LMFDB - Embedded newform 143.4.a.c.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [143,4,Mod(1,143)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(143, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("143.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 143 = 11 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	143.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:	$8.43727313082$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 59x^{7} - 12x^{6} + 1144x^{5} + 345x^{4} - 7888x^{3} - 2245x^{2} + 9710x - 2988 $ x^9 - 59x^7 - 12x^6 + 1144x^5 + 345x^4 - 7888x^3 - 2245x^2 + 9710*x - 2988
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$4.08298$ of defining polynomial
Character	$\chi$	$=$	143.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.08298 q^{2} +7.19985 q^{3} +8.67073 q^{4} -7.90460 q^{5} +29.3968 q^{6} +23.1330 q^{7} +2.73856 q^{8} +24.8378 q^{9} +O(q^{10})$	\(q+4.08298 q^{2} +7.19985 q^{3} +8.67073 q^{4} -7.90460 q^{5} +29.3968 q^{6} +23.1330 q^{7} +2.73856 q^{8} +24.8378 q^{9} -32.2743 q^{10} -11.0000 q^{11} +62.4279 q^{12} -13.0000 q^{13} +94.4517 q^{14} -56.9119 q^{15} -58.1843 q^{16} +100.093 q^{17} +101.412 q^{18} -54.0546 q^{19} -68.5386 q^{20} +166.554 q^{21} -44.9128 q^{22} -51.0260 q^{23} +19.7172 q^{24} -62.5174 q^{25} -53.0787 q^{26} -15.5675 q^{27} +200.580 q^{28} -258.146 q^{29} -232.370 q^{30} +153.477 q^{31} -259.474 q^{32} -79.1983 q^{33} +408.676 q^{34} -182.857 q^{35} +215.362 q^{36} -106.420 q^{37} -220.704 q^{38} -93.5980 q^{39} -21.6472 q^{40} +256.519 q^{41} +680.038 q^{42} +452.475 q^{43} -95.3780 q^{44} -196.333 q^{45} -208.338 q^{46} +208.882 q^{47} -418.918 q^{48} +192.137 q^{49} -255.257 q^{50} +720.652 q^{51} -112.719 q^{52} -320.975 q^{53} -63.5620 q^{54} +86.9506 q^{55} +63.3512 q^{56} -389.185 q^{57} -1054.00 q^{58} -477.404 q^{59} -493.467 q^{60} -132.810 q^{61} +626.643 q^{62} +574.574 q^{63} -593.952 q^{64} +102.760 q^{65} -323.365 q^{66} +808.985 q^{67} +867.876 q^{68} -367.380 q^{69} -746.603 q^{70} +645.982 q^{71} +68.0198 q^{72} -343.315 q^{73} -434.512 q^{74} -450.115 q^{75} -468.692 q^{76} -254.463 q^{77} -382.159 q^{78} +835.068 q^{79} +459.924 q^{80} -782.704 q^{81} +1047.36 q^{82} +88.0542 q^{83} +1444.15 q^{84} -791.192 q^{85} +1847.45 q^{86} -1858.61 q^{87} -30.1242 q^{88} -846.133 q^{89} -801.623 q^{90} -300.729 q^{91} -442.433 q^{92} +1105.01 q^{93} +852.862 q^{94} +427.280 q^{95} -1868.17 q^{96} +1466.21 q^{97} +784.493 q^{98} -273.216 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 8 q^{3} + 46 q^{4} + 30 q^{5} + 34 q^{6} + 25 q^{7} + 36 q^{8} + 91 q^{9}+O(q^{10}) $ 9 * q + 8 * q^3 + 46 * q^4 + 30 * q^5 + 34 * q^6 + 25 * q^7 + 36 * q^8 + 91 * q^9	\( 9 q + 8 q^{3} + 46 q^{4} + 30 q^{5} + 34 q^{6} + 25 q^{7} + 36 q^{8} + 91 q^{9} - 22 q^{10} - 99 q^{11} + 181 q^{12} - 117 q^{13} + 351 q^{15} + 130 q^{16} + 53 q^{17} + 33 q^{18} + 69 q^{19} + 282 q^{20} + 463 q^{21} + 216 q^{23} - 121 q^{24} + 617 q^{25} + 275 q^{27} + 279 q^{28} - 91 q^{29} + 29 q^{30} + 636 q^{31} + 663 q^{32} - 88 q^{33} + 423 q^{34} - 358 q^{35} - 252 q^{36} + 967 q^{37} - 101 q^{38} - 104 q^{39} + 652 q^{40} - 226 q^{41} - 1186 q^{42} + 42 q^{43} - 506 q^{44} + 5 q^{45} - 1127 q^{46} - 269 q^{47} - 1820 q^{48} + 228 q^{49} - 1374 q^{50} - 589 q^{51} - 598 q^{52} + 1227 q^{53} - 2438 q^{54} - 330 q^{55} - 659 q^{56} - 71 q^{57} + 471 q^{58} - 613 q^{59} - 859 q^{60} + 427 q^{61} - 1714 q^{62} + 305 q^{63} - 1194 q^{64} - 390 q^{65} - 374 q^{66} - 271 q^{67} - 2835 q^{68} - 846 q^{69} - 102 q^{70} + 2279 q^{71} - 2400 q^{72} + 3602 q^{73} - 4955 q^{74} - 883 q^{75} + 1126 q^{76} - 275 q^{77} - 442 q^{78} - 1182 q^{79} - 2360 q^{80} + 2697 q^{81} + 1007 q^{82} - 1877 q^{83} + 1618 q^{84} - 441 q^{85} + 830 q^{86} + 1942 q^{87} - 396 q^{88} + 1258 q^{89} - 5669 q^{90} - 325 q^{91} + 1046 q^{92} + 1556 q^{93} + 1439 q^{94} + 2032 q^{95} - 3417 q^{96} + 4002 q^{97} - 1855 q^{98} - 1001 q^{99}+O(q^{100}) \) 9 * q + 8 * q^3 + 46 * q^4 + 30 * q^5 + 34 * q^6 + 25 * q^7 + 36 * q^8 + 91 * q^9 - 22 * q^10 - 99 * q^11 + 181 * q^12 - 117 * q^13 + 351 * q^15 + 130 * q^16 + 53 * q^17 + 33 * q^18 + 69 * q^19 + 282 * q^20 + 463 * q^21 + 216 * q^23 - 121 * q^24 + 617 * q^25 + 275 * q^27 + 279 * q^28 - 91 * q^29 + 29 * q^30 + 636 * q^31 + 663 * q^32 - 88 * q^33 + 423 * q^34 - 358 * q^35 - 252 * q^36 + 967 * q^37 - 101 * q^38 - 104 * q^39 + 652 * q^40 - 226 * q^41 - 1186 * q^42 + 42 * q^43 - 506 * q^44 + 5 * q^45 - 1127 * q^46 - 269 * q^47 - 1820 * q^48 + 228 * q^49 - 1374 * q^50 - 589 * q^51 - 598 * q^52 + 1227 * q^53 - 2438 * q^54 - 330 * q^55 - 659 * q^56 - 71 * q^57 + 471 * q^58 - 613 * q^59 - 859 * q^60 + 427 * q^61 - 1714 * q^62 + 305 * q^63 - 1194 * q^64 - 390 * q^65 - 374 * q^66 - 271 * q^67 - 2835 * q^68 - 846 * q^69 - 102 * q^70 + 2279 * q^71 - 2400 * q^72 + 3602 * q^73 - 4955 * q^74 - 883 * q^75 + 1126 * q^76 - 275 * q^77 - 442 * q^78 - 1182 * q^79 - 2360 * q^80 + 2697 * q^81 + 1007 * q^82 - 1877 * q^83 + 1618 * q^84 - 441 * q^85 + 830 * q^86 + 1942 * q^87 - 396 * q^88 + 1258 * q^89 - 5669 * q^90 - 325 * q^91 + 1046 * q^92 + 1556 * q^93 + 1439 * q^94 + 2032 * q^95 - 3417 * q^96 + 4002 * q^97 - 1855 * q^98 - 1001 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	4.08298	1.44355	0.721776	−	0.692127i	$-0.243326\pi$
$2$	4.08298	1.44355	0.721776	+	0.692127i	$0.243326\pi$
$3$	7.19985	1.38561	0.692806	−	0.721124i	$-0.256374\pi$
$3$	7.19985	1.38561	0.692806	+	0.721124i	$0.256374\pi$
$4$	8.67073	1.08384
$5$	−7.90460	−0.707009	−0.353504	−	0.935433i	$-0.615010\pi$
$5$	−7.90460	−0.707009	−0.353504	+	0.935433i	$0.615010\pi$
$6$	29.3968	2.00020
$7$	23.1330	1.24907	0.624533	−	0.780998i	$-0.285289\pi$
$7$	23.1330	1.24907	0.624533	+	0.780998i	$0.285289\pi$
$8$	2.73856	0.121028
$9$	24.8378	0.919918
$10$	−32.2743	−1.02060
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	62.4279	1.50178
$13$	−13.0000	−0.277350
$13$	−13.0000	−0.277350
$14$	94.4517	1.80309
$15$	−56.9119	−0.979639
$16$	−58.1843	−0.909130
$17$	100.093	1.42800	0.714001	−	0.700145i	$-0.246881\pi$
$17$	100.093	1.42800	0.714001	+	0.700145i	$0.246881\pi$
$18$	101.412	1.32795
$19$	−54.0546	−0.652683	−0.326341	−	0.945252i	$-0.605816\pi$
$19$	−54.0546	−0.652683	−0.326341	+	0.945252i	$0.605816\pi$
