LMFDB - Embedded newform 667.4.a.a.1.35

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:	$1$
Dimension:	$35$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.35
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)

$f(q)$	$=$	$q+5.36967 q^{2} -3.86254 q^{3} +20.8334 q^{4} -16.8123 q^{5} -20.7406 q^{6} +34.1544 q^{7} +68.9109 q^{8} -12.0808 q^{9} +O(q^{10})$	\(q+5.36967 q^{2} -3.86254 q^{3} +20.8334 q^{4} -16.8123 q^{5} -20.7406 q^{6} +34.1544 q^{7} +68.9109 q^{8} -12.0808 q^{9} -90.2767 q^{10} -69.6108 q^{11} -80.4697 q^{12} -86.0619 q^{13} +183.398 q^{14} +64.9383 q^{15} +203.362 q^{16} -0.387905 q^{17} -64.8698 q^{18} -17.1294 q^{19} -350.257 q^{20} -131.923 q^{21} -373.787 q^{22} +23.0000 q^{23} -266.171 q^{24} +157.654 q^{25} -462.124 q^{26} +150.951 q^{27} +711.552 q^{28} -29.0000 q^{29} +348.697 q^{30} -97.9228 q^{31} +540.700 q^{32} +268.875 q^{33} -2.08292 q^{34} -574.216 q^{35} -251.683 q^{36} -8.18524 q^{37} -91.9794 q^{38} +332.418 q^{39} -1158.55 q^{40} -357.604 q^{41} -708.383 q^{42} -26.9554 q^{43} -1450.23 q^{44} +203.106 q^{45} +123.502 q^{46} -371.239 q^{47} -785.495 q^{48} +823.526 q^{49} +846.552 q^{50} +1.49830 q^{51} -1792.96 q^{52} -530.297 q^{53} +810.558 q^{54} +1170.32 q^{55} +2353.61 q^{56} +66.1631 q^{57} -155.720 q^{58} -11.8413 q^{59} +1352.88 q^{60} -412.187 q^{61} -525.813 q^{62} -412.612 q^{63} +1276.49 q^{64} +1446.90 q^{65} +1443.77 q^{66} +345.758 q^{67} -8.08136 q^{68} -88.8384 q^{69} -3083.35 q^{70} +43.8068 q^{71} -832.498 q^{72} +663.102 q^{73} -43.9521 q^{74} -608.946 q^{75} -356.864 q^{76} -2377.52 q^{77} +1784.97 q^{78} +303.315 q^{79} -3418.99 q^{80} -256.874 q^{81} -1920.21 q^{82} -3.15873 q^{83} -2748.40 q^{84} +6.52158 q^{85} -144.742 q^{86} +112.014 q^{87} -4796.95 q^{88} +469.312 q^{89} +1090.61 q^{90} -2939.40 q^{91} +479.167 q^{92} +378.231 q^{93} -1993.43 q^{94} +287.986 q^{95} -2088.48 q^{96} +584.952 q^{97} +4422.06 q^{98} +840.953 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 35 q - 6 q^{2} - 22 q^{3} + 116 q^{4} - 80 q^{5} - 52 q^{6} - 38 q^{7} + 12 q^{8} + 231 q^{9}+O(q^{10}) $ 35 * q - 6 * q^2 - 22 * q^3 + 116 * q^4 - 80 * q^5 - 52 * q^6 - 38 * q^7 + 12 * q^8 + 231 * q^9	\( 35 q - 6 q^{2} - 22 q^{3} + 116 q^{4} - 80 q^{5} - 52 q^{6} - 38 q^{7} + 12 q^{8} + 231 q^{9} - 52 q^{10} - 126 q^{11} - 173 q^{12} - 252 q^{13} + 112 q^{14} - 32 q^{15} + 312 q^{16} - 332 q^{17} - 225 q^{18} - 2 q^{19} - 747 q^{20} - 202 q^{21} - 127 q^{22} + 805 q^{23} - 494 q^{24} + 315 q^{25} - 677 q^{26} - 694 q^{27} - 529 q^{28} - 1015 q^{29} + 389 q^{30} - 652 q^{31} + 320 q^{32} - 290 q^{33} - 455 q^{34} - 940 q^{35} + 34 q^{36} - 528 q^{37} - 1218 q^{38} - 268 q^{39} - 806 q^{40} - 68 q^{41} - 1484 q^{42} - 162 q^{43} - 1817 q^{44} - 356 q^{45} - 138 q^{46} - 1200 q^{47} - 2153 q^{48} + 93 q^{49} - 1369 q^{50} - 270 q^{51} - 3134 q^{52} - 1892 q^{53} - 1221 q^{54} - 794 q^{55} + 191 q^{56} - 1764 q^{57} + 174 q^{58} - 1354 q^{59} + 159 q^{60} - 1274 q^{61} - 5413 q^{62} - 2904 q^{63} - 926 q^{64} - 548 q^{65} - 2477 q^{66} - 3212 q^{67} - 3901 q^{68} - 506 q^{69} - 2768 q^{70} - 2342 q^{71} - 2381 q^{72} + 916 q^{73} + 661 q^{74} - 4708 q^{75} - 2810 q^{76} - 5536 q^{77} - 2434 q^{78} + 2622 q^{79} - 5444 q^{80} + 607 q^{81} - 3687 q^{82} - 2702 q^{83} + 346 q^{84} - 3304 q^{85} - 5789 q^{86} + 638 q^{87} - 2252 q^{88} - 1620 q^{89} - 3933 q^{90} - 4016 q^{91} + 2668 q^{92} - 4942 q^{93} - 1413 q^{94} - 4528 q^{95} - 7920 q^{96} + 682 q^{97} + 152 q^{98} - 582 q^{99}+O(q^{100}) \) 35 * q - 6 * q^2 - 22 * q^3 + 116 * q^4 - 80 * q^5 - 52 * q^6 - 38 * q^7 + 12 * q^8 + 231 * q^9 - 52 * q^10 - 126 * q^11 - 173 * q^12 - 252 * q^13 + 112 * q^14 - 32 * q^15 + 312 * q^16 - 332 * q^17 - 225 * q^18 - 2 * q^19 - 747 * q^20 - 202 * q^21 - 127 * q^22 + 805 * q^23 - 494 * q^24 + 315 * q^25 - 677 * q^26 - 694 * q^27 - 529 * q^28 - 1015 * q^29 + 389 * q^30 - 652 * q^31 + 320 * q^32 - 290 * q^33 - 455 * q^34 - 940 * q^35 + 34 * q^36 - 528 * q^37 - 1218 * q^38 - 268 * q^39 - 806 * q^40 - 68 * q^41 - 1484 * q^42 - 162 * q^43 - 1817 * q^44 - 356 * q^45 - 138 * q^46 - 1200 * q^47 - 2153 * q^48 + 93 * q^49 - 1369 * q^50 - 270 * q^51 - 3134 * q^52 - 1892 * q^53 - 1221 * q^54 - 794 * q^55 + 191 * q^56 - 1764 * q^57 + 174 * q^58 - 1354 * q^59 + 159 * q^60 - 1274 * q^61 - 5413 * q^62 - 2904 * q^63 - 926 * q^64 - 548 * q^65 - 2477 * q^66 - 3212 * q^67 - 3901 * q^68 - 506 * q^69 - 2768 * q^70 - 2342 * q^71 - 2381 * q^72 + 916 * q^73 + 661 * q^74 - 4708 * q^75 - 2810 * q^76 - 5536 * q^77 - 2434 * q^78 + 2622 * q^79 - 5444 * q^80 + 607 * q^81 - 3687 * q^82 - 2702 * q^83 + 346 * q^84 - 3304 * q^85 - 5789 * q^86 + 638 * q^87 - 2252 * q^88 - 1620 * q^89 - 3933 * q^90 - 4016 * q^91 + 2668 * q^92 - 4942 * q^93 - 1413 * q^94 - 4528 * q^95 - 7920 * q^96 + 682 * q^97 + 152 * q^98 - 582 * 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 $

$2$	5.36967	1.89847	0.949233	−	0.314575i	$-0.101862\pi$
$2$	5.36967	1.89847	0.949233	+	0.314575i	$0.101862\pi$
$3$	−3.86254	−0.743346	−0.371673	−	0.928364i	$-0.621216\pi$
$3$	−3.86254	−0.743346	−0.371673	+	0.928364i	$0.621216\pi$
$4$	20.8334	2.60417
$5$	−16.8123	−1.50374	−0.751870	−	0.659311i	$-0.770848\pi$
$5$	−16.8123	−1.50374	−0.751870	+	0.659311i	$0.770848\pi$
$6$	−20.7406	−1.41122
$7$	34.1544	1.84417	0.922083	−	0.386992i	$-0.126486\pi$
$7$	34.1544	1.84417	0.922083	+	0.386992i	$0.126486\pi$
$8$	68.9109	3.04546
$9$	−12.0808	−0.447436
$10$	−90.2767	−2.85480
$11$	−69.6108	−1.90804	−0.954020	−	0.299741i	$-0.903100\pi$
$11$	−69.6108	−1.90804	−0.954020	+	0.299741i	$0.903100\pi$
$12$	−80.4697	−1.93580
$13$	−86.0619	−1.83610	−0.918050	−	0.396466i	$-0.870237\pi$
$13$	−86.0619	−1.83610	−0.918050	+	0.396466i	$0.870237\pi$
$14$	183.398	3.50109
$15$	64.9383	1.11780
$16$	203.362	3.17753
$17$	−0.387905	−0.00553416	−0.00276708	−	0.999996i	$-0.500881\pi$
$17$	−0.387905	−0.00553416	−0.00276708	+	0.999996i	$0.500881\pi$
$18$	−64.8698	−0.849442
$19$	−17.1294	−0.206829	−0.103415	−	0.994638i	$-0.532977\pi$
$19$	−17.1294	−0.206829	−0.103415	+	0.994638i	$0.532977\pi$
$20$	−350.257	−3.91600
$21$	−131.923	−1.37085
$22$	−373.787	−3.62235
$23$	23.0000	0.208514
$23$	23.0000	0.208514
$24$	−266.171	−2.26383
