LMFDB - Embedded newform 4033.2.a.e.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4033,2,Mod(1,4033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4033, 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("4033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4033 = 37 \cdot 109 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4033.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:	$32.2036671352$
Analytic rank:	$0$
Dimension:	$82$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	4033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.40882 q^{2} -0.455887 q^{3} +3.80243 q^{4} +1.02492 q^{5} +1.09815 q^{6} +3.87779 q^{7} -4.34175 q^{8} -2.79217 q^{9} +O(q^{10})$	\(q-2.40882 q^{2} -0.455887 q^{3} +3.80243 q^{4} +1.02492 q^{5} +1.09815 q^{6} +3.87779 q^{7} -4.34175 q^{8} -2.79217 q^{9} -2.46884 q^{10} +3.83167 q^{11} -1.73348 q^{12} -0.427906 q^{13} -9.34091 q^{14} -0.467245 q^{15} +2.85363 q^{16} -0.761140 q^{17} +6.72584 q^{18} +2.04100 q^{19} +3.89717 q^{20} -1.76783 q^{21} -9.22981 q^{22} +2.22677 q^{23} +1.97934 q^{24} -3.94955 q^{25} +1.03075 q^{26} +2.64057 q^{27} +14.7450 q^{28} -1.23494 q^{29} +1.12551 q^{30} -6.46416 q^{31} +1.80959 q^{32} -1.74681 q^{33} +1.83345 q^{34} +3.97440 q^{35} -10.6170 q^{36} -1.00000 q^{37} -4.91641 q^{38} +0.195076 q^{39} -4.44992 q^{40} +2.95531 q^{41} +4.25840 q^{42} +3.51598 q^{43} +14.5697 q^{44} -2.86174 q^{45} -5.36391 q^{46} -8.99411 q^{47} -1.30093 q^{48} +8.03723 q^{49} +9.51377 q^{50} +0.346994 q^{51} -1.62708 q^{52} +9.91289 q^{53} -6.36068 q^{54} +3.92714 q^{55} -16.8364 q^{56} -0.930465 q^{57} +2.97476 q^{58} +4.78754 q^{59} -1.77667 q^{60} +13.3796 q^{61} +15.5710 q^{62} -10.8274 q^{63} -10.0662 q^{64} -0.438567 q^{65} +4.20775 q^{66} -3.72281 q^{67} -2.89418 q^{68} -1.01516 q^{69} -9.57364 q^{70} +7.54528 q^{71} +12.1229 q^{72} -10.1105 q^{73} +2.40882 q^{74} +1.80055 q^{75} +7.76077 q^{76} +14.8584 q^{77} -0.469905 q^{78} +1.91669 q^{79} +2.92473 q^{80} +7.17270 q^{81} -7.11883 q^{82} +6.16523 q^{83} -6.72206 q^{84} -0.780104 q^{85} -8.46939 q^{86} +0.562994 q^{87} -16.6361 q^{88} +9.15644 q^{89} +6.89342 q^{90} -1.65933 q^{91} +8.46716 q^{92} +2.94693 q^{93} +21.6652 q^{94} +2.09185 q^{95} -0.824967 q^{96} +8.74595 q^{97} -19.3603 q^{98} -10.6987 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 82 q + 10 q^{2} + 17 q^{3} + 88 q^{4} + 22 q^{5} + 4 q^{6} + 15 q^{7} + 33 q^{8} + 91 q^{9}+O(q^{10}) $ 82 * q + 10 * q^2 + 17 * q^3 + 88 * q^4 + 22 * q^5 + 4 * q^6 + 15 * q^7 + 33 * q^8 + 91 * q^9	\( 82 q + 10 q^{2} + 17 q^{3} + 88 q^{4} + 22 q^{5} + 4 q^{6} + 15 q^{7} + 33 q^{8} + 91 q^{9} + 13 q^{10} + 2 q^{11} + 36 q^{12} + 23 q^{13} + 24 q^{14} + 35 q^{15} + 104 q^{16} + 43 q^{17} + 42 q^{18} + 15 q^{19} + 59 q^{20} + 9 q^{21} + 6 q^{22} + 70 q^{23} + 15 q^{24} + 98 q^{25} + 10 q^{26} + 65 q^{27} + 37 q^{28} + 27 q^{29} + 17 q^{30} + 59 q^{31} + 46 q^{32} + 16 q^{33} - 16 q^{34} + 80 q^{35} + 88 q^{36} - 82 q^{37} + 82 q^{38} + 13 q^{39} + 14 q^{40} + 3 q^{41} + 62 q^{42} + 7 q^{43} - 11 q^{44} + 42 q^{45} - 11 q^{46} + 123 q^{47} + 45 q^{48} + 105 q^{49} + 27 q^{50} + 3 q^{51} - 30 q^{52} + 82 q^{53} - 27 q^{54} + 37 q^{55} + 66 q^{56} + 29 q^{57} - 34 q^{58} + 60 q^{59} + 94 q^{60} + 9 q^{61} - 2 q^{62} + 106 q^{63} + 93 q^{64} + 9 q^{65} + 63 q^{66} + 113 q^{68} + 48 q^{69} + 47 q^{70} + 59 q^{71} + 63 q^{72} + 21 q^{73} - 10 q^{74} + 77 q^{75} + 22 q^{76} + 30 q^{77} + 29 q^{78} + 55 q^{79} + 88 q^{80} + 42 q^{81} + 4 q^{82} + 92 q^{83} + 43 q^{84} - 7 q^{85} + 17 q^{86} + 147 q^{87} - 13 q^{88} + 100 q^{89} + 91 q^{90} + 28 q^{91} + 127 q^{92} + 3 q^{93} + 30 q^{94} + 48 q^{95} - 31 q^{96} + 53 q^{97} + 101 q^{98} - 20 q^{99}+O(q^{100}) \) 82 * q + 10 * q^2 + 17 * q^3 + 88 * q^4 + 22 * q^5 + 4 * q^6 + 15 * q^7 + 33 * q^8 + 91 * q^9 + 13 * q^10 + 2 * q^11 + 36 * q^12 + 23 * q^13 + 24 * q^14 + 35 * q^15 + 104 * q^16 + 43 * q^17 + 42 * q^18 + 15 * q^19 + 59 * q^20 + 9 * q^21 + 6 * q^22 + 70 * q^23 + 15 * q^24 + 98 * q^25 + 10 * q^26 + 65 * q^27 + 37 * q^28 + 27 * q^29 + 17 * q^30 + 59 * q^31 + 46 * q^32 + 16 * q^33 - 16 * q^34 + 80 * q^35 + 88 * q^36 - 82 * q^37 + 82 * q^38 + 13 * q^39 + 14 * q^40 + 3 * q^41 + 62 * q^42 + 7 * q^43 - 11 * q^44 + 42 * q^45 - 11 * q^46 + 123 * q^47 + 45 * q^48 + 105 * q^49 + 27 * q^50 + 3 * q^51 - 30 * q^52 + 82 * q^53 - 27 * q^54 + 37 * q^55 + 66 * q^56 + 29 * q^57 - 34 * q^58 + 60 * q^59 + 94 * q^60 + 9 * q^61 - 2 * q^62 + 106 * q^63 + 93 * q^64 + 9 * q^65 + 63 * q^66 + 113 * q^68 + 48 * q^69 + 47 * q^70 + 59 * q^71 + 63 * q^72 + 21 * q^73 - 10 * q^74 + 77 * q^75 + 22 * q^76 + 30 * q^77 + 29 * q^78 + 55 * q^79 + 88 * q^80 + 42 * q^81 + 4 * q^82 + 92 * q^83 + 43 * q^84 - 7 * q^85 + 17 * q^86 + 147 * q^87 - 13 * q^88 + 100 * q^89 + 91 * q^90 + 28 * q^91 + 127 * q^92 + 3 * q^93 + 30 * q^94 + 48 * q^95 - 31 * q^96 + 53 * q^97 + 101 * q^98 - 20 * 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 $

$2$	−2.40882	−1.70330	−0.851648	−	0.524114i	$-0.824396\pi$
$2$	−2.40882	−1.70330	−0.851648	+	0.524114i	$0.824396\pi$
$3$	−0.455887	−0.263206	−0.131603	−	0.991302i	$-0.542012\pi$
$3$	−0.455887	−0.263206	−0.131603	+	0.991302i	$0.542012\pi$
$4$	3.80243	1.90122
$5$	1.02492	0.458356	0.229178	−	0.973385i	$-0.426396\pi$
$5$	1.02492	0.458356	0.229178	+	0.973385i	$0.426396\pi$
$6$	1.09815	0.448318
$7$	3.87779	1.46567	0.732833	−	0.680409i	$-0.238198\pi$
$7$	3.87779	1.46567	0.732833	+	0.680409i	$0.238198\pi$
$8$	−4.34175	−1.53504
$9$	−2.79217	−0.930722
$10$	−2.46884	−0.780716
$11$	3.83167	1.15529	0.577646	−	0.816288i	$-0.303972\pi$
$11$	3.83167	1.15529	0.577646	+	0.816288i	$0.303972\pi$
$12$	−1.73348	−0.500412
$13$	−0.427906	−0.118680	−0.0593398	−	0.998238i	$-0.518900\pi$
$13$	−0.427906	−0.118680	−0.0593398	+	0.998238i	$0.518900\pi$
$14$	−9.34091	−2.49646
$15$	−0.467245	−0.120642
$16$	2.85363	0.713409
$17$	−0.761140	−0.184604	−0.0923018	−	0.995731i	$-0.529422\pi$
$17$	−0.761140	−0.184604	−0.0923018	+	0.995731i	$0.529422\pi$
$18$	6.72584	1.58530
$19$	2.04100	0.468238	0.234119	−	0.972208i	$-0.424780\pi$
$19$	2.04100	0.468238	0.234119	+	0.972208i	$0.424780\pi$
$20$	3.89717	0.871434
$21$	−1.76783	−0.385773
$22$	−9.22981	−1.96780
