LMFDB - Embedded newform 1441.4.a.c.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1441,4,Mod(1,1441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1441, 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("1441.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1441 = 11 \cdot 131 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1441.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:	$85.0217523183$
Analytic rank:	$0$
Dimension:	$84$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	1441.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.49484 q^{2} -4.17061 q^{3} +12.2036 q^{4} +2.72170 q^{5} +18.7463 q^{6} +3.24249 q^{7} -18.8947 q^{8} -9.60598 q^{9} +O(q^{10})$	\(q-4.49484 q^{2} -4.17061 q^{3} +12.2036 q^{4} +2.72170 q^{5} +18.7463 q^{6} +3.24249 q^{7} -18.8947 q^{8} -9.60598 q^{9} -12.2336 q^{10} -11.0000 q^{11} -50.8966 q^{12} -3.41845 q^{13} -14.5745 q^{14} -11.3512 q^{15} -12.7005 q^{16} -57.9800 q^{17} +43.1774 q^{18} -150.779 q^{19} +33.2146 q^{20} -13.5232 q^{21} +49.4433 q^{22} -37.6079 q^{23} +78.8023 q^{24} -117.592 q^{25} +15.3654 q^{26} +152.669 q^{27} +39.5701 q^{28} -265.778 q^{29} +51.0217 q^{30} -9.05701 q^{31} +208.244 q^{32} +45.8768 q^{33} +260.611 q^{34} +8.82507 q^{35} -117.228 q^{36} +313.676 q^{37} +677.729 q^{38} +14.2571 q^{39} -51.4256 q^{40} -146.193 q^{41} +60.7845 q^{42} -223.148 q^{43} -134.240 q^{44} -26.1446 q^{45} +169.042 q^{46} -313.901 q^{47} +52.9688 q^{48} -332.486 q^{49} +528.559 q^{50} +241.812 q^{51} -41.7175 q^{52} -31.4452 q^{53} -686.225 q^{54} -29.9387 q^{55} -61.2657 q^{56} +628.842 q^{57} +1194.63 q^{58} +726.535 q^{59} -138.525 q^{60} -215.414 q^{61} +40.7098 q^{62} -31.1473 q^{63} -834.420 q^{64} -9.30400 q^{65} -206.209 q^{66} +312.730 q^{67} -707.567 q^{68} +156.848 q^{69} -39.6673 q^{70} -761.261 q^{71} +181.502 q^{72} +1058.98 q^{73} -1409.92 q^{74} +490.432 q^{75} -1840.05 q^{76} -35.6674 q^{77} -64.0832 q^{78} -812.979 q^{79} -34.5669 q^{80} -377.364 q^{81} +657.113 q^{82} +102.415 q^{83} -165.032 q^{84} -157.804 q^{85} +1003.02 q^{86} +1108.46 q^{87} +207.841 q^{88} +351.773 q^{89} +117.516 q^{90} -11.0843 q^{91} -458.953 q^{92} +37.7733 q^{93} +1410.94 q^{94} -410.376 q^{95} -868.505 q^{96} -914.681 q^{97} +1494.47 q^{98} +105.666 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q + 12 q^{2} + 14 q^{3} + 380 q^{4} + 38 q^{5} + 59 q^{6} + 11 q^{7} + 162 q^{8} + 856 q^{9}+O(q^{10}) $ 84 * q + 12 * q^2 + 14 * q^3 + 380 * q^4 + 38 * q^5 + 59 * q^6 + 11 * q^7 + 162 * q^8 + 856 * q^9	\( 84 q + 12 q^{2} + 14 q^{3} + 380 q^{4} + 38 q^{5} + 59 q^{6} + 11 q^{7} + 162 q^{8} + 856 q^{9} - 58 q^{10} - 924 q^{11} + 152 q^{12} - 202 q^{13} + 306 q^{14} + 630 q^{15} + 1720 q^{16} + 148 q^{17} + 251 q^{18} + 33 q^{19} + 510 q^{20} - 206 q^{21} - 132 q^{22} + 938 q^{23} + 518 q^{24} + 2288 q^{25} + 788 q^{26} + 506 q^{27} + 52 q^{28} + 197 q^{29} + 93 q^{30} + 1018 q^{31} + 1173 q^{32} - 154 q^{33} - 16 q^{34} + 1126 q^{35} + 6815 q^{36} + 1059 q^{37} + 3259 q^{38} + 1350 q^{39} + 2912 q^{40} + 523 q^{41} + 1171 q^{42} + 110 q^{43} - 4180 q^{44} + 572 q^{45} - 552 q^{46} + 3764 q^{47} + 6132 q^{48} + 6165 q^{49} + 2316 q^{50} + 1910 q^{51} + 137 q^{52} + 2586 q^{53} + 5126 q^{54} - 418 q^{55} + 3853 q^{56} + 1480 q^{57} + 2576 q^{58} + 5392 q^{59} + 10535 q^{60} - 3704 q^{61} + 3766 q^{62} + 1375 q^{63} + 7804 q^{64} + 3178 q^{65} - 649 q^{66} + 2095 q^{67} + 1751 q^{68} + 2690 q^{69} + 1475 q^{70} + 10220 q^{71} + 4930 q^{72} - 100 q^{73} + 4970 q^{74} + 312 q^{75} + 1005 q^{76} - 121 q^{77} + 2325 q^{78} + 810 q^{79} + 12763 q^{80} + 14368 q^{81} + 2363 q^{82} + 3097 q^{83} + 6017 q^{84} - 1102 q^{85} + 4884 q^{86} + 2552 q^{87} - 1782 q^{88} + 7493 q^{89} + 1052 q^{90} + 2238 q^{91} + 9134 q^{92} + 4776 q^{93} + 1885 q^{94} + 6782 q^{95} + 10849 q^{96} + 1180 q^{97} + 13073 q^{98} - 9416 q^{99}+O(q^{100}) \) 84 * q + 12 * q^2 + 14 * q^3 + 380 * q^4 + 38 * q^5 + 59 * q^6 + 11 * q^7 + 162 * q^8 + 856 * q^9 - 58 * q^10 - 924 * q^11 + 152 * q^12 - 202 * q^13 + 306 * q^14 + 630 * q^15 + 1720 * q^16 + 148 * q^17 + 251 * q^18 + 33 * q^19 + 510 * q^20 - 206 * q^21 - 132 * q^22 + 938 * q^23 + 518 * q^24 + 2288 * q^25 + 788 * q^26 + 506 * q^27 + 52 * q^28 + 197 * q^29 + 93 * q^30 + 1018 * q^31 + 1173 * q^32 - 154 * q^33 - 16 * q^34 + 1126 * q^35 + 6815 * q^36 + 1059 * q^37 + 3259 * q^38 + 1350 * q^39 + 2912 * q^40 + 523 * q^41 + 1171 * q^42 + 110 * q^43 - 4180 * q^44 + 572 * q^45 - 552 * q^46 + 3764 * q^47 + 6132 * q^48 + 6165 * q^49 + 2316 * q^50 + 1910 * q^51 + 137 * q^52 + 2586 * q^53 + 5126 * q^54 - 418 * q^55 + 3853 * q^56 + 1480 * q^57 + 2576 * q^58 + 5392 * q^59 + 10535 * q^60 - 3704 * q^61 + 3766 * q^62 + 1375 * q^63 + 7804 * q^64 + 3178 * q^65 - 649 * q^66 + 2095 * q^67 + 1751 * q^68 + 2690 * q^69 + 1475 * q^70 + 10220 * q^71 + 4930 * q^72 - 100 * q^73 + 4970 * q^74 + 312 * q^75 + 1005 * q^76 - 121 * q^77 + 2325 * q^78 + 810 * q^79 + 12763 * q^80 + 14368 * q^81 + 2363 * q^82 + 3097 * q^83 + 6017 * q^84 - 1102 * q^85 + 4884 * q^86 + 2552 * q^87 - 1782 * q^88 + 7493 * q^89 + 1052 * q^90 + 2238 * q^91 + 9134 * q^92 + 4776 * q^93 + 1885 * q^94 + 6782 * q^95 + 10849 * q^96 + 1180 * q^97 + 13073 * q^98 - 9416 * 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 $

$2$	−4.49484	−1.58917	−0.794584	−	0.607155i	$-0.792311\pi$
$2$	−4.49484	−1.58917	−0.794584	+	0.607155i	$0.792311\pi$
$3$	−4.17061	−0.802635	−0.401318	−	0.915939i	$-0.631448\pi$
$3$	−4.17061	−0.802635	−0.401318	+	0.915939i	$0.631448\pi$
$4$	12.2036	1.52545
$5$	2.72170	0.243436	0.121718	−	0.992565i	$-0.461160\pi$
$5$	2.72170	0.243436	0.121718	+	0.992565i	$0.461160\pi$
$6$	18.7463	1.27552
$7$	3.24249	0.175078	0.0875389	−	0.996161i	$-0.472100\pi$
$7$	3.24249	0.175078	0.0875389	+	0.996161i	$0.472100\pi$
$8$	−18.8947	−0.835034
$9$	−9.60598	−0.355777
$10$	−12.2336	−0.386861
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	−50.8966	−1.22438
$13$	−3.41845	−0.0729314	−0.0364657	−	0.999335i	$-0.511610\pi$
$13$	−3.41845	−0.0729314	−0.0364657	+	0.999335i	$0.511610\pi$
$14$	−14.5745	−0.278228
$15$	−11.3512	−0.195390
$16$	−12.7005	−0.198445
$17$	−57.9800	−0.827190	−0.413595	−	0.910461i	$-0.635727\pi$
$17$	−57.9800	−0.827190	−0.413595	+	0.910461i	$0.635727\pi$
$18$	43.1774	0.565389
