LMFDB - Embedded newform 4031.2.a.c.1.24

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			1.24
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)

$f(q)$	$=$	$q-0.705690 q^{2} -2.07165 q^{3} -1.50200 q^{4} +1.36937 q^{5} +1.46195 q^{6} -1.20985 q^{7} +2.47133 q^{8} +1.29175 q^{9} +O(q^{10})$	\(q-0.705690 q^{2} -2.07165 q^{3} -1.50200 q^{4} +1.36937 q^{5} +1.46195 q^{6} -1.20985 q^{7} +2.47133 q^{8} +1.29175 q^{9} -0.966352 q^{10} -5.09471 q^{11} +3.11163 q^{12} +0.515934 q^{13} +0.853776 q^{14} -2.83686 q^{15} +1.26001 q^{16} -4.55177 q^{17} -0.911576 q^{18} +6.78980 q^{19} -2.05680 q^{20} +2.50638 q^{21} +3.59529 q^{22} +3.04730 q^{23} -5.11974 q^{24} -3.12482 q^{25} -0.364090 q^{26} +3.53890 q^{27} +1.81719 q^{28} -1.00000 q^{29} +2.00195 q^{30} +0.516425 q^{31} -5.83183 q^{32} +10.5545 q^{33} +3.21214 q^{34} -1.65673 q^{35} -1.94021 q^{36} +4.59160 q^{37} -4.79150 q^{38} -1.06884 q^{39} +3.38416 q^{40} +4.88761 q^{41} -1.76873 q^{42} -5.56355 q^{43} +7.65227 q^{44} +1.76889 q^{45} -2.15045 q^{46} +4.43939 q^{47} -2.61031 q^{48} -5.53627 q^{49} +2.20516 q^{50} +9.42969 q^{51} -0.774933 q^{52} +3.55406 q^{53} -2.49737 q^{54} -6.97655 q^{55} -2.98993 q^{56} -14.0661 q^{57} +0.705690 q^{58} -1.30679 q^{59} +4.26097 q^{60} -6.94111 q^{61} -0.364436 q^{62} -1.56282 q^{63} +1.59545 q^{64} +0.706505 q^{65} -7.44820 q^{66} -0.645621 q^{67} +6.83676 q^{68} -6.31296 q^{69} +1.16914 q^{70} +9.52163 q^{71} +3.19234 q^{72} -0.281151 q^{73} -3.24024 q^{74} +6.47355 q^{75} -10.1983 q^{76} +6.16382 q^{77} +0.754268 q^{78} +5.72458 q^{79} +1.72542 q^{80} -11.2066 q^{81} -3.44914 q^{82} +15.9026 q^{83} -3.76459 q^{84} -6.23306 q^{85} +3.92614 q^{86} +2.07165 q^{87} -12.5907 q^{88} +14.4515 q^{89} -1.24829 q^{90} -0.624200 q^{91} -4.57705 q^{92} -1.06985 q^{93} -3.13283 q^{94} +9.29775 q^{95} +12.0815 q^{96} +2.55664 q^{97} +3.90689 q^{98} -6.58110 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.705690	−0.498998	−0.249499	−	0.968375i	$-0.580266\pi$
$2$	−0.705690	−0.498998	−0.249499	+	0.968375i	$0.580266\pi$
$3$	−2.07165	−1.19607	−0.598035	−	0.801470i	$-0.704052\pi$
$3$	−2.07165	−1.19607	−0.598035	+	0.801470i	$0.704052\pi$
$4$	−1.50200	−0.751001
$5$	1.36937	0.612401	0.306201	−	0.951967i	$-0.400942\pi$
$5$	1.36937	0.612401	0.306201	+	0.951967i	$0.400942\pi$
$6$	1.46195	0.596837
$7$	−1.20985	−0.457279	−0.228639	−	0.973511i	$-0.573428\pi$
$7$	−1.20985	−0.457279	−0.228639	+	0.973511i	$0.573428\pi$
$8$	2.47133	0.873746
$9$	1.29175	0.430584
$10$	−0.966352	−0.305587
$11$	−5.09471	−1.53611	−0.768057	−	0.640381i	$-0.778776\pi$
$11$	−5.09471	−1.53611	−0.768057	+	0.640381i	$0.778776\pi$
$12$	3.11163	0.898249
$13$	0.515934	0.143094	0.0715472	−	0.997437i	$-0.477206\pi$
$13$	0.515934	0.143094	0.0715472	+	0.997437i	$0.477206\pi$
$14$	0.853776	0.228181
$15$	−2.83686	−0.732475
$16$	1.26001	0.315003
$17$	−4.55177	−1.10397	−0.551983	−	0.833856i	$-0.686129\pi$
$17$	−4.55177	−1.10397	−0.551983	+	0.833856i	$0.686129\pi$
$18$	−0.911576	−0.214861
$19$	6.78980	1.55769	0.778843	−	0.627218i	$-0.215807\pi$
$19$	6.78980	1.55769	0.778843	+	0.627218i	$0.215807\pi$
$20$	−2.05680	−0.459914
$21$	2.50638	0.546937
$22$	3.59529	0.766519
$23$	3.04730	0.635406	0.317703	−	0.948190i	$-0.397088\pi$
$23$	3.04730	0.635406	0.317703	+	0.948190i	$0.397088\pi$
$24$	−5.11974	−1.04506
$25$	−3.12482	−0.624965
$26$	−0.364090	−0.0714038
$27$	3.53890	0.681062
$28$	1.81719	0.343416
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	2.00195	0.365504
$31$	0.516425	0.0927527	0.0463764	−	0.998924i	$-0.485233\pi$
$31$	0.516425	0.0927527	0.0463764	+	0.998924i	$0.485233\pi$
$32$	−5.83183	−1.03093
$33$	10.5545	1.83730
$34$	3.21214	0.550877
$35$	−1.65673	−0.280038
$36$	−1.94021	−0.323369
$37$	4.59160	0.754854	0.377427	−	0.926039i	$-0.376809\pi$
$37$	4.59160	0.754854	0.377427	+	0.926039i	$0.376809\pi$
$38$	−4.79150	−0.777283
$39$	−1.06884	−0.171151
$40$	3.38416	0.535083
$41$	4.88761	0.763316	0.381658	−	0.924304i	$-0.375353\pi$
$41$	4.88761	0.763316	0.381658	+	0.924304i	$0.375353\pi$
$42$	−1.76873	−0.272921
$43$	−5.56355	−0.848434	−0.424217	−	0.905561i	$-0.639451\pi$
$43$	−5.56355	−0.848434	−0.424217	+	0.905561i	$0.639451\pi$
$44$	7.65227	1.15362
$45$	1.76889	0.263690
$46$	−2.15045	−0.317067
$47$	4.43939	0.647551	0.323776	−	0.946134i	$-0.395048\pi$
$47$	4.43939	0.647551	0.323776	+	0.946134i	$0.395048\pi$
$48$	−2.61031	−0.376765
$49$	−5.53627	−0.790896
$50$	2.20516	0.311856
$51$	9.42969	1.32042
$52$	−0.774933	−0.107464
$53$	3.55406	0.488187	0.244094	−	0.969752i	$-0.421510\pi$
$53$	3.55406	0.488187	0.244094	+	0.969752i	$0.421510\pi$
$54$	−2.49737	−0.339849
$55$	−6.97655	−0.940718
$56$	−2.98993	−0.399546
$57$	−14.0661	−1.86310
$58$	0.705690	0.0926617
$59$	−1.30679	−0.170130	−0.0850648	−	0.996375i	$-0.527110\pi$
$59$	−1.30679	−0.170130	−0.0850648	+	0.996375i	$0.527110\pi$
$60$	4.26097	0.550089
$61$	−6.94111	−0.888718	−0.444359	−	0.895849i	$-0.646569\pi$
$61$	−6.94111	−0.888718	−0.444359	+	0.895849i	$0.646569\pi$
$62$	−0.364436	−0.0462835
$63$	−1.56282	−0.196897
$64$	1.59545	0.199431
$65$	0.706505	0.0876311
$66$	−7.44820	−0.916810
$67$	−0.645621	−0.0788752	−0.0394376	−	0.999222i	$-0.512557\pi$
$67$	−0.645621	−0.0788752	−0.0394376	+	0.999222i	$0.512557\pi$
$68$	6.83676	0.829079
$69$	−6.31296	−0.759991
$70$	1.16914	0.139738
$71$	9.52163	1.13001	0.565005	−	0.825088i	$-0.308874\pi$
$71$	9.52163	1.13001	0.565005	+	0.825088i	$0.308874\pi$
$72$	3.19234	0.376221
$73$	−0.281151	−0.0329062	−0.0164531	−	0.999865i	$-0.505237\pi$
$73$	−0.281151	−0.0329062	−0.0164531	+	0.999865i	$0.505237\pi$
