LMFDB - Embedded newform 6037.2.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6037,2,Mod(1,6037)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6037, 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("6037.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6037 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6037.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:	$48.2056877002$
Analytic rank:	$1$
Dimension:	$243$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	6037.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.80926 q^{2} -0.794746 q^{3} +5.89194 q^{4} -3.46470 q^{5} +2.23265 q^{6} -2.15218 q^{7} -10.9335 q^{8} -2.36838 q^{9} +O(q^{10})$	\(q-2.80926 q^{2} -0.794746 q^{3} +5.89194 q^{4} -3.46470 q^{5} +2.23265 q^{6} -2.15218 q^{7} -10.9335 q^{8} -2.36838 q^{9} +9.73325 q^{10} -4.73561 q^{11} -4.68259 q^{12} -0.736005 q^{13} +6.04604 q^{14} +2.75356 q^{15} +18.9311 q^{16} -6.42081 q^{17} +6.65339 q^{18} -4.26388 q^{19} -20.4138 q^{20} +1.71044 q^{21} +13.3035 q^{22} -9.40572 q^{23} +8.68933 q^{24} +7.00416 q^{25} +2.06763 q^{26} +4.26650 q^{27} -12.6805 q^{28} +10.2484 q^{29} -7.73546 q^{30} +3.74516 q^{31} -31.3154 q^{32} +3.76360 q^{33} +18.0377 q^{34} +7.45667 q^{35} -13.9543 q^{36} +4.27309 q^{37} +11.9783 q^{38} +0.584937 q^{39} +37.8812 q^{40} -8.07498 q^{41} -4.80506 q^{42} +4.14726 q^{43} -27.9019 q^{44} +8.20573 q^{45} +26.4231 q^{46} -10.9056 q^{47} -15.0454 q^{48} -2.36811 q^{49} -19.6765 q^{50} +5.10291 q^{51} -4.33650 q^{52} +8.12327 q^{53} -11.9857 q^{54} +16.4075 q^{55} +23.5308 q^{56} +3.38870 q^{57} -28.7903 q^{58} +13.4985 q^{59} +16.2238 q^{60} +8.88956 q^{61} -10.5211 q^{62} +5.09719 q^{63} +50.1108 q^{64} +2.55004 q^{65} -10.5729 q^{66} -2.97583 q^{67} -37.8310 q^{68} +7.47515 q^{69} -20.9477 q^{70} +6.02195 q^{71} +25.8946 q^{72} -4.69290 q^{73} -12.0042 q^{74} -5.56652 q^{75} -25.1225 q^{76} +10.1919 q^{77} -1.64324 q^{78} -14.4193 q^{79} -65.5905 q^{80} +3.71436 q^{81} +22.6847 q^{82} +7.18568 q^{83} +10.0778 q^{84} +22.2462 q^{85} -11.6507 q^{86} -8.14484 q^{87} +51.7766 q^{88} +15.4333 q^{89} -23.0520 q^{90} +1.58402 q^{91} -55.4179 q^{92} -2.97645 q^{93} +30.6367 q^{94} +14.7731 q^{95} +24.8877 q^{96} +2.13965 q^{97} +6.65263 q^{98} +11.2157 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 243 q - 47 q^{2} - 31 q^{3} + 229 q^{4} - 40 q^{5} - 18 q^{6} - 42 q^{7} - 135 q^{8} + 214 q^{9}+O(q^{10}) $ 243 * q - 47 * q^2 - 31 * q^3 + 229 * q^4 - 40 * q^5 - 18 * q^6 - 42 * q^7 - 135 * q^8 + 214 * q^9	\( 243 q - 47 q^{2} - 31 q^{3} + 229 q^{4} - 40 q^{5} - 18 q^{6} - 42 q^{7} - 135 q^{8} + 214 q^{9} - 14 q^{10} - 112 q^{11} - 54 q^{12} - 45 q^{13} - 35 q^{14} - 56 q^{15} + 213 q^{16} - 71 q^{17} - 135 q^{18} - 69 q^{19} - 107 q^{20} - 36 q^{21} - 24 q^{22} - 162 q^{23} - 57 q^{24} + 203 q^{25} - 55 q^{26} - 115 q^{27} - 87 q^{28} - 76 q^{29} - 64 q^{30} - 35 q^{31} - 302 q^{32} - 77 q^{33} - 9 q^{34} - 264 q^{35} + 173 q^{36} - 61 q^{37} - 71 q^{38} - 123 q^{39} - 16 q^{40} - 74 q^{41} - 70 q^{42} - 178 q^{43} - 209 q^{44} - 107 q^{45} - 11 q^{46} - 191 q^{47} - 65 q^{48} + 211 q^{49} - 188 q^{50} - 175 q^{51} - 95 q^{52} - 122 q^{53} - 36 q^{54} - 47 q^{55} - 69 q^{56} - 103 q^{57} - 37 q^{58} - 212 q^{59} - 79 q^{60} - 14 q^{61} - 152 q^{62} - 203 q^{63} + 217 q^{64} - 159 q^{65} + 5 q^{66} - 202 q^{67} - 176 q^{68} - 34 q^{69} + 45 q^{70} - 170 q^{71} - 347 q^{72} - 57 q^{73} - 68 q^{74} - 124 q^{75} - 74 q^{76} - 166 q^{77} - 63 q^{78} - 48 q^{79} - 222 q^{80} + 159 q^{81} - 27 q^{82} - 434 q^{83} - 52 q^{84} - 57 q^{85} - 77 q^{86} - 184 q^{87} - 15 q^{88} - 62 q^{89} - 24 q^{90} - 81 q^{91} - 330 q^{92} - 164 q^{93} + 40 q^{94} - 182 q^{95} - 66 q^{96} - 21 q^{97} - 254 q^{98} - 306 q^{99}+O(q^{100}) \) 243 * q - 47 * q^2 - 31 * q^3 + 229 * q^4 - 40 * q^5 - 18 * q^6 - 42 * q^7 - 135 * q^8 + 214 * q^9 - 14 * q^10 - 112 * q^11 - 54 * q^12 - 45 * q^13 - 35 * q^14 - 56 * q^15 + 213 * q^16 - 71 * q^17 - 135 * q^18 - 69 * q^19 - 107 * q^20 - 36 * q^21 - 24 * q^22 - 162 * q^23 - 57 * q^24 + 203 * q^25 - 55 * q^26 - 115 * q^27 - 87 * q^28 - 76 * q^29 - 64 * q^30 - 35 * q^31 - 302 * q^32 - 77 * q^33 - 9 * q^34 - 264 * q^35 + 173 * q^36 - 61 * q^37 - 71 * q^38 - 123 * q^39 - 16 * q^40 - 74 * q^41 - 70 * q^42 - 178 * q^43 - 209 * q^44 - 107 * q^45 - 11 * q^46 - 191 * q^47 - 65 * q^48 + 211 * q^49 - 188 * q^50 - 175 * q^51 - 95 * q^52 - 122 * q^53 - 36 * q^54 - 47 * q^55 - 69 * q^56 - 103 * q^57 - 37 * q^58 - 212 * q^59 - 79 * q^60 - 14 * q^61 - 152 * q^62 - 203 * q^63 + 217 * q^64 - 159 * q^65 + 5 * q^66 - 202 * q^67 - 176 * q^68 - 34 * q^69 + 45 * q^70 - 170 * q^71 - 347 * q^72 - 57 * q^73 - 68 * q^74 - 124 * q^75 - 74 * q^76 - 166 * q^77 - 63 * q^78 - 48 * q^79 - 222 * q^80 + 159 * q^81 - 27 * q^82 - 434 * q^83 - 52 * q^84 - 57 * q^85 - 77 * q^86 - 184 * q^87 - 15 * q^88 - 62 * q^89 - 24 * q^90 - 81 * q^91 - 330 * q^92 - 164 * q^93 + 40 * q^94 - 182 * q^95 - 66 * q^96 - 21 * q^97 - 254 * q^98 - 306 * 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 $

$2$	−2.80926	−1.98645	−0.993223	−	0.116222i	$-0.962922\pi$
$2$	−2.80926	−1.98645	−0.993223	+	0.116222i	$0.962922\pi$
$3$	−0.794746	−0.458847	−0.229423	−	0.973327i	$-0.573684\pi$
$3$	−0.794746	−0.458847	−0.229423	+	0.973327i	$0.573684\pi$
$4$	5.89194	2.94597
$5$	−3.46470	−1.54946	−0.774731	−	0.632291i	$-0.782115\pi$
$5$	−3.46470	−1.54946	−0.774731	+	0.632291i	$0.782115\pi$
$6$	2.23265	0.911474
$7$	−2.15218	−0.813449	−0.406724	−	0.913551i	$-0.633329\pi$
$7$	−2.15218	−0.813449	−0.406724	+	0.913551i	$0.633329\pi$
$8$	−10.9335	−3.86556
$9$	−2.36838	−0.789460
$10$	9.73325	3.07792
$11$	−4.73561	−1.42784	−0.713919	−	0.700228i	$-0.753082\pi$
$11$	−4.73561	−1.42784	−0.713919	+	0.700228i	$0.753082\pi$
$12$	−4.68259	−1.35175
$13$	−0.736005	−0.204131	−0.102066	−	0.994778i	$-0.532545\pi$
$13$	−0.736005	−0.204131	−0.102066	+	0.994778i	$0.532545\pi$
$14$	6.04604	1.61587
$15$	2.75356	0.710965
$16$	18.9311	4.73277
$17$	−6.42081	−1.55728	−0.778638	−	0.627474i	$-0.784089\pi$
$17$	−6.42081	−1.55728	−0.778638	+	0.627474i	$0.784089\pi$
$18$	6.65339	1.56822
$19$	−4.26388	−0.978201	−0.489101	−	0.872227i	$-0.662675\pi$
$19$	−4.26388	−0.978201	−0.489101	+	0.872227i	$0.662675\pi$
