LMFDB - Embedded newform 6002.2.a.d.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6002,2,Mod(1,6002)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6002, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6002.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6002 = 2 \cdot 3001 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6002.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:	$47.9262112932$
Analytic rank:	$0$
Dimension:	$79$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	6002.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -3.08764 q^{3} +1.00000 q^{4} -2.69580 q^{5} -3.08764 q^{6} -4.17911 q^{7} +1.00000 q^{8} +6.53354 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -3.08764 q^{3} +1.00000 q^{4} -2.69580 q^{5} -3.08764 q^{6} -4.17911 q^{7} +1.00000 q^{8} +6.53354 q^{9} -2.69580 q^{10} -1.29143 q^{11} -3.08764 q^{12} +2.13638 q^{13} -4.17911 q^{14} +8.32366 q^{15} +1.00000 q^{16} +4.90875 q^{17} +6.53354 q^{18} -4.90588 q^{19} -2.69580 q^{20} +12.9036 q^{21} -1.29143 q^{22} -6.89840 q^{23} -3.08764 q^{24} +2.26733 q^{25} +2.13638 q^{26} -10.9103 q^{27} -4.17911 q^{28} +0.990772 q^{29} +8.32366 q^{30} -6.94880 q^{31} +1.00000 q^{32} +3.98747 q^{33} +4.90875 q^{34} +11.2660 q^{35} +6.53354 q^{36} -8.43896 q^{37} -4.90588 q^{38} -6.59639 q^{39} -2.69580 q^{40} -7.89259 q^{41} +12.9036 q^{42} -9.61136 q^{43} -1.29143 q^{44} -17.6131 q^{45} -6.89840 q^{46} -6.71973 q^{47} -3.08764 q^{48} +10.4650 q^{49} +2.26733 q^{50} -15.1565 q^{51} +2.13638 q^{52} +8.35571 q^{53} -10.9103 q^{54} +3.48143 q^{55} -4.17911 q^{56} +15.1476 q^{57} +0.990772 q^{58} +1.09421 q^{59} +8.32366 q^{60} -11.6084 q^{61} -6.94880 q^{62} -27.3044 q^{63} +1.00000 q^{64} -5.75925 q^{65} +3.98747 q^{66} +13.7293 q^{67} +4.90875 q^{68} +21.2998 q^{69} +11.2660 q^{70} -5.74741 q^{71} +6.53354 q^{72} -6.20077 q^{73} -8.43896 q^{74} -7.00070 q^{75} -4.90588 q^{76} +5.39702 q^{77} -6.59639 q^{78} -12.5767 q^{79} -2.69580 q^{80} +14.0866 q^{81} -7.89259 q^{82} -9.45055 q^{83} +12.9036 q^{84} -13.2330 q^{85} -9.61136 q^{86} -3.05915 q^{87} -1.29143 q^{88} +2.19029 q^{89} -17.6131 q^{90} -8.92818 q^{91} -6.89840 q^{92} +21.4554 q^{93} -6.71973 q^{94} +13.2253 q^{95} -3.08764 q^{96} +18.7856 q^{97} +10.4650 q^{98} -8.43760 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 79 q + 79 q^{2} + 17 q^{3} + 79 q^{4} + 18 q^{5} + 17 q^{6} + 19 q^{7} + 79 q^{8} + 118 q^{9}+O(q^{10}) $ 79 * q + 79 * q^2 + 17 * q^3 + 79 * q^4 + 18 * q^5 + 17 * q^6 + 19 * q^7 + 79 * q^8 + 118 * q^9	\( 79 q + 79 q^{2} + 17 q^{3} + 79 q^{4} + 18 q^{5} + 17 q^{6} + 19 q^{7} + 79 q^{8} + 118 q^{9} + 18 q^{10} + 28 q^{11} + 17 q^{12} + 47 q^{13} + 19 q^{14} + 14 q^{15} + 79 q^{16} + 36 q^{17} + 118 q^{18} + 29 q^{19} + 18 q^{20} + 45 q^{21} + 28 q^{22} + 23 q^{23} + 17 q^{24} + 161 q^{25} + 47 q^{26} + 50 q^{27} + 19 q^{28} + 53 q^{29} + 14 q^{30} + 29 q^{31} + 79 q^{32} + 34 q^{33} + 36 q^{34} + 33 q^{35} + 118 q^{36} + 89 q^{37} + 29 q^{38} - 7 q^{39} + 18 q^{40} + 58 q^{41} + 45 q^{42} + 88 q^{43} + 28 q^{44} + 45 q^{45} + 23 q^{46} + 3 q^{47} + 17 q^{48} + 162 q^{49} + 161 q^{50} + 29 q^{51} + 47 q^{52} + 88 q^{53} + 50 q^{54} + 37 q^{55} + 19 q^{56} + 54 q^{57} + 53 q^{58} + 37 q^{59} + 14 q^{60} + 55 q^{61} + 29 q^{62} + 21 q^{63} + 79 q^{64} + 55 q^{65} + 34 q^{66} + 107 q^{67} + 36 q^{68} + 39 q^{69} + 33 q^{70} - 5 q^{71} + 118 q^{72} + 71 q^{73} + 89 q^{74} + 37 q^{75} + 29 q^{76} + 61 q^{77} - 7 q^{78} + 29 q^{79} + 18 q^{80} + 215 q^{81} + 58 q^{82} + 42 q^{83} + 45 q^{84} + 84 q^{85} + 88 q^{86} + 15 q^{87} + 28 q^{88} + 72 q^{89} + 45 q^{90} + 70 q^{91} + 23 q^{92} + 97 q^{93} + 3 q^{94} - 18 q^{95} + 17 q^{96} + 93 q^{97} + 162 q^{98} + 49 q^{99}+O(q^{100}) \) 79 * q + 79 * q^2 + 17 * q^3 + 79 * q^4 + 18 * q^5 + 17 * q^6 + 19 * q^7 + 79 * q^8 + 118 * q^9 + 18 * q^10 + 28 * q^11 + 17 * q^12 + 47 * q^13 + 19 * q^14 + 14 * q^15 + 79 * q^16 + 36 * q^17 + 118 * q^18 + 29 * q^19 + 18 * q^20 + 45 * q^21 + 28 * q^22 + 23 * q^23 + 17 * q^24 + 161 * q^25 + 47 * q^26 + 50 * q^27 + 19 * q^28 + 53 * q^29 + 14 * q^30 + 29 * q^31 + 79 * q^32 + 34 * q^33 + 36 * q^34 + 33 * q^35 + 118 * q^36 + 89 * q^37 + 29 * q^38 - 7 * q^39 + 18 * q^40 + 58 * q^41 + 45 * q^42 + 88 * q^43 + 28 * q^44 + 45 * q^45 + 23 * q^46 + 3 * q^47 + 17 * q^48 + 162 * q^49 + 161 * q^50 + 29 * q^51 + 47 * q^52 + 88 * q^53 + 50 * q^54 + 37 * q^55 + 19 * q^56 + 54 * q^57 + 53 * q^58 + 37 * q^59 + 14 * q^60 + 55 * q^61 + 29 * q^62 + 21 * q^63 + 79 * q^64 + 55 * q^65 + 34 * q^66 + 107 * q^67 + 36 * q^68 + 39 * q^69 + 33 * q^70 - 5 * q^71 + 118 * q^72 + 71 * q^73 + 89 * q^74 + 37 * q^75 + 29 * q^76 + 61 * q^77 - 7 * q^78 + 29 * q^79 + 18 * q^80 + 215 * q^81 + 58 * q^82 + 42 * q^83 + 45 * q^84 + 84 * q^85 + 88 * q^86 + 15 * q^87 + 28 * q^88 + 72 * q^89 + 45 * q^90 + 70 * q^91 + 23 * q^92 + 97 * q^93 + 3 * q^94 - 18 * q^95 + 17 * q^96 + 93 * q^97 + 162 * q^98 + 49 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−3.08764	−1.78265	−0.891326	−	0.453363i	$-0.850224\pi$
$3$	−3.08764	−1.78265	−0.891326	+	0.453363i	$0.850224\pi$
$4$	1.00000	0.500000
$5$	−2.69580	−1.20560	−0.602799	−	0.797893i	$-0.705948\pi$
$5$	−2.69580	−1.20560	−0.602799	+	0.797893i	$0.705948\pi$
$6$	−3.08764	−1.26053
$7$	−4.17911	−1.57956	−0.789778	−	0.613392i	$-0.789804\pi$
$7$	−4.17911	−1.57956	−0.789778	+	0.613392i	$0.789804\pi$
$8$	1.00000	0.353553
$9$	6.53354	2.17785
$10$	−2.69580	−0.852486
$11$	−1.29143	−0.389380	−0.194690	−	0.980865i	$-0.562370\pi$
$11$	−1.29143	−0.389380	−0.194690	+	0.980865i	$0.562370\pi$
$12$	−3.08764	−0.891326
$13$	2.13638	0.592526	0.296263	−	0.955106i	$-0.404260\pi$
$13$	2.13638	0.592526	0.296263	+	0.955106i	$0.404260\pi$
$14$	−4.17911	−1.11692
$15$	8.32366	2.14916
$16$	1.00000	0.250000
$17$	4.90875	1.19055	0.595273	−	0.803523i	$-0.297044\pi$
$17$	4.90875	1.19055	0.595273	+	0.803523i	$0.297044\pi$
$18$	6.53354	1.53997
$19$	−4.90588	−1.12549	−0.562743	−	0.826632i	$-0.690254\pi$
$19$	−4.90588	−1.12549	−0.562743	+	0.826632i	$0.690254\pi$
$20$	−2.69580	−0.602799
$21$	12.9036	2.81580
$22$	−1.29143	−0.275333
$23$	−6.89840	−1.43842	−0.719208	−	0.694795i	$-0.755495\pi$
$23$	−6.89840	−1.43842	−0.719208	+	0.694795i	$0.755495\pi$
