LMFDB - Embedded newform 6031.2.a.c.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6031,2,Mod(1,6031)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6031, 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("6031.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6031 = 37 \cdot 163 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6031.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:	$48.1577774590$
Analytic rank:	$1$
Dimension:	$110$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	6031.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.35892 q^{2} -1.34501 q^{3} +3.56450 q^{4} +0.355993 q^{5} +3.17276 q^{6} -3.31316 q^{7} -3.69052 q^{8} -1.19096 q^{9} +O(q^{10})$	\(q-2.35892 q^{2} -1.34501 q^{3} +3.56450 q^{4} +0.355993 q^{5} +3.17276 q^{6} -3.31316 q^{7} -3.69052 q^{8} -1.19096 q^{9} -0.839759 q^{10} +0.106247 q^{11} -4.79427 q^{12} -2.76889 q^{13} +7.81548 q^{14} -0.478813 q^{15} +1.57664 q^{16} +4.60394 q^{17} +2.80938 q^{18} +1.53949 q^{19} +1.26894 q^{20} +4.45622 q^{21} -0.250629 q^{22} -4.15036 q^{23} +4.96377 q^{24} -4.87327 q^{25} +6.53158 q^{26} +5.63686 q^{27} -11.8098 q^{28} -2.36605 q^{29} +1.12948 q^{30} -1.95096 q^{31} +3.66187 q^{32} -0.142903 q^{33} -10.8603 q^{34} -1.17946 q^{35} -4.24517 q^{36} -1.00000 q^{37} -3.63153 q^{38} +3.72417 q^{39} -1.31380 q^{40} +4.12223 q^{41} -10.5119 q^{42} -0.923859 q^{43} +0.378718 q^{44} -0.423974 q^{45} +9.79035 q^{46} +11.2365 q^{47} -2.12059 q^{48} +3.97705 q^{49} +11.4956 q^{50} -6.19232 q^{51} -9.86969 q^{52} +8.33034 q^{53} -13.2969 q^{54} +0.0378233 q^{55} +12.2273 q^{56} -2.07062 q^{57} +5.58132 q^{58} -11.6625 q^{59} -1.70673 q^{60} +2.88569 q^{61} +4.60215 q^{62} +3.94584 q^{63} -11.7913 q^{64} -0.985706 q^{65} +0.337097 q^{66} +12.3148 q^{67} +16.4107 q^{68} +5.58225 q^{69} +2.78226 q^{70} -8.79614 q^{71} +4.39526 q^{72} -10.3820 q^{73} +2.35892 q^{74} +6.55457 q^{75} +5.48751 q^{76} -0.352015 q^{77} -8.78501 q^{78} +2.26095 q^{79} +0.561274 q^{80} -4.00873 q^{81} -9.72400 q^{82} +9.37757 q^{83} +15.8842 q^{84} +1.63897 q^{85} +2.17931 q^{86} +3.18235 q^{87} -0.392108 q^{88} +12.3386 q^{89} +1.00012 q^{90} +9.17378 q^{91} -14.7939 q^{92} +2.62405 q^{93} -26.5059 q^{94} +0.548048 q^{95} -4.92523 q^{96} +9.04265 q^{97} -9.38153 q^{98} -0.126536 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 110 q - 9 q^{2} + 97 q^{4} - 26 q^{5} - 26 q^{6} - 4 q^{7} - 27 q^{8} + 62 q^{9}+O(q^{10}) $ 110 * q - 9 * q^2 + 97 * q^4 - 26 * q^5 - 26 * q^6 - 4 * q^7 - 27 * q^8 + 62 * q^9	\( 110 q - 9 q^{2} + 97 q^{4} - 26 q^{5} - 26 q^{6} - 4 q^{7} - 27 q^{8} + 62 q^{9} - 17 q^{10} - 9 q^{11} - 21 q^{13} - 29 q^{14} - 23 q^{15} + 79 q^{16} - 76 q^{17} - 31 q^{18} - 27 q^{19} - 67 q^{20} - 30 q^{21} - 28 q^{22} - 32 q^{23} - 63 q^{24} + 66 q^{25} - 55 q^{26} - 4 q^{28} - 81 q^{29} - 48 q^{30} - 30 q^{31} - 73 q^{32} - 53 q^{33} - 23 q^{34} - 78 q^{35} + 7 q^{36} - 110 q^{37} - 50 q^{38} - 64 q^{39} - 37 q^{40} - 123 q^{41} - 63 q^{42} - 40 q^{43} - 31 q^{44} - 73 q^{45} + 16 q^{46} - 37 q^{47} - 29 q^{48} + 46 q^{49} - 58 q^{50} - 73 q^{51} - 39 q^{52} - 16 q^{53} - 53 q^{54} - 59 q^{55} - 113 q^{56} - 39 q^{57} + 11 q^{58} - 93 q^{59} - 18 q^{60} - 66 q^{61} - 40 q^{62} - 21 q^{63} + 23 q^{64} - 92 q^{65} - 31 q^{66} + q^{67} - 121 q^{68} - 80 q^{69} - 3 q^{70} - 75 q^{71} - 114 q^{72} - 39 q^{73} + 9 q^{74} - 25 q^{75} - 58 q^{76} - 31 q^{77} + 68 q^{78} - 36 q^{79} - 82 q^{80} - 50 q^{81} - 18 q^{82} - 57 q^{83} - 9 q^{84} - 14 q^{85} - 58 q^{86} - 58 q^{87} - 15 q^{88} - 181 q^{89} + 8 q^{90} - 55 q^{91} - 116 q^{92} - 86 q^{93} - 39 q^{94} - 70 q^{95} - 127 q^{96} - 91 q^{97} - 19 q^{98} - 21 q^{99}+O(q^{100}) \) 110 * q - 9 * q^2 + 97 * q^4 - 26 * q^5 - 26 * q^6 - 4 * q^7 - 27 * q^8 + 62 * q^9 - 17 * q^10 - 9 * q^11 - 21 * q^13 - 29 * q^14 - 23 * q^15 + 79 * q^16 - 76 * q^17 - 31 * q^18 - 27 * q^19 - 67 * q^20 - 30 * q^21 - 28 * q^22 - 32 * q^23 - 63 * q^24 + 66 * q^25 - 55 * q^26 - 4 * q^28 - 81 * q^29 - 48 * q^30 - 30 * q^31 - 73 * q^32 - 53 * q^33 - 23 * q^34 - 78 * q^35 + 7 * q^36 - 110 * q^37 - 50 * q^38 - 64 * q^39 - 37 * q^40 - 123 * q^41 - 63 * q^42 - 40 * q^43 - 31 * q^44 - 73 * q^45 + 16 * q^46 - 37 * q^47 - 29 * q^48 + 46 * q^49 - 58 * q^50 - 73 * q^51 - 39 * q^52 - 16 * q^53 - 53 * q^54 - 59 * q^55 - 113 * q^56 - 39 * q^57 + 11 * q^58 - 93 * q^59 - 18 * q^60 - 66 * q^61 - 40 * q^62 - 21 * q^63 + 23 * q^64 - 92 * q^65 - 31 * q^66 + q^67 - 121 * q^68 - 80 * q^69 - 3 * q^70 - 75 * q^71 - 114 * q^72 - 39 * q^73 + 9 * q^74 - 25 * q^75 - 58 * q^76 - 31 * q^77 + 68 * q^78 - 36 * q^79 - 82 * q^80 - 50 * q^81 - 18 * q^82 - 57 * q^83 - 9 * q^84 - 14 * q^85 - 58 * q^86 - 58 * q^87 - 15 * q^88 - 181 * q^89 + 8 * q^90 - 55 * q^91 - 116 * q^92 - 86 * q^93 - 39 * q^94 - 70 * q^95 - 127 * q^96 - 91 * q^97 - 19 * q^98 - 21 * 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 $

$2$	−2.35892	−1.66801	−0.834004	−	0.551759i	$-0.813957\pi$
$2$	−2.35892	−1.66801	−0.834004	+	0.551759i	$0.813957\pi$
$3$	−1.34501	−0.776539	−0.388270	−	0.921546i	$-0.626927\pi$
$3$	−1.34501	−0.776539	−0.388270	+	0.921546i	$0.626927\pi$
$4$	3.56450	1.78225
$5$	0.355993	0.159205	0.0796025	−	0.996827i	$-0.474635\pi$
$5$	0.355993	0.159205	0.0796025	+	0.996827i	$0.474635\pi$
$6$	3.17276	1.29527
$7$	−3.31316	−1.25226	−0.626129	−	0.779720i	$-0.715362\pi$
$7$	−3.31316	−1.25226	−0.626129	+	0.779720i	$0.715362\pi$
$8$	−3.69052	−1.30480
$9$	−1.19096	−0.396987
$10$	−0.839759	−0.265555
$11$	0.106247	0.0320348	0.0160174	−	0.999872i	$-0.494901\pi$
$11$	0.106247	0.0320348	0.0160174	+	0.999872i	$0.494901\pi$
$12$	−4.79427	−1.38399
$13$	−2.76889	−0.767951	−0.383976	−	0.923343i	$-0.625445\pi$
$13$	−2.76889	−0.767951	−0.383976	+	0.923343i	$0.625445\pi$
$14$	7.81548	2.08878
$15$	−0.478813	−0.123629
$16$	1.57664	0.394160
$17$	4.60394	1.11662	0.558310	−	0.829633i	$-0.311450\pi$
$17$	4.60394	1.11662	0.558310	+	0.829633i	$0.311450\pi$
$18$	2.80938	0.662177
$19$	1.53949	0.353183	0.176592	−	0.984284i	$-0.443493\pi$
$19$	1.53949	0.353183	0.176592	+	0.984284i	$0.443493\pi$
$20$	1.26894	0.283743
$21$	4.45622	0.972427
$22$	−0.250629	−0.0534343
$23$	−4.15036	−0.865409	−0.432705	−	0.901536i	$-0.642441\pi$
