LMFDB - Embedded newform 6033.2.a.b.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6033,2,Mod(1,6033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6033, 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("6033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6033 = 3 \cdot 2011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6033.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:	$48.1737475394$
Analytic rank:	$1$
Dimension:	$71$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	6033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.47301 q^{2} +1.00000 q^{3} +4.11576 q^{4} -3.79557 q^{5} -2.47301 q^{6} -3.86713 q^{7} -5.23229 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.47301 q^{2} +1.00000 q^{3} +4.11576 q^{4} -3.79557 q^{5} -2.47301 q^{6} -3.86713 q^{7} -5.23229 q^{8} +1.00000 q^{9} +9.38648 q^{10} +3.08764 q^{11} +4.11576 q^{12} -4.78375 q^{13} +9.56345 q^{14} -3.79557 q^{15} +4.70797 q^{16} -0.299042 q^{17} -2.47301 q^{18} -1.83340 q^{19} -15.6217 q^{20} -3.86713 q^{21} -7.63575 q^{22} -1.89412 q^{23} -5.23229 q^{24} +9.40637 q^{25} +11.8303 q^{26} +1.00000 q^{27} -15.9162 q^{28} -2.38851 q^{29} +9.38648 q^{30} +4.00657 q^{31} -1.17826 q^{32} +3.08764 q^{33} +0.739532 q^{34} +14.6780 q^{35} +4.11576 q^{36} -0.401122 q^{37} +4.53400 q^{38} -4.78375 q^{39} +19.8596 q^{40} +12.3247 q^{41} +9.56345 q^{42} -6.34340 q^{43} +12.7080 q^{44} -3.79557 q^{45} +4.68418 q^{46} +7.25042 q^{47} +4.70797 q^{48} +7.95472 q^{49} -23.2620 q^{50} -0.299042 q^{51} -19.6888 q^{52} +7.38084 q^{53} -2.47301 q^{54} -11.7194 q^{55} +20.2340 q^{56} -1.83340 q^{57} +5.90681 q^{58} +4.85572 q^{59} -15.6217 q^{60} -6.83493 q^{61} -9.90829 q^{62} -3.86713 q^{63} -6.50210 q^{64} +18.1571 q^{65} -7.63575 q^{66} +5.82699 q^{67} -1.23078 q^{68} -1.89412 q^{69} -36.2988 q^{70} -11.5968 q^{71} -5.23229 q^{72} -9.13830 q^{73} +0.991978 q^{74} +9.40637 q^{75} -7.54583 q^{76} -11.9403 q^{77} +11.8303 q^{78} +6.56561 q^{79} -17.8695 q^{80} +1.00000 q^{81} -30.4791 q^{82} +6.94486 q^{83} -15.9162 q^{84} +1.13503 q^{85} +15.6873 q^{86} -2.38851 q^{87} -16.1554 q^{88} +10.7277 q^{89} +9.38648 q^{90} +18.4994 q^{91} -7.79575 q^{92} +4.00657 q^{93} -17.9303 q^{94} +6.95879 q^{95} -1.17826 q^{96} +8.56348 q^{97} -19.6721 q^{98} +3.08764 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 71 q - 11 q^{2} + 71 q^{3} + 53 q^{4} - 8 q^{5} - 11 q^{6} - 46 q^{7} - 33 q^{8} + 71 q^{9}+O(q^{10}) $ 71 * q - 11 * q^2 + 71 * q^3 + 53 * q^4 - 8 * q^5 - 11 * q^6 - 46 * q^7 - 33 * q^8 + 71 * q^9	\( 71 q - 11 q^{2} + 71 q^{3} + 53 q^{4} - 8 q^{5} - 11 q^{6} - 46 q^{7} - 33 q^{8} + 71 q^{9} - 41 q^{10} - 18 q^{11} + 53 q^{12} - 67 q^{13} - 7 q^{14} - 8 q^{15} + 21 q^{16} - 25 q^{17} - 11 q^{18} - 43 q^{19} - 8 q^{20} - 46 q^{21} - 49 q^{22} - 75 q^{23} - 33 q^{24} + 19 q^{25} + 71 q^{27} - 89 q^{28} - 35 q^{29} - 41 q^{30} - 82 q^{31} - 62 q^{32} - 18 q^{33} - 28 q^{34} - 51 q^{35} + 53 q^{36} - 66 q^{37} - 29 q^{38} - 67 q^{39} - 102 q^{40} + q^{41} - 7 q^{42} - 112 q^{43} - 25 q^{44} - 8 q^{45} - 36 q^{46} - 67 q^{47} + 21 q^{48} + 7 q^{49} - 24 q^{50} - 25 q^{51} - 134 q^{52} - 40 q^{53} - 11 q^{54} - 112 q^{55} + 9 q^{56} - 43 q^{57} - 47 q^{58} - 18 q^{59} - 8 q^{60} - 144 q^{61} - 19 q^{62} - 46 q^{63} - 17 q^{64} - 31 q^{65} - 49 q^{66} - 85 q^{67} - 22 q^{68} - 75 q^{69} - 11 q^{70} - 44 q^{71} - 33 q^{72} - 98 q^{73} + 6 q^{74} + 19 q^{75} - 85 q^{76} - 39 q^{77} - 126 q^{79} + 21 q^{80} + 71 q^{81} - 69 q^{82} - 43 q^{83} - 89 q^{84} - 112 q^{85} + 32 q^{86} - 35 q^{87} - 85 q^{88} + 8 q^{89} - 41 q^{90} - 40 q^{91} - 96 q^{92} - 82 q^{93} - 99 q^{94} - 103 q^{95} - 62 q^{96} - 67 q^{97} - 11 q^{98} - 18 q^{99}+O(q^{100}) \) 71 * q - 11 * q^2 + 71 * q^3 + 53 * q^4 - 8 * q^5 - 11 * q^6 - 46 * q^7 - 33 * q^8 + 71 * q^9 - 41 * q^10 - 18 * q^11 + 53 * q^12 - 67 * q^13 - 7 * q^14 - 8 * q^15 + 21 * q^16 - 25 * q^17 - 11 * q^18 - 43 * q^19 - 8 * q^20 - 46 * q^21 - 49 * q^22 - 75 * q^23 - 33 * q^24 + 19 * q^25 + 71 * q^27 - 89 * q^28 - 35 * q^29 - 41 * q^30 - 82 * q^31 - 62 * q^32 - 18 * q^33 - 28 * q^34 - 51 * q^35 + 53 * q^36 - 66 * q^37 - 29 * q^38 - 67 * q^39 - 102 * q^40 + q^41 - 7 * q^42 - 112 * q^43 - 25 * q^44 - 8 * q^45 - 36 * q^46 - 67 * q^47 + 21 * q^48 + 7 * q^49 - 24 * q^50 - 25 * q^51 - 134 * q^52 - 40 * q^53 - 11 * q^54 - 112 * q^55 + 9 * q^56 - 43 * q^57 - 47 * q^58 - 18 * q^59 - 8 * q^60 - 144 * q^61 - 19 * q^62 - 46 * q^63 - 17 * q^64 - 31 * q^65 - 49 * q^66 - 85 * q^67 - 22 * q^68 - 75 * q^69 - 11 * q^70 - 44 * q^71 - 33 * q^72 - 98 * q^73 + 6 * q^74 + 19 * q^75 - 85 * q^76 - 39 * q^77 - 126 * q^79 + 21 * q^80 + 71 * q^81 - 69 * q^82 - 43 * q^83 - 89 * q^84 - 112 * q^85 + 32 * q^86 - 35 * q^87 - 85 * q^88 + 8 * q^89 - 41 * q^90 - 40 * q^91 - 96 * q^92 - 82 * q^93 - 99 * q^94 - 103 * q^95 - 62 * q^96 - 67 * q^97 - 11 * q^98 - 18 * 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 $

$2$	−2.47301	−1.74868	−0.874340	−	0.485314i	$-0.838705\pi$
$2$	−2.47301	−1.74868	−0.874340	+	0.485314i	$0.838705\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.11576	2.05788
$5$	−3.79557	−1.69743	−0.848716	−	0.528849i	$-0.822624\pi$
$5$	−3.79557	−1.69743	−0.848716	+	0.528849i	$0.822624\pi$
$6$	−2.47301	−1.00960
$7$	−3.86713	−1.46164	−0.730819	−	0.682571i	$-0.760862\pi$
$7$	−3.86713	−1.46164	−0.730819	+	0.682571i	$0.760862\pi$
$8$	−5.23229	−1.84990
$9$	1.00000	0.333333
$10$	9.38648	2.96826
$11$	3.08764	0.930958	0.465479	−	0.885059i	$-0.345882\pi$
$11$	3.08764	0.930958	0.465479	+	0.885059i	$0.345882\pi$
$12$	4.11576	1.18812
$13$	−4.78375	−1.32677	−0.663387	−	0.748276i	$-0.730882\pi$
$13$	−4.78375	−1.32677	−0.663387	+	0.748276i	$0.730882\pi$
$14$	9.56345	2.55594
$15$	−3.79557	−0.980013
$16$	4.70797	1.17699
$17$	−0.299042	−0.0725282	−0.0362641	−	0.999342i	$-0.511546\pi$
$17$	−0.299042	−0.0725282	−0.0362641	+	0.999342i	$0.511546\pi$
$18$	−2.47301	−0.582893
$19$	−1.83340	−0.420610	−0.210305	−	0.977636i	$-0.567446\pi$
$19$	−1.83340	−0.420610	−0.210305	+	0.977636i	$0.567446\pi$
$20$	−15.6217	−3.49311
$21$	−3.86713	−0.843878
$22$	−7.63575	−1.62795
$23$	−1.89412	−0.394952	−0.197476	−	0.980308i	$-0.563274\pi$
