LMFDB - Embedded newform 6033.2.a.b.1.10

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			1.10
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)

$f(q)$	$=$	$q-2.28528 q^{2} +1.00000 q^{3} +3.22252 q^{4} -1.27062 q^{5} -2.28528 q^{6} -1.88714 q^{7} -2.79381 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.28528 q^{2} +1.00000 q^{3} +3.22252 q^{4} -1.27062 q^{5} -2.28528 q^{6} -1.88714 q^{7} -2.79381 q^{8} +1.00000 q^{9} +2.90374 q^{10} +1.58203 q^{11} +3.22252 q^{12} +2.22131 q^{13} +4.31266 q^{14} -1.27062 q^{15} -0.0604011 q^{16} -4.76522 q^{17} -2.28528 q^{18} -4.36525 q^{19} -4.09461 q^{20} -1.88714 q^{21} -3.61539 q^{22} -0.598551 q^{23} -2.79381 q^{24} -3.38552 q^{25} -5.07633 q^{26} +1.00000 q^{27} -6.08136 q^{28} +9.48258 q^{29} +2.90374 q^{30} +1.34807 q^{31} +5.72565 q^{32} +1.58203 q^{33} +10.8899 q^{34} +2.39785 q^{35} +3.22252 q^{36} +5.61496 q^{37} +9.97584 q^{38} +2.22131 q^{39} +3.54988 q^{40} +6.48741 q^{41} +4.31266 q^{42} -0.904939 q^{43} +5.09813 q^{44} -1.27062 q^{45} +1.36786 q^{46} -4.07467 q^{47} -0.0604011 q^{48} -3.43869 q^{49} +7.73686 q^{50} -4.76522 q^{51} +7.15823 q^{52} -0.221603 q^{53} -2.28528 q^{54} -2.01017 q^{55} +5.27231 q^{56} -4.36525 q^{57} -21.6704 q^{58} +9.31472 q^{59} -4.09461 q^{60} +12.7095 q^{61} -3.08071 q^{62} -1.88714 q^{63} -12.9639 q^{64} -2.82245 q^{65} -3.61539 q^{66} -14.5162 q^{67} -15.3560 q^{68} -0.598551 q^{69} -5.47976 q^{70} +4.01839 q^{71} -2.79381 q^{72} -11.7497 q^{73} -12.8318 q^{74} -3.38552 q^{75} -14.0671 q^{76} -2.98552 q^{77} -5.07633 q^{78} -1.48959 q^{79} +0.0767471 q^{80} +1.00000 q^{81} -14.8256 q^{82} -10.7772 q^{83} -6.08136 q^{84} +6.05480 q^{85} +2.06804 q^{86} +9.48258 q^{87} -4.41989 q^{88} +4.04574 q^{89} +2.90374 q^{90} -4.19194 q^{91} -1.92884 q^{92} +1.34807 q^{93} +9.31177 q^{94} +5.54659 q^{95} +5.72565 q^{96} +4.59420 q^{97} +7.85838 q^{98} +1.58203 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.28528	−1.61594	−0.807970	−	0.589224i	$-0.799434\pi$
$2$	−2.28528	−1.61594	−0.807970	+	0.589224i	$0.799434\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	3.22252	1.61126
$5$	−1.27062	−0.568240	−0.284120	−	0.958789i	$-0.591701\pi$
$5$	−1.27062	−0.568240	−0.284120	+	0.958789i	$0.591701\pi$
$6$	−2.28528	−0.932963
$7$	−1.88714	−0.713273	−0.356637	−	0.934243i	$-0.616077\pi$
$7$	−1.88714	−0.713273	−0.356637	+	0.934243i	$0.616077\pi$
$8$	−2.79381	−0.987760
$9$	1.00000	0.333333
$10$	2.90374	0.918242
$11$	1.58203	0.477001	0.238500	−	0.971142i	$-0.423344\pi$
$11$	1.58203	0.477001	0.238500	+	0.971142i	$0.423344\pi$
$12$	3.22252	0.930262
$13$	2.22131	0.616081	0.308041	−	0.951373i	$-0.400327\pi$
$13$	2.22131	0.616081	0.308041	+	0.951373i	$0.400327\pi$
$14$	4.31266	1.15261
$15$	−1.27062	−0.328074
$16$	−0.0604011	−0.0151003
$17$	−4.76522	−1.15573	−0.577867	−	0.816131i	$-0.696115\pi$
$17$	−4.76522	−1.15573	−0.577867	+	0.816131i	$0.696115\pi$
$18$	−2.28528	−0.538646
$19$	−4.36525	−1.00146	−0.500729	−	0.865604i	$-0.666935\pi$
$19$	−4.36525	−1.00146	−0.500729	+	0.865604i	$0.666935\pi$
$20$	−4.09461	−0.915583
$21$	−1.88714	−0.411808
$22$	−3.61539	−0.770804
$23$	−0.598551	−0.124807	−0.0624033	−	0.998051i	$-0.519876\pi$
$23$	−0.598551	−0.124807	−0.0624033	+	0.998051i	$0.519876\pi$
$24$	−2.79381	−0.570283
$25$	−3.38552	−0.677103
$26$	−5.07633	−0.995550
$27$	1.00000	0.192450
$28$	−6.08136	−1.14927
$29$	9.48258	1.76087	0.880435	−	0.474167i	$-0.157251\pi$
$29$	9.48258	1.76087	0.880435	+	0.474167i	$0.157251\pi$
$30$	2.90374	0.530147
$31$	1.34807	0.242120	0.121060	−	0.992645i	$-0.461371\pi$
$31$	1.34807	0.242120	0.121060	+	0.992645i	$0.461371\pi$
$32$	5.72565	1.01216
$33$	1.58203	0.275396
$34$	10.8899	1.86760
$35$	2.39785	0.405310
$36$	3.22252	0.537087
$37$	5.61496	0.923093	0.461546	−	0.887116i	$-0.347295\pi$
$37$	5.61496	0.923093	0.461546	+	0.887116i	$0.347295\pi$
$38$	9.97584	1.61829
$39$	2.22131	0.355695
$40$	3.54988	0.561285
$41$	6.48741	1.01316	0.506582	−	0.862192i	$-0.330909\pi$
$41$	6.48741	1.01316	0.506582	+	0.862192i	$0.330909\pi$
$42$	4.31266	0.665458
$43$	−0.904939	−0.138002	−0.0690009	−	0.997617i	$-0.521981\pi$
$43$	−0.904939	−0.138002	−0.0690009	+	0.997617i	$0.521981\pi$
$44$	5.09813	0.768572
$45$	−1.27062	−0.189413
$46$	1.36786	0.201680
$47$	−4.07467	−0.594351	−0.297176	−	0.954823i	$-0.596045\pi$
$47$	−4.07467	−0.594351	−0.297176	+	0.954823i	$0.596045\pi$
$48$	−0.0604011	−0.00871815
$49$	−3.43869	−0.491241
$50$	7.73686	1.09416
$51$	−4.76522	−0.667264
$52$	7.15823	0.992667
$53$	−0.221603	−0.0304395	−0.0152198	−	0.999884i	$-0.504845\pi$
$53$	−0.221603	−0.0304395	−0.0152198	+	0.999884i	$0.504845\pi$
$54$	−2.28528	−0.310988
$55$	−2.01017	−0.271051
$56$	5.27231	0.704543
$57$	−4.36525	−0.578192
$58$	−21.6704	−2.84546
$59$	9.31472	1.21267	0.606337	−	0.795208i	$-0.292638\pi$
$59$	9.31472	1.21267	0.606337	+	0.795208i	$0.292638\pi$
$60$	−4.09461	−0.528612
$61$	12.7095	1.62729	0.813643	−	0.581364i	$-0.197481\pi$
$61$	12.7095	1.62729	0.813643	+	0.581364i	$0.197481\pi$
$62$	−3.08071	−0.391251
$63$	−1.88714	−0.237758
$64$	−12.9639	−1.62049
$65$	−2.82245	−0.350082
$66$	−3.61539	−0.445024
$67$	−14.5162	−1.77343	−0.886715	−	0.462316i	$-0.847019\pi$
$67$	−14.5162	−1.77343	−0.886715	+	0.462316i	$0.847019\pi$
$68$	−15.3560	−1.86219
$69$	−0.598551	−0.0720571
$70$	−5.47976	−0.654957
$71$	4.01839	0.476895	0.238448	−	0.971155i	$-0.423361\pi$
$71$	4.01839	0.476895	0.238448	+	0.971155i	$0.423361\pi$
$72$	−2.79381	−0.329253
$73$	−11.7497	−1.37520	−0.687599	−	0.726090i	$-0.741335\pi$
$73$	−11.7497	−1.37520	−0.687599	+	0.726090i	$0.741335\pi$
