LMFDB - Embedded newform 6011.2.a.f.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6011,2,Mod(1,6011)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6011, 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("6011.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6011.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:	$47.9980766550$
Analytic rank:	$0$
Dimension:	$275$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	6011.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.59860 q^{2} +2.92349 q^{3} +4.75274 q^{4} -3.28865 q^{5} -7.59699 q^{6} +2.97734 q^{7} -7.15327 q^{8} +5.54680 q^{9} +O(q^{10})$	\(q-2.59860 q^{2} +2.92349 q^{3} +4.75274 q^{4} -3.28865 q^{5} -7.59699 q^{6} +2.97734 q^{7} -7.15327 q^{8} +5.54680 q^{9} +8.54591 q^{10} +0.976828 q^{11} +13.8946 q^{12} +5.78717 q^{13} -7.73692 q^{14} -9.61435 q^{15} +9.08305 q^{16} +2.45171 q^{17} -14.4139 q^{18} +4.43205 q^{19} -15.6301 q^{20} +8.70422 q^{21} -2.53839 q^{22} +3.42514 q^{23} -20.9125 q^{24} +5.81524 q^{25} -15.0386 q^{26} +7.44553 q^{27} +14.1505 q^{28} +1.43775 q^{29} +24.9839 q^{30} +3.85931 q^{31} -9.29668 q^{32} +2.85575 q^{33} -6.37102 q^{34} -9.79144 q^{35} +26.3625 q^{36} -1.32081 q^{37} -11.5171 q^{38} +16.9187 q^{39} +23.5246 q^{40} -4.36593 q^{41} -22.6188 q^{42} -7.41220 q^{43} +4.64261 q^{44} -18.2415 q^{45} -8.90057 q^{46} +3.86347 q^{47} +26.5542 q^{48} +1.86455 q^{49} -15.1115 q^{50} +7.16755 q^{51} +27.5049 q^{52} +4.03356 q^{53} -19.3480 q^{54} -3.21245 q^{55} -21.2977 q^{56} +12.9570 q^{57} -3.73614 q^{58} +11.0399 q^{59} -45.6945 q^{60} -6.95483 q^{61} -10.0288 q^{62} +16.5147 q^{63} +5.99230 q^{64} -19.0320 q^{65} -7.42095 q^{66} +6.29294 q^{67} +11.6523 q^{68} +10.0134 q^{69} +25.4441 q^{70} +2.39457 q^{71} -39.6778 q^{72} +14.3525 q^{73} +3.43225 q^{74} +17.0008 q^{75} +21.0644 q^{76} +2.90835 q^{77} -43.9651 q^{78} +6.02873 q^{79} -29.8710 q^{80} +5.12656 q^{81} +11.3453 q^{82} +6.83542 q^{83} +41.3689 q^{84} -8.06282 q^{85} +19.2614 q^{86} +4.20324 q^{87} -6.98752 q^{88} -12.9056 q^{89} +47.4024 q^{90} +17.2304 q^{91} +16.2788 q^{92} +11.2827 q^{93} -10.0396 q^{94} -14.5755 q^{95} -27.1788 q^{96} +2.56335 q^{97} -4.84522 q^{98} +5.41827 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 275 q + 16 q^{2} + 9 q^{3} + 316 q^{4} + 36 q^{5} + 30 q^{6} + 41 q^{7} + 36 q^{8} + 322 q^{9}+O(q^{10}) $ 275 * q + 16 * q^2 + 9 * q^3 + 316 * q^4 + 36 * q^5 + 30 * q^6 + 41 * q^7 + 36 * q^8 + 322 * q^9	\( 275 q + 16 q^{2} + 9 q^{3} + 316 q^{4} + 36 q^{5} + 30 q^{6} + 41 q^{7} + 36 q^{8} + 322 q^{9} + 44 q^{10} + 42 q^{11} + 26 q^{12} + 97 q^{13} + 24 q^{14} + 46 q^{15} + 386 q^{16} + 35 q^{17} + 47 q^{18} + 101 q^{19} + 60 q^{20} + 187 q^{21} + 72 q^{22} + 35 q^{23} + 73 q^{24} + 373 q^{25} + 21 q^{26} + 27 q^{27} + 97 q^{28} + 162 q^{29} + 13 q^{30} + 113 q^{31} + 58 q^{32} + 16 q^{33} + 52 q^{34} + 23 q^{35} + 426 q^{36} + 257 q^{37} + 8 q^{38} + 87 q^{39} + 126 q^{40} + 77 q^{41} - 7 q^{42} + 107 q^{43} + 133 q^{44} + 140 q^{45} + 207 q^{46} + 24 q^{47} + 4 q^{48} + 418 q^{49} + 65 q^{50} + 94 q^{51} + 142 q^{52} + 81 q^{53} + 79 q^{54} + 26 q^{55} + 62 q^{56} + 112 q^{57} + 44 q^{58} + 30 q^{59} + 83 q^{60} + 347 q^{61} + 5 q^{62} + 97 q^{63} + 508 q^{64} + 94 q^{65} + 4 q^{66} + 98 q^{67} + 28 q^{68} + 91 q^{69} + 17 q^{70} + 58 q^{71} + 99 q^{72} + 157 q^{73} + 80 q^{74} + 83 q^{75} + 264 q^{76} + 61 q^{77} + 5 q^{78} + 282 q^{79} + 49 q^{80} + 403 q^{81} + 46 q^{82} + 43 q^{83} + 318 q^{84} + 396 q^{85} + 57 q^{86} + 31 q^{87} + 180 q^{88} + 98 q^{89} + 67 q^{90} + 195 q^{91} + 97 q^{92} + 83 q^{93} + 96 q^{94} + 28 q^{95} + 127 q^{96} + 167 q^{97} + 24 q^{98} + 133 q^{99}+O(q^{100}) \) 275 * q + 16 * q^2 + 9 * q^3 + 316 * q^4 + 36 * q^5 + 30 * q^6 + 41 * q^7 + 36 * q^8 + 322 * q^9 + 44 * q^10 + 42 * q^11 + 26 * q^12 + 97 * q^13 + 24 * q^14 + 46 * q^15 + 386 * q^16 + 35 * q^17 + 47 * q^18 + 101 * q^19 + 60 * q^20 + 187 * q^21 + 72 * q^22 + 35 * q^23 + 73 * q^24 + 373 * q^25 + 21 * q^26 + 27 * q^27 + 97 * q^28 + 162 * q^29 + 13 * q^30 + 113 * q^31 + 58 * q^32 + 16 * q^33 + 52 * q^34 + 23 * q^35 + 426 * q^36 + 257 * q^37 + 8 * q^38 + 87 * q^39 + 126 * q^40 + 77 * q^41 - 7 * q^42 + 107 * q^43 + 133 * q^44 + 140 * q^45 + 207 * q^46 + 24 * q^47 + 4 * q^48 + 418 * q^49 + 65 * q^50 + 94 * q^51 + 142 * q^52 + 81 * q^53 + 79 * q^54 + 26 * q^55 + 62 * q^56 + 112 * q^57 + 44 * q^58 + 30 * q^59 + 83 * q^60 + 347 * q^61 + 5 * q^62 + 97 * q^63 + 508 * q^64 + 94 * q^65 + 4 * q^66 + 98 * q^67 + 28 * q^68 + 91 * q^69 + 17 * q^70 + 58 * q^71 + 99 * q^72 + 157 * q^73 + 80 * q^74 + 83 * q^75 + 264 * q^76 + 61 * q^77 + 5 * q^78 + 282 * q^79 + 49 * q^80 + 403 * q^81 + 46 * q^82 + 43 * q^83 + 318 * q^84 + 396 * q^85 + 57 * q^86 + 31 * q^87 + 180 * q^88 + 98 * q^89 + 67 * q^90 + 195 * q^91 + 97 * q^92 + 83 * q^93 + 96 * q^94 + 28 * q^95 + 127 * q^96 + 167 * q^97 + 24 * q^98 + 133 * 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 $

$2$	−2.59860	−1.83749	−0.918745	−	0.394851i	$-0.870796\pi$
$2$	−2.59860	−1.83749	−0.918745	+	0.394851i	$0.870796\pi$
$3$	2.92349	1.68788	0.843939	−	0.536439i	$-0.180231\pi$
$3$	2.92349	1.68788	0.843939	+	0.536439i	$0.180231\pi$
$4$	4.75274	2.37637
$5$	−3.28865	−1.47073	−0.735365	−	0.677671i	$-0.762989\pi$
$5$	−3.28865	−1.47073	−0.735365	+	0.677671i	$0.762989\pi$
$6$	−7.59699	−3.10146
$7$	2.97734	1.12533	0.562664	−	0.826686i	$-0.309776\pi$
$7$	2.97734	1.12533	0.562664	+	0.826686i	$0.309776\pi$
$8$	−7.15327	−2.52906
$9$	5.54680	1.84893
$10$	8.54591	2.70245
$11$	0.976828	0.294525	0.147262	−	0.989097i	$-0.452954\pi$
$11$	0.976828	0.294525	0.147262	+	0.989097i	$0.452954\pi$
$12$	13.8946	4.01102
$13$	5.78717	1.60507	0.802537	−	0.596603i	$-0.203483\pi$
$13$	5.78717	1.60507	0.802537	+	0.596603i	$0.203483\pi$
$14$	−7.73692	−2.06778
$15$	−9.61435	−2.48241
$16$	9.08305	2.27076
$17$	2.45171	0.594627	0.297314	−	0.954780i	$-0.403909\pi$
$17$	2.45171	0.594627	0.297314	+	0.954780i	$0.403909\pi$
$18$	−14.4139	−3.39739
$19$	4.43205	1.01678	0.508391	−	0.861127i	$-0.330241\pi$
$19$	4.43205	1.01678	0.508391	+	0.861127i	$0.330241\pi$
$20$	−15.6301	−3.49500
$21$	8.70422	1.89942
$22$	−2.53839	−0.541186
