LMFDB - Embedded newform 4033.2.a.f.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4033, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4033 = 37 \cdot 109 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4033.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$32.2036671352$
Analytic rank:	$0$
Dimension:	$85$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	4033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.49324 q^{2} -1.70202 q^{3} +4.21624 q^{4} -1.58478 q^{5} +4.24353 q^{6} +2.99306 q^{7} -5.52560 q^{8} -0.103143 q^{9} +O(q^{10})$	\(q-2.49324 q^{2} -1.70202 q^{3} +4.21624 q^{4} -1.58478 q^{5} +4.24353 q^{6} +2.99306 q^{7} -5.52560 q^{8} -0.103143 q^{9} +3.95124 q^{10} +1.39137 q^{11} -7.17610 q^{12} -6.59651 q^{13} -7.46240 q^{14} +2.69733 q^{15} +5.34417 q^{16} +4.23076 q^{17} +0.257160 q^{18} -3.71775 q^{19} -6.68182 q^{20} -5.09423 q^{21} -3.46902 q^{22} -5.72353 q^{23} +9.40466 q^{24} -2.48846 q^{25} +16.4467 q^{26} +5.28160 q^{27} +12.6194 q^{28} -2.80076 q^{29} -6.72508 q^{30} -6.13831 q^{31} -2.27308 q^{32} -2.36814 q^{33} -10.5483 q^{34} -4.74335 q^{35} -0.434875 q^{36} +1.00000 q^{37} +9.26925 q^{38} +11.2274 q^{39} +8.75688 q^{40} -0.116706 q^{41} +12.7011 q^{42} -9.64444 q^{43} +5.86635 q^{44} +0.163459 q^{45} +14.2701 q^{46} +1.53133 q^{47} -9.09586 q^{48} +1.95838 q^{49} +6.20432 q^{50} -7.20082 q^{51} -27.8124 q^{52} +0.281857 q^{53} -13.1683 q^{54} -2.20502 q^{55} -16.5384 q^{56} +6.32768 q^{57} +6.98297 q^{58} +8.00795 q^{59} +11.3726 q^{60} -8.40487 q^{61} +15.3043 q^{62} -0.308713 q^{63} -5.02100 q^{64} +10.4540 q^{65} +5.90433 q^{66} +12.5217 q^{67} +17.8379 q^{68} +9.74154 q^{69} +11.8263 q^{70} +7.06143 q^{71} +0.569927 q^{72} +6.50223 q^{73} -2.49324 q^{74} +4.23540 q^{75} -15.6749 q^{76} +4.16445 q^{77} -27.9925 q^{78} +1.04239 q^{79} -8.46935 q^{80} -8.67993 q^{81} +0.290976 q^{82} +1.37143 q^{83} -21.4785 q^{84} -6.70484 q^{85} +24.0459 q^{86} +4.76694 q^{87} -7.68817 q^{88} -4.27966 q^{89} -0.407543 q^{90} -19.7437 q^{91} -24.1318 q^{92} +10.4475 q^{93} -3.81796 q^{94} +5.89184 q^{95} +3.86882 q^{96} +6.81532 q^{97} -4.88272 q^{98} -0.143510 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 85 q + 11 q^{2} + 21 q^{3} + 93 q^{4} + 12 q^{5} + 4 q^{6} + 17 q^{7} + 30 q^{8} + 98 q^{9}+O(q^{10}) $ 85 * q + 11 * q^2 + 21 * q^3 + 93 * q^4 + 12 * q^5 + 4 * q^6 + 17 * q^7 + 30 * q^8 + 98 * q^9	\( 85 q + 11 q^{2} + 21 q^{3} + 93 q^{4} + 12 q^{5} + 4 q^{6} + 17 q^{7} + 30 q^{8} + 98 q^{9} + 9 q^{10} + 37 q^{11} + 44 q^{12} + 14 q^{13} + 26 q^{14} + 27 q^{15} + 85 q^{16} + 34 q^{17} + 3 q^{18} + 15 q^{19} + 15 q^{20} + 17 q^{21} + q^{22} + 72 q^{23} + 15 q^{24} + 85 q^{25} + 33 q^{26} + 69 q^{27} + 7 q^{28} + 19 q^{29} - 9 q^{30} + 23 q^{31} + 51 q^{32} + 32 q^{33} + 49 q^{34} + 40 q^{35} + 121 q^{36} + 85 q^{37} + 84 q^{38} + 39 q^{39} + 22 q^{40} + 55 q^{41} - 28 q^{42} + 78 q^{44} + 28 q^{45} + 17 q^{46} + 184 q^{47} + 97 q^{48} + 88 q^{49} + 26 q^{50} + 27 q^{51} + 73 q^{52} + 64 q^{53} + 31 q^{54} + 39 q^{55} + 68 q^{56} - 33 q^{57} + 28 q^{58} + 60 q^{59} - 22 q^{60} + 7 q^{61} + 70 q^{62} + 28 q^{63} + 102 q^{64} + 17 q^{65} - 15 q^{66} + 82 q^{67} + 92 q^{68} + 22 q^{69} - 41 q^{70} + 113 q^{71} - 19 q^{73} + 11 q^{74} + 45 q^{75} + 34 q^{76} + 64 q^{77} + 29 q^{78} + 23 q^{79} + 54 q^{80} + 149 q^{81} + 4 q^{82} + 100 q^{83} - 49 q^{84} - 5 q^{85} - 24 q^{86} + 65 q^{87} + 14 q^{88} + 84 q^{89} - 21 q^{90} + 32 q^{91} + 95 q^{92} + 19 q^{93} - 47 q^{94} + 102 q^{95} + 29 q^{96} + 7 q^{97} + 26 q^{98} + 107 q^{99}+O(q^{100}) \) 85 * q + 11 * q^2 + 21 * q^3 + 93 * q^4 + 12 * q^5 + 4 * q^6 + 17 * q^7 + 30 * q^8 + 98 * q^9 + 9 * q^10 + 37 * q^11 + 44 * q^12 + 14 * q^13 + 26 * q^14 + 27 * q^15 + 85 * q^16 + 34 * q^17 + 3 * q^18 + 15 * q^19 + 15 * q^20 + 17 * q^21 + q^22 + 72 * q^23 + 15 * q^24 + 85 * q^25 + 33 * q^26 + 69 * q^27 + 7 * q^28 + 19 * q^29 - 9 * q^30 + 23 * q^31 + 51 * q^32 + 32 * q^33 + 49 * q^34 + 40 * q^35 + 121 * q^36 + 85 * q^37 + 84 * q^38 + 39 * q^39 + 22 * q^40 + 55 * q^41 - 28 * q^42 + 78 * q^44 + 28 * q^45 + 17 * q^46 + 184 * q^47 + 97 * q^48 + 88 * q^49 + 26 * q^50 + 27 * q^51 + 73 * q^52 + 64 * q^53 + 31 * q^54 + 39 * q^55 + 68 * q^56 - 33 * q^57 + 28 * q^58 + 60 * q^59 - 22 * q^60 + 7 * q^61 + 70 * q^62 + 28 * q^63 + 102 * q^64 + 17 * q^65 - 15 * q^66 + 82 * q^67 + 92 * q^68 + 22 * q^69 - 41 * q^70 + 113 * q^71 - 19 * q^73 + 11 * q^74 + 45 * q^75 + 34 * q^76 + 64 * q^77 + 29 * q^78 + 23 * q^79 + 54 * q^80 + 149 * q^81 + 4 * q^82 + 100 * q^83 - 49 * q^84 - 5 * q^85 - 24 * q^86 + 65 * q^87 + 14 * q^88 + 84 * q^89 - 21 * q^90 + 32 * q^91 + 95 * q^92 + 19 * q^93 - 47 * q^94 + 102 * q^95 + 29 * q^96 + 7 * q^97 + 26 * q^98 + 107 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.49324	−1.76299	−0.881493	−	0.472198i	$-0.843461\pi$
$2$	−2.49324	−1.76299	−0.881493	+	0.472198i	$0.843461\pi$
$3$	−1.70202	−0.982659	−0.491330	−	0.870974i	$-0.663489\pi$
$3$	−1.70202	−0.982659	−0.491330	+	0.870974i	$0.663489\pi$
$4$	4.21624	2.10812
$5$	−1.58478	−0.708737	−0.354368	−	0.935106i	$-0.615304\pi$
$5$	−1.58478	−0.708737	−0.354368	+	0.935106i	$0.615304\pi$
$6$	4.24353	1.73241
$7$	2.99306	1.13127	0.565634	−	0.824656i	$-0.308631\pi$
$7$	2.99306	1.13127	0.565634	+	0.824656i	$0.308631\pi$
$8$	−5.52560	−1.95360
$9$	−0.103143	−0.0343810
$10$	3.95124	1.24949
$11$	1.39137	0.419514	0.209757	−	0.977754i	$-0.432733\pi$
$11$	1.39137	0.419514	0.209757	+	0.977754i	$0.432733\pi$
$12$	−7.17610	−2.07156
$13$	−6.59651	−1.82954	−0.914772	−	0.403972i	$-0.867629\pi$
$13$	−6.59651	−1.82954	−0.914772	+	0.403972i	$0.867629\pi$
$14$	−7.46240	−1.99441
$15$	2.69733	0.696447
$16$	5.34417	1.33604
$17$	4.23076	1.02611	0.513055	−	0.858356i	$-0.328514\pi$
$17$	4.23076	1.02611	0.513055	+	0.858356i	$0.328514\pi$
$18$	0.257160	0.0606132
$19$	−3.71775	−0.852911	−0.426456	−	0.904508i	$-0.640238\pi$
$19$	−3.71775	−0.852911	−0.426456	+	0.904508i	$0.640238\pi$
$20$	−6.68182	−1.49410
$21$	−5.09423	−1.11165
$22$	−3.46902	−0.739598
$23$	−5.72353	−1.19344	−0.596719	−	0.802450i	$-0.703529\pi$
$23$	−5.72353	−1.19344	−0.596719	+	0.802450i	$0.703529\pi$
$24$	9.40466	1.91972
$25$	−2.48846	−0.497692