$74$	−3.24024	−0.376671
$75$	6.47355	0.747502
$76$	−10.1983	−1.16982
$77$	6.16382	0.702432
$78$	0.754268	0.0854040
$79$	5.72458	0.644065	0.322033	−	0.946729i	$-0.395634\pi$
$79$	5.72458	0.644065	0.322033	+	0.946729i	$0.395634\pi$
$80$	1.72542	0.192908
$81$	−11.2066	−1.24518
$82$	−3.44914	−0.380894
$83$	15.9026	1.74553	0.872767	−	0.488138i	$-0.162324\pi$
$83$	15.9026	1.74553	0.872767	+	0.488138i	$0.162324\pi$
$84$	−3.76459	−0.410750
$85$	−6.23306	−0.676070
$86$	3.92614	0.423367
$87$	2.07165	0.222105
$88$	−12.5907	−1.34217
$89$	14.4515	1.53185	0.765926	−	0.642929i	$-0.222281\pi$
$89$	14.4515	1.53185	0.765926	+	0.642929i	$0.222281\pi$
$90$	−1.24829	−0.131581
$91$	−0.624200	−0.0654340
$92$	−4.57705	−0.477191
$93$	−1.06985	−0.110939
$94$	−3.13283	−0.323127
$95$	9.29775	0.953929
$96$	12.0815	1.23307
$97$	2.55664	0.259588	0.129794	−	0.991541i	$-0.458568\pi$
$97$	2.55664	0.259588	0.129794	+	0.991541i	$0.458568\pi$
$98$	3.90689	0.394656
$99$	−6.58110	−0.661426
$100$	4.69349	0.469349
$101$	−3.90231	−0.388294	−0.194147	−	0.980972i	$-0.562194\pi$
$101$	−3.90231	−0.388294	−0.194147	+	0.980972i	$0.562194\pi$
$102$	−6.65444	−0.658888
$103$	−1.09558	−0.107950	−0.0539752	−	0.998542i	$-0.517189\pi$
$103$	−1.09558	−0.107950	−0.0539752	+	0.998542i	$0.517189\pi$
$104$	1.27504	0.125028
$105$	3.43217	0.334945
$106$	−2.50806	−0.243605
$107$	−8.60063	−0.831455	−0.415727	−	0.909489i	$-0.636473\pi$
$107$	−8.60063	−0.831455	−0.415727	+	0.909489i	$0.636473\pi$
$108$	−5.31543	−0.511478
$109$	18.3815	1.76063	0.880313	−	0.474393i	$-0.157333\pi$
$109$	18.3815	1.76063	0.880313	+	0.474393i	$0.157333\pi$
$110$	4.92329	0.469417
$111$	−9.51220	−0.902858
$112$	−1.52442	−0.144044
$113$	−6.16025	−0.579507	−0.289754	−	0.957101i	$-0.593573\pi$
$113$	−6.16025	−0.579507	−0.289754	+	0.957101i	$0.593573\pi$
$114$	9.92632	0.929685
$115$	4.17289	0.389124
$116$	1.50200	0.139457
$117$	0.666458	0.0616141
$118$	0.922189	0.0848944
$119$	5.50693	0.504820
$120$	−7.01082	−0.639997
$121$	14.9561	1.35965
$122$	4.89828	0.443469
$123$	−10.1254	−0.912980
$124$	−0.775671	−0.0696573
$125$	−11.1259	−0.995130
$126$	1.10287	0.0982511
$127$	4.95500	0.439685	0.219842	−	0.975535i	$-0.429446\pi$
$127$	4.95500	0.439685	0.219842	+	0.975535i	$0.429446\pi$
$128$	10.5378	0.931416
$129$	11.5258	1.01479
$130$	−0.498574	−0.0437278
$131$	−7.15132	−0.624814	−0.312407	−	0.949948i	$-0.601135\pi$
$131$	−7.15132	−0.624814	−0.312407	+	0.949948i	$0.601135\pi$
$132$	−15.8529	−1.37981
$133$	−8.21461	−0.712297
$134$	0.455609	0.0393586
$135$	4.84607	0.417083
$136$	−11.2489	−0.964586
$137$	6.12981	0.523705	0.261852	−	0.965108i	$-0.415667\pi$
$137$	6.12981	0.523705	0.261852	+	0.965108i	$0.415667\pi$
$138$	4.45499	0.379234
$139$	−1.00000	−0.0848189
$139$	−1.00000	−0.0848189
$140$	2.48841	0.210309
$141$	−9.19688	−0.774517
$142$	−6.71932	−0.563873
$143$	−2.62854	−0.219809
$144$	1.62762	0.135635
$145$	−1.36937	−0.113720
$146$	0.198405	0.0164201
$147$	11.4692	0.945967
$148$	−6.89658	−0.566896
$149$	3.72515	0.305176	0.152588	−	0.988290i	$-0.451239\pi$
$149$	3.72515	0.305176	0.152588	+	0.988290i	$0.451239\pi$
$150$	−4.56832	−0.373002
$151$	−8.97954	−0.730745	−0.365372	−	0.930861i	$-0.619058\pi$
$151$	−8.97954	−0.730745	−0.365372	+	0.930861i	$0.619058\pi$
$152$	16.7798	1.36102
$153$	−5.87975	−0.475350
$154$	−4.34975	−0.350513
$155$	0.707178	0.0568019
$156$	1.60539	0.128534
$157$	9.10387	0.726568	0.363284	−	0.931679i	$-0.381656\pi$
$157$	9.10387	0.726568	0.363284	+	0.931679i	$0.381656\pi$
$158$	−4.03978	−0.321387
$159$	−7.36277	−0.583906
$160$	−7.98594	−0.631344
$161$	−3.68676	−0.290558
$162$	7.90841	0.621343
$163$	−7.74582	−0.606699	−0.303350	−	0.952879i	$-0.598105\pi$
$163$	−7.74582	−0.606699	−0.303350	+	0.952879i	$0.598105\pi$
$164$	−7.34120	−0.573251
$165$	14.4530	1.12517
$166$	−11.2223	−0.871018
$167$	−7.16689	−0.554591	−0.277295	−	0.960785i	$-0.589438\pi$
$167$	−7.16689	−0.554591	−0.277295	+	0.960785i	$0.589438\pi$
$168$	6.19409	0.477884
$169$	−12.7338	−0.979524
$170$	4.39861	0.337358
$171$	8.77073	0.670715
$172$	8.35646	0.637174
$173$	−16.2783	−1.23762	−0.618809	−	0.785542i	$-0.712384\pi$
$173$	−16.2783	−1.23762	−0.618809	+	0.785542i	$0.712384\pi$
$174$	−1.46195	−0.110830
$175$	3.78055	0.285783
$176$	−6.41939	−0.483880
$177$	2.70722	0.203487
$178$	−10.1983	−0.764392
$179$	−2.76598	−0.206739	−0.103370	−	0.994643i	$-0.532962\pi$
$179$	−2.76598	−0.206739	−0.103370	+	0.994643i	$0.532962\pi$
$180$	−2.65687	−0.198031
$181$	−15.4788	−1.15053	−0.575265	−	0.817967i	$-0.695101\pi$
$181$	−15.4788	−1.15053	−0.575265	+	0.817967i	$0.695101\pi$
$182$	0.440492	0.0326514
$183$	14.3796	1.06297
$184$	7.53088	0.555184
$185$	6.28760	0.462273
$186$	0.754986	0.0553583
$187$	23.1900	1.69582
$188$	−6.66797	−0.486312
$189$	−4.28152	−0.311435
$190$	−6.56133	−0.476009
$191$	3.98139	0.288083	0.144042	−	0.989572i	$-0.453990\pi$
$191$	3.98139	0.288083	0.144042	+	0.989572i	$0.453990\pi$
$192$	−3.30522	−0.238533
$193$	−3.19171	−0.229744	−0.114872	−	0.993380i	$-0.536646\pi$
$193$	−3.19171	−0.229744	−0.114872	+	0.993380i	$0.536646\pi$
$194$	−1.80420	−0.129534
$195$	−1.46363	−0.104813
$196$	8.31549	0.593964
$197$	3.65316	0.260277	0.130138	−	0.991496i	$-0.458458\pi$
$197$	3.65316	0.260277	0.130138	+	0.991496i	$0.458458\pi$
$198$	4.64422	0.330050
$199$	9.06208	0.642394	0.321197	−	0.947012i	$-0.395915\pi$
$199$	9.06208	0.642394	0.321197	+	0.947012i	$0.395915\pi$
$200$	−7.72247	−0.546061
$201$	1.33750	0.0943402
$202$	2.75382	0.193758
$203$	1.20985	0.0849145
$204$	−14.1634	−0.991636
$205$	6.69295	0.467456
$206$	0.773138	0.0538670