$20$	−20.4138	−4.56467
$21$	1.71044	0.373248
$22$	13.3035	2.83633
$23$	−9.40572	−1.96123	−0.980614	−	0.195950i	$-0.937221\pi$
$23$	−9.40572	−1.96123	−0.980614	+	0.195950i	$0.937221\pi$
$24$	8.68933	1.77370
$25$	7.00416	1.40083
$26$	2.06763	0.405496
$27$	4.26650	0.821088
$28$	−12.6805	−2.39640
$29$	10.2484	1.90307	0.951536	−	0.307536i	$-0.0995045\pi$
$29$	10.2484	1.90307	0.951536	+	0.307536i	$0.0995045\pi$
$30$	−7.73546	−1.41229
$31$	3.74516	0.672650	0.336325	−	0.941746i	$-0.390816\pi$
$31$	3.74516	0.672650	0.336325	+	0.941746i	$0.390816\pi$
$32$	−31.3154	−5.53583
$33$	3.76360	0.655159
$34$	18.0377	3.09344
$35$	7.45667	1.26041
$36$	−13.9543	−2.32572
$37$	4.27309	0.702492	0.351246	−	0.936283i	$-0.385758\pi$
$37$	4.27309	0.702492	0.351246	+	0.936283i	$0.385758\pi$
$38$	11.9783	1.94314
$39$	0.584937	0.0936649
$40$	37.8812	5.98954
$41$	−8.07498	−1.26110	−0.630550	−	0.776149i	$-0.717171\pi$
$41$	−8.07498	−1.26110	−0.630550	+	0.776149i	$0.717171\pi$
$42$	−4.80506	−0.741438
$43$	4.14726	0.632452	0.316226	−	0.948684i	$-0.397584\pi$
$43$	4.14726	0.632452	0.316226	+	0.948684i	$0.397584\pi$
$44$	−27.9019	−4.20637
$45$	8.20573	1.22324
$46$	26.4231	3.89587
$47$	−10.9056	−1.59075	−0.795374	−	0.606119i	$-0.792726\pi$
$47$	−10.9056	−1.59075	−0.795374	+	0.606119i	$0.792726\pi$
$48$	−15.0454	−2.17161
$49$	−2.36811	−0.338301
$50$	−19.6765	−2.78268
$51$	5.10291	0.714551
$52$	−4.33650	−0.601364
$53$	8.12327	1.11582	0.557909	−	0.829902i	$-0.311604\pi$
$53$	8.12327	1.11582	0.557909	+	0.829902i	$0.311604\pi$
$54$	−11.9857	−1.63105
$55$	16.4075	2.21238
$56$	23.5308	3.14444
$57$	3.38870	0.448844
$58$	−28.7903	−3.78035
$59$	13.4985	1.75736	0.878678	−	0.477414i	$-0.158426\pi$
$59$	13.4985	1.75736	0.878678	+	0.477414i	$0.158426\pi$
$60$	16.2238	2.09448
$61$	8.88956	1.13819	0.569096	−	0.822271i	$-0.307293\pi$
$61$	8.88956	1.13819	0.569096	+	0.822271i	$0.307293\pi$
$62$	−10.5211	−1.33618
$63$	5.09719	0.642185
$64$	50.1108	6.26385
$65$	2.55004	0.316293
$66$	−10.5729	−1.30144
$67$	−2.97583	−0.363555	−0.181778	−	0.983340i	$-0.558185\pi$
$67$	−2.97583	−0.363555	−0.181778	+	0.983340i	$0.558185\pi$
$68$	−37.8310	−4.58769
$69$	7.47515	0.899903
$70$	−20.9477	−2.50373
$71$	6.02195	0.714674	0.357337	−	0.933976i	$-0.383685\pi$
$71$	6.02195	0.714674	0.357337	+	0.933976i	$0.383685\pi$
$72$	25.8946	3.05171
$73$	−4.69290	−0.549263	−0.274631	−	0.961550i	$-0.588556\pi$
$73$	−4.69290	−0.549263	−0.274631	+	0.961550i	$0.588556\pi$
$74$	−12.0042	−1.39546
$75$	−5.56652	−0.642767
$76$	−25.1225	−2.88175
$77$	10.1919	1.16147
$78$	−1.64324	−0.186060
$79$	−14.4193	−1.62229	−0.811147	−	0.584843i	$-0.801156\pi$
$79$	−14.4193	−1.62229	−0.811147	+	0.584843i	$0.801156\pi$
$80$	−65.5905	−7.33324
$81$	3.71436	0.412706
$82$	22.6847	2.50511
$83$	7.18568	0.788731	0.394366	−	0.918954i	$-0.370964\pi$
$83$	7.18568	0.788731	0.394366	+	0.918954i	$0.370964\pi$
$84$	10.0778	1.09958
$85$	22.2462	2.41294
$86$	−11.6507	−1.25633
$87$	−8.14484	−0.873219
$88$	51.7766	5.51940
$89$	15.4333	1.63592	0.817962	−	0.575272i	$-0.195104\pi$
$89$	15.4333	1.63592	0.817962	+	0.575272i	$0.195104\pi$
$90$	−23.0520	−2.42990
$91$	1.58402	0.166050
$92$	−55.4179	−5.77772
$93$	−2.97645	−0.308643
$94$	30.6367	3.15994
$95$	14.7731	1.51569
$96$	24.8877	2.54010
$97$	2.13965	0.217249	0.108624	−	0.994083i	$-0.465355\pi$
$97$	2.13965	0.217249	0.108624	+	0.994083i	$0.465355\pi$
$98$	6.65263	0.672017
$99$	11.2157	1.12722
$100$	41.2681	4.12681
$101$	−0.645710	−0.0642505	−0.0321252	−	0.999484i	$-0.510228\pi$
$101$	−0.645710	−0.0642505	−0.0321252	+	0.999484i	$0.510228\pi$
$102$	−14.3354	−1.41942
$103$	0.290994	0.0286725	0.0143362	−	0.999897i	$-0.495436\pi$
$103$	0.290994	0.0286725	0.0143362	+	0.999897i	$0.495436\pi$
$104$	8.04709	0.789082
$105$	−5.92616	−0.578334
$106$	−22.8204	−2.21651
$107$	0.0490299	0.00473990	0.00236995	−	0.999997i	$-0.499246\pi$
$107$	0.0490299	0.00473990	0.00236995	+	0.999997i	$0.499246\pi$
$108$	25.1379	2.41890
$109$	−12.4040	−1.18809	−0.594044	−	0.804432i	$-0.702470\pi$
$109$	−12.4040	−1.18809	−0.594044	+	0.804432i	$0.702470\pi$
$110$	−46.0928	−4.39478
$111$	−3.39602	−0.322336
$112$	−40.7431	−3.84986
$113$	14.3760	1.35238	0.676190	−	0.736727i	$-0.263630\pi$
$113$	14.3760	1.35238	0.676190	+	0.736727i	$0.263630\pi$
$114$	−9.51974	−0.891605
$115$	32.5880	3.03885
$116$	60.3827	5.60640
$117$	1.74314	0.161153
$118$	−37.9208	−3.49090
$119$	13.8188	1.26676
$120$	−30.1059	−2.74828
$121$	11.4260	1.03872
$122$	−24.9731	−2.26096
$123$	6.41756	0.578652
$124$	22.0662	1.98161
$125$	−6.94381	−0.621073
$126$	−14.3193	−1.27567
$127$	−13.1242	−1.16459	−0.582294	−	0.812979i	$-0.697845\pi$
$127$	−13.1242	−1.16459	−0.582294	+	0.812979i	$0.697845\pi$
$128$	−78.1436	−6.90699
$129$	−3.29602	−0.290198
$130$	−7.16372	−0.628300
$131$	1.84491	0.161191	0.0805954	−	0.996747i	$-0.474318\pi$
$131$	1.84491	0.161191	0.0805954	+	0.996747i	$0.474318\pi$
$132$	22.1749	1.93008
$133$	9.17665	0.795717
$134$	8.35987	0.722183
$135$	−14.7821	−1.27224
$136$	70.2017	6.01975
$137$	4.47846	0.382621	0.191310	−	0.981530i	$-0.438726\pi$
$137$	4.47846	0.382621	0.191310	+	0.981530i	$0.438726\pi$
$138$	−20.9997	−1.78761
$139$	−12.3184	−1.04483	−0.522417	−	0.852690i	$-0.674970\pi$
$139$	−12.3184	−1.04483	−0.522417	+	0.852690i	$0.674970\pi$
$140$	43.9343	3.71312
$141$	8.66720	0.729910
$142$	−16.9172	−1.41966
$143$	3.48543	0.291466
$144$	−44.8360	−3.73633
$145$	−35.5075	−2.94874
$146$	13.1836	1.09108
$147$	1.88204	0.155228
$148$	25.1768	2.06952
$149$	−3.61307	−0.295994	−0.147997	−	0.988988i	$-0.547283\pi$
$149$	−3.61307	−0.295994	−0.147997	+	0.988988i	$0.547283\pi$
$150$	15.6378	1.27682
$151$	−7.00504	−0.570062	−0.285031	−	0.958518i	$-0.592004\pi$
$151$	−7.00504	−0.570062	−0.285031	+	0.958518i	$0.592004\pi$
$152$	46.6190	3.78130
$153$	15.2069	1.22941
$154$	−28.6317	−2.30721
$155$	−12.9759	−1.04225
$156$	3.44641	0.275934
$157$	−12.5817	−1.00413	−0.502066	−	0.864829i	$-0.667427\pi$
$157$	−12.5817	−1.00413	−0.502066	+	0.864829i	$0.667427\pi$
$158$	40.5074	3.22260
$159$	−6.45594	−0.511989
$160$	108.498	8.57755
$161$	20.2428	1.59536
$162$	−10.4346	−0.819819
$163$	−11.5812	−0.907109	−0.453555	−	0.891229i	$-0.649844\pi$
$163$	−11.5812	−0.907109	−0.453555	+	0.891229i	$0.649844\pi$
