LMFDB - Embedded newform 6041.2.a.d.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6041,2,Mod(1,6041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6041, 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("6041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6041 = 7 \cdot 863 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6041.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$48.2376278611$
Analytic rank:	$1$
Dimension:	$101$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	6041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.44864 q^{2} -2.39074 q^{3} +3.99581 q^{4} -0.961081 q^{5} +5.85406 q^{6} -1.00000 q^{7} -4.88702 q^{8} +2.71565 q^{9} +O(q^{10})$	\(q-2.44864 q^{2} -2.39074 q^{3} +3.99581 q^{4} -0.961081 q^{5} +5.85406 q^{6} -1.00000 q^{7} -4.88702 q^{8} +2.71565 q^{9} +2.35334 q^{10} -6.49032 q^{11} -9.55296 q^{12} -6.00183 q^{13} +2.44864 q^{14} +2.29770 q^{15} +3.97491 q^{16} -1.46964 q^{17} -6.64964 q^{18} -4.74615 q^{19} -3.84030 q^{20} +2.39074 q^{21} +15.8924 q^{22} -0.0229005 q^{23} +11.6836 q^{24} -4.07632 q^{25} +14.6963 q^{26} +0.679808 q^{27} -3.99581 q^{28} +1.53143 q^{29} -5.62622 q^{30} -7.07998 q^{31} +0.0409495 q^{32} +15.5167 q^{33} +3.59860 q^{34} +0.961081 q^{35} +10.8512 q^{36} +3.28981 q^{37} +11.6216 q^{38} +14.3488 q^{39} +4.69682 q^{40} +5.38315 q^{41} -5.85406 q^{42} +6.72181 q^{43} -25.9341 q^{44} -2.60996 q^{45} +0.0560749 q^{46} +0.369915 q^{47} -9.50298 q^{48} +1.00000 q^{49} +9.98143 q^{50} +3.51352 q^{51} -23.9822 q^{52} -1.08018 q^{53} -1.66460 q^{54} +6.23772 q^{55} +4.88702 q^{56} +11.3468 q^{57} -3.74993 q^{58} +5.19741 q^{59} +9.18117 q^{60} +7.25181 q^{61} +17.3363 q^{62} -2.71565 q^{63} -8.05008 q^{64} +5.76825 q^{65} -37.9947 q^{66} +14.1902 q^{67} -5.87239 q^{68} +0.0547491 q^{69} -2.35334 q^{70} +3.74629 q^{71} -13.2714 q^{72} +4.89573 q^{73} -8.05554 q^{74} +9.74544 q^{75} -18.9647 q^{76} +6.49032 q^{77} -35.1351 q^{78} -11.9070 q^{79} -3.82021 q^{80} -9.77220 q^{81} -13.1814 q^{82} +0.272919 q^{83} +9.55296 q^{84} +1.41244 q^{85} -16.4593 q^{86} -3.66127 q^{87} +31.7183 q^{88} +2.33883 q^{89} +6.39084 q^{90} +6.00183 q^{91} -0.0915060 q^{92} +16.9264 q^{93} -0.905786 q^{94} +4.56143 q^{95} -0.0978997 q^{96} +1.22106 q^{97} -2.44864 q^{98} -17.6254 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 101 q + 3 q^{2} - 17 q^{3} + 85 q^{4} - 12 q^{5} - 17 q^{6} - 101 q^{7} - 3 q^{8} + 88 q^{9}+O(q^{10}) $ 101 * q + 3 * q^2 - 17 * q^3 + 85 * q^4 - 12 * q^5 - 17 * q^6 - 101 * q^7 - 3 * q^8 + 88 * q^9	\( 101 q + 3 q^{2} - 17 q^{3} + 85 q^{4} - 12 q^{5} - 17 q^{6} - 101 q^{7} - 3 q^{8} + 88 q^{9} - 23 q^{10} - 13 q^{11} - 31 q^{12} - 35 q^{13} - 3 q^{14} - 20 q^{15} + 45 q^{16} - 19 q^{17} + 3 q^{18} - 59 q^{19} - 31 q^{20} + 17 q^{21} - 13 q^{22} - 29 q^{23} - 59 q^{24} + 103 q^{25} - 18 q^{26} - 47 q^{27} - 85 q^{28} - 26 q^{29} - 8 q^{30} - 125 q^{31} + 12 q^{32} - 18 q^{33} - 66 q^{34} + 12 q^{35} + 40 q^{36} + 22 q^{37} - 31 q^{38} - 94 q^{39} - 79 q^{40} - 39 q^{41} + 17 q^{42} - 5 q^{43} - 53 q^{44} - 50 q^{45} - 37 q^{46} - 47 q^{47} - 81 q^{48} + 101 q^{49} + 2 q^{50} - 23 q^{51} - 56 q^{52} - 5 q^{53} - 77 q^{54} - 155 q^{55} + 3 q^{56} + 61 q^{57} - 31 q^{58} - 33 q^{59} - 48 q^{60} - 96 q^{61} - 38 q^{62} - 88 q^{63} - 33 q^{64} - 8 q^{65} - 91 q^{66} + 8 q^{67} - 41 q^{68} - 91 q^{69} + 23 q^{70} - 116 q^{71} - 5 q^{72} - 62 q^{73} - 23 q^{74} - 94 q^{75} - 112 q^{76} + 13 q^{77} + 17 q^{78} - 127 q^{79} - 87 q^{80} + 37 q^{81} - 118 q^{82} - 58 q^{83} + 31 q^{84} - 6 q^{85} - 26 q^{86} - 82 q^{87} - 40 q^{88} - 57 q^{89} - 123 q^{90} + 35 q^{91} - 28 q^{92} - 10 q^{93} - 107 q^{94} - 70 q^{95} - 76 q^{96} - 69 q^{97} + 3 q^{98} - 67 q^{99}+O(q^{100}) \) 101 * q + 3 * q^2 - 17 * q^3 + 85 * q^4 - 12 * q^5 - 17 * q^6 - 101 * q^7 - 3 * q^8 + 88 * q^9 - 23 * q^10 - 13 * q^11 - 31 * q^12 - 35 * q^13 - 3 * q^14 - 20 * q^15 + 45 * q^16 - 19 * q^17 + 3 * q^18 - 59 * q^19 - 31 * q^20 + 17 * q^21 - 13 * q^22 - 29 * q^23 - 59 * q^24 + 103 * q^25 - 18 * q^26 - 47 * q^27 - 85 * q^28 - 26 * q^29 - 8 * q^30 - 125 * q^31 + 12 * q^32 - 18 * q^33 - 66 * q^34 + 12 * q^35 + 40 * q^36 + 22 * q^37 - 31 * q^38 - 94 * q^39 - 79 * q^40 - 39 * q^41 + 17 * q^42 - 5 * q^43 - 53 * q^44 - 50 * q^45 - 37 * q^46 - 47 * q^47 - 81 * q^48 + 101 * q^49 + 2 * q^50 - 23 * q^51 - 56 * q^52 - 5 * q^53 - 77 * q^54 - 155 * q^55 + 3 * q^56 + 61 * q^57 - 31 * q^58 - 33 * q^59 - 48 * q^60 - 96 * q^61 - 38 * q^62 - 88 * q^63 - 33 * q^64 - 8 * q^65 - 91 * q^66 + 8 * q^67 - 41 * q^68 - 91 * q^69 + 23 * q^70 - 116 * q^71 - 5 * q^72 - 62 * q^73 - 23 * q^74 - 94 * q^75 - 112 * q^76 + 13 * q^77 + 17 * q^78 - 127 * q^79 - 87 * q^80 + 37 * q^81 - 118 * q^82 - 58 * q^83 + 31 * q^84 - 6 * q^85 - 26 * q^86 - 82 * q^87 - 40 * q^88 - 57 * q^89 - 123 * q^90 + 35 * q^91 - 28 * q^92 - 10 * q^93 - 107 * q^94 - 70 * q^95 - 76 * q^96 - 69 * q^97 + 3 * q^98 - 67 * 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 $

$2$	−2.44864	−1.73145	−0.865723	−	0.500523i	$-0.833141\pi$
$2$	−2.44864	−1.73145	−0.865723	+	0.500523i	$0.833141\pi$
$3$	−2.39074	−1.38030	−0.690148	−	0.723668i	$-0.742455\pi$
$3$	−2.39074	−1.38030	−0.690148	+	0.723668i	$0.742455\pi$
$4$	3.99581	1.99791
$5$	−0.961081	−0.429808	−0.214904	−	0.976635i	$-0.568944\pi$
$5$	−0.961081	−0.429808	−0.214904	+	0.976635i	$0.568944\pi$
$6$	5.85406	2.38991
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−4.88702	−1.72782
$9$	2.71565	0.905217
$10$	2.35334	0.744190
$11$	−6.49032	−1.95691	−0.978453	−	0.206471i	$-0.933802\pi$
$11$	−6.49032	−1.95691	−0.978453	+	0.206471i	$0.933802\pi$
$12$	−9.55296	−2.75770
$13$	−6.00183	−1.66461	−0.832305	−	0.554318i	$-0.812979\pi$
$13$	−6.00183	−1.66461	−0.832305	+	0.554318i	$0.812979\pi$
$14$	2.44864	0.654425
$15$	2.29770	0.593263
$16$	3.97491	0.993727
$17$	−1.46964	−0.356439	−0.178220	−	0.983991i	$-0.557034\pi$
$17$	−1.46964	−0.356439	−0.178220	+	0.983991i	$0.557034\pi$
$18$	−6.64964	−1.56733
$19$	−4.74615	−1.08884	−0.544421	−	0.838812i	$-0.683250\pi$
$19$	−4.74615	−1.08884	−0.544421	+	0.838812i	$0.683250\pi$
$20$	−3.84030	−0.858717
$21$	2.39074	0.521703
$22$	15.8924	3.38828
$23$	−0.0229005	−0.00477508	−0.00238754	−	0.999997i	$-0.500760\pi$
