LMFDB - Embedded newform 667.4.a.b.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [667,4,Mod(1,667)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(667, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("667.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 667 = 23 \cdot 29 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	667.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:	$39.3542739738$
Analytic rank:	$1$
Dimension:	$38$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	667.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.460454 q^{2} +1.16842 q^{3} -7.78798 q^{4} +16.4926 q^{5} -0.538005 q^{6} -29.6525 q^{7} +7.26964 q^{8} -25.6348 q^{9} +O(q^{10})$	\(q-0.460454 q^{2} +1.16842 q^{3} -7.78798 q^{4} +16.4926 q^{5} -0.538005 q^{6} -29.6525 q^{7} +7.26964 q^{8} -25.6348 q^{9} -7.59408 q^{10} +24.8443 q^{11} -9.09966 q^{12} +85.0547 q^{13} +13.6536 q^{14} +19.2703 q^{15} +58.9565 q^{16} -85.5430 q^{17} +11.8036 q^{18} +20.2519 q^{19} -128.444 q^{20} -34.6466 q^{21} -11.4397 q^{22} -23.0000 q^{23} +8.49401 q^{24} +147.006 q^{25} -39.1638 q^{26} -61.4997 q^{27} +230.933 q^{28} +29.0000 q^{29} -8.87309 q^{30} +114.603 q^{31} -85.3039 q^{32} +29.0287 q^{33} +39.3886 q^{34} -489.046 q^{35} +199.643 q^{36} -269.148 q^{37} -9.32507 q^{38} +99.3799 q^{39} +119.895 q^{40} -326.361 q^{41} +15.9532 q^{42} -275.711 q^{43} -193.487 q^{44} -422.784 q^{45} +10.5904 q^{46} -8.69455 q^{47} +68.8862 q^{48} +536.270 q^{49} -67.6892 q^{50} -99.9505 q^{51} -662.405 q^{52} -560.892 q^{53} +28.3178 q^{54} +409.747 q^{55} -215.563 q^{56} +23.6628 q^{57} -13.3532 q^{58} +399.243 q^{59} -150.077 q^{60} -518.718 q^{61} -52.7694 q^{62} +760.135 q^{63} -432.374 q^{64} +1402.77 q^{65} -13.3664 q^{66} -412.547 q^{67} +666.208 q^{68} -26.8737 q^{69} +225.183 q^{70} +813.338 q^{71} -186.356 q^{72} +486.500 q^{73} +123.930 q^{74} +171.765 q^{75} -157.722 q^{76} -736.695 q^{77} -45.7598 q^{78} -662.469 q^{79} +972.346 q^{80} +620.282 q^{81} +150.274 q^{82} -1180.70 q^{83} +269.827 q^{84} -1410.83 q^{85} +126.952 q^{86} +33.8843 q^{87} +180.609 q^{88} -24.2301 q^{89} +194.673 q^{90} -2522.08 q^{91} +179.124 q^{92} +133.905 q^{93} +4.00344 q^{94} +334.006 q^{95} -99.6710 q^{96} -1520.10 q^{97} -246.927 q^{98} -636.878 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q - 8 q^{2} - 16 q^{3} + 152 q^{4} - 80 q^{5} - 16 q^{6} - 38 q^{7} - 138 q^{8} + 312 q^{9}+O(q^{10}) $ 38 * q - 8 * q^2 - 16 * q^3 + 152 * q^4 - 80 * q^5 - 16 * q^6 - 38 * q^7 - 138 * q^8 + 312 * q^9	\( 38 q - 8 q^{2} - 16 q^{3} + 152 q^{4} - 80 q^{5} - 16 q^{6} - 38 q^{7} - 138 q^{8} + 312 q^{9} + 30 q^{10} - 100 q^{11} - 173 q^{12} - 160 q^{13} - 304 q^{14} - 208 q^{15} + 552 q^{16} - 666 q^{17} - 315 q^{18} - 252 q^{19} - 747 q^{20} - 470 q^{21} - 323 q^{22} - 874 q^{23} - 114 q^{24} + 910 q^{25} - 119 q^{26} - 526 q^{27} - 619 q^{28} + 1102 q^{29} - 533 q^{30} + 358 q^{31} - 1272 q^{32} - 604 q^{33} - 553 q^{34} + 16 q^{35} + 1230 q^{36} - 1206 q^{37} - 2010 q^{38} - 240 q^{39} - 418 q^{40} - 1094 q^{41} - 1184 q^{42} - 936 q^{43} - 2153 q^{44} - 3654 q^{45} + 184 q^{46} - 1702 q^{47} - 1319 q^{48} + 1920 q^{49} - 1255 q^{50} - 270 q^{51} - 2202 q^{52} - 4640 q^{53} - 1529 q^{54} - 318 q^{55} - 2435 q^{56} - 1980 q^{57} - 232 q^{58} + 318 q^{59} - 3279 q^{60} - 2212 q^{61} - 541 q^{62} - 1044 q^{63} + 1186 q^{64} - 2438 q^{65} - 3503 q^{66} - 496 q^{67} - 6099 q^{68} + 368 q^{69} + 4068 q^{70} + 870 q^{71} - 3869 q^{72} - 2810 q^{73} - 2793 q^{74} - 3638 q^{75} + 1548 q^{76} - 6072 q^{77} + 2170 q^{78} - 3084 q^{79} - 6702 q^{80} + 362 q^{81} - 1183 q^{82} - 5566 q^{83} - 6518 q^{84} - 120 q^{85} - 2095 q^{86} - 464 q^{87} - 1220 q^{88} - 6506 q^{89} + 165 q^{90} + 44 q^{91} - 3496 q^{92} - 5928 q^{93} + 135 q^{94} - 2024 q^{95} - 3164 q^{96} - 7472 q^{97} - 6422 q^{98} - 944 q^{99}+O(q^{100}) \) 38 * q - 8 * q^2 - 16 * q^3 + 152 * q^4 - 80 * q^5 - 16 * q^6 - 38 * q^7 - 138 * q^8 + 312 * q^9 + 30 * q^10 - 100 * q^11 - 173 * q^12 - 160 * q^13 - 304 * q^14 - 208 * q^15 + 552 * q^16 - 666 * q^17 - 315 * q^18 - 252 * q^19 - 747 * q^20 - 470 * q^21 - 323 * q^22 - 874 * q^23 - 114 * q^24 + 910 * q^25 - 119 * q^26 - 526 * q^27 - 619 * q^28 + 1102 * q^29 - 533 * q^30 + 358 * q^31 - 1272 * q^32 - 604 * q^33 - 553 * q^34 + 16 * q^35 + 1230 * q^36 - 1206 * q^37 - 2010 * q^38 - 240 * q^39 - 418 * q^40 - 1094 * q^41 - 1184 * q^42 - 936 * q^43 - 2153 * q^44 - 3654 * q^45 + 184 * q^46 - 1702 * q^47 - 1319 * q^48 + 1920 * q^49 - 1255 * q^50 - 270 * q^51 - 2202 * q^52 - 4640 * q^53 - 1529 * q^54 - 318 * q^55 - 2435 * q^56 - 1980 * q^57 - 232 * q^58 + 318 * q^59 - 3279 * q^60 - 2212 * q^61 - 541 * q^62 - 1044 * q^63 + 1186 * q^64 - 2438 * q^65 - 3503 * q^66 - 496 * q^67 - 6099 * q^68 + 368 * q^69 + 4068 * q^70 + 870 * q^71 - 3869 * q^72 - 2810 * q^73 - 2793 * q^74 - 3638 * q^75 + 1548 * q^76 - 6072 * q^77 + 2170 * q^78 - 3084 * q^79 - 6702 * q^80 + 362 * q^81 - 1183 * q^82 - 5566 * q^83 - 6518 * q^84 - 120 * q^85 - 2095 * q^86 - 464 * q^87 - 1220 * q^88 - 6506 * q^89 + 165 * q^90 + 44 * q^91 - 3496 * q^92 - 5928 * q^93 + 135 * q^94 - 2024 * q^95 - 3164 * q^96 - 7472 * q^97 - 6422 * q^98 - 944 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.460454	−0.162795	−0.0813975	−	0.996682i	$-0.525938\pi$
$2$	−0.460454	−0.162795	−0.0813975	+	0.996682i	$0.525938\pi$
$3$	1.16842	0.224863	0.112432	−	0.993659i	$-0.464136\pi$
$3$	1.16842	0.224863	0.112432	+	0.993659i	$0.464136\pi$
$4$	−7.78798	−0.973498
$5$	16.4926	1.47514	0.737571	−	0.675270i	$-0.235973\pi$
$5$	16.4926	1.47514	0.737571	+	0.675270i	$0.235973\pi$
$6$	−0.538005	−0.0366066
$7$	−29.6525	−1.60108	−0.800542	−	0.599277i	$-0.795455\pi$
$7$	−29.6525	−1.60108	−0.800542	+	0.599277i	$0.795455\pi$
$8$	7.26964	0.321276
$9$	−25.6348	−0.949437
$10$	−7.59408	−0.240146
$11$	24.8443	0.680985	0.340493	−	0.940247i	$-0.389406\pi$
$11$	24.8443	0.680985	0.340493	+	0.940247i	$0.389406\pi$
$12$	−9.09966	−0.218904
$13$	85.0547	1.81461	0.907305	−	0.420473i	$-0.138136\pi$
$13$	85.0547	1.81461	0.907305	+	0.420473i	$0.138136\pi$
$14$	13.6536	0.260648
$15$	19.2703	0.331705
$16$	58.9565	0.921196
$17$	−85.5430	−1.22043	−0.610213	−	0.792238i	$-0.708916\pi$
$17$	−85.5430	−1.22043	−0.610213	+	0.792238i	$0.708916\pi$
$18$	11.8036	0.154564
