LMFDB - Embedded newform 4031.2.a.c.1.14

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			1.14
Character	$\chi$	$=$	4031.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.73344 q^{2} -1.78807 q^{3} +1.00480 q^{4} -2.76512 q^{5} +3.09951 q^{6} -4.11682 q^{7} +1.72512 q^{8} +0.197207 q^{9} +O(q^{10})$	\(q-1.73344 q^{2} -1.78807 q^{3} +1.00480 q^{4} -2.76512 q^{5} +3.09951 q^{6} -4.11682 q^{7} +1.72512 q^{8} +0.197207 q^{9} +4.79315 q^{10} -1.99041 q^{11} -1.79665 q^{12} -4.67393 q^{13} +7.13623 q^{14} +4.94423 q^{15} -4.99998 q^{16} -2.57995 q^{17} -0.341846 q^{18} -2.14491 q^{19} -2.77838 q^{20} +7.36117 q^{21} +3.45025 q^{22} -1.75275 q^{23} -3.08464 q^{24} +2.64587 q^{25} +8.10195 q^{26} +5.01160 q^{27} -4.13657 q^{28} -1.00000 q^{29} -8.57050 q^{30} +6.89231 q^{31} +5.21690 q^{32} +3.55900 q^{33} +4.47218 q^{34} +11.3835 q^{35} +0.198153 q^{36} +5.25840 q^{37} +3.71806 q^{38} +8.35733 q^{39} -4.77016 q^{40} -6.91323 q^{41} -12.7601 q^{42} -4.92517 q^{43} -1.99996 q^{44} -0.545301 q^{45} +3.03828 q^{46} -4.03679 q^{47} +8.94033 q^{48} +9.94817 q^{49} -4.58644 q^{50} +4.61314 q^{51} -4.69635 q^{52} +6.90102 q^{53} -8.68728 q^{54} +5.50372 q^{55} -7.10200 q^{56} +3.83526 q^{57} +1.73344 q^{58} -11.1107 q^{59} +4.96795 q^{60} -3.54169 q^{61} -11.9474 q^{62} -0.811866 q^{63} +0.956800 q^{64} +12.9240 q^{65} -6.16929 q^{66} +8.82546 q^{67} -2.59233 q^{68} +3.13405 q^{69} -19.7325 q^{70} +1.32126 q^{71} +0.340206 q^{72} +1.21852 q^{73} -9.11510 q^{74} -4.73101 q^{75} -2.15520 q^{76} +8.19415 q^{77} -14.4869 q^{78} -13.8652 q^{79} +13.8255 q^{80} -9.55273 q^{81} +11.9836 q^{82} +14.0747 q^{83} +7.39648 q^{84} +7.13386 q^{85} +8.53746 q^{86} +1.78807 q^{87} -3.43369 q^{88} +7.91115 q^{89} +0.945244 q^{90} +19.2417 q^{91} -1.76116 q^{92} -12.3240 q^{93} +6.99752 q^{94} +5.93093 q^{95} -9.32820 q^{96} +17.0121 q^{97} -17.2445 q^{98} -0.392523 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 61 q - q^{2} - 4 q^{3} + 43 q^{4} - 7 q^{5} - 13 q^{6} - 10 q^{7} - 6 q^{8} + 23 q^{9}+O(q^{10}) $ 61 * q - q^2 - 4 * q^3 + 43 * q^4 - 7 * q^5 - 13 * q^6 - 10 * q^7 - 6 * q^8 + 23 * q^9	\( 61 q - q^{2} - 4 q^{3} + 43 q^{4} - 7 q^{5} - 13 q^{6} - 10 q^{7} - 6 q^{8} + 23 q^{9} - 16 q^{10} - 3 q^{11} - 18 q^{12} - 28 q^{13} - 14 q^{14} - 12 q^{15} + 11 q^{16} - 21 q^{17} - 17 q^{18} - 36 q^{19} - 16 q^{20} - 12 q^{21} - 42 q^{22} - 15 q^{23} - 28 q^{24} - 16 q^{25} - 13 q^{26} - 10 q^{27} - 25 q^{28} - 61 q^{29} - 12 q^{30} - 18 q^{31} - 3 q^{32} - 42 q^{33} - 22 q^{34} - 29 q^{35} - 38 q^{36} - 30 q^{37} - 27 q^{38} - 31 q^{39} - 22 q^{40} - 28 q^{41} - 9 q^{42} - 58 q^{43} - 2 q^{44} - 31 q^{45} - 40 q^{46} - 6 q^{47} - 37 q^{48} - 37 q^{49} - 15 q^{50} - 44 q^{51} - 43 q^{52} - 27 q^{53} - 18 q^{54} - 38 q^{55} - 22 q^{56} - 50 q^{57} + q^{58} - 24 q^{59} + 6 q^{60} - 76 q^{61} - 17 q^{62} - 6 q^{63} - 60 q^{64} - 65 q^{65} - 7 q^{66} - 45 q^{67} - 31 q^{68} - 16 q^{69} - 48 q^{70} - 28 q^{71} - 40 q^{72} - 50 q^{73} - 17 q^{74} - 35 q^{75} - 100 q^{76} + q^{77} - 6 q^{78} - 66 q^{79} - 10 q^{80} - 63 q^{81} - 5 q^{82} - 9 q^{83} - 24 q^{84} - 77 q^{85} + 29 q^{86} + 4 q^{87} - 62 q^{88} - 30 q^{89} + 50 q^{90} - 52 q^{91} - 53 q^{92} - 42 q^{93} - 92 q^{94} - 20 q^{95} - 47 q^{96} - 34 q^{97} + 36 q^{98} - 29 q^{99}+O(q^{100}) \) 61 * q - q^2 - 4 * q^3 + 43 * q^4 - 7 * q^5 - 13 * q^6 - 10 * q^7 - 6 * q^8 + 23 * q^9 - 16 * q^10 - 3 * q^11 - 18 * q^12 - 28 * q^13 - 14 * q^14 - 12 * q^15 + 11 * q^16 - 21 * q^17 - 17 * q^18 - 36 * q^19 - 16 * q^20 - 12 * q^21 - 42 * q^22 - 15 * q^23 - 28 * q^24 - 16 * q^25 - 13 * q^26 - 10 * q^27 - 25 * q^28 - 61 * q^29 - 12 * q^30 - 18 * q^31 - 3 * q^32 - 42 * q^33 - 22 * q^34 - 29 * q^35 - 38 * q^36 - 30 * q^37 - 27 * q^38 - 31 * q^39 - 22 * q^40 - 28 * q^41 - 9 * q^42 - 58 * q^43 - 2 * q^44 - 31 * q^45 - 40 * q^46 - 6 * q^47 - 37 * q^48 - 37 * q^49 - 15 * q^50 - 44 * q^51 - 43 * q^52 - 27 * q^53 - 18 * q^54 - 38 * q^55 - 22 * q^56 - 50 * q^57 + q^58 - 24 * q^59 + 6 * q^60 - 76 * q^61 - 17 * q^62 - 6 * q^63 - 60 * q^64 - 65 * q^65 - 7 * q^66 - 45 * q^67 - 31 * q^68 - 16 * q^69 - 48 * q^70 - 28 * q^71 - 40 * q^72 - 50 * q^73 - 17 * q^74 - 35 * q^75 - 100 * q^76 + q^77 - 6 * q^78 - 66 * q^79 - 10 * q^80 - 63 * q^81 - 5 * q^82 - 9 * q^83 - 24 * q^84 - 77 * q^85 + 29 * q^86 + 4 * q^87 - 62 * q^88 - 30 * q^89 + 50 * q^90 - 52 * q^91 - 53 * q^92 - 42 * q^93 - 92 * q^94 - 20 * q^95 - 47 * q^96 - 34 * q^97 + 36 * q^98 - 29 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.73344	−1.22572	−0.612862	−	0.790190i	$-0.709982\pi$
$2$	−1.73344	−1.22572	−0.612862	+	0.790190i	$0.709982\pi$
$3$	−1.78807	−1.03234	−0.516172	−	0.856485i	$-0.672644\pi$
$3$	−1.78807	−1.03234	−0.516172	+	0.856485i	$0.672644\pi$
$4$	1.00480	0.502399
$5$	−2.76512	−1.23660	−0.618299	−	0.785943i	$-0.712178\pi$
$5$	−2.76512	−1.23660	−0.618299	+	0.785943i	$0.712178\pi$
$6$	3.09951	1.26537
$7$	−4.11682	−1.55601	−0.778005	−	0.628258i	$-0.783768\pi$
$7$	−4.11682	−1.55601	−0.778005	+	0.628258i	$0.783768\pi$
$8$	1.72512	0.609922
$9$	0.197207	0.0657357
$10$	4.79315	1.51573
$11$	−1.99041	−0.600131	−0.300066	−	0.953919i	$-0.597009\pi$
$11$	−1.99041	−0.600131	−0.300066	+	0.953919i	$0.597009\pi$
$12$	−1.79665	−0.518649
$13$	−4.67393	−1.29631	−0.648157	−	0.761506i	$-0.724460\pi$
$13$	−4.67393	−1.29631	−0.648157	+	0.761506i	$0.724460\pi$
$14$	7.13623	1.90724
$15$	4.94423	1.27660
$16$	−4.99998	−1.24999
$17$	−2.57995	−0.625730	−0.312865	−	0.949798i	$-0.601289\pi$
$17$	−2.57995	−0.625730	−0.312865	+	0.949798i	$0.601289\pi$
$18$	−0.341846	−0.0805738
$19$	−2.14491	−0.492076	−0.246038	−	0.969260i	$-0.579129\pi$
$19$	−2.14491	−0.492076	−0.246038	+	0.969260i	$0.579129\pi$
$20$	−2.77838	−0.621265
$21$	7.36117	1.60634
$22$	3.45025	0.735595
$23$	−1.75275	−0.365474	−0.182737	−	0.983162i	$-0.558496\pi$
