LMFDB - Embedded newform 6017.2.a.e.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6017,2,Mod(1,6017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6017, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6017 = 11 \cdot 547 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6017.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:	$48.0459868962$
Analytic rank:	$0$
Dimension:	$119$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	6017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.59415 q^{2} -0.508113 q^{3} +4.72962 q^{4} +4.04973 q^{5} +1.31812 q^{6} +4.63801 q^{7} -7.08105 q^{8} -2.74182 q^{9} +O(q^{10})$	\(q-2.59415 q^{2} -0.508113 q^{3} +4.72962 q^{4} +4.04973 q^{5} +1.31812 q^{6} +4.63801 q^{7} -7.08105 q^{8} -2.74182 q^{9} -10.5056 q^{10} +1.00000 q^{11} -2.40318 q^{12} -2.35739 q^{13} -12.0317 q^{14} -2.05772 q^{15} +8.91006 q^{16} +6.35123 q^{17} +7.11270 q^{18} -1.01166 q^{19} +19.1537 q^{20} -2.35664 q^{21} -2.59415 q^{22} +5.45854 q^{23} +3.59797 q^{24} +11.4003 q^{25} +6.11541 q^{26} +2.91750 q^{27} +21.9360 q^{28} +0.689000 q^{29} +5.33804 q^{30} +6.50413 q^{31} -8.95196 q^{32} -0.508113 q^{33} -16.4761 q^{34} +18.7827 q^{35} -12.9678 q^{36} -10.2243 q^{37} +2.62441 q^{38} +1.19782 q^{39} -28.6763 q^{40} -0.278631 q^{41} +6.11347 q^{42} +4.24292 q^{43} +4.72962 q^{44} -11.1036 q^{45} -14.1603 q^{46} -12.8925 q^{47} -4.52732 q^{48} +14.5112 q^{49} -29.5742 q^{50} -3.22714 q^{51} -11.1495 q^{52} -1.20884 q^{53} -7.56842 q^{54} +4.04973 q^{55} -32.8420 q^{56} +0.514039 q^{57} -1.78737 q^{58} +10.4337 q^{59} -9.73225 q^{60} +13.1445 q^{61} -16.8727 q^{62} -12.7166 q^{63} +5.40260 q^{64} -9.54678 q^{65} +1.31812 q^{66} -8.04520 q^{67} +30.0389 q^{68} -2.77356 q^{69} -48.7252 q^{70} -15.9334 q^{71} +19.4150 q^{72} +4.06009 q^{73} +26.5234 q^{74} -5.79266 q^{75} -4.78478 q^{76} +4.63801 q^{77} -3.10732 q^{78} -1.53717 q^{79} +36.0834 q^{80} +6.74304 q^{81} +0.722812 q^{82} +1.08452 q^{83} -11.1460 q^{84} +25.7208 q^{85} -11.0068 q^{86} -0.350090 q^{87} -7.08105 q^{88} +10.5127 q^{89} +28.8045 q^{90} -10.9336 q^{91} +25.8168 q^{92} -3.30484 q^{93} +33.4452 q^{94} -4.09696 q^{95} +4.54861 q^{96} +10.1455 q^{97} -37.6442 q^{98} -2.74182 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 119 q + 15 q^{2} + 15 q^{3} + 133 q^{4} + 6 q^{5} + 16 q^{6} + 72 q^{7} + 39 q^{8} + 128 q^{9}+O(q^{10}) $ 119 * q + 15 * q^2 + 15 * q^3 + 133 * q^4 + 6 * q^5 + 16 * q^6 + 72 * q^7 + 39 * q^8 + 128 * q^9	\( 119 q + 15 q^{2} + 15 q^{3} + 133 q^{4} + 6 q^{5} + 16 q^{6} + 72 q^{7} + 39 q^{8} + 128 q^{9} + 22 q^{10} + 119 q^{11} + 40 q^{12} + 67 q^{13} + 3 q^{14} + 22 q^{15} + 145 q^{16} + 57 q^{17} + 53 q^{18} + 68 q^{19} + 25 q^{20} + 21 q^{21} + 15 q^{22} + 21 q^{23} + 34 q^{24} + 137 q^{25} + 10 q^{26} + 54 q^{27} + 149 q^{28} + 46 q^{29} + 10 q^{30} + 87 q^{31} + 58 q^{32} + 15 q^{33} + 16 q^{34} + 40 q^{35} + 137 q^{36} + 39 q^{37} + 27 q^{38} + 72 q^{39} + 46 q^{40} + 50 q^{41} - 4 q^{42} + 122 q^{43} + 133 q^{44} + 12 q^{45} + 22 q^{46} + 92 q^{47} + 9 q^{48} + 161 q^{49} + 2 q^{50} - 12 q^{51} + 177 q^{52} + 12 q^{53} + 19 q^{54} + 6 q^{55} - 16 q^{56} + 43 q^{57} + 56 q^{58} + 39 q^{59} + 27 q^{60} + 114 q^{61} + 66 q^{62} + 196 q^{63} + 161 q^{64} + 7 q^{65} + 16 q^{66} + 59 q^{67} + 139 q^{68} - 24 q^{69} + 9 q^{70} + 11 q^{71} + 92 q^{72} + 123 q^{73} + q^{74} + 19 q^{75} + 92 q^{76} + 72 q^{77} - 101 q^{78} + 78 q^{79} - 34 q^{80} + 139 q^{81} + 73 q^{82} + 108 q^{83} - 31 q^{84} + 30 q^{85} - 18 q^{86} + 164 q^{87} + 39 q^{88} + 15 q^{89} - 41 q^{90} + 60 q^{91} - 26 q^{92} - 2 q^{93} + 45 q^{94} + 75 q^{95} + 42 q^{96} + 73 q^{97} + 32 q^{98} + 128 q^{99}+O(q^{100}) \) 119 * q + 15 * q^2 + 15 * q^3 + 133 * q^4 + 6 * q^5 + 16 * q^6 + 72 * q^7 + 39 * q^8 + 128 * q^9 + 22 * q^10 + 119 * q^11 + 40 * q^12 + 67 * q^13 + 3 * q^14 + 22 * q^15 + 145 * q^16 + 57 * q^17 + 53 * q^18 + 68 * q^19 + 25 * q^20 + 21 * q^21 + 15 * q^22 + 21 * q^23 + 34 * q^24 + 137 * q^25 + 10 * q^26 + 54 * q^27 + 149 * q^28 + 46 * q^29 + 10 * q^30 + 87 * q^31 + 58 * q^32 + 15 * q^33 + 16 * q^34 + 40 * q^35 + 137 * q^36 + 39 * q^37 + 27 * q^38 + 72 * q^39 + 46 * q^40 + 50 * q^41 - 4 * q^42 + 122 * q^43 + 133 * q^44 + 12 * q^45 + 22 * q^46 + 92 * q^47 + 9 * q^48 + 161 * q^49 + 2 * q^50 - 12 * q^51 + 177 * q^52 + 12 * q^53 + 19 * q^54 + 6 * q^55 - 16 * q^56 + 43 * q^57 + 56 * q^58 + 39 * q^59 + 27 * q^60 + 114 * q^61 + 66 * q^62 + 196 * q^63 + 161 * q^64 + 7 * q^65 + 16 * q^66 + 59 * q^67 + 139 * q^68 - 24 * q^69 + 9 * q^70 + 11 * q^71 + 92 * q^72 + 123 * q^73 + q^74 + 19 * q^75 + 92 * q^76 + 72 * q^77 - 101 * q^78 + 78 * q^79 - 34 * q^80 + 139 * q^81 + 73 * q^82 + 108 * q^83 - 31 * q^84 + 30 * q^85 - 18 * q^86 + 164 * q^87 + 39 * q^88 + 15 * q^89 - 41 * q^90 + 60 * q^91 - 26 * q^92 - 2 * q^93 + 45 * q^94 + 75 * q^95 + 42 * q^96 + 73 * q^97 + 32 * q^98 + 128 * 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 $

$2$	−2.59415	−1.83434	−0.917171	−	0.398494i	$-0.869533\pi$
$2$	−2.59415	−1.83434	−0.917171	+	0.398494i	$0.869533\pi$
$3$	−0.508113	−0.293359	−0.146680	−	0.989184i	$-0.546859\pi$
$3$	−0.508113	−0.293359	−0.146680	+	0.989184i	$0.546859\pi$
$4$	4.72962	2.36481
$5$	4.04973	1.81110	0.905548	−	0.424244i	$-0.139460\pi$
$5$	4.04973	1.81110	0.905548	+	0.424244i	$0.139460\pi$
$6$	1.31812	0.538121
$7$	4.63801	1.75300	0.876502	−	0.481397i	$-0.159871\pi$
$7$	4.63801	1.75300	0.876502	+	0.481397i	$0.159871\pi$
$8$	−7.08105	−2.50353
$9$	−2.74182	−0.913940
$10$	−10.5056	−3.32217
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−2.40318	−0.693739
$13$	−2.35739	−0.653821	−0.326911	−	0.945055i	$-0.606008\pi$
$13$	−2.35739	−0.653821	−0.326911	+	0.945055i	$0.606008\pi$
$14$	−12.0317	−3.21561
$15$	−2.05772	−0.531302
$16$	8.91006	2.22752
$17$	6.35123	1.54040	0.770200	−	0.637803i	$-0.220156\pi$
$17$	6.35123	1.54040	0.770200	+	0.637803i	$0.220156\pi$
$18$	7.11270	1.67648
$19$	−1.01166	−0.232091	−0.116046	−	0.993244i	$-0.537022\pi$
$19$	−1.01166	−0.232091	−0.116046	+	0.993244i	$0.537022\pi$
$20$	19.1537	4.28290
$21$	−2.35664	−0.514260
$22$	−2.59415	−0.553075
$23$	5.45854	1.13819	0.569093	−	0.822273i	$-0.307295\pi$
