LMFDB - Embedded newform 667.4.a.d.1.30

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:	$42$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.30
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)

$f(q)$	$=$	$q+3.22905 q^{2} +7.74829 q^{3} +2.42674 q^{4} +3.88662 q^{5} +25.0196 q^{6} +15.1282 q^{7} -17.9963 q^{8} +33.0359 q^{9} +O(q^{10})$	\(q+3.22905 q^{2} +7.74829 q^{3} +2.42674 q^{4} +3.88662 q^{5} +25.0196 q^{6} +15.1282 q^{7} -17.9963 q^{8} +33.0359 q^{9} +12.5501 q^{10} +63.2619 q^{11} +18.8031 q^{12} -20.4733 q^{13} +48.8497 q^{14} +30.1146 q^{15} -77.5249 q^{16} +71.1115 q^{17} +106.675 q^{18} -17.6078 q^{19} +9.43181 q^{20} +117.218 q^{21} +204.276 q^{22} +23.0000 q^{23} -139.441 q^{24} -109.894 q^{25} -66.1092 q^{26} +46.7682 q^{27} +36.7122 q^{28} +29.0000 q^{29} +97.2415 q^{30} -50.2200 q^{31} -106.361 q^{32} +490.171 q^{33} +229.622 q^{34} +58.7975 q^{35} +80.1697 q^{36} +0.966654 q^{37} -56.8565 q^{38} -158.633 q^{39} -69.9447 q^{40} +82.4000 q^{41} +378.501 q^{42} +436.013 q^{43} +153.520 q^{44} +128.398 q^{45} +74.2681 q^{46} -189.493 q^{47} -600.685 q^{48} -114.138 q^{49} -354.854 q^{50} +550.992 q^{51} -49.6834 q^{52} -75.3110 q^{53} +151.017 q^{54} +245.875 q^{55} -272.252 q^{56} -136.430 q^{57} +93.6424 q^{58} -343.534 q^{59} +73.0804 q^{60} +765.148 q^{61} -162.163 q^{62} +499.774 q^{63} +276.755 q^{64} -79.5718 q^{65} +1582.79 q^{66} -242.557 q^{67} +172.569 q^{68} +178.211 q^{69} +189.860 q^{70} -171.381 q^{71} -594.525 q^{72} +283.915 q^{73} +3.12137 q^{74} -851.492 q^{75} -42.7296 q^{76} +957.038 q^{77} -512.233 q^{78} +585.199 q^{79} -301.309 q^{80} -529.597 q^{81} +266.073 q^{82} -67.0958 q^{83} +284.457 q^{84} +276.383 q^{85} +1407.91 q^{86} +224.700 q^{87} -1138.48 q^{88} -373.386 q^{89} +414.603 q^{90} -309.724 q^{91} +55.8151 q^{92} -389.119 q^{93} -611.883 q^{94} -68.4349 q^{95} -824.115 q^{96} -1238.41 q^{97} -368.556 q^{98} +2089.92 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 42 q + 12 q^{2} + 32 q^{3} + 192 q^{4} + 80 q^{5} + 32 q^{6} + 18 q^{7} + 102 q^{8} + 492 q^{9}+O(q^{10}) $ 42 * q + 12 * q^2 + 32 * q^3 + 192 * q^4 + 80 * q^5 + 32 * q^6 + 18 * q^7 + 102 * q^8 + 492 * q^9	\( 42 q + 12 q^{2} + 32 q^{3} + 192 q^{4} + 80 q^{5} + 32 q^{6} + 18 q^{7} + 102 q^{8} + 492 q^{9} + 48 q^{10} + 50 q^{11} + 403 q^{12} + 236 q^{13} + 32 q^{14} + 12 q^{15} + 792 q^{16} + 456 q^{17} + 297 q^{18} + 166 q^{19} + 533 q^{20} + 258 q^{21} + 73 q^{22} + 966 q^{23} + 514 q^{24} + 1358 q^{25} + 497 q^{26} + 1250 q^{27} + 143 q^{28} + 1218 q^{29} + 593 q^{30} + 558 q^{31} + 1328 q^{32} - 464 q^{33} + 157 q^{34} + 48 q^{35} + 3030 q^{36} + 352 q^{37} + 218 q^{38} + 1080 q^{39} + 900 q^{40} + 182 q^{41} + 272 q^{42} + 870 q^{43} + 925 q^{44} + 1238 q^{45} + 276 q^{46} + 2058 q^{47} + 4057 q^{48} + 3340 q^{49} + 981 q^{50} + 750 q^{51} + 1850 q^{52} + 2412 q^{53} + 1643 q^{54} + 1506 q^{55} + 671 q^{56} + 516 q^{57} + 348 q^{58} + 2958 q^{59} + 2445 q^{60} + 902 q^{61} + 1123 q^{62} + 296 q^{63} + 3234 q^{64} + 682 q^{65} - 1007 q^{66} - 612 q^{67} + 6445 q^{68} + 736 q^{69} - 608 q^{70} + 1358 q^{71} + 3475 q^{72} + 3102 q^{73} + 777 q^{74} + 2362 q^{75} - 1034 q^{76} + 6440 q^{77} - 430 q^{78} + 614 q^{79} - 272 q^{80} + 6622 q^{81} + 3749 q^{82} + 1910 q^{83} - 582 q^{84} + 4156 q^{85} + 3071 q^{86} + 928 q^{87} + 2584 q^{88} + 3768 q^{89} + 6545 q^{90} - 844 q^{91} + 4416 q^{92} + 3032 q^{93} + 1671 q^{94} + 2432 q^{95} - 1812 q^{96} + 4086 q^{97} + 4714 q^{98} + 3490 q^{99}+O(q^{100}) \) 42 * q + 12 * q^2 + 32 * q^3 + 192 * q^4 + 80 * q^5 + 32 * q^6 + 18 * q^7 + 102 * q^8 + 492 * q^9 + 48 * q^10 + 50 * q^11 + 403 * q^12 + 236 * q^13 + 32 * q^14 + 12 * q^15 + 792 * q^16 + 456 * q^17 + 297 * q^18 + 166 * q^19 + 533 * q^20 + 258 * q^21 + 73 * q^22 + 966 * q^23 + 514 * q^24 + 1358 * q^25 + 497 * q^26 + 1250 * q^27 + 143 * q^28 + 1218 * q^29 + 593 * q^30 + 558 * q^31 + 1328 * q^32 - 464 * q^33 + 157 * q^34 + 48 * q^35 + 3030 * q^36 + 352 * q^37 + 218 * q^38 + 1080 * q^39 + 900 * q^40 + 182 * q^41 + 272 * q^42 + 870 * q^43 + 925 * q^44 + 1238 * q^45 + 276 * q^46 + 2058 * q^47 + 4057 * q^48 + 3340 * q^49 + 981 * q^50 + 750 * q^51 + 1850 * q^52 + 2412 * q^53 + 1643 * q^54 + 1506 * q^55 + 671 * q^56 + 516 * q^57 + 348 * q^58 + 2958 * q^59 + 2445 * q^60 + 902 * q^61 + 1123 * q^62 + 296 * q^63 + 3234 * q^64 + 682 * q^65 - 1007 * q^66 - 612 * q^67 + 6445 * q^68 + 736 * q^69 - 608 * q^70 + 1358 * q^71 + 3475 * q^72 + 3102 * q^73 + 777 * q^74 + 2362 * q^75 - 1034 * q^76 + 6440 * q^77 - 430 * q^78 + 614 * q^79 - 272 * q^80 + 6622 * q^81 + 3749 * q^82 + 1910 * q^83 - 582 * q^84 + 4156 * q^85 + 3071 * q^86 + 928 * q^87 + 2584 * q^88 + 3768 * q^89 + 6545 * q^90 - 844 * q^91 + 4416 * q^92 + 3032 * q^93 + 1671 * q^94 + 2432 * q^95 - 1812 * q^96 + 4086 * q^97 + 4714 * q^98 + 3490 * 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 $

$2$	3.22905	1.14164	0.570820	−	0.821075i	$-0.306625\pi$
$2$	3.22905	1.14164	0.570820	+	0.821075i	$0.306625\pi$
$3$	7.74829	1.49116	0.745579	−	0.666417i	$-0.232173\pi$
$3$	7.74829	1.49116	0.745579	+	0.666417i	$0.232173\pi$
$4$	2.42674	0.303343
$5$	3.88662	0.347629	0.173815	−	0.984778i	$-0.444391\pi$
$5$	3.88662	0.347629	0.173815	+	0.984778i	$0.444391\pi$
$6$	25.0196	1.70237
$7$	15.1282	0.816846	0.408423	−	0.912793i	$-0.366079\pi$
$7$	15.1282	0.816846	0.408423	+	0.912793i	$0.366079\pi$
$8$	−17.9963	−0.795332
$9$	33.0359	1.22355
$10$	12.5501	0.396868
$11$	63.2619	1.73402	0.867008	−	0.498294i	$-0.166040\pi$
$11$	63.2619	1.73402	0.867008	+	0.498294i	$0.166040\pi$
$12$	18.8031	0.452332
$13$	−20.4733	−0.436790	−0.218395	−	0.975860i	$-0.570082\pi$
$13$	−20.4733	−0.436790	−0.218395	+	0.975860i	$0.570082\pi$
$14$	48.8497	0.932544
$15$	30.1146	0.518371
$16$	−77.5249	−1.21133
$17$	71.1115	1.01453	0.507267	−	0.861789i	$-0.330656\pi$
$17$	71.1115	1.01453	0.507267	+	0.861789i	$0.330656\pi$
$18$	106.675	1.39686
$19$	−17.6078	−0.212606	−0.106303	−	0.994334i	$-0.533901\pi$
$19$	−17.6078	−0.212606	−0.106303	+	0.994334i	$0.533901\pi$
$20$	9.43181	0.105451
$21$	117.218	1.21805
$22$	204.276	1.97962
$23$	23.0000	0.208514
$23$	23.0000	0.208514
$24$	−139.441	−1.18597
$25$	−109.894	−0.879154
$26$	−66.1092	−0.498657
