LMFDB - Embedded newform 6001.2.a.d.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6001,2,Mod(1,6001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6001, 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("6001.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6001 = 17 \cdot 353 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6001.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$47.9182262530$
Analytic rank:	$0$
Dimension:	$121$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	6001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.24229 q^{2} +2.77352 q^{3} +3.02787 q^{4} +0.258648 q^{5} -6.21903 q^{6} +3.59133 q^{7} -2.30477 q^{8} +4.69240 q^{9} +O(q^{10})$	\(q-2.24229 q^{2} +2.77352 q^{3} +3.02787 q^{4} +0.258648 q^{5} -6.21903 q^{6} +3.59133 q^{7} -2.30477 q^{8} +4.69240 q^{9} -0.579964 q^{10} +1.04738 q^{11} +8.39784 q^{12} +1.78915 q^{13} -8.05280 q^{14} +0.717365 q^{15} -0.887758 q^{16} +1.00000 q^{17} -10.5217 q^{18} +2.63252 q^{19} +0.783152 q^{20} +9.96062 q^{21} -2.34854 q^{22} +8.20057 q^{23} -6.39233 q^{24} -4.93310 q^{25} -4.01179 q^{26} +4.69390 q^{27} +10.8741 q^{28} +9.95368 q^{29} -1.60854 q^{30} +0.457574 q^{31} +6.60016 q^{32} +2.90494 q^{33} -2.24229 q^{34} +0.928891 q^{35} +14.2080 q^{36} -0.988008 q^{37} -5.90288 q^{38} +4.96223 q^{39} -0.596126 q^{40} +2.03994 q^{41} -22.3346 q^{42} +4.37973 q^{43} +3.17134 q^{44} +1.21368 q^{45} -18.3881 q^{46} -7.94975 q^{47} -2.46221 q^{48} +5.89765 q^{49} +11.0614 q^{50} +2.77352 q^{51} +5.41730 q^{52} -12.8480 q^{53} -10.5251 q^{54} +0.270904 q^{55} -8.27721 q^{56} +7.30135 q^{57} -22.3191 q^{58} +4.08684 q^{59} +2.17209 q^{60} -6.93442 q^{61} -1.02601 q^{62} +16.8520 q^{63} -13.0240 q^{64} +0.462760 q^{65} -6.51371 q^{66} -0.0995187 q^{67} +3.02787 q^{68} +22.7444 q^{69} -2.08284 q^{70} -2.43494 q^{71} -10.8149 q^{72} +5.94332 q^{73} +2.21540 q^{74} -13.6820 q^{75} +7.97093 q^{76} +3.76150 q^{77} -11.1268 q^{78} +8.72057 q^{79} -0.229617 q^{80} -1.05859 q^{81} -4.57414 q^{82} -8.46331 q^{83} +30.1594 q^{84} +0.258648 q^{85} -9.82063 q^{86} +27.6067 q^{87} -2.41398 q^{88} -2.36482 q^{89} -2.72142 q^{90} +6.42542 q^{91} +24.8302 q^{92} +1.26909 q^{93} +17.8256 q^{94} +0.680897 q^{95} +18.3057 q^{96} -4.45176 q^{97} -13.2242 q^{98} +4.91474 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 121 q + 9 q^{2} + 21 q^{3} + 127 q^{4} + 27 q^{5} + 17 q^{6} + 39 q^{7} + 24 q^{8} + 134 q^{9}+O(q^{10}) $ 121 * q + 9 * q^2 + 21 * q^3 + 127 * q^4 + 27 * q^5 + 17 * q^6 + 39 * q^7 + 24 * q^8 + 134 * q^9	\( 121 q + 9 q^{2} + 21 q^{3} + 127 q^{4} + 27 q^{5} + 17 q^{6} + 39 q^{7} + 24 q^{8} + 134 q^{9} + 19 q^{10} + 48 q^{11} + 43 q^{12} + 6 q^{13} + 40 q^{14} + 49 q^{15} + 135 q^{16} + 121 q^{17} + 30 q^{19} + 50 q^{20} + 18 q^{21} + 24 q^{22} + 75 q^{23} + 24 q^{24} + 128 q^{25} + 59 q^{26} + 75 q^{27} + 52 q^{28} + 49 q^{29} - 34 q^{30} + 101 q^{31} + 47 q^{32} + 20 q^{33} + 9 q^{34} + 47 q^{35} + 138 q^{36} + 32 q^{37} + 30 q^{38} + 101 q^{39} + 36 q^{40} + 83 q^{41} - 11 q^{42} + 8 q^{43} + 98 q^{44} + 49 q^{45} + 45 q^{46} + 135 q^{47} + 54 q^{48} + 116 q^{49} + 3 q^{50} + 21 q^{51} - 5 q^{52} + 28 q^{53} + 10 q^{54} + 37 q^{55} + 75 q^{56} + 31 q^{58} + 150 q^{59} + 50 q^{60} + 36 q^{61} + 34 q^{62} + 118 q^{63} + 110 q^{64} + 18 q^{65} - 28 q^{66} - 6 q^{67} + 127 q^{68} + 25 q^{69} - 22 q^{70} + 223 q^{71} + q^{72} + 38 q^{73} - 10 q^{74} + 88 q^{75} - 4 q^{76} + 38 q^{77} + 42 q^{78} + 74 q^{79} + 106 q^{80} + 133 q^{81} + 28 q^{82} + 55 q^{83} + 10 q^{84} + 27 q^{85} + 64 q^{86} + 14 q^{87} + 56 q^{88} + 118 q^{89} + 51 q^{90} + 73 q^{91} + 82 q^{92} + 31 q^{93} + 33 q^{94} + 106 q^{95} + 38 q^{96} + 37 q^{97} + 88 q^{98} + 81 q^{99}+O(q^{100}) \) 121 * q + 9 * q^2 + 21 * q^3 + 127 * q^4 + 27 * q^5 + 17 * q^6 + 39 * q^7 + 24 * q^8 + 134 * q^9 + 19 * q^10 + 48 * q^11 + 43 * q^12 + 6 * q^13 + 40 * q^14 + 49 * q^15 + 135 * q^16 + 121 * q^17 + 30 * q^19 + 50 * q^20 + 18 * q^21 + 24 * q^22 + 75 * q^23 + 24 * q^24 + 128 * q^25 + 59 * q^26 + 75 * q^27 + 52 * q^28 + 49 * q^29 - 34 * q^30 + 101 * q^31 + 47 * q^32 + 20 * q^33 + 9 * q^34 + 47 * q^35 + 138 * q^36 + 32 * q^37 + 30 * q^38 + 101 * q^39 + 36 * q^40 + 83 * q^41 - 11 * q^42 + 8 * q^43 + 98 * q^44 + 49 * q^45 + 45 * q^46 + 135 * q^47 + 54 * q^48 + 116 * q^49 + 3 * q^50 + 21 * q^51 - 5 * q^52 + 28 * q^53 + 10 * q^54 + 37 * q^55 + 75 * q^56 + 31 * q^58 + 150 * q^59 + 50 * q^60 + 36 * q^61 + 34 * q^62 + 118 * q^63 + 110 * q^64 + 18 * q^65 - 28 * q^66 - 6 * q^67 + 127 * q^68 + 25 * q^69 - 22 * q^70 + 223 * q^71 + q^72 + 38 * q^73 - 10 * q^74 + 88 * q^75 - 4 * q^76 + 38 * q^77 + 42 * q^78 + 74 * q^79 + 106 * q^80 + 133 * q^81 + 28 * q^82 + 55 * q^83 + 10 * q^84 + 27 * q^85 + 64 * q^86 + 14 * q^87 + 56 * q^88 + 118 * q^89 + 51 * q^90 + 73 * q^91 + 82 * q^92 + 31 * q^93 + 33 * q^94 + 106 * q^95 + 38 * q^96 + 37 * q^97 + 88 * q^98 + 81 * 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 $

$2$	−2.24229	−1.58554	−0.792769	−	0.609522i	$-0.791362\pi$
$2$	−2.24229	−1.58554	−0.792769	+	0.609522i	$0.791362\pi$
$3$	2.77352	1.60129	0.800646	−	0.599138i	$-0.204490\pi$
$3$	2.77352	1.60129	0.800646	+	0.599138i	$0.204490\pi$
$4$	3.02787	1.51393
$5$	0.258648	0.115671	0.0578355	−	0.998326i	$-0.481580\pi$
$5$	0.258648	0.115671	0.0578355	+	0.998326i	$0.481580\pi$
$6$	−6.21903	−2.53891
$7$	3.59133	1.35740	0.678698	−	0.734418i	$-0.262545\pi$
$7$	3.59133	1.35740	0.678698	+	0.734418i	$0.262545\pi$
$8$	−2.30477	−0.814861
$9$	4.69240	1.56413
$10$	−0.579964	−0.183401
$11$	1.04738	0.315798	0.157899	−	0.987455i	$-0.449528\pi$
$11$	1.04738	0.315798	0.157899	+	0.987455i	$0.449528\pi$
$12$	8.39784	2.42425
$13$	1.78915	0.496220	0.248110	−	0.968732i	$-0.420190\pi$
$13$	1.78915	0.496220	0.248110	+	0.968732i	$0.420190\pi$
$14$	−8.05280	−2.15220
$15$	0.717365	0.185223
$16$	−0.887758	−0.221940
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−10.5217	−2.47999
$19$	2.63252	0.603943	0.301971	−	0.953317i	$-0.402355\pi$
$19$	2.63252	0.603943	0.301971	+	0.953317i	$0.402355\pi$
$20$	0.783152	0.175118
$21$	9.96062	2.17358
$22$	−2.34854	−0.500710
$23$	8.20057	1.70994	0.854969	−	0.518679i	$-0.173576\pi$
$23$	8.20057	1.70994	0.854969	+	0.518679i	$0.173576\pi$