$23$	5.45854	1.13819	0.569093	+	0.822273i	$0.307295\pi$
$24$	3.59797	0.734433
$25$	11.4003	2.28007
$26$	6.11541	1.19933
$27$	2.91750	0.561472
$28$	21.9360	4.14552
$29$	0.689000	0.127944	0.0639721	−	0.997952i	$-0.479623\pi$
$29$	0.689000	0.127944	0.0639721	+	0.997952i	$0.479623\pi$
$30$	5.33804	0.974589
$31$	6.50413	1.16818	0.584088	−	0.811690i	$-0.301452\pi$
$31$	6.50413	1.16818	0.584088	+	0.811690i	$0.301452\pi$
$32$	−8.95196	−1.58250
$33$	−0.508113	−0.0884512
$34$	−16.4761	−2.82562
$35$	18.7827	3.17486
$36$	−12.9678	−2.16130
$37$	−10.2243	−1.68086	−0.840431	−	0.541918i	$-0.817698\pi$
$37$	−10.2243	−1.68086	−0.840431	+	0.541918i	$0.817698\pi$
$38$	2.62441	0.425735
$39$	1.19782	0.191804
$40$	−28.6763	−4.53413
$41$	−0.278631	−0.0435149	−0.0217574	−	0.999763i	$-0.506926\pi$
$41$	−0.278631	−0.0435149	−0.0217574	+	0.999763i	$0.506926\pi$
$42$	6.11347	0.943329
$43$	4.24292	0.647040	0.323520	−	0.946221i	$-0.395134\pi$
$43$	4.24292	0.647040	0.323520	+	0.946221i	$0.395134\pi$
$44$	4.72962	0.713017
$45$	−11.1036	−1.65523
$46$	−14.1603	−2.08782
$47$	−12.8925	−1.88057	−0.940284	−	0.340391i	$-0.889441\pi$
$47$	−12.8925	−1.88057	−0.940284	+	0.340391i	$0.889441\pi$
$48$	−4.52732	−0.653462
$49$	14.5112	2.07303
$50$	−29.5742	−4.18242
$51$	−3.22714	−0.451891
$52$	−11.1495	−1.54616
$53$	−1.20884	−0.166047	−0.0830234	−	0.996548i	$-0.526458\pi$
$53$	−1.20884	−0.166047	−0.0830234	+	0.996548i	$0.526458\pi$
$54$	−7.56842	−1.02993
$55$	4.04973	0.546066
$56$	−32.8420	−4.38870
$57$	0.514039	0.0680862
$58$	−1.78737	−0.234693
$59$	10.4337	1.35835	0.679177	−	0.733975i	$-0.262337\pi$
$59$	10.4337	1.35835	0.679177	+	0.733975i	$0.262337\pi$
$60$	−9.73225	−1.25643
$61$	13.1445	1.68299	0.841493	−	0.540267i	$-0.181677\pi$
$61$	13.1445	1.68299	0.841493	+	0.540267i	$0.181677\pi$
$62$	−16.8727	−2.14284
$63$	−12.7166	−1.60214
$64$	5.40260	0.675326
$65$	−9.54678	−1.18413
$66$	1.31812	0.162250
$67$	−8.04520	−0.982878	−0.491439	−	0.870912i	$-0.663529\pi$
$67$	−8.04520	−0.982878	−0.491439	+	0.870912i	$0.663529\pi$
$68$	30.0389	3.64275
$69$	−2.77356	−0.333897
$70$	−48.7252	−5.82378
$71$	−15.9334	−1.89094	−0.945472	−	0.325703i	$-0.894399\pi$
$71$	−15.9334	−1.89094	−0.945472	+	0.325703i	$0.894399\pi$
$72$	19.4150	2.28807
$73$	4.06009	0.475197	0.237599	−	0.971363i	$-0.423640\pi$
$73$	4.06009	0.475197	0.237599	+	0.971363i	$0.423640\pi$
$74$	26.5234	3.08328
$75$	−5.79266	−0.668879
$76$	−4.78478	−0.548852
$77$	4.63801	0.528551
$78$	−3.10732	−0.351835
$79$	−1.53717	−0.172945	−0.0864725	−	0.996254i	$-0.527559\pi$
$79$	−1.53717	−0.172945	−0.0864725	+	0.996254i	$0.527559\pi$
$80$	36.0834	4.03424
$81$	6.74304	0.749227
$82$	0.722812	0.0798212
$83$	1.08452	0.119042	0.0595209	−	0.998227i	$-0.481043\pi$
$83$	1.08452	0.119042	0.0595209	+	0.998227i	$0.481043\pi$
$84$	−11.1460	−1.21613
$85$	25.7208	2.78981
$86$	−11.0068	−1.18689
$87$	−0.350090	−0.0375336
$88$	−7.08105	−0.754842
$89$	10.5127	1.11434	0.557172	−	0.830397i	$-0.311886\pi$
$89$	10.5127	1.11434	0.557172	+	0.830397i	$0.311886\pi$
$90$	28.8045	3.03626
$91$	−10.9336	−1.14615
$92$	25.8168	2.69159
$93$	−3.30484	−0.342696
$94$	33.4452	3.44960
$95$	−4.09696	−0.420340
$96$	4.54861	0.464240
$97$	10.1455	1.03012	0.515058	−	0.857155i	$-0.327770\pi$
$97$	10.1455	1.03012	0.515058	+	0.857155i	$0.327770\pi$
$98$	−37.6442	−3.80264
$99$	−2.74182	−0.275563
$100$	53.9192	5.39192
$101$	−7.14911	−0.711363	−0.355681	−	0.934607i	$-0.615751\pi$
$101$	−7.14911	−0.711363	−0.355681	+	0.934607i	$0.615751\pi$
$102$	8.37170	0.828922
$103$	−0.125733	−0.0123888	−0.00619442	−	0.999981i	$-0.501972\pi$
$103$	−0.125733	−0.0123888	−0.00619442	+	0.999981i	$0.501972\pi$
$104$	16.6928	1.63686
$105$	−9.54375	−0.931374
$106$	3.13591	0.304587
$107$	18.1556	1.75517	0.877583	−	0.479425i	$-0.159155\pi$
$107$	18.1556	1.75517	0.877583	+	0.479425i	$0.159155\pi$
$108$	13.7986	1.32778
$109$	−10.0616	−0.963726	−0.481863	−	0.876246i	$-0.660040\pi$
$109$	−10.0616	−0.963726	−0.481863	+	0.876246i	$0.660040\pi$
$110$	−10.5056	−1.00167
$111$	5.19510	0.493097
$112$	41.3250	3.90485
$113$	−13.9261	−1.31006	−0.655029	−	0.755603i	$-0.727344\pi$
$113$	−13.9261	−1.31006	−0.655029	+	0.755603i	$0.727344\pi$
$114$	−1.33350	−0.124893
$115$	22.1056	2.06136
$116$	3.25871	0.302564
$117$	6.46353	0.597553
$118$	−27.0666	−2.49168
$119$	29.4571	2.70033
$120$	14.5708	1.33013
$121$	1.00000	0.0909091
$122$	−34.0989	−3.08717
$123$	0.141576	0.0127655
$124$	30.7621	2.76252
$125$	25.9196	2.31832
$126$	32.9888	2.93888
$127$	−1.19322	−0.105881	−0.0529404	−	0.998598i	$-0.516859\pi$
$127$	−1.19322	−0.105881	−0.0529404	+	0.998598i	$0.516859\pi$
$128$	3.88874	0.343720
$129$	−2.15589	−0.189815
$130$	24.7658	2.17210
$131$	2.30692	0.201557	0.100778	−	0.994909i	$-0.467867\pi$
$131$	2.30692	0.201557	0.100778	+	0.994909i	$0.467867\pi$
$132$	−2.40318	−0.209170
$133$	−4.69211	−0.406857
$134$	20.8705	1.80293
$135$	11.8151	1.01688
$136$	−44.9734	−3.85643
$137$	−14.0621	−1.20141	−0.600703	−	0.799472i	$-0.705112\pi$
$137$	−14.0621	−1.20141	−0.600703	+	0.799472i	$0.705112\pi$
$138$	7.19503	0.612482
$139$	−10.2012	−0.865251	−0.432626	−	0.901574i	$-0.642413\pi$
$139$	−10.2012	−0.865251	−0.432626	+	0.901574i	$0.642413\pi$
$140$	88.8351	7.50794
$141$	6.55086	0.551682
$142$	41.3336	3.46864
$143$	−2.35739	−0.197134
$144$	−24.4298	−2.03582
$145$	2.79027	0.231719
$146$	−10.5325	−0.871674
$147$	−7.37332	−0.608141
$148$	−48.3570	−3.97492
$149$	9.05097	0.741484	0.370742	−	0.928736i	$-0.379103\pi$
$149$	9.05097	0.741484	0.370742	+	0.928736i	$0.379103\pi$
$150$	15.0270	1.22695
$151$	−1.46803	−0.119467	−0.0597335	−	0.998214i	$-0.519025\pi$
$151$	−1.46803	−0.119467	−0.0597335	+	0.998214i	$0.519025\pi$
$152$	7.16363	0.581047
$153$	−17.4139	−1.40783
$154$	−12.0317	−0.969543
$155$	26.3400	2.11568
$156$	5.66523	0.453581
$157$	14.2216	1.13501	0.567505	−	0.823370i	$-0.307909\pi$
$157$	14.2216	1.13501	0.567505	+	0.823370i	$0.307909\pi$
$158$	3.98765	0.317240
$159$	0.614227	0.0487114
$160$	−36.2530	−2.86605
$161$	25.3168	1.99524
$162$	−17.4925	−1.37434
$163$	19.7976	1.55067	0.775334	−	0.631551i	$-0.217582\pi$
$163$	19.7976	1.55067	0.775334	+	0.631551i	$0.217582\pi$
$164$	−1.31782	−0.102904
$165$	−2.05772	−0.160193
$166$	−2.81341	−0.218363
$167$	−19.7572	−1.52885	−0.764427	−	0.644710i	$-0.776978\pi$
