LMFDB - Embedded newform 667.4.a.b.1.1

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			1.1
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)

$f(q)$	$=$	$q-5.54069 q^{2} +7.25408 q^{3} +22.6992 q^{4} -1.00273 q^{5} -40.1926 q^{6} +21.1757 q^{7} -81.4436 q^{8} +25.6216 q^{9} +O(q^{10})$	\(q-5.54069 q^{2} +7.25408 q^{3} +22.6992 q^{4} -1.00273 q^{5} -40.1926 q^{6} +21.1757 q^{7} -81.4436 q^{8} +25.6216 q^{9} +5.55579 q^{10} -6.83052 q^{11} +164.662 q^{12} -55.9093 q^{13} -117.328 q^{14} -7.27385 q^{15} +269.660 q^{16} -87.3584 q^{17} -141.962 q^{18} +79.2178 q^{19} -22.7611 q^{20} +153.610 q^{21} +37.8458 q^{22} -23.0000 q^{23} -590.798 q^{24} -123.995 q^{25} +309.776 q^{26} -9.99866 q^{27} +480.671 q^{28} +29.0000 q^{29} +40.3021 q^{30} -271.886 q^{31} -842.552 q^{32} -49.5491 q^{33} +484.025 q^{34} -21.2334 q^{35} +581.591 q^{36} -218.538 q^{37} -438.921 q^{38} -405.570 q^{39} +81.6656 q^{40} -376.225 q^{41} -851.106 q^{42} +92.5915 q^{43} -155.047 q^{44} -25.6915 q^{45} +127.436 q^{46} -500.759 q^{47} +1956.13 q^{48} +105.410 q^{49} +687.015 q^{50} -633.705 q^{51} -1269.10 q^{52} -650.422 q^{53} +55.3995 q^{54} +6.84914 q^{55} -1724.63 q^{56} +574.652 q^{57} -160.680 q^{58} +794.662 q^{59} -165.111 q^{60} +531.256 q^{61} +1506.44 q^{62} +542.556 q^{63} +2511.04 q^{64} +56.0616 q^{65} +274.536 q^{66} +738.335 q^{67} -1982.97 q^{68} -166.844 q^{69} +117.648 q^{70} -3.29855 q^{71} -2086.72 q^{72} +371.088 q^{73} +1210.85 q^{74} -899.466 q^{75} +1798.18 q^{76} -144.641 q^{77} +2247.14 q^{78} -192.676 q^{79} -270.395 q^{80} -764.316 q^{81} +2084.54 q^{82} -547.320 q^{83} +3486.83 q^{84} +87.5965 q^{85} -513.020 q^{86} +210.368 q^{87} +556.303 q^{88} +195.065 q^{89} +142.348 q^{90} -1183.92 q^{91} -522.082 q^{92} -1972.28 q^{93} +2774.55 q^{94} -79.4337 q^{95} -6111.94 q^{96} +872.766 q^{97} -584.045 q^{98} -175.009 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−5.54069	−1.95893	−0.979464	−	0.201619i	$-0.935380\pi$
$2$	−5.54069	−1.95893	−0.979464	+	0.201619i	$0.935380\pi$
$3$	7.25408	1.39605	0.698024	−	0.716074i	$-0.254063\pi$
$3$	7.25408	1.39605	0.698024	+	0.716074i	$0.254063\pi$
$4$	22.6992	2.83740
$5$	−1.00273	−0.0896865	−0.0448432	−	0.998994i	$-0.514279\pi$
$5$	−1.00273	−0.0896865	−0.0448432	+	0.998994i	$0.514279\pi$
$6$	−40.1926	−2.73476
$7$	21.1757	1.14338	0.571690	−	0.820470i	$-0.306288\pi$
$7$	21.1757	1.14338	0.571690	+	0.820470i	$0.306288\pi$
$8$	−81.4436	−3.59933
$9$	25.6216	0.948950
$10$	5.55579	0.175689
$11$	−6.83052	−0.187225	−0.0936127	−	0.995609i	$-0.529842\pi$
$11$	−6.83052	−0.187225	−0.0936127	+	0.995609i	$0.529842\pi$
$12$	164.662	3.96115
$13$	−55.9093	−1.19280	−0.596401	−	0.802686i	$-0.703403\pi$
$13$	−55.9093	−1.19280	−0.596401	+	0.802686i	$0.703403\pi$
$14$	−117.328	−2.23980
$15$	−7.27385	−0.125207
$16$	269.660	4.21344
$17$	−87.3584	−1.24632	−0.623162	−	0.782092i	$-0.714152\pi$
$17$	−87.3584	−1.24632	−0.623162	+	0.782092i	$0.714152\pi$
$18$	−141.962	−1.85892
$19$	79.2178	0.956516	0.478258	−	0.878219i	$-0.341268\pi$
$19$	79.2178	0.956516	0.478258	+	0.878219i	$0.341268\pi$
$20$	−22.7611	−0.254476
$21$	153.610	1.59621
$22$	37.8458	0.366761
$23$	−23.0000	−0.208514
$23$	−23.0000	−0.208514
$24$	−590.798	−5.02484
$25$	−123.995	−0.991956
$26$	309.776	2.33662
$27$	−9.99866	−0.0712683
$28$	480.671	3.24423
$29$	29.0000	0.185695
$29$	29.0000	0.185695
$30$	40.3021	0.245271
$31$	−271.886	−1.57523	−0.787616	−	0.616166i	$-0.788685\pi$
$31$	−271.886	−1.57523	−0.787616	+	0.616166i	$0.788685\pi$
$32$	−842.552	−4.65449
$33$	−49.5491	−0.261376
$34$	484.025	2.44146
$35$	−21.2334	−0.102546
$36$	581.591	2.69255
$37$	−218.538	−0.971011	−0.485505	−	0.874234i	$-0.661364\pi$
$37$	−218.538	−0.971011	−0.485505	+	0.874234i	$0.661364\pi$
$38$	−438.921	−1.87375
$39$	−405.570	−1.66521
$40$	81.6656	0.322812
$41$	−376.225	−1.43308	−0.716542	−	0.697544i	$-0.754276\pi$
$41$	−376.225	−1.43308	−0.716542	+	0.697544i	$0.754276\pi$
$42$	−851.106	−3.12687
$43$	92.5915	0.328374	0.164187	−	0.986429i	$-0.447500\pi$
$43$	92.5915	0.328374	0.164187	+	0.986429i	$0.447500\pi$
$44$	−155.047	−0.531233
$45$	−25.6915	−0.0851080
$46$	127.436	0.408465
$47$	−500.759	−1.55411	−0.777056	−	0.629432i	$-0.783288\pi$
$47$	−500.759	−1.55411	−0.777056	+	0.629432i	$0.783288\pi$
$48$	1956.13	5.88216
$49$	105.410	0.307318
$50$	687.015	1.94317
$51$	−633.705	−1.73993
$52$	−1269.10	−3.38446
$53$	−650.422	−1.68570	−0.842852	−	0.538145i	$-0.819125\pi$
$53$	−650.422	−1.68570	−0.842852	+	0.538145i	$0.819125\pi$
$54$	55.3995	0.139609
$55$	6.84914	0.0167916
$56$	−1724.63	−4.11541
$57$	574.652	1.33534
$58$	−160.680	−0.363764
$59$	794.662	1.75349	0.876747	−	0.480952i	$-0.159709\pi$
$59$	794.662	1.75349	0.876747	+	0.480952i	$0.159709\pi$
$60$	−165.111	−0.355261
$61$	531.256	1.11509	0.557544	−	0.830147i	$-0.311744\pi$
$61$	531.256	1.11509	0.557544	+	0.830147i	$0.311744\pi$
$62$	1506.44	3.08577
$63$	542.556	1.08501
$64$	2511.04	4.90437
$65$	56.0616	0.106978
$66$	274.536	0.512016
$67$	738.335	1.34630	0.673149	−	0.739507i	$-0.264941\pi$
$67$	738.335	1.34630	0.673149	+	0.739507i	$0.264941\pi$
$68$	−1982.97	−3.53632
$69$	−166.844	−0.291096
$70$	117.648	0.200880
$71$	−3.29855	−0.00551360	−0.00275680	−	0.999996i	$-0.500878\pi$
$71$	−3.29855	−0.00551360	−0.00275680	+	0.999996i	$0.500878\pi$
$72$	−2086.72	−3.41559
$73$	371.088	0.594966	0.297483	−	0.954727i	$-0.403853\pi$
$73$	371.088	0.594966	0.297483	+	0.954727i	$0.403853\pi$
$74$	1210.85	1.90214
$75$	−899.466	−1.38482
$76$	1798.18	2.71402