$24$	−6.39233	−1.30483
$25$	−4.93310	−0.986620
$26$	−4.01179	−0.786777
$27$	4.69390	0.903341
$28$	10.8741	2.05501
$29$	9.95368	1.84835	0.924176	−	0.381966i	$-0.124753\pi$
$29$	9.95368	1.84835	0.924176	+	0.381966i	$0.124753\pi$
$30$	−1.60854	−0.293678
$31$	0.457574	0.0821827	0.0410914	−	0.999155i	$-0.486917\pi$
$31$	0.457574	0.0821827	0.0410914	+	0.999155i	$0.486917\pi$
$32$	6.60016	1.16675
$33$	2.90494	0.505685
$34$	−2.24229	−0.384550
$35$	0.928891	0.157011
$36$	14.2080	2.36799
$37$	−0.988008	−0.162427	−0.0812137	−	0.996697i	$-0.525880\pi$
$37$	−0.988008	−0.162427	−0.0812137	+	0.996697i	$0.525880\pi$
$38$	−5.90288	−0.957574
$39$	4.96223	0.794593
$40$	−0.596126	−0.0942557
$41$	2.03994	0.318585	0.159292	−	0.987231i	$-0.449079\pi$
$41$	2.03994	0.318585	0.159292	+	0.987231i	$0.449079\pi$
$42$	−22.3346	−3.44630
$43$	4.37973	0.667903	0.333951	−	0.942590i	$-0.391618\pi$
$43$	4.37973	0.667903	0.333951	+	0.942590i	$0.391618\pi$
$44$	3.17134	0.478097
$45$	1.21368	0.180925
$46$	−18.3881	−2.71117
$47$	−7.94975	−1.15959	−0.579795	−	0.814762i	$-0.696867\pi$
$47$	−7.94975	−1.15959	−0.579795	+	0.814762i	$0.696867\pi$
$48$	−2.46221	−0.355390
$49$	5.89765	0.842522
$50$	11.0614	1.56432
$51$	2.77352	0.388370
$52$	5.41730	0.751245
$53$	−12.8480	−1.76481	−0.882405	−	0.470491i	$-0.844077\pi$
$53$	−12.8480	−1.76481	−0.882405	+	0.470491i	$0.844077\pi$
$54$	−10.5251	−1.43228
$55$	0.270904	0.0365287
$56$	−8.27721	−1.10609
$57$	7.30135	0.967088
$58$	−22.3191	−2.93064
$59$	4.08684	0.532061	0.266031	−	0.963965i	$-0.414288\pi$
$59$	4.08684	0.532061	0.266031	+	0.963965i	$0.414288\pi$
$60$	2.17209	0.280415
$61$	−6.93442	−0.887862	−0.443931	−	0.896061i	$-0.646416\pi$
$61$	−6.93442	−0.887862	−0.443931	+	0.896061i	$0.646416\pi$
$62$	−1.02601	−0.130304
$63$	16.8520	2.12315
$64$	−13.0240	−1.62800
$65$	0.462760	0.0573983
$66$	−6.51371	−0.801783
$67$	−0.0995187	−0.0121581	−0.00607907	−	0.999982i	$-0.501935\pi$
$67$	−0.0995187	−0.0121581	−0.00607907	+	0.999982i	$0.501935\pi$
$68$	3.02787	0.367183
$69$	22.7444	2.73811
$70$	−2.08284	−0.248947
$71$	−2.43494	−0.288974	−0.144487	−	0.989507i	$-0.546153\pi$
$71$	−2.43494	−0.288974	−0.144487	+	0.989507i	$0.546153\pi$
$72$	−10.8149	−1.27455
$73$	5.94332	0.695613	0.347807	−	0.937566i	$-0.386927\pi$
$73$	5.94332	0.695613	0.347807	+	0.937566i	$0.386927\pi$
$74$	2.21540	0.257535
$75$	−13.6820	−1.57987
$76$	7.97093	0.914329
$77$	3.76150	0.428663
$78$	−11.1268	−1.25986
$79$	8.72057	0.981140	0.490570	−	0.871402i	$-0.336789\pi$
$79$	8.72057	0.981140	0.490570	+	0.871402i	$0.336789\pi$
$80$	−0.229617	−0.0256720
$81$	−1.05859	−0.117621
$82$	−4.57414	−0.505129
$83$	−8.46331	−0.928969	−0.464485	−	0.885581i	$-0.653760\pi$
$83$	−8.46331	−0.928969	−0.464485	+	0.885581i	$0.653760\pi$
$84$	30.1594	3.29066
$85$	0.258648	0.0280543
$86$	−9.82063	−1.05899
$87$	27.6067	2.95975
$88$	−2.41398	−0.257332
$89$	−2.36482	−0.250671	−0.125335	−	0.992114i	$-0.540001\pi$
$89$	−2.36482	−0.250671	−0.125335	+	0.992114i	$0.540001\pi$
$90$	−2.72142	−0.286863
$91$	6.42542	0.673567
$92$	24.8302	2.58873
$93$	1.26909	0.131598
$94$	17.8256	1.83858
$95$	0.680897	0.0698586
$96$	18.3057	1.86831
$97$	−4.45176	−0.452008	−0.226004	−	0.974126i	$-0.572566\pi$
$97$	−4.45176	−0.452008	−0.226004	+	0.974126i	$0.572566\pi$
$98$	−13.2242	−1.33585
$99$	4.91474	0.493950
$100$	−14.9368	−1.49368
$101$	10.4437	1.03918	0.519591	−	0.854415i	$-0.326084\pi$
$101$	10.4437	1.03918	0.519591	+	0.854415i	$0.326084\pi$
$102$	−6.21903	−0.615776
$103$	−8.43017	−0.830649	−0.415324	−	0.909673i	$-0.636332\pi$
$103$	−8.43017	−0.830649	−0.415324	+	0.909673i	$0.636332\pi$
$104$	−4.12358	−0.404351
$105$	2.57629	0.251421
$106$	28.8090	2.79817
$107$	−3.69819	−0.357518	−0.178759	−	0.983893i	$-0.557208\pi$
$107$	−3.69819	−0.357518	−0.178759	+	0.983893i	$0.557208\pi$
$108$	14.2125	1.36760
$109$	2.01455	0.192959	0.0964796	−	0.995335i	$-0.469242\pi$
$109$	2.01455	0.192959	0.0964796	+	0.995335i	$0.469242\pi$
$110$	−0.607445	−0.0579176
$111$	−2.74026	−0.260094
$112$	−3.18823	−0.301260
$113$	−3.71376	−0.349361	−0.174681	−	0.984625i	$-0.555889\pi$
$113$	−3.71376	−0.349361	−0.174681	+	0.984625i	$0.555889\pi$
$114$	−16.3718	−1.53336
$115$	2.12106	0.197790
$116$	30.1384	2.79828
$117$	8.39540	0.776155
$118$	−9.16388	−0.843603
$119$	3.59133	0.329217
$120$	−1.65336	−0.150931
$121$	−9.90299	−0.900272
$122$	15.5490	1.40774
$123$	5.65781	0.510147
$124$	1.38547	0.124419
$125$	−2.56918	−0.229794
$126$	−37.7870	−3.36633
$127$	−11.6349	−1.03243	−0.516216	−	0.856458i	$-0.672660\pi$
$127$	−11.6349	−1.03243	−0.516216	+	0.856458i	$0.672660\pi$
$128$	16.0032	1.41449
$129$	12.1473	1.06951
$130$	−1.03764	−0.0910072
$131$	6.07247	0.530554	0.265277	−	0.964172i	$-0.414537\pi$
$131$	6.07247	0.530554	0.265277	+	0.964172i	$0.414537\pi$
$132$	8.79576	0.765573
$133$	9.45426	0.819789
$134$	0.223150	0.0192772
$135$	1.21407	0.104490
$136$	−2.30477	−0.197633
$137$	4.49058	0.383656	0.191828	−	0.981429i	$-0.438558\pi$
$137$	4.49058	0.383656	0.191828	+	0.981429i	$0.438558\pi$
$138$	−50.9996	−4.34138
$139$	−5.38986	−0.457162	−0.228581	−	0.973525i	$-0.573409\pi$
$139$	−5.38986	−0.457162	−0.228581	+	0.973525i	$0.573409\pi$
$140$	2.81256	0.237704
$141$	−22.0488	−1.85684
$142$	5.45985	0.458180
$143$	1.87393	0.156706
$144$	−4.16572	−0.347143
$145$	2.57450	0.213801
$146$	−13.3267	−1.10292
$147$	16.3572	1.34912
$148$	−2.99156	−0.245904
$149$	−6.37695	−0.522420	−0.261210	−	0.965282i	$-0.584121\pi$
$149$	−6.37695	−0.522420	−0.261210	+	0.965282i	$0.584121\pi$
$150$	30.6791	2.50494
$151$	−18.9515	−1.54225	−0.771127	−	0.636681i	$-0.780307\pi$
$151$	−18.9515	−1.54225	−0.771127	+	0.636681i	$0.780307\pi$
$152$	−6.06738	−0.492129
$153$	4.69240	0.379358
$154$	−8.43438	−0.679662
$155$	0.118351	0.00950616
$156$	15.0250	1.20296
$157$	−5.15979	−0.411796	−0.205898	−	0.978573i	$-0.566012\pi$
$157$	−5.15979	−0.411796	−0.205898	+	0.978573i	$0.566012\pi$
$158$	−19.5540	−1.55564
$159$	−35.6342	−2.82597
$160$	1.70712	0.134960
$161$	29.4510	2.32106
$162$	2.37366	0.186492
$163$	20.8270	1.63130	0.815649	−	0.578547i	$-0.196380\pi$
$163$	20.8270	1.63130	0.815649	+	0.578547i	$0.196380\pi$
$164$	6.17666	0.482316
$165$	0.751357	0.0584930
$166$	18.9772	1.47292