$23$	−0.0229005	−0.00477508	−0.00238754	+	0.999997i	$0.500760\pi$
$24$	11.6836	2.38491
$25$	−4.07632	−0.815265
$26$	14.6963	2.88218
$27$	0.679808	0.130829
$28$	−3.99581	−0.755138
$29$	1.53143	0.284380	0.142190	−	0.989839i	$-0.454586\pi$
$29$	1.53143	0.284380	0.142190	+	0.989839i	$0.454586\pi$
$30$	−5.62622	−1.02720
$31$	−7.07998	−1.27160	−0.635801	−	0.771853i	$-0.719330\pi$
$31$	−7.07998	−1.27160	−0.635801	+	0.771853i	$0.719330\pi$
$32$	0.0409495	0.00723892
$33$	15.5167	2.70111
$34$	3.59860	0.617155
$35$	0.961081	0.162452
$36$	10.8512	1.80854
$37$	3.28981	0.540841	0.270421	−	0.962742i	$-0.412837\pi$
$37$	3.28981	0.540841	0.270421	+	0.962742i	$0.412837\pi$
$38$	11.6216	1.88527
$39$	14.3488	2.29765
$40$	4.69682	0.742633
$41$	5.38315	0.840707	0.420353	−	0.907361i	$-0.361906\pi$
$41$	5.38315	0.840707	0.420353	+	0.907361i	$0.361906\pi$
$42$	−5.85406	−0.903301
$43$	6.72181	1.02507	0.512533	−	0.858667i	$-0.328707\pi$
$43$	6.72181	1.02507	0.512533	+	0.858667i	$0.328707\pi$
$44$	−25.9341	−3.90972
$45$	−2.60996	−0.389070
$46$	0.0560749	0.00826779
$47$	0.369915	0.0539576	0.0269788	−	0.999636i	$-0.491411\pi$
$47$	0.369915	0.0539576	0.0269788	+	0.999636i	$0.491411\pi$
$48$	−9.50298	−1.37164
$49$	1.00000	0.142857
$50$	9.98143	1.41159
$51$	3.51352	0.491991
$52$	−23.9822	−3.32574
$53$	−1.08018	−0.148374	−0.0741868	−	0.997244i	$-0.523636\pi$
$53$	−1.08018	−0.148374	−0.0741868	+	0.997244i	$0.523636\pi$
$54$	−1.66460	−0.226524
$55$	6.23772	0.841094
$56$	4.88702	0.653056
$57$	11.3468	1.50292
$58$	−3.74993	−0.492389
$59$	5.19741	0.676645	0.338322	−	0.941030i	$-0.390141\pi$
$59$	5.19741	0.676645	0.338322	+	0.941030i	$0.390141\pi$
$60$	9.18117	1.18528
$61$	7.25181	0.928499	0.464249	−	0.885704i	$-0.346324\pi$
$61$	7.25181	0.928499	0.464249	+	0.885704i	$0.346324\pi$
$62$	17.3363	2.20171
$63$	−2.71565	−0.342140
$64$	−8.05008	−1.00626
$65$	5.76825	0.715463
$66$	−37.9947	−4.67683
$67$	14.1902	1.73361	0.866807	−	0.498644i	$-0.166168\pi$
$67$	14.1902	1.73361	0.866807	+	0.498644i	$0.166168\pi$
$68$	−5.87239	−0.712132
$69$	0.0547491	0.00659102
$70$	−2.35334	−0.281277
$71$	3.74629	0.444603	0.222301	−	0.974978i	$-0.428643\pi$
$71$	3.74629	0.444603	0.222301	+	0.974978i	$0.428643\pi$
$72$	−13.2714	−1.56405
$73$	4.89573	0.573002	0.286501	−	0.958080i	$-0.407508\pi$
$73$	4.89573	0.573002	0.286501	+	0.958080i	$0.407508\pi$
$74$	−8.05554	−0.936437
$75$	9.74544	1.12531
$76$	−18.9647	−2.17540
$77$	6.49032	0.739641
$78$	−35.1351	−3.97826
$79$	−11.9070	−1.33964	−0.669819	−	0.742525i	$-0.733628\pi$
$79$	−11.9070	−1.33964	−0.669819	+	0.742525i	$0.733628\pi$
$80$	−3.82021	−0.427112
$81$	−9.77220	−1.08580
$82$	−13.1814	−1.45564
$83$	0.272919	0.0299567	0.0149784	−	0.999888i	$-0.495232\pi$
$83$	0.272919	0.0299567	0.0149784	+	0.999888i	$0.495232\pi$
$84$	9.55296	1.04231
$85$	1.41244	0.153201
$86$	−16.4593	−1.77485
$87$	−3.66127	−0.392529
$88$	31.7183	3.38119
$89$	2.33883	0.247916	0.123958	−	0.992287i	$-0.460441\pi$
$89$	2.33883	0.247916	0.123958	+	0.992287i	$0.460441\pi$
$90$	6.39084	0.673653
$91$	6.00183	0.629163
$92$	−0.0915060	−0.00954016
$93$	16.9264	1.75519
$94$	−0.905786	−0.0934247
$95$	4.56143	0.467993
$96$	−0.0978997	−0.00999184
$97$	1.22106	0.123979	0.0619897	−	0.998077i	$-0.480255\pi$
$97$	1.22106	0.123979	0.0619897	+	0.998077i	$0.480255\pi$
$98$	−2.44864	−0.247350
$99$	−17.6254	−1.77142
$100$	−16.2882	−1.62882
$101$	1.80931	0.180033	0.0900166	−	0.995940i	$-0.471308\pi$
$101$	1.80931	0.180033	0.0900166	+	0.995940i	$0.471308\pi$
$102$	−8.60333	−0.851857
$103$	−15.5083	−1.52808	−0.764040	−	0.645169i	$-0.776787\pi$
$103$	−15.5083	−1.52808	−0.764040	+	0.645169i	$0.776787\pi$
$104$	29.3311	2.87615
$105$	−2.29770	−0.224232
$106$	2.64496	0.256901
$107$	8.33774	0.806039	0.403020	−	0.915191i	$-0.367961\pi$
$107$	8.33774	0.806039	0.403020	+	0.915191i	$0.367961\pi$
$108$	2.71639	0.261384
$109$	−1.66941	−0.159901	−0.0799504	−	0.996799i	$-0.525476\pi$
$109$	−1.66941	−0.159901	−0.0799504	+	0.996799i	$0.525476\pi$
$110$	−15.2739	−1.45631
$111$	−7.86508	−0.746521
$112$	−3.97491	−0.375593
$113$	−17.1929	−1.61737	−0.808685	−	0.588242i	$-0.799820\pi$
$113$	−17.1929	−1.61737	−0.808685	+	0.588242i	$0.799820\pi$
$114$	−27.7842	−2.60223
$115$	0.0220092	0.00205237
$116$	6.11933	0.568166
$117$	−16.2989	−1.50683
$118$	−12.7266	−1.17157
$119$	1.46964	0.134721
$120$	−11.2289	−1.02505
$121$	31.1243	2.82948
$122$	−17.7570	−1.60765
$123$	−12.8697	−1.16042
$124$	−28.2903	−2.54054
$125$	8.72308	0.780216
$126$	6.64964	0.592397
$127$	2.83526	0.251589	0.125794	−	0.992056i	$-0.459852\pi$
$127$	2.83526	0.251589	0.125794	+	0.992056i	$0.459852\pi$
$128$	19.6298	1.73505
$129$	−16.0701	−1.41490
$130$	−14.1243	−1.23879
$131$	−10.4213	−0.910514	−0.455257	−	0.890360i	$-0.650453\pi$
$131$	−10.4213	−0.910514	−0.455257	+	0.890360i	$0.650453\pi$
$132$	62.0018	5.39656
$133$	4.74615	0.411543
$134$	−34.7467	−3.00166
$135$	−0.653350	−0.0562314
$136$	7.18214	0.615864
$137$	5.51808	0.471441	0.235721	−	0.971821i	$-0.424255\pi$
$137$	5.51808	0.471441	0.235721	+	0.971821i	$0.424255\pi$
$138$	−0.134061	−0.0114120
$139$	−10.8715	−0.922108	−0.461054	−	0.887372i	$-0.652529\pi$
$139$	−10.8715	−0.922108	−0.461054	+	0.887372i	$0.652529\pi$
$140$	3.84030	0.324565
$141$	−0.884370	−0.0744774
$142$	−9.17329	−0.769806
$143$	38.9538	3.25748
$144$	10.7945	0.899538
$145$	−1.47183	−0.122229
$146$	−11.9879	−0.992123
$147$	−2.39074	−0.197185
$148$	13.1455	1.08055
$149$	6.73060	0.551392	0.275696	−	0.961245i	$-0.411092\pi$
$149$	6.73060	0.551392	0.275696	+	0.961245i	$0.411092\pi$
$150$	−23.8630	−1.94841
$151$	−18.3564	−1.49382	−0.746910	−	0.664925i	$-0.768464\pi$
$151$	−18.3564	−1.49382	−0.746910	+	0.664925i	$0.768464\pi$
$152$	23.1945	1.88132
$153$	−3.99102	−0.322655
$154$	−15.8924	−1.28065
$155$	6.80443	0.546545
$156$	57.3353	4.59050
$157$	−4.73165	−0.377627	−0.188813	−	0.982013i	$-0.560464\pi$
$157$	−4.73165	−0.377627	−0.188813	+	0.982013i	$0.560464\pi$
$158$	29.1558	2.31951
$159$	2.58242	0.204800
$160$	−0.0393558	−0.00311135
$161$	0.0229005	0.00180481
$162$	23.9285	1.88000
$163$	8.12064	0.636058	0.318029	−	0.948081i	$-0.396979\pi$
$163$	8.12064	0.636058	0.318029	+	0.948081i	$0.396979\pi$
$164$	21.5101	1.67965
$165$	−14.9128	−1.16096
$166$	−0.668278	−0.0518685