$23$	−1.89412	−0.394952	−0.197476	+	0.980308i	$0.563274\pi$
$24$	−5.23229	−1.06804
$25$	9.40637	1.88127
$26$	11.8303	2.32010
$27$	1.00000	0.192450
$28$	−15.9162	−3.00788
$29$	−2.38851	−0.443536	−0.221768	−	0.975099i	$-0.571183\pi$
$29$	−2.38851	−0.443536	−0.221768	+	0.975099i	$0.571183\pi$
$30$	9.38648	1.71373
$31$	4.00657	0.719602	0.359801	−	0.933029i	$-0.382845\pi$
$31$	4.00657	0.719602	0.359801	+	0.933029i	$0.382845\pi$
$32$	−1.17826	−0.208289
$33$	3.08764	0.537489
$34$	0.739532	0.126829
$35$	14.6780	2.48103
$36$	4.11576	0.685960
$37$	−0.401122	−0.0659441	−0.0329720	−	0.999456i	$-0.510497\pi$
$37$	−0.401122	−0.0659441	−0.0329720	+	0.999456i	$0.510497\pi$
$38$	4.53400	0.735513
$39$	−4.78375	−0.766014
$40$	19.8596	3.14007
$41$	12.3247	1.92480	0.962398	−	0.271643i	$-0.0875669\pi$
$41$	12.3247	1.92480	0.962398	+	0.271643i	$0.0875669\pi$
$42$	9.56345	1.47567
$43$	−6.34340	−0.967359	−0.483680	−	0.875245i	$-0.660700\pi$
$43$	−6.34340	−0.967359	−0.483680	+	0.875245i	$0.660700\pi$
$44$	12.7080	1.91580
$45$	−3.79557	−0.565811
$46$	4.68418	0.690644
$47$	7.25042	1.05758	0.528791	−	0.848752i	$-0.322645\pi$
$47$	7.25042	1.05758	0.528791	+	0.848752i	$0.322645\pi$
$48$	4.70797	0.679537
$49$	7.95472	1.13639
$50$	−23.2620	−3.28975
$51$	−0.299042	−0.0418742
$52$	−19.6888	−2.73034
$53$	7.38084	1.01384	0.506918	−	0.861994i	$-0.330785\pi$
$53$	7.38084	1.01384	0.506918	+	0.861994i	$0.330785\pi$
$54$	−2.47301	−0.336534
$55$	−11.7194	−1.58024
$56$	20.2340	2.70388
$57$	−1.83340	−0.242839
$58$	5.90681	0.775602
$59$	4.85572	0.632161	0.316081	−	0.948732i	$-0.397633\pi$
$59$	4.85572	0.632161	0.316081	+	0.948732i	$0.397633\pi$
$60$	−15.6217	−2.01675
$61$	−6.83493	−0.875123	−0.437561	−	0.899189i	$-0.644158\pi$
$61$	−6.83493	−0.875123	−0.437561	+	0.899189i	$0.644158\pi$
$62$	−9.90829	−1.25835
$63$	−3.86713	−0.487213
$64$	−6.50210	−0.812762
$65$	18.1571	2.25211
$66$	−7.63575	−0.939896
$67$	5.82699	0.711880	0.355940	−	0.934509i	$-0.384161\pi$
$67$	5.82699	0.711880	0.355940	+	0.934509i	$0.384161\pi$
$68$	−1.23078	−0.149254
$69$	−1.89412	−0.228025
$70$	−36.2988	−4.33853
$71$	−11.5968	−1.37629	−0.688143	−	0.725575i	$-0.741574\pi$
$71$	−11.5968	−1.37629	−0.688143	+	0.725575i	$0.741574\pi$
$72$	−5.23229	−0.616632
$73$	−9.13830	−1.06956	−0.534778	−	0.844992i	$-0.679605\pi$
$73$	−9.13830	−1.06956	−0.534778	+	0.844992i	$0.679605\pi$
$74$	0.991978	0.115315
$75$	9.40637	1.08615
$76$	−7.54583	−0.865566
$77$	−11.9403	−1.36072
$78$	11.8303	1.33951
$79$	6.56561	0.738689	0.369345	−	0.929293i	$-0.379582\pi$
$79$	6.56561	0.738689	0.369345	+	0.929293i	$0.379582\pi$
$80$	−17.8695	−1.99787
$81$	1.00000	0.111111
$82$	−30.4791	−3.36585
$83$	6.94486	0.762297	0.381149	−	0.924514i	$-0.375529\pi$
$83$	6.94486	0.762297	0.381149	+	0.924514i	$0.375529\pi$
$84$	−15.9162	−1.73660
$85$	1.13503	0.123112
$86$	15.6873	1.69160
$87$	−2.38851	−0.256076
$88$	−16.1554	−1.72217
$89$	10.7277	1.13713	0.568567	−	0.822637i	$-0.307498\pi$
$89$	10.7277	1.13713	0.568567	+	0.822637i	$0.307498\pi$
$90$	9.38648	0.989422
$91$	18.4994	1.93926
$92$	−7.79575	−0.812764
$93$	4.00657	0.415462
$94$	−17.9303	−1.84937
$95$	6.95879	0.713957
$96$	−1.17826	−0.120256
$97$	8.56348	0.869490	0.434745	−	0.900554i	$-0.356839\pi$
$97$	8.56348	0.869490	0.434745	+	0.900554i	$0.356839\pi$
$98$	−19.6721	−1.98718
$99$	3.08764	0.310319
$100$	38.7144	3.87144
$101$	−1.06475	−0.105946	−0.0529732	−	0.998596i	$-0.516870\pi$
$101$	−1.06475	−0.105946	−0.0529732	+	0.998596i	$0.516870\pi$
$102$	0.739532	0.0732245
$103$	−16.8710	−1.66234	−0.831172	−	0.556015i	$-0.812330\pi$
$103$	−16.8710	−1.66234	−0.831172	+	0.556015i	$0.812330\pi$
$104$	25.0300	2.45439
$105$	14.6780	1.43242
$106$	−18.2529	−1.77287
$107$	6.80257	0.657629	0.328814	−	0.944395i	$-0.393351\pi$
$107$	6.80257	0.657629	0.328814	+	0.944395i	$0.393351\pi$
$108$	4.11576	0.396039
$109$	9.50253	0.910177	0.455088	−	0.890446i	$-0.349608\pi$
$109$	9.50253	0.910177	0.455088	+	0.890446i	$0.349608\pi$
$110$	28.9820	2.76333
$111$	−0.401122	−0.0380728
$112$	−18.2064	−1.72034
$113$	−11.5431	−1.08588	−0.542940	−	0.839772i	$-0.682689\pi$
$113$	−11.5431	−1.08588	−0.542940	+	0.839772i	$0.682689\pi$
$114$	4.53400	0.424648
$115$	7.18928	0.670403
$116$	−9.83056	−0.912744
$117$	−4.78375	−0.442258
$118$	−12.0082	−1.10545
$119$	1.15643	0.106010
$120$	19.8596	1.81292
$121$	−1.46649	−0.133317
$122$	16.9028	1.53031
$123$	12.3247	1.11128
$124$	16.4901	1.48086
$125$	−16.7247	−1.49590
$126$	9.56345	0.851979
$127$	12.7294	1.12955	0.564774	−	0.825246i	$-0.308963\pi$
$127$	12.7294	1.12955	0.564774	+	0.825246i	$0.308963\pi$
$128$	18.4363	1.62955
$129$	−6.34340	−0.558505
$130$	−44.9026	−3.93822
$131$	−2.00252	−0.174961	−0.0874806	−	0.996166i	$-0.527882\pi$
$131$	−2.00252	−0.174961	−0.0874806	+	0.996166i	$0.527882\pi$
$132$	12.7080	1.10609
$133$	7.08999	0.614780
$134$	−14.4102	−1.24485
$135$	−3.79557	−0.326671
$136$	1.56467	0.134170
$137$	12.0105	1.02612	0.513062	−	0.858352i	$-0.328511\pi$
$137$	12.0105	1.02612	0.513062	+	0.858352i	$0.328511\pi$
$138$	4.68418	0.398743
$139$	−5.32111	−0.451331	−0.225665	−	0.974205i	$-0.572456\pi$
$139$	−5.32111	−0.451331	−0.225665	+	0.974205i	$0.572456\pi$
$140$	60.4111	5.10567
$141$	7.25042	0.610596
$142$	28.6789	2.40668
$143$	−14.7705	−1.23517
$144$	4.70797	0.392331
$145$	9.06578	0.752872
$146$	22.5991	1.87031
$147$	7.95472	0.656094
$148$	−1.65092	−0.135705
$149$	15.6300	1.28046	0.640231	−	0.768182i	$-0.278839\pi$
$149$	15.6300	1.28046	0.640231	+	0.768182i	$0.278839\pi$
$150$	−23.2620	−1.89934
$151$	11.4959	0.935526	0.467763	−	0.883854i	$-0.345060\pi$
$151$	11.4959	0.935526	0.467763	+	0.883854i	$0.345060\pi$
$152$	9.59287	0.778085
$153$	−0.299042	−0.0241761
$154$	29.5285	2.37947
$155$	−15.2072	−1.22148
$156$	−19.6888	−1.57636
$157$	−21.9276	−1.75001	−0.875005	−	0.484113i	$-0.839142\pi$
$157$	−21.9276	−1.75001	−0.875005	+	0.484113i	$0.839142\pi$
$158$	−16.2368	−1.29173
$159$	7.38084	0.585339
$160$	4.47218	0.353557
$161$	7.32482	0.577277
$162$	−2.47301	−0.194298
$163$	14.9236	1.16890	0.584452	−	0.811428i	$-0.301309\pi$
$163$	14.9236	1.16890	0.584452	+	0.811428i	$0.301309\pi$
$164$	50.7256	3.96100
$165$	−11.7194	−0.912351
$166$	−17.1747	−1.33301
$167$	−14.4744	−1.12006	−0.560032	−	0.828471i	$-0.689211\pi$