$23$	−1.75275	−0.365474	−0.182737	+	0.983162i	$0.558496\pi$
$24$	−3.08464	−0.629649
$25$	2.64587	0.529174
$26$	8.10195	1.58892
$27$	5.01160	0.964483
$28$	−4.13657	−0.781738
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	−8.57050	−1.56475
$31$	6.89231	1.23790	0.618948	−	0.785432i	$-0.287559\pi$
$31$	6.89231	1.23790	0.618948	+	0.785432i	$0.287559\pi$
$32$	5.21690	0.922226
$33$	3.55900	0.619542
$34$	4.47218	0.766972
$35$	11.3835	1.92416
$36$	0.198153	0.0330255
$37$	5.25840	0.864476	0.432238	−	0.901759i	$-0.357724\pi$
$37$	5.25840	0.864476	0.432238	+	0.901759i	$0.357724\pi$
$38$	3.71806	0.603149
$39$	8.35733	1.33824
$40$	−4.77016	−0.754228
$41$	−6.91323	−1.07967	−0.539833	−	0.841772i	$-0.681513\pi$
$41$	−6.91323	−1.07967	−0.539833	+	0.841772i	$0.681513\pi$
$42$	−12.7601	−1.96893
$43$	−4.92517	−0.751081	−0.375541	−	0.926806i	$-0.622543\pi$
$43$	−4.92517	−0.751081	−0.375541	+	0.926806i	$0.622543\pi$
$44$	−1.99996	−0.301505
$45$	−0.545301	−0.0812886
$46$	3.03828	0.447970
$47$	−4.03679	−0.588827	−0.294413	−	0.955678i	$-0.595124\pi$
$47$	−4.03679	−0.588827	−0.294413	+	0.955678i	$0.595124\pi$
$48$	8.94033	1.29043
$49$	9.94817	1.42117
$50$	−4.58644	−0.648621
$51$	4.61314	0.645969
$52$	−4.69635	−0.651267
$53$	6.90102	0.947928	0.473964	−	0.880544i	$-0.342823\pi$
$53$	6.90102	0.947928	0.473964	+	0.880544i	$0.342823\pi$
$54$	−8.68728	−1.18219
$55$	5.50372	0.742121
$56$	−7.10200	−0.949044
$57$	3.83526	0.507992
$58$	1.73344	0.227611
$59$	−11.1107	−1.44649	−0.723243	−	0.690594i	$-0.757349\pi$
$59$	−11.1107	−1.44649	−0.723243	+	0.690594i	$0.757349\pi$
$60$	4.96795	0.641360
$61$	−3.54169	−0.453467	−0.226734	−	0.973957i	$-0.572805\pi$
$61$	−3.54169	−0.453467	−0.226734	+	0.973957i	$0.572805\pi$
$62$	−11.9474	−1.51732
$63$	−0.811866	−0.102285
$64$	0.956800	0.119600
$65$	12.9240	1.60302
$66$	−6.16929	−0.759388
$67$	8.82546	1.07820	0.539101	−	0.842241i	$-0.318764\pi$
$67$	8.82546	1.07820	0.539101	+	0.842241i	$0.318764\pi$
$68$	−2.59233	−0.314366
$69$	3.13405	0.377295
$70$	−19.7325	−2.35849
$71$	1.32126	0.156805	0.0784025	−	0.996922i	$-0.475018\pi$
$71$	1.32126	0.156805	0.0784025	+	0.996922i	$0.475018\pi$
$72$	0.340206	0.0400936
$73$	1.21852	0.142616	0.0713082	−	0.997454i	$-0.477283\pi$
$73$	1.21852	0.142616	0.0713082	+	0.997454i	$0.477283\pi$
$74$	−9.11510	−1.05961
$75$	−4.73101	−0.546290
$76$	−2.15520	−0.247218
$77$	8.19415	0.933810
$78$	−14.4869	−1.64032
$79$	−13.8652	−1.55996	−0.779981	−	0.625804i	$-0.784771\pi$
$79$	−13.8652	−1.55996	−0.779981	+	0.625804i	$0.784771\pi$
$80$	13.8255	1.54574
$81$	−9.55273	−1.06141
$82$	11.9836	1.32337
$83$	14.0747	1.54490	0.772451	−	0.635075i	$-0.219031\pi$
$83$	14.0747	1.54490	0.772451	+	0.635075i	$0.219031\pi$
$84$	7.39648	0.807023
$85$	7.13386	0.773776
$86$	8.53746	0.920618
$87$	1.78807	0.191702
$88$	−3.43369	−0.366033
$89$	7.91115	0.838580	0.419290	−	0.907852i	$-0.362279\pi$
$89$	7.91115	0.838580	0.419290	+	0.907852i	$0.362279\pi$
$90$	0.945244	0.0996374
$91$	19.2417	2.01708
$92$	−1.76116	−0.183614
$93$	−12.3240	−1.27793
$94$	6.99752	0.721739
$95$	5.93093	0.608500
$96$	−9.32820	−0.952055
$97$	17.0121	1.72731	0.863657	−	0.504079i	$-0.168168\pi$
$97$	17.0121	1.72731	0.863657	+	0.504079i	$0.168168\pi$
$98$	−17.2445	−1.74196
$99$	−0.392523	−0.0394501
$100$	2.65856	0.265856
$101$	1.60717	0.159919	0.0799596	−	0.996798i	$-0.474521\pi$
$101$	1.60717	0.159919	0.0799596	+	0.996798i	$0.474521\pi$
$102$	−7.99658	−0.791780
$103$	8.06634	0.794800	0.397400	−	0.917646i	$-0.369913\pi$
$103$	8.06634	0.794800	0.397400	+	0.917646i	$0.369913\pi$
$104$	−8.06308	−0.790650
$105$	−20.3545	−1.98639
$106$	−11.9625	−1.16190
$107$	12.4805	1.20654	0.603270	−	0.797537i	$-0.293864\pi$
$107$	12.4805	1.20654	0.603270	+	0.797537i	$0.293864\pi$
$108$	5.03564	0.484555
$109$	−6.69103	−0.640884	−0.320442	−	0.947268i	$-0.603831\pi$
$109$	−6.69103	−0.640884	−0.320442	+	0.947268i	$0.603831\pi$
$110$	−9.54033	−0.909635
$111$	−9.40241	−0.892438
$112$	20.5840	1.94500
$113$	16.2832	1.53179	0.765897	−	0.642964i	$-0.222295\pi$
$113$	16.2832	1.53179	0.765897	+	0.642964i	$0.222295\pi$
$114$	−6.64817	−0.622658
$115$	4.84656	0.451944
$116$	−1.00480	−0.0932931
$117$	−0.921732	−0.0852142
$118$	19.2596	1.77299
$119$	10.6212	0.973642
$120$	8.52939	0.778623
$121$	−7.03827	−0.639843
$122$	6.13929	0.555825
$123$	12.3614	1.11459
$124$	6.92537	0.621917
$125$	6.50945	0.582223
$126$	1.40732	0.125374
$127$	−1.13446	−0.100667	−0.0503337	−	0.998732i	$-0.516028\pi$
$127$	−1.13446	−0.100667	−0.0503337	+	0.998732i	$0.516028\pi$
$128$	−12.0923	−1.06882
$129$	8.80656	0.775375
$130$	−22.4028	−1.96486
$131$	−17.6223	−1.53967	−0.769834	−	0.638244i	$-0.779661\pi$
$131$	−17.6223	−1.53967	−0.769834	+	0.638244i	$0.779661\pi$
$132$	3.57607	0.311257
$133$	8.83020	0.765675
$134$	−15.2984	−1.32158
$135$	−13.8577	−1.19268
$136$	−4.45072	−0.381646
$137$	−16.1735	−1.38180	−0.690898	−	0.722952i	$-0.742785\pi$
$137$	−16.1735	−1.38180	−0.690898	+	0.722952i	$0.742785\pi$
$138$	−5.43267	−0.462460
$139$	−1.00000	−0.0848189
$139$	−1.00000	−0.0848189
$140$	11.4381	0.966695
$141$	7.21808	0.607872
$142$	−2.29032	−0.192200
$143$	9.30303	0.777959
$144$	−0.986031	−0.0821693
$145$	2.76512	0.229630
$146$	−2.11222	−0.174808
$147$	−17.7881	−1.46713
$148$	5.28363	0.434312
$149$	4.67382	0.382895	0.191447	−	0.981503i	$-0.438682\pi$
$149$	4.67382	0.382895	0.191447	+	0.981503i	$0.438682\pi$
$150$	8.20089	0.669600
$151$	2.36916	0.192799	0.0963996	−	0.995343i	$-0.469267\pi$
$151$	2.36916	0.192799	0.0963996	+	0.995343i	$0.469267\pi$
$152$	−3.70023	−0.300128
$153$	−0.508785	−0.0411328
$154$	−14.2040	−1.14459
$155$	−19.0580	−1.53078
$156$	8.39742	0.672332
$157$	9.65761	0.770761	0.385381	−	0.922758i	$-0.374070\pi$
$157$	9.65761	0.770761	0.385381	+	0.922758i	$0.374070\pi$
$158$	24.0345	1.91208
$159$	−12.3395	−0.978589
$160$	−14.4253	−1.14042
$161$	7.21575	0.568681
$162$	16.5590	1.30100