$207$	3.93636	0.273596
$208$	0.650082	0.0450751
$209$	−34.5921	−2.39279
$210$	−2.42205	−0.167137
$211$	10.0085	0.689012	0.344506	−	0.938784i	$-0.388046\pi$
$211$	10.0085	0.689012	0.344506	+	0.938784i	$0.388046\pi$
$212$	−5.33820	−0.366629
$213$	−19.7255	−1.35157
$214$	6.06938	0.414894
$215$	−7.61856	−0.519582
$216$	8.74579	0.595075
$217$	−0.624795	−0.0424138
$218$	−12.9716	−0.878549
$219$	0.582447	0.0393581
$220$	10.4788	0.706480
$221$	−2.34841	−0.157971
$222$	6.71267	0.450525
$223$	−4.68137	−0.313488	−0.156744	−	0.987639i	$-0.550100\pi$
$223$	−4.68137	−0.313488	−0.156744	+	0.987639i	$0.550100\pi$
$224$	7.05562	0.471423
$225$	−4.03649	−0.269100
$226$	4.34723	0.289173
$227$	−2.60825	−0.173116	−0.0865578	−	0.996247i	$-0.527587\pi$
$227$	−2.60825	−0.173116	−0.0865578	+	0.996247i	$0.527587\pi$
$228$	21.1273	1.39919
$229$	−9.04868	−0.597954	−0.298977	−	0.954260i	$-0.596645\pi$
$229$	−9.04868	−0.597954	−0.298977	+	0.954260i	$0.596645\pi$
$230$	−2.94476	−0.194172
$231$	−12.7693	−0.840158
$232$	−2.47133	−0.162251
$233$	1.68086	0.110117	0.0550585	−	0.998483i	$-0.482465\pi$
$233$	1.68086	0.110117	0.0550585	+	0.998483i	$0.482465\pi$
$234$	−0.470313	−0.0307453
$235$	6.07917	0.396561
$236$	1.96280	0.127767
$237$	−11.8593	−0.770347
$238$	−3.88619	−0.251904
$239$	−1.55321	−0.100469	−0.0502344	−	0.998737i	$-0.515997\pi$
$239$	−1.55321	−0.100469	−0.0502344	+	0.998737i	$0.515997\pi$
$240$	−3.57448	−0.230731
$241$	−19.4607	−1.25357	−0.626787	−	0.779191i	$-0.715630\pi$
$241$	−19.4607	−1.25357	−0.626787	+	0.779191i	$0.715630\pi$
$242$	−10.5544	−0.678462
$243$	12.5996	0.808262
$244$	10.4256	0.667428
$245$	−7.58121	−0.484346
$246$	7.14542	0.455575
$247$	3.50309	0.222896
$248$	1.27626	0.0810424
$249$	−32.9446	−2.08778
$250$	7.85144	0.496568
$251$	−24.9209	−1.57299	−0.786497	−	0.617594i	$-0.788107\pi$
$251$	−24.9209	−1.57299	−0.786497	+	0.617594i	$0.788107\pi$
$252$	2.34736	0.147870
$253$	−15.5251	−0.976057
$254$	−3.49669	−0.219402
$255$	12.9127	0.808627
$256$	−10.6273	−0.664206
$257$	−20.1978	−1.25990	−0.629951	−	0.776635i	$-0.716925\pi$
$257$	−20.1978	−1.25990	−0.629951	+	0.776635i	$0.716925\pi$
$258$	−8.13361	−0.506377
$259$	−5.55512	−0.345178
$260$	−1.06117	−0.0658110
$261$	−1.29175	−0.0799574
$262$	5.04662	0.311781
$263$	−4.44581	−0.274141	−0.137070	−	0.990561i	$-0.543769\pi$
$263$	−4.44581	−0.274141	−0.137070	+	0.990561i	$0.543769\pi$
$264$	26.0836	1.60533
$265$	4.86682	0.298966
$266$	5.79697	0.355435
$267$	−29.9384	−1.83220
$268$	0.969724	0.0592353
$269$	−13.8412	−0.843914	−0.421957	−	0.906616i	$-0.638657\pi$
$269$	−13.8412	−0.843914	−0.421957	+	0.906616i	$0.638657\pi$
$270$	−3.41982	−0.208124
$271$	−2.79513	−0.169792	−0.0848960	−	0.996390i	$-0.527056\pi$
$271$	−2.79513	−0.169792	−0.0848960	+	0.996390i	$0.527056\pi$
$272$	−5.73527	−0.347752
$273$	1.29313	0.0782636
$274$	−4.32574	−0.261328
$275$	15.9201	0.960017
$276$	9.48207	0.570753
$277$	−25.3208	−1.52138	−0.760690	−	0.649115i	$-0.775139\pi$
$277$	−25.3208	−1.52138	−0.760690	+	0.649115i	$0.775139\pi$
$278$	0.705690	0.0423245
$279$	0.667093	0.0399378
$280$	−4.09432	−0.244682
$281$	−6.27626	−0.374410	−0.187205	−	0.982321i	$-0.559943\pi$
$281$	−6.27626	−0.374410	−0.187205	+	0.982321i	$0.559943\pi$
$282$	6.49015	0.386483
$283$	6.12719	0.364224	0.182112	−	0.983278i	$-0.441707\pi$
$283$	6.12719	0.364224	0.182112	+	0.983278i	$0.441707\pi$
$284$	−14.3015	−0.848638
$285$	−19.2617	−1.14097
$286$	1.85493	0.109684
$287$	−5.91325	−0.349048
$288$	−7.53328	−0.443903
$289$	3.71858	0.218740
$290$	0.966352	0.0567461
$291$	−5.29648	−0.310485
$292$	0.422289	0.0247126
$293$	−1.63621	−0.0955885	−0.0477943	−	0.998857i	$-0.515219\pi$
$293$	−1.63621	−0.0955885	−0.0477943	+	0.998857i	$0.515219\pi$
$294$	−8.09374	−0.472036
$295$	−1.78948	−0.104188
$296$	11.3473	0.659551
$297$	−18.0297	−1.04619
$298$	−2.62880	−0.152282
$299$	1.57221	0.0909230
$300$	−9.72329	−0.561374
$301$	6.73104	0.387971
$302$	6.33677	0.364640
$303$	8.08424	0.464427
$304$	8.55522	0.490675
$305$	−9.50496	−0.544252
$306$	4.14928	0.237199
$307$	−25.0980	−1.43242	−0.716209	−	0.697886i	$-0.754124\pi$
$307$	−25.0980	−1.43242	−0.716209	+	0.697886i	$0.754124\pi$
$308$	−9.25806	−0.527527
$309$	2.26966	0.129116
$310$	−0.499048	−0.0283440
$311$	19.9525	1.13141	0.565703	−	0.824609i	$-0.308605\pi$
$311$	19.9525	1.13141	0.565703	+	0.824609i	$0.308605\pi$
$312$	−2.64145	−0.149542
$313$	−8.19104	−0.462985	−0.231493	−	0.972837i	$-0.574361\pi$
$313$	−8.19104	−0.462985	−0.231493	+	0.972837i	$0.574361\pi$
$314$	−6.42451	−0.362556
$315$	−2.14008	−0.120580
$316$	−8.59832	−0.483693
$317$	−13.4714	−0.756629	−0.378315	−	0.925677i	$-0.623496\pi$
$317$	−13.4714	−0.756629	−0.378315	+	0.925677i	$0.623496\pi$
$318$	5.19584	0.291368
$319$	5.09471	0.285249
$320$	2.18476	0.122132
$321$	17.8175	0.994478
$322$	2.60171	0.144988
$323$	−30.9056	−1.71963
$324$	16.8324	0.935132
$325$	−1.61220	−0.0894289
$326$	5.46615	0.302742
$327$	−38.0801	−2.10583
$328$	12.0789	0.666945
$329$	−5.37097	−0.296111
$330$	−10.1993	−0.561456
$331$	9.31044	0.511748	0.255874	−	0.966710i	$-0.417637\pi$
$331$	9.31044	0.511748	0.255874	+	0.966710i	$0.417637\pi$
$332$	−23.8857	−1.31090
$333$	5.93120	0.325028
$334$	5.05760	0.276740
$335$	−0.884095	−0.0483032
$336$	3.15807	0.172287
$337$	4.56264	0.248543	0.124271	−	0.992248i	$-0.460341\pi$
$337$	4.56264	0.248543	0.124271	+	0.992248i	$0.460341\pi$
$338$	8.98613	0.488781
$339$	12.7619	0.693131
$340$	9.36206	0.507729
$341$	−2.63104	−0.142479
$342$	−6.18942	−0.334686
$343$	15.1670	0.818939
$344$	−13.7494	−0.741316
$345$	−8.64478	−0.465419
