LMFDB - Embedded newform 667.4.a.d.1.24

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			1.24
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)

$f(q)$	$=$	$q+1.18914 q^{2} +1.01380 q^{3} -6.58595 q^{4} -19.9715 q^{5} +1.20554 q^{6} +7.40802 q^{7} -17.3447 q^{8} -25.9722 q^{9} +O(q^{10})$	\(q+1.18914 q^{2} +1.01380 q^{3} -6.58595 q^{4} -19.9715 q^{5} +1.20554 q^{6} +7.40802 q^{7} -17.3447 q^{8} -25.9722 q^{9} -23.7489 q^{10} -20.2127 q^{11} -6.67682 q^{12} -22.3793 q^{13} +8.80916 q^{14} -20.2471 q^{15} +32.0624 q^{16} -27.2637 q^{17} -30.8845 q^{18} -151.173 q^{19} +131.532 q^{20} +7.51023 q^{21} -24.0357 q^{22} +23.0000 q^{23} -17.5840 q^{24} +273.863 q^{25} -26.6121 q^{26} -53.7031 q^{27} -48.7889 q^{28} +29.0000 q^{29} -24.0766 q^{30} +62.4279 q^{31} +176.884 q^{32} -20.4916 q^{33} -32.4203 q^{34} -147.950 q^{35} +171.052 q^{36} -70.5850 q^{37} -179.765 q^{38} -22.6880 q^{39} +346.401 q^{40} -55.6090 q^{41} +8.93070 q^{42} +65.6316 q^{43} +133.120 q^{44} +518.705 q^{45} +27.3502 q^{46} -314.750 q^{47} +32.5047 q^{48} -288.121 q^{49} +325.661 q^{50} -27.6399 q^{51} +147.389 q^{52} +419.994 q^{53} -63.8603 q^{54} +403.679 q^{55} -128.490 q^{56} -153.258 q^{57} +34.4850 q^{58} +893.817 q^{59} +133.346 q^{60} -115.378 q^{61} +74.2354 q^{62} -192.403 q^{63} -46.1592 q^{64} +446.949 q^{65} -24.3673 q^{66} +198.419 q^{67} +179.557 q^{68} +23.3173 q^{69} -175.933 q^{70} -807.127 q^{71} +450.480 q^{72} +614.455 q^{73} -83.9352 q^{74} +277.641 q^{75} +995.616 q^{76} -149.736 q^{77} -26.9792 q^{78} -474.863 q^{79} -640.335 q^{80} +646.806 q^{81} -66.1268 q^{82} +73.4270 q^{83} -49.4620 q^{84} +544.499 q^{85} +78.0450 q^{86} +29.4001 q^{87} +350.584 q^{88} -218.953 q^{89} +616.812 q^{90} -165.786 q^{91} -151.477 q^{92} +63.2892 q^{93} -374.281 q^{94} +3019.15 q^{95} +179.325 q^{96} -146.106 q^{97} -342.616 q^{98} +524.969 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.18914	0.420424	0.210212	−	0.977656i	$-0.432585\pi$
$2$	1.18914	0.420424	0.210212	+	0.977656i	$0.432585\pi$
$3$	1.01380	0.195105	0.0975526	−	0.995230i	$-0.468899\pi$
$3$	1.01380	0.195105	0.0975526	+	0.995230i	$0.468899\pi$
$4$	−6.58595	−0.823244
$5$	−19.9715	−1.78631	−0.893155	−	0.449749i	$-0.851513\pi$
$5$	−19.9715	−1.78631	−0.893155	+	0.449749i	$0.851513\pi$
$6$	1.20554	0.0820269
$7$	7.40802	0.399996	0.199998	−	0.979796i	$-0.435906\pi$
$7$	7.40802	0.399996	0.199998	+	0.979796i	$0.435906\pi$
$8$	−17.3447	−0.766535
$9$	−25.9722	−0.961934
$10$	−23.7489	−0.751007
$11$	−20.2127	−0.554033	−0.277016	−	0.960865i	$-0.589346\pi$
$11$	−20.2127	−0.554033	−0.277016	+	0.960865i	$0.589346\pi$
$12$	−6.67682	−0.160619
$13$	−22.3793	−0.477454	−0.238727	−	0.971087i	$-0.576730\pi$
$13$	−22.3793	−0.477454	−0.238727	+	0.971087i	$0.576730\pi$
$14$	8.80916	0.168168
$15$	−20.2471	−0.348518
$16$	32.0624	0.500974
$17$	−27.2637	−0.388966	−0.194483	−	0.980906i	$-0.562303\pi$
$17$	−27.2637	−0.388966	−0.194483	+	0.980906i	$0.562303\pi$
$18$	−30.8845	−0.404420
$19$	−151.173	−1.82534	−0.912668	−	0.408701i	$-0.865982\pi$
$19$	−151.173	−1.82534	−0.912668	+	0.408701i	$0.865982\pi$
$20$	131.532	1.47057
$21$	7.51023	0.0780413
$22$	−24.0357	−0.232929
$23$	23.0000	0.208514
$23$	23.0000	0.208514
$24$	−17.5840	−0.149555
$25$	273.863	2.19090
$26$	−26.6121	−0.200733
$27$	−53.7031	−0.382784
$28$	−48.7889	−0.329294
$29$	29.0000	0.185695
$29$	29.0000	0.185695
$30$	−24.0766	−0.146525
$31$	62.4279	0.361690	0.180845	−	0.983512i	$-0.442117\pi$
$31$	62.4279	0.361690	0.180845	+	0.983512i	$0.442117\pi$
$32$	176.884	0.977156
$33$	−20.4916	−0.108095
$34$	−32.4203	−0.163531
$35$	−147.950	−0.714516
$36$	171.052	0.791906
$37$	−70.5850	−0.313624	−0.156812	−	0.987628i	$-0.550122\pi$
$37$	−70.5850	−0.313624	−0.156812	+	0.987628i	$0.550122\pi$
$38$	−179.765	−0.767415
$39$	−22.6880	−0.0931537
$40$	346.401	1.36927
$41$	−55.6090	−0.211821	−0.105911	−	0.994376i	$-0.533776\pi$
$41$	−55.6090	−0.211821	−0.105911	+	0.994376i	$0.533776\pi$
$42$	8.93070	0.0328104
$43$	65.6316	0.232761	0.116381	−	0.993205i	$-0.462871\pi$
$43$	65.6316	0.232761	0.116381	+	0.993205i	$0.462871\pi$
$44$	133.120	0.456104
$45$	518.705	1.71831
$46$	27.3502	0.0876644
$47$	−314.750	−0.976830	−0.488415	−	0.872611i	$-0.662425\pi$
$47$	−314.750	−0.976830	−0.488415	+	0.872611i	$0.662425\pi$
$48$	32.5047	0.0977428
$49$	−288.121	−0.840003
$50$	325.661	0.921107
$51$	−27.6399	−0.0758893
$52$	147.389	0.393061
$53$	419.994	1.08850	0.544251	−	0.838922i	$-0.316814\pi$
$53$	419.994	1.08850	0.544251	+	0.838922i	$0.316814\pi$
$54$	−63.8603	−0.160931
$55$	403.679	0.989674
$56$	−128.490	−0.306611
$57$	−153.258	−0.356133
$58$	34.4850	0.0780707
$59$	893.817	1.97229	0.986145	−	0.165888i	$-0.0530489\pi$
$59$	893.817	1.97229	0.986145	+	0.165888i	$0.0530489\pi$
$60$	133.346	0.286916
$61$	−115.378	−0.242174	−0.121087	−	0.992642i	$-0.538638\pi$
$61$	−115.378	−0.242174	−0.121087	+	0.992642i	$0.538638\pi$
$62$	74.2354	0.152063
$63$	−192.403	−0.384769
$64$	−46.1592	−0.0901547
$65$	446.949	0.852880
$66$	−24.3673	−0.0454456
$67$	198.419	0.361803	0.180901	−	0.983501i	$-0.442098\pi$
$67$	198.419	0.361803	0.180901	+	0.983501i	$0.442098\pi$
$68$	179.557	0.320214
$69$	23.3173	0.0406823
$70$	−175.933	−0.300400
$71$	−807.127	−1.34913	−0.674566	−	0.738214i	$-0.735669\pi$
$71$	−807.127	−1.34913	−0.674566	+	0.738214i	$0.735669\pi$
$72$	450.480	0.737356
$73$	614.455	0.985157	0.492579	−	0.870268i	$-0.336054\pi$
$73$	614.455	0.985157	0.492579	+	0.870268i	$0.336054\pi$
$74$	−83.9352	−0.131855
$75$	277.641	0.427457
$76$	995.616	1.50270
$77$	−149.736	−0.221611