$163$	1.40430	0.109994	0.0549968	−	0.998487i	$-0.482485\pi$
$163$	1.40430	0.109994	0.0549968	+	0.998487i	$0.482485\pi$
$164$	−6.94640	−0.542423
$165$	−9.84105	−0.766125
$166$	−24.3976	−1.89362
$167$	23.2591	1.79984	0.899922	−	0.436050i	$-0.143623\pi$
$167$	23.2591	1.79984	0.899922	+	0.436050i	$0.143623\pi$
$168$	12.6989	0.979741
$169$	8.84561	0.680432
$170$	−12.3661	−0.948436
$171$	−0.422992	−0.0323470
$172$	−4.94880	−0.377342
$173$	3.38728	0.257530	0.128765	−	0.991675i	$-0.458899\pi$
$173$	3.38728	0.257530	0.128765	+	0.991675i	$0.458899\pi$
$174$	−3.09951	−0.234973
$175$	−10.8926	−0.823400
$176$	9.95200	0.750161
$177$	19.8667	1.49327
$178$	−13.7135	−1.02787
$179$	15.7211	1.17505	0.587524	−	0.809207i	$-0.300103\pi$
$179$	15.7211	1.17505	0.587524	+	0.809207i	$0.300103\pi$
$180$	−0.547917	−0.0408393
$181$	−17.1928	−1.27793	−0.638965	−	0.769236i	$-0.720637\pi$
$181$	−17.1928	−1.27793	−0.638965	+	0.769236i	$0.720637\pi$
$182$	−33.3542	−2.47238
$183$	6.33280	0.468134
$184$	−3.02370	−0.222910
$185$	−14.5401	−1.06901
$186$	21.3628	1.56639
$187$	5.13516	0.375520
$188$	−4.05616	−0.295826
$189$	−20.6318	−1.50075
$190$	−10.2809	−0.745853
$191$	4.86513	0.352028	0.176014	−	0.984388i	$-0.443680\pi$
$191$	4.86513	0.352028	0.176014	+	0.984388i	$0.443680\pi$
$192$	−1.71083	−0.123468
$193$	−25.5427	−1.83860	−0.919302	−	0.393553i	$-0.871246\pi$
$193$	−25.5427	−1.83860	−0.919302	+	0.393553i	$0.871246\pi$
$194$	−29.4893	−2.11721
$195$	−23.1090	−1.65487
$196$	9.99590	0.713993
$197$	−3.93826	−0.280590	−0.140295	−	0.990110i	$-0.544805\pi$
$197$	−3.93826	−0.280590	−0.140295	+	0.990110i	$0.544805\pi$
$198$	0.680413	0.0483549
$199$	8.92493	0.632671	0.316336	−	0.948647i	$-0.397547\pi$
$199$	8.92493	0.632671	0.316336	+	0.948647i	$0.397547\pi$
$200$	4.56444	0.322755
$201$	−15.7806	−1.11308
$202$	−2.78592	−0.196017
$203$	4.11682	0.288944
$204$	4.63527	0.324534
$205$	19.1159	1.33511
$206$	−13.9825	−0.974205
$207$	−0.345655	−0.0240247
$208$	23.3695	1.62039
$209$	4.26925	0.295310
$210$	35.2832	2.43477
$211$	−16.7727	−1.15468	−0.577341	−	0.816503i	$-0.695910\pi$
$211$	−16.7727	−1.15468	−0.577341	+	0.816503i	$0.695910\pi$
$212$	6.93413	0.476238
$213$	−2.36252	−0.161877
$214$	−21.6342	−1.47888
$215$	13.6187	0.928785
$216$	8.64561	0.588259
$217$	−28.3744	−1.92618
$218$	11.5985	0.785547
$219$	−2.17879	−0.147229
$220$	5.53012	0.372841
$221$	12.0585	0.811143
$222$	16.2985	1.09388
$223$	−9.42187	−0.630935	−0.315468	−	0.948936i	$-0.602161\pi$
$223$	−9.42187	−0.630935	−0.315468	+	0.948936i	$0.602161\pi$
$224$	−21.4770	−1.43499
$225$	0.521784	0.0347856
$226$	−28.2258	−1.87756
$227$	−18.5748	−1.23285	−0.616426	−	0.787413i	$-0.711420\pi$
$227$	−18.5748	−1.23285	−0.616426	+	0.787413i	$0.711420\pi$
$228$	3.85366	0.255215
$229$	−0.969783	−0.0640851	−0.0320425	−	0.999487i	$-0.510201\pi$
$229$	−0.969783	−0.0640851	−0.0320425	+	0.999487i	$0.510201\pi$
$230$	−8.40120	−0.553959
$231$	−14.6517	−0.964014
$232$	−1.72512	−0.113260
$233$	−9.93912	−0.651134	−0.325567	−	0.945519i	$-0.605555\pi$
$233$	−9.93912	−0.651134	−0.325567	+	0.945519i	$0.605555\pi$
$234$	1.59776	0.104449
$235$	11.1622	0.728142
$236$	−11.1640	−0.726713
$237$	24.7921	1.61042
$238$	−18.4111	−1.19342
$239$	−11.8610	−0.767227	−0.383613	−	0.923494i	$-0.625320\pi$
$239$	−11.8610	−0.767227	−0.383613	+	0.923494i	$0.625320\pi$
$240$	−24.7210	−1.59574
$241$	7.98266	0.514208	0.257104	−	0.966384i	$-0.417232\pi$
$241$	7.98266	0.514208	0.257104	+	0.966384i	$0.417232\pi$
$242$	12.2004	0.784270
$243$	2.04619	0.131263
$244$	−3.55868	−0.227821
$245$	−27.5079	−1.75741
$246$	−21.4276	−1.36618
$247$	10.0252	0.637885
$248$	11.8901	0.755019
$249$	−25.1666	−1.59487
$250$	−11.2837	−0.713644
$251$	20.3390	1.28379	0.641893	−	0.766794i	$-0.278149\pi$
$251$	20.3390	1.28379	0.641893	+	0.766794i	$0.278149\pi$
$252$	−0.815761	−0.0513881
$253$	3.48869	0.219332
$254$	1.96652	0.123390
$255$	−12.7559	−0.798804
$256$	19.0477	1.19048
$257$	23.5156	1.46686	0.733432	−	0.679762i	$-0.237917\pi$
$257$	23.5156	1.46686	0.733432	+	0.679762i	$0.237917\pi$
$258$	−15.2656	−0.950395
$259$	−21.6479	−1.34513
$260$	12.9860	0.805355
$261$	−0.197207	−0.0122068
$262$	30.5471	1.88721
$263$	−18.5188	−1.14192	−0.570958	−	0.820979i	$-0.693428\pi$
$263$	−18.5188	−1.14192	−0.570958	+	0.820979i	$0.693428\pi$
$264$	6.13970	0.377872
$265$	−19.0821	−1.17221
$266$	−15.3066	−0.938507
$267$	−14.1457	−0.865704
$268$	8.86780	0.541687
$269$	25.9852	1.58434	0.792171	−	0.610299i	$-0.208951\pi$
$269$	25.9852	1.58434	0.792171	+	0.610299i	$0.208951\pi$
$270$	24.0213	1.46189
$271$	−20.3772	−1.23783	−0.618913	−	0.785459i	$-0.712427\pi$
$271$	−20.3772	−1.23783	−0.618913	+	0.785459i	$0.712427\pi$
$272$	12.8997	0.782159
$273$	−34.4056	−2.08232
$274$	28.0357	1.69370
$275$	−5.26636	−0.317574
$276$	3.14908	0.189553
$277$	1.82620	0.109726	0.0548628	−	0.998494i	$-0.482528\pi$
$277$	1.82620	0.109726	0.0548628	+	0.998494i	$0.482528\pi$
$278$	1.73344	0.103965
$279$	1.35921	0.0813739
$280$	19.6378	1.17359
$281$	3.64692	0.217557	0.108778	−	0.994066i	$-0.465306\pi$
$281$	3.64692	0.217557	0.108778	+	0.994066i	$0.465306\pi$
$282$	−12.5121	−0.745083
$283$	−1.75521	−0.104337	−0.0521683	−	0.998638i	$-0.516613\pi$
$283$	−1.75521	−0.104337	−0.0521683	+	0.998638i	$0.516613\pi$
$284$	1.32760	0.0787787
$285$	−10.6049	−0.628182
$286$	−16.1262	−0.953563
$287$	28.4605	1.67997
$288$	1.02881	0.0606232
$289$	−10.3439	−0.608462
$290$	−4.79315	−0.281463
$291$	−30.4188	−1.78318
$292$	1.22436	0.0716503
$293$	10.6127	0.620003	0.310002	−	0.950736i	$-0.399670\pi$
$293$	10.6127	0.620003	0.310002	+	0.950736i	$0.399670\pi$
$294$	30.8345	1.79830
$295$	30.7223	1.78872
$296$	9.07137	0.527263
$297$	−9.97514	−0.578816
$298$	−8.10177	−0.469323
$299$	8.19224	0.473769
$300$	−4.75370	−0.274455
$301$	20.2760	1.16869
$302$	−4.10678	−0.236319
$303$	−2.87373	−0.165092
$304$	10.7245	0.615092
$305$	9.79319	0.560756