$74$	−12.8318	−1.49166
$75$	−3.38552	−0.390926
$76$	−14.0671	−1.61361
$77$	−2.98552	−0.340232
$78$	−5.07633	−0.574781
$79$	−1.48959	−0.167592	−0.0837960	−	0.996483i	$-0.526704\pi$
$79$	−1.48959	−0.167592	−0.0837960	+	0.996483i	$0.526704\pi$
$80$	0.0767471	0.00858058
$81$	1.00000	0.111111
$82$	−14.8256	−1.63721
$83$	−10.7772	−1.18295	−0.591475	−	0.806324i	$-0.701454\pi$
$83$	−10.7772	−1.18295	−0.591475	+	0.806324i	$0.701454\pi$
$84$	−6.08136	−0.663531
$85$	6.05480	0.656735
$86$	2.06804	0.223003
$87$	9.48258	1.01664
$88$	−4.41989	−0.471162
$89$	4.04574	0.428848	0.214424	−	0.976741i	$-0.431213\pi$
$89$	4.04574	0.428848	0.214424	+	0.976741i	$0.431213\pi$
$90$	2.90374	0.306081
$91$	−4.19194	−0.439434
$92$	−1.92884	−0.201096
$93$	1.34807	0.139788
$94$	9.31177	0.960436
$95$	5.54659	0.569068
$96$	5.72565	0.584371
$97$	4.59420	0.466470	0.233235	−	0.972420i	$-0.425069\pi$
$97$	4.59420	0.466470	0.233235	+	0.972420i	$0.425069\pi$
$98$	7.85838	0.793816
$99$	1.58203	0.159000
$100$	−10.9099	−1.09099
$101$	−5.75166	−0.572312	−0.286156	−	0.958183i	$-0.592377\pi$
$101$	−5.75166	−0.572312	−0.286156	+	0.958183i	$0.592377\pi$
$102$	10.8899	1.07826
$103$	4.41654	0.435174	0.217587	−	0.976041i	$-0.430181\pi$
$103$	4.41654	0.435174	0.217587	+	0.976041i	$0.430181\pi$
$104$	−6.20592	−0.608540
$105$	2.39785	0.234006
$106$	0.506426	0.0491884
$107$	−12.8481	−1.24207	−0.621037	−	0.783781i	$-0.713288\pi$
$107$	−12.8481	−1.24207	−0.621037	+	0.783781i	$0.713288\pi$
$108$	3.22252	0.310087
$109$	−4.89635	−0.468985	−0.234492	−	0.972118i	$-0.575343\pi$
$109$	−4.89635	−0.468985	−0.234492	+	0.972118i	$0.575343\pi$
$110$	4.59380	0.438002
$111$	5.61496	0.532948
$112$	0.113986	0.0107706
$113$	17.4013	1.63698	0.818489	−	0.574522i	$-0.194812\pi$
$113$	17.4013	1.63698	0.818489	+	0.574522i	$0.194812\pi$
$114$	9.97584	0.934323
$115$	0.760533	0.0709201
$116$	30.5578	2.83722
$117$	2.22131	0.205360
$118$	−21.2868	−1.95961
$119$	8.99264	0.824354
$120$	3.54988	0.324058
$121$	−8.49718	−0.772470
$122$	−29.0448	−2.62960
$123$	6.48741	0.584950
$124$	4.34417	0.390118
$125$	10.6548	0.952997
$126$	4.31266	0.384202
$127$	−8.09707	−0.718499	−0.359249	−	0.933242i	$-0.616967\pi$
$127$	−8.09707	−0.718499	−0.359249	+	0.933242i	$0.616967\pi$
$128$	18.1750	1.60645
$129$	−0.904939	−0.0796754
$130$	6.45010	0.565712
$131$	−5.37332	−0.469469	−0.234734	−	0.972060i	$-0.575422\pi$
$131$	−5.37332	−0.469469	−0.234734	+	0.972060i	$0.575422\pi$
$132$	5.09813	0.443735
$133$	8.23786	0.714313
$134$	33.1735	2.86576
$135$	−1.27062	−0.109358
$136$	13.3131	1.14159
$137$	1.34809	0.115175	0.0575877	−	0.998340i	$-0.481659\pi$
$137$	1.34809	0.115175	0.0575877	+	0.998340i	$0.481659\pi$
$138$	1.36786	0.116440
$139$	14.3225	1.21481	0.607407	−	0.794391i	$-0.292210\pi$
$139$	14.3225	1.21481	0.607407	+	0.794391i	$0.292210\pi$
$140$	7.72712	0.653061
$141$	−4.07467	−0.343149
$142$	−9.18316	−0.770634
$143$	3.51419	0.293871
$144$	−0.0604011	−0.00503343
$145$	−12.0488	−1.00060
$146$	26.8514	2.22224
$147$	−3.43869	−0.283618
$148$	18.0943	1.48734
$149$	8.95617	0.733718	0.366859	−	0.930277i	$-0.380433\pi$
$149$	8.95617	0.733718	0.366859	+	0.930277i	$0.380433\pi$
$150$	7.73686	0.631712
$151$	−15.3786	−1.25149	−0.625747	−	0.780026i	$-0.715206\pi$
$151$	−15.3786	−1.25149	−0.625747	+	0.780026i	$0.715206\pi$
$152$	12.1957	0.989199
$153$	−4.76522	−0.385245
$154$	6.82276	0.549794
$155$	−1.71288	−0.137582
$156$	7.15823	0.573117
$157$	−1.56185	−0.124649	−0.0623247	−	0.998056i	$-0.519851\pi$
$157$	−1.56185	−0.124649	−0.0623247	+	0.998056i	$0.519851\pi$
$158$	3.40413	0.270818
$159$	−0.221603	−0.0175743
$160$	−7.27514	−0.575151
$161$	1.12955	0.0890211
$162$	−2.28528	−0.179549
$163$	−4.02234	−0.315054	−0.157527	−	0.987515i	$-0.550352\pi$
$163$	−4.02234	−0.315054	−0.157527	+	0.987515i	$0.550352\pi$
$164$	20.9058	1.63247
$165$	−2.01017	−0.156491
$166$	24.6289	1.91157
$167$	−2.95622	−0.228759	−0.114379	−	0.993437i	$-0.536488\pi$
$167$	−2.95622	−0.228759	−0.114379	+	0.993437i	$0.536488\pi$
$168$	5.27231	0.406768
$169$	−8.06577	−0.620444
$170$	−13.8369	−1.06124
$171$	−4.36525	−0.333819
$172$	−2.91618	−0.222357
$173$	1.25127	0.0951325	0.0475662	−	0.998868i	$-0.484853\pi$
$173$	1.25127	0.0951325	0.0475662	+	0.998868i	$0.484853\pi$
$174$	−21.6704	−1.64283
$175$	6.38895	0.482959
$176$	−0.0955565	−0.00720284
$177$	9.31472	0.700137
$178$	−9.24567	−0.692992
$179$	−6.46327	−0.483088	−0.241544	−	0.970390i	$-0.577654\pi$
$179$	−6.46327	−0.483088	−0.241544	+	0.970390i	$0.577654\pi$
$180$	−4.09461	−0.305194
$181$	−12.7766	−0.949675	−0.474837	−	0.880074i	$-0.657493\pi$
$181$	−12.7766	−0.949675	−0.474837	+	0.880074i	$0.657493\pi$
$182$	9.57976	0.710099
$183$	12.7095	0.939514
$184$	1.67224	0.123279
$185$	−7.13450	−0.524539
$186$	−3.08071	−0.225889
$187$	−7.53872	−0.551286
$188$	−13.1307	−0.957655
$189$	−1.88714	−0.137269
$190$	−12.6755	−0.919580
$191$	−8.38230	−0.606522	−0.303261	−	0.952908i	$-0.598075\pi$
$191$	−8.38230	−0.606522	−0.303261	+	0.952908i	$0.598075\pi$
$192$	−12.9639	−0.935591
$193$	4.72238	0.339924	0.169962	−	0.985451i	$-0.445635\pi$
$193$	4.72238	0.339924	0.169962	+	0.985451i	$0.445635\pi$
$194$	−10.4990	−0.753787
$195$	−2.82245	−0.202120
$196$	−11.0813	−0.791518
$197$	−4.92854	−0.351144	−0.175572	−	0.984467i	$-0.556177\pi$
$197$	−4.92854	−0.351144	−0.175572	+	0.984467i	$0.556177\pi$
$198$	−3.61539	−0.256935
$199$	5.41341	0.383747	0.191873	−	0.981420i	$-0.438544\pi$
$199$	5.41341	0.383747	0.191873	+	0.981420i	$0.438544\pi$
$200$	9.45848	0.668815
$201$	−14.5162	−1.02389
$202$	13.1442	0.924821
$203$	−17.8950	−1.25598
$204$	−15.3560	−1.07514