$167$	−19.7572	−1.52885	−0.764427	+	0.644710i	$0.776978\pi$
$168$	16.6875	1.28746
$169$	−7.44273	−0.572518
$170$	−66.7236	−5.11747
$171$	2.77380	0.212118
$172$	20.0674	1.53013
$173$	−8.33109	−0.633401	−0.316701	−	0.948526i	$-0.602575\pi$
$173$	−8.33109	−0.633401	−0.316701	+	0.948526i	$0.602575\pi$
$174$	0.908187	0.0688494
$175$	52.8749	3.99697
$176$	8.91006	0.671621
$177$	−5.30151	−0.398486
$178$	−27.2715	−2.04409
$179$	−20.1158	−1.50352	−0.751761	−	0.659435i	$-0.770795\pi$
$179$	−20.1158	−1.50352	−0.751761	+	0.659435i	$0.770795\pi$
$180$	−52.5160	−3.91431
$181$	−9.64668	−0.717032	−0.358516	−	0.933524i	$-0.616717\pi$
$181$	−9.64668	−0.717032	−0.358516	+	0.933524i	$0.616717\pi$
$182$	28.3634	2.10243
$183$	−6.67892	−0.493720
$184$	−38.6522	−2.84948
$185$	−41.4056	−3.04420
$186$	8.57325	0.628621
$187$	6.35123	0.464448
$188$	−60.9767	−4.44719
$189$	13.5314	0.984263
$190$	10.6281	0.771047
$191$	−22.4584	−1.62504	−0.812518	−	0.582937i	$-0.801904\pi$
$191$	−22.4584	−1.62504	−0.812518	+	0.582937i	$0.801904\pi$
$192$	−2.74513	−0.198113
$193$	23.1862	1.66898	0.834488	−	0.551026i	$-0.185764\pi$
$193$	23.1862	1.66898	0.834488	+	0.551026i	$0.185764\pi$
$194$	−26.3189	−1.88959
$195$	4.85084	0.347376
$196$	68.6324	4.90231
$197$	20.3064	1.44677	0.723385	−	0.690445i	$-0.242585\pi$
$197$	20.3064	1.44677	0.723385	+	0.690445i	$0.242585\pi$
$198$	7.11270	0.505477
$199$	6.84104	0.484948	0.242474	−	0.970158i	$-0.422041\pi$
$199$	6.84104	0.484948	0.242474	+	0.970158i	$0.422041\pi$
$200$	−80.7263	−5.70821
$201$	4.08787	0.288336
$202$	18.5459	1.30488
$203$	3.19559	0.224287
$204$	−15.2632	−1.06864
$205$	−1.12838	−0.0788096
$206$	0.326170	0.0227254
$207$	−14.9664	−1.04023
$208$	−21.0045	−1.45640
$209$	−1.01166	−0.0699782
$210$	24.7579	1.70846
$211$	20.2855	1.39651	0.698257	−	0.715848i	$-0.253959\pi$
$211$	20.2855	1.39651	0.698257	+	0.715848i	$0.253959\pi$
$212$	−5.71735	−0.392669
$213$	8.09596	0.554726
$214$	−47.0983	−3.21957
$215$	17.1827	1.17185
$216$	−20.6589	−1.40566
$217$	30.1663	2.04782
$218$	26.1013	1.76780
$219$	−2.06298	−0.139403
$220$	19.1537	1.29134
$221$	−14.9723	−1.00715
$222$	−13.4769	−0.904508
$223$	11.6527	0.780320	0.390160	−	0.920747i	$-0.372420\pi$
$223$	11.6527	0.780320	0.390160	+	0.920747i	$0.372420\pi$
$224$	−41.5193	−2.77413
$225$	−31.2577	−2.08384
$226$	36.1264	2.40310
$227$	−16.6195	−1.10308	−0.551538	−	0.834150i	$-0.685959\pi$
$227$	−16.6195	−1.10308	−0.551538	+	0.834150i	$0.685959\pi$
$228$	2.43121	0.161011
$229$	2.72226	0.179892	0.0899459	−	0.995947i	$-0.471331\pi$
$229$	2.72226	0.179892	0.0899459	+	0.995947i	$0.471331\pi$
$230$	−57.3454	−3.78124
$231$	−2.35664	−0.155055
$232$	−4.87884	−0.320312
$233$	−6.17858	−0.404772	−0.202386	−	0.979306i	$-0.564870\pi$
$233$	−6.17858	−0.404772	−0.202386	+	0.979306i	$0.564870\pi$
$234$	−16.7674	−1.09612
$235$	−52.2113	−3.40589
$236$	49.3475	3.21225
$237$	0.781056	0.0507350
$238$	−76.4162	−4.95332
$239$	0.288685	0.0186735	0.00933675	−	0.999956i	$-0.497028\pi$
$239$	0.288685	0.0186735	0.00933675	+	0.999956i	$0.497028\pi$
$240$	−18.3344	−1.18348
$241$	19.9409	1.28451	0.642253	−	0.766493i	$-0.278000\pi$
$241$	19.9409	1.28451	0.642253	+	0.766493i	$0.278000\pi$
$242$	−2.59415	−0.166758
$243$	−12.1787	−0.781265
$244$	62.1687	3.97994
$245$	58.7664	3.75445
$246$	−0.367270	−0.0234163
$247$	2.38488	0.151746
$248$	−46.0561	−2.92456
$249$	−0.551060	−0.0349220
$250$	−67.2394	−4.25260
$251$	−18.9461	−1.19587	−0.597935	−	0.801544i	$-0.704012\pi$
$251$	−18.9461	−1.19587	−0.597935	+	0.801544i	$0.704012\pi$
$252$	−60.1447	−3.78876
$253$	5.45854	0.343176
$254$	3.09538	0.194222
$255$	−13.0691	−0.818417
$256$	−20.8932	−1.30582
$257$	−8.76710	−0.546876	−0.273438	−	0.961890i	$-0.588161\pi$
$257$	−8.76710	−0.546876	−0.273438	+	0.961890i	$0.588161\pi$
$258$	5.59269	0.348186
$259$	−47.4204	−2.94656
$260$	−45.1526	−2.80025
$261$	−1.88912	−0.116933
$262$	−5.98450	−0.369724
$263$	10.7673	0.663939	0.331969	−	0.943290i	$-0.392287\pi$
$263$	10.7673	0.663939	0.331969	+	0.943290i	$0.392287\pi$
$264$	3.59797	0.221440
$265$	−4.89547	−0.300727
$266$	12.1720	0.746315
$267$	−5.34164	−0.326903
$268$	−38.0507	−2.32432
$269$	16.2880	0.993099	0.496550	−	0.868008i	$-0.334600\pi$
$269$	16.2880	0.993099	0.496550	+	0.868008i	$0.334600\pi$
$270$	−30.6501	−1.86531
$271$	24.3371	1.47837	0.739187	−	0.673500i	$-0.235210\pi$
$271$	24.3371	1.47837	0.739187	+	0.673500i	$0.235210\pi$
$272$	56.5899	3.43126
$273$	5.55550	0.336234
$274$	36.4792	2.20379
$275$	11.4003	0.687466
$276$	−13.1179	−0.789603
$277$	−19.6149	−1.17855	−0.589273	−	0.807934i	$-0.700586\pi$
$277$	−19.6149	−1.17855	−0.589273	+	0.807934i	$0.700586\pi$
$278$	26.4634	1.58717
$279$	−17.8332	−1.06764
$280$	−133.001	−7.94835
$281$	0.479773	0.0286208	0.0143104	−	0.999898i	$-0.495445\pi$
$281$	0.479773	0.0286208	0.0143104	+	0.999898i	$0.495445\pi$
$282$	−16.9939	−1.01197
$283$	−4.56541	−0.271385	−0.135693	−	0.990751i	$-0.543326\pi$
$283$	−4.56541	−0.271385	−0.135693	+	0.990751i	$0.543326\pi$
$284$	−75.3588	−4.47172
$285$	2.08172	0.123311
$286$	6.11541	0.361612
$287$	−1.29230	−0.0762818
$288$	24.5447	1.44631
$289$	23.3381	1.37283
$290$	−7.23837	−0.425052
$291$	−5.15505	−0.302194
$292$	19.2027	1.12375
$293$	−11.7302	−0.685283	−0.342641	−	0.939466i	$-0.611322\pi$
$293$	−11.7302	−0.685283	−0.342641	+	0.939466i	$0.611322\pi$
$294$	19.1275	1.11554
$295$	42.2537	2.46011
$296$	72.3987	4.20809
$297$	2.91750	0.169290
$298$	−23.4796	−1.36014
$299$	−12.8679	−0.744169
$300$	−27.3971	−1.58177
$301$	19.6787	1.13426
$302$	3.80830	0.219143
$303$	3.63256	0.208685
$304$	−9.01398	−0.516987
$305$	53.2319	3.04805
$306$	45.1744	2.58245
$307$	12.3080	0.702454	0.351227	−	0.936290i	$-0.385764\pi$
$307$	12.3080	0.702454	0.351227	+	0.936290i	$0.385764\pi$
$308$	21.9360	1.24992
$309$	0.0638866	0.00363438
$310$	−68.3299	−3.88088
$311$	19.6650	1.11510	0.557549	−	0.830144i	$-0.311742\pi$
$311$	19.6650	1.11510	0.557549	+	0.830144i	$0.311742\pi$
$312$	−8.48181	−0.480188
$313$	−27.7705	−1.56968	−0.784841	−	0.619698i	$-0.787255\pi$
$313$	−27.7705	−1.56968	−0.784841	+	0.619698i	$0.787255\pi$
$314$	−36.8930	−2.08200
$315$	−51.4989	−2.90163
$316$	−7.27022	−0.408982
$317$	17.8963	1.00516	0.502578	−	0.864532i	$-0.332385\pi$
