LMFDB - Embedded newform 6031.2.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6031,2,Mod(1,6031)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6031, 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("6031.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6031 = 37 \cdot 163 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6031.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:	$48.1577774590$
Analytic rank:	$1$
Dimension:	$110$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	6031.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.78685 q^{2} -0.498757 q^{3} +5.76655 q^{4} +1.84399 q^{5} +1.38996 q^{6} -1.25608 q^{7} -10.4968 q^{8} -2.75124 q^{9} +O(q^{10})$	\(q-2.78685 q^{2} -0.498757 q^{3} +5.76655 q^{4} +1.84399 q^{5} +1.38996 q^{6} -1.25608 q^{7} -10.4968 q^{8} -2.75124 q^{9} -5.13894 q^{10} -0.523231 q^{11} -2.87611 q^{12} -0.0517683 q^{13} +3.50050 q^{14} -0.919706 q^{15} +17.7200 q^{16} +1.63094 q^{17} +7.66730 q^{18} -4.01873 q^{19} +10.6335 q^{20} +0.626477 q^{21} +1.45817 q^{22} +2.23029 q^{23} +5.23536 q^{24} -1.59968 q^{25} +0.144271 q^{26} +2.86847 q^{27} -7.24323 q^{28} -1.96250 q^{29} +2.56308 q^{30} +1.58649 q^{31} -28.3894 q^{32} +0.260965 q^{33} -4.54518 q^{34} -2.31620 q^{35} -15.8652 q^{36} -1.00000 q^{37} +11.1996 q^{38} +0.0258198 q^{39} -19.3561 q^{40} +0.308008 q^{41} -1.74590 q^{42} +8.98896 q^{43} -3.01723 q^{44} -5.07327 q^{45} -6.21550 q^{46} -9.26050 q^{47} -8.83797 q^{48} -5.42227 q^{49} +4.45808 q^{50} -0.813441 q^{51} -0.298525 q^{52} +9.31004 q^{53} -7.99401 q^{54} -0.964834 q^{55} +13.1848 q^{56} +2.00437 q^{57} +5.46920 q^{58} +13.6345 q^{59} -5.30353 q^{60} +12.4005 q^{61} -4.42131 q^{62} +3.45577 q^{63} +43.6770 q^{64} -0.0954605 q^{65} -0.727271 q^{66} +12.4336 q^{67} +9.40487 q^{68} -1.11238 q^{69} +6.45490 q^{70} -3.57614 q^{71} +28.8793 q^{72} +6.03045 q^{73} +2.78685 q^{74} +0.797854 q^{75} -23.1742 q^{76} +0.657218 q^{77} -0.0719561 q^{78} -4.26844 q^{79} +32.6756 q^{80} +6.82305 q^{81} -0.858372 q^{82} -1.90211 q^{83} +3.61261 q^{84} +3.00744 q^{85} -25.0509 q^{86} +0.978812 q^{87} +5.49226 q^{88} -5.82583 q^{89} +14.1385 q^{90} +0.0650250 q^{91} +12.8611 q^{92} -0.791272 q^{93} +25.8077 q^{94} -7.41053 q^{95} +14.1594 q^{96} -2.17725 q^{97} +15.1111 q^{98} +1.43953 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 110 q - 9 q^{2} + 97 q^{4} - 26 q^{5} - 26 q^{6} - 4 q^{7} - 27 q^{8} + 62 q^{9}+O(q^{10}) $ 110 * q - 9 * q^2 + 97 * q^4 - 26 * q^5 - 26 * q^6 - 4 * q^7 - 27 * q^8 + 62 * q^9	\( 110 q - 9 q^{2} + 97 q^{4} - 26 q^{5} - 26 q^{6} - 4 q^{7} - 27 q^{8} + 62 q^{9} - 17 q^{10} - 9 q^{11} - 21 q^{13} - 29 q^{14} - 23 q^{15} + 79 q^{16} - 76 q^{17} - 31 q^{18} - 27 q^{19} - 67 q^{20} - 30 q^{21} - 28 q^{22} - 32 q^{23} - 63 q^{24} + 66 q^{25} - 55 q^{26} - 4 q^{28} - 81 q^{29} - 48 q^{30} - 30 q^{31} - 73 q^{32} - 53 q^{33} - 23 q^{34} - 78 q^{35} + 7 q^{36} - 110 q^{37} - 50 q^{38} - 64 q^{39} - 37 q^{40} - 123 q^{41} - 63 q^{42} - 40 q^{43} - 31 q^{44} - 73 q^{45} + 16 q^{46} - 37 q^{47} - 29 q^{48} + 46 q^{49} - 58 q^{50} - 73 q^{51} - 39 q^{52} - 16 q^{53} - 53 q^{54} - 59 q^{55} - 113 q^{56} - 39 q^{57} + 11 q^{58} - 93 q^{59} - 18 q^{60} - 66 q^{61} - 40 q^{62} - 21 q^{63} + 23 q^{64} - 92 q^{65} - 31 q^{66} + q^{67} - 121 q^{68} - 80 q^{69} - 3 q^{70} - 75 q^{71} - 114 q^{72} - 39 q^{73} + 9 q^{74} - 25 q^{75} - 58 q^{76} - 31 q^{77} + 68 q^{78} - 36 q^{79} - 82 q^{80} - 50 q^{81} - 18 q^{82} - 57 q^{83} - 9 q^{84} - 14 q^{85} - 58 q^{86} - 58 q^{87} - 15 q^{88} - 181 q^{89} + 8 q^{90} - 55 q^{91} - 116 q^{92} - 86 q^{93} - 39 q^{94} - 70 q^{95} - 127 q^{96} - 91 q^{97} - 19 q^{98} - 21 q^{99}+O(q^{100}) \) 110 * q - 9 * q^2 + 97 * q^4 - 26 * q^5 - 26 * q^6 - 4 * q^7 - 27 * q^8 + 62 * q^9 - 17 * q^10 - 9 * q^11 - 21 * q^13 - 29 * q^14 - 23 * q^15 + 79 * q^16 - 76 * q^17 - 31 * q^18 - 27 * q^19 - 67 * q^20 - 30 * q^21 - 28 * q^22 - 32 * q^23 - 63 * q^24 + 66 * q^25 - 55 * q^26 - 4 * q^28 - 81 * q^29 - 48 * q^30 - 30 * q^31 - 73 * q^32 - 53 * q^33 - 23 * q^34 - 78 * q^35 + 7 * q^36 - 110 * q^37 - 50 * q^38 - 64 * q^39 - 37 * q^40 - 123 * q^41 - 63 * q^42 - 40 * q^43 - 31 * q^44 - 73 * q^45 + 16 * q^46 - 37 * q^47 - 29 * q^48 + 46 * q^49 - 58 * q^50 - 73 * q^51 - 39 * q^52 - 16 * q^53 - 53 * q^54 - 59 * q^55 - 113 * q^56 - 39 * q^57 + 11 * q^58 - 93 * q^59 - 18 * q^60 - 66 * q^61 - 40 * q^62 - 21 * q^63 + 23 * q^64 - 92 * q^65 - 31 * q^66 + q^67 - 121 * q^68 - 80 * q^69 - 3 * q^70 - 75 * q^71 - 114 * q^72 - 39 * q^73 + 9 * q^74 - 25 * q^75 - 58 * q^76 - 31 * q^77 + 68 * q^78 - 36 * q^79 - 82 * q^80 - 50 * q^81 - 18 * q^82 - 57 * q^83 - 9 * q^84 - 14 * q^85 - 58 * q^86 - 58 * q^87 - 15 * q^88 - 181 * q^89 + 8 * q^90 - 55 * q^91 - 116 * q^92 - 86 * q^93 - 39 * q^94 - 70 * q^95 - 127 * q^96 - 91 * q^97 - 19 * q^98 - 21 * 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 $

$2$	−2.78685	−1.97060	−0.985301	−	0.170826i	$-0.945356\pi$
$2$	−2.78685	−1.97060	−0.985301	+	0.170826i	$0.945356\pi$
$3$	−0.498757	−0.287958	−0.143979	−	0.989581i	$-0.545990\pi$
$3$	−0.498757	−0.287958	−0.143979	+	0.989581i	$0.545990\pi$
$4$	5.76655	2.88327
$5$	1.84399	0.824660	0.412330	−	0.911035i	$-0.364715\pi$
$5$	1.84399	0.824660	0.412330	+	0.911035i	$0.364715\pi$
$6$	1.38996	0.567450
$7$	−1.25608	−0.474752	−0.237376	−	0.971418i	$-0.576287\pi$
$7$	−1.25608	−0.474752	−0.237376	+	0.971418i	$0.576287\pi$
$8$	−10.4968	−3.71119
$9$	−2.75124	−0.917080
$10$	−5.13894	−1.62508
$11$	−0.523231	−0.157760	−0.0788800	−	0.996884i	$-0.525134\pi$
$11$	−0.523231	−0.157760	−0.0788800	+	0.996884i	$0.525134\pi$
$12$	−2.87611	−0.830261
$13$	−0.0517683	−0.0143579	−0.00717897	−	0.999974i	$-0.502285\pi$
$13$	−0.0517683	−0.0143579	−0.00717897	+	0.999974i	$0.502285\pi$
$14$	3.50050	0.935548
$15$	−0.919706	−0.237467
$16$	17.7200	4.43000
$17$	1.63094	0.395560	0.197780	−	0.980246i	$-0.436627\pi$
$17$	1.63094	0.395560	0.197780	+	0.980246i	$0.436627\pi$
$18$	7.66730	1.80720
$19$	−4.01873	−0.921961	−0.460981	−	0.887410i	$-0.652502\pi$
$19$	−4.01873	−0.921961	−0.460981	+	0.887410i	$0.652502\pi$
$20$	10.6335	2.37772
$21$	0.626477	0.136709
$22$	1.45817	0.310882
$23$	2.23029	0.465049	0.232524	−	0.972591i	$-0.425301\pi$