$205$	−8.24306	−0.575720
$206$	−10.0930	−0.703215
$207$	−0.598551	−0.0416022
$208$	−0.134170	−0.00930300
$209$	−6.90597	−0.477696
$210$	−5.47976	−0.378140
$211$	−5.83676	−0.401819	−0.200910	−	0.979610i	$-0.564390\pi$
$211$	−5.83676	−0.401819	−0.200910	+	0.979610i	$0.564390\pi$
$212$	−0.714121	−0.0490460
$213$	4.01839	0.275336
$214$	29.3616	2.00712
$215$	1.14984	0.0784182
$216$	−2.79381	−0.190094
$217$	−2.54399	−0.172697
$218$	11.1895	0.757851
$219$	−11.7497	−0.793971
$220$	−6.47781	−0.436734
$221$	−10.5850	−0.712026
$222$	−12.8318	−0.861212
$223$	11.1779	0.748528	0.374264	−	0.927322i	$-0.377895\pi$
$223$	11.1779	0.748528	0.374264	+	0.927322i	$0.377895\pi$
$224$	−10.8051	−0.721947
$225$	−3.38552	−0.225701
$226$	−39.7670	−2.64526
$227$	3.80844	0.252775	0.126388	−	0.991981i	$-0.459662\pi$
$227$	3.80844	0.252775	0.126388	+	0.991981i	$0.459662\pi$
$228$	−14.0671	−0.931617
$229$	5.27259	0.348422	0.174211	−	0.984708i	$-0.444262\pi$
$229$	5.27259	0.348422	0.174211	+	0.984708i	$0.444262\pi$
$230$	−1.73803	−0.114603
$231$	−2.98552	−0.196433
$232$	−26.4925	−1.73932
$233$	19.9689	1.30821	0.654105	−	0.756404i	$-0.273046\pi$
$233$	19.9689	1.30821	0.654105	+	0.756404i	$0.273046\pi$
$234$	−5.07633	−0.331850
$235$	5.17737	0.337734
$236$	30.0169	1.95393
$237$	−1.48959	−0.0967592
$238$	−20.5507	−1.33211
$239$	−12.9140	−0.835334	−0.417667	−	0.908600i	$-0.637152\pi$
$239$	−12.9140	−0.835334	−0.417667	+	0.908600i	$0.637152\pi$
$240$	0.0767471	0.00495400
$241$	−14.9953	−0.965929	−0.482965	−	0.875640i	$-0.660440\pi$
$241$	−14.9953	−0.965929	−0.482965	+	0.875640i	$0.660440\pi$
$242$	19.4185	1.24827
$243$	1.00000	0.0641500
$244$	40.9567	2.62198
$245$	4.36928	0.279143
$246$	−14.8256	−0.945244
$247$	−9.69659	−0.616979
$248$	−3.76623	−0.239156
$249$	−10.7772	−0.682976
$250$	−24.3493	−1.53999
$251$	5.48457	0.346183	0.173091	−	0.984906i	$-0.444624\pi$
$251$	5.48457	0.346183	0.173091	+	0.984906i	$0.444624\pi$
$252$	−6.08136	−0.383090
$253$	−0.946927	−0.0595328
$254$	18.5041	1.16105
$255$	6.05480	0.379166
$256$	−15.6071	−0.975442
$257$	6.84143	0.426756	0.213378	−	0.976970i	$-0.431553\pi$
$257$	6.84143	0.426756	0.213378	+	0.976970i	$0.431553\pi$
$258$	2.06804	0.128751
$259$	−10.5962	−0.658417
$260$	−9.09541	−0.564074
$261$	9.48258	0.586957
$262$	12.2795	0.758633
$263$	9.26938	0.571575	0.285787	−	0.958293i	$-0.407745\pi$
$263$	9.26938	0.571575	0.285787	+	0.958293i	$0.407745\pi$
$264$	−4.41989	−0.272026
$265$	0.281574	0.0172970
$266$	−18.8258	−1.15429
$267$	4.04574	0.247596
$268$	−46.7786	−2.85746
$269$	−23.9852	−1.46240	−0.731202	−	0.682161i	$-0.761040\pi$
$269$	−23.9852	−1.46240	−0.731202	+	0.682161i	$0.761040\pi$
$270$	2.90374	0.176716
$271$	−5.99910	−0.364419	−0.182210	−	0.983260i	$-0.558325\pi$
$271$	−5.99910	−0.364419	−0.182210	+	0.983260i	$0.558325\pi$
$272$	0.287824	0.0174519
$273$	−4.19194	−0.253707
$274$	−3.08077	−0.186116
$275$	−5.35599	−0.322979
$276$	−1.92884	−0.116103
$277$	0.0840055	0.00504740	0.00252370	−	0.999997i	$-0.499197\pi$
$277$	0.0840055	0.00504740	0.00252370	+	0.999997i	$0.499197\pi$
$278$	−32.7309	−1.96307
$279$	1.34807	0.0807066
$280$	−6.69913	−0.400349
$281$	24.1863	1.44284	0.721418	−	0.692500i	$-0.243491\pi$
$281$	24.1863	1.44284	0.721418	+	0.692500i	$0.243491\pi$
$282$	9.31177	0.554508
$283$	−4.84003	−0.287710	−0.143855	−	0.989599i	$-0.545950\pi$
$283$	−4.84003	−0.287710	−0.143855	+	0.989599i	$0.545950\pi$
$284$	12.9493	0.768402
$285$	5.54659	0.328552
$286$	−8.03091	−0.474878
$287$	−12.2427	−0.722662
$288$	5.72565	0.337387
$289$	5.70728	0.335722
$290$	27.5349	1.61690
$291$	4.59420	0.269317
$292$	−37.8637	−2.21580
$293$	1.45523	0.0850153	0.0425077	−	0.999096i	$-0.486465\pi$
$293$	1.45523	0.0850153	0.0425077	+	0.999096i	$0.486465\pi$
$294$	7.85838	0.458310
$295$	−11.8355	−0.689090
$296$	−15.6871	−0.911794
$297$	1.58203	0.0917988
$298$	−20.4674	−1.18564
$299$	−1.32957	−0.0768910
$300$	−10.9099	−0.629883
$301$	1.70775	0.0984330
$302$	35.1445	2.02234
$303$	−5.75166	−0.330424
$304$	0.263666	0.0151223
$305$	−16.1490	−0.924690
$306$	10.8899	0.622532
$307$	−3.90258	−0.222732	−0.111366	−	0.993779i	$-0.535523\pi$
$307$	−3.90258	−0.222732	−0.111366	+	0.993779i	$0.535523\pi$
$308$	−9.62090	−0.548202
$309$	4.41654	0.251248
$310$	3.91443	0.222324
$311$	−32.6923	−1.85381	−0.926905	−	0.375295i	$-0.877541\pi$
$311$	−32.6923	−1.85381	−0.926905	+	0.375295i	$0.877541\pi$
$312$	−6.20592	−0.351341
$313$	−26.4591	−1.49556	−0.747778	−	0.663949i	$-0.768879\pi$
$313$	−26.4591	−1.49556	−0.747778	+	0.663949i	$0.768879\pi$
$314$	3.56928	0.201426
$315$	2.39785	0.135103
$316$	−4.80023	−0.270034
$317$	−5.49207	−0.308465	−0.154233	−	0.988035i	$-0.549291\pi$
$317$	−5.49207	−0.308465	−0.154233	+	0.988035i	$0.549291\pi$
$318$	0.506426	0.0283990
$319$	15.0017	0.839936
$320$	16.4723	0.920828
$321$	−12.8481	−0.717111
$322$	−2.58135	−0.143853
$323$	20.8014	1.15742
$324$	3.22252	0.179029
$325$	−7.52029	−0.417151
$326$	9.19218	0.509108
$327$	−4.89635	−0.270769
$328$	−18.1246	−1.00076
$329$	7.68948	0.423935
$330$	4.59380	0.252880
$331$	3.38912	0.186283	0.0931415	−	0.995653i	$-0.470309\pi$
$331$	3.38912	0.186283	0.0931415	+	0.995653i	$0.470309\pi$
$332$	−34.7297	−1.90604
$333$	5.61496	0.307698
$334$	6.75580	0.369661
$335$	18.4446	1.00773
$336$	0.113986	0.00621842
$337$	−16.5929	−0.903872	−0.451936	−	0.892050i	$-0.649266\pi$
$337$	−16.5929	−0.903872	−0.451936	+	0.892050i	$0.649266\pi$
$338$	18.4326	1.00260
$339$	17.4013	0.945110
$340$	19.5117	1.05817
$341$	2.13268	0.115491
$342$	9.97584	0.539431
$343$	19.6993	1.06366
$344$	2.52822	0.136313
$345$	0.760533	0.0409457
