LMFDB - Embedded newform 4031.2.a.c.1.17

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			1.17
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)

$f(q)$	$=$	$q-1.44140 q^{2} +2.16928 q^{3} +0.0776255 q^{4} +0.0237256 q^{5} -3.12680 q^{6} +1.29161 q^{7} +2.77090 q^{8} +1.70580 q^{9} +O(q^{10})$	\(q-1.44140 q^{2} +2.16928 q^{3} +0.0776255 q^{4} +0.0237256 q^{5} -3.12680 q^{6} +1.29161 q^{7} +2.77090 q^{8} +1.70580 q^{9} -0.0341981 q^{10} +2.85722 q^{11} +0.168392 q^{12} +3.27002 q^{13} -1.86173 q^{14} +0.0514677 q^{15} -4.14923 q^{16} -2.63441 q^{17} -2.45873 q^{18} -6.32493 q^{19} +0.00184172 q^{20} +2.80188 q^{21} -4.11839 q^{22} -5.18950 q^{23} +6.01088 q^{24} -4.99944 q^{25} -4.71340 q^{26} -2.80750 q^{27} +0.100262 q^{28} -1.00000 q^{29} -0.0741854 q^{30} -5.53067 q^{31} +0.438871 q^{32} +6.19813 q^{33} +3.79722 q^{34} +0.0306444 q^{35} +0.132413 q^{36} +1.80794 q^{37} +9.11673 q^{38} +7.09360 q^{39} +0.0657415 q^{40} -3.80735 q^{41} -4.03862 q^{42} -8.83651 q^{43} +0.221793 q^{44} +0.0404711 q^{45} +7.48013 q^{46} -12.4492 q^{47} -9.00085 q^{48} -5.33173 q^{49} +7.20617 q^{50} -5.71477 q^{51} +0.253837 q^{52} -4.75313 q^{53} +4.04672 q^{54} +0.0677895 q^{55} +3.57894 q^{56} -13.7206 q^{57} +1.44140 q^{58} -7.95235 q^{59} +0.00399520 q^{60} -1.44128 q^{61} +7.97190 q^{62} +2.20323 q^{63} +7.66586 q^{64} +0.0775833 q^{65} -8.93397 q^{66} +8.26135 q^{67} -0.204497 q^{68} -11.2575 q^{69} -0.0441707 q^{70} -5.47640 q^{71} +4.72660 q^{72} +3.62545 q^{73} -2.60595 q^{74} -10.8452 q^{75} -0.490976 q^{76} +3.69043 q^{77} -10.2247 q^{78} +16.7698 q^{79} -0.0984430 q^{80} -11.2076 q^{81} +5.48790 q^{82} +16.7752 q^{83} +0.217497 q^{84} -0.0625030 q^{85} +12.7369 q^{86} -2.16928 q^{87} +7.91709 q^{88} +9.86238 q^{89} -0.0583349 q^{90} +4.22360 q^{91} -0.402837 q^{92} -11.9976 q^{93} +17.9442 q^{94} -0.150063 q^{95} +0.952037 q^{96} -6.95404 q^{97} +7.68515 q^{98} +4.87384 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.44140	−1.01922	−0.509611	−	0.860405i	$-0.670211\pi$
$2$	−1.44140	−1.01922	−0.509611	+	0.860405i	$0.670211\pi$
$3$	2.16928	1.25244	0.626219	−	0.779648i	$-0.284602\pi$
$3$	2.16928	1.25244	0.626219	+	0.779648i	$0.284602\pi$
$4$	0.0776255	0.0388128
$5$	0.0237256	0.0106104	0.00530522	−	0.999986i	$-0.498311\pi$
$5$	0.0237256	0.0106104	0.00530522	+	0.999986i	$0.498311\pi$
$6$	−3.12680	−1.27651
$7$	1.29161	0.488184	0.244092	−	0.969752i	$-0.421510\pi$
$7$	1.29161	0.488184	0.244092	+	0.969752i	$0.421510\pi$
$8$	2.77090	0.979663
$9$	1.70580	0.568599
$10$	−0.0341981	−0.0108144
$11$	2.85722	0.861485	0.430743	−	0.902475i	$-0.358252\pi$
$11$	2.85722	0.861485	0.430743	+	0.902475i	$0.358252\pi$
$12$	0.168392	0.0486105
$13$	3.27002	0.906940	0.453470	−	0.891271i	$-0.350186\pi$
$13$	3.27002	0.906940	0.453470	+	0.891271i	$0.350186\pi$
$14$	−1.86173	−0.497568
$15$	0.0514677	0.0132889
$16$	−4.14923	−1.03731
$17$	−2.63441	−0.638937	−0.319469	−	0.947597i	$-0.603504\pi$
$17$	−2.63441	−0.638937	−0.319469	+	0.947597i	$0.603504\pi$
$18$	−2.45873	−0.579528
$19$	−6.32493	−1.45104	−0.725519	−	0.688202i	$-0.758400\pi$
$19$	−6.32493	−1.45104	−0.725519	+	0.688202i	$0.758400\pi$
$20$	0.00184172	0.000411820 0
$21$	2.80188	0.611420
$22$	−4.11839	−0.878044
$23$	−5.18950	−1.08209	−0.541043	−	0.840995i	$-0.681970\pi$
$23$	−5.18950	−1.08209	−0.541043	+	0.840995i	$0.681970\pi$
$24$	6.01088	1.22697
$25$	−4.99944	−0.999887
$26$	−4.71340	−0.924373
$27$	−2.80750	−0.540303
$28$	0.100262	0.0189478
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	−0.0741854	−0.0135443
$31$	−5.53067	−0.993338	−0.496669	−	0.867940i	$-0.665444\pi$
$31$	−5.53067	−0.993338	−0.496669	+	0.867940i	$0.665444\pi$
$32$	0.438871	0.0775822
$33$	6.19813	1.07896
$34$	3.79722	0.651219
$35$	0.0306444	0.00517984
$36$	0.132413	0.0220689
$37$	1.80794	0.297223	0.148611	−	0.988896i	$-0.452520\pi$
$37$	1.80794	0.297223	0.148611	+	0.988896i	$0.452520\pi$
$38$	9.11673	1.47893
$39$	7.09360	1.13589
$40$	0.0657415	0.0103946
$41$	−3.80735	−0.594608	−0.297304	−	0.954783i	$-0.596087\pi$
$41$	−3.80735	−0.594608	−0.297304	+	0.954783i	$0.596087\pi$
$42$	−4.03862	−0.623172
$43$	−8.83651	−1.34755	−0.673777	−	0.738934i	$-0.735329\pi$
$43$	−8.83651	−1.34755	−0.673777	+	0.738934i	$0.735329\pi$
$44$	0.221793	0.0334366
$45$	0.0404711	0.00603308
$46$	7.48013	1.10288
$47$	−12.4492	−1.81590	−0.907952	−	0.419075i	$-0.862354\pi$
$47$	−12.4492	−1.81590	−0.907952	+	0.419075i	$0.862354\pi$
$48$	−9.00085	−1.29916
$49$	−5.33173	−0.761676
$50$	7.20617	1.01911
$51$	−5.71477	−0.800229
$52$	0.253837	0.0352008
$53$	−4.75313	−0.652892	−0.326446	−	0.945216i	$-0.605851\pi$
$53$	−4.75313	−0.652892	−0.326446	+	0.945216i	$0.605851\pi$
$54$	4.04672	0.550689
$55$	0.0677895	0.00914073
$56$	3.57894	0.478256
$57$	−13.7206	−1.81733
$58$	1.44140	0.189265
$59$	−7.95235	−1.03531	−0.517654	−	0.855590i	$-0.673194\pi$
$59$	−7.95235	−1.03531	−0.517654	+	0.855590i	$0.673194\pi$
$60$	0.00399520	0.000515779 0
$61$	−1.44128	−0.184536	−0.0922682	−	0.995734i	$-0.529412\pi$
$61$	−1.44128	−0.184536	−0.0922682	+	0.995734i	$0.529412\pi$
$62$	7.97190	1.01243
$63$	2.20323	0.277581
$64$	7.66586	0.958233
$65$	0.0775833	0.00962303
$66$	−8.93397	−1.09970
$67$	8.26135	1.00928	0.504642	−	0.863329i	$-0.331624\pi$
$67$	8.26135	1.00928	0.504642	+	0.863329i	$0.331624\pi$
$68$	−0.204497	−0.0247989
$69$	−11.2575	−1.35524
$70$	−0.0441707	−0.00527941
$71$	−5.47640	−0.649929	−0.324964	−	0.945726i	$-0.605352\pi$
$71$	−5.47640	−0.649929	−0.324964	+	0.945726i	$0.605352\pi$
$72$	4.72660	0.557035
$73$	3.62545	0.424327	0.212163	−	0.977234i	$-0.431949\pi$
$73$	3.62545	0.424327	0.212163	+	0.977234i	$0.431949\pi$
$74$	−2.60595	−0.302936
