LMFDB - Embedded newform 4031.2.a.c.1.51

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4031,2,Mod(1,4031)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4031, 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("4031.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4031 = 29 \cdot 139 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4031.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:	$32.1876970548$
Analytic rank:	$1$
Dimension:	$61$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.51
Character	$\chi$	$=$	4031.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.93031 q^{2} -2.44491 q^{3} +1.72610 q^{4} +1.84276 q^{5} -4.71944 q^{6} +1.02253 q^{7} -0.528718 q^{8} +2.97760 q^{9} +O(q^{10})$	\(q+1.93031 q^{2} -2.44491 q^{3} +1.72610 q^{4} +1.84276 q^{5} -4.71944 q^{6} +1.02253 q^{7} -0.528718 q^{8} +2.97760 q^{9} +3.55709 q^{10} +1.66439 q^{11} -4.22016 q^{12} -6.74710 q^{13} +1.97380 q^{14} -4.50538 q^{15} -4.47278 q^{16} +4.15288 q^{17} +5.74769 q^{18} -0.427076 q^{19} +3.18077 q^{20} -2.50000 q^{21} +3.21278 q^{22} +3.29374 q^{23} +1.29267 q^{24} -1.60425 q^{25} -13.0240 q^{26} +0.0547625 q^{27} +1.76499 q^{28} -1.00000 q^{29} -8.69678 q^{30} -8.07687 q^{31} -7.57642 q^{32} -4.06928 q^{33} +8.01635 q^{34} +1.88428 q^{35} +5.13963 q^{36} +4.05223 q^{37} -0.824389 q^{38} +16.4961 q^{39} -0.974299 q^{40} -4.43934 q^{41} -4.82578 q^{42} -8.08600 q^{43} +2.87289 q^{44} +5.48699 q^{45} +6.35793 q^{46} -3.83689 q^{47} +10.9356 q^{48} -5.95443 q^{49} -3.09670 q^{50} -10.1534 q^{51} -11.6461 q^{52} -1.26613 q^{53} +0.105709 q^{54} +3.06706 q^{55} -0.540631 q^{56} +1.04416 q^{57} -1.93031 q^{58} +7.32808 q^{59} -7.77672 q^{60} +7.48653 q^{61} -15.5909 q^{62} +3.04469 q^{63} -5.67928 q^{64} -12.4333 q^{65} -7.85498 q^{66} +0.652106 q^{67} +7.16828 q^{68} -8.05290 q^{69} +3.63724 q^{70} -7.72526 q^{71} -1.57431 q^{72} -1.29975 q^{73} +7.82206 q^{74} +3.92226 q^{75} -0.737174 q^{76} +1.70189 q^{77} +31.8425 q^{78} -4.20072 q^{79} -8.24225 q^{80} -9.06669 q^{81} -8.56929 q^{82} -5.86290 q^{83} -4.31524 q^{84} +7.65275 q^{85} -15.6085 q^{86} +2.44491 q^{87} -0.879993 q^{88} +10.8407 q^{89} +10.5916 q^{90} -6.89912 q^{91} +5.68531 q^{92} +19.7472 q^{93} -7.40638 q^{94} -0.786996 q^{95} +18.5237 q^{96} +5.31462 q^{97} -11.4939 q^{98} +4.95588 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 61 q - q^{2} - 4 q^{3} + 43 q^{4} - 7 q^{5} - 13 q^{6} - 10 q^{7} - 6 q^{8} + 23 q^{9}+O(q^{10}) $ 61 * q - q^2 - 4 * q^3 + 43 * q^4 - 7 * q^5 - 13 * q^6 - 10 * q^7 - 6 * q^8 + 23 * q^9	\( 61 q - q^{2} - 4 q^{3} + 43 q^{4} - 7 q^{5} - 13 q^{6} - 10 q^{7} - 6 q^{8} + 23 q^{9} - 16 q^{10} - 3 q^{11} - 18 q^{12} - 28 q^{13} - 14 q^{14} - 12 q^{15} + 11 q^{16} - 21 q^{17} - 17 q^{18} - 36 q^{19} - 16 q^{20} - 12 q^{21} - 42 q^{22} - 15 q^{23} - 28 q^{24} - 16 q^{25} - 13 q^{26} - 10 q^{27} - 25 q^{28} - 61 q^{29} - 12 q^{30} - 18 q^{31} - 3 q^{32} - 42 q^{33} - 22 q^{34} - 29 q^{35} - 38 q^{36} - 30 q^{37} - 27 q^{38} - 31 q^{39} - 22 q^{40} - 28 q^{41} - 9 q^{42} - 58 q^{43} - 2 q^{44} - 31 q^{45} - 40 q^{46} - 6 q^{47} - 37 q^{48} - 37 q^{49} - 15 q^{50} - 44 q^{51} - 43 q^{52} - 27 q^{53} - 18 q^{54} - 38 q^{55} - 22 q^{56} - 50 q^{57} + q^{58} - 24 q^{59} + 6 q^{60} - 76 q^{61} - 17 q^{62} - 6 q^{63} - 60 q^{64} - 65 q^{65} - 7 q^{66} - 45 q^{67} - 31 q^{68} - 16 q^{69} - 48 q^{70} - 28 q^{71} - 40 q^{72} - 50 q^{73} - 17 q^{74} - 35 q^{75} - 100 q^{76} + q^{77} - 6 q^{78} - 66 q^{79} - 10 q^{80} - 63 q^{81} - 5 q^{82} - 9 q^{83} - 24 q^{84} - 77 q^{85} + 29 q^{86} + 4 q^{87} - 62 q^{88} - 30 q^{89} + 50 q^{90} - 52 q^{91} - 53 q^{92} - 42 q^{93} - 92 q^{94} - 20 q^{95} - 47 q^{96} - 34 q^{97} + 36 q^{98} - 29 q^{99}+O(q^{100}) \) 61 * q - q^2 - 4 * q^3 + 43 * q^4 - 7 * q^5 - 13 * q^6 - 10 * q^7 - 6 * q^8 + 23 * q^9 - 16 * q^10 - 3 * q^11 - 18 * q^12 - 28 * q^13 - 14 * q^14 - 12 * q^15 + 11 * q^16 - 21 * q^17 - 17 * q^18 - 36 * q^19 - 16 * q^20 - 12 * q^21 - 42 * q^22 - 15 * q^23 - 28 * q^24 - 16 * q^25 - 13 * q^26 - 10 * q^27 - 25 * q^28 - 61 * q^29 - 12 * q^30 - 18 * q^31 - 3 * q^32 - 42 * q^33 - 22 * q^34 - 29 * q^35 - 38 * q^36 - 30 * q^37 - 27 * q^38 - 31 * q^39 - 22 * q^40 - 28 * q^41 - 9 * q^42 - 58 * q^43 - 2 * q^44 - 31 * q^45 - 40 * q^46 - 6 * q^47 - 37 * q^48 - 37 * q^49 - 15 * q^50 - 44 * q^51 - 43 * q^52 - 27 * q^53 - 18 * q^54 - 38 * q^55 - 22 * q^56 - 50 * q^57 + q^58 - 24 * q^59 + 6 * q^60 - 76 * q^61 - 17 * q^62 - 6 * q^63 - 60 * q^64 - 65 * q^65 - 7 * q^66 - 45 * q^67 - 31 * q^68 - 16 * q^69 - 48 * q^70 - 28 * q^71 - 40 * q^72 - 50 * q^73 - 17 * q^74 - 35 * q^75 - 100 * q^76 + q^77 - 6 * q^78 - 66 * q^79 - 10 * q^80 - 63 * q^81 - 5 * q^82 - 9 * q^83 - 24 * q^84 - 77 * q^85 + 29 * q^86 + 4 * q^87 - 62 * q^88 - 30 * q^89 + 50 * q^90 - 52 * q^91 - 53 * q^92 - 42 * q^93 - 92 * q^94 - 20 * q^95 - 47 * q^96 - 34 * q^97 + 36 * q^98 - 29 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.93031	1.36494	0.682468	−	0.730916i	$-0.260907\pi$
$2$	1.93031	1.36494	0.682468	+	0.730916i	$0.260907\pi$
$3$	−2.44491	−1.41157	−0.705786	−	0.708425i	$-0.749406\pi$
$3$	−2.44491	−1.41157	−0.705786	+	0.708425i	$0.749406\pi$
$4$	1.72610	0.863048
$5$	1.84276	0.824105	0.412053	−	0.911160i	$-0.364812\pi$
$5$	1.84276	0.824105	0.412053	+	0.911160i	$0.364812\pi$
$6$	−4.71944	−1.92670
$7$	1.02253	0.386480	0.193240	−	0.981151i	$-0.438100\pi$
$7$	1.02253	0.386480	0.193240	+	0.981151i	$0.438100\pi$
$8$	−0.528718	−0.186930
$9$	2.97760	0.992534
$10$	3.55709	1.12485
$11$	1.66439	0.501832	0.250916	−	0.968009i	$-0.419268\pi$
$11$	1.66439	0.501832	0.250916	+	0.968009i	$0.419268\pi$
$12$	−4.22016	−1.21825
$13$	−6.74710	−1.87131	−0.935654	−	0.352918i	$-0.885189\pi$
$13$	−6.74710	−1.87131	−0.935654	+	0.352918i	$0.885189\pi$
$14$	1.97380	0.527521
$15$	−4.50538	−1.16328
$16$	−4.47278	−1.11820
$17$	4.15288	1.00722	0.503611	−	0.863930i	$-0.332004\pi$
$17$	4.15288	1.00722	0.503611	+	0.863930i	$0.332004\pi$
$18$	5.74769	1.35474
$19$	−0.427076	−0.0979779	−0.0489890	−	0.998799i	$-0.515600\pi$
$19$	−0.427076	−0.0979779	−0.0489890	+	0.998799i	$0.515600\pi$
$20$	3.18077	0.711243
$21$	−2.50000	−0.545545
$22$	3.21278	0.684968
$23$	3.29374	0.686792	0.343396	−	0.939191i	$-0.388423\pi$
