LMFDB - Embedded newform 4027.2.a.c.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4027,2,Mod(1,4027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4027, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("4027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4027 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4027.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:	$32.1557568940$
Analytic rank:	$0$
Dimension:	$174$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	4027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.58182 q^{2} +1.87364 q^{3} +4.66582 q^{4} +2.74921 q^{5} -4.83740 q^{6} +4.58392 q^{7} -6.88267 q^{8} +0.510512 q^{9} +O(q^{10})$	\(q-2.58182 q^{2} +1.87364 q^{3} +4.66582 q^{4} +2.74921 q^{5} -4.83740 q^{6} +4.58392 q^{7} -6.88267 q^{8} +0.510512 q^{9} -7.09798 q^{10} +3.67809 q^{11} +8.74204 q^{12} +0.712583 q^{13} -11.8349 q^{14} +5.15102 q^{15} +8.43822 q^{16} -3.71085 q^{17} -1.31805 q^{18} +2.31918 q^{19} +12.8273 q^{20} +8.58860 q^{21} -9.49619 q^{22} +5.08992 q^{23} -12.8956 q^{24} +2.55817 q^{25} -1.83977 q^{26} -4.66439 q^{27} +21.3877 q^{28} +7.27085 q^{29} -13.2990 q^{30} -3.51421 q^{31} -8.02065 q^{32} +6.89141 q^{33} +9.58076 q^{34} +12.6022 q^{35} +2.38196 q^{36} -11.0544 q^{37} -5.98771 q^{38} +1.33512 q^{39} -18.9219 q^{40} -9.75528 q^{41} -22.1743 q^{42} -1.05940 q^{43} +17.1613 q^{44} +1.40351 q^{45} -13.1413 q^{46} +4.58609 q^{47} +15.8101 q^{48} +14.0123 q^{49} -6.60475 q^{50} -6.95278 q^{51} +3.32478 q^{52} +14.0244 q^{53} +12.0426 q^{54} +10.1119 q^{55} -31.5496 q^{56} +4.34529 q^{57} -18.7721 q^{58} -1.70745 q^{59} +24.0337 q^{60} -11.0038 q^{61} +9.07308 q^{62} +2.34015 q^{63} +3.83147 q^{64} +1.95904 q^{65} -17.7924 q^{66} -13.3228 q^{67} -17.3141 q^{68} +9.53666 q^{69} -32.5366 q^{70} +6.15065 q^{71} -3.51369 q^{72} +9.71356 q^{73} +28.5404 q^{74} +4.79308 q^{75} +10.8209 q^{76} +16.8601 q^{77} -3.44705 q^{78} +1.19637 q^{79} +23.1985 q^{80} -10.2709 q^{81} +25.1864 q^{82} +9.58215 q^{83} +40.0728 q^{84} -10.2019 q^{85} +2.73519 q^{86} +13.6229 q^{87} -25.3151 q^{88} +5.77873 q^{89} -3.62361 q^{90} +3.26643 q^{91} +23.7487 q^{92} -6.58436 q^{93} -11.8405 q^{94} +6.37591 q^{95} -15.0278 q^{96} -0.332297 q^{97} -36.1774 q^{98} +1.87771 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 174 q + 21 q^{2} + 17 q^{3} + 187 q^{4} + 72 q^{5} + 21 q^{6} + 24 q^{7} + 54 q^{8} + 197 q^{9}+O(q^{10}) $ 174 * q + 21 * q^2 + 17 * q^3 + 187 * q^4 + 72 * q^5 + 21 * q^6 + 24 * q^7 + 54 * q^8 + 197 * q^9	\( 174 q + 21 q^{2} + 17 q^{3} + 187 q^{4} + 72 q^{5} + 21 q^{6} + 24 q^{7} + 54 q^{8} + 197 q^{9} + 20 q^{10} + 35 q^{11} + 23 q^{12} + 91 q^{13} + 18 q^{14} + 16 q^{15} + 201 q^{16} + 148 q^{17} + 39 q^{18} + 36 q^{19} + 128 q^{20} + 57 q^{21} + 17 q^{22} + 96 q^{23} + 24 q^{24} + 226 q^{25} + 44 q^{26} + 62 q^{27} + 32 q^{28} + 122 q^{29} + 25 q^{30} + 23 q^{31} + 104 q^{32} + 91 q^{33} + 6 q^{34} + 80 q^{35} + 222 q^{36} + 71 q^{37} + 125 q^{38} + 16 q^{39} + 53 q^{40} + 97 q^{41} + 14 q^{42} + 38 q^{43} + 70 q^{44} + 185 q^{45} - 23 q^{46} + 110 q^{47} + 36 q^{48} + 210 q^{49} + 51 q^{50} + 33 q^{51} + 118 q^{52} + 214 q^{53} + 8 q^{54} + 37 q^{55} + 41 q^{56} + 76 q^{57} + 2 q^{58} + 66 q^{59} - 12 q^{60} + 114 q^{61} + 175 q^{62} + 62 q^{63} + 190 q^{64} + 128 q^{65} + 12 q^{66} - 6 q^{67} + 348 q^{68} + 115 q^{69} - 38 q^{70} + 54 q^{71} + 101 q^{72} + 107 q^{73} + 71 q^{74} - q^{75} + 31 q^{76} + 368 q^{77} - 14 q^{78} - 14 q^{79} + 205 q^{80} + 222 q^{81} + 26 q^{82} + 246 q^{83} + 41 q^{84} + 87 q^{85} + 33 q^{86} + 100 q^{87} - 6 q^{88} + 147 q^{89} + 50 q^{90} - 23 q^{91} + 189 q^{92} + 117 q^{93} + 23 q^{94} + 42 q^{95} + 38 q^{96} + 52 q^{97} + 148 q^{98} + 38 q^{99}+O(q^{100}) \) 174 * q + 21 * q^2 + 17 * q^3 + 187 * q^4 + 72 * q^5 + 21 * q^6 + 24 * q^7 + 54 * q^8 + 197 * q^9 + 20 * q^10 + 35 * q^11 + 23 * q^12 + 91 * q^13 + 18 * q^14 + 16 * q^15 + 201 * q^16 + 148 * q^17 + 39 * q^18 + 36 * q^19 + 128 * q^20 + 57 * q^21 + 17 * q^22 + 96 * q^23 + 24 * q^24 + 226 * q^25 + 44 * q^26 + 62 * q^27 + 32 * q^28 + 122 * q^29 + 25 * q^30 + 23 * q^31 + 104 * q^32 + 91 * q^33 + 6 * q^34 + 80 * q^35 + 222 * q^36 + 71 * q^37 + 125 * q^38 + 16 * q^39 + 53 * q^40 + 97 * q^41 + 14 * q^42 + 38 * q^43 + 70 * q^44 + 185 * q^45 - 23 * q^46 + 110 * q^47 + 36 * q^48 + 210 * q^49 + 51 * q^50 + 33 * q^51 + 118 * q^52 + 214 * q^53 + 8 * q^54 + 37 * q^55 + 41 * q^56 + 76 * q^57 + 2 * q^58 + 66 * q^59 - 12 * q^60 + 114 * q^61 + 175 * q^62 + 62 * q^63 + 190 * q^64 + 128 * q^65 + 12 * q^66 - 6 * q^67 + 348 * q^68 + 115 * q^69 - 38 * q^70 + 54 * q^71 + 101 * q^72 + 107 * q^73 + 71 * q^74 - q^75 + 31 * q^76 + 368 * q^77 - 14 * q^78 - 14 * q^79 + 205 * q^80 + 222 * q^81 + 26 * q^82 + 246 * q^83 + 41 * q^84 + 87 * q^85 + 33 * q^86 + 100 * q^87 - 6 * q^88 + 147 * q^89 + 50 * q^90 - 23 * q^91 + 189 * q^92 + 117 * q^93 + 23 * q^94 + 42 * q^95 + 38 * q^96 + 52 * q^97 + 148 * q^98 + 38 * 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 $

$2$	−2.58182	−1.82563	−0.912813	−	0.408378i	$-0.866094\pi$
$2$	−2.58182	−1.82563	−0.912813	+	0.408378i	$0.866094\pi$
$3$	1.87364	1.08174	0.540872	−	0.841105i	$-0.318094\pi$
$3$	1.87364	1.08174	0.540872	+	0.841105i	$0.318094\pi$
$4$	4.66582	2.33291
$5$	2.74921	1.22949	0.614743	−	0.788728i	$-0.289260\pi$
$5$	2.74921	1.22949	0.614743	+	0.788728i	$0.289260\pi$
$6$	−4.83740	−1.97486
$7$	4.58392	1.73256	0.866280	−	0.499559i	$-0.166505\pi$
$7$	4.58392	1.73256	0.866280	+	0.499559i	$0.166505\pi$
$8$	−6.88267	−2.43339
$9$	0.510512	0.170171
$10$	−7.09798	−2.24458
$11$	3.67809	1.10899	0.554493	−	0.832188i	$-0.312912\pi$
$11$	3.67809	1.10899	0.554493	+	0.832188i	$0.312912\pi$
$12$	8.74204	2.52361
$13$	0.712583	0.197635	0.0988175	−	0.995106i	$-0.468494\pi$
$13$	0.712583	0.197635	0.0988175	+	0.995106i	$0.468494\pi$
$14$	−11.8349	−3.16300
$15$	5.15102	1.32999
$16$	8.43822	2.10955
$17$	−3.71085	−0.900013	−0.450006	−	0.893025i	$-0.648578\pi$
$17$	−3.71085	−0.900013	−0.450006	+	0.893025i	$0.648578\pi$
$18$	−1.31805	−0.310668
$19$	2.31918	0.532056	0.266028	−	0.963965i	$-0.414289\pi$
$19$	2.31918	0.532056	0.266028	+	0.963965i	$0.414289\pi$
$20$	12.8273	2.86828
$21$	8.58860	1.87419