$164$	−47.5773	−3.71516
$165$	−13.0398	−1.01514
$166$	−20.1864	−1.56677
$167$	−6.38456	−0.494052	−0.247026	−	0.969009i	$-0.579453\pi$
$167$	−6.38456	−0.494052	−0.247026	+	0.969009i	$0.579453\pi$
$168$	−18.7010	−1.44282
$169$	−12.4583	−0.958330
$170$	−62.4953	−4.79317
$171$	10.0985	0.772251
$172$	24.4354	1.86318
$173$	0.0290512	0.00220872	0.00110436	−	0.999999i	$-0.499648\pi$
$173$	0.0290512	0.00220872	0.00110436	+	0.999999i	$0.499648\pi$
$174$	22.8810	1.73460
$175$	−15.0742	−1.13950
$176$	−89.6501	−6.75763
$177$	−10.7279	−0.806357
$178$	−43.3561	−3.24968
$179$	−13.3817	−1.00019	−0.500096	−	0.865970i	$-0.666702\pi$
$179$	−13.3817	−1.00019	−0.500096	+	0.865970i	$0.666702\pi$
$180$	48.3477	3.60362
$181$	−4.00034	−0.297343	−0.148671	−	0.988887i	$-0.547500\pi$
$181$	−4.00034	−0.297343	−0.148671	+	0.988887i	$0.547500\pi$
$182$	−4.44992	−0.329850
$183$	−7.06494	−0.522256
$184$	102.837	7.58125
$185$	−14.8050	−1.08849
$186$	8.36161	0.613103
$187$	30.4064	2.22354
$188$	−64.2553	−4.68630
$189$	−9.18228	−0.667913
$190$	−41.5014	−3.01083
$191$	6.32160	0.457415	0.228707	−	0.973495i	$-0.426550\pi$
$191$	6.32160	0.457415	0.228707	+	0.973495i	$0.426550\pi$
$192$	−39.8254	−2.87415
$193$	−9.80873	−0.706048	−0.353024	−	0.935614i	$-0.614847\pi$
$193$	−9.80873	−0.706048	−0.353024	+	0.935614i	$0.614847\pi$
$194$	−6.01084	−0.431553
$195$	−2.02663	−0.145130
$196$	−13.9528	−0.996625
$197$	19.2164	1.36911	0.684554	−	0.728962i	$-0.259997\pi$
$197$	19.2164	1.36911	0.684554	+	0.728962i	$0.259997\pi$
$198$	−31.5078	−2.23916
$199$	−11.7335	−0.831769	−0.415884	−	0.909418i	$-0.636528\pi$
$199$	−11.7335	−0.831769	−0.415884	+	0.909418i	$0.636528\pi$
$200$	−76.5797	−5.41501
$201$	2.36503	0.166816
$202$	1.81397	0.127630
$203$	−22.0563	−1.54805
$204$	30.0660	2.10504
$205$	27.9774	1.95403
$206$	−0.817478	−0.0569564
$207$	22.2763	1.54831
$208$	−13.9334	−0.966106
$209$	20.1921	1.39671
$210$	16.6481	1.14883
$211$	6.49384	0.447055	0.223527	−	0.974698i	$-0.428243\pi$
$211$	6.49384	0.447055	0.223527	+	0.974698i	$0.428243\pi$
$212$	47.8618	3.28716
$213$	−4.78592	−0.327926
$214$	−0.137738	−0.00941556
$215$	−14.3690	−0.979960
$216$	−46.6476	−3.17397
$217$	−8.06026	−0.547166
$218$	34.8461	2.36007
$219$	3.72966	0.252027
$220$	96.6718	6.51761
$221$	4.72575	0.317888
$222$	9.54031	0.640304
$223$	−5.06524	−0.339194	−0.169597	−	0.985514i	$-0.554247\pi$
$223$	−5.06524	−0.339194	−0.169597	+	0.985514i	$0.554247\pi$
$224$	67.3964	4.50311
$225$	−16.5885	−1.10590
$226$	−40.3859	−2.68643
$227$	−9.39863	−0.623809	−0.311905	−	0.950113i	$-0.600967\pi$
$227$	−9.39863	−0.623809	−0.311905	+	0.950113i	$0.600967\pi$
$228$	19.9660	1.32228
$229$	−2.72319	−0.179954	−0.0899768	−	0.995944i	$-0.528679\pi$
$229$	−2.72319	−0.179954	−0.0899768	+	0.995944i	$0.528679\pi$
$230$	−91.5482	−6.03651
$231$	−8.09996	−0.532938
$232$	−112.050	−7.35645
$233$	2.47793	0.162335	0.0811674	−	0.996700i	$-0.474135\pi$
$233$	2.47793	0.162335	0.0811674	+	0.996700i	$0.474135\pi$
$234$	−4.89693	−0.320123
$235$	37.7847	2.46480
$236$	79.5324	5.17712
$237$	11.4596	0.744384
$238$	−38.8205	−2.51636
$239$	−3.63333	−0.235020	−0.117510	−	0.993072i	$-0.537491\pi$
$239$	−3.63333	−0.235020	−0.117510	+	0.993072i	$0.537491\pi$
$240$	52.1278	3.36483
$241$	0.633694	0.0408198	0.0204099	−	0.999792i	$-0.493503\pi$
$241$	0.633694	0.0408198	0.0204099	+	0.999792i	$0.493503\pi$
$242$	−32.0985	−2.06337
$243$	−15.7515	−1.01046
$244$	52.3768	3.35308
$245$	8.20479	0.524185
$246$	−18.0286	−1.14946
$247$	3.13824	0.199681
$248$	−40.9476	−2.60017
$249$	−5.71079	−0.361907
$250$	19.5070	1.23373
$251$	24.9325	1.57373	0.786864	−	0.617126i	$-0.211703\pi$
$251$	24.9325	1.57373	0.786864	+	0.617126i	$0.211703\pi$
$252$	30.0323	1.89186
$253$	44.5418	2.80032
$254$	36.8694	2.31339
$255$	−17.6801	−1.10717
$256$	119.304	7.45650
$257$	6.90842	0.430935	0.215468	−	0.976511i	$-0.430872\pi$
$257$	6.90842	0.430935	0.215468	+	0.976511i	$0.430872\pi$
$258$	9.25937	0.576463
$259$	−9.19648	−0.571442
$260$	15.0247	0.931791
$261$	−24.2720	−1.50240
$262$	−5.18284	−0.320197
$263$	15.4808	0.954588	0.477294	−	0.878744i	$-0.341618\pi$
$263$	15.4808	0.954588	0.477294	+	0.878744i	$0.341618\pi$
$264$	−41.1492	−2.53256
$265$	−28.1447	−1.72892
$266$	−25.7796	−1.58065
$267$	−12.2655	−0.750638
$268$	−17.5334	−1.07102
$269$	20.4582	1.24736	0.623680	−	0.781679i	$-0.285637\pi$
$269$	20.4582	1.24736	0.623680	+	0.781679i	$0.285637\pi$
$270$	41.5269	2.52724
$271$	9.15221	0.555957	0.277979	−	0.960587i	$-0.410336\pi$
$271$	9.15221	0.555957	0.277979	+	0.960587i	$0.410336\pi$
$272$	−121.553	−7.37022
$273$	−1.25889	−0.0761916
$274$	−12.5812	−0.760056
$275$	−33.1689	−2.00016
$276$	44.0432	2.65109
$277$	3.07343	0.184664	0.0923321	−	0.995728i	$-0.470568\pi$
$277$	3.07343	0.184664	0.0923321	+	0.995728i	$0.470568\pi$
$278$	34.6056	2.07551
$279$	−8.86995	−0.531030
$280$	−81.5273	−4.87219
$281$	−0.394064	−0.0235079	−0.0117539	−	0.999931i	$-0.503741\pi$
$281$	−0.394064	−0.0235079	−0.0117539	+	0.999931i	$0.503741\pi$
$282$	−24.3484	−1.44993
$283$	−0.102619	−0.00610008	−0.00305004	−	0.999995i	$-0.500971\pi$
$283$	−0.102619	−0.00610008	−0.00305004	+	0.999995i	$0.500971\pi$
$284$	35.4810	2.10541
$285$	−11.7408	−0.695467
$286$	−9.79148	−0.578982
$287$	17.3788	1.02584
$288$	74.1667	4.37031
$289$	24.2268	1.42511
$290$	99.7498	5.85751
$291$	−1.70048	−0.0996839
$292$	−27.6503	−1.61811
$293$	−25.6564	−1.49886	−0.749431	−	0.662082i	$-0.769673\pi$
$293$	−25.6564	−1.49886	−0.749431	+	0.662082i	$0.769673\pi$
$294$	−5.28715	−0.308353
$295$	−46.7683	−2.72296
$296$	−46.7197	−2.71553
$297$	−20.2044	−1.17238
$298$	10.1500	0.587977
$299$	6.92266	0.400348
$300$	−32.7976	−1.89357
$301$	−8.92567	−0.514467
$302$	19.6790	1.13240
$303$	0.513175	0.0294811
$304$	−80.7198	−4.62960
$305$	−30.7997	−1.76358
$306$	−42.7202	−2.44215
$307$	10.4003	0.593577	0.296788	−	0.954943i	$-0.404084\pi$
$307$	10.4003	0.593577	0.296788	+	0.954943i	$0.404084\pi$
$308$	60.0500	3.42167
$309$	−0.231266	−0.0131563
$310$	36.4525	2.07036
$311$	9.91559	0.562262	0.281131	−	0.959669i	$-0.409291\pi$
$311$	9.91559	0.562262	0.281131	+	0.959669i	$0.409291\pi$
$312$	−6.39539	−0.362068
$313$	14.0907	0.796452	0.398226	−	0.917287i	$-0.369626\pi$
$313$	14.0907	0.796452	0.398226	+	0.917287i	$0.369626\pi$
