LMFDB - Embedded newform 4031.2.a.c.1.6

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			1.6
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)

$f(q)$	$=$	$q-2.31412 q^{2} +0.311751 q^{3} +3.35513 q^{4} +1.29585 q^{5} -0.721429 q^{6} -1.13716 q^{7} -3.13593 q^{8} -2.90281 q^{9} +O(q^{10})$	\(q-2.31412 q^{2} +0.311751 q^{3} +3.35513 q^{4} +1.29585 q^{5} -0.721429 q^{6} -1.13716 q^{7} -3.13593 q^{8} -2.90281 q^{9} -2.99874 q^{10} +2.78758 q^{11} +1.04597 q^{12} +3.93476 q^{13} +2.63152 q^{14} +0.403982 q^{15} +0.546648 q^{16} -3.61518 q^{17} +6.71744 q^{18} +4.23592 q^{19} +4.34773 q^{20} -0.354511 q^{21} -6.45077 q^{22} -0.383069 q^{23} -0.977632 q^{24} -3.32078 q^{25} -9.10550 q^{26} -1.84021 q^{27} -3.81532 q^{28} -1.00000 q^{29} -0.934860 q^{30} -10.0360 q^{31} +5.00686 q^{32} +0.869031 q^{33} +8.36595 q^{34} -1.47358 q^{35} -9.73931 q^{36} +3.45191 q^{37} -9.80241 q^{38} +1.22667 q^{39} -4.06368 q^{40} +2.80806 q^{41} +0.820379 q^{42} +4.55341 q^{43} +9.35268 q^{44} -3.76159 q^{45} +0.886466 q^{46} -11.7839 q^{47} +0.170418 q^{48} -5.70687 q^{49} +7.68468 q^{50} -1.12704 q^{51} +13.2017 q^{52} +0.380395 q^{53} +4.25846 q^{54} +3.61227 q^{55} +3.56605 q^{56} +1.32055 q^{57} +2.31412 q^{58} +6.87739 q^{59} +1.35541 q^{60} +2.49126 q^{61} +23.2244 q^{62} +3.30096 q^{63} -12.6797 q^{64} +5.09885 q^{65} -2.01104 q^{66} -9.83620 q^{67} -12.1294 q^{68} -0.119422 q^{69} +3.41004 q^{70} +3.25521 q^{71} +9.10302 q^{72} -1.79064 q^{73} -7.98813 q^{74} -1.03526 q^{75} +14.2121 q^{76} -3.16992 q^{77} -2.83865 q^{78} -8.48872 q^{79} +0.708371 q^{80} +8.13475 q^{81} -6.49817 q^{82} +11.7202 q^{83} -1.18943 q^{84} -4.68472 q^{85} -10.5371 q^{86} -0.311751 q^{87} -8.74165 q^{88} -14.2658 q^{89} +8.70477 q^{90} -4.47445 q^{91} -1.28525 q^{92} -3.12873 q^{93} +27.2694 q^{94} +5.48910 q^{95} +1.56090 q^{96} -3.70766 q^{97} +13.2064 q^{98} -8.09180 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.31412	−1.63633	−0.818164	−	0.574986i	$-0.805008\pi$
$2$	−2.31412	−1.63633	−0.818164	+	0.574986i	$0.805008\pi$
$3$	0.311751	0.179990	0.0899949	−	0.995942i	$-0.471315\pi$
$3$	0.311751	0.179990	0.0899949	+	0.995942i	$0.471315\pi$
$4$	3.35513	1.67757
$5$	1.29585	0.579520	0.289760	−	0.957099i	$-0.406425\pi$
$5$	1.29585	0.579520	0.289760	+	0.957099i	$0.406425\pi$
$6$	−0.721429	−0.294522
$7$	−1.13716	−0.429806	−0.214903	−	0.976635i	$-0.568943\pi$
$7$	−1.13716	−0.429806	−0.214903	+	0.976635i	$0.568943\pi$
$8$	−3.13593	−1.10872
$9$	−2.90281	−0.967604
$10$	−2.99874	−0.948284
$11$	2.78758	0.840486	0.420243	−	0.907412i	$-0.361945\pi$
$11$	2.78758	0.840486	0.420243	+	0.907412i	$0.361945\pi$
$12$	1.04597	0.301945
$13$	3.93476	1.09131	0.545654	−	0.838011i	$-0.316281\pi$
$13$	3.93476	1.09131	0.545654	+	0.838011i	$0.316281\pi$
$14$	2.63152	0.703303
$15$	0.403982	0.104308
$16$	0.546648	0.136662
$17$	−3.61518	−0.876811	−0.438405	−	0.898777i	$-0.644457\pi$
$17$	−3.61518	−0.876811	−0.438405	+	0.898777i	$0.644457\pi$
$18$	6.71744	1.58332
$19$	4.23592	0.971787	0.485893	−	0.874018i	$-0.338494\pi$
$19$	4.23592	0.971787	0.485893	+	0.874018i	$0.338494\pi$
$20$	4.34773	0.972183
$21$	−0.354511	−0.0773606
$22$	−6.45077	−1.37531
$23$	−0.383069	−0.0798754	−0.0399377	−	0.999202i	$-0.512716\pi$
$23$	−0.383069	−0.0798754	−0.0399377	+	0.999202i	$0.512716\pi$
$24$	−0.977632	−0.199558
$25$	−3.32078	−0.664157
$26$	−9.10550	−1.78574
$27$	−1.84021	−0.354149
$28$	−3.81532	−0.721027
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	−0.934860	−0.170681
$31$	−10.0360	−1.80251	−0.901257	−	0.433284i	$-0.857355\pi$
$31$	−10.0360	−1.80251	−0.901257	+	0.433284i	$0.857355\pi$
$32$	5.00686	0.885096
$33$	0.869031	0.151279
$34$	8.36595	1.43475
$35$	−1.47358	−0.249081
$36$	−9.73931	−1.62322
$37$	3.45191	0.567491	0.283745	−	0.958900i	$-0.408423\pi$
$37$	3.45191	0.567491	0.283745	+	0.958900i	$0.408423\pi$
$38$	−9.80241	−1.59016
$39$	1.22667	0.196424
$40$	−4.06368	−0.642525
$41$	2.80806	0.438545	0.219272	−	0.975664i	$-0.429632\pi$
$41$	2.80806	0.438545	0.219272	+	0.975664i	$0.429632\pi$
$42$	0.820379	0.126587
$43$	4.55341	0.694389	0.347194	−	0.937793i	$-0.387134\pi$
$43$	4.55341	0.694389	0.347194	+	0.937793i	$0.387134\pi$
$44$	9.35268	1.40997
$45$	−3.76159	−0.560745
$46$	0.886466	0.130702
$47$	−11.7839	−1.71886	−0.859432	−	0.511250i	$-0.829183\pi$
$47$	−11.7839	−1.71886	−0.859432	+	0.511250i	$0.829183\pi$
$48$	0.170418	0.0245977
$49$	−5.70687	−0.815267
$50$	7.68468	1.08678
$51$	−1.12704	−0.157817
$52$	13.2017	1.83074
$53$	0.380395	0.0522513	0.0261257	−	0.999659i	$-0.491683\pi$
$53$	0.380395	0.0522513	0.0261257	+	0.999659i	$0.491683\pi$
$54$	4.25846	0.579503
$55$	3.61227	0.487078
$56$	3.56605	0.476534
$57$	1.32055	0.174912
$58$	2.31412	0.303858
$59$	6.87739	0.895360	0.447680	−	0.894194i	$-0.352250\pi$
$59$	6.87739	0.895360	0.447680	+	0.894194i	$0.352250\pi$
$60$	1.35541	0.174983
$61$	2.49126	0.318973	0.159487	−	0.987200i	$-0.449016\pi$
$61$	2.49126	0.318973	0.159487	+	0.987200i	$0.449016\pi$
$62$	23.2244	2.94950
$63$	3.30096	0.415882
$64$	−12.6797	−1.58497
$65$	5.09885	0.632434
$66$	−2.01104	−0.247542
$67$	−9.83620	−1.20168	−0.600842	−	0.799368i	$-0.705168\pi$
$67$	−9.83620	−1.20168	−0.600842	+	0.799368i	$0.705168\pi$
$68$	−12.1294	−1.47091
$69$	−0.119422	−0.0143768
$70$	3.41004	0.407578
$71$	3.25521	0.386322	0.193161	−	0.981167i	$-0.438126\pi$
$71$	3.25521	0.386322	0.193161	+	0.981167i	$0.438126\pi$
$72$	9.10302	1.07280
$73$	−1.79064	−0.209579	−0.104789	−	0.994494i	$-0.533417\pi$
$73$	−1.79064	−0.209579	−0.104789	+	0.994494i	$0.533417\pi$
$74$	−7.98813	−0.928601