$22$	−9.49619	−2.02459
$23$	5.08992	1.06132	0.530661	−	0.847584i	$-0.321944\pi$
$23$	5.08992	1.06132	0.530661	+	0.847584i	$0.321944\pi$
$24$	−12.8956	−2.63231
$25$	2.55817	0.511634
$26$	−1.83977	−0.360808
$27$	−4.66439	−0.897663
$28$	21.3877	4.04190
$29$	7.27085	1.35016	0.675081	−	0.737743i	$-0.264108\pi$
$29$	7.27085	1.35016	0.675081	+	0.737743i	$0.264108\pi$
$30$	−13.2990	−2.42806
$31$	−3.51421	−0.631171	−0.315586	−	0.948897i	$-0.602201\pi$
$31$	−3.51421	−0.631171	−0.315586	+	0.948897i	$0.602201\pi$
$32$	−8.02065	−1.41786
$33$	6.89141	1.19964
$34$	9.58076	1.64309
$35$	12.6022	2.13016
$36$	2.38196	0.396993
$37$	−11.0544	−1.81733	−0.908663	−	0.417529i	$-0.862896\pi$
$37$	−11.0544	−1.81733	−0.908663	+	0.417529i	$0.862896\pi$
$38$	−5.98771	−0.971335
$39$	1.33512	0.213791
$40$	−18.9219	−2.99182
$41$	−9.75528	−1.52352	−0.761760	−	0.647860i	$-0.775664\pi$
$41$	−9.75528	−1.52352	−0.761760	+	0.647860i	$0.775664\pi$
$42$	−22.1743	−3.42156
$43$	−1.05940	−0.161557	−0.0807786	−	0.996732i	$-0.525741\pi$
$43$	−1.05940	−0.161557	−0.0807786	+	0.996732i	$0.525741\pi$
$44$	17.1613	2.58717
$45$	1.40351	0.209223
$46$	−13.1413	−1.93758
$47$	4.58609	0.668950	0.334475	−	0.942405i	$-0.391441\pi$
$47$	4.58609	0.668950	0.334475	+	0.942405i	$0.391441\pi$
$48$	15.8101	2.28200
$49$	14.0123	2.00176
$50$	−6.60475	−0.934053
$51$	−6.95278	−0.973584
$52$	3.32478	0.461065
$53$	14.0244	1.92640	0.963198	−	0.268794i	$-0.0866251\pi$
$53$	14.0244	1.92640	0.963198	+	0.268794i	$0.0866251\pi$
$54$	12.0426	1.63880
$55$	10.1119	1.36348
$56$	−31.5496	−4.21600
$57$	4.34529	0.575548
$58$	−18.7721	−2.46489
$59$	−1.70745	−0.222291	−0.111146	−	0.993804i	$-0.535452\pi$
$59$	−1.70745	−0.222291	−0.111146	+	0.993804i	$0.535452\pi$
$60$	24.0337	3.10274
$61$	−11.0038	−1.40890	−0.704448	−	0.709755i	$-0.748806\pi$
$61$	−11.0038	−1.40890	−0.704448	+	0.709755i	$0.748806\pi$
$62$	9.07308	1.15228
$63$	2.34015	0.294831
$64$	3.83147	0.478934
$65$	1.95904	0.242989
$66$	−17.7924	−2.19009
$67$	−13.3228	−1.62763	−0.813817	−	0.581122i	$-0.802614\pi$
$67$	−13.3228	−1.62763	−0.813817	+	0.581122i	$0.802614\pi$
$68$	−17.3141	−2.09965
$69$	9.53666	1.14808
$70$	−32.5366	−3.88887
$71$	6.15065	0.729948	0.364974	−	0.931018i	$-0.381078\pi$
$71$	6.15065	0.729948	0.364974	+	0.931018i	$0.381078\pi$
$72$	−3.51369	−0.414092
$73$	9.71356	1.13689	0.568443	−	0.822723i	$-0.307546\pi$
$73$	9.71356	1.13689	0.568443	+	0.822723i	$0.307546\pi$
$74$	28.5404	3.31776
$75$	4.79308	0.553458
$76$	10.8209	1.24124
$77$	16.8601	1.92139
$78$	−3.44705	−0.390302
$79$	1.19637	0.134603	0.0673013	−	0.997733i	$-0.478561\pi$
$79$	1.19637	0.134603	0.0673013	+	0.997733i	$0.478561\pi$
$80$	23.1985	2.59367
$81$	−10.2709	−1.14121
$82$	25.1864	2.78138
$83$	9.58215	1.05178	0.525889	−	0.850553i	$-0.323733\pi$
$83$	9.58215	1.05178	0.525889	+	0.850553i	$0.323733\pi$
$84$	40.0728	4.37230
$85$	−10.2019	−1.10655
$86$	2.73519	0.294943
$87$	13.6229	1.46053
$88$	−25.3151	−2.69860
$89$	5.77873	0.612544	0.306272	−	0.951944i	$-0.400918\pi$
$89$	5.77873	0.612544	0.306272	+	0.951944i	$0.400918\pi$
$90$	−3.62361	−0.381962
$91$	3.26643	0.342415
$92$	23.7487	2.47597
$93$	−6.58436	−0.682766
$94$	−11.8405	−1.22125
$95$	6.37591	0.654155
$96$	−15.0278	−1.53377
$97$	−0.332297	−0.0337396	−0.0168698	−	0.999858i	$-0.505370\pi$
$97$	−0.332297	−0.0337396	−0.0168698	+	0.999858i	$0.505370\pi$
$98$	−36.1774	−3.65447
$99$	1.87771	0.188717
$100$	11.9360	1.19360
$101$	−3.70414	−0.368576	−0.184288	−	0.982872i	$-0.558998\pi$
$101$	−3.70414	−0.368576	−0.184288	+	0.982872i	$0.558998\pi$
$102$	17.9509	1.77740
$103$	18.2236	1.79562	0.897811	−	0.440382i	$-0.145157\pi$
$103$	18.2236	1.79562	0.897811	+	0.440382i	$0.145157\pi$
$104$	−4.90448	−0.480924
$105$	23.6119	2.30428
$106$	−36.2085	−3.51688
$107$	1.96123	0.189599	0.0947996	−	0.995496i	$-0.469779\pi$
$107$	1.96123	0.189599	0.0947996	+	0.995496i	$0.469779\pi$
$108$	−21.7632	−2.09417
$109$	2.25868	0.216342	0.108171	−	0.994132i	$-0.465501\pi$
$109$	2.25868	0.216342	0.108171	+	0.994132i	$0.465501\pi$
$110$	−26.1071	−2.48921
$111$	−20.7119	−1.96588
$112$	38.6801	3.65493
$113$	−18.1321	−1.70572	−0.852862	−	0.522136i	$-0.825135\pi$
$113$	−18.1321	−1.70572	−0.852862	+	0.522136i	$0.825135\pi$
$114$	−11.2188	−1.05074
$115$	13.9933	1.30488
$116$	33.9245	3.14981
$117$	0.363783	0.0336317
$118$	4.40834	0.405820
$119$	−17.0102	−1.55933
$120$	−35.4528	−3.23638
$121$	2.52837	0.229852
$122$	28.4100	2.57212
$123$	−18.2779	−1.64806
$124$	−16.3967	−1.47246
$125$	−6.71311	−0.600438
$126$	−6.04185	−0.538251
$127$	−9.95974	−0.883784	−0.441892	−	0.897068i	$-0.645693\pi$
$127$	−9.95974	−0.883784	−0.441892	+	0.897068i	$0.645693\pi$
$128$	6.14911	0.543509
$129$	−1.98493	−0.174764
$130$	−5.05791	−0.443608
$131$	20.9465	1.83010	0.915051	−	0.403339i	$-0.132150\pi$
$131$	20.9465	1.83010	0.915051	+	0.403339i	$0.132150\pi$
$132$	32.1541	2.79865
$133$	10.6309	0.921818
$134$	34.3970	2.97145
$135$	−12.8234	−1.10366
$136$	25.5405	2.19008
$137$	16.3246	1.39470	0.697351	−	0.716730i	$-0.254362\pi$
$137$	16.3246	1.39470	0.697351	+	0.716730i	$0.254362\pi$
$138$	−24.6220	−2.09596
$139$	2.61179	0.221529	0.110765	−	0.993847i	$-0.464670\pi$
$139$	2.61179	0.221529	0.110765	+	0.993847i	$0.464670\pi$
$140$	58.7994	4.96946
$141$	8.59266	0.723633
$142$	−15.8799	−1.33261
$143$	2.62095	0.219175
$144$	4.30781	0.358985
$145$	19.9891	1.66001
$146$	−25.0787	−2.07553
$147$	26.2540	2.16539
$148$	−51.5777	−4.23966
$149$	2.53569	0.207732	0.103866	−	0.994591i	$-0.466879\pi$
$149$	2.53569	0.207732	0.103866	+	0.994591i	$0.466879\pi$
$150$	−12.3749	−1.01041
$151$	11.1125	0.904320	0.452160	−	0.891937i	$-0.350654\pi$
$151$	11.1125	0.904320	0.452160	+	0.891937i	$0.350654\pi$
$152$	−15.9621	−1.29470
$153$	−1.89443	−0.153156
$154$	−43.5298	−3.50773
$155$	−9.66132	−0.776016
$156$	6.22944	0.498754
$157$	−0.725607	−0.0579098	−0.0289549	−	0.999581i	$-0.509218\pi$
$157$	−0.725607	−0.0579098	−0.0289549	+	0.999581i	$0.509218\pi$
$158$	−3.08883	−0.245734
$159$	26.2766	2.08387
$160$	−22.0505	−1.74324
$161$	23.3318	1.83880
$162$	26.5177	2.08343
$163$	24.5696	1.92444	0.962218	−	0.272281i	$-0.0877779\pi$
$163$	24.5696	1.92444	0.962218	+	0.272281i	$0.0877779\pi$
$164$	−45.5164	−3.55423
$165$	18.9459	1.47494