$346$	11.4874	0.617569
$347$	12.2750	0.658957	0.329479	−	0.944163i	$-0.393127\pi$
$347$	12.2750	0.658957	0.329479	+	0.944163i	$0.393127\pi$
$348$	−3.11163	−0.166801
$349$	−13.4500	−0.719964	−0.359982	−	0.932959i	$-0.617217\pi$
$349$	−13.4500	−0.719964	−0.359982	+	0.932959i	$0.617217\pi$
$350$	−2.66790	−0.142605
$351$	1.82584	0.0974561
$352$	29.7115	1.58363
$353$	−15.4901	−0.824455	−0.412227	−	0.911081i	$-0.635249\pi$
$353$	−15.4901	−0.824455	−0.412227	+	0.911081i	$0.635249\pi$
$354$	−1.91046	−0.101540
$355$	13.0386	0.692019
$356$	−21.7061	−1.15042
$357$	−11.4085	−0.603800
$358$	1.95193	0.103163
$359$	−8.15845	−0.430587	−0.215293	−	0.976549i	$-0.569071\pi$
$359$	−8.15845	−0.430587	−0.215293	+	0.976549i	$0.569071\pi$
$360$	4.37150	0.230398
$361$	27.1014	1.42639
$362$	10.9232	0.574113
$363$	−30.9839	−1.62623
$364$	0.937549	0.0491409
$365$	−0.385000	−0.0201518
$366$	−10.1475	−0.530420
$367$	−2.90193	−0.151479	−0.0757397	−	0.997128i	$-0.524132\pi$
$367$	−2.90193	−0.151479	−0.0757397	+	0.997128i	$0.524132\pi$
$368$	3.83963	0.200155
$369$	6.31358	0.328672
$370$	−4.43710	−0.230674
$371$	−4.29986	−0.223237
$372$	1.60692	0.0833151
$373$	−30.7812	−1.59379	−0.796895	−	0.604118i	$-0.793525\pi$
$373$	−30.7812	−1.59379	−0.796895	+	0.604118i	$0.793525\pi$
$374$	−16.3649	−0.846210
$375$	23.0490	1.19025
$376$	10.9712	0.565796
$377$	−0.515934	−0.0265719
$378$	3.02143	0.155406
$379$	12.7614	0.655507	0.327754	−	0.944763i	$-0.393708\pi$
$379$	12.7614	0.655507	0.327754	+	0.944763i	$0.393708\pi$
$380$	−13.9652	−0.716402
$381$	−10.2650	−0.525894
$382$	−2.80963	−0.143753
$383$	−9.13761	−0.466910	−0.233455	−	0.972368i	$-0.575003\pi$
$383$	−9.13761	−0.466910	−0.233455	+	0.972368i	$0.575003\pi$
$384$	−21.8306	−1.11404
$385$	8.44055	0.430170
$386$	2.25236	0.114642
$387$	−7.18672	−0.365322
$388$	−3.84008	−0.194951
$389$	−5.48586	−0.278144	−0.139072	−	0.990282i	$-0.544412\pi$
$389$	−5.48586	−0.278144	−0.139072	+	0.990282i	$0.544412\pi$
$390$	1.03287	0.0523015
$391$	−13.8706	−0.701467
$392$	−13.6820	−0.691043
$393$	14.8151	0.747321
$394$	−2.57800	−0.129878
$395$	7.83907	0.394426
$396$	9.88483	0.496731
$397$	36.7265	1.84325	0.921626	−	0.388080i	$-0.126862\pi$
$397$	36.7265	1.84325	0.921626	+	0.388080i	$0.126862\pi$
$398$	−6.39502	−0.320554
$399$	17.0178	0.851957
$400$	−3.93731	−0.196865
$401$	−5.43788	−0.271555	−0.135777	−	0.990739i	$-0.543353\pi$
$401$	−5.43788	−0.271555	−0.135777	+	0.990739i	$0.543353\pi$
$402$	−0.943863	−0.0470756
$403$	0.266441	0.0132724
$404$	5.86128	0.291609
$405$	−15.3460	−0.762551
$406$	−0.853776	−0.0423722
$407$	−23.3929	−1.15954
$408$	23.3038	1.15371
$409$	−33.2543	−1.64432	−0.822160	−	0.569257i	$-0.807231\pi$
$409$	−33.2543	−1.64432	−0.822160	+	0.569257i	$0.807231\pi$
$410$	−4.72315	−0.233260
$411$	−12.6988	−0.626387
$412$	1.64556	0.0810708
$413$	1.58101	0.0777966
$414$	−2.77785	−0.136524
$415$	21.7765	1.06897
$416$	−3.00884	−0.147521
$417$	2.07165	0.101449
$418$	24.4113	1.19400
$419$	9.79061	0.478303	0.239151	−	0.970982i	$-0.423131\pi$
$419$	9.79061	0.478303	0.239151	+	0.970982i	$0.423131\pi$
$420$	−5.15512	−0.251544
$421$	−20.9023	−1.01872	−0.509359	−	0.860554i	$-0.670117\pi$
$421$	−20.9023	−1.01872	−0.509359	+	0.860554i	$0.670117\pi$
$422$	−7.06288	−0.343816
$423$	5.73459	0.278825
$424$	8.78324	0.426552
$425$	14.2235	0.689940
$426$	13.9201	0.674431
$427$	8.39767	0.406392
$428$	12.9182	0.624423
$429$	5.44542	0.262907
$430$	5.37635	0.259270
$431$	2.56590	0.123595	0.0617975	−	0.998089i	$-0.480317\pi$
$431$	2.56590	0.123595	0.0617975	+	0.998089i	$0.480317\pi$
$432$	4.45905	0.214536
$433$	−12.5807	−0.604588	−0.302294	−	0.953215i	$-0.597752\pi$
$433$	−12.5807	−0.604588	−0.302294	+	0.953215i	$0.597752\pi$
$434$	0.440912	0.0211644
$435$	2.83686	0.136017
$436$	−27.6090	−1.32223
$437$	20.6906	0.989764
$438$	−0.411027	−0.0196396
$439$	−40.3873	−1.92758	−0.963790	−	0.266663i	$-0.914079\pi$
$439$	−40.3873	−1.92758	−0.963790	+	0.266663i	$0.914079\pi$
$440$	−17.2414	−0.821949
$441$	−7.15149	−0.340547
$442$	1.65725	0.0788274
$443$	28.5222	1.35513	0.677565	−	0.735463i	$-0.263035\pi$
$443$	28.5222	1.35513	0.677565	+	0.735463i	$0.263035\pi$
$444$	14.2873	0.678047
$445$	19.7894	0.938108
$446$	3.30360	0.156430
$447$	−7.71722	−0.365012
$448$	−1.93025	−0.0911955
$449$	−10.5422	−0.497518	−0.248759	−	0.968565i	$-0.580023\pi$
$449$	−10.5422	−0.497518	−0.248759	+	0.968565i	$0.580023\pi$
$450$	2.84852	0.134280
$451$	−24.9010	−1.17254
$452$	9.25270	0.435210
$453$	18.6025	0.874022
$454$	1.84062	0.0863844
$455$	−0.854761	−0.0400718
$456$	−34.7620	−1.62788
$457$	14.5749	0.681784	0.340892	−	0.940102i	$-0.389271\pi$
$457$	14.5749	0.681784	0.340892	+	0.940102i	$0.389271\pi$
$458$	6.38557	0.298378
$459$	−16.1082	−0.751869
$460$	−6.26768	−0.292232
$461$	2.16358	0.100768	0.0503839	−	0.998730i	$-0.483956\pi$
$461$	2.16358	0.100768	0.0503839	+	0.998730i	$0.483956\pi$
$462$	9.01117	0.419238
$463$	7.73365	0.359413	0.179707	−	0.983720i	$-0.442485\pi$
$463$	7.73365	0.359413	0.179707	+	0.983720i	$0.442485\pi$
$464$	−1.26001	−0.0584945
$465$	−1.46503	−0.0679390
$466$	−1.18617	−0.0549482
$467$	34.3640	1.59018	0.795088	−	0.606495i	$-0.207425\pi$
$467$	34.3640	1.59018	0.795088	+	0.606495i	$0.207425\pi$
$468$	−1.00102	−0.0462722
$469$	0.781102	0.0360679
$470$	−4.29001	−0.197883
$471$	−18.8601	−0.869026
$472$	−3.22951	−0.148650
$473$	28.3447	1.30329
$474$	8.36902	0.384402
$475$	−21.2169	−0.973499
$476$	−8.27142	−0.379120
$477$	4.59096	0.210205
$478$	1.09609	0.0501338
$479$	−13.3744	−0.611091	−0.305546	−	0.952177i	$-0.598839\pi$
$479$	−13.3744	−0.611091	−0.305546	+	0.952177i	$0.598839\pi$
