LMFDB - Embedded newform 6010.2.a.f.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6010,2,Mod(1,6010)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6010, 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("6010.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6010 = 2 \cdot 5 \cdot 601 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6010.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:	$47.9900916148$
Analytic rank:	$1$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	6010.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.55148 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.55148 q^{6} +2.51624 q^{7} +1.00000 q^{8} -0.592901 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.55148 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.55148 q^{6} +2.51624 q^{7} +1.00000 q^{8} -0.592901 q^{9} -1.00000 q^{10} -5.46728 q^{11} -1.55148 q^{12} +3.57909 q^{13} +2.51624 q^{14} +1.55148 q^{15} +1.00000 q^{16} -1.82409 q^{17} -0.592901 q^{18} +0.145449 q^{19} -1.00000 q^{20} -3.90390 q^{21} -5.46728 q^{22} -3.72992 q^{23} -1.55148 q^{24} +1.00000 q^{25} +3.57909 q^{26} +5.57432 q^{27} +2.51624 q^{28} +5.42201 q^{29} +1.55148 q^{30} +5.70954 q^{31} +1.00000 q^{32} +8.48238 q^{33} -1.82409 q^{34} -2.51624 q^{35} -0.592901 q^{36} -3.40636 q^{37} +0.145449 q^{38} -5.55289 q^{39} -1.00000 q^{40} -1.32156 q^{41} -3.90390 q^{42} +4.63563 q^{43} -5.46728 q^{44} +0.592901 q^{45} -3.72992 q^{46} +0.489901 q^{47} -1.55148 q^{48} -0.668534 q^{49} +1.00000 q^{50} +2.83004 q^{51} +3.57909 q^{52} +4.04925 q^{53} +5.57432 q^{54} +5.46728 q^{55} +2.51624 q^{56} -0.225662 q^{57} +5.42201 q^{58} -9.44852 q^{59} +1.55148 q^{60} -7.07575 q^{61} +5.70954 q^{62} -1.49188 q^{63} +1.00000 q^{64} -3.57909 q^{65} +8.48238 q^{66} -7.43807 q^{67} -1.82409 q^{68} +5.78691 q^{69} -2.51624 q^{70} -5.82379 q^{71} -0.592901 q^{72} -10.3824 q^{73} -3.40636 q^{74} -1.55148 q^{75} +0.145449 q^{76} -13.7570 q^{77} -5.55289 q^{78} -9.84027 q^{79} -1.00000 q^{80} -6.86976 q^{81} -1.32156 q^{82} +6.30177 q^{83} -3.90390 q^{84} +1.82409 q^{85} +4.63563 q^{86} -8.41215 q^{87} -5.46728 q^{88} -14.4635 q^{89} +0.592901 q^{90} +9.00584 q^{91} -3.72992 q^{92} -8.85825 q^{93} +0.489901 q^{94} -0.145449 q^{95} -1.55148 q^{96} +11.9361 q^{97} -0.668534 q^{98} +3.24155 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 22 q^{2} - 6 q^{3} + 22 q^{4} - 22 q^{5} - 6 q^{6} - 12 q^{7} + 22 q^{8} + 12 q^{9}+O(q^{10}) $ 22 * q + 22 * q^2 - 6 * q^3 + 22 * q^4 - 22 * q^5 - 6 * q^6 - 12 * q^7 + 22 * q^8 + 12 * q^9	\( 22 q + 22 q^{2} - 6 q^{3} + 22 q^{4} - 22 q^{5} - 6 q^{6} - 12 q^{7} + 22 q^{8} + 12 q^{9} - 22 q^{10} - 4 q^{11} - 6 q^{12} - 20 q^{13} - 12 q^{14} + 6 q^{15} + 22 q^{16} - 23 q^{17} + 12 q^{18} + q^{19} - 22 q^{20} - 8 q^{21} - 4 q^{22} - 17 q^{23} - 6 q^{24} + 22 q^{25} - 20 q^{26} - 21 q^{27} - 12 q^{28} - 13 q^{29} + 6 q^{30} - 13 q^{31} + 22 q^{32} - 21 q^{33} - 23 q^{34} + 12 q^{35} + 12 q^{36} - 16 q^{37} + q^{38} - 4 q^{39} - 22 q^{40} - 31 q^{41} - 8 q^{42} - 9 q^{43} - 4 q^{44} - 12 q^{45} - 17 q^{46} - 41 q^{47} - 6 q^{48} - 6 q^{49} + 22 q^{50} - 7 q^{51} - 20 q^{52} - 15 q^{53} - 21 q^{54} + 4 q^{55} - 12 q^{56} - 26 q^{57} - 13 q^{58} - 32 q^{59} + 6 q^{60} - 22 q^{61} - 13 q^{62} - 55 q^{63} + 22 q^{64} + 20 q^{65} - 21 q^{66} - 19 q^{67} - 23 q^{68} - 37 q^{69} + 12 q^{70} - 36 q^{71} + 12 q^{72} - 47 q^{73} - 16 q^{74} - 6 q^{75} + q^{76} - 26 q^{77} - 4 q^{78} - 10 q^{79} - 22 q^{80} - 18 q^{81} - 31 q^{82} - 48 q^{83} - 8 q^{84} + 23 q^{85} - 9 q^{86} - 50 q^{87} - 4 q^{88} - 42 q^{89} - 12 q^{90} + 25 q^{91} - 17 q^{92} - 48 q^{93} - 41 q^{94} - q^{95} - 6 q^{96} - 67 q^{97} - 6 q^{98} - 3 q^{99}+O(q^{100}) \) 22 * q + 22 * q^2 - 6 * q^3 + 22 * q^4 - 22 * q^5 - 6 * q^6 - 12 * q^7 + 22 * q^8 + 12 * q^9 - 22 * q^10 - 4 * q^11 - 6 * q^12 - 20 * q^13 - 12 * q^14 + 6 * q^15 + 22 * q^16 - 23 * q^17 + 12 * q^18 + q^19 - 22 * q^20 - 8 * q^21 - 4 * q^22 - 17 * q^23 - 6 * q^24 + 22 * q^25 - 20 * q^26 - 21 * q^27 - 12 * q^28 - 13 * q^29 + 6 * q^30 - 13 * q^31 + 22 * q^32 - 21 * q^33 - 23 * q^34 + 12 * q^35 + 12 * q^36 - 16 * q^37 + q^38 - 4 * q^39 - 22 * q^40 - 31 * q^41 - 8 * q^42 - 9 * q^43 - 4 * q^44 - 12 * q^45 - 17 * q^46 - 41 * q^47 - 6 * q^48 - 6 * q^49 + 22 * q^50 - 7 * q^51 - 20 * q^52 - 15 * q^53 - 21 * q^54 + 4 * q^55 - 12 * q^56 - 26 * q^57 - 13 * q^58 - 32 * q^59 + 6 * q^60 - 22 * q^61 - 13 * q^62 - 55 * q^63 + 22 * q^64 + 20 * q^65 - 21 * q^66 - 19 * q^67 - 23 * q^68 - 37 * q^69 + 12 * q^70 - 36 * q^71 + 12 * q^72 - 47 * q^73 - 16 * q^74 - 6 * q^75 + q^76 - 26 * q^77 - 4 * q^78 - 10 * q^79 - 22 * q^80 - 18 * q^81 - 31 * q^82 - 48 * q^83 - 8 * q^84 + 23 * q^85 - 9 * q^86 - 50 * q^87 - 4 * q^88 - 42 * q^89 - 12 * q^90 + 25 * q^91 - 17 * q^92 - 48 * q^93 - 41 * q^94 - q^95 - 6 * q^96 - 67 * q^97 - 6 * q^98 - 3 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.55148	−0.895749	−0.447874	−	0.894096i	$-0.647819\pi$
$3$	−1.55148	−0.895749	−0.447874	+	0.894096i	$0.647819\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.55148	−0.633390
$7$	2.51624	0.951050	0.475525	−	0.879702i	$-0.342258\pi$
$7$	2.51624	0.951050	0.475525	+	0.879702i	$0.342258\pi$
$8$	1.00000	0.353553
$9$	−0.592901	−0.197634
$10$	−1.00000	−0.316228
$11$	−5.46728	−1.64845	−0.824223	−	0.566266i	$-0.808388\pi$
$11$	−5.46728	−1.64845	−0.824223	+	0.566266i	$0.808388\pi$
$12$	−1.55148	−0.447874
$13$	3.57909	0.992660	0.496330	−	0.868134i	$-0.334681\pi$
$13$	3.57909	0.992660	0.496330	+	0.868134i	$0.334681\pi$
$14$	2.51624	0.672494
$15$	1.55148	0.400591
$16$	1.00000	0.250000
$17$	−1.82409	−0.442406	−0.221203	−	0.975228i	$-0.570998\pi$
$17$	−1.82409	−0.442406	−0.221203	+	0.975228i	$0.570998\pi$
$18$	−0.592901	−0.139748
$19$	0.145449	0.0333684	0.0166842	−	0.999861i	$-0.494689\pi$
$19$	0.145449	0.0333684	0.0166842	+	0.999861i	$0.494689\pi$
$20$	−1.00000	−0.223607
$21$	−3.90390	−0.851902
$22$	−5.46728	−1.16563
$23$	−3.72992	−0.777743	−0.388871	−	0.921292i	$-0.627135\pi$
$23$	−3.72992	−0.777743	−0.388871	+	0.921292i	$0.627135\pi$
$24$	−1.55148	−0.316695
$25$	1.00000	0.200000
$26$	3.57909	0.701916
$27$	5.57432	1.07278
$28$	2.51624	0.475525
$29$	5.42201	1.00684	0.503421	−	0.864041i	$-0.332075\pi$
