LMFDB - Embedded newform 2671.2.a.b.1.36

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2671,2,Mod(1,2671)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2671, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("2671.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2671 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2671.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:	$21.3280423799$
Analytic rank:	$0$
Dimension:	$122$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.36
Character	$\chi$	$=$	2671.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.24322 q^{2} +2.17580 q^{3} -0.454407 q^{4} -1.92456 q^{5} -2.70499 q^{6} +3.86028 q^{7} +3.05136 q^{8} +1.73408 q^{9} +O(q^{10})$	\(q-1.24322 q^{2} +2.17580 q^{3} -0.454407 q^{4} -1.92456 q^{5} -2.70499 q^{6} +3.86028 q^{7} +3.05136 q^{8} +1.73408 q^{9} +2.39264 q^{10} +6.39231 q^{11} -0.988696 q^{12} +5.89226 q^{13} -4.79918 q^{14} -4.18744 q^{15} -2.88470 q^{16} +0.389348 q^{17} -2.15585 q^{18} +4.73358 q^{19} +0.874531 q^{20} +8.39919 q^{21} -7.94704 q^{22} -2.02688 q^{23} +6.63914 q^{24} -1.29609 q^{25} -7.32536 q^{26} -2.75437 q^{27} -1.75414 q^{28} +7.87245 q^{29} +5.20590 q^{30} -2.44648 q^{31} -2.51641 q^{32} +13.9084 q^{33} -0.484045 q^{34} -7.42933 q^{35} -0.787980 q^{36} -1.83759 q^{37} -5.88488 q^{38} +12.8203 q^{39} -5.87252 q^{40} +8.59181 q^{41} -10.4420 q^{42} -10.6178 q^{43} -2.90471 q^{44} -3.33734 q^{45} +2.51985 q^{46} +6.79343 q^{47} -6.27652 q^{48} +7.90179 q^{49} +1.61132 q^{50} +0.847142 q^{51} -2.67748 q^{52} -4.69437 q^{53} +3.42429 q^{54} -12.3023 q^{55} +11.7791 q^{56} +10.2993 q^{57} -9.78718 q^{58} -10.9630 q^{59} +1.90280 q^{60} +9.15861 q^{61} +3.04151 q^{62} +6.69406 q^{63} +8.89786 q^{64} -11.3400 q^{65} -17.2911 q^{66} -9.35304 q^{67} -0.176923 q^{68} -4.41007 q^{69} +9.23628 q^{70} +0.283346 q^{71} +5.29132 q^{72} -13.7145 q^{73} +2.28452 q^{74} -2.82002 q^{75} -2.15097 q^{76} +24.6761 q^{77} -15.9385 q^{78} -8.38187 q^{79} +5.55177 q^{80} -11.1952 q^{81} -10.6815 q^{82} -14.8123 q^{83} -3.81665 q^{84} -0.749322 q^{85} +13.2002 q^{86} +17.1288 q^{87} +19.5053 q^{88} +11.9110 q^{89} +4.14904 q^{90} +22.7458 q^{91} +0.921026 q^{92} -5.32303 q^{93} -8.44571 q^{94} -9.11004 q^{95} -5.47520 q^{96} -5.49047 q^{97} -9.82366 q^{98} +11.0848 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 122 q + 14 q^{2} + 10 q^{3} + 128 q^{4} + 33 q^{5} + 22 q^{6} + 6 q^{7} + 36 q^{8} + 162 q^{9}+O(q^{10}) $ 122 * q + 14 * q^2 + 10 * q^3 + 128 * q^4 + 33 * q^5 + 22 * q^6 + 6 * q^7 + 36 * q^8 + 162 * q^9	\( 122 q + 14 q^{2} + 10 q^{3} + 128 q^{4} + 33 q^{5} + 22 q^{6} + 6 q^{7} + 36 q^{8} + 162 q^{9} + 16 q^{10} + 43 q^{11} + 23 q^{12} + 25 q^{13} + 45 q^{14} + 12 q^{15} + 132 q^{16} + 103 q^{17} + 30 q^{18} + 37 q^{19} + 63 q^{20} + 81 q^{21} + 15 q^{23} + 60 q^{24} + 151 q^{25} + 59 q^{26} + 22 q^{27} - 3 q^{28} + 80 q^{29} - 9 q^{30} + 15 q^{31} + 66 q^{32} + 93 q^{33} + 30 q^{34} + 23 q^{35} + 162 q^{36} + 18 q^{37} + 41 q^{38} + 10 q^{39} + 29 q^{40} + 249 q^{41} - 8 q^{42} + 14 q^{43} + 100 q^{44} + 59 q^{45} + 11 q^{46} + 57 q^{47} + 33 q^{48} + 180 q^{49} + 63 q^{50} + 26 q^{51} + 31 q^{52} + 65 q^{53} + 65 q^{54} - 8 q^{55} + 120 q^{56} + 57 q^{57} - 31 q^{58} + 108 q^{59} - q^{60} + 70 q^{61} + 25 q^{62} - 7 q^{63} + 100 q^{64} + 171 q^{65} + 12 q^{66} - 6 q^{67} + 184 q^{68} + 64 q^{69} - 24 q^{70} + 47 q^{71} + 53 q^{72} + 76 q^{73} + 66 q^{74} + 40 q^{75} + 32 q^{76} + 73 q^{77} - 19 q^{78} + 8 q^{79} + 115 q^{80} + 250 q^{81} - 13 q^{82} + 116 q^{83} + 159 q^{84} + 31 q^{85} + 91 q^{86} + 25 q^{87} - 43 q^{88} + 361 q^{89} + 32 q^{90} + 7 q^{91} + 5 q^{92} + 18 q^{93} + 23 q^{94} + 42 q^{95} + 77 q^{96} + 79 q^{97} + 56 q^{98} + 74 q^{99}+O(q^{100}) \) 122 * q + 14 * q^2 + 10 * q^3 + 128 * q^4 + 33 * q^5 + 22 * q^6 + 6 * q^7 + 36 * q^8 + 162 * q^9 + 16 * q^10 + 43 * q^11 + 23 * q^12 + 25 * q^13 + 45 * q^14 + 12 * q^15 + 132 * q^16 + 103 * q^17 + 30 * q^18 + 37 * q^19 + 63 * q^20 + 81 * q^21 + 15 * q^23 + 60 * q^24 + 151 * q^25 + 59 * q^26 + 22 * q^27 - 3 * q^28 + 80 * q^29 - 9 * q^30 + 15 * q^31 + 66 * q^32 + 93 * q^33 + 30 * q^34 + 23 * q^35 + 162 * q^36 + 18 * q^37 + 41 * q^38 + 10 * q^39 + 29 * q^40 + 249 * q^41 - 8 * q^42 + 14 * q^43 + 100 * q^44 + 59 * q^45 + 11 * q^46 + 57 * q^47 + 33 * q^48 + 180 * q^49 + 63 * q^50 + 26 * q^51 + 31 * q^52 + 65 * q^53 + 65 * q^54 - 8 * q^55 + 120 * q^56 + 57 * q^57 - 31 * q^58 + 108 * q^59 - q^60 + 70 * q^61 + 25 * q^62 - 7 * q^63 + 100 * q^64 + 171 * q^65 + 12 * q^66 - 6 * q^67 + 184 * q^68 + 64 * q^69 - 24 * q^70 + 47 * q^71 + 53 * q^72 + 76 * q^73 + 66 * q^74 + 40 * q^75 + 32 * q^76 + 73 * q^77 - 19 * q^78 + 8 * q^79 + 115 * q^80 + 250 * q^81 - 13 * q^82 + 116 * q^83 + 159 * q^84 + 31 * q^85 + 91 * q^86 + 25 * q^87 - 43 * q^88 + 361 * q^89 + 32 * q^90 + 7 * q^91 + 5 * q^92 + 18 * q^93 + 23 * q^94 + 42 * q^95 + 77 * q^96 + 79 * q^97 + 56 * q^98 + 74 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.24322	−0.879089	−0.439544	−	0.898221i	$-0.644860\pi$
$2$	−1.24322	−0.879089	−0.439544	+	0.898221i	$0.644860\pi$
$3$	2.17580	1.25620	0.628098	−	0.778134i	$-0.283834\pi$
$3$	2.17580	1.25620	0.628098	+	0.778134i	$0.283834\pi$
$4$	−0.454407	−0.227203
$5$	−1.92456	−0.860687	−0.430344	−	0.902665i	$-0.641608\pi$
$5$	−1.92456	−0.860687	−0.430344	+	0.902665i	$0.641608\pi$
$6$	−2.70499	−1.10431
$7$	3.86028	1.45905	0.729525	−	0.683954i	$-0.239741\pi$
$7$	3.86028	1.45905	0.729525	+	0.683954i	$0.239741\pi$
$8$	3.05136	1.07882
$9$	1.73408	0.578028
$10$	2.39264	0.756620
$11$	6.39231	1.92735	0.963677	−	0.267072i	$-0.0860561\pi$
$11$	6.39231	1.92735	0.963677	+	0.267072i	$0.0860561\pi$
$12$	−0.988696	−0.285412
$13$	5.89226	1.63422	0.817109	−	0.576483i	$-0.195575\pi$
$13$	5.89226	1.63422	0.817109	+	0.576483i	$0.195575\pi$
$14$	−4.79918	−1.28263
$15$	−4.18744	−1.08119
$16$	−2.88470	−0.721175
$17$	0.389348	0.0944308	0.0472154	−	0.998885i	$-0.484965\pi$
$17$	0.389348	0.0944308	0.0472154	+	0.998885i	$0.484965\pi$
$18$	−2.15585	−0.508138
$19$	4.73358	1.08596	0.542979	−	0.839746i	$-0.317296\pi$
$19$	4.73358	1.08596	0.542979	+	0.839746i	$0.317296\pi$
$20$	0.874531	0.195551
$21$	8.39919	1.83285
$22$	−7.94704	−1.69431
