LMFDB - Embedded newform 6023.2.a.a.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6023,2,Mod(1,6023)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6023, 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("6023.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6023 = 19 \cdot 317 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6023.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:	$48.0938971374$
Analytic rank:	$1$
Dimension:	$98$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	6023.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.63244 q^{2} -2.81028 q^{3} +4.92974 q^{4} +1.41252 q^{5} +7.39789 q^{6} +3.18061 q^{7} -7.71236 q^{8} +4.89767 q^{9} +O(q^{10})$	\(q-2.63244 q^{2} -2.81028 q^{3} +4.92974 q^{4} +1.41252 q^{5} +7.39789 q^{6} +3.18061 q^{7} -7.71236 q^{8} +4.89767 q^{9} -3.71838 q^{10} +0.715727 q^{11} -13.8539 q^{12} -1.65990 q^{13} -8.37276 q^{14} -3.96958 q^{15} +10.4428 q^{16} +6.51375 q^{17} -12.8928 q^{18} +1.00000 q^{19} +6.96337 q^{20} -8.93840 q^{21} -1.88411 q^{22} -3.69982 q^{23} +21.6739 q^{24} -3.00478 q^{25} +4.36958 q^{26} -5.33297 q^{27} +15.6796 q^{28} +3.54363 q^{29} +10.4497 q^{30} +3.26636 q^{31} -12.0654 q^{32} -2.01139 q^{33} -17.1470 q^{34} +4.49268 q^{35} +24.1442 q^{36} -9.57448 q^{37} -2.63244 q^{38} +4.66478 q^{39} -10.8939 q^{40} -0.712498 q^{41} +23.5298 q^{42} +7.35785 q^{43} +3.52834 q^{44} +6.91806 q^{45} +9.73956 q^{46} -6.54066 q^{47} -29.3473 q^{48} +3.11627 q^{49} +7.90990 q^{50} -18.3054 q^{51} -8.18287 q^{52} +11.8429 q^{53} +14.0387 q^{54} +1.01098 q^{55} -24.5300 q^{56} -2.81028 q^{57} -9.32839 q^{58} +9.77617 q^{59} -19.5690 q^{60} -6.93487 q^{61} -8.59851 q^{62} +15.5776 q^{63} +10.8758 q^{64} -2.34464 q^{65} +5.29487 q^{66} -8.41543 q^{67} +32.1111 q^{68} +10.3975 q^{69} -11.8267 q^{70} -12.7819 q^{71} -37.7726 q^{72} -12.4423 q^{73} +25.2042 q^{74} +8.44427 q^{75} +4.92974 q^{76} +2.27645 q^{77} -12.2797 q^{78} +6.26390 q^{79} +14.7507 q^{80} +0.294134 q^{81} +1.87561 q^{82} -13.2155 q^{83} -44.0639 q^{84} +9.20082 q^{85} -19.3691 q^{86} -9.95858 q^{87} -5.51994 q^{88} +7.34484 q^{89} -18.2114 q^{90} -5.27949 q^{91} -18.2392 q^{92} -9.17939 q^{93} +17.2179 q^{94} +1.41252 q^{95} +33.9072 q^{96} -18.8104 q^{97} -8.20339 q^{98} +3.50539 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 98 q - 8 q^{2} - 25 q^{3} + 82 q^{4} - 10 q^{5} - 4 q^{6} - 18 q^{7} - 18 q^{8} + 61 q^{9}+O(q^{10}) $ 98 * q - 8 * q^2 - 25 * q^3 + 82 * q^4 - 10 * q^5 - 4 * q^6 - 18 * q^7 - 18 * q^8 + 61 * q^9	\( 98 q - 8 q^{2} - 25 q^{3} + 82 q^{4} - 10 q^{5} - 4 q^{6} - 18 q^{7} - 18 q^{8} + 61 q^{9} - 24 q^{10} - 12 q^{11} - 51 q^{12} - 58 q^{13} - 15 q^{14} - 18 q^{15} + 58 q^{16} - 25 q^{17} - 40 q^{18} + 98 q^{19} - 12 q^{20} - 24 q^{21} - 59 q^{22} - 38 q^{23} - 9 q^{24} - 12 q^{25} - 3 q^{26} - 85 q^{27} - 33 q^{28} - 24 q^{29} - 22 q^{30} - 56 q^{31} - 29 q^{32} - 51 q^{33} - 38 q^{34} - 10 q^{35} + 50 q^{36} - 124 q^{37} - 8 q^{38} - 4 q^{39} - 80 q^{40} - 28 q^{41} - 37 q^{42} - 63 q^{43} - 7 q^{44} - 32 q^{45} - 47 q^{46} - 10 q^{47} - 88 q^{48} + 6 q^{49} - 17 q^{50} - 22 q^{51} - 119 q^{52} - 65 q^{53} + 24 q^{54} - 30 q^{55} - 39 q^{56} - 25 q^{57} - 91 q^{58} - 26 q^{59} - 60 q^{60} - 60 q^{61} + 6 q^{62} - 26 q^{63} + 50 q^{64} - 40 q^{65} + 57 q^{66} - 108 q^{67} - 41 q^{68} - 15 q^{69} - 36 q^{70} - 19 q^{71} - 47 q^{72} - 136 q^{73} + 22 q^{74} - 48 q^{75} + 82 q^{76} - 35 q^{77} - 56 q^{78} - 98 q^{79} - 42 q^{80} + 6 q^{81} - 37 q^{82} - 31 q^{83} - 24 q^{84} - 71 q^{85} - 24 q^{86} + 7 q^{87} - 166 q^{88} - 38 q^{89} + 26 q^{90} - 100 q^{91} - 59 q^{92} - 21 q^{93} - 48 q^{94} - 10 q^{95} - 16 q^{96} - 190 q^{97} - 80 q^{98} - 17 q^{99}+O(q^{100}) \) 98 * q - 8 * q^2 - 25 * q^3 + 82 * q^4 - 10 * q^5 - 4 * q^6 - 18 * q^7 - 18 * q^8 + 61 * q^9 - 24 * q^10 - 12 * q^11 - 51 * q^12 - 58 * q^13 - 15 * q^14 - 18 * q^15 + 58 * q^16 - 25 * q^17 - 40 * q^18 + 98 * q^19 - 12 * q^20 - 24 * q^21 - 59 * q^22 - 38 * q^23 - 9 * q^24 - 12 * q^25 - 3 * q^26 - 85 * q^27 - 33 * q^28 - 24 * q^29 - 22 * q^30 - 56 * q^31 - 29 * q^32 - 51 * q^33 - 38 * q^34 - 10 * q^35 + 50 * q^36 - 124 * q^37 - 8 * q^38 - 4 * q^39 - 80 * q^40 - 28 * q^41 - 37 * q^42 - 63 * q^43 - 7 * q^44 - 32 * q^45 - 47 * q^46 - 10 * q^47 - 88 * q^48 + 6 * q^49 - 17 * q^50 - 22 * q^51 - 119 * q^52 - 65 * q^53 + 24 * q^54 - 30 * q^55 - 39 * q^56 - 25 * q^57 - 91 * q^58 - 26 * q^59 - 60 * q^60 - 60 * q^61 + 6 * q^62 - 26 * q^63 + 50 * q^64 - 40 * q^65 + 57 * q^66 - 108 * q^67 - 41 * q^68 - 15 * q^69 - 36 * q^70 - 19 * q^71 - 47 * q^72 - 136 * q^73 + 22 * q^74 - 48 * q^75 + 82 * q^76 - 35 * q^77 - 56 * q^78 - 98 * q^79 - 42 * q^80 + 6 * q^81 - 37 * q^82 - 31 * q^83 - 24 * q^84 - 71 * q^85 - 24 * q^86 + 7 * q^87 - 166 * q^88 - 38 * q^89 + 26 * q^90 - 100 * q^91 - 59 * q^92 - 21 * q^93 - 48 * q^94 - 10 * q^95 - 16 * q^96 - 190 * q^97 - 80 * q^98 - 17 * 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 $

$2$	−2.63244	−1.86142	−0.930708	−	0.365763i	$-0.880808\pi$
$2$	−2.63244	−1.86142	−0.930708	+	0.365763i	$0.880808\pi$
$3$	−2.81028	−1.62252	−0.811258	−	0.584689i	$-0.801217\pi$
$3$	−2.81028	−1.62252	−0.811258	+	0.584689i	$0.801217\pi$
$4$	4.92974	2.46487
$5$	1.41252	0.631699	0.315850	−	0.948809i	$-0.397710\pi$
$5$	1.41252	0.631699	0.315850	+	0.948809i	$0.397710\pi$
$6$	7.39789	3.02018
$7$	3.18061	1.20216	0.601078	−	0.799190i	$-0.294738\pi$
$7$	3.18061	1.20216	0.601078	+	0.799190i	$0.294738\pi$
$8$	−7.71236	−2.72673
$9$	4.89767	1.63256
$10$	−3.71838	−1.17586
$11$	0.715727	0.215800	0.107900	−	0.994162i	$-0.465587\pi$
$11$	0.715727	0.215800	0.107900	+	0.994162i	$0.465587\pi$
$12$	−13.8539	−3.99929
$13$	−1.65990	−0.460373	−0.230187	−	0.973147i	$-0.573934\pi$
$13$	−1.65990	−0.460373	−0.230187	+	0.973147i	$0.573934\pi$
$14$	−8.37276	−2.23771
$15$	−3.96958	−1.02494
$16$	10.4428	2.61071
$17$	6.51375	1.57982	0.789908	−	0.613225i	$-0.210128\pi$
$17$	6.51375	1.57982	0.789908	+	0.613225i	$0.210128\pi$
$18$	−12.8928	−3.03886
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	6.96337	1.55706
$21$	−8.93840	−1.95052
$22$	−1.88411	−0.401693
$23$	−3.69982	−0.771466	−0.385733	−	0.922610i	$-0.626051\pi$