$23$	3.29374	0.686792	0.343396	+	0.939191i	$0.388423\pi$
$24$	1.29267	0.263865
$25$	−1.60425	−0.320850
$26$	−13.0240	−2.55421
$27$	0.0547625	0.0105390
$28$	1.76499	0.333551
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	−8.69678	−1.58781
$31$	−8.07687	−1.45065	−0.725324	−	0.688407i	$-0.758310\pi$
$31$	−8.07687	−1.45065	−0.725324	+	0.688407i	$0.758310\pi$
$32$	−7.57642	−1.33933
$33$	−4.06928	−0.708372
$34$	8.01635	1.37479
$35$	1.88428	0.318501
$36$	5.13963	0.856605
$37$	4.05223	0.666183	0.333091	−	0.942895i	$-0.391908\pi$
$37$	4.05223	0.666183	0.333091	+	0.942895i	$0.391908\pi$
$38$	−0.824389	−0.133734
$39$	16.4961	2.64149
$40$	−0.974299	−0.154050
$41$	−4.43934	−0.693308	−0.346654	−	0.937993i	$-0.612682\pi$
$41$	−4.43934	−0.693308	−0.346654	+	0.937993i	$0.612682\pi$
$42$	−4.82578	−0.744633
$43$	−8.08600	−1.23310	−0.616552	−	0.787314i	$-0.711471\pi$
$43$	−8.08600	−1.23310	−0.616552	+	0.787314i	$0.711471\pi$
$44$	2.87289	0.433105
$45$	5.48699	0.817952
$46$	6.35793	0.937426
$47$	−3.83689	−0.559668	−0.279834	−	0.960048i	$-0.590279\pi$
$47$	−3.83689	−0.559668	−0.279834	+	0.960048i	$0.590279\pi$
$48$	10.9356	1.57841
$49$	−5.95443	−0.850633
$50$	−3.09670	−0.437940
$51$	−10.1534	−1.42177
$52$	−11.6461	−1.61503
$53$	−1.26613	−0.173917	−0.0869585	−	0.996212i	$-0.527715\pi$
$53$	−1.26613	−0.173917	−0.0869585	+	0.996212i	$0.527715\pi$
$54$	0.105709	0.0143851
$55$	3.06706	0.413562
$56$	−0.540631	−0.0722449
$57$	1.04416	0.138303
$58$	−1.93031	−0.253462
$59$	7.32808	0.954034	0.477017	−	0.878894i	$-0.341718\pi$
$59$	7.32808	0.954034	0.477017	+	0.878894i	$0.341718\pi$
$60$	−7.77672	−1.00397
$61$	7.48653	0.958552	0.479276	−	0.877664i	$-0.340899\pi$
$61$	7.48653	0.958552	0.479276	+	0.877664i	$0.340899\pi$
$62$	−15.5909	−1.98004
$63$	3.04469	0.383595
$64$	−5.67928	−0.709909
$65$	−12.4333	−1.54216
$66$	−7.85498	−0.966881
$67$	0.652106	0.0796675	0.0398337	−	0.999206i	$-0.487317\pi$
$67$	0.652106	0.0796675	0.0398337	+	0.999206i	$0.487317\pi$
$68$	7.16828	0.869282
$69$	−8.05290	−0.969456
$70$	3.63724	0.434733
$71$	−7.72526	−0.916819	−0.458410	−	0.888741i	$-0.651581\pi$
$71$	−7.72526	−0.916819	−0.458410	+	0.888741i	$0.651581\pi$
$72$	−1.57431	−0.185535
$73$	−1.29975	−0.152124	−0.0760622	−	0.997103i	$-0.524235\pi$
$73$	−1.29975	−0.152124	−0.0760622	+	0.997103i	$0.524235\pi$
$74$	7.82206	0.909296
$75$	3.92226	0.452903
$76$	−0.737174	−0.0845597
$77$	1.70189	0.193948
$78$	31.8425	3.60546
$79$	−4.20072	−0.472617	−0.236309	−	0.971678i	$-0.575938\pi$
$79$	−4.20072	−0.472617	−0.236309	+	0.971678i	$0.575938\pi$
$80$	−8.24225	−0.921511
$81$	−9.06669	−1.00741
$82$	−8.56929	−0.946320
$83$	−5.86290	−0.643536	−0.321768	−	0.946818i	$-0.604277\pi$
$83$	−5.86290	−0.643536	−0.321768	+	0.946818i	$0.604277\pi$
$84$	−4.31524	−0.470832
$85$	7.65275	0.830057
$86$	−15.6085	−1.68311
$87$	2.44491	0.262122
$88$	−0.879993	−0.0938075
$89$	10.8407	1.14911	0.574557	−	0.818464i	$-0.305174\pi$
$89$	10.8407	1.14911	0.574557	+	0.818464i	$0.305174\pi$
$90$	10.5916	1.11645
$91$	−6.89912	−0.723224
$92$	5.68531	0.592735
$93$	19.7472	2.04769
$94$	−7.40638	−0.763910
$95$	−0.786996	−0.0807441
$96$	18.5237	1.89057
$97$	5.31462	0.539618	0.269809	−	0.962914i	$-0.413039\pi$
$97$	5.31462	0.539618	0.269809	+	0.962914i	$0.413039\pi$
$98$	−11.4939	−1.16106
$99$	4.95588	0.498085
$100$	−2.76909	−0.276909
$101$	−5.13198	−0.510651	−0.255325	−	0.966855i	$-0.582183\pi$
$101$	−5.13198	−0.510651	−0.255325	+	0.966855i	$0.582183\pi$
$102$	−19.5993	−1.94062
$103$	11.5919	1.14218	0.571091	−	0.820887i	$-0.306520\pi$
$103$	11.5919	1.14218	0.571091	+	0.820887i	$0.306520\pi$
$104$	3.56731	0.349804
$105$	−4.60689	−0.449586
$106$	−2.44403	−0.237385
$107$	−5.78202	−0.558969	−0.279484	−	0.960150i	$-0.590164\pi$
$107$	−5.78202	−0.558969	−0.279484	+	0.960150i	$0.590164\pi$
$108$	0.0945253	0.00909570
$109$	−1.73097	−0.165796	−0.0828982	−	0.996558i	$-0.526418\pi$
$109$	−1.73097	−0.165796	−0.0828982	+	0.996558i	$0.526418\pi$
$110$	5.92038	0.564486
$111$	−9.90735	−0.940364
$112$	−4.57356	−0.432161
$113$	−15.3160	−1.44081	−0.720405	−	0.693554i	$-0.756044\pi$
$113$	−15.3160	−1.44081	−0.720405	+	0.693554i	$0.756044\pi$
$114$	2.01556	0.188774
$115$	6.06955	0.565989
$116$	−1.72610	−0.160264
$117$	−20.0902	−1.85734
$118$	14.1455	1.30220
$119$	4.24645	0.389272
$120$	2.38208	0.217453
$121$	−8.22981	−0.748165
$122$	14.4513	1.30836
$123$	10.8538	0.978653
$124$	−13.9415	−1.25198
$125$	−12.1700	−1.08852
$126$	5.87720	0.523582
$127$	−12.7094	−1.12778	−0.563888	−	0.825851i	$-0.690695\pi$
$127$	−12.7094	−1.12778	−0.563888	+	0.825851i	$0.690695\pi$
$128$	4.19008	0.370354
$129$	19.7696	1.74061
$130$	−24.0000	−2.10494
$131$	−21.4627	−1.87520	−0.937600	−	0.347715i	$-0.886958\pi$
$131$	−21.4627	−1.87520	−0.937600	+	0.347715i	$0.886958\pi$
$132$	−7.02398	−0.611359
$133$	−0.436698	−0.0378665
$134$	1.25877	0.108741
$135$	0.100914	0.00868528
$136$	−2.19571	−0.188280
$137$	−10.7666	−0.919851	−0.459925	−	0.887958i	$-0.652124\pi$
$137$	−10.7666	−0.919851	−0.459925	+	0.887958i	$0.652124\pi$
$138$	−15.5446	−1.32324
$139$	−1.00000	−0.0848189
$139$	−1.00000	−0.0848189
$140$	3.25244	0.274881
$141$	9.38086	0.790011
$142$	−14.9121	−1.25140
$143$	−11.2298	−0.939082
$144$	−13.3182	−1.10985
$145$	−1.84276	−0.153033
$146$	−2.50892	−0.207640
$147$	14.5581	1.20073
$148$	6.99454	0.574948
$149$	−17.1603	−1.40583	−0.702915	−	0.711274i	$-0.748119\pi$
$149$	−17.1603	−1.40583	−0.702915	+	0.711274i	$0.748119\pi$
$150$	7.57117	0.618183
$151$	20.8291	1.69505	0.847523	−	0.530759i	$-0.178093\pi$
$151$	20.8291	1.69505	0.847523	+	0.530759i	$0.178093\pi$
$152$	0.225803	0.0183150
$153$	12.3656	0.999702
$154$	3.28517	0.264727
$155$	−14.8837	−1.19549
$156$	28.4738	2.27973
$157$	−4.69026	−0.374324	−0.187162	−	0.982329i	$-0.559929\pi$
$157$	−4.69026	−0.374324	−0.187162	+	0.982329i	$0.559929\pi$
$158$	−8.10868	−0.645092
$159$	3.09559	0.245496
$160$	−13.9615	−1.10375
$161$	3.36795	0.265432
$162$	−17.5015	−1.37505
$163$	−1.84336	−0.144383	−0.0721914	−	0.997391i	$-0.522999\pi$
$163$	−1.84336	−0.144383	−0.0721914	+	0.997391i	$0.522999\pi$
$164$	−7.66272	−0.598358
$165$	−7.49870	−0.583773
$166$	−11.3172	−0.878386
$167$	−3.38414	−0.261872	−0.130936	−	0.991391i	$-0.541798\pi$