$23$	−2.02688	−0.422633	−0.211316	−	0.977418i	$-0.567775\pi$
$23$	−2.02688	−0.422633	−0.211316	+	0.977418i	$0.567775\pi$
$24$	6.63914	1.35521
$25$	−1.29609	−0.259217
$26$	−7.32536	−1.43662
$27$	−2.75437	−0.530079
$28$	−1.75414	−0.331501
$29$	7.87245	1.46188	0.730939	−	0.682443i	$-0.239083\pi$
$29$	7.87245	1.46188	0.730939	+	0.682443i	$0.239083\pi$
$30$	5.20590	0.950463
$31$	−2.44648	−0.439400	−0.219700	−	0.975567i	$-0.570508\pi$
$31$	−2.44648	−0.439400	−0.219700	+	0.975567i	$0.570508\pi$
$32$	−2.51641	−0.444844
$33$	13.9084	2.42113
$34$	−0.484045	−0.0830131
$35$	−7.42933	−1.25579
$36$	−0.787980	−0.131330
$37$	−1.83759	−0.302098	−0.151049	−	0.988526i	$-0.548265\pi$
$37$	−1.83759	−0.302098	−0.151049	+	0.988526i	$0.548265\pi$
$38$	−5.88488	−0.954653
$39$	12.8203	2.05290
$40$	−5.87252	−0.928527
$41$	8.59181	1.34182	0.670908	−	0.741541i	$-0.265905\pi$
$41$	8.59181	1.34182	0.670908	+	0.741541i	$0.265905\pi$
$42$	−10.4420	−1.61124
$43$	−10.6178	−1.61919	−0.809596	−	0.586987i	$-0.800314\pi$
$43$	−10.6178	−1.61919	−0.809596	+	0.586987i	$0.800314\pi$
$44$	−2.90471	−0.437901
$45$	−3.33734	−0.497501
$46$	2.51985	0.371532
$47$	6.79343	0.990923	0.495461	−	0.868630i	$-0.334999\pi$
$47$	6.79343	0.990923	0.495461	+	0.868630i	$0.334999\pi$
$48$	−6.27652	−0.905937
$49$	7.90179	1.12883
$50$	1.61132	0.227875
$51$	0.847142	0.118624
$52$	−2.67748	−0.371300
$53$	−4.69437	−0.644822	−0.322411	−	0.946600i	$-0.604493\pi$
$53$	−4.69437	−0.644822	−0.322411	+	0.946600i	$0.604493\pi$
$54$	3.42429	0.465987
$55$	−12.3023	−1.65885
$56$	11.7791	1.57405
$57$	10.2993	1.36418
$58$	−9.78718	−1.28512
$59$	−10.9630	−1.42726	−0.713628	−	0.700524i	$-0.752950\pi$
$59$	−10.9630	−1.42726	−0.713628	+	0.700524i	$0.752950\pi$
$60$	1.90280	0.245650
$61$	9.15861	1.17264	0.586320	−	0.810080i	$-0.300576\pi$
$61$	9.15861	1.17264	0.586320	+	0.810080i	$0.300576\pi$
$62$	3.04151	0.386272
$63$	6.69406	0.843372
$64$	8.89786	1.11223
$65$	−11.3400	−1.40655
$66$	−17.2911	−2.12839
$67$	−9.35304	−1.14266	−0.571328	−	0.820722i	$-0.693571\pi$
$67$	−9.35304	−1.14266	−0.571328	+	0.820722i	$0.693571\pi$
$68$	−0.176923	−0.0214550
$69$	−4.41007	−0.530910
$70$	9.23628	1.10395
$71$	0.283346	0.0336269	0.0168135	−	0.999859i	$-0.494648\pi$
$71$	0.283346	0.0336269	0.0168135	+	0.999859i	$0.494648\pi$
$72$	5.29132	0.623588
$73$	−13.7145	−1.60516	−0.802579	−	0.596546i	$-0.796539\pi$
$73$	−13.7145	−1.60516	−0.802579	+	0.596546i	$0.796539\pi$
$74$	2.28452	0.265571
$75$	−2.82002	−0.325628
$76$	−2.15097	−0.246733
$77$	24.6761	2.81211
$78$	−15.9385	−1.80468
$79$	−8.38187	−0.943034	−0.471517	−	0.881857i	$-0.656293\pi$
$79$	−8.38187	−0.943034	−0.471517	+	0.881857i	$0.656293\pi$
$80$	5.55177	0.620706
$81$	−11.1952	−1.24391
$82$	−10.6815	−1.17958
$83$	−14.8123	−1.62586	−0.812929	−	0.582363i	$-0.802128\pi$
$83$	−14.8123	−1.62586	−0.812929	+	0.582363i	$0.802128\pi$
$84$	−3.81665	−0.416430
$85$	−0.749322	−0.0812754
$86$	13.2002	1.42341
$87$	17.1288	1.83640
$88$	19.5053	2.07927
$89$	11.9110	1.26257	0.631283	−	0.775552i	$-0.282529\pi$
$89$	11.9110	1.26257	0.631283	+	0.775552i	$0.282529\pi$
$90$	4.14904	0.437348
$91$	22.7458	2.38441
$92$	0.921026	0.0960236
$93$	−5.32303	−0.551973
$94$	−8.44571	−0.871109
$95$	−9.11004	−0.934670
$96$	−5.47520	−0.558811
$97$	−5.49047	−0.557473	−0.278736	−	0.960368i	$-0.589916\pi$
$97$	−5.49047	−0.557473	−0.278736	+	0.960368i	$0.589916\pi$
$98$	−9.82366	−0.992339
$99$	11.0848	1.11406
$100$	0.588951	0.0588951
$101$	10.1987	1.01481	0.507404	−	0.861708i	$-0.330605\pi$
$101$	10.1987	1.01481	0.507404	+	0.861708i	$0.330605\pi$
$102$	−1.05318	−0.104281
$103$	−10.5041	−1.03500	−0.517501	−	0.855683i	$-0.673138\pi$
$103$	−10.5041	−1.03500	−0.517501	+	0.855683i	$0.673138\pi$
$104$	17.9794	1.76303
$105$	−16.1647	−1.57751
$106$	5.83613	0.566855
$107$	11.3075	1.09314	0.546569	−	0.837414i	$-0.315934\pi$
$107$	11.3075	1.09314	0.546569	+	0.837414i	$0.315934\pi$
$108$	1.25161	0.120436
$109$	−4.93022	−0.472229	−0.236115	−	0.971725i	$-0.575874\pi$
$109$	−4.93022	−0.472229	−0.236115	+	0.971725i	$0.575874\pi$
$110$	15.2945	1.45827
$111$	−3.99822	−0.379494
$112$	−11.1358	−1.05223
$113$	−21.0945	−1.98441	−0.992203	−	0.124629i	$-0.960226\pi$
$113$	−21.0945	−1.98441	−0.992203	+	0.124629i	$0.960226\pi$
$114$	−12.8043	−1.19923
$115$	3.90084	0.363755
$116$	−3.57729	−0.332143
$117$	10.2177	0.944624
$118$	13.6294	1.25469
$119$	1.50300	0.137779
$120$	−12.7774	−1.16641
$121$	29.8616	2.71469
$122$	−11.3862	−1.03085
$123$	18.6940	1.68558
$124$	1.11170	0.0998332
$125$	12.1172	1.08379
$126$	−8.32218	−0.741399
$127$	−8.02319	−0.711943	−0.355971	−	0.934497i	$-0.615850\pi$
$127$	−8.02319	−0.711943	−0.355971	+	0.934497i	$0.615850\pi$
$128$	−6.02915	−0.532907
$129$	−23.1021	−2.03402
$130$	14.0981	1.23648
$131$	12.5382	1.09547	0.547733	−	0.836653i	$-0.315491\pi$
$131$	12.5382	1.09547	0.547733	+	0.836653i	$0.315491\pi$
$132$	−6.32005	−0.550090
$133$	18.2730	1.58447
$134$	11.6279	1.00450
$135$	5.30094	0.456233
$136$	1.18804	0.101874
$137$	21.1081	1.80339	0.901695	−	0.432373i	$-0.142323\pi$
$137$	21.1081	1.80339	0.901695	+	0.432373i	$0.142323\pi$
$138$	5.48268	0.466717
$139$	1.19387	0.101263	0.0506315	−	0.998717i	$-0.483877\pi$
$139$	1.19387	0.101263	0.0506315	+	0.998717i	$0.483877\pi$
$140$	3.37594	0.285319
$141$	14.7811	1.24479
$142$	−0.352261	−0.0295611
$143$	37.6651	3.14972
$144$	−5.00231	−0.416860
$145$	−15.1510	−1.25822
$146$	17.0501	1.41108
$147$	17.1927	1.41803
$148$	0.835013	0.0686376
$149$	2.94047	0.240893	0.120446	−	0.992720i	$-0.461567\pi$
$149$	2.94047	0.240893	0.120446	+	0.992720i	$0.461567\pi$
$150$	3.50590	0.286256
$151$	−0.386936	−0.0314884	−0.0157442	−	0.999876i	$-0.505012\pi$
$151$	−0.386936	−0.0314884	−0.0157442	+	0.999876i	$0.505012\pi$
$152$	14.4439	1.17155
$153$	0.675163	0.0545837
$154$	−30.6778	−2.47209
$155$	4.70838	0.378186
$156$	−5.82565	−0.466425
$157$	−10.4148	−0.831188	−0.415594	−	0.909550i	$-0.636426\pi$
$157$	−10.4148	−0.831188	−0.415594	+	0.909550i	$0.636426\pi$
$158$	10.4205	0.829010
$159$	−10.2140	−0.810022
$160$	4.84298	0.382871
$161$	−7.82432	−0.616643
$162$	13.9181	1.09351
$163$	4.29963	0.336773	0.168386	−	0.985721i	$-0.446144\pi$
$163$	4.29963	0.336773	0.168386	+	0.985721i	$0.446144\pi$
$164$	−3.90418	−0.304865
$165$	−26.7674	−2.08384
$166$	18.4149	1.42927