$166$	−24.7394	−1.92015
$167$	−2.11436	−0.163614	−0.0818072	−	0.996648i	$-0.526069\pi$
$167$	−2.11436	−0.163614	−0.0818072	+	0.996648i	$0.526069\pi$
$168$	−59.1125	−4.56063
$169$	−12.4922	−0.960940
$170$	26.3395	2.02015
$171$	1.18397	0.0905404
$172$	−4.94297	−0.376898
$173$	−19.5009	−1.48262	−0.741312	−	0.671160i	$-0.765796\pi$
$173$	−19.5009	−1.48262	−0.741312	+	0.671160i	$0.765796\pi$
$174$	−35.1720	−2.66638
$175$	11.7265	0.886437
$176$	31.0365	2.33947
$177$	−3.19914	−0.240462
$178$	−14.9197	−1.11828
$179$	13.6972	1.02377	0.511887	−	0.859053i	$-0.328947\pi$
$179$	13.6972	1.02377	0.511887	+	0.859053i	$0.328947\pi$
$180$	6.54851	0.488097
$181$	−11.4379	−0.850172	−0.425086	−	0.905153i	$-0.639756\pi$
$181$	−11.4379	−0.850172	−0.425086	+	0.905153i	$0.639756\pi$
$182$	−8.43334	−0.625121
$183$	−20.6172	−1.52407
$184$	−35.0323	−2.58261
$185$	−30.3908	−2.23438
$186$	16.9997	1.24648
$187$	−13.6488	−0.998102
$188$	21.3979	1.56060
$189$	−21.3812	−1.55525
$190$	−16.4615	−1.19424
$191$	2.87314	0.207893	0.103947	−	0.994583i	$-0.466853\pi$
$191$	2.87314	0.207893	0.103947	+	0.994583i	$0.466853\pi$
$192$	7.17879	0.518084
$193$	−11.0309	−0.794022	−0.397011	−	0.917814i	$-0.629953\pi$
$193$	−11.0309	−0.794022	−0.397011	+	0.917814i	$0.629953\pi$
$194$	0.857932	0.0615959
$195$	3.67054	0.262852
$196$	65.3790	4.66993
$197$	−5.51546	−0.392960	−0.196480	−	0.980508i	$-0.562951\pi$
$197$	−5.51546	−0.392960	−0.196480	+	0.980508i	$0.562951\pi$
$198$	−4.84792	−0.344527
$199$	−24.8527	−1.76176	−0.880882	−	0.473337i	$-0.843049\pi$
$199$	−24.8527	−1.76176	−0.880882	+	0.473337i	$0.843049\pi$
$200$	−17.6071	−1.24501
$201$	−24.9620	−1.76068
$202$	9.56343	0.672881
$203$	33.3290	2.33924
$204$	−32.4404	−2.27128
$205$	−26.8193	−1.87314
$206$	−47.0500	−3.27813
$207$	2.59847	0.180606
$208$	6.01293	0.416922
$209$	8.53015	0.590043
$210$	−60.9618	−4.20676
$211$	7.12974	0.490831	0.245416	−	0.969418i	$-0.421076\pi$
$211$	7.12974	0.490831	0.245416	+	0.969418i	$0.421076\pi$
$212$	65.4351	4.49410
$213$	11.5241	0.789617
$214$	−5.06355	−0.346137
$215$	−2.91252	−0.198632
$216$	32.1035	2.18437
$217$	−16.1089	−1.09354
$218$	−5.83151	−0.394960
$219$	18.1997	1.22982
$220$	47.1801	3.18088
$221$	−2.64429	−0.177874
$222$	53.4744	3.58897
$223$	−23.0869	−1.54602	−0.773008	−	0.634396i	$-0.781249\pi$
$223$	−23.0869	−1.54602	−0.773008	+	0.634396i	$0.781249\pi$
$224$	−36.7660	−2.45653
$225$	1.30598	0.0870652
$226$	46.8139	3.11401
$227$	0.626585	0.0415879	0.0207939	−	0.999784i	$-0.493381\pi$
$227$	0.626585	0.0415879	0.0207939	+	0.999784i	$0.493381\pi$
$228$	20.2743	1.34270
$229$	−23.6709	−1.56422	−0.782109	−	0.623142i	$-0.785856\pi$
$229$	−23.6709	−1.56422	−0.782109	+	0.623142i	$0.785856\pi$
$230$	−36.1282	−2.38222
$231$	31.5897	2.07845
$232$	−50.0429	−3.28548
$233$	−10.4120	−0.682114	−0.341057	−	0.940043i	$-0.610785\pi$
$233$	−10.4120	−0.682114	−0.341057	+	0.940043i	$0.610785\pi$
$234$	−0.939223	−0.0613989
$235$	12.6081	0.822464
$236$	−7.96665	−0.518585
$237$	2.24157	0.145606
$238$	43.9174	2.84674
$239$	12.5188	0.809776	0.404888	−	0.914366i	$-0.367311\pi$
$239$	12.5188	0.809776	0.404888	+	0.914366i	$0.367311\pi$
$240$	43.4655	2.80568
$241$	−22.4684	−1.44732	−0.723658	−	0.690159i	$-0.757541\pi$
$241$	−22.4684	−1.44732	−0.723658	+	0.690159i	$0.757541\pi$
$242$	−6.52781	−0.419623
$243$	−5.25077	−0.336837
$244$	−51.3419	−3.28683
$245$	38.5229	2.46114
$246$	47.1902	3.00874
$247$	1.65261	0.105153
$248$	24.1872	1.53589
$249$	17.9535	1.13775
$250$	17.3321	1.09618
$251$	−18.3778	−1.15999	−0.579997	−	0.814618i	$-0.696946\pi$
$251$	−18.3778	−1.15999	−0.579997	+	0.814618i	$0.696946\pi$
$252$	10.9187	0.687814
$253$	18.7212	1.17699
$254$	25.7143	1.61346
$255$	−19.1147	−1.19701
$256$	−23.5389	−1.47118
$257$	−31.8146	−1.98454	−0.992270	−	0.124099i	$-0.960396\pi$
$257$	−31.8146	−1.98454	−0.992270	+	0.124099i	$0.960396\pi$
$258$	5.12475	0.319053
$259$	−50.6723	−3.14863
$260$	9.14054	0.566872
$261$	3.71186	0.229758
$262$	−54.0801	−3.34108
$263$	−11.9127	−0.734566	−0.367283	−	0.930109i	$-0.619712\pi$
$263$	−11.9127	−0.734566	−0.367283	+	0.930109i	$0.619712\pi$
$264$	−47.4313	−2.91920
$265$	38.5560	2.36847
$266$	−27.4472	−1.68289
$267$	10.8272	0.662616
$268$	−62.1615	−3.79712
$269$	−3.85198	−0.234859	−0.117430	−	0.993081i	$-0.537465\pi$
$269$	−3.85198	−0.234859	−0.117430	+	0.993081i	$0.537465\pi$
$270$	33.1078	2.01488
$271$	30.9797	1.88188	0.940940	−	0.338573i	$-0.109944\pi$
$271$	30.9797	1.88188	0.940940	+	0.338573i	$0.109944\pi$
$272$	−31.3129	−1.89863
$273$	6.12009	0.370405
$274$	−42.1472	−2.54620
$275$	9.40919	0.567396
$276$	44.4963	2.67836
$277$	9.15195	0.549888	0.274944	−	0.961460i	$-0.411341\pi$
$277$	9.15195	0.549888	0.274944	+	0.961460i	$0.411341\pi$
$278$	−6.74319	−0.404430
$279$	−1.79405	−0.107407
$280$	−86.7366	−5.18351
$281$	2.60464	0.155380	0.0776900	−	0.996978i	$-0.475246\pi$
$281$	2.60464	0.155380	0.0776900	+	0.996978i	$0.475246\pi$
$282$	−22.1847	−1.32108
$283$	12.6780	0.753627	0.376814	−	0.926289i	$-0.377020\pi$
$283$	12.6780	0.753627	0.376814	+	0.926289i	$0.377020\pi$
$284$	28.6978	1.70290
$285$	11.9461	0.707628
$286$	−6.76683	−0.400131
$287$	−44.7174	−2.63959
$288$	−4.09464	−0.241279
$289$	−3.22961	−0.189977
$290$	−51.6084	−3.03055
$291$	−0.622603	−0.0364977
$292$	45.3217	2.65225
$293$	3.50485	0.204756	0.102378	−	0.994746i	$-0.467355\pi$
$293$	3.50485	0.204756	0.102378	+	0.994746i	$0.467355\pi$
$294$	−67.7832	−3.95320
$295$	−4.69414	−0.273304
$296$	76.0836	4.42227
$297$	−17.1561	−0.995497
$298$	−6.54670	−0.379240
$299$	3.62700	0.209755
$300$	22.3636	1.29117
$301$	−4.85621	−0.279907
$302$	−28.6905	−1.65095
$303$	−6.94021	−0.398705
$304$	19.5697	1.12240
$305$	−30.2519	−1.73222
$306$	4.89110	0.279605
$307$	−6.11552	−0.349031	−0.174516	−	0.984654i	$-0.555836\pi$
$307$	−6.11552	−0.349031	−0.174516	+	0.984654i	$0.555836\pi$
$308$	78.6661	4.48242
$309$	34.1443	1.94240
$310$	24.9438	1.41671
$311$	−29.9333	−1.69736	−0.848680	−	0.528906i	$-0.822602\pi$
$311$	−29.9333	−1.69736	−0.848680	+	0.528906i	$0.822602\pi$
$312$	−9.18921	−0.520236
$313$	12.8066	0.723872	0.361936	−	0.932203i	$-0.382116\pi$
$313$	12.8066	0.723872	0.361936	+	0.932203i	$0.382116\pi$
$314$	1.87339	0.105722
$315$	6.43357	0.362490
$316$	5.58206	0.314015