$314$	35.3454	1.99466
$315$	−17.6602	−0.995041
$316$	−84.9574	−4.77923
$317$	7.13005	0.400464	0.200232	−	0.979749i	$-0.435830\pi$
$317$	7.13005	0.400464	0.200232	+	0.979749i	$0.435830\pi$
$318$	18.1364	1.01704
$319$	−48.5322	−2.71728
$320$	−173.619	−9.70560
$321$	−0.0389663	−0.00217489
$322$	−56.8674	−3.16909
$323$	27.3776	1.52333
$324$	21.8848	1.21582
$325$	−5.15510	−0.285953
$326$	32.5346	1.80192
$327$	9.85803	0.545150
$328$	88.2876	4.87486
$329$	23.4709	1.29399
$330$	36.6321	2.01653
$331$	−4.22791	−0.232387	−0.116193	−	0.993227i	$-0.537069\pi$
$331$	−4.22791	−0.232387	−0.116193	+	0.993227i	$0.537069\pi$
$332$	42.3376	2.32358
$333$	−10.1203	−0.554589
$334$	17.9359	0.981407
$335$	10.3104	0.563315
$336$	32.3804	1.76650
$337$	28.8218	1.57003	0.785013	−	0.619479i	$-0.212656\pi$
$337$	28.8218	1.57003	0.785013	+	0.619479i	$0.212656\pi$
$338$	34.9986	1.90367
$339$	−11.4253	−0.620535
$340$	131.073	7.10844
$341$	−17.7356	−0.960436
$342$	−28.3693	−1.53403
$343$	20.1619	1.08864
$344$	−45.3440	−2.44478
$345$	−25.8992	−1.39437
$346$	−0.0816123	−0.00438751
$347$	26.5600	1.42581	0.712907	−	0.701259i	$-0.247378\pi$
$347$	26.5600	1.42581	0.712907	+	0.701259i	$0.247378\pi$
$348$	−47.9889	−2.57248
$349$	27.6787	1.48161	0.740804	−	0.671722i	$-0.234445\pi$
$349$	27.6787	1.48161	0.740804	+	0.671722i	$0.234445\pi$
$350$	42.3474	2.26357
$351$	−3.14016	−0.167610
$352$	148.297	7.90427
$353$	−15.9120	−0.846910	−0.423455	−	0.905917i	$-0.639183\pi$
$353$	−15.9120	−0.846910	−0.423455	+	0.905917i	$0.639183\pi$
$354$	30.1374	1.60179
$355$	−20.8643	−1.10736
$356$	90.9319	4.81938
$357$	−10.9824	−0.581250
$358$	37.5925	1.98683
$359$	−15.5633	−0.821397	−0.410699	−	0.911771i	$-0.634715\pi$
$359$	−15.5633	−0.821397	−0.410699	+	0.911771i	$0.634715\pi$
$360$	−89.7171	−4.72850
$361$	−0.819319	−0.0431220
$362$	11.2380	0.590656
$363$	−9.08073	−0.476615
$364$	9.33294	0.489179
$365$	16.2595	0.851062
$366$	19.8473	1.03743
$367$	16.2807	0.849846	0.424923	−	0.905230i	$-0.360301\pi$
$367$	16.2807	0.849846	0.424923	+	0.905230i	$0.360301\pi$
$368$	−178.060	−9.28204
$369$	19.1246	0.995588
$370$	41.5911	2.16222
$371$	−17.4828	−0.907660
$372$	−17.5370	−0.909253
$373$	−7.47105	−0.386837	−0.193418	−	0.981116i	$-0.561957\pi$
$373$	−7.47105	−0.386837	−0.193418	+	0.981116i	$0.561957\pi$
$374$	−85.4195	−4.41694
$375$	5.51856	0.284977
$376$	119.236	6.14914
$377$	−7.54285	−0.388477
$378$	25.7954	1.32677
$379$	6.72920	0.345656	0.172828	−	0.984952i	$-0.444710\pi$
$379$	6.72920	0.345656	0.172828	+	0.984952i	$0.444710\pi$
$380$	87.0421	4.46516
$381$	10.4304	0.534367
$382$	−17.7590	−0.908630
$383$	18.1954	0.929744	0.464872	−	0.885378i	$-0.346100\pi$
$383$	18.1954	0.929744	0.464872	+	0.885378i	$0.346100\pi$
$384$	62.1043	3.16925
$385$	−35.3119	−1.79966
$386$	27.5553	1.40253
$387$	−9.82229	−0.499295
$388$	12.6067	0.640009
$389$	−23.2591	−1.17928	−0.589642	−	0.807665i	$-0.700731\pi$
$389$	−23.2591	−1.17928	−0.589642	+	0.807665i	$0.700731\pi$
$390$	5.69334	0.288293
$391$	60.3923	3.05417
$392$	25.8916	1.30773
$393$	−1.46624	−0.0739618
$394$	−53.9837	−2.71966
$395$	49.9584	2.51368
$396$	66.0823	3.32076
$397$	10.2150	0.512676	0.256338	−	0.966587i	$-0.417484\pi$
$397$	10.2150	0.512676	0.256338	+	0.966587i	$0.417484\pi$
$398$	32.9626	1.65226
$399$	−7.29310	−0.365112
$400$	132.596	6.62981
$401$	−35.3820	−1.76689	−0.883446	−	0.468533i	$-0.844783\pi$
$401$	−35.3820	−1.76689	−0.883446	+	0.468533i	$0.844783\pi$
$402$	−6.64397	−0.331371
$403$	−2.75646	−0.137309
$404$	−3.80448	−0.189280
$405$	−12.8691	−0.639473
$406$	61.9620	3.07512
$407$	−20.2357	−1.00305
$408$	−55.7925	−2.76214
$409$	24.4546	1.20920	0.604600	−	0.796529i	$-0.293333\pi$
$409$	24.4546	1.20920	0.604600	+	0.796529i	$0.293333\pi$
$410$	−78.5958	−3.88157
$411$	−3.55924	−0.175564
$412$	1.71452	0.0844683
$413$	−29.0513	−1.42952
$414$	−62.5799	−3.07564
$415$	−24.8962	−1.22211
$416$	23.0483	1.13003
$417$	9.79001	0.479419
$418$	−56.7247	−2.77450
$419$	16.7350	0.817556	0.408778	−	0.912634i	$-0.365955\pi$
$419$	16.7350	0.817556	0.408778	+	0.912634i	$0.365955\pi$
$420$	−34.9166	−1.70375
$421$	31.8064	1.55015	0.775074	−	0.631871i	$-0.217713\pi$
$421$	31.8064	1.55015	0.775074	+	0.631871i	$0.217713\pi$
$422$	−18.2429	−0.888050
$423$	25.8286	1.25583
$424$	−88.8156	−4.31326
$425$	−44.9724	−2.18148
$426$	13.4449	0.651407
$427$	−19.1320	−0.925861
$428$	0.288881	0.0139636
$429$	−2.77003	−0.133738
$430$	40.3663	1.94664
$431$	1.53692	0.0740310	0.0370155	−	0.999315i	$-0.488215\pi$
$431$	1.53692	0.0740310	0.0370155	+	0.999315i	$0.488215\pi$
$432$	80.7694	3.88602
$433$	12.8863	0.619277	0.309639	−	0.950854i	$-0.399792\pi$
$433$	12.8863	0.619277	0.309639	+	0.950854i	$0.399792\pi$
$434$	22.6434	1.08692
$435$	28.2194	1.35302
$436$	−73.0837	−3.50007
$437$	40.1049	1.91848
$438$	−10.4776	−0.500639
$439$	1.76583	0.0842784	0.0421392	−	0.999112i	$-0.486583\pi$
$439$	1.76583	0.0842784	0.0421392	+	0.999112i	$0.486583\pi$
$440$	−179.390	−8.55210
$441$	5.60858	0.267075
$442$	−13.2759	−0.631468
$443$	−30.3239	−1.44073	−0.720366	−	0.693594i	$-0.756026\pi$
$443$	−30.3239	−1.44073	−0.720366	+	0.693594i	$0.756026\pi$
$444$	−20.0092	−0.949593
$445$	−53.4717	−2.53480
$446$	14.2296	0.673790
$447$	2.87147	0.135816
$448$	−107.848	−5.09532
$449$	−10.4640	−0.493828	−0.246914	−	0.969037i	$-0.579416\pi$
$449$	−10.4640	−0.493828	−0.246914	+	0.969037i	$0.579416\pi$
$450$	46.6014	2.19681
$451$	38.2399	1.80065
$452$	84.7025	3.98407
$453$	5.56722	0.261571
$454$	26.4032	1.23916
$455$	−5.48815	−0.257289
$456$	−37.0503	−1.73504
$457$	−10.1516	−0.474874	−0.237437	−	0.971403i	$-0.576307\pi$
$457$	−10.1516	−0.474874	−0.237437	+	0.971403i	$0.576307\pi$
$458$	7.65015	0.357468
$459$	−27.3944	−1.27866
$460$	192.007	8.95235
$461$	22.5546	1.05047	0.525235	−	0.850957i	$-0.323977\pi$
$461$	22.5546	1.05047	0.525235	+	0.850957i	$0.323977\pi$
$462$	22.7549	1.05865
$463$	−16.7925	−0.780412	−0.390206	−	0.920728i	$-0.627596\pi$
$463$	−16.7925	−0.780412	−0.390206	+	0.920728i	$0.627596\pi$
$464$	194.012	9.00680
$465$	10.3125	0.478231
$466$	−6.96115	−0.322469
$467$	−5.06286	−0.234281	−0.117141	−	0.993115i	$-0.537373\pi$
$467$	−5.06286	−0.234281	−0.117141	+	0.993115i	$0.537373\pi$
$468$	10.2705	0.474753
$469$	6.40452	0.295733