$19$	−150.779	−1.82059	−0.910293	−	0.413964i	$-0.864144\pi$
$19$	−150.779	−1.82059	−0.910293	+	0.413964i	$0.864144\pi$
$20$	33.2146	0.371350
$21$	−13.5232	−0.140524
$22$	49.4433	0.479152
$23$	−37.6079	−0.340947	−0.170474	−	0.985362i	$-0.554530\pi$
$23$	−37.6079	−0.340947	−0.170474	+	0.985362i	$0.554530\pi$
$24$	78.8023	0.670227
$25$	−117.592	−0.940739
$26$	15.3654	0.115900
$27$	152.669	1.08819
$28$	39.5701	0.267073
$29$	−265.778	−1.70186	−0.850928	−	0.525283i	$-0.823959\pi$
$29$	−265.778	−1.70186	−0.850928	+	0.525283i	$0.823959\pi$
$30$	51.0217	0.310508
$31$	−9.05701	−0.0524738	−0.0262369	−	0.999656i	$-0.508352\pi$
$31$	−9.05701	−0.0524738	−0.0262369	+	0.999656i	$0.508352\pi$
$32$	208.244	1.15040
$33$	45.8768	0.242004
$34$	260.611	1.31454
$35$	8.82507	0.0426203
$36$	−117.228	−0.542721
$37$	313.676	1.39373	0.696865	−	0.717203i	$-0.254578\pi$
$37$	313.676	1.39373	0.696865	+	0.717203i	$0.254578\pi$
$38$	677.729	2.89322
$39$	14.2571	0.0585373
$40$	−51.4256	−0.203277
$41$	−146.193	−0.556865	−0.278432	−	0.960456i	$-0.589815\pi$
$41$	−146.193	−0.556865	−0.278432	+	0.960456i	$0.589815\pi$
$42$	60.7845	0.223316
$43$	−223.148	−0.791390	−0.395695	−	0.918382i	$-0.629496\pi$
$43$	−223.148	−0.791390	−0.395695	+	0.918382i	$0.629496\pi$
$44$	−134.240	−0.459942
$45$	−26.1446	−0.0866089
$46$	169.042	0.541822
$47$	−313.901	−0.974196	−0.487098	−	0.873347i	$-0.661945\pi$
$47$	−313.901	−0.974196	−0.487098	+	0.873347i	$0.661945\pi$
$48$	52.9688	0.159279
$49$	−332.486	−0.969348
$50$	528.559	1.49499
$51$	241.812	0.663932
$52$	−41.7175	−0.111253
$53$	−31.4452	−0.0814969	−0.0407485	−	0.999169i	$-0.512974\pi$
$53$	−31.4452	−0.0814969	−0.0407485	+	0.999169i	$0.512974\pi$
$54$	−686.225	−1.72932
$55$	−29.9387	−0.0733987
$56$	−61.2657	−0.146196
$57$	628.842	1.46127
$58$	1194.63	2.70453
$59$	726.535	1.60317	0.801583	−	0.597884i	$-0.203992\pi$
$59$	726.535	1.60317	0.801583	+	0.597884i	$0.203992\pi$
$60$	−138.525	−0.298059
$61$	−215.414	−0.452147	−0.226074	−	0.974110i	$-0.572589\pi$
$61$	−215.414	−0.452147	−0.226074	+	0.974110i	$0.572589\pi$
$62$	40.7098	0.0833896
$63$	−31.1473	−0.0622887
$64$	−834.420	−1.62973
$65$	−9.30400	−0.0177541
$66$	−206.209	−0.384584
$67$	312.730	0.570240	0.285120	−	0.958492i	$-0.407966\pi$
$67$	312.730	0.570240	0.285120	+	0.958492i	$0.407966\pi$
$68$	−707.567	−1.26184
$69$	156.848	0.273656
$70$	−39.6673	−0.0677307
$71$	−761.261	−1.27247	−0.636233	−	0.771497i	$-0.719508\pi$
$71$	−761.261	−1.27247	−0.636233	+	0.771497i	$0.719508\pi$
$72$	181.502	0.297086
$73$	1058.98	1.69787	0.848933	−	0.528500i	$-0.177245\pi$
$73$	1058.98	1.69787	0.848933	+	0.528500i	$0.177245\pi$
$74$	−1409.92	−2.21487
$75$	490.432	0.755070
$76$	−1840.05	−2.77722
$77$	−35.6674	−0.0527880
$78$	−64.0832	−0.0930256
$79$	−812.979	−1.15781	−0.578907	−	0.815394i	$-0.696521\pi$
$79$	−812.979	−1.15781	−0.578907	+	0.815394i	$0.696521\pi$
$80$	−34.5669	−0.0483087
$81$	−377.364	−0.517646
$82$	657.113	0.884951
$83$	102.415	0.135440	0.0677198	−	0.997704i	$-0.478428\pi$
$83$	102.415	0.135440	0.0677198	+	0.997704i	$0.478428\pi$
$84$	−165.032	−0.214362
$85$	−157.804	−0.201368
$86$	1003.02	1.25765
$87$	1108.46	1.36597
$88$	207.841	0.251772
$89$	351.773	0.418965	0.209482	−	0.977812i	$-0.432822\pi$
$89$	351.773	0.418965	0.209482	+	0.977812i	$0.432822\pi$
$90$	117.516	0.137636
$91$	−11.0843	−0.0127687
$92$	−458.953	−0.520099
$93$	37.7733	0.0421173
$94$	1410.94	1.54816
$95$	−410.376	−0.443196
$96$	−868.505	−0.923348
$97$	−914.681	−0.957441	−0.478721	−	0.877967i	$-0.658899\pi$
$97$	−914.681	−0.957441	−0.478721	+	0.877967i	$0.658899\pi$
$98$	1494.47	1.54046
$99$	105.666	0.107271
$100$	−1435.05	−1.43505
$101$	1363.72	1.34352	0.671758	−	0.740771i	$-0.265540\pi$
$101$	1363.72	1.34352	0.671758	+	0.740771i	$0.265540\pi$
$102$	−1086.91	−1.05510
$103$	−746.648	−0.714266	−0.357133	−	0.934054i	$-0.616246\pi$
$103$	−746.648	−0.714266	−0.357133	+	0.934054i	$0.616246\pi$
$104$	64.5905	0.0609002
$105$	−36.8060	−0.0342085
$106$	141.341	0.129512
$107$	−1417.59	−1.28078	−0.640390	−	0.768050i	$-0.721227\pi$
$107$	−1417.59	−1.28078	−0.640390	+	0.768050i	$0.721227\pi$
$108$	1863.12	1.65999
$109$	−716.192	−0.629346	−0.314673	−	0.949200i	$-0.601895\pi$
$109$	−716.192	−0.629346	−0.314673	+	0.949200i	$0.601895\pi$
$110$	134.570	0.116643
$111$	−1308.22	−1.11866
$112$	−41.1811	−0.0347433
$113$	−1655.18	−1.37793	−0.688966	−	0.724794i	$-0.741935\pi$
$113$	−1655.18	−1.37793	−0.688966	+	0.724794i	$0.741935\pi$
$114$	−2826.55	−2.32220
$115$	−102.357	−0.0829989
$116$	−3243.46	−2.59610
$117$	32.8376	0.0259473
$118$	−3265.66	−2.54770
$119$	−188.000	−0.144823
$120$	214.476	0.163158
$121$	121.000	0.0909091
$122$	968.254	0.718538
$123$	609.713	0.446959
$124$	−110.528	−0.0800463
$125$	−660.263	−0.472446
$126$	140.002	0.0989871
$127$	−2034.82	−1.42174	−0.710872	−	0.703322i	$-0.751699\pi$
$127$	−2034.82	−1.42174	−0.710872	+	0.703322i	$0.751699\pi$
$128$	2084.64	1.43951
$129$	930.665	0.635198
$130$	41.8200	0.0282143
$131$	−131.000	−0.0873704
$131$	−131.000	−0.0873704
$132$	559.863	0.369165
$133$	−488.900	−0.318744
$134$	−1405.67	−0.906207
$135$	415.520	0.264906
$136$	1095.51	0.690731
$137$	−3125.61	−1.94919	−0.974593	−	0.223982i	$-0.928094\pi$
$137$	−3125.61	−1.94919	−0.974593	+	0.223982i	$0.928094\pi$
$138$	−705.008	−0.434886
$139$	535.135	0.326544	0.163272	−	0.986581i	$-0.447795\pi$
$139$	535.135	0.326544	0.163272	+	0.986581i	$0.447795\pi$
$140$	107.698	0.0650152
$141$	1309.16	0.781924
$142$	3421.75	2.02216
$143$	37.6030	0.0219896
$144$	122.000	0.0706021
$145$	−723.368	−0.414293
$146$	−4759.95	−2.69819
$147$	1386.67	0.778033
$148$	3827.98	2.12607
$149$	2209.30	1.21472	0.607359	−	0.794428i	$-0.292229\pi$
$149$	2209.30	1.21472	0.607359	+	0.794428i	$0.292229\pi$
$150$	−2204.42	−1.19993
$151$	−1915.18	−1.03216	−0.516078	−	0.856542i	$-0.672609\pi$
$151$	−1915.18	−1.03216	−0.516078	+	0.856542i	$0.672609\pi$
$152$	2848.92	1.52025
$153$	556.955	0.294295
$154$	160.319	0.0838889
$155$	−24.6504	−0.0127740
$156$	173.988	0.0892960
$157$	8.53062	0.00433642	0.00216821	−	0.999998i	$-0.499310\pi$
$157$	8.53062	0.00433642	0.00216821	+	0.999998i	$0.499310\pi$
$158$	3654.22	1.83996
$159$	131.146	0.0654123
$160$	566.777	0.280048
$161$	−121.943	−0.0596923
$162$	1696.19	0.822626
$163$	−3763.25	−1.80835	−0.904173	−	0.427166i	$-0.859512\pi$