$23$	−3.69982	−0.771466	−0.385733	+	0.922610i	$0.626051\pi$
$24$	21.6739	4.42416
$25$	−3.00478	−0.600956
$26$	4.36958	0.856946
$27$	−5.33297	−1.02633
$28$	15.6796	2.96316
$29$	3.54363	0.658035	0.329018	−	0.944324i	$-0.393282\pi$
$29$	3.54363	0.658035	0.329018	+	0.944324i	$0.393282\pi$
$30$	10.4497	1.90784
$31$	3.26636	0.586656	0.293328	−	0.956012i	$-0.405237\pi$
$31$	3.26636	0.586656	0.293328	+	0.956012i	$0.405237\pi$
$32$	−12.0654	−2.13289
$33$	−2.01139	−0.350138
$34$	−17.1470	−2.94069
$35$	4.49268	0.759402
$36$	24.1442	4.02404
$37$	−9.57448	−1.57403	−0.787017	−	0.616931i	$-0.788376\pi$
$37$	−9.57448	−1.57403	−0.787017	+	0.616931i	$0.788376\pi$
$38$	−2.63244	−0.427038
$39$	4.66478	0.746962
$40$	−10.8939	−1.72247
$41$	−0.712498	−0.111273	−0.0556367	−	0.998451i	$-0.517719\pi$
$41$	−0.712498	−0.111273	−0.0556367	+	0.998451i	$0.517719\pi$
$42$	23.5298	3.63072
$43$	7.35785	1.12206	0.561031	−	0.827795i	$-0.310405\pi$
$43$	7.35785	1.12206	0.561031	+	0.827795i	$0.310405\pi$
$44$	3.52834	0.531918
$45$	6.91806	1.03128
$46$	9.73956	1.43602
$47$	−6.54066	−0.954054	−0.477027	−	0.878889i	$-0.658286\pi$
$47$	−6.54066	−0.954054	−0.477027	+	0.878889i	$0.658286\pi$
$48$	−29.3473	−4.23592
$49$	3.11627	0.445181
$50$	7.90990	1.11863
$51$	−18.3054	−2.56328
$52$	−8.18287	−1.13476
$53$	11.8429	1.62675	0.813376	−	0.581738i	$-0.197627\pi$
$53$	11.8429	1.62675	0.813376	+	0.581738i	$0.197627\pi$
$54$	14.0387	1.91043
$55$	1.01098	0.136321
$56$	−24.5300	−3.27796
$57$	−2.81028	−0.372230
$58$	−9.32839	−1.22488
$59$	9.77617	1.27275	0.636375	−	0.771380i	$-0.280433\pi$
$59$	9.77617	1.27275	0.636375	+	0.771380i	$0.280433\pi$
$60$	−19.5690	−2.52635
$61$	−6.93487	−0.887919	−0.443960	−	0.896047i	$-0.646427\pi$
$61$	−6.93487	−0.887919	−0.443960	+	0.896047i	$0.646427\pi$
$62$	−8.59851	−1.09201
$63$	15.5776	1.96259
$64$	10.8758	1.35948
$65$	−2.34464	−0.290817
$66$	5.29487	0.651753
$67$	−8.41543	−1.02811	−0.514054	−	0.857758i	$-0.671857\pi$
$67$	−8.41543	−1.02811	−0.514054	+	0.857758i	$0.671857\pi$
$68$	32.1111	3.89404
$69$	10.3975	1.25172
$70$	−11.8267	−1.41356
$71$	−12.7819	−1.51693	−0.758467	−	0.651711i	$-0.774051\pi$
$71$	−12.7819	−1.51693	−0.758467	+	0.651711i	$0.774051\pi$
$72$	−37.7726	−4.45154
$73$	−12.4423	−1.45627	−0.728133	−	0.685436i	$-0.759612\pi$
$73$	−12.4423	−1.45627	−0.728133	+	0.685436i	$0.759612\pi$
$74$	25.2042	2.92993
$75$	8.44427	0.975060
$76$	4.92974	0.565480
$77$	2.27645	0.259425
$78$	−12.2797	−1.39041
$79$	6.26390	0.704744	0.352372	−	0.935860i	$-0.385375\pi$
$79$	6.26390	0.704744	0.352372	+	0.935860i	$0.385375\pi$
$80$	14.7507	1.64918
$81$	0.294134	0.0326816
$82$	1.87561	0.207126
$83$	−13.2155	−1.45059	−0.725293	−	0.688440i	$-0.758296\pi$
$83$	−13.2155	−1.45059	−0.725293	+	0.688440i	$0.758296\pi$
$84$	−44.0639	−4.80777
$85$	9.20082	0.997969
$86$	−19.3691	−2.08862
$87$	−9.95858	−1.06767
$88$	−5.51994	−0.588428
$89$	7.34484	0.778551	0.389276	−	0.921121i	$-0.372725\pi$
$89$	7.34484	0.778551	0.389276	+	0.921121i	$0.372725\pi$
$90$	−18.2114	−1.91965
$91$	−5.27949	−0.553441
$92$	−18.2392	−1.90156
$93$	−9.17939	−0.951859
$94$	17.2179	1.77589
$95$	1.41252	0.144922
$96$	33.9072	3.46064
$97$	−18.8104	−1.90991	−0.954955	−	0.296751i	$-0.904097\pi$
$97$	−18.8104	−1.90991	−0.954955	+	0.296751i	$0.904097\pi$
$98$	−8.20339	−0.828667
$99$	3.50539	0.352305
$100$	−14.8128	−1.48128
$101$	−7.17992	−0.714429	−0.357214	−	0.934022i	$-0.616273\pi$
$101$	−7.17992	−0.714429	−0.357214	+	0.934022i	$0.616273\pi$
$102$	48.1880	4.77132
$103$	−10.8495	−1.06903	−0.534516	−	0.845158i	$-0.679506\pi$
$103$	−10.8495	−1.06903	−0.534516	+	0.845158i	$0.679506\pi$
$104$	12.8017	1.25531
$105$	−12.6257	−1.23214
$106$	−31.1758	−3.02806
$107$	−9.49256	−0.917681	−0.458840	−	0.888519i	$-0.651735\pi$
$107$	−9.49256	−0.917681	−0.458840	+	0.888519i	$0.651735\pi$
$108$	−26.2901	−2.52977
$109$	−19.3232	−1.85083	−0.925413	−	0.378961i	$-0.876282\pi$
$109$	−19.3232	−1.85083	−0.925413	+	0.378961i	$0.876282\pi$
$110$	−2.66134	−0.253749
$111$	26.9069	2.55389
$112$	33.2146	3.13848
$113$	−4.78346	−0.449990	−0.224995	−	0.974360i	$-0.572237\pi$
$113$	−4.78346	−0.449990	−0.224995	+	0.974360i	$0.572237\pi$
$114$	7.39789	0.692876
$115$	−5.22608	−0.487335
$116$	17.4692	1.62197
$117$	−8.12963	−0.751584
$118$	−25.7352	−2.36912
$119$	20.7177	1.89919
$120$	30.6148	2.79474
$121$	−10.4877	−0.953430
$122$	18.2556	1.65279
$123$	2.00232	0.180543
$124$	16.1023	1.44603
$125$	−11.3069	−1.01132
$126$	−41.0070	−3.65319
$127$	−15.9080	−1.41160	−0.705802	−	0.708410i	$-0.749413\pi$
$127$	−15.9080	−1.41160	−0.705802	+	0.708410i	$0.749413\pi$
$128$	−4.49912	−0.397670
$129$	−20.6776	−1.82056
$130$	6.17213	0.541332
$131$	−19.7689	−1.72722	−0.863609	−	0.504162i	$-0.831801\pi$
$131$	−19.7689	−1.72722	−0.863609	+	0.504162i	$0.831801\pi$
$132$	−9.91563	−0.863045
$133$	3.18061	0.275794
$134$	22.1531	1.91374
$135$	−7.53294	−0.648332
$136$	−50.2364	−4.30773
$137$	22.8533	1.95249	0.976243	−	0.216678i	$-0.0695223\pi$
$137$	22.8533	1.95249	0.976243	+	0.216678i	$0.0695223\pi$
$138$	−27.3709	−2.32996
$139$	13.7757	1.16844	0.584220	−	0.811595i	$-0.301401\pi$
$139$	13.7757	1.16844	0.584220	+	0.811595i	$0.301401\pi$
$140$	22.1477	1.87183
$141$	18.3811	1.54797
$142$	33.6476	2.82365
$143$	−1.18803	−0.0993484
$144$	51.1455	4.26213
$145$	5.00546	0.415680
$146$	32.7537	2.71072
$147$	−8.75758	−0.722313
$148$	−47.1997	−3.87979
$149$	−14.9659	−1.22606	−0.613028	−	0.790061i	$-0.710049\pi$
$149$	−14.9659	−1.22606	−0.613028	+	0.790061i	$0.710049\pi$
$150$	−22.2290	−1.81499
$151$	8.62263	0.701700	0.350850	−	0.936432i	$-0.385893\pi$
$151$	8.62263	0.701700	0.350850	+	0.936432i	$0.385893\pi$
$152$	−7.71236	−0.625555
$153$	31.9022	2.57914
$154$	−5.99261	−0.482898
$155$	4.61381	0.370590
$156$	22.9961	1.84116
$157$	−3.78409	−0.302003	−0.151002	−	0.988534i	$-0.548250\pi$
$157$	−3.78409	−0.302003	−0.151002	+	0.988534i	$0.548250\pi$
$158$	−16.4893	−1.31182
$159$	−33.2820	−2.63943
$160$	−17.0427	−1.34734
$161$	−11.7677	−0.927423
$162$	−0.774291	−0.0608340
$163$	6.30973	0.494216	0.247108	−	0.968988i	$-0.420520\pi$
$163$	6.30973	0.494216	0.247108	+	0.968988i	$0.420520\pi$
$164$	−3.51243	−0.274275
$165$	−2.84114	−0.221182