$167$	−24.5866	−1.90257	−0.951283	−	0.308318i	$-0.900234\pi$
$167$	−24.5866	−1.90257	−0.951283	+	0.308318i	$0.900234\pi$
$168$	25.6290	1.97732
$169$	21.7187	1.67067
$170$	0.931572	0.0714483
$171$	8.20843	0.627714
$172$	4.82478	0.367886
$173$	13.6045	1.03433	0.517166	−	0.855885i	$-0.326987\pi$
$173$	13.6045	1.03433	0.517166	+	0.855885i	$0.326987\pi$
$174$	−21.2949	−1.61436
$175$	−5.00326	−0.378211
$176$	−18.4399	−1.38996
$177$	−23.8532	−1.79291
$178$	−14.8080	−1.10991
$179$	7.22796	0.540243	0.270121	−	0.962826i	$-0.412936\pi$
$179$	7.22796	0.540243	0.270121	+	0.962826i	$0.412936\pi$
$180$	1.51651	0.113034
$181$	12.1429	0.902573	0.451287	−	0.892379i	$-0.350965\pi$
$181$	12.1429	0.902573	0.451287	+	0.892379i	$0.350965\pi$
$182$	−28.2780	−2.09610
$183$	19.9273	1.47307
$184$	−6.18474	−0.455945
$185$	3.53654	0.260012
$186$	6.61769	0.485233
$187$	2.48883	0.182002
$188$	−3.08698	−0.225141
$189$	−10.6327	−0.773413
$190$	11.3258	0.821658
$191$	3.13714	0.226995	0.113498	−	0.993538i	$-0.463795\pi$
$191$	3.13714	0.226995	0.113498	+	0.993538i	$0.463795\pi$
$192$	19.3599	1.39718
$193$	12.0397	0.866638	0.433319	−	0.901241i	$-0.357342\pi$
$193$	12.0397	0.866638	0.433319	+	0.901241i	$0.357342\pi$
$194$	6.82586	0.490068
$195$	−24.6735	−1.76690
$196$	−3.59063	−0.256473
$197$	−17.5665	−1.25156	−0.625780	−	0.780000i	$-0.715219\pi$
$197$	−17.5665	−1.25156	−0.625780	+	0.780000i	$0.715219\pi$
$198$	−13.7808	−0.979361
$199$	−0.316531	−0.0224383	−0.0112191	−	0.999937i	$-0.503571\pi$
$199$	−0.316531	−0.0224383	−0.0112191	+	0.999937i	$0.503571\pi$
$200$	−3.95484	−0.279649
$201$	−20.3503	−1.43540
$202$	−12.6792	−0.892107
$203$	30.3899	2.13295
$204$	−0.384947	−0.0269517
$205$	−16.5354	−1.15488
$206$	13.0589	0.909858
$207$	−3.51477	−0.244294
$208$	−16.9974	−1.17856
$209$	30.2585	2.09302
$210$	20.0963	1.38677
$211$	6.03201	0.415261	0.207630	−	0.978207i	$-0.433425\pi$
$211$	6.03201	0.415261	0.207630	+	0.978207i	$0.433425\pi$
$212$	2.13315	0.146506
$213$	0.616502	0.0422420
$214$	−14.0577	−0.960965
$215$	20.4345	1.39362
$216$	−8.40460	−0.571861
$217$	−9.44409	−0.641107
$218$	6.12934	0.415131
$219$	−29.8399	−2.01639
$220$	5.59027	0.376896
$221$	2.29414	0.154321
$222$	4.97066	0.333609
$223$	17.0877	1.14428	0.572140	−	0.820156i	$-0.306113\pi$
$223$	17.0877	1.14428	0.572140	+	0.820156i	$0.306113\pi$
$224$	−9.71408	−0.649049
$225$	−2.24752	−0.149835
$226$	26.2251	1.74447
$227$	−5.16723	−0.342961	−0.171480	−	0.985188i	$-0.554855\pi$
$227$	−5.16723	−0.342961	−0.171480	+	0.985188i	$0.554855\pi$
$228$	−4.68007	−0.309945
$229$	−21.6836	−1.43289	−0.716446	−	0.697643i	$-0.754232\pi$
$229$	−21.6836	−1.43289	−0.716446	+	0.697643i	$0.754232\pi$
$230$	−4.84959	−0.319773
$231$	53.6902	3.53255
$232$	24.0217	1.57710
$233$	−3.43964	−0.225339	−0.112669	−	0.993633i	$-0.535940\pi$
$233$	−3.43964	−0.225339	−0.112669	+	0.993633i	$0.535940\pi$
$234$	−12.7028	−0.830408
$235$	−13.0743	−0.852875
$236$	4.98165	0.324278
$237$	−18.2372	−1.18464
$238$	−1.86855	−0.121120
$239$	−25.5109	−1.65016	−0.825081	−	0.565014i	$-0.808871\pi$
$239$	−25.5109	−1.65016	−0.825081	+	0.565014i	$0.808871\pi$
$240$	12.0795	0.779729
$241$	4.42376	0.284959	0.142480	−	0.989798i	$-0.454492\pi$
$241$	4.42376	0.284959	0.142480	+	0.989798i	$0.454492\pi$
$242$	−37.1245	−2.38645
$243$	−16.0953	−1.03252
$244$	−4.16173	−0.266428
$245$	−15.2074	−0.971567
$246$	−23.2408	−1.48178
$247$	27.8915	1.77469
$248$	−7.46509	−0.474034
$249$	−32.2285	−2.04240
$250$	−15.0643	−0.952749
$251$	22.8171	1.44020	0.720101	−	0.693869i	$-0.244095\pi$
$251$	22.8171	1.44020	0.720101	+	0.693869i	$0.244095\pi$
$252$	−3.04182	−0.191617
$253$	−12.9564	−0.814563
$254$	9.97458	0.625861
$255$	−1.63037	−0.102098
$256$	−10.3002	−0.643760
$257$	−22.4933	−1.40309	−0.701546	−	0.712624i	$-0.747506\pi$
$257$	−22.4933	−1.40309	−0.701546	+	0.712624i	$0.747506\pi$
$258$	28.7209	1.78809
$259$	−7.09361	−0.440776
$260$	5.15296	0.319573
$261$	13.6515	0.845006
$262$	−15.5877	−0.963012
$263$	−17.5574	−1.08263	−0.541317	−	0.840819i	$-0.682074\pi$
$263$	−17.5574	−1.08263	−0.541317	+	0.840819i	$0.682074\pi$
$264$	42.4395	2.61197
$265$	9.03458	0.554990
$266$	−22.7173	−1.39289
$267$	25.9160	1.58603
$268$	4.25008	0.259615
$269$	−14.7766	−0.900943	−0.450472	−	0.892791i	$-0.648744\pi$
$269$	−14.7766	−0.900943	−0.450472	+	0.892791i	$0.648744\pi$
$270$	−6.59023	−0.401069
$271$	−18.2551	−1.10892	−0.554459	−	0.832211i	$-0.687075\pi$
$271$	−18.2551	−1.10892	−0.554459	+	0.832211i	$0.687075\pi$
$272$	−1.12315	−0.0681012
$273$	49.4902	2.99528
$274$	−26.2420	−1.58534
$275$	−8.28499	−0.499604
$276$	2.00396	0.120624
$277$	11.5287	0.692690	0.346345	−	0.938107i	$-0.387423\pi$
$277$	11.5287	0.692690	0.346345	+	0.938107i	$0.387423\pi$
$278$	−1.48425	−0.0890191
$279$	−4.24240	−0.253986
$280$	−22.6696	−1.35477
$281$	23.6148	1.40874	0.704370	−	0.709833i	$-0.251229\pi$
$281$	23.6148	1.40874	0.704370	+	0.709833i	$0.251229\pi$
$282$	−18.3761	−1.09428
$283$	5.19320	0.308704	0.154352	−	0.988016i	$-0.450671\pi$
$283$	5.19320	0.308704	0.154352	+	0.988016i	$0.450671\pi$
$284$	−0.128754	−0.00764015
$285$	−19.8216	−1.17413
$286$	−46.8260	−2.76888
$287$	33.1668	1.95778
$288$	−4.36368	−0.257132
$289$	−16.8484	−0.991083
$290$	18.8360	1.10609
$291$	−11.9461	−0.700295
$292$	6.23195	0.364697
$293$	−11.5243	−0.673257	−0.336629	−	0.941637i	$-0.609287\pi$
$293$	−11.5243	−0.673257	−0.336629	+	0.941637i	$0.609287\pi$
$294$	−21.3743	−1.24657
$295$	21.0988	1.22842
$296$	−5.60715	−0.325909
$297$	−17.6068	−1.02165
$298$	−3.65565	−0.211766
$299$	−11.9429	−0.690674
$300$	1.28144	0.0739838
$301$	−40.9876	−2.36248
$302$	0.481046	0.0276811
$303$	22.1903	1.27480
$304$	−13.6550	−0.783166
$305$	−17.6263	−1.00928
$306$	−0.839375	−0.0479839
$307$	−16.9045	−0.964789	−0.482395	−	0.875954i	$-0.660233\pi$
$307$	−16.9045	−0.964789	−0.482395	+	0.875954i	$0.660233\pi$
$308$	−11.2130	−0.638920
$309$	−22.8548	−1.30017
$310$	−5.85354	−0.332459
$311$	−9.21419	−0.522489	−0.261244	−	0.965273i	$-0.584133\pi$
$311$	−9.21419	−0.522489	−0.261244	+	0.965273i	$0.584133\pi$
$312$	39.1195	2.21471
$313$	−22.8591	−1.29207	−0.646036	−	0.763307i	$-0.723574\pi$
$313$	−22.8591	−1.29207	−0.646036	+	0.763307i	$0.723574\pi$
$314$	12.9478	0.730688
$315$	−12.8831	−0.725879
$316$	3.80878	0.214261