$20$	−68.5386	−0.766285
$21$	166.554	1.73072
$22$	−44.9128	−0.435247
$23$	−51.0260	−0.462594	−0.231297	−	0.972883i	$-0.574297\pi$
$23$	−51.0260	−0.462594	−0.231297	+	0.972883i	$0.574297\pi$
$24$	19.7172	0.167698
$25$	−62.5174	−0.500139
$26$	−53.0787	−0.400369
$27$	−15.5675	−0.110962
$28$	200.580	1.35379
$29$	−258.146	−1.65298	−0.826490	−	0.562951i	$-0.809666\pi$
$29$	−258.146	−1.65298	−0.826490	+	0.562951i	$0.809666\pi$
$30$	−232.370	−1.41416
$31$	153.477	0.889202	0.444601	−	0.895729i	$-0.353346\pi$
$31$	153.477	0.889202	0.444601	+	0.895729i	$0.353346\pi$
$32$	−259.474	−1.43340
$33$	−79.1983	−0.417777
$34$	408.676	2.06139
$35$	−182.857	−0.883101
$36$	215.362	0.997045
$37$	−106.420	−0.472848	−0.236424	−	0.971650i	$-0.575976\pi$
$37$	−106.420	−0.472848	−0.236424	+	0.971650i	$0.575976\pi$
$38$	−220.704	−0.942181
$39$	−93.5980	−0.384299
$40$	−21.6472	−0.0855682
$41$	256.519	0.977112	0.488556	−	0.872532i	$-0.337524\pi$
$41$	256.519	0.977112	0.488556	+	0.872532i	$0.337524\pi$
$42$	680.038	2.49838
$43$	452.475	1.60469	0.802347	−	0.596858i	$-0.203584\pi$
$43$	452.475	1.60469	0.802347	+	0.596858i	$0.203584\pi$
$44$	−95.3780	−0.326790
$45$	−196.333	−0.650390
$46$	−208.338	−0.667778
$47$	208.882	0.648268	0.324134	−	0.946011i	$-0.394927\pi$
$47$	208.882	0.648268	0.324134	+	0.946011i	$0.394927\pi$
$48$	−418.918	−1.25970
$49$	192.137	0.560167
$50$	−255.257	−0.721976
$51$	720.652	1.97866
$52$	−112.719	−0.300603
$53$	−320.975	−0.831875	−0.415937	−	0.909393i	$-0.636546\pi$
$53$	−320.975	−0.831875	−0.415937	+	0.909393i	$0.636546\pi$
$54$	−63.5620	−0.160179
$55$	86.9506	0.213171
$56$	63.3512	0.151173
$57$	−389.185	−0.904364
$58$	−1054.00	−2.38616
$59$	−477.404	−1.05343	−0.526717	−	0.850040i	$-0.676577\pi$
$59$	−477.404	−1.05343	−0.526717	+	0.850040i	$0.676577\pi$
$60$	−493.467	−1.06177
$61$	−132.810	−0.278763	−0.139382	−	0.990239i	$-0.544511\pi$
$61$	−132.810	−0.278763	−0.139382	+	0.990239i	$0.544511\pi$
$62$	626.643	1.28361
$63$	574.574	1.14904
$64$	−593.952	−1.16006
$65$	102.760	0.196089
$66$	−323.365	−0.603083
$67$	808.985	1.47512	0.737562	−	0.675280i	$-0.235977\pi$
$67$	808.985	1.47512	0.737562	+	0.675280i	$0.235977\pi$
$68$	867.876	1.54773
$69$	−367.380	−0.640975
$70$	−746.603	−1.27480
$71$	645.982	1.07977	0.539887	−	0.841737i	$-0.318467\pi$
$71$	645.982	1.07977	0.539887	+	0.841737i	$0.318467\pi$
$72$	68.0198	0.111336
$73$	−343.315	−0.550438	−0.275219	−	0.961382i	$-0.588750\pi$
$73$	−343.315	−0.550438	−0.275219	+	0.961382i	$0.588750\pi$
$74$	−434.512	−0.682581
$75$	−450.115	−0.692998
$76$	−468.692	−0.707404
$77$	−254.463	−0.376608
$78$	−382.159	−0.554756
$79$	835.068	1.18927	0.594636	−	0.803995i	$-0.297296\pi$
$79$	835.068	1.18927	0.594636	+	0.803995i	$0.297296\pi$
$80$	459.924	0.642763
$81$	−782.704	−1.07367
$82$	1047.36	1.41051
$83$	88.0542	0.116448	0.0582241	−	0.998304i	$-0.481456\pi$
$83$	88.0542	0.116448	0.0582241	+	0.998304i	$0.481456\pi$
$84$	1444.15	1.87583
$85$	−791.192	−1.00961
$86$	1847.45	2.31646
$87$	−1858.61	−2.29039
$88$	−30.1242	−0.0364915
$89$	−846.133	−1.00775	−0.503876	−	0.863776i	$-0.668093\pi$
$89$	−846.133	−1.00775	−0.503876	+	0.863776i	$0.668093\pi$
$90$	−801.623	−0.938872
$91$	−300.729	−0.346429
$92$	−442.433	−0.501378
$93$	1105.01	1.23209
$94$	852.862	0.935809
$95$	427.280	0.461452
$96$	−1868.17	−1.98614
$97$	1466.21	1.53475	0.767375	−	0.641199i	$-0.221563\pi$
$97$	1466.21	1.53475	0.767375	+	0.641199i	$0.221563\pi$
$98$	784.493	0.808630
$99$	−273.216	−0.277366
$100$	−542.071	−0.542071
$101$	623.597	0.614359	0.307179	−	0.951652i	$-0.400615\pi$
$101$	623.597	0.614359	0.307179	+	0.951652i	$0.400615\pi$
$102$	2942.41	2.85629
$103$	477.041	0.456352	0.228176	−	0.973620i	$-0.426724\pi$
$103$	477.041	0.456352	0.228176	+	0.973620i	$0.426724\pi$
$104$	−35.6013	−0.0335673
$105$	−1316.54	−1.22363
$106$	−1310.54	−1.20085
$107$	−1324.66	−1.19682	−0.598410	−	0.801190i	$-0.704201\pi$
$107$	−1324.66	−1.19682	−0.598410	+	0.801190i	$0.704201\pi$
$108$	−134.982	−0.120265
$109$	−580.596	−0.510193	−0.255096	−	0.966916i	$-0.582107\pi$
$109$	−580.596	−0.510193	−0.255096	+	0.966916i	$0.582107\pi$
$110$	355.017	0.307723
$111$	−766.210	−0.655184
$112$	−1345.98	−1.13556
$113$	888.162	0.739392	0.369696	−	0.929153i	$-0.379462\pi$
$113$	888.162	0.739392	0.369696	+	0.929153i	$0.379462\pi$
$114$	−1589.03	−1.30550
$115$	403.340	0.327058
$116$	−2238.31	−1.79157
$117$	−322.891	−0.255139
$118$	−1949.23	−1.52069
$119$	2315.45	1.78367
$120$	−155.857	−0.118564
$121$	121.000	0.0909091
$122$	−542.260	−0.402409
$123$	1846.90	1.35390
$124$	1330.76	0.963753
$125$	1482.25	1.06061
$126$	2345.97	1.65870
$127$	−1208.00	−0.844039	−0.422020	−	0.906587i	$-0.638679\pi$
$127$	−1208.00	−0.844039	−0.422020	+	0.906587i	$0.638679\pi$
$128$	−349.304	−0.241206
$129$	3257.75	2.22348
$130$	419.566	0.283064
$131$	−1413.27	−0.942582	−0.471291	−	0.881978i	$-0.656212\pi$
$131$	−1413.27	−0.942582	−0.471291	+	0.881978i	$0.656212\pi$
$132$	−686.707	−0.452804
$133$	−1250.45	−0.815244
$134$	3303.07	2.12942
$135$	123.055	0.0784511
$136$	274.110	0.172829
$137$	2002.38	1.24872	0.624361	−	0.781136i	$-0.285360\pi$
$137$	2002.38	1.24872	0.624361	+	0.781136i	$0.285360\pi$
$138$	−1500.00	−0.925281
$139$	2778.43	1.69542	0.847709	−	0.530462i	$-0.177981\pi$
$139$	2778.43	1.69542	0.847709	+	0.530462i	$0.177981\pi$
$140$	−1585.51	−0.957141
$141$	1503.92	0.898248
$142$	2637.53	1.55871
$143$	143.000	0.0836242
$144$	−1445.17	−0.836325
$145$	2040.54	1.16867
$146$	−1401.75	−0.794585
$147$	1383.36	0.776174
$148$	−922.742	−0.512492
$149$	−590.584	−0.324715	−0.162357	−	0.986732i	$-0.551910\pi$
$149$	−590.584	−0.324715	−0.162357	+	0.986732i	$0.551910\pi$
$150$	−1837.81	−1.00038
$151$	2322.26	1.25154	0.625772	−	0.780006i	$-0.284784\pi$
$151$	2322.26	1.25154	0.625772	+	0.780006i	$0.284784\pi$
$152$	−148.032	−0.0789932
$153$	2486.08	1.31365
$154$	−1038.97	−0.543653
$155$	−1213.17	−0.628673
$156$	−811.563	−0.416519
$157$	−1318.45	−0.670217	−0.335108	−	0.942180i	$-0.608773\pi$
$157$	−1318.45	−0.670217	−0.335108	+	0.942180i	$0.608773\pi$
$158$	3409.57	1.71678
$159$	−2310.97	−1.15265
$160$	2051.04	1.01343
$161$	−1180.39	−0.577811
$162$	−3195.77	−1.54990
$163$	1490.99	0.716464	0.358232	−	0.933633i	$-0.383380\pi$
$163$	1490.99	0.716464	0.358232	+	0.933633i	$0.383380\pi$