$29$	5.42201	1.00684	0.503421	+	0.864041i	$0.332075\pi$
$30$	1.55148	0.283261
$31$	5.70954	1.02546	0.512732	−	0.858549i	$-0.328633\pi$
$31$	5.70954	1.02546	0.512732	+	0.858549i	$0.328633\pi$
$32$	1.00000	0.176777
$33$	8.48238	1.47659
$34$	−1.82409	−0.312828
$35$	−2.51624	−0.425322
$36$	−0.592901	−0.0988169
$37$	−3.40636	−0.560001	−0.280001	−	0.960000i	$-0.590335\pi$
$37$	−3.40636	−0.560001	−0.280001	+	0.960000i	$0.590335\pi$
$38$	0.145449	0.0235950
$39$	−5.55289	−0.889174
$40$	−1.00000	−0.158114
$41$	−1.32156	−0.206393	−0.103196	−	0.994661i	$-0.532907\pi$
$41$	−1.32156	−0.206393	−0.103196	+	0.994661i	$0.532907\pi$
$42$	−3.90390	−0.602385
$43$	4.63563	0.706926	0.353463	−	0.935448i	$-0.385004\pi$
$43$	4.63563	0.706926	0.353463	+	0.935448i	$0.385004\pi$
$44$	−5.46728	−0.824223
$45$	0.592901	0.0883845
$46$	−3.72992	−0.549947
$47$	0.489901	0.0714594	0.0357297	−	0.999361i	$-0.488624\pi$
$47$	0.489901	0.0714594	0.0357297	+	0.999361i	$0.488624\pi$
$48$	−1.55148	−0.223937
$49$	−0.668534	−0.0955048
$50$	1.00000	0.141421
$51$	2.83004	0.396285
$52$	3.57909	0.496330
$53$	4.04925	0.556207	0.278104	−	0.960551i	$-0.410294\pi$
$53$	4.04925	0.556207	0.278104	+	0.960551i	$0.410294\pi$
$54$	5.57432	0.758569
$55$	5.46728	0.737207
$56$	2.51624	0.336247
$57$	−0.225662	−0.0298897
$58$	5.42201	0.711944
$59$	−9.44852	−1.23009	−0.615046	−	0.788491i	$-0.710863\pi$
$59$	−9.44852	−1.23009	−0.615046	+	0.788491i	$0.710863\pi$
$60$	1.55148	0.200296
$61$	−7.07575	−0.905956	−0.452978	−	0.891522i	$-0.649638\pi$
$61$	−7.07575	−0.905956	−0.452978	+	0.891522i	$0.649638\pi$
$62$	5.70954	0.725112
$63$	−1.49188	−0.187959
$64$	1.00000	0.125000
$65$	−3.57909	−0.443931
$66$	8.48238	1.04411
$67$	−7.43807	−0.908705	−0.454353	−	0.890822i	$-0.650129\pi$
$67$	−7.43807	−0.908705	−0.454353	+	0.890822i	$0.650129\pi$
$68$	−1.82409	−0.221203
$69$	5.78691	0.696662
$70$	−2.51624	−0.300748
$71$	−5.82379	−0.691157	−0.345578	−	0.938390i	$-0.612317\pi$
$71$	−5.82379	−0.691157	−0.345578	+	0.938390i	$0.612317\pi$
$72$	−0.592901	−0.0698741
$73$	−10.3824	−1.21517	−0.607584	−	0.794255i	$-0.707861\pi$
$73$	−10.3824	−1.21517	−0.607584	+	0.794255i	$0.707861\pi$
$74$	−3.40636	−0.395981
$75$	−1.55148	−0.179150
$76$	0.145449	0.0166842
$77$	−13.7570	−1.56775
$78$	−5.55289	−0.628741
$79$	−9.84027	−1.10712	−0.553559	−	0.832810i	$-0.686731\pi$
$79$	−9.84027	−1.10712	−0.553559	+	0.832810i	$0.686731\pi$
$80$	−1.00000	−0.111803
$81$	−6.86976	−0.763307
$82$	−1.32156	−0.145942
$83$	6.30177	0.691709	0.345855	−	0.938288i	$-0.387589\pi$
$83$	6.30177	0.691709	0.345855	+	0.938288i	$0.387589\pi$
$84$	−3.90390	−0.425951
$85$	1.82409	0.197850
$86$	4.63563	0.499872
$87$	−8.41215	−0.901877
$88$	−5.46728	−0.582814
$89$	−14.4635	−1.53313	−0.766565	−	0.642167i	$-0.778036\pi$
$89$	−14.4635	−1.53313	−0.766565	+	0.642167i	$0.778036\pi$
$90$	0.592901	0.0624973
$91$	9.00584	0.944068
$92$	−3.72992	−0.388871
$93$	−8.85825	−0.918558
$94$	0.489901	0.0505294
$95$	−0.145449	−0.0149228
$96$	−1.55148	−0.158348
$97$	11.9361	1.21193	0.605965	−	0.795491i	$-0.292787\pi$
$97$	11.9361	1.21193	0.605965	+	0.795491i	$0.292787\pi$
$98$	−0.668534	−0.0675321
$99$	3.24155	0.325789
$100$	1.00000	0.100000
$101$	−12.4271	−1.23654	−0.618271	−	0.785965i	$-0.712167\pi$
$101$	−12.4271	−1.23654	−0.618271	+	0.785965i	$0.712167\pi$
$102$	2.83004	0.280215
$103$	10.3220	1.01706	0.508531	−	0.861044i	$-0.330189\pi$
$103$	10.3220	1.01706	0.508531	+	0.861044i	$0.330189\pi$
$104$	3.57909	0.350958
$105$	3.90390	0.380982
$106$	4.04925	0.393298
$107$	10.9407	1.05767	0.528837	−	0.848724i	$-0.322628\pi$
$107$	10.9407	1.05767	0.528837	+	0.848724i	$0.322628\pi$
$108$	5.57432	0.536390
$109$	−17.9393	−1.71827	−0.859136	−	0.511747i	$-0.828998\pi$
$109$	−17.9393	−1.71827	−0.859136	+	0.511747i	$0.828998\pi$
$110$	5.46728	0.521284
$111$	5.28490	0.501621
$112$	2.51624	0.237762
$113$	2.10346	0.197877	0.0989385	−	0.995094i	$-0.468455\pi$
$113$	2.10346	0.197877	0.0989385	+	0.995094i	$0.468455\pi$
$114$	−0.225662	−0.0211352
$115$	3.72992	0.347817
$116$	5.42201	0.503421
$117$	−2.12204	−0.196183
$118$	−9.44852	−0.869806
$119$	−4.58984	−0.420750
$120$	1.55148	0.141630
$121$	18.8911	1.71737
$122$	−7.07575	−0.640608
$123$	2.05037	0.184876
$124$	5.70954	0.512732
$125$	−1.00000	−0.0894427
$126$	−1.49188	−0.132907
$127$	−10.8772	−0.965194	−0.482597	−	0.875843i	$-0.660306\pi$
$127$	−10.8772	−0.965194	−0.482597	+	0.875843i	$0.660306\pi$
$128$	1.00000	0.0883883
$129$	−7.19209	−0.633229
$130$	−3.57909	−0.313907
$131$	1.02115	0.0892183	0.0446091	−	0.999005i	$-0.485796\pi$
$131$	1.02115	0.0892183	0.0446091	+	0.999005i	$0.485796\pi$
$132$	8.48238	0.738297
$133$	0.365986	0.0317350
$134$	−7.43807	−0.642552
$135$	−5.57432	−0.479761
$136$	−1.82409	−0.156414
$137$	−3.04616	−0.260251	−0.130125	−	0.991498i	$-0.541538\pi$
$137$	−3.04616	−0.260251	−0.130125	+	0.991498i	$0.541538\pi$
$138$	5.78691	0.492614
$139$	19.5796	1.66072	0.830360	−	0.557228i	$-0.188135\pi$
$139$	19.5796	1.66072	0.830360	+	0.557228i	$0.188135\pi$
$140$	−2.51624	−0.212661
$141$	−0.760073	−0.0640097
$142$	−5.82379	−0.488721
$143$	−19.5678	−1.63635
$144$	−0.592901	−0.0494084
$145$	−5.42201	−0.450273
$146$	−10.3824	−0.859254
$147$	1.03722	0.0855484
$148$	−3.40636	−0.280001
$149$	2.10742	0.172647	0.0863233	−	0.996267i	$-0.472488\pi$
$149$	2.10742	0.172647	0.0863233	+	0.996267i	$0.472488\pi$
$150$	−1.55148	−0.126678
$151$	0.762679	0.0620659	0.0310330	−	0.999518i	$-0.490120\pi$
$151$	0.762679	0.0620659	0.0310330	+	0.999518i	$0.490120\pi$
$152$	0.145449	0.0117975
$153$	1.08150	0.0874343
$154$	−13.7570	−1.10857
$155$	−5.70954	−0.458601
$156$	−5.55289	−0.444587
$157$	−6.36772	−0.508200	−0.254100	−	0.967178i	$-0.581779\pi$
$157$	−6.36772	−0.508200	−0.254100	+	0.967178i	$0.581779\pi$
$158$	−9.84027	−0.782850
$159$	−6.28234	−0.498222
$160$	−1.00000	−0.0790569
$161$	−9.38538	−0.739672
$162$	−6.86976	−0.539740
$163$	−5.58787	−0.437676	−0.218838	−	0.975761i	$-0.570227\pi$
$163$	−5.58787	−0.437676	−0.218838	+	0.975761i	$0.570227\pi$
$164$	−1.32156	−0.103196
$165$	−8.48238	−0.660353
$166$	6.30177	0.489112
$167$	14.6115	1.13067	0.565334	−	0.824862i	$-0.308747\pi$
$167$	14.6115	1.13067	0.565334	+	0.824862i	$0.308747\pi$
$168$	−3.90390	−0.301193
$169$	−0.190150	−0.0146269