$167$	−3.38414	−0.261872	−0.130936	+	0.991391i	$0.541798\pi$
$168$	1.32180	0.101979
$169$	32.5233	2.50179
$170$	14.7722	1.13297
$171$	−1.27166	−0.0972464
$172$	−13.9572	−1.06423
$173$	−9.38300	−0.713376	−0.356688	−	0.934223i	$-0.616094\pi$
$173$	−9.38300	−0.713376	−0.356688	+	0.934223i	$0.616094\pi$
$174$	4.71944	0.357780
$175$	−1.64040	−0.124002
$176$	−7.44445	−0.561146
$177$	−17.9165	−1.34669
$178$	20.9260	1.56847
$179$	−1.52944	−0.114316	−0.0571578	−	0.998365i	$-0.518204\pi$
$179$	−1.52944	−0.114316	−0.0571578	+	0.998365i	$0.518204\pi$
$180$	9.47108	0.705932
$181$	0.512259	0.0380759	0.0190379	−	0.999819i	$-0.493940\pi$
$181$	0.512259	0.0380759	0.0190379	+	0.999819i	$0.493940\pi$
$182$	−13.3174	−0.987154
$183$	−18.3039	−1.35306
$184$	−1.74146	−0.128382
$185$	7.46727	0.549005
$186$	38.1183	2.79497
$187$	6.91201	0.505456
$188$	−6.62284	−0.483020
$189$	0.0559963	0.00407313
$190$	−1.51915	−0.110210
$191$	−13.5320	−0.979141	−0.489570	−	0.871964i	$-0.662846\pi$
$191$	−13.5320	−0.979141	−0.489570	+	0.871964i	$0.662846\pi$
$192$	13.8853	1.00209
$193$	−1.86506	−0.134250	−0.0671249	−	0.997745i	$-0.521383\pi$
$193$	−1.86506	−0.134250	−0.0671249	+	0.997745i	$0.521383\pi$
$194$	10.2589	0.736543
$195$	30.3982	2.17686
$196$	−10.2779	−0.734137
$197$	8.37065	0.596384	0.298192	−	0.954506i	$-0.403616\pi$
$197$	8.37065	0.596384	0.298192	+	0.954506i	$0.403616\pi$
$198$	9.56639	0.679854
$199$	−0.668973	−0.0474222	−0.0237111	−	0.999719i	$-0.507548\pi$
$199$	−0.668973	−0.0474222	−0.0237111	+	0.999719i	$0.507548\pi$
$200$	0.848197	0.0599766
$201$	−1.59434	−0.112456
$202$	−9.90631	−0.697005
$203$	−1.02253	−0.0717676
$204$	−17.5258	−1.22705
$205$	−8.18061	−0.571359
$206$	22.3759	1.55900
$207$	9.80744	0.681664
$208$	30.1783	2.09249
$209$	−0.710820	−0.0491684
$210$	−8.89273	−0.613656
$211$	23.2230	1.59874	0.799369	−	0.600840i	$-0.205167\pi$
$211$	23.2230	1.59874	0.799369	+	0.600840i	$0.205167\pi$
$212$	−2.18547	−0.150099
$213$	18.8876	1.29416
$214$	−11.1611	−0.762956
$215$	−14.9005	−1.01621
$216$	−0.0289539	−0.00197007
$217$	−8.25885	−0.560647
$218$	−3.34130	−0.226301
$219$	3.17778	0.214734
$220$	5.29404	0.356924
$221$	−28.0199	−1.88482
$222$	−19.1243	−1.28354
$223$	1.61445	0.108112	0.0540558	−	0.998538i	$-0.482785\pi$
$223$	1.61445	0.108112	0.0540558	+	0.998538i	$0.482785\pi$
$224$	−7.74713	−0.517627
$225$	−4.77682	−0.318455
$226$	−29.5647	−1.96661
$227$	17.3301	1.15024	0.575121	−	0.818068i	$-0.304955\pi$
$227$	17.3301	1.15024	0.575121	+	0.818068i	$0.304955\pi$
$228$	1.80233	0.119362
$229$	−20.7869	−1.37364	−0.686820	−	0.726827i	$-0.740994\pi$
$229$	−20.7869	−1.37364	−0.686820	+	0.726827i	$0.740994\pi$
$230$	11.7161	0.772538
$231$	−4.16097	−0.273772
$232$	0.528718	0.0347121
$233$	−19.2593	−1.26172	−0.630860	−	0.775897i	$-0.717298\pi$
$233$	−19.2593	−1.26172	−0.630860	+	0.775897i	$0.717298\pi$
$234$	−38.7803	−2.53514
$235$	−7.07045	−0.461225
$236$	12.6490	0.823378
$237$	10.2704	0.667133
$238$	8.19697	0.531331
$239$	17.3695	1.12354	0.561768	−	0.827295i	$-0.310121\pi$
$239$	17.3695	1.12354	0.561768	+	0.827295i	$0.310121\pi$
$240$	20.1516	1.30078
$241$	11.1623	0.719027	0.359514	−	0.933140i	$-0.382943\pi$
$241$	11.1623	0.719027	0.359514	+	0.933140i	$0.382943\pi$
$242$	−15.8861	−1.02120
$243$	22.0030	1.41149
$244$	12.9225	0.827277
$245$	−10.9726	−0.701011
$246$	20.9512	1.33580
$247$	2.88152	0.183347
$248$	4.27039	0.271170
$249$	14.3343	0.908398
$250$	−23.4919	−1.48576
$251$	6.26510	0.395449	0.197725	−	0.980258i	$-0.436645\pi$
$251$	6.26510	0.395449	0.197725	+	0.980258i	$0.436645\pi$
$252$	5.25543	0.331061
$253$	5.48206	0.344654
$254$	−24.5331	−1.53934
$255$	−18.7103	−1.17169
$256$	19.4467	1.21542
$257$	25.3280	1.57992	0.789959	−	0.613160i	$-0.210102\pi$
$257$	25.3280	1.57992	0.789959	+	0.613160i	$0.210102\pi$
$258$	38.1614	2.37583
$259$	4.14353	0.257467
$260$	−21.4610	−1.33095
$261$	−2.97760	−0.184309
$262$	−41.4296	−2.55953
$263$	−22.7842	−1.40493	−0.702466	−	0.711717i	$-0.747918\pi$
$263$	−22.7842	−1.40493	−0.702466	+	0.711717i	$0.747918\pi$
$264$	2.15151	0.132416
$265$	−2.33318	−0.143326
$266$	−0.842963	−0.0516854
$267$	−26.5046	−1.62206
$268$	1.12560	0.0687569
$269$	−1.72045	−0.104898	−0.0524489	−	0.998624i	$-0.516703\pi$
$269$	−1.72045	−0.104898	−0.0524489	+	0.998624i	$0.516703\pi$
$270$	0.194795	0.0118548
$271$	−7.91506	−0.480806	−0.240403	−	0.970673i	$-0.577280\pi$
$271$	−7.91506	−0.480806	−0.240403	+	0.970673i	$0.577280\pi$
$272$	−18.5750	−1.12627
$273$	16.8677	1.02088
$274$	−20.7828	−1.25554
$275$	−2.67010	−0.161013
$276$	−13.9001	−0.836687
$277$	−23.6788	−1.42272	−0.711361	−	0.702826i	$-0.751921\pi$
$277$	−23.6788	−1.42272	−0.711361	+	0.702826i	$0.751921\pi$
$278$	−1.93031	−0.115772
$279$	−24.0497	−1.43982
$280$	−0.996251	−0.0595374
$281$	−27.8986	−1.66429	−0.832144	−	0.554559i	$-0.812887\pi$
$281$	−27.8986	−1.66429	−0.832144	+	0.554559i	$0.812887\pi$
$282$	18.1080	1.07831
$283$	7.55132	0.448879	0.224440	−	0.974488i	$-0.427945\pi$
$283$	7.55132	0.448879	0.224440	+	0.974488i	$0.427945\pi$
$284$	−13.3345	−0.791259
$285$	1.92414	0.113976
$286$	−21.6770	−1.28179
$287$	−4.53936	−0.267950
$288$	−22.5596	−1.32934
$289$	0.246450	0.0144971
$290$	−3.55709	−0.208879
$291$	−12.9938	−0.761709
$292$	−2.24350	−0.131291
$293$	−3.93074	−0.229636	−0.114818	−	0.993387i	$-0.536629\pi$
$293$	−3.93074	−0.229636	−0.114818	+	0.993387i	$0.536629\pi$
$294$	28.1016	1.63892
$295$	13.5039	0.786225
$296$	−2.14249	−0.124530
$297$	0.0911460	0.00528883
$298$	−33.1248	−1.91887
$299$	−22.2232	−1.28520
$300$	6.77019	0.390877
$301$	−8.26819	−0.476571
$302$	40.2066	2.31363
$303$	12.5472	0.720820
$304$	1.91022	0.109558
$305$	13.7958	0.789948
$306$	23.8695	1.36453
$307$	16.9199	0.965671	0.482835	−	0.875711i	$-0.339607\pi$
$307$	16.9199	0.965671	0.482835	+	0.875711i	$0.339607\pi$
$308$	2.93762	0.167387
$309$	−28.3411	−1.61227
$310$	−28.7301	−1.63176
$311$	−2.46637	−0.139855	−0.0699276	−	0.997552i	$-0.522277\pi$
$311$	−2.46637	−0.139855	−0.0699276	+	0.997552i	$0.522277\pi$
$312$	−8.72178	−0.493773
$313$	−21.6124	−1.22161	−0.610803	−	0.791783i	$-0.709153\pi$
$313$	−21.6124	−1.22161	−0.610803	+	0.791783i	$0.709153\pi$
$314$	−9.05366	−0.510928
$315$	5.61062	0.316123
$316$	−7.25084	−0.407892
$317$	−8.91127	−0.500507	−0.250253	−	0.968180i	$-0.580514\pi$