$164$	2224.21	1.05903
$165$	626.031	0.295372
$166$	359.523	0.168099
$167$	3298.36	1.52835	0.764176	−	0.645008i	$-0.223146\pi$
$167$	3298.36	1.52835	0.764176	+	0.645008i	$0.223146\pi$
$168$	456.119	0.209466
$169$	169.000	0.0769231
$170$	−3230.42	−1.45742
$171$	−1342.60	−0.600415
$172$	3923.29	1.73923
$173$	−3820.43	−1.67897	−0.839486	−	0.543381i	$-0.817144\pi$
$173$	−3820.43	−1.67897	−0.839486	+	0.543381i	$0.817144\pi$
$174$	−7588.66	−3.30629
$175$	−1446.22	−0.624707
$176$	640.027	0.274113
$177$	−3437.23	−1.45965
$178$	−3454.74	−1.45474
$179$	2859.05	1.19383	0.596915	−	0.802304i	$-0.296393\pi$
$179$	2859.05	1.19383	0.596915	+	0.802304i	$0.296393\pi$
$180$	−1702.35	−0.704919
$181$	907.515	0.372680	0.186340	−	0.982485i	$-0.440337\pi$
$181$	907.515	0.372680	0.186340	+	0.982485i	$0.440337\pi$
$182$	−1227.87	−0.500088
$183$	−956.210	−0.386257
$184$	−139.738	−0.0559870
$185$	841.210	0.334308
$186$	4511.73	1.77858
$187$	−1101.02	−0.430559
$188$	1811.16	0.702620
$189$	−360.124	−0.138599
$190$	1744.57	0.666130
$191$	−2994.45	−1.13440	−0.567201	−	0.823579i	$-0.691974\pi$
$191$	−2994.45	−1.13440	−0.567201	+	0.823579i	$0.691974\pi$
$192$	−4276.37	−1.60740
$193$	−1176.75	−0.438884	−0.219442	−	0.975626i	$-0.570424\pi$
$193$	−1176.75	−0.438884	−0.219442	+	0.975626i	$0.570424\pi$
$194$	5986.49	2.21549
$195$	739.854	0.271703
$196$	1665.97	0.607132
$197$	−3866.89	−1.39850	−0.699250	−	0.714877i	$-0.746483\pi$
$197$	−3866.89	−1.39850	−0.699250	+	0.714877i	$0.746483\pi$
$198$	−1115.53	−0.400392
$199$	750.123	0.267210	0.133605	−	0.991035i	$-0.457345\pi$
$199$	750.123	0.267210	0.133605	+	0.991035i	$0.457345\pi$
$200$	−171.208	−0.0605310
$201$	5824.57	2.04395
$202$	2546.13	0.886858
$203$	−5971.69	−2.06468
$204$	6248.57	2.14455
$205$	−2027.68	−0.690827
$206$	1947.75	0.658768
$207$	−1267.37	−0.425549
$208$	756.396	0.252147
$209$	594.600	0.196791
$210$	−5375.43	−1.76638
$211$	244.573	0.0797967	0.0398983	−	0.999204i	$-0.487297\pi$
$211$	244.573	0.0797967	0.0398983	+	0.999204i	$0.487297\pi$
$212$	−2783.09	−0.901620
$213$	4650.97	1.49615
$214$	−5408.57	−1.72767
$215$	−3576.64	−1.13453
$216$	−42.6327	−0.0134296
$217$	3550.39	1.11067
$218$	−2370.56	−0.736490
$219$	−2471.81	−0.762693
$220$	753.924	0.231044
$221$	−1301.20	−0.396056
$222$	−3128.42	−0.945792
$223$	−3209.38	−0.963748	−0.481874	−	0.876241i	$-0.660044\pi$
$223$	−3209.38	−0.963748	−0.481874	+	0.876241i	$0.660044\pi$
$224$	−6002.42	−1.79042
$225$	−1552.79	−0.460087
$226$	3626.35	1.06735
$227$	−5482.27	−1.60296	−0.801478	−	0.598025i	$-0.795952\pi$
$227$	−5482.27	−1.60296	−0.801478	+	0.598025i	$0.795952\pi$
$228$	−3374.51	−0.980187
$229$	54.2712	0.0156609	0.00783044	−	0.999969i	$-0.497507\pi$
$229$	54.2712	0.0156609	0.00783044	+	0.999969i	$0.497507\pi$
$230$	1646.83	0.472125
$231$	−1832.10	−0.521832
$232$	−706.948	−0.200058
$233$	−37.4521	−0.0105303	−0.00526516	−	0.999986i	$-0.501676\pi$
$233$	−37.4521	−0.0105303	−0.00526516	+	0.999986i	$0.501676\pi$
$234$	−1318.36	−0.368307
$235$	−1651.13	−0.458331
$236$	−4139.44	−1.14176
$237$	6012.36	1.64787
$238$	9453.92	2.57482
$239$	−733.442	−0.198504	−0.0992520	−	0.995062i	$-0.531645\pi$
$239$	−733.442	−0.198504	−0.0992520	+	0.995062i	$0.531645\pi$
$240$	3311.38	0.890619
$241$	−4270.58	−1.14146	−0.570731	−	0.821137i	$-0.693340\pi$
$241$	−4270.58	−1.14146	−0.570731	+	0.821137i	$0.693340\pi$
$242$	494.041	0.131232
$243$	−5215.03	−1.37673
$244$	−1151.56	−0.302135
$245$	−1518.77	−0.396043
$246$	7540.86	1.95442
$247$	702.709	0.181022
$248$	420.306	0.107619
$249$	633.976	0.161352
$250$	6051.99	1.53105
$251$	3814.09	0.959135	0.479568	−	0.877505i	$-0.340793\pi$
$251$	3814.09	0.959135	0.479568	+	0.877505i	$0.340793\pi$
$252$	4981.97	1.24538
$253$	561.286	0.139477
$254$	−4932.26	−1.21841
$255$	−5696.46	−1.39893
$256$	3325.42	0.811869
$257$	2584.59	0.627324	0.313662	−	0.949535i	$-0.398444\pi$
$257$	2584.59	0.627324	0.313662	+	0.949535i	$0.398444\pi$
$258$	13301.3	3.20971
$259$	−2461.83	−0.590619
$260$	891.002	0.212529
$261$	−6411.77	−1.52061
$262$	−5770.37	−1.36067
$263$	−8011.92	−1.87847	−0.939233	−	0.343281i	$-0.888462\pi$
$263$	−8011.92	−1.87847	−0.939233	+	0.343281i	$0.888462\pi$
$264$	−216.889	−0.0505630
$265$	2537.18	0.588143
$266$	−5105.55	−1.17685
$267$	−6092.03	−1.39635
$268$	7014.49	1.59880
$269$	−6392.43	−1.44890	−0.724449	−	0.689329i	$-0.757906\pi$
$269$	−6392.43	−1.44890	−0.724449	+	0.689329i	$0.757906\pi$
$270$	502.432	0.113248
$271$	4985.07	1.11742	0.558711	−	0.829362i	$-0.311296\pi$
$271$	4985.07	1.11742	0.558711	+	0.829362i	$0.311296\pi$
$272$	−5823.82	−1.29824
$273$	−2165.21	−0.480016
$274$	8175.68	1.80259
$275$	687.691	0.150798
$276$	−3185.45	−0.694715
$277$	2986.78	0.647863	0.323932	−	0.946081i	$-0.394995\pi$
$277$	2986.78	0.647863	0.323932	+	0.946081i	$0.394995\pi$
$278$	11344.3	2.44742
$279$	3812.03	0.817993
$280$	−500.766	−0.106880
$281$	5654.29	1.20038	0.600189	−	0.799858i	$-0.295092\pi$
$281$	5654.29	1.20038	0.600189	+	0.799858i	$0.295092\pi$
$282$	6140.48	1.29667
$283$	−9291.29	−1.95163	−0.975813	−	0.218609i	$-0.929848\pi$
$283$	−9291.29	−1.95163	−0.975813	+	0.218609i	$0.929848\pi$
$284$	5601.14	1.17030
$285$	3076.35	0.639393
$286$	583.866	0.120716
$287$	5934.07	1.22048
$288$	−6444.76	−1.31861
$289$	5105.54	1.03919
$290$	8331.47	1.68704
$291$	10556.5	2.12657
$292$	−2976.79	−0.596587
$293$	−3807.05	−0.759079	−0.379539	−	0.925176i	$-0.623918\pi$
$293$	−3807.05	−0.759079	−0.379539	+	0.925176i	$0.623918\pi$
$294$	5648.23	1.12045
$295$	3773.68	0.744788
$296$	−291.439	−0.0572281
$297$	171.243	0.0334563
$298$	−2411.34	−0.468743
$299$	663.338	0.128300
$300$	−3902.83	−0.751099
$301$	10467.1	2.00437
$302$	9481.75	1.80667
$303$	4489.80	0.851262
$304$	3145.13	0.593373
$305$	1049.81	0.197088
$306$	10150.6	1.89631
$307$	5513.65	1.02502	0.512510	−	0.858682i	$-0.328716\pi$
$307$	5513.65	1.02502	0.512510	+	0.858682i	$0.328716\pi$
$308$	−2206.38	−0.408183
$309$	3434.62	0.632327
$310$	−4953.36	−0.907522
$311$	−5923.31	−1.08000	−0.540000	−	0.841665i	$-0.681576\pi$
$311$	−5923.31	−1.08000	−0.540000	+	0.841665i	$0.681576\pi$
$312$	−256.324	−0.0465112
$313$	−6967.84	−1.25829	−0.629147	−	0.777287i	$-0.716596\pi$
$313$	−6967.84	−1.25829	−0.629147	+	0.777287i	$0.716596\pi$
$314$	−5383.22	−0.967492