$75$	−1.03526	−0.119541
$76$	14.2121	1.63024
$77$	−3.16992	−0.361246
$78$	−2.83865	−0.321414
$79$	−8.48872	−0.955055	−0.477528	−	0.878617i	$-0.658467\pi$
$79$	−8.48872	−0.955055	−0.477528	+	0.878617i	$0.658467\pi$
$80$	0.708371	0.0791983
$81$	8.13475	0.903861
$82$	−6.49817	−0.717603
$83$	11.7202	1.28646	0.643231	−	0.765673i	$-0.277594\pi$
$83$	11.7202	1.28646	0.643231	+	0.765673i	$0.277594\pi$
$84$	−1.18943	−0.129778
$85$	−4.68472	−0.508129
$86$	−10.5371	−1.13625
$87$	−0.311751	−0.0334233
$88$	−8.74165	−0.931863
$89$	−14.2658	−1.51217	−0.756086	−	0.654472i	$-0.772891\pi$
$89$	−14.2658	−1.51217	−0.756086	+	0.654472i	$0.772891\pi$
$90$	8.70477	0.917563
$91$	−4.47445	−0.469050
$92$	−1.28525	−0.133996
$93$	−3.12873	−0.324434
$94$	27.2694	2.81262
$95$	5.48910	0.563170
$96$	1.56090	0.159308
$97$	−3.70766	−0.376456	−0.188228	−	0.982125i	$-0.560274\pi$
$97$	−3.70766	−0.376456	−0.188228	+	0.982125i	$0.560274\pi$
$98$	13.2064	1.33404
$99$	−8.09180	−0.813257
$100$	−11.1417	−1.11417
$101$	6.81077	0.677697	0.338848	−	0.940841i	$-0.389963\pi$
$101$	6.81077	0.677697	0.338848	+	0.940841i	$0.389963\pi$
$102$	2.60810	0.258240
$103$	0.353928	0.0348736	0.0174368	−	0.999848i	$-0.494449\pi$
$103$	0.353928	0.0348736	0.0174368	+	0.999848i	$0.494449\pi$
$104$	−12.3392	−1.20995
$105$	−0.459391	−0.0448320
$106$	−0.880279	−0.0855002
$107$	−10.9921	−1.06265	−0.531324	−	0.847169i	$-0.678305\pi$
$107$	−10.9921	−1.06265	−0.531324	+	0.847169i	$0.678305\pi$
$108$	−6.17415	−0.594108
$109$	2.39166	0.229079	0.114540	−	0.993419i	$-0.463461\pi$
$109$	2.39166	0.229079	0.114540	+	0.993419i	$0.463461\pi$
$110$	−8.35920	−0.797019
$111$	1.07614	0.102143
$112$	−0.621625	−0.0587381
$113$	−4.07855	−0.383678	−0.191839	−	0.981426i	$-0.561445\pi$
$113$	−4.07855	−0.383678	−0.191839	+	0.981426i	$0.561445\pi$
$114$	−3.05592	−0.286213
$115$	−0.496398	−0.0462894
$116$	−3.35513	−0.311516
$117$	−11.4219	−1.05595
$118$	−15.9151	−1.46510
$119$	4.11104	0.376858
$120$	−1.26686	−0.115648
$121$	−3.22942	−0.293584
$122$	−5.76507	−0.521945
$123$	0.875416	0.0789336
$124$	−33.6720	−3.02384
$125$	−10.7825	−0.964412
$126$	−7.63880	−0.680518
$127$	−3.37957	−0.299889	−0.149944	−	0.988694i	$-0.547909\pi$
$127$	−3.37957	−0.299889	−0.149944	+	0.988694i	$0.547909\pi$
$128$	19.3287	1.70843
$129$	1.41953	0.124983
$130$	−11.7993	−1.03487
$131$	−9.87230	−0.862547	−0.431273	−	0.902221i	$-0.641936\pi$
$131$	−9.87230	−0.862547	−0.431273	+	0.902221i	$0.641936\pi$
$132$	2.91571	0.253780
$133$	−4.81691	−0.417679
$134$	22.7621	1.96635
$135$	−2.38463	−0.205236
$136$	11.3370	0.972137
$137$	−7.89475	−0.674494	−0.337247	−	0.941416i	$-0.609496\pi$
$137$	−7.89475	−0.674494	−0.337247	+	0.941416i	$0.609496\pi$
$138$	0.276357	0.0235251
$139$	−1.00000	−0.0848189
$139$	−1.00000	−0.0848189
$140$	−4.94406	−0.417850
$141$	−3.67366	−0.309378
$142$	−7.53293	−0.632149
$143$	10.9685	0.917228
$144$	−1.58681	−0.132235
$145$	−1.29585	−0.107614
$146$	4.14375	0.342939
$147$	−1.77912	−0.146740
$148$	11.5816	0.952004
$149$	−2.67103	−0.218820	−0.109410	−	0.993997i	$-0.534896\pi$
$149$	−2.67103	−0.218820	−0.109410	+	0.993997i	$0.534896\pi$
$150$	2.39571	0.195609
$151$	−6.10750	−0.497021	−0.248511	−	0.968629i	$-0.579941\pi$
$151$	−6.10750	−0.497021	−0.248511	+	0.968629i	$0.579941\pi$
$152$	−13.2836	−1.07744
$153$	10.4942	0.848405
$154$	7.33555	0.591116
$155$	−13.0051	−1.04459
$156$	4.11563	0.329514
$157$	2.32296	0.185392	0.0926960	−	0.995694i	$-0.470452\pi$
$157$	2.32296	0.185392	0.0926960	+	0.995694i	$0.470452\pi$
$158$	19.6439	1.56278
$159$	0.118589	0.00940470
$160$	6.48812	0.512931
$161$	0.435610	0.0343309
$162$	−18.8247	−1.47901
$163$	16.8464	1.31951	0.659756	−	0.751480i	$-0.270660\pi$
$163$	16.8464	1.31951	0.659756	+	0.751480i	$0.270660\pi$
$164$	9.42140	0.735688
$165$	1.12613	0.0876691
$166$	−27.1219	−2.10507
$167$	3.54358	0.274211	0.137105	−	0.990556i	$-0.456220\pi$
$167$	3.54358	0.274211	0.137105	+	0.990556i	$0.456220\pi$
$168$	1.11172	0.0857713
$169$	2.48236	0.190951
$170$	10.8410	0.831465
$171$	−12.2961	−0.940304
$172$	15.2773	1.16488
$173$	19.2566	1.46405	0.732027	−	0.681276i	$-0.238575\pi$
$173$	19.2566	1.46405	0.732027	+	0.681276i	$0.238575\pi$
$174$	0.721429	0.0546914
$175$	3.77626	0.285458
$176$	1.52382	0.114862
$177$	2.14404	0.161156
$178$	33.0127	2.47441
$179$	−3.76009	−0.281042	−0.140521	−	0.990078i	$-0.544878\pi$
$179$	−3.76009	−0.281042	−0.140521	+	0.990078i	$0.544878\pi$
$180$	−12.6206	−0.940687
$181$	−5.05011	−0.375372	−0.187686	−	0.982229i	$-0.560099\pi$
$181$	−5.05011	−0.375372	−0.187686	+	0.982229i	$0.560099\pi$
$182$	10.3544	0.767519
$183$	0.776655	0.0574120
$184$	1.20128	0.0885594
$185$	4.47315	0.328872
$186$	7.24024	0.530880
$187$	−10.0776	−0.736947
$188$	−39.5367	−2.88351
$189$	2.09261	0.152215
$190$	−12.7024	−0.921530
$191$	23.4484	1.69666	0.848332	−	0.529465i	$-0.177607\pi$
$191$	23.4484	1.69666	0.848332	+	0.529465i	$0.177607\pi$
$192$	−3.95293	−0.285278
$193$	4.99663	0.359666	0.179833	−	0.983697i	$-0.442444\pi$
$193$	4.99663	0.359666	0.179833	+	0.983697i	$0.442444\pi$
$194$	8.57996	0.616005
$195$	1.58957	0.113832
$196$	−19.1473	−1.36766
$197$	−14.1743	−1.00988	−0.504939	−	0.863155i	$-0.668485\pi$
$197$	−14.1743	−1.00988	−0.504939	+	0.863155i	$0.668485\pi$
$198$	18.7254	1.33075
$199$	−2.26467	−0.160538	−0.0802692	−	0.996773i	$-0.525578\pi$
$199$	−2.26467	−0.160538	−0.0802692	+	0.996773i	$0.525578\pi$
$200$	10.4138	0.736364
$201$	−3.06645	−0.216291
$202$	−15.7609	−1.10893
$203$	1.13716	0.0798129
$204$	−3.78136	−0.264748
$205$	3.63881	0.254145
$206$	−0.819031	−0.0570646