$167$	−14.4744	−1.12006	−0.560032	+	0.828471i	$0.689211\pi$
$168$	20.2340	1.56109
$169$	9.88429	0.760330
$170$	−2.80695	−0.215283
$171$	−1.83340	−0.140203
$172$	−26.1079	−1.99071
$173$	8.81850	0.670458	0.335229	−	0.942137i	$-0.391186\pi$
$173$	8.81850	0.670458	0.335229	+	0.942137i	$0.391186\pi$
$174$	5.90681	0.447794
$175$	−36.3757	−2.74974
$176$	14.5365	1.09573
$177$	4.85572	0.364979
$178$	−26.5297	−1.98848
$179$	−19.2865	−1.44154	−0.720770	−	0.693174i	$-0.756212\pi$
$179$	−19.2865	−1.44154	−0.720770	+	0.693174i	$0.756212\pi$
$180$	−15.6217	−1.16437
$181$	19.5442	1.45271	0.726355	−	0.687319i	$-0.241213\pi$
$181$	19.5442	1.45271	0.726355	+	0.687319i	$0.241213\pi$
$182$	−45.7492	−3.39115
$183$	−6.83493	−0.505252
$184$	9.91060	0.730619
$185$	1.52249	0.111936
$186$	−9.90829	−0.726511
$187$	−0.923332	−0.0675207
$188$	29.8410	2.17638
$189$	−3.86713	−0.281293
$190$	−17.2091	−1.24848
$191$	−13.7124	−0.992194	−0.496097	−	0.868267i	$-0.665234\pi$
$191$	−13.7124	−0.992194	−0.496097	+	0.868267i	$0.665234\pi$
$192$	−6.50210	−0.469248
$193$	−10.7095	−0.770890	−0.385445	−	0.922731i	$-0.625952\pi$
$193$	−10.7095	−0.770890	−0.385445	+	0.922731i	$0.625952\pi$
$194$	−21.1776	−1.52046
$195$	18.1571	1.30026
$196$	32.7397	2.33855
$197$	−11.9209	−0.849330	−0.424665	−	0.905351i	$-0.639608\pi$
$197$	−11.9209	−0.849330	−0.424665	+	0.905351i	$0.639608\pi$
$198$	−7.63575	−0.542649
$199$	1.72970	0.122615	0.0613077	−	0.998119i	$-0.480473\pi$
$199$	1.72970	0.122615	0.0613077	+	0.998119i	$0.480473\pi$
$200$	−49.2169	−3.48016
$201$	5.82699	0.411004
$202$	2.63313	0.185266
$203$	9.23670	0.648289
$204$	−1.23078	−0.0861721
$205$	−46.7793	−3.26721
$206$	41.7220	2.90691
$207$	−1.89412	−0.131651
$208$	−22.5218	−1.56160
$209$	−5.66087	−0.391570
$210$	−36.2988	−2.50485
$211$	3.39753	0.233896	0.116948	−	0.993138i	$-0.462689\pi$
$211$	3.39753	0.233896	0.116948	+	0.993138i	$0.462689\pi$
$212$	30.3778	2.08635
$213$	−11.5968	−0.794599
$214$	−16.8228	−1.14998
$215$	24.0768	1.64203
$216$	−5.23229	−0.356013
$217$	−15.4940	−1.05180
$218$	−23.4998	−1.59161
$219$	−9.13830	−0.617509
$220$	−48.2341	−3.25194
$221$	1.43054	0.0962286
$222$	0.991978	0.0665772
$223$	2.85467	0.191163	0.0955813	−	0.995422i	$-0.469529\pi$
$223$	2.85467	0.191163	0.0955813	+	0.995422i	$0.469529\pi$
$224$	4.55650	0.304444
$225$	9.40637	0.627091
$226$	28.5461	1.89886
$227$	−19.1427	−1.27055	−0.635273	−	0.772288i	$-0.719112\pi$
$227$	−19.1427	−1.27055	−0.635273	+	0.772288i	$0.719112\pi$
$228$	−7.54583	−0.499735
$229$	−0.470029	−0.0310604	−0.0155302	−	0.999879i	$-0.504944\pi$
$229$	−0.470029	−0.0310604	−0.0155302	+	0.999879i	$0.504944\pi$
$230$	−17.7791	−1.17232
$231$	−11.9403	−0.785615
$232$	12.4974	0.820495
$233$	7.41332	0.485663	0.242831	−	0.970069i	$-0.421924\pi$
$233$	7.41332	0.485663	0.242831	+	0.970069i	$0.421924\pi$
$234$	11.8303	0.773368
$235$	−27.5195	−1.79517
$236$	19.9850	1.30091
$237$	6.56561	0.426482
$238$	−2.85987	−0.185378
$239$	−11.8019	−0.763404	−0.381702	−	0.924285i	$-0.624662\pi$
$239$	−11.8019	−0.763404	−0.381702	+	0.924285i	$0.624662\pi$
$240$	−17.8695	−1.15347
$241$	−12.8317	−0.826564	−0.413282	−	0.910603i	$-0.635618\pi$
$241$	−12.8317	−0.826564	−0.413282	+	0.910603i	$0.635618\pi$
$242$	3.62664	0.233129
$243$	1.00000	0.0641500
$244$	−28.1309	−1.80090
$245$	−30.1927	−1.92894
$246$	−30.4791	−1.94328
$247$	8.77052	0.558055
$248$	−20.9636	−1.33119
$249$	6.94486	0.440113
$250$	41.3603	2.61586
$251$	25.3510	1.60014	0.800070	−	0.599907i	$-0.204796\pi$
$251$	25.3510	1.60014	0.800070	+	0.599907i	$0.204796\pi$
$252$	−15.9162	−1.00263
$253$	−5.84836	−0.367683
$254$	−31.4798	−1.97522
$255$	1.13503	0.0710786
$256$	−32.5888	−2.03680
$257$	−17.4897	−1.09097	−0.545487	−	0.838119i	$-0.683655\pi$
$257$	−17.4897	−1.09097	−0.545487	+	0.838119i	$0.683655\pi$
$258$	15.6873	0.976646
$259$	1.55119	0.0963864
$260$	74.7302	4.63457
$261$	−2.38851	−0.147845
$262$	4.95225	0.305951
$263$	−1.71974	−0.106044	−0.0530219	−	0.998593i	$-0.516885\pi$
$263$	−1.71974	−0.106044	−0.0530219	+	0.998593i	$0.516885\pi$
$264$	−16.1554	−0.994298
$265$	−28.0145	−1.72092
$266$	−17.5336	−1.07505
$267$	10.7277	0.656525
$268$	23.9825	1.46496
$269$	22.8023	1.39028	0.695140	−	0.718874i	$-0.255342\pi$
$269$	22.8023	1.39028	0.695140	+	0.718874i	$0.255342\pi$
$270$	9.38648	0.571243
$271$	−16.4701	−1.00049	−0.500243	−	0.865885i	$-0.666756\pi$
$271$	−16.4701	−1.00049	−0.500243	+	0.865885i	$0.666756\pi$
$272$	−1.40788	−0.0853652
$273$	18.4994	1.11964
$274$	−29.7020	−1.79436
$275$	29.0435	1.75139
$276$	−7.79575	−0.469249
$277$	−15.2770	−0.917903	−0.458952	−	0.888461i	$-0.651775\pi$
$277$	−15.2770	−0.917903	−0.458952	+	0.888461i	$0.651775\pi$
$278$	13.1591	0.789233
$279$	4.00657	0.239867
$280$	−76.7995	−4.58965
$281$	4.68427	0.279440	0.139720	−	0.990191i	$-0.455380\pi$
$281$	4.68427	0.279440	0.139720	+	0.990191i	$0.455380\pi$
$282$	−17.9303	−1.06774
$283$	13.5180	0.803559	0.401780	−	0.915736i	$-0.368392\pi$
$283$	13.5180	0.803559	0.401780	+	0.915736i	$0.368392\pi$
$284$	−47.7296	−2.83223
$285$	6.95879	0.412203
$286$	36.5275	2.15992
$287$	−47.6613	−2.81336
$288$	−1.17826	−0.0694298
$289$	−16.9106	−0.994740
$290$	−22.4197	−1.31653
$291$	8.56348	0.502000
$292$	−37.6111	−2.20102
$293$	0.971189	0.0567375	0.0283687	−	0.999598i	$-0.490969\pi$
$293$	0.971189	0.0567375	0.0283687	+	0.999598i	$0.490969\pi$
$294$	−19.6721	−1.14730
$295$	−18.4303	−1.07305
$296$	2.09879	0.121990
$297$	3.08764	0.179163
$298$	−38.6532	−2.23912
$299$	9.06101	0.524012
$300$	38.7144	2.23518
$301$	24.5308	1.41393
$302$	−28.4295	−1.63594
$303$	−1.06475	−0.0611682
$304$	−8.63159	−0.495055
$305$	25.9425	1.48546
$306$	0.739532	0.0422762
$307$	−10.0391	−0.572960	−0.286480	−	0.958086i	$-0.592485\pi$
$307$	−10.0391	−0.572960	−0.286480	+	0.958086i	$0.592485\pi$
$308$	−49.1435	−2.80021
$309$	−16.8710	−0.959755
$310$	37.6076	2.13597
$311$	27.9275	1.58362	0.791812	−	0.610765i	$-0.209138\pi$
$311$	27.9275	1.58362	0.791812	+	0.610765i	$0.209138\pi$
$312$	25.0300	1.41704
$313$	24.1248	1.36361	0.681807	−	0.731532i	$-0.261194\pi$
$313$	24.1248	1.36361	0.681807	+	0.731532i	$0.261194\pi$
$314$	54.2270	3.06021
$315$	14.6780	0.827011
$316$	27.0225	1.52013
$317$	−14.3245	−0.804542	−0.402271	−	0.915521i	$-0.631779\pi$
