LMFDB - Embedded newform 6005.2.a.f.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6005,2,Mod(1,6005)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6005, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("6005.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6005 = 5 \cdot 1201 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6005.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:	$47.9501664138$
Analytic rank:	$0$
Dimension:	$111$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	6005.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.63642 q^{2} +3.34656 q^{3} +4.95072 q^{4} +1.00000 q^{5} -8.82296 q^{6} -3.64864 q^{7} -7.77935 q^{8} +8.19949 q^{9} +O(q^{10})$	\(q-2.63642 q^{2} +3.34656 q^{3} +4.95072 q^{4} +1.00000 q^{5} -8.82296 q^{6} -3.64864 q^{7} -7.77935 q^{8} +8.19949 q^{9} -2.63642 q^{10} -3.22202 q^{11} +16.5679 q^{12} -4.33134 q^{13} +9.61935 q^{14} +3.34656 q^{15} +10.6082 q^{16} +5.04761 q^{17} -21.6173 q^{18} -8.39943 q^{19} +4.95072 q^{20} -12.2104 q^{21} +8.49461 q^{22} -0.122181 q^{23} -26.0341 q^{24} +1.00000 q^{25} +11.4192 q^{26} +17.4004 q^{27} -18.0634 q^{28} +0.184441 q^{29} -8.82296 q^{30} +1.68269 q^{31} -12.4090 q^{32} -10.7827 q^{33} -13.3076 q^{34} -3.64864 q^{35} +40.5934 q^{36} -5.47798 q^{37} +22.1444 q^{38} -14.4951 q^{39} -7.77935 q^{40} +0.394032 q^{41} +32.1918 q^{42} +4.38959 q^{43} -15.9513 q^{44} +8.19949 q^{45} +0.322122 q^{46} +10.7897 q^{47} +35.5010 q^{48} +6.31256 q^{49} -2.63642 q^{50} +16.8922 q^{51} -21.4433 q^{52} -1.31567 q^{53} -45.8749 q^{54} -3.22202 q^{55} +28.3840 q^{56} -28.1092 q^{57} -0.486265 q^{58} +12.9908 q^{59} +16.5679 q^{60} +14.0944 q^{61} -4.43627 q^{62} -29.9170 q^{63} +11.4990 q^{64} -4.33134 q^{65} +28.4278 q^{66} +14.1551 q^{67} +24.9893 q^{68} -0.408888 q^{69} +9.61935 q^{70} -10.4859 q^{71} -63.7867 q^{72} +12.9997 q^{73} +14.4423 q^{74} +3.34656 q^{75} -41.5832 q^{76} +11.7560 q^{77} +38.2152 q^{78} +4.91587 q^{79} +10.6082 q^{80} +33.6332 q^{81} -1.03884 q^{82} +16.2346 q^{83} -60.4503 q^{84} +5.04761 q^{85} -11.5728 q^{86} +0.617244 q^{87} +25.0652 q^{88} -11.3890 q^{89} -21.6173 q^{90} +15.8035 q^{91} -0.604886 q^{92} +5.63121 q^{93} -28.4463 q^{94} -8.39943 q^{95} -41.5275 q^{96} +9.19002 q^{97} -16.6426 q^{98} -26.4190 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 111 q + 20 q^{2} + 40 q^{3} + 136 q^{4} + 111 q^{5} + 3 q^{6} + 39 q^{7} + 45 q^{8} + 139 q^{9}+O(q^{10}) $ 111 * q + 20 * q^2 + 40 * q^3 + 136 * q^4 + 111 * q^5 + 3 * q^6 + 39 * q^7 + 45 * q^8 + 139 * q^9	\( 111 q + 20 q^{2} + 40 q^{3} + 136 q^{4} + 111 q^{5} + 3 q^{6} + 39 q^{7} + 45 q^{8} + 139 q^{9} + 20 q^{10} + 36 q^{11} + 80 q^{12} + 36 q^{13} + 7 q^{14} + 40 q^{15} + 190 q^{16} + 38 q^{17} + 48 q^{18} + 77 q^{19} + 136 q^{20} + 11 q^{21} + 39 q^{22} + 82 q^{23} - 3 q^{24} + 111 q^{25} - 3 q^{26} + 130 q^{27} + 87 q^{28} + 20 q^{29} + 3 q^{30} + 41 q^{31} + 85 q^{32} + 33 q^{33} + 7 q^{34} + 39 q^{35} + 191 q^{36} + 80 q^{37} + 42 q^{38} + 21 q^{39} + 45 q^{40} + 16 q^{41} + 33 q^{42} + 164 q^{43} + 37 q^{44} + 139 q^{45} + 32 q^{46} + 148 q^{47} + 149 q^{48} + 160 q^{49} + 20 q^{50} + 51 q^{51} + 87 q^{52} + 83 q^{53} - 6 q^{54} + 36 q^{55} - 10 q^{56} + 28 q^{57} + 47 q^{58} + 14 q^{59} + 80 q^{60} + 20 q^{61} + 14 q^{62} + 120 q^{63} + 231 q^{64} + 36 q^{65} - 4 q^{66} + 253 q^{67} + 80 q^{68} + 6 q^{69} + 7 q^{70} + 5 q^{71} + 124 q^{72} + 64 q^{73} - 37 q^{74} + 40 q^{75} + 92 q^{76} + 63 q^{77} + 29 q^{78} + 91 q^{79} + 190 q^{80} + 187 q^{81} - 7 q^{82} + 63 q^{83} - 69 q^{84} + 38 q^{85} - 22 q^{86} + 57 q^{87} + 121 q^{88} - 6 q^{89} + 48 q^{90} + 119 q^{91} + 104 q^{92} + 14 q^{93} - q^{94} + 77 q^{95} - 38 q^{96} + 96 q^{97} + 81 q^{98} + 106 q^{99}+O(q^{100}) \) 111 * q + 20 * q^2 + 40 * q^3 + 136 * q^4 + 111 * q^5 + 3 * q^6 + 39 * q^7 + 45 * q^8 + 139 * q^9 + 20 * q^10 + 36 * q^11 + 80 * q^12 + 36 * q^13 + 7 * q^14 + 40 * q^15 + 190 * q^16 + 38 * q^17 + 48 * q^18 + 77 * q^19 + 136 * q^20 + 11 * q^21 + 39 * q^22 + 82 * q^23 - 3 * q^24 + 111 * q^25 - 3 * q^26 + 130 * q^27 + 87 * q^28 + 20 * q^29 + 3 * q^30 + 41 * q^31 + 85 * q^32 + 33 * q^33 + 7 * q^34 + 39 * q^35 + 191 * q^36 + 80 * q^37 + 42 * q^38 + 21 * q^39 + 45 * q^40 + 16 * q^41 + 33 * q^42 + 164 * q^43 + 37 * q^44 + 139 * q^45 + 32 * q^46 + 148 * q^47 + 149 * q^48 + 160 * q^49 + 20 * q^50 + 51 * q^51 + 87 * q^52 + 83 * q^53 - 6 * q^54 + 36 * q^55 - 10 * q^56 + 28 * q^57 + 47 * q^58 + 14 * q^59 + 80 * q^60 + 20 * q^61 + 14 * q^62 + 120 * q^63 + 231 * q^64 + 36 * q^65 - 4 * q^66 + 253 * q^67 + 80 * q^68 + 6 * q^69 + 7 * q^70 + 5 * q^71 + 124 * q^72 + 64 * q^73 - 37 * q^74 + 40 * q^75 + 92 * q^76 + 63 * q^77 + 29 * q^78 + 91 * q^79 + 190 * q^80 + 187 * q^81 - 7 * q^82 + 63 * q^83 - 69 * q^84 + 38 * q^85 - 22 * q^86 + 57 * q^87 + 121 * q^88 - 6 * q^89 + 48 * q^90 + 119 * q^91 + 104 * q^92 + 14 * q^93 - q^94 + 77 * q^95 - 38 * q^96 + 96 * q^97 + 81 * q^98 + 106 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.63642	−1.86423	−0.932116	−	0.362160i	$-0.882039\pi$
$2$	−2.63642	−1.86423	−0.932116	+	0.362160i	$0.882039\pi$
$3$	3.34656	1.93214	0.966070	−	0.258281i	$-0.0831559\pi$
$3$	3.34656	1.93214	0.966070	+	0.258281i	$0.0831559\pi$
$4$	4.95072	2.47536
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−8.82296	−3.60196
$7$	−3.64864	−1.37906	−0.689528	−	0.724259i	$-0.742182\pi$
$7$	−3.64864	−1.37906	−0.689528	+	0.724259i	$0.742182\pi$
$8$	−7.77935	−2.75041
$9$	8.19949	2.73316
$10$	−2.63642	−0.833710
$11$	−3.22202	−0.971477	−0.485738	−	0.874104i	$-0.661449\pi$
$11$	−3.22202	−0.971477	−0.485738	+	0.874104i	$0.661449\pi$
$12$	16.5679	4.78274
$13$	−4.33134	−1.20130	−0.600649	−	0.799513i	$-0.705091\pi$
$13$	−4.33134	−1.20130	−0.600649	+	0.799513i	$0.705091\pi$
$14$	9.61935	2.57088
$15$	3.34656	0.864079
$16$	10.6082	2.65205
$17$	5.04761	1.22423	0.612113	−	0.790771i	$-0.290320\pi$
$17$	5.04761	1.22423	0.612113	+	0.790771i	$0.290320\pi$
$18$	−21.6173	−5.09525
$19$	−8.39943	−1.92696	−0.963481	−	0.267778i	$-0.913711\pi$
$19$	−8.39943	−1.92696	−0.963481	+	0.267778i	$0.913711\pi$
$20$	4.95072	1.10702
$21$	−12.2104	−2.66453
$22$	8.49461	1.81106
$23$	−0.122181	−0.0254766	−0.0127383	−	0.999919i	$-0.504055\pi$