$163$	−3763.25	−1.80835	−0.904173	+	0.427166i	$0.859512\pi$
$164$	−1784.08	−0.849471
$165$	124.863	0.0589124
$166$	−460.339	−0.215236
$167$	887.789	0.411372	0.205686	−	0.978618i	$-0.434057\pi$
$167$	887.789	0.411372	0.205686	+	0.978618i	$0.434057\pi$
$168$	255.516	0.117342
$169$	−2185.31	−0.994681
$170$	709.305	0.320007
$171$	1448.38	0.647722
$172$	−2723.22	−1.20723
$173$	3650.03	1.60408	0.802041	−	0.597269i	$-0.203747\pi$
$173$	3650.03	1.60408	0.802041	+	0.597269i	$0.203747\pi$
$174$	−4982.35	−2.17075
$175$	−381.292	−0.164703
$176$	139.705	0.0598334
$177$	−3030.10	−1.28676
$178$	−1581.16	−0.665805
$179$	1446.76	0.604110	0.302055	−	0.953290i	$-0.402327\pi$
$179$	1446.76	0.604110	0.302055	+	0.953290i	$0.402327\pi$
$180$	−319.059	−0.132118
$181$	4209.38	1.72862	0.864311	−	0.502957i	$-0.167755\pi$
$181$	4209.38	1.72862	0.864311	+	0.502957i	$0.167755\pi$
$182$	49.8222	0.0202916
$183$	898.410	0.362909
$184$	710.588	0.284703
$185$	853.731	0.339284
$186$	−169.785	−0.0669314
$187$	637.780	0.249407
$188$	−3830.74	−1.48609
$189$	495.029	0.190519
$190$	1844.57	0.704313
$191$	3226.29	1.22223	0.611115	−	0.791542i	$-0.290721\pi$
$191$	3226.29	1.22223	0.611115	+	0.791542i	$0.290721\pi$
$192$	3480.05	1.30808
$193$	−3739.36	−1.39464	−0.697319	−	0.716761i	$-0.745624\pi$
$193$	−3739.36	−1.39464	−0.697319	+	0.716761i	$0.745624\pi$
$194$	4111.35	1.52153
$195$	38.8034	0.0142501
$196$	−4057.54	−1.47869
$197$	−1811.44	−0.655127	−0.327564	−	0.944829i	$-0.606228\pi$
$197$	−1811.44	−0.655127	−0.327564	+	0.944829i	$0.606228\pi$
$198$	−474.951	−0.170471
$199$	3357.87	1.19615	0.598074	−	0.801441i	$-0.295933\pi$
$199$	3357.87	1.19615	0.598074	+	0.801441i	$0.295933\pi$
$200$	2221.87	0.785549
$201$	−1304.28	−0.457695
$202$	−6129.70	−2.13507
$203$	−861.783	−0.297957
$204$	2950.99	1.01280
$205$	−397.892	−0.135561
$206$	3356.06	1.13509
$207$	361.261	0.121301
$208$	43.4160	0.0144729
$209$	1658.57	0.548927
$210$	165.437	0.0543631
$211$	−426.141	−0.139037	−0.0695185	−	0.997581i	$-0.522146\pi$
$211$	−426.141	−0.139037	−0.0695185	+	0.997581i	$0.522146\pi$
$212$	−383.746	−0.124320
$213$	3174.93	1.02133
$214$	6371.84	2.03537
$215$	−607.342	−0.192653
$216$	−2884.64	−0.908679
$217$	−29.3672	−0.00918699
$218$	3219.17	1.00014
$219$	−4416.60	−1.36277
$220$	−365.360	−0.111966
$221$	198.202	0.0603281
$222$	5880.25	1.77773
$223$	5273.00	1.58343	0.791717	−	0.610888i	$-0.209187\pi$
$223$	5273.00	1.58343	0.791717	+	0.610888i	$0.209187\pi$
$224$	675.228	0.201409
$225$	1129.59	0.334693
$226$	7439.78	2.18977
$227$	−3774.30	−1.10356	−0.551782	−	0.833989i	$-0.686052\pi$
$227$	−3774.30	−1.10356	−0.551782	+	0.833989i	$0.686052\pi$
$228$	7674.16	2.22909
$229$	346.168	0.0998928	0.0499464	−	0.998752i	$-0.484095\pi$
$229$	346.168	0.0998928	0.0499464	+	0.998752i	$0.484095\pi$
$230$	460.080	0.131899
$231$	148.755	0.0423695
$232$	5021.79	1.42111
$233$	1267.43	0.356360	0.178180	−	0.983998i	$-0.442979\pi$
$233$	1267.43	0.356360	0.178180	+	0.983998i	$0.442979\pi$
$234$	−147.600	−0.0412346
$235$	−854.345	−0.237155
$236$	8866.36	2.44555
$237$	3390.62	0.929302
$238$	845.029	0.230147
$239$	1520.29	0.411461	0.205730	−	0.978609i	$-0.434043\pi$
$239$	1520.29	0.411461	0.205730	+	0.978609i	$0.434043\pi$
$240$	144.165	0.0387742
$241$	−6437.82	−1.72073	−0.860366	−	0.509676i	$-0.829765\pi$
$241$	−6437.82	−1.72073	−0.860366	+	0.509676i	$0.829765\pi$
$242$	−543.876	−0.144470
$243$	−2548.23	−0.672713
$244$	−2628.84	−0.689729
$245$	−904.927	−0.235974
$246$	−2740.56	−0.710293
$247$	515.432	0.132778
$248$	171.129	0.0438174
$249$	−427.133	−0.108709
$250$	2967.78	0.750796
$251$	2474.89	0.622366	0.311183	−	0.950350i	$-0.399275\pi$
$251$	2474.89	0.622366	0.311183	+	0.950350i	$0.399275\pi$
$252$	−380.110	−0.0950184
$253$	413.687	0.102799
$254$	9146.22	2.25939
$255$	658.140	0.161625
$256$	−2694.76	−0.657901
$257$	2045.22	0.496409	0.248205	−	0.968708i	$-0.420159\pi$
$257$	2045.22	0.496409	0.248205	+	0.968708i	$0.420159\pi$
$258$	−4183.19	−1.00944
$259$	1017.09	0.244011
$260$	−113.543	−0.0270831
$261$	2553.06	0.605481
$262$	588.825	0.138846
$263$	3949.84	0.926074	0.463037	−	0.886339i	$-0.346760\pi$
$263$	3949.84	0.926074	0.463037	+	0.886339i	$0.346760\pi$
$264$	−866.826	−0.202081
$265$	−85.5844	−0.0198393
$266$	2197.53	0.506538
$267$	−1467.11	−0.336276
$268$	3816.45	0.869875
$269$	−659.271	−0.149429	−0.0747147	−	0.997205i	$-0.523805\pi$
$269$	−659.271	−0.149429	−0.0747147	+	0.997205i	$0.523805\pi$
$270$	−1867.70	−0.420980
$271$	2911.59	0.652645	0.326322	−	0.945259i	$-0.394190\pi$
$271$	2911.59	0.652645	0.326322	+	0.945259i	$0.394190\pi$
$272$	736.374	0.164152
$273$	46.2283	0.0102486
$274$	14049.1	3.09758
$275$	1293.52	0.283643
$276$	1914.12	0.417450
$277$	−1669.18	−0.362063	−0.181031	−	0.983477i	$-0.557944\pi$
$277$	−1669.18	−0.362063	−0.181031	+	0.983477i	$0.557944\pi$
$278$	−2405.35	−0.518932
$279$	87.0014	0.0186689
$280$	−166.747	−0.0355894
$281$	4177.66	0.886897	0.443448	−	0.896300i	$-0.353755\pi$
$281$	4177.66	0.886897	0.443448	+	0.896300i	$0.353755\pi$
$282$	−5884.48	−1.24261
$283$	715.412	0.150272	0.0751358	−	0.997173i	$-0.476061\pi$
$283$	715.412	0.150272	0.0751358	+	0.997173i	$0.476061\pi$
$284$	−9290.15	−1.94109
$285$	1711.52	0.355725
$286$	−169.020	−0.0349452
$287$	−474.028	−0.0974946
$288$	−2000.39	−0.409284
$289$	−1551.31	−0.315757
$290$	3251.43	0.658381
$291$	3814.78	0.768476
$292$	12923.4	2.59002
$293$	−1199.39	−0.239143	−0.119572	−	0.992826i	$-0.538152\pi$
$293$	−1199.39	−0.239143	−0.119572	+	0.992826i	$0.538152\pi$
$294$	−6232.88	−1.23642
$295$	1977.41	0.390268
$296$	−5926.80	−1.16381
$297$	−1679.36	−0.328103
$298$	−9930.46	−1.93039
$299$	128.561	0.0248658
$300$	5985.05	1.15182
$301$	−723.555	−0.138555
$302$	8608.46	1.64027
$303$	−5687.54	−1.07835
$304$	1914.97	0.361286
$305$	−586.293	−0.110069
$306$	−2503.43	−0.467684
$307$	−6226.86	−1.15761	−0.578804	−	0.815467i	$-0.696480\pi$
$307$	−6226.86	−1.15761	−0.578804	+	0.815467i	$0.696480\pi$
$308$	−435.271	−0.0805256
$309$	3113.98	0.573295
$310$	110.800	0.0203000
$311$	4043.08	0.737177	0.368588	−	0.929593i	$-0.379841\pi$
$311$	4043.08	0.737177	0.368588	+	0.929593i	$0.379841\pi$
$312$	−269.382	−0.0488806
$313$	6771.45	1.22283	0.611414	−	0.791311i	$-0.290601\pi$
$313$	6771.45	1.22283	0.611414	+	0.791311i	$0.290601\pi$
$314$	−38.3438	−0.00689129
$315$	−84.7734	−0.0151633