$24$	−3.08764	−0.630263
$25$	2.26733	0.453466
$26$	2.13638	0.418979
$27$	−10.9103	−2.09969
$28$	−4.17911	−0.789778
$29$	0.990772	0.183982	0.0919909	−	0.995760i	$-0.470677\pi$
$29$	0.990772	0.183982	0.0919909	+	0.995760i	$0.470677\pi$
$30$	8.32366	1.51969
$31$	−6.94880	−1.24804	−0.624021	−	0.781408i	$-0.714502\pi$
$31$	−6.94880	−1.24804	−0.624021	+	0.781408i	$0.714502\pi$
$32$	1.00000	0.176777
$33$	3.98747	0.694129
$34$	4.90875	0.841844
$35$	11.2660	1.90431
$36$	6.53354	1.08892
$37$	−8.43896	−1.38736	−0.693678	−	0.720285i	$-0.744011\pi$
$37$	−8.43896	−1.38736	−0.693678	+	0.720285i	$0.744011\pi$
$38$	−4.90588	−0.795838
$39$	−6.59639	−1.05627
$40$	−2.69580	−0.426243
$41$	−7.89259	−1.23262	−0.616308	−	0.787505i	$-0.711372\pi$
$41$	−7.89259	−1.23262	−0.616308	+	0.787505i	$0.711372\pi$
$42$	12.9036	1.99107
$43$	−9.61136	−1.46572	−0.732859	−	0.680380i	$-0.761815\pi$
$43$	−9.61136	−1.46572	−0.732859	+	0.680380i	$0.761815\pi$
$44$	−1.29143	−0.194690
$45$	−17.6131	−2.62561
$46$	−6.89840	−1.01711
$47$	−6.71973	−0.980173	−0.490087	−	0.871674i	$-0.663035\pi$
$47$	−6.71973	−0.980173	−0.490087	+	0.871674i	$0.663035\pi$
$48$	−3.08764	−0.445663
$49$	10.4650	1.49500
$50$	2.26733	0.320649
$51$	−15.1565	−2.12233
$52$	2.13638	0.296263
$53$	8.35571	1.14775	0.573873	−	0.818945i	$-0.305440\pi$
$53$	8.35571	1.14775	0.573873	+	0.818945i	$0.305440\pi$
$54$	−10.9103	−1.48471
$55$	3.48143	0.469436
$56$	−4.17911	−0.558458
$57$	15.1476	2.00635
$58$	0.990772	0.130095
$59$	1.09421	0.142455	0.0712273	−	0.997460i	$-0.477308\pi$
$59$	1.09421	0.142455	0.0712273	+	0.997460i	$0.477308\pi$
$60$	8.32366	1.07458
$61$	−11.6084	−1.48631	−0.743153	−	0.669122i	$-0.766670\pi$
$61$	−11.6084	−1.48631	−0.743153	+	0.669122i	$0.766670\pi$
$62$	−6.94880	−0.882498
$63$	−27.3044	−3.44003
$64$	1.00000	0.125000
$65$	−5.75925	−0.714348
$66$	3.98747	0.490823
$67$	13.7293	1.67730	0.838649	−	0.544673i	$-0.183346\pi$
$67$	13.7293	1.67730	0.838649	+	0.544673i	$0.183346\pi$
$68$	4.90875	0.595273
$69$	21.2998	2.56420
$70$	11.2660	1.34655
$71$	−5.74741	−0.682092	−0.341046	−	0.940047i	$-0.610781\pi$
$71$	−5.74741	−0.682092	−0.341046	+	0.940047i	$0.610781\pi$
$72$	6.53354	0.769986
$73$	−6.20077	−0.725746	−0.362873	−	0.931839i	$-0.618204\pi$
$73$	−6.20077	−0.725746	−0.362873	+	0.931839i	$0.618204\pi$
$74$	−8.43896	−0.981009
$75$	−7.00070	−0.808371
$76$	−4.90588	−0.562743
$77$	5.39702	0.615048
$78$	−6.59639	−0.746894
$79$	−12.5767	−1.41499	−0.707493	−	0.706720i	$-0.750174\pi$
$79$	−12.5767	−1.41499	−0.707493	+	0.706720i	$0.750174\pi$
$80$	−2.69580	−0.301399
$81$	14.0866	1.56517
$82$	−7.89259	−0.871591
$83$	−9.45055	−1.03733	−0.518666	−	0.854977i	$-0.673571\pi$
$83$	−9.45055	−1.03733	−0.518666	+	0.854977i	$0.673571\pi$
$84$	12.9036	1.40790
$85$	−13.2330	−1.43532
$86$	−9.61136	−1.03642
$87$	−3.05915	−0.327976
$88$	−1.29143	−0.137667
$89$	2.19029	0.232171	0.116085	−	0.993239i	$-0.462965\pi$
$89$	2.19029	0.232171	0.116085	+	0.993239i	$0.462965\pi$
$90$	−17.6131	−1.85659
$91$	−8.92818	−0.935928
$92$	−6.89840	−0.719208
$93$	21.4554	2.22482
$94$	−6.71973	−0.693087
$95$	13.2253	1.35688
$96$	−3.08764	−0.315131
$97$	18.7856	1.90739	0.953694	−	0.300778i	$-0.0972463\pi$
$97$	18.7856	1.90739	0.953694	+	0.300778i	$0.0972463\pi$
$98$	10.4650	1.05712
$99$	−8.43760	−0.848011
$100$	2.26733	0.226733
$101$	−7.02177	−0.698692	−0.349346	−	0.936994i	$-0.613596\pi$
$101$	−7.02177	−0.698692	−0.349346	+	0.936994i	$0.613596\pi$
$102$	−15.1565	−1.50071
$103$	−12.7904	−1.26028	−0.630140	−	0.776482i	$-0.717002\pi$
$103$	−12.7904	−1.26028	−0.630140	+	0.776482i	$0.717002\pi$
$104$	2.13638	0.209489
$105$	−34.7855	−3.39472
$106$	8.35571	0.811578
$107$	9.93739	0.960684	0.480342	−	0.877081i	$-0.340513\pi$
$107$	9.93739	0.960684	0.480342	+	0.877081i	$0.340513\pi$
$108$	−10.9103	−1.04985
$109$	−1.54915	−0.148381	−0.0741907	−	0.997244i	$-0.523637\pi$
$109$	−1.54915	−0.148381	−0.0741907	+	0.997244i	$0.523637\pi$
$110$	3.48143	0.331941
$111$	26.0565	2.47317
$112$	−4.17911	−0.394889
$113$	−7.26908	−0.683817	−0.341909	−	0.939733i	$-0.611073\pi$
$113$	−7.26908	−0.683817	−0.341909	+	0.939733i	$0.611073\pi$
$114$	15.1476	1.41870
$115$	18.5967	1.73415
$116$	0.990772	0.0919909
$117$	13.9581	1.29043
$118$	1.09421	0.100731
$119$	−20.5142	−1.88054
$120$	8.32366	0.759843
$121$	−9.33222	−0.848383
$122$	−11.6084	−1.05098
$123$	24.3695	2.19733
$124$	−6.94880	−0.624021
$125$	7.36673	0.658901
$126$	−27.3044	−2.43247
$127$	−4.49861	−0.399187	−0.199593	−	0.979879i	$-0.563962\pi$
$127$	−4.49861	−0.399187	−0.199593	+	0.979879i	$0.563962\pi$
$128$	1.00000	0.0883883
$129$	29.6765	2.61287
$130$	−5.75925	−0.505120
$131$	−2.38453	−0.208338	−0.104169	−	0.994560i	$-0.533218\pi$
$131$	−2.38453	−0.208338	−0.104169	+	0.994560i	$0.533218\pi$
$132$	3.98747	0.347065
$133$	20.5022	1.77777
$134$	13.7293	1.18603
$135$	29.4120	2.53139
$136$	4.90875	0.420922
$137$	15.5987	1.33268	0.666342	−	0.745646i	$-0.267859\pi$
$137$	15.5987	1.33268	0.666342	+	0.745646i	$0.267859\pi$
$138$	21.2998	1.81316
$139$	5.81430	0.493162	0.246581	−	0.969122i	$-0.420693\pi$
$139$	5.81430	0.493162	0.246581	+	0.969122i	$0.420693\pi$
$140$	11.2660	0.952155
$141$	20.7481	1.74731
$142$	−5.74741	−0.482312
$143$	−2.75898	−0.230718
$144$	6.53354	0.544462
$145$	−2.67092	−0.221808
$146$	−6.20077	−0.513180
$147$	−32.3122	−2.66506
$148$	−8.43896	−0.693678
$149$	−4.96071	−0.406397	−0.203199	−	0.979138i	$-0.565134\pi$
$149$	−4.96071	−0.406397	−0.203199	+	0.979138i	$0.565134\pi$
$150$	−7.00070	−0.571605
$151$	15.5634	1.26653	0.633267	−	0.773934i	$-0.281714\pi$
$151$	15.5634	1.26653	0.633267	+	0.773934i	$0.281714\pi$
$152$	−4.90588	−0.397919
$153$	32.0715	2.59283
$154$	5.39702	0.434904
$155$	18.7326	1.50464
$156$	−6.59639	−0.528134
$157$	−7.81193	−0.623460	−0.311730	−	0.950171i	$-0.600908\pi$
$157$	−7.81193	−0.623460	−0.311730	+	0.950171i	$0.600908\pi$
$158$	−12.5767	−1.00055
$159$	−25.7995	−2.04603
$160$	−2.69580	−0.213122
$161$	28.8292	2.27206
$162$	14.0866	1.10675
$163$	23.1954	1.81680	0.908401	−	0.418099i	$-0.137304\pi$
$163$	23.1954	1.81680	0.908401	+	0.418099i	$0.137304\pi$
$164$	−7.89259	−0.616308
$165$	−10.7494	−0.836840
$166$	−9.45055	−0.733505
$167$	0.564047	0.0436473	0.0218236	−	0.999762i	$-0.493053\pi$