$23$	2.22677	0.464315	0.232157	−	0.972678i	$-0.425422\pi$
$23$	2.22677	0.464315	0.232157	+	0.972678i	$0.425422\pi$
$24$	1.97934	0.404032
$25$	−3.94955	−0.789910
$26$	1.03075	0.202147
$27$	2.64057	0.508178
$28$	14.7450	2.78655
$29$	−1.23494	−0.229323	−0.114661	−	0.993405i	$-0.536578\pi$
$29$	−1.23494	−0.229323	−0.114661	+	0.993405i	$0.536578\pi$
$30$	1.12551	0.205489
$31$	−6.46416	−1.16100	−0.580499	−	0.814261i	$-0.697142\pi$
$31$	−6.46416	−1.16100	−0.580499	+	0.814261i	$0.697142\pi$
$32$	1.80959	0.319893
$33$	−1.74681	−0.304080
$34$	1.83345	0.314434
$35$	3.97440	0.671797
$36$	−10.6170	−1.76951
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	−4.91641	−0.797547
$39$	0.195076	0.0312372
$40$	−4.44992	−0.703595
$41$	2.95531	0.461542	0.230771	−	0.973008i	$-0.425875\pi$
$41$	2.95531	0.461542	0.230771	+	0.973008i	$0.425875\pi$
$42$	4.25840	0.657085
$43$	3.51598	0.536182	0.268091	−	0.963394i	$-0.413607\pi$
$43$	3.51598	0.536182	0.268091	+	0.963394i	$0.413607\pi$
$44$	14.5697	2.19646
$45$	−2.86174	−0.426602
$46$	−5.36391	−0.790865
$47$	−8.99411	−1.31193	−0.655963	−	0.754793i	$-0.727737\pi$
$47$	−8.99411	−1.31193	−0.655963	+	0.754793i	$0.727737\pi$
$48$	−1.30093	−0.187774
$49$	8.03723	1.14818
$50$	9.51377	1.34545
$51$	0.346994	0.0485888
$52$	−1.62708	−0.225636
$53$	9.91289	1.36164	0.680820	−	0.732451i	$-0.261624\pi$
$53$	9.91289	1.36164	0.680820	+	0.732451i	$0.261624\pi$
$54$	−6.36068	−0.865578
$55$	3.92714	0.529535
$56$	−16.8364	−2.24985
$57$	−0.930465	−0.123243
$58$	2.97476	0.390605
$59$	4.78754	0.623284	0.311642	−	0.950200i	$-0.399121\pi$
$59$	4.78754	0.623284	0.311642	+	0.950200i	$0.399121\pi$
$60$	−1.77667	−0.229367
$61$	13.3796	1.71308	0.856540	−	0.516080i	$-0.172609\pi$
$61$	13.3796	1.71308	0.856540	+	0.516080i	$0.172609\pi$
$62$	15.5710	1.97752
$63$	−10.8274	−1.36413
$64$	−10.0662	−1.25828
$65$	−0.438567	−0.0543975
$66$	4.20775	0.517938
$67$	−3.72281	−0.454814	−0.227407	−	0.973800i	$-0.573025\pi$
$67$	−3.72281	−0.454814	−0.227407	+	0.973800i	$0.573025\pi$
$68$	−2.89418	−0.350971
$69$	−1.01516	−0.122211
$70$	−9.57364	−1.14427
$71$	7.54528	0.895460	0.447730	−	0.894169i	$-0.352233\pi$
$71$	7.54528	0.895460	0.447730	+	0.894169i	$0.352233\pi$
$72$	12.1229	1.42870
$73$	−10.1105	−1.18334	−0.591672	−	0.806179i	$-0.701532\pi$
$73$	−10.1105	−1.18334	−0.591672	+	0.806179i	$0.701532\pi$
$74$	2.40882	0.280020
$75$	1.80055	0.207909
$76$	7.76077	0.890221
$77$	14.8584	1.69327
$78$	−0.469905	−0.0532063
$79$	1.91669	0.215645	0.107822	−	0.994170i	$-0.465612\pi$
$79$	1.91669	0.215645	0.107822	+	0.994170i	$0.465612\pi$
$80$	2.92473	0.326995
$81$	7.17270	0.796967
$82$	−7.11883	−0.786143
$83$	6.16523	0.676721	0.338361	−	0.941016i	$-0.390128\pi$
$83$	6.16523	0.676721	0.338361	+	0.941016i	$0.390128\pi$
$84$	−6.72206	−0.733437
$85$	−0.780104	−0.0846141
$86$	−8.46939	−0.913277
$87$	0.562994	0.0603592
$88$	−16.6361	−1.77342
$89$	9.15644	0.970581	0.485290	−	0.874353i	$-0.338714\pi$
$89$	9.15644	0.970581	0.485290	+	0.874353i	$0.338714\pi$
$90$	6.89342	0.726630
$91$	−1.65933	−0.173945
$92$	8.46716	0.882763
$93$	2.94693	0.305582
$94$	21.6652	2.23460
$95$	2.09185	0.214620
$96$	−0.824967	−0.0841978
$97$	8.74595	0.888017	0.444009	−	0.896023i	$-0.353556\pi$
$97$	8.74595	0.888017	0.444009	+	0.896023i	$0.353556\pi$
$98$	−19.3603	−1.95568
$99$	−10.6987	−1.07526
$100$	−15.0179	−1.50179
$101$	17.1193	1.70343	0.851717	−	0.524002i	$-0.175562\pi$
$101$	17.1193	1.70343	0.851717	+	0.524002i	$0.175562\pi$
$102$	−0.835846	−0.0827611
$103$	1.32572	0.130627	0.0653137	−	0.997865i	$-0.479195\pi$
$103$	1.32572	0.130627	0.0653137	+	0.997865i	$0.479195\pi$
$104$	1.85786	0.182178
$105$	−1.81188	−0.176821
$106$	−23.8784	−2.31928
$107$	6.33678	0.612599	0.306300	−	0.951935i	$-0.400909\pi$
$107$	6.33678	0.612599	0.306300	+	0.951935i	$0.400909\pi$
$108$	10.0406	0.966157
$109$	1.00000	0.0957826
$109$	1.00000	0.0957826
$110$	−9.45978	−0.901954
$111$	0.455887	0.0432709
$112$	11.0658	1.04562
$113$	7.64536	0.719215	0.359608	−	0.933104i	$-0.382911\pi$
$113$	7.64536	0.719215	0.359608	+	0.933104i	$0.382911\pi$
$114$	2.24133	0.209920
$115$	2.28226	0.212821
$116$	−4.69578	−0.435993
$117$	1.19478	0.110458
$118$	−11.5323	−1.06164
$119$	−2.95154	−0.270567
$120$	2.02866	0.185191
$121$	3.68167	0.334698
$122$	−32.2291	−2.91788
$123$	−1.34729	−0.121481
$124$	−24.5796	−2.20731
$125$	−9.17253	−0.820416
$126$	26.0814	2.32351
$127$	−4.57080	−0.405593	−0.202797	−	0.979221i	$-0.565003\pi$
$127$	−4.57080	−0.405593	−0.202797	+	0.979221i	$0.565003\pi$
$128$	20.6286	1.82333
$129$	−1.60289	−0.141127
$130$	1.05643	0.0926551
$131$	−8.12936	−0.710266	−0.355133	−	0.934816i	$-0.615564\pi$
$131$	−8.12936	−0.710266	−0.355133	+	0.934816i	$0.615564\pi$
$132$	−6.64212	−0.578122
$133$	7.91457	0.686280
$134$	8.96760	0.774683
$135$	2.70636	0.232927
$136$	3.30468	0.283374
$137$	−14.8418	−1.26802	−0.634010	−	0.773325i	$-0.718592\pi$
$137$	−14.8418	−1.26802	−0.634010	+	0.773325i	$0.718592\pi$
$138$	2.44534	0.208161
$139$	8.31180	0.704997	0.352499	−	0.935812i	$-0.385332\pi$
$139$	8.31180	0.704997	0.352499	+	0.935812i	$0.385332\pi$
$140$	15.1124	1.27723
$141$	4.10030	0.345307
$142$	−18.1752	−1.52523
$143$	−1.63959	−0.137110
$144$	−7.96783	−0.663985
$145$	−1.26571	−0.105112
$146$	24.3544	2.01559
$147$	−3.66407	−0.302207
$148$	−3.80243	−0.312558
$149$	4.24042	0.347389	0.173694	−	0.984800i	$-0.444430\pi$
$149$	4.24042	0.347389	0.173694	+	0.984800i	$0.444430\pi$
$150$	−4.33720	−0.354131
$151$	−9.71836	−0.790869	−0.395434	−	0.918494i	$-0.629406\pi$
$151$	−9.71836	−0.790869	−0.395434	+	0.918494i	$0.629406\pi$
$152$	−8.86151	−0.718763
$153$	2.12523	0.171815
$154$	−35.7912	−2.88414
$155$	−6.62522	−0.532151
$156$	0.741765	0.0593888
$157$	−5.76169	−0.459833	−0.229917	−	0.973210i	$-0.573845\pi$
$157$	−5.76169	−0.459833	−0.229917	+	0.973210i	$0.573845\pi$
$158$	−4.61697	−0.367307
$159$	−4.51915	−0.358392
$160$	1.85467	0.146625
$161$	8.63496	0.680530
$162$	−17.2778	−1.35747
$163$	14.7056	1.15184	0.575918	−	0.817508i	$-0.304645\pi$
$163$	14.7056	1.15184	0.575918	+	0.817508i	$0.304645\pi$
$164$	11.2374	0.877492
$165$	−1.79033	−0.139377
$166$	−14.8509	−1.15266
$167$	−4.37520	−0.338563	−0.169281	−	0.985568i	$-0.554145\pi$
$167$	−4.37520	−0.338563	−0.169281	+	0.985568i	$0.554145\pi$
