LMFDB - Embedded newform 667.4.a.a.1.8

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			1.8
Character	$\chi$	$=$	667.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.82659 q^{2} +3.57847 q^{3} +6.64282 q^{4} +6.65081 q^{5} -13.6933 q^{6} +1.73304 q^{7} +5.19338 q^{8} -14.1946 q^{9} +O(q^{10})$	\(q-3.82659 q^{2} +3.57847 q^{3} +6.64282 q^{4} +6.65081 q^{5} -13.6933 q^{6} +1.73304 q^{7} +5.19338 q^{8} -14.1946 q^{9} -25.4500 q^{10} +50.6314 q^{11} +23.7711 q^{12} -60.3796 q^{13} -6.63165 q^{14} +23.7997 q^{15} -73.0155 q^{16} +26.6935 q^{17} +54.3168 q^{18} -54.2134 q^{19} +44.1802 q^{20} +6.20164 q^{21} -193.746 q^{22} +23.0000 q^{23} +18.5843 q^{24} -80.7667 q^{25} +231.048 q^{26} -147.413 q^{27} +11.5123 q^{28} -29.0000 q^{29} -91.0719 q^{30} -98.9570 q^{31} +237.854 q^{32} +181.183 q^{33} -102.145 q^{34} +11.5261 q^{35} -94.2919 q^{36} +92.1894 q^{37} +207.453 q^{38} -216.066 q^{39} +34.5402 q^{40} -323.644 q^{41} -23.7312 q^{42} -169.785 q^{43} +336.336 q^{44} -94.4054 q^{45} -88.0117 q^{46} -304.648 q^{47} -261.284 q^{48} -339.997 q^{49} +309.061 q^{50} +95.5220 q^{51} -401.091 q^{52} +515.744 q^{53} +564.091 q^{54} +336.740 q^{55} +9.00035 q^{56} -194.001 q^{57} +110.971 q^{58} +685.641 q^{59} +158.097 q^{60} -88.8582 q^{61} +378.668 q^{62} -24.5998 q^{63} -326.045 q^{64} -401.573 q^{65} -693.314 q^{66} -18.0566 q^{67} +177.320 q^{68} +82.3048 q^{69} -44.1059 q^{70} +225.840 q^{71} -73.7177 q^{72} +751.524 q^{73} -352.771 q^{74} -289.021 q^{75} -360.130 q^{76} +87.7465 q^{77} +826.799 q^{78} -604.274 q^{79} -485.613 q^{80} -144.261 q^{81} +1238.45 q^{82} -556.713 q^{83} +41.1964 q^{84} +177.534 q^{85} +649.700 q^{86} -103.776 q^{87} +262.948 q^{88} -262.661 q^{89} +361.251 q^{90} -104.640 q^{91} +152.785 q^{92} -354.114 q^{93} +1165.77 q^{94} -360.563 q^{95} +851.152 q^{96} -1471.91 q^{97} +1301.03 q^{98} -718.691 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−3.82659	−1.35291	−0.676453	−	0.736486i	$-0.736484\pi$
$2$	−3.82659	−1.35291	−0.676453	+	0.736486i	$0.736484\pi$
$3$	3.57847	0.688677	0.344338	−	0.938846i	$-0.388103\pi$
$3$	3.57847	0.688677	0.344338	+	0.938846i	$0.388103\pi$
$4$	6.64282	0.830352
$5$	6.65081	0.594867	0.297433	−	0.954743i	$-0.403869\pi$
$5$	6.65081	0.594867	0.297433	+	0.954743i	$0.403869\pi$
$6$	−13.6933	−0.931714
$7$	1.73304	0.0935756	0.0467878	−	0.998905i	$-0.485102\pi$
$7$	1.73304	0.0935756	0.0467878	+	0.998905i	$0.485102\pi$
$8$	5.19338	0.229517
$9$	−14.1946	−0.525724
$10$	−25.4500	−0.804798
$11$	50.6314	1.38781	0.693907	−	0.720065i	$-0.255888\pi$
$11$	50.6314	1.38781	0.693907	+	0.720065i	$0.255888\pi$
$12$	23.7711	0.571844
$13$	−60.3796	−1.28818	−0.644088	−	0.764952i	$-0.722763\pi$
$13$	−60.3796	−1.28818	−0.644088	+	0.764952i	$0.722763\pi$
$14$	−6.63165	−0.126599
$15$	23.7997	0.409671
$16$	−73.0155	−1.14087
$17$	26.6935	0.380831	0.190416	−	0.981704i	$-0.439016\pi$
$17$	26.6935	0.380831	0.190416	+	0.981704i	$0.439016\pi$
$18$	54.3168	0.711255
$19$	−54.2134	−0.654601	−0.327300	−	0.944920i	$-0.606139\pi$
$19$	−54.2134	−0.654601	−0.327300	+	0.944920i	$0.606139\pi$
$20$	44.1802	0.493949
$21$	6.20164	0.0644433
$22$	−193.746	−1.87758
$23$	23.0000	0.208514
$23$	23.0000	0.208514
$24$	18.5843	0.158063
$25$	−80.7667	−0.646133
$26$	231.048	1.74278
$27$	−147.413	−1.05073
$28$	11.5123	0.0777007
$29$	−29.0000	−0.185695
$29$	−29.0000	−0.185695
$30$	−91.0719	−0.554246
$31$	−98.9570	−0.573329	−0.286664	−	0.958031i	$-0.592546\pi$
$31$	−98.9570	−0.573329	−0.286664	+	0.958031i	$0.592546\pi$
$32$	237.854	1.31397
$33$	181.183	0.955755
$34$	−102.145	−0.515229
$35$	11.5261	0.0556650
$36$	−94.2919	−0.436537
$37$	92.1894	0.409617	0.204809	−	0.978802i	$-0.434343\pi$
$37$	92.1894	0.409617	0.204809	+	0.978802i	$0.434343\pi$
$38$	207.453	0.885613
$39$	−216.066	−0.887137
$40$	34.5402	0.136532
$41$	−323.644	−1.23280	−0.616398	−	0.787435i	$-0.711409\pi$
$41$	−323.644	−1.23280	−0.616398	+	0.787435i	$0.711409\pi$
$42$	−23.7312	−0.0871857
$43$	−169.785	−0.602140	−0.301070	−	0.953602i	$-0.597344\pi$
$43$	−169.785	−0.602140	−0.301070	+	0.953602i	$0.597344\pi$
$44$	336.336	1.15237
$45$	−94.4054	−0.312736
$46$	−88.0117	−0.282100
$47$	−304.648	−0.945480	−0.472740	−	0.881202i	$-0.656735\pi$
$47$	−304.648	−0.945480	−0.472740	+	0.881202i	$0.656735\pi$
$48$	−261.284	−0.785689
$49$	−339.997	−0.991244
$50$	309.061	0.874157
$51$	95.5220	0.262270
$52$	−401.091	−1.06964
$53$	515.744	1.33666	0.668329	−	0.743866i	$-0.267010\pi$
$53$	515.744	1.33666	0.668329	+	0.743866i	$0.267010\pi$
$54$	564.091	1.42154
$55$	336.740	0.825565
$56$	9.00035	0.0214772
$57$	−194.001	−0.450808
$58$	110.971	0.251228
$59$	685.641	1.51293	0.756465	−	0.654035i	$-0.226925\pi$
$59$	685.641	1.51293	0.756465	+	0.654035i	$0.226925\pi$
$60$	158.097	0.340171
$61$	−88.8582	−0.186510	−0.0932551	−	0.995642i	$-0.529727\pi$
$61$	−88.8582	−0.186510	−0.0932551	+	0.995642i	$0.529727\pi$
$62$	378.668	0.775660
$63$	−24.5998	−0.0491950
$64$	−326.045	−0.636807
$65$	−401.573	−0.766293
$66$	−693.314	−1.29305
$67$	−18.0566	−0.0329248	−0.0164624	−	0.999864i	$-0.505240\pi$
$67$	−18.0566	−0.0329248	−0.0164624	+	0.999864i	$0.505240\pi$
$68$	177.320	0.316224
$69$	82.3048	0.143599
$70$	−44.1059	−0.0753095
$71$	225.840	0.377497	0.188749	−	0.982025i	$-0.439557\pi$
$71$	225.840	0.377497	0.188749	+	0.982025i	$0.439557\pi$
$72$	−73.7177	−0.120663
$73$	751.524	1.20492	0.602460	−	0.798149i	$-0.294187\pi$
$73$	751.524	1.20492	0.602460	+	0.798149i	$0.294187\pi$
$74$	−352.771	−0.554173
$75$	−289.021	−0.444977
$76$	−360.130	−0.543549
$77$	87.7465	0.129865