$23$	2.23029	0.465049	0.232524	+	0.972591i	$0.425301\pi$
$24$	5.23536	1.06866
$25$	−1.59968	−0.319937
$26$	0.144271	0.0282938
$27$	2.86847	0.552038
$28$	−7.24323	−1.36884
$29$	−1.96250	−0.364427	−0.182214	−	0.983259i	$-0.558326\pi$
$29$	−1.96250	−0.364427	−0.182214	+	0.983259i	$0.558326\pi$
$30$	2.56308	0.467953
$31$	1.58649	0.284942	0.142471	−	0.989799i	$-0.454495\pi$
$31$	1.58649	0.284942	0.142471	+	0.989799i	$0.454495\pi$
$32$	−28.3894	−5.01858
$33$	0.260965	0.0454282
$34$	−4.54518	−0.779492
$35$	−2.31620	−0.391509
$36$	−15.8652	−2.64419
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	11.1996	1.81682
$39$	0.0258198	0.00413448
$40$	−19.3561	−3.06046
$41$	0.308008	0.0481027	0.0240514	−	0.999711i	$-0.492343\pi$
$41$	0.308008	0.0481027	0.0240514	+	0.999711i	$0.492343\pi$
$42$	−1.74590	−0.269398
$43$	8.98896	1.37080	0.685402	−	0.728165i	$-0.259627\pi$
$43$	8.98896	1.37080	0.685402	+	0.728165i	$0.259627\pi$
$44$	−3.01723	−0.454865
$45$	−5.07327	−0.756279
$46$	−6.21550	−0.916426
$47$	−9.26050	−1.35078	−0.675392	−	0.737459i	$-0.736025\pi$
$47$	−9.26050	−1.35078	−0.675392	+	0.737459i	$0.736025\pi$
$48$	−8.83797	−1.27565
$49$	−5.42227	−0.774610
$50$	4.45808	0.630468
$51$	−0.813441	−0.113905
$52$	−0.298525	−0.0413979
$53$	9.31004	1.27883	0.639416	−	0.768861i	$-0.279176\pi$
$53$	9.31004	1.27883	0.639416	+	0.768861i	$0.279176\pi$
$54$	−7.99401	−1.08785
$55$	−0.964834	−0.130098
$56$	13.1848	1.76189
$57$	2.00437	0.265486
$58$	5.46920	0.718142
$59$	13.6345	1.77506	0.887529	−	0.460753i	$-0.152421\pi$
$59$	13.6345	1.77506	0.887529	+	0.460753i	$0.152421\pi$
$60$	−5.30353	−0.684682
$61$	12.4005	1.58773	0.793863	−	0.608097i	$-0.208067\pi$
$61$	12.4005	1.58773	0.793863	+	0.608097i	$0.208067\pi$
$62$	−4.42131	−0.561507
$63$	3.45577	0.435386
$64$	43.6770	5.45962
$65$	−0.0954605	−0.0118404
$66$	−0.727271	−0.0895209
$67$	12.4336	1.51901	0.759503	−	0.650503i	$-0.225442\pi$
$67$	12.4336	1.51901	0.759503	+	0.650503i	$0.225442\pi$
$68$	9.40487	1.14051
$69$	−1.11238	−0.133914
$70$	6.45490	0.771509
$71$	−3.57614	−0.424410	−0.212205	−	0.977225i	$-0.568064\pi$
$71$	−3.57614	−0.424410	−0.212205	+	0.977225i	$0.568064\pi$
$72$	28.8793	3.40346
$73$	6.03045	0.705811	0.352906	−	0.935659i	$-0.385194\pi$
$73$	6.03045	0.705811	0.352906	+	0.935659i	$0.385194\pi$
$74$	2.78685	0.323965
$75$	0.797854	0.0921282
$76$	−23.1742	−2.65827
$77$	0.657218	0.0748969
$78$	−0.0719561	−0.00814742
$79$	−4.26844	−0.480237	−0.240119	−	0.970744i	$-0.577186\pi$
$79$	−4.26844	−0.480237	−0.240119	+	0.970744i	$0.577186\pi$
$80$	32.6756	3.65324
$81$	6.82305	0.758117
$82$	−0.858372	−0.0947913
$83$	−1.90211	−0.208783	−0.104392	−	0.994536i	$-0.533290\pi$
$83$	−1.90211	−0.208783	−0.104392	+	0.994536i	$0.533290\pi$
$84$	3.61261	0.394168
$85$	3.00744	0.326202
$86$	−25.0509	−2.70131
$87$	0.978812	0.104940
$88$	5.49226	0.585476
$89$	−5.82583	−0.617536	−0.308768	−	0.951137i	$-0.599917\pi$
$89$	−5.82583	−0.617536	−0.308768	+	0.951137i	$0.599917\pi$
$90$	14.1385	1.49033
$91$	0.0650250	0.00681647
$92$	12.8611	1.34086
$93$	−0.791272	−0.0820511
$94$	25.8077	2.66186
$95$	−7.41053	−0.760304
$96$	14.1594	1.44514
$97$	−2.17725	−0.221066	−0.110533	−	0.993872i	$-0.535256\pi$
$97$	−2.17725	−0.221066	−0.110533	+	0.993872i	$0.535256\pi$
$98$	15.1111	1.52645
$99$	1.43953	0.144679
$100$	−9.22465	−0.922465
$101$	−16.0044	−1.59250	−0.796249	−	0.604969i	$-0.793185\pi$
$101$	−16.0044	−1.59250	−0.796249	+	0.604969i	$0.793185\pi$
$102$	2.26694	0.224461
$103$	−2.45150	−0.241553	−0.120777	−	0.992680i	$-0.538538\pi$
$103$	−2.45150	−0.241553	−0.120777	+	0.992680i	$0.538538\pi$
$104$	0.543403	0.0532850
$105$	1.15522	0.112738
$106$	−25.9457	−2.52007
$107$	−14.6124	−1.41264	−0.706319	−	0.707894i	$-0.749645\pi$
$107$	−14.6124	−1.41264	−0.706319	+	0.707894i	$0.749645\pi$
$108$	16.5412	1.59168
$109$	−5.81825	−0.557288	−0.278644	−	0.960395i	$-0.589885\pi$
$109$	−5.81825	−0.557288	−0.278644	+	0.960395i	$0.589885\pi$
$110$	2.68885	0.256372
$111$	0.498757	0.0473399
$112$	−22.2577	−2.10315
$113$	19.8779	1.86996	0.934980	−	0.354701i	$-0.115417\pi$
$113$	19.8779	1.86996	0.934980	+	0.354701i	$0.115417\pi$
$114$	−5.58589	−0.523167
$115$	4.11265	0.383507
$116$	−11.3169	−1.05074
$117$	0.142427	0.0131674
$118$	−37.9973	−3.49793
$119$	−2.04858	−0.187793
$120$	9.65398	0.881284
$121$	−10.7262	−0.975112
$122$	−34.5585	−3.12878
$123$	−0.153621	−0.0138515
$124$	9.14856	0.821565
$125$	−12.1698	−1.08850
$126$	−9.63072	−0.857973
$127$	13.9094	1.23426	0.617129	−	0.786862i	$-0.288296\pi$
$127$	13.9094	1.23426	0.617129	+	0.786862i	$0.288296\pi$
$128$	−64.9426	−5.74017
$129$	−4.48331	−0.394733
$130$	0.266034	0.0233328
$131$	−20.8135	−1.81849	−0.909243	−	0.416266i	$-0.863338\pi$
$131$	−20.8135	−1.81849	−0.909243	+	0.416266i	$0.863338\pi$
$132$	1.50487	0.130982
$133$	5.04784	0.437703
$134$	−34.6506	−2.99336
$135$	5.28945	0.455243
$136$	−17.1196	−1.46800
$137$	2.07075	0.176916	0.0884580	−	0.996080i	$-0.471806\pi$
$137$	2.07075	0.176916	0.0884580	+	0.996080i	$0.471806\pi$
$138$	3.10003	0.263892
$139$	12.4174	1.05323	0.526616	−	0.850103i	$-0.323460\pi$
$139$	12.4174	1.05323	0.526616	+	0.850103i	$0.323460\pi$
$140$	−13.3565	−1.12883
$141$	4.61874	0.388968
$142$	9.96617	0.836343
$143$	0.0270868	0.00226511
$144$	−48.7520	−4.06266
$145$	−3.61884	−0.300529
$146$	−16.8060	−1.39087
$147$	2.70440	0.223055
$148$	−5.76655	−0.474007
$149$	18.9016	1.54848	0.774239	−	0.632894i	$-0.218133\pi$
$149$	18.9016	1.54848	0.774239	+	0.632894i	$0.218133\pi$
$150$	−2.22350	−0.181548
$151$	10.2099	0.830874	0.415437	−	0.909622i	$-0.363629\pi$
$151$	10.2099	0.830874	0.415437	+	0.909622i	$0.363629\pi$
$152$	42.1839	3.42157
$153$	−4.48710	−0.362760
$154$	−1.83157	−0.147592
$155$	2.92547	0.234980
$156$	0.148891	0.0119208
$157$	−9.70196	−0.774301	−0.387150	−	0.922017i	$-0.626541\pi$
$157$	−9.70196	−0.774301	−0.387150	+	0.922017i	$0.626541\pi$
$158$	11.8955	0.946357
$159$	−4.64345	−0.368250
$160$	−52.3498	−4.13862
$161$	−2.80142	−0.220783
$162$	−19.0148	−1.49395
$163$	−1.00000	−0.0783260
$163$	−1.00000	−0.0783260
$164$	1.77614	0.138693
$165$	0.481218	0.0374628
$166$	5.30089	0.411429
$167$	−17.6777	−1.36794	−0.683969	−	0.729511i	$-0.739748\pi$
$167$	−17.6777	−1.36794	−0.683969	+	0.729511i	$0.739748\pi$
