LMFDB - Embedded newform 8029.2.a.h.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8029,2,Mod(1,8029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8029, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("8029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8029 = 7 \cdot 31 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8029.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:	$64.1118877829$
Analytic rank:	$0$
Dimension:	$71$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	8029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.28647 q^{2} -0.837618 q^{3} +3.22797 q^{4} +2.08578 q^{5} +1.91519 q^{6} -1.00000 q^{7} -2.80772 q^{8} -2.29840 q^{9} +O(q^{10})$	\(q-2.28647 q^{2} -0.837618 q^{3} +3.22797 q^{4} +2.08578 q^{5} +1.91519 q^{6} -1.00000 q^{7} -2.80772 q^{8} -2.29840 q^{9} -4.76908 q^{10} -1.28621 q^{11} -2.70380 q^{12} -2.15289 q^{13} +2.28647 q^{14} -1.74709 q^{15} -0.0361596 q^{16} -1.02517 q^{17} +5.25523 q^{18} -5.43559 q^{19} +6.73283 q^{20} +0.837618 q^{21} +2.94089 q^{22} +3.02379 q^{23} +2.35179 q^{24} -0.649527 q^{25} +4.92254 q^{26} +4.43803 q^{27} -3.22797 q^{28} -3.27660 q^{29} +3.99467 q^{30} -1.00000 q^{31} +5.69811 q^{32} +1.07735 q^{33} +2.34402 q^{34} -2.08578 q^{35} -7.41915 q^{36} +1.00000 q^{37} +12.4283 q^{38} +1.80330 q^{39} -5.85628 q^{40} -11.9189 q^{41} -1.91519 q^{42} +11.8261 q^{43} -4.15185 q^{44} -4.79395 q^{45} -6.91382 q^{46} -3.81198 q^{47} +0.0302879 q^{48} +1.00000 q^{49} +1.48513 q^{50} +0.858699 q^{51} -6.94947 q^{52} -4.33265 q^{53} -10.1474 q^{54} -2.68276 q^{55} +2.80772 q^{56} +4.55294 q^{57} +7.49186 q^{58} -5.09764 q^{59} -5.63954 q^{60} +6.16265 q^{61} +2.28647 q^{62} +2.29840 q^{63} -12.9563 q^{64} -4.49046 q^{65} -2.46334 q^{66} -12.9544 q^{67} -3.30921 q^{68} -2.53278 q^{69} +4.76908 q^{70} -8.68065 q^{71} +6.45325 q^{72} -1.82557 q^{73} -2.28647 q^{74} +0.544055 q^{75} -17.5459 q^{76} +1.28621 q^{77} -4.12320 q^{78} -4.93969 q^{79} -0.0754209 q^{80} +3.17781 q^{81} +27.2523 q^{82} -9.37127 q^{83} +2.70380 q^{84} -2.13827 q^{85} -27.0401 q^{86} +2.74454 q^{87} +3.61132 q^{88} +18.0914 q^{89} +10.9612 q^{90} +2.15289 q^{91} +9.76069 q^{92} +0.837618 q^{93} +8.71599 q^{94} -11.3374 q^{95} -4.77284 q^{96} -10.9476 q^{97} -2.28647 q^{98} +2.95623 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 71 q + 6 q^{2} + 8 q^{3} + 78 q^{4} + 5 q^{6} - 71 q^{7} + 18 q^{8} + 87 q^{9}+O(q^{10}) $ 71 * q + 6 * q^2 + 8 * q^3 + 78 * q^4 + 5 * q^6 - 71 * q^7 + 18 * q^8 + 87 * q^9	\( 71 q + 6 q^{2} + 8 q^{3} + 78 q^{4} + 5 q^{6} - 71 q^{7} + 18 q^{8} + 87 q^{9} + 4 q^{10} + 57 q^{11} + 21 q^{12} - 20 q^{13} - 6 q^{14} + 22 q^{15} + 88 q^{16} - 19 q^{17} + q^{18} + 23 q^{19} + 25 q^{20} - 8 q^{21} + 18 q^{22} + 34 q^{23} + 15 q^{24} + 81 q^{25} - 13 q^{26} + 20 q^{27} - 78 q^{28} + 16 q^{29} + 6 q^{30} - 71 q^{31} + 47 q^{32} - 16 q^{33} + 32 q^{34} + 125 q^{36} + 71 q^{37} + 13 q^{38} + 30 q^{39} + 31 q^{40} + 17 q^{41} - 5 q^{42} + 38 q^{43} + 80 q^{44} - q^{45} + 26 q^{46} + 32 q^{47} + 61 q^{48} + 71 q^{49} + 47 q^{50} + 73 q^{51} - 23 q^{52} + 31 q^{53} + 47 q^{54} + 11 q^{55} - 18 q^{56} + 17 q^{57} - 2 q^{58} + 97 q^{59} + 103 q^{60} - q^{61} - 6 q^{62} - 87 q^{63} + 100 q^{64} + 46 q^{65} + 43 q^{66} + 75 q^{67} - 43 q^{68} + 10 q^{69} - 4 q^{70} + 131 q^{71} - 11 q^{72} - 15 q^{73} + 6 q^{74} + 76 q^{75} + 41 q^{76} - 57 q^{77} + 89 q^{78} + 8 q^{79} + 10 q^{80} + 171 q^{81} + 14 q^{82} + 18 q^{83} - 21 q^{84} + 47 q^{85} + 90 q^{86} - 59 q^{87} + 13 q^{88} + 18 q^{89} + 69 q^{90} + 20 q^{91} + 110 q^{92} - 8 q^{93} + 39 q^{94} + 72 q^{95} + 100 q^{96} + 23 q^{97} + 6 q^{98} + 168 q^{99}+O(q^{100}) \) 71 * q + 6 * q^2 + 8 * q^3 + 78 * q^4 + 5 * q^6 - 71 * q^7 + 18 * q^8 + 87 * q^9 + 4 * q^10 + 57 * q^11 + 21 * q^12 - 20 * q^13 - 6 * q^14 + 22 * q^15 + 88 * q^16 - 19 * q^17 + q^18 + 23 * q^19 + 25 * q^20 - 8 * q^21 + 18 * q^22 + 34 * q^23 + 15 * q^24 + 81 * q^25 - 13 * q^26 + 20 * q^27 - 78 * q^28 + 16 * q^29 + 6 * q^30 - 71 * q^31 + 47 * q^32 - 16 * q^33 + 32 * q^34 + 125 * q^36 + 71 * q^37 + 13 * q^38 + 30 * q^39 + 31 * q^40 + 17 * q^41 - 5 * q^42 + 38 * q^43 + 80 * q^44 - q^45 + 26 * q^46 + 32 * q^47 + 61 * q^48 + 71 * q^49 + 47 * q^50 + 73 * q^51 - 23 * q^52 + 31 * q^53 + 47 * q^54 + 11 * q^55 - 18 * q^56 + 17 * q^57 - 2 * q^58 + 97 * q^59 + 103 * q^60 - q^61 - 6 * q^62 - 87 * q^63 + 100 * q^64 + 46 * q^65 + 43 * q^66 + 75 * q^67 - 43 * q^68 + 10 * q^69 - 4 * q^70 + 131 * q^71 - 11 * q^72 - 15 * q^73 + 6 * q^74 + 76 * q^75 + 41 * q^76 - 57 * q^77 + 89 * q^78 + 8 * q^79 + 10 * q^80 + 171 * q^81 + 14 * q^82 + 18 * q^83 - 21 * q^84 + 47 * q^85 + 90 * q^86 - 59 * q^87 + 13 * q^88 + 18 * q^89 + 69 * q^90 + 20 * q^91 + 110 * q^92 - 8 * q^93 + 39 * q^94 + 72 * q^95 + 100 * q^96 + 23 * q^97 + 6 * q^98 + 168 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.28647	−1.61678	−0.808391	−	0.588646i	$-0.799661\pi$
$2$	−2.28647	−1.61678	−0.808391	+	0.588646i	$0.799661\pi$
$3$	−0.837618	−0.483599	−0.241799	−	0.970326i	$-0.577738\pi$
$3$	−0.837618	−0.483599	−0.241799	+	0.970326i	$0.577738\pi$
$4$	3.22797	1.61398
$5$	2.08578	0.932789	0.466394	−	0.884577i	$-0.345553\pi$
$5$	2.08578	0.932789	0.466394	+	0.884577i	$0.345553\pi$
$6$	1.91519	0.781874
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−2.80772	−0.992678
$9$	−2.29840	−0.766132
$10$	−4.76908	−1.50812
$11$	−1.28621	−0.387808	−0.193904	−	0.981021i	$-0.562115\pi$
$11$	−1.28621	−0.387808	−0.193904	+	0.981021i	$0.562115\pi$
$12$	−2.70380	−0.780521
$13$	−2.15289	−0.597105	−0.298553	−	0.954393i	$-0.596504\pi$
$13$	−2.15289	−0.597105	−0.298553	+	0.954393i	$0.596504\pi$
$14$	2.28647	0.611086
$15$	−1.74709	−0.451096
$16$	−0.0361596	−0.00903990
$17$	−1.02517	−0.248640	−0.124320	−	0.992242i	$-0.539675\pi$
$17$	−1.02517	−0.248640	−0.124320	+	0.992242i	$0.539675\pi$
$18$	5.25523	1.23867
$19$	−5.43559	−1.24701	−0.623504	−	0.781820i	$-0.714292\pi$
$19$	−5.43559	−1.24701	−0.623504	+	0.781820i	$0.714292\pi$
$20$	6.73283	1.50551
$21$	0.837618	0.182783
$22$	2.94089	0.627001
$23$	3.02379	0.630503	0.315252	−	0.949008i	$-0.397911\pi$
$23$	3.02379	0.630503	0.315252	+	0.949008i	$0.397911\pi$
$24$	2.35179	0.480058