$23$	−4.15036	−0.865409	−0.432705	+	0.901536i	$0.642441\pi$
$24$	4.96377	1.01323
$25$	−4.87327	−0.974654
$26$	6.53158	1.28095
$27$	5.63686	1.08482
$28$	−11.8098	−2.23183
$29$	−2.36605	−0.439365	−0.219682	−	0.975571i	$-0.570502\pi$
$29$	−2.36605	−0.439365	−0.219682	+	0.975571i	$0.570502\pi$
$30$	1.12948	0.206214
$31$	−1.95096	−0.350402	−0.175201	−	0.984533i	$-0.556058\pi$
$31$	−1.95096	−0.350402	−0.175201	+	0.984533i	$0.556058\pi$
$32$	3.66187	0.647333
$33$	−0.142903	−0.0248763
$34$	−10.8603	−1.86253
$35$	−1.17946	−0.199366
$36$	−4.24517	−0.707529
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	−3.63153	−0.589112
$39$	3.72417	0.596345
$40$	−1.31380	−0.207730
$41$	4.12223	0.643784	0.321892	−	0.946776i	$-0.395681\pi$
$41$	4.12223	0.643784	0.321892	+	0.946776i	$0.395681\pi$
$42$	−10.5119	−1.62202
$43$	−0.923859	−0.140887	−0.0704436	−	0.997516i	$-0.522441\pi$
$43$	−0.923859	−0.140887	−0.0704436	+	0.997516i	$0.522441\pi$
$44$	0.378718	0.0570939
$45$	−0.423974	−0.0632023
$46$	9.79035	1.44351
$47$	11.2365	1.63901	0.819505	−	0.573072i	$-0.194249\pi$
$47$	11.2365	1.63901	0.819505	+	0.573072i	$0.194249\pi$
$48$	−2.12059	−0.306081
$49$	3.97705	0.568150
$50$	11.4956	1.62573
$51$	−6.19232	−0.867099
$52$	−9.86969	−1.36868
$53$	8.33034	1.14426	0.572130	−	0.820163i	$-0.306117\pi$
$53$	8.33034	1.14426	0.572130	+	0.820163i	$0.306117\pi$
$54$	−13.2969	−1.80948
$55$	0.0378233	0.00510010
$56$	12.2273	1.63394
$57$	−2.07062	−0.274261
$58$	5.58132	0.732864
$59$	−11.6625	−1.51832	−0.759162	−	0.650902i	$-0.774391\pi$
$59$	−11.6625	−1.51832	−0.759162	+	0.650902i	$0.774391\pi$
$60$	−1.70673	−0.220338
$61$	2.88569	0.369474	0.184737	−	0.982788i	$-0.440857\pi$
$61$	2.88569	0.369474	0.184737	+	0.982788i	$0.440857\pi$
$62$	4.60215	0.584473
$63$	3.94584	0.497130
$64$	−11.7913	−1.47392
$65$	−0.985706	−0.122262
$66$	0.337097	0.0414938
$67$	12.3148	1.50450	0.752249	−	0.658879i	$-0.228969\pi$
$67$	12.3148	1.50450	0.752249	+	0.658879i	$0.228969\pi$
$68$	16.4107	1.99009
$69$	5.58225	0.672024
$70$	2.78226	0.332544
$71$	−8.79614	−1.04391	−0.521955	−	0.852973i	$-0.674797\pi$
$71$	−8.79614	−1.04391	−0.521955	+	0.852973i	$0.674797\pi$
$72$	4.39526	0.517987
$73$	−10.3820	−1.21512	−0.607562	−	0.794273i	$-0.707852\pi$
$73$	−10.3820	−1.21512	−0.607562	+	0.794273i	$0.707852\pi$
$74$	2.35892	0.274219
$75$	6.55457	0.756857
$76$	5.48751	0.629460
$77$	−0.352015	−0.0401158
$78$	−8.78501	−0.994707
$79$	2.26095	0.254377	0.127188	−	0.991879i	$-0.459405\pi$
$79$	2.26095	0.254377	0.127188	+	0.991879i	$0.459405\pi$
$80$	0.561274	0.0627523
$81$	−4.00873	−0.445415
$82$	−9.72400	−1.07384
$83$	9.37757	1.02932	0.514661	−	0.857394i	$-0.327918\pi$
$83$	9.37757	1.02932	0.514661	+	0.857394i	$0.327918\pi$
$84$	15.8842	1.73311
$85$	1.63897	0.177771
$86$	2.17931	0.235001
$87$	3.18235	0.341184
$88$	−0.392108	−0.0417988
$89$	12.3386	1.30788	0.653942	−	0.756545i	$-0.273114\pi$
$89$	12.3386	1.30788	0.653942	+	0.756545i	$0.273114\pi$
$90$	1.00012	0.105422
$91$	9.17378	0.961673
$92$	−14.7939	−1.54237
$93$	2.62405	0.272101
$94$	−26.5059	−2.73388
$95$	0.548048	0.0562285
$96$	−4.92523	−0.502680
$97$	9.04265	0.918142	0.459071	−	0.888400i	$-0.348182\pi$
$97$	9.04265	0.918142	0.459071	+	0.888400i	$0.348182\pi$
$98$	−9.38153	−0.947678
$99$	−0.126536	−0.0127174
$100$	−17.3707	−1.73707
$101$	8.93133	0.888701	0.444350	−	0.895853i	$-0.353435\pi$
$101$	8.93133	0.888701	0.444350	+	0.895853i	$0.353435\pi$
$102$	14.6072	1.44633
$103$	11.3368	1.11705	0.558523	−	0.829489i	$-0.311368\pi$
$103$	11.3368	1.11705	0.558523	+	0.829489i	$0.311368\pi$
$104$	10.2186	1.00202
$105$	1.58639	0.154815
$106$	−19.6506	−1.90863
$107$	−0.392044	−0.0379003	−0.0189502	−	0.999820i	$-0.506032\pi$
$107$	−0.392044	−0.0379003	−0.0189502	+	0.999820i	$0.506032\pi$
$108$	20.0926	1.93341
$109$	−3.88932	−0.372530	−0.186265	−	0.982500i	$-0.559638\pi$
$109$	−3.88932	−0.372530	−0.186265	+	0.982500i	$0.559638\pi$
$110$	−0.0892222	−0.00850700
$111$	1.34501	0.127662
$112$	−5.22367	−0.493591
$113$	−8.99215	−0.845910	−0.422955	−	0.906151i	$-0.639007\pi$
$113$	−8.99215	−0.845910	−0.422955	+	0.906151i	$0.639007\pi$
$114$	4.88443	0.457469
$115$	−1.47750	−0.137778
$116$	−8.43378	−0.783057
$117$	3.29764	0.304867
$118$	27.5108	2.53258
$119$	−15.2536	−1.39829
$120$	1.76707	0.161311
$121$	−10.9887	−0.998974
$122$	−6.80710	−0.616286
$123$	−5.54442	−0.499923
$124$	−6.95418	−0.624503
$125$	−3.51482	−0.314375
$126$	−9.30793	−0.829216
$127$	17.1856	1.52498	0.762490	−	0.647000i	$-0.223977\pi$
$127$	17.1856	1.52498	0.762490	+	0.647000i	$0.223977\pi$
$128$	20.4911	1.81117
$129$	1.24260	0.109404
$130$	2.32520	0.203933
$131$	−14.2534	−1.24532	−0.622661	−	0.782492i	$-0.713948\pi$
$131$	−14.2534	−1.24532	−0.622661	+	0.782492i	$0.713948\pi$
$132$	−0.509378	−0.0443357
$133$	−5.10058	−0.442276
$134$	−29.0497	−2.50951
$135$	2.00669	0.172708
$136$	−16.9909	−1.45696
$137$	2.40802	0.205731	0.102865	−	0.994695i	$-0.467199\pi$
$137$	2.40802	0.205731	0.102865	+	0.994695i	$0.467199\pi$
$138$	−13.1681	−1.12094
$139$	20.9524	1.77716	0.888581	−	0.458720i	$-0.151692\pi$
$139$	20.9524	1.77716	0.888581	+	0.458720i	$0.151692\pi$
$140$	−4.20419	−0.355319
$141$	−15.1131	−1.27276
$142$	20.7494	1.74125
$143$	−0.294187	−0.0246012
$144$	−1.87772	−0.156476
$145$	−0.842299	−0.0699491
$146$	24.4903	2.02683
$147$	−5.34915	−0.441191
$148$	−3.56450	−0.293000
$149$	−19.2580	−1.57767	−0.788837	−	0.614603i	$-0.789316\pi$
$149$	−19.2580	−1.57767	−0.788837	+	0.614603i	$0.789316\pi$
$150$	−15.4617	−1.26244
$151$	−7.58407	−0.617183	−0.308591	−	0.951195i	$-0.599858\pi$
$151$	−7.58407	−0.617183	−0.308591	+	0.951195i	$0.599858\pi$
$152$	−5.68152	−0.460832
$153$	−5.48311	−0.443283
$154$	0.830374	0.0669135
$155$	−0.694527	−0.0557858
$156$	13.2748	1.06283
$157$	−5.16443	−0.412167	−0.206083	−	0.978534i	$-0.566072\pi$
$157$	−5.16443	−0.412167	−0.206083	+	0.978534i	$0.566072\pi$
$158$	−5.33340	−0.424302
$159$	−11.2044	−0.888563
$160$	1.30360	0.103059
$161$	13.7508	1.08372
$162$	9.45628	0.742955
$163$	−1.00000	−0.0783260
$163$	−1.00000	−0.0783260
$164$	14.6937	1.14738
$165$	−0.0508726	−0.00396043
$166$	−22.1209	−1.71692
$167$	−7.11997	−0.550960	−0.275480	−	0.961307i	$-0.588837\pi$
$167$	−7.11997	−0.550960	−0.275480	+	0.961307i	$0.588837\pi$
$168$	−16.4458	−1.26882
