LMFDB - Embedded newform 4015.2.a.g.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4015,2,Mod(1,4015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4015, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4015 = 5 \cdot 11 \cdot 73 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4015.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:	$32.0599364115$
Analytic rank:	$1$
Dimension:	$32$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	4015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.711670 q^{2} -2.33630 q^{3} -1.49353 q^{4} -1.00000 q^{5} +1.66268 q^{6} -3.28922 q^{7} +2.48624 q^{8} +2.45831 q^{9} +O(q^{10})$	\(q-0.711670 q^{2} -2.33630 q^{3} -1.49353 q^{4} -1.00000 q^{5} +1.66268 q^{6} -3.28922 q^{7} +2.48624 q^{8} +2.45831 q^{9} +0.711670 q^{10} -1.00000 q^{11} +3.48933 q^{12} -1.30591 q^{13} +2.34084 q^{14} +2.33630 q^{15} +1.21767 q^{16} -4.80787 q^{17} -1.74951 q^{18} -6.34213 q^{19} +1.49353 q^{20} +7.68461 q^{21} +0.711670 q^{22} +0.965774 q^{23} -5.80860 q^{24} +1.00000 q^{25} +0.929374 q^{26} +1.26555 q^{27} +4.91254 q^{28} +0.174660 q^{29} -1.66268 q^{30} +6.72799 q^{31} -5.83905 q^{32} +2.33630 q^{33} +3.42161 q^{34} +3.28922 q^{35} -3.67155 q^{36} +4.36644 q^{37} +4.51350 q^{38} +3.05099 q^{39} -2.48624 q^{40} +1.00503 q^{41} -5.46891 q^{42} +0.999338 q^{43} +1.49353 q^{44} -2.45831 q^{45} -0.687312 q^{46} +2.91024 q^{47} -2.84485 q^{48} +3.81897 q^{49} -0.711670 q^{50} +11.2326 q^{51} +1.95040 q^{52} -11.5665 q^{53} -0.900655 q^{54} +1.00000 q^{55} -8.17778 q^{56} +14.8171 q^{57} -0.124300 q^{58} -2.10338 q^{59} -3.48933 q^{60} +5.15845 q^{61} -4.78811 q^{62} -8.08592 q^{63} +1.72013 q^{64} +1.30591 q^{65} -1.66268 q^{66} +1.01620 q^{67} +7.18068 q^{68} -2.25634 q^{69} -2.34084 q^{70} +13.7094 q^{71} +6.11194 q^{72} -1.00000 q^{73} -3.10746 q^{74} -2.33630 q^{75} +9.47214 q^{76} +3.28922 q^{77} -2.17130 q^{78} +7.16676 q^{79} -1.21767 q^{80} -10.3316 q^{81} -0.715250 q^{82} +11.7069 q^{83} -11.4772 q^{84} +4.80787 q^{85} -0.711198 q^{86} -0.408059 q^{87} -2.48624 q^{88} +7.19431 q^{89} +1.74951 q^{90} +4.29541 q^{91} -1.44241 q^{92} -15.7186 q^{93} -2.07113 q^{94} +6.34213 q^{95} +13.6418 q^{96} -8.03629 q^{97} -2.71785 q^{98} -2.45831 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 5 q^{2} - 7 q^{3} + 37 q^{4} - 32 q^{5} - 3 q^{6} - 18 q^{8} + 29 q^{9}+O(q^{10}) $ 32 * q - 5 * q^2 - 7 * q^3 + 37 * q^4 - 32 * q^5 - 3 * q^6 - 18 * q^8 + 29 * q^9	\( 32 q - 5 q^{2} - 7 q^{3} + 37 q^{4} - 32 q^{5} - 3 q^{6} - 18 q^{8} + 29 q^{9} + 5 q^{10} - 32 q^{11} - 24 q^{12} - q^{13} - 5 q^{14} + 7 q^{15} + 47 q^{16} - 30 q^{17} - 11 q^{18} + 16 q^{19} - 37 q^{20} + q^{21} + 5 q^{22} - 26 q^{23} - 21 q^{24} + 32 q^{25} - q^{26} - 31 q^{27} - 24 q^{28} - 10 q^{29} + 3 q^{30} - 2 q^{31} - 31 q^{32} + 7 q^{33} - 14 q^{34} + 38 q^{36} - 28 q^{37} - 63 q^{38} - 2 q^{39} + 18 q^{40} - 62 q^{41} - 9 q^{42} + 8 q^{43} - 37 q^{44} - 29 q^{45} + 19 q^{46} - 21 q^{47} - 79 q^{48} + 34 q^{49} - 5 q^{50} + 17 q^{51} + 15 q^{52} - 32 q^{53} + 5 q^{54} + 32 q^{55} - 52 q^{56} - 57 q^{57} + 4 q^{58} - 37 q^{59} + 24 q^{60} + 15 q^{61} - 22 q^{62} + 5 q^{63} + 70 q^{64} + q^{65} + 3 q^{66} - 42 q^{67} - 81 q^{68} - 8 q^{69} + 5 q^{70} - 40 q^{71} - 27 q^{72} - 32 q^{73} - 17 q^{74} - 7 q^{75} + 21 q^{76} - 105 q^{78} + 18 q^{79} - 47 q^{80} + 12 q^{81} - 70 q^{82} - 26 q^{83} + 22 q^{84} + 30 q^{85} - 45 q^{86} - 18 q^{87} + 18 q^{88} - 83 q^{89} + 11 q^{90} - 18 q^{91} - 73 q^{92} - 68 q^{93} + 56 q^{94} - 16 q^{95} - 35 q^{96} - 99 q^{97} - 61 q^{98} - 29 q^{99}+O(q^{100}) \) 32 * q - 5 * q^2 - 7 * q^3 + 37 * q^4 - 32 * q^5 - 3 * q^6 - 18 * q^8 + 29 * q^9 + 5 * q^10 - 32 * q^11 - 24 * q^12 - q^13 - 5 * q^14 + 7 * q^15 + 47 * q^16 - 30 * q^17 - 11 * q^18 + 16 * q^19 - 37 * q^20 + q^21 + 5 * q^22 - 26 * q^23 - 21 * q^24 + 32 * q^25 - q^26 - 31 * q^27 - 24 * q^28 - 10 * q^29 + 3 * q^30 - 2 * q^31 - 31 * q^32 + 7 * q^33 - 14 * q^34 + 38 * q^36 - 28 * q^37 - 63 * q^38 - 2 * q^39 + 18 * q^40 - 62 * q^41 - 9 * q^42 + 8 * q^43 - 37 * q^44 - 29 * q^45 + 19 * q^46 - 21 * q^47 - 79 * q^48 + 34 * q^49 - 5 * q^50 + 17 * q^51 + 15 * q^52 - 32 * q^53 + 5 * q^54 + 32 * q^55 - 52 * q^56 - 57 * q^57 + 4 * q^58 - 37 * q^59 + 24 * q^60 + 15 * q^61 - 22 * q^62 + 5 * q^63 + 70 * q^64 + q^65 + 3 * q^66 - 42 * q^67 - 81 * q^68 - 8 * q^69 + 5 * q^70 - 40 * q^71 - 27 * q^72 - 32 * q^73 - 17 * q^74 - 7 * q^75 + 21 * q^76 - 105 * q^78 + 18 * q^79 - 47 * q^80 + 12 * q^81 - 70 * q^82 - 26 * q^83 + 22 * q^84 + 30 * q^85 - 45 * q^86 - 18 * q^87 + 18 * q^88 - 83 * q^89 + 11 * q^90 - 18 * q^91 - 73 * q^92 - 68 * q^93 + 56 * q^94 - 16 * q^95 - 35 * q^96 - 99 * q^97 - 61 * q^98 - 29 * 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 $

$2$	−0.711670	−0.503227	−0.251613	−	0.967828i	$-0.580961\pi$
$2$	−0.711670	−0.503227	−0.251613	+	0.967828i	$0.580961\pi$
$3$	−2.33630	−1.34886	−0.674432	−	0.738337i	$-0.735612\pi$
$3$	−2.33630	−1.34886	−0.674432	+	0.738337i	$0.735612\pi$
$4$	−1.49353	−0.746763
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	1.66268	0.678785
$7$	−3.28922	−1.24321	−0.621604	−	0.783332i	$-0.713519\pi$
$7$	−3.28922	−1.24321	−0.621604	+	0.783332i	$0.713519\pi$
$8$	2.48624	0.879018
$9$	2.45831	0.819437
$10$	0.711670	0.225050
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	3.48933	1.00728
$13$	−1.30591	−0.362193	−0.181097	−	0.983465i	$-0.557965\pi$
$13$	−1.30591	−0.362193	−0.181097	+	0.983465i	$0.557965\pi$
$14$	2.34084	0.625615
$15$	2.33630	0.603231
$16$	1.21767	0.304418
$17$	−4.80787	−1.16608	−0.583040	−	0.812444i	$-0.698137\pi$
$17$	−4.80787	−1.16608	−0.583040	+	0.812444i	$0.698137\pi$
$18$	−1.74951	−0.412362
$19$	−6.34213	−1.45498	−0.727492	−	0.686116i	$-0.759314\pi$
$19$	−6.34213	−1.45498	−0.727492	+	0.686116i	$0.759314\pi$
$20$	1.49353	0.333963
$21$	7.68461	1.67692
$22$	0.711670	0.151729
$23$	0.965774	0.201378	0.100689	−	0.994918i	$-0.467895\pi$
$23$	0.965774	0.201378	0.100689	+	0.994918i	$0.467895\pi$
$24$	−5.80860	−1.18568
$25$	1.00000	0.200000
$26$	0.929374	0.182265
$27$	1.26555	0.243555
$28$	4.91254	0.928382
$29$	0.174660	0.0324336	0.0162168	−	0.999868i	$-0.494838\pi$