$317$	−14.3245	−0.804542	−0.402271	+	0.915521i	$0.631779\pi$
$318$	−18.2529	−1.02357
$319$	−7.37487	−0.412913
$320$	24.6792	1.37961
$321$	6.80257	0.379682
$322$	−18.1143	−1.00947
$323$	0.548262	0.0305061
$324$	4.11576	0.228653
$325$	−44.9978	−2.49603
$326$	−36.9061	−2.04404
$327$	9.50253	0.525491
$328$	−64.4865	−3.56067
$329$	−28.0383	−1.54580
$330$	28.9820	1.59541
$331$	13.0435	0.716934	0.358467	−	0.933542i	$-0.383300\pi$
$331$	13.0435	0.716934	0.358467	+	0.933542i	$0.383300\pi$
$332$	28.5834	1.56872
$333$	−0.401122	−0.0219814
$334$	35.7953	1.95863
$335$	−22.1168	−1.20837
$336$	−18.2064	−0.993238
$337$	−14.7069	−0.801137	−0.400568	−	0.916267i	$-0.631187\pi$
$337$	−14.7069	−0.801137	−0.400568	+	0.916267i	$0.631187\pi$
$338$	−24.4439	−1.32957
$339$	−11.5431	−0.626933
$340$	4.67153	0.253349
$341$	12.3709	0.669919
$342$	4.53400	0.245171
$343$	−3.69201	−0.199350
$344$	33.1905	1.78951
$345$	7.18928	0.387058
$346$	−21.8082	−1.17242
$347$	−25.3602	−1.36141	−0.680704	−	0.732558i	$-0.738326\pi$
$347$	−25.3602	−1.36141	−0.680704	+	0.732558i	$0.738326\pi$
$348$	−9.83056	−0.526973
$349$	−15.6128	−0.835735	−0.417868	−	0.908508i	$-0.637222\pi$
$349$	−15.6128	−0.835735	−0.417868	+	0.908508i	$0.637222\pi$
$350$	89.9573	4.80842
$351$	−4.78375	−0.255338
$352$	−3.63805	−0.193909
$353$	31.9614	1.70114	0.850568	−	0.525865i	$-0.176258\pi$
$353$	31.9614	1.70114	0.850568	+	0.525865i	$0.176258\pi$
$354$	−12.0082	−0.638231
$355$	44.0165	2.33615
$356$	44.1527	2.34009
$357$	1.15643	0.0612049
$358$	47.6956	2.52079
$359$	26.0928	1.37713	0.688563	−	0.725177i	$-0.258242\pi$
$359$	26.0928	1.37713	0.688563	+	0.725177i	$0.258242\pi$
$360$	19.8596	1.04669
$361$	−15.6387	−0.823087
$362$	−48.3330	−2.54033
$363$	−1.46649	−0.0769707
$364$	76.1392	3.99078
$365$	34.6851	1.81550
$366$	16.9028	0.883525
$367$	−13.1634	−0.687125	−0.343563	−	0.939130i	$-0.611634\pi$
$367$	−13.1634	−0.687125	−0.343563	+	0.939130i	$0.611634\pi$
$368$	−8.91747	−0.464855
$369$	12.3247	0.641599
$370$	−3.76512	−0.195739
$371$	−28.5427	−1.48186
$372$	16.4901	0.854972
$373$	−14.2932	−0.740073	−0.370037	−	0.929017i	$-0.620655\pi$
$373$	−14.2932	−0.740073	−0.370037	+	0.929017i	$0.620655\pi$
$374$	2.28341	0.118072
$375$	−16.7247	−0.863660
$376$	−37.9363	−1.95642
$377$	11.4261	0.588472
$378$	9.56345	0.491891
$379$	4.04255	0.207652	0.103826	−	0.994595i	$-0.466892\pi$
$379$	4.04255	0.207652	0.103826	+	0.994595i	$0.466892\pi$
$380$	28.6407	1.46924
$381$	12.7294	0.652144
$382$	33.9108	1.73503
$383$	−8.70944	−0.445032	−0.222516	−	0.974929i	$-0.571427\pi$
$383$	−8.70944	−0.445032	−0.222516	+	0.974929i	$0.571427\pi$
$384$	18.4363	0.940821
$385$	45.3203	2.30974
$386$	26.4848	1.34804
$387$	−6.34340	−0.322453
$388$	35.2453	1.78931
$389$	0.534202	0.0270851	0.0135426	−	0.999908i	$-0.495689\pi$
$389$	0.534202	0.0270851	0.0135426	+	0.999908i	$0.495689\pi$
$390$	−44.9026	−2.27373
$391$	0.566421	0.0286451
$392$	−41.6214	−2.10220
$393$	−2.00252	−0.101014
$394$	29.4805	1.48521
$395$	−24.9203	−1.25387
$396$	12.7080	0.638600
$397$	27.8445	1.39747	0.698737	−	0.715378i	$-0.253746\pi$
$397$	27.8445	1.39747	0.698737	+	0.715378i	$0.253746\pi$
$398$	−4.27757	−0.214415
$399$	7.08999	0.354944
$400$	44.2850	2.21425
$401$	−26.7497	−1.33582	−0.667909	−	0.744243i	$-0.732811\pi$
$401$	−26.7497	−1.33582	−0.667909	+	0.744243i	$0.732811\pi$
$402$	−14.4102	−0.718715
$403$	−19.1665	−0.954750
$404$	−4.38225	−0.218025
$405$	−3.79557	−0.188604
$406$	−22.8424	−1.13365
$407$	−1.23852	−0.0613912
$408$	1.56467	0.0774629
$409$	−19.6344	−0.970860	−0.485430	−	0.874276i	$-0.661337\pi$
$409$	−19.6344	−0.970860	−0.485430	+	0.874276i	$0.661337\pi$
$410$	115.686	5.71330
$411$	12.0105	0.592433
$412$	−69.4368	−3.42091
$413$	−18.7777	−0.923992
$414$	4.68418	0.230215
$415$	−26.3597	−1.29395
$416$	5.63652	0.276353
$417$	−5.32111	−0.260576
$418$	13.9994	0.684731
$419$	14.5674	0.711665	0.355832	−	0.934550i	$-0.384197\pi$
$419$	14.5674	0.711665	0.355832	+	0.934550i	$0.384197\pi$
$420$	60.4111	2.94776
$421$	−9.30874	−0.453680	−0.226840	−	0.973932i	$-0.572839\pi$
$421$	−9.30874	−0.453680	−0.226840	+	0.973932i	$0.572839\pi$
$422$	−8.40213	−0.409009
$423$	7.25042	0.352528
$424$	−38.6187	−1.87549
$425$	−2.81290	−0.136445
$426$	28.6789	1.38950
$427$	26.4316	1.27911
$428$	27.9977	1.35332
$429$	−14.7705	−0.713126
$430$	−59.5422	−2.87138
$431$	−37.9311	−1.82708	−0.913538	−	0.406754i	$-0.866660\pi$
$431$	−37.9311	−1.82708	−0.913538	+	0.406754i	$0.866660\pi$
$432$	4.70797	0.226512
$433$	3.25202	0.156282	0.0781411	−	0.996942i	$-0.475102\pi$
$433$	3.25202	0.156282	0.0781411	+	0.996942i	$0.475102\pi$
$434$	38.3167	1.83926
$435$	9.06578	0.434671
$436$	39.1101	1.87304
$437$	3.47268	0.166121
$438$	22.5991	1.07983
$439$	5.69873	0.271986	0.135993	−	0.990710i	$-0.456578\pi$
$439$	5.69873	0.271986	0.135993	+	0.990710i	$0.456578\pi$
$440$	61.3191	2.92327
$441$	7.95472	0.378796
$442$	−3.53774	−0.168273
$443$	−25.7378	−1.22284	−0.611419	−	0.791307i	$-0.709401\pi$
$443$	−25.7378	−1.22284	−0.611419	+	0.791307i	$0.709401\pi$
$444$	−1.65092	−0.0783494
$445$	−40.7178	−1.93021
$446$	−7.05961	−0.334282
$447$	15.6300	0.739275
$448$	25.1445	1.18796
$449$	−4.04439	−0.190867	−0.0954334	−	0.995436i	$-0.530424\pi$
$449$	−4.04439	−0.190867	−0.0954334	+	0.995436i	$0.530424\pi$
$450$	−23.2620	−1.09658
$451$	38.0543	1.79190
$452$	−47.5085	−2.23461
$453$	11.4959	0.540126
$454$	47.3400	2.22178
$455$	−70.2158	−3.29177
$456$	9.59287	0.449228
$457$	3.48238	0.162899	0.0814495	−	0.996677i	$-0.474045\pi$
$457$	3.48238	0.162899	0.0814495	+	0.996677i	$0.474045\pi$
$458$	1.16238	0.0543147
$459$	−0.299042	−0.0139581
$460$	29.5893	1.37961
$461$	−31.4696	−1.46568	−0.732842	−	0.680399i	$-0.761806\pi$
$461$	−31.4696	−1.46568	−0.732842	+	0.680399i	$0.761806\pi$
$462$	29.5285	1.37379
$463$	−17.5089	−0.813706	−0.406853	−	0.913494i	$-0.633374\pi$
$463$	−17.5089	−0.813706	−0.406853	+	0.913494i	$0.633374\pi$
$464$	−11.2451	−0.522039
$465$	−15.2072	−0.705219
$466$	−18.3332	−0.849268
$467$	12.9973	0.601446	0.300723	−	0.953712i	$-0.402772\pi$
$467$	12.9973	0.601446	0.300723	+	0.953712i	$0.402772\pi$
$468$	−19.6888	−0.910115
$469$	−22.5337	−1.04051
$470$	68.0559	3.13918
$471$	−21.9276	−1.01037
