LMFDB - Embedded newform 4015.2.a.c.1.6

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:	$23$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
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)

$f(q)$	$=$	$q-1.63550 q^{2} +2.32797 q^{3} +0.674867 q^{4} +1.00000 q^{5} -3.80740 q^{6} -0.601850 q^{7} +2.16726 q^{8} +2.41945 q^{9} +O(q^{10})$	\(q-1.63550 q^{2} +2.32797 q^{3} +0.674867 q^{4} +1.00000 q^{5} -3.80740 q^{6} -0.601850 q^{7} +2.16726 q^{8} +2.41945 q^{9} -1.63550 q^{10} -1.00000 q^{11} +1.57107 q^{12} -3.12789 q^{13} +0.984326 q^{14} +2.32797 q^{15} -4.89429 q^{16} +4.94659 q^{17} -3.95701 q^{18} -6.49476 q^{19} +0.674867 q^{20} -1.40109 q^{21} +1.63550 q^{22} -2.90532 q^{23} +5.04531 q^{24} +1.00000 q^{25} +5.11568 q^{26} -1.35151 q^{27} -0.406169 q^{28} +3.92545 q^{29} -3.80740 q^{30} +0.264921 q^{31} +3.67010 q^{32} -2.32797 q^{33} -8.09016 q^{34} -0.601850 q^{35} +1.63281 q^{36} -7.71523 q^{37} +10.6222 q^{38} -7.28164 q^{39} +2.16726 q^{40} +0.925656 q^{41} +2.29148 q^{42} +1.12395 q^{43} -0.674867 q^{44} +2.41945 q^{45} +4.75165 q^{46} -0.578904 q^{47} -11.3938 q^{48} -6.63778 q^{49} -1.63550 q^{50} +11.5155 q^{51} -2.11091 q^{52} -5.06645 q^{53} +2.21040 q^{54} -1.00000 q^{55} -1.30436 q^{56} -15.1196 q^{57} -6.42008 q^{58} +0.0753517 q^{59} +1.57107 q^{60} +5.94570 q^{61} -0.433279 q^{62} -1.45614 q^{63} +3.78611 q^{64} -3.12789 q^{65} +3.80740 q^{66} -12.1340 q^{67} +3.33829 q^{68} -6.76349 q^{69} +0.984326 q^{70} +4.66312 q^{71} +5.24356 q^{72} +1.00000 q^{73} +12.6183 q^{74} +2.32797 q^{75} -4.38310 q^{76} +0.601850 q^{77} +11.9091 q^{78} -10.3046 q^{79} -4.89429 q^{80} -10.4046 q^{81} -1.51391 q^{82} -6.24520 q^{83} -0.945549 q^{84} +4.94659 q^{85} -1.83822 q^{86} +9.13832 q^{87} -2.16726 q^{88} -12.4339 q^{89} -3.95701 q^{90} +1.88252 q^{91} -1.96070 q^{92} +0.616729 q^{93} +0.946799 q^{94} -6.49476 q^{95} +8.54390 q^{96} -15.8286 q^{97} +10.8561 q^{98} -2.41945 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 23 q - 3 q^{2} - 5 q^{3} + 15 q^{4} + 23 q^{5} - 5 q^{6} - 6 q^{8} + 8 q^{9}+O(q^{10}) $ 23 * q - 3 * q^2 - 5 * q^3 + 15 * q^4 + 23 * q^5 - 5 * q^6 - 6 * q^8 + 8 * q^9	\( 23 q - 3 q^{2} - 5 q^{3} + 15 q^{4} + 23 q^{5} - 5 q^{6} - 6 q^{8} + 8 q^{9} - 3 q^{10} - 23 q^{11} - 18 q^{12} - 5 q^{13} - 17 q^{14} - 5 q^{15} - q^{16} - 36 q^{17} + q^{18} + 6 q^{19} + 15 q^{20} - 18 q^{21} + 3 q^{22} - 14 q^{23} - 7 q^{24} + 23 q^{25} - 21 q^{26} - 29 q^{27} + 28 q^{28} - 36 q^{29} - 5 q^{30} - 16 q^{31} - 5 q^{32} + 5 q^{33} - 28 q^{34} - 14 q^{36} - 24 q^{37} + q^{38} - 10 q^{39} - 6 q^{40} - 36 q^{41} - 5 q^{42} + 17 q^{43} - 15 q^{44} + 8 q^{45} - 25 q^{46} - 21 q^{47} - 17 q^{48} - 27 q^{49} - 3 q^{50} + 19 q^{51} - 21 q^{52} - 28 q^{53} - 15 q^{54} - 23 q^{55} - 46 q^{56} - 23 q^{57} - 16 q^{58} - 61 q^{59} - 18 q^{60} - 17 q^{61} - 22 q^{62} - 9 q^{63} - 18 q^{64} - 5 q^{65} + 5 q^{66} + 2 q^{67} - 39 q^{68} - 36 q^{69} - 17 q^{70} - 50 q^{71} + 15 q^{72} + 23 q^{73} + 17 q^{74} - 5 q^{75} - 21 q^{76} + 49 q^{78} - 18 q^{79} - q^{80} - 57 q^{81} + 14 q^{82} - 20 q^{83} - 38 q^{84} - 36 q^{85} - 45 q^{86} + 37 q^{87} + 6 q^{88} - 93 q^{89} + q^{90} - 42 q^{91} - 39 q^{92} - 18 q^{93} - 6 q^{94} + 6 q^{95} - 9 q^{96} - 31 q^{97} - 31 q^{98} - 8 q^{99}+O(q^{100}) \) 23 * q - 3 * q^2 - 5 * q^3 + 15 * q^4 + 23 * q^5 - 5 * q^6 - 6 * q^8 + 8 * q^9 - 3 * q^10 - 23 * q^11 - 18 * q^12 - 5 * q^13 - 17 * q^14 - 5 * q^15 - q^16 - 36 * q^17 + q^18 + 6 * q^19 + 15 * q^20 - 18 * q^21 + 3 * q^22 - 14 * q^23 - 7 * q^24 + 23 * q^25 - 21 * q^26 - 29 * q^27 + 28 * q^28 - 36 * q^29 - 5 * q^30 - 16 * q^31 - 5 * q^32 + 5 * q^33 - 28 * q^34 - 14 * q^36 - 24 * q^37 + q^38 - 10 * q^39 - 6 * q^40 - 36 * q^41 - 5 * q^42 + 17 * q^43 - 15 * q^44 + 8 * q^45 - 25 * q^46 - 21 * q^47 - 17 * q^48 - 27 * q^49 - 3 * q^50 + 19 * q^51 - 21 * q^52 - 28 * q^53 - 15 * q^54 - 23 * q^55 - 46 * q^56 - 23 * q^57 - 16 * q^58 - 61 * q^59 - 18 * q^60 - 17 * q^61 - 22 * q^62 - 9 * q^63 - 18 * q^64 - 5 * q^65 + 5 * q^66 + 2 * q^67 - 39 * q^68 - 36 * q^69 - 17 * q^70 - 50 * q^71 + 15 * q^72 + 23 * q^73 + 17 * q^74 - 5 * q^75 - 21 * q^76 + 49 * q^78 - 18 * q^79 - q^80 - 57 * q^81 + 14 * q^82 - 20 * q^83 - 38 * q^84 - 36 * q^85 - 45 * q^86 + 37 * q^87 + 6 * q^88 - 93 * q^89 + q^90 - 42 * q^91 - 39 * q^92 - 18 * q^93 - 6 * q^94 + 6 * q^95 - 9 * q^96 - 31 * q^97 - 31 * q^98 - 8 * 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 $

$2$	−1.63550	−1.15647	−0.578237	−	0.815869i	$-0.696259\pi$
$2$	−1.63550	−1.15647	−0.578237	+	0.815869i	$0.696259\pi$
$3$	2.32797	1.34405	0.672027	−	0.740526i	$-0.265424\pi$
$3$	2.32797	1.34405	0.672027	+	0.740526i	$0.265424\pi$
$4$	0.674867	0.337434
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−3.80740	−1.55436
$7$	−0.601850	−0.227478	−0.113739	−	0.993511i	$-0.536283\pi$
$7$	−0.601850	−0.227478	−0.113739	+	0.993511i	$0.536283\pi$
$8$	2.16726	0.766241
$9$	2.41945	0.806482
$10$	−1.63550	−0.517191
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	1.57107	0.453529
$13$	−3.12789	−0.867521	−0.433761	−	0.901028i	$-0.642814\pi$
$13$	−3.12789	−0.867521	−0.433761	+	0.901028i	$0.642814\pi$
$14$	0.984326	0.263072
$15$	2.32797	0.601079
$16$	−4.89429	−1.22357
$17$	4.94659	1.19973	0.599863	−	0.800103i	$-0.295222\pi$
$17$	4.94659	1.19973	0.599863	+	0.800103i	$0.295222\pi$
$18$	−3.95701	−0.932676
$19$	−6.49476	−1.49000	−0.745000	−	0.667065i	$-0.767551\pi$
$19$	−6.49476	−1.49000	−0.745000	+	0.667065i	$0.767551\pi$
$20$	0.674867	0.150905
$21$	−1.40109	−0.305743
$22$	1.63550	0.348690
$23$	−2.90532	−0.605801	−0.302900	−	0.953022i	$-0.597955\pi$
$23$	−2.90532	−0.605801	−0.302900	+	0.953022i	$0.597955\pi$
$24$	5.04531	1.02987
$25$	1.00000	0.200000
$26$	5.11568	1.00327
$27$	−1.35151	−0.260098
$28$	−0.406169	−0.0767587
$29$	3.92545	0.728937	0.364469	−	0.931216i	$-0.381251\pi$
$29$	3.92545	0.728937	0.364469	+	0.931216i	$0.381251\pi$
$30$	−3.80740	−0.695133
$31$	0.264921	0.0475813	0.0237906	−	0.999717i	$-0.492426\pi$
$31$	0.264921	0.0475813	0.0237906	+	0.999717i	$0.492426\pi$
$32$	3.67010	0.648789
$33$	−2.32797	−0.405248
$34$	−8.09016	−1.38745
$35$	−0.601850	−0.101731