$29$	0.174660	0.0324336	0.0162168	+	0.999868i	$0.494838\pi$
$30$	−1.66268	−0.303562
$31$	6.72799	1.20838	0.604192	−	0.796839i	$-0.293496\pi$
$31$	6.72799	1.20838	0.604192	+	0.796839i	$0.293496\pi$
$32$	−5.83905	−1.03221
$33$	2.33630	0.406698
$34$	3.42161	0.586802
$35$	3.28922	0.555980
$36$	−3.67155	−0.611925
$37$	4.36644	0.717838	0.358919	−	0.933369i	$-0.383145\pi$
$37$	4.36644	0.717838	0.358919	+	0.933369i	$0.383145\pi$
$38$	4.51350	0.732187
$39$	3.05099	0.488550
$40$	−2.48624	−0.393109
$41$	1.00503	0.156959	0.0784797	−	0.996916i	$-0.474993\pi$
$41$	1.00503	0.156959	0.0784797	+	0.996916i	$0.474993\pi$
$42$	−5.46891	−0.843871
$43$	0.999338	0.152398	0.0761988	−	0.997093i	$-0.475722\pi$
$43$	0.999338	0.152398	0.0761988	+	0.997093i	$0.475722\pi$
$44$	1.49353	0.225158
$45$	−2.45831	−0.366463
$46$	−0.687312	−0.101339
$47$	2.91024	0.424502	0.212251	−	0.977215i	$-0.431920\pi$
$47$	2.91024	0.424502	0.212251	+	0.977215i	$0.431920\pi$
$48$	−2.84485	−0.410619
$49$	3.81897	0.545567
$50$	−0.711670	−0.100645
$51$	11.2326	1.57288
$52$	1.95040	0.270472
$53$	−11.5665	−1.58878	−0.794391	−	0.607407i	$-0.792210\pi$
$53$	−11.5665	−1.58878	−0.794391	+	0.607407i	$0.792210\pi$
$54$	−0.900655	−0.122564
$55$	1.00000	0.134840
$56$	−8.17778	−1.09280
$57$	14.8171	1.96258
$58$	−0.124300	−0.0163215
$59$	−2.10338	−0.273837	−0.136919	−	0.990582i	$-0.543720\pi$
$59$	−2.10338	−0.273837	−0.136919	+	0.990582i	$0.543720\pi$
$60$	−3.48933	−0.450470
$61$	5.15845	0.660472	0.330236	−	0.943898i	$-0.392872\pi$
$61$	5.15845	0.660472	0.330236	+	0.943898i	$0.392872\pi$
$62$	−4.78811	−0.608091
$63$	−8.08592	−1.01873
$64$	1.72013	0.215017
$65$	1.30591	0.161978
$66$	−1.66268	−0.204661
$67$	1.01620	0.124149	0.0620744	−	0.998072i	$-0.480228\pi$
$67$	1.01620	0.124149	0.0620744	+	0.998072i	$0.480228\pi$
$68$	7.18068	0.870785
$69$	−2.25634	−0.271631
$70$	−2.34084	−0.279784
$71$	13.7094	1.62701	0.813505	−	0.581558i	$-0.197557\pi$
$71$	13.7094	1.62701	0.813505	+	0.581558i	$0.197557\pi$
$72$	6.11194	0.720299
$73$	−1.00000	−0.117041
$73$	−1.00000	−0.117041
$74$	−3.10746	−0.361235
$75$	−2.33630	−0.269773
$76$	9.47214	1.08653
$77$	3.28922	0.374841
$78$	−2.17130	−0.245851
$79$	7.16676	0.806323	0.403162	−	0.915129i	$-0.367911\pi$
$79$	7.16676	0.806323	0.403162	+	0.915129i	$0.367911\pi$
$80$	−1.21767	−0.136140
$81$	−10.3316	−1.14796
$82$	−0.715250	−0.0789862
$83$	11.7069	1.28500	0.642501	−	0.766285i	$-0.277897\pi$
$83$	11.7069	1.28500	0.642501	+	0.766285i	$0.277897\pi$
$84$	−11.4772	−1.25226
$85$	4.80787	0.521486
$86$	−0.711198	−0.0766905
$87$	−0.408059	−0.0437486
$88$	−2.48624	−0.265034
$89$	7.19431	0.762595	0.381297	−	0.924452i	$-0.375477\pi$
$89$	7.19431	0.762595	0.381297	+	0.924452i	$0.375477\pi$
$90$	1.74951	0.184414
$91$	4.29541	0.450281
$92$	−1.44241	−0.150381
$93$	−15.7186	−1.62995
$94$	−2.07113	−0.213621
$95$	6.34213	0.650689
$96$	13.6418	1.39231
$97$	−8.03629	−0.815961	−0.407981	−	0.912991i	$-0.633767\pi$
$97$	−8.03629	−0.815961	−0.407981	+	0.912991i	$0.633767\pi$
$98$	−2.71785	−0.274544
$99$	−2.45831	−0.247069
$100$	−1.49353	−0.149353
$101$	9.86773	0.981876	0.490938	−	0.871194i	$-0.336654\pi$
$101$	9.86773	0.981876	0.490938	+	0.871194i	$0.336654\pi$
$102$	−7.99393	−0.791517
$103$	−10.9958	−1.08345	−0.541724	−	0.840557i	$-0.682228\pi$
$103$	−10.9958	−1.08345	−0.541724	+	0.840557i	$0.682228\pi$
$104$	−3.24679	−0.318374
$105$	−7.68461	−0.749942
$106$	8.23153	0.799517
$107$	10.0224	0.968900	0.484450	−	0.874819i	$-0.339020\pi$
$107$	10.0224	0.968900	0.484450	+	0.874819i	$0.339020\pi$
$108$	−1.89013	−0.181878
$109$	17.9108	1.71554	0.857769	−	0.514035i	$-0.171850\pi$
$109$	17.9108	1.71554	0.857769	+	0.514035i	$0.171850\pi$
$110$	−0.711670	−0.0678551
$111$	−10.2013	−0.968267
$112$	−4.00519	−0.378455
$113$	16.4074	1.54348	0.771739	−	0.635940i	$-0.219387\pi$
$113$	16.4074	1.54348	0.771739	+	0.635940i	$0.219387\pi$
$114$	−10.5449	−0.987621
$115$	−0.965774	−0.0900589
$116$	−0.260860	−0.0242202
$117$	−3.21032	−0.296794
$118$	1.49692	0.137802
$119$	15.8141	1.44968
$120$	5.80860	0.530250
$121$	1.00000	0.0909091
$122$	−3.67111	−0.332367
$123$	−2.34806	−0.211717
$124$	−10.0484	−0.902376
$125$	−1.00000	−0.0894427
$126$	5.75451	0.512652
$127$	1.26844	0.112556	0.0562781	−	0.998415i	$-0.482077\pi$
$127$	1.26844	0.112556	0.0562781	+	0.998415i	$0.482077\pi$
$128$	10.4539	0.924007
$129$	−2.33475	−0.205564
$130$	−0.929374	−0.0815115
$131$	21.5546	1.88323	0.941617	−	0.336687i	$-0.109306\pi$
$131$	21.5546	1.88323	0.941617	+	0.336687i	$0.109306\pi$
$132$	−3.48933	−0.303707
$133$	20.8607	1.80885
$134$	−0.723201	−0.0624750
$135$	−1.26555	−0.108921
$136$	−11.9535	−1.02500
$137$	−10.7912	−0.921955	−0.460978	−	0.887412i	$-0.652501\pi$
$137$	−10.7912	−0.921955	−0.460978	+	0.887412i	$0.652501\pi$
$138$	1.60577	0.136692
$139$	9.71380	0.823913	0.411957	−	0.911203i	$-0.364846\pi$
$139$	9.71380	0.823913	0.411957	+	0.911203i	$0.364846\pi$
$140$	−4.91254	−0.415185
$141$	−6.79921	−0.572597
$142$	−9.75659	−0.818755
$143$	1.30591	0.109205
$144$	2.99342	0.249451
$145$	−0.174660	−0.0145048
$146$	0.711670	0.0588982
$147$	−8.92227	−0.735896
$148$	−6.52139	−0.536055
$149$	−17.8657	−1.46362	−0.731808	−	0.681511i	$-0.761323\pi$
$149$	−17.8657	−1.46362	−0.731808	+	0.681511i	$0.761323\pi$
$150$	1.66268	0.135757
$151$	−16.8798	−1.37366	−0.686831	−	0.726817i	$-0.740999\pi$
$151$	−16.8798	−1.37366	−0.686831	+	0.726817i	$0.740999\pi$
$152$	−15.7680	−1.27896
$153$	−11.8192	−0.955528
$154$	−2.34084	−0.188630
$155$	−6.72799	−0.540405
$156$	−4.55673	−0.364831
$157$	−13.0413	−1.04081	−0.520403	−	0.853921i	$-0.674218\pi$
$157$	−13.0413	−1.04081	−0.520403	+	0.853921i	$0.674218\pi$
$158$	−5.10037	−0.405763
$159$	27.0229	2.14305
$160$	5.83905	0.461618
$161$	−3.17664	−0.250354
$162$	7.35272	0.577684
$163$	−17.8771	−1.40025	−0.700123	−	0.714023i	$-0.746871\pi$
$163$	−17.8771	−1.40025	−0.700123	+	0.714023i	$0.746871\pi$
$164$	−1.50104	−0.117212
$165$	−2.33630	−0.181881
$166$	−8.33147	−0.646647
$167$	−14.5367	−1.12489	−0.562443	−	0.826836i	$-0.690138\pi$
$167$	−14.5367	−1.12489	−0.562443	+	0.826836i	$0.690138\pi$
$168$	19.1058	1.47404
$169$	−11.2946	−0.868816
$170$	−3.42161	−0.262426
$171$	−15.5909	−1.19227
$172$	−1.49254	−0.113805