$78$	−26.9792	−0.0391640
$79$	−474.863	−0.676282	−0.338141	−	0.941095i	$-0.609798\pi$
$79$	−474.863	−0.676282	−0.338141	+	0.941095i	$0.609798\pi$
$80$	−640.335	−0.894895
$81$	646.806	0.887251
$82$	−66.1268	−0.0890547
$83$	73.4270	0.0971043	0.0485521	−	0.998821i	$-0.484539\pi$
$83$	73.4270	0.0971043	0.0485521	+	0.998821i	$0.484539\pi$
$84$	−49.4620	−0.0642470
$85$	544.499	0.694814
$86$	78.0450	0.0978582
$87$	29.4001	0.0362301
$88$	350.584	0.424686
$89$	−218.953	−0.260775	−0.130387	−	0.991463i	$-0.541622\pi$
$89$	−218.953	−0.260775	−0.130387	+	0.991463i	$0.541622\pi$
$90$	616.812	0.722419
$91$	−165.786	−0.190979
$92$	−151.477	−0.171658
$93$	63.2892	0.0705676
$94$	−374.281	−0.410683
$95$	3019.15	3.26062
$96$	179.325	0.190648
$97$	−146.106	−0.152937	−0.0764684	−	0.997072i	$-0.524364\pi$
$97$	−146.106	−0.152937	−0.0764684	+	0.997072i	$0.524364\pi$
$98$	−342.616	−0.353157
$99$	524.969	0.532943
$100$	−1803.65	−1.80365
$101$	1330.90	1.31118	0.655592	−	0.755116i	$-0.272419\pi$
$101$	1330.90	1.31118	0.655592	+	0.755116i	$0.272419\pi$
$102$	−32.8676	−0.0319057
$103$	484.695	0.463674	0.231837	−	0.972755i	$-0.425526\pi$
$103$	484.695	0.463674	0.231837	+	0.972755i	$0.425526\pi$
$104$	388.162	0.365985
$105$	−149.991	−0.139406
$106$	499.431	0.457632
$107$	−1510.00	−1.36427	−0.682136	−	0.731225i	$-0.738949\pi$
$107$	−1510.00	−1.36427	−0.682136	+	0.731225i	$0.738949\pi$
$108$	353.686	0.315124
$109$	−795.990	−0.699468	−0.349734	−	0.936849i	$-0.613728\pi$
$109$	−795.990	−0.699468	−0.349734	+	0.936849i	$0.613728\pi$
$110$	480.030	0.416083
$111$	−71.5588	−0.0611897
$112$	237.519	0.200388
$113$	776.364	0.646320	0.323160	−	0.946344i	$-0.395255\pi$
$113$	776.364	0.646320	0.323160	+	0.946344i	$0.395255\pi$
$114$	−182.245	−0.149727
$115$	−459.346	−0.372471
$116$	−190.993	−0.152873
$117$	581.240	0.459279
$118$	1062.87	0.829197
$119$	−201.970	−0.155585
$120$	351.180	0.267152
$121$	−922.446	−0.693048
$122$	−137.200	−0.101815
$123$	−56.3763	−0.0413274
$124$	−411.147	−0.297759
$125$	−2973.02	−2.12732
$126$	−228.793	−0.161766
$127$	−1751.23	−1.22359	−0.611796	−	0.791016i	$-0.709553\pi$
$127$	−1751.23	−1.22359	−0.611796	+	0.791016i	$0.709553\pi$
$128$	−1469.96	−1.01506
$129$	66.5371	0.0454129
$130$	531.484	0.358571
$131$	917.502	0.611927	0.305964	−	0.952043i	$-0.401021\pi$
$131$	917.502	0.611927	0.305964	+	0.952043i	$0.401021\pi$
$132$	134.957	0.0889883
$133$	−1119.89	−0.730127
$134$	235.948	0.152111
$135$	1072.53	0.683770
$136$	472.881	0.298156
$137$	−583.011	−0.363576	−0.181788	−	0.983338i	$-0.558189\pi$
$137$	−583.011	−0.363576	−0.181788	+	0.983338i	$0.558189\pi$
$138$	27.7275	0.0171038
$139$	−914.276	−0.557899	−0.278949	−	0.960306i	$-0.589986\pi$
$139$	−914.276	−0.557899	−0.278949	+	0.960306i	$0.589986\pi$
$140$	974.390	0.588221
$141$	−319.093	−0.190585
$142$	−959.786	−0.567207
$143$	452.346	0.264525
$144$	−832.731	−0.481904
$145$	−579.175	−0.331709
$146$	730.671	0.414183
$147$	−292.096	−0.163889
$148$	464.869	0.258189
$149$	−1751.08	−0.962778	−0.481389	−	0.876507i	$-0.659868\pi$
$149$	−1751.08	−0.962778	−0.481389	+	0.876507i	$0.659868\pi$
$150$	330.154	0.179713
$151$	−1818.34	−0.979962	−0.489981	−	0.871733i	$-0.662996\pi$
$151$	−1818.34	−0.979962	−0.489981	+	0.871733i	$0.662996\pi$
$152$	2622.05	1.39918
$153$	708.099	0.374160
$154$	−178.057	−0.0931704
$155$	−1246.78	−0.646090
$156$	149.422	0.0766882
$157$	−3671.42	−1.86632	−0.933158	−	0.359467i	$-0.882959\pi$
$157$	−3671.42	−1.86632	−0.933158	+	0.359467i	$0.882959\pi$
$158$	−564.678	−0.284325
$159$	425.789	0.212373
$160$	−3532.65	−1.74550
$161$	170.385	0.0834049
$162$	769.141	0.373021
$163$	917.066	0.440676	0.220338	−	0.975424i	$-0.429284\pi$
$163$	917.066	0.440676	0.220338	+	0.975424i	$0.429284\pi$
$164$	366.238	0.174381
$165$	409.249	0.193091
$166$	87.3148	0.0408249
$167$	1839.72	0.852464	0.426232	−	0.904614i	$-0.359841\pi$
$167$	1839.72	0.852464	0.426232	+	0.904614i	$0.359841\pi$
$168$	−130.263	−0.0598214
$169$	−1696.17	−0.772038
$170$	647.484	0.292116
$171$	3926.29	1.75585
$172$	−432.246	−0.191619
$173$	3812.99	1.67570	0.837850	−	0.545900i	$-0.183812\pi$
$173$	3812.99	1.67570	0.837850	+	0.545900i	$0.183812\pi$
$174$	34.9608	0.0152320
$175$	2028.78	0.876351
$176$	−648.067	−0.277556
$177$	906.149	0.384804
$178$	−260.365	−0.109636
$179$	3921.54	1.63748	0.818742	−	0.574162i	$-0.194672\pi$
$179$	3921.54	1.63748	0.818742	+	0.574162i	$0.194672\pi$
$180$	−3416.17	−1.41459
$181$	−1730.82	−0.710778	−0.355389	−	0.934719i	$-0.615652\pi$
$181$	−1730.82	−0.710778	−0.355389	+	0.934719i	$0.615652\pi$
$182$	−197.143	−0.0802923
$183$	−116.969	−0.0472493
$184$	−398.928	−0.159834
$185$	1409.69	0.560230
$186$	75.2596	0.0296683
$187$	551.074	0.215500
$188$	2072.93	0.804170
$189$	−397.834	−0.153112
$190$	3590.19	1.37084
$191$	3539.44	1.34086	0.670431	−	0.741972i	$-0.266109\pi$
$191$	3539.44	1.34086	0.670431	+	0.741972i	$0.266109\pi$
$192$	−46.7960	−0.0175897
$193$	−599.584	−0.223622	−0.111811	−	0.993729i	$-0.535665\pi$
$193$	−599.584	−0.223622	−0.111811	+	0.993729i	$0.535665\pi$
$194$	−173.741	−0.0642982
$195$	453.115	0.166401
$196$	1897.55	0.691528
$197$	−3219.78	−1.16447	−0.582233	−	0.813022i	$-0.697821\pi$
$197$	−3219.78	−1.16447	−0.582233	+	0.813022i	$0.697821\pi$
$198$	624.260	0.224062
$199$	−839.508	−0.299051	−0.149526	−	0.988758i	$-0.547775\pi$
$199$	−839.508	−0.299051	−0.149526	+	0.988758i	$0.547775\pi$
$200$	−4750.07	−1.67940
$201$	201.157	0.0705897
$202$	1582.62	0.551252
$203$	214.833	0.0742773
$204$	182.035	0.0624754
$205$	1110.60	0.378378
$206$	576.369	0.194940
