LMFDB - Embedded newform 667.4.a.c.1.11

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:	$0$
Dimension:	$39$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
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)

$f(q)$	$=$	$q-2.59264 q^{2} -9.20361 q^{3} -1.27821 q^{4} +4.17679 q^{5} +23.8617 q^{6} -28.9309 q^{7} +24.0551 q^{8} +57.7064 q^{9} +O(q^{10})$	\(q-2.59264 q^{2} -9.20361 q^{3} -1.27821 q^{4} +4.17679 q^{5} +23.8617 q^{6} -28.9309 q^{7} +24.0551 q^{8} +57.7064 q^{9} -10.8289 q^{10} -45.2000 q^{11} +11.7641 q^{12} +47.8885 q^{13} +75.0074 q^{14} -38.4415 q^{15} -52.1405 q^{16} -17.6848 q^{17} -149.612 q^{18} -36.5310 q^{19} -5.33881 q^{20} +266.269 q^{21} +117.187 q^{22} -23.0000 q^{23} -221.393 q^{24} -107.554 q^{25} -124.158 q^{26} -282.610 q^{27} +36.9797 q^{28} -29.0000 q^{29} +99.6651 q^{30} -222.786 q^{31} -57.2589 q^{32} +416.003 q^{33} +45.8504 q^{34} -120.838 q^{35} -73.7609 q^{36} -133.607 q^{37} +94.7118 q^{38} -440.747 q^{39} +100.473 q^{40} -241.816 q^{41} -690.339 q^{42} -456.287 q^{43} +57.7750 q^{44} +241.027 q^{45} +59.6308 q^{46} -93.8153 q^{47} +479.881 q^{48} +493.996 q^{49} +278.850 q^{50} +162.764 q^{51} -61.2115 q^{52} -687.318 q^{53} +732.706 q^{54} -188.791 q^{55} -695.935 q^{56} +336.217 q^{57} +75.1866 q^{58} -406.643 q^{59} +49.1363 q^{60} +243.492 q^{61} +577.604 q^{62} -1669.50 q^{63} +565.576 q^{64} +200.020 q^{65} -1078.55 q^{66} +396.726 q^{67} +22.6049 q^{68} +211.683 q^{69} +313.290 q^{70} -409.697 q^{71} +1388.13 q^{72} -335.557 q^{73} +346.396 q^{74} +989.889 q^{75} +46.6943 q^{76} +1307.68 q^{77} +1142.70 q^{78} +147.341 q^{79} -217.780 q^{80} +1042.96 q^{81} +626.942 q^{82} -696.516 q^{83} -340.347 q^{84} -73.8658 q^{85} +1182.99 q^{86} +266.905 q^{87} -1087.29 q^{88} -1440.88 q^{89} -624.898 q^{90} -1385.46 q^{91} +29.3988 q^{92} +2050.43 q^{93} +243.229 q^{94} -152.582 q^{95} +526.989 q^{96} +734.183 q^{97} -1280.76 q^{98} -2608.33 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 39 q + 6 q^{2} + 2 q^{3} + 156 q^{4} + 80 q^{5} - 4 q^{6} + 18 q^{7} + 156 q^{8} + 411 q^{9}+O(q^{10}) $ 39 * q + 6 * q^2 + 2 * q^3 + 156 * q^4 + 80 * q^5 - 4 * q^6 + 18 * q^7 + 156 * q^8 + 411 * q^9	\( 39 q + 6 q^{2} + 2 q^{3} + 156 q^{4} + 80 q^{5} - 4 q^{6} + 18 q^{7} + 156 q^{8} + 411 q^{9} + 130 q^{10} + 76 q^{11} + 115 q^{12} + 184 q^{13} + 336 q^{14} + 228 q^{15} + 776 q^{16} + 314 q^{17} + 27 q^{18} + 36 q^{19} + 533 q^{20} + 246 q^{21} + 269 q^{22} - 897 q^{23} + 30 q^{24} + 1267 q^{25} + 787 q^{26} + 122 q^{27} + 53 q^{28} - 1131 q^{29} + 703 q^{30} + 140 q^{31} + 1304 q^{32} + 2210 q^{33} + 59 q^{34} + 1828 q^{35} + 1834 q^{36} + 430 q^{37} + 1874 q^{38} - 340 q^{39} + 276 q^{40} + 1936 q^{41} + 756 q^{42} + 96 q^{43} - 671 q^{44} + 3392 q^{45} - 138 q^{46} + 1808 q^{47} + 535 q^{48} + 2201 q^{49} + 395 q^{50} + 750 q^{51} - 530 q^{52} + 4200 q^{53} - 937 q^{54} + 902 q^{55} + 3805 q^{56} + 300 q^{57} - 174 q^{58} + 726 q^{59} + 195 q^{60} + 736 q^{61} + 1851 q^{62} + 796 q^{63} + 2914 q^{64} + 2572 q^{65} + 307 q^{66} + 1192 q^{67} + 1235 q^{68} - 46 q^{69} + 5268 q^{70} + 1714 q^{71} + 643 q^{72} + 2012 q^{73} + 3307 q^{74} - 1708 q^{75} + 5244 q^{76} + 6592 q^{77} + 6406 q^{78} + 1768 q^{79} + 8606 q^{80} + 5363 q^{81} - 2059 q^{82} + 3766 q^{83} + 3818 q^{84} + 1260 q^{85} - 2355 q^{86} - 58 q^{87} + 3448 q^{88} + 1634 q^{89} - 1313 q^{90} + 1240 q^{91} - 3588 q^{92} + 3954 q^{93} + 2315 q^{94} + 1656 q^{95} + 1480 q^{96} - 788 q^{97} + 3128 q^{98} + 4488 q^{99}+O(q^{100}) \) 39 * q + 6 * q^2 + 2 * q^3 + 156 * q^4 + 80 * q^5 - 4 * q^6 + 18 * q^7 + 156 * q^8 + 411 * q^9 + 130 * q^10 + 76 * q^11 + 115 * q^12 + 184 * q^13 + 336 * q^14 + 228 * q^15 + 776 * q^16 + 314 * q^17 + 27 * q^18 + 36 * q^19 + 533 * q^20 + 246 * q^21 + 269 * q^22 - 897 * q^23 + 30 * q^24 + 1267 * q^25 + 787 * q^26 + 122 * q^27 + 53 * q^28 - 1131 * q^29 + 703 * q^30 + 140 * q^31 + 1304 * q^32 + 2210 * q^33 + 59 * q^34 + 1828 * q^35 + 1834 * q^36 + 430 * q^37 + 1874 * q^38 - 340 * q^39 + 276 * q^40 + 1936 * q^41 + 756 * q^42 + 96 * q^43 - 671 * q^44 + 3392 * q^45 - 138 * q^46 + 1808 * q^47 + 535 * q^48 + 2201 * q^49 + 395 * q^50 + 750 * q^51 - 530 * q^52 + 4200 * q^53 - 937 * q^54 + 902 * q^55 + 3805 * q^56 + 300 * q^57 - 174 * q^58 + 726 * q^59 + 195 * q^60 + 736 * q^61 + 1851 * q^62 + 796 * q^63 + 2914 * q^64 + 2572 * q^65 + 307 * q^66 + 1192 * q^67 + 1235 * q^68 - 46 * q^69 + 5268 * q^70 + 1714 * q^71 + 643 * q^72 + 2012 * q^73 + 3307 * q^74 - 1708 * q^75 + 5244 * q^76 + 6592 * q^77 + 6406 * q^78 + 1768 * q^79 + 8606 * q^80 + 5363 * q^81 - 2059 * q^82 + 3766 * q^83 + 3818 * q^84 + 1260 * q^85 - 2355 * q^86 - 58 * q^87 + 3448 * q^88 + 1634 * q^89 - 1313 * q^90 + 1240 * q^91 - 3588 * q^92 + 3954 * q^93 + 2315 * q^94 + 1656 * q^95 + 1480 * q^96 - 788 * q^97 + 3128 * q^98 + 4488 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.59264	−0.916637	−0.458319	−	0.888788i	$-0.651548\pi$
$2$	−2.59264	−0.916637	−0.458319	+	0.888788i	$0.651548\pi$
$3$	−9.20361	−1.77124	−0.885618	−	0.464415i	$-0.846265\pi$
$3$	−9.20361	−1.77124	−0.885618	+	0.464415i	$0.846265\pi$
$4$	−1.27821	−0.159776
$5$	4.17679	0.373583	0.186792	−	0.982400i	$-0.440191\pi$
$5$	4.17679	0.373583	0.186792	+	0.982400i	$0.440191\pi$
$6$	23.8617	1.62358
$7$	−28.9309	−1.56212	−0.781061	−	0.624455i	$-0.785321\pi$
$7$	−28.9309	−1.56212	−0.781061	+	0.624455i	$0.785321\pi$
$8$	24.0551	1.06309
$9$	57.7064	2.13727
$10$	−10.8289	−0.342440
$11$	−45.2000	−1.23894	−0.619469	−	0.785021i	$-0.712652\pi$
$11$	−45.2000	−1.23894	−0.619469	+	0.785021i	$0.712652\pi$
$12$	11.7641	0.283001
$13$	47.8885	1.02168	0.510841	−	0.859675i	$-0.329334\pi$
$13$	47.8885	1.02168	0.510841	+	0.859675i	$0.329334\pi$
$14$	75.0074	1.43190
$15$	−38.4415	−0.661704
$16$	−52.1405	−0.814695
$17$	−17.6848	−0.252306	−0.126153	−	0.992011i	$-0.540263\pi$
$17$	−17.6848	−0.252306	−0.126153	+	0.992011i	$0.540263\pi$
$18$	−149.612	−1.95911
$19$	−36.5310	−0.441094	−0.220547	−	0.975376i	$-0.570784\pi$
$19$	−36.5310	−0.441094	−0.220547	+	0.975376i	$0.570784\pi$
$20$	−5.33881	−0.0596897
$21$	266.269	2.76688
$22$	117.187	1.13566
$23$	−23.0000	−0.208514
$23$	−23.0000	−0.208514
$24$	−221.393	−1.88299
