LMFDB - Embedded newform 6041.2.a.d.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6041,2,Mod(1,6041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6041, 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("6041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6041 = 7 \cdot 863 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6041.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:	$48.2376278611$
Analytic rank:	$1$
Dimension:	$101$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	6041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00569 q^{2} +2.11059 q^{3} +2.02278 q^{4} +3.12491 q^{5} -4.23318 q^{6} -1.00000 q^{7} -0.0456843 q^{8} +1.45460 q^{9} +O(q^{10})$	\(q-2.00569 q^{2} +2.11059 q^{3} +2.02278 q^{4} +3.12491 q^{5} -4.23318 q^{6} -1.00000 q^{7} -0.0456843 q^{8} +1.45460 q^{9} -6.26760 q^{10} -0.771038 q^{11} +4.26926 q^{12} -6.22175 q^{13} +2.00569 q^{14} +6.59542 q^{15} -3.95393 q^{16} +4.85290 q^{17} -2.91747 q^{18} +3.82696 q^{19} +6.32101 q^{20} -2.11059 q^{21} +1.54646 q^{22} -4.73458 q^{23} -0.0964208 q^{24} +4.76509 q^{25} +12.4789 q^{26} -3.26171 q^{27} -2.02278 q^{28} -3.76331 q^{29} -13.2283 q^{30} -1.21109 q^{31} +8.02170 q^{32} -1.62735 q^{33} -9.73340 q^{34} -3.12491 q^{35} +2.94233 q^{36} -5.06516 q^{37} -7.67569 q^{38} -13.1316 q^{39} -0.142759 q^{40} -11.9257 q^{41} +4.23318 q^{42} -2.61923 q^{43} -1.55964 q^{44} +4.54549 q^{45} +9.49607 q^{46} -10.1998 q^{47} -8.34512 q^{48} +1.00000 q^{49} -9.55727 q^{50} +10.2425 q^{51} -12.5852 q^{52} +3.20749 q^{53} +6.54197 q^{54} -2.40943 q^{55} +0.0456843 q^{56} +8.07716 q^{57} +7.54802 q^{58} +6.53712 q^{59} +13.3411 q^{60} +5.92838 q^{61} +2.42908 q^{62} -1.45460 q^{63} -8.18117 q^{64} -19.4424 q^{65} +3.26395 q^{66} +12.5436 q^{67} +9.81634 q^{68} -9.99276 q^{69} +6.26760 q^{70} -3.96749 q^{71} -0.0664522 q^{72} -9.41914 q^{73} +10.1591 q^{74} +10.0572 q^{75} +7.74110 q^{76} +0.771038 q^{77} +26.3378 q^{78} +0.911513 q^{79} -12.3557 q^{80} -11.2479 q^{81} +23.9192 q^{82} +15.7651 q^{83} -4.26926 q^{84} +15.1649 q^{85} +5.25335 q^{86} -7.94281 q^{87} +0.0352243 q^{88} -18.6989 q^{89} -9.11683 q^{90} +6.22175 q^{91} -9.57699 q^{92} -2.55613 q^{93} +20.4575 q^{94} +11.9589 q^{95} +16.9305 q^{96} +2.64546 q^{97} -2.00569 q^{98} -1.12155 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 101 q + 3 q^{2} - 17 q^{3} + 85 q^{4} - 12 q^{5} - 17 q^{6} - 101 q^{7} - 3 q^{8} + 88 q^{9}+O(q^{10}) $ 101 * q + 3 * q^2 - 17 * q^3 + 85 * q^4 - 12 * q^5 - 17 * q^6 - 101 * q^7 - 3 * q^8 + 88 * q^9	\( 101 q + 3 q^{2} - 17 q^{3} + 85 q^{4} - 12 q^{5} - 17 q^{6} - 101 q^{7} - 3 q^{8} + 88 q^{9} - 23 q^{10} - 13 q^{11} - 31 q^{12} - 35 q^{13} - 3 q^{14} - 20 q^{15} + 45 q^{16} - 19 q^{17} + 3 q^{18} - 59 q^{19} - 31 q^{20} + 17 q^{21} - 13 q^{22} - 29 q^{23} - 59 q^{24} + 103 q^{25} - 18 q^{26} - 47 q^{27} - 85 q^{28} - 26 q^{29} - 8 q^{30} - 125 q^{31} + 12 q^{32} - 18 q^{33} - 66 q^{34} + 12 q^{35} + 40 q^{36} + 22 q^{37} - 31 q^{38} - 94 q^{39} - 79 q^{40} - 39 q^{41} + 17 q^{42} - 5 q^{43} - 53 q^{44} - 50 q^{45} - 37 