$19$	20.2519	0.244532	0.122266	−	0.992497i	$-0.460984\pi$
$19$	20.2519	0.244532	0.122266	+	0.992497i	$0.460984\pi$
$20$	−128.444	−1.43605
$21$	−34.6466	−0.360025
$22$	−11.4397	−0.110861
$23$	−23.0000	−0.208514
$23$	−23.0000	−0.208514
$24$	8.49401	0.0722430
$25$	147.006	1.17604
$26$	−39.1638	−0.295409
$27$	−61.4997	−0.438356
$28$	230.933	1.55865
$29$	29.0000	0.185695
$29$	29.0000	0.185695
$30$	−8.87309	−0.0539999
$31$	114.603	0.663978	0.331989	−	0.943283i	$-0.392280\pi$
$31$	114.603	0.663978	0.331989	+	0.943283i	$0.392280\pi$
$32$	−85.3039	−0.471242
$33$	29.0287	0.153129
$34$	39.3886	0.198679
$35$	−489.046	−2.36183
$36$	199.643	0.924274
$37$	−269.148	−1.19588	−0.597942	−	0.801539i	$-0.704015\pi$
$37$	−269.148	−1.19588	−0.597942	+	0.801539i	$0.704015\pi$
$38$	−9.32507	−0.0398086
$39$	99.3799	0.408039
$40$	119.895	0.473927
$41$	−326.361	−1.24315	−0.621573	−	0.783356i	$-0.713506\pi$
$41$	−326.361	−1.24315	−0.621573	+	0.783356i	$0.713506\pi$
$42$	15.9532	0.0586102
$43$	−275.711	−0.977803	−0.488902	−	0.872339i	$-0.662602\pi$
$43$	−275.711	−0.977803	−0.488902	+	0.872339i	$0.662602\pi$
$44$	−193.487	−0.662938
$45$	−422.784	−1.40055
$46$	10.5904	0.0339451
$47$	−8.69455	−0.0269836	−0.0134918	−	0.999909i	$-0.504295\pi$
$47$	−8.69455	−0.0269836	−0.0134918	+	0.999909i	$0.504295\pi$
$48$	68.8862	0.207143
$49$	536.270	1.56347
$50$	−67.6892	−0.191454
$51$	−99.9505	−0.274429
$52$	−662.405	−1.76652
$53$	−560.892	−1.45367	−0.726835	−	0.686812i	$-0.759009\pi$
$53$	−560.892	−1.45367	−0.726835	+	0.686812i	$0.759009\pi$
$54$	28.3178	0.0713622
$55$	409.747	1.00455
$56$	−215.563	−0.514389
$57$	23.6628	0.0549862
$58$	−13.3532	−0.0302303
$59$	399.243	0.880967	0.440483	−	0.897761i	$-0.354807\pi$
$59$	399.243	0.880967	0.440483	+	0.897761i	$0.354807\pi$
$60$	−150.077	−0.322914
$61$	−518.718	−1.08877	−0.544385	−	0.838835i	$-0.683237\pi$
$61$	−518.718	−1.08877	−0.544385	+	0.838835i	$0.683237\pi$
$62$	−52.7694	−0.108092
$63$	760.135	1.52013
$64$	−432.374	−0.844480
$65$	1402.77	2.67681
$66$	−13.3664	−0.0249286
$67$	−412.547	−0.752249	−0.376124	−	0.926569i	$-0.622743\pi$
$67$	−412.547	−0.752249	−0.376124	+	0.926569i	$0.622743\pi$
$68$	666.208	1.18808
$69$	−26.8737	−0.0468872
$70$	225.183	0.384493
$71$	813.338	1.35951	0.679757	−	0.733437i	$-0.262085\pi$
$71$	813.338	1.35951	0.679757	+	0.733437i	$0.262085\pi$
$72$	−186.356	−0.305031
$73$	486.500	0.780006	0.390003	−	0.920814i	$-0.372474\pi$
$73$	486.500	0.780006	0.390003	+	0.920814i	$0.372474\pi$
$74$	123.930	0.194684
$75$	171.765	0.264449
$76$	−157.722	−0.238051
$77$	−736.695	−1.09031
$78$	−45.7598	−0.0664267
$79$	−662.469	−0.943463	−0.471731	−	0.881742i	$-0.656371\pi$
$79$	−662.469	−0.943463	−0.471731	+	0.881742i	$0.656371\pi$
$80$	972.346	1.35889
$81$	620.282	0.850866
$82$	150.274	0.202378
$83$	−1180.70	−1.56143	−0.780714	−	0.624888i	$-0.785144\pi$
$83$	−1180.70	−1.56143	−0.780714	+	0.624888i	$0.785144\pi$
$84$	269.827	0.350483
$85$	−1410.83	−1.80030
$86$	126.952	0.159181
$87$	33.8843	0.0417560
$88$	180.609	0.218784
$89$	−24.2301	−0.0288582	−0.0144291	−	0.999896i	$-0.504593\pi$
$89$	−24.2301	−0.0288582	−0.0144291	+	0.999896i	$0.504593\pi$
$90$	194.673	0.228003
$91$	−2522.08	−2.90534
$92$	179.124	0.202988
$93$	133.905	0.149304
$94$	4.00344	0.00439280
$95$	334.006	0.360719
$96$	−99.6710	−0.105965
$97$	−1520.10	−1.59116	−0.795580	−	0.605849i	$-0.792834\pi$
$97$	−1520.10	−1.59116	−0.795580	+	0.605849i	$0.792834\pi$
$98$	−246.927	−0.254525
$99$	−636.878	−0.646552
$100$	−1144.88	−1.14488
$101$	−990.104	−0.975436	−0.487718	−	0.873001i	$-0.662171\pi$
$101$	−990.104	−0.975436	−0.487718	+	0.873001i	$0.662171\pi$
$102$	46.0226	0.0446756
$103$	114.035	0.109089	0.0545445	−	0.998511i	$-0.482629\pi$
$103$	114.035	0.109089	0.0545445	+	0.998511i	$0.482629\pi$
$104$	618.317	0.582990
$105$	−571.413	−0.531088
$106$	258.265	0.236650
$107$	276.433	0.249755	0.124878	−	0.992172i	$-0.460146\pi$
$107$	276.433	0.249755	0.124878	+	0.992172i	$0.460146\pi$
$108$	478.959	0.426739
$109$	1431.07	1.25754	0.628771	−	0.777591i	$-0.283558\pi$
$109$	1431.07	1.25754	0.628771	+	0.777591i	$0.283558\pi$
$110$	−188.670	−0.163536
$111$	−314.479	−0.268910
$112$	−1748.21	−1.47491
$113$	−2150.73	−1.79047	−0.895235	−	0.445593i	$-0.852993\pi$
$113$	−2150.73	−1.79047	−0.895235	+	0.445593i	$0.852993\pi$
$114$	−10.8956	−0.00895148
$115$	−379.330	−0.307588
$116$	−225.851	−0.180774
$117$	−2180.36	−1.72286
$118$	−183.833	−0.143417
$119$	2536.56	1.95400
$120$	140.088	0.106569
$121$	−713.761	−0.536259
$122$	238.846	0.177246
$123$	−381.327	−0.279538
$124$	−892.527	−0.646381
$125$	362.928	0.259690
$126$	−350.007	−0.247469
$127$	1982.50	1.38518	0.692590	−	0.721331i	$-0.256469\pi$
$127$	1982.50	1.38518	0.692590	+	0.721331i	$0.256469\pi$
$128$	881.519	0.608719
$129$	−322.147	−0.219872
$130$	−645.912	−0.435771
$131$	−554.280	−0.369677	−0.184839	−	0.982769i	$-0.559176\pi$
$131$	−554.280	−0.369677	−0.184839	+	0.982769i	$0.559176\pi$
$132$	−226.075	−0.149070
$133$	−600.519	−0.391516
$134$	189.959	0.122462
$135$	−1014.29	−0.646638
$136$	−621.867	−0.392093
$137$	−460.543	−0.287203	−0.143602	−	0.989636i	$-0.545868\pi$
$137$	−460.543	−0.287203	−0.143602	+	0.989636i	$0.545868\pi$
$138$	12.3741	0.00763300
$139$	−808.022	−0.493061	−0.246531	−	0.969135i	$-0.579291\pi$
$139$	−808.022	−0.493061	−0.246531	+	0.969135i	$0.579291\pi$
$140$	3808.68	2.29923
$141$	−10.1589	−0.00606762
$142$	−374.505	−0.221322
$143$	2113.12	1.23572
$144$	−1511.34	−0.874617
$145$	478.285	0.273927
$146$	−224.011	−0.126981
$147$	626.590	0.351567
$148$	2096.12	1.16419
$149$	−2520.94	−1.38606	−0.693032	−	0.720906i	$-0.743726\pi$
$149$	−2520.94	−1.38606	−0.693032	+	0.720906i	$0.743726\pi$
$150$	−79.0897	−0.0430510
$151$	−2093.24	−1.12812	−0.564058	−	0.825735i	$-0.690761\pi$
$151$	−2093.24	−1.12812	−0.564058	+	0.825735i	$0.690761\pi$
$152$	147.224	0.0785621
$153$	2192.88	1.15872
$154$	339.214	0.177498
$155$	1890.10	0.979462
$156$	−773.969	−0.397225
$157$	−3474.70	−1.76631	−0.883156	−	0.469078i	$-0.844586\pi$
$157$	−3474.70	−1.76631	−0.883156	+	0.469078i	$0.844586\pi$
$158$	305.036	0.153591
$159$	−655.360	−0.326877
$160$	−1406.88	−0.695148
$161$	682.007	0.333849
$162$	−285.611	−0.138517
$163$	−3340.04	−1.60498	−0.802491	−	0.596664i	$-0.796492\pi$
$163$	−3340.04	−1.60498	−0.802491	+	0.596664i	$0.796492\pi$
$164$	2541.69	1.21020