$25$	−107.554	−0.860436
$26$	−124.158	−0.936512
$27$	−282.610	−2.01438
$28$	36.9797	0.249590
$29$	−29.0000	−0.185695
$29$	−29.0000	−0.185695
$30$	99.6651	0.606543
$31$	−222.786	−1.29076	−0.645380	−	0.763862i	$-0.723301\pi$
$31$	−222.786	−1.29076	−0.645380	+	0.763862i	$0.723301\pi$
$32$	−57.2589	−0.316314
$33$	416.003	2.19445
$34$	45.8504	0.231273
$35$	−120.838	−0.583582
$36$	−73.7609	−0.341485
$37$	−133.607	−0.593647	−0.296823	−	0.954932i	$-0.595927\pi$
$37$	−133.607	−0.593647	−0.296823	+	0.954932i	$0.595927\pi$
$38$	94.7118	0.404323
$39$	−440.747	−1.80964
$40$	100.473	0.397154
$41$	−241.816	−0.921105	−0.460552	−	0.887633i	$-0.652349\pi$
$41$	−241.816	−0.921105	−0.460552	+	0.887633i	$0.652349\pi$
$42$	−690.339	−2.53623
$43$	−456.287	−1.61821	−0.809106	−	0.587662i	$-0.800048\pi$
$43$	−456.287	−1.61821	−0.809106	+	0.587662i	$0.800048\pi$
$44$	57.7750	0.197953
$45$	241.027	0.798450
$46$	59.6308	0.191132
$47$	−93.8153	−0.291157	−0.145578	−	0.989347i	$-0.546504\pi$
$47$	−93.8153	−0.291157	−0.145578	+	0.989347i	$0.546504\pi$
$48$	479.881	1.44302
$49$	493.996	1.44022
$50$	278.850	0.788707
$51$	162.764	0.446893
$52$	−61.2115	−0.163240
$53$	−687.318	−1.78133	−0.890664	−	0.454663i	$-0.849760\pi$
$53$	−687.318	−1.78133	−0.890664	+	0.454663i	$0.849760\pi$
$54$	732.706	1.84646
$55$	−188.791	−0.462846
$56$	−695.935	−1.66068
$57$	336.217	0.781282
$58$	75.1866	0.170215
$59$	−406.643	−0.897295	−0.448647	−	0.893709i	$-0.648094\pi$
$59$	−406.643	−0.897295	−0.448647	+	0.893709i	$0.648094\pi$
$60$	49.1363	0.105724
$61$	243.492	0.511082	0.255541	−	0.966798i	$-0.417746\pi$
$61$	243.492	0.511082	0.255541	+	0.966798i	$0.417746\pi$
$62$	577.604	1.18316
$63$	−1669.50	−3.33868
$64$	565.576	1.10464
$65$	200.020	0.381683
$66$	−1078.55	−2.01151
$67$	396.726	0.723400	0.361700	−	0.932294i	$-0.382196\pi$
$67$	396.726	0.723400	0.361700	+	0.932294i	$0.382196\pi$
$68$	22.6049	0.0403125
$69$	211.683	0.369328
$70$	313.290	0.534933
$71$	−409.697	−0.684818	−0.342409	−	0.939551i	$-0.611243\pi$
$71$	−409.697	−0.684818	−0.342409	+	0.939551i	$0.611243\pi$
$72$	1388.13	2.27212
$73$	−335.557	−0.537999	−0.269000	−	0.963140i	$-0.586693\pi$
$73$	−335.557	−0.537999	−0.269000	+	0.963140i	$0.586693\pi$
$74$	346.396	0.544159
$75$	989.889	1.52403
$76$	46.6943	0.0704763
$77$	1307.68	1.93537
$78$	1142.70	1.65878
$79$	147.341	0.209837	0.104919	−	0.994481i	$-0.466542\pi$
$79$	147.341	0.209837	0.104919	+	0.994481i	$0.466542\pi$
$80$	−217.780	−0.304357
$81$	1042.96	1.43067
$82$	626.942	0.844319
$83$	−696.516	−0.921116	−0.460558	−	0.887630i	$-0.652351\pi$
$83$	−696.516	−0.921116	−0.460558	+	0.887630i	$0.652351\pi$
$84$	−340.347	−0.442082
$85$	−73.8658	−0.0942573
$86$	1182.99	1.48331
$87$	266.905	0.328910
$88$	−1087.29	−1.31711
$89$	−1440.88	−1.71610	−0.858049	−	0.513568i	$-0.828323\pi$
$89$	−1440.88	−1.71610	−0.858049	+	0.513568i	$0.828323\pi$
$90$	−624.898	−0.731889
$91$	−1385.46	−1.59599
$92$	29.3988	0.0333156
$93$	2050.43	2.28624
$94$	243.229	0.266885
$95$	−152.582	−0.164785
$96$	526.989	0.560266
$97$	734.183	0.768505	0.384253	−	0.923228i	$-0.374459\pi$
$97$	734.183	0.768505	0.384253	+	0.923228i	$0.374459\pi$
$98$	−1280.76	−1.32016
$99$	−2608.33	−2.64795
$100$	137.477	0.137477
$101$	427.270	0.420940	0.210470	−	0.977600i	$-0.432501\pi$
$101$	427.270	0.420940	0.210470	+	0.977600i	$0.432501\pi$
$102$	−421.989	−0.409639
$103$	822.982	0.787290	0.393645	−	0.919263i	$-0.371214\pi$
$103$	822.982	0.787290	0.393645	+	0.919263i	$0.371214\pi$
$104$	1151.96	1.08614
$105$	1112.15	1.03366
$106$	1781.97	1.63283
$107$	1707.94	1.54311	0.771553	−	0.636165i	$-0.219480\pi$
$107$	1707.94	1.54311	0.771553	+	0.636165i	$0.219480\pi$
$108$	361.234	0.321850
$109$	−1515.89	−1.33207	−0.666035	−	0.745920i	$-0.732010\pi$
$109$	−1515.89	−1.33207	−0.666035	+	0.745920i	$0.732010\pi$
$110$	489.467	0.424262
$111$	1229.67	1.05149
$112$	1508.47	1.27265
$113$	1363.98	1.13551	0.567753	−	0.823199i	$-0.307813\pi$
$113$	1363.98	1.13551	0.567753	+	0.823199i	$0.307813\pi$
$114$	−871.691	−0.716152
$115$	−96.0661	−0.0778975
$116$	37.0681	0.0296697
$117$	2763.47	2.18362
$118$	1054.28	0.822494
$119$	511.638	0.394132
$120$	−924.714	−0.703454
$121$	712.039	0.534966
$122$	−631.288	−0.468476
$123$	2225.58	1.63149
$124$	284.767	0.206233
$125$	−971.331	−0.695028
$126$	4328.41	3.06036
$127$	1471.56	1.02819	0.514093	−	0.857734i	$-0.328129\pi$
$127$	1471.56	1.02819	0.514093	+	0.857734i	$0.328129\pi$
$128$	−1008.26	−0.696241
$129$	4199.49	2.86624
$130$	−518.580	−0.349865
$131$	−1431.48	−0.954726	−0.477363	−	0.878706i	$-0.658407\pi$
$131$	−1431.48	−0.954726	−0.477363	+	0.878706i	$0.658407\pi$
$132$	−531.739	−0.350621
$133$	1056.87	0.689043
$134$	−1028.57	−0.663096
$135$	−1180.40	−0.752539
$136$	−425.410	−0.268225
$137$	−1842.11	−1.14878	−0.574388	−	0.818583i	$-0.694760\pi$
$137$	−1842.11	−1.14878	−0.574388	+	0.818583i	$0.694760\pi$
$138$	−548.818	−0.338540
$139$	−1519.25	−0.927056	−0.463528	−	0.886082i	$-0.653417\pi$
$139$	−1519.25	−0.927056	−0.463528	+	0.886082i	$0.653417\pi$
$140$	154.456	0.0932425
$141$	863.439	0.515707
$142$	1062.20	0.627730
$143$	−2164.56	−1.26580
$144$	−3008.84	−1.74123
$145$	−121.127	−0.0693727
$146$	869.978	0.493150
$147$	−4546.55	−2.55097
$148$	170.778	0.0948506
$149$	1370.25	0.753392	0.376696	−	0.926337i	$-0.377060\pi$
$149$	1370.25	0.753392	0.376696	+	0.926337i	$0.377060\pi$
$150$	−2566.43	−1.39699
$151$	1107.93	0.597102	0.298551	−	0.954394i	$-0.403497\pi$
$151$	1107.93	0.597102	0.298551	+	0.954394i	$0.403497\pi$
$152$	−878.756	−0.468925
$153$	−1020.53	−0.539247
$154$	−3390.34	−1.77403
$155$	−930.530	−0.482206
$156$	563.366	0.289137
$157$	297.597	0.151279	0.0756397	−	0.997135i	$-0.475900\pi$
$157$	297.597	0.151279	0.0756397	+	0.997135i	$0.475900\pi$
$158$	−382.002	−0.192344
$159$	6325.80	3.15515
$160$	−239.158	−0.118170
$161$	665.410	0.325725
$162$	−2704.01	−1.31140
$163$	−2578.04	−1.23882	−0.619411	−	0.785067i	$-0.712628\pi$
$163$	−2578.04	−1.23882	−0.619411	+	0.785067i	$0.712628\pi$
$164$	309.091	0.147171
$165$	1737.56	0.819810
$166$	1805.82	0.844329
$167$	−2741.95	−1.27053	−0.635265	−	0.772295i	$-0.719109\pi$
$167$	−2741.95	−1.27053	−0.635265	+	0.772295i	$0.719109\pi$
$168$	6405.11	2.94146
$169$	96.3050	0.0438348