$23$	−0.122181	−0.0254766	−0.0127383	+	0.999919i	$0.504055\pi$
$24$	−26.0341	−5.31419
$25$	1.00000	0.200000
$26$	11.4192	2.23950
$27$	17.4004	3.34872
$28$	−18.0634	−3.41366
$29$	0.184441	0.0342499	0.0171249	−	0.999853i	$-0.494549\pi$
$29$	0.184441	0.0342499	0.0171249	+	0.999853i	$0.494549\pi$
$30$	−8.82296	−1.61084
$31$	1.68269	0.302219	0.151110	−	0.988517i	$-0.451715\pi$
$31$	1.68269	0.302219	0.151110	+	0.988517i	$0.451715\pi$
$32$	−12.4090	−2.19362
$33$	−10.7827	−1.87703
$34$	−13.3076	−2.28224
$35$	−3.64864	−0.616732
$36$	40.5934	6.76557
$37$	−5.47798	−0.900575	−0.450287	−	0.892884i	$-0.648678\pi$
$37$	−5.47798	−0.900575	−0.450287	+	0.892884i	$0.648678\pi$
$38$	22.1444	3.59230
$39$	−14.4951	−2.32108
$40$	−7.77935	−1.23002
$41$	0.394032	0.0615375	0.0307688	−	0.999527i	$-0.490204\pi$
$41$	0.394032	0.0615375	0.0307688	+	0.999527i	$0.490204\pi$
$42$	32.1918	4.96730
$43$	4.38959	0.669407	0.334703	−	0.942324i	$-0.391364\pi$
$43$	4.38959	0.669407	0.334703	+	0.942324i	$0.391364\pi$
$44$	−15.9513	−2.40476
$45$	8.19949	1.22231
$46$	0.322122	0.0474942
$47$	10.7897	1.57384	0.786922	−	0.617052i	$-0.211673\pi$
$47$	10.7897	1.57384	0.786922	+	0.617052i	$0.211673\pi$
$48$	35.5010	5.12413
$49$	6.31256	0.901794
$50$	−2.63642	−0.372846
$51$	16.8922	2.36537
$52$	−21.4433	−2.97365
$53$	−1.31567	−0.180721	−0.0903605	−	0.995909i	$-0.528802\pi$
$53$	−1.31567	−0.180721	−0.0903605	+	0.995909i	$0.528802\pi$
$54$	−45.8749	−6.24278
$55$	−3.22202	−0.434458
$56$	28.3840	3.79297
$57$	−28.1092	−3.72316
$58$	−0.486265	−0.0638497
$59$	12.9908	1.69126	0.845628	−	0.533773i	$-0.179226\pi$
$59$	12.9908	1.69126	0.845628	+	0.533773i	$0.179226\pi$
$60$	16.5679	2.13891
$61$	14.0944	1.80461	0.902304	−	0.431101i	$-0.141875\pi$
$61$	14.0944	1.80461	0.902304	+	0.431101i	$0.141875\pi$
$62$	−4.43627	−0.563407
$63$	−29.9170	−3.76918
$64$	11.4990	1.43737
$65$	−4.33134	−0.537237
$66$	28.4278	3.49922
$67$	14.1551	1.72932	0.864658	−	0.502361i	$-0.167535\pi$
$67$	14.1551	1.72932	0.864658	+	0.502361i	$0.167535\pi$
$68$	24.9893	3.03040
$69$	−0.408888	−0.0492243
$70$	9.61935	1.14973
$71$	−10.4859	−1.24444	−0.622222	−	0.782841i	$-0.713770\pi$
$71$	−10.4859	−1.24444	−0.622222	+	0.782841i	$0.713770\pi$
$72$	−63.7867	−7.51734
$73$	12.9997	1.52150	0.760751	−	0.649044i	$-0.224831\pi$
$73$	12.9997	1.52150	0.760751	+	0.649044i	$0.224831\pi$
$74$	14.4423	1.67888
$75$	3.34656	0.386428
$76$	−41.5832	−4.76993
$77$	11.7560	1.33972
$78$	38.2152	4.32702
$79$	4.91587	0.553079	0.276539	−	0.961003i	$-0.410812\pi$
$79$	4.91587	0.553079	0.276539	+	0.961003i	$0.410812\pi$
$80$	10.6082	1.18603
$81$	33.6332	3.73702
$82$	−1.03884	−0.114720
$83$	16.2346	1.78198	0.890991	−	0.454021i	$-0.150011\pi$
$83$	16.2346	1.78198	0.890991	+	0.454021i	$0.150011\pi$
$84$	−60.4503	−6.59567
$85$	5.04761	0.547490
$86$	−11.5728	−1.24793
$87$	0.617244	0.0661755
$88$	25.0652	2.67196
$89$	−11.3890	−1.20724	−0.603618	−	0.797274i	$-0.706275\pi$
$89$	−11.3890	−1.20724	−0.603618	+	0.797274i	$0.706275\pi$
$90$	−21.6173	−2.27867
$91$	15.8035	1.65666
$92$	−0.604886	−0.0630637
$93$	5.63121	0.583930
$94$	−28.4463	−2.93401
$95$	−8.39943	−0.861763
$96$	−41.5275	−4.23838
$97$	9.19002	0.933106	0.466553	−	0.884493i	$-0.345496\pi$
$97$	9.19002	0.933106	0.466553	+	0.884493i	$0.345496\pi$
$98$	−16.6426	−1.68115
$99$	−26.4190	−2.65521
$100$	4.95072	0.495072
$101$	−3.73138	−0.371286	−0.185643	−	0.982617i	$-0.559437\pi$
$101$	−3.73138	−0.371286	−0.185643	+	0.982617i	$0.559437\pi$
$102$	−44.5348	−4.40961
$103$	1.98493	0.195580	0.0977902	−	0.995207i	$-0.468823\pi$
$103$	1.98493	0.195580	0.0977902	+	0.995207i	$0.468823\pi$
$104$	33.6950	3.30407
$105$	−12.2104	−1.19161
$106$	3.46866	0.336906
$107$	2.16580	0.209376	0.104688	−	0.994505i	$-0.466616\pi$
$107$	2.16580	0.209376	0.104688	+	0.994505i	$0.466616\pi$
$108$	86.1447	8.28928
$109$	−7.24105	−0.693567	−0.346783	−	0.937945i	$-0.612726\pi$
$109$	−7.24105	−0.693567	−0.346783	+	0.937945i	$0.612726\pi$
$110$	8.49461	0.809930
$111$	−18.3324	−1.74004
$112$	−38.7055	−3.65732
$113$	−10.5253	−0.990133	−0.495067	−	0.868855i	$-0.664856\pi$
$113$	−10.5253	−0.990133	−0.495067	+	0.868855i	$0.664856\pi$
$114$	74.1078	6.94083
$115$	−0.122181	−0.0113935
$116$	0.913117	0.0847807
$117$	−35.5148	−3.28335
$118$	−34.2492	−3.15289
$119$	−18.4169	−1.68827
$120$	−26.0341	−2.37658
$121$	−0.618564	−0.0562331
$122$	−37.1589	−3.36421
$123$	1.31865	0.118899
$124$	8.33051	0.748102
$125$	1.00000	0.0894427
$126$	78.8738	7.02664
$127$	1.38727	0.123100	0.0615500	−	0.998104i	$-0.480396\pi$
$127$	1.38727	0.123100	0.0615500	+	0.998104i	$0.480396\pi$
$128$	−5.49812	−0.485969
$129$	14.6901	1.29339
$130$	11.4192	1.00153
$131$	−17.4157	−1.52162	−0.760809	−	0.648976i	$-0.775198\pi$
$131$	−17.4157	−1.52162	−0.760809	+	0.648976i	$0.775198\pi$
$132$	−53.3822	−4.64632
$133$	30.6465	2.65739
$134$	−37.3187	−3.22385
$135$	17.4004	1.49759
$136$	−39.2671	−3.36713
$137$	−0.616492	−0.0526705	−0.0263352	−	0.999653i	$-0.508384\pi$
$137$	−0.616492	−0.0526705	−0.0263352	+	0.999653i	$0.508384\pi$
$138$	1.07800	0.0917655
$139$	15.7498	1.33588	0.667941	−	0.744214i	$-0.267176\pi$
$139$	15.7498	1.33588	0.667941	+	0.744214i	$0.267176\pi$
$140$	−18.0634	−1.52663
$141$	36.1085	3.04089
$142$	27.6452	2.31993
$143$	13.9557	1.16703
$144$	86.9819	7.24849
$145$	0.184441	0.0153170
$146$	−34.2727	−2.83643
$147$	21.1254	1.74239
$148$	−27.1200	−2.22925
$149$	10.1157	0.828708	0.414354	−	0.910116i	$-0.364008\pi$
$149$	10.1157	0.828708	0.414354	+	0.910116i	$0.364008\pi$
$150$	−8.82296	−0.720391
$151$	4.18276	0.340388	0.170194	−	0.985411i	$-0.445561\pi$
$151$	4.18276	0.340388	0.170194	+	0.985411i	$0.445561\pi$
$152$	65.3421	5.29994
$153$	41.3878	3.34601
$154$	−30.9938	−2.49755
$155$	1.68269	0.135157
$156$	−71.7613	−5.74550
$157$	−6.26815	−0.500253	−0.250126	−	0.968213i	$-0.580472\pi$
$157$	−6.26815	−0.500253	−0.250126	+	0.968213i	$0.580472\pi$
$158$	−12.9603	−1.03107
$159$	−4.40297	−0.349178
$160$	−12.4090	−0.981018
$161$	0.445795	0.0351336
$162$	−88.6713	−6.96668
$163$	11.2046	0.877611	0.438805	−	0.898582i	$-0.355402\pi$
$163$	11.2046	0.877611	0.438805	+	0.898582i	$0.355402\pi$
$164$	1.95074	0.152328
$165$	−10.7827	−0.839433
$166$	−42.8013	−3.32203