$480$	16.5441	0.755132
$481$	2.36896	0.108015
$482$	13.7332	0.625531
$483$	7.63770	0.347527
$484$	−22.4641	−1.02110
$485$	3.50099	0.158972
$486$	−8.89139	−0.403322
$487$	−2.63480	−0.119394	−0.0596971	−	0.998217i	$-0.519013\pi$
$487$	−2.63480	−0.119394	−0.0596971	+	0.998217i	$0.519013\pi$
$488$	−17.1538	−0.776515
$489$	16.0467	0.725655
$490$	5.34999	0.241688
$491$	19.5666	0.883029	0.441515	−	0.897254i	$-0.354441\pi$
$491$	19.5666	0.883029	0.441515	+	0.897254i	$0.354441\pi$
$492$	15.2084	0.685648
$493$	4.55177	0.205001
$494$	−2.47209	−0.111225
$495$	−9.01197	−0.405058
$496$	0.650701	0.0292173
$497$	−11.5197	−0.516729
$498$	23.2487	1.04180
$499$	−25.5969	−1.14588	−0.572938	−	0.819598i	$-0.694197\pi$
$499$	−25.5969	−1.14588	−0.572938	+	0.819598i	$0.694197\pi$
$500$	16.7111	0.747344
$501$	14.8473	0.663329
$502$	17.5864	0.784921
$503$	32.1156	1.43197	0.715983	−	0.698118i	$-0.245979\pi$
$503$	32.1156	1.43197	0.715983	+	0.698118i	$0.245979\pi$
$504$	−3.86224	−0.172038
$505$	−5.34371	−0.237792
$506$	10.9559	0.487051
$507$	26.3801	1.17158
$508$	−7.44241	−0.330204
$509$	−26.3578	−1.16829	−0.584144	−	0.811650i	$-0.698570\pi$
$509$	−26.3578	−1.16829	−0.584144	+	0.811650i	$0.698570\pi$
$510$	−9.11239	−0.403504
$511$	0.340149	0.0150473
$512$	−13.5760	−0.599979
$513$	24.0284	1.06088
$514$	14.2534	0.628689
$515$	−1.50025	−0.0661089
$516$	−17.3117	−0.762105
$517$	−22.6174	−0.994713
$518$	3.92019	0.172243
$519$	33.7230	1.48028
$520$	1.74601	0.0765674
$521$	44.0504	1.92988	0.964942	−	0.262463i	$-0.0845349\pi$
$521$	44.0504	1.92988	0.964942	+	0.262463i	$0.0845349\pi$
$522$	0.911576	0.0398986
$523$	12.4744	0.545469	0.272734	−	0.962089i	$-0.412072\pi$
$523$	12.4744	0.545469	0.272734	+	0.962089i	$0.412072\pi$
$524$	10.7413	0.469235
$525$	−7.83200	−0.341816
$526$	3.13737	0.136796
$527$	−2.35065	−0.102396
$528$	13.2988	0.578754
$529$	−13.7140	−0.596259
$530$	−3.43447	−0.149184
$531$	−1.68805	−0.0732550
$532$	12.3384	0.534935
$533$	2.52168	0.109226
$534$	21.1273	0.914266
$535$	−11.7775	−0.509184
$536$	−1.59554	−0.0689169
$537$	5.73016	0.247275
$538$	9.76761	0.421112
$539$	28.2057	1.21491
$540$	−7.27880	−0.313230
$541$	−11.6214	−0.499644	−0.249822	−	0.968292i	$-0.580372\pi$
$541$	−11.6214	−0.499644	−0.249822	+	0.968292i	$0.580372\pi$
$542$	1.97250	0.0847259
$543$	32.0667	1.37611
$544$	26.5451	1.13811
$545$	25.1711	1.07821
$546$	−0.912547	−0.0390534
$547$	−2.86158	−0.122352	−0.0611761	−	0.998127i	$-0.519485\pi$
$547$	−2.86158	−0.122352	−0.0611761	+	0.998127i	$0.519485\pi$
$548$	−9.20697	−0.393302
$549$	−8.96619	−0.382668
$550$	−11.2346	−0.479047
$551$	−6.78980	−0.289255
$552$	−15.6014	−0.664039
$553$	−6.92585	−0.294517
$554$	17.8687	0.759166
$555$	−13.0257	−0.552911
$556$	1.50200	0.0636990
$557$	−4.19770	−0.177862	−0.0889312	−	0.996038i	$-0.528345\pi$
$557$	−4.19770	−0.177862	−0.0889312	+	0.996038i	$0.528345\pi$
$558$	−0.470761	−0.0199289
$559$	−2.87042	−0.121406
$560$	−2.08749	−0.0882127
$561$	−48.0416	−2.02832
$562$	4.42910	0.186830
$563$	−4.61687	−0.194578	−0.0972889	−	0.995256i	$-0.531017\pi$
$563$	−4.61687	−0.194578	−0.0972889	+	0.995256i	$0.531017\pi$
$564$	13.8137	0.581663
$565$	−8.43566	−0.354891
$566$	−4.32390	−0.181747
$567$	13.5583	0.569395
$568$	23.5311	0.987342
$569$	25.4242	1.06584	0.532919	−	0.846166i	$-0.321095\pi$
$569$	25.4242	1.06584	0.532919	+	0.846166i	$0.321095\pi$
$570$	13.5928	0.569340
$571$	−37.7606	−1.58023	−0.790116	−	0.612957i	$-0.789980\pi$
$571$	−37.7606	−1.58023	−0.790116	+	0.612957i	$0.789980\pi$
$572$	3.94806	0.165077
$573$	−8.24807	−0.344568
$574$	4.17292	0.174174
$575$	−9.52228	−0.397107
$576$	2.06092	0.0858717
$577$	6.74091	0.280628	0.140314	−	0.990107i	$-0.455189\pi$
$577$	6.74091	0.280628	0.140314	+	0.990107i	$0.455189\pi$
$578$	−2.62416	−0.109151
$579$	6.61212	0.274790
$580$	2.05680	0.0854038
$581$	−19.2396	−0.798195
$582$	3.73767	0.154932
$583$	−18.1069	−0.749911
$584$	−0.694816	−0.0287517
$585$	0.912628	0.0377325
$586$	1.15466	0.0476985
$587$	−17.3076	−0.714361	−0.357181	−	0.934035i	$-0.616262\pi$
$587$	−17.3076	−0.714361	−0.357181	+	0.934035i	$0.616262\pi$
$588$	−17.2268	−0.710422
$589$	3.50642	0.144480
$590$	1.26282	0.0519894
$591$	−7.56808	−0.311309
$592$	5.78546	0.237781
$593$	2.27069	0.0932461	0.0466231	−	0.998913i	$-0.485154\pi$
$593$	2.27069	0.0932461	0.0466231	+	0.998913i	$0.485154\pi$
$594$	12.7234	0.522046
$595$	7.54103	0.309152
$596$	−5.59518	−0.229187
$597$	−18.7735	−0.768348
$598$	−1.10949	−0.0453704
$599$	−13.7563	−0.562067	−0.281034	−	0.959698i	$-0.590677\pi$
$599$	−13.7563	−0.562067	−0.281034	+	0.959698i	$0.590677\pi$
$600$	15.9983	0.653127
$601$	−34.6009	−1.41140	−0.705701	−	0.708510i	$-0.749368\pi$
$601$	−34.6009	−1.41140	−0.705701	+	0.708510i	$0.749368\pi$
$602$	−4.75003	−0.193597
$603$	−0.833982	−0.0339624
$604$	13.4873	0.548790
$605$	20.4805	0.832650
$606$	−5.70497	−0.231749
$607$	27.0348	1.09731	0.548653	−	0.836050i	$-0.315141\pi$
$607$	27.0348	1.09731	0.548653	+	0.836050i	$0.315141\pi$
$608$	−39.5970	−1.60587
$609$	−2.50638	−0.101564
$610$	6.70756	0.271581
$611$	2.29043	0.0926609
$612$	8.83139	0.356988
$613$	−10.5421	−0.425791	−0.212895	−	0.977075i	$-0.568289\pi$
$613$	−10.5421	−0.425791	−0.212895	+	0.977075i	$0.568289\pi$
$614$	17.7114	0.714774
$615$	−13.8655	−0.559110
$616$	15.2328	0.613748
$617$	−22.3493	−0.899750	−0.449875	−	0.893092i	$-0.648531\pi$
$617$	−22.3493	−0.899750	−0.449875	+	0.893092i	$0.648531\pi$
$618$	−1.60167	−0.0644288
$619$	3.96483	0.159360	0.0796799	−	0.996821i	$-0.474610\pi$
$619$	3.96483	0.159360	0.0796799	+	0.996821i	$0.474610\pi$
