LMFDB - Embedded newform 667.4.a.d.1.27

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			1.27
Character	$\chi$	$=$	667.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.32902 q^{2} -4.43884 q^{3} -2.57566 q^{4} +20.5248 q^{5} -10.3382 q^{6} -30.5748 q^{7} -24.6309 q^{8} -7.29667 q^{9} +O(q^{10})$	\(q+2.32902 q^{2} -4.43884 q^{3} -2.57566 q^{4} +20.5248 q^{5} -10.3382 q^{6} -30.5748 q^{7} -24.6309 q^{8} -7.29667 q^{9} +47.8028 q^{10} -66.2006 q^{11} +11.4330 q^{12} +27.5845 q^{13} -71.2094 q^{14} -91.1065 q^{15} -36.7607 q^{16} +108.958 q^{17} -16.9941 q^{18} +70.9503 q^{19} -52.8650 q^{20} +135.717 q^{21} -154.183 q^{22} +23.0000 q^{23} +109.333 q^{24} +296.269 q^{25} +64.2449 q^{26} +152.238 q^{27} +78.7504 q^{28} +29.0000 q^{29} -212.189 q^{30} -95.1901 q^{31} +111.431 q^{32} +293.854 q^{33} +253.765 q^{34} -627.543 q^{35} +18.7938 q^{36} -231.899 q^{37} +165.245 q^{38} -122.443 q^{39} -505.546 q^{40} +323.128 q^{41} +316.087 q^{42} -223.669 q^{43} +170.510 q^{44} -149.763 q^{45} +53.5675 q^{46} +426.293 q^{47} +163.175 q^{48} +591.820 q^{49} +690.016 q^{50} -483.647 q^{51} -71.0484 q^{52} -104.695 q^{53} +354.564 q^{54} -1358.76 q^{55} +753.087 q^{56} -314.937 q^{57} +67.5416 q^{58} +640.152 q^{59} +234.660 q^{60} +216.972 q^{61} -221.700 q^{62} +223.095 q^{63} +553.611 q^{64} +566.168 q^{65} +684.393 q^{66} +539.080 q^{67} -280.639 q^{68} -102.093 q^{69} -1461.56 q^{70} -972.122 q^{71} +179.724 q^{72} -377.177 q^{73} -540.097 q^{74} -1315.09 q^{75} -182.744 q^{76} +2024.07 q^{77} -285.173 q^{78} +526.383 q^{79} -754.507 q^{80} -478.748 q^{81} +752.571 q^{82} +479.088 q^{83} -349.561 q^{84} +2236.35 q^{85} -520.929 q^{86} -128.726 q^{87} +1630.58 q^{88} -1607.17 q^{89} -348.801 q^{90} -843.392 q^{91} -59.2402 q^{92} +422.534 q^{93} +992.845 q^{94} +1456.24 q^{95} -494.625 q^{96} +82.8888 q^{97} +1378.36 q^{98} +483.045 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.32902	0.823433	0.411717	−	0.911312i	$-0.364929\pi$
$2$	2.32902	0.823433	0.411717	+	0.911312i	$0.364929\pi$
$3$	−4.43884	−0.854256	−0.427128	−	0.904191i	$-0.640475\pi$
$3$	−4.43884	−0.854256	−0.427128	+	0.904191i	$0.640475\pi$
$4$	−2.57566	−0.321958
$5$	20.5248	1.83580	0.917899	−	0.396815i	$-0.129885\pi$
$5$	20.5248	1.83580	0.917899	+	0.396815i	$0.129885\pi$
$6$	−10.3382	−0.703423
$7$	−30.5748	−1.65089	−0.825443	−	0.564486i	$-0.809075\pi$
$7$	−30.5748	−1.65089	−0.825443	+	0.564486i	$0.809075\pi$
$8$	−24.6309	−1.08854
$9$	−7.29667	−0.270247
$10$	47.8028	1.51166
$11$	−66.2006	−1.81457	−0.907284	−	0.420519i	$-0.861848\pi$
$11$	−66.2006	−1.81457	−0.907284	+	0.420519i	$0.861848\pi$
$12$	11.4330	0.275034
$13$	27.5845	0.588505	0.294253	−	0.955728i	$-0.404929\pi$
$13$	27.5845	0.588505	0.294253	+	0.955728i	$0.404929\pi$
$14$	−71.2094	−1.35939
$15$	−91.1065	−1.56824
$16$	−36.7607	−0.574386
$17$	108.958	1.55448	0.777241	−	0.629203i	$-0.216619\pi$
$17$	108.958	1.55448	0.777241	+	0.629203i	$0.216619\pi$
$18$	−16.9941	−0.222531
$19$	70.9503	0.856690	0.428345	−	0.903615i	$-0.359097\pi$
$19$	70.9503	0.856690	0.428345	+	0.903615i	$0.359097\pi$
$20$	−52.8650	−0.591049
$21$	135.717	1.41028
$22$	−154.183	−1.49418
$23$	23.0000	0.208514
$23$	23.0000	0.208514
$24$	109.333	0.929895
$25$	296.269	2.37015
$26$	64.2449	0.484595
$27$	152.238	1.08512
$28$	78.7504	0.531515
$29$	29.0000	0.185695
$29$	29.0000	0.185695
$30$	−212.189	−1.29134
$31$	−95.1901	−0.551505	−0.275752	−	0.961229i	$-0.588927\pi$
$31$	−95.1901	−0.551505	−0.275752	+	0.961229i	$0.588927\pi$
$32$	111.431	0.615576
$33$	293.854	1.55010
$34$	253.765	1.28001
$35$	−627.543	−3.03069
$36$	18.7938	0.0870082
$37$	−231.899	−1.03038	−0.515188	−	0.857077i	$-0.672278\pi$
$37$	−231.899	−1.03038	−0.515188	+	0.857077i	$0.672278\pi$
$38$	165.245	0.705427
$39$	−122.443	−0.502734
$40$	−505.546	−1.99835
$41$	323.128	1.23083	0.615416	−	0.788203i	$-0.288988\pi$
$41$	323.128	1.23083	0.615416	+	0.788203i	$0.288988\pi$
$42$	316.087	1.16127
$43$	−223.669	−0.793236	−0.396618	−	0.917984i	$-0.629816\pi$
$43$	−223.669	−0.793236	−0.396618	+	0.917984i	$0.629816\pi$
$44$	170.510	0.584214
$45$	−149.763	−0.496119
$46$	53.5675	0.171698
$47$	426.293	1.32300	0.661502	−	0.749943i	$-0.269919\pi$
$47$	426.293	1.32300	0.661502	+	0.749943i	$0.269919\pi$
$48$	163.175	0.490672
$49$	591.820	1.72542
$50$	690.016	1.95166
$51$	−483.647	−1.32793
$52$	−71.0484	−0.189474
$53$	−104.695	−0.271340	−0.135670	−	0.990754i	$-0.543319\pi$
$53$	−104.695	−0.271340	−0.135670	+	0.990754i	$0.543319\pi$
$54$	354.564	0.893521
$55$	−1358.76	−3.33118
$56$	753.087	1.79706
$57$	−314.937	−0.731833
$58$	67.5416	0.152908
$59$	640.152	1.41255	0.706277	−	0.707936i	$-0.250373\pi$
$59$	640.152	1.41255	0.706277	+	0.707936i	$0.250373\pi$
$60$	234.660	0.504907
$61$	216.972	0.455416	0.227708	−	0.973729i	$-0.426877\pi$
$61$	216.972	0.455416	0.227708	+	0.973729i	$0.426877\pi$
$62$	−221.700	−0.454127
$63$	223.095	0.446147
$64$	553.611	1.08127
$65$	566.168	1.08038
$66$	684.393	1.27641
$67$	539.080	0.982972	0.491486	−	0.870886i	$-0.336454\pi$
$67$	539.080	0.982972	0.491486	+	0.870886i	$0.336454\pi$
$68$	−280.639	−0.500477
$69$	−102.093	−0.178125
$70$	−1461.56	−2.49557
$71$	−972.122	−1.62492	−0.812462	−	0.583014i	$-0.801873\pi$
$71$	−972.122	−1.62492	−0.812462	+	0.583014i	$0.801873\pi$
$72$	179.724	0.294176
$73$	−377.177	−0.604729	−0.302364	−	0.953192i	$-0.597776\pi$
$73$	−377.177	−0.604729	−0.302364	+	0.953192i	$0.597776\pi$
$74$	−540.097	−0.848446
$75$	−1315.09	−2.02472
$76$	−182.744	−0.275818
$77$	2024.07	2.99564