$173$	7.20731	0.547962	0.273981	−	0.961735i	$-0.411659\pi$
$173$	7.20731	0.547962	0.273981	+	0.961735i	$0.411659\pi$
$174$	0.290404	0.0220154
$175$	−3.28922	−0.248642
$176$	−1.21767	−0.0917855
$177$	4.91414	0.369370
$178$	−5.11997	−0.383758
$179$	5.21182	0.389550	0.194775	−	0.980848i	$-0.437602\pi$
$179$	5.21182	0.389550	0.194775	+	0.980848i	$0.437602\pi$
$180$	3.67155	0.273661
$181$	−5.66977	−0.421431	−0.210715	−	0.977547i	$-0.567579\pi$
$181$	−5.66977	−0.421431	−0.210715	+	0.977547i	$0.567579\pi$
$182$	−3.05691	−0.226594
$183$	−12.0517	−0.890887
$184$	2.40114	0.177015
$185$	−4.36644	−0.321027
$186$	11.1865	0.820232
$187$	4.80787	0.351586
$188$	−4.34652	−0.317003
$189$	−4.16268	−0.302790
$190$	−4.51350	−0.327444
$191$	−21.0799	−1.52529	−0.762645	−	0.646817i	$-0.776100\pi$
$191$	−21.0799	−1.52529	−0.762645	+	0.646817i	$0.776100\pi$
$192$	−4.01876	−0.290029
$193$	−11.8809	−0.855206	−0.427603	−	0.903967i	$-0.640642\pi$
$193$	−11.8809	−0.855206	−0.427603	+	0.903967i	$0.640642\pi$
$194$	5.71918	0.410613
$195$	−3.05099	−0.218486
$196$	−5.70373	−0.407409
$197$	0.731995	0.0521525	0.0260763	−	0.999660i	$-0.491699\pi$
$197$	0.731995	0.0521525	0.0260763	+	0.999660i	$0.491699\pi$
$198$	1.74951	0.124332
$199$	5.15534	0.365452	0.182726	−	0.983164i	$-0.441508\pi$
$199$	5.15534	0.365452	0.182726	+	0.983164i	$0.441508\pi$
$200$	2.48624	0.175804
$201$	−2.37416	−0.167460
$202$	−7.02257	−0.494106
$203$	−0.574496	−0.0403217
$204$	−16.7762	−1.17457
$205$	−1.00503	−0.0701944
$206$	7.82537	0.545219
$207$	2.37417	0.165016
$208$	−1.59017	−0.110258
$209$	6.34213	0.438694
$210$	5.46891	0.377390
$211$	18.6561	1.28434	0.642171	−	0.766561i	$-0.278034\pi$
$211$	18.6561	1.28434	0.642171	+	0.766561i	$0.278034\pi$
$212$	17.2749	1.18644
$213$	−32.0294	−2.19462
$214$	−7.13262	−0.487576
$215$	−0.999338	−0.0681543
$216$	3.14646	0.214090
$217$	−22.1299	−1.50227
$218$	−12.7465	−0.863305
$219$	2.33630	0.157873
$220$	−1.49353	−0.100694
$221$	6.27862	0.422346
$222$	7.25998	0.487258
$223$	−2.19996	−0.147320	−0.0736602	−	0.997283i	$-0.523468\pi$
$223$	−2.19996	−0.147320	−0.0736602	+	0.997283i	$0.523468\pi$
$224$	19.2059	1.28325
$225$	2.45831	0.163887
$226$	−11.6766	−0.776719
$227$	−9.12945	−0.605943	−0.302971	−	0.953000i	$-0.597979\pi$
$227$	−9.12945	−0.605943	−0.302971	+	0.953000i	$0.597979\pi$
$228$	−22.1298	−1.46558
$229$	−9.53883	−0.630343	−0.315172	−	0.949035i	$-0.602062\pi$
$229$	−9.53883	−0.630343	−0.315172	+	0.949035i	$0.602062\pi$
$230$	0.687312	0.0453200
$231$	−7.68461	−0.505610
$232$	0.434247	0.0285097
$233$	−5.24880	−0.343861	−0.171930	−	0.985109i	$-0.555000\pi$
$233$	−5.24880	−0.343861	−0.171930	+	0.985109i	$0.555000\pi$
$234$	2.28469	0.149355
$235$	−2.91024	−0.189843
$236$	3.14146	0.204492
$237$	−16.7437	−1.08762
$238$	−11.2544	−0.729517
$239$	−8.18117	−0.529196	−0.264598	−	0.964359i	$-0.585239\pi$
$239$	−8.18117	−0.529196	−0.264598	+	0.964359i	$0.585239\pi$
$240$	2.84485	0.183634
$241$	−21.4488	−1.38164	−0.690819	−	0.723027i	$-0.742750\pi$
$241$	−21.4488	−1.38164	−0.690819	+	0.723027i	$0.742750\pi$
$242$	−0.711670	−0.0457479
$243$	20.3412	1.30489
$244$	−7.70428	−0.493216
$245$	−3.81897	−0.243985
$246$	1.67104	0.106542
$247$	8.28223	0.526985
$248$	16.7274	1.06219
$249$	−27.3509	−1.73329
$250$	0.711670	0.0450100
$251$	7.94505	0.501487	0.250744	−	0.968054i	$-0.419325\pi$
$251$	7.94505	0.501487	0.250744	+	0.968054i	$0.419325\pi$
$252$	12.0765	0.760750
$253$	−0.965774	−0.0607177
$254$	−0.902713	−0.0566412
$255$	−11.2326	−0.703415
$256$	−10.8800	−0.680002
$257$	−22.2824	−1.38994	−0.694968	−	0.719041i	$-0.744582\pi$
$257$	−22.2824	−1.38994	−0.694968	+	0.719041i	$0.744582\pi$
$258$	1.66157	0.103445
$259$	−14.3622	−0.892423
$260$	−1.95040	−0.120959
$261$	0.429369	0.0265773
$262$	−15.3398	−0.947693
$263$	23.0860	1.42354	0.711771	−	0.702412i	$-0.247894\pi$
$263$	23.0860	1.42354	0.711771	+	0.702412i	$0.247894\pi$
$264$	5.80860	0.357495
$265$	11.5665	0.710525
$266$	−14.8459	−0.910261
$267$	−16.8081	−1.02864
$268$	−1.51772	−0.0927098
$269$	−12.9867	−0.791812	−0.395906	−	0.918291i	$-0.629569\pi$
$269$	−12.9867	−0.791812	−0.395906	+	0.918291i	$0.629569\pi$
$270$	0.900655	0.0548121
$271$	23.9769	1.45649	0.728247	−	0.685315i	$-0.240335\pi$
$271$	23.9769	1.45649	0.728247	+	0.685315i	$0.240335\pi$
$272$	−5.85441	−0.354976
$273$	−10.0354	−0.607369
$274$	7.67978	0.463952
$275$	−1.00000	−0.0603023
$276$	3.36990	0.202844
$277$	21.6358	1.29997	0.649985	−	0.759947i	$-0.274775\pi$
$277$	21.6358	1.29997	0.649985	+	0.759947i	$0.274775\pi$
$278$	−6.91301	−0.414615
$279$	16.5395	0.990194
$280$	8.17778	0.488716
$281$	27.6765	1.65104	0.825521	−	0.564372i	$-0.190882\pi$
$281$	27.6765	1.65104	0.825521	+	0.564372i	$0.190882\pi$
$282$	4.83879	0.288146
$283$	−3.56883	−0.212145	−0.106073	−	0.994358i	$-0.533828\pi$
$283$	−3.56883	−0.212145	−0.106073	+	0.994358i	$0.533828\pi$
$284$	−20.4754	−1.21499
$285$	−14.8171	−0.877691
$286$	−0.929374	−0.0549550
$287$	−3.30577	−0.195133
$288$	−14.3542	−0.845830
$289$	6.11559	0.359741
$290$	0.124300	0.00729918
$291$	18.7752	1.10062
$292$	1.49353	0.0874020
$293$	−26.2108	−1.53125	−0.765627	−	0.643285i	$-0.777571\pi$
$293$	−26.2108	−1.53125	−0.765627	+	0.643285i	$0.777571\pi$
$294$	6.34971	0.370323
$295$	2.10338	0.122464
$296$	10.8560	0.630993
$297$	−1.26555	−0.0734347
$298$	12.7145	0.736530
$299$	−1.26121	−0.0729376
$300$	3.48933	0.201456
$301$	−3.28704	−0.189462
$302$	12.0129	0.691263
$303$	−23.0540	−1.32442
$304$	−7.72264	−0.442924
$305$	−5.15845	−0.295372
$306$	8.41139	0.480847
$307$	−13.6620	−0.779730	−0.389865	−	0.920872i	$-0.627478\pi$
$307$	−13.6620	−0.779730	−0.389865	+	0.920872i	$0.627478\pi$
$308$	−4.91254	−0.279918
$309$	25.6895	1.46142
$310$	4.78811	0.271946
$311$	−10.5230	−0.596705	−0.298352	−	0.954456i	$-0.596437\pi$
$311$	−10.5230	−0.596705	−0.298352	+	0.954456i	$0.596437\pi$
$312$	7.58549	0.429444
$313$	−3.49189	−0.197373	−0.0986866	−	0.995119i	$-0.531464\pi$
$313$	−3.49189	−0.197373	−0.0986866	+	0.995119i	$0.531464\pi$
$314$	9.28107	0.523761
$315$	8.08592	0.455590
$316$	−10.7037	−0.602132
$317$	−20.2259	−1.13600	−0.567999	−	0.823029i	$-0.692282\pi$
$317$	−20.2259	−1.13600	−0.567999	+	0.823029i	$0.692282\pi$
$318$	−19.2314	−1.07844