$168$	−6.57602	−0.507351
$169$	−12.9973	−0.999794
$170$	−8.38129	−0.642815
$171$	11.0565	0.845512
$172$	51.8353	3.95240
$173$	−24.1911	−1.83922	−0.919608	−	0.392838i	$-0.871493\pi$
$173$	−24.1911	−1.83922	−0.919608	+	0.392838i	$0.871493\pi$
$174$	−2.72781	−0.206794
$175$	2.00932	0.151891
$176$	−9.27164	−0.698876
$177$	−6.80029	−0.511141
$178$	16.2357	1.21692
$179$	−24.8171	−1.85492	−0.927458	−	0.373928i	$-0.878011\pi$
$179$	−24.8171	−1.85492	−0.927458	+	0.373928i	$0.878011\pi$
$180$	−29.2553	−2.18056
$181$	−18.0151	−1.33905	−0.669524	−	0.742790i	$-0.733502\pi$
$181$	−18.0151	−1.33905	−0.669524	+	0.742790i	$0.733502\pi$
$182$	−0.181215	−0.0134326
$183$	−6.18486	−0.457198
$184$	−23.4110	−1.72588
$185$	−1.84399	−0.135573
$186$	2.20516	0.161690
$187$	−0.853356	−0.0624035
$188$	−53.4011	−3.89468
$189$	−3.60302	−0.262081
$190$	20.6520	1.49826
$191$	6.67936	0.483301	0.241651	−	0.970363i	$-0.422311\pi$
$191$	6.67936	0.483301	0.241651	+	0.970363i	$0.422311\pi$
$192$	−21.7842	−1.57214
$193$	22.3015	1.60530	0.802650	−	0.596450i	$-0.203423\pi$
$193$	22.3015	1.60530	0.802650	+	0.596450i	$0.203423\pi$
$194$	6.06767	0.435633
$195$	0.0476116	0.00340954
$196$	−31.2678	−2.23341
$197$	15.5534	1.10814	0.554068	−	0.832471i	$-0.313075\pi$
$197$	15.5534	1.10814	0.554068	+	0.832471i	$0.313075\pi$
$198$	−4.01177	−0.285104
$199$	3.00246	0.212839	0.106419	−	0.994321i	$-0.466061\pi$
$199$	3.00246	0.212839	0.106419	+	0.994321i	$0.466061\pi$
$200$	16.7916	1.18734
$201$	−6.20135	−0.437410
$202$	44.6019	3.13818
$203$	2.46505	0.173013
$204$	−4.69075	−0.328418
$205$	0.567965	0.0396684
$206$	6.83196	0.476005
$207$	−6.13608	−0.426487
$208$	−0.917334	−0.0636057
$209$	2.10273	0.145449
$210$	−3.21943	−0.222162
$211$	−4.19193	−0.288584	−0.144292	−	0.989535i	$-0.546090\pi$
$211$	−4.19193	−0.288584	−0.144292	+	0.989535i	$0.546090\pi$
$212$	53.6868	3.68723
$213$	1.78363	0.122212
$214$	40.7227	2.78375
$215$	16.5756	1.13045
$216$	−30.1098	−2.04871
$217$	−1.99275	−0.135277
$218$	16.2146	1.09819
$219$	−3.00773	−0.203244
$220$	−5.56376	−0.375109
$221$	−0.0844308	−0.00567943
$222$	−1.38996	−0.0932882
$223$	26.7713	1.79274	0.896371	−	0.443305i	$-0.146194\pi$
$223$	26.7713	1.79274	0.896371	+	0.443305i	$0.146194\pi$
$224$	35.6592	2.38258
$225$	4.40112	0.293408
$226$	−55.3969	−3.68495
$227$	−27.9518	−1.85523	−0.927613	−	0.373542i	$-0.878143\pi$
$227$	−27.9518	−1.85523	−0.927613	+	0.373542i	$0.878143\pi$
$228$	11.5583	0.765468
$229$	1.61214	0.106533	0.0532664	−	0.998580i	$-0.483037\pi$
$229$	1.61214	0.106533	0.0532664	+	0.998580i	$0.483037\pi$
$230$	−11.4614	−0.755739
$231$	−0.327792	−0.0215671
$232$	20.6000	1.35246
$233$	−18.9485	−1.24135	−0.620677	−	0.784066i	$-0.713142\pi$
$233$	−18.9485	−1.24135	−0.620677	+	0.784066i	$0.713142\pi$
$234$	−0.396924	−0.0259477
$235$	−17.0763	−1.11394
$236$	78.6238	5.11798
$237$	2.12892	0.138288
$238$	5.70909	0.370065
$239$	20.2555	1.31022	0.655110	−	0.755534i	$-0.272622\pi$
$239$	20.2555	1.31022	0.655110	+	0.755534i	$0.272622\pi$
$240$	−16.2972	−1.05198
$241$	−21.7509	−1.40110	−0.700548	−	0.713605i	$-0.747061\pi$
$241$	−21.7509	−1.40110	−0.700548	+	0.713605i	$0.747061\pi$
$242$	29.8924	1.92156
$243$	−12.0085	−0.770343
$244$	71.5083	4.57785
$245$	−9.99864	−0.638790
$246$	0.428119	0.0272959
$247$	0.208043	0.0132375
$248$	−16.6531	−1.05747
$249$	0.948689	0.0601207
$250$	33.9154	2.14500
$251$	−29.4713	−1.86021	−0.930106	−	0.367292i	$-0.880285\pi$
$251$	−29.4713	−1.86021	−0.930106	+	0.367292i	$0.880285\pi$
$252$	19.9279	1.25534
$253$	−1.16696	−0.0733660
$254$	−38.7634	−2.43223
$255$	−1.49998	−0.0939325
$256$	93.6316	5.85197
$257$	9.91817	0.618678	0.309339	−	0.950952i	$-0.399892\pi$
$257$	9.91817	0.618678	0.309339	+	0.950952i	$0.399892\pi$
$258$	12.4943	0.777862
$259$	1.25608	0.0780488
$260$	−0.550478	−0.0341392
$261$	5.39932	0.334209
$262$	58.0042	3.58351
$263$	−5.94941	−0.366857	−0.183428	−	0.983033i	$-0.558719\pi$
$263$	−5.94941	−0.366857	−0.183428	+	0.983033i	$0.558719\pi$
$264$	−2.73930	−0.168592
$265$	17.1677	1.05460
$266$	−14.0676	−0.862539
$267$	2.90567	0.177824
$268$	71.6990	4.37971
$269$	−16.9165	−1.03142	−0.515708	−	0.856764i	$-0.672471\pi$
$269$	−16.9165	−1.03142	−0.515708	+	0.856764i	$0.672471\pi$
$270$	−14.7409	−0.897104
$271$	−23.1520	−1.40638	−0.703191	−	0.711001i	$-0.748242\pi$
$271$	−23.1520	−1.40638	−0.703191	+	0.711001i	$0.748242\pi$
$272$	28.9002	1.75233
$273$	−0.0324317	−0.00196285
$274$	−5.77087	−0.348631
$275$	0.837003	0.0504732
$276$	−6.41457	−0.386112
$277$	−6.92814	−0.416271	−0.208136	−	0.978100i	$-0.566740\pi$
$277$	−6.92814	−0.416271	−0.208136	+	0.978100i	$0.566740\pi$
$278$	−34.6056	−2.07550
$279$	−4.36481	−0.261314
$280$	24.3127	1.45296
$281$	−23.5840	−1.40690	−0.703452	−	0.710743i	$-0.748359\pi$
$281$	−23.5840	−1.40690	−0.703452	+	0.710743i	$0.748359\pi$
$282$	−12.8718	−0.766502
$283$	−19.4201	−1.15441	−0.577204	−	0.816600i	$-0.695856\pi$
$283$	−19.4201	−1.15441	−0.577204	+	0.816600i	$0.695856\pi$
$284$	−20.6220	−1.22369
$285$	3.69605	0.218935
$286$	−0.0754868	−0.00446363
$287$	−0.386881	−0.0228369
$288$	78.1060	4.60244
$289$	−14.3400	−0.843532
$290$	10.0852	0.592222
$291$	1.08592	0.0636576
$292$	34.7749	2.03505
$293$	−1.03593	−0.0605199	−0.0302599	−	0.999542i	$-0.509634\pi$
$293$	−1.03593	−0.0605199	−0.0302599	+	0.999542i	$0.509634\pi$
$294$	−7.53676	−0.439553
$295$	25.1419	1.46382
$296$	10.4968	0.610115
$297$	−1.50087	−0.0870895
$298$	−52.6759	−3.05143
$299$	−0.115459	−0.00667714
$300$	4.60086	0.265631
$301$	−11.2908	−0.650792
$302$	−28.4536	−1.63732
$303$	7.98231	0.458572
$304$	−71.2119	−4.08428
$305$	22.8665	1.30933
$306$	12.5049	0.714857
$307$	24.9920	1.42637	0.713183	−	0.700977i	$-0.247253\pi$
$307$	24.9920	1.42637	0.713183	+	0.700977i	$0.247253\pi$
$308$	3.78988	0.215948
$309$	1.22270	0.0695571
$310$	−8.15287	−0.463052
$311$	−12.2079	−0.692245	−0.346122	−	0.938189i	$-0.612502\pi$
$311$	−12.2079	−0.692245	−0.346122	+	0.938189i	$0.612502\pi$
$312$	−0.271026	−0.0153438
$313$	9.87308	0.558059	0.279030	−	0.960282i	$-0.409987\pi$
$313$	9.87308	0.558059	0.279030	+	0.960282i	$0.409987\pi$
$314$	27.0379	1.52584
$315$	6.37242	0.359045
$316$	−24.6142	−1.38466
$317$	10.9334	0.614080	0.307040	−	0.951697i	$-0.400661\pi$
$317$	10.9334	0.614080	0.307040	+	0.951697i	$0.400661\pi$