$78$	−285.173	−0.413968
$79$	526.383	0.749655	0.374827	−	0.927095i	$-0.377702\pi$
$79$	526.383	0.749655	0.374827	+	0.927095i	$0.377702\pi$
$80$	−754.507	−1.05446
$81$	−478.748	−0.656719
$82$	752.571	1.01351
$83$	479.088	0.633576	0.316788	−	0.948496i	$-0.397396\pi$
$83$	479.088	0.633576	0.316788	+	0.948496i	$0.397396\pi$
$84$	−349.561	−0.454050
$85$	2236.35	2.85371
$86$	−520.929	−0.653177
$87$	−128.726	−0.158631
$88$	1630.58	1.97524
$89$	−1607.17	−1.91415	−0.957076	−	0.289837i	$-0.906399\pi$
$89$	−1607.17	−1.91415	−0.957076	+	0.289837i	$0.906399\pi$
$90$	−348.801	−0.408521
$91$	−843.392	−0.971555
$92$	−59.2402	−0.0671328
$93$	422.534	0.471126
$94$	992.845	1.08941
$95$	1456.24	1.57271
$96$	−494.625	−0.525859
$97$	82.8888	0.0867637	0.0433819	−	0.999059i	$-0.486187\pi$
$97$	82.8888	0.0867637	0.0433819	+	0.999059i	$0.486187\pi$
$98$	1378.36	1.42077
$99$	483.045	0.490382
$100$	−763.088	−0.763088
$101$	1503.01	1.48074	0.740372	−	0.672198i	$-0.234649\pi$
$101$	1503.01	1.48074	0.740372	+	0.672198i	$0.234649\pi$
$102$	−1126.43	−1.09346
$103$	−1641.20	−1.57002	−0.785009	−	0.619484i	$-0.787342\pi$
$103$	−1641.20	−1.57002	−0.785009	+	0.619484i	$0.787342\pi$
$104$	−679.433	−0.640614
$105$	2785.57	2.58899
$106$	−243.838	−0.223430
$107$	−391.486	−0.353704	−0.176852	−	0.984237i	$-0.556591\pi$
$107$	−391.486	−0.353704	−0.176852	+	0.984237i	$0.556591\pi$
$108$	−392.112	−0.349361
$109$	240.625	0.211447	0.105724	−	0.994396i	$-0.466284\pi$
$109$	240.625	0.211447	0.105724	+	0.994396i	$0.466284\pi$
$110$	−3164.57	−2.74300
$111$	1029.36	0.880205
$112$	1123.95	0.948245
$113$	335.119	0.278985	0.139492	−	0.990223i	$-0.455453\pi$
$113$	335.119	0.278985	0.139492	+	0.990223i	$0.455453\pi$
$114$	−733.496	−0.602615
$115$	472.071	0.382790
$116$	−74.6942	−0.0597860
$117$	−201.275	−0.159042
$118$	1490.93	1.16314
$119$	−3331.37	−2.56627
$120$	2244.04	1.70710
$121$	3051.53	2.29266
$122$	505.331	0.375005
$123$	−1434.31	−1.05144
$124$	245.177	0.177561
$125$	3515.27	2.51532
$126$	519.592	0.367372
$127$	2502.28	1.74836	0.874179	−	0.485604i	$-0.161400\pi$
$127$	2502.28	1.74836	0.874179	+	0.485604i	$0.161400\pi$
$128$	397.922	0.274779
$129$	992.830	0.677627
$130$	1318.62	0.889618
$131$	2374.21	1.58348	0.791738	−	0.610861i	$-0.209176\pi$
$131$	2374.21	1.58348	0.791738	+	0.610861i	$0.209176\pi$
$132$	−756.869	−0.499068
$133$	−2169.29	−1.41430
$134$	1255.53	0.809412
$135$	3124.65	1.99205
$136$	−2683.74	−1.69212
$137$	−333.499	−0.207976	−0.103988	−	0.994579i	$-0.533160\pi$
$137$	−333.499	−0.207976	−0.103988	+	0.994579i	$0.533160\pi$
$138$	−237.778	−0.146674
$139$	1614.73	0.985319	0.492660	−	0.870222i	$-0.336025\pi$
$139$	1614.73	0.985319	0.492660	+	0.870222i	$0.336025\pi$
$140$	1616.34	0.975754
$141$	−1892.25	−1.13018
$142$	−2264.09	−1.33802
$143$	−1826.11	−1.06788
$144$	268.231	0.155226
$145$	595.220	0.340899
$146$	−878.453	−0.497954
$147$	−2627.00	−1.47395
$148$	597.293	0.331737
$149$	1209.89	0.665221	0.332611	−	0.943064i	$-0.392071\pi$
$149$	1209.89	0.665221	0.332611	+	0.943064i	$0.392071\pi$
$150$	−3062.87	−1.66722
$151$	2755.27	1.48490	0.742452	−	0.669899i	$-0.233663\pi$
$151$	2755.27	1.48490	0.742452	+	0.669899i	$0.233663\pi$
$152$	−1747.57	−0.932545
$153$	−795.031	−0.420094
$154$	4714.11	2.46671
$155$	−1953.76	−1.01245
$156$	315.373	0.161859
$157$	−1737.66	−0.883316	−0.441658	−	0.897183i	$-0.645610\pi$
$157$	−1737.66	−0.883316	−0.441658	+	0.897183i	$0.645610\pi$
$158$	1225.96	0.617291
$159$	464.726	0.231794
$160$	2287.11	1.13007
$161$	−703.221	−0.344233
$162$	−1115.01	−0.540764
$163$	−1603.00	−0.770286	−0.385143	−	0.922857i	$-0.625848\pi$
$163$	−1603.00	−0.770286	−0.385143	+	0.922857i	$0.625848\pi$
$164$	−832.268	−0.396275
$165$	6031.31	2.84568
$166$	1115.81	0.521707
$167$	201.021	0.0931465	0.0465732	−	0.998915i	$-0.485170\pi$
$167$	201.021	0.0931465	0.0465732	+	0.998915i	$0.485170\pi$
$168$	−3342.83	−1.53515
$169$	−1436.09	−0.653662
$170$	5208.50	2.34984
$171$	−517.701	−0.231518
$172$	576.095	0.255388
$173$	−1073.39	−0.471725	−0.235863	−	0.971786i	$-0.575792\pi$
$173$	−1073.39	−0.471725	−0.235863	+	0.971786i	$0.575792\pi$
$174$	−299.807	−0.130622
$175$	−9058.37	−3.91285
$176$	2433.58	1.04226
$177$	−2841.53	−1.20668
$178$	−3743.13	−1.57618
$179$	−914.525	−0.381870	−0.190935	−	0.981603i	$-0.561152\pi$
$179$	−914.525	−0.381870	−0.190935	+	0.981603i	$0.561152\pi$
$180$	385.739	0.159729
$181$	−459.489	−0.188693	−0.0943467	−	0.995539i	$-0.530076\pi$
$181$	−459.489	−0.188693	−0.0943467	+	0.995539i	$0.530076\pi$
$182$	−1964.28	−0.800011
$183$	−963.103	−0.389042
$184$	−566.512	−0.226977
$185$	−4759.68	−1.89156
$186$	984.090	0.387941
$187$	−7213.09	−2.82071
$188$	−1097.99	−0.425951
$189$	−4654.64	−1.79140
$190$	3391.62	1.29502
$191$	−3290.91	−1.24671	−0.623355	−	0.781939i	$-0.714231\pi$
$191$	−3290.91	−1.24671	−0.623355	+	0.781939i	$0.714231\pi$
$192$	−2457.39	−0.923682
$193$	639.900	0.238658	0.119329	−	0.992855i	$-0.461926\pi$
$193$	639.900	0.238658	0.119329	+	0.992855i	$0.461926\pi$
$194$	193.050	0.0714441
$195$	−2513.13	−0.922918
$196$	−1524.33	−0.555513
$197$	1069.69	0.386865	0.193432	−	0.981114i	$-0.438038\pi$
$197$	1069.69	0.386865	0.193432	+	0.981114i	$0.438038\pi$
$198$	1125.02	0.403797
$199$	1571.71	0.559879	0.279939	−	0.960018i	$-0.409686\pi$
$199$	1571.71	0.559879	0.279939	+	0.960018i	$0.409686\pi$
$200$	−7297.38	−2.58001
$201$	−2392.89	−0.839709
$202$	3500.54	1.21929
$203$	−886.670	−0.306562
$204$	1245.71	0.427536
$205$	6632.14	2.25956
$206$	−3822.38	−1.29281