$306$	0.881946	0.0504175
$307$	−0.258382	−0.0147467	−0.00737333	−	0.999973i	$-0.502347\pi$
$307$	−0.258382	−0.0147467	−0.00737333	+	0.999973i	$0.502347\pi$
$308$	8.23346	0.469145
$309$	−14.4232	−0.820507
$310$	33.0359	1.87631
$311$	24.4312	1.38536	0.692682	−	0.721243i	$-0.256429\pi$
$311$	24.4312	1.38536	0.692682	+	0.721243i	$0.256429\pi$
$312$	14.4174	0.816224
$313$	10.9772	0.620467	0.310234	−	0.950660i	$-0.399593\pi$
$313$	10.9772	0.620467	0.310234	+	0.950660i	$0.399593\pi$
$314$	−16.7408	−0.944741
$315$	2.24490	0.126486
$316$	−13.9318	−0.783723
$317$	−26.5903	−1.49346	−0.746729	−	0.665129i	$-0.768377\pi$
$317$	−26.5903	−1.49346	−0.746729	+	0.665129i	$0.768377\pi$
$318$	21.3898	1.19948
$319$	1.99041	0.111442
$320$	−2.64566	−0.147897
$321$	−22.3161	−1.24556
$322$	−12.5080	−0.697046
$323$	5.53376	0.307907
$324$	−9.59856	−0.533253
$325$	−12.3666	−0.685976
$326$	−2.43427	−0.134822
$327$	11.9641	0.661614
$328$	−11.9262	−0.658512
$329$	16.6187	0.916220
$330$	17.0588	0.939057
$331$	−23.1894	−1.27461	−0.637304	−	0.770613i	$-0.719950\pi$
$331$	−23.1894	−1.27461	−0.637304	+	0.770613i	$0.719950\pi$
$332$	14.1422	0.776156
$333$	1.03700	0.0568270
$334$	−40.3182	−2.20611
$335$	−24.4034	−1.33330
$336$	−36.8057	−2.00791
$337$	12.7774	0.696029	0.348015	−	0.937489i	$-0.386856\pi$
$337$	12.7774	0.696029	0.348015	+	0.937489i	$0.386856\pi$
$338$	−15.3333	−0.834021
$339$	−29.1155	−1.58134
$340$	7.16809	0.388744
$341$	−13.7185	−0.742899
$342$	0.733229	0.0396485
$343$	−12.1371	−0.655341
$344$	−8.49650	−0.458101
$345$	−8.66601	−0.466562
$346$	−5.87164	−0.315661
$347$	−16.1604	−0.867536	−0.433768	−	0.901025i	$-0.642816\pi$
$347$	−16.1604	−0.867536	−0.433768	+	0.901025i	$0.642816\pi$
$348$	1.79665	0.0963106
$349$	−27.3766	−1.46544	−0.732719	−	0.680531i	$-0.761749\pi$
$349$	−27.3766	−1.46544	−0.732719	+	0.680531i	$0.761749\pi$
$350$	18.8815	1.00926
$351$	−23.4239	−1.25027
$352$	−10.3838	−0.553457
$353$	−8.09900	−0.431066	−0.215533	−	0.976497i	$-0.569149\pi$
$353$	−8.09900	−0.431066	−0.215533	+	0.976497i	$0.569149\pi$
$354$	−34.4376	−1.83034
$355$	−3.65345	−0.193905
$356$	7.94910	0.421302
$357$	−18.9915	−1.00513
$358$	−27.2515	−1.44028
$359$	4.45481	0.235116	0.117558	−	0.993066i	$-0.462493\pi$
$359$	4.45481	0.235116	0.117558	+	0.993066i	$0.462493\pi$
$360$	−0.940709	−0.0495797
$361$	−14.3994	−0.757861
$362$	29.8026	1.56639
$363$	12.5849	0.660538
$364$	19.3340	1.01338
$365$	−3.36934	−0.176359
$366$	−10.9775	−0.573803
$367$	−1.13040	−0.0590064	−0.0295032	−	0.999565i	$-0.509393\pi$
$367$	−1.13040	−0.0590064	−0.0295032	+	0.999565i	$0.509393\pi$
$368$	8.76372	0.456840
$369$	−1.36334	−0.0709726
$370$	25.2043	1.31031
$371$	−28.4102	−1.47499
$372$	−12.3831	−0.642033
$373$	−21.0857	−1.09178	−0.545889	−	0.837857i	$-0.683808\pi$
$373$	−21.0857	−1.09178	−0.545889	+	0.837857i	$0.683808\pi$
$374$	−8.90147	−0.460284
$375$	−11.6394	−0.601055
$376$	−6.96395	−0.359138
$377$	4.67393	0.240720
$378$	35.7639	1.83950
$379$	35.6204	1.82970	0.914848	−	0.403798i	$-0.132310\pi$
$379$	35.6204	1.82970	0.914848	+	0.403798i	$0.132310\pi$
$380$	5.95938	0.305710
$381$	2.02850	0.103923
$382$	−8.43339	−0.431490
$383$	−1.78014	−0.0909608	−0.0454804	−	0.998965i	$-0.514482\pi$
$383$	−1.78014	−0.0909608	−0.0454804	+	0.998965i	$0.514482\pi$
$384$	21.6220	1.10339
$385$	−22.6578	−1.15475
$386$	44.2766	2.25362
$387$	−0.971279	−0.0493729
$388$	17.0937	0.867801
$389$	1.43693	0.0728552	0.0364276	−	0.999336i	$-0.488402\pi$
$389$	1.43693	0.0728552	0.0364276	+	0.999336i	$0.488402\pi$
$390$	40.0579	2.02841
$391$	4.52201	0.228688
$392$	17.1618	0.866801
$393$	31.5100	1.58947
$394$	6.82673	0.343926
$395$	38.3390	1.92904
$396$	−0.394406	−0.0198197
$397$	−38.4081	−1.92765	−0.963823	−	0.266543i	$-0.914119\pi$
$397$	−38.4081	−1.92765	−0.963823	+	0.266543i	$0.914119\pi$
$398$	−15.4708	−0.775480
$399$	−15.7890	−0.790441
$400$	−13.2293	−0.661464
$401$	−15.8959	−0.793804	−0.396902	−	0.917861i	$-0.629915\pi$
$401$	−15.8959	−0.793804	−0.396902	+	0.917861i	$0.629915\pi$
$402$	27.3546	1.36432
$403$	−32.2142	−1.60470
$404$	1.61488	0.0803432
$405$	26.4144	1.31254
$406$	−7.13623	−0.354165
$407$	−10.4664	−0.518799
$408$	7.95822	0.393991
$409$	−6.52618	−0.322699	−0.161349	−	0.986897i	$-0.551585\pi$
$409$	−6.52618	−0.322699	−0.161349	+	0.986897i	$0.551585\pi$
$410$	−33.1362	−1.63648
$411$	28.9194	1.42649
$412$	8.10503	0.399306
$413$	45.7406	2.25075
$414$	0.599171	0.0294476
$415$	−38.9182	−1.91042
$416$	−24.3834	−1.19549
$417$	1.78807	0.0875623
$418$	−7.40047	−0.361969
$419$	17.4463	0.852308	0.426154	−	0.904651i	$-0.359868\pi$
$419$	17.4463	0.852308	0.426154	+	0.904651i	$0.359868\pi$
$420$	−20.4521	−0.997962
$421$	21.5524	1.05040	0.525201	−	0.850978i	$-0.323990\pi$
$421$	21.5524	1.05040	0.525201	+	0.850978i	$0.323990\pi$
$422$	29.0744	1.41532
$423$	−0.796084	−0.0387069
$424$	11.9051	0.578162
$425$	−6.82621	−0.331120
$426$	4.09527	0.198416
$427$	14.5805	0.705599
$428$	12.5404	0.606164
$429$	−16.6345	−0.803122
$430$	−23.6071	−1.13843
$431$	−17.7399	−0.854501	−0.427250	−	0.904133i	$-0.640518\pi$
$431$	−17.7399	−0.854501	−0.427250	+	0.904133i	$0.640518\pi$
$432$	−25.0579	−1.20560
$433$	−33.3143	−1.60098	−0.800492	−	0.599344i	$-0.795428\pi$
$433$	−33.3143	−1.60098	−0.800492	+	0.599344i	$0.795428\pi$
$434$	49.1851	2.36096
$435$	−4.94423	−0.237058
$436$	−6.72313	−0.321979
$437$	3.75949	0.179841
$438$	3.77680	0.180462
$439$	39.5485	1.88754	0.943772	−	0.330596i	$-0.107250\pi$
$439$	39.5485	1.88754	0.943772	+	0.330596i	$0.107250\pi$
$440$	9.49456	0.452636
$441$	1.96185	0.0934215
$442$	−20.9026	−0.994237
$443$	35.8764	1.70454	0.852269	−	0.523104i	$-0.175226\pi$
$443$	35.8764	1.70454	0.852269	+	0.523104i	$0.175226\pi$
$444$	−9.44752	−0.448360
$445$	−21.8753	−1.03699
$446$	16.3322	0.773352
$447$	−8.35714	−0.395279
$448$	−3.93897	−0.186099
$449$	−28.0027	−1.32153	−0.660765	−	0.750592i	$-0.729768\pi$