$26$	16.4467	3.22546
$27$	5.28160	1.01644
$28$	12.6194	2.38485
$29$	−2.80076	−0.520088	−0.260044	−	0.965597i	$-0.583737\pi$
$29$	−2.80076	−0.520088	−0.260044	+	0.965597i	$0.583737\pi$
$30$	−6.72508	−1.22783
$31$	−6.13831	−1.10247	−0.551236	−	0.834349i	$-0.685844\pi$
$31$	−6.13831	−1.10247	−0.551236	+	0.834349i	$0.685844\pi$
$32$	−2.27308	−0.401828
$33$	−2.36814	−0.412240
$34$	−10.5483	−1.80902
$35$	−4.74335	−0.801772
$36$	−0.434875	−0.0724792
$37$	1.00000	0.164399
$37$	1.00000	0.164399
$38$	9.26925	1.50367
$39$	11.2274	1.79782
$40$	8.75688	1.38458
$41$	−0.116706	−0.0182265	−0.00911323	−	0.999958i	$-0.502901\pi$
$41$	−0.116706	−0.0182265	−0.00911323	+	0.999958i	$0.502901\pi$
$42$	12.7011	1.95983
$43$	−9.64444	−1.47076	−0.735381	−	0.677654i	$-0.762997\pi$
$43$	−9.64444	−1.47076	−0.735381	+	0.677654i	$0.762997\pi$
$44$	5.86635	0.884386
$45$	0.163459	0.0243671
$46$	14.2701	2.10401
$47$	1.53133	0.223367	0.111683	−	0.993744i	$-0.464376\pi$
$47$	1.53133	0.223367	0.111683	+	0.993744i	$0.464376\pi$
$48$	−9.09586	−1.31287
$49$	1.95838	0.279769
$50$	6.20432	0.877424
$51$	−7.20082	−1.00832
$52$	−27.8124	−3.85689
$53$	0.281857	0.0387160	0.0193580	−	0.999813i	$-0.493838\pi$
$53$	0.281857	0.0387160	0.0193580	+	0.999813i	$0.493838\pi$
$54$	−13.1683	−1.79198
$55$	−2.20502	−0.297325
$56$	−16.5384	−2.21004
$57$	6.32768	0.838121
$58$	6.98297	0.916908
$59$	8.00795	1.04255	0.521273	−	0.853390i	$-0.325457\pi$
$59$	8.00795	1.04255	0.521273	+	0.853390i	$0.325457\pi$
$60$	11.3726	1.46819
$61$	−8.40487	−1.07613	−0.538067	−	0.842902i	$-0.680845\pi$
$61$	−8.40487	−1.07613	−0.538067	+	0.842902i	$0.680845\pi$
$62$	15.3043	1.94364
$63$	−0.308713	−0.0388942
$64$	−5.02100	−0.627626
$65$	10.4540	1.29666
$66$	5.90433	0.726772
$67$	12.5217	1.52977	0.764884	−	0.644168i	$-0.222796\pi$
$67$	12.5217	1.52977	0.764884	+	0.644168i	$0.222796\pi$
$68$	17.8379	2.16316
$69$	9.74154	1.17274
$70$	11.8263	1.41351
$71$	7.06143	0.838037	0.419019	−	0.907978i	$-0.362374\pi$
$71$	7.06143	0.838037	0.419019	+	0.907978i	$0.362374\pi$
$72$	0.569927	0.0671666
$73$	6.50223	0.761029	0.380514	−	0.924775i	$-0.375747\pi$
$73$	6.50223	0.761029	0.380514	+	0.924775i	$0.375747\pi$
$74$	−2.49324	−0.289833
$75$	4.23540	0.489062
$76$	−15.6749	−1.79804
$77$	4.16445	0.474584
$78$	−27.9925	−3.16953
$79$	1.04239	0.117278	0.0586388	−	0.998279i	$-0.481324\pi$
$79$	1.04239	0.117278	0.0586388	+	0.998279i	$0.481324\pi$
$80$	−8.46935	−0.946902
$81$	−8.67993	−0.964437
$82$	0.290976	0.0321330
$83$	1.37143	0.150533	0.0752667	−	0.997163i	$-0.476019\pi$
$83$	1.37143	0.150533	0.0752667	+	0.997163i	$0.476019\pi$
$84$	−21.4785	−2.34349
$85$	−6.70484	−0.727242
$86$	24.0459	2.59293
$87$	4.76694	0.511070
$88$	−7.68817	−0.819561
$89$	−4.27966	−0.453643	−0.226821	−	0.973936i	$-0.572833\pi$
$89$	−4.27966	−0.453643	−0.226821	+	0.973936i	$0.572833\pi$
$90$	−0.407543	−0.0429588
$91$	−19.7437	−2.06971
$92$	−24.1318	−2.51591
$93$	10.4475	1.08335
$94$	−3.81796	−0.393793
$95$	5.89184	0.604490
$96$	3.86882	0.394860
$97$	6.81532	0.691990	0.345995	−	0.938236i	$-0.387541\pi$
$97$	6.81532	0.691990	0.345995	+	0.938236i	$0.387541\pi$
$98$	−4.88272	−0.493229
$99$	−0.143510	−0.0144233
$100$	−10.4919	−1.04919
$101$	−6.41017	−0.637836	−0.318918	−	0.947782i	$-0.603319\pi$
$101$	−6.41017	−0.637836	−0.318918	+	0.947782i	$0.603319\pi$
$102$	17.9534	1.77765
$103$	−8.92590	−0.879495	−0.439747	−	0.898122i	$-0.644932\pi$
$103$	−8.92590	−0.879495	−0.439747	+	0.898122i	$0.644932\pi$
$104$	36.4497	3.57419
$105$	8.07325	0.787869
$106$	−0.702736	−0.0682557
$107$	−13.3330	−1.28895	−0.644477	−	0.764624i	$-0.722925\pi$
$107$	−13.3330	−1.28895	−0.644477	+	0.764624i	$0.722925\pi$
$108$	22.2685	2.14278
$109$	−1.00000	−0.0957826
$109$	−1.00000	−0.0957826
$110$	5.49765	0.524180
$111$	−1.70202	−0.161548
$112$	15.9954	1.51142
$113$	6.07191	0.571197	0.285599	−	0.958349i	$-0.407808\pi$
$113$	6.07191	0.571197	0.285599	+	0.958349i	$0.407808\pi$
$114$	−15.7764	−1.47760
$115$	9.07056	0.845834
$116$	−11.8087	−1.09641
$117$	0.680384	0.0629015
$118$	−19.9657	−1.83799
$119$	12.6629	1.16081
$120$	−14.9044	−1.36058
$121$	−9.06408	−0.824008
$122$	20.9553	1.89721
$123$	0.198636	0.0179104
$124$	−25.8805	−2.32414
$125$	11.8676	1.06147
$126$	0.769695	0.0685699
$127$	−15.1401	−1.34347	−0.671733	−	0.740793i	$-0.734450\pi$
$127$	−15.1401	−1.34347	−0.671733	+	0.740793i	$0.734450\pi$
$128$	17.0647	1.50832
$129$	16.4150	1.44526
$130$	−26.0644	−2.28600
$131$	−14.9529	−1.30644	−0.653219	−	0.757169i	$-0.726582\pi$
$131$	−14.9529	−1.30644	−0.653219	+	0.757169i	$0.726582\pi$
$132$	−9.98462	−0.869050
$133$	−11.1274	−0.964872
$134$	−31.2196	−2.69696
$135$	−8.37019	−0.720391
$136$	−23.3775	−2.00460
$137$	14.7596	1.26100	0.630501	−	0.776189i	$-0.282850\pi$
$137$	14.7596	1.26100	0.630501	+	0.776189i	$0.282850\pi$
$138$	−24.2880	−2.06753
$139$	−10.3731	−0.879835	−0.439917	−	0.898038i	$-0.644992\pi$
$139$	−10.3731	−0.879835	−0.439917	+	0.898038i	$0.644992\pi$
$140$	−19.9991	−1.69023
$141$	−2.60634	−0.219494
$142$	−17.6058	−1.47745
$143$	−9.17820	−0.767520
$144$	−0.551214	−0.0459345
$145$	4.43860	0.368606
$146$	−16.2116	−1.34168
$147$	−3.33320	−0.274918
$148$	4.21624	0.346572
$149$	4.59761	0.376651	0.188326	−	0.982107i	$-0.439694\pi$
$149$	4.59761	0.376651	0.188326	+	0.982107i	$0.439694\pi$
$150$	−10.5599	−0.862209
$151$	0.152984	0.0124497	0.00622484	−	0.999981i	$-0.498019\pi$
$151$	0.152984	0.0124497	0.00622484	+	0.999981i	$0.498019\pi$
$152$	20.5428	1.66624
$153$	−0.436374	−0.0352787
$154$	−10.3830	−0.836684
$155$	9.72789	0.781363
$156$	47.3372	3.79001
$157$	−3.31183	−0.264313	−0.132156	−	0.991229i	$-0.542190\pi$
$157$	−3.31183	−0.264313	−0.132156	+	0.991229i	$0.542190\pi$
$158$	−2.59892	−0.206759
$159$	−0.479724	−0.0380446
$160$	3.60234	0.284790
$161$	−17.1308	−1.35010
$162$	21.6411	1.70029
$163$	−15.4073	−1.20679	−0.603394	−	0.797443i	$-0.706186\pi$
$163$	−15.4073	−1.20679	−0.603394	+	0.797443i	$0.706186\pi$
$164$	−0.492061	−0.0384235
$165$	3.75298	0.292169
$166$	−3.41929	−0.265388
$167$	−1.62391	−0.125662	−0.0628312	−	0.998024i	$-0.520013\pi$
$167$	−1.62391	−0.125662	−0.0628312	+	0.998024i	$0.520013\pi$
$168$	28.1487	2.17172
$169$	30.5140	2.34723
$170$	16.7168	1.28212