$317$	−8.91127	−0.500507	−0.250253	+	0.968180i	$0.580514\pi$
$318$	5.97545	0.335086
$319$	−1.66439	−0.0931878
$320$	−10.4655	−0.585040
$321$	14.1365	0.789024
$322$	6.50119	0.362297
$323$	−1.77360	−0.0986855
$324$	−15.6500	−0.869444
$325$	10.8240	0.600410
$326$	−3.55825	−0.197073
$327$	4.23206	0.234033
$328$	2.34716	0.129600
$329$	−3.92334	−0.216301
$330$	−14.4748	−0.796812
$331$	26.6461	1.46460	0.732302	−	0.680980i	$-0.238446\pi$
$331$	26.6461	1.46460	0.732302	+	0.680980i	$0.238446\pi$
$332$	−10.1199	−0.555403
$333$	12.0659	0.661209
$334$	−6.53243	−0.357439
$335$	1.20167	0.0656544
$336$	11.1820	0.610026
$337$	−2.46433	−0.134241	−0.0671204	−	0.997745i	$-0.521381\pi$
$337$	−2.46433	−0.134241	−0.0671204	+	0.997745i	$0.521381\pi$
$338$	62.7801	3.41479
$339$	37.4463	2.03381
$340$	13.2094	0.716380
$341$	−13.4430	−0.727982
$342$	−2.45470	−0.132735
$343$	−13.2463	−0.715233
$344$	4.27522	0.230504
$345$	−14.8395	−0.798934
$346$	−18.1121	−0.973713
$347$	−0.749214	−0.0402199	−0.0201100	−	0.999798i	$-0.506402\pi$
$347$	−0.749214	−0.0402199	−0.0201100	+	0.999798i	$0.506402\pi$
$348$	4.22016	0.226224
$349$	9.65069	0.516590	0.258295	−	0.966066i	$-0.416839\pi$
$349$	9.65069	0.516590	0.258295	+	0.966066i	$0.416839\pi$
$350$	−3.16648	−0.169255
$351$	−0.369488	−0.0197218
$352$	−12.6101	−0.672121
$353$	−13.9489	−0.742424	−0.371212	−	0.928548i	$-0.621058\pi$
$353$	−13.9489	−0.742424	−0.371212	+	0.928548i	$0.621058\pi$
$354$	−34.5844	−1.83814
$355$	−14.2358	−0.755556
$356$	18.7121	0.991741
$357$	−10.3822	−0.549485
$358$	−2.95229	−0.156033
$359$	−5.80727	−0.306496	−0.153248	−	0.988188i	$-0.548973\pi$
$359$	−5.80727	−0.306496	−0.153248	+	0.988188i	$0.548973\pi$
$360$	−2.90107	−0.152900
$361$	−18.8176	−0.990400
$362$	0.988818	0.0519711
$363$	20.1212	1.05609
$364$	−11.9085	−0.624177
$365$	−2.39512	−0.125367
$366$	−35.3322	−1.84685
$367$	25.6587	1.33937	0.669686	−	0.742644i	$-0.266429\pi$
$367$	25.6587	1.33937	0.669686	+	0.742644i	$0.266429\pi$
$368$	−14.7322	−0.767968
$369$	−13.2186	−0.688131
$370$	14.4141	0.749356
$371$	−1.29466	−0.0672155
$372$	34.0857	1.76726
$373$	11.2418	0.582079	0.291039	−	0.956711i	$-0.405999\pi$
$373$	11.2418	0.582079	0.291039	+	0.956711i	$0.405999\pi$
$374$	13.3423	0.689915
$375$	29.7546	1.53652
$376$	2.02863	0.104619
$377$	6.74710	0.347493
$378$	0.108090	0.00555957
$379$	6.06634	0.311607	0.155804	−	0.987788i	$-0.450203\pi$
$379$	6.06634	0.311607	0.155804	+	0.987788i	$0.450203\pi$
$380$	−1.35843	−0.0696861
$381$	31.0734	1.59194
$382$	−26.1209	−1.33646
$383$	29.1489	1.48944	0.744720	−	0.667377i	$-0.232583\pi$
$383$	29.1489	1.48944	0.744720	+	0.667377i	$0.232583\pi$
$384$	−10.2444	−0.522782
$385$	3.13617	0.159834
$386$	−3.60014	−0.183242
$387$	−24.0769	−1.22390
$388$	9.17355	0.465716
$389$	25.4559	1.29067	0.645333	−	0.763902i	$-0.276719\pi$
$389$	25.4559	1.29067	0.645333	+	0.763902i	$0.276719\pi$
$390$	58.6780	2.97128
$391$	13.6785	0.691752
$392$	3.14822	0.159009
$393$	52.4743	2.64698
$394$	16.1580	0.814026
$395$	−7.74089	−0.389487
$396$	8.55434	0.429872
$397$	5.14992	0.258467	0.129233	−	0.991614i	$-0.458748\pi$
$397$	5.14992	0.258467	0.129233	+	0.991614i	$0.458748\pi$
$398$	−1.29132	−0.0647282
$399$	1.06769	0.0534513
$400$	7.17547	0.358774
$401$	−0.110526	−0.00551942	−0.00275971	−	0.999996i	$-0.500878\pi$
$401$	−0.110526	−0.00551942	−0.00275971	+	0.999996i	$0.500878\pi$
$402$	−3.07758	−0.153496
$403$	54.4954	2.71461
$404$	−8.85829	−0.440716
$405$	−16.7077	−0.830212
$406$	−1.97380	−0.0979582
$407$	6.74448	0.334312
$408$	5.36831	0.265771
$409$	−24.4548	−1.20921	−0.604605	−	0.796525i	$-0.706669\pi$
$409$	−24.4548	−1.20921	−0.604605	+	0.796525i	$0.706669\pi$
$410$	−15.7911	−0.779867
$411$	26.3233	1.29843
$412$	20.0087	0.985758
$413$	7.49319	0.368716
$414$	18.9314	0.930427
$415$	−10.8039	−0.530342
$416$	51.1189	2.50631
$417$	2.44491	0.119728
$418$	−1.37210	−0.0671117
$419$	0.642090	0.0313682	0.0156841	−	0.999877i	$-0.495007\pi$
$419$	0.642090	0.0313682	0.0156841	+	0.999877i	$0.495007\pi$
$420$	−7.95194	−0.388015
$421$	17.7196	0.863598	0.431799	−	0.901970i	$-0.357879\pi$
$421$	17.7196	0.863598	0.431799	+	0.901970i	$0.357879\pi$
$422$	44.8276	2.18217
$423$	−11.4247	−0.555489
$424$	0.669429	0.0325103
$425$	−6.66227	−0.323168
$426$	36.4589	1.76644
$427$	7.65521	0.370462
$428$	−9.98032	−0.482417
$429$	27.4559	1.32558
$430$	−28.7626	−1.38706
$431$	26.4068	1.27197	0.635985	−	0.771701i	$-0.280594\pi$
$431$	26.4068	1.27197	0.635985	+	0.771701i	$0.280594\pi$
$432$	−0.244941	−0.0117847
$433$	23.6129	1.13476	0.567381	−	0.823456i	$-0.307957\pi$
$433$	23.6129	1.13476	0.567381	+	0.823456i	$0.307957\pi$
$434$	−15.9421	−0.765247
$435$	4.50538	0.216016
$436$	−2.98781	−0.143090
$437$	−1.40668	−0.0672904
$438$	6.13410	0.293099
$439$	−1.38419	−0.0660637	−0.0330319	−	0.999454i	$-0.510516\pi$
$439$	−1.38419	−0.0660637	−0.0330319	+	0.999454i	$0.510516\pi$
$440$	−1.62161	−0.0773073
$441$	−17.7299	−0.844282
$442$	−54.0871	−2.57266
$443$	28.5007	1.35411	0.677054	−	0.735934i	$-0.263256\pi$
$443$	28.5007	1.35411	0.677054	+	0.735934i	$0.263256\pi$
$444$	−17.1010	−0.811580
$445$	19.9768	0.946991
$446$	3.11639	0.147565
$447$	41.9556	1.98443
$448$	−5.80724	−0.274366
$449$	29.9602	1.41391	0.706954	−	0.707260i	$-0.250069\pi$
$449$	29.9602	1.41391	0.706954	+	0.707260i	$0.250069\pi$
$450$	−9.22075	−0.434670
$451$	−7.38878	−0.347924
$452$	−26.4369	−1.24349
$453$	−50.9253	−2.39268
$454$	33.4525	1.57001
$455$	−12.7134	−0.596013
$456$	−0.552068	−0.0258530
$457$	−4.03386	−0.188696	−0.0943480	−	0.995539i	$-0.530077\pi$
$457$	−4.03386	−0.188696	−0.0943480	+	0.995539i	$0.530077\pi$
$458$	−40.1253	−1.87493
$459$	0.227422	0.0106152
$460$	10.4766	0.488476
$461$	11.7979	0.549481	0.274741	−	0.961518i	$-0.411408\pi$
$461$	11.7979	0.549481	0.274741	+	0.961518i	$0.411408\pi$
$462$	−8.03196	−0.373681
$463$	35.9336	1.66998	0.834988	−	0.550268i	$-0.185474\pi$
$463$	35.9336	1.66998	0.834988	+	0.550268i	$0.185474\pi$
$464$	4.47278	0.207644
$465$	36.3893	1.68752
$466$	−37.1764	−1.72217
$467$	−19.2879	−0.892536	−0.446268	−	0.894899i	$-0.647247\pi$
$467$	−19.2879	−0.892536	−0.446268	+	0.894899i	$0.647247\pi$
$468$	−34.6776	−1.60297
$469$	0.666799	0.0307899
$470$	−13.6482	−0.629542
$471$	11.4673	0.528385
