LMFDB - Embedded newform 667.4.a.c.1.31

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("667.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 667 = 23 \cdot 29 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	667.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$39.3542739738$
Analytic rank:	$0$
Dimension:	$39$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.31
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)

$f(q)$	$=$	$q+3.80690 q^{2} +8.79577 q^{3} +6.49250 q^{4} +3.70166 q^{5} +33.4846 q^{6} +30.8046 q^{7} -5.73891 q^{8} +50.3656 q^{9} +O(q^{10})$	\(q+3.80690 q^{2} +8.79577 q^{3} +6.49250 q^{4} +3.70166 q^{5} +33.4846 q^{6} +30.8046 q^{7} -5.73891 q^{8} +50.3656 q^{9} +14.0919 q^{10} -22.6287 q^{11} +57.1065 q^{12} +38.6941 q^{13} +117.270 q^{14} +32.5589 q^{15} -73.7875 q^{16} +17.7442 q^{17} +191.737 q^{18} -94.4803 q^{19} +24.0330 q^{20} +270.950 q^{21} -86.1451 q^{22} -23.0000 q^{23} -50.4782 q^{24} -111.298 q^{25} +147.305 q^{26} +205.518 q^{27} +199.999 q^{28} -29.0000 q^{29} +123.949 q^{30} +103.035 q^{31} -234.990 q^{32} -199.037 q^{33} +67.5506 q^{34} +114.028 q^{35} +326.998 q^{36} +67.1876 q^{37} -359.677 q^{38} +340.345 q^{39} -21.2435 q^{40} -6.05699 q^{41} +1031.48 q^{42} -286.956 q^{43} -146.917 q^{44} +186.436 q^{45} -87.5587 q^{46} -313.475 q^{47} -649.017 q^{48} +605.921 q^{49} -423.699 q^{50} +156.074 q^{51} +251.222 q^{52} +404.902 q^{53} +782.387 q^{54} -83.7637 q^{55} -176.785 q^{56} -831.027 q^{57} -110.400 q^{58} -247.840 q^{59} +211.389 q^{60} -351.344 q^{61} +392.245 q^{62} +1551.49 q^{63} -304.285 q^{64} +143.233 q^{65} -757.713 q^{66} +671.235 q^{67} +115.204 q^{68} -202.303 q^{69} +434.093 q^{70} -255.865 q^{71} -289.044 q^{72} +950.477 q^{73} +255.776 q^{74} -978.949 q^{75} -613.413 q^{76} -697.066 q^{77} +1295.66 q^{78} -1305.65 q^{79} -273.136 q^{80} +447.819 q^{81} -23.0584 q^{82} +704.274 q^{83} +1759.14 q^{84} +65.6832 q^{85} -1092.41 q^{86} -255.077 q^{87} +129.864 q^{88} +960.231 q^{89} +709.744 q^{90} +1191.96 q^{91} -149.327 q^{92} +906.275 q^{93} -1193.37 q^{94} -349.734 q^{95} -2066.92 q^{96} +1325.51 q^{97} +2306.68 q^{98} -1139.71 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 39 q + 6 q^{2} + 2 q^{3} + 156 q^{4} + 80 q^{5} - 4 q^{6} + 18 q^{7} + 156 q^{8} + 411 q^{9}+O(q^{10}) $ 39 * q + 6 * q^2 + 2 * q^3 + 156 * q^4 + 80 * q^5 - 4 * q^6 + 18 * q^7 + 156 * q^8 + 411 * q^9	\( 39 q + 6 q^{2} + 2 q^{3} + 156 q^{4} + 80 q^{5} - 4 q^{6} + 18 q^{7} + 156 q^{8} + 411 q^{9} + 130 q^{10} + 76 q^{11} + 115 q^{12} + 184 q^{13} + 336 q^{14} + 228 q^{15} + 776 q^{16} + 314 q^{17} + 27 q^{18} + 36 q^{19} + 533 q^{20} + 246 q^{21} + 269 q^{22} - 897 q^{23} + 30 q^{24} + 1267 q^{25} + 787 q^{26} + 122 q^{27} + 53 q^{28} - 1131 q^{29} + 703 q^{30} + 140 q^{31} + 1304 q^{32} + 2210 q^{33} + 59 q^{34} + 1828 q^{35} + 1834 q^{36} + 430 q^{37} + 1874 q^{38} - 340 q^{39} + 276 q^{40} + 1936 q^{41} + 756 q^{42} + 96 q^{43} - 671 q^{44} + 3392 q^{45} - 138 q^{46} + 1808 q^{47} + 535 q^{48} + 2201 q^{49} + 395 q^{50} + 750 q^{51} - 530 q^{52} + 4200 q^{53} - 937 q^{54} + 902 q^{55} + 3805 q^{56} + 300 q^{57} - 174 q^{58} + 726 q^{59} + 195 q^{60} + 736 q^{61} + 1851 q^{62} + 796 q^{63} + 2914 q^{64} + 2572 q^{65} + 307 q^{66} + 1192 q^{67} + 1235 q^{68} - 46 q^{69} + 5268 q^{70} + 1714 q^{71} + 643 q^{72} + 2012 q^{73} + 3307 q^{74} - 1708 q^{75} + 5244 q^{76} + 6592 q^{77} + 6406 q^{78} + 1768 q^{79} + 8606 q^{80} + 5363 q^{81} - 2059 q^{82} + 3766 q^{83} + 3818 q^{84} + 1260 q^{85} - 2355 q^{86} - 58 q^{87} + 3448 q^{88} + 1634 q^{89} - 1313 q^{90} + 1240 q^{91} - 3588 q^{92} + 3954 q^{93} + 2315 q^{94} + 1656 q^{95} + 1480 q^{96} - 788 q^{97} + 3128 q^{98} + 4488 q^{99}+O(q^{100}) \) 39 * q + 6 * q^2 + 2 * q^3 + 156 * q^4 + 80 * q^5 - 4 * q^6 + 18 * q^7 + 156 * q^8 + 411 * q^9 + 130 * q^10 + 76 * q^11 + 115 * q^12 + 184 * q^13 + 336 * q^14 + 228 * q^15 + 776 * q^16 + 314 * q^17 + 27 * q^18 + 36 * q^19 + 533 * q^20 + 246 * q^21 + 269 * q^22 - 897 * q^23 + 30 * q^24 + 1267 * q^25 + 787 * q^26 + 122 * q^27 + 53 * q^28 - 1131 * q^29 + 703 * q^30 + 140 * q^31 + 1304 * q^32 + 2210 * q^33 + 59 * q^34 + 1828 * q^35 + 1834 * q^36 + 430 * q^37 + 1874 * q^38 - 340 * q^39 + 276 * q^40 + 1936 * q^41 + 756 * q^42 + 96 * q^43 - 671 * q^44 + 3392 * q^45 - 138 * q^46 + 1808 * q^47 + 535 * q^48 + 2201 * q^49 + 395 * q^50 + 750 * q^51 - 530 * q^52 + 4200 * q^53 - 937 * q^54 + 902 * q^55 + 3805 * q^56 + 300 * q^57 - 174 * q^58 + 726 * q^59 + 195 * q^60 + 736 * q^61 + 1851 * q^62 + 796 * q^63 + 2914 * q^64 + 2572 * q^65 + 307 * q^66 + 1192 * q^67 + 1235 * q^68 - 46 * q^69 + 5268 * q^70 + 1714 * q^71 + 643 * q^72 + 2012 * q^73 + 3307 * q^74 - 1708 * q^75 + 5244 * q^76 + 6592 * q^77 + 6406 * q^78 + 1768 * q^79 + 8606 * q^80 + 5363 * q^81 - 2059 * q^82 + 3766 * q^83 + 3818 * q^84 + 1260 * q^85 - 2355 * q^86 - 58 * q^87 + 3448 * q^88 + 1634 * q^89 - 1313 * q^90 + 1240 * q^91 - 3588 * q^92 + 3954 * q^93 + 2315 * q^94 + 1656 * q^95 + 1480 * q^96 - 788 * q^97 + 3128 * q^98 + 4488 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	3.80690	1.34594	0.672971	−	0.739668i	$-0.265018\pi$
$2$	3.80690	1.34594	0.672971	+	0.739668i	$0.265018\pi$
$3$	8.79577	1.69275	0.846373	−	0.532590i	$-0.178781\pi$
$3$	8.79577	1.69275	0.846373	+	0.532590i	$0.178781\pi$
$4$	6.49250	0.811562
$5$	3.70166	0.331087	0.165543	−	0.986203i	$-0.447062\pi$
$5$	3.70166	0.331087	0.165543	+	0.986203i	$0.447062\pi$
$6$	33.4846	2.27834
$7$	30.8046	1.66329	0.831645	−	0.555308i	$-0.187399\pi$
$7$	30.8046	1.66329	0.831645	+	0.555308i	$0.187399\pi$
$8$	−5.73891	−0.253627
$9$	50.3656	1.86539
$10$	14.0919	0.445624
$11$	−22.6287	−0.620255	−0.310127	−	0.950695i	$-0.600372\pi$
$11$	−22.6287	−0.620255	−0.310127	+	0.950695i	$0.600372\pi$
$12$	57.1065	1.37377
$13$	38.6941	0.825525	0.412762	−	0.910839i	$-0.364564\pi$
$13$	38.6941	0.825525	0.412762	+	0.910839i	$0.364564\pi$
$14$	117.270	2.23869
$15$	32.5589	0.560446
$16$	−73.7875	−1.15293
$17$	17.7442	0.253154	0.126577	−	0.991957i	$-0.459601\pi$
$17$	17.7442	0.253154	0.126577	+	0.991957i	$0.459601\pi$
$18$	191.737	2.51071
$19$	−94.4803	−1.14080	−0.570402	−	0.821366i	$-0.693213\pi$
$19$	−94.4803	−1.14080	−0.570402	+	0.821366i	$0.693213\pi$
