LMFDB - Embedded newform 6019.2.a.d.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6019,2,Mod(1,6019)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6019, 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("6019.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6019 = 13 \cdot 463 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6019.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:	$48.0619569766$
Analytic rank:	$0$
Dimension:	$123$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	6019.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.47080 q^{2} +2.36731 q^{3} +4.10488 q^{4} -1.23232 q^{5} -5.84916 q^{6} +4.18566 q^{7} -5.20074 q^{8} +2.60415 q^{9} +O(q^{10})$	\(q-2.47080 q^{2} +2.36731 q^{3} +4.10488 q^{4} -1.23232 q^{5} -5.84916 q^{6} +4.18566 q^{7} -5.20074 q^{8} +2.60415 q^{9} +3.04483 q^{10} +4.61067 q^{11} +9.71751 q^{12} -1.00000 q^{13} -10.3419 q^{14} -2.91729 q^{15} +4.64025 q^{16} +3.52008 q^{17} -6.43434 q^{18} +4.71376 q^{19} -5.05853 q^{20} +9.90874 q^{21} -11.3921 q^{22} +8.60604 q^{23} -12.3117 q^{24} -3.48138 q^{25} +2.47080 q^{26} -0.937102 q^{27} +17.1816 q^{28} +7.02093 q^{29} +7.20804 q^{30} +7.12264 q^{31} -1.06368 q^{32} +10.9149 q^{33} -8.69743 q^{34} -5.15808 q^{35} +10.6897 q^{36} -8.24225 q^{37} -11.6468 q^{38} -2.36731 q^{39} +6.40898 q^{40} +11.5312 q^{41} -24.4826 q^{42} +0.601146 q^{43} +18.9262 q^{44} -3.20915 q^{45} -21.2638 q^{46} -9.24564 q^{47} +10.9849 q^{48} +10.5197 q^{49} +8.60182 q^{50} +8.33312 q^{51} -4.10488 q^{52} +1.51230 q^{53} +2.31540 q^{54} -5.68183 q^{55} -21.7685 q^{56} +11.1589 q^{57} -17.3473 q^{58} -7.64877 q^{59} -11.9751 q^{60} +4.97357 q^{61} -17.5987 q^{62} +10.9001 q^{63} -6.65235 q^{64} +1.23232 q^{65} -26.9685 q^{66} -13.7229 q^{67} +14.4495 q^{68} +20.3732 q^{69} +12.7446 q^{70} -8.73630 q^{71} -13.5435 q^{72} +11.5769 q^{73} +20.3650 q^{74} -8.24151 q^{75} +19.3494 q^{76} +19.2987 q^{77} +5.84916 q^{78} -8.38504 q^{79} -5.71829 q^{80} -10.0309 q^{81} -28.4912 q^{82} +11.0864 q^{83} +40.6741 q^{84} -4.33787 q^{85} -1.48531 q^{86} +16.6207 q^{87} -23.9789 q^{88} +13.1365 q^{89} +7.92918 q^{90} -4.18566 q^{91} +35.3267 q^{92} +16.8615 q^{93} +22.8442 q^{94} -5.80887 q^{95} -2.51807 q^{96} -3.96289 q^{97} -25.9922 q^{98} +12.0069 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 123 q + 10 q^{2} + q^{3} + 136 q^{4} + 46 q^{5} + 16 q^{6} + 12 q^{7} + 30 q^{8} + 154 q^{9}+O(q^{10}) $ 123 * q + 10 * q^2 + q^3 + 136 * q^4 + 46 * q^5 + 16 * q^6 + 12 * q^7 + 30 * q^8 + 154 * q^9	\( 123 q + 10 q^{2} + q^{3} + 136 q^{4} + 46 q^{5} + 16 q^{6} + 12 q^{7} + 30 q^{8} + 154 q^{9} + 5 q^{10} + 53 q^{11} - 6 q^{12} - 123 q^{13} + 21 q^{14} + 29 q^{15} + 166 q^{16} - 35 q^{17} + 28 q^{18} + 23 q^{19} + 93 q^{20} + 72 q^{21} + 8 q^{22} + 42 q^{23} + 55 q^{24} + 153 q^{25} - 10 q^{26} + 7 q^{27} + 39 q^{28} + 86 q^{29} + 44 q^{30} + 16 q^{31} + 70 q^{32} + 40 q^{33} + 10 q^{34} + 6 q^{35} + 222 q^{36} + 52 q^{37} + 12 q^{38} - q^{39} + 14 q^{40} + 80 q^{41} + 29 q^{42} + 2 q^{43} + 143 q^{44} + 137 q^{45} + 39 q^{46} + 45 q^{47} - 27 q^{48} + 163 q^{49} + 102 q^{50} + 48 q^{51} - 136 q^{52} + 117 q^{53} + 75 q^{54} + 20 q^{55} + 88 q^{56} + 67 q^{57} + 56 q^{58} + 88 q^{59} + 96 q^{60} + 57 q^{61} - 13 q^{62} + 48 q^{63} + 228 q^{64} - 46 q^{65} + 28 q^{66} + 43 q^{67} - 56 q^{68} + 92 q^{69} + 14 q^{70} + 90 q^{71} + 98 q^{72} + 25 q^{73} + 80 q^{74} + 21 q^{75} + 75 q^{76} + 112 q^{77} - 16 q^{78} + 36 q^{79} + 208 q^{80} + 231 q^{81} - 27 q^{82} + 93 q^{83} + 175 q^{84} + 77 q^{85} + 199 q^{86} + 15 q^{87} + 43 q^{88} + 140 q^{89} + 11 q^{90} - 12 q^{91} + 93 q^{92} + 140 q^{93} + 4 q^{94} + 23 q^{95} + 105 q^{96} + 43 q^{97} + 67 q^{98} + 140 q^{99}+O(q^{100}) \) 123 * q + 10 * q^2 + q^3 + 136 * q^4 + 46 * q^5 + 16 * q^6 + 12 * q^7 + 30 * q^8 + 154 * q^9 + 5 * q^10 + 53 * q^11 - 6 * q^12 - 123 * q^13 + 21 * q^14 + 29 * q^15 + 166 * q^16 - 35 * q^17 + 28 * q^18 + 23 * q^19 + 93 * q^20 + 72 * q^21 + 8 * q^22 + 42 * q^23 + 55 * q^24 + 153 * q^25 - 10 * q^26 + 7 * q^27 + 39 * q^28 + 86 * q^29 + 44 * q^30 + 16 * q^31 + 70 * q^32 + 40 * q^33 + 10 * q^34 + 6 * q^35 + 222 * q^36 + 52 * q^37 + 12 * q^38 - q^39 + 14 * q^40 + 80 * q^41 + 29 * q^42 + 2 * q^43 + 143 * q^44 + 137 * q^45 + 39 * q^46 + 45 * q^47 - 27 * q^48 + 163 * q^49 + 102 * q^50 + 48 * q^51 - 136 * q^52 + 117 * q^53 + 75 * q^54 + 20 * q^55 + 88 * q^56 + 67 * q^57 + 56 * q^58 + 88 * q^59 + 96 * q^60 + 57 * q^61 - 13 * q^62 + 48 * q^63 + 228 * q^64 - 46 * q^65 + 28 * q^66 + 43 * q^67 - 56 * q^68 + 92 * q^69 + 14 * q^70 + 90 * q^71 + 98 * q^72 + 25 * q^73 + 80 * q^74 + 21 * q^75 + 75 * q^76 + 112 * q^77 - 16 * q^78 + 36 * q^79 + 208 * q^80 + 231 * q^81 - 27 * q^82 + 93 * q^83 + 175 * q^84 + 77 * q^85 + 199 * q^86 + 15 * q^87 + 43 * q^88 + 140 * q^89 + 11 * q^90 - 12 * q^91 + 93 * q^92 + 140 * q^93 + 4 * q^94 + 23 * q^95 + 105 * q^96 + 43 * q^97 + 67 * q^98 + 140 * 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 $

$2$	−2.47080	−1.74712	−0.873561	−	0.486714i	$-0.838195\pi$
$2$	−2.47080	−1.74712	−0.873561	+	0.486714i	$0.838195\pi$
$3$	2.36731	1.36677	0.683383	−	0.730060i	$-0.260508\pi$
$3$	2.36731	1.36677	0.683383	+	0.730060i	$0.260508\pi$
$4$	4.10488	2.05244
$5$	−1.23232	−0.551111	−0.275556	−	0.961285i	$-0.588862\pi$
$5$	−1.23232	−0.551111	−0.275556	+	0.961285i	$0.588862\pi$
$6$	−5.84916	−2.38791
$7$	4.18566	1.58203	0.791015	−	0.611797i	$-0.209553\pi$
$7$	4.18566	1.58203	0.791015	+	0.611797i	$0.209553\pi$
$8$	−5.20074	−1.83874
$9$	2.60415	0.868050
$10$	3.04483	0.962859
$11$	4.61067	1.39017	0.695085	−	0.718928i	$-0.255367\pi$
$11$	4.61067	1.39017	0.695085	+	0.718928i	$0.255367\pi$
$12$	9.71751	2.80520
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−10.3419	−2.76400
$15$	−2.91729	−0.753240
$16$	4.64025	1.16006
$17$	3.52008	0.853745	0.426873	−	0.904312i	$-0.359615\pi$
$17$	3.52008	0.853745	0.426873	+	0.904312i	$0.359615\pi$
$18$	−6.43434	−1.51659
$19$	4.71376	1.08141	0.540705	−	0.841212i	$-0.318158\pi$
$19$	4.71376	1.08141	0.540705	+	0.841212i	$0.318158\pi$
$20$	−5.05853	−1.13112
$21$	9.90874	2.16226
$22$	−11.3921	−2.42880
$23$	8.60604	1.79448	0.897242	−	0.441540i	$-0.145568\pi$