$167$	−13.6357	−1.05516	−0.527581	−	0.849504i	$-0.676901\pi$
$167$	−13.6357	−1.05516	−0.527581	+	0.849504i	$0.676901\pi$
$168$	−22.9570	−1.77117
$169$	−9.79895	−0.753765
$170$	−0.579964	−0.0444812
$171$	12.3529	0.944647
$172$	13.2612	1.01116
$173$	20.4789	1.55698	0.778490	−	0.627657i	$-0.215986\pi$
$173$	20.4789	1.55698	0.778490	+	0.627657i	$0.215986\pi$
$174$	−61.9023	−4.69280
$175$	−17.7164	−1.33923
$176$	−0.929824	−0.0700881
$177$	11.3349	0.851985
$178$	5.30262	0.397448
$179$	21.1761	1.58277	0.791387	−	0.611315i	$-0.209359\pi$
$179$	21.1761	1.58277	0.791387	+	0.611315i	$0.209359\pi$
$180$	3.67486	0.273908
$181$	−5.44323	−0.404592	−0.202296	−	0.979324i	$-0.564840\pi$
$181$	−5.44323	−0.404592	−0.202296	+	0.979324i	$0.564840\pi$
$182$	−14.4077	−1.06797
$183$	−19.2327	−1.42172
$184$	−18.9005	−1.39336
$185$	−0.255546	−0.0187881
$186$	−2.84567	−0.208655
$187$	1.04738	0.0765923
$188$	−24.0708	−1.75554
$189$	16.8573	1.22619
$190$	−1.52677	−0.110764
$191$	−12.7225	−0.920569	−0.460284	−	0.887771i	$-0.652253\pi$
$191$	−12.7225	−0.920569	−0.460284	+	0.887771i	$0.652253\pi$
$192$	−36.1222	−2.60689
$193$	−4.08332	−0.293924	−0.146962	−	0.989142i	$-0.546949\pi$
$193$	−4.08332	−0.293924	−0.146962	+	0.989142i	$0.546949\pi$
$194$	9.98214	0.716676
$195$	1.28347	0.0919114
$196$	17.8573	1.27552
$197$	13.0564	0.930231	0.465116	−	0.885250i	$-0.346013\pi$
$197$	13.0564	0.930231	0.465116	+	0.885250i	$0.346013\pi$
$198$	−11.0203	−0.783178
$199$	17.2319	1.22154	0.610768	−	0.791809i	$-0.290861\pi$
$199$	17.2319	1.22154	0.610768	+	0.791809i	$0.290861\pi$
$200$	11.3697	0.803958
$201$	−0.276017	−0.0194687
$202$	−23.4177	−1.64766
$203$	35.7470	2.50895
$204$	8.39784	0.587966
$205$	0.527626	0.0368510
$206$	18.9029	1.31703
$207$	38.4804	2.67457
$208$	−1.58833	−0.110131
$209$	2.75726	0.190724
$210$	−5.77680	−0.398637
$211$	−21.7765	−1.49916	−0.749579	−	0.661915i	$-0.769744\pi$
$211$	−21.7765	−1.49916	−0.749579	+	0.661915i	$0.769744\pi$
$212$	−38.9021	−2.67180
$213$	−6.75335	−0.462732
$214$	8.29242	0.566858
$215$	1.13281	0.0772570
$216$	−10.8184	−0.736098
$217$	1.64330	0.111554
$218$	−4.51722	−0.305944
$219$	16.4839	1.11388
$220$	0.820261	0.0553020
$221$	1.78915	0.120351
$222$	6.14445	0.412389
$223$	7.02715	0.470573	0.235286	−	0.971926i	$-0.424397\pi$
$223$	7.02715	0.470573	0.235286	+	0.971926i	$0.424397\pi$
$224$	23.7034	1.58375
$225$	−23.1481	−1.54321
$226$	8.32733	0.553926
$227$	−9.11686	−0.605107	−0.302554	−	0.953132i	$-0.597839\pi$
$227$	−9.11686	−0.605107	−0.302554	+	0.953132i	$0.597839\pi$
$228$	22.1075	1.46411
$229$	−23.6000	−1.55953	−0.779764	−	0.626073i	$-0.784661\pi$
$229$	−23.6000	−1.55953	−0.779764	+	0.626073i	$0.784661\pi$
$230$	−4.75604	−0.313604
$231$	10.4326	0.686414
$232$	−22.9410	−1.50615
$233$	0.931390	0.0610174	0.0305087	−	0.999535i	$-0.490287\pi$
$233$	0.931390	0.0610174	0.0305087	+	0.999535i	$0.490287\pi$
$234$	−18.8249	−1.23062
$235$	−2.05619	−0.134131
$236$	12.3744	0.805505
$237$	24.1866	1.57109
$238$	−8.05280	−0.521986
$239$	20.3762	1.31802	0.659012	−	0.752133i	$-0.270975\pi$
$239$	20.3762	1.31802	0.659012	+	0.752133i	$0.270975\pi$
$240$	−0.636847	−0.0411083
$241$	−11.0296	−0.710477	−0.355238	−	0.934776i	$-0.615600\pi$
$241$	−11.0296	−0.710477	−0.355238	+	0.934776i	$0.615600\pi$
$242$	22.2054	1.42742
$243$	−17.0177	−1.09169
$244$	−20.9965	−1.34416
$245$	1.52542	0.0974553
$246$	−12.6864	−0.808858
$247$	4.70998	0.299689
$248$	−1.05461	−0.0669675
$249$	−23.4731	−1.48755
$250$	5.76084	0.364348
$251$	−1.68230	−0.106186	−0.0530929	−	0.998590i	$-0.516908\pi$
$251$	−1.68230	−0.106186	−0.0530929	+	0.998590i	$0.516908\pi$
$252$	51.0255	3.21430
$253$	8.58915	0.539995
$254$	26.0889	1.63696
$255$	0.717365	0.0449231
$256$	−9.83586	−0.614741
$257$	13.0149	0.811850	0.405925	−	0.913906i	$-0.366949\pi$
$257$	13.0149	0.811850	0.405925	+	0.913906i	$0.366949\pi$
$258$	−27.2377	−1.69574
$259$	−3.54826	−0.220478
$260$	1.40117	0.0868972
$261$	46.7067	2.89107
$262$	−13.6162	−0.841214
$263$	6.09649	0.375926	0.187963	−	0.982176i	$-0.439812\pi$
$263$	6.09649	0.375926	0.187963	+	0.982176i	$0.439812\pi$
$264$	−6.69523	−0.412063
$265$	−3.32311	−0.204137
$266$	−21.1992	−1.29981
$267$	−6.55888	−0.401397
$268$	−0.301329	−0.0184066
$269$	−13.4226	−0.818391	−0.409196	−	0.912447i	$-0.634191\pi$
$269$	−13.4226	−0.818391	−0.409196	+	0.912447i	$0.634191\pi$
$270$	−2.72229	−0.165673
$271$	−25.8215	−1.56854	−0.784272	−	0.620417i	$-0.786963\pi$
$271$	−25.8215	−1.56854	−0.784272	+	0.620417i	$0.786963\pi$
$272$	−0.887758	−0.0538283
$273$	17.8210	1.07858
$274$	−10.0692	−0.608301
$275$	−5.16685	−0.311573
$276$	68.8671	4.14531
$277$	−26.6230	−1.59962	−0.799810	−	0.600253i	$-0.795067\pi$
$277$	−26.6230	−1.59962	−0.799810	+	0.600253i	$0.795067\pi$
$278$	12.0856	0.724848
$279$	2.14712	0.128545
$280$	−2.14088	−0.127942
$281$	23.3833	1.39493	0.697466	−	0.716618i	$-0.254311\pi$
$281$	23.3833	1.39493	0.697466	+	0.716618i	$0.254311\pi$
$282$	49.4397	2.94409
$283$	3.58458	0.213081	0.106541	−	0.994308i	$-0.466023\pi$
$283$	3.58458	0.213081	0.106541	+	0.994308i	$0.466023\pi$
$284$	−7.37268	−0.437488
$285$	1.88848	0.111864
$286$	−4.20188	−0.248463
$287$	7.32609	0.432446
$288$	30.9706	1.82496
$289$	1.00000	0.0588235
$290$	−5.77278	−0.338989
$291$	−12.3470	−0.723796
$292$	17.9956	1.05311
$293$	10.0477	0.586992	0.293496	−	0.955960i	$-0.405181\pi$
$293$	10.0477	0.586992	0.293496	+	0.955960i	$0.405181\pi$
$294$	−36.6777	−2.13909
$295$	1.05705	0.0615440
$296$	2.27714	0.132356
$297$	4.91632	0.285274
$298$	14.2990	0.828317
$299$	14.6720	0.848506
$300$	−41.4274	−2.39181
$301$	15.7291	0.906608
$302$	42.4949	2.44530
$303$	28.9657	1.66403
$304$	−2.33705	−0.134039
$305$	−1.79357	−0.102700
$306$	−10.5217	−0.601487
$307$	5.64621	0.322246	0.161123	−	0.986934i	$-0.448488\pi$
$307$	5.64621	0.322246	0.161123	+	0.986934i	$0.448488\pi$
$308$	11.3893	0.648967
$309$	−23.3812	−1.33011
$310$	−0.265377	−0.0150724
$311$	−26.2048	−1.48594	−0.742968	−	0.669327i	$-0.766583\pi$
$311$	−26.2048	−1.48594	−0.742968	+	0.669327i	$0.766583\pi$
$312$	−11.4368	−0.647483
$313$	19.7246	1.11490	0.557450	−	0.830210i	$-0.311780\pi$
$313$	19.7246	1.11490	0.557450	+	0.830210i	$0.311780\pi$
$314$	11.5697	0.652919
$315$	4.35873	0.245586
$316$	26.4047	1.48538