$169$	−5.33326	−0.410250
$170$	−3.86620	−0.296524
$171$	−1.83347	−0.140209
$172$	−3.29309	−0.251096
$173$	−23.9478	−1.82072	−0.910360	−	0.413816i	$-0.864196\pi$
$173$	−23.9478	−1.82072	−0.910360	+	0.413816i	$0.864196\pi$
$174$	−7.50691	−0.569097
$175$	16.1459	1.22052
$176$	0.167514	0.0126268
$177$	15.6861	1.17904
$178$	−29.1056	−2.18156
$179$	−13.3489	−0.997742	−0.498871	−	0.866676i	$-0.666252\pi$
$179$	−13.3489	−0.997742	−0.498871	+	0.866676i	$0.666252\pi$
$180$	−1.51125	−0.112642
$181$	10.2204	0.759676	0.379838	−	0.925053i	$-0.375980\pi$
$181$	10.2204	0.759676	0.379838	+	0.925053i	$0.375980\pi$
$182$	−21.6402	−1.60408
$183$	−3.88127	−0.286911
$184$	15.3170	1.12918
$185$	−0.355993	−0.0261731
$186$	−6.18991	−0.453866
$187$	0.489156	0.0357706
$188$	40.0524	2.92112
$189$	−18.6758	−1.35847
$190$	−1.29280	−0.0937896
$191$	18.2536	1.32079	0.660394	−	0.750920i	$-0.270389\pi$
$191$	18.2536	1.32079	0.660394	+	0.750920i	$0.270389\pi$
$192$	15.8594	1.14455
$193$	−5.51922	−0.397282	−0.198641	−	0.980072i	$-0.563653\pi$
$193$	−5.51922	−0.397282	−0.198641	+	0.980072i	$0.563653\pi$
$194$	−21.3309	−1.53147
$195$	1.32578	0.0949411
$196$	14.1762	1.01258
$197$	13.5571	0.965902	0.482951	−	0.875647i	$-0.339565\pi$
$197$	13.5571	0.965902	0.482951	+	0.875647i	$0.339565\pi$
$198$	0.298489	0.0212127
$199$	24.5240	1.73846	0.869230	−	0.494408i	$-0.164615\pi$
$199$	24.5240	1.73846	0.869230	+	0.494408i	$0.164615\pi$
$200$	17.9849	1.27172
$201$	−16.5635	−1.16830
$202$	−21.0683	−1.48236
$203$	7.83912	0.550198
$204$	−22.0725	−1.54538
$205$	1.46749	0.102494
$206$	−26.7425	−1.86324
$207$	4.94291	0.343556
$208$	−4.36555	−0.302696
$209$	0.163567	0.0113141
$210$	−3.74215	−0.258233
$211$	−18.0867	−1.24514	−0.622571	−	0.782563i	$-0.713912\pi$
$211$	−18.0867	−1.24514	−0.622571	+	0.782563i	$0.713912\pi$
$212$	29.6935	2.03936
$213$	11.8309	0.810637
$214$	0.924800	0.0632180
$215$	−0.328888	−0.0224299
$216$	−20.8030	−1.41546
$217$	6.46383	0.438794
$218$	9.17460	0.621382
$219$	13.9639	0.943591
$220$	0.134821	0.00908964
$221$	−12.7478	−0.857509
$222$	−3.17276	−0.212942
$223$	−12.1115	−0.811045	−0.405522	−	0.914085i	$-0.632910\pi$
$223$	−12.1115	−0.811045	−0.405522	+	0.914085i	$0.632910\pi$
$224$	−12.1324	−0.810628
$225$	5.80387	0.386925
$226$	21.2117	1.41098
$227$	16.6503	1.10512	0.552559	−	0.833474i	$-0.313651\pi$
$227$	16.6503	1.10512	0.552559	+	0.833474i	$0.313651\pi$
$228$	−7.38073	−0.488800
$229$	14.7564	0.975129	0.487564	−	0.873087i	$-0.337885\pi$
$229$	14.7564	0.975129	0.487564	+	0.873087i	$0.337885\pi$
$230$	3.48530	0.229814
$231$	0.473462	0.0311515
$232$	8.73196	0.573281
$233$	−17.9166	−1.17376	−0.586879	−	0.809674i	$-0.699644\pi$
$233$	−17.9166	−1.17376	−0.586879	+	0.809674i	$0.699644\pi$
$234$	−7.77885	−0.508520
$235$	4.00011	0.260939
$236$	−41.5708	−2.70603
$237$	−3.04099	−0.197534
$238$	35.9820	2.33237
$239$	−6.03671	−0.390482	−0.195241	−	0.980755i	$-0.562549\pi$
$239$	−6.03671	−0.390482	−0.195241	+	0.980755i	$0.562549\pi$
$240$	−0.754917	−0.0487297
$241$	10.3417	0.666168	0.333084	−	0.942897i	$-0.391911\pi$
$241$	10.3417	0.666168	0.333084	+	0.942897i	$0.391911\pi$
$242$	25.9215	1.66630
$243$	−11.5188	−0.738933
$244$	10.2860	0.658495
$245$	1.41580	0.0904523
$246$	13.0788	0.833876
$247$	−4.26268	−0.271228
$248$	7.20004	0.457203
$249$	−12.6129	−0.799309
$250$	8.29117	0.524379
$251$	21.8586	1.37970	0.689851	−	0.723952i	$-0.257676\pi$
$251$	21.8586	1.37970	0.689851	+	0.723952i	$0.257676\pi$
$252$	14.0649	0.886009
$253$	−0.440965	−0.0277232
$254$	−40.5395	−2.54368
$255$	−2.20443	−0.138046
$256$	−24.7541	−1.54713
$257$	4.62898	0.288748	0.144374	−	0.989523i	$-0.453883\pi$
$257$	4.62898	0.288748	0.144374	+	0.989523i	$0.453883\pi$
$258$	−2.93118	−0.182487
$259$	3.31316	0.205870
$260$	−3.51354	−0.217901
$261$	2.81787	0.174422
$262$	33.6225	2.07721
$263$	24.5730	1.51524	0.757618	−	0.652698i	$-0.226363\pi$
$263$	24.5730	1.51524	0.757618	+	0.652698i	$0.226363\pi$
$264$	0.527387	0.0324584
$265$	2.96554	0.182172
$266$	12.0319	0.737720
$267$	−16.5954	−1.01562
$268$	43.8962	2.68139
$269$	6.56029	0.399988	0.199994	−	0.979797i	$-0.435908\pi$
$269$	6.56029	0.399988	0.199994	+	0.979797i	$0.435908\pi$
$270$	−4.73361	−0.288078
$271$	20.1490	1.22397	0.611983	−	0.790871i	$-0.290372\pi$
$271$	20.1490	1.22397	0.611983	+	0.790871i	$0.290372\pi$
$272$	7.25876	0.440127
$273$	−12.3388	−0.746777
$274$	−5.68032	−0.343161
$275$	−0.517772	−0.0312228
$276$	19.8979	1.19771
$277$	23.3449	1.40266	0.701329	−	0.712837i	$-0.252590\pi$
$277$	23.3449	1.40266	0.701329	+	0.712837i	$0.252590\pi$
$278$	−49.4251	−2.96432
$279$	2.32351	0.139105
$280$	4.35283	0.260132
$281$	28.6228	1.70749	0.853745	−	0.520691i	$-0.174326\pi$
$281$	28.6228	1.70749	0.853745	+	0.520691i	$0.174326\pi$
$282$	35.6506	2.12297
$283$	30.9301	1.83861	0.919303	−	0.393551i	$-0.128754\pi$
$283$	30.9301	1.83861	0.919303	+	0.393551i	$0.128754\pi$
$284$	−31.3538	−1.86051
$285$	−0.737128	−0.0436637
$286$	0.693963	0.0410349
$287$	−13.6576	−0.806183
$288$	−4.36114	−0.256983
$289$	4.19625	0.246838
$290$	1.98691	0.116676
$291$	−12.1624	−0.712973
$292$	−37.0067	−2.16565
$293$	8.29439	0.484564	0.242282	−	0.970206i	$-0.422104\pi$
$293$	8.29439	0.484564	0.242282	+	0.970206i	$0.422104\pi$
$294$	12.6182	0.735909
$295$	−4.15176	−0.241725
$296$	3.69052	0.214507
$297$	0.598902	0.0347518
$298$	45.4280	2.63157
$299$	11.4919	0.664592
$300$	23.3638	1.34891
$301$	3.06090	0.176427
$302$	17.8902	1.02947
$303$	−12.0127	−0.690111
$304$	2.42722	0.139211
$305$	1.02729	0.0588222
$306$	12.9342	0.739399
$307$	−9.12437	−0.520755	−0.260378	−	0.965507i	$-0.583847\pi$
$307$	−9.12437	−0.520755	−0.260378	+	0.965507i	$0.583847\pi$
$308$	−1.25476	−0.0714963
$309$	−15.2480	−0.867430
$310$	1.63833	0.0930511
$311$	−30.7122	−1.74153	−0.870765	−	0.491700i	$-0.836376\pi$
$311$	−30.7122	−1.74153	−0.870765	+	0.491700i	$0.836376\pi$
$312$	−13.7441	−0.778108
$313$	21.0280	1.18857	0.594287	−	0.804253i	$-0.297434\pi$
$313$	21.0280	1.18857	0.594287	+	0.804253i	$0.297434\pi$
$314$	12.1825	0.687497
$315$	1.40469	0.0791456
$316$	8.05915	0.453363
$317$	−3.58180	−0.201174	−0.100587	−	0.994928i	$-0.532072\pi$
$317$	−3.58180	−0.201174	−0.100587	+	0.994928i	$0.532072\pi$
$318$	26.4302	1.48213