$20$	24.0330	0.268697
$21$	270.950	2.81553
$22$	−86.1451	−0.834827
$23$	−23.0000	−0.208514
$23$	−23.0000	−0.208514
$24$	−50.4782	−0.429325
$25$	−111.298	−0.890382
$26$	147.305	1.11111
$27$	205.518	1.46489
$28$	199.999	1.34986
$29$	−29.0000	−0.185695
$29$	−29.0000	−0.185695
$30$	123.949	0.754328
$31$	103.035	0.596958	0.298479	−	0.954416i	$-0.403521\pi$
$31$	103.035	0.596958	0.298479	+	0.954416i	$0.403521\pi$
$32$	−234.990	−1.29815
$33$	−199.037	−1.04993
$34$	67.5506	0.340730
$35$	114.028	0.550693
$36$	326.998	1.51388
$37$	67.1876	0.298529	0.149264	−	0.988797i	$-0.452309\pi$
$37$	67.1876	0.298529	0.149264	+	0.988797i	$0.452309\pi$
$38$	−359.677	−1.53546
$39$	340.345	1.39740
$40$	−21.2435	−0.0839723
$41$	−6.05699	−0.0230718	−0.0115359	−	0.999933i	$-0.503672\pi$
$41$	−6.05699	−0.0230718	−0.0115359	+	0.999933i	$0.503672\pi$
$42$	1031.48	3.78954
$43$	−286.956	−1.01768	−0.508841	−	0.860860i	$-0.669926\pi$
$43$	−286.956	−1.01768	−0.508841	+	0.860860i	$0.669926\pi$
$44$	−146.917	−0.503375
$45$	186.436	0.617606
$46$	−87.5587	−0.280648
$47$	−313.475	−0.972873	−0.486436	−	0.873716i	$-0.661703\pi$
$47$	−313.475	−0.972873	−0.486436	+	0.873716i	$0.661703\pi$
$48$	−649.017	−1.95162
$49$	605.921	1.76653
$50$	−423.699	−1.19840
$51$	156.074	0.428525
$52$	251.222	0.669965
$53$	404.902	1.04939	0.524694	−	0.851291i	$-0.324180\pi$
$53$	404.902	1.04939	0.524694	+	0.851291i	$0.324180\pi$
$54$	782.387	1.97165
$55$	−83.7637	−0.205358
$56$	−176.785	−0.421854
$57$	−831.027	−1.93109
$58$	−110.400	−0.249935
$59$	−247.840	−0.546882	−0.273441	−	0.961889i	$-0.588162\pi$
$59$	−247.840	−0.546882	−0.273441	+	0.961889i	$0.588162\pi$
$60$	211.389	0.454836
$61$	−351.344	−0.737458	−0.368729	−	0.929537i	$-0.620207\pi$
$61$	−351.344	−0.737458	−0.368729	+	0.929537i	$0.620207\pi$
$62$	392.245	0.803471
$63$	1551.49	3.10269
$64$	−304.285	−0.594307
$65$	143.233	0.273320
$66$	−757.713	−1.41315
$67$	671.235	1.22395	0.611973	−	0.790879i	$-0.290376\pi$
$67$	671.235	1.22395	0.611973	+	0.790879i	$0.290376\pi$
$68$	115.204	0.205450
$69$	−202.303	−0.352962
$70$	434.093	0.741201
$71$	−255.865	−0.427684	−0.213842	−	0.976868i	$-0.568598\pi$
$71$	−255.865	−0.427684	−0.213842	+	0.976868i	$0.568598\pi$
$72$	−289.044	−0.473113
$73$	950.477	1.52390	0.761952	−	0.647634i	$-0.224241\pi$
$73$	950.477	1.52390	0.761952	+	0.647634i	$0.224241\pi$
$74$	255.776	0.401803
$75$	−978.949	−1.50719
$76$	−613.413	−0.925833
$77$	−697.066	−1.03166
$78$	1295.66	1.88083
$79$	−1305.65	−1.85946	−0.929731	−	0.368238i	$-0.879961\pi$
$79$	−1305.65	−1.85946	−0.929731	+	0.368238i	$0.879961\pi$
$80$	−273.136	−0.381719
$81$	447.819	0.614292
$82$	−23.0584	−0.0310533
$83$	704.274	0.931374	0.465687	−	0.884949i	$-0.345807\pi$
$83$	704.274	0.931374	0.465687	+	0.884949i	$0.345807\pi$
$84$	1759.14	2.28498
$85$	65.6832	0.0838158
$86$	−1092.41	−1.36974
$87$	−255.077	−0.314335
$88$	129.864	0.157313
$89$	960.231	1.14364	0.571822	−	0.820378i	$-0.306237\pi$
$89$	960.231	1.14364	0.571822	+	0.820378i	$0.306237\pi$
$90$	709.744	0.831262
$91$	1191.96	1.37309
$92$	−149.327	−0.169222
$93$	906.275	1.01050
$94$	−1193.37	−1.30943
$95$	−349.734	−0.377705
$96$	−2066.92	−2.19744
$97$	1325.51	1.38747	0.693736	−	0.720229i	$-0.255963\pi$
$97$	1325.51	1.38747	0.693736	+	0.720229i	$0.255963\pi$
$98$	2306.68	2.37765
$99$	−1139.71	−1.15702
$100$	−722.600	−0.722600
$101$	1330.76	1.31104	0.655521	−	0.755177i	$-0.272449\pi$
$101$	1330.76	1.31104	0.655521	+	0.755177i	$0.272449\pi$
$102$	594.159	0.576770
$103$	−1782.11	−1.70482	−0.852411	−	0.522872i	$-0.824861\pi$
$103$	−1782.11	−1.70482	−0.852411	+	0.522872i	$0.824861\pi$
$104$	−222.062	−0.209375
$105$	1002.96	0.932184
$106$	1541.42	1.41242
$107$	−350.368	−0.316554	−0.158277	−	0.987395i	$-0.550594\pi$
$107$	−350.368	−0.316554	−0.158277	+	0.987395i	$0.550594\pi$
$108$	1334.33	1.18885
$109$	−174.025	−0.152923	−0.0764613	−	0.997073i	$-0.524362\pi$
$109$	−174.025	−0.152923	−0.0764613	+	0.997073i	$0.524362\pi$
$110$	−318.880	−0.276400
$111$	590.966	0.505334
$112$	−2272.99	−1.91766
$113$	199.379	0.165983	0.0829913	−	0.996550i	$-0.473553\pi$
$113$	199.379	0.165983	0.0829913	+	0.996550i	$0.473553\pi$
$114$	−3163.64	−2.59914
$115$	−85.1382	−0.0690363
$116$	−188.282	−0.150703
$117$	1948.85	1.53993
$118$	−943.503	−0.736072
$119$	546.604	0.421068
$120$	−186.853	−0.142144
$121$	−818.943	−0.615284
$122$	−1337.53	−0.992576
$123$	−53.2759	−0.0390547
$124$	668.957	0.484469
$125$	−874.694	−0.625880
$126$	5906.36	4.17604
$127$	−2476.65	−1.73045	−0.865224	−	0.501385i	$-0.832824\pi$
$127$	−2476.65	−1.73045	−0.865224	+	0.501385i	$0.832824\pi$
$128$	721.539	0.498247
$129$	−2524.00	−1.72268
$130$	545.272	0.367873
$131$	−1692.92	−1.12909	−0.564545	−	0.825403i	$-0.690948\pi$
$131$	−1692.92	−1.12909	−0.564545	+	0.825403i	$0.690948\pi$
$132$	−1292.24	−0.852087
$133$	−2910.42	−1.89749
$134$	2555.32	1.64736
$135$	760.758	0.485004
$136$	−101.833	−0.0642065
$137$	1513.58	0.943899	0.471949	−	0.881626i	$-0.343550\pi$
$137$	1513.58	0.943899	0.471949	+	0.881626i	$0.343550\pi$
$138$	−770.146	−0.475067
$139$	−1266.75	−0.772981	−0.386490	−	0.922293i	$-0.626313\pi$
$139$	−1266.75	−0.772981	−0.386490	+	0.922293i	$0.626313\pi$
$140$	740.327	0.446922
$141$	−2757.25	−1.64683
$142$	−974.052	−0.575638
$143$	−875.597	−0.512036
$144$	−3716.35	−2.15066
$145$	−107.348	−0.0614812
$146$	3618.37	2.05109
$147$	5329.54	2.99029
$148$	436.215	0.242275
$149$	3060.51	1.68273	0.841364	−	0.540469i	$-0.181753\pi$
$149$	3060.51	1.68273	0.841364	+	0.540469i	$0.181753\pi$
$150$	−3726.76	−2.02859
$151$	48.3684	0.0260673	0.0130336	−	0.999915i	$-0.495851\pi$
$151$	48.3684	0.0260673	0.0130336	+	0.999915i	$0.495851\pi$
$152$	542.214	0.289338
$153$	893.699	0.472230
$154$	−2653.66	−1.38856
$155$	381.402	0.197645
$156$	2209.69	1.13408
$157$	−183.454	−0.0932561	−0.0466280	−	0.998912i	$-0.514848\pi$
$157$	−183.454	−0.0932561	−0.0466280	+	0.998912i	$0.514848\pi$
$158$	−4970.50	−2.50273
$159$	3561.42	1.77635
$160$	−869.854	−0.429800
$161$	−708.505	−0.346820
$162$	1704.80	0.826802
$163$	−14.8510	−0.00713630	−0.00356815	−	0.999994i	$-0.501136\pi$
$163$	−14.8510	−0.00713630	−0.00356815	+	0.999994i	$0.501136\pi$
$164$	−39.3250	−0.0187242
$165$	−736.766	−0.347619
$166$	2681.10	1.25358
$167$	−1320.33	−0.611797	−0.305898	−	0.952064i	$-0.598957\pi$