$346$	−2.85951	−0.153728
$347$	−35.9321	−1.92894	−0.964469	−	0.264195i	$-0.914894\pi$
$347$	−35.9321	−1.92894	−0.964469	+	0.264195i	$0.914894\pi$
$348$	30.5578	1.63807
$349$	23.1689	1.24020	0.620102	−	0.784521i	$-0.287091\pi$
$349$	23.1689	1.24020	0.620102	+	0.784521i	$0.287091\pi$
$350$	−14.6006	−0.780433
$351$	2.22131	0.118565
$352$	9.05816	0.482801
$353$	−25.7848	−1.37239	−0.686194	−	0.727418i	$-0.740720\pi$
$353$	−25.7848	−1.37239	−0.686194	+	0.727418i	$0.740720\pi$
$354$	−21.2868	−1.13138
$355$	−5.10586	−0.270991
$356$	13.0375	0.690986
$357$	8.99264	0.475941
$358$	14.7704	0.780641
$359$	0.337428	0.0178087	0.00890437	−	0.999960i	$-0.497166\pi$
$359$	0.337428	0.0178087	0.00890437	+	0.999960i	$0.497166\pi$
$360$	3.54988	0.187095
$361$	0.0554197	0.00291683
$362$	29.1981	1.53462
$363$	−8.49718	−0.445986
$364$	−13.5086	−0.708043
$365$	14.9295	0.781443
$366$	−29.0448	−1.51820
$367$	6.06734	0.316712	0.158356	−	0.987382i	$-0.449381\pi$
$367$	6.06734	0.316712	0.158356	+	0.987382i	$0.449381\pi$
$368$	0.0361531	0.00188461
$369$	6.48741	0.337721
$370$	16.3043	0.847622
$371$	0.418197	0.0217117
$372$	4.34417	0.225235
$373$	−17.6137	−0.912003	−0.456001	−	0.889979i	$-0.650719\pi$
$373$	−17.6137	−0.912003	−0.456001	+	0.889979i	$0.650719\pi$
$374$	17.2281	0.890845
$375$	10.6548	0.550213
$376$	11.3838	0.587076
$377$	21.0638	1.08484
$378$	4.31266	0.221819
$379$	−0.566463	−0.0290973	−0.0145486	−	0.999894i	$-0.504631\pi$
$379$	−0.566463	−0.0290973	−0.0145486	+	0.999894i	$0.504631\pi$
$380$	17.8740	0.916917
$381$	−8.09707	−0.414826
$382$	19.1559	0.980103
$383$	30.8337	1.57553	0.787764	−	0.615977i	$-0.211239\pi$
$383$	30.8337	1.57553	0.787764	+	0.615977i	$0.211239\pi$
$384$	18.1750	0.927487
$385$	3.79347	0.193333
$386$	−10.7920	−0.549297
$387$	−0.904939	−0.0460006
$388$	14.8049	0.751605
$389$	2.58015	0.130819	0.0654094	−	0.997859i	$-0.479165\pi$
$389$	2.58015	0.130819	0.0654094	+	0.997859i	$0.479165\pi$
$390$	6.45010	0.326614
$391$	2.85222	0.144243
$392$	9.60704	0.485229
$393$	−5.37332	−0.271048
$394$	11.2631	0.567427
$395$	1.89271	0.0952325
$396$	5.09813	0.256191
$397$	−1.66930	−0.0837799	−0.0418900	−	0.999122i	$-0.513338\pi$
$397$	−1.66930	−0.0837799	−0.0418900	+	0.999122i	$0.513338\pi$
$398$	−12.3712	−0.620111
$399$	8.23786	0.412409
$400$	0.204489	0.0102244
$401$	27.1317	1.35489	0.677446	−	0.735572i	$-0.263087\pi$
$401$	27.1317	1.35489	0.677446	+	0.735572i	$0.263087\pi$
$402$	33.1735	1.65455
$403$	2.99447	0.149165
$404$	−18.5348	−0.922143
$405$	−1.27062	−0.0631378
$406$	40.8951	2.02959
$407$	8.88304	0.440316
$408$	13.3131	0.659096
$409$	−4.82065	−0.238366	−0.119183	−	0.992872i	$-0.538027\pi$
$409$	−4.82065	−0.238366	−0.119183	+	0.992872i	$0.538027\pi$
$410$	18.8377	0.930329
$411$	1.34809	0.0664965
$412$	14.2324	0.701179
$413$	−17.5782	−0.864968
$414$	1.36786	0.0672266
$415$	13.6937	0.672199
$416$	12.7185	0.623573
$417$	14.3225	0.701374
$418$	15.7821	0.771927
$419$	−18.4342	−0.900571	−0.450285	−	0.892885i	$-0.648678\pi$
$419$	−18.4342	−0.900571	−0.450285	+	0.892885i	$0.648678\pi$
$420$	7.72712	0.377045
$421$	−10.9665	−0.534473	−0.267237	−	0.963631i	$-0.586111\pi$
$421$	−10.9665	−0.534473	−0.267237	+	0.963631i	$0.586111\pi$
$422$	13.3386	0.649315
$423$	−4.07467	−0.198117
$424$	0.619116	0.0300670
$425$	16.1327	0.782551
$426$	−9.18316	−0.444926
$427$	−23.9847	−1.16070
$428$	−41.4033	−2.00130
$429$	3.51419	0.169667
$430$	−2.62770	−0.126719
$431$	1.37465	0.0662144	0.0331072	−	0.999452i	$-0.489460\pi$
$431$	1.37465	0.0662144	0.0331072	+	0.999452i	$0.489460\pi$
$432$	−0.0604011	−0.00290605
$433$	−36.9376	−1.77511	−0.887554	−	0.460703i	$-0.847597\pi$
$433$	−36.9376	−1.77511	−0.887554	+	0.460703i	$0.847597\pi$
$434$	5.81374	0.279069
$435$	−12.0488	−0.577695
$436$	−15.7786	−0.755657
$437$	2.61283	0.124988
$438$	26.8514	1.28301
$439$	−4.06428	−0.193978	−0.0969888	−	0.995285i	$-0.530921\pi$
$439$	−4.06428	−0.193978	−0.0969888	+	0.995285i	$0.530921\pi$
$440$	5.61602	0.267733
$441$	−3.43869	−0.163747
$442$	24.1898	1.15059
$443$	15.4897	0.735940	0.367970	−	0.929838i	$-0.380053\pi$
$443$	15.4897	0.735940	0.367970	+	0.929838i	$0.380053\pi$
$444$	18.0943	0.858718
$445$	−5.14062	−0.243689
$446$	−25.5447	−1.20958
$447$	8.95617	0.423612
$448$	24.4648	1.15585
$449$	9.39372	0.443317	0.221659	−	0.975124i	$-0.428853\pi$
$449$	9.39372	0.443317	0.221659	+	0.975124i	$0.428853\pi$
$450$	7.73686	0.364719
$451$	10.2633	0.483280
$452$	56.0761	2.63760
$453$	−15.3786	−0.722550
$454$	−8.70337	−0.408469
$455$	5.32637	0.249704
$456$	12.1957	0.571115
$457$	16.6255	0.777708	0.388854	−	0.921299i	$-0.372871\pi$
$457$	16.6255	0.777708	0.388854	+	0.921299i	$0.372871\pi$
$458$	−12.0494	−0.563029
$459$	−4.76522	−0.222421
$460$	2.45083	0.114271
$461$	−22.6257	−1.05378	−0.526891	−	0.849933i	$-0.676642\pi$
$461$	−22.6257	−1.05378	−0.526891	+	0.849933i	$0.676642\pi$
$462$	6.82276	0.317424
$463$	−17.3237	−0.805101	−0.402551	−	0.915398i	$-0.631876\pi$
$463$	−17.3237	−0.805101	−0.402551	+	0.915398i	$0.631876\pi$
$464$	−0.572758	−0.0265896
$465$	−1.71288	−0.0794331
$466$	−45.6347	−2.11399
$467$	13.8369	0.640293	0.320147	−	0.947368i	$-0.396268\pi$
$467$	13.8369	0.640293	0.320147	+	0.947368i	$0.396268\pi$
$468$	7.15823	0.330889
$469$	27.3941	1.26494
$470$	−11.8318	−0.545758
$471$	−1.56185	−0.0719664
$472$	−26.0235	−1.19783
$473$	−1.43164	−0.0658270
$474$	3.40413	0.156357
$475$	14.7786	0.678090
$476$	28.9790	1.32825
$477$	−0.221603	−0.0101465
$478$	29.5120	1.34985
$479$	−13.9463	−0.637221	−0.318610	−	0.947886i	$-0.603216\pi$
$479$	−13.9463	−0.637221	−0.318610	+	0.947886i	$0.603216\pi$