$36$	1.63281	0.272134
$37$	−7.71523	−1.26838	−0.634188	−	0.773179i	$-0.718666\pi$
$37$	−7.71523	−1.26838	−0.634188	+	0.773179i	$0.718666\pi$
$38$	10.6222	1.72315
$39$	−7.28164	−1.16600
$40$	2.16726	0.342674
$41$	0.925656	0.144563	0.0722816	−	0.997384i	$-0.476972\pi$
$41$	0.925656	0.144563	0.0722816	+	0.997384i	$0.476972\pi$
$42$	2.29148	0.353584
$43$	1.12395	0.171401	0.0857004	−	0.996321i	$-0.472687\pi$
$43$	1.12395	0.171401	0.0857004	+	0.996321i	$0.472687\pi$
$44$	−0.674867	−0.101740
$45$	2.41945	0.360670
$46$	4.75165	0.700593
$47$	−0.578904	−0.0844418	−0.0422209	−	0.999108i	$-0.513443\pi$
$47$	−0.578904	−0.0844418	−0.0422209	+	0.999108i	$0.513443\pi$
$48$	−11.3938	−1.64455
$49$	−6.63778	−0.948254
$50$	−1.63550	−0.231295
$51$	11.5155	1.61250
$52$	−2.11091	−0.292731
$53$	−5.06645	−0.695931	−0.347965	−	0.937507i	$-0.613127\pi$
$53$	−5.06645	−0.695931	−0.347965	+	0.937507i	$0.613127\pi$
$54$	2.21040	0.300797
$55$	−1.00000	−0.134840
$56$	−1.30436	−0.174303
$57$	−15.1196	−2.00264
$58$	−6.42008	−0.842997
$59$	0.0753517	0.00980996	0.00490498	−	0.999988i	$-0.498439\pi$
$59$	0.0753517	0.00980996	0.00490498	+	0.999988i	$0.498439\pi$
$60$	1.57107	0.202824
$61$	5.94570	0.761269	0.380634	−	0.924726i	$-0.375706\pi$
$61$	5.94570	0.761269	0.380634	+	0.924726i	$0.375706\pi$
$62$	−0.433279	−0.0550265
$63$	−1.45614	−0.183457
$64$	3.78611	0.473264
$65$	−3.12789	−0.387967
$66$	3.80740	0.468659
$67$	−12.1340	−1.48241	−0.741205	−	0.671279i	$-0.765745\pi$
$67$	−12.1340	−1.48241	−0.741205	+	0.671279i	$0.765745\pi$
$68$	3.33829	0.404828
$69$	−6.76349	−0.814229
$70$	0.984326	0.117650
$71$	4.66312	0.553411	0.276705	−	0.960955i	$-0.410757\pi$
$71$	4.66312	0.553411	0.276705	+	0.960955i	$0.410757\pi$
$72$	5.24356	0.617960
$73$	1.00000	0.117041
$73$	1.00000	0.117041
$74$	12.6183	1.46685
$75$	2.32797	0.268811
$76$	−4.38310	−0.502776
$77$	0.601850	0.0685871
$78$	11.9091	1.34844
$79$	−10.3046	−1.15936	−0.579680	−	0.814844i	$-0.696822\pi$
$79$	−10.3046	−1.15936	−0.579680	+	0.814844i	$0.696822\pi$
$80$	−4.89429	−0.547198
$81$	−10.4046	−1.15607
$82$	−1.51391	−0.167184
$83$	−6.24520	−0.685500	−0.342750	−	0.939427i	$-0.611358\pi$
$83$	−6.24520	−0.685500	−0.342750	+	0.939427i	$0.611358\pi$
$84$	−0.945549	−0.103168
$85$	4.94659	0.536533
$86$	−1.83822	−0.198221
$87$	9.13832	0.979731
$88$	−2.16726	−0.231030
$89$	−12.4339	−1.31799	−0.658993	−	0.752149i	$-0.729017\pi$
$89$	−12.4339	−1.31799	−0.658993	+	0.752149i	$0.729017\pi$
$90$	−3.95701	−0.417106
$91$	1.88252	0.197342
$92$	−1.96070	−0.204417
$93$	0.616729	0.0639518
$94$	0.946799	0.0976548
$95$	−6.49476	−0.666348
$96$	8.54390	0.872008
$97$	−15.8286	−1.60715	−0.803573	−	0.595206i	$-0.797070\pi$
$97$	−15.8286	−1.60715	−0.803573	+	0.595206i	$0.797070\pi$
$98$	10.8561	1.09663
$99$	−2.41945	−0.243164
$100$	0.674867	0.0674867
$101$	6.62658	0.659370	0.329685	−	0.944091i	$-0.393058\pi$
$101$	6.62658	0.659370	0.329685	+	0.944091i	$0.393058\pi$
$102$	−18.8337	−1.86481
$103$	0.0864846	0.00852158	0.00426079	−	0.999991i	$-0.498644\pi$
$103$	0.0864846	0.00852158	0.00426079	+	0.999991i	$0.498644\pi$
$104$	−6.77895	−0.664731
$105$	−1.40109	−0.136732
$106$	8.28619	0.804826
$107$	12.5719	1.21537	0.607684	−	0.794179i	$-0.292099\pi$
$107$	12.5719	1.21537	0.607684	+	0.794179i	$0.292099\pi$
$108$	−0.912090	−0.0877659
$109$	−6.25940	−0.599542	−0.299771	−	0.954011i	$-0.596910\pi$
$109$	−6.25940	−0.599542	−0.299771	+	0.954011i	$0.596910\pi$
$110$	1.63550	0.155939
$111$	−17.9608	−1.70477
$112$	2.94563	0.278336
$113$	20.2555	1.90547	0.952737	−	0.303796i	$-0.0982541\pi$
$113$	20.2555	1.90547	0.952737	+	0.303796i	$0.0982541\pi$
$114$	24.7282	2.31600
$115$	−2.90532	−0.270922
$116$	2.64915	0.245968
$117$	−7.56777	−0.699641
$118$	−0.123238	−0.0113450
$119$	−2.97711	−0.272911
$120$	5.04531	0.460572
$121$	1.00000	0.0909091
$122$	−9.72420	−0.880388
$123$	2.15490	0.194301
$124$	0.178787	0.0160555
$125$	1.00000	0.0894427
$126$	2.38153	0.212163
$127$	1.57052	0.139361	0.0696807	−	0.997569i	$-0.477802\pi$
$127$	1.57052	0.139361	0.0696807	+	0.997569i	$0.477802\pi$
$128$	−13.5324	−1.19611
$129$	2.61652	0.230372
$130$	5.11568	0.448674
$131$	16.7558	1.46396	0.731980	−	0.681326i	$-0.238596\pi$
$131$	16.7558	1.46396	0.731980	+	0.681326i	$0.238596\pi$
$132$	−1.57107	−0.136744
$133$	3.90887	0.338942
$134$	19.8453	1.71437
$135$	−1.35151	−0.116319
$136$	10.7205	0.919279
$137$	−9.79735	−0.837044	−0.418522	−	0.908207i	$-0.637452\pi$
$137$	−9.79735	−0.837044	−0.418522	+	0.908207i	$0.637452\pi$
$138$	11.0617	0.941635
$139$	−5.20813	−0.441748	−0.220874	−	0.975302i	$-0.570891\pi$
$139$	−5.20813	−0.441748	−0.220874	+	0.975302i	$0.570891\pi$
$140$	−0.406169	−0.0343275
$141$	−1.34767	−0.113494
$142$	−7.62655	−0.640006
$143$	3.12789	0.261568
$144$	−11.8415	−0.986789
$145$	3.92545	0.325991
$146$	−1.63550	−0.135355
$147$	−15.4525	−1.27450
$148$	−5.20676	−0.427993
$149$	−16.7394	−1.37135	−0.685673	−	0.727909i	$-0.740492\pi$
$149$	−16.7394	−1.37135	−0.685673	+	0.727909i	$0.740492\pi$
$150$	−3.80740	−0.310873
$151$	3.21063	0.261278	0.130639	−	0.991430i	$-0.458297\pi$
$151$	3.21063	0.261278	0.130639	+	0.991430i	$0.458297\pi$
$152$	−14.0758	−1.14170
$153$	11.9680	0.967557
$154$	−0.984326	−0.0793193
$155$	0.264921	0.0212790
$156$	−4.91414	−0.393446
$157$	1.77720	0.141836	0.0709180	−	0.997482i	$-0.477407\pi$
$157$	1.77720	0.141836	0.0709180	+	0.997482i	$0.477407\pi$
$158$	16.8532	1.34077
$159$	−11.7945	−0.935368
$160$	3.67010	0.290147
$161$	1.74856	0.137806
$162$	17.0168	1.33696
$163$	−21.7349	−1.70241	−0.851206	−	0.524832i	$-0.824128\pi$
$163$	−21.7349	−1.70241	−0.851206	+	0.524832i	$0.824128\pi$
$164$	0.624695	0.0487805
$165$	−2.32797	−0.181232
$166$	10.2140	0.792763
$167$	2.58127	0.199745	0.0998724	−	0.995000i	$-0.468157\pi$
$167$	2.58127	0.199745	0.0998724	+	0.995000i	$0.468157\pi$
$168$	−3.03652	−0.234273
$169$	−3.21629	−0.247407
$170$	−8.09016	−0.620487
$171$	−15.7137	−1.20166
$172$	0.758517	0.0578364
$173$	−19.7687	−1.50299	−0.751494	−	0.659740i	$-0.770667\pi$
$173$	−19.7687	−1.50299	−0.751494	+	0.659740i	$0.770667\pi$
$174$	−14.9457	−1.13303
$175$	−0.601850	−0.0454956
$176$	4.89429	0.368921
$177$	0.175417	0.0131851