$23$	8.60604	1.79448	0.897242	+	0.441540i	$0.145568\pi$
$24$	−12.3117	−2.51312
$25$	−3.48138	−0.696276
$26$	2.47080	0.484565
$27$	−0.937102	−0.180345
$28$	17.1816	3.24702
$29$	7.02093	1.30375	0.651877	−	0.758325i	$-0.273982\pi$
$29$	7.02093	1.30375	0.651877	+	0.758325i	$0.273982\pi$
$30$	7.20804	1.31600
$31$	7.12264	1.27926	0.639632	−	0.768681i	$-0.279087\pi$
$31$	7.12264	1.27926	0.639632	+	0.768681i	$0.279087\pi$
$32$	−1.06368	−0.188035
$33$	10.9149	1.90004
$34$	−8.69743	−1.49160
$35$	−5.15808	−0.871874
$36$	10.6897	1.78162
$37$	−8.24225	−1.35502	−0.677509	−	0.735514i	$-0.736941\pi$
$37$	−8.24225	−1.35502	−0.677509	+	0.735514i	$0.736941\pi$
$38$	−11.6468	−1.88936
$39$	−2.36731	−0.379073
$40$	6.40898	1.01335
$41$	11.5312	1.80086	0.900432	−	0.434998i	$-0.143251\pi$
$41$	11.5312	1.80086	0.900432	+	0.434998i	$0.143251\pi$
$42$	−24.4826	−3.77774
$43$	0.601146	0.0916739	0.0458370	−	0.998949i	$-0.485405\pi$
$43$	0.601146	0.0916739	0.0458370	+	0.998949i	$0.485405\pi$
$44$	18.9262	2.85324
$45$	−3.20915	−0.478392
$46$	−21.2638	−3.13518
$47$	−9.24564	−1.34862	−0.674308	−	0.738451i	$-0.735558\pi$
$47$	−9.24564	−1.34862	−0.674308	+	0.738451i	$0.735558\pi$
$48$	10.9849	1.58553
$49$	10.5197	1.50282
$50$	8.60182	1.21648
$51$	8.33312	1.16687
$52$	−4.10488	−0.569244
$53$	1.51230	0.207730	0.103865	−	0.994591i	$-0.466879\pi$
$53$	1.51230	0.207730	0.103865	+	0.994591i	$0.466879\pi$
$54$	2.31540	0.315086
$55$	−5.68183	−0.766138
$56$	−21.7685	−2.90894
$57$	11.1589	1.47803
$58$	−17.3473	−2.27782
$59$	−7.64877	−0.995785	−0.497892	−	0.867239i	$-0.665893\pi$
$59$	−7.64877	−0.995785	−0.497892	+	0.867239i	$0.665893\pi$
$60$	−11.9751	−1.54598
$61$	4.97357	0.636800	0.318400	−	0.947956i	$-0.396854\pi$
$61$	4.97357	0.636800	0.318400	+	0.947956i	$0.396854\pi$
$62$	−17.5987	−2.23503
$63$	10.9001	1.37328
$64$	−6.65235	−0.831544
$65$	1.23232	0.152851
$66$	−26.9685	−3.31960
$67$	−13.7229	−1.67652	−0.838261	−	0.545269i	$-0.816428\pi$
$67$	−13.7229	−1.67652	−0.838261	+	0.545269i	$0.816428\pi$
$68$	14.4495	1.75226
$69$	20.3732	2.45264
$70$	12.7446	1.52327
$71$	−8.73630	−1.03681	−0.518404	−	0.855136i	$-0.673474\pi$
$71$	−8.73630	−1.03681	−0.518404	+	0.855136i	$0.673474\pi$
$72$	−13.5435	−1.59612
$73$	11.5769	1.35497	0.677485	−	0.735536i	$-0.263070\pi$
$73$	11.5769	1.35497	0.677485	+	0.735536i	$0.263070\pi$
$74$	20.3650	2.36738
$75$	−8.24151	−0.951647
$76$	19.3494	2.21953
$77$	19.2987	2.19929
$78$	5.84916	0.662287
$79$	−8.38504	−0.943391	−0.471695	−	0.881762i	$-0.656358\pi$
$79$	−8.38504	−0.943391	−0.471695	+	0.881762i	$0.656358\pi$
$80$	−5.71829	−0.639324
$81$	−10.0309	−1.11454
$82$	−28.4912	−3.14633
$83$	11.0864	1.21689	0.608446	−	0.793595i	$-0.291793\pi$
$83$	11.0864	1.21689	0.608446	+	0.793595i	$0.291793\pi$
$84$	40.6741	4.43791
$85$	−4.33787	−0.470508
$86$	−1.48531	−0.160166
$87$	16.6207	1.78193
$88$	−23.9789	−2.55616
$89$	13.1365	1.39247	0.696234	−	0.717815i	$-0.254858\pi$
$89$	13.1365	1.39247	0.696234	+	0.717815i	$0.254858\pi$
$90$	7.92918	0.835809
$91$	−4.18566	−0.438776
$92$	35.3267	3.68307
$93$	16.8615	1.74846
$94$	22.8442	2.35620
$95$	−5.80887	−0.595977
$96$	−2.51807	−0.256999
$97$	−3.96289	−0.402370	−0.201185	−	0.979553i	$-0.564479\pi$
$97$	−3.96289	−0.402370	−0.201185	+	0.979553i	$0.564479\pi$
$98$	−25.9922	−2.62561
$99$	12.0069	1.20674
$100$	−14.2906	−1.42906
$101$	−2.45637	−0.244418	−0.122209	−	0.992504i	$-0.538998\pi$
$101$	−2.45637	−0.244418	−0.122209	+	0.992504i	$0.538998\pi$
$102$	−20.5895	−2.03866
$103$	−14.8919	−1.46734	−0.733671	−	0.679505i	$-0.762195\pi$
$103$	−14.8919	−1.46734	−0.733671	+	0.679505i	$0.762195\pi$
$104$	5.20074	0.509974
$105$	−12.2108	−1.19165
$106$	−3.73659	−0.362930
$107$	−11.6698	−1.12816	−0.564079	−	0.825721i	$-0.690769\pi$
$107$	−11.6698	−1.12816	−0.564079	+	0.825721i	$0.690769\pi$
$108$	−3.84669	−0.370148
$109$	4.43772	0.425057	0.212528	−	0.977155i	$-0.431830\pi$
$109$	4.43772	0.425057	0.212528	+	0.977155i	$0.431830\pi$
$110$	14.0387	1.33854
$111$	−19.5120	−1.85199
$112$	19.4225	1.83525
$113$	−15.2889	−1.43825	−0.719127	−	0.694879i	$-0.755458\pi$
$113$	−15.2889	−1.43825	−0.719127	+	0.694879i	$0.755458\pi$
$114$	−27.5715	−2.58231
$115$	−10.6054	−0.988960
$116$	28.8200	2.67587
$117$	−2.60415	−0.240754
$118$	18.8986	1.73976
$119$	14.7339	1.35065
$120$	15.1720	1.38501
$121$	10.2583	0.932573
$122$	−12.2887	−1.11257
$123$	27.2978	2.46136
$124$	29.2376	2.62561
$125$	10.4518	0.934837
$126$	−26.9320	−2.39929
$127$	−10.1605	−0.901599	−0.450800	−	0.892625i	$-0.648861\pi$
$127$	−10.1605	−0.901599	−0.450800	+	0.892625i	$0.648861\pi$
$128$	18.5640	1.64084
$129$	1.42310	0.125297
$130$	−3.04483	−0.267049
$131$	−2.93911	−0.256791	−0.128396	−	0.991723i	$-0.540983\pi$
$131$	−2.93911	−0.256791	−0.128396	+	0.991723i	$0.540983\pi$
$132$	44.8042	3.89971
$133$	19.7302	1.71082
$134$	33.9067	2.92909
$135$	1.15481	0.0993904
$136$	−18.3070	−1.56981
$137$	−11.0918	−0.947638	−0.473819	−	0.880622i	$-0.657125\pi$
$137$	−11.0918	−0.947638	−0.473819	+	0.880622i	$0.657125\pi$
$138$	−50.3381	−4.28506
$139$	−13.2352	−1.12259	−0.561297	−	0.827614i	$-0.689697\pi$
$139$	−13.2352	−1.12259	−0.561297	+	0.827614i	$0.689697\pi$
$140$	−21.1733	−1.78947
$141$	−21.8873	−1.84324
$142$	21.5857	1.81143
$143$	−4.61067	−0.385564
$144$	12.0839	1.00699
$145$	−8.65204	−0.718513
$146$	−28.6042	−2.36730
$147$	24.9034	2.05400
$148$	−33.8334	−2.78109
$149$	2.67880	0.219456	0.109728	−	0.993962i	$-0.465002\pi$
$149$	2.67880	0.219456	0.109728	+	0.993962i	$0.465002\pi$
$150$	20.3631	1.66264
$151$	4.81506	0.391844	0.195922	−	0.980619i	$-0.437230\pi$
$151$	4.81506	0.391844	0.195922	+	0.980619i	$0.437230\pi$
$152$	−24.5150	−1.98843
$153$	9.16681	0.741093
$154$	−47.6833	−3.84243
$155$	−8.77739	−0.705017
$156$	−9.71751	−0.778023
$157$	−19.4823	−1.55486	−0.777428	−	0.628971i	$-0.783476\pi$
$157$	−19.4823	−1.55486	−0.777428	+	0.628971i	$0.783476\pi$
$158$	20.7178	1.64822
$159$	3.58008	0.283919
$160$	1.31080	0.103628
$161$	36.0219	2.83893
$162$	24.7843	1.94724
$163$	5.23123	0.409741	0.204871	−	0.978789i	$-0.434323\pi$
$163$	5.23123	0.409741	0.204871	+	0.978789i	$0.434323\pi$
$164$	47.3339	3.69616
$165$	−13.4507	−1.04713
$166$	−27.3924	−2.12606