q^{46} - 47 q^{47} - 81 q^{48} + 101 q^{49} + 2 q^{50} - 23 q^{51} - 56 q^{52} - 5 q^{53} - 77 q^{54} - 155 q^{55} + 3 q^{56} + 61 q^{57} - 31 q^{58} - 33 q^{59} - 48 q^{60} - 96 q^{61} - 38 q^{62} - 88 q^{63} - 33 q^{64} - 8 q^{65} - 91 q^{66} + 8 q^{67} - 41 q^{68} - 91 q^{69} + 23 q^{70} - 116 q^{71} - 5 q^{72} - 62 q^{73} - 23 q^{74} - 94 q^{75} - 112 q^{76} + 13 q^{77} + 17 q^{78} - 127 q^{79} - 87 q^{80} + 37 q^{81} - 118 q^{82} - 58 q^{83} + 31 q^{84} - 6 q^{85} - 26 q^{86} - 82 q^{87} - 40 q^{88} - 57 q^{89} - 123 q^{90} + 35 q^{91} - 28 q^{92} - 10 q^{93} - 107 q^{94} - 70 q^{95} - 76 q^{96} - 69 q^{97} + 3 q^{98} - 67 q^{99}+O(q^{100}) \) 101 * q + 3 * q^2 - 17 * q^3 + 85 * q^4 - 12 * q^5 - 17 * q^6 - 101 * q^7 - 3 * q^8 + 88 * q^9 - 23 * q^10 - 13 * q^11 - 31 * q^12 - 35 * q^13 - 3 * q^14 - 20 * q^15 + 45 * q^16 - 19 * q^17 + 3 * q^18 - 59 * q^19 - 31 * q^20 + 17 * q^21 - 13 * q^22 - 29 * q^23 - 59 * q^24 + 103 * q^25 - 18 * q^26 - 47 * q^27 - 85 * q^28 - 26 * q^29 - 8 * q^30 - 125 * q^31 + 12 * q^32 - 18 * q^33 - 66 * q^34 + 12 * q^35 + 40 * q^36 + 22 * q^37 - 31 * q^38 - 94 * q^39 - 79 * q^40 - 39 * q^41 + 17 * q^42 - 5 * q^43 - 53 * q^44 - 50 * q^45 - 37 * q^46 - 47 * q^47 - 81 * q^48 + 101 * q^49 + 2 * q^50 - 23 * q^51 - 56 * q^52 - 5 * q^53 - 77 * q^54 - 155 * q^55 + 3 * q^56 + 61 * q^57 - 31 * q^58 - 33 * q^59 - 48 * q^60 - 96 * q^61 - 38 * q^62 - 88 * q^63 - 33 * q^64 - 8 * q^65 - 91 * q^66 + 8 * q^67 - 41 * q^68 - 91 * q^69 + 23 * q^70 - 116 * q^71 - 5 * q^72 - 62 * q^73 - 23 * q^74 - 94 * q^75 - 112 * q^76 + 13 * q^77 + 17 * q^78 - 127 * q^79 - 87 * q^80 + 37 * q^81 - 118 * q^82 - 58 * q^83 + 31 * q^84 - 6 * q^85 - 26 * q^86 - 82 * q^87 - 40 * q^88 - 57 * q^89 - 123 * q^90 + 35 * q^91 - 28 * q^92 - 10 * q^93 - 107 * q^94 - 70 * q^95 - 76 * q^96 - 69 * q^97 + 3 * q^98 - 67 * 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 $

$2$	−2.00569	−1.41823	−0.709117	−	0.705091i	$-0.750906\pi$
$2$	−2.00569	−1.41823	−0.709117	+	0.705091i	$0.750906\pi$
$3$	2.11059	1.21855	0.609275	−	0.792959i	$-0.291460\pi$
$3$	2.11059	1.21855	0.609275	+	0.792959i	$0.291460\pi$
$4$	2.02278	1.01139
$5$	3.12491	1.39750	0.698752	−	0.715364i	$-0.253739\pi$
$5$	3.12491	1.39750	0.698752	+	0.715364i	$0.253739\pi$
$6$	−4.23318	−1.72819
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−0.0456843	−0.0161518
$9$	1.45460	0.484866
$10$	−6.26760	−1.98199
$11$	−0.771038	−0.232477	−0.116238	−	0.993221i	$-0.537084\pi$
$11$	−0.771038	−0.232477	−0.116238	+	0.993221i	$0.537084\pi$
$12$	4.26926	1.23243
$13$	−6.22175	−1.72560	−0.862802	−	0.505543i	$-0.831292\pi$
$13$	−6.22175	−1.72560	−0.862802	+	0.505543i	$0.831292\pi$
$14$	2.00569	0.536042
$15$	6.59542	1.70293
$16$	−3.95393	−0.988482
$17$	4.85290	1.17700	0.588501	−	0.808496i	$-0.299718\pi$
$17$	4.85290	1.17700	0.588501	+	0.808496i	$0.299718\pi$
$18$	−2.91747	−0.687653
$19$	3.82696	0.877966	0.438983	−	0.898495i	$-0.355339\pi$
$19$	3.82696	0.877966	0.438983	+	0.898495i	$0.355339\pi$
$20$	6.32101	1.41342
$21$	−2.11059	−0.460569
$22$	1.54646	0.329706