$317$	17.8963	1.00516	0.502578	+	0.864532i	$0.332385\pi$
$318$	−1.59340	−0.0893533
$319$	0.689000	0.0385766
$320$	21.8791	1.22308
$321$	−9.22509	−0.514894
$322$	−65.6756	−3.65996
$323$	−6.42530	−0.357514
$324$	31.8920	1.77178
$325$	−26.8750	−1.49076
$326$	−51.3580	−2.84445
$327$	5.11243	0.282718
$328$	1.97300	0.108941
$329$	−59.7957	−3.29664
$330$	5.33804	0.293850
$331$	2.71631	0.149302	0.0746508	−	0.997210i	$-0.476216\pi$
$331$	2.71631	0.149302	0.0746508	+	0.997210i	$0.476216\pi$
$332$	5.12938	0.281511
$333$	28.0332	1.53621
$334$	51.2530	2.80444
$335$	−32.5809	−1.78008
$336$	−20.9978	−1.14552
$337$	−0.934893	−0.0509268	−0.0254634	−	0.999676i	$-0.508106\pi$
$337$	−0.934893	−0.0509268	−0.0254634	+	0.999676i	$0.508106\pi$
$338$	19.3076	1.05019
$339$	7.07604	0.384318
$340$	121.650	6.59737
$341$	6.50413	0.352219
$342$	−7.19565	−0.389096
$343$	34.8370	1.88102
$344$	−30.0443	−1.61988
$345$	−11.2322	−0.604720
$346$	21.6121	1.16187
$347$	23.0207	1.23582	0.617908	−	0.786251i	$-0.287981\pi$
$347$	23.0207	1.23582	0.617908	+	0.786251i	$0.287981\pi$
$348$	−1.65579	−0.0887598
$349$	−27.6667	−1.48096	−0.740481	−	0.672077i	$-0.765402\pi$
$349$	−27.6667	−1.48096	−0.740481	+	0.672077i	$0.765402\pi$
$350$	−137.165	−7.33180
$351$	−6.87766	−0.367102
$352$	−8.95196	−0.477141
$353$	−18.2488	−0.971287	−0.485644	−	0.874157i	$-0.661415\pi$
$353$	−18.2488	−0.971287	−0.485644	+	0.874157i	$0.661415\pi$
$354$	13.7529	0.730959
$355$	−64.5259	−3.42468
$356$	49.7211	2.63521
$357$	−14.9675	−0.792166
$358$	52.1833	2.75797
$359$	−17.8825	−0.943804	−0.471902	−	0.881651i	$-0.656432\pi$
$359$	−17.8825	−0.943804	−0.471902	+	0.881651i	$0.656432\pi$
$360$	78.6254	4.14392
$361$	−17.9765	−0.946134
$362$	25.0249	1.31528
$363$	−0.508113	−0.0266690
$364$	−51.7117	−2.71043
$365$	16.4423	0.860627
$366$	17.3261	0.905651
$367$	21.4434	1.11934	0.559668	−	0.828717i	$-0.310929\pi$
$367$	21.4434	1.11934	0.559668	+	0.828717i	$0.310929\pi$
$368$	48.6360	2.53533
$369$	0.763957	0.0397700
$370$	107.412	5.58411
$371$	−5.60661	−0.291081
$372$	−15.6306	−0.810410
$373$	30.9108	1.60050	0.800250	−	0.599666i	$-0.204700\pi$
$373$	30.9108	1.60050	0.800250	+	0.599666i	$0.204700\pi$
$374$	−16.4761	−0.851956
$375$	−13.1701	−0.680101
$376$	91.2926	4.70805
$377$	−1.62424	−0.0836526
$378$	−35.1025	−1.80548
$379$	7.68443	0.394723	0.197361	−	0.980331i	$-0.436763\pi$
$379$	7.68443	0.394723	0.197361	+	0.980331i	$0.436763\pi$
$380$	−19.3771	−0.994023
$381$	0.606289	0.0310611
$382$	58.2606	2.98087
$383$	−11.8901	−0.607557	−0.303779	−	0.952743i	$-0.598248\pi$
$383$	−11.8901	−0.607557	−0.303779	+	0.952743i	$0.598248\pi$
$384$	−1.97592	−0.100833
$385$	18.7827	0.957256
$386$	−60.1484	−3.06147
$387$	−11.6333	−0.591356
$388$	47.9842	2.43603
$389$	−27.6484	−1.40183	−0.700914	−	0.713246i	$-0.747224\pi$
$389$	−27.6484	−1.40183	−0.700914	+	0.713246i	$0.747224\pi$
$390$	−12.5838	−0.637207
$391$	34.6685	1.75326
$392$	−102.754	−5.18988
$393$	−1.17218	−0.0591285
$394$	−52.6778	−2.65387
$395$	−6.22512	−0.313220
$396$	−12.9678	−0.651655
$397$	11.3198	0.568126	0.284063	−	0.958806i	$-0.408317\pi$
$397$	11.3198	0.568126	0.284063	+	0.958806i	$0.408317\pi$
$398$	−17.7467	−0.889561
$399$	2.38412	0.119355
$400$	101.578	5.07888
$401$	14.4060	0.719400	0.359700	−	0.933068i	$-0.382879\pi$
$401$	14.4060	0.719400	0.359700	+	0.933068i	$0.382879\pi$
$402$	−10.6046	−0.528907
$403$	−15.3327	−0.763779
$404$	−33.8126	−1.68224
$405$	27.3075	1.35692
$406$	−8.28985	−0.411418
$407$	−10.2243	−0.506799
$408$	22.8516	1.13132
$409$	−23.0962	−1.14203	−0.571016	−	0.820939i	$-0.693450\pi$
$409$	−23.0962	−1.14203	−0.571016	+	0.820939i	$0.693450\pi$
$410$	2.92719	0.144564
$411$	7.14513	0.352444
$412$	−0.594669	−0.0292972
$413$	48.3917	2.38120
$414$	38.8250	1.90814
$415$	4.39203	0.215596
$416$	21.1032	1.03467
$417$	5.18334	0.253829
$418$	2.62441	0.128364
$419$	−12.6051	−0.615800	−0.307900	−	0.951419i	$-0.599626\pi$
$419$	−12.6051	−0.615800	−0.307900	+	0.951419i	$0.599626\pi$
$420$	−45.1383	−2.20252
$421$	−9.66519	−0.471052	−0.235526	−	0.971868i	$-0.575681\pi$
$421$	−9.66519	−0.471052	−0.235526	+	0.971868i	$0.575681\pi$
$422$	−52.6237	−2.56168
$423$	35.3490	1.71873
$424$	8.55984	0.415703
$425$	72.4061	3.51221
$426$	−21.0021	−1.01756
$427$	60.9646	2.95028
$428$	85.8690	4.15063
$429$	1.19782	0.0578312
$430$	−44.5745	−2.14958
$431$	−3.08792	−0.148740	−0.0743699	−	0.997231i	$-0.523695\pi$
$431$	−3.08792	−0.148740	−0.0743699	+	0.997231i	$0.523695\pi$
$432$	25.9951	1.25069
$433$	−19.5148	−0.937820	−0.468910	−	0.883246i	$-0.655353\pi$
$433$	−19.5148	−0.937820	−0.468910	+	0.883246i	$0.655353\pi$
$434$	−78.2559	−3.75640
$435$	−1.41777	−0.0679769
$436$	−47.5875	−2.27903
$437$	−5.52221	−0.264163
$438$	5.35169	0.255714
$439$	−5.29969	−0.252940	−0.126470	−	0.991970i	$-0.540365\pi$
$439$	−5.29969	−0.252940	−0.126470	+	0.991970i	$0.540365\pi$
$440$	−28.6763	−1.36709
$441$	−39.7871	−1.89462
$442$	38.8404	1.84745
$443$	13.8119	0.656224	0.328112	−	0.944639i	$-0.393588\pi$
$443$	13.8119	0.656224	0.328112	+	0.944639i	$0.393588\pi$
$444$	24.5708	1.16608
$445$	42.5736	2.01818
$446$	−30.2288	−1.43137
$447$	−4.59892	−0.217521
$448$	25.0574	1.18385
$449$	−21.6457	−1.02153	−0.510763	−	0.859722i	$-0.670637\pi$
$449$	−21.6457	−1.02153	−0.510763	+	0.859722i	$0.670637\pi$
$450$	81.0871	3.82248
$451$	−0.278631	−0.0131202
$452$	−65.8652	−3.09804
$453$	0.745928	0.0350468
$454$	43.1135	2.02342
$455$	−44.2781	−2.07579
$456$	−3.63994	−0.170456
$457$	32.3583	1.51366	0.756829	−	0.653613i	$-0.226747\pi$
$457$	32.3583	1.51366	0.756829	+	0.653613i	$0.226747\pi$
$458$	−7.06194	−0.329983
$459$	18.5297	0.864892
$460$	104.551	4.87473
$461$	−10.3489	−0.481995	−0.240997	−	0.970526i	$-0.577475\pi$
$461$	−10.3489	−0.481995	−0.240997	+	0.970526i	$0.577475\pi$
$462$	6.11347	0.284424
$463$	7.47718	0.347494	0.173747	−	0.984790i	$-0.444413\pi$
$463$	7.47718	0.347494	0.173747	+	0.984790i	$0.444413\pi$
$464$	6.13903	0.284998
$465$	−13.3837	−0.620654
$466$	16.0282	0.742491
$467$	−22.0377	−1.01978	−0.509891	−	0.860239i	$-0.670314\pi$
$467$	−22.0377	−1.01978	−0.509891	+	0.860239i	$0.670314\pi$
$468$	30.5700	1.41310
$469$	−37.3138	−1.72299
$470$	135.444	6.24756
$471$	−7.22620	−0.332966