$75$	−10.8452	−1.25230
$76$	−0.490976	−0.0563188
$77$	3.69043	0.420563
$78$	−10.2247	−1.15772
$79$	16.7698	1.88675	0.943374	−	0.331730i	$-0.107632\pi$
$79$	16.7698	1.88675	0.943374	+	0.331730i	$0.107632\pi$
$80$	−0.0984430	−0.0110063
$81$	−11.2076	−1.24529
$82$	5.48790	0.606037
$83$	16.7752	1.84131	0.920656	−	0.390374i	$-0.127654\pi$
$83$	16.7752	1.84131	0.920656	+	0.390374i	$0.127654\pi$
$84$	0.217497	0.0237309
$85$	−0.0625030	−0.00677940
$86$	12.7369	1.37346
$87$	−2.16928	−0.232572
$88$	7.91709	0.843965
$89$	9.86238	1.04541	0.522705	−	0.852514i	$-0.324923\pi$
$89$	9.86238	1.04541	0.522705	+	0.852514i	$0.324923\pi$
$90$	−0.0583349	−0.00614904
$91$	4.22360	0.442754
$92$	−0.402837	−0.0419987
$93$	−11.9976	−1.24409
$94$	17.9442	1.85081
$95$	−0.150063	−0.0153961
$96$	0.952037	0.0971668
$97$	−6.95404	−0.706076	−0.353038	−	0.935609i	$-0.614851\pi$
$97$	−6.95404	−0.706076	−0.353038	+	0.935609i	$0.614851\pi$
$98$	7.68515	0.776317
$99$	4.87384	0.489839
$100$	−0.388084	−0.0388084
$101$	−15.7816	−1.57033	−0.785166	−	0.619285i	$-0.787422\pi$
$101$	−15.7816	−1.57033	−0.785166	+	0.619285i	$0.787422\pi$
$102$	8.23726	0.815610
$103$	−0.497893	−0.0490589	−0.0245294	−	0.999699i	$-0.507809\pi$
$103$	−0.497893	−0.0490589	−0.0245294	+	0.999699i	$0.507809\pi$
$104$	9.06091	0.888496
$105$	0.0664764	0.00648743
$106$	6.85114	0.665442
$107$	−8.37042	−0.809199	−0.404599	−	0.914494i	$-0.632589\pi$
$107$	−8.37042	−0.809199	−0.404599	+	0.914494i	$0.632589\pi$
$108$	−0.217933	−0.0209706
$109$	−7.74654	−0.741984	−0.370992	−	0.928636i	$-0.620982\pi$
$109$	−7.74654	−0.741984	−0.370992	+	0.928636i	$0.620982\pi$
$110$	−0.0977115	−0.00931643
$111$	3.92193	0.372253
$112$	−5.35920	−0.506396
$113$	11.6979	1.10045	0.550223	−	0.835018i	$-0.314543\pi$
$113$	11.6979	1.10045	0.550223	+	0.835018i	$0.314543\pi$
$114$	19.7768	1.85227
$115$	−0.123124	−0.0114814
$116$	−0.0776255	−0.00720735
$117$	5.57799	0.515685
$118$	11.4625	1.05521
$119$	−3.40263	−0.311919
$120$	0.142612	0.0130186
$121$	−2.83628	−0.257843
$122$	2.07745	0.188083
$123$	−8.25922	−0.744709
$124$	−0.429321	−0.0385542
$125$	−0.237243	−0.0212197
$126$	−3.17573	−0.282916
$127$	19.5139	1.73158	0.865790	−	0.500407i	$-0.166816\pi$
$127$	19.5139	1.73158	0.865790	+	0.500407i	$0.166816\pi$
$128$	−11.9273	−1.05423
$129$	−19.1689	−1.68773
$130$	−0.111828	−0.00980800
$131$	21.9921	1.92146	0.960728	−	0.277492i	$-0.0895031\pi$
$131$	21.9921	1.92146	0.960728	+	0.277492i	$0.0895031\pi$
$132$	0.481133	0.0418773
$133$	−8.16937	−0.708374
$134$	−11.9079	−1.02868
$135$	−0.0666097	−0.00573285
$136$	−7.29969	−0.625943
$137$	2.79068	0.238424	0.119212	−	0.992869i	$-0.461963\pi$
$137$	2.79068	0.238424	0.119212	+	0.992869i	$0.461963\pi$
$138$	16.2265	1.38129
$139$	−1.00000	−0.0848189
$139$	−1.00000	−0.0848189
$140$	0.00237878	0.000201044 0
$141$	−27.0059	−2.27430
$142$	7.89366	0.662422
$143$	9.34318	0.781316
$144$	−7.07773	−0.589811
$145$	−0.0237256	−0.00197031
$146$	−5.22572	−0.432483
$147$	−11.5660	−0.953952
$148$	0.140342	0.0115360
$149$	16.7366	1.37111	0.685557	−	0.728019i	$-0.259559\pi$
$149$	16.7366	1.37111	0.685557	+	0.728019i	$0.259559\pi$
$150$	15.6322	1.27637
$151$	−18.4167	−1.49873	−0.749363	−	0.662159i	$-0.769640\pi$
$151$	−18.4167	−1.49873	−0.749363	+	0.662159i	$0.769640\pi$
$152$	−17.5258	−1.42153
$153$	−4.49376	−0.363299
$154$	−5.31937	−0.428647
$155$	−0.131219	−0.0105397
$156$	0.550645	0.0440868
$157$	−3.27599	−0.261452	−0.130726	−	0.991419i	$-0.541731\pi$
$157$	−3.27599	−0.261452	−0.130726	+	0.991419i	$0.541731\pi$
$158$	−24.1719	−1.92302
$159$	−10.3109	−0.817706
$160$	0.0104125	0.000823181 0
$161$	−6.70283	−0.528257
$162$	16.1547	1.26923
$163$	7.71572	0.604341	0.302171	−	0.953254i	$-0.402289\pi$
$163$	7.71572	0.604341	0.302171	+	0.953254i	$0.402289\pi$
$164$	−0.295547	−0.0230784
$165$	0.147055	0.0114482
$166$	−24.1797	−1.87671
$167$	−7.06534	−0.546732	−0.273366	−	0.961910i	$-0.588137\pi$
$167$	−7.06534	−0.546732	−0.273366	+	0.961910i	$0.588137\pi$
$168$	7.76374	0.598985
$169$	−2.30697	−0.177459
$170$	0.0900916	0.00690971
$171$	−10.7890	−0.825058
$172$	−0.685938	−0.0523023
$173$	5.53623	0.420912	0.210456	−	0.977603i	$-0.432505\pi$
$173$	5.53623	0.420912	0.210456	+	0.977603i	$0.432505\pi$
$174$	3.12680	0.237042
$175$	−6.45734	−0.488129
$176$	−11.8553	−0.893624
$177$	−17.2509	−1.29666
$178$	−14.2156	−1.06550
$179$	8.51694	0.636586	0.318293	−	0.947992i	$-0.396890\pi$
$179$	8.51694	0.636586	0.318293	+	0.947992i	$0.396890\pi$
$180$	0.00314159	0.000234160 0
$181$	9.46279	0.703364	0.351682	−	0.936120i	$-0.385610\pi$
$181$	9.46279	0.703364	0.351682	+	0.936120i	$0.385610\pi$
$182$	−6.08789	−0.451264
$183$	−3.12654	−0.231120
$184$	−14.3796	−1.06008
$185$	0.0428944	0.00315366
$186$	17.2933	1.26801
$187$	−7.52708	−0.550435
$188$	−0.966376	−0.0704802
$189$	−3.62620	−0.263767
$190$	0.216300	0.0156921
$191$	−1.04842	−0.0758610	−0.0379305	−	0.999280i	$-0.512077\pi$
$191$	−1.04842	−0.0758610	−0.0379305	+	0.999280i	$0.512077\pi$
$192$	16.6294	1.20013
$193$	−12.1742	−0.876317	−0.438159	−	0.898898i	$-0.644369\pi$
$193$	−12.1742	−0.876317	−0.438159	+	0.898898i	$0.644369\pi$
$194$	10.0235	0.719648
$195$	0.168300	0.0120522
$196$	−0.413879	−0.0295628
$197$	−16.0708	−1.14500	−0.572498	−	0.819906i	$-0.694025\pi$
$197$	−16.0708	−1.14500	−0.572498	+	0.819906i	$0.694025\pi$
$198$	−7.02514	−0.499255
$199$	−8.15113	−0.577818	−0.288909	−	0.957357i	$-0.593293\pi$
$199$	−8.15113	−0.577818	−0.288909	+	0.957357i	$0.593293\pi$
$200$	−13.8530	−0.979553
$201$	17.9212	1.26407
$202$	22.7476	1.60052
$203$	−1.29161	−0.0906535
$204$	−0.443612	−0.0310591
$205$	−0.0903318	−0.00630905
$206$	0.717662	0.0500019