$23$	−4.73458	−0.987227	−0.493614	−	0.869681i	$-0.664324\pi$
$23$	−4.73458	−0.987227	−0.493614	+	0.869681i	$0.664324\pi$
$24$	−0.0964208	−0.0196818
$25$	4.76509	0.953017
$26$	12.4789	2.44731
$27$	−3.26171	−0.627717
$28$	−2.02278	−0.382269
$29$	−3.76331	−0.698829	−0.349415	−	0.936968i	$-0.613620\pi$
$29$	−3.76331	−0.698829	−0.349415	+	0.936968i	$0.613620\pi$
$30$	−13.2283	−2.41515
$31$	−1.21109	−0.217519	−0.108759	−	0.994068i	$-0.534688\pi$
$31$	−1.21109	−0.217519	−0.108759	+	0.994068i	$0.534688\pi$
$32$	8.02170	1.41805
$33$	−1.62735	−0.283285
$34$	−9.73340	−1.66926
$35$	−3.12491	−0.528207
$36$	2.94233	0.490388
$37$	−5.06516	−0.832707	−0.416354	−	0.909203i	$-0.636692\pi$
$37$	−5.06516	−0.832707	−0.416354	+	0.909203i	$0.636692\pi$
$38$	−7.67569	−1.24516
$39$	−13.1316	−2.10273
$40$	−0.142759	−0.0225722
$41$	−11.9257	−1.86248	−0.931239	−	0.364408i	$-0.881271\pi$
$41$	−11.9257	−1.86248	−0.931239	+	0.364408i	$0.881271\pi$
$42$	4.23318	0.653195
$43$	−2.61923	−0.399429	−0.199714	−	0.979854i	$-0.564001\pi$
$43$	−2.61923	−0.399429	−0.199714	+	0.979854i	$0.564001\pi$
$44$	−1.55964	−0.235124
$45$	4.54549	0.677602
$46$	9.49607	1.40012
$47$	−10.1998	−1.48779	−0.743895	−	0.668297i	$-0.767024\pi$
$47$	−10.1998	−1.48779	−0.743895	+	0.668297i	$0.767024\pi$
$48$	−8.34512	−1.20451
$49$	1.00000	0.142857
$50$	−9.55727	−1.35160
$51$	10.2425	1.43424
$52$	−12.5852	−1.74526
$53$	3.20749	0.440583	0.220291	−	0.975434i	$-0.429299\pi$
$53$	3.20749	0.440583	0.220291	+	0.975434i	$0.429299\pi$
$54$	6.54197	0.890250
$55$	−2.40943	−0.324887
$56$	0.0456843	0.00610482
$57$	8.07716	1.06985
$58$	7.54802	0.991104
$59$	6.53712	0.851060	0.425530	−	0.904944i	$-0.360088\pi$
$59$	6.53712	0.851060	0.425530	+	0.904944i	$0.360088\pi$
$60$	13.3411	1.72232
$61$	5.92838	0.759051	0.379525	−	0.925181i	$-0.376087\pi$
$61$	5.92838	0.759051	0.379525	+	0.925181i	$0.376087\pi$
$62$	2.42908	0.308493
$63$	−1.45460	−0.183262
$64$	−8.18117	−1.02265
$65$	−19.4424	−2.41154
$66$	3.26395	0.401764
$67$	12.5436	1.53245	0.766223	−	0.642574i	$-0.222134\pi$
$67$	12.5436	1.53245	0.766223	+	0.642574i	$0.222134\pi$
$68$	9.81634	1.19041
$69$	−9.99276	−1.20299
$70$	6.26760	0.749121
$71$	−3.96749	−0.470854	−0.235427	−	0.971892i	$-0.575649\pi$
$71$	−3.96749	−0.470854	−0.235427	+	0.971892i	$0.575649\pi$
$72$	−0.0664522	−0.00783147
$73$	−9.41914	−1.10243	−0.551214	−	0.834364i	$-0.685835\pi$
$73$	−9.41914	−1.10243	−0.551214	+	0.834364i	$0.685835\pi$
$74$	10.1591	1.18097
$75$	10.0572	1.16130
$76$	7.74110	0.887965
$77$	0.771038	0.0878679
$78$	26.3378	2.98217
$79$	0.911513	0.102553	0.0512766	−	0.998684i	$-0.483671\pi$
$79$	0.911513	0.102553	0.0512766	+	0.998684i	$0.483671\pi$
$80$	−12.3557	−1.38141
$81$	−11.2479	−1.24977
$82$	23.9192	2.64143
$83$	15.7651	1.73045	0.865225	−	0.501384i	$-0.167176\pi$
$83$	15.7651	1.73045	0.865225	+	0.501384i	$0.167176\pi$
$84$	−4.26926	−0.465814
$85$	15.1649	1.64487
$86$	5.25335	0.566484
$87$	−7.94281	−0.851559
$88$	0.0352243	0.00375492
$89$	−18.6989	−1.98208	−0.991040	−	0.133566i	$-0.957357\pi$
$89$	−18.6989	−1.98208	−0.991040	+	0.133566i	$0.957357\pi$
$90$	−9.11683	−0.960998