$317$	24.8695	1.39681	0.698406	−	0.715702i	$-0.253893\pi$
$317$	24.8695	1.39681	0.698406	+	0.715702i	$0.253893\pi$
$318$	12.6982	0.712081
$319$	50.3231	2.81755
$320$	−17.1244	−0.957284
$321$	24.6028	1.37320
$322$	9.72734	0.542083
$323$	1.84301	0.102548
$324$	5.08718	0.282621
$325$	−7.63688	−0.423618
$326$	−5.34538	−0.296053
$327$	−10.7271	−0.593212
$328$	26.2168	1.44758
$329$	26.2245	1.44581
$330$	33.2777	1.83188
$331$	−0.285726	−0.0157049	−0.00785247	−	0.999969i	$-0.502500\pi$
$331$	−0.285726	−0.0157049	−0.00785247	+	0.999969i	$0.502500\pi$
$332$	6.73079	0.369400
$333$	−3.18653	−0.174621
$334$	30.5665	1.67252
$335$	18.0004	0.983469
$336$	−24.2291	−1.32181
$337$	16.3613	0.891255	0.445628	−	0.895218i	$-0.352981\pi$
$337$	16.3613	0.891255	0.445628	+	0.895218i	$0.352981\pi$
$338$	−27.0011	−1.46866
$339$	−45.8974	−2.49280
$340$	0.340497	0.0184661
$341$	−15.6386	−0.846879
$342$	−10.2049	−0.551816
$343$	3.48117	0.187966
$344$	−32.3987	−1.74682
$345$	8.48742	0.456947
$346$	−16.9134	−0.909269
$347$	4.92788	0.264542	0.132271	−	0.991214i	$-0.457773\pi$
$347$	4.92788	0.264542	0.132271	+	0.991214i	$0.457773\pi$
$348$	−7.78346	−0.417237
$349$	−9.21724	−0.493387	−0.246694	−	0.969093i	$-0.579344\pi$
$349$	−9.21724	−0.493387	−0.246694	+	0.969093i	$0.579344\pi$
$350$	6.22015	0.332481
$351$	−16.2295	−0.866265
$352$	−16.0857	−0.857371
$353$	6.07970	0.323590	0.161795	−	0.986824i	$-0.448272\pi$
$353$	6.07970	0.323590	0.161795	+	0.986824i	$0.448272\pi$
$354$	29.6547	1.57613
$355$	−0.545314	−0.0289423
$356$	−5.41245	−0.286859
$357$	3.27021	0.173078
$358$	−8.98593	−0.474921
$359$	28.2721	1.49215	0.746073	−	0.665864i	$-0.231937\pi$
$359$	28.2721	1.49215	0.746073	+	0.665864i	$0.231937\pi$
$360$	−10.1834	−0.536715
$361$	3.40679	0.179305
$362$	−15.0963	−0.793442
$363$	64.9727	3.41018
$364$	−10.3358	−0.541745
$365$	26.3943	1.38154
$366$	−24.7739	−1.29495
$367$	−11.0247	−0.575485	−0.287743	−	0.957708i	$-0.592905\pi$
$367$	−11.0247	−0.575485	−0.287743	+	0.957708i	$0.592905\pi$
$368$	5.84693	0.304792
$369$	14.8989	0.775607
$370$	−4.39669	−0.228573
$371$	−18.1216	−0.940827
$372$	2.41882	0.125410
$373$	33.6038	1.73994	0.869970	−	0.493104i	$-0.164138\pi$
$373$	33.6038	1.73994	0.869970	+	0.493104i	$0.164138\pi$
$374$	−3.09417	−0.159996
$375$	26.3645	1.36146
$376$	20.7292	1.06903
$377$	46.3865	2.38903
$378$	13.2187	0.679898
$379$	1.84863	0.0949576	0.0474788	−	0.998872i	$-0.484881\pi$
$379$	1.84863	0.0949576	0.0474788	+	0.998872i	$0.484881\pi$
$380$	4.13966	0.212360
$381$	−17.4568	−0.894339
$382$	−3.90015	−0.199549
$383$	0.253069	0.0129312	0.00646562	−	0.999979i	$-0.497942\pi$
$383$	0.253069	0.0129312	0.00646562	+	0.999979i	$0.497942\pi$
$384$	−13.1182	−0.669435
$385$	−47.4906	−2.42034
$386$	−14.9680	−0.761852
$387$	−18.4121	−0.935939
$388$	2.49491	0.126660
$389$	2.85311	0.144658	0.0723291	−	0.997381i	$-0.476957\pi$
$389$	2.85311	0.144658	0.0723291	+	0.997381i	$0.476957\pi$
$390$	30.6745	1.55326
$391$	−0.789161	−0.0399096
$392$	24.1112	1.21780
$393$	27.2805	1.37612
$394$	21.8390	1.10023
$395$	16.1314	0.811657
$396$	−5.03701	−0.253119
$397$	−18.4539	−0.926173	−0.463086	−	0.886313i	$-0.653258\pi$
$397$	−18.4539	−0.926173	−0.463086	+	0.886313i	$0.653258\pi$
$398$	0.393517	0.0197252
$399$	39.7582	1.99040
$400$	3.73882	0.186941
$401$	33.6566	1.68073	0.840366	−	0.542019i	$-0.182340\pi$
$401$	33.6566	1.68073	0.840366	+	0.542019i	$0.182340\pi$
$402$	25.2999	1.26184
$403$	−14.4153	−0.718075
$404$	−4.63436	−0.230568
$405$	21.5458	1.07062
$406$	−37.7813	−1.87505
$407$	−11.7464	−0.582249
$408$	2.58494	0.127974
$409$	−9.00111	−0.445076	−0.222538	−	0.974924i	$-0.571434\pi$
$409$	−9.00111	−0.445076	−0.222538	+	0.974924i	$0.571434\pi$
$410$	20.5571	1.01525
$411$	45.9270	2.26541
$412$	4.77314	0.235156
$413$	−42.3202	−2.08244
$414$	4.36963	0.214756
$415$	28.5070	1.39935
$416$	−14.8274	−0.726971
$417$	2.59762	0.127206
$418$	−37.6179	−1.83995
$419$	36.9788	1.80653	0.903266	−	0.429080i	$-0.141162\pi$
$419$	36.9788	1.80653	0.903266	+	0.429080i	$0.141162\pi$
$420$	7.34535	0.358416
$421$	30.4158	1.48237	0.741187	−	0.671299i	$-0.234263\pi$
$421$	30.4158	1.48237	0.741187	+	0.671299i	$0.234263\pi$
$422$	−7.49911	−0.365051
$423$	11.7804	0.572781
$424$	−14.3242	−0.695647
$425$	−0.504629	−0.0244781
$426$	−0.766447	−0.0371345
$427$	35.3548	1.71094
$428$	−5.13821	−0.248365
$429$	81.9516	3.95666
$430$	−25.4045	−1.22511
$431$	−25.7249	−1.23913	−0.619563	−	0.784947i	$-0.712690\pi$
$431$	−25.7249	−1.23913	−0.619563	+	0.784947i	$0.712690\pi$
$432$	7.94554	0.382280
$433$	7.45375	0.358204	0.179102	−	0.983830i	$-0.442681\pi$
$433$	7.45375	0.358204	0.179102	+	0.983830i	$0.442681\pi$
$434$	11.7411	0.563590
$435$	−32.9654	−1.58057
$436$	2.24032	0.107292
$437$	−9.59438	−0.458962
$438$	37.0975	1.77259
$439$	−8.81231	−0.420588	−0.210294	−	0.977638i	$-0.567442\pi$
$439$	−8.81231	−0.420588	−0.210294	+	0.977638i	$0.567442\pi$
$440$	−37.5390	−1.78960
$441$	13.7024	0.652494
$442$	−2.85212	−0.135661
$443$	15.8376	0.752466	0.376233	−	0.926525i	$-0.377219\pi$
$443$	15.8376	0.752466	0.376233	+	0.926525i	$0.377219\pi$
$444$	1.81682	0.0862223
$445$	−22.9234	−1.08667
$446$	−21.2438	−1.00592
$447$	6.39786	0.302609
$448$	34.3483	1.62280
$449$	1.88783	0.0890923	0.0445462	−	0.999007i	$-0.485816\pi$
$449$	1.88783	0.0890923	0.0445462	+	0.999007i	$0.485816\pi$
$450$	2.79416	0.131718
$451$	54.9215	2.58615
$452$	9.58550	0.450864
$453$	−0.841894	−0.0395556
$454$	6.42399	0.301493
$455$	−43.7755	−2.05223
$456$	31.4269	1.47170
$457$	−10.1611	−0.475316	−0.237658	−	0.971349i	$-0.576380\pi$
$457$	−10.1611	−0.475316	−0.237658	+	0.971349i	$0.576380\pi$
$458$	26.9574	1.25964
$459$	−1.07241	−0.0500559
$460$	−1.77257	−0.0826463
$461$	−9.12546	−0.425015	−0.212507	−	0.977159i	$-0.568163\pi$
$461$	−9.12546	−0.425015	−0.212507	+	0.977159i	$0.568163\pi$
$462$	−66.7487	−3.10543
$463$	−18.1384	−0.842963	−0.421481	−	0.906837i	$-0.638490\pi$
$463$	−18.1384	−0.842963	−0.421481	+	0.906837i	$0.638490\pi$
$464$	−22.7097	−1.05427
$465$	10.2445	0.475076
$466$	4.27623	0.198093
$467$	−0.673646	−0.0311726	−0.0155863	−	0.999879i	$-0.504961\pi$
$467$	−0.673646	−0.0311726	−0.0155863	+	0.999879i	$0.504961\pi$
$468$	−4.64298	−0.214622
$469$	−36.1054	−1.66719
$470$	16.2542	0.749752
$471$	−22.6604	−1.04413