$168$	7.67548	0.592176
$169$	−12.8169	−0.985915
$170$	1.87913	0.144123
$171$	−5.69882	−0.435799
$172$	13.3693	1.01940
$173$	9.06112	0.688905	0.344452	−	0.938804i	$-0.388065\pi$
$173$	9.06112	0.688905	0.344452	+	0.938804i	$0.388065\pi$
$174$	−1.35615	−0.102810
$175$	−15.3155	−1.15774
$176$	10.9342	0.824195
$177$	−2.18257	−0.164052
$178$	−22.0563	−1.65319
$179$	−9.05178	−0.676562	−0.338281	−	0.941045i	$-0.609845\pi$
$179$	−9.05178	−0.676562	−0.338281	+	0.941045i	$0.609845\pi$
$180$	−10.8816	−0.811064
$181$	−18.2742	−1.35831	−0.679157	−	0.733993i	$-0.737654\pi$
$181$	−18.2742	−1.35831	−0.679157	+	0.733993i	$0.737654\pi$
$182$	3.99703	0.296279
$183$	−6.09958	−0.450894
$184$	−9.66809	−0.712741
$185$	−1.02492	−0.0753533
$186$	−7.09863	−0.520497
$187$	−2.91643	−0.213271
$188$	−34.1995	−2.49425
$189$	10.2396	0.744820
$190$	−5.03891	−0.365561
$191$	9.37516	0.678363	0.339182	−	0.940721i	$-0.389850\pi$
$191$	9.37516	0.678363	0.339182	+	0.940721i	$0.389850\pi$
$192$	4.58907	0.331188
$193$	24.0017	1.72768	0.863840	−	0.503766i	$-0.168053\pi$
$193$	24.0017	1.72768	0.863840	+	0.503766i	$0.168053\pi$
$194$	−21.0675	−1.51256
$195$	0.199937	0.0143178
$196$	30.5610	2.18293
$197$	2.01479	0.143548	0.0717740	−	0.997421i	$-0.477134\pi$
$197$	2.01479	0.143548	0.0717740	+	0.997421i	$0.477134\pi$
$198$	25.7712	1.83148
$199$	−4.85032	−0.343830	−0.171915	−	0.985112i	$-0.554996\pi$
$199$	−4.85032	−0.343830	−0.171915	+	0.985112i	$0.554996\pi$
$200$	17.1479	1.21254
$201$	1.69718	0.119710
$202$	−41.2374	−2.90145
$203$	−4.78884	−0.336111
$204$	1.31942	0.0923779
$205$	3.02895	0.211551
$206$	−3.19343	−0.222497
$207$	−6.21753	−0.432148
$208$	−1.22109	−0.0846671
$209$	7.82044	0.540951
$210$	4.36450	0.301179
$211$	−22.5797	−1.55445	−0.777224	−	0.629224i	$-0.783373\pi$
$211$	−22.5797	−1.55445	−0.777224	+	0.629224i	$0.783373\pi$
$212$	37.6931	2.58877
$213$	−3.43979	−0.235691
$214$	−15.2642	−1.04344
$215$	3.60359	0.245763
$216$	−11.4647	−0.780074
$217$	−25.0666	−1.70163
$218$	−2.40882	−0.163146
$219$	4.60924	0.311464
$220$	14.9327	1.00676
$221$	0.325696	0.0219087
$222$	−1.09815	−0.0737031
$223$	6.35963	0.425873	0.212936	−	0.977066i	$-0.431697\pi$
$223$	6.35963	0.425873	0.212936	+	0.977066i	$0.431697\pi$
$224$	7.01719	0.468856
$225$	11.0278	0.735187
$226$	−18.4163	−1.22504
$227$	17.1167	1.13608	0.568038	−	0.823002i	$-0.307703\pi$
$227$	17.1167	1.13608	0.568038	+	0.823002i	$0.307703\pi$
$228$	−3.53803	−0.234312
$229$	1.40859	0.0930822	0.0465411	−	0.998916i	$-0.485180\pi$
$229$	1.40859	0.0930822	0.0465411	+	0.998916i	$0.485180\pi$
$230$	−5.49755	−0.362498
$231$	−6.77374	−0.445680
$232$	5.36180	0.352020
$233$	7.64358	0.500748	0.250374	−	0.968149i	$-0.419446\pi$
$233$	7.64358	0.500748	0.250374	+	0.968149i	$0.419446\pi$
$234$	−2.87802	−0.188142
$235$	−9.21820	−0.601329
$236$	18.2043	1.18500
$237$	−0.873794	−0.0567590
$238$	7.10973	0.460856
$239$	−3.78263	−0.244678	−0.122339	−	0.992488i	$-0.539040\pi$
$239$	−3.78263	−0.244678	−0.122339	+	0.992488i	$0.539040\pi$
$240$	−1.33335	−0.0860672
$241$	8.32828	0.536472	0.268236	−	0.963353i	$-0.413559\pi$
$241$	8.32828	0.536472	0.268236	+	0.963353i	$0.413559\pi$
$242$	−8.86851	−0.570089
$243$	−11.1917	−0.717945
$244$	50.8750	3.25694
$245$	8.23748	0.526273
$246$	3.24538	0.206918
$247$	−0.873356	−0.0555703
$248$	28.0658	1.78218
$249$	−2.81064	−0.178117
$250$	22.0950	1.39741
$251$	−17.5375	−1.10696	−0.553479	−	0.832863i	$-0.686700\pi$
$251$	−17.5375	−1.10696	−0.553479	+	0.832863i	$0.686700\pi$
$252$	−41.1706	−2.59350
$253$	8.53226	0.536419
$254$	11.0103	0.690845
$255$	0.355639	0.0222710
$256$	−29.5583	−1.84739
$257$	−11.9519	−0.745537	−0.372769	−	0.927924i	$-0.621591\pi$
$257$	−11.9519	−0.745537	−0.372769	+	0.927924i	$0.621591\pi$
$258$	3.86108	0.240380
$259$	−3.87779	−0.240954
$260$	−1.66762	−0.103422
$261$	3.44816	0.213436
$262$	19.5822	1.20979
$263$	8.69199	0.535971	0.267986	−	0.963423i	$-0.413642\pi$
$263$	8.69199	0.535971	0.267986	+	0.963423i	$0.413642\pi$
$264$	7.58419	0.466775
$265$	10.1599	0.624116
$266$	−19.0648	−1.16894
$267$	−4.17430	−0.255463
$268$	−14.1557	−0.864700
$269$	25.4857	1.55389	0.776946	−	0.629567i	$-0.216768\pi$
$269$	25.4857	1.55389	0.776946	+	0.629567i	$0.216768\pi$
$270$	−6.51915	−0.396743
$271$	−28.2716	−1.71738	−0.858689	−	0.512497i	$-0.828721\pi$
$271$	−28.2716	−1.71738	−0.858689	+	0.512497i	$0.828721\pi$
$272$	−2.17201	−0.131698
$273$	0.756465	0.0457833
$274$	35.7513	2.15981
$275$	−15.1334	−0.912576
$276$	−3.86007	−0.232349
$277$	27.7652	1.66825	0.834124	−	0.551577i	$-0.185974\pi$
$277$	27.7652	1.66825	0.834124	+	0.551577i	$0.185974\pi$
$278$	−20.0217	−1.20082
$279$	18.0490	1.08057
$280$	−17.2559	−1.03123
$281$	13.9853	0.834294	0.417147	−	0.908839i	$-0.363030\pi$
$281$	13.9853	0.834294	0.417147	+	0.908839i	$0.363030\pi$
$282$	−9.87689	−0.588160
$283$	20.0791	1.19358	0.596790	−	0.802397i	$-0.296443\pi$
$283$	20.0791	1.19358	0.596790	+	0.802397i	$0.296443\pi$
$284$	28.6904	1.70246
$285$	−0.953648	−0.0564893
$286$	3.94949	0.233538
$287$	11.4601	0.676467
$288$	−5.05267	−0.297731
$289$	−16.4207	−0.965922
$290$	3.04887	0.179036
$291$	−3.98716	−0.233732
$292$	−38.4445	−2.24979
$293$	−9.46201	−0.552776	−0.276388	−	0.961046i	$-0.589138\pi$
$293$	−9.46201	−0.552776	−0.276388	+	0.961046i	$0.589138\pi$
$294$	8.82609	0.514748
$295$	4.90682	0.285686
$296$	4.34175	0.252359
$297$	10.1178	0.587094
$298$	−10.2144	−0.591706
$299$	−0.952849	−0.0551047
$300$	6.84646	0.395281
$301$	13.6342	0.785864
$302$	23.4098	1.34708
$303$	−7.80446	−0.448355
$304$	5.82427	0.334045
$305$	13.7129	0.785201
$306$	−5.11930	−0.292651
$307$	27.4795	1.56834	0.784169	−	0.620548i	$-0.213090\pi$
$307$	27.4795	1.56834	0.784169	+	0.620548i	$0.213090\pi$
$308$	56.4980	3.21927
$309$	−0.604380	−0.0343820
$310$	15.9590	0.906410
$311$	−18.3318	−1.03950	−0.519752	−	0.854317i	$-0.673975\pi$
$311$	−18.3318	−1.03950	−0.519752	+	0.854317i	$0.673975\pi$
$312$	−0.846972	−0.0479504
$313$	−10.6204	−0.600300	−0.300150	−	0.953892i	$-0.597037\pi$
$313$	−10.6204	−0.600300	−0.300150	+	0.953892i	$0.597037\pi$
$314$	13.8789	0.783232
$315$	−11.0972	−0.625256
$316$	7.28809	0.409987
$317$	20.1599	1.13229	0.566145	−	0.824305i	$-0.308434\pi$
$317$	20.1599	1.13229	0.566145	+	0.824305i	$0.308434\pi$
