.8	−2.51089
$563$	−24463.2	−1.83126	−0.915630	−	0.402022i	$-0.868307\pi$
$563$	−24463.2	−1.83126	−0.915630	+	0.402022i	$0.868307\pi$
$564$	−25360.2	−1.89337
$565$	407.586	0.0303491
$566$	−22167.0	−1.64620
$567$	−567.000	−0.0419961
$568$	37642.5	2.78071
$569$	−8582.14	−0.632306	−0.316153	−	0.948708i	$-0.602391\pi$
$569$	−8582.14	−0.632306	−0.316153	+	0.948708i	$0.602391\pi$
$570$	−2786.31	−0.204747
$571$	17580.8	1.28850	0.644248	−	0.764816i	$-0.277170\pi$
$571$	17580.8	1.28850	0.644248	+	0.764816i	$0.277170\pi$
$572$	29564.7	2.16112
$573$	−8980.32	−0.654727
$574$	15129.2	1.10014
$575$	5186.17	0.376136
$576$	24199.6	1.75055
$577$	−8692.57	−0.627169	−0.313585	−	0.949560i	$-0.601530\pi$
$577$	−8692.57	−0.627169	−0.313585	+	0.949560i	$0.601530\pi$
$578$	3300.36	0.237503
$579$	−3927.95	−0.281935
$580$	21689.2	1.55275
$581$	−166.250	−0.0118713
$582$	867.381	0.0617768
$583$	−15401.7	−1.09412
$584$	−1830.47	−0.129701
$585$	1725.94	0.121981
$586$	13848.3	0.976227
$587$	3584.61	0.252049	0.126024	−	0.992027i	$-0.459778\pi$
$587$	3584.61	0.252049	0.126024	+	0.992027i	$0.459778\pi$
$588$	−3370.84	−0.236413
$589$	6750.33	0.472228
$590$	7124.79	0.497158
$591$	3424.13	0.238325
$592$	−4599.56	−0.319326
$593$	−21853.6	−1.51335	−0.756676	−	0.653790i	$-0.773178\pi$
$593$	−21853.6	−1.51335	−0.756676	+	0.653790i	$0.773178\pi$
$594$	−5047.77	−0.348674
$595$	2300.32	0.158494
$596$	−45937.1	−3.15714
$597$	−7110.69	−0.487472
$598$	44250.2	3.02596
$599$	9090.48	0.620078	0.310039	−	0.950724i	$-0.399658\pi$
$599$	9090.48	0.620078	0.310039	+	0.950724i	$0.399658\pi$
$600$	6227.91	0.423756
$601$	−19546.1	−1.32663	−0.663314	−	0.748341i	$-0.730851\pi$
$601$	−19546.1	−1.32663	−0.663314	+	0.748341i	$0.730851\pi$
$602$	1627.87	0.110211
$603$	−3026.49	−0.204392
$604$	62852.6	4.23416
$605$	1004.98	0.0675344
$606$	23847.4	1.59857
$607$	−15726.0	−1.05157	−0.525783	−	0.850619i	$-0.676227\pi$
$607$	−15726.0	−1.05157	−0.525783	+	0.850619i	$0.676227\pi$
$608$	−29522.0	−1.96920
$609$	−3972.58	−0.264330
$610$	−3434.57	−0.227970
$611$	−14139.2	−0.936186
$612$	13563.9	0.895894
$613$	−13572.5	−0.894269	−0.447135	−	0.894467i	$-0.647556\pi$
$613$	−13572.5	−0.894269	−0.447135	+	0.894467i	$0.647556\pi$
$614$	788.921	0.0518538
$615$	5829.26	0.382209
$616$	−19539.8	−1.27805
$617$	17378.5	1.13393	0.566964	−	0.823743i	$-0.308118\pi$
$617$	17378.5	1.13393	0.566964	+	0.823743i	$0.308118\pi$
$618$	7244.68	0.471560
$619$	−25113.3	−1.63068	−0.815338	−	0.578985i	$-0.803449\pi$
$619$	−25113.3	−1.63068	−0.815338	+	0.578985i	$0.803449\pi$
$620$	−23172.6	−1.50102
$621$	−5601.07	−0.361937
$622$	−11634.3	−0.749989
$623$	10379.7	0.667501
$624$	32030.8	2.05490
$625$	625.000	0.0400000
$626$	−30707.8	−1.96059
$627$	3368.24	0.214537
$628$	83565.1	5.30989
$629$	−1085.93	−0.0688377