$317$	−10.4285	−0.585724	−0.292862	−	0.956155i	$-0.594608\pi$
$317$	−10.4285	−0.585724	−0.292862	+	0.956155i	$0.594608\pi$
$318$	−67.8415	−3.80436
$319$	26.7429	1.49731
$320$	10.5335	0.588842
$321$	3.67463	0.205098
$322$	−60.2386	−3.35697
$323$	−8.60611	−0.478857
$324$	−47.9222	−2.66234
$325$	1.82291	0.101117
$326$	−63.4343	−3.51330
$327$	4.23194	0.234027
$328$	67.1424	3.70732
$329$	21.0223	1.15900
$330$	−48.9151	−2.69269
$331$	7.98352	0.438814	0.219407	−	0.975633i	$-0.429588\pi$
$331$	7.98352	0.438814	0.219407	+	0.975633i	$0.429588\pi$
$332$	44.7086	2.45370
$333$	−5.64339	−0.309256
$334$	5.45891	0.298699
$335$	−36.6271	−2.00115
$336$	72.4725	3.95370
$337$	−11.2684	−0.613830	−0.306915	−	0.951737i	$-0.599297\pi$
$337$	−11.2684	−0.613830	−0.306915	+	0.951737i	$0.599297\pi$
$338$	32.2527	1.75432
$339$	−33.9730	−1.84516
$340$	−47.6002	−2.58149
$341$	−12.9256	−0.699961
$342$	−3.05680	−0.165293
$343$	32.1440	1.73561
$344$	7.29151	0.393132
$345$	26.2183	1.41155
$346$	50.3479	2.70672
$347$	6.57310	0.352862	0.176431	−	0.984313i	$-0.443545\pi$
$347$	6.57310	0.352862	0.176431	+	0.984313i	$0.443545\pi$
$348$	63.5621	3.40729
$349$	22.4225	1.20025	0.600125	−	0.799906i	$-0.295118\pi$
$349$	22.4225	1.20025	0.600125	+	0.799906i	$0.295118\pi$
$350$	−30.2757	−1.61830
$351$	−3.32377	−0.177410
$352$	−29.5007	−1.57239
$353$	−20.1950	−1.07487	−0.537436	−	0.843304i	$-0.680607\pi$
$353$	−20.1950	−1.07487	−0.537436	+	0.843304i	$0.680607\pi$
$354$	8.25962	0.438994
$355$	16.9095	0.897461
$356$	26.9625	1.42901
$357$	−31.8710	−1.68679
$358$	−35.3637	−1.86903
$359$	−14.1975	−0.749317	−0.374658	−	0.927163i	$-0.622240\pi$
$359$	−14.1975	−0.749317	−0.374658	+	0.927163i	$0.622240\pi$
$360$	−9.65988	−0.509120
$361$	−13.6214	−0.716917
$362$	29.5307	1.55210
$363$	4.73725	0.248641
$364$	15.2405	0.798822
$365$	26.7046	1.39778
$366$	53.2299	2.78237
$367$	29.1992	1.52419	0.762094	−	0.647466i	$-0.224171\pi$
$367$	29.1992	1.52419	0.762094	+	0.647466i	$0.224171\pi$
$368$	42.9499	2.23892
$369$	−4.98019	−0.259259
$370$	78.4637	4.07914
$371$	64.2866	3.33759
$372$	−30.7214	−1.59283
$373$	−13.3216	−0.689765	−0.344882	−	0.938646i	$-0.612081\pi$
$373$	−13.3216	−0.689765	−0.344882	+	0.938646i	$0.612081\pi$
$374$	35.2389	1.82216
$375$	−12.5779	−0.649521
$376$	−31.5645	−1.62782
$377$	5.18109	0.266840
$378$	55.2025	2.83931
$379$	−11.8223	−0.607271	−0.303636	−	0.952788i	$-0.598201\pi$
$379$	−11.8223	−0.607271	−0.303636	+	0.952788i	$0.598201\pi$
$380$	29.7488	1.52608
$381$	−18.6609	−0.956028
$382$	−7.41796	−0.379536
$383$	13.8347	0.706920	0.353460	−	0.935450i	$-0.385005\pi$
$383$	13.8347	0.706920	0.353460	+	0.935450i	$0.385005\pi$
$384$	11.5212	0.587938
$385$	46.3520	2.36232
$386$	28.4799	1.44959
$387$	−0.540838	−0.0274923
$388$	−1.55044	−0.0787115
$389$	−12.4510	−0.631290	−0.315645	−	0.948877i	$-0.602221\pi$
$389$	−12.4510	−0.631290	−0.315645	+	0.948877i	$0.602221\pi$
$390$	−9.47668	−0.479870
$391$	−18.8879	−0.955204
$392$	−96.4423	−4.87107
$393$	39.2461	1.97970
$394$	14.2400	0.717399
$395$	3.28909	0.165492
$396$	8.76106	0.440260
$397$	−11.0832	−0.556251	−0.278125	−	0.960545i	$-0.589713\pi$
$397$	−11.0832	−0.556251	−0.278125	+	0.960545i	$0.589713\pi$
$398$	64.1654	3.21632
$399$	19.9185	0.997171
$400$	21.5864	1.07932
$401$	−17.3857	−0.868200	−0.434100	−	0.900865i	$-0.642934\pi$
$401$	−17.3857	−0.868200	−0.434100	+	0.900865i	$0.642934\pi$
$402$	64.4475	3.21435
$403$	−2.50417	−0.124742
$404$	−17.2828	−0.859853
$405$	−28.2369	−1.40310
$406$	−86.0496	−4.27057
$407$	−40.6590	−2.01539
$408$	47.8537	2.36911
$409$	30.6973	1.51788	0.758941	−	0.651159i	$-0.225717\pi$
$409$	30.6973	1.51788	0.758941	+	0.651159i	$0.225717\pi$
$410$	69.2429	3.41966
$411$	30.5863	1.50871
$412$	85.0278	4.18902
$413$	−7.82681	−0.385132
$414$	−6.70879	−0.329719
$415$	26.3434	1.29314
$416$	−5.71538	−0.280220
$417$	4.89355	0.239638
$418$	−22.0234	−1.07720
$419$	29.0148	1.41747	0.708734	−	0.705476i	$-0.249267\pi$
$419$	29.0148	1.41747	0.708734	+	0.705476i	$0.249267\pi$
$420$	110.169	5.37568
$421$	−13.9572	−0.680232	−0.340116	−	0.940383i	$-0.610466\pi$
$421$	−13.9572	−0.680232	−0.340116	+	0.940383i	$0.610466\pi$
$422$	−18.4077	−0.896074
$423$	2.34126	0.113836
$424$	−96.5251	−4.68768
$425$	−9.49298	−0.460477
$426$	−29.7532	−1.44155
$427$	−50.4407	−2.44100
$428$	9.15074	0.442318
$429$	4.91070	0.237091
$430$	7.51962	0.362628
$431$	21.8494	1.05245	0.526225	−	0.850345i	$-0.323607\pi$
$431$	21.8494	1.05245	0.526225	+	0.850345i	$0.323607\pi$
$432$	−39.3592	−1.89367
$433$	−17.3546	−0.834010	−0.417005	−	0.908904i	$-0.636920\pi$
$433$	−17.3546	−0.834010	−0.417005	+	0.908904i	$0.636920\pi$
$434$	41.5903	1.99640
$435$	37.4523	1.79570
$436$	10.5386	0.504707
$437$	11.8044	0.564683
$438$	−46.9884	−2.24519
$439$	8.49182	0.405292	0.202646	−	0.979252i	$-0.435046\pi$
$439$	8.49182	0.405292	0.202646	+	0.979252i	$0.435046\pi$
$440$	−69.5966	−3.31789
$441$	7.15347	0.340641
$442$	6.82709	0.324731
$443$	4.30519	0.204546	0.102273	−	0.994756i	$-0.467389\pi$
$443$	4.30519	0.204546	0.102273	+	0.994756i	$0.467389\pi$
$444$	−96.6378	−4.58623
$445$	15.8870	0.753114
$446$	59.6065	2.82245
$447$	4.75096	0.224713
$448$	17.5632	0.829782
$449$	14.8433	0.700499	0.350250	−	0.936656i	$-0.386097\pi$
$449$	14.8433	0.700499	0.350250	+	0.936656i	$0.386097\pi$
$450$	−3.37181	−0.158949
$451$	−35.8808	−1.68956
$452$	−84.6011	−3.97930
$453$	20.8207	0.978243
$454$	−1.61773	−0.0759239
$455$	8.98010	0.420994
$456$	−29.9072	−1.40053
$457$	12.8672	0.601902	0.300951	−	0.953640i	$-0.402696\pi$
$457$	12.8672	0.601902	0.300951	+	0.953640i	$0.402696\pi$
$458$	61.1141	2.85568
$459$	17.3089	0.807908
$460$	65.2901	3.04417
$461$	−40.2633	−1.87525	−0.937624	−	0.347651i	$-0.886979\pi$
$461$	−40.2633	−1.87525	−0.937624	+	0.347651i	$0.886979\pi$
$462$	−81.5590	−3.79447
$463$	−6.62642	−0.307956	−0.153978	−	0.988074i	$-0.549208\pi$
$463$	−6.62642	−0.307956	−0.153978	+	0.988074i	$0.549208\pi$
$464$	61.3530	2.84824
$465$	−18.1018	−0.839451
$466$	26.8820	1.24528
$467$	5.82392	0.269499	0.134749	−	0.990880i	$-0.456977\pi$
$467$	5.82392	0.269499	0.134749	+	0.990880i	$0.456977\pi$
$468$	1.69734	0.0784597
$469$	−61.0704	−2.81997
$470$	−32.5520	−1.50151
$471$	−1.35952	−0.0626436
$472$	11.7518	0.540921