$317$	11.3334	0.636550	0.318275	−	0.947998i	$-0.396896\pi$
$317$	11.3334	0.636550	0.318275	+	0.947998i	$0.396896\pi$
$318$	79.9022	4.48069
$319$	10.4253	0.583706
$320$	−3.36862	−0.188312
$321$	−10.2570	−0.572490
$322$	−66.0376	−3.68013
$323$	2.63252	0.146478
$324$	−3.20526	−0.178070
$325$	−8.82605	−0.489581
$326$	−46.7002	−2.58649
$327$	5.58740	0.308984
$328$	−4.70160	−0.259602
$329$	−28.5502	−1.57402
$330$	−1.68476	−0.0927430
$331$	4.01321	0.220586	0.110293	−	0.993899i	$-0.464821\pi$
$331$	4.01321	0.220586	0.110293	+	0.993899i	$0.464821\pi$
$332$	−25.6258	−1.40640
$333$	−4.63613	−0.254058
$334$	30.5752	1.67300
$335$	−0.0257403	−0.00140634
$336$	−8.84262	−0.482405
$337$	−19.1692	−1.04421	−0.522106	−	0.852881i	$-0.674853\pi$
$337$	−19.1692	−1.04421	−0.522106	+	0.852881i	$0.674853\pi$
$338$	21.9721	1.19512
$339$	−10.3002	−0.559429
$340$	0.783152	0.0424724
$341$	0.479256	0.0259532
$342$	−27.6987	−1.49777
$343$	−3.95890	−0.213760
$344$	−10.0943	−0.544248
$345$	5.88280	0.316720
$346$	−45.9196	−2.46865
$347$	3.06838	0.164719	0.0823597	−	0.996603i	$-0.473754\pi$
$347$	3.06838	0.164719	0.0823597	+	0.996603i	$0.473754\pi$
$348$	83.5895	4.48087
$349$	16.3185	0.873508	0.436754	−	0.899581i	$-0.356128\pi$
$349$	16.3185	0.873508	0.436754	+	0.899581i	$0.356128\pi$
$350$	39.7253	2.12341
$351$	8.39808	0.448256
$352$	6.91290	0.368459
$353$	−1.00000	−0.0532246
$353$	−1.00000	−0.0532246
$354$	−25.4162	−1.35085
$355$	−0.629793	−0.0334259
$356$	−7.16037	−0.379499
$357$	9.96062	0.527172
$358$	−47.4829	−2.50955
$359$	27.6205	1.45775	0.728877	−	0.684645i	$-0.240043\pi$
$359$	27.6205	1.45775	0.728877	+	0.684645i	$0.240043\pi$
$360$	−2.79726	−0.147428
$361$	−12.0698	−0.635253
$362$	12.2053	0.641497
$363$	−27.4661	−1.44160
$364$	19.4553	1.01974
$365$	1.53723	0.0804622
$366$	43.1254	2.25420
$367$	5.40277	0.282022	0.141011	−	0.990008i	$-0.454965\pi$
$367$	5.40277	0.282022	0.141011	+	0.990008i	$0.454965\pi$
$368$	−7.28013	−0.379503
$369$	9.57221	0.498309
$370$	0.573009	0.0297893
$371$	−46.1414	−2.39554
$372$	3.84263	0.199231
$373$	−16.7246	−0.865966	−0.432983	−	0.901402i	$-0.642539\pi$
$373$	−16.7246	−0.865966	−0.432983	+	0.901402i	$0.642539\pi$
$374$	−2.34854	−0.121440
$375$	−7.12566	−0.367967
$376$	18.3224	0.944905
$377$	17.8086	0.917190
$378$	−37.7991	−1.94417
$379$	−25.1388	−1.29129	−0.645647	−	0.763636i	$-0.723412\pi$
$379$	−25.1388	−1.29129	−0.645647	+	0.763636i	$0.723412\pi$
$380$	2.06167	0.105761
$381$	−32.2697	−1.65322
$382$	28.5276	1.45960
$383$	12.4483	0.636076	0.318038	−	0.948078i	$-0.396976\pi$
$383$	12.4483	0.636076	0.318038	+	0.948078i	$0.396976\pi$
$384$	44.3851	2.26502
$385$	0.972905	0.0495838
$386$	9.15598	0.466027
$387$	20.5515	1.04469
$388$	−13.4793	−0.684309
$389$	10.4541	0.530043	0.265022	−	0.964242i	$-0.414621\pi$
$389$	10.4541	0.530043	0.265022	+	0.964242i	$0.414621\pi$
$390$	−2.87792	−0.145729
$391$	8.20057	0.414721
$392$	−13.5928	−0.686538
$393$	16.8421	0.849571
$394$	−29.2763	−1.47492
$395$	2.25556	0.113489
$396$	14.8812	0.747808
$397$	−8.80292	−0.441806	−0.220903	−	0.975296i	$-0.570900\pi$
$397$	−8.80292	−0.441806	−0.220903	+	0.975296i	$0.570900\pi$
$398$	−38.6389	−1.93679
$399$	26.2216	1.31272
$400$	4.37940	0.218970
$401$	−25.1831	−1.25758	−0.628791	−	0.777574i	$-0.716450\pi$
$401$	−25.1831	−1.25758	−0.628791	+	0.777574i	$0.716450\pi$
$402$	0.618910	0.0308684
$403$	0.818668	0.0407808
$404$	31.6220	1.57325
$405$	−0.273801	−0.0136053
$406$	−80.1551	−3.97803
$407$	−1.03482	−0.0512943
$408$	−6.39233	−0.316468
$409$	−23.2562	−1.14994	−0.574972	−	0.818173i	$-0.694987\pi$
$409$	−23.2562	−1.14994	−0.574972	+	0.818173i	$0.694987\pi$
$410$	−1.18309	−0.0584287
$411$	12.4547	0.614344
$412$	−25.5254	−1.25755
$413$	14.6772	0.722217
$414$	−86.2842	−4.24064
$415$	−2.18902	−0.107455
$416$	11.8087	0.578968
$417$	−14.9489	−0.732049
$418$	−6.18259	−0.302400
$419$	3.34458	0.163393	0.0816967	−	0.996657i	$-0.473966\pi$
$419$	3.34458	0.163393	0.0816967	+	0.996657i	$0.473966\pi$
$420$	7.80067	0.380634
$421$	−5.73812	−0.279659	−0.139829	−	0.990176i	$-0.544655\pi$
$421$	−5.73812	−0.279659	−0.139829	+	0.990176i	$0.544655\pi$
$422$	48.8293	2.37697
$423$	−37.3034	−1.81375
$424$	29.6118	1.43807
$425$	−4.93310	−0.239291
$426$	15.1430	0.733680
$427$	−24.9038	−1.20518
$428$	−11.1976	−0.541258
$429$	5.19736	0.250931
$430$	−2.54009	−0.122494
$431$	20.0619	0.966349	0.483174	−	0.875524i	$-0.339484\pi$
$431$	20.0619	0.966349	0.483174	+	0.875524i	$0.339484\pi$
$432$	−4.16705	−0.200487
$433$	25.0529	1.20396	0.601982	−	0.798510i	$-0.294378\pi$
$433$	25.0529	1.20396	0.601982	+	0.798510i	$0.294378\pi$
$434$	−3.68476	−0.176874
$435$	7.14042	0.342357
$436$	6.09980	0.292127
$437$	21.5882	1.03270
$438$	−36.9617	−1.76610
$439$	2.44243	0.116571	0.0582853	−	0.998300i	$-0.481437\pi$
$439$	2.44243	0.116571	0.0582853	+	0.998300i	$0.481437\pi$
$440$	−0.624372	−0.0297658
$441$	27.6741	1.31782
$442$	−4.01179	−0.190821
$443$	−20.5611	−0.976887	−0.488444	−	0.872595i	$-0.662435\pi$
$443$	−20.5611	−0.976887	−0.488444	+	0.872595i	$0.662435\pi$
$444$	−8.29713	−0.393764
$445$	−0.611657	−0.0289953
$446$	−15.7569	−0.746111
$447$	−17.6866	−0.836546
$448$	−46.7733	−2.20983
$449$	13.9589	0.658759	0.329380	−	0.944198i	$-0.393160\pi$
$449$	13.9589	0.658759	0.329380	+	0.944198i	$0.393160\pi$
$450$	51.9047	2.44681
$451$	2.13660	0.100609
$452$	−11.2448	−0.528910
$453$	−52.5624	−2.46960
$454$	20.4427	0.959421
$455$	1.66192	0.0779122
$456$	−16.8280	−0.788042
$457$	−3.07697	−0.143934	−0.0719672	−	0.997407i	$-0.522928\pi$
$457$	−3.07697	−0.143934	−0.0719672	+	0.997407i	$0.522928\pi$
$458$	52.9179	2.47269
$459$	4.69390	0.219092
$460$	6.42229	0.299441
$461$	−16.1174	−0.750660	−0.375330	−	0.926891i	$-0.622471\pi$
$461$	−16.1174	−0.750660	−0.375330	+	0.926891i	$0.622471\pi$
$462$	−23.3929	−1.08834
$463$	−17.7718	−0.825923	−0.412962	−	0.910748i	$-0.635506\pi$
$463$	−17.7718	−0.825923	−0.412962	+	0.910748i	$0.635506\pi$
$464$	−8.83647	−0.410223
$465$	0.328248	0.0152221
$466$	−2.08845	−0.0967454
$467$	−23.8307	−1.10275	−0.551377	−	0.834256i	$-0.685898\pi$
$467$	−23.8307	−1.10275	−0.551377	+	0.834256i	$0.685898\pi$
$468$	25.4201	1.17505
$469$	−0.357405	−0.0165034
$470$	4.61057	0.212670
$471$	−14.3108	−0.659405
$472$	−9.41924	−0.433556
$473$	4.58726	0.210923