$630$	−1751.89	−0.110789
$631$	−10814.4	−0.682276	−0.341138	−	0.940013i	$-0.610812\pi$
$631$	−10814.4	−0.682276	−0.341138	+	0.940013i	$0.610812\pi$
$632$	−32004.5	−2.01436
$633$	2061.48	0.129441
$634$	−29763.4	−1.86444
$635$	1684.92	0.105298
$636$	−31518.9	−1.96510
$637$	−1879.35	−0.116896
$638$	−35366.3	−2.19461
$639$	−4079.81	−0.252574
$640$	39414.7	2.43438
$641$	−16359.0	−1.00802	−0.504010	−	0.863698i	$-0.668143\pi$
$641$	−16359.0	−1.00802	−0.504010	+	0.863698i	$0.668143\pi$
$642$	11117.1	0.683422
$643$	8819.47	0.540911	0.270456	−	0.962732i	$-0.412826\pi$
$643$	8819.47	0.540911	0.270456	+	0.962732i	$0.412826\pi$
$644$	−33298.6	−2.03750
$645$	627.216	0.0382893
$646$	−12208.4	−0.743549
$647$	−13828.8	−0.840290	−0.420145	−	0.907457i	$-0.638021\pi$
$647$	−13828.8	−0.840290	−0.420145	+	0.907457i	$0.638021\pi$
$648$	−6726.14	−0.407759
$649$	−8612.83	−0.520930
$650$	5332.72	0.321794
$651$	4244.27	0.255524
$652$	63616.4	3.82118
$653$	23988.7	1.43760	0.718798	−	0.695219i	$-0.244693\pi$
$653$	23988.7	1.43760	0.718798	+	0.695219i	$0.244693\pi$
$654$	−20013.4	−1.19662
$655$	−14655.8	−0.874271
$656$	108182.	6.43874
$657$	198.392	0.0117809
$658$	14351.8	0.850289
$659$	3109.28	0.183794	0.0918972	−	0.995769i	$-0.470707\pi$
$659$	3109.28	0.183794	0.0918972	+	0.995769i	$0.470707\pi$
$660$	−11562.5	−0.681924
$661$	22695.0	1.33545	0.667726	−	0.744407i	$-0.267268\pi$
$661$	22695.0	1.33545	0.667726	+	0.744407i	$0.267268\pi$
$662$	24379.2	1.43131
$663$	7562.31	0.442980
$664$	−1972.18	−0.115264
$665$	1168.99	0.0681675
$666$	827.028	0.0481182
$667$	−39242.8	−2.27809
$668$	26483.2	1.53393
$669$	−2971.49	−0.171726
$670$	−9351.10	−0.539201
$671$	4151.90	0.238871
$672$	−18562.0	−1.06554
$673$	22073.4	1.26429	0.632145	−	0.774850i	$-0.282175\pi$
$673$	22073.4	1.26429	0.632145	+	0.774850i	$0.282175\pi$
$674$	39623.7	2.26446
$675$	−675.000	−0.0384900
$676$	−16646.9	−0.947136
$677$	−2489.50	−0.141328	−0.0706642	−	0.997500i	$-0.522512\pi$
$677$	−2489.50	−0.141328	−0.0706642	+	0.997500i	$0.522512\pi$
$678$	−1360.09	−0.0770410
$679$	−363.907	−0.0205677
$680$	27288.0	1.53889
$681$	−4437.75	−0.249714
$682$	37785.0	2.12150
$683$	7970.98	0.446561	0.223280	−	0.974754i	$-0.428323\pi$
$683$	7970.98	0.446561	0.223280	+	0.974754i	$0.428323\pi$
$684$	6892.94	0.385319
$685$	7925.33	0.442060
$686$	1907.61	0.106171
$687$	−20113.4	−1.11699
$688$	11640.2	0.645027
$689$	−17572.8	−0.971656
$690$	−17305.9	−0.954818
$691$	−23892.7	−1.31537	−0.657687	−	0.753292i	$-0.728465\pi$
$691$	−23892.7	−1.31537	−0.657687	+	0.753292i	$0.728465\pi$
$692$	−77677.4	−4.26712
$693$	2117.78	0.116086
$694$	−2823.84	−0.154454
$695$	6494.25	0.354447
$696$	−47125.5	−2.56650
$697$	25541.3	1.38801
$698$	−34232.1	−1.85631
$699$	5247.28	0.283935
$700$	−4012.90	−0.216676