$170$	1.82409	0.139901
$171$	−0.0862371	−0.00659472
$172$	4.63563	0.353463
$173$	15.5139	1.17950	0.589751	−	0.807585i	$-0.299226\pi$
$173$	15.5139	1.17950	0.589751	+	0.807585i	$0.299226\pi$
$174$	−8.41215	−0.637723
$175$	2.51624	0.190210
$176$	−5.46728	−0.412111
$177$	14.6592	1.10185
$178$	−14.4635	−1.08409
$179$	−19.6240	−1.46676	−0.733382	−	0.679817i	$-0.762059\pi$
$179$	−19.6240	−1.46676	−0.733382	+	0.679817i	$0.762059\pi$
$180$	0.592901	0.0441923
$181$	−1.83064	−0.136070	−0.0680351	−	0.997683i	$-0.521673\pi$
$181$	−1.83064	−0.136070	−0.0680351	+	0.997683i	$0.521673\pi$
$182$	9.00584	0.667557
$183$	10.9779	0.811509
$184$	−3.72992	−0.274974
$185$	3.40636	0.250440
$186$	−8.85825	−0.649519
$187$	9.97278	0.729282
$188$	0.489901	0.0357297
$189$	14.0263	1.02027
$190$	−0.145449	−0.0105520
$191$	23.8359	1.72471	0.862353	−	0.506307i	$-0.168990\pi$
$191$	23.8359	1.72471	0.862353	+	0.506307i	$0.168990\pi$
$192$	−1.55148	−0.111969
$193$	−12.5740	−0.905099	−0.452550	−	0.891739i	$-0.649485\pi$
$193$	−12.5740	−0.905099	−0.452550	+	0.891739i	$0.649485\pi$
$194$	11.9361	0.856964
$195$	5.55289	0.397651
$196$	−0.668534	−0.0477524
$197$	−19.5142	−1.39033	−0.695164	−	0.718851i	$-0.744668\pi$
$197$	−19.5142	−1.39033	−0.695164	+	0.718851i	$0.744668\pi$
$198$	3.24155	0.230367
$199$	−18.9541	−1.34362	−0.671809	−	0.740724i	$-0.734483\pi$
$199$	−18.9541	−1.34362	−0.671809	+	0.740724i	$0.734483\pi$
$200$	1.00000	0.0707107
$201$	11.5400	0.813972
$202$	−12.4271	−0.874367
$203$	13.6431	0.957556
$204$	2.83004	0.198142
$205$	1.32156	0.0923016
$206$	10.3220	0.719171
$207$	2.21148	0.153708
$208$	3.57909	0.248165
$209$	−0.795212	−0.0550060
$210$	3.90390	0.269395
$211$	−7.85599	−0.540828	−0.270414	−	0.962744i	$-0.587161\pi$
$211$	−7.85599	−0.540828	−0.270414	+	0.962744i	$0.587161\pi$
$212$	4.04925	0.278104
$213$	9.03551	0.619103
$214$	10.9407	0.747888
$215$	−4.63563	−0.316147
$216$	5.57432	0.379285
$217$	14.3666	0.975267
$218$	−17.9393	−1.21500
$219$	16.1081	1.08849
$220$	5.46728	0.368604
$221$	−6.52856	−0.439158
$222$	5.28490	0.354699
$223$	−3.51095	−0.235111	−0.117555	−	0.993066i	$-0.537506\pi$
$223$	−3.51095	−0.235111	−0.117555	+	0.993066i	$0.537506\pi$
$224$	2.51624	0.168123
$225$	−0.592901	−0.0395268
$226$	2.10346	0.139920
$227$	−27.3524	−1.81544	−0.907721	−	0.419575i	$-0.862179\pi$
$227$	−27.3524	−1.81544	−0.907721	+	0.419575i	$0.862179\pi$
$228$	−0.225662	−0.0149448
$229$	7.64016	0.504876	0.252438	−	0.967613i	$-0.418768\pi$
$229$	7.64016	0.504876	0.252438	+	0.967613i	$0.418768\pi$
$230$	3.72992	0.245944
$231$	21.3437	1.40431
$232$	5.42201	0.355972
$233$	−27.7661	−1.81902	−0.909510	−	0.415683i	$-0.863543\pi$
$233$	−27.7661	−1.81902	−0.909510	+	0.415683i	$0.863543\pi$
$234$	−2.12204	−0.138722
$235$	−0.489901	−0.0319576
$236$	−9.44852	−0.615046
$237$	15.2670	0.991699
$238$	−4.58984	−0.297515
$239$	−25.6990	−1.66233	−0.831164	−	0.556027i	$-0.812325\pi$
$239$	−25.6990	−1.66233	−0.831164	+	0.556027i	$0.812325\pi$
$240$	1.55148	0.100148
$241$	23.1891	1.49374	0.746871	−	0.664969i	$-0.231555\pi$
$241$	23.1891	1.49374	0.746871	+	0.664969i	$0.231555\pi$
$242$	18.8911	1.21437
$243$	−6.06465	−0.389048
$244$	−7.07575	−0.452978
$245$	0.668534	0.0427111
$246$	2.05037	0.130727
$247$	0.520576	0.0331234
$248$	5.70954	0.362556
$249$	−9.77709	−0.619598
$250$	−1.00000	−0.0632456
$251$	−13.6544	−0.861857	−0.430928	−	0.902386i	$-0.641814\pi$
$251$	−13.6544	−0.861857	−0.430928	+	0.902386i	$0.641814\pi$
$252$	−1.49188	−0.0939797
$253$	20.3925	1.28207
$254$	−10.8772	−0.682495
$255$	−2.83004	−0.177224
$256$	1.00000	0.0625000
$257$	−30.4866	−1.90170	−0.950852	−	0.309647i	$-0.899789\pi$
$257$	−30.4866	−1.90170	−0.950852	+	0.309647i	$0.899789\pi$
$258$	−7.19209	−0.447760
$259$	−8.57121	−0.532589
$260$	−3.57909	−0.221965
$261$	−3.21471	−0.198986
$262$	1.02115	0.0630869
$263$	−19.7667	−1.21887	−0.609435	−	0.792836i	$-0.708604\pi$
$263$	−19.7667	−1.21887	−0.609435	+	0.792836i	$0.708604\pi$
$264$	8.48238	0.522055
$265$	−4.04925	−0.248743
$266$	0.365986	0.0224400
$267$	22.4399	1.37330
$268$	−7.43807	−0.454353
$269$	−4.43544	−0.270433	−0.135217	−	0.990816i	$-0.543173\pi$
$269$	−4.43544	−0.270433	−0.135217	+	0.990816i	$0.543173\pi$
$270$	−5.57432	−0.339243
$271$	−9.41500	−0.571921	−0.285960	−	0.958241i	$-0.592313\pi$
$271$	−9.41500	−0.571921	−0.285960	+	0.958241i	$0.592313\pi$
$272$	−1.82409	−0.110601
$273$	−13.9724	−0.845648
$274$	−3.04616	−0.184025
$275$	−5.46728	−0.329689
$276$	5.78691	0.348331
$277$	20.3179	1.22079	0.610393	−	0.792099i	$-0.291012\pi$
$277$	20.3179	1.22079	0.610393	+	0.792099i	$0.291012\pi$
$278$	19.5796	1.17431
$279$	−3.38519	−0.202666
$280$	−2.51624	−0.150374
$281$	−30.4025	−1.81366	−0.906831	−	0.421495i	$-0.861506\pi$
$281$	−30.4025	−1.81366	−0.906831	+	0.421495i	$0.861506\pi$
$282$	−0.760073	−0.0452617
$283$	−18.0465	−1.07275	−0.536377	−	0.843978i	$-0.680208\pi$
$283$	−18.0465	−1.07275	−0.536377	+	0.843978i	$0.680208\pi$
$284$	−5.82379	−0.345578
$285$	0.225662	0.0133671
$286$	−19.5678	−1.15707
$287$	−3.32536	−0.196290
$288$	−0.592901	−0.0349370
$289$	−13.6727	−0.804277
$290$	−5.42201	−0.318391
$291$	−18.5187	−1.08558
$292$	−10.3824	−0.607584
$293$	−1.24949	−0.0729961	−0.0364980	−	0.999334i	$-0.511620\pi$
$293$	−1.24949	−0.0729961	−0.0364980	+	0.999334i	$0.511620\pi$
$294$	1.03722	0.0604918
$295$	9.44852	0.550114
$296$	−3.40636	−0.197990
$297$	−30.4764	−1.76842
$298$	2.10742	0.122080
$299$	−13.3497	−0.772034
$300$	−1.55148	−0.0895749
$301$	11.6643	0.672322
$302$	0.762679	0.0438872
$303$	19.2804	1.10763
$304$	0.145449	0.00834209
$305$	7.07575	0.405156
$306$	1.08150	0.0618254
$307$	−5.14385	−0.293575	−0.146788	−	0.989168i	$-0.546893\pi$
$307$	−5.14385	−0.293575	−0.146788	+	0.989168i	$0.546893\pi$
$308$	−13.7570	−0.783877
$309$	−16.0145	−0.911032
$310$	−5.70954	−0.324280
$311$	24.7438	1.40309	0.701546	−	0.712624i	$-0.252493\pi$
$311$	24.7438	1.40309	0.701546	+	0.712624i	$0.252493\pi$
$312$	−5.55289	−0.314370
$313$	11.4595	0.647727	0.323863	−	0.946104i	$-0.395018\pi$
$313$	11.4595	0.647727	0.323863	+	0.946104i	$0.395018\pi$
$314$	−6.36772	−0.359351
$315$	1.49188	0.0840580
$316$	−9.84027	−0.553559
$317$	−2.61938	−0.147119	−0.0735595	−	0.997291i	$-0.523436\pi$
$317$	−2.61938	−0.147119	−0.0735595	+	0.997291i	$0.523436\pi$