$318$	12.9406	0.725674
$319$	1.02684	0.0574921
$320$	80.5401	4.50233
$321$	7.28806	0.406780
$322$	7.80715	0.435075
$323$	−6.55430	−0.364691
$324$	39.3455	2.18586
$325$	0.0828129	0.00459364
$326$	2.78685	0.154350
$327$	2.90190	0.160475
$328$	−3.23310	−0.178518
$329$	11.6319	0.641287
$330$	−1.34108	−0.0738243
$331$	5.21036	0.286387	0.143194	−	0.989695i	$-0.454263\pi$
$331$	5.21036	0.286387	0.143194	+	0.989695i	$0.454263\pi$
$332$	−10.9686	−0.601980
$333$	2.75124	0.150767
$334$	49.2650	2.69566
$335$	22.9275	1.25266
$336$	11.1012	0.605618
$337$	−14.2249	−0.774878	−0.387439	−	0.921895i	$-0.626640\pi$
$337$	−14.2249	−0.774878	−0.387439	+	0.921895i	$0.626640\pi$
$338$	36.2216	1.97020
$339$	−9.91427	−0.538469
$340$	17.3425	0.940531
$341$	−0.830099	−0.0449524
$342$	−30.8129	−1.66617
$343$	15.6033	0.842500
$344$	−94.3554	−5.08730
$345$	−2.05121	−0.110434
$346$	67.4170	3.62436
$347$	6.89595	0.370194	0.185097	−	0.982720i	$-0.440740\pi$
$347$	6.89595	0.370194	0.185097	+	0.982720i	$0.440740\pi$
$348$	5.64437	0.302570
$349$	18.3578	0.982669	0.491334	−	0.870971i	$-0.336509\pi$
$349$	18.3578	0.982669	0.491334	+	0.870971i	$0.336509\pi$
$350$	−5.59969	−0.299316
$351$	−0.148496	−0.00792613
$352$	14.8542	0.791731
$353$	−23.8759	−1.27079	−0.635393	−	0.772189i	$-0.719162\pi$
$353$	−23.8759	−1.27079	−0.635393	+	0.772189i	$0.719162\pi$
$354$	18.9514	1.00726
$355$	−6.59438	−0.349993
$356$	−33.5949	−1.78053
$357$	1.02174	0.0540764
$358$	69.1616	3.65530
$359$	3.14684	0.166084	0.0830420	−	0.996546i	$-0.473536\pi$
$359$	3.14684	0.166084	0.0830420	+	0.996546i	$0.473536\pi$
$360$	53.2532	2.80669
$361$	−2.84977	−0.149988
$362$	50.2053	2.63873
$363$	5.34978	0.280791
$364$	0.374970	0.0196538
$365$	11.1201	0.582054
$366$	17.2363	0.900955
$367$	19.0016	0.991877	0.495939	−	0.868358i	$-0.334824\pi$
$367$	19.0016	0.991877	0.495939	+	0.868358i	$0.334824\pi$
$368$	39.5208	2.06016
$369$	−0.847403	−0.0441141
$370$	5.13894	0.267161
$371$	−11.6941	−0.607129
$372$	−4.56291	−0.236576
$373$	−24.5950	−1.27348	−0.636739	−	0.771079i	$-0.719717\pi$
$373$	−24.5950	−1.27348	−0.636739	+	0.771079i	$0.719717\pi$
$374$	2.37818	0.122973
$375$	6.06977	0.313441
$376$	97.2058	5.01301
$377$	0.101595	0.00523243
$378$	10.0411	0.516458
$379$	15.1002	0.775645	0.387823	−	0.921734i	$-0.373227\pi$
$379$	15.1002	0.775645	0.387823	+	0.921734i	$0.373227\pi$
$380$	−42.7332	−2.19216
$381$	−6.93740	−0.355414
$382$	−18.6144	−0.952395
$383$	3.08415	0.157593	0.0787964	−	0.996891i	$-0.474892\pi$
$383$	3.08415	0.157593	0.0787964	+	0.996891i	$0.474892\pi$
$384$	32.3906	1.65293
$385$	1.21191	0.0617644
$386$	−62.1511	−3.16341
$387$	−24.7308	−1.25714
$388$	−12.5552	−0.637394
$389$	31.2261	1.58323	0.791614	−	0.611022i	$-0.209241\pi$
$389$	31.2261	1.58323	0.791614	+	0.611022i	$0.209241\pi$
$390$	−0.132687	−0.00671885
$391$	3.63747	0.183955
$392$	56.9166	2.87472
$393$	10.3809	0.523647
$394$	−43.3451	−2.18370
$395$	−7.87099	−0.396032
$396$	8.30114	0.417148
$397$	−10.6470	−0.534357	−0.267178	−	0.963647i	$-0.586091\pi$
$397$	−10.6470	−0.534357	−0.267178	+	0.963647i	$0.586091\pi$
$398$	−8.36742	−0.419421
$399$	−2.51765	−0.126040
$400$	−28.3464	−1.41732
$401$	26.3393	1.31532	0.657662	−	0.753313i	$-0.271546\pi$
$401$	26.3393	1.31532	0.657662	+	0.753313i	$0.271546\pi$
$402$	17.2823	0.861960
$403$	−0.0821298	−0.00409118
$404$	−92.2902	−4.59161
$405$	12.5817	0.625188
$406$	−6.86974	−0.340939
$407$	0.523231	0.0259356
$408$	8.53854	0.422721
$409$	−7.53003	−0.372336	−0.186168	−	0.982518i	$-0.559607\pi$
$409$	−7.53003	−0.372336	−0.186168	+	0.982518i	$0.559607\pi$
$410$	−1.58283	−0.0781706
$411$	−1.03280	−0.0509443
$412$	−14.1367	−0.696464
$413$	−17.1259	−0.842712
$414$	17.1003	0.840436
$415$	−3.50747	−0.172175
$416$	1.46967	0.0720565
$417$	−6.19328	−0.303286
$418$	−5.85999	−0.286621
$419$	4.26653	0.208434	0.104217	−	0.994555i	$-0.466766\pi$
$419$	4.26653	0.208434	0.104217	+	0.994555i	$0.466766\pi$
$420$	6.66164	0.325055
$421$	2.29002	0.111609	0.0558043	−	0.998442i	$-0.482228\pi$
$421$	2.29002	0.111609	0.0558043	+	0.998442i	$0.482228\pi$
$422$	11.6823	0.568684
$423$	25.4779	1.23878
$424$	−97.7258	−4.74598
$425$	−2.60898	−0.126554
$426$	−4.97070	−0.240831
$427$	−15.5760	−0.753777
$428$	−84.2633	−4.07302
$429$	−0.0135097	−0.000652256 0
$430$	−46.1937	−2.22766
$431$	−2.29309	−0.110454	−0.0552271	−	0.998474i	$-0.517588\pi$
$431$	−2.29309	−0.110454	−0.0552271	+	0.998474i	$0.517588\pi$
$432$	50.8293	2.44553
$433$	9.81363	0.471613	0.235807	−	0.971800i	$-0.424227\pi$
$433$	9.81363	0.471613	0.235807	+	0.971800i	$0.424227\pi$
$434$	5.55350	0.266577
$435$	1.80492	0.0865395
$436$	−33.5512	−1.60681
$437$	−8.96296	−0.428757
$438$	8.38211	0.400513
$439$	−32.5115	−1.55169	−0.775845	−	0.630924i	$-0.782676\pi$
$439$	−32.5115	−1.55169	−0.775845	+	0.630924i	$0.782676\pi$
$440$	10.1277	0.482819
$441$	14.9180	0.710380
$442$	0.235296	0.0111919
$443$	6.99605	0.332392	0.166196	−	0.986093i	$-0.446851\pi$
$443$	6.99605	0.332392	0.166196	+	0.986093i	$0.446851\pi$
$444$	2.87611	0.136494
$445$	−10.7428	−0.509257
$446$	−74.6078	−3.53278
$447$	−9.42730	−0.445896
$448$	−54.8616	−2.59197
$449$	−22.6432	−1.06860	−0.534300	−	0.845295i	$-0.679425\pi$
$449$	−22.6432	−1.06860	−0.534300	+	0.845295i	$0.679425\pi$
$450$	−12.2653	−0.578190
$451$	−0.161159	−0.00758868
$452$	114.627	5.39161
$453$	−5.09229	−0.239256
$454$	77.8976	3.65591
$455$	0.119906	0.00562127
$456$	−21.0395	−0.985267
$457$	−16.4975	−0.771722	−0.385861	−	0.922557i	$-0.626096\pi$
$457$	−16.4975	−0.771722	−0.385861	+	0.922557i	$0.626096\pi$
$458$	−4.49278	−0.209934
$459$	4.67830	0.218364
$460$	23.7158	1.10575
$461$	11.8680	0.552750	0.276375	−	0.961050i	$-0.410867\pi$
$461$	11.8680	0.552750	0.276375	+	0.961050i	$0.410867\pi$
$462$	0.913508	0.0425002
$463$	30.8028	1.43153	0.715763	−	0.698344i	$-0.246079\pi$
$463$	30.8028	1.43153	0.715763	+	0.698344i	$0.246079\pi$
$464$	−34.7755	−1.61441
$465$	−1.45910	−0.0676642
$466$	52.8065	2.44622
$467$	−18.7871	−0.869365	−0.434683	−	0.900584i	$-0.643139\pi$
$467$	−18.7871	−0.869365	−0.434683	+	0.900584i	$0.643139\pi$
$468$	0.821313	0.0379652
$469$	−15.6176	−0.721152
$470$	47.5892	2.19513
$471$	4.83892	0.222966
$472$	−143.119	−6.58757
$473$	−4.70330	−0.216258