$207$	−167.824	−0.0563504
$208$	−1014.03	−0.338029
$209$	−4696.96	−1.55452
$210$	6487.64	2.13186
$211$	−536.574	−0.175068	−0.0875339	−	0.996162i	$-0.527899\pi$
$211$	−536.574	−0.175068	−0.0875339	+	0.996162i	$0.527899\pi$
$212$	269.660	0.0873599
$213$	4315.10	1.38810
$214$	−911.779	−0.291252
$215$	−4590.76	−1.45622
$216$	−3749.75	−1.18120
$217$	2910.42	0.910471
$218$	560.422	0.174113
$219$	1674.23	0.516593
$220$	3499.70	1.07250
$221$	3005.55	0.914821
$222$	2397.41	0.724790
$223$	3641.34	1.09346	0.546732	−	0.837308i	$-0.315872\pi$
$223$	3641.34	1.09346	0.546732	+	0.837308i	$0.315872\pi$
$224$	−3406.99	−1.01625
$225$	−2161.78	−0.640527
$226$	780.498	0.229725
$227$	−3213.22	−0.939511	−0.469756	−	0.882796i	$-0.655658\pi$
$227$	−3213.22	−0.939511	−0.469756	+	0.882796i	$0.655658\pi$
$228$	811.172	0.235619
$229$	5150.12	1.48615	0.743077	−	0.669206i	$-0.233366\pi$
$229$	5150.12	1.48615	0.743077	+	0.669206i	$0.233366\pi$
$230$	1099.46	0.315202
$231$	−8984.54	−2.55905
$232$	−714.297	−0.202138
$233$	−2400.13	−0.674841	−0.337421	−	0.941354i	$-0.609554\pi$
$233$	−2400.13	−0.674841	−0.337421	+	0.941354i	$0.609554\pi$
$234$	−468.774	−0.130960
$235$	8749.59	2.42877
$236$	−1648.81	−0.454782
$237$	−2336.53	−0.640397
$238$	−7758.84	−2.11315
$239$	957.763	0.259216	0.129608	−	0.991565i	$-0.458628\pi$
$239$	957.763	0.259216	0.129608	+	0.991565i	$0.458628\pi$
$240$	3349.14	0.900775
$241$	5081.38	1.35818	0.679088	−	0.734057i	$-0.262375\pi$
$241$	5081.38	1.35818	0.679088	+	0.734057i	$0.262375\pi$
$242$	7107.07	1.88785
$243$	−1985.33	−0.524110
$244$	−558.845	−0.146625
$245$	12147.0	3.16753
$246$	−3340.55	−0.865794
$247$	1957.13	0.504167
$248$	2344.62	0.600337
$249$	−2126.60	−0.541236
$250$	8187.13	2.07120
$251$	−4981.45	−1.25270	−0.626348	−	0.779544i	$-0.715451\pi$
$251$	−4981.45	−1.25270	−0.626348	+	0.779544i	$0.715451\pi$
$252$	−574.616	−0.143641
$253$	−1522.61	−0.378364
$254$	5827.86	1.43966
$255$	−9926.78	−2.43780
$256$	−3502.12	−0.855009
$257$	−4705.46	−1.14210	−0.571048	−	0.820917i	$-0.693463\pi$
$257$	−4705.46	−1.14210	−0.571048	+	0.820917i	$0.693463\pi$
$258$	2312.32	0.557980
$259$	7090.26	1.70103
$260$	−1458.26	−0.347835
$261$	−211.604	−0.0501836
$262$	5529.58	1.30389
$263$	7074.54	1.65869	0.829344	−	0.558739i	$-0.188714\pi$
$263$	7074.54	1.65869	0.829344	+	0.558739i	$0.188714\pi$
$264$	−7237.91	−1.68736
$265$	−2148.86	−0.498125
$266$	−5052.33	−1.16458
$267$	7133.97	1.63518
$268$	−1388.49	−0.316475
$269$	−4304.98	−0.975759	−0.487879	−	0.872911i	$-0.662229\pi$
$269$	−4304.98	−0.975759	−0.487879	+	0.872911i	$0.662229\pi$
$270$	7277.38	1.64032
$271$	−610.061	−0.136747	−0.0683737	−	0.997660i	$-0.521781\pi$
$271$	−610.061	−0.136747	−0.0683737	+	0.997660i	$0.521781\pi$
$272$	−4005.37	−0.892872
$273$	3743.68	0.829956
$274$	−776.726	−0.171255
$275$	−19613.2	−4.30080
$276$	262.958	0.0573486
$277$	−3811.72	−0.826801	−0.413400	−	0.910549i	$-0.635659\pi$
$277$	−3811.72	−0.826801	−0.413400	+	0.910549i	$0.635659\pi$
$278$	3760.73	0.811345
$279$	694.571	0.149043
$280$	15457.0	3.29904
$281$	6086.22	1.29208	0.646039	−	0.763305i	$-0.276424\pi$
$281$	6086.22	1.29208	0.646039	+	0.763305i	$0.276424\pi$
$282$	−4407.08	−0.930631
$283$	2678.67	0.562652	0.281326	−	0.959612i	$-0.409226\pi$
$283$	2678.67	0.562652	0.281326	+	0.959612i	$0.409226\pi$
$284$	2503.86	0.523157
$285$	−6464.04	−1.34350
$286$	−4253.06	−0.879330
$287$	−9879.58	−2.03196
$288$	−813.076	−0.166358
$289$	6958.85	1.41642
$290$	1386.28	0.280708
$291$	−367.930	−0.0741184
$292$	971.479	0.194697
$293$	4443.28	0.885936	0.442968	−	0.896538i	$-0.353926\pi$
$293$	4443.28	0.885936	0.442968	+	0.896538i	$0.353926\pi$
$294$	−6118.33	−1.21370
$295$	13139.0	2.59316
$296$	5711.88	1.12161
$297$	−10078.2	−1.96902
$298$	2817.86	0.547765
$299$	634.444	0.122712
$300$	3387.23	0.651873
$301$	6838.63	1.30954
$302$	6417.08	1.22272
$303$	−6671.63	−1.26493
$304$	−2608.18	−0.492071
$305$	4453.31	0.836051
$306$	−1851.64	−0.345920
$307$	5805.56	1.07929	0.539643	−	0.841894i	$-0.318559\pi$
$307$	5805.56	1.07929	0.539643	+	0.841894i	$0.318559\pi$
$308$	−5213.33	−0.964470
$309$	7285.01	1.34120
$310$	−4550.35	−0.833685
$311$	2734.02	0.498495	0.249247	−	0.968440i	$-0.419817\pi$
$311$	2734.02	0.498495	0.249247	+	0.968440i	$0.419817\pi$
$312$	3015.89	0.547248
$313$	−3699.77	−0.668125	−0.334063	−	0.942551i	$-0.608420\pi$
$313$	−3699.77	−0.668125	−0.334063	+	0.942551i	$0.608420\pi$
$314$	−4047.05	−0.727352
$315$	4578.98	0.819036
$316$	−1355.78	−0.241357
$317$	416.509	0.0737964	0.0368982	−	0.999319i	$-0.488252\pi$
$317$	416.509	0.0737964	0.0368982	+	0.999319i	$0.488252\pi$
$318$	1082.36	0.190867
$319$	−1919.82	−0.336957
$320$	11362.8	1.98499
$321$	1737.74	0.302154
$322$	−1637.82	−0.283453
$323$	7730.60	1.33171
$324$	1233.09	0.211436
$325$	8172.43	1.39485
$326$	−3733.42	−0.634279
$327$	−1068.10	−0.180630
$328$	−7958.94	−1.33981
$329$	−13033.8	−2.18413
$330$	14047.0	2.34323
$331$	597.597	0.0992353	0.0496176	−	0.998768i	$-0.484200\pi$
$331$	597.597	0.0992353	0.0496176	+	0.998768i	$0.484200\pi$
$332$	−1233.97	−0.203985
$333$	1692.09	0.278456
$334$	468.182	0.0766999
$335$	11064.5	1.80454
$336$	−4989.04	−0.810044
$337$	5567.28	0.899909	0.449954	−	0.893052i	$-0.351440\pi$
$337$	5567.28	0.899909	0.449954	+	0.893052i	$0.351440\pi$
$338$	−3344.69	−0.538247
$339$	−1487.54	−0.238324
$340$	−5760.07	−0.918775
$341$	6301.64	1.00074
$342$	−1205.74	−0.190640
$343$	−7607.64	−1.19759
$344$	5509.17	0.863472
$345$	−2095.45	−0.327001
$346$	−2499.95	−0.388434