$167$	18.7430	1.45038	0.725189	−	0.688550i	$-0.241752\pi$
$167$	18.7430	1.45038	0.725189	+	0.688550i	$0.241752\pi$
$168$	−51.5327	−3.97584
$169$	1.00000	0.0769231
$170$	10.7180	0.822036
$171$	12.2753	0.938717
$172$	2.46763	0.188155
$173$	−12.6015	−0.958074	−0.479037	−	0.877795i	$-0.659014\pi$
$173$	−12.6015	−0.958074	−0.479037	+	0.877795i	$0.659014\pi$
$174$	−41.0665	−3.11324
$175$	−14.5719	−1.10153
$176$	21.3947	1.61268
$177$	−18.1070	−1.36100
$178$	−32.4578	−2.43281
$179$	−20.9479	−1.56572	−0.782858	−	0.622200i	$-0.786239\pi$
$179$	−20.9479	−1.56572	−0.782858	+	0.622200i	$0.786239\pi$
$180$	−13.1732	−0.981869
$181$	17.1221	1.27268	0.636338	−	0.771411i	$-0.280448\pi$
$181$	17.1221	1.27268	0.636338	+	0.771411i	$0.280448\pi$
$182$	10.3419	0.766596
$183$	11.7740	0.870357
$184$	−44.7577	−3.29958
$185$	10.1571	0.746766
$186$	−41.6615	−3.05477
$187$	16.2299	1.18685
$188$	−37.9522	−2.76795
$189$	−3.92239	−0.285312
$190$	14.3526	1.04125
$191$	−7.39963	−0.535419	−0.267709	−	0.963500i	$-0.586267\pi$
$191$	−7.39963	−0.535419	−0.267709	+	0.963500i	$0.586267\pi$
$192$	−15.7482	−1.13653
$193$	−22.5832	−1.62557	−0.812787	−	0.582561i	$-0.802051\pi$
$193$	−22.5832	−1.62557	−0.812787	+	0.582561i	$0.802051\pi$
$194$	9.79152	0.702990
$195$	2.91729	0.208911
$196$	43.1822	3.08444
$197$	8.03532	0.572493	0.286246	−	0.958156i	$-0.407592\pi$
$197$	8.03532	0.572493	0.286246	+	0.958156i	$0.407592\pi$
$198$	−29.6666	−2.10832
$199$	−13.1940	−0.935295	−0.467648	−	0.883915i	$-0.654898\pi$
$199$	−13.1940	−0.935295	−0.467648	+	0.883915i	$0.654898\pi$
$200$	18.1058	1.28027
$201$	−32.4864	−2.29141
$202$	6.06922	0.427029
$203$	29.3872	2.06258
$204$	34.2064	2.39493
$205$	−14.2101	−0.992476
$206$	36.7950	2.56363
$207$	22.4114	1.55770
$208$	−4.64025	−0.321744
$209$	21.7336	1.50334
$210$	30.1704	2.08196
$211$	11.3904	0.784146	0.392073	−	0.919934i	$-0.371758\pi$
$211$	11.3904	0.784146	0.392073	+	0.919934i	$0.371758\pi$
$212$	6.20780	0.426353
$213$	−20.6815	−1.41707
$214$	28.8337	1.97103
$215$	−0.740806	−0.0505225
$216$	4.87362	0.331608
$217$	29.8129	2.02383
$218$	−10.9647	−0.742626
$219$	27.4060	1.85193
$220$	−23.3232	−1.57245
$221$	−3.52008	−0.236786
$222$	48.2102	3.23566
$223$	19.3317	1.29454	0.647272	−	0.762259i	$-0.275910\pi$
$223$	19.3317	1.29454	0.647272	+	0.762259i	$0.275910\pi$
$224$	−4.45222	−0.297476
$225$	−9.06604	−0.604402
$226$	37.7758	2.51281
$227$	−0.268468	−0.0178188	−0.00890942	−	0.999960i	$-0.502836\pi$
$227$	−0.268468	−0.0178188	−0.00890942	+	0.999960i	$0.502836\pi$
$228$	45.8060	3.03357
$229$	15.6513	1.03426	0.517132	−	0.855906i	$-0.327000\pi$
$229$	15.6513	1.03426	0.517132	+	0.855906i	$0.327000\pi$
$230$	26.2039	1.72783
$231$	45.6860	3.00592
$232$	−36.5140	−2.39726
$233$	−15.0464	−0.985721	−0.492861	−	0.870108i	$-0.664049\pi$
$233$	−15.0464	−0.985721	−0.492861	+	0.870108i	$0.664049\pi$
$234$	6.43434	0.420626
$235$	11.3936	0.743237
$236$	−31.3972	−2.04379
$237$	−19.8500	−1.28939
$238$	−36.4045	−2.35975
$239$	8.72318	0.564255	0.282128	−	0.959377i	$-0.408960\pi$
$239$	8.72318	0.564255	0.282128	+	0.959377i	$0.408960\pi$
$240$	−13.5369	−0.873806
$241$	−1.29734	−0.0835688	−0.0417844	−	0.999127i	$-0.513304\pi$
$241$	−1.29734	−0.0835688	−0.0417844	+	0.999127i	$0.513304\pi$
$242$	−25.3463	−1.62932
$243$	−20.9348	−1.34297
$244$	20.4159	1.30699
$245$	−12.9637	−0.828220
$246$	−67.4475	−4.30030
$247$	−4.71376	−0.299929
$248$	−37.0430	−2.35223
$249$	26.2450	1.66321
$250$	−25.8243	−1.63327
$251$	13.3820	0.844663	0.422331	−	0.906442i	$-0.361212\pi$
$251$	13.3820	0.844663	0.422331	+	0.906442i	$0.361212\pi$
$252$	44.7434	2.81857
$253$	39.6796	2.49464
$254$	25.1046	1.57520
$255$	−10.2691	−0.643075
$256$	−32.5634	−2.03521
$257$	−0.693755	−0.0432752	−0.0216376	−	0.999766i	$-0.506888\pi$
$257$	−0.693755	−0.0432752	−0.0216376	+	0.999766i	$0.506888\pi$
$258$	−3.51620	−0.218909
$259$	−34.4992	−2.14368
$260$	5.05853	0.313717
$261$	18.2835	1.13172
$262$	7.26196	0.448646
$263$	23.1018	1.42452	0.712260	−	0.701916i	$-0.247672\pi$
$263$	23.1018	1.42452	0.712260	+	0.701916i	$0.247672\pi$
$264$	−56.7654	−3.49367
$265$	−1.86364	−0.114482
$266$	−48.7494	−2.98902
$267$	31.0982	1.90318
$268$	−56.3309	−3.44096
$269$	13.4921	0.822627	0.411313	−	0.911494i	$-0.365070\pi$
$269$	13.4921	0.822627	0.411313	+	0.911494i	$0.365070\pi$
$270$	−2.85332	−0.173647
$271$	−11.1145	−0.675159	−0.337579	−	0.941297i	$-0.609608\pi$
$271$	−11.1145	−0.675159	−0.337579	+	0.941297i	$0.609608\pi$
$272$	16.3341	0.990398
$273$	−9.90874	−0.599704
$274$	27.4057	1.65564
$275$	−16.0515	−0.967943
$276$	83.6292	5.03389
$277$	−17.9325	−1.07746	−0.538730	−	0.842478i	$-0.681096\pi$
$277$	−17.9325	−1.07746	−0.538730	+	0.842478i	$0.681096\pi$
$278$	32.7016	1.96131
$279$	18.5484	1.11046
$280$	26.8258	1.60315
$281$	−30.6666	−1.82942	−0.914709	−	0.404113i	$-0.867580\pi$
$281$	−30.6666	−1.82942	−0.914709	+	0.404113i	$0.867580\pi$
$282$	54.0792	3.22037
$283$	−18.8311	−1.11939	−0.559696	−	0.828698i	$-0.689082\pi$
$283$	−18.8311	−1.11939	−0.559696	+	0.828698i	$0.689082\pi$
$284$	−35.8614	−2.12798
$285$	−13.7514	−0.814561
$286$	11.3921	0.673627
$287$	48.2654	2.84902
$288$	−2.76999	−0.163223
$289$	−4.60903	−0.271119
$290$	21.3775	1.25533
$291$	−9.38138	−0.549946
$292$	47.5216	2.78099
$293$	29.2146	1.70674	0.853369	−	0.521308i	$-0.174556\pi$
$293$	29.2146	1.70674	0.853369	+	0.521308i	$0.174556\pi$
$294$	−61.5315	−3.58859
$295$	9.42575	0.548788
$296$	42.8658	2.49152
$297$	−4.32067	−0.250711
$298$	−6.61879	−0.383416
$299$	−8.60604	−0.497700
$300$	−33.8304	−1.95320
$301$	2.51619	0.145031
$302$	−11.8971	−0.684600
$303$	−5.81499	−0.334063
$304$	21.8730	1.25450
$305$	−6.12904	−0.350948
$306$	−22.6494	−1.29478
$307$	−9.90994	−0.565590	−0.282795	−	0.959180i	$-0.591262\pi$
$307$	−9.90994	−0.565590	−0.282795	+	0.959180i	$0.591262\pi$
$308$	79.2187	4.51391
$309$	−35.2537	−2.00551
$310$	21.6872	1.23175
$311$	5.15447	0.292283	0.146141	−	0.989264i	$-0.453315\pi$
$311$	5.15447	0.292283	0.146141	+	0.989264i	$0.453315\pi$
$312$	12.3117	0.697015
$313$	−8.91393	−0.503845	−0.251923	−	0.967747i	$-0.581063\pi$
$313$	−8.91393	−0.503845	−0.251923	+	0.967747i	$0.581063\pi$
$314$	48.1370	2.71653
$315$	−13.4324	−0.756830