$701$	12197.0	0.657170	0.328585	−	0.944474i	$-0.393428\pi$
$701$	12197.0	0.657170	0.328585	+	0.944474i	$0.393428\pi$
$702$	−5759.33	−0.309647
$703$	−551.853	−0.0296067
$704$	−90387.0	−4.83891
$705$	5529.72	0.295406
$706$	35758.4	1.90621
$707$	−10005.1	−0.532221
$708$	−17625.8	−0.935617
$709$	−8982.28	−0.475792	−0.237896	−	0.971291i	$-0.576458\pi$
$709$	−8982.28	−0.475792	−0.237896	+	0.971291i	$0.576458\pi$
$710$	−12605.6	−0.666310
$711$	3468.75	0.182965
$712$	123131.	6.48107
$713$	41926.7	2.20220
$714$	−7676.02	−0.402336
$715$	−6446.48	−0.337181
$716$	36765.6	1.91899
$717$	18962.7	0.987690
$718$	−56035.0	−2.91255
$719$	−6501.61	−0.337231	−0.168616	−	0.985682i	$-0.553930\pi$
$719$	−6501.61	−0.337231	−0.168616	+	0.985682i	$0.553930\pi$
$720$	−12527.0	−0.648408
$721$	−3039.49	−0.156999
$722$	31942.6	1.64651
$723$	−10078.9	−0.518446
$724$	12479.4	0.640600
$725$	−4729.26	−0.242263
$726$	−3353.55	−0.171435
$727$	−24228.7	−1.23603	−0.618013	−	0.786168i	$-0.712062\pi$
$727$	−24228.7	−1.23603	−0.618013	+	0.786168i	$0.712062\pi$
$728$	−22294.2	−1.13500
$729$	729.000	0.0370370
$730$	612.983	0.0310788
$731$	2748.19	0.139050
$732$	8496.67	0.429024
$733$	36719.1	1.85027	0.925136	−	0.379636i	$-0.123951\pi$
$733$	36719.1	1.85027	0.925136	+	0.379636i	$0.123951\pi$
$734$	−4543.22	−0.228465
$735$	735.000	0.0368856
$736$	−183363.	−9.18321
$737$	11304.1	0.564983
$738$	−19451.8	−0.970234
$739$	23304.5	1.16004	0.580021	−	0.814602i	$-0.303044\pi$
$739$	23304.5	1.16004	0.580021	+	0.814602i	$0.303044\pi$
$740$	1894.40	0.0941076
$741$	3843.04	0.190523
$742$	17837.0	0.882505
$743$	6875.35	0.339478	0.169739	−	0.985489i	$-0.445708\pi$
$743$	6875.35	0.339478	0.169739	+	0.985489i	$0.445708\pi$
$744$	50348.4	2.48100
$745$	10016.4	0.492582
$746$	20788.3	1.02026
$747$	213.751	0.0104695
$748$	−50661.8	−2.47644
$749$	−4664.15	−0.227536
$750$	−2085.58	−0.101540
$751$	1182.65	0.0574640	0.0287320	−	0.999587i	$-0.490853\pi$
$751$	1182.65	0.0574640	0.0287320	+	0.999587i	$0.490853\pi$
$752$	102623.	4.97645
$753$	3991.49	0.193171
$754$	−40351.7	−1.94897
$755$	−13704.8	−0.660620
$756$	4333.93	0.208497
$757$	25226.8	1.21121	0.605604	−	0.795766i	$-0.292932\pi$
$757$	25226.8	1.21121	0.605604	+	0.795766i	$0.292932\pi$
$758$	−10847.7	−0.519795
$759$	20920.3	1.00047
$760$	13867.3	0.661870
$761$	−10909.2	−0.519655	−0.259827	−	0.965655i	$-0.583666\pi$
$761$	−10909.2	−0.519655	−0.259827	+	0.965655i	$0.583666\pi$
$762$	−5622.48	−0.267298
$763$	8396.58	0.398397
$764$	68642.2	3.25051
$765$	−2957.56	−0.139779
$766$	−37607.6	−1.77391
$767$	−9826.95	−0.462621
$768$	−66991.9	−3.14761
$769$	−12771.6	−0.598903	−0.299451	−	0.954112i	$-0.596804\pi$
$769$	−12771.6	−0.598903	−0.299451	+	0.954112i	$0.596804\pi$
$770$	6543.41	0.306244
$771$	7430.84	0.347101
$772$	30023.8	1.39972