$207$	1.11198	0.0772877
$208$	2.15093	0.149140
$209$	11.8079	0.816773
$210$	1.06308	0.0733598
$211$	13.4434	0.925479	0.462740	−	0.886494i	$-0.346867\pi$
$211$	13.4434	0.925479	0.462740	+	0.886494i	$0.346867\pi$
$212$	1.27628	0.0876550
$213$	1.01482	0.0695340
$214$	25.4370	1.73884
$215$	5.90052	0.402412
$216$	5.77077	0.392651
$217$	11.4125	0.774731
$218$	−5.53457	−0.374849
$219$	−0.558235	−0.0377220
$220$	12.1196	0.817105
$221$	−14.2249	−0.956870
$222$	−2.49031	−0.167139
$223$	−2.36637	−0.158464	−0.0792318	−	0.996856i	$-0.525247\pi$
$223$	−2.36637	−0.158464	−0.0792318	+	0.996856i	$0.525247\pi$
$224$	−5.69360	−0.380419
$225$	9.63961	0.642641
$226$	9.43824	0.627822
$227$	−18.6957	−1.24088	−0.620438	−	0.784255i	$-0.713045\pi$
$227$	−18.6957	−1.24088	−0.620438	+	0.784255i	$0.713045\pi$
$228$	4.43063	0.293426
$229$	−25.3115	−1.67263	−0.836317	−	0.548246i	$-0.815296\pi$
$229$	−25.3115	−1.67263	−0.836317	+	0.548246i	$0.815296\pi$
$230$	1.14872	0.0757445
$231$	−0.988226	−0.0650205
$232$	3.13593	0.205884
$233$	25.9601	1.70070	0.850352	−	0.526215i	$-0.176389\pi$
$233$	25.9601	1.70070	0.850352	+	0.526215i	$0.176389\pi$
$234$	26.4315	1.72788
$235$	−15.2702	−0.996115
$236$	23.0746	1.50203
$237$	−2.64637	−0.171900
$238$	−9.51342	−0.616663
$239$	−8.50889	−0.550395	−0.275197	−	0.961388i	$-0.588743\pi$
$239$	−8.50889	−0.550395	−0.275197	+	0.961388i	$0.588743\pi$
$240$	0.220836	0.0142549
$241$	−7.50867	−0.483676	−0.241838	−	0.970317i	$-0.577750\pi$
$241$	−7.50867	−0.483676	−0.241838	+	0.970317i	$0.577750\pi$
$242$	7.47326	0.480399
$243$	8.05665	0.516834
$244$	8.35851	0.535099
$245$	−7.39522	−0.472463
$246$	−2.02581	−0.129161
$247$	16.6673	1.06052
$248$	31.4722	1.99848
$249$	3.65379	0.231550
$250$	24.9518	1.57809
$251$	5.84509	0.368939	0.184469	−	0.982838i	$-0.440943\pi$
$251$	5.84509	0.368939	0.184469	+	0.982838i	$0.440943\pi$
$252$	11.0751	0.697669
$253$	−1.06783	−0.0671341
$254$	7.82072	0.490716
$255$	−1.46047	−0.0914580
$256$	−19.3693	−1.21058
$257$	16.5272	1.03094	0.515468	−	0.856909i	$-0.327618\pi$
$257$	16.5272	1.03094	0.515468	+	0.856909i	$0.327618\pi$
$258$	−3.28496	−0.204513
$259$	−3.92537	−0.243911
$260$	17.1073	1.06095
$261$	2.90281	0.179679
$262$	22.8456	1.41141
$263$	−5.36913	−0.331075	−0.165537	−	0.986204i	$-0.552936\pi$
$263$	−5.36913	−0.331075	−0.165537	+	0.986204i	$0.552936\pi$
$264$	−2.72522	−0.167726
$265$	0.492933	0.0302807
$266$	11.1469	0.683460
$267$	−4.44738	−0.272175
$268$	−33.0018	−2.01590
$269$	15.9452	0.972196	0.486098	−	0.873904i	$-0.338420\pi$
$269$	15.9452	0.972196	0.486098	+	0.873904i	$0.338420\pi$
$270$	5.51830	0.335833
$271$	−6.23858	−0.378967	−0.189483	−	0.981884i	$-0.560681\pi$
$271$	−6.23858	−0.378967	−0.189483	+	0.981884i	$0.560681\pi$
$272$	−1.97623	−0.119827
$273$	−1.39492	−0.0844242
$274$	18.2694	1.10369
$275$	−9.25694	−0.558214
$276$	−0.400678	−0.0241180
$277$	−10.6406	−0.639329	−0.319664	−	0.947531i	$-0.603570\pi$
$277$	−10.6406	−0.639329	−0.319664	+	0.947531i	$0.603570\pi$
$278$	2.31412	0.138791
$279$	29.1325	1.74412
$280$	4.62106	0.276161
$281$	−6.35189	−0.378922	−0.189461	−	0.981888i	$-0.560674\pi$
$281$	−6.35189	−0.378922	−0.189461	+	0.981888i	$0.560674\pi$
$282$	8.50127	0.506243
$283$	−10.8965	−0.647730	−0.323865	−	0.946103i	$-0.604982\pi$
$283$	−10.8965	−0.647730	−0.323865	+	0.946103i	$0.604982\pi$
$284$	10.9216	0.648081
$285$	1.71123	0.101365
$286$	−25.3823	−1.50088
$287$	−3.19321	−0.188489
$288$	−14.5340	−0.856422
$289$	−3.93045	−0.231203
$290$	2.99874	0.176092
$291$	−1.15587	−0.0677582
$292$	−6.00784	−0.351582
$293$	2.69708	0.157565	0.0787826	−	0.996892i	$-0.474897\pi$
$293$	2.69708	0.157565	0.0787826	+	0.996892i	$0.474897\pi$
$294$	4.11710	0.240114
$295$	8.91204	0.518879
$296$	−10.8250	−0.629188
$297$	−5.12972	−0.297657
$298$	6.18108	0.358060
$299$	−1.50729	−0.0871686
$300$	−3.47343	−0.200539
$301$	−5.17795	−0.298452
$302$	14.1335	0.813290
$303$	2.12327	0.121978
$304$	2.31556	0.132806
$305$	3.22829	0.184851
$306$	−24.2848	−1.38827
$307$	−15.7417	−0.898427	−0.449213	−	0.893424i	$-0.648296\pi$
$307$	−15.7417	−0.898427	−0.449213	+	0.893424i	$0.648296\pi$
$308$	−10.6355	−0.606013
$309$	0.110338	0.00627689
$310$	30.0953	1.70930
$311$	−17.8191	−1.01043	−0.505214	−	0.862994i	$-0.668586\pi$
$311$	−17.8191	−1.01043	−0.505214	+	0.862994i	$0.668586\pi$
$312$	−3.84675	−0.217779
$313$	−13.6759	−0.773009	−0.386504	−	0.922288i	$-0.626318\pi$
$313$	−13.6759	−0.773009	−0.386504	+	0.922288i	$0.626318\pi$
$314$	−5.37559	−0.303362
$315$	4.27753	0.241012
$316$	−28.4808	−1.60217
$317$	20.8956	1.17361	0.586806	−	0.809728i	$-0.300385\pi$
$317$	20.8956	1.17361	0.586806	+	0.809728i	$0.300385\pi$
$318$	−0.274428	−0.0153892
$319$	−2.78758	−0.156074
$320$	−16.4310	−0.918521
$321$	−3.42681	−0.191266
$322$	−1.00805	−0.0561766
$323$	−15.3136	−0.852073
$324$	27.2931	1.51629
$325$	−13.0665	−0.724799
$326$	−38.9845	−2.15915
$327$	0.745603	0.0412319
$328$	−8.80588	−0.486223
$329$	13.4002	0.738777
$330$	−2.60599	−0.143455
$331$	−25.3733	−1.39464	−0.697322	−	0.716758i	$-0.745625\pi$
$331$	−25.3733	−1.39464	−0.697322	+	0.716758i	$0.745625\pi$
$332$	39.3229	2.15812
$333$	−10.0203	−0.549106
$334$	−8.20026	−0.448698
$335$	−12.7462	−0.696399
$336$	−0.193793	−0.0105722
$337$	2.82593	0.153938	0.0769690	−	0.997033i	$-0.475476\pi$
$337$	2.82593	0.153938	0.0769690	+	0.997033i	$0.475476\pi$
$338$	−5.74448	−0.312458
$339$	−1.27149	−0.0690581
$340$	−15.7178	−0.852420
$341$	−27.9760	−1.51499
$342$	28.4545	1.53865
$343$	14.4497	0.780212
$344$	−14.2792	−0.769883
$345$	−0.154753	−0.00833161
$346$	−44.5620	−2.39567