$316$	−34.4195	−1.93625
$317$	−7.06004	−0.396531	−0.198266	−	0.980148i	$-0.563531\pi$
$317$	−7.06004	−0.396531	−0.198266	+	0.980148i	$0.563531\pi$
$318$	−8.84567	−0.496041
$319$	32.3712	1.81244
$320$	8.19784	0.458273
$321$	−27.6259	−1.54193
$322$	−89.0032	−4.95995
$323$	16.5928	0.923249
$324$	−41.1754	−2.28752
$325$	3.48138	0.193112
$326$	−12.9253	−0.715869
$327$	10.5055	0.580953
$328$	−59.9705	−3.31132
$329$	−38.6991	−2.13355
$330$	33.2339	1.82947
$331$	−15.3188	−0.841997	−0.420998	−	0.907061i	$-0.638320\pi$
$331$	−15.3188	−0.841997	−0.420998	+	0.907061i	$0.638320\pi$
$332$	45.5084	2.49760
$333$	−21.4641	−1.17622
$334$	−46.3103	−2.53399
$335$	16.9111	0.923950
$336$	45.9791	2.50836
$337$	−8.03882	−0.437902	−0.218951	−	0.975736i	$-0.570264\pi$
$337$	−8.03882	−0.437902	−0.218951	+	0.975736i	$0.570264\pi$
$338$	−2.47080	−0.134394
$339$	−36.1934	−1.96576
$340$	−17.8064	−0.965689
$341$	32.8402	1.77839
$342$	−30.3299	−1.64005
$343$	14.7324	0.795473
$344$	−3.12640	−0.168564
$345$	−25.1063	−1.35168
$346$	31.1358	1.67387
$347$	10.1355	0.544100	0.272050	−	0.962283i	$-0.412298\pi$
$347$	10.1355	0.544100	0.272050	+	0.962283i	$0.412298\pi$
$348$	68.2259	3.65729
$349$	−17.8061	−0.953141	−0.476570	−	0.879136i	$-0.658120\pi$
$349$	−17.8061	−0.953141	−0.476570	+	0.879136i	$0.658120\pi$
$350$	36.0043	1.92451
$351$	0.937102	0.0500188
$352$	−4.90430	−0.261400
$353$	14.4369	0.768400	0.384200	−	0.923250i	$-0.374477\pi$
$353$	14.4369	0.768400	0.384200	+	0.923250i	$0.374477\pi$
$354$	44.7388	2.37784
$355$	10.7659	0.571396
$356$	53.9237	2.85795
$357$	34.8796	1.84602
$358$	51.7581	2.73550
$359$	−22.1574	−1.16942	−0.584711	−	0.811241i	$-0.698792\pi$
$359$	−22.1574	−1.16942	−0.584711	+	0.811241i	$0.698792\pi$
$360$	16.6899	0.879637
$361$	3.21951	0.169448
$362$	−42.3054	−2.22352
$363$	24.2846	1.27461
$364$	−17.1816	−0.900561
$365$	−14.2664	−0.746739
$366$	−29.0912	−1.52062
$367$	33.7721	1.76289	0.881445	−	0.472288i	$-0.156572\pi$
$367$	33.7721	1.76289	0.881445	+	0.472288i	$0.156572\pi$
$368$	39.9342	2.08171
$369$	30.0288	1.56324
$370$	−25.0962	−1.30469
$371$	6.32996	0.328635
$372$	69.2143	3.58860
$373$	−35.4887	−1.83753	−0.918767	−	0.394801i	$-0.870814\pi$
$373$	−35.4887	−1.83753	−0.918767	+	0.394801i	$0.870814\pi$
$374$	−40.1010	−2.07357
$375$	24.7426	1.27770
$376$	48.0841	2.47975
$377$	−7.02093	−0.361596
$378$	9.69146	0.498475
$379$	−16.8595	−0.866016	−0.433008	−	0.901390i	$-0.642548\pi$
$379$	−16.8595	−0.866016	−0.433008	+	0.901390i	$0.642548\pi$
$380$	−23.8447	−1.22321
$381$	−24.0530	−1.23227
$382$	18.2830	0.935442
$383$	−28.0861	−1.43513	−0.717567	−	0.696490i	$-0.754744\pi$
$383$	−28.0861	−1.43513	−0.717567	+	0.696490i	$0.754744\pi$
$384$	43.9468	2.24265
$385$	−23.7822	−1.21205
$386$	55.7987	2.84008
$387$	1.56547	0.0795775
$388$	−16.2672	−0.825840
$389$	27.5717	1.39794	0.698970	−	0.715151i	$-0.253642\pi$
$389$	27.5717	1.39794	0.698970	+	0.715151i	$0.253642\pi$
$390$	−7.20804	−0.364994
$391$	30.2940	1.53203
$392$	−54.7103	−2.76329
$393$	−6.95777	−0.350973
$394$	−19.8537	−1.00021
$395$	10.3331	0.519913
$396$	49.2867	2.47675
$397$	14.0606	0.705682	0.352841	−	0.935683i	$-0.385216\pi$
$397$	14.0606	0.705682	0.352841	+	0.935683i	$0.385216\pi$
$398$	32.5997	1.63408
$399$	46.7074	2.33829
$400$	−16.1545	−0.807725
$401$	7.83995	0.391509	0.195754	−	0.980653i	$-0.437285\pi$
$401$	7.83995	0.391509	0.195754	+	0.980653i	$0.437285\pi$
$402$	80.2676	4.00338
$403$	−7.12264	−0.354804
$404$	−10.0831	−0.501653
$405$	12.3612	0.614235
$406$	−72.6100	−3.60357
$407$	−38.0023	−1.88371
$408$	−43.3383	−2.14557
$409$	−16.6215	−0.821878	−0.410939	−	0.911663i	$-0.634799\pi$
$409$	−16.6215	−0.821878	−0.410939	+	0.911663i	$0.634799\pi$
$410$	35.1104	1.73398
$411$	−26.2577	−1.29520
$412$	−61.1294	−3.01163
$413$	−32.0151	−1.57536
$414$	−55.3742	−2.72149
$415$	−13.6620	−0.670643
$416$	1.06368	0.0521514
$417$	−31.3318	−1.53432
$418$	−53.6995	−2.62653
$419$	12.1407	0.593112	0.296556	−	0.955016i	$-0.404162\pi$
$419$	12.1407	0.593112	0.296556	+	0.955016i	$0.404162\pi$
$420$	−50.1237	−2.44578
$421$	−14.3289	−0.698350	−0.349175	−	0.937058i	$-0.613538\pi$
$421$	−14.3289	−0.698350	−0.349175	+	0.937058i	$0.613538\pi$
$422$	−28.1434	−1.37000
$423$	−24.0770	−1.17066
$424$	−7.86507	−0.381961
$425$	−12.2547	−0.594443
$426$	51.1000	2.47580
$427$	20.8177	1.00744
$428$	−47.9029	−2.31547
$429$	−10.9149	−0.526975
$430$	1.83039	0.0882690
$431$	−26.0568	−1.25511	−0.627557	−	0.778571i	$-0.715945\pi$
$431$	−26.0568	−1.25511	−0.627557	+	0.778571i	$0.715945\pi$
$432$	−4.34839	−0.209212
$433$	28.7303	1.38069	0.690344	−	0.723481i	$-0.257459\pi$
$433$	28.7303	1.38069	0.690344	+	0.723481i	$0.257459\pi$
$434$	−73.6620	−3.53589
$435$	−20.4821	−0.982039
$436$	18.2163	0.872403
$437$	40.5668	1.94057
$438$	−67.7149	−3.23554
$439$	−31.0478	−1.48183	−0.740916	−	0.671597i	$-0.765609\pi$
$439$	−31.0478	−1.48183	−0.740916	+	0.671597i	$0.765609\pi$
$440$	29.5497	1.40873
$441$	27.3949	1.30452
$442$	8.69743	0.413695
$443$	−6.77053	−0.321678	−0.160839	−	0.986981i	$-0.551420\pi$
$443$	−6.77053	−0.321678	−0.160839	+	0.986981i	$0.551420\pi$
$444$	−80.0941	−3.80110
$445$	−16.1884	−0.767404
$446$	−47.7648	−2.26173
$447$	6.34154	0.299945
$448$	−27.8445	−1.31553
$449$	−21.7948	−1.02856	−0.514281	−	0.857622i	$-0.671941\pi$
$449$	−21.7948	−1.02856	−0.514281	+	0.857622i	$0.671941\pi$
$450$	22.4004	1.05597
$451$	53.1664	2.50351
$452$	−62.7588	−2.95193
$453$	11.3987	0.535559
$454$	0.663332	0.0311317
$455$	5.15808	0.241814
$456$	−58.0346	−2.71772
$457$	16.8156	0.786603	0.393301	−	0.919410i	$-0.371333\pi$
$457$	16.8156	0.786603	0.393301	+	0.919410i	$0.371333\pi$
$458$	−38.6712	−1.80699
$459$	−3.29868	−0.153969
$460$	−43.5339	−2.02978
$461$	37.2511	1.73496	0.867479	−	0.497474i	$-0.165739\pi$
$461$	37.2511	1.73496	0.867479	+	0.497474i	$0.165739\pi$
$462$	−112.881	−5.25170
$463$	1.00000	0.0464739
$463$	1.00000	0.0464739
$464$	32.5789	1.51244
$465$	−20.7788	−0.963593
$466$	37.1767	1.72218
$467$	−0.774669	−0.0358474	−0.0179237	−	0.999839i	$-0.505706\pi$
$467$	−0.774669	−0.0358474	−0.0179237	+	0.999839i	$0.505706\pi$
$468$	−10.6897	−0.494132
$469$	−57.4395	−2.65231
$470$	−28.1514	−1.29853
$471$	−46.1206	−2.12513
$472$	39.7792	1.83099