$207$	−597.361	−0.200577
$208$	−717.533	−0.239192
$209$	3055.61	1.01130
$210$	−178.360	−0.0586095
$211$	3707.35	1.20960	0.604798	−	0.796379i	$-0.293254\pi$
$211$	3707.35	1.20960	0.604798	+	0.796379i	$0.293254\pi$
$212$	−2766.06	−0.896103
$213$	−818.263	−0.263223
$214$	−1795.60	−0.573573
$215$	−1310.76	−0.415783
$216$	931.464	0.293417
$217$	462.468	0.144674
$218$	−946.542	−0.294073
$219$	622.932	0.192209
$220$	−2658.61	−0.814743
$221$	610.142	0.185713
$222$	−85.0933	−0.0257256
$223$	1615.89	0.485238	0.242619	−	0.970122i	$-0.421993\pi$
$223$	1615.89	0.485238	0.242619	+	0.970122i	$0.421993\pi$
$224$	1310.36	0.390858
$225$	−7112.82	−2.10750
$226$	923.204	0.271728
$227$	66.8134	0.0195355	0.00976775	−	0.999952i	$-0.496891\pi$
$227$	66.8134	0.0195355	0.00976775	+	0.999952i	$0.496891\pi$
$228$	1009.35	0.293184
$229$	5808.28	1.67608	0.838039	−	0.545611i	$-0.183702\pi$
$229$	5808.28	1.67608	0.838039	+	0.545611i	$0.183702\pi$
$230$	−546.225	−0.156596
$231$	−151.802	−0.0432374
$232$	−502.996	−0.142342
$233$	−5485.95	−1.54247	−0.771237	−	0.636548i	$-0.780362\pi$
$233$	−5485.95	−1.54247	−0.771237	+	0.636548i	$0.780362\pi$
$234$	691.174	0.193092
$235$	6286.05	1.74492
$236$	−5886.64	−1.62368
$237$	−481.415	−0.131946
$238$	−240.170	−0.0654115
$239$	2271.07	0.614658	0.307329	−	0.951603i	$-0.400565\pi$
$239$	2271.07	0.614658	0.307329	+	0.951603i	$0.400565\pi$
$240$	−649.170	−0.174599
$241$	1224.69	0.327340	0.163670	−	0.986515i	$-0.447667\pi$
$241$	1224.69	0.327340	0.163670	+	0.986515i	$0.447667\pi$
$242$	−1096.92	−0.291374
$243$	2105.71	0.555891
$244$	759.871	0.199368
$245$	5754.23	1.50051
$246$	−67.0391	−0.0173750
$247$	3383.14	0.871514
$248$	−1082.79	−0.277248
$249$	74.4400	0.0189456
$250$	−3535.33	−0.894375
$251$	1101.11	0.276898	0.138449	−	0.990370i	$-0.455788\pi$
$251$	1101.11	0.276898	0.138449	+	0.990370i	$0.455788\pi$
$252$	1267.16	0.316759
$253$	−464.892	−0.115524
$254$	−2082.45	−0.514427
$255$	552.011	0.135562
$256$	−1378.72	−0.336600
$257$	−2485.92	−0.603375	−0.301687	−	0.953407i	$-0.597550\pi$
$257$	−2485.92	−0.603375	−0.301687	+	0.953407i	$0.597550\pi$
$258$	79.1218	0.0190927
$259$	−522.895	−0.125448
$260$	−2943.58	−0.702128
$261$	−753.194	−0.178627
$262$	1091.04	0.257269
$263$	2830.63	0.663666	0.331833	−	0.943338i	$-0.392333\pi$
$263$	2830.63	0.663666	0.331833	+	0.943338i	$0.392333\pi$
$264$	355.420	0.0828584
$265$	−8387.93	−1.94440
$266$	−1331.70	−0.306963
$267$	−221.974	−0.0508785
$268$	−1306.78	−0.297852
$269$	1673.09	0.379219	0.189610	−	0.981860i	$-0.439278\pi$
$269$	1673.09	0.379219	0.189610	+	0.981860i	$0.439278\pi$
$270$	1275.39	0.287473
$271$	−3469.05	−0.777600	−0.388800	−	0.921322i	$-0.627110\pi$
$271$	−3469.05	−0.777600	−0.388800	+	0.921322i	$0.627110\pi$
$272$	−874.139	−0.194862
$273$	−168.074	−0.0372611
$274$	−693.280	−0.152856
$275$	−5535.51	−1.21383
$276$	−153.567	−0.0334914
$277$	−4280.28	−0.928437	−0.464219	−	0.885721i	$-0.653665\pi$
$277$	−4280.28	−0.928437	−0.464219	+	0.885721i	$0.653665\pi$
$278$	−1087.20	−0.234554
$279$	−1621.39	−0.347922
$280$	2566.14	0.547702
$281$	−2964.90	−0.629435	−0.314718	−	0.949185i	$-0.601910\pi$
$281$	−2964.90	−0.629435	−0.314718	+	0.949185i	$0.601910\pi$
$282$	−379.445	−0.0801263
$283$	5278.88	1.10882	0.554411	−	0.832243i	$-0.312944\pi$
$283$	5278.88	1.10882	0.554411	+	0.832243i	$0.312944\pi$
$284$	5315.70	1.11067
$285$	3060.81	0.636164
$286$	537.902	0.111213
$287$	−411.953	−0.0847276
$288$	−4594.08	−0.939960
$289$	−4169.69	−0.848705
$290$	−688.719	−0.139458
$291$	−148.122	−0.0298388
$292$	−4046.77	−0.811025
$293$	−6847.44	−1.36530	−0.682648	−	0.730748i	$-0.739172\pi$
$293$	−6847.44	−1.36530	−0.682648	+	0.730748i	$0.739172\pi$
$294$	−347.343	−0.0689029
$295$	−17850.9	−3.52312
$296$	1224.28	0.240404
$297$	1085.48	0.212075
$298$	−2082.27	−0.404775
$299$	−514.724	−0.0995560
$300$	−1828.53	−0.351901
$301$	486.200	0.0931034
$302$	−2162.26	−0.411999
$303$	1349.26	0.255819
$304$	−4846.95	−0.914447
$305$	2304.27	0.432597
$306$	842.027	0.157306
$307$	6746.86	1.25428	0.627139	−	0.778907i	$-0.284226\pi$
$307$	6746.86	1.25428	0.627139	+	0.778907i	$0.284226\pi$
$308$	986.156	0.182440
$309$	491.382	0.0904653
$310$	−1482.60	−0.271632
$311$	−5307.03	−0.967633	−0.483817	−	0.875169i	$-0.660750\pi$
$311$	−5307.03	−0.967633	−0.483817	+	0.875169i	$0.660750\pi$
$312$	393.517	0.0714056
$313$	6832.60	1.23387	0.616935	−	0.787014i	$-0.288374\pi$
$313$	6832.60	1.23387	0.616935	+	0.787014i	$0.288374\pi$
$314$	−4365.83	−0.784643
$315$	3842.58	0.687317
$316$	3127.43	0.556745
$317$	5400.67	0.956882	0.478441	−	0.878120i	$-0.341202\pi$
$317$	5400.67	0.956882	0.478441	+	0.878120i	$0.341202\pi$
$318$	506.321	0.0892864
$319$	−586.169	−0.102881
$320$	921.870	0.161044
$321$	−1530.83	−0.266177
$322$	202.611	0.0350654
$323$	4121.53	0.709994
$324$	−4259.83	−0.730424
$325$	−6128.85	−1.04605
$326$	1090.52	0.185271
$327$	−806.972	−0.136470
$328$	964.522	0.162368
$329$	−2331.68	−0.390728
$330$	486.653	0.0811799
$331$	−4818.52	−0.800150	−0.400075	−	0.916482i	$-0.631016\pi$
$331$	−4818.52	−0.800150	−0.400075	+	0.916482i	$0.631016\pi$
$332$	−483.586	−0.0799405
$333$	1833.25	0.301686
$334$	2187.67	0.358396
$335$	−3962.74	−0.646292
$336$	240.796	0.0390967
$337$	−6946.46	−1.12284	−0.561421	−	0.827530i	$-0.689745\pi$
$337$	−6946.46	−1.12284	−0.561421	+	0.827530i	$0.689745\pi$
$338$	−2016.98	−0.324583
$339$	787.075	0.126100
$340$	−3586.04	−0.572001
$341$	−1261.84	−0.200388
$342$	4668.90	0.738202
$343$	−4675.36	−0.735994
$344$	−1138.36	−0.178419
$345$	−465.683	−0.0726711
$346$	4534.17	0.704504