$171$	0.383461	0.0293240
$172$	−40.6632	−3.10054
$173$	9.00680	0.684774	0.342387	−	0.939559i	$-0.388765\pi$
$173$	9.00680	0.684774	0.342387	+	0.939559i	$0.388765\pi$
$174$	−11.8851	−0.901008
$175$	−7.44810	−0.563024
$176$	7.43573	0.560489
$177$	−13.6297	−1.02447
$178$	10.6702	0.799766
$179$	−21.0962	−1.57681	−0.788403	−	0.615159i	$-0.789092\pi$
$179$	−21.0962	−1.57681	−0.788403	+	0.615159i	$0.789092\pi$
$180$	0.689183	0.0513687
$181$	9.68809	0.720110	0.360055	−	0.932931i	$-0.382758\pi$
$181$	9.68809	0.720110	0.360055	+	0.932931i	$0.382758\pi$
$182$	49.2258	3.64886
$183$	14.3052	1.05747
$184$	31.6259	2.33150
$185$	−1.58478	−0.116516
$186$	−26.0481	−1.90994
$187$	5.88656	0.430468
$188$	6.45643	0.470884
$189$	15.8081	1.14987
$190$	−14.6898	−1.06571
$191$	−0.385765	−0.0279130	−0.0139565	−	0.999903i	$-0.504443\pi$
$191$	−0.385765	−0.0279130	−0.0139565	+	0.999903i	$0.504443\pi$
$192$	8.54583	0.616742
$193$	17.5219	1.26125	0.630625	−	0.776088i	$-0.282799\pi$
$193$	17.5219	1.26125	0.630625	+	0.776088i	$0.282799\pi$
$194$	−16.9922	−1.21997
$195$	−17.7929	−1.27418
$196$	8.25701	0.589786
$197$	−7.33608	−0.522674	−0.261337	−	0.965248i	$-0.584163\pi$
$197$	−7.33608	−0.522674	−0.261337	+	0.965248i	$0.584163\pi$
$198$	0.357805	0.0254281
$199$	26.9955	1.91366	0.956831	−	0.290646i	$-0.0938703\pi$
$199$	26.9955	1.91366	0.956831	+	0.290646i	$0.0938703\pi$
$200$	13.7502	0.972289
$201$	−21.3121	−1.50324
$202$	15.9821	1.12450
$203$	−8.38284	−0.588360
$204$	−30.3604	−2.12565
$205$	0.184954	0.0129178
$206$	22.2544	1.55054
$207$	0.590342	0.0410316
$208$	−35.2529	−2.44435
$209$	−5.17278	−0.357809
$210$	−20.1285	−1.38900
$211$	6.40928	0.441233	0.220617	−	0.975361i	$-0.429193\pi$
$211$	6.40928	0.441233	0.220617	+	0.975361i	$0.429193\pi$
$212$	1.18837	0.0816179
$213$	−12.0187	−0.823505
$214$	33.2424	2.27241
$215$	15.2843	1.04238
$216$	−29.1840	−1.98572
$217$	−18.3723	−1.24719
$218$	2.49324	0.168863
$219$	−11.0669	−0.747832
$220$	−9.29690	−0.626797
$221$	−27.9083	−1.87731
$222$	4.24353	0.284807
$223$	−12.6122	−0.844578	−0.422289	−	0.906461i	$-0.638773\pi$
$223$	−12.6122	−0.844578	−0.422289	+	0.906461i	$0.638773\pi$
$224$	−6.80346	−0.454575
$225$	0.256667	0.0171112
$226$	−15.1387	−1.00701
$227$	3.48278	0.231160	0.115580	−	0.993298i	$-0.463127\pi$
$227$	3.48278	0.231160	0.115580	+	0.993298i	$0.463127\pi$
$228$	26.6790	1.76686
$229$	−22.7805	−1.50538	−0.752688	−	0.658378i	$-0.771243\pi$
$229$	−22.7805	−1.50538	−0.752688	+	0.658378i	$0.771243\pi$
$230$	−22.6151	−1.49119
$231$	−7.08797	−0.466354
$232$	15.4759	1.01604
$233$	−27.6590	−1.81200	−0.906002	−	0.423273i	$-0.860881\pi$
$233$	−27.6590	−1.81200	−0.906002	+	0.423273i	$0.860881\pi$
$234$	−1.69636	−0.110895
$235$	−2.42682	−0.158308
$236$	33.7634	2.19781
$237$	−1.77416	−0.115244
$238$	−31.5716	−2.04649
$239$	−0.479899	−0.0310421	−0.0155210	−	0.999880i	$-0.504941\pi$
$239$	−0.479899	−0.0310421	−0.0155210	+	0.999880i	$0.504941\pi$
$240$	14.4150	0.930482
$241$	−19.9683	−1.28627	−0.643137	−	0.765751i	$-0.722367\pi$
$241$	−19.9683	−1.28627	−0.643137	+	0.765751i	$0.722367\pi$
$242$	22.5989	1.45271
$243$	−1.07141	−0.0687312
$244$	−35.4369	−2.26862
$245$	−3.10362	−0.198283
$246$	−0.495246	−0.0315758
$247$	24.5242	1.56044
$248$	33.9178	2.15378
$249$	−2.33419	−0.147923
$250$	−29.5887	−1.87136
$251$	−20.2738	−1.27967	−0.639836	−	0.768511i	$-0.720998\pi$
$251$	−20.2738	−1.27967	−0.639836	+	0.768511i	$0.720998\pi$
$252$	−1.30161	−0.0819935
$253$	−7.96356	−0.500665
$254$	37.7479	2.36851
$255$	11.4117	0.714631
$256$	−32.5044	−2.03153
$257$	19.2125	1.19844	0.599220	−	0.800584i	$-0.295477\pi$
$257$	19.2125	1.19844	0.599220	+	0.800584i	$0.295477\pi$
$258$	−40.9264	−2.54797
$259$	2.99306	0.185979
$260$	44.0767	2.73352
$261$	0.288879	0.0178812
$262$	37.2811	2.30323
$263$	31.2820	1.92893	0.964466	−	0.264206i	$-0.0851097\pi$
$263$	31.2820	1.92893	0.964466	+	0.264206i	$0.0851097\pi$
$264$	13.0854	0.805349
$265$	−0.446682	−0.0274394
$266$	27.7434	1.70106
$267$	7.28404	0.445776
$268$	52.7944	3.22493
$269$	2.81973	0.171922	0.0859611	−	0.996298i	$-0.472604\pi$
$269$	2.81973	0.171922	0.0859611	+	0.996298i	$0.472604\pi$
$270$	20.8689	1.27004
$271$	−5.56203	−0.337870	−0.168935	−	0.985627i	$-0.554033\pi$
$271$	−5.56203	−0.337870	−0.168935	+	0.985627i	$0.554033\pi$
$272$	22.6099	1.37093
$273$	33.6041	2.03381
$274$	−36.7993	−2.22313
$275$	−3.46237	−0.208789
$276$	41.0726	2.47228
$277$	6.07053	0.364743	0.182371	−	0.983230i	$-0.441623\pi$
$277$	6.07053	0.364743	0.182371	+	0.983230i	$0.441623\pi$
$278$	25.8626	1.55114
$279$	0.633123	0.0379041
$280$	26.2098	1.56634
$281$	−12.5779	−0.750337	−0.375168	−	0.926957i	$-0.622415\pi$
$281$	−12.5779	−0.750337	−0.375168	+	0.926957i	$0.622415\pi$
$282$	6.49823	0.386964
$283$	14.5908	0.867331	0.433665	−	0.901074i	$-0.357220\pi$
$283$	14.5908	0.867331	0.433665	+	0.901074i	$0.357220\pi$
$284$	29.7726	1.76668
$285$	−10.0280	−0.594007
$286$	22.8834	1.35313
$287$	−0.349308	−0.0206190
$288$	0.234453	0.0138152
$289$	0.899343	0.0529025
$290$	−11.0665	−0.649847
$291$	−11.5998	−0.679991
$292$	27.4149	1.60434
$293$	32.0991	1.87525	0.937623	−	0.347653i	$-0.113021\pi$
$293$	32.0991	1.87525	0.937623	+	0.347653i	$0.113021\pi$
$294$	8.31046	0.484676
$295$	−12.6909	−0.738891
$296$	−5.52560	−0.321169
$297$	7.34867	0.426413
$298$	−11.4629	−0.664031
$299$	37.7553	2.18345
$300$	17.8574	1.03100
$301$	−28.8663	−1.66383
$302$	−0.381426	−0.0219486
$303$	10.9102	0.626775
$304$	−19.8683	−1.13953
$305$	13.3199	0.762695
$306$	1.08798	0.0621959
$307$	−12.4742	−0.711941	−0.355971	−	0.934497i	$-0.615850\pi$
$307$	−12.4742	−0.711941	−0.355971	+	0.934497i	$0.615850\pi$
$308$	17.5583	1.00048
$309$	15.1920	0.864243
$310$	−24.2539	−1.37753
$311$	1.96281	0.111301	0.0556504	−	0.998450i	$-0.482277\pi$
$311$	1.96281	0.111301	0.0556504	+	0.998450i	$0.482277\pi$
$312$	−62.0379	−3.51221
$313$	2.19086	0.123835	0.0619174	−	0.998081i	$-0.480278\pi$
$313$	2.19086	0.123835	0.0619174	+	0.998081i	$0.480278\pi$
$314$	8.25717	0.465979
$315$	0.489243	0.0275657
$316$	4.39495	0.247235
$317$	28.2527	1.58683	0.793414	−	0.608683i	$-0.208302\pi$
$317$	28.2527	1.58683	0.793414	+	0.608683i	$0.208302\pi$
$318$	1.19607	0.0670721
$319$	−3.89690	−0.218185