$319$	−0.174660	−0.00977910
$320$	−1.72013	−0.0961585
$321$	−23.4153	−1.30691
$322$	2.26072	0.125985
$323$	30.4921	1.69663
$324$	15.4306	0.857254
$325$	−1.30591	−0.0724386
$326$	12.7226	0.704641
$327$	−41.8449	−2.31403
$328$	2.49875	0.137970
$329$	−9.57243	−0.527745
$330$	1.66268	0.0915273
$331$	28.0579	1.54220	0.771101	−	0.636713i	$-0.219706\pi$
$331$	28.0579	1.54220	0.771101	+	0.636713i	$0.219706\pi$
$332$	−17.4846	−0.959592
$333$	10.7341	0.588223
$334$	10.3454	0.566072
$335$	−1.01620	−0.0555211
$336$	9.35734	0.510485
$337$	11.6836	0.636444	0.318222	−	0.948016i	$-0.396914\pi$
$337$	11.6836	0.636444	0.318222	+	0.948016i	$0.396914\pi$
$338$	8.03803	0.437211
$339$	−38.3326	−2.08194
$340$	−7.18068	−0.389427
$341$	−6.72799	−0.364341
$342$	11.0956	0.599981
$343$	10.4631	0.564955
$344$	2.48459	0.133960
$345$	2.25634	0.121477
$346$	−5.12923	−0.275749
$347$	6.48076	0.347906	0.173953	−	0.984754i	$-0.444346\pi$
$347$	6.48076	0.347906	0.173953	+	0.984754i	$0.444346\pi$
$348$	0.609447	0.0326698
$349$	24.9965	1.33803	0.669017	−	0.743247i	$-0.266715\pi$
$349$	24.9965	1.33803	0.669017	+	0.743247i	$0.266715\pi$
$350$	2.34084	0.125123
$351$	−1.65269	−0.0882141
$352$	5.83905	0.311223
$353$	−13.3322	−0.709601	−0.354800	−	0.934942i	$-0.615451\pi$
$353$	−13.3322	−0.709601	−0.354800	+	0.934942i	$0.615451\pi$
$354$	−3.49725	−0.185877
$355$	−13.7094	−0.727621
$356$	−10.7449	−0.569478
$357$	−36.9466	−1.95542
$358$	−3.70910	−0.196032
$359$	−29.9158	−1.57890	−0.789449	−	0.613816i	$-0.789634\pi$
$359$	−29.9158	−1.57890	−0.789449	+	0.613816i	$0.789634\pi$
$360$	−6.11194	−0.322128
$361$	21.2226	1.11698
$362$	4.03500	0.212075
$363$	−2.33630	−0.122624
$364$	−6.41531	−0.336254
$365$	1.00000	0.0523424
$366$	8.57683	0.448318
$367$	15.7013	0.819601	0.409800	−	0.912175i	$-0.365598\pi$
$367$	15.7013	0.819601	0.409800	+	0.912175i	$0.365598\pi$
$368$	1.17600	0.0613030
$369$	2.47068	0.128618
$370$	3.10746	0.161549
$371$	38.0448	1.97519
$372$	23.4762	1.21718
$373$	35.4191	1.83393	0.916965	−	0.398967i	$-0.130631\pi$
$373$	35.4191	1.83393	0.916965	+	0.398967i	$0.130631\pi$
$374$	−3.42161	−0.176927
$375$	2.33630	0.120646
$376$	7.23555	0.373145
$377$	−0.228090	−0.0117472
$378$	2.96245	0.152372
$379$	4.39693	0.225855	0.112927	−	0.993603i	$-0.463977\pi$
$379$	4.39693	0.225855	0.112927	+	0.993603i	$0.463977\pi$
$380$	−9.47214	−0.485910
$381$	−2.96347	−0.151823
$382$	15.0019	0.767566
$383$	15.0716	0.770120	0.385060	−	0.922891i	$-0.374181\pi$
$383$	15.0716	0.770120	0.385060	+	0.922891i	$0.374181\pi$
$384$	−24.4236	−1.24636
$385$	−3.28922	−0.167634
$386$	8.45527	0.430362
$387$	2.45668	0.124880
$388$	12.0024	0.609330
$389$	−24.0467	−1.21922	−0.609609	−	0.792702i	$-0.708674\pi$
$389$	−24.0467	−1.21922	−0.609609	+	0.792702i	$0.708674\pi$
$390$	2.17130	0.109948
$391$	−4.64331	−0.234822
$392$	9.49486	0.479563
$393$	−50.3580	−2.54023
$394$	−0.520939	−0.0262445
$395$	−7.16676	−0.360599
$396$	3.67155	0.184502
$397$	−7.39784	−0.371287	−0.185643	−	0.982617i	$-0.559437\pi$
$397$	−7.39784	−0.371287	−0.185643	+	0.982617i	$0.559437\pi$
$398$	−3.66890	−0.183905
$399$	−48.7368	−2.43989
$400$	1.21767	0.0608836
$401$	−2.43734	−0.121715	−0.0608574	−	0.998146i	$-0.519383\pi$
$401$	−2.43734	−0.121715	−0.0608574	+	0.998146i	$0.519383\pi$
$402$	1.68962	0.0842704
$403$	−8.78613	−0.437668
$404$	−14.7377	−0.733229
$405$	10.3316	0.513383
$406$	0.408852	0.0202910
$407$	−4.36644	−0.216436
$408$	27.9270	1.38259
$409$	32.2805	1.59617	0.798084	−	0.602546i	$-0.205847\pi$
$409$	32.2805	1.59617	0.798084	+	0.602546i	$0.205847\pi$
$410$	0.715250	0.0353237
$411$	25.2115	1.24359
$412$	16.4225	0.809078
$413$	6.91850	0.340437
$414$	−1.68963	−0.0830406
$415$	−11.7069	−0.574671
$416$	7.62526	0.373859
$417$	−22.6944	−1.11135
$418$	−4.51350	−0.220763
$419$	−5.36465	−0.262080	−0.131040	−	0.991377i	$-0.541832\pi$
$419$	−5.36465	−0.262080	−0.131040	+	0.991377i	$0.541832\pi$
$420$	11.4772	0.560029
$421$	−34.1863	−1.66614	−0.833068	−	0.553170i	$-0.813418\pi$
$421$	−34.1863	−1.66614	−0.833068	+	0.553170i	$0.813418\pi$
$422$	−13.2770	−0.646315
$423$	7.15428	0.347853
$424$	−28.7571	−1.39657
$425$	−4.80787	−0.233216
$426$	22.7943	1.10439
$427$	−16.9673	−0.821104
$428$	−14.9687	−0.723538
$429$	−3.05099	−0.147303
$430$	0.711198	0.0342970
$431$	34.1409	1.64451	0.822254	−	0.569121i	$-0.192716\pi$
$431$	34.1409	1.64451	0.822254	+	0.569121i	$0.192716\pi$
$432$	1.54103	0.0741427
$433$	−17.0788	−0.820753	−0.410377	−	0.911916i	$-0.634603\pi$
$433$	−17.0788	−0.820753	−0.410377	+	0.911916i	$0.634603\pi$
$434$	15.7491	0.755983
$435$	0.408059	0.0195650
$436$	−26.7502	−1.28110
$437$	−6.12506	−0.293001
$438$	−1.66268	−0.0794457
$439$	−28.2770	−1.34959	−0.674794	−	0.738006i	$-0.735767\pi$
$439$	−28.2770	−1.34959	−0.674794	+	0.738006i	$0.735767\pi$
$440$	2.48624	0.118527
$441$	9.38821	0.447058
$442$	−4.46831	−0.212536
$443$	6.99801	0.332485	0.166243	−	0.986085i	$-0.446836\pi$
$443$	6.99801	0.332485	0.166243	+	0.986085i	$0.446836\pi$
$444$	15.2359	0.723066
$445$	−7.19431	−0.341043
$446$	1.56565	0.0741355
$447$	41.7397	1.97422
$448$	−5.65790	−0.267311
$449$	15.0935	0.712306	0.356153	−	0.934428i	$-0.384088\pi$
$449$	15.0935	0.712306	0.356153	+	0.934428i	$0.384088\pi$
$450$	−1.74951	−0.0824725
$451$	−1.00503	−0.0473251
$452$	−24.5049	−1.15261
$453$	39.4364	1.85288
$454$	6.49715	0.304926
$455$	−4.29541	−0.201372
$456$	36.8389	1.72514
$457$	7.53993	0.352703	0.176352	−	0.984327i	$-0.443570\pi$
$457$	7.53993	0.352703	0.176352	+	0.984327i	$0.443570\pi$
$458$	6.78849	0.317206
$459$	−6.08460	−0.284005
$460$	1.44241	0.0672526
$461$	−17.1823	−0.800259	−0.400130	−	0.916459i	$-0.631035\pi$
$461$	−17.1823	−0.800259	−0.400130	+	0.916459i	$0.631035\pi$
$462$	5.46891	0.254437
$463$	15.2997	0.711039	0.355519	−	0.934669i	$-0.384304\pi$
$463$	15.2997	0.711039	0.355519	+	0.934669i	$0.384304\pi$
$464$	0.212679	0.00987338
$465$	15.7186	0.728934
$466$	3.73541	0.173040
$467$	−40.7408	−1.88526	−0.942629	−	0.333842i	$-0.891655\pi$
$467$	−40.7408	−1.88526	−0.942629	+	0.333842i	$0.891655\pi$
$468$	4.79470	0.221635
$469$	−3.34251	−0.154343
$470$	2.07113	0.0955342
$471$	30.4683	1.40391
$472$	−5.22951	−0.240708
$473$	−0.999338	−0.0459496
$474$	11.9160	0.547320
$475$	−6.34213	−0.290997