$178$	20.3356	1.52422
$179$	19.8610	1.48448	0.742240	−	0.670134i	$-0.233763\pi$
$179$	19.8610	1.48448	0.742240	+	0.670134i	$0.233763\pi$
$180$	1.63281	0.121702
$181$	−16.4980	−1.22629	−0.613143	−	0.789972i	$-0.710095\pi$
$181$	−16.4980	−1.22629	−0.613143	+	0.789972i	$0.710095\pi$
$182$	−3.07887	−0.228221
$183$	13.8414	1.02319
$184$	−6.29657	−0.464189
$185$	−7.71523	−0.567235
$186$	−1.00866	−0.0739587
$187$	−4.94659	−0.361731
$188$	−0.390683	−0.0284935
$189$	0.813406	0.0591666
$190$	10.6222	0.770615
$191$	−21.1652	−1.53146	−0.765730	−	0.643163i	$-0.777622\pi$
$191$	−21.1652	−1.53146	−0.765730	+	0.643163i	$0.777622\pi$
$192$	8.81396	0.636093
$193$	27.5185	1.98083	0.990414	−	0.138131i	$-0.0441096\pi$
$193$	27.5185	1.98083	0.990414	+	0.138131i	$0.0441096\pi$
$194$	25.8876	1.85862
$195$	−7.28164	−0.521449
$196$	−4.47962	−0.319973
$197$	−15.6625	−1.11591	−0.557954	−	0.829872i	$-0.688414\pi$
$197$	−15.6625	−1.11591	−0.557954	+	0.829872i	$0.688414\pi$
$198$	3.95701	0.281213
$199$	24.3935	1.72921	0.864606	−	0.502450i	$-0.167568\pi$
$199$	24.3935	1.72921	0.864606	+	0.502450i	$0.167568\pi$
$200$	2.16726	0.153248
$201$	−28.2477	−1.99244
$202$	−10.8378	−0.762544
$203$	−2.36253	−0.165817
$204$	7.77145	0.544110
$205$	0.925656	0.0646506
$206$	−0.141446	−0.00985499
$207$	−7.02926	−0.488568
$208$	15.3088	1.06148
$209$	6.49476	0.449252
$210$	2.29148	0.158127
$211$	−14.8067	−1.01934	−0.509668	−	0.860371i	$-0.670232\pi$
$211$	−14.8067	−1.01934	−0.509668	+	0.860371i	$0.670232\pi$
$212$	−3.41918	−0.234830
$213$	10.8556	0.743814
$214$	−20.5613	−1.40554
$215$	1.12395	0.0766527
$216$	−2.92907	−0.199298
$217$	−0.159443	−0.0108237
$218$	10.2373	0.693355
$219$	2.32797	0.157310
$220$	−0.674867	−0.0454995
$221$	−15.4724	−1.04079
$222$	29.3750	1.97152
$223$	24.6313	1.64943	0.824716	−	0.565548i	$-0.191335\pi$
$223$	24.6313	1.64943	0.824716	+	0.565548i	$0.191335\pi$
$224$	−2.20885	−0.147585
$225$	2.41945	0.161296
$226$	−33.1279	−2.20363
$227$	0.875791	0.0581283	0.0290641	−	0.999578i	$-0.490747\pi$
$227$	0.875791	0.0581283	0.0290641	+	0.999578i	$0.490747\pi$
$228$	−10.2037	−0.675758
$229$	−10.4119	−0.688035	−0.344018	−	0.938963i	$-0.611788\pi$
$229$	−10.4119	−0.688035	−0.344018	+	0.938963i	$0.611788\pi$
$230$	4.75165	0.313315
$231$	1.40109	0.0921848
$232$	8.50745	0.558542
$233$	−20.3502	−1.33318	−0.666592	−	0.745423i	$-0.732248\pi$
$233$	−20.3502	−1.33318	−0.666592	+	0.745423i	$0.732248\pi$
$234$	12.3771	0.809117
$235$	−0.578904	−0.0377635
$236$	0.0508524	0.00331021
$237$	−23.9888	−1.55824
$238$	4.86906	0.315614
$239$	19.0203	1.23032	0.615160	−	0.788403i	$-0.289092\pi$
$239$	19.0203	1.23032	0.615160	+	0.788403i	$0.289092\pi$
$240$	−11.3938	−0.735464
$241$	−11.5392	−0.743308	−0.371654	−	0.928371i	$-0.621209\pi$
$241$	−11.5392	−0.743308	−0.371654	+	0.928371i	$0.621209\pi$
$242$	−1.63550	−0.105134
$243$	−20.1671	−1.29372
$244$	4.01256	0.256878
$245$	−6.63778	−0.424072
$246$	−3.52434	−0.224704
$247$	20.3149	1.29261
$248$	0.574153	0.0364587
$249$	−14.5386	−0.921349
$250$	−1.63550	−0.103438
$251$	25.0704	1.58243	0.791214	−	0.611540i	$-0.209450\pi$
$251$	25.0704	1.58243	0.791214	+	0.611540i	$0.209450\pi$
$252$	−0.982703	−0.0619045
$253$	2.90532	0.182656
$254$	−2.56859	−0.161168
$255$	11.5155	0.721130
$256$	14.5601	0.910003
$257$	−2.27010	−0.141605	−0.0708024	−	0.997490i	$-0.522556\pi$
$257$	−2.27010	−0.141605	−0.0708024	+	0.997490i	$0.522556\pi$
$258$	−4.27933	−0.266419
$259$	4.64341	0.288527
$260$	−2.11091	−0.130913
$261$	9.49741	0.587875
$262$	−27.4041	−1.69303
$263$	17.3570	1.07028	0.535140	−	0.844763i	$-0.320259\pi$
$263$	17.3570	1.07028	0.535140	+	0.844763i	$0.320259\pi$
$264$	−5.04531	−0.310517
$265$	−5.06645	−0.311230
$266$	−6.39296	−0.391978
$267$	−28.9457	−1.77145
$268$	−8.18887	−0.500215
$269$	−21.4132	−1.30559	−0.652794	−	0.757536i	$-0.726403\pi$
$269$	−21.4132	−1.30559	−0.652794	+	0.757536i	$0.726403\pi$
$270$	2.21040	0.134521
$271$	20.6973	1.25727	0.628637	−	0.777699i	$-0.283613\pi$
$271$	20.6973	1.25727	0.628637	+	0.777699i	$0.283613\pi$
$272$	−24.2101	−1.46795
$273$	4.38245	0.265238
$274$	16.0236	0.968020
$275$	−1.00000	−0.0603023
$276$	−4.56446	−0.274748
$277$	14.0245	0.842653	0.421327	−	0.906909i	$-0.361565\pi$
$277$	14.0245	0.842653	0.421327	+	0.906909i	$0.361565\pi$
$278$	8.51791	0.510871
$279$	0.640963	0.0383735
$280$	−1.30436	−0.0779506
$281$	−27.7253	−1.65395	−0.826976	−	0.562237i	$-0.809941\pi$
$281$	−27.7253	−1.65395	−0.826976	+	0.562237i	$0.809941\pi$
$282$	2.20412	0.131253
$283$	11.7674	0.699498	0.349749	−	0.936843i	$-0.386267\pi$
$283$	11.7674	0.699498	0.349749	+	0.936843i	$0.386267\pi$
$284$	3.14699	0.186739
$285$	−15.1196	−0.895608
$286$	−5.11568	−0.302496
$287$	−0.557106	−0.0328849
$288$	8.87962	0.523237
$289$	7.46879	0.439340
$290$	−6.42008	−0.377000
$291$	−36.8484	−2.16009
$292$	0.674867	0.0394936
$293$	16.5165	0.964903	0.482452	−	0.875923i	$-0.339746\pi$
$293$	16.5165	0.964903	0.482452	+	0.875923i	$0.339746\pi$
$294$	25.2727	1.47393
$295$	0.0753517	0.00438715
$296$	−16.7209	−0.971882
$297$	1.35151	0.0784226
$298$	27.3774	1.58593
$299$	9.08752	0.525545
$300$	1.57107	0.0907058
$301$	−0.676449	−0.0389899
$302$	−5.25100	−0.302161
$303$	15.4265	0.886229
$304$	31.7872	1.82312
$305$	5.94570	0.340450
$306$	−19.5737	−1.11896
$307$	4.21421	0.240518	0.120259	−	0.992743i	$-0.461628\pi$
$307$	4.21421	0.240518	0.120259	+	0.992743i	$0.461628\pi$
$308$	0.406169	0.0231436
$309$	0.201334	0.0114535
$310$	−0.433279	−0.0246086
$311$	−15.5584	−0.882236	−0.441118	−	0.897449i	$-0.645418\pi$
$311$	−15.5584	−0.882236	−0.441118	+	0.897449i	$0.645418\pi$
$312$	−15.7812	−0.893434
$313$	−2.44156	−0.138005	−0.0690027	−	0.997616i	$-0.521982\pi$
$313$	−2.44156	−0.138005	−0.0690027	+	0.997616i	$0.521982\pi$
$314$	−2.90662	−0.164030
$315$	−1.45614	−0.0820444
$316$	−6.95424	−0.391207
$317$	17.4383	0.979434	0.489717	−	0.871881i	$-0.337100\pi$
$317$	17.4383	0.979434	0.489717	+	0.871881i	$0.337100\pi$
$318$	19.2900	1.08173
$319$	−3.92545	−0.219783
$320$	3.78611	0.211650
$321$	29.2669	1.63352
$322$	−2.85978	−0.159369
$323$	−32.1269	−1.78759
$324$	−7.02173	−0.390096
$325$	−3.12789	−0.173504
$326$	35.5475	1.96880