$320$	7.95721	0.444821
$321$	22.6930	1.26660
$322$	42.7113	2.38021
$323$	−15.7289	−0.875181
$324$	−36.5966	−2.03315
$325$	16.4152	0.910549
$326$	38.4139	2.12755
$327$	1.70202	0.0941217
$328$	0.644872	0.0356071
$329$	4.58335	0.252688
$330$	−9.35708	−0.515090
$331$	31.4677	1.72962	0.864810	−	0.502100i	$-0.167439\pi$
$331$	31.4677	1.72962	0.864810	+	0.502100i	$0.167439\pi$
$332$	5.78225	0.317342
$333$	−0.103143	−0.00565220
$334$	4.04881	0.221541
$335$	−19.8442	−1.08420
$336$	−27.2244	−1.48521
$337$	8.37852	0.456407	0.228204	−	0.973613i	$-0.426715\pi$
$337$	8.37852	0.456407	0.228204	+	0.973613i	$0.426715\pi$
$338$	−76.0786	−4.13813
$339$	−10.3345	−0.561292
$340$	−28.2692	−1.53311
$341$	−8.54066	−0.462503
$342$	−0.956058	−0.0516977
$343$	−15.0898	−0.814775
$344$	53.2913	2.87327
$345$	−15.4382	−0.831166
$346$	−22.4561	−1.20725
$347$	24.9518	1.33948	0.669742	−	0.742594i	$-0.266405\pi$
$347$	24.9518	1.33948	0.669742	+	0.742594i	$0.266405\pi$
$348$	20.0985	1.07739
$349$	19.3970	1.03830	0.519148	−	0.854684i	$-0.326249\pi$
$349$	19.3970	1.03830	0.519148	+	0.854684i	$0.326249\pi$
$350$	18.5699	0.992602
$351$	−34.8401	−1.85963
$352$	−3.16270	−0.168573
$353$	−2.85115	−0.151751	−0.0758757	−	0.997117i	$-0.524175\pi$
$353$	−2.85115	−0.151751	−0.0758757	+	0.997117i	$0.524175\pi$
$354$	33.9820	1.80612
$355$	−11.1908	−0.593948
$356$	−18.0440	−0.956332
$357$	−21.5525	−1.14068
$358$	52.5979	2.77988
$359$	20.2350	1.06796	0.533982	−	0.845496i	$-0.320695\pi$
$359$	20.2350	1.06796	0.533982	+	0.845496i	$0.320695\pi$
$360$	−0.903212	−0.0476034
$361$	−5.17830	−0.272542
$362$	−24.1547	−1.26954
$363$	15.4272	0.809719
$364$	−83.2442	−4.36318
$365$	−10.3046	−0.539369
$366$	−35.6663	−1.86431
$367$	11.5117	0.600905	0.300453	−	0.953797i	$-0.402862\pi$
$367$	11.5117	0.600905	0.300453	+	0.953797i	$0.402862\pi$
$368$	−30.5875	−1.59448
$369$	0.0120374	0.000626644 0
$370$	3.95124	0.205415
$371$	0.843613	0.0437982
$372$	44.0491	2.28384
$373$	−13.9839	−0.724061	−0.362030	−	0.932166i	$-0.617916\pi$
$373$	−13.9839	−0.724061	−0.362030	+	0.932166i	$0.617916\pi$
$374$	−14.6766	−0.758909
$375$	−20.1988	−1.04306
$376$	−8.46150	−0.436368
$377$	18.4753	0.951524
$378$	−39.4134	−2.02721
$379$	−34.2917	−1.76145	−0.880724	−	0.473630i	$-0.842943\pi$
$379$	−34.2917	−1.76145	−0.880724	+	0.473630i	$0.842943\pi$
$380$	24.8414	1.27434
$381$	25.7687	1.32017
$382$	0.961804	0.0492102
$383$	35.4624	1.81205	0.906023	−	0.423228i	$-0.139103\pi$
$383$	35.4624	1.81205	0.906023	+	0.423228i	$0.139103\pi$
$384$	−29.0444	−1.48217
$385$	−6.59976	−0.336355
$386$	−43.6861	−2.22357
$387$	0.994756	0.0505663
$388$	28.7350	1.45880
$389$	2.63939	0.133822	0.0669112	−	0.997759i	$-0.478686\pi$
$389$	2.63939	0.133822	0.0669112	+	0.997759i	$0.478686\pi$
$390$	44.3620	2.24636
$391$	−24.2149	−1.22460
$392$	−10.8213	−0.546556
$393$	25.4500	1.28378
$394$	18.2906	0.921467
$395$	−1.65196	−0.0831190
$396$	−0.605073	−0.0304061
$397$	23.0194	1.15531	0.577654	−	0.816282i	$-0.303968\pi$
$397$	23.0194	1.15531	0.577654	+	0.816282i	$0.303968\pi$
$398$	−67.3062	−3.37376
$399$	18.9391	0.948140
$400$	−13.2988	−0.664938
$401$	2.88188	0.143914	0.0719571	−	0.997408i	$-0.477076\pi$
$401$	2.88188	0.143914	0.0719571	+	0.997408i	$0.477076\pi$
$402$	53.1362	2.65019
$403$	40.4914	2.01702
$404$	−27.0268	−1.34463
$405$	13.7558	0.683532
$406$	20.9004	1.03727
$407$	1.39137	0.0689677
$408$	39.7889	1.96984
$409$	0.923529	0.0456656	0.0228328	−	0.999739i	$-0.492731\pi$
$409$	0.923529	0.0456656	0.0228328	+	0.999739i	$0.492731\pi$
$410$	−0.461135	−0.0227738
$411$	−25.1211	−1.23913
$412$	−37.6337	−1.85408
$413$	23.9682	1.17940
$414$	−1.47186	−0.0723382
$415$	−2.17341	−0.106689
$416$	14.9944	0.735161
$417$	17.6552	0.864578
$418$	12.8970	0.630811
$419$	−2.34142	−0.114386	−0.0571928	−	0.998363i	$-0.518215\pi$
$419$	−2.34142	−0.114386	−0.0571928	+	0.998363i	$0.518215\pi$
$420$	34.0387	1.66092
$421$	−12.7400	−0.620912	−0.310456	−	0.950588i	$-0.600482\pi$
$421$	−12.7400	−0.620912	−0.310456	+	0.950588i	$0.600482\pi$
$422$	−15.9799	−0.777888
$423$	−0.157946	−0.00767958
$424$	−1.55743	−0.0756354
$425$	−10.5281	−0.510687
$426$	29.9654	1.45183
$427$	−25.1562	−1.21740
$428$	−56.2152	−2.71727
$429$	15.6214	0.754210
$430$	−38.1075	−1.83771
$431$	14.2316	0.685514	0.342757	−	0.939424i	$-0.388639\pi$
$431$	14.2316	0.685514	0.342757	+	0.939424i	$0.388639\pi$
$432$	28.2258	1.35801
$433$	15.5467	0.747129	0.373565	−	0.927604i	$-0.378135\pi$
$433$	15.5467	0.747129	0.373565	+	0.927604i	$0.378135\pi$
$434$	45.8065	2.19878
$435$	−7.55457	−0.362214
$436$	−4.21624	−0.201921
$437$	21.2787	1.01790
$438$	27.5924	1.31842
$439$	40.7184	1.94338	0.971692	−	0.236251i	$-0.0759187\pi$
$439$	40.7184	1.94338	0.971692	+	0.236251i	$0.0759187\pi$
$440$	12.1841	0.580853
$441$	−0.201994	−0.00961875
$442$	69.5819	3.30968
$443$	−17.4186	−0.827581	−0.413790	−	0.910372i	$-0.635795\pi$
$443$	−17.4186	−0.827581	−0.413790	+	0.910372i	$0.635795\pi$
$444$	−7.17610	−0.340563
$445$	6.78233	0.321513
$446$	31.4453	1.48898
$447$	−7.82521	−0.370120
$448$	−15.0281	−0.710013
$449$	13.0979	0.618130	0.309065	−	0.951041i	$-0.399984\pi$
$449$	13.0979	0.618130	0.309065	+	0.951041i	$0.399984\pi$
$450$	−0.639933	−0.0301667
$451$	−0.162382	−0.00764626
$452$	25.6006	1.20415
$453$	−0.260381	−0.0122338
$454$	−8.68340	−0.407532
$455$	31.2895	1.46688
$456$	−34.9642	−1.63735
$457$	15.5419	0.727017	0.363509	−	0.931591i	$-0.381579\pi$
$457$	15.5419	0.727017	0.363509	+	0.931591i	$0.381579\pi$
$458$	56.7971	2.65395
$459$	22.3452	1.04298
$460$	38.2436	1.78312
$461$	17.1571	0.799086	0.399543	−	0.916714i	$-0.369169\pi$
$461$	17.1571	0.799086	0.399543	+	0.916714i	$0.369169\pi$
$462$	17.6720	0.822175
$463$	20.5558	0.955308	0.477654	−	0.878548i	$-0.341487\pi$
$463$	20.5558	0.955308	0.477654	+	0.878548i	$0.341487\pi$
$464$	−14.9677	−0.694860
$465$	−16.5570	−0.767813
$466$	68.9606	3.19454
$467$	−1.13738	−0.0526316	−0.0263158	−	0.999654i	$-0.508378\pi$
$467$	−1.13738	−0.0526316	−0.0263158	+	0.999654i	$0.508378\pi$
$468$	2.86866	0.132604
$469$	37.4781	1.73058
$470$	6.05064	0.279095
$471$	5.63678	0.259729
$472$	−44.2487	−2.03671
$473$	−13.4190	−0.617006
$474$	4.42340	0.203173
$475$	9.25149	0.424487
$476$	53.3898	2.44712