$167$	2.87798	0.222705	0.111352	−	0.993781i	$-0.464482\pi$
$167$	2.87798	0.222705	0.111352	+	0.993781i	$0.464482\pi$
$168$	−11.6836	−0.901410
$169$	23.0220	1.77092
$170$	−3.45855	−0.265258
$171$	−12.8889	−0.985637
$172$	26.8591	2.04799
$173$	26.1384	1.98727	0.993635	−	0.112651i	$-0.0359342\pi$
$173$	26.1384	1.98727	0.993635	+	0.112651i	$0.0359342\pi$
$174$	8.96511	0.679643
$175$	4.07632	0.308141
$176$	−25.7984	−1.94463
$177$	−12.4257	−0.933970
$178$	−5.72695	−0.429253
$179$	−9.27266	−0.693071	−0.346536	−	0.938037i	$-0.612642\pi$
$179$	−9.27266	−0.693071	−0.346536	+	0.938037i	$0.612642\pi$
$180$	−10.4289	−0.777325
$181$	−3.58624	−0.266563	−0.133282	−	0.991078i	$-0.542551\pi$
$181$	−3.58624	−0.266563	−0.133282	+	0.991078i	$0.542551\pi$
$182$	−14.6963	−1.08936
$183$	−17.3372	−1.28160
$184$	0.111915	0.00825049
$185$	−3.16177	−0.232458
$186$	−41.4466	−3.03901
$187$	9.53841	0.697518
$188$	1.47811	0.107802
$189$	−0.679808	−0.0494488
$190$	−11.1693	−0.810305
$191$	18.7285	1.35515	0.677574	−	0.735454i	$-0.263031\pi$
$191$	18.7285	1.35515	0.677574	+	0.735454i	$0.263031\pi$
$192$	19.2457	1.38894
$193$	−19.8636	−1.42981	−0.714905	−	0.699221i	$-0.753530\pi$
$193$	−19.8636	−1.42981	−0.714905	+	0.699221i	$0.753530\pi$
$194$	−2.98992	−0.214664
$195$	−13.7904	−0.987551
$196$	3.99581	0.285415
$197$	9.05130	0.644878	0.322439	−	0.946590i	$-0.395497\pi$
$197$	9.05130	0.644878	0.322439	+	0.946590i	$0.395497\pi$
$198$	43.1583	3.06712
$199$	−15.5490	−1.10224	−0.551121	−	0.834425i	$-0.685800\pi$
$199$	−15.5490	−1.10224	−0.551121	+	0.834425i	$0.685800\pi$
$200$	19.9211	1.40863
$201$	−33.9252	−2.39290
$202$	−4.43034	−0.311718
$203$	−1.53143	−0.107486
$204$	14.0394	0.982953
$205$	−5.17364	−0.361343
$206$	37.9742	2.64579
$207$	−0.0621897	−0.00432248
$208$	−23.8567	−1.65417
$209$	30.8040	2.13076
$210$	5.62622	0.388246
$211$	13.3285	0.917572	0.458786	−	0.888547i	$-0.348284\pi$
$211$	13.3285	0.917572	0.458786	+	0.888547i	$0.348284\pi$
$212$	−4.31618	−0.296437
$213$	−8.95641	−0.613683
$214$	−20.4161	−1.39561
$215$	−6.46020	−0.440582
$216$	−3.32224	−0.226050
$217$	7.07998	0.480620
$218$	4.08779	0.276860
$219$	−11.7044	−0.790913
$220$	24.9248	1.68043
$221$	8.82051	0.593332
$222$	19.2587	1.29256
$223$	4.58677	0.307153	0.153576	−	0.988137i	$-0.450921\pi$
$223$	4.58677	0.307153	0.153576	+	0.988137i	$0.450921\pi$
$224$	−0.0409495	−0.00273605
$225$	−11.0699	−0.737991
$226$	42.0991	2.80039
$227$	7.66466	0.508722	0.254361	−	0.967109i	$-0.418135\pi$
$227$	7.66466	0.508722	0.254361	+	0.967109i	$0.418135\pi$
$228$	45.3398	3.00270
$229$	9.62462	0.636013	0.318006	−	0.948089i	$-0.396987\pi$
$229$	9.62462	0.636013	0.318006	+	0.948089i	$0.396987\pi$
$230$	−0.0538925	−0.00355357
$231$	−15.5167	−1.02092
$232$	−7.48416	−0.491359
$233$	22.7828	1.49255	0.746276	−	0.665637i	$-0.231840\pi$
$233$	22.7828	1.49255	0.746276	+	0.665637i	$0.231840\pi$
$234$	39.9100	2.60900
$235$	−0.355518	−0.0231914
$236$	20.7679	1.35187
$237$	28.4665	1.84910
$238$	−3.59860	−0.233263
$239$	10.5256	0.680845	0.340423	−	0.940272i	$-0.389430\pi$
$239$	10.5256	0.680845	0.340423	+	0.940272i	$0.389430\pi$
$240$	9.13313	0.589541
$241$	−11.8581	−0.763849	−0.381925	−	0.924194i	$-0.624739\pi$
$241$	−11.8581	−0.763849	−0.381925	+	0.924194i	$0.624739\pi$
$242$	−76.2120	−4.89909
$243$	21.3234	1.36790
$244$	28.9769	1.85505
$245$	−0.961081	−0.0614012
$246$	31.5133	2.00921
$247$	28.4856	1.81249
$248$	34.6000	2.19710
$249$	−0.652478	−0.0413491
$250$	−21.3596	−1.35090
$251$	0.413897	0.0261250	0.0130625	−	0.999915i	$-0.495842\pi$
$251$	0.413897	0.0261250	0.0130625	+	0.999915i	$0.495842\pi$
$252$	−10.8512	−0.683563
$253$	0.148631	0.00934438
$254$	−6.94252	−0.435613
$255$	−3.37678	−0.211462
$256$	−31.9661	−1.99788
$257$	2.83755	0.177001	0.0885007	−	0.996076i	$-0.471792\pi$
$257$	2.83755	0.177001	0.0885007	+	0.996076i	$0.471792\pi$
$258$	39.3499	2.44982
$259$	−3.28981	−0.204419
$260$	23.0488	1.42943
$261$	4.15884	0.257426
$262$	25.5180	1.57651
$263$	−0.210463	−0.0129777	−0.00648885	−	0.999979i	$-0.502065\pi$
$263$	−0.210463	−0.0129777	−0.00648885	+	0.999979i	$0.502065\pi$
$264$	−75.8304	−4.66704
$265$	1.03814	0.0637722
$266$	−11.6216	−0.712565
$267$	−5.59155	−0.342197
$268$	56.7016	3.46360
$269$	−30.3879	−1.85278	−0.926391	−	0.376563i	$-0.877106\pi$
$269$	−30.3879	−1.85278	−0.926391	+	0.376563i	$0.877106\pi$
$270$	1.59982	0.0973617
$271$	−13.3265	−0.809529	−0.404765	−	0.914421i	$-0.632647\pi$
$271$	−13.3265	−0.809529	−0.404765	+	0.914421i	$0.632647\pi$
$272$	−5.84167	−0.354203
$273$	−14.3488	−0.868431
$274$	−13.5118	−0.816275
$275$	26.4567	1.59540
$276$	0.218767	0.0131682
$277$	−0.549908	−0.0330408	−0.0165204	−	0.999864i	$-0.505259\pi$
$277$	−0.549908	−0.0330408	−0.0165204	+	0.999864i	$0.505259\pi$
$278$	26.6203	1.59658
$279$	−19.2267	−1.15108
$280$	−4.69682	−0.280689
$281$	4.94231	0.294834	0.147417	−	0.989074i	$-0.452904\pi$
$281$	4.94231	0.294834	0.147417	+	0.989074i	$0.452904\pi$
$282$	2.16550	0.128954
$283$	−5.63476	−0.334952	−0.167476	−	0.985876i	$-0.553562\pi$
$283$	−5.63476	−0.334952	−0.167476	+	0.985876i	$0.553562\pi$
$284$	14.9695	0.888275
$285$	−10.9052	−0.645969
$286$	−95.3837	−5.64016
$287$	−5.38315	−0.317757
$288$	0.111204	0.00655279
$289$	−14.8402	−0.872951
$290$	3.60398	0.211633
$291$	−2.91923	−0.171128
$292$	19.5624	1.14481
$293$	−14.3798	−0.840076	−0.420038	−	0.907507i	$-0.637983\pi$
$293$	−14.3798	−0.840076	−0.420038	+	0.907507i	$0.637983\pi$
$294$	5.85406	0.341416
$295$	−4.99513	−0.290828
$296$	−16.0774	−0.934478
$297$	−4.41217	−0.256020
$298$	−16.4808	−0.954706
$299$	0.137445	0.00794864
$300$	38.9410	2.24826
$301$	−6.72181	−0.387439
$302$	44.9481	2.58647
$303$	−4.32560	−0.248499
$304$	−18.8655	−1.08201
$305$	−6.96957	−0.399077
$306$	9.77255	0.558659
$307$	−17.9705	−1.02563	−0.512816	−	0.858499i	$-0.671398\pi$
$307$	−17.9705	−1.02563	−0.512816	+	0.858499i	$0.671398\pi$
$308$	25.9341	1.47773
$309$	37.0764	2.10920
$310$	−16.6616	−0.946314
$311$	−3.51930	−0.199561	−0.0997806	−	0.995009i	$-0.531814\pi$
$311$	−3.51930	−0.199561	−0.0997806	+	0.995009i	$0.531814\pi$
$312$	−70.1231	−3.96994
$313$	−4.61679	−0.260956	−0.130478	−	0.991451i	$-0.541651\pi$
$313$	−4.61679	−0.260956	−0.130478	+	0.991451i	$0.541651\pi$
$314$	11.5861	0.653841
$315$	2.60996	0.147055
$316$	−47.5780	−2.67647