$474$	−54.2335	−2.49103
$475$	−12.9865	−0.595862
$476$	10.8741	0.498412
$477$	−60.2880	−2.76040
$478$	−45.6893	−2.08978
$479$	−40.6516	−1.85742	−0.928709	−	0.370810i	$-0.879080\pi$
$479$	−40.6516	−1.85742	−0.928709	+	0.370810i	$0.879080\pi$
$480$	4.73472	0.216110
$481$	−1.76769	−0.0805998
$482$	24.7315	1.12649
$483$	81.6828	3.71669
$484$	−29.9849	−1.36295
$485$	−1.15144	−0.0522841
$486$	38.1586	1.73091
$487$	15.9016	0.720569	0.360285	−	0.932842i	$-0.382680\pi$
$487$	15.9016	0.720569	0.360285	+	0.932842i	$0.382680\pi$
$488$	15.9823	0.723484
$489$	57.7641	2.61218
$490$	−3.42043	−0.154519
$491$	34.3728	1.55122	0.775611	−	0.631212i	$-0.217442\pi$
$491$	34.3728	1.55122	0.775611	+	0.631212i	$0.217442\pi$
$492$	17.1311	0.772329
$493$	9.95368	0.448291
$494$	−10.5611	−0.475168
$495$	1.27119	0.0571357
$496$	−0.406215	−0.0182396
$497$	−8.74468	−0.392252
$498$	52.6336	2.35857
$499$	−2.29217	−0.102611	−0.0513057	−	0.998683i	$-0.516338\pi$
$499$	−2.29217	−0.102611	−0.0513057	+	0.998683i	$0.516338\pi$
$500$	−7.77913	−0.347893
$501$	−37.8189	−1.68962
$502$	3.77220	0.168362
$503$	−1.96361	−0.0875532	−0.0437766	−	0.999041i	$-0.513939\pi$
$503$	−1.96361	−0.0875532	−0.0437766	+	0.999041i	$0.513939\pi$
$504$	−38.8400	−1.73007
$505$	2.70123	0.120203
$506$	−19.2594	−0.856183
$507$	−27.1776	−1.20700
$508$	−35.2290	−1.56303
$509$	13.5156	0.599070	0.299535	−	0.954085i	$-0.403168\pi$
$509$	13.5156	0.599070	0.299535	+	0.954085i	$0.403168\pi$
$510$	−1.60854	−0.0712274
$511$	21.3444	0.944222
$512$	−9.95151	−0.439799
$513$	12.3568	0.545566
$514$	−29.1833	−1.28722
$515$	−2.18045	−0.0960819
$516$	36.7803	1.61916
$517$	−8.32644	−0.366196
$518$	7.95623	0.349577
$519$	56.7985	2.49318
$520$	−1.06656	−0.0467716
$521$	0.274929	0.0120448	0.00602242	−	0.999982i	$-0.498083\pi$
$521$	0.274929	0.0120448	0.00602242	+	0.999982i	$0.498083\pi$
$522$	−104.730	−4.58390
$523$	−4.64897	−0.203285	−0.101643	−	0.994821i	$-0.532410\pi$
$523$	−4.64897	−0.203285	−0.101643	+	0.994821i	$0.532410\pi$
$524$	18.3866	0.803223
$525$	−49.1367	−2.14450
$526$	−13.6701	−0.596045
$527$	0.457574	0.0199322
$528$	−2.57888	−0.112231
$529$	44.2494	1.92389
$530$	7.45138	0.323667
$531$	19.1771	0.832214
$532$	28.6262	1.24111
$533$	3.64975	0.158088
$534$	14.7069	0.636431
$535$	−0.956530	−0.0413544
$536$	0.229368	0.00990720
$537$	58.7322	2.53448
$538$	30.0974	1.29759
$539$	6.17711	0.266067
$540$	3.67604	0.158191
$541$	6.77060	0.291091	0.145545	−	0.989352i	$-0.453506\pi$
$541$	6.77060	0.291091	0.145545	+	0.989352i	$0.453506\pi$
$542$	57.8993	2.48699
$543$	−15.0969	−0.647870
$544$	6.60016	0.282980
$545$	0.521061	0.0223198
$546$	−39.9599	−1.71013
$547$	18.1744	0.777080	0.388540	−	0.921432i	$-0.372980\pi$
$547$	18.1744	0.777080	0.388540	+	0.921432i	$0.372980\pi$
$548$	13.5969	0.580829
$549$	−32.5391	−1.38873
$550$	11.5856	0.494011
$551$	26.2033	1.11630
$552$	−52.4208	−2.23118
$553$	31.3184	1.33180
$554$	59.6965	2.53626
$555$	−0.708762	−0.0300853
$556$	−16.3198	−0.692113
$557$	−1.95955	−0.0830288	−0.0415144	−	0.999138i	$-0.513218\pi$
$557$	−1.95955	−0.0830288	−0.0415144	+	0.999138i	$0.513218\pi$
$558$	−4.81447	−0.203813
$559$	7.83599	0.331427
$560$	−0.824630	−0.0348470
$561$	2.90494	0.122647
$562$	−52.4322	−2.21172
$563$	−24.8639	−1.04789	−0.523943	−	0.851753i	$-0.675540\pi$
$563$	−24.8639	−1.04789	−0.523943	+	0.851753i	$0.675540\pi$
$564$	−66.7607	−2.81113
$565$	−0.960558	−0.0404110
$566$	−8.03767	−0.337848
$567$	−3.80173	−0.159658
$568$	5.61199	0.235474
$569$	25.2778	1.05970	0.529850	−	0.848091i	$-0.322248\pi$
$569$	25.2778	1.05970	0.529850	+	0.848091i	$0.322248\pi$
$570$	−4.23452	−0.177365
$571$	−17.4454	−0.730068	−0.365034	−	0.930994i	$-0.618943\pi$
$571$	−17.4454	−0.730068	−0.365034	+	0.930994i	$0.618943\pi$
$572$	5.67400	0.237242
$573$	−35.2861	−1.47410
$574$	−16.4272	−0.685659
$575$	−40.4543	−1.68706
$576$	−61.1136	−2.54640
$577$	0.686171	0.0285657	0.0142828	−	0.999898i	$-0.495453\pi$
$577$	0.686171	0.0285657	0.0142828	+	0.999898i	$0.495453\pi$
$578$	−2.24229	−0.0932670
$579$	−11.3251	−0.470657
$580$	7.79525	0.323680
$581$	−30.3946	−1.26098
$582$	27.6856	1.14761
$583$	−13.4568	−0.557324
$584$	−13.6980	−0.566828
$585$	2.17145	0.0897786
$586$	−22.5298	−0.930699
$587$	−16.6202	−0.685990	−0.342995	−	0.939337i	$-0.611441\pi$
$587$	−16.6202	−0.685990	−0.342995	+	0.939337i	$0.611441\pi$
$588$	49.5275	2.04248
$589$	1.20458	0.0496337
$590$	−2.37022	−0.0975804
$591$	36.2122	1.48957
$592$	0.877112	0.0360491
$593$	12.4402	0.510859	0.255430	−	0.966828i	$-0.417783\pi$
$593$	12.4402	0.510859	0.255430	+	0.966828i	$0.417783\pi$
$594$	−11.0238	−0.452312
$595$	0.928891	0.0380808
$596$	−19.3085	−0.790909
$597$	47.7930	1.95604
$598$	−32.8990	−1.34534
$599$	10.6327	0.434438	0.217219	−	0.976123i	$-0.430301\pi$
$599$	10.6327	0.434438	0.217219	+	0.976123i	$0.430301\pi$
$600$	31.5340	1.28737
$601$	28.8198	1.17558	0.587792	−	0.809012i	$-0.299997\pi$
$601$	28.8198	1.17558	0.587792	+	0.809012i	$0.299997\pi$
$602$	−35.2691	−1.43746
$603$	−0.466982	−0.0190170
$604$	−57.3827	−2.33487
$605$	−2.56139	−0.104135
$606$	−64.9495	−2.63839
$607$	−19.0495	−0.773194	−0.386597	−	0.922249i	$-0.626350\pi$
$607$	−19.0495	−0.773194	−0.386597	+	0.922249i	$0.626350\pi$
$608$	17.3751	0.704653
$609$	99.1448	4.01755
$610$	4.02171	0.162834
$611$	−14.2233	−0.575412
$612$	14.2080	0.574323
$613$	−12.5793	−0.508073	−0.254037	−	0.967195i	$-0.581758\pi$
$613$	−12.5793	−0.508073	−0.254037	+	0.967195i	$0.581758\pi$
$614$	−12.6604	−0.510934
$615$	1.46338	0.0590092
$616$	−8.66941	−0.349301
$617$	1.80701	0.0727475	0.0363737	−	0.999338i	$-0.488419\pi$
$617$	1.80701	0.0727475	0.0363737	+	0.999338i	$0.488419\pi$
$618$	52.4275	2.10894
$619$	33.0958	1.33023	0.665115	−	0.746741i	$-0.268382\pi$
$619$	33.0958	1.33023	0.665115	+	0.746741i	$0.268382\pi$
$620$	0.358350	0.0143917
$621$	38.4927	1.54466
$622$	58.7587	2.35601
$623$	−8.49287	−0.340259
$624$	−4.40526	−0.176352
$625$	24.0010	0.960040
$626$	−44.2283	−1.76772
$627$	7.64732	0.305405
$628$	−15.6232	−0.623432
$629$	−0.988008	−0.0393945
$630$	−9.77353	−0.389387
$631$	−26.9155	−1.07149	−0.535744	−	0.844380i	$-0.679969\pi$
$631$	−26.9155	−1.07149	−0.535744	+	0.844380i	$0.679969\pi$
$632$	−20.0989	−0.799493
$633$	−60.3976	−2.40059