$473$	2.77169	0.127442
$474$	49.0454	2.25273
$475$	−16.4104	−0.752960
$476$	60.4806	2.77213
$477$	3.93825	0.180320
$478$	−21.5533	−0.985823
$479$	−6.01878	−0.275005	−0.137503	−	0.990501i	$-0.543908\pi$
$479$	−6.01878	−0.275005	−0.137503	+	0.990501i	$0.543908\pi$
$480$	3.10307	0.141635
$481$	8.24225	0.375814
$482$	3.20547	0.146005
$483$	85.2750	3.88015
$484$	42.1090	1.91405
$485$	4.88355	0.221751
$486$	51.7259	2.34633
$487$	−23.7763	−1.07740	−0.538702	−	0.842496i	$-0.681085\pi$
$487$	−23.7763	−1.07740	−0.538702	+	0.842496i	$0.681085\pi$
$488$	−25.8662	−1.17091
$489$	12.3839	0.560021
$490$	32.0307	1.44700
$491$	22.2482	1.00405	0.502025	−	0.864853i	$-0.332589\pi$
$491$	22.2482	1.00405	0.502025	+	0.864853i	$0.332589\pi$
$492$	112.054	5.05179
$493$	24.7142	1.11307
$494$	11.6468	0.524013
$495$	−14.7963	−0.665046
$496$	33.0509	1.48403
$497$	−36.5672	−1.64026
$498$	−64.8462	−2.90583
$499$	−13.4792	−0.603412	−0.301706	−	0.953401i	$-0.597556\pi$
$499$	−13.4792	−0.603412	−0.301706	+	0.953401i	$0.597556\pi$
$500$	42.9033	1.91869
$501$	44.3705	1.98233
$502$	−33.0642	−1.47573
$503$	−27.7294	−1.23639	−0.618196	−	0.786024i	$-0.712136\pi$
$503$	−27.7294	−1.23639	−0.618196	+	0.786024i	$0.712136\pi$
$504$	−56.6884	−2.52510
$505$	3.02704	0.134702
$506$	−98.0406	−4.35844
$507$	2.36731	0.105136
$508$	−41.7076	−1.85048
$509$	−9.23108	−0.409161	−0.204580	−	0.978850i	$-0.565583\pi$
$509$	−9.23108	−0.409161	−0.204580	+	0.978850i	$0.565583\pi$
$510$	25.3729	1.12353
$511$	48.4568	2.14360
$512$	43.3297	1.91492
$513$	−4.41727	−0.195027
$514$	1.71413	0.0756072
$515$	18.3516	0.808669
$516$	5.84164	0.257164
$517$	−42.6286	−1.87480
$518$	85.2409	3.74527
$519$	−29.8316	−1.30946
$520$	−6.40898	−0.281052
$521$	−12.8997	−0.565145	−0.282573	−	0.959246i	$-0.591188\pi$
$521$	−12.8997	−0.565145	−0.282573	+	0.959246i	$0.591188\pi$
$522$	−45.1750	−1.97726
$523$	3.22711	0.141112	0.0705559	−	0.997508i	$-0.477523\pi$
$523$	3.22711	0.141112	0.0705559	+	0.997508i	$0.477523\pi$
$524$	−12.0647	−0.527048
$525$	−34.4961	−1.50553
$526$	−57.0801	−2.48881
$527$	25.0723	1.09217
$528$	50.6478	2.20416
$529$	51.0639	2.22017
$530$	4.60469	0.200015
$531$	−19.9185	−0.864391
$532$	80.9899	3.51136
$533$	−11.5312	−0.499470
$534$	−76.8375	−3.32508
$535$	14.3809	0.621740
$536$	71.3693	3.08269
$537$	−49.5900	−2.13997
$538$	−33.3363	−1.43723
$539$	48.5030	2.08917
$540$	4.74036	0.203993
$541$	10.9983	0.472855	0.236428	−	0.971649i	$-0.424023\pi$
$541$	10.9983	0.472855	0.236428	+	0.971649i	$0.424023\pi$
$542$	27.4618	1.17959
$543$	40.5333	1.73945
$544$	−3.74425	−0.160534
$545$	−5.46870	−0.234254
$546$	24.4826	1.04776
$547$	23.0678	0.986309	0.493155	−	0.869942i	$-0.335844\pi$
$547$	23.0678	0.986309	0.493155	+	0.869942i	$0.335844\pi$
$548$	−45.5305	−1.94497
$549$	12.9519	0.552774
$550$	39.6602	1.69111
$551$	33.0949	1.40989
$552$	−105.955	−4.50976
$553$	−35.0969	−1.49247
$554$	44.3078	1.88246
$555$	24.0450	1.02065
$556$	−54.3288	−2.30405
$557$	2.48578	0.105326	0.0526630	−	0.998612i	$-0.483229\pi$
$557$	2.48578	0.105326	0.0526630	+	0.998612i	$0.483229\pi$
$558$	−45.8295	−1.94012
$559$	−0.601146	−0.0254258
$560$	−23.9348	−1.01143
$561$	38.4213	1.62215
$562$	75.7713	3.19622
$563$	−0.447412	−0.0188562	−0.00942808	−	0.999956i	$-0.503001\pi$
$563$	−0.447412	−0.0188562	−0.00942808	+	0.999956i	$0.503001\pi$
$564$	−89.8446	−3.78314
$565$	18.8408	0.792638
$566$	46.5279	1.95571
$567$	−41.9857	−1.76323
$568$	45.4352	1.90642
$569$	−27.2712	−1.14327	−0.571634	−	0.820509i	$-0.693690\pi$
$569$	−27.2712	−1.14327	−0.571634	+	0.820509i	$0.693690\pi$
$570$	33.9770	1.42314
$571$	9.39218	0.393051	0.196525	−	0.980499i	$-0.437034\pi$
$571$	9.39218	0.393051	0.196525	+	0.980499i	$0.437034\pi$
$572$	−18.9262	−0.791346
$573$	−17.5172	−0.731792
$574$	−119.254	−4.97759
$575$	−29.9609	−1.24946
$576$	−17.3237	−0.721821
$577$	11.9486	0.497428	0.248714	−	0.968577i	$-0.419992\pi$
$577$	11.9486	0.497428	0.248714	+	0.968577i	$0.419992\pi$
$578$	11.3880	0.473679
$579$	−53.4614	−2.22178
$580$	−35.5156	−1.47470
$581$	46.4040	1.92516
$582$	23.1796	0.960823
$583$	6.97271	0.288780
$584$	−60.2083	−2.49144
$585$	3.20915	0.132682
$586$	−72.1837	−2.98188
$587$	−4.91793	−0.202985	−0.101492	−	0.994836i	$-0.532362\pi$
$587$	−4.91793	−0.202985	−0.101492	+	0.994836i	$0.532362\pi$
$588$	102.226	4.21571
$589$	33.5744	1.38341
$590$	−23.2892	−0.958800
$591$	19.0221	0.782463
$592$	−38.2461	−1.57191
$593$	33.4440	1.37338	0.686690	−	0.726951i	$-0.259063\pi$
$593$	33.4440	1.37338	0.686690	+	0.726951i	$0.259063\pi$
$594$	10.6755	0.438023
$595$	−18.1569	−0.744358
$596$	10.9961	0.450419
$597$	−31.2342	−1.27833
$598$	21.2638	0.869543
$599$	31.2747	1.27785	0.638925	−	0.769269i	$-0.279379\pi$
$599$	31.2747	1.27785	0.638925	+	0.769269i	$0.279379\pi$
$600$	42.8619	1.74983
$601$	39.6560	1.61760	0.808801	−	0.588082i	$-0.200117\pi$
$601$	39.6560	1.61760	0.808801	+	0.588082i	$0.200117\pi$
$602$	−6.21702	−0.253387
$603$	−35.7365	−1.45530
$604$	19.7652	0.804235
$605$	−12.6415	−0.513951
$606$	14.3677	0.583649
$607$	−21.2801	−0.863731	−0.431865	−	0.901938i	$-0.642144\pi$
$607$	−21.2801	−0.863731	−0.431865	+	0.901938i	$0.642144\pi$
$608$	−5.01395	−0.203342
$609$	69.5685	2.81906
$610$	15.1437	0.613149
$611$	9.24564	0.374039
$612$	37.6286	1.52105
$613$	21.9082	0.884862	0.442431	−	0.896802i	$-0.354116\pi$
$613$	21.9082	0.884862	0.442431	+	0.896802i	$0.354116\pi$
$614$	24.4855	0.988156
$615$	−33.6397	−1.35648
$616$	−100.367	−4.04392
$617$	15.7139	0.632617	0.316308	−	0.948656i	$-0.397557\pi$
$617$	15.7139	0.632617	0.316308	+	0.948656i	$0.397557\pi$
$618$	87.1050	3.50388
$619$	1.50841	0.0606283	0.0303141	−	0.999540i	$-0.490349\pi$
$619$	1.50841	0.0606283	0.0303141	+	0.999540i	$0.490349\pi$
$620$	−36.0301	−1.44700
$621$	−8.06474	−0.323627
$622$	−12.7357	−0.510654
$623$	54.9849	2.20293
$624$	−10.9849	−0.439748
$625$	4.52693	0.181077
$626$	22.0246	0.880279
$627$	51.4501	2.05472
$628$	−79.9724	−3.19125
$629$	−29.0134	−1.15684
$630$	33.1888	1.32227
$631$	−16.1581	−0.643243	−0.321622	−	0.946868i	$-0.604228\pi$
$631$	−16.1581	−0.643243	−0.321622	+	0.946868i	$0.604228\pi$
$632$	43.6084	1.73465
$633$	26.9645	1.07174
$634$	17.4440	0.692789
$635$	12.5210	0.496881