$347$	−4.66332	−0.250340	−0.125170	−	0.992135i	$-0.539948\pi$
$347$	−4.66332	−0.250340	−0.125170	+	0.992135i	$0.539948\pi$
$348$	−1.04597	−0.0560697
$349$	−9.24866	−0.495069	−0.247535	−	0.968879i	$-0.579620\pi$
$349$	−9.24866	−0.495069	−0.247535	+	0.968879i	$0.579620\pi$
$350$	−8.73870	−0.467103
$351$	−7.24079	−0.386485
$352$	13.9570	0.743911
$353$	13.4304	0.714828	0.357414	−	0.933946i	$-0.383658\pi$
$353$	13.4304	0.714828	0.357414	+	0.933946i	$0.383658\pi$
$354$	−4.96155	−0.263703
$355$	4.21824	0.223881
$356$	−47.8636	−2.53677
$357$	1.28162	0.0678306
$358$	8.70128	0.459877
$359$	−4.02047	−0.212192	−0.106096	−	0.994356i	$-0.533835\pi$
$359$	−4.02047	−0.212192	−0.106096	+	0.994356i	$0.533835\pi$
$360$	11.7961	0.621709
$361$	−1.05698	−0.0556306
$362$	11.6865	0.614231
$363$	−1.00678	−0.0528421
$364$	−15.0124	−0.786862
$365$	−2.32040	−0.121455
$366$	−1.79727	−0.0939447
$367$	10.6338	0.555078	0.277539	−	0.960714i	$-0.410481\pi$
$367$	10.6338	0.555078	0.277539	+	0.960714i	$0.410481\pi$
$368$	−0.209404	−0.0109159
$369$	−8.15126	−0.424338
$370$	−10.3514	−0.538142
$371$	−0.432570	−0.0224579
$372$	−10.4973	−0.544260
$373$	−12.5870	−0.651729	−0.325864	−	0.945416i	$-0.605655\pi$
$373$	−12.5870	−0.651729	−0.325864	+	0.945416i	$0.605655\pi$
$374$	23.3207	1.20589
$375$	−3.36144	−0.173584
$376$	36.9536	1.90574
$377$	−3.93476	−0.202651
$378$	−4.84254	−0.249074
$379$	−3.89244	−0.199941	−0.0999706	−	0.994990i	$-0.531875\pi$
$379$	−3.89244	−0.199941	−0.0999706	+	0.994990i	$0.531875\pi$
$380$	18.4166	0.944754
$381$	−1.05359	−0.0539769
$382$	−54.2622	−2.77630
$383$	−15.5423	−0.794175	−0.397087	−	0.917781i	$-0.629979\pi$
$383$	−15.5423	−0.794175	−0.397087	+	0.917781i	$0.629979\pi$
$384$	6.02575	0.307500
$385$	−4.10772	−0.209349
$386$	−11.5628	−0.588530
$387$	−13.2177	−0.671893
$388$	−12.4397	−0.631530
$389$	−16.6122	−0.842274	−0.421137	−	0.906997i	$-0.638369\pi$
$389$	−16.6122	−0.842274	−0.421137	+	0.906997i	$0.638369\pi$
$390$	−3.67845	−0.186266
$391$	1.38486	0.0700356
$392$	17.8964	0.903903
$393$	−3.07770	−0.155250
$394$	32.8010	1.65249
$395$	−11.0001	−0.553473
$396$	−27.1491	−1.36429
$397$	−26.7036	−1.34022	−0.670108	−	0.742264i	$-0.733752\pi$
$397$	−26.7036	−1.34022	−0.670108	+	0.742264i	$0.733752\pi$
$398$	5.24072	0.262693
$399$	−1.50168	−0.0751780
$400$	−1.81530	−0.0907649
$401$	6.88089	0.343615	0.171808	−	0.985131i	$-0.445039\pi$
$401$	6.88089	0.343615	0.171808	+	0.985131i	$0.445039\pi$
$402$	7.09612	0.353922
$403$	−39.4892	−1.96710
$404$	22.8510	1.13688
$405$	10.5414	0.523805
$406$	−2.63152	−0.130600
$407$	9.62247	0.476968
$408$	3.53432	0.174975
$409$	−25.7580	−1.27365	−0.636826	−	0.771007i	$-0.719753\pi$
$409$	−25.7580	−1.27365	−0.636826	+	0.771007i	$0.719753\pi$
$410$	−8.42062	−0.415865
$411$	−2.46120	−0.121402
$412$	1.18748	0.0585028
$413$	−7.82069	−0.384831
$414$	−2.57324	−0.126468
$415$	15.1876	0.745530
$416$	19.7008	0.965912
$417$	−0.311751	−0.0152665
$418$	−27.3250	−1.33651
$419$	−22.2355	−1.08628	−0.543138	−	0.839644i	$-0.682764\pi$
$419$	−22.2355	−1.08628	−0.543138	+	0.839644i	$0.682764\pi$
$420$	−1.54132	−0.0752087
$421$	11.3874	0.554987	0.277493	−	0.960728i	$-0.410496\pi$
$421$	11.3874	0.554987	0.277493	+	0.960728i	$0.410496\pi$
$422$	−31.1095	−1.51439
$423$	34.2065	1.66318
$424$	−1.19289	−0.0579320
$425$	12.0052	0.582340
$426$	−2.34840	−0.113780
$427$	−2.83296	−0.137097
$428$	−36.8800	−1.78266
$429$	3.41943	0.165092
$430$	−13.6545	−0.658478
$431$	−36.4535	−1.75590	−0.877952	−	0.478749i	$-0.841091\pi$
$431$	−36.4535	−1.75590	−0.877952	+	0.478749i	$0.841091\pi$
$432$	−1.00595	−0.0483986
$433$	−16.3500	−0.785729	−0.392865	−	0.919596i	$-0.628516\pi$
$433$	−16.3500	−0.785729	−0.392865	+	0.919596i	$0.628516\pi$
$434$	−26.4099	−1.26771
$435$	−0.403982	−0.0193694
$436$	8.02433	0.384296
$437$	−1.62265	−0.0776218
$438$	1.29182	0.0617256
$439$	−23.9011	−1.14074	−0.570369	−	0.821389i	$-0.693200\pi$
$439$	−23.9011	−1.14074	−0.570369	+	0.821389i	$0.693200\pi$
$440$	−11.3278	−0.540033
$441$	16.5660	0.788855
$442$	32.9180	1.56575
$443$	16.4236	0.780309	0.390155	−	0.920749i	$-0.372422\pi$
$443$	16.4236	0.780309	0.390155	+	0.920749i	$0.372422\pi$
$444$	3.61059	0.171351
$445$	−18.4863	−0.876333
$446$	5.47605	0.259298
$447$	−0.832698	−0.0393853
$448$	14.4189	0.681229
$449$	−10.6997	−0.504951	−0.252475	−	0.967603i	$-0.581245\pi$
$449$	−10.6997	−0.504951	−0.252475	+	0.967603i	$0.581245\pi$
$450$	−22.3072	−1.05157
$451$	7.82767	0.368591
$452$	−13.6841	−0.643645
$453$	−1.90402	−0.0894588
$454$	43.2640	2.03048
$455$	−5.79820	−0.271824
$456$	−4.14117	−0.193928
$457$	−33.1942	−1.55276	−0.776381	−	0.630264i	$-0.782947\pi$
$457$	−33.1942	−1.55276	−0.776381	+	0.630264i	$0.782947\pi$
$458$	58.5738	2.73698
$459$	6.65269	0.310521
$460$	−1.66548	−0.0776535
$461$	31.2733	1.45654	0.728271	−	0.685289i	$-0.240324\pi$
$461$	31.2733	1.45654	0.728271	+	0.685289i	$0.240324\pi$
$462$	2.28687	0.106395
$463$	−2.15877	−0.100326	−0.0501632	−	0.998741i	$-0.515974\pi$
$463$	−2.15877	−0.100326	−0.0501632	+	0.998741i	$0.515974\pi$
$464$	−0.546648	−0.0253775
$465$	−4.05435	−0.188016
$466$	−60.0747	−2.78291
$467$	13.9210	0.644187	0.322094	−	0.946708i	$-0.395613\pi$
$467$	13.9210	0.644187	0.322094	+	0.946708i	$0.395613\pi$
$468$	−38.3219	−1.77143
$469$	11.1853	0.516490
$470$	35.3369	1.62997
$471$	0.724185	0.0333687
$472$	−21.5670	−0.992704
$473$	12.6930	0.583624
$474$	6.12401	0.281285
$475$	−14.0666	−0.645419
$476$	13.7931	0.632205
$477$	−1.10422	−0.0505586
$478$	19.6906	0.900626
$479$	21.6989	0.991447	0.495724	−	0.868480i	$-0.334903\pi$