$207$	−8.85222	−0.615272
$208$	−13.5680	−0.940775
$209$	−18.0717	−1.25005
$210$	−0.0958188	−0.00661213
$211$	7.85756	0.540937	0.270469	−	0.962729i	$-0.412821\pi$
$211$	7.85756	0.540937	0.270469	+	0.962729i	$0.412821\pi$
$212$	−0.368964	−0.0253405
$213$	−11.8799	−0.813995
$214$	12.0651	0.824753
$215$	−0.209652	−0.0142981
$216$	−7.77931	−0.529315
$217$	−7.14350	−0.484932
$218$	11.1658	0.756246
$219$	7.86464	0.531443
$220$	0.00526219	0.000354777 0
$221$	−8.61456	−0.579478
$222$	−5.65305	−0.379408
$223$	−5.31289	−0.355777	−0.177889	−	0.984051i	$-0.556927\pi$
$223$	−5.31289	−0.355777	−0.177889	+	0.984051i	$0.556927\pi$
$224$	0.566852	0.0378744
$225$	−8.52802	−0.568535
$226$	−16.8613	−1.12160
$227$	5.65697	0.375466	0.187733	−	0.982220i	$-0.439886\pi$
$227$	5.65697	0.375466	0.187733	+	0.982220i	$0.439886\pi$
$228$	−1.06507	−0.0705357
$229$	−17.8459	−1.17929	−0.589645	−	0.807662i	$-0.700732\pi$
$229$	−17.8459	−1.17929	−0.589645	+	0.807662i	$0.700732\pi$
$230$	0.177471	0.0117021
$231$	8.00559	0.526729
$232$	−2.77090	−0.181919
$233$	8.17627	0.535646	0.267823	−	0.963468i	$-0.413696\pi$
$233$	8.17627	0.535646	0.267823	+	0.963468i	$0.413696\pi$
$234$	−8.04009	−0.525597
$235$	−0.295365	−0.0192675
$236$	−0.617305	−0.0401831
$237$	36.3784	2.36303
$238$	4.90455	0.317915
$239$	15.9450	1.03140	0.515699	−	0.856770i	$-0.327532\pi$
$239$	15.9450	1.03140	0.515699	+	0.856770i	$0.327532\pi$
$240$	−0.213551	−0.0137847
$241$	19.3879	1.24888	0.624441	−	0.781072i	$-0.285327\pi$
$241$	19.3879	1.24888	0.624441	+	0.781072i	$0.285327\pi$
$242$	4.08820	0.262799
$243$	−15.8901	−1.01935
$244$	−0.111880	−0.00716236
$245$	−0.126499	−0.00808171
$246$	11.9048	0.759024
$247$	−20.6826	−1.31600
$248$	−15.3250	−0.973137
$249$	36.3901	2.30613
$250$	0.341961	0.0216275
$251$	3.92085	0.247482	0.123741	−	0.992315i	$-0.460511\pi$
$251$	3.92085	0.247482	0.123741	+	0.992315i	$0.460511\pi$
$252$	0.171027	0.0107737
$253$	−14.8276	−0.932200
$254$	−28.1273	−1.76486
$255$	−0.135587	−0.00849077
$256$	1.86024	0.116265
$257$	−7.58448	−0.473107	−0.236554	−	0.971618i	$-0.576018\pi$
$257$	−7.58448	−0.473107	−0.236554	+	0.971618i	$0.576018\pi$
$258$	27.6300	1.72017
$259$	2.33515	0.145099
$260$	0.00602244	0.000373496 0
$261$	−1.70580	−0.105586
$262$	−31.6993	−1.95839
$263$	6.86867	0.423540	0.211770	−	0.977320i	$-0.432077\pi$
$263$	6.86867	0.423540	0.211770	+	0.977320i	$0.432077\pi$
$264$	17.1744	1.05701
$265$	−0.112771	−0.00692747
$266$	11.7753	0.721990
$267$	21.3943	1.30931
$268$	0.641292	0.0391731
$269$	15.9476	0.972345	0.486173	−	0.873863i	$-0.338393\pi$
$269$	15.9476	0.972345	0.486173	+	0.873863i	$0.338393\pi$
$270$	0.0960110	0.00584304
$271$	−9.26938	−0.563075	−0.281537	−	0.959550i	$-0.590844\pi$
$271$	−9.26938	−0.563075	−0.281537	+	0.959550i	$0.590844\pi$
$272$	10.9307	0.662773
$273$	9.16220	0.554521
$274$	−4.02248	−0.243007
$275$	−14.2845	−0.861388
$276$	−0.873869	−0.0526007
$277$	0.202309	0.0121555	0.00607777	−	0.999982i	$-0.498065\pi$
$277$	0.202309	0.0121555	0.00607777	+	0.999982i	$0.498065\pi$
$278$	1.44140	0.0864493
$279$	−9.43420	−0.564811
$280$	0.0849126	0.00507450
$281$	26.8704	1.60296	0.801478	−	0.598024i	$-0.204047\pi$
$281$	26.8704	1.60296	0.801478	+	0.598024i	$0.204047\pi$
$282$	38.9262	2.31802
$283$	−3.93348	−0.233821	−0.116911	−	0.993142i	$-0.537299\pi$
$283$	−3.93348	−0.233821	−0.116911	+	0.993142i	$0.537299\pi$
$284$	−0.425108	−0.0252255
$285$	−0.325529	−0.0192827
$286$	−13.4672	−0.796334
$287$	−4.91762	−0.290278
$288$	0.748625	0.0441131
$289$	−10.0599	−0.591759
$290$	0.0341981	0.00200818
$291$	−15.0853	−0.884316
$292$	0.281428	0.0164693
$293$	−13.0407	−0.761844	−0.380922	−	0.924607i	$-0.624393\pi$
$293$	−13.0407	−0.761844	−0.380922	+	0.924607i	$0.624393\pi$
$294$	16.6713	0.972288
$295$	−0.188675	−0.0109851
$296$	5.00962	0.291178
$297$	−8.02164	−0.465463
$298$	−24.1241	−1.39747
$299$	−16.9698	−0.981387
$300$	−0.841864	−0.0486051
$301$	−11.4134	−0.657855
$302$	26.5457	1.52753
$303$	−34.2349	−1.96674
$304$	26.2436	1.50517
$305$	−0.0341952	−0.00195801
$306$	6.47729	0.370282
$307$	4.23978	0.241977	0.120988	−	0.992654i	$-0.461394\pi$
$307$	4.23978	0.241977	0.120988	+	0.992654i	$0.461394\pi$
$308$	0.286471	0.0163232
$309$	−1.08007	−0.0614432
$310$	0.189138	0.0107423
$311$	22.6470	1.28420	0.642098	−	0.766623i	$-0.278064\pi$
$311$	22.6470	1.28420	0.642098	+	0.766623i	$0.278064\pi$
$312$	19.6557	1.11278
$313$	10.2916	0.581713	0.290856	−	0.956767i	$-0.406060\pi$
$313$	10.2916	0.581713	0.290856	+	0.956767i	$0.406060\pi$
$314$	4.72200	0.266478
$315$	0.0522730	0.00294525
$316$	1.30176	0.0732299
$317$	−19.8157	−1.11296	−0.556480	−	0.830861i	$-0.687849\pi$
$317$	−19.8157	−1.11296	−0.556480	+	0.830861i	$0.687849\pi$
$318$	14.8621	0.833424
$319$	−2.85722	−0.159974
$320$	0.181878	0.0101673
$321$	−18.1578	−1.01347
$322$	9.66144	0.538411
$323$	16.6624	0.927122
$324$	−0.869999	−0.0483333
$325$	−16.3483	−0.906838
$326$	−11.1214	−0.615958
$327$	−16.8044	−0.929288
$328$	−10.5498	−0.582515
$329$	−16.0796	−0.886495
$330$	−0.211964	−0.0116682
$331$	−27.5993	−1.51700	−0.758498	−	0.651675i	$-0.774067\pi$
$331$	−27.5993	−1.51700	−0.758498	+	0.651675i	$0.774067\pi$
$332$	1.30218	0.0714664
$333$	3.08397	0.169000
$334$	10.1840	0.557241
$335$	0.196006	0.0107089
$336$	−11.6256	−0.634230
$337$	13.8453	0.754203	0.377101	−	0.926172i	$-0.376921\pi$
$337$	13.8453	0.754203	0.377101	+	0.926172i	$0.376921\pi$
$338$	3.32526	0.180870
$339$	25.3761	1.37824
$340$	−0.00485182	−0.000263127 0
$341$	−15.8024	−0.855746
$342$	15.5513	0.840917
$343$	−15.9278	−0.860022
$344$	−24.4851	−1.32015
$345$	−0.267091	−0.0143797
$346$	−7.97991	−0.429003
$347$	4.21277	0.226153	0.113077	−	0.993586i	$-0.463929\pi$