$470$	−106.147	−4.89620
$471$	9.99929	0.460743
$472$	−147.586	−6.79318
$473$	−19.6398	−0.903039
$474$	−32.1931	−1.47868
$475$	−29.8649	−1.37030
$476$	81.4193	3.73185
$477$	−19.2390	−0.880893
$478$	10.2070	0.466856
$479$	4.93634	0.225547	0.112774	−	0.993621i	$-0.464027\pi$
$479$	4.93634	0.225547	0.112774	+	0.993621i	$0.464027\pi$
$480$	−86.2286	−3.93578
$481$	−3.14502	−0.143401
$482$	−1.78021	−0.0810864
$483$	−16.0879	−0.732025
$484$	67.3211	3.06005
$485$	−7.41326	−0.336619
$486$	44.2499	2.00722
$487$	−22.1159	−1.00217	−0.501084	−	0.865398i	$-0.667065\pi$
$487$	−22.1159	−1.00217	−0.501084	+	0.865398i	$0.667065\pi$
$488$	−97.1938	−4.39975
$489$	9.20410	0.416224
$490$	−23.0494	−1.04127
$491$	−33.7938	−1.52509	−0.762546	−	0.646934i	$-0.776051\pi$
$491$	−33.7938	−1.52509	−0.762546	+	0.646934i	$0.776051\pi$
$492$	37.8119	1.70469
$493$	−65.8028	−2.96361
$494$	−8.81613	−0.396656
$495$	−38.8591	−1.74659
$496$	70.8998	3.18350
$497$	−12.9603	−0.581351
$498$	16.0431	0.718908
$499$	9.08577	0.406735	0.203367	−	0.979102i	$-0.434811\pi$
$499$	9.08577	0.406735	0.203367	+	0.979102i	$0.434811\pi$
$500$	−40.9125	−1.82966
$501$	5.07410	0.226694
$502$	−70.0420	−3.12613
$503$	−14.0207	−0.625154	−0.312577	−	0.949892i	$-0.601192\pi$
$503$	−14.0207	−0.625154	−0.312577	+	0.949892i	$0.601192\pi$
$504$	−55.7299	−2.48241
$505$	2.23719	0.0995537
$506$	−125.129	−5.56268
$507$	9.90118	0.439727
$508$	−77.3272	−3.43084
$509$	−25.4260	−1.12699	−0.563493	−	0.826121i	$-0.690543\pi$
$509$	−25.4260	−1.12699	−0.563493	+	0.826121i	$0.690543\pi$
$510$	49.6679	2.19933
$511$	10.1000	0.446797
$512$	−178.869	−7.90496
$513$	−18.1918	−0.803189
$514$	−19.4075	−0.856030
$515$	−1.00821	−0.0444269
$516$	−19.4199	−0.854915
$517$	51.6447	2.27133
$518$	25.8353	1.13514
$519$	−0.0230883	−0.00101346
$520$	−27.8808	−1.22265
$521$	20.4205	0.894639	0.447319	−	0.894374i	$-0.352379\pi$
$521$	20.4205	0.894639	0.447319	+	0.894374i	$0.352379\pi$
$522$	68.1864	2.98444
$523$	−29.9321	−1.30884	−0.654420	−	0.756131i	$-0.727087\pi$
$523$	−29.9321	−1.30884	−0.654420	+	0.756131i	$0.727087\pi$
$524$	10.8701	0.474863
$525$	11.9802	0.522858
$526$	−43.4896	−1.89624
$527$	−24.0469	−1.04750
$528$	71.2490	3.10072
$529$	65.4675	2.84642
$530$	79.0658	3.43440
$531$	−31.9696	−1.38736
$532$	54.0683	2.34416
$533$	5.94323	0.257430
$534$	34.4571	1.49110
$535$	−0.169874	−0.00734430
$536$	32.5361	1.40535
$537$	10.6350	0.458935
$538$	−57.4725	−2.47782
$539$	11.2144	0.483040
$540$	−87.0955	−3.74799
$541$	7.26347	0.312281	0.156140	−	0.987735i	$-0.450095\pi$
$541$	7.26347	0.312281	0.156140	+	0.987735i	$0.450095\pi$
$542$	−25.7109	−1.10438
$543$	3.17925	0.136435
$544$	201.070	8.62081
$545$	42.9762	1.84090
$546$	3.53655	0.151351
$547$	10.0687	0.430507	0.215254	−	0.976558i	$-0.430942\pi$
$547$	10.0687	0.430507	0.215254	+	0.976558i	$0.430942\pi$
$548$	26.3868	1.12719
$549$	−21.0539	−0.898557
$550$	93.1801	3.97321
$551$	−43.6978	−1.86159
$552$	−81.7294	−3.47863
$553$	31.0329	1.31965
$554$	−8.63405	−0.366826
$555$	11.7662	0.499448
$556$	−72.5794	−3.07805
$557$	−20.9175	−0.886304	−0.443152	−	0.896446i	$-0.646140\pi$
$557$	−20.9175	−0.886304	−0.443152	+	0.896446i	$0.646140\pi$
$558$	24.9180	1.05486
$559$	−3.05241	−0.129103
$560$	141.163	5.96522
$561$	−24.1654	−1.02026
$562$	1.10703	0.0466971
$563$	28.5577	1.20356	0.601781	−	0.798661i	$-0.294458\pi$
$563$	28.5577	1.20356	0.601781	+	0.798661i	$0.294458\pi$
$564$	51.0666	2.15029
$565$	−49.8085	−2.09546
$566$	0.288284	0.0121175
$567$	−7.99398	−0.335716
$568$	−65.8408	−2.76262
$569$	−4.51678	−0.189353	−0.0946767	−	0.995508i	$-0.530182\pi$
$569$	−4.51678	−0.189353	−0.0946767	+	0.995508i	$0.530182\pi$
$570$	32.9831	1.38151
$571$	39.0013	1.63216	0.816078	−	0.577942i	$-0.196144\pi$
$571$	39.0013	1.63216	0.816078	+	0.577942i	$0.196144\pi$
$572$	20.5360	0.858651
$573$	−5.02406	−0.209883
$574$	−48.8217	−2.03778
$575$	−65.8791	−2.74735
$576$	−118.681	−4.94506
$577$	0.485567	0.0202144	0.0101072	−	0.999949i	$-0.496783\pi$
$577$	0.485567	0.0202144	0.0101072	+	0.999949i	$0.496783\pi$
$578$	−68.0594	−2.83090
$579$	7.79544	0.323968
$580$	−209.208	−8.68689
$581$	−15.4649	−0.641592
$582$	4.77709	0.198017
$583$	−38.4686	−1.59321
$584$	51.3097	2.12321
$585$	−6.03946	−0.249701
$586$	72.0755	2.97741
$587$	11.9687	0.494003	0.247001	−	0.969015i	$-0.420555\pi$
$587$	11.9687	0.494003	0.247001	+	0.969015i	$0.420555\pi$
$588$	11.0889	0.457298
$589$	−15.9689	−0.657987
$590$	131.384	5.40901
$591$	−15.2721	−0.628211
$592$	80.8943	3.32473
$593$	−27.8390	−1.14321	−0.571606	−	0.820528i	$-0.693679\pi$
$593$	−27.8390	−1.14321	−0.571606	+	0.820528i	$0.693679\pi$
$594$	56.7595	2.32887
$595$	−47.8779	−1.96280
$596$	−21.2880	−0.871990
$597$	9.32518	0.381654
$598$	−19.4476	−0.795270
$599$	13.9345	0.569347	0.284673	−	0.958625i	$-0.408115\pi$
$599$	13.9345	0.569347	0.284673	+	0.958625i	$0.408115\pi$
$600$	60.8614	2.48466
$601$	−20.1910	−0.823610	−0.411805	−	0.911272i	$-0.635101\pi$
$601$	−20.1910	−0.823610	−0.411805	+	0.911272i	$0.635101\pi$
$602$	25.0745	1.02196
$603$	7.04789	0.287012
$604$	−41.2733	−1.67939
$605$	−39.5875	−1.60946
$606$	−1.44164	−0.0585627
$607$	8.87524	0.360235	0.180117	−	0.983645i	$-0.442352\pi$
$607$	8.87524	0.360235	0.180117	+	0.983645i	$0.442352\pi$
$608$	133.525	5.41515
$609$	17.5292	0.710319
$610$	86.5243	3.50327
$611$	8.02660	0.324721
$612$	89.5982	3.62179
$613$	−9.52365	−0.384656	−0.192328	−	0.981331i	$-0.561604\pi$
$613$	−9.52365	−0.384656	−0.192328	+	0.981331i	$0.561604\pi$
$614$	−29.2172	−1.17911
$615$	−22.2349	−0.896599
$616$	−111.433	−4.48975
$617$	−23.0682	−0.928692	−0.464346	−	0.885654i	$-0.653711\pi$
$617$	−23.0682	−0.928692	−0.464346	+	0.885654i	$0.653711\pi$
$618$	0.649687	0.0261342
$619$	21.8610	0.878666	0.439333	−	0.898324i	$-0.355215\pi$
$619$	21.8610	0.878666	0.439333	+	0.898324i	$0.355215\pi$
$620$	−76.4529	−3.07042
$621$	−40.1295	−1.61034
$622$	−27.8555	−1.11690
$623$	−33.2152	−1.33074
$624$	11.0735	0.443294
$625$	−10.9626	−0.438502
$626$	−39.5844	−1.58211
$627$	−16.0476	−0.640877
$628$	−74.1309	−2.95814
$629$	−27.4367	−1.09397
$630$	49.6122	1.97660
$631$	−24.9412	−0.992893	−0.496446	−	0.868067i	$-0.665362\pi$
$631$	−24.9412	−0.992893	−0.496446	+	0.868067i	$0.665362\pi$
$632$	157.652	6.27108
$633$	−5.16095	−0.205129