$620$	−1.06218	−0.0426582
$621$	10.7841	0.432751
$622$	−14.0803	−0.564569
$623$	−17.4840	−0.700483
$624$	−1.34674	−0.0539129
$625$	0.388642	0.0155457
$626$	5.78034	0.231029
$627$	71.6629	2.86194
$628$	−13.6740	−0.545653
$629$	−20.8999	−0.833332
$630$	1.51023	0.0601691
$631$	49.8537	1.98464	0.992322	−	0.123682i	$-0.0394704\pi$
$631$	49.8537	1.98464	0.992322	+	0.123682i	$0.0394704\pi$
$632$	14.1473	0.562750
$633$	−20.7341	−0.824106
$634$	9.50664	0.377557
$635$	6.78523	0.269264
$636$	11.0589	0.438514
$637$	−2.85635	−0.113173
$638$	−3.59529	−0.142339
$639$	12.2996	0.486564
$640$	14.4301	0.570401
$641$	9.00297	0.355596	0.177798	−	0.984067i	$-0.443103\pi$
$641$	9.00297	0.355596	0.177798	+	0.984067i	$0.443103\pi$
$642$	−12.5737	−0.496243
$643$	−10.8851	−0.429267	−0.214633	−	0.976695i	$-0.568856\pi$
$643$	−10.8851	−0.429267	−0.214633	+	0.976695i	$0.568856\pi$
$644$	5.53752	0.218209
$645$	15.7830	0.621456
$646$	21.8098	0.858094
$647$	27.5281	1.08224	0.541120	−	0.840945i	$-0.318000\pi$
$647$	27.5281	1.08224	0.541120	+	0.840945i	$0.318000\pi$
$648$	−27.6953	−1.08797
$649$	6.65772	0.261339
$650$	1.13772	0.0446249
$651$	1.29436	0.0507299
$652$	11.6342	0.455632
$653$	−33.0317	−1.29263	−0.646316	−	0.763070i	$-0.723691\pi$
$653$	−33.0317	−1.29263	−0.646316	+	0.763070i	$0.723691\pi$
$654$	26.8727	1.05081
$655$	−9.79281	−0.382637
$656$	6.15844	0.240447
$657$	−0.363177	−0.0141689
$658$	3.79024	0.147759
$659$	31.2778	1.21841	0.609206	−	0.793012i	$-0.291488\pi$
$659$	31.2778	1.21841	0.609206	+	0.793012i	$0.291488\pi$
$660$	−21.7084	−0.845000
$661$	−20.2976	−0.789485	−0.394742	−	0.918792i	$-0.629166\pi$
$661$	−20.2976	−0.789485	−0.394742	+	0.918792i	$0.629166\pi$
$662$	−6.57029	−0.255361
$663$	4.86509	0.188945
$664$	39.3005	1.52515
$665$	−11.2488	−0.436211
$666$	−4.18559	−0.162188
$667$	−3.04730	−0.117992
$668$	10.7647	0.416498
$669$	9.69819	0.374954
$670$	0.623897	0.0241032
$671$	35.3630	1.36517
$672$	−14.6168	−0.563855
$673$	4.14455	0.159761	0.0798804	−	0.996804i	$-0.474546\pi$
$673$	4.14455	0.159761	0.0798804	+	0.996804i	$0.474546\pi$
$674$	−3.21981	−0.124022
$675$	−11.0584	−0.425640
$676$	19.1262	0.735623
$677$	6.40694	0.246239	0.123119	−	0.992392i	$-0.460710\pi$
$677$	6.40694	0.246239	0.123119	+	0.992392i	$0.460710\pi$
$678$	−9.00595	−0.345871
$679$	−3.09314	−0.118704
$680$	−15.4039	−0.590714
$681$	5.40339	0.207058
$682$	1.85670	0.0710967
$683$	10.8110	0.413670	0.206835	−	0.978376i	$-0.433684\pi$
$683$	10.8110	0.413670	0.206835	+	0.978376i	$0.433684\pi$
$684$	−13.1737	−0.503707
$685$	8.39398	0.320717
$686$	−10.7032	−0.408649
$687$	18.7457	0.715195
$688$	−7.01013	−0.267259
$689$	1.83366	0.0698568
$690$	6.10053	0.232243
$691$	29.1135	1.10753	0.553766	−	0.832672i	$-0.313190\pi$
$691$	29.1135	1.10753	0.553766	+	0.832672i	$0.313190\pi$
$692$	24.4500	0.929451
$693$	7.96212	0.302456
$694$	−8.66236	−0.328819
$695$	−1.36937	−0.0519432
$696$	5.11974	0.194063
$697$	−22.2473	−0.842675
$698$	9.49156	0.359261
$699$	−3.48216	−0.131708
$700$	−5.67840	−0.214623
$701$	31.9484	1.20667	0.603337	−	0.797487i	$-0.293838\pi$
$701$	31.9484	1.20667	0.603337	+	0.797487i	$0.293838\pi$
$702$	−1.28848	−0.0486304
$703$	31.1760	1.17583
$704$	−8.12835	−0.306349
$705$	−12.5939	−0.474315
$706$	10.9312	0.411402
$707$	4.72119	0.177559
$708$	−4.06624	−0.152819
$709$	−22.8071	−0.856538	−0.428269	−	0.903651i	$-0.640877\pi$
$709$	−22.8071	−0.856538	−0.428269	+	0.903651i	$0.640877\pi$
$710$	−9.20124	−0.345316
$711$	7.39473	0.277324
$712$	35.7143	1.33845
$713$	1.57370	0.0589357
$714$	8.05084	0.301295
$715$	−3.59944	−0.134611
$716$	4.15451	0.155261
$717$	3.21772	0.120168
$718$	5.75734	0.214862
$719$	−32.0847	−1.19656	−0.598280	−	0.801287i	$-0.704149\pi$
$719$	−32.0847	−1.19656	−0.598280	+	0.801287i	$0.704149\pi$
$720$	2.22881	0.0830630
$721$	1.32548	0.0493634
$722$	−19.1252	−0.711766
$723$	40.3158	1.49936
$724$	23.2492	0.864049
$725$	3.12482	0.116053
$726$	21.8650	0.811488
$727$	20.4208	0.757366	0.378683	−	0.925526i	$-0.376377\pi$
$727$	20.4208	0.757366	0.378683	+	0.925526i	$0.376377\pi$
$728$	−1.54260	−0.0571727
$729$	7.51796	0.278443
$730$	0.271691	0.0100557
$731$	25.3240	0.936641
$732$	−21.5982	−0.798291
$733$	−16.4478	−0.607512	−0.303756	−	0.952750i	$-0.598241\pi$
$733$	−16.4478	−0.607512	−0.303756	+	0.952750i	$0.598241\pi$
$734$	2.04786	0.0755880
$735$	15.7056	0.579312
$736$	−17.7714	−0.655061
$737$	3.28926	0.121161
$738$	−4.45543	−0.164007
$739$	−35.8708	−1.31953	−0.659764	−	0.751473i	$-0.729344\pi$
$739$	−35.8708	−1.31953	−0.659764	+	0.751473i	$0.729344\pi$
$740$	−9.44398	−0.347168
$741$	−7.25719	−0.266599
$742$	3.03437	0.111395
$743$	42.3255	1.55277	0.776386	−	0.630258i	$-0.217051\pi$
$743$	42.3255	1.55277	0.776386	+	0.630258i	$0.217051\pi$
$744$	−2.64396	−0.0969323
$745$	5.10111	0.186890
$746$	21.7220	0.795298
$747$	20.5422	0.751598
$748$	−34.8313	−1.27356
$749$	10.4054	0.380206
$750$	−16.2655	−0.593931
$751$	52.1136	1.90165	0.950827	−	0.309723i	$-0.100236\pi$
$751$	52.1136	1.90165	0.950827	+	0.309723i	$0.100236\pi$
$752$	5.59367	0.203980
$753$	51.6275	1.88141
$754$	0.364090	0.0132594
$755$	−12.2963	−0.447509
$756$	6.43085	0.233888
$757$	−14.1788	−0.515336	−0.257668	−	0.966234i	$-0.582954\pi$
$757$	−14.1788	−0.515336	−0.257668	+	0.966234i	$0.582954\pi$
$758$	−9.00557	−0.327097
$759$	32.1627	1.16743
$760$	22.9778	0.833492
$761$	−23.5634	−0.854174	−0.427087	−	0.904210i	$-0.640460\pi$
$761$	−23.5634	−0.854174	−0.427087	+	0.904210i	$0.640460\pi$
$762$	7.24394	0.262420
$763$	−22.2387	−0.805097
$764$	−5.98006	−0.216351
$765$	−8.05156	−0.291105