$77$	−144.641	−0.214070
$78$	2247.14	3.26203
$79$	−192.676	−0.274402	−0.137201	−	0.990543i	$-0.543811\pi$
$79$	−192.676	−0.274402	−0.137201	+	0.990543i	$0.543811\pi$
$80$	−270.395	−0.377888
$81$	−764.316	−1.04844
$82$	2084.54	2.80731
$83$	−547.320	−0.723809	−0.361904	−	0.932215i	$-0.617873\pi$
$83$	−547.320	−0.723809	−0.361904	+	0.932215i	$0.617873\pi$
$84$	3486.83	4.52910
$85$	87.5965	0.111779
$86$	−513.020	−0.643261
$87$	210.368	0.259240
$88$	556.303	0.673887
$89$	195.065	0.232324	0.116162	−	0.993230i	$-0.462941\pi$
$89$	195.065	0.232324	0.116162	+	0.993230i	$0.462941\pi$
$90$	142.348	0.166720
$91$	−1183.92	−1.36383
$92$	−522.082	−0.591639
$93$	−1972.28	−2.19910
$94$	2774.55	3.04439
$95$	−79.4337	−0.0857865
$96$	−6111.94	−6.49789
$97$	872.766	0.913566	0.456783	−	0.889578i	$-0.349002\pi$
$97$	872.766	0.913566	0.456783	+	0.889578i	$0.349002\pi$
$98$	−584.045	−0.602015
$99$	−175.009	−0.177668
$100$	−2814.58	−2.81458
$101$	85.9200	0.0846471	0.0423235	−	0.999104i	$-0.486524\pi$
$101$	85.9200	0.0846471	0.0423235	+	0.999104i	$0.486524\pi$
$102$	3511.16	3.40840
$103$	−782.500	−0.748563	−0.374282	−	0.927315i	$-0.622111\pi$
$103$	−782.500	−0.748563	−0.374282	+	0.927315i	$0.622111\pi$
$104$	4553.45	4.29330
$105$	−154.029	−0.143159
$106$	3603.78	3.30217
$107$	604.066	0.545769	0.272884	−	0.962047i	$-0.412022\pi$
$107$	604.066	0.545769	0.272884	+	0.962047i	$0.412022\pi$
$108$	−226.962	−0.202217
$109$	1661.98	1.46045	0.730223	−	0.683209i	$-0.239416\pi$
$109$	1661.98	1.46045	0.730223	+	0.683209i	$0.239416\pi$
$110$	−37.9489	−0.0328935
$111$	−1585.29	−1.35558
$112$	5710.24	4.81756
$113$	719.584	0.599051	0.299526	−	0.954088i	$-0.403172\pi$
$113$	719.584	0.599051	0.299526	+	0.954088i	$0.403172\pi$
$114$	−3183.96	−2.61584
$115$	23.0627	0.0187009
$116$	658.277	0.526892
$117$	−1432.49	−1.13191
$118$	−4402.97	−3.43497
$119$	−1849.88	−1.42502
$120$	592.409	0.450661
$121$	−1284.34	−0.964947
$122$	−2943.52	−2.18438
$123$	−2729.16	−2.00065
$124$	−6171.60	−4.46956
$125$	249.673	0.178652
$126$	−3006.13	−2.12546
$127$	−810.794	−0.566506	−0.283253	−	0.959045i	$-0.591414\pi$
$127$	−810.794	−0.566506	−0.283253	+	0.959045i	$0.591414\pi$
$128$	−7172.45	−4.95282
$129$	671.666	0.458426
$130$	−310.620	−0.209563
$131$	2290.54	1.52767	0.763836	−	0.645410i	$-0.223314\pi$
$131$	2290.54	1.52767	0.763836	+	0.645410i	$0.223314\pi$
$132$	−1124.73	−0.741627
$133$	1677.49	1.09366
$134$	−4090.88	−2.63730
$135$	10.0259	0.00639180
$136$	7114.78	4.48594
$137$	−2978.31	−1.85733	−0.928666	−	0.370917i	$-0.879043\pi$
$137$	−2978.31	−1.85733	−0.928666	+	0.370917i	$0.879043\pi$
$138$	924.429	0.570236
$139$	−1545.00	−0.942772	−0.471386	−	0.881927i	$-0.656246\pi$
$139$	−1545.00	−0.942772	−0.471386	+	0.881927i	$0.656246\pi$
$140$	−481.981	−0.290963
$141$	−3632.55	−2.16961
$142$	18.2762	0.0108007
$143$	381.889	0.223323
$144$	6909.13	3.99834
$145$	−29.0790	−0.0166544
$146$	−2056.08	−1.16550
$147$	764.654	0.429031
$148$	−4960.63	−2.75515
$149$	2315.97	1.27337	0.636684	−	0.771125i	$-0.280306\pi$
$149$	2315.97	1.27337	0.636684	+	0.771125i	$0.280306\pi$
$150$	4983.66	2.71276
$151$	−2063.00	−1.11182	−0.555910	−	0.831242i	$-0.687630\pi$
$151$	−2063.00	−1.11182	−0.555910	+	0.831242i	$0.687630\pi$
$152$	−6451.78	−3.44282
$153$	−2238.27	−1.18270
$154$	801.411	0.419348
$155$	272.627	0.141277
$156$	−9206.12	−4.72487
$157$	2514.75	1.27834	0.639168	−	0.769067i	$-0.279279\pi$
$157$	2514.75	1.27834	0.639168	+	0.769067i	$0.279279\pi$
$158$	1067.56	0.537534
$159$	−4718.21	−2.35332
$160$	844.848	0.417445
$161$	−487.041	−0.238411
$162$	4234.83	2.05383
$163$	−1042.10	−0.500760	−0.250380	−	0.968148i	$-0.580556\pi$
$163$	−1042.10	−0.500760	−0.250380	+	0.968148i	$0.580556\pi$
$164$	−8540.00	−4.06623
$165$	49.6842	0.0234419
$166$	3032.53	1.41789
$167$	975.395	0.451966	0.225983	−	0.974131i	$-0.427441\pi$
$167$	975.395	0.451966	0.225983	+	0.974131i	$0.427441\pi$
$168$	−12510.6	−5.74531
$169$	928.845	0.422779
$170$	−485.345	−0.218966
$171$	2029.69	0.907686
$172$	2101.75	0.931728
$173$	−106.883	−0.0469722	−0.0234861	−	0.999724i	$-0.507477\pi$
$173$	−106.883	−0.0469722	−0.0234861	+	0.999724i	$0.507477\pi$
$174$	−1165.58	−0.507832
$175$	−2625.67	−1.13418
$176$	−1841.92	−0.788863
$177$	5764.54	2.44796
$178$	−1080.79	−0.455105
$179$	−73.0788	−0.0305149	−0.0152574	−	0.999884i	$-0.504857\pi$
$179$	−73.0788	−0.0305149	−0.0152574	+	0.999884i	$0.504857\pi$
$180$	−583.176	−0.241485
$181$	1528.26	0.627596	0.313798	−	0.949490i	$-0.398398\pi$
$181$	1528.26	0.627596	0.313798	+	0.949490i	$0.398398\pi$
$182$	6559.71	2.67164
$183$	3853.77	1.55672
$184$	1873.20	0.750513
$185$	219.133	0.0870865
$186$	10927.8	4.30788
$187$	596.703	0.233344
$188$	−11366.8	−4.40964
$189$	−211.729	−0.0814868
$190$	440.117	0.168050
$191$	−1838.98	−0.696669	−0.348335	−	0.937370i	$-0.613253\pi$
$191$	−1838.98	−0.696669	−0.348335	+	0.937370i	$0.613253\pi$
$192$	18215.3	6.84673
$193$	−2107.86	−0.786152	−0.393076	−	0.919506i	$-0.628589\pi$
$193$	−2107.86	−0.786152	−0.393076	+	0.919506i	$0.628589\pi$
$194$	−4835.72	−1.78961
$195$	406.675	0.149347
$196$	2392.73	0.871985
$197$	−98.1104	−0.0354826	−0.0177413	−	0.999843i	$-0.505648\pi$
$197$	−98.1104	−0.0354826	−0.0177413	+	0.999843i	$0.505648\pi$
$198$	969.671	0.348038
$199$	1576.46	0.561570	0.280785	−	0.959771i	$-0.409405\pi$
$199$	1576.46	0.561570	0.280785	+	0.959771i	$0.409405\pi$
$200$	10098.6	3.57038
$201$	5355.94	1.87950
$202$	−476.056	−0.165818
$203$	614.095	0.212320
$204$	−14384.6	−4.93687
$205$	377.250	0.128528