$319$	−0.251387	−0.0140750
$320$	−4.19764	−0.234655
$321$	0.527302	0.0294311
$322$	−32.4370	−1.80765
$323$	7.08772	0.394371
$324$	−14.2891	−0.793840
$325$	13.4935	0.748487
$326$	2.35892	0.130648
$327$	5.23116	0.289284
$328$	−15.2132	−0.840006
$329$	−37.2283	−2.05246
$330$	0.120004	0.00660602
$331$	−22.8222	−1.25442	−0.627210	−	0.778850i	$-0.715803\pi$
$331$	−22.8222	−1.25442	−0.627210	+	0.778850i	$0.715803\pi$
$332$	33.4263	1.83451
$333$	1.19096	0.0652642
$334$	16.7954	0.919005
$335$	4.38400	0.239524
$336$	7.02587	0.383292
$337$	−0.410814	−0.0223785	−0.0111892	−	0.999937i	$-0.503562\pi$
$337$	−0.410814	−0.0223785	−0.0111892	+	0.999937i	$0.503562\pi$
$338$	12.5807	0.684301
$339$	12.0945	0.656882
$340$	5.84211	0.316833
$341$	−0.207284	−0.0112251
$342$	4.32501	0.233870
$343$	10.0155	0.540788
$344$	3.40952	0.183829
$345$	1.98724	0.106990
$346$	56.4910	3.03698
$347$	6.29238	0.337793	0.168896	−	0.985634i	$-0.445980\pi$
$347$	6.29238	0.337793	0.168896	+	0.985634i	$0.445980\pi$
$348$	11.3435	0.608075
$349$	−5.09539	−0.272750	−0.136375	−	0.990657i	$-0.543545\pi$
$349$	−5.09539	−0.272750	−0.136375	+	0.990657i	$0.543545\pi$
$350$	−38.0869	−2.03583
$351$	−15.6078	−0.833085
$352$	0.389064	0.0207372
$353$	8.48347	0.451530	0.225765	−	0.974182i	$-0.427512\pi$
$353$	8.48347	0.451530	0.225765	+	0.974182i	$0.427512\pi$
$354$	−37.0022	−1.96664
$355$	−3.13137	−0.166196
$356$	43.9807	2.33097
$357$	20.5162	1.08583
$358$	31.4889	1.66424
$359$	−36.9243	−1.94879	−0.974394	−	0.224847i	$-0.927812\pi$
$359$	−36.9243	−1.94879	−0.974394	+	0.224847i	$0.927812\pi$
$360$	1.56468	0.0824661
$361$	−16.6300	−0.875262
$362$	−24.1091	−1.26714
$363$	14.7799	0.775742
$364$	32.6999	1.71394
$365$	−3.69593	−0.193454
$366$	9.15559	0.478570
$367$	−10.0471	−0.524454	−0.262227	−	0.965006i	$-0.584457\pi$
$367$	−10.0471	−0.524454	−0.262227	+	0.965006i	$0.584457\pi$
$368$	−6.54363	−0.341110
$369$	−4.90941	−0.255574
$370$	0.839759	0.0436570
$371$	−27.5998	−1.43291
$372$	9.35340	0.484951
$373$	−29.4044	−1.52250	−0.761250	−	0.648459i	$-0.775414\pi$
$373$	−29.4044	−1.52250	−0.761250	+	0.648459i	$0.775414\pi$
$374$	−1.15388	−0.0596657
$375$	4.72745	0.244124
$376$	−41.4685	−2.13857
$377$	6.55133	0.337411
$378$	44.0548	2.26593
$379$	9.99362	0.513338	0.256669	−	0.966499i	$-0.417375\pi$
$379$	9.99362	0.513338	0.256669	+	0.966499i	$0.417375\pi$
$380$	1.95352	0.100213
$381$	−23.1148	−1.18421
$382$	−43.0589	−2.20308
$383$	6.66032	0.340326	0.170163	−	0.985416i	$-0.445571\pi$
$383$	6.66032	0.340326	0.170163	+	0.985416i	$0.445571\pi$
$384$	−27.5606	−1.40645
$385$	−0.125315	−0.00638664
$386$	13.0194	0.662669
$387$	1.10028	0.0559303
$388$	32.2325	1.63636
$389$	−2.28672	−0.115941	−0.0579705	−	0.998318i	$-0.518463\pi$
$389$	−2.28672	−0.115941	−0.0579705	+	0.998318i	$0.518463\pi$
$390$	−3.12741	−0.158362
$391$	−19.1080	−0.966333
$392$	−14.6774	−0.741319
$393$	19.1709	0.967042
$394$	−31.9801	−1.61113
$395$	0.804883	0.0404981
$396$	−0.451038	−0.0226655
$397$	3.44574	0.172937	0.0864684	−	0.996255i	$-0.472442\pi$
$397$	3.44574	0.172937	0.0864684	+	0.996255i	$0.472442\pi$
$398$	−57.8501	−2.89976
$399$	6.86031	0.343445
$400$	−7.68340	−0.384170
$401$	−21.3529	−1.06631	−0.533155	−	0.846017i	$-0.678994\pi$
$401$	−21.3529	−1.06631	−0.533155	+	0.846017i	$0.678994\pi$
$402$	39.0720	1.94874
$403$	5.40198	0.269092
$404$	31.8357	1.58389
$405$	−1.42708	−0.0709123
$406$	−18.4918	−0.917734
$407$	−0.106247	−0.00526649
$408$	22.8529	1.13139
$409$	−15.2722	−0.755164	−0.377582	−	0.925976i	$-0.623244\pi$
$409$	−15.2722	−0.755164	−0.377582	+	0.925976i	$0.623244\pi$
$410$	−3.46168	−0.170960
$411$	−3.23880	−0.159758
$412$	40.4099	1.99085
$413$	38.6397	1.90133
$414$	−11.6599	−0.573054
$415$	3.33835	0.163873
$416$	−10.1393	−0.497120
$417$	−28.1811	−1.38004
$418$	−0.385841	−0.0188721
$419$	−32.7963	−1.60220	−0.801102	−	0.598528i	$-0.795753\pi$
$419$	−32.7963	−1.60220	−0.801102	+	0.598528i	$0.795753\pi$
$420$	5.65466	0.275919
$421$	−35.0809	−1.70974	−0.854869	−	0.518843i	$-0.826363\pi$
$421$	−35.0809	−1.70974	−0.854869	+	0.518843i	$0.826363\pi$
$422$	42.6651	2.07691
$423$	−13.3822	−0.650665
$424$	−30.7433	−1.49303
$425$	−22.4362	−1.08832
$426$	−27.9080	−1.35215
$427$	−9.56075	−0.462677
$428$	−1.39744	−0.0675478
$429$	0.395683	0.0191038
$430$	0.775819	0.0374133
$431$	−21.8169	−1.05088	−0.525441	−	0.850830i	$-0.676100\pi$
$431$	−21.8169	−1.05088	−0.525441	+	0.850830i	$0.676100\pi$
$432$	8.88732	0.427591
$433$	−32.0898	−1.54214	−0.771069	−	0.636751i	$-0.780278\pi$
$433$	−32.0898	−1.54214	−0.771069	+	0.636751i	$0.780278\pi$
$434$	−15.2477	−0.731911
$435$	1.13290	0.0543182
$436$	−13.8635	−0.663940
$437$	−6.38943	−0.305648
$438$	−32.9396	−1.57392
$439$	35.6708	1.70247	0.851237	−	0.524782i	$-0.175853\pi$
$439$	35.6708	1.70247	0.851237	+	0.524782i	$0.175853\pi$
$440$	−0.139588	−0.00665459
$441$	−4.73651	−0.225548
$442$	30.0710	1.43033
$443$	19.7951	0.940495	0.470248	−	0.882534i	$-0.344165\pi$
$443$	19.7951	0.940495	0.470248	+	0.882534i	$0.344165\pi$
$444$	4.79427	0.227526
$445$	4.39244	0.208222
$446$	28.5700	1.35283
$447$	25.9021	1.22513
$448$	39.0666	1.84572
$449$	−19.8013	−0.934483	−0.467242	−	0.884130i	$-0.654752\pi$
$449$	−19.8013	−0.934483	−0.467242	+	0.884130i	$0.654752\pi$
$450$	−13.6909	−0.645393
$451$	0.437976	0.0206235
$452$	−32.0525	−1.50762
$453$	10.2006	0.479267
$454$	−39.2767	−1.84335
$455$	3.26580	0.153103
$456$	7.64167	0.357854
$457$	−18.5890	−0.869558	−0.434779	−	0.900537i	$-0.643173\pi$
$457$	−18.5890	−0.869558	−0.434779	+	0.900537i	$0.643173\pi$
$458$	−34.8091	−1.62652
$459$	25.9518	1.21133
$460$	−5.26654	−0.245554
$461$	9.63609	0.448797	0.224399	−	0.974497i	$-0.427958\pi$
$461$	9.63609	0.448797	0.224399	+	0.974497i	$0.427958\pi$
$462$	−1.11686	−0.0519609
$463$	8.38692	0.389773	0.194887	−	0.980826i	$-0.437566\pi$
$463$	8.38692	0.389773	0.194887	+	0.980826i	$0.437566\pi$
$464$	−3.73042	−0.173180
$465$	0.934143	0.0433198
$466$	42.2639	1.95784
$467$	−2.44997	−0.113371	−0.0566855	−	0.998392i	$-0.518053\pi$
$467$	−2.44997	−0.113371	−0.0566855	+	0.998392i	$0.518053\pi$
$468$	11.7544	0.543348
$469$	−40.8011	−1.88402
$470$	−9.43594	−0.435247
$471$	6.94619	0.320064
$472$	43.0406	1.98110
$473$	−0.0981576	−0.00451329
$474$	7.17345	0.329488
$475$	−7.50235	−0.344231