$766$	6.44833	0.232987
$767$	−0.674217	−0.0243446
$768$	22.0161	0.794437
$769$	−20.3503	−0.733850	−0.366925	−	0.930251i	$-0.619589\pi$
$769$	−20.3503	−0.733850	−0.366925	+	0.930251i	$0.619589\pi$
$770$	−5.95641	−0.214654
$771$	41.8428	1.50693
$772$	4.79395	0.172538
$773$	13.3627	0.480623	0.240311	−	0.970696i	$-0.422750\pi$
$773$	13.3627	0.480623	0.240311	+	0.970696i	$0.422750\pi$
$774$	5.07160	0.182295
$775$	−1.61374	−0.0579672
$776$	6.31830	0.226814
$777$	11.5083	0.412858
$778$	3.87132	0.138793
$779$	33.1859	1.18901
$780$	2.19838	0.0787146
$781$	−48.5100	−1.73582
$782$	9.78835	0.350031
$783$	−3.53890	−0.126470
$784$	−6.97576	−0.249134
$785$	12.4666	0.444951
$786$	−10.4548	−0.372912
$787$	−51.1581	−1.82359	−0.911795	−	0.410645i	$-0.865304\pi$
$787$	−51.1581	−1.82359	−0.911795	+	0.410645i	$0.865304\pi$
$788$	−5.48705	−0.195468
$789$	9.21019	0.327891
$790$	−5.53195	−0.196818
$791$	7.45295	0.264996
$792$	−16.2641	−0.577918
$793$	−3.58115	−0.127171
$794$	−25.9176	−0.919779
$795$	−10.0824	−0.357585
$796$	−13.6113	−0.482438
$797$	13.1956	0.467413	0.233707	−	0.972307i	$-0.424914\pi$
$797$	13.1956	0.467413	0.233707	+	0.972307i	$0.424914\pi$
$798$	−12.0093	−0.425125
$799$	−20.2071	−0.714874
$800$	18.2235	0.644296
$801$	18.6677	0.659590
$802$	3.83746	0.135505
$803$	1.43238	0.0505477
$804$	−2.00893	−0.0708496
$805$	−5.04855	−0.177938
$806$	−0.188025	−0.00662290
$807$	28.6742	1.00938
$808$	−9.64389	−0.339271
$809$	−31.7465	−1.11615	−0.558073	−	0.829792i	$-0.688459\pi$
$809$	−31.7465	−1.11615	−0.558073	+	0.829792i	$0.688459\pi$
$810$	10.8295	0.380512
$811$	12.3887	0.435026	0.217513	−	0.976057i	$-0.430206\pi$
$811$	12.3887	0.435026	0.217513	+	0.976057i	$0.430206\pi$
$812$	−1.81719	−0.0637708
$813$	5.79054	0.203083
$814$	16.5081	0.578609
$815$	−10.6069	−0.371543
$816$	11.8815	0.415936
$817$	−37.7754	−1.32159
$818$	23.4672	0.820513
$819$	−0.806311	−0.0281748
$820$	−10.0528	−0.351060
$821$	−12.7939	−0.446511	−0.223256	−	0.974760i	$-0.571668\pi$
$821$	−12.7939	−0.446511	−0.223256	+	0.974760i	$0.571668\pi$
$822$	8.96145	0.312566
$823$	29.1806	1.01717	0.508586	−	0.861011i	$-0.330168\pi$
$823$	29.1806	1.01717	0.508586	+	0.861011i	$0.330168\pi$
$824$	−2.70753	−0.0943212
$825$	−32.9809	−1.14825
$826$	−1.11571	−0.0388204
$827$	44.0368	1.53131	0.765654	−	0.643252i	$-0.222415\pi$
$827$	44.0368	1.53131	0.765654	+	0.643252i	$0.222415\pi$
$828$	−5.91241	−0.205470
$829$	52.4473	1.82157	0.910786	−	0.412879i	$-0.135477\pi$
$829$	52.4473	1.82157	0.910786	+	0.412879i	$0.135477\pi$
$830$	−15.3675	−0.533413
$831$	52.4560	1.81968
$832$	0.823146	0.0285374
$833$	25.1998	0.873122
$834$	−1.46195	−0.0506231
$835$	−9.81413	−0.339632
$836$	51.9574	1.79698
$837$	1.82758	0.0631703
$838$	−6.90914	−0.238672
$839$	−39.1172	−1.35047	−0.675237	−	0.737601i	$-0.735959\pi$
$839$	−39.1172	−1.35047	−0.675237	+	0.737601i	$0.735959\pi$
$840$	8.48201	0.292657
$841$	1.00000	0.0344828
$842$	14.7506	0.508339
$843$	13.0022	0.447821
$844$	−15.0327	−0.517448
$845$	−17.4373	−0.599862
$846$	−4.04684	−0.139133
$847$	−18.0946	−0.621738
$848$	4.47815	0.153780
$849$	−12.6934	−0.435637
$850$	−10.0374	−0.344279
$851$	13.9920	0.479639
$852$	29.6278	1.01503
$853$	−16.2850	−0.557589	−0.278794	−	0.960351i	$-0.589935\pi$
$853$	−16.2850	−0.557589	−0.278794	+	0.960351i	$0.589935\pi$
$854$	−5.92616	−0.202789
$855$	12.0104	0.410746
$856$	−21.2550	−0.726481
$857$	−4.57275	−0.156202	−0.0781011	−	0.996945i	$-0.524886\pi$
$857$	−4.57275	−0.156202	−0.0781011	+	0.996945i	$0.524886\pi$
$858$	−3.84278	−0.131190
$859$	23.3742	0.797517	0.398758	−	0.917056i	$-0.369441\pi$
$859$	23.3742	0.797517	0.398758	+	0.917056i	$0.369441\pi$
$860$	11.4431	0.390206
$861$	12.2502	0.417486
$862$	−1.81073	−0.0616737
$863$	−46.3891	−1.57910	−0.789552	−	0.613683i	$-0.789687\pi$
$863$	−46.3891	−1.57910	−0.789552	+	0.613683i	$0.789687\pi$
$864$	−20.6383	−0.702129
$865$	−22.2910	−0.757918
$866$	8.87805	0.301689
$867$	−7.70361	−0.261628
$868$	0.938442	0.0318528
$869$	−29.1651	−0.989358
$870$	−2.00195	−0.0678723
$871$	−0.333098	−0.0112866
$872$	45.4267	1.53834
$873$	3.30255	0.111774
$874$	−14.6011	−0.493891
$875$	13.4606	0.455052
$876$	−0.874837	−0.0295580
$877$	3.08146	0.104053	0.0520267	−	0.998646i	$-0.483432\pi$
$877$	3.08146	0.104053	0.0520267	+	0.998646i	$0.483432\pi$
$878$	28.5009	0.961859
$879$	3.38967	0.114331
$880$	−8.79053	−0.296329
$881$	−10.6177	−0.357719	−0.178859	−	0.983875i	$-0.557241\pi$
$881$	−10.6177	−0.357719	−0.178859	+	0.983875i	$0.557241\pi$
$882$	5.04674	0.169932
$883$	7.77796	0.261749	0.130875	−	0.991399i	$-0.458221\pi$
$883$	7.77796	0.261749	0.130875	+	0.991399i	$0.458221\pi$
$884$	3.52732	0.118636
$885$	3.70719	0.124616
$886$	−20.1278	−0.676208
$887$	−6.40648	−0.215108	−0.107554	−	0.994199i	$-0.534302\pi$
$887$	−6.40648	−0.215108	−0.107554	+	0.994199i	$0.534302\pi$
$888$	−23.5078	−0.788869
$889$	−5.99478	−0.201058
$890$	−13.9652	−0.468114
$891$	57.0946	1.91274
$892$	7.03143	0.235430
$893$	30.1426	1.00868
$894$	5.44597	0.182140
$895$	−3.78765	−0.126607
$896$	−12.7491	−0.425917
$897$	−3.25707	−0.108750
$898$	7.43954	0.248261
$899$	−0.516425	−0.0172237
$900$	6.06282	0.202094
$901$	−16.1772	−0.538942
$902$	17.5724	0.585096
$903$	−13.9444	−0.464040
$904$	−15.2240	−0.506342
$905$	−21.1962	−0.704586
$906$	−13.1276	−0.436136
$907$	−12.8406	−0.426364	−0.213182	−	0.977013i	$-0.568383\pi$
$907$	−12.8406	−0.426364	−0.213182	+	0.977013i	$0.568383\pi$
$908$	3.91759	0.130010
$909$	−5.04082	−0.167193
$910$	0.603197	0.0199958
$911$	−12.6737	−0.419900	−0.209950	−	0.977712i	$-0.567330\pi$