$91$	6.22175	0.652217
$92$	−9.57699	−0.998470
$93$	−2.55613	−0.265058
$94$	20.4575	2.11003
$95$	11.9589	1.22696
$96$	16.9305	1.72797
$97$	2.64546	0.268605	0.134303	−	0.990940i	$-0.457121\pi$
$97$	2.64546	0.268605	0.134303	+	0.990940i	$0.457121\pi$
$98$	−2.00569	−0.202605
$99$	−1.12155	−0.112720
$100$	9.63871	0.963871
$101$	2.52439	0.251186	0.125593	−	0.992082i	$-0.459917\pi$
$101$	2.52439	0.251186	0.125593	+	0.992082i	$0.459917\pi$
$102$	−20.5432	−2.03408
$103$	−2.53847	−0.250123	−0.125061	−	0.992149i	$-0.539913\pi$
$103$	−2.53847	−0.250123	−0.125061	+	0.992149i	$0.539913\pi$
$104$	0.284236	0.0278716
$105$	−6.59542	−0.643647
$106$	−6.43322	−0.624850
$107$	−18.9068	−1.82779	−0.913893	−	0.405954i	$-0.866939\pi$
$107$	−18.9068	−1.82779	−0.913893	+	0.405954i	$0.866939\pi$
$108$	−6.59772	−0.634866
$109$	−2.79582	−0.267791	−0.133896	−	0.990995i	$-0.542749\pi$
$109$	−2.79582	−0.267791	−0.133896	+	0.990995i	$0.542749\pi$
$110$	4.83255	0.460766
$111$	−10.6905	−1.01470
$112$	3.95393	0.373611
$113$	−15.5647	−1.46420	−0.732100	−	0.681197i	$-0.761460\pi$
$113$	−15.5647	−1.46420	−0.732100	+	0.681197i	$0.761460\pi$
$114$	−16.2002	−1.51729
$115$	−14.7951	−1.37965
$116$	−7.61234	−0.706788
$117$	−9.05014	−0.836686
$118$	−13.1114	−1.20700
$119$	−4.85290	−0.444865
$120$	−0.301307	−0.0275054
$121$	−10.4055	−0.945955
$122$	−11.8905	−1.07651
$123$	−25.1702	−2.26952
$124$	−2.44977	−0.219996
$125$	−0.734082	−0.0656583
$126$	2.91747	0.259909
$127$	11.8505	1.05157	0.525783	−	0.850619i	$-0.323772\pi$
$127$	11.8505	1.05157	0.525783	+	0.850619i	$0.323772\pi$
$128$	0.365450	0.0323016
$129$	−5.52812	−0.486724
$130$	38.9954	3.42013
$131$	8.13597	0.710843	0.355421	−	0.934706i	$-0.384337\pi$
$131$	8.13597	0.710843	0.355421	+	0.934706i	$0.384337\pi$
$132$	−3.29176	−0.286511
$133$	−3.82696	−0.331840
$134$	−25.1586	−2.17337
$135$	−10.1926	−0.877237
$136$	−0.221701	−0.0190107
$137$	5.55604	0.474684	0.237342	−	0.971426i	$-0.423724\pi$
$137$	5.55604	0.474684	0.237342	+	0.971426i	$0.423724\pi$
$138$	20.0423	1.70612
$139$	−15.3926	−1.30558	−0.652792	−	0.757538i	$-0.726402\pi$
$139$	−15.3926	−1.30558	−0.652792	+	0.757538i	$0.726402\pi$
$140$	−6.32101	−0.534222
$141$	−21.5276	−1.81295
$142$	7.95753	0.667781
$143$	4.79720	0.401162
$144$	−5.75137	−0.479281
$145$	−11.7600	−0.976617
$146$	18.8918	1.56350
$147$	2.11059	0.174079
$148$	−10.2457	−0.842191
$149$	4.01682	0.329071	0.164536	−	0.986371i	$-0.447387\pi$
$149$	4.01682	0.329071	0.164536	+	0.986371i	$0.447387\pi$
$150$	−20.1715	−1.64700
$151$	3.59819	0.292816	0.146408	−	0.989224i	$-0.453229\pi$
$151$	3.59819	0.292816	0.146408	+	0.989224i	$0.453229\pi$
$152$	−0.174832	−0.0141807
$153$	7.05902	0.570688
$154$	−1.54646	−0.124617
$155$	−3.78457	−0.303984
$156$	−26.5623	−2.12668
$157$	23.0912	1.84288	0.921441	−	0.388519i	$-0.127013\pi$
$157$	23.0912	1.84288	0.921441	+	0.388519i	$0.127013\pi$
$158$	−1.82821	−0.145444
$159$	6.76970	0.536872
$160$	25.0671	1.98173
$161$	4.73458	0.373137
$162$	22.5598	1.77247
$163$	−16.4927	−1.29181	−0.645905	−	0.763418i	$-0.723520\pi$
$163$	−16.4927	−1.29181	−0.645905	+	0.763418i	$0.723520\pi$