$473$	−3.89658	−0.179165
$474$	−5.78734	−0.265821
$475$	5.93285	0.272218
$476$	−79.3666	−3.63776
$477$	7.15962	0.327816
$478$	−32.3214	−1.47835
$479$	−34.0824	−1.55726	−0.778632	−	0.627480i	$-0.784086\pi$
$479$	−34.0824	−1.55726	−0.778632	+	0.627480i	$0.784086\pi$
$480$	−41.3146	−1.88574
$481$	−7.87716	−0.359168
$482$	58.0094	2.64226
$483$	43.7153	1.98912
$484$	11.7969	0.536223
$485$	−0.913555	−0.0414824
$486$	13.5566	0.614939
$487$	36.6195	1.65939	0.829695	−	0.558218i	$-0.188515\pi$
$487$	36.6195	1.65939	0.829695	+	0.558218i	$0.188515\pi$
$488$	75.7358	3.42840
$489$	46.0344	2.08175
$490$	−99.4593	−4.49311
$491$	11.1836	0.504710	0.252355	−	0.967635i	$-0.418795\pi$
$491$	11.1836	0.504710	0.252355	+	0.967635i	$0.418795\pi$
$492$	−85.2811	−3.84477
$493$	−26.9810	−1.21516
$494$	−4.26674	−0.191970
$495$	5.16223	0.232025
$496$	−29.6537	−1.33149
$497$	28.1941	1.26468
$498$	−46.3527	−2.07711
$499$	22.7648	1.01909	0.509547	−	0.860443i	$-0.329813\pi$
$499$	22.7648	1.01909	0.509547	+	0.860443i	$0.329813\pi$
$500$	−31.3221	−1.40077
$501$	−3.96155	−0.176989
$502$	47.4482	2.11772
$503$	29.4992	1.31530	0.657651	−	0.753323i	$-0.271550\pi$
$503$	29.4992	1.31530	0.657651	+	0.753323i	$0.271550\pi$
$504$	−16.1065	−0.717439
$505$	−10.1835	−0.453158
$506$	−48.3349	−2.14875
$507$	−23.4059	−1.03949
$508$	−46.4703	−2.06179
$509$	−0.0808782	−0.00358486	−0.00179243	−	0.999998i	$-0.500571\pi$
$509$	−0.0808782	−0.00358486	−0.00179243	+	0.999998i	$0.500571\pi$
$510$	49.3507	2.18529
$511$	44.5262	1.96972
$512$	48.4750	2.14231
$513$	−10.8176	−0.477607
$514$	82.1397	3.62303
$515$	50.1005	2.20769
$516$	−9.26134	−0.407708
$517$	16.8681	0.741857
$518$	130.827	5.74821
$519$	−36.5376	−1.60382
$520$	−13.4835	−0.591289
$521$	41.1915	1.80463	0.902317	−	0.431074i	$-0.141865\pi$
$521$	41.1915	1.80463	0.902317	+	0.431074i	$0.141865\pi$
$522$	−9.58337	−0.419453
$523$	2.12049	0.0927227	0.0463614	−	0.998925i	$-0.485237\pi$
$523$	2.12049	0.0927227	0.0463614	+	0.998925i	$0.485237\pi$
$524$	97.7324	4.26946
$525$	21.9711	0.958898
$526$	30.7564	1.34104
$527$	13.0407	0.568062
$528$	58.1512	2.53071
$529$	2.90732	0.126405
$530$	−99.5448	−4.32395
$531$	−0.871674	−0.0378274
$532$	49.6020	2.15052
$533$	−6.95145	−0.301101
$534$	−27.9540	−1.20969
$535$	5.39184	0.233110
$536$	91.6961	3.96067
$537$	25.6635	1.10746
$538$	9.94513	0.428765
$539$	51.5387	2.21993
$540$	−59.8317	−2.57475
$541$	−3.88414	−0.166992	−0.0834962	−	0.996508i	$-0.526609\pi$
$541$	−3.88414	−0.166992	−0.0834962	+	0.996508i	$0.526609\pi$
$542$	−79.9840	−3.43561
$543$	−21.4305	−0.919669
$544$	29.7634	1.27610
$545$	6.20959	0.265990
$546$	−15.8010	−0.676221
$547$	−5.24979	−0.224465	−0.112233	−	0.993682i	$-0.535800\pi$
$547$	−5.24979	−0.224465	−0.112233	+	0.993682i	$0.535800\pi$
$548$	76.1674	3.25371
$549$	−5.61759	−0.239753
$550$	−24.2929	−1.03585
$551$	16.8624	0.718362
$552$	−65.6377	−2.79373
$553$	5.48408	0.233207
$554$	−23.6287	−1.00389
$555$	−56.9413	−2.41702
$556$	12.1862	0.516808
$557$	14.9906	0.635174	0.317587	−	0.948229i	$-0.397127\pi$
$557$	14.9906	0.635174	0.317587	+	0.948229i	$0.397127\pi$
$558$	4.63192	0.196085
$559$	−0.754912	−0.0319294
$560$	106.340	4.49368
$561$	−25.5730	−1.07969
$562$	−6.72473	−0.283666
$563$	16.4771	0.694429	0.347214	−	0.937786i	$-0.387128\pi$
$563$	16.4771	0.694429	0.347214	+	0.937786i	$0.387128\pi$
$564$	40.0918	1.68817
$565$	−49.8490	−2.09716
$566$	−32.7323	−1.37584
$567$	−47.0811	−1.97722
$568$	−42.3329	−1.77625
$569$	−21.0167	−0.881068	−0.440534	−	0.897736i	$-0.645211\pi$
$569$	−21.0167	−0.881068	−0.440534	+	0.897736i	$0.645211\pi$
$570$	−30.8428	−1.29186
$571$	−15.8066	−0.661488	−0.330744	−	0.943721i	$-0.607300\pi$
$571$	−15.8066	−0.661488	−0.330744	+	0.943721i	$0.607300\pi$
$572$	12.2289	0.511315
$573$	5.38323	0.224888
$574$	115.453	4.81890
$575$	13.0209	0.543009
$576$	1.95601	0.0815006
$577$	−8.21551	−0.342016	−0.171008	−	0.985270i	$-0.554702\pi$
$577$	−8.21551	−0.342016	−0.171008	+	0.985270i	$0.554702\pi$
$578$	8.33829	0.346827
$579$	−20.6679	−0.858929
$580$	93.2655	3.87264
$581$	43.9238	1.82227
$582$	1.60745	0.0666311
$583$	51.5829	2.13635
$584$	−66.8552	−2.76649
$585$	1.00012	0.0413497
$586$	−9.04892	−0.373807
$587$	27.2374	1.12421	0.562105	−	0.827066i	$-0.309992\pi$
$587$	27.2374	1.12421	0.562105	+	0.827066i	$0.309992\pi$
$588$	122.496	5.05167
$589$	−8.15008	−0.335818
$590$	12.1195	0.498950
$591$	−10.3340	−0.425083
$592$	−93.2791	−3.83375
$593$	17.8641	0.733589	0.366794	−	0.930302i	$-0.380455\pi$
$593$	17.8641	0.733589	0.366794	+	0.930302i	$0.380455\pi$
$594$	44.2940	1.81740
$595$	−46.7647	−1.91717
$596$	11.8311	0.484619
$597$	−46.5650	−1.90578
$598$	−9.36427	−0.382933
$599$	−2.09953	−0.0857846	−0.0428923	−	0.999080i	$-0.513657\pi$
$599$	−2.09953	−0.0857846	−0.0428923	+	0.999080i	$0.513657\pi$
$600$	−32.9892	−1.34678
$601$	−1.28774	−0.0525280	−0.0262640	−	0.999655i	$-0.508361\pi$
$601$	−1.28774	−0.0525280	−0.0262640	+	0.999655i	$0.508361\pi$
$602$	12.5379	0.511006
$603$	−6.80143	−0.276976
$604$	51.8488	2.10970
$605$	6.95103	0.282600
$606$	17.9184	0.727885
$607$	−27.6412	−1.12192	−0.560960	−	0.827843i	$-0.689568\pi$
$607$	−27.6412	−1.12192	−0.560960	+	0.827843i	$0.689568\pi$
$608$	−18.6013	−0.754382
$609$	62.4464	2.53046
$610$	78.1051	3.16238
$611$	3.26797	0.132208
$612$	−8.83908	−0.357299
$613$	−38.8082	−1.56745	−0.783725	−	0.621108i	$-0.786683\pi$
$613$	−38.8082	−1.56745	−0.783725	+	0.621108i	$0.786683\pi$
$614$	15.7892	0.637200
$615$	−50.2497	−2.02626
$616$	−116.042	−4.67548
$617$	−13.8383	−0.557109	−0.278554	−	0.960420i	$-0.589855\pi$
$617$	−13.8383	−0.557109	−0.278554	+	0.960420i	$0.589855\pi$
$618$	−88.1547	−3.54610
$619$	−21.4773	−0.863247	−0.431623	−	0.902054i	$-0.642059\pi$
$619$	−21.4773	−0.863247	−0.431623	+	0.902054i	$0.642059\pi$
$620$	−45.0780	−1.81037
$621$	−23.7414	−0.952710
$622$	77.2825	3.09874
$623$	26.4892	1.06127
$624$	11.2660	0.451003
$625$	−31.2466	−1.24986
$626$	−33.0644	−1.32152
$627$	15.9824	0.638276
$628$	−3.38555	−0.135098
$629$	41.0211	1.63562
$630$	−16.6103	−0.661772
$631$	13.3799	0.532644	0.266322	−	0.963884i	$-0.414191\pi$
$631$	13.3799	0.532644	0.266322	+	0.963884i	$0.414191\pi$
$632$	−8.23425	−0.327541
$633$	13.3585	0.530954
$634$	26.9246	1.06931