$480$	−7.27514	−0.332063
$481$	12.4726	0.568700
$482$	34.2684	1.56088
$483$	1.12955	0.0513964
$484$	−27.3823	−1.24465
$485$	−5.83750	−0.265067
$486$	−2.28528	−0.103663
$487$	−17.6312	−0.798947	−0.399474	−	0.916745i	$-0.630807\pi$
$487$	−17.6312	−0.798947	−0.399474	+	0.916745i	$0.630807\pi$
$488$	−35.5079	−1.60737
$489$	−4.02234	−0.181896
$490$	−9.98505	−0.451078
$491$	−24.3869	−1.10056	−0.550282	−	0.834979i	$-0.685480\pi$
$491$	−24.3869	−1.10056	−0.550282	+	0.834979i	$0.685480\pi$
$492$	20.9058	0.942507
$493$	−45.1865	−2.03510
$494$	22.1595	0.997001
$495$	−2.01017	−0.0903503
$496$	−0.0814246	−0.00365607
$497$	−7.58328	−0.340156
$498$	24.6289	1.10365
$499$	−20.7982	−0.931055	−0.465527	−	0.885034i	$-0.654135\pi$
$499$	−20.7982	−0.931055	−0.465527	+	0.885034i	$0.654135\pi$
$500$	34.3354	1.53553
$501$	−2.95622	−0.132074
$502$	−12.5338	−0.559411
$503$	−23.3056	−1.03914	−0.519572	−	0.854427i	$-0.673908\pi$
$503$	−23.3056	−1.03914	−0.519572	+	0.854427i	$0.673908\pi$
$504$	5.27231	0.234848
$505$	7.30820	0.325210
$506$	2.16400	0.0962014
$507$	−8.06577	−0.358213
$508$	−26.0930	−1.15769
$509$	−32.3328	−1.43312	−0.716562	−	0.697523i	$-0.754286\pi$
$509$	−32.3328	−1.43312	−0.716562	+	0.697523i	$0.754286\pi$
$510$	−13.8369	−0.612709
$511$	22.1734	0.980892
$512$	−0.683333	−0.0301994
$513$	−4.36525	−0.192731
$514$	−15.6346	−0.689613
$515$	−5.61176	−0.247284
$516$	−2.91618	−0.128378
$517$	−6.44625	−0.283506
$518$	24.2154	1.06396
$519$	1.25127	0.0549248
$520$	7.88539	0.345797
$521$	−12.7851	−0.560125	−0.280063	−	0.959982i	$-0.590355\pi$
$521$	−12.7851	−0.560125	−0.280063	+	0.959982i	$0.590355\pi$
$522$	−21.6704	−0.948487
$523$	10.3320	0.451785	0.225893	−	0.974152i	$-0.427470\pi$
$523$	10.3320	0.451785	0.225893	+	0.974152i	$0.427470\pi$
$524$	−17.3156	−0.756436
$525$	6.38895	0.278837
$526$	−21.1832	−0.923630
$527$	−6.42382	−0.279826
$528$	−0.0955565	−0.00415856
$529$	−22.6417	−0.984423
$530$	−0.643477	−0.0279509
$531$	9.31472	0.404225
$532$	26.5467	1.15094
$533$	14.4106	0.624191
$534$	−9.24567	−0.400099
$535$	16.3251	0.705796
$536$	40.5553	1.75172
$537$	−6.46327	−0.278911
$538$	54.8130	2.36316
$539$	−5.44012	−0.234322
$540$	−4.09461	−0.176204
$541$	16.2403	0.698224	0.349112	−	0.937081i	$-0.386483\pi$
$541$	16.2403	0.698224	0.349112	+	0.937081i	$0.386483\pi$
$542$	13.7096	0.588880
$543$	−12.7766	−0.548295
$544$	−27.2839	−1.16979
$545$	6.22141	0.266496
$546$	9.57976	0.409976
$547$	−9.52469	−0.407246	−0.203623	−	0.979049i	$-0.565272\pi$
$547$	−9.52469	−0.407246	−0.203623	+	0.979049i	$0.565272\pi$
$548$	4.34426	0.185577
$549$	12.7095	0.542429
$550$	12.2400	0.521914
$551$	−41.3938	−1.76344
$552$	1.67224	0.0711751
$553$	2.81107	0.119539
$554$	−0.191976	−0.00815629
$555$	−7.13450	−0.302842
$556$	46.1544	1.95738
$557$	13.1143	0.555670	0.277835	−	0.960629i	$-0.410383\pi$
$557$	13.1143	0.555670	0.277835	+	0.960629i	$0.410383\pi$
$558$	−3.08071	−0.130417
$559$	−2.01015	−0.0850204
$560$	−0.144833	−0.00612030
$561$	−7.53872	−0.318285
$562$	−55.2726	−2.33153
$563$	−45.2101	−1.90538	−0.952689	−	0.303946i	$-0.901696\pi$
$563$	−45.2101	−1.90538	−0.952689	+	0.303946i	$0.901696\pi$
$564$	−13.1307	−0.552902
$565$	−22.1105	−0.930197
$566$	11.0608	0.464922
$567$	−1.88714	−0.0792526
$568$	−11.2266	−0.471058
$569$	24.0210	1.00701	0.503507	−	0.863991i	$-0.332043\pi$
$569$	24.0210	1.00701	0.503507	+	0.863991i	$0.332043\pi$
$570$	−12.6755	−0.530920
$571$	−16.0803	−0.672939	−0.336470	−	0.941694i	$-0.609233\pi$
$571$	−16.0803	−0.672939	−0.336470	+	0.941694i	$0.609233\pi$
$572$	11.3245	0.473503
$573$	−8.38230	−0.350176
$574$	27.9780	1.16778
$575$	2.02640	0.0845069
$576$	−12.9639	−0.540164
$577$	23.7935	0.990537	0.495269	−	0.868740i	$-0.335070\pi$
$577$	23.7935	0.990537	0.495269	+	0.868740i	$0.335070\pi$
$578$	−13.0427	−0.542507
$579$	4.72238	0.196255
$580$	−38.8275	−1.61222
$581$	20.3381	0.843766
$582$	−10.4990	−0.435199
$583$	−0.350583	−0.0145197
$584$	32.8264	1.35837
$585$	−2.82245	−0.116694
$586$	−3.32561	−0.137380
$587$	0.494052	0.0203917	0.0101959	−	0.999948i	$-0.496755\pi$
$587$	0.494052	0.0203917	0.0101959	+	0.999948i	$0.496755\pi$
$588$	−11.0813	−0.456983
$589$	−5.88464	−0.242473
$590$	27.0475	1.11353
$591$	−4.92854	−0.202733
$592$	−0.339149	−0.0139390
$593$	−17.3519	−0.712556	−0.356278	−	0.934380i	$-0.615954\pi$
$593$	−17.3519	−0.712556	−0.356278	+	0.934380i	$0.615954\pi$
$594$	−3.61539	−0.148341
$595$	−11.4263	−0.468431
$596$	28.8614	1.18221
$597$	5.41341	0.221556
$598$	3.03844	0.124251
$599$	−8.55564	−0.349574	−0.174787	−	0.984606i	$-0.555924\pi$
$599$	−8.55564	−0.349574	−0.174787	+	0.984606i	$0.555924\pi$
$600$	9.45848	0.386141
$601$	−24.0093	−0.979360	−0.489680	−	0.871902i	$-0.662886\pi$
$601$	−24.0093	−0.979360	−0.489680	+	0.871902i	$0.662886\pi$
$602$	−3.90269	−0.159062
$603$	−14.5162	−0.591143
$604$	−49.5579	−2.01648
$605$	10.7967	0.438949
$606$	13.1442	0.533946
$607$	−4.48207	−0.181922	−0.0909608	−	0.995854i	$-0.528994\pi$
$607$	−4.48207	−0.181922	−0.0909608	+	0.995854i	$0.528994\pi$
$608$	−24.9939	−1.01364
$609$	−17.8950	−0.725141
$610$	36.9051	1.49424
$611$	−9.05111	−0.366169
$612$	−15.3560	−0.620730
$613$	−29.8453	−1.20544	−0.602721	−	0.797952i	$-0.705917\pi$
$613$	−29.8453	−1.20544	−0.602721	+	0.797952i	$0.705917\pi$
$614$	8.91851	0.359922
$615$	−8.24306	−0.332392
$616$	8.34097	0.336067
$617$	−14.7355	−0.593229	−0.296615	−	0.954997i	$-0.595858\pi$
$617$	−14.7355	−0.593229	−0.296615	+	0.954997i	$0.595858\pi$
$618$	−10.0930	−0.406002
$619$	40.9761	1.64697	0.823484	−	0.567339i	$-0.192027\pi$
$619$	40.9761	1.64697	0.823484	+	0.567339i	$0.192027\pi$