$167$	20.9899	1.62425	0.812123	−	0.583486i	$-0.198312\pi$
$167$	20.9899	1.62425	0.812123	+	0.583486i	$0.198312\pi$
$168$	94.9889	7.32856
$169$	5.76052	0.443117
$170$	−13.3076	−1.02065
$171$	−68.8711	−5.26670
$172$	21.7317	1.65702
$173$	−1.74192	−0.132436	−0.0662179	−	0.997805i	$-0.521093\pi$
$173$	−1.74192	−0.132436	−0.0662179	+	0.997805i	$0.521093\pi$
$174$	−1.62732	−0.123367
$175$	−3.64864	−0.275811
$176$	−34.1799	−2.57640
$177$	43.4745	3.26774
$178$	30.0263	2.25057
$179$	−3.47649	−0.259845	−0.129922	−	0.991524i	$-0.541473\pi$
$179$	−3.47649	−0.259845	−0.129922	+	0.991524i	$0.541473\pi$
$180$	40.5934	3.02565
$181$	20.8767	1.55175	0.775877	−	0.630884i	$-0.217308\pi$
$181$	20.8767	1.55175	0.775877	+	0.630884i	$0.217308\pi$
$182$	−41.6647	−3.08839
$183$	47.1679	3.48675
$184$	0.950491	0.0700711
$185$	−5.47798	−0.402749
$186$	−14.8463	−1.08858
$187$	−16.2635	−1.18931
$188$	53.4170	3.89583
$189$	−63.4879	−4.61806
$190$	22.1444	1.60653
$191$	6.41249	0.463991	0.231996	−	0.972717i	$-0.425474\pi$
$191$	6.41249	0.463991	0.231996	+	0.972717i	$0.425474\pi$
$192$	38.4820	2.77720
$193$	16.5194	1.18909	0.594546	−	0.804062i	$-0.297332\pi$
$193$	16.5194	1.18909	0.594546	+	0.804062i	$0.297332\pi$
$194$	−24.2288	−1.73953
$195$	−14.4951	−1.03802
$196$	31.2517	2.23226
$197$	19.9337	1.42022	0.710110	−	0.704091i	$-0.248645\pi$
$197$	19.9337	1.42022	0.710110	+	0.704091i	$0.248645\pi$
$198$	69.6515	4.94992
$199$	−3.05282	−0.216409	−0.108204	−	0.994129i	$-0.534510\pi$
$199$	−3.05282	−0.216409	−0.108204	+	0.994129i	$0.534510\pi$
$200$	−7.77935	−0.550083
$201$	47.3708	3.34128
$202$	9.83749	0.692163
$203$	−0.672959	−0.0472324
$204$	83.6283	5.85515
$205$	0.394032	0.0275204
$206$	−5.23310	−0.364607
$207$	−1.00182	−0.0696316
$208$	−45.9477	−3.18590
$209$	27.0632	1.87200
$210$	32.1918	2.22144
$211$	8.79955	0.605786	0.302893	−	0.953025i	$-0.402048\pi$
$211$	8.79955	0.605786	0.302893	+	0.953025i	$0.402048\pi$
$212$	−6.51351	−0.447350
$213$	−35.0916	−2.40444
$214$	−5.70996	−0.390325
$215$	4.38959	0.299368
$216$	−135.364	−9.21036
$217$	−6.13951	−0.416777
$218$	19.0905	1.29297
$219$	43.5044	2.93975
$220$	−15.9513	−1.07544
$221$	−21.8629	−1.47066
$222$	48.3320	3.24383
$223$	−20.0651	−1.34366	−0.671829	−	0.740706i	$-0.734491\pi$
$223$	−20.0651	−1.34366	−0.671829	+	0.740706i	$0.734491\pi$
$224$	45.2759	3.02513
$225$	8.19949	0.546633
$226$	27.7490	1.84584
$227$	−1.07741	−0.0715105	−0.0357552	−	0.999361i	$-0.511384\pi$
$227$	−1.07741	−0.0715105	−0.0357552	+	0.999361i	$0.511384\pi$
$228$	−139.161	−9.21616
$229$	5.30422	0.350513	0.175256	−	0.984523i	$-0.443925\pi$
$229$	5.30422	0.350513	0.175256	+	0.984523i	$0.443925\pi$
$230$	0.322122	0.0212401
$231$	39.3422	2.58853
$232$	−1.43483	−0.0942013
$233$	5.90081	0.386575	0.193288	−	0.981142i	$-0.438085\pi$
$233$	5.90081	0.386575	0.193288	+	0.981142i	$0.438085\pi$
$234$	93.6320	6.12092
$235$	10.7897	0.703845
$236$	64.3137	4.18647
$237$	16.4513	1.06863
$238$	48.5547	3.14733
$239$	−5.26710	−0.340700	−0.170350	−	0.985384i	$-0.554490\pi$
$239$	−5.26710	−0.340700	−0.170350	+	0.985384i	$0.554490\pi$
$240$	35.5010	2.29158
$241$	−1.18771	−0.0765074	−0.0382537	−	0.999268i	$-0.512179\pi$
$241$	−1.18771	−0.0765074	−0.0382537	+	0.999268i	$0.512179\pi$
$242$	1.63080	0.104832
$243$	60.3544	3.87174
$244$	69.7776	4.46705
$245$	6.31256	0.403294
$246$	−3.47653	−0.221655
$247$	36.3808	2.31486
$248$	−13.0902	−0.831228
$249$	54.3302	3.44304
$250$	−2.63642	−0.166742
$251$	−2.46613	−0.155661	−0.0778304	−	0.996967i	$-0.524799\pi$
$251$	−2.46613	−0.155661	−0.0778304	+	0.996967i	$0.524799\pi$
$252$	−148.111	−9.33009
$253$	0.393671	0.0247499
$254$	−3.65742	−0.229487
$255$	16.8922	1.05783
$256$	−8.50257	−0.531411
$257$	−16.1073	−1.00475	−0.502373	−	0.864651i	$-0.667540\pi$
$257$	−16.1073	−1.00475	−0.502373	+	0.864651i	$0.667540\pi$
$258$	−38.7292	−2.41117
$259$	19.9872	1.24194
$260$	−21.4433	−1.32985
$261$	1.51232	0.0936105
$262$	45.9152	2.83665
$263$	−15.2425	−0.939890	−0.469945	−	0.882696i	$-0.655726\pi$
$263$	−15.2425	−0.939890	−0.469945	+	0.882696i	$0.655726\pi$
$264$	83.8824	5.16261
$265$	−1.31567	−0.0808209
$266$	−80.7971	−4.95398
$267$	−38.1141	−2.33255
$268$	70.0778	4.28068
$269$	−21.6159	−1.31794	−0.658972	−	0.752167i	$-0.729008\pi$
$269$	−21.6159	−1.31794	−0.658972	+	0.752167i	$0.729008\pi$
$270$	−45.8749	−2.79186
$271$	−3.64239	−0.221260	−0.110630	−	0.993862i	$-0.535287\pi$
$271$	−3.64239	−0.221260	−0.110630	+	0.993862i	$0.535287\pi$
$272$	53.5461	3.24671
$273$	52.8874	3.20089
$274$	1.62533	0.0981900
$275$	−3.22202	−0.194295
$276$	−2.02429	−0.121848
$277$	−6.37440	−0.383001	−0.191500	−	0.981493i	$-0.561335\pi$
$277$	−6.37440	−0.383001	−0.191500	+	0.981493i	$0.561335\pi$
$278$	−41.5232	−2.49039
$279$	13.7972	0.826015
$280$	28.3840	1.69627
$281$	−2.19089	−0.130698	−0.0653488	−	0.997862i	$-0.520816\pi$
$281$	−2.19089	−0.130698	−0.0653488	+	0.997862i	$0.520816\pi$
$282$	−95.1973	−5.66892
$283$	19.2233	1.14271	0.571353	−	0.820704i	$-0.306419\pi$
$283$	19.2233	1.14271	0.571353	+	0.820704i	$0.306419\pi$
$284$	−51.9126	−3.08045
$285$	−28.1092	−1.66505
$286$	−36.7931	−2.17562
$287$	−1.43768	−0.0848636
$288$	−101.748	−5.99553
$289$	8.47836	0.498727
$290$	−0.486265	−0.0285544
$291$	30.7550	1.80289
$292$	64.3580	3.76627
$293$	13.4366	0.784977	0.392489	−	0.919757i	$-0.371614\pi$
$293$	13.4366	0.784977	0.392489	+	0.919757i	$0.371614\pi$
$294$	−55.6954	−3.24822
$295$	12.9908	0.756352
$296$	42.6151	2.47695
$297$	−56.0646	−3.25320
$298$	−26.6692	−1.54490
$299$	0.529209	0.0306049
$300$	16.5679	0.956549
$301$	−16.0160	−0.923149
$302$	−11.0275	−0.634562
$303$	−12.4873	−0.717377
$304$	−89.1028	−5.11040
$305$	14.0944	0.807045
$306$	−109.116	−6.23774
$307$	5.05989	0.288783	0.144392	−	0.989521i	$-0.453878\pi$
$307$	5.05989	0.288783	0.144392	+	0.989521i	$0.453878\pi$
$308$	58.2007	3.31629
$309$	6.64268	0.377889
$310$	−4.43627	−0.251963
$311$	−27.7458	−1.57332	−0.786659	−	0.617388i	$-0.788191\pi$
$311$	−27.7458	−1.57332	−0.786659	+	0.617388i	$0.788191\pi$
$312$	112.763	6.38392
$313$	−7.33560	−0.414633	−0.207316	−	0.978274i	$-0.566473\pi$
$313$	−7.33560	−0.414633	−0.207316	+	0.978274i	$0.566473\pi$
$314$	16.5255	0.932587
$315$	−29.9170	−1.68563
$316$	24.3371	1.36907