$170$	191.507	0.0863997
$171$	−2108.07	−0.942740
$172$	583.230	0.258552
$173$	−3256.91	−1.43132	−0.715660	−	0.698449i	$-0.753874\pi$
$173$	−3256.91	−1.43132	−0.715660	+	0.698449i	$0.753874\pi$
$174$	−691.988	−0.301491
$175$	3111.65	1.34410
$176$	2356.75	1.00936
$177$	3742.58	1.58932
$178$	3735.68	1.57304
$179$	3437.77	1.43548	0.717741	−	0.696311i	$-0.245176\pi$
$179$	3437.77	1.43548	0.717741	+	0.696311i	$0.245176\pi$
$180$	−308.083	−0.127573
$181$	−2530.04	−1.03898	−0.519492	−	0.854475i	$-0.673879\pi$
$181$	−2530.04	−1.03898	−0.519492	+	0.854475i	$0.673879\pi$
$182$	3591.99	1.46295
$183$	−2241.01	−0.905246
$184$	−553.267	−0.221670
$185$	−558.050	−0.221777
$186$	−5316.04	−2.09565
$187$	799.354	0.312591
$188$	119.916	0.0465199
$189$	8176.15	3.14671
$190$	395.591	0.151048
$191$	−1163.79	−0.440884	−0.220442	−	0.975400i	$-0.570750\pi$
$191$	−1163.79	−0.440884	−0.220442	+	0.975400i	$0.570750\pi$
$192$	−5205.34	−1.95658
$193$	−1302.00	−0.485597	−0.242799	−	0.970077i	$-0.578065\pi$
$193$	−1302.00	−0.485597	−0.242799	+	0.970077i	$0.578065\pi$
$194$	−1903.47	−0.704441
$195$	−1840.91	−0.676051
$196$	−631.431	−0.230113
$197$	2176.39	0.787112	0.393556	−	0.919301i	$-0.371245\pi$
$197$	2176.39	0.787112	0.393556	+	0.919301i	$0.371245\pi$
$198$	6762.46	2.42721
$199$	−1755.73	−0.625430	−0.312715	−	0.949847i	$-0.601239\pi$
$199$	−1755.73	−0.625430	−0.312715	+	0.949847i	$0.601239\pi$
$200$	−2587.23	−0.914724
$201$	−3651.31	−1.28131
$202$	−1107.76	−0.385849
$203$	838.996	0.290079
$204$	−208.047	−0.0714028
$205$	−1010.01	−0.344109
$206$	−2133.70	−0.721659
$207$	−1327.25	−0.445653
$208$	−2496.93	−0.832360
$209$	1651.20	0.546488
$210$	−2883.40	−0.947493
$211$	−3274.04	−1.06822	−0.534109	−	0.845416i	$-0.679353\pi$
$211$	−3274.04	−1.06822	−0.534109	+	0.845416i	$0.679353\pi$
$212$	878.536	0.284614
$213$	3770.69	1.21297
$214$	−4428.07	−1.41447
$215$	−1905.82	−0.604537
$216$	−6798.20	−2.14148
$217$	6445.40	2.01632
$218$	3930.15	1.22103
$219$	3088.33	0.952923
$220$	241.314	0.0739518
$221$	−846.899	−0.257776
$222$	−3188.10	−0.963833
$223$	2421.38	0.727120	0.363560	−	0.931571i	$-0.381561\pi$
$223$	2421.38	0.727120	0.363560	+	0.931571i	$0.381561\pi$
$224$	1656.55	0.494120
$225$	−6206.58	−1.83899
$226$	−3536.30	−1.04085
$227$	−398.715	−0.116580	−0.0582900	−	0.998300i	$-0.518565\pi$
$227$	−398.715	−0.116580	−0.0582900	+	0.998300i	$0.518565\pi$
$228$	−429.756	−0.124830
$229$	−6532.33	−1.88502	−0.942508	−	0.334183i	$-0.891540\pi$
$229$	−6532.33	−1.88502	−0.942508	+	0.334183i	$0.891540\pi$
$230$	249.065	0.0714038
$231$	−12035.3	−3.42800
$232$	−697.597	−0.197412
$233$	384.826	0.108201	0.0541004	−	0.998536i	$-0.482771\pi$
$233$	384.826	0.108201	0.0541004	+	0.998536i	$0.482771\pi$
$234$	−7164.69	−2.00158
$235$	−391.847	−0.108771
$236$	519.775	0.143366
$237$	−1356.07	−0.371671
$238$	−1326.49	−0.361276
$239$	−4519.34	−1.22315	−0.611573	−	0.791188i	$-0.709463\pi$
$239$	−4519.34	−1.22315	−0.611573	+	0.791188i	$0.709463\pi$
$240$	2004.36	0.539087
$241$	152.215	0.0406848	0.0203424	−	0.999793i	$-0.493524\pi$
$241$	152.215	0.0406848	0.0203424	+	0.999793i	$0.493524\pi$
$242$	−1846.06	−0.490369
$243$	−1968.50	−0.519669
$244$	−311.234	−0.0816586
$245$	2063.32	0.538043
$246$	−5770.13	−1.49549
$247$	−1749.41	−0.450658
$248$	−5359.13	−1.37220
$249$	6410.46	1.63151
$250$	2518.31	0.637088
$251$	1369.37	0.344359	0.172179	−	0.985066i	$-0.444919\pi$
$251$	1369.37	0.344359	0.172179	+	0.985066i	$0.444919\pi$
$252$	2133.97	0.533442
$253$	1039.60	0.258336
$254$	−3815.22	−0.942474
$255$	679.832	0.166952
$256$	−1910.54	−0.466440
$257$	6127.63	1.48728	0.743640	−	0.668580i	$-0.233097\pi$
$257$	6127.63	1.48728	0.743640	+	0.668580i	$0.233097\pi$
$258$	−10887.8	−2.62730
$259$	3865.38	0.927348
$260$	−255.667	−0.0609839
$261$	−1673.49	−0.396882
$262$	3711.32	0.875137
$263$	4478.46	1.05001	0.525007	−	0.851098i	$-0.324063\pi$
$263$	4478.46	1.05001	0.525007	+	0.851098i	$0.324063\pi$
$264$	10007.0	2.33291
$265$	−2870.78	−0.665474
$266$	−2740.10	−0.631602
$267$	13261.3	3.03961
$268$	−507.099	−0.115582
$269$	2734.91	0.619891	0.309946	−	0.950754i	$-0.399689\pi$
$269$	2734.91	0.619891	0.309946	+	0.950754i	$0.399689\pi$
$270$	3060.36	0.689805
$271$	−2153.19	−0.482646	−0.241323	−	0.970445i	$-0.577581\pi$
$271$	−2153.19	−0.482646	−0.241323	+	0.970445i	$0.577581\pi$
$272$	922.096	0.205552
$273$	12751.2	2.82688
$274$	4775.94	1.05301
$275$	4861.46	1.06603
$276$	−270.575	−0.0590098
$277$	−2917.31	−0.632795	−0.316397	−	0.948627i	$-0.602473\pi$
$277$	−2917.31	−0.632795	−0.316397	+	0.948627i	$0.602473\pi$
$278$	3938.86	0.849775
$279$	−12856.2	−2.75871
$280$	−2906.77	−0.620403
$281$	6339.09	1.34576	0.672879	−	0.739752i	$-0.265057\pi$
$281$	6339.09	1.34576	0.672879	+	0.739752i	$0.265057\pi$
$282$	−2238.59	−0.472716
$283$	5355.83	1.12499	0.562493	−	0.826802i	$-0.309843\pi$
$283$	5355.83	1.12499	0.562493	+	0.826802i	$0.309843\pi$
$284$	523.678	0.109418
$285$	1404.31	0.291874
$286$	5611.92	1.16028
$287$	6995.95	1.43888
$288$	−3304.21	−0.676049
$289$	−4600.25	−0.936342
$290$	314.039	0.0635896
$291$	−6757.14	−1.36120
$292$	428.912	0.0859594
$293$	8396.96	1.67425	0.837126	−	0.547010i	$-0.184234\pi$
$293$	8396.96	1.67425	0.837126	+	0.547010i	$0.184234\pi$
$294$	11787.6	2.33832
$295$	−1698.46	−0.335214
$296$	−3213.94	−0.631102
$297$	12774.0	2.49569
$298$	−3552.57	−0.690587
$299$	−1101.43	−0.213035
$300$	−1265.28	−0.243504
$301$	13200.8	2.52784
$302$	−2872.47	−0.547326
$303$	−3932.43	−0.745584
$304$	1904.75	0.359357
$305$	1017.02	0.190932
$306$	2645.86	0.494294
$307$	−1686.82	−0.313590	−0.156795	−	0.987631i	$-0.550116\pi$
$307$	−1686.82	−0.313590	−0.156795	+	0.987631i	$0.550116\pi$
$308$	−1671.48	−0.309226
$309$	−7574.41	−1.39448
$310$	2412.53	0.442008
$311$	−10055.1	−1.83336	−0.916678	−	0.399626i	$-0.869140\pi$
$311$	−10055.1	−1.83336	−0.916678	+	0.399626i	$0.869140\pi$
$312$	−10602.2	−1.92382
$313$	665.817	0.120237	0.0601185	−	0.998191i	$-0.480852\pi$
$313$	665.817	0.120237	0.0601185	+	0.998191i	$0.480852\pi$
$314$	−771.564	−0.138668
$315$	−6973.14	−1.24728
$316$	−188.332	−0.0335269
$317$	2410.82	0.427146	0.213573	−	0.976927i	$-0.431490\pi$
$317$	2410.82	0.427146	0.213573	+	0.976927i	$0.431490\pi$
$318$	−16400.5	−2.89213
$319$	1310.80	0.230065