$620$	−5.51980	−0.221681
$621$	−0.598551	−0.0240190
$622$	74.7112	2.99565
$623$	−7.63490	−0.305886
$624$	−0.134170	−0.00537109
$625$	3.38929	0.135572
$626$	60.4665	2.41673
$627$	−6.90597	−0.275798
$628$	−5.03311	−0.200843
$629$	−26.7565	−1.06685
$630$	−5.47976	−0.218319
$631$	−3.97362	−0.158187	−0.0790937	−	0.996867i	$-0.525203\pi$
$631$	−3.97362	−0.158187	−0.0790937	+	0.996867i	$0.525203\pi$
$632$	4.16163	0.165541
$633$	−5.83676	−0.231990
$634$	12.5509	0.498461
$635$	10.2883	0.408280
$636$	−0.714121	−0.0283167
$637$	−7.63841	−0.302645
$638$	−34.2832	−1.35729
$639$	4.01839	0.158965
$640$	−23.0935	−0.912852
$641$	34.6427	1.36830	0.684151	−	0.729340i	$-0.260173\pi$
$641$	34.6427	1.36830	0.684151	+	0.729340i	$0.260173\pi$
$642$	29.3616	1.15881
$643$	−20.1844	−0.795995	−0.397998	−	0.917386i	$-0.630295\pi$
$643$	−20.1844	−0.795995	−0.397998	+	0.917386i	$0.630295\pi$
$644$	3.64000	0.143436
$645$	1.14984	0.0452748
$646$	−47.5370	−1.87032
$647$	27.8512	1.09494	0.547472	−	0.836824i	$-0.315590\pi$
$647$	27.8512	1.09494	0.547472	+	0.836824i	$0.315590\pi$
$648$	−2.79381	−0.109751
$649$	14.7362	0.578446
$650$	17.1860	0.674090
$651$	−2.54399	−0.0997069
$652$	−12.9621	−0.507634
$653$	−20.3886	−0.797868	−0.398934	−	0.916980i	$-0.630620\pi$
$653$	−20.3886	−0.797868	−0.398934	+	0.916980i	$0.630620\pi$
$654$	11.1895	0.437546
$655$	6.82746	0.266771
$656$	−0.391847	−0.0152990
$657$	−11.7497	−0.458400
$658$	−17.5726	−0.685053
$659$	−14.7797	−0.575735	−0.287867	−	0.957670i	$-0.592946\pi$
$659$	−14.7797	−0.575735	−0.287867	+	0.957670i	$0.592946\pi$
$660$	−6.47781	−0.252148
$661$	−43.7323	−1.70099	−0.850494	−	0.525984i	$-0.823697\pi$
$661$	−43.7323	−1.70099	−0.850494	+	0.525984i	$0.823697\pi$
$662$	−7.74510	−0.301022
$663$	−10.5850	−0.411089
$664$	30.1094	1.16847
$665$	−10.4672	−0.405901
$666$	−12.8318	−0.497221
$667$	−5.67581	−0.219768
$668$	−9.52647	−0.368590
$669$	11.1779	0.432163
$670$	−42.1511	−1.62844
$671$	20.1069	0.776217
$672$	−10.8051	−0.416816
$673$	−22.7318	−0.876248	−0.438124	−	0.898914i	$-0.644357\pi$
$673$	−22.7318	−0.876248	−0.438124	+	0.898914i	$0.644357\pi$
$674$	37.9194	1.46060
$675$	−3.38552	−0.130309
$676$	−25.9921	−0.999697
$677$	−27.3298	−1.05037	−0.525185	−	0.850988i	$-0.676004\pi$
$677$	−27.3298	−1.05037	−0.525185	+	0.850988i	$0.676004\pi$
$678$	−39.7670	−1.52724
$679$	−8.66991	−0.332721
$680$	−16.9159	−0.648696
$681$	3.80844	0.145940
$682$	−4.87378	−0.186627
$683$	10.2698	0.392963	0.196482	−	0.980508i	$-0.437048\pi$
$683$	10.2698	0.392963	0.196482	+	0.980508i	$0.437048\pi$
$684$	−14.0671	−0.537870
$685$	−1.71292	−0.0654473
$686$	−45.0185	−1.71881
$687$	5.27259	0.201162
$688$	0.0546593	0.00208387
$689$	−0.492250	−0.0187532
$690$	−1.73803	−0.0661658
$691$	−26.6434	−1.01356	−0.506781	−	0.862075i	$-0.669165\pi$
$691$	−26.6434	−1.01356	−0.506781	+	0.862075i	$0.669165\pi$
$692$	4.03225	0.153283
$693$	−2.98552	−0.113411
$694$	82.1151	3.11705
$695$	−18.1984	−0.690306
$696$	−26.4925	−1.00420
$697$	−30.9139	−1.17095
$698$	−52.9475	−2.00409
$699$	19.9689	0.755295
$700$	20.5885	0.778173
$701$	20.4215	0.771311	0.385655	−	0.922643i	$-0.373975\pi$
$701$	20.4215	0.771311	0.385655	+	0.922643i	$0.373975\pi$
$702$	−5.07633	−0.191594
$703$	−24.5107	−0.924438
$704$	−20.5093	−0.772975
$705$	5.17737	0.194991
$706$	58.9257	2.21770
$707$	10.8542	0.408215
$708$	30.0169	1.12810
$709$	44.2419	1.66154	0.830770	−	0.556616i	$-0.187900\pi$
$709$	44.2419	1.66154	0.830770	+	0.556616i	$0.187900\pi$
$710$	11.6683	0.437905
$711$	−1.48959	−0.0558640
$712$	−11.3030	−0.423599
$713$	−0.806886	−0.0302181
$714$	−20.5507	−0.769092
$715$	−4.46521	−0.166989
$716$	−20.8280	−0.778380
$717$	−12.9140	−0.482280
$718$	−0.771118	−0.0287779
$719$	27.5853	1.02876	0.514379	−	0.857563i	$-0.328022\pi$
$719$	27.5853	1.02876	0.514379	+	0.857563i	$0.328022\pi$
$720$	0.0767471	0.00286019
$721$	−8.33464	−0.310398
$722$	−0.126650	−0.00471341
$723$	−14.9953	−0.557680
$724$	−41.1728	−1.53017
$725$	−32.1034	−1.19229
$726$	19.4185	0.720686
$727$	−9.35222	−0.346854	−0.173427	−	0.984847i	$-0.555484\pi$
$727$	−9.35222	−0.346854	−0.173427	+	0.984847i	$0.555484\pi$
$728$	11.7115	0.434056
$729$	1.00000	0.0370370
$730$	−34.1180	−1.26276
$731$	4.31223	0.159494
$732$	40.9567	1.51380
$733$	−36.0520	−1.33161	−0.665806	−	0.746125i	$-0.731912\pi$
$733$	−36.0520	−1.33161	−0.665806	+	0.746125i	$0.731912\pi$
$734$	−13.8656	−0.511788
$735$	4.36928	0.161163
$736$	−3.42709	−0.126324
$737$	−22.9650	−0.845927
$738$	−14.8256	−0.545737
$739$	−1.67556	−0.0616366	−0.0308183	−	0.999525i	$-0.509811\pi$
$739$	−1.67556	−0.0616366	−0.0308183	+	0.999525i	$0.509811\pi$
$740$	−22.9911	−0.845168
$741$	−9.69659	−0.356213
$742$	−0.955699	−0.0350848
$743$	8.51595	0.312420	0.156210	−	0.987724i	$-0.450072\pi$
$743$	8.51595	0.312420	0.156210	+	0.987724i	$0.450072\pi$
$744$	−3.76623	−0.138077
$745$	−11.3799	−0.416928
$746$	40.2523	1.47374
$747$	−10.7772	−0.394316
$748$	−24.2937	−0.888265
$749$	24.2462	0.885938
$750$	−24.3493	−0.889111
$751$	18.5489	0.676860	0.338430	−	0.940992i	$-0.390104\pi$
$751$	18.5489	0.676860	0.338430	+	0.940992i	$0.390104\pi$
$752$	0.246114	0.00897487
$753$	5.48457	0.199869
$754$	−48.1367	−1.75303
$755$	19.5404	0.711149
$756$	−6.08136	−0.221177
$757$	10.4425	0.379540	0.189770	−	0.981829i	$-0.439226\pi$
$757$	10.4425	0.379540	0.189770	+	0.981829i	$0.439226\pi$
$758$	1.29453	0.0470194
$759$	−0.946927	−0.0343713
$760$	−15.4961	−0.562103
$761$	10.5085	0.380933	0.190467	−	0.981694i	$-0.439000\pi$
$761$	10.5085	0.380933	0.190467	+	0.981694i	$0.439000\pi$
$762$	18.5041	0.670333
$763$	9.24011	0.334514