$472$	−3.87449	−0.178338
$473$	−13.4582	−0.618811
$474$	19.8250	0.910594
$475$	0.685137	0.0314362
$476$	7.32979	0.335960
$477$	−3.77004	−0.172618
$478$	33.5284	1.53356
$479$	28.7037	1.31151	0.655753	−	0.754976i	$-0.272351\pi$
$479$	28.7037	1.31151	0.655753	+	0.754976i	$0.272351\pi$
$480$	34.1346	1.55803
$481$	−27.3408	−1.24663
$482$	21.5467	0.981426
$483$	−8.23435	−0.374676
$484$	−14.2055	−0.645702
$485$	9.79354	0.444702
$486$	42.4726	1.92660
$487$	−25.4534	−1.15340	−0.576702	−	0.816954i	$-0.695661\pi$
$487$	−25.4534	−1.15340	−0.576702	+	0.816954i	$0.695661\pi$
$488$	−3.95827	−0.179182
$489$	4.50684	0.203807
$490$	−21.1804	−0.956835
$491$	19.7373	0.890732	0.445366	−	0.895348i	$-0.353073\pi$
$491$	19.7373	0.890732	0.445366	+	0.895348i	$0.353073\pi$
$492$	18.7347	0.844625
$493$	−4.15288	−0.187037
$494$	5.56223	0.250257
$495$	9.13248	0.410475
$496$	36.1261	1.62211
$497$	−7.89932	−0.354333
$498$	27.6696	1.23990
$499$	−7.19587	−0.322131	−0.161066	−	0.986944i	$-0.551493\pi$
$499$	−7.19587	−0.322131	−0.161066	+	0.986944i	$0.551493\pi$
$500$	−21.0066	−0.939445
$501$	8.27392	0.369652
$502$	12.0936	0.539763
$503$	−0.256870	−0.0114533	−0.00572664	−	0.999984i	$-0.501823\pi$
$503$	−0.256870	−0.0114533	−0.00572664	+	0.999984i	$0.501823\pi$
$504$	−1.60978	−0.0717055
$505$	−9.45698	−0.420830
$506$	10.5821	0.470430
$507$	−79.5167	−3.53146
$508$	−21.9377	−0.973326
$509$	7.41992	0.328882	0.164441	−	0.986387i	$-0.447418\pi$
$509$	7.41992	0.328882	0.164441	+	0.986387i	$0.447418\pi$
$510$	−36.1167	−1.59927
$511$	−1.32904	−0.0587931
$512$	29.1580	1.28861
$513$	−0.0233877	−0.00103259
$514$	48.8909	2.15648
$515$	21.3610	0.941278
$516$	34.1242	1.50223
$517$	−6.38607	−0.280859
$518$	7.99830	0.351425
$519$	22.9406	1.00698
$520$	6.57369	0.288275
$521$	−16.1767	−0.708713	−0.354357	−	0.935110i	$-0.615300\pi$
$521$	−16.1767	−0.708713	−0.354357	+	0.935110i	$0.615300\pi$
$522$	−5.74769	−0.251570
$523$	−13.3028	−0.581692	−0.290846	−	0.956770i	$-0.593937\pi$
$523$	−13.3028	−0.581692	−0.290846	+	0.956770i	$0.593937\pi$
$524$	−37.0466	−1.61839
$525$	4.01063	0.175038
$526$	−43.9805	−1.91764
$527$	−33.5423	−1.46113
$528$	18.2010	0.792098
$529$	−12.1513	−0.528317
$530$	−4.50375	−0.195631
$531$	21.8201	0.946911
$532$	−0.753784	−0.0326807
$533$	29.9526	1.29739
$534$	−51.1622	−2.21400
$535$	−10.6548	−0.460649
$536$	−0.344781	−0.0148923
$537$	3.73934	0.161365
$538$	−3.32100	−0.143179
$539$	−9.91048	−0.426875
$540$	0.174187	0.00749582
$541$	−20.7571	−0.892418	−0.446209	−	0.894929i	$-0.647226\pi$
$541$	−20.7571	−0.892418	−0.446209	+	0.894929i	$0.647226\pi$
$542$	−15.2785	−0.656269
$543$	−1.25243	−0.0537468
$544$	−31.4640	−1.34901
$545$	−3.18975	−0.136634
$546$	32.5600	1.39344
$547$	−10.8236	−0.462784	−0.231392	−	0.972861i	$-0.574328\pi$
$547$	−10.8236	−0.462784	−0.231392	+	0.972861i	$0.574328\pi$
$548$	−18.5842	−0.793876
$549$	22.2919	0.951395
$550$	−5.15412	−0.219772
$551$	0.427076	0.0181940
$552$	4.25772	0.181221
$553$	−4.29536	−0.182657
$554$	−45.7075	−1.94192
$555$	−18.2568	−0.774959
$556$	−1.72610	−0.0732028
$557$	14.4510	0.612308	0.306154	−	0.951982i	$-0.400958\pi$
$557$	14.4510	0.612308	0.306154	+	0.951982i	$0.400958\pi$
$558$	−46.4234	−1.96526
$559$	54.5571	2.30752
$560$	−8.42796	−0.356146
$561$	−16.8993	−0.713488
$562$	−53.8529	−2.27165
$563$	36.7321	1.54807	0.774037	−	0.633141i	$-0.218235\pi$
$563$	36.7321	1.54807	0.774037	+	0.633141i	$0.218235\pi$
$564$	16.1923	0.681817
$565$	−28.2237	−1.18738
$566$	14.5764	0.612691
$567$	−9.27098	−0.389344
$568$	4.08449	0.171381
$569$	−38.1702	−1.60018	−0.800090	−	0.599880i	$-0.795215\pi$
$569$	−38.1702	−1.60018	−0.800090	+	0.599880i	$0.795215\pi$
$570$	3.71418	0.155570
$571$	19.5031	0.816178	0.408089	−	0.912942i	$-0.366195\pi$
$571$	19.5031	0.816178	0.408089	+	0.912942i	$0.366195\pi$
$572$	−19.3837	−0.810473
$573$	33.0846	1.38213
$574$	−8.76237	−0.365734
$575$	−5.28398	−0.220357
$576$	−16.9106	−0.704609
$577$	27.7460	1.15508	0.577542	−	0.816361i	$-0.304012\pi$
$577$	27.7460	1.15508	0.577542	+	0.816361i	$0.304012\pi$
$578$	0.475726	0.0197876
$579$	4.55990	0.189503
$580$	−3.18077	−0.132074
$581$	−5.99499	−0.248714
$582$	−25.0820	−1.03968
$583$	−2.10734	−0.0872771
$584$	0.687203	0.0284366
$585$	−37.0213	−1.53064
$586$	−7.58755	−0.313439
$587$	25.4843	1.05185	0.525926	−	0.850531i	$-0.323719\pi$
$587$	25.4843	1.05185	0.525926	+	0.850531i	$0.323719\pi$
$588$	25.1286	1.03629
$589$	3.44944	0.142132
$590$	26.0666	1.07315
$591$	−20.4655	−0.841839
$592$	−18.1248	−0.744923
$593$	−9.28563	−0.381315	−0.190658	−	0.981657i	$-0.561062\pi$
$593$	−9.28563	−0.381315	−0.190658	+	0.981657i	$0.561062\pi$
$594$	0.175940	0.00721891
$595$	7.82518	0.320801
$596$	−29.6204	−1.21330
$597$	1.63558	0.0669398
$598$	−42.8976	−1.75421
$599$	24.1185	0.985454	0.492727	−	0.870184i	$-0.336000\pi$
$599$	24.1185	0.985454	0.492727	+	0.870184i	$0.336000\pi$
$600$	−2.07377	−0.0846613
$601$	−10.8163	−0.441205	−0.220603	−	0.975364i	$-0.570802\pi$
$601$	−10.8163	−0.441205	−0.220603	+	0.975364i	$0.570802\pi$
$602$	−15.9602	−0.650488
$603$	1.94171	0.0790726
$604$	35.9530	1.46291
$605$	−15.1655	−0.616567
$606$	24.2201	0.983873
$607$	14.7089	0.597017	0.298509	−	0.954407i	$-0.403511\pi$
$607$	14.7089	0.597017	0.298509	+	0.954407i	$0.403511\pi$
$608$	3.23571	0.131225
$609$	2.50000	0.101305
$610$	26.6303	1.07823
$611$	25.8879	1.04731
$612$	21.3443	0.862791
$613$	−45.7453	−1.84763	−0.923817	−	0.382835i	$-0.874948\pi$
$613$	−45.7453	−1.84763	−0.923817	+	0.382835i	$0.874948\pi$
$614$	32.6607	1.31808
$615$	20.0009	0.806513
$616$	−0.899820	−0.0362548
$617$	19.8795	0.800317	0.400159	−	0.916446i	$-0.368955\pi$
$617$	19.8795	0.800317	0.400159	+	0.916446i	$0.368955\pi$
$618$	−54.7072	−2.20064
$619$	−34.9455	−1.40458	−0.702289	−	0.711892i	$-0.747839\pi$
$619$	−34.9455	−1.40458	−0.702289	+	0.711892i	$0.747839\pi$
$620$	−25.6907	−1.03176
$621$	0.180373	0.00723813
$622$	−4.76087	−0.190893
$623$	11.0850	0.444110
$624$	−73.7834	−2.95370
$625$	−14.4051	−0.576205
$626$	−41.7186	−1.66741
$627$	1.73789	0.0694048
$628$	−8.09585	−0.323059
$629$	16.8284	0.670994
$630$	10.8302	0.431487
$631$	−35.0894	−1.39689	−0.698443	−	0.715665i	$-0.746124\pi$
$631$	−35.0894	−1.39689	−0.698443	+	0.715665i	$0.746124\pi$
$632$	2.22100	0.0883465