$472$	−25.4066	−1.16943
$473$	−19.5861	−0.900571
$474$	−16.2368	−0.745781
$475$	−17.2456	−0.791283
$476$	4.75960	0.218156
$477$	7.38084	0.337945
$478$	29.1863	1.33495
$479$	33.5689	1.53380	0.766901	−	0.641765i	$-0.221798\pi$
$479$	33.5689	1.53380	0.766901	+	0.641765i	$0.221798\pi$
$480$	4.47218	0.204126
$481$	1.91887	0.0874929
$482$	31.7329	1.44540
$483$	7.32482	0.333291
$484$	−6.03572	−0.274351
$485$	−32.5033	−1.47590
$486$	−2.47301	−0.112178
$487$	8.38476	0.379950	0.189975	−	0.981789i	$-0.439159\pi$
$487$	8.38476	0.379950	0.189975	+	0.981789i	$0.439159\pi$
$488$	35.7624	1.61889
$489$	14.9236	0.674867
$490$	74.6668	3.37310
$491$	30.6588	1.38361	0.691806	−	0.722083i	$-0.256815\pi$
$491$	30.6588	1.38361	0.691806	+	0.722083i	$0.256815\pi$
$492$	50.7256	2.28689
$493$	0.714265	0.0321689
$494$	−21.6896	−0.975859
$495$	−11.7194	−0.526746
$496$	18.8628	0.846967
$497$	44.8463	2.01163
$498$	−17.1747	−0.769616
$499$	−4.33632	−0.194121	−0.0970603	−	0.995279i	$-0.530944\pi$
$499$	−4.33632	−0.194121	−0.0970603	+	0.995279i	$0.530944\pi$
$500$	−68.8349	−3.07839
$501$	−14.4744	−0.646669
$502$	−62.6932	−2.79813
$503$	−25.1115	−1.11966	−0.559832	−	0.828606i	$-0.689135\pi$
$503$	−25.1115	−1.11966	−0.559832	+	0.828606i	$0.689135\pi$
$504$	20.2340	0.901293
$505$	4.04133	0.179837
$506$	14.4630	0.642961
$507$	9.88429	0.438977
$508$	52.3910	2.32447
$509$	24.4006	1.08154	0.540769	−	0.841171i	$-0.318133\pi$
$509$	24.4006	1.08154	0.540769	+	0.841171i	$0.318133\pi$
$510$	−2.80695	−0.124294
$511$	35.3390	1.56331
$512$	43.7198	1.93216
$513$	−1.83340	−0.0809465
$514$	43.2520	1.90777
$515$	64.0349	2.82172
$516$	−26.1079	−1.14934
$517$	22.3867	0.984565
$518$	−3.83611	−0.168549
$519$	8.81850	0.387089
$520$	−95.0032	−4.16617
$521$	8.91620	0.390626	0.195313	−	0.980741i	$-0.437428\pi$
$521$	8.91620	0.390626	0.195313	+	0.980741i	$0.437428\pi$
$522$	5.90681	0.258534
$523$	6.69625	0.292807	0.146403	−	0.989225i	$-0.453230\pi$
$523$	6.69625	0.292807	0.146403	+	0.989225i	$0.453230\pi$
$524$	−8.24190	−0.360049
$525$	−36.3757	−1.58757
$526$	4.25293	0.185437
$527$	−1.19813	−0.0521915
$528$	14.5365	0.632621
$529$	−19.4123	−0.844013
$530$	69.2801	3.00933
$531$	4.85572	0.210720
$532$	29.1807	1.26514
$533$	−58.9584	−2.55377
$534$	−26.5297	−1.14805
$535$	−25.8196	−1.11628
$536$	−30.4885	−1.31690
$537$	−19.2865	−0.832274
$538$	−56.3902	−2.43116
$539$	24.5613	1.05793
$540$	−15.6217	−0.672250
$541$	−25.4086	−1.09240	−0.546201	−	0.837654i	$-0.683926\pi$
$541$	−25.4086	−1.09240	−0.546201	+	0.837654i	$0.683926\pi$
$542$	40.7306	1.74953
$543$	19.5442	0.838723
$544$	0.352349	0.0151069
$545$	−36.0675	−1.54496
$546$	−45.7492	−1.95788
$547$	7.58119	0.324148	0.162074	−	0.986779i	$-0.448182\pi$
$547$	7.58119	0.324148	0.162074	+	0.986779i	$0.448182\pi$
$548$	49.4323	2.11164
$549$	−6.83493	−0.291708
$550$	−71.8247	−3.06262
$551$	4.37910	0.186556
$552$	9.91060	0.421823
$553$	−25.3901	−1.07970
$554$	37.7800	1.60512
$555$	1.52249	0.0646260
$556$	−21.9004	−0.928785
$557$	−42.9910	−1.82159	−0.910793	−	0.412863i	$-0.864529\pi$
$557$	−42.9910	−1.82159	−0.910793	+	0.412863i	$0.864529\pi$
$558$	−9.90829	−0.419451
$559$	30.3452	1.28347
$560$	69.1036	2.92016
$561$	−0.923332	−0.0389831
$562$	−11.5842	−0.488651
$563$	−41.9273	−1.76702	−0.883512	−	0.468408i	$-0.844828\pi$
$563$	−41.9273	−1.76702	−0.883512	+	0.468408i	$0.844828\pi$
$564$	29.8410	1.25653
$565$	43.8125	1.84321
$566$	−33.4300	−1.40517
$567$	−3.86713	−0.162404
$568$	60.6778	2.54598
$569$	17.2823	0.724513	0.362256	−	0.932078i	$-0.382006\pi$
$569$	17.2823	0.724513	0.362256	+	0.932078i	$0.382006\pi$
$570$	−17.2091	−0.720812
$571$	22.4462	0.939346	0.469673	−	0.882841i	$-0.344372\pi$
$571$	22.4462	0.939346	0.469673	+	0.882841i	$0.344372\pi$
$572$	−60.7919	−2.54184
$573$	−13.7124	−0.572844
$574$	117.867	4.91966
$575$	−17.8168	−0.743012
$576$	−6.50210	−0.270921
$577$	−4.25377	−0.177087	−0.0885434	−	0.996072i	$-0.528221\pi$
$577$	−4.25377	−0.177087	−0.0885434	+	0.996072i	$0.528221\pi$
$578$	41.8200	1.73948
$579$	−10.7095	−0.445073
$580$	37.3126	1.54932
$581$	−26.8567	−1.11420
$582$	−21.1776	−0.877838
$583$	22.7894	0.943839
$584$	47.8142	1.97857
$585$	18.1571	0.750703
$586$	−2.40176	−0.0992157
$587$	43.5419	1.79716	0.898582	−	0.438805i	$-0.144598\pi$
$587$	43.5419	1.79716	0.898582	+	0.438805i	$0.144598\pi$
$588$	32.7397	1.35016
$589$	−7.34564	−0.302672
$590$	45.5781	1.87642
$591$	−11.9209	−0.490361
$592$	−1.88847	−0.0776158
$593$	−10.7729	−0.442389	−0.221195	−	0.975230i	$-0.570996\pi$
$593$	−10.7729	−0.442389	−0.221195	+	0.975230i	$0.570996\pi$
$594$	−7.63575	−0.313299
$595$	−4.38933	−0.179945
$596$	64.3295	2.63504
$597$	1.72970	0.0707920
$598$	−22.4079	−0.916329
$599$	1.87805	0.0767349	0.0383674	−	0.999264i	$-0.487784\pi$
$599$	1.87805	0.0767349	0.0383674	+	0.999264i	$0.487784\pi$
$600$	−49.2169	−2.00927
$601$	−30.5370	−1.24563	−0.622816	−	0.782368i	$-0.714011\pi$
$601$	−30.5370	−1.24563	−0.622816	+	0.782368i	$0.714011\pi$
$602$	−60.6647	−2.47251
$603$	5.82699	0.237293
$604$	47.3146	1.92520
$605$	5.56616	0.226297
$606$	2.63313	0.106964
$607$	9.89804	0.401749	0.200875	−	0.979617i	$-0.435622\pi$
$607$	9.89804	0.401749	0.200875	+	0.979617i	$0.435622\pi$
$608$	2.16022	0.0876086
$609$	9.23670	0.374290
$610$	−64.1559	−2.59760
$611$	−34.6842	−1.40317
$612$	−1.23078	−0.0497515
$613$	−28.9640	−1.16984	−0.584922	−	0.811089i	$-0.698875\pi$
$613$	−28.9640	−1.16984	−0.584922	+	0.811089i	$0.698875\pi$
$614$	24.8267	1.00192
$615$	−46.7793	−1.88632
$616$	62.4752	2.51720
$617$	−22.4457	−0.903630	−0.451815	−	0.892112i	$-0.649223\pi$
$617$	−22.4457	−0.903630	−0.451815	+	0.892112i	$0.649223\pi$
$618$	41.7220	1.67830
$619$	29.9962	1.20565	0.602824	−	0.797874i	$-0.294042\pi$
$619$	29.9962	1.20565	0.602824	+	0.797874i	$0.294042\pi$
$620$	−62.5894	−2.51365
$621$	−1.89412	−0.0760085
$622$	−69.0649	−2.76925
$623$	−41.4855	−1.66208
$624$	−22.5218	−0.901593
$625$	16.4480	0.657919
$626$	−59.6608	−2.38453
$627$	−5.66087	−0.226073
$628$	−90.2487	−3.60131
$629$	0.119952	0.00478281
$630$	−36.2988	−1.44618
$631$	−24.6684	−0.982034	−0.491017	−	0.871150i	$-0.663375\pi$
$631$	−24.6684	−0.982034	−0.491017	+	0.871150i	$0.663375\pi$
$632$	−34.3532	−1.36650
$633$	3.39753	0.135040
$634$	35.4245	1.40689