$27$	46.7682	0.333353
$28$	36.7122	0.247784
$29$	29.0000	0.185695
$29$	29.0000	0.185695
$30$	97.2415	0.591793
$31$	−50.2200	−0.290961	−0.145480	−	0.989361i	$-0.546473\pi$
$31$	−50.2200	−0.290961	−0.145480	+	0.989361i	$0.546473\pi$
$32$	−106.361	−0.587566
$33$	490.171	2.58569
$34$	229.622	1.15823
$35$	58.7975	0.283960
$36$	80.1697	0.371156
$37$	0.966654	0.00429505	0.00214753	−	0.999998i	$-0.499316\pi$
$37$	0.966654	0.00429505	0.00214753	+	0.999998i	$0.499316\pi$
$38$	−56.8565	−0.242719
$39$	−158.633	−0.651323
$40$	−69.9447	−0.276481
$41$	82.4000	0.313871	0.156936	−	0.987609i	$-0.449838\pi$
$41$	82.4000	0.313871	0.156936	+	0.987609i	$0.449838\pi$
$42$	378.501	1.39057
$43$	436.013	1.54631	0.773156	−	0.634216i	$-0.218677\pi$
$43$	436.013	1.54631	0.773156	+	0.634216i	$0.218677\pi$
$44$	153.520	0.526001
$45$	128.398	0.425343
$46$	74.2681	0.238048
$47$	−189.493	−0.588095	−0.294047	−	0.955791i	$-0.595002\pi$
$47$	−189.493	−0.588095	−0.294047	+	0.955791i	$0.595002\pi$
$48$	−600.685	−1.80628
$49$	−114.138	−0.332763
$50$	−354.854	−1.00368
$51$	550.992	1.51283
$52$	−49.6834	−0.132497
$53$	−75.3110	−0.195184	−0.0975921	−	0.995227i	$-0.531114\pi$
$53$	−75.3110	−0.195184	−0.0975921	+	0.995227i	$0.531114\pi$
$54$	151.017	0.380570
$55$	245.875	0.602795
$56$	−272.252	−0.649664
$57$	−136.430	−0.317029
$58$	93.6424	0.211997
$59$	−343.534	−0.758039	−0.379019	−	0.925389i	$-0.623739\pi$
$59$	−343.534	−0.758039	−0.379019	+	0.925389i	$0.623739\pi$
$60$	73.0804	0.157244
$61$	765.148	1.60602	0.803010	−	0.595966i	$-0.203231\pi$
$61$	765.148	1.60602	0.803010	+	0.595966i	$0.203231\pi$
$62$	−162.163	−0.332173
$63$	499.774	0.999455
$64$	276.755	0.540536
$65$	−79.5718	−0.151841
$66$	1582.79	2.95193
$67$	−242.557	−0.442285	−0.221142	−	0.975242i	$-0.570979\pi$
$67$	−242.557	−0.442285	−0.221142	+	0.975242i	$0.570979\pi$
$68$	172.569	0.307751
$69$	178.211	0.310928
$70$	189.860	0.324180
$71$	−171.381	−0.286467	−0.143234	−	0.989689i	$-0.545750\pi$
$71$	−171.381	−0.286467	−0.143234	+	0.989689i	$0.545750\pi$
$72$	−594.525	−0.973131
$73$	283.915	0.455203	0.227601	−	0.973754i	$-0.426912\pi$
$73$	283.915	0.455203	0.227601	+	0.973754i	$0.426912\pi$
$74$	3.12137	0.00490340
$75$	−851.492	−1.31096
$76$	−42.7296	−0.0644925
$77$	957.038	1.41642
$78$	−512.233	−0.743576
$79$	585.199	0.833418	0.416709	−	0.909040i	$-0.363183\pi$
$79$	585.199	0.833418	0.416709	+	0.909040i	$0.363183\pi$
$80$	−301.309	−0.421093
$81$	−529.597	−0.726471
$82$	266.073	0.358328
$83$	−67.0958	−0.0887316	−0.0443658	−	0.999015i	$-0.514127\pi$
$83$	−67.0958	−0.0887316	−0.0443658	+	0.999015i	$0.514127\pi$
$84$	284.457	0.369486
$85$	276.383	0.352682
$86$	1407.91	1.76533
$87$	224.700	0.276901
$88$	−1138.48	−1.37912
$89$	−373.386	−0.444706	−0.222353	−	0.974966i	$-0.571374\pi$
$89$	−373.386	−0.444706	−0.222353	+	0.974966i	$0.571374\pi$
$90$	414.603	0.485589
$91$	−309.724	−0.356790
$92$	55.8151	0.0632513
$93$	−389.119	−0.433869
$94$	−611.883	−0.671393
$95$	−68.4349	−0.0739081
$96$	−824.115	−0.876155
$97$	−1238.41	−1.29630	−0.648150	−	0.761513i	$-0.724457\pi$
$97$	−1238.41	−1.29630	−0.648150	+	0.761513i	$0.724457\pi$
$98$	−368.556	−0.379895
$99$	2089.92	2.12166
$100$	−266.685	−0.266685
$101$	−1788.48	−1.76198	−0.880991	−	0.473134i	$-0.843123\pi$
$101$	−1788.48	−1.76198	−0.880991	+	0.473134i	$0.843123\pi$
$102$	1779.18	1.72711
$103$	1036.94	0.991964	0.495982	−	0.868333i	$-0.334808\pi$
$103$	1036.94	0.991964	0.495982	+	0.868333i	$0.334808\pi$
$104$	368.444	0.347393
$105$	455.580	0.423429
$106$	−243.183	−0.222830
$107$	−2085.72	−1.88443	−0.942216	−	0.335005i	$-0.891262\pi$
$107$	−2085.72	−1.88443	−0.942216	+	0.335005i	$0.891262\pi$
$108$	113.494	0.101120
$109$	−268.850	−0.236249	−0.118124	−	0.992999i	$-0.537688\pi$
$109$	−268.850	−0.236249	−0.118124	+	0.992999i	$0.537688\pi$
$110$	793.941	0.688175
$111$	7.48991	0.00640460
$112$	−1172.81	−0.989467
$113$	−287.253	−0.239137	−0.119568	−	0.992826i	$-0.538151\pi$
$113$	−287.253	−0.239137	−0.119568	+	0.992826i	$0.538151\pi$
$114$	−440.540	−0.361933
$115$	89.3922	0.0724858
$116$	70.3755	0.0563293
$117$	−676.354	−0.534436
$118$	−1109.29	−0.865408
$119$	1075.79	0.828717
$120$	−541.952	−0.412277
$121$	2671.07	2.00681
$122$	2470.70	1.83350
$123$	638.459	0.468032
$124$	−121.871	−0.0882608
$125$	−912.944	−0.653249
$126$	1613.79	1.14102
$127$	112.882	0.0788715	0.0394358	−	0.999222i	$-0.487444\pi$
$127$	112.882	0.0788715	0.0394358	+	0.999222i	$0.487444\pi$
$128$	1744.54	1.20466
$129$	3378.36	2.30580
$130$	−256.941	−0.173348
$131$	367.073	0.244819	0.122410	−	0.992480i	$-0.460938\pi$
$131$	367.073	0.244819	0.122410	+	0.992480i	$0.460938\pi$
$132$	1189.52	0.784351
$133$	−266.375	−0.173666
$134$	−783.228	−0.504930
$135$	181.770	0.115883
$136$	−1279.74	−0.806891
$137$	−2418.82	−1.50842	−0.754210	−	0.656633i	$-0.771980\pi$
$137$	−2418.82	−1.50842	−0.754210	+	0.656633i	$0.771980\pi$
$138$	575.450	0.354968
$139$	936.487	0.571452	0.285726	−	0.958311i	$-0.407765\pi$
$139$	936.487	0.571452	0.285726	+	0.958311i	$0.407765\pi$
$140$	142.686	0.0861371
$141$	−1468.25	−0.876942
$142$	−553.397	−0.327042
$143$	−1295.18	−0.757400
$144$	−2561.11	−1.48212
$145$	112.712	0.0645532
$146$	916.776	0.519678
$147$	−884.371	−0.496202
$148$	2.34582	0.00130287
$149$	−1557.71	−0.856460	−0.428230	−	0.903670i	$-0.640863\pi$
$149$	−1557.71	−0.856460	−0.428230	+	0.903670i	$0.640863\pi$
$150$	−2749.51	−1.49664
$151$	−2382.76	−1.28415	−0.642073	−	0.766644i	$-0.721925\pi$
$151$	−2382.76	−1.28415	−0.642073	+	0.766644i	$0.721925\pi$
$152$	316.876	0.169092
$153$	2349.23	1.24134
$154$	3090.32	1.61705
$155$	−195.186	−0.101147
$156$	−384.961	−0.197574
$157$	−2248.84	−1.14316	−0.571582	−	0.820545i	$-0.693670\pi$
$157$	−2248.84	−1.14316	−0.571582	+	0.820545i	$0.693670\pi$
$158$	1889.63	0.951464
$159$	−583.531	−0.291050
$160$	−413.384	−0.204255
$161$	347.949	0.170324
$162$	−1710.09	−0.829368
$163$	−2215.69	−1.06470	−0.532350	−	0.846525i	$-0.678691\pi$
$163$	−2215.69	−1.06470	−0.532350	+	0.846525i	$0.678691\pi$
$164$	199.964	0.0952105
$165$	1905.11	0.898863
$166$	−216.656	−0.101300
$167$	−1115.97	−0.517104	−0.258552	−	0.965997i	$-0.583245\pi$
$167$	−1115.97	−0.517104	−0.258552	+	0.965997i	$0.583245\pi$
$168$	−2109.48	−0.968752
$169$	−1777.84	−0.809215
$170$	892.454	0.402636