$474$	−5.93298	−0.272511
$475$	6.42870	0.294969
$476$	−11.8132	−0.541459
$477$	−25.6142	−1.17279
$478$	−56.4491	−2.58192
$479$	−6.58971	−0.301091	−0.150546	−	0.988603i	$-0.548103\pi$
$479$	−6.58971	−0.301091	−0.150546	+	0.988603i	$0.548103\pi$
$480$	26.1099	1.19175
$481$	0.0517683	0.00236043
$482$	60.6165	2.76101
$483$	1.39723	0.0635761
$484$	−61.8533	−2.81151
$485$	−4.01483	−0.182304
$486$	33.4658	1.51804
$487$	24.3384	1.10288	0.551440	−	0.834214i	$-0.314079\pi$
$487$	24.3384	1.10288	0.551440	+	0.834214i	$0.314079\pi$
$488$	−130.166	−5.89235
$489$	0.498757	0.0225546
$490$	27.8647	1.25880
$491$	15.6443	0.706019	0.353009	−	0.935620i	$-0.385158\pi$
$491$	15.6443	0.706019	0.353009	+	0.935620i	$0.385158\pi$
$492$	−0.885863	−0.0399378
$493$	−3.20072	−0.144153
$494$	−0.579786	−0.0260858
$495$	2.65449	0.119311
$496$	28.1125	1.26229
$497$	4.49190	0.201489
$498$	−2.64386	−0.118474
$499$	14.7365	0.659697	0.329848	−	0.944034i	$-0.393002\pi$
$499$	14.7365	0.659697	0.329848	+	0.944034i	$0.393002\pi$
$500$	−70.1776	−3.13844
$501$	8.81686	0.393908
$502$	82.1321	3.66574
$503$	−19.7354	−0.879959	−0.439980	−	0.898008i	$-0.645014\pi$
$503$	−19.7354	−0.879959	−0.439980	+	0.898008i	$0.645014\pi$
$504$	−36.2746	−1.61580
$505$	−29.5120	−1.31327
$506$	3.25214	0.144575
$507$	6.48251	0.287898
$508$	80.2091	3.55870
$509$	−25.2514	−1.11925	−0.559625	−	0.828746i	$-0.689055\pi$
$509$	−25.2514	−1.11925	−0.559625	+	0.828746i	$0.689055\pi$
$510$	4.18023	0.185104
$511$	−7.57471	−0.335085
$512$	−131.052	−5.79174
$513$	−11.5276	−0.508957
$514$	−27.6405	−1.21917
$515$	−4.52055	−0.199199
$516$	−25.8532	−1.13812
$517$	4.84538	0.213100
$518$	−3.50050	−0.153803
$519$	12.0655	0.529616
$520$	1.00203	0.0439420
$521$	3.19205	0.139846	0.0699232	−	0.997552i	$-0.477725\pi$
$521$	3.19205	0.139846	0.0699232	+	0.997552i	$0.477725\pi$
$522$	−15.0471	−0.658594
$523$	22.4865	0.983264	0.491632	−	0.870803i	$-0.336401\pi$
$523$	22.4865	0.983264	0.491632	+	0.870803i	$0.336401\pi$
$524$	−120.022	−5.24319
$525$	−1.00217	−0.0437381
$526$	16.5801	0.722928
$527$	2.58746	0.112712
$528$	4.62430	0.201247
$529$	−18.0258	−0.783730
$530$	−47.8438	−2.07820
$531$	−37.5117	−1.62787
$532$	29.1086	1.26202
$533$	−0.0159450	−0.000690656 0
$534$	−8.09768	−0.350421
$535$	−26.9453	−1.16494
$536$	−130.513	−5.63731
$537$	12.3777	0.534137
$538$	47.1437	2.03251
$539$	2.83710	0.122202
$540$	30.5019	1.31259
$541$	−20.3501	−0.874919	−0.437459	−	0.899238i	$-0.644122\pi$
$541$	−20.3501	−0.874919	−0.437459	+	0.899238i	$0.644122\pi$
$542$	64.5211	2.77142
$543$	8.98514	0.385589
$544$	−46.3012	−1.98515
$545$	−10.7288	−0.459572
$546$	0.0903823	0.00386801
$547$	−0.549704	−0.0235037	−0.0117518	−	0.999931i	$-0.503741\pi$
$547$	−0.549704	−0.0235037	−0.0117518	+	0.999931i	$0.503741\pi$
$548$	11.9411	0.510097
$549$	−34.1169	−1.45607
$550$	−2.33261	−0.0994626
$551$	7.88678	0.335988
$552$	11.6764	0.496981
$553$	5.36149	0.227994
$554$	19.3077	0.820305
$555$	0.919706	0.0390393
$556$	71.6057	3.03676
$557$	−42.6139	−1.80561	−0.902805	−	0.430049i	$-0.858496\pi$
$557$	−42.6139	−1.80561	−0.902805	+	0.430049i	$0.858496\pi$
$558$	12.1641	0.514947
$559$	−0.465343	−0.0196819
$560$	−41.0430	−1.73438
$561$	0.425617	0.0179696
$562$	65.7251	2.77245
$563$	−12.5741	−0.529935	−0.264967	−	0.964257i	$-0.585361\pi$
$563$	−12.5741	−0.529935	−0.264967	+	0.964257i	$0.585361\pi$
$564$	26.6342	1.12150
$565$	36.6548	1.54208
$566$	54.1211	2.27488
$567$	−8.57027	−0.359918
$568$	37.5381	1.57506
$569$	−15.8594	−0.664862	−0.332431	−	0.943128i	$-0.607869\pi$
$569$	−15.8594	−0.664862	−0.332431	+	0.943128i	$0.607869\pi$
$570$	−10.3004	−0.431434
$571$	−35.8791	−1.50149	−0.750747	−	0.660590i	$-0.770306\pi$
$571$	−35.8791	−1.50149	−0.750747	+	0.660590i	$0.770306\pi$
$572$	0.156197	0.00653093
$573$	−3.33138	−0.139170
$574$	1.07818	0.0450024
$575$	−3.56776	−0.148786
$576$	−120.166	−5.00691
$577$	20.5504	0.855524	0.427762	−	0.903891i	$-0.359302\pi$
$577$	20.5504	0.855524	0.427762	+	0.903891i	$0.359302\pi$
$578$	39.9636	1.66227
$579$	−11.1231	−0.462258
$580$	−20.8682	−0.866506
$581$	2.38919	0.0991204
$582$	−3.02629	−0.125444
$583$	−4.87130	−0.201749
$584$	−63.3006	−2.61940
$585$	0.262635	0.0108586
$586$	2.88700	0.119261
$587$	18.3744	0.758391	0.379196	−	0.925317i	$-0.376201\pi$
$587$	18.3744	0.758391	0.379196	+	0.925317i	$0.376201\pi$
$588$	15.5950	0.643129
$589$	−6.37567	−0.262705
$590$	−70.0668	−2.88460
$591$	−7.75738	−0.319096
$592$	−17.7200	−0.728287
$593$	−30.9644	−1.27156	−0.635778	−	0.771872i	$-0.719321\pi$
$593$	−30.9644	−1.27156	−0.635778	+	0.771872i	$0.719321\pi$
$594$	4.18271	0.171619
$595$	−3.77757	−0.154865
$596$	108.997	4.46468
$597$	−1.49750	−0.0612886
$598$	0.321766	0.0131580
$599$	18.7697	0.766908	0.383454	−	0.923560i	$-0.374734\pi$
$599$	18.7697	0.766908	0.383454	+	0.923560i	$0.374734\pi$
$600$	−8.37492	−0.341905
$601$	−18.1353	−0.739755	−0.369878	−	0.929081i	$-0.620600\pi$
$601$	−18.1353	−0.739755	−0.369878	+	0.929081i	$0.620600\pi$
$602$	31.4658	1.28245
$603$	−34.2078	−1.39305
$604$	58.8762	2.39564
$605$	−19.7791	−0.804135
$606$	−22.2455	−0.903663
$607$	−28.9481	−1.17497	−0.587484	−	0.809236i	$-0.699881\pi$
$607$	−28.9481	−1.17497	−0.587484	+	0.809236i	$0.699881\pi$
$608$	114.089	4.62693
$609$	−1.22946	−0.0498203
$610$	−63.7256	−2.58018
$611$	0.479401	0.0193945
$612$	−25.8751	−1.04594
$613$	−26.0682	−1.05289	−0.526443	−	0.850211i	$-0.676474\pi$
$613$	−26.0682	−1.05289	−0.526443	+	0.850211i	$0.676474\pi$
$614$	−69.6489	−2.81080
$615$	−0.283276	−0.0114228
$616$	−6.89869	−0.277956
$617$	4.17885	0.168234	0.0841170	−	0.996456i	$-0.473193\pi$
$617$	4.17885	0.168234	0.0841170	+	0.996456i	$0.473193\pi$
$618$	−3.40749	−0.137069
$619$	13.0236	0.523461	0.261731	−	0.965141i	$-0.415707\pi$
$619$	13.0236	0.523461	0.261731	+	0.965141i	$0.415707\pi$
$620$	16.8699	0.677511
$621$	6.39754	0.256724
$622$	34.0215	1.36414
$623$	7.31768	0.293177
$624$	0.457527	0.0183157
$625$	−14.4426	−0.577704
$626$	−27.5148	−1.09971
$627$	−1.04875	−0.0418830
$628$	−55.9468	−2.23252
$629$	−1.63094	−0.0650297
$630$	−17.7590	−0.707535
$631$	−18.3633	−0.731031	−0.365516	−	0.930805i	$-0.619107\pi$
$631$	−18.3633	−0.731031	−0.365516	+	0.930805i	$0.619107\pi$
$632$	44.8051	1.78225
$633$	2.09075	0.0831000