$347$	−1348.25	−0.208582	−0.104291	−	0.994547i	$-0.533257\pi$
$347$	−1348.25	−0.208582	−0.104291	+	0.994547i	$0.533257\pi$
$348$	−193.628	−0.0298262
$349$	−995.424	−0.152676	−0.0763379	−	0.997082i	$-0.524323\pi$
$349$	−995.424	−0.152676	−0.0763379	+	0.997082i	$0.524323\pi$
$350$	2412.50	0.368439
$351$	1201.84	0.182761
$352$	−3575.31	−0.541377
$353$	−9507.47	−1.43352	−0.716759	−	0.697321i	$-0.754375\pi$
$353$	−9507.47	−1.43352	−0.716759	+	0.697321i	$0.754375\pi$
$354$	1077.54	0.161781
$355$	16119.6	2.40997
$356$	1442.01	0.214681
$357$	−204.757	−0.0303554
$358$	4663.25	0.688437
$359$	6568.60	0.965675	0.482837	−	0.875710i	$-0.339606\pi$
$359$	6568.60	0.965675	0.482837	+	0.875710i	$0.339606\pi$
$360$	−8996.79	−1.31715
$361$	15994.2	2.33185
$362$	−2058.18	−0.298828
$363$	−935.173	−0.135217
$364$	1091.86	0.157223
$365$	−12271.6	−1.75980
$366$	−139.093	−0.0198647
$367$	−9901.83	−1.40837	−0.704184	−	0.710017i	$-0.748687\pi$
$367$	−9901.83	−1.40837	−0.704184	+	0.710017i	$0.748687\pi$
$368$	737.434	0.104460
$369$	1444.29	0.203758
$370$	1676.32	0.235534
$371$	3111.33	0.435396
$372$	−416.820	−0.0580944
$373$	8028.66	1.11450	0.557250	−	0.830345i	$-0.311857\pi$
$373$	8028.66	1.11450	0.557250	+	0.830345i	$0.311857\pi$
$374$	655.302	0.0906013
$375$	−3014.04	−0.415051
$376$	5459.25	0.748775
$377$	−648.999	−0.0886609
$378$	−473.079	−0.0643718
$379$	7118.34	0.964761	0.482381	−	0.875962i	$-0.339772\pi$
$379$	7118.34	0.964761	0.482381	+	0.875962i	$0.339772\pi$
$380$	−19884.0	−2.68428
$381$	−1775.39	−0.238729
$382$	4208.88	0.563730
$383$	9957.54	1.32848	0.664238	−	0.747521i	$-0.268756\pi$
$383$	9957.54	1.32848	0.664238	+	0.747521i	$0.268756\pi$
$384$	−1490.24	−0.198044
$385$	2990.47	0.395865
$386$	−712.988	−0.0940159
$387$	−1704.60	−0.223901
$388$	962.250	0.125904
$389$	11367.9	1.48169	0.740846	−	0.671675i	$-0.234425\pi$
$389$	11367.9	1.48169	0.740846	+	0.671675i	$0.234425\pi$
$390$	538.817	0.0699591
$391$	−627.065	−0.0811050
$392$	4997.38	0.643892
$393$	930.160	0.119390
$394$	−3828.76	−0.489569
$395$	9483.75	1.20805
$396$	−3457.42	−0.438742
$397$	8277.94	1.04649	0.523247	−	0.852181i	$-0.324721\pi$
$397$	8277.94	1.04649	0.523247	+	0.852181i	$0.324721\pi$
$398$	−998.291	−0.125728
$399$	−1135.34	−0.142452
$400$	8780.69	1.09759
$401$	2673.61	0.332952	0.166476	−	0.986046i	$-0.446761\pi$
$401$	2673.61	0.332952	0.166476	+	0.986046i	$0.446761\pi$
$402$	239.203	0.0296776
$403$	−1397.09	−0.172690
$404$	−8765.24	−1.07942
$405$	−12917.7	−1.58490
$406$	255.466	0.0312280
$407$	1426.71	0.173758
$408$	479.405	0.0581718
$409$	−10751.6	−1.29984	−0.649918	−	0.760004i	$-0.725197\pi$
$409$	−10751.6	−1.29984	−0.649918	+	0.760004i	$0.725197\pi$
$410$	1320.65	0.159079
$411$	−591.054	−0.0709357
$412$	−3192.18	−0.381717
$413$	6621.42	0.788907
$414$	−710.345	−0.0843274
$415$	−1466.45	−0.173458
$416$	−3958.54	−0.466547
$417$	−926.891	−0.108849
$418$	3633.54	0.425173
$419$	14879.4	1.73486	0.867430	−	0.497558i	$-0.165770\pi$
$419$	14879.4	1.73486	0.867430	+	0.497558i	$0.165770\pi$
$420$	987.833	0.114765
$421$	7674.65	0.888455	0.444227	−	0.895914i	$-0.353478\pi$
$421$	7674.65	0.888455	0.444227	+	0.895914i	$0.353478\pi$
$422$	4408.55	0.508543
$423$	8174.76	0.939646
$424$	−7284.67	−0.834375
$425$	−7466.51	−0.852186
$426$	−973.028	−0.110665
$427$	−854.720	−0.0968684
$428$	9944.78	1.12313
$429$	458.587	0.0516102
$430$	−1558.68	−0.174805
$431$	−15417.8	−1.72308	−0.861542	−	0.507686i	$-0.830501\pi$
$431$	−15417.8	−1.72308	−0.861542	+	0.507686i	$0.830501\pi$
$432$	−1721.85	−0.191765
$433$	3419.01	0.379463	0.189731	−	0.981836i	$-0.439238\pi$
$433$	3419.01	0.379463	0.189731	+	0.981836i	$0.439238\pi$
$434$	549.938	0.0608246
$435$	−587.166	−0.0647182
$436$	5242.35	0.575833
$437$	−3476.97	−0.380609
$438$	740.752	0.0808094
$439$	295.578	0.0321347	0.0160674	−	0.999871i	$-0.494885\pi$
$439$	295.578	0.0321347	0.0160674	+	0.999871i	$0.494885\pi$
$440$	−7001.70	−0.758620
$441$	7483.15	0.808028
$442$	725.543	0.0780782
$443$	−11424.1	−1.22522	−0.612611	−	0.790384i	$-0.709881\pi$
$443$	−11424.1	−1.22522	−0.612611	+	0.790384i	$0.709881\pi$
$444$	471.283	0.0503741
$445$	4372.83	0.465824
$446$	1921.52	0.204006
$447$	−1775.24	−0.187843
$448$	−341.948	−0.0360615
$449$	8220.75	0.864056	0.432028	−	0.901860i	$-0.357798\pi$
$449$	8220.75	0.864056	0.432028	+	0.901860i	$0.357798\pi$
$450$	−8458.13	−0.886044
$451$	1124.01	0.117356
$452$	−5113.09	−0.532079
$453$	−1843.43	−0.191196
$454$	79.4503	0.00821319
$455$	3311.01	0.341148
$456$	2658.22	0.272988
$457$	−11999.6	−1.22826	−0.614132	−	0.789203i	$-0.710494\pi$
$457$	−11999.6	−1.22826	−0.614132	+	0.789203i	$0.710494\pi$
$458$	6906.84	0.704663
$459$	1464.14	0.148890
$460$	3025.23	0.306635
$461$	6810.97	0.688109	0.344055	−	0.938950i	$-0.388199\pi$
$461$	6810.97	0.688109	0.344055	+	0.938950i	$0.388199\pi$
$462$	−180.514	−0.0181780
$463$	7426.79	0.745469	0.372735	−	0.927938i	$-0.378420\pi$
$463$	7426.79	0.745469	0.372735	+	0.927938i	$0.378420\pi$
$464$	929.809	0.0930286
$465$	−1263.98	−0.126056
$466$	−6523.55	−0.648493
$467$	2234.21	0.221385	0.110693	−	0.993855i	$-0.464693\pi$
$467$	2234.21	0.221385	0.110693	+	0.993855i	$0.464693\pi$
$468$	−3828.02	−0.378098
$469$	1469.90	0.144720
$470$	7474.98	0.733606
$471$	−3722.08	−0.364128
$472$	−15503.0	−1.51183
$473$	−1326.59	−0.128957
$474$	−572.469	−0.0554733
$475$	−41400.6	−3.99913
$476$	1330.17	0.128084
$477$	−10908.2	−1.04707
$478$	2700.62	0.258417
$479$	−12101.9	−1.15438	−0.577192	−	0.816609i	$-0.695851\pi$
$479$	−12101.9	−1.15438	−0.577192	+	0.816609i	$0.695851\pi$
$480$	−3581.39	−0.340557