$317$	−13.1483	−0.738483	−0.369241	−	0.929334i	$-0.620382\pi$
$317$	−13.1483	−0.738483	−0.369241	+	0.929334i	$0.620382\pi$
$318$	11.6081	0.650949
$319$	−0.594274	−0.0332729
$320$	11.4990	0.642811
$321$	7.24798	0.404543
$322$	−1.17530	−0.0654972
$323$	−42.3970	−2.35903
$324$	166.509	9.25048
$325$	−4.33134	−0.240260
$326$	−29.5400	−1.63607
$327$	−24.2326	−1.34007
$328$	−3.06531	−0.169254
$329$	−39.3678	−2.17042
$330$	28.4278	1.56490
$331$	30.5235	1.67772	0.838861	−	0.544346i	$-0.183222\pi$
$331$	30.5235	1.67772	0.838861	+	0.544346i	$0.183222\pi$
$332$	80.3731	4.41105
$333$	−44.9167	−2.46142
$334$	−55.3382	−3.02797
$335$	14.1551	0.773374
$336$	−129.530	−7.06646
$337$	−15.9905	−0.871057	−0.435529	−	0.900175i	$-0.643439\pi$
$337$	−15.9905	−0.871057	−0.435529	+	0.900175i	$0.643439\pi$
$338$	−15.1872	−0.826073
$339$	−35.2235	−1.91308
$340$	24.9893	1.35524
$341$	−5.42165	−0.293599
$342$	181.573	9.81836
$343$	2.50824	0.135432
$344$	−34.1482	−1.84115
$345$	−0.408888	−0.0220138
$346$	4.59244	0.246891
$347$	−20.1976	−1.08426	−0.542132	−	0.840294i	$-0.682383\pi$
$347$	−20.1976	−1.08426	−0.542132	+	0.840294i	$0.682383\pi$
$348$	3.05580	0.163808
$349$	−34.1587	−1.82847	−0.914236	−	0.405183i	$-0.867208\pi$
$349$	−34.1587	−1.82847	−0.914236	+	0.405183i	$0.867208\pi$
$350$	9.61935	0.514176
$351$	−75.3672	−4.02281
$352$	39.9821	2.13105
$353$	−11.7193	−0.623757	−0.311879	−	0.950122i	$-0.600958\pi$
$353$	−11.7193	−0.623757	−0.311879	+	0.950122i	$0.600958\pi$
$354$	−114.617	−6.09183
$355$	−10.4859	−0.556532
$356$	−56.3839	−2.98834
$357$	−61.6333	−3.26198
$358$	9.16548	0.484411
$359$	−14.3632	−0.758061	−0.379031	−	0.925384i	$-0.623742\pi$
$359$	−14.3632	−0.758061	−0.379031	+	0.925384i	$0.623742\pi$
$360$	−63.7867	−3.36185
$361$	51.5504	2.71318
$362$	−55.0399	−2.89283
$363$	−2.07007	−0.108650
$364$	78.2387	4.10082
$365$	12.9997	0.680436
$366$	−124.355	−6.50012
$367$	26.0045	1.35742	0.678711	−	0.734405i	$-0.262539\pi$
$367$	26.0045	1.35742	0.678711	+	0.734405i	$0.262539\pi$
$368$	−1.29612	−0.0675651
$369$	3.23086	0.168192
$370$	14.4423	0.750818
$371$	4.80040	0.249224
$372$	27.8786	1.44544
$373$	−32.0360	−1.65876	−0.829381	−	0.558684i	$-0.811307\pi$
$373$	−32.0360	−1.65876	−0.829381	+	0.558684i	$0.811307\pi$
$374$	42.8775	2.21714
$375$	3.34656	0.172816
$376$	−83.9371	−4.32872
$377$	−0.798877	−0.0411443
$378$	167.381	8.60914
$379$	8.44996	0.434046	0.217023	−	0.976167i	$-0.430365\pi$
$379$	8.44996	0.434046	0.217023	+	0.976167i	$0.430365\pi$
$380$	−41.5832	−2.13318
$381$	4.64258	0.237846
$382$	−16.9060	−0.864987
$383$	27.2769	1.39378	0.696891	−	0.717177i	$-0.254566\pi$
$383$	27.2769	1.39378	0.696891	+	0.717177i	$0.254566\pi$
$384$	−18.3998	−0.938961
$385$	11.7560	0.599141
$386$	−43.5521	−2.21674
$387$	35.9924	1.82960
$388$	45.4972	2.30977
$389$	2.25641	0.114405	0.0572023	−	0.998363i	$-0.481782\pi$
$389$	2.25641	0.114405	0.0572023	+	0.998363i	$0.481782\pi$
$390$	38.2152	1.93510
$391$	−0.616724	−0.0311891
$392$	−49.1076	−2.48031
$393$	−58.2828	−2.93998
$394$	−52.5537	−2.64762
$395$	4.91587	0.247344
$396$	−130.793	−6.57259
$397$	−7.22456	−0.362590	−0.181295	−	0.983429i	$-0.558029\pi$
$397$	−7.22456	−0.362590	−0.181295	+	0.983429i	$0.558029\pi$
$398$	8.04852	0.403436
$399$	102.560	5.13444
$400$	10.6082	0.530410
$401$	−16.1749	−0.807738	−0.403869	−	0.914817i	$-0.632335\pi$
$401$	−16.1749	−0.807738	−0.403869	+	0.914817i	$0.632335\pi$
$402$	−124.890	−6.22892
$403$	−7.28828	−0.363055
$404$	−18.4730	−0.919067
$405$	33.6332	1.67125
$406$	1.77420	0.0880522
$407$	17.6502	0.874888
$408$	−131.410	−6.50576
$409$	−21.2884	−1.05264	−0.526322	−	0.850286i	$-0.676429\pi$
$409$	−21.2884	−1.05264	−0.526322	+	0.850286i	$0.676429\pi$
$410$	−1.03884	−0.0513044
$411$	−2.06313	−0.101767
$412$	9.82681	0.484132
$413$	−47.3986	−2.33233
$414$	2.64123	0.129810
$415$	16.2346	0.796927
$416$	53.7476	2.63519
$417$	52.7078	2.58111
$418$	−71.3499	−3.48984
$419$	31.3841	1.53321	0.766606	−	0.642118i	$-0.221944\pi$
$419$	31.3841	1.53321	0.766606	+	0.642118i	$0.221944\pi$
$420$	−60.4503	−2.94967
$421$	26.8373	1.30797	0.653984	−	0.756508i	$-0.273096\pi$
$421$	26.8373	1.30797	0.653984	+	0.756508i	$0.273096\pi$
$422$	−23.1993	−1.12933
$423$	88.4703	4.30158
$424$	10.2350	0.497058
$425$	5.04761	0.244845
$426$	92.5164	4.48243
$427$	−51.4255	−2.48865
$428$	10.7223	0.518280
$429$	46.7036	2.25487
$430$	−11.5728	−0.558091
$431$	5.76390	0.277637	0.138819	−	0.990318i	$-0.455670\pi$
$431$	5.76390	0.277637	0.138819	+	0.990318i	$0.455670\pi$
$432$	184.587	8.88096
$433$	35.1445	1.68894	0.844469	−	0.535604i	$-0.179916\pi$
$433$	35.1445	1.68894	0.844469	+	0.535604i	$0.179916\pi$
$434$	16.1863	0.776969
$435$	0.617244	0.0295946
$436$	−35.8484	−1.71683
$437$	1.02625	0.0490924
$438$	−114.696	−5.48038
$439$	16.1281	0.769750	0.384875	−	0.922969i	$-0.374245\pi$
$439$	16.1281	0.769750	0.384875	+	0.922969i	$0.374245\pi$
$440$	25.0652	1.19494
$441$	51.7598	2.46475
$442$	57.6399	2.74165
$443$	−5.34536	−0.253966	−0.126983	−	0.991905i	$-0.540529\pi$
$443$	−5.34536	−0.253966	−0.126983	+	0.991905i	$0.540529\pi$
$444$	−90.7587	−4.30722
$445$	−11.3890	−0.539892
$446$	52.9001	2.50489
$447$	33.8527	1.60118
$448$	−41.9555	−1.98221
$449$	34.0064	1.60486	0.802431	−	0.596745i	$-0.203540\pi$
$449$	34.0064	1.60486	0.802431	+	0.596745i	$0.203540\pi$
$450$	−21.6173	−1.01905
$451$	−1.26958	−0.0597822
$452$	−52.1076	−2.45094
$453$	13.9979	0.657677
$454$	2.84052	0.133312
$455$	15.8035	0.740879
$456$	218.672	10.2402
$457$	2.00471	0.0937765	0.0468882	−	0.998900i	$-0.485070\pi$
$457$	2.00471	0.0937765	0.0468882	+	0.998900i	$0.485070\pi$
$458$	−13.9842	−0.653437
$459$	87.8306	4.09958
$460$	−0.604886	−0.0282029
$461$	−5.18242	−0.241369	−0.120685	−	0.992691i	$-0.538509\pi$
$461$	−5.18242	−0.241369	−0.120685	+	0.992691i	$0.538509\pi$
$462$	−103.723	−4.82561
$463$	−5.99964	−0.278827	−0.139413	−	0.990234i	$-0.544522\pi$
$463$	−5.99964	−0.278827	−0.139413	+	0.990234i	$0.544522\pi$
$464$	1.95659	0.0908323
$465$	5.63121	0.261141
$466$	−15.5570	−0.720666
$467$	−30.6729	−1.41937	−0.709686	−	0.704518i	$-0.751163\pi$
$467$	−30.6729	−1.41937	−0.709686	+	0.704518i	$0.751163\pi$
$468$	−175.824	−8.12746
$469$	−51.6467	−2.38482
$470$	−28.4463	−1.31213
$471$	−20.9768	−0.966558