$327$	−14.5717	−0.805817
$328$	2.00614	0.110770
$329$	0.348413	0.0192086
$330$	3.80740	0.209591
$331$	23.2163	1.27609	0.638043	−	0.770001i	$-0.279744\pi$
$331$	23.2163	1.27609	0.638043	+	0.770001i	$0.279744\pi$
$332$	−4.21468	−0.231311
$333$	−18.6666	−1.02292
$334$	−4.22168	−0.231000
$335$	−12.1340	−0.662954
$336$	6.85733	0.374098
$337$	−10.5210	−0.573116	−0.286558	−	0.958063i	$-0.592511\pi$
$337$	−10.5210	−0.573116	−0.286558	+	0.958063i	$0.592511\pi$
$338$	5.26024	0.286119
$339$	47.1541	2.56106
$340$	3.33829	0.181044
$341$	−0.264921	−0.0143463
$342$	25.6998	1.38969
$343$	8.20789	0.443185
$344$	2.43589	0.131334
$345$	−6.76349	−0.364134
$346$	32.3318	1.73817
$347$	−24.3488	−1.30711	−0.653555	−	0.756879i	$-0.726723\pi$
$347$	−24.3488	−1.30711	−0.653555	+	0.756879i	$0.726723\pi$
$348$	6.16715	0.330594
$349$	21.6028	1.15637	0.578186	−	0.815905i	$-0.303761\pi$
$349$	21.6028	1.15637	0.578186	+	0.815905i	$0.303761\pi$
$350$	0.984326	0.0526145
$351$	4.22738	0.225641
$352$	−3.67010	−0.195617
$353$	13.2200	0.703631	0.351815	−	0.936069i	$-0.385564\pi$
$353$	13.2200	0.703631	0.351815	+	0.936069i	$0.385564\pi$
$354$	−0.286894	−0.0152483
$355$	4.66312	0.247493
$356$	−8.39120	−0.444733
$357$	−6.93061	−0.366807
$358$	−32.4827	−1.71676
$359$	−9.48017	−0.500344	−0.250172	−	0.968201i	$-0.580487\pi$
$359$	−9.48017	−0.500344	−0.250172	+	0.968201i	$0.580487\pi$
$360$	5.24356	0.276360
$361$	23.1819	1.22010
$362$	26.9825	1.41817
$363$	2.32797	0.122187
$364$	1.27045	0.0665898
$365$	1.00000	0.0523424
$366$	−22.6377	−1.18329
$367$	−37.8304	−1.97473	−0.987364	−	0.158466i	$-0.949345\pi$
$367$	−37.8304	−1.97473	−0.987364	+	0.158466i	$0.949345\pi$
$368$	14.2195	0.741241
$369$	2.23958	0.116588
$370$	12.6183	0.655993
$371$	3.04924	0.158309
$372$	0.416210	0.0215795
$373$	3.75539	0.194447	0.0972234	−	0.995263i	$-0.469004\pi$
$373$	3.75539	0.194447	0.0972234	+	0.995263i	$0.469004\pi$
$374$	8.09016	0.418332
$375$	2.32797	0.120216
$376$	−1.25463	−0.0647028
$377$	−12.2784	−0.632369
$378$	−1.33033	−0.0684246
$379$	15.9914	0.821424	0.410712	−	0.911765i	$-0.365280\pi$
$379$	15.9914	0.821424	0.410712	+	0.911765i	$0.365280\pi$
$380$	−4.38310	−0.224848
$381$	3.65613	0.187309
$382$	34.6157	1.77109
$383$	−6.62501	−0.338522	−0.169261	−	0.985571i	$-0.554138\pi$
$383$	−6.62501	−0.338522	−0.169261	+	0.985571i	$0.554138\pi$
$384$	−31.5030	−1.60763
$385$	0.601850	0.0306731
$386$	−45.0066	−2.29078
$387$	2.71934	0.138232
$388$	−10.6822	−0.542305
$389$	2.01159	0.101992	0.0509959	−	0.998699i	$-0.483760\pi$
$389$	2.01159	0.101992	0.0509959	+	0.998699i	$0.483760\pi$
$390$	11.9091	0.603043
$391$	−14.3714	−0.726794
$392$	−14.3858	−0.726591
$393$	39.0070	1.96764
$394$	25.6161	1.29052
$395$	−10.3046	−0.518481
$396$	−1.63281	−0.0820516
$397$	13.0436	0.654640	0.327320	−	0.944914i	$-0.393855\pi$
$397$	13.0436	0.654640	0.327320	+	0.944914i	$0.393855\pi$
$398$	−39.8957	−1.99979
$399$	9.09973	0.455556
$400$	−4.89429	−0.244714
$401$	−11.4246	−0.570518	−0.285259	−	0.958450i	$-0.592080\pi$
$401$	−11.4246	−0.570518	−0.285259	+	0.958450i	$0.592080\pi$
$402$	46.1992	2.30420
$403$	−0.828645	−0.0412778
$404$	4.47206	0.222493
$405$	−10.4046	−0.517010
$406$	3.86392	0.191763
$407$	7.71523	0.382430
$408$	24.9571	1.23556
$409$	−19.3566	−0.957121	−0.478561	−	0.878054i	$-0.658841\pi$
$409$	−19.3566	−0.957121	−0.478561	+	0.878054i	$0.658841\pi$
$410$	−1.51391	−0.0747668
$411$	−22.8079	−1.12503
$412$	0.0583656	0.00287547
$413$	−0.0453504	−0.00223155
$414$	11.4964	0.565016
$415$	−6.24520	−0.306565
$416$	−11.4797	−0.562838
$417$	−12.1244	−0.593734
$418$	−10.6222	−0.519548
$419$	−16.2653	−0.794613	−0.397306	−	0.917686i	$-0.630055\pi$
$419$	−16.2653	−0.794613	−0.397306	+	0.917686i	$0.630055\pi$
$420$	−0.945549	−0.0461380
$421$	−26.2074	−1.27727	−0.638636	−	0.769509i	$-0.720501\pi$
$421$	−26.2074	−1.27727	−0.638636	+	0.769509i	$0.720501\pi$
$422$	24.2164	1.17884
$423$	−1.40063	−0.0681008
$424$	−10.9803	−0.533251
$425$	4.94659	0.239945
$426$	−17.7544	−0.860202
$427$	−3.57842	−0.173172
$428$	8.48433	0.410106
$429$	7.28164	0.351561
$430$	−1.83822	−0.0886469
$431$	−37.7497	−1.81834	−0.909169	−	0.416427i	$-0.863282\pi$
$431$	−37.7497	−1.81834	−0.909169	+	0.416427i	$0.863282\pi$
$432$	6.61468	0.318249
$433$	−6.18274	−0.297123	−0.148562	−	0.988903i	$-0.547464\pi$
$433$	−6.18274	−0.297123	−0.148562	+	0.988903i	$0.547464\pi$
$434$	0.260769	0.0125173
$435$	9.13832	0.438149
$436$	−4.22427	−0.202306
$437$	18.8693	0.902643
$438$	−3.80740	−0.181925
$439$	7.94257	0.379078	0.189539	−	0.981873i	$-0.439301\pi$
$439$	7.94257	0.379078	0.189539	+	0.981873i	$0.439301\pi$
$440$	−2.16726	−0.103320
$441$	−16.0597	−0.764750
$442$	25.3052	1.20364
$443$	8.22856	0.390951	0.195475	−	0.980709i	$-0.437375\pi$
$443$	8.22856	0.390951	0.195475	+	0.980709i	$0.437375\pi$
$444$	−12.1212	−0.575246
$445$	−12.4339	−0.589421
$446$	−40.2845	−1.90753
$447$	−38.9689	−1.84316
$448$	−2.27867	−0.107657
$449$	−32.1719	−1.51829	−0.759144	−	0.650923i	$-0.774382\pi$
$449$	−32.1719	−1.51829	−0.759144	+	0.650923i	$0.774382\pi$
$450$	−3.95701	−0.186535
$451$	−0.925656	−0.0435874
$452$	13.6698	0.642971
$453$	7.47426	0.351171
$454$	−1.43236	−0.0672239
$455$	1.88252	0.0882540
$456$	−32.7681	−1.53451
$457$	−21.0081	−0.982715	−0.491358	−	0.870958i	$-0.663499\pi$
$457$	−21.0081	−0.982715	−0.491358	+	0.870958i	$0.663499\pi$
$458$	17.0286	0.795695
$459$	−6.68537	−0.312046
$460$	−1.96070	−0.0914183
$461$	36.1398	1.68320	0.841599	−	0.540103i	$-0.181615\pi$
$461$	36.1398	1.68320	0.841599	+	0.540103i	$0.181615\pi$
$462$	−2.29148	−0.106609
$463$	−8.78905	−0.408462	−0.204231	−	0.978923i	$-0.565469\pi$
$463$	−8.78905	−0.408462	−0.204231	+	0.978923i	$0.565469\pi$
$464$	−19.2123	−0.891907
$465$	0.616729	0.0286001
$466$	33.2828	1.54179
$467$	−18.2019	−0.842285	−0.421142	−	0.906995i	$-0.638371\pi$
$467$	−18.2019	−0.842285	−0.421142	+	0.906995i	$0.638371\pi$
$468$	−5.10724	−0.236082
$469$	7.30287	0.337215
$470$	0.946799	0.0436726
$471$	4.13727	0.190635
$472$	0.163307	0.00751679
$473$	−1.12395	−0.0516793
$474$	39.2338	1.80207
$475$	−6.49476	−0.298000
$476$	−2.00915	−0.0920893
$477$	−12.2580	−0.561256
$478$	−31.1077	−1.42283