$25$	157.654	1.26123
$26$	−462.124	−3.48577
$27$	150.951	1.07595
$28$	711.552	4.80252
$29$	−29.0000	−0.185695
$29$	−29.0000	−0.185695
$30$	348.697	2.12210
$31$	−97.9228	−0.567337	−0.283669	−	0.958922i	$-0.591552\pi$
$31$	−97.9228	−0.567337	−0.283669	+	0.958922i	$0.591552\pi$
$32$	540.700	2.98698
$33$	268.875	1.41834
$34$	−2.08292	−0.0105064
$35$	−574.216	−2.77315
$36$	−251.683	−1.16520
$37$	−8.18524	−0.0363688	−0.0181844	−	0.999835i	$-0.505789\pi$
$37$	−8.18524	−0.0363688	−0.0181844	+	0.999835i	$0.505789\pi$
$38$	−91.9794	−0.392659
$39$	332.418	1.36486
$40$	−1158.55	−4.57958
$41$	−357.604	−1.36215	−0.681077	−	0.732212i	$-0.738488\pi$
$41$	−357.604	−1.36215	−0.681077	+	0.732212i	$0.738488\pi$
$42$	−708.383	−2.60252
$43$	−26.9554	−0.0955967	−0.0477984	−	0.998857i	$-0.515220\pi$
$43$	−26.9554	−0.0955967	−0.0477984	+	0.998857i	$0.515220\pi$
$44$	−1450.23	−4.96886
$45$	203.106	0.672828
$46$	123.502	0.395857
$47$	−371.239	−1.15215	−0.576073	−	0.817398i	$-0.695415\pi$
$47$	−371.239	−1.15215	−0.576073	+	0.817398i	$0.695415\pi$
$48$	−785.495	−2.36201
$49$	823.526	2.40095
$50$	846.552	2.39441
$51$	1.49830	0.00411380
$52$	−1792.96	−4.78152
$53$	−530.297	−1.37438	−0.687188	−	0.726480i	$-0.741155\pi$
$53$	−530.297	−1.37438	−0.687188	+	0.726480i	$0.741155\pi$
$54$	810.558	2.04265
$55$	1170.32	2.86920
$56$	2353.61	5.61634
$57$	66.1631	0.153746
$58$	−155.720	−0.352536
$59$	−11.8413	−0.0261289	−0.0130644	−	0.999915i	$-0.504159\pi$
$59$	−11.8413	−0.0261289	−0.0130644	+	0.999915i	$0.504159\pi$
$60$	1352.88	2.91094
$61$	−412.187	−0.865166	−0.432583	−	0.901594i	$-0.642398\pi$
$61$	−412.187	−0.865166	−0.432583	+	0.901594i	$0.642398\pi$
$62$	−525.813	−1.07707
$63$	−412.612	−0.825147
$64$	1276.49	2.49314
$65$	1446.90	2.76102
$66$	1443.77	2.69266
$67$	345.758	0.630463	0.315232	−	0.949015i	$-0.397918\pi$
$67$	345.758	0.630463	0.315232	+	0.949015i	$0.397918\pi$
$68$	−8.08136	−0.0144119
$69$	−88.8384	−0.154998
$70$	−3083.35	−5.26472
$71$	43.8068	0.0732240	0.0366120	−	0.999330i	$-0.488343\pi$
$71$	43.8068	0.0732240	0.0366120	+	0.999330i	$0.488343\pi$
$72$	−832.498	−1.36265
$73$	663.102	1.06315	0.531576	−	0.847010i	$-0.321600\pi$
$73$	663.102	1.06315	0.531576	+	0.847010i	$0.321600\pi$
$74$	−43.9521	−0.0690449
$75$	−608.946	−0.937534
$76$	−356.864	−0.538619
$77$	−2377.52	−3.51874
$78$	1784.97	2.59113
$79$	303.315	0.431969	0.215985	−	0.976397i	$-0.430704\pi$
$79$	303.315	0.431969	0.215985	+	0.976397i	$0.430704\pi$
$80$	−3418.99	−4.77818
$81$	−256.874	−0.352365
$82$	−1920.21	−2.58600
$83$	−3.15873	−0.00417730	−0.00208865	−	0.999998i	$-0.500665\pi$
$83$	−3.15873	−0.00417730	−0.00208865	+	0.999998i	$0.500665\pi$
$84$	−2748.40	−3.56994
$85$	6.52158	0.00832194
$86$	−144.742	−0.181487
$87$	112.014	0.138036
$88$	−4796.95	−5.81087
$89$	469.312	0.558955	0.279477	−	0.960152i	$-0.409839\pi$
$89$	469.312	0.558955	0.279477	+	0.960152i	$0.409839\pi$
$90$	1090.61	1.27734
$91$	−2939.40	−3.38607
$92$	479.167	0.543007
$93$	378.231	0.421728
$94$	−1993.43	−2.18731
$95$	287.986	0.311018
$96$	−2088.48	−2.22036
$97$	584.952	0.612298	0.306149	−	0.951984i	$-0.400959\pi$
$97$	584.952	0.612298	0.306149	+	0.951984i	$0.400959\pi$
$98$	4422.06	4.55812
$99$	840.953	0.853727
$100$	3284.47	3.28447
$101$	−1051.88	−1.03629	−0.518147	−	0.855291i	$-0.673378\pi$
$101$	−1051.88	−1.03629	−0.518147	+	0.855291i	$0.673378\pi$
$102$	8.04537	0.00780990
$103$	−932.578	−0.892133	−0.446066	−	0.895000i	$-0.647175\pi$
$103$	−932.578	−0.892133	−0.446066	+	0.895000i	$0.647175\pi$
$104$	−5930.61	−5.59177
$105$	2217.93	2.06141
$106$	−2847.52	−2.60920
$107$	−123.091	−0.111212	−0.0556058	−	0.998453i	$-0.517709\pi$
$107$	−123.091	−0.111212	−0.0556058	+	0.998453i	$0.517709\pi$
$108$	3144.82	2.80195
$109$	−604.524	−0.531219	−0.265609	−	0.964081i	$-0.585573\pi$
$109$	−604.524	−0.531219	−0.265609	+	0.964081i	$0.585573\pi$
$110$	6284.23	5.44707
$111$	31.6158	0.0270346
$112$	6945.72	5.85990
$113$	1314.44	1.09427	0.547134	−	0.837045i	$-0.315719\pi$
$113$	1314.44	1.09427	0.547134	+	0.837045i	$0.315719\pi$
$114$	355.274	0.291881
$115$	−386.684	−0.313552
$116$	−604.168	−0.483582
$117$	1039.70	0.821537
$118$	−63.5838	−0.0496047
$119$	−13.2487	−0.0102059
$120$	4474.96	3.40422
$121$	3514.67	2.64062
$122$	−2213.31	−1.64249
$123$	1381.26	1.01255
$124$	−2040.06	−1.47744
$125$	−548.995	−0.392829
$126$	−2215.59	−1.56651
$127$	622.206	0.434739	0.217369	−	0.976089i	$-0.430252\pi$
$127$	622.206	0.434739	0.217369	+	0.976089i	$0.430252\pi$
$128$	2528.70	1.74616
$129$	104.116	0.0710615
$130$	7769.38	5.24169
$131$	−409.316	−0.272993	−0.136497	−	0.990641i	$-0.543584\pi$
$131$	−409.316	−0.272993	−0.136497	+	0.990641i	$0.543584\pi$
$132$	5601.56	3.69359
$133$	−585.046	−0.381428
$134$	1856.61	1.19691
$135$	−2537.84	−1.61794
$136$	−26.7309	−0.0168541
$137$	1167.40	0.728012	0.364006	−	0.931397i	$-0.381409\pi$
$137$	1167.40	0.728012	0.364006	+	0.931397i	$0.381409\pi$
$138$	−477.033	−0.294259
$139$	−3002.52	−1.83216	−0.916082	−	0.400992i	$-0.868665\pi$
$139$	−3002.52	−1.83216	−0.916082	+	0.400992i	$0.868665\pi$
$140$	−11962.8	−7.22175
$141$	1433.93	0.856443
$142$	235.228	0.139013
$143$	5990.84	3.50335
$144$	−2456.77	−1.42174
$145$	487.557	0.279238
$146$	3560.64	2.01836
$147$	−3180.90	−1.78474
$148$	−170.526	−0.0947105
$149$	2945.99	1.61977	0.809883	−	0.586591i	$-0.199530\pi$
$149$	2945.99	1.61977	0.809883	+	0.586591i	$0.199530\pi$
$150$	−3269.84	−1.77988
$151$	−2740.22	−1.47680	−0.738398	−	0.674365i	$-0.764417\pi$
$151$	−2740.22	−1.47680	−0.738398	+	0.674365i	$0.764417\pi$
$152$	−1180.40	−0.629891
$153$	4.68619	0.00247618
$154$	−12766.5	−6.68022
$155$	1646.31	0.853128
$156$	6925.38	3.55432
$157$	3473.89	1.76590	0.882951	−	0.469466i	$-0.155553\pi$
$157$	3473.89	1.76590	0.882951	+	0.469466i	$0.155553\pi$
$158$	1628.70	0.820079
$159$	2048.29	1.02164
$160$	−9090.43	−4.49163
$161$	785.552	0.384535
$162$	−1379.33	−0.668952
$163$	3722.58	1.78880	0.894402	−	0.447265i	$-0.147602\pi$
$163$	3722.58	1.78880	0.894402	+	0.447265i	$0.147602\pi$
$164$	−7450.09	−3.54728
$165$	−4520.41	−2.13281
$166$	−16.9613	−0.00793046
$167$	−3759.15	−1.74187	−0.870934	−	0.491400i	$-0.836486\pi$
$167$	−3759.15	−1.74187	−0.870934	+	0.491400i	$0.836486\pi$
$168$	−9090.93	−4.17489
$169$	5209.66	2.37126