$472$	−73.8816	−3.40068
$473$	4.24292	0.195090
$474$	−2.02618	−0.0930653
$475$	−11.5333	−0.529184
$476$	139.321	6.38576
$477$	3.31442	0.151757
$478$	−0.748893	−0.0342536
$479$	−15.4424	−0.705581	−0.352791	−	0.935702i	$-0.614767\pi$
$479$	−15.4424	−0.705581	−0.352791	+	0.935702i	$0.614767\pi$
$480$	18.4206	0.840784
$481$	24.1026	1.09898
$482$	−51.7297	−2.35622
$483$	−12.8638	−0.585323
$484$	4.72962	0.214983
$485$	41.0864	1.86564
$486$	31.5934	1.43311
$487$	−33.7292	−1.52842	−0.764209	−	0.644969i	$-0.776870\pi$
$487$	−33.7292	−1.52842	−0.764209	+	0.644969i	$0.776870\pi$
$488$	−93.0771	−4.21340
$489$	−10.0594	−0.454903
$490$	−152.449	−6.88694
$491$	−2.49801	−0.112734	−0.0563669	−	0.998410i	$-0.517952\pi$
$491$	−2.49801	−0.112734	−0.0563669	+	0.998410i	$0.517952\pi$
$492$	0.669602	0.0301880
$493$	4.37600	0.197085
$494$	−6.18674	−0.278354
$495$	−11.1036	−0.499072
$496$	57.9522	2.60213
$497$	−73.8992	−3.31483
$498$	1.42953	0.0640589
$499$	−15.8958	−0.711593	−0.355797	−	0.934563i	$-0.615790\pi$
$499$	−15.8958	−0.711593	−0.355797	+	0.934563i	$0.615790\pi$
$500$	122.590	5.48239
$501$	10.0389	0.448504
$502$	49.1492	2.19363
$503$	−20.1702	−0.899346	−0.449673	−	0.893193i	$-0.648459\pi$
$503$	−20.1702	−0.899346	−0.449673	+	0.893193i	$0.648459\pi$
$504$	90.0469	4.01101
$505$	−28.9520	−1.28835
$506$	−14.1603	−0.629502
$507$	3.78175	0.167954
$508$	−5.64346	−0.250388
$509$	−2.48946	−0.110343	−0.0551716	−	0.998477i	$-0.517571\pi$
$509$	−2.48946	−0.110343	−0.0551716	+	0.998477i	$0.517571\pi$
$510$	33.9031	1.50126
$511$	18.8307	0.833023
$512$	46.4226	2.05161
$513$	−2.95152	−0.130313
$514$	22.7432	1.00316
$515$	−0.509185	−0.0224374
$516$	−10.1965	−0.448877
$517$	−12.8925	−0.567013
$518$	123.016	5.40500
$519$	4.23314	0.185814
$520$	67.6012	2.96451
$521$	−12.9522	−0.567445	−0.283723	−	0.958906i	$-0.591569\pi$
$521$	−12.9522	−0.567445	−0.283723	+	0.958906i	$0.591569\pi$
$522$	4.90065	0.214496
$523$	−3.92643	−0.171691	−0.0858453	−	0.996308i	$-0.527359\pi$
$523$	−3.92643	−0.171691	−0.0858453	+	0.996308i	$0.527359\pi$
$524$	10.9109	0.476643
$525$	−26.8664	−1.17255
$526$	−27.9319	−1.21789
$527$	41.3093	1.79946
$528$	−4.52732	−0.197026
$529$	6.79571	0.295466
$530$	12.6996	0.551635
$531$	−28.6074	−1.24145
$532$	−22.1919	−0.962140
$533$	0.656841	0.0284510
$534$	13.8570	0.599652
$535$	73.5252	3.17877
$536$	56.9684	2.46066
$537$	10.2211	0.441072
$538$	−42.2536	−1.82168
$539$	14.5112	0.625041
$540$	55.8808	2.40473
$541$	−10.9415	−0.470414	−0.235207	−	0.971945i	$-0.575577\pi$
$541$	−10.9415	−0.470414	−0.235207	+	0.971945i	$0.575577\pi$
$542$	−63.1341	−2.71184
$543$	4.90160	0.210348
$544$	−56.8559	−2.43768
$545$	−40.7468	−1.74540
$546$	−14.4118	−0.616768
$547$	−1.00000	−0.0427569
$547$	−1.00000	−0.0427569
$548$	−66.5083	−2.84110
$549$	−36.0400	−1.53815
$550$	−29.5742	−1.26105
$551$	−0.697036	−0.0296947
$552$	19.6397	0.835921
$553$	−7.12941	−0.303173
$554$	50.8840	2.16185
$555$	21.0388	0.893045
$556$	−48.2476	−2.04615
$557$	23.9235	1.01367	0.506836	−	0.862042i	$-0.330815\pi$
$557$	23.9235	1.01367	0.506836	+	0.862042i	$0.330815\pi$
$558$	46.2619	1.95842
$559$	−10.0022	−0.423048
$560$	167.355	7.07205
$561$	−3.22714	−0.136250
$562$	−1.24460	−0.0525004
$563$	20.2479	0.853349	0.426675	−	0.904405i	$-0.359685\pi$
$563$	20.2479	0.853349	0.426675	+	0.904405i	$0.359685\pi$
$564$	30.9831	1.30462
$565$	−56.3970	−2.37264
$566$	11.8434	0.497814
$567$	31.2743	1.31340
$568$	112.825	4.73403
$569$	34.5268	1.44744	0.723719	−	0.690095i	$-0.242431\pi$
$569$	34.5268	1.44744	0.723719	+	0.690095i	$0.242431\pi$
$570$	−5.40030	−0.226194
$571$	0.207601	0.00868783	0.00434392	−	0.999991i	$-0.498617\pi$
$571$	0.207601	0.00868783	0.00434392	+	0.999991i	$0.498617\pi$
$572$	−11.1495	−0.466186
$573$	11.4114	0.476719
$574$	3.35241	0.139927
$575$	62.2292	2.59514
$576$	−14.8130	−0.617207
$577$	20.4727	0.852290	0.426145	−	0.904655i	$-0.359871\pi$
$577$	20.4727	0.852290	0.426145	+	0.904655i	$0.359871\pi$
$578$	−60.5426	−2.51824
$579$	−11.7812	−0.489610
$580$	13.1969	0.547971
$581$	5.03003	0.208681
$582$	13.3730	0.554328
$583$	−1.20884	−0.0500650
$584$	−28.7496	−1.18967
$585$	26.1756	1.08223
$586$	30.4298	1.25704
$587$	−6.96905	−0.287644	−0.143822	−	0.989604i	$-0.545939\pi$
$587$	−6.96905	−0.287644	−0.143822	+	0.989604i	$0.545939\pi$
$588$	−34.8730	−1.43814
$589$	−6.57999	−0.271124
$590$	−109.613	−4.51268
$591$	−10.3179	−0.424424
$592$	−91.0991	−3.74415
$593$	−43.2101	−1.77443	−0.887214	−	0.461359i	$-0.847362\pi$
$593$	−43.2101	−1.77443	−0.887214	+	0.461359i	$0.847362\pi$
$594$	−7.56842	−0.310536
$595$	119.293	4.89055
$596$	42.8076	1.75347
$597$	−3.47602	−0.142264
$598$	33.3813	1.36506
$599$	10.5682	0.431804	0.215902	−	0.976415i	$-0.430731\pi$
$599$	10.5682	0.431804	0.215902	+	0.976415i	$0.430731\pi$
$600$	41.0181	1.67456
$601$	0.716910	0.0292434	0.0146217	−	0.999893i	$-0.495346\pi$
$601$	0.716910	0.0292434	0.0146217	+	0.999893i	$0.495346\pi$
$602$	−51.0496	−2.08063
$603$	22.0585	0.898291
$604$	−6.94325	−0.282517
$605$	4.04973	0.164645
$606$	−9.42340	−0.382800
$607$	38.1424	1.54815	0.774076	−	0.633092i	$-0.218215\pi$
$607$	38.1424	1.54815	0.774076	+	0.633092i	$0.218215\pi$
$608$	9.05636	0.367284
$609$	−1.62372	−0.0657966
$610$	−138.092	−5.59116
$611$	30.3926	1.22955
$612$	−82.3613	−3.32926
$613$	−43.5327	−1.75827	−0.879135	−	0.476573i	$-0.841879\pi$
$613$	−43.5327	−1.75827	−0.879135	+	0.476573i	$0.841879\pi$
$614$	−31.9288	−1.28854
$615$	0.573346	0.0231195
$616$	−32.8420	−1.32324
$617$	36.2915	1.46104	0.730521	−	0.682891i	$-0.239278\pi$
$617$	36.2915	1.46104	0.730521	+	0.682891i	$0.239278\pi$
$618$	−0.165731	−0.00666669
$619$	5.03080	0.202205	0.101102	−	0.994876i	$-0.467763\pi$
$619$	5.03080	0.202205	0.101102	+	0.994876i	$0.467763\pi$
$620$	124.578	5.00318
$621$	15.9253	0.639059
$622$	−51.0139	−2.04547
$623$	48.7581	1.95345
$624$	10.6726	0.427248
$625$	47.9659	1.91864
$626$	72.0409	2.87933
$627$	0.514039	0.0205288
$628$	67.2629	2.68408
$629$	−64.9368	−2.58920
$630$	133.596	5.32258
$631$	7.16862	0.285378	0.142689	−	0.989768i	$-0.454425\pi$
$631$	7.16862	0.285378	0.142689	+	0.989768i	$0.454425\pi$
$632$	10.8848	0.432972
$633$	−10.3073	−0.409680
$634$	−46.4257	−1.84380
$635$	−4.83220	−0.191760