$78$	826.799	1.20021
$79$	−604.274	−0.860584	−0.430292	−	0.902690i	$-0.641589\pi$
$79$	−604.274	−0.860584	−0.430292	+	0.902690i	$0.641589\pi$
$80$	−485.613	−0.678664
$81$	−144.261	−0.197889
$82$	1238.45	1.66786
$83$	−556.713	−0.736231	−0.368115	−	0.929780i	$-0.619997\pi$
$83$	−556.713	−0.736231	−0.368115	+	0.929780i	$0.619997\pi$
$84$	41.1964	0.0535107
$85$	177.534	0.226544
$86$	649.700	0.814639
$87$	−103.776	−0.127884
$88$	262.948	0.318527
$89$	−262.661	−0.312831	−0.156416	−	0.987691i	$-0.549994\pi$
$89$	−262.661	−0.312831	−0.156416	+	0.987691i	$0.549994\pi$
$90$	361.251	0.423102
$91$	−104.640	−0.120542
$92$	152.785	0.173140
$93$	−354.114	−0.394838
$94$	1165.77	1.27914
$95$	−360.563	−0.389400
$96$	851.152	0.904899
$97$	−1471.91	−1.54072	−0.770359	−	0.637611i	$-0.779923\pi$
$97$	−1471.91	−1.54072	−0.770359	+	0.637611i	$0.779923\pi$
$98$	1301.03	1.34106
$99$	−718.691	−0.729608
$100$	−536.518	−0.536518
$101$	620.051	0.610865	0.305432	−	0.952214i	$-0.401199\pi$
$101$	620.051	0.610865	0.305432	+	0.952214i	$0.401199\pi$
$102$	−365.524	−0.354826
$103$	−495.074	−0.473603	−0.236801	−	0.971558i	$-0.576099\pi$
$103$	−495.074	−0.473603	−0.236801	+	0.971558i	$0.576099\pi$
$104$	−313.574	−0.295658
$105$	41.2460	0.0383352
$106$	−1973.54	−1.80837
$107$	−264.955	−0.239384	−0.119692	−	0.992811i	$-0.538191\pi$
$107$	−264.955	−0.239384	−0.119692	+	0.992811i	$0.538191\pi$
$108$	−979.241	−0.872477
$109$	1467.04	1.28915	0.644574	−	0.764542i	$-0.277035\pi$
$109$	1467.04	1.28915	0.644574	+	0.764542i	$0.277035\pi$
$110$	−1288.57	−1.11691
$111$	329.897	0.282094
$112$	−126.539	−0.106757
$113$	−742.440	−0.618078	−0.309039	−	0.951049i	$-0.600007\pi$
$113$	−742.440	−0.618078	−0.309039	+	0.951049i	$0.600007\pi$
$114$	742.363	0.609901
$115$	152.969	0.124038
$116$	−192.642	−0.154193
$117$	857.062	0.677225
$118$	−2623.67	−2.04685
$119$	46.2611	0.0356365
$120$	123.601	0.0940264
$121$	1232.54	0.926028
$122$	340.024	0.252331
$123$	−1158.15	−0.848998
$124$	−657.353	−0.476065
$125$	−1368.52	−0.979230
$126$	94.1334	0.0665561
$127$	−829.667	−0.579694	−0.289847	−	0.957073i	$-0.593604\pi$
$127$	−829.667	−0.579694	−0.289847	+	0.957073i	$0.593604\pi$
$128$	−655.186	−0.452428
$129$	−607.572	−0.414680
$130$	1536.66	1.03672
$131$	−1381.62	−0.921468	−0.460734	−	0.887538i	$-0.652414\pi$
$131$	−1381.62	−0.921468	−0.460734	+	0.887538i	$0.652414\pi$
$132$	1203.57	0.793614
$133$	−93.9542	−0.0612546
$134$	69.0952	0.0445441
$135$	−980.419	−0.625045
$136$	138.630	0.0874073
$137$	−1951.39	−1.21693	−0.608463	−	0.793582i	$-0.708214\pi$
$137$	−1951.39	−1.21693	−0.608463	+	0.793582i	$0.708214\pi$
$138$	−314.947	−0.194276
$139$	−187.688	−0.114529	−0.0572643	−	0.998359i	$-0.518238\pi$
$139$	−187.688	−0.114529	−0.0572643	+	0.998359i	$0.518238\pi$
$140$	76.5661	0.0462216
$141$	−1090.17	−0.651130
$142$	−864.198	−0.510718
$143$	−3057.11	−1.78775
$144$	1036.42	0.599782
$145$	−192.874	−0.110464
$146$	−2875.78	−1.63014
$147$	−1216.67	−0.682646
$148$	612.397	0.340127
$149$	−1772.44	−0.974526	−0.487263	−	0.873255i	$-0.662005\pi$
$149$	−1772.44	−0.974526	−0.487263	+	0.873255i	$0.662005\pi$
$150$	1105.97	0.602012
$151$	−1937.44	−1.04415	−0.522075	−	0.852900i	$-0.674842\pi$
$151$	−1937.44	−1.04415	−0.522075	+	0.852900i	$0.674842\pi$
$152$	−281.551	−0.150242
$153$	−378.903	−0.200212
$154$	−335.770	−0.175696
$155$	−658.144	−0.341054
$156$	−1435.29	−0.736636
$157$	1787.37	0.908585	0.454293	−	0.890853i	$-0.349892\pi$
$157$	1787.37	0.908585	0.454293	+	0.890853i	$0.349892\pi$
$158$	2312.31	1.16429
$159$	1845.57	0.920525
$160$	1581.92	0.781636
$161$	39.8600	0.0195119
$162$	552.029	0.267725
$163$	−2827.37	−1.35863	−0.679316	−	0.733846i	$-0.737723\pi$
$163$	−2827.37	−1.35863	−0.679316	+	0.733846i	$0.737723\pi$
$164$	−2149.91	−1.02366
$165$	1205.01	0.568547
$166$	2130.31	0.996051
$167$	−2619.55	−1.21381	−0.606906	−	0.794774i	$-0.707590\pi$
$167$	−2619.55	−1.21381	−0.606906	+	0.794774i	$0.707590\pi$
$168$	32.2075	0.0147908
$169$	1448.69	0.659397
$170$	−679.350	−0.306493
$171$	769.536	0.344140
$172$	−1127.85	−0.499989
$173$	−328.298	−0.144278	−0.0721388	−	0.997395i	$-0.522982\pi$
$173$	−328.298	−0.144278	−0.0721388	+	0.997395i	$0.522982\pi$
$174$	397.107	0.173015
$175$	−139.972	−0.0604623
$176$	−3696.88	−1.58331
$177$	2453.54	1.04192
$178$	1005.10	0.423231
$179$	−2549.39	−1.06453	−0.532263	−	0.846579i	$-0.678658\pi$
$179$	−2549.39	−1.06453	−0.532263	+	0.846579i	$0.678658\pi$
$180$	−627.118	−0.259681
$181$	−1087.00	−0.446388	−0.223194	−	0.974774i	$-0.571648\pi$
$181$	−1087.00	−0.446388	−0.223194	+	0.974774i	$0.571648\pi$
$182$	400.416	0.163082
$183$	−317.976	−0.128445
$184$	119.448	0.0478576
$185$	613.134	0.243668
$186$	1355.05	0.534179
$187$	1351.53	0.528523
$188$	−2023.72	−0.785081
$189$	−255.474	−0.0983227
$190$	1379.73	0.526822
$191$	−1262.02	−0.478097	−0.239049	−	0.971008i	$-0.576836\pi$
$191$	−1262.02	−0.478097	−0.239049	+	0.971008i	$0.576836\pi$
$192$	−1166.74	−0.438554
$193$	2429.69	0.906183	0.453091	−	0.891464i	$-0.350321\pi$
$193$	2429.69	0.906183	0.453091	+	0.891464i	$0.350321\pi$
$194$	5632.39	2.08445
$195$	−1437.02	−0.527728
$196$	−2258.54	−0.823082
$197$	2263.80	0.818727	0.409364	−	0.912371i	$-0.365751\pi$
$197$	2263.80	0.818727	0.409364	+	0.912371i	$0.365751\pi$
$198$	2750.14	0.987090
$199$	−3512.76	−1.25132	−0.625661	−	0.780095i	$-0.715171\pi$
$199$	−3512.76	−1.25132	−0.625661	+	0.780095i	$0.715171\pi$
$200$	−419.452	−0.148299
$201$	−64.6149	−0.0226745
$202$	−2372.68	−0.826442
$203$	−50.2583	−0.0173765
$204$	634.535	0.217776
$205$	−2152.49	−0.733349
$206$	1894.45	0.640739