$634$	−30.4697	−1.21011
$635$	25.6488	1.01784
$636$	−26.7767	−1.06176
$637$	0.280702	0.0111218
$638$	−2.86166	−0.113294
$639$	9.83882	0.389218
$640$	−119.754	−4.73369
$641$	24.6314	0.972883	0.486442	−	0.873713i	$-0.338295\pi$
$641$	24.6314	0.972883	0.486442	+	0.873713i	$0.338295\pi$
$642$	−20.3107	−0.801601
$643$	37.3094	1.47134	0.735670	−	0.677340i	$-0.236867\pi$
$643$	37.3094	1.47134	0.735670	+	0.677340i	$0.236867\pi$
$644$	−16.1545	−0.636577
$645$	−8.26719	−0.325520
$646$	18.2659	0.718661
$647$	−3.73596	−0.146876	−0.0734378	−	0.997300i	$-0.523397\pi$
$647$	−3.73596	−0.146876	−0.0734378	+	0.997300i	$0.523397\pi$
$648$	−71.6203	−2.81351
$649$	−7.13397	−0.280033
$650$	−0.230787	−0.00905223
$651$	0.993898	0.0389539
$652$	−5.76655	−0.225835
$653$	−14.0164	−0.548505	−0.274252	−	0.961658i	$-0.588430\pi$
$653$	−14.0164	−0.548505	−0.274252	+	0.961658i	$0.588430\pi$
$654$	−8.08716	−0.316233
$655$	−38.3800	−1.49963
$656$	5.45789	0.213095
$657$	−16.5912	−0.647286
$658$	−32.4164	−1.26372
$659$	−6.73408	−0.262323	−0.131161	−	0.991361i	$-0.541871\pi$
$659$	−6.73408	−0.262323	−0.131161	+	0.991361i	$0.541871\pi$
$660$	2.77497	0.108015
$661$	−38.6239	−1.50230	−0.751148	−	0.660134i	$-0.770499\pi$
$661$	−38.6239	−1.50230	−0.751148	+	0.660134i	$0.770499\pi$
$662$	−14.5205	−0.564355
$663$	0.0421105	0.00163544
$664$	19.9661	0.774834
$665$	9.30819	0.360956
$666$	−7.66730	−0.297102
$667$	−4.37696	−0.169476
$668$	−101.939	−3.94414
$669$	−13.3524	−0.516234
$670$	−63.8956	−2.46850
$671$	−6.48834	−0.250480
$672$	−17.7853	−0.686082
$673$	29.9518	1.15456	0.577279	−	0.816547i	$-0.304115\pi$
$673$	29.9518	1.15456	0.577279	+	0.816547i	$0.304115\pi$
$674$	39.6426	1.52698
$675$	−4.58865	−0.176617
$676$	−74.9497	−2.88268
$677$	12.5191	0.481149	0.240575	−	0.970631i	$-0.422664\pi$
$677$	12.5191	0.481149	0.240575	+	0.970631i	$0.422664\pi$
$678$	27.6296	1.06111
$679$	2.73479	0.104952
$680$	−31.5685	−1.21060
$681$	13.9412	0.534226
$682$	2.31336	0.0885833
$683$	19.9840	0.764667	0.382333	−	0.924024i	$-0.375121\pi$
$683$	19.9840	0.764667	0.382333	+	0.924024i	$0.375121\pi$
$684$	63.7579	2.43784
$685$	3.81845	0.145895
$686$	−43.4842	−1.66023
$687$	−0.804064	−0.0306770
$688$	159.284	6.07265
$689$	−0.481965	−0.0183614
$690$	5.71643	0.217621
$691$	33.4134	1.27110	0.635552	−	0.772058i	$-0.280772\pi$
$691$	33.4134	1.27110	0.635552	+	0.772058i	$0.280772\pi$
$692$	−139.499	−5.30296
$693$	−1.80816	−0.0686865
$694$	−19.2180	−0.729505
$695$	22.8977	0.868558
$696$	−10.2744	−0.389451
$697$	0.502341	0.0190275
$698$	−51.1604	−1.93645
$699$	9.45068	0.357457
$700$	11.5869	0.437942
$701$	−15.6665	−0.591717	−0.295858	−	0.955232i	$-0.595606\pi$
$701$	−15.6665	−0.591717	−0.295858	+	0.955232i	$0.595606\pi$
$702$	0.413837	0.0156193
$703$	4.01873	0.151569
$704$	−22.8531	−0.861310
$705$	8.51694	0.320766
$706$	66.5387	2.50422
$707$	20.1028	0.756042
$708$	−39.2142	−1.47376
$709$	9.93599	0.373154	0.186577	−	0.982440i	$-0.440261\pi$
$709$	9.93599	0.373154	0.186577	+	0.982440i	$0.440261\pi$
$710$	18.3776	0.689698
$711$	11.7435	0.440416
$712$	61.1526	2.29179
$713$	3.53833	0.132512
$714$	−2.84745	−0.106563
$715$	0.0499479	0.00186794
$716$	−143.109	−5.34823
$717$	−10.1026	−0.377288
$718$	−8.76979	−0.327286
$719$	16.9174	0.630914	0.315457	−	0.948940i	$-0.397842\pi$
$719$	16.9174	0.630914	0.315457	+	0.948940i	$0.397842\pi$
$720$	−89.8983	−3.35031
$721$	3.07927	0.114678
$722$	7.94189	0.295567
$723$	10.8484	0.403457
$724$	−103.885	−3.86085
$725$	3.13938	0.116594
$726$	−14.9091	−0.553327
$727$	5.80726	0.215379	0.107690	−	0.994185i	$-0.465655\pi$
$727$	5.80726	0.215379	0.107690	+	0.994185i	$0.465655\pi$
$728$	−0.682555	−0.0252972
$729$	−14.4798	−0.536291
$730$	−30.9902	−1.14700
$731$	14.6604	0.542235
$732$	−35.6653	−1.31823
$733$	4.09355	0.151199	0.0755994	−	0.997138i	$-0.475913\pi$
$733$	4.09355	0.151199	0.0755994	+	0.997138i	$0.475913\pi$
$734$	−52.9548	−1.95460
$735$	4.98689	0.183944
$736$	−63.3166	−2.33388
$737$	−6.50564	−0.239638
$738$	2.36159	0.0869313
$739$	−0.467196	−0.0171861	−0.00859304	−	0.999963i	$-0.502735\pi$
$739$	−0.467196	−0.0171861	−0.00859304	+	0.999963i	$0.502735\pi$
$740$	−10.6335	−0.390895
$741$	−0.103763	−0.00381183
$742$	32.5898	1.19641
$743$	14.6841	0.538707	0.269353	−	0.963041i	$-0.413190\pi$
$743$	14.6841	0.538707	0.269353	+	0.963041i	$0.413190\pi$
$744$	8.30584	0.304507
$745$	34.8544	1.27697
$746$	68.5425	2.50952
$747$	5.23315	0.191471
$748$	−4.92092	−0.179927
$749$	18.3543	0.670653
$750$	−16.9155	−0.617668
$751$	−12.1314	−0.442681	−0.221340	−	0.975197i	$-0.571043\pi$
$751$	−12.1314	−0.442681	−0.221340	+	0.975197i	$0.571043\pi$
$752$	−164.096	−5.98397
$753$	14.6990	0.535662
$754$	−0.283132	−0.0103110
$755$	18.8271	0.685188
$756$	−20.7770	−0.755652
$757$	13.0763	0.475267	0.237633	−	0.971355i	$-0.423628\pi$
$757$	13.0763	0.475267	0.237633	+	0.971355i	$0.423628\pi$
$758$	−42.0820	−1.52849
$759$	0.582029	0.0211263
$760$	77.7869	2.82163
$761$	−15.1576	−0.549462	−0.274731	−	0.961521i	$-0.588589\pi$
$761$	−15.1576	−0.549462	−0.274731	+	0.961521i	$0.588589\pi$
$762$	19.3335	0.700379
$763$	7.30817	0.264574
$764$	38.5168	1.39349
$765$	−8.27419	−0.299154
$766$	−8.59507	−0.310553
$767$	−0.705834	−0.0254862
$768$	−46.6994	−1.68512
$769$	25.9457	0.935625	0.467813	−	0.883828i	$-0.345042\pi$
$769$	25.9457	0.935625	0.467813	+	0.883828i	$0.345042\pi$
$770$	−3.37740	−0.121713
$771$	−4.94676	−0.178153
$772$	128.603	4.62852
$773$	−33.5697	−1.20742	−0.603709	−	0.797205i	$-0.706311\pi$
$773$	−33.5697	−1.20742	−0.603709	+	0.797205i	$0.706311\pi$
$774$	68.9211	2.47732
$775$	−2.53788	−0.0911633
$776$	22.8542	0.820416
$777$	−0.626477	−0.0224747
$778$	−87.0226	−3.11991
$779$	−1.23780	−0.0443488
$780$	0.274555	0.00983064
$781$	1.87115	0.0669549
$782$	−10.1371	−0.362501
$783$	−5.62938	−0.201178
$784$	−96.0826	−3.43152
$785$	−17.8904	−0.638534
$786$	−28.9300	−1.03190
$787$	−10.4845	−0.373733	−0.186866	−	0.982385i	$-0.559833\pi$
$787$	−10.4845	−0.373733	−0.186866	+	0.982385i	$0.559833\pi$
$788$	89.6896	3.19506
$789$	2.96731	0.105639
$790$	21.9353	0.780422
$791$	−24.9682	−0.887768
$792$	−15.1105	−0.536929
$793$	−0.641955	−0.0227965
$794$	29.6716	1.05300
$795$	−8.56250	−0.303681
$796$	17.3138	0.613673
$797$	−7.32708	−0.259538	−0.129769	−	0.991544i	$-0.541424\pi$