$25$	−0.649527	−0.129905
$26$	4.92254	0.965389
$27$	4.43803	0.854100
$28$	−3.22797	−0.610029
$29$	−3.27660	−0.608449	−0.304224	−	0.952600i	$-0.598397\pi$
$29$	−3.27660	−0.608449	−0.304224	+	0.952600i	$0.598397\pi$
$30$	3.99467	0.729323
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	5.69811	1.00729
$33$	1.07735	0.187543
$34$	2.34402	0.401996
$35$	−2.08578	−0.352561
$36$	−7.41915	−1.23652
$37$	1.00000	0.164399
$37$	1.00000	0.164399
$38$	12.4283	2.01614
$39$	1.80330	0.288759
$40$	−5.85628	−0.925959
$41$	−11.9189	−1.86142	−0.930711	−	0.365755i	$-0.880811\pi$
$41$	−11.9189	−1.86142	−0.930711	+	0.365755i	$0.880811\pi$
$42$	−1.91519	−0.295521
$43$	11.8261	1.80347	0.901733	−	0.432293i	$-0.142295\pi$
$43$	11.8261	1.80347	0.901733	+	0.432293i	$0.142295\pi$
$44$	−4.15185	−0.625915
$45$	−4.79395	−0.714639
$46$	−6.91382	−1.01939
$47$	−3.81198	−0.556034	−0.278017	−	0.960576i	$-0.589677\pi$
$47$	−3.81198	−0.556034	−0.278017	+	0.960576i	$0.589677\pi$
$48$	0.0302879	0.00437168
$49$	1.00000	0.142857
$50$	1.48513	0.210029
$51$	0.858699	0.120242
$52$	−6.94947	−0.963718
$53$	−4.33265	−0.595136	−0.297568	−	0.954701i	$-0.596175\pi$
$53$	−4.33265	−0.595136	−0.297568	+	0.954701i	$0.596175\pi$
$54$	−10.1474	−1.38089
$55$	−2.68276	−0.361743
$56$	2.80772	0.375197
$57$	4.55294	0.603052
$58$	7.49186	0.983729
$59$	−5.09764	−0.663657	−0.331828	−	0.943340i	$-0.607666\pi$
$59$	−5.09764	−0.663657	−0.331828	+	0.943340i	$0.607666\pi$
$60$	−5.63954	−0.728061
$61$	6.16265	0.789047	0.394523	−	0.918886i	$-0.370910\pi$
$61$	6.16265	0.789047	0.394523	+	0.918886i	$0.370910\pi$
$62$	2.28647	0.290383
$63$	2.29840	0.289571
$64$	−12.9563	−1.61953
$65$	−4.49046	−0.556973
$66$	−2.46334	−0.303217
$67$	−12.9544	−1.58264	−0.791319	−	0.611404i	$-0.790605\pi$
$67$	−12.9544	−1.58264	−0.791319	+	0.611404i	$0.790605\pi$
$68$	−3.30921	−0.401301
$69$	−2.53278	−0.304911
$70$	4.76908	0.570014
$71$	−8.68065	−1.03020	−0.515102	−	0.857129i	$-0.672246\pi$
$71$	−8.68065	−1.03020	−0.515102	+	0.857129i	$0.672246\pi$
$72$	6.45325	0.760523
$73$	−1.82557	−0.213666	−0.106833	−	0.994277i	$-0.534071\pi$
$73$	−1.82557	−0.213666	−0.106833	+	0.994277i	$0.534071\pi$
$74$	−2.28647	−0.265797
$75$	0.544055	0.0628221
$76$	−17.5459	−2.01265
$77$	1.28621	0.146578
$78$	−4.12320	−0.466861
$79$	−4.93969	−0.555759	−0.277879	−	0.960616i	$-0.589632\pi$
$79$	−4.93969	−0.555759	−0.277879	+	0.960616i	$0.589632\pi$
$80$	−0.0754209	−0.00843231
$81$	3.17781	0.353091
$82$	27.2523	3.00951
$83$	−9.37127	−1.02863	−0.514316	−	0.857601i	$-0.671954\pi$
$83$	−9.37127	−1.02863	−0.514316	+	0.857601i	$0.671954\pi$
$84$	2.70380	0.295009
$85$	−2.13827	−0.231928
$86$	−27.0401	−2.91581
$87$	2.74454	0.294245
$88$	3.61132	0.384968
$89$	18.0914	1.91769	0.958844	−	0.283934i	$-0.0916395\pi$
$89$	18.0914	1.91769	0.958844	+	0.283934i	$0.0916395\pi$
$90$	10.9612	1.15542
$91$	2.15289	0.225685
$92$	9.76069	1.01762
$93$	0.837618	0.0868569
$94$	8.71599	0.898985
$95$	−11.3374	−1.16320
$96$	−4.77284	−0.487126
$97$	−10.9476	−1.11156	−0.555781	−	0.831329i	$-0.687581\pi$
$97$	−10.9476	−1.11156	−0.555781	+	0.831329i	$0.687581\pi$
$98$	−2.28647	−0.230969
$99$	2.95623	0.297112
$100$	−2.09665	−0.209665
$101$	−0.311985	−0.0310436	−0.0155218	−	0.999880i	$-0.504941\pi$
$101$	−0.311985	−0.0310436	−0.0155218	+	0.999880i	$0.504941\pi$
$102$	−1.96339	−0.194405
$103$	17.1665	1.69146	0.845731	−	0.533609i	$-0.179164\pi$
$103$	17.1665	1.69146	0.845731	+	0.533609i	$0.179164\pi$
$104$	6.04472	0.592733
$105$	1.74709	0.170498
$106$	9.90650	0.962204
$107$	−3.79349	−0.366730	−0.183365	−	0.983045i	$-0.558699\pi$
$107$	−3.79349	−0.366730	−0.183365	+	0.983045i	$0.558699\pi$
$108$	14.3258	1.37850
$109$	11.9627	1.14582	0.572910	−	0.819618i	$-0.305814\pi$
$109$	11.9627	1.14582	0.572910	+	0.819618i	$0.305814\pi$
$110$	6.13405	0.584859
$111$	−0.837618	−0.0795032
$112$	0.0361596	0.00341676
$113$	1.58130	0.148756	0.0743780	−	0.997230i	$-0.476303\pi$
$113$	1.58130	0.148756	0.0743780	+	0.997230i	$0.476303\pi$
$114$	−10.4102	−0.975004
$115$	6.30695	0.588126
$116$	−10.5768	−0.982027
$117$	4.94820	0.457461
$118$	11.6556	1.07299
$119$	1.02517	0.0939770
$120$	4.90532	0.447793
$121$	−9.34566	−0.849605
$122$	−14.0907	−1.27572
$123$	9.98350	0.900182
$124$	−3.22797	−0.289880
$125$	−11.7837	−1.05396
$126$	−5.25523	−0.468173
$127$	−3.64875	−0.323774	−0.161887	−	0.986809i	$-0.551758\pi$
$127$	−3.64875	−0.323774	−0.161887	+	0.986809i	$0.551758\pi$
$128$	18.2280	1.61114
$129$	−9.90577	−0.872154
$130$	10.2673	0.900504
$131$	−20.2777	−1.77167	−0.885834	−	0.464002i	$-0.846413\pi$
$131$	−20.2777	−1.77167	−0.885834	+	0.464002i	$0.846413\pi$
$132$	3.47767	0.302692
$133$	5.43559	0.471325
$134$	29.6200	2.55878
$135$	9.25675	0.796694
$136$	2.87838	0.246819
$137$	7.18745	0.614065	0.307033	−	0.951699i	$-0.400664\pi$
$137$	7.18745	0.614065	0.307033	+	0.951699i	$0.400664\pi$
$138$	5.79113	0.492974
$139$	5.97587	0.506866	0.253433	−	0.967353i	$-0.418440\pi$
$139$	5.97587	0.506866	0.253433	+	0.967353i	$0.418440\pi$
$140$	−6.73283	−0.569028
$141$	3.19298	0.268897
$142$	19.8481	1.66561
$143$	2.76908	0.231562
$144$	0.0831091	0.00692575
$145$	−6.83426	−0.567554
$146$	4.17411	0.345452
$147$	−0.837618	−0.0690856
$148$	3.22797	0.265337
$149$	4.55563	0.373212	0.186606	−	0.982435i	$-0.440251\pi$
$149$	4.55563	0.373212	0.186606	+	0.982435i	$0.440251\pi$
$150$	−1.24397	−0.101570
$151$	18.2116	1.48204	0.741021	−	0.671482i	$-0.234342\pi$
$151$	18.2116	1.48204	0.741021	+	0.671482i	$0.234342\pi$
$152$	15.2616	1.23788
$153$	2.35624	0.190491
$154$	−2.94089	−0.236984
$155$	−2.08578	−0.167534
$156$	5.82100	0.466053
$157$	−9.87463	−0.788082	−0.394041	−	0.919093i	$-0.628923\pi$
$157$	−9.87463	−0.788082	−0.394041	+	0.919093i	$0.628923\pi$
$158$	11.2945	0.898540
$159$	3.62911	0.287807
$160$	11.8850	0.939592
$161$	−3.02379	−0.238308
$162$	−7.26599	−0.570870
$163$	12.2780	0.961689	0.480844	−	0.876806i	$-0.340330\pi$
$163$	12.2780	0.961689	0.480844	+	0.876806i	$0.340330\pi$
$164$	−38.4739	−3.00431
$165$	2.24712	0.174938
$166$	21.4272	1.66307
$167$	−20.4683	−1.58389	−0.791944	−	0.610594i	$-0.790931\pi$
$167$	−20.4683	−1.58389	−0.791944	+	0.610594i	$0.790931\pi$
$168$	−2.35179	−0.181445
$169$	−8.36505	−0.643466
$170$	4.88911	0.374978