$315$	−4541.77	−0.812381
$316$	7240.65	1.28898
$317$	241.618	0.0428095	0.0214048	−	0.999771i	$-0.493186\pi$
$317$	241.618	0.0428095	0.0214048	+	0.999771i	$0.493186\pi$
$318$	−9435.66	−1.66392
$319$	2839.60	0.498392
$320$	4694.95	0.820174
$321$	−9537.36	−1.65833
$322$	−4819.50	−0.834099
$323$	−5410.46	−0.932032
$324$	−6786.62	−1.16369
$325$	812.726	0.138714
$326$	6087.70	1.03425
$327$	−4180.20	−0.706929
$328$	702.494	0.118258
$329$	4832.08	0.809730
$330$	2556.07	0.426385
$331$	4934.26	0.819370	0.409685	−	0.912227i	$-0.365639\pi$
$331$	4934.26	0.819370	0.409685	+	0.912227i	$0.365639\pi$
$332$	763.493	0.126211
$333$	−2643.25	−0.434982
$334$	13467.1	2.20626
$335$	−6394.70	−1.04293
$336$	−9690.85	−1.57345
$337$	−5106.34	−0.825400	−0.412700	−	0.910867i	$-0.635414\pi$
$337$	−5106.34	−0.825400	−0.412700	+	0.910867i	$0.635414\pi$
$338$	690.024	0.111042
$339$	6394.63	1.02451
$340$	−6860.21	−1.09426
$341$	−1688.25	−0.268104
$342$	−5481.79	−0.866729
$343$	−3489.91	−0.549380
$344$	1239.13	0.194214
$345$	2903.99	0.453175
$346$	−15598.8	−2.42368
$347$	−7418.96	−1.14775	−0.573877	−	0.818942i	$-0.694561\pi$
$347$	−7418.96	−1.14775	−0.573877	+	0.818942i	$0.694561\pi$
$348$	−16115.5	−2.48242
$349$	−3374.51	−0.517574	−0.258787	−	0.965934i	$-0.583323\pi$
$349$	−3374.51	−0.517574	−0.258787	+	0.965934i	$0.583323\pi$
$350$	−5904.87	−0.901796
$351$	202.378	0.0307753
$352$	2854.21	0.432188
$353$	−2043.75	−0.308152	−0.154076	−	0.988059i	$-0.549240\pi$
$353$	−2043.75	−0.308152	−0.154076	+	0.988059i	$0.549240\pi$
$354$	−14034.2	−2.10708
$355$	−5106.23	−0.763410
$356$	−7336.59	−1.09224
$357$	16670.9	2.47147
$358$	11673.5	1.72336
$359$	−8737.04	−1.28447	−0.642233	−	0.766510i	$-0.721992\pi$
$359$	−8737.04	−1.28447	−0.642233	+	0.766510i	$0.721992\pi$
$360$	−537.669	−0.0787157
$361$	−3937.10	−0.574005
$362$	3705.36	0.537982
$363$	871.181	0.125965
$364$	−2607.54	−0.375474
$365$	2713.77	0.389164
$366$	−3904.19	−0.557582
$367$	−8283.21	−1.17815	−0.589074	−	0.808079i	$-0.700507\pi$
$367$	−8283.21	−1.17815	−0.589074	+	0.808079i	$0.700507\pi$
$368$	2968.91	0.420558
$369$	6371.38	0.898863
$370$	3434.64	0.482591
$371$	−7425.13	−1.03907
$372$	9581.24	1.33539
$373$	1498.35	0.207993	0.103997	−	0.994578i	$-0.466837\pi$
$373$	1498.35	0.207993	0.103997	+	0.994578i	$0.466837\pi$
$374$	−4495.44	−0.621534
$375$	10672.0	1.46959
$376$	572.037	0.0784589
$377$	3355.89	0.458454
$378$	−1470.38	−0.200075
$379$	14420.2	1.95439	0.977197	−	0.212333i	$-0.0681060\pi$
$379$	14420.2	1.95439	0.977197	+	0.212333i	$0.0681060\pi$
$380$	3704.82	0.500141
$381$	−8697.44	−1.16951
$382$	−12226.3	−1.63757
$383$	−8477.42	−1.13101	−0.565504	−	0.824745i	$-0.691318\pi$
$383$	−8477.42	−1.13101	−0.565504	+	0.824745i	$0.691318\pi$
$384$	−2514.93	−0.334218
$385$	2011.43	0.266265
$386$	−4804.66	−0.633551
$387$	11238.5	1.47619
$388$	12713.1	1.66342
$389$	−1753.78	−0.228587	−0.114293	−	0.993447i	$-0.536460\pi$
$389$	−1753.78	−0.228587	−0.114293	+	0.993447i	$0.536460\pi$
$390$	3020.81	0.392217
$391$	−5107.33	−0.660585
$392$	526.180	0.0677962
$393$	−10175.3	−1.30605
$394$	−15788.4	−2.01881
$395$	−6600.88	−0.840825
$396$	−2368.98	−0.300620
$397$	6224.80	0.786937	0.393468	−	0.919338i	$-0.371275\pi$
$397$	6224.80	0.786937	0.393468	+	0.919338i	$0.371275\pi$
$398$	3062.74	0.385731
$399$	−9003.02	−1.12961
$400$	3637.53	0.454691
$401$	6038.15	0.751947	0.375974	−	0.926630i	$-0.377308\pi$
$401$	6038.15	0.751947	0.375974	+	0.926630i	$0.377308\pi$
$402$	23781.6	2.95054
$403$	−1995.20	−0.246620
$404$	5407.04	0.665867
$405$	6186.96	0.759093
$406$	−24382.3	−2.98048
$407$	1170.62	0.142569
$408$	1973.55	0.239474
$409$	16311.3	1.97199	0.985993	−	0.166786i	$-0.0533387\pi$
$409$	16311.3	1.97199	0.985993	+	0.166786i	$0.0533387\pi$
$410$	−8278.99	−0.997244
$411$	14416.8	1.73024
$412$	4136.29	0.494613
$413$	−11043.8	−1.31581
$414$	−5174.66	−0.614301
$415$	−696.033	−0.0823299
$416$	3373.16	0.397555
$417$	20004.2	2.34919
$418$	2427.74	0.284078
$419$	16057.5	1.87222	0.936110	−	0.351707i	$-0.114399\pi$
$419$	16057.5	1.87222	0.936110	+	0.351707i	$0.114399\pi$
$420$	−11415.4	−1.32622
$421$	4643.75	0.537583	0.268791	−	0.963198i	$-0.413376\pi$
$421$	4643.75	0.537583	0.268791	+	0.963198i	$0.413376\pi$
$422$	998.587	0.115191
$423$	5188.18	0.596354
$424$	−879.011	−0.100681
$425$	−6257.53	−0.714199
$426$	18989.8	2.15977
$427$	−3072.29	−0.348194
$428$	−11485.8	−1.29716
$429$	1029.58	0.115871
$430$	−14603.3	−1.63776
$431$	−12139.7	−1.35673	−0.678365	−	0.734725i	$-0.737311\pi$
$431$	−12139.7	−1.35673	−0.678365	+	0.734725i	$0.737311\pi$
$432$	905.787	0.100879
$433$	6439.61	0.714707	0.357353	−	0.933969i	$-0.383679\pi$
$433$	6439.61	0.714707	0.357353	+	0.933969i	$0.383679\pi$
$434$	14496.2	1.60331
$435$	14691.6	1.61932
$436$	−5034.19	−0.552968
$437$	2758.19	0.301927
$438$	−10092.4	−1.10099
$439$	−14005.2	−1.52262	−0.761311	−	0.648387i	$-0.775444\pi$
$439$	−14005.2	−1.52262	−0.761311	+	0.648387i	$0.775444\pi$
$440$	238.119	0.0257998
$441$	4772.27	0.515308
$442$	−5312.79	−0.571728
$443$	17348.6	1.86063	0.930314	−	0.366764i	$-0.119534\pi$
$443$	17348.6	1.86063	0.930314	+	0.366764i	$0.119534\pi$
$444$	−6643.60	−0.710115
$445$	6688.34	0.712489
$446$	−13103.8	−1.39122
$447$	−4252.11	−0.449929
$448$	−13739.9	−1.44900
$449$	10837.1	1.13905	0.569527	−	0.821972i	$-0.307126\pi$
$449$	10837.1	1.13905	0.569527	+	0.821972i	$0.307126\pi$
$450$	−6340.02	−0.664159
$451$	−2821.71	−0.294610
$452$	7701.01	0.801383
$453$	16719.9	1.73415
$454$	−22384.0	−2.31395
$455$	2377.15	0.244928
$456$	−1065.81	−0.109454
$457$	−14609.4	−1.49541	−0.747703	−	0.664034i	$-0.768843\pi$
$457$	−14609.4	−1.49541	−0.747703	+	0.664034i	$0.768843\pi$
$458$	221.588	0.0226073
$459$	−1558.20	−0.158454
$460$	3497.25	0.354479
$461$	−4021.16	−0.406256	−0.203128	−	0.979152i	$-0.565111\pi$
$461$	−4021.16	−0.406256	−0.203128	+	0.979152i	$0.565111\pi$
$462$	−7480.42	−0.753291
$463$	−1103.64	−0.110778	−0.0553892	−	0.998465i	$-0.517640\pi$
$463$	−1103.64	−0.110778	−0.0553892	+	0.998465i	$0.517640\pi$
$464$	15020.0	1.50277
$465$	−8734.66	−0.871097
$466$	−152.916	−0.0152011
$467$	−4814.12	−0.477025	−0.238513	−	0.971139i	$-0.576660\pi$
$467$	−4814.12	−0.477025	−0.238513	+	0.971139i	$0.576660\pi$
$468$	−2799.70	−0.276531
$469$	18714.3	1.84253
$470$	−6741.53	−0.661625