$317$	27.4041	1.53917	0.769584	−	0.638546i	$-0.220464\pi$
$317$	27.4041	1.53917	0.769584	+	0.638546i	$0.220464\pi$
$318$	−6.32341	−0.354599
$319$	−9.93950	−0.556505
$320$	7.73678	0.432499
$321$	−19.9334	−1.11257
$322$	−0.0560749	−0.00312493
$323$	6.97511	0.388106
$324$	−39.0479	−2.16933
$325$	24.4654	1.35710
$326$	−19.8845	−1.10130
$327$	3.99114	0.220711
$328$	−26.3076	−1.45259
$329$	−0.369915	−0.0203940
$330$	36.5160	2.01014
$331$	21.7317	1.19448	0.597242	−	0.802061i	$-0.296263\pi$
$331$	21.7317	1.19448	0.597242	+	0.802061i	$0.296263\pi$
$332$	1.09053	0.0598507
$333$	8.93397	0.489578
$334$	−7.04712	−0.385601
$335$	−13.6380	−0.745122
$336$	9.50298	0.518430
$337$	35.9458	1.95809	0.979045	−	0.203644i	$-0.0652784\pi$
$337$	35.9458	1.95809	0.979045	+	0.203644i	$0.0652784\pi$
$338$	−56.3725	−3.06626
$339$	41.1037	2.23245
$340$	5.64384	0.306080
$341$	45.9513	2.48840
$342$	31.5602	1.70658
$343$	−1.00000	−0.0539949
$344$	−32.8496	−1.77113
$345$	−0.0526183	−0.00283288
$346$	−64.0035	−3.44085
$347$	18.3914	0.987301	0.493651	−	0.869660i	$-0.335662\pi$
$347$	18.3914	0.987301	0.493651	+	0.869660i	$0.335662\pi$
$348$	−14.6297	−0.784237
$349$	−12.4141	−0.664512	−0.332256	−	0.943189i	$-0.607810\pi$
$349$	−12.4141	−0.664512	−0.332256	+	0.943189i	$0.607810\pi$
$350$	−9.98143	−0.533530
$351$	−4.08010	−0.217779
$352$	−0.265775	−0.0141659
$353$	23.9489	1.27467	0.637336	−	0.770586i	$-0.280036\pi$
$353$	23.9489	1.27467	0.637336	+	0.770586i	$0.280036\pi$
$354$	30.4259	1.61712
$355$	−3.60049	−0.191094
$356$	9.34555	0.495313
$357$	−3.51352	−0.185955
$358$	22.7054	1.20002
$359$	−31.2857	−1.65120	−0.825598	−	0.564258i	$-0.809162\pi$
$359$	−31.2857	−1.65120	−0.825598	+	0.564258i	$0.809162\pi$
$360$	12.7549	0.672244
$361$	3.52592	0.185575
$362$	8.78139	0.461540
$363$	−74.4101	−3.90552
$364$	23.9822	1.25701
$365$	−4.70520	−0.246281
$366$	42.4525	2.21903
$367$	−6.58042	−0.343495	−0.171747	−	0.985141i	$-0.554941\pi$
$367$	−6.58042	−0.343495	−0.171747	+	0.985141i	$0.554941\pi$
$368$	−0.0910272	−0.00474512
$369$	14.6187	0.761022
$370$	7.74202	0.402489
$371$	1.08018	0.0560800
$372$	67.6348	3.50670
$373$	−17.4590	−0.903993	−0.451997	−	0.892020i	$-0.649288\pi$
$373$	−17.4590	−0.903993	−0.451997	+	0.892020i	$0.649288\pi$
$374$	−23.3561	−1.20771
$375$	−20.8546	−1.07693
$376$	−1.80778	−0.0932292
$377$	−9.19142	−0.473382
$378$	1.66460	0.0856179
$379$	−7.23588	−0.371682	−0.185841	−	0.982580i	$-0.559501\pi$
$379$	−7.23588	−0.371682	−0.185841	+	0.982580i	$0.559501\pi$
$380$	18.2266	0.935007
$381$	−6.77838	−0.347267
$382$	−45.8593	−2.34637
$383$	10.9423	0.559124	0.279562	−	0.960128i	$-0.409811\pi$
$383$	10.9423	0.559124	0.279562	+	0.960128i	$0.409811\pi$
$384$	−46.9298	−2.39488
$385$	−6.23772	−0.317904
$386$	48.6386	2.47564
$387$	18.2541	0.927907
$388$	4.87912	0.247700
$389$	25.4621	1.29098	0.645491	−	0.763768i	$-0.276653\pi$
$389$	25.4621	1.29098	0.645491	+	0.763768i	$0.276653\pi$
$390$	33.7676	1.70989
$391$	0.0336554	0.00170202
$392$	−4.88702	−0.246832
$393$	24.9147	1.25678
$394$	−22.1633	−1.11657
$395$	11.4435	0.575787
$396$	−70.4280	−3.53914
$397$	−27.7107	−1.39076	−0.695379	−	0.718643i	$-0.744764\pi$
$397$	−27.7107	−1.39076	−0.695379	+	0.718643i	$0.744764\pi$
$398$	38.0739	1.90847
$399$	−11.3468	−0.568051
$400$	−16.2030	−0.810150
$401$	−2.24864	−0.112292	−0.0561458	−	0.998423i	$-0.517881\pi$
$401$	−2.24864	−0.112292	−0.0561458	+	0.998423i	$0.517881\pi$
$402$	83.0705	4.14318
$403$	42.4929	2.11672
$404$	7.22967	0.359690
$405$	9.39187	0.466686
$406$	3.74993	0.186106
$407$	−21.3519	−1.05837
$408$	−17.1707	−0.850074
$409$	2.27491	0.112487	0.0562435	−	0.998417i	$-0.482088\pi$
$409$	2.27491	0.112487	0.0562435	+	0.998417i	$0.482088\pi$
$410$	12.6684	0.625646
$411$	−13.1923	−0.650728
$412$	−61.9684	−3.05296
$413$	−5.19741	−0.255748
$414$	0.152280	0.00748414
$415$	−0.262297	−0.0128756
$416$	−0.245772	−0.0120500
$417$	25.9909	1.27278
$418$	−75.4278	−3.68930
$419$	−2.92385	−0.142839	−0.0714197	−	0.997446i	$-0.522753\pi$
$419$	−2.92385	−0.142839	−0.0714197	+	0.997446i	$0.522753\pi$
$420$	−9.18117	−0.447995
$421$	36.2170	1.76511	0.882553	−	0.470213i	$-0.155823\pi$
$421$	36.2170	1.76511	0.882553	+	0.470213i	$0.155823\pi$
$422$	−32.6366	−1.58873
$423$	1.00456	0.0488433
$424$	5.27885	0.256363
$425$	5.99071	0.290592
$426$	21.9310	1.06256
$427$	−7.25181	−0.350940
$428$	33.3160	1.61039
$429$	−93.1286	−4.49629
$430$	15.8187	0.762844
$431$	−22.8388	−1.10011	−0.550054	−	0.835129i	$-0.685393\pi$
$431$	−22.8388	−1.10011	−0.550054	+	0.835129i	$0.685393\pi$
$432$	2.70217	0.130008
$433$	17.0324	0.818524	0.409262	−	0.912417i	$-0.365786\pi$
$433$	17.0324	0.818524	0.409262	+	0.912417i	$0.365786\pi$
$434$	−17.3363	−0.832168
$435$	3.51877	0.168712
$436$	−6.67067	−0.319467
$437$	0.108689	0.00519930
$438$	28.6599	1.36942
$439$	3.69950	0.176567	0.0882836	−	0.996095i	$-0.471862\pi$
$439$	3.69950	0.176567	0.0882836	+	0.996095i	$0.471862\pi$
$440$	−30.4839	−1.45326
$441$	2.71565	0.129317
$442$	−21.5982	−1.02732
$443$	13.6107	0.646662	0.323331	−	0.946286i	$-0.395197\pi$
$443$	13.6107	0.646662	0.323331	+	0.946286i	$0.395197\pi$
$444$	−31.4274	−1.49148
$445$	−2.24781	−0.106556
$446$	−11.2313	−0.531819
$447$	−16.0911	−0.761084
$448$	8.05008	0.380331
$449$	24.3902	1.15105	0.575523	−	0.817786i	$-0.304799\pi$
$449$	24.3902	1.15105	0.575523	+	0.817786i	$0.304799\pi$
$450$	27.1061	1.27779
$451$	−34.9384	−1.64518
$452$	−68.6996	−3.23136
$453$	43.8854	2.06191
$454$	−18.7680	−0.880824
$455$	−5.76825	−0.270420
$456$	−55.4522	−2.59679
$457$	16.2235	0.758904	0.379452	−	0.925211i	$-0.376112\pi$
$457$	16.2235	0.758904	0.379452	+	0.925211i	$0.376112\pi$
$458$	−23.5672	−1.10122
$459$	−0.999070	−0.0466326
$460$	0.0879447	0.00410044
$461$	−3.84983	−0.179305	−0.0896523	−	0.995973i	$-0.528576\pi$
$461$	−3.84983	−0.179305	−0.0896523	+	0.995973i	$0.528576\pi$
$462$	37.9947	1.76767
$463$	−7.75659	−0.360479	−0.180240	−	0.983623i	$-0.557687\pi$
$463$	−7.75659	−0.360479	−0.180240	+	0.983623i	$0.557687\pi$
$464$	6.08731	0.282596
$465$	−16.2676	−0.754394
$466$	−55.7868	−2.58427
$467$	−16.2524	−0.752070	−0.376035	−	0.926605i	$-0.622713\pi$
$467$	−16.2524	−0.752070	−0.376035	+	0.926605i	$0.622713\pi$
$468$	−65.1273	−3.01051
$469$	−14.1902	−0.655244
$470$	0.870533	0.0401547