$165$	478.758	0.225886
$166$	543.657	0.254193
$167$	−1406.08	−0.651533	−0.325766	−	0.945450i	$-0.605622\pi$
$167$	−1406.08	−0.651533	−0.325766	+	0.945450i	$0.605622\pi$
$168$	−251.869	−0.115667
$169$	5037.30	2.29281
$170$	649.620	0.293080
$171$	−519.153	−0.232168
$172$	2147.23	0.951889
$173$	2436.15	1.07062	0.535309	−	0.844656i	$-0.320195\pi$
$173$	2436.15	1.07062	0.535309	+	0.844656i	$0.320195\pi$
$174$	−15.6021	−0.00679767
$175$	−4359.08	−1.88294
$176$	1464.73	0.627321
$177$	466.485	0.198097
$178$	11.1568	0.00469797
$179$	2341.21	0.977601	0.488801	−	0.872396i	$-0.337435\pi$
$179$	2341.21	0.977601	0.488801	+	0.872396i	$0.337435\pi$
$180$	3292.63	1.36344
$181$	−338.852	−0.139153	−0.0695764	−	0.997577i	$-0.522165\pi$
$181$	−338.852	−0.139153	−0.0695764	+	0.997577i	$0.522165\pi$
$182$	1161.30	0.472975
$183$	−606.082	−0.244824
$184$	−167.202	−0.0669906
$185$	−4438.96	−1.76410
$186$	−61.6570	−0.0243060
$187$	−2125.26	−0.831092
$188$	67.7130	0.0262685
$189$	1823.62	0.701845
$190$	−153.795	−0.0587233
$191$	98.8248	0.0374383	0.0187191	−	0.999825i	$-0.494041\pi$
$191$	98.8248	0.0374383	0.0187191	+	0.999825i	$0.494041\pi$
$192$	−505.195	−0.189892
$193$	1613.71	0.601851	0.300926	−	0.953648i	$-0.402704\pi$
$193$	1613.71	0.601851	0.300926	+	0.953648i	$0.402704\pi$
$194$	699.935	0.259033
$195$	1639.03	0.601915
$196$	−4176.46	−1.52203
$197$	2661.67	0.962618	0.481309	−	0.876551i	$-0.340161\pi$
$197$	2661.67	0.962618	0.481309	+	0.876551i	$0.340161\pi$
$198$	293.253	0.105256
$199$	417.289	0.148647	0.0743237	−	0.997234i	$-0.476320\pi$
$199$	417.289	0.148647	0.0743237	+	0.997234i	$0.476320\pi$
$200$	1068.68	0.377834
$201$	−482.030	−0.169153
$202$	455.897	0.158796
$203$	−859.922	−0.297314
$204$	778.412	0.267156
$205$	−5382.53	−1.83382
$206$	−52.5077	−0.0177592
$207$	589.600	0.197971
$208$	5014.53	1.67161
$209$	503.145	0.166523
$210$	263.109	0.0864584
$211$	3246.09	1.05910	0.529550	−	0.848279i	$-0.322361\pi$
$211$	3246.09	1.05910	0.529550	+	0.848279i	$0.322361\pi$
$212$	4368.22	1.41514
$213$	950.323	0.305705
$214$	−127.285	−0.0406589
$215$	−4547.19	−1.44240
$216$	−447.080	−0.140833
$217$	−3398.27	−1.06308
$218$	−658.944	−0.204722
$219$	568.437	0.175395
$220$	−3191.10	−0.977927
$221$	−7275.84	−2.21460
$222$	144.803	0.0437773
$223$	2488.11	0.747159	0.373579	−	0.927598i	$-0.378130\pi$
$223$	2488.11	0.747159	0.373579	+	0.927598i	$0.378130\pi$
$224$	2529.47	0.754497
$225$	−3768.45	−1.11658
$226$	990.310	0.291480
$227$	4490.13	1.31287	0.656433	−	0.754385i	$-0.272065\pi$
$227$	4490.13	1.31287	0.656433	+	0.754385i	$0.272065\pi$
$228$	−184.285	−0.0535290
$229$	2874.77	0.829565	0.414782	−	0.909921i	$-0.363858\pi$
$229$	2874.77	0.829565	0.414782	+	0.909921i	$0.363858\pi$
$230$	174.664	0.0500739
$231$	−860.772	−0.245172
$232$	210.819	0.0596594
$233$	3746.04	1.05327	0.526634	−	0.850092i	$-0.323454\pi$
$233$	3746.04	1.05327	0.526634	+	0.850092i	$0.323454\pi$
$234$	1003.95	0.280473
$235$	−143.396	−0.0398047
$236$	−3109.30	−0.857619
$237$	−774.044	−0.212150
$238$	−1167.97	−0.318102
$239$	2775.91	0.751291	0.375645	−	0.926764i	$-0.377421\pi$
$239$	2775.91	0.751291	0.375645	+	0.926764i	$0.377421\pi$
$240$	1136.11	0.305565
$241$	−5363.07	−1.43347	−0.716734	−	0.697347i	$-0.754364\pi$
$241$	−5363.07	−1.43347	−0.716734	+	0.697347i	$0.754364\pi$
$242$	328.654	0.0873003
$243$	2385.24	0.629685
$244$	4039.77	1.05992
$245$	8844.48	2.30634
$246$	175.584	0.0455073
$247$	1722.52	0.443730
$248$	833.123	0.213320
$249$	−1379.56	−0.351108
$250$	−167.111	−0.0422762
$251$	−2040.00	−0.513002	−0.256501	−	0.966544i	$-0.582570\pi$
$251$	−2040.00	−0.513002	−0.256501	+	0.966544i	$0.582570\pi$
$252$	−5919.92	−1.47984
$253$	−571.419	−0.141995
$254$	−912.847	−0.225501
$255$	−1648.44	−0.404821
$256$	3053.09	0.745384
$257$	−3671.11	−0.891042	−0.445521	−	0.895272i	$-0.646981\pi$
$257$	−3671.11	−0.891042	−0.445521	+	0.895272i	$0.646981\pi$
$258$	148.334	0.0357940
$259$	7980.92	1.91471
$260$	−10924.8	−2.60587
$261$	−743.409	−0.176306
$262$	255.220	0.0601816
$263$	1800.83	0.422220	0.211110	−	0.977462i	$-0.432292\pi$
$263$	1800.83	0.422220	0.211110	+	0.977462i	$0.432292\pi$
$264$	211.028	0.0491965
$265$	−9250.57	−2.14437
$266$	276.511	0.0637369
$267$	−28.3110	−0.00648915
$268$	3212.91	0.732312
$269$	−1989.44	−0.450924	−0.225462	−	0.974252i	$-0.572389\pi$
$269$	−1989.44	−0.450924	−0.225462	+	0.974252i	$0.572389\pi$
$270$	467.033	0.105269
$271$	7124.18	1.59691	0.798456	−	0.602053i	$-0.205650\pi$
$271$	7124.18	1.59691	0.798456	+	0.602053i	$0.205650\pi$
$272$	−5043.32	−1.12425
$273$	−2946.86	−0.653304
$274$	212.059	0.0467553
$275$	3652.25	0.800869
$276$	209.292	0.0456446
$277$	1444.04	0.313226	0.156613	−	0.987660i	$-0.449942\pi$
$277$	1444.04	0.313226	0.156613	+	0.987660i	$0.449942\pi$
$278$	372.057	0.0802679
$279$	−2937.83	−0.630405
$280$	−3555.19	−0.758797
$281$	3255.18	0.691059	0.345530	−	0.938408i	$-0.387699\pi$
$281$	3255.18	0.691059	0.345530	+	0.938408i	$0.387699\pi$
$282$	4.67771	0.000987778 0
$283$	−1042.41	−0.218957	−0.109479	−	0.993989i	$-0.534918\pi$
$283$	−1042.41	−0.218957	−0.109479	+	0.993989i	$0.534918\pi$
$284$	−6334.27	−1.32348
$285$	390.261	0.0811125
$286$	−972.996	−0.201170
$287$	9677.41	1.99038
$288$	2186.75	0.447414
$289$	2404.61	0.489439
$290$	−220.228	−0.0445939
$291$	−1776.12	−0.357793
$292$	−3788.85	−0.759334
$293$	−1015.85	−0.202547	−0.101274	−	0.994859i	$-0.532292\pi$
$293$	−1015.85	−0.202547	−0.101274	+	0.994859i	$0.532292\pi$
$294$	−288.516	−0.0572333
$295$	6584.56	1.29955
$296$	−1956.61	−0.384209
$297$	−1527.92	−0.298514
$298$	1160.78	0.225644
$299$	−1956.26	−0.378372
$300$	−1337.70	−0.257440
$301$	8175.52	1.56554
$302$	963.841	0.183652
$303$	−1156.86	−0.219340
$304$	1193.98	0.225262
$305$	−8555.00	−1.60609
$306$	−1009.72	−0.188633
$307$	1500.38	0.278928	0.139464	−	0.990227i	$-0.455462\pi$
$307$	1500.38	0.278928	0.139464	+	0.990227i	$0.455462\pi$
$308$	5737.37	1.06142
$309$	133.241	0.0245301
$310$	−870.305	−0.159452
$311$	3624.31	0.660822	0.330411	−	0.943837i	$-0.392813\pi$
$311$	3624.31	0.660822	0.330411	+	0.943837i	$0.392813\pi$
$312$	722.456	0.131093
$313$	−3647.68	−0.658719	−0.329359	−	0.944205i	$-0.606833\pi$
$313$	−3647.68	−0.658719	−0.329359	+	0.944205i	$0.606833\pi$
$314$	1599.94	0.287547
$315$	12536.6	2.24240
$316$	5159.29	0.918459
$317$	3206.50	0.568123	0.284062	−	0.958806i	$-0.408318\pi$