$636$	2.90506	0.115193
$637$	−34.2084	−1.35539
$638$	−1.78737	−0.0707627
$639$	43.6865	1.72821
$640$	15.7484	0.622509
$641$	−20.3739	−0.804723	−0.402361	−	0.915481i	$-0.631810\pi$
$641$	−20.3739	−0.804723	−0.402361	+	0.915481i	$0.631810\pi$
$642$	23.9313	0.944492
$643$	14.5487	0.573746	0.286873	−	0.957969i	$-0.407384\pi$
$643$	14.5487	0.573746	0.286873	+	0.957969i	$0.407384\pi$
$644$	119.739	4.71837
$645$	−8.73076	−0.343773
$646$	16.6682	0.655802
$647$	16.3361	0.642238	0.321119	−	0.947039i	$-0.395941\pi$
$647$	16.3361	0.642238	0.321119	+	0.947039i	$0.395941\pi$
$648$	−47.7478	−1.87571
$649$	10.4337	0.409559
$650$	69.7177	2.73455
$651$	−15.3279	−0.600747
$652$	93.6351	3.66703
$653$	−37.3247	−1.46063	−0.730315	−	0.683111i	$-0.760627\pi$
$653$	−37.3247	−1.46063	−0.730315	+	0.683111i	$0.760627\pi$
$654$	−13.2624	−0.518602
$655$	9.34242	0.365038
$656$	−2.48262	−0.0969301
$657$	−11.1320	−0.434302
$658$	155.119	6.04717
$659$	−8.72632	−0.339929	−0.169965	−	0.985450i	$-0.554365\pi$
$659$	−8.72632	−0.339929	−0.169965	+	0.985450i	$0.554365\pi$
$660$	−9.73225	−0.378827
$661$	17.3159	0.673512	0.336756	−	0.941592i	$-0.390670\pi$
$661$	17.3159	0.673512	0.336756	+	0.941592i	$0.390670\pi$
$662$	−7.04651	−0.273870
$663$	7.60762	0.295456
$664$	−7.67955	−0.298024
$665$	−19.0018	−0.736857
$666$	−72.7223	−2.81793
$667$	3.76094	0.145624
$668$	−93.4438	−3.61545
$669$	−5.92087	−0.228914
$670$	84.5198	3.26528
$671$	13.1445	0.507440
$672$	21.0965	0.813816
$673$	−4.31441	−0.166308	−0.0831541	−	0.996537i	$-0.526499\pi$
$673$	−4.31441	−0.166308	−0.0831541	+	0.996537i	$0.526499\pi$
$674$	2.42525	0.0934172
$675$	33.2604	1.28019
$676$	−35.2013	−1.35390
$677$	31.1093	1.19563	0.597814	−	0.801635i	$-0.296036\pi$
$677$	31.1093	1.19563	0.597814	+	0.801635i	$0.296036\pi$
$678$	−18.3563	−0.704970
$679$	47.0548	1.80580
$680$	−182.130	−6.98437
$681$	8.44459	0.323597
$682$	−16.8727	−0.646089
$683$	22.7296	0.869723	0.434861	−	0.900497i	$-0.356797\pi$
$683$	22.7296	0.869723	0.434861	+	0.900497i	$0.356797\pi$
$684$	13.1190	0.501618
$685$	−56.9477	−2.17586
$686$	−90.3724	−3.45043
$687$	−1.38321	−0.0527729
$688$	37.8047	1.44129
$689$	2.84970	0.108565
$690$	29.1379	1.10926
$691$	−18.4822	−0.703096	−0.351548	−	0.936170i	$-0.614345\pi$
$691$	−18.4822	−0.703096	−0.351548	+	0.936170i	$0.614345\pi$
$692$	−39.4029	−1.49787
$693$	−12.7166	−0.483064
$694$	−59.7192	−2.26691
$695$	−41.3120	−1.56705
$696$	2.47900	0.0939664
$697$	−1.76965	−0.0670303
$698$	71.7715	2.71659
$699$	3.13942	0.118744
$700$	250.078	9.45207
$701$	−30.6655	−1.15822	−0.579110	−	0.815250i	$-0.696600\pi$
$701$	−30.6655	−1.15822	−0.579110	+	0.815250i	$0.696600\pi$
$702$	17.8417	0.673391
$703$	10.3435	0.390114
$704$	5.40260	0.203618
$705$	26.5292	0.999149
$706$	47.3402	1.78167
$707$	−33.1577	−1.24702
$708$	−25.0741	−0.942343
$709$	6.59658	0.247740	0.123870	−	0.992298i	$-0.460469\pi$
$709$	6.59658	0.247740	0.123870	+	0.992298i	$0.460469\pi$
$710$	167.390	6.28203
$711$	4.21464	0.158061
$712$	−74.4409	−2.78979
$713$	35.5031	1.32960
$714$	38.8281	1.45310
$715$	−9.54678	−0.357029
$716$	−95.1399	−3.55554
$717$	−0.146685	−0.00547804
$718$	46.3900	1.73126
$719$	2.68034	0.0999599	0.0499799	−	0.998750i	$-0.484084\pi$
$719$	2.68034	0.0999599	0.0499799	+	0.998750i	$0.484084\pi$
$720$	−98.9341	−3.68706
$721$	−0.583151	−0.0217177
$722$	46.6339	1.73553
$723$	−10.1322	−0.376822
$724$	−45.6251	−1.69564
$725$	7.85483	0.291721
$726$	1.31812	0.0489201
$727$	30.4857	1.13065	0.565326	−	0.824867i	$-0.308750\pi$
$727$	30.4857	1.13065	0.565326	+	0.824867i	$0.308750\pi$
$728$	77.4212	2.86942
$729$	−14.0410	−0.520036
$730$	−42.6537	−1.57868
$731$	26.9478	0.996700
$732$	−31.5887	−1.16755
$733$	−25.3670	−0.936951	−0.468475	−	0.883477i	$-0.655197\pi$
$733$	−25.3670	−0.936951	−0.468475	+	0.883477i	$0.655197\pi$
$734$	−55.6274	−2.05324
$735$	−29.8600	−1.10140
$736$	−48.8647	−1.80118
$737$	−8.04520	−0.296349
$738$	−1.98182	−0.0729518
$739$	−18.2677	−0.671990	−0.335995	−	0.941864i	$-0.609073\pi$
$739$	−18.2677	−0.671990	−0.335995	+	0.941864i	$0.609073\pi$
$740$	−195.833	−7.19896
$741$	−1.21179	−0.0445162
$742$	14.5444	0.533942
$743$	51.9405	1.90551	0.952757	−	0.303735i	$-0.0982336\pi$
$743$	51.9405	1.90551	0.952757	+	0.303735i	$0.0982336\pi$
$744$	23.4017	0.857948
$745$	36.6540	1.34290
$746$	−80.1873	−2.93587
$747$	−2.97357	−0.108797
$748$	30.0389	1.09833
$749$	84.2058	3.07681
$750$	34.1652	1.24754
$751$	25.4212	0.927631	0.463815	−	0.885932i	$-0.346480\pi$
$751$	25.4212	0.927631	0.463815	+	0.885932i	$0.346480\pi$
$752$	−114.873	−4.18899
$753$	9.62679	0.350820
$754$	4.21352	0.153447
$755$	−5.94515	−0.216366
$756$	63.9983	2.32760
$757$	−39.8421	−1.44809	−0.724043	−	0.689755i	$-0.757718\pi$
$757$	−39.8421	−1.44809	−0.724043	+	0.689755i	$0.757718\pi$
$758$	−19.9346	−0.724056
$759$	−2.77356	−0.100674
$760$	29.0108	1.05233
$761$	−10.0429	−0.364054	−0.182027	−	0.983294i	$-0.558266\pi$
$761$	−10.0429	−0.364054	−0.182027	+	0.983294i	$0.558266\pi$
$762$	−1.57280	−0.0569767
$763$	−46.6658	−1.68942
$764$	−106.220	−3.84290
$765$	−70.5218	−2.54972
$766$	30.8448	1.11447
$767$	−24.5963	−0.888120
$768$	10.6161	0.383076
$769$	36.2082	1.30570	0.652851	−	0.757486i	$-0.273573\pi$
$769$	36.2082	1.30570	0.652851	+	0.757486i	$0.273573\pi$
$770$	−48.7252	−1.75593
$771$	4.45468	0.160431
$772$	109.662	3.94681
$773$	7.86228	0.282787	0.141393	−	0.989953i	$-0.454842\pi$
$773$	7.86228	0.282787	0.141393	+	0.989953i	$0.454842\pi$
$774$	30.1786	1.08475
$775$	74.1493	2.66352
$776$	−71.8405	−2.57893
$777$	24.0949	0.864401
$778$	71.7241	2.57143
$779$	0.281881	0.0100994
$780$	22.9427	0.821479
$781$	−15.9334	−0.570141
$782$	−89.9353	−3.21608
$783$	2.01015	0.0718371
$784$	129.296	4.61770
$785$	57.5938	2.05561
$786$	3.04081	0.108462
$787$	16.5885	0.591317	0.295658	−	0.955294i	$-0.404461\pi$
$787$	16.5885	0.591317	0.295658	+	0.955294i	$0.404461\pi$
$788$	96.0415	3.42134
$789$	−5.47100	−0.194773
$790$	16.1489	0.574552
$791$	−64.5895	−2.29654
$792$	19.4150	0.689881
$793$	−30.9868	−1.10037
$794$	−29.3654	−1.04214
$795$	2.48746	0.0882210
$796$	32.3555	1.14681
$797$	−10.2877	−0.364408	−0.182204	−	0.983261i	$-0.558323\pi$
$797$	−10.2877	−0.364408	−0.182204	+	0.983261i	$0.558323\pi$
$798$	−6.18477	−0.218939