$471$	11.3122	0.521237
$472$	−25.3999	−1.16912
$473$	−43.6267	−2.00596
$474$	−69.7040	−3.20161
$475$	19.3468	0.887694
$476$	5.87239	0.269161
$477$	−2.93338	−0.134310
$478$	−25.7734	−1.17885
$479$	−35.2849	−1.61221	−0.806104	−	0.591774i	$-0.798428\pi$
$479$	−35.2849	−1.61221	−0.806104	+	0.591774i	$0.798428\pi$
$480$	0.0940895	0.00429458
$481$	−19.7449	−0.900289
$482$	29.0362	1.32256
$483$	−0.0547491	−0.00249117
$484$	124.367	5.65304
$485$	−1.17353	−0.0532874
$486$	−52.2132	−2.36844
$487$	−33.4845	−1.51733	−0.758664	−	0.651482i	$-0.774147\pi$
$487$	−33.4845	−1.51733	−0.758664	+	0.651482i	$0.774147\pi$
$488$	−35.4398	−1.60428
$489$	−19.4144	−0.877948
$490$	2.35334	0.106313
$491$	19.1734	0.865283	0.432641	−	0.901566i	$-0.357582\pi$
$491$	19.1734	0.865283	0.432641	+	0.901566i	$0.357582\pi$
$492$	−51.4250	−2.31842
$493$	−2.25065	−0.101364
$494$	−69.7508	−3.13824
$495$	16.9395	0.761373
$496$	−28.1423	−1.26362
$497$	−3.74629	−0.168044
$498$	1.59768	0.0715938
$499$	−27.1237	−1.21423	−0.607113	−	0.794616i	$-0.707672\pi$
$499$	−27.1237	−1.21423	−0.607113	+	0.794616i	$0.707672\pi$
$500$	34.8558	1.55880
$501$	−6.88051	−0.307399
$502$	−1.01348	−0.0452340
$503$	−17.0603	−0.760679	−0.380340	−	0.924847i	$-0.624193\pi$
$503$	−17.0603	−0.760679	−0.380340	+	0.924847i	$0.624193\pi$
$504$	13.2714	0.591157
$505$	−1.73889	−0.0773797
$506$	−0.363944	−0.0161793
$507$	−55.0397	−2.44440
$508$	11.3292	0.502651
$509$	−18.8976	−0.837620	−0.418810	−	0.908074i	$-0.637553\pi$
$509$	−18.8976	−0.837620	−0.418810	+	0.908074i	$0.637553\pi$
$510$	8.26850	0.366135
$511$	−4.89573	−0.216575
$512$	39.0137	1.72418
$513$	−3.22647	−0.142452
$514$	−6.94812	−0.306468
$515$	14.9047	0.656782
$516$	−64.2132	−2.82683
$517$	−2.40086	−0.105590
$518$	8.05554	0.353940
$519$	−62.4903	−2.74302
$520$	−28.1896	−1.23619
$521$	15.8707	0.695308	0.347654	−	0.937623i	$-0.386978\pi$
$521$	15.8707	0.695308	0.347654	+	0.937623i	$0.386978\pi$
$522$	−10.1835	−0.445719
$523$	−2.53761	−0.110962	−0.0554809	−	0.998460i	$-0.517669\pi$
$523$	−2.53761	−0.110962	−0.0554809	+	0.998460i	$0.517669\pi$
$524$	−41.6416	−1.81912
$525$	−9.74544	−0.425326
$526$	0.515347	0.0224702
$527$	10.4050	0.453249
$528$	61.6774	2.68416
$529$	−22.9995	−0.999977
$530$	−2.54202	−0.110418
$531$	14.1143	0.612510
$532$	18.9647	0.822225
$533$	−32.3088	−1.39945
$534$	13.6917	0.592496
$535$	−8.01324	−0.346442
$536$	−69.3480	−2.99538
$537$	22.1685	0.956643
$538$	74.4089	3.20799
$539$	−6.49032	−0.279558
$540$	−2.61067	−0.112345
$541$	4.89054	0.210261	0.105130	−	0.994458i	$-0.466474\pi$
$541$	4.89054	0.210261	0.105130	+	0.994458i	$0.466474\pi$
$542$	32.6318	1.40166
$543$	8.57377	0.367936
$544$	−0.0601808	−0.00258023
$545$	1.60444	0.0687267
$546$	35.1351	1.50364
$547$	−39.8645	−1.70448	−0.852242	−	0.523148i	$-0.824758\pi$
$547$	−39.8645	−1.70448	−0.852242	+	0.523148i	$0.824758\pi$
$548$	22.0492	0.941896
$549$	19.6934	0.840493
$550$	−64.7827	−2.76234
$551$	−7.26842	−0.309645
$552$	−0.267560	−0.0113881
$553$	11.9070	0.506335
$554$	1.34652	0.0572083
$555$	7.55898	0.320861
$556$	−43.4405	−1.84229
$557$	−39.7098	−1.68256	−0.841278	−	0.540602i	$-0.818196\pi$
$557$	−39.7098	−1.68256	−0.841278	+	0.540602i	$0.818196\pi$
$558$	47.0793	1.99303
$559$	−40.3432	−1.70634
$560$	3.82021	0.161433
$561$	−22.8039	−0.962781
$562$	−12.1019	−0.510489
$563$	34.4400	1.45147	0.725737	−	0.687972i	$-0.241499\pi$
$563$	34.4400	1.45147	0.725737	+	0.687972i	$0.241499\pi$
$564$	−3.53378	−0.148799
$565$	16.5237	0.695159
$566$	13.7975	0.579951
$567$	9.77220	0.410394
$568$	−18.3082	−0.768195
$569$	−28.2937	−1.18614	−0.593068	−	0.805153i	$-0.702083\pi$
$569$	−28.2937	−1.18614	−0.593068	+	0.805153i	$0.702083\pi$
$570$	26.7029	1.11846
$571$	17.8763	0.748100	0.374050	−	0.927409i	$-0.377969\pi$
$571$	17.8763	0.748100	0.374050	+	0.927409i	$0.377969\pi$
$572$	155.652	6.50815
$573$	−44.7751	−1.87051
$574$	13.1814	0.550180
$575$	0.0933497	0.00389295
$576$	−21.8612	−0.910884
$577$	−8.09239	−0.336891	−0.168445	−	0.985711i	$-0.553875\pi$
$577$	−8.09239	−0.336891	−0.168445	+	0.985711i	$0.553875\pi$
$578$	36.3382	1.51147
$579$	47.4887	1.97356
$580$	−5.88117	−0.244202
$581$	−0.272919	−0.0113226
$582$	7.14813	0.296300
$583$	7.01069	0.290353
$584$	−23.9256	−0.990047
$585$	15.6645	0.647649
$586$	35.2108	1.45455
$587$	41.6016	1.71708	0.858541	−	0.512745i	$-0.171371\pi$
$587$	41.6016	1.71708	0.858541	+	0.512745i	$0.171371\pi$
$588$	−9.55296	−0.393958
$589$	33.6026	1.38457
$590$	12.2312	0.503553
$591$	−21.6393	−0.890123
$592$	13.0767	0.537448
$593$	−2.98536	−0.122594	−0.0612969	−	0.998120i	$-0.519524\pi$
$593$	−2.98536	−0.122594	−0.0612969	+	0.998120i	$0.519524\pi$
$594$	10.8038	0.443285
$595$	−1.41244	−0.0579043
$596$	26.8942	1.10163
$597$	37.1737	1.52142
$598$	−0.336552	−0.0137626
$599$	−15.0504	−0.614945	−0.307472	−	0.951557i	$-0.599483\pi$
$599$	−15.0504	−0.614945	−0.307472	+	0.951557i	$0.599483\pi$
$600$	−47.6262	−1.94433
$601$	32.0792	1.30854	0.654268	−	0.756263i	$-0.272977\pi$
$601$	32.0792	1.30854	0.654268	+	0.756263i	$0.272977\pi$
$602$	16.4593	0.670830
$603$	38.5357	1.56930
$604$	−73.3487	−2.98451
$605$	−29.9129	−1.21613
$606$	10.5918	0.430263
$607$	39.9522	1.62161	0.810806	−	0.585315i	$-0.199029\pi$
$607$	39.9522	1.62161	0.810806	+	0.585315i	$0.199029\pi$
$608$	−0.194352	−0.00788203
$609$	3.66127	0.148362
$610$	17.0659	0.690980
$611$	−2.22017	−0.0898183
$612$	−15.9474	−0.644634
$613$	−20.5265	−0.829059	−0.414530	−	0.910036i	$-0.636054\pi$
$613$	−20.5265	−0.829059	−0.414530	+	0.910036i	$0.636054\pi$
$614$	44.0032	1.77583
$615$	12.3688	0.498760
$616$	−31.7183	−1.27797
$617$	13.2114	0.531870	0.265935	−	0.963991i	$-0.414319\pi$
$617$	13.2114	0.531870	0.265935	+	0.963991i	$0.414319\pi$
$618$	−90.7866	−3.65197
$619$	28.1742	1.13242	0.566208	−	0.824262i	$-0.308410\pi$
$619$	28.1742	1.13242	0.566208	+	0.824262i	$0.308410\pi$
$620$	27.1892	1.09195
$621$	−0.0155679	−0.000624719 0
$622$	8.61749	0.345530
$623$	−2.33883	−0.0937034
$624$	57.0353	2.28324
$625$	11.9980	0.479921
$626$	11.3048	0.451832
$627$	−73.6445	−2.94108
$628$	−18.9068	−0.754464
$629$	−4.83482	−0.192777
$630$	−6.39084	−0.254617
$631$	41.6960	1.65989	0.829946	−	0.557843i	$-0.188371\pi$
$631$	41.6960	1.65989	0.829946	+	0.557843i	$0.188371\pi$
$632$	58.1896	2.31466