$636$	14.6958	0.582725
$637$	−10.5197	−0.416807
$638$	−79.9829	−3.16655
$639$	−22.7506	−0.900001
$640$	−22.8769	−0.904287
$641$	−16.2922	−0.643504	−0.321752	−	0.946824i	$-0.604272\pi$
$641$	−16.2922	−0.643504	−0.321752	+	0.946824i	$0.604272\pi$
$642$	68.2582	2.69394
$643$	−20.5678	−0.811116	−0.405558	−	0.914069i	$-0.632923\pi$
$643$	−20.5678	−0.811116	−0.405558	+	0.914069i	$0.632923\pi$
$644$	147.866	5.82672
$645$	−1.75372	−0.0690525
$646$	−40.9976	−1.61303
$647$	−20.9688	−0.824370	−0.412185	−	0.911100i	$-0.635234\pi$
$647$	−20.9688	−0.824370	−0.412185	+	0.911100i	$0.635234\pi$
$648$	52.1678	2.04935
$649$	−35.2660	−1.38431
$650$	−8.60182	−0.337391
$651$	70.5764	2.76611
$652$	21.4735	0.840969
$653$	−31.5888	−1.23617	−0.618083	−	0.786113i	$-0.712090\pi$
$653$	−31.5888	−1.23617	−0.618083	+	0.786113i	$0.712090\pi$
$654$	−25.9569	−1.01500
$655$	3.62193	0.141520
$656$	53.5074	2.08911
$657$	30.1479	1.17618
$658$	95.6179	3.72757
$659$	39.6308	1.54380	0.771899	−	0.635745i	$-0.219307\pi$
$659$	39.6308	1.54380	0.771899	+	0.635745i	$0.219307\pi$
$660$	−55.2132	−2.14917
$661$	−11.7861	−0.458424	−0.229212	−	0.973376i	$-0.573615\pi$
$661$	−11.7861	−0.458424	−0.229212	+	0.973376i	$0.573615\pi$
$662$	37.8497	1.47107
$663$	−8.33312	−0.323631
$664$	−57.6575	−2.23755
$665$	−24.3139	−0.942854
$666$	53.0335	2.05501
$667$	60.4224	2.33956
$668$	76.9377	2.97681
$669$	45.7640	1.76934
$670$	−41.7839	−1.61425
$671$	22.9315	0.885261
$672$	−10.5398	−0.406580
$673$	18.3604	0.707742	0.353871	−	0.935294i	$-0.384865\pi$
$673$	18.3604	0.707742	0.353871	+	0.935294i	$0.384865\pi$
$674$	19.8624	0.765069
$675$	3.26241	0.125570
$676$	4.10488	0.157880
$677$	43.4719	1.67076	0.835381	−	0.549672i	$-0.185247\pi$
$677$	43.4719	1.67076	0.835381	+	0.549672i	$0.185247\pi$
$678$	89.4269	3.43442
$679$	−16.5873	−0.636562
$680$	22.5601	0.865142
$681$	−0.635546	−0.0243542
$682$	−81.1416	−3.10707
$683$	1.38098	0.0528418	0.0264209	−	0.999651i	$-0.491589\pi$
$683$	1.38098	0.0528418	0.0264209	+	0.999651i	$0.491589\pi$
$684$	50.3887	1.92666
$685$	13.6687	0.522254
$686$	−36.4008	−1.38979
$687$	37.0513	1.41360
$688$	2.78947	0.106348
$689$	−1.51230	−0.0576140
$690$	62.0327	2.36155
$691$	−3.32345	−0.126430	−0.0632151	−	0.998000i	$-0.520135\pi$
$691$	−3.32345	−0.126430	−0.0632151	+	0.998000i	$0.520135\pi$
$692$	−51.7275	−1.96639
$693$	50.2567	1.90909
$694$	−25.0428	−0.950610
$695$	16.3100	0.618674
$696$	−86.4399	−3.27649
$697$	40.5906	1.53748
$698$	43.9955	1.66525
$699$	−35.6194	−1.34725
$700$	−59.8157	−2.26082
$701$	23.4694	0.886426	0.443213	−	0.896416i	$-0.353839\pi$
$701$	23.4694	0.886426	0.443213	+	0.896416i	$0.353839\pi$
$702$	−2.31540	−0.0873890
$703$	−38.8520	−1.46533
$704$	−30.6718	−1.15599
$705$	26.9722	1.01583
$706$	−35.6708	−1.34249
$707$	−10.2815	−0.386677
$708$	−74.3270	−2.79338
$709$	27.5718	1.03548	0.517741	−	0.855538i	$-0.326773\pi$
$709$	27.5718	1.03548	0.517741	+	0.855538i	$0.326773\pi$
$710$	−26.6005	−0.998300
$711$	−21.8359	−0.818910
$712$	−68.3195	−2.56038
$713$	61.2978	2.29562
$714$	−86.1806	−3.22523
$715$	5.68183	0.212489
$716$	−85.9884	−3.21354
$717$	20.6504	0.771205
$718$	54.7466	2.04313
$719$	−15.2117	−0.567302	−0.283651	−	0.958928i	$-0.591546\pi$
$719$	−15.2117	−0.567302	−0.283651	+	0.958928i	$0.591546\pi$
$720$	−14.8913	−0.554965
$721$	−62.3324	−2.32138
$722$	−7.95477	−0.296046
$723$	−3.07120	−0.114219
$724$	70.2841	2.61209
$725$	−24.4425	−0.907773
$726$	−60.0024	−2.22690
$727$	7.20787	0.267325	0.133662	−	0.991027i	$-0.457326\pi$
$727$	7.20787	0.267325	0.133662	+	0.991027i	$0.457326\pi$
$728$	21.7685	0.806794
$729$	−19.4666	−0.720985
$730$	35.2496	1.30465
$731$	2.11608	0.0782662
$732$	48.3307	1.78635
$733$	39.1392	1.44564	0.722820	−	0.691036i	$-0.242845\pi$
$733$	39.1392	1.44564	0.722820	+	0.691036i	$0.242845\pi$
$734$	−83.4443	−3.07998
$735$	−30.6891	−1.13198
$736$	−9.15411	−0.337425
$737$	−63.2719	−2.33065
$738$	−74.1954	−2.73117
$739$	22.7942	0.838499	0.419249	−	0.907871i	$-0.362293\pi$
$739$	22.7942	0.838499	0.419249	+	0.907871i	$0.362293\pi$
$740$	41.6937	1.53269
$741$	−11.1589	−0.409933
$742$	−15.6401	−0.574166
$743$	47.5723	1.74526	0.872629	−	0.488384i	$-0.162414\pi$
$743$	47.5723	1.74526	0.872629	+	0.488384i	$0.162414\pi$
$744$	−87.6922	−3.21495
$745$	−3.30114	−0.120945
$746$	87.6855	3.21040
$747$	28.8707	1.05632
$748$	66.6219	2.43594
$749$	−48.8456	−1.78478
$750$	−61.1342	−2.23230
$751$	−13.5522	−0.494527	−0.247263	−	0.968948i	$-0.579531\pi$
$751$	−13.5522	−0.494527	−0.247263	+	0.968948i	$0.579531\pi$
$752$	−42.9021	−1.56448
$753$	31.6793	1.15446
$754$	17.3473	0.631753
$755$	−5.93370	−0.215950
$756$	−16.1009	−0.585585
$757$	−14.1014	−0.512522	−0.256261	−	0.966608i	$-0.582491\pi$
$757$	−14.1014	−0.512522	−0.256261	+	0.966608i	$0.582491\pi$
$758$	41.6566	1.51304
$759$	93.9339	3.40959
$760$	30.2104	1.09585
$761$	−48.1495	−1.74542	−0.872709	−	0.488240i	$-0.837639\pi$
$761$	−48.1495	−1.74542	−0.872709	+	0.488240i	$0.837639\pi$
$762$	59.4304	2.15294
$763$	18.5748	0.672453
$764$	−30.3746	−1.09891
$765$	−11.2965	−0.408425
$766$	69.3953	2.50735
$767$	7.64877	0.276181
$768$	−77.0875	−2.78166
$769$	49.1634	1.77288	0.886439	−	0.462846i	$-0.153172\pi$
$769$	49.1634	1.77288	0.886439	+	0.462846i	$0.153172\pi$
$770$	58.7612	2.11761
$771$	−1.64233	−0.0591471
$772$	−92.7012	−3.33639
$773$	37.8667	1.36197	0.680986	−	0.732297i	$-0.261552\pi$
$773$	37.8667	1.36197	0.680986	+	0.732297i	$0.261552\pi$
$774$	−3.86798	−0.139032
$775$	−24.7966	−0.890722
$776$	20.6099	0.739854
$777$	−81.6704	−2.92991
$778$	−68.1243	−2.44237
$779$	54.3550	1.94747
$780$	11.9751	0.428777
$781$	−40.2802	−1.44134
$782$	−74.8505	−2.67665
$783$	−6.57933	−0.235126
$784$	48.8142	1.74336
$785$	24.0085	0.856899
$786$	17.1913	0.613193
$787$	29.1381	1.03866	0.519330	−	0.854574i	$-0.326181\pi$
$787$	29.1381	1.03866	0.519330	+	0.854574i	$0.326181\pi$
$788$	32.9840	1.17501
$789$	54.6891	1.94698
$790$	−25.5310	−0.908352
$791$	−63.9939	−2.27536
$792$	−62.4446	−2.21887
$793$	−4.97357	−0.176617
$794$	−34.7410	−1.23291
$795$	−4.41181	−0.156471
$796$	−54.1596	−1.91964
$797$	−15.3207	−0.542686	−0.271343	−	0.962483i	$-0.587468\pi$
$797$	−15.3207	−0.542686	−0.271343	+	0.962483i	$0.587468\pi$