$166$	34.7889	2.70014
$167$	−7.22888	−0.559388	−0.279694	−	0.960089i	$-0.590233\pi$
$167$	−7.22888	−0.559388	−0.279694	+	0.960089i	$0.590233\pi$
$168$	68.9361	5.31854
$169$	−10.2447	−0.788057
$170$	−24.2206	−1.85763
$171$	4.89767	0.374534
$172$	36.2723	2.76573
$173$	−6.17205	−0.469252	−0.234626	−	0.972086i	$-0.575387\pi$
$173$	−6.17205	−0.469252	−0.234626	+	0.972086i	$0.575387\pi$
$174$	26.2154	1.98738
$175$	−9.55703	−0.722443
$176$	7.47422	0.563390
$177$	−27.4738	−2.06506
$178$	−19.3348	−1.44921
$179$	22.5154	1.68288	0.841439	−	0.540353i	$-0.181709\pi$
$179$	22.5154	1.68288	0.841439	+	0.540353i	$0.181709\pi$
$180$	34.1042	2.54198
$181$	9.31404	0.692307	0.346153	−	0.938178i	$-0.387488\pi$
$181$	9.31404	0.692307	0.346153	+	0.938178i	$0.387488\pi$
$182$	13.8979	1.03018
$183$	19.4889	1.44066
$184$	28.5344	2.10358
$185$	−13.5242	−0.994316
$186$	24.1642	1.77181
$187$	4.66206	0.340924
$188$	−32.2437	−2.35162
$189$	−16.9621	−1.23381
$190$	−3.71838	−0.269760
$191$	5.05103	0.365480	0.182740	−	0.983161i	$-0.441503\pi$
$191$	5.05103	0.365480	0.182740	+	0.983161i	$0.441503\pi$
$192$	−30.5641	−2.20578
$193$	−7.73714	−0.556931	−0.278466	−	0.960446i	$-0.589826\pi$
$193$	−7.73714	−0.556931	−0.278466	+	0.960446i	$0.589826\pi$
$194$	49.5173	3.55514
$195$	6.58910	0.471855
$196$	15.3624	1.09731
$197$	11.6252	0.828264	0.414132	−	0.910217i	$-0.364085\pi$
$197$	11.6252	0.828264	0.414132	+	0.910217i	$0.364085\pi$
$198$	−9.22773	−0.655786
$199$	7.92663	0.561904	0.280952	−	0.959722i	$-0.409350\pi$
$199$	7.92663	0.561904	0.280952	+	0.959722i	$0.409350\pi$
$200$	23.1739	1.63865
$201$	23.6497	1.66812
$202$	18.9007	1.32985
$203$	11.2709	0.791062
$204$	−90.2411	−6.31814
$205$	−1.00642	−0.0702914
$206$	28.5606	1.98991
$207$	−18.1205	−1.25946
$208$	−17.3341	−1.20190
$209$	0.715727	0.0495078
$210$	33.2364	2.29353
$211$	0.894548	0.0615832	0.0307916	−	0.999526i	$-0.490197\pi$
$211$	0.894548	0.0615832	0.0307916	+	0.999526i	$0.490197\pi$
$212$	58.3826	4.00973
$213$	35.9207	2.46125
$214$	24.9886	1.70819
$215$	10.3931	0.708805
$216$	41.1298	2.79853
$217$	10.3890	0.705253
$218$	50.8671	3.44516
$219$	34.9664	2.36281
$220$	4.98387	0.336012
$221$	−10.8122	−0.727305
$222$	−70.8309	−4.75386
$223$	−19.5787	−1.31109	−0.655544	−	0.755157i	$-0.727561\pi$
$223$	−19.5787	−1.31109	−0.655544	+	0.755157i	$0.727561\pi$
$224$	−38.3754	−2.56406
$225$	−14.7164	−0.981094
$226$	12.5922	0.837619
$227$	14.0467	0.932310	0.466155	−	0.884703i	$-0.345639\pi$
$227$	14.0467	0.932310	0.466155	+	0.884703i	$0.345639\pi$
$228$	−13.8539	−0.917499
$229$	−2.18964	−0.144696	−0.0723478	−	0.997379i	$-0.523049\pi$
$229$	−2.18964	−0.144696	−0.0723478	+	0.997379i	$0.523049\pi$
$230$	13.7573	0.907132
$231$	−6.39745	−0.420921
$232$	−27.3297	−1.79428
$233$	−20.6099	−1.35020	−0.675100	−	0.737726i	$-0.735900\pi$
$233$	−20.6099	−1.35020	−0.675100	+	0.737726i	$0.735900\pi$
$234$	21.4008	1.39901
$235$	−9.23883	−0.602675
$236$	48.1940	3.13716
$237$	−17.6033	−1.14346
$238$	−54.5380	−3.53518
$239$	11.2709	0.729055	0.364528	−	0.931193i	$-0.381230\pi$
$239$	11.2709	0.729055	0.364528	+	0.931193i	$0.381230\pi$
$240$	−41.4537	−2.67583
$241$	20.6022	1.32711	0.663554	−	0.748129i	$-0.269047\pi$
$241$	20.6022	1.32711	0.663554	+	0.748129i	$0.269047\pi$
$242$	27.6083	1.77473
$243$	15.1723	0.973304
$244$	−34.1871	−2.18860
$245$	4.40180	0.281221
$246$	−5.27098	−0.336065
$247$	−1.65990	−0.105617
$248$	−25.1914	−1.59965
$249$	37.1391	2.35360
$250$	29.7648	1.88249
$251$	14.0783	0.888613	0.444306	−	0.895875i	$-0.353450\pi$
$251$	14.0783	0.888613	0.444306	+	0.895875i	$0.353450\pi$
$252$	76.7933	4.83752
$253$	−2.64806	−0.166482
$254$	41.8767	2.62758
$255$	−25.8569	−1.61922
$256$	−9.90802	−0.619251
$257$	−20.7435	−1.29395	−0.646973	−	0.762513i	$-0.723965\pi$
$257$	−20.7435	−1.29395	−0.646973	+	0.762513i	$0.723965\pi$
$258$	54.4325	3.38882
$259$	−30.4527	−1.89224
$260$	−11.5585	−0.716827
$261$	17.3555	1.07428
$262$	52.0405	3.21507
$263$	−9.00380	−0.555198	−0.277599	−	0.960697i	$-0.589539\pi$
$263$	−9.00380	−0.555198	−0.277599	+	0.960697i	$0.589539\pi$
$264$	15.5126	0.954733
$265$	16.7284	1.02762
$266$	−8.37276	−0.513367
$267$	−20.6410	−1.26321
$268$	−41.4858	−2.53415
$269$	−11.4408	−0.697558	−0.348779	−	0.937205i	$-0.613404\pi$
$269$	−11.4408	−0.697558	−0.348779	+	0.937205i	$0.613404\pi$
$270$	19.8300	1.20682
$271$	3.48533	0.211719	0.105859	−	0.994381i	$-0.466241\pi$
$271$	3.48533	0.211719	0.105859	+	0.994381i	$0.466241\pi$
$272$	68.0220	4.12444
$273$	14.8368	0.897966
$274$	−60.1598	−3.63439
$275$	−2.15060	−0.129686
$276$	51.2571	3.08531
$277$	−25.6648	−1.54205	−0.771025	−	0.636805i	$-0.780256\pi$
$277$	−25.6648	−1.54205	−0.771025	+	0.636805i	$0.780256\pi$
$278$	−36.2637	−2.17495
$279$	15.9976	0.957749
$280$	−34.6492	−2.07068
$281$	5.41233	0.322872	0.161436	−	0.986883i	$-0.448387\pi$
$281$	5.41233	0.322872	0.161436	+	0.986883i	$0.448387\pi$
$282$	−48.3871	−2.88141
$283$	19.0675	1.13344	0.566722	−	0.823909i	$-0.308211\pi$
$283$	19.0675	1.13344	0.566722	+	0.823909i	$0.308211\pi$
$284$	−63.0115	−3.73904
$285$	−3.96958	−0.235138
$286$	3.12743	0.184929
$287$	−2.26618	−0.133768
$288$	−59.0924	−3.48206
$289$	25.4289	1.49582
$290$	−13.1766	−0.773754
$291$	52.8625	3.09886
$292$	−61.3375	−3.58950
$293$	15.4819	0.904461	0.452230	−	0.891901i	$-0.350628\pi$
$293$	15.4819	0.904461	0.452230	+	0.891901i	$0.350628\pi$
$294$	23.0538	1.34453
$295$	13.8091	0.803995
$296$	73.8418	4.29197
$297$	−3.81695	−0.221482
$298$	39.3969	2.28220
$299$	6.14133	0.355162
$300$	41.6280	2.40340
$301$	23.4024	1.34889
$302$	−22.6986	−1.30615
$303$	20.1776	1.15917
$304$	10.4428	0.598938
$305$	−9.79566	−0.560898
$306$	−83.9805	−4.80085
$307$	−29.2918	−1.67177	−0.835886	−	0.548903i	$-0.815046\pi$
$307$	−29.2918	−1.67177	−0.835886	+	0.548903i	$0.815046\pi$
$308$	11.2223	0.639449
$309$	30.4901	1.73452
$310$	−12.1456	−0.689823
$311$	−7.88718	−0.447241	−0.223621	−	0.974676i	$-0.571788\pi$
$311$	−7.88718	−0.447241	−0.223621	+	0.974676i	$0.571788\pi$
$312$	−35.9764	−2.03676
$313$	−30.9158	−1.74746	−0.873731	−	0.486409i	$-0.838306\pi$
$313$	−30.9158	−1.74746	−0.873731	+	0.486409i	$0.838306\pi$
$314$	9.96139	0.562154
$315$	22.0036	1.23977