$911$	−12.6737	−0.419900	−0.209950	+	0.977712i	$0.567330\pi$
$912$	−17.7235	−0.586882
$913$	−81.0190	−2.68134
$914$	−10.2854	−0.340209
$915$	19.6910	0.650964
$916$	13.5911	0.449064
$917$	8.65199	0.285714
$918$	11.3674	0.375181
$919$	−40.2427	−1.32748	−0.663741	−	0.747962i	$-0.731032\pi$
$919$	−40.2427	−1.32748	−0.663741	+	0.747962i	$0.731032\pi$
$920$	10.3126	0.339995
$921$	51.9944	1.71327
$922$	−1.52681	−0.0502830
$923$	4.91253	0.161698
$924$	19.1795	0.630959
$925$	−14.3479	−0.471757
$926$	−5.45756	−0.179347
$927$	−1.41521	−0.0464817
$928$	5.83183	0.191439
$929$	5.28943	0.173541	0.0867703	−	0.996228i	$-0.472345\pi$
$929$	5.28943	0.173541	0.0867703	+	0.996228i	$0.472345\pi$
$930$	1.03386	0.0339015
$931$	−37.5902	−1.23197
$932$	−2.52466	−0.0826979
$933$	−41.3348	−1.35324
$934$	−24.2503	−0.793495
$935$	31.7556	1.03852
$936$	1.64704	0.0538351
$937$	13.7310	0.448573	0.224287	−	0.974523i	$-0.427995\pi$
$937$	13.7310	0.448573	0.224287	+	0.974523i	$0.427995\pi$
$938$	−0.551216	−0.0179978
$939$	16.9690	0.553763
$940$	−9.13092	−0.297818
$941$	−48.3608	−1.57652	−0.788259	−	0.615344i	$-0.789017\pi$
$941$	−48.3608	−1.57652	−0.788259	+	0.615344i	$0.789017\pi$
$942$	13.3094	0.433642
$943$	14.8940	0.485016
$944$	−1.64657	−0.0535913
$945$	−5.86299	−0.190723
$946$	−20.0026	−0.650340
$947$	36.4336	1.18393	0.591967	−	0.805962i	$-0.298352\pi$
$947$	36.4336	1.18393	0.591967	+	0.805962i	$0.298352\pi$
$948$	17.8127	0.578531
$949$	−0.145055	−0.00470869
$950$	14.9726	0.485775
$951$	27.9081	0.904982
$952$	13.6094	0.441084
$953$	−23.1765	−0.750761	−0.375380	−	0.926871i	$-0.622488\pi$
$953$	−23.1765	−0.750761	−0.375380	+	0.926871i	$0.622488\pi$
$954$	−3.23979	−0.104892
$955$	5.45200	0.176423
$956$	2.33292	0.0754522
$957$	−10.5545	−0.341178
$958$	9.43818	0.304934
$959$	−7.41612	−0.239479
$960$	−4.52607	−0.146078
$961$	−30.7333	−0.991397
$962$	−1.67175	−0.0538994
$963$	−11.1099	−0.358011
$964$	29.2300	0.941434
$965$	−4.37063	−0.140696
$966$	−5.38985	−0.173416
$967$	−13.4607	−0.432868	−0.216434	−	0.976297i	$-0.569443\pi$
$967$	−13.4607	−0.432868	−0.216434	+	0.976297i	$0.569443\pi$
$968$	36.9615	1.18799
$969$	64.0257	2.05680
$970$	−2.47062	−0.0793267
$971$	−30.5484	−0.980344	−0.490172	−	0.871626i	$-0.663066\pi$
$971$	−30.5484	−0.980344	−0.490172	+	0.871626i	$0.663066\pi$
$972$	−18.9246	−0.607006
$973$	1.20985	0.0387859
$974$	1.85935	0.0595775
$975$	3.33993	0.106963
$976$	−8.74587	−0.279949
$977$	−1.48628	−0.0475503	−0.0237751	−	0.999717i	$-0.507569\pi$
$977$	−1.48628	−0.0475503	−0.0237751	+	0.999717i	$0.507569\pi$
$978$	−11.3240	−0.362101
$979$	−73.6261	−2.35310
$980$	11.3870	0.363744
$981$	23.7443	0.758097
$982$	−13.8080	−0.440630
$983$	−11.6631	−0.371995	−0.185998	−	0.982550i	$-0.559552\pi$
$983$	−11.6631	−0.371995	−0.185998	+	0.982550i	$0.559552\pi$
$984$	−25.0233	−0.797713
$985$	5.00253	0.159394
$986$	−3.21214	−0.102295
$987$	11.1268	0.354170
$988$	−5.26164	−0.167395
$989$	−16.9538	−0.539100
$990$	6.35966	0.202123
$991$	−2.55591	−0.0811913	−0.0405957	−	0.999176i	$-0.512926\pi$
$991$	−2.55591	−0.0811913	−0.0405957	+	0.999176i	$0.512926\pi$
$992$	−3.01171	−0.0956218
$993$	−19.2880	−0.612086
$994$	8.12934	0.257847
$995$	12.4094	0.393403
$996$	49.4829	1.56792
$997$	13.4710	0.426631	0.213315	−	0.976983i	$-0.431574\pi$
$997$	13.4710	0.426631	0.213315	+	0.976983i	$0.431574\pi$
$998$	18.0635	0.571791
$999$	16.2492	0.514102

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4031.2.a.c.1.24	✓	61

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4031.2.a.c.1.24	✓	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)

\(f(q)\)	\(=\)	\(q-0.705690 q^{2} -2.07165 q^{3} -1.50200 q^{4} +1.36937 q^{5} +1.46195 q^{6} -1.20985 q^{7} +2.47133 q^{8} +1.29175 q^{9} +O(q^{10})\)	\(q-0.705690 q^{2} -2.07165 q^{3} -1.50200 q^{4} +1.36937 q^{5} +1.46195 q^{6} -1.20985 q^{7} +2.47133 q^{8} +1.29175 q^{9} -0.966352 q^{10} -5.09471 q^{11} +3.11163 q^{12} +0.515934 q^{13} +0.853776 q^{14} -2.83686 q^{15} +1.26001 q^{16} -4.55177 q^{17} -0.911576 q^{18} +6.78980 q^{19} -2.05680 q^{20} +2.50638 q^{21} +3.59529 q^{22} +3.04730 q^{23} -5.11974 q^{24} -3.12482 q^{25} -0.364090 q^{26} +3.53890 q^{27} +1.81719 q^{28} -1.00000 q^{29} +2.00195 q^{30} +0.516425 q^{31} -5.83183 q^{32} +10.5545 q^{33} +3.21214 q^{34} -1.65673 q^{35} -1.94021 q^{36} +4.59160 q^{37} -4.79150 q^{38} -1.06884 q^{39} +3.38416 q^{40} +4.88761 q^{41} -1.76873 q^{42} -5.56355 q^{43} +7.65227 q^{44} +1.76889 q^{45} -2.15045 q^{46} +4.43939 q^{47} -2.61031 q^{48} -5.53627 q^{49} +2.20516 q^{50} +9.42969 q^{51} -0.774933 q^{52} +3.55406 q^{53} -2.49737 q^{54} -6.97655 q^{55} -2.98993 q^{56} -14.0661 q^{57} +0.705690 q^{58} -1.30679 q^{59} +4.26097 q^{60} -6.94111 q^{61} -0.364436 q^{62} -1.56282 q^{63} +1.59545 q^{64} +0.706505 q^{65} -7.44820 q^{66} -0.645621 q^{67} +6.83676 q^{68} -6.31296 q^{69} +1.16914 q^{70} +9.52163 q^{71} +3.19234 q^{72} -0.281151 q^{73} -3.24024 q^{74} +6.47355 q^{75} -10.1983 q^{76} +6.16382 q^{77} +0.754268 q^{78} +5.72458 q^{79} +1.72542 q^{80} -11.2066 q^{81} -3.44914 q^{82} +15.9026 q^{83} -3.76459 q^{84} -6.23306 q^{85} +3.92614 q^{86} +2.07165 q^{87} -12.5907 q^{88} +14.4515 q^{89} -1.24829 q^{90} -0.624200 q^{91} -4.57705 q^{92} -1.06985 q^{93} -3.13283 q^{94} +9.29775 q^{95} +12.0815 q^{96} +2.55664 q^{97} +3.90689 q^{98} -6.58110 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 61 q - q^{2} - 4 q^{3} + 43 q^{4} - 7 q^{5} - 13 q^{6} - 10 q^{7} - 6 q^{8} + 23 q^{9}+O(q^{10}) \) 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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