$317$	3206.50	0.568123	0.284062	+	0.958806i	$0.408318\pi$
$318$	301.763	0.0532139
$319$	720.485	0.126456
$320$	−7130.96	−1.24573
$321$	322.991	0.0561608
$322$	−314.033	−0.0543490
$323$	−1732.41	−0.298433
$324$	−4830.74	−0.828317
$325$	12503.5	2.13406
$326$	1537.93	0.261283
$327$	1672.10	0.282775
$328$	−2372.52	−0.399392
$329$	257.815	0.0432030
$330$	−220.446	−0.0367732
$331$	−3826.85	−0.635477	−0.317738	−	0.948178i	$-0.602923\pi$
$331$	−3826.85	−0.635477	−0.317738	+	0.948178i	$0.602923\pi$
$332$	9195.26	1.52005
$333$	6899.56	1.13542
$334$	647.436	0.106066
$335$	−6803.97	−1.10967
$336$	−2042.65	−0.331653
$337$	−9735.35	−1.57365	−0.786823	−	0.617179i	$-0.788275\pi$
$337$	−9735.35	−1.57365	−0.786823	+	0.617179i	$0.788275\pi$
$338$	−2319.45	−0.373258
$339$	−2512.96	−0.402611
$340$	10987.5	1.75259
$341$	2847.23	0.452160
$342$	239.046	0.0377957
$343$	−5730.93	−0.902161
$344$	−2004.32	−0.314144
$345$	−443.217	−0.0691653
$346$	−1121.73	−0.174291
$347$	−8462.84	−1.30925	−0.654624	−	0.755955i	$-0.727173\pi$
$347$	−8462.84	−1.30925	−0.654624	+	0.755955i	$0.727173\pi$
$348$	−263.890	−0.0406494
$349$	3373.47	0.517414	0.258707	−	0.965956i	$-0.416704\pi$
$349$	3373.47	0.517414	0.258707	+	0.965956i	$0.416704\pi$
$350$	2007.15	0.306534
$351$	−5230.84	−0.795446
$352$	−2119.31	−0.320909
$353$	−10473.1	−1.57911	−0.789557	−	0.613677i	$-0.789690\pi$
$353$	−10473.1	−1.57911	−0.789557	+	0.613677i	$0.789690\pi$
$354$	−214.795	−0.0322492
$355$	13414.1	2.00548
$356$	188.703	0.0280934
$357$	2963.78	0.439383
$358$	−1078.02	−0.159149
$359$	12229.5	1.79791	0.898956	−	0.438040i	$-0.144327\pi$
$359$	12229.5	1.79791	0.898956	+	0.438040i	$0.144327\pi$
$360$	−3073.49	−0.449964
$361$	−6448.86	−0.940204
$362$	156.026	0.0226534
$363$	−833.974	−0.120585
$364$	19641.9	2.82834
$365$	8023.64	1.15062
$366$	279.073	0.0398562
$367$	10997.8	1.56425	0.782127	−	0.623119i	$-0.214135\pi$
$367$	10997.8	1.56425	0.782127	+	0.623119i	$0.214135\pi$
$368$	−1356.00	−0.192083
$369$	8366.19	1.18029
$370$	2043.93	0.287187
$371$	16631.9	2.32745
$372$	−1042.85	−0.145347
$373$	5992.61	0.831866	0.415933	−	0.909395i	$-0.363455\pi$
$373$	5992.61	0.831866	0.415933	+	0.909395i	$0.363455\pi$
$374$	978.583	0.135298
$375$	424.053	0.0583947
$376$	−63.2062	−0.00866918
$377$	2466.59	0.336965
$378$	−839.692	−0.114257
$379$	659.628	0.0894006	0.0447003	−	0.999000i	$-0.485767\pi$
$379$	659.628	0.0894006	0.0447003	+	0.999000i	$0.485767\pi$
$380$	−2601.24	−0.351159
$381$	2316.39	0.311476
$382$	−45.5043	−0.00609477
$383$	6620.63	0.883286	0.441643	−	0.897191i	$-0.354396\pi$
$383$	6620.63	0.883286	0.441643	+	0.897191i	$0.354396\pi$
$384$	1029.99	0.136878
$385$	−12150.0	−1.60837
$386$	−743.038	−0.0979784
$387$	7067.79	0.928362
$388$	11838.5	1.54899
$389$	−1059.57	−0.138103	−0.0690515	−	0.997613i	$-0.521997\pi$
$389$	−1059.57	−0.138103	−0.0690515	+	0.997613i	$0.521997\pi$
$390$	−754.698	−0.0979888
$391$	1967.49	0.254476
$392$	3898.49	0.502304
$393$	−647.634	−0.0831267
$394$	−1225.57	−0.156709
$395$	−10925.8	−1.39174
$396$	4960.00	0.629417
$397$	−12260.6	−1.54998	−0.774992	−	0.631971i	$-0.782246\pi$
$397$	−12260.6	−1.54998	−0.774992	+	0.631971i	$0.782246\pi$
$398$	−192.142	−0.0241991
$399$	−701.661	−0.0880375
$400$	8666.93	1.08337
$401$	−4288.00	−0.533996	−0.266998	−	0.963697i	$-0.586032\pi$
$401$	−4288.00	−0.533996	−0.266998	+	0.963697i	$0.586032\pi$
$402$	221.952	0.0275373
$403$	9747.54	1.20486
$404$	7710.91	0.949585
$405$	10230.0	1.25515
$406$	395.954	0.0484012
$407$	−6686.81	−0.814380
$408$	−726.604	−0.0881673
$409$	−6275.23	−0.758656	−0.379328	−	0.925262i	$-0.623845\pi$
$409$	−6275.23	−0.758656	−0.379328	+	0.925262i	$0.623845\pi$
$410$	2478.41	0.298536
$411$	−538.109	−0.0645815
$412$	−888.100	−0.106198
$413$	−11838.6	−1.41050
$414$	−271.484	−0.0322287
$415$	−19472.8	−2.30333
$416$	−7255.49	−0.855120
$417$	−944.112	−0.110871
$418$	−231.675	−0.0271091
$419$	−8846.10	−1.03141	−0.515704	−	0.856767i	$-0.672470\pi$
$419$	−8846.10	−1.03141	−0.515704	+	0.856767i	$0.672470\pi$
$420$	4450.15	0.517013
$421$	11295.1	1.30758	0.653791	−	0.756676i	$-0.273178\pi$
$421$	11295.1	1.30758	0.653791	+	0.756676i	$0.273178\pi$
$422$	−1494.67	−0.172416
$423$	222.883	0.0256192
$424$	−4077.48	−0.467029
$425$	−12575.3	−1.43527
$426$	−437.580	−0.0497672
$427$	15381.3	1.74321
$428$	−2152.86	−0.243136
$429$	2469.02	0.277869
$430$	2093.77	0.234815
$431$	−5626.30	−0.628792	−0.314396	−	0.949292i	$-0.601802\pi$
$431$	−5626.30	−0.628792	−0.314396	+	0.949292i	$0.601802\pi$
$432$	−3625.81	−0.403812
$433$	11192.9	1.24226	0.621130	−	0.783708i	$-0.286674\pi$
$433$	11192.9	1.24226	0.621130	+	0.783708i	$0.286674\pi$
$434$	1564.75	0.173065
$435$	558.839	0.0615961
$436$	−11145.2	−1.22421
$437$	−465.794	−0.0509884
$438$	−261.739	−0.0285534
$439$	−1037.60	−0.112806	−0.0564031	−	0.998408i	$-0.517963\pi$
$439$	−1037.60	−0.112806	−0.0564031	+	0.998408i	$0.517963\pi$
$440$	2978.71	0.322737
$441$	−13747.2	−1.48441
$442$	3350.19	0.360525
$443$	−8639.92	−0.926625	−0.463313	−	0.886195i	$-0.653339\pi$
$443$	−8639.92	−0.926625	−0.463313	+	0.886195i	$0.653339\pi$
$444$	2449.16	0.261784
$445$	−399.616	−0.0425700
$446$	−1145.66	−0.121634
$447$	−2945.53	−0.311675
$448$	12821.0	1.35208
$449$	−291.807	−0.0306709	−0.0153355	−	0.999882i	$-0.504882\pi$
$449$	−291.807	−0.0306709	−0.0153355	+	0.999882i	$0.504882\pi$
$450$	1735.20	0.181774
$451$	−8108.20	−0.846564
$452$	16749.8	1.74302
$453$	−2445.79	−0.253672
$454$	−2067.50	−0.213728
$455$	−41595.7	−4.28579
$456$	172.020	0.0176657
$457$	115.820	0.0118552	0.00592760	−	0.999982i	$-0.498113\pi$
$457$	115.820	0.0118552	0.00592760	+	0.999982i	$0.498113\pi$
$458$	−1323.70	−0.135049
$459$	5260.87	0.534981
$460$	2954.21	0.299437
$461$	−11941.2	−1.20641	−0.603205	−	0.797586i	$-0.706110\pi$
$461$	−11941.2	−1.20641	−0.603205	+	0.797586i	$0.706110\pi$
$462$	396.346	0.0399127
$463$	−1306.33	−0.131124	−0.0655619	−	0.997849i	$-0.520884\pi$
$463$	−1306.33	−0.131124	−0.0655619	+	0.997849i	$0.520884\pi$
$464$	1709.74	0.171062
$465$	2208.44	0.220245
$466$	−1724.88	−0.171467
$467$	1550.96	0.153683	0.0768413	−	0.997043i	$-0.475517\pi$
$467$	1550.96	0.153683	0.0768413	+	0.997043i	$0.475517\pi$
$468$	16980.6	1.67720
$469$	12233.0	1.20441
$470$	66.0270	0.00648000
$471$	−4059.92	−0.397179
$472$	2902.35	0.283033
$473$	−6849.85	−0.665870