$170$	35.0187	0.0157989
$171$	206.937	0.0925430
$172$	−561.572	−0.248950
$173$	443.521	0.194915	0.0974574	−	0.995240i	$-0.468929\pi$
$173$	443.521	0.194915	0.0974574	+	0.995240i	$0.468929\pi$
$174$	601.477	0.262056
$175$	5384.59	2.32593
$176$	−14156.2	−6.06286
$177$	45.7374	0.0194228
$178$	2520.05	1.06116
$179$	952.889	0.397890	0.198945	−	0.980011i	$-0.436249\pi$
$179$	952.889	0.397890	0.198945	+	0.980011i	$0.436249\pi$
$180$	4231.38	1.75216
$181$	765.682	0.314435	0.157217	−	0.987564i	$-0.449748\pi$
$181$	765.682	0.314435	0.157217	+	0.987564i	$0.449748\pi$
$182$	−15783.6	−6.42834
$183$	1592.09	0.643118
$184$	1584.95	0.635023
$185$	137.613	0.0546892
$186$	2030.98	0.800636
$187$	27.0024	0.0105594
$188$	−7734.17	−3.00038
$189$	5155.65	1.98422
$190$	1546.39	0.590457
$191$	369.146	0.139845	0.0699227	−	0.997552i	$-0.477725\pi$
$191$	369.146	0.139845	0.0699227	+	0.997552i	$0.477725\pi$
$192$	−4930.48	−1.85326
$193$	−751.364	−0.280230	−0.140115	−	0.990135i	$-0.544747\pi$
$193$	−751.364	−0.280230	−0.140115	+	0.990135i	$0.544747\pi$
$194$	3141.00	1.16243
$195$	−5588.72	−2.05239
$196$	17156.8	6.25248
$197$	1794.13	0.648866	0.324433	−	0.945909i	$-0.394827\pi$
$197$	1794.13	0.648866	0.324433	+	0.945909i	$0.394827\pi$
$198$	4515.64	1.62077
$199$	1033.97	0.368323	0.184162	−	0.982896i	$-0.441043\pi$
$199$	1033.97	0.368323	0.184162	+	0.982896i	$0.441043\pi$
$200$	10864.1	3.84104
$201$	−1335.50	−0.468653
$202$	−5648.24	−1.96737
$203$	−990.479	−0.342453
$204$	31.2146	0.0107130
$205$	6012.15	2.04832
$206$	−5007.64	−1.69368
$207$	−277.858	−0.0932969
$208$	−17501.7	−5.83427
$209$	1192.39	0.394639
$210$	11909.6	3.91351
$211$	−2137.46	−0.697387	−0.348694	−	0.937237i	$-0.613375\pi$
$211$	−2137.46	−0.697387	−0.348694	+	0.937237i	$0.613375\pi$
$212$	−11047.9	−3.57911
$213$	−169.205	−0.0544308
$214$	−660.958	−0.211131
$215$	453.183	0.143753
$216$	10402.2	3.27675
$217$	−3344.50	−1.04626
$218$	−3246.09	−1.00850
$219$	−2561.26	−0.790291
$220$	24381.7	7.47188
$221$	33.3838	0.0101613
$222$	169.767	0.0513243
$223$	2257.88	0.678020	0.339010	−	0.940783i	$-0.389908\pi$
$223$	2257.88	0.678020	0.339010	+	0.940783i	$0.389908\pi$
$224$	18467.3	5.50848
$225$	−1904.59	−0.564322
$226$	7058.12	2.07743
$227$	3078.48	0.900113	0.450056	−	0.893000i	$-0.351404\pi$
$227$	3078.48	0.900113	0.450056	+	0.893000i	$0.351404\pi$
$228$	1378.40	0.400381
$229$	−2808.74	−0.810511	−0.405255	−	0.914204i	$-0.632817\pi$
$229$	−2808.74	−0.810511	−0.405255	+	0.914204i	$0.632817\pi$
$230$	−2076.36	−0.595267
$231$	9183.26	2.61565
$232$	−1998.42	−0.565528
$233$	−1123.77	−0.315969	−0.157984	−	0.987442i	$-0.550500\pi$
$233$	−1123.77	−0.315969	−0.157984	+	0.987442i	$0.550500\pi$
$234$	5582.82	1.55966
$235$	6241.40	1.73253
$236$	−246.694	−0.0680440
$237$	−1171.57	−0.321103
$238$	−71.1410	−0.0193756
$239$	−4960.42	−1.34252	−0.671261	−	0.741221i	$-0.734247\pi$
$239$	−4960.42	−1.34252	−0.671261	+	0.741221i	$0.734247\pi$
$240$	13206.0	3.55185
$241$	−3920.75	−1.04796	−0.523979	−	0.851731i	$-0.675553\pi$
$241$	−3920.75	−1.04796	−0.523979	+	0.851731i	$0.675553\pi$
$242$	18872.6	5.01313
$243$	−3083.49	−0.814017
$244$	−8587.24	−2.25304
$245$	−13845.4	−3.61040
$246$	7416.90	1.92229
$247$	1474.19	0.379759
$248$	−6747.95	−1.72780
$249$	12.2007	0.00310518
$250$	−2947.92	−0.745772
$251$	−6614.59	−1.66338	−0.831691	−	0.555238i	$-0.812627\pi$
$251$	−6614.59	−1.66338	−0.831691	+	0.555238i	$0.812627\pi$
$252$	−8596.10	−2.14882
$253$	−1601.05	−0.397854
$254$	3341.04	0.825337
$255$	−25.1899	−0.00618608
$256$	3366.42	0.821880
$257$	−5248.91	−1.27400	−0.637001	−	0.770863i	$-0.719825\pi$
$257$	−5248.91	−1.27400	−0.637001	+	0.770863i	$0.719825\pi$
$258$	559.070	0.134908
$259$	−279.562	−0.0670701
$260$	30143.8	7.19016
$261$	350.343	0.0830868
$262$	−2197.89	−0.518268
$263$	−2151.39	−0.504413	−0.252206	−	0.967673i	$-0.581156\pi$
$263$	−2151.39	−0.504413	−0.252206	+	0.967673i	$0.581156\pi$
$264$	18528.4	4.31949
$265$	8915.52	2.06670
$266$	−3141.50	−0.724128
$267$	−1812.74	−0.415497
$268$	7203.30	1.64183
$269$	−1238.49	−0.280714	−0.140357	−	0.990101i	$-0.544825\pi$
$269$	−1238.49	−0.280714	−0.140357	+	0.990101i	$0.544825\pi$
$270$	−13627.4	−3.07161
$271$	−8204.03	−1.83897	−0.919483	−	0.393131i	$-0.871392\pi$
$271$	−8204.03	−1.83897	−0.919483	+	0.393131i	$0.871392\pi$
$272$	−78.8852	−0.0175850
$273$	11353.5	2.51702
$274$	6268.55	1.38210
$275$	−10974.4	−2.40649
$276$	−1850.80	−0.403642
$277$	2503.45	0.543025	0.271513	−	0.962435i	$-0.412476\pi$
$277$	2503.45	0.543025	0.271513	+	0.962435i	$0.412476\pi$
$278$	−16122.6	−3.47830
$279$	1182.98	0.253847
$280$	−39569.7	−8.44551
$281$	871.973	0.185116	0.0925579	−	0.995707i	$-0.470496\pi$
$281$	871.973	0.185116	0.0925579	+	0.995707i	$0.470496\pi$
$282$	7699.72	1.62593
$283$	2199.92	0.462091	0.231046	−	0.972943i	$-0.425785\pi$
$283$	2199.92	0.462091	0.231046	+	0.972943i	$0.425785\pi$
$284$	912.642	0.190688
$285$	−1112.36	−0.231194
$286$	32168.8	6.65099
$287$	−12213.7	−2.51204
$288$	−6532.08	−1.33648
$289$	−4912.85	−0.999969
$290$	2618.02	0.530123
$291$	−2259.40	−0.455149
$292$	13814.6	2.76863
$293$	−2782.56	−0.554809	−0.277404	−	0.960753i	$-0.589474\pi$
$293$	−2782.56	−0.554809	−0.277404	+	0.960753i	$0.589474\pi$
$294$	−17080.4	−3.38826
$295$	199.079	0.0392910
$296$	−564.053	−0.110760
$297$	−10507.8	−2.05295
$298$	15819.0	3.07507
$299$	−1979.42	−0.382853
$300$	−12686.4	−2.44150
$301$	−920.646	−0.176296
$302$	−14714.1	−2.80365
$303$	4062.92	0.770326
$304$	−3483.48	−0.657208
$305$	6929.82	1.30098
$306$	25.1633	0.00470095
$307$	9234.81	1.71680	0.858401	−	0.512979i	$-0.171458\pi$
$307$	9234.81	1.71680	0.858401	+	0.512979i	$0.171458\pi$
$308$	−49531.7	−9.16341
$309$	3602.12	0.663164
$310$	8840.15	1.61963
$311$	6828.83	1.24510	0.622552	−	0.782579i	$-0.286096\pi$
$311$	6828.83	1.24510	0.622552	+	0.782579i	$0.286096\pi$
$312$	22907.2	4.15662
$313$	3135.38	0.566205	0.283103	−	0.959090i	$-0.408636\pi$
$313$	3135.38	0.566205	0.283103	+	0.959090i	$0.408636\pi$
$314$	18653.6	3.35250
$315$	6936.97	1.24081
$316$	6319.07	1.12492
$317$	937.931	0.166181	0.0830907	−	0.996542i	$-0.473521\pi$
$317$	937.931	0.166181	0.0830907	+	0.996542i	$0.473521\pi$
$318$	10998.7	1.93954
$319$	2018.71	0.354314
$320$	−21460.7	−3.74903