$479$	−20.2754	−0.926405	−0.463203	−	0.886252i	$-0.653300\pi$
$479$	−20.2754	−0.926405	−0.463203	+	0.886252i	$0.653300\pi$
$480$	8.54390	0.389974
$481$	24.1324	1.10034
$482$	18.8725	0.859617
$483$	4.07061	0.185219
$484$	0.674867	0.0306758
$485$	−15.8286	−0.718738
$486$	32.9834	1.49616
$487$	22.3012	1.01056	0.505282	−	0.862954i	$-0.331388\pi$
$487$	22.3012	1.01056	0.505282	+	0.862954i	$0.331388\pi$
$488$	12.8859	0.583316
$489$	−50.5983	−2.28813
$490$	10.8561	0.490429
$491$	18.3321	0.827315	0.413657	−	0.910433i	$-0.364251\pi$
$491$	18.3321	0.827315	0.413657	+	0.910433i	$0.364251\pi$
$492$	1.45427	0.0655636
$493$	19.4176	0.874524
$494$	−33.2251	−1.49487
$495$	−2.41945	−0.108746
$496$	−1.29660	−0.0582191
$497$	−2.80650	−0.125889
$498$	23.7780	1.06552
$499$	−22.8626	−1.02347	−0.511736	−	0.859143i	$-0.670997\pi$
$499$	−22.8626	−1.02347	−0.511736	+	0.859143i	$0.670997\pi$
$500$	0.674867	0.0301810
$501$	6.00912	0.268468
$502$	−41.0026	−1.83004
$503$	−9.53369	−0.425086	−0.212543	−	0.977152i	$-0.568175\pi$
$503$	−9.53369	−0.425086	−0.212543	+	0.977152i	$0.568175\pi$
$504$	−3.15584	−0.140572
$505$	6.62658	0.294879
$506$	−4.75165	−0.211237
$507$	−7.48742	−0.332528
$508$	1.05989	0.0470252
$509$	−3.32704	−0.147468	−0.0737341	−	0.997278i	$-0.523492\pi$
$509$	−3.32704	−0.147468	−0.0737341	+	0.997278i	$0.523492\pi$
$510$	−18.8337	−0.833969
$511$	−0.601850	−0.0266243
$512$	3.25182	0.143711
$513$	8.77773	0.387546
$514$	3.71275	0.163762
$515$	0.0864846	0.00381097
$516$	1.76580	0.0777352
$517$	0.578904	0.0254602
$518$	−7.59431	−0.333675
$519$	−46.0210	−2.02010
$520$	−6.77895	−0.297277
$521$	9.20883	0.403446	0.201723	−	0.979443i	$-0.435346\pi$
$521$	9.20883	0.403446	0.201723	+	0.979443i	$0.435346\pi$
$522$	−15.5330	−0.679862
$523$	22.4671	0.982416	0.491208	−	0.871042i	$-0.336556\pi$
$523$	22.4671	0.982416	0.491208	+	0.871042i	$0.336556\pi$
$524$	11.3079	0.493989
$525$	−1.40109	−0.0611485
$526$	−28.3875	−1.23775
$527$	1.31046	0.0570844
$528$	11.3938	0.495850
$529$	−14.5591	−0.633006
$530$	8.28619	0.359929
$531$	0.182309	0.00791156
$532$	2.63797	0.114370
$533$	−2.89535	−0.125412
$534$	47.3407	2.04863
$535$	12.5719	0.543529
$536$	−26.2976	−1.13588
$537$	46.2358	1.99522
$538$	35.0214	1.50988
$539$	6.63778	0.285909
$540$	−0.912090	−0.0392501
$541$	−19.3025	−0.829878	−0.414939	−	0.909849i	$-0.636197\pi$
$541$	−19.3025	−0.829878	−0.414939	+	0.909849i	$0.636197\pi$
$542$	−33.8505	−1.45400
$543$	−38.4069	−1.64820
$544$	18.1545	0.778368
$545$	−6.25940	−0.268123
$546$	−7.16751	−0.306741
$547$	−12.7936	−0.547014	−0.273507	−	0.961870i	$-0.588184\pi$
$547$	−12.7936	−0.547014	−0.273507	+	0.961870i	$0.588184\pi$
$548$	−6.61191	−0.282447
$549$	14.3853	0.613950
$550$	1.63550	0.0697380
$551$	−25.4948	−1.08612
$552$	−14.6582	−0.623896
$553$	6.20183	0.263729
$554$	−22.9372	−0.974507
$555$	−17.9608	−0.762395
$556$	−3.51480	−0.149061
$557$	29.4817	1.24918	0.624590	−	0.780953i	$-0.285266\pi$
$557$	29.4817	1.24918	0.624590	+	0.780953i	$0.285266\pi$
$558$	−1.04830	−0.0443779
$559$	−3.51559	−0.148694
$560$	2.94563	0.124475
$561$	−11.5155	−0.486186
$562$	45.3448	1.91275
$563$	34.2308	1.44266	0.721329	−	0.692593i	$-0.243532\pi$
$563$	34.2308	1.44266	0.721329	+	0.692593i	$0.243532\pi$
$564$	−0.909499	−0.0382968
$565$	20.2555	0.852154
$566$	−19.2456	−0.808952
$567$	6.26202	0.262980
$568$	10.1062	0.424046
$569$	1.96606	0.0824216	0.0412108	−	0.999150i	$-0.486878\pi$
$569$	1.96606	0.0824216	0.0412108	+	0.999150i	$0.486878\pi$
$570$	24.7282	1.03575
$571$	−42.1153	−1.76247	−0.881234	−	0.472680i	$-0.843287\pi$
$571$	−42.1153	−1.76247	−0.881234	+	0.472680i	$0.843287\pi$
$572$	2.11091	0.0882617
$573$	−49.2719	−2.05836
$574$	0.911148	0.0380306
$575$	−2.90532	−0.121160
$576$	9.16030	0.381679
$577$	−35.0375	−1.45863	−0.729315	−	0.684178i	$-0.760161\pi$
$577$	−35.0375	−1.45863	−0.729315	+	0.684178i	$0.760161\pi$
$578$	−12.2152	−0.508086
$579$	64.0624	2.66234
$580$	2.64915	0.110000
$581$	3.75867	0.155936
$582$	60.2656	2.49809
$583$	5.06645	0.209831
$584$	2.16726	0.0896818
$585$	−7.56777	−0.312889
$586$	−27.0127	−1.11589
$587$	33.1049	1.36639	0.683193	−	0.730238i	$-0.260591\pi$
$587$	33.1049	1.36639	0.683193	+	0.730238i	$0.260591\pi$
$588$	−10.4284	−0.430061
$589$	−1.72060	−0.0708961
$590$	−0.123238	−0.00507362
$591$	−36.4619	−1.49984
$592$	37.7606	1.55195
$593$	−33.3779	−1.37066	−0.685332	−	0.728231i	$-0.740343\pi$
$593$	−33.3779	−1.37066	−0.685332	+	0.728231i	$0.740343\pi$
$594$	−2.21040	−0.0906937
$595$	−2.97711	−0.122049
$596$	−11.2969	−0.462738
$597$	56.7875	2.32416
$598$	−14.8627	−0.607779
$599$	−13.2418	−0.541044	−0.270522	−	0.962714i	$-0.587196\pi$
$599$	−13.2418	−0.541044	−0.270522	+	0.962714i	$0.587196\pi$
$600$	5.04531	0.205974
$601$	−10.6330	−0.433730	−0.216865	−	0.976202i	$-0.569583\pi$
$601$	−10.6330	−0.433730	−0.216865	+	0.976202i	$0.569583\pi$
$602$	1.10633	0.0450908
$603$	−29.3577	−1.19554
$604$	2.16675	0.0881638
$605$	1.00000	0.0406558
$606$	−25.2301	−1.02490
$607$	6.62384	0.268853	0.134427	−	0.990924i	$-0.457081\pi$
$607$	6.62384	0.268853	0.134427	+	0.990924i	$0.457081\pi$
$608$	−23.8364	−0.966695
$609$	−5.49990	−0.222867
$610$	−9.72420	−0.393721
$611$	1.81075	0.0732551
$612$	8.07682	0.326486
$613$	−3.99432	−0.161329	−0.0806645	−	0.996741i	$-0.525704\pi$
$613$	−3.99432	−0.161329	−0.0806645	+	0.996741i	$0.525704\pi$
$614$	−6.89235	−0.278152
$615$	2.15490	0.0868940
$616$	1.30436	0.0525543
$617$	26.3564	1.06107	0.530534	−	0.847664i	$-0.321991\pi$
$617$	26.3564	1.06107	0.530534	+	0.847664i	$0.321991\pi$
$618$	−0.329281	−0.0132456
$619$	26.9164	1.08186	0.540930	−	0.841067i	$-0.318072\pi$
$619$	26.9164	1.08186	0.540930	+	0.841067i	$0.318072\pi$
$620$	0.178787	0.00718025
$621$	3.92657	0.157568
$622$	25.4458	1.02028
$623$	7.48331	0.299813
$624$	35.6385	1.42668
$625$	1.00000	0.0400000
$626$	3.99318	0.159600
$627$	15.1196	0.603819
$628$	1.19937	0.0478603
$629$	−38.1641	−1.52170
$630$	2.38153	0.0948823
$631$	19.4346	0.773678	0.386839	−	0.922147i	$-0.373567\pi$
$631$	19.4346	0.773678	0.386839	+	0.922147i	$0.373567\pi$
$632$	−22.3327	−0.888349
$633$	−34.4696	−1.37004
$634$	−28.5204	−1.13269
$635$	1.57052	0.0623243
$636$	−7.95975	−0.315625