$206$	4335.59	1.46638
$207$	−589.298	−0.197870
$208$	−15076.5	−5.02580
$209$	−541.099	−0.179084
$210$	853.425	0.280438
$211$	−84.2207	−0.0274786	−0.0137393	−	0.999906i	$-0.504373\pi$
$211$	−84.2207	−0.0274786	−0.0137393	+	0.999906i	$0.504373\pi$
$212$	−14764.1	−4.78302
$213$	−23.9279	−0.00769725
$214$	−3346.94	−1.06912
$215$	−92.8439	−0.0294507
$216$	814.328	0.256518
$217$	−5757.38	−1.80109
$218$	−9208.50	−2.86091
$219$	2691.90	0.830601
$220$	155.470	0.0476445
$221$	4884.14	1.48662
$222$	8783.60	2.65548
$223$	2297.15	0.689815	0.344907	−	0.938637i	$-0.387910\pi$
$223$	2297.15	0.689815	0.344907	+	0.938637i	$0.387910\pi$
$224$	−17841.6	−5.32185
$225$	−3176.94	−0.941317
$226$	−3986.99	−1.17350
$227$	6105.58	1.78520	0.892602	−	0.450845i	$-0.148877\pi$
$227$	6105.58	1.78520	0.892602	+	0.450845i	$0.148877\pi$
$228$	13044.1	3.78890
$229$	−3776.25	−1.08970	−0.544851	−	0.838533i	$-0.683414\pi$
$229$	−3776.25	−1.08970	−0.544851	+	0.838533i	$0.683414\pi$
$230$	−127.783	−0.0366338
$231$	−1049.24	−0.298852
$232$	−2361.87	−0.668380
$233$	−1567.30	−0.440673	−0.220337	−	0.975424i	$-0.570716\pi$
$233$	−1567.30	−0.440673	−0.220337	+	0.975424i	$0.570716\pi$
$234$	7936.96	2.21733
$235$	502.124	0.139383
$236$	18038.2	4.97536
$237$	−1397.69	−0.383078
$238$	10249.6	2.79152
$239$	835.744	0.226191	0.113096	−	0.993584i	$-0.463923\pi$
$239$	835.744	0.226191	0.113096	+	0.993584i	$0.463923\pi$
$240$	−1961.47	−0.527550
$241$	−2474.50	−0.661395	−0.330698	−	0.943737i	$-0.607284\pi$
$241$	−2474.50	−0.661395	−0.330698	+	0.943737i	$0.607284\pi$
$242$	7116.15	1.89026
$243$	−5274.44	−1.39241
$244$	12059.1	3.16395
$245$	−105.698	−0.0275623
$246$	15121.4	3.91914
$247$	−4429.01	−1.14093
$248$	22143.4	5.66979
$249$	−3970.30	−1.01047
$250$	−1383.36	−0.349966
$251$	−5957.92	−1.49825	−0.749124	−	0.662429i	$-0.769525\pi$
$251$	−5957.92	−1.49825	−0.749124	+	0.662429i	$0.769525\pi$
$252$	12315.6	3.07861
$253$	157.102	0.0390392
$254$	4492.35	1.10975
$255$	635.432	0.156048
$256$	19652.0	4.79785
$257$	2181.66	0.529526	0.264763	−	0.964313i	$-0.414706\pi$
$257$	2181.66	0.529526	0.264763	+	0.964313i	$0.414706\pi$
$258$	−3721.49	−0.898023
$259$	−4627.69	−1.11023
$260$	1272.55	0.303540
$261$	743.028	0.176216
$262$	−12691.1	−2.99260
$263$	−2044.93	−0.479451	−0.239725	−	0.970841i	$-0.577057\pi$
$263$	−2044.93	−0.479451	−0.239725	+	0.970841i	$0.577057\pi$
$264$	4035.46	0.940778
$265$	652.195	0.151185
$266$	−9294.45	−2.14240
$267$	1415.01	0.324335
$268$	16759.6	3.81998
$269$	−3661.78	−0.829972	−0.414986	−	0.909828i	$-0.636214\pi$
$269$	−3661.78	−0.829972	−0.414986	+	0.909828i	$0.636214\pi$
$270$	−55.5504	−0.0125211
$271$	−5113.43	−1.14619	−0.573097	−	0.819487i	$-0.694258\pi$
$271$	−5113.43	−1.14619	−0.573097	+	0.819487i	$0.694258\pi$
$272$	−23557.1	−5.25131
$273$	−8588.23	−1.90397
$274$	16501.9	3.63838
$275$	846.947	0.185719
$276$	−3787.22	−0.825956
$277$	2856.89	0.619689	0.309845	−	0.950787i	$-0.399723\pi$
$277$	2856.89	0.619689	0.309845	+	0.950787i	$0.399723\pi$
$278$	8560.37	1.84682
$279$	−6966.17	−1.49482
$280$	1729.33	0.369096
$281$	−1829.11	−0.388312	−0.194156	−	0.980971i	$-0.562197\pi$
$281$	−1829.11	−0.388312	−0.194156	+	0.980971i	$0.562197\pi$
$282$	20126.8	4.25012
$283$	5553.93	1.16660	0.583298	−	0.812258i	$-0.301762\pi$
$283$	5553.93	1.16660	0.583298	+	0.812258i	$0.301762\pi$
$284$	−74.8744	−0.0156443
$285$	−576.218	−0.119762
$286$	−2115.93	−0.437474
$287$	−7966.82	−1.63856
$288$	−21587.6	−4.41687
$289$	2718.49	0.553326
$290$	161.118	0.0326247
$291$	6331.11	1.27538
$292$	8423.39	1.68816
$293$	8154.48	1.62590	0.812952	−	0.582330i	$-0.197859\pi$
$293$	8154.48	1.62590	0.812952	+	0.582330i	$0.197859\pi$
$294$	−4236.71	−0.840441
$295$	−796.827	−0.157265
$296$	17798.5	3.49499
$297$	68.2961	0.0133432
$298$	−12832.1	−2.49444
$299$	1285.91	0.248717
$300$	−20417.2	−3.92928
$301$	1960.69	0.375456
$302$	11430.5	2.17798
$303$	623.270	0.118171
$304$	21361.9	4.03022
$305$	−532.704	−0.100008
$306$	12401.5	2.31682
$307$	−1435.40	−0.266849	−0.133425	−	0.991059i	$-0.542597\pi$
$307$	−1435.40	−0.266849	−0.133425	+	0.991059i	$0.542597\pi$
$308$	−3283.24	−0.607402
$309$	−5676.32	−1.04503
$310$	−1510.54	−0.276752
$311$	−10816.2	−1.97212	−0.986059	−	0.166396i	$-0.946787\pi$
$311$	−10816.2	−1.97212	−0.986059	+	0.166396i	$0.946787\pi$
$312$	33031.1	5.99365
$313$	−5673.83	−1.02461	−0.512306	−	0.858803i	$-0.671209\pi$
$313$	−5673.83	−1.02461	−0.512306	+	0.858803i	$0.671209\pi$
$314$	−13933.4	−2.50417
$315$	−544.035	−0.0973108
$316$	−4373.59	−0.778588
$317$	6873.20	1.21778	0.608892	−	0.793253i	$-0.291614\pi$
$317$	6873.20	1.21778	0.608892	+	0.793253i	$0.291614\pi$
$318$	26142.1	4.60999
$319$	−198.085	−0.0347669
$320$	−2517.88	−0.439856
$321$	4381.94	0.761920
$322$	2698.54	0.467031
$323$	−6920.34	−1.19213
$324$	−17349.4	−2.97485
$325$	6932.44	1.18321
$326$	5773.97	0.980953
$327$	12056.1	2.03885
$328$	30641.1	5.15814
$329$	−10603.9	−1.77694
$330$	−275.284	−0.0459209
$331$	1109.81	0.184292	0.0921460	−	0.995746i	$-0.470627\pi$
$331$	1109.81	0.184292	0.0921460	+	0.995746i	$0.470627\pi$
$332$	−12423.7	−2.05374
$333$	−5599.30	−0.921441
$334$	−5404.36	−0.885369
$335$	−740.347	−0.120745
$336$	41422.5	6.72555
$337$	3577.60	0.578292	0.289146	−	0.957285i	$-0.406629\pi$
$337$	3577.60	0.578292	0.289146	+	0.957285i	$0.406629\pi$
$338$	−5146.44	−0.828193
$339$	5219.92	0.836304
$340$	1988.37	0.317160
$341$	1857.13	0.294924
$342$	−11245.9	−1.77809
$343$	−5031.13	−0.791998
$344$	−7540.99	−1.18193
$345$	167.299	0.0261074