$171$	−581.691	−0.260135
$172$	1058.09	0.469063
$173$	790.290	0.347310	0.173655	−	0.984807i	$-0.444442\pi$
$173$	790.290	0.347310	0.173655	+	0.984807i	$0.444442\pi$
$174$	725.568	0.316122
$175$	−1662.50	−0.718133
$176$	−4904.37	−2.10046
$177$	−2661.80	−1.13036
$178$	−1205.68	−0.507694
$179$	4365.68	1.82294	0.911470	−	0.411366i	$-0.134948\pi$
$179$	4365.68	1.82294	0.911470	+	0.411366i	$0.134948\pi$
$180$	311.589	0.129025
$181$	270.546	0.111103	0.0555513	−	0.998456i	$-0.482308\pi$
$181$	270.546	0.111103	0.0555513	+	0.998456i	$0.482308\pi$
$182$	−1000.11	−0.407326
$183$	5928.59	2.39483
$184$	−413.915	−0.165838
$185$	3.75701	0.00149309
$186$	−1256.48	−0.495322
$187$	4498.65	1.75922
$188$	−459.851	−0.178394
$189$	707.518	0.272298
$190$	−220.979	−0.0843764
$191$	4756.63	1.80198	0.900988	−	0.433844i	$-0.142843\pi$
$191$	4756.63	1.80198	0.900988	+	0.433844i	$0.142843\pi$
$192$	2144.37	0.806025
$193$	−1974.10	−0.736263	−0.368132	−	0.929774i	$-0.620002\pi$
$193$	−1974.10	−0.736263	−0.368132	+	0.929774i	$0.620002\pi$
$194$	−3998.87	−1.47991
$195$	−616.545	−0.226419
$196$	−276.983	−0.100941
$197$	1665.90	0.602490	0.301245	−	0.953547i	$-0.402598\pi$
$197$	1665.90	0.602490	0.301245	+	0.953547i	$0.402598\pi$
$198$	6748.44	2.42217
$199$	402.793	0.143483	0.0717417	−	0.997423i	$-0.477144\pi$
$199$	402.793	0.143483	0.0717417	+	0.997423i	$0.477144\pi$
$200$	1977.69	0.699219
$201$	−1879.40	−0.659516
$202$	−5775.08	−2.01155
$203$	438.718	0.151684
$204$	1337.12	0.458906
$205$	320.257	0.109111
$206$	3348.31	1.13247
$207$	759.827	0.255129
$208$	1587.19	0.529095
$209$	−1113.90	−0.368662
$210$	1471.09	0.483404
$211$	−5125.57	−1.67232	−0.836159	−	0.548487i	$-0.815204\pi$
$211$	−5125.57	−1.67232	−0.836159	+	0.548487i	$0.815204\pi$
$212$	−182.760	−0.0592077
$213$	−1327.91	−0.427168
$214$	−6734.89	−2.15134
$215$	1694.62	0.537544
$216$	−841.655	−0.265127
$217$	−759.738	−0.237670
$218$	−868.128	−0.269711
$219$	2199.86	0.678779
$220$	596.674	0.182854
$221$	−1455.89	−0.443138
$222$	24.1853	0.00731175
$223$	4357.96	1.30866	0.654329	−	0.756210i	$-0.272951\pi$
$223$	4357.96	1.30866	0.654329	+	0.756210i	$0.272951\pi$
$224$	−1609.05	−0.479951
$225$	−3630.46	−1.07569
$226$	−927.552	−0.273008
$227$	1029.13	0.300907	0.150453	−	0.988617i	$-0.451927\pi$
$227$	1029.13	0.300907	0.150453	+	0.988617i	$0.451927\pi$
$228$	−331.082	−0.0961685
$229$	1673.08	0.482797	0.241399	−	0.970426i	$-0.422394\pi$
$229$	1673.08	0.482797	0.241399	+	0.970426i	$0.422394\pi$
$230$	288.651	0.0827527
$231$	7415.41	2.11211
$232$	−521.893	−0.147689
$233$	3407.98	0.958216	0.479108	−	0.877756i	$-0.340960\pi$
$233$	3407.98	0.958216	0.479108	+	0.877756i	$0.340960\pi$
$234$	−2183.98	−0.610133
$235$	−736.488	−0.204439
$236$	−833.668	−0.229946
$237$	4534.29	1.24276
$238$	3473.77	0.946097
$239$	−24.0829	−0.00651796	−0.00325898	−	0.999995i	$-0.501037\pi$
$239$	−24.0829	−0.00651796	−0.00325898	+	0.999995i	$0.501037\pi$
$240$	−2334.63	−0.627916
$241$	1104.35	0.295176	0.147588	−	0.989049i	$-0.452849\pi$
$241$	1104.35	0.295176	0.147588	+	0.989049i	$0.452849\pi$
$242$	8625.00	2.29106
$243$	−5366.21	−1.41664
$244$	1856.82	0.487174
$245$	−443.609	−0.115678
$246$	2061.61	0.534324
$247$	360.490	0.0928641
$248$	903.775	0.231410
$249$	−519.878	−0.132313
$250$	−2947.94	−0.745776
$251$	−4740.43	−1.19208	−0.596042	−	0.802953i	$-0.703261\pi$
$251$	−4740.43	−1.19208	−0.596042	+	0.802953i	$0.703261\pi$
$252$	1212.82	0.303177
$253$	1455.02	0.361567
$254$	364.502	0.0900429
$255$	2141.49	0.525904
$256$	3419.17	0.834757
$257$	−4324.06	−1.04952	−0.524761	−	0.851249i	$-0.675845\pi$
$257$	−4324.06	−1.04952	−0.524761	+	0.851249i	$0.675845\pi$
$258$	10908.9	2.63239
$259$	14.6237	0.00350840
$260$	−193.100	−0.0460599
$261$	958.042	0.227208
$262$	1185.30	0.279495
$263$	5489.00	1.28694	0.643472	−	0.765470i	$-0.277493\pi$
$263$	5489.00	1.28694	0.643472	+	0.765470i	$0.277493\pi$
$264$	−8821.27	−2.05648
$265$	−292.705	−0.0678518
$266$	−860.136	−0.198264
$267$	−2893.10	−0.663127
$268$	−588.623	−0.134164
$269$	−3743.29	−0.848448	−0.424224	−	0.905557i	$-0.639453\pi$
$269$	−3743.29	−0.848448	−0.424224	+	0.905557i	$0.639453\pi$
$270$	586.944	0.132297
$271$	2732.32	0.612461	0.306230	−	0.951957i	$-0.400932\pi$
$271$	2732.32	0.612461	0.306230	+	0.951957i	$0.400932\pi$
$272$	−5512.91	−1.22893
$273$	−2399.83	−0.532030
$274$	−7810.47	−1.72207
$275$	−6952.12	−1.52447
$276$	432.471	0.0943178
$277$	5744.29	1.24600	0.622998	−	0.782223i	$-0.285914\pi$
$277$	5744.29	1.24600	0.622998	+	0.782223i	$0.285914\pi$
$278$	3023.96	0.652392
$279$	−1659.07	−0.356006
$280$	−1058.14	−0.225842
$281$	−3490.91	−0.741104	−0.370552	−	0.928812i	$-0.620832\pi$
$281$	−3490.91	−0.741104	−0.370552	+	0.928812i	$0.620832\pi$
$282$	−4741.04	−1.00115
$283$	7380.57	1.55028	0.775141	−	0.631789i	$-0.217679\pi$
$283$	7380.57	1.55028	0.775141	+	0.631789i	$0.217679\pi$
$284$	−415.897	−0.0868977
$285$	−530.253	−0.110209
$286$	−4182.19	−0.864679
$287$	1246.56	0.256384
$288$	−3513.73	−0.718919
$289$	143.843	0.0292780
$290$	363.952	0.0736965
$291$	−9595.52	−1.93299
$292$	688.989	0.138082
$293$	7743.02	1.54386	0.771932	−	0.635705i	$-0.219290\pi$
$293$	7743.02	1.54386	0.771932	+	0.635705i	$0.219290\pi$
$294$	−2855.67	−0.566484
$295$	−1335.18	−0.263517
$296$	−17.3962	−0.00341599
$297$	2958.64	0.578040
$298$	−5029.92	−0.977769
$299$	−470.886	−0.0910770
$300$	−2066.35	−0.397669
$301$	6596.10	1.26310
$302$	−7694.03	−1.46603
$303$	−13857.6	−2.62739
$304$	1365.04	0.257535
$305$	2973.84	0.558300
$306$	7585.79	1.41716
$307$	4766.47	0.886113	0.443057	−	0.896494i	$-0.353894\pi$
$307$	4766.47	0.886113	0.443057	+	0.896494i	$0.353894\pi$
$308$	2322.49	0.429662
$309$	8034.48	1.47918
$310$	−630.264	−0.115473
$311$	−1776.31	−0.323876	−0.161938	−	0.986801i	$-0.551774\pi$
$311$	−1776.31	−0.323876	−0.161938	+	0.986801i	$0.551774\pi$
$312$	2854.81	0.518018
$313$	4676.33	0.844478	0.422239	−	0.906485i	$-0.361244\pi$
$313$	4676.33	0.844478	0.422239	+	0.906485i	$0.361244\pi$
$314$	−7261.60	−1.30508
$315$	1942.43	0.347440
$316$	1420.13	0.252811
$317$	−7565.31	−1.34041	−0.670206	−	0.742175i	$-0.733794\pi$
$317$	−7565.31	−1.34041	−0.670206	+	0.742175i	$0.733794\pi$
$318$	−1884.25	−0.332275
$319$	1834.59	0.321999
$320$	1075.64	0.187906