$474$	356.411	0.0345370
$475$	2977.14	0.287580
$476$	−19754.7	−1.90222
$477$	14378.4	1.38017
$478$	−1278.18	−0.122306
$479$	3095.25	0.295252	0.147626	−	0.989043i	$-0.452837\pi$
$479$	3095.25	0.295252	0.147626	+	0.989043i	$0.452837\pi$
$480$	−1643.83	−0.156313
$481$	−22892.3	−2.17006
$482$	2469.45	0.233361
$483$	796.873	0.0750703
$484$	5558.75	0.522047
$485$	−25070.3	−2.34719
$486$	−1098.29	−0.102510
$487$	−2914.06	−0.271148	−0.135574	−	0.990767i	$-0.543288\pi$
$487$	−2914.06	−0.271148	−0.135574	+	0.990767i	$0.543288\pi$
$488$	−3770.89	−0.349796
$489$	−3902.58	−0.360901
$490$	−4072.47	−0.375460
$491$	−5436.17	−0.499655	−0.249828	−	0.968290i	$-0.580374\pi$
$491$	−5436.17	−0.499655	−0.249828	+	0.968290i	$0.580374\pi$
$492$	2969.77	0.272129
$493$	−2480.75	−0.226627
$494$	−793.141	−0.0722371
$495$	−10503.8	−0.953757
$496$	6756.60	0.611654
$497$	−24117.5	−2.17670
$498$	635.222	0.0571586
$499$	−11798.1	−1.05843	−0.529213	−	0.848489i	$-0.677513\pi$
$499$	−11798.1	−1.05843	−0.529213	+	0.848489i	$0.677513\pi$
$500$	−2826.47	−0.252808
$501$	−1642.90	−0.146506
$502$	939.325	0.0835142
$503$	15946.4	1.41355	0.706776	−	0.707438i	$-0.250149\pi$
$503$	15946.4	1.41355	0.706776	+	0.707438i	$0.250149\pi$
$504$	5525.91	0.488380
$505$	−16329.4	−1.43891
$506$	263.112	0.0231161
$507$	5885.70	0.515568
$508$	−15439.6	−1.34847
$509$	−12303.0	−1.07136	−0.535678	−	0.844422i	$-0.679944\pi$
$509$	−12303.0	−1.07136	−0.535678	+	0.844422i	$0.679944\pi$
$510$	759.031	0.0659029
$511$	−14425.9	−1.24886
$512$	−8457.96	−0.730064
$513$	−1245.49	−0.107192
$514$	1690.38	0.145057
$515$	1880.73	0.160922
$516$	2508.88	0.214045
$517$	−216.010	−0.0183754
$518$	−3674.85	−0.311706
$519$	2846.45	0.240742
$520$	10197.6	0.859993
$521$	22531.1	1.89464	0.947320	−	0.320290i	$-0.103780\pi$
$521$	22531.1	1.89464	0.947320	+	0.320290i	$0.103780\pi$
$522$	342.305	0.0287017
$523$	−15068.8	−1.25987	−0.629935	−	0.776648i	$-0.716918\pi$
$523$	−15068.8	−1.25987	−0.629935	+	0.776648i	$0.716918\pi$
$524$	4316.73	0.359880
$525$	−5093.25	−0.423405
$526$	−829.198	−0.0687353
$527$	−9803.50	−0.810336
$528$	1711.43	0.141061
$529$	529.000	0.0434783
$530$	4259.46	0.349093
$531$	−10234.5	−0.836422
$532$	4676.84	0.381140
$533$	−27758.5	−2.25582
$534$	13.0359	0.00105640
$535$	4559.10	0.368425
$536$	−2999.07	−0.241679
$537$	2735.53	0.219826
$538$	916.046	0.0734081
$539$	13323.3	1.06470
$540$	7899.27	0.629501
$541$	292.985	0.0232836	0.0116418	−	0.999932i	$-0.496294\pi$
$541$	292.985	0.0232836	0.0116418	+	0.999932i	$0.496294\pi$
$542$	−3280.36	−0.259969
$543$	−395.922	−0.0312903
$544$	7297.15	0.575115
$545$	23602.1	1.85505
$546$	1356.89	0.106355
$547$	−5533.85	−0.432560	−0.216280	−	0.976331i	$-0.569392\pi$
$547$	−5533.85	−0.432560	−0.216280	+	0.976331i	$0.569392\pi$
$548$	3586.70	0.279592
$549$	13297.2	1.03372
$550$	−1681.69	−0.130377
$551$	587.305	0.0454084
$552$	−195.362	−0.0150637
$553$	19643.8	1.51056
$554$	−664.911	−0.0509917
$555$	−5186.58	−0.396681
$556$	6292.86	0.479994
$557$	7643.89	0.581476	0.290738	−	0.956803i	$-0.406099\pi$
$557$	7643.89	0.581476	0.290738	+	0.956803i	$0.406099\pi$
$558$	1352.73	0.102627
$559$	−23450.5	−1.77433
$560$	−28832.5	−2.17570
$561$	−2483.20	−0.186882
$562$	−1498.86	−0.112501
$563$	17651.8	1.32137	0.660687	−	0.750662i	$-0.270265\pi$
$563$	17651.8	1.32137	0.660687	+	0.750662i	$0.270265\pi$
$564$	79.1174	0.00590681
$565$	−35471.0	−2.64120
$566$	479.982	0.0356451
$567$	−18392.9	−1.36231
$568$	5912.68	0.436779
$569$	−15919.6	−1.17291	−0.586453	−	0.809983i	$-0.699476\pi$
$569$	−15919.6	−1.17291	−0.586453	+	0.809983i	$0.699476\pi$
$570$	−179.697	−0.0132047
$571$	−8515.75	−0.624121	−0.312061	−	0.950062i	$-0.601019\pi$
$571$	−8515.75	−0.624121	−0.312061	+	0.950062i	$0.601019\pi$
$572$	−16457.0	−1.20297
$573$	115.469	0.00841849
$574$	−4456.00	−0.324024
$575$	−3381.13	−0.245222
$576$	11083.8	0.801780
$577$	2553.24	0.184216	0.0921081	−	0.995749i	$-0.470639\pi$
$577$	2553.24	0.184216	0.0921081	+	0.995749i	$0.470639\pi$
$578$	−1107.21	−0.0796782
$579$	1885.49	0.135334
$580$	−3724.88	−0.266667
$581$	35010.7	2.49998
$582$	817.820	0.0582470
$583$	−13935.0	−0.989928
$584$	3536.68	0.250597
$585$	−35959.8	−2.54146
$586$	467.750	0.0329737
$587$	13308.2	0.935755	0.467877	−	0.883793i	$-0.345019\pi$
$587$	13308.2	0.935755	0.467877	+	0.883793i	$0.345019\pi$
$588$	−4879.87	−0.342249
$589$	2320.93	0.162364
$590$	−3031.88	−0.211560
$591$	3109.95	0.216457
$592$	−15868.1	−1.10164
$593$	5629.06	0.389811	0.194906	−	0.980822i	$-0.437560\pi$
$593$	5629.06	0.389811	0.194906	+	0.980822i	$0.437560\pi$
$594$	703.535	0.0485966
$595$	41834.5	2.88243
$596$	19633.1	1.34933
$597$	487.570	0.0334253
$598$	900.767	0.0615971
$599$	6453.49	0.440205	0.220102	−	0.975477i	$-0.429361\pi$
$599$	6453.49	0.440205	0.220102	+	0.975477i	$0.429361\pi$
$600$	1248.67	0.0849610
$601$	28207.1	1.91446	0.957230	−	0.289328i	$-0.0934317\pi$
$601$	28207.1	1.91446	0.957230	+	0.289328i	$0.0934317\pi$
$602$	−3764.45	−0.254863
$603$	10575.6	0.714212
$604$	16302.1	1.09822
$605$	−11771.8	−0.791058
$606$	532.681	0.0357074
$607$	−1591.63	−0.106429	−0.0532144	−	0.998583i	$-0.516947\pi$
$607$	−1591.63	−0.106429	−0.0532144	+	0.998583i	$0.516947\pi$
$608$	−1727.57	−0.115234
$609$	−1004.75	−0.0668549
$610$	3939.18	0.261464
$611$	−739.512	−0.0489647
$612$	−17078.1	−1.12801
$613$	11426.6	0.752883	0.376441	−	0.926440i	$-0.377148\pi$
$613$	11426.6	0.752883	0.376441	+	0.926440i	$0.377148\pi$
$614$	−690.853	−0.0454081
$615$	−6289.08	−0.412358
$616$	−5355.51	−0.350291
$617$	16794.9	1.09584	0.547922	−	0.836529i	$-0.315419\pi$
$617$	16794.9	1.09584	0.547922	+	0.836529i	$0.315419\pi$
$618$	−61.3512	−0.00399338
$619$	−19120.7	−1.24156	−0.620779	−	0.783986i	$-0.713184\pi$
$619$	−19120.7	−1.24156	−0.620779	+	0.783986i	$0.713184\pi$
$620$	−14720.1	−0.953504
$621$	1414.49	0.0914036
$622$	−1668.83	−0.107579
$623$	718.482	0.0462044
$624$	5859.09	0.375884
$625$	−12390.1	−0.792964
$626$	1679.59	0.107236
$627$	587.886	0.0374448
$628$	27060.9	1.71950
$629$	23023.8	1.45949
$630$	−5772.52	−0.365052
$631$	10637.0	0.671078	0.335539	−	0.942026i	$-0.391082\pi$
$631$	10637.0	0.671078	0.335539	+	0.942026i	$0.391082\pi$
$632$	−4815.91	−0.303112
$633$	3792.81	0.238152
$634$	−1476.45	−0.0924876
$635$	32696.5	2.04334
$636$	5103.93	0.318214
$637$	45612.3	2.83709