$476$	−54.3714	−2.49211
$477$	−9.92110	−0.454256
$478$	14.2401	0.651327
$479$	−8.36374	−0.382149	−0.191074	−	0.981576i	$-0.561197\pi$
$479$	−8.36374	−0.382149	−0.191074	+	0.981576i	$0.561197\pi$
$480$	−1.75335	−0.0800291
$481$	2.76889	0.126250
$482$	−24.3952	−1.11117
$483$	−18.4949	−0.841548
$484$	−39.1692	−1.78042
$485$	3.21912	0.146173
$486$	27.1720	1.23255
$487$	33.6729	1.52586	0.762932	−	0.646479i	$-0.223759\pi$
$487$	33.6729	1.52586	0.762932	+	0.646479i	$0.223759\pi$
$488$	−10.6497	−0.482089
$489$	1.34501	0.0608233
$490$	−3.33976	−0.150875
$491$	−19.0339	−0.858990	−0.429495	−	0.903069i	$-0.641308\pi$
$491$	−19.0339	−0.858990	−0.429495	+	0.903069i	$0.641308\pi$
$492$	−19.7631	−0.890987
$493$	−10.8932	−0.490603
$494$	10.0553	0.452410
$495$	−0.0450461	−0.00202467
$496$	−3.07596	−0.138115
$497$	29.1430	1.30724
$498$	29.7528	1.33325
$499$	−27.4971	−1.23094	−0.615470	−	0.788160i	$-0.711034\pi$
$499$	−27.4971	−1.23094	−0.615470	+	0.788160i	$0.711034\pi$
$500$	−12.5286	−0.560294
$501$	9.57640	0.427842
$502$	−51.5626	−2.30135
$503$	3.40366	0.151762	0.0758808	−	0.997117i	$-0.475823\pi$
$503$	3.40366	0.151762	0.0758808	+	0.997117i	$0.475823\pi$
$504$	−14.5622	−0.648653
$505$	3.17949	0.141486
$506$	1.04020	0.0462425
$507$	7.17326	0.318576
$508$	61.2582	2.71789
$509$	−29.1964	−1.29411	−0.647053	−	0.762445i	$-0.723999\pi$
$509$	−29.1964	−1.29411	−0.647053	+	0.762445i	$0.723999\pi$
$510$	5.20006	0.230263
$511$	34.3973	1.52165
$512$	17.4107	0.769452
$513$	8.67790	0.383138
$514$	−10.9194	−0.481634
$515$	4.03582	0.177839
$516$	4.42923	0.194986
$517$	1.19385	0.0525053
$518$	−7.81548	−0.343393
$519$	32.2100	1.41386
$520$	3.63777	0.159527
$521$	38.2292	1.67485	0.837426	−	0.546550i	$-0.184059\pi$
$521$	38.2292	1.67485	0.837426	+	0.546550i	$0.184059\pi$
$522$	−6.64713	−0.290937
$523$	5.15700	0.225500	0.112750	−	0.993623i	$-0.464034\pi$
$523$	5.15700	0.225500	0.112750	+	0.993623i	$0.464034\pi$
$524$	−50.8061	−2.21947
$525$	−21.7164	−0.947780
$526$	−57.9657	−2.52743
$527$	−8.98208	−0.391266
$528$	−0.225307	−0.00980524
$529$	−5.77453	−0.251067
$530$	−6.99548	−0.303864
$531$	13.8895	0.602755
$532$	−18.1810	−0.788246
$533$	−11.4140	−0.494395
$534$	39.1472	1.69407
$535$	−0.139565	−0.00603393
$536$	−45.4482	−1.96306
$537$	17.9543	0.774786
$538$	−15.4752	−0.667183
$539$	0.422551	0.0182006
$540$	7.15282	0.307809
$541$	−12.8820	−0.553841	−0.276920	−	0.960893i	$-0.589314\pi$
$541$	−12.8820	−0.553841	−0.276920	+	0.960893i	$0.589314\pi$
$542$	−47.5299	−2.04158
$543$	−13.7465	−0.589918
$544$	16.8590	0.722825
$545$	−1.38457	−0.0593086
$546$	29.1062	1.24563
$547$	−22.3361	−0.955024	−0.477512	−	0.878625i	$-0.658461\pi$
$547$	−22.3361	−0.955024	−0.477512	+	0.878625i	$0.658461\pi$
$548$	8.58337	0.366663
$549$	−3.43674	−0.146676
$550$	1.22138	0.0520799
$551$	−3.64251	−0.155176
$552$	−20.6014	−0.876854
$553$	−7.49090	−0.318545
$554$	−55.0687	−2.33964
$555$	0.478813	0.0203245
$556$	74.6849	3.16734
$557$	−21.4286	−0.907960	−0.453980	−	0.891012i	$-0.649996\pi$
$557$	−21.4286	−0.907960	−0.453980	+	0.891012i	$0.649996\pi$
$558$	−5.48097	−0.232028
$559$	2.55806	0.108195
$560$	−1.85959	−0.0785821
$561$	−0.657918	−0.0277773
$562$	−67.5187	−2.84811
$563$	−21.8493	−0.920839	−0.460419	−	0.887702i	$-0.652301\pi$
$563$	−21.8493	−0.920839	−0.460419	+	0.887702i	$0.652301\pi$
$564$	−53.8707	−2.26837
$565$	−3.20114	−0.134673
$566$	−72.9617	−3.06681
$567$	13.2816	0.557774
$568$	32.4623	1.36209
$569$	20.1059	0.842883	0.421441	−	0.906856i	$-0.361524\pi$
$569$	20.1059	0.842883	0.421441	+	0.906856i	$0.361524\pi$
$570$	1.73882	0.0728313
$571$	11.8083	0.494161	0.247080	−	0.968995i	$-0.420529\pi$
$571$	11.8083	0.494161	0.247080	+	0.968995i	$0.420529\pi$
$572$	−1.04863	−0.0438454
$573$	−24.5512	−1.02564
$574$	32.2172	1.34472
$575$	20.2258	0.843474
$576$	14.0430	0.585125
$577$	−9.85160	−0.410127	−0.205064	−	0.978749i	$-0.565740\pi$
$577$	−9.85160	−0.410127	−0.205064	+	0.978749i	$0.565740\pi$
$578$	−9.89861	−0.411728
$579$	7.42338	0.308505
$580$	−3.00237	−0.124667
$581$	−31.0694	−1.28898
$582$	28.6901	1.18924
$583$	0.885076	0.0366561
$584$	38.3150	1.58549
$585$	1.17394	0.0485363
$586$	−19.5658	−0.808256
$587$	−18.7107	−0.772275	−0.386137	−	0.922441i	$-0.626191\pi$
$587$	−18.7107	−0.772275	−0.386137	+	0.922441i	$0.626191\pi$
$588$	−19.0670	−0.786311
$589$	−3.00348	−0.123756
$590$	9.79367	0.403199
$591$	−18.2344	−0.750061
$592$	−1.57664	−0.0647996
$593$	−8.45822	−0.347337	−0.173669	−	0.984804i	$-0.555562\pi$
$593$	−8.45822	−0.347337	−0.173669	+	0.984804i	$0.555562\pi$
$594$	−1.41276	−0.0579663
$595$	−5.43018	−0.222616
$596$	−68.6449	−2.81181
$597$	−32.9849	−1.34998
$598$	−27.1084	−1.10854
$599$	0.870276	0.0355585	0.0177792	−	0.999842i	$-0.494340\pi$
$599$	0.870276	0.0355585	0.0177792	+	0.999842i	$0.494340\pi$
$600$	−24.1898	−0.987544
$601$	13.0061	0.530531	0.265266	−	0.964175i	$-0.414540\pi$
$601$	13.0061	0.530531	0.265266	+	0.964175i	$0.414540\pi$
$602$	−7.22040	−0.294282
$603$	−14.6665	−0.597266
$604$	−27.0334	−1.09997
$605$	−3.91191	−0.159042
$606$	28.3370	1.15111
$607$	−13.1087	−0.532065	−0.266033	−	0.963964i	$-0.585713\pi$
$607$	−13.1087	−0.532065	−0.266033	+	0.963964i	$0.585713\pi$
$608$	5.63741	0.228627
$609$	−10.5437	−0.427250
$610$	−2.42328	−0.0981158
$611$	−31.1126	−1.25868
$612$	−19.5445	−0.790040
$613$	41.8751	1.69132	0.845660	−	0.533723i	$-0.179207\pi$
$613$	41.8751	1.69132	0.845660	+	0.533723i	$0.179207\pi$
$614$	21.5236	0.868623
$615$	−1.97378	−0.0795903
$616$	1.29912	0.0523429
$617$	20.2161	0.813868	0.406934	−	0.913458i	$-0.366598\pi$
$617$	20.2161	0.813868	0.406934	+	0.913458i	$0.366598\pi$
$618$	35.9689	1.44688
$619$	35.7978	1.43884	0.719418	−	0.694578i	$-0.244409\pi$
$619$	35.7978	1.43884	0.719418	+	0.694578i	$0.244409\pi$
$620$	−2.47564	−0.0994241
$621$	−23.3950	−0.938809
$622$	72.4476	2.90488
$623$	−40.8796	−1.63781
$624$	5.87168	0.235055
$625$	23.1151	0.924604
$626$	−49.6034	−1.98255
$627$	−0.219998	−0.00878588
$628$	−18.4086	−0.734584
$629$	−4.60394	−0.183571
$630$	−3.31356	−0.132015
$631$	−27.9403	−1.11229	−0.556144	−	0.831086i	$-0.687720\pi$
$631$	−27.9403	−1.11229	−0.556144	+	0.831086i	$0.687720\pi$
$632$	−8.34408	−0.331910
$633$	24.3268	0.966902
$634$	8.44917	0.335559