$171$	12.4931	0.955374
$172$	38.1743	2.91077
$173$	10.6674	0.811029	0.405515	−	0.914089i	$-0.367092\pi$
$173$	10.6674	0.811029	0.405515	+	0.914089i	$0.367092\pi$
$174$	−6.27531	−0.475730
$175$	0.649527	0.0490996
$176$	0.0465089	0.00350574
$177$	4.26988	0.320944
$178$	−41.3656	−3.10048
$179$	23.4364	1.75172	0.875859	−	0.482567i	$-0.160295\pi$
$179$	23.4364	1.75172	0.875859	+	0.482567i	$0.160295\pi$
$180$	−15.4747	−1.15342
$181$	3.12821	0.232518	0.116259	−	0.993219i	$-0.462910\pi$
$181$	3.12821	0.232518	0.116259	+	0.993219i	$0.462910\pi$
$182$	−4.92254	−0.364883
$183$	−5.16195	−0.381582
$184$	−8.48994	−0.625887
$185$	2.08578	0.153350
$186$	−1.91519	−0.140429
$187$	1.31858	0.0964245
$188$	−12.3049	−0.897430
$189$	−4.43803	−0.322819
$190$	25.9228	1.88063
$191$	16.2863	1.17844	0.589218	−	0.807974i	$-0.299436\pi$
$191$	16.2863	1.17844	0.589218	+	0.807974i	$0.299436\pi$
$192$	10.8524	0.783205
$193$	0.507691	0.0365444	0.0182722	−	0.999833i	$-0.494183\pi$
$193$	0.507691	0.0365444	0.0182722	+	0.999833i	$0.494183\pi$
$194$	25.0314	1.79715
$195$	3.76129	0.269351
$196$	3.22797	0.230569
$197$	25.1375	1.79097	0.895485	−	0.445092i	$-0.146829\pi$
$197$	25.1375	1.79097	0.895485	+	0.445092i	$0.146829\pi$
$198$	−6.75934	−0.480365
$199$	−27.2057	−1.92856	−0.964282	−	0.264878i	$-0.914668\pi$
$199$	−27.2057	−1.92856	−0.964282	+	0.264878i	$0.914668\pi$
$200$	1.82369	0.128954
$201$	10.8509	0.765362
$202$	0.713345	0.0501908
$203$	3.27660	0.229972
$204$	2.77185	0.194069
$205$	−24.8602	−1.73631
$206$	−39.2507	−2.73473
$207$	−6.94986	−0.483049
$208$	0.0778477	0.00539777
$209$	6.99132	0.483600
$210$	−3.99467	−0.275658
$211$	−8.61607	−0.593154	−0.296577	−	0.955009i	$-0.595845\pi$
$211$	−8.61607	−0.593154	−0.296577	+	0.955009i	$0.595845\pi$
$212$	−13.9857	−0.960539
$213$	7.27106	0.498205
$214$	8.67371	0.592923
$215$	24.6667	1.68225
$216$	−12.4607	−0.847846
$217$	1.00000	0.0678844
$218$	−27.3525	−1.85254
$219$	1.52913	0.103329
$220$	−8.65985	−0.583847
$221$	2.20708	0.148464
$222$	1.91519	0.128539
$223$	14.5385	0.973571	0.486785	−	0.873522i	$-0.338169\pi$
$223$	14.5385	0.973571	0.486785	+	0.873522i	$0.338169\pi$
$224$	−5.69811	−0.380721
$225$	1.49287	0.0995247
$226$	−3.61560	−0.240506
$227$	−1.48119	−0.0983099	−0.0491549	−	0.998791i	$-0.515653\pi$
$227$	−1.48119	−0.0983099	−0.0491549	+	0.998791i	$0.515653\pi$
$228$	14.6968	0.973316
$229$	5.35838	0.354092	0.177046	−	0.984203i	$-0.443346\pi$
$229$	5.35838	0.354092	0.177046	+	0.984203i	$0.443346\pi$
$230$	−14.4207	−0.950872
$231$	−1.07735	−0.0708847
$232$	9.19976	0.603994
$233$	1.37191	0.0898767	0.0449384	−	0.998990i	$-0.485691\pi$
$233$	1.37191	0.0898767	0.0449384	+	0.998990i	$0.485691\pi$
$234$	−11.3139	−0.739615
$235$	−7.95094	−0.518662
$236$	−16.4550	−1.07113
$237$	4.13757	0.268764
$238$	−2.34402	−0.151940
$239$	17.8315	1.15342	0.576710	−	0.816949i	$-0.304336\pi$
$239$	17.8315	1.15342	0.576710	+	0.816949i	$0.304336\pi$
$240$	0.0631739	0.00407786
$241$	10.6061	0.683199	0.341600	−	0.939846i	$-0.389031\pi$
$241$	10.6061	0.683199	0.341600	+	0.939846i	$0.389031\pi$
$242$	21.3686	1.37363
$243$	−15.9759	−1.02485
$244$	19.8928	1.27351
$245$	2.08578	0.133256
$246$	−22.8270	−1.45540
$247$	11.7022	0.744595
$248$	2.80772	0.178290
$249$	7.84955	0.497445
$250$	26.9431	1.70403
$251$	8.50210	0.536648	0.268324	−	0.963329i	$-0.413530\pi$
$251$	8.50210	0.536648	0.268324	+	0.963329i	$0.413530\pi$
$252$	7.41915	0.467362
$253$	−3.88923	−0.244514
$254$	8.34278	0.523473
$255$	1.79106	0.112160
$256$	−15.7652	−0.985328
$257$	13.1914	0.822856	0.411428	−	0.911442i	$-0.365030\pi$
$257$	13.1914	0.822856	0.411428	+	0.911442i	$0.365030\pi$
$258$	22.6493	1.41008
$259$	−1.00000	−0.0621370
$260$	−14.4951	−0.898945
$261$	7.53092	0.466152
$262$	46.3644	2.86440
$263$	−22.8685	−1.41013	−0.705066	−	0.709142i	$-0.749083\pi$
$263$	−22.8685	−1.41013	−0.705066	+	0.709142i	$0.749083\pi$
$264$	−3.02491	−0.186170
$265$	−9.03695	−0.555136
$266$	−12.4283	−0.762030
$267$	−15.1537	−0.927392
$268$	−41.8165	−2.55435
$269$	11.0810	0.675620	0.337810	−	0.941214i	$-0.390314\pi$
$269$	11.0810	0.675620	0.337810	+	0.941214i	$0.390314\pi$
$270$	−21.1653	−1.28808
$271$	−1.02101	−0.0620218	−0.0310109	−	0.999519i	$-0.509873\pi$
$271$	−1.02101	−0.0620218	−0.0310109	+	0.999519i	$0.509873\pi$
$272$	0.0370697	0.00224768
$273$	−1.80330	−0.109141
$274$	−16.4339	−0.992809
$275$	0.835430	0.0503783
$276$	−8.17573	−0.492121
$277$	−22.8991	−1.37588	−0.687938	−	0.725769i	$-0.741484\pi$
$277$	−22.8991	−1.37588	−0.687938	+	0.725769i	$0.741484\pi$
$278$	−13.6637	−0.819492
$279$	2.29840	0.137601
$280$	5.85628	0.349980
$281$	15.2452	0.909450	0.454725	−	0.890632i	$-0.349738\pi$
$281$	15.2452	0.909450	0.454725	+	0.890632i	$0.349738\pi$
$282$	−7.30067	−0.434748
$283$	−7.05166	−0.419177	−0.209589	−	0.977790i	$-0.567213\pi$
$283$	−7.05166	−0.419177	−0.209589	+	0.977790i	$0.567213\pi$
$284$	−28.0208	−1.66273
$285$	9.49643	0.562520
$286$	−6.33143	−0.374385
$287$	11.9189	0.703552
$288$	−13.0965	−0.771720
$289$	−15.9490	−0.938178
$290$	15.6264	0.917611
$291$	9.16991	0.537550
$292$	−5.89287	−0.344854
$293$	0.273987	0.0160065	0.00800326	−	0.999968i	$-0.497452\pi$
$293$	0.273987	0.0160065	0.00800326	+	0.999968i	$0.497452\pi$
$294$	1.91519	0.111696
$295$	−10.6326	−0.619052
$296$	−2.80772	−0.163195
$297$	−5.70825	−0.331226
$298$	−10.4163	−0.603402
$299$	−6.50989	−0.376477
$300$	1.75619	0.101394
$301$	−11.8261	−0.681646
$302$	−41.6405	−2.39614
$303$	0.261324	0.0150127
$304$	0.196549	0.0112728
$305$	12.8539	0.736014
$306$	−5.38749	−0.307982
$307$	−3.29630	−0.188130	−0.0940649	−	0.995566i	$-0.529986\pi$
$307$	−3.29630	−0.188130	−0.0940649	+	0.995566i	$0.529986\pi$
$308$	4.15185	0.236574
$309$	−14.3789	−0.817990
$310$	4.76908	0.270866
$311$	12.3802	0.702019	0.351010	−	0.936372i	$-0.385838\pi$
$311$	12.3802	0.702019	0.351010	+	0.936372i	$0.385838\pi$
$312$	−5.06316	−0.286645
$313$	−12.4468	−0.703534	−0.351767	−	0.936088i	$-0.614419\pi$
$313$	−12.4468	−0.703534	−0.351767	+	0.936088i	$0.614419\pi$
$314$	22.5781	1.27416
$315$	4.79395	0.270108
$316$	−15.9452	−0.896985
$317$	−2.60409	−0.146260	−0.0731302	−	0.997322i	$-0.523299\pi$
$317$	−2.60409	−0.146260	−0.0731302	+	0.997322i	$0.523299\pi$
$318$	−8.29786	−0.465321