$471$	−9492.66	−0.928660
$472$	−1307.40	−0.127496
$473$	−4977.23	−0.483833
$474$	24548.4	2.37878
$475$	3379.35	0.326432
$476$	20076.6	1.93321
$477$	−7972.32	−0.765257
$478$	−2994.63	−0.286551
$479$	11043.5	1.05342	0.526711	−	0.850045i	$-0.323425\pi$
$479$	11043.5	1.05342	0.526711	+	0.850045i	$0.323425\pi$
$480$	14767.1	1.40422
$481$	1383.46	0.131145
$482$	−17436.7	−1.64776
$483$	−8498.60	−0.800621
$484$	1049.16	0.0985310
$485$	−11589.8	−1.08508
$486$	−21292.9	−1.98737
$487$	7012.58	0.652506	0.326253	−	0.945283i	$-0.394214\pi$
$487$	7012.58	0.652506	0.326253	+	0.945283i	$0.394214\pi$
$488$	−363.708	−0.0337383
$489$	10734.9	0.992741
$490$	−6201.10	−0.571709
$491$	−4379.09	−0.402496	−0.201248	−	0.979540i	$-0.564500\pi$
$491$	−4379.09	−0.402496	−0.201248	+	0.979540i	$0.564500\pi$
$492$	16014.0	1.46741
$493$	−25838.5	−2.36046
$494$	2869.15	0.261314
$495$	2159.66	0.196100
$496$	−8929.94	−0.808400
$497$	14943.5	1.34871
$498$	2588.51	0.232920
$499$	−7711.79	−0.691838	−0.345919	−	0.938264i	$-0.612433\pi$
$499$	−7711.79	−0.691838	−0.345919	+	0.938264i	$0.612433\pi$
$500$	12852.2	1.14953
$501$	23747.7	2.11770
$502$	15572.8	1.38456
$503$	−15095.4	−1.33812	−0.669058	−	0.743210i	$-0.733302\pi$
$503$	−15095.4	−1.33812	−0.669058	+	0.743210i	$0.733302\pi$
$504$	1573.51	0.139066
$505$	−4929.28	−0.434357
$506$	2291.72	0.201343
$507$	1216.77	0.106585
$508$	−10474.3	−0.914804
$509$	5674.90	0.494176	0.247088	−	0.968993i	$-0.420526\pi$
$509$	5674.90	0.494176	0.247088	+	0.968993i	$0.420526\pi$
$510$	−23258.5	−2.01942
$511$	−7941.92	−0.687534
$512$	16372.0	1.41318
$513$	841.497	0.0724230
$514$	10552.8	0.905575
$515$	−3770.82	−0.322645
$516$	28247.1	2.40990
$517$	−2297.71	−0.195460
$518$	−10051.6	−0.852589
$519$	−27506.5	−2.32640
$520$	281.414	0.0237323
$521$	4808.48	0.404344	0.202172	−	0.979350i	$-0.435200\pi$
$521$	4808.48	0.404344	0.202172	+	0.979350i	$0.435200\pi$
$522$	−26179.1	−2.19507
$523$	4520.04	0.377912	0.188956	−	0.981986i	$-0.439490\pi$
$523$	4520.04	0.377912	0.188956	+	0.981986i	$0.439490\pi$
$524$	−12254.1	−1.02161
$525$	−10412.5	−0.865601
$526$	−32712.5	−2.71166
$527$	15361.9	1.26978
$528$	4608.10	0.379814
$529$	−9563.35	−0.786007
$530$	10359.3	0.849014
$531$	−11857.7	−0.969074
$532$	−10842.3	−0.883595
$533$	−3334.75	−0.271002
$534$	−24873.6	−2.01571
$535$	10470.9	0.846163
$536$	2215.46	0.178532
$537$	20584.8	1.65419
$538$	−26100.2	−2.09156
$539$	−2113.51	−0.168897
$540$	1066.98	0.0850285
$541$	−4588.52	−0.364651	−0.182325	−	0.983238i	$-0.558362\pi$
$541$	−4588.52	−0.364651	−0.182325	+	0.983238i	$0.558362\pi$
$542$	20353.9	1.61306
$543$	6533.97	0.516389
$544$	−25971.4	−2.04690
$545$	4589.38	0.360711
$546$	−8840.49	−0.692927
$547$	8217.35	0.642319	0.321160	−	0.947025i	$-0.395927\pi$
$547$	8217.35	0.642319	0.321160	+	0.947025i	$0.395927\pi$
$548$	17362.1	1.35342
$549$	−3298.70	−0.256439
$550$	2807.83	0.217684
$551$	13953.9	1.07887
$552$	−1006.09	−0.0775763
$553$	19317.7	1.48548
$554$	12195.0	0.935224
$555$	6056.58	0.463221
$556$	24091.0	1.83756
$557$	6872.47	0.522793	0.261397	−	0.965231i	$-0.415817\pi$
$557$	6872.47	0.522793	0.261397	+	0.965231i	$0.415817\pi$
$558$	15564.4	1.18081
$559$	−5882.18	−0.445062
$560$	10639.4	0.802853
$561$	−7927.17	−0.596587
$562$	23086.3	1.73281
$563$	15461.0	1.15737	0.578687	−	0.815550i	$-0.303565\pi$
$563$	15461.0	1.15737	0.578687	+	0.815550i	$0.303565\pi$
$564$	13040.1	0.973558
$565$	−7020.56	−0.522756
$566$	−37936.2	−2.81727
$567$	−18106.3	−1.34108
$568$	1769.06	0.130683
$569$	11434.8	0.842478	0.421239	−	0.906950i	$-0.361595\pi$
$569$	11434.8	0.842478	0.421239	+	0.906950i	$0.361595\pi$
$570$	12560.7	0.922997
$571$	18340.2	1.34416	0.672079	−	0.740480i	$-0.265402\pi$
$571$	18340.2	1.34416	0.672079	+	0.740480i	$0.265402\pi$
$572$	1239.91	0.0906353
$573$	−21559.6	−1.57184
$574$	24228.7	1.76182
$575$	3190.01	0.231361
$576$	−14752.5	−1.06716
$577$	11117.5	0.802128	0.401064	−	0.916050i	$-0.368641\pi$
$577$	11117.5	0.802128	0.401064	+	0.916050i	$0.368641\pi$
$578$	20845.8	1.50012
$579$	−8472.45	−0.608122
$580$	17692.9	1.26665
$581$	2036.96	0.145452
$582$	43101.8	3.06981
$583$	3530.73	0.250820
$584$	−940.189	−0.0666187
$585$	2552.33	0.180386
$586$	−15544.1	−1.09577
$587$	−3405.84	−0.239479	−0.119739	−	0.992805i	$-0.538206\pi$
$587$	−3405.84	−0.239479	−0.119739	+	0.992805i	$0.538206\pi$
$588$	11994.7	0.841249
$589$	−8296.12	−0.580366
$590$	15407.9	1.07514
$591$	−27841.0	−1.93778
$592$	6191.99	0.429881
$593$	−18335.5	−1.26973	−0.634865	−	0.772623i	$-0.718944\pi$
$593$	−18335.5	−1.26973	−0.634865	+	0.772623i	$0.718944\pi$
$594$	699.182	0.0482959
$595$	−18302.7	−1.26107
$596$	−5120.79	−0.351939
$597$	5400.77	0.370249
$598$	2708.40	0.185208
$599$	−21733.7	−1.48249	−0.741246	−	0.671233i	$-0.765765\pi$
$599$	−21733.7	−1.48249	−0.741246	+	0.671233i	$0.765765\pi$
$600$	−1232.67	−0.0838725
$601$	−21429.3	−1.45444	−0.727221	−	0.686404i	$-0.759188\pi$
$601$	−21429.3	−1.45444	−0.727221	+	0.686404i	$0.759188\pi$
$602$	42737.1	2.89341
$603$	20093.4	1.35699
$604$	20135.7	1.35647
$605$	−956.456	−0.0642735
$606$	18331.8	1.22884
$607$	21233.2	1.41982	0.709909	−	0.704293i	$-0.248736\pi$
$607$	21233.2	1.41982	0.709909	+	0.704293i	$0.248736\pi$
$608$	14025.7	0.935558
$609$	−42995.3	−2.86085
$610$	4286.34	0.284507
$611$	−2715.47	−0.179797
$612$	21556.1	1.42378
$613$	25855.1	1.70355	0.851776	−	0.523906i	$-0.175526\pi$
$613$	25855.1	1.70355	0.851776	+	0.523906i	$0.175526\pi$
$614$	22512.1	1.47967
$615$	−14599.0	−0.957217
$616$	−696.864	−0.0455803
$617$	15792.0	1.03041	0.515205	−	0.857067i	$-0.327716\pi$
$617$	15792.0	1.03041	0.515205	+	0.857067i	$0.327716\pi$
$618$	14023.5	0.912796
$619$	−28082.5	−1.82348	−0.911739	−	0.410771i	$-0.865260\pi$
$619$	−28082.5	−1.82348	−0.911739	+	0.410771i	$0.865260\pi$
$620$	−10519.1	−0.681382
$621$	794.350	0.0513304
$622$	−24184.8	−1.55904
$623$	−19573.6	−1.25875
$624$	5445.94	0.349378
$625$	−3901.91	−0.249722
$626$	−28449.6	−1.81641
$627$	4281.03	0.272676
$628$	−11431.9	−0.726408
$629$	−10651.9	−0.675229
$630$	−18544.0	−1.17271
$631$	−14210.8	−0.896550	−0.448275	−	0.893896i	$-0.647962\pi$
$631$	−14210.8	−0.896550	−0.448275	+	0.893896i	$0.647962\pi$
$632$	2286.89	0.143936
$633$	1760.89	0.110567
$634$	986.522	0.0617978
$635$	9548.78	0.596743
$636$	−20037.8	−1.24929