$167$	−1320.33	−0.611797	−0.305898	+	0.952064i	$0.598957\pi$
$168$	−1554.96	−0.714093
$169$	−699.764	−0.318509
$170$	250.049	0.112811
$171$	−4758.55	−2.12804
$172$	−1863.06	−0.825913
$173$	−4125.01	−1.81282	−0.906412	−	0.422395i	$-0.861190\pi$
$173$	−4125.01	−1.81282	−0.906412	+	0.422395i	$0.861190\pi$
$174$	−971.054	−0.423077
$175$	−3428.48	−1.48096
$176$	1669.71	0.715110
$177$	−2179.94	−0.925733
$178$	3655.50	1.53928
$179$	2122.85	0.886421	0.443210	−	0.896418i	$-0.353839\pi$
$179$	2122.85	0.886421	0.443210	+	0.896418i	$0.353839\pi$
$180$	1210.44	0.501225
$181$	−4121.40	−1.69250	−0.846248	−	0.532790i	$-0.821144\pi$
$181$	−4121.40	−1.69250	−0.846248	+	0.532790i	$0.821144\pi$
$182$	4537.66	1.84810
$183$	−3090.34	−1.24833
$184$	131.995	0.0528848
$185$	248.706	0.0988389
$186$	3450.10	1.36007
$187$	−401.529	−0.157020
$188$	−2035.23	−0.789547
$189$	6330.89	2.43653
$190$	−1331.40	−0.508369
$191$	1992.27	0.754741	0.377370	−	0.926062i	$-0.376828\pi$
$191$	1992.27	0.754741	0.377370	+	0.926062i	$0.376828\pi$
$192$	−2676.42	−1.00601
$193$	3023.88	1.12779	0.563895	−	0.825847i	$-0.309302\pi$
$193$	3023.88	1.12779	0.563895	+	0.825847i	$0.309302\pi$
$194$	5046.07	1.86746
$195$	1259.84	0.462662
$196$	3933.94	1.43365
$197$	3739.76	1.35252	0.676262	−	0.736662i	$-0.263599\pi$
$197$	3739.76	1.35252	0.676262	+	0.736662i	$0.263599\pi$
$198$	−4338.75	−1.55728
$199$	3193.36	1.13754	0.568771	−	0.822496i	$-0.307419\pi$
$199$	3193.36	1.13754	0.568771	+	0.822496i	$0.307419\pi$
$200$	638.728	0.225824
$201$	5904.03	2.07183
$202$	5066.06	1.76459
$203$	−893.332	−0.308865
$204$	1013.31	0.347775
$205$	−22.4209	−0.00763875
$206$	−6784.32	−2.29459
$207$	−1158.41	−0.388961
$208$	−2855.14	−0.951771
$209$	2137.96	0.707589
$210$	3818.19	1.25467
$211$	−1402.88	−0.457715	−0.228858	−	0.973460i	$-0.573499\pi$
$211$	−1402.88	−0.457715	−0.228858	+	0.973460i	$0.573499\pi$
$212$	2628.82	0.851643
$213$	−2250.53	−0.723961
$214$	−1333.81	−0.426064
$215$	−1062.21	−0.336941
$216$	−1179.45	−0.371534
$217$	3173.96	0.992914
$218$	−662.496	−0.205825
$219$	8360.18	2.57958
$220$	−543.835	−0.166661
$221$	686.598	0.208985
$222$	2249.75	0.680150
$223$	3922.99	1.17804	0.589021	−	0.808118i	$-0.299514\pi$
$223$	3922.99	1.17804	0.589021	+	0.808118i	$0.299514\pi$
$224$	−7238.77	−2.15920
$225$	−5605.57	−1.66091
$226$	759.017	0.223403
$227$	2364.63	0.691393	0.345697	−	0.938346i	$-0.387643\pi$
$227$	2364.63	0.691393	0.345697	+	0.938346i	$0.387643\pi$
$228$	−5395.44	−1.56720
$229$	−1056.06	−0.304744	−0.152372	−	0.988323i	$-0.548691\pi$
$229$	−1056.06	−0.304744	−0.152372	+	0.988323i	$0.548691\pi$
$230$	−324.113	−0.0929189
$231$	−6131.23	−1.74634
$232$	166.428	0.0470973
$233$	961.100	0.270231	0.135115	−	0.990830i	$-0.456860\pi$
$233$	961.100	0.270231	0.135115	+	0.990830i	$0.456860\pi$
$234$	7419.09	2.07265
$235$	−1160.38	−0.322105
$236$	−1609.10	−0.443829
$237$	−11484.2	−3.14760
$238$	2080.87	0.566733
$239$	−361.342	−0.0977961	−0.0488980	−	0.998804i	$-0.515571\pi$
$239$	−361.342	−0.0977961	−0.0488980	+	0.998804i	$0.515571\pi$
$240$	−2402.44	−0.646154
$241$	3268.51	0.873624	0.436812	−	0.899553i	$-0.356108\pi$
$241$	3268.51	0.873624	0.436812	+	0.899553i	$0.356108\pi$
$242$	−3117.64	−0.828137
$243$	−1610.07	−0.425046
$244$	−2281.10	−0.598493
$245$	2242.91	0.584875
$246$	−202.816	−0.0525653
$247$	−3655.83	−0.941762
$248$	−591.311	−0.151404
$249$	6194.63	1.57658
$250$	−3329.87	−0.842399
$251$	−3037.08	−0.763741	−0.381871	−	0.924216i	$-0.624720\pi$
$251$	−3037.08	−0.763741	−0.381871	+	0.924216i	$0.624720\pi$
$252$	10073.0	2.51802
$253$	520.459	0.129332
$254$	−9428.35	−2.32908
$255$	577.734	0.141879
$256$	5181.11	1.26492
$257$	2173.63	0.527576	0.263788	−	0.964581i	$-0.415028\pi$
$257$	2173.63	0.527576	0.263788	+	0.964581i	$0.415028\pi$
$258$	−9608.61	−2.31863
$259$	2069.68	0.496540
$260$	929.937	0.221816
$261$	−1460.60	−0.346394
$262$	−6444.76	−1.51969
$263$	6070.68	1.42332	0.711662	−	0.702523i	$-0.247943\pi$
$263$	6070.68	1.42332	0.711662	+	0.702523i	$0.247943\pi$
$264$	1142.25	0.266291
$265$	1498.81	0.347438
$266$	−11079.7	−2.55391
$267$	8445.97	1.93590
$268$	4357.99	0.993308
$269$	−3884.55	−0.880466	−0.440233	−	0.897884i	$-0.645104\pi$
$269$	−3884.55	−0.880466	−0.440233	+	0.897884i	$0.645104\pi$
$270$	2896.13	0.652788
$271$	−3451.28	−0.773618	−0.386809	−	0.922160i	$-0.626423\pi$
$271$	−3451.28	−0.773618	−0.386809	+	0.922160i	$0.626423\pi$
$272$	−1309.30	−0.291868
$273$	10484.2	2.32429
$274$	5762.06	1.27043
$275$	2518.52	0.552263
$276$	−1313.45	−0.286451
$277$	−5252.30	−1.13928	−0.569640	−	0.821895i	$-0.692917\pi$
$277$	−5252.30	−1.13928	−0.569640	+	0.821895i	$0.692917\pi$
$278$	−4822.39	−1.04039
$279$	5189.43	1.11356
$280$	−654.397	−0.139670
$281$	−6430.66	−1.36520	−0.682600	−	0.730793i	$-0.739151\pi$
$281$	−6430.66	−1.36520	−0.682600	+	0.730793i	$0.739151\pi$
$282$	−10496.6	−2.21653
$283$	4043.79	0.849393	0.424696	−	0.905336i	$-0.360381\pi$
$283$	4043.79	0.849393	0.424696	+	0.905336i	$0.360381\pi$
$284$	−1661.20	−0.347092
$285$	−3076.18	−0.639358
$286$	−3333.31	−0.689171
$287$	−186.583	−0.0383750
$288$	−11835.4	−2.42156
$289$	−4598.14	−0.935913
$290$	−408.664	−0.0827502
$291$	11658.8	2.34864
$292$	6170.97	1.23674
$293$	1114.94	0.222305	0.111152	−	0.993803i	$-0.464546\pi$
$293$	1114.94	0.222305	0.111152	+	0.993803i	$0.464546\pi$
$294$	20289.0	4.02476
$295$	−917.420	−0.181065
$296$	−385.584	−0.0757148
$297$	−4650.60	−0.908603
$298$	11651.0	2.26485
$299$	−889.965	−0.172134
$300$	−6355.82	−1.22318
$301$	−8839.55	−1.69270
$302$	184.134	0.0350851
$303$	11705.0	2.21926
$304$	6971.46	1.31527
$305$	−1300.55	−0.244162
$306$	3402.22	0.635595
$307$	1342.68	0.249611	0.124805	−	0.992181i	$-0.460169\pi$
$307$	1342.68	0.249611	0.124805	+	0.992181i	$0.460169\pi$
$308$	−4525.70	−0.837259
$309$	−15675.0	−2.88583
$310$	1451.96	0.266019
$311$	−2852.09	−0.520023	−0.260011	−	0.965606i	$-0.583726\pi$
$311$	−2852.09	−0.520023	−0.260011	+	0.965606i	$0.583726\pi$
$312$	−1953.21	−0.354419
$313$	−147.223	−0.0265864	−0.0132932	−	0.999912i	$-0.504231\pi$
$313$	−147.223	−0.0265864	−0.0132932	+	0.999912i	$0.504231\pi$
$314$	−698.390	−0.125517
$315$	5743.08	1.02726
$316$	−8476.96	−1.50907
$317$	6231.37	1.10406	0.552032	−	0.833823i	$-0.313852\pi$