$321$	−16160.8	−2.80999
$322$	1123.54	0.194449
$323$	−1252.12	−0.215696
$324$	−1285.20	−0.220370
$325$	2249.90	0.384005
$326$	−7154.56	−1.21550
$327$	−2083.12	−0.352284
$328$	−1482.90	−0.249632
$329$	−2866.69	−0.480383
$330$	6151.68	1.02618
$331$	−6353.53	−1.05505	−0.527525	−	0.849539i	$-0.676880\pi$
$331$	−6353.53	−1.05505	−0.527525	+	0.849539i	$0.676880\pi$
$332$	−162.824	−0.0269161
$333$	31.9343	0.00525523
$334$	−3603.52	−0.590346
$335$	−942.726	−0.153751
$336$	−9087.28	−1.47545
$337$	−1978.62	−0.319829	−0.159914	−	0.987131i	$-0.551122\pi$
$337$	−1978.62	−0.319829	−0.159914	+	0.987131i	$0.551122\pi$
$338$	−5740.74	−0.923832
$339$	−2225.71	−0.356591
$340$	670.710	0.106983
$341$	−3177.01	−0.504531
$342$	−1878.31	−0.296980
$343$	−6915.67	−1.08866
$344$	−7846.63	−1.22983
$345$	692.636	0.108088
$346$	2551.88	0.396503
$347$	4914.18	0.760251	0.380126	−	0.924935i	$-0.375881\pi$
$347$	4914.18	0.760251	0.380126	+	0.924935i	$0.375881\pi$
$348$	545.290	0.0839960
$349$	383.748	0.0588584	0.0294292	−	0.999567i	$-0.490631\pi$
$349$	383.748	0.0588584	0.0294292	+	0.999567i	$0.490631\pi$
$350$	−5368.29	−0.819850
$351$	−957.498	−0.145605
$352$	−6728.59	−1.01885
$353$	−9021.04	−1.36017	−0.680087	−	0.733132i	$-0.738058\pi$
$353$	−9021.04	−1.36017	−0.680087	+	0.733132i	$0.738058\pi$
$354$	−8595.07	−1.29046
$355$	−666.092	−0.0995844
$356$	−906.111	−0.134898
$357$	8335.52	1.23575
$358$	14097.0	2.08114
$359$	4936.29	0.725703	0.362851	−	0.931847i	$-0.381803\pi$
$359$	4936.29	0.725703	0.362851	+	0.931847i	$0.381803\pi$
$360$	−2310.69	−0.338289
$361$	−6548.96	−0.954799
$362$	873.607	0.126839
$363$	20696.2	2.99247
$364$	−751.620	−0.108230
$365$	1103.47	0.158242
$366$	19143.7	2.73403
$367$	−3783.56	−0.538147	−0.269074	−	0.963120i	$-0.586718\pi$
$367$	−3783.56	−0.538147	−0.269074	+	0.963120i	$0.586718\pi$
$368$	−1783.07	−0.252579
$369$	2722.16	0.384038
$370$	12.1316	0.00170457
$371$	−1139.32	−0.159435
$372$	−944.292	−0.131611
$373$	1151.10	0.159791	0.0798953	−	0.996803i	$-0.474541\pi$
$373$	1151.10	0.159791	0.0798953	+	0.996803i	$0.474541\pi$
$374$	14526.3	2.00839
$375$	−7073.75	−0.974098
$376$	3410.18	0.467731
$377$	−593.725	−0.0811098
$378$	2284.61	0.310867
$379$	−8135.26	−1.10259	−0.551293	−	0.834312i	$-0.685865\pi$
$379$	−8135.26	−1.10259	−0.551293	+	0.834312i	$0.685865\pi$
$380$	−166.074	−0.0224195
$381$	874.645	0.117610
$382$	15359.4	2.05721
$383$	−4670.76	−0.623145	−0.311573	−	0.950222i	$-0.600856\pi$
$383$	−4670.76	−0.623145	−0.311573	+	0.950222i	$0.600856\pi$
$384$	13517.2	1.79635
$385$	3719.64	0.492391
$386$	−6374.46	−0.840548
$387$	14404.1	1.89200
$388$	−3005.29	−0.393223
$389$	−1217.77	−0.158723	−0.0793616	−	0.996846i	$-0.525288\pi$
$389$	−1217.77	−0.158723	−0.0793616	+	0.996846i	$0.525288\pi$
$390$	−1990.85	−0.258489
$391$	1635.56	0.211545
$392$	2054.06	0.264657
$393$	2844.19	0.365064
$394$	5379.27	0.687827
$395$	2274.44	0.289721
$396$	5071.69	0.643590
$397$	−14248.2	−1.80125	−0.900623	−	0.434600i	$-0.856890\pi$
$397$	−14248.2	−1.80125	−0.900623	+	0.434600i	$0.856890\pi$
$398$	1300.64	0.163807
$399$	−2063.95	−0.258964
$400$	8519.53	1.06494
$401$	−1578.50	−0.196575	−0.0982877	−	0.995158i	$-0.531337\pi$
$401$	−1578.50	−0.196575	−0.0982877	+	0.995158i	$0.531337\pi$
$402$	−6068.68	−0.752930
$403$	1028.17	0.127089
$404$	−4340.17	−0.534484
$405$	−2058.34	−0.252543
$406$	1416.64	0.173169
$407$	61.1524	0.00744769
$408$	−9915.83	−1.20320
$409$	779.782	0.0942732	0.0471366	−	0.998888i	$-0.484990\pi$
$409$	779.782	0.0942732	0.0471366	+	0.998888i	$0.484990\pi$
$410$	1034.13	0.124565
$411$	−18741.7	−2.24929
$412$	2516.38	0.300905
$413$	−5197.05	−0.619201
$414$	2453.52	0.291265
$415$	−260.776	−0.0308457
$416$	2177.56	0.256643
$417$	7256.17	0.852125
$418$	−3596.85	−0.420879
$419$	5927.01	0.691058	0.345529	−	0.938408i	$-0.387699\pi$
$419$	5927.01	0.691058	0.345529	+	0.938408i	$0.387699\pi$
$420$	1105.57	0.128444
$421$	7063.26	0.817678	0.408839	−	0.912607i	$-0.365934\pi$
$421$	7063.26	0.817678	0.408839	+	0.912607i	$0.365934\pi$
$422$	−16550.7	−1.90919
$423$	−6260.09	−0.719565
$424$	1355.32	0.155236
$425$	−7814.74	−0.891931
$426$	−4287.88	−0.487672
$427$	11575.3	1.31187
$428$	−5061.51	−0.571629
$429$	−10035.4	−1.12940
$430$	5472.00	0.613682
$431$	13349.8	1.49196	0.745981	−	0.665967i	$-0.231981\pi$
$431$	13349.8	1.49196	0.745981	+	0.665967i	$0.231981\pi$
$432$	−3625.70	−0.403800
$433$	5764.62	0.639792	0.319896	−	0.947453i	$-0.396352\pi$
$433$	5764.62	0.639792	0.319896	+	0.947453i	$0.396352\pi$
$434$	−2453.23	−0.271334
$435$	873.324	0.0962590
$436$	−652.428	−0.0716644
$437$	−404.980	−0.0443314
$438$	7103.44	0.774922
$439$	5931.28	0.644839	0.322420	−	0.946597i	$-0.395504\pi$
$439$	5931.28	0.644839	0.322420	+	0.946597i	$0.395504\pi$
$440$	−4424.84	−0.479422
$441$	−3770.64	−0.407153
$442$	−4701.12	−0.505904
$443$	3022.96	0.324210	0.162105	−	0.986774i	$-0.448172\pi$
$443$	3022.96	0.324210	0.162105	+	0.986774i	$0.448172\pi$
$444$	18.1761	0.00194279
$445$	−1451.21	−0.154593
$446$	14072.1	1.49402
$447$	−12069.6	−1.27712
$448$	4186.80	0.441535
$449$	−1489.39	−0.156544	−0.0782722	−	0.996932i	$-0.524940\pi$
$449$	−1489.39	−0.156544	−0.0782722	+	0.996932i	$0.524940\pi$
$450$	−11722.9	−1.22805
$451$	5212.78	0.544258
$452$	−697.088	−0.0725404
$453$	−18462.3	−1.91486
$454$	3323.12	0.343528
$455$	−1203.78	−0.124031
$456$	2455.25	0.252143
$457$	1794.35	0.183668	0.0918341	−	0.995774i	$-0.470727\pi$
$457$	1794.35	0.183668	0.0918341	+	0.995774i	$0.470727\pi$
$458$	5402.47	0.551181
$459$	3325.76	0.338198
$460$	216.932	0.0219880
$461$	8559.36	0.864748	0.432374	−	0.901694i	$-0.357676\pi$
$461$	8559.36	0.864748	0.432374	+	0.901694i	$0.357676\pi$
$462$	23944.7	2.41127
$463$	14204.4	1.42578	0.712890	−	0.701276i	$-0.247386\pi$
$463$	14204.4	1.42578	0.712890	+	0.701276i	$0.247386\pi$
$464$	−2248.22	−0.224938
$465$	−1512.36	−0.150825
$466$	11004.5	1.09394
$467$	5697.34	0.564543	0.282272	−	0.959335i	$-0.408912\pi$
$467$	5697.34	0.564543	0.282272	+	0.959335i	$0.408912\pi$
$468$	−1641.34	−0.162117
$469$	−3669.45	−0.361278
$470$	−2378.15	−0.233396
$471$	−17424.6	−1.70464
$472$	6182.34	0.602893
$473$	27583.0	2.68133
$474$	14641.4	1.41878
$475$	1935.00	0.186913
$476$	2610.66	0.251385
$477$	−2487.97	−0.238818
$478$	−77.7648	−0.00744117