$476$	−23.6188	−1.08257
$477$	−28.4341	−1.30191
$478$	5.82229	0.266305
$479$	−20.2764	−0.926450	−0.463225	−	0.886241i	$-0.653308\pi$
$479$	−20.2764	−0.926450	−0.463225	+	0.886241i	$0.653308\pi$
$480$	−13.6418	−0.622660
$481$	−5.70216	−0.259996
$482$	15.2645	0.695277
$483$	7.42160	0.337694
$484$	−1.49353	−0.0678875
$485$	8.03629	0.364909
$486$	−14.4762	−0.656654
$487$	−2.43231	−0.110218	−0.0551092	−	0.998480i	$-0.517551\pi$
$487$	−2.43231	−0.110218	−0.0551092	+	0.998480i	$0.517551\pi$
$488$	12.8251	0.580566
$489$	41.7664	1.88874
$490$	2.71785	0.122780
$491$	34.6464	1.56357	0.781785	−	0.623548i	$-0.214309\pi$
$491$	34.6464	1.56357	0.781785	+	0.623548i	$0.214309\pi$
$492$	3.50688	0.158103
$493$	−0.839744	−0.0378202
$494$	−5.89421	−0.265193
$495$	2.45831	0.110493
$496$	8.19249	0.367854
$497$	−45.0933	−2.02271
$498$	19.4648	0.872240
$499$	2.16750	0.0970306	0.0485153	−	0.998822i	$-0.484551\pi$
$499$	2.16750	0.0970306	0.0485153	+	0.998822i	$0.484551\pi$
$500$	1.49353	0.0667925
$501$	33.9622	1.51732
$502$	−5.65425	−0.252362
$503$	7.13527	0.318146	0.159073	−	0.987267i	$-0.449150\pi$
$503$	7.13527	0.318146	0.159073	+	0.987267i	$0.449150\pi$
$504$	−20.1035	−0.895482
$505$	−9.86773	−0.439108
$506$	0.687312	0.0305547
$507$	26.3876	1.17192
$508$	−1.89445	−0.0840528
$509$	22.6889	1.00567	0.502835	−	0.864383i	$-0.332290\pi$
$509$	22.6889	1.00567	0.502835	+	0.864383i	$0.332290\pi$
$510$	7.99393	0.353977
$511$	3.28922	0.145507
$512$	−13.1649	−0.581812
$513$	−8.02629	−0.354370
$514$	15.8577	0.699453
$515$	10.9958	0.484532
$516$	3.48702	0.153507
$517$	−2.91024	−0.127992
$518$	10.2211	0.449091
$519$	−16.8385	−0.739127
$520$	3.24679	0.142381
$521$	−5.40909	−0.236976	−0.118488	−	0.992955i	$-0.537805\pi$
$521$	−5.40909	−0.236976	−0.118488	+	0.992955i	$0.537805\pi$
$522$	−0.305569	−0.0133744
$523$	15.4275	0.674599	0.337299	−	0.941397i	$-0.390487\pi$
$523$	15.4275	0.674599	0.337299	+	0.941397i	$0.390487\pi$
$524$	−32.1923	−1.40633
$525$	7.68461	0.335384
$526$	−16.4296	−0.716364
$527$	−32.3473	−1.40907
$528$	2.84485	0.123806
$529$	−22.0673	−0.959447
$530$	−8.23153	−0.357555
$531$	−5.17077	−0.224392
$532$	−31.1559	−1.35078
$533$	−1.31248	−0.0568496
$534$	11.9618	0.517638
$535$	−10.0224	−0.433305
$536$	2.52652	0.109129
$537$	−12.1764	−0.525450
$538$	9.24223	0.398461
$539$	−3.81897	−0.164495
$540$	1.89013	0.0813384
$541$	40.8364	1.75569	0.877847	−	0.478942i	$-0.158979\pi$
$541$	40.8364	1.75569	0.877847	+	0.478942i	$0.158979\pi$
$542$	−17.0636	−0.732946
$543$	13.2463	0.568453
$544$	28.0734	1.20364
$545$	−17.9108	−0.767212
$546$	7.14188	0.305644
$547$	2.71340	0.116017	0.0580083	−	0.998316i	$-0.481525\pi$
$547$	2.71340	0.116017	0.0580083	+	0.998316i	$0.481525\pi$
$548$	16.1169	0.688482
$549$	12.6811	0.541215
$550$	0.711670	0.0303457
$551$	−1.10772	−0.0471904
$552$	−5.60979	−0.238769
$553$	−23.5730	−1.00243
$554$	−15.3976	−0.654179
$555$	10.2013	0.433022
$556$	−14.5078	−0.615268
$557$	−22.9948	−0.974320	−0.487160	−	0.873313i	$-0.661967\pi$
$557$	−22.9948	−0.974320	−0.487160	+	0.873313i	$0.661967\pi$
$558$	−11.7707	−0.498292
$559$	−1.30504	−0.0551973
$560$	4.00519	0.169250
$561$	−11.2326	−0.474242
$562$	−19.6965	−0.830848
$563$	−5.29592	−0.223196	−0.111598	−	0.993753i	$-0.535597\pi$
$563$	−5.29592	−0.223196	−0.111598	+	0.993753i	$0.535597\pi$
$564$	10.1548	0.427594
$565$	−16.4074	−0.690264
$566$	2.53983	0.106757
$567$	33.9830	1.42715
$568$	34.0849	1.43017
$569$	−0.704689	−0.0295421	−0.0147711	−	0.999891i	$-0.504702\pi$
$569$	−0.704689	−0.0295421	−0.0147711	+	0.999891i	$0.504702\pi$
$570$	10.5449	0.441678
$571$	−3.67918	−0.153969	−0.0769845	−	0.997032i	$-0.524529\pi$
$571$	−3.67918	−0.153969	−0.0769845	+	0.997032i	$0.524529\pi$
$572$	−1.95040	−0.0815505
$573$	49.2491	2.05741
$574$	2.35262	0.0981963
$575$	0.965774	0.0402755
$576$	4.22862	0.176193
$577$	−3.88166	−0.161596	−0.0807978	−	0.996731i	$-0.525747\pi$
$577$	−3.88166	−0.161596	−0.0807978	+	0.996731i	$0.525747\pi$
$578$	−4.35228	−0.181031
$579$	27.7574	1.15356
$580$	0.260860	0.0108316
$581$	−38.5067	−1.59753
$582$	−13.3617	−0.553862
$583$	11.5665	0.479036
$584$	−2.48624	−0.102881
$585$	3.21032	0.132730
$586$	18.6535	0.770567
$587$	13.2163	0.545497	0.272749	−	0.962085i	$-0.412067\pi$
$587$	13.2163	0.545497	0.272749	+	0.962085i	$0.412067\pi$
$588$	13.3256	0.549540
$589$	−42.6698	−1.75818
$590$	−1.49692	−0.0616270
$591$	−1.71016	−0.0703467
$592$	5.31689	0.218523
$593$	−23.6109	−0.969584	−0.484792	−	0.874629i	$-0.661105\pi$
$593$	−23.6109	−0.969584	−0.484792	+	0.874629i	$0.661105\pi$
$594$	0.900655	0.0369543
$595$	−15.8141	−0.648316
$596$	26.6829	1.09297
$597$	−12.0444	−0.492946
$598$	0.897565	0.0367041
$599$	26.7203	1.09176	0.545880	−	0.837863i	$-0.316195\pi$
$599$	26.7203	1.09176	0.545880	+	0.837863i	$0.316195\pi$
$600$	−5.80860	−0.237135
$601$	16.3647	0.667532	0.333766	−	0.942656i	$-0.391680\pi$
$601$	16.3647	0.667532	0.333766	+	0.942656i	$0.391680\pi$
$602$	2.33929	0.0953423
$603$	2.49814	0.101732
$604$	25.2105	1.02580
$605$	−1.00000	−0.0406558
$606$	16.4068	0.666482
$607$	−6.84434	−0.277803	−0.138902	−	0.990306i	$-0.544357\pi$
$607$	−6.84434	−0.277803	−0.138902	+	0.990306i	$0.544357\pi$
$608$	37.0320	1.50185
$609$	1.34220	0.0543886
$610$	3.67111	0.148639
$611$	−3.80050	−0.153752
$612$	17.6523	0.713553
$613$	−3.87975	−0.156701	−0.0783507	−	0.996926i	$-0.524965\pi$
$613$	−3.87975	−0.156701	−0.0783507	+	0.996926i	$0.524965\pi$
$614$	9.72281	0.392381
$615$	2.34806	0.0946828
$616$	8.17778	0.329492
$617$	25.8381	1.04020	0.520102	−	0.854104i	$-0.325894\pi$
$617$	25.8381	1.04020	0.520102	+	0.854104i	$0.325894\pi$
$618$	−18.2824	−0.735427
$619$	4.38536	0.176262	0.0881312	−	0.996109i	$-0.471911\pi$
$619$	4.38536	0.176262	0.0881312	+	0.996109i	$0.471911\pi$
$620$	10.0484	0.403555
$621$	1.22224	0.0490466
$622$	7.48890	0.300278
$623$	−23.6637	−0.948064
$624$	3.71511	0.148723
$625$	1.00000	0.0400000
$626$	2.48507	0.0993234
$627$	−14.8171	−0.591739
$628$	19.4775	0.777235
$629$	−20.9933	−0.837056
$630$	−5.75451	−0.229265
$631$	−36.1060	−1.43736	−0.718679	−	0.695342i	$-0.755253\pi$
$631$	−36.1060	−1.43736	−0.718679	+	0.695342i	$0.755253\pi$
$632$	17.8183	0.708772
$633$	−43.5864	−1.73240