$318$	10.8858	0.610448
$319$	−4.73188	−0.264935
$320$	−10.3171	−0.576741
$321$	−2.88885	−0.161240
$322$	−20.8001	−1.15914
$323$	−1.55349	−0.0864383
$324$	27.2737	1.51521
$325$	1.69003	0.0937462
$326$	−35.4233	−1.96192
$327$	−0.455887	−0.0252106
$328$	−12.8312	−0.708485
$329$	−34.8772	−1.92284
$330$	4.31259	0.237400
$331$	−25.1550	−1.38264	−0.691322	−	0.722547i	$-0.742971\pi$
$331$	−25.1550	−1.38264	−0.691322	+	0.722547i	$0.742971\pi$
$332$	23.4429	1.28659
$333$	2.79217	0.153010
$334$	10.5391	0.576673
$335$	−3.81557	−0.208467
$336$	−5.04475	−0.275213
$337$	−19.8166	−1.07948	−0.539739	−	0.841833i	$-0.681477\pi$
$337$	−19.8166	−1.07948	−0.539739	+	0.841833i	$0.681477\pi$
$338$	30.8737	1.67931
$339$	−3.48542	−0.189302
$340$	−2.96629	−0.160870
$341$	−24.7685	−1.34129
$342$	13.7274	0.742295
$343$	4.02215	0.217176
$344$	−15.2655	−0.823061
$345$	−1.04045	−0.0560160
$346$	−21.8267	−1.17341
$347$	20.8434	1.11893	0.559467	−	0.828852i	$-0.311006\pi$
$347$	20.8434	1.11893	0.559467	+	0.828852i	$0.311006\pi$
$348$	2.14075	0.114756
$349$	7.76076	0.415424	0.207712	−	0.978190i	$-0.433398\pi$
$349$	7.76076	0.415424	0.207712	+	0.978190i	$0.433398\pi$
$350$	36.8924	1.97198
$351$	−1.12992	−0.0603104
$352$	6.93374	0.369569
$353$	−26.4948	−1.41018	−0.705088	−	0.709120i	$-0.749093\pi$
$353$	−26.4948	−1.41018	−0.705088	+	0.709120i	$0.749093\pi$
$354$	5.25744	0.279430
$355$	7.73327	0.410439
$356$	34.8168	1.84528
$357$	1.34557	0.0712150
$358$	21.8042	1.15239
$359$	12.1169	0.639506	0.319753	−	0.947501i	$-0.396400\pi$
$359$	12.1169	0.639506	0.319753	+	0.947501i	$0.396400\pi$
$360$	12.4249	0.654851
$361$	−14.8343	−0.780753
$362$	44.0194	2.31361
$363$	−1.67843	−0.0880946
$364$	−6.30948	−0.330707
$365$	−10.3624	−0.542393
$366$	14.6928	0.768006
$367$	−15.7364	−0.821436	−0.410718	−	0.911762i	$-0.634722\pi$
$367$	−15.7364	−0.821436	−0.410718	+	0.911762i	$0.634722\pi$
$368$	6.35440	0.331246
$369$	−8.25173	−0.429568
$370$	2.46884	0.128349
$371$	38.4401	1.99571
$372$	11.2055	0.580978
$373$	24.2907	1.25772	0.628861	−	0.777517i	$-0.283521\pi$
$373$	24.2907	1.25772	0.628861	+	0.777517i	$0.283521\pi$
$374$	7.02518	0.363263
$375$	4.18164	0.215939
$376$	39.0501	2.01386
$377$	0.528438	0.0272160
$378$	−24.6653	−1.26865
$379$	37.8567	1.94457	0.972285	−	0.233798i	$-0.0751156\pi$
$379$	37.8567	1.94457	0.972285	+	0.233798i	$0.0751156\pi$
$380$	7.95413	0.408038
$381$	2.08377	0.106755
$382$	−22.5831	−1.15545
$383$	8.81238	0.450291	0.225146	−	0.974325i	$-0.427714\pi$
$383$	8.81238	0.450291	0.225146	+	0.974325i	$0.427714\pi$
$384$	−9.40433	−0.479913
$385$	15.2286	0.776121
$386$	−57.8159	−2.94275
$387$	−9.81721	−0.499037
$388$	33.2559	1.68831
$389$	12.7736	0.647648	0.323824	−	0.946117i	$-0.395031\pi$
$389$	12.7736	0.647648	0.323824	+	0.946117i	$0.395031\pi$
$390$	−0.481613	−0.0243874
$391$	−1.69489	−0.0857141
$392$	−34.8956	−1.76249
$393$	3.70607	0.186946
$394$	−4.85328	−0.244505
$395$	1.96445	0.0988420
$396$	−40.6809	−2.04429
$397$	−0.0247509	−0.00124221	−0.000621106	−	1.00000i	$-0.500198\pi$
$397$	−0.0247509	−0.00124221	−0.000621106		1.00000i	$0.500198\pi$
$398$	11.6836	0.585645
$399$	−3.60815	−0.180633
$400$	−11.2706	−0.563528
$401$	25.5251	1.27466	0.637330	−	0.770591i	$-0.280039\pi$
$401$	25.5251	1.27466	0.637330	+	0.770591i	$0.280039\pi$
$402$	−4.08821	−0.203901
$403$	2.76605	0.137787
$404$	65.0950	3.23860
$405$	7.35141	0.365295
$406$	11.5355	0.572496
$407$	−3.83167	−0.189929
$408$	−1.50656	−0.0745857
$409$	15.8022	0.781371	0.390685	−	0.920524i	$-0.372238\pi$
$409$	15.8022	0.781371	0.390685	+	0.920524i	$0.372238\pi$
$410$	−7.29620	−0.360333
$411$	6.76618	0.333751
$412$	5.04097	0.248351
$413$	18.5650	0.913526
$414$	14.9769	0.736076
$415$	6.31883	0.310179
$416$	−0.774332	−0.0379648
$417$	−3.78924	−0.185560
$418$	−18.8381	−0.921399
$419$	7.38566	0.360813	0.180407	−	0.983592i	$-0.442259\pi$
$419$	7.38566	0.360813	0.180407	+	0.983592i	$0.442259\pi$
$420$	−6.88955	−0.336175
$421$	−36.5669	−1.78216	−0.891081	−	0.453845i	$-0.850052\pi$
$421$	−36.5669	−1.78216	−0.891081	+	0.453845i	$0.850052\pi$
$422$	54.3904	2.64769
$423$	25.1131	1.22104
$424$	−43.0392	−2.09017
$425$	3.00616	0.145820
$426$	8.28586	0.401451
$427$	51.8832	2.51080
$428$	24.0952	1.16468
$429$	0.747468	0.0360881
$430$	−8.68041	−0.418606
$431$	15.5096	0.747070	0.373535	−	0.927616i	$-0.378146\pi$
$431$	15.5096	0.747070	0.373535	+	0.927616i	$0.378146\pi$
$432$	7.53523	0.362539
$433$	11.0826	0.532596	0.266298	−	0.963891i	$-0.414199\pi$
$433$	11.0826	0.532596	0.266298	+	0.963891i	$0.414199\pi$
$434$	60.3811	2.89839
$435$	0.577021	0.0276660
$436$	3.80243	0.182104
$437$	4.54485	0.217410
$438$	−11.1029	−0.530515
$439$	16.5199	0.788451	0.394225	−	0.919014i	$-0.371013\pi$
$439$	16.5199	0.788451	0.394225	+	0.919014i	$0.371013\pi$
$440$	−17.0506	−0.812857
$441$	−22.4413	−1.06863
$442$	−0.784544	−0.0373170
$443$	19.9769	0.949132	0.474566	−	0.880220i	$-0.342605\pi$
$443$	19.9769	0.949132	0.474566	+	0.880220i	$0.342605\pi$
$444$	1.73348	0.0822673
$445$	9.38458	0.444872
$446$	−15.3192	−0.725387
$447$	−1.93315	−0.0914349
$448$	−39.0348	−1.84422
$449$	−18.0804	−0.853266	−0.426633	−	0.904425i	$-0.640300\pi$
$449$	−18.0804	−0.853266	−0.426633	+	0.904425i	$0.640300\pi$
$450$	−26.5640	−1.25224
$451$	11.3238	0.533216
$452$	29.0710	1.36738
$453$	4.43047	0.208162
$454$	−41.2311	−1.93507
$455$	−1.70067	−0.0797286
$456$	4.03984	0.189183
$457$	25.0149	1.17015	0.585073	−	0.810981i	$-0.301066\pi$
$457$	25.0149	1.17015	0.585073	+	0.810981i	$0.301066\pi$
$458$	−3.39304	−0.158547
$459$	−2.00984	−0.0938115
$460$	8.67813	0.404620
$461$	36.3115	1.69119	0.845597	−	0.533821i	$-0.179245\pi$
$461$	36.3115	1.69119	0.845597	+	0.533821i	$0.179245\pi$
$462$	16.3168	0.759124
$463$	−20.5441	−0.954765	−0.477382	−	0.878696i	$-0.658414\pi$
$463$	−20.5441	−0.954765	−0.477382	+	0.878696i	$0.658414\pi$
$464$	−3.52407	−0.163601
$465$	3.02035	0.140065
$466$	−18.4120	−0.852922
$467$	0.213372	0.00987369	0.00493684	−	0.999988i	$-0.498429\pi$
$467$	0.213372	0.00987369	0.00493684	+	0.999988i	$0.498429\pi$
$468$	4.54309	0.210004
$469$	−14.4363	−0.666605
$470$	22.2050	1.02424
$471$	2.62668	0.121031
$472$	−20.7863	−0.956765
$473$	13.4721	0.619447
$474$	2.10482	0.0966774