$635$	−48.3152	−1.91733
$636$	30.3778	1.20456
$637$	−38.0534	−1.50773
$638$	18.2381	0.722053
$639$	−11.5968	−0.458762
$640$	−69.9761	−2.76605
$641$	−19.8674	−0.784714	−0.392357	−	0.919813i	$-0.628340\pi$
$641$	−19.8674	−0.784714	−0.392357	+	0.919813i	$0.628340\pi$
$642$	−16.8228	−0.663943
$643$	−34.1262	−1.34581	−0.672903	−	0.739731i	$-0.734953\pi$
$643$	−34.1262	−1.34581	−0.672903	+	0.739731i	$0.734953\pi$
$644$	30.1472	1.18797
$645$	24.0768	0.948024
$646$	−1.35586	−0.0533454
$647$	−10.1471	−0.398925	−0.199463	−	0.979905i	$-0.563920\pi$
$647$	−10.1471	−0.398925	−0.199463	+	0.979905i	$0.563920\pi$
$648$	−5.23229	−0.205544
$649$	14.9927	0.588516
$650$	111.280	4.36475
$651$	−15.4940	−0.607256
$652$	61.4219	2.40547
$653$	40.4428	1.58265	0.791325	−	0.611396i	$-0.209392\pi$
$653$	40.4428	1.58265	0.791325	+	0.611396i	$0.209392\pi$
$654$	−23.4998	−0.918915
$655$	7.60072	0.296985
$656$	58.0244	2.26547
$657$	−9.13830	−0.356519
$658$	69.3390	2.70312
$659$	−8.61627	−0.335642	−0.167821	−	0.985817i	$-0.553673\pi$
$659$	−8.61627	−0.335642	−0.167821	+	0.985817i	$0.553673\pi$
$660$	−48.2341	−1.87751
$661$	−8.19572	−0.318777	−0.159388	−	0.987216i	$-0.550952\pi$
$661$	−8.19572	−0.318777	−0.159388	+	0.987216i	$0.550952\pi$
$662$	−32.2566	−1.25369
$663$	1.43054	0.0555576
$664$	−36.3375	−1.41017
$665$	−26.9106	−1.04355
$666$	0.991978	0.0384384
$667$	4.52414	0.175175
$668$	−59.5732	−2.30496
$669$	2.85467	0.110368
$670$	54.6949	2.11305
$671$	−21.1038	−0.814703
$672$	4.55650	0.175771
$673$	−47.5468	−1.83279	−0.916397	−	0.400270i	$-0.868916\pi$
$673$	−47.5468	−1.83279	−0.916397	+	0.400270i	$0.868916\pi$
$674$	36.3703	1.40093
$675$	9.40637	0.362051
$676$	40.6814	1.56467
$677$	3.83613	0.147434	0.0737172	−	0.997279i	$-0.476514\pi$
$677$	3.83613	0.147434	0.0737172	+	0.997279i	$0.476514\pi$
$678$	28.5461	1.09630
$679$	−33.1161	−1.27088
$680$	−5.93883	−0.227744
$681$	−19.1427	−0.733550
$682$	−30.5932	−1.17147
$683$	−22.9865	−0.879553	−0.439776	−	0.898107i	$-0.644942\pi$
$683$	−22.9865	−0.879553	−0.439776	+	0.898107i	$0.644942\pi$
$684$	−7.54583	−0.288522
$685$	−45.5866	−1.74178
$686$	9.13038	0.348599
$687$	−0.470029	−0.0179327
$688$	−29.8645	−1.13858
$689$	−35.3081	−1.34513
$690$	−17.7791	−0.676840
$691$	32.1532	1.22317	0.611583	−	0.791180i	$-0.290533\pi$
$691$	32.1532	1.22317	0.611583	+	0.791180i	$0.290533\pi$
$692$	36.2949	1.37972
$693$	−11.9403	−0.453575
$694$	62.7160	2.38067
$695$	20.1967	0.766103
$696$	12.4974	0.473713
$697$	−3.68560	−0.139602
$698$	38.6106	1.46143
$699$	7.41332	0.280397
$700$	−149.714	−5.65865
$701$	1.65383	0.0624642	0.0312321	−	0.999512i	$-0.490057\pi$
$701$	1.65383	0.0624642	0.0312321	+	0.999512i	$0.490057\pi$
$702$	11.8303	0.446504
$703$	0.735417	0.0277368
$704$	−20.0761	−0.756647
$705$	−27.5195	−1.03644
$706$	−79.0409	−2.97474
$707$	4.11752	0.154855
$708$	19.9850	0.751082
$709$	49.2189	1.84845	0.924227	−	0.381844i	$-0.124711\pi$
$709$	49.2189	1.84845	0.924227	+	0.381844i	$0.124711\pi$
$710$	−108.853	−4.08518
$711$	6.56561	0.246230
$712$	−56.1305	−2.10358
$713$	−7.58894	−0.284208
$714$	−2.85987	−0.107028
$715$	56.0625	2.09662
$716$	−79.3786	−2.96652
$717$	−11.8019	−0.440752
$718$	−64.5277	−2.40815
$719$	−46.4017	−1.73049	−0.865246	−	0.501348i	$-0.832838\pi$
$719$	−46.4017	−1.73049	−0.865246	+	0.501348i	$0.832838\pi$
$720$	−17.8695	−0.665955
$721$	65.2422	2.42975
$722$	38.6745	1.43932
$723$	−12.8317	−0.477217
$724$	80.4394	2.98951
$725$	−22.4673	−0.834413
$726$	3.62664	0.134597
$727$	30.8860	1.14550	0.572750	−	0.819730i	$-0.305877\pi$
$727$	30.8860	1.14550	0.572750	+	0.819730i	$0.305877\pi$
$728$	−96.7943	−3.58744
$729$	1.00000	0.0370370
$730$	−85.7764	−3.17473
$731$	1.89694	0.0701608
$732$	−28.1309	−1.03975
$733$	43.6707	1.61301	0.806506	−	0.591226i	$-0.201356\pi$
$733$	43.6707	1.61301	0.806506	+	0.591226i	$0.201356\pi$
$734$	32.5532	1.20156
$735$	−30.1927	−1.11367
$736$	2.23177	0.0822642
$737$	17.9916	0.662731
$738$	−30.4791	−1.12195
$739$	−29.7713	−1.09515	−0.547577	−	0.836755i	$-0.684450\pi$
$739$	−29.7713	−1.09515	−0.547577	+	0.836755i	$0.684450\pi$
$740$	6.26620	0.230350
$741$	8.77052	0.322193
$742$	70.5862	2.59130
$743$	−37.3360	−1.36972	−0.684862	−	0.728673i	$-0.740137\pi$
$743$	−37.3360	−1.36972	−0.684862	+	0.728673i	$0.740137\pi$
$744$	−20.9636	−0.768562
$745$	−59.3249	−2.17350
$746$	35.3471	1.29415
$747$	6.94486	0.254099
$748$	−3.80022	−0.138950
$749$	−26.3064	−0.961216
$750$	41.3603	1.51026
$751$	−39.0514	−1.42500	−0.712502	−	0.701670i	$-0.752438\pi$
$751$	−39.0514	−1.42500	−0.712502	+	0.701670i	$0.752438\pi$
$752$	34.1348	1.24477
$753$	25.3510	0.923841
$754$	−28.2567	−1.02905
$755$	−43.6337	−1.58799
$756$	−15.9162	−0.578867
$757$	43.0572	1.56494	0.782471	−	0.622687i	$-0.213959\pi$
$757$	43.0572	1.56494	0.782471	+	0.622687i	$0.213959\pi$
$758$	−9.99724	−0.363116
$759$	−5.84836	−0.212282
$760$	−36.4105	−1.32075
$761$	−7.54980	−0.273680	−0.136840	−	0.990593i	$-0.543695\pi$
$761$	−7.54980	−0.273680	−0.136840	+	0.990593i	$0.543695\pi$
$762$	−31.4798	−1.14039
$763$	−36.7475	−1.33035
$764$	−56.4370	−2.04182
$765$	1.13503	0.0410372
$766$	21.5385	0.778218
$767$	−23.2286	−0.838736
$768$	−32.5888	−1.17595
$769$	−26.0584	−0.939689	−0.469844	−	0.882749i	$-0.655690\pi$
$769$	−26.0584	−0.939689	−0.469844	+	0.882749i	$0.655690\pi$
$770$	−112.077	−4.03899
$771$	−17.4897	−0.629875
$772$	−44.0779	−1.58640
$773$	10.2998	0.370459	0.185229	−	0.982695i	$-0.440697\pi$
$773$	10.2998	0.370459	0.185229	+	0.982695i	$0.440697\pi$
$774$	15.6873	0.563867
$775$	37.6873	1.35377
$776$	−44.8067	−1.60847
$777$	1.55119	0.0556487
$778$	−1.32109	−0.0473632
$779$	−22.5961	−0.809589
$780$	74.7302	2.67577
$781$	−35.8067	−1.28126
$782$	−1.40076	−0.0500912
$783$	−2.38851	−0.0853585
$784$	37.4506	1.33752
$785$	83.2277	2.97052
$786$	4.95225	0.176641
$787$	−40.9206	−1.45866	−0.729330	−	0.684162i	$-0.760168\pi$
$787$	−40.9206	−1.45866	−0.729330	+	0.684162i	$0.760168\pi$
$788$	−49.0636	−1.74782
$789$	−1.71974	−0.0612244
$790$	61.6280	2.19262
$791$	44.6385	1.58716
$792$	−16.1554	−0.574058
$793$	32.6966	1.16109
$794$	−68.8596	−2.44374
$795$	−28.0145	−0.993572
$796$	7.11905	0.252328
$797$	−10.9285	−0.387108	−0.193554	−	0.981090i	$-0.562001\pi$