$449$	−28.0027	−1.32153	−0.660765	+	0.750592i	$0.729768\pi$
$450$	−0.904479	−0.0426376
$451$	13.7602	0.647941
$452$	16.3613	0.769571
$453$	−4.23623	−0.199035
$454$	32.1982	1.51114
$455$	−53.2056	−2.49431
$456$	6.61628	0.309835
$457$	−17.0996	−0.799885	−0.399942	−	0.916540i	$-0.630970\pi$
$457$	−17.0996	−0.799885	−0.399942	+	0.916540i	$0.630970\pi$
$458$	1.68106	0.0785506
$459$	−12.9297	−0.603506
$460$	4.86981	0.227056
$461$	16.1459	0.751990	0.375995	−	0.926622i	$-0.377301\pi$
$461$	16.1459	0.751990	0.375995	+	0.926622i	$0.377301\pi$
$462$	25.3979	1.18161
$463$	−10.3594	−0.481444	−0.240722	−	0.970594i	$-0.577384\pi$
$463$	−10.3594	−0.481444	−0.240722	+	0.970594i	$0.577384\pi$
$464$	4.99998	0.232118
$465$	34.0772	1.58029
$466$	17.2288	0.798110
$467$	10.9627	0.507291	0.253646	−	0.967297i	$-0.418370\pi$
$467$	10.9627	0.507291	0.253646	+	0.967297i	$0.418370\pi$
$468$	−0.926154	−0.0428115
$469$	−36.3328	−1.67769
$470$	−19.3489	−0.892500
$471$	−17.2685	−0.795692
$472$	−19.1672	−0.882243
$473$	9.80310	0.450747
$474$	−42.9754	−1.97393
$475$	−5.67515	−0.260394
$476$	10.6721	0.489157
$477$	1.36093	0.0623127
$478$	20.5603	0.940408
$479$	30.5134	1.39419	0.697096	−	0.716978i	$-0.254475\pi$
$479$	30.5134	1.39419	0.697096	+	0.716978i	$0.254475\pi$
$480$	25.7936	1.17731
$481$	−24.5774	−1.12063
$482$	−13.8374	−0.630277
$483$	−12.9023	−0.587075
$484$	−7.07203	−0.321456
$485$	−47.0404	−2.13599
$486$	−3.54693	−0.160892
$487$	12.1141	0.548942	0.274471	−	0.961595i	$-0.411497\pi$
$487$	12.1141	0.548942	0.274471	+	0.961595i	$0.411497\pi$
$488$	−6.10984	−0.276579
$489$	−2.51100	−0.113551
$490$	47.6831	2.15410
$491$	22.9920	1.03762	0.518808	−	0.854891i	$-0.326376\pi$
$491$	22.9920	1.03762	0.518808	+	0.854891i	$0.326376\pi$
$492$	12.4207	0.559967
$493$	2.57995	0.116195
$494$	−17.3780	−0.781871
$495$	1.08537	0.0487839
$496$	−34.4614	−1.54736
$497$	−5.43940	−0.243990
$498$	43.6247	1.95487
$499$	1.13345	0.0507403	0.0253702	−	0.999678i	$-0.491924\pi$
$499$	1.13345	0.0507403	0.0253702	+	0.999678i	$0.491924\pi$
$500$	6.54068	0.292508
$501$	−41.5890	−1.85806
$502$	−35.2564	−1.57357
$503$	−11.3333	−0.505329	−0.252664	−	0.967554i	$-0.581307\pi$
$503$	−11.3333	−0.505329	−0.252664	+	0.967554i	$0.581307\pi$
$504$	−1.40056	−0.0623861
$505$	−4.44401	−0.197756
$506$	−6.04742	−0.268841
$507$	−15.8166	−0.702440
$508$	−1.13991	−0.0505751
$509$	31.3002	1.38735	0.693677	−	0.720286i	$-0.255989\pi$
$509$	31.3002	1.38735	0.693677	+	0.720286i	$0.255989\pi$
$510$	22.1115	0.979113
$511$	−5.01640	−0.221913
$512$	−8.83326	−0.390378
$513$	−10.7494	−0.474599
$514$	−40.7628	−1.79797
$515$	−22.3044	−0.982847
$516$	8.84881	0.389547
$517$	8.03487	0.353373
$518$	37.5252	1.64876
$519$	−6.05671	−0.265860
$520$	22.2954	0.977716
$521$	25.8744	1.13358	0.566788	−	0.823863i	$-0.308186\pi$
$521$	25.8744	1.13358	0.566788	+	0.823863i	$0.308186\pi$
$522$	0.341846	0.0149622
$523$	−15.6465	−0.684173	−0.342086	−	0.939668i	$-0.611134\pi$
$523$	−15.6465	−0.684173	−0.342086	+	0.939668i	$0.611134\pi$
$524$	−17.7068	−0.773527
$525$	19.4767	0.850032
$526$	32.1011	1.39967
$527$	−17.7818	−0.774588
$528$	−17.7949	−0.774424
$529$	−19.9279	−0.866429
$530$	33.0776	1.43680
$531$	−2.19110	−0.0950858
$532$	8.87256	0.384674
$533$	32.3120	1.39959
$534$	24.5207	1.06111
$535$	−34.5101	−1.49200
$536$	15.2250	0.657618
$537$	−28.1104	−1.21305
$538$	−45.0436	−1.94197
$539$	−19.8009	−0.852887
$540$	−13.9241	−0.599199
$541$	−29.2020	−1.25549	−0.627746	−	0.778418i	$-0.716022\pi$
$541$	−29.2020	−1.25549	−0.627746	+	0.778418i	$0.716022\pi$
$542$	35.3226	1.51723
$543$	30.7420	1.31926
$544$	−13.4593	−0.577064
$545$	18.5015	0.792516
$546$	59.6398	2.55235
$547$	4.68008	0.200106	0.100053	−	0.994982i	$-0.468099\pi$
$547$	4.68008	0.200106	0.100053	+	0.994982i	$0.468099\pi$
$548$	−16.2511	−0.694213
$549$	−0.698447	−0.0298090
$550$	9.12890	0.389258
$551$	2.14491	0.0913762
$552$	5.40661	0.230120
$553$	57.0806	2.42732
$554$	−3.16560	−0.134493
$555$	25.9988	1.10359
$556$	−1.00480	−0.0426129
$557$	−3.30413	−0.140001	−0.0700003	−	0.997547i	$-0.522300\pi$
$557$	−3.30413	−0.140001	−0.0700003	+	0.997547i	$0.522300\pi$
$558$	−2.35611	−0.0997420
$559$	23.0199	0.973637
$560$	−56.9171	−2.40519
$561$	−9.18204	−0.387666
$562$	−6.32170	−0.266665
$563$	12.0632	0.508404	0.254202	−	0.967151i	$-0.418187\pi$
$563$	12.0632	0.508404	0.254202	+	0.967151i	$0.418187\pi$
$564$	7.25271	0.305394
$565$	−45.0249	−1.89421
$566$	3.04255	0.127888
$567$	39.3268	1.65157
$568$	2.27934	0.0956388
$569$	−40.9608	−1.71717	−0.858584	−	0.512673i	$-0.828655\pi$
$569$	−40.9608	−1.71717	−0.858584	+	0.512673i	$0.828655\pi$
$570$	18.3830	0.769978
$571$	2.49342	0.104346	0.0521731	−	0.998638i	$-0.483385\pi$
$571$	2.49342	0.104346	0.0521731	+	0.998638i	$0.483385\pi$
$572$	9.34767	0.390846
$573$	−8.69921	−0.363415
$574$	−49.3344	−2.05918
$575$	−4.63755	−0.193399
$576$	0.188688	0.00786199
$577$	25.4492	1.05946	0.529732	−	0.848165i	$-0.322292\pi$
$577$	25.4492	1.05946	0.529732	+	0.848165i	$0.322292\pi$
$578$	17.9304	0.745806
$579$	45.6722	1.89807
$580$	2.77838	0.115366
$581$	−57.9430	−2.40388
$582$	52.7291	2.18569
$583$	−13.7359	−0.568881
$584$	2.10208	0.0869848
$585$	2.54870	0.105376
$586$	−18.3965	−0.759953
$587$	29.2319	1.20653	0.603264	−	0.797542i	$-0.293867\pi$
$587$	29.2319	1.20653	0.603264	+	0.797542i	$0.293867\pi$
$588$	−17.8734	−0.737087
$589$	−14.7834	−0.609139
$590$	−53.2551	−2.19248
$591$	7.04191	0.289665
$592$	−26.2919	−1.08059
$593$	28.0472	1.15176	0.575880	−	0.817534i	$-0.304659\pi$
$593$	28.0472	1.15176	0.575880	+	0.817534i	$0.304659\pi$
$594$	17.2913	0.709469
$595$	−29.3688	−1.20400
$596$	4.69625	0.192366
$597$	−15.9584	−0.653135
$598$	−14.2007	−0.580710
$599$	24.6296	1.00634	0.503169	−	0.864188i	$-0.332167\pi$
$599$	24.6296	1.00634	0.503169	+	0.864188i	$0.332167\pi$
$600$	−8.16155	−0.333194
$601$	−35.0948	−1.43155	−0.715774	−	0.698332i	$-0.753926\pi$