$475$	−8.06103	−0.369866
$476$	−11.2230	−0.514407
$477$	−27.6784	−1.26731
$478$	9.11169	0.416759
$479$	17.1280	0.782599	0.391299	−	0.920263i	$-0.372026\pi$
$479$	17.1280	0.782599	0.391299	+	0.920263i	$0.372026\pi$
$480$	−0.845521	−0.0385926
$481$	0.427906	0.0195108
$482$	−20.0614	−0.913770
$483$	−3.93656	−0.179120
$484$	13.9993	0.636333
$485$	8.96386	0.407028
$486$	26.9587	1.22287
$487$	17.1311	0.776282	0.388141	−	0.921600i	$-0.373117\pi$
$487$	17.1311	0.776282	0.388141	+	0.921600i	$0.373117\pi$
$488$	−58.0908	−2.62965
$489$	−6.70411	−0.303170
$490$	−19.8426	−0.896399
$491$	−27.5904	−1.24514	−0.622570	−	0.782564i	$-0.713911\pi$
$491$	−27.5904	−1.24514	−0.622570	+	0.782564i	$0.713911\pi$
$492$	−5.12297	−0.230961
$493$	0.939963	0.0423338
$494$	2.10376	0.0946526
$495$	−10.9652	−0.492850
$496$	−18.4464	−0.828266
$497$	29.2590	1.31244
$498$	6.77035	0.303387
$499$	−27.8904	−1.24854	−0.624272	−	0.781207i	$-0.714604\pi$
$499$	−27.8904	−1.24854	−0.624272	+	0.781207i	$0.714604\pi$
$500$	−34.8779	−1.55979
$501$	1.99459	0.0891119
$502$	42.2448	1.88548
$503$	9.40824	0.419493	0.209746	−	0.977756i	$-0.432736\pi$
$503$	9.40824	0.419493	0.209746	+	0.977756i	$0.432736\pi$
$504$	47.0099	2.09399
$505$	17.5458	0.780779
$506$	−20.5527	−0.913680
$507$	5.84305	0.259499
$508$	−17.3802	−0.771121
$509$	29.4115	1.30364	0.651821	−	0.758373i	$-0.274005\pi$
$509$	29.4115	1.30364	0.651821	+	0.758373i	$0.274005\pi$
$510$	−0.856672	−0.0379341
$511$	−39.2063	−1.73439
$512$	29.9434	1.32332
$513$	5.38941	0.237948
$514$	28.7900	1.26987
$515$	1.35875	0.0598738
$516$	−6.09489	−0.268312
$517$	−34.4624	−1.51566
$518$	9.34091	0.410416
$519$	−4.13085	−0.181324
$520$	1.90415	0.0835023
$521$	31.7997	1.39317	0.696585	−	0.717475i	$-0.254702\pi$
$521$	31.7997	1.39317	0.696585	+	0.717475i	$0.254702\pi$
$522$	−8.30602	−0.363545
$523$	23.1618	1.01280	0.506398	−	0.862300i	$-0.330977\pi$
$523$	23.1618	1.01280	0.506398	+	0.862300i	$0.330977\pi$
$524$	−30.9114	−1.35037
$525$	6.98214	0.304725
$526$	−20.9375	−0.912917
$527$	4.92013	0.214324
$528$	−4.98475	−0.216933
$529$	−18.0415	−0.784412
$530$	−24.4733	−1.06305
$531$	−13.3676	−0.580104
$532$	30.0946	1.30477
$533$	−1.26459	−0.0547757
$534$	10.0552	0.435129
$535$	6.49466	0.280789
$536$	16.1635	0.698157
$537$	4.12659	0.178075
$538$	−61.3906	−2.64674
$539$	30.7960	1.32648
$540$	10.2908	0.442844
$541$	−6.79401	−0.292097	−0.146049	−	0.989277i	$-0.546656\pi$
$541$	−6.79401	−0.292097	−0.146049	+	0.989277i	$0.546656\pi$
$542$	68.1013	2.92520
$543$	8.33098	0.357517
$544$	−1.37735	−0.0590533
$545$	1.02492	0.0439026
$546$	−1.82219	−0.0779826
$547$	−5.81040	−0.248435	−0.124217	−	0.992255i	$-0.539642\pi$
$547$	−5.81040	−0.248435	−0.124217	+	0.992255i	$0.539642\pi$
$548$	−56.4349	−2.41078
$549$	−37.3581	−1.59440
$550$	36.4536	1.55439
$551$	−2.52052	−0.107378
$552$	4.40756	0.187598
$553$	7.43252	0.316063
$554$	−66.8814	−2.84152
$555$	0.467245	0.0198335
$556$	31.6051	1.34035
$557$	8.16598	0.346004	0.173002	−	0.984921i	$-0.444653\pi$
$557$	8.16598	0.346004	0.173002	+	0.984921i	$0.444653\pi$
$558$	−43.4769	−1.84053
$559$	−1.50451	−0.0636339
$560$	11.3415	0.479266
$561$	1.32956	0.0561342
$562$	−33.6882	−1.42105
$563$	23.0959	0.973378	0.486689	−	0.873575i	$-0.338205\pi$
$563$	23.0959	0.973378	0.486689	+	0.873575i	$0.338205\pi$
$564$	15.5911	0.656504
$565$	7.83585	0.329657
$566$	−48.3671	−2.03302
$567$	27.8142	1.16809
$568$	−32.7597	−1.37457
$569$	−36.2425	−1.51937	−0.759683	−	0.650293i	$-0.774646\pi$
$569$	−36.2425	−1.51937	−0.759683	+	0.650293i	$0.774646\pi$
$570$	2.29717	0.0962179
$571$	23.6427	0.989416	0.494708	−	0.869059i	$-0.335275\pi$
$571$	23.6427	0.989416	0.494708	+	0.869059i	$0.335275\pi$
$572$	−6.23444	−0.260675
$573$	−4.27401	−0.178549
$574$	−27.6053	−1.15222
$575$	−8.79475	−0.366767
$576$	28.1066	1.17111
$577$	41.6831	1.73529	0.867645	−	0.497184i	$-0.165633\pi$
$577$	41.6831	1.73529	0.867645	+	0.497184i	$0.165633\pi$
$578$	39.5545	1.64525
$579$	−10.9421	−0.454736
$580$	−4.81278	−0.199840
$581$	23.9074	0.991847
$582$	9.60438	0.398114
$583$	37.9829	1.57309
$584$	43.8972	1.81648
$585$	1.22455	0.0506290
$586$	22.7923	0.941542
$587$	−24.7954	−1.02342	−0.511709	−	0.859159i	$-0.670987\pi$
$587$	−24.7954	−1.02342	−0.511709	+	0.859159i	$0.670987\pi$
$588$	−13.9324	−0.574561
$589$	−13.1934	−0.543623
$590$	−11.8197	−0.486608
$591$	−0.918517	−0.0377827
$592$	−2.85363	−0.117284
$593$	−27.7354	−1.13896	−0.569478	−	0.822007i	$-0.692855\pi$
$593$	−27.7354	−1.13896	−0.569478	+	0.822007i	$0.692855\pi$
$594$	−24.3720	−0.999995
$595$	−3.02508	−0.124016
$596$	16.1239	0.660461
$597$	2.21120	0.0904984
$598$	2.29525	0.0938596
$599$	−41.5967	−1.69959	−0.849797	−	0.527110i	$-0.823275\pi$
$599$	−41.5967	−1.69959	−0.849797	+	0.527110i	$0.823275\pi$
$600$	−7.81752	−0.319149
$601$	−30.3759	−1.23906	−0.619529	−	0.784974i	$-0.712676\pi$
$601$	−30.3759	−1.23906	−0.619529	+	0.784974i	$0.712676\pi$
$602$	−32.8425	−1.33856
$603$	10.3947	0.423305
$604$	−36.9534	−1.50361
$605$	3.77340	0.153411
$606$	18.7996	0.763681
$607$	28.2806	1.14787	0.573937	−	0.818899i	$-0.305415\pi$
$607$	28.2806	1.14787	0.573937	+	0.818899i	$0.305415\pi$
$608$	3.69337	0.149786
$609$	2.18317	0.0884665
$610$	−33.0321	−1.33743
$611$	3.84863	0.155699
$612$	8.08104	0.326657
$613$	−17.4678	−0.705518	−0.352759	−	0.935714i	$-0.614757\pi$
$613$	−17.4678	−0.705518	−0.352759	+	0.935714i	$0.614757\pi$
$614$	−66.1933	−2.67134
$615$	−1.38086	−0.0556815
$616$	−64.5113	−2.59924
$617$	−10.0384	−0.404131	−0.202066	−	0.979372i	$-0.564765\pi$
$617$	−10.0384	−0.404131	−0.202066	+	0.979372i	$0.564765\pi$
$618$	1.45584	0.0585626
$619$	26.2110	1.05351	0.526755	−	0.850017i	$-0.323409\pi$
$619$	26.2110	1.05351	0.526755	+	0.850017i	$0.323409\pi$
$620$	−25.1920	−1.01173
$621$	5.87996	0.235955
$622$	44.1582	1.77058
$623$	35.5067	1.42255
$624$	0.556677	0.0222849
$625$	10.3467	0.413867
$626$	25.5827	1.02249
$627$	−3.56523	−0.142382
$628$	−21.9085	−0.874243
$629$	0.761140	0.0303486
$630$	26.7312	1.06500
$631$	11.6689	0.464533	0.232266	−	0.972652i	$-0.425386\pi$
$631$	11.6689	0.464533	0.232266	+	0.972652i	$0.425386\pi$
$632$	−8.32178	−0.331023
$633$	10.2938	0.409141
$634$	−48.5616	−1.92863
$635$	−4.68469	−0.185906
$636$	−17.1838	−0.681381
$637$	−3.43917	−0.136265