$319$	4.21440	0.235961
$320$	−27.0239	−1.51068
$321$	3.17749	0.177350
$322$	6.91382	0.385292
$323$	5.57239	0.310056
$324$	10.2579	0.569882
$325$	1.39836	0.0775671
$326$	−28.0734	−1.55484
$327$	−10.0202	−0.554118
$328$	33.4650	1.84779
$329$	3.81198	0.210161
$330$	−5.13799	−0.282837
$331$	5.51385	0.303068	0.151534	−	0.988452i	$-0.451579\pi$
$331$	5.51385	0.303068	0.151534	+	0.988452i	$0.451579\pi$
$332$	−30.2502	−1.66019
$333$	−2.29840	−0.125951
$334$	46.8003	2.56080
$335$	−27.0201	−1.47627
$336$	−0.0302879	−0.00165234
$337$	−1.11543	−0.0607613	−0.0303807	−	0.999538i	$-0.509672\pi$
$337$	−1.11543	−0.0607613	−0.0303807	+	0.999538i	$0.509672\pi$
$338$	19.1265	1.04034
$339$	−1.32452	−0.0719382
$340$	−6.90228	−0.374329
$341$	1.28621	0.0696523
$342$	−28.5652	−1.54463
$343$	−1.00000	−0.0539949
$344$	−33.2044	−1.79026
$345$	−5.28282	−0.284417
$346$	−24.3908	−1.31126
$347$	−0.544170	−0.0292126	−0.0146063	−	0.999893i	$-0.504649\pi$
$347$	−0.544170	−0.0292126	−0.0146063	+	0.999893i	$0.504649\pi$
$348$	8.85927	0.474907
$349$	−21.6121	−1.15687	−0.578436	−	0.815728i	$-0.696337\pi$
$349$	−21.6121	−1.15687	−0.578436	+	0.815728i	$0.696337\pi$
$350$	−1.48513	−0.0793834
$351$	−9.55461	−0.509987
$352$	−7.32899	−0.390636
$353$	−24.9411	−1.32748	−0.663740	−	0.747964i	$-0.731032\pi$
$353$	−24.9411	−1.32748	−0.663740	+	0.747964i	$0.731032\pi$
$354$	−9.76297	−0.518896
$355$	−18.1059	−0.960962
$356$	58.3986	3.09512
$357$	−0.858699	−0.0454472
$358$	−53.5867	−2.83215
$359$	22.6369	1.19473	0.597365	−	0.801970i	$-0.296215\pi$
$359$	22.6369	1.19473	0.597365	+	0.801970i	$0.296215\pi$
$360$	13.4600	0.709407
$361$	10.5456	0.555031
$362$	−7.15258	−0.375931
$363$	7.82809	0.410868
$364$	6.94947	0.364251
$365$	−3.80773	−0.199306
$366$	11.8027	0.616935
$367$	8.39171	0.438044	0.219022	−	0.975720i	$-0.429713\pi$
$367$	8.39171	0.438044	0.219022	+	0.975720i	$0.429713\pi$
$368$	−0.109339	−0.00569968
$369$	27.3944	1.42610
$370$	−4.76908	−0.247933
$371$	4.33265	0.224940
$372$	2.70380	0.140186
$373$	−14.1695	−0.733670	−0.366835	−	0.930286i	$-0.619559\pi$
$373$	−14.1695	−0.733670	−0.366835	+	0.930286i	$0.619559\pi$
$374$	−3.01491	−0.155897
$375$	9.87021	0.509695
$376$	10.7030	0.551963
$377$	7.05416	0.363308
$378$	10.1474	0.521928
$379$	−21.5617	−1.10755	−0.553775	−	0.832666i	$-0.686813\pi$
$379$	−21.5617	−1.10755	−0.553775	+	0.832666i	$0.686813\pi$
$380$	−36.5969	−1.87738
$381$	3.05626	0.156577
$382$	−37.2383	−1.90528
$383$	14.1579	0.723437	0.361719	−	0.932287i	$-0.382190\pi$
$383$	14.1579	0.723437	0.361719	+	0.932287i	$0.382190\pi$
$384$	−15.2681	−0.779146
$385$	2.68276	0.136726
$386$	−1.16082	−0.0590843
$387$	−27.1811	−1.38169
$388$	−35.3385	−1.79404
$389$	24.3921	1.23673	0.618365	−	0.785891i	$-0.287795\pi$
$389$	24.3921	1.23673	0.618365	+	0.785891i	$0.287795\pi$
$390$	−8.60009	−0.435483
$391$	−3.09989	−0.156768
$392$	−2.80772	−0.141811
$393$	16.9849	0.856777
$394$	−57.4762	−2.89561
$395$	−10.3031	−0.518405
$396$	9.54260	0.479534
$397$	−34.0130	−1.70706	−0.853531	−	0.521042i	$-0.825544\pi$
$397$	−34.0130	−1.70706	−0.853531	+	0.521042i	$0.825544\pi$
$398$	62.2052	3.11807
$399$	−4.55294	−0.227932
$400$	0.0234866	0.00117433
$401$	13.2295	0.660650	0.330325	−	0.943867i	$-0.392842\pi$
$401$	13.2295	0.660650	0.330325	+	0.943867i	$0.392842\pi$
$402$	−24.8103	−1.23742
$403$	2.15289	0.107243
$404$	−1.00708	−0.0501039
$405$	6.62822	0.329359
$406$	−7.49186	−0.371815
$407$	−1.28621	−0.0637552
$408$	−2.41099	−0.119362
$409$	6.37095	0.315023	0.157512	−	0.987517i	$-0.449653\pi$
$409$	6.37095	0.315023	0.157512	+	0.987517i	$0.449653\pi$
$410$	56.8423	2.80724
$411$	−6.02033	−0.296961
$412$	55.4128	2.72999
$413$	5.09764	0.250839
$414$	15.8907	0.780985
$415$	−19.5464	−0.959495
$416$	−12.2674	−0.601460
$417$	−5.00549	−0.245120
$418$	−15.9855	−0.781875
$419$	−8.59700	−0.419991	−0.209996	−	0.977702i	$-0.567345\pi$
$419$	−8.59700	−0.419991	−0.209996	+	0.977702i	$0.567345\pi$
$420$	5.63954	0.275181
$421$	1.31688	0.0641808	0.0320904	−	0.999485i	$-0.489784\pi$
$421$	1.31688	0.0641808	0.0320904	+	0.999485i	$0.489784\pi$
$422$	19.7004	0.959001
$423$	8.76143	0.425995
$424$	12.1649	0.590778
$425$	0.665874	0.0322997
$426$	−16.6251	−0.805489
$427$	−6.16265	−0.298232
$428$	−12.2453	−0.591897
$429$	−2.31943	−0.111983
$430$	−56.3997	−2.71984
$431$	35.7494	1.72199	0.860994	−	0.508614i	$-0.169842\pi$
$431$	35.7494	1.72199	0.860994	+	0.508614i	$0.169842\pi$
$432$	−0.160477	−0.00772097
$433$	−0.682176	−0.0327833	−0.0163917	−	0.999866i	$-0.505218\pi$
$433$	−0.682176	−0.0327833	−0.0163917	+	0.999866i	$0.505218\pi$
$434$	−2.28647	−0.109754
$435$	5.72450	0.274469
$436$	38.6153	1.84934
$437$	−16.4361	−0.786243
$438$	−3.49631	−0.167060
$439$	14.1443	0.675069	0.337535	−	0.941313i	$-0.390407\pi$
$439$	14.1443	0.675069	0.337535	+	0.941313i	$0.390407\pi$
$440$	7.53242	0.359094
$441$	−2.29840	−0.109447
$442$	−5.04643	−0.240034
$443$	−5.42238	−0.257625	−0.128813	−	0.991669i	$-0.541117\pi$
$443$	−5.42238	−0.257625	−0.128813	+	0.991669i	$0.541117\pi$
$444$	−2.70380	−0.128317
$445$	37.7347	1.78880
$446$	−33.2419	−1.57405
$447$	−3.81587	−0.180485
$448$	12.9563	0.612126
$449$	9.42444	0.444767	0.222383	−	0.974959i	$-0.428616\pi$
$449$	9.42444	0.444767	0.222383	+	0.974959i	$0.428616\pi$
$450$	−3.41341	−0.160910
$451$	15.3303	0.721874
$452$	5.10438	0.240090
$453$	−15.2544	−0.716714
$454$	3.38670	0.158946
$455$	4.49046	0.210516
$456$	−12.7834	−0.598637
$457$	4.80814	0.224915	0.112458	−	0.993657i	$-0.464128\pi$
$457$	4.80814	0.224915	0.112458	+	0.993657i	$0.464128\pi$
$458$	−12.2518	−0.572489
$459$	−4.54973	−0.212363
$460$	20.3586	0.949226
$461$	7.95301	0.370409	0.185204	−	0.982700i	$-0.440705\pi$
$461$	7.95301	0.370409	0.185204	+	0.982700i	$0.440705\pi$
$462$	2.46334	0.114605
$463$	2.68624	0.124840	0.0624201	−	0.998050i	$-0.480118\pi$
$463$	2.68624	0.124840	0.0624201	+	0.998050i	$0.480118\pi$
$464$	0.118480	0.00550031
$465$	1.74709	0.0810192
$466$	−3.13683	−0.145311
$467$	0.450243	0.0208348	0.0104174	−	0.999946i	$-0.496684\pi$
$467$	0.450243	0.0208348	0.0104174	+	0.999946i	$0.496684\pi$
$468$	15.9726	0.738335
$469$	12.9544	0.598181
$470$	18.1796	0.838563
$471$	8.27117	0.381115
$472$	14.3127	0.658798
$473$	−15.2109	−0.699398