$347$	4.21277	0.226153	0.113077	+	0.993586i	$0.463929\pi$
$348$	−0.168392	−0.00902675
$349$	33.4756	1.79191	0.895954	−	0.444146i	$-0.146493\pi$
$349$	33.4756	1.79191	0.895954	+	0.444146i	$0.146493\pi$
$350$	9.30759	0.497512
$351$	−9.18057	−0.490023
$352$	1.25395	0.0668359
$353$	−14.4749	−0.770419	−0.385210	−	0.922829i	$-0.625871\pi$
$353$	−14.4749	−0.770419	−0.385210	+	0.922829i	$0.625871\pi$
$354$	24.8654	1.32158
$355$	−0.129931	−0.00689603
$356$	0.765572	0.0405752
$357$	−7.38128	−0.390659
$358$	−12.2763	−0.648823
$359$	6.42843	0.339280	0.169640	−	0.985506i	$-0.445740\pi$
$359$	6.42843	0.339280	0.169640	+	0.985506i	$0.445740\pi$
$360$	0.112142	0.00591038
$361$	21.0047	1.10551
$362$	−13.6396	−0.716884
$363$	−6.15269	−0.322932
$364$	0.327859	0.0171845
$365$	0.0860162	0.00450229
$366$	4.50658	0.235563
$367$	−26.1769	−1.36642	−0.683212	−	0.730221i	$-0.739417\pi$
$367$	−26.1769	−1.36642	−0.683212	+	0.730221i	$0.739417\pi$
$368$	21.5324	1.12245
$369$	−6.49456	−0.338093
$370$	−0.0618279	−0.00321428
$371$	−6.13920	−0.318732
$372$	−0.931320	−0.0482867
$373$	−16.8675	−0.873366	−0.436683	−	0.899615i	$-0.643847\pi$
$373$	−16.8675	−0.873366	−0.436683	+	0.899615i	$0.643847\pi$
$374$	10.8495	0.561015
$375$	−0.514648	−0.0265763
$376$	−34.4956	−1.77897
$377$	−3.27002	−0.168415
$378$	5.22680	0.268837
$379$	−9.79954	−0.503369	−0.251684	−	0.967809i	$-0.580984\pi$
$379$	−9.79954	−0.503369	−0.251684	+	0.967809i	$0.580984\pi$
$380$	−0.0116487	−0.000597567 0
$381$	42.3313	2.16870
$382$	1.51119	0.0773192
$383$	33.7504	1.72456	0.862282	−	0.506429i	$-0.169035\pi$
$383$	33.7504	1.72456	0.862282	+	0.506429i	$0.169035\pi$
$384$	−25.8737	−1.32036
$385$	0.0875578	0.00446236
$386$	17.5478	0.893161
$387$	−15.0733	−0.766218
$388$	−0.539811	−0.0274048
$389$	27.7919	1.40911	0.704553	−	0.709651i	$-0.251147\pi$
$389$	27.7919	1.40911	0.704553	+	0.709651i	$0.251147\pi$
$390$	−0.242588	−0.0122839
$391$	13.6712	0.691384
$392$	−14.7737	−0.746186
$393$	47.7071	2.40650
$394$	23.1644	1.16700
$395$	0.397874	0.0200192
$396$	0.378334	0.0190120
$397$	13.4653	0.675802	0.337901	−	0.941182i	$-0.390283\pi$
$397$	13.4653	0.675802	0.337901	+	0.941182i	$0.390283\pi$
$398$	11.7490	0.588925
$399$	−17.7217	−0.887194
$400$	20.7438	1.03719
$401$	11.7256	0.585550	0.292775	−	0.956181i	$-0.405421\pi$
$401$	11.7256	0.585550	0.292775	+	0.956181i	$0.405421\pi$
$402$	−25.8316	−1.28836
$403$	−18.0854	−0.900899
$404$	−1.22506	−0.0609489
$405$	−0.265909	−0.0132131
$406$	1.86173	0.0923960
$407$	5.16567	0.256053
$408$	−15.8351	−0.783954
$409$	39.1642	1.93654	0.968272	−	0.249898i	$-0.0803971\pi$
$409$	39.1642	1.93654	0.968272	+	0.249898i	$0.0803971\pi$
$410$	0.130204	0.00643032
$411$	6.05378	0.298611
$412$	−0.0386492	−0.00190411
$413$	−10.2714	−0.505421
$414$	12.7596	0.627099
$415$	0.398001	0.0195371
$416$	1.43512	0.0703624
$417$	−2.16928	−0.106230
$418$	26.0485	1.27408
$419$	14.0821	0.687956	0.343978	−	0.938978i	$-0.388225\pi$
$419$	14.0821	0.687956	0.343978	+	0.938978i	$0.388225\pi$
$420$	0.00516026	0.000251795 0
$421$	13.5069	0.658286	0.329143	−	0.944280i	$-0.393240\pi$
$421$	13.5069	0.658286	0.329143	+	0.944280i	$0.393240\pi$
$422$	−11.3259	−0.551335
$423$	−21.2358	−1.03252
$424$	−13.1705	−0.639614
$425$	13.1705	0.638865
$426$	17.1236	0.829641
$427$	−1.86157	−0.0900877
$428$	−0.649758	−0.0314072
$429$	20.2680	0.978549
$430$	0.302192	0.0145730
$431$	−25.7758	−1.24157	−0.620787	−	0.783979i	$-0.713187\pi$
$431$	−25.7758	−1.24157	−0.620787	+	0.783979i	$0.713187\pi$
$432$	11.6489	0.560460
$433$	−3.31352	−0.159237	−0.0796187	−	0.996825i	$-0.525370\pi$
$433$	−3.31352	−0.159237	−0.0796187	+	0.996825i	$0.525370\pi$
$434$	10.2966	0.494253
$435$	−0.0514677	−0.00246769
$436$	−0.601329	−0.0287984
$437$	32.8232	1.57015
$438$	−11.3361	−0.541658
$439$	13.5199	0.645270	0.322635	−	0.946523i	$-0.395431\pi$
$439$	13.5199	0.645270	0.322635	+	0.946523i	$0.395431\pi$
$440$	0.187838	0.00895483
$441$	−9.09485	−0.433088
$442$	12.4170	0.590616
$443$	2.35544	0.111910	0.0559552	−	0.998433i	$-0.482180\pi$
$443$	2.35544	0.111910	0.0559552	+	0.998433i	$0.482180\pi$
$444$	0.304442	0.0144482
$445$	0.233991	0.0110922
$446$	7.65798	0.362616
$447$	36.3064	1.71723
$448$	9.90133	0.467794
$449$	4.42492	0.208825	0.104413	−	0.994534i	$-0.466704\pi$
$449$	4.42492	0.208825	0.104413	+	0.994534i	$0.466704\pi$
$450$	12.2923	0.579463
$451$	−10.8784	−0.512246
$452$	0.908056	0.0427113
$453$	−39.9510	−1.87706
$454$	−8.15394	−0.382683
$455$	0.100208	0.00469781
$456$	−38.0184	−1.78037
$457$	−37.2863	−1.74418	−0.872089	−	0.489348i	$-0.837235\pi$
$457$	−37.2863	−1.74418	−0.872089	+	0.489348i	$0.837235\pi$
$458$	25.7230	1.20196
$459$	7.39608	0.345220
$460$	−0.00955758	−0.000445624 0
$461$	3.78948	0.176494	0.0882469	−	0.996099i	$-0.471874\pi$
$461$	3.78948	0.176494	0.0882469	+	0.996099i	$0.471874\pi$
$462$	−11.5392	−0.536854
$463$	5.94468	0.276273	0.138136	−	0.990413i	$-0.455889\pi$
$463$	5.94468	0.276273	0.138136	+	0.990413i	$0.455889\pi$
$464$	4.14923	0.192623
$465$	−0.284651	−0.0132004
$466$	−11.7853	−0.545942
$467$	−15.8081	−0.731510	−0.365755	−	0.930711i	$-0.619189\pi$
$467$	−15.8081	−0.731510	−0.365755	+	0.930711i	$0.619189\pi$
$468$	0.432994	0.0200152
$469$	10.6705	0.492717
$470$	0.425739	0.0196379
$471$	−7.10655	−0.327453
$472$	−22.0352	−1.01425
$473$	−25.2479	−1.16090
$474$	−52.4358	−2.40846
$475$	31.6211	1.45087
$476$	−0.264131	−0.0121064
$477$	−8.10786	−0.371234
$478$	−22.9831	−1.05122
$479$	15.0571	0.687975	0.343988	−	0.938974i	$-0.388222\pi$
$479$	15.0571	0.687975	0.343988	+	0.938974i	$0.388222\pi$
$480$	0.0225877	0.00103098
$481$	5.91198	0.269563
$482$	−27.9456	−1.27289