$317$	6231.37	1.10406	0.552032	+	0.833823i	$0.313852\pi$
$318$	13558.0	2.39086
$319$	656.232	0.115178
$320$	−1126.36	−0.196767
$321$	−3081.75	−0.535846
$322$	−2697.21	−0.466800
$323$	−1676.48	−0.288799
$324$	2907.46	0.498536
$325$	−4306.57	−0.735032
$326$	−56.5361	−0.00960505
$327$	−1530.68	−0.258859
$328$	34.7605	0.00585161
$329$	−9656.46	−1.61817
$330$	−2804.79	−0.467875
$331$	−6116.21	−1.01564	−0.507820	−	0.861463i	$-0.669549\pi$
$331$	−6116.21	−1.01564	−0.507820	+	0.861463i	$0.669549\pi$
$332$	4572.49	0.755868
$333$	3383.94	0.556873
$334$	−5026.36	−0.823443
$335$	2484.68	0.405232
$336$	−19992.7	−3.24610
$337$	−3131.30	−0.506151	−0.253075	−	0.967447i	$-0.581442\pi$
$337$	−3131.30	−0.506151	−0.253075	+	0.967447i	$0.581442\pi$
$338$	−2663.93	−0.428695
$339$	1753.69	0.280966
$340$	426.448	0.0680217
$341$	−2331.55	−0.370266
$342$	−18115.3	−2.86423
$343$	8099.17	1.27497
$344$	1646.81	0.258111
$345$	−748.856	−0.116861
$346$	−15703.5	−2.43996
$347$	−8535.83	−1.32054	−0.660270	−	0.751028i	$-0.729558\pi$
$347$	−8535.83	−1.32054	−0.660270	+	0.751028i	$0.729558\pi$
$348$	−1656.09	−0.255103
$349$	685.601	0.105156	0.0525779	−	0.998617i	$-0.483256\pi$
$349$	685.601	0.105156	0.0525779	+	0.998617i	$0.483256\pi$
$350$	−13051.9	−1.99329
$351$	7952.34	1.20930
$352$	5317.52	0.805184
$353$	−8519.73	−1.28459	−0.642294	−	0.766459i	$-0.722017\pi$
$353$	−8519.73	−1.28459	−0.642294	+	0.766459i	$0.722017\pi$
$354$	−8298.83	−1.24598
$355$	−947.125	−0.141600
$356$	6234.30	0.928138
$357$	4807.80	0.712761
$358$	8081.48	1.19307
$359$	967.974	0.142306	0.0711528	−	0.997465i	$-0.477332\pi$
$359$	967.974	0.142306	0.0711528	+	0.997465i	$0.477332\pi$
$360$	−1069.94	−0.156641
$361$	2067.53	0.301433
$362$	−15689.8	−2.27800
$363$	−7203.23	−1.04152
$364$	7738.77	1.11435
$365$	3518.34	0.504544
$366$	−11764.6	−1.68018
$367$	9239.65	1.31419	0.657093	−	0.753810i	$-0.271786\pi$
$367$	9239.65	1.31419	0.657093	+	0.753810i	$0.271786\pi$
$368$	1697.11	0.240402
$369$	−305.064	−0.0430379
$370$	946.797	0.133031
$371$	12472.8	1.74544
$372$	5883.99	0.820082
$373$	6844.75	0.950155	0.475077	−	0.879944i	$-0.342420\pi$
$373$	6844.75	0.950155	0.475077	+	0.879944i	$0.342420\pi$
$374$	−1528.58	−0.211340
$375$	−7693.60	−1.05946
$376$	1799.01	0.246746
$377$	−1122.13	−0.153296
$378$	24101.1	3.27943
$379$	6387.01	0.865643	0.432822	−	0.901480i	$-0.357518\pi$
$379$	6387.01	0.865643	0.432822	+	0.901480i	$0.357518\pi$
$380$	−2270.65	−0.306531
$381$	−21784.0	−2.92921
$382$	7584.37	1.01584
$383$	5089.71	0.679040	0.339520	−	0.940599i	$-0.389735\pi$
$383$	5089.71	0.679040	0.339520	+	0.940599i	$0.389735\pi$
$384$	6346.49	0.843406
$385$	−2580.30	−0.341570
$386$	11511.6	1.51794
$387$	−14452.7	−1.89838
$388$	8605.85	1.12602
$389$	11667.3	1.52071	0.760355	−	0.649508i	$-0.225025\pi$
$389$	11667.3	1.52071	0.760355	+	0.649508i	$0.225025\pi$
$390$	4796.09	0.622716
$391$	−408.118	−0.0527862
$392$	−3477.33	−0.448040
$393$	−14890.5	−1.91126
$394$	14236.9	1.82042
$395$	−4833.09	−0.615643
$396$	−7399.54	−0.938992
$397$	7561.93	0.955976	0.477988	−	0.878366i	$-0.341366\pi$
$397$	7561.93	0.955976	0.477988	+	0.878366i	$0.341366\pi$
$398$	12156.8	1.53107
$399$	−25599.4	−3.21197
$400$	8212.38	1.02655
$401$	7295.24	0.908496	0.454248	−	0.890875i	$-0.349908\pi$
$401$	7295.24	0.908496	0.454248	+	0.890875i	$0.349908\pi$
$402$	22476.0	2.78856
$403$	3986.86	0.492804
$404$	8639.94	1.06399
$405$	1657.67	0.203384
$406$	−3400.83	−0.415715
$407$	−1520.37	−0.185164
$408$	−895.697	−0.108685
$409$	−7399.07	−0.894524	−0.447262	−	0.894403i	$-0.647601\pi$
$409$	−7399.07	−0.894524	−0.447262	+	0.894403i	$0.647601\pi$
$410$	−85.3542	−0.0102813
$411$	13313.1	1.59778
$412$	−11570.4	−1.38357
$413$	−7634.61	−0.909623
$414$	−4409.94	−0.523519
$415$	2606.98	0.308365
$416$	−9092.75	−1.07166
$417$	−11142.0	−1.30846
$418$	8139.02	0.952374
$419$	1333.36	0.155462	0.0777311	−	0.996974i	$-0.475232\pi$
$419$	1333.36	0.155462	0.0777311	+	0.996974i	$0.475232\pi$
$420$	6511.74	0.756525
$421$	−10470.4	−1.21210	−0.606051	−	0.795426i	$-0.707247\pi$
$421$	−10470.4	−1.21210	−0.606051	+	0.795426i	$0.707247\pi$
$422$	−5340.61	−0.616059
$423$	−15788.3	−1.81479
$424$	−2323.70	−0.266152
$425$	−1974.89	−0.225403
$426$	−8567.54	−0.974410
$427$	−10823.0	−1.22661
$428$	−2274.76	−0.256904
$429$	−7701.55	−0.866747
$430$	−4043.74	−0.453503
$431$	11947.6	1.33525	0.667627	−	0.744496i	$-0.267310\pi$
$431$	11947.6	1.33525	0.667627	+	0.744496i	$0.267310\pi$
$432$	−15164.7	−1.68891
$433$	5597.39	0.621232	0.310616	−	0.950535i	$-0.399465\pi$
$433$	5597.39	0.621232	0.310616	+	0.950535i	$0.399465\pi$
$434$	12082.9	1.33641
$435$	−944.209	−0.104072
$436$	−1129.86	−0.124106
$437$	2173.05	0.237874
$438$	31826.4	3.47197
$439$	−4198.01	−0.456401	−0.228200	−	0.973614i	$-0.573284\pi$
$439$	−4198.01	−0.456401	−0.228200	+	0.973614i	$0.573284\pi$
$440$	480.712	0.0520842
$441$	30517.5	3.29528
$442$	2613.81	0.281281
$443$	12953.3	1.38923	0.694617	−	0.719379i	$-0.255574\pi$
$443$	12953.3	1.38923	0.694617	+	0.719379i	$0.255574\pi$
$444$	3836.85	0.410110
$445$	3554.45	0.378645
$446$	14934.5	1.58558
$447$	26919.5	2.84843
$448$	−9373.37	−0.988505
$449$	6363.07	0.668802	0.334401	−	0.942431i	$-0.391466\pi$
$449$	6363.07	0.668802	0.334401	+	0.942431i	$0.391466\pi$
$450$	−21339.9	−2.23549
$451$	137.062	0.0143104
$452$	1294.47	0.134705
$453$	425.437	0.0441253
$454$	9001.93	0.930576
$455$	4412.22	0.454611
$456$	4769.19	0.489776
$457$	6769.37	0.692906	0.346453	−	0.938067i	$-0.387386\pi$
$457$	6769.37	0.692906	0.346453	+	0.938067i	$0.387386\pi$
$458$	−4020.31	−0.410167
$459$	3646.76	0.370842
$460$	−552.759	−0.0560273
$461$	2635.44	0.266258	0.133129	−	0.991099i	$-0.457498\pi$
$461$	2635.44	0.266258	0.133129	+	0.991099i	$0.457498\pi$
$462$	−23341.0	−2.35048
$463$	−17804.5	−1.78714	−0.893569	−	0.448927i	$-0.851806\pi$
$463$	−17804.5	−1.78714	−0.893569	+	0.448927i	$0.851806\pi$
$464$	2139.84	0.214094
$465$	3354.72	0.334562
$466$	3658.81	0.363715
$467$	−6392.37	−0.633412	−0.316706	−	0.948524i	$-0.602577\pi$
$467$	−6392.37	−0.633412	−0.316706	+	0.948524i	$0.602577\pi$
$468$	12652.9	1.24975
$469$	20677.1	2.03578
$470$	−4417.44	−0.433535
$471$	−1613.62	−0.157859
$472$	1422.33	0.138704
$473$	6493.43	0.631222
$474$	−43719.3	−4.23649
$475$	10515.4	1.01575
$476$	3548.82	0.341723