$318$	−6.28234	−0.352296
$319$	−29.6436	−1.65972
$320$	−1.00000	−0.0559017
$321$	−16.9742	−0.947410
$322$	−9.38538	−0.523027
$323$	−0.265312	−0.0147624
$324$	−6.86976	−0.381654
$325$	3.57909	0.198532
$326$	−5.58787	−0.309483
$327$	27.8325	1.53914
$328$	−1.32156	−0.0729708
$329$	1.23271	0.0679614
$330$	−8.48238	−0.466940
$331$	1.16765	0.0641797	0.0320899	−	0.999485i	$-0.489784\pi$
$331$	1.16765	0.0641797	0.0320899	+	0.999485i	$0.489784\pi$
$332$	6.30177	0.345855
$333$	2.01963	0.110675
$334$	14.6115	0.799503
$335$	7.43807	0.406385
$336$	−3.90390	−0.212975
$337$	16.8666	0.918782	0.459391	−	0.888234i	$-0.348068\pi$
$337$	16.8666	0.918782	0.459391	+	0.888234i	$0.348068\pi$
$338$	−0.190150	−0.0103428
$339$	−3.26348	−0.177248
$340$	1.82409	0.0989249
$341$	−31.2156	−1.69042
$342$	−0.0862371	−0.00466317
$343$	−19.2959	−1.04188
$344$	4.63563	0.249936
$345$	−5.78691	−0.311557
$346$	15.5139	0.834034
$347$	−24.9640	−1.34014	−0.670068	−	0.742299i	$-0.733735\pi$
$347$	−24.9640	−1.34014	−0.670068	+	0.742299i	$0.733735\pi$
$348$	−8.41215	−0.450938
$349$	−16.6940	−0.893607	−0.446804	−	0.894632i	$-0.647438\pi$
$349$	−16.6940	−0.893607	−0.446804	+	0.894632i	$0.647438\pi$
$350$	2.51624	0.134499
$351$	19.9510	1.06490
$352$	−5.46728	−0.291407
$353$	−14.6126	−0.777751	−0.388876	−	0.921290i	$-0.627136\pi$
$353$	−14.6126	−0.777751	−0.388876	+	0.921290i	$0.627136\pi$
$354$	14.6592	0.779128
$355$	5.82379	0.309095
$356$	−14.4635	−0.766565
$357$	7.12105	0.376886
$358$	−19.6240	−1.03716
$359$	26.7279	1.41065	0.705323	−	0.708886i	$-0.250802\pi$
$359$	26.7279	1.41065	0.705323	+	0.708886i	$0.250802\pi$
$360$	0.592901	0.0312486
$361$	−18.9788	−0.998887
$362$	−1.83064	−0.0962161
$363$	−29.3092	−1.53834
$364$	9.00584	0.472034
$365$	10.3824	0.543440
$366$	10.9779	0.573824
$367$	11.1395	0.581479	0.290740	−	0.956802i	$-0.406099\pi$
$367$	11.1395	0.581479	0.290740	+	0.956802i	$0.406099\pi$
$368$	−3.72992	−0.194436
$369$	0.783553	0.0407902
$370$	3.40636	0.177088
$371$	10.1889	0.528981
$372$	−8.85825	−0.459279
$373$	11.8887	0.615574	0.307787	−	0.951455i	$-0.400412\pi$
$373$	11.8887	0.615574	0.307787	+	0.951455i	$0.400412\pi$
$374$	9.97278	0.515680
$375$	1.55148	0.0801182
$376$	0.489901	0.0252647
$377$	19.4058	0.999451
$378$	14.0263	0.721437
$379$	10.6392	0.546497	0.273249	−	0.961943i	$-0.411902\pi$
$379$	10.6392	0.546497	0.273249	+	0.961943i	$0.411902\pi$
$380$	−0.145449	−0.00746140
$381$	16.8758	0.864572
$382$	23.8359	1.21955
$383$	−9.95657	−0.508757	−0.254379	−	0.967105i	$-0.581871\pi$
$383$	−9.95657	−0.508757	−0.254379	+	0.967105i	$0.581871\pi$
$384$	−1.55148	−0.0791738
$385$	13.7570	0.701121
$386$	−12.5740	−0.640002
$387$	−2.74847	−0.139713
$388$	11.9361	0.605965
$389$	36.4354	1.84735	0.923674	−	0.383179i	$-0.125171\pi$
$389$	36.4354	1.84735	0.923674	+	0.383179i	$0.125171\pi$
$390$	5.55289	0.281181
$391$	6.80370	0.344078
$392$	−0.668534	−0.0337661
$393$	−1.58430	−0.0799172
$394$	−19.5142	−0.983110
$395$	9.84027	0.495118
$396$	3.24155	0.162894
$397$	27.8635	1.39843	0.699215	−	0.714911i	$-0.253533\pi$
$397$	27.8635	1.39843	0.699215	+	0.714911i	$0.253533\pi$
$398$	−18.9541	−0.950082
$399$	−0.567820	−0.0284266
$400$	1.00000	0.0500000
$401$	−34.1005	−1.70290	−0.851449	−	0.524437i	$-0.824276\pi$
$401$	−34.1005	−1.70290	−0.851449	+	0.524437i	$0.824276\pi$
$402$	11.5400	0.575565
$403$	20.4349	1.01794
$404$	−12.4271	−0.618271
$405$	6.86976	0.341361
$406$	13.6431	0.677094
$407$	18.6235	0.923132
$408$	2.83004	0.140108
$409$	22.1772	1.09659	0.548297	−	0.836284i	$-0.315276\pi$
$409$	22.1772	1.09659	0.548297	+	0.836284i	$0.315276\pi$
$410$	1.32156	0.0652671
$411$	4.72606	0.233119
$412$	10.3220	0.508531
$413$	−23.7747	−1.16988
$414$	2.21148	0.108688
$415$	−6.30177	−0.309342
$416$	3.57909	0.175479
$417$	−30.3774	−1.48759
$418$	−0.795212	−0.0388951
$419$	−10.6393	−0.519765	−0.259883	−	0.965640i	$-0.583684\pi$
$419$	−10.6393	−0.519765	−0.259883	+	0.965640i	$0.583684\pi$
$420$	3.90390	0.190491
$421$	11.9313	0.581495	0.290747	−	0.956800i	$-0.406096\pi$
$421$	11.9313	0.581495	0.290747	+	0.956800i	$0.406096\pi$
$422$	−7.85599	−0.382423
$423$	−0.290463	−0.0141228
$424$	4.04925	0.196649
$425$	−1.82409	−0.0884811
$426$	9.03551	0.437772
$427$	−17.8043	−0.861609
$428$	10.9407	0.528837
$429$	30.3592	1.46575
$430$	−4.63563	−0.223550
$431$	25.9953	1.25215	0.626074	−	0.779764i	$-0.284661\pi$
$431$	25.9953	1.25215	0.626074	+	0.779764i	$0.284661\pi$
$432$	5.57432	0.268195
$433$	−38.9736	−1.87295	−0.936476	−	0.350732i	$-0.885933\pi$
$433$	−38.9736	−1.87295	−0.936476	+	0.350732i	$0.885933\pi$
$434$	14.3666	0.689618
$435$	8.41215	0.403332
$436$	−17.9393	−0.859136
$437$	−0.542515	−0.0259520
$438$	16.1081	0.769676
$439$	−1.41102	−0.0673445	−0.0336722	−	0.999433i	$-0.510720\pi$
$439$	−1.41102	−0.0673445	−0.0336722	+	0.999433i	$0.510720\pi$
$440$	5.46728	0.260642
$441$	0.396375	0.0188750
$442$	−6.52856	−0.310532
$443$	13.8606	0.658538	0.329269	−	0.944236i	$-0.393198\pi$
$443$	13.8606	0.658538	0.329269	+	0.944236i	$0.393198\pi$
$444$	5.28490	0.250810
$445$	14.4635	0.685637
$446$	−3.51095	−0.166248
$447$	−3.26963	−0.154648
$448$	2.51624	0.118881
$449$	13.3849	0.631673	0.315837	−	0.948814i	$-0.397715\pi$
$449$	13.3849	0.631673	0.315837	+	0.948814i	$0.397715\pi$
$450$	−0.592901	−0.0279496
$451$	7.22532	0.340227
$452$	2.10346	0.0989385
$453$	−1.18328	−0.0555955
$454$	−27.3524	−1.28371
$455$	−9.00584	−0.422200
$456$	−0.225662	−0.0105676
$457$	22.3038	1.04333	0.521664	−	0.853151i	$-0.325312\pi$
$457$	22.3038	1.04333	0.521664	+	0.853151i	$0.325312\pi$
$458$	7.64016	0.357001
$459$	−10.1680	−0.474604
$460$	3.72992	0.173909
$461$	−12.2682	−0.571385	−0.285693	−	0.958321i	$-0.592224\pi$
$461$	−12.2682	−0.571385	−0.285693	+	0.958321i	$0.592224\pi$
$462$	21.3437	0.993000
$463$	11.1839	0.519762	0.259881	−	0.965641i	$-0.416317\pi$
$463$	11.1839	0.519762	0.259881	+	0.965641i	$0.416317\pi$
$464$	5.42201	0.251710
$465$	8.85825	0.410792
$466$	−27.7661	−1.28624
$467$	20.5147	0.949307	0.474654	−	0.880173i	$-0.342573\pi$
$467$	20.5147	0.949307	0.474654	+	0.880173i	$0.342573\pi$
$468$	−2.12204	−0.0980915
$469$	−18.7160	−0.864224
$470$	−0.489901	−0.0225974
$471$	9.87941	0.455219
$472$	−9.44852	−0.434903
$473$	−25.3442	−1.16533