$346$	592.207	0.0920151
$347$	−5404.57	−0.836117	−0.418059	−	0.908420i	$-0.637289\pi$
$347$	−5404.57	−0.836117	−0.418059	+	0.908420i	$0.637289\pi$
$348$	4775.19	0.735566
$349$	10217.8	1.56719	0.783594	−	0.621273i	$-0.213384\pi$
$349$	10217.8	1.56719	0.783594	+	0.621273i	$0.213384\pi$
$350$	14548.0	2.22178
$351$	559.018	0.0850090
$352$	5755.07	0.871438
$353$	−10114.3	−1.52501	−0.762507	−	0.646980i	$-0.776032\pi$
$353$	−10114.3	−1.52501	−0.762507	+	0.646980i	$0.776032\pi$
$354$	−31939.5	−4.79538
$355$	3.30754	0.000494496 0
$356$	4427.81	0.659195
$357$	−13419.1	−1.98940
$358$	404.907	0.0597765
$359$	151.966	0.0223411	0.0111706	−	0.999938i	$-0.496444\pi$
$359$	151.966	0.0223411	0.0111706	+	0.999938i	$0.496444\pi$
$360$	2092.41	0.306332
$361$	−583.548	−0.0850777
$362$	−8467.63	−1.22942
$363$	−9316.73	−1.34711
$364$	−26874.0	−3.86972
$365$	−372.099	−0.0533604
$366$	−21352.6	−3.04950
$367$	−7134.35	−1.01474	−0.507371	−	0.861728i	$-0.669383\pi$
$367$	−7134.35	−1.01474	−0.507371	+	0.861728i	$0.669383\pi$
$368$	−6202.18	−0.878562
$369$	−9639.49	−1.35992
$370$	−1214.15	−0.170596
$371$	−13773.1	−1.92740
$372$	−44769.3	−6.23973
$373$	−11921.2	−1.65484	−0.827422	−	0.561581i	$-0.810193\pi$
$373$	−11921.2	−1.65484	−0.827422	+	0.561581i	$0.810193\pi$
$374$	−3306.15	−0.457104
$375$	1811.15	0.249406
$376$	40783.7	5.59377
$377$	−1621.37	−0.221498
$378$	1173.12	0.159627
$379$	−138.747	−0.0188046	−0.00940229	−	0.999956i	$-0.502993\pi$
$379$	−138.747	−0.0188046	−0.00940229	+	0.999956i	$0.502993\pi$
$380$	−1803.08	−0.243411
$381$	−5881.56	−0.790870
$382$	10189.2	1.36472
$383$	10167.2	1.35645	0.678224	−	0.734856i	$-0.262750\pi$
$383$	10167.2	1.35645	0.678224	+	0.734856i	$0.262750\pi$
$384$	−52029.5	−6.91437
$385$	145.035	0.0191992
$386$	11679.0	1.54002
$387$	2372.35	0.311610
$388$	19811.1	2.59215
$389$	−5880.08	−0.766406	−0.383203	−	0.923664i	$-0.625179\pi$
$389$	−5880.08	−0.766406	−0.383203	+	0.923664i	$0.625179\pi$
$390$	−2253.26	−0.292560
$391$	2009.24	0.259877
$392$	−8584.99	−1.10614
$393$	16615.7	2.13270
$394$	543.599	0.0695079
$395$	193.201	0.0246102
$396$	−3972.57	−0.504114
$397$	−5902.09	−0.746139	−0.373069	−	0.927803i	$-0.621695\pi$
$397$	−5902.09	−0.746139	−0.373069	+	0.927803i	$0.621695\pi$
$398$	−8734.68	−1.10008
$399$	12168.7	1.52680
$400$	−33436.4	−4.17955
$401$	3237.76	0.403207	0.201603	−	0.979467i	$-0.435385\pi$
$401$	3237.76	0.403207	0.201603	+	0.979467i	$0.435385\pi$
$402$	−29675.6	−3.68180
$403$	15201.0	1.87894
$404$	1950.31	0.240178
$405$	766.399	0.0940313
$406$	−3402.51	−0.415920
$407$	1492.73	0.181798
$408$	51611.2	6.26259
$409$	8633.71	1.04379	0.521894	−	0.853010i	$-0.325226\pi$
$409$	8633.71	1.04379	0.521894	+	0.853010i	$0.325226\pi$
$410$	−2090.22	−0.251778
$411$	−21604.9	−2.59292
$412$	−17762.1	−2.12397
$413$	16827.5	2.00491
$414$	3265.11	0.387613
$415$	548.811	0.0649159
$416$	47106.5	5.55188
$417$	−11207.6	−1.31616
$418$	2998.06	0.350813
$419$	−7692.20	−0.896870	−0.448435	−	0.893815i	$-0.648018\pi$
$419$	−7692.20	−0.896870	−0.448435	+	0.893815i	$0.648018\pi$
$420$	−3496.33	−0.406199
$421$	5624.29	0.651096	0.325548	−	0.945526i	$-0.394451\pi$
$421$	5624.29	0.651096	0.325548	+	0.945526i	$0.394451\pi$
$422$	466.640	0.0538287
$423$	−12830.3	−1.47477
$424$	52972.7	6.06741
$425$	10832.0	1.23630
$426$	132.577	0.0150784
$427$	11249.7	1.27497
$428$	13711.8	1.54856
$429$	2770.26	0.311770
$430$	514.419	0.0576918
$431$	72.5532	0.00810851	0.00405425	−	0.999992i	$-0.498709\pi$
$431$	72.5532	0.00810851	0.00405425	+	0.999992i	$0.498709\pi$
$432$	−2696.24	−0.300284
$433$	3760.43	0.417355	0.208678	−	0.977984i	$-0.433084\pi$
$433$	3760.43	0.417355	0.208678	+	0.977984i	$0.433084\pi$
$434$	31899.8	3.52821
$435$	−210.942	−0.0232503
$436$	37725.6	4.14387
$437$	−1822.01	−0.199447
$438$	−14915.0	−1.62709
$439$	6127.73	0.666198	0.333099	−	0.942892i	$-0.391906\pi$
$439$	6127.73	0.666198	0.333099	+	0.942892i	$0.391906\pi$
$440$	−557.819	−0.0604386
$441$	2700.78	0.291630
$442$	−27061.5	−2.91218
$443$	−14631.9	−1.56926	−0.784629	−	0.619965i	$-0.787147\pi$
$443$	−14631.9	−1.56926	−0.784629	+	0.619965i	$0.787147\pi$
$444$	−35984.8	−3.84632
$445$	−195.596	−0.0208363
$446$	−12727.8	−1.35130
$447$	16800.2	1.77768
$448$	53172.9	5.60756
$449$	16044.8	1.68641	0.843207	−	0.537589i	$-0.180665\pi$
$449$	16044.8	1.68641	0.843207	+	0.537589i	$0.180665\pi$
$450$	17602.5	1.84397
$451$	2569.81	0.268310
$452$	16334.0	1.69975
$453$	−14965.2	−1.55215
$454$	−33829.1	−3.49709
$455$	1187.14	0.122317
$456$	−46801.7	−4.80634
$457$	21.0294	0.00215255	0.00107627	−	0.999999i	$-0.499657\pi$
$457$	21.0294	0.00215255	0.00107627	+	0.999999i	$0.499657\pi$
$458$	20923.0	2.13465
$459$	873.467	0.0888234
$460$	523.504	0.0530620
$461$	13843.7	1.39862	0.699311	−	0.714818i	$-0.253490\pi$
$461$	13843.7	1.39862	0.699311	+	0.714818i	$0.253490\pi$
$462$	5813.50	0.585429
$463$	−6986.76	−0.701301	−0.350651	−	0.936506i	$-0.614039\pi$
$463$	−6986.76	−0.701301	−0.350651	+	0.936506i	$0.614039\pi$
$464$	7820.14	0.782416
$465$	1977.66	0.197230
$466$	8683.89	0.863248
$467$	−4752.90	−0.470959	−0.235480	−	0.971879i	$-0.575666\pi$
$467$	−4752.90	−0.470959	−0.235480	+	0.971879i	$0.575666\pi$
$468$	−32516.3	−3.21168
$469$	15634.8	1.53933
$470$	−2782.11	−0.273041
$471$	18242.2	1.78462
$472$	−64720.1	−6.31141
$473$	−632.448	−0.0614799
$474$	7744.15	0.750423
$475$	−9822.57	−0.948822
$476$	−41990.7	−4.04336
$477$	−16664.9	−1.59965
$478$	−4630.59	−0.443093
$479$	10019.4	0.955741	0.477871	−	0.878430i	$-0.341409\pi$