$472$	−101.060	−4.65165
$473$	−14.1434	−0.650313
$474$	−43.3725	−1.99217
$475$	−8.39943	−0.385392
$476$	−91.1769	−4.17909
$477$	−10.7878	−0.493940
$478$	13.8863	0.635145
$479$	−41.9304	−1.91585	−0.957924	−	0.287023i	$-0.907334\pi$
$479$	−41.9304	−1.91585	−0.957924	+	0.287023i	$0.907334\pi$
$480$	−41.5275	−1.89546
$481$	23.7270	1.08186
$482$	3.13131	0.142627
$483$	1.49188	0.0678830
$484$	−3.06234	−0.139197
$485$	9.19002	0.417297
$486$	−159.120	−7.21781
$487$	5.63633	0.255406	0.127703	−	0.991812i	$-0.459240\pi$
$487$	5.63633	0.255406	0.127703	+	0.991812i	$0.459240\pi$
$488$	−109.645	−4.96342
$489$	37.4969	1.69567
$490$	−16.6426	−0.751834
$491$	−20.2047	−0.911826	−0.455913	−	0.890024i	$-0.650687\pi$
$491$	−20.2047	−0.911826	−0.455913	+	0.890024i	$0.650687\pi$
$492$	6.52829	0.294318
$493$	0.930987	0.0419295
$494$	−95.9152	−4.31543
$495$	−26.4190	−1.18744
$496$	17.8503	0.801500
$497$	38.2591	1.71616
$498$	−143.237	−6.41862
$499$	−37.2321	−1.66674	−0.833369	−	0.552718i	$-0.813591\pi$
$499$	−37.2321	−1.66674	−0.833369	+	0.552718i	$0.813591\pi$
$500$	4.95072	0.221403
$501$	70.2440	3.13827
$502$	6.50176	0.290188
$503$	29.0752	1.29640	0.648200	−	0.761470i	$-0.275522\pi$
$503$	29.0752	1.29640	0.648200	+	0.761470i	$0.275522\pi$
$504$	232.735	10.3668
$505$	−3.73138	−0.166044
$506$	−1.03788	−0.0461395
$507$	19.2780	0.856164
$508$	6.86797	0.304717
$509$	7.97981	0.353699	0.176849	−	0.984238i	$-0.443409\pi$
$509$	7.97981	0.353699	0.176849	+	0.984238i	$0.443409\pi$
$510$	−44.5348	−1.97204
$511$	−47.4313	−2.09824
$512$	33.4126	1.47664
$513$	−146.154	−6.45285
$514$	42.4657	1.87308
$515$	1.98493	0.0874663
$516$	72.7264	3.20160
$517$	−34.7648	−1.52895
$518$	−52.6946	−2.31527
$519$	−5.82945	−0.255884
$520$	33.6950	1.47762
$521$	17.6880	0.774925	0.387462	−	0.921886i	$-0.373352\pi$
$521$	17.6880	0.774925	0.387462	+	0.921886i	$0.373352\pi$
$522$	−3.98712	−0.174512
$523$	−17.1219	−0.748689	−0.374344	−	0.927290i	$-0.622132\pi$
$523$	−17.1219	−0.748689	−0.374344	+	0.927290i	$0.622132\pi$
$524$	−86.2203	−3.76655
$525$	−12.2104	−0.532906
$526$	40.1855	1.75217
$527$	8.49354	0.369984
$528$	−114.385	−4.97797
$529$	−22.9851	−0.999351
$530$	3.46866	0.150669
$531$	106.518	4.62248
$532$	151.722	6.57799
$533$	−1.70669	−0.0739249
$534$	100.485	4.34841
$535$	2.16580	0.0936356
$536$	−110.117	−4.75634
$537$	−11.6343	−0.502056
$538$	56.9886	2.45695
$539$	−20.3392	−0.876071
$540$	86.1447	3.70708
$541$	−41.2402	−1.77305	−0.886527	−	0.462676i	$-0.846889\pi$
$541$	−41.2402	−1.77305	−0.886527	+	0.462676i	$0.846889\pi$
$542$	9.60289	0.412479
$543$	69.8653	2.99821
$544$	−62.6358	−2.68549
$545$	−7.24105	−0.310172
$546$	−139.434	−5.96721
$547$	−41.6278	−1.77987	−0.889937	−	0.456083i	$-0.849252\pi$
$547$	−41.6278	−1.77987	−0.889937	+	0.456083i	$0.849252\pi$
$548$	−3.05208	−0.130378
$549$	115.567	4.93229
$550$	8.49461	0.362212
$551$	−1.54920	−0.0659982
$552$	3.18088	0.135387
$553$	−17.9362	−0.762726
$554$	16.8056	0.714002
$555$	−18.3324	−0.778168
$556$	77.9730	3.30679
$557$	−26.6641	−1.12979	−0.564896	−	0.825162i	$-0.691084\pi$
$557$	−26.6641	−1.12979	−0.564896	+	0.825162i	$0.691084\pi$
$558$	−36.3752	−1.53988
$559$	−19.0128	−0.804157
$560$	−38.7055	−1.63561
$561$	−54.4269	−2.29791
$562$	5.77611	0.243651
$563$	30.6695	1.29257	0.646283	−	0.763098i	$-0.276323\pi$
$563$	30.6695	1.29257	0.646283	+	0.763098i	$0.276323\pi$
$564$	178.763	7.52729
$565$	−10.5253	−0.442801
$566$	−50.6807	−2.13027
$567$	−122.715	−5.15356
$568$	81.5732	3.42274
$569$	17.8149	0.746840	0.373420	−	0.927662i	$-0.378185\pi$
$569$	17.8149	0.746840	0.373420	+	0.927662i	$0.378185\pi$
$570$	74.1078	3.10403
$571$	26.1776	1.09550	0.547749	−	0.836642i	$-0.315485\pi$
$571$	26.1776	1.09550	0.547749	+	0.836642i	$0.315485\pi$
$572$	69.0907	2.88883
$573$	21.4598	0.896496
$574$	3.79033	0.158205
$575$	−0.122181	−0.00509531
$576$	94.2857	3.92857
$577$	−33.9410	−1.41298	−0.706491	−	0.707722i	$-0.749723\pi$
$577$	−33.9410	−1.41298	−0.706491	+	0.707722i	$0.749723\pi$
$578$	−22.3525	−0.929743
$579$	55.2832	2.29749
$580$	0.913117	0.0379151
$581$	−59.2343	−2.45745
$582$	−81.0832	−3.36101
$583$	4.23912	0.175566
$584$	−101.129	−4.18476
$585$	−35.5148	−1.46836
$586$	−35.4247	−1.46338
$587$	−41.6446	−1.71886	−0.859429	−	0.511256i	$-0.829181\pi$
$587$	−41.6446	−1.71886	−0.859429	+	0.511256i	$0.829181\pi$
$588$	104.586	4.31305
$589$	−14.1336	−0.582365
$590$	−34.2492	−1.41002
$591$	66.7095	2.74406
$592$	−58.1115	−2.38837
$593$	10.1109	0.415206	0.207603	−	0.978213i	$-0.433434\pi$
$593$	10.1109	0.415206	0.207603	+	0.978213i	$0.433434\pi$
$594$	147.810	6.06472
$595$	−18.4169	−0.755019
$596$	50.0799	2.05135
$597$	−10.2165	−0.418132
$598$	−1.39522	−0.0570547
$599$	7.00520	0.286225	0.143112	−	0.989706i	$-0.454289\pi$
$599$	7.00520	0.286225	0.143112	+	0.989706i	$0.454289\pi$
$600$	−26.0341	−1.06284
$601$	19.7459	0.805451	0.402725	−	0.915321i	$-0.368063\pi$
$601$	19.7459	0.805451	0.402725	+	0.915321i	$0.368063\pi$
$602$	42.2250	1.72096
$603$	116.064	4.72651
$604$	20.7077	0.842583
$605$	−0.618564	−0.0251482
$606$	32.9218	1.33736
$607$	−35.9385	−1.45870	−0.729350	−	0.684141i	$-0.760177\pi$
$607$	−35.9385	−1.45870	−0.729350	+	0.684141i	$0.760177\pi$
$608$	104.229	4.22703
$609$	−2.25210	−0.0912597
$610$	−37.1589	−1.50452
$611$	−46.7340	−1.89066
$612$	204.900	8.28258
$613$	−12.0608	−0.487133	−0.243566	−	0.969884i	$-0.578317\pi$
$613$	−12.0608	−0.487133	−0.243566	+	0.969884i	$0.578317\pi$
$614$	−13.3400	−0.538359
$615$	1.31865	0.0531733
$616$	−91.4540	−3.68479
$617$	14.0323	0.564917	0.282459	−	0.959279i	$-0.408850\pi$
$617$	14.0323	0.564917	0.282459	+	0.959279i	$0.408850\pi$
$618$	−17.5129	−0.704472
$619$	−5.08055	−0.204204	−0.102102	−	0.994774i	$-0.532557\pi$
$619$	−5.08055	−0.204204	−0.102102	+	0.994774i	$0.532557\pi$
$620$	8.33051	0.334561
$621$	−2.12601	−0.0853138
$622$	73.1496	2.93303
$623$	41.5545	1.66484
$624$	−153.767	−6.15561
$625$	1.00000	0.0400000
$626$	19.3397	0.772972
$627$	90.5686	3.61696
$628$	−31.0319	−1.23831
$629$	−27.6507	−1.10251
$630$	78.8738	3.14241
$631$	37.7437	1.50255	0.751276	−	0.659988i	$-0.229439\pi$
$631$	37.7437	1.50255	0.751276	+	0.659988i	$0.229439\pi$
$632$	−38.2423	−1.52120
$633$	29.4483	1.17046
$634$	34.6645	1.37670