$474$	15.2670	0.701237
$475$	0.145449	0.00667368
$476$	−4.58984	−0.210375
$477$	−2.40080	−0.109925
$478$	−25.6990	−1.17544
$479$	−1.73507	−0.0792773	−0.0396386	−	0.999214i	$-0.512621\pi$
$479$	−1.73507	−0.0792773	−0.0396386	+	0.999214i	$0.512621\pi$
$480$	1.55148	0.0708152
$481$	−12.1916	−0.555891
$482$	23.1891	1.05623
$483$	14.5613	0.662560
$484$	18.8911	0.858687
$485$	−11.9361	−0.541991
$486$	−6.06465	−0.275098
$487$	13.8303	0.626709	0.313354	−	0.949636i	$-0.398547\pi$
$487$	13.8303	0.626709	0.313354	+	0.949636i	$0.398547\pi$
$488$	−7.07575	−0.320304
$489$	8.66948	0.392047
$490$	0.668534	0.0302013
$491$	7.76245	0.350315	0.175157	−	0.984540i	$-0.443957\pi$
$491$	7.76245	0.350315	0.175157	+	0.984540i	$0.443957\pi$
$492$	2.05037	0.0924380
$493$	−9.89020	−0.445432
$494$	0.520576	0.0234218
$495$	−3.24155	−0.145697
$496$	5.70954	0.256366
$497$	−14.6541	−0.657324
$498$	−9.77709	−0.438122
$499$	22.5863	1.01110	0.505550	−	0.862797i	$-0.331290\pi$
$499$	22.5863	1.01110	0.505550	+	0.862797i	$0.331290\pi$
$500$	−1.00000	−0.0447214
$501$	−22.6694	−1.01280
$502$	−13.6544	−0.609425
$503$	−1.12416	−0.0501239	−0.0250620	−	0.999686i	$-0.507978\pi$
$503$	−1.12416	−0.0501239	−0.0250620	+	0.999686i	$0.507978\pi$
$504$	−1.49188	−0.0664537
$505$	12.4271	0.552998
$506$	20.3925	0.906558
$507$	0.295014	0.0131020
$508$	−10.8772	−0.482597
$509$	18.7787	0.832351	0.416175	−	0.909284i	$-0.363370\pi$
$509$	18.7787	0.832351	0.416175	+	0.909284i	$0.363370\pi$
$510$	−2.83004	−0.125316
$511$	−26.1246	−1.15569
$512$	1.00000	0.0441942
$513$	0.810782	0.0357969
$514$	−30.4866	−1.34471
$515$	−10.3220	−0.454844
$516$	−7.19209	−0.316614
$517$	−2.67842	−0.117797
$518$	−8.57121	−0.376597
$519$	−24.0696	−1.05654
$520$	−3.57909	−0.156953
$521$	−8.13561	−0.356428	−0.178214	−	0.983992i	$-0.557032\pi$
$521$	−8.13561	−0.356428	−0.178214	+	0.983992i	$0.557032\pi$
$522$	−3.21471	−0.140704
$523$	−5.19466	−0.227147	−0.113573	−	0.993530i	$-0.536230\pi$
$523$	−5.19466	−0.227147	−0.113573	+	0.993530i	$0.536230\pi$
$524$	1.02115	0.0446091
$525$	−3.90390	−0.170380
$526$	−19.7667	−0.861871
$527$	−10.4147	−0.453671
$528$	8.48238	0.369148
$529$	−9.08768	−0.395117
$530$	−4.04925	−0.175888
$531$	5.60204	0.243108
$532$	0.365986	0.0158675
$533$	−4.72997	−0.204878
$534$	22.4399	0.971070
$535$	−10.9407	−0.473006
$536$	−7.43807	−0.321276
$537$	30.4462	1.31385
$538$	−4.43544	−0.191225
$539$	3.65506	0.157435
$540$	−5.57432	−0.239881
$541$	7.68632	0.330461	0.165230	−	0.986255i	$-0.447163\pi$
$541$	7.68632	0.330461	0.165230	+	0.986255i	$0.447163\pi$
$542$	−9.41500	−0.404409
$543$	2.84020	0.121885
$544$	−1.82409	−0.0782070
$545$	17.9393	0.768435
$546$	−13.9724	−0.597964
$547$	21.5266	0.920412	0.460206	−	0.887812i	$-0.347776\pi$
$547$	21.5266	0.920412	0.460206	+	0.887812i	$0.347776\pi$
$548$	−3.04616	−0.130125
$549$	4.19522	0.179048
$550$	−5.46728	−0.233125
$551$	0.788627	0.0335967
$552$	5.78691	0.246307
$553$	−24.7605	−1.05292
$554$	20.3179	0.863226
$555$	−5.28490	−0.224332
$556$	19.5796	0.830360
$557$	7.22629	0.306188	0.153094	−	0.988212i	$-0.451076\pi$
$557$	7.22629	0.306188	0.153094	+	0.988212i	$0.451076\pi$
$558$	−3.38519	−0.143307
$559$	16.5913	0.701737
$560$	−2.51624	−0.106331
$561$	−15.4726	−0.653254
$562$	−30.4025	−1.28245
$563$	−23.9006	−1.00729	−0.503645	−	0.863911i	$-0.668008\pi$
$563$	−23.9006	−1.00729	−0.503645	+	0.863911i	$0.668008\pi$
$564$	−0.760073	−0.0320048
$565$	−2.10346	−0.0884933
$566$	−18.0465	−0.758552
$567$	−17.2860	−0.725943
$568$	−5.82379	−0.244361
$569$	−24.7625	−1.03810	−0.519050	−	0.854744i	$-0.673714\pi$
$569$	−24.7625	−1.03810	−0.519050	+	0.854744i	$0.673714\pi$
$570$	0.225662	0.00945195
$571$	36.9038	1.54437	0.772187	−	0.635395i	$-0.219163\pi$
$571$	36.9038	1.54437	0.772187	+	0.635395i	$0.219163\pi$
$572$	−19.5678	−0.818173
$573$	−36.9810	−1.54490
$574$	−3.32536	−0.138798
$575$	−3.72992	−0.155549
$576$	−0.592901	−0.0247042
$577$	1.14216	0.0475489	0.0237744	−	0.999717i	$-0.492432\pi$
$577$	1.14216	0.0475489	0.0237744	+	0.999717i	$0.492432\pi$
$578$	−13.6727	−0.568710
$579$	19.5084	0.810742
$580$	−5.42201	−0.225137
$581$	15.8568	0.657850
$582$	−18.5187	−0.767624
$583$	−22.1384	−0.916877
$584$	−10.3824	−0.429627
$585$	2.12204	0.0877357
$586$	−1.24949	−0.0516160
$587$	−40.9148	−1.68873	−0.844367	−	0.535766i	$-0.820023\pi$
$587$	−40.9148	−1.68873	−0.844367	+	0.535766i	$0.820023\pi$
$588$	1.03722	0.0427742
$589$	0.830449	0.0342181
$590$	9.44852	0.388989
$591$	30.2759	1.24539
$592$	−3.40636	−0.140000
$593$	−22.6383	−0.929642	−0.464821	−	0.885405i	$-0.653881\pi$
$593$	−22.6383	−0.929642	−0.464821	+	0.885405i	$0.653881\pi$
$594$	−30.4764	−1.25046
$595$	4.58984	0.188165
$596$	2.10742	0.0863233
$597$	29.4069	1.20354
$598$	−13.3497	−0.545910
$599$	−23.1312	−0.945117	−0.472559	−	0.881299i	$-0.656669\pi$
$599$	−23.1312	−0.945117	−0.472559	+	0.881299i	$0.656669\pi$
$600$	−1.55148	−0.0633390
$601$	1.00000	0.0407909
$601$	1.00000	0.0407909
$602$	11.6643	0.475403
$603$	4.41004	0.179591
$604$	0.762679	0.0310330
$605$	−18.8911	−0.768033
$606$	19.2804	0.783213
$607$	−2.86711	−0.116373	−0.0581863	−	0.998306i	$-0.518532\pi$
$607$	−2.86711	−0.116373	−0.0581863	+	0.998306i	$0.518532\pi$
$608$	0.145449	0.00589875
$609$	−21.1670	−0.857730
$610$	7.07575	0.286489
$611$	1.75340	0.0709349
$612$	1.08150	0.0437172
$613$	−15.5517	−0.628129	−0.314064	−	0.949402i	$-0.601691\pi$
$613$	−15.5517	−0.628129	−0.314064	+	0.949402i	$0.601691\pi$
$614$	−5.14385	−0.207589
$615$	−2.05037	−0.0826791
$616$	−13.7570	−0.554285
$617$	−34.1572	−1.37512	−0.687558	−	0.726129i	$-0.741317\pi$
$617$	−34.1572	−1.37512	−0.687558	+	0.726129i	$0.741317\pi$
$618$	−16.0145	−0.644197
$619$	−6.10077	−0.245211	−0.122605	−	0.992456i	$-0.539125\pi$
$619$	−6.10077	−0.245211	−0.122605	+	0.992456i	$0.539125\pi$
$620$	−5.70954	−0.229301
$621$	−20.7918	−0.834346
$622$	24.7438	0.992137
$623$	−36.3937	−1.45808
$624$	−5.55289	−0.222293
$625$	1.00000	0.0400000
$626$	11.4595	0.458012
$627$	1.23376	0.0492715
$628$	−6.36772	−0.254100
$629$	6.21348	0.247748
$630$	1.49188	0.0594380
$631$	37.7230	1.50173	0.750864	−	0.660456i	$-0.229637\pi$
$631$	37.7230	1.50173	0.750864	+	0.660456i	$0.229637\pi$
$632$	−9.84027	−0.391425
$633$	12.1884	0.484447
$634$	−2.61938	−0.104029