$773$	2199.06	0.102322	0.0511610	−	0.998690i	$-0.483708\pi$
$773$	2199.06	0.102322	0.0511610	+	0.998690i	$0.483708\pi$
$774$	−2092.98	−0.0971971
$775$	5052.70	0.234191
$776$	−4316.92	−0.199701
$777$	−346.977	−0.0160203
$778$	14193.0	0.654041
$779$	12979.7	0.596977
$780$	−13192.4	−0.605595
$781$	15238.3	0.698170
$782$	−75827.0	−3.46748
$783$	5107.60	0.233117
$784$	13640.5	0.621379
$785$	−18221.1	−0.828457
$786$	48905.3	2.21933
$787$	−19587.7	−0.887201	−0.443601	−	0.896225i	$-0.646299\pi$
$787$	−19587.7	−0.887201	−0.443601	+	0.896225i	$0.646299\pi$
$788$	−26172.8	−1.18321
$789$	15457.7	0.697476
$790$	10717.6	0.482676
$791$	570.620	0.0256497
$792$	25122.5	1.12713
$793$	4737.17	0.212134
$794$	22790.9	1.01866
$795$	6872.58	0.306598
$796$	54351.4	2.42014
$797$	21699.3	0.964401	0.482200	−	0.876061i	$-0.339838\pi$
$797$	21699.3	0.964401	0.482200	+	0.876061i	$0.339838\pi$
$798$	−3900.83	−0.173042
$799$	24228.8	1.07278
$800$	−22097.6	−0.976583
$801$	−13345.3	−0.588680
$802$	5821.89	0.256332
$803$	−741.007	−0.0325649
$804$	23133.3	1.01474
$805$	7260.64	0.317893
$806$	43111.4	1.88404
$807$	3452.90	0.150617
$808$	−118687.	−5.16758
$809$	−15649.4	−0.680103	−0.340051	−	0.940407i	$-0.610444\pi$
$809$	−15649.4	−0.680103	−0.340051	+	0.940407i	$0.610444\pi$
$810$	2252.43	0.0977065
$811$	−33267.3	−1.44041	−0.720206	−	0.693760i	$-0.755953\pi$
$811$	−33267.3	−1.44041	−0.720206	+	0.693760i	$0.755953\pi$
$812$	30364.9	1.31231
$813$	−5514.97	−0.237907
$814$	−3089.00	−0.133009
$815$	−13871.3	−0.596186
$816$	−54887.9	−2.35473
$817$	1396.59	0.0598046
$818$	−36244.2	−1.54920
$819$	2416.31	0.103093
$820$	−44556.7	−1.89754
$821$	5158.58	0.219288	0.109644	−	0.993971i	$-0.465029\pi$
$821$	5158.58	0.219288	0.109644	+	0.993971i	$0.465029\pi$
$822$	−26446.3	−1.12217
$823$	26333.6	1.11535	0.557674	−	0.830060i	$-0.311694\pi$
$823$	26333.6	1.11535	0.557674	+	0.830060i	$0.311694\pi$
$824$	−36056.5	−1.52438
$825$	2521.16	0.106395
$826$	9974.71	0.420175
$827$	19572.7	0.822988	0.411494	−	0.911413i	$-0.365007\pi$
$827$	19572.7	0.822988	0.411494	+	0.911413i	$0.365007\pi$
$828$	42812.5	1.79690
$829$	9642.26	0.403968	0.201984	−	0.979389i	$-0.435261\pi$
$829$	9642.26	0.403968	0.201984	+	0.979389i	$0.435261\pi$
$830$	660.436	0.0276194
$831$	−1705.34	−0.0711885
$832$	−103128.	−4.29728
$833$	3220.45	0.133952
$834$	−21670.9	−0.899761
$835$	−5774.57	−0.239326
$836$	−25745.5	−1.06511
$837$	−5456.91	−0.225351
$838$	−68290.7	−2.81511
$839$	−31081.1	−1.27895	−0.639475	−	0.768812i	$-0.720848\pi$
$839$	−31081.1	−1.27895	−0.639475	+	0.768812i	$0.720848\pi$
$840$	8719.08	0.358139
$841$	11396.5	0.467278
$842$	−56432.3	−2.30972
$843$	−18045.0	−0.737252
$844$	−15757.1	−0.642634
$845$	3629.79	0.147774
$846$	−18452.3	−0.749885
$847$	1406.97	0.0570770