$483$	−14.5403	−0.661608
$484$	−0.220167	−0.0100076
$485$	−0.164989	−0.00749177
$486$	22.9039	1.03894
$487$	−16.7173	−0.757532	−0.378766	−	0.925492i	$-0.623652\pi$
$487$	−16.7173	−0.757532	−0.378766	+	0.925492i	$0.623652\pi$
$488$	−3.99364	−0.180783
$489$	16.7376	0.756900
$490$	0.182335	0.00823706
$491$	−20.5445	−0.927159	−0.463579	−	0.886055i	$-0.653435\pi$
$491$	−20.5445	−0.927159	−0.463579	+	0.886055i	$0.653435\pi$
$492$	−0.641126	−0.0289042
$493$	2.63441	0.118648
$494$	29.8119	1.34130
$495$	0.115635	0.00519741
$496$	22.9480	1.03040
$497$	−7.07339	−0.317285
$498$	−52.4526	−2.35046
$499$	−35.2627	−1.57857	−0.789287	−	0.614025i	$-0.789549\pi$
$499$	−35.2627	−1.57857	−0.789287	+	0.614025i	$0.789549\pi$
$500$	−0.0184161	−0.000823594 0
$501$	−15.3267	−0.684748
$502$	−5.65151	−0.252239
$503$	−2.94724	−0.131411	−0.0657055	−	0.997839i	$-0.520930\pi$
$503$	−2.94724	−0.131411	−0.0657055	+	0.997839i	$0.520930\pi$
$504$	6.10494	0.271936
$505$	−0.374430	−0.0166619
$506$	21.3724	0.950119
$507$	−5.00448	−0.222257
$508$	1.51478	0.0672074
$509$	−32.5256	−1.44167	−0.720836	−	0.693106i	$-0.756242\pi$
$509$	−32.5256	−1.44167	−0.720836	+	0.693106i	$0.756242\pi$
$510$	0.195434	0.00865398
$511$	4.68268	0.207150
$512$	21.1732	0.935734
$513$	17.7572	0.784000
$514$	10.9323	0.482201
$515$	−0.0118128	−0.000520536 0
$516$	−1.48800	−0.0655054
$517$	−35.5702	−1.56437
$518$	−3.36588	−0.147888
$519$	12.0097	0.527166
$520$	0.214976	0.00942732
$521$	−21.0994	−0.924380	−0.462190	−	0.886781i	$-0.652936\pi$
$521$	−21.0994	−0.924380	−0.462190	+	0.886781i	$0.652936\pi$
$522$	2.45873	0.107616
$523$	−2.03896	−0.0891576	−0.0445788	−	0.999006i	$-0.514195\pi$
$523$	−2.03896	−0.0891576	−0.0445788	+	0.999006i	$0.514195\pi$
$524$	1.70715	0.0745770
$525$	−14.0078	−0.611351
$526$	−9.90048	−0.431681
$527$	14.5700	0.634681
$528$	−25.7174	−1.11921
$529$	3.93089	0.170908
$530$	0.162548	0.00706062
$531$	−13.5651	−0.588674
$532$	−0.634151	−0.0274939
$533$	−12.4501	−0.539274
$534$	−30.8377	−1.33448
$535$	−0.198594	−0.00858595
$536$	22.8914	0.988759
$537$	18.4757	0.797284
$538$	−22.9869	−0.991035
$539$	−15.2340	−0.656173
$540$	−0.00517061	−0.000222508 0
$541$	−16.7240	−0.719021	−0.359511	−	0.933141i	$-0.617056\pi$
$541$	−16.7240	−0.719021	−0.359511	+	0.933141i	$0.617056\pi$
$542$	13.3609	0.573898
$543$	20.5275	0.880919
$544$	−1.15616	−0.0495702
$545$	−0.183792	−0.00787277
$546$	−13.2064	−0.565180
$547$	32.9566	1.40912	0.704562	−	0.709643i	$-0.251144\pi$
$547$	32.9566	1.40912	0.704562	+	0.709643i	$0.251144\pi$
$548$	0.216628	0.00925388
$549$	−2.45852	−0.104927
$550$	20.5896	0.877945
$551$	6.32493	0.269451
$552$	−31.1935	−1.32768
$553$	21.6601	0.921081
$554$	−0.291607	−0.0123892
$555$	0.0930502	0.00394976
$556$	−0.0776255	−0.00329205
$557$	30.8339	1.30647	0.653236	−	0.757154i	$-0.273411\pi$
$557$	30.8339	1.30647	0.653236	+	0.757154i	$0.273411\pi$
$558$	13.5984	0.575668
$559$	−28.8956	−1.22215
$560$	−0.127150	−0.00537308
$561$	−16.3284	−0.689385
$562$	−38.7310	−1.63377
$563$	−34.0004	−1.43295	−0.716474	−	0.697614i	$-0.754245\pi$
$563$	−34.0004	−1.43295	−0.716474	+	0.697614i	$0.754245\pi$
$564$	−2.09634	−0.0882720
$565$	0.277540	0.0116762
$566$	5.66971	0.238316
$567$	−14.4760	−0.607933
$568$	−15.1746	−0.636711
$569$	3.02396	0.126771	0.0633856	−	0.997989i	$-0.479810\pi$
$569$	3.02396	0.126771	0.0633856	+	0.997989i	$0.479810\pi$
$570$	0.469217	0.0196533
$571$	0.857273	0.0358757	0.0179379	−	0.999839i	$-0.494290\pi$
$571$	0.857273	0.0358757	0.0179379	+	0.999839i	$0.494290\pi$
$572$	0.725269	0.0303250
$573$	−2.27432	−0.0950111
$574$	7.08825	0.295858
$575$	25.9446	1.08196
$576$	13.0764	0.544850
$577$	−40.7432	−1.69616	−0.848082	−	0.529866i	$-0.822242\pi$
$577$	−40.7432	−1.69616	−0.848082	+	0.529866i	$0.822242\pi$
$578$	14.5003	0.603134
$579$	−26.4093	−1.09753
$580$	−0.00184172	−7.64731e−5 0
$581$	21.6670	0.898900
$582$	21.7439	0.901314
$583$	−13.5807	−0.562457
$584$	10.0458	0.415697
$585$	0.132341	0.00547164
$586$	18.7968	0.776488
$587$	−19.5934	−0.808705	−0.404353	−	0.914603i	$-0.632503\pi$
$587$	−19.5934	−0.808705	−0.404353	+	0.914603i	$0.632503\pi$
$588$	−0.897820	−0.0370255
$589$	34.9811	1.44137
$590$	0.271955	0.0111962
$591$	−34.8621	−1.43403
$592$	−7.50153	−0.308311
$593$	1.62330	0.0666611	0.0333305	−	0.999444i	$-0.489389\pi$
$593$	1.62330	0.0666611	0.0333305	+	0.999444i	$0.489389\pi$
$594$	11.5624	0.474410
$595$	−0.0807297	−0.00330959
$596$	1.29919	0.0532167
$597$	−17.6821	−0.723681
$598$	24.4602	1.00025
$599$	−42.3633	−1.73092	−0.865458	−	0.500981i	$-0.832973\pi$
$599$	−42.3633	−1.73092	−0.865458	+	0.500981i	$0.832973\pi$
$600$	−30.0510	−1.22683
$601$	−39.5236	−1.61220	−0.806100	−	0.591780i	$-0.798425\pi$
$601$	−39.5236	−1.61220	−0.806100	+	0.591780i	$0.798425\pi$
$602$	16.4512	0.670500
$603$	14.0922	0.573878
$604$	−1.42960	−0.0581697
$605$	−0.0672925	−0.00273583
$606$	49.3460	2.00455
$607$	42.8241	1.73818	0.869088	−	0.494658i	$-0.164706\pi$
$607$	42.8241	1.73818	0.869088	+	0.494658i	$0.164706\pi$
$608$	−2.77583	−0.112575
$609$	−2.80188	−0.113538
$610$	0.0492888	0.00199565
$611$	−40.7091	−1.64692
$612$	−0.348830	−0.0141006
$613$	−3.16702	−0.127915	−0.0639573	−	0.997953i	$-0.520372\pi$
$613$	−3.16702	−0.127915	−0.0639573	+	0.997953i	$0.520372\pi$
$614$	−6.11120	−0.246628
$615$	−0.195955	−0.00790168
$616$	10.2258	0.412010
$617$	20.9486	0.843360	0.421680	−	0.906745i	$-0.361441\pi$
$617$	20.9486	0.843360	0.421680	+	0.906745i	$0.361441\pi$
$618$	1.55681	0.0626242
$619$	−18.9591	−0.762029	−0.381014	−	0.924569i	$-0.624425\pi$
$619$	−18.9591	−0.762029	−0.381014	+	0.924569i	$0.624425\pi$
$620$	−0.0101859	−0.000409077 0
$621$	14.5695	0.584654