$799$	−81.8834	−2.89683
$800$	−102.055	−3.60820
$801$	−28.8239	−1.01844
$802$	−37.3713	−1.31963
$803$	4.06009	0.143277
$804$	19.3341	0.681860
$805$	102.526	3.61358
$806$	39.7755	1.40103
$807$	−8.27617	−0.291335
$808$	50.6232	1.78092
$809$	−26.9420	−0.947229	−0.473614	−	0.880732i	$-0.657051\pi$
$809$	−26.9420	−0.947229	−0.473614	+	0.880732i	$0.657051\pi$
$810$	−70.8398	−2.48906
$811$	−10.7273	−0.376687	−0.188343	−	0.982103i	$-0.560312\pi$
$811$	−10.7273	−0.376687	−0.188343	+	0.982103i	$0.560312\pi$
$812$	15.1139	0.530395
$813$	−12.3660	−0.433695
$814$	26.5234	0.929643
$815$	80.1750	2.80841
$816$	−28.7541	−1.00659
$817$	−4.29241	−0.150172
$818$	59.9149	2.09488
$819$	29.9779	1.04751
$820$	−5.33682	−0.186370
$821$	−41.1553	−1.43633	−0.718166	−	0.695872i	$-0.755018\pi$
$821$	−41.1553	−1.43633	−0.718166	+	0.695872i	$0.755018\pi$
$822$	−18.5356	−0.646502
$823$	3.56214	0.124168	0.0620842	−	0.998071i	$-0.480225\pi$
$823$	3.56214	0.124168	0.0620842	+	0.998071i	$0.480225\pi$
$824$	0.890321	0.0310158
$825$	−5.79266	−0.201675
$826$	−125.535	−4.36794
$827$	−24.6896	−0.858541	−0.429270	−	0.903176i	$-0.641229\pi$
$827$	−24.6896	−0.858541	−0.429270	+	0.903176i	$0.641229\pi$
$828$	−70.7852	−2.45995
$829$	12.5960	0.437476	0.218738	−	0.975784i	$-0.429806\pi$
$829$	12.5960	0.437476	0.218738	+	0.975784i	$0.429806\pi$
$830$	−11.3936	−0.395477
$831$	9.96659	0.345737
$832$	−12.7360	−0.441542
$833$	92.1639	3.19329
$834$	−13.4464	−0.465610
$835$	−80.0112	−2.76890
$836$	−4.78478	−0.165485
$837$	18.9758	0.655899
$838$	32.6996	1.12959
$839$	−34.6936	−1.19776	−0.598878	−	0.800840i	$-0.704387\pi$
$839$	−34.6936	−1.19776	−0.598878	+	0.800840i	$0.704387\pi$
$840$	67.5797	2.33172
$841$	−28.5253	−0.983630
$842$	25.0730	0.864071
$843$	−0.243779	−0.00839619
$844$	95.9428	3.30249
$845$	−30.1411	−1.03688
$846$	−91.7006	−3.15273
$847$	4.63801	0.159364
$848$	−10.7708	−0.369872
$849$	2.31975	0.0796134
$850$	−187.832	−6.44260
$851$	−55.8097	−1.91313
$852$	38.2908	1.31182
$853$	−24.4251	−0.836301	−0.418150	−	0.908378i	$-0.637321\pi$
$853$	−24.4251	−0.836301	−0.418150	+	0.908378i	$0.637321\pi$
$854$	−158.151	−5.41183
$855$	11.2331	0.384165
$856$	−128.560	−4.39411
$857$	−29.1993	−0.997428	−0.498714	−	0.866767i	$-0.666194\pi$
$857$	−29.1993	−0.997428	−0.498714	+	0.866767i	$0.666194\pi$
$858$	−3.10732	−0.106082
$859$	−53.0184	−1.80896	−0.904482	−	0.426511i	$-0.859743\pi$
$859$	−53.0184	−1.80896	−0.904482	+	0.426511i	$0.859743\pi$
$860$	81.2677	2.77120
$861$	0.656633	0.0223780
$862$	8.01053	0.272840
$863$	−8.42795	−0.286891	−0.143445	−	0.989658i	$-0.545818\pi$
$863$	−8.42795	−0.286891	−0.143445	+	0.989658i	$0.545818\pi$
$864$	−26.1173	−0.888528
$865$	−33.7387	−1.14715
$866$	50.6243	1.72028
$867$	−11.8584	−0.402733
$868$	142.675	4.84270
$869$	−1.53717	−0.0521449
$870$	3.67791	0.124693
$871$	18.9656	0.642626
$872$	71.2466	2.41272
$873$	−27.8171	−0.941465
$874$	14.3254	0.484565
$875$	120.216	4.06403
$876$	−9.75713	−0.329663
$877$	14.5412	0.491022	0.245511	−	0.969394i	$-0.421044\pi$
$877$	14.5412	0.491022	0.245511	+	0.969394i	$0.421044\pi$
$878$	13.7482	0.463979
$879$	5.96025	0.201034
$880$	36.0834	1.21637
$881$	−7.87449	−0.265298	−0.132649	−	0.991163i	$-0.542348\pi$
$881$	−7.87449	−0.265298	−0.132649	+	0.991163i	$0.542348\pi$
$882$	103.214	3.47538
$883$	−2.80517	−0.0944013	−0.0472007	−	0.998885i	$-0.515030\pi$
$883$	−2.80517	−0.0944013	−0.0472007	+	0.998885i	$0.515030\pi$
$884$	−70.8133	−2.38171
$885$	−21.4697	−0.721696
$886$	−35.8302	−1.20374
$887$	44.5767	1.49674	0.748370	−	0.663281i	$-0.230837\pi$
$887$	44.5767	1.49674	0.748370	+	0.663281i	$0.230837\pi$
$888$	−36.7867	−1.23448
$889$	−5.53415	−0.185609
$890$	−110.442	−3.70204
$891$	6.74304	0.225901
$892$	55.1127	1.84531
$893$	13.0429	0.436464
$894$	11.9303	0.399008
$895$	−81.4634	−2.72302
$896$	18.0361	0.602542
$897$	6.53835	0.218309
$898$	56.1523	1.87383
$899$	4.48135	0.149461
$900$	−147.837	−4.92790
$901$	−7.67762	−0.255778
$902$	0.722812	0.0240670
$903$	−9.99903	−0.332747
$904$	98.6115	3.27977
$905$	−39.0665	−1.29861
$906$	−1.93505	−0.0642877
$907$	2.98390	0.0990787	0.0495393	−	0.998772i	$-0.484225\pi$
$907$	2.98390	0.0990787	0.0495393	+	0.998772i	$0.484225\pi$
$908$	−78.6040	−2.60856
$909$	19.6016	0.650143
$910$	114.864	3.80771
$911$	46.4485	1.53891	0.769454	−	0.638702i	$-0.220528\pi$
$911$	46.4485	1.53891	0.769454	+	0.638702i	$0.220528\pi$
$912$	4.58012	0.151663
$913$	1.08452	0.0358925
$914$	−83.9424	−2.77657
$915$	−27.0478	−0.894174
$916$	12.8752	0.425410
$917$	10.6995	0.353330
$918$	−48.0688	−1.58651
$919$	6.83850	0.225581	0.112791	−	0.993619i	$-0.464021\pi$
$919$	6.83850	0.225581	0.112791	+	0.993619i	$0.464021\pi$
$920$	−156.531	−5.16068
$921$	−6.25386	−0.206072
$922$	26.8465	0.884143
$923$	37.5611	1.23634
$924$	−11.1460	−0.366676
$925$	−116.560	−3.83248
$926$	−19.3969	−0.637423
$927$	0.344737	0.0113227
$928$	−6.16790	−0.202471
$929$	2.01249	0.0660276	0.0330138	−	0.999455i	$-0.489489\pi$
$929$	2.01249	0.0660276	0.0330138	+	0.999455i	$0.489489\pi$
$930$	34.7193	1.13849
$931$	−14.6804	−0.481131
$932$	−29.2223	−0.957210
$933$	−9.99202	−0.327124
$934$	57.1690	1.87063
$935$	25.7208	0.841160
$936$	−45.7685	−1.49599
$937$	16.0677	0.524910	0.262455	−	0.964944i	$-0.415468\pi$
$937$	16.0677	0.524910	0.262455	+	0.964944i	$0.415468\pi$
$938$	96.7975	3.16055
$939$	14.1106	0.460481
$940$	−246.939	−8.05428
$941$	48.9608	1.59608	0.798038	−	0.602607i	$-0.205871\pi$
$941$	48.9608	1.59608	0.798038	+	0.602607i	$0.205871\pi$
$942$	18.7458	0.610773
$943$	−1.52092	−0.0495280
$944$	92.9650	3.02575
$945$	54.7985	1.78260
$946$	−11.0068	−0.357862
$947$	−49.0035	−1.59240	−0.796201	−	0.605033i	$-0.793160\pi$
$947$	−49.0035	−1.59240	−0.796201	+	0.605033i	$0.793160\pi$
$948$	3.69410	0.119979
$949$	−9.57118	−0.310694
$950$	29.9191	0.970704
$951$	−9.09334	−0.294872
$952$	−208.587	−6.76035
$953$	59.2136	1.91812	0.959058	−	0.283209i	$-0.0913989\pi$
$953$	59.2136	1.91812	0.959058	+	0.283209i	$0.0913989\pi$
$954$	−8.59811	−0.278374
$955$	−90.9506	−2.94309
$956$	1.36537	0.0441593
$957$	−0.350090	−0.0113168
$958$	40.0599	1.29428
$959$	−65.2202	−2.10607
$960$	−11.1171	−0.358802
$961$	11.3038	0.364637
$962$	−62.5258	−2.01591
$963$	−49.7793	−1.60412