$601$	−35.0948	−1.43155	−0.715774	+	0.698332i	$0.753926\pi$
$602$	−35.1471	−1.43249
$603$	1.74044	0.0708763
$604$	2.38052	0.0968621
$605$	19.4616	0.791228
$606$	4.98143	0.202357
$607$	14.8389	0.602293	0.301147	−	0.953578i	$-0.402631\pi$
$607$	14.8389	0.602293	0.301147	+	0.953578i	$0.402631\pi$
$608$	−11.1898	−0.453805
$609$	−7.36117	−0.298290
$610$	−16.9759	−0.687332
$611$	18.8677	0.763304
$612$	−0.511226	−0.0206651
$613$	27.5300	1.11193	0.555963	−	0.831207i	$-0.312350\pi$
$613$	27.5300	1.11193	0.555963	+	0.831207i	$0.312350\pi$
$614$	0.447889	0.0180753
$615$	−34.1806	−1.37830
$616$	14.1359	0.569551
$617$	−27.9004	−1.12323	−0.561613	−	0.827400i	$-0.689819\pi$
$617$	−27.9004	−1.12323	−0.561613	+	0.827400i	$0.689819\pi$
$618$	25.0017	1.00572
$619$	16.9797	0.682470	0.341235	−	0.939978i	$-0.389155\pi$
$619$	16.9797	0.682470	0.341235	+	0.939978i	$0.389155\pi$
$620$	−19.1495	−0.769061
$621$	−8.78409	−0.352493
$622$	−42.3498	−1.69807
$623$	−32.5688	−1.30484
$624$	−41.7865	−1.67280
$625$	−31.2287	−1.24915
$626$	−19.0282	−0.760521
$627$	−7.63373	−0.304862
$628$	9.70395	0.387230
$629$	−13.5664	−0.540929
$630$	−3.89139	−0.155037
$631$	0.523279	0.0208314	0.0104157	−	0.999946i	$-0.496685\pi$
$631$	0.523279	0.0208314	0.0104157	+	0.999946i	$0.496685\pi$
$632$	−23.9192	−0.951454
$633$	29.9909	1.19203
$634$	46.0925	1.83057
$635$	3.13692	0.124485
$636$	−12.3987	−0.491642
$637$	−46.4971	−1.84228
$638$	−3.45025	−0.136597
$639$	0.260563	0.0103077
$640$	33.4367	1.32170
$641$	−13.3609	−0.527726	−0.263863	−	0.964560i	$-0.584997\pi$
$641$	−13.3609	−0.527726	−0.263863	+	0.964560i	$0.584997\pi$
$642$	38.6836	1.52672
$643$	−9.81732	−0.387157	−0.193579	−	0.981085i	$-0.562009\pi$
$643$	−9.81732	−0.387157	−0.193579	+	0.981085i	$0.562009\pi$
$644$	7.25037	0.285705
$645$	−24.3512	−0.958826
$646$	−9.59242	−0.377409
$647$	6.90779	0.271573	0.135787	−	0.990738i	$-0.456644\pi$
$647$	6.90779	0.271573	0.135787	+	0.990738i	$0.456644\pi$
$648$	−16.4796	−0.647380
$649$	22.1148	0.868081
$650$	21.4367	0.840817
$651$	50.7355	1.98848
$652$	1.41104	0.0552607
$653$	13.6257	0.533214	0.266607	−	0.963805i	$-0.414097\pi$
$653$	13.6257	0.533214	0.266607	+	0.963805i	$0.414097\pi$
$654$	−20.7389	−0.810956
$655$	48.7277	1.90395
$656$	34.5660	1.34958
$657$	0.240300	0.00937499
$658$	−28.8075	−1.12303
$659$	−13.6298	−0.530942	−0.265471	−	0.964119i	$-0.585527\pi$
$659$	−13.6298	−0.530942	−0.265471	+	0.964119i	$0.585527\pi$
$660$	−9.88826	−0.384900
$661$	29.9549	1.16511	0.582556	−	0.812791i	$-0.302053\pi$
$661$	29.9549	1.16511	0.582556	+	0.812791i	$0.302053\pi$
$662$	40.1974	1.56232
$663$	−21.5615	−0.837379
$664$	24.2806	0.942269
$665$	−24.4165	−0.946832
$666$	−1.79756	−0.0696542
$667$	1.75275	0.0678668
$668$	23.3707	0.904240
$669$	16.8470	0.651343
$670$	42.3017	1.63426
$671$	7.04942	0.272140
$672$	38.4025	1.48141
$673$	−10.3738	−0.399882	−0.199941	−	0.979808i	$-0.564075\pi$
$673$	−10.3738	−0.399882	−0.199941	+	0.979808i	$0.564075\pi$
$674$	−22.1488	−0.853139
$675$	13.2600	0.510379
$676$	8.88805	0.341848
$677$	−12.4111	−0.476997	−0.238498	−	0.971143i	$-0.576655\pi$
$677$	−12.4111	−0.476997	−0.238498	+	0.971143i	$0.576655\pi$
$678$	50.4699	1.93828
$679$	−70.0356	−2.68772
$680$	12.3068	0.471943
$681$	33.2131	1.27273
$682$	23.7802	0.910590
$683$	37.1084	1.41991	0.709956	−	0.704246i	$-0.248715\pi$
$683$	37.1084	1.41991	0.709956	+	0.704246i	$0.248715\pi$
$684$	−0.425021	−0.0162511
$685$	44.7216	1.70873
$686$	21.0388	0.803267
$687$	1.73404	0.0661579
$688$	24.6257	0.938847
$689$	−32.2549	−1.22881
$690$	15.0220	0.571876
$691$	15.0165	0.571253	0.285627	−	0.958341i	$-0.407798\pi$
$691$	15.0165	0.571253	0.285627	+	0.958341i	$0.407798\pi$
$692$	3.40353	0.129383
$693$	1.61595	0.0613847
$694$	28.0130	1.06336
$695$	2.76512	0.104887
$696$	3.08464	0.116923
$697$	17.8358	0.675579
$698$	47.4556	1.79622
$699$	17.7719	0.672194
$700$	−10.9448	−0.413675
$701$	−32.5487	−1.22935	−0.614673	−	0.788782i	$-0.710712\pi$
$701$	−32.5487	−1.22935	−0.614673	+	0.788782i	$0.710712\pi$
$702$	40.6037	1.53249
$703$	−11.2788	−0.425388
$704$	−1.90442	−0.0717757
$705$	−19.9588	−0.751693
$706$	14.0391	0.528368
$707$	−6.61641	−0.248836
$708$	19.9620	0.750218
$709$	39.9748	1.50128	0.750642	−	0.660709i	$-0.229744\pi$
$709$	39.9748	1.50128	0.750642	+	0.660709i	$0.229744\pi$
$710$	6.33301	0.237674
$711$	−2.73433	−0.102545
$712$	13.6477	0.511468
$713$	−12.0805	−0.452418
$714$	32.9205	1.23202
$715$	−25.7240	−0.962022
$716$	15.7965	0.590343
$717$	21.2084	0.792043
$718$	−7.72213	−0.288187
$719$	0.921437	0.0343638	0.0171819	−	0.999852i	$-0.494531\pi$
$719$	0.921437	0.0343638	0.0171819	+	0.999852i	$0.494531\pi$
$720$	2.72649	0.101610
$721$	−33.2076	−1.23672
$722$	24.9604	0.928928
$723$	−14.2736	−0.530840
$724$	−17.2753	−0.642031
$725$	−2.64587	−0.0982651
$726$	−21.8152	−0.809637
$727$	21.5936	0.800862	0.400431	−	0.916327i	$-0.368860\pi$
$727$	21.5936	0.800862	0.400431	+	0.916327i	$0.368860\pi$
$728$	33.1942	1.23026
$729$	24.9995	0.925906
$730$	5.84053	0.216168
$731$	12.7067	0.469974
$732$	6.36319	0.235190
$733$	−22.0973	−0.816183	−0.408092	−	0.912941i	$-0.633806\pi$
$733$	−22.0973	−0.816183	−0.408092	+	0.912941i	$0.633806\pi$
$734$	1.95947	0.0723255
$735$	49.1861	1.81426
$736$	−9.14392	−0.337050
$737$	−17.5663	−0.647062
$738$	2.36326	0.0869928
$739$	42.3637	1.55837	0.779187	−	0.626792i	$-0.215632\pi$
$739$	42.3637	1.55837	0.779187	+	0.626792i	$0.215632\pi$
$740$	−14.6099	−0.537069
$741$	−17.9257	−0.658518
$742$	49.2473	1.80792
$743$	2.31320	0.0848630	0.0424315	−	0.999099i	$-0.486490\pi$
$743$	2.31320	0.0848630	0.0424315	+	0.999099i	$0.486490\pi$
$744$	−21.2603	−0.779440
$745$	−12.9237	−0.473486
$746$	36.5508	1.33822
$747$	2.77564	0.101555
$748$	5.15980	0.188661
$749$	−51.3801	−1.87739
$750$	20.1761	0.736727
$751$	−18.2167	−0.664736	−0.332368	−	0.943150i	$-0.607848\pi$