$635$	−27.3814	−1.08660
$636$	122.602	4.86147
$637$	9.98495	0.395618
$638$	−69.0454	−2.73353
$639$	3.13999	0.124216
$640$	16.9052	0.668237
$641$	−13.1260	−0.518447	−0.259223	−	0.965817i	$-0.583467\pi$
$641$	−13.1260	−0.518447	−0.259223	+	0.965817i	$0.583467\pi$
$642$	−9.48725	−0.374432
$643$	6.15698	0.242808	0.121404	−	0.992603i	$-0.461260\pi$
$643$	6.15698	0.242808	0.121404	+	0.992603i	$0.461260\pi$
$644$	108.862	4.28976
$645$	−5.45700	−0.214869
$646$	22.2195	0.874213
$647$	−14.6103	−0.574390	−0.287195	−	0.957872i	$-0.592723\pi$
$647$	−14.6103	−0.574390	−0.287195	+	0.957872i	$0.592723\pi$
$648$	70.6913	2.77702
$649$	−6.28016	−0.246518
$650$	−4.70644	−0.184602
$651$	−30.1822	−1.18293
$652$	114.637	4.48953
$653$	22.1990	0.868715	0.434357	−	0.900741i	$-0.356975\pi$
$653$	22.1990	0.868715	0.434357	+	0.900741i	$0.356975\pi$
$654$	−10.9261	−0.427246
$655$	57.5863	2.25008
$656$	−82.3172	−3.21395
$657$	4.95889	0.193465
$658$	−54.2758	−2.11589
$659$	−25.2871	−0.985044	−0.492522	−	0.870300i	$-0.663925\pi$
$659$	−25.2871	−0.985044	−0.492522	+	0.870300i	$0.663925\pi$
$660$	88.3983	3.44090
$661$	8.09077	0.314695	0.157347	−	0.987543i	$-0.449706\pi$
$661$	8.09077	0.314695	0.157347	+	0.987543i	$0.449706\pi$
$662$	−20.6120	−0.801110
$663$	−4.95443	−0.192414
$664$	−65.9508	−2.55939
$665$	29.2267	1.13336
$666$	14.5702	0.564586
$667$	37.0081	1.43296
$668$	−9.86523	−0.381697
$669$	−43.2565	−1.67239
$670$	94.5647	3.65335
$671$	−40.4731	−1.56245
$672$	−68.8861	−2.65734
$673$	23.2076	0.894587	0.447293	−	0.894387i	$-0.352388\pi$
$673$	23.2076	0.894587	0.447293	+	0.894387i	$0.352388\pi$
$674$	29.0931	1.12062
$675$	−11.9323	−0.459275
$676$	−58.2864	−2.24179
$677$	10.9028	0.419028	0.209514	−	0.977806i	$-0.432812\pi$
$677$	10.9028	0.419028	0.209514	+	0.977806i	$0.432812\pi$
$678$	87.7122	3.36857
$679$	−1.52322	−0.0584559
$680$	70.2164	2.69268
$681$	1.17399	0.0449875
$682$	33.3716	1.27787
$683$	−44.3659	−1.69761	−0.848806	−	0.528704i	$-0.822678\pi$
$683$	−44.3659	−1.69761	−0.848806	+	0.528704i	$0.822678\pi$
$684$	5.52418	0.211222
$685$	44.8797	1.71477
$686$	−82.9901	−3.16858
$687$	−44.3507	−1.69208
$688$	−8.93946	−0.340814
$689$	9.99353	0.380723
$690$	−67.6911	−2.57696
$691$	−25.9198	−0.986035	−0.493017	−	0.870019i	$-0.664106\pi$
$691$	−25.9198	−0.986035	−0.493017	+	0.870019i	$0.664106\pi$
$692$	−90.9876	−3.45883
$693$	8.60729	0.326964
$694$	−16.9706	−0.644194
$695$	7.18038	0.272367
$696$	−93.7621	−3.55404
$697$	36.2004	1.37119
$698$	−57.8910	−2.19121
$699$	−19.5083	−0.737873
$700$	54.7135	2.06798
$701$	−10.5159	−0.397180	−0.198590	−	0.980083i	$-0.563636\pi$
$701$	−10.5159	−0.397180	−0.198590	+	0.980083i	$0.563636\pi$
$702$	8.58139	0.323884
$703$	−25.6370	−0.966919
$704$	14.0925	0.531132
$705$	23.6231	0.889696
$706$	52.1400	1.96231
$707$	−16.9795	−0.638579
$708$	−14.9266	−0.560976
$709$	−49.7491	−1.86837	−0.934183	−	0.356793i	$-0.883870\pi$
$709$	−49.7491	−1.86837	−0.934183	+	0.356793i	$0.883870\pi$
$710$	−43.6572	−1.63843
$711$	0.610764	0.0229054
$712$	−39.7731	−1.49056
$713$	−17.8871	−0.669876
$714$	82.2853	3.07945
$715$	7.20555	0.269472
$716$	63.9084	2.38837
$717$	23.4557	0.875971
$718$	36.6555	1.36797
$719$	18.2259	0.679710	0.339855	−	0.940478i	$-0.389622\pi$
$719$	18.2259	0.679710	0.339855	+	0.940478i	$0.389622\pi$
$720$	11.8431	0.441366
$721$	83.5354	3.11102
$722$	35.1681	1.30882
$723$	−42.0976	−1.56563
$724$	−53.3672	−1.98337
$725$	18.6001	0.690790
$726$	−12.2307	−0.453925
$727$	−22.2465	−0.825077	−0.412539	−	0.910940i	$-0.635358\pi$
$727$	−22.2465	−0.825077	−0.412539	+	0.910940i	$0.635358\pi$
$728$	−22.4817	−0.833229
$729$	20.9747	0.776841
$730$	−68.9467	−2.55183
$731$	3.93128	0.145404
$732$	−96.1960	−3.55551
$733$	26.5229	0.979647	0.489824	−	0.871822i	$-0.337061\pi$
$733$	26.5229	0.979647	0.489824	+	0.871822i	$0.337061\pi$
$734$	−75.3873	−2.78260
$735$	72.1779	2.66232
$736$	−40.8245	−1.50481
$737$	−49.0023	−1.80502
$738$	12.8580	0.473309
$739$	−18.5361	−0.681863	−0.340932	−	0.940088i	$-0.610742\pi$
$739$	−18.5361	−0.681863	−0.340932	+	0.940088i	$0.610742\pi$
$740$	−141.798	−5.21260
$741$	3.09638	0.113749
$742$	−165.977	−6.09320
$743$	0.313050	0.0114847	0.00574235	−	0.999984i	$-0.498172\pi$
$743$	0.313050	0.0114847	0.00574235	+	0.999984i	$0.498172\pi$
$744$	45.3180	1.66144
$745$	6.97115	0.255403
$746$	34.3940	1.25925
$747$	4.89181	0.178982
$748$	−63.6830	−2.32848
$749$	8.99012	0.328492
$750$	32.4740	1.18578
$751$	−30.2827	−1.10503	−0.552515	−	0.833503i	$-0.686332\pi$
$751$	−30.2827	−1.10503	−0.552515	+	0.833503i	$0.686332\pi$
$752$	38.6984	1.41119
$753$	−34.4333	−1.25482
$754$	−13.3767	−0.487149
$755$	30.5506	1.11185
$756$	−99.7608	−3.62827
$757$	2.88608	0.104896	0.0524482	−	0.998624i	$-0.483298\pi$
$757$	2.88608	0.104896	0.0524482	+	0.998624i	$0.483298\pi$
$758$	30.5231	1.10865
$759$	35.0767	1.27321
$760$	−43.8833	−1.59181
$761$	25.6050	0.928181	0.464090	−	0.885788i	$-0.346381\pi$
$761$	25.6050	0.928181	0.464090	+	0.885788i	$0.346381\pi$
$762$	48.1792	1.74535
$763$	10.3536	0.374826
$764$	13.4056	0.484996
$765$	−5.20820	−0.188303
$766$	−35.7188	−1.29057
$767$	−1.21670	−0.0439325
$768$	−44.1033	−1.59144
$769$	12.9019	0.465254	0.232627	−	0.972566i	$-0.425268\pi$
$769$	12.9019	0.465254	0.232627	+	0.972566i	$0.425268\pi$
$770$	−119.673	−4.31270
$771$	−59.6090	−2.14676
$772$	−51.4682	−1.85238
$773$	−26.8433	−0.965486	−0.482743	−	0.875762i	$-0.660359\pi$
$773$	−26.8433	−0.965486	−0.482743	+	0.875762i	$0.660359\pi$
$774$	1.39635	0.0501907
$775$	−8.98996	−0.322929
$776$	2.28709	0.0821018
$777$	−94.9415	−3.40601
$778$	32.1463	1.15250
$779$	−22.6242	−0.810597
$780$	17.1260	0.613211
$781$	22.6227	0.809503
$782$	48.7653	1.74384
$783$	−33.9141	−1.21199
$784$	118.239	4.22282
$785$	−1.99485	−0.0711992
$786$	−101.326	−3.61419
$787$	−10.6432	−0.379388	−0.189694	−	0.981843i	$-0.560750\pi$
$787$	−10.6432	−0.379388	−0.189694	+	0.981843i	$0.560750\pi$
$788$	−25.7341	−0.916741
$789$	−22.3200	−0.794613
$790$	−8.49184	−0.302126
$791$	−83.1161	−2.95527
$792$	−12.9237	−0.459223
$793$	−7.84115	−0.278447
$794$	28.6149	1.01551
$795$	72.2399	2.56208
$796$	−115.958	−4.11003
$797$	24.9106	0.882379	0.441189	−	0.897414i	$-0.354557\pi$
$797$	24.9106	0.882379	0.441189	+	0.897414i	$0.354557\pi$