$347$	−8238.58	−1.27455	−0.637277	−	0.770635i	$-0.719939\pi$
$347$	−8238.58	−1.27455	−0.637277	+	0.770635i	$0.719939\pi$
$348$	331.556	0.0510726
$349$	−6698.68	−1.02743	−0.513713	−	0.857962i	$-0.671731\pi$
$349$	−6698.68	−1.02743	−0.513713	+	0.857962i	$0.671731\pi$
$350$	−21097.1	−3.22197
$351$	4199.40	0.638596
$352$	−7376.81	−1.11700
$353$	4817.41	0.726359	0.363179	−	0.931719i	$-0.381691\pi$
$353$	4817.41	0.726359	0.363179	+	0.931719i	$0.381691\pi$
$354$	−6617.99	−0.993622
$355$	−19952.6	−2.98303
$356$	4139.52	0.616276
$357$	14787.4	2.19225
$358$	−2129.95	−0.314445
$359$	2099.54	0.308661	0.154331	−	0.988019i	$-0.450678\pi$
$359$	2099.54	0.308661	0.154331	+	0.988019i	$0.450678\pi$
$360$	3688.80	0.540047
$361$	−1825.05	−0.266082
$362$	−1070.16	−0.155376
$363$	−13545.2	−1.95851
$364$	2172.29	0.312800
$365$	−7741.49	−1.11016
$366$	−2243.09	−0.320350
$367$	4473.60	0.636294	0.318147	−	0.948041i	$-0.396939\pi$
$367$	4473.60	0.636294	0.318147	+	0.948041i	$0.396939\pi$
$368$	−845.496	−0.119768
$369$	−2357.76	−0.332629
$370$	−11085.4	−1.55757
$371$	3201.04	0.447951
$372$	−1088.30	−0.151683
$373$	2528.73	0.351026	0.175513	−	0.984477i	$-0.443842\pi$
$373$	2528.73	0.351026	0.175513	+	0.984477i	$0.443842\pi$
$374$	−16799.4	−2.32267
$375$	−15603.7	−2.14873
$376$	−10500.0	−1.44015
$377$	799.951	0.109283
$378$	−10840.7	−1.47510
$379$	−2339.98	−0.317141	−0.158571	−	0.987348i	$-0.550689\pi$
$379$	−2339.98	−0.317141	−0.158571	+	0.987348i	$0.550689\pi$
$380$	−3750.79	−0.506346
$381$	−11107.2	−1.49354
$382$	−7664.59	−1.02658
$383$	8564.40	1.14261	0.571306	−	0.820737i	$-0.306437\pi$
$383$	8564.40	1.14261	0.571306	+	0.820737i	$0.306437\pi$
$384$	−1766.32	−0.234731
$385$	41543.8	5.49939
$386$	1490.34	0.196519
$387$	1632.04	0.214370
$388$	−213.493	−0.0279342
$389$	6514.16	0.849052	0.424526	−	0.905416i	$-0.360441\pi$
$389$	6514.16	0.849052	0.424526	+	0.905416i	$0.360441\pi$
$390$	−5853.13	−0.759961
$391$	2506.03	0.324132
$392$	−14577.1	−1.87820
$393$	−10538.7	−1.35269
$394$	2491.33	0.318557
$395$	10803.9	1.37621
$396$	−1244.16	−0.157882
$397$	1211.95	0.153214	0.0766071	−	0.997061i	$-0.475591\pi$
$397$	1211.95	0.153214	0.0766071	+	0.997061i	$0.475591\pi$
$398$	3660.56	0.461023
$399$	9629.15	1.20817
$400$	−10891.0	−1.36138
$401$	−7705.03	−0.959529	−0.479764	−	0.877397i	$-0.659278\pi$
$401$	−7705.03	−0.959529	−0.479764	+	0.877397i	$0.659278\pi$
$402$	−5573.10	−0.691445
$403$	−2625.77	−0.324563
$404$	−3871.25	−0.476737
$405$	−9826.23	−1.20560
$406$	−2065.07	−0.252433
$407$	15351.8	1.86969
$408$	11912.7	1.44551
$409$	7788.44	0.941598	0.470799	−	0.882241i	$-0.343966\pi$
$409$	7788.44	0.941598	0.470799	+	0.882241i	$0.343966\pi$
$410$	15446.4	1.86059
$411$	1480.35	0.177665
$412$	4227.17	0.505479
$413$	−19572.5	−2.33196
$414$	−390.864	−0.0464008
$415$	9833.21	1.16312
$416$	3073.77	0.362270
$417$	−7167.52	−0.841715
$418$	−10939.3	−1.28005
$419$	8871.77	1.03440	0.517201	−	0.855864i	$-0.326974\pi$
$419$	8871.77	1.03440	0.517201	+	0.855864i	$0.326974\pi$
$420$	−7174.68	−0.833544
$421$	−4459.50	−0.516254	−0.258127	−	0.966111i	$-0.583105\pi$
$421$	−4459.50	−0.516254	−0.258127	+	0.966111i	$0.583105\pi$
$422$	−1249.69	−0.144157
$423$	−3110.52	−0.357538
$424$	2578.74	0.295365
$425$	32280.9	3.68436
$426$	10050.0	1.14301
$427$	−6633.87	−0.751840
$428$	1008.33	0.113878
$429$	8105.83	0.912245
$430$	−10692.0	−1.19910
$431$	−5643.31	−0.630693	−0.315347	−	0.948977i	$-0.602121\pi$
$431$	−5643.31	−0.630693	−0.315347	+	0.948977i	$0.602121\pi$
$432$	−5596.36	−0.623275
$433$	7784.01	0.863916	0.431958	−	0.901894i	$-0.357823\pi$
$433$	7784.01	0.863916	0.431958	+	0.901894i	$0.357823\pi$
$434$	6778.43	0.749712
$435$	−2642.09	−0.291215
$436$	−619.770	−0.0680770
$437$	1631.86	0.178632
$438$	3899.31	0.425380
$439$	−9644.57	−1.04854	−0.524271	−	0.851551i	$-0.675662\pi$
$439$	−9644.57	−1.04854	−0.524271	+	0.851551i	$0.675662\pi$
$440$	33467.5	3.62613
$441$	−4318.32	−0.466291
$442$	7000.00	0.753294
$443$	−2792.12	−0.299453	−0.149726	−	0.988727i	$-0.547839\pi$
$443$	−2792.12	−0.299453	−0.149726	+	0.988727i	$0.547839\pi$
$444$	−2651.29	−0.283389
$445$	−32986.9	−3.51400
$446$	8480.77	0.900395
$447$	−5370.51	−0.568269
$448$	−16926.6	−1.78506
$449$	14198.0	1.49231	0.746155	−	0.665773i	$-0.231898\pi$
$449$	14198.0	1.49231	0.746155	+	0.665773i	$0.231898\pi$
$450$	−5034.83	−0.527431
$451$	−21391.3	−2.23343
$452$	−863.152	−0.0898213
$453$	−12230.2	−1.26849
$454$	−7483.66	−0.773625
$455$	−17310.5	−1.78358
$456$	7757.20	0.796632
$457$	3901.14	0.399316	0.199658	−	0.979866i	$-0.436017\pi$
$457$	3901.14	0.399316	0.199658	+	0.979866i	$0.436017\pi$
$458$	11994.7	1.22375
$459$	16587.5	1.68679
$460$	−1215.90	−0.123242
$461$	−7719.89	−0.779937	−0.389969	−	0.920828i	$-0.627514\pi$
$461$	−7719.89	−0.779937	−0.389969	+	0.920828i	$0.627514\pi$
$462$	−20925.2	−2.10720
$463$	15580.5	1.56390	0.781950	−	0.623341i	$-0.214225\pi$
$463$	15580.5	1.56390	0.781950	+	0.623341i	$0.214225\pi$
$464$	−1066.06	−0.106661
$465$	8672.44	0.864892
$466$	−5589.96	−0.555687
$467$	10727.0	1.06292	0.531461	−	0.847082i	$-0.321643\pi$
$467$	10727.0	1.06292	0.531461	+	0.847082i	$0.321643\pi$
$468$	518.417	0.0512048
$469$	−16482.3	−1.62277
$470$	20378.0	1.99993
$471$	7713.21	0.754578
$472$	−15767.5	−1.53763
$473$	14807.0	1.43938
$474$	−5441.83	−0.527324
$475$	21020.4	2.03049
$476$	8580.49	0.826231
$477$	763.928	0.0733288
$478$	2230.65	0.213447
$479$	−2181.68	−0.208107	−0.104054	−	0.994572i	$-0.533181\pi$
$479$	−2181.68	−0.208107	−0.104054	+	0.994572i	$0.533181\pi$