$848$	127545.	5.16499
$849$	−11957.2	−0.483359
$850$	−9138.11	−0.368747
$851$	−3427.59	−0.138068
$852$	31184.5	1.25395
$853$	25780.9	1.03484	0.517421	−	0.855731i	$-0.326892\pi$
$853$	25780.9	1.03484	0.517421	+	0.855731i	$0.326892\pi$
$854$	−4808.40	−0.192670
$855$	−1502.98	−0.0601181
$856$	−55329.3	−2.20925
$857$	14452.6	0.576069	0.288035	−	0.957620i	$-0.406998\pi$
$857$	14452.6	0.576069	0.288035	+	0.957620i	$0.406998\pi$
$858$	21511.5	0.855931
$859$	889.366	0.0353257	0.0176628	−	0.999844i	$-0.494377\pi$
$859$	889.366	0.0353257	0.0176628	+	0.999844i	$0.494377\pi$
$860$	−4794.20	−0.190094
$861$	8160.97	0.323025
$862$	−39259.2	−1.55125
$863$	41460.3	1.63537	0.817685	−	0.575665i	$-0.195257\pi$
$863$	41460.3	1.63537	0.817685	+	0.575665i	$0.195257\pi$
$864$	23865.4	0.939718
$865$	16937.3	0.665763
$866$	−35977.6	−1.41174
$867$	1780.27	0.0697361
$868$	−32441.6	−1.26859
$869$	−12956.0	−0.505756
$870$	15781.2	0.614981
$871$	12897.6	0.501744
$872$	99606.0	3.86822
$873$	467.880	0.0181390
$874$	−38534.1	−1.49134
$875$	875.000	0.0338062
$876$	−1516.44	−0.0584882
$877$	21173.0	0.815236	0.407618	−	0.913153i	$-0.366360\pi$
$877$	21173.0	0.815236	0.407618	+	0.913153i	$0.366360\pi$
$878$	−26512.6	−1.01909
$879$	7470.03	0.286642
$880$	46789.1	1.79234
$881$	9883.39	0.377957	0.188978	−	0.981981i	$-0.439482\pi$
$881$	9883.39	0.377957	0.188978	+	0.981981i	$0.439482\pi$
$882$	−2452.64	−0.0936336
$883$	−45273.9	−1.72547	−0.862734	−	0.505658i	$-0.831250\pi$
$883$	−45273.9	−1.72547	−0.862734	+	0.505658i	$0.831250\pi$
$884$	−57803.4	−2.19925
$885$	3843.24	0.145976
$886$	−13161.7	−0.499069
$887$	644.388	0.0243928	0.0121964	−	0.999926i	$-0.496118\pi$
$887$	644.388	0.0243928	0.0121964	+	0.999926i	$0.496118\pi$
$888$	−4116.08	−0.155548
$889$	2358.89	0.0889930
$890$	−41233.6	−1.55298
$891$	−2722.86	−0.102378
$892$	22712.9	0.852562
$893$	12312.7	0.461398
$894$	−33424.2	−1.25042
$895$	−8016.62	−0.299403
$896$	55180.6	2.05743
$897$	23869.4	0.888489
$898$	−10089.6	−0.374937
$899$	−38232.8	−1.41839
$900$	5159.45	0.191091
$901$	30112.7	1.11343
$902$	72653.8	2.68194
$903$	878.103	0.0323604
$904$	6769.09	0.249045
$905$	−2721.10	−0.0999474
$906$	45732.0	1.67698
$907$	−15065.2	−0.551522	−0.275761	−	0.961226i	$-0.588930\pi$
$907$	−15065.2	−0.551522	−0.275761	+	0.961226i	$0.588930\pi$
$908$	33920.5	1.23975
$909$	12863.7	0.469375
$910$	7465.80	0.271966
$911$	28789.9	1.04704	0.523520	−	0.852014i	$-0.324619\pi$
$911$	28789.9	1.04704	0.523520	+	0.852014i	$0.324619\pi$
$912$	−27893.1	−1.01276
$913$	−798.371	−0.0289400
$914$	−46072.6	−1.66734
$915$	−1852.67	−0.0669370
$916$	153739.	5.54552
$917$	−20518.1	−0.738894
$918$	9869.16	0.354827
$919$	−24163.8	−0.867345	−0.433673	−	0.901070i	$-0.642783\pi$
$919$	−24163.8	−0.867345	−0.433673	+	0.901070i	$0.642783\pi$