$635$	10.8772	0.431648
$636$	−6.28234	−0.249111
$637$	−2.39274	−0.0948038
$638$	−29.6436	−1.17360
$639$	3.45293	0.136596
$640$	−1.00000	−0.0395285
$641$	−11.9883	−0.473511	−0.236755	−	0.971569i	$-0.576084\pi$
$641$	−11.9883	−0.473511	−0.236755	+	0.971569i	$0.576084\pi$
$642$	−16.9742	−0.669920
$643$	−15.2082	−0.599752	−0.299876	−	0.953978i	$-0.596945\pi$
$643$	−15.2082	−0.599752	−0.299876	+	0.953978i	$0.596945\pi$
$644$	−9.38538	−0.369836
$645$	7.19209	0.283188
$646$	−0.265312	−0.0104386
$647$	27.1690	1.06812	0.534061	−	0.845446i	$-0.320665\pi$
$647$	27.1690	1.06812	0.534061	+	0.845446i	$0.320665\pi$
$648$	−6.86976	−0.269870
$649$	51.6576	2.02774
$650$	3.57909	0.140383
$651$	−22.2895	−0.873594
$652$	−5.58787	−0.218838
$653$	−28.4827	−1.11462	−0.557308	−	0.830306i	$-0.688166\pi$
$653$	−28.4827	−1.11462	−0.557308	+	0.830306i	$0.688166\pi$
$654$	27.8325	1.08834
$655$	−1.02115	−0.0398996
$656$	−1.32156	−0.0515982
$657$	6.15574	0.240158
$658$	1.23271	0.0480560
$659$	33.0918	1.28907	0.644537	−	0.764573i	$-0.277050\pi$
$659$	33.0918	1.28907	0.644537	+	0.764573i	$0.277050\pi$
$660$	−8.48238	−0.330176
$661$	26.4739	1.02972	0.514858	−	0.857276i	$-0.327845\pi$
$661$	26.4739	1.02972	0.514858	+	0.857276i	$0.327845\pi$
$662$	1.16765	0.0453819
$663$	10.1289	0.393376
$664$	6.30177	0.244556
$665$	−0.365986	−0.0141923
$666$	2.01963	0.0782592
$667$	−20.2237	−0.783063
$668$	14.6115	0.565334
$669$	5.44718	0.210600
$670$	7.43807	0.287358
$671$	38.6851	1.49342
$672$	−3.90390	−0.150596
$673$	−24.0971	−0.928874	−0.464437	−	0.885606i	$-0.653743\pi$
$673$	−24.0971	−0.928874	−0.464437	+	0.885606i	$0.653743\pi$
$674$	16.8666	0.649677
$675$	5.57432	0.214556
$676$	−0.190150	−0.00731345
$677$	−20.6102	−0.792113	−0.396057	−	0.918226i	$-0.629622\pi$
$677$	−20.6102	−0.792113	−0.396057	+	0.918226i	$0.629622\pi$
$678$	−3.26348	−0.125333
$679$	30.0342	1.15261
$680$	1.82409	0.0699505
$681$	42.4367	1.62618
$682$	−31.2156	−1.19531
$683$	30.8689	1.18117	0.590584	−	0.806976i	$-0.298898\pi$
$683$	30.8689	1.18117	0.590584	+	0.806976i	$0.298898\pi$
$684$	−0.0862371	−0.00329736
$685$	3.04616	0.116388
$686$	−19.2959	−0.736720
$687$	−11.8536	−0.452242
$688$	4.63563	0.176732
$689$	14.4926	0.552124
$690$	−5.78691	−0.220304
$691$	43.3335	1.64848	0.824242	−	0.566238i	$-0.191602\pi$
$691$	43.3335	1.64848	0.824242	+	0.566238i	$0.191602\pi$
$692$	15.5139	0.589751
$693$	8.15653	0.309841
$694$	−24.9640	−0.947620
$695$	−19.5796	−0.742696
$696$	−8.41215	−0.318862
$697$	2.41063	0.0913093
$698$	−16.6940	−0.631876
$699$	43.0787	1.62938
$700$	2.51624	0.0951050
$701$	2.63592	0.0995572	0.0497786	−	0.998760i	$-0.484148\pi$
$701$	2.63592	0.0995572	0.0497786	+	0.998760i	$0.484148\pi$
$702$	19.9510	0.753001
$703$	−0.495452	−0.0186863
$704$	−5.46728	−0.206056
$705$	0.760073	0.0286260
$706$	−14.6126	−0.549953
$707$	−31.2695	−1.17601
$708$	14.6592	0.550927
$709$	26.4124	0.991940	0.495970	−	0.868340i	$-0.334813\pi$
$709$	26.4124	0.991940	0.495970	+	0.868340i	$0.334813\pi$
$710$	5.82379	0.218563
$711$	5.83431	0.218804
$712$	−14.4635	−0.542043
$713$	−21.2961	−0.797547
$714$	7.12105	0.266499
$715$	19.5678	0.731796
$716$	−19.6240	−0.733382
$717$	39.8715	1.48903
$718$	26.7279	0.997478
$719$	−13.3752	−0.498812	−0.249406	−	0.968399i	$-0.580235\pi$
$719$	−13.3752	−0.498812	−0.249406	+	0.968399i	$0.580235\pi$
$720$	0.592901	0.0220961
$721$	25.9728	0.967276
$722$	−18.9788	−0.706319
$723$	−35.9775	−1.33802
$724$	−1.83064	−0.0680351
$725$	5.42201	0.201368
$726$	−29.3092	−1.08777
$727$	19.3869	0.719021	0.359511	−	0.933141i	$-0.382944\pi$
$727$	19.3869	0.719021	0.359511	+	0.933141i	$0.382944\pi$
$728$	9.00584	0.333779
$729$	30.0185	1.11180
$730$	10.3824	0.384270
$731$	−8.45578	−0.312748
$732$	10.9779	0.405755
$733$	17.3910	0.642350	0.321175	−	0.947020i	$-0.395922\pi$
$733$	17.3910	0.642350	0.321175	+	0.947020i	$0.395922\pi$
$734$	11.1395	0.411168
$735$	−1.03722	−0.0382584
$736$	−3.72992	−0.137487
$737$	40.6660	1.49795
$738$	0.783553	0.0288430
$739$	23.0877	0.849294	0.424647	−	0.905359i	$-0.360398\pi$
$739$	23.0877	0.849294	0.424647	+	0.905359i	$0.360398\pi$
$740$	3.40636	0.125220
$741$	−0.807664	−0.0296703
$742$	10.1889	0.374046
$743$	−13.1459	−0.482277	−0.241138	−	0.970491i	$-0.577521\pi$
$743$	−13.1459	−0.482277	−0.241138	+	0.970491i	$0.577521\pi$
$744$	−8.85825	−0.324759
$745$	−2.10742	−0.0772099
$746$	11.8887	0.435277
$747$	−3.73633	−0.136705
$748$	9.97278	0.364641
$749$	27.5293	1.00590
$750$	1.55148	0.0566521
$751$	−6.51140	−0.237604	−0.118802	−	0.992918i	$-0.537905\pi$
$751$	−6.51140	−0.237604	−0.118802	+	0.992918i	$0.537905\pi$
$752$	0.489901	0.0178649
$753$	21.1845	0.772007
$754$	19.4058	0.706718
$755$	−0.762679	−0.0277567
$756$	14.0263	0.510133
$757$	13.9842	0.508266	0.254133	−	0.967169i	$-0.418210\pi$
$757$	13.9842	0.508266	0.254133	+	0.967169i	$0.418210\pi$
$758$	10.6392	0.386432
$759$	−31.6386	−1.14841
$760$	−0.145449	−0.00527600
$761$	−17.9055	−0.649074	−0.324537	−	0.945873i	$-0.605209\pi$
$761$	−17.9055	−0.649074	−0.324537	+	0.945873i	$0.605209\pi$
$762$	16.8758	0.611344
$763$	−45.1396	−1.63416
$764$	23.8359	0.862353
$765$	−1.08150	−0.0391018
$766$	−9.95657	−0.359746
$767$	−33.8170	−1.22106
$768$	−1.55148	−0.0559843
$769$	−16.4585	−0.593507	−0.296753	−	0.954954i	$-0.595904\pi$
$769$	−16.4585	−0.593507	−0.296753	+	0.954954i	$0.595904\pi$
$770$	13.7570	0.495767
$771$	47.2995	1.70345
$772$	−12.5740	−0.452550
$773$	5.32778	0.191627	0.0958135	−	0.995399i	$-0.469455\pi$
$773$	5.32778	0.191627	0.0958135	+	0.995399i	$0.469455\pi$
$774$	−2.74847	−0.0987917
$775$	5.70954	0.205093
$776$	11.9361	0.428482
$777$	13.2981	0.477066
$778$	36.4354	1.30627
$779$	−0.192220	−0.00688699
$780$	5.55289	0.198825
$781$	31.8403	1.13933
$782$	6.80370	0.243300
$783$	30.2240	1.08012
$784$	−0.668534	−0.0238762
$785$	6.36772	0.227274
$786$	−1.58430	−0.0565100
$787$	−8.73035	−0.311203	−0.155602	−	0.987820i	$-0.549732\pi$
$787$	−8.73035	−0.311203	−0.155602	+	0.987820i	$0.549732\pi$
$788$	−19.5142	−0.695164
$789$	30.6678	1.09180
$790$	9.84027	0.350101
$791$	5.29281	0.188191
$792$	3.24155	0.115184
$793$	−25.3247	−0.899306
$794$	27.8635	0.988840
$795$	6.28234	0.222812
$796$	−18.9541	−0.671809
$797$	19.9866	0.707963	0.353981	−	0.935253i	$-0.384828\pi$