$637$	20.7623	0.822631
$638$	6.42008	0.254173
$639$	11.2822	0.446316
$640$	−13.5324	−0.534915
$641$	−47.5547	−1.87830	−0.939149	−	0.343509i	$-0.888385\pi$
$641$	−47.5547	−1.87830	−0.939149	+	0.343509i	$0.888385\pi$
$642$	−47.8661	−1.88912
$643$	43.2545	1.70579	0.852895	−	0.522083i	$-0.174845\pi$
$643$	43.2545	1.70579	0.852895	+	0.522083i	$0.174845\pi$
$644$	1.18005	0.0465004
$645$	2.61652	0.103025
$646$	52.5437	2.06730
$647$	34.9684	1.37475	0.687374	−	0.726304i	$-0.258763\pi$
$647$	34.9684	1.37475	0.687374	+	0.726304i	$0.258763\pi$
$648$	−22.5495	−0.885827
$649$	−0.0753517	−0.00295781
$650$	5.11568	0.200653
$651$	−0.371178	−0.0145476
$652$	−14.6682	−0.574451
$653$	−2.80145	−0.109629	−0.0548146	−	0.998497i	$-0.517457\pi$
$653$	−2.80145	−0.109629	−0.0548146	+	0.998497i	$0.517457\pi$
$654$	23.8321	0.931907
$655$	16.7558	0.654703
$656$	−4.53043	−0.176884
$657$	2.41945	0.0943916
$658$	−0.569830	−0.0222143
$659$	−3.88391	−0.151296	−0.0756478	−	0.997135i	$-0.524102\pi$
$659$	−3.88391	−0.151296	−0.0756478	+	0.997135i	$0.524102\pi$
$660$	−1.57107	−0.0611539
$661$	−4.36649	−0.169837	−0.0849184	−	0.996388i	$-0.527063\pi$
$661$	−4.36649	−0.169837	−0.0849184	+	0.996388i	$0.527063\pi$
$662$	−37.9704	−1.47576
$663$	−36.0193	−1.39887
$664$	−13.5350	−0.525258
$665$	3.90887	0.151579
$666$	30.5293	1.18298
$667$	−11.4047	−0.441591
$668$	1.74202	0.0674006
$669$	57.3408	2.21693
$670$	19.8453	0.766689
$671$	−5.94570	−0.229531
$672$	−5.14214	−0.198362
$673$	−13.0978	−0.504881	−0.252441	−	0.967612i	$-0.581233\pi$
$673$	−13.0978	−0.504881	−0.252441	+	0.967612i	$0.581233\pi$
$674$	17.2071	0.662794
$675$	−1.35151	−0.0520197
$676$	−2.17057	−0.0834833
$677$	−17.0544	−0.655455	−0.327728	−	0.944772i	$-0.606283\pi$
$677$	−17.0544	−0.655455	−0.327728	+	0.944772i	$0.606283\pi$
$678$	−77.1207	−2.96180
$679$	9.52641	0.365590
$680$	10.7205	0.411114
$681$	2.03882	0.0781276
$682$	0.433279	0.0165911
$683$	19.4848	0.745566	0.372783	−	0.927919i	$-0.378404\pi$
$683$	19.4848	0.745566	0.372783	+	0.927919i	$0.378404\pi$
$684$	−10.6047	−0.405480
$685$	−9.79735	−0.374337
$686$	−13.4240	−0.512532
$687$	−24.2385	−0.924757
$688$	−5.50093	−0.209721
$689$	15.8473	0.603735
$690$	11.0617	0.421112
$691$	−42.2963	−1.60903	−0.804514	−	0.593933i	$-0.797574\pi$
$691$	−42.2963	−1.60903	−0.804514	+	0.593933i	$0.797574\pi$
$692$	−13.3413	−0.507159
$693$	1.45614	0.0553143
$694$	39.8225	1.51164
$695$	−5.20813	−0.197556
$696$	19.8051	0.750710
$697$	4.57885	0.173436
$698$	−35.3314	−1.33731
$699$	−47.3746	−1.79187
$700$	−0.406169	−0.0153517
$701$	34.4005	1.29929	0.649644	−	0.760238i	$-0.274918\pi$
$701$	34.4005	1.29929	0.649644	+	0.760238i	$0.274918\pi$
$702$	−6.91389	−0.260948
$703$	50.1086	1.88988
$704$	−3.78611	−0.142695
$705$	−1.34767	−0.0507562
$706$	−21.6214	−0.813731
$707$	−3.98821	−0.149992
$708$	0.118383	0.00444910
$709$	−29.0335	−1.09038	−0.545188	−	0.838314i	$-0.683542\pi$
$709$	−29.0335	−1.09038	−0.545188	+	0.838314i	$0.683542\pi$
$710$	−7.62655	−0.286219
$711$	−24.9315	−0.935003
$712$	−26.9474	−1.00990
$713$	−0.769681	−0.0288248
$714$	11.3350	0.424203
$715$	3.12789	0.116977
$716$	13.4035	0.500914
$717$	44.2786	1.65362
$718$	15.5048	0.578636
$719$	−16.6871	−0.622326	−0.311163	−	0.950357i	$-0.600718\pi$
$719$	−16.6871	−0.622326	−0.311163	+	0.950357i	$0.600718\pi$
$720$	−11.8415	−0.441306
$721$	−0.0520507	−0.00193847
$722$	−37.9140	−1.41101
$723$	−26.8630	−0.999046
$724$	−11.1340	−0.413790
$725$	3.92545	0.145787
$726$	−3.80740	−0.141306
$727$	−39.1323	−1.45134	−0.725668	−	0.688045i	$-0.758469\pi$
$727$	−39.1323	−1.45134	−0.725668	+	0.688045i	$0.758469\pi$
$728$	4.07991	0.151211
$729$	−15.7346	−0.582763
$730$	−1.63550	−0.0605326
$731$	5.55972	0.205634
$732$	9.34112	0.345258
$733$	16.8396	0.621986	0.310993	−	0.950412i	$-0.399338\pi$
$733$	16.8396	0.621986	0.310993	+	0.950412i	$0.399338\pi$
$734$	61.8716	2.28372
$735$	−15.4525	−0.569976
$736$	−10.6628	−0.393037
$737$	12.1340	0.446963
$738$	−3.66283	−0.134831
$739$	46.7217	1.71869	0.859343	−	0.511400i	$-0.170873\pi$
$739$	46.7217	1.71869	0.859343	+	0.511400i	$0.170873\pi$
$740$	−5.20676	−0.191404
$741$	47.2925	1.73733
$742$	−4.98704	−0.183080
$743$	−23.3616	−0.857055	−0.428528	−	0.903529i	$-0.640967\pi$
$743$	−23.3616	−0.857055	−0.428528	+	0.903529i	$0.640967\pi$
$744$	1.33661	0.0490025
$745$	−16.7394	−0.613285
$746$	−6.14195	−0.224873
$747$	−15.1099	−0.552844
$748$	−3.33829	−0.122060
$749$	−7.56637	−0.276469
$750$	−3.80740	−0.139027
$751$	3.53900	0.129140	0.0645701	−	0.997913i	$-0.479432\pi$
$751$	3.53900	0.129140	0.0645701	+	0.997913i	$0.479432\pi$
$752$	2.83332	0.103321
$753$	58.3631	2.12687
$754$	20.0813	0.731318
$755$	3.21063	0.116847
$756$	0.548941	0.0199648
$757$	43.8360	1.59325	0.796624	−	0.604475i	$-0.206617\pi$
$757$	43.8360	1.59325	0.796624	+	0.604475i	$0.206617\pi$
$758$	−26.1540	−0.949956
$759$	6.76349	0.245499
$760$	−14.0758	−0.510583
$761$	31.0534	1.12568	0.562842	−	0.826565i	$-0.309708\pi$
$761$	31.0534	1.12568	0.562842	+	0.826565i	$0.309708\pi$
$762$	−5.97961	−0.216618
$763$	3.76722	0.136382
$764$	−14.2837	−0.516766
$765$	11.9680	0.432705
$766$	10.8352	0.391492
$767$	−0.235692	−0.00851035
$768$	33.8954	1.22309
$769$	−54.2503	−1.95632	−0.978158	−	0.207861i	$-0.933350\pi$
$769$	−54.2503	−1.95632	−0.978158	+	0.207861i	$0.933350\pi$
$770$	−0.984326	−0.0354727
$771$	−5.28472	−0.190325
$772$	18.5714	0.668398
$773$	−0.00494361	−0.000177809 0	−8.89047e−5	−	1.00000i	$-0.500028\pi$
$773$	−0.00494361	−0.000177809 0	−8.89047e−5		1.00000i	$0.500028\pi$
$774$	−4.44748	−0.159861
$775$	0.264921	0.00951625
$776$	−34.3046	−1.23146
$777$	10.8097	0.387797
$778$	−3.28996	−0.117951
$779$	−6.01191	−0.215399
$780$	−4.91414	−0.175955
$781$	−4.66312	−0.166860
$782$	23.5045	0.840519
$783$	−5.30528	−0.189595
$784$	32.4872	1.16026
$785$	1.77720	0.0634310
$786$	−63.7960	−2.27553
$787$	−17.6190	−0.628050	−0.314025	−	0.949415i	$-0.601678\pi$
$787$	−17.6190	−0.628050	−0.314025	+	0.949415i	$0.601678\pi$
$788$	−10.5701	−0.376545
$789$	40.4067	1.43851
$790$	16.8532	0.599610
$791$	−12.1907	−0.433453
$792$	−5.24356	−0.186322
$793$	−18.5975	−0.660417
$794$	−21.3328	−0.757074
$795$	−11.7945	−0.418310