$23$	3.42514	0.714190	0.357095	−	0.934068i	$-0.383767\pi$
$23$	3.42514	0.714190	0.357095	+	0.934068i	$0.383767\pi$
$24$	−20.9125	−4.26875
$25$	5.81524	1.16305
$26$	−15.0386	−2.94931
$27$	7.44553	1.43289
$28$	14.1505	2.67420
$29$	1.43775	0.266983	0.133492	−	0.991050i	$-0.457381\pi$
$29$	1.43775	0.266983	0.133492	+	0.991050i	$0.457381\pi$
$30$	24.9839	4.56141
$31$	3.85931	0.693153	0.346576	−	0.938022i	$-0.387344\pi$
$31$	3.85931	0.693153	0.346576	+	0.938022i	$0.387344\pi$
$32$	−9.29668	−1.64344
$33$	2.85575	0.497122
$34$	−6.37102	−1.09262
$35$	−9.79144	−1.65505
$36$	26.3625	4.39374
$37$	−1.32081	−0.217139	−0.108570	−	0.994089i	$-0.534627\pi$
$37$	−1.32081	−0.217139	−0.108570	+	0.994089i	$0.534627\pi$
$38$	−11.5171	−1.86833
$39$	16.9187	2.70917
$40$	23.5246	3.71957
$41$	−4.36593	−0.681844	−0.340922	−	0.940092i	$-0.610739\pi$
$41$	−4.36593	−0.681844	−0.340922	+	0.940092i	$0.610739\pi$
$42$	−22.6188	−3.49016
$43$	−7.41220	−1.13035	−0.565175	−	0.824971i	$-0.691191\pi$
$43$	−7.41220	−1.13035	−0.565175	+	0.824971i	$0.691191\pi$
$44$	4.64261	0.699900
$45$	−18.2415	−2.71928
$46$	−8.90057	−1.31232
$47$	3.86347	0.563545	0.281772	−	0.959481i	$-0.409078\pi$
$47$	3.86347	0.563545	0.281772	+	0.959481i	$0.409078\pi$
$48$	26.5542	3.83277
$49$	1.86455	0.266364
$50$	−15.1115	−2.13709
$51$	7.16755	1.00366
$52$	27.5049	3.81425
$53$	4.03356	0.554052	0.277026	−	0.960862i	$-0.410651\pi$
$53$	4.03356	0.554052	0.277026	+	0.960862i	$0.410651\pi$
$54$	−19.3480	−2.63293
$55$	−3.21245	−0.433167
$56$	−21.2977	−2.84603
$57$	12.9570	1.71620
$58$	−3.73614	−0.490579
$59$	11.0399	1.43728	0.718638	−	0.695385i	$-0.244766\pi$
$59$	11.0399	1.43728	0.718638	+	0.695385i	$0.244766\pi$
$60$	−45.6945	−5.89913
$61$	−6.95483	−0.890474	−0.445237	−	0.895413i	$-0.646881\pi$
$61$	−6.95483	−0.890474	−0.445237	+	0.895413i	$0.646881\pi$
$62$	−10.0288	−1.27366
$63$	16.5147	2.08066
$64$	5.99230	0.749037
$65$	−19.0320	−2.36063
$66$	−7.42095	−0.913456
$67$	6.29294	0.768806	0.384403	−	0.923165i	$-0.374407\pi$
$67$	6.29294	0.768806	0.384403	+	0.923165i	$0.374407\pi$
$68$	11.6523	1.41305
$69$	10.0134	1.20547
$70$	25.4441	3.04115
$71$	2.39457	0.284184	0.142092	−	0.989853i	$-0.454617\pi$
$71$	2.39457	0.284184	0.142092	+	0.989853i	$0.454617\pi$
$72$	−39.6778	−4.67607
$73$	14.3525	1.67983	0.839916	−	0.542716i	$-0.182604\pi$
$73$	14.3525	1.67983	0.839916	+	0.542716i	$0.182604\pi$
$74$	3.43225	0.398991
$75$	17.0008	1.96308
$76$	21.0644	2.41625
$77$	2.90835	0.331437
$78$	−43.9651	−4.97807
$79$	6.02873	0.678286	0.339143	−	0.940735i	$-0.389863\pi$
$79$	6.02873	0.678286	0.339143	+	0.940735i	$0.389863\pi$
$80$	−29.8710	−3.33968
$81$	5.12656	0.569617
$82$	11.3453	1.25288
$83$	6.83542	0.750285	0.375143	−	0.926967i	$-0.377594\pi$
$83$	6.83542	0.750285	0.375143	+	0.926967i	$0.377594\pi$
$84$	41.3689	4.51372
$85$	−8.06282	−0.874536
$86$	19.2614	2.07701
$87$	4.20324	0.450635
$88$	−6.98752	−0.744872
$89$	−12.9056	−1.36799	−0.683994	−	0.729488i	$-0.739758\pi$
$89$	−12.9056	−1.36799	−0.683994	+	0.729488i	$0.739758\pi$
$90$	47.4024	4.99665
$91$	17.2304	1.80623
$92$	16.2788	1.69718
$93$	11.2827	1.16996
$94$	−10.0396	−1.03551
$95$	−14.5755	−1.49541
$96$	−27.1788	−2.77392
$97$	2.56335	0.260269	0.130135	−	0.991496i	$-0.458459\pi$
$97$	2.56335	0.260269	0.130135	+	0.991496i	$0.458459\pi$
$98$	−4.84522	−0.489441
$99$	5.41827	0.544556
$100$	27.6383	2.76383
$101$	−19.1978	−1.91026	−0.955128	−	0.296194i	$-0.904282\pi$
$101$	−19.1978	−1.91026	−0.955128	+	0.296194i	$0.904282\pi$
$102$	−18.6256	−1.84421
$103$	−2.98094	−0.293721	−0.146860	−	0.989157i	$-0.546917\pi$
$103$	−2.98094	−0.293721	−0.146860	+	0.989157i	$0.546917\pi$
$104$	−41.3972	−4.05933
$105$	−28.6252	−2.79353
$106$	−10.4816	−1.01806
$107$	−4.27468	−0.413249	−0.206624	−	0.978420i	$-0.566248\pi$
$107$	−4.27468	−0.413249	−0.206624	+	0.978420i	$0.566248\pi$
$108$	35.3867	3.40508
$109$	−3.89927	−0.373483	−0.186741	−	0.982409i	$-0.559793\pi$
$109$	−3.89927	−0.373483	−0.186741	+	0.982409i	$0.559793\pi$
$110$	8.34788	0.795939
$111$	−3.86136	−0.366504
$112$	27.0433	2.55535
$113$	−10.7791	−1.01401	−0.507005	−	0.861943i	$-0.669248\pi$
$113$	−10.7791	−1.01401	−0.507005	+	0.861943i	$0.669248\pi$
$114$	−33.6702	−3.15350
$115$	−11.2641	−1.05038
$116$	6.83324	0.634450
$117$	32.1003	2.96767
$118$	−28.6884	−2.64098
$119$	7.29957	0.669151
$120$	68.7741	6.27818
$121$	−10.0458	−0.913255
$122$	18.0728	1.63624
$123$	−12.7638	−1.15087
$124$	18.3423	1.64719
$125$	−2.68105	−0.239800
$126$	−42.9151	−3.82318
$127$	−5.59495	−0.496471	−0.248236	−	0.968700i	$-0.579851\pi$
$127$	−5.59495	−0.496471	−0.248236	+	0.968700i	$0.579851\pi$
$128$	3.02177	0.267089
$129$	−21.6695	−1.90789
$130$	49.4566	4.33763
$131$	5.98534	0.522942	0.261471	−	0.965211i	$-0.415792\pi$
$131$	5.98534	0.522942	0.261471	+	0.965211i	$0.415792\pi$
$132$	13.5726	1.18134
$133$	13.1957	1.14421
$134$	−16.3529	−1.41267
$135$	−24.4858	−2.10740
$136$	−17.5378	−1.50385
$137$	−20.4851	−1.75016	−0.875080	−	0.483979i	$-0.839191\pi$
$137$	−20.4851	−1.75016	−0.875080	+	0.483979i	$0.839191\pi$
$138$	−26.0207	−2.21503
$139$	1.21175	0.102779	0.0513895	−	0.998679i	$-0.483635\pi$
$139$	1.21175	0.102779	0.0513895	+	0.998679i	$0.483635\pi$
$140$	−46.5361	−3.93302
$141$	11.2948	0.951194
$142$	−6.22255	−0.522185
$143$	5.65307	0.472734
$144$	50.3818	4.19848
$145$	−4.72825	−0.392660
$146$	−37.2964	−3.08668
$147$	5.45099	0.449590
$148$	−6.27744	−0.516003
$149$	9.71261	0.795688	0.397844	−	0.917453i	$-0.369759\pi$
$149$	9.71261	0.795688	0.397844	+	0.917453i	$0.369759\pi$
$150$	−44.1783	−3.60715
$151$	−14.1974	−1.15537	−0.577684	−	0.816260i	$-0.696043\pi$
$151$	−14.1974	−1.15537	−0.577684	+	0.816260i	$0.696043\pi$
$152$	−31.7036	−2.57151
$153$	13.5991	1.09942
$154$	−7.55764	−0.609012
$155$	−12.6919	−1.01944
$156$	80.4104	6.43798
$157$	−14.6642	−1.17033	−0.585163	−	0.810915i	$-0.698970\pi$
$157$	−14.6642	−1.17033	−0.585163	+	0.810915i	$0.698970\pi$
$158$	−15.6663	−1.24634
$159$	11.7921	0.935172
$160$	30.5736	2.41705
$161$	10.1978	0.803699
$162$	−13.3219	−1.04667
$163$	2.33206	0.182661	0.0913307	−	0.995821i	$-0.470888\pi$
$163$	2.33206	0.182661	0.0913307	+	0.995821i	$0.470888\pi$
$164$	−20.7501	−1.62031
$165$	−9.39156	−0.731132