$316$	−9921.30	−1.76619
$317$	−5068.44	−0.898018	−0.449009	−	0.893527i	$-0.648223\pi$
$317$	−5068.44	−0.898018	−0.449009	+	0.893527i	$0.648223\pi$
$318$	−589.481	−0.103951
$319$	2923.56	0.513129
$320$	−2271.04	−0.396734
$321$	5912.21	1.02800
$322$	548.115	0.0948611
$323$	8742.19	1.50597
$324$	−4605.21	−0.789645
$325$	401.984	0.0686094
$326$	16915.2	2.87376
$327$	2986.96	0.505135
$328$	2762.26	0.465001
$329$	−1017.82	−0.170560
$330$	−561.238	−0.0936217
$331$	1609.13	0.267208	0.133604	−	0.991035i	$-0.457345\pi$
$331$	1609.13	0.267208	0.133604	+	0.991035i	$0.457345\pi$
$332$	1249.83	0.206607
$333$	−3013.16	−0.495857
$334$	−3990.47	−0.653740
$335$	851.158	0.138817
$336$	171.751	0.0278862
$337$	5191.58	0.839180	0.419590	−	0.907714i	$-0.362174\pi$
$337$	5191.58	0.839180	0.419590	+	0.907714i	$0.362174\pi$
$338$	9822.65	1.58071
$339$	6903.12	1.10598
$340$	−1925.78	−0.307177
$341$	99.6271	0.0158214
$342$	−6510.25	−1.02934
$343$	−2190.26	−0.344789
$344$	4216.31	0.660838
$345$	426.893	0.0666178
$346$	−16406.3	−2.54916
$347$	7295.93	1.12872	0.564360	−	0.825529i	$-0.309123\pi$
$347$	7295.93	1.12872	0.564360	+	0.825529i	$0.309123\pi$
$348$	13527.2	2.08372
$349$	−4823.18	−0.739768	−0.369884	−	0.929078i	$-0.620603\pi$
$349$	−4823.18	−0.739768	−0.369884	+	0.929078i	$0.620603\pi$
$350$	1713.85	0.261740
$351$	−521.893	−0.0793635
$352$	−2290.68	−0.346857
$353$	−4606.37	−0.694539	−0.347270	−	0.937765i	$-0.612891\pi$
$353$	−4606.37	−0.694539	−0.347270	+	0.937765i	$0.612891\pi$
$354$	13619.8	2.04487
$355$	−2071.92	−0.309764
$356$	4292.91	0.639111
$357$	784.074	0.116240
$358$	−6502.95	−0.960033
$359$	7414.91	1.09010	0.545048	−	0.838405i	$-0.316512\pi$
$359$	7414.91	1.09010	0.545048	+	0.838405i	$0.316512\pi$
$360$	493.993	0.0723214
$361$	15875.4	2.31453
$362$	−18920.5	−2.74707
$363$	−504.644	−0.0729668
$364$	−135.269	−0.0194780
$365$	2882.22	0.413322
$366$	−4038.21	−0.576723
$367$	−12550.5	−1.78509	−0.892546	−	0.450956i	$-0.851083\pi$
$367$	−12550.5	−1.78509	−0.892546	+	0.450956i	$0.851083\pi$
$368$	477.638	0.0676593
$369$	1404.32	0.198120
$370$	−3837.39	−0.539179
$371$	−101.961	−0.0142683
$372$	460.971	0.0642479
$373$	−12176.3	−1.69025	−0.845126	−	0.534568i	$-0.820474\pi$
$373$	−12176.3	−1.69025	−0.845126	+	0.534568i	$0.820474\pi$
$374$	−2866.72	−0.396350
$375$	2753.70	0.379202
$376$	5931.06	0.813487
$377$	908.551	0.124119
$378$	−2225.08	−0.302766
$379$	3323.75	0.450474	0.225237	−	0.974304i	$-0.427684\pi$
$379$	3323.75	0.450474	0.225237	+	0.974304i	$0.427684\pi$
$380$	−5008.07	−0.676075
$381$	8486.47	1.14114
$382$	−14501.7	−1.94233
$383$	10061.9	1.34240	0.671198	−	0.741279i	$-0.265780\pi$
$383$	10061.9	1.34240	0.671198	+	0.741279i	$0.265780\pi$
$384$	−8694.22	−1.15540
$385$	−97.0758	−0.0128505
$386$	16807.9	2.21631
$387$	2143.56	0.281558
$388$	−11162.4	−1.46053
$389$	1586.30	0.206758	0.103379	−	0.994642i	$-0.467035\pi$
$389$	1586.30	0.206758	0.103379	+	0.994642i	$0.467035\pi$
$390$	−174.415	−0.0226458
$391$	2180.51	0.282028
$392$	6282.21	0.809438
$393$	546.350	0.0701266
$394$	8142.16	1.04111
$395$	−2212.68	−0.281854
$396$	1289.51	0.163637
$397$	2446.75	0.309317	0.154659	−	0.987968i	$-0.450572\pi$
$397$	2446.75	0.309317	0.154659	+	0.987968i	$0.450572\pi$
$398$	−15093.1	−1.90088
$399$	2039.01	0.255835
$400$	1493.48	0.186685
$401$	5089.55	0.633816	0.316908	−	0.948456i	$-0.397355\pi$
$401$	5089.55	0.633816	0.316908	+	0.948456i	$0.397355\pi$
$402$	5862.53	0.727354
$403$	30.9610	0.00382698
$404$	16642.3	2.04947
$405$	−1027.07	−0.126014
$406$	3873.58	0.473504
$407$	−3450.43	−0.420225
$408$	−4568.96	−0.554405
$409$	−13207.4	−1.59674	−0.798368	−	0.602170i	$-0.794303\pi$
$409$	−13207.4	−1.59674	−0.798368	+	0.602170i	$0.794303\pi$
$410$	1788.46	0.215429
$411$	13035.7	1.56449
$412$	−9111.81	−1.08958
$413$	2355.78	0.280679
$414$	−1623.81	−0.192768
$415$	278.742	0.0329709
$416$	−711.872	−0.0839000
$417$	−2231.84	−0.262095
$418$	−7455.02	−0.872338
$419$	2342.39	0.273110	0.136555	−	0.990632i	$-0.456397\pi$
$419$	2342.39	0.273110	0.136555	+	0.990632i	$0.456397\pi$
$420$	−449.166	−0.0521835
$421$	−13415.8	−1.55308	−0.776541	−	0.630067i	$-0.783027\pi$
$421$	−13415.8	−1.55308	−0.776541	+	0.630067i	$0.783027\pi$
$422$	1915.44	0.220953
$423$	3015.33	0.346597
$424$	594.147	0.0680527
$425$	6818.01	0.778170
$426$	−14270.8	−1.62306
$427$	−698.478	−0.0791609
$428$	−17299.7	−1.95377
$429$	−156.828	−0.0176497
$430$	2729.91	0.306158
$431$	−5005.21	−0.559379	−0.279689	−	0.960091i	$-0.590231\pi$
$431$	−5005.21	−0.559379	−0.279689	+	0.960091i	$0.590231\pi$
$432$	−1938.97	−0.215947
$433$	1315.19	0.145968	0.0729839	−	0.997333i	$-0.476748\pi$
$433$	1315.19	0.145968	0.0729839	+	0.997333i	$0.476748\pi$
$434$	132.001	0.0145997
$435$	3016.89	0.332526
$436$	−8740.14	−0.960038
$437$	5670.49	0.620724
$438$	19851.9	2.16567
$439$	−11575.7	−1.25849	−0.629245	−	0.777207i	$-0.716636\pi$
$439$	−11575.7	−1.25849	−0.629245	+	0.777207i	$0.716636\pi$
$440$	565.681	0.0612904
$441$	3193.86	0.344872
$442$	−890.888	−0.0958715
$443$	8878.77	0.952242	0.476121	−	0.879380i	$-0.342043\pi$
$443$	8878.77	0.952242	0.476121	+	0.879380i	$0.342043\pi$
$444$	−15965.0	−1.70646
$445$	957.420	0.101991
$446$	−23701.3	−2.51634
$447$	−9214.14	−0.974975
$448$	−2705.60	−0.285329
$449$	−4904.83	−0.515530	−0.257765	−	0.966208i	$-0.582986\pi$
$449$	−4904.83	−0.515530	−0.257765	+	0.966208i	$0.582986\pi$
$450$	−5077.33	−0.531884
$451$	1608.12	0.167901
$452$	−20199.2	−2.10197
$453$	7987.50	0.828444
$454$	16964.9	1.75375
$455$	−30.1681	−0.00310836
$456$	−11881.8	−1.22021
$457$	11799.0	1.20773	0.603866	−	0.797086i	$-0.293626\pi$
$457$	11799.0	1.20773	0.603866	+	0.797086i	$0.293626\pi$
$458$	−1555.97	−0.158746
$459$	−8851.78	−0.900143
$460$	−1249.13	−0.126611
$461$	−18170.8	−1.83579	−0.917896	−	0.396820i	$-0.870114\pi$
$461$	−18170.8	−1.83579	−0.917896	+	0.396820i	$0.870114\pi$
$462$	−668.630	−0.0673322
$463$	10369.3	1.04083	0.520413	−	0.853915i	$-0.325778\pi$
$463$	10369.3	1.04083	0.520413	+	0.853915i	$0.325778\pi$
$464$	3375.51	0.337725
$465$	102.807	0.0102529
$466$	−5696.88	−0.566316
$467$	15365.6	1.52256	0.761278	−	0.648425i	$-0.224572\pi$
$467$	15365.6	1.52256	0.761278	+	0.648425i	$0.224572\pi$
$468$	400.738	0.0395814
$469$	1014.02	0.0998365
$470$	3840.15	0.376878
$471$	−35.5779	−0.00348056
$472$	−13727.6	−1.33870