$164$	−24.1230	−1.88369
$165$	−5.08532	−0.395891
$166$	−31.6199	−2.45418
$167$	−4.89635	−0.378891	−0.189446	−	0.981891i	$-0.560669\pi$
$167$	−4.89635	−0.378891	−0.189446	+	0.981891i	$0.560669\pi$
$168$	0.0964208	0.00743903
$169$	25.7102	1.97771
$170$	−30.4160	−2.33280
$171$	5.56669	0.425696
$172$	−5.29812	−0.403978
$173$	−11.8069	−0.897665	−0.448833	−	0.893616i	$-0.648160\pi$
$173$	−11.8069	−0.897665	−0.448833	+	0.893616i	$0.648160\pi$
$174$	15.9308	1.20771
$175$	−4.76509	−0.360207
$176$	3.04863	0.229799
$177$	13.7972	1.03706
$178$	37.5041	2.81105
$179$	−2.86361	−0.214036	−0.107018	−	0.994257i	$-0.534130\pi$
$179$	−2.86361	−0.214036	−0.107018	+	0.994257i	$0.534130\pi$
$180$	9.19452	0.685319
$181$	4.48582	0.333428	0.166714	−	0.986005i	$-0.446684\pi$
$181$	4.48582	0.333428	0.166714	+	0.986005i	$0.446684\pi$
$182$	−12.4789	−0.924996
$183$	12.5124	0.924942
$184$	0.216296	0.0159455
$185$	−15.8282	−1.16371
$186$	5.12679	0.375914
$187$	−3.74177	−0.273625
$188$	−20.6319	−1.50473
$189$	3.26171	0.237255
$190$	−23.9859	−1.74012
$191$	19.4151	1.40483	0.702415	−	0.711768i	$-0.252105\pi$
$191$	19.4151	1.40483	0.702415	+	0.711768i	$0.252105\pi$
$192$	−17.2671	−1.24615
$193$	2.35746	0.169693	0.0848467	−	0.996394i	$-0.472960\pi$
$193$	2.35746	0.169693	0.0848467	+	0.996394i	$0.472960\pi$
$194$	−5.30595	−0.380945
$195$	−41.0350	−2.93858
$196$	2.02278	0.144484
$197$	−22.5535	−1.60687	−0.803436	−	0.595392i	$-0.796997\pi$
$197$	−22.5535	−1.60687	−0.803436	+	0.595392i	$0.796997\pi$
$198$	2.24948	0.159863
$199$	−24.9026	−1.76530	−0.882649	−	0.470033i	$-0.844242\pi$
$199$	−24.9026	−1.76530	−0.882649	+	0.470033i	$0.844242\pi$
$200$	−0.217690	−0.0153930
$201$	26.4745	1.86736
$202$	−5.06313	−0.356241
$203$	3.76331	0.264133
$204$	20.7183	1.45057
$205$	−37.2667	−2.60282
$206$	5.09137	0.354733
$207$	−6.88690	−0.478673
$208$	24.6003	1.70573
$209$	−2.95073	−0.204106
$210$	13.2283	0.912842
$211$	−20.7211	−1.42650	−0.713248	−	0.700912i	$-0.752777\pi$
$211$	−20.7211	−1.42650	−0.713248	+	0.700912i	$0.752777\pi$
$212$	6.48804	0.445600
$213$	−8.37374	−0.573760
$214$	37.9211	2.59223
$215$	−8.18487	−0.558203
$216$	0.149009	0.0101388
$217$	1.21109	0.0822144
$218$	5.60755	0.379791
$219$	−19.8800	−1.34336
$220$	−4.87373	−0.328587
$221$	−30.1936	−2.03104
$222$	21.4418	1.43908
$223$	−6.82709	−0.457175	−0.228588	−	0.973523i	$-0.573411\pi$
$223$	−6.82709	−0.457175	−0.228588	+	0.973523i	$0.573411\pi$
$224$	−8.02170	−0.535973
$225$	6.93128	0.462086
$226$	31.2178	2.07658
$227$	19.7353	1.30988	0.654939	−	0.755681i	$-0.272694\pi$
$227$	19.7353	1.30988	0.654939	+	0.755681i	$0.272694\pi$
$228$	16.3383	1.08203
$229$	−18.1789	−1.20130	−0.600649	−	0.799513i	$-0.705091\pi$
$229$	−18.1789	−1.20130	−0.600649	+	0.799513i	$0.705091\pi$
$230$	29.6744	1.95667
$231$	1.62735	0.107071
$232$	0.171924	0.0112874
$233$	24.5394	1.60763	0.803816	−	0.594878i	$-0.202800\pi$
$233$	24.5394	1.60763	0.803816	+	0.594878i	$0.202800\pi$
$234$	18.1517	1.18662
$235$	−31.8734	−2.07919
$236$	13.2231	0.860753
$237$	1.92383	0.124966
$238$	9.73340	0.630923