$798$	−115.405	−4.08529
$799$	−32.5454	−1.15137
$800$	3.70309	0.130924
$801$	34.2094	1.20873
$802$	−19.3710	−0.684013
$803$	53.3772	1.88364
$804$	−133.353	−4.70299
$805$	−44.3906	−1.56456
$806$	17.5987	0.619886
$807$	31.9399	1.12434
$808$	12.7750	0.449421
$809$	8.00106	0.281302	0.140651	−	0.990059i	$-0.455080\pi$
$809$	8.00106	0.281302	0.140651	+	0.990059i	$0.455080\pi$
$810$	−30.5422	−1.07314
$811$	22.3065	0.783288	0.391644	−	0.920117i	$-0.371906\pi$
$811$	22.3065	0.783288	0.391644	+	0.920117i	$0.371906\pi$
$812$	120.631	4.23331
$813$	−26.3115	−0.922784
$814$	93.8963	3.29106
$815$	−6.44656	−0.225813
$816$	38.6678	1.35364
$817$	2.83366	0.0991371
$818$	41.0684	1.43592
$819$	−10.9001	−0.380879
$820$	−58.3307	−2.03699
$821$	22.0420	0.769271	0.384635	−	0.923069i	$-0.374327\pi$
$821$	22.0420	0.769271	0.384635	+	0.923069i	$0.374327\pi$
$822$	64.8778	2.26287
$823$	−15.9570	−0.556226	−0.278113	−	0.960548i	$-0.589709\pi$
$823$	−15.9570	−0.556226	−0.278113	+	0.960548i	$0.589709\pi$
$824$	77.4488	2.69806
$825$	−37.9989	−1.32295
$826$	79.1031	2.75235
$827$	−19.9534	−0.693849	−0.346925	−	0.937893i	$-0.612774\pi$
$827$	−19.9534	−0.693849	−0.346925	+	0.937893i	$0.612774\pi$
$828$	91.9960	3.19708
$829$	37.9327	1.31746	0.658728	−	0.752381i	$-0.271095\pi$
$829$	37.9327	1.31746	0.658728	+	0.752381i	$0.271095\pi$
$830$	33.7562	1.17170
$831$	−42.4518	−1.47264
$832$	6.65235	0.230629
$833$	37.0303	1.28302
$834$	77.4147	2.68065
$835$	−23.0974	−0.799319
$836$	89.2137	3.08552
$837$	−6.67465	−0.230710
$838$	−29.9973	−1.03624
$839$	0.0762804	0.00263349	0.00131675	−	0.999999i	$-0.499581\pi$
$839$	0.0762804	0.00263349	0.00131675	+	0.999999i	$0.499581\pi$
$840$	63.5049	2.19113
$841$	20.2934	0.699773
$842$	35.4040	1.22010
$843$	−72.5974	−2.50039
$844$	46.7561	1.60941
$845$	−1.23232	−0.0423932
$846$	59.4896	2.04529
$847$	42.9377	1.47536
$848$	7.01745	0.240980
$849$	−44.5790	−1.52995
$850$	30.2791	1.03856
$851$	−70.9332	−2.43156
$852$	−84.8950	−2.90846
$853$	16.9214	0.579377	0.289688	−	0.957121i	$-0.406448\pi$
$853$	16.9214	0.579377	0.289688	+	0.957121i	$0.406448\pi$
$854$	−51.4364	−1.76012
$855$	−15.1272	−0.517338
$856$	60.6913	2.07439
$857$	−49.4155	−1.68800	−0.844001	−	0.536342i	$-0.819806\pi$
$857$	−49.4155	−1.68800	−0.844001	+	0.536342i	$0.819806\pi$
$858$	26.9685	0.920691
$859$	19.8923	0.678716	0.339358	−	0.940657i	$-0.389790\pi$
$859$	19.8923	0.678716	0.339358	+	0.940657i	$0.389790\pi$
$860$	−3.04091	−0.103694
$861$	114.259	3.89394
$862$	64.3813	2.19284
$863$	−14.8469	−0.505393	−0.252697	−	0.967546i	$-0.581317\pi$
$863$	−14.8469	−0.505393	−0.252697	+	0.967546i	$0.581317\pi$
$864$	0.996781	0.0339112
$865$	15.5291	0.528005
$866$	−70.9869	−2.41223
$867$	−10.9110	−0.370557
$868$	122.378	4.15379
$869$	−38.6607	−1.31147
$870$	50.6071	1.71574
$871$	13.7229	0.464984
$872$	−23.0794	−0.781568
$873$	−10.3199	−0.349277
$874$	−100.233	−3.39042
$875$	43.7476	1.47894
$876$	112.498	3.80097
$877$	17.1939	0.580597	0.290298	−	0.956936i	$-0.406245\pi$
$877$	17.1939	0.580597	0.290298	+	0.956936i	$0.406245\pi$
$878$	76.7132	2.58894
$879$	69.1601	2.33271
$880$	−26.3651	−0.888769
$881$	−27.1871	−0.915957	−0.457978	−	0.888963i	$-0.651426\pi$
$881$	−27.1871	−0.915957	−0.457978	+	0.888963i	$0.651426\pi$
$882$	−67.6875	−2.27916
$883$	−7.37786	−0.248285	−0.124142	−	0.992264i	$-0.539618\pi$
$883$	−7.37786	−0.248285	−0.124142	+	0.992264i	$0.539618\pi$
$884$	−14.4495	−0.485989
$885$	22.3136	0.750065
$886$	16.7287	0.562010
$887$	14.6516	0.491954	0.245977	−	0.969276i	$-0.420891\pi$
$887$	14.6516	0.491954	0.245977	+	0.969276i	$0.420891\pi$
$888$	101.477	3.40533
$889$	−42.5284	−1.42636
$890$	39.9984	1.34075
$891$	−46.2490	−1.54940
$892$	79.3541	2.65697
$893$	−43.5817	−1.45841
$894$	−15.6687	−0.524040
$895$	25.8145	0.862884
$896$	77.7026	2.59586
$897$	−20.3732	−0.680240
$898$	53.8508	1.79702
$899$	50.0076	1.66785
$900$	−37.2150	−1.24050
$901$	5.32341	0.177349
$902$	−131.364	−4.37393
$903$	5.95660	0.198223
$904$	79.5133	2.64457
$905$	−21.0999	−0.701386
$906$	−28.1640	−0.935688
$907$	51.0415	1.69480	0.847402	−	0.530951i	$-0.178165\pi$
$907$	51.0415	1.69480	0.847402	+	0.530951i	$0.178165\pi$
$908$	−1.10203	−0.0365721
$909$	−6.39676	−0.212167
$910$	−12.7446	−0.422479
$911$	−24.9223	−0.825714	−0.412857	−	0.910796i	$-0.635469\pi$
$911$	−24.9223	−0.825714	−0.412857	+	0.910796i	$0.635469\pi$
$912$	51.7802	1.71461
$913$	51.1158	1.69169
$914$	−41.5482	−1.37429
$915$	−14.5093	−0.479664
$916$	64.2464	2.12276
$917$	−12.3021	−0.406251
$918$	8.15039	0.269003
$919$	−0.980735	−0.0323515	−0.0161757	−	0.999869i	$-0.505149\pi$
$919$	−0.980735	−0.0323515	−0.0161757	+	0.999869i	$0.505149\pi$
$920$	55.1560	1.81844
$921$	−23.4599	−0.773030
$922$	−92.0403	−3.03119
$923$	8.73630	0.287559
$924$	187.535	6.16945
$925$	28.6944	0.943467
$926$	−2.47080	−0.0811957
$927$	−38.7807	−1.27373
$928$	−7.46805	−0.245151
$929$	24.3300	0.798241	0.399120	−	0.916898i	$-0.369316\pi$
$929$	24.3300	0.798241	0.399120	+	0.916898i	$0.369316\pi$
$930$	51.3403	1.68352
$931$	49.5874	1.62516
$932$	−61.7635	−2.02313
$933$	12.2022	0.399482
$934$	1.91406	0.0626298
$935$	−20.0005	−0.654087
$936$	13.5435	0.442683
$937$	−16.2922	−0.532244	−0.266122	−	0.963939i	$-0.585742\pi$
$937$	−16.2922	−0.532244	−0.266122	+	0.963939i	$0.585742\pi$
$938$	141.922	4.63391
$939$	−21.1020	−0.688638
$940$	46.7693	1.52545
$941$	26.8106	0.874000	0.437000	−	0.899461i	$-0.356041\pi$
$941$	26.8106	0.874000	0.437000	+	0.899461i	$0.356041\pi$
$942$	113.955	3.71286
$943$	99.2375	3.23162
$944$	−35.4922	−1.15517
$945$	4.83365	0.157239
$946$	−6.84830	−0.222657
$947$	−28.9351	−0.940265	−0.470132	−	0.882596i	$-0.655794\pi$
$947$	−28.9351	−0.940265	−0.470132	+	0.882596i	$0.655794\pi$
$948$	−81.4817	−2.64640
$949$	−11.5769	−0.375801
$950$	40.5469	1.31551
$951$	−16.7133	−0.541965
$952$	−76.6269	−2.48349
$953$	−38.5486	−1.24871	−0.624356	−	0.781140i	$-0.714638\pi$
$953$	−38.5486	−1.24871	−0.624356	+	0.781140i	$0.714638\pi$
$954$	−9.73065	−0.315041
$955$	9.11873	0.295075
$956$	35.8076	1.15810
$957$	76.6326	2.47718
$958$	14.8712	0.480468
$959$	−46.4265	−1.49919
$960$	19.4068	0.626352
$961$	19.7320	0.636517
$962$	−20.3650	−0.656594
$963$	−30.3898	−0.979297