$638$	−331.750	−0.0205864
$639$	−20849.8	−1.29077
$640$	14538.5	0.897947
$641$	16206.3	0.998615	0.499307	−	0.866425i	$-0.333588\pi$
$641$	16206.3	0.998615	0.499307	+	0.866425i	$0.333588\pi$
$642$	−148.723	−0.00914269
$643$	−4553.54	−0.279275	−0.139638	−	0.990203i	$-0.544594\pi$
$643$	−4553.54	−0.279275	−0.139638	+	0.990203i	$0.544594\pi$
$644$	−5311.46	−0.325001
$645$	−5313.04	−0.324342
$646$	797.695	0.0485834
$647$	20892.3	1.26949	0.634747	−	0.772720i	$-0.281105\pi$
$647$	20892.3	1.26949	0.634747	+	0.772720i	$0.281105\pi$
$648$	4509.22	0.273363
$649$	9918.92	0.599926
$650$	−5757.29	−0.347415
$651$	−3970.61	−0.239049
$652$	26012.2	1.56245
$653$	−13070.9	−0.783314	−0.391657	−	0.920111i	$-0.628098\pi$
$653$	−13070.9	−0.783314	−0.391657	+	0.920111i	$0.628098\pi$
$654$	−769.925	−0.0460343
$655$	−9141.52	−0.545326
$656$	−19241.1	−1.14518
$657$	−12471.3	−0.740567
$658$	−118.712	−0.00703324
$659$	−26121.2	−1.54406	−0.772030	−	0.635586i	$-0.780759\pi$
$659$	−26121.2	−1.54406	−0.772030	+	0.635586i	$0.780759\pi$
$660$	−3728.56	−0.219900
$661$	−2530.91	−0.148927	−0.0744636	−	0.997224i	$-0.523724\pi$
$661$	−2530.91	−0.148927	−0.0744636	+	0.997224i	$0.523724\pi$
$662$	1762.09	0.103452
$663$	−8501.26	−0.497981
$664$	−8583.25	−0.501649
$665$	−9904.12	−0.577542
$666$	−3176.93	−0.184840
$667$	−667.000	−0.0387202
$668$	10950.6	0.634266
$669$	2907.17	0.168008
$670$	3132.91	0.180649
$671$	−12887.2	−0.741437
$672$	2955.49	0.169659
$673$	21759.7	1.24632	0.623161	−	0.782094i	$-0.285848\pi$
$673$	21759.7	1.24632	0.623161	+	0.782094i	$0.285848\pi$
$674$	4482.68	0.256182
$675$	−9040.79	−0.515526
$676$	−39230.4	−2.23205
$677$	−19708.8	−1.11886	−0.559431	−	0.828877i	$-0.688980\pi$
$677$	−19708.8	−1.11886	−0.559431	+	0.828877i	$0.688980\pi$
$678$	1157.10	0.0655430
$679$	45074.7	2.54758
$680$	−10256.2	−0.578393
$681$	5246.37	0.295215
$682$	−1311.02	−0.0736093
$683$	−5930.54	−0.332249	−0.166124	−	0.986105i	$-0.553125\pi$
$683$	−5930.54	−0.332249	−0.166124	+	0.986105i	$0.553125\pi$
$684$	4043.16	0.226015
$685$	−7595.55	−0.423666
$686$	2638.83	0.146867
$687$	3358.95	0.186538
$688$	−16255.0	−0.900748
$689$	−47706.5	−2.63784
$690$	204.081	0.0112598
$691$	25983.2	1.43046	0.715229	−	0.698890i	$-0.246322\pi$
$691$	25983.2	1.43046	0.715229	+	0.698890i	$0.246322\pi$
$692$	−18972.7	−1.04224
$693$	18885.0	1.03518
$694$	3896.75	0.213139
$695$	−13326.4	−0.727336
$696$	246.326	0.0134152
$697$	27917.9	1.51717
$698$	−1553.33	−0.0842324
$699$	4376.96	0.236841
$700$	33948.4	1.83304
$701$	−4612.93	−0.248542	−0.124271	−	0.992248i	$-0.539659\pi$
$701$	−4612.93	−0.248542	−0.124271	+	0.992248i	$0.539659\pi$
$702$	2408.56	0.129495
$703$	−5450.77	−0.292432
$704$	−10742.0	−0.575078
$705$	−167.547	−0.00895060
$706$	4822.38	0.257072
$707$	29359.0	1.56175
$708$	−3632.98	−0.192847
$709$	−2568.99	−0.136079	−0.0680397	−	0.997683i	$-0.521674\pi$
$709$	−2568.99	−0.136079	−0.0680397	+	0.997683i	$0.521674\pi$
$710$	−6176.55	−0.326482
$711$	16982.2	0.895758
$712$	−176.144	−0.00927144
$713$	−2635.87	−0.138449
$714$	−1364.68	−0.0715294
$715$	34850.9	1.82287
$716$	−18233.3	−0.951693
$717$	3243.43	0.168938
$718$	−5631.14	−0.292691
$719$	1617.76	0.0839116	0.0419558	−	0.999119i	$-0.486641\pi$
$719$	1617.76	0.0839116	0.0419558	+	0.999119i	$0.486641\pi$
$720$	−24925.9	−1.29018
$721$	−3381.41	−0.174661
$722$	2969.40	0.153061
$723$	−6266.34	−0.322334
$724$	2638.97	0.135465
$725$	4263.16	0.218386
$726$	384.007	0.0196306
$727$	−34456.4	−1.75780	−0.878898	−	0.477010i	$-0.841721\pi$
$727$	−34456.4	−1.75780	−0.878898	+	0.477010i	$0.841721\pi$
$728$	−18334.6	−0.933416
$729$	−13960.6	−0.709273
$730$	−3694.51	−0.187315
$731$	23585.2	1.19334
$732$	4720.16	0.238336
$733$	−987.142	−0.0497420	−0.0248710	−	0.999691i	$-0.507918\pi$
$733$	−987.142	−0.0497420	−0.0248710	+	0.999691i	$0.507918\pi$
$734$	−5063.99	−0.254653
$735$	10334.1	0.518611
$736$	1961.99	0.0982607
$737$	−10249.4	−0.512270
$738$	−3852.24	−0.192145
$739$	−33457.7	−1.66544	−0.832722	−	0.553692i	$-0.813219\pi$
$739$	−33457.7	−1.66544	−0.832722	+	0.553692i	$0.813219\pi$
$740$	34570.5	1.71735
$741$	2012.63	0.0997786
$742$	−7658.20	−0.378897
$743$	−35556.6	−1.75565	−0.877823	−	0.478985i	$-0.841005\pi$
$743$	−35556.6	−1.75565	−0.877823	+	0.478985i	$0.841005\pi$
$744$	973.440	0.0479678
$745$	−41576.9	−2.04464
$746$	−2759.32	−0.135424
$747$	30267.0	1.48248
$748$	16551.5	0.809066
$749$	−8196.94	−0.399879
$750$	−195.257	−0.00950636
$751$	−39320.5	−1.91055	−0.955277	−	0.295714i	$-0.904443\pi$
$751$	−39320.5	−1.91055	−0.955277	+	0.295714i	$0.904443\pi$
$752$	−512.600	−0.0248572
$753$	−2383.58	−0.115355
$754$	−1135.75	−0.0548562
$755$	−34523.0	−1.66413
$756$	−14202.3	−0.683245
$757$	−9529.61	−0.457542	−0.228771	−	0.973480i	$-0.573471\pi$
$757$	−9529.61	−0.457542	−0.228771	+	0.973480i	$0.573471\pi$
$758$	−303.728	−0.0145540
$759$	−667.659	−0.0319295
$760$	2428.11	0.115890
$761$	15314.5	0.729503	0.364752	−	0.931105i	$-0.381154\pi$
$761$	15314.5	0.729503	0.364752	+	0.931105i	$0.381154\pi$
$762$	−1066.59	−0.0507068
$763$	−42434.9	−2.01343
$764$	−769.646	−0.0364461
$765$	36166.2	1.70927
$766$	−3048.50	−0.143795
$767$	33957.5	1.59861
$768$	3567.30	0.167609
$769$	−7495.02	−0.351466	−0.175733	−	0.984438i	$-0.556230\pi$
$769$	−7495.02	−0.351466	−0.175733	+	0.984438i	$0.556230\pi$
$770$	5594.52	0.261834
$771$	−4289.41	−0.200362
$772$	−12567.5	−0.585901
$773$	36212.8	1.68497	0.842487	−	0.538716i	$-0.181090\pi$
$773$	36212.8	1.68497	0.842487	+	0.538716i	$0.181090\pi$
$774$	−3254.39	−0.151133
$775$	16847.3	0.780868
$776$	−11050.6	−0.511201
$777$	9325.09	0.430548
$778$	487.881	0.0224825
$779$	−6609.43	−0.303989
$780$	−12764.7	−0.585963
$781$	20206.8	0.925809
$782$	−905.938	−0.0414275
$783$	−1783.49	−0.0814007
$784$	31616.6	1.44026
$785$	−57306.8	−2.60556
$786$	298.206	0.0135326
$787$	25032.3	1.13380	0.566902	−	0.823785i	$-0.308142\pi$
$787$	25032.3	1.13380	0.566902	+	0.823785i	$0.308142\pi$
$788$	−20729.0	−0.937107
$789$	2104.13	0.0949417
$790$	5030.84	0.226569
$791$	63774.3	2.86669
$792$	−4629.87	−0.207722
$793$	−44119.4	−1.97569
$794$	5645.46	0.252330
$795$	−10808.6	−0.482190
$796$	−3249.84	−0.144708
$797$	14044.4	0.624189	0.312094	−	0.950051i	$-0.398970\pi$
$797$	14044.4	0.624189	0.312094	+	0.950051i	$0.398970\pi$
$798$	323.082	0.0143321
$799$	743.758	0.0329315
$800$	−12540.1	−0.554201