$316$	30.8794	1.73710
$317$	1.00000	0.0561656
$317$	1.00000	0.0561656
$318$	87.6127	4.91308
$319$	2.53627	0.142004
$320$	15.3624	0.858782
$321$	26.6767	1.48895
$322$	30.9777	1.72632
$323$	6.51375	0.362435
$324$	1.45001	0.0805559
$325$	4.98763	0.276664
$326$	−16.6100	−0.919942
$327$	54.3035	3.00299
$328$	5.49504	0.303413
$329$	−20.8033	−1.14692
$330$	7.47912	0.411712
$331$	1.22825	0.0675110	0.0337555	−	0.999430i	$-0.489253\pi$
$331$	1.22825	0.0675110	0.0337555	+	0.999430i	$0.489253\pi$
$332$	−65.1488	−3.57550
$333$	−46.8926	−2.56970
$334$	19.0296	1.04125
$335$	−11.8870	−0.649455
$336$	−93.3422	−5.09224
$337$	8.54164	0.465293	0.232646	−	0.972561i	$-0.425262\pi$
$337$	8.54164	0.465293	0.232646	+	0.972561i	$0.425262\pi$
$338$	26.9686	1.46690
$339$	13.4429	0.730116
$340$	45.3576	2.45986
$341$	2.33782	0.126600
$342$	−12.8928	−0.697163
$343$	−12.3526	−0.666979
$344$	−56.7463	−3.05956
$345$	14.6867	0.790708
$346$	16.2475	0.873474
$347$	−19.9934	−1.07330	−0.536651	−	0.843804i	$-0.680311\pi$
$347$	−19.9934	−1.07330	−0.536651	+	0.843804i	$0.680311\pi$
$348$	−49.0932	−2.63167
$349$	23.3115	1.24783	0.623917	−	0.781490i	$-0.285540\pi$
$349$	23.3115	1.24783	0.623917	+	0.781490i	$0.285540\pi$
$350$	25.1583	1.34477
$351$	8.85219	0.472495
$352$	−8.63555	−0.460276
$353$	21.9043	1.16585	0.582923	−	0.812527i	$-0.301909\pi$
$353$	21.9043	1.16585	0.582923	+	0.812527i	$0.301909\pi$
$354$	72.3230	3.84393
$355$	−18.0547	−0.958246
$356$	36.2081	1.91903
$357$	−58.2225	−3.08146
$358$	−59.2703	−3.13253
$359$	22.4398	1.18433	0.592164	−	0.805817i	$-0.298274\pi$
$359$	22.4398	1.18433	0.592164	+	0.805817i	$0.298274\pi$
$360$	−53.3546	−2.81203
$361$	1.00000	0.0526316
$362$	−24.5186	−1.28867
$363$	29.4735	1.54696
$364$	−26.0265	−1.36416
$365$	−17.5751	−0.919922
$366$	−51.3034	−2.68167
$367$	4.03893	0.210830	0.105415	−	0.994428i	$-0.466383\pi$
$367$	4.03893	0.210830	0.105415	+	0.994428i	$0.466383\pi$
$368$	−38.6366	−2.01407
$369$	−3.48958	−0.181660
$370$	35.6015	1.85084
$371$	37.6677	1.95561
$372$	−45.2520	−2.34621
$373$	−4.86841	−0.252077	−0.126038	−	0.992025i	$-0.540226\pi$
$373$	−4.86841	−0.252077	−0.126038	+	0.992025i	$0.540226\pi$
$374$	−12.2726	−0.634601
$375$	31.7756	1.64089
$376$	50.4439	2.60145
$377$	−5.88206	−0.302942
$378$	44.6517	2.29663
$379$	16.0300	0.823404	0.411702	−	0.911319i	$-0.364934\pi$
$379$	16.0300	0.823404	0.411702	+	0.911319i	$0.364934\pi$
$380$	6.96337	0.357213
$381$	44.7058	2.29035
$382$	−13.2965	−0.680310
$383$	12.0472	0.615582	0.307791	−	0.951454i	$-0.400410\pi$
$383$	12.0472	0.615582	0.307791	+	0.951454i	$0.400410\pi$
$384$	12.6438	0.645225
$385$	3.21553	0.163879
$386$	20.3676	1.03668
$387$	36.0363	1.83183
$388$	−92.7305	−4.70768
$389$	−27.3646	−1.38744	−0.693720	−	0.720244i	$-0.744030\pi$
$389$	−27.3646	−1.38744	−0.693720	+	0.720244i	$0.744030\pi$
$390$	−17.3454	−0.878319
$391$	−24.0997	−1.21877
$392$	−24.0338	−1.21389
$393$	55.5562	2.80244
$394$	−30.6027	−1.54174
$395$	8.84790	0.445186
$396$	17.2807	0.868386
$397$	−28.2590	−1.41828	−0.709139	−	0.705069i	$-0.750916\pi$
$397$	−28.2590	−1.41828	−0.709139	+	0.705069i	$0.750916\pi$
$398$	−20.8664	−1.04594
$399$	−8.93840	−0.447479
$400$	−31.3784	−1.56892
$401$	8.75871	0.437389	0.218694	−	0.975793i	$-0.429820\pi$
$401$	8.75871	0.437389	0.218694	+	0.975793i	$0.429820\pi$
$402$	−62.2564	−3.10507
$403$	−5.42183	−0.270081
$404$	−35.3951	−1.76097
$405$	0.415471	0.0206449
$406$	−29.6699	−1.47249
$407$	−6.85271	−0.339676
$408$	141.178	6.98936
$409$	−18.9117	−0.935123	−0.467561	−	0.883961i	$-0.654867\pi$
$409$	−18.9117	−0.935123	−0.467561	+	0.883961i	$0.654867\pi$
$410$	2.64934	0.130841
$411$	−64.2240	−3.16794
$412$	−53.4852	−2.63502
$413$	31.0942	1.53004
$414$	47.7011	2.34438
$415$	−18.6671	−0.916334
$416$	20.0274	0.981924
$417$	−38.7136	−1.89581
$418$	−1.88411	−0.0921547
$419$	−22.1120	−1.08024	−0.540122	−	0.841587i	$-0.681622\pi$
$419$	−22.1120	−1.08024	−0.540122	+	0.841587i	$0.681622\pi$
$420$	−62.2413	−3.03707
$421$	8.66910	0.422506	0.211253	−	0.977431i	$-0.432246\pi$
$421$	8.66910	0.422506	0.211253	+	0.977431i	$0.432246\pi$
$422$	−2.35484	−0.114632
$423$	−32.0340	−1.55755
$424$	−91.3370	−4.43572
$425$	−19.5724	−0.949400
$426$	−94.5592	−4.58141
$427$	−22.0571	−1.06742
$428$	−46.7958	−2.26196
$429$	3.33871	0.161194
$430$	−27.3593	−1.31938
$431$	−14.7810	−0.711975	−0.355987	−	0.934491i	$-0.615855\pi$
$431$	−14.7810	−0.711975	−0.355987	+	0.934491i	$0.615855\pi$
$432$	−55.6914	−2.67945
$433$	15.2884	0.734714	0.367357	−	0.930080i	$-0.380263\pi$
$433$	15.2884	0.734714	0.367357	+	0.930080i	$0.380263\pi$
$434$	−27.3485	−1.31277
$435$	−14.0667	−0.674448
$436$	−95.2582	−4.56204
$437$	−3.69982	−0.176986
$438$	−92.0471	−4.39818
$439$	−12.4427	−0.593858	−0.296929	−	0.954900i	$-0.595962\pi$
$439$	−12.4427	−0.593858	−0.296929	+	0.954900i	$0.595962\pi$
$440$	−7.79704	−0.371709
$441$	15.2624	0.726783
$442$	28.4624	1.35382
$443$	13.7563	0.653583	0.326792	−	0.945096i	$-0.394032\pi$
$443$	13.7563	0.653583	0.326792	+	0.945096i	$0.394032\pi$
$444$	132.644	6.29501
$445$	10.3747	0.491810
$446$	51.5398	2.44048
$447$	42.0584	1.98930
$448$	34.5918	1.63431
$449$	−26.6703	−1.25865	−0.629324	−	0.777143i	$-0.716668\pi$
$449$	−26.6703	−1.25865	−0.629324	+	0.777143i	$0.716668\pi$
$450$	38.7401	1.82622
$451$	−0.509954	−0.0240128
$452$	−23.5812	−1.10917
$453$	−24.2320	−1.13852
$454$	−36.9770	−1.73542
$455$	−7.45739	−0.349608
$456$	21.6739	1.01497
$457$	24.7435	1.15745	0.578726	−	0.815522i	$-0.303550\pi$
$457$	24.7435	1.15745	0.578726	+	0.815522i	$0.303550\pi$
$458$	5.76410	0.269339
$459$	−34.7376	−1.62141
$460$	−25.7632	−1.20122
$461$	27.5042	1.28100	0.640499	−	0.767959i	$-0.278728\pi$
$461$	27.5042	1.28100	0.640499	+	0.767959i	$0.278728\pi$
$462$	16.8409	0.783509
$463$	−12.1842	−0.566247	−0.283123	−	0.959083i	$-0.591371\pi$
$463$	−12.1842	−0.566247	−0.283123	+	0.959083i	$0.591371\pi$
$464$	37.0055	1.71794
$465$	−12.9661	−0.601289
$466$	54.2543	2.51328
$467$	23.2657	1.07661	0.538305	−	0.842750i	$-0.319065\pi$
$467$	23.2657	1.07661	0.538305	+	0.842750i	$0.319065\pi$
$468$	−40.0769	−1.85256
$469$	−26.7662	−1.23595
$470$	24.3207	1.12183
$471$	10.6343	0.490005
$472$	−75.3974	−3.47044
$473$	5.26621	0.242140