$166$	−17.7625	−1.37864
$167$	−11.5453	−0.893404	−0.446702	−	0.894683i	$-0.647402\pi$
$167$	−11.5453	−0.893404	−0.446702	+	0.894683i	$0.647402\pi$
$168$	−62.2637	−4.80375
$169$	20.4914	1.57626
$170$	20.9521	1.60695
$171$	24.5837	1.87996
$172$	−35.2282	−2.68613
$173$	10.8923	0.828124	0.414062	−	0.910249i	$-0.364110\pi$
$173$	10.8923	0.828124	0.414062	+	0.910249i	$0.364110\pi$
$174$	−10.9226	−0.828037
$175$	17.3139	1.30881
$176$	8.87257	0.668795
$177$	32.2751	2.42595
$178$	33.5364	2.51366
$179$	−8.95923	−0.669645	−0.334822	−	0.942281i	$-0.608676\pi$
$179$	−8.95923	−0.669645	−0.334822	+	0.942281i	$0.608676\pi$
$180$	−86.6970	−6.46202
$181$	−6.48746	−0.482209	−0.241104	−	0.970499i	$-0.577510\pi$
$181$	−6.48746	−0.482209	−0.241104	+	0.970499i	$0.577510\pi$
$182$	−44.7749	−3.31894
$183$	−20.3324	−1.50301
$184$	−24.5009	−1.80623
$185$	4.34367	0.319353
$186$	−29.3192	−2.14978
$187$	2.39490	0.175132
$188$	18.3620	1.33919
$189$	22.1679	1.61248
$190$	37.8759	2.74780
$191$	1.54757	0.111978	0.0559892	−	0.998431i	$-0.482169\pi$
$191$	1.54757	0.111978	0.0559892	+	0.998431i	$0.482169\pi$
$192$	17.5184	1.26428
$193$	21.6540	1.55869	0.779346	−	0.626594i	$-0.215552\pi$
$193$	21.6540	1.55869	0.779346	+	0.626594i	$0.215552\pi$
$194$	−6.66114	−0.478242
$195$	−55.6399	−3.98446
$196$	8.86171	0.632979
$197$	−25.6644	−1.82851	−0.914256	−	0.405136i	$-0.867224\pi$
$197$	−25.6644	−1.82851	−0.914256	+	0.405136i	$0.867224\pi$
$198$	−14.0799	−1.00062
$199$	−3.59073	−0.254540	−0.127270	−	0.991868i	$-0.540621\pi$
$199$	−3.59073	−0.254540	−0.127270	+	0.991868i	$0.540621\pi$
$200$	−41.5980	−2.94142
$201$	18.3974	1.29765
$202$	49.8875	3.51008
$203$	4.28066	0.300444
$204$	34.0655	2.38506
$205$	14.3580	1.00281
$206$	7.74628	0.539709
$207$	18.9985	1.32049
$208$	52.5652	3.64474
$209$	4.32935	0.299467
$210$	74.3855	5.13308
$211$	−24.6536	−1.69722	−0.848612	−	0.529015i	$-0.822561\pi$
$211$	−24.6536	−1.69722	−0.848612	+	0.529015i	$0.822561\pi$
$212$	19.1704	1.31663
$213$	7.00052	0.479667
$214$	11.1082	0.759340
$215$	24.3761	1.66244
$216$	−53.2599	−3.62388
$217$	11.4905	0.780024
$218$	10.1327	0.686270
$219$	41.9594	2.83535
$220$	−15.2679	−1.02936
$221$	14.1885	0.954420
$222$	10.0341	0.673448
$223$	18.1846	1.21773	0.608867	−	0.793272i	$-0.291624\pi$
$223$	18.1846	1.21773	0.608867	+	0.793272i	$0.291624\pi$
$224$	−27.6794	−1.84941
$225$	32.2560	2.15040
$226$	28.0106	1.86323
$227$	−15.9483	−1.05852	−0.529262	−	0.848458i	$-0.677531\pi$
$227$	−15.9483	−1.05852	−0.529262	+	0.848458i	$0.677531\pi$
$228$	61.5814	4.07833
$229$	13.5202	0.893441	0.446720	−	0.894674i	$-0.352592\pi$
$229$	13.5202	0.893441	0.446720	+	0.894674i	$0.352592\pi$
$230$	29.2709	1.93007
$231$	8.50253	0.559425
$232$	−10.2846	−0.675217
$233$	−22.0353	−1.44358	−0.721791	−	0.692111i	$-0.756681\pi$
$233$	−22.0353	−1.44358	−0.721791	+	0.692111i	$0.756681\pi$
$234$	−83.4159	−5.45307
$235$	−12.7056	−0.828822
$236$	52.4699	3.41550
$237$	17.6249	1.14486
$238$	−18.9687	−1.22956
$239$	25.4991	1.64940	0.824700	−	0.565570i	$-0.191344\pi$
$239$	25.4991	1.64940	0.824700	+	0.565570i	$0.191344\pi$
$240$	−87.3276	−5.63697
$241$	17.5202	1.12857	0.564286	−	0.825579i	$-0.309151\pi$
$241$	17.5202	1.12857	0.564286	+	0.825579i	$0.309151\pi$
$242$	26.1051	1.67810
$243$	−7.34916	−0.471449
$244$	−33.0545	−2.11610
$245$	−6.13185	−0.391750
$246$	33.1679	2.11471
$247$	25.6490	1.63201
$248$	−27.6067	−1.75303
$249$	19.9833	1.26639
$250$	6.96698	0.440631
$251$	7.21983	0.455712	0.227856	−	0.973695i	$-0.426829\pi$
$251$	7.21983	0.455712	0.227856	+	0.973695i	$0.426829\pi$
$252$	78.4900	4.94441
$253$	3.34577	0.210347
$254$	14.5390	0.912261
$255$	−23.5716	−1.47611
$256$	−19.8370	−1.23981
$257$	4.03841	0.251909	0.125955	−	0.992036i	$-0.459801\pi$
$257$	4.03841	0.251909	0.125955	+	0.992036i	$0.459801\pi$
$258$	56.3104	3.50573
$259$	−3.93249	−0.244353
$260$	−90.4542	−5.60973
$261$	7.97489	0.493634
$262$	−15.5535	−0.960900
$263$	−9.18076	−0.566110	−0.283055	−	0.959104i	$-0.591348\pi$
$263$	−9.18076	−0.566110	−0.283055	+	0.959104i	$0.591348\pi$
$264$	−20.4279	−1.25725
$265$	−13.2650	−0.814861
$266$	−34.2904	−2.10248
$267$	−37.7293	−2.30900
$268$	29.9087	1.82697
$269$	14.0435	0.856248	0.428124	−	0.903720i	$-0.359175\pi$
$269$	14.0435	0.856248	0.428124	+	0.903720i	$0.359175\pi$
$270$	63.6288	3.87233
$271$	−0.494288	−0.0300258	−0.0150129	−	0.999887i	$-0.504779\pi$
$271$	−0.494288	−0.0300258	−0.0150129	+	0.999887i	$0.504779\pi$
$272$	22.2690	1.35026
$273$	50.3729	3.04870
$274$	53.2326	3.21590
$275$	5.68049	0.342547
$276$	47.5908	2.86463
$277$	−21.8318	−1.31174	−0.655872	−	0.754872i	$-0.727699\pi$
$277$	−21.8318	−1.31174	−0.655872	+	0.754872i	$0.727699\pi$
$278$	−3.14885	−0.188855
$279$	21.4068	1.28159
$280$	70.0408	4.18574
$281$	−14.4238	−0.860454	−0.430227	−	0.902721i	$-0.641566\pi$
$281$	−14.4238	−0.860454	−0.430227	+	0.902721i	$0.641566\pi$
$282$	−29.3507	−1.74781
$283$	20.3004	1.20674	0.603368	−	0.797463i	$-0.293825\pi$
$283$	20.3004	1.20674	0.603368	+	0.797463i	$0.293825\pi$
$284$	11.3808	0.675326
$285$	−42.6112	−2.52407
$286$	−14.6901	−0.868644
$287$	−12.9989	−0.767298
$288$	−51.5668	−3.03860
$289$	−10.9891	−0.646419
$290$	12.2869	0.721509
$291$	7.49394	0.439303
$292$	68.2136	3.99190
$293$	12.8845	0.752721	0.376361	−	0.926473i	$-0.377175\pi$
$293$	12.8845	0.752721	0.376361	+	0.926473i	$0.377175\pi$
$294$	−14.1650	−0.826117
$295$	−36.3065	−2.11384
$296$	9.44808	0.549159
$297$	7.27301	0.422023
$298$	−25.2392	−1.46207
$299$	19.8219	1.14633
$300$	80.8004	4.66501
$301$	−22.0686	−1.27201
$302$	36.8934	2.12298
$303$	−56.1247	−3.22428
$304$	40.2565	2.30887
$305$	22.8720	1.30965
$306$	−35.3388	−2.02018
$307$	5.64088	0.321942	0.160971	−	0.986959i	$-0.448537\pi$
$307$	5.64088	0.321942	0.160971	+	0.986959i	$0.448537\pi$
$308$	13.8226	0.787617
$309$	−8.71475	−0.495765
$310$	32.9813	1.87321
$311$	2.34635	0.133049	0.0665246	−	0.997785i	$-0.478809\pi$
$311$	2.34635	0.133049	0.0665246	+	0.997785i	$0.478809\pi$
$312$	−121.024	−6.85166
$313$	13.9311	0.787434	0.393717	−	0.919232i	$-0.371189\pi$
$313$	13.9311	0.787434	0.393717	+	0.919232i	$0.371189\pi$
$314$	38.1063	2.15046
$315$	−54.3111	−3.06008
$316$	28.6530	1.61186