$477$	−0.0290716	−0.00133109
$478$	1.19650	0.0547267
$479$	−2.01624	−0.0921242	−0.0460621	−	0.998939i	$-0.514667\pi$
$479$	−2.01624	−0.0921242	−0.0460621	+	0.998939i	$0.514667\pi$
$480$	−6.13124	−0.279852
$481$	−6.59651	−0.300775
$482$	49.7858	2.26768
$483$	29.1570	1.32669
$484$	−38.2163	−1.73711
$485$	−10.8008	−0.490439
$486$	2.67129	0.121172
$487$	−23.3912	−1.05996	−0.529978	−	0.848011i	$-0.677800\pi$
$487$	−23.3912	−1.05996	−0.529978	+	0.848011i	$0.677800\pi$
$488$	46.4420	2.10233
$489$	26.2234	1.18586
$490$	7.73805	0.349570
$491$	−43.5025	−1.96324	−0.981620	−	0.190844i	$-0.938878\pi$
$491$	−43.5025	−1.96324	−0.981620	+	0.190844i	$0.938878\pi$
$492$	0.837495	0.0377572
$493$	−11.8494	−0.533668
$494$	−61.1447	−2.75103
$495$	0.227433	0.0102223
$496$	−32.8041	−1.47295
$497$	21.1352	0.948045
$498$	5.81968	0.260786
$499$	−10.8956	−0.487752	−0.243876	−	0.969806i	$-0.578419\pi$
$499$	−10.8956	−0.487752	−0.243876	+	0.969806i	$0.578419\pi$
$500$	50.0366	2.23770
$501$	2.76393	0.123483
$502$	50.5475	2.25604
$503$	10.7096	0.477516	0.238758	−	0.971079i	$-0.423260\pi$
$503$	10.7096	0.477516	0.238758	+	0.971079i	$0.423260\pi$
$504$	1.70582	0.0759835
$505$	10.1587	0.452058
$506$	19.8550	0.882664
$507$	−51.9352	−2.30652
$508$	−63.8342	−2.83219
$509$	−21.4863	−0.952365	−0.476183	−	0.879346i	$-0.657980\pi$
$509$	−21.4863	−0.952365	−0.476183	+	0.879346i	$0.657980\pi$
$510$	−28.4522	−1.25988
$511$	19.4615	0.860928
$512$	46.9118	2.07323
$513$	−19.6357	−0.866937
$514$	−47.9012	−2.11283
$515$	14.1456	0.623330
$516$	69.2094	3.04677
$517$	2.13064	0.0937056
$518$	−7.46240	−0.327879
$519$	−15.3297	−0.672899
$520$	−57.7649	−2.53316
$521$	−5.53992	−0.242708	−0.121354	−	0.992609i	$-0.538724\pi$
$521$	−5.53992	−0.242708	−0.121354	+	0.992609i	$0.538724\pi$
$522$	−0.720244	−0.0315242
$523$	6.77666	0.296323	0.148161	−	0.988963i	$-0.452665\pi$
$523$	6.77666	0.296323	0.148161	+	0.988963i	$0.452665\pi$
$524$	−63.0448	−2.75413
$525$	12.6768	0.553260
$526$	−77.9936	−3.40068
$527$	−25.9697	−1.13126
$528$	−12.6557	−0.550770
$529$	9.75880	0.424296
$530$	1.11368	0.0483753
$531$	−0.825964	−0.0358438
$532$	−46.9159	−2.03406
$533$	0.769854	0.0333461
$534$	−18.1609	−0.785897
$535$	21.1300	0.913529
$536$	−69.1899	−2.98855
$537$	35.9061	1.54946
$538$	−7.03026	−0.303096
$539$	2.72484	0.117367
$540$	−35.2907	−1.51867
$541$	−0.708751	−0.0304716	−0.0152358	−	0.999884i	$-0.504850\pi$
$541$	−0.708751	−0.0304716	−0.0152358	+	0.999884i	$0.504850\pi$
$542$	13.8675	0.595659
$543$	−16.4893	−0.707623
$544$	−9.61687	−0.412320
$545$	1.58478	0.0678847
$546$	−83.7831	−3.58559
$547$	13.2615	0.567020	0.283510	−	0.958969i	$-0.408501\pi$
$547$	13.2615	0.567020	0.283510	+	0.958969i	$0.408501\pi$
$548$	62.2301	2.65834
$549$	0.866904	0.0369985
$550$	8.63252	0.368092
$551$	10.4125	0.443589
$552$	−53.8279	−2.29107
$553$	3.11992	0.132673
$554$	−15.1353	−0.643037
$555$	2.69733	0.114495
$556$	−43.7354	−1.85479
$557$	−14.6434	−0.620460	−0.310230	−	0.950662i	$-0.600406\pi$
$557$	−14.6434	−0.620460	−0.310230	+	0.950662i	$0.600406\pi$
$558$	−1.57853	−0.0668244
$559$	63.6196	2.69082
$560$	−25.3492	−1.07120
$561$	−10.0190	−0.423003
$562$	31.3598	1.32283
$563$	11.6698	0.491822	0.245911	−	0.969292i	$-0.420913\pi$
$563$	11.6698	0.491822	0.245911	+	0.969292i	$0.420913\pi$
$564$	−10.9889	−0.462718
$565$	−9.62266	−0.404828
$566$	−36.3782	−1.52909
$567$	−25.9795	−1.09104
$568$	−39.0186	−1.63719
$569$	−16.7665	−0.702888	−0.351444	−	0.936209i	$-0.614309\pi$
$569$	−16.7665	−0.702888	−0.351444	+	0.936209i	$0.614309\pi$
$570$	25.0022	1.04723
$571$	35.2518	1.47524	0.737621	−	0.675215i	$-0.235949\pi$
$571$	35.2518	1.47524	0.737621	+	0.675215i	$0.235949\pi$
$572$	−38.6974	−1.61802
$573$	0.656578	0.0274289
$574$	0.870909	0.0363510
$575$	14.2428	0.593965
$576$	0.517882	0.0215784
$577$	−18.2934	−0.761563	−0.380782	−	0.924665i	$-0.624345\pi$
$577$	−18.2934	−0.761563	−0.380782	+	0.924665i	$0.624345\pi$
$578$	−2.24228	−0.0932664
$579$	−29.8225	−1.23938
$580$	18.7142	0.777064
$581$	4.10475	0.170294
$582$	28.9210	1.19881
$583$	0.392167	0.0162419
$584$	−35.9288	−1.48674
$585$	−1.07826	−0.0445806
$586$	−80.0306	−3.30603
$587$	13.0575	0.538942	0.269471	−	0.963008i	$-0.413151\pi$
$587$	13.0575	0.538942	0.269471	+	0.963008i	$0.413151\pi$
$588$	−14.0536	−0.579559
$589$	22.8207	0.940311
$590$	31.6413	1.30265
$591$	12.4861	0.513610
$592$	5.34417	0.219644
$593$	−14.7763	−0.606788	−0.303394	−	0.952865i	$-0.598120\pi$
$593$	−14.7763	−0.606788	−0.303394	+	0.952865i	$0.598120\pi$
$594$	−18.3220	−0.751760
$595$	−20.0680	−0.822707
$596$	19.3846	0.794025
$597$	−45.9468	−1.88048
$598$	−94.1330	−3.84939
$599$	29.5946	1.20920	0.604601	−	0.796529i	$-0.293333\pi$
$599$	29.5946	1.20920	0.604601	+	0.796529i	$0.293333\pi$
$600$	−23.4031	−0.955429
$601$	16.4013	0.669023	0.334512	−	0.942392i	$-0.391429\pi$
$601$	16.4013	0.669023	0.334512	+	0.942392i	$0.391429\pi$
$602$	71.9706	2.93330
$603$	−1.29153	−0.0525950
$604$	0.645017	0.0262454
$605$	14.3646	0.584005
$606$	−27.2017	−1.10500
$607$	16.7133	0.678371	0.339186	−	0.940720i	$-0.389849\pi$
$607$	16.7133	0.678371	0.339186	+	0.940720i	$0.389849\pi$
$608$	8.45076	0.342724
$609$	14.2677	0.578157
$610$	−33.2097	−1.34462
$611$	−10.1014	−0.408659
$612$	−1.83985	−0.0743717
$613$	−17.7616	−0.717383	−0.358692	−	0.933456i	$-0.616777\pi$
$613$	−17.7616	−0.717383	−0.358692	+	0.933456i	$0.616777\pi$
$614$	31.1012	1.25514
$615$	−0.314795	−0.0126938
$616$	−23.0111	−0.927144
$617$	5.76633	0.232144	0.116072	−	0.993241i	$-0.462970\pi$
$617$	5.76633	0.232144	0.116072	+	0.993241i	$0.462970\pi$
$618$	−37.8773	−1.52365
$619$	−10.1536	−0.408108	−0.204054	−	0.978960i	$-0.565412\pi$
$619$	−10.1536	−0.408108	−0.204054	+	0.978960i	$0.565412\pi$
$620$	41.0151	1.64720
$621$	−30.2294	−1.21306
$622$	−4.89376	−0.196222
$623$	−12.8093	−0.513192
$624$	60.0009	2.40196
$625$	−6.36526	−0.254611
$626$	−5.46234	−0.218319
$627$	8.80415	0.351604
$628$	−13.9634	−0.557202
$629$	4.23076	0.168692
$630$	−1.21980	−0.0485980
$631$	36.5881	1.45655	0.728274	−	0.685286i	$-0.240323\pi$
$631$	36.5881	1.45655	0.728274	+	0.685286i	$0.240323\pi$
$632$	−5.75981	−0.229113
$633$	−10.9087	−0.433582
$634$	−70.4406	−2.79755
$635$	23.9938	0.952164