$474$	46.3397	2.12845
$475$	−3.00478	−0.137869
$476$	102.133	4.68125
$477$	58.0028	2.65576
$478$	−29.6700	−1.35708
$479$	−22.7752	−1.04063	−0.520313	−	0.853976i	$-0.674185\pi$
$479$	−22.7752	−1.04063	−0.520313	+	0.853976i	$0.674185\pi$
$480$	47.8947	2.18608
$481$	15.8927	0.724643
$482$	−54.2342	−2.47030
$483$	33.0705	1.50476
$484$	−51.7018	−2.35008
$485$	−26.5702	−1.20649
$486$	−39.9402	−1.81172
$487$	−7.69884	−0.348868	−0.174434	−	0.984669i	$-0.555810\pi$
$487$	−7.69884	−0.348868	−0.174434	+	0.984669i	$0.555810\pi$
$488$	53.4842	2.42112
$489$	−17.7321	−0.801874
$490$	−11.5875	−0.523469
$491$	−28.5394	−1.28797	−0.643983	−	0.765040i	$-0.722719\pi$
$491$	−28.5394	−1.28797	−0.643983	+	0.765040i	$0.722719\pi$
$492$	9.87090	0.445015
$493$	23.0823	1.03957
$494$	4.36958	0.196597
$495$	4.95144	0.222551
$496$	34.1101	1.53159
$497$	−40.6543	−1.82359
$498$	−97.7665	−4.38102
$499$	12.4670	0.558100	0.279050	−	0.960277i	$-0.409980\pi$
$499$	12.4670	0.558100	0.279050	+	0.960277i	$0.409980\pi$
$500$	−55.7402	−2.49278
$501$	20.3152	0.907615
$502$	−37.0602	−1.65408
$503$	13.8632	0.618130	0.309065	−	0.951041i	$-0.399984\pi$
$503$	13.8632	0.618130	0.309065	+	0.951041i	$0.399984\pi$
$504$	−120.140	−5.35145
$505$	−10.1418	−0.451304
$506$	6.97086	0.309893
$507$	28.7906	1.27863
$508$	−78.4221	−3.47942
$509$	26.3910	1.16976	0.584880	−	0.811120i	$-0.301142\pi$
$509$	26.3910	1.16976	0.584880	+	0.811120i	$0.301142\pi$
$510$	68.0666	3.01404
$511$	−39.5742	−1.75066
$512$	35.0805	1.55035
$513$	−5.33297	−0.235456
$514$	54.6061	2.40857
$515$	−15.3252	−0.675307
$516$	−101.935	−4.48744
$517$	−4.68133	−0.205884
$518$	80.1648	3.52224
$519$	17.3452	0.761369
$520$	18.0827	0.792980
$521$	−11.2975	−0.494952	−0.247476	−	0.968894i	$-0.579601\pi$
$521$	−11.2975	−0.494952	−0.247476	+	0.968894i	$0.579601\pi$
$522$	−45.6873	−1.99968
$523$	−10.6050	−0.463723	−0.231861	−	0.972749i	$-0.574482\pi$
$523$	−10.6050	−0.463723	−0.231861	+	0.972749i	$0.574482\pi$
$524$	−97.4556	−4.25737
$525$	26.8579	1.17218
$526$	23.7020	1.03345
$527$	21.2763	0.926809
$528$	−21.0046	−0.914110
$529$	−9.31132	−0.404840
$530$	−44.0365	−1.91283
$531$	47.8804	2.07783
$532$	15.6796	0.679795
$533$	1.18267	0.0512273
$534$	54.3363	2.35136
$535$	−13.4085	−0.579698
$536$	64.9028	2.80337
$537$	−63.2744	−2.73049
$538$	30.1172	1.29845
$539$	2.23040	0.0960700
$540$	−37.1354	−1.59805
$541$	13.5649	0.583202	0.291601	−	0.956540i	$-0.405812\pi$
$541$	13.5649	0.583202	0.291601	+	0.956540i	$0.405812\pi$
$542$	−9.17493	−0.394097
$543$	−26.1750	−1.12328
$544$	−78.5912	−3.36957
$545$	−27.2944	−1.16917
$546$	−39.0571	−1.67149
$547$	20.6344	0.882262	0.441131	−	0.897443i	$-0.354577\pi$
$547$	20.6344	0.882262	0.441131	+	0.897443i	$0.354577\pi$
$548$	112.661	4.81262
$549$	−33.9647	−1.44958
$550$	5.66133	0.241400
$551$	3.54363	0.150964
$552$	−80.1895	−3.41309
$553$	19.9230	0.847213
$554$	67.5611	2.87040
$555$	38.0067	1.61329
$556$	67.9106	2.88005
$557$	18.1345	0.768384	0.384192	−	0.923253i	$-0.374480\pi$
$557$	18.1345	0.768384	0.384192	+	0.923253i	$0.374480\pi$
$558$	−42.1126	−1.78277
$559$	−12.2133	−0.516567
$560$	46.9163	1.98258
$561$	−13.1017	−0.553154
$562$	−14.2476	−0.601000
$563$	20.3944	0.859522	0.429761	−	0.902943i	$-0.358598\pi$
$563$	20.3944	0.859522	0.429761	+	0.902943i	$0.358598\pi$
$564$	90.6139	3.81553
$565$	−6.75675	−0.284258
$566$	−50.1940	−2.10981
$567$	0.935526	0.0392884
$568$	98.5787	4.13627
$569$	6.42396	0.269307	0.134653	−	0.990893i	$-0.457008\pi$
$569$	6.42396	0.269307	0.134653	+	0.990893i	$0.457008\pi$
$570$	10.4497	0.437689
$571$	−34.4955	−1.44359	−0.721795	−	0.692107i	$-0.756683\pi$
$571$	−34.4955	−1.44359	−0.721795	+	0.692107i	$0.756683\pi$
$572$	−5.85669	−0.244881
$573$	−14.1948	−0.592997
$574$	5.96557	0.248998
$575$	11.1172	0.463617
$576$	53.2662	2.21943
$577$	−8.40107	−0.349741	−0.174871	−	0.984591i	$-0.555951\pi$
$577$	−8.40107	−0.349741	−0.174871	+	0.984591i	$0.555951\pi$
$578$	−66.9401	−2.78434
$579$	21.7435	0.903630
$580$	24.6756	1.02460
$581$	−42.0332	−1.74383
$582$	−139.157	−5.76826
$583$	8.47631	0.351053
$584$	95.9598	3.97084
$585$	−11.4833	−0.474775
$586$	−40.7551	−1.68358
$587$	−11.9999	−0.495287	−0.247644	−	0.968851i	$-0.579656\pi$
$587$	−11.9999	−0.495287	−0.247644	+	0.968851i	$0.579656\pi$
$588$	−43.1726	−1.78041
$589$	3.26636	0.134588
$590$	−36.3515	−1.49657
$591$	−32.6702	−1.34387
$592$	−99.9847	−4.10935
$593$	−11.2292	−0.461126	−0.230563	−	0.973057i	$-0.574057\pi$
$593$	−11.2292	−0.461126	−0.230563	+	0.973057i	$0.574057\pi$
$594$	10.0479	0.412270
$595$	29.2642	1.19971
$596$	−73.7781	−3.02207
$597$	−22.2760	−0.911697
$598$	−16.1667	−0.661105
$599$	27.2862	1.11489	0.557443	−	0.830215i	$-0.311783\pi$
$599$	27.2862	1.11489	0.557443	+	0.830215i	$0.311783\pi$
$600$	−65.1252	−2.65873
$601$	−18.9471	−0.772869	−0.386434	−	0.922317i	$-0.626293\pi$
$601$	−18.9471	−0.772869	−0.386434	+	0.922317i	$0.626293\pi$
$602$	−61.6055	−2.51085
$603$	−41.2159	−1.67844
$604$	42.5073	1.72960
$605$	−14.8142	−0.602281
$606$	−53.1162	−2.15770
$607$	6.11590	0.248237	0.124118	−	0.992267i	$-0.460390\pi$
$607$	6.11590	0.248237	0.124118	+	0.992267i	$0.460390\pi$
$608$	−12.0654	−0.489318
$609$	−31.6744	−1.28351
$610$	25.7865	1.04406
$611$	10.8568	0.439221
$612$	157.269	6.35723
$613$	−13.0910	−0.528741	−0.264371	−	0.964421i	$-0.585164\pi$
$613$	−13.0910	−0.528741	−0.264371	+	0.964421i	$0.585164\pi$
$614$	77.1089	3.11186
$615$	2.82832	0.114049
$616$	−17.5568	−0.707382
$617$	20.1244	0.810179	0.405089	−	0.914277i	$-0.367240\pi$
$617$	20.1244	0.810179	0.405089	+	0.914277i	$0.367240\pi$
$618$	−80.2633	−3.22867
$619$	22.5742	0.907332	0.453666	−	0.891172i	$-0.350116\pi$
$619$	22.5742	0.907332	0.453666	+	0.891172i	$0.350116\pi$
$620$	22.7449	0.913457
$621$	19.7310	0.791779
$622$	20.7625	0.832502
$623$	23.3610	0.935940
$624$	48.7135	1.95010
$625$	−0.947396	−0.0378958
$626$	81.3839	3.25275
$627$	−2.01139	−0.0803272
$628$	−18.6546	−0.744398
$629$	−62.3657	−2.48668
$630$	−57.9233	−2.30772
$631$	30.0327	1.19558	0.597791	−	0.801652i	$-0.296045\pi$
$631$	30.0327	1.19558	0.597791	+	0.801652i	$0.296045\pi$
$632$	−48.3095	−1.92165
$633$	−2.51393	−0.0999197
$634$	−2.63244	−0.104548
$635$	−22.4704	−0.891709