$472$	−33.4520	−1.53975
$473$	−67.8720	−3.12076
$474$	22.6729	1.04140
$475$	−6.13513	−0.281499
$476$	−0.682971	−0.0313039
$477$	−8.14044	−0.372725
$478$	31.7156	1.45064
$479$	−14.6429	−0.669053	−0.334527	−	0.942386i	$-0.608576\pi$
$479$	−14.6429	−0.669053	−0.334527	+	0.942386i	$0.608576\pi$
$480$	10.5373	0.480961
$481$	−10.8275	−0.493693
$482$	−5.49970	−0.250504
$483$	−17.0241	−0.774624
$484$	−13.5693	−0.616787
$485$	10.5667	0.479810
$486$	20.0100	0.907674
$487$	−19.2998	−0.874555	−0.437278	−	0.899327i	$-0.644057\pi$
$487$	−19.2998	−0.874555	−0.437278	+	0.899327i	$0.644057\pi$
$488$	27.9463	1.26507
$489$	9.35511	0.423053
$490$	18.9062	0.854094
$491$	30.5775	1.37994	0.689971	−	0.723837i	$-0.257623\pi$
$491$	30.5775	1.37994	0.689971	+	0.723837i	$0.257623\pi$
$492$	−8.49469	−0.382970
$493$	3.06512	0.138046
$494$	−34.6752	−1.56011
$495$	−21.3333	−0.958861
$496$	7.05735	0.316884
$497$	1.09379	0.0490634
$498$	40.0670	1.79545
$499$	−4.71664	−0.211146	−0.105573	−	0.994412i	$-0.533668\pi$
$499$	−4.71664	−0.211146	−0.105573	+	0.994412i	$0.533668\pi$
$500$	−5.50612	−0.246241
$501$	−53.4954	−2.39000
$502$	−28.3666	−1.26606
$503$	−22.2151	−0.990522	−0.495261	−	0.868744i	$-0.664927\pi$
$503$	−22.2151	−0.990522	−0.495261	+	0.868744i	$0.664927\pi$
$504$	20.4260	0.909847
$505$	−19.6280	−0.873433
$506$	16.1077	0.716073
$507$	47.2554	2.09869
$508$	3.64579	0.161756
$509$	−27.4438	−1.21642	−0.608212	−	0.793775i	$-0.708113\pi$
$509$	−27.4438	−1.21642	−0.608212	+	0.793775i	$0.708113\pi$
$510$	2.02691	0.0897531
$511$	−52.9418	−2.34201
$512$	24.8637	1.09883
$513$	−13.0381	−0.575644
$514$	27.9641	1.23344
$515$	20.2158	0.890813
$516$	10.4977	0.462137
$517$	43.4257	1.90986
$518$	8.81891	0.387481
$519$	29.6006	1.29932
$520$	−34.6024	−1.51742
$521$	−37.1339	−1.62686	−0.813432	−	0.581660i	$-0.802404\pi$
$521$	−37.1339	−1.62686	−0.813432	+	0.581660i	$0.802404\pi$
$522$	−16.9718	−0.742835
$523$	−7.46577	−0.326455	−0.163228	−	0.986588i	$-0.552191\pi$
$523$	−7.46577	−0.326455	−0.163228	+	0.986588i	$0.552191\pi$
$524$	−5.69743	−0.248894
$525$	−10.8861	−0.475107
$526$	21.8277	0.951731
$527$	−0.952531	−0.0414929
$528$	−40.1214	−1.74606
$529$	−18.8918	−0.821381
$530$	−11.2320	−0.487885
$531$	−19.0107	−0.824995
$532$	−8.30336	−0.359996
$533$	50.6252	2.19282
$534$	−32.2192	−1.39426
$535$	−21.7619	−0.940850
$536$	−28.5395	−1.23272
$537$	15.7265	0.678651
$538$	18.3705	0.792009
$539$	50.5107	2.17565
$540$	−2.40878	−0.103658
$541$	−15.5709	−0.669447	−0.334723	−	0.942316i	$-0.608643\pi$
$541$	−15.5709	−0.669447	−0.334723	+	0.942316i	$0.608643\pi$
$542$	22.6951	0.974837
$543$	26.4204	1.13381
$544$	−0.979762	−0.0420069
$545$	9.48847	0.406442
$546$	−61.5271	−2.63312
$547$	41.0975	1.75720	0.878602	−	0.477554i	$-0.158477\pi$
$547$	41.0975	1.75720	0.878602	+	0.477554i	$0.158477\pi$
$548$	−9.59168	−0.409736
$549$	15.8818	0.677819
$550$	10.3001	0.439196
$551$	37.2649	1.58754
$552$	−13.4567	−0.572756
$553$	−32.3564	−1.37593
$554$	−14.3326	−0.608936
$555$	7.69479	0.326626
$556$	−0.542504	−0.0230073
$557$	−0.571247	−0.0242045	−0.0121023	−	0.999927i	$-0.503852\pi$
$557$	−0.571247	−0.0242045	−0.0121023	+	0.999927i	$0.503852\pi$
$558$	5.27423	0.223276
$559$	−62.5625	−2.64611
$560$	21.4314	0.905642
$561$	5.41519	0.228630
$562$	−29.3584	−1.23841
$563$	−18.0101	−0.759037	−0.379518	−	0.925184i	$-0.623910\pi$
$563$	−18.0101	−0.759037	−0.379518	+	0.925184i	$0.623910\pi$
$564$	−6.71663	−0.282821
$565$	40.5976	1.70795
$566$	−6.45629	−0.271378
$567$	−43.2167	−1.81493
$568$	0.864591	0.0362774
$569$	37.1618	1.55790	0.778952	−	0.627084i	$-0.215752\pi$
$569$	37.1618	1.55790	0.778952	+	0.627084i	$0.215752\pi$
$570$	24.6426	1.03216
$571$	−33.5506	−1.40405	−0.702025	−	0.712152i	$-0.747721\pi$
$571$	−33.5506	−1.40405	−0.702025	+	0.712152i	$0.747721\pi$
$572$	−17.1153	−0.715626
$573$	6.82577	0.285150
$574$	−41.2336	−1.72106
$575$	2.62701	0.109554
$576$	15.4296	0.642901
$577$	27.2808	1.13571	0.567857	−	0.823127i	$-0.307773\pi$
$577$	27.2808	1.13571	0.567857	+	0.823127i	$0.307773\pi$
$578$	20.9463	0.871250
$579$	26.1960	1.08867
$580$	6.88470	0.285872
$581$	−57.1796	−2.37221
$582$	14.8517	0.615621
$583$	−30.0079	−1.24280
$584$	−41.8479	−1.73168
$585$	−19.6645	−0.813026
$586$	14.3272	0.591853
$587$	−1.00732	−0.0415765	−0.0207882	−	0.999784i	$-0.506618\pi$
$587$	−1.00732	−0.0415765	−0.0207882	+	0.999784i	$0.506618\pi$
$588$	−7.81247	−0.322181
$589$	−11.5806	−0.477170
$590$	−26.2305	−1.07989
$591$	−38.2211	−1.57220
$592$	5.30089	0.217865
$593$	−13.4768	−0.553424	−0.276712	−	0.960953i	$-0.589245\pi$
$593$	−13.4768	−0.553424	−0.276712	+	0.960953i	$0.589245\pi$
$594$	21.8891	0.898121
$595$	−2.89260	−0.118585
$596$	−1.33617	−0.0547317
$597$	−0.688706	−0.0281869
$598$	14.8476	0.607164
$599$	−39.9738	−1.63329	−0.816643	−	0.577143i	$-0.804167\pi$
$599$	−39.9738	−1.63329	−0.816643	+	0.577143i	$0.804167\pi$
$600$	−8.60491	−0.351294
$601$	−14.9484	−0.609757	−0.304878	−	0.952391i	$-0.598616\pi$
$601$	−14.9484	−0.609757	−0.304878	+	0.952391i	$0.598616\pi$
$602$	50.9565	2.07683
$603$	−16.2190	−0.660487
$604$	0.175826	0.00715427
$605$	−57.4703	−2.33650
$606$	−27.5874	−1.12066
$607$	24.9001	1.01066	0.505331	−	0.862926i	$-0.331370\pi$
$607$	24.9001	1.01066	0.505331	+	0.862926i	$0.331370\pi$
$608$	−11.9117	−0.483081
$609$	66.1222	2.67941
$610$	21.9133	0.887243
$611$	40.0286	1.61938
$612$	−0.306799	−0.0124016
$613$	−10.2686	−0.414744	−0.207372	−	0.978262i	$-0.566491\pi$
$613$	−10.2686	−0.414744	−0.207372	+	0.978262i	$0.566491\pi$
$614$	21.0160	0.848135
$615$	−35.9777	−1.45076
$616$	75.2959	3.03376
$617$	−5.08754	−0.204817	−0.102408	−	0.994742i	$-0.532655\pi$
$617$	−5.08754	−0.204817	−0.102408	+	0.994742i	$0.532655\pi$
$618$	28.4135	1.14296
$619$	−39.3585	−1.58195	−0.790976	−	0.611847i	$-0.790427\pi$
$619$	−39.3585	−1.58195	−0.790976	+	0.611847i	$0.790427\pi$
$620$	−2.13952	−0.0859251
$621$	5.58277	0.224029
$622$	11.4553	0.459314
$623$	45.9799	1.84215
$624$	−36.9829	−1.48050
$625$	−16.8397	−0.673589
$626$	28.4188	1.13585
$627$	65.8363	2.62925
$628$	4.73253	0.188849
$629$	−0.715462	−0.0285273
$630$	16.0165	0.638112
$631$	−10.8173	−0.430630	−0.215315	−	0.976545i	$-0.569078\pi$
$631$	−10.8173	−0.430630	−0.215315	+	0.976545i	$0.569078\pi$
$632$	−25.5761	−1.01736