$479$	−9194.60	−0.877061	−0.438530	−	0.898716i	$-0.644501\pi$
$479$	−9194.60	−0.877061	−0.438530	+	0.898716i	$0.644501\pi$
$480$	−3203.02	−0.304577
$481$	−19.7906	−0.00187603
$482$	3565.99	0.336985
$483$	2696.01	0.253980
$484$	6481.99	0.608752
$485$	−4813.21	−0.450632
$486$	−17327.7	−1.61729
$487$	11008.4	1.02431	0.512155	−	0.858893i	$-0.328848\pi$
$487$	11008.4	1.02431	0.512155	+	0.858893i	$0.328848\pi$
$488$	−13769.8	−1.27732
$489$	−17167.8	−1.58764
$490$	−1432.43	−0.132063
$491$	18486.7	1.69917	0.849586	−	0.527451i	$-0.176852\pi$
$491$	18486.7	1.69917	0.849586	+	0.527451i	$0.176852\pi$
$492$	1549.37	0.141974
$493$	2062.23	0.188394
$494$	1164.04	0.106017
$495$	8122.70	0.737552
$496$	3893.30	0.352448
$497$	−2592.68	−0.234000
$498$	−1678.71	−0.151054
$499$	−15380.1	−1.37977	−0.689886	−	0.723918i	$-0.742339\pi$
$499$	−15380.1	−1.37977	−0.689886	+	0.723918i	$0.742339\pi$
$500$	−2215.48	−0.198158
$501$	−8646.85	−0.771084
$502$	−15307.1	−1.36093
$503$	9466.79	0.839172	0.419586	−	0.907716i	$-0.362175\pi$
$503$	9466.79	0.839172	0.419586	+	0.907716i	$0.362175\pi$
$504$	−8994.09	−0.794898
$505$	−6951.12	−0.612517
$506$	4698.34	0.412780
$507$	−13775.2	−1.20667
$508$	273.936	0.0239251
$509$	3324.41	0.289493	0.144747	−	0.989469i	$-0.453763\pi$
$509$	3324.41	0.289493	0.144747	+	0.989469i	$0.453763\pi$
$510$	6914.99	0.600394
$511$	4295.13	0.371830
$512$	−2915.68	−0.251672
$513$	−823.486	−0.0708729
$514$	−13962.6	−1.19818
$515$	4030.17	0.344836
$516$	8198.40	0.699447
$517$	−11987.7	−1.01977
$518$	47.2207	0.00400533
$519$	6123.39	0.517894
$520$	1432.00	0.120764
$521$	8699.50	0.731539	0.365770	−	0.930705i	$-0.380806\pi$
$521$	8699.50	0.731539	0.365770	+	0.930705i	$0.380806\pi$
$522$	3093.56	0.259390
$523$	−7587.23	−0.634353	−0.317176	−	0.948367i	$-0.602735\pi$
$523$	−7587.23	−0.634353	−0.317176	+	0.948367i	$0.602735\pi$
$524$	890.791	0.0742641
$525$	−12881.5	−1.07085
$526$	17724.2	1.46923
$527$	−3571.22	−0.295189
$528$	−38000.5	−3.13212
$529$	529.000	0.0434783
$530$	−945.158	−0.0774623
$531$	−11349.0	−0.927501
$532$	−646.423	−0.0526804
$533$	−1687.00	−0.137096
$534$	−9341.96	−0.757052
$535$	−8106.40	−0.655084
$536$	4365.13	0.351763
$537$	33826.5	2.71829
$538$	−12087.3	−0.968623
$539$	−7220.56	−0.577016
$540$	441.109	0.0351524
$541$	3936.14	0.312806	0.156403	−	0.987693i	$-0.450010\pi$
$541$	3936.14	0.312806	0.156403	+	0.987693i	$0.450010\pi$
$542$	8822.80	0.699210
$543$	2096.27	0.165672
$544$	−7563.48	−0.596106
$545$	−1044.92	−0.0821270
$546$	−7749.16	−0.607387
$547$	9174.77	0.717157	0.358578	−	0.933500i	$-0.383262\pi$
$547$	9174.77	0.717157	0.358578	+	0.933500i	$0.383262\pi$
$548$	−5869.85	−0.457568
$549$	25277.4	1.96505
$550$	−22448.7	−1.74039
$551$	−510.627	−0.0394799
$552$	−3207.13	−0.247291
$553$	8853.01	0.680774
$554$	18548.6	1.42248
$555$	29.1104	0.00222643
$556$	2272.61	0.173346
$557$	−6120.40	−0.465583	−0.232791	−	0.972527i	$-0.574786\pi$
$557$	−6120.40	−0.465583	−0.232791	+	0.972527i	$0.574786\pi$
$558$	−5357.20	−0.406431
$559$	−8926.63	−0.675413
$560$	−4558.27	−0.343968
$561$	34856.8	2.62327
$562$	−11272.3	−0.846075
$563$	−8425.26	−0.630697	−0.315349	−	0.948976i	$-0.602121\pi$
$563$	−8425.26	−0.630697	−0.315349	+	0.948976i	$0.602121\pi$
$564$	−3563.06	−0.266014
$565$	−1116.44	−0.0831310
$566$	23832.2	1.76986
$567$	−8011.85	−0.593415
$568$	3084.22	0.227837
$569$	−10143.8	−0.747362	−0.373681	−	0.927557i	$-0.621904\pi$
$569$	−10143.8	−0.747362	−0.373681	+	0.927557i	$0.621904\pi$
$570$	−1712.21	−0.125819
$571$	13873.7	1.01681	0.508403	−	0.861119i	$-0.330236\pi$
$571$	13873.7	1.01681	0.508403	+	0.861119i	$0.330236\pi$
$572$	−3143.06	−0.229752
$573$	36855.7	2.68703
$574$	4025.21	0.292699
$575$	−2527.57	−0.183316
$576$	9142.85	0.661375
$577$	10844.4	0.782420	0.391210	−	0.920301i	$-0.372057\pi$
$577$	10844.4	0.782420	0.391210	+	0.920301i	$0.372057\pi$
$578$	464.476	0.0334250
$579$	−15295.9	−1.09788
$580$	273.523	0.0195817
$581$	−1015.04	−0.0724801
$582$	−30984.4	−2.20678
$583$	−4764.31	−0.338452
$584$	−5109.43	−0.362037
$585$	−2628.73	−0.185786
$586$	25002.6	1.76254
$587$	18428.9	1.29581	0.647907	−	0.761720i	$-0.275645\pi$
$587$	18428.9	1.29581	0.647907	+	0.761720i	$0.275645\pi$
$588$	−2146.14	−0.150519
$589$	884.265	0.0618600
$590$	−4311.37	−0.300841
$591$	12907.9	0.898408
$592$	−74.9397	−0.00520271
$593$	3920.60	0.271500	0.135750	−	0.990743i	$-0.456656\pi$
$593$	3920.60	0.271500	0.135750	+	0.990743i	$0.456656\pi$
$594$	9553.60	0.659914
$595$	4181.18	0.288087
$596$	−3780.16	−0.259801
$597$	3120.95	0.213957
$598$	−1520.51	−0.103977
$599$	4164.23	0.284050	0.142025	−	0.989863i	$-0.454639\pi$
$599$	4164.23	0.284050	0.142025	+	0.989863i	$0.454639\pi$
$600$	15323.7	1.04265
$601$	−15472.2	−1.05012	−0.525061	−	0.851065i	$-0.675958\pi$
$601$	−15472.2	−1.05012	−0.525061	+	0.851065i	$0.675958\pi$
$602$	21299.1	1.44200
$603$	−8013.10	−0.541159
$604$	−5782.34	−0.389536
$605$	10381.4	0.697627
$606$	−44746.9	−2.99954
$607$	12890.8	0.861977	0.430989	−	0.902357i	$-0.358165\pi$
$607$	12890.8	0.861977	0.430989	+	0.902357i	$0.358165\pi$
$608$	1872.78	0.124920
$609$	3399.31	0.226186
$610$	9602.66	0.637377
$611$	3879.55	0.256874
$612$	5700.99	0.376550
$613$	12888.2	0.849185	0.424593	−	0.905385i	$-0.360417\pi$
$613$	12888.2	0.849185	0.424593	+	0.905385i	$0.360417\pi$
$614$	15391.2	1.01162
$615$	2481.44	0.162702
$616$	−17223.2	−1.12653
$617$	8707.19	0.568133	0.284067	−	0.958805i	$-0.408316\pi$
$617$	8707.19	0.568133	0.284067	+	0.958805i	$0.408316\pi$
$618$	25943.7	1.68869
$619$	24738.2	1.60632	0.803159	−	0.595765i	$-0.203151\pi$
$619$	24738.2	1.60632	0.803159	+	0.595765i	$0.203151\pi$
$620$	−473.666	−0.0306821
$621$	1075.67	0.0695090
$622$	−5735.80	−0.369750
$623$	−5648.66	−0.363256
$624$	12298.0	0.788964
$625$	10188.5	0.652065
$626$	15100.1	0.964090
$627$	−8630.85	−0.549734
$628$	−5457.35	−0.346771
$629$	68.7402	0.00435747
$630$	6272.20	0.396651
$631$	12064.2	0.761122	0.380561	−	0.924756i	$-0.375731\pi$
$631$	12064.2	0.761122	0.380561	+	0.924756i	$0.375731\pi$
$632$	−10531.4	−0.662844
$633$	−39714.4	−2.49369
$634$	−24428.8	−1.53027
$635$	438.730	0.0274181
$636$	−1416.08	−0.0882880
$637$	2336.77	0.145347
$638$	5923.99	0.367607
$639$	−5661.73	−0.350508
$640$	6780.36	0.418777