$633$	−31.8650	−1.26652
$634$	−67.1027	−2.66499
$635$	−2.72491	−0.108135
$636$	10.3189	0.409170
$637$	−6.00183	−0.237801
$638$	24.3382	0.963559
$639$	10.1736	0.402462
$640$	−18.8658	−0.745738
$641$	−1.72782	−0.0682450	−0.0341225	−	0.999418i	$-0.510864\pi$
$641$	−1.72782	−0.0682450	−0.0341225	+	0.999418i	$0.510864\pi$
$642$	48.8096	1.92636
$643$	−5.74081	−0.226395	−0.113198	−	0.993572i	$-0.536109\pi$
$643$	−5.74081	−0.226395	−0.113198	+	0.993572i	$0.536109\pi$
$644$	0.0915060	0.00360584
$645$	15.4447	0.608134
$646$	−17.0795	−0.671984
$647$	45.3195	1.78169	0.890847	−	0.454303i	$-0.150112\pi$
$647$	45.3195	1.78169	0.890847	+	0.454303i	$0.150112\pi$
$648$	47.7569	1.87607
$649$	−33.7329	−1.32413
$650$	−59.9069	−2.34974
$651$	−16.9264	−0.663398
$652$	32.4486	1.27078
$653$	34.2389	1.33987	0.669936	−	0.742419i	$-0.266321\pi$
$653$	34.2389	1.33987	0.669936	+	0.742419i	$0.266321\pi$
$654$	−9.77284	−0.382148
$655$	10.0157	0.391347
$656$	21.3975	0.835432
$657$	13.2951	0.518691
$658$	0.905786	0.0353112
$659$	−49.1783	−1.91571	−0.957857	−	0.287246i	$-0.907260\pi$
$659$	−49.1783	−1.91571	−0.957857	+	0.287246i	$0.907260\pi$
$660$	−59.5887	−2.31949
$661$	43.8395	1.70516	0.852580	−	0.522597i	$-0.175037\pi$
$661$	43.8395	1.70516	0.852580	+	0.522597i	$0.175037\pi$
$662$	−53.2131	−2.06818
$663$	−21.0876	−0.818974
$664$	−1.33376	−0.0517599
$665$	−4.56143	−0.176885
$666$	−21.8760	−0.847679
$667$	−0.0350706	−0.00135794
$668$	11.4999	0.444944
$669$	−10.9658	−0.423962
$670$	33.3944	1.29014
$671$	−47.0666	−1.81698
$672$	0.0978997	0.00377656
$673$	41.6646	1.60605	0.803027	−	0.595943i	$-0.203222\pi$
$673$	41.6646	1.60605	0.803027	+	0.595943i	$0.203222\pi$
$674$	−88.0181	−3.39033
$675$	−2.77112	−0.106660
$676$	91.9917	3.53814
$677$	17.7319	0.681492	0.340746	−	0.940155i	$-0.389320\pi$
$677$	17.7319	0.681492	0.340746	+	0.940155i	$0.389320\pi$
$678$	−100.648	−3.86537
$679$	−1.22106	−0.0468598
$680$	−6.90262	−0.264703
$681$	−18.3242	−0.702186
$682$	−112.518	−4.30854
$683$	−23.1276	−0.884952	−0.442476	−	0.896780i	$-0.645900\pi$
$683$	−23.1276	−0.884952	−0.442476	+	0.896780i	$0.645900\pi$
$684$	−51.5016	−1.96921
$685$	−5.30332	−0.202629
$686$	2.44864	0.0934893
$687$	−23.0100	−0.877886
$688$	26.7186	1.01864
$689$	6.48304	0.246984
$690$	0.128843	0.00490497
$691$	−22.0412	−0.838485	−0.419243	−	0.907874i	$-0.637704\pi$
$691$	−22.0412	−0.838485	−0.419243	+	0.907874i	$0.637704\pi$
$692$	104.444	3.97038
$693$	17.6254	0.669535
$694$	−45.0338	−1.70946
$695$	10.4484	0.396330
$696$	17.8927	0.678221
$697$	−7.91127	−0.299661
$698$	30.3976	1.15057
$699$	−54.4678	−2.06016
$700$	16.2882	0.615637
$701$	36.8951	1.39351	0.696755	−	0.717310i	$-0.254627\pi$
$701$	36.8951	1.39351	0.696755	+	0.717310i	$0.254627\pi$
$702$	9.99066	0.377073
$703$	−15.6139	−0.588890
$704$	52.2476	1.96916
$705$	0.849951	0.0320110
$706$	−58.6422	−2.20703
$707$	−1.80931	−0.0680461
$708$	−49.6507	−1.86599
$709$	−3.02448	−0.113587	−0.0567934	−	0.998386i	$-0.518088\pi$
$709$	−3.02448	−0.113587	−0.0567934	+	0.998386i	$0.518088\pi$
$710$	8.81628	0.330869
$711$	−32.3351	−1.21266
$712$	−11.4299	−0.428355
$713$	0.162135	0.00607200
$714$	8.60333	0.321972
$715$	−37.4378	−1.40009
$716$	−37.0518	−1.38469
$717$	−25.1640	−0.939768
$718$	76.6073	2.85896
$719$	−36.1480	−1.34809	−0.674046	−	0.738689i	$-0.735445\pi$
$719$	−36.1480	−1.34809	−0.674046	+	0.738689i	$0.735445\pi$
$720$	−10.3743	−0.386629
$721$	15.5083	0.577560
$722$	−8.63369	−0.321313
$723$	28.3497	1.05434
$724$	−14.3299	−0.532568
$725$	−6.24262	−0.231845
$726$	182.203	6.76220
$727$	−40.3699	−1.49724	−0.748618	−	0.663001i	$-0.769282\pi$
$727$	−40.3699	−1.49724	−0.748618	+	0.663001i	$0.769282\pi$
$728$	−29.3311	−1.08708
$729$	−21.6621	−0.802301
$730$	11.5213	0.426423
$731$	−9.87862	−0.365374
$732$	−69.2763	−2.56052
$733$	28.8623	1.06605	0.533026	−	0.846099i	$-0.321055\pi$
$733$	28.8623	1.06605	0.533026	+	0.846099i	$0.321055\pi$
$734$	16.1130	0.594743
$735$	2.29770	0.0847518
$736$	−0.000937762 0	−3.45664e−5 0
$737$	−92.0992	−3.39252
$738$	−35.7960	−1.31767
$739$	25.9985	0.956371	0.478186	−	0.878259i	$-0.341295\pi$
$739$	25.9985	0.956371	0.478186	+	0.878259i	$0.341295\pi$
$740$	−12.6338	−0.464430
$741$	−68.1017	−2.50178
$742$	−2.64496	−0.0970995
$743$	35.9161	1.31763	0.658817	−	0.752303i	$-0.271057\pi$
$743$	35.9161	1.31763	0.658817	+	0.752303i	$0.271057\pi$
$744$	−82.7197	−3.03265
$745$	−6.46865	−0.236993
$746$	42.7507	1.56522
$747$	0.741152	0.0271173
$748$	38.1137	1.39358
$749$	−8.33774	−0.304654
$750$	51.0654	1.86464
$751$	−33.4699	−1.22133	−0.610667	−	0.791887i	$-0.709099\pi$
$751$	−33.4699	−1.22133	−0.610667	+	0.791887i	$0.709099\pi$
$752$	1.47038	0.0536191
$753$	−0.989521	−0.0360602
$754$	22.5064	0.819636
$755$	17.6420	0.642056
$756$	−2.71639	−0.0987940
$757$	3.84638	0.139799	0.0698995	−	0.997554i	$-0.477732\pi$
$757$	3.84638	0.139799	0.0698995	+	0.997554i	$0.477732\pi$
$758$	17.7180	0.643548
$759$	−0.355339	−0.0128980
$760$	−22.2918	−0.808609
$761$	34.5018	1.25069	0.625344	−	0.780349i	$-0.284959\pi$
$761$	34.5018	1.25069	0.625344	+	0.780349i	$0.284959\pi$
$762$	16.5978	0.601274
$763$	1.66941	0.0604368
$764$	74.8357	2.70746
$765$	3.83569	0.138680
$766$	−26.7936	−0.968094
$767$	−31.1940	−1.12635
$768$	76.4227	2.75767
$769$	27.6778	0.998087	0.499043	−	0.866577i	$-0.333685\pi$
$769$	27.6778	0.998087	0.499043	+	0.866577i	$0.333685\pi$
$770$	15.2739	0.550433
$771$	−6.78384	−0.244314
$772$	−79.3711	−2.85663
$773$	−2.37438	−0.0854006	−0.0427003	−	0.999088i	$-0.513596\pi$
$773$	−2.37438	−0.0854006	−0.0427003	+	0.999088i	$0.513596\pi$
$774$	−44.6976	−1.60662
$775$	28.8603	1.03669
$776$	−5.96733	−0.214215
$777$	7.86508	0.282158
$778$	−62.3475	−2.23527
$779$	−25.5492	−0.915396
$780$	−55.1039	−1.97303
$781$	−24.3146	−0.870045
$782$	−0.0824097	−0.00294696
$783$	1.04108	0.0372052
$784$	3.97491	0.141961
$785$	4.54750	0.162307
$786$	−61.0070	−2.17605
$787$	7.13463	0.254322	0.127161	−	0.991882i	$-0.459413\pi$
$787$	7.13463	0.254322	0.127161	+	0.991882i	$0.459413\pi$
$788$	36.1673	1.28841
$789$	0.503163	0.0179131
$790$	−28.0211	−0.996945
$791$	17.1929	0.611308
$792$	86.1359	3.06071
$793$	−43.5242	−1.54559
$794$	67.8533	2.40802
$795$	−2.48192	−0.0880245
$796$	−62.1311	−2.20218
$797$	−22.9216	−0.811924	−0.405962	−	0.913890i	$-0.633063\pi$