$964$	−5.32541	−0.171520
$965$	27.8298	0.895872
$966$	−210.698	−6.77909
$967$	30.2059	0.971357	0.485678	−	0.874138i	$-0.338573\pi$
$967$	30.2059	0.971357	0.485678	+	0.874138i	$0.338573\pi$
$968$	−53.3507	−1.71476
$969$	39.2803	1.26186
$970$	−12.0663	−0.387426
$971$	34.5606	1.10910	0.554552	−	0.832149i	$-0.312890\pi$
$971$	34.5606	1.10910	0.554552	+	0.832149i	$0.312890\pi$
$972$	−85.9348	−2.75636
$973$	−55.3980	−1.77598
$974$	58.7465	1.88236
$975$	8.24151	0.263939
$976$	23.0786	0.738729
$977$	27.1906	0.869903	0.434951	−	0.900454i	$-0.356766\pi$
$977$	27.1906	0.869903	0.434951	+	0.900454i	$0.356766\pi$
$978$	−30.5983	−0.978425
$979$	60.5682	1.93577
$980$	−53.2143	−1.69987
$981$	11.5565	0.368970
$982$	−54.9711	−1.75420
$983$	51.0854	1.62937	0.814686	−	0.579902i	$-0.196909\pi$
$983$	51.0854	1.62937	0.814686	+	0.579902i	$0.196909\pi$
$984$	−141.969	−4.52579
$985$	−9.90210	−0.315507
$986$	−61.0640	−1.94467
$987$	−91.6126	−2.91606
$988$	−19.3494	−0.615586
$989$	5.17349	0.164507
$990$	36.5589	1.16192
$991$	32.5359	1.03354	0.516769	−	0.856125i	$-0.327135\pi$
$991$	32.5359	1.03354	0.516769	+	0.856125i	$0.327135\pi$
$992$	−7.57624	−0.240546
$993$	−36.2643	−1.15081
$994$	90.3503	2.86574
$995$	16.2592	0.515452
$996$	107.732	3.41363
$997$	−49.3826	−1.56396	−0.781981	−	0.623303i	$-0.785791\pi$
$997$	−49.3826	−1.56396	−0.781981	+	0.623303i	$0.785791\pi$
$998$	33.3045	1.05424
$999$	7.72384	0.244371

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6019.2.a.d.1.11	✓	123

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6019.2.a.d.1.11	✓	123	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:	\( N \)	\(=\)	\( 6019 = 13 \cdot 463 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6019.a (trivial)

\(f(q)\)	\(=\)	\(q-2.47080 q^{2} +2.36731 q^{3} +4.10488 q^{4} -1.23232 q^{5} -5.84916 q^{6} +4.18566 q^{7} -5.20074 q^{8} +2.60415 q^{9} +O(q^{10})\)	\(q-2.47080 q^{2} +2.36731 q^{3} +4.10488 q^{4} -1.23232 q^{5} -5.84916 q^{6} +4.18566 q^{7} -5.20074 q^{8} +2.60415 q^{9} +3.04483 q^{10} +4.61067 q^{11} +9.71751 q^{12} -1.00000 q^{13} -10.3419 q^{14} -2.91729 q^{15} +4.64025 q^{16} +3.52008 q^{17} -6.43434 q^{18} +4.71376 q^{19} -5.05853 q^{20} +9.90874 q^{21} -11.3921 q^{22} +8.60604 q^{23} -12.3117 q^{24} -3.48138 q^{25} +2.47080 q^{26} -0.937102 q^{27} +17.1816 q^{28} +7.02093 q^{29} +7.20804 q^{30} +7.12264 q^{31} -1.06368 q^{32} +10.9149 q^{33} -8.69743 q^{34} -5.15808 q^{35} +10.6897 q^{36} -8.24225 q^{37} -11.6468 q^{38} -2.36731 q^{39} +6.40898 q^{40} +11.5312 q^{41} -24.4826 q^{42} +0.601146 q^{43} +18.9262 q^{44} -3.20915 q^{45} -21.2638 q^{46} -9.24564 q^{47} +10.9849 q^{48} +10.5197 q^{49} +8.60182 q^{50} +8.33312 q^{51} -4.10488 q^{52} +1.51230 q^{53} +2.31540 q^{54} -5.68183 q^{55} -21.7685 q^{56} +11.1589 q^{57} -17.3473 q^{58} -7.64877 q^{59} -11.9751 q^{60} +4.97357 q^{61} -17.5987 q^{62} +10.9001 q^{63} -6.65235 q^{64} +1.23232 q^{65} -26.9685 q^{66} -13.7229 q^{67} +14.4495 q^{68} +20.3732 q^{69} +12.7446 q^{70} -8.73630 q^{71} -13.5435 q^{72} +11.5769 q^{73} +20.3650 q^{74} -8.24151 q^{75} +19.3494 q^{76} +19.2987 q^{77} +5.84916 q^{78} -8.38504 q^{79} -5.71829 q^{80} -10.0309 q^{81} -28.4912 q^{82} +11.0864 q^{83} +40.6741 q^{84} -4.33787 q^{85} -1.48531 q^{86} +16.6207 q^{87} -23.9789 q^{88} +13.1365 q^{89} +7.92918 q^{90} -4.18566 q^{91} +35.3267 q^{92} +16.8615 q^{93} +22.8442 q^{94} -5.80887 q^{95} -2.51807 q^{96} -3.96289 q^{97} -25.9922 q^{98} +12.0069 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 123 q + 10 q^{2} + q^{3} + 136 q^{4} + 46 q^{5} + 16 q^{6} + 12 q^{7} + 30 q^{8} + 154 q^{9}+O(q^{10}) \) 123 * q + 10 * q^2 + q^3 + 136 * q^4 + 46 * q^5 + 16 * q^6 + 12 * q^7 + 30 * q^8 + 154 * q^9	\( 123 q + 10 q^{2} + q^{3} + 136 q^{4} + 46 q^{5} + 16 q^{6} + 12 q^{7} + 30 q^{8} + 154 q^{9} + 5 q^{10} + 53 q^{11} - 6 q^{12} - 123 q^{13} + 21 q^{14} + 29 q^{15} + 166 q^{16} - 35 q^{17} + 28 q^{18} + 23 q^{19} + 93 q^{20} + 72 q^{21} + 8 q^{22} + 42 q^{23} + 55 q^{24} + 153 q^{25} - 10 q^{26} + 7 q^{27} + 39 q^{28} + 86 q^{29} + 44 q^{30} + 16 q^{31} + 70 q^{32} + 40 q^{33} + 10 q^{34} + 6 q^{35} + 222 q^{36} + 52 q^{37} + 12 q^{38} - q^{39} + 14 q^{40} + 80 q^{41} + 29 q^{42} + 2 q^{43} + 143 q^{44} + 137 q^{45} + 39 q^{46} + 45 q^{47} - 27 q^{48} + 163 q^{49} + 102 q^{50} + 48 q^{51} - 136 q^{52} + 117 q^{53} + 75 q^{54} + 20 q^{55} + 88 q^{56} + 67 q^{57} + 56 q^{58} + 88 q^{59} + 96 q^{60} + 57 q^{61} - 13 q^{62} + 48 q^{63} + 228 q^{64} - 46 q^{65} + 28 q^{66} + 43 q^{67} - 56 q^{68} + 92 q^{69} + 14 q^{70} + 90 q^{71} + 98 q^{72} + 25 q^{73} + 80 q^{74} + 21 q^{75} + 75 q^{76} + 112 q^{77} - 16 q^{78} + 36 q^{79} + 208 q^{80} + 231 q^{81} - 27 q^{82} + 93 q^{83} + 175 q^{84} + 77 q^{85} + 199 q^{86} + 15 q^{87} + 43 q^{88} + 140 q^{89} + 11 q^{90} - 12 q^{91} + 93 q^{92} + 140 q^{93} + 4 q^{94} + 23 q^{95} + 105 q^{96} + 43 q^{97} + 67 q^{98} + 140 q^{99}+O(q^{100}) \) 123 * q + 10 * q^2 + q^3 + 136 * q^4 + 46 * q^5 + 16 * q^6 + 12 * q^7 + 30 * q^8 + 154 * q^9 + 5 * q^10 + 53 * q^11 - 6 * q^12 - 123 * q^13 + 21 * q^14 + 29 * q^15 + 166 * q^16 - 35 * q^17 + 28 * q^18 + 23 * q^19 + 93 * q^20 + 72 * q^21 + 8 * q^22 + 42 * q^23 + 55 * q^24 + 153 * q^25 - 10 * q^26 + 7 * q^27 + 39 * q^28 + 86 * q^29 + 44 * q^30 + 16 * q^31 + 70 * q^32 + 40 * q^33 + 10 * q^34 + 6 * q^35 + 222 * q^36 + 52 * q^37 + 12 * q^38 - q^39 + 14 * q^40 + 80 * q^41 + 29 * q^42 + 2 * q^43 + 143 * q^44 + 137 * q^45 + 39 * q^46 + 45 * q^47 - 27 * q^48 + 163 * q^49 + 102 * q^50 + 48 * q^51 - 136 * q^52 + 117 * q^53 + 75 * q^54 + 20 * q^55 + 88 * q^56 + 67 * q^57 + 56 * q^58 + 88 * q^59 + 96 * q^60 + 57 * q^61 - 13 * q^62 + 48 * q^63 + 228 * q^64 - 46 * q^65 + 28 * q^66 + 43 * q^67 - 56 * q^68 + 92 * q^69 + 14 * q^70 + 90 * q^71 + 98 * q^72 + 25 * q^73 + 80 * q^74 + 21 * q^75 + 75 * q^76 + 112 * q^77 - 16 * q^78 + 36 * q^79 + 208 * q^80 + 231 * q^81 - 27 * q^82 + 93 * q^83 + 175 * q^84 + 77 * q^85 + 199 * q^86 + 15 * q^87 + 43 * q^88 + 140 * q^89 + 11 * q^90 - 12 * q^91 + 93 * q^92 + 140 * q^93 + 4 * q^94 + 23 * q^95 + 105 * q^96 + 43 * q^97 + 67 * q^98 + 140 * q^99

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