$798$	−51.4260	−1.82046
$799$	−17.0183	−0.602063
$800$	−20.5182	−0.725428
$801$	2.95011	0.104237
$802$	44.8868	1.58501
$803$	35.7274	1.26079
$804$	−116.468	−4.10751
$805$	64.1441	2.26078
$806$	6.46533	0.227731
$807$	−7.21721	−0.254058
$808$	25.4944	0.896889
$809$	9.70851	0.341333	0.170666	−	0.985329i	$-0.445408\pi$
$809$	9.70851	0.341333	0.170666	+	0.985329i	$0.445408\pi$
$810$	72.9028	2.56154
$811$	48.9866	1.72015	0.860076	−	0.510166i	$-0.170416\pi$
$811$	48.9866	1.72015	0.860076	+	0.510166i	$0.170416\pi$
$812$	155.507	5.45723
$813$	58.0446	2.03571
$814$	104.974	3.67935
$815$	67.5469	2.36607
$816$	−58.6690	−2.05383
$817$	−2.45694	−0.0859575
$818$	−79.2550	−2.77109
$819$	1.66755	0.0582690
$820$	−125.134	−4.36988
$821$	52.7951	1.84256	0.921281	−	0.388897i	$-0.127144\pi$
$821$	52.7951	1.84256	0.921281	+	0.388897i	$0.127144\pi$
$822$	−78.9684	−2.75434
$823$	18.4765	0.644049	0.322024	−	0.946731i	$-0.395637\pi$
$823$	18.4765	0.644049	0.322024	+	0.946731i	$0.395637\pi$
$824$	−125.427	−4.36945
$825$	17.6294	0.613777
$826$	20.2075	0.703107
$827$	14.8922	0.517851	0.258926	−	0.965897i	$-0.416632\pi$
$827$	14.8922	0.517851	0.258926	+	0.965897i	$0.416632\pi$
$828$	12.1240	0.421338
$829$	−38.9566	−1.35302	−0.676510	−	0.736434i	$-0.736508\pi$
$829$	−38.9566	−1.35302	−0.676510	+	0.736434i	$0.736508\pi$
$830$	−68.0139	−2.36080
$831$	17.1474	0.594838
$832$	2.73024	0.0946542
$833$	−51.9976	−1.80161
$834$	−12.6343	−0.437490
$835$	−5.81284	−0.201161
$836$	39.8001	1.37652
$837$	16.3917	0.566579
$838$	−74.9112	−2.58777
$839$	34.0858	1.17677	0.588387	−	0.808579i	$-0.299763\pi$
$839$	34.0858	1.17677	0.588387	+	0.808579i	$0.299763\pi$
$840$	−162.513	−5.60723
$841$	23.8652	0.822940
$842$	36.0350	1.24185
$843$	4.88015	0.168081
$844$	33.2661	1.14506
$845$	−34.3438	−1.18146
$846$	−6.04471	−0.207821
$847$	11.5899	0.398232
$848$	118.341	4.06383
$849$	23.7539	0.815232
$850$	24.5092	0.840659
$851$	−56.2659	−1.92877
$852$	53.7693	1.84211
$853$	15.4810	0.530060	0.265030	−	0.964240i	$-0.414618\pi$
$853$	15.4810	0.530060	0.265030	+	0.964240i	$0.414618\pi$
$854$	130.229	4.45635
$855$	3.25498	0.111318
$856$	−13.4985	−0.461369
$857$	55.6474	1.90088	0.950440	−	0.310907i	$-0.100633\pi$
$857$	55.6474	1.90088	0.950440	+	0.310907i	$0.100633\pi$
$858$	−12.6786	−0.432839
$859$	1.48731	0.0507465	0.0253732	−	0.999678i	$-0.491923\pi$
$859$	1.48731	0.0507465	0.0253732	+	0.999678i	$0.491923\pi$
$860$	−13.5893	−0.463391
$861$	−83.7842	−2.85536
$862$	−56.4114	−1.92138
$863$	−1.15526	−0.0393255	−0.0196628	−	0.999807i	$-0.506259\pi$
$863$	−1.15526	−0.0393255	−0.0196628	+	0.999807i	$0.506259\pi$
$864$	37.4115	1.27276
$865$	−53.6121	−1.82287
$866$	44.8066	1.52259
$867$	−6.05112	−0.205507
$868$	−75.1611	−2.55113
$869$	4.40037	0.149272
$870$	−96.6953	−3.27828
$871$	−9.49357	−0.321677
$872$	−15.5457	−0.526445
$873$	−0.169642	−0.00574150
$874$	−30.4770	−1.03090
$875$	−30.7723	−1.04030
$876$	84.9163	2.86906
$877$	−49.1255	−1.65885	−0.829424	−	0.558619i	$-0.811331\pi$
$877$	−49.1255	−1.65885	−0.829424	+	0.558619i	$0.811331\pi$
$878$	−21.9244	−0.739912
$879$	6.56682	0.221493
$880$	85.3261	2.87634
$881$	−19.5061	−0.657179	−0.328589	−	0.944473i	$-0.606573\pi$
$881$	−19.5061	−0.657179	−0.328589	+	0.944473i	$0.606573\pi$
$882$	−18.4690	−0.621884
$883$	−6.33877	−0.213317	−0.106658	−	0.994296i	$-0.534015\pi$
$883$	−6.33877	−0.213317	−0.106658	+	0.994296i	$0.534015\pi$
$884$	−12.3378	−0.414964
$885$	−8.79512	−0.295645
$886$	−11.1152	−0.373424
$887$	49.0081	1.64553	0.822765	−	0.568382i	$-0.192430\pi$
$887$	49.0081	1.64553	0.822765	+	0.568382i	$0.192430\pi$
$888$	142.553	4.78376
$889$	−45.6547	−1.53121
$890$	−41.0173	−1.37490
$891$	−37.7774	−1.26559
$892$	−107.719	−3.60672
$893$	10.6360	0.355919
$894$	−12.2661	−0.410241
$895$	37.6564	1.25871
$896$	28.1870	0.941662
$897$	6.79567	0.226901
$898$	−38.3228	−1.27885
$899$	−25.5513	−0.852184
$900$	6.09346	0.203115
$901$	−52.0423	−1.73378
$902$	92.6380	3.08451
$903$	−9.09878	−0.302788
$904$	124.797	4.15070
$905$	−31.4452	−1.04527
$906$	−53.7555	−1.78591
$907$	23.4597	0.778967	0.389483	−	0.921034i	$-0.372654\pi$
$907$	23.4597	0.778967	0.389483	+	0.921034i	$0.372654\pi$
$908$	2.92353	0.0970208
$909$	−1.89101	−0.0627208
$910$	−23.1850	−0.768577
$911$	−8.73940	−0.289549	−0.144775	−	0.989465i	$-0.546246\pi$
$911$	−8.73940	−0.289549	−0.144775	+	0.989465i	$0.546246\pi$
$912$	36.6665	1.21415
$913$	35.2440	1.16641
$914$	−33.2208	−1.09885
$915$	−56.6810	−1.87382
$916$	−110.444	−3.64918
$917$	96.0169	3.17076
$918$	−44.6884	−1.47494
$919$	−18.8856	−0.622980	−0.311490	−	0.950249i	$-0.600828\pi$
$919$	−18.8856	−0.622980	−0.311490	+	0.950249i	$0.600828\pi$
$920$	−96.3112	−3.17529
$921$	−11.4583	−0.377562
$922$	103.953	3.42350
$923$	4.38285	0.144263
$924$	147.392	4.84883
$925$	−28.2790	−0.929807
$926$	17.1082	0.562212
$927$	9.30336	0.305562
$928$	−58.3169	−1.91435
$929$	−23.5243	−0.771808	−0.385904	−	0.922539i	$-0.626110\pi$
$929$	−23.5243	−0.771808	−0.385904	+	0.922539i	$0.626110\pi$
$930$	46.7357	1.53252
$931$	32.4971	1.06505
$932$	−48.5806	−1.59131
$933$	−56.0841	−1.83611
$934$	−15.0363	−0.492004
$935$	−37.5236	−1.22715
$936$	−2.50380	−0.0818392
$937$	40.4819	1.32249	0.661244	−	0.750171i	$-0.270029\pi$
$937$	40.4819	1.32249	0.661244	+	0.750171i	$0.270029\pi$
$938$	157.673	5.14821
$939$	23.9949	0.783044
$940$	58.8273	1.91873
$941$	−49.7853	−1.62295	−0.811477	−	0.584385i	$-0.801336\pi$
$941$	−49.7853	−1.62295	−0.811477	+	0.584385i	$0.801336\pi$
$942$	3.51005	0.114364
$943$	−49.6536	−1.61695
$944$	−14.4078	−0.468935
$945$	−58.7815	−1.91216
$946$	10.0603	0.327088
$947$	−35.6643	−1.15893	−0.579467	−	0.814996i	$-0.696739\pi$
$947$	−35.6643	−1.15893	−0.579467	+	0.814996i	$0.696739\pi$
$948$	10.4588	0.339684
$949$	6.92172	0.224689
$950$	−15.3176	−0.496968
$951$	−19.5392	−0.633603
$952$	117.076	3.79445
$953$	3.90283	0.126425	0.0632125	−	0.998000i	$-0.479865\pi$
$953$	3.90283	0.126425	0.0632125	+	0.998000i	$0.479865\pi$
$954$	−18.4849	−0.598470
$955$	7.89889	0.255602
$956$	58.4106	1.88913
$957$	50.1064	1.61971
$958$	87.9948	2.84298
$959$	74.8305	2.41640
$960$	19.7360	0.636977
$961$	−18.6503	−0.601623
$962$	20.3374	0.655705
$963$	1.00123	0.0322643
$964$	−104.833	−3.37646