$167$	0.564047	0.0436473	0.0218236	+	0.999762i	$0.493053\pi$
$168$	12.9036	0.995536
$169$	−8.43587	−0.648913
$170$	−13.2330	−1.01492
$171$	−32.0528	−2.45114
$172$	−9.61136	−0.732859
$173$	−5.58439	−0.424573	−0.212287	−	0.977207i	$-0.568091\pi$
$173$	−5.58439	−0.424573	−0.212287	+	0.977207i	$0.568091\pi$
$174$	−3.05915	−0.231914
$175$	−9.47542	−0.716275
$176$	−1.29143	−0.0973450
$177$	−3.37854	−0.253947
$178$	2.19029	0.164170
$179$	17.5211	1.30959	0.654793	−	0.755808i	$-0.272756\pi$
$179$	17.5211	1.30959	0.654793	+	0.755808i	$0.272756\pi$
$180$	−17.6131	−1.31280
$181$	7.58916	0.564098	0.282049	−	0.959400i	$-0.408986\pi$
$181$	7.58916	0.564098	0.282049	+	0.959400i	$0.408986\pi$
$182$	−8.92818	−0.661801
$183$	35.8427	2.64957
$184$	−6.89840	−0.508557
$185$	22.7497	1.67259
$186$	21.4554	1.57319
$187$	−6.33929	−0.463575
$188$	−6.71973	−0.490087
$189$	45.5955	3.31658
$190$	13.2253	0.959461
$191$	16.6517	1.20487	0.602437	−	0.798166i	$-0.294196\pi$
$191$	16.6517	1.20487	0.602437	+	0.798166i	$0.294196\pi$
$192$	−3.08764	−0.222832
$193$	−20.3973	−1.46823	−0.734116	−	0.679024i	$-0.762403\pi$
$193$	−20.3973	−1.46823	−0.734116	+	0.679024i	$0.762403\pi$
$194$	18.7856	1.34873
$195$	17.7825	1.27343
$196$	10.4650	0.747499
$197$	−12.0571	−0.859030	−0.429515	−	0.903060i	$-0.641316\pi$
$197$	−12.0571	−0.859030	−0.429515	+	0.903060i	$0.641316\pi$
$198$	−8.43760	−0.599634
$199$	−9.91476	−0.702839	−0.351420	−	0.936218i	$-0.614301\pi$
$199$	−9.91476	−0.702839	−0.351420	+	0.936218i	$0.614301\pi$
$200$	2.26733	0.160324
$201$	−42.3911	−2.99004
$202$	−7.02177	−0.494050
$203$	−4.14055	−0.290610
$204$	−15.1565	−1.06117
$205$	21.2768	1.48604
$206$	−12.7904	−0.891152
$207$	−45.0710	−3.13265
$208$	2.13638	0.148131
$209$	6.33558	0.438242
$210$	−34.7855	−2.40043
$211$	19.4621	1.33983	0.669913	−	0.742440i	$-0.266331\pi$
$211$	19.4621	1.33983	0.669913	+	0.742440i	$0.266331\pi$
$212$	8.35571	0.573873
$213$	17.7460	1.21593
$214$	9.93739	0.679306
$215$	25.9103	1.76707
$216$	−10.9103	−0.742354
$217$	29.0398	1.97135
$218$	−1.54915	−0.104921
$219$	19.1458	1.29375
$220$	3.48143	0.234718
$221$	10.4870	0.705429
$222$	26.0565	1.74880
$223$	13.1248	0.878901	0.439450	−	0.898267i	$-0.355173\pi$
$223$	13.1248	0.878901	0.439450	+	0.898267i	$0.355173\pi$
$224$	−4.17911	−0.279229
$225$	14.8137	0.987579
$226$	−7.26908	−0.483532
$227$	19.0273	1.26289	0.631444	−	0.775421i	$-0.282462\pi$
$227$	19.0273	1.26289	0.631444	+	0.775421i	$0.282462\pi$
$228$	15.1476	1.00317
$229$	−21.2027	−1.40112	−0.700558	−	0.713595i	$-0.747066\pi$
$229$	−21.2027	−1.40112	−0.700558	+	0.713595i	$0.747066\pi$
$230$	18.5967	1.22623
$231$	−16.6641	−1.09642
$232$	0.990772	0.0650474
$233$	10.6736	0.699252	0.349626	−	0.936889i	$-0.386309\pi$
$233$	10.6736	0.699252	0.349626	+	0.936889i	$0.386309\pi$
$234$	13.9581	0.912472
$235$	18.1150	1.18169
$236$	1.09421	0.0712273
$237$	38.8323	2.52243
$238$	−20.5142	−1.32974
$239$	−23.2884	−1.50640	−0.753200	−	0.657792i	$-0.771491\pi$
$239$	−23.2884	−1.50640	−0.753200	+	0.657792i	$0.771491\pi$
$240$	8.32366	0.537290
$241$	1.53730	0.0990263	0.0495131	−	0.998773i	$-0.484233\pi$
$241$	1.53730	0.0990263	0.0495131	+	0.998773i	$0.484233\pi$
$242$	−9.33222	−0.599898
$243$	−10.7633	−0.690468
$244$	−11.6084	−0.743153
$245$	−28.2115	−1.80237
$246$	24.3695	1.55374
$247$	−10.4808	−0.666879
$248$	−6.94880	−0.441249
$249$	29.1799	1.84920
$250$	7.36673	0.465913
$251$	−2.71120	−0.171130	−0.0855648	−	0.996333i	$-0.527269\pi$
$251$	−2.71120	−0.171130	−0.0855648	+	0.996333i	$0.527269\pi$
$252$	−27.3044	−1.72002
$253$	8.90878	0.560090
$254$	−4.49861	−0.282268
$255$	40.8588	2.55868
$256$	1.00000	0.0625000
$257$	−16.9330	−1.05625	−0.528126	−	0.849166i	$-0.677105\pi$
$257$	−16.9330	−1.05625	−0.528126	+	0.849166i	$0.677105\pi$
$258$	29.6765	1.84758
$259$	35.2674	2.19141
$260$	−5.75925	−0.357174
$261$	6.47326	0.400684
$262$	−2.38453	−0.147317
$263$	1.55081	0.0956269	0.0478134	−	0.998856i	$-0.484775\pi$
$263$	1.55081	0.0956269	0.0478134	+	0.998856i	$0.484775\pi$
$264$	3.98747	0.245412
$265$	−22.5253	−1.38372
$266$	20.5022	1.25707
$267$	−6.76285	−0.413880
$268$	13.7293	0.838649
$269$	−15.8901	−0.968834	−0.484417	−	0.874837i	$-0.660968\pi$
$269$	−15.8901	−0.968834	−0.484417	+	0.874837i	$0.660968\pi$
$270$	29.4120	1.78996
$271$	−15.0293	−0.912964	−0.456482	−	0.889733i	$-0.650891\pi$
$271$	−15.0293	−0.912964	−0.456482	+	0.889733i	$0.650891\pi$
$272$	4.90875	0.297637
$273$	27.5670	1.66843
$274$	15.5987	0.942350
$275$	−2.92809	−0.176570
$276$	21.2998	1.28210
$277$	16.9726	1.01978	0.509892	−	0.860238i	$-0.329685\pi$
$277$	16.9726	1.01978	0.509892	+	0.860238i	$0.329685\pi$
$278$	5.81430	0.348718
$279$	−45.4003	−2.71804
$280$	11.2660	0.673275
$281$	−9.79694	−0.584436	−0.292218	−	0.956352i	$-0.594393\pi$
$281$	−9.79694	−0.584436	−0.292218	+	0.956352i	$0.594393\pi$
$282$	20.7481	1.23553
$283$	−10.9322	−0.649850	−0.324925	−	0.945740i	$-0.605339\pi$
$283$	−10.9322	−0.649850	−0.324925	+	0.945740i	$0.605339\pi$
$284$	−5.74741	−0.341046
$285$	−40.8349	−2.41885
$286$	−2.75898	−0.163142
$287$	32.9840	1.94699
$288$	6.53354	0.384993
$289$	7.09582	0.417401
$290$	−2.67092	−0.156842
$291$	−58.0032	−3.40021
$292$	−6.20077	−0.362873
$293$	−13.4646	−0.786609	−0.393304	−	0.919408i	$-0.628668\pi$
$293$	−13.4646	−0.786609	−0.393304	+	0.919408i	$0.628668\pi$
$294$	−32.3122	−1.88448
$295$	−2.94978	−0.171743
$296$	−8.43896	−0.490505
$297$	14.0899	0.817579
$298$	−4.96071	−0.287366
$299$	−14.7376	−0.852298
$300$	−7.00070	−0.404186
$301$	40.1670	2.31519
$302$	15.5634	0.895574
$303$	21.6807	1.24552
$304$	−4.90588	−0.281371
$305$	31.2939	1.79189
$306$	32.0715	1.83341
$307$	−17.9088	−1.02211	−0.511056	−	0.859548i	$-0.670745\pi$
$307$	−17.9088	−1.02211	−0.511056	+	0.859548i	$0.670745\pi$
$308$	5.39702	0.307524
$309$	39.4923	2.24664
$310$	18.7326	1.06394
$311$	−6.02340	−0.341556	−0.170778	−	0.985310i	$-0.554628\pi$
$311$	−6.02340	−0.341556	−0.170778	+	0.985310i	$0.554628\pi$
$312$	−6.59639	−0.373447
$313$	2.01957	0.114153	0.0570764	−	0.998370i	$-0.481822\pi$
$313$	2.01957	0.114153	0.0570764	+	0.998370i	$0.481822\pi$
$314$	−7.81193	−0.440853
$315$	73.6072	4.14730
$316$	−12.5767	−0.707493
$317$	−2.90553	−0.163191	−0.0815954	−	0.996666i	$-0.526002\pi$