$479$	21.6989	0.991447	0.495724	+	0.868480i	$0.334903\pi$
$480$	2.02268	0.0923223
$481$	13.5825	0.619307
$482$	17.3759	0.791453
$483$	0.135802	0.00617921
$484$	−10.8351	−0.492506
$485$	−4.80456	−0.218164
$486$	−18.6440	−0.845710
$487$	4.77561	0.216403	0.108202	−	0.994129i	$-0.465491\pi$
$487$	4.77561	0.216403	0.108202	+	0.994129i	$0.465491\pi$
$488$	−7.81243	−0.353652
$489$	5.25189	0.237499
$490$	17.1134	0.773104
$491$	13.1760	0.594623	0.297311	−	0.954781i	$-0.403910\pi$
$491$	13.1760	0.594623	0.297311	+	0.954781i	$0.403910\pi$
$492$	2.93714	0.132416
$493$	3.61518	0.162820
$494$	−38.5702	−1.73535
$495$	−10.4857	−0.471298
$496$	−5.48614	−0.246335
$497$	−3.70169	−0.166043
$498$	−8.45530	−0.378891
$499$	−17.2531	−0.772355	−0.386178	−	0.922424i	$-0.626205\pi$
$499$	−17.2531	−0.772355	−0.386178	+	0.922424i	$0.626205\pi$
$500$	−36.1765	−1.61786
$501$	1.10472	0.0493551
$502$	−13.5262	−0.603704
$503$	4.26936	0.190362	0.0951808	−	0.995460i	$-0.469657\pi$
$503$	4.26936	0.190362	0.0951808	+	0.995460i	$0.469657\pi$
$504$	−10.3516	−0.461096
$505$	8.82570	0.392739
$506$	2.47109	0.109853
$507$	0.773881	0.0343693
$508$	−11.3389	−0.503083
$509$	−7.43591	−0.329591	−0.164795	−	0.986328i	$-0.552696\pi$
$509$	−7.43591	−0.329591	−0.164795	+	0.986328i	$0.552696\pi$
$510$	3.37969	0.149655
$511$	2.03624	0.0900782
$512$	6.16549	0.272479
$513$	−7.79498	−0.344157
$514$	−38.2458	−1.68695
$515$	0.458637	0.0202099
$516$	4.76272	0.209667
$517$	−32.8486	−1.44468
$518$	9.08377	0.399118
$519$	6.00328	0.263515
$520$	−15.9896	−0.701192
$521$	−26.6066	−1.16565	−0.582827	−	0.812596i	$-0.698054\pi$
$521$	−26.6066	−1.16565	−0.582827	+	0.812596i	$0.698054\pi$
$522$	−6.71744	−0.294014
$523$	0.223778	0.00978514	0.00489257	−	0.999988i	$-0.498443\pi$
$523$	0.223778	0.00978514	0.00489257	+	0.999988i	$0.498443\pi$
$524$	−33.1229	−1.44698
$525$	1.17725	0.0513796
$526$	12.4248	0.541747
$527$	36.2819	1.58046
$528$	0.475053	0.0206740
$529$	−22.8533	−0.993620
$530$	−1.14071	−0.0495491
$531$	−19.9638	−0.866354
$532$	−16.1614	−0.700685
$533$	11.0490	0.478587
$534$	10.2918	0.445368
$535$	−14.2441	−0.615825
$536$	30.8457	1.33233
$537$	−1.17221	−0.0505847
$538$	−36.8990	−1.59083
$539$	−15.9083	−0.685220
$540$	−8.00074	−0.344297
$541$	−19.8094	−0.851671	−0.425836	−	0.904801i	$-0.640020\pi$
$541$	−19.8094	−0.851671	−0.425836	+	0.904801i	$0.640020\pi$
$542$	14.4368	0.620113
$543$	−1.57438	−0.0675630
$544$	−18.1007	−0.776062
$545$	3.09922	0.132756
$546$	3.22800	0.138146
$547$	−2.27235	−0.0971586	−0.0485793	−	0.998819i	$-0.515469\pi$
$547$	−2.27235	−0.0971586	−0.0485793	+	0.998819i	$0.515469\pi$
$548$	−26.4879	−1.13151
$549$	−7.23166	−0.308640
$550$	21.4216	0.913421
$551$	−4.23592	−0.180456
$552$	0.374500	0.0159398
$553$	9.65302	0.410488
$554$	24.6235	1.04615
$555$	1.39451	0.0591936
$556$	−3.35513	−0.142289
$557$	−3.27832	−0.138907	−0.0694535	−	0.997585i	$-0.522126\pi$
$557$	−3.27832	−0.138907	−0.0694535	+	0.997585i	$0.522126\pi$
$558$	−67.4161	−2.85395
$559$	17.9166	0.757792
$560$	−0.805530	−0.0340399
$561$	−3.14170	−0.132643
$562$	14.6990	0.620040
$563$	23.6327	0.995998	0.497999	−	0.867178i	$-0.334068\pi$
$563$	23.6327	0.995998	0.497999	+	0.867178i	$0.334068\pi$
$564$	−12.3256	−0.519002
$565$	−5.28517	−0.222349
$566$	25.2158	1.05990
$567$	−9.25050	−0.388484
$568$	−10.2081	−0.428323
$569$	2.04529	0.0857432	0.0428716	−	0.999081i	$-0.486349\pi$
$569$	2.04529	0.0857432	0.0428716	+	0.999081i	$0.486349\pi$
$570$	−3.95999	−0.165866
$571$	−44.1233	−1.84650	−0.923251	−	0.384197i	$-0.874478\pi$
$571$	−44.1233	−1.84650	−0.923251	+	0.384197i	$0.874478\pi$
$572$	36.8006	1.53871
$573$	7.31006	0.305382
$574$	7.38945	0.308430
$575$	1.27209	0.0530498
$576$	36.8069	1.53362
$577$	31.7503	1.32178	0.660891	−	0.750482i	$-0.270179\pi$
$577$	31.7503	1.32178	0.660891	+	0.750482i	$0.270179\pi$
$578$	9.09552	0.378324
$579$	1.55771	0.0647361
$580$	−4.34773	−0.180530
$581$	−13.3278	−0.552928
$582$	2.67482	0.110875
$583$	1.06038	0.0439165
$584$	5.61533	0.232364
$585$	−14.8010	−0.611945
$586$	−6.24136	−0.257828
$587$	32.8234	1.35477	0.677384	−	0.735630i	$-0.263114\pi$
$587$	32.8234	1.35477	0.677384	+	0.735630i	$0.263114\pi$
$588$	−5.96920	−0.246166
$589$	−42.5116	−1.75166
$590$	−20.6235	−0.849056
$591$	−4.41887	−0.181768
$592$	1.88698	0.0775544
$593$	−7.81354	−0.320864	−0.160432	−	0.987047i	$-0.551289\pi$
$593$	−7.81354	−0.320864	−0.160432	+	0.987047i	$0.551289\pi$
$594$	11.8708	0.487064
$595$	5.32727	0.218397
$596$	−8.96167	−0.367084
$597$	−0.706015	−0.0288953
$598$	3.48803	0.142636
$599$	−2.23550	−0.0913399	−0.0456700	−	0.998957i	$-0.514542\pi$
$599$	−2.23550	−0.0913399	−0.0456700	+	0.998957i	$0.514542\pi$
$600$	3.24650	0.132538
$601$	−6.43562	−0.262514	−0.131257	−	0.991348i	$-0.541901\pi$
$601$	−6.43562	−0.262514	−0.131257	+	0.991348i	$0.541901\pi$
$602$	11.9824	0.488366
$603$	28.5526	1.16275
$604$	−20.4915	−0.833786
$605$	−4.18483	−0.170138
$606$	−4.91348	−0.199597
$607$	−24.5469	−0.996329	−0.498164	−	0.867083i	$-0.665992\pi$
$607$	−24.5469	−0.996329	−0.498164	+	0.867083i	$0.665992\pi$
$608$	21.2087	0.860125
$609$	0.354511	0.0143655
$610$	−7.47064	−0.302477
$611$	−46.3670	−1.87581
$612$	35.2094	1.42326
$613$	−5.78251	−0.233554	−0.116777	−	0.993158i	$-0.537256\pi$
$613$	−5.78251	−0.233554	−0.116777	+	0.993158i	$0.537256\pi$
$614$	36.4281	1.47012
$615$	1.13440	0.0457436
$616$	9.94065	0.400520
$617$	0.963831	0.0388024	0.0194012	−	0.999812i	$-0.493824\pi$
$617$	0.963831	0.0388024	0.0194012	+	0.999812i	$0.493824\pi$
$618$	−0.255334	−0.0102710
$619$	2.86259	0.115057	0.0575285	−	0.998344i	$-0.481678\pi$