$207$	−326.475	−0.109621
$208$	4408.65	1.46964
$209$	−2744.90	−0.908464
$210$	−157.832	−0.0518639
$211$	2132.12	0.695645	0.347823	−	0.937560i	$-0.386921\pi$
$211$	2132.12	0.695645	0.347823	+	0.937560i	$0.386921\pi$
$212$	3425.99	1.10990
$213$	808.162	0.259973
$214$	1013.87	0.323864
$215$	−1129.21	−0.358193
$216$	−765.574	−0.241161
$217$	−171.497	−0.0536496
$218$	−5613.77	−1.74409
$219$	2689.30	0.829801
$220$	2236.91	0.685510
$221$	−1611.74	−0.490578
$222$	−1262.38	−0.381646
$223$	−456.359	−0.137041	−0.0685203	−	0.997650i	$-0.521828\pi$
$223$	−456.359	−0.137041	−0.0685203	+	0.997650i	$0.521828\pi$
$224$	412.211	0.122955
$225$	1146.45	0.339688
$226$	2841.02	0.836201
$227$	2971.84	0.868934	0.434467	−	0.900688i	$-0.356937\pi$
$227$	2971.84	0.868934	0.434467	+	0.900688i	$0.356937\pi$
$228$	−1288.71	−0.374330
$229$	−4482.75	−1.29357	−0.646787	−	0.762671i	$-0.723888\pi$
$229$	−4482.75	−1.29357	−0.646787	+	0.762671i	$0.723888\pi$
$230$	−585.349	−0.167812
$231$	313.998	0.0894353
$232$	−150.608	−0.0426202
$233$	3428.59	0.964011	0.482005	−	0.876168i	$-0.339909\pi$
$233$	3428.59	0.964011	0.482005	+	0.876168i	$0.339909\pi$
$234$	−3279.63	−0.916222
$235$	−2026.16	−0.562434
$236$	4554.59	1.25626
$237$	−2162.38	−0.592664
$238$	−177.022	−0.0482128
$239$	579.043	0.156716	0.0783581	−	0.996925i	$-0.475032\pi$
$239$	579.043	0.156716	0.0783581	+	0.996925i	$0.475032\pi$
$240$	−1737.75	−0.467380
$241$	−1461.24	−0.390567	−0.195284	−	0.980747i	$-0.562563\pi$
$241$	−1461.24	−0.390567	−0.195284	+	0.980747i	$0.562563\pi$
$242$	−4716.44	−1.25283
$243$	3463.93	0.914449
$244$	−590.269	−0.154869
$245$	−2261.25	−0.589658
$246$	4431.76	1.14861
$247$	3273.38	0.843241
$248$	−513.921	−0.131589
$249$	−1992.18	−0.507025
$250$	5236.75	1.32481
$251$	4545.21	1.14299	0.571496	−	0.820605i	$-0.306363\pi$
$251$	4545.21	1.14299	0.571496	+	0.820605i	$0.306363\pi$
$252$	−163.412	−0.0408492
$253$	1164.52	0.289379
$254$	3174.80	0.784270
$255$	635.299	0.156016
$256$	5115.49	1.24890
$257$	2696.39	0.654461	0.327230	−	0.944945i	$-0.393885\pi$
$257$	2696.39	0.654461	0.327230	+	0.944945i	$0.393885\pi$
$258$	2324.93	0.561023
$259$	159.768	0.0383302
$260$	−2667.58	−0.636293
$261$	411.642	0.0976246
$262$	5286.88	1.24666
$263$	3068.79	0.719505	0.359753	−	0.933048i	$-0.382861\pi$
$263$	3068.79	0.719505	0.359753	+	0.933048i	$0.382861\pi$
$264$	940.952	0.219362
$265$	3430.12	0.795134
$266$	359.525	0.0828717
$267$	−939.924	−0.215440
$268$	−119.947	−0.0273392
$269$	4831.84	1.09518	0.547588	−	0.836748i	$-0.315546\pi$
$269$	4831.84	1.09518	0.547588	+	0.836748i	$0.315546\pi$
$270$	3751.67	0.845627
$271$	2738.43	0.613829	0.306915	−	0.951737i	$-0.400703\pi$
$271$	2738.43	0.613829	0.306915	+	0.951737i	$0.400703\pi$
$272$	−1949.04	−0.434478
$273$	−374.453	−0.0830143
$274$	7467.19	1.64639
$275$	−4089.33	−0.896713
$276$	546.736	0.119238
$277$	5891.03	1.27782	0.638912	−	0.769280i	$-0.279385\pi$
$277$	5891.03	1.27782	0.638912	+	0.769280i	$0.279385\pi$
$278$	718.205	0.154946
$279$	1404.65	0.301413
$280$	59.8596	0.0127761
$281$	−2672.80	−0.567424	−0.283712	−	0.958910i	$-0.591566\pi$
$281$	−2672.80	−0.567424	−0.283712	+	0.958910i	$0.591566\pi$
$282$	4171.66	0.880917
$283$	−2409.97	−0.506211	−0.253106	−	0.967439i	$-0.581452\pi$
$283$	−2409.97	−0.506211	−0.253106	+	0.967439i	$0.581452\pi$
$284$	1500.22	0.313456
$285$	−1290.26	−0.268171
$286$	11698.3	2.41865
$287$	−560.888	−0.115360
$288$	−3376.23	−0.690785
$289$	−4200.45	−0.854967
$290$	738.049	0.149447
$291$	−5267.18	−1.06106
$292$	4992.24	1.00051
$293$	−2376.98	−0.473940	−0.236970	−	0.971517i	$-0.576154\pi$
$293$	−2376.98	−0.473940	−0.236970	+	0.971517i	$0.576154\pi$
$294$	4655.69	0.923556
$295$	4560.07	0.899992
$296$	478.774	0.0940141
$297$	−7463.76	−1.45822
$298$	6782.43	1.31844
$299$	−1388.73	−0.268603
$300$	−1919.91	−0.369488
$301$	−294.246	−0.0563456
$302$	7413.80	1.41264
$303$	2218.83	0.420688
$304$	3958.42	0.746812
$305$	−590.979	−0.110949
$306$	1449.91	0.270868
$307$	−4113.44	−0.764711	−0.382355	−	0.924015i	$-0.624887\pi$
$307$	−4113.44	−0.764711	−0.382355	+	0.924015i	$0.624887\pi$
$308$	582.884	0.107834
$309$	−1771.61	−0.326159
$310$	2518.45	0.461414
$311$	5094.09	0.928809	0.464404	−	0.885623i	$-0.346268\pi$
$311$	5094.09	0.928809	0.464404	+	0.885623i	$0.346268\pi$
$312$	−1122.11	−0.203613
$313$	3339.80	0.603121	0.301560	−	0.953447i	$-0.402493\pi$
$313$	3339.80	0.603121	0.301560	+	0.953447i	$0.402493\pi$
$314$	−6839.55	−1.22923
$315$	−163.609	−0.0292644
$316$	−4014.08	−0.714588
$317$	−9127.87	−1.61726	−0.808631	−	0.588316i	$-0.799791\pi$
$317$	−9127.87	−1.61726	−0.808631	+	0.588316i	$0.799791\pi$
$318$	−7062.26	−1.24538
$319$	−1468.31	−0.257711
$320$	−2168.47	−0.378815
$321$	−948.132	−0.164858
$322$	−152.528	−0.0263977
$323$	−1447.15	−0.249292
$324$	−958.302	−0.164318
$325$	4876.66	0.832333
$326$	10819.2	1.83810
$327$	5249.76	0.887805
$328$	−1680.80	−0.282948
$329$	−527.969	−0.0884738
$330$	−4611.10	−0.769190
$331$	6360.16	1.05615	0.528075	−	0.849198i	$-0.322914\pi$
$331$	6360.16	1.05615	0.528075	+	0.849198i	$0.322914\pi$
$332$	−3698.14	−0.611331
$333$	−1308.59	−0.215346
$334$	10023.9	1.64217
$335$	−120.091	−0.0195859
$336$	−452.816	−0.0735212
$337$	−4150.65	−0.670921	−0.335460	−	0.942054i	$-0.608892\pi$
$337$	−4150.65	−0.670921	−0.335460	+	0.942054i	$0.608892\pi$
$338$	−5543.57	−0.892101
$339$	−2656.80	−0.425656
$340$	1179.32	0.188111
$341$	−5010.34	−0.795674
$342$	−2944.70	−0.465588
$343$	−1183.66	−0.186332
$344$	−881.760	−0.138201
$345$	547.394	0.0854223
$346$	1256.26	0.195194