$801$	621.132	0.0273990
$802$	1974.42	0.0869318
$803$	12086.7	0.531173
$804$	3754.04	0.164670
$805$	11248.1	0.492475
$806$	−4488.29	−0.196145
$807$	−2324.51	−0.101396
$808$	−7197.70	−0.313384
$809$	8714.13	0.378705	0.189353	−	0.981909i	$-0.439361\pi$
$809$	8714.13	0.378705	0.189353	+	0.981909i	$0.439361\pi$
$810$	−4710.47	−0.204332
$811$	16334.5	0.707254	0.353627	−	0.935386i	$-0.384948\pi$
$811$	16334.5	0.707254	0.353627	+	0.935386i	$0.384948\pi$
$812$	6697.06	0.289434
$813$	8324.06	0.359087
$814$	3078.97	0.132577
$815$	−55085.9	−2.36758
$816$	−5892.73	−0.252803
$817$	−5583.67	−0.239104
$818$	2889.46	0.123505
$819$	64653.1	2.75844
$820$	41919.1	1.78522
$821$	−23641.7	−1.00500	−0.502498	−	0.864578i	$-0.667586\pi$
$821$	−23641.7	−1.00500	−0.502498	+	0.864578i	$0.667586\pi$
$822$	247.775	0.0105135
$823$	−26488.0	−1.12189	−0.560945	−	0.827853i	$-0.689562\pi$
$823$	−26488.0	−1.12189	−0.560945	+	0.827853i	$0.689562\pi$
$824$	828.991	0.0350477
$825$	4267.37	0.180086
$826$	5451.11	0.229623
$827$	−44929.9	−1.88920	−0.944598	−	0.328228i	$-0.893548\pi$
$827$	−44929.9	−1.88920	−0.944598	+	0.328228i	$0.893548\pi$
$828$	−4591.80	−0.192725
$829$	6468.58	0.271005	0.135502	−	0.990777i	$-0.456735\pi$
$829$	6468.58	0.271005	0.135502	+	0.990777i	$0.456735\pi$
$830$	8966.32	0.374970
$831$	1687.24	0.0704330
$832$	−36775.4	−1.53240
$833$	−45874.2	−1.90810
$834$	434.720	0.0180493
$835$	−23190.0	−0.961104
$836$	−3918.48	−0.162109
$837$	−7048.06	−0.291059
$838$	4073.22	0.167908
$839$	26959.1	1.10934	0.554668	−	0.832072i	$-0.312845\pi$
$839$	26959.1	1.10934	0.554668	+	0.832072i	$0.312845\pi$
$840$	−4153.96	−0.170625
$841$	841.000	0.0344828
$842$	−5200.89	−0.212868
$843$	3803.43	0.155394
$844$	−25280.5	−1.03103
$845$	83078.2	3.38222
$846$	−102.627	−0.00417068
$847$	21164.8	0.858595
$848$	−33068.3	−1.33911
$849$	−1217.98	−0.0492354
$850$	5790.34	0.233655
$851$	6190.42	0.249359
$852$	−7401.10	−0.297603
$853$	4831.85	0.193950	0.0969750	−	0.995287i	$-0.469083\pi$
$853$	4831.85	0.193950	0.0969750	+	0.995287i	$0.469083\pi$
$854$	−7082.37	−0.283786
$855$	−8562.18	−0.342480
$856$	2009.57	0.0802403
$857$	−5290.63	−0.210880	−0.105440	−	0.994426i	$-0.533625\pi$
$857$	−5290.63	−0.210880	−0.105440	+	0.994426i	$0.533625\pi$
$858$	−1136.87	−0.0452356
$859$	−10026.4	−0.398249	−0.199125	−	0.979974i	$-0.563810\pi$
$859$	−10026.4	−0.398249	−0.199125	+	0.979974i	$0.563810\pi$
$860$	35413.4	1.40417
$861$	11307.3	0.447563
$862$	2590.65	0.102364
$863$	−30269.5	−1.19396	−0.596979	−	0.802257i	$-0.703632\pi$
$863$	−30269.5	−1.19396	−0.596979	+	0.802257i	$0.703632\pi$
$864$	5246.16	0.206572
$865$	40178.4	1.57931
$866$	−5153.83	−0.202234
$867$	2809.61	0.110057
$868$	26465.6	1.03491
$869$	−16458.6	−0.642484
$870$	−257.320	−0.0100275
$871$	−35089.1	−1.36504
$872$	10403.4	0.404018
$873$	38967.4	1.51071
$874$	214.477	0.00830066
$875$	−10761.7	−0.415785
$876$	−4426.98	−0.170746
$877$	−31205.2	−1.20151	−0.600755	−	0.799433i	$-0.705133\pi$
$877$	−31205.2	−1.20151	−0.600755	+	0.799433i	$0.705133\pi$
$878$	477.767	0.0183643
$879$	−1186.94	−0.0455454
$880$	24157.3	0.925387
$881$	16139.6	0.617204	0.308602	−	0.951191i	$-0.400139\pi$
$881$	16139.6	0.617204	0.308602	+	0.951191i	$0.400139\pi$
$882$	6329.93	0.241655
$883$	19755.2	0.752905	0.376453	−	0.926436i	$-0.377144\pi$
$883$	19755.2	0.752905	0.376453	+	0.926436i	$0.377144\pi$
$884$	56664.1	2.15591
$885$	7693.55	0.292221
$886$	3978.28	0.150850
$887$	−8582.53	−0.324885	−0.162443	−	0.986718i	$-0.551937\pi$
$887$	−8582.53	−0.324885	−0.162443	+	0.986718i	$0.551937\pi$
$888$	−2286.15	−0.0863944
$889$	−58785.9	−2.21779
$890$	184.005	0.00693018
$891$	15410.5	0.579428
$892$	−19377.4	−0.727358
$893$	−176.081	−0.00659836
$894$	1356.28	0.0507391
$895$	38612.7	1.44210
$896$	−26139.2	−0.974610
$897$	−2285.74	−0.0850820
$898$	134.364	0.00499307
$899$	3323.49	0.123298
$900$	29348.7	1.08699
$901$	47980.4	1.77410
$902$	3733.45	0.137816
$903$	9552.46	0.352033
$904$	−15635.0	−0.575235
$905$	−5588.54	−0.205270
$906$	1126.17	0.0412965
$907$	40568.8	1.48519	0.742593	−	0.669743i	$-0.233596\pi$
$907$	40568.8	1.48519	0.742593	+	0.669743i	$0.233596\pi$
$908$	−34969.1	−1.27807
$909$	25381.1	0.926115
$910$	19152.9	0.697706
$911$	29974.8	1.09013	0.545065	−	0.838394i	$-0.316505\pi$
$911$	29974.8	1.09013	0.545065	+	0.838394i	$0.316505\pi$
$912$	1395.08	0.0506531
$913$	−29333.6	−1.06331
$914$	−53.3297	−0.00192997
$915$	−9995.86	−0.361151
$916$	−22388.7	−0.807579
$917$	16435.8	0.591884
$918$	−2422.39	−0.0870923
$919$	43243.2	1.55219	0.776095	−	0.630616i	$-0.217198\pi$
$919$	43243.2	1.55219	0.776095	+	0.630616i	$0.217198\pi$
$920$	−2757.59	−0.0988206
$921$	1753.07	0.0627207
$922$	5498.35	0.196398
$923$	69178.3	2.46699
$924$	6703.68	0.238674
$925$	−39566.3	−1.40641
$926$	601.505	0.0213463
$927$	−2923.26	−0.103573
$928$	−2473.81	−0.0875074
$929$	−2185.69	−0.0771908	−0.0385954	−	0.999255i	$-0.512288\pi$
$929$	−2185.69	−0.0771908	−0.0385954	+	0.999255i	$0.512288\pi$
$930$	−1016.88	−0.0358548
$931$	10860.5	0.382318
$932$	−29174.1	−1.02535
$933$	4234.73	0.148595
$934$	−714.145	−0.0250188
$935$	−35051.0	−1.22598
$936$	−15850.4	−0.553512
$937$	38195.2	1.33168	0.665840	−	0.746095i	$-0.268073\pi$
$937$	38195.2	1.33168	0.665840	+	0.746095i	$0.268073\pi$
$938$	−5632.75	−0.196072
$939$	−4262.03	−0.148122
$940$	1116.76	0.0387498
$941$	−33303.7	−1.15374	−0.576870	−	0.816836i	$-0.695726\pi$
$941$	−33303.7	−1.15374	−0.576870	+	0.816836i	$0.695726\pi$
$942$	1869.40	0.0646587
$943$	7506.30	0.259214
$944$	23538.0	0.811543
$945$	30076.2	1.03532
$946$	3154.04	0.108400
$947$	−10998.7	−0.377412	−0.188706	−	0.982034i	$-0.560429\pi$
$947$	−10998.7	−0.377412	−0.188706	+	0.982034i	$0.560429\pi$
$948$	6028.24	0.206528
$949$	41379.1	1.41541
$950$	−1370.84	−0.0468166
$951$	3746.55	0.127750
$952$	18439.9	0.627774
$953$	15497.9	0.526785	0.263393	−	0.964689i	$-0.415159\pi$
$953$	15497.9	0.526785	0.263393	+	0.964689i	$0.415159\pi$
$954$	−6620.57	−0.224684
$955$	1629.88	0.0552268
$956$	−21618.7	−0.731380
$957$	841.831	0.0284352
$958$	−1425.22	−0.0480655
$959$	13656.3	0.459837
$960$	−8331.98	−0.280118
$961$	−16657.1	−0.559133
$962$	10540.9	0.353276
$963$	−7086.31	−0.237127
$964$	41767.5	1.39548
$965$	26614.2	0.887816
$966$	−366.923	−0.0122211
$967$	−22383.8	−0.744380	−0.372190	−	0.928156i	$-0.621393\pi$