$474$	−9.46046	−0.434533
$475$	3.53056	0.161993
$476$	3.30921	0.151677
$477$	9.95815	0.455952
$478$	−40.7712	−1.86483
$479$	−7.52287	−0.343729	−0.171864	−	0.985121i	$-0.554979\pi$
$479$	−7.52287	−0.343729	−0.171864	+	0.985121i	$0.554979\pi$
$480$	−9.95509	−0.454386
$481$	−2.15289	−0.0981635
$482$	−24.2506	−1.10458
$483$	2.53278	0.115245
$484$	−30.1675	−1.37125
$485$	−22.8343	−1.03685
$486$	36.5285	1.65696
$487$	13.9050	0.630095	0.315047	−	0.949076i	$-0.397980\pi$
$487$	13.9050	0.630095	0.315047	+	0.949076i	$0.397980\pi$
$488$	−17.3030	−0.783269
$489$	−10.2843	−0.465072
$490$	−4.76908	−0.215445
$491$	−27.8477	−1.25675	−0.628375	−	0.777910i	$-0.716280\pi$
$491$	−27.8477	−1.25675	−0.628375	+	0.777910i	$0.716280\pi$
$492$	32.2264	1.45288
$493$	3.35906	0.151285
$494$	−26.7569	−1.20385
$495$	6.16603	0.277143
$496$	0.0361596	0.00162361
$497$	8.68065	0.389380
$498$	−17.9478	−0.804260
$499$	6.22716	0.278766	0.139383	−	0.990239i	$-0.455488\pi$
$499$	6.22716	0.278766	0.139383	+	0.990239i	$0.455488\pi$
$500$	−38.0373	−1.70108
$501$	17.1446	0.765966
$502$	−19.4398	−0.867642
$503$	1.48036	0.0660060	0.0330030	−	0.999455i	$-0.489493\pi$
$503$	1.48036	0.0660060	0.0330030	+	0.999455i	$0.489493\pi$
$504$	−6.45325	−0.287451
$505$	−0.650731	−0.0289572
$506$	8.89264	0.395326
$507$	7.00672	0.311179
$508$	−11.7781	−0.522567
$509$	43.7138	1.93758	0.968790	−	0.247883i	$-0.0797348\pi$
$509$	43.7138	1.93758	0.968790	+	0.247883i	$0.0797348\pi$
$510$	−4.09521	−0.181339
$511$	1.82557	0.0807583
$512$	−0.409093	−0.0180795
$513$	−24.1233	−1.06507
$514$	−30.1618	−1.33038
$515$	35.8055	1.57778
$516$	−31.9755	−1.40764
$517$	4.90301	0.215634
$518$	2.28647	0.100462
$519$	−8.93523	−0.392213
$520$	12.6079	0.552895
$521$	−41.0197	−1.79710	−0.898552	−	0.438867i	$-0.855380\pi$
$521$	−41.0197	−1.79710	−0.898552	+	0.438867i	$0.855380\pi$
$522$	−17.2193	−0.753666
$523$	−23.6422	−1.03380	−0.516900	−	0.856046i	$-0.672914\pi$
$523$	−23.6422	−1.03380	−0.516900	+	0.856046i	$0.672914\pi$
$524$	−65.4557	−2.85944
$525$	−0.544055	−0.0237445
$526$	52.2882	2.27988
$527$	1.02517	0.0446570
$528$	−0.0389567	−0.00169537
$529$	−13.8567	−0.602466
$530$	20.6628	0.897533
$531$	11.7164	0.508449
$532$	17.5459	0.760711
$533$	25.6602	1.11146
$534$	34.6486	1.49939
$535$	−7.91237	−0.342082
$536$	36.3724	1.57105
$537$	−19.6307	−0.847129
$538$	−25.3364	−1.09233
$539$	−1.28621	−0.0554011
$540$	29.8805	1.28585
$541$	−38.0088	−1.63412	−0.817062	−	0.576550i	$-0.804399\pi$
$541$	−38.0088	−1.63412	−0.817062	+	0.576550i	$0.804399\pi$
$542$	2.33451	0.100276
$543$	−2.62025	−0.112445
$544$	−5.84153	−0.250453
$545$	24.9516	1.06881
$546$	4.12320	0.176457
$547$	−13.1082	−0.560468	−0.280234	−	0.959932i	$-0.590412\pi$
$547$	−13.1082	−0.560468	−0.280234	+	0.959932i	$0.590412\pi$
$548$	23.2008	0.991091
$549$	−14.1642	−0.604514
$550$	−1.91019	−0.0814507
$551$	17.8102	0.758741
$552$	7.11133	0.302678
$553$	4.93969	0.210057
$554$	52.3583	2.22449
$555$	−1.74709	−0.0741596
$556$	19.2899	0.818074
$557$	−12.7192	−0.538929	−0.269465	−	0.963010i	$-0.586847\pi$
$557$	−12.7192	−0.538929	−0.269465	+	0.963010i	$0.586847\pi$
$558$	−5.25523	−0.222471
$559$	−25.4604	−1.07686
$560$	0.0754209	0.00318711
$561$	−1.10447	−0.0466308
$562$	−34.8577	−1.47038
$563$	32.8182	1.38312	0.691562	−	0.722317i	$-0.256923\pi$
$563$	32.8182	1.38312	0.691562	+	0.722317i	$0.256923\pi$
$564$	10.3068	0.433996
$565$	3.29824	0.138758
$566$	16.1234	0.677718
$567$	−3.17781	−0.133456
$568$	24.3728	1.02266
$569$	−12.1987	−0.511396	−0.255698	−	0.966757i	$-0.582305\pi$
$569$	−12.1987	−0.511396	−0.255698	+	0.966757i	$0.582305\pi$
$570$	−21.7134	−0.909472
$571$	43.9142	1.83775	0.918876	−	0.394548i	$-0.129099\pi$
$571$	43.9142	1.83775	0.918876	+	0.394548i	$0.129099\pi$
$572$	8.93850	0.373737
$573$	−13.6417	−0.569891
$574$	−27.2523	−1.13749
$575$	−1.96403	−0.0819058
$576$	29.7787	1.24078
$577$	39.2637	1.63457	0.817284	−	0.576235i	$-0.195479\pi$
$577$	39.2637	1.63457	0.817284	+	0.576235i	$0.195479\pi$
$578$	36.4671	1.51683
$579$	−0.425251	−0.0176728
$580$	−22.0608	−0.916023
$581$	9.37127	0.388786
$582$	−20.9668	−0.869101
$583$	5.57271	0.230798
$584$	5.12568	0.212102
$585$	10.3209	0.426715
$586$	−0.626465	−0.0258790
$587$	27.2764	1.12582	0.562909	−	0.826519i	$-0.309682\pi$
$587$	27.2764	1.12582	0.562909	+	0.826519i	$0.309682\pi$
$588$	−2.70380	−0.111503
$589$	5.43559	0.223969
$590$	24.3111	1.00087
$591$	−21.0556	−0.866111
$592$	−0.0361596	−0.00148615
$593$	−6.61877	−0.271800	−0.135900	−	0.990723i	$-0.543393\pi$
$593$	−6.61877	−0.271800	−0.135900	+	0.990723i	$0.543393\pi$
$594$	13.0518	0.535521
$595$	2.13827	0.0876607
$596$	14.7054	0.602357
$597$	22.7880	0.932651
$598$	14.8847	0.608681
$599$	−21.9013	−0.894863	−0.447432	−	0.894318i	$-0.647661\pi$
$599$	−21.9013	−0.894863	−0.447432	+	0.894318i	$0.647661\pi$
$600$	−1.52755	−0.0623621
$601$	12.3287	0.502898	0.251449	−	0.967871i	$-0.419093\pi$
$601$	12.3287	0.502898	0.251449	+	0.967871i	$0.419093\pi$
$602$	27.0401	1.10207
$603$	29.7745	1.21251
$604$	58.7866	2.39199
$605$	−19.4930	−0.792502
$606$	−0.597511	−0.0242722
$607$	41.1979	1.67217	0.836086	−	0.548599i	$-0.184838\pi$
$607$	41.1979	1.67217	0.836086	+	0.548599i	$0.184838\pi$
$608$	−30.9726	−1.25610
$609$	−2.74454	−0.111214
$610$	−29.3902	−1.18997
$611$	8.20678	0.332011
$612$	7.60588	0.307449
$613$	−43.0785	−1.73992	−0.869962	−	0.493119i	$-0.835857\pi$
$613$	−43.0785	−1.73992	−0.869962	+	0.493119i	$0.835857\pi$
$614$	7.53690	0.304165
$615$	20.8234	0.839679
$616$	−3.61132	−0.145504
$617$	32.6233	1.31337	0.656683	−	0.754167i	$-0.271959\pi$
$617$	32.6233	1.31337	0.656683	+	0.754167i	$0.271959\pi$
$618$	32.8771	1.32251
$619$	29.1016	1.16969	0.584847	−	0.811144i	$-0.301155\pi$
$619$	29.1016	1.16969	0.584847	+	0.811144i	$0.301155\pi$
$620$	−6.73283	−0.270397
$621$	13.4197	0.538513
$622$	−28.3071	−1.13501
$623$	−18.0914	−0.724818
$624$	−0.0652066	−0.00261035
$625$	−21.3305	−0.853219
$626$	28.4593	1.13746
$627$	−5.85605	−0.233868
$628$	−31.8750	−1.27195
$629$	−1.02517	−0.0408761
$630$	−10.9612	−0.436706
$631$	4.35386	0.173324	0.0866622	−	0.996238i	$-0.472380\pi$
$631$	4.35386	0.173324	0.0866622	+	0.996238i	$0.472380\pi$
$632$	13.8693	0.551689
$633$	7.21697	0.286849