$347$	−593.240	−0.0917775	−0.0458888	−	0.998947i	$-0.514612\pi$
$347$	−593.240	−0.0917775	−0.0458888	+	0.998947i	$0.514612\pi$
$348$	−689.363	−0.106189
$349$	−5206.17	−0.798510	−0.399255	−	0.916840i	$-0.630731\pi$
$349$	−5206.17	−0.798510	−0.399255	+	0.916840i	$0.630731\pi$
$350$	535.617	0.0817997
$351$	8900.76	1.35353
$352$	12042.9	1.82354
$353$	11004.2	1.65919	0.829594	−	0.558367i	$-0.188572\pi$
$353$	11004.2	1.65919	0.829594	+	0.558367i	$0.188572\pi$
$354$	−9388.72	−1.40962
$355$	1502.02	0.224560
$356$	−1744.81	−0.259760
$357$	165.544	0.0245420
$358$	9755.46	1.44020
$359$	−3681.61	−0.541248	−0.270624	−	0.962685i	$-0.587230\pi$
$359$	−3681.61	−0.541248	−0.270624	+	0.962685i	$0.587230\pi$
$360$	−490.283	−0.0717782
$361$	−3919.91	−0.571498
$362$	4159.52	0.603921
$363$	4410.62	0.637734
$364$	−695.108	−0.100092
$365$	4998.24	0.716767
$366$	1216.77	0.173774
$367$	−7879.00	−1.12066	−0.560328	−	0.828271i	$-0.689325\pi$
$367$	−7879.00	−1.12066	−0.560328	+	0.828271i	$0.689325\pi$
$368$	−1679.36	−0.237887
$369$	4593.98	0.648111
$370$	−2346.22	−0.329659
$371$	893.807	0.125079
$372$	−2352.32	−0.327855
$373$	−5341.03	−0.741415	−0.370708	−	0.928750i	$-0.620885\pi$
$373$	−5341.03	−0.741415	−0.370708	+	0.928750i	$0.620885\pi$
$374$	−5171.77	−0.715042
$375$	−4897.19	−0.674373
$376$	−1582.15	−0.217004
$377$	1751.01	0.239208
$378$	977.595	0.133021
$379$	11451.0	1.55198	0.775989	−	0.630746i	$-0.217251\pi$
$379$	11451.0	1.55198	0.775989	+	0.630746i	$0.217251\pi$
$380$	−2395.16	−0.323339
$381$	−2968.94	−0.399221
$382$	4829.24	0.646820
$383$	−48.5940	−0.00648312	−0.00324156	−	0.999995i	$-0.501032\pi$
$383$	−48.5940	−0.00648312	−0.00324156	+	0.999995i	$0.501032\pi$
$384$	−2344.56	−0.311577
$385$	583.586	0.0772527
$386$	−9297.45	−1.22598
$387$	2410.03	0.316560
$388$	−9777.62	−1.27934
$389$	4764.66	0.621022	0.310511	−	0.950570i	$-0.399500\pi$
$389$	4764.66	0.621022	0.310511	+	0.950570i	$0.399500\pi$
$390$	5498.88	0.713966
$391$	613.951	0.0794088
$392$	−1765.73	−0.227507
$393$	−4944.07	−0.634594
$394$	−8662.66	−1.10766
$395$	−4018.91	−0.511933
$396$	−4774.14	−0.605832
$397$	−458.395	−0.0579501	−0.0289750	−	0.999580i	$-0.509224\pi$
$397$	−458.395	−0.0579501	−0.0289750	+	0.999580i	$0.509224\pi$
$398$	13441.9	1.69292
$399$	−336.212	−0.0421846
$400$	5897.22	0.737152
$401$	−1373.17	−0.171004	−0.0855021	−	0.996338i	$-0.527249\pi$
$401$	−1373.17	−0.171004	−0.0855021	+	0.996338i	$0.527249\pi$
$402$	247.255	0.0306765
$403$	5974.98	0.738548
$404$	4118.89	0.507233
$405$	−959.455	−0.117718
$406$	192.318	0.0235088
$407$	4667.68	0.568473
$408$	496.082	0.0601954
$409$	−1620.06	−0.195860	−0.0979301	−	0.995193i	$-0.531222\pi$
$409$	−1620.06	−0.195860	−0.0979301	+	0.995193i	$0.531222\pi$
$410$	8236.72	0.992152
$411$	−6983.00	−0.838069
$412$	−3288.69	−0.393257
$413$	1188.25	0.141573
$414$	1249.29	0.148307
$415$	−3702.59	−0.437959
$416$	−14361.5	−1.69262
$417$	−671.635	−0.0788732
$418$	10503.6	1.22907
$419$	−1069.87	−0.124741	−0.0623706	−	0.998053i	$-0.519866\pi$
$419$	−1069.87	−0.124741	−0.0623706	+	0.998053i	$0.519866\pi$
$420$	273.990	0.0318317
$421$	13558.3	1.56958	0.784789	−	0.619762i	$-0.212771\pi$
$421$	13558.3	1.56958	0.784789	+	0.619762i	$0.212771\pi$
$422$	−8158.76	−0.941142
$423$	4324.35	0.497062
$424$	2678.45	0.306786
$425$	−2155.95	−0.246068
$426$	−3092.51	−0.351719
$427$	−153.995	−0.0174528
$428$	−1760.05	−0.198773
$429$	−10939.8	−1.23118
$430$	4321.03	0.484602
$431$	−7943.48	−0.887759	−0.443879	−	0.896087i	$-0.646398\pi$
$431$	−7943.48	−0.887759	−0.443879	+	0.896087i	$0.646398\pi$
$432$	10763.5	1.19874
$433$	7530.06	0.835732	0.417866	−	0.908509i	$-0.362778\pi$
$433$	7530.06	0.835732	0.417866	+	0.908509i	$0.362778\pi$
$434$	656.248	0.0725828
$435$	−690.192	−0.0760740
$436$	9745.29	1.07045
$437$	−1246.91	−0.136494
$438$	−10290.9	−1.12264
$439$	6604.71	0.718053	0.359027	−	0.933327i	$-0.383109\pi$
$439$	6604.71	0.718053	0.359027	+	0.933327i	$0.383109\pi$
$440$	1748.82	0.189481
$441$	4826.10	0.521121
$442$	6167.49	0.663705
$443$	−5171.95	−0.554688	−0.277344	−	0.960771i	$-0.589454\pi$
$443$	−5171.95	−0.554688	−0.277344	+	0.960771i	$0.589454\pi$
$444$	2191.44	0.234237
$445$	−1746.91	−0.186093
$446$	1746.30	0.185403
$447$	−6342.64	−0.671133
$448$	−565.051	−0.0595896
$449$	4487.75	0.471692	0.235846	−	0.971790i	$-0.424214\pi$
$449$	4487.75	0.471692	0.235846	+	0.971790i	$0.424214\pi$
$450$	−4386.99	−0.459566
$451$	−16386.5	−1.71089
$452$	−4931.89	−0.513223
$453$	−6933.07	−0.719082
$454$	−11372.0	−1.17559
$455$	−695.944	−0.0717063
$456$	−1007.52	−0.103468
$457$	713.057	0.0729877	0.0364939	−	0.999334i	$-0.488381\pi$
$457$	713.057	0.0729877	0.0364939	+	0.999334i	$0.488381\pi$
$458$	17153.7	1.75008
$459$	−3934.99	−0.400151
$460$	1016.14	0.102996
$461$	−10857.3	−1.09690	−0.548452	−	0.836182i	$-0.684783\pi$
$461$	−10857.3	−1.09690	−0.548452	+	0.836182i	$0.684783\pi$
$462$	−1201.54	−0.120998
$463$	227.834	0.0228689	0.0114345	−	0.999935i	$-0.496360\pi$
$463$	227.834	0.0228689	0.0114345	+	0.999935i	$0.496360\pi$
$464$	2117.45	0.211854
$465$	−2355.15	−0.234876
$466$	−13119.8	−1.30422
$467$	12085.8	1.19757	0.598784	−	0.800911i	$-0.295651\pi$
$467$	12085.8	1.19757	0.598784	+	0.800911i	$0.295651\pi$
$468$	5693.31	0.562336
$469$	−31.2928	−0.00308096
$470$	7753.29	0.760920
$471$	6396.06	0.625721
$472$	3560.79	0.347243
$473$	−8596.48	−0.835659
$474$	8274.53	0.801818
$475$	4378.64	0.422959
$476$	307.304	0.0295909
$477$	−7320.76	−0.702714
$478$	−2215.76	−0.212022
$479$	−2547.42	−0.242995	−0.121498	−	0.992592i	$-0.538770\pi$
$479$	−2547.42	−0.242995	−0.121498	+	0.992592i	$0.538770\pi$