$796$	16.4624	0.583494
$797$	−25.3542	−0.898091	−0.449045	−	0.893509i	$-0.648236\pi$
$797$	−25.3542	−0.898091	−0.449045	+	0.893509i	$0.648236\pi$
$798$	−14.8826	−0.526839
$799$	−2.86360	−0.101307
$800$	3.67010	0.129758
$801$	−30.0831	−1.06293
$802$	18.6850	0.659790
$803$	−1.00000	−0.0352892
$804$	−19.0634	−0.672316
$805$	1.74856	0.0616288
$806$	1.35525	0.0477367
$807$	−49.8494	−1.75478
$808$	14.3615	0.505236
$809$	−19.0019	−0.668073	−0.334036	−	0.942560i	$-0.608411\pi$
$809$	−19.0019	−0.668073	−0.334036	+	0.942560i	$0.608411\pi$
$810$	17.0168	0.597908
$811$	−24.1909	−0.849456	−0.424728	−	0.905321i	$-0.639630\pi$
$811$	−24.1909	−0.849456	−0.424728	+	0.905321i	$0.639630\pi$
$812$	−1.59439	−0.0559522
$813$	48.1828	1.68984
$814$	−12.6183	−0.442270
$815$	−21.7349	−0.761342
$816$	−56.3603	−1.97301
$817$	−7.29978	−0.255387
$818$	31.6577	1.10689
$819$	4.55466	0.159153
$820$	0.624695	0.0218153
$821$	35.4891	1.23858	0.619288	−	0.785164i	$-0.287421\pi$
$821$	35.4891	1.23858	0.619288	+	0.785164i	$0.287421\pi$
$822$	37.3024	1.30107
$823$	32.9507	1.14859	0.574295	−	0.818648i	$-0.305276\pi$
$823$	32.9507	1.14859	0.574295	+	0.818648i	$0.305276\pi$
$824$	0.187434	0.00652958
$825$	−2.32797	−0.0810495
$826$	0.0741707	0.00258073
$827$	−3.13886	−0.109149	−0.0545744	−	0.998510i	$-0.517380\pi$
$827$	−3.13886	−0.109149	−0.0545744	+	0.998510i	$0.517380\pi$
$828$	−4.74382	−0.164859
$829$	−21.4419	−0.744707	−0.372354	−	0.928091i	$-0.621449\pi$
$829$	−21.4419	−0.744707	−0.372354	+	0.928091i	$0.621449\pi$
$830$	10.2140	0.354535
$831$	32.6487	1.13257
$832$	−11.8426	−0.410567
$833$	−32.8344	−1.13764
$834$	19.8295	0.686638
$835$	2.58127	0.0893286
$836$	4.38310	0.151593
$837$	−0.358044	−0.0123758
$838$	26.6020	0.918949
$839$	−16.2138	−0.559763	−0.279882	−	0.960035i	$-0.590295\pi$
$839$	−16.2138	−0.559763	−0.279882	+	0.960035i	$0.590295\pi$
$840$	−3.03652	−0.104770
$841$	−13.5909	−0.468651
$842$	42.8623	1.47713
$843$	−64.5437	−2.22300
$844$	−9.99255	−0.343958
$845$	−3.21629	−0.110644
$846$	2.29073	0.0787569
$847$	−0.601850	−0.0206798
$848$	24.7967	0.851521
$849$	27.3941	0.940163
$850$	−8.09016	−0.277490
$851$	22.4152	0.768383
$852$	7.32610	0.250988
$853$	39.5387	1.35378	0.676890	−	0.736084i	$-0.263327\pi$
$853$	39.5387	1.35378	0.676890	+	0.736084i	$0.263327\pi$
$854$	5.85251	0.200269
$855$	−15.7137	−0.537398
$856$	27.2465	0.931265
$857$	16.7796	0.573181	0.286590	−	0.958053i	$-0.407478\pi$
$857$	16.7796	0.573181	0.286590	+	0.958053i	$0.407478\pi$
$858$	−11.9091	−0.406571
$859$	20.6732	0.705361	0.352680	−	0.935744i	$-0.385270\pi$
$859$	20.6732	0.705361	0.352680	+	0.935744i	$0.385270\pi$
$860$	0.758517	0.0258652
$861$	−1.29693	−0.0441991
$862$	61.7397	2.10286
$863$	26.6364	0.906715	0.453358	−	0.891329i	$-0.350226\pi$
$863$	26.6364	0.906715	0.453358	+	0.891329i	$0.350226\pi$
$864$	−4.96018	−0.168749
$865$	−19.7687	−0.672157
$866$	10.1119	0.343616
$867$	17.3871	0.590497
$868$	−0.107603	−0.00365227
$869$	10.3046	0.349560
$870$	−14.9457	−0.506708
$871$	37.9540	1.28602
$872$	−13.5657	−0.459394
$873$	−38.2963	−1.29613
$874$	−30.8608	−1.04388
$875$	−0.601850	−0.0203462
$876$	1.57107	0.0530816
$877$	−11.3839	−0.384406	−0.192203	−	0.981355i	$-0.561563\pi$
$877$	−11.3839	−0.384406	−0.192203	+	0.981355i	$0.561563\pi$
$878$	−12.9901	−0.438395
$879$	38.4499	1.29688
$880$	4.89429	0.164986
$881$	35.3979	1.19259	0.596293	−	0.802767i	$-0.296640\pi$
$881$	35.3979	1.19259	0.596293	+	0.802767i	$0.296640\pi$
$882$	26.2658	0.884414
$883$	48.1577	1.62063	0.810317	−	0.585992i	$-0.199295\pi$
$883$	48.1577	1.62063	0.810317	+	0.585992i	$0.199295\pi$
$884$	−10.4418	−0.351197
$885$	0.175417	0.00589656
$886$	−13.4578	−0.452125
$887$	22.6071	0.759071	0.379536	−	0.925177i	$-0.376084\pi$
$887$	22.6071	0.759071	0.379536	+	0.925177i	$0.376084\pi$
$888$	−38.9258	−1.30626
$889$	−0.945218	−0.0317016
$890$	20.3356	0.681651
$891$	10.4046	0.348568
$892$	16.6228	0.556573
$893$	3.75984	0.125818
$894$	63.7337	2.13157
$895$	19.8610	0.663880
$896$	8.14447	0.272088
$897$	21.1555	0.706361
$898$	52.6173	1.75586
$899$	1.03993	0.0346838
$900$	1.63281	0.0544268
$901$	−25.0617	−0.834925
$902$	1.51391	0.0504078
$903$	−1.57475	−0.0524045
$904$	43.8988	1.46005
$905$	−16.4980	−0.548412
$906$	−12.2242	−0.406121
$907$	47.1000	1.56393	0.781965	−	0.623322i	$-0.214217\pi$
$907$	47.1000	1.56393	0.781965	+	0.623322i	$0.214217\pi$
$908$	0.591042	0.0196144
$909$	16.0327	0.531770
$910$	−3.07887	−0.102063
$911$	−11.0100	−0.364779	−0.182389	−	0.983226i	$-0.558383\pi$
$911$	−11.0100	−0.364779	−0.182389	+	0.983226i	$0.558383\pi$
$912$	73.9997	2.45038
$913$	6.24520	0.206686
$914$	34.3587	1.13649
$915$	13.8414	0.457583
$916$	−7.02663	−0.232166
$917$	−10.0845	−0.333018
$918$	10.9339	0.360874
$919$	23.2245	0.766105	0.383052	−	0.923727i	$-0.374873\pi$
$919$	23.2245	0.766105	0.383052	+	0.923727i	$0.374873\pi$
$920$	−6.29657	−0.207592
$921$	9.81055	0.323269
$922$	−59.1067	−1.94658
$923$	−14.5857	−0.480096
$924$	0.945549	0.0311063
$925$	−7.71523	−0.253675
$926$	14.3745	0.472376
$927$	0.209245	0.00687250
$928$	14.4068	0.472926
$929$	−45.4514	−1.49121	−0.745606	−	0.666387i	$-0.767840\pi$
$929$	−45.4514	−1.49121	−0.745606	+	0.666387i	$0.767840\pi$
$930$	−1.00866	−0.0330753
$931$	43.1108	1.41290
$932$	−13.7337	−0.449861
$933$	−36.2195	−1.18577
$934$	29.7693	0.974081
$935$	−4.94659	−0.161771
$936$	−16.4013	−0.536094
$937$	42.2522	1.38032	0.690160	−	0.723657i	$-0.257540\pi$
$937$	42.2522	1.38032	0.690160	+	0.723657i	$0.257540\pi$
$938$	−11.9439	−0.389981
$939$	−5.68389	−0.185487
$940$	−0.390683	−0.0127427
$941$	37.2558	1.21450	0.607251	−	0.794510i	$-0.292272\pi$
$941$	37.2558	1.21450	0.607251	+	0.794510i	$0.292272\pi$
$942$	−6.76652	−0.220465
$943$	−2.68933	−0.0875765
$944$	−0.368793	−0.0120032
$945$	0.813406	0.0264601
$946$	1.83822	0.0597657
$947$	−39.7561	−1.29190	−0.645949	−	0.763380i	$-0.723538\pi$
$947$	−39.7561	−1.29190	−0.645949	+	0.763380i	$0.723538\pi$
$948$	−16.1893	−0.525803
$949$	−3.12789	−0.101536
$950$	10.6222	0.344629
$951$	40.5959	1.31641
$952$	−6.45215	−0.209116
$953$	28.2590	0.915400	0.457700	−	0.889107i	$-0.348673\pi$
$953$	28.2590	0.915400	0.457700	+	0.889107i	$0.348673\pi$