$473$	2454.63	0.238613
$474$	−15240.3	−1.47682
$475$	17730.5	1.71270
$476$	−2294.28	−0.220920
$477$	302.062	0.0289947
$478$	−6833.44	−0.653880
$479$	−12530.7	−1.19528	−0.597642	−	0.801763i	$-0.703896\pi$
$479$	−12530.7	−1.19528	−0.597642	+	0.801763i	$0.703896\pi$
$480$	−2363.81	−0.224776
$481$	−1072.29	−0.101647
$482$	28937.0	2.73453
$483$	508.578	0.0479112
$484$	1476.64	0.138678
$485$	−2489.49	−0.233076
$486$	11453.9	1.06905
$487$	−3267.16	−0.304003	−0.152001	−	0.988380i	$-0.548572\pi$
$487$	−3267.16	−0.304003	−0.152001	+	0.988380i	$0.548572\pi$
$488$	4070.18	0.377558
$489$	15695.1	1.45144
$490$	4067.51	0.375003
$491$	−1348.30	−0.123926	−0.0619631	−	0.998078i	$-0.519736\pi$
$491$	−1348.30	−0.123926	−0.0619631	+	0.998078i	$0.519736\pi$
$492$	7440.71	0.681815
$493$	15409.8	1.40776
$494$	−2316.79	−0.211006
$495$	287.590	0.0261136
$496$	115.028	0.0104132
$497$	−2468.38	−0.222781
$498$	1919.90	0.172756
$499$	−1280.25	−0.114853	−0.0574266	−	0.998350i	$-0.518290\pi$
$499$	−1280.25	−0.114853	−0.0574266	+	0.998350i	$0.518290\pi$
$500$	−8057.61	−0.720694
$501$	−3702.63	−0.330182
$502$	−11124.3	−0.989044
$503$	10450.7	0.926390	0.463195	−	0.886256i	$-0.346703\pi$
$503$	10450.7	0.926390	0.463195	+	0.886256i	$0.346703\pi$
$504$	588.517	0.0520131
$505$	3711.63	0.327060
$506$	−1859.46	−0.163366
$507$	9114.10	0.798366
$508$	−24832.2	−2.16880
$509$	12672.5	1.10354	0.551768	−	0.833998i	$-0.313953\pi$
$509$	12672.5	1.10354	0.551768	+	0.833998i	$0.313953\pi$
$510$	−2958.24	−0.256849
$511$	3433.73	0.297259
$512$	−4564.57	−0.393999
$513$	−23019.4	−1.98115
$514$	−9192.94	−0.788878
$515$	−2032.15	−0.173878
$516$	11357.5	0.968964
$517$	3452.92	0.293731
$518$	−4571.66	−0.387775
$519$	−15222.8	−1.28749
$520$	175.796	0.0148253
$521$	−8004.66	−0.673111	−0.336555	−	0.941664i	$-0.609262\pi$
$521$	−8004.66	−0.673111	−0.336555	+	0.941664i	$0.609262\pi$
$522$	−11475.6	−0.962210
$523$	5386.05	0.450316	0.225158	−	0.974322i	$-0.427710\pi$
$523$	5386.05	0.450316	0.225158	+	0.974322i	$0.427710\pi$
$524$	−1598.68	−0.133279
$525$	1590.22	0.132196
$526$	−17753.9	−1.47169
$527$	525.126	0.0434057
$528$	−582.657	−0.0480244
$529$	−10752.6	−0.883755
$530$	384.689	0.0315279
$531$	−6979.07	−0.570369
$532$	−5966.35	−0.486230
$533$	499.753	0.0406129
$534$	6594.43	0.534399
$535$	−3858.25	−0.311788
$536$	−5908.93	−0.476170
$537$	−6033.87	−0.484880
$538$	2963.32	0.237468
$539$	3657.35	0.292269
$540$	5070.85	0.404101
$541$	3202.27	0.254485	0.127243	−	0.991872i	$-0.459387\pi$
$541$	3202.27	0.254485	0.127243	+	0.991872i	$0.459387\pi$
$542$	−13087.2	−1.03716
$543$	−17555.7	−1.38745
$544$	−12074.0	−0.951596
$545$	−1949.26	−0.153206
$546$	−207.789	−0.0162867
$547$	−14159.7	−1.10681	−0.553405	−	0.832912i	$-0.686672\pi$
$547$	−14159.7	−1.10681	−0.553405	+	0.832912i	$0.686672\pi$
$548$	−38143.7	−2.97339
$549$	2069.26	0.160864
$550$	−5814.15	−0.450757
$551$	40073.9	3.09837
$552$	−2963.59	−0.228512
$553$	−2636.07	−0.202708
$554$	7502.71	0.575378
$555$	−3560.58	−0.272321
$556$	6530.59	0.498127
$557$	−8809.14	−0.670117	−0.335058	−	0.942197i	$-0.608756\pi$
$557$	−8809.14	−0.670117	−0.335058	+	0.942197i	$0.608756\pi$
$558$	−391.058	−0.0296681
$559$	762.822	0.0577172
$560$	−112.083	−0.00845778
$561$	−2659.94	−0.200183
$562$	−18777.9	−1.40943
$563$	22129.5	1.65656	0.828282	−	0.560311i	$-0.189318\pi$
$563$	22129.5	1.65656	0.828282	+	0.560311i	$0.189318\pi$
$564$	15976.5	1.19279
$565$	−4504.90	−0.335438
$566$	−3215.67	−0.238807
$567$	−1223.60	−0.0906283
$568$	14383.8	1.06255
$569$	23096.9	1.70171	0.850854	−	0.525402i	$-0.176085\pi$
$569$	23096.9	1.70171	0.850854	+	0.525402i	$0.176085\pi$
$570$	−7693.01	−0.565306
$571$	−18256.1	−1.33799	−0.668995	−	0.743267i	$-0.733275\pi$
$571$	−18256.1	−1.33799	−0.668995	+	0.743267i	$0.733275\pi$
$572$	458.893	0.0335442
$573$	−13455.6	−0.981005
$574$	2130.68	0.154935
$575$	4422.40	0.320742
$576$	8015.42	0.579819
$577$	7671.27	0.553482	0.276741	−	0.960944i	$-0.410746\pi$
$577$	7671.27	0.553482	0.276741	+	0.960944i	$0.410746\pi$
$578$	6972.92	0.501791
$579$	15595.4	1.11939
$580$	−8827.72	−0.631985
$581$	332.079	0.0237125
$582$	−17146.9	−1.22124
$583$	345.898	0.0245722
$584$	−20009.1	−1.41778
$585$	89.3740	0.00631651
$586$	5391.06	0.380039
$587$	−7717.23	−0.542631	−0.271315	−	0.962491i	$-0.587459\pi$
$587$	−7717.23	−0.542631	−0.271315	+	0.962491i	$0.587459\pi$
$588$	16922.4	1.18685
$589$	1365.61	0.0955330
$590$	−8888.14	−0.620202
$591$	7554.83	0.525828
$592$	−3983.83	−0.276579
$593$	−10910.9	−0.755578	−0.377789	−	0.925892i	$-0.623316\pi$
$593$	−10910.9	−0.755578	−0.377789	+	0.925892i	$0.623316\pi$
$594$	7548.48	0.521410
$595$	−511.678	−0.0352550
$596$	26961.5	1.85300
$597$	−14004.4	−0.960070
$598$	−577.861	−0.0395159
$599$	−19533.7	−1.33243	−0.666214	−	0.745760i	$-0.732086\pi$
$599$	−19533.7	−1.33243	−0.666214	+	0.745760i	$0.732086\pi$
$600$	−9266.55	−0.630509
$601$	10285.4	0.698089	0.349045	−	0.937106i	$-0.386506\pi$
$601$	10285.4	0.698089	0.349045	+	0.937106i	$0.386506\pi$
$602$	3252.27	0.220187
$603$	−3004.08	−0.202878
$604$	−23372.2	−1.57451
$605$	329.325	0.0221306
$606$	25564.6	1.71368
$607$	3118.50	0.208527	0.104264	−	0.994550i	$-0.466751\pi$
$607$	3118.50	0.208527	0.104264	+	0.994550i	$0.466751\pi$
$608$	−31398.9	−2.09440
$609$	3594.16	0.239151
$610$	2635.29	0.174918
$611$	1073.06	0.0710495
$612$	6796.87	0.448933
$613$	639.338	0.0421250	0.0210625	−	0.999778i	$-0.493295\pi$
$613$	639.338	0.0421250	0.0210625	+	0.999778i	$0.493295\pi$
$614$	27988.8	1.83963
$615$	1659.45	0.108806
$616$	673.923	0.0440797
$617$	14825.9	0.967374	0.483687	−	0.875241i	$-0.339297\pi$
$617$	14825.9	0.967374	0.483687	+	0.875241i	$0.339297\pi$
$618$	−13996.9	−0.911061
$619$	11310.9	0.734447	0.367223	−	0.930133i	$-0.380308\pi$
$619$	11310.9	0.734447	0.367223	+	0.930133i	$0.380308\pi$
$620$	−300.825	−0.0194861
$621$	−5741.58	−0.371017
$622$	−18173.0	−1.17150
$623$	1140.62	0.0733514
$624$	−181.071	−0.0116164
$625$	12902.0	0.825729
$626$	−30436.6	−1.94328
$627$	−6917.26	−0.440588
$628$	104.104	0.00661500
$629$	−18186.9	−1.15288
$630$	381.043	0.0240970
$631$	12713.4	0.802082	0.401041	−	0.916060i	$-0.368648\pi$
$631$	12713.4	0.802082	0.401041	+	0.916060i	$0.368648\pi$
$632$	15361.0	0.966814
$633$	1777.27	0.111596
$634$	22781.8	1.42710
$635$	−5538.18	−0.346104
$636$	1600.46	0.0997834