$920$	86130.8	3.08657
$921$	425.558	0.0152254
$922$	−7700.65	−0.275062
$923$	17386.4	0.620023
$924$	−16187.5	−0.576331
$925$	−413.068	−0.0146828
$926$	73469.5	2.60730
$927$	3907.91	0.138460
$928$	167208.	5.91474
$929$	−35115.4	−1.24015	−0.620075	−	0.784542i	$-0.712898\pi$
$929$	−35115.4	−1.24015	−0.620075	+	0.784542i	$0.712898\pi$
$930$	−16860.5	−0.594492
$931$	1636.58	0.0576120
$932$	−40108.2	−1.40964
$933$	−6275.75	−0.220213
$934$	25439.9	0.891239
$935$	11046.6	0.386379
$936$	28664.0	1.00097
$937$	−15512.6	−0.540849	−0.270424	−	0.962741i	$-0.587164\pi$
$937$	−15512.6	−0.540849	−0.270424	+	0.962741i	$0.587164\pi$
$938$	−13091.5	−0.455708
$939$	−16564.3	−0.575672
$940$	−42267.1	−1.46660
$941$	−53283.8	−1.84591	−0.922956	−	0.384905i	$-0.874234\pi$
$941$	−53283.8	−1.84591	−0.922956	+	0.384905i	$0.874234\pi$
$942$	60802.5	2.10303
$943$	80617.5	2.78395
$944$	71324.8	2.45914
$945$	−945.000	−0.0325300
$946$	7817.39	0.268674
$947$	−55509.7	−1.90478	−0.952388	−	0.304890i	$-0.901380\pi$
$947$	−55509.7	−1.90478	−0.952388	+	0.304890i	$0.901380\pi$
$948$	−26513.8	−0.908364
$949$	−845.464	−0.0289198
$950$	−4643.84	−0.158596
$951$	−16054.9	−0.547441
$952$	38203.2	1.30060
$953$	−28080.6	−0.954480	−0.477240	−	0.878773i	$-0.658363\pi$
$953$	−28080.6	−0.954480	−0.477240	+	0.878773i	$0.658363\pi$
$954$	−22933.3	−0.778296
$955$	−14967.2	−0.507149
$956$	−144943.	−4.90356
$957$	−19077.2	−0.644387
$958$	61353.9	2.06916
$959$	11095.5	0.373609
$960$	40332.7	1.35597
$961$	11056.6	0.371140
$962$	−3524.44	−0.118121
$963$	5996.76	0.200668
$964$	77039.0	2.57392
$965$	−6546.59	−0.218386
$966$	−24228.3	−0.806969
$967$	56609.3	1.88256	0.941278	−	0.337634i	$-0.109626\pi$
$967$	56609.3	1.88256	0.941278	+	0.337634i	$0.109626\pi$
$968$	16690.5	0.554187
$969$	−6585.42	−0.218322
$970$	1445.63	0.0478521
$971$	−6782.17	−0.224151	−0.112075	−	0.993700i	$-0.535750\pi$
$971$	−6782.17	−0.224151	−0.112075	+	0.993700i	$0.535750\pi$
$972$	−5572.20	−0.183877
$973$	9091.95	0.299563
$974$	28887.0	0.950309
$975$	2876.56	0.0944859
$976$	−34382.8	−1.12763
$977$	−45655.0	−1.49502	−0.747509	−	0.664252i	$-0.768750\pi$
$977$	−45655.0	−1.49502	−0.747509	+	0.664252i	$0.768750\pi$
$978$	46287.7	1.51341
$979$	49845.5	1.62724
$980$	−5618.06	−0.183125
$981$	−10795.6	−0.351353
$982$	−66486.8	−2.16057
$983$	−10102.3	−0.327785	−0.163893	−	0.986478i	$-0.552405\pi$
$983$	−10102.3	−0.327785	−0.163893	+	0.986478i	$0.552405\pi$
$984$	96811.0	3.13640
$985$	5706.88	0.184606
$986$	69146.4	2.23334
$987$	7741.60	0.249664
$988$	−29374.8	−0.945887
$989$	8674.27	0.278894
$990$	−8412.95	−0.270082
$991$	25416.2	0.814705	0.407353	−	0.913271i	$-0.366452\pi$
$991$	25416.2	0.814705	0.407353	+	0.913271i	$0.366452\pi$
$992$	−178644.	−5.71768
$993$	13150.6	0.420262
$994$	−17647.8	−0.563135