$764$	−27.0121	−0.977265
$765$	6.05480	0.218912
$766$	−70.4637	−2.54596
$767$	20.6909	0.747106
$768$	−15.6071	−0.563171
$769$	21.1076	0.761161	0.380580	−	0.924748i	$-0.375724\pi$
$769$	21.1076	0.761161	0.380580	+	0.924748i	$0.375724\pi$
$770$	−8.66916	−0.312415
$771$	6.84143	0.246388
$772$	15.2180	0.547707
$773$	−33.0950	−1.19035	−0.595173	−	0.803598i	$-0.702916\pi$
$773$	−33.0950	−1.19035	−0.595173	+	0.803598i	$0.702916\pi$
$774$	2.06804	0.0743342
$775$	−4.56390	−0.163940
$776$	−12.8353	−0.460760
$777$	−10.5962	−0.380137
$778$	−5.89637	−0.211395
$779$	−28.3192	−1.01464
$780$	−9.09541	−0.325668
$781$	6.35722	0.227479
$782$	−6.51814	−0.233088
$783$	9.48258	0.338880
$784$	0.207701	0.00741788
$785$	1.98453	0.0708308
$786$	12.2795	0.437997
$787$	20.3649	0.725930	0.362965	−	0.931803i	$-0.381765\pi$
$787$	20.3649	0.725930	0.362965	+	0.931803i	$0.381765\pi$
$788$	−15.8823	−0.565784
$789$	9.26938	0.329999
$790$	−4.32537	−0.153890
$791$	−32.8388	−1.16761
$792$	−4.41989	−0.157054
$793$	28.2318	1.00254
$794$	3.81483	0.135383
$795$	0.281574	0.00998641
$796$	17.4448	0.618316
$797$	−43.6561	−1.54638	−0.773189	−	0.634176i	$-0.781340\pi$
$797$	−43.6561	−1.54638	−0.773189	+	0.634176i	$0.781340\pi$
$798$	−18.8258	−0.666427
$799$	19.4167	0.686912
$800$	−19.3843	−0.685337
$801$	4.04574	0.142949
$802$	−62.0036	−2.18942
$803$	−18.5884	−0.655971
$804$	−46.7786	−1.64975
$805$	−1.43523	−0.0505854
$806$	−6.84322	−0.241042
$807$	−23.9852	−0.844319
$808$	16.0690	0.565306
$809$	−20.5459	−0.722357	−0.361178	−	0.932497i	$-0.617625\pi$
$809$	−20.5459	−0.722357	−0.361178	+	0.932497i	$0.617625\pi$
$810$	2.90374	0.102027
$811$	24.8152	0.871378	0.435689	−	0.900097i	$-0.356505\pi$
$811$	24.8152	0.871378	0.435689	+	0.900097i	$0.356505\pi$
$812$	−57.6670	−2.02371
$813$	−5.99910	−0.210398
$814$	−20.3003	−0.711524
$815$	5.11088	0.179026
$816$	0.287824	0.0100759
$817$	3.95029	0.138203
$818$	11.0165	0.385184
$819$	−4.19194	−0.146478
$820$	−26.5634	−0.927635
$821$	1.26408	0.0441168	0.0220584	−	0.999757i	$-0.492978\pi$
$821$	1.26408	0.0441168	0.0220584	+	0.999757i	$0.492978\pi$
$822$	−3.08077	−0.107454
$823$	−16.8523	−0.587433	−0.293717	−	0.955893i	$-0.594892\pi$
$823$	−16.8523	−0.587433	−0.293717	+	0.955893i	$0.594892\pi$
$824$	−12.3390	−0.429848
$825$	−5.35599	−0.186472
$826$	40.1712	1.39774
$827$	−52.3267	−1.81958	−0.909788	−	0.415073i	$-0.863756\pi$
$827$	−52.3267	−1.81958	−0.909788	+	0.415073i	$0.863756\pi$
$828$	−1.92884	−0.0670319
$829$	44.4375	1.54338	0.771690	−	0.635999i	$-0.219412\pi$
$829$	44.4375	1.54338	0.771690	+	0.635999i	$0.219412\pi$
$830$	−31.2941	−1.08623
$831$	0.0840055	0.00291412
$832$	−28.7969	−0.998354
$833$	16.3861	0.567745
$834$	−32.7309	−1.13338
$835$	3.75624	0.129990
$836$	−22.2546	−0.769692
$837$	1.34807	0.0465960
$838$	42.1274	1.45527
$839$	28.3527	0.978844	0.489422	−	0.872047i	$-0.337208\pi$
$839$	28.3527	0.978844	0.489422	+	0.872047i	$0.337208\pi$
$840$	−6.69913	−0.231142
$841$	60.9193	2.10066
$842$	25.0615	0.863676
$843$	24.1863	0.833021
$844$	−18.8091	−0.647435
$845$	10.2486	0.352561
$846$	9.31177	0.320145
$847$	16.0354	0.550982
$848$	0.0133851	0.000459645 0
$849$	−4.84003	−0.166109
$850$	−36.8678	−1.26456
$851$	−3.36084	−0.115208
$852$	12.9493	0.443637
$853$	−23.2666	−0.796633	−0.398316	−	0.917248i	$-0.630405\pi$
$853$	−23.2666	−0.796633	−0.398316	+	0.917248i	$0.630405\pi$
$854$	54.8118	1.87562
$855$	5.54659	0.189689
$856$	35.8951	1.22687
$857$	27.3777	0.935206	0.467603	−	0.883939i	$-0.345118\pi$
$857$	27.3777	0.935206	0.467603	+	0.883939i	$0.345118\pi$
$858$	−8.03091	−0.274171
$859$	−32.3054	−1.10225	−0.551123	−	0.834424i	$-0.685800\pi$
$859$	−32.3054	−1.10225	−0.551123	+	0.834424i	$0.685800\pi$
$860$	3.70537	0.126352
$861$	−12.2427	−0.417229
$862$	−3.14146	−0.106999
$863$	−9.77132	−0.332620	−0.166310	−	0.986074i	$-0.553185\pi$
$863$	−9.77132	−0.332620	−0.166310	+	0.986074i	$0.553185\pi$
$864$	5.72565	0.194790
$865$	−1.58990	−0.0540581
$866$	84.4129	2.86847
$867$	5.70728	0.193829
$868$	−8.19807	−0.278261
$869$	−2.35658	−0.0799414
$870$	27.5349	0.933520
$871$	−32.2449	−1.09258
$872$	13.6794	0.463244
$873$	4.59420	0.155490
$874$	−5.97105	−0.201974
$875$	−20.1072	−0.679747
$876$	−37.8637	−1.27929
$877$	−6.25237	−0.211128	−0.105564	−	0.994413i	$-0.533665\pi$
$877$	−6.25237	−0.211128	−0.105564	+	0.994413i	$0.533665\pi$
$878$	9.28804	0.313456
$879$	1.45523	0.0490836
$880$	0.121416	0.00409294
$881$	17.0942	0.575918	0.287959	−	0.957643i	$-0.407023\pi$
$881$	17.0942	0.575918	0.287959	+	0.957643i	$0.407023\pi$
$882$	7.85838	0.264605
$883$	9.56284	0.321815	0.160908	−	0.986969i	$-0.448558\pi$
$883$	9.56284	0.321815	0.160908	+	0.986969i	$0.448558\pi$
$884$	−34.1105	−1.14726
$885$	−11.8355	−0.397846
$886$	−35.3984	−1.18923
$887$	−43.1389	−1.44846	−0.724230	−	0.689558i	$-0.757805\pi$
$887$	−43.1389	−1.44846	−0.724230	+	0.689558i	$0.757805\pi$
$888$	−15.6871	−0.526425
$889$	15.2803	0.512486
$890$	11.7478	0.393786
$891$	1.58203	0.0530001
$892$	36.0210	1.20607
$893$	17.7869	0.595218
$894$	−20.4674	−0.684532
$895$	8.21239	0.274510
$896$	−34.2987	−1.14584
$897$	−1.32957	−0.0443930
$898$	−21.4673	−0.716374
$899$	12.7831	0.426341
$900$	−10.9099	−0.363663
$901$	1.05599	0.0351800
$902$	−23.4545	−0.780950
$903$	1.70775	0.0568303
$904$	−48.6159	−1.61694
$905$	16.2342	0.539643
$906$	35.1445	1.16760
$907$	−36.1397	−1.20000	−0.599999	−	0.800001i	$-0.704832\pi$
$907$	−36.1397	−1.20000	−0.599999	+	0.800001i	$0.704832\pi$
$908$	12.2728	0.407286
$909$	−5.75166	−0.190771
$910$	−12.1723	−0.403507
$911$	−19.7487	−0.654304	−0.327152	−	0.944972i	$-0.606089\pi$