$634$	14.3941	0.571664
$635$	−1.26844	−0.0503366
$636$	−40.3593	−1.60035
$637$	−4.98721	−0.197601
$638$	0.124300	0.00492110
$639$	33.7020	1.33323
$640$	−10.4539	−0.413228
$641$	30.1634	1.19138	0.595691	−	0.803213i	$-0.296878\pi$
$641$	30.1634	1.19138	0.595691	+	0.803213i	$0.296878\pi$
$642$	16.6640	0.657674
$643$	−13.4900	−0.531994	−0.265997	−	0.963974i	$-0.585701\pi$
$643$	−13.4900	−0.531994	−0.265997	+	0.963974i	$0.585701\pi$
$644$	4.74440	0.186955
$645$	2.33475	0.0919309
$646$	−21.7003	−0.853788
$647$	1.63775	0.0643864	0.0321932	−	0.999482i	$-0.489751\pi$
$647$	1.63775	0.0643864	0.0321932	+	0.999482i	$0.489751\pi$
$648$	−25.6869	−1.00908
$649$	2.10338	0.0825651
$650$	0.929374	0.0364530
$651$	51.7020	2.02636
$652$	26.7000	1.04565
$653$	1.82152	0.0712814	0.0356407	−	0.999365i	$-0.488653\pi$
$653$	1.82152	0.0712814	0.0356407	+	0.999365i	$0.488653\pi$
$654$	29.7798	1.16448
$655$	−21.5546	−0.842207
$656$	1.22380	0.0477813
$657$	−2.45831	−0.0959078
$658$	6.81241	0.265575
$659$	28.3099	1.10280	0.551398	−	0.834243i	$-0.314095\pi$
$659$	28.3099	1.10280	0.551398	+	0.834243i	$0.314095\pi$
$660$	3.48933	0.135822
$661$	37.4055	1.45490	0.727452	−	0.686159i	$-0.240704\pi$
$661$	37.4055	1.45490	0.727452	+	0.686159i	$0.240704\pi$
$662$	−19.9680	−0.776077
$663$	−14.6688	−0.569688
$664$	29.1062	1.12954
$665$	−20.8607	−0.808942
$666$	−7.63911	−0.296010
$667$	0.168682	0.00653141
$668$	21.7110	0.840023
$669$	5.13978	0.198715
$670$	0.723201	0.0279397
$671$	−5.15845	−0.199140
$672$	−44.8709	−1.73093
$673$	42.0687	1.62163	0.810815	−	0.585302i	$-0.199024\pi$
$673$	42.0687	1.62163	0.810815	+	0.585302i	$0.199024\pi$
$674$	−8.31484	−0.320276
$675$	1.26555	0.0487111
$676$	16.8688	0.648800
$677$	−40.5543	−1.55863	−0.779313	−	0.626635i	$-0.784432\pi$
$677$	−40.5543	−1.55863	−0.779313	+	0.626635i	$0.784432\pi$
$678$	27.2802	1.04769
$679$	26.4331	1.01441
$680$	11.9535	0.458396
$681$	21.3292	0.817335
$682$	4.78811	0.183346
$683$	2.71143	0.103750	0.0518750	−	0.998654i	$-0.483480\pi$
$683$	2.71143	0.103750	0.0518750	+	0.998654i	$0.483480\pi$
$684$	23.2855	0.890342
$685$	10.7912	0.412311
$686$	−7.44628	−0.284300
$687$	22.2856	0.850248
$688$	1.21687	0.0463926
$689$	15.1048	0.575446
$690$	−1.60577	−0.0611306
$691$	21.3059	0.810515	0.405258	−	0.914202i	$-0.367182\pi$
$691$	21.3059	0.810515	0.405258	+	0.914202i	$0.367182\pi$
$692$	−10.7643	−0.409198
$693$	8.08592	0.307159
$694$	−4.61216	−0.175075
$695$	−9.71380	−0.368465
$696$	−1.01453	−0.0384558
$697$	−4.83206	−0.183027
$698$	−17.7893	−0.673334
$699$	12.2628	0.463821
$700$	4.91254	0.185676
$701$	−21.9313	−0.828333	−0.414166	−	0.910201i	$-0.635927\pi$
$701$	−21.9313	−0.828333	−0.414166	+	0.910201i	$0.635927\pi$
$702$	1.17617	0.0443917
$703$	−27.6925	−1.04444
$704$	−1.72013	−0.0648300
$705$	6.79921	0.256073
$706$	9.48811	0.357090
$707$	−32.4571	−1.22068
$708$	−7.33940	−0.275832
$709$	11.9095	0.447270	0.223635	−	0.974673i	$-0.428208\pi$
$709$	11.9095	0.447270	0.223635	+	0.974673i	$0.428208\pi$
$710$	9.75659	0.366158
$711$	17.6181	0.660731
$712$	17.8867	0.670334
$713$	6.49772	0.243341
$714$	26.2938	0.984020
$715$	−1.30591	−0.0488381
$716$	−7.78399	−0.290901
$717$	19.1137	0.713814
$718$	21.2902	0.794543
$719$	5.91488	0.220588	0.110294	−	0.993899i	$-0.464821\pi$
$719$	5.91488	0.220588	0.110294	+	0.993899i	$0.464821\pi$
$720$	−2.99342	−0.111558
$721$	36.1676	1.34695
$722$	−15.1035	−0.562094
$723$	50.1109	1.86364
$724$	8.46795	0.314709
$725$	0.174660	0.00648672
$726$	1.66268	0.0617077
$727$	32.0858	1.19000	0.594999	−	0.803727i	$-0.297153\pi$
$727$	32.0858	1.19000	0.594999	+	0.803727i	$0.297153\pi$
$728$	10.6794	0.395805
$729$	−16.5282	−0.612157
$730$	−0.711670	−0.0263401
$731$	−4.80468	−0.177708
$732$	17.9995	0.665282
$733$	14.1458	0.522488	0.261244	−	0.965273i	$-0.415867\pi$
$733$	14.1458	0.522488	0.261244	+	0.965273i	$0.415867\pi$
$734$	−11.1741	−0.412445
$735$	8.92227	0.329103
$736$	−5.63920	−0.207864
$737$	−1.01620	−0.0374323
$738$	−1.75831	−0.0647242
$739$	−0.210118	−0.00772932	−0.00386466	−	0.999993i	$-0.501230\pi$
$739$	−0.210118	−0.00772932	−0.00386466	+	0.999993i	$0.501230\pi$
$740$	6.52139	0.239731
$741$	−19.3498	−0.710832
$742$	−27.0753	−0.993966
$743$	−21.8580	−0.801894	−0.400947	−	0.916101i	$-0.631319\pi$
$743$	−21.8580	−0.801894	−0.400947	+	0.916101i	$0.631319\pi$
$744$	−39.0802	−1.43275
$745$	17.8657	0.654549
$746$	−25.2067	−0.922883
$747$	28.7793	1.05298
$748$	−7.18068	−0.262551
$749$	−32.9658	−1.20454
$750$	−1.66268	−0.0607123
$751$	−32.2972	−1.17854	−0.589271	−	0.807936i	$-0.700585\pi$
$751$	−32.2972	−1.17854	−0.589271	+	0.807936i	$0.700585\pi$
$752$	3.54372	0.129226
$753$	−18.5620	−0.676439
$754$	0.162325	0.00591152
$755$	16.8798	0.614320
$756$	6.21707	0.226113
$757$	−19.9825	−0.726278	−0.363139	−	0.931735i	$-0.618295\pi$
$757$	−19.9825	−0.726278	−0.363139	+	0.931735i	$0.618295\pi$
$758$	−3.12916	−0.113656
$759$	2.25634	0.0818999
$760$	15.7680	0.571967
$761$	17.4684	0.633228	0.316614	−	0.948554i	$-0.397454\pi$
$761$	17.4684	0.633228	0.316614	+	0.948554i	$0.397454\pi$
$762$	2.10901	0.0764014
$763$	−58.9124	−2.13277
$764$	31.4834	1.13903
$765$	11.8192	0.427325
$766$	−10.7260	−0.387545
$767$	2.74682	0.0991820
$768$	25.4190	0.917230
$769$	−1.55156	−0.0559508	−0.0279754	−	0.999609i	$-0.508906\pi$
$769$	−1.55156	−0.0559508	−0.0279754	+	0.999609i	$0.508906\pi$
$770$	2.34084	0.0843580
$771$	52.0584	1.87484
$772$	17.7444	0.638636
$773$	−10.3330	−0.371653	−0.185827	−	0.982583i	$-0.559496\pi$
$773$	−10.3330	−0.371653	−0.185827	+	0.982583i	$0.559496\pi$
$774$	−1.74835	−0.0628430
$775$	6.72799	0.241677
$776$	−19.9801	−0.717244
$777$	33.5544	1.20376
$778$	17.1133	0.613543
$779$	−6.37404	−0.228374
$780$	4.55673	0.163157
$781$	−13.7094	−0.490562
$782$	3.30450	0.118169
$783$	0.221042	0.00789938
$784$	4.65025	0.166080
$785$	13.0413	0.465463
$786$	35.8383	1.27831
$787$	41.6827	1.48583	0.742915	−	0.669386i	$-0.233443\pi$
$787$	41.6827	1.48583	0.742915	+	0.669386i	$0.233443\pi$
$788$	−1.09325	−0.0389456
$789$	−53.9358	−1.92016
$790$	5.10037	0.181463
$791$	−53.9675	−1.91886
$792$	−6.11194	−0.217178
$793$	−6.73645	−0.239218
$794$	5.26482	0.186841
$795$	−27.0229	−0.958402
$796$	−7.69963	−0.272906