$481$	1579.64	0.149741
$482$	1456.32	0.137621
$483$	172.735	0.0162727
$484$	6075.19	0.570547
$485$	2917.97	0.273192
$486$	2503.98	0.233710
$487$	12750.7	1.18642	0.593212	−	0.805047i	$-0.297860\pi$
$487$	12750.7	1.18642	0.593212	+	0.805047i	$0.297860\pi$
$488$	2001.19	0.185634
$489$	929.719	0.0859782
$490$	6842.57	0.630848
$491$	19623.8	1.80368	0.901841	−	0.432067i	$-0.142216\pi$
$491$	19623.8	1.80368	0.901841	+	0.432067i	$0.142216\pi$
$492$	371.291	0.0340226
$493$	−790.648	−0.0722292
$494$	4023.02	0.366405
$495$	−10484.4	−0.952001
$496$	2001.59	0.181197
$497$	−5979.22	−0.539647
$498$	88.5194	0.00796516
$499$	5791.05	0.519525	0.259762	−	0.965673i	$-0.416356\pi$
$499$	5791.05	0.519525	0.259762	+	0.965673i	$0.416356\pi$
$500$	19580.2	1.75130
$501$	1865.10	0.166320
$502$	1309.37	0.116414
$503$	−11859.8	−1.05129	−0.525646	−	0.850703i	$-0.676176\pi$
$503$	−11859.8	−1.05129	−0.525646	+	0.850703i	$0.676176\pi$
$504$	3337.17	0.294939
$505$	−26580.1	−2.34218
$506$	−552.821	−0.0485690
$507$	−1719.57	−0.150629
$508$	11533.5	1.00731
$509$	17593.0	1.53201	0.766007	−	0.642833i	$-0.222241\pi$
$509$	17593.0	1.53201	0.766007	+	0.642833i	$0.222241\pi$
$510$	656.417	0.0569934
$511$	4551.90	0.394059
$512$	10120.2	0.873545
$513$	8118.44	0.698709
$514$	−2956.10	−0.253673
$515$	−9680.11	−0.828266
$516$	−438.210	−0.0373859
$517$	6361.95	0.541196
$518$	−621.794	−0.0527415
$519$	3865.60	0.326938
$520$	−7752.20	−0.653762
$521$	−2681.21	−0.225462	−0.112731	−	0.993626i	$-0.535960\pi$
$521$	−2681.21	−0.225462	−0.112731	+	0.993626i	$0.535960\pi$
$522$	−895.652	−0.0750989
$523$	10724.5	0.896654	0.448327	−	0.893870i	$-0.352020\pi$
$523$	10724.5	0.896654	0.448327	+	0.893870i	$0.352020\pi$
$524$	−6042.62	−0.503766
$525$	2056.77	0.170981
$526$	3366.01	0.279021
$527$	−1702.02	−0.140685
$528$	−657.009	−0.0541527
$529$	529.000	0.0434783
$530$	−9974.40	−0.817473
$531$	−23214.4	−1.89721
$532$	7375.55	0.601073
$533$	1244.49	0.101135
$534$	−263.957	−0.0213905
$535$	30157.0	2.43701
$536$	−3441.53	−0.277335
$537$	3975.64	0.319482
$538$	1989.53	0.159433
$539$	5823.71	0.465390
$540$	−7063.65	−0.562910
$541$	21218.7	1.68626	0.843129	−	0.537712i	$-0.180711\pi$
$541$	21218.7	1.68626	0.843129	+	0.537712i	$0.180711\pi$
$542$	−4125.18	−0.326922
$543$	−1754.70	−0.138677
$544$	−4822.52	−0.380081
$545$	15897.2	1.24947
$546$	−199.863	−0.0156654
$547$	−2203.99	−0.172278	−0.0861388	−	0.996283i	$-0.527453\pi$
$547$	−2203.99	−0.172278	−0.0861388	+	0.996283i	$0.527453\pi$
$548$	3839.68	0.299312
$549$	2996.61	0.232955
$550$	−6582.48	−0.510324
$551$	−4384.01	−0.338957
$552$	−404.432	−0.0311844
$553$	−3517.80	−0.270510
$554$	−5089.84	−0.390337
$555$	1429.14	0.109304
$556$	6021.38	0.459287
$557$	24681.5	1.87754	0.938771	−	0.344543i	$-0.111966\pi$
$557$	24681.5	1.87754	0.938771	+	0.344543i	$0.111966\pi$
$558$	−1928.06	−0.146275
$559$	−1468.79	−0.111133
$560$	−4743.62	−0.357954
$561$	558.677	0.0420452
$562$	−3525.68	−0.264630
$563$	−22172.9	−1.65982	−0.829908	−	0.557901i	$-0.811607\pi$
$563$	−22172.9	−1.65982	−0.829908	+	0.557901i	$0.811607\pi$
$564$	2101.53	0.156898
$565$	−15505.2	−1.15453
$566$	6277.31	0.466175
$567$	4791.55	0.354897
$568$	13999.4	1.03416
$569$	9875.84	0.727622	0.363811	−	0.931473i	$-0.381475\pi$
$569$	9875.84	0.727622	0.363811	+	0.931473i	$0.381475\pi$
$570$	3639.72	0.267458
$571$	−10070.8	−0.738090	−0.369045	−	0.929412i	$-0.620315\pi$
$571$	−10070.8	−0.738090	−0.369045	+	0.929412i	$0.620315\pi$
$572$	−2979.13	−0.217769
$573$	3588.27	0.261609
$574$	−489.869	−0.0356215
$575$	6298.84	0.456835
$576$	1198.86	0.0867228
$577$	−871.424	−0.0628732	−0.0314366	−	0.999506i	$-0.510008\pi$
$577$	−871.424	−0.0628732	−0.0314366	+	0.999506i	$0.510008\pi$
$578$	−4958.34	−0.356816
$579$	−607.857	−0.0436298
$580$	3814.42	0.273078
$581$	543.949	0.0388413
$582$	−176.138	−0.0125449
$583$	−8489.22	−0.603066
$584$	−10657.5	−0.755157
$585$	−11608.3	−0.820414
$586$	−8142.54	−0.574002
$587$	−18755.2	−1.31876	−0.659378	−	0.751811i	$-0.729180\pi$
$587$	−18755.2	−1.31876	−0.659378	+	0.751811i	$0.729180\pi$
$588$	1923.73	0.134921
$589$	−9437.40	−0.660206
$590$	−21227.2	−1.48120
$591$	−3264.20	−0.227193
$592$	−2263.12	−0.157118
$593$	11956.7	0.828000	0.414000	−	0.910277i	$-0.364131\pi$
$593$	11956.7	0.828000	0.414000	+	0.910277i	$0.364131\pi$
$594$	1290.79	0.0891613
$595$	4033.66	0.277922
$596$	11532.5	0.792601
$597$	−851.091	−0.0583465
$598$	−612.077	−0.0418557
$599$	12103.8	0.825619	0.412810	−	0.910817i	$-0.364547\pi$
$599$	12103.8	0.825619	0.412810	+	0.910817i	$0.364547\pi$
$600$	−4815.60	−0.327660
$601$	12375.8	0.839966	0.419983	−	0.907532i	$-0.362036\pi$
$601$	12375.8	0.839966	0.419983	+	0.907532i	$0.362036\pi$
$602$	578.159	0.0391429
$603$	−5153.39	−0.348030
$604$	11975.5	0.806748
$605$	18422.7	1.23800
$606$	1604.46	0.107552
$607$	−814.934	−0.0544928	−0.0272464	−	0.999629i	$-0.508674\pi$
$607$	−814.934	−0.0544928	−0.0272464	+	0.999629i	$0.508674\pi$
$608$	−26740.1	−1.78364
$609$	217.797	0.0144919
$610$	2740.09	0.181874
$611$	7043.88	0.466391
$612$	−4663.51	−0.308025
$613$	−21951.6	−1.44636	−0.723179	−	0.690661i	$-0.757320\pi$
$613$	−21951.6	−1.44636	−0.723179	+	0.690661i	$0.757320\pi$
$614$	8022.94	0.527328
$615$	1125.92	0.0738236
$616$	2597.13	0.169872
$617$	5349.82	0.349069	0.174535	−	0.984651i	$-0.444158\pi$
$617$	5349.82	0.349069	0.174535	+	0.984651i	$0.444158\pi$
$618$	584.321	0.0380337
$619$	9256.77	0.601068	0.300534	−	0.953771i	$-0.402835\pi$
$619$	9256.77	0.601068	0.300534	+	0.953771i	$0.402835\pi$
$620$	8211.25	0.531890
$621$	−1235.17	−0.0798159