$797$	−22.9216	−0.811924	−0.405962	+	0.913890i	$0.633063\pi$
$798$	27.7842	0.983551
$799$	−0.543640	−0.0192326
$800$	−0.166923	−0.00590163
$801$	6.35146	0.224418
$802$	5.50610	0.194427
$803$	−31.7749	−1.12131
$804$	−135.559	−4.78079
$805$	−0.0220092	−0.000775722 0
$806$	−104.050	−3.66499
$807$	72.6496	2.55739
$808$	−8.84214	−0.311065
$809$	−49.7030	−1.74747	−0.873733	−	0.486406i	$-0.838307\pi$
$809$	−49.7030	−1.74747	−0.873733	+	0.486406i	$0.838307\pi$
$810$	−22.9973	−0.808041
$811$	−9.49901	−0.333555	−0.166778	−	0.985995i	$-0.553336\pi$
$811$	−9.49901	−0.333555	−0.166778	+	0.985995i	$0.553336\pi$
$812$	−6.11933	−0.214746
$813$	31.8603	1.11739
$814$	52.2830	1.83252
$815$	−7.80459	−0.273383
$816$	13.9659	0.488905
$817$	−31.9027	−1.11613
$818$	−5.57042	−0.194765
$819$	16.2989	0.569529
$820$	−20.6729	−0.721929
$821$	−3.01574	−0.105250	−0.0526251	−	0.998614i	$-0.516759\pi$
$821$	−3.01574	−0.105250	−0.0526251	+	0.998614i	$0.516759\pi$
$822$	32.3031	1.12670
$823$	−50.5907	−1.76348	−0.881741	−	0.471734i	$-0.843628\pi$
$823$	−50.5907	−1.76348	−0.881741	+	0.471734i	$0.843628\pi$
$824$	75.7895	2.64025
$825$	−63.2510	−2.20212
$826$	12.7266	0.442814
$827$	−34.2307	−1.19032	−0.595159	−	0.803608i	$-0.702911\pi$
$827$	−34.2307	−1.19032	−0.595159	+	0.803608i	$0.702911\pi$
$828$	−0.248498	−0.00863591
$829$	−1.47859	−0.0513536	−0.0256768	−	0.999670i	$-0.508174\pi$
$829$	−1.47859	−0.0513536	−0.0256768	+	0.999670i	$0.508174\pi$
$830$	0.642269	0.0222935
$831$	1.31469	0.0456060
$832$	48.3153	1.67503
$833$	−1.46964	−0.0509199
$834$	−63.6423	−2.20375
$835$	−2.76597	−0.0957204
$836$	123.087	4.25706
$837$	−4.81303	−0.166363
$838$	7.15944	0.247319
$839$	25.5647	0.882593	0.441296	−	0.897361i	$-0.354519\pi$
$839$	25.5647	0.882593	0.441296	+	0.897361i	$0.354519\pi$
$840$	11.2289	0.387434
$841$	−26.6547	−0.919128
$842$	−88.6821	−3.05619
$843$	−11.8158	−0.406958
$844$	53.2582	1.83322
$845$	−22.1260	−0.761158
$846$	−2.45980	−0.0845696
$847$	−31.1243	−1.06944
$848$	−4.29360	−0.147443
$849$	13.4713	0.462333
$850$	−14.6691	−0.503145
$851$	−0.0753381	−0.00258256
$852$	−35.7882	−1.22608
$853$	7.28208	0.249334	0.124667	−	0.992199i	$-0.460214\pi$
$853$	7.28208	0.249334	0.124667	+	0.992199i	$0.460214\pi$
$854$	17.7570	0.607633
$855$	12.3872	0.423635
$856$	−40.7467	−1.39269
$857$	0.959637	0.0327806	0.0163903	−	0.999866i	$-0.494783\pi$
$857$	0.959637	0.0327806	0.0163903	+	0.999866i	$0.494783\pi$
$858$	228.038	7.78509
$859$	−11.3521	−0.387327	−0.193664	−	0.981068i	$-0.562037\pi$
$859$	−11.3521	−0.387327	−0.193664	+	0.981068i	$0.562037\pi$
$860$	−25.8138	−0.880242
$861$	12.8697	0.438599
$862$	55.9239	1.90478
$863$	−1.00000	−0.0340404
$863$	−1.00000	−0.0340404
$864$	0.0278378	0.000947061 0
$865$	−25.1212	−0.854145
$866$	−41.7061	−1.41723
$867$	35.4790	1.20493
$868$	28.2903	0.960235
$869$	77.2800	2.62154
$870$	−8.61619	−0.292116
$871$	−85.1675	−2.88579
$872$	8.15846	0.276280
$873$	3.31596	0.112228
$874$	−0.266140	−0.00900231
$875$	−8.72308	−0.294894
$876$	−46.7688	−1.58017
$877$	19.0652	0.643787	0.321894	−	0.946776i	$-0.395681\pi$
$877$	19.0652	0.643787	0.321894	+	0.946776i	$0.395681\pi$
$878$	−9.05871	−0.305717
$879$	34.3784	1.15955
$880$	24.7944	0.835818
$881$	−20.8129	−0.701204	−0.350602	−	0.936525i	$-0.614023\pi$
$881$	−20.8129	−0.701204	−0.350602	+	0.936525i	$0.614023\pi$
$882$	−6.64964	−0.223905
$883$	−5.40775	−0.181985	−0.0909926	−	0.995852i	$-0.529004\pi$
$883$	−5.40775	−0.181985	−0.0909926	+	0.995852i	$0.529004\pi$
$884$	35.2451	1.18542
$885$	11.9421	0.401428
$886$	−33.3275	−1.11966
$887$	−29.1529	−0.978859	−0.489429	−	0.872043i	$-0.662795\pi$
$887$	−29.1529	−0.978859	−0.489429	+	0.872043i	$0.662795\pi$
$888$	38.4368	1.28986
$889$	−2.83526	−0.0950916
$890$	5.50406	0.184497
$891$	63.4247	2.12481
$892$	18.3279	0.613663
$893$	−1.75567	−0.0587512
$894$	39.4013	1.31778
$895$	8.91178	0.297888
$896$	−19.6298	−0.655786
$897$	−0.328595	−0.0109715
$898$	−59.7227	−1.99297
$899$	−10.8425	−0.361619
$900$	−44.2331	−1.47444
$901$	1.58747	0.0528862
$902$	85.5513	2.84855
$903$	16.0701	0.534780
$904$	84.0220	2.79453
$905$	3.44666	0.114571
$906$	−107.459	−3.57009
$907$	55.4212	1.84023	0.920115	−	0.391649i	$-0.128095\pi$
$907$	55.4212	1.84023	0.920115	+	0.391649i	$0.128095\pi$
$908$	30.6266	1.01638
$909$	4.91345	0.162969
$910$	14.1243	0.468217
$911$	24.2932	0.804869	0.402434	−	0.915449i	$-0.368164\pi$
$911$	24.2932	0.804869	0.402434	+	0.915449i	$0.368164\pi$
$912$	45.1025	1.49349
$913$	−1.77133	−0.0586225
$914$	−39.7255	−1.31400
$915$	16.6625	0.550844
$916$	38.4582	1.27069
$917$	10.4213	0.344142
$918$	2.44636	0.0807419
$919$	48.5462	1.60139	0.800696	−	0.599071i	$-0.204463\pi$
$919$	48.5462	1.60139	0.800696	+	0.599071i	$0.204463\pi$
$920$	−0.107559	−0.00354613
$921$	42.9629	1.41567
$922$	9.42683	0.310456
$923$	−22.4846	−0.740090
$924$	−62.0018	−2.03971
$925$	−13.4103	−0.440929
$926$	18.9931	0.624151
$927$	−42.1152	−1.38324
$928$	0.0627115	0.00205861
$929$	4.20201	0.137863	0.0689317	−	0.997621i	$-0.478041\pi$
$929$	4.20201	0.137863	0.0689317	+	0.997621i	$0.478041\pi$
$930$	39.8335	1.30619
$931$	−4.74615	−0.155549
$932$	91.0359	2.98198
$933$	8.41374	0.275454
$934$	39.7961	1.30217
$935$	−9.16718	−0.299799
$936$	79.6530	2.60354
$937$	−16.6967	−0.545456	−0.272728	−	0.962091i	$-0.587926\pi$
$937$	−16.6967	−0.545456	−0.272728	+	0.962091i	$0.587926\pi$
$938$	34.7467	1.13452
$939$	11.0376	0.360197
$940$	−1.42058	−0.0463343
$941$	16.3270	0.532244	0.266122	−	0.963939i	$-0.414258\pi$
$941$	16.3270	0.532244	0.266122	+	0.963939i	$0.414258\pi$
$942$	−27.6994	−0.902494
$943$	−0.123277	−0.00401444
$944$	20.6592	0.672400
$945$	0.653350	0.0212535
$946$	106.826	3.47321
$947$	9.89970	0.321697	0.160849	−	0.986979i	$-0.448577\pi$
$947$	9.89970	0.321697	0.160849	+	0.986979i	$0.448577\pi$
$948$	113.747	3.69432
$949$	−29.3834	−0.953825
$950$	−47.3733	−1.53699
$951$	−65.5162	−2.12451
$952$	−7.18214	−0.232775
$953$	−40.6682	−1.31737	−0.658686	−	0.752418i	$-0.728888\pi$
$953$	−40.6682	−1.31737	−0.658686	+	0.752418i	$0.728888\pi$
$954$	7.18278	0.232551
$955$	−17.9996	−0.582454
$956$	42.0584	1.36027
$957$	23.7628	0.768142
$958$	86.3999	2.79145
$959$	−5.51808	−0.178188
$960$	−18.4966	−0.596977
$961$	19.1261	0.616972
$962$	48.3480	1.55880