$634$	−20.0302	−0.795500
$635$	45.4715	1.80448
$636$	−38.0380	−1.50830
$637$	1.74294	0.0690578
$638$	136.340	5.39773
$639$	−14.2623	−0.564206
$640$	270.744	10.7021
$641$	6.65919	0.263022	0.131511	−	0.991315i	$-0.458017\pi$
$641$	6.65919	0.263022	0.131511	+	0.991315i	$0.458017\pi$
$642$	0.109467	0.00432030
$643$	−0.329872	−0.0130089	−0.00650445	−	0.999979i	$-0.502070\pi$
$643$	−0.329872	−0.0130089	−0.00650445	+	0.999979i	$0.502070\pi$
$644$	119.270	4.69988
$645$	11.4197	0.449651
$646$	−76.9107	−3.02601
$647$	13.4437	0.528528	0.264264	−	0.964450i	$-0.414871\pi$
$647$	13.4437	0.528528	0.264264	+	0.964450i	$0.414871\pi$
$648$	−40.6108	−1.59534
$649$	−63.9236	−2.50922
$650$	14.4820	0.568031
$651$	6.40586	0.251065
$652$	−68.2357	−2.67232
$653$	26.6016	1.04100	0.520501	−	0.853861i	$-0.325745\pi$
$653$	26.6016	1.04100	0.520501	+	0.853861i	$0.325745\pi$
$654$	−27.6938	−1.08291
$655$	−6.39207	−0.249759
$656$	−152.868	−5.96849
$657$	11.1146	0.433621
$658$	−65.9358	−2.57045
$659$	20.6342	0.803793	0.401896	−	0.915685i	$-0.368351\pi$
$659$	20.6342	0.803793	0.401896	+	0.915685i	$0.368351\pi$
$660$	−76.8295	−2.99058
$661$	1.59400	0.0619996	0.0309998	−	0.999519i	$-0.490131\pi$
$661$	1.59400	0.0619996	0.0309998	+	0.999519i	$0.490131\pi$
$662$	11.8773	0.461624
$663$	−3.75577	−0.145862
$664$	−78.5644	−3.04889
$665$	−31.7944	−1.23293
$666$	28.4306	1.10166
$667$	−96.3932	−3.73236
$668$	−37.6174	−1.45546
$669$	4.02558	0.155638
$670$	−28.9645	−1.11899
$671$	−42.0975	−1.62515
$672$	−53.5630	−2.06624
$673$	26.7645	1.03170	0.515848	−	0.856680i	$-0.327477\pi$
$673$	26.7645	1.03170	0.515848	+	0.856680i	$0.327477\pi$
$674$	−80.9680	−3.11877
$675$	29.8832	1.15021
$676$	−73.4035	−2.82321
$677$	−21.5194	−0.827057	−0.413528	−	0.910491i	$-0.635704\pi$
$677$	−21.5194	−0.827057	−0.413528	+	0.910491i	$0.635704\pi$
$678$	32.0965	1.23266
$679$	−4.60493	−0.176721
$680$	−243.228	−9.32737
$681$	7.46952	0.286233
$682$	49.8239	1.90785
$683$	−25.2383	−0.965717	−0.482859	−	0.875698i	$-0.660402\pi$
$683$	−25.2383	−0.965717	−0.482859	+	0.875698i	$0.660402\pi$
$684$	59.4997	2.27503
$685$	−15.5165	−0.592856
$686$	−56.6400	−2.16252
$687$	2.16424	0.0825711
$688$	78.5121	2.99325
$689$	−5.97877	−0.227773
$690$	72.7575	2.76983
$691$	26.6220	1.01275	0.506375	−	0.862314i	$-0.330985\pi$
$691$	26.6220	1.01275	0.506375	+	0.862314i	$0.330985\pi$
$692$	0.171168	0.00650682
$693$	−24.1383	−0.916937
$694$	−74.6138	−2.83230
$695$	42.6796	1.61893
$696$	89.0514	3.37548
$697$	51.8479	1.96388
$698$	−77.7567	−2.94313
$699$	−1.96933	−0.0744867
$700$	−88.8165	−3.35695
$701$	27.7483	1.04804	0.524020	−	0.851706i	$-0.324432\pi$
$701$	27.7483	1.04804	0.524020	+	0.851706i	$0.324432\pi$
$702$	8.82154	0.332947
$703$	−18.2200	−0.687179
$704$	−237.305	−8.94377
$705$	−30.0293	−1.13097
$706$	44.7009	1.68234
$707$	1.38968	0.0522645
$708$	−63.2081	−2.37550
$709$	10.8575	0.407763	0.203882	−	0.978996i	$-0.434644\pi$
$709$	10.8575	0.407763	0.203882	+	0.978996i	$0.434644\pi$
$710$	58.6131	2.19971
$711$	34.1503	1.28074
$712$	−168.739	−6.32377
$713$	−35.2259	−1.31922
$714$	30.8524	1.15462
$715$	−12.0760	−0.451616
$716$	−78.8439	−2.94653
$717$	2.88757	0.107838
$718$	43.7212	1.63166
$719$	−13.8564	−0.516757	−0.258378	−	0.966044i	$-0.583188\pi$
$719$	−13.8564	−0.516757	−0.258378	+	0.966044i	$0.583188\pi$
$720$	155.343	5.78930
$721$	−0.626272	−0.0233236
$722$	2.30168	0.0856596
$723$	−0.503626	−0.0187300
$724$	−23.5698	−0.875963
$725$	71.7811	2.66588
$726$	25.5101	0.946770
$727$	−24.0100	−0.890483	−0.445241	−	0.895411i	$-0.646882\pi$
$727$	−24.0100	−0.890483	−0.445241	+	0.895411i	$0.646882\pi$
$728$	−17.3188	−0.641878
$729$	1.37533	0.0509382
$730$	−45.6772	−1.69059
$731$	−26.6288	−0.984901
$732$	−41.6262	−1.53855
$733$	−28.6081	−1.05666	−0.528331	−	0.849038i	$-0.677182\pi$
$733$	−28.6081	−1.05666	−0.528331	+	0.849038i	$0.677182\pi$
$734$	−45.7367	−1.68817
$735$	−6.52072	−0.240520
$736$	294.543	10.8570
$737$	14.0923	0.519098
$738$	−53.7260	−1.97768
$739$	−3.03236	−0.111547	−0.0557737	−	0.998443i	$-0.517763\pi$
$739$	−3.03236	−0.111547	−0.0557737	+	0.998443i	$0.517763\pi$
$740$	−87.2302	−3.20664
$741$	−2.49410	−0.0916232
$742$	49.1136	1.80302
$743$	2.19820	0.0806441	0.0403220	−	0.999187i	$-0.487162\pi$
$743$	2.19820	0.0806441	0.0403220	+	0.999187i	$0.487162\pi$
$744$	32.5429	1.19308
$745$	12.5182	0.458632
$746$	20.9881	0.768430
$747$	−17.0184	−0.622671
$748$	179.153	6.55048
$749$	−0.105521	−0.00385567
$750$	−15.5031	−0.566092
$751$	37.4193	1.36545	0.682724	−	0.730676i	$-0.260795\pi$
$751$	37.4193	1.36545	0.682724	+	0.730676i	$0.260795\pi$
$752$	−206.455	−7.52864
$753$	−19.8150	−0.722100
$754$	21.1898	0.771688
$755$	24.2704	0.883289
$756$	−54.1014	−1.96765
$757$	−12.4272	−0.451675	−0.225837	−	0.974165i	$-0.572512\pi$
$757$	−12.4272	−0.451675	−0.225837	+	0.974165i	$0.572512\pi$
$758$	−18.9041	−0.686627
$759$	−35.3994	−1.28492
$760$	−161.521	−5.85898
$761$	−24.1741	−0.876310	−0.438155	−	0.898899i	$-0.644368\pi$
$761$	−24.1741	−0.876310	−0.438155	+	0.898899i	$0.644368\pi$
$762$	−29.3018	−1.06149
$763$	26.6957	0.966449
$764$	37.2465	1.34753
$765$	−52.6874	−1.90492
$766$	−51.1157	−1.84689
$767$	−9.93498	−0.358731
$768$	−94.8164	−3.42139
$769$	13.2561	0.478026	0.239013	−	0.971016i	$-0.423176\pi$
$769$	13.2561	0.478026	0.239013	+	0.971016i	$0.423176\pi$
$770$	99.2002	3.57493
$771$	−5.49044	−0.197733
$772$	−57.7924	−2.07999
$773$	−2.44127	−0.0878065	−0.0439032	−	0.999036i	$-0.513979\pi$
$773$	−2.44127	−0.0878065	−0.0439032	+	0.999036i	$0.513979\pi$
$774$	27.5934	0.991823
$775$	26.2317	0.942269
$776$	−23.3938	−0.839790
$777$	7.30886	0.262204
$778$	65.3409	2.34258
$779$	34.4308	1.23361
$780$	−11.9408	−0.427549
$781$	−28.5176	−1.02044
$782$	−169.658	−6.06695
$783$	43.7246	1.56259
$784$	−44.8308	−1.60110
$785$	43.5920	1.55586
$786$	4.11904	0.146921
$787$	10.0299	0.357526	0.178763	−	0.983892i	$-0.442791\pi$
$787$	10.0299	0.357526	0.178763	+	0.983892i	$0.442791\pi$
$788$	113.222	4.03335
$789$	−12.3033	−0.438009
$790$	−140.346	−4.99329
$791$	−30.9398	−1.10009
$792$	−122.627	−4.35735
$793$	−6.54277	−0.232340
$794$	−28.6966	−1.01840
$795$	22.3679	0.793307
$796$	−69.1333	−2.45037
$797$	44.2657	1.56797	0.783986	−	0.620778i	$-0.213183\pi$