$797$	22.5883	0.800117	0.400059	−	0.916490i	$-0.368990\pi$
$797$	22.5883	0.800117	0.400059	+	0.916490i	$0.368990\pi$
$798$	34.6845	1.22782
$799$	−13.9921	−0.495003
$800$	−5.83905	−0.206442
$801$	17.6858	0.624898
$802$	1.73458	0.0612501
$803$	1.00000	0.0352892
$804$	3.54586	0.125053
$805$	3.17664	0.111962
$806$	6.25282	0.220246
$807$	30.3408	1.06805
$808$	24.5335	0.863086
$809$	16.9304	0.595242	0.297621	−	0.954684i	$-0.403807\pi$
$809$	16.9304	0.595242	0.297621	+	0.954684i	$0.403807\pi$
$810$	−7.35272	−0.258348
$811$	−44.6820	−1.56900	−0.784498	−	0.620131i	$-0.787080\pi$
$811$	−44.6820	−1.56900	−0.784498	+	0.620131i	$0.787080\pi$
$812$	0.858025	0.0301108
$813$	−56.0173	−1.96461
$814$	3.10746	0.108917
$815$	17.8771	0.626209
$816$	13.6777	0.478814
$817$	−6.33793	−0.221736
$818$	−22.9731	−0.803234
$819$	10.5595	0.368977
$820$	1.50104	0.0524186
$821$	6.93411	0.242002	0.121001	−	0.992652i	$-0.461390\pi$
$821$	6.93411	0.242002	0.121001	+	0.992652i	$0.461390\pi$
$822$	−17.9423	−0.625809
$823$	−53.4828	−1.86429	−0.932147	−	0.362081i	$-0.882066\pi$
$823$	−53.4828	−1.86429	−0.932147	+	0.362081i	$0.882066\pi$
$824$	−27.3381	−0.952369
$825$	2.33630	0.0813396
$826$	−4.92368	−0.171317
$827$	12.2424	0.425709	0.212854	−	0.977084i	$-0.431724\pi$
$827$	12.2424	0.425709	0.212854	+	0.977084i	$0.431724\pi$
$828$	−3.54589	−0.123228
$829$	6.36119	0.220933	0.110467	−	0.993880i	$-0.464765\pi$
$829$	6.36119	0.220933	0.110467	+	0.993880i	$0.464765\pi$
$830$	8.33147	0.289189
$831$	−50.5478	−1.75348
$832$	−2.24633	−0.0778776
$833$	−18.3611	−0.636174
$834$	16.1509	0.559260
$835$	14.5367	0.503064
$836$	−9.47214	−0.327601
$837$	8.51462	0.294308
$838$	3.81786	0.131886
$839$	−27.9174	−0.963816	−0.481908	−	0.876222i	$-0.660056\pi$
$839$	−27.9174	−0.963816	−0.481908	+	0.876222i	$0.660056\pi$
$840$	−19.1058	−0.659212
$841$	−28.9695	−0.998948
$842$	24.3293	0.838444
$843$	−64.6607	−2.22703
$844$	−27.8634	−0.959099
$845$	11.2946	0.388546
$846$	−5.09148	−0.175049
$847$	−3.28922	−0.113019
$848$	−14.0842	−0.483654
$849$	8.33787	0.286155
$850$	3.42161	0.117360
$851$	4.21699	0.144557
$852$	47.8367	1.63886
$853$	−6.12545	−0.209731	−0.104866	−	0.994486i	$-0.533441\pi$
$853$	−6.12545	−0.209731	−0.104866	+	0.994486i	$0.533441\pi$
$854$	12.0751	0.413201
$855$	15.5909	0.533198
$856$	24.9180	0.851680
$857$	16.4327	0.561329	0.280665	−	0.959806i	$-0.409445\pi$
$857$	16.4327	0.561329	0.280665	+	0.959806i	$0.409445\pi$
$858$	2.17130	0.0741269
$859$	30.5752	1.04321	0.521607	−	0.853186i	$-0.325333\pi$
$859$	30.5752	1.04321	0.521607	+	0.853186i	$0.325333\pi$
$860$	1.49254	0.0508951
$861$	7.72328	0.263209
$862$	−24.2970	−0.827560
$863$	58.5378	1.99265	0.996325	−	0.0856555i	$-0.0272985\pi$
$863$	58.5378	1.99265	0.996325	+	0.0856555i	$0.0272985\pi$
$864$	−7.38962	−0.251400
$865$	−7.20731	−0.245056
$866$	12.1544	0.413025
$867$	−14.2879	−0.485242
$868$	33.0515	1.12184
$869$	−7.16676	−0.243116
$870$	−0.290404	−0.00984560
$871$	−1.32706	−0.0449659
$872$	44.5304	1.50799
$873$	−19.7557	−0.668629
$874$	4.35902	0.147446
$875$	3.28922	0.111196
$876$	−3.48933	−0.117893
$877$	46.1343	1.55784	0.778922	−	0.627121i	$-0.215767\pi$
$877$	46.1343	1.55784	0.778922	+	0.627121i	$0.215767\pi$
$878$	20.1239	0.679148
$879$	61.2364	2.06545
$880$	1.21767	0.0410477
$881$	−43.0611	−1.45076	−0.725382	−	0.688347i	$-0.758337\pi$
$881$	−43.0611	−1.45076	−0.725382	+	0.688347i	$0.758337\pi$
$882$	−6.68131	−0.224971
$883$	39.8997	1.34273	0.671366	−	0.741126i	$-0.265708\pi$
$883$	39.8997	1.34273	0.671366	+	0.741126i	$0.265708\pi$
$884$	−9.37729	−0.315392
$885$	−4.91414	−0.165187
$886$	−4.98027	−0.167315
$887$	−8.59411	−0.288562	−0.144281	−	0.989537i	$-0.546087\pi$
$887$	−8.59411	−0.288562	−0.144281	+	0.989537i	$0.546087\pi$
$888$	−25.3629	−0.851124
$889$	−4.17219	−0.139931
$890$	5.11997	0.171622
$891$	10.3316	0.346123
$892$	3.28570	0.110013
$893$	−18.4571	−0.617645
$894$	−29.7049	−0.993480
$895$	−5.21182	−0.174212
$896$	−34.3853	−1.14873
$897$	2.94657	0.0983830
$898$	−10.7416	−0.358451
$899$	1.17511	0.0391922
$900$	−3.67155	−0.122385
$901$	55.6102	1.85265
$902$	0.715250	0.0238152
$903$	7.67952	0.255559
$904$	40.7927	1.35674
$905$	5.66977	0.188470
$906$	−28.0657	−0.932420
$907$	−12.7751	−0.424191	−0.212095	−	0.977249i	$-0.568029\pi$
$907$	−12.7751	−0.424191	−0.212095	+	0.977249i	$0.568029\pi$
$908$	13.6351	0.452496
$909$	24.2579	0.804585
$910$	3.05691	0.101336
$911$	−36.7775	−1.21849	−0.609247	−	0.792981i	$-0.708528\pi$
$911$	−36.7775	−1.21849	−0.609247	+	0.792981i	$0.708528\pi$
$912$	18.0424	0.597444
$913$	−11.7069	−0.387443
$914$	−5.36594	−0.177490
$915$	12.0517	0.398417
$916$	14.2465	0.470717
$917$	−70.8978	−2.34125
$918$	4.33023	0.142919
$919$	14.2007	0.468439	0.234219	−	0.972184i	$-0.424747\pi$
$919$	14.2007	0.468439	0.234219	+	0.972184i	$0.424747\pi$
$920$	−2.40114	−0.0791633
$921$	31.9185	1.05175
$922$	12.2281	0.402712
$923$	−17.9032	−0.589292
$924$	11.4772	0.377571
$925$	4.36644	0.143568
$926$	−10.8884	−0.357814
$927$	−27.0311	−0.887816
$928$	−1.01985	−0.0334783
$929$	3.81753	0.125249	0.0626245	−	0.998037i	$-0.480053\pi$
$929$	3.81753	0.125249	0.0626245	+	0.998037i	$0.480053\pi$
$930$	−11.1865	−0.366819
$931$	−24.2204	−0.793792
$932$	7.83922	0.256782
$933$	24.5849	0.804874
$934$	28.9940	0.948712
$935$	−4.80787	−0.157234
$936$	−7.98162	−0.260887
$937$	−42.2231	−1.37937	−0.689684	−	0.724110i	$-0.742251\pi$
$937$	−42.2231	−1.37937	−0.689684	+	0.724110i	$0.742251\pi$
$938$	2.37877	0.0776695
$939$	8.15811	0.266230
$940$	4.34652	0.141768
$941$	−23.6860	−0.772143	−0.386071	−	0.922469i	$-0.626168\pi$
$941$	−23.6860	−0.772143	−0.386071	+	0.922469i	$0.626168\pi$
$942$	−21.6834	−0.706483
$943$	0.970632	0.0316081
$944$	−2.56123	−0.0833610
$945$	4.16268	0.135412
$946$	0.711198	0.0231231
$947$	−10.5138	−0.341651	−0.170826	−	0.985301i	$-0.554643\pi$
$947$	−10.5138	−0.341651	−0.170826	+	0.985301i	$0.554643\pi$
$948$	25.0072	0.812195
$949$	1.30591	0.0423915
$950$	4.51350	0.146437
$951$	47.2537	1.53231
$952$	39.3177	1.27429
$953$	1.70238	0.0551455	0.0275728	−	0.999620i	$-0.491222\pi$
$953$	1.70238	0.0551455	0.0275728	+	0.999620i	$0.491222\pi$
$954$	20.2357	0.655154
$955$	21.0799	0.682130
$956$	12.2188	0.395184
$957$	0.408059	0.0131907