$634$	−25.4129	−1.00927
$635$	−3.00935	−0.119422
$636$	−107.896	−4.27834
$637$	10.5518	0.418076
$638$	−23.3766	−0.925489
$639$	−11.4257	−0.451994
$640$	4.13919	0.163616
$641$	−24.0217	−0.948801	−0.474401	−	0.880309i	$-0.657335\pi$
$641$	−24.0217	−0.948801	−0.474401	+	0.880309i	$0.657335\pi$
$642$	22.9992	0.907705
$643$	15.1679	0.598165	0.299083	−	0.954227i	$-0.403319\pi$
$643$	15.1679	0.598165	0.299083	+	0.954227i	$0.403319\pi$
$644$	89.1736	3.51393
$645$	3.14187	0.123711
$646$	−5.90288	−0.232246
$647$	1.41870	0.0557747	0.0278874	−	0.999611i	$-0.491122\pi$
$647$	1.41870	0.0557747	0.0278874	+	0.999611i	$0.491122\pi$
$648$	2.43980	0.0958445
$649$	4.28049	0.168024
$650$	19.7906	0.776250
$651$	4.55772	0.178631
$652$	63.0614	2.46968
$653$	46.7022	1.82760	0.913799	−	0.406166i	$-0.133134\pi$
$653$	46.7022	1.82760	0.913799	+	0.406166i	$0.133134\pi$
$654$	−12.5286	−0.489906
$655$	1.57063	0.0613697
$656$	−1.81097	−0.0707066
$657$	27.8884	1.08803
$658$	64.0178	2.49567
$659$	−4.78889	−0.186549	−0.0932743	−	0.995640i	$-0.529733\pi$
$659$	−4.78889	−0.186549	−0.0932743	+	0.995640i	$0.529733\pi$
$660$	2.27501	0.0885545
$661$	27.2045	1.05813	0.529065	−	0.848581i	$-0.322543\pi$
$661$	27.2045	1.05813	0.529065	+	0.848581i	$0.322543\pi$
$662$	−8.99878	−0.349748
$663$	4.96223	0.192717
$664$	19.5060	0.756981
$665$	2.44533	0.0948257
$666$	10.3955	0.402819
$667$	81.6259	3.16057
$668$	−41.2871	−1.59745
$669$	19.4899	0.753524
$670$	0.0577173	0.00222981
$671$	−7.26300	−0.280385
$672$	65.7417	2.53604
$673$	−32.5710	−1.25552	−0.627760	−	0.778407i	$-0.716028\pi$
$673$	−32.5710	−1.25552	−0.627760	+	0.778407i	$0.716028\pi$
$674$	42.9829	1.65564
$675$	−23.1555	−0.891255
$676$	−29.6699	−1.14115
$677$	1.44429	0.0555086	0.0277543	−	0.999615i	$-0.491164\pi$
$677$	1.44429	0.0555086	0.0277543	+	0.999615i	$0.491164\pi$
$678$	23.0960	0.886997
$679$	−15.9877	−0.613553
$680$	−0.596126	−0.0228604
$681$	−25.2858	−0.968953
$682$	−1.07463	−0.0411497
$683$	9.08456	0.347611	0.173806	−	0.984780i	$-0.444394\pi$
$683$	9.08456	0.347611	0.173806	+	0.984780i	$0.444394\pi$
$684$	37.4028	1.43013
$685$	1.16148	0.0443778
$686$	8.87700	0.338925
$687$	−65.4549	−2.49726
$688$	−3.88814	−0.148234
$689$	−22.9870	−0.875735
$690$	−13.1910	−0.502171
$691$	48.1281	1.83088	0.915439	−	0.402457i	$-0.131844\pi$
$691$	48.1281	1.83088	0.915439	+	0.402457i	$0.131844\pi$
$692$	62.0073	2.35716
$693$	17.6505	0.670486
$694$	−6.88021	−0.261169
$695$	−1.39408	−0.0528803
$696$	−63.6273	−2.41179
$697$	2.03994	0.0772682
$698$	−36.5908	−1.38498
$699$	2.58323	0.0977066
$700$	−53.6429	−2.02751
$701$	11.4232	0.431449	0.215724	−	0.976454i	$-0.430789\pi$
$701$	11.4232	0.431449	0.215724	+	0.976454i	$0.430789\pi$
$702$	−18.8309	−0.710728
$703$	−2.60095	−0.0980969
$704$	−13.6411	−0.514118
$705$	−5.70287	−0.214783
$706$	2.24229	0.0843897
$707$	37.5066	1.41058
$708$	34.3206	1.28985
$709$	4.66813	0.175315	0.0876577	−	0.996151i	$-0.472062\pi$
$709$	4.66813	0.175315	0.0876577	+	0.996151i	$0.472062\pi$
$710$	1.41218	0.0529981
$711$	40.9204	1.53463
$712$	5.45039	0.204262
$713$	3.75237	0.140527
$714$	−22.3346	−0.835851
$715$	0.484687	0.0181263
$716$	64.1183	2.39621
$717$	56.5136	2.11054
$718$	−61.9332	−2.31133
$719$	−15.7575	−0.587656	−0.293828	−	0.955858i	$-0.594929\pi$
$719$	−15.7575	−0.587656	−0.293828	+	0.955858i	$0.594929\pi$
$720$	−1.07745	−0.0401544
$721$	−30.2755	−1.12752
$722$	27.0640	1.00722
$723$	−30.5907	−1.13768
$724$	−16.4814	−0.612526
$725$	−49.1025	−1.82362
$726$	61.5870	2.28571
$727$	−17.6293	−0.653836	−0.326918	−	0.945053i	$-0.606010\pi$
$727$	−17.6293	−0.653836	−0.326918	+	0.945053i	$0.606010\pi$
$728$	−14.8091	−0.548864
$729$	−44.0231	−1.63049
$730$	−3.44691	−0.127576
$731$	4.37973	0.161990
$732$	−58.2342	−2.15240
$733$	14.1992	0.524460	0.262230	−	0.965005i	$-0.415542\pi$
$733$	14.1992	0.524460	0.262230	+	0.965005i	$0.415542\pi$
$734$	−12.1146	−0.447157
$735$	4.23077	0.156054
$736$	54.1251	1.99508
$737$	−0.104234	−0.00383952
$738$	−21.4637	−0.790089
$739$	12.9712	0.477153	0.238576	−	0.971124i	$-0.423319\pi$
$739$	12.9712	0.477153	0.238576	+	0.971124i	$0.423319\pi$
$740$	−0.773760	−0.0284440
$741$	13.0632	0.479889
$742$	103.463	3.79823
$743$	−29.8536	−1.09522	−0.547611	−	0.836733i	$-0.684463\pi$
$743$	−29.8536	−1.09522	−0.547611	+	0.836733i	$0.684463\pi$
$744$	−2.92497	−0.107234
$745$	−1.64938	−0.0604288
$746$	37.5014	1.37302
$747$	−39.7132	−1.45303
$748$	3.17134	0.115956
$749$	−13.2814	−0.485293
$750$	15.9778	0.583427
$751$	−5.59982	−0.204340	−0.102170	−	0.994767i	$-0.532579\pi$
$751$	−5.59982	−0.204340	−0.102170	+	0.994767i	$0.532579\pi$
$752$	7.05746	0.257359
$753$	−4.66589	−0.170034
$754$	−39.9321	−1.45424
$755$	−4.90178	−0.178394
$756$	51.0418	1.85637
$757$	12.0124	0.436596	0.218298	−	0.975882i	$-0.429949\pi$
$757$	12.0124	0.436596	0.218298	+	0.975882i	$0.429949\pi$
$758$	56.3685	2.04740
$759$	23.8222	0.864690
$760$	−1.56932	−0.0569250
$761$	−7.81185	−0.283180	−0.141590	−	0.989925i	$-0.545221\pi$
$761$	−7.81185	−0.283180	−0.141590	+	0.989925i	$0.545221\pi$
$762$	72.3580	2.62125
$763$	7.23493	0.261922
$764$	−38.5221	−1.39368
$765$	1.21368	0.0438807
$766$	−27.9126	−1.00852
$767$	7.31196	0.264020
$768$	−27.2799	−0.984379
$769$	−11.1644	−0.402598	−0.201299	−	0.979530i	$-0.564516\pi$
$769$	−11.1644	−0.402598	−0.201299	+	0.979530i	$0.564516\pi$
$770$	−2.18154	−0.0786171
$771$	36.0972	1.30001
$772$	−12.3637	−0.444981
$773$	43.1464	1.55187	0.775934	−	0.630814i	$-0.217279\pi$
$773$	43.1464	1.55187	0.775934	+	0.630814i	$0.217279\pi$
$774$	−46.0823	−1.65640
$775$	−2.25726	−0.0810832
$776$	10.2603	0.368323
$777$	−9.84117	−0.353050
$778$	−23.4411	−0.840404
$779$	5.37019	0.192407
$780$	3.88618	0.139148
$781$	−2.55032	−0.0912576
$782$	−18.3881	−0.657556
$783$	46.7216	1.66969
$784$	−5.23569	−0.186989
$785$	−1.33457	−0.0476328
$786$	−37.7649	−1.34703
$787$	−7.56238	−0.269570	−0.134785	−	0.990875i	$-0.543034\pi$
$787$	−7.56238	−0.269570	−0.134785	+	0.990875i	$0.543034\pi$
$788$	39.5331	1.40831
$789$	16.9087	0.601966
$790$	−5.05762	−0.179942
$791$	−13.3373	−0.474221
$792$	−11.3274	−0.402501
$793$	−12.4067	−0.440575
$794$	19.7387	0.700500
$795$	−9.21671	−0.326883
$796$	52.1759	1.84932
$797$	42.9869	1.52268	0.761338	−	0.648355i	$-0.224543\pi$