$634$	5.95419	0.236471
$635$	−7.61049	−0.302013
$636$	11.7146	0.464516
$637$	−2.15289	−0.0853007
$638$	−9.63612	−0.381498
$639$	19.9516	0.789272
$640$	38.0195	1.50285
$641$	−19.4209	−0.767077	−0.383539	−	0.923525i	$-0.625295\pi$
$641$	−19.4209	−0.767077	−0.383539	+	0.923525i	$0.625295\pi$
$642$	−7.26526	−0.286737
$643$	9.88719	0.389913	0.194956	−	0.980812i	$-0.437543\pi$
$643$	9.88719	0.389913	0.194956	+	0.980812i	$0.437543\pi$
$644$	−9.76069	−0.384625
$645$	−20.6612	−0.813536
$646$	−12.7411	−0.501293
$647$	−6.55080	−0.257539	−0.128769	−	0.991675i	$-0.541103\pi$
$647$	−6.55080	−0.257539	−0.128769	+	0.991675i	$0.541103\pi$
$648$	−8.92241	−0.350505
$649$	6.55666	0.257371
$650$	−3.19732	−0.125409
$651$	−0.837618	−0.0328288
$652$	39.6331	1.55215
$653$	2.01617	0.0788987	0.0394493	−	0.999222i	$-0.487440\pi$
$653$	2.01617	0.0788987	0.0394493	+	0.999222i	$0.487440\pi$
$654$	22.9109	0.895888
$655$	−42.2947	−1.65259
$656$	0.430983	0.0168271
$657$	4.19588	0.163697
$658$	−8.71599	−0.339785
$659$	−31.7937	−1.23851	−0.619254	−	0.785191i	$-0.712565\pi$
$659$	−31.7937	−1.23851	−0.619254	+	0.785191i	$0.712565\pi$
$660$	7.25364	0.282348
$661$	−18.0289	−0.701242	−0.350621	−	0.936517i	$-0.614029\pi$
$661$	−18.0289	−0.701242	−0.350621	+	0.936517i	$0.614029\pi$
$662$	−12.6073	−0.489996
$663$	−1.84869	−0.0717971
$664$	26.3119	1.02110
$665$	11.3374	0.439647
$666$	5.25523	0.203636
$667$	−9.90773	−0.383629
$668$	−66.0711	−2.55637
$669$	−12.1777	−0.470818
$670$	61.7808	2.38680
$671$	−7.92648	−0.305998
$672$	4.77284	0.184116
$673$	−41.0534	−1.58249	−0.791245	−	0.611499i	$-0.790567\pi$
$673$	−41.0534	−1.58249	−0.791245	+	0.611499i	$0.790567\pi$
$674$	2.55040	0.0982378
$675$	−2.88262	−0.110952
$676$	−27.0021	−1.03854
$677$	19.8340	0.762282	0.381141	−	0.924517i	$-0.375531\pi$
$677$	19.8340	0.762282	0.381141	+	0.924517i	$0.375531\pi$
$678$	3.02849	0.116308
$679$	10.9476	0.420131
$680$	6.00367	0.230230
$681$	1.24067	0.0475425
$682$	−2.94089	−0.112613
$683$	30.3336	1.16068	0.580342	−	0.814373i	$-0.302919\pi$
$683$	30.3336	1.16068	0.580342	+	0.814373i	$0.302919\pi$
$684$	40.3274	1.54196
$685$	14.9914	0.572793
$686$	2.28647	0.0872980
$687$	−4.48828	−0.171238
$688$	−0.427628	−0.0163031
$689$	9.32774	0.355358
$690$	12.0790	0.459841
$691$	32.6876	1.24350	0.621748	−	0.783218i	$-0.286423\pi$
$691$	32.6876	1.24350	0.621748	+	0.783218i	$0.286423\pi$
$692$	34.4341	1.30899
$693$	−2.95623	−0.112298
$694$	1.24423	0.0472304
$695$	12.4643	0.472799
$696$	−7.70588	−0.292091
$697$	12.2189	0.462824
$698$	49.4156	1.87041
$699$	−1.14914	−0.0434643
$700$	2.09665	0.0792460
$701$	−16.3131	−0.616138	−0.308069	−	0.951364i	$-0.599683\pi$
$701$	−16.3131	−0.616138	−0.308069	+	0.951364i	$0.599683\pi$
$702$	21.8464	0.824538
$703$	−5.43559	−0.205007
$704$	16.6645	0.628068
$705$	6.65985	0.250824
$706$	57.0271	2.14624
$707$	0.311985	0.0117334
$708$	13.7830	0.517998
$709$	45.3966	1.70490	0.852452	−	0.522805i	$-0.175114\pi$
$709$	45.3966	1.70490	0.852452	+	0.522805i	$0.175114\pi$
$710$	41.3987	1.55367
$711$	11.3534	0.425784
$712$	−50.7956	−1.90365
$713$	−3.02379	−0.113242
$714$	1.96339	0.0734782
$715$	5.77568	0.215998
$716$	75.6519	2.82725
$717$	−14.9359	−0.557793
$718$	−51.7587	−1.93162
$719$	45.3878	1.69268	0.846339	−	0.532644i	$-0.178802\pi$
$719$	45.3878	1.69268	0.846339	+	0.532644i	$0.178802\pi$
$720$	0.173347	0.00646026
$721$	−17.1665	−0.639313
$722$	−24.1122	−0.897365
$723$	−8.88386	−0.330394
$724$	10.0978	0.375280
$725$	2.12824	0.0790408
$726$	−17.8987	−0.664284
$727$	6.45265	0.239315	0.119658	−	0.992815i	$-0.461820\pi$
$727$	6.45265	0.239315	0.119658	+	0.992815i	$0.461820\pi$
$728$	−6.04472	−0.224032
$729$	3.84824	0.142528
$730$	8.70628	0.322234
$731$	−12.1238	−0.448414
$732$	−16.6626	−0.615867
$733$	28.9699	1.07003	0.535014	−	0.844843i	$-0.320306\pi$
$733$	28.9699	1.07003	0.535014	+	0.844843i	$0.320306\pi$
$734$	−19.1874	−0.708221
$735$	−1.74709	−0.0644422
$736$	17.2299	0.635102
$737$	16.6622	0.613759
$738$	−62.6366	−2.30569
$739$	9.68333	0.356207	0.178104	−	0.984012i	$-0.443004\pi$
$739$	9.68333	0.356207	0.178104	+	0.984012i	$0.443004\pi$
$740$	6.73283	0.247504
$741$	−9.80200	−0.360085
$742$	−9.90650	−0.363679
$743$	15.3600	0.563505	0.281752	−	0.959487i	$-0.409084\pi$
$743$	15.3600	0.563505	0.281752	+	0.959487i	$0.409084\pi$
$744$	−2.35179	−0.0862210
$745$	9.50203	0.348127
$746$	32.3983	1.18618
$747$	21.5389	0.788067
$748$	4.25635	0.155628
$749$	3.79349	0.138611
$750$	−22.5680	−0.824066
$751$	52.0105	1.89789	0.948946	−	0.315440i	$-0.102152\pi$
$751$	52.0105	1.89789	0.948946	+	0.315440i	$0.102152\pi$
$752$	0.137839	0.00502649
$753$	−7.12151	−0.259522
$754$	−16.1292	−0.587390
$755$	37.9855	1.38243
$756$	−14.3258	−0.521025
$757$	11.9875	0.435694	0.217847	−	0.975983i	$-0.430097\pi$
$757$	11.9875	0.435694	0.217847	+	0.975983i	$0.430097\pi$
$758$	49.3003	1.79067
$759$	3.25769	0.118247
$760$	31.8323	1.15468
$761$	20.5075	0.743397	0.371698	−	0.928354i	$-0.378776\pi$
$761$	20.5075	0.743397	0.371698	+	0.928354i	$0.378776\pi$
$762$	−6.98806	−0.253151
$763$	−11.9627	−0.433080
$764$	52.5717	1.90198
$765$	4.91460	0.177688
$766$	−32.3718	−1.16964
$767$	10.9747	0.396273
$768$	13.2053	0.476504
$769$	−26.3080	−0.948692	−0.474346	−	0.880338i	$-0.657316\pi$
$769$	−26.3080	−0.948692	−0.474346	+	0.880338i	$0.657316\pi$
$770$	−6.13405	−0.221056
$771$	−11.0493	−0.397932
$772$	1.63881	0.0589821
$773$	−36.6991	−1.31997	−0.659987	−	0.751277i	$-0.729438\pi$
$773$	−36.6991	−1.31997	−0.659987	+	0.751277i	$0.729438\pi$
$774$	62.1489	2.23390
$775$	0.649527	0.0233317
$776$	30.7378	1.10342
$777$	0.837618	0.0300494
$778$	−55.7720	−1.99952
$779$	64.7863	2.32121
$780$	12.1413	0.434729
$781$	11.1652	0.399521
$782$	7.08782	0.253460
$783$	−14.5416	−0.519676
$784$	−0.0361596	−0.00129141
$785$	−20.5963	−0.735114
$786$	−38.8356	−1.38522
$787$	25.8948	0.923050	0.461525	−	0.887127i	$-0.347303\pi$
$787$	25.8948	0.923050	0.461525	+	0.887127i	$0.347303\pi$
$788$	81.1429	2.89060
$789$	19.1551	0.681938
$790$	23.5578	0.838148
$791$	−1.58130	−0.0562245
$792$	−8.30025	−0.294937
$793$	−13.2675	−0.471144
$794$	77.7698	2.75995
$795$	7.56951	0.268463
$796$	−87.8192	−3.11267
$797$	40.8305	1.44629	0.723145	−	0.690696i	$-0.242696\pi$