$958$	14.4301	0.466214
$959$	35.4947	1.14618
$960$	4.01876	0.129705
$961$	14.2659	0.460190
$962$	4.05806	0.130837
$963$	24.6381	0.793952
$964$	32.0343	1.03176
$965$	11.8809	0.382460
$966$	−5.28173	−0.169937
$967$	−14.3467	−0.461360	−0.230680	−	0.973030i	$-0.574095\pi$
$967$	−14.3467	−0.461360	−0.230680	+	0.973030i	$0.574095\pi$
$968$	2.48624	0.0799107
$969$	−71.2388	−2.28852
$970$	−5.71918	−0.183632
$971$	−17.6688	−0.567018	−0.283509	−	0.958970i	$-0.591499\pi$
$971$	−17.6688	−0.567018	−0.283509	+	0.958970i	$0.591499\pi$
$972$	−30.3801	−0.974442
$973$	−31.9508	−1.02430
$974$	1.73100	0.0554648
$975$	3.05099	0.0977099
$976$	6.28130	0.201060
$977$	5.26555	0.168460	0.0842300	−	0.996446i	$-0.473157\pi$
$977$	5.26555	0.168460	0.0842300	+	0.996446i	$0.473157\pi$
$978$	−29.7239	−0.950465
$979$	−7.19431	−0.229931
$980$	5.70373	0.182199
$981$	44.0302	1.40578
$982$	−24.6568	−0.786830
$983$	−25.5534	−0.815028	−0.407514	−	0.913199i	$-0.633604\pi$
$983$	−25.5534	−0.815028	−0.407514	+	0.913199i	$0.633604\pi$
$984$	−5.83783	−0.186103
$985$	−0.731995	−0.0233233
$986$	0.597620	0.0190321
$987$	22.3641	0.711857
$988$	−12.3697	−0.393533
$989$	0.965134	0.0306895
$990$	−1.74951	−0.0556029
$991$	−23.8776	−0.758496	−0.379248	−	0.925295i	$-0.623817\pi$
$991$	−23.8776	−0.758496	−0.379248	+	0.925295i	$0.623817\pi$
$992$	−39.2851	−1.24730
$993$	−65.5517	−2.08022
$994$	32.0916	1.01788
$995$	−5.15534	−0.163435
$996$	40.8493	1.29436
$997$	−38.3852	−1.21567	−0.607835	−	0.794063i	$-0.707962\pi$
$997$	−38.3852	−1.21567	−0.607835	+	0.794063i	$0.707962\pi$
$998$	−1.54254	−0.0488284
$999$	5.52596	0.174833

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4015.2.a.g.1.15	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4015.2.a.g.1.15	✓	32	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:	\( N \)	\(=\)	\( 4015 = 5 \cdot 11 \cdot 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4015.a (trivial)

\(f(q)\)	\(=\)	\(q-0.711670 q^{2} -2.33630 q^{3} -1.49353 q^{4} -1.00000 q^{5} +1.66268 q^{6} -3.28922 q^{7} +2.48624 q^{8} +2.45831 q^{9} +O(q^{10})\)	\(q-0.711670 q^{2} -2.33630 q^{3} -1.49353 q^{4} -1.00000 q^{5} +1.66268 q^{6} -3.28922 q^{7} +2.48624 q^{8} +2.45831 q^{9} +0.711670 q^{10} -1.00000 q^{11} +3.48933 q^{12} -1.30591 q^{13} +2.34084 q^{14} +2.33630 q^{15} +1.21767 q^{16} -4.80787 q^{17} -1.74951 q^{18} -6.34213 q^{19} +1.49353 q^{20} +7.68461 q^{21} +0.711670 q^{22} +0.965774 q^{23} -5.80860 q^{24} +1.00000 q^{25} +0.929374 q^{26} +1.26555 q^{27} +4.91254 q^{28} +0.174660 q^{29} -1.66268 q^{30} +6.72799 q^{31} -5.83905 q^{32} +2.33630 q^{33} +3.42161 q^{34} +3.28922 q^{35} -3.67155 q^{36} +4.36644 q^{37} +4.51350 q^{38} +3.05099 q^{39} -2.48624 q^{40} +1.00503 q^{41} -5.46891 q^{42} +0.999338 q^{43} +1.49353 q^{44} -2.45831 q^{45} -0.687312 q^{46} +2.91024 q^{47} -2.84485 q^{48} +3.81897 q^{49} -0.711670 q^{50} +11.2326 q^{51} +1.95040 q^{52} -11.5665 q^{53} -0.900655 q^{54} +1.00000 q^{55} -8.17778 q^{56} +14.8171 q^{57} -0.124300 q^{58} -2.10338 q^{59} -3.48933 q^{60} +5.15845 q^{61} -4.78811 q^{62} -8.08592 q^{63} +1.72013 q^{64} +1.30591 q^{65} -1.66268 q^{66} +1.01620 q^{67} +7.18068 q^{68} -2.25634 q^{69} -2.34084 q^{70} +13.7094 q^{71} +6.11194 q^{72} -1.00000 q^{73} -3.10746 q^{74} -2.33630 q^{75} +9.47214 q^{76} +3.28922 q^{77} -2.17130 q^{78} +7.16676 q^{79} -1.21767 q^{80} -10.3316 q^{81} -0.715250 q^{82} +11.7069 q^{83} -11.4772 q^{84} +4.80787 q^{85} -0.711198 q^{86} -0.408059 q^{87} -2.48624 q^{88} +7.19431 q^{89} +1.74951 q^{90} +4.29541 q^{91} -1.44241 q^{92} -15.7186 q^{93} -2.07113 q^{94} +6.34213 q^{95} +13.6418 q^{96} -8.03629 q^{97} -2.71785 q^{98} -2.45831 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 5 q^{2} - 7 q^{3} + 37 q^{4} - 32 q^{5} - 3 q^{6} - 18 q^{8} + 29 q^{9}+O(q^{10}) \) 32 * q - 5 * q^2 - 7 * q^3 + 37 * q^4 - 32 * q^5 - 3 * q^6 - 18 * q^8 + 29 * q^9	\( 32 q - 5 q^{2} - 7 q^{3} + 37 q^{4} - 32 q^{5} - 3 q^{6} - 18 q^{8} + 29 q^{9} + 5 q^{10} - 32 q^{11} - 24 q^{12} - q^{13} - 5 q^{14} + 7 q^{15} + 47 q^{16} - 30 q^{17} - 11 q^{18} + 16 q^{19} - 37 q^{20} + q^{21} + 5 q^{22} - 26 q^{23} - 21 q^{24} + 32 q^{25} - q^{26} - 31 q^{27} - 24 q^{28} - 10 q^{29} + 3 q^{30} - 2 q^{31} - 31 q^{32} + 7 q^{33} - 14 q^{34} + 38 q^{36} - 28 q^{37} - 63 q^{38} - 2 q^{39} + 18 q^{40} - 62 q^{41} - 9 q^{42} + 8 q^{43} - 37 q^{44} - 29 q^{45} + 19 q^{46} - 21 q^{47} - 79 q^{48} + 34 q^{49} - 5 q^{50} + 17 q^{51} + 15 q^{52} - 32 q^{53} + 5 q^{54} + 32 q^{55} - 52 q^{56} - 57 q^{57} + 4 q^{58} - 37 q^{59} + 24 q^{60} + 15 q^{61} - 22 q^{62} + 5 q^{63} + 70 q^{64} + q^{65} + 3 q^{66} - 42 q^{67} - 81 q^{68} - 8 q^{69} + 5 q^{70} - 40 q^{71} - 27 q^{72} - 32 q^{73} - 17 q^{74} - 7 q^{75} + 21 q^{76} - 105 q^{78} + 18 q^{79} - 47 q^{80} + 12 q^{81} - 70 q^{82} - 26 q^{83} + 22 q^{84} + 30 q^{85} - 45 q^{86} - 18 q^{87} + 18 q^{88} - 83 q^{89} + 11 q^{90} - 18 q^{91} - 73 q^{92} - 68 q^{93} + 56 q^{94} - 16 q^{95} - 35 q^{96} - 99 q^{97} - 61 q^{98} - 29 q^{99}+O(q^{100}) \) 32 * q - 5 * q^2 - 7 * q^3 + 37 * q^4 - 32 * q^5 - 3 * q^6 - 18 * q^8 + 29 * q^9 + 5 * q^10 - 32 * q^11 - 24 * q^12 - q^13 - 5 * q^14 + 7 * q^15 + 47 * q^16 - 30 * q^17 - 11 * q^18 + 16 * q^19 - 37 * q^20 + q^21 + 5 * q^22 - 26 * q^23 - 21 * q^24 + 32 * q^25 - q^26 - 31 * q^27 - 24 * q^28 - 10 * q^29 + 3 * q^30 - 2 * q^31 - 31 * q^32 + 7 * q^33 - 14 * q^34 + 38 * q^36 - 28 * q^37 - 63 * q^38 - 2 * q^39 + 18 * q^40 - 62 * q^41 - 9 * q^42 + 8 * q^43 - 37 * q^44 - 29 * q^45 + 19 * q^46 - 21 * q^47 - 79 * q^48 + 34 * q^49 - 5 * q^50 + 17 * q^51 + 15 * q^52 - 32 * q^53 + 5 * q^54 + 32 * q^55 - 52 * q^56 - 57 * q^57 + 4 * q^58 - 37 * q^59 + 24 * q^60 + 15 * q^61 - 22 * q^62 + 5 * q^63 + 70 * q^64 + q^65 + 3 * q^66 - 42 * q^67 - 81 * q^68 - 8 * q^69 + 5 * q^70 - 40 * q^71 - 27 * q^72 - 32 * q^73 - 17 * q^74 - 7 * q^75 + 21 * q^76 - 105 * q^78 + 18 * q^79 - 47 * q^80 + 12 * q^81 - 70 * q^82 - 26 * q^83 + 22 * q^84 + 30 * q^85 - 45 * q^86 - 18 * q^87 + 18 * q^88 - 83 * q^89 + 11 * q^90 - 18 * q^91 - 73 * q^92 - 68 * q^93 + 56 * q^94 - 16 * q^95 - 35 * q^96 - 99 * q^97 - 61 * q^98 - 29 * q^99

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