$619$	2.86259	0.115057	0.0575285	+	0.998344i	$0.481678\pi$
$620$	−43.6337	−1.75237
$621$	0.704927	0.0282878
$622$	41.2354	1.65339
$623$	16.2225	0.649940
$624$	0.670555	0.0268437
$625$	2.63153	0.105261
$626$	31.6477	1.26489
$627$	3.68114	0.147011
$628$	7.79382	0.311007
$629$	−12.4793	−0.497582
$630$	−9.89870	−0.394374
$631$	−4.96291	−0.197570	−0.0987851	−	0.995109i	$-0.531496\pi$
$631$	−4.96291	−0.197570	−0.0987851	+	0.995109i	$0.531496\pi$
$632$	26.6200	1.05889
$633$	4.19099	0.166577
$634$	−48.3548	−1.92041
$635$	−4.37940	−0.173791
$636$	0.397881	0.0157770
$637$	−22.4552	−0.889707
$638$	6.45077	0.255389
$639$	−9.44925	−0.373807
$640$	25.0470	0.990069
$641$	−24.8544	−0.981691	−0.490846	−	0.871247i	$-0.663312\pi$
$641$	−24.8544	−0.981691	−0.490846	+	0.871247i	$0.663312\pi$
$642$	7.93003	0.312973
$643$	−18.8363	−0.742830	−0.371415	−	0.928467i	$-0.621127\pi$
$643$	−18.8363	−0.742830	−0.371415	+	0.928467i	$0.621127\pi$
$644$	1.46153	0.0575923
$645$	1.83950	0.0724301
$646$	35.4375	1.39427
$647$	8.58381	0.337464	0.168732	−	0.985662i	$-0.446033\pi$
$647$	8.58381	0.337464	0.168732	+	0.985662i	$0.446033\pi$
$648$	−25.5100	−1.00213
$649$	19.1713	0.752537
$650$	30.2374	1.18601
$651$	3.55786	0.139444
$652$	56.5219	2.21357
$653$	−8.16296	−0.319441	−0.159721	−	0.987162i	$-0.551059\pi$
$653$	−8.16296	−0.319441	−0.159721	+	0.987162i	$0.551059\pi$
$654$	−1.72541	−0.0674689
$655$	−12.7930	−0.499863
$656$	1.53502	0.0599324
$657$	5.19790	0.202789
$658$	−31.0096	−1.20888
$659$	−24.3059	−0.946823	−0.473411	−	0.880842i	$-0.656978\pi$
$659$	−24.3059	−0.946823	−0.473411	+	0.880842i	$0.656978\pi$
$660$	3.77831	0.147071
$661$	−10.9894	−0.427437	−0.213719	−	0.976895i	$-0.568558\pi$
$661$	−10.9894	−0.427437	−0.213719	+	0.976895i	$0.568558\pi$
$662$	58.7168	2.28209
$663$	−4.43463	−0.172227
$664$	−36.7538	−1.42632
$665$	−6.24198	−0.242053
$666$	23.1880	0.898518
$667$	0.383069	0.0148325
$668$	11.8892	0.460006
$669$	−0.737718	−0.0285218
$670$	29.4962	1.13954
$671$	6.94458	0.268093
$672$	−1.77499	−0.0684716
$673$	−23.9288	−0.922386	−0.461193	−	0.887300i	$-0.652578\pi$
$673$	−23.9288	−0.922386	−0.461193	+	0.887300i	$0.652578\pi$
$674$	−6.53952	−0.251893
$675$	6.11094	0.235210
$676$	8.32866	0.320333
$677$	33.6028	1.29146	0.645731	−	0.763565i	$-0.276553\pi$
$677$	33.6028	1.29146	0.645731	+	0.763565i	$0.276553\pi$
$678$	2.94239	0.113002
$679$	4.21620	0.161803
$680$	14.6910	0.563373
$681$	−5.82841	−0.223345
$682$	64.7398	2.47902
$683$	21.7767	0.833263	0.416632	−	0.909075i	$-0.363210\pi$
$683$	21.7767	0.833263	0.416632	+	0.909075i	$0.363210\pi$
$684$	−41.2550	−1.57742
$685$	−10.2304	−0.390883
$686$	−33.4384	−1.27668
$687$	−7.89091	−0.301057
$688$	2.48911	0.0948965
$689$	1.49677	0.0570222
$690$	0.358116	0.0136332
$691$	16.2195	0.617021	0.308510	−	0.951221i	$-0.400170\pi$
$691$	16.2195	0.617021	0.308510	+	0.951221i	$0.400170\pi$
$692$	64.6085	2.45605
$693$	9.20167	0.349542
$694$	10.7915	0.409638
$695$	−1.29585	−0.0491542
$696$	0.977632	0.0370570
$697$	−10.1516	−0.384521
$698$	21.4025	0.810095
$699$	8.09310	0.306109
$700$	12.6699	0.478875
$701$	28.2550	1.06718	0.533589	−	0.845744i	$-0.320843\pi$
$701$	28.2550	1.06718	0.533589	+	0.845744i	$0.320843\pi$
$702$	16.7560	0.632416
$703$	14.6220	0.551480
$704$	−35.3458	−1.33214
$705$	−4.76049	−0.179291
$706$	−31.0795	−1.16969
$707$	−7.74493	−0.291278
$708$	7.19353	0.270349
$709$	−32.7292	−1.22917	−0.614585	−	0.788850i	$-0.710677\pi$
$709$	−32.7292	−1.22917	−0.614585	+	0.788850i	$0.710677\pi$
$710$	−9.76151	−0.366343
$711$	24.6411	0.924115
$712$	44.7366	1.67657
$713$	3.84447	0.143977
$714$	−2.96582	−0.110993
$715$	14.2134	0.531552
$716$	−12.6156	−0.471467
$717$	−2.65266	−0.0990654
$718$	9.30383	0.347216
$719$	9.90783	0.369500	0.184750	−	0.982786i	$-0.440852\pi$
$719$	9.90783	0.369500	0.184750	+	0.982786i	$0.440852\pi$
$720$	−2.05627	−0.0766325
$721$	−0.402473	−0.0149889
$722$	2.44598	0.0910298
$723$	−2.34084	−0.0870568
$724$	−16.9438	−0.629710
$725$	3.32078	0.123331
$726$	2.32980	0.0864670
$727$	41.0757	1.52341	0.761706	−	0.647923i	$-0.224362\pi$
$727$	41.0757	1.52341	0.761706	+	0.647923i	$0.224362\pi$
$728$	14.0316	0.520045
$729$	−21.8926	−0.810836
$730$	5.36966	0.198740
$731$	−16.4614	−0.608848
$732$	2.60578	0.0963123
$733$	−4.60030	−0.169916	−0.0849581	−	0.996385i	$-0.527076\pi$
$733$	−4.60030	−0.169916	−0.0849581	+	0.996385i	$0.527076\pi$
$734$	−24.6078	−0.908289
$735$	−2.30547	−0.0850386
$736$	−1.91797	−0.0706974
$737$	−27.4191	−1.01000
$738$	18.8630	0.694355
$739$	22.5825	0.830709	0.415355	−	0.909660i	$-0.363657\pi$
$739$	22.5825	0.830709	0.415355	+	0.909660i	$0.363657\pi$
$740$	15.0080	0.551705
$741$	5.19607	0.190882
$742$	1.00102	0.0367485
$743$	−36.8186	−1.35074	−0.675372	−	0.737477i	$-0.736017\pi$
$743$	−36.8186	−1.35074	−0.675372	+	0.737477i	$0.736017\pi$
$744$	9.81149	0.359707
$745$	−3.46125	−0.126810
$746$	29.1277	1.06644
$747$	−34.0216	−1.24478
$748$	−33.8117	−1.23628
$749$	12.4998	0.456732
$750$	7.77877	0.284041
$751$	4.12722	0.150604	0.0753022	−	0.997161i	$-0.476008\pi$
$751$	4.12722	0.150604	0.0753022	+	0.997161i	$0.476008\pi$
$752$	−6.44166	−0.234903
$753$	1.82221	0.0664052
$754$	9.10550	0.331603
$755$	−7.91438	−0.288034
$756$	7.02099	0.255351
$757$	−19.2373	−0.699192	−0.349596	−	0.936900i	$-0.613681\pi$
$757$	−19.2373	−0.699192	−0.349596	+	0.936900i	$0.613681\pi$
$758$	9.00756	0.327169
$759$	−0.332899	−0.0120835
$760$	−17.2134	−0.624397
$761$	4.51141	0.163538	0.0817692	−	0.996651i	$-0.473943\pi$
$761$	4.51141	0.163538	0.0817692	+	0.996651i	$0.473943\pi$
$762$	2.43812	0.0883238
$763$	−2.71970	−0.0984596