$317$	15.5019	0.870675	0.435338	−	0.900267i	$-0.356629\pi$
$317$	15.5019	0.870675	0.435338	+	0.900267i	$0.356629\pi$
$318$	−30.6429	−1.71837
$319$	1.40443	0.0786331
$320$	−19.7066	−1.10163
$321$	−12.4970	−0.697513
$322$	−26.5000	−1.47679
$323$	10.8661	0.604606
$324$	24.3652	1.35362
$325$	33.6538	1.86678
$326$	−6.06011	−0.335638
$327$	−11.3995	−0.630393
$328$	31.2307	1.72443
$329$	11.5029	0.634173
$330$	24.4049	1.34345
$331$	10.8891	0.598520	0.299260	−	0.954172i	$-0.403260\pi$
$331$	10.8891	0.598520	0.299260	+	0.954172i	$0.403260\pi$
$332$	32.4870	1.78295
$333$	−7.32624	−0.401475
$334$	30.0017	1.64162
$335$	−20.6953	−1.13071
$336$	79.0609	4.31312
$337$	−22.2605	−1.21261	−0.606304	−	0.795233i	$-0.707349\pi$
$337$	−22.2605	−1.21261	−0.606304	+	0.795233i	$0.707349\pi$
$338$	−53.2490	−2.89636
$339$	−31.5125	−1.71153
$340$	−38.3205	−2.07822
$341$	3.76988	0.204151
$342$	−63.8832	−3.45441
$343$	−15.2900	−0.825581
$344$	53.0215	2.85873
$345$	−32.9304	−1.77292
$346$	−28.3047	−1.52167
$347$	−11.5892	−0.622141	−0.311071	−	0.950387i	$-0.600688\pi$
$347$	−11.5892	−0.622141	−0.311071	+	0.950387i	$0.600688\pi$
$348$	19.9769	1.07087
$349$	0.604990	0.0323844	0.0161922	−	0.999869i	$-0.494846\pi$
$349$	0.604990	0.0323844	0.0161922	+	0.999869i	$0.494846\pi$
$350$	−44.9921	−2.40493
$351$	43.0886	2.29990
$352$	−9.08126	−0.484033
$353$	24.6460	1.31177	0.655886	−	0.754860i	$-0.272295\pi$
$353$	24.6460	1.31177	0.655886	+	0.754860i	$0.272295\pi$
$354$	−83.8702	−4.45765
$355$	−7.87493	−0.417958
$356$	−61.3368	−3.25084
$357$	21.3402	1.12944
$358$	23.2815	1.23047
$359$	34.4147	1.81634	0.908170	−	0.418601i	$-0.137480\pi$
$359$	34.4147	1.81634	0.908170	+	0.418601i	$0.137480\pi$
$360$	130.486	6.87724
$361$	0.643037	0.0338440
$362$	16.8583	0.886054
$363$	−29.3688	−1.54146
$364$	81.8915	4.29228
$365$	−47.2004	−2.47058
$366$	52.8357	2.76177
$367$	14.8995	0.777745	0.388873	−	0.921292i	$-0.372865\pi$
$367$	14.8995	0.777745	0.388873	+	0.921292i	$0.372865\pi$
$368$	31.1107	1.62176
$369$	−24.2169	−1.26068
$370$	−11.2875	−0.586808
$371$	12.0093	0.623490
$372$	53.6235	2.78025
$373$	19.6806	1.01902	0.509512	−	0.860463i	$-0.329826\pi$
$373$	19.6806	1.01902	0.509512	+	0.860463i	$0.329826\pi$
$374$	−6.22339	−0.321804
$375$	−7.83802	−0.404754
$376$	−27.6364	−1.42524
$377$	8.32050	0.428527
$378$	−57.6055	−2.96291
$379$	−32.0283	−1.64518	−0.822591	−	0.568634i	$-0.807472\pi$
$379$	−32.0283	−1.64518	−0.822591	+	0.568634i	$0.807472\pi$
$380$	−69.2734	−3.55365
$381$	−16.3568	−0.837983
$382$	−4.02153	−0.205759
$383$	−2.53660	−0.129614	−0.0648071	−	0.997898i	$-0.520643\pi$
$383$	−2.53660	−0.129614	−0.0648071	+	0.997898i	$0.520643\pi$
$384$	8.83410	0.450813
$385$	−9.56455	−0.487455
$386$	−56.2702	−2.86408
$387$	−41.1139	−2.08994
$388$	12.1830	0.618496
$389$	−15.6064	−0.791278	−0.395639	−	0.918406i	$-0.629477\pi$
$389$	−15.6064	−0.791278	−0.395639	+	0.918406i	$0.629477\pi$
$390$	144.586	7.32140
$391$	8.39744	0.424677
$392$	−13.3376	−0.673652
$393$	17.4981	0.882662
$394$	66.6916	3.35987
$395$	−19.8264	−0.997575
$396$	25.7516	1.29407
$397$	21.6231	1.08523	0.542617	−	0.839980i	$-0.317433\pi$
$397$	21.6231	1.08523	0.542617	+	0.839980i	$0.317433\pi$
$398$	9.33088	0.467715
$399$	38.5775	1.93129
$400$	52.8201	2.64101
$401$	27.5375	1.37516	0.687578	−	0.726111i	$-0.258674\pi$
$401$	27.5375	1.37516	0.687578	+	0.726111i	$0.258674\pi$
$402$	−47.8074	−2.38442
$403$	22.3345	1.11256
$404$	−91.2423	−4.53947
$405$	−16.8595	−0.837754
$406$	−11.1237	−0.552062
$407$	−1.29020	−0.0639528
$408$	−51.2715	−2.53832
$409$	−20.1279	−0.995259	−0.497630	−	0.867390i	$-0.665796\pi$
$409$	−20.1279	−0.995259	−0.497630	+	0.867390i	$0.665796\pi$
$410$	−37.3108	−1.84265
$411$	−59.8880	−2.95406
$412$	−14.1676	−0.697989
$413$	32.8696	1.61741
$414$	−49.3696	−2.42639
$415$	−22.4793	−1.10347
$416$	−53.8015	−2.63784
$417$	3.54253	0.173478
$418$	−11.2503	−0.550268
$419$	33.9655	1.65932	0.829662	−	0.558266i	$-0.188533\pi$
$419$	33.9655	1.65932	0.829662	+	0.558266i	$0.188533\pi$
$420$	−136.048	−6.63846
$421$	−32.6426	−1.59090	−0.795451	−	0.606017i	$-0.792766\pi$
$421$	−32.6426	−1.59090	−0.795451	+	0.606017i	$0.792766\pi$
$422$	64.0650	3.11863
$423$	21.4299	1.04196
$424$	−28.8531	−1.40123
$425$	14.2573	0.691580
$426$	−18.1916	−0.881384
$427$	−20.7069	−1.00208
$428$	−20.3164	−0.982031
$429$	16.5267	0.797917
$430$	−63.3439	−3.05472
$431$	−0.571922	−0.0275485	−0.0137743	−	0.999905i	$-0.504385\pi$
$431$	−0.571922	−0.0275485	−0.0137743	+	0.999905i	$0.504385\pi$
$432$	67.6281	3.25376
$433$	17.7228	0.851706	0.425853	−	0.904792i	$-0.359974\pi$
$433$	17.7228	0.851706	0.425853	+	0.904792i	$0.359974\pi$
$434$	−29.8592	−1.43329
$435$	−13.8230	−0.662762
$436$	−18.5322	−0.887532
$437$	15.1804	0.726175
$438$	−109.036	−5.20993
$439$	−23.8147	−1.13662	−0.568308	−	0.822816i	$-0.692402\pi$
$439$	−23.8147	−1.13662	−0.568308	+	0.822816i	$0.692402\pi$
$440$	22.9795	1.09551
$441$	10.3423	0.492489
$442$	−36.8702	−1.75374
$443$	−14.1008	−0.669948	−0.334974	−	0.942227i	$-0.608728\pi$
$443$	−14.1008	−0.669948	−0.334974	+	0.942227i	$0.608728\pi$
$444$	−18.3520	−0.870949
$445$	42.4419	2.01194
$446$	−47.2547	−2.23757
$447$	28.3947	1.34302
$448$	17.8411	0.842913
$449$	−36.2644	−1.71142	−0.855712	−	0.517452i	$-0.826881\pi$
$449$	−36.2644	−1.71142	−0.855712	+	0.517452i	$0.826881\pi$
$450$	−83.8204	−3.95133
$451$	−4.26476	−0.200820
$452$	−51.2302	−2.40966
$453$	−41.5060	−1.95012
$454$	41.4432	1.94503
$455$	−56.6648	−2.65648
$456$	−92.6853	−4.34039
$457$	−12.8324	−0.600276	−0.300138	−	0.953896i	$-0.597033\pi$
$457$	−12.8324	−0.600276	−0.300138	+	0.953896i	$0.597033\pi$
$458$	−35.1337	−1.64169
$459$	18.2543	0.852037
$460$	−53.5352	−2.49609
$461$	−22.1515	−1.03170	−0.515849	−	0.856680i	$-0.672523\pi$
$461$	−22.1515	−1.03170	−0.515849	+	0.856680i	$0.672523\pi$
$462$	−22.0947	−1.02794
$463$	−3.12307	−0.145141	−0.0725706	−	0.997363i	$-0.523120\pi$
$463$	−3.12307	−0.145141	−0.0725706	+	0.997363i	$0.523120\pi$
$464$	13.0591	0.606255
$465$	−37.1048	−1.72069
$466$	57.2611	2.65257
$467$	20.7518	0.960280	0.480140	−	0.877192i	$-0.340586\pi$
$467$	20.7518	0.960280	0.480140	+	0.877192i	$0.340586\pi$
$468$	152.564	7.05228
$469$	18.7362	0.865159
$470$	33.0168	1.52295