$480$	−10152.1	−0.965371
$481$	−6396.81	−0.606382
$482$	11834.6	1.11837
$483$	3121.49	0.294063
$484$	−7859.70	−0.738138
$485$	1701.28	0.159281
$486$	−4623.86	−0.431569
$487$	6013.62	0.559555	0.279778	−	0.960065i	$-0.409739\pi$
$487$	6013.62	0.559555	0.279778	+	0.960065i	$0.409739\pi$
$488$	−5344.21	−0.495740
$489$	7115.46	0.658021
$490$	28290.7	2.60825
$491$	298.071	0.0273966	0.0136983	−	0.999906i	$-0.495640\pi$
$491$	298.071	0.0273966	0.0136983	+	0.999906i	$0.495640\pi$
$492$	3694.30	0.338521
$493$	3159.78	0.288660
$494$	4558.20	0.415148
$495$	9914.41	0.900242
$496$	3499.25	0.316776
$497$	29722.5	2.68256
$498$	−4952.89	−0.445671
$499$	11405.4	1.02320	0.511599	−	0.859224i	$-0.329053\pi$
$499$	11405.4	1.02320	0.511599	+	0.859224i	$0.329053\pi$
$500$	−9054.13	−0.809826
$501$	−892.300	−0.0795709
$502$	−11601.9	−1.03151
$503$	8096.98	0.717747	0.358873	−	0.933386i	$-0.383161\pi$
$503$	8096.98	0.717747	0.358873	+	0.933386i	$0.383161\pi$
$504$	−5495.03	−0.485651
$505$	30849.0	2.71834
$506$	−3546.20	−0.311557
$507$	6374.60	0.558394
$508$	−6445.03	−0.562897
$509$	−12646.6	−1.10128	−0.550638	−	0.834744i	$-0.685615\pi$
$509$	−12646.6	−1.10128	−0.550638	+	0.834744i	$0.685615\pi$
$510$	−23119.7	−2.00737
$511$	11532.1	0.998338
$512$	−11339.9	−0.978822
$513$	10801.3	0.929608
$514$	−10959.1	−0.940440
$515$	−33685.3	−2.88223
$516$	−2557.19	−0.218167
$517$	−28220.9	−2.40068
$518$	16513.4	1.40069
$519$	4764.62	0.402974
$520$	−13945.2	−1.17604
$521$	−11627.4	−0.977746	−0.488873	−	0.872355i	$-0.662592\pi$
$521$	−11627.4	−0.977746	−0.488873	+	0.872355i	$0.662592\pi$
$522$	−492.829	−0.0413229
$523$	−6839.95	−0.571874	−0.285937	−	0.958248i	$-0.592305\pi$
$523$	−6839.95	−0.571874	−0.285937	+	0.958248i	$0.592305\pi$
$524$	−6115.15	−0.509812
$525$	40208.7	3.34257
$526$	16476.8	1.36582
$527$	−10371.7	−0.857304
$528$	−10802.3	−0.890358
$529$	529.000	0.0434783
$530$	−5004.73	−0.410173
$531$	−4670.98	−0.381739
$532$	5587.37	0.455344
$533$	8913.32	0.724351
$534$	16615.2	1.34646
$535$	−8035.18	−0.649329
$536$	−13278.0	−1.07001
$537$	4059.43	0.326215
$538$	−10026.4	−0.803472
$539$	−39178.9	−3.13090
$540$	−8048.04	−0.641357
$541$	77.0685	0.00612465	0.00306233	−	0.999995i	$-0.499025\pi$
$541$	77.0685	0.00612465	0.00306233	+	0.999995i	$0.499025\pi$
$542$	−1420.84	−0.112602
$543$	2039.60	0.161192
$544$	12141.3	0.956901
$545$	4938.80	0.388174
$546$	8719.12	0.683414
$547$	8401.23	0.656692	0.328346	−	0.944558i	$-0.393509\pi$
$547$	8401.23	0.656692	0.328346	+	0.944558i	$0.393509\pi$
$548$	858.980	0.0669595
$549$	−1583.17	−0.123075
$550$	−45679.5	−3.54142
$551$	2057.56	0.159083
$552$	2514.66	0.193896
$553$	−16094.1	−1.23759
$554$	−8877.57	−0.680815
$555$	21127.5	1.61588
$556$	−4158.99	−0.317231
$557$	−1318.74	−0.100317	−0.0501586	−	0.998741i	$-0.515973\pi$
$557$	−1318.74	−0.100317	−0.0501586	+	0.998741i	$0.515973\pi$
$558$	1617.67	0.122727
$559$	−6169.79	−0.466824
$560$	23068.9	1.74079
$561$	32017.8	2.40961
$562$	14174.9	1.06394
$563$	10572.4	0.791429	0.395715	−	0.918374i	$-0.370497\pi$
$563$	10572.4	0.791429	0.395715	+	0.918374i	$0.370497\pi$
$564$	4873.79	0.363871
$565$	6878.25	0.512160
$566$	6238.68	0.463306
$567$	14637.6	1.08417
$568$	23944.3	1.76880
$569$	−19806.1	−1.45925	−0.729625	−	0.683847i	$-0.760305\pi$
$569$	−19806.1	−1.45925	−0.729625	+	0.683847i	$0.760305\pi$
$570$	−15054.9	−1.10628
$571$	−3652.05	−0.267659	−0.133830	−	0.991004i	$-0.542728\pi$
$571$	−3652.05	−0.267659	−0.133830	+	0.991004i	$0.542728\pi$
$572$	4703.45	0.343813
$573$	14607.8	1.06501
$574$	−23009.7	−1.67318
$575$	6814.18	0.494211
$576$	−4039.52	−0.292210
$577$	15706.6	1.13323	0.566616	−	0.823982i	$-0.308252\pi$
$577$	15706.6	1.13323	0.566616	+	0.823982i	$0.308252\pi$
$578$	16207.3	1.16632
$579$	−2840.41	−0.203875
$580$	−1533.09	−0.109755
$581$	−14648.0	−1.04596
$582$	−856.917	−0.0610316
$583$	6930.90	0.492365
$584$	9290.22	0.658274
$585$	−4131.14	−0.291969
$586$	10348.5	0.729509
$587$	−21002.7	−1.47679	−0.738393	−	0.674371i	$-0.764415\pi$
$587$	−21002.7	−1.47679	−0.738393	+	0.674371i	$0.764415\pi$
$588$	6766.26	0.474550
$589$	−6753.77	−0.472469
$590$	30601.0	2.13530
$591$	−4748.19	−0.330481
$592$	8524.75	0.591833
$593$	3135.04	0.217101	0.108550	−	0.994091i	$-0.465379\pi$
$593$	3135.04	0.217101	0.108550	+	0.994091i	$0.465379\pi$
$594$	−23472.4	−1.62135
$595$	−68375.9	−4.71116
$596$	−3116.26	−0.214173
$597$	−6976.59	−0.478280
$598$	1477.63	0.101045
$599$	−11620.5	−0.792653	−0.396327	−	0.918110i	$-0.629715\pi$
$599$	−11620.5	−0.792653	−0.396327	+	0.918110i	$0.629715\pi$
$600$	32391.9	2.20399
$601$	3461.71	0.234952	0.117476	−	0.993076i	$-0.462520\pi$
$601$	3461.71	0.234952	0.117476	+	0.993076i	$0.462520\pi$
$602$	15927.3	1.07832
$603$	−3933.49	−0.265645
$604$	−7096.64	−0.478076
$605$	62632.1	4.20885
$606$	−15538.4	−1.04159
$607$	−19856.7	−1.32777	−0.663886	−	0.747834i	$-0.731094\pi$
$607$	−19856.7	−1.32777	−0.663886	+	0.747834i	$0.731094\pi$
$608$	7906.07	0.527358
$609$	3935.79	0.261882
$610$	10371.8	0.688432
$611$	11759.1	0.778595
$612$	2047.73	0.135253
$613$	11612.6	0.765134	0.382567	−	0.923928i	$-0.375040\pi$
$613$	11612.6	0.765134	0.382567	+	0.923928i	$0.375040\pi$
$614$	13521.3	0.888719
$615$	−29439.0	−1.93024
$616$	−49854.8	−3.26089
$617$	14737.8	0.961623	0.480812	−	0.876824i	$-0.340342\pi$
$617$	14737.8	0.961623	0.480812	+	0.876824i	$0.340342\pi$
$618$	16966.9	1.10439
$619$	22049.0	1.43170	0.715850	−	0.698254i	$-0.246039\pi$
$619$	22049.0	1.43170	0.715850	+	0.698254i	$0.246039\pi$
$620$	5032.23	0.325966