$764$	78.6723	2.84627
$765$	13.5989	0.491668
$766$	35.9667	1.29953
$767$	27.0609	0.977113
$768$	−6.03841	−0.217893
$769$	15.5928	0.562291	0.281145	−	0.959665i	$-0.409286\pi$
$769$	15.5928	0.562291	0.281145	+	0.959665i	$0.409286\pi$
$770$	9.50574	0.342563
$771$	5.15237	0.185558
$772$	16.7644	0.603363
$773$	−41.1797	−1.48113	−0.740566	−	0.671984i	$-0.765442\pi$
$773$	−41.1797	−1.48113	−0.740566	+	0.671984i	$0.765442\pi$
$774$	30.5873	1.09944
$775$	33.3273	1.19715
$776$	11.6270	0.417384
$777$	−1.22374	−0.0439015
$778$	38.4427	1.37824
$779$	11.8947	0.426172
$780$	5.33323	0.190960
$781$	9.07413	0.324698
$782$	−3.20474	−0.114601
$783$	1.84021	0.0657637
$784$	−3.11965	−0.111416
$785$	3.01019	0.107438
$786$	7.12216	0.254039
$787$	−19.5882	−0.698246	−0.349123	−	0.937077i	$-0.613520\pi$
$787$	−19.5882	−0.698246	−0.349123	+	0.937077i	$0.613520\pi$
$788$	−47.5567	−1.69414
$789$	−1.67383	−0.0595901
$790$	25.4554	0.905663
$791$	4.63796	0.164907
$792$	25.3754	0.901674
$793$	9.80253	0.348098
$794$	61.7953	2.19303
$795$	0.153673	0.00545021
$796$	−7.59828	−0.269314
$797$	17.2477	0.610944	0.305472	−	0.952201i	$-0.401186\pi$
$797$	17.2477	0.610944	0.305472	+	0.952201i	$0.401186\pi$
$798$	3.47506	0.123016
$799$	42.6011	1.50712
$800$	−16.6267	−0.587843
$801$	41.4109	1.46318
$802$	−15.9232	−0.562267
$803$	−4.99155	−0.176148
$804$	−10.2883	−0.362842
$805$	0.564484	0.0198954
$806$	91.3826	3.21881
$807$	4.97094	0.174985
$808$	−21.3581	−0.751376
$809$	6.65883	0.234112	0.117056	−	0.993125i	$-0.462654\pi$
$809$	6.65883	0.234112	0.117056	+	0.993125i	$0.462654\pi$
$810$	−24.3940	−0.857116
$811$	21.7342	0.763189	0.381595	−	0.924330i	$-0.375375\pi$
$811$	21.7342	0.763189	0.381595	+	0.924330i	$0.375375\pi$
$812$	3.81532	0.133891
$813$	−1.94489	−0.0682101
$814$	−22.2675	−0.780476
$815$	21.8303	0.764683
$816$	−0.616093	−0.0215676
$817$	19.2879	0.674798
$818$	59.6071	2.08411
$819$	12.9885	0.453855
$820$	12.2087	0.426346
$821$	13.3231	0.464980	0.232490	−	0.972599i	$-0.425313\pi$
$821$	13.3231	0.464980	0.232490	+	0.972599i	$0.425313\pi$
$822$	5.69550	0.198653
$823$	18.7951	0.655157	0.327578	−	0.944824i	$-0.393767\pi$
$823$	18.7951	0.655157	0.327578	+	0.944824i	$0.393767\pi$
$824$	−1.10990	−0.0386651
$825$	−2.88586	−0.100473
$826$	18.0980	0.629709
$827$	27.6050	0.959919	0.479959	−	0.877291i	$-0.340651\pi$
$827$	27.6050	0.959919	0.479959	+	0.877291i	$0.340651\pi$
$828$	3.73083	0.129655
$829$	−26.1151	−0.907016	−0.453508	−	0.891252i	$-0.649828\pi$
$829$	−26.1151	−0.907016	−0.453508	+	0.891252i	$0.649828\pi$
$830$	−35.1458	−1.21993
$831$	−3.31721	−0.115073
$832$	−49.8918	−1.72969
$833$	20.6314	0.714835
$834$	0.721429	0.0249810
$835$	4.59193	0.158910
$836$	39.6172	1.37019
$837$	18.4683	0.638358
$838$	51.4555	1.77750
$839$	30.7252	1.06075	0.530377	−	0.847762i	$-0.322051\pi$
$839$	30.7252	1.06075	0.530377	+	0.847762i	$0.322051\pi$
$840$	1.44062	0.0497061
$841$	1.00000	0.0344828
$842$	−26.3517	−0.908140
$843$	−1.98021	−0.0682020
$844$	45.1042	1.55255
$845$	3.21676	0.110660
$846$	−79.1579	−2.72150
$847$	3.67237	0.126184
$848$	0.207942	0.00714076
$849$	−3.39700	−0.116585
$850$	−27.7815	−0.952898
$851$	−1.32232	−0.0453286
$852$	3.40484	0.116648
$853$	34.0611	1.16623	0.583115	−	0.812390i	$-0.301834\pi$
$853$	34.0611	1.16623	0.583115	+	0.812390i	$0.301834\pi$
$854$	6.55580	0.224335
$855$	−15.9338	−0.544925
$856$	34.4705	1.17818
$857$	−14.9393	−0.510315	−0.255158	−	0.966899i	$-0.582127\pi$
$857$	−14.9393	−0.510315	−0.255158	+	0.966899i	$0.582127\pi$
$858$	−7.91296	−0.270144
$859$	−39.4619	−1.34642	−0.673211	−	0.739450i	$-0.735086\pi$
$859$	−39.4619	−1.34642	−0.673211	+	0.739450i	$0.735086\pi$
$860$	19.7970	0.675073
$861$	−0.995487	−0.0339261
$862$	84.3577	2.87323
$863$	−5.79967	−0.197423	−0.0987116	−	0.995116i	$-0.531472\pi$
$863$	−5.79967	−0.197423	−0.0987116	+	0.995116i	$0.531472\pi$
$864$	−9.21367	−0.313455
$865$	24.9536	0.848448
$866$	37.8357	1.28571
$867$	−1.22532	−0.0416142
$868$	38.2905	1.29966
$869$	−23.6629	−0.802710
$870$	0.934860	0.0316947
$871$	−38.7031	−1.31141
$872$	−7.50008	−0.253985
$873$	10.7626	0.364260
$874$	3.75500	0.127015
$875$	12.2614	0.414510
$876$	−1.87295	−0.0632812
$877$	1.22011	0.0412001	0.0206001	−	0.999788i	$-0.493442\pi$
$877$	1.22011	0.0412001	0.0206001	+	0.999788i	$0.493442\pi$
$878$	55.3099	1.86662
$879$	0.840819	0.0283601
$880$	1.97464	0.0665650
$881$	23.8129	0.802277	0.401139	−	0.916017i	$-0.368615\pi$
$881$	23.8129	0.802277	0.401139	+	0.916017i	$0.368615\pi$
$882$	−38.3356	−1.29083
$883$	47.8692	1.61093	0.805464	−	0.592645i	$-0.201916\pi$
$883$	47.8692	1.61093	0.805464	+	0.592645i	$0.201916\pi$
$884$	−47.7264	−1.60521
$885$	2.77834	0.0933929
$886$	−38.0061	−1.27684
$887$	−26.7351	−0.897676	−0.448838	−	0.893613i	$-0.648162\pi$
$887$	−26.7351	−0.897676	−0.448838	+	0.893613i	$0.648162\pi$
$888$	−3.37470	−0.113247
$889$	3.84311	0.128894
$890$	42.7794	1.43397
$891$	22.6762	0.759682
$892$	−7.93947	−0.265833
$893$	−49.9158	−1.67037
$894$	1.92696	0.0644472
$895$	−4.87249	−0.162870
$896$	−21.9798	−0.734293
$897$	−0.469898	−0.0156895
$898$	24.7604	0.826264
$899$	10.0360	0.334719
$900$	32.3422	1.07807
$901$	−1.37520	−0.0458145
$902$	−18.1141	−0.603135
$903$	−1.61423	−0.0537184
$904$	12.7901	0.425391
$905$	−6.54416	−0.217535
$906$	4.40613	0.146384
$907$	56.4278	1.87365	0.936827	−	0.349792i	$-0.113748\pi$
$907$	56.4278	1.87365	0.936827	+	0.349792i	$0.113748\pi$
$908$	−62.7265	−2.08165
$909$	−19.7704	−0.655742
$910$	13.4177	0.444792
$911$	8.50374	0.281741	0.140871	−	0.990028i	$-0.455010\pi$