$637$	−2497.79	−0.155362
$638$	11594.0	0.719455
$639$	16044.8	0.993304
$640$	2761.11	0.170535
$641$	420.062	0.0258837	0.0129419	−	0.999916i	$-0.495880\pi$
$641$	420.062	0.0258837	0.0129419	+	0.999916i	$0.495880\pi$
$642$	−38940.8	−2.39388
$643$	2055.22	0.126050	0.0630248	−	0.998012i	$-0.479925\pi$
$643$	2055.22	0.126050	0.0630248	+	0.998012i	$0.479925\pi$
$644$	−10234.8	−0.626255
$645$	−25751.2	−1.57202
$646$	−22090.8	−1.34544
$647$	19884.9	1.20828	0.604138	−	0.796880i	$-0.293518\pi$
$647$	19884.9	1.20828	0.604138	+	0.796880i	$0.293518\pi$
$648$	−2143.48	−0.129944
$649$	5251.44	0.317623
$650$	3318.34	0.200240
$651$	25562.2	1.53896
$652$	12928.0	0.776533
$653$	−1378.77	−0.0826272	−0.0413136	−	0.999146i	$-0.513154\pi$
$653$	−1378.77	−0.0826272	−0.0413136	+	0.999146i	$0.513154\pi$
$654$	−17067.7	−1.02049
$655$	11171.4	0.666413
$656$	−14925.4	−0.888322
$657$	−8527.18	−0.506358
$658$	19729.3	1.16889
$659$	16598.2	0.981145	0.490572	−	0.871400i	$-0.336788\pi$
$659$	16598.2	0.981145	0.490572	+	0.871400i	$0.336788\pi$
$660$	5428.14	0.320137
$661$	−6922.64	−0.407352	−0.203676	−	0.979038i	$-0.565289\pi$
$661$	−6922.64	−0.407352	−0.203676	+	0.979038i	$0.565289\pi$
$662$	20146.5	1.18280
$663$	−9368.47	−0.548780
$664$	241.142	0.0140935
$665$	9884.27	0.576385
$666$	−10792.3	−0.627919
$667$	13172.1	0.764659
$668$	28599.2	1.65649
$669$	−23107.0	−1.33538
$670$	−26109.4	−1.50552
$671$	1460.91	0.0840503
$672$	−43216.5	−2.48082
$673$	28758.7	1.64720	0.823600	−	0.567172i	$-0.191962\pi$
$673$	28758.7	1.64720	0.823600	+	0.567172i	$0.191962\pi$
$674$	−20849.1	−1.19151
$675$	973.241	0.0554964
$676$	1465.35	0.0833724
$677$	−24543.4	−1.39332	−0.696660	−	0.717401i	$-0.745331\pi$
$677$	−24543.4	−1.39332	−0.696660	+	0.717401i	$0.745331\pi$
$678$	26109.1	1.47893
$679$	33917.8	1.91700
$680$	−2166.73	−0.122191
$681$	−39471.5	−2.22107
$682$	−6893.07	−0.387022
$683$	17920.9	1.00399	0.501994	−	0.864871i	$-0.332600\pi$
$683$	17920.9	1.00399	0.501994	+	0.864871i	$0.332600\pi$
$684$	−11641.3	−0.650754
$685$	−15828.0	−0.882857
$686$	−14249.2	−0.793059
$687$	390.744	0.0216999
$688$	−26327.0	−1.45888
$689$	4172.68	0.230721
$690$	11856.9	0.654182
$691$	1159.09	0.0638119	0.0319059	−	0.999491i	$-0.489842\pi$
$691$	1159.09	0.0638119	0.0319059	+	0.999491i	$0.489842\pi$
$692$	−33125.9	−1.81974
$693$	−6320.31	−0.346448
$694$	−30291.5	−1.65684
$695$	−21962.3	−1.19867
$696$	−5089.92	−0.277202
$697$	25675.7	1.39532
$698$	−13778.0	−0.747144
$699$	−269.649	−0.0145909
$700$	−12539.7	−0.677083
$701$	−9161.83	−0.493634	−0.246817	−	0.969062i	$-0.579385\pi$
$701$	−9161.83	−0.493634	−0.246817	+	0.969062i	$0.579385\pi$
$702$	826.305	0.0444258
$703$	5752.51	0.308620
$704$	6533.47	0.349772
$705$	−11887.9	−0.635069
$706$	−8344.58	−0.444833
$707$	14425.7	0.767375
$708$	−29803.3	−1.58203
$709$	26126.5	1.38392	0.691961	−	0.721935i	$-0.256747\pi$
$709$	26126.5	1.38392	0.691961	+	0.721935i	$0.256747\pi$
$710$	−20848.6	−1.10202
$711$	20741.2	1.09403
$712$	−2317.19	−0.121967
$713$	−7831.31	−0.411339
$714$	68066.8	3.56770
$715$	−1130.36	−0.0591230
$716$	24790.1	1.29392
$717$	−5280.67	−0.275049
$718$	−35673.1	−1.85419
$719$	12274.6	0.636672	0.318336	−	0.947978i	$-0.396876\pi$
$719$	12274.6	0.636672	0.318336	+	0.947978i	$0.396876\pi$
$720$	11423.5	0.591289
$721$	11035.4	0.570014
$722$	−16075.1	−0.828606
$723$	−30747.5	−1.58162
$724$	7868.81	0.403925
$725$	16138.6	0.826720
$726$	3557.02	0.181836
$727$	17052.2	0.869919	0.434959	−	0.900450i	$-0.356763\pi$
$727$	17052.2	0.869919	0.434959	+	0.900450i	$0.356763\pi$
$728$	−823.566	−0.0419277
$729$	−16414.4	−0.833937
$730$	11080.3	0.561779
$731$	45289.5	2.29151
$732$	−8291.04	−0.418641
$733$	13561.6	0.683368	0.341684	−	0.939815i	$-0.389003\pi$
$733$	13561.6	0.683368	0.341684	+	0.939815i	$0.389003\pi$
$734$	−33820.2	−1.70072
$735$	−10934.9	−0.548762
$736$	13239.9	0.663084
$737$	−8898.84	−0.444767
$738$	26014.2	1.29756
$739$	34216.0	1.70319	0.851594	−	0.524202i	$-0.175636\pi$
$739$	34216.0	1.70319	0.851594	+	0.524202i	$0.175636\pi$
$740$	7293.90	0.362337
$741$	5059.40	0.250826
$742$	−30316.7	−1.49995
$743$	−24013.0	−1.18567	−0.592835	−	0.805324i	$-0.701991\pi$
$743$	−24013.0	−1.18567	−0.592835	+	0.805324i	$0.701991\pi$
$744$	3026.14	0.149118
$745$	4668.33	0.229576
$746$	6117.73	0.300249
$747$	2187.07	0.107123
$748$	−9546.63	−0.466657
$749$	−30643.4	−1.49491
$750$	43573.4	2.12144
$751$	−22818.4	−1.10873	−0.554365	−	0.832274i	$-0.687039\pi$
$751$	−22818.4	−1.10873	−0.554365	+	0.832274i	$0.687039\pi$
$752$	−12153.7	−0.589360
$753$	27460.8	1.32899
$754$	13702.0	0.661802
$755$	−18356.5	−0.884852
$756$	−3122.54	−0.150219
$757$	26225.7	1.25917	0.629584	−	0.776932i	$-0.283225\pi$
$757$	26225.7	1.25917	0.629584	+	0.776932i	$0.283225\pi$
$758$	58877.4	2.82127
$759$	4041.17	0.193261
$760$	1170.13	0.0558488
$761$	−19905.3	−0.948184	−0.474092	−	0.880475i	$-0.657224\pi$
$761$	−19905.3	−0.948184	−0.474092	+	0.880475i	$0.657224\pi$
$762$	−35511.5	−1.68825
$763$	−13431.0	−0.637265
$764$	−25964.1	−1.22951
$765$	−19651.5	−0.928758
$766$	−34613.2	−1.63267
$767$	6206.25	0.292170
$768$	23942.5	1.12494
$769$	15268.7	0.715998	0.357999	−	0.933722i	$-0.383459\pi$
$769$	15268.7	0.715998	0.357999	+	0.933722i	$0.383459\pi$
$770$	8212.63	0.384367
$771$	18608.7	0.869228
$772$	−10203.3	−0.475680
$773$	5536.42	0.257608	0.128804	−	0.991670i	$-0.458886\pi$
$773$	5536.42	0.257608	0.128804	+	0.991670i	$0.458886\pi$
$774$	45886.5	2.13095
$775$	−9594.97	−0.444724
$776$	4015.30	0.185748
$777$	−17724.8	−0.818369
$778$	−7160.65	−0.329977
$779$	−13866.0	−0.637744
$780$	6415.08	0.294483
$781$	−7105.81	−0.325564
$782$	−20853.1	−0.953588
$783$	4018.69	0.183418
$784$	−11179.4	−0.509265
$785$	10421.8	0.473849
$786$	−41545.7	−1.88535
$787$	−27861.4	−1.26195	−0.630974	−	0.775804i	$-0.717345\pi$
$787$	−27861.4	−1.26195	−0.630974	+	0.775804i	$0.717345\pi$
$788$	−33528.8	−1.51575
$789$	−57684.6	−2.60282
$790$	−26951.2	−1.21377
$791$	20545.9	0.923549
$792$	−748.218	−0.0335692
$793$	1726.53	0.0773150
$794$	25415.8	1.13598
$795$	18267.3	0.814937
$796$	6504.11	0.289613
$797$	−25126.6	−1.11673	−0.558363	−	0.829596i	$-0.688571\pi$
$797$	−25126.6	−1.11673	−0.558363	+	0.829596i	$0.688571\pi$
$798$	−36759.2	−1.63065
$799$	20907.6	0.925729
$800$	16221.6	0.716901
$801$	−21016.1	−0.927049