$964$	94.3129	3.03761
$965$	93.8977	3.02267
$966$	33.3707	1.07368
$967$	6.61037	0.212575	0.106288	−	0.994335i	$-0.466104\pi$
$967$	6.61037	0.212575	0.106288	+	0.994335i	$0.466104\pi$
$968$	−7.08105	−0.227593
$969$	3.26478	0.104880
$970$	−106.584	−3.42222
$971$	−13.2177	−0.424176	−0.212088	−	0.977251i	$-0.568026\pi$
$971$	−13.2177	−0.424176	−0.212088	+	0.977251i	$0.568026\pi$
$972$	−57.6007	−1.84754
$973$	−47.3131	−1.51679
$974$	87.4987	2.80364
$975$	13.6555	0.437327
$976$	117.119	3.74888
$977$	18.8431	0.602844	0.301422	−	0.953491i	$-0.402539\pi$
$977$	18.8431	0.602844	0.301422	+	0.953491i	$0.402539\pi$
$978$	26.0957	0.834447
$979$	10.5127	0.335987
$980$	277.943	8.87855
$981$	27.5871	0.880788
$982$	6.48023	0.206792
$983$	29.9458	0.955122	0.477561	−	0.878599i	$-0.341521\pi$
$983$	29.9458	0.955122	0.477561	+	0.878599i	$0.341521\pi$
$984$	−1.00251	−0.0319588
$985$	82.2354	2.62024
$986$	−11.3520	−0.361521
$987$	30.3830	0.967101
$988$	11.2796	0.358851
$989$	23.1602	0.736451
$990$	28.8045	0.915468
$991$	23.0986	0.733753	0.366876	−	0.930270i	$-0.380427\pi$
$991$	23.0986	0.733753	0.366876	+	0.930270i	$0.380427\pi$
$992$	−58.2247	−1.84864
$993$	−1.38019	−0.0437990
$994$	191.706	6.08054
$995$	27.7044	0.878288
$996$	−2.60630	−0.0825839
$997$	−27.1273	−0.859130	−0.429565	−	0.903036i	$-0.641333\pi$
$997$	−27.1273	−0.859130	−0.429565	+	0.903036i	$0.641333\pi$
$998$	41.2361	1.30531
$999$	−29.8293	−0.943758

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6017.2.a.e.1.7	✓	119

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6017.2.a.e.1.7	✓	119	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:	\( N \)	\(=\)	\( 6017 = 11 \cdot 547 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6017.a (trivial)

\(f(q)\)	\(=\)	\(q-2.59415 q^{2} -0.508113 q^{3} +4.72962 q^{4} +4.04973 q^{5} +1.31812 q^{6} +4.63801 q^{7} -7.08105 q^{8} -2.74182 q^{9} +O(q^{10})\)	\(q-2.59415 q^{2} -0.508113 q^{3} +4.72962 q^{4} +4.04973 q^{5} +1.31812 q^{6} +4.63801 q^{7} -7.08105 q^{8} -2.74182 q^{9} -10.5056 q^{10} +1.00000 q^{11} -2.40318 q^{12} -2.35739 q^{13} -12.0317 q^{14} -2.05772 q^{15} +8.91006 q^{16} +6.35123 q^{17} +7.11270 q^{18} -1.01166 q^{19} +19.1537 q^{20} -2.35664 q^{21} -2.59415 q^{22} +5.45854 q^{23} +3.59797 q^{24} +11.4003 q^{25} +6.11541 q^{26} +2.91750 q^{27} +21.9360 q^{28} +0.689000 q^{29} +5.33804 q^{30} +6.50413 q^{31} -8.95196 q^{32} -0.508113 q^{33} -16.4761 q^{34} +18.7827 q^{35} -12.9678 q^{36} -10.2243 q^{37} +2.62441 q^{38} +1.19782 q^{39} -28.6763 q^{40} -0.278631 q^{41} +6.11347 q^{42} +4.24292 q^{43} +4.72962 q^{44} -11.1036 q^{45} -14.1603 q^{46} -12.8925 q^{47} -4.52732 q^{48} +14.5112 q^{49} -29.5742 q^{50} -3.22714 q^{51} -11.1495 q^{52} -1.20884 q^{53} -7.56842 q^{54} +4.04973 q^{55} -32.8420 q^{56} +0.514039 q^{57} -1.78737 q^{58} +10.4337 q^{59} -9.73225 q^{60} +13.1445 q^{61} -16.8727 q^{62} -12.7166 q^{63} +5.40260 q^{64} -9.54678 q^{65} +1.31812 q^{66} -8.04520 q^{67} +30.0389 q^{68} -2.77356 q^{69} -48.7252 q^{70} -15.9334 q^{71} +19.4150 q^{72} +4.06009 q^{73} +26.5234 q^{74} -5.79266 q^{75} -4.78478 q^{76} +4.63801 q^{77} -3.10732 q^{78} -1.53717 q^{79} +36.0834 q^{80} +6.74304 q^{81} +0.722812 q^{82} +1.08452 q^{83} -11.1460 q^{84} +25.7208 q^{85} -11.0068 q^{86} -0.350090 q^{87} -7.08105 q^{88} +10.5127 q^{89} +28.8045 q^{90} -10.9336 q^{91} +25.8168 q^{92} -3.30484 q^{93} +33.4452 q^{94} -4.09696 q^{95} +4.54861 q^{96} +10.1455 q^{97} -37.6442 q^{98} -2.74182 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 119 q + 15 q^{2} + 15 q^{3} + 133 q^{4} + 6 q^{5} + 16 q^{6} + 72 q^{7} + 39 q^{8} + 128 q^{9}+O(q^{10}) \) 119 * q + 15 * q^2 + 15 * q^3 + 133 * q^4 + 6 * q^5 + 16 * q^6 + 72 * q^7 + 39 * q^8 + 128 * q^9	\( 119 q + 15 q^{2} + 15 q^{3} + 133 q^{4} + 6 q^{5} + 16 q^{6} + 72 q^{7} + 39 q^{8} + 128 q^{9} + 22 q^{10} + 119 q^{11} + 40 q^{12} + 67 q^{13} + 3 q^{14} + 22 q^{15} + 145 q^{16} + 57 q^{17} + 53 q^{18} + 68 q^{19} + 25 q^{20} + 21 q^{21} + 15 q^{22} + 21 q^{23} + 34 q^{24} + 137 q^{25} + 10 q^{26} + 54 q^{27} + 149 q^{28} + 46 q^{29} + 10 q^{30} + 87 q^{31} + 58 q^{32} + 15 q^{33} + 16 q^{34} + 40 q^{35} + 137 q^{36} + 39 q^{37} + 27 q^{38} + 72 q^{39} + 46 q^{40} + 50 q^{41} - 4 q^{42} + 122 q^{43} + 133 q^{44} + 12 q^{45} + 22 q^{46} + 92 q^{47} + 9 q^{48} + 161 q^{49} + 2 q^{50} - 12 q^{51} + 177 q^{52} + 12 q^{53} + 19 q^{54} + 6 q^{55} - 16 q^{56} + 43 q^{57} + 56 q^{58} + 39 q^{59} + 27 q^{60} + 114 q^{61} + 66 q^{62} + 196 q^{63} + 161 q^{64} + 7 q^{65} + 16 q^{66} + 59 q^{67} + 139 q^{68} - 24 q^{69} + 9 q^{70} + 11 q^{71} + 92 q^{72} + 123 q^{73} + q^{74} + 19 q^{75} + 92 q^{76} + 72 q^{77} - 101 q^{78} + 78 q^{79} - 34 q^{80} + 139 q^{81} + 73 q^{82} + 108 q^{83} - 31 q^{84} + 30 q^{85} - 18 q^{86} + 164 q^{87} + 39 q^{88} + 15 q^{89} - 41 q^{90} + 60 q^{91} - 26 q^{92} - 2 q^{93} + 45 q^{94} + 75 q^{95} + 42 q^{96} + 73 q^{97} + 32 q^{98} + 128 q^{99}+O(q^{100}) \) 119 * q + 15 * q^2 + 15 * q^3 + 133 * q^4 + 6 * q^5 + 16 * q^6 + 72 * q^7 + 39 * q^8 + 128 * q^9 + 22 * q^10 + 119 * q^11 + 40 * q^12 + 67 * q^13 + 3 * q^14 + 22 * q^15 + 145 * q^16 + 57 * q^17 + 53 * q^18 + 68 * q^19 + 25 * q^20 + 21 * q^21 + 15 * q^22 + 21 * q^23 + 34 * q^24 + 137 * q^25 + 10 * q^26 + 54 * q^27 + 149 * q^28 + 46 * q^29 + 10 * q^30 + 87 * q^31 + 58 * q^32 + 15 * q^33 + 16 * q^34 + 40 * q^35 + 137 * q^36 + 39 * q^37 + 27 * q^38 + 72 * q^39 + 46 * q^40 + 50 * q^41 - 4 * q^42 + 122 * q^43 + 133 * q^44 + 12 * q^45 + 22 * q^46 + 92 * q^47 + 9 * q^48 + 161 * q^49 + 2 * q^50 - 12 * q^51 + 177 * q^52 + 12 * q^53 + 19 * q^54 + 6 * q^55 - 16 * q^56 + 43 * q^57 + 56 * q^58 + 39 * q^59 + 27 * q^60 + 114 * q^61 + 66 * q^62 + 196 * q^63 + 161 * q^64 + 7 * q^65 + 16 * q^66 + 59 * q^67 + 139 * q^68 - 24 * q^69 + 9 * q^70 + 11 * q^71 + 92 * q^72 + 123 * q^73 + q^74 + 19 * q^75 + 92 * q^76 + 72 * q^77 - 101 * q^78 + 78 * q^79 - 34 * q^80 + 139 * q^81 + 73 * q^82 + 108 * q^83 - 31 * q^84 + 30 * q^85 - 18 * q^86 + 164 * q^87 + 39 * q^88 + 15 * q^89 - 41 * q^90 + 60 * q^91 - 26 * q^92 - 2 * q^93 + 45 * q^94 + 75 * q^95 + 42 * q^96 + 73 * q^97 + 32 * q^98 + 128 * q^99

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