$797$	−7.32708	−0.259538	−0.129769	+	0.991544i	$0.541424\pi$
$798$	7.01631	0.248375
$799$	−15.1033	−0.534316
$800$	45.4140	1.60563
$801$	16.0283	0.566331
$802$	−73.4039	−2.59198
$803$	−3.15532	−0.111349
$804$	−35.7604	−1.26117
$805$	−5.16580	−0.182071
$806$	0.228884	0.00806208
$807$	8.43722	0.297004
$808$	167.995	5.91005
$809$	13.6549	0.480080	0.240040	−	0.970763i	$-0.422839\pi$
$809$	13.6549	0.480080	0.240040	+	0.970763i	$0.422839\pi$
$810$	−35.0633	−1.23200
$811$	11.3086	0.397100	0.198550	−	0.980091i	$-0.436377\pi$
$811$	11.3086	0.397100	0.198550	+	0.980091i	$0.436377\pi$
$812$	14.2148	0.498843
$813$	11.5472	0.404978
$814$	−1.45817	−0.0511087
$815$	−1.84399	−0.0645923
$816$	−14.4142	−0.504597
$817$	−36.1242	−1.26383
$818$	20.9851	0.733726
$819$	−0.178899	−0.00625125
$820$	3.27520	0.114375
$821$	−39.7555	−1.38748	−0.693739	−	0.720227i	$-0.744038\pi$
$821$	−39.7555	−1.38748	−0.693739	+	0.720227i	$0.744038\pi$
$822$	2.87826	0.100391
$823$	24.0339	0.837771	0.418885	−	0.908039i	$-0.362421\pi$
$823$	24.0339	0.837771	0.418885	+	0.908039i	$0.362421\pi$
$824$	25.7329	0.896448
$825$	−0.417461	−0.0145341
$826$	47.7275	1.66065
$827$	26.4092	0.918338	0.459169	−	0.888349i	$-0.348147\pi$
$827$	26.4092	0.918338	0.459169	+	0.888349i	$0.348147\pi$
$828$	−35.3840	−1.22968
$829$	−32.0859	−1.11439	−0.557194	−	0.830382i	$-0.688122\pi$
$829$	−32.0859	−1.11439	−0.557194	+	0.830382i	$0.688122\pi$
$830$	9.77482	0.339289
$831$	3.45546	0.119869
$832$	−2.26108	−0.0783890
$833$	−8.84338	−0.306405
$834$	17.2598	0.597657
$835$	−32.5975	−1.12808
$836$	12.1255	0.419368
$837$	4.55080	0.157299
$838$	−11.8902	−0.410740
$839$	−38.3641	−1.32448	−0.662239	−	0.749293i	$-0.730393\pi$
$839$	−38.3641	−1.32448	−0.662239	+	0.749293i	$0.730393\pi$
$840$	−12.1261	−0.418392
$841$	−25.1486	−0.867193
$842$	−6.38194	−0.219936
$843$	11.7627	0.405128
$844$	−24.1729	−0.832067
$845$	−23.9670	−0.824490
$846$	−71.0031	−2.44114
$847$	13.4730	0.462937
$848$	164.974	5.66522
$849$	9.68594	0.332420
$850$	7.27085	0.249388
$851$	−2.23029	−0.0764535
$852$	10.2854	0.352371
$853$	−5.46110	−0.186985	−0.0934923	−	0.995620i	$-0.529803\pi$
$853$	−5.46110	−0.186985	−0.0934923	+	0.995620i	$0.529803\pi$
$854$	43.4081	1.48539
$855$	20.3881	0.697260
$856$	153.384	5.24256
$857$	−15.1780	−0.518469	−0.259235	−	0.965814i	$-0.583470\pi$
$857$	−15.1780	−0.518469	−0.259235	+	0.965814i	$0.583470\pi$
$858$	0.0376496	0.00128534
$859$	−34.2526	−1.16868	−0.584342	−	0.811508i	$-0.698647\pi$
$859$	−34.2526	−1.16868	−0.584342	+	0.811508i	$0.698647\pi$
$860$	95.5839	3.25939
$861$	0.192960	0.00657605
$862$	6.39050	0.217661
$863$	−47.7278	−1.62467	−0.812337	−	0.583188i	$-0.801805\pi$
$863$	−47.7278	−1.62467	−0.812337	+	0.583188i	$0.801805\pi$
$864$	−81.4341	−2.77044
$865$	−44.6083	−1.51673
$866$	−27.3492	−0.929362
$867$	7.15220	0.242902
$868$	−11.4913	−0.390040
$869$	2.23338	0.0757622
$870$	−5.03006	−0.170535
$871$	−0.643667	−0.0218098
$872$	61.0731	2.06820
$873$	5.99013	0.202735
$874$	24.9785	0.844909
$875$	15.2862	0.516767
$876$	−17.3442	−0.586007
$877$	50.0979	1.69169	0.845843	−	0.533433i	$-0.179098\pi$
$877$	50.0979	1.69169	0.845843	+	0.533433i	$0.179098\pi$
$878$	90.6048	3.05776
$879$	0.516679	0.0174272
$880$	−17.0969	−0.576335
$881$	29.3753	0.989678	0.494839	−	0.868985i	$-0.335227\pi$
$881$	29.3753	0.989678	0.494839	+	0.868985i	$0.335227\pi$
$882$	−41.5742	−1.39988
$883$	−42.9667	−1.44594	−0.722972	−	0.690877i	$-0.757225\pi$
$883$	−42.9667	−1.44594	−0.722972	+	0.690877i	$0.757225\pi$
$884$	−0.486874	−0.0163754
$885$	−12.5397	−0.421517
$886$	−19.4970	−0.655013
$887$	24.9589	0.838038	0.419019	−	0.907977i	$-0.362374\pi$
$887$	24.9589	0.838038	0.419019	+	0.907977i	$0.362374\pi$
$888$	−5.23536	−0.175687
$889$	−17.4712	−0.585966
$890$	29.9386	1.00354
$891$	−3.57003	−0.119600
$892$	154.378	5.16897
$893$	37.2155	1.24537
$894$	26.2725	0.878683
$895$	−45.7626	−1.52967
$896$	81.5729	2.72516
$897$	0.0575858	0.00192273
$898$	63.1033	2.10579
$899$	−3.11348	−0.103841
$900$	25.3792	0.845975
$901$	15.1841	0.505855
$902$	0.449127	0.0149543
$903$	5.63138	0.187400
$904$	−208.655	−6.93977
$905$	−33.2197	−1.10426
$906$	14.1914	0.471479
$907$	36.5305	1.21298	0.606488	−	0.795092i	$-0.292578\pi$
$907$	36.5305	1.21298	0.606488	+	0.795092i	$0.292578\pi$
$908$	−161.185	−5.34913
$909$	44.0320	1.46045
$910$	−0.334160	−0.0110773
$911$	−8.82634	−0.292430	−0.146215	−	0.989253i	$-0.546709\pi$
$911$	−8.82634	−0.292430	−0.146215	+	0.989253i	$0.546709\pi$
$912$	35.5175	1.17610
$913$	0.995240	0.0329377
$914$	45.9762	1.52076
$915$	−11.4048	−0.377033
$916$	9.29646	0.307164
$917$	26.1434	0.863330
$918$	−13.0377	−0.430309
$919$	−33.9710	−1.12060	−0.560300	−	0.828289i	$-0.689314\pi$
$919$	−33.9710	−1.12060	−0.560300	+	0.828289i	$0.689314\pi$
$920$	−43.1697	−1.42326
$921$	−12.4649	−0.410733
$922$	−33.0745	−1.08925
$923$	0.185131	0.00609365
$924$	−1.89023	−0.0621840
$925$	1.59968	0.0525973
$926$	−85.8427	−2.82097
$927$	6.74466	0.221524
$928$	55.7142	1.82891
$929$	34.3828	1.12806	0.564032	−	0.825753i	$-0.309250\pi$
$929$	34.3828	1.12806	0.564032	+	0.825753i	$0.309250\pi$
$930$	4.06630	0.133339
$931$	21.7907	0.714160
$932$	−109.267	−3.57916
$933$	6.08876	0.199337
$934$	52.3570	1.71317
$935$	−1.57358	−0.0514617
$936$	−1.49503	−0.0488666
$937$	−52.7474	−1.72318	−0.861592	−	0.507602i	$-0.830532\pi$
$937$	−52.7474	−1.72318	−0.861592	+	0.507602i	$0.830532\pi$
$938$	43.5238	1.42110
$939$	−4.92427	−0.160697
$940$	−98.4714	−3.21178
$941$	−10.0318	−0.327027	−0.163514	−	0.986541i	$-0.552283\pi$
$941$	−10.0318	−0.327027	−0.163514	+	0.986541i	$0.552283\pi$
$942$	−13.4854	−0.439377
$943$	0.686948	0.0223701
$944$	241.603	7.86350
$945$	−6.64395	−0.216128
$946$	13.1074	0.426158
$947$	−17.7679	−0.577378	−0.288689	−	0.957423i	$-0.593219\pi$
$947$	−17.7679	−0.577378	−0.288689	+	0.957423i	$0.593219\pi$
$948$	12.2765	0.398722
$949$	−0.312186	−0.0101340
$950$	−17.9159	−0.581267
$951$	−5.45310	−0.176829
$952$	21.5036	0.696935
$953$	−36.2188	−1.17324	−0.586621	−	0.809862i	$-0.699542\pi$
$953$	−36.2188	−1.17324	−0.586621	+	0.809862i	$0.699542\pi$
$954$	71.3829	2.31111
$955$	12.3167	0.398559
$956$	116.804	3.77772
$957$	−0.512144	−0.0165553
$958$	18.3645	0.593332
$959$	−2.60102	−0.0839913