$802$	24653.7	1.08547
$803$	3776.46	0.165963
$804$	50503.3	2.21531
$805$	9330.48	0.408517
$806$	−8146.36	−0.356009
$807$	−46024.5	−2.00761
$808$	1707.76	0.0743549
$809$	−23284.0	−1.01190	−0.505948	−	0.862564i	$-0.668857\pi$
$809$	−23284.0	−1.01190	−0.505948	+	0.862564i	$0.668857\pi$
$810$	25261.2	1.09579
$811$	1713.56	0.0741937	0.0370969	−	0.999312i	$-0.488189\pi$
$811$	1713.56	0.0741937	0.0370969	+	0.999312i	$0.488189\pi$
$812$	−51778.9	−2.23779
$813$	35891.7	1.54831
$814$	4779.63	0.205806
$815$	−11785.7	−0.506546
$816$	−41930.6	−1.79885
$817$	−24458.4	−1.04736
$818$	66598.8	2.84666
$819$	−7469.46	−0.318686
$820$	−17581.5	−0.748746
$821$	34054.5	1.44764	0.723819	−	0.689990i	$-0.242385\pi$
$821$	34054.5	1.44764	0.723819	+	0.689990i	$0.242385\pi$
$822$	58863.6	2.49769
$823$	26103.7	1.10561	0.552806	−	0.833310i	$-0.313557\pi$
$823$	26103.7	1.10561	0.552806	+	0.833310i	$0.313557\pi$
$824$	1306.41	0.0552316
$825$	4951.27	0.208947
$826$	−45091.6	−1.89944
$827$	10887.7	0.457802	0.228901	−	0.973450i	$-0.426487\pi$
$827$	10887.7	0.457802	0.228901	+	0.973450i	$0.426487\pi$
$828$	−10989.1	−0.461227
$829$	−43276.9	−1.81311	−0.906556	−	0.422086i	$-0.861298\pi$
$829$	−43276.9	−1.81311	−0.906556	+	0.422086i	$0.861298\pi$
$830$	−2841.89	−0.118847
$831$	21504.3	0.897686
$832$	7721.38	0.321744
$833$	19231.5	0.799920
$834$	81676.9	3.39118
$835$	−26072.2	−1.08056
$836$	5155.62	0.213290
$837$	−2389.26	−0.0986676
$838$	65562.5	2.70265
$839$	15155.9	0.623648	0.311824	−	0.950140i	$-0.399060\pi$
$839$	15155.9	0.623648	0.311824	+	0.950140i	$0.399060\pi$
$840$	−3605.44	−0.148095
$841$	42250.2	1.73234
$842$	18960.3	0.776029
$843$	40710.0	1.66326
$844$	2120.63	0.0864869
$845$	−1335.88	−0.0543853
$846$	21183.2	0.860868
$847$	2799.10	0.113552
$848$	18675.7	0.756282
$849$	−66895.9	−2.70419
$850$	−25549.4	−1.03098
$851$	5430.21	0.218737
$852$	40327.3	1.62159
$853$	−14099.3	−0.565943	−0.282972	−	0.959128i	$-0.591320\pi$
$853$	−14099.3	−0.565943	−0.282972	+	0.959128i	$0.591320\pi$
$854$	−12544.1	−0.502636
$855$	10612.7	0.424498
$856$	−3627.67	−0.144849
$857$	−22155.2	−0.883089	−0.441545	−	0.897239i	$-0.645569\pi$
$857$	−22155.2	−0.883089	−0.441545	+	0.897239i	$0.645569\pi$
$858$	4203.75	0.167265
$859$	−16200.3	−0.643476	−0.321738	−	0.946829i	$-0.604267\pi$
$859$	−16200.3	−0.643476	−0.321738	+	0.946829i	$0.604267\pi$
$860$	−31012.0	−1.22965
$861$	42724.4	1.69111
$862$	−49566.3	−1.95851
$863$	−9756.57	−0.384840	−0.192420	−	0.981313i	$-0.561634\pi$
$863$	−9756.57	−0.384840	−0.192420	+	0.981313i	$0.561634\pi$
$864$	4039.37	0.159053
$865$	30199.0	1.18705
$866$	26292.8	1.03172
$867$	36759.1	1.43991
$868$	30784.4	1.20379
$869$	−9185.75	−0.358579
$870$	59985.3	2.33758
$871$	−10516.8	−0.409126
$872$	−1590.00	−0.0617479
$873$	36417.3	1.41184
$874$	11261.6	0.435847
$875$	34288.9	1.32477
$876$	−21432.4	−0.826638
$877$	29588.3	1.13925	0.569627	−	0.821903i	$-0.307088\pi$
$877$	29588.3	1.13925	0.569627	+	0.821903i	$0.307088\pi$
$878$	−57182.9	−2.19798
$879$	−27410.2	−1.05179
$880$	−5059.16	−0.193800
$881$	37205.4	1.42279	0.711396	−	0.702791i	$-0.248063\pi$
$881$	37205.4	1.42279	0.711396	+	0.702791i	$0.248063\pi$
$882$	19485.1	0.743874
$883$	−35092.8	−1.33745	−0.668725	−	0.743510i	$-0.733160\pi$
$883$	−35092.8	−1.33745	−0.668725	+	0.743510i	$0.733160\pi$
$884$	−11282.4	−0.429262
$885$	27169.9	1.03199
$886$	70834.1	2.68591
$887$	−25549.0	−0.967138	−0.483569	−	0.875306i	$-0.660660\pi$
$887$	−25549.0	−0.967138	−0.483569	+	0.875306i	$0.660660\pi$
$888$	−2098.31	−0.0792959
$889$	−27944.8	−1.05426
$890$	27308.4	1.02851
$891$	8609.75	0.323723
$892$	−27827.6	−1.04455
$893$	−11291.0	−0.423113
$894$	−17361.3	−0.649495
$895$	−22599.7	−0.844049
$896$	−8080.46	−0.301283
$897$	4775.93	0.177775
$898$	44247.8	1.64428
$899$	−39619.4	−1.46983
$900$	−13463.8	−0.498661
$901$	−32127.3	−1.18792
$902$	−11521.0	−0.425285
$903$	75361.7	2.77728
$904$	2432.29	0.0894874
$905$	−7173.54	−0.263488
$906$	68267.1	2.50334
$907$	−1157.05	−0.0423587	−0.0211794	−	0.999776i	$-0.506742\pi$
$907$	−1157.05	−0.0423587	−0.0211794	+	0.999776i	$0.506742\pi$
$908$	−47535.2	−1.73735
$909$	15488.8	0.565160
$910$	9705.84	0.353566
$911$	−16077.6	−0.584715	−0.292358	−	0.956309i	$-0.594440\pi$
$911$	−16077.6	−0.584715	−0.292358	+	0.956309i	$0.594440\pi$
$912$	22644.4	0.822185
$913$	−968.596	−0.0351104
$914$	−59650.0	−2.15869
$915$	7558.46	0.273087
$916$	470.570	0.0169739
$917$	−32693.3	−1.17735
$918$	−6362.08	−0.228736
$919$	19988.1	0.717463	0.358731	−	0.933441i	$-0.383209\pi$
$919$	19988.1	0.717463	0.358731	+	0.933441i	$0.383209\pi$
$920$	1104.57	0.0395833
$921$	39697.5	1.42028
$922$	−16418.3	−0.586452
$923$	−8397.77	−0.299476
$924$	−15885.6	−0.565583
$925$	6653.12	0.236490
$926$	−4506.13	−0.159914
$927$	11848.7	0.419807
$928$	66982.0	2.36939
$929$	−36505.2	−1.28923	−0.644616	−	0.764506i	$-0.722983\pi$
$929$	−36505.2	−1.28923	−0.644616	+	0.764506i	$0.722983\pi$
$930$	−35663.4	−1.25747
$931$	−10385.9	−0.365611
$932$	−324.737	−0.0114132
$933$	−42646.9	−1.49646
$934$	−19655.9	−0.688611
$935$	8703.11	0.304409
$936$	−884.258	−0.0308791
$937$	−19159.6	−0.668001	−0.334000	−	0.942573i	$-0.608399\pi$
$937$	−19159.6	−0.668001	−0.334000	+	0.942573i	$0.608399\pi$
$938$	76410.1	2.65978
$939$	−50167.4	−1.74351
$940$	−14316.5	−0.496758
$941$	24590.0	0.851871	0.425935	−	0.904754i	$-0.359945\pi$
$941$	24590.0	0.851871	0.425935	+	0.904754i	$0.359945\pi$
$942$	−38758.3	−1.34057
$943$	−13089.2	−0.452006
$944$	27777.4	0.957709
$945$	2846.64	0.0979907
$946$	−20321.9	−0.698439
$947$	−53885.3	−1.84904	−0.924518	−	0.381139i	$-0.875532\pi$
$947$	−53885.3	−1.84904	−0.924518	+	0.381139i	$0.875532\pi$
$948$	52131.5	1.78603
$949$	4463.09	0.152664
$950$	13797.8	0.471221
$951$	1739.61	0.0593174
$952$	6340.99	0.215875
$953$	−14645.2	−0.497802	−0.248901	−	0.968529i	$-0.580069\pi$
$953$	−14645.2	−0.497802	−0.248901	+	0.968529i	$0.580069\pi$
$954$	−32550.8	−1.10469
$955$	23669.9	0.802032
$956$	−6359.48	−0.215147
$957$	20444.7	0.690578
$958$	45090.2	1.52067
$959$	46321.1	1.55974
$960$	33802.9	1.13644
$961$	−6235.86	−0.209320
$962$	5648.66	0.189314
$963$	−32901.7	−1.10098
$964$	−37029.0	−1.23716
$965$	9301.76	0.310295
$966$	−34699.6	−1.15574
$967$	−27135.1	−0.902385	−0.451193	−	0.892427i	$-0.649001\pi$