$621$	3501.46	0.226262
$622$	6367.58	0.410477
$623$	49138.9	3.16005
$624$	4501.10	0.288763
$625$	35116.6	2.24747
$626$	−8616.84	−0.550157
$627$	20849.1	1.32796
$628$	4475.63	0.284390
$629$	−25267.2	−1.60170
$630$	10664.5	0.674421
$631$	−6247.38	−0.394143	−0.197071	−	0.980389i	$-0.563143\pi$
$631$	−6247.38	−0.394143	−0.197071	+	0.980389i	$0.563143\pi$
$632$	−12965.3	−0.816032
$633$	2381.77	0.149553
$634$	970.058	0.0607664
$635$	51358.9	3.20963
$636$	−1196.98	−0.0746277
$637$	16325.1	1.01542
$638$	−4471.30	−0.277461
$639$	7093.26	0.439131
$640$	8167.29	0.504438
$641$	−29060.5	−1.79067	−0.895336	−	0.445391i	$-0.853065\pi$
$641$	−29060.5	−1.79067	−0.895336	+	0.445391i	$0.853065\pi$
$642$	4047.24	0.248804
$643$	−29316.0	−1.79799	−0.898997	−	0.437954i	$-0.855703\pi$
$643$	−29316.0	−1.79799	−0.898997	+	0.437954i	$0.855703\pi$
$644$	1811.26	0.110829
$645$	20377.7	1.24398
$646$	18004.7	1.09657
$647$	14896.4	0.905157	0.452579	−	0.891724i	$-0.350504\pi$
$647$	14896.4	0.905157	0.452579	+	0.891724i	$0.350504\pi$
$648$	11792.0	0.714868
$649$	−42378.5	−2.56317
$650$	19033.8	1.14856
$651$	−12918.9	−0.777775
$652$	4128.78	0.247999
$653$	4447.36	0.266522	0.133261	−	0.991081i	$-0.457455\pi$
$653$	4447.36	0.266522	0.133261	+	0.991081i	$0.457455\pi$
$654$	−2487.62	−0.148737
$655$	48730.2	2.90694
$656$	−11878.4	−0.706972
$657$	2752.14	0.163426
$658$	−30356.1	−1.79848
$659$	4907.31	0.290079	0.145039	−	0.989426i	$-0.453669\pi$
$659$	4907.31	0.290079	0.145039	+	0.989426i	$0.453669\pi$
$660$	−15534.6	−0.916188
$661$	−17607.1	−1.03606	−0.518030	−	0.855362i	$-0.673335\pi$
$661$	−17607.1	−1.03606	−0.518030	+	0.855362i	$0.673335\pi$
$662$	1391.82	0.0817136
$663$	−13341.2	−0.781491
$664$	−11800.4	−0.689675
$665$	−44524.4	−2.59636
$666$	3940.91	0.229290
$667$	667.000	0.0387202
$668$	−517.762	−0.0299892
$669$	−16163.4	−0.934098
$670$	25769.5	1.48592
$671$	−14363.7	−0.826383
$672$	15123.1	0.868133
$673$	−14422.7	−0.826083	−0.413042	−	0.910712i	$-0.635534\pi$
$673$	−14422.7	−0.826083	−0.413042	+	0.910712i	$0.635534\pi$
$674$	12966.3	0.741015
$675$	45103.3	2.57189
$676$	3698.89	0.210451
$677$	−16003.4	−0.908507	−0.454254	−	0.890872i	$-0.650094\pi$
$677$	−16003.4	−0.908507	−0.454254	+	0.890872i	$0.650094\pi$
$678$	−3464.51	−0.196244
$679$	−2534.31	−0.143237
$680$	−55083.3	−3.10639
$681$	14263.0	0.802583
$682$	14676.7	0.824045
$683$	−2760.08	−0.154629	−0.0773145	−	0.997007i	$-0.524635\pi$
$683$	−2760.08	−0.154629	−0.0773145	+	0.997007i	$0.524635\pi$
$684$	1333.42	0.0745390
$685$	−6845.01	−0.381802
$686$	−17718.4	−0.986137
$687$	−22860.6	−1.26956
$688$	8222.21	0.455623
$689$	−2887.97	−0.159685
$690$	−4880.35	−0.269263
$691$	18830.3	1.03667	0.518335	−	0.855178i	$-0.326552\pi$
$691$	18830.3	1.03667	0.518335	+	0.855178i	$0.326552\pi$
$692$	2764.69	0.151875
$693$	−14769.0	−0.809564
$694$	−19187.8	−1.04951
$695$	33142.0	1.80885
$696$	3170.65	0.172677
$697$	35207.4	1.91331
$698$	−15601.4	−0.846018
$699$	10653.8	0.576487
$700$	23331.3	1.25977
$701$	−8638.11	−0.465416	−0.232708	−	0.972547i	$-0.574759\pi$
$701$	−8638.11	−0.465416	−0.232708	+	0.972547i	$0.574759\pi$
$702$	9780.49	0.525842
$703$	−16453.3	−0.882713
$704$	−36649.4	−1.96204
$705$	−38838.1	−2.07479
$706$	11219.8	0.598108
$707$	−45954.3	−2.44454
$708$	7318.83	0.388500
$709$	26147.4	1.38503	0.692514	−	0.721405i	$-0.256503\pi$
$709$	26147.4	1.38503	0.692514	+	0.721405i	$0.256503\pi$
$710$	−46470.1	−2.45633
$711$	−3840.85	−0.202592
$712$	39586.1	2.08364
$713$	−2189.37	−0.114997
$714$	34440.3	1.80517
$715$	−37480.7	−1.96042
$716$	2355.51	0.122946
$717$	−4251.36	−0.221436
$718$	4889.87	0.254162
$719$	22922.0	1.18894	0.594470	−	0.804118i	$-0.297362\pi$
$719$	22922.0	1.18894	0.594470	+	0.804118i	$0.297362\pi$
$720$	5505.39	0.284964
$721$	50179.3	2.59192
$722$	−4250.59	−0.219100
$723$	−22555.5	−1.16023
$724$	1183.49	0.0607513
$725$	8591.80	0.440126
$726$	−31547.2	−1.61271
$727$	1498.66	0.0764544	0.0382272	−	0.999269i	$-0.487829\pi$
$727$	1498.66	0.0764544	0.0382272	+	0.999269i	$0.487829\pi$
$728$	20773.5	1.05758
$729$	21738.8	1.10444
$730$	−18030.1	−0.914142
$731$	−24370.5	−1.23307
$732$	2480.63	0.125255
$733$	25056.5	1.26260	0.631299	−	0.775540i	$-0.282522\pi$
$733$	25056.5	1.26260	0.631299	+	0.775540i	$0.282522\pi$
$734$	10419.1	0.523945
$735$	−53918.7	−2.70588
$736$	2562.92	0.128356
$737$	−35687.4	−1.78367
$738$	−5491.27	−0.273898
$739$	−12522.7	−0.623350	−0.311675	−	0.950189i	$-0.600890\pi$
$739$	−12522.7	−0.623350	−0.311675	+	0.950189i	$0.600890\pi$
$740$	12259.3	0.609003
$741$	−8687.39	−0.430687
$742$	7455.30	0.368858
$743$	10881.8	0.537300	0.268650	−	0.963238i	$-0.413423\pi$
$743$	10881.8	0.537300	0.268650	+	0.963238i	$0.413423\pi$
$744$	−10407.4	−0.512841
$745$	24832.8	1.22121
$746$	5889.47	0.289047
$747$	−3495.75	−0.171222
$748$	18578.5	0.908150
$749$	11969.6	0.583925
$750$	−36341.4	−1.76933
$751$	−25648.3	−1.24623	−0.623115	−	0.782130i	$-0.714133\pi$
$751$	−25648.3	−1.24623	−0.623115	+	0.782130i	$0.714133\pi$
$752$	−15670.8	−0.759915
$753$	22111.9	1.07012
$754$	1863.10	0.0899870
$755$	56551.4	2.72598
$756$	11988.8	0.576756
$757$	−9347.44	−0.448796	−0.224398	−	0.974498i	$-0.572042\pi$
$757$	−9347.44	−0.448796	−0.224398	+	0.974498i	$0.572042\pi$
$758$	−5449.85	−0.261145
$759$	6758.65	0.323219
$760$	−35868.6	−1.71196
$761$	8876.05	0.422807	0.211404	−	0.977399i	$-0.432197\pi$
$761$	8876.05	0.422807	0.211404	+	0.977399i	$0.432197\pi$
$762$	−25869.0	−1.22983
$763$	−7357.08	−0.349075
$764$	8476.26	0.401388
$765$	−16317.9	−0.771208