$635$	6.11797	0.242784
$636$	−39.9379	−1.58364
$637$	−11.0120	−0.436311
$638$	0.593001	0.0234771
$639$	10.4759	0.414418
$640$	7.29468	0.288348
$641$	−35.5917	−1.40579	−0.702894	−	0.711294i	$-0.748109\pi$
$641$	−35.5917	−1.40579	−0.702894	+	0.711294i	$0.748109\pi$
$642$	−1.24386	−0.0490913
$643$	−35.9323	−1.41703	−0.708516	−	0.705695i	$-0.750635\pi$
$643$	−35.9323	−1.41703	−0.708516	+	0.705695i	$0.750635\pi$
$644$	49.0147	1.93145
$645$	0.442356	0.0174177
$646$	−16.7193	−0.657814
$647$	−37.1944	−1.46226	−0.731131	−	0.682237i	$-0.761007\pi$
$647$	−37.1944	−1.46226	−0.731131	+	0.682237i	$0.761007\pi$
$648$	14.7943	0.581175
$649$	−1.23911	−0.0486392
$650$	−31.8302	−1.24848
$651$	−8.69389	−0.340741
$652$	−3.56450	−0.139596
$653$	19.7230	0.771822	0.385911	−	0.922536i	$-0.373887\pi$
$653$	19.7230	0.771822	0.385911	+	0.922536i	$0.373887\pi$
$654$	−12.3399	−0.482528
$655$	−5.07410	−0.198262
$656$	6.49928	0.253754
$657$	12.3646	0.482388
$658$	87.8185	3.42352
$659$	−28.7029	−1.11811	−0.559053	−	0.829132i	$-0.688835\pi$
$659$	−28.7029	−1.11811	−0.559053	+	0.829132i	$0.688835\pi$
$660$	−0.181335	−0.00705846
$661$	14.0299	0.545700	0.272850	−	0.962057i	$-0.412034\pi$
$661$	14.0299	0.545700	0.272850	+	0.962057i	$0.412034\pi$
$662$	53.8356	2.09238
$663$	17.1459	0.665890
$664$	−34.6081	−1.34306
$665$	−1.81577	−0.0704126
$666$	−2.80938	−0.108861
$667$	9.81996	0.380230
$668$	−25.3791	−0.981947
$669$	16.2900	0.629808
$670$	−10.3415	−0.399527
$671$	0.306597	0.0118360
$672$	16.3181	0.629485
$673$	−42.5253	−1.63923	−0.819615	−	0.572915i	$-0.805813\pi$
$673$	−42.5253	−1.63923	−0.819615	+	0.572915i	$0.805813\pi$
$674$	0.969077	0.0373274
$675$	−27.4700	−1.05732
$676$	−19.0104	−0.731168
$677$	−22.4174	−0.861569	−0.430785	−	0.902455i	$-0.641763\pi$
$677$	−22.4174	−0.861569	−0.430785	+	0.902455i	$0.641763\pi$
$678$	−28.5299	−1.09568
$679$	−29.9598	−1.14975
$680$	−6.04866	−0.231955
$681$	−22.3947	−0.858168
$682$	0.488966	0.0187235
$683$	−17.5348	−0.670952	−0.335476	−	0.942049i	$-0.608897\pi$
$683$	−17.5348	−0.670952	−0.335476	+	0.942049i	$0.608897\pi$
$684$	−6.53540	−0.249887
$685$	0.857238	0.0327534
$686$	−23.6258	−0.902038
$687$	−19.8474	−0.757226
$688$	−1.45659	−0.0555322
$689$	−23.0658	−0.878736
$690$	−4.68775	−0.178460
$691$	30.7503	1.16980	0.584898	−	0.811107i	$-0.301135\pi$
$691$	30.7503	1.16980	0.584898	+	0.811107i	$0.301135\pi$
$692$	−85.3620	−3.24498
$693$	0.419236	0.0159254
$694$	−14.8432	−0.563440
$695$	7.45892	0.282933
$696$	−11.7445	−0.445175
$697$	18.9785	0.718861
$698$	12.0196	0.454949
$699$	24.0980	0.911470
$700$	57.5521	2.17527
$701$	−22.6869	−0.856871	−0.428435	−	0.903572i	$-0.640935\pi$
$701$	−22.6869	−0.856871	−0.428435	+	0.903572i	$0.640935\pi$
$702$	36.8176	1.38959
$703$	−1.53949	−0.0580630
$704$	−1.25280	−0.0472166
$705$	−5.38017	−0.202629
$706$	−20.0118	−0.753155
$707$	−29.5910	−1.11288
$708$	55.9130	2.10134
$709$	−31.1046	−1.16816	−0.584078	−	0.811698i	$-0.698544\pi$
$709$	−31.1046	−1.16816	−0.584078	+	0.811698i	$0.698544\pi$
$710$	7.38664	0.277216
$711$	−2.69270	−0.100984
$712$	−45.5357	−1.70652
$713$	8.09716	0.303241
$714$	−48.3960	−1.81117
$715$	−0.104729	−0.00391663
$716$	−47.5820	−1.77822
$717$	8.11941	0.303225
$718$	87.1013	3.25059
$719$	20.7449	0.773652	0.386826	−	0.922153i	$-0.373571\pi$
$719$	20.7449	0.773652	0.386826	+	0.922153i	$0.373571\pi$
$720$	−0.668455	−0.0249118
$721$	−37.5606	−1.39883
$722$	39.2287	1.45994
$723$	−13.9097	−0.517306
$724$	36.4305	1.35393
$725$	11.5304	0.428229
$726$	−34.8645	−1.29394
$727$	−41.3865	−1.53494	−0.767470	−	0.641085i	$-0.778485\pi$
$727$	−41.3865	−1.53494	−0.767470	+	0.641085i	$0.778485\pi$
$728$	−33.8560	−1.25479
$729$	27.5191	1.01923
$730$	8.71839	0.322682
$731$	−4.25339	−0.157317
$732$	−13.8348	−0.511347
$733$	−33.0786	−1.22179	−0.610893	−	0.791713i	$-0.709189\pi$
$733$	−33.0786	−1.22179	−0.610893	+	0.791713i	$0.709189\pi$
$734$	23.7003	0.874793
$735$	−1.90426	−0.0702398
$736$	−15.1981	−0.560208
$737$	1.30842	0.0481963
$738$	11.5809	0.426299
$739$	2.81915	0.103704	0.0518520	−	0.998655i	$-0.483488\pi$
$739$	2.81915	0.103704	0.0518520	+	0.998655i	$0.483488\pi$
$740$	−1.26894	−0.0466470
$741$	5.73332	0.210619
$742$	65.1056	2.39010
$743$	29.8177	1.09391	0.546953	−	0.837163i	$-0.315788\pi$
$743$	29.8177	1.09391	0.546953	+	0.837163i	$0.315788\pi$
$744$	−9.68409	−0.355036
$745$	−6.85570	−0.251174
$746$	69.3625	2.53954
$747$	−11.1683	−0.408627
$748$	1.74360	0.0637522
$749$	1.29891	0.0474610
$750$	−11.1517	−0.407201
$751$	41.7054	1.52185	0.760926	−	0.648838i	$-0.224745\pi$
$751$	41.7054	1.52185	0.760926	+	0.648838i	$0.224745\pi$
$752$	17.7159	0.646033
$753$	−29.3999	−1.07139
$754$	−15.4541	−0.562804
$755$	−2.69988	−0.0982586
$756$	−66.5700	−2.42113
$757$	−19.9803	−0.726196	−0.363098	−	0.931751i	$-0.618281\pi$
$757$	−19.9803	−0.726196	−0.363098	+	0.931751i	$0.618281\pi$
$758$	−23.5741	−0.856251
$759$	0.593100	0.0215282
$760$	−2.02258	−0.0733668
$761$	−45.8747	−1.66296	−0.831479	−	0.555556i	$-0.812505\pi$
$761$	−45.8747	−1.66296	−0.831479	+	0.555556i	$0.812505\pi$
$762$	54.5259	1.97527
$763$	12.8860	0.466503
$764$	65.0650	2.35397
$765$	−1.95195	−0.0705729
$766$	−15.7111	−0.567667
$767$	32.2921	1.16600
$768$	33.2944	1.20141
$769$	−1.37895	−0.0497262	−0.0248631	−	0.999691i	$-0.507915\pi$
$769$	−1.37895	−0.0497262	−0.0248631	+	0.999691i	$0.507915\pi$
$770$	0.295608	0.0106530
$771$	−6.22601	−0.224224
$772$	−19.6732	−0.708055
$773$	−14.1450	−0.508761	−0.254380	−	0.967104i	$-0.581872\pi$
$773$	−14.1450	−0.508761	−0.254380	+	0.967104i	$0.581872\pi$
$774$	−2.59547	−0.0932922
$775$	9.50753	0.341521
$776$	−33.3721	−1.19799
$777$	−4.45622	−0.159866
$778$	5.39417	0.193391
$779$	6.34613	0.227374
$780$	4.72574	0.169209
$781$	−0.934567	−0.0334414
$782$	45.0742	1.61185
$783$	−13.3371	−0.476630
$784$	6.27038	0.223942
$785$	−1.83850	−0.0656190
$786$	−45.2225	−1.61303
$787$	5.13881	0.183179	0.0915894	−	0.995797i	$-0.470805\pi$
$787$	5.13881	0.183179	0.0915894	+	0.995797i	$0.470805\pi$
$788$	48.3242	1.72148
$789$	−33.0508	−1.17664
$790$	−1.89865	−0.0675511
$791$	29.7924	1.05930
$792$	0.466985	0.0165936
$793$	−7.99015	−0.283738
$794$	−8.12823	−0.288460
$795$	−3.98867	−0.141464
$796$	87.4157	3.09837
$797$	−46.3738	−1.64264	−0.821321	−	0.570466i	$-0.806763\pi$