$317$	−2.90553	−0.163191	−0.0815954	+	0.996666i	$0.526002\pi$
$318$	−25.7995	−1.44676
$319$	−1.27951	−0.0716388
$320$	−2.69580	−0.150700
$321$	−30.6831	−1.71257
$322$	28.8292	1.60659
$323$	−24.0817	−1.33994
$324$	14.0866	0.782587
$325$	4.84388	0.268690
$326$	23.1954	1.28467
$327$	4.78321	0.264512
$328$	−7.89259	−0.435796
$329$	28.0825	1.54824
$330$	−10.7494	−0.591735
$331$	21.2377	1.16733	0.583665	−	0.811995i	$-0.301618\pi$
$331$	21.2377	1.16733	0.583665	+	0.811995i	$0.301618\pi$
$332$	−9.45055	−0.518666
$333$	−55.1363	−3.02145
$334$	0.564047	0.0308633
$335$	−37.0113	−2.02215
$336$	12.9036	0.703950
$337$	−4.91296	−0.267626	−0.133813	−	0.991007i	$-0.542722\pi$
$337$	−4.91296	−0.267626	−0.133813	+	0.991007i	$0.542722\pi$
$338$	−8.43587	−0.458851
$339$	22.4443	1.21901
$340$	−13.2330	−0.717660
$341$	8.97387	0.485962
$342$	−32.0528	−1.73322
$343$	−14.4806	−0.781879
$344$	−9.61136	−0.518210
$345$	−57.4200	−3.09139
$346$	−5.58439	−0.300219
$347$	19.9856	1.07288	0.536441	−	0.843938i	$-0.319768\pi$
$347$	19.9856	1.07288	0.536441	+	0.843938i	$0.319768\pi$
$348$	−3.05915	−0.163988
$349$	−8.52974	−0.456586	−0.228293	−	0.973592i	$-0.573314\pi$
$349$	−8.52974	−0.456586	−0.228293	+	0.973592i	$0.573314\pi$
$350$	−9.47542	−0.506483
$351$	−23.3086	−1.24412
$352$	−1.29143	−0.0688333
$353$	−10.5560	−0.561838	−0.280919	−	0.959731i	$-0.590639\pi$
$353$	−10.5560	−0.561838	−0.280919	+	0.959731i	$0.590639\pi$
$354$	−3.37854	−0.179568
$355$	15.4939	0.822329
$356$	2.19029	0.116085
$357$	63.3406	3.35234
$358$	17.5211	0.926017
$359$	−0.461744	−0.0243699	−0.0121850	−	0.999926i	$-0.503879\pi$
$359$	−0.461744	−0.0243699	−0.0121850	+	0.999926i	$0.503879\pi$
$360$	−17.6131	−0.928293
$361$	5.06763	0.266718
$362$	7.58916	0.398878
$363$	28.8146	1.51237
$364$	−8.92818	−0.467964
$365$	16.7160	0.874957
$366$	35.8427	1.87353
$367$	13.8040	0.720561	0.360281	−	0.932844i	$-0.382681\pi$
$367$	13.8040	0.720561	0.360281	+	0.932844i	$0.382681\pi$
$368$	−6.89840	−0.359604
$369$	−51.5666	−2.68445
$370$	22.7497	1.18270
$371$	−34.9195	−1.81293
$372$	21.4554	1.11241
$373$	−24.7293	−1.28043	−0.640216	−	0.768195i	$-0.721155\pi$
$373$	−24.7293	−1.28043	−0.640216	+	0.768195i	$0.721155\pi$
$374$	−6.33929	−0.327797
$375$	−22.7458	−1.17459
$376$	−6.71973	−0.346544
$377$	2.11667	0.109014
$378$	45.5955	2.34518
$379$	−21.1369	−1.08573	−0.542865	−	0.839820i	$-0.682660\pi$
$379$	−21.1369	−1.08573	−0.542865	+	0.839820i	$0.682660\pi$
$380$	13.2253	0.678441
$381$	13.8901	0.711611
$382$	16.6517	0.851975
$383$	−25.6133	−1.30878	−0.654388	−	0.756159i	$-0.727074\pi$
$383$	−25.6133	−1.30878	−0.654388	+	0.756159i	$0.727074\pi$
$384$	−3.08764	−0.157566
$385$	−14.5493	−0.741500
$386$	−20.3973	−1.03820
$387$	−62.7963	−3.19211
$388$	18.7856	0.953694
$389$	2.93124	0.148620	0.0743099	−	0.997235i	$-0.476325\pi$
$389$	2.93124	0.148620	0.0743099	+	0.997235i	$0.476325\pi$
$390$	17.7825	0.900453
$391$	−33.8625	−1.71250
$392$	10.4650	0.528562
$393$	7.36259	0.371394
$394$	−12.0571	−0.607426
$395$	33.9042	1.70590
$396$	−8.43760	−0.424005
$397$	36.5726	1.83552	0.917762	−	0.397130i	$-0.129994\pi$
$397$	36.5726	1.83552	0.917762	+	0.397130i	$0.129994\pi$
$398$	−9.91476	−0.496982
$399$	−63.3036	−3.16914
$400$	2.26733	0.113366
$401$	17.1978	0.858818	0.429409	−	0.903110i	$-0.358722\pi$
$401$	17.1978	0.858818	0.429409	+	0.903110i	$0.358722\pi$
$402$	−42.3911	−2.11428
$403$	−14.8453	−0.739496
$404$	−7.02177	−0.349346
$405$	−37.9746	−1.88697
$406$	−4.14055	−0.205492
$407$	10.8983	0.540209
$408$	−15.1565	−0.750357
$409$	−9.99197	−0.494071	−0.247036	−	0.969006i	$-0.579456\pi$
$409$	−9.99197	−0.494071	−0.247036	+	0.969006i	$0.579456\pi$
$410$	21.2768	1.05079
$411$	−48.1631	−2.37571
$412$	−12.7904	−0.630140
$413$	−4.57285	−0.225015
$414$	−45.0710	−2.21512
$415$	25.4768	1.25061
$416$	2.13638	0.104745
$417$	−17.9525	−0.879137
$418$	6.33558	0.309884
$419$	−9.53692	−0.465909	−0.232954	−	0.972488i	$-0.574839\pi$
$419$	−9.53692	−0.465909	−0.232954	+	0.972488i	$0.574839\pi$
$420$	−34.7855	−1.69736
$421$	−9.12685	−0.444816	−0.222408	−	0.974954i	$-0.571392\pi$
$421$	−9.12685	−0.444816	−0.222408	+	0.974954i	$0.571392\pi$
$422$	19.4621	0.947400
$423$	−43.9037	−2.13467
$424$	8.35571	0.405789
$425$	11.1297	0.539872
$426$	17.7460	0.859794
$427$	48.5129	2.34770
$428$	9.93739	0.480342
$429$	8.51875	0.411289
$430$	25.9103	1.24951
$431$	−10.7543	−0.518016	−0.259008	−	0.965875i	$-0.583396\pi$
$431$	−10.7543	−0.518016	−0.259008	+	0.965875i	$0.583396\pi$
$432$	−10.9103	−0.524923
$433$	26.0183	1.25036	0.625180	−	0.780481i	$-0.285026\pi$
$433$	26.0183	1.25036	0.625180	+	0.780481i	$0.285026\pi$
$434$	29.0398	1.39396
$435$	8.24686	0.395407
$436$	−1.54915	−0.0741907
$437$	33.8427	1.61892
$438$	19.1458	0.914821
$439$	34.8169	1.66172	0.830859	−	0.556483i	$-0.187849\pi$
$439$	34.8169	1.66172	0.830859	+	0.556483i	$0.187849\pi$
$440$	3.48143	0.165971
$441$	68.3735	3.25588
$442$	10.4870	0.498814
$443$	35.8120	1.70148	0.850739	−	0.525588i	$-0.176155\pi$
$443$	35.8120	1.70148	0.850739	+	0.525588i	$0.176155\pi$
$444$	26.0565	1.23659
$445$	−5.90459	−0.279905
$446$	13.1248	0.621477
$447$	15.3169	0.724465
$448$	−4.17911	−0.197445
$449$	−14.4096	−0.680033	−0.340016	−	0.940419i	$-0.610433\pi$
$449$	−14.4096	−0.680033	−0.340016	+	0.940419i	$0.610433\pi$
$450$	14.8137	0.698324
$451$	10.1927	0.479956
$452$	−7.26908	−0.341909
$453$	−48.0543	−2.25779
$454$	19.0273	0.892997
$455$	24.0686	1.12835
$456$	15.1476	0.709351
$457$	38.2949	1.79136	0.895680	−	0.444699i	$-0.146689\pi$
$457$	38.2949	1.79136	0.895680	+	0.444699i	$0.146689\pi$
$458$	−21.2027	−0.990739
$459$	−53.5561	−2.49978
$460$	18.5967	0.867076
$461$	25.5033	1.18781	0.593904	−	0.804536i	$-0.297586\pi$
$461$	25.5033	1.18781	0.593904	+	0.804536i	$0.297586\pi$
$462$	−16.6641	−0.775283
$463$	40.7458	1.89362	0.946808	−	0.321799i	$-0.104287\pi$
$463$	40.7458	1.89362	0.946808	+	0.321799i	$0.104287\pi$
$464$	0.990772	0.0459955
$465$	−57.8395	−2.68224
$466$	10.6736	0.494445
$467$	18.3937	0.851161	0.425581	−	0.904921i	$-0.360070\pi$
$467$	18.3937	0.851161	0.425581	+	0.904921i	$0.360070\pi$
$468$	13.9581	0.645215
$469$	−57.3762	−2.64939
$470$	18.1150	0.835584
$471$	24.1205	1.11141
$472$	1.09421	0.0503653