$995$	−11851.1	−0.377595
$996$	−1633.83	−0.0519777
$997$	48152.5	1.52959	0.764797	−	0.644271i	$-0.222839\pi$
$997$	48152.5	1.52959	0.764797	+	0.644271i	$0.222839\pi$
$998$	−14271.2	−0.452653
$999$	446.114	0.0141285

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.4.a.c.1.1	✓	2
3.2	odd	2		315.4.a.m.1.2		2
4.3	odd	2		1680.4.a.bk.1.2		2
5.2	odd	4		525.4.d.i.274.1		4
5.3	odd	4		525.4.d.i.274.4		4
5.4	even	2		525.4.a.p.1.2		2
7.6	odd	2		735.4.a.k.1.1		2
15.14	odd	2		1575.4.a.m.1.1		2
21.20	even	2		2205.4.a.bh.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.4.a.c.1.1	✓	2	1.1	even	1	trivial
315.4.a.m.1.2		2	3.2	odd	2
525.4.a.p.1.2		2	5.4	even	2
525.4.d.i.274.1		4	5.2	odd	4
525.4.d.i.274.4		4	5.3	odd	4
735.4.a.k.1.1		2	7.6	odd	2
1575.4.a.m.1.1		2	15.14	odd	2
1680.4.a.bk.1.2		2	4.3	odd	2
2205.4.a.bh.1.2		2	21.20	even	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:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	105.a (trivial)

\(f(q)\)	\(=\)	\(q-5.56155 q^{2} -3.00000 q^{3} +22.9309 q^{4} -5.00000 q^{5} +16.6847 q^{6} -7.00000 q^{7} -83.0388 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-5.56155 q^{2} -3.00000 q^{3} +22.9309 q^{4} -5.00000 q^{5} +16.6847 q^{6} -7.00000 q^{7} -83.0388 q^{8} +9.00000 q^{9} +27.8078 q^{10} -33.6155 q^{11} -68.7926 q^{12} -38.3542 q^{13} +38.9309 q^{14} +15.0000 q^{15} +278.378 q^{16} +65.7235 q^{17} -50.0540 q^{18} +33.3996 q^{19} -114.654 q^{20} +21.0000 q^{21} +186.955 q^{22} +207.447 q^{23} +249.116 q^{24} +25.0000 q^{25} +213.309 q^{26} -27.0000 q^{27} -160.516 q^{28} -189.170 q^{29} -83.4233 q^{30} +202.108 q^{31} -883.902 q^{32} +100.847 q^{33} -365.525 q^{34} +35.0000 q^{35} +206.378 q^{36} -16.5227 q^{37} -185.754 q^{38} +115.062 q^{39} +415.194 q^{40} +388.617 q^{41} -116.793 q^{42} +41.8144 q^{43} -770.833 q^{44} -45.0000 q^{45} -1153.73 q^{46} +368.648 q^{47} -835.133 q^{48} +49.0000 q^{49} -139.039 q^{50} -197.170 q^{51} -879.494 q^{52} +458.172 q^{53} +150.162 q^{54} +168.078 q^{55} +581.272 q^{56} -100.199 q^{57} +1052.08 q^{58} +256.216 q^{59} +343.963 q^{60} -123.511 q^{61} -1124.03 q^{62} -63.0000 q^{63} +2688.85 q^{64} +191.771 q^{65} -560.864 q^{66} -336.277 q^{67} +1507.10 q^{68} -622.341 q^{69} -194.654 q^{70} -453.312 q^{71} -747.349 q^{72} +22.0436 q^{73} +91.8920 q^{74} -75.0000 q^{75} +765.882 q^{76} +235.309 q^{77} -639.926 q^{78} +385.417 q^{79} -1391.89 q^{80} +81.0000 q^{81} -2161.32 q^{82} +23.7501 q^{83} +481.548 q^{84} -328.617 q^{85} -232.553 q^{86} +567.511 q^{87} +2791.39 q^{88} -1482.81 q^{89} +250.270 q^{90} +268.479 q^{91} +4756.94 q^{92} -606.324 q^{93} -2050.25 q^{94} -166.998 q^{95} +2651.71 q^{96} +51.9867 q^{97} -272.516 q^{98} -302.540 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 7 q^{2} - 