$797$	42.9869	1.52268	0.761338	+	0.648355i	$0.224543\pi$
$798$	−58.7964	−2.08137
$799$	−7.94975	−0.281242
$800$	−32.5593	−1.15114
$801$	−11.0967	−0.392083
$802$	56.4677	1.99394
$803$	6.22494	0.219673
$804$	−0.835742	−0.0294744
$805$	7.61744	0.268479
$806$	−1.83569	−0.0646595
$807$	−37.2279	−1.31048
$808$	−24.0703	−0.846790
$809$	1.06032	0.0372789	0.0186394	−	0.999826i	$-0.494067\pi$
$809$	1.06032	0.0372789	0.0186394	+	0.999826i	$0.494067\pi$
$810$	0.613942	0.0215717
$811$	47.3065	1.66116	0.830578	−	0.556902i	$-0.188010\pi$
$811$	47.3065	1.66116	0.830578	+	0.556902i	$0.188010\pi$
$812$	108.237	3.79838
$813$	−71.6164	−2.51170
$814$	2.32038	0.0813291
$815$	5.38687	0.188694
$816$	−2.46221	−0.0861947
$817$	11.5298	0.403375
$818$	52.1471	1.82328
$819$	30.1506	1.05355
$820$	1.59758	0.0557900
$821$	−36.5810	−1.27668	−0.638342	−	0.769753i	$-0.720379\pi$
$821$	−36.5810	−1.27668	−0.638342	+	0.769753i	$0.720379\pi$
$822$	−27.9270	−0.974067
$823$	54.1160	1.88637	0.943183	−	0.332274i	$-0.107816\pi$
$823$	54.1160	1.88637	0.943183	+	0.332274i	$0.107816\pi$
$824$	19.4296	0.676863
$825$	−14.3304	−0.498919
$826$	−32.9105	−1.14510
$827$	46.6636	1.62265	0.811327	−	0.584593i	$-0.198746\pi$
$827$	46.6636	1.62265	0.811327	+	0.584593i	$0.198746\pi$
$828$	116.513	4.04912
$829$	35.5682	1.23533	0.617667	−	0.786440i	$-0.288078\pi$
$829$	35.5682	1.23533	0.617667	+	0.786440i	$0.288078\pi$
$830$	4.90842	0.170374
$831$	−73.8393	−2.56146
$832$	−23.3018	−0.807845
$833$	5.89765	0.204342
$834$	33.5197	1.16069
$835$	−3.52685	−0.122052
$836$	8.34863	0.288743
$837$	2.14781	0.0742391
$838$	−7.49952	−0.259067
$839$	−7.20767	−0.248836	−0.124418	−	0.992230i	$-0.539706\pi$
$839$	−7.20767	−0.248836	−0.124418	+	0.992230i	$0.539706\pi$
$840$	−5.93778	−0.204873
$841$	70.0758	2.41641
$842$	12.8665	0.443410
$843$	64.8541	2.23369
$844$	−65.9364	−2.26962
$845$	−2.53448	−0.0871887
$846$	83.6451	2.87578
$847$	−35.5649	−1.22202
$848$	11.4059	0.391681
$849$	9.94189	0.341205
$850$	11.0614	0.379404
$851$	−8.10223	−0.277741
$852$	−20.4482	−0.700545
$853$	35.8698	1.22816	0.614079	−	0.789245i	$-0.289528\pi$
$853$	35.8698	1.22816	0.614079	+	0.789245i	$0.289528\pi$
$854$	55.8415	1.91086
$855$	3.19504	0.109268
$856$	8.52350	0.291327
$857$	29.0155	0.991152	0.495576	−	0.868565i	$-0.334957\pi$
$857$	29.0155	0.991152	0.495576	+	0.868565i	$0.334957\pi$
$858$	−11.6540	−0.397861
$859$	20.4675	0.698343	0.349172	−	0.937059i	$-0.386463\pi$
$859$	20.4675	0.698343	0.349172	+	0.937059i	$0.386463\pi$
$860$	3.43000	0.116962
$861$	20.3190	0.692471
$862$	−44.9847	−1.53218
$863$	17.7562	0.604429	0.302214	−	0.953240i	$-0.402274\pi$
$863$	17.7562	0.604429	0.302214	+	0.953240i	$0.402274\pi$
$864$	30.9805	1.05398
$865$	5.29682	0.180097
$866$	−56.1758	−1.90893
$867$	2.77352	0.0941936
$868$	4.97569	0.168886
$869$	9.13378	0.309842
$870$	−16.0109	−0.542821
$871$	−0.178054	−0.00603312
$872$	−4.64309	−0.157235
$873$	−20.8894	−0.707000
$874$	−48.4070	−1.63739
$875$	−9.22676	−0.311922
$876$	49.9111	1.68634
$877$	−15.3350	−0.517827	−0.258913	−	0.965901i	$-0.583364\pi$
$877$	−15.3350	−0.517827	−0.258913	+	0.965901i	$0.583364\pi$
$878$	−5.47663	−0.184827
$879$	27.8674	0.939945
$880$	−0.240497	−0.00810716
$881$	32.5068	1.09518	0.547592	−	0.836746i	$-0.315545\pi$
$881$	32.5068	1.09518	0.547592	+	0.836746i	$0.315545\pi$
$882$	−62.0535	−2.08945
$883$	−55.6882	−1.87406	−0.937028	−	0.349254i	$-0.886435\pi$
$883$	−55.6882	−1.87406	−0.937028	+	0.349254i	$0.886435\pi$
$884$	5.41730	0.182204
$885$	2.93175	0.0985499
$886$	46.1040	1.54889
$887$	35.8222	1.20279	0.601395	−	0.798952i	$-0.294612\pi$
$887$	35.8222	1.20279	0.601395	+	0.798952i	$0.294612\pi$
$888$	6.31567	0.211940
$889$	−41.7849	−1.40142
$890$	1.37151	0.0459732
$891$	−1.10875	−0.0371444
$892$	21.2773	0.712416
$893$	−20.9279	−0.700326
$894$	39.6584	1.32638
$895$	5.47715	0.183081
$896$	57.4727	1.92003
$897$	40.6932	1.35871
$898$	−31.2998	−1.04449
$899$	4.55455	0.151903
$900$	−70.0893	−2.33631
$901$	−12.8480	−0.428029
$902$	−4.79088	−0.159519
$903$	43.6248	1.45174
$904$	8.55939	0.284681
$905$	−1.40788	−0.0467996
$906$	117.860	3.91564
$907$	−13.7643	−0.457034	−0.228517	−	0.973540i	$-0.573388\pi$
$907$	−13.7643	−0.457034	−0.228517	+	0.973540i	$0.573388\pi$
$908$	−27.6046	−0.916092
$909$	49.0058	1.62542
$910$	−3.72651	−0.123533
$911$	29.5818	0.980087	0.490044	−	0.871698i	$-0.336981\pi$
$911$	29.5818	0.980087	0.490044	+	0.871698i	$0.336981\pi$
$912$	−6.48184	−0.214635
$913$	−8.86434	−0.293367
$914$	6.89946	0.228214
$915$	−4.97451	−0.164452
$916$	−71.4575	−2.36102
$917$	21.8082	0.720171
$918$	−10.5251	−0.347380
$919$	−26.9933	−0.890426	−0.445213	−	0.895425i	$-0.646872\pi$
$919$	−26.9933	−0.890426	−0.445213	+	0.895425i	$0.646872\pi$
$920$	−4.88857	−0.161171
$921$	15.6599	0.516010
$922$	36.1398	1.19020
$923$	−4.35647	−0.143395
$924$	31.5885	1.03919
$925$	4.87394	0.160254
$926$	39.8494	1.30953
$927$	−39.5577	−1.29925
$928$	65.6959	2.15657
$929$	−48.5772	−1.59377	−0.796883	−	0.604134i	$-0.793519\pi$
$929$	−48.5772	−1.59377	−0.796883	+	0.604134i	$0.793519\pi$
$930$	−0.736027	−0.0241353
$931$	15.5257	0.508835
$932$	2.82012	0.0923762
$933$	−72.6794	−2.37942
$934$	53.4354	1.74846
$935$	0.270904	0.00885950
$936$	−19.3495	−0.632458
$937$	57.9308	1.89252	0.946259	−	0.323409i	$-0.104829\pi$
$937$	57.9308	1.89252	0.946259	+	0.323409i	$0.104829\pi$
$938$	0.801405	0.0261668
$939$	54.7065	1.78528
$940$	−6.22586	−0.203065
$941$	45.9864	1.49911	0.749557	−	0.661940i	$-0.230267\pi$
$941$	45.9864	1.49911	0.749557	+	0.661940i	$0.230267\pi$
$942$	32.0889	1.04551
$943$	16.7287	0.544760
$944$	−3.62812	−0.118085
$945$	4.36012	0.141835
$946$	−10.2860	−0.334426
$947$	41.1110	1.33593	0.667964	−	0.744194i	$-0.267166\pi$
$947$	41.1110	1.33593	0.667964	+	0.744194i	$0.267166\pi$
$948$	73.2339	2.37853
$949$	10.6335	0.345177
$950$	29.1195	0.944762
$951$	31.4335	1.01930
$952$	−8.27721	−0.268266
$953$	−12.8160	−0.415149	−0.207575	−	0.978219i	$-0.566557\pi$
$953$	−12.8160	−0.415149	−0.207575	+	0.978219i	$0.566557\pi$
$954$	135.183	4.37672
$955$	−3.29065	−0.106483
$956$	61.6963	1.99540
$957$	28.9148	0.934684
$958$	91.1526	2.94501
$959$	16.1271	0.520772
$960$	−9.34293	−0.301542
$961$	−30.7906	−0.993246
$962$	3.96368	0.127794