$636$	−164.071	−6.50585
$637$	−5.17269	−0.204949
$638$	−6.67658	−0.264328
$639$	−62.6016	−2.47648
$640$	−6.35510	−0.251208
$641$	−8.06523	−0.318557	−0.159279	−	0.987234i	$-0.550917\pi$
$641$	−8.06523	−0.318557	−0.159279	+	0.987234i	$0.550917\pi$
$642$	−70.2249	−2.77156
$643$	15.4982	0.611189	0.305595	−	0.952162i	$-0.401145\pi$
$643$	15.4982	0.611189	0.305595	+	0.952162i	$0.401145\pi$
$644$	−58.0116	−2.28598
$645$	−29.2076	−1.15005
$646$	−17.1470	−0.674642
$647$	24.6254	0.968123	0.484061	−	0.875034i	$-0.339161\pi$
$647$	24.6254	0.968123	0.484061	+	0.875034i	$0.339161\pi$
$648$	−2.26847	−0.0891139
$649$	6.99707	0.274659
$650$	−13.1296	−0.514987
$651$	−29.1961	−1.14428
$652$	31.1053	1.21818
$653$	38.2044	1.49505	0.747526	−	0.664233i	$-0.231242\pi$
$653$	38.2044	1.49505	0.747526	+	0.664233i	$0.231242\pi$
$654$	−142.951	−5.58982
$655$	−27.9240	−1.09108
$656$	−7.44050	−0.290503
$657$	−60.9384	−2.37743
$658$	54.7634	2.13490
$659$	6.79851	0.264832	0.132416	−	0.991194i	$-0.457726\pi$
$659$	6.79851	0.264832	0.132416	+	0.991194i	$0.457726\pi$
$660$	−14.0061	−0.545185
$661$	26.3034	1.02308	0.511542	−	0.859258i	$-0.329074\pi$
$661$	26.3034	1.02308	0.511542	+	0.859258i	$0.329074\pi$
$662$	−3.23330	−0.125666
$663$	30.3852	1.18006
$664$	101.922	3.95536
$665$	4.49268	0.174219
$666$	123.442	4.78328
$667$	−13.1108	−0.507652
$668$	−35.6365	−1.37882
$669$	55.0216	2.12726
$670$	31.2917	1.20891
$671$	−4.96347	−0.191613
$672$	107.846	4.16023
$673$	−37.5187	−1.44624	−0.723120	−	0.690722i	$-0.757293\pi$
$673$	−37.5187	−1.44624	−0.723120	+	0.690722i	$0.757293\pi$
$674$	−22.4854	−0.866104
$675$	16.0244	0.616780
$676$	−50.5039	−1.94246
$677$	−32.0171	−1.23052	−0.615258	−	0.788326i	$-0.710948\pi$
$677$	−32.0171	−1.23052	−0.615258	+	0.788326i	$0.710948\pi$
$678$	−35.3875	−1.35905
$679$	−59.8286	−2.29601
$680$	−70.9600	−2.72119
$681$	−39.4751	−1.51269
$682$	−6.15418	−0.235656
$683$	37.8005	1.44639	0.723197	−	0.690642i	$-0.242672\pi$
$683$	37.8005	1.44639	0.723197	+	0.690642i	$0.242672\pi$
$684$	24.1442	0.923177
$685$	32.2808	1.23338
$686$	32.5175	1.24153
$687$	6.15350	0.234771
$688$	76.8368	2.92938
$689$	−19.6581	−0.748913
$690$	−38.6620	−1.47184
$691$	−9.73010	−0.370151	−0.185075	−	0.982724i	$-0.559253\pi$
$691$	−9.73010	−0.370151	−0.185075	+	0.982724i	$0.559253\pi$
$692$	−30.4266	−1.15665
$693$	11.1493	0.423526
$694$	52.6315	1.99786
$695$	19.4585	0.738103
$696$	76.8042	2.91125
$697$	−4.64103	−0.175792
$698$	−61.3660	−2.32274
$699$	57.9196	2.19072
$700$	−47.1136	−1.78073
$701$	−13.3962	−0.505967	−0.252983	−	0.967471i	$-0.581412\pi$
$701$	−13.3962	−0.505967	−0.252983	+	0.967471i	$0.581412\pi$
$702$	−23.3029	−0.879510
$703$	−9.57448	−0.361108
$704$	7.78412	0.293375
$705$	25.9637	0.977849
$706$	−57.6617	−2.17013
$707$	−22.8365	−0.858855
$708$	−135.439	−5.09009
$709$	24.2151	0.909416	0.454708	−	0.890641i	$-0.349744\pi$
$709$	24.2151	0.909416	0.454708	+	0.890641i	$0.349744\pi$
$710$	47.5280	1.78370
$711$	30.6785	1.15053
$712$	−56.6460	−2.12290
$713$	−12.0850	−0.452586
$714$	153.267	5.73588
$715$	−1.67812	−0.0627583
$716$	110.995	4.14807
$717$	−31.6744	−1.18290
$718$	−59.0715	−2.20453
$719$	−24.3652	−0.908669	−0.454334	−	0.890831i	$-0.650123\pi$
$719$	−24.3652	−0.908669	−0.454334	+	0.890831i	$0.650123\pi$
$720$	72.2442	2.69238
$721$	−34.5080	−1.28514
$722$	−2.63244	−0.0979693
$723$	−57.8980	−2.15325
$724$	45.9158	1.70645
$725$	−10.6478	−0.395450
$726$	−77.5871	−2.87953
$727$	41.4588	1.53762	0.768810	−	0.639477i	$-0.220849\pi$
$727$	41.4588	1.53762	0.768810	+	0.639477i	$0.220849\pi$
$728$	40.7173	1.50908
$729$	−43.5208	−1.61188
$730$	46.2654	1.71236
$731$	47.9272	1.77265
$732$	96.0753	3.55104
$733$	27.1274	1.00197	0.500987	−	0.865455i	$-0.332970\pi$
$733$	27.1274	1.00197	0.500987	+	0.865455i	$0.332970\pi$
$734$	−10.6322	−0.392443
$735$	−12.3703	−0.456285
$736$	44.6399	1.64545
$737$	−6.02314	−0.221865
$738$	9.18610	0.338145
$739$	−2.57801	−0.0948337	−0.0474169	−	0.998875i	$-0.515099\pi$
$739$	−2.57801	−0.0948337	−0.0474169	+	0.998875i	$0.515099\pi$
$740$	−66.6706	−2.45086
$741$	4.66478	0.171365
$742$	−99.1581	−3.64021
$743$	21.2982	0.781357	0.390678	−	0.920527i	$-0.372240\pi$
$743$	21.2982	0.781357	0.390678	+	0.920527i	$0.372240\pi$
$744$	70.7948	2.59546
$745$	−21.1397	−0.774499
$746$	12.8158	0.469220
$747$	−64.7249	−2.36816
$748$	22.9827	0.840332
$749$	−30.1921	−1.10320
$750$	−83.6474	−3.05437
$751$	40.0771	1.46243	0.731217	−	0.682145i	$-0.238953\pi$
$751$	40.0771	1.46243	0.731217	+	0.682145i	$0.238953\pi$
$752$	−68.3031	−2.49076
$753$	−39.5639	−1.44179
$754$	15.4842	0.563901
$755$	12.1797	0.443263
$756$	−83.6187	−3.04118
$757$	13.8538	0.503523	0.251762	−	0.967789i	$-0.418990\pi$
$757$	13.8538	0.503523	0.251762	+	0.967789i	$0.418990\pi$
$758$	−42.1979	−1.53270
$759$	7.44179	0.270120
$760$	−10.8939	−0.395163
$761$	−18.3404	−0.664839	−0.332420	−	0.943132i	$-0.607865\pi$
$761$	−18.3404	−0.664839	−0.332420	+	0.943132i	$0.607865\pi$
$762$	−117.685	−4.26329
$763$	−61.4595	−2.22498
$764$	24.9003	0.900860
$765$	45.0625	1.62924
$766$	−31.7135	−1.14585
$767$	−16.2275	−0.585940
$768$	27.8443	1.00474
$769$	−14.8338	−0.534921	−0.267461	−	0.963569i	$-0.586185\pi$
$769$	−14.8338	−0.534921	−0.267461	+	0.963569i	$0.586185\pi$
$770$	−8.46469	−0.305046
$771$	58.2951	2.09945
$772$	−38.1421	−1.37276
$773$	17.3327	0.623415	0.311708	−	0.950178i	$-0.399099\pi$
$773$	17.3327	0.623415	0.311708	+	0.950178i	$0.399099\pi$
$774$	−94.8633	−3.40979
$775$	−9.81471	−0.352555
$776$	145.073	5.20781
$777$	85.5805	3.07018
$778$	72.0357	2.58260
$779$	−0.712498	−0.0255279
$780$	32.4826	1.16306
$781$	−9.14836	−0.327354
$782$	63.4410	2.26865
$783$	−18.8981	−0.675362
$784$	32.5427	1.16224
$785$	−5.34511	−0.190775
$786$	−146.248	−5.21650
$787$	−11.2670	−0.401624	−0.200812	−	0.979630i	$-0.564358\pi$
$787$	−11.2670	−0.401624	−0.200812	+	0.979630i	$0.564358\pi$
$788$	57.3094	2.04156
$789$	25.3032	0.900817
$790$	−23.2916	−0.828677
$791$	−15.2143	−0.540959
$792$	−27.0348	−0.960641
$793$	11.5112	0.408774
$794$	74.3901	2.64000
$795$	−47.0115	−1.66733
$796$	39.0762	1.38502
$797$	9.06936	0.321253	0.160627	−	0.987015i	$-0.448649\pi$
$797$	9.06936	0.321253	0.160627	+	0.987015i	$0.448649\pi$