$797$	−10.9285	−0.387108	−0.193554	+	0.981090i	$0.562001\pi$
$798$	−17.5336	−0.620683
$799$	−2.16818	−0.0767046
$800$	−11.0832	−0.391849
$801$	10.7277	0.379045
$802$	66.1523	2.33592
$803$	−28.2158	−0.995712
$804$	23.9825	0.845798
$805$	−27.8019	−0.979888
$806$	47.3988	1.66955
$807$	22.8023	0.802679
$808$	5.57108	0.195990
$809$	19.5101	0.685939	0.342970	−	0.939346i	$-0.388567\pi$
$809$	19.5101	0.685939	0.342970	+	0.939346i	$0.388567\pi$
$810$	9.38648	0.329807
$811$	−4.75107	−0.166833	−0.0834163	−	0.996515i	$-0.526583\pi$
$811$	−4.75107	−0.166833	−0.0834163	+	0.996515i	$0.526583\pi$
$812$	38.0161	1.33410
$813$	−16.4701	−0.577631
$814$	3.06287	0.107354
$815$	−56.6435	−1.98414
$816$	−1.40788	−0.0492856
$817$	11.6300	0.406881
$818$	48.5561	1.69772
$819$	18.4994	0.646422
$820$	−192.533	−6.72353
$821$	−18.9456	−0.661205	−0.330602	−	0.943770i	$-0.607252\pi$
$821$	−18.9456	−0.661205	−0.330602	+	0.943770i	$0.607252\pi$
$822$	−29.7020	−1.03598
$823$	55.8935	1.94832	0.974162	−	0.225851i	$-0.0725163\pi$
$823$	55.8935	1.94832	0.974162	+	0.225851i	$0.0725163\pi$
$824$	88.2738	3.07516
$825$	29.0435	1.01116
$826$	46.4374	1.61577
$827$	−3.23396	−0.112456	−0.0562278	−	0.998418i	$-0.517907\pi$
$827$	−3.23396	−0.112456	−0.0562278	+	0.998418i	$0.517907\pi$
$828$	−7.79575	−0.270921
$829$	41.5909	1.44451	0.722256	−	0.691626i	$-0.243105\pi$
$829$	41.5909	1.44451	0.722256	+	0.691626i	$0.243105\pi$
$830$	65.1877	2.26270
$831$	−15.2770	−0.529952
$832$	31.1044	1.07835
$833$	−2.37879	−0.0824202
$834$	13.1591	0.455664
$835$	54.9387	1.90123
$836$	−23.2988	−0.805805
$837$	4.00657	0.138487
$838$	−36.0253	−1.24447
$839$	−10.3108	−0.355968	−0.177984	−	0.984033i	$-0.556958\pi$
$839$	−10.3108	−0.355968	−0.177984	+	0.984033i	$0.556958\pi$
$840$	−76.7995	−2.64984
$841$	−23.2950	−0.803276
$842$	23.0206	0.793341
$843$	4.68427	0.161335
$844$	13.9834	0.481330
$845$	−37.5166	−1.29061
$846$	−17.9303	−0.616458
$847$	5.67111	0.194862
$848$	34.7488	1.19328
$849$	13.5180	0.463935
$850$	6.95631	0.238599
$851$	0.759774	0.0260447
$852$	−47.7296	−1.63519
$853$	11.8396	0.405380	0.202690	−	0.979243i	$-0.435032\pi$
$853$	11.8396	0.405380	0.202690	+	0.979243i	$0.435032\pi$
$854$	−65.3655	−2.23676
$855$	6.95879	0.237986
$856$	−35.5930	−1.21654
$857$	1.57471	0.0537912	0.0268956	−	0.999638i	$-0.491438\pi$
$857$	1.57471	0.0537912	0.0268956	+	0.999638i	$0.491438\pi$
$858$	36.5275	1.24703
$859$	−6.69058	−0.228280	−0.114140	−	0.993465i	$-0.536411\pi$
$859$	−6.69058	−0.228280	−0.114140	+	0.993465i	$0.536411\pi$
$860$	99.0945	3.37909
$861$	−47.6613	−1.62429
$862$	93.8038	3.19497
$863$	−26.3025	−0.895347	−0.447673	−	0.894197i	$-0.647747\pi$
$863$	−26.3025	−0.895347	−0.447673	+	0.894197i	$0.647747\pi$
$864$	−1.17826	−0.0400853
$865$	−33.4713	−1.13806
$866$	−8.04227	−0.273287
$867$	−16.9106	−0.574313
$868$	−63.7694	−2.16448
$869$	20.2722	0.687689
$870$	−22.4197	−0.760100
$871$	−27.8749	−0.944504
$872$	−49.7200	−1.68373
$873$	8.56348	0.289830
$874$	−8.58796	−0.290492
$875$	64.6767	2.18647
$876$	−37.6111	−1.27076
$877$	35.3083	1.19228	0.596139	−	0.802882i	$-0.296701\pi$
$877$	35.3083	1.19228	0.596139	+	0.802882i	$0.296701\pi$
$878$	−14.0930	−0.475616
$879$	0.971189	0.0327574
$880$	−55.1744	−1.85993
$881$	−17.2783	−0.582120	−0.291060	−	0.956705i	$-0.594008\pi$
$881$	−17.2783	−0.582120	−0.291060	+	0.956705i	$0.594008\pi$
$882$	−19.6721	−0.662393
$883$	20.6978	0.696538	0.348269	−	0.937395i	$-0.386770\pi$
$883$	20.6978	0.696538	0.348269	+	0.937395i	$0.386770\pi$
$884$	5.88777	0.198027
$885$	−18.4303	−0.619526
$886$	63.6497	2.13835
$887$	−24.2546	−0.814389	−0.407194	−	0.913342i	$-0.633493\pi$
$887$	−24.2546	−0.814389	−0.407194	+	0.913342i	$0.633493\pi$
$888$	2.09879	0.0704308
$889$	−49.2261	−1.65099
$890$	100.695	3.37532
$891$	3.08764	0.103440
$892$	11.7491	0.393390
$893$	−13.2929	−0.444830
$894$	−38.6532	−1.29276
$895$	73.2033	2.44692
$896$	−71.2954	−2.38181
$897$	9.06101	0.302538
$898$	10.0018	0.333765
$899$	−9.56976	−0.319169
$900$	38.7144	1.29048
$901$	−2.20718	−0.0735317
$902$	−94.1084	−3.13347
$903$	24.5308	0.816333
$904$	60.3967	2.00876
$905$	−74.1815	−2.46588
$906$	−28.4295	−0.944508
$907$	−43.4278	−1.44199	−0.720997	−	0.692938i	$-0.756316\pi$
$907$	−43.4278	−1.44199	−0.720997	+	0.692938i	$0.756316\pi$
$908$	−78.7868	−2.61463
$909$	−1.06475	−0.0353155
$910$	173.644	5.75625
$911$	4.19985	0.139147	0.0695736	−	0.997577i	$-0.477836\pi$
$911$	4.19985	0.139147	0.0695736	+	0.997577i	$0.477836\pi$
$912$	−8.63159	−0.285820
$913$	21.4432	0.709667
$914$	−8.61195	−0.284858
$915$	25.9425	0.857632
$916$	−1.93453	−0.0639186
$917$	7.74402	0.255730
$918$	0.739532	0.0244082
$919$	−16.3779	−0.540258	−0.270129	−	0.962824i	$-0.587066\pi$
$919$	−16.3779	−0.540258	−0.270129	+	0.962824i	$0.587066\pi$
$920$	−37.6164	−1.24018
$921$	−10.0391	−0.330798
$922$	77.8244	2.56301
$923$	55.4762	1.82602
$924$	−49.1435	−1.61670
$925$	−3.77310	−0.124059
$926$	43.2995	1.42291
$927$	−16.8710	−0.554115
$928$	2.81430	0.0923838
$929$	36.1402	1.18572	0.592860	−	0.805305i	$-0.297999\pi$
$929$	36.1402	1.18572	0.592860	+	0.805305i	$0.297999\pi$
$930$	37.6076	1.23320
$931$	−14.5842	−0.477976
$932$	30.5114	0.999436
$933$	27.9275	0.914305
$934$	−32.1425	−1.05174
$935$	3.50457	0.114612
$936$	25.0300	0.818131
$937$	−3.55692	−0.116199	−0.0580997	−	0.998311i	$-0.518504\pi$
$937$	−3.55692	−0.116199	−0.0580997	+	0.998311i	$0.518504\pi$
$938$	55.7261	1.81952
$939$	24.1248	0.787283
$940$	−113.264	−3.69426
$941$	34.0458	1.10986	0.554931	−	0.831897i	$-0.312745\pi$
$941$	34.0458	1.10986	0.554931	+	0.831897i	$0.312745\pi$
$942$	54.2270	1.76681
$943$	−23.3445	−0.760202
$944$	22.8606	0.744050
$945$	14.6780	0.477475
$946$	48.4366	1.57481
$947$	20.8030	0.676005	0.338003	−	0.941145i	$-0.390249\pi$
$947$	20.8030	0.676005	0.338003	+	0.941145i	$0.390249\pi$
$948$	27.0225	0.877650
$949$	43.7153	1.41906
$950$	42.6485	1.38370
$951$	−14.3245	−0.464503
$952$	−6.05080	−0.196108
$953$	−16.6029	−0.537822	−0.268911	−	0.963165i	$-0.586664\pi$
$953$	−16.6029	−0.537822	−0.268911	+	0.963165i	$0.586664\pi$
$954$	−18.2529	−0.590958
$955$	52.0464	1.68418
$956$	−48.5740	−1.57100
$957$	−7.37487	−0.238396
$958$	−83.0161	−2.68213
$959$	−46.4461	−1.49982
$960$	24.6792	0.796517
$961$	−14.9474	−0.482173