$967$	−27135.1	−0.902385	−0.451193	+	0.892427i	$0.649001\pi$
$968$	331.366	0.0110026
$969$	−38954.5	−1.29143
$970$	−47320.8	−1.56637
$971$	−21403.8	−0.707395	−0.353698	−	0.935360i	$-0.615076\pi$
$971$	−21403.8	−0.707395	−0.353698	+	0.935360i	$0.615076\pi$
$972$	−45218.1	−1.49215
$973$	64273.4	2.11769
$974$	28632.2	0.941926
$975$	5851.50	0.192203
$976$	7727.45	0.253432
$977$	16330.6	0.534763	0.267382	−	0.963591i	$-0.413842\pi$
$977$	16330.6	0.534763	0.267382	+	0.963591i	$0.413842\pi$
$978$	43830.5	1.43307
$979$	9307.46	0.303849
$980$	−13168.8	−0.429248
$981$	−14420.7	−0.469336
$982$	−17879.7	−0.581023
$983$	−40861.7	−1.32582	−0.662912	−	0.748698i	$-0.730680\pi$
$983$	−40861.7	−1.32582	−0.662912	+	0.748698i	$0.730680\pi$
$984$	5057.85	0.163860
$985$	30566.2	0.988752
$986$	−105498.	−3.40744
$987$	34790.3	1.12197
$988$	6093.00	0.196199
$989$	−23088.0	−0.742322
$990$	8817.85	0.283080
$991$	13405.5	0.429708	0.214854	−	0.976646i	$-0.431072\pi$
$991$	13405.5	0.429708	0.214854	+	0.976646i	$0.431072\pi$
$992$	−39823.2	−1.27459
$993$	35525.9	1.13533
$994$	61014.1	1.94693
$995$	−5929.42	−0.188920
$996$	5497.04	0.174880
$997$	49438.4	1.57044	0.785221	−	0.619215i	$-0.212549\pi$
$997$	49438.4	1.57044	0.785221	+	0.619215i	$0.212549\pi$
$998$	−31487.1	−0.998703
$999$	1656.70	0.0524682

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.a.c.1.8	✓	9
3.2	odd	2		1287.4.a.k.1.2		9
4.3	odd	2		2288.4.a.r.1.3		9
11.10	odd	2		1573.4.a.e.1.2		9
13.12	even	2		1859.4.a.d.1.2		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.a.c.1.8	✓	9	1.1	even	1	trivial
1287.4.a.k.1.2		9	3.2	odd	2
1573.4.a.e.1.2		9	11.10	odd	2
1859.4.a.d.1.2		9	13.12	even	2
2288.4.a.r.1.3		9	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	143.a (trivial)

\(f(q)\)	\(=\)	\(q+4.08298 q^{2} +7.19985 q^{3} +8.67073 q^{4} -7.90460 q^{5} +29.3968 q^{6} +23.1330 q^{7} +2.73856 q^{8} +24.8378 q^{9} +O(q^{10})\)	\(q+4.08298 q^{2} +7.19985 q^{3} +8.67073 q^{4} -7.90460 q^{5} +29.3968 q^{6} +23.1330 q^{7} +2.73856 q^{8} +24.8378 q^{9} -32.2743 q^{10} -11.0000 q^{11} +62.4279 q^{12} -13.0000 q^{13} +94.4517 q^{14} -56.9119 q^{15} -58.1843 q^{16} +100.093 q^{17} +101.412 q^{18} -54.0546 q^{19} -68.5386 q^{20} +166.554 q^{21} -44.9128 q^{22} -51.0260 q^{23} +19.7172 q^{24} -62.5174 q^{25} -53.0787 q^{26} -15.5675 q^{27} +200.580 q^{28} -258.146 q^{29} -232.370 q^{30} +153.477 q^{31} -259.474 q^{32} -79.1983 q^{33} +408.676 q^{34} -182.857 q^{35} +215.362 q^{36} -106.420 q^{37} -220.704 q^{38} -93.5980 q^{39} -21.6472 q^{40} +256.519 q^{41} +680.038 q^{42} +452.475 q^{43} -95.3780 q^{44} -196.333 q^{45} -208.338 q^{46} +208.882 q^{47} -418.918 q^{48} +192.137 q^{49} -255.257 q^{50} +720.652 q^{51} -112.719 q^{52} -320.975 q^{53} -63.5620 q^{54} +86.9506 q^{55} +63.3512 q^{56} -389.185 q^{57} -1054.00 q^{58} -477.404 q^{59} -493.467 q^{60} -132.810 q^{61} +626.643 q^{62} +574.574 q^{63} -593.952 q^{64} +102.760 q^{65} -323.365 q^{66} +808.985 q^{67} +867.876 q^{68} -367.380 q^{69} -746.603 q^{70} +645.982 q^{71} +68.0198 q^{72} -343.315 q^{73} -434.512 q^{74} -450.115 q^{75} -468.692 q^{76} -254.463 q^{77} -382.159 q^{78} +835.068 q^{79} +459.924 q^{80} -782.704 q^{81} +1047.36 q^{82} +88.0542 q^{83} +1444.15 q^{84} -791.192 q^{85} +1847.45 q^{86} -1858.61 q^{87} -30.1242 q^{88} -846.133 q^{89} -801.623 q^{90} -300.729 q^{91} -442.433 q^{92} +1105.01 q^{93} +852.862 q^{94} +427.280 q^{95} -1868.17 q^{96} +1466.21 q^{97} +784.493 q^{98} -273.216 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 8 q^{3} + 46 q^{4} + 30 q^{5} + 34 q^{6} + 25 q^{7} + 36 q^{8} + 91 q^{9}+O(q^{10}) \) 9 * q + 8 * q^3 + 46 * q^4 + 30 * q^5 + 34 * q^6 + 25 * q^7 + 36 * q^8 + 91 * q^9	\( 9 q + 8 q^{3} + 46 q^{4} + 30 q^{5} + 34 q^{6} + 25 q^{7} + 36 q^{8} + 91 q^{9} - 22 q^{10} - 99 q^{11} + 181 q^{12} - 117 q^{13} + 351 q^{15} + 130 q^{16} + 53 q^{17} + 33 q^{18} + 69 q^{19} + 282 q^{20} + 463 q^{21} + 216 q^{23} - 121 q^{24} + 617 q^{25} + 275 q^{27} + 279 q^{28} - 91 q^{29} + 29 q^{30} + 636 q^{31} + 663 q^{32} - 88 q^{33} + 423 q^{34} - 358 q^{35} - 252 q^{36} + 967 q^{37} - 101 q^{38} - 104 q^{39} + 652 q^{40} - 226 q^{41} - 1186 q^{42} + 42 q^{43} - 506 q^{44} + 5 q^{45} - 1127 q^{46} - 269 q^{47} - 1820 q^{48} + 228 q^{49} - 1374 q^{50} - 589 q^{51} - 598 q^{52} + 1227 q^{53} - 2438 q^{54} - 330 q^{55} - 659 q^{56} - 71 q^{57} + 471 q^{58} - 613 q^{59} - 859 q^{60} + 427 q^{61} - 1714 q^{62} + 305 q^{63} - 1194 q^{64} - 390 q^{65} - 374 q^{66} - 271 q^{67} - 2835 q^{68} - 846 q^{69} - 102 q^{70} + 2279 q^{71} - 2400 q^{72} + 3602 q^{73} - 4955 q^{74} - 883 q^{75} + 1126 q^{76} - 275 q^{77} - 442 q^{78} - 1182 q^{79} - 2360 q^{80} + 2697 q^{81} + 1007 q^{82} - 1877 q^{83} + 1618 q^{84} - 441 q^{85} + 830 q^{86} + 1942 q^{87} - 396 q^{88} + 1258 q^{89} - 5669 q^{90} - 325 q^{91} + 1046 q^{92} + 1556 q^{93} + 1439 q^{94} + 2032 q^{95} - 3417 q^{96} + 4002 q^{97} - 1855 q^{98} - 1001 q^{99}+O(q^{100}) \) 9 * q + 8 * q^3 + 46 * q^4 + 30 * q^5 + 34 * q^6 + 25 * q^7 + 36 * q^8 + 91 * q^9 - 22 * q^10 - 99 * q^11 + 181 * q^12 - 117 * q^13 + 351 * q^15 + 130 * q^16 + 53 * q^17 + 33 * q^18 + 69 * q^19 + 282 * q^20 + 463 * q^21 + 216 * q^23 - 121 * q^24 + 617 * q^25 + 275 * q^27 + 279 * q^28 - 91 * q^29 + 29 * q^30 + 636 * q^31 + 663 * q^32 - 88 * q^33 + 423 * q^34 - 358 * q^35 - 252 * q^36 + 967 * q^37 - 101 * q^38 - 104 * q^39 + 652 * q^40 - 226 * q^41 - 1186 * q^42 + 42 * q^43 - 506 * q^44 + 5 * q^45 - 1127 * q^46 - 269 * q^47 - 1820 * q^48 + 228 * q^49 - 1374 * q^50 - 589 * q^51 - 598 * q^52 + 1227 * q^53 - 2438 * q^54 - 330 * q^55 - 659 * q^56 - 71 * q^57 + 471 * q^58 - 613 * q^59 - 859 * q^60 + 427 * q^61 - 1714 * q^62 + 305 * q^63 - 1194 * q^64 - 390 * q^65 - 374 * q^66 - 271 * q^67 - 2835 * q^68 - 846 * q^69 - 102 * q^70 + 2279 * q^71 - 2400 * q^72 + 3602 * q^73 - 4955 * q^74 - 883 * q^75 + 1126 * q^76 - 275 * q^77 - 442 * q^78 - 1182 * q^79 - 2360 * q^80 + 2697 * q^81 + 1007 * q^82 - 1877 * q^83 + 1618 * q^84 - 441 * q^85 + 830 * q^86 + 1942 * q^87 - 396 * q^88 + 1258 * q^89 - 5669 * q^90 - 325 * q^91 + 1046 * q^92 + 1556 * q^93 + 1439 * q^94 + 2032 * q^95 - 3417 * q^96 + 4002 * q^97 - 1855 * q^98 - 1001 * q^99

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