$480$	5660.85	0.538295
$481$	−5566.36	−0.527659
$482$	5591.57	0.528400
$483$	142.638	0.0134374
$484$	8187.56	0.768930
$485$	−9789.39	−0.916522
$486$	−13255.0	−1.23716
$487$	−8091.15	−0.752864	−0.376432	−	0.926444i	$-0.622849\pi$
$487$	−8091.15	−0.752864	−0.376432	+	0.926444i	$0.622849\pi$
$488$	−461.474	−0.0428073
$489$	−10117.7	−0.935658
$490$	8652.90	0.797751
$491$	19691.4	1.80990	0.904949	−	0.425520i	$-0.139909\pi$
$491$	19691.4	1.80990	0.904949	+	0.425520i	$0.139909\pi$
$492$	−7693.37	−0.704967
$493$	−774.113	−0.0707186
$494$	−12525.9	−1.14082
$495$	−4779.88	−0.434020
$496$	7225.39	0.654092
$497$	391.391	0.0353245
$498$	7623.26	0.685957
$499$	5734.91	0.514489	0.257244	−	0.966346i	$-0.417185\pi$
$499$	5734.91	0.514489	0.257244	+	0.966346i	$0.417185\pi$
$500$	−9090.80	−0.813106
$501$	−9373.96	−0.835924
$502$	−17392.7	−1.54636
$503$	−2989.45	−0.264996	−0.132498	−	0.991183i	$-0.542300\pi$
$503$	−2989.45	−0.264996	−0.132498	+	0.991183i	$0.542300\pi$
$504$	−127.756	−0.0112911
$505$	4123.84	0.363383
$506$	−4456.16	−0.391503
$507$	5184.11	0.454111
$508$	−5511.33	−0.481350
$509$	−19778.1	−1.72229	−0.861147	−	0.508355i	$-0.830254\pi$
$509$	−19778.1	−1.72229	−0.861147	+	0.508355i	$0.830254\pi$
$510$	−2431.03	−0.211074
$511$	1302.42	0.112751
$512$	−14333.4	−1.23721
$513$	7991.79	0.687809
$514$	−10318.0	−0.885423
$515$	−3292.64	−0.281731
$516$	−4035.99	−0.344331
$517$	−15424.8	−1.31215
$518$	−611.368	−0.0518571
$519$	−1174.80	−0.0993606
$520$	−2085.52	−0.175877
$521$	−12224.7	−1.02797	−0.513985	−	0.857799i	$-0.671831\pi$
$521$	−12224.7	−1.02797	−0.513985	+	0.857799i	$0.671831\pi$
$522$	−1575.19	−0.132077
$523$	−3371.73	−0.281903	−0.140952	−	0.990016i	$-0.545016\pi$
$523$	−3371.73	−0.281903	−0.140952	+	0.990016i	$0.545016\pi$
$524$	−9177.83	−0.765144
$525$	−500.886	−0.0416390
$526$	−11743.0	−0.973422
$527$	−2641.51	−0.218342
$528$	−13229.2	−1.09039
$529$	529.000	0.0434783
$530$	−13125.7	−1.07574
$531$	−9732.37	−0.795384
$532$	−624.121	−0.0508629
$533$	19541.5	1.58806
$534$	3596.71	0.291469
$535$	−1762.16	−0.142402
$536$	−93.7746	−0.00755680
$537$	−9122.90	−0.733114
$538$	−18489.5	−1.48167
$539$	−17214.5	−1.37566
$540$	−6512.75	−0.519008
$541$	7157.25	0.568788	0.284394	−	0.958708i	$-0.408208\pi$
$541$	7157.25	0.568788	0.284394	+	0.958708i	$0.408208\pi$
$542$	−10478.9	−0.830453
$543$	−3889.81	−0.307417
$544$	6349.16	0.500400
$545$	9757.02	0.766871
$546$	1432.88	0.112310
$547$	−17826.8	−1.39345	−0.696726	−	0.717337i	$-0.745361\pi$
$547$	−17826.8	−1.39345	−0.696726	+	0.717337i	$0.745361\pi$
$548$	−12962.8	−1.01048
$549$	1261.30	0.0980530
$550$	15648.2	1.21317
$551$	1572.19	0.121556
$552$	427.440	0.0329584
$553$	−1047.23	−0.0805296
$554$	−22542.6	−1.72878
$555$	2194.08	0.167808
$556$	−1246.78	−0.0950991
$557$	5668.64	0.431217	0.215609	−	0.976480i	$-0.430826\pi$
$557$	5668.64	0.431217	0.215609	+	0.976480i	$0.430826\pi$
$558$	−5375.03	−0.407783
$559$	10251.6	0.775663
$560$	−841.588	−0.0635064
$561$	4836.42	0.363982
$562$	10227.7	0.767670
$563$	7331.10	0.548790	0.274395	−	0.961617i	$-0.411522\pi$
$563$	7331.10	0.548790	0.274395	+	0.961617i	$0.411522\pi$
$564$	−7241.84	−0.540667
$565$	−4937.83	−0.367674
$566$	9221.97	0.684856
$567$	−250.011	−0.0185176
$568$	1172.87	0.0866420
$569$	18955.7	1.39660	0.698300	−	0.715806i	$-0.253940\pi$
$569$	18955.7	1.39660	0.698300	+	0.715806i	$0.253940\pi$
$570$	4937.32	0.362810
$571$	26882.3	1.97021	0.985106	−	0.171951i	$-0.0550070\pi$
$571$	26882.3	1.97021	0.985106	+	0.171951i	$0.0550070\pi$
$572$	−20307.8	−1.48446
$573$	−4516.10	−0.329254
$574$	2146.29	0.156071
$575$	−1857.63	−0.134728
$576$	4628.07	0.334785
$577$	−24816.2	−1.79049	−0.895246	−	0.445572i	$-0.853000\pi$
$577$	−24816.2	−1.79049	−0.895246	+	0.445572i	$0.853000\pi$
$578$	16073.4	1.15669
$579$	8694.59	0.624067
$580$	−1281.22	−0.0917241
$581$	−964.807	−0.0688932
$582$	20155.3	1.43551
$583$	26112.9	1.85503
$584$	3902.95	0.276550
$585$	5700.16	0.402859
$586$	9095.73	0.641196
$587$	−17217.2	−1.21061	−0.605307	−	0.795992i	$-0.706950\pi$
$587$	−17217.2	−1.21061	−0.605307	+	0.795992i	$0.706950\pi$
$588$	−8082.10	−0.566837
$589$	5364.80	0.375301
$590$	−17449.5	−1.21760
$591$	8100.95	0.563838
$592$	−6731.25	−0.467319
$593$	−5980.48	−0.414146	−0.207073	−	0.978325i	$-0.566394\pi$
$593$	−5980.48	−0.414146	−0.207073	+	0.978325i	$0.566394\pi$
$594$	28560.8	1.97283
$595$	307.674	0.0211990
$596$	−11774.0	−0.809200
$597$	−12570.3	−0.861756
$598$	5314.11	0.363395
$599$	27293.5	1.86174	0.930870	−	0.365351i	$-0.119051\pi$
$599$	27293.5	1.86174	0.930870	+	0.365351i	$0.119051\pi$
$600$	−1501.00	−0.102130
$601$	−20503.6	−1.39161	−0.695806	−	0.718229i	$-0.744953\pi$
$601$	−20503.6	−1.39161	−0.695806	+	0.718229i	$0.744953\pi$
$602$	1125.96	0.0762303
$603$	256.305	0.0173094
$604$	−12870.1	−0.867013
$605$	8197.42	0.550863
$606$	−8490.57	−0.569152
$607$	−2416.41	−0.161580	−0.0807900	−	0.996731i	$-0.525744\pi$
$607$	−2416.41	−0.161580	−0.0807900	+	0.996731i	$0.525744\pi$
$608$	−12894.9	−0.860124
$609$	−179.848	−0.0119668
$610$	2261.44	0.150103
$611$	18394.5	1.21794
$612$	−2516.98	−0.166247
$613$	10326.7	0.680408	0.340204	−	0.940352i	$-0.389504\pi$
$613$	10326.7	0.680408	0.340204	+	0.940352i	$0.389504\pi$
$614$	15740.4	1.03458
$615$	−7702.63	−0.505041
$616$	455.701	0.0298063
$617$	−16021.8	−1.04540	−0.522701	−	0.852516i	$-0.675075\pi$
$617$	−16021.8	−1.04540	−0.522701	+	0.852516i	$0.675075\pi$
$618$	6779.22	0.441262
$619$	5100.48	0.331188	0.165594	−	0.986194i	$-0.447046\pi$
$619$	5100.48	0.331188	0.165594	+	0.986194i	$0.447046\pi$