$473$	12.4124	0.570722
$474$	38.8323	1.78363
$475$	−11.1232	−0.510369
$476$	−20.5142	−0.940268
$477$	54.5924	2.49961
$478$	−23.2884	−1.06519
$479$	3.35867	0.153461	0.0767307	−	0.997052i	$-0.475552\pi$
$479$	3.35867	0.153461	0.0767307	+	0.997052i	$0.475552\pi$
$480$	8.32366	0.379922
$481$	−18.0288	−0.822045
$482$	1.53730	0.0700221
$483$	−89.0143	−4.05029
$484$	−9.33222	−0.424192
$485$	−50.6422	−2.29954
$486$	−10.7633	−0.488235
$487$	−4.70517	−0.213211	−0.106606	−	0.994301i	$-0.533998\pi$
$487$	−4.70517	−0.213211	−0.106606	+	0.994301i	$0.533998\pi$
$488$	−11.6084	−0.525488
$489$	−71.6191	−3.23873
$490$	−28.2115	−1.27447
$491$	−15.6209	−0.704962	−0.352481	−	0.935819i	$-0.614662\pi$
$491$	−15.6209	−0.704962	−0.352481	+	0.935819i	$0.614662\pi$
$492$	24.3695	1.09866
$493$	4.86345	0.219039
$494$	−10.4808	−0.471555
$495$	22.7461	1.02236
$496$	−6.94880	−0.312010
$497$	24.0191	1.07740
$498$	29.1799	1.30758
$499$	26.3680	1.18039	0.590197	−	0.807259i	$-0.299050\pi$
$499$	26.3680	1.18039	0.590197	+	0.807259i	$0.299050\pi$
$500$	7.36673	0.329450
$501$	−1.74158	−0.0778079
$502$	−2.71120	−0.121007
$503$	−9.77144	−0.435687	−0.217844	−	0.975984i	$-0.569902\pi$
$503$	−9.77144	−0.435687	−0.217844	+	0.975984i	$0.569902\pi$
$504$	−27.3044	−1.21624
$505$	18.9293	0.842342
$506$	8.90878	0.396044
$507$	26.0470	1.15679
$508$	−4.49861	−0.199593
$509$	−13.7059	−0.607503	−0.303751	−	0.952751i	$-0.598239\pi$
$509$	−13.7059	−0.607503	−0.303751	+	0.952751i	$0.598239\pi$
$510$	40.8588	1.80926
$511$	25.9137	1.14636
$512$	1.00000	0.0441942
$513$	53.5247	2.36317
$514$	−16.9330	−0.746883
$515$	34.4805	1.51939
$516$	29.6765	1.30643
$517$	8.67804	0.381660
$518$	35.2674	1.54956
$519$	17.2426	0.756867
$520$	−5.75925	−0.252560
$521$	−16.2683	−0.712726	−0.356363	−	0.934348i	$-0.615983\pi$
$521$	−16.2683	−0.712726	−0.356363	+	0.934348i	$0.615983\pi$
$522$	6.47326	0.283327
$523$	24.3291	1.06384	0.531919	−	0.846795i	$-0.321471\pi$
$523$	24.3291	1.06384	0.531919	+	0.846795i	$0.321471\pi$
$524$	−2.38453	−0.104169
$525$	29.2567	1.27687
$526$	1.55081	0.0676184
$527$	−34.1099	−1.48585
$528$	3.98747	0.173532
$529$	24.5879	1.06904
$530$	−22.5253	−0.978437
$531$	7.14910	0.310244
$532$	20.5022	0.888884
$533$	−16.8616	−0.730357
$534$	−6.76285	−0.292657
$535$	−26.7892	−1.15820
$536$	13.7293	0.593014
$537$	−54.0988	−2.33454
$538$	−15.8901	−0.685069
$539$	−13.5148	−0.582123
$540$	29.4120	1.26569
$541$	20.5092	0.881758	0.440879	−	0.897567i	$-0.354667\pi$
$541$	20.5092	0.881758	0.440879	+	0.897567i	$0.354667\pi$
$542$	−15.0293	−0.645563
$543$	−23.4326	−1.00559
$544$	4.90875	0.210461
$545$	4.17619	0.178888
$546$	27.5670	1.17976
$547$	−14.5144	−0.620590	−0.310295	−	0.950640i	$-0.600428\pi$
$547$	−14.5144	−0.620590	−0.310295	+	0.950640i	$0.600428\pi$
$548$	15.5987	0.666342
$549$	−75.8441	−3.23695
$550$	−2.92809	−0.124854
$551$	−4.86061	−0.207069
$552$	21.2998	0.906580
$553$	52.5594	2.23505
$554$	16.9726	0.721096
$555$	−70.2431	−2.98165
$556$	5.81430	0.246581
$557$	35.5975	1.50831	0.754157	−	0.656694i	$-0.228046\pi$
$557$	35.5975	1.50831	0.754157	+	0.656694i	$0.228046\pi$
$558$	−45.4003	−1.92195
$559$	−20.5335	−0.868476
$560$	11.2660	0.476077
$561$	19.5735	0.826393
$562$	−9.79694	−0.413259
$563$	−2.10690	−0.0887953	−0.0443976	−	0.999014i	$-0.514137\pi$
$563$	−2.10690	−0.0887953	−0.0443976	+	0.999014i	$0.514137\pi$
$564$	20.7481	0.873654
$565$	19.5960	0.824408
$566$	−10.9322	−0.459513
$567$	−58.8694	−2.47228
$568$	−5.74741	−0.241156
$569$	−29.9982	−1.25759	−0.628795	−	0.777571i	$-0.716451\pi$
$569$	−29.9982	−1.25759	−0.628795	+	0.777571i	$0.716451\pi$
$570$	−40.8349	−1.71038
$571$	25.8494	1.08177	0.540883	−	0.841098i	$-0.318090\pi$
$571$	25.8494	1.08177	0.540883	+	0.841098i	$0.318090\pi$
$572$	−2.75898	−0.115359
$573$	−51.4145	−2.14787
$574$	32.9840	1.37673
$575$	−15.6409	−0.652272
$576$	6.53354	0.272231
$577$	−19.0476	−0.792962	−0.396481	−	0.918043i	$-0.629769\pi$
$577$	−19.0476	−0.792962	−0.396481	+	0.918043i	$0.629769\pi$
$578$	7.09582	0.295147
$579$	62.9797	2.61735
$580$	−2.67092	−0.110904
$581$	39.4949	1.63852
$582$	−58.0032	−2.40431
$583$	−10.7908	−0.446909
$584$	−6.20077	−0.256590
$585$	−37.6283	−1.55574
$586$	−13.4646	−0.556217
$587$	4.15709	0.171581	0.0857907	−	0.996313i	$-0.472658\pi$
$587$	4.15709	0.171581	0.0857907	+	0.996313i	$0.472658\pi$
$588$	−32.3122	−1.33253
$589$	34.0900	1.40465
$590$	−2.94978	−0.121441
$591$	37.2279	1.53135
$592$	−8.43896	−0.346839
$593$	−40.3225	−1.65584	−0.827922	−	0.560843i	$-0.810477\pi$
$593$	−40.3225	−1.65584	−0.827922	+	0.560843i	$0.810477\pi$
$594$	14.0899	0.578115
$595$	55.3022	2.26717
$596$	−4.96071	−0.203199
$597$	30.6133	1.25292
$598$	−14.7376	−0.602666
$599$	35.3936	1.44614	0.723072	−	0.690773i	$-0.242730\pi$
$599$	35.3936	1.44614	0.723072	+	0.690773i	$0.242730\pi$
$600$	−7.00070	−0.285802
$601$	−38.4490	−1.56837	−0.784184	−	0.620528i	$-0.786918\pi$
$601$	−38.4490	−1.56837	−0.784184	+	0.620528i	$0.786918\pi$
$602$	40.1670	1.63708
$603$	89.7008	3.65290
$604$	15.5634	0.633267
$605$	25.1578	1.02281
$606$	21.6807	0.880719
$607$	23.8523	0.968137	0.484068	−	0.875030i	$-0.339159\pi$
$607$	23.8523	0.968137	0.484068	+	0.875030i	$0.339159\pi$
$608$	−4.90588	−0.198960
$609$	12.7845	0.518056
$610$	31.2939	1.26705
$611$	−14.3559	−0.580778
$612$	32.0715	1.29641
$613$	−32.9272	−1.32992	−0.664958	−	0.746880i	$-0.731551\pi$
$613$	−32.9272	−1.32992	−0.664958	+	0.746880i	$0.731551\pi$
$614$	−17.9088	−0.722742
$615$	−65.6953	−2.64909
$616$	5.39702	0.217452
$617$	3.17034	0.127633	0.0638166	−	0.997962i	$-0.479673\pi$
$617$	3.17034	0.127633	0.0638166	+	0.997962i	$0.479673\pi$
$618$	39.4923	1.58861
$619$	2.70064	0.108548	0.0542740	−	0.998526i	$-0.482716\pi$
$619$	2.70064	0.108548	0.0542740	+	0.998526i	$0.482716\pi$
$620$	18.7326	0.752318
$621$	75.2638	3.02023
$622$	−6.02340	−0.241516
$623$	−9.15349	−0.366727
$624$	−6.59639	−0.264067
$625$	−31.1959	−1.24783
$626$	2.01957	0.0807182
$627$	−19.5620	−0.781232
$628$	−7.81193	−0.311730
$629$	−41.4248	−1.65171
$630$	73.6072	2.93258
$631$	−7.35304	−0.292720	−0.146360	−	0.989231i	$-0.546756\pi$
$631$	−7.35304	−0.292720	−0.146360	+	0.989231i	$0.546756\pi$
$632$	−12.5767	−0.500273
$633$	−60.0920	−2.38844
$634$	−2.90553	−0.115393