$471$	−42.8705	−1.97537
$472$	−78.9716	−3.63496
$473$	−7.24044	−0.332916
$474$	−45.8002	−2.10367
$475$	25.7734	1.18257
$476$	34.6930	1.59015
$477$	22.3733	1.02440
$478$	−66.2621	−3.03076
$479$	13.3768	0.611200	0.305600	−	0.952160i	$-0.401143\pi$
$479$	13.3768	0.611200	0.305600	+	0.952160i	$0.401143\pi$
$480$	89.3815	4.07969
$481$	−7.64373	−0.348524
$482$	−45.5279	−2.07374
$483$	29.8131	1.35655
$484$	−47.7451	−2.17023
$485$	−8.42998	−0.382786
$486$	19.0976	0.866283
$487$	1.37902	0.0624893	0.0312447	−	0.999512i	$-0.490053\pi$
$487$	1.37902	0.0624893	0.0312447	+	0.999512i	$0.490053\pi$
$488$	49.7498	2.25207
$489$	6.81777	0.308310
$490$	15.9343	0.719836
$491$	25.8570	1.16691	0.583456	−	0.812145i	$-0.301700\pi$
$491$	25.8570	1.16691	0.583456	+	0.812145i	$0.301700\pi$
$492$	−60.6628	−2.73489
$493$	3.52494	0.158755
$494$	−66.6516	−2.99880
$495$	−17.8188	−0.800895
$496$	35.0543	1.57398
$497$	7.12946	0.319800
$498$	−51.9286	−2.32698
$499$	−28.6298	−1.28165	−0.640824	−	0.767688i	$-0.721407\pi$
$499$	−28.6298	−1.28165	−0.640824	+	0.767688i	$0.721407\pi$
$500$	−12.7423	−0.569854
$501$	−33.7527	−1.50796
$502$	−18.7615	−0.837365
$503$	43.5202	1.94047	0.970234	−	0.242170i	$-0.0778591\pi$
$503$	43.5202	1.94047	0.970234	+	0.242170i	$0.0778591\pi$
$504$	−118.134	−5.26211
$505$	63.1350	2.80947
$506$	−8.69433	−0.386510
$507$	59.9064	2.66054
$508$	−26.5913	−1.17980
$509$	8.93361	0.395975	0.197988	−	0.980204i	$-0.436559\pi$
$509$	8.93361	0.395975	0.197988	+	0.980204i	$0.436559\pi$
$510$	61.2532	2.71234
$511$	42.7322	1.89036
$512$	45.5049	2.01105
$513$	32.9989	1.45694
$514$	−10.4942	−0.462880
$515$	9.80328	0.431984
$516$	−102.989	−4.53386
$517$	3.77394	0.165978
$518$	10.2190	0.448996
$519$	31.8434	1.39777
$520$	136.141	5.97019
$521$	−17.8614	−0.782524	−0.391262	−	0.920279i	$-0.627961\pi$
$521$	−17.8614	−0.782524	−0.391262	+	0.920279i	$0.627961\pi$
$522$	−20.7236	−0.907047
$523$	44.6241	1.95128	0.975639	−	0.219384i	$-0.0704049\pi$
$523$	44.6241	1.95128	0.975639	+	0.219384i	$0.0704049\pi$
$524$	28.4468	1.24270
$525$	50.6172	2.20911
$526$	23.8572	1.04022
$527$	9.46191	0.412167
$528$	25.9389	1.12885
$529$	−11.2684	−0.489932
$530$	34.4704	1.49730
$531$	61.2362	2.65742
$532$	62.7157	2.71907
$533$	−25.2664	−1.09441
$534$	98.0435	4.24276
$535$	14.0579	0.607777
$536$	−45.0152	−1.94436
$537$	−26.1922	−1.13028
$538$	−36.4935	−1.57335
$539$	1.82134	0.0784508
$540$	−116.375	−5.00796
$541$	−5.56003	−0.239044	−0.119522	−	0.992832i	$-0.538136\pi$
$541$	−5.56003	−0.239044	−0.119522	+	0.992832i	$0.538136\pi$
$542$	1.28446	0.0551722
$543$	−18.9660	−0.813910
$544$	−22.7928	−0.977232
$545$	12.8234	0.549292
$546$	−130.899	−5.60196
$547$	12.7361	0.544554	0.272277	−	0.962219i	$-0.412223\pi$
$547$	12.7361	0.544554	0.272277	+	0.962219i	$0.412223\pi$
$548$	−97.3603	−4.15903
$549$	−38.5770	−1.64643
$550$	−14.7613	−0.629426
$551$	6.37217	0.271463
$552$	−71.6283	−3.04870
$553$	17.9496	0.763294
$554$	56.7321	2.41032
$555$	12.6987	0.539029
$556$	5.75911	0.244241
$557$	15.0321	0.636928	0.318464	−	0.947935i	$-0.396833\pi$
$557$	15.0321	0.636928	0.318464	+	0.947935i	$0.396833\pi$
$558$	−55.6278	−2.35491
$559$	−42.8957	−1.81429
$560$	−88.9361	−3.75823
$561$	7.00146	0.295602
$562$	37.4818	1.58108
$563$	−16.6314	−0.700932	−0.350466	−	0.936576i	$-0.613977\pi$
$563$	−16.6314	−0.700932	−0.350466	+	0.936576i	$0.613977\pi$
$564$	53.6813	2.26039
$565$	35.4487	1.49134
$566$	−52.7528	−2.21736
$567$	15.2635	0.641007
$568$	−17.1291	−0.718719
$569$	4.75885	0.199501	0.0997506	−	0.995012i	$-0.468195\pi$
$569$	4.75885	0.199501	0.0997506	+	0.995012i	$0.468195\pi$
$570$	110.730	4.63796
$571$	−20.2559	−0.847683	−0.423842	−	0.905736i	$-0.639319\pi$
$571$	−20.2559	−0.847683	−0.423842	+	0.905736i	$0.639319\pi$
$572$	26.8676	1.12339
$573$	4.52431	0.189006
$574$	33.7789	1.40990
$575$	19.9180	0.830638
$576$	33.2380	1.38492
$577$	−23.5087	−0.978678	−0.489339	−	0.872094i	$-0.662762\pi$
$577$	−23.5087	−0.978678	−0.489339	+	0.872094i	$0.662762\pi$
$578$	28.5564	1.18779
$579$	63.3054	2.63088
$580$	−22.4722	−0.933106
$581$	20.3514	0.844317
$582$	−19.4738	−0.807214
$583$	3.94009	0.163182
$584$	−102.667	−4.24840
$585$	−105.567	−4.36464
$586$	−33.4817	−1.38312
$587$	−23.6726	−0.977074	−0.488537	−	0.872543i	$-0.662469\pi$
$587$	−23.6726	−0.977074	−0.488537	+	0.872543i	$0.662469\pi$
$588$	25.9071	1.06839
$589$	17.1046	0.704785
$590$	94.3461	3.88417
$591$	−75.0296	−3.08631
$592$	−11.9969	−0.493071
$593$	−37.0085	−1.51976	−0.759879	−	0.650065i	$-0.774742\pi$
$593$	−37.0085	−1.51976	−0.759879	+	0.650065i	$0.774742\pi$
$594$	−18.8997	−0.775462
$595$	−24.0058	−0.984140
$596$	46.1615	1.89085
$597$	−10.4975	−0.429633
$598$	−51.5091	−2.10637
$599$	46.3935	1.89559	0.947794	−	0.318884i	$-0.103308\pi$
$599$	46.3935	1.89559	0.947794	+	0.318884i	$0.103308\pi$
$600$	−121.611	−4.96477
$601$	−31.9050	−1.30143	−0.650716	−	0.759321i	$-0.725531\pi$
$601$	−31.9050	−1.30143	−0.650716	+	0.759321i	$0.725531\pi$
$602$	57.3476	2.33731
$603$	34.9057	1.42147
$604$	−67.4765	−2.74558
$605$	33.0372	1.34315
$606$	145.846	5.92458
$607$	23.9280	0.971208	0.485604	−	0.874179i	$-0.338600\pi$
$607$	23.9280	0.971208	0.485604	+	0.874179i	$0.338600\pi$
$608$	−41.2033	−1.67102
$609$	12.5145	0.507112
$610$	−59.4353	−2.40646
$611$	22.3586	0.904530
$612$	64.6331	2.61264
$613$	28.0580	1.13325	0.566626	−	0.823975i	$-0.308248\pi$
$613$	28.0580	1.13325	0.566626	+	0.823975i	$0.308248\pi$
$614$	−14.6584	−0.591565
$615$	41.9756	1.69262
$616$	−20.8042	−0.838226
$617$	16.3067	0.656484	0.328242	−	0.944594i	$-0.393544\pi$
$617$	16.3067	0.656484	0.328242	+	0.944594i	$0.393544\pi$
$618$	22.6462	0.910963
$619$	28.4544	1.14368	0.571839	−	0.820366i	$-0.306230\pi$
$619$	28.4544	1.14368	0.571839	+	0.820366i	$0.306230\pi$
$620$	−60.3215	−2.42257
$621$	25.5020	1.02336
$622$	−6.09723	−0.244477
$623$	−38.4242	−1.53943
$624$	153.674	6.15187
$625$	−20.2592	−0.810367
$626$	−36.2015	−1.44690
$627$	12.6568	0.505464
$628$	−69.6949	−2.78113
$629$	−3.23823	−0.129117
$630$	141.133	5.62287
$631$	−23.6703	−0.942301	−0.471150	−	0.882053i	$-0.656161\pi$
$631$	−23.6703	−0.942301	−0.471150	+	0.882053i	$0.656161\pi$
$632$	−43.1252	−1.71543
$633$	−72.0746	−2.86471