$633$	13.1244	0.521649
$634$	−30.9182	−1.22792
$635$	15.4411	0.612760
$636$	4.64131	0.184040
$637$	46.5594	1.84475
$638$	−62.5626	−2.47688
$639$	0.491345	0.0194373
$640$	11.6034	0.458666
$641$	−2.59977	−0.102685	−0.0513424	−	0.998681i	$-0.516350\pi$
$641$	−2.59977	−0.102685	−0.0513424	+	0.998681i	$0.516350\pi$
$642$	−30.5867	−1.20716
$643$	14.5202	0.572623	0.286311	−	0.958137i	$-0.407571\pi$
$643$	14.5202	0.572623	0.286311	+	0.958137i	$0.407571\pi$
$644$	3.55542	0.140103
$645$	44.4612	1.75066
$646$	−2.29127	−0.0901487
$647$	24.4393	0.960806	0.480403	−	0.877048i	$-0.340490\pi$
$647$	24.4393	0.960806	0.480403	+	0.877048i	$0.340490\pi$
$648$	−34.1607	−1.34196
$649$	−70.0787	−2.75083
$650$	9.49431	0.372398
$651$	−20.5484	−0.805356
$652$	−1.95378	−0.0765159
$653$	31.3209	1.22568	0.612841	−	0.790206i	$-0.290026\pi$
$653$	31.3209	1.22568	0.612841	+	0.790206i	$0.290026\pi$
$654$	13.3362	0.521486
$655$	−24.1304	−0.942854
$656$	−24.7848	−0.967685
$657$	−23.7821	−0.927826
$658$	−32.6029	−1.27099
$659$	29.5071	1.14943	0.574717	−	0.818352i	$-0.305112\pi$
$659$	29.5071	1.14943	0.574717	+	0.818352i	$0.305112\pi$
$660$	12.1633	0.473455
$661$	2.10348	0.0818161	0.0409080	−	0.999163i	$-0.486975\pi$
$661$	2.10348	0.0818161	0.0409080	+	0.999163i	$0.486975\pi$
$662$	0.355220	0.0138060
$663$	4.99158	0.193857
$664$	−45.1976	−1.75401
$665$	−35.1673	−1.36373
$666$	3.96156	0.153507
$667$	−15.9565	−0.617837
$668$	11.1723	0.432270
$669$	37.1794	1.43744
$670$	−22.3785	−0.864556
$671$	58.5447	2.26009
$672$	−21.1358	−0.815333
$673$	20.7542	0.800015	0.400007	−	0.916512i	$-0.369008\pi$
$673$	20.7542	0.800015	0.400007	+	0.916512i	$0.369008\pi$
$674$	−20.3406	−0.783492
$675$	3.56991	0.137406
$676$	−9.86912	−0.379581
$677$	−20.3219	−0.781035	−0.390518	−	0.920595i	$-0.627704\pi$
$677$	−20.3219	−0.781035	−0.390518	+	0.920595i	$0.627704\pi$
$678$	57.0605	2.19140
$679$	−21.1948	−0.813381
$680$	−2.28646	−0.0876816
$681$	−11.2428	−0.430826
$682$	19.4422	0.744482
$683$	8.86162	0.339080	0.169540	−	0.985523i	$-0.445772\pi$
$683$	8.86162	0.339080	0.169540	+	0.985523i	$0.445772\pi$
$684$	−3.72996	−0.142619
$685$	−40.6238	−1.55215
$686$	−4.32786	−0.165238
$687$	−47.1790	−1.79999
$688$	30.6291	1.16772
$689$	−27.6604	−1.05378
$690$	−10.5517	−0.401697
$691$	39.2994	1.49502	0.747510	−	0.664251i	$-0.231249\pi$
$691$	39.2994	1.49502	0.747510	+	0.664251i	$0.231249\pi$
$692$	−6.18198	−0.235004
$693$	42.7905	1.62548
$694$	−6.12643	−0.232556
$695$	−2.29767	−0.0871557
$696$	52.2663	1.98115
$697$	3.34521	0.126709
$698$	11.4590	0.433731
$699$	−7.48396	−0.283069
$700$	2.27352	0.0859309
$701$	−7.99521	−0.301975	−0.150987	−	0.988536i	$-0.548245\pi$
$701$	−7.99521	−0.301975	−0.150987	+	0.988536i	$0.548245\pi$
$702$	20.1768	0.761524
$703$	−8.69837	−0.328065
$704$	56.8778	2.14366
$705$	−28.4470	−1.07138
$706$	−7.55840	−0.284464
$707$	39.3699	1.48066
$708$	10.8390	0.407356
$709$	6.76033	0.253889	0.126945	−	0.991910i	$-0.459483\pi$
$709$	6.76033	0.253889	0.126945	+	0.991910i	$0.459483\pi$
$710$	0.677945	0.0254428
$711$	−14.5349	−0.545100
$712$	36.3449	1.36208
$713$	4.95870	0.185705
$714$	−4.06559	−0.152151
$715$	−72.4886	−2.71092
$716$	−3.28443	−0.122745
$717$	−55.5065	−2.07293
$718$	−35.1484	−1.31173
$719$	−10.7936	−0.402533	−0.201267	−	0.979537i	$-0.564506\pi$
$719$	−10.7936	−0.402533	−0.201267	+	0.979537i	$0.564506\pi$
$720$	9.62723	0.358786
$721$	−40.5489	−1.51012
$722$	−4.23539	−0.157625
$723$	9.62519	0.357965
$724$	−5.51781	−0.205068
$725$	−10.2034	−0.378944
$726$	−80.7753	−2.99785
$727$	−11.9156	−0.441926	−0.220963	−	0.975282i	$-0.570920\pi$
$727$	−11.9156	−0.441926	−0.220963	+	0.975282i	$0.570920\pi$
$728$	69.4057	2.57235
$729$	−1.43457	−0.0531322
$730$	−32.8138	−1.21450
$731$	−4.13401	−0.152902
$732$	−9.05508	−0.334685
$733$	−1.97035	−0.0727764	−0.0363882	−	0.999338i	$-0.511585\pi$
$733$	−1.97035	−0.0727764	−0.0363882	+	0.999338i	$0.511585\pi$
$734$	13.7061	0.505902
$735$	−33.0883	−1.22048
$736$	5.10046	0.188006
$737$	−59.7875	−2.20230
$738$	−18.5226	−0.681827
$739$	24.1083	0.886838	0.443419	−	0.896315i	$-0.353765\pi$
$739$	24.1083	0.886838	0.443419	+	0.896315i	$0.353765\pi$
$740$	−1.60703	−0.0590755
$741$	60.6861	2.22936
$742$	22.5291	0.827070
$743$	−24.6964	−0.906024	−0.453012	−	0.891504i	$-0.649651\pi$
$743$	−24.6964	−0.906024	−0.453012	+	0.891504i	$0.649651\pi$
$744$	−16.2425	−0.595479
$745$	−5.65910	−0.207333
$746$	−41.7769	−1.52956
$747$	−25.6857	−0.939791
$748$	−1.13094	−0.0413514
$749$	43.6502	1.59494
$750$	−32.7768	−1.19684
$751$	30.4067	1.10956	0.554779	−	0.831998i	$-0.312803\pi$
$751$	30.4067	1.10956	0.554779	+	0.831998i	$0.312803\pi$
$752$	−19.5970	−0.714629
$753$	49.6453	1.80918
$754$	−57.6686	−2.10016
$755$	0.744680	0.0271017
$756$	4.83155	0.175722
$757$	−25.0938	−0.912050	−0.456025	−	0.889967i	$-0.650727\pi$
$757$	−25.0938	−0.912050	−0.456025	+	0.889967i	$0.650727\pi$
$758$	−2.29825	−0.0834761
$759$	−28.1905	−1.02325
$760$	−27.7981	−1.00834
$761$	10.3630	0.375657	0.187829	−	0.982202i	$-0.439855\pi$
$761$	10.3630	0.375657	0.187829	+	0.982202i	$0.439855\pi$
$762$	21.7026	0.786204
$763$	−19.0320	−0.689006
$764$	−1.42554	−0.0515741
$765$	−1.29939	−0.0469795
$766$	−0.314621	−0.0113677
$767$	−64.5966	−2.33245
$768$	−22.4110	−0.808688
$769$	11.2847	0.406935	0.203468	−	0.979082i	$-0.434779\pi$
$769$	11.2847	0.406935	0.203468	+	0.979082i	$0.434779\pi$
$770$	59.0412	2.12770
$771$	−48.9407	−1.76256
$772$	−5.47093	−0.196903
$773$	2.25523	0.0811150	0.0405575	−	0.999177i	$-0.487087\pi$
$773$	2.25523	0.0811150	0.0405575	+	0.999177i	$0.487087\pi$
$774$	22.8903	0.822773
$775$	3.17085	0.113900
$776$	−16.7534	−0.601413
$777$	−15.4342	−0.553701
$778$	−3.54704	−0.127167
$779$	40.6701	1.45716
$780$	11.2118	0.401446
$781$	1.81123	0.0648110
$782$	0.981100	0.0350841
$783$	−21.6837	−0.774911
$784$	−22.7943	−0.814082
$785$	20.0438	0.715393
$786$	−33.9156	−1.20973
$787$	−11.7777	−0.419830	−0.209915	−	0.977720i	$-0.567319\pi$
$787$	−11.7777	−0.419830	−0.209915	+	0.977720i	$0.567319\pi$
$788$	7.98233	0.284359
$789$	−38.2012	−1.36000
$790$	−20.0548	−0.713519
$791$	−81.4309	−2.89535
$792$	33.8238	1.20188
$793$	53.9649	1.91635
$794$	22.9422	0.814188
$795$	19.6574	0.697176
$796$	0.143834	0.00509805
$797$	12.4401	0.440652	0.220326	−	0.975426i	$-0.429288\pi$