$622$	−6310.79	−0.406816
$623$	−1622.01	−0.104309
$624$	−727.432	−0.0466676
$625$	25143.0	1.60915
$626$	8124.90	0.518748
$627$	3097.77	0.197309
$628$	24179.8	1.53643
$629$	1924.41	0.121989
$630$	4569.36	0.288965
$631$	8175.17	0.515766	0.257883	−	0.966176i	$-0.416975\pi$
$631$	8175.17	0.515766	0.257883	+	0.966176i	$0.416975\pi$
$632$	8236.36	0.518394
$633$	3758.50	0.235998
$634$	6422.14	0.402296
$635$	34974.7	2.18571
$636$	−2804.22	−0.174834
$637$	6447.95	0.401063
$638$	−697.035	−0.0432538
$639$	20962.9	1.29778
$640$	29357.4	1.81321
$641$	3159.98	0.194714	0.0973570	−	0.995250i	$-0.468961\pi$
$641$	3159.98	0.194714	0.0973570	+	0.995250i	$0.468961\pi$
$642$	−1820.37	−0.111907
$643$	−1662.03	−0.101935	−0.0509674	−	0.998700i	$-0.516230\pi$
$643$	−1662.03	−0.101935	−0.0509674	+	0.998700i	$0.516230\pi$
$644$	−1122.14	−0.0686626
$645$	−1328.85	−0.0811215
$646$	4901.07	0.298498
$647$	30508.6	1.85381	0.926907	−	0.375291i	$-0.122457\pi$
$647$	30508.6	1.85381	0.926907	+	0.375291i	$0.122457\pi$
$648$	−11218.7	−0.680109
$649$	−18066.5	−1.09271
$650$	−7288.05	−0.439786
$651$	468.848	0.0282267
$652$	−6039.75	−0.362784
$653$	7661.76	0.459154	0.229577	−	0.973290i	$-0.426266\pi$
$653$	7661.76	0.459154	0.229577	+	0.973290i	$0.426266\pi$
$654$	−959.601	−0.0573752
$655$	−18323.9	−1.09309
$656$	−1782.96	−0.106117
$657$	−15958.7	−0.947656
$658$	−2772.68	−0.164271
$659$	3102.13	0.183371	0.0916857	−	0.995788i	$-0.470774\pi$
$659$	3102.13	0.183371	0.0916857	+	0.995788i	$0.470774\pi$
$660$	−2695.29	−0.158961
$661$	8669.59	0.510148	0.255074	−	0.966921i	$-0.417900\pi$
$661$	8669.59	0.510148	0.255074	+	0.966921i	$0.417900\pi$
$662$	−5729.88	−0.336402
$663$	618.560	0.0362336
$664$	−1273.57	−0.0744338
$665$	22366.0	1.30423
$666$	2179.98	0.126836
$667$	667.000	0.0387202
$668$	−12116.3	−0.701785
$669$	1638.19	0.0946726
$670$	−4712.25	−0.271716
$671$	2332.09	0.134172
$672$	1328.44	0.0762585
$673$	10923.6	0.625669	0.312835	−	0.949808i	$-0.398721\pi$
$673$	10923.6	0.625669	0.312835	+	0.949808i	$0.398721\pi$
$674$	−8260.30	−0.472069
$675$	−14707.3	−0.838641
$676$	11170.9	0.635576
$677$	−7712.61	−0.437843	−0.218922	−	0.975742i	$-0.570254\pi$
$677$	−7712.61	−0.437843	−0.218922	+	0.975742i	$0.570254\pi$
$678$	935.941	0.0530156
$679$	−1082.36	−0.0611741
$680$	−9444.17	−0.532599
$681$	67.7352	0.00381148
$682$	−1500.50	−0.0842479
$683$	17956.4	1.00598	0.502989	−	0.864293i	$-0.332233\pi$
$683$	17956.4	1.00598	0.502989	+	0.864293i	$0.332233\pi$
$684$	−25858.4	−1.44550
$685$	11643.6	0.649460
$686$	−5559.65	−0.309429
$687$	5888.41	0.327012
$688$	2104.30	0.116607
$689$	−9399.16	−0.519709
$690$	−553.761	−0.0305527
$691$	21127.1	1.16312	0.581558	−	0.813505i	$-0.302443\pi$
$691$	21127.1	1.16312	0.581558	+	0.813505i	$0.302443\pi$
$692$	−25112.2	−1.37951
$693$	3888.98	0.213175
$694$	−1603.25	−0.0876926
$695$	18259.5	0.996580
$696$	−509.936	−0.0277717
$697$	1516.11	0.0823913
$698$	−1183.70	−0.0641885
$699$	−5561.64	−0.300945
$700$	−13361.5	−0.721451
$701$	5875.92	0.316591	0.158296	−	0.987392i	$-0.449400\pi$
$701$	5875.92	0.316591	0.158296	+	0.987392i	$0.449400\pi$
$702$	1429.15	0.0768372
$703$	10670.5	0.572470
$704$	933.002	0.0499487
$705$	6372.77	0.340443
$706$	−11305.7	−0.602685
$707$	9859.34	0.524468
$708$	−5967.85	−0.316788
$709$	−28935.1	−1.53270	−0.766349	−	0.642425i	$-0.777928\pi$
$709$	−28935.1	−1.53270	−0.766349	+	0.642425i	$0.777928\pi$
$710$	19168.4	1.01321
$711$	12333.2	0.650539
$712$	3797.67	0.199893
$713$	1435.84	0.0754176
$714$	−243.484	−0.0127621
$715$	−9034.05	−0.472524
$716$	−25827.1	−1.34805
$717$	2302.40	0.119923
$718$	7810.97	0.405993
$719$	−17769.5	−0.921684	−0.460842	−	0.887482i	$-0.652452\pi$
$719$	−17769.5	−0.921684	−0.460842	+	0.887482i	$0.652452\pi$
$720$	16630.9	0.860830
$721$	3590.63	0.185468
$722$	19019.3	0.980367
$723$	1241.58	0.0638658
$724$	11399.1	0.585144
$725$	7942.02	0.406840
$726$	−1112.05	−0.0568485
$727$	26123.3	1.33268	0.666342	−	0.745646i	$-0.267859\pi$
$727$	26123.3	1.33268	0.666342	+	0.745646i	$0.267859\pi$
$728$	2875.51	0.146392
$729$	−15329.0	−0.778794
$730$	−14592.6	−0.739860
$731$	−1789.36	−0.0905361
$732$	770.355	0.0388977
$733$	−36719.3	−1.85029	−0.925143	−	0.379618i	$-0.876055\pi$
$733$	−36719.3	−1.85029	−0.925143	+	0.379618i	$0.876055\pi$
$734$	−11774.6	−0.592111
$735$	5833.62	0.292757
$736$	4068.34	0.203751
$737$	−4010.60	−0.200451
$738$	1717.46	0.0856647
$739$	−26922.0	−1.34011	−0.670056	−	0.742310i	$-0.733730\pi$
$739$	−26922.0	−1.34011	−0.670056	+	0.742310i	$0.733730\pi$
$740$	−9284.16	−0.461206
$741$	3429.81	0.170037
$742$	3699.80	0.183051
$743$	−28494.5	−1.40695	−0.703473	−	0.710722i	$-0.748368\pi$
$743$	−28494.5	−1.40695	−0.703473	+	0.710722i	$0.748368\pi$
$744$	−1097.73	−0.0540925
$745$	34971.8	1.71982
$746$	9547.18	0.468562
$747$	−1907.06	−0.0934079
$748$	−3629.34	−0.177409
$749$	−11186.1	−0.545703
$750$	−3584.11	−0.174497
$751$	−6275.76	−0.304934	−0.152467	−	0.988309i	$-0.548722\pi$
$751$	−6275.76	−0.304934	−0.152467	+	0.988309i	$0.548722\pi$
$752$	−10091.6	−0.489367
$753$	1116.30	0.0540242
$754$	−771.750	−0.0372751
$755$	36315.0	1.75052
$756$	2620.11	0.126048
$757$	−26634.6	−1.27880	−0.639398	−	0.768876i	$-0.720817\pi$
$757$	−26634.6	−1.27880	−0.639398	+	0.768876i	$0.720817\pi$
$758$	8464.69	0.405609
$759$	−471.306	−0.0225393
$760$	−52366.3	−2.49938
$761$	−6036.70	−0.287556	−0.143778	−	0.989610i	$-0.545925\pi$
$761$	−6036.70	−0.287556	−0.143778	+	0.989610i	$0.545925\pi$
$762$	−2111.18	−0.100367
$763$	−5896.71	−0.279784
$764$	−23310.6	−1.10386
$765$	−14141.8	−0.668365