$479$	10019.4	0.955741	0.477871	+	0.878430i	$0.341409\pi$
$480$	6128.60	0.582773
$481$	12218.3	1.15822
$482$	13710.4	1.29563
$483$	−3533.03	−0.332834
$484$	−29153.6	−2.73794
$485$	−875.144	−0.0819346
$486$	29224.0	2.72763
$487$	−14386.0	−1.33858	−0.669292	−	0.742999i	$-0.733403\pi$
$487$	−14386.0	−1.33858	−0.669292	+	0.742999i	$0.733403\pi$
$488$	−43267.4	−4.01358
$489$	−7559.51	−0.699085
$490$	585.637	0.0539926
$491$	10967.1	1.00802	0.504012	−	0.863697i	$-0.331857\pi$
$491$	10967.1	1.00802	0.504012	+	0.863697i	$0.331857\pi$
$492$	−61949.8	−5.67665
$493$	−2533.39	−0.231437
$494$	24539.7	2.23501
$495$	175.486	0.0159344
$496$	−73316.8	−6.63714
$497$	−69.8491	−0.00630414
$498$	21998.2	1.97944
$499$	−12736.2	−1.14258	−0.571292	−	0.820747i	$-0.693558\pi$
$499$	−12736.2	−1.14258	−0.571292	+	0.820747i	$0.693558\pi$
$500$	5667.38	0.506906
$501$	7075.59	0.630966
$502$	33010.9	2.93496
$503$	−17414.5	−1.54369	−0.771845	−	0.635811i	$-0.780666\pi$
$503$	−17414.5	−1.54369	−0.771845	+	0.635811i	$0.780666\pi$
$504$	−44187.8	−3.90532
$505$	−86.1541	−0.00759170
$506$	−870.453	−0.0764750
$507$	6737.91	0.590219
$508$	−18404.4	−1.60740
$509$	2002.14	0.174348	0.0871741	−	0.996193i	$-0.472216\pi$
$509$	2002.14	0.174348	0.0871741	+	0.996193i	$0.472216\pi$
$510$	−3520.73	−0.305687
$511$	7858.04	0.680272
$512$	−51505.9	−4.44582
$513$	−792.072	−0.0681692
$514$	−12087.9	−1.03730
$515$	784.633	0.0671360
$516$	15246.3	1.30074
$517$	3420.45	0.290969
$518$	25640.6	2.17487
$519$	−775.340	−0.0655754
$520$	−4565.86	−0.385051
$521$	14095.3	1.18527	0.592637	−	0.805470i	$-0.298087\pi$
$521$	14095.3	1.18527	0.592637	+	0.805470i	$0.298087\pi$
$522$	−4116.88	−0.345194
$523$	3228.70	0.269945	0.134973	−	0.990849i	$-0.456905\pi$
$523$	3228.70	0.269945	0.134973	+	0.990849i	$0.456905\pi$
$524$	51993.3	4.33462
$525$	−19046.8	−1.58337
$526$	11330.3	0.939209
$527$	23751.5	1.96325
$528$	−13361.4	−1.10129
$529$	529.000	0.0434783
$530$	−3613.60	−0.296160
$531$	20360.5	1.66398
$532$	38077.7	3.10315
$533$	21034.4	1.70939
$534$	−7840.15	−0.635349
$535$	−605.712	−0.0489481
$536$	−60132.6	−4.84577
$537$	−530.119	−0.0426002
$538$	20288.8	1.62586
$539$	−720.007	−0.0575378
$540$	227.580	0.0181361
$541$	−8589.72	−0.682626	−0.341313	−	0.939950i	$-0.610872\pi$
$541$	−8589.72	−0.682626	−0.341313	+	0.939950i	$0.610872\pi$
$542$	28331.9	2.24531
$543$	11086.1	0.876155
$544$	73604.0	5.80100
$545$	−1666.51	−0.130982
$546$	47584.7	3.72974
$547$	−14460.0	−1.13028	−0.565142	−	0.824994i	$-0.691179\pi$
$547$	−14460.0	−1.13028	−0.565142	+	0.824994i	$0.691179\pi$
$548$	−67605.3	−5.26999
$549$	13611.7	1.05816
$550$	−4692.67	−0.363811
$551$	2297.31	0.177621
$552$	13588.4	1.04775
$553$	−4080.05	−0.313746
$554$	−15829.1	−1.21393
$555$	1589.61	0.121577
$556$	−35070.3	−2.67502
$557$	10577.3	0.804623	0.402311	−	0.915503i	$-0.368207\pi$
$557$	10577.3	0.804623	0.402311	+	0.915503i	$0.368207\pi$
$558$	38597.4	2.92824
$559$	−5176.72	−0.391685
$560$	−5725.80	−0.432070
$561$	4328.53	0.325759
$562$	10134.5	0.760675
$563$	−5849.83	−0.437906	−0.218953	−	0.975735i	$-0.570264\pi$
$563$	−5849.83	−0.437906	−0.218953	+	0.975735i	$0.570264\pi$
$564$	−82455.9	−6.15606
$565$	−721.546	−0.0537268
$566$	−30772.6	−2.28528
$567$	−16184.9	−1.19877
$568$	268.646	0.0198453
$569$	21309.0	1.56998	0.784991	−	0.619508i	$-0.212668\pi$
$569$	21309.0	1.56998	0.784991	+	0.619508i	$0.212668\pi$
$570$	3192.64	0.234605
$571$	−13667.2	−1.00167	−0.500834	−	0.865543i	$-0.666973\pi$
$571$	−13667.2	−1.00167	−0.500834	+	0.865543i	$0.666973\pi$
$572$	8668.58	0.633657
$573$	−13340.1	−0.972583
$574$	44141.6	3.20982
$575$	2851.87	0.206837
$576$	64336.9	4.65400
$577$	−466.999	−0.0336939	−0.0168470	−	0.999858i	$-0.505363\pi$
$577$	−466.999	−0.0336939	−0.0168470	+	0.999858i	$0.505363\pi$
$578$	−15062.3	−1.08393
$579$	−15290.6	−1.09751
$580$	−660.071	−0.0472551
$581$	−11589.9	−0.827589
$582$	−35078.7	−2.49838
$583$	4442.72	0.315607
$584$	−30222.7	−2.14148
$585$	1436.39	0.101517
$586$	−45181.4	−3.18503
$587$	12157.1	0.854815	0.427408	−	0.904059i	$-0.359427\pi$
$587$	12157.1	0.854815	0.427408	+	0.904059i	$0.359427\pi$
$588$	17357.0	1.21733
$589$	−21538.2	−1.50673
$590$	4414.97	0.308070
$591$	−711.701	−0.0495354
$592$	−58930.9	−4.09129
$593$	5532.67	0.383135	0.191568	−	0.981479i	$-0.438643\pi$
$593$	5532.67	0.383135	0.191568	+	0.981479i	$0.438643\pi$
$594$	−378.407	−0.0261384
$595$	1854.92	0.127805
$596$	52570.7	3.61305
$597$	11435.8	0.783979
$598$	−7124.84	−0.487218
$599$	−19277.9	−1.31498	−0.657491	−	0.753462i	$-0.728382\pi$
$599$	−19277.9	−1.31498	−0.657491	+	0.753462i	$0.728382\pi$
$600$	73255.8	4.98442
$601$	10158.6	0.689481	0.344740	−	0.938698i	$-0.387967\pi$
$601$	10158.6	0.689481	0.344740	+	0.938698i	$0.387967\pi$
$602$	−10863.6	−0.735492
$603$	18917.4	1.27757
$604$	−46828.5	−3.15468
$605$	1287.84	0.0865427
$606$	−3453.34	−0.231489
$607$	−15668.8	−1.04774	−0.523868	−	0.851799i	$-0.675512\pi$
$607$	−15668.8	−1.04774	−0.523868	+	0.851799i	$0.675512\pi$
$608$	−66745.1	−4.45209
$609$	4454.70	0.296409
$610$	2951.55	0.195909
$611$	27997.1	1.85375
$612$	−50806.8	−3.35579
$613$	17912.6	1.18023	0.590116	−	0.807318i	$-0.299082\pi$
$613$	17912.6	1.18023	0.590116	+	0.807318i	$0.299082\pi$
$614$	7953.11	0.522738
$615$	2736.60	0.179432
$616$	11780.1	0.770509
$617$	14321.8	0.934477	0.467239	−	0.884131i	$-0.345249\pi$
$617$	14321.8	0.934477	0.467239	+	0.884131i	$0.345249\pi$
$618$	31450.7	2.04714
$619$	10845.0	0.704197	0.352098	−	0.935963i	$-0.385468\pi$
$619$	10845.0	0.704197	0.352098	+	0.935963i	$0.385468\pi$