$963$	22.6424	0.729640
$964$	−47.3829	−1.52610
$965$	19.0905	0.614544
$966$	0.134061	0.00431333
$967$	18.8031	0.604666	0.302333	−	0.953202i	$-0.402235\pi$
$967$	18.8031	0.604666	0.302333	+	0.953202i	$0.402235\pi$
$968$	−152.105	−4.88884
$969$	−16.6757	−0.535700
$970$	2.87356	0.0922643
$971$	−27.7777	−0.891430	−0.445715	−	0.895175i	$-0.647050\pi$
$971$	−27.7777	−0.891430	−0.445715	+	0.895175i	$0.647050\pi$
$972$	85.2043	2.73293
$973$	10.8715	0.348524
$974$	81.9913	2.62717
$975$	−58.4905	−1.87320
$976$	28.8253	0.922674
$977$	−28.9390	−0.925841	−0.462921	−	0.886400i	$-0.653198\pi$
$977$	−28.9390	−0.925841	−0.462921	+	0.886400i	$0.653198\pi$
$978$	47.5387	1.52012
$979$	−15.1798	−0.485148
$980$	−3.84030	−0.122674
$981$	−4.53354	−0.144745
$982$	−46.9486	−1.49819
$983$	2.53827	0.0809583	0.0404791	−	0.999180i	$-0.487112\pi$
$983$	2.53827	0.0809583	0.0404791	+	0.999180i	$0.487112\pi$
$984$	62.8946	2.00501
$985$	−8.69903	−0.277174
$986$	5.51103	0.175507
$987$	0.884370	0.0281498
$988$	113.823	3.62120
$989$	−0.153933	−0.00489477
$990$	−41.4786	−1.31828
$991$	−1.34397	−0.0426927	−0.0213463	−	0.999772i	$-0.506795\pi$
$991$	−1.34397	−0.0426927	−0.0213463	+	0.999772i	$0.506795\pi$
$992$	−0.289922	−0.00920502
$993$	−51.9550	−1.64874
$994$	9.17329	0.290959
$995$	14.9439	0.473753
$996$	−2.60718	−0.0826117
$997$	10.0394	0.317950	0.158975	−	0.987283i	$-0.449181\pi$
$997$	10.0394	0.317950	0.158975	+	0.987283i	$0.449181\pi$
$998$	66.4162	2.10237
$999$	2.23644	0.0707578

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6041.2.a.d.1.5	✓	101

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6041.2.a.d.1.5	✓	101	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:	\( N \)	\(=\)	\( 6041 = 7 \cdot 863 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6041.a (trivial)

\(f(q)\)	\(=\)	\(q-2.44864 q^{2} -2.39074 q^{3} +3.99581 q^{4} -0.961081 q^{5} +5.85406 q^{6} -1.00000 q^{7} -4.88702 q^{8} +2.71565 q^{9} +O(q^{10})\)	\(q-2.44864 q^{2} -2.39074 q^{3} +3.99581 q^{4} -0.961081 q^{5} +5.85406 q^{6} -1.00000 q^{7} -4.88702 q^{8} +2.71565 q^{9} +2.35334 q^{10} -6.49032 q^{11} -9.55296 q^{12} -6.00183 q^{13} +2.44864 q^{14} +2.29770 q^{15} +3.97491 q^{16} -1.46964 q^{17} -6.64964 q^{18} -4.74615 q^{19} -3.84030 q^{20} +2.39074 q^{21} +15.8924 q^{22} -0.0229005 q^{23} +11.6836 q^{24} -4.07632 q^{25} +14.6963 q^{26} +0.679808 q^{27} -3.99581 q^{28} +1.53143 q^{29} -5.62622 q^{30} -7.07998 q^{31} +0.0409495 q^{32} +15.5167 q^{33} +3.59860 q^{34} +0.961081 q^{35} +10.8512 q^{36} +3.28981 q^{37} +11.6216 q^{38} +14.3488 q^{39} +4.69682 q^{40} +5.38315 q^{41} -5.85406 q^{42} +6.72181 q^{43} -25.9341 q^{44} -2.60996 q^{45} +0.0560749 q^{46} +0.369915 q^{47} -9.50298 q^{48} +1.00000 q^{49} +9.98143 q^{50} +3.51352 q^{51} -23.9822 q^{52} -1.08018 q^{53} -1.66460 q^{54} +6.23772 q^{55} +4.88702 q^{56} +11.3468 q^{57} -3.74993 q^{58} +5.19741 q^{59} +9.18117 q^{60} +7.25181 q^{61} +17.3363 q^{62} -2.71565 q^{63} -8.05008 q^{64} +5.76825 q^{65} -37.9947 q^{66} +14.1902 q^{67} -5.87239 q^{68} +0.0547491 q^{69} -2.35334 q^{70} +3.74629 q^{71} -13.2714 q^{72} +4.89573 q^{73} -8.05554 q^{74} +9.74544 q^{75} -18.9647 q^{76} +6.49032 q^{77} -35.1351 q^{78} -11.9070 q^{79} -3.82021 q^{80} -9.77220 q^{81} -13.1814 q^{82} +0.272919 q^{83} +9.55296 q^{84} +1.41244 q^{85} -16.4593 q^{86} -3.66127 q^{87} +31.7183 q^{88} +2.33883 q^{89} +6.39084 q^{90} +6.00183 q^{91} -0.0915060 q^{92} +16.9264 q^{93} -0.905786 q^{94} +4.56143 q^{95} -0.0978997 q^{96} +1.22106 q^{97} -2.44864 q^{98} -17.6254 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 101 q + 3 q^{2} - 17 q^{3} + 85 q^{4} - 12 q^{5} - 17 q^{6} - 101 q^{7} - 3 q^{8} + 88 q^{9}+O(q^{10}) \) 101 * q + 3 * q^2 - 17 * q^3 + 85 * q^4 - 12 * q^5 - 17 * q^6 - 101 * q^7 - 3 * q^8 + 88 * q^9	\( 101 q + 3 q^{2} - 17 q^{3} + 85 q^{4} - 12 q^{5} - 17 q^{6} - 101 q^{7} - 3 q^{8} + 88 q^{9} - 23 q^{10} - 13 q^{11} - 31 q^{12} - 35 q^{13} - 3 q^{14} - 20 q^{15} + 45 q^{16} - 19 q^{17} + 3 q^{18} - 59 q^{19} - 31 q^{20} + 17 q^{21} - 13 q^{22} - 29 q^{23} - 59 q^{24} + 103 q^{25} - 18 q^{26} - 47 q^{27} - 85 q^{28} - 26 q^{29} - 8 q^{30} - 125 q^{31} + 12 q^{32} - 18 q^{33} - 66 q^{34} + 12 q^{35} + 40 q^{36} + 22 q^{37} - 31 q^{38} - 94 q^{39} - 79 q^{40} - 39 q^{41} + 17 q^{42} - 5 q^{43} - 53 q^{44} - 50 q^{45} - 37 q^{46} - 47 q^{47} - 81 q^{48} + 101 q^{49} + 2 q^{50} - 23 q^{51} - 56 q^{52} - 5 q^{53} - 77 q^{54} - 155 q^{55} + 3 q^{56} + 61 q^{57} - 31 q^{58} - 33 q^{59} - 48 q^{60} - 96 q^{61} - 38 q^{62} - 88 q^{63} - 33 q^{64} - 8 q^{65} - 91 q^{66} + 8 q^{67} - 41 q^{68} - 91 q^{69} + 23 q^{70} - 116 q^{71} - 5 q^{72} - 62 q^{73} - 23 q^{74} - 94 q^{75} - 112 q^{76} + 13 q^{77} + 17 q^{78} - 127 q^{79} - 87 q^{80} + 37 q^{81} - 118 q^{82} - 58 q^{83} + 31 q^{84} - 6 q^{85} - 26 q^{86} - 82 q^{87} - 40 q^{88} - 57 q^{89} - 123 q^{90} + 35 q^{91} - 28 q^{92} - 10 q^{93} - 107 q^{94} - 70 q^{95} - 76 q^{96} - 69 q^{97} + 3 q^{98} - 67 q^{99}+O(q^{100}) \) 101 * q + 3 * q^2 - 17 * q^3 + 85 * q^4 - 12 * q^5 - 17 * q^6 - 101 * q^7 - 3 * q^8 + 88 * q^9 - 23 * q^10 - 13 * q^11 - 31 * q^12 - 35 * q^13 - 3 * q^14 - 20 * q^15 + 45 * q^16 - 19 * q^17 + 3 * q^18 - 59 * q^19 - 31 * q^20 + 17 * q^21 - 13 * q^22 - 29 * q^23 - 59 * q^24 + 103 * q^25 - 18 * q^26 - 47 * q^27 - 85 * q^28 - 26 * q^29 - 8 * q^30 - 125 * q^31 + 12 * q^32 - 18 * q^33 - 66 * q^34 + 12 * q^35 + 40 * q^36 + 22 * q^37 - 31 * q^38 - 94 * q^39 - 79 * q^40 - 39 * q^41 + 17 * q^42 - 5 * q^43 - 53 * q^44 - 50 * q^45 - 37 * q^46 - 47 * q^47 - 81 * q^48 + 101 * q^49 + 2 * q^50 - 23 * q^51 - 56 * q^52 - 5 * q^53 - 77 * q^54 - 155 * q^55 + 3 * q^56 + 61 * q^57 - 31 * q^58 - 33 * q^59 - 48 * q^60 - 96 * q^61 - 38 * q^62 - 88 * q^63 - 33 * q^64 - 8 * q^65 - 91 * q^66 + 8 * q^67 - 41 * q^68 - 91 * q^69 + 23 * q^70 - 116 * q^71 - 5 * q^72 - 62 * q^73 - 23 * q^74 - 94 * q^75 - 112 * q^76 + 13 * q^77 + 17 * q^78 - 127 * q^79 - 87 * q^80 + 37 * q^81 - 118 * q^82 - 58 * q^83 + 31 * q^84 - 6 * q^85 - 26 * q^86 - 82 * q^87 - 40 * q^88 - 57 * q^89 - 123 * q^90 + 35 * q^91 - 28 * q^92 - 10 * q^93 - 107 * q^94 - 70 * q^95 - 76 * q^96 - 69 * q^97 + 3 * q^98 - 67 * q^99

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