$321$	475.444	0.0826688
$322$	4218.16	0.730027
$323$	6.64459	0.00114463
$324$	−5351.55	−0.917618
$325$	−13568.0	−2.31575
$326$	19989.0	3.39598
$327$	2335.00	0.394880
$328$	−24642.8	−4.14839
$329$	−12679.5	−2.12475
$330$	−24273.1	−4.04906
$331$	−155.783	−0.0258689	−0.0129345	−	0.999916i	$-0.504117\pi$
$331$	−155.783	−0.0258689	−0.0129345	+	0.999916i	$0.504117\pi$
$332$	−65.8070	−0.0108784
$333$	98.8841	0.0162727
$334$	−20185.4	−3.30688
$335$	−5812.99	−0.948053
$336$	−26828.1	−4.35594
$337$	−5242.99	−0.847489	−0.423745	−	0.905782i	$-0.639285\pi$
$337$	−5242.99	−0.847489	−0.423745	+	0.905782i	$0.639285\pi$
$338$	27974.1	4.50175
$339$	−5077.09	−0.813420
$340$	135.866	0.0216718
$341$	6816.49	1.08250
$342$	1111.18	0.175690
$343$	16412.1	2.58358
$344$	−1857.52	−0.291136
$345$	1493.58	0.233077
$346$	2381.56	0.370039
$347$	−1349.57	−0.208785	−0.104393	−	0.994536i	$-0.533290\pi$
$347$	−1349.57	−0.208785	−0.104393	+	0.994536i	$0.533290\pi$
$348$	2333.62	0.359469
$349$	−9088.64	−1.39399	−0.696997	−	0.717074i	$-0.745481\pi$
$349$	−9088.64	−1.39399	−0.696997	+	0.717074i	$0.745481\pi$
$350$	28913.5	4.41569
$351$	−12991.1	−1.97554
$352$	−37638.6	−5.69927
$353$	−8756.58	−1.32030	−0.660150	−	0.751134i	$-0.729507\pi$
$353$	−8756.58	−1.32030	−0.660150	+	0.751134i	$0.729507\pi$
$354$	245.595	0.0368735
$355$	−736.494	−0.110110
$356$	9777.35	1.45561
$357$	51.1735	0.00758653
$358$	5116.70	0.755380
$359$	−6045.77	−0.888813	−0.444406	−	0.895825i	$-0.646585\pi$
$359$	−6045.77	−0.888813	−0.444406	+	0.895825i	$0.646585\pi$
$360$	13996.2	2.04907
$361$	−6565.58	−0.957222
$362$	4111.46	0.596943
$363$	−13575.5	−1.96290
$364$	−61237.5	−8.81791
$365$	−11148.3	−1.59871
$366$	8548.99	1.22094
$367$	2556.73	0.363652	0.181826	−	0.983331i	$-0.441799\pi$
$367$	2556.73	0.363652	0.181826	+	0.983331i	$0.441799\pi$
$368$	4677.33	0.662562
$369$	4320.13	0.609477
$370$	738.936	0.103826
$371$	−18112.0	−2.53458
$372$	7879.82	1.09825
$373$	1262.28	0.175224	0.0876120	−	0.996155i	$-0.472076\pi$
$373$	1262.28	0.175224	0.0876120	+	0.996155i	$0.472076\pi$
$374$	144.994	0.0200467
$375$	2120.52	0.292008
$376$	−25582.5	−3.50882
$377$	2495.80	0.340955
$378$	27684.1	3.76698
$379$	2811.61	0.381062	0.190531	−	0.981681i	$-0.438979\pi$
$379$	2811.61	0.381062	0.190531	+	0.981681i	$0.438979\pi$
$380$	5999.71	0.809943
$381$	−2403.30	−0.323162
$382$	1982.19	0.265492
$383$	2590.43	0.345600	0.172800	−	0.984957i	$-0.444719\pi$
$383$	2590.43	0.345600	0.172800	+	0.984957i	$0.444719\pi$
$384$	−9767.22	−1.29800
$385$	39971.6	5.29128
$386$	−4034.58	−0.532006
$387$	325.642	0.0427734
$388$	12186.5	1.59453
$389$	4227.50	0.551009	0.275505	−	0.961300i	$-0.411155\pi$
$389$	4227.50	0.551009	0.275505	+	0.961300i	$0.411155\pi$
$390$	−30009.6	−3.89639
$391$	−8.92181	−0.00115395
$392$	56749.9	7.31200
$393$	1581.00	0.202929
$394$	9633.90	1.23185
$395$	−5099.43	−0.649570
$396$	17519.9	2.22325
$397$	−6985.48	−0.883101	−0.441551	−	0.897236i	$-0.645571\pi$
$397$	−6985.48	−0.883101	−0.441551	+	0.897236i	$0.645571\pi$
$398$	5552.09	0.699249
$399$	2259.76	0.283533
$400$	32060.9	4.00762
$401$	10755.6	1.33942	0.669709	−	0.742623i	$-0.266419\pi$
$401$	10755.6	1.33942	0.669709	+	0.742623i	$0.266419\pi$
$402$	−7171.22	−0.889721
$403$	8427.43	1.04169
$404$	−21914.2	−2.69869
$405$	4318.65	0.529865
$406$	−5318.54	−0.650135
$407$	569.781	0.0693932
$408$	103.249	0.0125284
$409$	−5314.78	−0.642540	−0.321270	−	0.946988i	$-0.604110\pi$
$409$	−5314.78	−0.642540	−0.321270	+	0.946988i	$0.604110\pi$
$410$	32283.3	3.88867
$411$	−4509.12	−0.541165
$412$	−19428.7	−2.32327
$413$	−404.432	−0.0481860
$414$	−1492.01	−0.177121
$415$	53.1056	0.00628157
$416$	−46533.7	−5.48438
$417$	11597.4	1.36193
$418$	6402.76	0.749209
$419$	−9168.47	−1.06900	−0.534498	−	0.845170i	$-0.679499\pi$
$419$	−9168.47	−1.06900	−0.534498	+	0.845170i	$0.679499\pi$
$420$	46207.0	5.36826
$421$	−3474.47	−0.402221	−0.201111	−	0.979569i	$-0.564455\pi$
$421$	−3474.47	−0.402221	−0.201111	+	0.979569i	$0.564455\pi$
$422$	−11477.4	−1.32397
$423$	4484.86	0.515512
$424$	−36543.3	−4.18561
$425$	−61.1549	−0.00697987
$426$	−908.578	−0.103335
$427$	−14078.0	−1.59551
$428$	−2564.40	−0.289614
$429$	−23139.9	−2.60420
$430$	2433.44	0.272909
$431$	−240.988	−0.0269327	−0.0134664	−	0.999909i	$-0.504287\pi$
$431$	−240.988	−0.0269327	−0.0134664	+	0.999909i	$0.504287\pi$
$432$	30697.7	3.41886
$433$	13118.2	1.45594	0.727969	−	0.685611i	$-0.240465\pi$
$433$	13118.2	1.45594	0.727969	+	0.685611i	$0.240465\pi$
$434$	−17958.9	−1.98630
$435$	−1883.21	−0.207570
$436$	−12594.3	−1.38338
$437$	−393.977	−0.0431269
$438$	−13753.1	−1.50034
$439$	155.594	0.0169159	0.00845796	−	0.999964i	$-0.497308\pi$
$439$	155.594	0.0169159	0.00845796	+	0.999964i	$0.497308\pi$
$440$	80647.8	8.73803
$441$	−9948.83	−1.07427
$442$	179.260	0.0192908
$443$	−9049.14	−0.970514	−0.485257	−	0.874372i	$-0.661274\pi$
$443$	−9049.14	−0.970514	−0.485257	+	0.874372i	$0.661274\pi$
$444$	658.664	0.0704027
$445$	−7890.23	−0.840523
$446$	12124.1	1.28720
$447$	−11379.0	−1.20405
$448$	43597.6	4.59776
$449$	−2047.76	−0.215233	−0.107617	−	0.994192i	$-0.534322\pi$
$449$	−2047.76	−0.215233	−0.107617	+	0.994192i	$0.534322\pi$
$450$	−10227.0	−1.07135
$451$	24893.1	2.59904
$452$	27384.2	2.84966
$453$	10584.2	1.09777
$454$	16530.4	1.70883
$455$	49418.1	5.09177
$456$	4559.36	0.468227
$457$	−16348.7	−1.67343	−0.836717	−	0.547635i	$-0.815528\pi$
$457$	−16348.7	−1.67343	−0.836717	+	0.547635i	$0.815528\pi$
$458$	−15082.0	−1.53873
$459$	−58.5547	−0.00595446
$460$	−8055.92	−0.816542
$461$	−129.898	−0.0131236	−0.00656178	−	0.999978i	$-0.502089\pi$
$461$	−129.898	−0.0131236	−0.00656178	+	0.999978i	$0.502089\pi$
$462$	49311.1	4.96571
$463$	3431.37	0.344427	0.172213	−	0.985060i	$-0.444908\pi$
$463$	3431.37	0.344427	0.172213	+	0.985060i	$0.444908\pi$
$464$	−5897.50	−0.590053
$465$	−6358.94	−0.634170
$466$	−6034.28	−0.599856
$467$	12950.4	1.28324	0.641620	−	0.767022i	$-0.278262\pi$
$467$	12950.4	1.28324	0.641620	+	0.767022i	$0.278262\pi$
$468$	21660.3	2.13942
$469$	11809.2	1.16268
$470$	33514.3	3.28914
$471$	−13418.0	−1.31268
$472$	−815.993	−0.0795745
$473$	1876.39	0.182402
$474$	−6290.92	−0.609603
$475$	−2700.53	−0.260860
$476$	−276.014	−0.0265779
$477$	6406.40	0.614945
$478$	−26635.8	−2.54873