$622$	−32.6434	−1.30888
$623$	12.7384	0.510353
$624$	−29.4330	−1.17826
$625$	24.9916	0.999662
$626$	−14.8342	−0.592894
$627$	−39.2027	−1.56561
$628$	−0.254300	−0.0101477
$629$	−4.76283	−0.189907
$630$	−0.0753462	−0.00300186
$631$	−14.0990	−0.561274	−0.280637	−	0.959814i	$-0.590546\pi$
$631$	−14.0990	−0.561274	−0.280637	+	0.959814i	$0.590546\pi$
$632$	46.4675	1.84838
$633$	17.0453	0.677490
$634$	28.5623	1.13435
$635$	0.462980	0.0183728
$636$	−0.800388	−0.0317374
$637$	−17.4349	−0.690795
$638$	4.11839	0.163049
$639$	−9.34162	−0.369549
$640$	−0.282983	−0.0111859
$641$	−0.143017	−0.00564884	−0.00282442	−	0.999996i	$-0.500899\pi$
$641$	−0.143017	−0.00564884	−0.00282442	+	0.999996i	$0.500899\pi$
$642$	26.1726	1.03295
$643$	−12.4764	−0.492022	−0.246011	−	0.969267i	$-0.579120\pi$
$643$	−12.4764	−0.492022	−0.246011	+	0.969267i	$0.579120\pi$
$644$	−0.520310	−0.0205031
$645$	−0.454794	−0.0179075
$646$	−24.0172	−0.944943
$647$	−28.2334	−1.10997	−0.554984	−	0.831861i	$-0.687276\pi$
$647$	−28.2334	−1.10997	−0.554984	+	0.831861i	$0.687276\pi$
$648$	−31.0553	−1.21997
$649$	−22.7216	−0.891902
$650$	23.5643	0.924269
$651$	−15.4963	−0.607347
$652$	0.598936	0.0234562
$653$	−29.5921	−1.15803	−0.579014	−	0.815318i	$-0.696562\pi$
$653$	−29.5921	−1.15803	−0.579014	+	0.815318i	$0.696562\pi$
$654$	24.2219	0.947150
$655$	0.521776	0.0203875
$656$	15.7975	0.616791
$657$	6.18428	0.241272
$658$	23.1770	0.903535
$659$	28.3564	1.10461	0.552304	−	0.833643i	$-0.313749\pi$
$659$	28.3564	1.10461	0.552304	+	0.833643i	$0.313749\pi$
$660$	0.0114152	0.000444336 0
$661$	−11.3046	−0.439696	−0.219848	−	0.975534i	$-0.570556\pi$
$661$	−11.3046	−0.439696	−0.219848	+	0.975534i	$0.570556\pi$
$662$	39.7816	1.54616
$663$	−18.6874	−0.725759
$664$	46.4824	1.80387
$665$	−0.193823	−0.00751615
$666$	−4.44522	−0.172249
$667$	5.18950	0.200938
$668$	−0.548450	−0.0212202
$669$	−11.5252	−0.445589
$670$	−0.282522	−0.0109148
$671$	−4.11804	−0.158975
$672$	1.22966	0.0474353
$673$	−17.0891	−0.658735	−0.329367	−	0.944202i	$-0.606835\pi$
$673$	−17.0891	−0.658735	−0.329367	+	0.944202i	$0.606835\pi$
$674$	−19.9566	−0.768700
$675$	14.0359	0.540242
$676$	−0.179080	−0.00688769
$677$	−28.8172	−1.10753	−0.553767	−	0.832672i	$-0.686810\pi$
$677$	−28.8172	−1.10753	−0.553767	+	0.832672i	$0.686810\pi$
$678$	−36.5770	−1.40473
$679$	−8.98194	−0.344695
$680$	−0.173190	−0.00664152
$681$	12.2716	0.470248
$682$	22.7775	0.872195
$683$	10.6669	0.408158	0.204079	−	0.978954i	$-0.434580\pi$
$683$	10.6669	0.408158	0.204079	+	0.978954i	$0.434580\pi$
$684$	−0.837505	−0.0320228
$685$	0.0662106	0.00252978
$686$	22.9583	0.876553
$687$	−38.7128	−1.47699
$688$	36.6647	1.39783
$689$	−15.5428	−0.592134
$690$	0.384985	0.0146561
$691$	10.5226	0.400300	0.200150	−	0.979765i	$-0.435857\pi$
$691$	10.5226	0.400300	0.200150	+	0.979765i	$0.435857\pi$
$692$	0.429753	0.0163368
$693$	6.29512	0.239132
$694$	−6.07227	−0.230500
$695$	−0.0237256	−0.000899965 0
$696$	−6.01088	−0.227842
$697$	10.0301	0.379917
$698$	−48.2516	−1.82635
$699$	17.7367	0.670862
$700$	−0.501254	−0.0189456
$701$	−5.17967	−0.195633	−0.0978167	−	0.995204i	$-0.531186\pi$
$701$	−5.17967	−0.195633	−0.0978167	+	0.995204i	$0.531186\pi$
$702$	13.2328	0.499442
$703$	−11.4351	−0.431282
$704$	21.9031	0.825503
$705$	−0.640732	−0.0241314
$706$	20.8640	0.785228
$707$	−20.3838	−0.766611
$708$	−1.33911	−0.0503268
$709$	11.9938	0.450435	0.225218	−	0.974308i	$-0.427691\pi$
$709$	11.9938	0.450435	0.225218	+	0.974308i	$0.427691\pi$
$710$	0.187282	0.00702858
$711$	28.6058	1.07280
$712$	27.3277	1.02415
$713$	28.7014	1.07488
$714$	10.6394	0.398168
$715$	0.221673	0.00829009
$716$	0.661132	0.0247077
$717$	34.5893	1.29176
$718$	−9.26592	−0.345801
$719$	22.1622	0.826511	0.413256	−	0.910615i	$-0.364392\pi$
$719$	22.1622	0.826511	0.413256	+	0.910615i	$0.364392\pi$
$720$	−0.167924	−0.00625815
$721$	−0.643086	−0.0239498
$722$	−30.2762	−1.12676
$723$	42.0578	1.56415
$724$	0.734554	0.0272995
$725$	4.99944	0.185674
$726$	8.86847	0.329140
$727$	29.8138	1.10573	0.552866	−	0.833270i	$-0.313534\pi$
$727$	29.8138	1.10573	0.552866	+	0.833270i	$0.313534\pi$
$728$	11.7032	0.433749
$729$	−0.847182	−0.0313771
$730$	−0.123983	−0.00458883
$731$	23.2789	0.861003
$732$	−0.242699	−0.00897041
$733$	−14.3713	−0.530816	−0.265408	−	0.964136i	$-0.585507\pi$
$733$	−14.3713	−0.530816	−0.265408	+	0.964136i	$0.585507\pi$
$734$	37.7313	1.39269
$735$	−0.274412	−0.0101218
$736$	−2.27752	−0.0839506
$737$	23.6045	0.869484
$738$	9.36124	0.344592
$739$	−12.0779	−0.444293	−0.222147	−	0.975013i	$-0.571306\pi$
$739$	−12.0779	−0.444293	−0.222147	+	0.975013i	$0.571306\pi$
$740$	0.00332970	0.000122402 0
$741$	−44.8665	−1.64821
$742$	8.84903	0.324858
$743$	30.2748	1.11067	0.555337	−	0.831626i	$-0.312589\pi$
$743$	30.2748	1.11067	0.555337	+	0.831626i	$0.312589\pi$
$744$	−33.2442	−1.21879
$745$	0.397086	0.0145481
$746$	24.3128	0.890154
$747$	28.6150	1.04697
$748$	−0.584294	−0.0213639
$749$	−10.8113	−0.395038
$750$	0.741812	0.0270871
$751$	−17.2916	−0.630980	−0.315490	−	0.948929i	$-0.602169\pi$
$751$	−17.2916	−0.630980	−0.315490	+	0.948929i	$0.602169\pi$
$752$	51.6546	1.88365
$753$	8.50545	0.309956
$754$	4.71340	0.171652
$755$	−0.436947	−0.0159021
$756$	−0.281486	−0.0102375
$757$	−5.14268	−0.186914	−0.0934569	−	0.995623i	$-0.529792\pi$
$757$	−5.14268	−0.186914	−0.0934569	+	0.995623i	$0.529792\pi$
$758$	14.1250	0.513044
$759$	−32.1652	−1.16752
$760$	−0.415810	−0.0150830
$761$	−2.61328	−0.0947313	−0.0473657	−	0.998878i	$-0.515083\pi$
$761$	−2.61328	−0.0947313	−0.0473657	+	0.998878i	$0.515083\pi$
$762$	−61.0161	−2.21038
$763$	−10.0055	−0.362225
$764$	−0.0813841	−0.00294437
$765$	−0.106617	−0.00385476