$635$	12.1273	0.481259
$636$	−25.7995	−1.02302
$637$	22.3572	0.885825
$638$	−1.27951	−0.0506563
$639$	−37.5510	−1.48549
$640$	−2.69580	−0.106561
$641$	−35.2496	−1.39228	−0.696138	−	0.717908i	$-0.745100\pi$
$641$	−35.2496	−1.39228	−0.696138	+	0.717908i	$0.745100\pi$
$642$	−30.6831	−1.21097
$643$	−21.3135	−0.840523	−0.420262	−	0.907403i	$-0.638062\pi$
$643$	−21.3135	−0.840523	−0.420262	+	0.907403i	$0.638062\pi$
$644$	28.8292	1.13603
$645$	−80.0018	−3.15007
$646$	−24.0817	−0.947483
$647$	−2.14315	−0.0842561	−0.0421281	−	0.999112i	$-0.513414\pi$
$647$	−2.14315	−0.0842561	−0.0421281	+	0.999112i	$0.513414\pi$
$648$	14.0866	0.553373
$649$	−1.41310	−0.0554690
$650$	4.84388	0.189993
$651$	−89.6646	−3.51423
$652$	23.1954	0.908401
$653$	41.9428	1.64135	0.820675	−	0.571395i	$-0.193598\pi$
$653$	41.9428	1.64135	0.820675	+	0.571395i	$0.193598\pi$
$654$	4.78321	0.187038
$655$	6.42822	0.251171
$656$	−7.89259	−0.308154
$657$	−40.5130	−1.58056
$658$	28.0825	1.09477
$659$	9.32875	0.363396	0.181698	−	0.983354i	$-0.441841\pi$
$659$	9.32875	0.363396	0.181698	+	0.983354i	$0.441841\pi$
$660$	−10.7494	−0.418420
$661$	−0.529128	−0.0205807	−0.0102903	−	0.999947i	$-0.503276\pi$
$661$	−0.529128	−0.0205807	−0.0102903	+	0.999947i	$0.503276\pi$
$662$	21.2377	0.825427
$663$	−32.3800	−1.25754
$664$	−9.45055	−0.366752
$665$	−55.2698	−2.14327
$666$	−55.1363	−2.13649
$667$	−6.83475	−0.264642
$668$	0.564047	0.0218236
$669$	−40.5247	−1.56677
$670$	−37.0113	−1.42987
$671$	14.9914	0.578738
$672$	12.9036	0.497768
$673$	−21.7275	−0.837534	−0.418767	−	0.908094i	$-0.637538\pi$
$673$	−21.7275	−0.837534	−0.418767	+	0.908094i	$0.637538\pi$
$674$	−4.91296	−0.189240
$675$	−24.7373	−0.952139
$676$	−8.43587	−0.324457
$677$	−22.6034	−0.868718	−0.434359	−	0.900740i	$-0.643025\pi$
$677$	−22.6034	−0.868718	−0.434359	+	0.900740i	$0.643025\pi$
$678$	22.4443	0.861969
$679$	−78.5072	−3.01283
$680$	−13.2330	−0.507462
$681$	−58.7497	−2.25129
$682$	8.97387	0.343627
$683$	9.22940	0.353153	0.176577	−	0.984287i	$-0.443498\pi$
$683$	9.22940	0.353153	0.176577	+	0.984287i	$0.443498\pi$
$684$	−32.0528	−1.22557
$685$	−42.0509	−1.60668
$686$	−14.4806	−0.552872
$687$	65.4665	2.49770
$688$	−9.61136	−0.366430
$689$	17.8510	0.680068
$690$	−57.4200	−2.18594
$691$	48.7730	1.85541	0.927706	−	0.373312i	$-0.121778\pi$
$691$	48.7730	1.85541	0.927706	+	0.373312i	$0.121778\pi$
$692$	−5.58439	−0.212287
$693$	35.2617	1.33948
$694$	19.9856	0.758643
$695$	−15.6742	−0.594555
$696$	−3.05915	−0.115957
$697$	−38.7428	−1.46749
$698$	−8.52974	−0.322855
$699$	−32.9563	−1.24652
$700$	−9.47542	−0.358137
$701$	−43.4623	−1.64155	−0.820773	−	0.571254i	$-0.806457\pi$
$701$	−43.4623	−1.64155	−0.820773	+	0.571254i	$0.806457\pi$
$702$	−23.3086	−0.879727
$703$	41.4005	1.56145
$704$	−1.29143	−0.0486725
$705$	−55.9328	−2.10655
$706$	−10.5560	−0.397280
$707$	29.3448	1.10362
$708$	−3.37854	−0.126973
$709$	8.04245	0.302040	0.151020	−	0.988531i	$-0.451744\pi$
$709$	8.04245	0.302040	0.151020	+	0.988531i	$0.451744\pi$
$710$	15.4939	0.581474
$711$	−82.1703	−3.08163
$712$	2.19029	0.0820848
$713$	47.9356	1.79520
$714$	63.3406	2.37046
$715$	7.43766	0.278153
$716$	17.5211	0.654793
$717$	71.9062	2.68539
$718$	−0.461744	−0.0172321
$719$	4.13641	0.154262	0.0771310	−	0.997021i	$-0.475424\pi$
$719$	4.13641	0.154262	0.0771310	+	0.997021i	$0.475424\pi$
$720$	−17.6131	−0.656402
$721$	53.4527	1.99068
$722$	5.06763	0.188598
$723$	−4.74664	−0.176529
$724$	7.58916	0.282049
$725$	2.24641	0.0834294
$726$	28.8146	1.06941
$727$	−11.3233	−0.419956	−0.209978	−	0.977706i	$-0.567339\pi$
$727$	−11.3233	−0.419956	−0.209978	+	0.977706i	$0.567339\pi$
$728$	−8.92818	−0.330900
$729$	−9.02638	−0.334310
$730$	16.7160	0.618688
$731$	−47.1798	−1.74501
$732$	35.8427	1.32478
$733$	−33.3325	−1.23116	−0.615582	−	0.788073i	$-0.711079\pi$
$733$	−33.3325	−1.23116	−0.615582	+	0.788073i	$0.711079\pi$
$734$	13.8040	0.509514
$735$	87.1071	3.21299
$736$	−6.89840	−0.254278
$737$	−17.7304	−0.653106
$738$	−51.5666	−1.89819
$739$	17.2507	0.634578	0.317289	−	0.948329i	$-0.397228\pi$
$739$	17.2507	0.634578	0.317289	+	0.948329i	$0.397228\pi$
$740$	22.7497	0.836297
$741$	32.3611	1.18881
$742$	−34.9195	−1.28193
$743$	−22.1198	−0.811498	−0.405749	−	0.913985i	$-0.632989\pi$
$743$	−22.1198	−0.811498	−0.405749	+	0.913985i	$0.632989\pi$
$744$	21.4554	0.786594
$745$	13.3731	0.489951
$746$	−24.7293	−0.905402
$747$	−61.7456	−2.25915
$748$	−6.33929	−0.231788
$749$	−41.5295	−1.51745
$750$	−22.7458	−0.830561
$751$	21.3572	0.779334	0.389667	−	0.920956i	$-0.372590\pi$
$751$	21.3572	0.779334	0.389667	+	0.920956i	$0.372590\pi$
$752$	−6.71973	−0.245043
$753$	8.37123	0.305065
$754$	2.11667	0.0770845
$755$	−41.9558	−1.52693
$756$	45.5955	1.65829
$757$	50.8474	1.84808	0.924041	−	0.382294i	$-0.124866\pi$
$757$	50.8474	1.84808	0.924041	+	0.382294i	$0.124866\pi$
$758$	−21.1369	−0.767727
$759$	−27.5072	−0.998446
$760$	13.2253	0.479730
$761$	−32.5426	−1.17967	−0.589833	−	0.807525i	$-0.700807\pi$
$761$	−32.5426	−1.17967	−0.589833	+	0.807525i	$0.700807\pi$
$762$	13.8901	0.503185
$763$	6.47406	0.234377
$764$	16.6517	0.602437
$765$	−86.4584	−3.12591
$766$	−25.6133	−0.925444
$767$	2.33766	0.0844080
$768$	−3.08764	−0.111416
$769$	−29.1255	−1.05029	−0.525146	−	0.851012i	$-0.675989\pi$
$769$	−29.1255	−1.05029	−0.525146	+	0.851012i	$0.675989\pi$
$770$	−14.5493	−0.524320
$771$	52.2831	1.88293
$772$	−20.3973	−0.734116
$773$	28.7137	1.03276	0.516379	−	0.856360i	$-0.327280\pi$
$773$	28.7137	1.03276	0.516379	+	0.856360i	$0.327280\pi$
$774$	−62.7963	−2.25717
$775$	−15.7552	−0.565944
$776$	18.7856	0.674364
$777$	−108.893	−3.90652
$778$	2.93124	0.105090
$779$	38.7201	1.38729
$780$	17.7825	0.636717
$781$	7.42236	0.265593
$782$	−33.8625	−1.21092
$783$	−10.8097	−0.386305
$784$	10.4650	0.373750
$785$	21.0594	0.751642
$786$	7.36259	0.262615
$787$	−27.3603	−0.975289	−0.487644	−	0.873042i	$-0.662144\pi$
$787$	−27.3603	−0.975289	−0.487644	+	0.873042i	$0.662144\pi$
$788$	−12.0571	−0.429515
$789$	−4.78834	−0.170469
$790$	33.9042	1.20626
$791$	30.3783	1.08013
$792$	−8.43760	−0.299817
$793$	−24.8000	−0.880674
$794$	36.5726	1.29791
$795$	69.5501	2.46669
$796$	−9.91476	−0.351420
$797$	46.9551	1.66323	0.831617	−	0.555349i	$-0.187415\pi$