$479$	−12522.8	−1.19453	−0.597265	−	0.802044i	$-0.703746\pi$
$479$	−12522.8	−1.19453	−0.597265	+	0.802044i	$0.703746\pi$
$480$	35112.2	3.33884
$481$	704.438	0.0667767
$482$	−21053.2	−1.98951
$483$	−3034.23	−0.285843
$484$	73222.3	6.87663
$485$	−9834.41	−0.920737
$486$	−16557.3	−1.54538
$487$	6813.12	0.633947	0.316973	−	0.948434i	$-0.397333\pi$
$487$	6813.12	0.633947	0.316973	+	0.948434i	$0.397333\pi$
$488$	−28404.2	−2.63483
$489$	−14378.6	−1.32970
$490$	−74345.2	−6.85423
$491$	81.5942	0.00749958	0.00374979	−	0.999993i	$-0.498806\pi$
$491$	81.5942	0.00749958	0.00374979	+	0.999993i	$0.498806\pi$
$492$	28776.3	2.63686
$493$	11.2492	0.00102767
$494$	7915.92	0.720960
$495$	−14138.4	−1.28378
$496$	−19913.8	−1.80273
$497$	1496.20	0.135037
$498$	65.5139	0.00589508
$499$	−14466.0	−1.29777	−0.648886	−	0.760886i	$-0.724765\pi$
$499$	−14466.0	−1.29777	−0.648886	+	0.760886i	$0.724765\pi$
$500$	−11437.4	−1.02299
$501$	14519.9	1.29481
$502$	−35518.2	−3.15787
$503$	6829.91	0.605429	0.302714	−	0.953081i	$-0.402107\pi$
$503$	6829.91	0.605429	0.302714	+	0.953081i	$0.402107\pi$
$504$	−28433.5	−2.51295
$505$	17684.5	1.55832
$506$	−8597.10	−0.755312
$507$	−20122.5	−1.76267
$508$	12962.6	1.13213
$509$	−17728.5	−1.54382	−0.771909	−	0.635733i	$-0.780698\pi$
$509$	−17728.5	−1.54382	−0.771909	+	0.635733i	$0.780698\pi$
$510$	−135.261	−0.0117441
$511$	22647.9	1.96063
$512$	−2153.05	−0.185844
$513$	−2585.71	−0.222537
$514$	−28184.9	−2.41865
$515$	15678.8	1.34154
$516$	2169.09	0.185056
$517$	25842.3	2.19834
$518$	−1501.16	−0.127330
$519$	−1713.12	−0.144889
$520$	99707.3	8.40857
$521$	3302.59	0.277715	0.138857	−	0.990312i	$-0.455657\pi$
$521$	3302.59	0.277715	0.138857	+	0.990312i	$0.455657\pi$
$522$	1881.22	0.157737
$523$	12716.5	1.06320	0.531598	−	0.846997i	$-0.321592\pi$
$523$	12716.5	1.06320	0.531598	+	0.846997i	$0.321592\pi$
$524$	−8527.43	−0.710921
$525$	−20798.2	−1.72897
$526$	−11552.3	−0.957610
$527$	37.9847	0.00313974
$528$	54678.9	4.50681
$529$	529.000	0.0434783
$530$	47873.4	3.92356
$531$	143.052	0.0116910
$532$	−12188.5	−0.993303
$533$	30776.1	2.50105
$534$	−9733.80	−0.788807
$535$	2069.44	0.167233
$536$	23826.5	1.92005
$537$	−3680.57	−0.295770
$538$	−6650.29	−0.532927
$539$	−57326.3	−4.58111
$540$	−52871.7	−4.21340
$541$	−7811.49	−0.620780	−0.310390	−	0.950609i	$-0.600460\pi$
$541$	−7811.49	−0.620780	−0.310390	+	0.950609i	$0.600460\pi$
$542$	−44053.0	−3.49121
$543$	−2957.48	−0.233734
$544$	−209.740	−0.0165304
$545$	10163.4	0.798815
$546$	60964.8	4.77848
$547$	−13224.3	−1.03369	−0.516847	−	0.856078i	$-0.672894\pi$
$547$	−13224.3	−1.03369	−0.516847	+	0.856078i	$0.672894\pi$
$548$	24320.8	1.89587
$549$	4979.54	0.387106
$550$	−58929.2	−4.56863
$551$	496.753	0.0384073
$552$	−6121.94	−0.472042
$553$	10359.5	0.796624
$554$	13442.7	1.03091
$555$	−531.536	−0.0406530
$556$	−62552.7	−4.77126
$557$	−6962.38	−0.529633	−0.264816	−	0.964299i	$-0.585311\pi$
$557$	−6962.38	−0.529633	−0.264816	+	0.964299i	$0.585311\pi$
$558$	6352.23	0.481920
$559$	2319.83	0.175525
$560$	−116774.	−8.81177
$561$	−104.298	−0.00784930
$562$	4682.21	0.351436
$563$	−17773.2	−1.33046	−0.665231	−	0.746637i	$-0.731667\pi$
$563$	−17773.2	−1.33046	−0.665231	+	0.746637i	$0.731667\pi$
$564$	29873.5	2.23032
$565$	−22098.8	−1.64549
$566$	11812.9	0.877264
$567$	−8773.38	−0.649819
$568$	3018.77	0.223001
$569$	−461.774	−0.0340221	−0.0170110	−	0.999855i	$-0.505415\pi$
$569$	−461.774	−0.0340221	−0.0170110	+	0.999855i	$0.505415\pi$
$570$	−5972.98	−0.438914
$571$	14893.1	1.09152	0.545759	−	0.837942i	$-0.316242\pi$
$571$	14893.1	1.09152	0.545759	+	0.837942i	$0.316242\pi$
$572$	124809.	9.12333
$573$	−1425.84	−0.103954
$574$	−65583.8	−4.76902
$575$	3626.05	0.262986
$576$	−15420.9	−1.11552
$577$	−195.395	−0.0140977	−0.00704887	−	0.999975i	$-0.502244\pi$
$577$	−195.395	−0.0140977	−0.00704887	+	0.999975i	$0.502244\pi$
$578$	−26380.4	−1.89841
$579$	2902.17	0.208308
$580$	10157.5	0.727182
$581$	−107.885	−0.00770363
$582$	−12132.2	−0.864085
$583$	36914.4	2.62236
$584$	45694.9	3.23779
$585$	−17479.7	−1.23538
$586$	−14941.4	−1.05328
$587$	23867.5	1.67822	0.839110	−	0.543962i	$-0.183076\pi$
$587$	23867.5	1.67822	0.839110	+	0.543962i	$0.183076\pi$
$588$	−66268.9	−4.64776
$589$	1677.36	0.117342
$590$	1068.99	0.0745926
$591$	−6929.91	−0.482332
$592$	−1664.57	−0.115563
$593$	14031.1	0.971653	0.485826	−	0.874055i	$-0.338519\pi$
$593$	14031.1	0.971653	0.485826	+	0.874055i	$0.338519\pi$
$594$	−56423.6	−3.89745
$595$	222.741	0.0153470
$596$	61375.0	4.21815
$597$	−3993.76	−0.273792
$598$	−10628.9	−0.726833
$599$	−20620.8	−1.40658	−0.703292	−	0.710901i	$-0.748288\pi$
$599$	−20620.8	−1.40658	−0.703292	+	0.710901i	$0.748288\pi$
$600$	−41963.1	−2.85522
$601$	−6575.94	−0.446320	−0.223160	−	0.974782i	$-0.571637\pi$
$601$	−6575.94	−0.446320	−0.223160	+	0.974782i	$0.571637\pi$
$602$	−4943.57	−0.334692
$603$	−4177.02	−0.282092
$604$	−57088.1	−3.84583
$605$	−59089.7	−3.97081
$606$	21816.6	1.46244
$607$	5896.24	0.394268	0.197134	−	0.980377i	$-0.436837\pi$
$607$	5896.24	0.394268	0.197134	+	0.980377i	$0.436837\pi$
$608$	−9261.89	−0.617795
$609$	3825.76	0.254561
$610$	37210.8	2.46987
$611$	31949.6	2.11545
$612$	97.6291	0.00644840
$613$	−23731.6	−1.56364	−0.781818	−	0.623507i	$-0.785707\pi$
$613$	−23731.6	−1.56364	−0.781818	+	0.623507i	$0.785707\pi$
$614$	49587.9	3.25929
$615$	−23222.2	−1.52261
$616$	−163837.	−10.7162
$617$	−12212.2	−0.796831	−0.398416	−	0.917205i	$-0.630440\pi$
$617$	−12212.2	−0.796831	−0.398416	+	0.917205i	$0.630440\pi$
$618$	19342.2	1.25899
$619$	10115.8	0.656844	0.328422	−	0.944531i	$-0.393483\pi$
$619$	10115.8	0.656844	0.328422	+	0.944531i	$0.393483\pi$
$620$	34298.2	2.22169
$621$	3471.88	0.224350
$622$	36668.6	2.36379
$623$	16029.1	1.03081
$624$	67601.2	4.33688
$625$	−10476.9	−0.670522
$626$	16836.0	1.07492
$627$	−4605.67	−0.293354
$628$	72372.8	4.59871
$629$	3.17509	0.000201271 0
$630$	37249.2	2.35563
$631$	−18761.2	−1.18363	−0.591816	−	0.806073i	$-0.701589\pi$
$631$	−18761.2	−1.18363	−0.591816	+	0.806073i	$0.701589\pi$
$632$	20901.7	1.31555
$633$	8256.02	0.518400
$634$	5036.38	0.315489
$635$	−10460.7	−0.653734
$636$	42672.8	2.66052
$637$	−70874.2	−4.40838
$638$	10839.8	0.672653
$639$	−529.220	−0.0327631
$640$	−42513.4	−2.62576