$634$	−40.2834	−1.59986
$635$	18.3998	0.730175
$636$	56.0446	2.22231
$637$	10.7905	0.427534
$638$	−3.64956	−0.144488
$639$	13.2822	0.525436
$640$	−9.93754	−0.392816
$641$	16.2775	0.642923	0.321462	−	0.946923i	$-0.395826\pi$
$641$	16.2775	0.642923	0.321462	+	0.946923i	$0.395826\pi$
$642$	32.4747	1.28167
$643$	25.2088	0.994137	0.497069	−	0.867711i	$-0.334410\pi$
$643$	25.2088	0.994137	0.497069	+	0.867711i	$0.334410\pi$
$644$	48.4674	1.90988
$645$	71.2634	2.80599
$646$	−28.2367	−1.11096
$647$	−34.8393	−1.36968	−0.684838	−	0.728695i	$-0.740127\pi$
$647$	−34.8393	−1.36968	−0.684838	+	0.728695i	$0.740127\pi$
$648$	−36.6717	−1.44060
$649$	10.7841	0.423313
$650$	−87.4529	−3.43019
$651$	33.5923	1.31659
$652$	11.0837	0.434071
$653$	17.7476	0.694518	0.347259	−	0.937769i	$-0.387112\pi$
$653$	17.7476	0.694518	0.347259	+	0.937769i	$0.387112\pi$
$654$	29.6227	1.15834
$655$	−19.6837	−0.769106
$656$	−39.6559	−1.54830
$657$	79.6104	3.10590
$658$	−29.8913	−1.16529
$659$	36.5761	1.42480	0.712400	−	0.701773i	$-0.247608\pi$
$659$	36.5761	1.42480	0.712400	+	0.701773i	$0.247608\pi$
$660$	−44.6356	−1.73744
$661$	−17.6954	−0.688270	−0.344135	−	0.938920i	$-0.611828\pi$
$661$	−17.6954	−0.688270	−0.344135	+	0.938920i	$0.611828\pi$
$662$	−28.2965	−1.09977
$663$	41.4799	1.61094
$664$	−48.8957	−1.89752
$665$	−43.3961	−1.68283
$666$	19.0380	0.737707
$667$	4.92448	0.190677
$668$	−54.8719	−2.12306
$669$	53.1626	2.05539
$670$	53.7789	2.07766
$671$	−6.79367	−0.262267
$672$	−80.9204	−3.12157
$673$	−14.3157	−0.551831	−0.275915	−	0.961182i	$-0.588981\pi$
$673$	−14.3157	−0.551831	−0.275915	+	0.961182i	$0.588981\pi$
$674$	57.8463	2.22816
$675$	43.2976	1.66652
$676$	97.3902	3.74578
$677$	21.3801	0.821703	0.410851	−	0.911702i	$-0.365232\pi$
$677$	21.3801	0.821703	0.410851	+	0.911702i	$0.365232\pi$
$678$	81.8886	3.14491
$679$	7.63197	0.292888
$680$	57.6756	2.21176
$681$	−46.6246	−1.78666
$682$	−9.79643	−0.375125
$683$	−35.6594	−1.36447	−0.682234	−	0.731134i	$-0.738991\pi$
$683$	−35.6594	−1.36447	−0.682234	+	0.731134i	$0.738991\pi$
$684$	116.840	4.46748
$685$	67.3684	2.57401
$686$	39.7326	1.51700
$687$	39.5262	1.50802
$688$	−67.3253	−2.56675
$689$	23.3429	0.889293
$690$	85.5732	3.25771
$691$	−9.21031	−0.350377	−0.175188	−	0.984535i	$-0.556053\pi$
$691$	−9.21031	−0.350377	−0.175188	+	0.984535i	$0.556053\pi$
$692$	51.7681	1.96793
$693$	16.1320	0.612805
$694$	30.1158	1.14318
$695$	−3.98501	−0.151160
$696$	−30.0669	−1.13968
$697$	−10.7040	−0.405443
$698$	−1.57213	−0.0595060
$699$	−64.4201	−2.43659
$700$	82.2887	3.11022
$701$	44.7666	1.69081	0.845405	−	0.534125i	$-0.179359\pi$
$701$	44.7666	1.69081	0.845405	+	0.534125i	$0.179359\pi$
$702$	−111.970	−4.22604
$703$	−5.85387	−0.220783
$704$	5.85344	0.220610
$705$	−37.1447	−1.39895
$706$	−64.0451	−2.41037
$707$	−57.1585	−2.14966
$708$	153.395	5.76494
$709$	−7.13427	−0.267933	−0.133966	−	0.990986i	$-0.542771\pi$
$709$	−7.13427	−0.267933	−0.133966	+	0.990986i	$0.542771\pi$
$710$	20.4638	0.767993
$711$	33.4402	1.25410
$712$	92.3170	3.45973
$713$	13.2187	0.495043
$714$	−55.4548	−2.07534
$715$	−18.5910	−0.695264
$716$	−42.5809	−1.59132
$717$	74.5464	2.78399
$718$	−89.4302	−3.33751
$719$	44.2741	1.65115	0.825573	−	0.564295i	$-0.190852\pi$
$719$	44.2741	1.65115	0.825573	+	0.564295i	$0.190852\pi$
$720$	−165.688	−6.17484
$721$	−8.87527	−0.330532
$722$	−1.67100	−0.0621881
$723$	51.2200	1.90489
$724$	−30.8332	−1.14591
$725$	8.36085	0.310514
$726$	76.3179	2.83242
$727$	47.0517	1.74505	0.872525	−	0.488569i	$-0.162481\pi$
$727$	47.0517	1.74505	0.872525	+	0.488569i	$0.162481\pi$
$728$	−123.254	−4.56808
$729$	−36.8649	−1.36537
$730$	122.655	4.53967
$731$	−18.1726	−0.672136
$732$	−96.6344	−3.57171
$733$	−30.4256	−1.12379	−0.561897	−	0.827207i	$-0.689928\pi$
$733$	−30.4256	−1.12379	−0.561897	+	0.827207i	$0.689928\pi$
$734$	−38.7178	−1.42910
$735$	−17.9264	−0.661226
$736$	−31.8424	−1.17373
$737$	6.14712	0.226432
$738$	62.9302	2.31649
$739$	−38.4087	−1.41289	−0.706444	−	0.707769i	$-0.749702\pi$
$739$	−38.4087	−1.41289	−0.706444	+	0.707769i	$0.749702\pi$
$740$	20.6443	0.758901
$741$	74.9847	2.75463
$742$	−31.2073	−1.14566
$743$	−15.4937	−0.568408	−0.284204	−	0.958764i	$-0.591729\pi$
$743$	−15.4937	−0.568408	−0.284204	+	0.958764i	$0.591729\pi$
$744$	−80.7080	−2.95890
$745$	−31.9414	−1.17024
$746$	−51.1421	−1.87245
$747$	37.9147	1.38723
$748$	11.3823	0.416179
$749$	−12.7272	−0.465040
$750$	20.3679	0.743731
$751$	−2.69838	−0.0984654	−0.0492327	−	0.998787i	$-0.515678\pi$
$751$	−2.69838	−0.0984654	−0.0492327	+	0.998787i	$0.515678\pi$
$752$	35.0920	1.27968
$753$	21.1071	0.769185
$754$	−21.6217	−0.787415
$755$	46.6903	1.69924
$756$	105.358	3.83184
$757$	35.4114	1.28705	0.643524	−	0.765426i	$-0.277472\pi$
$757$	35.4114	1.28705	0.643524	+	0.765426i	$0.277472\pi$
$758$	83.2287	3.02300
$759$	9.78132	0.355040
$760$	104.262	3.78199
$761$	−19.1536	−0.694316	−0.347158	−	0.937807i	$-0.612853\pi$
$761$	−19.1536	−0.694316	−0.347158	+	0.937807i	$0.612853\pi$
$762$	42.5048	1.53978
$763$	−11.6095	−0.420291
$764$	7.35521	0.266102
$765$	−44.7228	−1.61696
$766$	6.59162	0.238165
$767$	63.8899	2.30693
$768$	−57.9932	−2.09265
$769$	46.7088	1.68436	0.842181	−	0.539195i	$-0.181271\pi$
$769$	46.7088	1.68436	0.842181	+	0.539195i	$0.181271\pi$
$770$	24.8545	0.895693
$771$	11.8063	0.425192
$772$	102.916	3.70403
$773$	−54.9140	−1.97512	−0.987560	−	0.157244i	$-0.949739\pi$
$773$	−54.9140	−1.97512	−0.987560	+	0.157244i	$0.949739\pi$
$774$	106.839	3.84024
$775$	22.4428	0.806170
$776$	−18.3364	−0.658238
$777$	−11.4966	−0.412438
$778$	40.5550	1.45397
$779$	−19.3500	−0.693286
$780$	−264.442	−9.46854
$781$	2.33909	0.0836991
$782$	−21.8216	−0.780339
$783$	10.7048	0.382558
$784$	16.9358	0.604849
$785$	48.2253	1.72124
$786$	−45.4706	−1.62188
$787$	−11.5720	−0.412497	−0.206248	−	0.978500i	$-0.566125\pi$
$787$	−11.5720	−0.412497	−0.206248	+	0.978500i	$0.566125\pi$
$788$	−121.976	−4.34522
$789$	−26.8399	−0.955524
$790$	51.5210	1.83303
$791$	−32.0930	−1.14110
$792$	−38.7583	−1.37722
$793$	−40.2488	−1.42928
$794$	−56.1900	−1.99411
$795$	−38.7800	−1.37539
$796$	−17.0658	−0.604881
$797$	−44.8622	−1.58910	−0.794551	−	0.607197i	$-0.792294\pi$
$797$	−44.8622	−1.58910	−0.794551	+	0.607197i	$0.792294\pi$