$797$	46.9551	1.66323	0.831617	+	0.555349i	$0.187415\pi$
$798$	−63.3036	−2.24092
$799$	−32.9855	−1.16694
$800$	2.26733	0.0801621
$801$	14.3104	0.505633
$802$	17.1978	0.607276
$803$	8.00785	0.282591
$804$	−42.3911	−1.49502
$805$	−77.7177	−2.73919
$806$	−14.8453	−0.522903
$807$	49.0628	1.72709
$808$	−7.02177	−0.247025
$809$	35.4050	1.24477	0.622386	−	0.782710i	$-0.286163\pi$
$809$	35.4050	1.24477	0.622386	+	0.782710i	$0.286163\pi$
$810$	−37.9746	−1.33429
$811$	−50.9628	−1.78955	−0.894773	−	0.446521i	$-0.852663\pi$
$811$	−50.9628	−1.78955	−0.894773	+	0.446521i	$0.852663\pi$
$812$	−4.14055	−0.145305
$813$	46.4051	1.62750
$814$	10.8983	0.381985
$815$	−62.5301	−2.19033
$816$	−15.1565	−0.530583
$817$	47.1522	1.64965
$818$	−9.99197	−0.349361
$819$	−58.3327	−2.03831
$820$	21.2768	0.743019
$821$	9.63463	0.336251	0.168125	−	0.985766i	$-0.446229\pi$
$821$	9.63463	0.336251	0.168125	+	0.985766i	$0.446229\pi$
$822$	−48.1631	−1.67988
$823$	42.0984	1.46746	0.733729	−	0.679442i	$-0.237778\pi$
$823$	42.0984	1.46746	0.733729	+	0.679442i	$0.237778\pi$
$824$	−12.7904	−0.445576
$825$	9.04090	0.314764
$826$	−4.57285	−0.159110
$827$	−43.2813	−1.50504	−0.752520	−	0.658570i	$-0.771162\pi$
$827$	−43.2813	−1.50504	−0.752520	+	0.658570i	$0.771162\pi$
$828$	−45.0710	−1.56633
$829$	−15.0744	−0.523556	−0.261778	−	0.965128i	$-0.584309\pi$
$829$	−15.0744	−0.523556	−0.261778	+	0.965128i	$0.584309\pi$
$830$	25.4768	0.884311
$831$	−52.4053	−1.81792
$832$	2.13638	0.0740657
$833$	51.3700	1.77987
$834$	−17.9525	−0.621643
$835$	−1.52056	−0.0526211
$836$	6.33558	0.219121
$837$	75.8137	2.62050
$838$	−9.53692	−0.329447
$839$	42.3453	1.46192	0.730961	−	0.682419i	$-0.239072\pi$
$839$	42.3453	1.46192	0.730961	+	0.682419i	$0.239072\pi$
$840$	−34.7855	−1.20022
$841$	−28.0184	−0.966151
$842$	−9.12685	−0.314532
$843$	30.2495	1.04185
$844$	19.4621	0.669913
$845$	22.7414	0.782328
$846$	−43.9037	−1.50944
$847$	39.0004	1.34007
$848$	8.35571	0.286936
$849$	33.7547	1.15846
$850$	11.1297	0.381747
$851$	58.2154	1.99560
$852$	17.7460	0.607966
$853$	18.4867	0.632972	0.316486	−	0.948597i	$-0.397497\pi$
$853$	18.4867	0.632972	0.316486	+	0.948597i	$0.397497\pi$
$854$	48.5129	1.66008
$855$	86.4078	2.95508
$856$	9.93739	0.339653
$857$	33.4962	1.14421	0.572104	−	0.820181i	$-0.306127\pi$
$857$	33.4962	1.14421	0.572104	+	0.820181i	$0.306127\pi$
$858$	8.51875	0.290825
$859$	−52.3763	−1.78705	−0.893527	−	0.449008i	$-0.851777\pi$
$859$	−52.3763	−1.78705	−0.893527	+	0.449008i	$0.851777\pi$
$860$	25.9103	0.883534
$861$	−101.843	−3.47080
$862$	−10.7543	−0.366292
$863$	25.5233	0.868824	0.434412	−	0.900714i	$-0.356956\pi$
$863$	25.5233	0.868824	0.434412	+	0.900714i	$0.356956\pi$
$864$	−10.9103	−0.371177
$865$	15.0544	0.511865
$866$	26.0183	0.884137
$867$	−21.9094	−0.744081
$868$	29.0398	0.985676
$869$	16.2419	0.550967
$870$	8.24686	0.279595
$871$	29.3310	0.993842
$872$	−1.54915	−0.0524607
$873$	122.737	4.15400
$874$	33.8427	1.14475
$875$	−30.7864	−1.04077
$876$	19.1458	0.646876
$877$	−5.36556	−0.181182	−0.0905911	−	0.995888i	$-0.528876\pi$
$877$	−5.36556	−0.181182	−0.0905911	+	0.995888i	$0.528876\pi$
$878$	34.8169	1.17501
$879$	41.5738	1.40225
$880$	3.48143	0.117359
$881$	33.1284	1.11612	0.558062	−	0.829799i	$-0.311545\pi$
$881$	33.1284	1.11612	0.558062	+	0.829799i	$0.311545\pi$
$882$	68.3735	2.30226
$883$	43.2071	1.45403	0.727017	−	0.686619i	$-0.240906\pi$
$883$	43.2071	1.45403	0.727017	+	0.686619i	$0.240906\pi$
$884$	10.4870	0.352715
$885$	9.10787	0.306158
$886$	35.8120	1.20313
$887$	−39.6084	−1.32992	−0.664960	−	0.746879i	$-0.731551\pi$
$887$	−39.6084	−1.32992	−0.664960	+	0.746879i	$0.731551\pi$
$888$	26.0565	0.874399
$889$	18.8002	0.630538
$890$	−5.90459	−0.197922
$891$	−18.1918	−0.609448
$892$	13.1248	0.439450
$893$	32.9662	1.10317
$894$	15.3169	0.512274
$895$	−47.2333	−1.57883
$896$	−4.17911	−0.139614
$897$	45.5045	1.51935
$898$	−14.4096	−0.480856
$899$	−6.88468	−0.229617
$900$	14.8137	0.493790
$901$	41.0161	1.36644
$902$	10.1927	0.339380
$903$	−124.021	−4.12717
$904$	−7.26908	−0.241766
$905$	−20.4589	−0.680075
$906$	−48.0543	−1.59650
$907$	19.5347	0.648638	0.324319	−	0.945948i	$-0.394865\pi$
$907$	19.5347	0.648638	0.324319	+	0.945948i	$0.394865\pi$
$908$	19.0273	0.631444
$909$	−45.8770	−1.52165
$910$	24.0686	0.797866
$911$	19.2279	0.637049	0.318524	−	0.947915i	$-0.396813\pi$
$911$	19.2279	0.637049	0.318524	+	0.947915i	$0.396813\pi$
$912$	15.1476	0.501587
$913$	12.2047	0.403916
$914$	38.2949	1.26668
$915$	−96.6246	−3.19431
$916$	−21.2027	−0.700558
$917$	9.96524	0.329081
$918$	−53.5561	−1.76761
$919$	2.29292	0.0756366	0.0378183	−	0.999285i	$-0.487959\pi$
$919$	2.29292	0.0756366	0.0378183	+	0.999285i	$0.487959\pi$
$920$	18.5967	0.613115
$921$	55.2961	1.82207
$922$	25.5033	0.839907
$923$	−12.2787	−0.404157
$924$	−16.6641	−0.548208
$925$	−19.1339	−0.629119
$926$	40.7458	1.33899
$927$	−83.5669	−2.74470
$928$	0.990772	0.0325237
$929$	−1.01290	−0.0332321	−0.0166161	−	0.999862i	$-0.505289\pi$
$929$	−1.01290	−0.0332321	−0.0166161	+	0.999862i	$0.505289\pi$
$930$	−57.8395	−1.89663
$931$	−51.3400	−1.68260
$932$	10.6736	0.349626
$933$	18.5981	0.608875
$934$	18.3937	0.601862
$935$	17.0895	0.558885
$936$	13.9581	0.456236
$937$	40.3418	1.31791	0.658954	−	0.752183i	$-0.270999\pi$
$937$	40.3418	1.31791	0.658954	+	0.752183i	$0.270999\pi$
$938$	−57.3762	−1.87340
$939$	−6.23571	−0.203495
$940$	18.1150	0.590847
$941$	52.7113	1.71834	0.859170	−	0.511691i	$-0.170981\pi$
$941$	52.7113	1.71834	0.859170	+	0.511691i	$0.170981\pi$
$942$	24.1205	0.785887
$943$	54.4463	1.77301
$944$	1.09421	0.0356136
$945$	−122.916	−3.99847
$946$	12.4124	0.403561
$947$	−43.7219	−1.42077	−0.710385	−	0.703813i	$-0.751479\pi$
$947$	−43.7219	−1.42077	−0.710385	+	0.703813i	$0.751479\pi$
$948$	38.8323	1.26121
$949$	−13.2472	−0.430023
$950$	−11.1232	−0.360885
$951$	8.97124	0.290912
$952$	−20.5142	−0.664870
$953$	35.4402	1.14802	0.574010	−	0.818848i	$-0.305387\pi$
$953$	35.4402	1.14802	0.574010	+	0.818848i	$0.305387\pi$
$954$	54.5924	1.76749
$955$	−44.8896	−1.45259
$956$	−23.2884	−0.753200
$957$	3.95067	0.127707
$958$	3.35867	0.108514
$959$	−65.1886	−2.10505
$960$	8.32366	0.268645
$961$	17.2858	0.557607
$962$	−18.0288	−0.581273
$963$	64.9264	2.09222
$964$	1.53730	0.0495131