$620$	−4371.93	−0.283195
$621$	−3390.51	−0.219093
$622$	−19493.0	−1.25659
$623$	−455.203	−0.0292734
$624$	15776.2	1.01210
$625$	994.091	0.0636218
$626$	−12780.1	−0.815965
$627$	−9822.55	−0.625638
$628$	11873.2	0.754446
$629$	2460.86	0.155995
$630$	626.064	0.0395920
$631$	−23260.2	−1.46747	−0.733736	−	0.679434i	$-0.762225\pi$
$631$	−23260.2	−1.46747	−0.733736	+	0.679434i	$0.762225\pi$
$632$	−3138.22	−0.197519
$633$	7629.73	0.479075
$634$	34928.6	2.18800
$635$	−5517.96	−0.344841
$636$	12259.8	0.764361
$637$	20528.9	1.27690
$638$	5618.63	0.348658
$639$	−3205.70	−0.198459
$640$	−4357.52	−0.269135
$641$	22789.0	1.40423	0.702116	−	0.712062i	$-0.252239\pi$
$641$	22789.0	1.40423	0.702116	+	0.712062i	$0.252239\pi$
$642$	3628.12	0.223038
$643$	5706.01	0.349958	0.174979	−	0.984572i	$-0.444014\pi$
$643$	5706.01	0.349958	0.174979	+	0.984572i	$0.444014\pi$
$644$	264.783	0.0162017
$645$	−4040.85	−0.246679
$646$	5537.65	0.337269
$647$	−6165.96	−0.374666	−0.187333	−	0.982296i	$-0.559984\pi$
$647$	−6165.96	−0.374666	−0.187333	+	0.982296i	$0.559984\pi$
$648$	−749.203	−0.0454190
$649$	34715.0	2.09966
$650$	−18661.0	−1.12607
$651$	−613.696	−0.0369472
$652$	−18781.7	−1.12814
$653$	21127.6	1.26614	0.633069	−	0.774096i	$-0.281795\pi$
$653$	21127.6	1.26614	0.633069	+	0.774096i	$0.281795\pi$
$654$	−20088.7	−1.20112
$655$	−9188.87	−0.548151
$656$	23631.0	1.40646
$657$	−10667.5	−0.633456
$658$	2020.32	0.119697
$659$	3723.23	0.220085	0.110043	−	0.993927i	$-0.464901\pi$
$659$	3723.23	0.220085	0.110043	+	0.993927i	$0.464901\pi$
$660$	8004.70	0.472095
$661$	31776.0	1.86981	0.934903	−	0.354902i	$-0.115486\pi$
$661$	31776.0	1.86981	0.934903	+	0.354902i	$0.115486\pi$
$662$	−24337.7	−1.42887
$663$	−5767.58	−0.337849
$664$	−2891.22	−0.168978
$665$	−624.872	−0.0364383
$666$	5007.43	0.291342
$667$	−667.000	−0.0387202
$668$	−17401.2	−1.00789
$669$	−1633.07	−0.0943767
$670$	459.539	0.0264978
$671$	−4499.02	−0.258842
$672$	1475.08	0.0846764
$673$	31717.4	1.81667	0.908333	−	0.418247i	$-0.137355\pi$
$673$	31717.4	1.81667	0.908333	+	0.418247i	$0.137355\pi$
$674$	15882.9	0.907692
$675$	11906.1	0.678912
$676$	9623.42	0.547532
$677$	−18640.4	−1.05821	−0.529107	−	0.848555i	$-0.677473\pi$
$677$	−18640.4	−1.05821	−0.529107	+	0.848555i	$0.677473\pi$
$678$	10166.5	0.575872
$679$	−2550.88	−0.144174
$680$	922.000	0.0519957
$681$	10634.6	0.598414
$682$	19172.5	1.07647
$683$	6320.66	0.354104	0.177052	−	0.984201i	$-0.443344\pi$
$683$	6320.66	0.354104	0.177052	+	0.984201i	$0.443344\pi$
$684$	5111.89	0.285757
$685$	−12978.4	−0.723909
$686$	4529.40	0.252089
$687$	−16041.4	−0.890854
$688$	12397.0	0.686962
$689$	−31140.4	−1.72185
$690$	−2094.65	−0.115568
$691$	33809.7	1.86133	0.930666	−	0.365870i	$-0.119229\pi$
$691$	33809.7	1.86133	0.930666	+	0.365870i	$0.119229\pi$
$692$	−2180.82	−0.119801
$693$	−1245.52	−0.0682735
$694$	2270.09	0.124166
$695$	−1248.28	−0.0681293
$696$	−538.946	−0.0293516
$697$	−8639.19	−0.469487
$698$	19921.9	1.08031
$699$	12269.1	0.663892
$700$	−929.810	−0.0502050
$701$	4684.60	0.252403	0.126202	−	0.992005i	$-0.459721\pi$
$701$	4684.60	0.252403	0.126202	+	0.992005i	$0.459721\pi$
$702$	−34059.6	−1.83119
$703$	−4997.90	−0.268136
$704$	−16508.1	−0.883770
$705$	−7250.55	−0.387335
$706$	−42108.5	−2.24472
$707$	1074.57	0.0571620
$708$	16298.5	0.865160
$709$	17362.3	0.919684	0.459842	−	0.888001i	$-0.347906\pi$
$709$	17362.3	0.919684	0.459842	+	0.888001i	$0.347906\pi$
$710$	−5747.62	−0.303809
$711$	8577.40	0.452430
$712$	−1364.10	−0.0718001
$713$	−2276.01	−0.119547
$714$	−633.469	−0.0332030
$715$	−20332.2	−1.06347
$716$	−16935.1	−0.883931
$717$	2072.09	0.107927
$718$	14088.0	0.732258
$719$	−11995.1	−0.622174	−0.311087	−	0.950382i	$-0.600693\pi$
$719$	−11995.1	−0.622174	−0.311087	+	0.950382i	$0.600693\pi$
$720$	6893.06	0.356790
$721$	−857.984	−0.0443176
$722$	14999.9	0.773183
$723$	−5229.00	−0.268975
$724$	−7220.76	−0.370660
$725$	2342.23	0.119984
$726$	−16877.6	−0.862794
$727$	−28428.1	−1.45026	−0.725130	−	0.688612i	$-0.758220\pi$
$727$	−28428.1	−1.45026	−0.725130	+	0.688612i	$0.758220\pi$
$728$	−543.437	−0.0276664
$729$	16290.6	0.827649
$730$	−19126.3	−0.969718
$731$	−4532.17	−0.229314
$732$	−2112.26	−0.106655
$733$	1316.12	0.0663191	0.0331595	−	0.999450i	$-0.489443\pi$
$733$	1316.12	0.0663191	0.0331595	+	0.999450i	$0.489443\pi$
$734$	30149.7	1.51614
$735$	−8091.83	−0.406084
$736$	5470.63	0.273981
$737$	−914.231	−0.0456935
$738$	−17579.3	−0.876833
$739$	13324.7	0.663271	0.331635	−	0.943408i	$-0.392400\pi$
$739$	13324.7	0.663271	0.331635	+	0.943408i	$0.392400\pi$
$740$	4072.94	0.202330
$741$	11713.7	0.580720
$742$	−3420.24	−0.169219
$743$	5984.25	0.295479	0.147740	−	0.989026i	$-0.452800\pi$
$743$	5984.25	0.295479	0.147740	+	0.989026i	$0.452800\pi$
$744$	−1839.05	−0.0906221
$745$	−11788.2	−0.579713
$746$	20437.9	1.00306
$747$	7902.29	0.387055
$748$	8977.99	0.438861
$749$	−459.178	−0.0224005
$750$	18739.6	0.912363
$751$	−18331.5	−0.890712	−0.445356	−	0.895354i	$-0.646923\pi$
$751$	−18331.5	−0.890712	−0.445356	+	0.895354i	$0.646923\pi$
$752$	22244.1	1.07867
$753$	16264.9	0.787152
$754$	−6700.40	−0.323626
$755$	−12885.6	−0.621130
$756$	−1697.07	−0.0816425
$757$	−5585.52	−0.268176	−0.134088	−	0.990969i	$-0.542810\pi$
$757$	−5585.52	−0.268176	−0.134088	+	0.990969i	$0.542810\pi$
$758$	−43818.4	−2.09968
$759$	4167.21	0.199289
$760$	−1872.54	−0.0893740
$761$	4505.96	0.214640	0.107320	−	0.994225i	$-0.465773\pi$
$761$	4505.96	0.214640	0.107320	+	0.994225i	$0.465773\pi$
$762$	11360.9	0.540109
$763$	2542.45	0.120633
$764$	−8383.37	−0.396989