$798$	23.5298	0.832945
$799$	−42.6042	−1.50723
$800$	36.2540	1.28177
$801$	35.9726	1.27103
$802$	−23.0568	−0.814163
$803$	−8.90532	−0.314262
$804$	116.587	4.11170
$805$	−16.6221	−0.585853
$806$	14.2726	0.502733
$807$	32.1518	1.13180
$808$	55.3741	1.94805
$809$	−25.7353	−0.904807	−0.452403	−	0.891813i	$-0.649433\pi$
$809$	−25.7353	−0.904807	−0.452403	+	0.891813i	$0.649433\pi$
$810$	−1.09370	−0.0384288
$811$	38.5268	1.35286	0.676430	−	0.736507i	$-0.263526\pi$
$811$	38.5268	1.35286	0.676430	+	0.736507i	$0.263526\pi$
$812$	55.5626	1.94986
$813$	−9.79476	−0.343517
$814$	18.0393	0.632278
$815$	8.91264	0.312196
$816$	−191.161	−6.69197
$817$	7.35785	0.257418
$818$	49.7839	1.74065
$819$	−25.8572	−0.903522
$820$	−4.96138	−0.173259
$821$	−50.2647	−1.75425	−0.877124	−	0.480263i	$-0.840541\pi$
$821$	−50.2647	−1.75425	−0.877124	+	0.480263i	$0.840541\pi$
$822$	169.066	5.89685
$823$	11.1479	0.388590	0.194295	−	0.980943i	$-0.437758\pi$
$823$	11.1479	0.388590	0.194295	+	0.980943i	$0.437758\pi$
$824$	83.6752	2.91496
$825$	6.04379	0.210418
$826$	−81.8535	−2.84805
$827$	−48.1889	−1.67569	−0.837846	−	0.545906i	$-0.816186\pi$
$827$	−48.1889	−1.67569	−0.837846	+	0.545906i	$0.816186\pi$
$828$	−89.3293	−3.10441
$829$	−18.7671	−0.651809	−0.325904	−	0.945403i	$-0.605669\pi$
$829$	−18.7671	−0.651809	−0.325904	+	0.945403i	$0.605669\pi$
$830$	49.1401	1.70568
$831$	72.1253	2.50200
$832$	−18.0528	−0.625868
$833$	20.2986	0.703304
$834$	101.911	3.52889
$835$	−10.2110	−0.353365
$836$	3.52834	0.122030
$837$	−17.4194	−0.602103
$838$	58.2086	2.01078
$839$	−13.9421	−0.481335	−0.240668	−	0.970608i	$-0.577366\pi$
$839$	−13.9421	−0.481335	−0.240668	+	0.970608i	$0.577366\pi$
$840$	97.3738	3.35972
$841$	−16.4427	−0.566990
$842$	−22.8209	−0.786459
$843$	−15.2101	−0.523865
$844$	4.40989	0.151795
$845$	−14.4709	−0.497815
$846$	84.3275	2.89924
$847$	−33.3574	−1.14617
$848$	123.674	4.24698
$849$	−53.5849	−1.83903
$850$	51.5231	1.76723
$851$	35.4239	1.21431
$852$	177.080	6.06666
$853$	−25.5021	−0.873176	−0.436588	−	0.899662i	$-0.643813\pi$
$853$	−25.5021	−0.873176	−0.436588	+	0.899662i	$0.643813\pi$
$854$	58.0640	1.98691
$855$	6.91806	0.236593
$856$	73.2100	2.50227
$857$	28.0365	0.957708	0.478854	−	0.877895i	$-0.341052\pi$
$857$	28.0365	0.957708	0.478854	+	0.877895i	$0.341052\pi$
$858$	−8.78894	−0.300049
$859$	2.79430	0.0953402	0.0476701	−	0.998863i	$-0.484820\pi$
$859$	2.79430	0.0953402	0.0476701	+	0.998863i	$0.484820\pi$
$860$	51.2354	1.74711
$861$	6.36859	0.217041
$862$	38.9100	1.32528
$863$	36.4749	1.24162	0.620810	−	0.783961i	$-0.286804\pi$
$863$	36.4749	1.24162	0.620810	+	0.783961i	$0.286804\pi$
$864$	64.3446	2.18905
$865$	−8.71816	−0.296426
$866$	−40.2458	−1.36761
$867$	−71.4623	−2.42699
$868$	51.2152	1.73836
$869$	4.48324	0.152084
$870$	37.0298	1.25543
$871$	13.9688	0.473313
$872$	149.027	5.04670
$873$	−92.1272	−3.11803
$874$	9.73956	0.329445
$875$	−35.9629	−1.21577
$876$	172.375	5.82403
$877$	20.9756	0.708297	0.354149	−	0.935189i	$-0.384771\pi$
$877$	20.9756	0.708297	0.354149	+	0.935189i	$0.384771\pi$
$878$	32.7547	1.10542
$879$	−43.5084	−1.46750
$880$	10.5575	0.355893
$881$	−41.3136	−1.39189	−0.695945	−	0.718095i	$-0.745014\pi$
$881$	−41.3136	−1.39189	−0.695945	+	0.718095i	$0.745014\pi$
$882$	−40.1775	−1.35285
$883$	−46.8988	−1.57827	−0.789135	−	0.614219i	$-0.789471\pi$
$883$	−46.8988	−1.57827	−0.789135	+	0.614219i	$0.789471\pi$
$884$	−53.3011	−1.79271
$885$	−38.8073	−1.30449
$886$	−36.2127	−1.21659
$887$	−3.32966	−0.111799	−0.0558996	−	0.998436i	$-0.517803\pi$
$887$	−3.32966	−0.111799	−0.0558996	+	0.998436i	$0.517803\pi$
$888$	−207.516	−6.96378
$889$	−50.5970	−1.69697
$890$	−27.3109	−0.915463
$891$	0.210520	0.00705268
$892$	−96.5179	−3.23166
$893$	−6.54066	−0.218875
$894$	−110.716	−3.70291
$895$	31.8035	1.06307
$896$	−14.3099	−0.478061
$897$	−17.2588	−0.576256
$898$	70.2079	2.34287
$899$	11.5748	0.386041
$900$	−72.5480	−2.41827
$901$	77.1419	2.56997
$902$	1.34242	0.0446978
$903$	−65.7673	−2.18860
$904$	36.8918	1.22700
$905$	13.1563	0.437330
$906$	63.7893	2.11926
$907$	−44.8344	−1.48870	−0.744351	−	0.667789i	$-0.767241\pi$
$907$	−44.8344	−1.48870	−0.744351	+	0.667789i	$0.767241\pi$
$908$	69.2464	2.29802
$909$	−35.1648	−1.16634
$910$	19.6311	0.650766
$911$	39.5481	1.31029	0.655144	−	0.755504i	$-0.272608\pi$
$911$	39.5481	1.31029	0.655144	+	0.755504i	$0.272608\pi$
$912$	−29.3473	−0.971786
$913$	−9.45866	−0.313036
$914$	−65.1357	−2.15450
$915$	27.5285	0.910066
$916$	−10.7944	−0.356656
$917$	−62.8772	−2.07639
$918$	91.4447	3.01812
$919$	−17.2726	−0.569771	−0.284886	−	0.958562i	$-0.591956\pi$
$919$	−17.2726	−0.569771	−0.284886	+	0.958562i	$0.591956\pi$
$920$	40.3054	1.32883
$921$	82.3182	2.71248
$922$	−72.4031	−2.38447
$923$	21.2167	0.698356
$924$	−31.5377	−1.03752
$925$	28.7692	0.945925
$926$	32.0741	1.05402
$927$	−53.1372	−1.74525
$928$	−42.7554	−1.40351
$929$	8.74137	0.286795	0.143398	−	0.989665i	$-0.454197\pi$
$929$	8.74137	0.286795	0.143398	+	0.989665i	$0.454197\pi$
$930$	34.1325	1.11925
$931$	3.11627	0.102132
$932$	−101.601	−3.32807
$933$	22.1652	0.725656
$934$	−61.2457	−2.00402
$935$	6.58527	0.215361
$936$	62.6986	2.04937
$937$	30.0786	0.982624	0.491312	−	0.870984i	$-0.336517\pi$
$937$	30.0786	0.982624	0.491312	+	0.870984i	$0.336517\pi$
$938$	70.4603	2.30061
$939$	86.8819	2.83528
$940$	−45.5450	−1.48551
$941$	−42.2933	−1.37872	−0.689362	−	0.724417i	$-0.742109\pi$
$941$	−42.2933	−1.37872	−0.689362	+	0.724417i	$0.742109\pi$
$942$	−27.9943	−0.912103
$943$	2.63612	0.0858437
$944$	102.091	3.32278
$945$	−23.9593	−0.779397
$946$	−13.8630	−0.450724
$947$	−7.48364	−0.243186	−0.121593	−	0.992580i	$-0.538800\pi$
$947$	−7.48364	−0.243186	−0.121593	+	0.992580i	$0.538800\pi$
$948$	−86.7797	−2.81847
$949$	20.6530	0.670426
$950$	7.90990	0.256631
$951$	−2.81028	−0.0911295
$952$	−159.782	−5.17857
$953$	8.02459	0.259942	0.129971	−	0.991518i	$-0.458512\pi$
$953$	8.02459	0.259942	0.129971	+	0.991518i	$0.458512\pi$
$954$	−152.689	−4.94348
$955$	7.13470	0.230873
$956$	55.5627	1.79703
$957$	−7.12762	−0.230403
$958$	59.9543	1.93704
$959$	72.6873	2.34719
$960$	−43.1725	−1.39339
$961$	−20.3309	−0.655834
$962$	−41.8365	−1.34886
$963$	−46.4914	−1.49816