$638$	11.3983	0.451262
$639$	−21.0677	−0.833424
$640$	21.1426	0.835735
$641$	4.47150	0.176614	0.0883069	−	0.996093i	$-0.471854\pi$
$641$	4.47150	0.176614	0.0883069	+	0.996093i	$0.471854\pi$
$642$	6.95874	0.274639
$643$	3.21450	0.126767	0.0633837	−	0.997989i	$-0.479811\pi$
$643$	3.21450	0.126767	0.0633837	+	0.997989i	$0.479811\pi$
$644$	32.8339	1.29384
$645$	−1.64283	−0.0646863
$646$	3.74208	0.147230
$647$	−12.7818	−0.502504	−0.251252	−	0.967922i	$-0.580842\pi$
$647$	−12.7818	−0.502504	−0.251252	+	0.967922i	$0.580842\pi$
$648$	−31.1420	−1.22337
$649$	18.3442	0.720075
$650$	−4.07099	−0.159677
$651$	11.4276	0.447881
$652$	55.9173	2.18989
$653$	−1.41250	−0.0552756	−0.0276378	−	0.999618i	$-0.508798\pi$
$653$	−1.41250	−0.0552756	−0.0276378	+	0.999618i	$0.508798\pi$
$654$	1.09815	0.0429411
$655$	−8.33191	−0.325555
$656$	8.43338	0.329268
$657$	28.2302	1.10136
$658$	84.0131	3.27517
$659$	−6.04705	−0.235560	−0.117780	−	0.993040i	$-0.537578\pi$
$659$	−6.04705	−0.235560	−0.117780	+	0.993040i	$0.537578\pi$
$660$	−6.80761	−0.264986
$661$	21.3399	0.830025	0.415012	−	0.909816i	$-0.363777\pi$
$661$	21.3399	0.830025	0.415012	+	0.909816i	$0.363777\pi$
$662$	60.5940	2.35505
$663$	−0.148480	−0.00576650
$664$	−26.7678	−1.03879
$665$	8.11176	0.314561
$666$	−6.72584	−0.260621
$667$	−2.74994	−0.106478
$668$	−16.6364	−0.643682
$669$	−2.89927	−0.112092
$670$	9.19103	0.355081
$671$	51.2661	1.97911
$672$	−3.19905	−0.123406
$673$	−26.8183	−1.03377	−0.516885	−	0.856055i	$-0.672909\pi$
$673$	−26.8183	−1.03377	−0.516885	+	0.856055i	$0.672909\pi$
$674$	47.7346	1.83867
$675$	−10.4291	−0.401415
$676$	−48.7354	−1.87444
$677$	1.64115	0.0630745	0.0315372	−	0.999503i	$-0.489960\pi$
$677$	1.64115	0.0630745	0.0315372	+	0.999503i	$0.489960\pi$
$678$	8.39577	0.322437
$679$	33.9149	1.30154
$680$	3.38701	0.129886
$681$	−7.80328	−0.299022
$682$	59.6630	2.28462
$683$	2.93958	0.112480	0.0562400	−	0.998417i	$-0.482089\pi$
$683$	2.93958	0.112480	0.0562400	+	0.998417i	$0.482089\pi$
$684$	−21.6694	−0.828549
$685$	−15.2116	−0.581205
$686$	−9.68866	−0.369915
$687$	−0.642157	−0.0244998
$688$	10.0333	0.382517
$689$	−4.24178	−0.161599
$690$	2.50626	0.0954118
$691$	−32.8438	−1.24944	−0.624718	−	0.780850i	$-0.714786\pi$
$691$	−32.8438	−1.24944	−0.624718	+	0.780850i	$0.714786\pi$
$692$	34.4543	1.30976
$693$	−41.4871	−1.57596
$694$	−50.2082	−1.90588
$695$	8.51889	0.323140
$696$	−2.44437	−0.0926538
$697$	−2.24941	−0.0852023
$698$	−18.6943	−0.707590
$699$	−3.48461	−0.131800
$700$	−58.2362	−2.20112
$701$	−22.1100	−0.835084	−0.417542	−	0.908658i	$-0.637108\pi$
$701$	−22.1100	−0.835084	−0.417542	+	0.908658i	$0.637108\pi$
$702$	2.72177	0.102727
$703$	−2.04100	−0.0769778
$704$	−38.5705	−1.45368
$705$	4.20246	0.158274
$706$	63.8213	2.40195
$707$	66.3850	2.49666
$708$	−8.29909	−0.311899
$709$	−0.539159	−0.0202485	−0.0101243	−	0.999949i	$-0.503223\pi$
$709$	−0.539159	−0.0202485	−0.0101243	+	0.999949i	$0.503223\pi$
$710$	−18.6281	−0.699100
$711$	−5.35172	−0.200705
$712$	−39.7549	−1.48988
$713$	−14.3942	−0.539068
$714$	−3.24123	−0.121300
$715$	−1.68044	−0.0628450
$716$	−34.4188	−1.28629
$717$	1.72445	0.0644008
$718$	−29.1875	−1.08927
$719$	2.02263	0.0754315	0.0377158	−	0.999289i	$-0.487992\pi$
$719$	2.02263	0.0754315	0.0377158	+	0.999289i	$0.487992\pi$
$720$	−8.16635	−0.304342
$721$	5.14087	0.191456
$722$	35.7333	1.32985
$723$	−3.79675	−0.141203
$724$	−69.4866	−2.58245
$725$	4.87746	0.181144
$726$	4.04303	0.150051
$727$	32.7385	1.21420	0.607101	−	0.794624i	$-0.292332\pi$
$727$	32.7385	1.21420	0.607101	+	0.794624i	$0.292332\pi$
$728$	7.20437	0.267012
$729$	−16.4160	−0.607999
$730$	24.9612	0.923856
$731$	−2.67615	−0.0989812
$732$	−23.1932	−0.857247
$733$	18.6821	0.690038	0.345019	−	0.938596i	$-0.387872\pi$
$733$	18.6821	0.690038	0.345019	+	0.938596i	$0.387872\pi$
$734$	37.9063	1.39915
$735$	−3.75536	−0.138518
$736$	4.02954	0.148531
$737$	−14.2646	−0.525442
$738$	19.8770	0.731681
$739$	34.0403	1.25219	0.626097	−	0.779745i	$-0.284651\pi$
$739$	34.0403	1.25219	0.626097	+	0.779745i	$0.284651\pi$
$740$	−3.89717	−0.143263
$741$	0.398151	0.0146265
$742$	−92.5953	−3.39928
$743$	5.49036	0.201422	0.100711	−	0.994916i	$-0.467888\pi$
$743$	5.49036	0.201422	0.100711	+	0.994916i	$0.467888\pi$
$744$	−12.7948	−0.469080
$745$	4.34607	0.159228
$746$	−58.5119	−2.14227
$747$	−17.2143	−0.629840
$748$	−11.0895	−0.405474
$749$	24.5727	0.897866
$750$	−10.0728	−0.367808
$751$	7.34208	0.267916	0.133958	−	0.990987i	$-0.457231\pi$
$751$	7.34208	0.267916	0.133958	+	0.990987i	$0.457231\pi$
$752$	−25.6659	−0.935939
$753$	7.99512	0.291358
$754$	−1.27291	−0.0463568
$755$	−9.96049	−0.362500
$756$	38.9353	1.41606
$757$	13.0006	0.472514	0.236257	−	0.971691i	$-0.424079\pi$
$757$	13.0006	0.472514	0.236257	+	0.971691i	$0.424079\pi$
$758$	−91.1902	−3.31218
$759$	−3.88974	−0.141189
$760$	−9.08230	−0.329449
$761$	−31.4960	−1.14173	−0.570865	−	0.821044i	$-0.693392\pi$
$761$	−31.4960	−1.14173	−0.570865	+	0.821044i	$0.693392\pi$
$762$	−5.01943	−0.181835
$763$	3.87779	0.140385
$764$	35.6484	1.28972
$765$	2.17818	0.0787523
$766$	−21.2275	−0.766979
$767$	−2.04861	−0.0739711
$768$	13.4752	0.486246
$769$	11.8133	0.425998	0.212999	−	0.977052i	$-0.431677\pi$
$769$	11.8133	0.425998	0.212999	+	0.977052i	$0.431677\pi$
$770$	−36.6830	−1.32196
$771$	5.44870	0.196230
$772$	91.2649	3.28469
$773$	5.80967	0.208959	0.104480	−	0.994527i	$-0.466682\pi$
$773$	5.80967	0.208959	0.104480	+	0.994527i	$0.466682\pi$
$774$	23.6479	0.850008
$775$	25.5305	0.917084
$776$	−37.9727	−1.36314
$777$	1.76783	0.0634206
$778$	−30.7694	−1.10314
$779$	6.03180	0.216111
$780$	0.760247	0.0272212
$781$	28.9110	1.03452
$782$	4.08268	0.145996
$783$	−3.26095	−0.116537
$784$	22.9353	0.819119
$785$	−5.90525	−0.210767
$786$	−8.92727	−0.318425
$787$	−30.1012	−1.07299	−0.536496	−	0.843903i	$-0.680252\pi$
$787$	−30.1012	−1.07299	−0.536496	+	0.843903i	$0.680252\pi$
$788$	7.66111	0.272916
$789$	−3.96256	−0.141071
$790$	−4.73201	−0.168357
$791$	29.6471	1.05413
$792$	46.4508	1.65056
$793$	−5.72520	−0.203308
$794$	0.0596205	0.00211585
$795$	−4.63175	−0.164271
$796$	−18.4430	−0.653696
$797$	−26.8951	−0.952673	−0.476336	−	0.879263i	$-0.658036\pi$
$797$	−26.8951	−0.952673	−0.476336	+	0.879263i	$0.658036\pi$