$766$	−48.6477	−1.75771
$767$	−26.0043	−0.938962
$768$	4.03539	0.145615
$769$	−43.4797	−1.56792	−0.783959	−	0.620813i	$-0.786803\pi$
$769$	−43.4797	−1.56792	−0.783959	+	0.620813i	$0.786803\pi$
$770$	−0.126206	−0.00454813
$771$	−16.4529	−0.592537
$772$	−0.945027	−0.0340123
$773$	3.95881	0.142389	0.0711943	−	0.997462i	$-0.477319\pi$
$773$	3.95881	0.142389	0.0711943	+	0.997462i	$0.477319\pi$
$774$	21.7266	0.780946
$775$	27.6503	0.993227
$776$	−19.2690	−0.691717
$777$	5.06561	0.181728
$778$	−40.0592	−1.43619
$779$	24.0812	0.862799
$780$	0.0130644	0.000467780 0
$781$	−15.6473	−0.559904
$782$	−19.7057	−0.704674
$783$	2.80750	0.100332
$784$	22.1226	0.790092
$785$	−0.0777249	−0.00277412
$786$	−68.7648	−2.45276
$787$	−40.1335	−1.43061	−0.715303	−	0.698815i	$-0.753711\pi$
$787$	−40.1335	−1.43061	−0.715303	+	0.698815i	$0.753711\pi$
$788$	−1.24750	−0.0444404
$789$	14.9001	0.530457
$790$	−0.573494	−0.0204040
$791$	15.1092	0.537220
$792$	13.5049	0.479877
$793$	−4.71300	−0.167363
$794$	−19.4088	−0.688792
$795$	−0.244632	−0.00867622
$796$	−0.632736	−0.0224267
$797$	24.6515	0.873202	0.436601	−	0.899655i	$-0.356182\pi$
$797$	24.6515	0.873202	0.436601	+	0.899655i	$0.356182\pi$
$798$	25.5440	0.904247
$799$	32.7963	1.16025
$800$	−2.19411	−0.0775735
$801$	16.8232	0.594419
$802$	−16.9013	−0.596805
$803$	10.3587	0.365551
$804$	1.39114	0.0490619
$805$	−0.159029	−0.00560503
$806$	26.0683	0.918215
$807$	34.5950	1.21780
$808$	−43.7294	−1.53840
$809$	23.6805	0.832562	0.416281	−	0.909236i	$-0.363333\pi$
$809$	23.6805	0.832562	0.416281	+	0.909236i	$0.363333\pi$
$810$	0.383280	0.0134671
$811$	0.268429	0.00942581	0.00471291	−	0.999989i	$-0.498500\pi$
$811$	0.268429	0.00942581	0.00471291	+	0.999989i	$0.498500\pi$
$812$	−0.100262	−0.00351851
$813$	−20.1079	−0.705215
$814$	−7.44579	−0.260975
$815$	0.183060	0.00641232
$816$	23.7119	0.830082
$817$	55.8903	1.95535
$818$	−56.4511	−1.97377
$819$	7.20460	0.251749
$820$	−0.00701205	−0.000244871 0
$821$	−13.3248	−0.465038	−0.232519	−	0.972592i	$-0.574697\pi$
$821$	−13.3248	−0.465038	−0.232519	+	0.972592i	$0.574697\pi$
$822$	−8.72590	−0.304351
$823$	25.0905	0.874598	0.437299	−	0.899316i	$-0.355935\pi$
$823$	25.0905	0.874598	0.437299	+	0.899316i	$0.355935\pi$
$824$	−1.37961	−0.0480612
$825$	−30.9872	−1.07883
$826$	14.8051	0.515136
$827$	−12.1457	−0.422348	−0.211174	−	0.977449i	$-0.567729\pi$
$827$	−12.1457	−0.422348	−0.211174	+	0.977449i	$0.567729\pi$
$828$	−0.687158	−0.0238804
$829$	−27.9464	−0.970617	−0.485309	−	0.874343i	$-0.661293\pi$
$829$	−27.9464	−0.970617	−0.485309	+	0.874343i	$0.661293\pi$
$830$	−0.573678	−0.0199127
$831$	0.438865	0.0152240
$832$	25.0675	0.869060
$833$	14.0459	0.486663
$834$	3.12680	0.108272
$835$	−0.167630	−0.00580106
$836$	−1.40283	−0.0485178
$837$	15.5274	0.536704
$838$	−20.2979	−0.701180
$839$	48.9226	1.68900	0.844498	−	0.535558i	$-0.179899\pi$
$839$	48.9226	1.68900	0.844498	+	0.535558i	$0.179899\pi$
$840$	0.184200	0.00635549
$841$	1.00000	0.0344828
$842$	−19.4688	−0.670939
$843$	58.2896	2.00760
$844$	0.609947	0.0209953
$845$	−0.0547344	−0.00188292
$846$	30.6092	1.05237
$847$	−3.66337	−0.125875
$848$	19.7218	0.677249
$849$	−8.53284	−0.292846
$850$	−18.9840	−0.651145
$851$	−9.38228	−0.321620
$852$	−0.922181	−0.0315934
$853$	−31.5562	−1.08046	−0.540232	−	0.841516i	$-0.681664\pi$
$853$	−31.5562	−1.08046	−0.540232	+	0.841516i	$0.681664\pi$
$854$	2.68326	0.0918194
$855$	−0.255977	−0.00875422
$856$	−23.1936	−0.792742
$857$	−42.8914	−1.46514	−0.732571	−	0.680691i	$-0.761680\pi$
$857$	−42.8914	−1.46514	−0.732571	+	0.680691i	$0.761680\pi$
$858$	−29.2142	−0.997358
$859$	9.26195	0.316014	0.158007	−	0.987438i	$-0.449493\pi$
$859$	9.26195	0.316014	0.158007	+	0.987438i	$0.449493\pi$
$860$	−0.0162743	−0.000554950 0
$861$	−10.6677	−0.363555
$862$	37.1531	1.26544
$863$	−14.6948	−0.500216	−0.250108	−	0.968218i	$-0.580466\pi$
$863$	−14.6948	−0.500216	−0.250108	+	0.968218i	$0.580466\pi$
$864$	−1.23213	−0.0419179
$865$	0.131351	0.00446606
$866$	4.77609	0.162298
$867$	−21.8228	−0.741141
$868$	−0.554517	−0.0188215
$869$	47.9150	1.62541
$870$	0.0741854	0.00251512
$871$	27.0148	0.915361
$872$	−21.4649	−0.726894
$873$	−11.8622	−0.401474
$874$	−47.3113	−1.60033
$875$	−0.306426	−0.0103591
$876$	0.610496	0.0206268
$877$	−22.3081	−0.753290	−0.376645	−	0.926358i	$-0.622922\pi$
$877$	−22.3081	−0.753290	−0.376645	+	0.926358i	$0.622922\pi$
$878$	−19.4876	−0.657673
$879$	−28.2889	−0.954162
$880$	−0.281274	−0.00948174
$881$	42.2608	1.42380	0.711902	−	0.702279i	$-0.247834\pi$
$881$	42.2608	1.42380	0.711902	+	0.702279i	$0.247834\pi$
$882$	13.1093	0.441413
$883$	−38.1070	−1.28240	−0.641202	−	0.767372i	$-0.721564\pi$
$883$	−38.1070	−1.28240	−0.641202	+	0.767372i	$0.721564\pi$
$884$	−0.668709	−0.0224911
$885$	−0.409289	−0.0137581
$886$	−3.39512	−0.114061
$887$	24.0823	0.808606	0.404303	−	0.914625i	$-0.367514\pi$
$887$	24.0823	0.808606	0.404303	+	0.914625i	$0.367514\pi$
$888$	10.8673	0.364682
$889$	25.2045	0.845330
$890$	−0.337274	−0.0113055
$891$	−32.0228	−1.07280
$892$	−0.412416	−0.0138087
$893$	78.7403	2.63495
$894$	−52.3320	−1.75024
$895$	0.202070	0.00675445
$896$	−15.4055	−0.514660
$897$	−36.8122	−1.22912
$898$	−6.37807	−0.212839
$899$	5.53067	0.184458
$900$	−0.661992	−0.0220664
$901$	12.5217	0.417157
$902$	15.6802	0.522092
$903$	−24.7588	−0.823922
$904$	32.4138	1.07807
$905$	0.224511	0.00746299
$906$	57.5852	1.91314
$907$	−21.9045	−0.727326	−0.363663	−	0.931531i	$-0.618474\pi$
$907$	−21.9045	−0.727326	−0.363663	+	0.931531i	$0.618474\pi$
$908$	0.439125	0.0145729
$909$	−26.9203	−0.892889
$910$	−0.144439	−0.00478811
$911$	−24.6992	−0.818319	−0.409160	−	0.912463i	$-0.634178\pi$