$641$	13769.0	0.848430	0.424215	−	0.905562i	$-0.360550\pi$
$641$	13769.0	0.848430	0.424215	+	0.905562i	$0.360550\pi$
$642$	−52183.9	−3.20800
$643$	8592.49	0.526990	0.263495	−	0.964661i	$-0.415125\pi$
$643$	8592.49	0.526990	0.263495	+	0.964661i	$0.415125\pi$
$644$	844.381	0.0516666
$645$	13130.4	0.801563
$646$	−4043.15	−0.246247
$647$	19250.3	1.16972	0.584859	−	0.811135i	$-0.301150\pi$
$647$	19250.3	1.16972	0.584859	+	0.811135i	$0.301150\pi$
$648$	9530.79	0.577785
$649$	−21732.6	−1.31445
$650$	7265.02	0.438396
$651$	−5886.67	−0.354404
$652$	−5376.90	−0.322969
$653$	14782.4	0.885879	0.442939	−	0.896552i	$-0.353936\pi$
$653$	14782.4	0.885879	0.442939	+	0.896552i	$0.353936\pi$
$654$	−6726.50	−0.402182
$655$	1426.67	0.0851063
$656$	−6388.05	−0.380200
$657$	9379.41	0.556965
$658$	−9256.69	−0.548424
$659$	19128.3	1.13070	0.565352	−	0.824850i	$-0.308740\pi$
$659$	19128.3	1.13070	0.565352	+	0.824850i	$0.308740\pi$
$660$	4623.20	0.272664
$661$	−30507.9	−1.79519	−0.897593	−	0.440825i	$-0.854686\pi$
$661$	−30507.9	−1.79519	−0.897593	+	0.440825i	$0.854686\pi$
$662$	−20515.9	−1.20449
$663$	−11280.6	−0.660789
$664$	1207.48	0.0705711
$665$	−1035.30	−0.0603715
$666$	103.117	0.00599958
$667$	667.000	0.0387202
$668$	−2708.17	−0.156860
$669$	33766.8	1.95142
$670$	−3044.11	−0.175529
$671$	48404.7	2.78486
$672$	−12467.4	−0.715683
$673$	−19648.1	−1.12538	−0.562689	−	0.826669i	$-0.690233\pi$
$673$	−19648.1	−1.12538	−0.562689	+	0.826669i	$0.690233\pi$
$674$	−6389.06	−0.365129
$675$	−5139.55	−0.293069
$676$	−4314.37	−0.245469
$677$	−13235.4	−0.751373	−0.375687	−	0.926747i	$-0.622593\pi$
$677$	−13235.4	−0.751373	−0.375687	+	0.926747i	$0.622593\pi$
$678$	−7186.94	−0.407098
$679$	−18734.9	−1.05888
$680$	−4973.87	−0.280499
$681$	7974.01	0.448700
$682$	−10258.7	−0.575992
$683$	−309.808	−0.0173565	−0.00867824	−	0.999962i	$-0.502762\pi$
$683$	−309.808	−0.0173565	−0.00867824	+	0.999962i	$0.502762\pi$
$684$	−1411.61	−0.0789100
$685$	−9401.01	−0.524371
$686$	−22331.0	−1.24286
$687$	12963.5	0.719927
$688$	−33801.9	−1.87309
$689$	1541.86	0.0852544
$690$	2236.55	0.123397
$691$	16379.8	0.901759	0.450879	−	0.892585i	$-0.351110\pi$
$691$	16379.8	0.901759	0.450879	+	0.892585i	$0.351110\pi$
$692$	1917.83	0.105354
$693$	31616.7	1.73307
$694$	15868.1	0.867934
$695$	3639.76	0.198653
$696$	−4043.78	−0.220228
$697$	5859.59	0.318433
$698$	1239.14	0.0671951
$699$	26406.0	1.42885
$700$	−4034.46	−0.217840
$701$	28396.1	1.52997	0.764983	−	0.644050i	$-0.222747\pi$
$701$	28396.1	1.52997	0.764983	+	0.644050i	$0.222747\pi$
$702$	−3091.81	−0.166229
$703$	−17.0207	−0.000913153 0
$704$	17508.0	0.937299
$705$	−5706.52	−0.304851
$706$	−29129.3	−1.55283
$707$	−27056.4	−1.43927
$708$	−6459.50	−0.342885
$709$	7251.41	0.384108	0.192054	−	0.981384i	$-0.438485\pi$
$709$	7251.41	0.384108	0.192054	+	0.981384i	$0.438485\pi$
$710$	−2150.84	−0.113690
$711$	19332.6	1.01973
$712$	6719.57	0.353689
$713$	−1155.06	−0.0606695
$714$	26915.8	1.41078
$715$	−5033.86	−0.263295
$716$	10594.4	0.552976
$717$	−186.601	−0.00971931
$718$	15939.5	0.828491
$719$	4320.18	0.224083	0.112041	−	0.993704i	$-0.464261\pi$
$719$	4320.18	0.224083	0.112041	+	0.993704i	$0.464261\pi$
$720$	−9954.04	−0.515229
$721$	15687.0	0.810282
$722$	−21146.9	−1.09004
$723$	8556.81	0.440154
$724$	656.546	0.0337022
$725$	−3186.93	−0.163255
$726$	66829.0	3.41633
$727$	11013.1	0.561835	0.280917	−	0.959732i	$-0.409361\pi$
$727$	11013.1	0.561835	0.280917	+	0.959732i	$0.409361\pi$
$728$	5573.89	0.283766
$729$	−27279.8	−1.38596
$730$	3563.16	0.180655
$731$	31005.6	1.56879
$732$	14387.1	0.726454
$733$	36059.7	1.81705	0.908525	−	0.417832i	$-0.137210\pi$
$733$	36059.7	1.81705	0.908525	+	0.417832i	$0.137210\pi$
$734$	−12217.3	−0.614371
$735$	−3437.21	−0.172494
$736$	−2446.30	−0.122516
$737$	−15344.6	−0.766929
$738$	8789.99	0.438433
$739$	6764.59	0.336724	0.168362	−	0.985725i	$-0.446152\pi$
$739$	6764.59	0.336724	0.168362	+	0.985725i	$0.446152\pi$
$740$	9.11730	0.000452917 0
$741$	2793.18	0.138475
$742$	−3678.92	−0.182018
$743$	−1119.22	−0.0552629	−0.0276314	−	0.999618i	$-0.508796\pi$
$743$	−1119.22	−0.0552629	−0.0276314	+	0.999618i	$0.508796\pi$
$744$	7002.71	0.345070
$745$	−6054.22	−0.297731
$746$	3716.97	0.182423
$747$	−2216.57	−0.108568
$748$	10917.1	0.533646
$749$	−31553.2	−1.53929
$750$	−22841.5	−1.11207
$751$	10671.6	0.518527	0.259263	−	0.965807i	$-0.416520\pi$
$751$	10671.6	0.518527	0.259263	+	0.965807i	$0.416520\pi$
$752$	14690.4	0.712374
$753$	−36730.2	−1.77759
$754$	−1917.17	−0.0925982
$755$	−9260.86	−0.446407
$756$	1716.96	0.0825997
$757$	−15764.1	−0.756879	−0.378439	−	0.925626i	$-0.623539\pi$
$757$	−15764.1	−0.756879	−0.378439	+	0.925626i	$0.623539\pi$
$758$	−26269.1	−1.25876
$759$	11273.9	0.539154
$760$	1231.57	0.0587815
$761$	16560.2	0.788842	0.394421	−	0.918930i	$-0.370945\pi$
$761$	16560.2	0.788842	0.394421	+	0.918930i	$0.370945\pi$
$762$	2824.27	0.134268
$763$	−4067.21	−0.192979
$764$	11543.1	0.546616
$765$	9130.57	0.431525
$766$	−15082.1	−0.711408
$767$	7033.26	0.331104
$768$	26492.7	1.24476
$769$	18701.5	0.876974	0.438487	−	0.898738i	$-0.355515\pi$
$769$	18701.5	0.876974	0.438487	+	0.898738i	$0.355515\pi$
$770$	12010.9	0.562133
$771$	−33504.0	−1.56500
$772$	−4790.63	−0.223340
$773$	−29544.4	−1.37470	−0.687348	−	0.726328i	$-0.741225\pi$
$773$	−29544.4	−1.37470	−0.687348	+	0.726328i	$0.741225\pi$
$774$	46511.6	2.15998
$775$	5518.89	0.255799
$776$	22286.7	1.03099
$777$	113.309	0.00523157
$778$	−3932.23	−0.181205
$779$	−1450.88	−0.0667309
$780$	−1496.20	−0.0686826
$781$	−10841.9	−0.496739
$782$	5281.31	0.241508
$783$	1356.28	0.0619022
$784$	8848.50	0.403084
$785$	−8740.37	−0.397398
$786$	9184.01	0.416772
$787$	−20406.3	−0.924279	−0.462139	−	0.886807i	$-0.652918\pi$
$787$	−20406.3	−0.924279	−0.462139	+	0.886807i	$0.652918\pi$
$788$	4042.71	0.182761
$789$	42530.3	1.91904
$790$	7344.29	0.330757
$791$	−4345.61	−0.195338
$792$	−37610.8	−1.68743
$793$	−15665.1	−0.701493
$794$	−46008.0	−2.05638
$795$	−2267.96	−0.101178
$796$	977.474	0.0435247
$797$	−18856.0	−0.838036	−0.419018	−	0.907978i	$-0.637626\pi$
$797$	−18856.0	−0.838036	−0.419018	+	0.907978i	$0.637626\pi$
$798$	−6664.58	−0.295644
$799$	−13475.2	−0.596642
$800$	11688.4	0.516561
$801$	−12335.2	−0.544121
$802$	−5097.06	−0.224418