$633$	−56.7783	−2.25673
$634$	−17.2015	−0.683159
$635$	−23.4203	−0.929407
$636$	5.34329	0.211875
$637$	40.1751	1.59180
$638$	−3.21278	−0.127195
$639$	−23.0027	−0.909974
$640$	7.72130	0.305211
$641$	27.9860	1.10538	0.552689	−	0.833387i	$-0.313602\pi$
$641$	27.9860	1.10538	0.552689	+	0.833387i	$0.313602\pi$
$642$	27.2879	1.07697
$643$	18.9692	0.748071	0.374036	−	0.927414i	$-0.377974\pi$
$643$	18.9692	0.748071	0.374036	+	0.927414i	$0.377974\pi$
$644$	5.81341	0.229080
$645$	36.4305	1.43445
$646$	−3.42359	−0.134699
$647$	22.0191	0.865661	0.432830	−	0.901475i	$-0.357515\pi$
$647$	22.0191	0.865661	0.432830	+	0.901475i	$0.357515\pi$
$648$	4.79373	0.188315
$649$	12.1968	0.478765
$650$	20.8938	0.819521
$651$	20.1922	0.791394
$652$	−3.18181	−0.124609
$653$	30.3306	1.18693	0.593463	−	0.804861i	$-0.297760\pi$
$653$	30.3306	1.18693	0.593463	+	0.804861i	$0.297760\pi$
$654$	8.16919	0.319441
$655$	−39.5504	−1.54536
$656$	19.8562	0.775254
$657$	−3.87014	−0.150989
$658$	−7.57326	−0.295236
$659$	23.1839	0.903116	0.451558	−	0.892242i	$-0.350868\pi$
$659$	23.1839	0.903116	0.451558	+	0.892242i	$0.350868\pi$
$660$	−12.9435	−0.503824
$661$	7.08081	0.275411	0.137706	−	0.990473i	$-0.456027\pi$
$661$	7.08081	0.275411	0.137706	+	0.990473i	$0.456027\pi$
$662$	51.4353	1.99909
$663$	68.5063	2.66056
$664$	3.09982	0.120296
$665$	−0.804728	−0.0312060
$666$	23.2910	0.902507
$667$	−3.29374	−0.127534
$668$	−5.84135	−0.226008
$669$	−3.94719	−0.152607
$670$	2.31960	0.0896140
$671$	12.4605	0.481032
$672$	18.9411	0.730667
$673$	14.5174	0.559604	0.279802	−	0.960058i	$-0.409731\pi$
$673$	14.5174	0.559604	0.279802	+	0.960058i	$0.409731\pi$
$674$	−4.75693	−0.183230
$675$	−0.0878528	−0.00338146
$676$	56.1384	2.15917
$677$	21.0011	0.807139	0.403569	−	0.914949i	$-0.367769\pi$
$677$	21.0011	0.807139	0.403569	+	0.914949i	$0.367769\pi$
$678$	72.2830	2.77601
$679$	5.43436	0.208552
$680$	−4.04615	−0.155163
$681$	−42.3707	−1.62365
$682$	−25.9492	−0.993648
$683$	1.91057	0.0731059	0.0365529	−	0.999332i	$-0.488362\pi$
$683$	1.91057	0.0731059	0.0365529	+	0.999332i	$0.488362\pi$
$684$	−2.19501	−0.0839283
$685$	−19.8402	−0.758054
$686$	−25.5695	−0.976247
$687$	50.8223	1.93899
$688$	36.1669	1.37885
$689$	8.54273	0.325452
$690$	−28.6449	−1.09049
$691$	3.07043	0.116804	0.0584022	−	0.998293i	$-0.481399\pi$
$691$	3.07043	0.116804	0.0584022	+	0.998293i	$0.481399\pi$
$692$	−16.1960	−0.615678
$693$	5.06755	0.192500
$694$	−1.44622	−0.0548976
$695$	−1.84276	−0.0698997
$696$	−1.29267	−0.0489986
$697$	−18.4360	−0.698315
$698$	18.6288	0.705111
$699$	47.0874	1.78101
$700$	−2.83148	−0.107020
$701$	48.7447	1.84106	0.920530	−	0.390672i	$-0.127757\pi$
$701$	48.7447	1.84106	0.920530	+	0.390672i	$0.127757\pi$
$702$	−0.713226	−0.0269190
$703$	−1.73061	−0.0652712
$704$	−9.45252	−0.356255
$705$	17.2866	0.651052
$706$	−26.9257	−1.01336
$707$	−5.24761	−0.197357
$708$	−30.9256	−1.16226
$709$	−33.9042	−1.27330	−0.636649	−	0.771154i	$-0.719680\pi$
$709$	−33.9042	−1.27330	−0.636649	+	0.771154i	$0.719680\pi$
$710$	−27.4794	−1.03128
$711$	−12.5081	−0.469089
$712$	−5.73169	−0.214804
$713$	−26.6031	−0.996294
$714$	−20.0409	−0.750011
$715$	−20.6938	−0.773903
$716$	−2.63996	−0.0986599
$717$	−42.4668	−1.58595
$718$	−11.2098	−0.418347
$719$	2.11591	0.0789102	0.0394551	−	0.999221i	$-0.487438\pi$
$719$	2.11591	0.0789102	0.0394551	+	0.999221i	$0.487438\pi$
$720$	−24.5421	−0.914631
$721$	11.8531	0.441431
$722$	−36.3238	−1.35183
$723$	−27.2909	−1.01496
$724$	0.884208	0.0328613
$725$	1.60425	0.0595804
$726$	38.8401	1.44149
$727$	50.2643	1.86420	0.932099	−	0.362203i	$-0.117975\pi$
$727$	50.2643	1.86420	0.932099	+	0.362203i	$0.117975\pi$
$728$	3.64769	0.135192
$729$	−26.5953	−0.985012
$730$	−4.62333	−0.171117
$731$	−33.5802	−1.24201
$732$	−31.5943	−1.16776
$733$	16.3129	0.602533	0.301266	−	0.953540i	$-0.402591\pi$
$733$	16.3129	0.602533	0.301266	+	0.953540i	$0.402591\pi$
$734$	49.5292	1.82816
$735$	26.8270	0.989527
$736$	−24.9547	−0.919844
$737$	1.08536	0.0399797
$738$	−25.5159	−0.939255
$739$	32.4605	1.19408	0.597039	−	0.802212i	$-0.296344\pi$
$739$	32.4605	1.19408	0.597039	+	0.802212i	$0.296344\pi$
$740$	12.8892	0.473818
$741$	−7.04507	−0.258807
$742$	−2.49910	−0.0917448
$743$	−16.5242	−0.606214	−0.303107	−	0.952956i	$-0.598024\pi$
$743$	−16.5242	−0.606214	−0.303107	+	0.952956i	$0.598024\pi$
$744$	−10.4407	−0.382776
$745$	−31.6223	−1.15855
$746$	21.7002	0.794500
$747$	−17.4574	−0.638732
$748$	11.9308	0.436233
$749$	−5.91229	−0.216030
$750$	57.4357	2.09726
$751$	−21.6370	−0.789545	−0.394773	−	0.918779i	$-0.629177\pi$
$751$	−21.6370	−0.789545	−0.394773	+	0.918779i	$0.629177\pi$
$752$	17.1616	0.625818
$753$	−15.3176	−0.558205
$754$	13.0240	0.474306
$755$	38.3829	1.39690
$756$	0.0966551	0.00351531
$757$	−38.5489	−1.40108	−0.700541	−	0.713612i	$-0.747058\pi$
$757$	−38.5489	−1.40108	−0.700541	+	0.713612i	$0.747058\pi$
$758$	11.7099	0.425324
$759$	−13.4032	−0.486504
$760$	0.416099	0.0150935
$761$	−37.3932	−1.35550	−0.677751	−	0.735292i	$-0.737045\pi$
$761$	−37.3932	−1.35550	−0.677751	+	0.735292i	$0.737045\pi$
$762$	59.9813	2.17289
$763$	−1.76997	−0.0640771
$764$	−23.3575	−0.845046
$765$	22.7868	0.823860
$766$	56.2664	2.03299
$767$	−49.4433	−1.78529
$768$	−47.5455	−1.71565
$769$	13.7957	0.497487	0.248743	−	0.968569i	$-0.419982\pi$
$769$	13.7957	0.497487	0.248743	+	0.968569i	$0.419982\pi$
$770$	6.05377	0.218163
$771$	−61.9248	−2.23017
$772$	−3.21927	−0.115864
$773$	−21.5564	−0.775328	−0.387664	−	0.921801i	$-0.626718\pi$
$773$	−21.5564	−0.775328	−0.387664	+	0.921801i	$0.626718\pi$
$774$	−46.4759	−1.67054
$775$	12.9573	0.465441
$776$	−2.80994	−0.100871
$777$	−10.1306	−0.363432
$778$	49.1378	1.76167
$779$	1.89593	0.0679288
$780$	52.4703	1.87874
$781$	−12.8578	−0.460089
$782$	26.4038	0.944197
$783$	−0.0547625	−0.00195705
$784$	26.6329	0.951174
$785$	−8.64301	−0.308482
$786$	101.292	3.61296
$787$	−18.1088	−0.645509	−0.322754	−	0.946483i	$-0.604609\pi$
$787$	−18.1088	−0.645509	−0.322754	+	0.946483i	$0.604609\pi$
$788$	14.4486	0.514708
$789$	55.7053	1.98316
$790$	−14.9423	−0.531624
$791$	−15.6611	−0.556845
$792$	−2.62027	−0.0931071
$793$	−50.5124	−1.79375
$794$	9.94093	0.352791
$795$	5.70442	0.202315
$796$	−1.15471	−0.0409277
$797$	10.1364	0.359048	0.179524	−	0.983754i	$-0.442544\pi$