$965$	−30.3263	−0.976238
$966$	−112.865	−3.63138
$967$	−14.9555	−0.480935	−0.240468	−	0.970657i	$-0.577301\pi$
$967$	−14.9555	−0.480935	−0.240468	+	0.970657i	$0.577301\pi$
$968$	−17.4019	−0.559320
$969$	−16.1247	−0.518001
$970$	2.35864	0.0757313
$971$	−35.0620	−1.12519	−0.562597	−	0.826732i	$-0.690198\pi$
$971$	−35.0620	−1.12519	−0.562597	+	0.826732i	$0.690198\pi$
$972$	−24.4992	−0.785811
$973$	11.9723	0.383813
$974$	−94.5452	−3.02942
$975$	3.41547	0.109383
$976$	−92.8527	−2.97214
$977$	38.5713	1.23400	0.617002	−	0.786961i	$-0.288347\pi$
$977$	38.5713	1.23400	0.617002	+	0.786961i	$0.288347\pi$
$978$	−118.853	−3.80049
$979$	21.2547	0.679303
$980$	179.741	5.74161
$981$	1.15308	0.0368151
$982$	−28.8742	−0.921412
$983$	0.342307	0.0109179	0.00545894	−	0.999985i	$-0.498262\pi$
$983$	0.342307	0.0109179	0.00545894	+	0.999985i	$0.498262\pi$
$984$	125.800	4.01037
$985$	−15.1632	−0.483139
$986$	69.6602	2.21843
$987$	39.3881	1.25374
$988$	7.71076	0.245312
$989$	−5.39227	−0.171464
$990$	−13.3280	−0.423591
$991$	−31.6194	−1.00442	−0.502211	−	0.864745i	$-0.667480\pi$
$991$	−31.6194	−1.00442	−0.502211	+	0.864745i	$0.667480\pi$
$992$	28.1863	0.894915
$993$	14.9582	0.474684
$994$	−72.7922	−2.30883
$995$	−68.3254	−2.16606
$996$	83.7676	2.65428
$997$	−55.8895	−1.77004	−0.885018	−	0.465556i	$-0.845854\pi$
$997$	−55.8895	−1.77004	−0.885018	+	0.465556i	$0.845854\pi$
$998$	−58.7748	−1.86048
$999$	51.5619	1.63135

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4027.2.a.c.1.7	✓	174

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4027.2.a.c.1.7	✓	174	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:	\( N \)	\(=\)	\( 4027 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4027.a (trivial)

\(f(q)\)	\(=\)	\(q-2.58182 q^{2} +1.87364 q^{3} +4.66582 q^{4} +2.74921 q^{5} -4.83740 q^{6} +4.58392 q^{7} -6.88267 q^{8} +0.510512 q^{9} +O(q^{10})\)	\(q-2.58182 q^{2} +1.87364 q^{3} +4.66582 q^{4} +2.74921 q^{5} -4.83740 q^{6} +4.58392 q^{7} -6.88267 q^{8} +0.510512 q^{9} -7.09798 q^{10} +3.67809 q^{11} +8.74204 q^{12} +0.712583 q^{13} -11.8349 q^{14} +5.15102 q^{15} +8.43822 q^{16} -3.71085 q^{17} -1.31805 q^{18} +2.31918 q^{19} +12.8273 q^{20} +8.58860 q^{21} -9.49619 q^{22} +5.08992 q^{23} -12.8956 q^{24} +2.55817 q^{25} -1.83977 q^{26} -4.66439 q^{27} +21.3877 q^{28} +7.27085 q^{29} -13.2990 q^{30} -3.51421 q^{31} -8.02065 q^{32} +6.89141 q^{33} +9.58076 q^{34} +12.6022 q^{35} +2.38196 q^{36} -11.0544 q^{37} -5.98771 q^{38} +1.33512 q^{39} -18.9219 q^{40} -9.75528 q^{41} -22.1743 q^{42} -1.05940 q^{43} +17.1613 q^{44} +1.40351 q^{45} -13.1413 q^{46} +4.58609 q^{47} +15.8101 q^{48} +14.0123 q^{49} -6.60475 q^{50} -6.95278 q^{51} +3.32478 q^{52} +14.0244 q^{53} +12.0426 q^{54} +10.1119 q^{55} -31.5496 q^{56} +4.34529 q^{57} -18.7721 q^{58} -1.70745 q^{59} +24.0337 q^{60} -11.0038 q^{61} +9.07308 q^{62} +2.34015 q^{63} +3.83147 q^{64} +1.95904 q^{65} -17.7924 q^{66} -13.3228 q^{67} -17.3141 q^{68} +9.53666 q^{69} -32.5366 q^{70} +6.15065 q^{71} -3.51369 q^{72} +9.71356 q^{73} +28.5404 q^{74} +4.79308 q^{75} +10.8209 q^{76} +16.8601 q^{77} -3.44705 q^{78} +1.19637 q^{79} +23.1985 q^{80} -10.2709 q^{81} +25.1864 q^{82} +9.58215 q^{83} +40.0728 q^{84} -10.2019 q^{85} +2.73519 q^{86} +13.6229 q^{87} -25.3151 q^{88} +5.77873 q^{89} -3.62361 q^{90} +3.26643 q^{91} +23.7487 q^{92} -6.58436 q^{93} -11.8405 q^{94} +6.37591 q^{95} -15.0278 q^{96} -0.332297 q^{97} -36.1774 q^{98} +1.87771 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 174 q + 21 q^{2} + 17 q^{3} + 187 q^{4} + 72 q^{5} + 21 q^{6} + 24 q^{7} + 54 q^{8} + 197 q^{9}+O(q^{10}) \) 174 * q + 21 * q^2 + 17 * q^3 + 187 * q^4 + 72 * q^5 + 21 * q^6 + 24 * q^7 + 54 * q^8 + 197 * q^9	\( 174 q + 21 q^{2} + 17 q^{3} + 187 q^{4} + 72 q^{5} + 21 q^{6} + 24 q^{7} + 54 q^{8} + 197 q^{9} + 20 q^{10} + 35 q^{11} + 23 q^{12} + 91 q^{13} + 18 q^{14} + 16 q^{15} + 201 q^{16} + 148 q^{17} + 39 q^{18} + 36 q^{19} + 128 q^{20} + 57 q^{21} + 17 q^{22} + 96 q^{23} + 24 q^{24} + 226 q^{25} + 44 q^{26} + 62 q^{27} + 32 q^{28} + 122 q^{29} + 25 q^{30} + 23 q^{31} + 104 q^{32} + 91 q^{33} + 6 q^{34} + 80 q^{35} + 222 q^{36} + 71 q^{37} + 125 q^{38} + 16 q^{39} + 53 q^{40} + 97 q^{41} + 14 q^{42} + 38 q^{43} + 70 q^{44} + 185 q^{45} - 23 q^{46} + 110 q^{47} + 36 q^{48} + 210 q^{49} + 51 q^{50} + 33 q^{51} + 118 q^{52} + 214 q^{53} + 8 q^{54} + 37 q^{55} + 41 q^{56} + 76 q^{57} + 2 q^{58} + 66 q^{59} - 12 q^{60} + 114 q^{61} + 175 q^{62} + 62 q^{63} + 190 q^{64} + 128 q^{65} + 12 q^{66} - 6 q^{67} + 348 q^{68} + 115 q^{69} - 38 q^{70} + 54 q^{71} + 101 q^{72} + 107 q^{73} + 71 q^{74} - q^{75} + 31 q^{76} + 368 q^{77} - 14 q^{78} - 14 q^{79} + 205 q^{80} + 222 q^{81} + 26 q^{82} + 246 q^{83} + 41 q^{84} + 87 q^{85} + 33 q^{86} + 100 q^{87} - 6 q^{88} + 147 q^{89} + 50 q^{90} - 23 q^{91} + 189 q^{92} + 117 q^{93} + 23 q^{94} + 42 q^{95} + 38 q^{96} + 52 q^{97} + 148 q^{98} + 38 q^{99}+O(q^{100}) \) 174 * q + 21 * q^2 + 17 * q^3 + 187 * q^4 + 72 * q^5 + 21 * q^6 + 24 * q^7 + 54 * q^8 + 197 * q^9 + 20 * q^10 + 35 * q^11 + 23 * q^12 + 91 * q^13 + 18 * q^14 + 16 * q^15 + 201 * q^16 + 148 * q^17 + 39 * q^18 + 36 * q^19 + 128 * q^20 + 57 * q^21 + 17 * q^22 + 96 * q^23 + 24 * q^24 + 226 * q^25 + 44 * q^26 + 62 * q^27 + 32 * q^28 + 122 * q^29 + 25 * q^30 + 23 * q^31 + 104 * q^32 + 91 * q^33 + 6 * q^34 + 80 * q^35 + 222 * q^36 + 71 * q^37 + 125 * q^38 + 16 * q^39 + 53 * q^40 + 97 * q^41 + 14 * q^42 + 38 * q^43 + 70 * q^44 + 185 * q^45 - 23 * q^46 + 110 * q^47 + 36 * q^48 + 210 * q^49 + 51 * q^50 + 33 * q^51 + 118 * q^52 + 214 * q^53 + 8 * q^54 + 37 * q^55 + 41 * q^56 + 76 * q^57 + 2 * q^58 + 66 * q^59 - 12 * q^60 + 114 * q^61 + 175 * q^62 + 62 * q^63 + 190 * q^64 + 128 * q^65 + 12 * q^66 - 6 * q^67 + 348 * q^68 + 115 * q^69 - 38 * q^70 + 54 * q^71 + 101 * q^72 + 107 * q^73 + 71 * q^74 - q^75 + 31 * q^76 + 368 * q^77 - 14 * q^78 - 14 * q^79 + 205 * q^80 + 222 * q^81 + 26 * q^82 + 246 * q^83 + 41 * q^84 + 87 * q^85 + 33 * q^86 + 100 * q^87 - 6 * q^88 + 147 * q^89 + 50 * q^90 - 23 * q^91 + 189 * q^92 + 117 * q^93 + 23 * q^94 + 42 * q^95 + 38 * q^96 + 52 * q^97 + 148 * q^98 + 38 * q^99

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