$765$	−2520.01	−0.119100
$766$	185.949	0.00877105
$767$	−41398.7	−1.94892
$768$	18305.6	0.860088
$769$	−4637.18	−0.217453	−0.108726	−	0.994072i	$-0.534677\pi$
$769$	−4637.18	−0.217453	−0.108726	+	0.994072i	$0.534677\pi$
$770$	−2233.15	−0.104516
$771$	9648.96	0.450712
$772$	16140.0	0.752451
$773$	−3706.72	−0.172473	−0.0862364	−	0.996275i	$-0.527484\pi$
$773$	−3706.72	−0.172473	−0.0862364	+	0.996275i	$0.527484\pi$
$774$	−9222.20	−0.428276
$775$	7992.43	0.370447
$776$	−7644.17	−0.353621
$777$	571.725	0.0263971
$778$	−18232.4	−0.840184
$779$	17545.8	0.806989
$780$	−9545.85	−0.438200
$781$	11434.6	0.523896
$782$	−2349.34	−0.107433
$783$	4274.99	0.195116
$784$	24825.0	1.13088
$785$	11887.5	0.540487
$786$	18918.9	0.858545
$787$	14920.8	0.675817	0.337908	−	0.941179i	$-0.390281\pi$
$787$	14920.8	0.675817	0.337908	+	0.941179i	$0.390281\pi$
$788$	15038.0	0.679832
$789$	10981.6	0.495506
$790$	15378.8	0.692597
$791$	−1286.68	−0.0578370
$792$	−3732.43	−0.167457
$793$	5365.22	0.240258
$794$	1754.09	0.0784010
$795$	12274.6	0.547590
$796$	−23334.6	−1.03904
$797$	−12506.5	−0.555837	−0.277918	−	0.960605i	$-0.589644\pi$
$797$	−12506.5	−0.555837	−0.277918	+	0.960605i	$0.589644\pi$
$798$	1286.55	0.0570718
$799$	−8132.14	−0.360068
$800$	−19210.6	−0.848999
$801$	3728.36	0.164463
$802$	5254.55	0.231352
$803$	38050.7	1.67221
$804$	−429.225	−0.0188279
$805$	265.101	0.0116070
$806$	−22863.8	−0.999186
$807$	17290.6	0.754222
$808$	3220.16	0.140204
$809$	−2251.56	−0.0978500	−0.0489250	−	0.998802i	$-0.515580\pi$
$809$	−2251.56	−0.0978500	−0.0489250	+	0.998802i	$0.515580\pi$
$810$	3671.44	0.159261
$811$	29509.8	1.27772	0.638859	−	0.769324i	$-0.279407\pi$
$811$	29509.8	1.27772	0.638859	+	0.769324i	$0.279407\pi$
$812$	−333.857	−0.0144287
$813$	9799.38	0.422730
$814$	−17861.3	−0.769090
$815$	−18804.3	−0.808205
$816$	−6974.59	−0.299215
$817$	9204.65	0.394161
$818$	6199.31	0.264980
$819$	1485.33	0.0633717
$820$	−14298.6	−0.608939
$821$	19789.0	0.841218	0.420609	−	0.907242i	$-0.361816\pi$
$821$	19789.0	0.841218	0.420609	+	0.907242i	$0.361816\pi$
$822$	26721.1	1.13383
$823$	27077.8	1.14687	0.573434	−	0.819252i	$-0.305611\pi$
$823$	27077.8	1.14687	0.573434	+	0.819252i	$0.305611\pi$
$824$	−2571.10	−0.108700
$825$	−14633.6	−0.617545
$826$	−4546.93	−0.191535
$827$	−12684.9	−0.533372	−0.266686	−	0.963783i	$-0.585929\pi$
$827$	−12684.9	−0.533372	−0.266686	+	0.963783i	$0.585929\pi$
$828$	−2168.71	−0.0910242
$829$	14479.2	0.606616	0.303308	−	0.952893i	$-0.401909\pi$
$829$	14479.2	0.606616	0.303308	+	0.952893i	$0.401909\pi$
$830$	14168.3	0.592517
$831$	21080.8	0.880008
$832$	19686.5	0.820320
$833$	−9075.71	−0.377497
$834$	2570.07	0.106708
$835$	−17422.1	−0.722056
$836$	−18233.9	−0.754345
$837$	14587.6	0.602414
$838$	4093.95	0.168763
$839$	39735.7	1.63508	0.817538	−	0.575874i	$-0.195338\pi$
$839$	39735.7	1.63508	0.817538	+	0.575874i	$0.195338\pi$
$840$	214.206	0.00879858
$841$	841.000	0.0344828
$842$	−51882.2	−2.12349
$843$	−9564.54	−0.390771
$844$	14163.3	0.577631
$845$	9635.00	0.392253
$846$	−16547.5	−0.672477
$847$	2136.05	0.0866536
$848$	−37657.3	−1.52495
$849$	−8624.00	−0.348616
$850$	8249.94	0.332907
$851$	2120.36	0.0854111
$852$	5368.47	0.215870
$853$	9185.52	0.368706	0.184353	−	0.982860i	$-0.440981\pi$
$853$	9185.52	0.368706	0.184353	+	0.982860i	$0.440981\pi$
$854$	589.277	0.0236120
$855$	5118.04	0.204717
$856$	−1376.01	−0.0549428
$857$	−26359.6	−1.05067	−0.525336	−	0.850895i	$-0.676060\pi$
$857$	−26359.6	−1.05067	−0.525336	+	0.850895i	$0.676060\pi$
$858$	41862.0	1.66567
$859$	−18038.9	−0.716508	−0.358254	−	0.933624i	$-0.616628\pi$
$859$	−18038.9	−0.716508	−0.358254	+	0.933624i	$0.616628\pi$
$860$	−7501.15	−0.297427
$861$	−2007.12	−0.0794454
$862$	30396.5	1.20105
$863$	−37723.0	−1.48796	−0.743978	−	0.668204i	$-0.767063\pi$
$863$	−37723.0	−1.48796	−0.743978	+	0.668204i	$0.767063\pi$
$864$	−35062.8	−1.38063
$865$	−2183.45	−0.0858260
$866$	−28814.5	−1.13067
$867$	−15031.2	−0.588796
$868$	−1139.22	−0.0445481
$869$	−30595.3	−1.19433
$870$	2641.08	0.102921
$871$	1090.25	0.0424129
$872$	7618.90	0.295881
$873$	20893.1	0.809993
$874$	4771.41	0.184663
$875$	−2371.70	−0.0916320
$876$	17864.6	0.689027
$877$	19054.5	0.733666	0.366833	−	0.930287i	$-0.380442\pi$
$877$	19054.5	0.733666	0.366833	+	0.930287i	$0.380442\pi$
$878$	−25273.5	−0.971458
$879$	−8505.94	−0.326392
$880$	−24587.3	−0.941860
$881$	−5052.41	−0.193212	−0.0966061	−	0.995323i	$-0.530799\pi$
$881$	−5052.41	−0.193212	−0.0966061	+	0.995323i	$0.530799\pi$
$882$	−18467.5	−0.705027
$883$	−1452.60	−0.0553610	−0.0276805	−	0.999617i	$-0.508812\pi$
$883$	−1452.60	−0.0553610	−0.0276805	+	0.999617i	$0.508812\pi$
$884$	−10706.5	−0.407352
$885$	16318.1	0.619803
$886$	19790.9	0.750440
$887$	32924.9	1.24635	0.623175	−	0.782083i	$-0.285843\pi$
$887$	32924.9	1.24635	0.623175	+	0.782083i	$0.285843\pi$
$888$	1713.28	0.0647453
$889$	−1437.85	−0.0542451
$890$	6684.71	0.251766
$891$	−7304.16	−0.274634
$892$	−3031.51	−0.113792
$893$	16516.0	0.618911
$894$	24270.7	0.907979
$895$	−16955.5	−0.633251
$896$	−1135.47	−0.0423362
$897$	−4969.53	−0.184981
$898$	−17172.8	−0.638155
$899$	2869.75	0.106465
$900$	7615.64	0.282061
$901$	13767.0	0.509042
$902$	62704.6	2.31467
$903$	−1052.95	−0.0388039
$904$	−3855.77	−0.141859
$905$	−7229.45	−0.265542
$906$	26530.0	0.972850
$907$	−43349.9	−1.58700	−0.793501	−	0.608569i	$-0.791744\pi$
$907$	−43349.9	−1.58700	−0.793501	+	0.608569i	$0.791744\pi$
$908$	19741.4	0.721521
$909$	−8801.35	−0.321147
$910$	2663.10	0.0970118
$911$	−37995.6	−1.38183	−0.690916	−	0.722935i	$-0.742793\pi$