$751$	−18.2167	−0.664736	−0.332368	+	0.943150i	$0.607848\pi$
$752$	20.1839	0.736030
$753$	−36.3676	−1.32531
$754$	−8.10195	−0.295056
$755$	−6.55100	−0.238415
$756$	−20.7308	−0.753972
$757$	12.5485	0.456083	0.228041	−	0.973651i	$-0.426768\pi$
$757$	12.5485	0.456083	0.228041	+	0.973651i	$0.426768\pi$
$758$	−61.7456	−2.24270
$759$	−6.23804	−0.226427
$760$	10.2316	0.371137
$761$	24.6831	0.894763	0.447382	−	0.894343i	$-0.352357\pi$
$761$	24.6831	0.894763	0.447382	+	0.894343i	$0.352357\pi$
$762$	−3.51628	−0.127381
$763$	27.5457	0.997223
$764$	4.88847	0.176859
$765$	1.40685	0.0508647
$766$	3.08575	0.111493
$767$	51.9305	1.87510
$768$	−34.0587	−1.22899
$769$	−35.7018	−1.28744	−0.643720	−	0.765261i	$-0.722610\pi$
$769$	−35.7018	−1.28744	−0.643720	+	0.765261i	$0.722610\pi$
$770$	39.2758	1.41540
$771$	−42.0477	−1.51431
$772$	−25.6652	−0.923712
$773$	−7.51031	−0.270127	−0.135064	−	0.990837i	$-0.543124\pi$
$773$	−7.51031	−0.270127	−0.135064	+	0.990837i	$0.543124\pi$
$774$	1.68365	0.0605175
$775$	18.2361	0.655062
$776$	29.3479	1.05353
$777$	38.7080	1.38864
$778$	−2.49082	−0.0893003
$779$	14.8283	0.531278
$780$	−23.2199	−0.831404
$781$	−2.62986	−0.0941036
$782$	−7.83862	−0.280308
$783$	−5.01160	−0.179100
$784$	−49.7406	−1.77645
$785$	−26.7044	−0.953122
$786$	−54.6205	−1.94825
$787$	4.92388	0.175518	0.0877588	−	0.996142i	$-0.472030\pi$
$787$	4.92388	0.175518	0.0877588	+	0.996142i	$0.472030\pi$
$788$	−3.95716	−0.140968
$789$	33.1129	1.17885
$790$	−66.4582	−2.36448
$791$	−67.0349	−2.38349
$792$	−0.677149	−0.0240614
$793$	16.5536	0.587836
$794$	66.5779	2.36276
$795$	34.1202	1.21012
$796$	8.96774	0.317853
$797$	−44.0689	−1.56100	−0.780499	−	0.625157i	$-0.785035\pi$
$797$	−44.0689	−1.56100	−0.780499	+	0.625157i	$0.785035\pi$
$798$	27.3693	0.968862
$799$	10.4147	0.368446
$800$	13.8032	0.488018
$801$	1.56014	0.0551247
$802$	27.5545	0.972985
$803$	−2.42534	−0.0855885
$804$	−15.8563	−0.559208
$805$	−19.9524	−0.703230
$806$	55.8412	1.96692
$807$	−46.4634	−1.63559
$808$	2.77256	0.0975382
$809$	35.8140	1.25915	0.629577	−	0.776938i	$-0.283228\pi$
$809$	35.8140	1.25915	0.629577	+	0.776938i	$0.283228\pi$
$810$	−45.7877	−1.60881
$811$	−28.5435	−1.00230	−0.501149	−	0.865361i	$-0.667089\pi$
$811$	−28.5435	−1.00230	−0.501149	+	0.865361i	$0.667089\pi$
$812$	4.13657	0.145165
$813$	36.4359	1.27786
$814$	18.1428	0.635905
$815$	−3.88307	−0.136018
$816$	−23.0656	−0.807458
$817$	10.5640	0.369589
$818$	11.3127	0.395540
$819$	3.79460	0.132594
$820$	19.2076	0.670759
$821$	0.641300	0.0223815	0.0111908	−	0.999937i	$-0.496438\pi$
$821$	0.641300	0.0223815	0.0111908	+	0.999937i	$0.496438\pi$
$822$	−50.1300	−1.74848
$823$	17.8126	0.620907	0.310453	−	0.950589i	$-0.399519\pi$
$823$	17.8126	0.620907	0.310453	+	0.950589i	$0.399519\pi$
$824$	13.9154	0.484766
$825$	9.41664	0.327845
$826$	−79.2883	−2.75879
$827$	38.6438	1.34378	0.671889	−	0.740652i	$-0.265483\pi$
$827$	38.6438	1.34378	0.671889	+	0.740652i	$0.265483\pi$
$828$	−0.347313	−0.0120700
$829$	39.9589	1.38783	0.693916	−	0.720056i	$-0.255884\pi$
$829$	39.9589	1.38783	0.693916	+	0.720056i	$0.255884\pi$
$830$	67.4622	2.34165
$831$	−3.26538	−0.113275
$832$	−4.47202	−0.155039
$833$	−25.6658	−0.889267
$834$	−3.09951	−0.107327
$835$	−64.3142	−2.22568
$836$	4.28973	0.148363
$837$	34.5415	1.19393
$838$	−30.2420	−1.04469
$839$	−1.46409	−0.0505462	−0.0252731	−	0.999681i	$-0.508046\pi$
$839$	−1.46409	−0.0505462	−0.0252731	+	0.999681i	$0.508046\pi$
$840$	−35.1139	−1.21155
$841$	1.00000	0.0344828
$842$	−37.3598	−1.28750
$843$	−6.52096	−0.224594
$844$	−16.8532	−0.580111
$845$	−24.4591	−0.841420
$846$	1.37996	0.0474440
$847$	28.9753	0.995602
$848$	−34.5049	−1.18490
$849$	3.13845	0.107711
$850$	11.8328	0.405861
$851$	−9.21668	−0.315944
$852$	−2.37385	−0.0813268
$853$	57.5784	1.97145	0.985723	−	0.168376i	$-0.0538522\pi$
$853$	57.5784	1.97145	0.985723	+	0.168376i	$0.0538522\pi$
$854$	−25.2743	−0.864870
$855$	1.16962	0.0400002
$856$	21.5304	0.735894
$857$	8.96067	0.306091	0.153045	−	0.988219i	$-0.451092\pi$
$857$	8.96067	0.306091	0.153045	+	0.988219i	$0.451092\pi$
$858$	28.8348	0.984405
$859$	−37.8543	−1.29157	−0.645786	−	0.763518i	$-0.723470\pi$
$859$	−37.8543	−1.29157	−0.645786	+	0.763518i	$0.723470\pi$
$860$	13.6840	0.466620
$861$	−50.8895	−1.73431
$862$	30.7510	1.04738
$863$	14.1478	0.481596	0.240798	−	0.970575i	$-0.422591\pi$
$863$	14.1478	0.481596	0.240798	+	0.970575i	$0.422591\pi$
$864$	26.1450	0.889471
$865$	−9.36623	−0.318461
$866$	57.7482	1.96236
$867$	18.4956	0.628142
$868$	−28.5105	−0.967709
$869$	27.5975	0.936182
$870$	8.57050	0.290567
$871$	−41.2496	−1.39769
$872$	−11.5428	−0.390889
$873$	3.35490	0.113546
$874$	−6.51684	−0.220435
$875$	−26.7982	−0.905944
$876$	−2.18925	−0.0739678
$877$	1.85034	0.0624817	0.0312408	−	0.999512i	$-0.490054\pi$
$877$	1.85034	0.0624817	0.0312408	+	0.999512i	$0.490054\pi$
$878$	−68.5547	−2.31361
$879$	−18.9764	−0.640057
$880$	−27.5184	−0.927647
$881$	−53.7460	−1.81075	−0.905375	−	0.424613i	$-0.860410\pi$
$881$	−53.7460	−1.81075	−0.905375	+	0.424613i	$0.860410\pi$
$882$	−3.40074	−0.114509
$883$	28.7143	0.966312	0.483156	−	0.875534i	$-0.339490\pi$
$883$	28.7143	0.966312	0.483156	+	0.875534i	$0.339490\pi$
$884$	12.1164	0.407517
$885$	−54.9337	−1.84658
$886$	−62.1894	−2.08929
$887$	−13.0560	−0.438377	−0.219188	−	0.975683i	$-0.570341\pi$
$887$	−13.0560	−0.438377	−0.219188	+	0.975683i	$0.570341\pi$
$888$	−16.2203	−0.544317
$889$	4.67038	0.156639
$890$	37.9193	1.27106
$891$	19.0139	0.636988
$892$	−9.46708	−0.316981
$893$	8.65856	0.289748
$894$	14.4866	0.484503
$895$	−43.4706	−1.45306
$896$	49.7820	1.66310
$897$	−14.6483	−0.489093
$898$	48.5409	1.61983
$899$	−6.89231	−0.229871
$900$	0.524288	0.0174763
$901$	−17.8043	−0.593147
$902$	−23.8524	−0.794197
$903$	−36.2550	−1.20649
$904$	28.0904	0.934274
$905$	47.5401	1.58029
$906$	7.34323	0.243962