$635$	1.38727	0.0550520
$636$	−21.7979	−0.864342
$637$	−27.3418	−1.08332
$638$	1.56676	0.0620285
$639$	−85.9788	−3.40127
$640$	−5.49812	−0.217332
$641$	−34.5586	−1.36498	−0.682491	−	0.730894i	$-0.739103\pi$
$641$	−34.5586	−1.36498	−0.682491	+	0.730894i	$0.739103\pi$
$642$	−19.1087	−0.754162
$643$	17.4380	0.687689	0.343844	−	0.939027i	$-0.388271\pi$
$643$	17.4380	0.687689	0.343844	+	0.939027i	$0.388271\pi$
$644$	2.20701	0.0869683
$645$	14.6901	0.578420
$646$	111.777	4.39779
$647$	9.65394	0.379535	0.189768	−	0.981829i	$-0.439227\pi$
$647$	9.65394	0.379535	0.189768	+	0.981829i	$0.439227\pi$
$648$	−261.644	−10.2784
$649$	−41.8566	−1.64301
$650$	11.4192	0.447900
$651$	−20.5463	−0.805271
$652$	55.4708	2.17240
$653$	−8.44711	−0.330561	−0.165281	−	0.986247i	$-0.552853\pi$
$653$	−8.44711	−0.330561	−0.165281	+	0.986247i	$0.552853\pi$
$654$	63.8874	2.49820
$655$	−17.4157	−0.680488
$656$	4.17997	0.163201
$657$	106.591	4.15851
$658$	103.790	4.04616
$659$	43.4904	1.69415	0.847073	−	0.531476i	$-0.178362\pi$
$659$	43.4904	1.69415	0.847073	+	0.531476i	$0.178362\pi$
$660$	−53.3822	−2.07790
$661$	−6.39016	−0.248549	−0.124274	−	0.992248i	$-0.539660\pi$
$661$	−6.39016	−0.248549	−0.124274	+	0.992248i	$0.539660\pi$
$662$	−80.4728	−3.12766
$663$	−73.1657	−2.84152
$664$	−126.295	−4.90119
$665$	30.6465	1.18842
$666$	118.419	4.58866
$667$	−0.0225353	−0.000872569 0
$668$	103.915	4.02059
$669$	−67.1491	−2.59614
$670$	−37.3187	−1.44175
$671$	−45.4126	−1.75313
$672$	151.519	5.84497
$673$	5.66515	0.218376	0.109188	−	0.994021i	$-0.465175\pi$
$673$	5.66515	0.218376	0.109188	+	0.994021i	$0.465175\pi$
$674$	42.1577	1.62385
$675$	17.4004	0.669743
$676$	28.5187	1.09687
$677$	−12.5264	−0.481428	−0.240714	−	0.970596i	$-0.577382\pi$
$677$	−12.5264	−0.481428	−0.240714	+	0.970596i	$0.577382\pi$
$678$	92.8639	3.56642
$679$	−33.5311	−1.28680
$680$	−39.2671	−1.50582
$681$	−3.60564	−0.138168
$682$	14.2938	0.547336
$683$	38.2523	1.46368	0.731842	−	0.681475i	$-0.238661\pi$
$683$	38.2523	1.46368	0.731842	+	0.681475i	$0.238661\pi$
$684$	−340.962	−13.0370
$685$	−0.616492	−0.0235549
$686$	−6.61277	−0.252477
$687$	17.7509	0.677240
$688$	46.5657	1.77530
$689$	5.69861	0.217100
$690$	1.07800	0.0410388
$691$	13.2562	0.504290	0.252145	−	0.967689i	$-0.418864\pi$
$691$	13.2562	0.504290	0.252145	+	0.967689i	$0.418864\pi$
$692$	−8.62376	−0.327826
$693$	96.3932	3.66168
$694$	53.2494	2.02132
$695$	15.7498	0.597425
$696$	−4.80176	−0.182010
$697$	1.98892	0.0753358
$698$	90.0566	3.40869
$699$	19.7474	0.746917
$700$	−18.0634	−0.682732
$701$	5.77932	0.218282	0.109141	−	0.994026i	$-0.465190\pi$
$701$	5.77932	0.218282	0.109141	+	0.994026i	$0.465190\pi$
$702$	198.700	7.49944
$703$	46.0119	1.73537
$704$	−37.0499	−1.39637
$705$	36.1085	1.35993
$706$	30.8971	1.16283
$707$	13.6144	0.512024
$708$	215.230	8.08884
$709$	12.3263	0.462924	0.231462	−	0.972844i	$-0.425649\pi$
$709$	12.3263	0.462924	0.231462	+	0.972844i	$0.425649\pi$
$710$	27.6452	1.03751
$711$	40.3076	1.51165
$712$	88.5993	3.32040
$713$	−0.205593	−0.00769951
$714$	162.491	6.08109
$715$	13.9557	0.521913
$716$	−17.2111	−0.643210
$717$	−17.6267	−0.658281
$718$	37.8675	1.41320
$719$	−2.81668	−0.105044	−0.0525221	−	0.998620i	$-0.516726\pi$
$719$	−2.81668	−0.105044	−0.0525221	+	0.998620i	$0.516726\pi$
$720$	86.9819	3.24162
$721$	−7.24227	−0.269716
$722$	−135.909	−5.05800
$723$	−3.97476	−0.147823
$724$	103.355	3.84115
$725$	0.184441	0.00684997
$726$	5.45757	0.202549
$727$	13.5923	0.504111	0.252055	−	0.967713i	$-0.418894\pi$
$727$	13.5923	0.504111	0.252055	+	0.967713i	$0.418894\pi$
$728$	−122.941	−4.55649
$729$	101.080	3.74371
$730$	−34.2727	−1.26849
$731$	22.1570	0.819505
$732$	233.515	8.63097
$733$	−25.4493	−0.939993	−0.469997	−	0.882668i	$-0.655745\pi$
$733$	−25.4493	−0.939993	−0.469997	+	0.882668i	$0.655745\pi$
$734$	−68.5588	−2.53055
$735$	21.1254	0.779221
$736$	1.51615	0.0558860
$737$	−45.6079	−1.67999
$738$	−8.51792	−0.313549
$739$	−27.1981	−1.00050	−0.500249	−	0.865882i	$-0.666758\pi$
$739$	−27.1981	−1.00050	−0.500249	+	0.865882i	$0.666758\pi$
$740$	−27.1200	−0.996950
$741$	121.751	4.47262
$742$	−12.6559	−0.464612
$743$	12.8485	0.471365	0.235682	−	0.971830i	$-0.424268\pi$
$743$	12.8485	0.471365	0.235682	+	0.971830i	$0.424268\pi$
$744$	−43.8072	−1.60605
$745$	10.1157	0.370609
$746$	84.4604	3.09232
$747$	133.116	4.87045
$748$	−80.5161	−2.94396
$749$	−7.90221	−0.288741
$750$	−8.82296	−0.322169
$751$	−1.82020	−0.0664201	−0.0332101	−	0.999448i	$-0.510573\pi$
$751$	−1.82020	−0.0664201	−0.0332101	+	0.999448i	$0.510573\pi$
$752$	114.460	4.17391
$753$	−8.25306	−0.300758
$754$	2.10618	0.0767025
$755$	4.18276	0.152226
$756$	−314.311	−11.4314
$757$	−40.7904	−1.48255	−0.741275	−	0.671201i	$-0.765779\pi$
$757$	−40.7904	−1.48255	−0.741275	+	0.671201i	$0.765779\pi$
$758$	−22.2777	−0.809162
$759$	1.31745	0.0478202
$760$	65.3421	2.37021
$761$	−17.7173	−0.642253	−0.321127	−	0.947036i	$-0.604061\pi$
$761$	−17.7173	−0.642253	−0.321127	+	0.947036i	$0.604061\pi$
$762$	−12.2398	−0.443401
$763$	26.4200	0.956467
$764$	31.7464	1.14855
$765$	41.3878	1.49638
$766$	−71.9133	−2.59833
$767$	−56.2675	−2.03170
$768$	−28.4544	−1.02676
$769$	0.534006	0.0192568	0.00962838	−	0.999954i	$-0.496935\pi$
$769$	0.534006	0.0192568	0.00962838	+	0.999954i	$0.496935\pi$
$770$	−30.9938	−1.11694
$771$	−53.9041	−1.94131
$772$	81.7829	2.94343
$773$	29.0009	1.04309	0.521545	−	0.853224i	$-0.325356\pi$
$773$	29.0009	1.04309	0.521545	+	0.853224i	$0.325356\pi$
$774$	−94.8913	−3.41080
$775$	1.68269	0.0604438
$776$	−71.4924	−2.56643
$777$	66.8884	2.39961
$778$	−5.94886	−0.213277
$779$	−3.30965	−0.118580
$780$	−71.7613	−2.56947
$781$	33.7857	1.20895
$782$	1.62594	0.0581436
$783$	3.20936	0.114693
$784$	66.9649	2.39160
$785$	−6.26815	−0.223720
$786$	153.658	5.48080
$787$	46.7809	1.66756	0.833779	−	0.552098i	$-0.186173\pi$
$787$	46.7809	1.66756	0.833779	+	0.552098i	$0.186173\pi$
$788$	98.6864	3.51556
$789$	−51.0099	−1.81600
$790$	−12.9603	−0.461107
$791$	38.4029	1.36545
$792$	205.522	7.30292
$793$	−61.0478	−2.16787
$794$	19.0470	0.675953
$795$	−4.40297	−0.156157
$796$	−15.1137	−0.535689
$797$	27.5733	0.976695	0.488347	−	0.872649i	$-0.337600\pi$
$797$	27.5733	0.976695	0.488347	+	0.872649i	$0.337600\pi$