$766$	19946.7	0.940865
$767$	17658.3	0.831295
$768$	15545.3	0.730396
$769$	−7124.83	−0.334107	−0.167053	−	0.985948i	$-0.553425\pi$
$769$	−7124.83	−0.334107	−0.167053	+	0.985948i	$0.553425\pi$
$770$	96756.3	4.52838
$771$	20886.8	0.975642
$772$	−1648.16	−0.0768377
$773$	12808.6	0.595979	0.297989	−	0.954569i	$-0.403684\pi$
$773$	12808.6	0.595979	0.297989	+	0.954569i	$0.403684\pi$
$774$	3801.05	0.176519
$775$	−28201.9	−1.30715
$776$	−2041.63	−0.0944461
$777$	−31472.6	−1.45312
$778$	15171.6	0.699137
$779$	22926.0	1.05444
$780$	6472.97	0.297140
$781$	64355.1	2.94854
$782$	5836.61	0.266901
$783$	4414.89	0.201501
$784$	−21755.7	−0.991059
$785$	−35665.2	−1.62159
$786$	−24544.9	−1.11385
$787$	−39467.7	−1.78764	−0.893819	−	0.448427i	$-0.851984\pi$
$787$	−39467.7	−1.78764	−0.893819	+	0.448427i	$0.851984\pi$
$788$	−2755.16	−0.124554
$789$	−31402.8	−1.41694
$790$	25162.6	1.13322
$791$	−10246.2	−0.460572
$792$	−11897.8	−0.533802
$793$	5985.06	0.268015
$794$	2822.66	0.126162
$795$	9538.43	0.425526
$796$	−4048.20	−0.180257
$797$	−6719.39	−0.298636	−0.149318	−	0.988789i	$-0.547708\pi$
$797$	−6719.39	−0.298636	−0.149318	+	0.988789i	$0.547708\pi$
$798$	22426.5	0.994849
$799$	46448.0	2.05659
$800$	33013.6	1.45901
$801$	11727.0	0.517294
$802$	−17945.2	−0.790108
$803$	24969.3	1.09732
$804$	6163.28	0.270351
$805$	−14433.5	−0.631943
$806$	−6115.48	−0.267256
$807$	19109.1	0.833548
$808$	−37020.6	−1.61185
$809$	−27301.1	−1.18647	−0.593235	−	0.805029i	$-0.702149\pi$
$809$	−27301.1	−1.18647	−0.593235	+	0.805029i	$0.702149\pi$
$810$	−22885.5	−0.992734
$811$	−6119.13	−0.264947	−0.132473	−	0.991187i	$-0.542292\pi$
$811$	−6119.13	−0.264947	−0.132473	+	0.991187i	$0.542292\pi$
$812$	2283.76	0.0986999
$813$	2707.96	0.116817
$814$	35754.8	1.53956
$815$	−32901.3	−1.41409
$816$	17779.2	0.762741
$817$	−15869.4	−0.679558
$818$	18139.4	0.775343
$819$	6153.96	0.262560
$820$	−17082.2	−0.727481
$821$	2737.97	0.116390	0.0581948	−	0.998305i	$-0.481466\pi$
$821$	2737.97	0.116390	0.0581948	+	0.998305i	$0.481466\pi$
$822$	3447.77	0.146295
$823$	16608.0	0.703425	0.351712	−	0.936108i	$-0.385600\pi$
$823$	16608.0	0.703425	0.351712	+	0.936108i	$0.385600\pi$
$824$	40424.2	1.70903
$825$	87059.9	3.67398
$826$	−45584.8	−1.92022
$827$	−2606.20	−0.109585	−0.0547924	−	0.998498i	$-0.517450\pi$
$827$	−2606.20	−0.109585	−0.0547924	+	0.998498i	$0.517450\pi$
$828$	432.257	0.0181425
$829$	13614.4	0.570385	0.285192	−	0.958470i	$-0.407943\pi$
$829$	13614.4	0.570385	0.285192	+	0.958470i	$0.407943\pi$
$830$	22901.8	0.957749
$831$	16919.6	0.706299
$832$	15271.1	0.636334
$833$	64483.6	2.68214
$834$	−16693.3	−0.693096
$835$	4125.92	0.170998
$836$	12097.8	0.500490
$837$	−14491.5	−0.598446
$838$	20662.5	0.851761
$839$	10701.5	0.440355	0.220177	−	0.975460i	$-0.429336\pi$
$839$	10701.5	0.440355	0.220177	+	0.975460i	$0.429336\pi$
$840$	−68611.1	−2.81822
$841$	841.000	0.0344828
$842$	−10386.3	−0.425101
$843$	−27015.8	−1.10376
$844$	1382.03	0.0563644
$845$	−29475.6	−1.19999
$846$	−7244.47	−0.294409
$847$	−93299.9	−3.78491
$848$	3848.67	0.155854
$849$	−11890.2	−0.480649
$850$	75182.8	3.03382
$851$	−5333.67	−0.214848
$852$	−11114.2	−0.446910
$853$	42065.6	1.68851	0.844254	−	0.535943i	$-0.180044\pi$
$853$	42065.6	1.68851	0.844254	+	0.535943i	$0.180044\pi$
$854$	−15450.4	−0.619090
$855$	−10625.7	−0.425020
$856$	9642.66	0.385023
$857$	−36922.7	−1.47171	−0.735856	−	0.677138i	$-0.763220\pi$
$857$	−36922.7	−1.47171	−0.735856	+	0.677138i	$0.763220\pi$
$858$	18878.6	0.751173
$859$	34546.9	1.37221	0.686104	−	0.727504i	$-0.259320\pi$
$859$	34546.9	1.37221	0.686104	+	0.727504i	$0.259320\pi$
$860$	11824.3	0.468841
$861$	43853.9	1.73581
$862$	−13143.4	−0.519334
$863$	34460.0	1.35925	0.679625	−	0.733560i	$-0.262143\pi$
$863$	34460.0	1.35925	0.679625	+	0.733560i	$0.262143\pi$
$864$	16964.0	0.667971
$865$	−22031.2	−0.865991
$866$	18129.1	0.711377
$867$	−30889.2	−1.20998
$868$	−7496.26	−0.293133
$869$	−34846.9	−1.36030
$870$	−6153.48	−0.239796
$871$	14870.3	0.578484
$872$	−5926.83	−0.230170
$873$	−604.813	−0.0234477
$874$	3800.63	0.147092
$875$	−107479.	−4.15251
$876$	−4312.24	−0.166321
$877$	29332.8	1.12941	0.564707	−	0.825291i	$-0.308989\pi$
$877$	29332.8	1.12941	0.564707	+	0.825291i	$0.308989\pi$
$878$	−22462.4	−0.863405
$879$	−19723.0	−0.756816
$880$	49948.8	1.91338
$881$	31901.9	1.21998	0.609991	−	0.792408i	$-0.291173\pi$
$881$	31901.9	1.21998	0.609991	+	0.792408i	$0.291173\pi$
$882$	−10057.5	−0.383959
$883$	43486.0	1.65733	0.828665	−	0.559745i	$-0.189101\pi$
$883$	43486.0	1.65733	0.828665	+	0.559745i	$0.189101\pi$
$884$	−7741.29	−0.294534
$885$	−58322.0	−2.21522
$886$	−6502.90	−0.246579
$887$	−14556.8	−0.551036	−0.275518	−	0.961296i	$-0.588849\pi$
$887$	−14556.8	−0.551036	−0.275518	+	0.961296i	$0.588849\pi$
$888$	−25354.1	−0.958141
$889$	−76506.8	−2.88634
$890$	−76827.1	−2.89354
$891$	31693.4	1.19166
$892$	−9378.87	−0.352049
$893$	30245.6	1.13341
$894$	−12508.0	−0.467932
$895$	−18770.5	−0.701036
$896$	−12166.4	−0.453629
$897$	−2816.20	−0.104827
$898$	33067.5	1.22882
$899$	−2760.51	−0.102412
$900$	5568.01	0.206222
$901$	−11407.4	−0.421793
$902$	−49820.7	−1.83908
$903$	−30355.6	−1.11868
$904$	−8254.28	−0.303687
$905$	−9430.93	−0.346403
$906$	−28484.4	−1.04451
$907$	1101.46	0.0403235	0.0201618	−	0.999797i	$-0.493582\pi$
$907$	1101.46	0.0403235	0.0201618	+	0.999797i	$0.493582\pi$
$908$	8276.17	0.302483
$909$	−10967.0	−0.400167
$910$	−40316.5	−1.46866
$911$	23042.4	0.838013	0.419007	−	0.907983i	$-0.362378\pi$