$907$	43.7318	1.45209	0.726045	−	0.687648i	$-0.241357\pi$
$907$	43.7318	1.45209	0.726045	+	0.687648i	$0.241357\pi$
$908$	−18.6639	−0.619383
$909$	0.316945	0.0105124
$910$	92.2284	3.05734
$911$	−5.69697	−0.188749	−0.0943746	−	0.995537i	$-0.530085\pi$
$911$	−5.69697	−0.188749	−0.0943746	+	0.995537i	$0.530085\pi$
$912$	−19.1762	−0.634987
$913$	−28.0145	−0.927143
$914$	29.6410	0.980438
$915$	−17.5109	−0.578894
$916$	−0.974435	−0.0321962
$917$	72.5478	2.39574
$918$	22.4128	0.739732
$919$	29.1840	0.962691	0.481345	−	0.876531i	$-0.340148\pi$
$919$	29.1840	0.962691	0.481345	+	0.876531i	$0.340148\pi$
$920$	8.36090	0.275651
$921$	0.462007	0.0152236
$922$	−27.9879	−0.921732
$923$	−6.17549	−0.203269
$924$	−14.7220	−0.484319
$925$	13.9130	0.457458
$926$	17.9574	0.590117
$927$	1.59074	0.0522467
$928$	−5.21690	−0.171253
$929$	27.8507	0.913750	0.456875	−	0.889531i	$-0.348969\pi$
$929$	27.8507	0.913750	0.456875	+	0.889531i	$0.348969\pi$
$930$	−59.0706	−1.93700
$931$	−21.3379	−0.699323
$932$	−9.98681	−0.327129
$933$	−43.6847	−1.43017
$934$	−19.0031	−0.621799
$935$	−14.1993	−0.464367
$936$	−1.59010	−0.0519740
$937$	−13.5946	−0.444116	−0.222058	−	0.975033i	$-0.571277\pi$
$937$	−13.5946	−0.444116	−0.222058	+	0.975033i	$0.571277\pi$
$938$	62.9805	2.05639
$939$	−19.6280	−0.640536
$940$	11.2157	0.365817
$941$	47.4444	1.54664	0.773322	−	0.634014i	$-0.218594\pi$
$941$	47.4444	1.54664	0.773322	+	0.634014i	$0.218594\pi$
$942$	29.9339	0.975298
$943$	12.1172	0.394590
$944$	55.5531	1.80810
$945$	57.0494	1.85582
$946$	−16.9930	−0.552492
$947$	31.7174	1.03068	0.515338	−	0.856987i	$-0.327666\pi$
$947$	31.7174	1.03068	0.515338	+	0.856987i	$0.327666\pi$
$948$	24.9110	0.809072
$949$	−5.69525	−0.184876
$950$	9.83750	0.319171
$951$	47.5453	1.54176
$952$	18.3228	0.593846
$953$	−3.23737	−0.104869	−0.0524343	−	0.998624i	$-0.516698\pi$
$953$	−3.23737	−0.104869	−0.0524343	+	0.998624i	$0.516698\pi$
$954$	−2.35909	−0.0763782
$955$	−13.4527	−0.435318
$956$	−11.9179	−0.385454
$957$	−3.55900	−0.115046
$958$	−52.8930	−1.70889
$959$	66.5834	2.15009
$960$	4.73064	0.152681
$961$	16.5039	0.532384
$962$	42.6033	1.37359
$963$	2.46125	0.0793127
$964$	8.02095	0.258338
$965$	70.6285	2.27361
$966$	22.3653	0.719592
$967$	41.2621	1.32690	0.663450	−	0.748221i	$-0.269092\pi$
$967$	41.2621	1.32690	0.663450	+	0.748221i	$0.269092\pi$
$968$	−12.1419	−0.390254
$969$	−9.89478	−0.317866
$970$	81.5414	2.61814
$971$	14.4091	0.462411	0.231206	−	0.972905i	$-0.425733\pi$
$971$	14.4091	0.462411	0.231206	+	0.972905i	$0.425733\pi$
$972$	2.05600	0.0659463
$973$	4.11682	0.131979
$974$	−20.9990	−0.672851
$975$	22.1124	0.708163
$976$	17.7084	0.566831
$977$	43.1375	1.38009	0.690045	−	0.723766i	$-0.257591\pi$
$977$	43.1375	1.38009	0.690045	+	0.723766i	$0.257591\pi$
$978$	4.35266	0.139183
$979$	−15.7464	−0.503258
$980$	−27.6398	−0.882922
$981$	−1.31952	−0.0421290
$982$	−39.8552	−1.27183
$983$	−23.1476	−0.738293	−0.369146	−	0.929371i	$-0.620350\pi$
$983$	−23.1476	−0.738293	−0.369146	+	0.929371i	$0.620350\pi$
$984$	21.3248	0.679811
$985$	10.8898	0.346977
$986$	−4.47218	−0.142423
$987$	−29.7155	−0.945855
$988$	10.0733	0.320473
$989$	8.63259	0.274501
$990$	−1.88142	−0.0597955
$991$	−32.6835	−1.03823	−0.519113	−	0.854706i	$-0.673738\pi$
$991$	−32.6835	−1.03823	−0.519113	+	0.854706i	$0.673738\pi$
$992$	35.9565	1.14162
$993$	41.4644	1.31583
$994$	9.42884	0.299065
$995$	−24.6785	−0.782360
$996$	−25.2874	−0.801261
$997$	18.0248	0.570852	0.285426	−	0.958401i	$-0.407865\pi$
$997$	18.0248	0.570852	0.285426	+	0.958401i	$0.407865\pi$
$998$	−1.96477	−0.0621936
$999$	26.3530	0.833773

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4031.2.a.c.1.14	✓	61

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4031.2.a.c.1.14	✓	61	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4031 = 29 \cdot 139 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4031.a (trivial)

\(f(q)\)	\(=\)	\(q-1.73344 q^{2} -1.78807 q^{3} +1.00480 q^{4} -2.76512 q^{5} +3.09951 q^{6} -4.11682 q^{7} +1.72512 q^{8} +0.197207 q^{9} +O(q^{10})\)	\(q-1.73344 q^{2} -1.78807 q^{3} +1.00480 q^{4} -2.76512 q^{5} +3.09951 q^{6} -4.11682 q^{7} +1.72512 q^{8} +0.197207 q^{9} +4.79315 q^{10} -1.99041 q^{11} -1.79665 q^{12} -4.67393 q^{13} +7.13623 q^{14} +4.94423 q^{15} -4.99998 q^{16} -2.57995 q^{17} -0.341846 q^{18} -2.14491 q^{19} -2.77838 q^{20} +7.36117 q^{21} +3.45025 q^{22} -1.75275 q^{23} -3.08464 q^{24} +2.64587 q^{25} +8.10195 q^{26} +5.01160 q^{27} -4.13657 q^{28} -1.00000 q^{29} -8.57050 q^{30} +6.89231 q^{31} +5.21690 q^{32} +3.55900 q^{33} +4.47218 q^{34} +11.3835 q^{35} +0.198153 q^{36} +5.25840 q^{37} +3.71806 q^{38} +8.35733 q^{39} -4.77016 q^{40} -6.91323 q^{41} -12.7601 q^{42} -4.92517 q^{43} -1.99996 q^{44} -0.545301 q^{45} +3.03828 q^{46} -4.03679 q^{47} +8.94033 q^{48} +9.94817 q^{49} -4.58644 q^{50} +4.61314 q^{51} -4.69635 q^{52} +6.90102 q^{53} -8.68728 q^{54} +5.50372 q^{55} -7.10200 q^{56} +3.83526 q^{57} +1.73344 q^{58} -11.1107 q^{59} +4.96795 q^{60} -3.54169 q^{61} -11.9474 q^{62} -0.811866 q^{63} +0.956800 q^{64} +12.9240 q^{65} -6.16929 q^{66} +8.82546 q^{67} -2.59233 q^{68} +3.13405 q^{69} -19.7325 q^{70} +1.32126 q^{71} +0.340206 q^{72} +1.21852 q^{73} -9.11510 q^{74} -4.73101 q^{75} -2.15520 q^{76} +8.19415 q^{77} -14.4869 q^{78} -13.8652 q^{79} +13.8255 q^{80} -9.55273 q^{81} +11.9836 q^{82} +14.0747 q^{83} +7.39648 q^{84} +7.13386 q^{85} +8.53746 q^{86} +1.78807 q^{87} -3.43369 q^{88} +7.91115 q^{89} +0.945244 q^{90} +19.2417 q^{91} -1.76116 q^{92} -12.3240 q^{93} +6.99752 q^{94} +5.93093 q^{95} -9.32820 q^{96} +17.0121 q^{97} -17.2445 q^{98} -0.392523 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 61 q - q^{2} - 4 q^{3} + 43 q^{4} - 7 q^{5} - 13 q^{6} - 10 q^{7} - 6 q^{8} + 23 q^{9}+O(q^{10}) \) 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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