$320$	2362.29	0.412675
$321$	−15719.2	−2.73321
$322$	−1725.17	−0.298571
$323$	646.045	0.111291
$324$	−1333.12	−0.228587
$325$	−5150.62	−0.879092
$326$	6683.94	1.13555
$327$	13951.6	2.35941
$328$	−5816.90	−0.979221
$329$	2714.16	0.454822
$330$	−4504.86	−0.751468
$331$	2258.11	0.374975	0.187488	−	0.982267i	$-0.439966\pi$
$331$	2258.11	0.374975	0.187488	+	0.982267i	$0.439966\pi$
$332$	890.293	0.147172
$333$	−7710.01	−1.26879
$334$	7108.89	1.16461
$335$	1657.04	0.270250
$336$	−13883.4	−2.25417
$337$	1659.82	0.268297	0.134148	−	0.990961i	$-0.457170\pi$
$337$	1659.82	0.268297	0.134148	+	0.990961i	$0.457170\pi$
$338$	−249.684	−0.0401806
$339$	−12553.5	−2.01125
$340$	94.4159	0.0150601
$341$	10069.9	1.59917
$342$	5465.48	0.864150
$343$	−4368.46	−0.687681
$344$	−10976.0	−1.72031
$345$	884.155	0.137975
$346$	8444.00	1.31200
$347$	11800.1	1.82553	0.912767	−	0.408482i	$-0.133942\pi$
$347$	11800.1	1.82553	0.912767	+	0.408482i	$0.133942\pi$
$348$	−341.160	−0.0525520
$349$	6872.90	1.05415	0.527075	−	0.849819i	$-0.323289\pi$
$349$	6872.90	1.05415	0.527075	+	0.849819i	$0.323289\pi$
$350$	−8067.38	−1.23206
$351$	−13533.8	−2.05806
$352$	2588.10	0.391893
$353$	−1791.27	−0.270084	−0.135042	−	0.990840i	$-0.543117\pi$
$353$	−1791.27	−0.270084	−0.135042	+	0.990840i	$0.543117\pi$
$354$	−9703.17	−1.45683
$355$	−1711.22	−0.255837
$356$	1841.74	0.274191
$357$	−4708.91	−0.698101
$358$	−8912.91	−1.31582
$359$	−10790.3	−1.58632	−0.793160	−	0.609013i	$-0.791566\pi$
$359$	−10790.3	−1.58632	−0.793160	+	0.609013i	$0.791566\pi$
$360$	5797.93	0.848828
$361$	−5524.48	−0.805436
$362$	6559.48	0.952372
$363$	−6553.33	−0.947550
$364$	1770.90	0.255001
$365$	−1401.55	−0.200988
$366$	5810.13	0.829782
$367$	243.576	0.0346446	0.0173223	−	0.999850i	$-0.494486\pi$
$367$	243.576	0.0346446	0.0173223	+	0.999850i	$0.494486\pi$
$368$	1199.23	0.169876
$369$	−13954.3	−1.96865
$370$	1446.82	0.203289
$371$	19884.7	2.78265
$372$	−2620.88	−0.365286
$373$	−4007.44	−0.556293	−0.278147	−	0.960539i	$-0.589720\pi$
$373$	−4007.44	−0.556293	−0.278147	+	0.960539i	$0.589720\pi$
$374$	−2072.44	−0.286533
$375$	8939.75	1.23106
$376$	−2256.73	−0.309527
$377$	−1388.77	−0.189722
$378$	−21197.8	−2.88439
$379$	−7833.43	−1.06168	−0.530839	−	0.847472i	$-0.678123\pi$
$379$	−7833.43	−1.06168	−0.530839	+	0.847472i	$0.678123\pi$
$380$	195.032	0.0263288
$381$	−13543.6	−1.82116
$382$	3017.29	0.404131
$383$	13784.7	1.83907	0.919536	−	0.393006i	$-0.128565\pi$
$383$	13784.7	1.83907	0.919536	+	0.393006i	$0.128565\pi$
$384$	9279.67	1.23321
$385$	5461.89	0.723022
$386$	3375.63	0.445117
$387$	−26330.7	−3.45857
$388$	−938.440	−0.122789
$389$	−5577.24	−0.726934	−0.363467	−	0.931607i	$-0.618407\pi$
$389$	−5577.24	−0.726934	−0.363467	+	0.931607i	$0.618407\pi$
$390$	4772.81	0.619694
$391$	406.751	0.0526094
$392$	11883.1	1.53109
$393$	13174.8	1.69104
$394$	−5642.59	−0.721496
$395$	615.411	0.0783916
$396$	3333.99	0.423079
$397$	−8098.82	−1.02385	−0.511925	−	0.859030i	$-0.671067\pi$
$397$	−8098.82	−1.02385	−0.511925	+	0.859030i	$0.671067\pi$
$398$	4551.99	0.573293
$399$	−9727.06	−1.22046
$400$	5607.94	0.700993
$401$	1905.19	0.237259	0.118629	−	0.992939i	$-0.462150\pi$
$401$	1905.19	0.237259	0.118629	+	0.992939i	$0.462150\pi$
$402$	9466.55	1.17450
$403$	−10668.9	−1.31875
$404$	−546.140	−0.0672562
$405$	4356.21	0.534474
$406$	−2175.22	−0.265897
$407$	6039.06	0.735491
$408$	3915.30	0.475089
$409$	−13103.6	−1.58418	−0.792091	−	0.610403i	$-0.791008\pi$
$409$	−13103.6	−1.58418	−0.792091	+	0.610403i	$0.791008\pi$
$410$	2618.60	0.315423
$411$	16954.1	2.03475
$412$	−1051.94	−0.125790
$413$	11764.5	1.40168
$414$	3441.08	0.408502
$415$	−2909.20	−0.344113
$416$	−2742.04	−0.323172
$417$	13982.6	1.64204
$418$	−4280.97	−0.500931
$419$	−2467.95	−0.287750	−0.143875	−	0.989596i	$-0.545956\pi$
$419$	−2467.95	−0.287750	−0.143875	+	0.989596i	$0.545956\pi$
$420$	−1421.56	−0.165154
$421$	−10665.1	−1.23464	−0.617321	−	0.786711i	$-0.711782\pi$
$421$	−10665.1	−1.23464	−0.617321	+	0.786711i	$0.711782\pi$
$422$	8488.41	0.979169
$423$	−5413.74	−0.622282
$424$	−16533.5	−1.89372
$425$	1902.08	0.217093
$426$	−9776.05	−1.11186
$427$	−7044.45	−0.798371
$428$	−2183.10	−0.246552
$429$	19921.7	2.24203
$430$	4941.10	0.554141
$431$	−7566.67	−0.845647	−0.422823	−	0.906212i	$-0.638961\pi$
$431$	−7566.67	−0.845647	−0.422823	+	0.906212i	$0.638961\pi$
$432$	14735.4	1.64111
$433$	976.857	0.108417	0.0542087	−	0.998530i	$-0.482736\pi$
$433$	976.857	0.108417	0.0542087	+	0.998530i	$0.482736\pi$
$434$	−16710.6	−1.84824
$435$	1114.80	0.122875
$436$	1937.62	0.212833
$437$	840.213	0.0919745
$438$	−8006.94	−0.873485
$439$	18316.5	1.99134	0.995670	−	0.0929599i	$-0.0296328\pi$
$439$	18316.5	1.99134	0.995670	+	0.0929599i	$0.0296328\pi$
$440$	−4541.38	−0.492049
$441$	28506.8	3.07815
$442$	2195.71	0.236288
$443$	14478.6	1.55281	0.776407	−	0.630231i	$-0.217040\pi$
$443$	14478.6	1.55281	0.776407	+	0.630231i	$0.217040\pi$
$444$	−1571.78	−0.168003
$445$	−6018.24	−0.641106
$446$	−6277.78	−0.666505
$447$	−12611.3	−1.33443
$448$	−16362.6	−1.72558
$449$	−11523.2	−1.21116	−0.605581	−	0.795784i	$-0.707059\pi$
$449$	−11523.2	−1.21116	−0.605581	+	0.795784i	$0.707059\pi$
$450$	16091.4	1.68568
$451$	10930.1	1.14119
$452$	−1743.45	−0.181427
$453$	−10197.0	−1.05761
$454$	1033.73	0.106862
$455$	−5786.76	−0.596236
$456$	8087.73	0.830576
$457$	15277.9	1.56383	0.781915	−	0.623385i	$-0.214243\pi$
$457$	15277.9	1.56383	0.781915	+	0.623385i	$0.214243\pi$
$458$	16936.0	1.72788
$459$	4997.91	0.508240
$460$	122.793	0.0124462
$461$	7675.19	0.775421	0.387711	−	0.921781i	$-0.373266\pi$
$461$	7675.19	0.775421	0.387711	+	0.921781i	$0.373266\pi$
$462$	31203.3	3.14223
$463$	2297.71	0.230635	0.115317	−	0.993329i	$-0.463212\pi$
$463$	2297.71	0.230635	0.115317	+	0.993329i	$0.463212\pi$
$464$	1512.07	0.151285
$465$	8564.23	0.854101
$466$	−997.715	−0.0991808
$467$	2825.49	0.279974	0.139987	−	0.990153i	$-0.455294\pi$
$467$	2825.49	0.279974	0.139987	+	0.990153i	$0.455294\pi$
$468$	−3532.29	−0.348890
$469$	−11477.6	−1.13004
$470$	1015.92	0.0997038
$471$	−2738.97	−0.267951
$472$	−9781.82	−0.953909
$473$	20624.2	2.00486
$474$	3515.79	0.340687
$475$	3929.07	0.379533
$476$	−653.980	−0.0629729
$477$	−39662.6	−3.80719