$636$	−2.02263	−0.0802025
$637$	−12.9185	−0.511850
$638$	9.71590	0.384656
$639$	−0.728337	−0.0288126
$640$	−27.0439	−1.06900
$641$	−9.14572	−0.361234	−0.180617	−	0.983553i	$-0.557809\pi$
$641$	−9.14572	−0.361234	−0.180617	+	0.983553i	$0.557809\pi$
$642$	−56.5791	−2.23300
$643$	13.4331	0.529750	0.264875	−	0.964283i	$-0.414669\pi$
$643$	13.4331	0.529750	0.264875	+	0.964283i	$0.414669\pi$
$644$	−72.2277	−2.84617
$645$	−26.0142	−1.02431
$646$	39.2160	1.54293
$647$	36.7502	1.44480	0.722399	−	0.691477i	$-0.243040\pi$
$647$	36.7502	1.44480	0.722399	+	0.691477i	$0.243040\pi$
$648$	47.9618	1.88412
$649$	11.1420	0.437363
$650$	−40.9269	−1.60528
$651$	31.2699	1.22557
$652$	−64.9606	−2.54405
$653$	−32.4830	−1.27116	−0.635579	−	0.772036i	$-0.719239\pi$
$653$	−32.4830	−1.27116	−0.635579	+	0.772036i	$0.719239\pi$
$654$	−4.24353	−0.165935
$655$	23.6971	0.925921
$656$	−0.623698	−0.0243513
$657$	−0.670660	−0.0261649
$658$	−11.4274	−0.445485
$659$	−0.877630	−0.0341876	−0.0170938	−	0.999854i	$-0.505441\pi$
$659$	−0.877630	−0.0341876	−0.0170938	+	0.999854i	$0.505441\pi$
$660$	15.8235	0.615927
$661$	43.5286	1.69307	0.846534	−	0.532335i	$-0.178685\pi$
$661$	43.5286	1.69307	0.846534	+	0.532335i	$0.178685\pi$
$662$	−78.4564	−3.04929
$663$	47.5003	1.84476
$664$	−7.57795	−0.294081
$665$	17.6346	0.683840
$666$	0.257160	0.00996475
$667$	16.0302	0.620694
$668$	−6.84681	−0.264911
$669$	21.4662	0.829932
$670$	49.4763	1.91143
$671$	−11.6943	−0.451453
$672$	11.5796	0.446693
$673$	25.2504	0.973331	0.486665	−	0.873588i	$-0.338213\pi$
$673$	25.2504	0.973331	0.486665	+	0.873588i	$0.338213\pi$
$674$	−20.8897	−0.804639
$675$	−13.1430	−0.505876
$676$	128.654	4.94823
$677$	22.6393	0.870098	0.435049	−	0.900407i	$-0.356731\pi$
$677$	22.6393	0.870098	0.435049	+	0.900407i	$0.356731\pi$
$678$	25.7663	0.989550
$679$	20.3986	0.782827
$680$	37.0483	1.42074
$681$	−5.92775	−0.227152
$682$	21.2939	0.815386
$683$	14.7272	0.563521	0.281761	−	0.959485i	$-0.409082\pi$
$683$	14.7272	0.563521	0.281761	+	0.959485i	$0.409082\pi$
$684$	1.61676	0.0618184
$685$	−23.3908	−0.893718
$686$	37.6226	1.43644
$687$	38.7727	1.47927
$688$	−51.5415	−1.96500
$689$	−1.85927	−0.0708326
$690$	38.4912	1.46533
$691$	15.2634	0.580647	0.290324	−	0.956929i	$-0.406237\pi$
$691$	15.2634	0.580647	0.290324	+	0.956929i	$0.406237\pi$
$692$	37.9748	1.44358
$693$	−0.429534	−0.0163167
$694$	−62.2108	−2.36149
$695$	16.4391	0.623571
$696$	−26.3402	−0.998423
$697$	−0.493756	−0.0187024
$698$	−48.3613	−1.83050
$699$	47.0761	1.78058
$700$	−31.4029	−1.18692
$701$	8.54458	0.322724	0.161362	−	0.986895i	$-0.448411\pi$
$701$	8.54458	0.322724	0.161362	+	0.986895i	$0.448411\pi$
$702$	86.8647	3.27850
$703$	−3.71775	−0.140218
$704$	−6.98608	−0.263298
$705$	4.13049	0.155563
$706$	7.10860	0.267536
$707$	−19.1860	−0.721564
$708$	−57.4658	−2.15970
$709$	5.11377	0.192052	0.0960258	−	0.995379i	$-0.469387\pi$
$709$	5.11377	0.192052	0.0960258	+	0.995379i	$0.469387\pi$
$710$	27.9014	1.04712
$711$	−0.107515	−0.00403212
$712$	23.6477	0.886234
$713$	35.1328	1.31573
$714$	53.7354	2.01100
$715$	14.5455	0.543969
$716$	−88.9466	−3.32409
$717$	0.816795	0.0305038
$718$	−50.4508	−1.88281
$719$	−26.8457	−1.00117	−0.500587	−	0.865686i	$-0.666882\pi$
$719$	−26.8457	−1.00117	−0.500587	+	0.865686i	$0.666882\pi$
$720$	0.873555	0.0325555
$721$	−26.7157	−0.994945
$722$	12.9107	0.480488
$723$	33.9864	1.26397
$724$	40.8473	1.51808
$725$	6.96958	0.258844
$726$	−38.4637	−1.42752
$727$	−50.0337	−1.85565	−0.927823	−	0.373021i	$-0.878322\pi$
$727$	−50.0337	−1.85565	−0.927823	+	0.373021i	$0.878322\pi$
$728$	109.096	4.04337
$729$	27.8634	1.03198
$730$	25.6919	0.950900
$731$	−40.8033	−1.50916
$732$	60.3142	2.22928
$733$	−38.2718	−1.41360	−0.706801	−	0.707412i	$-0.749862\pi$
$733$	−38.2718	−1.41360	−0.706801	+	0.707412i	$0.749862\pi$
$734$	−28.7014	−1.05939
$735$	5.28240	0.194844
$736$	13.0101	0.479557
$737$	17.4223	0.641760
$738$	−0.0300122	−0.00110476
$739$	17.5963	0.647290	0.323645	−	0.946179i	$-0.395092\pi$
$739$	17.5963	0.647290	0.323645	+	0.946179i	$0.395092\pi$
$740$	−6.68182	−0.245629
$741$	−41.7406	−1.53338
$742$	−2.10333	−0.0772156
$743$	−36.5220	−1.33986	−0.669930	−	0.742424i	$-0.733676\pi$
$743$	−36.5220	−1.33986	−0.669930	+	0.742424i	$0.733676\pi$
$744$	−57.7287	−2.11644
$745$	−7.28622	−0.266947
$746$	34.8653	1.27651
$747$	−0.141453	−0.00517549
$748$	24.8191	0.907477
$749$	−39.9065	−1.45815
$750$	50.3605	1.83890
$751$	38.0589	1.38879	0.694395	−	0.719594i	$-0.255672\pi$
$751$	38.0589	1.38879	0.694395	+	0.719594i	$0.255672\pi$
$752$	8.18367	0.298428
$753$	34.5064	1.25748
$754$	−46.0632	−1.67752
$755$	−0.242447	−0.00882354
$756$	66.6507	2.42406
$757$	31.9110	1.15982	0.579912	−	0.814679i	$-0.303087\pi$
$757$	31.9110	1.15982	0.579912	+	0.814679i	$0.303087\pi$
$758$	85.4974	3.10541
$759$	13.5541	0.491983
$760$	−32.5559	−1.18093
$761$	1.04214	0.0377777	0.0188888	−	0.999822i	$-0.493987\pi$
$761$	1.04214	0.0377777	0.0188888	+	0.999822i	$0.493987\pi$
$762$	−64.2475	−2.32744
$763$	−2.99306	−0.108356
$764$	−1.62648	−0.0588438
$765$	0.691558	0.0250033
$766$	−88.4163	−3.19461
$767$	−52.8245	−1.90738
$768$	55.3230	1.99630
$769$	−5.16536	−0.186268	−0.0931338	−	0.995654i	$-0.529688\pi$
$769$	−5.16536	−0.186268	−0.0931338	+	0.995654i	$0.529688\pi$
$770$	16.4548	0.592989
$771$	−32.6999	−1.17766
$772$	73.8762	2.65886
$773$	35.1011	1.26250	0.631250	−	0.775579i	$-0.282542\pi$
$773$	35.1011	1.26250	0.631250	+	0.775579i	$0.282542\pi$
$774$	−2.48016	−0.0891477
$775$	15.2749	0.548692
$776$	−37.6587	−1.35187
$777$	−5.09423	−0.182754
$778$	−6.58062	−0.235927
$779$	0.433885	0.0155456
$780$	−75.0192	−2.68612
$781$	9.82507	0.351569
$782$	60.3735	2.15895
$783$	−14.7925	−0.528641
$784$	10.4659	0.373784
$785$	5.24853	0.187328
$786$	−63.4529	−2.26329
$787$	−37.3326	−1.33077	−0.665383	−	0.746503i	$-0.731732\pi$
$787$	−37.3326	−1.33077	−0.665383	+	0.746503i	$0.731732\pi$
$788$	−30.9306	−1.10186
$789$	−53.2425	−1.89548
$790$	4.11872	0.146538
$791$	18.1736	0.646177
$792$	0.792981	0.0281773
$793$	55.4428	1.96883
$794$	−57.3927	−2.03679
$795$	0.760259	0.0269636
$796$	113.819	4.03422
$797$	−25.5257	−0.904167	−0.452084	−	0.891976i	$-0.649319\pi$
$797$	−25.5257	−0.904167	−0.452084	+	0.891976i	$0.649319\pi$