$797$	−46.3738	−1.64264	−0.821321	+	0.570466i	$0.806763\pi$
$798$	−16.1829	−0.572869
$799$	51.7321	1.83015
$800$	−17.8453	−0.630926
$801$	−14.6947	−0.519213
$802$	50.3696	1.77861
$803$	−1.10306	−0.0389262
$804$	−59.0407	−2.08220
$805$	4.89520	0.172533
$806$	−12.7428	−0.448847
$807$	−8.82363	−0.310606
$808$	−32.9613	−1.15957
$809$	45.7776	1.60946	0.804728	−	0.593644i	$-0.202311\pi$
$809$	45.7776	1.60946	0.804728	+	0.593644i	$0.202311\pi$
$810$	3.36637	0.118282
$811$	46.7774	1.64258	0.821289	−	0.570513i	$-0.193255\pi$
$811$	46.7774	1.64258	0.821289	+	0.570513i	$0.193255\pi$
$812$	27.9425	0.980589
$813$	−27.1005	−0.950458
$814$	0.250629	0.00878454
$815$	−0.355993	−0.0124699
$816$	−9.76308	−0.341776
$817$	−1.42227	−0.0497590
$818$	36.0260	1.25962
$819$	−10.9256	−0.381772
$820$	5.23085	0.182669
$821$	−4.44914	−0.155276	−0.0776380	−	0.996982i	$-0.524738\pi$
$821$	−4.44914	−0.155276	−0.0776380	+	0.996982i	$0.524738\pi$
$822$	7.64006	0.266478
$823$	−6.27595	−0.218766	−0.109383	−	0.994000i	$-0.534888\pi$
$823$	−6.27595	−0.218766	−0.109383	+	0.994000i	$0.534888\pi$
$824$	−41.8386	−1.45752
$825$	0.696406	0.0242457
$826$	−91.1478	−3.17144
$827$	−13.9289	−0.484356	−0.242178	−	0.970232i	$-0.577862\pi$
$827$	−13.9289	−0.484356	−0.242178	+	0.970232i	$0.577862\pi$
$828$	17.6190	0.612302
$829$	15.7078	0.545553	0.272777	−	0.962077i	$-0.412058\pi$
$829$	15.7078	0.545553	0.272777	+	0.962077i	$0.412058\pi$
$830$	−7.87490	−0.273342
$831$	−31.3990	−1.08922
$832$	32.6489	1.13190
$833$	18.3101	0.634407
$834$	66.4770	2.30191
$835$	−2.53466	−0.0877155
$836$	0.583033	0.0201646
$837$	−10.9973	−0.380121
$838$	77.3638	2.67249
$839$	35.9228	1.24019	0.620096	−	0.784526i	$-0.287093\pi$
$839$	35.9228	1.24019	0.620096	+	0.784526i	$0.287093\pi$
$840$	−5.85459	−0.202002
$841$	−23.4018	−0.806959
$842$	82.7530	2.85186
$843$	−38.4978	−1.32593
$844$	−64.4701	−2.21915
$845$	−1.89860	−0.0653139
$846$	31.5675	1.08531
$847$	36.4074	1.25097
$848$	13.1340	0.451022
$849$	−41.6012	−1.42775
$850$	52.9252	1.81532
$851$	4.15036	0.142272
$852$	42.1711	1.44476
$853$	−9.53721	−0.326548	−0.163274	−	0.986581i	$-0.552205\pi$
$853$	−9.53721	−0.326548	−0.163274	+	0.986581i	$0.552205\pi$
$854$	22.5530	0.771749
$855$	−0.652703	−0.0223220
$856$	1.44685	0.0494522
$857$	−37.0392	−1.26524	−0.632618	−	0.774464i	$-0.718019\pi$
$857$	−37.0392	−1.26524	−0.632618	+	0.774464i	$0.718019\pi$
$858$	−0.933385	−0.0318652
$859$	7.54799	0.257534	0.128767	−	0.991675i	$-0.458898\pi$
$859$	7.54799	0.257534	0.128767	+	0.991675i	$0.458898\pi$
$860$	−1.17232	−0.0399757
$861$	18.3696	0.626033
$862$	51.4642	1.75288
$863$	−32.1897	−1.09575	−0.547876	−	0.836560i	$-0.684563\pi$
$863$	−32.1897	−1.09575	−0.547876	+	0.836560i	$0.684563\pi$
$864$	20.6415	0.702237
$865$	−8.52527	−0.289868
$866$	75.6973	2.57230
$867$	−5.64398	−0.191679
$868$	23.0403	0.782039
$869$	0.240220	0.00814891
$870$	−2.67241	−0.0906032
$871$	−34.0984	−1.15538
$872$	14.3536	0.486075
$873$	−10.7694	−0.364490
$874$	15.0722	0.509823
$875$	11.6452	0.393678
$876$	49.7742	1.68171
$877$	−4.27782	−0.144452	−0.0722258	−	0.997388i	$-0.523010\pi$
$877$	−4.27782	−0.144452	−0.0722258	+	0.997388i	$0.523010\pi$
$878$	−84.1445	−2.83974
$879$	−11.1560	−0.376283
$880$	0.0596339	0.00201026
$881$	−32.2898	−1.08787	−0.543935	−	0.839127i	$-0.683066\pi$
$881$	−32.2898	−1.08787	−0.543935	+	0.839127i	$0.683066\pi$
$882$	11.1730	0.376215
$883$	−55.9293	−1.88217	−0.941086	−	0.338168i	$-0.890193\pi$
$883$	−55.9293	−1.88217	−0.941086	+	0.338168i	$0.890193\pi$
$884$	−45.4395	−1.52829
$885$	5.58414	0.187709
$886$	−46.6951	−1.56875
$887$	−42.6302	−1.43138	−0.715691	−	0.698417i	$-0.753888\pi$
$887$	−42.6302	−1.43138	−0.715691	+	0.698417i	$0.753888\pi$
$888$	−4.96377	−0.166573
$889$	−56.9388	−1.90967
$890$	−10.3614	−0.347315
$891$	−0.425917	−0.0142688
$892$	−43.1713	−1.44548
$893$	17.2985	0.578871
$894$	−61.1009	−2.04352
$895$	−4.75211	−0.158845
$896$	−67.8902	−2.26805
$897$	−15.4566	−0.516082
$898$	46.7098	1.55872
$899$	4.61606	0.153954
$900$	20.6879	0.689596
$901$	38.3524	1.27770
$902$	−1.03315	−0.0344001
$903$	−4.11692	−0.137003
$904$	33.1857	1.10374
$905$	3.63839	0.120944
$906$	−24.0624	−0.799420
$907$	24.7860	0.823007	0.411503	−	0.911408i	$-0.365004\pi$
$907$	24.7860	0.823007	0.411503	+	0.911408i	$0.365004\pi$
$908$	59.3499	1.96960
$909$	−10.6369	−0.352802
$910$	−7.70376	−0.255377
$911$	−2.75247	−0.0911934	−0.0455967	−	0.998960i	$-0.514519\pi$
$911$	−2.75247	−0.0911934	−0.0455967	+	0.998960i	$0.514519\pi$
$912$	−3.26463	−0.108103
$913$	0.996342	0.0329741
$914$	43.8500	1.45043
$915$	−1.38170	−0.0456777
$916$	52.5990	1.73792
$917$	47.2237	1.55946
$918$	−61.2181	−2.02050
$919$	18.1940	0.600164	0.300082	−	0.953913i	$-0.402986\pi$
$919$	18.1940	0.600164	0.300082	+	0.953913i	$0.402986\pi$
$920$	5.45274	0.179772
$921$	12.2723	0.404387
$922$	−22.7307	−0.748597
$923$	24.3555	0.801672
$924$	1.68765	0.0555197
$925$	4.87327	0.160232
$926$	−19.7841	−0.650144
$927$	−13.5017	−0.443452
$928$	−8.66417	−0.284415
$929$	26.7017	0.876054	0.438027	−	0.898962i	$-0.355677\pi$
$929$	26.7017	0.876054	0.438027	+	0.898962i	$0.355677\pi$
$930$	−2.20357	−0.0722578
$931$	6.12262	0.200661
$932$	−63.8638	−2.09193
$933$	41.3081	1.35237
$934$	5.77927	0.189104
$935$	0.174136	0.00569487
$936$	−12.1700	−0.397789
$937$	22.6236	0.739081	0.369540	−	0.929215i	$-0.379515\pi$
$937$	22.6236	0.739081	0.369540	+	0.929215i	$0.379515\pi$
$938$	96.2465	3.14256
$939$	−28.2828	−0.922975
$940$	14.2584	0.465057
$941$	55.9208	1.82297	0.911484	−	0.411336i	$-0.134938\pi$
$941$	55.9208	1.82297	0.911484	+	0.411336i	$0.134938\pi$
$942$	−16.3855	−0.533869
$943$	−17.1087	−0.557136
$944$	−18.3875	−0.598463
$945$	−6.64848	−0.216275
$946$	0.231546	0.00752820
$947$	−4.91529	−0.159726	−0.0798628	−	0.996806i	$-0.525448\pi$
$947$	−4.91529	−0.159726	−0.0798628	+	0.996806i	$0.525448\pi$
$948$	−10.8396	−0.352054
$949$	28.7466	0.933156
$950$	17.6974	0.574180
$951$	4.81754	0.156219
$952$	56.2937	1.82449
$953$	−39.1997	−1.26980	−0.634902	−	0.772593i	$-0.718960\pi$
$953$	−39.1997	−1.26980	−0.634902	+	0.772593i	$0.718960\pi$
$954$	23.4031	0.757702
$955$	6.49817	0.210276
$956$	−21.5178	−0.695936
$957$	0.338117	0.0109298
$958$	19.7294	0.637427