$803$	17961.0	0.789329
$804$	−4560.82	−0.200059
$805$	1352.34	0.0592097
$806$	3320.00	0.145090
$807$	−29004.1	−1.26517
$808$	32186.0	1.40136
$809$	38230.4	1.66145	0.830723	−	0.556685i	$-0.187927\pi$
$809$	38230.4	1.66145	0.830723	+	0.556685i	$0.187927\pi$
$810$	−6646.48	−0.288313
$811$	−25579.7	−1.10755	−0.553777	−	0.832665i	$-0.686814\pi$
$811$	−25579.7	−1.10755	−0.553777	+	0.832665i	$0.686814\pi$
$812$	1064.65	0.0460124
$813$	21170.8	0.913276
$814$	197.464	0.00850258
$815$	−8611.53	−0.370121
$816$	−42715.6	−1.83253
$817$	−7677.25	−0.328755
$818$	2517.95	0.107626
$819$	−10232.0	−0.436552
$820$	777.181	0.0330980
$821$	273.385	0.0116214	0.00581071	−	0.999983i	$-0.498150\pi$
$821$	273.385	0.0116214	0.00581071	+	0.999983i	$0.498150\pi$
$822$	−60517.8	−2.56788
$823$	14642.5	0.620175	0.310087	−	0.950708i	$-0.399642\pi$
$823$	14642.5	0.620175	0.310087	+	0.950708i	$0.399642\pi$
$824$	−18661.0	−0.788941
$825$	−53867.0	−2.27322
$826$	−16781.5	−0.706905
$827$	5042.66	0.212032	0.106016	−	0.994364i	$-0.466190\pi$
$827$	5042.66	0.212032	0.106016	+	0.994364i	$0.466190\pi$
$828$	1843.90	0.0773914
$829$	−23231.6	−0.973303	−0.486651	−	0.873596i	$-0.661782\pi$
$829$	−23231.6	−0.973303	−0.486651	+	0.873596i	$0.661782\pi$
$830$	−842.057	−0.0352147
$831$	44508.4	1.85798
$832$	−5666.07	−0.236101
$833$	−8116.49	−0.337599
$834$	23430.5	0.972820
$835$	−4337.35	−0.179760
$836$	−2703.16	−0.111831
$837$	−2348.70	−0.0969928
$838$	19138.6	0.788940
$839$	−45842.8	−1.88637	−0.943187	−	0.332262i	$-0.892188\pi$
$839$	−45842.8	−1.88637	−0.943187	+	0.332262i	$0.892188\pi$
$840$	−8198.76	−0.336767
$841$	841.000	0.0344828
$842$	22807.6	0.933494
$843$	−27048.6	−1.10510
$844$	−12438.4	−0.507285
$845$	−6909.80	−0.281307
$846$	−20214.1	−0.821485
$847$	40408.4	1.63926
$848$	5838.47	0.236432
$849$	57186.8	2.31171
$850$	−25234.2	−1.01826
$851$	22.2330	0.000895580 0
$852$	−3222.49	−0.129578
$853$	−39611.1	−1.58999	−0.794994	−	0.606618i	$-0.792526\pi$
$853$	−39611.1	−1.58999	−0.794994	+	0.606618i	$0.792526\pi$
$854$	37377.2	1.49768
$855$	−2260.81	−0.0904305
$856$	37535.3	1.49875
$857$	−22352.5	−0.890952	−0.445476	−	0.895294i	$-0.646966\pi$
$857$	−22352.5	−0.890952	−0.445476	+	0.895294i	$0.646966\pi$
$858$	−32404.8	−1.28937
$859$	−5364.76	−0.213089	−0.106544	−	0.994308i	$-0.533979\pi$
$859$	−5364.76	−0.213089	−0.106544	+	0.994308i	$0.533979\pi$
$860$	4112.40	0.163060
$861$	9658.73	0.382310
$862$	43107.0	1.70328
$863$	−20283.3	−0.800061	−0.400030	−	0.916502i	$-0.631000\pi$
$863$	−20283.3	−0.800061	−0.400030	+	0.916502i	$0.631000\pi$
$864$	−4974.31	−0.195867
$865$	3071.55	0.120735
$866$	18614.2	0.730413
$867$	1114.54	0.0436582
$868$	−1843.69	−0.0720955
$869$	37020.8	1.44516
$870$	2820.00	0.109893
$871$	4965.94	0.193185
$872$	4838.30	0.187896
$873$	−40911.9	−1.58609
$874$	−1307.70	−0.0506105
$875$	−13811.2	−0.533604
$876$	5338.49	0.205903
$877$	47021.6	1.81050	0.905250	−	0.424880i	$-0.139684\pi$
$877$	47021.6	1.81050	0.905250	+	0.424880i	$0.139684\pi$
$878$	19152.4	0.736174
$879$	59995.2	2.30215
$880$	−19061.4	−0.730181
$881$	−32694.2	−1.25028	−0.625138	−	0.780514i	$-0.714958\pi$
$881$	−32694.2	−1.25028	−0.625138	+	0.780514i	$0.714958\pi$
$882$	−12175.6	−0.464822
$883$	−32327.5	−1.23206	−0.616028	−	0.787724i	$-0.711259\pi$
$883$	−32327.5	−1.23206	−0.616028	+	0.787724i	$0.711259\pi$
$884$	−3533.06	−0.134423
$885$	−10345.4	−0.392945
$886$	9761.27	0.370131
$887$	4729.79	0.179043	0.0895213	−	0.995985i	$-0.471466\pi$
$887$	4729.79	0.179043	0.0895213	+	0.995985i	$0.471466\pi$
$888$	−134.791	−0.00509379
$889$	1707.71	0.0644259
$890$	−4686.02	−0.176489
$891$	−33503.3	−1.25971
$892$	10575.7	0.396972
$893$	3336.57	0.125032
$894$	−38973.2	−1.45801
$895$	16967.7	0.633708
$896$	26391.8	0.984025
$897$	−3648.56	−0.135810
$898$	−4809.30	−0.178717
$899$	−1456.38	−0.0540300
$900$	−8810.19	−0.326303
$901$	−5355.48	−0.198021
$902$	16832.3	0.621347
$903$	51108.5	1.88348
$904$	5169.49	0.190193
$905$	1051.51	0.0386225
$906$	−59615.6	−2.18609
$907$	−30256.3	−1.10765	−0.553827	−	0.832632i	$-0.686833\pi$
$907$	−30256.3	−1.10765	−0.553827	+	0.832632i	$0.686833\pi$
$908$	2497.44	0.0912779
$909$	−59084.0	−2.15588
$910$	−3887.05	−0.141598
$911$	53719.2	1.95367	0.976837	−	0.213987i	$-0.0686449\pi$
$911$	53719.2	1.95367	0.976837	+	0.213987i	$0.0686449\pi$
$912$	10576.8	0.384026
$913$	−4244.61	−0.153862
$914$	5794.05	0.209683
$915$	23042.1	0.832513
$916$	4060.14	0.146453
$917$	5553.15	0.199979
$918$	10739.0	0.386101
$919$	−36148.7	−1.29754	−0.648768	−	0.760987i	$-0.724715\pi$
$919$	−36148.7	−1.29754	−0.648768	+	0.760987i	$0.724715\pi$
$920$	−1608.73	−0.0576502
$921$	36932.0	1.32134
$922$	27638.6	0.987232
$923$	3508.73	0.125126
$924$	17995.3	0.640694
$925$	−106.230	−0.00377601
$926$	45866.8	1.62773
$927$	34256.2	1.21372
$928$	−3084.47	−0.109108
$929$	−16686.9	−0.589321	−0.294660	−	0.955602i	$-0.595206\pi$
$929$	−16686.9	−0.589321	−0.294660	+	0.955602i	$0.595206\pi$
$930$	−4883.47	−0.172188
$931$	2009.72	0.0707473
$932$	8270.29	0.290668
$933$	−13763.4	−0.482950
$934$	18397.0	0.644505
$935$	17484.5	0.611556
$936$	12171.9	0.425054
$937$	−21858.7	−0.762104	−0.381052	−	0.924554i	$-0.624438\pi$
$937$	−21858.7	−0.762104	−0.381052	+	0.924554i	$0.624438\pi$
$938$	−11848.8	−0.412450
$939$	36233.5	1.25925
$940$	−1787.27	−0.0620151
$941$	14412.5	0.499292	0.249646	−	0.968337i	$-0.419686\pi$
$941$	14412.5	0.499292	0.249646	+	0.968337i	$0.419686\pi$
$942$	−56265.0	−1.94608
$943$	1895.20	0.0654467
$944$	26632.4	0.918232
$945$	2749.85	0.0946590
$946$	89066.9	3.06112
$947$	33421.9	1.14685	0.573424	−	0.819259i	$-0.305615\pi$
$947$	33421.9	1.14685	0.573424	+	0.819259i	$0.305615\pi$
$948$	11003.6	0.376982
$949$	−5812.68	−0.198828
$950$	6248.20	0.213388
$951$	−58618.2	−1.99877
$952$	−19360.2	−0.659106
$953$	−37734.0	−1.28261	−0.641304	−	0.767287i	$-0.721606\pi$
$953$	−37734.0	−1.28261	−0.641304	+	0.767287i	$0.721606\pi$
$954$	−8033.77	−0.272644
$955$	18487.2	0.626420
$956$	−58.4430	−0.00197718
$957$	14215.0	0.480151
$958$	−29689.8	−1.00129
$959$	−36592.4	−1.23215
$960$	8334.36	0.280198
$961$	−27268.9	−0.915342
$962$	−63.9047	−0.00214176
$963$	−68903.8	−2.30570
$964$	2679.97	0.0895394
$965$	−7672.57	−0.255947
$966$	8705.53	0.289954
$967$	10586.2	0.352047	0.176024	−	0.984386i	$-0.443676\pi$