$239$	20.0021	1.29383	0.646915	−	0.762562i	$-0.276059\pi$
$239$	20.0021	1.29383	0.646915	+	0.762562i	$0.276059\pi$
$240$	−26.0778	−1.68331
$241$	26.7659	1.72414	0.862071	−	0.506787i	$-0.169167\pi$
$241$	26.7659	1.72414	0.862071	+	0.506787i	$0.169167\pi$
$242$	20.8702	1.34159
$243$	−13.9547	−0.895192
$244$	11.9918	0.767695
$245$	3.12491	0.199643
$246$	50.4836	3.21872
$247$	−23.8104	−1.51502
$248$	0.0553280	0.00351333
$249$	33.2738	2.10864
$250$	1.47234	0.0931189
$251$	1.78833	0.112878	0.0564391	−	0.998406i	$-0.482025\pi$
$251$	1.78833	0.112878	0.0564391	+	0.998406i	$0.482025\pi$
$252$	−2.94233	−0.185349
$253$	3.65054	0.229507
$254$	−23.7685	−1.49137
$255$	32.0069	2.00435
$256$	15.6294	0.976835
$257$	6.50145	0.405549	0.202775	−	0.979225i	$-0.435004\pi$
$257$	6.50145	0.405549	0.202775	+	0.979225i	$0.435004\pi$
$258$	11.0877	0.690289
$259$	5.06516	0.314734
$260$	−39.3277	−2.43900
$261$	−5.47410	−0.338838
$262$	−16.3182	−1.00814
$263$	−10.4149	−0.642208	−0.321104	−	0.947044i	$-0.604054\pi$
$263$	−10.4149	−0.642208	−0.321104	+	0.947044i	$0.604054\pi$
$264$	0.0743441	0.00457556
$265$	10.0231	0.615716
$266$	7.67569	0.470627
$267$	−39.4658	−2.41526
$268$	25.3729	1.54990
$269$	−12.7238	−0.775786	−0.387893	−	0.921704i	$-0.626797\pi$
$269$	−12.7238	−0.775786	−0.387893	+	0.921704i	$0.626797\pi$
$270$	20.4431	1.24413
$271$	−23.5750	−1.43208	−0.716041	−	0.698058i	$-0.754048\pi$
$271$	−23.5750	−1.43208	−0.716041	+	0.698058i	$0.754048\pi$
$272$	−19.1880	−1.16344
$273$	13.1316	0.794759
$274$	−11.1437	−0.673213
$275$	−3.67406	−0.221554
$276$	−20.2131	−1.21669
$277$	14.7630	0.887025	0.443512	−	0.896268i	$-0.353732\pi$
$277$	14.7630	0.887025	0.443512	+	0.896268i	$0.353732\pi$
$278$	30.8727	1.85162
$279$	−1.76165	−0.105468
$280$	0.142759	0.00853151
$281$	−12.9458	−0.772284	−0.386142	−	0.922439i	$-0.626193\pi$
$281$	−12.9458	−0.772284	−0.386142	+	0.922439i	$0.626193\pi$
$282$	43.1775	2.57118
$283$	−12.8173	−0.761911	−0.380956	−	0.924593i	$-0.624405\pi$
$283$	−12.8173	−0.761911	−0.380956	+	0.924593i	$0.624405\pi$
$284$	−8.02534	−0.476216
$285$	25.2404	1.49511
$286$	−9.62169	−0.568942
$287$	11.9257	0.703951
$288$	11.6684	0.687564
$289$	6.55067	0.385334
$290$	23.5869	1.38507
$291$	5.58348	0.327309
$292$	−19.0528	−1.11498
$293$	−1.72629	−0.100851	−0.0504255	−	0.998728i	$-0.516058\pi$
$293$	−1.72629	−0.100851	−0.0504255	+	0.998728i	$0.516058\pi$
$294$	−4.23318	−0.246884
$295$	20.4279	1.18936
$296$	0.231398	0.0134497
$297$	2.51490	0.145930
$298$	−8.05649	−0.466700
$299$	29.4573	1.70356
$300$	20.3434	1.17453
$301$	2.61923	0.150970
$302$	−7.21683	−0.415282
$303$	5.32795	0.306083
$304$	−15.1315	−0.867853
$305$	18.5257	1.06078
$306$	−14.1582	−0.809369
$307$	26.3131	1.50177	0.750883	−	0.660435i	$-0.229628\pi$
$307$	26.3131	1.50177	0.750883	+	0.660435i	$0.229628\pi$
$308$	1.55964	0.0888686
$309$	−5.35767	−0.304787
$310$	7.59065	0.431120
$311$	−9.21831	−0.522723	−0.261361	−	0.965241i	$-0.584171\pi$
$311$	−9.21831	−0.522723	−0.261361	+	0.965241i	$0.584171\pi$
$312$	0.599906	0.0339630
$313$	3.12656	0.176723	0.0883617	−	0.996088i	$-0.471837\pi$