$620$	6188.42	0.400860
$621$	229.969	0.0148605
$622$	59929.0	3.86324
$623$	4130.63	0.265634
$624$	−109366.	−7.01626
$625$	15249.0	0.975934
$626$	31436.9	2.00714
$627$	−3925.17	−0.250010
$628$	57082.7	3.62715
$629$	19091.1	1.21019
$630$	3014.33	0.190625
$631$	4368.26	0.275591	0.137795	−	0.990461i	$-0.455998\pi$
$631$	4368.26	0.275591	0.137795	+	0.990461i	$0.455998\pi$
$632$	15692.2	0.987665
$633$	−610.943	−0.0383615
$634$	−38082.2	−2.38555
$635$	813.003	0.0508080
$636$	−107100.	−6.67732
$637$	−5893.41	−0.366570
$638$	1097.53	0.0681058
$639$	−84.5142	−0.00523213
$640$	7191.99	0.444201
$641$	−28233.3	−1.73970	−0.869849	−	0.493318i	$-0.835784\pi$
$641$	−28233.3	−1.73970	−0.869849	+	0.493318i	$0.835784\pi$
$642$	−24279.0	−1.49255
$643$	−21154.5	−1.29743	−0.648717	−	0.761030i	$-0.724694\pi$
$643$	−21154.5	−1.29743	−0.648717	+	0.761030i	$0.724694\pi$
$644$	−11055.4	−0.676468
$645$	−673.497	−0.0411146
$646$	38343.4	2.33530
$647$	21761.4	1.32230	0.661152	−	0.750252i	$-0.270068\pi$
$647$	21761.4	1.32230	0.661152	+	0.750252i	$0.270068\pi$
$648$	62248.6	3.77370
$649$	−5427.95	−0.328299
$650$	−38410.5	−2.31782
$651$	−41764.5	−2.51441
$652$	−23654.9	−1.42086
$653$	−4312.86	−0.258461	−0.129231	−	0.991615i	$-0.541251\pi$
$653$	−4312.86	−0.258461	−0.129231	+	0.991615i	$0.541251\pi$
$654$	−66799.1	−3.99397
$655$	−2296.78	−0.137012
$656$	−101453.	−6.03821
$657$	9507.88	0.564593
$658$	58753.0	3.48090
$659$	−17763.0	−1.05000	−0.524998	−	0.851104i	$-0.675934\pi$
$659$	−17763.0	−1.05000	−0.524998	+	0.851104i	$0.675934\pi$
$660$	1127.79	0.0665140
$661$	8637.52	0.508261	0.254131	−	0.967170i	$-0.418211\pi$
$661$	8637.52	0.508261	0.254131	+	0.967170i	$0.418211\pi$
$662$	−6149.11	−0.361015
$663$	35430.0	2.07539
$664$	44575.7	2.60523
$665$	−1682.06	−0.0980866
$666$	31024.0	1.80504
$667$	−667.000	−0.0387202
$668$	22140.7	1.28241
$669$	16663.7	0.963015
$670$	4102.03	0.236530
$671$	−3628.76	−0.208773
$672$	−129425.	−7.42955
$673$	−13690.9	−0.784169	−0.392084	−	0.919929i	$-0.628246\pi$
$673$	−13690.9	−0.784169	−0.392084	+	0.919929i	$0.628246\pi$
$674$	−19822.4	−1.13283
$675$	1239.78	0.0706950
$676$	21084.0	1.19959
$677$	−22052.5	−1.25192	−0.625958	−	0.779857i	$-0.715292\pi$
$677$	−22052.5	−1.25192	−0.625958	+	0.779857i	$0.715292\pi$
$678$	−28921.9	−1.63826
$679$	18481.4	1.04455
$680$	−7134.18	−0.402328
$681$	44290.3	2.49223
$682$	−10289.7	−0.577734
$683$	26723.7	1.49715	0.748575	−	0.663051i	$-0.230739\pi$
$683$	26723.7	1.49715	0.748575	+	0.663051i	$0.230739\pi$
$684$	46072.3	2.57547
$685$	2986.43	0.166578
$686$	27875.9	1.55147
$687$	−27393.2	−1.52128
$688$	24968.2	1.38358
$689$	36364.6	2.01071
$690$	−926.949	−0.0511425
$691$	20665.6	1.13771	0.568853	−	0.822439i	$-0.307387\pi$
$691$	20665.6	1.13771	0.568853	+	0.822439i	$0.307387\pi$
$692$	−2426.16	−0.133279
$693$	−3705.94	−0.203142
$694$	29945.0	1.63789
$695$	1549.21	0.0845539
$696$	−17133.2	−0.933090
$697$	32866.4	1.78609
$698$	−56613.9	−3.07001
$699$	−11369.3	−0.615201
$700$	−59600.6	−3.21813
$701$	7469.66	0.402461	0.201231	−	0.979544i	$-0.435506\pi$
$701$	7469.66	0.402461	0.201231	+	0.979544i	$0.435506\pi$
$702$	−3097.34	−0.166527
$703$	−17312.1	−0.928787
$704$	−17151.7	−0.918222
$705$	3642.45	0.194585
$706$	56040.2	2.98739
$707$	1819.42	0.0967838
$708$	130850.	6.94584
$709$	−14168.7	−0.750519	−0.375260	−	0.926920i	$-0.622446\pi$
$709$	−14168.7	−0.750519	−0.375260	+	0.926920i	$0.622446\pi$
$710$	−18.3260	−0.000968681 0
$711$	−4936.68	−0.260394
$712$	−15886.8	−0.836210
$713$	6253.38	0.328459
$714$	74351.2	3.89709
$715$	−382.930	−0.0200291
$716$	−1658.83	−0.0865829
$717$	6062.55	0.315774
$718$	−841.996	−0.0437647
$719$	12477.5	0.647191	0.323596	−	0.946195i	$-0.395108\pi$
$719$	12477.5	0.647191	0.323596	+	0.946195i	$0.395108\pi$
$720$	−6927.96	−0.358597
$721$	−16570.0	−0.855893
$722$	3233.26	0.166661
$723$	−17950.2	−0.923340
$724$	34690.4	1.78074
$725$	−3595.84	−0.184202
$726$	51621.1	2.63890
$727$	−26176.3	−1.33538	−0.667692	−	0.744438i	$-0.732718\pi$
$727$	−26176.3	−1.33538	−0.667692	+	0.744438i	$0.732718\pi$
$728$	96422.5	4.90887
$729$	−17624.7	−0.895427
$730$	2061.68	0.104529
$731$	−8088.65	−0.409260
$732$	87477.6	4.41703
$733$	−29201.1	−1.47144	−0.735720	−	0.677286i	$-0.763156\pi$
$733$	−29201.1	−1.47144	−0.735720	+	0.677286i	$0.763156\pi$
$734$	39529.2	1.98781
$735$	−766.738	−0.0384783
$736$	19378.7	0.970527
$737$	−5043.21	−0.252061
$738$	53409.4	2.66399
$739$	4853.92	0.241616	0.120808	−	0.992676i	$-0.461451\pi$
$739$	4853.92	0.241616	0.120808	+	0.992676i	$0.461451\pi$
$740$	4974.15	0.247099
$741$	−32128.4	−1.59280
$742$	76312.6	3.77564
$743$	−11269.5	−0.556444	−0.278222	−	0.960517i	$-0.589745\pi$
$743$	−11269.5	−0.556444	−0.278222	+	0.960517i	$0.589745\pi$
$744$	160630.	7.91530
$745$	−2322.28	−0.114204
$746$	66051.7	3.24172
$747$	−14023.2	−0.686858
$748$	13544.7	0.662089
$749$	12791.5	0.624021
$750$	−10035.0	−0.488569
$751$	31445.5	1.52791	0.763956	−	0.645269i	$-0.223255\pi$
$751$	31445.5	1.52791	0.763956	+	0.645269i	$0.223255\pi$
$752$	−135035.	−6.54815
$753$	−43219.2	−2.09163
$754$	8983.49	0.433899
$755$	2068.63	0.0997153
$756$	−4806.07	−0.231211
$757$	8436.12	0.405041	0.202520	−	0.979278i	$-0.435087\pi$
$757$	8436.12	0.405041	0.202520	+	0.979278i	$0.435087\pi$
$758$	768.752	0.0368368
$759$	1139.63	0.0545006
$760$	6469.37	0.308774
$761$	13735.9	0.654306	0.327153	−	0.944971i	$-0.393911\pi$
$761$	13735.9	0.654306	0.327153	+	0.944971i	$0.393911\pi$
$762$	32587.9	1.54926
$763$	35193.5	1.66984