$478$	11717.0	1.12118
$479$	15137.0	1.44390	0.721949	−	0.691947i	$-0.243247\pi$
$479$	15137.0	1.44390	0.721949	+	0.691947i	$0.243247\pi$
$480$	2201.12	0.209306
$481$	−6398.26	−0.606518
$482$	−394.639	−0.0372932
$483$	−6124.18	−0.576935
$484$	−910.135	−0.0854747
$485$	3066.53	0.287101
$486$	5103.63	0.476348
$487$	1608.39	0.149657	0.0748285	−	0.997196i	$-0.476159\pi$
$487$	1608.39	0.149657	0.0748285	+	0.997196i	$0.476159\pi$
$488$	5857.22	0.543328
$489$	23727.3	2.19424
$490$	−5349.45	−0.493190
$491$	12990.3	1.19398	0.596988	−	0.802250i	$-0.296364\pi$
$491$	12990.3	1.19398	0.596988	+	0.802250i	$0.296364\pi$
$492$	−2844.75	−0.260674
$493$	512.860	0.0468520
$494$	4535.60	0.413090
$495$	−10894.4	−0.989230
$496$	11616.2	1.05158
$497$	11852.9	1.06977
$498$	−16620.0	−1.49551
$499$	9983.56	0.895643	0.447821	−	0.894123i	$-0.352200\pi$
$499$	9983.56	0.895643	0.447821	+	0.894123i	$0.352200\pi$
$500$	1241.56	0.111049
$501$	25235.8	2.25041
$502$	−3550.29	−0.315652
$503$	−6070.70	−0.538130	−0.269065	−	0.963122i	$-0.586715\pi$
$503$	−6070.70	−0.538130	−0.269065	+	0.963122i	$0.586715\pi$
$504$	−40159.9	−3.54933
$505$	1784.62	0.157256
$506$	−2695.31	−0.236801
$507$	−886.353	−0.0776417
$508$	−1880.96	−0.164280
$509$	15148.5	1.31915	0.659575	−	0.751639i	$-0.270736\pi$
$509$	15148.5	1.31915	0.659575	+	0.751639i	$0.270736\pi$
$510$	−1762.56	−0.153034
$511$	9707.96	0.840420
$512$	13019.5	1.12380
$513$	10324.0	0.888532
$514$	−15886.8	−1.36330
$515$	3437.42	0.294118
$516$	−5367.82	−0.457956
$517$	4240.45	0.360725
$518$	−10021.6	−0.850042
$519$	29975.3	2.53520
$520$	4811.49	0.405765
$521$	−9143.90	−0.768909	−0.384454	−	0.923144i	$-0.625610\pi$
$521$	−9143.90	−0.768909	−0.384454	+	0.923144i	$0.625610\pi$
$522$	4338.75	0.363797
$523$	21064.6	1.76117	0.880585	−	0.473888i	$-0.157150\pi$
$523$	21064.6	1.76117	0.880585	+	0.473888i	$0.157150\pi$
$524$	1829.73	0.152542
$525$	−28638.4	−2.38073
$526$	−11611.0	−0.962482
$527$	3939.93	0.325666
$528$	−21690.6	−1.78781
$529$	529.000	0.0434783
$530$	7442.91	0.609998
$531$	−23465.9	−1.91777
$532$	−1350.91	−0.110093
$533$	−11580.2	−0.941076
$534$	−34381.7	−2.78622
$535$	7133.69	0.576479
$536$	9543.28	0.769043
$537$	−31639.9	−2.54258
$538$	−7090.65	−0.568215
$539$	−22328.6	−1.78435
$540$	1508.80	0.120238
$541$	−12935.2	−1.02797	−0.513983	−	0.857800i	$-0.671831\pi$
$541$	−12935.2	−1.02797	−0.513983	+	0.857800i	$0.671831\pi$
$542$	5582.45	0.442411
$543$	23285.5	1.84029
$544$	1012.61	0.0798078
$545$	−6331.54	−0.497639
$546$	−33059.3	−2.59122
$547$	−15823.7	−1.23688	−0.618441	−	0.785831i	$-0.712235\pi$
$547$	−15823.7	−1.23688	−0.618441	+	0.785831i	$0.712235\pi$
$548$	2354.61	0.183547
$549$	14051.1	1.09232
$550$	−12604.0	−0.977159
$551$	1059.40	0.0819091
$552$	5092.05	0.392630
$553$	−4262.70	−0.327791
$554$	7563.54	0.580043
$555$	5136.08	0.392818
$556$	1941.92	0.148121
$557$	9494.77	0.722273	0.361137	−	0.932513i	$-0.382389\pi$
$557$	9494.77	0.722273	0.361137	+	0.932513i	$0.382389\pi$
$558$	33331.5	2.52873
$559$	−21850.9	−1.65330
$560$	6300.57	0.475442
$561$	−7356.94	−0.553673
$562$	−16435.0	−1.23357
$563$	7510.03	0.562185	0.281092	−	0.959681i	$-0.409303\pi$
$563$	7510.03	0.562185	0.281092	+	0.959681i	$0.409303\pi$
$564$	−1103.66	−0.0823977
$565$	5697.04	0.424206
$566$	−13885.7	−1.03120
$567$	−30173.7	−2.23488
$568$	−9855.29	−0.728026
$569$	1201.36	0.0885125	0.0442563	−	0.999020i	$-0.485908\pi$
$569$	1201.36	0.0885125	0.0442563	+	0.999020i	$0.485908\pi$
$570$	−3640.87	−0.267542
$571$	7503.60	0.549940	0.274970	−	0.961453i	$-0.411332\pi$
$571$	7503.60	0.549940	0.274970	+	0.961453i	$0.411332\pi$
$572$	2766.76	0.202245
$573$	10711.1	0.780910
$574$	−18138.0	−1.31893
$575$	2473.75	0.179413
$576$	32637.4	2.36092
$577$	−25201.7	−1.81830	−0.909152	−	0.416465i	$-0.863269\pi$
$577$	−25201.7	−1.81830	−0.909152	+	0.416465i	$0.863269\pi$
$578$	11926.8	0.858286
$579$	11983.1	0.860107
$580$	154.825	0.0110841
$581$	20150.8	1.43889
$582$	17518.8	1.24773
$583$	31066.8	2.20695
$584$	−8071.84	−0.571944
$585$	11542.4	0.815762
$586$	−21770.3	−1.53468
$587$	−16521.6	−1.16171	−0.580853	−	0.814009i	$-0.697281\pi$
$587$	−16521.6	−1.16171	−0.580853	+	0.814009i	$0.697281\pi$
$588$	5811.44	0.407585
$589$	8138.60	0.569347
$590$	4403.50	0.307270
$591$	−20030.6	−1.39416
$592$	6966.36	0.483641
$593$	−3736.57	−0.258756	−0.129378	−	0.991595i	$-0.541298\pi$
$593$	−3736.57	−0.258756	−0.129378	+	0.991595i	$0.541298\pi$
$594$	−33118.3	−2.28764
$595$	2137.00	0.147241
$596$	−1751.47	−0.120374
$597$	16159.1	1.10778
$598$	2855.63	0.195276
$599$	22042.0	1.50353	0.751764	−	0.659433i	$-0.229203\pi$
$599$	22042.0	1.50353	0.751764	+	0.659433i	$0.229203\pi$
$600$	23811.9	1.62019
$601$	−6226.17	−0.422580	−0.211290	−	0.977423i	$-0.567766\pi$
$601$	−6226.17	−0.422580	−0.211290	+	0.977423i	$0.567766\pi$
$602$	−34224.9	−2.31712
$603$	22893.7	1.54611
$604$	−1416.17	−0.0954026
$605$	2974.04	0.199854
$606$	10195.4	0.683430
$607$	−9479.25	−0.633857	−0.316928	−	0.948449i	$-0.602651\pi$
$607$	−9479.25	−0.633857	−0.316928	+	0.948449i	$0.602651\pi$
$608$	2091.73	0.139524
$609$	−7721.79	−0.513798
$610$	−2636.76	−0.175015
$611$	−4492.67	−0.297470
$612$	1304.45	0.0861588
$613$	−12787.4	−0.842540	−0.421270	−	0.906935i	$-0.638416\pi$
$613$	−12787.4	−0.842540	−0.421270	+	0.906935i	$0.638416\pi$
$614$	4373.33	0.287448
$615$	9295.77	0.609499
$616$	31456.2	2.05748
$617$	−4874.19	−0.318035	−0.159017	−	0.987276i	$-0.550833\pi$
$617$	−4874.19	−0.318035	−0.159017	+	0.987276i	$0.550833\pi$
$618$	19637.7	1.27823
$619$	−4364.10	−0.283373	−0.141687	−	0.989912i	$-0.545253\pi$
$619$	−4364.10	−0.283373	−0.141687	+	0.989912i	$0.545253\pi$
$620$	1189.41	0.0770450
$621$	6500.03	0.420027
$622$	26069.3	1.68052
$623$	41685.9	2.68075
$624$	22980.8	1.47431
$625$	9387.26	0.600785
$626$	−1726.22	−0.110214
$627$	−15197.0	−0.967959
$628$	−380.392	−0.0241708
$629$	2362.82	0.149781
$630$	18078.9	1.14330
$631$	23963.8	1.51186	0.755929	−	0.654654i	$-0.227186\pi$
$631$	23963.8	1.51186	0.755929	+	0.654654i	$0.227186\pi$
$632$	3544.29	0.223077
$633$	30133.0	1.89207
$634$	−6250.40	−0.391538
$635$	6146.39	0.384113
$636$	−8085.70	−0.504118
$637$	23656.7	1.47145
$638$	−3398.43	−0.210886
$639$	−23642.2	−1.46364
$640$	−4211.31	−0.260104