$798$	8.69139	0.307672
$799$	6.84577	0.242186
$800$	−7.14705	−0.252686
$801$	−25.5663	−0.903341
$802$	−61.4854	−2.17112
$803$	−38.7401	−1.36711
$804$	6.45342	0.227595
$805$	8.85010	0.311925
$806$	−6.66293	−0.234692
$807$	−11.6186	−0.408994
$808$	−74.3276	−2.61484
$809$	4.59067	0.161399	0.0806996	−	0.996738i	$-0.474285\pi$
$809$	4.59067	0.161399	0.0806996	+	0.996738i	$0.474285\pi$
$810$	−17.7083	−0.622205
$811$	−48.0065	−1.68574	−0.842868	−	0.538120i	$-0.819135\pi$
$811$	−48.0065	−1.68574	−0.842868	+	0.538120i	$0.819135\pi$
$812$	−18.2092	−0.639019
$813$	12.8887	0.452025
$814$	9.22981	0.323505
$815$	15.0720	0.527951
$816$	0.990193	0.0346637
$817$	7.17613	0.251061
$818$	−38.0648	−1.33091
$819$	4.63312	0.161894
$820$	11.5174	0.402204
$821$	−48.0886	−1.67831	−0.839153	−	0.543896i	$-0.816949\pi$
$821$	−48.0886	−1.67831	−0.839153	+	0.543896i	$0.816949\pi$
$822$	−16.2985	−0.568476
$823$	9.66978	0.337067	0.168534	−	0.985696i	$-0.446097\pi$
$823$	9.66978	0.337067	0.168534	+	0.985696i	$0.446097\pi$
$824$	−5.75595	−0.200518
$825$	6.89910	0.240196
$826$	−44.7199	−1.55601
$827$	−10.6757	−0.371229	−0.185614	−	0.982623i	$-0.559428\pi$
$827$	−10.6757	−0.371229	−0.185614	+	0.982623i	$0.559428\pi$
$828$	−23.6417	−0.821607
$829$	20.7852	0.721900	0.360950	−	0.932585i	$-0.382452\pi$
$829$	20.7852	0.721900	0.360950	+	0.932585i	$0.382452\pi$
$830$	−15.2210	−0.528327
$831$	−12.6578	−0.439093
$832$	4.30740	0.149332
$833$	−6.11745	−0.211957
$834$	9.12761	0.316063
$835$	−4.48421	−0.155182
$836$	29.7367	1.02846
$837$	−17.0691	−0.589994
$838$	−17.7908	−0.614572
$839$	−15.5831	−0.537989	−0.268994	−	0.963142i	$-0.586691\pi$
$839$	−15.5831	−0.537989	−0.268994	+	0.963142i	$0.586691\pi$
$840$	7.86671	0.271427
$841$	−27.4749	−0.947411
$842$	88.0832	3.03555
$843$	−6.37572	−0.219592
$844$	−85.8577	−2.95534
$845$	−13.1362	−0.451900
$846$	−60.4929	−2.07979
$847$	14.2767	0.490555
$848$	28.2878	0.971406
$849$	−9.15381	−0.314158
$850$	−7.24131	−0.248375
$851$	−2.22677	−0.0763329
$852$	−13.0796	−0.448099
$853$	−43.8917	−1.50282	−0.751412	−	0.659833i	$-0.770627\pi$
$853$	−43.8917	−1.50282	−0.751412	+	0.659833i	$0.770627\pi$
$854$	−124.977	−4.27664
$855$	−5.84080	−0.199751
$856$	−27.5127	−0.940364
$857$	−0.301424	−0.0102965	−0.00514823	−	0.999987i	$-0.501639\pi$
$857$	−0.301424	−0.0102965	−0.00514823	+	0.999987i	$0.501639\pi$
$858$	−1.80052	−0.0614687
$859$	−37.5493	−1.28117	−0.640583	−	0.767889i	$-0.721307\pi$
$859$	−37.5493	−1.28117	−0.640583	+	0.767889i	$0.721307\pi$
$860$	13.7024	0.467248
$861$	−5.22449	−0.178050
$862$	−37.3598	−1.27248
$863$	10.5815	0.360198	0.180099	−	0.983648i	$-0.442358\pi$
$863$	10.5815	0.360198	0.180099	+	0.983648i	$0.442358\pi$
$864$	4.77835	0.162563
$865$	9.28689	0.315764
$866$	−26.6960	−0.907169
$867$	7.48597	0.254237
$868$	−95.3143	−3.23518
$869$	7.34412	0.249132
$870$	−1.38994	−0.0471234
$871$	1.59301	0.0539771
$872$	−4.34175	−0.147030
$873$	−24.4202	−0.826497
$874$	−10.9477	−0.370313
$875$	−35.5691	−1.20246
$876$	17.5263	0.592160
$877$	33.8450	1.14286	0.571432	−	0.820650i	$-0.306388\pi$
$877$	33.8450	1.14286	0.571432	+	0.820650i	$0.306388\pi$
$878$	−39.7935	−1.34296
$879$	4.31360	0.145494
$880$	11.2066	0.377775
$881$	−41.3103	−1.39178	−0.695890	−	0.718148i	$-0.744990\pi$
$881$	−41.3103	−1.39178	−0.695890	+	0.718148i	$0.744990\pi$
$882$	54.0571	1.82020
$883$	−6.44559	−0.216911	−0.108456	−	0.994101i	$-0.534591\pi$
$883$	−6.44559	−0.216911	−0.108456	+	0.994101i	$0.534591\pi$
$884$	1.23844	0.0416531
$885$	−2.23695	−0.0751944
$886$	−48.1209	−1.61665
$887$	−25.0661	−0.841636	−0.420818	−	0.907145i	$-0.638257\pi$
$887$	−25.0661	−0.841636	−0.420818	+	0.907145i	$0.638257\pi$
$888$	−1.97934	−0.0664225
$889$	−17.7246	−0.594464
$890$	−22.6058	−0.757748
$891$	27.4834	0.920728
$892$	24.1821	0.809676
$893$	−18.3570	−0.614293
$894$	4.65662	0.155741
$895$	−9.27731	−0.310106
$896$	79.9935	2.67239
$897$	0.434391	0.0145039
$898$	43.5524	1.45336
$899$	7.98286	0.266243
$900$	41.9325	1.39775
$901$	−7.54509	−0.251363
$902$	−27.2770	−0.908224
$903$	−6.21567	−0.206844
$904$	−33.1942	−1.10402
$905$	−18.7295	−0.622591
$906$	−10.6722	−0.354561
$907$	23.7012	0.786986	0.393493	−	0.919328i	$-0.371267\pi$
$907$	23.7012	0.786986	0.393493	+	0.919328i	$0.371267\pi$
$908$	65.0852	2.15993
$909$	−47.7999	−1.58542
$910$	4.09661	0.135801
$911$	−26.4270	−0.875565	−0.437782	−	0.899081i	$-0.644236\pi$
$911$	−26.4270	−0.875565	−0.437782	+	0.899081i	$0.644236\pi$
$912$	−2.65521	−0.0879227
$913$	23.6231	0.781810
$914$	−60.2564	−1.99310
$915$	−6.25155	−0.206670
$916$	5.35607	0.176969
$917$	−31.5239	−1.04101
$918$	4.84136	0.159789
$919$	41.5537	1.37073	0.685365	−	0.728199i	$-0.259643\pi$
$919$	41.5537	1.37073	0.685365	+	0.728199i	$0.259643\pi$
$920$	−9.90898	−0.326689
$921$	−12.5275	−0.412796
$922$	−87.4680	−2.88060
$923$	−3.22867	−0.106273
$924$	−25.7567	−0.847334
$925$	3.94955	0.129860
$926$	49.4871	1.62625
$927$	−3.70164	−0.121578
$928$	−2.23473	−0.0733588
$929$	37.6470	1.23516	0.617579	−	0.786509i	$-0.288114\pi$
$929$	37.6470	1.23516	0.617579	+	0.786509i	$0.288114\pi$
$930$	−7.27549	−0.238573
$931$	16.4040	0.537619
$932$	29.0642	0.952030
$933$	8.35724	0.273604
$934$	−0.513976	−0.0168178
$935$	−2.98910	−0.0977540
$936$	−5.18745	−0.169557
$937$	1.71765	0.0561132	0.0280566	−	0.999606i	$-0.491068\pi$
$937$	1.71765	0.0561132	0.0280566	+	0.999606i	$0.491068\pi$
$938$	34.7744	1.13543
$939$	4.84170	0.158003
$940$	−35.0516	−1.14326
$941$	−43.9507	−1.43275	−0.716377	−	0.697714i	$-0.754201\pi$
$941$	−43.9507	−1.43275	−0.716377	+	0.697714i	$0.754201\pi$
$942$	−6.32721	−0.206152
$943$	6.58082	0.214301
$944$	13.6619	0.444656
$945$	10.4947	0.341393
$946$	−32.4519	−1.05510
$947$	22.7959	0.740766	0.370383	−	0.928879i	$-0.379226\pi$
$947$	22.7959	0.740766	0.370383	+	0.928879i	$0.379226\pi$
$948$	−3.32254	−0.107911
$949$	4.32634	0.140439
$950$	19.4176	0.629990
$951$	−9.19061	−0.298026
$952$	12.8148	0.415331
$953$	56.6847	1.83620	0.918099	−	0.396351i	$-0.129724\pi$
$953$	56.6847	1.83620	0.918099	+	0.396351i	$0.129724\pi$
$954$	66.6725	2.15860
$955$	9.60875	0.310932
$956$	−14.3832	−0.465186
$957$	2.15720	0.0697325
$958$	−41.2584	−1.33300
$959$	−57.5533	−1.85849
$960$	4.70341	0.151802
$961$	10.7854	0.347916
$962$	−1.03075	−0.0332327