6 q^{3} + 17 q^{4} - 10 q^{5} + 21 q^{6} - 14 q^{7} - 63 q^{8} + 18 q^{9}+O(q^{10}) \) 2 * q - 7 * q^2 - 6 * q^3 + 17 * q^4 - 10 * q^5 + 21 * q^6 - 14 * q^7 - 63 * q^8 + 18 * q^9	\( 2 q - 7 q^{2} - 6 q^{3} + 17 q^{4} - 10 q^{5} + 21 q^{6} - 14 q^{7} - 63 q^{8} + 18 q^{9} + 35 q^{10} - 26 q^{11} - 51 q^{12} + 14 q^{13} + 49 q^{14} + 30 q^{15} + 297 q^{16} + 16 q^{17} - 63 q^{18} + 174 q^{19} - 85 q^{20} + 42 q^{21} + 176 q^{22} + 184 q^{23} + 189 q^{24} + 50 q^{25} + 138 q^{26} - 54 q^{27} - 119 q^{28} - 32 q^{29} - 105 q^{30} + 330 q^{31} - 1071 q^{32} + 78 q^{33} - 294 q^{34} + 70 q^{35} + 153 q^{36} - 132 q^{37} - 388 q^{38} - 42 q^{39} + 315 q^{40} + 200 q^{41} - 147 q^{42} + 364 q^{43} - 816 q^{44} - 90 q^{45} - 1120 q^{46} + 292 q^{47} - 891 q^{48} + 98 q^{49} - 175 q^{50} - 48 q^{51} - 1190 q^{52} + 34 q^{53} + 189 q^{54} + 130 q^{55} + 441 q^{56} - 522 q^{57} + 826 q^{58} + 364 q^{59} + 255 q^{60} + 792 q^{61} - 1308 q^{62} - 126 q^{63} + 2809 q^{64} - 70 q^{65} - 528 q^{66} - 788 q^{67} + 1802 q^{68} - 552 q^{69} - 245 q^{70} + 454 q^{71} - 567 q^{72} + 778 q^{73} + 258 q^{74} - 150 q^{75} - 68 q^{76} + 182 q^{77} - 414 q^{78} + 408 q^{79} - 1485 q^{80} + 162 q^{81} - 1890 q^{82} + 1136 q^{83} + 357 q^{84} - 80 q^{85} - 696 q^{86} + 96 q^{87} + 2944 q^{88} + 36 q^{89} + 315 q^{90} - 98 q^{91} + 4896 q^{92} - 990 q^{93} - 1940 q^{94} - 870 q^{95} + 3213 q^{96} - 498 q^{97} - 343 q^{98} - 234 q^{99}+O(q^{100}) \) 2 * q - 7 * q^2 - 6 * q^3 + 17 * q^4 - 10 * q^5 + 21 * q^6 - 14 * q^7 - 63 * q^8 + 18 * q^9 + 35 * q^10 - 26 * q^11 - 51 * q^12 + 14 * q^13 + 49 * q^14 + 30 * q^15 + 297 * q^16 + 16 * q^17 - 63 * q^18 + 174 * q^19 - 85 * q^20 + 42 * q^21 + 176 * q^22 + 184 * q^23 + 189 * q^24 + 50 * q^25 + 138 * q^26 - 54 * q^27 - 119 * q^28 - 32 * q^29 - 105 * q^30 + 330 * q^31 - 1071 * q^32 + 78 * q^33 - 294 * q^34 + 70 * q^35 + 153 * q^36 - 132 * q^37 - 388 * q^38 - 42 * q^39 + 315 * q^40 + 200 * q^41 - 147 * q^42 + 364 * q^43 - 816 * q^44 - 90 * q^45 - 1120 * q^46 + 292 * q^47 - 891 * q^48 + 98 * q^49 - 175 * q^50 - 48 * q^51 - 1190 * q^52 + 34 * q^53 + 189 * q^54 + 130 * q^55 + 441 * q^56 - 522 * q^57 + 826 * q^58 + 364 * q^59 + 255 * q^60 + 792 * q^61 - 1308 * q^62 - 126 * q^63 + 2809 * q^64 - 70 * q^65 - 528 * q^66 - 788 * q^67 + 1802 * q^68 - 552 * q^69 - 245 * q^70 + 454 * q^71 - 567 * q^72 + 778 * q^73 + 258 * q^74 - 150 * q^75 - 68 * q^76 + 182 * q^77 - 414 * q^78 + 408 * q^79 - 1485 * q^80 + 162 * q^81 - 1890 * q^82 + 1136 * q^83 + 357 * q^84 - 80 * q^85 - 696 * q^86 + 96 * q^87 + 2944 * q^88 + 36 * q^89 + 315 * q^90 - 98 * q^91 + 4896 * q^92 - 990 * q^93 - 1940 * q^94 - 870 * q^95 + 3213 * q^96 - 498 * q^97 - 343 * q^98 - 234 * q^99

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