$797$	12.4401	0.440652	0.220326	+	0.975426i	$0.429288\pi$
$798$	−49.4282	−1.74974
$799$	2.64501	0.0935737
$800$	3.26149	0.115311
$801$	20.6547	0.729799
$802$	−41.8426	−1.47751
$803$	−87.6671	−3.09371
$804$	9.24731	0.326128
$805$	15.0583	0.530736
$806$	17.9213	0.631252
$807$	−32.1508	−1.13176
$808$	31.1200	1.09480
$809$	11.9965	0.421774	0.210887	−	0.977510i	$-0.432365\pi$
$809$	11.9965	0.421774	0.210887	+	0.977510i	$0.432365\pi$
$810$	−26.7861	−0.941169
$811$	20.2483	0.711012	0.355506	−	0.934674i	$-0.384308\pi$
$811$	20.2483	0.711012	0.355506	+	0.934674i	$0.384308\pi$
$812$	−13.8094	−0.484614
$813$	−39.7193	−1.39302
$814$	14.6034	0.511848
$815$	−8.27487	−0.289856
$816$	−2.44375	−0.0855484
$817$	−50.2600	−1.75838
$818$	11.1904	0.391262
$819$	39.4431	1.37825
$820$	7.51381	0.262394
$821$	7.63903	0.266604	0.133302	−	0.991075i	$-0.457442\pi$
$821$	7.63903	0.266604	0.133302	+	0.991075i	$0.457442\pi$
$822$	−57.0973	−1.99150
$823$	46.7326	1.62900	0.814498	−	0.580166i	$-0.197012\pi$
$823$	46.7326	1.62900	0.814498	+	0.580166i	$0.197012\pi$
$824$	−32.0519	−1.11658
$825$	−18.0264	−0.627600
$826$	52.6132	1.83065
$827$	−26.8899	−0.935054	−0.467527	−	0.883979i	$-0.654855\pi$
$827$	−26.8899	−0.935054	−0.467527	+	0.883979i	$0.654855\pi$
$828$	1.59714	0.0555043
$829$	13.0776	0.454205	0.227103	−	0.973871i	$-0.427075\pi$
$829$	13.0776	0.454205	0.227103	+	0.973871i	$0.427075\pi$
$830$	−35.4405	−1.23016
$831$	25.0840	0.870154
$832$	52.4285	1.81763
$833$	3.07655	0.106596
$834$	−3.22941	−0.111825
$835$	47.3182	1.63752
$836$	−13.7497	−0.475542
$837$	6.73851	0.232917
$838$	−45.9727	−1.58810
$839$	13.0730	0.451329	0.225665	−	0.974205i	$-0.427545\pi$
$839$	13.0730	0.451329	0.225665	+	0.974205i	$0.427545\pi$
$840$	−49.3244	−1.70185
$841$	32.9754	1.13708
$842$	−37.8134	−1.30314
$843$	51.3810	1.76965
$844$	−2.74098	−0.0943486
$845$	−41.7988	−1.43792
$846$	−14.6456	−0.503525
$847$	115.274	3.96087
$848$	13.5419	0.465029
$849$	11.2993	0.387792
$850$	0.627365	0.0215184
$851$	3.72456	0.127676
$852$	−0.280143	−0.00959753
$853$	−14.7626	−0.505461	−0.252731	−	0.967537i	$-0.581329\pi$
$853$	−14.7626	−0.505461	−0.252731	+	0.967537i	$0.581329\pi$
$854$	−43.9538	−1.50407
$855$	−15.7976	−0.540266
$856$	34.5033	1.17930
$857$	−0.673685	−0.0230127	−0.0115063	−	0.999934i	$-0.503663\pi$
$857$	−0.673685	−0.0230127	−0.0115063	+	0.999934i	$0.503663\pi$
$858$	−101.884	−3.47825
$859$	24.3809	0.831867	0.415933	−	0.909395i	$-0.363455\pi$
$859$	24.3809	0.831867	0.415933	+	0.909395i	$0.363455\pi$
$860$	−9.28556	−0.316635
$861$	72.1643	2.45935
$862$	31.9817	1.08930
$863$	−8.97182	−0.305404	−0.152702	−	0.988272i	$-0.548797\pi$
$863$	−8.97182	−0.305404	−0.152702	+	0.988272i	$0.548797\pi$
$864$	6.93115	0.235802
$865$	−26.1826	−0.890236
$866$	−9.26664	−0.314893
$867$	−36.6587	−1.24499
$868$	4.29146	0.145662
$869$	−53.5795	−1.81756
$870$	40.9832	1.38946
$871$	−55.1105	−1.86735
$872$	−15.0439	−0.509450
$873$	−9.52094	−0.322235
$874$	11.9279	0.403468
$875$	46.7757	1.58131
$876$	13.5594	0.458131
$877$	−21.8996	−0.739496	−0.369748	−	0.929132i	$-0.620556\pi$
$877$	−21.8996	−0.739496	−0.369748	+	0.929132i	$0.620556\pi$
$878$	10.9556	0.369735
$879$	−25.0745	−0.845743
$880$	35.4886	1.19632
$881$	22.9261	0.772400	0.386200	−	0.922415i	$-0.373787\pi$
$881$	22.9261	0.772400	0.386200	+	0.922415i	$0.373787\pi$
$882$	−17.0350	−0.573600
$883$	−37.3233	−1.25603	−0.628014	−	0.778202i	$-0.716132\pi$
$883$	−37.3233	−1.25603	−0.628014	+	0.778202i	$0.716132\pi$
$884$	−1.04247	−0.0350622
$885$	45.9067	1.54314
$886$	−19.6896	−0.661485
$887$	−8.42873	−0.283009	−0.141505	−	0.989938i	$-0.545194\pi$
$887$	−8.42873	−0.283009	−0.141505	+	0.989938i	$0.545194\pi$
$888$	−12.2000	−0.409406
$889$	−30.9718	−1.03876
$890$	28.4988	0.955283
$891$	−71.5632	−2.39746
$892$	−7.76478	−0.259984
$893$	32.1572	1.07610
$894$	−7.95394	−0.266020
$895$	−13.9106	−0.464980
$896$	−23.2742	−0.777538
$897$	−25.9852	−0.867622
$898$	−2.34699	−0.0783200
$899$	−19.2598	−0.642349
$900$	1.02129	0.0340430
$901$	−1.82775	−0.0608911
$902$	−68.2795	−2.27346
$903$	−89.1805	−2.96774
$904$	−64.3671	−2.14082
$905$	−23.3696	−0.776833
$906$	1.04666	0.0347729
$907$	12.1150	0.402271	0.201136	−	0.979563i	$-0.435537\pi$
$907$	12.1150	0.402271	0.201136	+	0.979563i	$0.435537\pi$
$908$	2.34802	0.0779218
$909$	17.6854	0.586588
$910$	54.4225	1.80409
$911$	−36.8980	−1.22249	−0.611243	−	0.791443i	$-0.709330\pi$
$911$	−36.8980	−1.22249	−0.611243	+	0.791443i	$0.709330\pi$
$912$	−29.7104	−0.983810
$913$	−94.6846	−3.13360
$914$	12.6325	0.417845
$915$	−38.3511	−1.26785
$916$	9.85317	0.325558
$917$	48.4009	1.59834
$918$	1.33324	0.0440035
$919$	36.5024	1.20410	0.602052	−	0.798457i	$-0.294350\pi$
$919$	36.5024	1.20410	0.602052	+	0.798457i	$0.294350\pi$
$920$	11.9029	0.392426
$921$	−36.7807	−1.21196
$922$	11.3449	0.373626
$923$	1.66955	0.0549537
$924$	−24.3972	−0.802608
$925$	2.38168	0.0783090
$926$	22.5500	0.741039
$927$	−18.2150	−0.598260
$928$	−19.8103	−0.650307
$929$	−1.68580	−0.0553094	−0.0276547	−	0.999618i	$-0.508804\pi$
$929$	−1.68580	−0.0553094	−0.0276547	+	0.999618i	$0.508804\pi$
$930$	−12.7361	−0.417634
$931$	37.4038	1.22586
$932$	1.56300	0.0511977
$933$	−20.0482	−0.656348
$934$	0.837489	0.0274035
$935$	−4.78990	−0.156646
$936$	31.1778	1.01908
$937$	−3.93479	−0.128544	−0.0642720	−	0.997932i	$-0.520473\pi$
$937$	−3.93479	−0.128544	−0.0642720	+	0.997932i	$0.520473\pi$
$938$	44.8869	1.46561
$939$	−49.7367	−1.62309
$940$	5.94106	0.193776
$941$	54.7679	1.78538	0.892691	−	0.450670i	$-0.148815\pi$
$941$	54.7679	1.78538	0.892691	+	0.450670i	$0.148815\pi$
$942$	28.1718	0.917887
$943$	−17.4145	−0.567096
$944$	31.6249	1.02930
$945$	20.4631	0.665666
$946$	84.3797	2.74342
$947$	−30.8248	−1.00167	−0.500836	−	0.865542i	$-0.666974\pi$
$947$	−30.8248	−1.00167	−0.500836	+	0.865542i	$0.666974\pi$
$948$	8.28712	0.269153
$949$	−80.8092	−2.62318
$950$	7.62731	0.247463
$951$	54.1110	1.75467
$952$	4.58619	0.148639
$953$	60.2594	1.95199	0.975997	−	0.217784i	$-0.0698828\pi$
$953$	60.2594	1.95199	0.975997	+	0.217784i	$0.0698828\pi$
$954$	10.1203	0.327658
$955$	−6.03759	−0.195372
$956$	11.5923	0.374922
$957$	109.493	3.53940
$958$	18.2044	0.588157
$959$	81.4834	2.63124
$960$	−37.2592	−1.20254
$961$	−25.0148	−0.806928