$911$	23042.4	0.838013	0.419007	+	0.907983i	$0.362378\pi$
$912$	11577.3	0.420354
$913$	−31716.0	−1.14967
$914$	9085.83	0.328810
$915$	−19767.5	−0.714201
$916$	−13265.0	−0.478479
$917$	−72591.0	−2.61414
$918$	38632.6	1.38896
$919$	−6047.28	−0.217063	−0.108532	−	0.994093i	$-0.534615\pi$
$919$	−6047.28	−0.217063	−0.108532	+	0.994093i	$0.534615\pi$
$920$	−11627.6	−0.416684
$921$	−25770.0	−0.921986
$922$	−17979.8	−0.642226
$923$	−26815.5	−0.956277
$924$	23141.1	0.823904
$925$	−68704.4	−2.44215
$926$	36287.2	1.28777
$927$	11975.3	0.424293
$928$	3231.50	0.114310
$929$	−10993.7	−0.388258	−0.194129	−	0.980976i	$-0.562188\pi$
$929$	−10993.7	−0.388258	−0.194129	+	0.980976i	$0.562188\pi$
$930$	20198.3	0.712181
$931$	41989.8	1.47815
$932$	6181.93	0.217270
$933$	−12135.9	−0.425842
$934$	24983.3	0.875246
$935$	−148047.	−5.17826
$936$	4957.60	0.173124
$937$	7023.02	0.244858	0.122429	−	0.992477i	$-0.460932\pi$
$937$	7023.02	0.244858	0.122429	+	0.992477i	$0.460932\pi$
$938$	−38387.6	−1.33625
$939$	16422.7	0.570750
$940$	−22536.0	−0.781960
$941$	−47120.7	−1.63240	−0.816201	−	0.577768i	$-0.803924\pi$
$941$	−47120.7	−1.63240	−0.816201	+	0.577768i	$0.803924\pi$
$942$	17964.2	0.621344
$943$	7431.94	0.256646
$944$	−23532.4	−0.811350
$945$	−95535.7	−3.28865
$946$	34485.8	1.18523
$947$	43677.2	1.49875	0.749376	−	0.662144i	$-0.230353\pi$
$947$	43677.2	1.49875	0.749376	+	0.662144i	$0.230353\pi$
$948$	6018.12	0.206181
$949$	−10404.2	−0.355886
$950$	48956.9	1.67197
$951$	−1848.82	−0.0630410
$952$	82054.8	2.79350
$953$	27584.6	0.937621	0.468811	−	0.883299i	$-0.344683\pi$
$953$	27584.6	0.937621	0.468811	+	0.883299i	$0.344683\pi$
$954$	1779.20	0.0603814
$955$	−67545.3	−2.28871
$956$	−2466.87	−0.0834565
$957$	8521.77	0.287847
$958$	−5081.17	−0.171362
$959$	10196.7	0.343345
$960$	−50437.6	−1.69569
$961$	−20729.9	−0.695843
$962$	−14898.3	−0.499315
$963$	2856.54	0.0955876
$964$	−13087.9	−0.437275
$965$	13133.8	0.438128
$966$	7270.01	0.242142
$967$	−34884.7	−1.16010	−0.580050	−	0.814581i	$-0.696967\pi$
$967$	−34884.7	−1.16010	−0.580050	+	0.814581i	$0.696967\pi$
$968$	−75161.9	−2.49566
$969$	−34314.9	−1.13762
$970$	3962.31	0.131157
$971$	32993.2	1.09043	0.545213	−	0.838298i	$-0.316449\pi$
$971$	32993.2	1.09043	0.545213	+	0.838298i	$0.316449\pi$
$972$	5113.53	0.168741
$973$	−49370.0	−1.62665
$974$	14005.9	0.460756
$975$	−36276.2	−1.19156
$976$	−7976.02	−0.261584
$977$	−7326.74	−0.239921	−0.119961	−	0.992779i	$-0.538277\pi$
$977$	−7326.74	−0.239921	−0.119961	+	0.992779i	$0.538277\pi$
$978$	16572.1	0.541836
$979$	106396.	3.47336
$980$	−31286.6	−1.01981
$981$	−1755.77	−0.0571430
$982$	694.213	0.0225593
$983$	22262.5	0.722344	0.361172	−	0.932499i	$-0.382377\pi$
$983$	22262.5	0.722344	0.361172	+	0.932499i	$0.382377\pi$
$984$	35328.5	1.14454
$985$	21955.2	0.710205
$986$	7359.20	0.237692
$987$	57855.1	1.86580
$988$	−5040.90	−0.162320
$989$	−5144.38	−0.165401
$990$	23090.9	0.741289
$991$	−17251.5	−0.552989	−0.276495	−	0.961015i	$-0.589173\pi$
$991$	−17251.5	−0.552989	−0.276495	+	0.961015i	$0.589173\pi$
$992$	−10607.1	−0.339493
$993$	−2652.64	−0.0847723
$994$	69224.2	2.20891
$995$	32259.2	1.02782
$996$	5477.40	0.174255
$997$	9530.34	0.302737	0.151369	−	0.988477i	$-0.451632\pi$
$997$	9530.34	0.302737	0.151369	+	0.988477i	$0.451632\pi$
$998$	26563.4	0.842536
$999$	−35303.7	−1.11808

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	667.4.a.d.1.27	✓	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
667.4.a.d.1.27	✓	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)

\(f(q)\)	\(=\)	\(q+2.32902 q^{2} -4.43884 q^{3} -2.57566 q^{4} +20.5248 q^{5} -10.3382 q^{6} -30.5748 q^{7} -24.6309 q^{8} -7.29667 q^{9} +O(q^{10})\)	\(q+2.32902 q^{2} -4.43884 q^{3} -2.57566 q^{4} +20.5248 q^{5} -10.3382 q^{6} -30.5748 q^{7} -24.6309 q^{8} -7.29667 q^{9} +47.8028 q^{10} -66.2006 q^{11} +11.4330 q^{12} +27.5845 q^{13} -71.2094 q^{14} -91.1065 q^{15} -36.7607 q^{16} +108.958 q^{17} -16.9941 q^{18} +70.9503 q^{19} -52.8650 q^{20} +135.717 q^{21} -154.183 q^{22} +23.0000 q^{23} +109.333 q^{24} +296.269 q^{25} +64.2449 q^{26} +152.238 q^{27} +78.7504 q^{28} +29.0000 q^{29} -212.189 q^{30} -95.1901 q^{31} +111.431 q^{32} +293.854 q^{33} +253.765 q^{34} -627.543 q^{35} +18.7938 q^{36} -231.899 q^{37} +165.245 q^{38} -122.443 q^{39} -505.546 q^{40} +323.128 q^{41} +316.087 q^{42} -223.669 q^{43} +170.510 q^{44} -149.763 q^{45} +53.5675 q^{46} +426.293 q^{47} +163.175 q^{48} +591.820 q^{49} +690.016 q^{50} -483.647 q^{51} -71.0484 q^{52} -104.695 q^{53} +354.564 q^{54} -1358.76 q^{55} +753.087 q^{56} -314.937 q^{57} +67.5416 q^{58} +640.152 q^{59} +234.660 q^{60} +216.972 q^{61} -221.700 q^{62} +223.095 q^{63} +553.611 q^{64} +566.168 q^{65} +684.393 q^{66} +539.080 q^{67} -280.639 q^{68} -102.093 q^{69} -1461.56 q^{70} -972.122 q^{71} +179.724 q^{72} -377.177 q^{73} -540.097 q^{74} -1315.09 q^{75} -182.744 q^{76} +2024.07 q^{77} -285.173 q^{78} +526.383 q^{79} -754.507 q^{80} -478.748 q^{81} +752.571 q^{82} +479.088 q^{83} -349.561 q^{84} +2236.35 q^{85} -520.929 q^{86} -128.726 q^{87} +1630.58 q^{88} -1607.17 q^{89} -348.801 q^{90} -843.392 q^{91} -59.2402 q^{92} +422.534 q^{93} +992.845 q^{94} +1456.24 q^{95} -494.625 q^{96} +82.8888 q^{97} +1378.36 q^{98} +483.045 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q + 12 q^{2} + 32 q^{3} + 192 q^{4} + 80 q^{5} + 32 q^{6} + 18 q^{7} + 102 q^{8} + 492 q^{9}+O(q^{10}) \) 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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