$641$	14233.7	0.877061	0.438530	−	0.898716i	$-0.355499\pi$
$641$	14233.7	0.877061	0.438530	+	0.898716i	$0.355499\pi$
$642$	40754.2	2.50536
$643$	2348.18	0.144017	0.0720085	−	0.997404i	$-0.477059\pi$
$643$	2348.18	0.144017	0.0720085	+	0.997404i	$0.477059\pi$
$644$	−850.534	−0.0520430
$645$	17540.4	1.07078
$646$	−1674.96	−0.102013
$647$	−27529.9	−1.67281	−0.836407	−	0.548108i	$-0.815348\pi$
$647$	−27529.9	−1.67281	−0.836407	+	0.548108i	$0.815348\pi$
$648$	25088.4	1.52093
$649$	18380.3	1.11169
$650$	13353.7	0.805808
$651$	−59320.9	−3.57138
$652$	3295.28	0.197934
$653$	−22577.3	−1.35302	−0.676508	−	0.736435i	$-0.736508\pi$
$653$	−22577.3	−1.35302	−0.676508	+	0.736435i	$0.736508\pi$
$654$	−36171.6	−2.16272
$655$	−5978.99	−0.356670
$656$	12608.4	0.750420
$657$	−19363.8	−1.14985
$658$	−7036.84	−0.416907
$659$	−8486.96	−0.501677	−0.250838	−	0.968029i	$-0.580706\pi$
$659$	−8486.96	−0.501677	−0.250838	+	0.968029i	$0.580706\pi$
$660$	−2220.96	−0.130986
$661$	22458.4	1.32153	0.660764	−	0.750594i	$-0.270233\pi$
$661$	22458.4	1.32153	0.660764	+	0.750594i	$0.270233\pi$
$662$	−5854.47	−0.343716
$663$	7794.53	0.456583
$664$	−16754.8	−0.979233
$665$	4414.34	0.257415
$666$	19989.3	1.16302
$667$	667.000	0.0387202
$668$	3504.78	0.203000
$669$	−22285.5	−1.28790
$670$	−4296.12	−0.247722
$671$	−11005.8	−0.633198
$672$	−15246.2	−0.875204
$673$	5000.95	0.286438	0.143219	−	0.989691i	$-0.454255\pi$
$673$	5000.95	0.286438	0.143219	+	0.989691i	$0.454255\pi$
$674$	−4303.31	−0.245931
$675$	30395.9	1.73325
$676$	−123.098	−0.00700375
$677$	15531.7	0.881729	0.440865	−	0.897574i	$-0.354672\pi$
$677$	15531.7	0.881729	0.440865	+	0.897574i	$0.354672\pi$
$678$	32546.8	1.84359
$679$	−21240.6	−1.20050
$680$	−1776.85	−0.100204
$681$	3669.62	0.206491
$682$	−26107.7	−1.46586
$683$	−8743.09	−0.489817	−0.244909	−	0.969546i	$-0.578758\pi$
$683$	−8743.09	−0.489817	−0.244909	+	0.969546i	$0.578758\pi$
$684$	2694.56	0.150627
$685$	−7694.12	−0.429164
$686$	11325.9	0.630354
$687$	60121.0	3.33881
$688$	23791.1	1.31835
$689$	−32914.6	−1.81995
$690$	−2292.30	−0.126473
$691$	7524.53	0.414250	0.207125	−	0.978314i	$-0.433589\pi$
$691$	7524.53	0.414250	0.207125	+	0.978314i	$0.433589\pi$
$692$	4163.01	0.228691
$693$	75461.3	4.13642
$694$	−30593.3	−1.67335
$695$	−6345.57	−0.346333
$696$	6420.41	0.349662
$697$	4276.47	0.232400
$698$	−17819.0	−0.966272
$699$	−3541.78	−0.191649
$700$	−3977.33	−0.214756
$701$	20319.5	1.09480	0.547402	−	0.836870i	$-0.315617\pi$
$701$	20319.5	1.09480	0.547402	+	0.836870i	$0.315617\pi$
$702$	35088.2	1.88649
$703$	4880.82	0.261854
$704$	−25564.0	−1.36858
$705$	3606.40	0.192660
$706$	4644.12	0.247569
$707$	−12361.3	−0.657560
$708$	−4783.80	−0.253935
$709$	−18129.2	−0.960307	−0.480153	−	0.877185i	$-0.659419\pi$
$709$	−18129.2	−0.960307	−0.480153	+	0.877185i	$0.659419\pi$
$710$	4436.58	0.234509
$711$	8502.51	0.448479
$712$	−34660.4	−1.82437
$713$	5124.08	0.269142
$714$	12208.5	0.639906
$715$	−9040.90	−0.472882
$716$	−4394.19	−0.229356
$717$	41594.2	2.16648
$718$	27975.3	1.45408
$719$	−11942.0	−0.619416	−0.309708	−	0.950832i	$-0.600231\pi$
$719$	−11942.0	−0.619416	−0.309708	+	0.950832i	$0.600231\pi$
$720$	−12567.3	−0.650494
$721$	−23809.6	−1.22984
$722$	14323.0	0.738293
$723$	−1400.93	−0.0720623
$724$	3233.92	0.166005
$725$	3119.08	0.159779
$726$	16990.4	0.868560
$727$	−31074.9	−1.58529	−0.792643	−	0.609686i	$-0.791296\pi$
$727$	−31074.9	−1.58529	−0.792643	+	0.609686i	$0.791296\pi$
$728$	−33327.2	−1.69669
$729$	−10042.5	−0.510212
$730$	3633.72	0.184233
$731$	8069.36	0.408285
$732$	2864.47	0.144637
$733$	−20025.6	−1.00909	−0.504545	−	0.863386i	$-0.668340\pi$
$733$	−20025.6	−1.00909	−0.504545	+	0.863386i	$0.668340\pi$
$734$	−631.505	−0.0317565
$735$	−18990.0	−0.953001
$736$	1316.95	0.0659560
$737$	−17932.0	−0.896248
$738$	36178.6	1.80454
$739$	−35864.5	−1.78525	−0.892624	−	0.450803i	$-0.851138\pi$
$739$	−35864.5	−1.78525	−0.892624	+	0.450803i	$0.851138\pi$
$740$	713.305	0.0354346
$741$	16100.9	0.798222
$742$	−51553.9	−2.55068
$743$	−5864.73	−0.289578	−0.144789	−	0.989463i	$-0.546250\pi$
$743$	−5864.73	−0.289578	−0.144789	+	0.989463i	$0.546250\pi$
$744$	49323.4	2.43049
$745$	5723.25	0.281455
$746$	10389.9	0.509919
$747$	−40193.5	−1.96868
$748$	−1021.74	−0.0499446
$749$	−49412.1	−2.41052
$750$	−23177.6	−1.12843
$751$	10618.2	0.515930	0.257965	−	0.966154i	$-0.416948\pi$
$751$	10618.2	0.515930	0.257965	+	0.966154i	$0.416948\pi$
$752$	4891.58	0.237204
$753$	−12603.2	−0.609940
$754$	3600.57	0.173906
$755$	4627.60	0.223067
$756$	−10450.8	−0.502769
$757$	32966.9	1.58283	0.791416	−	0.611279i	$-0.209344\pi$
$757$	32966.9	1.58283	0.791416	+	0.611279i	$0.209344\pi$
$758$	20309.3	0.973174
$759$	−9568.07	−0.457574
$760$	−3670.38	−0.175182
$761$	−33647.2	−1.60277	−0.801386	−	0.598147i	$-0.795904\pi$
$761$	−33647.2	−1.60277	−0.801386	+	0.598147i	$0.795904\pi$
$762$	35113.8	1.66934
$763$	43856.0	2.08086
$764$	1487.57	0.0704428
$765$	−4262.53	−0.201454
$766$	−35738.8	−1.68576
$767$	−19473.5	−0.916750
$768$	17583.9	0.826175
$769$	26031.9	1.22072	0.610361	−	0.792123i	$-0.291024\pi$
$769$	26031.9	1.22072	0.610361	+	0.792123i	$0.291024\pi$
$770$	−14160.7	−0.662749
$771$	−56396.3	−2.63432
$772$	1664.23	0.0775869
$773$	−20324.4	−0.945688	−0.472844	−	0.881146i	$-0.656773\pi$
$773$	−20324.4	−0.945688	−0.472844	+	0.881146i	$0.656773\pi$
$774$	68266.1	3.17025
$775$	23961.6	1.11062
$776$	17660.8	0.816994
$777$	−35575.5	−1.64255
$778$	14459.8	0.666334
$779$	8833.78	0.406294
$780$	2353.06	0.108017
$781$	18518.3	0.848447
$782$	−1054.56	−0.0482237
$783$	8195.69	0.374061
$784$	−25757.2	−1.17334
$785$	1243.00	0.0565154
$786$	−34157.5	−1.55007
$787$	4362.32	0.197586	0.0987929	−	0.995108i	$-0.468502\pi$
$787$	4362.32	0.197586	0.0987929	+	0.995108i	$0.468502\pi$
$788$	−2781.88	−0.125762
$789$	−41218.0	−1.85982
$790$	−1595.54	−0.0718567
$791$	−39461.1	−1.77380
$792$	−62743.6	−2.81502
$793$	11660.5	0.522163
$794$	20997.3	0.938498
$795$	26421.5	1.17871
$796$	2244.19	0.0999288
$797$	−6523.13	−0.289914	−0.144957	−	0.989438i	$-0.546304\pi$
$797$	−6523.13	−0.289914	−0.144957	+	0.989438i	$0.546304\pi$
$798$	25218.8	1.11872
$799$	1659.11	0.0734605
$800$	6158.45	0.272168
$801$	−83147.9	−3.66777
$802$	−4939.48	−0.217480