$911$	8.50374	0.281741	0.140871	+	0.990028i	$0.455010\pi$
$912$	0.721878	0.0239038
$913$	32.6710	1.08125
$914$	76.8153	2.54083
$915$	1.00642	0.0332714
$916$	−84.9236	−2.80595
$917$	11.2264	0.370727
$918$	−15.3951	−0.508114
$919$	15.7155	0.518406	0.259203	−	0.965823i	$-0.416540\pi$
$919$	15.7155	0.518406	0.259203	+	0.965823i	$0.416540\pi$
$920$	1.55667	0.0513219
$921$	−4.90750	−0.161708
$922$	−72.3700	−2.38338
$923$	12.8085	0.421596
$924$	−3.31563	−0.109076
$925$	−11.4631	−0.376903
$926$	4.99564	0.164167
$927$	−1.02739	−0.0337438
$928$	−5.00686	−0.164358
$929$	−17.4172	−0.571440	−0.285720	−	0.958313i	$-0.592233\pi$
$929$	−17.4172	−0.571440	−0.285720	+	0.958313i	$0.592233\pi$
$930$	9.38224	0.307656
$931$	−24.1738	−0.792266
$932$	87.0996	2.85304
$933$	−5.55513	−0.181867
$934$	−32.2148	−1.05410
$935$	−13.0590	−0.427075
$936$	35.8182	1.17076
$937$	−6.07434	−0.198440	−0.0992200	−	0.995066i	$-0.531635\pi$
$937$	−6.07434	−0.198440	−0.0992200	+	0.995066i	$0.531635\pi$
$938$	−25.8841	−0.845147
$939$	−4.26349	−0.139134
$940$	−51.2334	−1.67105
$941$	−29.2591	−0.953821	−0.476910	−	0.878952i	$-0.658243\pi$
$941$	−29.2591	−0.953821	−0.476910	+	0.878952i	$0.658243\pi$
$942$	−1.67585	−0.0546020
$943$	−1.07568	−0.0350289
$944$	3.75951	0.122362
$945$	2.71170	0.0882116
$946$	−29.3730	−0.955000
$947$	3.77521	0.122678	0.0613389	−	0.998117i	$-0.480463\pi$
$947$	3.77521	0.122678	0.0613389	+	0.998117i	$0.480463\pi$
$948$	−8.87892	−0.288374
$949$	−7.04575	−0.228715
$950$	32.5517	1.05612
$951$	6.51422	0.211238
$952$	−12.8919	−0.417830
$953$	−21.5188	−0.697061	−0.348530	−	0.937297i	$-0.613319\pi$
$953$	−21.5188	−0.697061	−0.348530	+	0.937297i	$0.613319\pi$
$954$	2.55528	0.0827303
$955$	30.3855	0.983250
$956$	−28.5485	−0.923323
$957$	−0.869031	−0.0280918
$958$	−50.2137	−1.62233
$959$	8.97759	0.289901
$960$	−5.12239	−0.165324
$961$	69.7209	2.24906
$962$	−31.4314	−1.01339
$963$	31.9080	1.02822
$964$	−25.1926	−0.811399
$965$	6.47487	0.208433
$966$	−0.314262	−0.0101112
$967$	−30.8925	−0.993435	−0.496718	−	0.867912i	$-0.665462\pi$
$967$	−30.8925	−0.993435	−0.496718	+	0.867912i	$0.665462\pi$
$968$	10.1273	0.325502
$969$	−4.77404	−0.153364
$970$	11.1183	0.356987
$971$	−42.9351	−1.37785	−0.688926	−	0.724831i	$-0.741918\pi$
$971$	−42.9351	−1.37785	−0.688926	+	0.724831i	$0.741918\pi$
$972$	27.0311	0.867024
$973$	1.13716	0.0364556
$974$	−11.0513	−0.354107
$975$	−4.07350	−0.130456
$976$	1.36184	0.0435915
$977$	−19.3023	−0.617536	−0.308768	−	0.951137i	$-0.599917\pi$
$977$	−19.3023	−0.617536	−0.308768	+	0.951137i	$0.599917\pi$
$978$	−12.1535	−0.388625
$979$	−39.7670	−1.27096
$980$	−24.8119	−0.792588
$981$	−6.94253	−0.221658
$982$	−30.4907	−0.972997
$983$	10.6594	0.339981	0.169991	−	0.985446i	$-0.445626\pi$
$983$	10.6594	0.339981	0.169991	+	0.985446i	$0.445626\pi$
$984$	−2.74525	−0.0875152
$985$	−18.3677	−0.585245
$986$	−8.36595	−0.266426
$987$	4.17753	0.132972
$988$	55.9211	1.77909
$989$	−1.74427	−0.0554646
$990$	24.2652	0.771198
$991$	40.8739	1.29840	0.649202	−	0.760616i	$-0.275103\pi$
$991$	40.8739	1.29840	0.649202	+	0.760616i	$0.275103\pi$
$992$	−50.2487	−1.59540
$993$	−7.91017	−0.251022
$994$	8.56613	0.271701
$995$	−2.93467	−0.0930352
$996$	12.2590	0.388440
$997$	12.9519	0.410189	0.205095	−	0.978742i	$-0.434250\pi$
$997$	12.9519	0.410189	0.205095	+	0.978742i	$0.434250\pi$
$998$	39.9257	1.26383
$999$	−6.35224	−0.200976

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4031.2.a.c.1.6	✓	61

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4031.2.a.c.1.6	✓	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)

\(f(q)\)	\(=\)	\(q-2.31412 q^{2} +0.311751 q^{3} +3.35513 q^{4} +1.29585 q^{5} -0.721429 q^{6} -1.13716 q^{7} -3.13593 q^{8} -2.90281 q^{9} +O(q^{10})\)	\(q-2.31412 q^{2} +0.311751 q^{3} +3.35513 q^{4} +1.29585 q^{5} -0.721429 q^{6} -1.13716 q^{7} -3.13593 q^{8} -2.90281 q^{9} -2.99874 q^{10} +2.78758 q^{11} +1.04597 q^{12} +3.93476 q^{13} +2.63152 q^{14} +0.403982 q^{15} +0.546648 q^{16} -3.61518 q^{17} +6.71744 q^{18} +4.23592 q^{19} +4.34773 q^{20} -0.354511 q^{21} -6.45077 q^{22} -0.383069 q^{23} -0.977632 q^{24} -3.32078 q^{25} -9.10550 q^{26} -1.84021 q^{27} -3.81532 q^{28} -1.00000 q^{29} -0.934860 q^{30} -10.0360 q^{31} +5.00686 q^{32} +0.869031 q^{33} +8.36595 q^{34} -1.47358 q^{35} -9.73931 q^{36} +3.45191 q^{37} -9.80241 q^{38} +1.22667 q^{39} -4.06368 q^{40} +2.80806 q^{41} +0.820379 q^{42} +4.55341 q^{43} +9.35268 q^{44} -3.76159 q^{45} +0.886466 q^{46} -11.7839 q^{47} +0.170418 q^{48} -5.70687 q^{49} +7.68468 q^{50} -1.12704 q^{51} +13.2017 q^{52} +0.380395 q^{53} +4.25846 q^{54} +3.61227 q^{55} +3.56605 q^{56} +1.32055 q^{57} +2.31412 q^{58} +6.87739 q^{59} +1.35541 q^{60} +2.49126 q^{61} +23.2244 q^{62} +3.30096 q^{63} -12.6797 q^{64} +5.09885 q^{65} -2.01104 q^{66} -9.83620 q^{67} -12.1294 q^{68} -0.119422 q^{69} +3.41004 q^{70} +3.25521 q^{71} +9.10302 q^{72} -1.79064 q^{73} -7.98813 q^{74} -1.03526 q^{75} +14.2121 q^{76} -3.16992 q^{77} -2.83865 q^{78} -8.48872 q^{79} +0.708371 q^{80} +8.13475 q^{81} -6.49817 q^{82} +11.7202 q^{83} -1.18943 q^{84} -4.68472 q^{85} -10.5371 q^{86} -0.311751 q^{87} -8.74165 q^{88} -14.2658 q^{89} +8.70477 q^{90} -4.47445 q^{91} -1.28525 q^{92} -3.12873 q^{93} +27.2694 q^{94} +5.48910 q^{95} +1.56090 q^{96} -3.70766 q^{97} +13.2064 q^{98} -8.09180 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 61 q - q^{2} - 4 q^{3} + 43 q^{4} - 7 q^{5} - 13 q^{6} - 10 q^{7} - 6 q^{8} + 23 q^{9}+O(q^{10}) \) 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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