$477$	20393.1	1.95752
$478$	−1375.59	−0.131628
$479$	−4675.46	−0.445986	−0.222993	−	0.974820i	$-0.571583\pi$
$479$	−4675.46	−0.445986	−0.222993	+	0.974820i	$0.571583\pi$
$480$	−7651.04	−0.727542
$481$	2599.76	0.246443
$482$	12442.9	1.17585
$483$	−6231.85	−0.587078
$484$	−5316.99	−0.499341
$485$	4906.57	0.459373
$486$	−6129.39	−0.572088
$487$	−11038.6	−1.02712	−0.513560	−	0.858054i	$-0.671674\pi$
$487$	−11038.6	−1.02712	−0.513560	+	0.858054i	$0.671674\pi$
$488$	2016.33	0.187039
$489$	−130.626	−0.0120799
$490$	8538.55	0.787209
$491$	−646.686	−0.0594389	−0.0297195	−	0.999558i	$-0.509461\pi$
$491$	−646.686	−0.0594389	−0.0297195	+	0.999558i	$0.509461\pi$
$492$	−345.893	−0.0316953
$493$	−514.583	−0.0470095
$494$	−13917.4	−1.26756
$495$	−4218.80	−0.383073
$496$	−7602.72	−0.688250
$497$	−7881.80	−0.711363
$498$	23582.3	2.12199
$499$	−16825.5	−1.50944	−0.754721	−	0.656046i	$-0.772228\pi$
$499$	−16825.5	−1.50944	−0.754721	+	0.656046i	$0.772228\pi$
$500$	−5678.95	−0.507940
$501$	−11613.3	−1.03562
$502$	−11561.9	−1.02795
$503$	−12085.6	−1.07131	−0.535657	−	0.844436i	$-0.679936\pi$
$503$	−12085.6	−1.07131	−0.535657	+	0.844436i	$0.679936\pi$
$504$	−8903.86	−0.786923
$505$	4926.01	0.434069
$506$	1981.34	0.174074
$507$	−6154.96	−0.539155
$508$	−16079.6	−1.40437
$509$	13782.8	1.20022	0.600111	−	0.799917i	$-0.295123\pi$
$509$	13782.8	1.20022	0.600111	+	0.799917i	$0.295123\pi$
$510$	2199.38	0.190961
$511$	29279.0	2.53469
$512$	13951.7	1.20426
$513$	−19417.4	−1.67115
$514$	8274.78	0.710087
$515$	−6596.77	−0.564444
$516$	−16387.0	−1.39806
$517$	7093.52	0.603429
$518$	7879.08	0.668315
$519$	−36282.6	−3.06865
$520$	−821.999	−0.0693212
$521$	−9780.87	−0.822471	−0.411236	−	0.911529i	$-0.634903\pi$
$521$	−9780.87	−0.822471	−0.411236	+	0.911529i	$0.634903\pi$
$522$	−5560.36	−0.466227
$523$	12861.3	1.07531	0.537653	−	0.843166i	$-0.319311\pi$
$523$	12861.3	1.07531	0.537653	+	0.843166i	$0.319311\pi$
$524$	−10991.2	−0.916326
$525$	−30156.1	−2.50689
$526$	23110.5	1.91571
$527$	1828.28	0.151122
$528$	14686.4	1.21050
$529$	529.000	0.0434783
$530$	5705.81	0.467632
$531$	−12482.6	−1.02015
$532$	−18895.9	−1.53993
$533$	−234.370	−0.0190463
$534$	32153.0	2.60561
$535$	−1296.94	−0.104807
$536$	−3852.16	−0.310425
$537$	18672.1	1.50049
$538$	−14788.1	−1.18506
$539$	−13711.2	−1.09570
$540$	4939.22	0.393611
$541$	14093.3	1.11999	0.559996	−	0.828495i	$-0.310802\pi$
$541$	14093.3	1.11999	0.559996	+	0.828495i	$0.310802\pi$
$542$	−13138.7	−1.04125
$543$	−36250.9	−2.86497
$544$	−4169.73	−0.328631
$545$	−644.181	−0.0506306
$546$	39912.2	3.12836
$547$	14840.3	1.16001	0.580006	−	0.814612i	$-0.303050\pi$
$547$	14840.3	1.16001	0.580006	+	0.814612i	$0.303050\pi$
$548$	9826.94	0.766033
$549$	−17695.6	−1.37565
$550$	9587.76	0.743315
$551$	2739.93	0.211842
$552$	1161.00	0.0895205
$553$	−40220.1	−3.09283
$554$	−19995.0	−1.53341
$555$	2187.56	0.167309
$556$	−8224.37	−0.627322
$557$	4962.40	0.377493	0.188746	−	0.982026i	$-0.439558\pi$
$557$	4962.40	0.377493	0.188746	+	0.982026i	$0.439558\pi$
$558$	19755.7	1.49879
$559$	−11103.5	−0.840122
$560$	−8413.84	−0.634910
$561$	−3531.75	−0.265795
$562$	−24480.9	−1.83748
$563$	4130.74	0.309218	0.154609	−	0.987976i	$-0.450588\pi$
$563$	4130.74	0.309218	0.154609	+	0.987976i	$0.450588\pi$
$564$	−17901.5	−1.33650
$565$	738.034	0.0549546
$566$	15394.3	1.14323
$567$	13794.9	1.02175
$568$	1468.39	0.108472
$569$	792.658	0.0584006	0.0292003	−	0.999574i	$-0.490704\pi$
$569$	792.658	0.0584006	0.0292003	+	0.999574i	$0.490704\pi$
$570$	−11710.7	−0.860540
$571$	25636.7	1.87892	0.939461	−	0.342657i	$-0.111327\pi$
$571$	25636.7	1.87892	0.939461	+	0.342657i	$0.111327\pi$
$572$	−5684.81	−0.415549
$573$	17523.5	1.27758
$574$	−710.303	−0.0516506
$575$	2559.85	0.185657
$576$	−15325.5	−1.10861
$577$	1133.74	0.0817995	0.0408997	−	0.999163i	$-0.486978\pi$
$577$	1133.74	0.0817995	0.0408997	+	0.999163i	$0.486978\pi$
$578$	−17504.7	−1.25969
$579$	26597.3	1.90906
$580$	−696.958	−0.0498958
$581$	21694.8	1.54915
$582$	44384.1	3.16113
$583$	−9162.39	−0.650887
$584$	−5454.71	−0.386502
$585$	7213.99	0.509849
$586$	4244.45	0.299210
$587$	1177.38	0.0827864	0.0413932	−	0.999143i	$-0.486820\pi$
$587$	1177.38	0.0827864	0.0413932	+	0.999143i	$0.486820\pi$
$588$	34602.0	2.42681
$589$	−9734.81	−0.681012
$590$	−3492.53	−0.243704
$591$	32894.1	2.28948
$592$	−4957.60	−0.344183
$593$	−12617.7	−0.873772	−0.436886	−	0.899517i	$-0.643919\pi$
$593$	−12617.7	−0.873772	−0.436886	+	0.899517i	$0.643919\pi$
$594$	−17704.4	−1.22293
$595$	2023.34	0.139410
$596$	19870.3	1.36564
$597$	28088.0	1.92557
$598$	−3388.01	−0.231682
$599$	20599.4	1.40512	0.702562	−	0.711622i	$-0.252039\pi$
$599$	20599.4	1.40512	0.702562	+	0.711622i	$0.252039\pi$
$600$	5618.10	0.382263
$601$	−10430.4	−0.707930	−0.353965	−	0.935259i	$-0.615167\pi$
$601$	−10430.4	−0.707930	−0.353965	+	0.935259i	$0.615167\pi$
$602$	−33651.3	−2.27828
$603$	33807.1	2.28314
$604$	314.031	0.0211552
$605$	−3031.45	−0.203712
$606$	44559.9	2.98700
$607$	−10190.4	−0.681412	−0.340706	−	0.940170i	$-0.610666\pi$
$607$	−10190.4	−0.681412	−0.340706	+	0.940170i	$0.610666\pi$
$608$	22202.0	1.48093
$609$	−7857.54	−0.522830
$610$	−4951.08	−0.328629
$611$	−12129.6	−0.803130
$612$	5802.34	0.383244
$613$	23917.1	1.57586	0.787930	−	0.615765i	$-0.211153\pi$
$613$	23917.1	1.57586	0.787930	+	0.615765i	$0.211153\pi$
$614$	5111.43	0.335962
$615$	−197.209	−0.0129305
$616$	4000.40	0.261657
$617$	−10904.5	−0.711507	−0.355753	−	0.934580i	$-0.615776\pi$
$617$	−10904.5	−0.711507	−0.355753	+	0.934580i	$0.615776\pi$
$618$	−59673.3	−3.88417
$619$	−13180.8	−0.855867	−0.427933	−	0.903810i	$-0.640758\pi$
$619$	−13180.8	−0.855867	−0.427933	+	0.903810i	$0.640758\pi$
$620$	2476.25	0.160401
$621$	−4726.91	−0.305450
$622$	−10857.6	−0.699921
$623$	29579.5	1.90221
$624$	−25113.2	−1.61111
$625$	10674.4	0.683161
$626$	−560.464	−0.0357838
$627$	18805.0	1.19777
$628$	−1191.07	−0.0756831
$629$	1192.19	0.0755737
$630$	21863.4	1.38263
$631$	14689.5	0.926752	0.463376	−	0.886162i	$-0.346638\pi$
$631$	14689.5	0.926752	0.463376	+	0.886162i	$0.346638\pi$
$632$	7493.04	0.471609
$633$	−12339.4	−0.774796
$634$	23722.2	1.48601
$635$	−9167.71	−0.572928
$636$	23122.5	1.44162
$637$	23445.6	1.45832
$638$	2498.21	0.155024
$639$	−12886.8	−0.797798