$797$	44.2657	1.56797	0.783986	+	0.620778i	$0.213183\pi$
$798$	20.4882	0.725275
$799$	70.0229	2.47723
$800$	−219.338	−7.75476
$801$	−36.5519	−1.29150
$802$	99.3972	3.50984
$803$	22.2237	0.784259
$804$	13.9346	0.491435
$805$	−70.1354	−2.47195
$806$	7.74360	0.272757
$807$	−16.2591	−0.572347
$808$	7.05984	0.248364
$809$	25.8096	0.907416	0.453708	−	0.891150i	$-0.350101\pi$
$809$	25.8096	0.907416	0.453708	+	0.891150i	$0.350101\pi$
$810$	36.1528	1.27028
$811$	−7.25463	−0.254744	−0.127372	−	0.991855i	$-0.540654\pi$
$811$	−7.25463	−0.254744	−0.127372	+	0.991855i	$0.540654\pi$
$812$	−129.955	−4.56051
$813$	−7.27368	−0.255099
$814$	56.8473	1.99250
$815$	40.1254	1.40553
$816$	96.6036	3.38180
$817$	−17.6834	−0.618665
$818$	−68.6992	−2.40201
$819$	−3.75156	−0.131090
$820$	164.841	5.75650
$821$	−35.4311	−1.23655	−0.618277	−	0.785960i	$-0.712169\pi$
$821$	−35.4311	−1.23655	−0.618277	+	0.785960i	$0.712169\pi$
$822$	9.99883	0.348749
$823$	24.4948	0.853837	0.426918	−	0.904290i	$-0.359599\pi$
$823$	24.4948	0.853837	0.426918	+	0.904290i	$0.359599\pi$
$824$	−3.18157	−0.110835
$825$	26.3609	0.917767
$826$	81.6126	2.83966
$827$	8.93029	0.310537	0.155268	−	0.987872i	$-0.450376\pi$
$827$	8.93029	0.310537	0.155268	+	0.987872i	$0.450376\pi$
$828$	131.251	4.56128
$829$	5.08664	0.176666	0.0883332	−	0.996091i	$-0.471846\pi$
$829$	5.08664	0.176666	0.0883332	+	0.996091i	$0.471846\pi$
$830$	69.9400	2.42765
$831$	−2.44259	−0.0847326
$832$	−36.8818	−1.27865
$833$	15.2052	0.526828
$834$	−27.5027	−0.952340
$835$	22.1206	0.765514
$836$	118.970	4.11468
$837$	15.9787	0.552305
$838$	−47.0128	−1.62403
$839$	−17.5064	−0.604386	−0.302193	−	0.953247i	$-0.597719\pi$
$839$	−17.5064	−0.604386	−0.302193	+	0.953247i	$0.597719\pi$
$840$	64.7935	2.23559
$841$	76.0289	2.62169
$842$	−89.3524	−3.07929
$843$	0.313180	0.0107865
$844$	38.2613	1.31701
$845$	43.1643	1.48490
$846$	−72.5594	−2.49464
$847$	−24.5908	−0.844948
$848$	153.782	5.28091
$849$	0.0815562	0.00279900
$850$	126.339	4.33339
$851$	−40.1915	−1.37775
$852$	−28.1983	−0.966059
$853$	9.47388	0.324379	0.162190	−	0.986760i	$-0.448144\pi$
$853$	9.47388	0.324379	0.162190	+	0.986760i	$0.448144\pi$
$854$	53.7467	1.83917
$855$	−34.9882	−1.19657
$856$	−0.536067	−0.0183224
$857$	−44.8869	−1.53331	−0.766654	−	0.642061i	$-0.778080\pi$
$857$	−44.8869	−1.53331	−0.766654	+	0.642061i	$0.778080\pi$
$858$	7.78174	0.265664
$859$	19.6712	0.671174	0.335587	−	0.942009i	$-0.391065\pi$
$859$	19.6712	0.671174	0.335587	+	0.942009i	$0.391065\pi$
$860$	−84.6615	−2.88693
$861$	−13.8118	−0.470703
$862$	−4.31762	−0.147059
$863$	4.53546	0.154389	0.0771945	−	0.997016i	$-0.475404\pi$
$863$	4.53546	0.154389	0.0771945	+	0.997016i	$0.475404\pi$
$864$	−133.607	−4.54540
$865$	−0.100654	−0.00342233
$866$	−36.2010	−1.23016
$867$	−19.2542	−0.653905
$868$	−47.4906	−1.61194
$869$	68.2839	2.31637
$870$	−79.2757	−2.68770
$871$	2.19022	0.0742129
$872$	135.619	4.59263
$873$	−5.06751	−0.171509
$874$	−112.665	−3.81095
$875$	14.9443	0.505211
$876$	21.9750	0.742465
$877$	4.84972	0.163763	0.0818816	−	0.996642i	$-0.473907\pi$
$877$	4.84972	0.163763	0.0818816	+	0.996642i	$0.473907\pi$
$878$	−4.96067	−0.167415
$879$	20.3903	0.687748
$880$	310.611	10.4707
$881$	54.4822	1.83555	0.917775	−	0.397100i	$-0.129983\pi$
$881$	54.4822	1.83555	0.917775	+	0.397100i	$0.129983\pi$
$882$	−15.7560	−0.530531
$883$	−30.3765	−1.02225	−0.511125	−	0.859506i	$-0.670771\pi$
$883$	−30.3765	−1.02225	−0.511125	+	0.859506i	$0.670771\pi$
$884$	27.8438	0.936490
$885$	37.1689	1.24942
$886$	85.1878	2.86194
$887$	18.6367	0.625760	0.312880	−	0.949793i	$-0.398706\pi$
$887$	18.6367	0.625760	0.312880	+	0.949793i	$0.398706\pi$
$888$	37.1303	1.24601
$889$	28.2457	0.947332
$890$	150.216	5.03525
$891$	−17.5897	−0.589278
$892$	−29.8441	−0.999254
$893$	46.5003	1.55607
$894$	−8.06671	−0.269791
$895$	46.3634	1.54976
$896$	168.179	5.61848
$897$	−5.50175	−0.183698
$898$	29.3961	0.980962
$899$	38.3817	1.28010
$900$	−97.7385	−3.25795
$901$	−52.1580	−1.73763
$902$	−107.426	−3.57689
$903$	7.09364	0.236061
$904$	−157.180	−5.22771
$905$	13.8600	0.460722
$906$	−15.6398	−0.519597
$907$	20.8802	0.693316	0.346658	−	0.937992i	$-0.387316\pi$
$907$	20.8802	0.693316	0.346658	+	0.937992i	$0.387316\pi$
$908$	−55.3762	−1.83772
$909$	1.52928	0.0507232
$910$	15.4176	0.511090
$911$	−58.8633	−1.95023	−0.975115	−	0.221701i	$-0.928839\pi$
$911$	−58.8633	−1.95023	−0.975115	+	0.221701i	$0.928839\pi$
$912$	64.1517	2.12428
$913$	−34.0286	−1.12618
$914$	28.5186	0.943311
$915$	24.4779	0.809215
$916$	−16.0449	−0.530138
$917$	−3.97059	−0.131120
$918$	76.9579	2.53999
$919$	27.4991	0.907111	0.453555	−	0.891228i	$-0.350155\pi$
$919$	27.4991	0.907111	0.453555	+	0.891228i	$0.350155\pi$
$920$	−356.300	−11.7469
$921$	−8.26560	−0.272361
$922$	−63.3616	−2.08670
$923$	−4.43219	−0.145887
$924$	−47.7245	−1.57002
$925$	29.9294	0.984074
$926$	47.1744	1.55025
$927$	−0.689184	−0.0226358
$928$	−320.931	−10.5351
$929$	−20.6304	−0.676860	−0.338430	−	0.940992i	$-0.609896\pi$
$929$	−20.6304	−0.676860	−0.338430	+	0.940992i	$0.609896\pi$
$930$	−28.9705	−0.949980
$931$	10.0973	0.330927
$932$	14.5998	0.478233
$933$	−7.88037	−0.257992
$934$	14.2229	0.465387
$935$	−105.349	−3.44529
$936$	−19.0586	−0.622949
$937$	−13.0128	−0.425110	−0.212555	−	0.977149i	$-0.568179\pi$
$937$	−13.0128	−0.425110	−0.212555	+	0.977149i	$0.568179\pi$
$938$	−17.9920	−0.587459
$939$	−11.1985	−0.365450
$940$	222.625	7.26124
$941$	38.1004	1.24204	0.621020	−	0.783795i	$-0.286719\pi$
$941$	38.1004	1.24204	0.621020	+	0.783795i	$0.286719\pi$
$942$	−28.0906	−0.915241
$943$	75.9510	2.47330
$944$	255.541	8.31716
$945$	31.8139	1.03491
$946$	55.1733	1.79384
$947$	14.8313	0.481953	0.240977	−	0.970531i	$-0.422532\pi$
$947$	14.8313	0.481953	0.240977	+	0.970531i	$0.422532\pi$
$948$	67.5195	2.19293
$949$	3.45400	0.112122
$950$	83.8982	2.72202
$951$	−5.66658	−0.183751
$952$	−151.087	−4.89676
$953$	−18.1151	−0.586805	−0.293403	−	0.955989i	$-0.594788\pi$
$953$	−18.1151	−0.586805	−0.293403	+	0.955989i	$0.594788\pi$
$954$	54.0473	1.74985
$955$	−21.9024	−0.708747
$956$	−21.4073	−0.692363
$957$	38.5708	1.24682
$958$	−13.8675	−0.448037
$959$	−9.63847	−0.311242
$960$	137.983	4.45338
$961$	−16.9738	−0.547542
$962$	8.83518	0.284858
$963$	−0.116121	−0.00374196
$964$	3.73369	0.120254