$641$	1399.48	0.0862342	0.0431171	−	0.999070i	$-0.486271\pi$
$641$	1399.48	0.0862342	0.0431171	+	0.999070i	$0.486271\pi$
$642$	2552.98	0.156944
$643$	3035.38	0.186164	0.0930821	−	0.995658i	$-0.470328\pi$
$643$	3035.38	0.186164	0.0930821	+	0.995658i	$0.470328\pi$
$644$	16365.7	1.00140
$645$	−1750.44	−0.106858
$646$	35.6792	0.00217304
$647$	20320.6	1.23475	0.617375	−	0.786669i	$-0.288196\pi$
$647$	20320.6	1.23475	0.617375	+	0.786669i	$0.288196\pi$
$648$	−17701.4	−1.07311
$649$	824.281	0.0498549
$650$	−72855.9	−4.39637
$651$	12918.3	0.777737
$652$	77553.9	4.65835
$653$	−23307.0	−1.39674	−0.698371	−	0.715736i	$-0.746092\pi$
$653$	−23307.0	−1.39674	−0.698371	+	0.715736i	$0.746092\pi$
$654$	12538.2	0.749665
$655$	6881.56	0.410511
$656$	−72723.0	−4.32829
$657$	−8010.78	−0.475693
$658$	−68084.6	−4.03376
$659$	−5013.26	−0.296341	−0.148171	−	0.988962i	$-0.547338\pi$
$659$	−5013.26	−0.296341	−0.148171	+	0.988962i	$0.547338\pi$
$660$	−94175.3	−5.55420
$661$	−13768.5	−0.810183	−0.405092	−	0.914276i	$-0.632760\pi$
$661$	−13768.5	−0.810183	−0.405092	+	0.914276i	$0.632760\pi$
$662$	−836.504	−0.0491112
$663$	−128.946	−0.00755334
$664$	−217.671	−0.0127218
$665$	9835.98	0.573569
$666$	530.975	0.0308932
$667$	−667.000	−0.0387202
$668$	−78315.8	−4.53612
$669$	−8721.14	−0.504004
$670$	−31213.9	−1.79985
$671$	28692.7	1.65077
$672$	−71330.8	−4.09471
$673$	5064.75	0.290092	0.145046	−	0.989425i	$-0.453667\pi$
$673$	5064.75	0.290092	0.145046	+	0.989425i	$0.453667\pi$
$674$	−28153.1	−1.60893
$675$	23798.1	1.35702
$676$	108535.	6.17517
$677$	18602.9	1.05608	0.528041	−	0.849219i	$-0.322927\pi$
$677$	18602.9	1.05608	0.528041	+	0.849219i	$0.322927\pi$
$678$	−27262.3	−1.54425
$679$	19978.7	1.12918
$680$	449.408	0.0253442
$681$	−11890.7	−0.669096
$682$	36602.3	2.05509
$683$	−20047.4	−1.12312	−0.561560	−	0.827436i	$-0.689799\pi$
$683$	−20047.4	−1.12312	−0.561560	+	0.827436i	$0.689799\pi$
$684$	4311.19	0.240998
$685$	−19626.7	−1.09474
$686$	88127.5	4.90485
$687$	10848.9	0.602490
$688$	−5481.71	−0.303762
$689$	45638.4	2.52349
$690$	8020.04	0.442489
$691$	−20652.9	−1.13701	−0.568504	−	0.822681i	$-0.692477\pi$
$691$	−20652.9	−1.13701	−0.568504	+	0.822681i	$0.692477\pi$
$692$	9240.03	0.507591
$693$	28722.3	1.57441
$694$	−7246.73	−0.396372
$695$	50479.4	2.75510
$696$	7718.97	0.420383
$697$	138.716	0.00753838
$698$	−48803.0	−2.64645
$699$	4340.61	0.234874
$700$	112179.	6.05711
$701$	−1445.33	−0.0778733	−0.0389366	−	0.999242i	$-0.512397\pi$
$701$	−1445.33	−0.0778733	−0.0389366	+	0.999242i	$0.512397\pi$
$702$	−69758.2	−3.75050
$703$	140.209	0.00752214
$704$	−88857.2	−4.75700
$705$	−24107.7	−1.28787
$706$	−47020.0	−2.50654
$707$	−35926.3	−1.91110
$708$	952.864	0.0505803
$709$	18902.3	1.00126	0.500629	−	0.865662i	$-0.333102\pi$
$709$	18902.3	1.00126	0.500629	+	0.865662i	$0.333102\pi$
$710$	−3954.73	−0.209040
$711$	−3664.28	−0.193279
$712$	32340.7	1.70228
$713$	−2252.23	−0.118298
$714$	274.785	0.0144028
$715$	−100720.	−5.26813
$716$	19851.9	1.03617
$717$	19159.8	0.997960
$718$	−32463.8	−1.68738
$719$	16392.7	0.850273	0.425136	−	0.905129i	$-0.360226\pi$
$719$	16392.7	0.850273	0.425136	+	0.905129i	$0.360226\pi$
$720$	41304.1	2.13793
$721$	−31851.7	−1.64524
$722$	−35255.0	−1.81725
$723$	15144.1	0.778996
$724$	15951.7	0.818841
$725$	−4571.98	−0.234205
$726$	−72896.2	−3.72649
$727$	−14548.6	−0.742196	−0.371098	−	0.928594i	$-0.621019\pi$
$727$	−14548.6	−0.742196	−0.371098	+	0.928594i	$0.621019\pi$
$728$	−202557.	−10.3122
$729$	18845.7	0.957462
$730$	−59862.6	−3.03509
$731$	10.4561	0.000529048 0
$732$	33168.6	1.67479
$733$	25965.7	1.30841	0.654206	−	0.756316i	$-0.273003\pi$
$733$	25965.7	1.30841	0.654206	+	0.756316i	$0.273003\pi$
$734$	13728.8	0.690381
$735$	53478.4	2.68378
$736$	12436.1	0.622827
$737$	−24068.5	−1.20295
$738$	23197.7	1.15707
$739$	7145.67	0.355694	0.177847	−	0.984058i	$-0.443087\pi$
$739$	7145.67	0.355694	0.177847	+	0.984058i	$0.443087\pi$
$740$	2866.94	0.142420
$741$	−5694.13	−0.282293
$742$	−97255.4	−4.81181
$743$	739.291	0.0365033	0.0182516	−	0.999833i	$-0.494190\pi$
$743$	739.291	0.0365033	0.0182516	+	0.999833i	$0.494190\pi$
$744$	26064.2	1.28436
$745$	−49529.0	−2.43571
$746$	6778.04	0.332657
$747$	38.1599	0.00186907
$748$	562.550	0.0274985
$749$	−4204.10	−0.205093
$750$	11386.5	0.554367
$751$	−10486.6	−0.509535	−0.254767	−	0.967002i	$-0.581999\pi$
$751$	−10486.6	−0.509535	−0.254767	+	0.967002i	$0.581999\pi$
$752$	−75496.0	−3.66098
$753$	25549.1	1.23647
$754$	13401.6	0.647291
$755$	46069.5	2.22072
$756$	107410.	5.16726
$757$	−11859.6	−0.569409	−0.284705	−	0.958615i	$-0.591896\pi$
$757$	−11859.6	−0.569409	−0.284705	+	0.958615i	$0.591896\pi$
$758$	15097.4	0.723433
$759$	6184.12	0.295743
$760$	19845.4	0.947193
$761$	−32064.4	−1.52738	−0.763689	−	0.645585i	$-0.776614\pi$
$761$	−32064.4	−1.52738	−0.763689	+	0.645585i	$0.776614\pi$
$762$	−12904.9	−0.613511
$763$	−20647.2	−0.979656
$764$	7690.55	0.364181
$765$	−78.7858	−0.00372354
$766$	13909.7	0.656109
$767$	1019.08	0.0479752
$768$	−13002.9	−0.610942
$769$	−7315.05	−0.343026	−0.171513	−	0.985182i	$-0.554866\pi$
$769$	−7315.05	−0.343026	−0.171513	+	0.985182i	$0.554866\pi$
$770$	214634.	10.0453
$771$	20274.1	0.947024
$772$	−15653.4	−0.729766
$773$	18724.0	0.871223	0.435612	−	0.900135i	$-0.356532\pi$
$773$	18724.0	0.871223	0.435612	+	0.900135i	$0.356532\pi$
$774$	1748.59	0.0812039
$775$	−15438.0	−0.715546
$776$	40309.6	1.86473
$777$	1079.82	0.0498563
$778$	22700.3	1.04607
$779$	6125.54	0.281734
$780$	−116432.	−5.34478
$781$	−3049.43	−0.139714
$782$	−47.9072	−0.00219074
$783$	−4377.58	−0.199798
$784$	167474.	7.62910
$785$	−58404.2	−2.65546
$786$	8489.45	0.385253
$787$	20080.1	0.909500	0.454750	−	0.890619i	$-0.349729\pi$
$787$	20080.1	0.909500	0.454750	+	0.890619i	$0.349729\pi$
$788$	37377.8	1.68976
$789$	8309.84	0.374953
$790$	−27382.3	−1.23319
$791$	44894.0	2.01801
$792$	57950.8	2.59999
$793$	35473.6	1.58853
$794$	−37509.7	−1.67654
$795$	−34436.6	−1.53628
$796$	21541.1	0.959177
$797$	−13151.0	−0.584481	−0.292240	−	0.956345i	$-0.594401\pi$
$797$	−13151.0	−0.584481	−0.292240	+	0.956345i	$0.594401\pi$
$798$	12134.2	0.538278
$799$	144.006	0.00637616
$800$	85243.7	3.76728
$801$	−5669.66	−0.250097
$802$	57753.8	2.54284