$766$	11840.9	0.558523
$767$	−20003.0	−0.941677
$768$	−1397.74	−0.0656725
$769$	−6030.48	−0.282789	−0.141394	−	0.989953i	$-0.545159\pi$
$769$	−6030.48	−0.282789	−0.141394	+	0.989953i	$0.545159\pi$
$770$	3556.08	0.166431
$771$	−2520.22	−0.117722
$772$	3948.83	0.184095
$773$	1346.29	0.0626423	0.0313212	−	0.999509i	$-0.490029\pi$
$773$	1346.29	0.0626423	0.0313212	+	0.999509i	$0.490029\pi$
$774$	−2027.00	−0.0941332
$775$	17096.7	0.792427
$776$	2534.17	0.117231
$777$	−530.109	−0.0244756
$778$	13518.1	0.622938
$779$	8406.57	0.386645
$780$	−2984.20	−0.136989
$781$	16314.2	0.747464
$782$	−745.667	−0.0340985
$783$	−1557.39	−0.0710811
$784$	−9237.85	−0.420820
$785$	73324.0	3.33382
$786$	1106.09	0.0501945
$787$	−40961.0	−1.85527	−0.927637	−	0.373483i	$-0.878163\pi$
$787$	−40961.0	−1.85527	−0.927637	+	0.373483i	$0.878163\pi$
$788$	21205.3	0.958639
$789$	2869.68	0.129485
$790$	11277.5	0.507892
$791$	5751.32	0.258525
$792$	−9105.43	−0.408519
$793$	2582.07	0.115627
$794$	9843.61	0.439970
$795$	−8503.66	−0.379363
$796$	5528.96	0.246192
$797$	25390.1	1.12844	0.564218	−	0.825626i	$-0.309178\pi$
$797$	25390.1	1.12844	0.564218	+	0.825626i	$0.309178\pi$
$798$	−1350.08	−0.0598900
$799$	8581.26	0.379954
$800$	48442.0	2.14085
$801$	5686.69	0.250848
$802$	3179.29	0.139981
$803$	−12419.8	−0.545810
$804$	−1324.81	−0.0581125
$805$	−3402.84	−0.148987
$806$	−1661.34	−0.0726030
$807$	1696.17	0.0739877
$808$	−23084.1	−1.00507
$809$	14814.3	0.643809	0.321905	−	0.946772i	$-0.395677\pi$
$809$	14814.3	0.643809	0.321905	+	0.946772i	$0.395677\pi$
$810$	−15360.9	−0.666331
$811$	21117.8	0.914362	0.457181	−	0.889374i	$-0.348859\pi$
$811$	21117.8	0.914362	0.457181	+	0.889374i	$0.348859\pi$
$812$	−1414.88	−0.0611484
$813$	−3516.91	−0.151714
$814$	1696.56	0.0730520
$815$	−18315.2	−0.787184
$816$	−886.199	−0.0380186
$817$	−9921.71	−0.424867
$818$	−12785.1	−0.546482
$819$	4305.84	0.183710
$820$	−7314.35	−0.311498
$821$	14428.7	0.613358	0.306679	−	0.951813i	$-0.400782\pi$
$821$	14428.7	0.613358	0.306679	+	0.951813i	$0.400782\pi$
$822$	−702.845	−0.0298230
$823$	−5346.50	−0.226449	−0.113224	−	0.993569i	$-0.536118\pi$
$823$	−5346.50	−0.226449	−0.113224	+	0.993569i	$0.536118\pi$
$824$	−8406.90	−0.355422
$825$	−5611.88	−0.236825
$826$	7873.78	0.331675
$827$	−32534.7	−1.36801	−0.684004	−	0.729478i	$-0.739763\pi$
$827$	−32534.7	−1.36801	−0.684004	+	0.729478i	$0.739763\pi$
$828$	3934.19	0.165124
$829$	43997.1	1.84329	0.921643	−	0.388040i	$-0.126848\pi$
$829$	43997.1	1.84329	0.921643	+	0.388040i	$0.126848\pi$
$830$	−1743.81	−0.0729260
$831$	−4339.33	−0.181143
$832$	1033.01	0.0430447
$833$	7855.25	0.326733
$834$	−1102.20	−0.0457627
$835$	−36742.0	−1.52276
$836$	−20124.1	−0.832544
$837$	−3352.57	−0.138449
$838$	17693.7	0.729377
$839$	−4834.78	−0.198945	−0.0994726	−	0.995040i	$-0.531716\pi$
$839$	−4834.78	−0.198945	−0.0994726	+	0.995040i	$0.531716\pi$
$840$	2601.55	0.106859
$841$	841.000	0.0344828
$842$	9126.22	0.373527
$843$	−3005.81	−0.122806
$844$	−24416.4	−0.995792
$845$	33875.1	1.37910
$846$	9720.91	0.395050
$847$	−6833.50	−0.277216
$848$	13466.0	0.545312
$849$	5351.71	0.216337
$850$	−8878.72	−0.358279
$851$	−1623.45	−0.0653952
$852$	5389.04	0.216697
$853$	−1052.26	−0.0422377	−0.0211188	−	0.999777i	$-0.506723\pi$
$853$	−1052.26	−0.0422377	−0.0211188	+	0.999777i	$0.506723\pi$
$854$	−1016.38	−0.0407258
$855$	−78414.1	−3.13650
$856$	26190.5	1.04576
$857$	25247.6	1.00635	0.503175	−	0.864184i	$-0.332165\pi$
$857$	25247.6	1.00635	0.503175	+	0.864184i	$0.332165\pi$
$858$	545.323	0.0216982
$859$	−8918.98	−0.354263	−0.177131	−	0.984187i	$-0.556682\pi$
$859$	−8918.98	−0.354263	−0.177131	+	0.984187i	$0.556682\pi$
$860$	8632.63	0.342291
$861$	−417.637	−0.0165308
$862$	−18333.9	−0.724426
$863$	−20452.9	−0.806750	−0.403375	−	0.915035i	$-0.632163\pi$
$863$	−20452.9	−0.806750	−0.403375	+	0.915035i	$0.632163\pi$
$864$	−9499.22	−0.374040
$865$	−76151.3	−2.99332
$866$	4065.68	0.159535
$867$	−4227.22	−0.165587
$868$	−3045.79	−0.119102
$869$	9598.27	0.374683
$870$	−698.221	−0.0272091
$871$	−4440.49	−0.172744
$872$	13806.2	0.536167
$873$	3794.71	0.147115
$874$	−4134.60	−0.160017
$875$	−22024.2	−0.850919
$876$	−4102.60	−0.158235
$877$	−16941.2	−0.652294	−0.326147	−	0.945319i	$-0.605750\pi$
$877$	−16941.2	−0.652294	−0.326147	+	0.945319i	$0.605750\pi$
$878$	351.482	0.0135102
$879$	−6941.91	−0.266376
$880$	12942.9	0.495802
$881$	15829.6	0.605348	0.302674	−	0.953094i	$-0.402121\pi$
$881$	15829.6	0.605348	0.302674	+	0.953094i	$0.402121\pi$
$882$	8898.49	0.339714
$883$	−31341.0	−1.19446	−0.597229	−	0.802070i	$-0.703732\pi$
$883$	−31341.0	−1.19446	−0.597229	+	0.802070i	$0.703732\pi$
$884$	−4018.37	−0.152887
$885$	−18097.2	−0.687379
$886$	−13584.8	−0.515112
$887$	−3752.65	−0.142054	−0.0710268	−	0.997474i	$-0.522628\pi$
$887$	−3752.65	−0.142054	−0.0710268	+	0.997474i	$0.522628\pi$
$888$	1241.17	0.0469041
$889$	−12973.1	−0.489431
$890$	5199.89	0.195844
$891$	−13073.7	−0.491566
$892$	−10642.2	−0.399470
$893$	47581.6	1.78304
$894$	−2111.00	−0.0789737
$895$	−78319.2	−2.92505
$896$	−10889.5	−0.406020
$897$	−521.825	−0.0194239
$898$	9775.61	0.363270
$899$	1810.41	0.0671641
$900$	46844.7	1.73499
$901$	−11450.6	−0.423390
$902$	1336.60	0.0493392
$903$	492.908	0.0181650
$904$	−13465.8	−0.495427
$905$	34567.1	1.26967
$906$	−2192.09	−0.0803833
$907$	28127.0	1.02970	0.514852	−	0.857279i	$-0.327847\pi$
$907$	28127.0	1.02970	0.514852	+	0.857279i	$0.327847\pi$
$908$	−440.030	−0.0160825
$909$	−34566.4	−1.26127
$910$	3937.25	0.143427
$911$	28236.8	1.02692	0.513462	−	0.858112i	$-0.328363\pi$