$640$	2670.89	0.164963
$641$	−13157.2	−0.810732	−0.405366	−	0.914155i	$-0.632856\pi$
$641$	−13157.2	−0.810732	−0.405366	+	0.914155i	$0.632856\pi$
$642$	−11731.9	−0.721218
$643$	−4075.37	−0.249949	−0.124974	−	0.992160i	$-0.539885\pi$
$643$	−4075.37	−0.249949	−0.124974	+	0.992160i	$0.539885\pi$
$644$	−4599.97	−0.281466
$645$	−9342.98	−0.570356
$646$	−6382.20	−0.388706
$647$	20473.3	1.24403	0.622016	−	0.783005i	$-0.286314\pi$
$647$	20473.3	1.24403	0.622016	+	0.783005i	$0.286314\pi$
$648$	−2569.99	−0.155801
$649$	5608.29	0.339206
$650$	−16394.7	−0.989311
$651$	27917.4	1.68075
$652$	−96.4198	−0.00579155
$653$	3926.11	0.235284	0.117642	−	0.993056i	$-0.462466\pi$
$653$	3926.11	0.235284	0.117642	+	0.993056i	$0.462466\pi$
$654$	−5827.16	−0.348410
$655$	−6266.60	−0.373826
$656$	446.930	0.0266001
$657$	47871.3	2.84268
$658$	−36761.2	−2.17796
$659$	27760.4	1.64096	0.820480	−	0.571676i	$-0.193706\pi$
$659$	27760.4	1.64096	0.820480	+	0.571676i	$0.193706\pi$
$660$	−4783.45	−0.282114
$661$	9456.05	0.556426	0.278213	−	0.960519i	$-0.410258\pi$
$661$	9456.05	0.556426	0.278213	+	0.960519i	$0.410258\pi$
$662$	−23283.8	−1.36699
$663$	6039.16	0.353758
$664$	−4041.76	−0.236221
$665$	−10773.4	−0.628232
$666$	12882.3	0.749519
$667$	667.000	0.0387202
$668$	−8572.23	−0.496511
$669$	34505.8	1.99412
$670$	9458.94	0.545419
$671$	7950.44	0.457412
$672$	−63670.6	−3.65498
$673$	32669.4	1.87120	0.935598	−	0.353068i	$-0.114862\pi$
$673$	32669.4	1.87120	0.935598	+	0.353068i	$0.114862\pi$
$674$	−11920.5	−0.681250
$675$	−22873.7	−1.30431
$676$	−4543.21	−0.258490
$677$	−19137.7	−1.08644	−0.543221	−	0.839590i	$-0.682795\pi$
$677$	−19137.7	−1.08644	−0.543221	+	0.839590i	$0.682795\pi$
$678$	6676.14	0.378165
$679$	40831.6	2.30777
$680$	−376.950	−0.0212579
$681$	20798.8	1.17035
$682$	−8875.99	−0.498357
$683$	22765.3	1.27539	0.637693	−	0.770291i	$-0.279889\pi$
$683$	22765.3	1.27539	0.637693	+	0.770291i	$0.279889\pi$
$684$	−30894.9	−1.72704
$685$	5602.77	0.312512
$686$	30832.7	1.71603
$687$	−9288.84	−0.515854
$688$	21173.7	1.17332
$689$	15667.3	0.866295
$690$	−2850.82	−0.157288
$691$	31992.0	1.76126	0.880632	−	0.473800i	$-0.157118\pi$
$691$	31992.0	1.76126	0.880632	+	0.473800i	$0.157118\pi$
$692$	−26781.6	−1.47122
$693$	−35108.1	−1.92446
$694$	−32495.1	−1.77737
$695$	−4689.08	−0.255924
$696$	1463.87	0.0797237
$697$	−107.477	−0.00584070
$698$	2610.01	0.141534
$699$	8453.61	0.457432
$700$	−22259.4	−1.20189
$701$	17351.8	0.934905	0.467453	−	0.884018i	$-0.345172\pi$
$701$	17351.8	0.934905	0.467453	+	0.884018i	$0.345172\pi$
$702$	30273.8	1.62765
$703$	−6347.90	−0.340563
$704$	6885.57	0.368622
$705$	−10206.4	−0.545242
$706$	−32433.8	−1.72898
$707$	40993.4	2.18064
$708$	−14153.3	−0.751290
$709$	−25778.9	−1.36551	−0.682754	−	0.730648i	$-0.739218\pi$
$709$	−25778.9	−1.36551	−0.682754	+	0.730648i	$0.739218\pi$
$710$	−3605.61	−0.190586
$711$	−65760.0	−3.46862
$712$	−5510.68	−0.290058
$713$	−2369.81	−0.124474
$714$	18302.8	0.959336
$715$	−3241.16	−0.169528
$716$	13782.6	0.719386
$717$	−3178.28	−0.165544
$718$	3684.98	0.191535
$719$	34926.3	1.81159	0.905794	−	0.423719i	$-0.139276\pi$
$719$	34926.3	1.81159	0.905794	+	0.423719i	$0.139276\pi$
$720$	−13756.6	−0.712056
$721$	−54897.2	−2.83561
$722$	7870.88	0.405712
$723$	28749.1	1.47882
$724$	−26758.2	−1.37357
$725$	3227.63	0.165340
$726$	−27422.0	−1.40183
$727$	16664.9	0.850163	0.425081	−	0.905155i	$-0.360245\pi$
$727$	16664.9	0.850163	0.425081	+	0.905155i	$0.360245\pi$
$728$	−6840.53	−0.348251
$729$	−26253.0	−1.33379
$730$	13394.0	0.679087
$731$	−5091.81	−0.257630
$732$	−20064.0	−1.01310
$733$	9322.07	0.469739	0.234869	−	0.972027i	$-0.424534\pi$
$733$	9322.07	0.469739	0.234869	+	0.972027i	$0.424534\pi$
$734$	35174.4	1.76882
$735$	19728.1	0.990046
$736$	5404.78	0.270683
$737$	−15189.2	−0.759158
$738$	−1161.35	−0.0579265
$739$	−11105.8	−0.552818	−0.276409	−	0.961040i	$-0.589144\pi$
$739$	−11105.8	−0.552818	−0.276409	+	0.961040i	$0.589144\pi$
$740$	1614.72	0.0802139
$741$	−32155.9	−1.59416
$742$	47482.8	2.34926
$743$	−14487.4	−0.715334	−0.357667	−	0.933849i	$-0.616428\pi$
$743$	−14487.4	−0.715334	−0.357667	+	0.933849i	$0.616428\pi$
$744$	−5201.04	−0.256289
$745$	11328.9	0.557128
$746$	26057.3	1.27885
$747$	35471.1	1.73738
$748$	−2606.92	−0.127431
$749$	−10792.9	−0.526522
$750$	−29288.8	−1.42597
$751$	6995.53	0.339908	0.169954	−	0.985452i	$-0.445638\pi$
$751$	6995.53	0.339908	0.169954	+	0.985452i	$0.445638\pi$
$752$	23130.5	1.12165
$753$	−26713.5	−1.29282
$754$	−4271.84	−0.206328
$755$	179.043	0.00863053
$756$	41103.3	1.97740
$757$	18092.5	0.868672	0.434336	−	0.900751i	$-0.356983\pi$
$757$	18092.5	0.868672	0.434336	+	0.900751i	$0.356983\pi$
$758$	24314.7	1.16511
$759$	4577.84	0.218926
$760$	2007.09	0.0957959
$761$	24728.5	1.17794	0.588968	−	0.808157i	$-0.299535\pi$
$761$	24728.5	1.17794	0.588968	+	0.808157i	$0.299535\pi$
$762$	−82929.6	−3.94255
$763$	−5360.76	−0.254355
$764$	12934.8	0.612519
$765$	3308.17	0.156349
$766$	19376.0	0.913948
$767$	−9589.96	−0.451465
$768$	45571.8	2.14119
$769$	−13368.2	−0.626878	−0.313439	−	0.949608i	$-0.601481\pi$
$769$	−13368.2	−0.626878	−0.313439	+	0.949608i	$0.601481\pi$
$770$	−9822.96	−0.459734
$771$	19118.7	0.893052
$772$	19632.5	0.915271
$773$	23349.8	1.08646	0.543229	−	0.839584i	$-0.317201\pi$
$773$	23349.8	1.08646	0.543229	+	0.839584i	$0.317201\pi$
$774$	−55020.0	−2.55511
$775$	−11467.6	−0.531520
$776$	−7606.97	−0.351900
$777$	18204.5	0.840517
$778$	44416.3	2.04679
$779$	572.266	0.0263204
$780$	8179.51	0.375479
$781$	5789.88	0.265273
$782$	−1553.66	−0.0710472
$783$	−5960.02	−0.272023
$784$	−44709.4	−2.03669
$785$	−679.083	−0.0308758
$786$	−56686.6	−2.57245
$787$	1800.71	0.0815610	0.0407805	−	0.999168i	$-0.487016\pi$
$787$	1800.71	0.0815610	0.0407805	+	0.999168i	$0.487016\pi$
$788$	24280.4	1.09766
$789$	53396.3	2.40933
$790$	−18399.1	−0.828620
$791$	6141.79	0.276077
$792$	6540.67	0.293450
$793$	−13594.9	−0.608790
$794$	28787.5	1.28669
$795$	13183.2	0.588124
$796$	20732.9	0.923187
$797$	−31454.5	−1.39796	−0.698980	−	0.715141i	$-0.746362\pi$
$797$	−31454.5	−1.39796	−0.698980	+	0.715141i	$0.746362\pi$
$798$	−97454.5	−4.32312
$799$	−5562.38	−0.246286
$800$	26153.9	1.15585
$801$	48362.6	2.13334
$802$	27772.3	1.22278
$803$	−21508.0	−0.945208
$804$	38331.9	1.68142