$798$	−100.248	−3.54873
$799$	9.47210	0.335099
$800$	−54.0625	−1.91140
$801$	−71.5845	−2.52931
$802$	−71.5590	−2.52684
$803$	14.0199	0.494752
$804$	87.4379	3.08370
$805$	−33.5370	−1.18202
$806$	−58.0385	−2.04432
$807$	41.0561	1.44524
$808$	137.327	4.83116
$809$	22.6555	0.796525	0.398262	−	0.917272i	$-0.369613\pi$
$809$	22.6555	0.796525	0.398262	+	0.917272i	$0.369613\pi$
$810$	43.8111	1.53936
$811$	29.3201	1.02957	0.514784	−	0.857320i	$-0.327872\pi$
$811$	29.3201	1.02957	0.514784	+	0.857320i	$0.327872\pi$
$812$	20.3449	0.713965
$813$	−1.44505	−0.0506800
$814$	3.35272	0.117513
$815$	−7.66935	−0.268646
$816$	65.1032	2.27907
$817$	−32.8512	−1.14932
$818$	52.3043	1.82878
$819$	95.5734	3.33960
$820$	68.2400	2.38304
$821$	32.2558	1.12573	0.562867	−	0.826547i	$-0.309698\pi$
$821$	32.2558	1.12573	0.562867	+	0.826547i	$0.309698\pi$
$822$	155.625	5.42805
$823$	−38.2945	−1.33486	−0.667431	−	0.744672i	$-0.732606\pi$
$823$	−38.2945	−1.33486	−0.667431	+	0.744672i	$0.732606\pi$
$824$	21.3235	0.742839
$825$	16.6069	0.578177
$826$	−85.4150	−2.97197
$827$	36.9617	1.28528	0.642642	−	0.766167i	$-0.277838\pi$
$827$	36.9617	1.28528	0.642642	+	0.766167i	$0.277838\pi$
$828$	90.2950	3.13797
$829$	−7.47402	−0.259583	−0.129792	−	0.991541i	$-0.541431\pi$
$829$	−7.47402	−0.259583	−0.129792	+	0.991541i	$0.541431\pi$
$830$	58.4149	2.02761
$831$	−63.8250	−2.21406
$832$	34.6785	1.20226
$833$	4.57133	0.158387
$834$	−9.20562	−0.318765
$835$	37.9686	1.31396
$836$	20.5763	0.711645
$837$	28.7346	0.993214
$838$	−88.2629	−3.04899
$839$	43.2116	1.49183	0.745914	−	0.666042i	$-0.232013\pi$
$839$	43.2116	1.49183	0.745914	+	0.666042i	$0.232013\pi$
$840$	204.764	7.06502
$841$	−26.9329	−0.928720
$842$	84.8252	2.92327
$843$	−42.1679	−1.45234
$844$	−117.172	−4.03323
$845$	−67.3891	−2.31825
$846$	−55.6877	−1.91458
$847$	−29.9098	−1.02771
$848$	36.6370	1.25812
$849$	59.3481	2.03682
$850$	−37.0490	−1.27077
$851$	−4.52394	−0.155079
$852$	33.2716	1.13987
$853$	35.6850	1.22183	0.610916	−	0.791696i	$-0.290801\pi$
$853$	35.6850	1.22183	0.610916	+	0.791696i	$0.290801\pi$
$854$	53.8090	1.84130
$855$	−80.8471	−2.76491
$856$	30.5779	1.04513
$857$	−3.13430	−0.107066	−0.0535328	−	0.998566i	$-0.517048\pi$
$857$	−3.13430	−0.107066	−0.0535328	+	0.998566i	$0.517048\pi$
$858$	−42.9464	−1.46616
$859$	−21.4786	−0.732840	−0.366420	−	0.930449i	$-0.619417\pi$
$859$	−21.4786	−0.732840	−0.366420	+	0.930449i	$0.619417\pi$
$860$	115.853	3.95057
$861$	−38.0020	−1.29511
$862$	1.48620	0.0506201
$863$	10.0266	0.341311	0.170656	−	0.985331i	$-0.445411\pi$
$863$	10.0266	0.341311	0.170656	+	0.985331i	$0.445411\pi$
$864$	−69.2188	−2.35487
$865$	−35.8209	−1.21795
$866$	−46.0546	−1.56500
$867$	−32.1266	−1.09108
$868$	54.6112	1.85363
$869$	5.88904	0.199772
$870$	35.9205	1.21782
$871$	36.4184	1.23399
$872$	27.8926	0.944561
$873$	14.2184	0.481220
$874$	−39.4477	−1.33434
$875$	−7.98239	−0.269854
$876$	199.422	6.73784
$877$	−5.39700	−0.182244	−0.0911219	−	0.995840i	$-0.529045\pi$
$877$	−5.39700	−0.182244	−0.0911219	+	0.995840i	$0.529045\pi$
$878$	61.8851	2.08852
$879$	37.6677	1.27050
$880$	−29.1788	−0.983618
$881$	37.8173	1.27410	0.637049	−	0.770824i	$-0.280155\pi$
$881$	37.8173	1.27410	0.637049	+	0.770824i	$0.280155\pi$
$882$	−26.8755	−0.904944
$883$	−0.866436	−0.0291579	−0.0145789	−	0.999894i	$-0.504641\pi$
$883$	−0.866436	−0.0291579	−0.0145789	+	0.999894i	$0.504641\pi$
$884$	67.4341	2.26805
$885$	−106.142	−3.56791
$886$	36.6423	1.23102
$887$	−23.0548	−0.774103	−0.387052	−	0.922058i	$-0.626506\pi$
$887$	−23.0548	−0.774103	−0.387052	+	0.922058i	$0.626506\pi$
$888$	27.6214	0.926913
$889$	−16.6581	−0.558693
$890$	−110.290	−3.69692
$891$	5.00776	0.167766
$892$	86.4269	2.89379
$893$	17.1231	0.573002
$894$	−73.7866	−2.46779
$895$	29.4638	0.984867
$896$	8.99682	0.300563
$897$	57.9490	1.93486
$898$	94.2369	3.14473
$899$	5.54872	0.185060
$900$	153.304	5.11014
$901$	9.88911	0.329454
$902$	11.0824	0.369004
$903$	−64.5174	−2.14700
$904$	77.1057	2.56450
$905$	21.3350	0.709199
$906$	107.858	3.58333
$907$	−15.8261	−0.525499	−0.262749	−	0.964864i	$-0.584629\pi$
$907$	−15.8261	−0.525499	−0.262749	+	0.964864i	$0.584629\pi$
$908$	−75.7980	−2.51544
$909$	−106.486	−3.53193
$910$	147.249	4.88126
$911$	16.6557	0.551828	0.275914	−	0.961182i	$-0.411020\pi$
$911$	16.6557	0.551828	0.275914	+	0.961182i	$0.411020\pi$
$912$	117.689	3.89709
$913$	6.67703	0.220978
$914$	33.3464	1.10300
$915$	66.8661	2.21053
$916$	64.2580	2.12315
$917$	17.8204	0.588481
$918$	−47.4357	−1.56561
$919$	−8.51076	−0.280744	−0.140372	−	0.990099i	$-0.544830\pi$
$919$	−8.51076	−0.280744	−0.140372	+	0.990099i	$0.544830\pi$
$920$	80.5751	2.65648
$921$	16.4911	0.543399
$922$	57.5630	1.89573
$923$	13.8578	0.456136
$924$	40.4103	1.32940
$925$	−7.68080	−0.252543
$926$	8.11561	0.266695
$927$	−16.5347	−0.543070
$928$	−13.3663	−0.438770
$929$	−34.2283	−1.12299	−0.561496	−	0.827479i	$-0.689774\pi$
$929$	−34.2283	−1.12299	−0.561496	+	0.827479i	$0.689774\pi$
$930$	96.4205	3.16175
$931$	8.26377	0.270834
$932$	−104.728	−3.43049
$933$	6.85953	0.224571
$934$	−53.9258	−1.76451
$935$	−7.87599	−0.257573
$936$	−229.622	−7.50543
$937$	−33.5963	−1.09754	−0.548771	−	0.835973i	$-0.684904\pi$
$937$	−33.5963	−1.09754	−0.548771	+	0.835973i	$0.684904\pi$
$938$	−48.6880	−1.58972
$939$	40.7275	1.32909
$940$	−60.3864	−1.96959
$941$	−53.9227	−1.75783	−0.878915	−	0.476979i	$-0.841732\pi$
$941$	−53.9227	−1.75783	−0.878915	+	0.476979i	$0.841732\pi$
$942$	111.403	3.62972
$943$	−14.9539	−0.486966
$944$	100.276	3.26371
$945$	−72.9025	−2.37152
$946$	18.8150	0.611730
$947$	29.2505	0.950514	0.475257	−	0.879847i	$-0.342355\pi$
$947$	29.2505	0.950514	0.475257	+	0.879847i	$0.342355\pi$
$948$	83.7668	2.72062
$949$	83.0604	2.69625
$950$	−66.9749	−2.17295
$951$	45.3197	1.46959
$952$	−52.2158	−1.69233
$953$	37.5064	1.21495	0.607475	−	0.794339i	$-0.292183\pi$
$953$	37.5064	1.21495	0.607475	+	0.794339i	$0.292183\pi$
$954$	−58.1394	−1.88233
$955$	−5.08943	−0.164690
$956$	121.191	3.91958
$957$	4.10584	0.132723
$958$	−34.7609	−1.12307
$959$	−60.9911	−1.96950
$960$	−57.6120	−1.85942
$961$	−16.1057	−0.519539
$962$	19.8630	0.640410
$963$	−23.7108	−0.764068
$964$	83.2687	2.68191