$964$	101.564	3.27114
$965$	−10.9289	−0.351813
$966$	−87.0560	−2.80098
$967$	33.6007	1.08053	0.540263	−	0.841497i	$-0.318325\pi$
$967$	33.6007	1.08053	0.540263	+	0.841497i	$0.318325\pi$
$968$	80.8852	2.59975
$969$	−18.3054	−0.588056
$970$	69.9443	2.24578
$971$	48.9149	1.56975	0.784877	−	0.619651i	$-0.212726\pi$
$971$	48.9149	1.56975	0.784877	+	0.619651i	$0.212726\pi$
$972$	74.7955	2.39907
$973$	43.8151	1.40465
$974$	20.2667	0.649388
$975$	−14.0166	−0.448891
$976$	−72.4198	−2.31810
$977$	−30.2087	−0.966461	−0.483231	−	0.875493i	$-0.660537\pi$
$977$	−30.2087	−0.966461	−0.483231	+	0.875493i	$0.660537\pi$
$978$	46.6787	1.49262
$979$	5.25689	0.168011
$980$	21.6997	0.693172
$981$	−94.6385	−3.02158
$982$	75.1283	2.39744
$983$	−15.8625	−0.505935	−0.252968	−	0.967475i	$-0.581407\pi$
$983$	−15.8625	−0.505935	−0.252968	+	0.967475i	$0.581407\pi$
$984$	−15.4426	−0.492292
$985$	16.4209	0.523214
$986$	−60.7628	−1.93508
$987$	58.4630	1.86090
$988$	−8.18287	−0.260332
$989$	−27.2227	−0.865632
$990$	−13.0344	−0.414260
$991$	−26.7461	−0.849619	−0.424810	−	0.905283i	$-0.639659\pi$
$991$	−26.7461	−0.849619	−0.424810	+	0.905283i	$0.639659\pi$
$992$	−39.4101	−1.25127
$993$	−3.45174	−0.109538
$994$	107.020	3.39447
$995$	11.1965	0.354954
$996$	183.086	5.80131
$997$	36.2498	1.14804	0.574022	−	0.818840i	$-0.305383\pi$
$997$	36.2498	1.14804	0.574022	+	0.818840i	$0.305383\pi$
$998$	−32.8187	−1.03886
$999$	51.0604	1.61548

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6023.2.a.a.1.4	✓	98

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6023.2.a.a.1.4	✓	98	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:	\( N \)	\(=\)	\( 6023 = 19 \cdot 317 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6023.a (trivial)

\(f(q)\)	\(=\)	\(q-2.63244 q^{2} -2.81028 q^{3} +4.92974 q^{4} +1.41252 q^{5} +7.39789 q^{6} +3.18061 q^{7} -7.71236 q^{8} +4.89767 q^{9} +O(q^{10})\)	\(q-2.63244 q^{2} -2.81028 q^{3} +4.92974 q^{4} +1.41252 q^{5} +7.39789 q^{6} +3.18061 q^{7} -7.71236 q^{8} +4.89767 q^{9} -3.71838 q^{10} +0.715727 q^{11} -13.8539 q^{12} -1.65990 q^{13} -8.37276 q^{14} -3.96958 q^{15} +10.4428 q^{16} +6.51375 q^{17} -12.8928 q^{18} +1.00000 q^{19} +6.96337 q^{20} -8.93840 q^{21} -1.88411 q^{22} -3.69982 q^{23} +21.6739 q^{24} -3.00478 q^{25} +4.36958 q^{26} -5.33297 q^{27} +15.6796 q^{28} +3.54363 q^{29} +10.4497 q^{30} +3.26636 q^{31} -12.0654 q^{32} -2.01139 q^{33} -17.1470 q^{34} +4.49268 q^{35} +24.1442 q^{36} -9.57448 q^{37} -2.63244 q^{38} +4.66478 q^{39} -10.8939 q^{40} -0.712498 q^{41} +23.5298 q^{42} +7.35785 q^{43} +3.52834 q^{44} +6.91806 q^{45} +9.73956 q^{46} -6.54066 q^{47} -29.3473 q^{48} +3.11627 q^{49} +7.90990 q^{50} -18.3054 q^{51} -8.18287 q^{52} +11.8429 q^{53} +14.0387 q^{54} +1.01098 q^{55} -24.5300 q^{56} -2.81028 q^{57} -9.32839 q^{58} +9.77617 q^{59} -19.5690 q^{60} -6.93487 q^{61} -8.59851 q^{62} +15.5776 q^{63} +10.8758 q^{64} -2.34464 q^{65} +5.29487 q^{66} -8.41543 q^{67} +32.1111 q^{68} +10.3975 q^{69} -11.8267 q^{70} -12.7819 q^{71} -37.7726 q^{72} -12.4423 q^{73} +25.2042 q^{74} +8.44427 q^{75} +4.92974 q^{76} +2.27645 q^{77} -12.2797 q^{78} +6.26390 q^{79} +14.7507 q^{80} +0.294134 q^{81} +1.87561 q^{82} -13.2155 q^{83} -44.0639 q^{84} +9.20082 q^{85} -19.3691 q^{86} -9.95858 q^{87} -5.51994 q^{88} +7.34484 q^{89} -18.2114 q^{90} -5.27949 q^{91} -18.2392 q^{92} -9.17939 q^{93} +17.2179 q^{94} +1.41252 q^{95} +33.9072 q^{96} -18.8104 q^{97} -8.20339 q^{98} +3.50539 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 98 q - 8 q^{2} - 25 q^{3} + 82 q^{4} - 10 q^{5} - 4 q^{6} - 18 q^{7} - 18 q^{8} + 61 q^{9}+O(q^{10}) \) 98 * q - 8 * q^2 - 25 * q^3 + 82 * q^4 - 10 * q^5 - 4 * q^6 - 18 * q^7 - 18 * q^8 + 61 * q^9	\( 98 q - 8 q^{2} - 25 q^{3} + 82 q^{4} - 10 q^{5} - 4 q^{6} - 18 q^{7} - 18 q^{8} + 61 q^{9} - 24 q^{10} - 12 q^{11} - 51 q^{12} - 58 q^{13} - 15 q^{14} - 18 q^{15} + 58 q^{16} - 25 q^{17} - 40 q^{18} + 98 q^{19} - 12 q^{20} - 24 q^{21} - 59 q^{22} - 38 q^{23} - 9 q^{24} - 12 q^{25} - 3 q^{26} - 85 q^{27} - 33 q^{28} - 24 q^{29} - 22 q^{30} - 56 q^{31} - 29 q^{32} - 51 q^{33} - 38 q^{34} - 10 q^{35} + 50 q^{36} - 124 q^{37} - 8 q^{38} - 4 q^{39} - 80 q^{40} - 28 q^{41} - 37 q^{42} - 63 q^{43} - 7 q^{44} - 32 q^{45} - 47 q^{46} - 10 q^{47} - 88 q^{48} + 6 q^{49} - 17 q^{50} - 22 q^{51} - 119 q^{52} - 65 q^{53} + 24 q^{54} - 30 q^{55} - 39 q^{56} - 25 q^{57} - 91 q^{58} - 26 q^{59} - 60 q^{60} - 60 q^{61} + 6 q^{62} - 26 q^{63} + 50 q^{64} - 40 q^{65} + 57 q^{66} - 108 q^{67} - 41 q^{68} - 15 q^{69} - 36 q^{70} - 19 q^{71} - 47 q^{72} - 136 q^{73} + 22 q^{74} - 48 q^{75} + 82 q^{76} - 35 q^{77} - 56 q^{78} - 98 q^{79} - 42 q^{80} + 6 q^{81} - 37 q^{82} - 31 q^{83} - 24 q^{84} - 71 q^{85} - 24 q^{86} + 7 q^{87} - 166 q^{88} - 38 q^{89} + 26 q^{90} - 100 q^{91} - 59 q^{92} - 21 q^{93} - 48 q^{94} - 10 q^{95} - 16 q^{96} - 190 q^{97} - 80 q^{98} - 17 q^{99}+O(q^{100}) \) 98 * q - 8 * q^2 - 25 * q^3 + 82 * q^4 - 10 * q^5 - 4 * q^6 - 18 * q^7 - 18 * q^8 + 61 * q^9 - 24 * q^10 - 12 * q^11 - 51 * q^12 - 58 * q^13 - 15 * q^14 - 18 * q^15 + 58 * q^16 - 25 * q^17 - 40 * q^18 + 98 * q^19 - 12 * q^20 - 24 * q^21 - 59 * q^22 - 38 * q^23 - 9 * q^24 - 12 * q^25 - 3 * q^26 - 85 * q^27 - 33 * q^28 - 24 * q^29 - 22 * q^30 - 56 * q^31 - 29 * q^32 - 51 * q^33 - 38 * q^34 - 10 * q^35 + 50 * q^36 - 124 * q^37 - 8 * q^38 - 4 * q^39 - 80 * q^40 - 28 * q^41 - 37 * q^42 - 63 * q^43 - 7 * q^44 - 32 * q^45 - 47 * q^46 - 10 * q^47 - 88 * q^48 + 6 * q^49 - 17 * q^50 - 22 * q^51 - 119 * q^52 - 65 * q^53 + 24 * q^54 - 30 * q^55 - 39 * q^56 - 25 * q^57 - 91 * q^58 - 26 * q^59 - 60 * q^60 - 60 * q^61 + 6 * q^62 - 26 * q^63 + 50 * q^64 - 40 * q^65 + 57 * q^66 - 108 * q^67 - 41 * q^68 - 15 * q^69 - 36 * q^70 - 19 * q^71 - 47 * q^72 - 136 * q^73 + 22 * q^74 - 48 * q^75 + 82 * q^76 - 35 * q^77 - 56 * q^78 - 98 * q^79 - 42 * q^80 + 6 * q^81 - 37 * q^82 - 31 * q^83 - 24 * q^84 - 71 * q^85 - 24 * q^86 + 7 * q^87 - 166 * q^88 - 38 * q^89 + 26 * q^90 - 100 * q^91 - 59 * q^92 - 21 * q^93 - 48 * q^94 - 10 * q^95 - 16 * q^96 - 190 * q^97 - 80 * q^98 - 17 * q^99

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