$797$	40.8305	1.44629	0.723145	+	0.690696i	$0.242696\pi$
$798$	10.4102	0.368517
$799$	3.90792	0.138252
$800$	−3.70108	−0.130853
$801$	−41.5813	−1.46920
$802$	−30.2489	−1.06813
$803$	2.34807	0.0828615
$804$	35.0263	1.23528
$805$	−6.30695	−0.222291
$806$	−4.92254	−0.173389
$807$	−9.28164	−0.326729
$808$	0.875965	0.0308163
$809$	−18.8451	−0.662559	−0.331280	−	0.943533i	$-0.607480\pi$
$809$	−18.8451	−0.662559	−0.331280	+	0.943533i	$0.607480\pi$
$810$	−15.1553	−0.532501
$811$	51.6903	1.81509	0.907546	−	0.419952i	$-0.137953\pi$
$811$	51.6903	1.81509	0.907546	+	0.419952i	$0.137953\pi$
$812$	10.5768	0.371171
$813$	0.855214	0.0299937
$814$	2.94089	0.103078
$815$	25.6092	0.897052
$816$	−0.0310502	−0.00108697
$817$	−64.2819	−2.24894
$818$	−14.5670	−0.509324
$819$	−4.94820	−0.172904
$820$	−80.2480	−2.80238
$821$	19.3620	0.675737	0.337869	−	0.941193i	$-0.390294\pi$
$821$	19.3620	0.675737	0.337869	+	0.941193i	$0.390294\pi$
$822$	13.7653	0.480121
$823$	−27.4299	−0.956146	−0.478073	−	0.878320i	$-0.658665\pi$
$823$	−27.4299	−0.956146	−0.478073	+	0.878320i	$0.658665\pi$
$824$	−48.1986	−1.67908
$825$	−0.699771	−0.0243629
$826$	−11.6556	−0.405551
$827$	11.9197	0.414490	0.207245	−	0.978289i	$-0.433550\pi$
$827$	11.9197	0.414490	0.207245	+	0.978289i	$0.433550\pi$
$828$	−22.4339	−0.779633
$829$	−13.2481	−0.460126	−0.230063	−	0.973176i	$-0.573893\pi$
$829$	−13.2481	−0.460126	−0.230063	+	0.973176i	$0.573893\pi$
$830$	44.6924	1.55129
$831$	19.1807	0.665372
$832$	27.8935	0.967032
$833$	−1.02517	−0.0355200
$834$	11.4449	0.396306
$835$	−42.6924	−1.47743
$836$	22.5678	0.780522
$837$	−4.43803	−0.153401
$838$	19.6568	0.679034
$839$	−13.4415	−0.464054	−0.232027	−	0.972709i	$-0.574536\pi$
$839$	−13.4415	−0.464054	−0.232027	+	0.972709i	$0.574536\pi$
$840$	−4.90532	−0.169250
$841$	−18.2639	−0.629790
$842$	−3.01101	−0.103766
$843$	−12.7696	−0.439809
$844$	−27.8124	−0.957342
$845$	−17.4476	−0.600217
$846$	−20.0328	−0.688742
$847$	9.34566	0.321121
$848$	0.156667	0.00537996
$849$	5.90659	0.202714
$850$	−1.52251	−0.0522215
$851$	3.02379	0.103654
$852$	23.4708	0.804095
$853$	27.5506	0.943313	0.471657	−	0.881782i	$-0.343656\pi$
$853$	27.5506	0.943313	0.471657	+	0.881782i	$0.343656\pi$
$854$	14.0907	0.482175
$855$	26.0579	0.891162
$856$	10.6510	0.364045
$857$	−47.8184	−1.63344	−0.816722	−	0.577031i	$-0.804211\pi$
$857$	−47.8184	−1.63344	−0.816722	+	0.577031i	$0.804211\pi$
$858$	5.30332	0.181052
$859$	57.4928	1.96163	0.980815	−	0.194940i	$-0.0624512\pi$
$859$	57.4928	1.96163	0.980815	+	0.194940i	$0.0624512\pi$
$860$	79.6232	2.71513
$861$	−9.98350	−0.340237
$862$	−81.7401	−2.78408
$863$	33.5978	1.14368	0.571841	−	0.820365i	$-0.306230\pi$
$863$	33.5978	1.14368	0.571841	+	0.820365i	$0.306230\pi$
$864$	25.2884	0.860329
$865$	22.2499	0.756519
$866$	1.55978	0.0530035
$867$	13.3592	0.453702
$868$	3.22797	0.109564
$869$	6.35349	0.215527
$870$	−13.0889	−0.443756
$871$	27.8895	0.945001
$872$	−33.5879	−1.13743
$873$	25.1619	0.851603
$874$	37.5806	1.27118
$875$	11.7837	0.398361
$876$	4.93597	0.166771
$877$	−24.8348	−0.838610	−0.419305	−	0.907845i	$-0.637726\pi$
$877$	−24.8348	−0.838610	−0.419305	+	0.907845i	$0.637726\pi$
$878$	−32.3405	−1.09144
$879$	−0.229497	−0.00774073
$880$	0.0970073	0.00327012
$881$	−15.9447	−0.537189	−0.268595	−	0.963253i	$-0.586559\pi$
$881$	−15.9447	−0.537189	−0.268595	+	0.963253i	$0.586559\pi$
$882$	5.25523	0.176953
$883$	−23.4883	−0.790446	−0.395223	−	0.918585i	$-0.629333\pi$
$883$	−23.4883	−0.790446	−0.395223	+	0.918585i	$0.629333\pi$
$884$	7.12438	0.239619
$885$	8.90602	0.299373
$886$	12.3981	0.416524
$887$	29.6737	0.996345	0.498172	−	0.867078i	$-0.334005\pi$
$887$	29.6737	0.996345	0.498172	+	0.867078i	$0.334005\pi$
$888$	2.35179	0.0789210
$889$	3.64875	0.122375
$890$	−86.2795	−2.89210
$891$	−4.08735	−0.136931
$892$	46.9298	1.57133
$893$	20.7203	0.693379
$894$	8.72490	0.291804
$895$	48.8831	1.63398
$896$	−18.2280	−0.608954
$897$	5.45280	0.182064
$898$	−21.5487	−0.719091
$899$	3.27660	0.109281
$900$	4.81894	0.160631
$901$	4.44170	0.147974
$902$	−35.0523	−1.16711
$903$	9.90577	0.329643
$904$	−4.43984	−0.147667
$905$	6.52476	0.216890
$906$	34.8788	1.15877
$907$	2.30500	0.0765364	0.0382682	−	0.999268i	$-0.487816\pi$
$907$	2.30500	0.0765364	0.0382682	+	0.999268i	$0.487816\pi$
$908$	−4.78123	−0.158671
$909$	0.717065	0.0237835
$910$	−10.2673	−0.340358
$911$	−41.2896	−1.36799	−0.683993	−	0.729488i	$-0.739758\pi$
$911$	−41.2896	−1.36799	−0.683993	+	0.729488i	$0.739758\pi$
$912$	−0.164633	−0.00545153
$913$	12.0535	0.398911
$914$	−10.9937	−0.363639
$915$	−10.7667	−0.355935
$916$	17.2967	0.571498
$917$	20.2777	0.669628
$918$	10.4028	0.343345
$919$	56.7467	1.87190	0.935951	−	0.352130i	$-0.114543\pi$
$919$	56.7467	1.87190	0.935951	+	0.352130i	$0.114543\pi$
$920$	−17.7081	−0.583820
$921$	2.76104	0.0909793
$922$	−18.1844	−0.598870
$923$	18.6885	0.615139
$924$	−3.47767	−0.114407
$925$	−0.649527	−0.0213563
$926$	−6.14202	−0.201839
$927$	−39.4554	−1.29588
$928$	−18.6704	−0.612887
$929$	49.3565	1.61933	0.809667	−	0.586889i	$-0.199648\pi$
$929$	49.3565	1.61933	0.809667	+	0.586889i	$0.199648\pi$
$930$	−3.99467	−0.130990
$931$	−5.43559	−0.178144
$932$	4.42848	0.145060
$933$	−10.3699	−0.339496
$934$	−1.02947	−0.0336853
$935$	2.75028	0.0899436
$936$	−13.8932	−0.454112
$937$	−34.2587	−1.11918	−0.559592	−	0.828768i	$-0.689042\pi$
$937$	−34.2587	−1.11918	−0.559592	+	0.828768i	$0.689042\pi$
$938$	−29.6200	−0.967128
$939$	10.4257	0.340228
$940$	−25.6654	−0.837112
$941$	−18.7099	−0.609925	−0.304963	−	0.952364i	$-0.598644\pi$
$941$	−18.7099	−0.609925	−0.304963	+	0.952364i	$0.598644\pi$
$942$	−18.9118	−0.616180
$943$	−36.0403	−1.17363
$944$	0.184329	0.00599939
$945$	−9.25675	−0.301122
$946$	34.7794	1.13077
$947$	−1.83553	−0.0596468	−0.0298234	−	0.999555i	$-0.509494\pi$
$947$	−1.83553	−0.0596468	−0.0298234	+	0.999555i	$0.509494\pi$
$948$	13.3560	0.433781
$949$	3.93025	0.127581
$950$	−8.07253	−0.261908
$951$	2.18124	0.0707314
$952$	−2.87838	−0.0932889
$953$	−7.64210	−0.247552	−0.123776	−	0.992310i	$-0.539500\pi$
$953$	−7.64210	−0.247552	−0.123776	+	0.992310i	$0.539500\pi$
$954$	−22.7691	−0.737176
$955$	33.9697	1.09923
$956$	57.5594	1.86160
$957$	−3.53006	−0.114111
$958$	17.2009	0.555735