$965$	54.9871	1.77010
$966$	−89.0143	−2.86399
$967$	−18.4537	−0.593431	−0.296716	−	0.954966i	$-0.595891\pi$
$967$	−18.4537	−0.593431	−0.296716	+	0.954966i	$0.595891\pi$
$968$	−9.33222	−0.299949
$969$	74.3558	2.38865
$970$	−50.6422	−1.62602
$971$	−47.9297	−1.53814	−0.769068	−	0.639167i	$-0.779279\pi$
$971$	−47.9297	−1.53814	−0.769068	+	0.639167i	$0.779279\pi$
$972$	−10.7633	−0.345234
$973$	−24.2986	−0.778978
$974$	−4.70517	−0.150763
$975$	−14.9562	−0.478981
$976$	−11.6084	−0.371576
$977$	−46.5549	−1.48942	−0.744712	−	0.667386i	$-0.767413\pi$
$977$	−46.5549	−1.48942	−0.744712	+	0.667386i	$0.767413\pi$
$978$	−71.6191	−2.29013
$979$	−2.82861	−0.0904027
$980$	−28.2115	−0.901184
$981$	−10.1214	−0.323152
$982$	−15.6209	−0.498484
$983$	34.6655	1.10566	0.552829	−	0.833295i	$-0.313548\pi$
$983$	34.6655	1.10566	0.552829	+	0.833295i	$0.313548\pi$
$984$	24.3695	0.776872
$985$	32.5034	1.03565
$986$	4.86345	0.154884
$987$	−86.7088	−2.75997
$988$	−10.4808	−0.333440
$989$	66.3030	2.10831
$990$	22.7461	0.722917
$991$	−29.3600	−0.932652	−0.466326	−	0.884613i	$-0.654423\pi$
$991$	−29.3600	−0.932652	−0.466326	+	0.884613i	$0.654423\pi$
$992$	−6.94880	−0.220625
$993$	−65.5744	−2.08094
$994$	24.0191	0.761839
$995$	26.7282	0.847341
$996$	29.1799	0.924601
$997$	−27.2249	−0.862221	−0.431110	−	0.902299i	$-0.641878\pi$
$997$	−27.2249	−0.862221	−0.431110	+	0.902299i	$0.641878\pi$
$998$	26.3680	0.834665
$999$	92.0718	2.91302

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6002.2.a.d.1.5	✓	79

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6002.2.a.d.1.5	✓	79	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:	\( N \)	\(=\)	\( 6002 = 2 \cdot 3001 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6002.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -3.08764 q^{3} +1.00000 q^{4} -2.69580 q^{5} -3.08764 q^{6} -4.17911 q^{7} +1.00000 q^{8} +6.53354 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -3.08764 q^{3} +1.00000 q^{4} -2.69580 q^{5} -3.08764 q^{6} -4.17911 q^{7} +1.00000 q^{8} +6.53354 q^{9} -2.69580 q^{10} -1.29143 q^{11} -3.08764 q^{12} +2.13638 q^{13} -4.17911 q^{14} +8.32366 q^{15} +1.00000 q^{16} +4.90875 q^{17} +6.53354 q^{18} -4.90588 q^{19} -2.69580 q^{20} +12.9036 q^{21} -1.29143 q^{22} -6.89840 q^{23} -3.08764 q^{24} +2.26733 q^{25} +2.13638 q^{26} -10.9103 q^{27} -4.17911 q^{28} +0.990772 q^{29} +8.32366 q^{30} -6.94880 q^{31} +1.00000 q^{32} +3.98747 q^{33} +4.90875 q^{34} +11.2660 q^{35} +6.53354 q^{36} -8.43896 q^{37} -4.90588 q^{38} -6.59639 q^{39} -2.69580 q^{40} -7.89259 q^{41} +12.9036 q^{42} -9.61136 q^{43} -1.29143 q^{44} -17.6131 q^{45} -6.89840 q^{46} -6.71973 q^{47} -3.08764 q^{48} +10.4650 q^{49} +2.26733 q^{50} -15.1565 q^{51} +2.13638 q^{52} +8.35571 q^{53} -10.9103 q^{54} +3.48143 q^{55} -4.17911 q^{56} +15.1476 q^{57} +0.990772 q^{58} +1.09421 q^{59} +8.32366 q^{60} -11.6084 q^{61} -6.94880 q^{62} -27.3044 q^{63} +1.00000 q^{64} -5.75925 q^{65} +3.98747 q^{66} +13.7293 q^{67} +4.90875 q^{68} +21.2998 q^{69} +11.2660 q^{70} -5.74741 q^{71} +6.53354 q^{72} -6.20077 q^{73} -8.43896 q^{74} -7.00070 q^{75} -4.90588 q^{76} +5.39702 q^{77} -6.59639 q^{78} -12.5767 q^{79} -2.69580 q^{80} +14.0866 q^{81} -7.89259 q^{82} -9.45055 q^{83} +12.9036 q^{84} -13.2330 q^{85} -9.61136 q^{86} -3.05915 q^{87} -1.29143 q^{88} +2.19029 q^{89} -17.6131 q^{90} -8.92818 q^{91} -6.89840 q^{92} +21.4554 q^{93} -6.71973 q^{94} +13.2253 q^{95} -3.08764 q^{96} +18.7856 q^{97} +10.4650 q^{98} -8.43760 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 79 q + 79 q^{2} + 17 q^{3} + 79 q^{4} + 18 q^{5} + 17 q^{6} + 19 q^{7} + 79 q^{8} + 118 q^{9}+O(q^{10}) \) 79 * q + 79 * q^2 + 17 * q^3 + 79 * q^4 + 18 * q^5 + 17 * q^6 + 19 * q^7 + 79 * q^8 + 118 * q^9	\( 79 q + 79 q^{2} + 17 q^{3} + 79 q^{4} + 18 q^{5} + 17 q^{6} + 19 q^{7} + 79 q^{8} + 118 q^{9} + 18 q^{10} + 28 q^{11} + 17 q^{12} + 47 q^{13} + 19 q^{14} + 14 q^{15} + 79 q^{16} + 36 q^{17} + 118 q^{18} + 29 q^{19} + 18 q^{20} + 45 q^{21} + 28 q^{22} + 23 q^{23} + 17 q^{24} + 161 q^{25} + 47 q^{26} + 50 q^{27} + 19 q^{28} + 53 q^{29} + 14 q^{30} + 29 q^{31} + 79 q^{32} + 34 q^{33} + 36 q^{34} + 33 q^{35} + 118 q^{36} + 89 q^{37} + 29 q^{38} - 7 q^{39} + 18 q^{40} + 58 q^{41} + 45 q^{42} + 88 q^{43} + 28 q^{44} + 45 q^{45} + 23 q^{46} + 3 q^{47} + 17 q^{48} + 162 q^{49} + 161 q^{50} + 29 q^{51} + 47 q^{52} + 88 q^{53} + 50 q^{54} + 37 q^{55} + 19 q^{56} + 54 q^{57} + 53 q^{58} + 37 q^{59} + 14 q^{60} + 55 q^{61} + 29 q^{62} + 21 q^{63} + 79 q^{64} + 55 q^{65} + 34 q^{66} + 107 q^{67} + 36 q^{68} + 39 q^{69} + 33 q^{70} - 5 q^{71} + 118 q^{72} + 71 q^{73} + 89 q^{74} + 37 q^{75} + 29 q^{76} + 61 q^{77} - 7 q^{78} + 29 q^{79} + 18 q^{80} + 215 q^{81} + 58 q^{82} + 42 q^{83} + 45 q^{84} + 84 q^{85} + 88 q^{86} + 15 q^{87} + 28 q^{88} + 72 q^{89} + 45 q^{90} + 70 q^{91} + 23 q^{92} + 97 q^{93} + 3 q^{94} - 18 q^{95} + 17 q^{96} + 93 q^{97} + 162 q^{98} + 49 q^{99}+O(q^{100}) \) 79 * q + 79 * q^2 + 17 * q^3 + 79 * q^4 + 18 * q^5 + 17 * q^6 + 19 * q^7 + 79 * q^8 + 118 * q^9 + 18 * q^10 + 28 * q^11 + 17 * q^12 + 47 * q^13 + 19 * q^14 + 14 * q^15 + 79 * q^16 + 36 * q^17 + 118 * q^18 + 29 * q^19 + 18 * q^20 + 45 * q^21 + 28 * q^22 + 23 * q^23 + 17 * q^24 + 161 * q^25 + 47 * q^26 + 50 * q^27 + 19 * q^28 + 53 * q^29 + 14 * q^30 + 29 * q^31 + 79 * q^32 + 34 * q^33 + 36 * q^34 + 33 * q^35 + 118 * q^36 + 89 * q^37 + 29 * q^38 - 7 * q^39 + 18 * q^40 + 58 * q^41 + 45 * q^42 + 88 * q^43 + 28 * q^44 + 45 * q^45 + 23 * q^46 + 3 * q^47 + 17 * q^48 + 162 * q^49 + 161 * q^50 + 29 * q^51 + 47 * q^52 + 88 * q^53 + 50 * q^54 + 37 * q^55 + 19 * q^56 + 54 * q^57 + 53 * q^58 + 37 * q^59 + 14 * q^60 + 55 * q^61 + 29 * q^62 + 21 * q^63 + 79 * q^64 + 55 * q^65 + 34 * q^66 + 107 * q^67 + 36 * q^68 + 39 * q^69 + 33 * q^70 - 5 * q^71 + 118 * q^72 + 71 * q^73 + 89 * q^74 + 37 * q^75 + 29 * q^76 + 61 * q^77 - 7 * q^78 + 29 * q^79 + 18 * q^80 + 215 * q^81 + 58 * q^82 + 42 * q^83 + 45 * q^84 + 84 * q^85 + 88 * q^86 + 15 * q^87 + 28 * q^88 + 72 * q^89 + 45 * q^90 + 70 * q^91 + 23 * q^92 + 97 * q^93 + 3 * q^94 - 18 * q^95 + 17 * q^96 + 93 * q^97 + 162 * q^98 + 49 * q^99

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