$963$	−17.3534	−0.559205
$964$	−33.3961	−1.07561
$965$	−1.05614	−0.0339984
$966$	−183.156	−5.89296
$967$	13.5822	0.436773	0.218386	−	0.975862i	$-0.429921\pi$
$967$	13.5822	0.436773	0.218386	+	0.975862i	$0.429921\pi$
$968$	22.8242	0.733596
$969$	7.30135	0.234553
$970$	2.58186	0.0828985
$971$	−38.8817	−1.24777	−0.623886	−	0.781515i	$-0.714447\pi$
$971$	−38.8817	−1.24777	−0.623886	+	0.781515i	$0.714447\pi$
$972$	−51.5273	−1.65274
$973$	−19.3568	−0.620549
$974$	−35.6559	−1.14249
$975$	−24.4792	−0.783962
$976$	6.15609	0.197052
$977$	62.3859	1.99590	0.997951	−	0.0639817i	$-0.0203799\pi$
$977$	62.3859	1.99590	0.997951	+	0.0639817i	$0.0203799\pi$
$978$	−129.524	−4.14172
$979$	−2.47688	−0.0791614
$980$	4.61876	0.147541
$981$	9.45309	0.301814
$982$	−77.0737	−2.45952
$983$	−0.0798366	−0.00254639	−0.00127320	−	0.999999i	$-0.500405\pi$
$983$	−0.0798366	−0.00254639	−0.00127320	+	0.999999i	$0.500405\pi$
$984$	−13.0400	−0.415699
$985$	3.37702	0.107601
$986$	−22.3191	−0.710783
$987$	−79.1844	−2.52047
$988$	14.2612	0.453709
$989$	35.9163	1.14207
$990$	−2.85038	−0.0905909
$991$	30.0863	0.955722	0.477861	−	0.878435i	$-0.341412\pi$
$991$	30.0863	0.955722	0.477861	+	0.878435i	$0.341412\pi$
$992$	3.02006	0.0958871
$993$	11.1307	0.353222
$994$	19.6081	0.621931
$995$	4.45700	0.141296
$996$	−71.0735	−2.25205
$997$	−32.4348	−1.02722	−0.513610	−	0.858024i	$-0.671692\pi$
$997$	−32.4348	−1.02722	−0.513610	+	0.858024i	$0.671692\pi$
$998$	5.13970	0.162694
$999$	−4.63761	−0.146727

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6001.2.a.d.1.15	✓	121

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6001.2.a.d.1.15	✓	121	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:	\( N \)	\(=\)	\( 6001 = 17 \cdot 353 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6001.a (trivial)

\(f(q)\)	\(=\)	\(q-2.24229 q^{2} +2.77352 q^{3} +3.02787 q^{4} +0.258648 q^{5} -6.21903 q^{6} +3.59133 q^{7} -2.30477 q^{8} +4.69240 q^{9} +O(q^{10})\)	\(q-2.24229 q^{2} +2.77352 q^{3} +3.02787 q^{4} +0.258648 q^{5} -6.21903 q^{6} +3.59133 q^{7} -2.30477 q^{8} +4.69240 q^{9} -0.579964 q^{10} +1.04738 q^{11} +8.39784 q^{12} +1.78915 q^{13} -8.05280 q^{14} +0.717365 q^{15} -0.887758 q^{16} +1.00000 q^{17} -10.5217 q^{18} +2.63252 q^{19} +0.783152 q^{20} +9.96062 q^{21} -2.34854 q^{22} +8.20057 q^{23} -6.39233 q^{24} -4.93310 q^{25} -4.01179 q^{26} +4.69390 q^{27} +10.8741 q^{28} +9.95368 q^{29} -1.60854 q^{30} +0.457574 q^{31} +6.60016 q^{32} +2.90494 q^{33} -2.24229 q^{34} +0.928891 q^{35} +14.2080 q^{36} -0.988008 q^{37} -5.90288 q^{38} +4.96223 q^{39} -0.596126 q^{40} +2.03994 q^{41} -22.3346 q^{42} +4.37973 q^{43} +3.17134 q^{44} +1.21368 q^{45} -18.3881 q^{46} -7.94975 q^{47} -2.46221 q^{48} +5.89765 q^{49} +11.0614 q^{50} +2.77352 q^{51} +5.41730 q^{52} -12.8480 q^{53} -10.5251 q^{54} +0.270904 q^{55} -8.27721 q^{56} +7.30135 q^{57} -22.3191 q^{58} +4.08684 q^{59} +2.17209 q^{60} -6.93442 q^{61} -1.02601 q^{62} +16.8520 q^{63} -13.0240 q^{64} +0.462760 q^{65} -6.51371 q^{66} -0.0995187 q^{67} +3.02787 q^{68} +22.7444 q^{69} -2.08284 q^{70} -2.43494 q^{71} -10.8149 q^{72} +5.94332 q^{73} +2.21540 q^{74} -13.6820 q^{75} +7.97093 q^{76} +3.76150 q^{77} -11.1268 q^{78} +8.72057 q^{79} -0.229617 q^{80} -1.05859 q^{81} -4.57414 q^{82} -8.46331 q^{83} +30.1594 q^{84} +0.258648 q^{85} -9.82063 q^{86} +27.6067 q^{87} -2.41398 q^{88} -2.36482 q^{89} -2.72142 q^{90} +6.42542 q^{91} +24.8302 q^{92} +1.26909 q^{93} +17.8256 q^{94} +0.680897 q^{95} +18.3057 q^{96} -4.45176 q^{97} -13.2242 q^{98} +4.91474 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 121 q + 9 q^{2} + 21 q^{3} + 127 q^{4} + 27 q^{5} + 17 q^{6} + 39 q^{7} + 24 q^{8} + 134 q^{9}+O(q^{10}) \) 121 * q + 9 * q^2 + 21 * q^3 + 127 * q^4 + 27 * q^5 + 17 * q^6 + 39 * q^7 + 24 * q^8 + 134 * q^9	\( 121 q + 9 q^{2} + 21 q^{3} + 127 q^{4} + 27 q^{5} + 17 q^{6} + 39 q^{7} + 24 q^{8} + 134 q^{9} + 19 q^{10} + 48 q^{11} + 43 q^{12} + 6 q^{13} + 40 q^{14} + 49 q^{15} + 135 q^{16} + 121 q^{17} + 30 q^{19} + 50 q^{20} + 18 q^{21} + 24 q^{22} + 75 q^{23} + 24 q^{24} + 128 q^{25} + 59 q^{26} + 75 q^{27} + 52 q^{28} + 49 q^{29} - 34 q^{30} + 101 q^{31} + 47 q^{32} + 20 q^{33} + 9 q^{34} + 47 q^{35} + 138 q^{36} + 32 q^{37} + 30 q^{38} + 101 q^{39} + 36 q^{40} + 83 q^{41} - 11 q^{42} + 8 q^{43} + 98 q^{44} + 49 q^{45} + 45 q^{46} + 135 q^{47} + 54 q^{48} + 116 q^{49} + 3 q^{50} + 21 q^{51} - 5 q^{52} + 28 q^{53} + 10 q^{54} + 37 q^{55} + 75 q^{56} + 31 q^{58} + 150 q^{59} + 50 q^{60} + 36 q^{61} + 34 q^{62} + 118 q^{63} + 110 q^{64} + 18 q^{65} - 28 q^{66} - 6 q^{67} + 127 q^{68} + 25 q^{69} - 22 q^{70} + 223 q^{71} + q^{72} + 38 q^{73} - 10 q^{74} + 88 q^{75} - 4 q^{76} + 38 q^{77} + 42 q^{78} + 74 q^{79} + 106 q^{80} + 133 q^{81} + 28 q^{82} + 55 q^{83} + 10 q^{84} + 27 q^{85} + 64 q^{86} + 14 q^{87} + 56 q^{88} + 118 q^{89} + 51 q^{90} + 73 q^{91} + 82 q^{92} + 31 q^{93} + 33 q^{94} + 106 q^{95} + 38 q^{96} + 37 q^{97} + 88 q^{98} + 81 q^{99}+O(q^{100}) \) 121 * q + 9 * q^2 + 21 * q^3 + 127 * q^4 + 27 * q^5 + 17 * q^6 + 39 * q^7 + 24 * q^8 + 134 * q^9 + 19 * q^10 + 48 * q^11 + 43 * q^12 + 6 * q^13 + 40 * q^14 + 49 * q^15 + 135 * q^16 + 121 * q^17 + 30 * q^19 + 50 * q^20 + 18 * q^21 + 24 * q^22 + 75 * q^23 + 24 * q^24 + 128 * q^25 + 59 * q^26 + 75 * q^27 + 52 * q^28 + 49 * q^29 - 34 * q^30 + 101 * q^31 + 47 * q^32 + 20 * q^33 + 9 * q^34 + 47 * q^35 + 138 * q^36 + 32 * q^37 + 30 * q^38 + 101 * q^39 + 36 * q^40 + 83 * q^41 - 11 * q^42 + 8 * q^43 + 98 * q^44 + 49 * q^45 + 45 * q^46 + 135 * q^47 + 54 * q^48 + 116 * q^49 + 3 * q^50 + 21 * q^51 - 5 * q^52 + 28 * q^53 + 10 * q^54 + 37 * q^55 + 75 * q^56 + 31 * q^58 + 150 * q^59 + 50 * q^60 + 36 * q^61 + 34 * q^62 + 118 * q^63 + 110 * q^64 + 18 * q^65 - 28 * q^66 - 6 * q^67 + 127 * q^68 + 25 * q^69 - 22 * q^70 + 223 * q^71 + q^72 + 38 * q^73 - 10 * q^74 + 88 * q^75 - 4 * q^76 + 38 * q^77 + 42 * q^78 + 74 * q^79 + 106 * q^80 + 133 * q^81 + 28 * q^82 + 55 * q^83 + 10 * q^84 + 27 * q^85 + 64 * q^86 + 14 * q^87 + 56 * q^88 + 118 * q^89 + 51 * q^90 + 73 * q^91 + 82 * q^92 + 31 * q^93 + 33 * q^94 + 106 * q^95 + 38 * q^96 + 37 * q^97 + 88 * q^98 + 81 * q^99

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