$959$	−7.18745	−0.232095
$960$	22.6357	0.730565
$961$	1.00000	0.0322581
$962$	4.92254	0.158709
$963$	8.71893	0.280964
$964$	34.2362	1.10267
$965$	1.05893	0.0340882
$966$	−5.79113	−0.186327
$967$	26.1673	0.841482	0.420741	−	0.907181i	$-0.361770\pi$
$967$	26.1673	0.841482	0.420741	+	0.907181i	$0.361770\pi$
$968$	26.2400	0.843384
$969$	−4.66753	−0.149943
$970$	52.2100	1.67636
$971$	57.4580	1.84392	0.921958	−	0.387290i	$-0.126589\pi$
$971$	57.4580	1.84392	0.921958	+	0.387290i	$0.126589\pi$
$972$	−51.5697	−1.65410
$973$	−5.97587	−0.191577
$974$	−31.7934	−1.01873
$975$	−1.17129	−0.0375114
$976$	−0.222839	−0.00713290
$977$	−7.33974	−0.234819	−0.117410	−	0.993084i	$-0.537459\pi$
$977$	−7.33974	−0.234819	−0.117410	+	0.993084i	$0.537459\pi$
$978$	23.5148	0.751919
$979$	−23.2694	−0.743694
$980$	6.73283	0.215072
$981$	−27.4951	−0.877850
$982$	63.6731	2.03189
$983$	40.5905	1.29464	0.647318	−	0.762220i	$-0.275891\pi$
$983$	40.5905	1.29464	0.647318	+	0.762220i	$0.275891\pi$
$984$	−28.0308	−0.893591
$985$	52.4312	1.67060
$986$	−7.68042	−0.244594
$987$	−3.19298	−0.101634
$988$	37.7744	1.20176
$989$	35.7597	1.13709
$990$	−14.0985	−0.448079
$991$	55.8932	1.77551	0.887753	−	0.460321i	$-0.152266\pi$
$991$	55.8932	1.77551	0.887753	+	0.460321i	$0.152266\pi$
$992$	−5.69811	−0.180915
$993$	−4.61850	−0.146564
$994$	−19.8481	−0.629543
$995$	−56.7452	−1.79894
$996$	25.3381	0.802868
$997$	31.0310	0.982762	0.491381	−	0.870945i	$-0.336492\pi$
$997$	31.0310	0.982762	0.491381	+	0.870945i	$0.336492\pi$
$998$	−14.2382	−0.450704
$999$	4.43803	0.140413

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8029.2.a.h.1.9	✓	71

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8029.2.a.h.1.9	✓	71	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:	\( N \)	\(=\)	\( 8029 = 7 \cdot 31 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8029.a (trivial)

\(f(q)\)	\(=\)	\(q-2.28647 q^{2} -0.837618 q^{3} +3.22797 q^{4} +2.08578 q^{5} +1.91519 q^{6} -1.00000 q^{7} -2.80772 q^{8} -2.29840 q^{9} +O(q^{10})\)	\(q-2.28647 q^{2} -0.837618 q^{3} +3.22797 q^{4} +2.08578 q^{5} +1.91519 q^{6} -1.00000 q^{7} -2.80772 q^{8} -2.29840 q^{9} -4.76908 q^{10} -1.28621 q^{11} -2.70380 q^{12} -2.15289 q^{13} +2.28647 q^{14} -1.74709 q^{15} -0.0361596 q^{16} -1.02517 q^{17} +5.25523 q^{18} -5.43559 q^{19} +6.73283 q^{20} +0.837618 q^{21} +2.94089 q^{22} +3.02379 q^{23} +2.35179 q^{24} -0.649527 q^{25} +4.92254 q^{26} +4.43803 q^{27} -3.22797 q^{28} -3.27660 q^{29} +3.99467 q^{30} -1.00000 q^{31} +5.69811 q^{32} +1.07735 q^{33} +2.34402 q^{34} -2.08578 q^{35} -7.41915 q^{36} +1.00000 q^{37} +12.4283 q^{38} +1.80330 q^{39} -5.85628 q^{40} -11.9189 q^{41} -1.91519 q^{42} +11.8261 q^{43} -4.15185 q^{44} -4.79395 q^{45} -6.91382 q^{46} -3.81198 q^{47} +0.0302879 q^{48} +1.00000 q^{49} +1.48513 q^{50} +0.858699 q^{51} -6.94947 q^{52} -4.33265 q^{53} -10.1474 q^{54} -2.68276 q^{55} +2.80772 q^{56} +4.55294 q^{57} +7.49186 q^{58} -5.09764 q^{59} -5.63954 q^{60} +6.16265 q^{61} +2.28647 q^{62} +2.29840 q^{63} -12.9563 q^{64} -4.49046 q^{65} -2.46334 q^{66} -12.9544 q^{67} -3.30921 q^{68} -2.53278 q^{69} +4.76908 q^{70} -8.68065 q^{71} +6.45325 q^{72} -1.82557 q^{73} -2.28647 q^{74} +0.544055 q^{75} -17.5459 q^{76} +1.28621 q^{77} -4.12320 q^{78} -4.93969 q^{79} -0.0754209 q^{80} +3.17781 q^{81} +27.2523 q^{82} -9.37127 q^{83} +2.70380 q^{84} -2.13827 q^{85} -27.0401 q^{86} +2.74454 q^{87} +3.61132 q^{88} +18.0914 q^{89} +10.9612 q^{90} +2.15289 q^{91} +9.76069 q^{92} +0.837618 q^{93} +8.71599 q^{94} -11.3374 q^{95} -4.77284 q^{96} -10.9476 q^{97} -2.28647 q^{98} +2.95623 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 71 q + 6 q^{2} + 8 q^{3} + 78 q^{4} + 5 q^{6} - 71 q^{7} + 18 q^{8} + 87 q^{9}+O(q^{10}) \) 71 * q + 6 * q^2 + 8 * q^3 + 78 * q^4 + 5 * q^6 - 71 * q^7 + 18 * q^8 + 87 * q^9	\( 71 q + 6 q^{2} + 8 q^{3} + 78 q^{4} + 5 q^{6} - 71 q^{7} + 18 q^{8} + 87 q^{9} + 4 q^{10} + 57 q^{11} + 21 q^{12} - 20 q^{13} - 6 q^{14} + 22 q^{15} + 88 q^{16} - 19 q^{17} + q^{18} + 23 q^{19} + 25 q^{20} - 8 q^{21} + 18 q^{22} + 34 q^{23} + 15 q^{24} + 81 q^{25} - 13 q^{26} + 20 q^{27} - 78 q^{28} + 16 q^{29} + 6 q^{30} - 71 q^{31} + 47 q^{32} - 16 q^{33} + 32 q^{34} + 125 q^{36} + 71 q^{37} + 13 q^{38} + 30 q^{39} + 31 q^{40} + 17 q^{41} - 5 q^{42} + 38 q^{43} + 80 q^{44} - q^{45} + 26 q^{46} + 32 q^{47} + 61 q^{48} + 71 q^{49} + 47 q^{50} + 73 q^{51} - 23 q^{52} + 31 q^{53} + 47 q^{54} + 11 q^{55} - 18 q^{56} + 17 q^{57} - 2 q^{58} + 97 q^{59} + 103 q^{60} - q^{61} - 6 q^{62} - 87 q^{63} + 100 q^{64} + 46 q^{65} + 43 q^{66} + 75 q^{67} - 43 q^{68} + 10 q^{69} - 4 q^{70} + 131 q^{71} - 11 q^{72} - 15 q^{73} + 6 q^{74} + 76 q^{75} + 41 q^{76} - 57 q^{77} + 89 q^{78} + 8 q^{79} + 10 q^{80} + 171 q^{81} + 14 q^{82} + 18 q^{83} - 21 q^{84} + 47 q^{85} + 90 q^{86} - 59 q^{87} + 13 q^{88} + 18 q^{89} + 69 q^{90} + 20 q^{91} + 110 q^{92} - 8 q^{93} + 39 q^{94} + 72 q^{95} + 100 q^{96} + 23 q^{97} + 6 q^{98} + 168 q^{99}+O(q^{100}) \) 71 * q + 6 * q^2 + 8 * q^3 + 78 * q^4 + 5 * q^6 - 71 * q^7 + 18 * q^8 + 87 * q^9 + 4 * q^10 + 57 * q^11 + 21 * q^12 - 20 * q^13 - 6 * q^14 + 22 * q^15 + 88 * q^16 - 19 * q^17 + q^18 + 23 * q^19 + 25 * q^20 - 8 * q^21 + 18 * q^22 + 34 * q^23 + 15 * q^24 + 81 * q^25 - 13 * q^26 + 20 * q^27 - 78 * q^28 + 16 * q^29 + 6 * q^30 - 71 * q^31 + 47 * q^32 - 16 * q^33 + 32 * q^34 + 125 * q^36 + 71 * q^37 + 13 * q^38 + 30 * q^39 + 31 * q^40 + 17 * q^41 - 5 * q^42 + 38 * q^43 + 80 * q^44 - q^45 + 26 * q^46 + 32 * q^47 + 61 * q^48 + 71 * q^49 + 47 * q^50 + 73 * q^51 - 23 * q^52 + 31 * q^53 + 47 * q^54 + 11 * q^55 - 18 * q^56 + 17 * q^57 - 2 * q^58 + 97 * q^59 + 103 * q^60 - q^61 - 6 * q^62 - 87 * q^63 + 100 * q^64 + 46 * q^65 + 43 * q^66 + 75 * q^67 - 43 * q^68 + 10 * q^69 - 4 * q^70 + 131 * q^71 - 11 * q^72 - 15 * q^73 + 6 * q^74 + 76 * q^75 + 41 * q^76 - 57 * q^77 + 89 * q^78 + 8 * q^79 + 10 * q^80 + 171 * q^81 + 14 * q^82 + 18 * q^83 - 21 * q^84 + 47 * q^85 + 90 * q^86 - 59 * q^87 + 13 * q^88 + 18 * q^89 + 69 * q^90 + 20 * q^91 + 110 * q^92 - 8 * q^93 + 39 * q^94 + 72 * q^95 + 100 * q^96 + 23 * q^97 + 6 * q^98 + 168 * q^99

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