$803$	15167.2	0.666547
$804$	4667.14	0.204723
$805$	2779.28	0.121685
$806$	27660.6	1.20881
$807$	−25171.1	−1.09797
$808$	10278.0	0.447499
$809$	−40247.0	−1.74908	−0.874541	−	0.484951i	$-0.838837\pi$
$809$	−40247.0	−1.74908	−0.874541	+	0.484951i	$0.838837\pi$
$810$	−11294.1	−0.489919
$811$	37329.4	1.61629	0.808147	−	0.588981i	$-0.200471\pi$
$811$	37329.4	1.61629	0.808147	+	0.588981i	$0.200471\pi$
$812$	−1072.41	−0.0463476
$813$	19817.1	0.854879
$814$	−15657.1	−0.674179
$815$	−10767.9	−0.462803
$816$	−8486.61	−0.364082
$817$	16668.6	0.713784
$818$	33972.9	1.45212
$819$	−79949.7	−3.41107
$820$	1291.01	0.0549805
$821$	−30309.4	−1.28844	−0.644218	−	0.764842i	$-0.722817\pi$
$821$	−30309.4	−1.28844	−0.644218	+	0.764842i	$0.722817\pi$
$822$	−43955.9	−1.86513
$823$	16482.9	0.698128	0.349064	−	0.937099i	$-0.386500\pi$
$823$	16482.9	0.698128	0.349064	+	0.937099i	$0.386500\pi$
$824$	19796.9	0.836963
$825$	−44743.0	−1.88818
$826$	−30501.2	−1.28484
$827$	−33755.9	−1.41935	−0.709677	−	0.704527i	$-0.751159\pi$
$827$	−33755.9	−1.41935	−0.709677	+	0.704527i	$0.751159\pi$
$828$	1696.50	0.0712046
$829$	16862.0	0.706444	0.353222	−	0.935540i	$-0.385086\pi$
$829$	16862.0	0.706444	0.353222	+	0.935540i	$0.385086\pi$
$830$	7542.52	0.315427
$831$	26849.8	1.12083
$832$	27084.6	1.12859
$833$	−8736.24	−0.363377
$834$	−36251.8	−1.50515
$835$	−11452.5	−0.474648
$836$	−2110.58	−0.0873157
$837$	62961.5	2.60008
$838$	6398.50	0.263762
$839$	31071.1	1.27854	0.639269	−	0.768983i	$-0.279237\pi$
$839$	31071.1	1.27854	0.639269	+	0.768983i	$0.279237\pi$
$840$	26752.8	1.09888
$841$	841.000	0.0344828
$842$	27650.8	1.13172
$843$	−58342.5	−2.38366
$844$	4184.90	0.170676
$845$	402.245	0.0163759
$846$	14035.9	0.570407
$847$	−20599.9	−0.835681
$848$	35837.1	1.45124
$849$	−49292.9	−1.99261
$850$	−4931.42	−0.198995
$851$	3072.97	0.123784
$852$	−4819.73	−0.193804
$853$	−24040.4	−0.964980	−0.482490	−	0.875902i	$-0.660268\pi$
$853$	−24040.4	−0.964980	−0.482490	+	0.875902i	$0.660268\pi$
$854$	18263.7	0.731817
$855$	−8804.98	−0.352192
$856$	41084.5	1.64047
$857$	−18729.3	−0.746536	−0.373268	−	0.927724i	$-0.621763\pi$
$857$	−18729.3	−0.746536	−0.373268	+	0.927724i	$0.621763\pi$
$858$	−51650.0	−2.05513
$859$	1412.28	0.0560960	0.0280480	−	0.999607i	$-0.491071\pi$
$859$	1412.28	0.0560960	0.0280480	+	0.999607i	$0.491071\pi$
$860$	2436.03	0.0965906
$861$	−64388.0	−2.54859
$862$	19617.7	0.775152
$863$	−24094.0	−0.950369	−0.475185	−	0.879886i	$-0.657619\pi$
$863$	−24094.0	−0.950369	−0.475185	+	0.879886i	$0.657619\pi$
$864$	16181.9	0.637176
$865$	−13603.4	−0.534717
$866$	−2532.64	−0.0993794
$867$	42338.9	1.65848
$868$	−8238.56	−0.322160
$869$	−6659.80	−0.259975
$870$	−2890.29	−0.112632
$871$	18998.6	0.739085
$872$	−36464.8	−1.41612
$873$	42367.1	1.64251
$874$	−2178.37	−0.0843073
$875$	28101.5	1.08572
$876$	−3947.53	−0.152254
$877$	−47682.1	−1.83593	−0.917965	−	0.396661i	$-0.870169\pi$
$877$	−47682.1	−1.83593	−0.917965	+	0.396661i	$0.870169\pi$
$878$	−47488.1	−1.82534
$879$	−77282.4	−2.96549
$880$	9843.65	0.377079
$881$	27014.5	1.03308	0.516538	−	0.856264i	$-0.327220\pi$
$881$	27014.5	1.03308	0.516538	+	0.856264i	$0.327220\pi$
$882$	−73907.8	−2.82155
$883$	3605.92	0.137428	0.0687139	−	0.997636i	$-0.478110\pi$
$883$	3605.92	0.137428	0.0687139	+	0.997636i	$0.478110\pi$
$884$	1082.51	0.0411865
$885$	15632.0	0.593744
$886$	−37537.7	−1.42337
$887$	−21940.6	−0.830545	−0.415272	−	0.909697i	$-0.636314\pi$
$887$	−21940.6	−0.830545	−0.415272	+	0.909697i	$0.636314\pi$
$888$	29579.8	1.11783
$889$	−42573.5	−1.60615
$890$	15603.1	0.587661
$891$	−47141.7	−1.77251
$892$	−3095.03	−0.116176
$893$	3427.17	0.128428
$894$	32696.5	1.22319
$895$	14358.8	0.536272
$896$	29170.0	1.08761
$897$	10137.2	0.377336
$898$	29875.4	1.11020
$899$	6460.79	0.239688
$900$	7933.31	0.293826
$901$	12155.1	0.449439
$902$	−28337.8	−1.04606
$903$	−121495.	−4.47741
$904$	32810.6	1.20715
$905$	−10567.4	−0.388147
$906$	26437.1	0.969442
$907$	−5493.93	−0.201128	−0.100564	−	0.994931i	$-0.532065\pi$
$907$	−5493.93	−0.201128	−0.100564	+	0.994931i	$0.532065\pi$
$908$	509.641	0.0186267
$909$	24656.2	0.899665
$910$	15003.0	0.546532
$911$	−28703.1	−1.04388	−0.521942	−	0.852981i	$-0.674792\pi$
$911$	−28703.1	−1.04388	−0.521942	+	0.852981i	$0.674792\pi$
$912$	−17530.5	−0.636507
$913$	31482.5	1.14120
$914$	−39610.1	−1.43347
$915$	−9360.21	−0.338185
$916$	8349.69	0.301181
$917$	41414.0	1.49140
$918$	−12957.8	−0.465872
$919$	−39341.0	−1.41212	−0.706061	−	0.708151i	$-0.749530\pi$
$919$	−39341.0	−1.41212	−0.706061	+	0.708151i	$0.749530\pi$
$920$	−2310.88	−0.0828124
$921$	15524.9	0.555442
$922$	−19899.0	−0.710780
$923$	−19619.8	−0.699667
$924$	15383.7	0.547712
$925$	14370.1	0.510795
$926$	−5957.15	−0.211408
$927$	47491.4	1.68265
$928$	1660.51	0.0587380
$929$	27001.1	0.953582	0.476791	−	0.879017i	$-0.341800\pi$
$929$	27001.1	0.953582	0.476791	+	0.879017i	$0.341800\pi$
$930$	−22204.0	−0.782900
$931$	−18046.2	−0.635274
$932$	−491.888	−0.0172879
$933$	92543.4	3.24731
$934$	−7325.47	−0.256635
$935$	3338.73	0.116779
$936$	66475.5	2.32139
$937$	−8078.87	−0.281671	−0.140835	−	0.990033i	$-0.544979\pi$
$937$	−8078.87	−0.281671	−0.140835	+	0.990033i	$0.544979\pi$
$938$	29757.4	1.03584
$939$	−6127.92	−0.212968
$940$	500.862	0.0173791
$941$	49866.9	1.72754	0.863769	−	0.503888i	$-0.168098\pi$
$941$	49866.9	1.72754	0.863769	+	0.503888i	$0.168098\pi$
$942$	7101.17	0.245614
$943$	5561.76	0.192064
$944$	21202.6	0.731022
$945$	34150.1	1.17556
$946$	−53471.1	−1.83773
$947$	41237.3	1.41503	0.707515	−	0.706698i	$-0.249816\pi$
$947$	41237.3	1.41503	0.707515	+	0.706698i	$0.249816\pi$
$948$	1733.34	0.0593841
$949$	−16069.3	−0.549664
$950$	−10186.7	−0.347894
$951$	−22188.3	−0.756576
$952$	12307.5	0.419000
$953$	−21276.5	−0.723203	−0.361602	−	0.932333i	$-0.617770\pi$
$953$	−21276.5	−0.723203	−0.361602	+	0.932333i	$0.617770\pi$
$954$	102831.	3.48981
$955$	−4860.91	−0.164707
$956$	5776.66	0.195429
$957$	−12064.1	−0.407499
$958$	−39244.8	−1.32353
$959$	53294.0	1.79453
$960$	−21741.6	−0.730945
$961$	19842.6	0.666060
$962$	16588.4	0.555957
$963$	98558.9	3.29804
$964$	−194.562	−0.00650045
$965$	−5438.20	−0.181411
$966$	15877.8	0.528840
$967$	−46430.0	−1.54404	−0.772020	−	0.635598i	$-0.780753\pi$