$798$	−47.2197	−1.67156
$799$	6.47868	0.229199
$800$	5.65647	0.199987
$801$	0.441417	0.0155967
$802$	−7.18521	−0.253719
$803$	9.04702	0.319263
$804$	−89.8569	−3.16901
$805$	27.1487	0.956866
$806$	−100.955	−3.55598
$807$	−4.79923	−0.168941
$808$	35.4200	1.24607
$809$	−28.4137	−0.998974	−0.499487	−	0.866322i	$-0.666478\pi$
$809$	−28.4137	−0.998974	−0.499487	+	0.866322i	$0.666478\pi$
$810$	−34.2965	−1.20506
$811$	16.7788	0.589183	0.294592	−	0.955623i	$-0.404816\pi$
$811$	16.7788	0.589183	0.294592	+	0.955623i	$0.404816\pi$
$812$	−35.3440	−1.24033
$813$	9.46667	0.332011
$814$	−3.46902	−0.121589
$815$	24.4172	0.855296
$816$	−38.4824	−1.34715
$817$	35.8556	1.25443
$818$	−2.30258	−0.0805077
$819$	2.03643	0.0711586
$820$	0.779810	0.0272322
$821$	32.6332	1.13891	0.569453	−	0.822024i	$-0.307155\pi$
$821$	32.6332	1.13891	0.569453	+	0.822024i	$0.307155\pi$
$822$	62.6330	2.18458
$823$	−9.43933	−0.329034	−0.164517	−	0.986374i	$-0.552607\pi$
$823$	−9.43933	−0.329034	−0.164517	+	0.986374i	$0.552607\pi$
$824$	49.3209	1.71818
$825$	5.89301	0.205168
$826$	−59.7585	−2.07926
$827$	−21.6195	−0.751784	−0.375892	−	0.926663i	$-0.622664\pi$
$827$	−21.6195	−0.751784	−0.375892	+	0.926663i	$0.622664\pi$
$828$	2.48902	0.0864995
$829$	−53.5917	−1.86132	−0.930659	−	0.365887i	$-0.880766\pi$
$829$	−53.5917	−1.86132	−0.930659	+	0.365887i	$0.880766\pi$
$830$	5.41883	0.188090
$831$	−10.3321	−0.358418
$832$	33.1211	1.14827
$833$	8.28546	0.287074
$834$	−44.0185	−1.52424
$835$	2.57355	0.0890615
$836$	−21.8097	−0.754303
$837$	−32.4201	−1.12060
$838$	5.83771	0.201660
$839$	27.9506	0.964961	0.482480	−	0.875907i	$-0.339736\pi$
$839$	27.9506	0.964961	0.482480	+	0.875907i	$0.339736\pi$
$840$	−44.6096	−1.53918
$841$	−21.1557	−0.729508
$842$	31.7640	1.09466
$843$	21.4078	0.737325
$844$	27.0230	0.930172
$845$	−48.3580	−1.66357
$846$	0.393796	0.0135390
$847$	−27.1293	−0.932174
$848$	1.50629	0.0517262
$849$	−24.8337	−0.852291
$850$	26.2490	0.900334
$851$	−5.72353	−0.196200
$852$	−50.6735	−1.73605
$853$	−1.60888	−0.0550869	−0.0275435	−	0.999621i	$-0.508768\pi$
$853$	−1.60888	−0.0550869	−0.0275435	+	0.999621i	$0.508768\pi$
$854$	62.7205	2.14625
$855$	−0.607702	−0.0207830
$856$	73.6731	2.51809
$857$	33.7948	1.15441	0.577204	−	0.816600i	$-0.304144\pi$
$857$	33.7948	1.15441	0.577204	+	0.816600i	$0.304144\pi$
$858$	−38.9480	−1.32966
$859$	20.1705	0.688207	0.344104	−	0.938932i	$-0.388183\pi$
$859$	20.1705	0.688207	0.344104	+	0.938932i	$0.388183\pi$
$860$	64.4424	2.19747
$861$	0.594528	0.0202615
$862$	−35.4829	−1.20855
$863$	13.8311	0.470817	0.235408	−	0.971897i	$-0.424357\pi$
$863$	13.8311	0.470817	0.235408	+	0.971897i	$0.424357\pi$
$864$	−12.0055	−0.408436
$865$	−14.2738	−0.485325
$866$	−38.7617	−1.31718
$867$	−1.53070	−0.0519852
$868$	−77.4619	−2.62923
$869$	1.45035	0.0491997
$870$	18.8353	0.638578
$871$	−82.5995	−2.79878
$872$	5.52560	0.187120
$873$	−0.702952	−0.0237913
$874$	−53.0528	−1.79454
$875$	35.5204	1.20081
$876$	−46.6607	−1.57652
$877$	29.2667	0.988265	0.494133	−	0.869387i	$-0.335486\pi$
$877$	29.2667	0.988265	0.494133	+	0.869387i	$0.335486\pi$
$878$	−101.521	−3.42616
$879$	−54.6331	−1.84273
$880$	−11.7840	−0.397239
$881$	10.0474	0.338506	0.169253	−	0.985573i	$-0.445865\pi$
$881$	10.0474	0.338506	0.169253	+	0.985573i	$0.445865\pi$
$882$	0.503618	0.0169577
$883$	19.9527	0.671461	0.335731	−	0.941958i	$-0.391017\pi$
$883$	19.9527	0.671461	0.335731	+	0.941958i	$0.391017\pi$
$884$	−117.668	−3.95760
$885$	21.6000	0.726078
$886$	43.4286	1.45901
$887$	45.4250	1.52522	0.762612	−	0.646856i	$-0.223917\pi$
$887$	45.4250	1.52522	0.762612	+	0.646856i	$0.223917\pi$
$888$	9.40466	0.315600
$889$	−45.3152	−1.51982
$890$	−16.9100	−0.566823
$891$	−12.0770	−0.404595
$892$	−53.1762	−1.78047
$893$	−5.69310	−0.190512
$894$	19.5101	0.652516
$895$	33.4329	1.11754
$896$	51.0757	1.70632
$897$	−64.2602	−2.14558
$898$	−32.6563	−1.08975
$899$	17.1919	0.573383
$900$	1.08217	0.0360723
$901$	1.19247	0.0397269
$902$	0.404856	0.0134802
$903$	49.1310	1.63498
$904$	−33.5509	−1.11589
$905$	−15.3535	−0.510369
$906$	0.649193	0.0215680
$907$	−59.6667	−1.98120	−0.990600	−	0.136791i	$-0.956321\pi$
$907$	−59.6667	−1.98120	−0.990600	+	0.136791i	$0.956321\pi$
$908$	14.6842	0.487313
$909$	0.661164	0.0219294
$910$	−78.0123	−2.58608
$911$	41.4942	1.37476	0.687382	−	0.726296i	$-0.258760\pi$
$911$	41.4942	1.37476	0.687382	+	0.726296i	$0.258760\pi$
$912$	33.8162	1.11977
$913$	1.90816	0.0631510
$914$	−38.7496	−1.28172
$915$	−22.6707	−0.749469
$916$	−96.0478	−3.17351
$917$	−44.7548	−1.47793
$918$	−55.7119	−1.83877
$919$	−5.00036	−0.164947	−0.0824733	−	0.996593i	$-0.526282\pi$
$919$	−5.00036	−0.164947	−0.0824733	+	0.996593i	$0.526282\pi$
$920$	−50.1203	−1.65242
$921$	21.2313	0.699596
$922$	−42.7767	−1.40878
$923$	−46.5808	−1.53323
$924$	−29.8845	−0.983129
$925$	−2.48846	−0.0818201
$926$	−51.2504	−1.68419
$927$	0.920644	0.0302379
$928$	6.36636	0.208986
$929$	−33.9925	−1.11526	−0.557629	−	0.830090i	$-0.688289\pi$
$929$	−33.9925	−1.11526	−0.557629	+	0.830090i	$0.688289\pi$
$930$	41.2806	1.35364
$931$	−7.28079	−0.238618
$932$	−116.617	−3.81992
$933$	−3.34074	−0.109371
$934$	2.83576	0.0927887
$935$	−9.32893	−0.305089
$936$	−3.75953	−0.122884
$937$	32.1542	1.05043	0.525216	−	0.850969i	$-0.323984\pi$
$937$	32.1542	1.05043	0.525216	+	0.850969i	$0.323984\pi$
$938$	−93.4419	−3.05099
$939$	−3.72888	−0.121687
$940$	−10.2320	−0.333733
$941$	10.3603	0.337736	0.168868	−	0.985639i	$-0.445989\pi$
$941$	10.3603	0.337736	0.168868	+	0.985639i	$0.445989\pi$
$942$	−14.0538	−0.457899
$943$	0.667972	0.0217522
$944$	42.7958	1.39289
$945$	−25.0524	−0.814956
$946$	33.4567	1.08777
$947$	−8.59632	−0.279343	−0.139671	−	0.990198i	$-0.544605\pi$
$947$	−8.59632	−0.279343	−0.139671	+	0.990198i	$0.544605\pi$
$948$	−7.48027	−0.242948
$949$	−42.8921	−1.39234
$950$	−23.0662	−0.748365
$951$	−48.0865	−1.55931
$952$	−69.9702	−2.26775
$953$	−28.2227	−0.914221	−0.457111	−	0.889410i	$-0.651116\pi$
$953$	−28.2227	−0.914221	−0.457111	+	0.889410i	$0.651116\pi$
$954$	0.0724823	0.00234670
$955$	0.611354	0.0197830
$956$	−2.02337	−0.0654404
$957$	6.63259	0.214401
$958$	5.02696	0.162414
$959$	44.1764	1.42653
$960$	−13.5433	−0.437108