$954$	20.0480	0.649078
$955$	−21.1652	−0.684889
$956$	12.8362	0.415151
$957$	−9.13832	−0.295400
$958$	33.1604	1.07136
$959$	5.89653	0.190409
$960$	8.81396	0.284469
$961$	−30.9298	−0.997736
$962$	−39.4686	−1.27252
$963$	30.4169	0.980172
$964$	−7.78745	−0.250817
$965$	27.5185	0.885853
$966$	−6.65749	−0.214201
$967$	17.0994	0.549879	0.274939	−	0.961462i	$-0.411342\pi$
$967$	17.0994	0.549879	0.274939	+	0.961462i	$0.411342\pi$
$968$	2.16726	0.0696583
$969$	−74.7906	−2.40262
$970$	25.8876	0.831202
$971$	−51.2389	−1.64433	−0.822167	−	0.569247i	$-0.807235\pi$
$971$	−51.2389	−1.64433	−0.822167	+	0.569247i	$0.807235\pi$
$972$	−13.6101	−0.436545
$973$	3.13451	0.100488
$974$	−36.4737	−1.16869
$975$	−7.28164	−0.233199
$976$	−29.1000	−0.931467
$977$	−13.3767	−0.427959	−0.213979	−	0.976838i	$-0.568643\pi$
$977$	−13.3767	−0.427959	−0.213979	+	0.976838i	$0.568643\pi$
$978$	82.7536	2.64617
$979$	12.4339	0.397388
$980$	−4.47962	−0.143096
$981$	−15.1443	−0.483520
$982$	−29.9821	−0.956769
$983$	−13.2836	−0.423682	−0.211841	−	0.977304i	$-0.567946\pi$
$983$	−13.2836	−0.423682	−0.211841	+	0.977304i	$0.567946\pi$
$984$	4.67022	0.148881
$985$	−15.6625	−0.499050
$986$	−31.7575	−1.01136
$987$	0.811096	0.0258175
$988$	13.7099	0.436169
$989$	−3.26543	−0.103835
$990$	3.95701	0.125762
$991$	23.6750	0.752060	0.376030	−	0.926608i	$-0.377289\pi$
$991$	23.6750	0.752060	0.376030	+	0.926608i	$0.377289\pi$
$992$	0.972289	0.0308702
$993$	54.0469	1.71513
$994$	4.59003	0.145587
$995$	24.3935	0.773327
$996$	−9.81166	−0.310894
$997$	51.8821	1.64312	0.821561	−	0.570121i	$-0.193104\pi$
$997$	51.8821	1.64312	0.821561	+	0.570121i	$0.193104\pi$
$998$	37.3918	1.18362
$999$	10.4272	0.329902

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4015.2.a.c.1.6	✓	23

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4015.2.a.c.1.6	✓	23	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)

\(f(q)\)	\(=\)	\(q-1.63550 q^{2} +2.32797 q^{3} +0.674867 q^{4} +1.00000 q^{5} -3.80740 q^{6} -0.601850 q^{7} +2.16726 q^{8} +2.41945 q^{9} +O(q^{10})\)	\(q-1.63550 q^{2} +2.32797 q^{3} +0.674867 q^{4} +1.00000 q^{5} -3.80740 q^{6} -0.601850 q^{7} +2.16726 q^{8} +2.41945 q^{9} -1.63550 q^{10} -1.00000 q^{11} +1.57107 q^{12} -3.12789 q^{13} +0.984326 q^{14} +2.32797 q^{15} -4.89429 q^{16} +4.94659 q^{17} -3.95701 q^{18} -6.49476 q^{19} +0.674867 q^{20} -1.40109 q^{21} +1.63550 q^{22} -2.90532 q^{23} +5.04531 q^{24} +1.00000 q^{25} +5.11568 q^{26} -1.35151 q^{27} -0.406169 q^{28} +3.92545 q^{29} -3.80740 q^{30} +0.264921 q^{31} +3.67010 q^{32} -2.32797 q^{33} -8.09016 q^{34} -0.601850 q^{35} +1.63281 q^{36} -7.71523 q^{37} +10.6222 q^{38} -7.28164 q^{39} +2.16726 q^{40} +0.925656 q^{41} +2.29148 q^{42} +1.12395 q^{43} -0.674867 q^{44} +2.41945 q^{45} +4.75165 q^{46} -0.578904 q^{47} -11.3938 q^{48} -6.63778 q^{49} -1.63550 q^{50} +11.5155 q^{51} -2.11091 q^{52} -5.06645 q^{53} +2.21040 q^{54} -1.00000 q^{55} -1.30436 q^{56} -15.1196 q^{57} -6.42008 q^{58} +0.0753517 q^{59} +1.57107 q^{60} +5.94570 q^{61} -0.433279 q^{62} -1.45614 q^{63} +3.78611 q^{64} -3.12789 q^{65} +3.80740 q^{66} -12.1340 q^{67} +3.33829 q^{68} -6.76349 q^{69} +0.984326 q^{70} +4.66312 q^{71} +5.24356 q^{72} +1.00000 q^{73} +12.6183 q^{74} +2.32797 q^{75} -4.38310 q^{76} +0.601850 q^{77} +11.9091 q^{78} -10.3046 q^{79} -4.89429 q^{80} -10.4046 q^{81} -1.51391 q^{82} -6.24520 q^{83} -0.945549 q^{84} +4.94659 q^{85} -1.83822 q^{86} +9.13832 q^{87} -2.16726 q^{88} -12.4339 q^{89} -3.95701 q^{90} +1.88252 q^{91} -1.96070 q^{92} +0.616729 q^{93} +0.946799 q^{94} -6.49476 q^{95} +8.54390 q^{96} -15.8286 q^{97} +10.8561 q^{98} -2.41945 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 23 q - 3 q^{2} - 5 q^{3} + 15 q^{4} + 23 q^{5} - 5 q^{6} - 6 q^{8} + 8 q^{9}+O(q^{10}) \) 23 * q - 3 * q^2 - 5 * q^3 + 15 * q^4 + 23 * q^5 - 5 * q^6 - 6 * q^8 + 8 * q^9	\( 23 q - 3 q^{2} - 5 q^{3} + 15 q^{4} + 23 q^{5} - 5 q^{6} - 6 q^{8} + 8 q^{9} - 3 q^{10} - 23 q^{11} - 18 q^{12} - 5 q^{13} - 17 q^{14} - 5 q^{15} - q^{16} - 36 q^{17} + q^{18} + 6 q^{19} + 15 q^{20} - 18 q^{21} + 3 q^{22} - 14 q^{23} - 7 q^{24} + 23 q^{25} - 21 q^{26} - 29 q^{27} + 28 q^{28} - 36 q^{29} - 5 q^{30} - 16 q^{31} - 5 q^{32} + 5 q^{33} - 28 q^{34} - 14 q^{36} - 24 q^{37} + q^{38} - 10 q^{39} - 6 q^{40} - 36 q^{41} - 5 q^{42} + 17 q^{43} - 15 q^{44} + 8 q^{45} - 25 q^{46} - 21 q^{47} - 17 q^{48} - 27 q^{49} - 3 q^{50} + 19 q^{51} - 21 q^{52} - 28 q^{53} - 15 q^{54} - 23 q^{55} - 46 q^{56} - 23 q^{57} - 16 q^{58} - 61 q^{59} - 18 q^{60} - 17 q^{61} - 22 q^{62} - 9 q^{63} - 18 q^{64} - 5 q^{65} + 5 q^{66} + 2 q^{67} - 39 q^{68} - 36 q^{69} - 17 q^{70} - 50 q^{71} + 15 q^{72} + 23 q^{73} + 17 q^{74} - 5 q^{75} - 21 q^{76} + 49 q^{78} - 18 q^{79} - q^{80} - 57 q^{81} + 14 q^{82} - 20 q^{83} - 38 q^{84} - 36 q^{85} - 45 q^{86} + 37 q^{87} + 6 q^{88} - 93 q^{89} + q^{90} - 42 q^{91} - 39 q^{92} - 18 q^{93} - 6 q^{94} + 6 q^{95} - 9 q^{96} - 31 q^{97} - 31 q^{98} - 8 q^{99}+O(q^{100}) \) 23 * q - 3 * q^2 - 5 * q^3 + 15 * q^4 + 23 * q^5 - 5 * q^6 - 6 * q^8 + 8 * q^9 - 3 * q^10 - 23 * q^11 - 18 * q^12 - 5 * q^13 - 17 * q^14 - 5 * q^15 - q^16 - 36 * q^17 + q^18 + 6 * q^19 + 15 * q^20 - 18 * q^21 + 3 * q^22 - 14 * q^23 - 7 * q^24 + 23 * q^25 - 21 * q^26 - 29 * q^27 + 28 * q^28 - 36 * q^29 - 5 * q^30 - 16 * q^31 - 5 * q^32 + 5 * q^33 - 28 * q^34 - 14 * q^36 - 24 * q^37 + q^38 - 10 * q^39 - 6 * q^40 - 36 * q^41 - 5 * q^42 + 17 * q^43 - 15 * q^44 + 8 * q^45 - 25 * q^46 - 21 * q^47 - 17 * q^48 - 27 * q^49 - 3 * q^50 + 19 * q^51 - 21 * q^52 - 28 * q^53 - 15 * q^54 - 23 * q^55 - 46 * q^56 - 23 * q^57 - 16 * q^58 - 61 * q^59 - 18 * q^60 - 17 * q^61 - 22 * q^62 - 9 * q^63 - 18 * q^64 - 5 * q^65 + 5 * q^66 + 2 * q^67 - 39 * q^68 - 36 * q^69 - 17 * q^70 - 50 * q^71 + 15 * q^72 + 23 * q^73 + 17 * q^74 - 5 * q^75 - 21 * q^76 + 49 * q^78 - 18 * q^79 - q^80 - 57 * q^81 + 14 * q^82 - 20 * q^83 - 38 * q^84 - 36 * q^85 - 45 * q^86 + 37 * q^87 + 6 * q^88 - 93 * q^89 + q^90 - 42 * q^91 - 39 * q^92 - 18 * q^93 - 6 * q^94 + 6 * q^95 - 9 * q^96 - 31 * q^97 - 31 * q^98 - 8 * q^99

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