$962$	−4.74538	−0.152997
$963$	6.80257	0.219210
$964$	−52.8123	−1.70097
$965$	40.6489	1.30853
$966$	−18.1143	−0.582819
$967$	52.3814	1.68447	0.842237	−	0.539108i	$-0.181238\pi$
$967$	52.3814	1.68447	0.842237	+	0.539108i	$0.181238\pi$
$968$	7.67310	0.246623
$969$	0.548262	0.0176127
$970$	80.3809	2.58088
$971$	3.53651	0.113492	0.0567461	−	0.998389i	$-0.481927\pi$
$971$	3.53651	0.113492	0.0567461	+	0.998389i	$0.481927\pi$
$972$	4.11576	0.132013
$973$	20.5775	0.659683
$974$	−20.7356	−0.664410
$975$	−44.9978	−1.44108
$976$	−32.1787	−1.03001
$977$	−49.9612	−1.59840	−0.799200	−	0.601065i	$-0.794743\pi$
$977$	−49.9612	−1.59840	−0.799200	+	0.601065i	$0.794743\pi$
$978$	−36.9061	−1.18013
$979$	33.1233	1.05862
$980$	−124.266	−3.96953
$981$	9.50253	0.303392
$982$	−75.8194	−2.41950
$983$	−30.3493	−0.967992	−0.483996	−	0.875070i	$-0.660815\pi$
$983$	−30.3493	−0.967992	−0.483996	+	0.875070i	$0.660815\pi$
$984$	−64.4865	−2.05575
$985$	45.2467	1.44168
$986$	−1.76638	−0.0562531
$987$	−28.0383	−0.892470
$988$	36.0974	1.14841
$989$	12.0152	0.382060
$990$	28.9820	0.921110
$991$	−15.5117	−0.492747	−0.246373	−	0.969175i	$-0.579239\pi$
$991$	−15.5117	−0.492747	−0.246373	+	0.969175i	$0.579239\pi$
$992$	−4.72080	−0.149885
$993$	13.0435	0.413922
$994$	−110.905	−3.51770
$995$	−6.56521	−0.208131
$996$	28.5834	0.905699
$997$	10.5350	0.333647	0.166824	−	0.985987i	$-0.446649\pi$
$997$	10.5350	0.333647	0.166824	+	0.985987i	$0.446649\pi$
$998$	10.7238	0.339455
$999$	−0.401122	−0.0126909

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6033.2.a.b.1.6	✓	71

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6033.2.a.b.1.6	✓	71	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:	\( N \)	\(=\)	\( 6033 = 3 \cdot 2011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6033.a (trivial)

\(f(q)\)	\(=\)	\(q-2.47301 q^{2} +1.00000 q^{3} +4.11576 q^{4} -3.79557 q^{5} -2.47301 q^{6} -3.86713 q^{7} -5.23229 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.47301 q^{2} +1.00000 q^{3} +4.11576 q^{4} -3.79557 q^{5} -2.47301 q^{6} -3.86713 q^{7} -5.23229 q^{8} +1.00000 q^{9} +9.38648 q^{10} +3.08764 q^{11} +4.11576 q^{12} -4.78375 q^{13} +9.56345 q^{14} -3.79557 q^{15} +4.70797 q^{16} -0.299042 q^{17} -2.47301 q^{18} -1.83340 q^{19} -15.6217 q^{20} -3.86713 q^{21} -7.63575 q^{22} -1.89412 q^{23} -5.23229 q^{24} +9.40637 q^{25} +11.8303 q^{26} +1.00000 q^{27} -15.9162 q^{28} -2.38851 q^{29} +9.38648 q^{30} +4.00657 q^{31} -1.17826 q^{32} +3.08764 q^{33} +0.739532 q^{34} +14.6780 q^{35} +4.11576 q^{36} -0.401122 q^{37} +4.53400 q^{38} -4.78375 q^{39} +19.8596 q^{40} +12.3247 q^{41} +9.56345 q^{42} -6.34340 q^{43} +12.7080 q^{44} -3.79557 q^{45} +4.68418 q^{46} +7.25042 q^{47} +4.70797 q^{48} +7.95472 q^{49} -23.2620 q^{50} -0.299042 q^{51} -19.6888 q^{52} +7.38084 q^{53} -2.47301 q^{54} -11.7194 q^{55} +20.2340 q^{56} -1.83340 q^{57} +5.90681 q^{58} +4.85572 q^{59} -15.6217 q^{60} -6.83493 q^{61} -9.90829 q^{62} -3.86713 q^{63} -6.50210 q^{64} +18.1571 q^{65} -7.63575 q^{66} +5.82699 q^{67} -1.23078 q^{68} -1.89412 q^{69} -36.2988 q^{70} -11.5968 q^{71} -5.23229 q^{72} -9.13830 q^{73} +0.991978 q^{74} +9.40637 q^{75} -7.54583 q^{76} -11.9403 q^{77} +11.8303 q^{78} +6.56561 q^{79} -17.8695 q^{80} +1.00000 q^{81} -30.4791 q^{82} +6.94486 q^{83} -15.9162 q^{84} +1.13503 q^{85} +15.6873 q^{86} -2.38851 q^{87} -16.1554 q^{88} +10.7277 q^{89} +9.38648 q^{90} +18.4994 q^{91} -7.79575 q^{92} +4.00657 q^{93} -17.9303 q^{94} +6.95879 q^{95} -1.17826 q^{96} +8.56348 q^{97} -19.6721 q^{98} +3.08764 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 71 q - 11 q^{2} + 71 q^{3} + 53 q^{4} - 8 q^{5} - 11 q^{6} - 46 q^{7} - 33 q^{8} + 71 q^{9}+O(q^{10}) \) 71 * q - 11 * q^2 + 71 * q^3 + 53 * q^4 - 8 * q^5 - 11 * q^6 - 46 * q^7 - 33 * q^8 + 71 * q^9	\( 71 q - 11 q^{2} + 71 q^{3} + 53 q^{4} - 8 q^{5} - 11 q^{6} - 46 q^{7} - 33 q^{8} + 71 q^{9} - 41 q^{10} - 18 q^{11} + 53 q^{12} - 67 q^{13} - 7 q^{14} - 8 q^{15} + 21 q^{16} - 25 q^{17} - 11 q^{18} - 43 q^{19} - 8 q^{20} - 46 q^{21} - 49 q^{22} - 75 q^{23} - 33 q^{24} + 19 q^{25} + 71 q^{27} - 89 q^{28} - 35 q^{29} - 41 q^{30} - 82 q^{31} - 62 q^{32} - 18 q^{33} - 28 q^{34} - 51 q^{35} + 53 q^{36} - 66 q^{37} - 29 q^{38} - 67 q^{39} - 102 q^{40} + q^{41} - 7 q^{42} - 112 q^{43} - 25 q^{44} - 8 q^{45} - 36 q^{46} - 67 q^{47} + 21 q^{48} + 7 q^{49} - 24 q^{50} - 25 q^{51} - 134 q^{52} - 40 q^{53} - 11 q^{54} - 112 q^{55} + 9 q^{56} - 43 q^{57} - 47 q^{58} - 18 q^{59} - 8 q^{60} - 144 q^{61} - 19 q^{62} - 46 q^{63} - 17 q^{64} - 31 q^{65} - 49 q^{66} - 85 q^{67} - 22 q^{68} - 75 q^{69} - 11 q^{70} - 44 q^{71} - 33 q^{72} - 98 q^{73} + 6 q^{74} + 19 q^{75} - 85 q^{76} - 39 q^{77} - 126 q^{79} + 21 q^{80} + 71 q^{81} - 69 q^{82} - 43 q^{83} - 89 q^{84} - 112 q^{85} + 32 q^{86} - 35 q^{87} - 85 q^{88} + 8 q^{89} - 41 q^{90} - 40 q^{91} - 96 q^{92} - 82 q^{93} - 99 q^{94} - 103 q^{95} - 62 q^{96} - 67 q^{97} - 11 q^{98} - 18 q^{99}+O(q^{100}) \) 71 * q - 11 * q^2 + 71 * q^3 + 53 * q^4 - 8 * q^5 - 11 * q^6 - 46 * q^7 - 33 * q^8 + 71 * q^9 - 41 * q^10 - 18 * q^11 + 53 * q^12 - 67 * q^13 - 7 * q^14 - 8 * q^15 + 21 * q^16 - 25 * q^17 - 11 * q^18 - 43 * q^19 - 8 * q^20 - 46 * q^21 - 49 * q^22 - 75 * q^23 - 33 * q^24 + 19 * q^25 + 71 * q^27 - 89 * q^28 - 35 * q^29 - 41 * q^30 - 82 * q^31 - 62 * q^32 - 18 * q^33 - 28 * q^34 - 51 * q^35 + 53 * q^36 - 66 * q^37 - 29 * q^38 - 67 * q^39 - 102 * q^40 + q^41 - 7 * q^42 - 112 * q^43 - 25 * q^44 - 8 * q^45 - 36 * q^46 - 67 * q^47 + 21 * q^48 + 7 * q^49 - 24 * q^50 - 25 * q^51 - 134 * q^52 - 40 * q^53 - 11 * q^54 - 112 * q^55 + 9 * q^56 - 43 * q^57 - 47 * q^58 - 18 * q^59 - 8 * q^60 - 144 * q^61 - 19 * q^62 - 46 * q^63 - 17 * q^64 - 31 * q^65 - 49 * q^66 - 85 * q^67 - 22 * q^68 - 75 * q^69 - 11 * q^70 - 44 * q^71 - 33 * q^72 - 98 * q^73 + 6 * q^74 + 19 * q^75 - 85 * q^76 - 39 * q^77 - 126 * q^79 + 21 * q^80 + 71 * q^81 - 69 * q^82 - 43 * q^83 - 89 * q^84 - 112 * q^85 + 32 * q^86 - 35 * q^87 - 85 * q^88 + 8 * q^89 - 41 * q^90 - 40 * q^91 - 96 * q^92 - 82 * q^93 - 99 * q^94 - 103 * q^95 - 62 * q^96 - 67 * q^97 - 11 * q^98 - 18 * q^99

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