$803$	−46159.0	−2.02854
$804$	−27823.0	−1.22045
$805$	−13207.0	−0.578241
$806$	45252.5	1.97761
$807$	4783.72	0.208668
$808$	−72485.9	−3.15600
$809$	−22918.3	−0.996002	−0.498001	−	0.867177i	$-0.665932\pi$
$809$	−22918.3	−0.996002	−0.498001	+	0.867177i	$0.665932\pi$
$810$	23189.7	1.00593
$811$	45507.1	1.97037	0.985185	−	0.171493i	$-0.0548592\pi$
$811$	45507.1	1.97037	0.985185	+	0.171493i	$0.0548592\pi$
$812$	−20635.0	−0.891806
$813$	31688.4	1.36699
$814$	3059.54	0.131740
$815$	−62585.2	−2.68990
$816$	304.697	0.0130717
$817$	461.730	0.0197722
$818$	−28538.6	−1.21984
$819$	35510.2	1.51505
$820$	125253.	5.33419
$821$	21496.8	0.913816	0.456908	−	0.889514i	$-0.348957\pi$
$821$	21496.8	0.913816	0.456908	+	0.889514i	$0.348957\pi$
$822$	−24212.5	−1.02738
$823$	38201.5	1.61801	0.809005	−	0.587802i	$-0.200007\pi$
$823$	38201.5	1.61801	0.809005	+	0.587802i	$0.200007\pi$
$824$	−64264.8	−2.71696
$825$	42389.2	1.78885
$826$	−2171.67	−0.0914794
$827$	23958.4	1.00739	0.503697	−	0.863880i	$-0.331973\pi$
$827$	23958.4	1.00739	0.503697	+	0.863880i	$0.331973\pi$
$828$	−5788.71	−0.242961
$829$	−1608.70	−0.0673976	−0.0336988	−	0.999432i	$-0.510729\pi$
$829$	−1608.70	−0.0673976	−0.0336988	+	0.999432i	$0.510729\pi$
$830$	285.160	0.0119253
$831$	−9669.69	−0.403656
$832$	−109857.	−4.57764
$833$	−319.450	−0.0132872
$834$	62274.0	2.58558
$835$	63200.1	2.61932
$836$	24841.6	1.02771
$837$	−14781.6	−0.610425
$838$	−49231.7	−2.02945
$839$	22499.4	0.925824	0.462912	−	0.886404i	$-0.346805\pi$
$839$	22499.4	0.925824	0.462912	+	0.886404i	$0.346805\pi$
$840$	152840.	6.27794
$841$	841.000	0.0344828
$842$	−18656.7	−0.763603
$843$	−3368.03	−0.137605
$844$	−44530.4	−1.81612
$845$	−87586.5	−3.56576
$846$	24082.2	0.978681
$847$	120041.	4.86974
$848$	−107842.	−4.36712
$849$	−8497.29	−0.343494
$850$	−328.382	−0.0132511
$851$	−188.261	−0.00758342
$852$	−3525.12	−0.141747
$853$	11941.0	0.479310	0.239655	−	0.970858i	$-0.422966\pi$
$853$	11941.0	0.479310	0.239655	+	0.970858i	$0.422966\pi$
$854$	−75594.3	−3.02902
$855$	−3479.09	−0.139161
$856$	−8482.31	−0.338691
$857$	10210.8	0.406995	0.203498	−	0.979075i	$-0.434769\pi$
$857$	10210.8	0.406995	0.203498	+	0.979075i	$0.434769\pi$
$858$	−124253.	−4.94399
$859$	−15068.7	−0.598528	−0.299264	−	0.954170i	$-0.596741\pi$
$859$	−15068.7	−0.598528	−0.299264	+	0.954170i	$0.596741\pi$
$860$	9441.32	0.374356
$861$	47176.1	1.86731
$862$	−1294.03	−0.0511308
$863$	−21406.8	−0.844373	−0.422187	−	0.906509i	$-0.638737\pi$
$863$	−21406.8	−0.844373	−0.422187	+	0.906509i	$0.638737\pi$
$864$	81619.3	3.21383
$865$	−7456.62	−0.293101
$866$	70440.5	2.76405
$867$	18976.1	0.743324
$868$	−69677.2	−2.72465
$869$	−21114.0	−0.824215
$870$	−10112.2	−0.394065
$871$	−29756.6	−1.15759
$872$	−41658.3	−1.61781
$873$	−7066.68	−0.273964
$874$	−2115.53	−0.0818750
$875$	−18750.6	−0.724442
$876$	−53359.6	−2.05805
$877$	38564.0	1.48485	0.742425	−	0.669929i	$-0.233675\pi$
$877$	38564.0	1.48485	0.742425	+	0.669929i	$0.233675\pi$
$878$	835.488	0.0321143
$879$	10747.8	0.412415
$880$	237999.	9.11697
$881$	−15248.0	−0.583108	−0.291554	−	0.956554i	$-0.594172\pi$
$881$	−15248.0	−0.583108	−0.291554	+	0.956554i	$0.594172\pi$
$882$	−53421.9	−2.03947
$883$	−39498.2	−1.50535	−0.752673	−	0.658394i	$-0.771236\pi$
$883$	−39498.2	−1.50535	−0.752673	+	0.658394i	$0.771236\pi$
$884$	695.498	0.0264617
$885$	−768.952	−0.0292068
$886$	−48590.9	−1.84249
$887$	22306.4	0.844392	0.422196	−	0.906505i	$-0.361259\pi$
$887$	22306.4	0.844392	0.422196	+	0.906505i	$0.361259\pi$
$888$	2178.68	0.0823329
$889$	21251.1	0.801731
$890$	−42367.9	−1.59570
$891$	17881.2	0.672326
$892$	47039.2	1.76568
$893$	6359.12	0.238298
$894$	−61101.6	−2.28584
$895$	−16020.3	−0.598323
$896$	86366.4	3.22020
$897$	7645.61	0.284592
$898$	−10995.8	−0.408613
$899$	2839.76	0.105352
$900$	−39678.9	−1.46959
$901$	205.705	0.00760601
$902$	133668.	4.93420
$903$	3556.03	0.131049
$904$	90579.4	3.33255
$905$	−12872.9	−0.472828
$906$	56833.8	2.08408
$907$	−20887.0	−0.764656	−0.382328	−	0.924027i	$-0.624878\pi$
$907$	−20887.0	−0.764656	−0.382328	+	0.924027i	$0.624878\pi$
$908$	64135.0	2.34405
$909$	12707.5	0.463676
$910$	265359.	9.66655
$911$	6776.54	0.246451	0.123225	−	0.992379i	$-0.460676\pi$
$911$	6776.54	0.246451	0.123225	+	0.992379i	$0.460676\pi$
$912$	13455.1	0.488533
$913$	219.882	0.00797046
$914$	−87787.1	−3.17696
$915$	−26766.7	−0.967082
$916$	−58515.6	−2.11071
$917$	−13980.0	−0.503445
$918$	−314.419	−0.0113043
$919$	−11995.1	−0.430559	−0.215279	−	0.976553i	$-0.569066\pi$
$919$	−11995.1	−0.430559	−0.215279	+	0.976553i	$0.569066\pi$
$920$	−26646.7	−0.954909
$921$	−35669.8	−1.27618
$922$	−697.511	−0.0249146
$923$	−3770.10	−0.134447
$924$	191318.	6.81159
$925$	−1290.44	−0.0458696
$926$	18425.3	0.653882
$927$	11266.3	0.399172
$928$	−15680.3	−0.554667
$929$	−19119.3	−0.675223	−0.337612	−	0.941285i	$-0.609619\pi$
$929$	−19119.3	−0.675223	−0.337612	+	0.941285i	$0.609619\pi$
$930$	−34145.4	−1.20395
$931$	−14106.5	−0.496587
$932$	−23411.9	−0.822837
$933$	−26376.6	−0.925543
$934$	69539.4	2.43619
$935$	−453.973	−0.0158786
$936$	71646.4	2.50196
$937$	−37372.6	−1.30300	−0.651500	−	0.758649i	$-0.725860\pi$
$937$	−37372.6	−1.30300	−0.651500	+	0.758649i	$0.725860\pi$
$938$	63411.3	2.20731
$939$	−12110.5	−0.420887
$940$	130029.	4.51180
$941$	−10032.8	−0.347565	−0.173783	−	0.984784i	$-0.555599\pi$
$941$	−10032.8	−0.347565	−0.173783	+	0.984784i	$0.555599\pi$
$942$	−72050.5	−2.49207
$943$	−8224.88	−0.284029
$944$	−2408.07	−0.0830253
$945$	−86678.5	−2.98376
$946$	10075.6	0.346285
$947$	−17488.6	−0.600109	−0.300054	−	0.953922i	$-0.597005\pi$
$947$	−17488.6	−0.600109	−0.300054	+	0.953922i	$0.597005\pi$
$948$	−24407.7	−0.836207
$949$	−57067.8	−1.95205
$950$	−14500.9	−0.495235
$951$	−3622.80	−0.123530
$952$	−912.978	−0.0310817
$953$	−10340.8	−0.351491	−0.175745	−	0.984436i	$-0.556234\pi$
$953$	−10340.8	−0.351491	−0.175745	+	0.984436i	$0.556234\pi$
$954$	34400.2	1.16745
$955$	−6206.20	−0.210291
$956$	−103342.	−3.49616
$957$	−7797.36	−0.263378
$958$	−67243.1	−2.26777
$959$	39871.8	1.34257
$960$	82892.8	2.78683
$961$	−20202.1	−0.678128
$962$	3782.60	0.126773
$963$	1487.03	0.0497601
$964$	−81682.5	−2.72906
$965$	12632.2	0.421393
$966$	−16292.8	−0.542663
$967$	51857.0	1.72452	0.862259	−	0.506468i	$-0.169049\pi$