$960$	−40.1700	−1.29648
$961$	−28.4831	−0.918808
$962$	−0.144271	−0.00465147
$963$	40.2023	1.29550
$964$	−125.427	−4.03975
$965$	41.1239	1.32383
$966$	−3.89387	−0.125283
$967$	−49.7572	−1.60008	−0.800042	−	0.599944i	$-0.795189\pi$
$967$	−49.7572	−1.60008	−0.800042	+	0.599944i	$0.795189\pi$
$968$	112.591	3.61882
$969$	3.26900	0.105016
$970$	11.1887	0.359249
$971$	−11.6022	−0.372332	−0.186166	−	0.982518i	$-0.559606\pi$
$971$	−11.6022	−0.372332	−0.186166	+	0.982518i	$0.559606\pi$
$972$	−69.2474	−2.22111
$973$	−15.5972	−0.500025
$974$	−67.8277	−2.17334
$975$	−0.0413035	−0.00132277
$976$	219.737	7.03362
$977$	50.7585	1.62391	0.811955	−	0.583721i	$-0.198404\pi$
$977$	50.7585	1.62391	0.811955	+	0.583721i	$0.198404\pi$
$978$	−1.38996	−0.0444461
$979$	3.04825	0.0974225
$980$	−57.6576	−1.84181
$981$	16.0074	0.511077
$982$	−43.5984	−1.39128
$983$	27.2906	0.870436	0.435218	−	0.900325i	$-0.356671\pi$
$983$	27.2906	0.870436	0.435218	+	0.900325i	$0.356671\pi$
$984$	1.61253	0.0514056
$985$	28.6804	0.913835
$986$	8.91992	0.284068
$987$	−5.80149	−0.184664
$988$	1.19969	0.0381673
$989$	20.0480	0.637490
$990$	−7.39768	−0.235114
$991$	31.7729	1.00930	0.504650	−	0.863324i	$-0.331622\pi$
$991$	31.7729	1.00930	0.504650	+	0.863324i	$0.331622\pi$
$992$	−45.0394	−1.43000
$993$	−2.59870	−0.0824674
$994$	−12.5183	−0.397056
$995$	5.53652	0.175520
$996$	5.47066	0.173345
$997$	−56.5570	−1.79118	−0.895589	−	0.444882i	$-0.853246\pi$
$997$	−56.5570	−1.79118	−0.895589	+	0.444882i	$0.853246\pi$
$998$	−41.0685	−1.30000
$999$	−2.86847	−0.0907545

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6031.2.a.c.1.1	✓	110

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6031.2.a.c.1.1	✓	110	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:	\( N \)	\(=\)	\( 6031 = 37 \cdot 163 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6031.a (trivial)

\(f(q)\)	\(=\)	\(q-2.78685 q^{2} -0.498757 q^{3} +5.76655 q^{4} +1.84399 q^{5} +1.38996 q^{6} -1.25608 q^{7} -10.4968 q^{8} -2.75124 q^{9} +O(q^{10})\)	\(q-2.78685 q^{2} -0.498757 q^{3} +5.76655 q^{4} +1.84399 q^{5} +1.38996 q^{6} -1.25608 q^{7} -10.4968 q^{8} -2.75124 q^{9} -5.13894 q^{10} -0.523231 q^{11} -2.87611 q^{12} -0.0517683 q^{13} +3.50050 q^{14} -0.919706 q^{15} +17.7200 q^{16} +1.63094 q^{17} +7.66730 q^{18} -4.01873 q^{19} +10.6335 q^{20} +0.626477 q^{21} +1.45817 q^{22} +2.23029 q^{23} +5.23536 q^{24} -1.59968 q^{25} +0.144271 q^{26} +2.86847 q^{27} -7.24323 q^{28} -1.96250 q^{29} +2.56308 q^{30} +1.58649 q^{31} -28.3894 q^{32} +0.260965 q^{33} -4.54518 q^{34} -2.31620 q^{35} -15.8652 q^{36} -1.00000 q^{37} +11.1996 q^{38} +0.0258198 q^{39} -19.3561 q^{40} +0.308008 q^{41} -1.74590 q^{42} +8.98896 q^{43} -3.01723 q^{44} -5.07327 q^{45} -6.21550 q^{46} -9.26050 q^{47} -8.83797 q^{48} -5.42227 q^{49} +4.45808 q^{50} -0.813441 q^{51} -0.298525 q^{52} +9.31004 q^{53} -7.99401 q^{54} -0.964834 q^{55} +13.1848 q^{56} +2.00437 q^{57} +5.46920 q^{58} +13.6345 q^{59} -5.30353 q^{60} +12.4005 q^{61} -4.42131 q^{62} +3.45577 q^{63} +43.6770 q^{64} -0.0954605 q^{65} -0.727271 q^{66} +12.4336 q^{67} +9.40487 q^{68} -1.11238 q^{69} +6.45490 q^{70} -3.57614 q^{71} +28.8793 q^{72} +6.03045 q^{73} +2.78685 q^{74} +0.797854 q^{75} -23.1742 q^{76} +0.657218 q^{77} -0.0719561 q^{78} -4.26844 q^{79} +32.6756 q^{80} +6.82305 q^{81} -0.858372 q^{82} -1.90211 q^{83} +3.61261 q^{84} +3.00744 q^{85} -25.0509 q^{86} +0.978812 q^{87} +5.49226 q^{88} -5.82583 q^{89} +14.1385 q^{90} +0.0650250 q^{91} +12.8611 q^{92} -0.791272 q^{93} +25.8077 q^{94} -7.41053 q^{95} +14.1594 q^{96} -2.17725 q^{97} +15.1111 q^{98} +1.43953 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 110 q - 9 q^{2} + 97 q^{4} - 26 q^{5} - 26 q^{6} - 4 q^{7} - 27 q^{8} + 62 q^{9}+O(q^{10}) \) 110 * q - 9 * q^2 + 97 * q^4 - 26 * q^5 - 26 * q^6 - 4 * q^7 - 27 * q^8 + 62 * q^9	\( 110 q - 9 q^{2} + 97 q^{4} - 26 q^{5} - 26 q^{6} - 4 q^{7} - 27 q^{8} + 62 q^{9} - 17 q^{10} - 9 q^{11} - 21 q^{13} - 29 q^{14} - 23 q^{15} + 79 q^{16} - 76 q^{17} - 31 q^{18} - 27 q^{19} - 67 q^{20} - 30 q^{21} - 28 q^{22} - 32 q^{23} - 63 q^{24} + 66 q^{25} - 55 q^{26} - 4 q^{28} - 81 q^{29} - 48 q^{30} - 30 q^{31} - 73 q^{32} - 53 q^{33} - 23 q^{34} - 78 q^{35} + 7 q^{36} - 110 q^{37} - 50 q^{38} - 64 q^{39} - 37 q^{40} - 123 q^{41} - 63 q^{42} - 40 q^{43} - 31 q^{44} - 73 q^{45} + 16 q^{46} - 37 q^{47} - 29 q^{48} + 46 q^{49} - 58 q^{50} - 73 q^{51} - 39 q^{52} - 16 q^{53} - 53 q^{54} - 59 q^{55} - 113 q^{56} - 39 q^{57} + 11 q^{58} - 93 q^{59} - 18 q^{60} - 66 q^{61} - 40 q^{62} - 21 q^{63} + 23 q^{64} - 92 q^{65} - 31 q^{66} + q^{67} - 121 q^{68} - 80 q^{69} - 3 q^{70} - 75 q^{71} - 114 q^{72} - 39 q^{73} + 9 q^{74} - 25 q^{75} - 58 q^{76} - 31 q^{77} + 68 q^{78} - 36 q^{79} - 82 q^{80} - 50 q^{81} - 18 q^{82} - 57 q^{83} - 9 q^{84} - 14 q^{85} - 58 q^{86} - 58 q^{87} - 15 q^{88} - 181 q^{89} + 8 q^{90} - 55 q^{91} - 116 q^{92} - 86 q^{93} - 39 q^{94} - 70 q^{95} - 127 q^{96} - 91 q^{97} - 19 q^{98} - 21 q^{99}+O(q^{100}) \) 110 * q - 9 * q^2 + 97 * q^4 - 26 * q^5 - 26 * q^6 - 4 * q^7 - 27 * q^8 + 62 * q^9 - 17 * q^10 - 9 * q^11 - 21 * q^13 - 29 * q^14 - 23 * q^15 + 79 * q^16 - 76 * q^17 - 31 * q^18 - 27 * q^19 - 67 * q^20 - 30 * q^21 - 28 * q^22 - 32 * q^23 - 63 * q^24 + 66 * q^25 - 55 * q^26 - 4 * q^28 - 81 * q^29 - 48 * q^30 - 30 * q^31 - 73 * q^32 - 53 * q^33 - 23 * q^34 - 78 * q^35 + 7 * q^36 - 110 * q^37 - 50 * q^38 - 64 * q^39 - 37 * q^40 - 123 * q^41 - 63 * q^42 - 40 * q^43 - 31 * q^44 - 73 * q^45 + 16 * q^46 - 37 * q^47 - 29 * q^48 + 46 * q^49 - 58 * q^50 - 73 * q^51 - 39 * q^52 - 16 * q^53 - 53 * q^54 - 59 * q^55 - 113 * q^56 - 39 * q^57 + 11 * q^58 - 93 * q^59 - 18 * q^60 - 66 * q^61 - 40 * q^62 - 21 * q^63 + 23 * q^64 - 92 * q^65 - 31 * q^66 + q^67 - 121 * q^68 - 80 * q^69 - 3 * q^70 - 75 * q^71 - 114 * q^72 - 39 * q^73 + 9 * q^74 - 25 * q^75 - 58 * q^76 - 31 * q^77 + 68 * q^78 - 36 * q^79 - 82 * q^80 - 50 * q^81 - 18 * q^82 - 57 * q^83 - 9 * q^84 - 14 * q^85 - 58 * q^86 - 58 * q^87 - 15 * q^88 - 181 * q^89 + 8 * q^90 - 55 * q^91 - 116 * q^92 - 86 * q^93 - 39 * q^94 - 70 * q^95 - 127 * q^96 - 91 * q^97 - 19 * q^98 - 21 * q^99

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