$961$	6.67879	0.215445
$962$	16.4467	0.530262
$963$	1.37521	0.0443155
$964$	−84.1912	−2.71162
$965$	−27.7683	−0.893895
$966$	−72.6953	−2.33893
$967$	35.4158	1.13889	0.569447	−	0.822028i	$-0.307157\pi$
$967$	35.4158	1.13889	0.569447	+	0.822028i	$0.307157\pi$
$968$	50.0845	1.60978
$969$	26.7709	0.860005
$970$	26.9290	0.864637
$971$	−32.1471	−1.03165	−0.515825	−	0.856694i	$-0.672515\pi$
$971$	−32.1471	−1.03165	−0.515825	+	0.856694i	$0.672515\pi$
$972$	−4.51733	−0.144893
$973$	−31.0473	−0.995330
$974$	58.3198	1.86869
$975$	−27.9389	−0.894759
$976$	−44.9170	−1.43776
$977$	−56.5001	−1.80760	−0.903800	−	0.427955i	$-0.859234\pi$
$977$	−56.5001	−1.80760	−0.903800	+	0.427955i	$0.859234\pi$
$978$	−65.3811	−2.09066
$979$	−5.95459	−0.190310
$980$	−13.0856	−0.418003
$981$	0.103143	0.00329310
$982$	108.462	3.46117
$983$	−28.6677	−0.914357	−0.457179	−	0.889375i	$-0.651140\pi$
$983$	−28.6677	−0.914357	−0.457179	+	0.889375i	$0.651140\pi$
$984$	−1.09758	−0.0349897
$985$	11.6261	0.370438
$986$	29.5433	0.940849
$987$	−7.80092	−0.248306
$988$	103.400	3.28959
$989$	55.2002	1.75526
$990$	−0.567044	−0.0180218
$991$	11.2638	0.357806	0.178903	−	0.983867i	$-0.442745\pi$
$991$	11.2638	0.357806	0.178903	+	0.983867i	$0.442745\pi$
$992$	13.9529	0.443004
$993$	−53.5585	−1.69963
$994$	−52.6952	−1.67139
$995$	−42.7820	−1.35628
$996$	−9.84148	−0.311839
$997$	−38.7561	−1.22742	−0.613710	−	0.789532i	$-0.710323\pi$
$997$	−38.7561	−1.22742	−0.613710	+	0.789532i	$0.710323\pi$
$998$	27.1652	0.859900
$999$	5.28160	0.167102

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4033.2.a.f.1.5	✓	85

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4033.2.a.f.1.5	✓	85	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 4033 = 37 \cdot 109 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4033.a (trivial)

\(f(q)\)	\(=\)	\(q-2.49324 q^{2} -1.70202 q^{3} +4.21624 q^{4} -1.58478 q^{5} +4.24353 q^{6} +2.99306 q^{7} -5.52560 q^{8} -0.103143 q^{9} +O(q^{10})\)	\(q-2.49324 q^{2} -1.70202 q^{3} +4.21624 q^{4} -1.58478 q^{5} +4.24353 q^{6} +2.99306 q^{7} -5.52560 q^{8} -0.103143 q^{9} +3.95124 q^{10} +1.39137 q^{11} -7.17610 q^{12} -6.59651 q^{13} -7.46240 q^{14} +2.69733 q^{15} +5.34417 q^{16} +4.23076 q^{17} +0.257160 q^{18} -3.71775 q^{19} -6.68182 q^{20} -5.09423 q^{21} -3.46902 q^{22} -5.72353 q^{23} +9.40466 q^{24} -2.48846 q^{25} +16.4467 q^{26} +5.28160 q^{27} +12.6194 q^{28} -2.80076 q^{29} -6.72508 q^{30} -6.13831 q^{31} -2.27308 q^{32} -2.36814 q^{33} -10.5483 q^{34} -4.74335 q^{35} -0.434875 q^{36} +1.00000 q^{37} +9.26925 q^{38} +11.2274 q^{39} +8.75688 q^{40} -0.116706 q^{41} +12.7011 q^{42} -9.64444 q^{43} +5.86635 q^{44} +0.163459 q^{45} +14.2701 q^{46} +1.53133 q^{47} -9.09586 q^{48} +1.95838 q^{49} +6.20432 q^{50} -7.20082 q^{51} -27.8124 q^{52} +0.281857 q^{53} -13.1683 q^{54} -2.20502 q^{55} -16.5384 q^{56} +6.32768 q^{57} +6.98297 q^{58} +8.00795 q^{59} +11.3726 q^{60} -8.40487 q^{61} +15.3043 q^{62} -0.308713 q^{63} -5.02100 q^{64} +10.4540 q^{65} +5.90433 q^{66} +12.5217 q^{67} +17.8379 q^{68} +9.74154 q^{69} +11.8263 q^{70} +7.06143 q^{71} +0.569927 q^{72} +6.50223 q^{73} -2.49324 q^{74} +4.23540 q^{75} -15.6749 q^{76} +4.16445 q^{77} -27.9925 q^{78} +1.04239 q^{79} -8.46935 q^{80} -8.67993 q^{81} +0.290976 q^{82} +1.37143 q^{83} -21.4785 q^{84} -6.70484 q^{85} +24.0459 q^{86} +4.76694 q^{87} -7.68817 q^{88} -4.27966 q^{89} -0.407543 q^{90} -19.7437 q^{91} -24.1318 q^{92} +10.4475 q^{93} -3.81796 q^{94} +5.89184 q^{95} +3.86882 q^{96} +6.81532 q^{97} -4.88272 q^{98} -0.143510 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 85 q + 11 q^{2} + 21 q^{3} + 93 q^{4} + 12 q^{5} + 4 q^{6} + 17 q^{7} + 30 q^{8} + 98 q^{9}+O(q^{10}) \) 85 * q + 11 * q^2 + 21 * q^3 + 93 * q^4 + 12 * q^5 + 4 * q^6 + 17 * q^7 + 30 * q^8 + 98 * q^9	\( 85 q + 11 q^{2} + 21 q^{3} + 93 q^{4} + 12 q^{5} + 4 q^{6} + 17 q^{7} + 30 q^{8} + 98 q^{9} + 9 q^{10} + 37 q^{11} + 44 q^{12} + 14 q^{13} + 26 q^{14} + 27 q^{15} + 85 q^{16} + 34 q^{17} + 3 q^{18} + 15 q^{19} + 15 q^{20} + 17 q^{21} + q^{22} + 72 q^{23} + 15 q^{24} + 85 q^{25} + 33 q^{26} + 69 q^{27} + 7 q^{28} + 19 q^{29} - 9 q^{30} + 23 q^{31} + 51 q^{32} + 32 q^{33} + 49 q^{34} + 40 q^{35} + 121 q^{36} + 85 q^{37} + 84 q^{38} + 39 q^{39} + 22 q^{40} + 55 q^{41} - 28 q^{42} + 78 q^{44} + 28 q^{45} + 17 q^{46} + 184 q^{47} + 97 q^{48} + 88 q^{49} + 26 q^{50} + 27 q^{51} + 73 q^{52} + 64 q^{53} + 31 q^{54} + 39 q^{55} + 68 q^{56} - 33 q^{57} + 28 q^{58} + 60 q^{59} - 22 q^{60} + 7 q^{61} + 70 q^{62} + 28 q^{63} + 102 q^{64} + 17 q^{65} - 15 q^{66} + 82 q^{67} + 92 q^{68} + 22 q^{69} - 41 q^{70} + 113 q^{71} - 19 q^{73} + 11 q^{74} + 45 q^{75} + 34 q^{76} + 64 q^{77} + 29 q^{78} + 23 q^{79} + 54 q^{80} + 149 q^{81} + 4 q^{82} + 100 q^{83} - 49 q^{84} - 5 q^{85} - 24 q^{86} + 65 q^{87} + 14 q^{88} + 84 q^{89} - 21 q^{90} + 32 q^{91} + 95 q^{92} + 19 q^{93} - 47 q^{94} + 102 q^{95} + 29 q^{96} + 7 q^{97} + 26 q^{98} + 107 q^{99}+O(q^{100}) \) 85 * q + 11 * q^2 + 21 * q^3 + 93 * q^4 + 12 * q^5 + 4 * q^6 + 17 * q^7 + 30 * q^8 + 98 * q^9 + 9 * q^10 + 37 * q^11 + 44 * q^12 + 14 * q^13 + 26 * q^14 + 27 * q^15 + 85 * q^16 + 34 * q^17 + 3 * q^18 + 15 * q^19 + 15 * q^20 + 17 * q^21 + q^22 + 72 * q^23 + 15 * q^24 + 85 * q^25 + 33 * q^26 + 69 * q^27 + 7 * q^28 + 19 * q^29 - 9 * q^30 + 23 * q^31 + 51 * q^32 + 32 * q^33 + 49 * q^34 + 40 * q^35 + 121 * q^36 + 85 * q^37 + 84 * q^38 + 39 * q^39 + 22 * q^40 + 55 * q^41 - 28 * q^42 + 78 * q^44 + 28 * q^45 + 17 * q^46 + 184 * q^47 + 97 * q^48 + 88 * q^49 + 26 * q^50 + 27 * q^51 + 73 * q^52 + 64 * q^53 + 31 * q^54 + 39 * q^55 + 68 * q^56 - 33 * q^57 + 28 * q^58 + 60 * q^59 - 22 * q^60 + 7 * q^61 + 70 * q^62 + 28 * q^63 + 102 * q^64 + 17 * q^65 - 15 * q^66 + 82 * q^67 + 92 * q^68 + 22 * q^69 - 41 * q^70 + 113 * q^71 - 19 * q^73 + 11 * q^74 + 45 * q^75 + 34 * q^76 + 64 * q^77 + 29 * q^78 + 23 * q^79 + 54 * q^80 + 149 * q^81 + 4 * q^82 + 100 * q^83 - 49 * q^84 - 5 * q^85 - 24 * q^86 + 65 * q^87 + 14 * q^88 + 84 * q^89 - 21 * q^90 + 32 * q^91 + 95 * q^92 + 19 * q^93 - 47 * q^94 + 102 * q^95 + 29 * q^96 + 7 * q^97 + 26 * q^98 + 107 * q^99

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