$967$	51857.0	1.72452	0.862259	+	0.506468i	$0.169049\pi$
$968$	242199.	8.04191
$969$	−25.6650	−0.000850855 0
$970$	−52807.5	−1.74799
$971$	−52217.0	−1.72577	−0.862885	−	0.505400i	$-0.831345\pi$
$971$	−52217.0	−1.72577	−0.862885	+	0.505400i	$0.831345\pi$
$972$	−64239.6	−2.11984
$973$	−102549.	−3.37881
$974$	36584.2	1.20353
$975$	52407.1	1.72141
$976$	−83823.2	−2.74909
$977$	21798.1	0.713801	0.356900	−	0.934142i	$-0.383834\pi$
$977$	21798.1	0.713801	0.356900	+	0.934142i	$0.383834\pi$
$978$	−77208.4	−2.52439
$979$	−32669.2	−1.06651
$980$	−288446.	−9.40211
$981$	7303.12	0.237687
$982$	438.134	0.0142377
$983$	478.947	0.0155402	0.00777010	−	0.999970i	$-0.497527\pi$
$983$	478.947	0.0155402	0.00777010	+	0.999970i	$0.497527\pi$
$984$	95183.8	3.08369
$985$	−30163.5	−0.975726
$986$	60.4047	0.00195099
$987$	48975.0	1.57942
$988$	30712.4	0.988958
$989$	−619.974	−0.0199333
$990$	−75918.4	−2.43722
$991$	39735.8	1.27371	0.636856	−	0.770983i	$-0.280234\pi$
$991$	39735.8	1.27371	0.636856	+	0.770983i	$0.280234\pi$
$992$	−52946.9	−1.69462
$993$	601.718	0.0192296
$994$	8034.08	0.256364
$995$	−17383.5	−0.553863
$996$	254.182	0.00808642
$997$	53212.1	1.69031	0.845157	−	0.534518i	$-0.179507\pi$
$997$	53212.1	1.69031	0.845157	+	0.534518i	$0.179507\pi$
$998$	−77677.7	−2.46377
$999$	−1235.57	−0.0391309

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	667.4.a.a.1.35	✓	35

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
667.4.a.a.1.35	✓	35	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)

\(f(q)\)	\(=\)	\(q+5.36967 q^{2} -3.86254 q^{3} +20.8334 q^{4} -16.8123 q^{5} -20.7406 q^{6} +34.1544 q^{7} +68.9109 q^{8} -12.0808 q^{9} +O(q^{10})\)	\(q+5.36967 q^{2} -3.86254 q^{3} +20.8334 q^{4} -16.8123 q^{5} -20.7406 q^{6} +34.1544 q^{7} +68.9109 q^{8} -12.0808 q^{9} -90.2767 q^{10} -69.6108 q^{11} -80.4697 q^{12} -86.0619 q^{13} +183.398 q^{14} +64.9383 q^{15} +203.362 q^{16} -0.387905 q^{17} -64.8698 q^{18} -17.1294 q^{19} -350.257 q^{20} -131.923 q^{21} -373.787 q^{22} +23.0000 q^{23} -266.171 q^{24} +157.654 q^{25} -462.124 q^{26} +150.951 q^{27} +711.552 q^{28} -29.0000 q^{29} +348.697 q^{30} -97.9228 q^{31} +540.700 q^{32} +268.875 q^{33} -2.08292 q^{34} -574.216 q^{35} -251.683 q^{36} -8.18524 q^{37} -91.9794 q^{38} +332.418 q^{39} -1158.55 q^{40} -357.604 q^{41} -708.383 q^{42} -26.9554 q^{43} -1450.23 q^{44} +203.106 q^{45} +123.502 q^{46} -371.239 q^{47} -785.495 q^{48} +823.526 q^{49} +846.552 q^{50} +1.49830 q^{51} -1792.96 q^{52} -530.297 q^{53} +810.558 q^{54} +1170.32 q^{55} +2353.61 q^{56} +66.1631 q^{57} -155.720 q^{58} -11.8413 q^{59} +1352.88 q^{60} -412.187 q^{61} -525.813 q^{62} -412.612 q^{63} +1276.49 q^{64} +1446.90 q^{65} +1443.77 q^{66} +345.758 q^{67} -8.08136 q^{68} -88.8384 q^{69} -3083.35 q^{70} +43.8068 q^{71} -832.498 q^{72} +663.102 q^{73} -43.9521 q^{74} -608.946 q^{75} -356.864 q^{76} -2377.52 q^{77} +1784.97 q^{78} +303.315 q^{79} -3418.99 q^{80} -256.874 q^{81} -1920.21 q^{82} -3.15873 q^{83} -2748.40 q^{84} +6.52158 q^{85} -144.742 q^{86} +112.014 q^{87} -4796.95 q^{88} +469.312 q^{89} +1090.61 q^{90} -2939.40 q^{91} +479.167 q^{92} +378.231 q^{93} -1993.43 q^{94} +287.986 q^{95} -2088.48 q^{96} +584.952 q^{97} +4422.06 q^{98} +840.953 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 35 q - 6 q^{2} - 22 q^{3} + 116 q^{4} - 80 q^{5} - 52 q^{6} - 38 q^{7} + 12 q^{8} + 231 q^{9}+O(q^{10}) \) 35 * q - 6 * q^2 - 22 * q^3 + 116 * q^4 - 80 * q^5 - 52 * q^6 - 38 * q^7 + 12 * q^8 + 231 * q^9	\( 35 q - 6 q^{2} - 22 q^{3} + 116 q^{4} - 80 q^{5} - 52 q^{6} - 38 q^{7} + 12 q^{8} + 231 q^{9} - 52 q^{10} - 126 q^{11} - 173 q^{12} - 252 q^{13} + 112 q^{14} - 32 q^{15} + 312 q^{16} - 332 q^{17} - 225 q^{18} - 2 q^{19} - 747 q^{20} - 202 q^{21} - 127 q^{22} + 805 q^{23} - 494 q^{24} + 315 q^{25} - 677 q^{26} - 694 q^{27} - 529 q^{28} - 1015 q^{29} + 389 q^{30} - 652 q^{31} + 320 q^{32} - 290 q^{33} - 455 q^{34} - 940 q^{35} + 34 q^{36} - 528 q^{37} - 1218 q^{38} - 268 q^{39} - 806 q^{40} - 68 q^{41} - 1484 q^{42} - 162 q^{43} - 1817 q^{44} - 356 q^{45} - 138 q^{46} - 1200 q^{47} - 2153 q^{48} + 93 q^{49} - 1369 q^{50} - 270 q^{51} - 3134 q^{52} - 1892 q^{53} - 1221 q^{54} - 794 q^{55} + 191 q^{56} - 1764 q^{57} + 174 q^{58} - 1354 q^{59} + 159 q^{60} - 1274 q^{61} - 5413 q^{62} - 2904 q^{63} - 926 q^{64} - 548 q^{65} - 2477 q^{66} - 3212 q^{67} - 3901 q^{68} - 506 q^{69} - 2768 q^{70} - 2342 q^{71} - 2381 q^{72} + 916 q^{73} + 661 q^{74} - 4708 q^{75} - 2810 q^{76} - 5536 q^{77} - 2434 q^{78} + 2622 q^{79} - 5444 q^{80} + 607 q^{81} - 3687 q^{82} - 2702 q^{83} + 346 q^{84} - 3304 q^{85} - 5789 q^{86} + 638 q^{87} - 2252 q^{88} - 1620 q^{89} - 3933 q^{90} - 4016 q^{91} + 2668 q^{92} - 4942 q^{93} - 1413 q^{94} - 4528 q^{95} - 7920 q^{96} + 682 q^{97} + 152 q^{98} - 582 q^{99}+O(q^{100}) \) 35 * q - 6 * q^2 - 22 * q^3 + 116 * q^4 - 80 * q^5 - 52 * q^6 - 38 * q^7 + 12 * q^8 + 231 * q^9 - 52 * q^10 - 126 * q^11 - 173 * q^12 - 252 * q^13 + 112 * q^14 - 32 * q^15 + 312 * q^16 - 332 * q^17 - 225 * q^18 - 2 * q^19 - 747 * q^20 - 202 * q^21 - 127 * q^22 + 805 * q^23 - 494 * q^24 + 315 * q^25 - 677 * q^26 - 694 * q^27 - 529 * q^28 - 1015 * q^29 + 389 * q^30 - 652 * q^31 + 320 * q^32 - 290 * q^33 - 455 * q^34 - 940 * q^35 + 34 * q^36 - 528 * q^37 - 1218 * q^38 - 268 * q^39 - 806 * q^40 - 68 * q^41 - 1484 * q^42 - 162 * q^43 - 1817 * q^44 - 356 * q^45 - 138 * q^46 - 1200 * q^47 - 2153 * q^48 + 93 * q^49 - 1369 * q^50 - 270 * q^51 - 3134 * q^52 - 1892 * q^53 - 1221 * q^54 - 794 * q^55 + 191 * q^56 - 1764 * q^57 + 174 * q^58 - 1354 * q^59 + 159 * q^60 - 1274 * q^61 - 5413 * q^62 - 2904 * q^63 - 926 * q^64 - 548 * q^65 - 2477 * q^66 - 3212 * q^67 - 3901 * q^68 - 506 * q^69 - 2768 * q^70 - 2342 * q^71 - 2381 * q^72 + 916 * q^73 + 661 * q^74 - 4708 * q^75 - 2810 * q^76 - 5536 * q^77 - 2434 * q^78 + 2622 * q^79 - 5444 * q^80 + 607 * q^81 - 3687 * q^82 - 2702 * q^83 + 346 * q^84 - 3304 * q^85 - 5789 * q^86 + 638 * q^87 - 2252 * q^88 - 1620 * q^89 - 3933 * q^90 - 4016 * q^91 + 2668 * q^92 - 4942 * q^93 - 1413 * q^94 - 4528 * q^95 - 7920 * q^96 + 682 * q^97 + 152 * q^98 - 582 * q^99

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