$797$	10.1364	0.359048	0.179524	+	0.983754i	$0.442544\pi$
$798$	2.06097	0.0729576
$799$	−15.9342	−0.563710
$800$	12.1545	0.429726
$801$	32.2794	1.14053
$802$	−0.213350	−0.00753365
$803$	−2.16329	−0.0763409
$804$	−2.75199	−0.0970552
$805$	6.20631	0.218744
$806$	105.193	3.70527
$807$	4.20635	0.148071
$808$	2.71337	0.0954561
$809$	−36.0249	−1.26657	−0.633283	−	0.773920i	$-0.718293\pi$
$809$	−36.0249	−1.26657	−0.633283	+	0.773920i	$0.718293\pi$
$810$	−32.2510	−1.13319
$811$	−28.7653	−1.01009	−0.505043	−	0.863094i	$-0.668523\pi$
$811$	−28.7653	−1.01009	−0.505043	+	0.863094i	$0.668523\pi$
$812$	−1.76499	−0.0619389
$813$	19.3516	0.678692
$814$	13.0189	0.456314
$815$	−3.39685	−0.118987
$816$	45.4142	1.58981
$817$	3.45334	0.120817
$818$	−47.2053	−1.65049
$819$	−20.5428	−0.717824
$820$	−14.1205	−0.493110
$821$	−9.59629	−0.334913	−0.167456	−	0.985879i	$-0.553555\pi$
$821$	−9.59629	−0.334913	−0.167456	+	0.985879i	$0.553555\pi$
$822$	50.8122	1.77228
$823$	36.2383	1.26319	0.631595	−	0.775299i	$-0.282401\pi$
$823$	36.2383	1.26319	0.631595	+	0.775299i	$0.282401\pi$
$824$	−6.12884	−0.213508
$825$	6.52816	0.227281
$826$	14.4642	0.503273
$827$	−20.3113	−0.706292	−0.353146	−	0.935568i	$-0.614888\pi$
$827$	−20.3113	−0.706292	−0.353146	+	0.935568i	$0.614888\pi$
$828$	16.9286	0.588309
$829$	−1.15275	−0.0400367	−0.0200183	−	0.999800i	$-0.506372\pi$
$829$	−1.15275	−0.0400367	−0.0200183	+	0.999800i	$0.506372\pi$
$830$	−20.8548	−0.723882
$831$	57.8927	2.00827
$832$	38.3186	1.32846
$833$	−24.7281	−0.856776
$834$	4.71944	0.163421
$835$	−6.23614	−0.215810
$836$	−1.22694	−0.0424347
$837$	−0.442309	−0.0152884
$838$	1.23943	0.0428155
$839$	−51.8837	−1.79122	−0.895611	−	0.444838i	$-0.853261\pi$
$839$	−51.8837	−1.79122	−0.895611	+	0.444838i	$0.853261\pi$
$840$	2.43575	0.0840413
$841$	1.00000	0.0344828
$842$	34.2042	1.17876
$843$	68.2096	2.34926
$844$	40.0852	1.37979
$845$	59.9325	2.06174
$846$	−22.0533	−0.758207
$847$	−8.41524	−0.289151
$848$	5.66315	0.194473
$849$	−18.4623	−0.633625
$850$	−12.8602	−0.441103
$851$	13.3470	0.457529
$852$	32.6018	1.11692
$853$	55.3896	1.89650	0.948251	−	0.317522i	$-0.102851\pi$
$853$	55.3896	1.89650	0.948251	+	0.317522i	$0.102851\pi$
$854$	14.7769	0.505656
$855$	−2.34336	−0.0801413
$856$	3.05706	0.104488
$857$	−2.25058	−0.0768782	−0.0384391	−	0.999261i	$-0.512239\pi$
$857$	−2.25058	−0.0768782	−0.0384391	+	0.999261i	$0.512239\pi$
$858$	52.9983	1.80933
$859$	14.4654	0.493554	0.246777	−	0.969072i	$-0.420629\pi$
$859$	14.4654	0.493554	0.246777	+	0.969072i	$0.420629\pi$
$860$	−25.7198	−0.877036
$861$	11.0983	0.378230
$862$	50.9733	1.73616
$863$	−14.5524	−0.495369	−0.247685	−	0.968841i	$-0.579670\pi$
$863$	−14.5524	−0.495369	−0.247685	+	0.968841i	$0.579670\pi$
$864$	−0.414904	−0.0141153
$865$	−17.2906	−0.587897
$866$	45.5801	1.54888
$867$	−0.602550	−0.0204637
$868$	−14.2556	−0.483866
$869$	−6.99162	−0.237174
$870$	8.69678	0.294848
$871$	−4.39982	−0.149082
$872$	0.915193	0.0309924
$873$	15.8248	0.535589
$874$	−2.71532	−0.0918471
$875$	−12.4442	−0.420692
$876$	5.48515	0.185326
$877$	1.33444	0.0450609	0.0225305	−	0.999746i	$-0.492828\pi$
$877$	1.33444	0.0450609	0.0225305	+	0.999746i	$0.492828\pi$
$878$	−2.67191	−0.0901727
$879$	9.61032	0.324148
$880$	−13.7183	−0.462444
$881$	−35.3124	−1.18970	−0.594852	−	0.803835i	$-0.702789\pi$
$881$	−35.3124	−1.18970	−0.594852	+	0.803835i	$0.702789\pi$
$882$	−34.2242	−1.15239
$883$	−44.8765	−1.51022	−0.755108	−	0.655601i	$-0.772415\pi$
$883$	−44.8765	−1.51022	−0.755108	+	0.655601i	$0.772415\pi$
$884$	−48.3651	−1.62669
$885$	−33.0158	−1.10981
$886$	55.0151	1.84827
$887$	−20.5375	−0.689581	−0.344791	−	0.938680i	$-0.612050\pi$
$887$	−20.5375	−0.689581	−0.344791	+	0.938680i	$0.612050\pi$
$888$	5.23820	0.175782
$889$	−12.9958	−0.435864
$890$	38.5614	1.29258
$891$	−15.0905	−0.505551
$892$	2.78670	0.0933055
$893$	1.63864	0.0548351
$894$	80.9872	2.70862
$895$	−2.81838	−0.0942081
$896$	4.28449	0.143135
$897$	54.3337	1.81415
$898$	57.8324	1.92989
$899$	8.07687	0.269379
$900$	−8.24526	−0.274842
$901$	−5.25811	−0.175173
$902$	−14.2626	−0.474894
$903$	20.2150	0.672713
$904$	8.09786	0.269331
$905$	0.943968	0.0313785
$906$	−98.3016	−3.26585
$907$	57.4968	1.90915	0.954575	−	0.297972i	$-0.0963103\pi$
$907$	57.4968	1.90915	0.954575	+	0.297972i	$0.0963103\pi$
$908$	29.9135	0.992714
$909$	−15.2810	−0.506838
$910$	−24.5408	−0.813519
$911$	−31.0637	−1.02919	−0.514593	−	0.857435i	$-0.672057\pi$
$911$	−31.0637	−1.02919	−0.514593	+	0.857435i	$0.672057\pi$
$912$	−4.67032	−0.154650
$913$	−9.75813	−0.322947
$914$	−7.78660	−0.257558
$915$	−33.7296	−1.11507
$916$	−35.8803	−1.18552
$917$	−21.9462	−0.724728
$918$	0.438995	0.0144890
$919$	−6.83396	−0.225431	−0.112716	−	0.993627i	$-0.535955\pi$
$919$	−6.83396	−0.225431	−0.112716	+	0.993627i	$0.535955\pi$
$920$	−3.20909	−0.105800
$921$	−41.3677	−1.36311
$922$	22.7735	0.750006
$923$	52.1231	1.71565
$924$	−7.18224	−0.236278
$925$	−6.50080	−0.213745
$926$	69.3630	2.27941
$927$	34.5160	1.13365
$928$	7.57642	0.248708
$929$	−38.7658	−1.27186	−0.635932	−	0.771745i	$-0.719384\pi$
$929$	−38.7658	−1.27186	−0.635932	+	0.771745i	$0.719384\pi$
$930$	70.2427	2.30335
$931$	2.54299	0.0833432
$932$	−33.2434	−1.08892
$933$	6.03007	0.197416
$934$	−37.2315	−1.21825
$935$	12.7371	0.416549
$936$	10.6220	0.347192
$937$	26.0777	0.851921	0.425960	−	0.904742i	$-0.359936\pi$
$937$	26.0777	0.851921	0.425960	+	0.904742i	$0.359936\pi$
$938$	1.28713	0.0420262
$939$	52.8405	1.72438
$940$	−12.2043	−0.398060
$941$	12.3117	0.401349	0.200675	−	0.979658i	$-0.435687\pi$
$941$	12.3117	0.401349	0.200675	+	0.979658i	$0.435687\pi$
$942$	22.1354	0.721211
$943$	−14.6220	−0.476158
$944$	−32.7769	−1.06680
$945$	0.103188	0.00335669
$946$	−25.9786	−0.844637
$947$	43.9916	1.42954	0.714768	−	0.699362i	$-0.246532\pi$
$947$	43.9916	1.42954	0.714768	+	0.699362i	$0.246532\pi$
$948$	17.7277	0.575768
$949$	8.76955	0.284672
$950$	1.32253	0.0429084
$951$	21.7873	0.706501
$952$	−2.24518	−0.0727667
$953$	−3.83272	−0.124154	−0.0620770	−	0.998071i	$-0.519772\pi$
$953$	−3.83272	−0.124154	−0.0620770	+	0.998071i	$0.519772\pi$
$954$	−7.27735	−0.235613
$955$	−24.9362	−0.806915
$956$	29.9814	0.969667
$957$	4.06928	0.131541
$958$	55.4070	1.79012
$959$	−11.0092	−0.355504