$965$	−71.2126	−2.29242
$966$	−77.4725	−2.49264
$967$	39.0595	1.25607	0.628035	−	0.778185i	$-0.283859\pi$
$967$	39.0595	1.25607	0.628035	+	0.778185i	$0.283859\pi$
$968$	71.8604	2.30968
$969$	31.7669	1.02050
$970$	21.9062	0.703365
$971$	15.9465	0.511749	0.255874	−	0.966710i	$-0.417637\pi$
$971$	15.9465	0.511749	0.255874	+	0.966710i	$0.417637\pi$
$972$	−34.9286	−1.12034
$973$	3.60778	0.115660
$974$	−3.58352	−0.114824
$975$	98.3866	3.15089
$976$	−63.1710	−2.02205
$977$	4.19889	0.134334	0.0671672	−	0.997742i	$-0.478604\pi$
$977$	4.19889	0.134334	0.0671672	+	0.997742i	$0.478604\pi$
$978$	−17.7167	−0.566517
$979$	−12.6065	−0.402906
$980$	−29.1431	−0.930942
$981$	−21.6285	−0.690544
$982$	−67.1922	−2.14419
$983$	−42.1244	−1.34356	−0.671780	−	0.740751i	$-0.734470\pi$
$983$	−42.1244	−1.34356	−0.671780	+	0.740751i	$0.734470\pi$
$984$	91.3027	2.91062
$985$	84.4013	2.68925
$986$	−9.15992	−0.291711
$987$	33.6285	1.07041
$988$	121.903	3.87825
$989$	−25.3878	−0.807284
$990$	46.3040	1.47164
$991$	10.6138	0.337160	0.168580	−	0.985688i	$-0.446082\pi$
$991$	10.6138	0.337160	0.168580	+	0.985688i	$0.446082\pi$
$992$	−35.8788	−1.13915
$993$	31.8342	1.01023
$994$	−18.5266	−0.587629
$995$	11.8087	0.374360
$996$	94.9754	3.00941
$997$	39.4665	1.24992	0.624958	−	0.780658i	$-0.285116\pi$
$997$	39.4665	1.24992	0.624958	+	0.780658i	$0.285116\pi$
$998$	74.3976	2.35501
$999$	−9.83410	−0.311137

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6011.2.a.f.1.17	✓	275

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6011.2.a.f.1.17	✓	275	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:	\( N \)	\(=\)	\( 6011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6011.a (trivial)

\(f(q)\)	\(=\)	\(q-2.59860 q^{2} +2.92349 q^{3} +4.75274 q^{4} -3.28865 q^{5} -7.59699 q^{6} +2.97734 q^{7} -7.15327 q^{8} +5.54680 q^{9} +O(q^{10})\)	\(q-2.59860 q^{2} +2.92349 q^{3} +4.75274 q^{4} -3.28865 q^{5} -7.59699 q^{6} +2.97734 q^{7} -7.15327 q^{8} +5.54680 q^{9} +8.54591 q^{10} +0.976828 q^{11} +13.8946 q^{12} +5.78717 q^{13} -7.73692 q^{14} -9.61435 q^{15} +9.08305 q^{16} +2.45171 q^{17} -14.4139 q^{18} +4.43205 q^{19} -15.6301 q^{20} +8.70422 q^{21} -2.53839 q^{22} +3.42514 q^{23} -20.9125 q^{24} +5.81524 q^{25} -15.0386 q^{26} +7.44553 q^{27} +14.1505 q^{28} +1.43775 q^{29} +24.9839 q^{30} +3.85931 q^{31} -9.29668 q^{32} +2.85575 q^{33} -6.37102 q^{34} -9.79144 q^{35} +26.3625 q^{36} -1.32081 q^{37} -11.5171 q^{38} +16.9187 q^{39} +23.5246 q^{40} -4.36593 q^{41} -22.6188 q^{42} -7.41220 q^{43} +4.64261 q^{44} -18.2415 q^{45} -8.90057 q^{46} +3.86347 q^{47} +26.5542 q^{48} +1.86455 q^{49} -15.1115 q^{50} +7.16755 q^{51} +27.5049 q^{52} +4.03356 q^{53} -19.3480 q^{54} -3.21245 q^{55} -21.2977 q^{56} +12.9570 q^{57} -3.73614 q^{58} +11.0399 q^{59} -45.6945 q^{60} -6.95483 q^{61} -10.0288 q^{62} +16.5147 q^{63} +5.99230 q^{64} -19.0320 q^{65} -7.42095 q^{66} +6.29294 q^{67} +11.6523 q^{68} +10.0134 q^{69} +25.4441 q^{70} +2.39457 q^{71} -39.6778 q^{72} +14.3525 q^{73} +3.43225 q^{74} +17.0008 q^{75} +21.0644 q^{76} +2.90835 q^{77} -43.9651 q^{78} +6.02873 q^{79} -29.8710 q^{80} +5.12656 q^{81} +11.3453 q^{82} +6.83542 q^{83} +41.3689 q^{84} -8.06282 q^{85} +19.2614 q^{86} +4.20324 q^{87} -6.98752 q^{88} -12.9056 q^{89} +47.4024 q^{90} +17.2304 q^{91} +16.2788 q^{92} +11.2827 q^{93} -10.0396 q^{94} -14.5755 q^{95} -27.1788 q^{96} +2.56335 q^{97} -4.84522 q^{98} +5.41827 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 275 q + 16 q^{2} + 9 q^{3} + 316 q^{4} + 36 q^{5} + 30 q^{6} + 41 q^{7} + 36 q^{8} + 322 q^{9}+O(q^{10}) \) 275 * q + 16 * q^2 + 9 * q^3 + 316 * q^4 + 36 * q^5 + 30 * q^6 + 41 * q^7 + 36 * q^8 + 322 * q^9	\( 275 q + 16 q^{2} + 9 q^{3} + 316 q^{4} + 36 q^{5} + 30 q^{6} + 41 q^{7} + 36 q^{8} + 322 q^{9} + 44 q^{10} + 42 q^{11} + 26 q^{12} + 97 q^{13} + 24 q^{14} + 46 q^{15} + 386 q^{16} + 35 q^{17} + 47 q^{18} + 101 q^{19} + 60 q^{20} + 187 q^{21} + 72 q^{22} + 35 q^{23} + 73 q^{24} + 373 q^{25} + 21 q^{26} + 27 q^{27} + 97 q^{28} + 162 q^{29} + 13 q^{30} + 113 q^{31} + 58 q^{32} + 16 q^{33} + 52 q^{34} + 23 q^{35} + 426 q^{36} + 257 q^{37} + 8 q^{38} + 87 q^{39} + 126 q^{40} + 77 q^{41} - 7 q^{42} + 107 q^{43} + 133 q^{44} + 140 q^{45} + 207 q^{46} + 24 q^{47} + 4 q^{48} + 418 q^{49} + 65 q^{50} + 94 q^{51} + 142 q^{52} + 81 q^{53} + 79 q^{54} + 26 q^{55} + 62 q^{56} + 112 q^{57} + 44 q^{58} + 30 q^{59} + 83 q^{60} + 347 q^{61} + 5 q^{62} + 97 q^{63} + 508 q^{64} + 94 q^{65} + 4 q^{66} + 98 q^{67} + 28 q^{68} + 91 q^{69} + 17 q^{70} + 58 q^{71} + 99 q^{72} + 157 q^{73} + 80 q^{74} + 83 q^{75} + 264 q^{76} + 61 q^{77} + 5 q^{78} + 282 q^{79} + 49 q^{80} + 403 q^{81} + 46 q^{82} + 43 q^{83} + 318 q^{84} + 396 q^{85} + 57 q^{86} + 31 q^{87} + 180 q^{88} + 98 q^{89} + 67 q^{90} + 195 q^{91} + 97 q^{92} + 83 q^{93} + 96 q^{94} + 28 q^{95} + 127 q^{96} + 167 q^{97} + 24 q^{98} + 133 q^{99}+O(q^{100}) \) 275 * q + 16 * q^2 + 9 * q^3 + 316 * q^4 + 36 * q^5 + 30 * q^6 + 41 * q^7 + 36 * q^8 + 322 * q^9 + 44 * q^10 + 42 * q^11 + 26 * q^12 + 97 * q^13 + 24 * q^14 + 46 * q^15 + 386 * q^16 + 35 * q^17 + 47 * q^18 + 101 * q^19 + 60 * q^20 + 187 * q^21 + 72 * q^22 + 35 * q^23 + 73 * q^24 + 373 * q^25 + 21 * q^26 + 27 * q^27 + 97 * q^28 + 162 * q^29 + 13 * q^30 + 113 * q^31 + 58 * q^32 + 16 * q^33 + 52 * q^34 + 23 * q^35 + 426 * q^36 + 257 * q^37 + 8 * q^38 + 87 * q^39 + 126 * q^40 + 77 * q^41 - 7 * q^42 + 107 * q^43 + 133 * q^44 + 140 * q^45 + 207 * q^46 + 24 * q^47 + 4 * q^48 + 418 * q^49 + 65 * q^50 + 94 * q^51 + 142 * q^52 + 81 * q^53 + 79 * q^54 + 26 * q^55 + 62 * q^56 + 112 * q^57 + 44 * q^58 + 30 * q^59 + 83 * q^60 + 347 * q^61 + 5 * q^62 + 97 * q^63 + 508 * q^64 + 94 * q^65 + 4 * q^66 + 98 * q^67 + 28 * q^68 + 91 * q^69 + 17 * q^70 + 58 * q^71 + 99 * q^72 + 157 * q^73 + 80 * q^74 + 83 * q^75 + 264 * q^76 + 61 * q^77 + 5 * q^78 + 282 * q^79 + 49 * q^80 + 403 * q^81 + 46 * q^82 + 43 * q^83 + 318 * q^84 + 396 * q^85 + 57 * q^86 + 31 * q^87 + 180 * q^88 + 98 * q^89 + 67 * q^90 + 195 * q^91 + 97 * q^92 + 83 * q^93 + 96 * q^94 + 28 * q^95 + 127 * q^96 + 167 * q^97 + 24 * q^98 + 133 * q^99

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