$798$	−270.393	−9.57179
$799$	54.4624	1.92674
$800$	−12.4090	−0.438724
$801$	−93.3843	−3.29957
$802$	42.6440	1.50581
$803$	−41.8854	−1.47810
$804$	234.520	8.27088
$805$	0.445795	0.0157122
$806$	19.2150	0.676819
$807$	−72.3390	−2.54645
$808$	29.0277	1.02119
$809$	−26.0413	−0.915563	−0.457782	−	0.889065i	$-0.651356\pi$
$809$	−26.0413	−0.915563	−0.457782	+	0.889065i	$0.651356\pi$
$810$	−88.6713	−3.11559
$811$	−18.9335	−0.664844	−0.332422	−	0.943131i	$-0.607866\pi$
$811$	−18.9335	−0.664844	−0.332422	+	0.943131i	$0.607866\pi$
$812$	−3.33163	−0.116917
$813$	−12.1895	−0.427505
$814$	−46.5334	−1.63099
$815$	11.2046	0.392479
$816$	179.195	6.27309
$817$	−36.8701	−1.28992
$818$	56.1252	1.96237
$819$	129.581	4.52791
$820$	1.95074	0.0681229
$821$	−24.8548	−0.867437	−0.433718	−	0.901048i	$-0.642799\pi$
$821$	−24.8548	−0.867437	−0.433718	+	0.901048i	$0.642799\pi$
$822$	5.43928	0.189717
$823$	13.5078	0.470851	0.235426	−	0.971892i	$-0.424352\pi$
$823$	13.5078	0.470851	0.235426	+	0.971892i	$0.424352\pi$
$824$	−15.4414	−0.537927
$825$	−10.7827	−0.375406
$826$	124.963	4.34801
$827$	4.45119	0.154783	0.0773915	−	0.997001i	$-0.475341\pi$
$827$	4.45119	0.154783	0.0773915	+	0.997001i	$0.475341\pi$
$828$	−4.95976	−0.172363
$829$	10.6894	0.371258	0.185629	−	0.982620i	$-0.440568\pi$
$829$	10.6894	0.371258	0.185629	+	0.982620i	$0.440568\pi$
$830$	−42.8013	−1.48566
$831$	−21.3323	−0.740011
$832$	−49.8059	−1.72671
$833$	31.8633	1.10400
$834$	−138.960	−4.81179
$835$	20.9899	0.726385
$836$	133.982	4.63387
$837$	29.2795	1.01205
$838$	−82.7417	−2.85826
$839$	21.6460	0.747303	0.373652	−	0.927569i	$-0.378106\pi$
$839$	21.6460	0.747303	0.373652	+	0.927569i	$0.378106\pi$
$840$	94.9889	3.27743
$841$	−28.9660	−0.998827
$842$	−70.7544	−2.43836
$843$	−7.33196	−0.252526
$844$	43.5641	1.49954
$845$	5.76052	0.198168
$846$	−233.245	−8.01913
$847$	2.25692	0.0775486
$848$	−13.9569	−0.479281
$849$	64.3320	2.20787
$850$	−13.3076	−0.456448
$851$	0.669307	0.0229436
$852$	−173.729	−5.95186
$853$	25.5256	0.873981	0.436991	−	0.899466i	$-0.356044\pi$
$853$	25.5256	0.873981	0.436991	+	0.899466i	$0.356044\pi$
$854$	135.579	4.63943
$855$	−68.8711	−2.35534
$856$	−16.8485	−0.575870
$857$	41.5816	1.42040	0.710201	−	0.703999i	$-0.248604\pi$
$857$	41.5816	1.42040	0.710201	+	0.703999i	$0.248604\pi$
$858$	−123.130	−4.20360
$859$	51.6373	1.76184	0.880921	−	0.473264i	$-0.156924\pi$
$859$	51.6373	1.76184	0.880921	+	0.473264i	$0.156924\pi$
$860$	21.7317	0.741043
$861$	−4.81129	−0.163968
$862$	−15.1961	−0.517580
$863$	−7.12651	−0.242589	−0.121295	−	0.992617i	$-0.538705\pi$
$863$	−7.12651	−0.242589	−0.121295	+	0.992617i	$0.538705\pi$
$864$	−215.922	−7.34582
$865$	−1.74192	−0.0592271
$866$	−92.6558	−3.14857
$867$	28.3734	0.963611
$868$	−30.3950	−1.03167
$869$	−15.8391	−0.537303
$870$	−1.62732	−0.0551712
$871$	−61.3104	−2.07742
$872$	56.3306	1.90760
$873$	75.3535	2.55033
$874$	−2.70564	−0.0915196
$875$	−3.64864	−0.123346
$876$	215.378	7.27695
$877$	−29.3749	−0.991920	−0.495960	−	0.868345i	$-0.665184\pi$
$877$	−29.3749	−0.991920	−0.495960	+	0.868345i	$0.665184\pi$
$878$	−42.5204	−1.43499
$879$	44.9666	1.51669
$880$	−34.1799	−1.15220
$881$	−5.77057	−0.194416	−0.0972078	−	0.995264i	$-0.530991\pi$
$881$	−5.77057	−0.194416	−0.0972078	+	0.995264i	$0.530991\pi$
$882$	−136.461	−4.59487
$883$	16.4115	0.552291	0.276145	−	0.961116i	$-0.410943\pi$
$883$	16.4115	0.552291	0.276145	+	0.961116i	$0.410943\pi$
$884$	−108.237	−3.64041
$885$	43.4745	1.46138
$886$	14.0926	0.473451
$887$	31.0088	1.04117	0.520587	−	0.853808i	$-0.325713\pi$
$887$	31.0088	1.04117	0.520587	+	0.853808i	$0.325713\pi$
$888$	142.614	4.78582
$889$	−5.06163	−0.169762
$890$	30.0263	1.00648
$891$	−108.367	−3.63043
$892$	−99.3367	−3.32604
$893$	−90.6276	−3.03274
$894$	−89.2501	−2.98497
$895$	−3.47649	−0.116206
$896$	20.0606	0.670179
$897$	1.77103	0.0591330
$898$	−89.6552	−2.99183
$899$	0.310356	0.0103510
$900$	40.5934	1.35311
$901$	−6.64098	−0.221243
$902$	3.34715	0.111448
$903$	−53.5987	−1.78365
$904$	81.8797	2.72328
$905$	20.8767	0.693966
$906$	−36.9043	−1.22606
$907$	55.2637	1.83500	0.917501	−	0.397734i	$-0.130203\pi$
$907$	55.2637	1.83500	0.917501	+	0.397734i	$0.130203\pi$
$908$	−5.33398	−0.177014
$909$	−30.5954	−1.01479
$910$	−41.6647	−1.38117
$911$	8.81668	0.292110	0.146055	−	0.989277i	$-0.453342\pi$
$911$	8.81668	0.292110	0.146055	+	0.989277i	$0.453342\pi$
$912$	−298.188	−9.87401
$913$	−52.3084	−1.73115
$914$	−5.28527	−0.174821
$915$	47.1679	1.55932
$916$	26.2597	0.867646
$917$	63.5436	2.09840
$918$	−231.559	−7.64257
$919$	−8.80545	−0.290465	−0.145232	−	0.989398i	$-0.546393\pi$
$919$	−8.80545	−0.290465	−0.145232	+	0.989398i	$0.546393\pi$
$920$	0.950491	0.0313368
$921$	16.9332	0.557969
$922$	13.6631	0.449969
$923$	45.4179	1.49495
$924$	194.772	6.40754
$925$	−5.47798	−0.180115
$926$	15.8176	0.519798
$927$	16.2754	0.534554
$928$	−2.28873	−0.0751312
$929$	−51.1717	−1.67889	−0.839444	−	0.543446i	$-0.817119\pi$
$929$	−51.1717	−1.67889	−0.839444	+	0.543446i	$0.817119\pi$
$930$	−14.8463	−0.486828
$931$	−53.0219	−1.73772
$932$	29.2133	0.956913
$933$	−92.8530	−3.03987
$934$	80.8667	2.64604
$935$	−16.2635	−0.531874
$936$	276.282	9.03056
$937$	11.8173	0.386054	0.193027	−	0.981193i	$-0.438169\pi$
$937$	11.8173	0.386054	0.193027	+	0.981193i	$0.438169\pi$
$938$	136.162	4.44586
$939$	−24.5491	−0.801128
$940$	53.4170	1.74227
$941$	−13.8763	−0.452353	−0.226177	−	0.974086i	$-0.572623\pi$
$941$	−13.8763	−0.452353	−0.226177	+	0.974086i	$0.572623\pi$
$942$	55.3036	1.80189
$943$	−0.0481434	−0.00156776
$944$	137.809	4.48529
$945$	−63.4879	−2.06526
$946$	37.2879	1.21233
$947$	−31.2082	−1.01413	−0.507065	−	0.861908i	$-0.669270\pi$
$947$	−31.2082	−1.01413	−0.507065	+	0.861908i	$0.669270\pi$
$948$	81.4457	2.64523
$949$	−56.3062	−1.82778
$950$	22.1444	0.718461
$951$	−44.0017	−1.42685
$952$	143.271	4.64345
$953$	−7.55968	−0.244882	−0.122441	−	0.992476i	$-0.539072\pi$
$953$	−7.55968	−0.244882	−0.122441	+	0.992476i	$0.539072\pi$
$954$	28.4412	0.920819
$955$	6.41249	0.207503
$956$	−26.0760	−0.843357
$957$	−1.98877	−0.0642880
$958$	110.546	3.57158
$959$	2.24936	0.0726355
$960$	38.4820	1.24200
$961$	−28.1686	−0.908664
$962$	−62.5544	−2.01684
$963$	17.7584	0.572258