$959$	−7.97815	−0.257628
$960$	5.64584	0.182219
$961$	−27.1938	−0.877218
$962$	−6.53158	−0.210587
$963$	0.466909	0.0150459
$964$	36.8630	1.18728
$965$	−1.96480	−0.0632493
$966$	43.6280	1.40371
$967$	22.7832	0.732657	0.366329	−	0.930486i	$-0.380615\pi$
$967$	22.7832	0.732657	0.366329	+	0.930486i	$0.380615\pi$
$968$	40.5541	1.30346
$969$	−9.53302	−0.306245
$970$	−7.59365	−0.243817
$971$	−19.6183	−0.629582	−0.314791	−	0.949161i	$-0.601934\pi$
$971$	−19.6183	−0.629582	−0.314791	+	0.949161i	$0.601934\pi$
$972$	−41.0588	−1.31696
$973$	−69.4188	−2.22546
$974$	−79.4315	−2.54515
$975$	−18.1489	−0.581229
$976$	4.54970	0.145632
$977$	−37.6628	−1.20494	−0.602470	−	0.798142i	$-0.705817\pi$
$977$	−37.6628	−1.20494	−0.602470	+	0.798142i	$0.705817\pi$
$978$	−3.17276	−0.101454
$979$	1.31094	0.0418978
$980$	5.04662	0.161208
$981$	4.63203	0.147889
$982$	44.8995	1.43280
$983$	−3.34959	−0.106835	−0.0534176	−	0.998572i	$-0.517011\pi$
$983$	−3.34959	−0.106835	−0.0534176	+	0.998572i	$0.517011\pi$
$984$	20.4618	0.652298
$985$	4.82623	0.153777
$986$	25.6961	0.818330
$987$	50.0723	1.59382
$988$	−15.1943	−0.483395
$989$	3.83434	0.121925
$990$	0.106260	0.00337717
$991$	−10.1765	−0.323266	−0.161633	−	0.986851i	$-0.551676\pi$
$991$	−10.1765	−0.323266	−0.161633	+	0.986851i	$0.551676\pi$
$992$	−7.14415	−0.226827
$993$	30.6959	0.974106
$994$	−68.7461	−2.18049
$995$	8.73038	0.276771
$996$	−44.9586	−1.42457
$997$	18.6870	0.591823	0.295912	−	0.955215i	$-0.404377\pi$
$997$	18.6870	0.591823	0.295912	+	0.955215i	$0.404377\pi$
$998$	64.8635	2.05322
$999$	−5.63686	−0.178343

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6031.2.a.c.1.12	✓	110

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6031.2.a.c.1.12	✓	110	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:	\( N \)	\(=\)	\( 6031 = 37 \cdot 163 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6031.a (trivial)

\(f(q)\)	\(=\)	\(q-2.35892 q^{2} -1.34501 q^{3} +3.56450 q^{4} +0.355993 q^{5} +3.17276 q^{6} -3.31316 q^{7} -3.69052 q^{8} -1.19096 q^{9} +O(q^{10})\)	\(q-2.35892 q^{2} -1.34501 q^{3} +3.56450 q^{4} +0.355993 q^{5} +3.17276 q^{6} -3.31316 q^{7} -3.69052 q^{8} -1.19096 q^{9} -0.839759 q^{10} +0.106247 q^{11} -4.79427 q^{12} -2.76889 q^{13} +7.81548 q^{14} -0.478813 q^{15} +1.57664 q^{16} +4.60394 q^{17} +2.80938 q^{18} +1.53949 q^{19} +1.26894 q^{20} +4.45622 q^{21} -0.250629 q^{22} -4.15036 q^{23} +4.96377 q^{24} -4.87327 q^{25} +6.53158 q^{26} +5.63686 q^{27} -11.8098 q^{28} -2.36605 q^{29} +1.12948 q^{30} -1.95096 q^{31} +3.66187 q^{32} -0.142903 q^{33} -10.8603 q^{34} -1.17946 q^{35} -4.24517 q^{36} -1.00000 q^{37} -3.63153 q^{38} +3.72417 q^{39} -1.31380 q^{40} +4.12223 q^{41} -10.5119 q^{42} -0.923859 q^{43} +0.378718 q^{44} -0.423974 q^{45} +9.79035 q^{46} +11.2365 q^{47} -2.12059 q^{48} +3.97705 q^{49} +11.4956 q^{50} -6.19232 q^{51} -9.86969 q^{52} +8.33034 q^{53} -13.2969 q^{54} +0.0378233 q^{55} +12.2273 q^{56} -2.07062 q^{57} +5.58132 q^{58} -11.6625 q^{59} -1.70673 q^{60} +2.88569 q^{61} +4.60215 q^{62} +3.94584 q^{63} -11.7913 q^{64} -0.985706 q^{65} +0.337097 q^{66} +12.3148 q^{67} +16.4107 q^{68} +5.58225 q^{69} +2.78226 q^{70} -8.79614 q^{71} +4.39526 q^{72} -10.3820 q^{73} +2.35892 q^{74} +6.55457 q^{75} +5.48751 q^{76} -0.352015 q^{77} -8.78501 q^{78} +2.26095 q^{79} +0.561274 q^{80} -4.00873 q^{81} -9.72400 q^{82} +9.37757 q^{83} +15.8842 q^{84} +1.63897 q^{85} +2.17931 q^{86} +3.18235 q^{87} -0.392108 q^{88} +12.3386 q^{89} +1.00012 q^{90} +9.17378 q^{91} -14.7939 q^{92} +2.62405 q^{93} -26.5059 q^{94} +0.548048 q^{95} -4.92523 q^{96} +9.04265 q^{97} -9.38153 q^{98} -0.126536 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 110 q - 9 q^{2} + 97 q^{4} - 26 q^{5} - 26 q^{6} - 4 q^{7} - 27 q^{8} + 62 q^{9}+O(q^{10}) \) 110 * q - 9 * q^2 + 97 * q^4 - 26 * q^5 - 26 * q^6 - 4 * q^7 - 27 * q^8 + 62 * q^9	\( 110 q - 9 q^{2} + 97 q^{4} - 26 q^{5} - 26 q^{6} - 4 q^{7} - 27 q^{8} + 62 q^{9} - 17 q^{10} - 9 q^{11} - 21 q^{13} - 29 q^{14} - 23 q^{15} + 79 q^{16} - 76 q^{17} - 31 q^{18} - 27 q^{19} - 67 q^{20} - 30 q^{21} - 28 q^{22} - 32 q^{23} - 63 q^{24} + 66 q^{25} - 55 q^{26} - 4 q^{28} - 81 q^{29} - 48 q^{30} - 30 q^{31} - 73 q^{32} - 53 q^{33} - 23 q^{34} - 78 q^{35} + 7 q^{36} - 110 q^{37} - 50 q^{38} - 64 q^{39} - 37 q^{40} - 123 q^{41} - 63 q^{42} - 40 q^{43} - 31 q^{44} - 73 q^{45} + 16 q^{46} - 37 q^{47} - 29 q^{48} + 46 q^{49} - 58 q^{50} - 73 q^{51} - 39 q^{52} - 16 q^{53} - 53 q^{54} - 59 q^{55} - 113 q^{56} - 39 q^{57} + 11 q^{58} - 93 q^{59} - 18 q^{60} - 66 q^{61} - 40 q^{62} - 21 q^{63} + 23 q^{64} - 92 q^{65} - 31 q^{66} + q^{67} - 121 q^{68} - 80 q^{69} - 3 q^{70} - 75 q^{71} - 114 q^{72} - 39 q^{73} + 9 q^{74} - 25 q^{75} - 58 q^{76} - 31 q^{77} + 68 q^{78} - 36 q^{79} - 82 q^{80} - 50 q^{81} - 18 q^{82} - 57 q^{83} - 9 q^{84} - 14 q^{85} - 58 q^{86} - 58 q^{87} - 15 q^{88} - 181 q^{89} + 8 q^{90} - 55 q^{91} - 116 q^{92} - 86 q^{93} - 39 q^{94} - 70 q^{95} - 127 q^{96} - 91 q^{97} - 19 q^{98} - 21 q^{99}+O(q^{100}) \) 110 * q - 9 * q^2 + 97 * q^4 - 26 * q^5 - 26 * q^6 - 4 * q^7 - 27 * q^8 + 62 * q^9 - 17 * q^10 - 9 * q^11 - 21 * q^13 - 29 * q^14 - 23 * q^15 + 79 * q^16 - 76 * q^17 - 31 * q^18 - 27 * q^19 - 67 * q^20 - 30 * q^21 - 28 * q^22 - 32 * q^23 - 63 * q^24 + 66 * q^25 - 55 * q^26 - 4 * q^28 - 81 * q^29 - 48 * q^30 - 30 * q^31 - 73 * q^32 - 53 * q^33 - 23 * q^34 - 78 * q^35 + 7 * q^36 - 110 * q^37 - 50 * q^38 - 64 * q^39 - 37 * q^40 - 123 * q^41 - 63 * q^42 - 40 * q^43 - 31 * q^44 - 73 * q^45 + 16 * q^46 - 37 * q^47 - 29 * q^48 + 46 * q^49 - 58 * q^50 - 73 * q^51 - 39 * q^52 - 16 * q^53 - 53 * q^54 - 59 * q^55 - 113 * q^56 - 39 * q^57 + 11 * q^58 - 93 * q^59 - 18 * q^60 - 66 * q^61 - 40 * q^62 - 21 * q^63 + 23 * q^64 - 92 * q^65 - 31 * q^66 + q^67 - 121 * q^68 - 80 * q^69 - 3 * q^70 - 75 * q^71 - 114 * q^72 - 39 * q^73 + 9 * q^74 - 25 * q^75 - 58 * q^76 - 31 * q^77 + 68 * q^78 - 36 * q^79 - 82 * q^80 - 50 * q^81 - 18 * q^82 - 57 * q^83 - 9 * q^84 - 14 * q^85 - 58 * q^86 - 58 * q^87 - 15 * q^88 - 181 * q^89 + 8 * q^90 - 55 * q^91 - 116 * q^92 - 86 * q^93 - 39 * q^94 - 70 * q^95 - 127 * q^96 - 91 * q^97 - 19 * q^98 - 21 * q^99

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