$764$	−41743.3	−1.97673
$765$	2244.37	0.106072
$766$	−56333.2	−2.65718
$767$	−44428.9	−2.09157
$768$	142557.	6.69802
$769$	33519.6	1.57184	0.785922	−	0.618325i	$-0.212189\pi$
$769$	33519.6	1.57184	0.785922	+	0.618325i	$0.212189\pi$
$770$	−803.595	−0.0376098
$771$	15825.9	0.739244
$772$	−47846.8	−2.23063
$773$	−8567.11	−0.398626	−0.199313	−	0.979936i	$-0.563871\pi$
$773$	−8567.11	−0.398626	−0.199313	+	0.979936i	$0.563871\pi$
$774$	−13144.4	−0.610422
$775$	33712.4	1.56256
$776$	−71081.2	−3.28823
$777$	−33569.6	−1.54994
$778$	32579.7	1.50133
$779$	−29803.7	−1.37077
$780$	9231.21	0.423757
$781$	22.5308	0.00103229
$782$	−11132.6	−0.509080
$783$	−289.961	−0.0132342
$784$	28424.9	1.29487
$785$	−2521.60	−0.114649
$786$	−92062.5	−4.17781
$787$	4576.41	0.207282	0.103641	−	0.994615i	$-0.466951\pi$
$787$	4576.41	0.207282	0.103641	+	0.994615i	$0.466951\pi$
$788$	−2227.03	−0.100678
$789$	−14834.0	−0.669336
$790$	−1070.47	−0.0482095
$791$	15237.7	0.684943
$792$	14253.4	0.639485
$793$	−29702.1	−1.33008
$794$	32701.6	1.46163
$795$	4731.07	0.211061
$796$	35784.4	1.59340
$797$	−35647.9	−1.58433	−0.792166	−	0.610306i	$-0.791046\pi$
$797$	−35647.9	−1.58433	−0.792166	+	0.610306i	$0.791046\pi$
$798$	−67422.7	−2.99090
$799$	43745.5	1.93693
$800$	104472.	4.61705
$801$	4997.88	0.220464
$802$	−17939.4	−0.789853
$803$	−2534.72	−0.111393
$804$	121575.	5.33288
$805$	488.368	0.0213823
$806$	−84223.7	−3.68071
$807$	−26562.8	−1.15868
$808$	−6997.63	−0.304673
$809$	−2784.72	−0.121021	−0.0605103	−	0.998168i	$-0.519273\pi$
$809$	−2784.72	−0.121021	−0.0605103	+	0.998168i	$0.519273\pi$
$810$	−4246.37	−0.184200
$811$	17825.5	0.771811	0.385906	−	0.922538i	$-0.373889\pi$
$811$	17825.5	0.771811	0.385906	+	0.922538i	$0.373889\pi$
$812$	13939.5	0.602438
$813$	−37093.2	−1.60014
$814$	−8270.73	−0.356129
$815$	1044.94	0.0449114
$816$	−170885.	−7.33108
$817$	7334.89	0.314095
$818$	−47836.7	−2.04471
$819$	−30333.9	−1.29420
$820$	8563.27	0.364686
$821$	−10685.6	−0.454240	−0.227120	−	0.973867i	$-0.572931\pi$
$821$	−10685.6	−0.454240	−0.227120	+	0.973867i	$0.572931\pi$
$822$	119706.	5.07935
$823$	26567.2	1.12524	0.562622	−	0.826715i	$-0.309793\pi$
$823$	26567.2	1.12524	0.562622	+	0.826715i	$0.309793\pi$
$824$	63729.7	2.69433
$825$	6143.82	0.259273
$826$	−93236.0	−3.92747
$827$	34262.6	1.44066	0.720331	−	0.693631i	$-0.243990\pi$
$827$	34262.6	1.44066	0.720331	+	0.693631i	$0.243990\pi$
$828$	−13376.6	−0.561436
$829$	464.312	0.0194526	0.00972631	−	0.999953i	$-0.496904\pi$
$829$	464.312	0.0194526	0.00972631	+	0.999953i	$0.496904\pi$
$830$	−3040.79	−0.127166
$831$	20724.1	0.865116
$832$	−140390.	−5.84994
$833$	−9208.47	−0.383019
$834$	62097.6	2.57825
$835$	−978.053	−0.0405352
$836$	−12282.5	−0.508133
$837$	2718.50	0.112264
$838$	42620.1	1.75690
$839$	−10873.9	−0.447449	−0.223724	−	0.974652i	$-0.571822\pi$
$839$	−10873.9	−0.447449	−0.223724	+	0.974652i	$0.571822\pi$
$840$	12544.7	0.515276
$841$	841.000	0.0344828
$842$	−31162.4	−1.27545
$843$	−13268.5	−0.542102
$844$	−1911.74	−0.0779679
$845$	−931.376	−0.0379175
$846$	71088.6	2.88898
$847$	−27196.9	−1.10330
$848$	−175393.	−7.10261
$849$	40288.6	1.62862
$850$	−60016.5	−2.42182
$851$	5026.37	0.202470
$852$	−543.145	−0.0218402
$853$	−43672.7	−1.75302	−0.876510	−	0.481384i	$-0.840134\pi$
$853$	−43672.7	−1.75302	−0.876510	+	0.481384i	$0.840134\pi$
$854$	−62331.2	−2.49757
$855$	−2035.22	−0.0814071
$856$	−49197.3	−1.96440
$857$	10245.2	0.408364	0.204182	−	0.978933i	$-0.434547\pi$
$857$	10245.2	0.408364	0.204182	+	0.978933i	$0.434547\pi$
$858$	−15349.1	−0.610734
$859$	22227.9	0.882893	0.441446	−	0.897288i	$-0.354466\pi$
$859$	22227.9	0.882893	0.441446	+	0.897288i	$0.354466\pi$
$860$	−2107.48	−0.0835634
$861$	−57791.9	−2.28751
$862$	−401.995	−0.0158840
$863$	22608.0	0.891756	0.445878	−	0.895094i	$-0.352892\pi$
$863$	22608.0	0.891756	0.445878	+	0.895094i	$0.352892\pi$
$864$	8424.39	0.331717
$865$	107.175	0.00421277
$866$	−20835.4	−0.817569
$867$	19720.1	0.772469
$868$	−130688.	−5.11041
$869$	1316.08	0.0513751
$870$	1168.76	0.0455456
$871$	−41279.7	−1.60587
$872$	−135357.	−5.25663
$873$	22361.7	0.866929
$874$	10095.2	0.390703
$875$	5287.00	0.204267
$876$	61103.9	2.35675
$877$	−40790.2	−1.57057	−0.785283	−	0.619137i	$-0.787483\pi$
$877$	−40790.2	−1.57057	−0.785283	+	0.619137i	$0.787483\pi$
$878$	−33951.8	−1.30503
$879$	59153.3	2.26984
$880$	1846.94	0.0707503
$881$	−14156.5	−0.541369	−0.270685	−	0.962668i	$-0.587250\pi$
$881$	−14156.5	−0.541369	−0.270685	+	0.962668i	$0.587250\pi$
$882$	−14964.2	−0.571282
$883$	29945.8	1.14129	0.570644	−	0.821198i	$-0.306694\pi$
$883$	29945.8	1.14129	0.570644	+	0.821198i	$0.306694\pi$
$884$	110866.	4.21813
$885$	−5780.25	−0.219549
$886$	81070.6	3.07406
$887$	−40734.0	−1.54196	−0.770978	−	0.636862i	$-0.780232\pi$
$887$	−40734.0	−1.54196	−0.770978	+	0.636862i	$0.780232\pi$
$888$	129112.	4.87918
$889$	−17169.1	−0.647732
$890$	1083.74	0.0408168
$891$	5220.67	0.196295
$892$	52143.5	1.95728
$893$	−39669.0	−1.48653
$894$	−93084.8	−3.48235
$895$	73.2780	0.00273677
$896$	−151882.	−5.66295
$897$	9328.11	0.347220
$898$	−88899.1	−3.30356
$899$	−7884.70	−0.292513
$900$	−72114.1	−2.67089
$901$	56819.8	2.10093
$902$	−14238.5	−0.525599
$903$	14223.0	0.524155
$904$	−58605.6	−2.15619
$905$	−1532.43	−0.0562869
$906$	82917.4	3.04056
$907$	25664.0	0.939537	0.469768	−	0.882790i	$-0.344337\pi$
$907$	25664.0	0.939537	0.469768	+	0.882790i	$0.344337\pi$
$908$	138592.	5.06534
$909$	2201.41	0.0803259
$910$	−6577.59	−0.239610