$911$	28236.8	1.02692	0.513462	+	0.858112i	$0.328363\pi$
$912$	−4913.83	−0.178413
$913$	−1484.16	−0.0537990
$914$	−14269.2	−0.516392
$915$	2336.06	0.0844019
$916$	−38253.0	−1.37982
$917$	6796.87	0.244768
$918$	1741.07	0.0625968
$919$	−5177.07	−0.185828	−0.0929138	−	0.995674i	$-0.529618\pi$
$919$	−5177.07	−0.185828	−0.0929138	+	0.995674i	$0.529618\pi$
$920$	7967.21	0.285512
$921$	6839.94	0.244716
$922$	8099.18	0.289297
$923$	18062.9	0.644148
$924$	999.762	0.0355950
$925$	−19330.6	−0.687120
$926$	8831.48	0.313413
$927$	−12588.6	−0.446024
$928$	5129.64	0.181453
$929$	43417.3	1.53334	0.766671	−	0.642040i	$-0.221912\pi$
$929$	43417.3	1.53334	0.766671	+	0.642040i	$0.221912\pi$
$930$	−1503.05	−0.0529968
$931$	43556.1	1.53329
$932$	36130.2	1.26983
$933$	−5380.25	−0.188790
$934$	2656.79	0.0930757
$935$	−11005.8	−0.384950
$936$	−10081.4	−0.352053
$937$	11889.3	0.414520	0.207260	−	0.978286i	$-0.433545\pi$
$937$	11889.3	0.414520	0.207260	+	0.978286i	$0.433545\pi$
$938$	1747.91	0.0608436
$939$	6926.86	0.240734
$940$	−41399.6	−1.43650
$941$	−5370.21	−0.186040	−0.0930200	−	0.995664i	$-0.529652\pi$
$941$	−5370.21	−0.186040	−0.0930200	+	0.995664i	$0.529652\pi$
$942$	−4426.06	−0.153088
$943$	−1279.01	−0.0441678
$944$	28657.9	0.988067
$945$	7945.35	0.273505
$946$	−1577.50	−0.0542167
$947$	−13559.8	−0.465296	−0.232648	−	0.972561i	$-0.574739\pi$
$947$	−13559.8	−0.465296	−0.232648	+	0.972561i	$0.574739\pi$
$948$	3170.57	0.108624
$949$	−13751.1	−0.470367
$950$	−49231.0	−1.68133
$951$	5475.18	0.186693
$952$	3503.11	0.119261
$953$	4644.04	0.157855	0.0789273	−	0.996880i	$-0.474851\pi$
$953$	4644.04	0.157855	0.0789273	+	0.996880i	$0.474851\pi$
$954$	−12971.3	−0.440212
$955$	−70688.0	−2.39520
$956$	−14957.2	−0.506014
$957$	−594.256	−0.0200727
$958$	−14390.8	−0.485330
$959$	−4318.96	−0.145429
$960$	934.589	0.0314206
$961$	−25893.8	−0.869180
$962$	1878.41	0.0629547
$963$	39218.0	1.31234
$964$	−8065.72	−0.269481
$965$	11974.6	0.399458
$966$	205.406	0.00684144
$967$	21077.7	0.700943	0.350472	−	0.936573i	$-0.386021\pi$
$967$	21077.7	0.700943	0.350472	+	0.936573i	$0.386021\pi$
$968$	15999.6	0.531245
$969$	4178.39	0.138524
$970$	3469.87	0.114857
$971$	11682.9	0.386121	0.193060	−	0.981187i	$-0.438159\pi$
$971$	11682.9	0.386121	0.193060	+	0.981187i	$0.438159\pi$
$972$	−13868.1	−0.457634
$973$	−6772.98	−0.223157
$974$	15162.3	0.498800
$975$	−6213.41	−0.204091
$976$	−3699.28	−0.121323
$977$	−25984.7	−0.850895	−0.425447	−	0.904983i	$-0.639883\pi$
$977$	−25984.7	−0.850895	−0.425447	+	0.904983i	$0.639883\pi$
$978$	1105.56	0.0361473
$979$	4425.63	0.144478
$980$	−37897.1	−1.23528
$981$	20673.6	0.672842
$982$	23335.4	0.758311
$983$	27109.7	0.879617	0.439809	−	0.898092i	$-0.355046\pi$
$983$	27109.7	0.879617	0.439809	+	0.898092i	$0.355046\pi$
$984$	977.830	0.0316789
$985$	64304.0	2.08010
$986$	−940.189	−0.0303669
$987$	−2363.85	−0.0762331
$988$	−22281.2	−0.717468
$989$	1509.53	0.0485340
$990$	−12467.4	−0.400244
$991$	−19662.0	−0.630256	−0.315128	−	0.949049i	$-0.602047\pi$
$991$	−19662.0	−0.630256	−0.315128	+	0.949049i	$0.602047\pi$
$992$	11042.5	0.353428
$993$	−4885.00	−0.156114
$994$	−7110.12	−0.226880
$995$	16766.3	0.534198
$996$	−490.258	−0.0155968
$997$	15114.1	0.480110	0.240055	−	0.970759i	$-0.422835\pi$
$997$	15114.1	0.480110	0.240055	+	0.970759i	$0.422835\pi$
$998$	6886.35	0.218421
$999$	3790.63	0.120050

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	667.4.a.d.1.24	✓	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
667.4.a.d.1.24	✓	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)

\(f(q)\)	\(=\)	\(q+1.18914 q^{2} +1.01380 q^{3} -6.58595 q^{4} -19.9715 q^{5} +1.20554 q^{6} +7.40802 q^{7} -17.3447 q^{8} -25.9722 q^{9} +O(q^{10})\)	\(q+1.18914 q^{2} +1.01380 q^{3} -6.58595 q^{4} -19.9715 q^{5} +1.20554 q^{6} +7.40802 q^{7} -17.3447 q^{8} -25.9722 q^{9} -23.7489 q^{10} -20.2127 q^{11} -6.67682 q^{12} -22.3793 q^{13} +8.80916 q^{14} -20.2471 q^{15} +32.0624 q^{16} -27.2637 q^{17} -30.8845 q^{18} -151.173 q^{19} +131.532 q^{20} +7.51023 q^{21} -24.0357 q^{22} +23.0000 q^{23} -17.5840 q^{24} +273.863 q^{25} -26.6121 q^{26} -53.7031 q^{27} -48.7889 q^{28} +29.0000 q^{29} -24.0766 q^{30} +62.4279 q^{31} +176.884 q^{32} -20.4916 q^{33} -32.4203 q^{34} -147.950 q^{35} +171.052 q^{36} -70.5850 q^{37} -179.765 q^{38} -22.6880 q^{39} +346.401 q^{40} -55.6090 q^{41} +8.93070 q^{42} +65.6316 q^{43} +133.120 q^{44} +518.705 q^{45} +27.3502 q^{46} -314.750 q^{47} +32.5047 q^{48} -288.121 q^{49} +325.661 q^{50} -27.6399 q^{51} +147.389 q^{52} +419.994 q^{53} -63.8603 q^{54} +403.679 q^{55} -128.490 q^{56} -153.258 q^{57} +34.4850 q^{58} +893.817 q^{59} +133.346 q^{60} -115.378 q^{61} +74.2354 q^{62} -192.403 q^{63} -46.1592 q^{64} +446.949 q^{65} -24.3673 q^{66} +198.419 q^{67} +179.557 q^{68} +23.3173 q^{69} -175.933 q^{70} -807.127 q^{71} +450.480 q^{72} +614.455 q^{73} -83.9352 q^{74} +277.641 q^{75} +995.616 q^{76} -149.736 q^{77} -26.9792 q^{78} -474.863 q^{79} -640.335 q^{80} +646.806 q^{81} -66.1268 q^{82} +73.4270 q^{83} -49.4620 q^{84} +544.499 q^{85} +78.0450 q^{86} +29.4001 q^{87} +350.584 q^{88} -218.953 q^{89} +616.812 q^{90} -165.786 q^{91} -151.477 q^{92} +63.2892 q^{93} -374.281 q^{94} +3019.15 q^{95} +179.325 q^{96} -146.106 q^{97} -342.616 q^{98} +524.969 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q + 12 q^{2} + 32 q^{3} + 192 q^{4} + 80 q^{5} + 32 q^{6} + 18 q^{7} + 102 q^{8} + 492 q^{9}+O(q^{10}) \) 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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