$965$	33.9843	1.09399
$966$	45.1951	1.45413
$967$	28.9187	0.929964	0.464982	−	0.885320i	$-0.346061\pi$
$967$	28.9187	0.929964	0.464982	+	0.885320i	$0.346061\pi$
$968$	−124.925	−4.01525
$969$	−21.7582	−0.698974
$970$	20.8258	0.668675
$971$	26.9941	0.866281	0.433140	−	0.901326i	$-0.357405\pi$
$971$	26.9941	0.866281	0.433140	+	0.901326i	$0.357405\pi$
$972$	−92.8066	−2.97677
$973$	26.5115	0.849919
$974$	62.1294	1.99075
$975$	4.09699	0.131209
$976$	168.289	5.38680
$977$	−46.5876	−1.49047	−0.745235	−	0.666802i	$-0.767663\pi$
$977$	−46.5876	−1.49047	−0.745235	+	0.666802i	$0.767663\pi$
$978$	−25.8567	−0.826807
$979$	−73.0859	−2.33584
$980$	48.3421	1.54423
$981$	29.3774	0.937948
$982$	94.9355	3.02951
$983$	12.9574	0.413278	0.206639	−	0.978417i	$-0.433747\pi$
$983$	12.9574	0.413278	0.206639	+	0.978417i	$0.433747\pi$
$984$	−70.1662	−2.23682
$985$	−66.5789	−2.12138
$986$	184.857	5.88705
$987$	−18.6534	−0.593744
$988$	18.4903	0.588255
$989$	−39.0080	−1.24038
$990$	109.165	3.46950
$991$	16.6704	0.529554	0.264777	−	0.964310i	$-0.414702\pi$
$991$	16.6704	0.529554	0.264777	+	0.964310i	$0.414702\pi$
$992$	−117.281	−3.72367
$993$	3.36011	0.106630
$994$	36.4090	1.15482
$995$	40.6532	1.28879
$996$	−33.6476	−1.06617
$997$	3.78855	0.119985	0.0599923	−	0.998199i	$-0.480892\pi$
$997$	3.78855	0.119985	0.0599923	+	0.998199i	$0.480892\pi$
$998$	−25.5243	−0.807957
$999$	18.2311	0.576808

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6037.2.a.a.1.2	✓	243

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6037.2.a.a.1.2	✓	243	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:	\( N \)	\(=\)	\( 6037 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6037.a (trivial)

\(f(q)\)	\(=\)	\(q-2.80926 q^{2} -0.794746 q^{3} +5.89194 q^{4} -3.46470 q^{5} +2.23265 q^{6} -2.15218 q^{7} -10.9335 q^{8} -2.36838 q^{9} +O(q^{10})\)	\(q-2.80926 q^{2} -0.794746 q^{3} +5.89194 q^{4} -3.46470 q^{5} +2.23265 q^{6} -2.15218 q^{7} -10.9335 q^{8} -2.36838 q^{9} +9.73325 q^{10} -4.73561 q^{11} -4.68259 q^{12} -0.736005 q^{13} +6.04604 q^{14} +2.75356 q^{15} +18.9311 q^{16} -6.42081 q^{17} +6.65339 q^{18} -4.26388 q^{19} -20.4138 q^{20} +1.71044 q^{21} +13.3035 q^{22} -9.40572 q^{23} +8.68933 q^{24} +7.00416 q^{25} +2.06763 q^{26} +4.26650 q^{27} -12.6805 q^{28} +10.2484 q^{29} -7.73546 q^{30} +3.74516 q^{31} -31.3154 q^{32} +3.76360 q^{33} +18.0377 q^{34} +7.45667 q^{35} -13.9543 q^{36} +4.27309 q^{37} +11.9783 q^{38} +0.584937 q^{39} +37.8812 q^{40} -8.07498 q^{41} -4.80506 q^{42} +4.14726 q^{43} -27.9019 q^{44} +8.20573 q^{45} +26.4231 q^{46} -10.9056 q^{47} -15.0454 q^{48} -2.36811 q^{49} -19.6765 q^{50} +5.10291 q^{51} -4.33650 q^{52} +8.12327 q^{53} -11.9857 q^{54} +16.4075 q^{55} +23.5308 q^{56} +3.38870 q^{57} -28.7903 q^{58} +13.4985 q^{59} +16.2238 q^{60} +8.88956 q^{61} -10.5211 q^{62} +5.09719 q^{63} +50.1108 q^{64} +2.55004 q^{65} -10.5729 q^{66} -2.97583 q^{67} -37.8310 q^{68} +7.47515 q^{69} -20.9477 q^{70} +6.02195 q^{71} +25.8946 q^{72} -4.69290 q^{73} -12.0042 q^{74} -5.56652 q^{75} -25.1225 q^{76} +10.1919 q^{77} -1.64324 q^{78} -14.4193 q^{79} -65.5905 q^{80} +3.71436 q^{81} +22.6847 q^{82} +7.18568 q^{83} +10.0778 q^{84} +22.2462 q^{85} -11.6507 q^{86} -8.14484 q^{87} +51.7766 q^{88} +15.4333 q^{89} -23.0520 q^{90} +1.58402 q^{91} -55.4179 q^{92} -2.97645 q^{93} +30.6367 q^{94} +14.7731 q^{95} +24.8877 q^{96} +2.13965 q^{97} +6.65263 q^{98} +11.2157 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 243 q - 47 q^{2} - 31 q^{3} + 229 q^{4} - 40 q^{5} - 18 q^{6} - 42 q^{7} - 135 q^{8} + 214 q^{9}+O(q^{10}) \) 243 * q - 47 * q^2 - 31 * q^3 + 229 * q^4 - 40 * q^5 - 18 * q^6 - 42 * q^7 - 135 * q^8 + 214 * q^9	\( 243 q - 47 q^{2} - 31 q^{3} + 229 q^{4} - 40 q^{5} - 18 q^{6} - 42 q^{7} - 135 q^{8} + 214 q^{9} - 14 q^{10} - 112 q^{11} - 54 q^{12} - 45 q^{13} - 35 q^{14} - 56 q^{15} + 213 q^{16} - 71 q^{17} - 135 q^{18} - 69 q^{19} - 107 q^{20} - 36 q^{21} - 24 q^{22} - 162 q^{23} - 57 q^{24} + 203 q^{25} - 55 q^{26} - 115 q^{27} - 87 q^{28} - 76 q^{29} - 64 q^{30} - 35 q^{31} - 302 q^{32} - 77 q^{33} - 9 q^{34} - 264 q^{35} + 173 q^{36} - 61 q^{37} - 71 q^{38} - 123 q^{39} - 16 q^{40} - 74 q^{41} - 70 q^{42} - 178 q^{43} - 209 q^{44} - 107 q^{45} - 11 q^{46} - 191 q^{47} - 65 q^{48} + 211 q^{49} - 188 q^{50} - 175 q^{51} - 95 q^{52} - 122 q^{53} - 36 q^{54} - 47 q^{55} - 69 q^{56} - 103 q^{57} - 37 q^{58} - 212 q^{59} - 79 q^{60} - 14 q^{61} - 152 q^{62} - 203 q^{63} + 217 q^{64} - 159 q^{65} + 5 q^{66} - 202 q^{67} - 176 q^{68} - 34 q^{69} + 45 q^{70} - 170 q^{71} - 347 q^{72} - 57 q^{73} - 68 q^{74} - 124 q^{75} - 74 q^{76} - 166 q^{77} - 63 q^{78} - 48 q^{79} - 222 q^{80} + 159 q^{81} - 27 q^{82} - 434 q^{83} - 52 q^{84} - 57 q^{85} - 77 q^{86} - 184 q^{87} - 15 q^{88} - 62 q^{89} - 24 q^{90} - 81 q^{91} - 330 q^{92} - 164 q^{93} + 40 q^{94} - 182 q^{95} - 66 q^{96} - 21 q^{97} - 254 q^{98} - 306 q^{99}+O(q^{100}) \) 243 * q - 47 * q^2 - 31 * q^3 + 229 * q^4 - 40 * q^5 - 18 * q^6 - 42 * q^7 - 135 * q^8 + 214 * q^9 - 14 * q^10 - 112 * q^11 - 54 * q^12 - 45 * q^13 - 35 * q^14 - 56 * q^15 + 213 * q^16 - 71 * q^17 - 135 * q^18 - 69 * q^19 - 107 * q^20 - 36 * q^21 - 24 * q^22 - 162 * q^23 - 57 * q^24 + 203 * q^25 - 55 * q^26 - 115 * q^27 - 87 * q^28 - 76 * q^29 - 64 * q^30 - 35 * q^31 - 302 * q^32 - 77 * q^33 - 9 * q^34 - 264 * q^35 + 173 * q^36 - 61 * q^37 - 71 * q^38 - 123 * q^39 - 16 * q^40 - 74 * q^41 - 70 * q^42 - 178 * q^43 - 209 * q^44 - 107 * q^45 - 11 * q^46 - 191 * q^47 - 65 * q^48 + 211 * q^49 - 188 * q^50 - 175 * q^51 - 95 * q^52 - 122 * q^53 - 36 * q^54 - 47 * q^55 - 69 * q^56 - 103 * q^57 - 37 * q^58 - 212 * q^59 - 79 * q^60 - 14 * q^61 - 152 * q^62 - 203 * q^63 + 217 * q^64 - 159 * q^65 + 5 * q^66 - 202 * q^67 - 176 * q^68 - 34 * q^69 + 45 * q^70 - 170 * q^71 - 347 * q^72 - 57 * q^73 - 68 * q^74 - 124 * q^75 - 74 * q^76 - 166 * q^77 - 63 * q^78 - 48 * q^79 - 222 * q^80 + 159 * q^81 - 27 * q^82 - 434 * q^83 - 52 * q^84 - 57 * q^85 - 77 * q^86 - 184 * q^87 - 15 * q^88 - 62 * q^89 - 24 * q^90 - 81 * q^91 - 330 * q^92 - 164 * q^93 + 40 * q^94 - 182 * q^95 - 66 * q^96 - 21 * q^97 - 254 * q^98 - 306 * q^99

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