$805$	−2622.64	−0.114827
$806$	15177.6	0.663286
$807$	−34167.6	−1.49041
$808$	−7637.10	−0.332515
$809$	−26951.7	−1.17129	−0.585643	−	0.810569i	$-0.699158\pi$
$809$	−26951.7	−1.17129	−0.585643	+	0.810569i	$0.699158\pi$
$810$	6310.60	0.273743
$811$	−25652.6	−1.11071	−0.555355	−	0.831613i	$-0.687418\pi$
$811$	−25652.6	−1.11071	−0.555355	+	0.831613i	$0.687418\pi$
$812$	−5799.96	−0.250663
$813$	−30356.7	−1.30954
$814$	−5787.88	−0.249220
$815$	−54.9732	−0.00236273
$816$	−11516.3	−0.494059
$817$	27111.7	1.16098
$818$	−28167.5	−1.20398
$819$	60033.5	2.56134
$820$	−145.568	−0.00619932
$821$	40184.3	1.70821	0.854106	−	0.520100i	$-0.174105\pi$
$821$	40184.3	1.70821	0.854106	+	0.520100i	$0.174105\pi$
$822$	50681.8	2.15052
$823$	13946.4	0.590693	0.295347	−	0.955390i	$-0.404565\pi$
$823$	13946.4	0.590693	0.295347	+	0.955390i	$0.404565\pi$
$824$	10227.4	0.432388
$825$	22152.3	0.934842
$826$	−29064.2	−1.22430
$827$	−44648.1	−1.87735	−0.938673	−	0.344808i	$-0.887944\pi$
$827$	−44648.1	−1.87735	−0.938673	+	0.344808i	$0.887944\pi$
$828$	−7520.96	−0.315666
$829$	−12187.5	−0.510603	−0.255302	−	0.966861i	$-0.582175\pi$
$829$	−12187.5	−0.510603	−0.255302	+	0.966861i	$0.582175\pi$
$830$	9924.52	0.415042
$831$	−46198.1	−1.92851
$832$	−11774.0	−0.490615
$833$	10751.6	0.447204
$834$	−42416.7	−1.76111
$835$	−4887.40	−0.202558
$836$	13880.7	0.574252
$837$	21175.6	0.874476
$838$	5075.95	0.209243
$839$	−31430.1	−1.29331	−0.646656	−	0.762782i	$-0.723833\pi$
$839$	−31430.1	−1.29331	−0.646656	+	0.762782i	$0.723833\pi$
$840$	−5755.92	−0.236426
$841$	841.000	0.0344828
$842$	−39859.7	−1.63142
$843$	−56562.6	−2.31094
$844$	−9108.17	−0.371465
$845$	−2590.29	−0.105454
$846$	−60104.6	−2.44260
$847$	−25227.2	−1.02340
$848$	−29876.7	−1.20987
$849$	35568.2	1.43781
$850$	−7518.23	−0.303380
$851$	−1545.31	−0.0622476
$852$	−14611.5	−0.587539
$853$	−530.342	−0.0212879	−0.0106439	−	0.999943i	$-0.503388\pi$
$853$	−530.342	−0.0212879	−0.0106439	+	0.999943i	$0.503388\pi$
$854$	−41202.0	−1.65094
$855$	−17614.5	−0.704567
$856$	2010.73	0.0802866
$857$	−33875.4	−1.35025	−0.675124	−	0.737704i	$-0.735910\pi$
$857$	−33875.4	−1.35025	−0.675124	+	0.737704i	$0.735910\pi$
$858$	−29319.0	−1.16659
$859$	19442.4	0.772253	0.386126	−	0.922446i	$-0.373813\pi$
$859$	19442.4	0.772253	0.386126	+	0.922446i	$0.373813\pi$
$860$	−6896.41	−0.273449
$861$	−1641.14	−0.0649592
$862$	45483.2	1.79718
$863$	−3995.05	−0.157582	−0.0787909	−	0.996891i	$-0.525106\pi$
$863$	−3995.05	−0.157582	−0.0787909	+	0.996891i	$0.525106\pi$
$864$	−48294.7	−1.90164
$865$	−15269.4	−0.600202
$866$	21308.7	0.836143
$867$	−40444.2	−1.58426
$868$	20606.9	0.805812
$869$	29545.2	1.15334
$870$	−3594.51	−0.140075
$871$	25972.8	1.01040
$872$	998.714	0.0387852
$873$	66759.9	2.58818
$874$	8272.58	0.320165
$875$	−26944.6	−1.04102
$876$	54278.4	2.09349
$877$	−5036.40	−0.193919	−0.0969596	−	0.995288i	$-0.530912\pi$
$877$	−5036.40	−0.193919	−0.0969596	+	0.995288i	$0.530912\pi$
$878$	−15981.4	−0.614289
$879$	9806.73	0.376306
$880$	6180.71	0.236763
$881$	14760.9	0.564481	0.282240	−	0.959344i	$-0.408922\pi$
$881$	14760.9	0.564481	0.282240	+	0.959344i	$0.408922\pi$
$882$	116177.	4.43525
$883$	20845.5	0.794460	0.397230	−	0.917719i	$-0.369971\pi$
$883$	20845.5	0.794460	0.397230	+	0.917719i	$0.369971\pi$
$884$	4457.74	0.169604
$885$	−8069.41	−0.306498
$886$	49312.0	1.86983
$887$	−274.645	−0.0103965	−0.00519824	−	0.999986i	$-0.501655\pi$
$887$	−274.645	−0.0103965	−0.00519824	+	0.999986i	$0.501655\pi$
$888$	−3391.50	−0.128166
$889$	−76292.0	−2.87824
$890$	13531.4	0.509634
$891$	−10133.5	−0.381018
$892$	25470.0	0.956054
$893$	29617.2	1.10986
$894$	102480.	3.83383
$895$	7858.07	0.293482
$896$	22226.7	0.828729
$897$	−7827.93	−0.291379
$898$	24223.6	0.900169
$899$	−2988.03	−0.110852
$900$	−36394.2	−1.34793
$901$	7184.67	0.265656
$902$	521.780	0.0192609
$903$	−77750.6	−2.86531
$904$	−1144.22	−0.0420976
$905$	−15256.0	−0.560362
$906$	1619.60	0.0593902
$907$	−38240.5	−1.39995	−0.699976	−	0.714166i	$-0.746806\pi$
$907$	−38240.5	−1.39995	−0.699976	+	0.714166i	$0.746806\pi$
$908$	15352.4	0.561109
$909$	67024.3	2.44561
$910$	16796.9	0.611880
$911$	38222.1	1.39007	0.695036	−	0.718975i	$-0.255389\pi$
$911$	38222.1	1.39007	0.695036	+	0.718975i	$0.255389\pi$
$912$	61319.4	2.22641
$913$	−15936.8	−0.577689
$914$	25770.3	0.932612
$915$	−11439.4	−0.413305
$916$	−6856.45	−0.247318
$917$	−52149.5	−1.87800
$918$	13882.9	0.499132
$919$	25717.6	0.923119	0.461560	−	0.887109i	$-0.347290\pi$
$919$	25717.6	0.923119	0.461560	+	0.887109i	$0.347290\pi$
$920$	488.601	0.0175094
$921$	11809.9	0.422528
$922$	10032.9	0.358368
$923$	−9900.47	−0.353064
$924$	−39807.0	−1.41727
$925$	−7477.82	−0.265805
$926$	−67779.9	−2.40538
$927$	−89757.1	−3.18016
$928$	6814.72	0.241060
$929$	−45637.7	−1.61176	−0.805880	−	0.592079i	$-0.798308\pi$
$929$	−45637.7	−1.61176	−0.805880	+	0.592079i	$0.798308\pi$
$930$	12771.1	0.450302
$931$	−57247.6	−2.01527
$932$	6239.94	0.219309
$933$	−25086.3	−0.880267
$934$	−24335.1	−0.852537
$935$	−1486.32	−0.0519871
$936$	−11184.3	−0.390566
$937$	9137.53	0.318581	0.159290	−	0.987232i	$-0.449079\pi$
$937$	9137.53	0.318581	0.159290	+	0.987232i	$0.449079\pi$
$938$	78715.6	2.74004
$939$	−1294.94	−0.0450040
$940$	−7533.75	−0.261408
$941$	19639.9	0.680384	0.340192	−	0.940356i	$-0.389508\pi$
$941$	19639.9	0.680384	0.340192	+	0.940356i	$0.389508\pi$
$942$	−6142.88	−0.212469
$943$	139.311	0.00481080
$944$	18287.5	0.630516
$945$	23434.8	0.806703
$946$	24719.8	0.849589
$947$	−38772.6	−1.33045	−0.665227	−	0.746641i	$-0.731665\pi$
$947$	−38772.6	−1.33045	−0.665227	+	0.746641i	$0.731665\pi$
$948$	−74561.3	−2.55447
$949$	36777.9	1.25802
$950$	40031.3	1.36714
$951$	54809.7	1.86890
$952$	−3136.91	−0.106794
$953$	17255.2	0.586516	0.293258	−	0.956033i	$-0.405261\pi$
$953$	17255.2	0.586516	0.293258	+	0.956033i	$0.405261\pi$
$954$	77634.5	2.63471
$955$	7374.70	0.249885
$956$	−2346.01	−0.0793676
$957$	5772.06	0.194968
$958$	−17799.0	−0.600271
$959$	46625.3	1.56998
$960$	−9907.20	−0.333077
$961$	−19174.7	−0.643641
$962$	9897.05	0.331698
$963$	−17646.5	−0.590498
$964$	21220.8	0.709000
$965$	11193.4	0.373396
$966$	−23724.0	−0.790174
$967$	2806.27	0.0933233	0.0466616	−	0.998911i	$-0.485142\pi$
$967$	2806.27	0.0933233	0.0466616	+	0.998911i	$0.485142\pi$