$967$	10586.2	0.352047	0.176024	+	0.984386i	$0.443676\pi$
$968$	−48069.3	−1.59608
$969$	−9701.77	−0.321637
$970$	−15542.1	−0.514460
$971$	45559.8	1.50575	0.752876	−	0.658163i	$-0.228666\pi$
$971$	45559.8	1.50575	0.752876	+	0.658163i	$0.228666\pi$
$972$	−13022.4	−0.429726
$973$	14167.4	0.466788
$974$	35546.7	1.16939
$975$	17432.8	0.572613
$976$	−59318.0	−1.94541
$977$	54697.0	1.79111	0.895554	−	0.444953i	$-0.146780\pi$
$977$	54697.0	1.79111	0.895554	+	0.444953i	$0.146780\pi$
$978$	−55435.6	−1.81251
$979$	−23621.1	−0.771127
$980$	−1076.52	−0.0350901
$981$	−8881.70	−0.289063
$982$	59694.4	1.93984
$983$	−61312.8	−1.98939	−0.994697	−	0.102847i	$-0.967205\pi$
$983$	−61312.8	−1.98939	−0.994697	+	0.102847i	$0.967205\pi$
$984$	−11489.9	−0.372241
$985$	6474.72	0.209443
$986$	6659.05	0.215078
$987$	−22212.0	−0.716327
$988$	874.816	0.0281696
$989$	10028.3	0.322428
$990$	26228.6	0.842019
$991$	−4288.92	−0.137479	−0.0687397	−	0.997635i	$-0.521898\pi$
$991$	−4288.92	−0.137479	−0.0687397	+	0.997635i	$0.521898\pi$
$992$	5341.45	0.170959
$993$	−49229.0	−1.57325
$994$	−8371.90	−0.267143
$995$	1565.50	0.0498791
$996$	−1261.61	−0.0401362
$997$	−41458.6	−1.31696	−0.658479	−	0.752599i	$-0.728800\pi$
$997$	−41458.6	−1.31696	−0.658479	+	0.752599i	$0.728800\pi$
$998$	−49663.0	−1.57520
$999$	45.2087	0.00143177

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	667.4.a.d.1.30	✓	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
667.4.a.d.1.30	✓	42	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)

\(f(q)\)	\(=\)	\(q+3.22905 q^{2} +7.74829 q^{3} +2.42674 q^{4} +3.88662 q^{5} +25.0196 q^{6} +15.1282 q^{7} -17.9963 q^{8} +33.0359 q^{9} +O(q^{10})\)	\(q+3.22905 q^{2} +7.74829 q^{3} +2.42674 q^{4} +3.88662 q^{5} +25.0196 q^{6} +15.1282 q^{7} -17.9963 q^{8} +33.0359 q^{9} +12.5501 q^{10} +63.2619 q^{11} +18.8031 q^{12} -20.4733 q^{13} +48.8497 q^{14} +30.1146 q^{15} -77.5249 q^{16} +71.1115 q^{17} +106.675 q^{18} -17.6078 q^{19} +9.43181 q^{20} +117.218 q^{21} +204.276 q^{22} +23.0000 q^{23} -139.441 q^{24} -109.894 q^{25} -66.1092 q^{26} +46.7682 q^{27} +36.7122 q^{28} +29.0000 q^{29} +97.2415 q^{30} -50.2200 q^{31} -106.361 q^{32} +490.171 q^{33} +229.622 q^{34} +58.7975 q^{35} +80.1697 q^{36} +0.966654 q^{37} -56.8565 q^{38} -158.633 q^{39} -69.9447 q^{40} +82.4000 q^{41} +378.501 q^{42} +436.013 q^{43} +153.520 q^{44} +128.398 q^{45} +74.2681 q^{46} -189.493 q^{47} -600.685 q^{48} -114.138 q^{49} -354.854 q^{50} +550.992 q^{51} -49.6834 q^{52} -75.3110 q^{53} +151.017 q^{54} +245.875 q^{55} -272.252 q^{56} -136.430 q^{57} +93.6424 q^{58} -343.534 q^{59} +73.0804 q^{60} +765.148 q^{61} -162.163 q^{62} +499.774 q^{63} +276.755 q^{64} -79.5718 q^{65} +1582.79 q^{66} -242.557 q^{67} +172.569 q^{68} +178.211 q^{69} +189.860 q^{70} -171.381 q^{71} -594.525 q^{72} +283.915 q^{73} +3.12137 q^{74} -851.492 q^{75} -42.7296 q^{76} +957.038 q^{77} -512.233 q^{78} +585.199 q^{79} -301.309 q^{80} -529.597 q^{81} +266.073 q^{82} -67.0958 q^{83} +284.457 q^{84} +276.383 q^{85} +1407.91 q^{86} +224.700 q^{87} -1138.48 q^{88} -373.386 q^{89} +414.603 q^{90} -309.724 q^{91} +55.8151 q^{92} -389.119 q^{93} -611.883 q^{94} -68.4349 q^{95} -824.115 q^{96} -1238.41 q^{97} -368.556 q^{98} +2089.92 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q + 12 q^{2} + 32 q^{3} + 192 q^{4} + 80 q^{5} + 32 q^{6} + 18 q^{7} + 102 q^{8} + 492 q^{9}+O(q^{10}) \) 42 * q + 12 * q^2 + 32 * q^3 + 192 * q^4 + 80 * q^5 + 32 * q^6 + 18 * q^7 + 102 * q^8 + 492 * q^9	\( 42 q + 12 q^{2} + 32 q^{3} + 192 q^{4} + 80 q^{5} + 32 q^{6} + 18 q^{7} + 102 q^{8} + 492 q^{9} + 48 q^{10} + 50 q^{11} + 403 q^{12} + 236 q^{13} + 32 q^{14} + 12 q^{15} + 792 q^{16} + 456 q^{17} + 297 q^{18} + 166 q^{19} + 533 q^{20} + 258 q^{21} + 73 q^{22} + 966 q^{23} + 514 q^{24} + 1358 q^{25} + 497 q^{26} + 1250 q^{27} + 143 q^{28} + 1218 q^{29} + 593 q^{30} + 558 q^{31} + 1328 q^{32} - 464 q^{33} + 157 q^{34} + 48 q^{35} + 3030 q^{36} + 352 q^{37} + 218 q^{38} + 1080 q^{39} + 900 q^{40} + 182 q^{41} + 272 q^{42} + 870 q^{43} + 925 q^{44} + 1238 q^{45} + 276 q^{46} + 2058 q^{47} + 4057 q^{48} + 3340 q^{49} + 981 q^{50} + 750 q^{51} + 1850 q^{52} + 2412 q^{53} + 1643 q^{54} + 1506 q^{55} + 671 q^{56} + 516 q^{57} + 348 q^{58} + 2958 q^{59} + 2445 q^{60} + 902 q^{61} + 1123 q^{62} + 296 q^{63} + 3234 q^{64} + 682 q^{65} - 1007 q^{66} - 612 q^{67} + 6445 q^{68} + 736 q^{69} - 608 q^{70} + 1358 q^{71} + 3475 q^{72} + 3102 q^{73} + 777 q^{74} + 2362 q^{75} - 1034 q^{76} + 6440 q^{77} - 430 q^{78} + 614 q^{79} - 272 q^{80} + 6622 q^{81} + 3749 q^{82} + 1910 q^{83} - 582 q^{84} + 4156 q^{85} + 3071 q^{86} + 928 q^{87} + 2584 q^{88} + 3768 q^{89} + 6545 q^{90} - 844 q^{91} + 4416 q^{92} + 3032 q^{93} + 1671 q^{94} + 2432 q^{95} - 1812 q^{96} + 4086 q^{97} + 4714 q^{98} + 3490 q^{99}+O(q^{100}) \) 42 * q + 12 * q^2 + 32 * q^3 + 192 * q^4 + 80 * q^5 + 32 * q^6 + 18 * q^7 + 102 * q^8 + 492 * q^9 + 48 * q^10 + 50 * q^11 + 403 * q^12 + 236 * q^13 + 32 * q^14 + 12 * q^15 + 792 * q^16 + 456 * q^17 + 297 * q^18 + 166 * q^19 + 533 * q^20 + 258 * q^21 + 73 * q^22 + 966 * q^23 + 514 * q^24 + 1358 * q^25 + 497 * q^26 + 1250 * q^27 + 143 * q^28 + 1218 * q^29 + 593 * q^30 + 558 * q^31 + 1328 * q^32 - 464 * q^33 + 157 * q^34 + 48 * q^35 + 3030 * q^36 + 352 * q^37 + 218 * q^38 + 1080 * q^39 + 900 * q^40 + 182 * q^41 + 272 * q^42 + 870 * q^43 + 925 * q^44 + 1238 * q^45 + 276 * q^46 + 2058 * q^47 + 4057 * q^48 + 3340 * q^49 + 981 * q^50 + 750 * q^51 + 1850 * q^52 + 2412 * q^53 + 1643 * q^54 + 1506 * q^55 + 671 * q^56 + 516 * q^57 + 348 * q^58 + 2958 * q^59 + 2445 * q^60 + 902 * q^61 + 1123 * q^62 + 296 * q^63 + 3234 * q^64 + 682 * q^65 - 1007 * q^66 - 612 * q^67 + 6445 * q^68 + 736 * q^69 - 608 * q^70 + 1358 * q^71 + 3475 * q^72 + 3102 * q^73 + 777 * q^74 + 2362 * q^75 - 1034 * q^76 + 6440 * q^77 - 430 * q^78 + 614 * q^79 - 272 * q^80 + 6622 * q^81 + 3749 * q^82 + 1910 * q^83 - 582 * q^84 + 4156 * q^85 + 3071 * q^86 + 928 * q^87 + 2584 * q^88 + 3768 * q^89 + 6545 * q^90 - 844 * q^91 + 4416 * q^92 + 3032 * q^93 + 1671 * q^94 + 2432 * q^95 - 1812 * q^96 + 4086 * q^97 + 4714 * q^98 + 3490 * q^99

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