$797$	19.9866	0.707963	0.353981	+	0.935253i	$0.384828\pi$
$798$	−0.567820	−0.0201006
$799$	−0.893621	−0.0316141
$800$	1.00000	0.0353553
$801$	8.57544	0.302998
$802$	−34.1005	−1.20413
$803$	56.7635	2.00314
$804$	11.5400	0.406986
$805$	9.38538	0.330791
$806$	20.4349	0.719790
$807$	6.88151	0.242241
$808$	−12.4271	−0.437183
$809$	−25.9308	−0.911678	−0.455839	−	0.890062i	$-0.650661\pi$
$809$	−25.9308	−0.911678	−0.455839	+	0.890062i	$0.650661\pi$
$810$	6.86976	0.241379
$811$	21.5605	0.757092	0.378546	−	0.925582i	$-0.376424\pi$
$811$	21.5605	0.757092	0.378546	+	0.925582i	$0.376424\pi$
$812$	13.6431	0.478778
$813$	14.6072	0.512297
$814$	18.6235	0.652753
$815$	5.58787	0.195734
$816$	2.83004	0.0990711
$817$	0.674249	0.0235890
$818$	22.1772	0.775409
$819$	−5.33957	−0.186580
$820$	1.32156	0.0461508
$821$	27.7170	0.967328	0.483664	−	0.875254i	$-0.339306\pi$
$821$	27.7170	0.967328	0.483664	+	0.875254i	$0.339306\pi$
$822$	4.72606	0.164840
$823$	−26.3416	−0.918211	−0.459105	−	0.888382i	$-0.651830\pi$
$823$	−26.3416	−0.918211	−0.459105	+	0.888382i	$0.651830\pi$
$824$	10.3220	0.359586
$825$	8.48238	0.295319
$826$	−23.7747	−0.827229
$827$	8.21849	0.285785	0.142893	−	0.989738i	$-0.454360\pi$
$827$	8.21849	0.285785	0.142893	+	0.989738i	$0.454360\pi$
$828$	2.21148	0.0768541
$829$	−32.9255	−1.14355	−0.571775	−	0.820410i	$-0.693745\pi$
$829$	−32.9255	−1.14355	−0.571775	+	0.820410i	$0.693745\pi$
$830$	−6.30177	−0.218738
$831$	−31.5229	−1.09352
$832$	3.57909	0.124082
$833$	1.21946	0.0422519
$834$	−30.3774	−1.05188
$835$	−14.6115	−0.505650
$836$	−0.795212	−0.0275030
$837$	31.8268	1.10010
$838$	−10.6393	−0.367529
$839$	47.2275	1.63048	0.815238	−	0.579127i	$-0.196606\pi$
$839$	47.2275	1.63048	0.815238	+	0.579127i	$0.196606\pi$
$840$	3.90390	0.134697
$841$	0.398147	0.0137292
$842$	11.9313	0.411179
$843$	47.1690	1.62459
$844$	−7.85599	−0.270414
$845$	0.190150	0.00654135
$846$	−0.290463	−0.00998632
$847$	47.5346	1.63331
$848$	4.04925	0.139052
$849$	27.9989	0.960919
$850$	−1.82409	−0.0625656
$851$	12.7054	0.435537
$852$	9.03551	0.309551
$853$	−50.4700	−1.72806	−0.864029	−	0.503442i	$-0.832067\pi$
$853$	−50.4700	−1.72806	−0.864029	+	0.503442i	$0.832067\pi$
$854$	−17.8043	−0.609250
$855$	0.0862371	0.00294925
$856$	10.9407	0.373944
$857$	12.2242	0.417570	0.208785	−	0.977962i	$-0.433049\pi$
$857$	12.2242	0.417570	0.208785	+	0.977962i	$0.433049\pi$
$858$	30.3592	1.03645
$859$	−40.0372	−1.36605	−0.683027	−	0.730393i	$-0.739337\pi$
$859$	−40.0372	−1.36605	−0.683027	+	0.730393i	$0.739337\pi$
$860$	−4.63563	−0.158074
$861$	5.15923	0.175826
$862$	25.9953	0.885402
$863$	1.11980	0.0381183	0.0190592	−	0.999818i	$-0.493933\pi$
$863$	1.11980	0.0381183	0.0190592	+	0.999818i	$0.493933\pi$
$864$	5.57432	0.189642
$865$	−15.5139	−0.527489
$866$	−38.9736	−1.32438
$867$	21.2130	0.720430
$868$	14.3666	0.487633
$869$	53.7995	1.82502
$870$	8.41215	0.285199
$871$	−26.6215	−0.902035
$872$	−17.9393	−0.607501
$873$	−7.07694	−0.239518
$874$	−0.542515	−0.0183508
$875$	−2.51624	−0.0850645
$876$	16.1081	0.544243
$877$	33.9482	1.14635	0.573175	−	0.819433i	$-0.305712\pi$
$877$	33.9482	1.14635	0.573175	+	0.819433i	$0.305712\pi$
$878$	−1.41102	−0.0476197
$879$	1.93856	0.0653861
$880$	5.46728	0.184302
$881$	7.10550	0.239390	0.119695	−	0.992811i	$-0.461808\pi$
$881$	7.10550	0.239390	0.119695	+	0.992811i	$0.461808\pi$
$882$	0.396375	0.0133466
$883$	23.7184	0.798188	0.399094	−	0.916910i	$-0.369325\pi$
$883$	23.7184	0.798188	0.399094	+	0.916910i	$0.369325\pi$
$884$	−6.52856	−0.219579
$885$	−14.6592	−0.492764
$886$	13.8606	0.465657
$887$	46.5020	1.56138	0.780691	−	0.624917i	$-0.214867\pi$
$887$	46.5020	1.56138	0.780691	+	0.624917i	$0.214867\pi$
$888$	5.28490	0.177350
$889$	−27.3696	−0.917947
$890$	14.4635	0.484818
$891$	37.5589	1.25827
$892$	−3.51095	−0.117555
$893$	0.0712558	0.00238448
$894$	−3.26963	−0.109353
$895$	19.6240	0.655956
$896$	2.51624	0.0840617
$897$	20.7118	0.691548
$898$	13.3849	0.446660
$899$	30.9572	1.03248
$900$	−0.592901	−0.0197634
$901$	−7.38618	−0.246069
$902$	7.22532	0.240577
$903$	−18.0970	−0.602232
$904$	2.10346	0.0699601
$905$	1.83064	0.0608524
$906$	−1.18328	−0.0393120
$907$	4.63245	0.153818	0.0769089	−	0.997038i	$-0.475495\pi$
$907$	4.63245	0.153818	0.0769089	+	0.997038i	$0.475495\pi$
$908$	−27.3524	−0.907721
$909$	7.36804	0.244382
$910$	−9.00584	−0.298541
$911$	25.8592	0.856753	0.428376	−	0.903600i	$-0.359086\pi$
$911$	25.8592	0.856753	0.428376	+	0.903600i	$0.359086\pi$
$912$	−0.225662	−0.00747242
$913$	−34.4535	−1.14025
$914$	22.3038	0.737744
$915$	−10.9779	−0.362918
$916$	7.64016	0.252438
$917$	2.56946	0.0848510
$918$	−10.1680	−0.335595
$919$	−4.14275	−0.136657	−0.0683284	−	0.997663i	$-0.521767\pi$
$919$	−4.14275	−0.136657	−0.0683284	+	0.997663i	$0.521767\pi$
$920$	3.72992	0.122972
$921$	7.98060	0.262970
$922$	−12.2682	−0.404030
$923$	−20.8438	−0.686083
$924$	21.3437	0.702157
$925$	−3.40636	−0.112000
$926$	11.1839	0.367527
$927$	−6.11996	−0.201006
$928$	5.42201	0.177986
$929$	3.94302	0.129366	0.0646832	−	0.997906i	$-0.479396\pi$
$929$	3.94302	0.129366	0.0646832	+	0.997906i	$0.479396\pi$
$930$	8.85825	0.290474
$931$	−0.0972378	−0.00318684
$932$	−27.7661	−0.909510
$933$	−38.3896	−1.25682
$934$	20.5147	0.671262
$935$	−9.97278	−0.326145
$936$	−2.12204	−0.0693612
$937$	−38.9091	−1.27111	−0.635553	−	0.772058i	$-0.719228\pi$
$937$	−38.9091	−1.27111	−0.635553	+	0.772058i	$0.719228\pi$
$938$	−18.7160	−0.611099
$939$	−17.7792	−0.580201
$940$	−0.489901	−0.0159788
$941$	−49.5008	−1.61368	−0.806841	−	0.590769i	$-0.798824\pi$
$941$	−49.5008	−1.61368	−0.806841	+	0.590769i	$0.798824\pi$
$942$	9.87941	0.321889
$943$	4.92931	0.160520
$944$	−9.44852	−0.307523
$945$	−14.0263	−0.456277
$946$	−25.3442	−0.824013
$947$	55.3492	1.79861	0.899304	−	0.437325i	$-0.144074\pi$
$947$	55.3492	1.79861	0.899304	+	0.437325i	$0.144074\pi$
$948$	15.2670	0.495850
$949$	−37.1595	−1.20625
$950$	0.145449	0.00471900
$951$	4.06392	0.131782
$952$	−4.58984	−0.148758
$953$	−6.33124	−0.205089	−0.102544	−	0.994728i	$-0.532698\pi$
$953$	−6.33124	−0.205089	−0.102544	+	0.994728i	$0.532698\pi$
$954$	−2.40080	−0.0777289
$955$	−23.8359	−0.771312
$956$	−25.6990	−0.831164
$957$	45.9915	1.48670
$958$	−1.73507	−0.0560575
$959$	−7.66487	−0.247512
$960$	1.55148	0.0500739