$968$	4699.84	0.156052
$969$	−14745.9	−0.488863
$970$	18678.8	0.618290
$971$	−18665.9	−0.616908	−0.308454	−	0.951239i	$-0.599812\pi$
$971$	−18665.9	−0.616908	−0.308454	+	0.951239i	$0.599812\pi$
$972$	−10453.4	−0.344952
$973$	−39021.7	−1.28569
$974$	−42022.9	−1.38244
$975$	−37879.6	−1.24422
$976$	25924.7	0.850237
$977$	−34582.6	−1.13244	−0.566221	−	0.824254i	$-0.691595\pi$
$977$	−34582.6	−1.13244	−0.566221	+	0.824254i	$0.691595\pi$
$978$	−497.279	−0.0162589
$979$	−21728.7	−0.709350
$980$	14562.1	0.474663
$981$	−8764.86	−0.285260
$982$	−2461.87	−0.0800014
$983$	−23083.6	−0.748984	−0.374492	−	0.927230i	$-0.622183\pi$
$983$	−23083.6	−0.748984	−0.374492	+	0.927230i	$0.622183\pi$
$984$	305.746	0.00990530
$985$	13843.3	0.447802
$986$	−1958.97	−0.0632720
$987$	−84936.0	−2.73915
$988$	−23735.5	−0.764298
$989$	6599.98	0.212201
$990$	−16060.6	−0.515594
$991$	9171.59	0.293991	0.146996	−	0.989137i	$-0.453040\pi$
$991$	9171.59	0.293991	0.146996	+	0.989137i	$0.453040\pi$
$992$	−24212.3	−0.774941
$993$	−53796.7	−1.71922
$994$	−30005.3	−0.957454
$995$	11820.7	0.376625
$996$	40218.6	1.27949
$997$	−52379.3	−1.66386	−0.831931	−	0.554879i	$-0.812765\pi$
$997$	−52379.3	−1.66386	−0.831931	+	0.554879i	$0.812765\pi$
$998$	−64052.9	−2.03162
$999$	13808.3	0.437311

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	667.4.a.c.1.31	✓	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
667.4.a.c.1.31	✓	39	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 667 = 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	667.a (trivial)

\(f(q)\)	\(=\)	\(q+3.80690 q^{2} +8.79577 q^{3} +6.49250 q^{4} +3.70166 q^{5} +33.4846 q^{6} +30.8046 q^{7} -5.73891 q^{8} +50.3656 q^{9} +O(q^{10})\)	\(q+3.80690 q^{2} +8.79577 q^{3} +6.49250 q^{4} +3.70166 q^{5} +33.4846 q^{6} +30.8046 q^{7} -5.73891 q^{8} +50.3656 q^{9} +14.0919 q^{10} -22.6287 q^{11} +57.1065 q^{12} +38.6941 q^{13} +117.270 q^{14} +32.5589 q^{15} -73.7875 q^{16} +17.7442 q^{17} +191.737 q^{18} -94.4803 q^{19} +24.0330 q^{20} +270.950 q^{21} -86.1451 q^{22} -23.0000 q^{23} -50.4782 q^{24} -111.298 q^{25} +147.305 q^{26} +205.518 q^{27} +199.999 q^{28} -29.0000 q^{29} +123.949 q^{30} +103.035 q^{31} -234.990 q^{32} -199.037 q^{33} +67.5506 q^{34} +114.028 q^{35} +326.998 q^{36} +67.1876 q^{37} -359.677 q^{38} +340.345 q^{39} -21.2435 q^{40} -6.05699 q^{41} +1031.48 q^{42} -286.956 q^{43} -146.917 q^{44} +186.436 q^{45} -87.5587 q^{46} -313.475 q^{47} -649.017 q^{48} +605.921 q^{49} -423.699 q^{50} +156.074 q^{51} +251.222 q^{52} +404.902 q^{53} +782.387 q^{54} -83.7637 q^{55} -176.785 q^{56} -831.027 q^{57} -110.400 q^{58} -247.840 q^{59} +211.389 q^{60} -351.344 q^{61} +392.245 q^{62} +1551.49 q^{63} -304.285 q^{64} +143.233 q^{65} -757.713 q^{66} +671.235 q^{67} +115.204 q^{68} -202.303 q^{69} +434.093 q^{70} -255.865 q^{71} -289.044 q^{72} +950.477 q^{73} +255.776 q^{74} -978.949 q^{75} -613.413 q^{76} -697.066 q^{77} +1295.66 q^{78} -1305.65 q^{79} -273.136 q^{80} +447.819 q^{81} -23.0584 q^{82} +704.274 q^{83} +1759.14 q^{84} +65.6832 q^{85} -1092.41 q^{86} -255.077 q^{87} +129.864 q^{88} +960.231 q^{89} +709.744 q^{90} +1191.96 q^{91} -149.327 q^{92} +906.275 q^{93} -1193.37 q^{94} -349.734 q^{95} -2066.92 q^{96} +1325.51 q^{97} +2306.68 q^{98} -1139.71 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q + 6 q^{2} + 2 q^{3} + 156 q^{4} + 80 q^{5} - 4 q^{6} + 18 q^{7} + 156 q^{8} + 411 q^{9}+O(q^{10}) \) 39 * q + 6 * q^2 + 2 * q^3 + 156 * q^4 + 80 * q^5 - 4 * q^6 + 18 * q^7 + 156 * q^8 + 411 * q^9	\( 39 q + 6 q^{2} + 2 q^{3} + 156 q^{4} + 80 q^{5} - 4 q^{6} + 18 q^{7} + 156 q^{8} + 411 q^{9} + 130 q^{10} + 76 q^{11} + 115 q^{12} + 184 q^{13} + 336 q^{14} + 228 q^{15} + 776 q^{16} + 314 q^{17} + 27 q^{18} + 36 q^{19} + 533 q^{20} + 246 q^{21} + 269 q^{22} - 897 q^{23} + 30 q^{24} + 1267 q^{25} + 787 q^{26} + 122 q^{27} + 53 q^{28} - 1131 q^{29} + 703 q^{30} + 140 q^{31} + 1304 q^{32} + 2210 q^{33} + 59 q^{34} + 1828 q^{35} + 1834 q^{36} + 430 q^{37} + 1874 q^{38} - 340 q^{39} + 276 q^{40} + 1936 q^{41} + 756 q^{42} + 96 q^{43} - 671 q^{44} + 3392 q^{45} - 138 q^{46} + 1808 q^{47} + 535 q^{48} + 2201 q^{49} + 395 q^{50} + 750 q^{51} - 530 q^{52} + 4200 q^{53} - 937 q^{54} + 902 q^{55} + 3805 q^{56} + 300 q^{57} - 174 q^{58} + 726 q^{59} + 195 q^{60} + 736 q^{61} + 1851 q^{62} + 796 q^{63} + 2914 q^{64} + 2572 q^{65} + 307 q^{66} + 1192 q^{67} + 1235 q^{68} - 46 q^{69} + 5268 q^{70} + 1714 q^{71} + 643 q^{72} + 2012 q^{73} + 3307 q^{74} - 1708 q^{75} + 5244 q^{76} + 6592 q^{77} + 6406 q^{78} + 1768 q^{79} + 8606 q^{80} + 5363 q^{81} - 2059 q^{82} + 3766 q^{83} + 3818 q^{84} + 1260 q^{85} - 2355 q^{86} - 58 q^{87} + 3448 q^{88} + 1634 q^{89} - 1313 q^{90} + 1240 q^{91} - 3588 q^{92} + 3954 q^{93} + 2315 q^{94} + 1656 q^{95} + 1480 q^{96} - 788 q^{97} + 3128 q^{98} + 4488 q^{99}+O(q^{100}) \) 39 * q + 6 * q^2 + 2 * q^3 + 156 * q^4 + 80 * q^5 - 4 * q^6 + 18 * q^7 + 156 * q^8 + 411 * q^9 + 130 * q^10 + 76 * q^11 + 115 * q^12 + 184 * q^13 + 336 * q^14 + 228 * q^15 + 776 * q^16 + 314 * q^17 + 27 * q^18 + 36 * q^19 + 533 * q^20 + 246 * q^21 + 269 * q^22 - 897 * q^23 + 30 * q^24 + 1267 * q^25 + 787 * q^26 + 122 * q^27 + 53 * q^28 - 1131 * q^29 + 703 * q^30 + 140 * q^31 + 1304 * q^32 + 2210 * q^33 + 59 * q^34 + 1828 * q^35 + 1834 * q^36 + 430 * q^37 + 1874 * q^38 - 340 * q^39 + 276 * q^40 + 1936 * q^41 + 756 * q^42 + 96 * q^43 - 671 * q^44 + 3392 * q^45 - 138 * q^46 + 1808 * q^47 + 535 * q^48 + 2201 * q^49 + 395 * q^50 + 750 * q^51 - 530 * q^52 + 4200 * q^53 - 937 * q^54 + 902 * q^55 + 3805 * q^56 + 300 * q^57 - 174 * q^58 + 726 * q^59 + 195 * q^60 + 736 * q^61 + 1851 * q^62 + 796 * q^63 + 2914 * q^64 + 2572 * q^65 + 307 * q^66 + 1192 * q^67 + 1235 * q^68 - 46 * q^69 + 5268 * q^70 + 1714 * q^71 + 643 * q^72 + 2012 * q^73 + 3307 * q^74 - 1708 * q^75 + 5244 * q^76 + 6592 * q^77 + 6406 * q^78 + 1768 * q^79 + 8606 * q^80 + 5363 * q^81 - 2059 * q^82 + 3766 * q^83 + 3818 * q^84 + 1260 * q^85 - 2355 * q^86 - 58 * q^87 + 3448 * q^88 + 1634 * q^89 - 1313 * q^90 + 1240 * q^91 - 3588 * q^92 + 3954 * q^93 + 2315 * q^94 + 1656 * q^95 + 1480 * q^96 - 788 * q^97 + 3128 * q^98 + 4488 * q^99

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