$911$	−24.6992	−0.818319	−0.409160	+	0.912463i	$0.634178\pi$
$912$	56.9297	1.88513
$913$	47.9304	1.58626
$914$	53.7443	1.77770
$915$	−0.0741791	−0.00245228
$916$	−1.38530	−0.0457715
$917$	28.4053	0.938024
$918$	−10.6607	−0.351855
$919$	−14.9096	−0.491823	−0.245912	−	0.969292i	$-0.579087\pi$
$919$	−14.9096	−0.491823	−0.245912	+	0.969292i	$0.579087\pi$
$920$	−0.341165	−0.0112479
$921$	9.19729	0.303061
$922$	−5.46215	−0.179886
$923$	−17.9079	−0.589447
$924$	0.621438	0.0204438
$925$	−9.03866	−0.297189
$926$	−8.56864	−0.281583
$927$	−0.849304	−0.0278948
$928$	−0.438871	−0.0144067
$929$	35.2255	1.15571	0.577856	−	0.816139i	$-0.303890\pi$
$929$	35.2255	1.15571	0.577856	+	0.816139i	$0.303890\pi$
$930$	0.410295	0.0134541
$931$	33.7228	1.10522
$932$	0.634687	0.0207899
$933$	49.1279	1.60837
$934$	22.7857	0.745570
$935$	−0.178585	−0.00584035
$936$	15.4561	0.505197
$937$	−26.5636	−0.867796	−0.433898	−	0.900962i	$-0.642862\pi$
$937$	−26.5636	−0.867796	−0.433898	+	0.900962i	$0.642862\pi$
$938$	−15.3804	−0.502188
$939$	22.3253	0.728559
$940$	−0.0229279	−0.000747825 0
$941$	32.4804	1.05883	0.529415	−	0.848363i	$-0.322411\pi$
$941$	32.4804	1.05883	0.529415	+	0.848363i	$0.322411\pi$
$942$	10.2434	0.333747
$943$	19.7582	0.643416
$944$	32.9961	1.07393
$945$	−0.0860340	−0.00279869
$946$	36.3922	1.18321
$947$	−12.0046	−0.390098	−0.195049	−	0.980793i	$-0.562487\pi$
$947$	−12.0046	−0.390098	−0.195049	+	0.980793i	$0.562487\pi$
$948$	2.82390	0.0917159
$949$	11.8553	0.384839
$950$	−45.5785	−1.47876
$951$	−42.9859	−1.39391
$952$	−9.42838	−0.305575
$953$	10.0335	0.325017	0.162508	−	0.986707i	$-0.448042\pi$
$953$	10.0335	0.325017	0.162508	+	0.986707i	$0.448042\pi$
$954$	11.6867	0.378369
$955$	−0.0248744	−0.000804918 0
$956$	1.23774	0.0400314
$957$	−6.19813	−0.200357
$958$	−21.7032	−0.701199
$959$	3.60448	0.116395
$960$	0.394544	0.0127339
$961$	−0.411638	−0.0132786
$962$	−8.52152	−0.274745
$963$	−14.2782	−0.460109
$964$	1.50499	0.0484726
$965$	−0.288840	−0.00929810
$966$	20.9584	0.674326
$967$	27.1988	0.874656	0.437328	−	0.899302i	$-0.355925\pi$
$967$	27.1988	0.874656	0.437328	+	0.899302i	$0.355925\pi$
$968$	−7.85905	−0.252599
$969$	36.1455	1.16116
$970$	0.237815	0.00763578
$971$	38.7602	1.24387	0.621937	−	0.783067i	$-0.286346\pi$
$971$	38.7602	1.24387	0.621937	+	0.783067i	$0.286346\pi$
$972$	−1.23348	−0.0395638
$973$	−1.29161	−0.0414072
$974$	24.0962	0.772093
$975$	−35.4640	−1.13576
$976$	5.98017	0.191421
$977$	−13.2799	−0.424860	−0.212430	−	0.977176i	$-0.568138\pi$
$977$	−13.2799	−0.424860	−0.212430	+	0.977176i	$0.568138\pi$
$978$	−24.1255	−0.771449
$979$	28.1790	0.900605
$980$	−0.00981953	−0.000313674 0
$981$	−13.2140	−0.421891
$982$	29.6127	0.944981
$983$	33.2638	1.06095	0.530476	−	0.847700i	$-0.322013\pi$
$983$	33.2638	1.06095	0.530476	+	0.847700i	$0.322013\pi$
$984$	−22.8855	−0.729564
$985$	−0.381289	−0.0121489
$986$	−3.79722	−0.120928
$987$	−34.8812	−1.11028
$988$	−1.60550	−0.0510778
$989$	45.8570	1.45817
$990$	−0.166676	−0.00529731
$991$	−29.3560	−0.932523	−0.466262	−	0.884647i	$-0.654399\pi$
$991$	−29.3560	−0.932523	−0.466262	+	0.884647i	$0.654399\pi$
$992$	−2.42725	−0.0770654
$993$	−59.8708	−1.89994
$994$	10.1956	0.323384
$995$	−0.193391	−0.00613090
$996$	2.82480	0.0895072
$997$	−20.9366	−0.663070	−0.331535	−	0.943443i	$-0.607566\pi$
$997$	−20.9366	−0.663070	−0.331535	+	0.943443i	$0.607566\pi$
$998$	50.8275	1.60892
$999$	−5.07577	−0.160590

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4031.2.a.c.1.17	✓	61

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4031.2.a.c.1.17	✓	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)

\(f(q)\)	\(=\)	\(q-1.44140 q^{2} +2.16928 q^{3} +0.0776255 q^{4} +0.0237256 q^{5} -3.12680 q^{6} +1.29161 q^{7} +2.77090 q^{8} +1.70580 q^{9} +O(q^{10})\)	\(q-1.44140 q^{2} +2.16928 q^{3} +0.0776255 q^{4} +0.0237256 q^{5} -3.12680 q^{6} +1.29161 q^{7} +2.77090 q^{8} +1.70580 q^{9} -0.0341981 q^{10} +2.85722 q^{11} +0.168392 q^{12} +3.27002 q^{13} -1.86173 q^{14} +0.0514677 q^{15} -4.14923 q^{16} -2.63441 q^{17} -2.45873 q^{18} -6.32493 q^{19} +0.00184172 q^{20} +2.80188 q^{21} -4.11839 q^{22} -5.18950 q^{23} +6.01088 q^{24} -4.99944 q^{25} -4.71340 q^{26} -2.80750 q^{27} +0.100262 q^{28} -1.00000 q^{29} -0.0741854 q^{30} -5.53067 q^{31} +0.438871 q^{32} +6.19813 q^{33} +3.79722 q^{34} +0.0306444 q^{35} +0.132413 q^{36} +1.80794 q^{37} +9.11673 q^{38} +7.09360 q^{39} +0.0657415 q^{40} -3.80735 q^{41} -4.03862 q^{42} -8.83651 q^{43} +0.221793 q^{44} +0.0404711 q^{45} +7.48013 q^{46} -12.4492 q^{47} -9.00085 q^{48} -5.33173 q^{49} +7.20617 q^{50} -5.71477 q^{51} +0.253837 q^{52} -4.75313 q^{53} +4.04672 q^{54} +0.0677895 q^{55} +3.57894 q^{56} -13.7206 q^{57} +1.44140 q^{58} -7.95235 q^{59} +0.00399520 q^{60} -1.44128 q^{61} +7.97190 q^{62} +2.20323 q^{63} +7.66586 q^{64} +0.0775833 q^{65} -8.93397 q^{66} +8.26135 q^{67} -0.204497 q^{68} -11.2575 q^{69} -0.0441707 q^{70} -5.47640 q^{71} +4.72660 q^{72} +3.62545 q^{73} -2.60595 q^{74} -10.8452 q^{75} -0.490976 q^{76} +3.69043 q^{77} -10.2247 q^{78} +16.7698 q^{79} -0.0984430 q^{80} -11.2076 q^{81} +5.48790 q^{82} +16.7752 q^{83} +0.217497 q^{84} -0.0625030 q^{85} +12.7369 q^{86} -2.16928 q^{87} +7.91709 q^{88} +9.86238 q^{89} -0.0583349 q^{90} +4.22360 q^{91} -0.402837 q^{92} -11.9976 q^{93} +17.9442 q^{94} -0.150063 q^{95} +0.952037 q^{96} -6.95404 q^{97} +7.68515 q^{98} +4.87384 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 61 q - q^{2} - 4 q^{3} + 43 q^{4} - 7 q^{5} - 13 q^{6} - 10 q^{7} - 6 q^{8} + 23 q^{9}+O(q^{10}) \) 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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