$637$	1136.59	0.0706959
$638$	−13141.0	−0.815447
$639$	7312.66	0.452714
$640$	5673.76	0.350430
$641$	12272.8	0.756237	0.378119	−	0.925757i	$-0.376571\pi$
$641$	12272.8	0.756237	0.378119	+	0.925757i	$0.376571\pi$
$642$	−26574.5	−1.63366
$643$	17321.4	1.06235	0.531174	−	0.847263i	$-0.321751\pi$
$643$	17321.4	1.06235	0.531174	+	0.847263i	$0.321751\pi$
$644$	−1488.15	−0.0910579
$645$	2532.99	0.154630
$646$	−39294.8	−2.39324
$647$	−9915.93	−0.602528	−0.301264	−	0.953541i	$-0.597409\pi$
$647$	−9915.93	−0.602528	−0.301264	+	0.953541i	$0.597409\pi$
$648$	7130.16	0.432252
$649$	−7991.88	−0.483373
$650$	−1806.86	−0.109032
$651$	122.479	0.00737380
$652$	−45925.3	−2.75855
$653$	−4946.90	−0.296458	−0.148229	−	0.988953i	$-0.547357\pi$
$653$	−4946.90	−0.296458	−0.148229	+	0.988953i	$0.547357\pi$
$654$	−13425.9	−0.802745
$655$	−356.542	−0.0212691
$656$	1856.72	0.110507
$657$	−10172.5	−0.604062
$658$	4574.95	0.271049
$659$	−33191.0	−1.96197	−0.980984	−	0.194086i	$-0.937826\pi$
$659$	−33191.0	−1.96197	−0.980984	+	0.194086i	$0.937826\pi$
$660$	1523.78	0.0898681
$661$	16539.8	0.973259	0.486630	−	0.873608i	$-0.338226\pi$
$661$	16539.8	0.973259	0.486630	+	0.873608i	$0.338226\pi$
$662$	−7232.80	−0.424639
$663$	−826.624	−0.0484215
$664$	−1935.09	−0.113097
$665$	−1330.64	−0.0775939
$666$	13543.7	0.787999
$667$	9995.36	0.580243
$668$	10834.2	0.627529
$669$	−21991.6	−1.27092
$670$	−3825.82	−0.220604
$671$	2369.56	0.136327
$672$	−2816.12	−0.161658
$673$	−25566.0	−1.46433	−0.732166	−	0.681126i	$-0.761491\pi$
$673$	−25566.0	−1.46433	−0.732166	+	0.681126i	$0.761491\pi$
$674$	−23335.4	−1.33360
$675$	−17952.8	−1.02371
$676$	−26668.8	−1.51734
$677$	−5462.95	−0.310130	−0.155065	−	0.987904i	$-0.549559\pi$
$677$	−5462.95	−0.310130	−0.155065	+	0.987904i	$0.549559\pi$
$678$	−31028.5	−1.75758
$679$	−2965.84	−0.167627
$680$	2981.66	0.168149
$681$	15741.1	0.885759
$682$	−447.808	−0.0251429
$683$	6011.33	0.336775	0.168388	−	0.985721i	$-0.446144\pi$
$683$	6011.33	0.336775	0.168388	+	0.985721i	$0.446144\pi$
$684$	17675.5	0.988071
$685$	−8506.96	−0.474502
$686$	9844.86	0.547928
$687$	−1443.74	−0.0801775
$688$	2834.09	0.157047
$689$	107.494	0.00594368
$690$	−1918.82	−0.105867
$691$	1123.29	0.0618406	0.0309203	−	0.999522i	$-0.490156\pi$
$691$	1123.29	0.0618406	0.0309203	+	0.999522i	$0.490156\pi$
$692$	44543.6	2.44695
$693$	342.620	0.0187807
$694$	−32794.1	−1.79373
$695$	1456.48	0.0794925
$696$	−20944.0	−1.14063
$697$	8476.25	0.460633
$698$	21679.5	1.17562
$699$	−5285.95	−0.286027
$700$	−4653.14	−0.251246
$701$	−3157.29	−0.170113	−0.0850565	−	0.996376i	$-0.527107\pi$
$701$	−3157.29	−0.170113	−0.0850565	+	0.996376i	$0.527107\pi$
$702$	2345.83	0.126122
$703$	−47295.8	−2.53740
$704$	9178.62	0.491381
$705$	3563.14	0.190349
$706$	20704.9	1.10374
$707$	4421.84	0.235220
$708$	−36978.2	−1.96289
$709$	19974.1	1.05803	0.529015	−	0.848612i	$-0.322561\pi$
$709$	19974.1	1.05803	0.529015	+	0.848612i	$0.322561\pi$
$710$	9312.97	0.492267
$711$	7809.46	0.411924
$712$	−6646.63	−0.349850
$713$	340.615	0.0178908
$714$	−3524.29	−0.184724
$715$	102.344	0.00535307
$716$	17655.7	0.921542
$717$	−6340.52	−0.330253
$718$	−33328.9	−1.73234
$719$	−23211.4	−1.20395	−0.601974	−	0.798516i	$-0.705619\pi$
$719$	−23211.4	−1.20395	−0.601974	+	0.798516i	$0.705619\pi$
$720$	332.048	0.0171871
$721$	−2421.00	−0.125052
$722$	−71357.4	−3.67818
$723$	26849.7	1.38112
$724$	51369.7	2.63693
$725$	31253.5	1.60100
$726$	2268.30	0.115957
$727$	−25535.3	−1.30268	−0.651342	−	0.758784i	$-0.725794\pi$
$727$	−25535.3	−1.30268	−0.651342	+	0.758784i	$0.725794\pi$
$728$	209.434	0.0106623
$729$	20816.5	1.05759
$730$	−12955.2	−0.656838
$731$	12938.1	0.654630
$732$	10963.9	0.553601
$733$	5070.26	0.255490	0.127745	−	0.991807i	$-0.459226\pi$
$733$	5070.26	0.255490	0.127745	+	0.991807i	$0.459226\pi$
$734$	56412.4	2.83681
$735$	3774.10	0.189401
$736$	−7831.62	−0.392224
$737$	−3440.03	−0.171934
$738$	−6312.21	−0.314845
$739$	14562.1	0.724867	0.362433	−	0.932010i	$-0.381946\pi$
$739$	14562.1	0.724867	0.362433	+	0.932010i	$0.381946\pi$
$740$	10418.6	0.517562
$741$	−2149.67	−0.106572
$742$	458.298	0.0226747
$743$	16379.4	0.808752	0.404376	−	0.914593i	$-0.367489\pi$
$743$	16379.4	0.808752	0.404376	+	0.914593i	$0.367489\pi$
$744$	−713.713	−0.0351693
$745$	6013.05	0.295706
$746$	54730.5	2.68609
$747$	−983.794	−0.0481863
$748$	7783.24	0.380459
$749$	−4596.51	−0.224236
$750$	−12377.5	−0.602615
$751$	30735.4	1.49341	0.746704	−	0.665157i	$-0.231635\pi$
$751$	30735.4	1.49341	0.746704	+	0.665157i	$0.231635\pi$
$752$	3986.70	0.193324
$753$	−10321.8	−0.499533
$754$	−4083.80	−0.197245
$755$	−5212.55	−0.251264
$756$	6041.15	0.290627
$757$	25113.3	1.20576	0.602880	−	0.797832i	$-0.294020\pi$
$757$	25113.3	1.20576	0.602880	+	0.797832i	$0.294020\pi$
$758$	−14939.7	−0.715878
$759$	−1725.33	−0.0825105
$760$	7753.91	0.370084
$761$	−25807.8	−1.22935	−0.614673	−	0.788782i	$-0.710712\pi$
$761$	−25807.8	−1.22935	−0.614673	+	0.788782i	$0.710712\pi$
$762$	−38145.3	−1.81346
$763$	−2322.24	−0.110185
$764$	39372.4	1.86446
$765$	1515.86	0.0716420
$766$	−45226.5	−2.13329
$767$	−2483.62	−0.116921
$768$	11238.8	0.528054
$769$	−174.306	−0.00817376	−0.00408688	−	0.999992i	$-0.501301\pi$
$769$	−174.306	−0.00817376	−0.00408688	+	0.999992i	$0.501301\pi$
$770$	436.341	0.0204216
$771$	−8529.82	−0.398436
$772$	−45633.8	−2.12746
$773$	358.475	0.0166798	0.00833989	−	0.999965i	$-0.497345\pi$
$773$	358.475	0.0166798	0.00833989	+	0.999965i	$0.497345\pi$
$774$	−9634.95	−0.447443
$775$	1065.03	0.0493641
$776$	17282.6	0.799496
$777$	−4241.89	−0.195852
$778$	−7130.19	−0.328573
$779$	22042.8	1.01382
$780$	473.542	0.0217379
$781$	8373.87	0.383663
$782$	−9801.04	−0.448190
$783$	−40576.2	−1.85195
$784$	4222.73	0.192362
$785$	23.2178	0.00105564
$786$	−2455.76	−0.111443
$787$	−12083.2	−0.547291	−0.273646	−	0.961831i	$-0.588230\pi$
$787$	−12083.2	−0.547291	−0.273646	+	0.961831i	$0.588230\pi$
$788$	−22106.2	−0.999366
$789$	−16473.3	−0.743300
$790$	9945.67	0.447913
$791$	−5366.90	−0.241245
$792$	−1996.52	−0.0895747
$793$	736.384	0.0329757
$794$	−10997.8	−0.491557
$795$	356.940	0.0159237
$796$	40978.2	1.82467
$797$	2572.44	0.114329	0.0571647	−	0.998365i	$-0.481794\pi$
$797$	2572.44	0.114329	0.0571647	+	0.998365i	$0.481794\pi$
$798$	−9165.05	−0.406565
$799$	18200.0	0.805845
$800$	−24487.9	−1.08222