$911$	−19.7487	−0.654304	−0.327152	+	0.944972i	$0.606089\pi$
$912$	0.263666	0.00873085
$913$	−17.0498	−0.564267
$914$	−37.9940	−1.25673
$915$	−16.1490	−0.533870
$916$	16.9910	0.561399
$917$	10.1402	0.334859
$918$	10.8899	0.359419
$919$	33.4186	1.10238	0.551188	−	0.834381i	$-0.314175\pi$
$919$	33.4186	1.10238	0.551188	+	0.834381i	$0.314175\pi$
$920$	−2.12478	−0.0700520
$921$	−3.90258	−0.128594
$922$	51.7061	1.70285
$923$	8.92610	0.293806
$924$	−9.62090	−0.316504
$925$	−19.0095	−0.625029
$926$	39.5896	1.30100
$927$	4.41654	0.145058
$928$	54.2939	1.78228
$929$	7.07464	0.232112	0.116056	−	0.993243i	$-0.462975\pi$
$929$	7.07464	0.232112	0.116056	+	0.993243i	$0.462975\pi$
$930$	3.91443	0.128359
$931$	15.0107	0.491957
$932$	64.3504	2.10787
$933$	−32.6923	−1.07030
$934$	−31.6211	−1.03468
$935$	9.57888	0.313263
$936$	−6.20592	−0.202847
$937$	13.7519	0.449255	0.224627	−	0.974445i	$-0.427883\pi$
$937$	13.7519	0.449255	0.224627	+	0.974445i	$0.427883\pi$
$938$	−62.6032	−2.04407
$939$	−26.4591	−0.863459
$940$	16.6842	0.544178
$941$	−47.1661	−1.53757	−0.768786	−	0.639506i	$-0.779139\pi$
$941$	−47.1661	−1.53757	−0.768786	+	0.639506i	$0.779139\pi$
$942$	3.56928	0.116293
$943$	−3.88305	−0.126449
$944$	−0.562620	−0.0183117
$945$	2.39785	0.0780020
$946$	3.27171	0.106372
$947$	16.0435	0.521345	0.260672	−	0.965427i	$-0.416056\pi$
$947$	16.0435	0.521345	0.260672	+	0.965427i	$0.416056\pi$
$948$	−4.80023	−0.155904
$949$	−26.0998	−0.847234
$950$	−33.7734	−1.09575
$951$	−5.49207	−0.178092
$952$	−25.1237	−0.814264
$953$	22.1365	0.717072	0.358536	−	0.933516i	$-0.383276\pi$
$953$	22.1365	0.717072	0.358536	+	0.933516i	$0.383276\pi$
$954$	0.506426	0.0163961
$955$	10.6508	0.344650
$956$	−41.6155	−1.34594
$957$	15.0017	0.484937
$958$	31.8712	1.02971
$959$	−2.54404	−0.0821515
$960$	16.4723	0.531640
$961$	−29.1827	−0.941378
$962$	−28.5034	−0.918985
$963$	−12.8481	−0.414024
$964$	−48.3225	−1.55636
$965$	−6.00037	−0.193159
$966$	−2.58135	−0.0830534
$967$	−8.02996	−0.258226	−0.129113	−	0.991630i	$-0.541213\pi$
$967$	−8.02996	−0.258226	−0.129113	+	0.991630i	$0.541213\pi$
$968$	23.7395	0.763015
$969$	20.8014	0.668236
$970$	13.3403	0.428332
$971$	9.14570	0.293500	0.146750	−	0.989174i	$-0.453119\pi$
$971$	9.14570	0.293500	0.146750	+	0.989174i	$0.453119\pi$
$972$	3.22252	0.103362
$973$	−27.0285	−0.866495
$974$	40.2923	1.29105
$975$	−7.52029	−0.240842
$976$	−0.767669	−0.0245725
$977$	−39.0663	−1.24984	−0.624921	−	0.780688i	$-0.714869\pi$
$977$	−39.0663	−1.24984	−0.624921	+	0.780688i	$0.714869\pi$
$978$	9.19218	0.293934
$979$	6.40050	0.204561
$980$	14.0801	0.449772
$981$	−4.89635	−0.156328
$982$	55.7309	1.77844
$983$	−33.1529	−1.05741	−0.528707	−	0.848804i	$-0.677323\pi$
$983$	−33.1529	−1.05741	−0.528707	+	0.848804i	$0.677323\pi$
$984$	−18.1246	−0.577790
$985$	6.26232	0.199534
$986$	103.264	3.28860
$987$	7.68948	0.244759
$988$	−31.2475	−0.994114
$989$	0.541652	0.0172235
$990$	4.59380	0.146001
$991$	−19.3543	−0.614810	−0.307405	−	0.951579i	$-0.599461\pi$
$991$	−19.3543	−0.614810	−0.307405	+	0.951579i	$0.599461\pi$
$992$	7.71855	0.245064
$993$	3.38912	0.107551
$994$	17.3299	0.549672
$995$	−6.87841	−0.218060
$996$	−34.7297	−1.10045
$997$	−50.9072	−1.61225	−0.806123	−	0.591748i	$-0.798438\pi$
$997$	−50.9072	−1.61225	−0.806123	+	0.591748i	$0.798438\pi$
$998$	47.5297	1.50453
$999$	5.61496	0.177649

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6033.2.a.b.1.10	✓	71

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6033.2.a.b.1.10	✓	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)

\(f(q)\)	\(=\)	\(q-2.28528 q^{2} +1.00000 q^{3} +3.22252 q^{4} -1.27062 q^{5} -2.28528 q^{6} -1.88714 q^{7} -2.79381 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.28528 q^{2} +1.00000 q^{3} +3.22252 q^{4} -1.27062 q^{5} -2.28528 q^{6} -1.88714 q^{7} -2.79381 q^{8} +1.00000 q^{9} +2.90374 q^{10} +1.58203 q^{11} +3.22252 q^{12} +2.22131 q^{13} +4.31266 q^{14} -1.27062 q^{15} -0.0604011 q^{16} -4.76522 q^{17} -2.28528 q^{18} -4.36525 q^{19} -4.09461 q^{20} -1.88714 q^{21} -3.61539 q^{22} -0.598551 q^{23} -2.79381 q^{24} -3.38552 q^{25} -5.07633 q^{26} +1.00000 q^{27} -6.08136 q^{28} +9.48258 q^{29} +2.90374 q^{30} +1.34807 q^{31} +5.72565 q^{32} +1.58203 q^{33} +10.8899 q^{34} +2.39785 q^{35} +3.22252 q^{36} +5.61496 q^{37} +9.97584 q^{38} +2.22131 q^{39} +3.54988 q^{40} +6.48741 q^{41} +4.31266 q^{42} -0.904939 q^{43} +5.09813 q^{44} -1.27062 q^{45} +1.36786 q^{46} -4.07467 q^{47} -0.0604011 q^{48} -3.43869 q^{49} +7.73686 q^{50} -4.76522 q^{51} +7.15823 q^{52} -0.221603 q^{53} -2.28528 q^{54} -2.01017 q^{55} +5.27231 q^{56} -4.36525 q^{57} -21.6704 q^{58} +9.31472 q^{59} -4.09461 q^{60} +12.7095 q^{61} -3.08071 q^{62} -1.88714 q^{63} -12.9639 q^{64} -2.82245 q^{65} -3.61539 q^{66} -14.5162 q^{67} -15.3560 q^{68} -0.598551 q^{69} -5.47976 q^{70} +4.01839 q^{71} -2.79381 q^{72} -11.7497 q^{73} -12.8318 q^{74} -3.38552 q^{75} -14.0671 q^{76} -2.98552 q^{77} -5.07633 q^{78} -1.48959 q^{79} +0.0767471 q^{80} +1.00000 q^{81} -14.8256 q^{82} -10.7772 q^{83} -6.08136 q^{84} +6.05480 q^{85} +2.06804 q^{86} +9.48258 q^{87} -4.41989 q^{88} +4.04574 q^{89} +2.90374 q^{90} -4.19194 q^{91} -1.92884 q^{92} +1.34807 q^{93} +9.31177 q^{94} +5.54659 q^{95} +5.72565 q^{96} +4.59420 q^{97} +7.85838 q^{98} +1.58203 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 71 q - 11 q^{2} + 71 q^{3} + 53 q^{4} - 8 q^{5} - 11 q^{6} - 46 q^{7} - 33 q^{8} + 71 q^{9}+O(q^{10}) \) 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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