$964$	−5.88004	−0.189383
$965$	16.5194	0.531778
$966$	−3.93323	−0.126550
$967$	4.46433	0.143563	0.0717815	−	0.997420i	$-0.477132\pi$
$967$	4.46433	0.143563	0.0717815	+	0.997420i	$0.477132\pi$
$968$	4.81203	0.154664
$969$	−141.884	−4.55799
$970$	−24.2288	−0.777939
$971$	44.5444	1.42950	0.714748	−	0.699382i	$-0.246541\pi$
$971$	44.5444	1.42950	0.714748	+	0.699382i	$0.246541\pi$
$972$	298.798	9.58394
$973$	−57.4654	−1.84226
$974$	−14.8597	−0.476137
$975$	−14.4951	−0.464215
$976$	149.517	4.78591
$977$	−58.0332	−1.85665	−0.928323	−	0.371776i	$-0.878749\pi$
$977$	−58.0332	−1.85665	−0.928323	+	0.371776i	$0.878749\pi$
$978$	−98.8575	−3.16112
$979$	36.6957	1.17280
$980$	31.2517	0.998299
$981$	−59.3729	−1.89563
$982$	53.2681	1.69985
$983$	−33.5870	−1.07126	−0.535630	−	0.844453i	$-0.679926\pi$
$983$	−33.5870	−1.07126	−0.535630	+	0.844453i	$0.679926\pi$
$984$	−10.2583	−0.327022
$985$	19.9337	0.635142
$986$	−2.45447	−0.0781664
$987$	−131.747	−4.19355
$988$	180.111	5.73010
$989$	−0.536326	−0.0170542
$990$	69.6515	2.21367
$991$	14.4897	0.460280	0.230140	−	0.973158i	$-0.426082\pi$
$991$	14.4897	0.460280	0.230140	+	0.973158i	$0.426082\pi$
$992$	−20.8804	−0.662955
$993$	102.149	3.24159
$994$	−100.867	−3.19931
$995$	−3.05282	−0.0967809
$996$	268.974	8.52276
$997$	52.1864	1.65276	0.826379	−	0.563114i	$-0.190397\pi$
$997$	52.1864	1.65276	0.826379	+	0.563114i	$0.190397\pi$
$998$	98.1595	3.10718
$999$	−95.3193	−3.01577

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6005.2.a.f.1.5	✓	111

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6005.2.a.f.1.5	✓	111	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:	\( N \)	\(=\)	\( 6005 = 5 \cdot 1201 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6005.a (trivial)

\(f(q)\)	\(=\)	\(q-2.63642 q^{2} +3.34656 q^{3} +4.95072 q^{4} +1.00000 q^{5} -8.82296 q^{6} -3.64864 q^{7} -7.77935 q^{8} +8.19949 q^{9} +O(q^{10})\)	\(q-2.63642 q^{2} +3.34656 q^{3} +4.95072 q^{4} +1.00000 q^{5} -8.82296 q^{6} -3.64864 q^{7} -7.77935 q^{8} +8.19949 q^{9} -2.63642 q^{10} -3.22202 q^{11} +16.5679 q^{12} -4.33134 q^{13} +9.61935 q^{14} +3.34656 q^{15} +10.6082 q^{16} +5.04761 q^{17} -21.6173 q^{18} -8.39943 q^{19} +4.95072 q^{20} -12.2104 q^{21} +8.49461 q^{22} -0.122181 q^{23} -26.0341 q^{24} +1.00000 q^{25} +11.4192 q^{26} +17.4004 q^{27} -18.0634 q^{28} +0.184441 q^{29} -8.82296 q^{30} +1.68269 q^{31} -12.4090 q^{32} -10.7827 q^{33} -13.3076 q^{34} -3.64864 q^{35} +40.5934 q^{36} -5.47798 q^{37} +22.1444 q^{38} -14.4951 q^{39} -7.77935 q^{40} +0.394032 q^{41} +32.1918 q^{42} +4.38959 q^{43} -15.9513 q^{44} +8.19949 q^{45} +0.322122 q^{46} +10.7897 q^{47} +35.5010 q^{48} +6.31256 q^{49} -2.63642 q^{50} +16.8922 q^{51} -21.4433 q^{52} -1.31567 q^{53} -45.8749 q^{54} -3.22202 q^{55} +28.3840 q^{56} -28.1092 q^{57} -0.486265 q^{58} +12.9908 q^{59} +16.5679 q^{60} +14.0944 q^{61} -4.43627 q^{62} -29.9170 q^{63} +11.4990 q^{64} -4.33134 q^{65} +28.4278 q^{66} +14.1551 q^{67} +24.9893 q^{68} -0.408888 q^{69} +9.61935 q^{70} -10.4859 q^{71} -63.7867 q^{72} +12.9997 q^{73} +14.4423 q^{74} +3.34656 q^{75} -41.5832 q^{76} +11.7560 q^{77} +38.2152 q^{78} +4.91587 q^{79} +10.6082 q^{80} +33.6332 q^{81} -1.03884 q^{82} +16.2346 q^{83} -60.4503 q^{84} +5.04761 q^{85} -11.5728 q^{86} +0.617244 q^{87} +25.0652 q^{88} -11.3890 q^{89} -21.6173 q^{90} +15.8035 q^{91} -0.604886 q^{92} +5.63121 q^{93} -28.4463 q^{94} -8.39943 q^{95} -41.5275 q^{96} +9.19002 q^{97} -16.6426 q^{98} -26.4190 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 111 q + 20 q^{2} + 40 q^{3} + 136 q^{4} + 111 q^{5} + 3 q^{6} + 39 q^{7} + 45 q^{8} + 139 q^{9}+O(q^{10}) \) 111 * q + 20 * q^2 + 40 * q^3 + 136 * q^4 + 111 * q^5 + 3 * q^6 + 39 * q^7 + 45 * q^8 + 139 * q^9	\( 111 q + 20 q^{2} + 40 q^{3} + 136 q^{4} + 111 q^{5} + 3 q^{6} + 39 q^{7} + 45 q^{8} + 139 q^{9} + 20 q^{10} + 36 q^{11} + 80 q^{12} + 36 q^{13} + 7 q^{14} + 40 q^{15} + 190 q^{16} + 38 q^{17} + 48 q^{18} + 77 q^{19} + 136 q^{20} + 11 q^{21} + 39 q^{22} + 82 q^{23} - 3 q^{24} + 111 q^{25} - 3 q^{26} + 130 q^{27} + 87 q^{28} + 20 q^{29} + 3 q^{30} + 41 q^{31} + 85 q^{32} + 33 q^{33} + 7 q^{34} + 39 q^{35} + 191 q^{36} + 80 q^{37} + 42 q^{38} + 21 q^{39} + 45 q^{40} + 16 q^{41} + 33 q^{42} + 164 q^{43} + 37 q^{44} + 139 q^{45} + 32 q^{46} + 148 q^{47} + 149 q^{48} + 160 q^{49} + 20 q^{50} + 51 q^{51} + 87 q^{52} + 83 q^{53} - 6 q^{54} + 36 q^{55} - 10 q^{56} + 28 q^{57} + 47 q^{58} + 14 q^{59} + 80 q^{60} + 20 q^{61} + 14 q^{62} + 120 q^{63} + 231 q^{64} + 36 q^{65} - 4 q^{66} + 253 q^{67} + 80 q^{68} + 6 q^{69} + 7 q^{70} + 5 q^{71} + 124 q^{72} + 64 q^{73} - 37 q^{74} + 40 q^{75} + 92 q^{76} + 63 q^{77} + 29 q^{78} + 91 q^{79} + 190 q^{80} + 187 q^{81} - 7 q^{82} + 63 q^{83} - 69 q^{84} + 38 q^{85} - 22 q^{86} + 57 q^{87} + 121 q^{88} - 6 q^{89} + 48 q^{90} + 119 q^{91} + 104 q^{92} + 14 q^{93} - q^{94} + 77 q^{95} - 38 q^{96} + 96 q^{97} + 81 q^{98} + 106 q^{99}+O(q^{100}) \) 111 * q + 20 * q^2 + 40 * q^3 + 136 * q^4 + 111 * q^5 + 3 * q^6 + 39 * q^7 + 45 * q^8 + 139 * q^9 + 20 * q^10 + 36 * q^11 + 80 * q^12 + 36 * q^13 + 7 * q^14 + 40 * q^15 + 190 * q^16 + 38 * q^17 + 48 * q^18 + 77 * q^19 + 136 * q^20 + 11 * q^21 + 39 * q^22 + 82 * q^23 - 3 * q^24 + 111 * q^25 - 3 * q^26 + 130 * q^27 + 87 * q^28 + 20 * q^29 + 3 * q^30 + 41 * q^31 + 85 * q^32 + 33 * q^33 + 7 * q^34 + 39 * q^35 + 191 * q^36 + 80 * q^37 + 42 * q^38 + 21 * q^39 + 45 * q^40 + 16 * q^41 + 33 * q^42 + 164 * q^43 + 37 * q^44 + 139 * q^45 + 32 * q^46 + 148 * q^47 + 149 * q^48 + 160 * q^49 + 20 * q^50 + 51 * q^51 + 87 * q^52 + 83 * q^53 - 6 * q^54 + 36 * q^55 - 10 * q^56 + 28 * q^57 + 47 * q^58 + 14 * q^59 + 80 * q^60 + 20 * q^61 + 14 * q^62 + 120 * q^63 + 231 * q^64 + 36 * q^65 - 4 * q^66 + 253 * q^67 + 80 * q^68 + 6 * q^69 + 7 * q^70 + 5 * q^71 + 124 * q^72 + 64 * q^73 - 37 * q^74 + 40 * q^75 + 92 * q^76 + 63 * q^77 + 29 * q^78 + 91 * q^79 + 190 * q^80 + 187 * q^81 - 7 * q^82 + 63 * q^83 - 69 * q^84 + 38 * q^85 - 22 * q^86 + 57 * q^87 + 121 * q^88 - 6 * q^89 + 48 * q^90 + 119 * q^91 + 104 * q^92 + 14 * q^93 - q^94 + 77 * q^95 - 38 * q^96 + 96 * q^97 + 81 * q^98 + 106 * q^99

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