$801$	−3379.12	−0.149058
$802$	−22876.8	−1.00724
$803$	−11648.8	−0.511926
$804$	−15916.9	−0.698192
$805$	−331.892	−0.0145313
$806$	−139.165	−0.00608172
$807$	2749.57	0.119937
$808$	−25767.0	−1.12188
$809$	20705.6	0.899841	0.449920	−	0.893069i	$-0.351452\pi$
$809$	20705.6	0.899841	0.449920	+	0.893069i	$0.351452\pi$
$810$	4616.52	0.200257
$811$	35447.9	1.53483	0.767414	−	0.641152i	$-0.221543\pi$
$811$	35447.9	1.53483	0.767414	+	0.641152i	$0.221543\pi$
$812$	−10516.9	−0.454520
$813$	−12143.1	−0.523836
$814$	15509.2	0.667808
$815$	−10242.4	−0.440217
$816$	−3071.13	−0.131754
$817$	33646.1	1.44079
$818$	59365.3	2.53748
$819$	106.475	0.00454280
$820$	−4855.73	−0.206792
$821$	−17215.7	−0.731828	−0.365914	−	0.930649i	$-0.619244\pi$
$821$	−17215.7	−0.731828	−0.365914	+	0.930649i	$0.619244\pi$
$822$	−58593.4	−2.48623
$823$	3448.35	0.146053	0.0730266	−	0.997330i	$-0.476734\pi$
$823$	3448.35	0.146053	0.0730266	+	0.997330i	$0.476734\pi$
$824$	14107.7	0.596436
$825$	−5394.76	−0.227662
$826$	−10588.9	−0.446046
$827$	29071.0	1.22237	0.611183	−	0.791489i	$-0.290694\pi$
$827$	29071.0	1.22237	0.611183	+	0.791489i	$0.290694\pi$
$828$	4408.69	0.185039
$829$	7306.76	0.306121	0.153061	−	0.988217i	$-0.451087\pi$
$829$	7306.76	0.306121	0.153061	+	0.988217i	$0.451087\pi$
$830$	−1252.90	−0.0523963
$831$	6961.51	0.290604
$832$	2852.43	0.118858
$833$	19277.6	0.801835
$834$	10031.8	0.416513
$835$	2416.29	0.100143
$836$	20240.6	0.837363
$837$	−1382.73	−0.0571016
$838$	−10528.7	−0.434018
$839$	27627.5	1.13684	0.568420	−	0.822739i	$-0.307555\pi$
$839$	27627.5	1.13684	0.568420	+	0.822739i	$0.307555\pi$
$840$	695.436	0.0285653
$841$	46249.1	1.89631
$842$	60302.0	2.46811
$843$	−17423.4	−0.711855
$844$	−5200.47	−0.212094
$845$	−5947.76	−0.242141
$846$	−13553.4	−0.550800
$847$	392.341	0.0159162
$848$	399.370	0.0161726
$849$	−2983.71	−0.120613
$850$	−30645.9	−1.23664
$851$	−11796.7	−0.475188
$852$	38745.6	1.55798
$853$	−42433.6	−1.70328	−0.851640	−	0.524127i	$-0.824392\pi$
$853$	−42433.6	−1.70328	−0.851640	+	0.524127i	$0.824392\pi$
$854$	3139.55	0.125800
$855$	3942.06	0.157679
$856$	26784.8	1.06949
$857$	−6502.69	−0.259192	−0.129596	−	0.991567i	$-0.541368\pi$
$857$	−6502.69	−0.259192	−0.129596	+	0.991567i	$0.541368\pi$
$858$	704.916	0.0280483
$859$	27043.1	1.07416	0.537078	−	0.843532i	$-0.319528\pi$
$859$	27043.1	1.07416	0.537078	+	0.843532i	$0.319528\pi$
$860$	−7411.78	−0.293883
$861$	1976.99	0.0782526
$862$	22497.6	0.888947
$863$	11126.9	0.438892	0.219446	−	0.975625i	$-0.429575\pi$
$863$	11126.9	0.438892	0.219446	+	0.975625i	$0.429575\pi$
$864$	31792.5	1.25185
$865$	9934.27	0.390492
$866$	−5911.58	−0.231967
$867$	6469.93	0.253438
$868$	−358.387	−0.0140143
$869$	8942.77	0.349094
$870$	−13560.5	−0.528440
$871$	−1069.05	−0.0415884
$872$	13532.2	0.525525
$873$	8786.41	0.340635
$874$	−25488.0	−0.986434
$875$	−2140.89	−0.0827148
$876$	−53898.5	−2.07884
$877$	−37992.7	−1.46285	−0.731426	−	0.681921i	$-0.761145\pi$
$877$	−37992.7	−1.46285	−0.731426	+	0.681921i	$0.761145\pi$
$878$	52030.9	1.99995
$879$	5002.19	0.191945
$880$	380.235	0.0145656
$881$	21730.0	0.830990	0.415495	−	0.909595i	$-0.363608\pi$
$881$	21730.0	0.830990	0.415495	+	0.909595i	$0.363608\pi$
$882$	−14355.9	−0.548059
$883$	−38693.5	−1.47468	−0.737338	−	0.675524i	$-0.763917\pi$
$883$	−38693.5	−1.47468	−0.737338	+	0.675524i	$0.763917\pi$
$884$	2418.78	0.0920277
$885$	−8247.01	−0.313243
$886$	−39908.7	−1.51327
$887$	37316.9	1.41260	0.706302	−	0.707910i	$-0.250362\pi$
$887$	37316.9	1.41260	0.706302	+	0.707910i	$0.250362\pi$
$888$	24718.4	0.934116
$889$	−6597.89	−0.248916
$890$	−4303.45	−0.162081
$891$	4151.00	0.156076
$892$	64349.7	2.41546
$893$	47329.8	1.77361
$894$	41416.1	1.54940
$895$	3937.64	0.147062
$896$	6759.41	0.252027
$897$	−536.178	−0.0199581
$898$	22046.4	0.819264
$899$	2407.16	0.0893027
$900$	13785.1	0.510559
$901$	1823.20	0.0674134
$902$	−7228.24	−0.266823
$903$	3017.67	0.111209
$904$	31274.1	1.15062
$905$	11456.7	0.420809
$906$	−35902.6	−1.31654
$907$	−49752.2	−1.82138	−0.910691	−	0.413087i	$-0.864450\pi$
$907$	−49752.2	−1.82138	−0.910691	+	0.413087i	$0.864450\pi$
$908$	−46060.1	−1.68343
$909$	−13099.8	−0.477992
$910$	135.601	0.00493970
$911$	45474.6	1.65383	0.826917	−	0.562325i	$-0.190093\pi$
$911$	45474.6	1.65383	0.826917	+	0.562325i	$0.190093\pi$
$912$	−7986.59	−0.289981
$913$	−1126.56	−0.0408366
$914$	−53034.6	−1.91929
$915$	2445.20	0.0883452
$916$	4224.51	0.152382
$917$	−424.766	−0.0152966
$918$	39787.4	1.43048
$919$	11931.5	0.428274	0.214137	−	0.976804i	$-0.431306\pi$
$919$	11931.5	0.428274	0.214137	+	0.976804i	$0.431306\pi$
$920$	1934.01	0.0693069
$921$	25969.8	0.929137
$922$	81675.1	2.91738
$923$	2602.34	0.0928027
$924$	1815.35	0.0646327
$925$	−36885.9	−1.31114
$926$	−46608.4	−1.65405
$927$	7172.28	0.254119
$928$	−55346.7	−1.95781
$929$	−17847.8	−0.630320	−0.315160	−	0.949039i	$-0.602058\pi$
$929$	−17847.8	−0.630320	−0.315160	+	0.949039i	$0.602058\pi$
$930$	−462.104	−0.0162935
$931$	50132.0	1.76478
$932$	15467.2	0.543610
$933$	−16862.1	−0.591684
$934$	−69065.9	−2.41960
$935$	1735.85	0.0607147
$936$	−620.455	−0.0216669
$937$	15578.9	0.543160	0.271580	−	0.962416i	$-0.412454\pi$
$937$	15578.9	0.543160	0.271580	+	0.962416i	$0.412454\pi$
$938$	−4557.88	−0.158657
$939$	−28241.1	−0.981485
$940$	−10426.1	−0.361768
$941$	17389.4	0.602421	0.301210	−	0.953558i	$-0.402609\pi$
$941$	17389.4	0.602421	0.301210	+	0.953558i	$0.402609\pi$
$942$	159.917	0.00553119
$943$	5498.00	0.189861
$944$	−9227.34	−0.318140
$945$	1347.32	0.0463791
$946$	−11033.2	−0.379196
$947$	24907.7	0.854690	0.427345	−	0.904089i	$-0.359449\pi$
$947$	24907.7	0.854690	0.427345	+	0.904089i	$0.359449\pi$
$948$	41377.9	1.41761
$949$	−3620.07	−0.123828
$950$	−79695.8	−2.72176
$951$	21138.5	0.720781
$952$	3552.19	0.120932
$953$	50097.2	1.70284	0.851420	−	0.524484i	$-0.175742\pi$
$953$	50097.2	1.70284	0.851420	+	0.524484i	$0.175742\pi$
$954$	−1357.72	−0.0460775
$955$	8780.98	0.297535
$956$	18553.0	0.627664
$957$	−12193.0	−0.411855
$958$	56323.4	1.89951
$959$	−10134.7	−0.341259
$960$	9471.63	0.318433
$961$	−29709.0	−0.997247
$962$	4819.76	0.161534
$963$	13617.3	0.455672
$964$	−78564.8	−2.62490
$965$	−10177.4	−0.339505
$966$	−2285.98	−0.0761389
$967$	54354.5	1.80757	0.903786	−	0.427984i	$-0.140776\pi$
$967$	54354.5	1.80757	0.903786	+	0.427984i	$0.140776\pi$