$313$	3.12656	0.176723	0.0883617	+	0.996088i	$0.471837\pi$
$314$	−46.3138	−2.61364
$315$	−4.54549	−0.256109
$316$	1.84379	0.103721
$317$	16.1712	0.908266	0.454133	−	0.890934i	$-0.349949\pi$
$317$	16.1712	0.908266	0.454133	+	0.890934i	$0.349949\pi$
$318$	−13.5779	−0.761411
$319$	2.90166	0.162462
$320$	−25.5655	−1.42915
$321$	−39.9045	−2.22725
$322$	−9.49607	−0.529195
$323$	18.5719	1.03337
$324$	−22.7521	−1.26400
$325$	−29.6472	−1.64453
$326$	33.0793	1.83209
$327$	−5.90084	−0.326317
$328$	0.544816	0.0300824
$329$	10.1998	0.562332
$330$	10.1995	0.561467
$331$	17.6124	0.968067	0.484033	−	0.875050i	$-0.339171\pi$
$331$	17.6124	0.968067	0.484033	+	0.875050i	$0.339171\pi$
$332$	31.8894	1.75016
$333$	−7.36777	−0.403751
$334$	9.82055	0.537357
$335$	39.1977	2.14160
$336$	8.34512	0.455264
$337$	35.6942	1.94439	0.972193	−	0.234182i	$-0.0752411\pi$
$337$	35.6942	1.94439	0.972193	+	0.234182i	$0.0752411\pi$
$338$	−51.5666	−2.80485
$339$	−32.8507	−1.78420
$340$	30.6752	1.66360
$341$	0.933800	0.0505681
$342$	−11.1650	−0.603736
$343$	−1.00000	−0.0539949
$344$	0.119658	0.00645150
$345$	−31.2265	−1.68118
$346$	23.6810	1.27310
$347$	−27.4590	−1.47408	−0.737038	−	0.675851i	$-0.763776\pi$
$347$	−27.4590	−1.47408	−0.737038	+	0.675851i	$0.763776\pi$
$348$	−16.0665	−0.861257
$349$	−30.2502	−1.61926	−0.809628	−	0.586944i	$-0.800331\pi$
$349$	−30.2502	−1.61926	−0.809628	+	0.586944i	$0.800331\pi$
$350$	9.55727	0.510858
$351$	20.2936	1.08319
$352$	−6.18504	−0.329664
$353$	15.3659	0.817847	0.408923	−	0.912569i	$-0.365904\pi$
$353$	15.3659	0.817847	0.408923	+	0.912569i	$0.365904\pi$
$354$	−27.6728	−1.47079
$355$	−12.3981	−0.658020
$356$	−37.8237	−2.00465
$357$	−10.2425	−0.542091
$358$	5.74350	0.303553
$359$	4.42568	0.233578	0.116789	−	0.993157i	$-0.462740\pi$
$359$	4.42568	0.233578	0.116789	+	0.993157i	$0.462740\pi$
$360$	−0.207657	−0.0109445
$361$	−4.35435	−0.229176
$362$	−8.99714	−0.472879
$363$	−21.9618	−1.15269
$364$	12.5852	0.659645
$365$	−29.4340	−1.54065
$366$	−25.0959	−1.31178
$367$	−27.9945	−1.46130	−0.730649	−	0.682753i	$-0.760783\pi$
$367$	−27.9945	−1.46130	−0.730649	+	0.682753i	$0.760783\pi$
$368$	18.7202	0.975856
$369$	−17.3471	−0.903052
$370$	31.7464	1.65042
$371$	−3.20749	−0.166525
$372$	−5.17047	−0.268077
$373$	27.9679	1.44812	0.724061	−	0.689736i	$-0.242273\pi$
$373$	27.9679	1.44812	0.724061	+	0.689736i	$0.242273\pi$
$374$	7.50482	0.388065
$375$	−1.54935	−0.0800080
$376$	0.465969	0.0240305
$377$	23.4144	1.20590
$378$	−6.54197	−0.336483
$379$	19.6439	1.00904	0.504519	−	0.863401i	$-0.331670\pi$
$379$	19.6439	1.00904	0.504519	+	0.863401i	$0.331670\pi$
$380$	24.1903	1.24093
$381$	25.0117	1.28139
$382$	−38.9407	−1.99238
$383$	5.67950	0.290209	0.145104	−	0.989416i	$-0.453648\pi$
$383$	5.67950	0.290209	0.145104	+	0.989416i	$0.453648\pi$
$384$	0.771317	0.0393611
$385$	2.40943	0.122796
$386$	−4.72832	−0.240665
$387$	−3.80992	−0.193669
$388$	5.35117	0.271664
$389$	22.0772	1.11936	0.559679	−	0.828709i	$-0.310924\pi$
$389$	22.0772	1.11936	0.559679	+	0.828709i	$0.310924\pi$
$390$	82.3034	4.16760
$391$	−22.9764	−1.16197
$392$	−0.0456843	−0.00230740