$967$	−22383.8	−0.744380	−0.372190	+	0.928156i	$0.621393\pi$
$968$	−5188.78	−0.172287
$969$	−2024.19	−0.0671066
$970$	11543.7	0.382110
$971$	1539.05	0.0508655	0.0254327	−	0.999677i	$-0.491904\pi$
$971$	1539.05	0.0508655	0.0254327	+	0.999677i	$0.491904\pi$
$972$	−18576.2	−0.612997
$973$	23959.9	0.789433
$974$	1341.79	0.0441415
$975$	14609.4	0.479872
$976$	−30581.8	−1.00297
$977$	12963.7	0.424510	0.212255	−	0.977214i	$-0.431919\pi$
$977$	12963.7	0.424510	0.212255	+	0.977214i	$0.431919\pi$
$978$	1796.96	0.0587529
$979$	−601.979	−0.0196520
$980$	−68880.6	−2.24522
$981$	−36685.3	−1.19396
$982$	2503.10	0.0813414
$983$	31946.4	1.03655	0.518276	−	0.855213i	$-0.326574\pi$
$983$	31946.4	1.03655	0.518276	+	0.855213i	$0.326574\pi$
$984$	−2772.11	−0.0898086
$985$	43897.8	1.42000
$986$	1142.27	0.0368938
$987$	301.237	0.00971477
$988$	−13415.0	−0.431970
$989$	6341.35	0.203886
$990$	4836.50	0.155267
$991$	20056.0	0.642887	0.321443	−	0.946929i	$-0.395832\pi$
$991$	20056.0	0.642887	0.321443	+	0.946929i	$0.395832\pi$
$992$	−9776.09	−0.312894
$993$	−4471.38	−0.142895
$994$	11105.0	0.354355
$995$	6882.18	0.219276
$996$	10744.0	0.341803
$997$	−48896.0	−1.55321	−0.776605	−	0.629988i	$-0.783060\pi$
$997$	−48896.0	−1.55321	−0.776605	+	0.629988i	$0.783060\pi$
$998$	5432.47	0.172307
$999$	16552.6	0.524224

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	667.4.a.b.1.18	✓	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
667.4.a.b.1.18	✓	38	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:	\( N \)	\(=\)	\( 667 = 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	667.a (trivial)

\(f(q)\)	\(=\)	\(q-0.460454 q^{2} +1.16842 q^{3} -7.78798 q^{4} +16.4926 q^{5} -0.538005 q^{6} -29.6525 q^{7} +7.26964 q^{8} -25.6348 q^{9} +O(q^{10})\)	\(q-0.460454 q^{2} +1.16842 q^{3} -7.78798 q^{4} +16.4926 q^{5} -0.538005 q^{6} -29.6525 q^{7} +7.26964 q^{8} -25.6348 q^{9} -7.59408 q^{10} +24.8443 q^{11} -9.09966 q^{12} +85.0547 q^{13} +13.6536 q^{14} +19.2703 q^{15} +58.9565 q^{16} -85.5430 q^{17} +11.8036 q^{18} +20.2519 q^{19} -128.444 q^{20} -34.6466 q^{21} -11.4397 q^{22} -23.0000 q^{23} +8.49401 q^{24} +147.006 q^{25} -39.1638 q^{26} -61.4997 q^{27} +230.933 q^{28} +29.0000 q^{29} -8.87309 q^{30} +114.603 q^{31} -85.3039 q^{32} +29.0287 q^{33} +39.3886 q^{34} -489.046 q^{35} +199.643 q^{36} -269.148 q^{37} -9.32507 q^{38} +99.3799 q^{39} +119.895 q^{40} -326.361 q^{41} +15.9532 q^{42} -275.711 q^{43} -193.487 q^{44} -422.784 q^{45} +10.5904 q^{46} -8.69455 q^{47} +68.8862 q^{48} +536.270 q^{49} -67.6892 q^{50} -99.9505 q^{51} -662.405 q^{52} -560.892 q^{53} +28.3178 q^{54} +409.747 q^{55} -215.563 q^{56} +23.6628 q^{57} -13.3532 q^{58} +399.243 q^{59} -150.077 q^{60} -518.718 q^{61} -52.7694 q^{62} +760.135 q^{63} -432.374 q^{64} +1402.77 q^{65} -13.3664 q^{66} -412.547 q^{67} +666.208 q^{68} -26.8737 q^{69} +225.183 q^{70} +813.338 q^{71} -186.356 q^{72} +486.500 q^{73} +123.930 q^{74} +171.765 q^{75} -157.722 q^{76} -736.695 q^{77} -45.7598 q^{78} -662.469 q^{79} +972.346 q^{80} +620.282 q^{81} +150.274 q^{82} -1180.70 q^{83} +269.827 q^{84} -1410.83 q^{85} +126.952 q^{86} +33.8843 q^{87} +180.609 q^{88} -24.2301 q^{89} +194.673 q^{90} -2522.08 q^{91} +179.124 q^{92} +133.905 q^{93} +4.00344 q^{94} +334.006 q^{95} -99.6710 q^{96} -1520.10 q^{97} -246.927 q^{98} -636.878 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q - 8 q^{2} - 16 q^{3} + 152 q^{4} - 80 q^{5} - 16 q^{6} - 38 q^{7} - 138 q^{8} + 312 q^{9}+O(q^{10}) \) 38 * q - 8 * q^2 - 16 * q^3 + 152 * q^4 - 80 * q^5 - 16 * q^6 - 38 * q^7 - 138 * q^8 + 312 * q^9	\( 38 q - 8 q^{2} - 16 q^{3} + 152 q^{4} - 80 q^{5} - 16 q^{6} - 38 q^{7} - 138 q^{8} + 312 q^{9} + 30 q^{10} - 100 q^{11} - 173 q^{12} - 160 q^{13} - 304 q^{14} - 208 q^{15} + 552 q^{16} - 666 q^{17} - 315 q^{18} - 252 q^{19} - 747 q^{20} - 470 q^{21} - 323 q^{22} - 874 q^{23} - 114 q^{24} + 910 q^{25} - 119 q^{26} - 526 q^{27} - 619 q^{28} + 1102 q^{29} - 533 q^{30} + 358 q^{31} - 1272 q^{32} - 604 q^{33} - 553 q^{34} + 16 q^{35} + 1230 q^{36} - 1206 q^{37} - 2010 q^{38} - 240 q^{39} - 418 q^{40} - 1094 q^{41} - 1184 q^{42} - 936 q^{43} - 2153 q^{44} - 3654 q^{45} + 184 q^{46} - 1702 q^{47} - 1319 q^{48} + 1920 q^{49} - 1255 q^{50} - 270 q^{51} - 2202 q^{52} - 4640 q^{53} - 1529 q^{54} - 318 q^{55} - 2435 q^{56} - 1980 q^{57} - 232 q^{58} + 318 q^{59} - 3279 q^{60} - 2212 q^{61} - 541 q^{62} - 1044 q^{63} + 1186 q^{64} - 2438 q^{65} - 3503 q^{66} - 496 q^{67} - 6099 q^{68} + 368 q^{69} + 4068 q^{70} + 870 q^{71} - 3869 q^{72} - 2810 q^{73} - 2793 q^{74} - 3638 q^{75} + 1548 q^{76} - 6072 q^{77} + 2170 q^{78} - 3084 q^{79} - 6702 q^{80} + 362 q^{81} - 1183 q^{82} - 5566 q^{83} - 6518 q^{84} - 120 q^{85} - 2095 q^{86} - 464 q^{87} - 1220 q^{88} - 6506 q^{89} + 165 q^{90} + 44 q^{91} - 3496 q^{92} - 5928 q^{93} + 135 q^{94} - 2024 q^{95} - 3164 q^{96} - 7472 q^{97} - 6422 q^{98} - 944 q^{99}+O(q^{100}) \) 38 * q - 8 * q^2 - 16 * q^3 + 152 * q^4 - 80 * q^5 - 16 * q^6 - 38 * q^7 - 138 * q^8 + 312 * q^9 + 30 * q^10 - 100 * q^11 - 173 * q^12 - 160 * q^13 - 304 * q^14 - 208 * q^15 + 552 * q^16 - 666 * q^17 - 315 * q^18 - 252 * q^19 - 747 * q^20 - 470 * q^21 - 323 * q^22 - 874 * q^23 - 114 * q^24 + 910 * q^25 - 119 * q^26 - 526 * q^27 - 619 * q^28 + 1102 * q^29 - 533 * q^30 + 358 * q^31 - 1272 * q^32 - 604 * q^33 - 553 * q^34 + 16 * q^35 + 1230 * q^36 - 1206 * q^37 - 2010 * q^38 - 240 * q^39 - 418 * q^40 - 1094 * q^41 - 1184 * q^42 - 936 * q^43 - 2153 * q^44 - 3654 * q^45 + 184 * q^46 - 1702 * q^47 - 1319 * q^48 + 1920 * q^49 - 1255 * q^50 - 270 * q^51 - 2202 * q^52 - 4640 * q^53 - 1529 * q^54 - 318 * q^55 - 2435 * q^56 - 1980 * q^57 - 232 * q^58 + 318 * q^59 - 3279 * q^60 - 2212 * q^61 - 541 * q^62 - 1044 * q^63 + 1186 * q^64 - 2438 * q^65 - 3503 * q^66 - 496 * q^67 - 6099 * q^68 + 368 * q^69 + 4068 * q^70 + 870 * q^71 - 3869 * q^72 - 2810 * q^73 - 2793 * q^74 - 3638 * q^75 + 1548 * q^76 - 6072 * q^77 + 2170 * q^78 - 3084 * q^79 - 6702 * q^80 + 362 * q^81 - 1183 * q^82 - 5566 * q^83 - 6518 * q^84 - 120 * q^85 - 2095 * q^86 - 464 * q^87 - 1220 * q^88 - 6506 * q^89 + 165 * q^90 + 44 * q^91 - 3496 * q^92 - 5928 * q^93 + 135 * q^94 - 2024 * q^95 - 3164 * q^96 - 7472 * q^97 - 6422 * q^98 - 944 * q^99

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