$961$	1.59885	0.0515759
$962$	−12.1916	−0.393074
$963$	−6.48673	−0.209032
$964$	23.1891	0.746871
$965$	12.5740	0.404773
$966$	14.5613	0.468501
$967$	−52.7599	−1.69664	−0.848322	−	0.529480i	$-0.822387\pi$
$967$	−52.7599	−1.69664	−0.848322	+	0.529480i	$0.822387\pi$
$968$	18.8911	0.607183
$969$	0.411627	0.0132234
$970$	−11.9361	−0.383246
$971$	5.49741	0.176420	0.0882102	−	0.996102i	$-0.471885\pi$
$971$	5.49741	0.176420	0.0882102	+	0.996102i	$0.471885\pi$
$972$	−6.06465	−0.194524
$973$	49.2670	1.57943
$974$	13.8303	0.443150
$975$	−5.55289	−0.177835
$976$	−7.07575	−0.226489
$977$	−39.3947	−1.26035	−0.630174	−	0.776454i	$-0.717016\pi$
$977$	−39.3947	−1.26035	−0.630174	+	0.776454i	$0.717016\pi$
$978$	8.66948	0.277219
$979$	79.0761	2.52728
$980$	0.668534	0.0213555
$981$	10.6362	0.339589
$982$	7.76245	0.247710
$983$	56.4958	1.80194	0.900968	−	0.433886i	$-0.142858\pi$
$983$	56.4958	1.80194	0.900968	+	0.433886i	$0.142858\pi$
$984$	2.05037	0.0653635
$985$	19.5142	0.621774
$986$	−9.89020	−0.314968
$987$	−1.91253	−0.0608764
$988$	0.520576	0.0165617
$989$	−17.2905	−0.549807
$990$	−3.24155	−0.103023
$991$	24.3651	0.773984	0.386992	−	0.922083i	$-0.373514\pi$
$991$	24.3651	0.773984	0.386992	+	0.922083i	$0.373514\pi$
$992$	5.70954	0.181278
$993$	−1.81158	−0.0574889
$994$	−14.6541	−0.464798
$995$	18.9541	0.600884
$996$	−9.77709	−0.309799
$997$	−46.2630	−1.46516	−0.732581	−	0.680680i	$-0.761685\pi$
$997$	−46.2630	−1.46516	−0.732581	+	0.680680i	$0.761685\pi$
$998$	22.5863	0.714955
$999$	−18.9881	−0.600758

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6010.2.a.f.1.7	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6010.2.a.f.1.7	✓	22	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:	\( N \)	\(=\)	\( 6010 = 2 \cdot 5 \cdot 601 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6010.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.55148 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.55148 q^{6} +2.51624 q^{7} +1.00000 q^{8} -0.592901 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.55148 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.55148 q^{6} +2.51624 q^{7} +1.00000 q^{8} -0.592901 q^{9} -1.00000 q^{10} -5.46728 q^{11} -1.55148 q^{12} +3.57909 q^{13} +2.51624 q^{14} +1.55148 q^{15} +1.00000 q^{16} -1.82409 q^{17} -0.592901 q^{18} +0.145449 q^{19} -1.00000 q^{20} -3.90390 q^{21} -5.46728 q^{22} -3.72992 q^{23} -1.55148 q^{24} +1.00000 q^{25} +3.57909 q^{26} +5.57432 q^{27} +2.51624 q^{28} +5.42201 q^{29} +1.55148 q^{30} +5.70954 q^{31} +1.00000 q^{32} +8.48238 q^{33} -1.82409 q^{34} -2.51624 q^{35} -0.592901 q^{36} -3.40636 q^{37} +0.145449 q^{38} -5.55289 q^{39} -1.00000 q^{40} -1.32156 q^{41} -3.90390 q^{42} +4.63563 q^{43} -5.46728 q^{44} +0.592901 q^{45} -3.72992 q^{46} +0.489901 q^{47} -1.55148 q^{48} -0.668534 q^{49} +1.00000 q^{50} +2.83004 q^{51} +3.57909 q^{52} +4.04925 q^{53} +5.57432 q^{54} +5.46728 q^{55} +2.51624 q^{56} -0.225662 q^{57} +5.42201 q^{58} -9.44852 q^{59} +1.55148 q^{60} -7.07575 q^{61} +5.70954 q^{62} -1.49188 q^{63} +1.00000 q^{64} -3.57909 q^{65} +8.48238 q^{66} -7.43807 q^{67} -1.82409 q^{68} +5.78691 q^{69} -2.51624 q^{70} -5.82379 q^{71} -0.592901 q^{72} -10.3824 q^{73} -3.40636 q^{74} -1.55148 q^{75} +0.145449 q^{76} -13.7570 q^{77} -5.55289 q^{78} -9.84027 q^{79} -1.00000 q^{80} -6.86976 q^{81} -1.32156 q^{82} +6.30177 q^{83} -3.90390 q^{84} +1.82409 q^{85} +4.63563 q^{86} -8.41215 q^{87} -5.46728 q^{88} -14.4635 q^{89} +0.592901 q^{90} +9.00584 q^{91} -3.72992 q^{92} -8.85825 q^{93} +0.489901 q^{94} -0.145449 q^{95} -1.55148 q^{96} +11.9361 q^{97} -0.668534 q^{98} +3.24155 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 22 q^{2} - 6 q^{3} + 22 q^{4} - 22 q^{5} - 6 q^{6} - 12 q^{7} + 22 q^{8} + 12 q^{9}+O(q^{10}) \) 22 * q + 22 * q^2 - 6 * q^3 + 22 * q^4 - 22 * q^5 - 6 * q^6 - 12 * q^7 + 22 * q^8 + 12 * q^9	\( 22 q + 22 q^{2} - 6 q^{3} + 22 q^{4} - 22 q^{5} - 6 q^{6} - 12 q^{7} + 22 q^{8} + 12 q^{9} - 22 q^{10} - 4 q^{11} - 6 q^{12} - 20 q^{13} - 12 q^{14} + 6 q^{15} + 22 q^{16} - 23 q^{17} + 12 q^{18} + q^{19} - 22 q^{20} - 8 q^{21} - 4 q^{22} - 17 q^{23} - 6 q^{24} + 22 q^{25} - 20 q^{26} - 21 q^{27} - 12 q^{28} - 13 q^{29} + 6 q^{30} - 13 q^{31} + 22 q^{32} - 21 q^{33} - 23 q^{34} + 12 q^{35} + 12 q^{36} - 16 q^{37} + q^{38} - 4 q^{39} - 22 q^{40} - 31 q^{41} - 8 q^{42} - 9 q^{43} - 4 q^{44} - 12 q^{45} - 17 q^{46} - 41 q^{47} - 6 q^{48} - 6 q^{49} + 22 q^{50} - 7 q^{51} - 20 q^{52} - 15 q^{53} - 21 q^{54} + 4 q^{55} - 12 q^{56} - 26 q^{57} - 13 q^{58} - 32 q^{59} + 6 q^{60} - 22 q^{61} - 13 q^{62} - 55 q^{63} + 22 q^{64} + 20 q^{65} - 21 q^{66} - 19 q^{67} - 23 q^{68} - 37 q^{69} + 12 q^{70} - 36 q^{71} + 12 q^{72} - 47 q^{73} - 16 q^{74} - 6 q^{75} + q^{76} - 26 q^{77} - 4 q^{78} - 10 q^{79} - 22 q^{80} - 18 q^{81} - 31 q^{82} - 48 q^{83} - 8 q^{84} + 23 q^{85} - 9 q^{86} - 50 q^{87} - 4 q^{88} - 42 q^{89} - 12 q^{90} + 25 q^{91} - 17 q^{92} - 48 q^{93} - 41 q^{94} - q^{95} - 6 q^{96} - 67 q^{97} - 6 q^{98} - 3 q^{99}+O(q^{100}) \) 22 * q + 22 * q^2 - 6 * q^3 + 22 * q^4 - 22 * q^5 - 6 * q^6 - 12 * q^7 + 22 * q^8 + 12 * q^9 - 22 * q^10 - 4 * q^11 - 6 * q^12 - 20 * q^13 - 12 * q^14 + 6 * q^15 + 22 * q^16 - 23 * q^17 + 12 * q^18 + q^19 - 22 * q^20 - 8 * q^21 - 4 * q^22 - 17 * q^23 - 6 * q^24 + 22 * q^25 - 20 * q^26 - 21 * q^27 - 12 * q^28 - 13 * q^29 + 6 * q^30 - 13 * q^31 + 22 * q^32 - 21 * q^33 - 23 * q^34 + 12 * q^35 + 12 * q^36 - 16 * q^37 + q^38 - 4 * q^39 - 22 * q^40 - 31 * q^41 - 8 * q^42 - 9 * q^43 - 4 * q^44 - 12 * q^45 - 17 * q^46 - 41 * q^47 - 6 * q^48 - 6 * q^49 + 22 * q^50 - 7 * q^51 - 20 * q^52 - 15 * q^53 - 21 * q^54 + 4 * q^55 - 12 * q^56 - 26 * q^57 - 13 * q^58 - 32 * q^59 + 6 * q^60 - 22 * q^61 - 13 * q^62 - 55 * q^63 + 22 * q^64 + 20 * q^65 - 21 * q^66 - 19 * q^67 - 23 * q^68 - 37 * q^69 + 12 * q^70 - 36 * q^71 + 12 * q^72 - 47 * q^73 - 16 * q^74 - 6 * q^75 + q^76 - 26 * q^77 - 4 * q^78 - 10 * q^79 - 22 * q^80 - 18 * q^81 - 31 * q^82 - 48 * q^83 - 8 * q^84 + 23 * q^85 - 9 * q^86 - 50 * q^87 - 4 * q^88 - 42 * q^89 - 12 * q^90 + 25 * q^91 - 17 * q^92 - 48 * q^93 - 41 * q^94 - q^95 - 6 * q^96 - 67 * q^97 - 6 * q^98 - 3 * q^99

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