$967$	−46430.0	−1.54404	−0.772020	+	0.635598i	$0.780753\pi$
$968$	17128.2	0.568719
$969$	−5945.94	−0.197122
$970$	−7950.41	−0.263167
$971$	14812.4	0.489551	0.244776	−	0.969580i	$-0.421286\pi$
$971$	14812.4	0.489551	0.244776	+	0.969580i	$0.421286\pi$
$972$	2516.16	0.0830307
$973$	43953.2	1.44817
$974$	−4169.97	−0.137181
$975$	47404.3	1.55708
$976$	−12695.8	−0.416376
$977$	−54167.3	−1.77376	−0.886881	−	0.461998i	$-0.847133\pi$
$977$	−54167.3	−1.77376	−0.886881	+	0.461998i	$0.847133\pi$
$978$	−61516.4	−2.01133
$979$	65127.6	2.12614
$980$	−2637.35	−0.0859664
$981$	−87476.5	−2.84700
$982$	−33679.1	−1.09444
$983$	18686.6	0.606319	0.303159	−	0.952940i	$-0.401959\pi$
$983$	18686.6	0.606319	0.303159	+	0.952940i	$0.401959\pi$
$984$	53536.5	1.73443
$985$	9090.31	0.294052
$986$	−1329.66	−0.0429463
$987$	−24980.1	−0.805597
$988$	2236.12	0.0720044
$989$	10494.6	0.337421
$990$	28245.4	0.906765
$991$	−6517.45	−0.208914	−0.104457	−	0.994529i	$-0.533310\pi$
$991$	−6517.45	−0.208914	−0.104457	+	0.994529i	$0.533310\pi$
$992$	12756.5	0.408285
$993$	−20782.7	−0.664170
$994$	−30730.3	−0.980590
$995$	−7333.33	−0.233650
$996$	−8193.91	−0.260677
$997$	8933.67	0.283784	0.141892	−	0.989882i	$-0.454682\pi$
$997$	8933.67	0.283784	0.141892	+	0.989882i	$0.454682\pi$
$998$	−25883.8	−0.820980
$999$	37758.8	1.19583

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	667.4.a.c.1.11	✓	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
667.4.a.c.1.11	✓	39	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)

\(f(q)\)	\(=\)	\(q-2.59264 q^{2} -9.20361 q^{3} -1.27821 q^{4} +4.17679 q^{5} +23.8617 q^{6} -28.9309 q^{7} +24.0551 q^{8} +57.7064 q^{9} +O(q^{10})\)	\(q-2.59264 q^{2} -9.20361 q^{3} -1.27821 q^{4} +4.17679 q^{5} +23.8617 q^{6} -28.9309 q^{7} +24.0551 q^{8} +57.7064 q^{9} -10.8289 q^{10} -45.2000 q^{11} +11.7641 q^{12} +47.8885 q^{13} +75.0074 q^{14} -38.4415 q^{15} -52.1405 q^{16} -17.6848 q^{17} -149.612 q^{18} -36.5310 q^{19} -5.33881 q^{20} +266.269 q^{21} +117.187 q^{22} -23.0000 q^{23} -221.393 q^{24} -107.554 q^{25} -124.158 q^{26} -282.610 q^{27} +36.9797 q^{28} -29.0000 q^{29} +99.6651 q^{30} -222.786 q^{31} -57.2589 q^{32} +416.003 q^{33} +45.8504 q^{34} -120.838 q^{35} -73.7609 q^{36} -133.607 q^{37} +94.7118 q^{38} -440.747 q^{39} +100.473 q^{40} -241.816 q^{41} -690.339 q^{42} -456.287 q^{43} +57.7750 q^{44} +241.027 q^{45} +59.6308 q^{46} -93.8153 q^{47} +479.881 q^{48} +493.996 q^{49} +278.850 q^{50} +162.764 q^{51} -61.2115 q^{52} -687.318 q^{53} +732.706 q^{54} -188.791 q^{55} -695.935 q^{56} +336.217 q^{57} +75.1866 q^{58} -406.643 q^{59} +49.1363 q^{60} +243.492 q^{61} +577.604 q^{62} -1669.50 q^{63} +565.576 q^{64} +200.020 q^{65} -1078.55 q^{66} +396.726 q^{67} +22.6049 q^{68} +211.683 q^{69} +313.290 q^{70} -409.697 q^{71} +1388.13 q^{72} -335.557 q^{73} +346.396 q^{74} +989.889 q^{75} +46.6943 q^{76} +1307.68 q^{77} +1142.70 q^{78} +147.341 q^{79} -217.780 q^{80} +1042.96 q^{81} +626.942 q^{82} -696.516 q^{83} -340.347 q^{84} -73.8658 q^{85} +1182.99 q^{86} +266.905 q^{87} -1087.29 q^{88} -1440.88 q^{89} -624.898 q^{90} -1385.46 q^{91} +29.3988 q^{92} +2050.43 q^{93} +243.229 q^{94} -152.582 q^{95} +526.989 q^{96} +734.183 q^{97} -1280.76 q^{98} -2608.33 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q + 6 q^{2} + 2 q^{3} + 156 q^{4} + 80 q^{5} - 4 q^{6} + 18 q^{7} + 156 q^{8} + 411 q^{9}+O(q^{10}) \) 39 * q + 6 * q^2 + 2 * q^3 + 156 * q^4 + 80 * q^5 - 4 * q^6 + 18 * q^7 + 156 * q^8 + 411 * q^9	\( 39 q + 6 q^{2} + 2 q^{3} + 156 q^{4} + 80 q^{5} - 4 q^{6} + 18 q^{7} + 156 q^{8} + 411 q^{9} + 130 q^{10} + 76 q^{11} + 115 q^{12} + 184 q^{13} + 336 q^{14} + 228 q^{15} + 776 q^{16} + 314 q^{17} + 27 q^{18} + 36 q^{19} + 533 q^{20} + 246 q^{21} + 269 q^{22} - 897 q^{23} + 30 q^{24} + 1267 q^{25} + 787 q^{26} + 122 q^{27} + 53 q^{28} - 1131 q^{29} + 703 q^{30} + 140 q^{31} + 1304 q^{32} + 2210 q^{33} + 59 q^{34} + 1828 q^{35} + 1834 q^{36} + 430 q^{37} + 1874 q^{38} - 340 q^{39} + 276 q^{40} + 1936 q^{41} + 756 q^{42} + 96 q^{43} - 671 q^{44} + 3392 q^{45} - 138 q^{46} + 1808 q^{47} + 535 q^{48} + 2201 q^{49} + 395 q^{50} + 750 q^{51} - 530 q^{52} + 4200 q^{53} - 937 q^{54} + 902 q^{55} + 3805 q^{56} + 300 q^{57} - 174 q^{58} + 726 q^{59} + 195 q^{60} + 736 q^{61} + 1851 q^{62} + 796 q^{63} + 2914 q^{64} + 2572 q^{65} + 307 q^{66} + 1192 q^{67} + 1235 q^{68} - 46 q^{69} + 5268 q^{70} + 1714 q^{71} + 643 q^{72} + 2012 q^{73} + 3307 q^{74} - 1708 q^{75} + 5244 q^{76} + 6592 q^{77} + 6406 q^{78} + 1768 q^{79} + 8606 q^{80} + 5363 q^{81} - 2059 q^{82} + 3766 q^{83} + 3818 q^{84} + 1260 q^{85} - 2355 q^{86} - 58 q^{87} + 3448 q^{88} + 1634 q^{89} - 1313 q^{90} + 1240 q^{91} - 3588 q^{92} + 3954 q^{93} + 2315 q^{94} + 1656 q^{95} + 1480 q^{96} - 788 q^{97} + 3128 q^{98} + 4488 q^{99}+O(q^{100}) \) 39 * q + 6 * q^2 + 2 * q^3 + 156 * q^4 + 80 * q^5 - 4 * q^6 + 18 * q^7 + 156 * q^8 + 411 * q^9 + 130 * q^10 + 76 * q^11 + 115 * q^12 + 184 * q^13 + 336 * q^14 + 228 * q^15 + 776 * q^16 + 314 * q^17 + 27 * q^18 + 36 * q^19 + 533 * q^20 + 246 * q^21 + 269 * q^22 - 897 * q^23 + 30 * q^24 + 1267 * q^25 + 787 * q^26 + 122 * q^27 + 53 * q^28 - 1131 * q^29 + 703 * q^30 + 140 * q^31 + 1304 * q^32 + 2210 * q^33 + 59 * q^34 + 1828 * q^35 + 1834 * q^36 + 430 * q^37 + 1874 * q^38 - 340 * q^39 + 276 * q^40 + 1936 * q^41 + 756 * q^42 + 96 * q^43 - 671 * q^44 + 3392 * q^45 - 138 * q^46 + 1808 * q^47 + 535 * q^48 + 2201 * q^49 + 395 * q^50 + 750 * q^51 - 530 * q^52 + 4200 * q^53 - 937 * q^54 + 902 * q^55 + 3805 * q^56 + 300 * q^57 - 174 * q^58 + 726 * q^59 + 195 * q^60 + 736 * q^61 + 1851 * q^62 + 796 * q^63 + 2914 * q^64 + 2572 * q^65 + 307 * q^66 + 1192 * q^67 + 1235 * q^68 - 46 * q^69 + 5268 * q^70 + 1714 * q^71 + 643 * q^72 + 2012 * q^73 + 3307 * q^74 - 1708 * q^75 + 5244 * q^76 + 6592 * q^77 + 6406 * q^78 + 1768 * q^79 + 8606 * q^80 + 5363 * q^81 - 2059 * q^82 + 3766 * q^83 + 3818 * q^84 + 1260 * q^85 - 2355 * q^86 - 58 * q^87 + 3448 * q^88 + 1634 * q^89 - 1313 * q^90 + 1240 * q^91 - 3588 * q^92 + 3954 * q^93 + 2315 * q^94 + 1656 * q^95 + 1480 * q^96 - 788 * q^97 + 3128 * q^98 + 4488 * q^99

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