$960$	25.5873	0.825826
$961$	34.2358	1.10438
$962$	−52.7762	−1.70157
$963$	−17.2165	−0.554795
$964$	19.2672	0.620555
$965$	−3.43684	−0.110636
$966$	−15.8948	−0.511408
$967$	−48.8173	−1.56986	−0.784930	−	0.619585i	$-0.787301\pi$
$967$	−48.8173	−1.56986	−0.784930	+	0.619585i	$0.787301\pi$
$968$	4.35125	0.139855
$969$	4.33629	0.139302
$970$	18.9046	0.606989
$971$	−38.6858	−1.24149	−0.620744	−	0.784014i	$-0.713169\pi$
$971$	−38.6858	−1.24149	−0.620744	+	0.784014i	$0.713169\pi$
$972$	37.9793	1.21819
$973$	−1.02253	−0.0327808
$974$	−49.1330	−1.57432
$975$	−26.4638	−0.847521
$976$	−33.4856	−1.07185
$977$	48.9355	1.56558	0.782792	−	0.622283i	$-0.213795\pi$
$977$	48.9355	1.56558	0.782792	+	0.622283i	$0.213795\pi$
$978$	8.69961	0.278183
$979$	18.0432	0.576662
$980$	−18.9397	−0.605006
$981$	−5.15412	−0.164559
$982$	38.0991	1.21579
$983$	31.6541	1.00961	0.504805	−	0.863234i	$-0.331565\pi$
$983$	31.6541	1.00961	0.504805	+	0.863234i	$0.331565\pi$
$984$	−5.73860	−0.182940
$985$	15.4251	0.491483
$986$	−8.01635	−0.255293
$987$	9.59222	0.305324
$988$	4.97379	0.158237
$989$	−26.6332	−0.846886
$990$	17.6285	0.560271
$991$	−59.2994	−1.88371	−0.941853	−	0.336024i	$-0.890918\pi$
$991$	−59.2994	−1.88371	−0.941853	+	0.336024i	$0.890918\pi$
$992$	61.1938	1.94290
$993$	−65.1475	−2.06739
$994$	−15.2481	−0.483641
$995$	−1.23275	−0.0390809
$996$	24.7423	0.783991
$997$	51.5879	1.63381	0.816903	−	0.576775i	$-0.195689\pi$
$997$	51.5879	1.63381	0.816903	+	0.576775i	$0.195689\pi$
$998$	−13.8903	−0.439689
$999$	0.221910	0.00702093

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4031.2.a.c.1.51	✓	61

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4031.2.a.c.1.51	✓	61	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:	\( N \)	\(=\)	\( 4031 = 29 \cdot 139 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4031.a (trivial)

\(f(q)\)	\(=\)	\(q+1.93031 q^{2} -2.44491 q^{3} +1.72610 q^{4} +1.84276 q^{5} -4.71944 q^{6} +1.02253 q^{7} -0.528718 q^{8} +2.97760 q^{9} +O(q^{10})\)	\(q+1.93031 q^{2} -2.44491 q^{3} +1.72610 q^{4} +1.84276 q^{5} -4.71944 q^{6} +1.02253 q^{7} -0.528718 q^{8} +2.97760 q^{9} +3.55709 q^{10} +1.66439 q^{11} -4.22016 q^{12} -6.74710 q^{13} +1.97380 q^{14} -4.50538 q^{15} -4.47278 q^{16} +4.15288 q^{17} +5.74769 q^{18} -0.427076 q^{19} +3.18077 q^{20} -2.50000 q^{21} +3.21278 q^{22} +3.29374 q^{23} +1.29267 q^{24} -1.60425 q^{25} -13.0240 q^{26} +0.0547625 q^{27} +1.76499 q^{28} -1.00000 q^{29} -8.69678 q^{30} -8.07687 q^{31} -7.57642 q^{32} -4.06928 q^{33} +8.01635 q^{34} +1.88428 q^{35} +5.13963 q^{36} +4.05223 q^{37} -0.824389 q^{38} +16.4961 q^{39} -0.974299 q^{40} -4.43934 q^{41} -4.82578 q^{42} -8.08600 q^{43} +2.87289 q^{44} +5.48699 q^{45} +6.35793 q^{46} -3.83689 q^{47} +10.9356 q^{48} -5.95443 q^{49} -3.09670 q^{50} -10.1534 q^{51} -11.6461 q^{52} -1.26613 q^{53} +0.105709 q^{54} +3.06706 q^{55} -0.540631 q^{56} +1.04416 q^{57} -1.93031 q^{58} +7.32808 q^{59} -7.77672 q^{60} +7.48653 q^{61} -15.5909 q^{62} +3.04469 q^{63} -5.67928 q^{64} -12.4333 q^{65} -7.85498 q^{66} +0.652106 q^{67} +7.16828 q^{68} -8.05290 q^{69} +3.63724 q^{70} -7.72526 q^{71} -1.57431 q^{72} -1.29975 q^{73} +7.82206 q^{74} +3.92226 q^{75} -0.737174 q^{76} +1.70189 q^{77} +31.8425 q^{78} -4.20072 q^{79} -8.24225 q^{80} -9.06669 q^{81} -8.56929 q^{82} -5.86290 q^{83} -4.31524 q^{84} +7.65275 q^{85} -15.6085 q^{86} +2.44491 q^{87} -0.879993 q^{88} +10.8407 q^{89} +10.5916 q^{90} -6.89912 q^{91} +5.68531 q^{92} +19.7472 q^{93} -7.40638 q^{94} -0.786996 q^{95} +18.5237 q^{96} +5.31462 q^{97} -11.4939 q^{98} +4.95588 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 61 q - q^{2} - 4 q^{3} + 43 q^{4} - 7 q^{5} - 13 q^{6} - 10 q^{7} - 6 q^{8} + 23 q^{9}+O(q^{10}) \) 61 * q - q^2 - 4 * q^3 + 43 * q^4 - 7 * q^5 - 13 * q^6 - 10 * q^7 - 6 * q^8 + 23 * q^9	\( 61 q - q^{2} - 4 q^{3} + 43 q^{4} - 7 q^{5} - 13 q^{6} - 10 q^{7} - 6 q^{8} + 23 q^{9} - 16 q^{10} - 3 q^{11} - 18 q^{12} - 28 q^{13} - 14 q^{14} - 12 q^{15} + 11 q^{16} - 21 q^{17} - 17 q^{18} - 36 q^{19} - 16 q^{20} - 12 q^{21} - 42 q^{22} - 15 q^{23} - 28 q^{24} - 16 q^{25} - 13 q^{26} - 10 q^{27} - 25 q^{28} - 61 q^{29} - 12 q^{30} - 18 q^{31} - 3 q^{32} - 42 q^{33} - 22 q^{34} - 29 q^{35} - 38 q^{36} - 30 q^{37} - 27 q^{38} - 31 q^{39} - 22 q^{40} - 28 q^{41} - 9 q^{42} - 58 q^{43} - 2 q^{44} - 31 q^{45} - 40 q^{46} - 6 q^{47} - 37 q^{48} - 37 q^{49} - 15 q^{50} - 44 q^{51} - 43 q^{52} - 27 q^{53} - 18 q^{54} - 38 q^{55} - 22 q^{56} - 50 q^{57} + q^{58} - 24 q^{59} + 6 q^{60} - 76 q^{61} - 17 q^{62} - 6 q^{63} - 60 q^{64} - 65 q^{65} - 7 q^{66} - 45 q^{67} - 31 q^{68} - 16 q^{69} - 48 q^{70} - 28 q^{71} - 40 q^{72} - 50 q^{73} - 17 q^{74} - 35 q^{75} - 100 q^{76} + q^{77} - 6 q^{78} - 66 q^{79} - 10 q^{80} - 63 q^{81} - 5 q^{82} - 9 q^{83} - 24 q^{84} - 77 q^{85} + 29 q^{86} + 4 q^{87} - 62 q^{88} - 30 q^{89} + 50 q^{90} - 52 q^{91} - 53 q^{92} - 42 q^{93} - 92 q^{94} - 20 q^{95} - 47 q^{96} - 34 q^{97} + 36 q^{98} - 29 q^{99}+O(q^{100}) \) 61 * q - q^2 - 4 * q^3 + 43 * q^4 - 7 * q^5 - 13 * q^6 - 10 * q^7 - 6 * q^8 + 23 * q^9 - 16 * q^10 - 3 * q^11 - 18 * q^12 - 28 * q^13 - 14 * q^14 - 12 * q^15 + 11 * q^16 - 21 * q^17 - 17 * q^18 - 36 * q^19 - 16 * q^20 - 12 * q^21 - 42 * q^22 - 15 * q^23 - 28 * q^24 - 16 * q^25 - 13 * q^26 - 10 * q^27 - 25 * q^28 - 61 * q^29 - 12 * q^30 - 18 * q^31 - 3 * q^32 - 42 * q^33 - 22 * q^34 - 29 * q^35 - 38 * q^36 - 30 * q^37 - 27 * q^38 - 31 * q^39 - 22 * q^40 - 28 * q^41 - 9 * q^42 - 58 * q^43 - 2 * q^44 - 31 * q^45 - 40 * q^46 - 6 * q^47 - 37 * q^48 - 37 * q^49 - 15 * q^50 - 44 * q^51 - 43 * q^52 - 27 * q^53 - 18 * q^54 - 38 * q^55 - 22 * q^56 - 50 * q^57 + q^58 - 24 * q^59 + 6 * q^60 - 76 * q^61 - 17 * q^62 - 6 * q^63 - 60 * q^64 - 65 * q^65 - 7 * q^66 - 45 * q^67 - 31 * q^68 - 16 * q^69 - 48 * q^70 - 28 * q^71 - 40 * q^72 - 50 * q^73 - 17 * q^74 - 35 * q^75 - 100 * q^76 + q^77 - 6 * q^78 - 66 * q^79 - 10 * q^80 - 63 * q^81 - 5 * q^82 - 9 * q^83 - 24 * q^84 - 77 * q^85 + 29 * q^86 + 4 * q^87 - 62 * q^88 - 30 * q^89 + 50 * q^90 - 52 * q^91 - 53 * q^92 - 42 * q^93 - 92 * q^94 - 20 * q^95 - 47 * q^96 - 34 * q^97 + 36 * q^98 - 29 * q^99

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