$968$	−2286.25	−0.0759122
$969$	−36460.3	−1.20874
$970$	11189.9	0.370396
$971$	49778.9	1.64519	0.822596	−	0.568626i	$-0.192525\pi$
$971$	49778.9	1.64519	0.822596	+	0.568626i	$0.192525\pi$
$972$	−31097.7	−1.02619
$973$	1735.17	0.0571705
$974$	14685.4	0.483111
$975$	−1676.52	−0.0550683
$976$	2735.86	0.0897263
$977$	49175.2	1.61029	0.805146	−	0.593077i	$-0.202087\pi$
$977$	49175.2	1.61029	0.805146	+	0.593077i	$0.202087\pi$
$978$	−70546.9	−2.30658
$979$	−3869.50	−0.126323
$980$	−11043.4	−0.359968
$981$	6879.72	0.223907
$982$	6060.38	0.196939
$983$	−48291.3	−1.56689	−0.783446	−	0.621460i	$-0.786540\pi$
$983$	−48291.3	−1.56689	−0.783446	+	0.621460i	$0.786540\pi$
$984$	−11520.3	−0.373226
$985$	−4930.20	−0.159482
$986$	−69264.8	−2.23716
$987$	4244.94	0.136898
$988$	6290.14	0.202547
$989$	8392.13	0.269822
$990$	−1292.67	−0.0414988
$991$	−31717.1	−1.01668	−0.508338	−	0.861157i	$-0.669740\pi$
$991$	−31717.1	−1.01668	−0.508338	+	0.861157i	$0.669740\pi$
$992$	−1886.07	−0.0603656
$993$	−6711.07	−0.214471
$994$	11095.0	0.354036
$995$	9139.12	0.291185
$996$	−5212.57	−0.165830
$997$	21595.4	0.685991	0.342996	−	0.939337i	$-0.388558\pi$
$997$	21595.4	0.685991	0.342996	+	0.939337i	$0.388558\pi$
$998$	5754.51	0.182521
$999$	47888.7	1.51665

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1441.4.a.c.1.12	✓	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1441.4.a.c.1.12	✓	84	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1441 = 11 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1441.a (trivial)

\(f(q)\)	\(=\)	\(q-4.49484 q^{2} -4.17061 q^{3} +12.2036 q^{4} +2.72170 q^{5} +18.7463 q^{6} +3.24249 q^{7} -18.8947 q^{8} -9.60598 q^{9} +O(q^{10})\)	\(q-4.49484 q^{2} -4.17061 q^{3} +12.2036 q^{4} +2.72170 q^{5} +18.7463 q^{6} +3.24249 q^{7} -18.8947 q^{8} -9.60598 q^{9} -12.2336 q^{10} -11.0000 q^{11} -50.8966 q^{12} -3.41845 q^{13} -14.5745 q^{14} -11.3512 q^{15} -12.7005 q^{16} -57.9800 q^{17} +43.1774 q^{18} -150.779 q^{19} +33.2146 q^{20} -13.5232 q^{21} +49.4433 q^{22} -37.6079 q^{23} +78.8023 q^{24} -117.592 q^{25} +15.3654 q^{26} +152.669 q^{27} +39.5701 q^{28} -265.778 q^{29} +51.0217 q^{30} -9.05701 q^{31} +208.244 q^{32} +45.8768 q^{33} +260.611 q^{34} +8.82507 q^{35} -117.228 q^{36} +313.676 q^{37} +677.729 q^{38} +14.2571 q^{39} -51.4256 q^{40} -146.193 q^{41} +60.7845 q^{42} -223.148 q^{43} -134.240 q^{44} -26.1446 q^{45} +169.042 q^{46} -313.901 q^{47} +52.9688 q^{48} -332.486 q^{49} +528.559 q^{50} +241.812 q^{51} -41.7175 q^{52} -31.4452 q^{53} -686.225 q^{54} -29.9387 q^{55} -61.2657 q^{56} +628.842 q^{57} +1194.63 q^{58} +726.535 q^{59} -138.525 q^{60} -215.414 q^{61} +40.7098 q^{62} -31.1473 q^{63} -834.420 q^{64} -9.30400 q^{65} -206.209 q^{66} +312.730 q^{67} -707.567 q^{68} +156.848 q^{69} -39.6673 q^{70} -761.261 q^{71} +181.502 q^{72} +1058.98 q^{73} -1409.92 q^{74} +490.432 q^{75} -1840.05 q^{76} -35.6674 q^{77} -64.0832 q^{78} -812.979 q^{79} -34.5669 q^{80} -377.364 q^{81} +657.113 q^{82} +102.415 q^{83} -165.032 q^{84} -157.804 q^{85} +1003.02 q^{86} +1108.46 q^{87} +207.841 q^{88} +351.773 q^{89} +117.516 q^{90} -11.0843 q^{91} -458.953 q^{92} +37.7733 q^{93} +1410.94 q^{94} -410.376 q^{95} -868.505 q^{96} -914.681 q^{97} +1494.47 q^{98} +105.666 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q + 12 q^{2} + 14 q^{3} + 380 q^{4} + 38 q^{5} + 59 q^{6} + 11 q^{7} + 162 q^{8} + 856 q^{9}+O(q^{10}) \) 84 * q + 12 * q^2 + 14 * q^3 + 380 * q^4 + 38 * q^5 + 59 * q^6 + 11 * q^7 + 162 * q^8 + 856 * q^9	\( 84 q + 12 q^{2} + 14 q^{3} + 380 q^{4} + 38 q^{5} + 59 q^{6} + 11 q^{7} + 162 q^{8} + 856 q^{9} - 58 q^{10} - 924 q^{11} + 152 q^{12} - 202 q^{13} + 306 q^{14} + 630 q^{15} + 1720 q^{16} + 148 q^{17} + 251 q^{18} + 33 q^{19} + 510 q^{20} - 206 q^{21} - 132 q^{22} + 938 q^{23} + 518 q^{24} + 2288 q^{25} + 788 q^{26} + 506 q^{27} + 52 q^{28} + 197 q^{29} + 93 q^{30} + 1018 q^{31} + 1173 q^{32} - 154 q^{33} - 16 q^{34} + 1126 q^{35} + 6815 q^{36} + 1059 q^{37} + 3259 q^{38} + 1350 q^{39} + 2912 q^{40} + 523 q^{41} + 1171 q^{42} + 110 q^{43} - 4180 q^{44} + 572 q^{45} - 552 q^{46} + 3764 q^{47} + 6132 q^{48} + 6165 q^{49} + 2316 q^{50} + 1910 q^{51} + 137 q^{52} + 2586 q^{53} + 5126 q^{54} - 418 q^{55} + 3853 q^{56} + 1480 q^{57} + 2576 q^{58} + 5392 q^{59} + 10535 q^{60} - 3704 q^{61} + 3766 q^{62} + 1375 q^{63} + 7804 q^{64} + 3178 q^{65} - 649 q^{66} + 2095 q^{67} + 1751 q^{68} + 2690 q^{69} + 1475 q^{70} + 10220 q^{71} + 4930 q^{72} - 100 q^{73} + 4970 q^{74} + 312 q^{75} + 1005 q^{76} - 121 q^{77} + 2325 q^{78} + 810 q^{79} + 12763 q^{80} + 14368 q^{81} + 2363 q^{82} + 3097 q^{83} + 6017 q^{84} - 1102 q^{85} + 4884 q^{86} + 2552 q^{87} - 1782 q^{88} + 7493 q^{89} + 1052 q^{90} + 2238 q^{91} + 9134 q^{92} + 4776 q^{93} + 1885 q^{94} + 6782 q^{95} + 10849 q^{96} + 1180 q^{97} + 13073 q^{98} - 9416 q^{99}+O(q^{100}) \) 84 * q + 12 * q^2 + 14 * q^3 + 380 * q^4 + 38 * q^5 + 59 * q^6 + 11 * q^7 + 162 * q^8 + 856 * q^9 - 58 * q^10 - 924 * q^11 + 152 * q^12 - 202 * q^13 + 306 * q^14 + 630 * q^15 + 1720 * q^16 + 148 * q^17 + 251 * q^18 + 33 * q^19 + 510 * q^20 - 206 * q^21 - 132 * q^22 + 938 * q^23 + 518 * q^24 + 2288 * q^25 + 788 * q^26 + 506 * q^27 + 52 * q^28 + 197 * q^29 + 93 * q^30 + 1018 * q^31 + 1173 * q^32 - 154 * q^33 - 16 * q^34 + 1126 * q^35 + 6815 * q^36 + 1059 * q^37 + 3259 * q^38 + 1350 * q^39 + 2912 * q^40 + 523 * q^41 + 1171 * q^42 + 110 * q^43 - 4180 * q^44 + 572 * q^45 - 552 * q^46 + 3764 * q^47 + 6132 * q^48 + 6165 * q^49 + 2316 * q^50 + 1910 * q^51 + 137 * q^52 + 2586 * q^53 + 5126 * q^54 - 418 * q^55 + 3853 * q^56 + 1480 * q^57 + 2576 * q^58 + 5392 * q^59 + 10535 * q^60 - 3704 * q^61 + 3766 * q^62 + 1375 * q^63 + 7804 * q^64 + 3178 * q^65 - 649 * q^66 + 2095 * q^67 + 1751 * q^68 + 2690 * q^69 + 1475 * q^70 + 10220 * q^71 + 4930 * q^72 - 100 * q^73 + 4970 * q^74 + 312 * q^75 + 1005 * q^76 - 121 * q^77 + 2325 * q^78 + 810 * q^79 + 12763 * q^80 + 14368 * q^81 + 2363 * q^82 + 3097 * q^83 + 6017 * q^84 - 1102 * q^85 + 4884 * q^86 + 2552 * q^87 - 1782 * q^88 + 7493 * q^89 + 1052 * q^90 + 2238 * q^91 + 9134 * q^92 + 4776 * q^93 + 1885 * q^94 + 6782 * q^95 + 10849 * q^96 + 1180 * q^97 + 13073 * q^98 - 9416 * q^99

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