$963$	−17.6933	−0.570160
$964$	31.6677	1.01995
$965$	24.5997	0.791893
$966$	9.48249	0.305094
$967$	−0.529174	−0.0170171	−0.00850855	−	0.999964i	$-0.502708\pi$
$967$	−0.529174	−0.0170171	−0.00850855	+	0.999964i	$0.502708\pi$
$968$	−15.9849	−0.513774
$969$	0.708214	0.0227511
$970$	−21.5924	−0.693289
$971$	49.5411	1.58985	0.794924	−	0.606709i	$-0.207511\pi$
$971$	49.5411	1.58985	0.794924	+	0.606709i	$0.207511\pi$
$972$	−42.5555	−1.36497
$973$	32.2314	1.03329
$974$	−41.2657	−1.32224
$975$	−0.770464	−0.0246746
$976$	38.1805	1.22213
$977$	−0.743194	−0.0237769	−0.0118884	−	0.999929i	$-0.503784\pi$
$977$	−0.743194	−0.0237769	−0.0118884	+	0.999929i	$0.503784\pi$
$978$	16.1490	0.516389
$979$	35.0844	1.12130
$980$	31.3225	1.00056
$981$	−2.79217	−0.0891470
$982$	66.4605	2.12084
$983$	40.2440	1.28358	0.641792	−	0.766878i	$-0.278191\pi$
$983$	40.2440	1.28358	0.641792	+	0.766878i	$0.278191\pi$
$984$	5.84958	0.186478
$985$	2.06499	0.0657961
$986$	−2.26421	−0.0721070
$987$	15.9001	0.506105
$988$	−3.32088	−0.105651
$989$	7.82930	0.248957
$990$	26.4133	0.839469
$991$	−11.6072	−0.368715	−0.184357	−	0.982859i	$-0.559020\pi$
$991$	−11.6072	−0.368715	−0.184357	+	0.982859i	$0.559020\pi$
$992$	−11.6975	−0.371395
$993$	11.4678	0.363921
$994$	−70.4797	−2.23548
$995$	−4.97117	−0.157597
$996$	−10.6873	−0.338640
$997$	−37.6832	−1.19344	−0.596719	−	0.802450i	$-0.703529\pi$
$997$	−37.6832	−1.19344	−0.596719	+	0.802450i	$0.703529\pi$
$998$	67.1830	2.12664
$999$	−2.64057	−0.0835440

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4033.2.a.e.1.7	✓	82

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4033.2.a.e.1.7	✓	82	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:	\( N \)	\(=\)	\( 4033 = 37 \cdot 109 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4033.a (trivial)

\(f(q)\)	\(=\)	\(q-2.40882 q^{2} -0.455887 q^{3} +3.80243 q^{4} +1.02492 q^{5} +1.09815 q^{6} +3.87779 q^{7} -4.34175 q^{8} -2.79217 q^{9} +O(q^{10})\)	\(q-2.40882 q^{2} -0.455887 q^{3} +3.80243 q^{4} +1.02492 q^{5} +1.09815 q^{6} +3.87779 q^{7} -4.34175 q^{8} -2.79217 q^{9} -2.46884 q^{10} +3.83167 q^{11} -1.73348 q^{12} -0.427906 q^{13} -9.34091 q^{14} -0.467245 q^{15} +2.85363 q^{16} -0.761140 q^{17} +6.72584 q^{18} +2.04100 q^{19} +3.89717 q^{20} -1.76783 q^{21} -9.22981 q^{22} +2.22677 q^{23} +1.97934 q^{24} -3.94955 q^{25} +1.03075 q^{26} +2.64057 q^{27} +14.7450 q^{28} -1.23494 q^{29} +1.12551 q^{30} -6.46416 q^{31} +1.80959 q^{32} -1.74681 q^{33} +1.83345 q^{34} +3.97440 q^{35} -10.6170 q^{36} -1.00000 q^{37} -4.91641 q^{38} +0.195076 q^{39} -4.44992 q^{40} +2.95531 q^{41} +4.25840 q^{42} +3.51598 q^{43} +14.5697 q^{44} -2.86174 q^{45} -5.36391 q^{46} -8.99411 q^{47} -1.30093 q^{48} +8.03723 q^{49} +9.51377 q^{50} +0.346994 q^{51} -1.62708 q^{52} +9.91289 q^{53} -6.36068 q^{54} +3.92714 q^{55} -16.8364 q^{56} -0.930465 q^{57} +2.97476 q^{58} +4.78754 q^{59} -1.77667 q^{60} +13.3796 q^{61} +15.5710 q^{62} -10.8274 q^{63} -10.0662 q^{64} -0.438567 q^{65} +4.20775 q^{66} -3.72281 q^{67} -2.89418 q^{68} -1.01516 q^{69} -9.57364 q^{70} +7.54528 q^{71} +12.1229 q^{72} -10.1105 q^{73} +2.40882 q^{74} +1.80055 q^{75} +7.76077 q^{76} +14.8584 q^{77} -0.469905 q^{78} +1.91669 q^{79} +2.92473 q^{80} +7.17270 q^{81} -7.11883 q^{82} +6.16523 q^{83} -6.72206 q^{84} -0.780104 q^{85} -8.46939 q^{86} +0.562994 q^{87} -16.6361 q^{88} +9.15644 q^{89} +6.89342 q^{90} -1.65933 q^{91} +8.46716 q^{92} +2.94693 q^{93} +21.6652 q^{94} +2.09185 q^{95} -0.824967 q^{96} +8.74595 q^{97} -19.3603 q^{98} -10.6987 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 82 q + 10 q^{2} + 17 q^{3} + 88 q^{4} + 22 q^{5} + 4 q^{6} + 15 q^{7} + 33 q^{8} + 91 q^{9}+O(q^{10}) \) 82 * q + 10 * q^2 + 17 * q^3 + 88 * q^4 + 22 * q^5 + 4 * q^6 + 15 * q^7 + 33 * q^8 + 91 * q^9	\( 82 q + 10 q^{2} + 17 q^{3} + 88 q^{4} + 22 q^{5} + 4 q^{6} + 15 q^{7} + 33 q^{8} + 91 q^{9} + 13 q^{10} + 2 q^{11} + 36 q^{12} + 23 q^{13} + 24 q^{14} + 35 q^{15} + 104 q^{16} + 43 q^{17} + 42 q^{18} + 15 q^{19} + 59 q^{20} + 9 q^{21} + 6 q^{22} + 70 q^{23} + 15 q^{24} + 98 q^{25} + 10 q^{26} + 65 q^{27} + 37 q^{28} + 27 q^{29} + 17 q^{30} + 59 q^{31} + 46 q^{32} + 16 q^{33} - 16 q^{34} + 80 q^{35} + 88 q^{36} - 82 q^{37} + 82 q^{38} + 13 q^{39} + 14 q^{40} + 3 q^{41} + 62 q^{42} + 7 q^{43} - 11 q^{44} + 42 q^{45} - 11 q^{46} + 123 q^{47} + 45 q^{48} + 105 q^{49} + 27 q^{50} + 3 q^{51} - 30 q^{52} + 82 q^{53} - 27 q^{54} + 37 q^{55} + 66 q^{56} + 29 q^{57} - 34 q^{58} + 60 q^{59} + 94 q^{60} + 9 q^{61} - 2 q^{62} + 106 q^{63} + 93 q^{64} + 9 q^{65} + 63 q^{66} + 113 q^{68} + 48 q^{69} + 47 q^{70} + 59 q^{71} + 63 q^{72} + 21 q^{73} - 10 q^{74} + 77 q^{75} + 22 q^{76} + 30 q^{77} + 29 q^{78} + 55 q^{79} + 88 q^{80} + 42 q^{81} + 4 q^{82} + 92 q^{83} + 43 q^{84} - 7 q^{85} + 17 q^{86} + 147 q^{87} - 13 q^{88} + 100 q^{89} + 91 q^{90} + 28 q^{91} + 127 q^{92} + 3 q^{93} + 30 q^{94} + 48 q^{95} - 31 q^{96} + 53 q^{97} + 101 q^{98} - 20 q^{99}+O(q^{100}) \) 82 * q + 10 * q^2 + 17 * q^3 + 88 * q^4 + 22 * q^5 + 4 * q^6 + 15 * q^7 + 33 * q^8 + 91 * q^9 + 13 * q^10 + 2 * q^11 + 36 * q^12 + 23 * q^13 + 24 * q^14 + 35 * q^15 + 104 * q^16 + 43 * q^17 + 42 * q^18 + 15 * q^19 + 59 * q^20 + 9 * q^21 + 6 * q^22 + 70 * q^23 + 15 * q^24 + 98 * q^25 + 10 * q^26 + 65 * q^27 + 37 * q^28 + 27 * q^29 + 17 * q^30 + 59 * q^31 + 46 * q^32 + 16 * q^33 - 16 * q^34 + 80 * q^35 + 88 * q^36 - 82 * q^37 + 82 * q^38 + 13 * q^39 + 14 * q^40 + 3 * q^41 + 62 * q^42 + 7 * q^43 - 11 * q^44 + 42 * q^45 - 11 * q^46 + 123 * q^47 + 45 * q^48 + 105 * q^49 + 27 * q^50 + 3 * q^51 - 30 * q^52 + 82 * q^53 - 27 * q^54 + 37 * q^55 + 66 * q^56 + 29 * q^57 - 34 * q^58 + 60 * q^59 + 94 * q^60 + 9 * q^61 - 2 * q^62 + 106 * q^63 + 93 * q^64 + 9 * q^65 + 63 * q^66 + 113 * q^68 + 48 * q^69 + 47 * q^70 + 59 * q^71 + 63 * q^72 + 21 * q^73 - 10 * q^74 + 77 * q^75 + 22 * q^76 + 30 * q^77 + 29 * q^78 + 55 * q^79 + 88 * q^80 + 42 * q^81 + 4 * q^82 + 92 * q^83 + 43 * q^84 - 7 * q^85 + 17 * q^86 + 147 * q^87 - 13 * q^88 + 100 * q^89 + 91 * q^90 + 28 * q^91 + 127 * q^92 + 3 * q^93 + 30 * q^94 + 48 * q^95 - 31 * q^96 + 53 * q^97 + 101 * q^98 - 20 * q^99

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