$911$	−37995.6	−1.38183	−0.690916	+	0.722935i	$0.742793\pi$
$912$	14165.1	0.514312
$913$	−28187.2	−1.02175
$914$	−2728.58	−0.0987455
$915$	−2114.80	−0.0764078
$916$	−29778.1	−1.07412
$917$	−2394.40	−0.0862269
$918$	15057.6	0.541367
$919$	16278.3	0.584299	0.292150	−	0.956373i	$-0.405629\pi$
$919$	16278.3	0.584299	0.292150	+	0.956373i	$0.405629\pi$
$920$	794.424	0.0284689
$921$	−14719.8	−0.526638
$922$	41546.3	1.48401
$923$	−13636.1	−0.486282
$924$	2085.83	0.0742628
$925$	−7445.83	−0.264667
$926$	−871.826	−0.0309395
$927$	7027.36	0.248984
$928$	−6897.76	−0.243998
$929$	−36689.2	−1.29573	−0.647866	−	0.761754i	$-0.724338\pi$
$929$	−36689.2	−1.29573	−0.647866	+	0.761754i	$0.724338\pi$
$930$	9012.20	0.317765
$931$	18432.4	0.648869
$932$	22775.5	0.800469
$933$	18229.1	0.639649
$934$	−46247.4	−1.62020
$935$	8988.79	0.314401
$936$	4451.04	0.155435
$937$	−36671.8	−1.27857	−0.639283	−	0.768971i	$-0.720769\pi$
$937$	−36671.8	−1.27857	−0.639283	+	0.768971i	$0.720769\pi$
$938$	119.745	0.00416824
$939$	11951.4	0.415355
$940$	−13459.4	−0.467019
$941$	50993.8	1.76658	0.883290	−	0.468827i	$-0.155323\pi$
$941$	50993.8	1.76658	0.883290	+	0.468827i	$0.155323\pi$
$942$	−24475.1	−0.846542
$943$	−7443.80	−0.257056
$944$	−50062.4	−1.72605
$945$	−1699.11	−0.0584889
$946$	32895.2	1.13057
$947$	2334.12	0.0800936	0.0400468	−	0.999198i	$-0.487249\pi$
$947$	2334.12	0.0800936	0.0400468	+	0.999198i	$0.487249\pi$
$948$	−14364.3	−0.492120
$949$	−45376.7	−1.55215
$950$	−16755.3	−0.572224
$951$	−32663.8	−1.11377
$952$	240.251	0.00817918
$953$	37727.4	1.28238	0.641191	−	0.767381i	$-0.278441\pi$
$953$	37727.4	1.28238	0.641191	+	0.767381i	$0.278441\pi$
$954$	28013.6	0.950705
$955$	−8393.46	−0.284404
$956$	3846.48	0.130130
$957$	−5254.31	−0.177479
$958$	9747.95	0.328749
$959$	−3381.85	−0.113875
$960$	−7759.79	−0.260881
$961$	−19998.5	−0.671294
$962$	21300.2	0.713873
$963$	3760.92	0.125850
$964$	−9706.75	−0.324309
$965$	16159.4	0.539058
$966$	−545.817	−0.0181795
$967$	−42475.6	−1.41254	−0.706268	−	0.707944i	$-0.749623\pi$
$967$	−42475.6	−1.41254	−0.706268	+	0.707944i	$0.749623\pi$
$968$	6401.06	0.212539
$969$	−5178.57	−0.171682
$970$	37460.0	1.23997
$971$	−23013.6	−0.760599	−0.380299	−	0.924863i	$-0.624179\pi$
$971$	−23013.6	−0.760599	−0.380299	+	0.924863i	$0.624179\pi$
$972$	23010.3	0.759315
$973$	−325.271	−0.0107171
$974$	30961.5	1.01855
$975$	17451.0	0.573209
$976$	6488.03	0.212783
$977$	−27077.8	−0.886690	−0.443345	−	0.896351i	$-0.646208\pi$
$977$	−27077.8	−0.886690	−0.443345	+	0.896351i	$0.646208\pi$
$978$	38716.2	1.26586
$979$	−13298.9	−0.434152
$980$	−15021.1	−0.489624
$981$	−20824.0	−0.677736
$982$	−75351.0	−2.44862
$983$	−41344.3	−1.34148	−0.670742	−	0.741690i	$-0.734024\pi$
$983$	−41344.3	−1.34148	−0.670742	+	0.741690i	$0.734024\pi$
$984$	−6014.70	−0.194859
$985$	15056.1	0.487034
$986$	2962.21	0.0956756
$987$	−1889.32	−0.0609298
$988$	21744.5	0.700187
$989$	−3905.07	−0.125555
$990$	18290.7	0.587187
$991$	32463.6	1.04060	0.520302	−	0.853982i	$-0.325819\pi$
$991$	32463.6	1.04060	0.520302	+	0.853982i	$0.325819\pi$
$992$	−23537.3	−0.753336
$993$	22759.6	0.727346
$994$	−1497.69	−0.0477907
$995$	−23362.7	−0.744370
$996$	−13233.7	−0.421009
$997$	8818.89	0.280137	0.140069	−	0.990142i	$-0.455268\pi$
$997$	8818.89	0.280137	0.140069	+	0.990142i	$0.455268\pi$
$998$	−21945.2	−0.696055
$999$	−13590.0	−0.430397

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	667.4.a.a.1.8	✓	35

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
667.4.a.a.1.8	✓	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)

\(f(q)\)	\(=\)	\(q-3.82659 q^{2} +3.57847 q^{3} +6.64282 q^{4} +6.65081 q^{5} -13.6933 q^{6} +1.73304 q^{7} +5.19338 q^{8} -14.1946 q^{9} +O(q^{10})\)	\(q-3.82659 q^{2} +3.57847 q^{3} +6.64282 q^{4} +6.65081 q^{5} -13.6933 q^{6} +1.73304 q^{7} +5.19338 q^{8} -14.1946 q^{9} -25.4500 q^{10} +50.6314 q^{11} +23.7711 q^{12} -60.3796 q^{13} -6.63165 q^{14} +23.7997 q^{15} -73.0155 q^{16} +26.6935 q^{17} +54.3168 q^{18} -54.2134 q^{19} +44.1802 q^{20} +6.20164 q^{21} -193.746 q^{22} +23.0000 q^{23} +18.5843 q^{24} -80.7667 q^{25} +231.048 q^{26} -147.413 q^{27} +11.5123 q^{28} -29.0000 q^{29} -91.0719 q^{30} -98.9570 q^{31} +237.854 q^{32} +181.183 q^{33} -102.145 q^{34} +11.5261 q^{35} -94.2919 q^{36} +92.1894 q^{37} +207.453 q^{38} -216.066 q^{39} +34.5402 q^{40} -323.644 q^{41} -23.7312 q^{42} -169.785 q^{43} +336.336 q^{44} -94.4054 q^{45} -88.0117 q^{46} -304.648 q^{47} -261.284 q^{48} -339.997 q^{49} +309.061 q^{50} +95.5220 q^{51} -401.091 q^{52} +515.744 q^{53} +564.091 q^{54} +336.740 q^{55} +9.00035 q^{56} -194.001 q^{57} +110.971 q^{58} +685.641 q^{59} +158.097 q^{60} -88.8582 q^{61} +378.668 q^{62} -24.5998 q^{63} -326.045 q^{64} -401.573 q^{65} -693.314 q^{66} -18.0566 q^{67} +177.320 q^{68} +82.3048 q^{69} -44.1059 q^{70} +225.840 q^{71} -73.7177 q^{72} +751.524 q^{73} -352.771 q^{74} -289.021 q^{75} -360.130 q^{76} +87.7465 q^{77} +826.799 q^{78} -604.274 q^{79} -485.613 q^{80} -144.261 q^{81} +1238.45 q^{82} -556.713 q^{83} +41.1964 q^{84} +177.534 q^{85} +649.700 q^{86} -103.776 q^{87} +262.948 q^{88} -262.661 q^{89} +361.251 q^{90} -104.640 q^{91} +152.785 q^{92} -354.114 q^{93} +1165.77 q^{94} -360.563 q^{95} +851.152 q^{96} -1471.91 q^{97} +1301.03 q^{98} -718.691 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 35 q - 6 q^{2} - 22 q^{3} + 116 q^{4} - 80 q^{5} - 52 q^{6} - 38 q^{7} + 12 q^{8} + 231 q^{9}+O(q^{10}) \) 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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