$911$	−32351.5	−1.17657	−0.588284	−	0.808654i	$-0.700196\pi$
$911$	−32351.5	−1.17657	−0.588284	+	0.808654i	$0.700196\pi$
$912$	154961.	5.62638
$913$	3738.48	0.135515
$914$	−116.517	−0.00421668
$915$	−3864.28	−0.139616
$916$	−85717.9	−3.09192
$917$	48503.7	1.74671
$918$	−4839.61	−0.173999
$919$	−20665.7	−0.741785	−0.370892	−	0.928676i	$-0.620948\pi$
$919$	−20665.7	−0.741785	−0.370892	+	0.928676i	$0.620948\pi$
$920$	−1878.31	−0.0673109
$921$	−10412.5	−0.372534
$922$	−76703.5	−2.73980
$923$	184.419	0.00657664
$924$	−23816.9	−0.847962
$925$	27097.5	0.963200
$926$	38711.5	1.37380
$927$	−20048.9	−0.710349
$928$	−24434.0	−0.864316
$929$	44264.1	1.56325	0.781625	−	0.623748i	$-0.214391\pi$
$929$	44264.1	1.56325	0.781625	+	0.623748i	$0.214391\pi$
$930$	−10957.6	−0.386359
$931$	8350.36	0.293955
$932$	−35576.3	−1.25037
$933$	−78461.3	−2.75317
$934$	26334.3	0.922575
$935$	−598.330	−0.0209278
$936$	116667.	4.07412
$937$	−38724.5	−1.35013	−0.675066	−	0.737757i	$-0.735885\pi$
$937$	−38724.5	−1.35013	−0.675066	+	0.737757i	$0.735885\pi$
$938$	−86627.2	−3.01544
$939$	−41158.4	−1.43041
$940$	11397.8	0.395485
$941$	−15211.8	−0.526983	−0.263491	−	0.964662i	$-0.584874\pi$
$941$	−15211.8	−0.526983	−0.263491	+	0.964662i	$0.584874\pi$
$942$	−101074.	−3.49594
$943$	8653.17	0.298819
$944$	214288.	7.38823
$945$	212.306	0.00730826
$946$	3504.20	0.120435
$947$	6313.57	0.216646	0.108323	−	0.994116i	$-0.465452\pi$
$947$	6313.57	0.216646	0.108323	+	0.994116i	$0.465452\pi$
$948$	−31726.4	−1.08695
$949$	−20747.2	−0.709677
$950$	54423.8	1.85867
$951$	49858.7	1.70008
$952$	150661.	5.12913
$953$	27793.0	0.944704	0.472352	−	0.881410i	$-0.343405\pi$
$953$	27793.0	0.944704	0.472352	+	0.881410i	$0.343405\pi$
$954$	92334.9	3.13360
$955$	1843.99	0.0624818
$956$	18970.7	0.641796
$957$	−1436.93	−0.0485363
$958$	−55514.6	−1.87223
$959$	−63067.9	−2.12364
$960$	−18264.9	−0.614059
$961$	44131.1	1.48136
$962$	−67697.7	−2.26888
$963$	15477.2	0.517907
$964$	−56169.1	−1.87664
$965$	2113.61	0.0705072
$966$	19575.4	0.651997
$967$	−39615.7	−1.31743	−0.658716	−	0.752392i	$-0.728900\pi$
$967$	−39615.7	−1.31743	−0.658716	+	0.752392i	$0.728900\pi$
$968$	104602.	3.47316
$969$	−50200.7	−1.66427
$970$	4848.90	0.160504
$971$	33408.9	1.10416	0.552082	−	0.833790i	$-0.313833\pi$
$971$	33408.9	1.10416	0.552082	+	0.833790i	$0.313833\pi$
$972$	−119726.	−3.95082
$973$	−32716.5	−1.07795
$974$	79708.2	2.62219
$975$	50288.5	1.65182
$976$	143259.	4.69835
$977$	39986.2	1.30939	0.654694	−	0.755894i	$-0.272797\pi$
$977$	39986.2	1.30939	0.654694	+	0.755894i	$0.272797\pi$
$978$	41884.9	1.36946
$979$	−1332.39	−0.0434969
$980$	−2399.25	−0.0782053
$981$	42582.6	1.38589
$982$	−60765.4	−1.97464
$983$	−17847.0	−0.579076	−0.289538	−	0.957167i	$-0.593502\pi$
$983$	−17847.0	−0.579076	−0.289538	+	0.957167i	$0.593502\pi$
$984$	222273.	7.20102
$985$	98.3778	0.00318231
$986$	14036.7	0.453368
$987$	−76921.7	−2.48069
$988$	−100535.	−3.23729
$989$	−2129.60	−0.0684707
$990$	−972.314	−0.0312143
$991$	17882.2	0.573204	0.286602	−	0.958050i	$-0.407474\pi$
$991$	17882.2	0.573204	0.286602	+	0.958050i	$0.407474\pi$
$992$	229078.	7.33190
$993$	8050.65	0.257281
$994$	387.012	0.0123494
$995$	−1580.76	−0.0503652
$996$	−90122.6	−2.86711
$997$	−56674.2	−1.80029	−0.900145	−	0.435591i	$-0.856539\pi$
$997$	−56674.2	−1.80029	−0.900145	+	0.435591i	$0.856539\pi$
$998$	70567.2	2.23824
$999$	2185.09	0.0692023

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
667.4.a.b.1.1	✓	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)

\(f(q)\)	\(=\)	\(q-5.54069 q^{2} +7.25408 q^{3} +22.6992 q^{4} -1.00273 q^{5} -40.1926 q^{6} +21.1757 q^{7} -81.4436 q^{8} +25.6216 q^{9} +O(q^{10})\)	\(q-5.54069 q^{2} +7.25408 q^{3} +22.6992 q^{4} -1.00273 q^{5} -40.1926 q^{6} +21.1757 q^{7} -81.4436 q^{8} +25.6216 q^{9} +5.55579 q^{10} -6.83052 q^{11} +164.662 q^{12} -55.9093 q^{13} -117.328 q^{14} -7.27385 q^{15} +269.660 q^{16} -87.3584 q^{17} -141.962 q^{18} +79.2178 q^{19} -22.7611 q^{20} +153.610 q^{21} +37.8458 q^{22} -23.0000 q^{23} -590.798 q^{24} -123.995 q^{25} +309.776 q^{26} -9.99866 q^{27} +480.671 q^{28} +29.0000 q^{29} +40.3021 q^{30} -271.886 q^{31} -842.552 q^{32} -49.5491 q^{33} +484.025 q^{34} -21.2334 q^{35} +581.591 q^{36} -218.538 q^{37} -438.921 q^{38} -405.570 q^{39} +81.6656 q^{40} -376.225 q^{41} -851.106 q^{42} +92.5915 q^{43} -155.047 q^{44} -25.6915 q^{45} +127.436 q^{46} -500.759 q^{47} +1956.13 q^{48} +105.410 q^{49} +687.015 q^{50} -633.705 q^{51} -1269.10 q^{52} -650.422 q^{53} +55.3995 q^{54} +6.84914 q^{55} -1724.63 q^{56} +574.652 q^{57} -160.680 q^{58} +794.662 q^{59} -165.111 q^{60} +531.256 q^{61} +1506.44 q^{62} +542.556 q^{63} +2511.04 q^{64} +56.0616 q^{65} +274.536 q^{66} +738.335 q^{67} -1982.97 q^{68} -166.844 q^{69} +117.648 q^{70} -3.29855 q^{71} -2086.72 q^{72} +371.088 q^{73} +1210.85 q^{74} -899.466 q^{75} +1798.18 q^{76} -144.641 q^{77} +2247.14 q^{78} -192.676 q^{79} -270.395 q^{80} -764.316 q^{81} +2084.54 q^{82} -547.320 q^{83} +3486.83 q^{84} +87.5965 q^{85} -513.020 q^{86} +210.368 q^{87} +556.303 q^{88} +195.065 q^{89} +142.348 q^{90} -1183.92 q^{91} -522.082 q^{92} -1972.28 q^{93} +2774.55 q^{94} -79.4337 q^{95} -6111.94 q^{96} +872.766 q^{97} -584.045 q^{98} -175.009 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q - 8 q^{2} - 16 q^{3} + 152 q^{4} - 80 q^{5} - 16 q^{6} - 38 q^{7} - 138 q^{8} + 312 q^{9}+O(q^{10}) \) 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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