$962$	13.4610	0.434000
$963$	19.6082	0.631865
$964$	−2.01018	−0.0647437
$965$	−23.1711	−0.745905
$966$	21.1647	0.680963
$967$	2.86745	0.0922110	0.0461055	−	0.998937i	$-0.485319\pi$
$967$	2.86745	0.0922110	0.0461055	+	0.998937i	$0.485319\pi$
$968$	91.1186	2.92866
$969$	4.01002	0.128820
$970$	−13.1367	−0.421795
$971$	21.0855	0.676667	0.338333	−	0.941026i	$-0.390137\pi$
$971$	21.0855	0.676667	0.338333	+	0.941026i	$0.390137\pi$
$972$	7.31384	0.234591
$973$	4.60869	0.147748
$974$	23.9938	0.768812
$975$	−16.6163	−0.532147
$976$	−26.4199	−0.845679
$977$	19.3085	0.617734	0.308867	−	0.951105i	$-0.400050\pi$
$977$	19.3085	0.617734	0.308867	+	0.951105i	$0.400050\pi$
$978$	−11.6304	−0.371901
$979$	76.1389	2.43341
$980$	6.91036	0.220743
$981$	−8.54941	−0.272962
$982$	−38.0145	−1.21309
$983$	−23.1416	−0.738101	−0.369051	−	0.929409i	$-0.620317\pi$
$983$	−23.1416	−0.738101	−0.369051	+	0.929409i	$0.620317\pi$
$984$	57.0423	1.81844
$985$	33.8077	1.07720
$986$	−3.81062	−0.121355
$987$	57.0592	1.81622
$988$	−12.6741	−0.403216
$989$	21.5209	0.684324
$990$	26.5220	0.842924
$991$	−36.0572	−1.14540	−0.572698	−	0.819766i	$-0.694103\pi$
$991$	−36.0572	−1.14540	−0.572698	+	0.819766i	$0.694103\pi$
$992$	6.15635	0.195464
$993$	−0.621682	−0.0197285
$994$	−1.35983	−0.0431311
$995$	0.609181	0.0193123
$996$	14.6448	0.464039
$997$	−28.4620	−0.901400	−0.450700	−	0.892676i	$-0.648826\pi$
$997$	−28.4620	−0.901400	−0.450700	+	0.892676i	$0.648826\pi$
$998$	5.86382	0.185616
$999$	5.06141	0.160136

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2671.2.a.b.1.36	✓	122

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2671.2.a.b.1.36	✓	122	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:	\( N \)	\(=\)	\( 2671 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2671.a (trivial)

\(f(q)\)	\(=\)	\(q-1.24322 q^{2} +2.17580 q^{3} -0.454407 q^{4} -1.92456 q^{5} -2.70499 q^{6} +3.86028 q^{7} +3.05136 q^{8} +1.73408 q^{9} +O(q^{10})\)	\(q-1.24322 q^{2} +2.17580 q^{3} -0.454407 q^{4} -1.92456 q^{5} -2.70499 q^{6} +3.86028 q^{7} +3.05136 q^{8} +1.73408 q^{9} +2.39264 q^{10} +6.39231 q^{11} -0.988696 q^{12} +5.89226 q^{13} -4.79918 q^{14} -4.18744 q^{15} -2.88470 q^{16} +0.389348 q^{17} -2.15585 q^{18} +4.73358 q^{19} +0.874531 q^{20} +8.39919 q^{21} -7.94704 q^{22} -2.02688 q^{23} +6.63914 q^{24} -1.29609 q^{25} -7.32536 q^{26} -2.75437 q^{27} -1.75414 q^{28} +7.87245 q^{29} +5.20590 q^{30} -2.44648 q^{31} -2.51641 q^{32} +13.9084 q^{33} -0.484045 q^{34} -7.42933 q^{35} -0.787980 q^{36} -1.83759 q^{37} -5.88488 q^{38} +12.8203 q^{39} -5.87252 q^{40} +8.59181 q^{41} -10.4420 q^{42} -10.6178 q^{43} -2.90471 q^{44} -3.33734 q^{45} +2.51985 q^{46} +6.79343 q^{47} -6.27652 q^{48} +7.90179 q^{49} +1.61132 q^{50} +0.847142 q^{51} -2.67748 q^{52} -4.69437 q^{53} +3.42429 q^{54} -12.3023 q^{55} +11.7791 q^{56} +10.2993 q^{57} -9.78718 q^{58} -10.9630 q^{59} +1.90280 q^{60} +9.15861 q^{61} +3.04151 q^{62} +6.69406 q^{63} +8.89786 q^{64} -11.3400 q^{65} -17.2911 q^{66} -9.35304 q^{67} -0.176923 q^{68} -4.41007 q^{69} +9.23628 q^{70} +0.283346 q^{71} +5.29132 q^{72} -13.7145 q^{73} +2.28452 q^{74} -2.82002 q^{75} -2.15097 q^{76} +24.6761 q^{77} -15.9385 q^{78} -8.38187 q^{79} +5.55177 q^{80} -11.1952 q^{81} -10.6815 q^{82} -14.8123 q^{83} -3.81665 q^{84} -0.749322 q^{85} +13.2002 q^{86} +17.1288 q^{87} +19.5053 q^{88} +11.9110 q^{89} +4.14904 q^{90} +22.7458 q^{91} +0.921026 q^{92} -5.32303 q^{93} -8.44571 q^{94} -9.11004 q^{95} -5.47520 q^{96} -5.49047 q^{97} -9.82366 q^{98} +11.0848 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 122 q + 14 q^{2} + 10 q^{3} + 128 q^{4} + 33 q^{5} + 22 q^{6} + 6 q^{7} + 36 q^{8} + 162 q^{9}+O(q^{10}) \) 122 * q + 14 * q^2 + 10 * q^3 + 128 * q^4 + 33 * q^5 + 22 * q^6 + 6 * q^7 + 36 * q^8 + 162 * q^9	\( 122 q + 14 q^{2} + 10 q^{3} + 128 q^{4} + 33 q^{5} + 22 q^{6} + 6 q^{7} + 36 q^{8} + 162 q^{9} + 16 q^{10} + 43 q^{11} + 23 q^{12} + 25 q^{13} + 45 q^{14} + 12 q^{15} + 132 q^{16} + 103 q^{17} + 30 q^{18} + 37 q^{19} + 63 q^{20} + 81 q^{21} + 15 q^{23} + 60 q^{24} + 151 q^{25} + 59 q^{26} + 22 q^{27} - 3 q^{28} + 80 q^{29} - 9 q^{30} + 15 q^{31} + 66 q^{32} + 93 q^{33} + 30 q^{34} + 23 q^{35} + 162 q^{36} + 18 q^{37} + 41 q^{38} + 10 q^{39} + 29 q^{40} + 249 q^{41} - 8 q^{42} + 14 q^{43} + 100 q^{44} + 59 q^{45} + 11 q^{46} + 57 q^{47} + 33 q^{48} + 180 q^{49} + 63 q^{50} + 26 q^{51} + 31 q^{52} + 65 q^{53} + 65 q^{54} - 8 q^{55} + 120 q^{56} + 57 q^{57} - 31 q^{58} + 108 q^{59} - q^{60} + 70 q^{61} + 25 q^{62} - 7 q^{63} + 100 q^{64} + 171 q^{65} + 12 q^{66} - 6 q^{67} + 184 q^{68} + 64 q^{69} - 24 q^{70} + 47 q^{71} + 53 q^{72} + 76 q^{73} + 66 q^{74} + 40 q^{75} + 32 q^{76} + 73 q^{77} - 19 q^{78} + 8 q^{79} + 115 q^{80} + 250 q^{81} - 13 q^{82} + 116 q^{83} + 159 q^{84} + 31 q^{85} + 91 q^{86} + 25 q^{87} - 43 q^{88} + 361 q^{89} + 32 q^{90} + 7 q^{91} + 5 q^{92} + 18 q^{93} + 23 q^{94} + 42 q^{95} + 77 q^{96} + 79 q^{97} + 56 q^{98} + 74 q^{99}+O(q^{100}) \) 122 * q + 14 * q^2 + 10 * q^3 + 128 * q^4 + 33 * q^5 + 22 * q^6 + 6 * q^7 + 36 * q^8 + 162 * q^9 + 16 * q^10 + 43 * q^11 + 23 * q^12 + 25 * q^13 + 45 * q^14 + 12 * q^15 + 132 * q^16 + 103 * q^17 + 30 * q^18 + 37 * q^19 + 63 * q^20 + 81 * q^21 + 15 * q^23 + 60 * q^24 + 151 * q^25 + 59 * q^26 + 22 * q^27 - 3 * q^28 + 80 * q^29 - 9 * q^30 + 15 * q^31 + 66 * q^32 + 93 * q^33 + 30 * q^34 + 23 * q^35 + 162 * q^36 + 18 * q^37 + 41 * q^38 + 10 * q^39 + 29 * q^40 + 249 * q^41 - 8 * q^42 + 14 * q^43 + 100 * q^44 + 59 * q^45 + 11 * q^46 + 57 * q^47 + 33 * q^48 + 180 * q^49 + 63 * q^50 + 26 * q^51 + 31 * q^52 + 65 * q^53 + 65 * q^54 - 8 * q^55 + 120 * q^56 + 57 * q^57 - 31 * q^58 + 108 * q^59 - q^60 + 70 * q^61 + 25 * q^62 - 7 * q^63 + 100 * q^64 + 171 * q^65 + 12 * q^66 - 6 * q^67 + 184 * q^68 + 64 * q^69 - 24 * q^70 + 47 * q^71 + 53 * q^72 + 76 * q^73 + 66 * q^74 + 40 * q^75 + 32 * q^76 + 73 * q^77 - 19 * q^78 + 8 * q^79 + 115 * q^80 + 250 * q^81 - 13 * q^82 + 116 * q^83 + 159 * q^84 + 31 * q^85 + 91 * q^86 + 25 * q^87 - 43 * q^88 + 361 * q^89 + 32 * q^90 + 7 * q^91 + 5 * q^92 + 18 * q^93 + 23 * q^94 + 42 * q^95 + 77 * q^96 + 79 * q^97 + 56 * q^98 + 74 * q^99

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