$393$	17.1717	0.866198
$394$	45.2353	2.27892
$395$	2.84840	0.143318
$396$	−2.26864	−0.114004
$397$	−22.6632	−1.13743	−0.568716	−	0.822534i	$-0.692560\pi$
$397$	−22.6632	−1.13743	−0.568716	+	0.822534i	$0.692560\pi$
$398$	49.9468	2.50361
$399$	−8.07716	−0.404364
$400$	−18.8408	−0.942040
$401$	30.6099	1.52859	0.764294	−	0.644868i	$-0.223088\pi$
$401$	30.6099	1.52859	0.764294	+	0.644868i	$0.223088\pi$
$402$	−53.0995	−2.64836
$403$	7.53513	0.375351
$404$	5.10627	0.254047
$405$	−35.1488	−1.74656
$406$	−7.54802	−0.374602
$407$	3.90543	0.193585
$408$	−0.467921	−0.0231655
$409$	17.1361	0.847324	0.423662	−	0.905820i	$-0.360744\pi$
$409$	17.1361	0.847324	0.423662	+	0.905820i	$0.360744\pi$
$410$	74.7454	3.69141
$411$	11.7265	0.578427
$412$	−5.13476	−0.252971
$413$	−6.53712	−0.321671
$414$	13.8130	0.678870
$415$	49.2647	2.41831
$416$	−49.9090	−2.44699
$417$	−32.4875	−1.59092
$418$	5.91825	0.289471
$419$	17.2356	0.842014	0.421007	−	0.907057i	$-0.361677\pi$
$419$	17.2356	0.842014	0.421007	+	0.907057i	$0.361677\pi$
$420$	−13.3411	−0.650977
$421$	−19.0845	−0.930121	−0.465061	−	0.885279i	$-0.653967\pi$
$421$	−19.0845	−0.930121	−0.465061	+	0.885279i	$0.653967\pi$
$422$	41.5599	2.02311
$423$	−14.8366	−0.721378
$424$	−0.146532	−0.00711622
$425$	23.1245	1.12170
$426$	16.7951	0.813725
$427$	−5.92838	−0.286894
$428$	−38.2442	−1.84860
$429$	10.1249	0.488837
$430$	16.4163	0.791663
$431$	−13.1957	−0.635613	−0.317807	−	0.948156i	$-0.602946\pi$
$431$	−13.1957	−0.635613	−0.317807	+	0.948156i	$0.602946\pi$
$432$	12.8966	0.620487
$433$	−23.2472	−1.11719	−0.558595	−	0.829440i	$-0.688660\pi$
$433$	−23.2472	−1.11719	−0.558595	+	0.829440i	$0.688660\pi$
$434$	−2.42908	−0.116599
$435$	−24.8206	−1.19006
$436$	−5.65533	−0.270841
$437$	−18.1190	−0.866752
$438$	39.8730	1.90520
$439$	−15.1041	−0.720881	−0.360440	−	0.932782i	$-0.617374\pi$
$439$	−15.1041	−0.720881	−0.360440	+	0.932782i	$0.617374\pi$
$440$	0.110073	0.00524752
$441$	1.45460	0.0692665
$442$	60.5588	2.88049
$443$	7.89103	0.374914	0.187457	−	0.982273i	$-0.439975\pi$
$443$	7.89103	0.374914	0.187457	+	0.982273i	$0.439975\pi$
$444$	−21.6245	−1.02625
$445$	−58.4325	−2.76996
$446$	13.6930	0.648382
$447$	8.47787	0.400990
$448$	8.18117	0.386524
$449$	−37.4671	−1.76818	−0.884090	−	0.467316i	$-0.845221\pi$
$449$	−37.4671	−1.76818	−0.884090	+	0.467316i	$0.845221\pi$
$450$	−13.9020	−0.655346
$451$	9.19515	0.432983
$452$	−31.4839	−1.48088
$453$	7.59430	0.356811
$454$	−39.5829	−1.85772
$455$	19.4424	0.911475
$456$	−0.368999	−0.0172800
$457$	21.6017	1.01048	0.505241	−	0.862978i	$-0.331403\pi$
$457$	21.6017	1.01048	0.505241	+	0.862978i	$0.331403\pi$
$458$	36.4613	1.70372
$459$	−15.8288	−0.738824
$460$	−29.9273	−1.39537
$461$	−7.70410	−0.358816	−0.179408	−	0.983775i	$-0.557418\pi$
$461$	−7.70410	−0.358816	−0.179408	+	0.983775i	$0.557418\pi$
$462$	−3.26395	−0.151852
$463$	16.7646	0.779118	0.389559	−	0.921002i	$-0.372627\pi$
$463$	16.7646	0.779118	0.389559	+	0.921002i	$0.372627\pi$
$464$	14.8799	0.690780
$465$	−7.98767	−0.370419
$466$	−49.2184	−2.28000
$467$	−29.3351	−1.35747	−0.678733	−	0.734386i	$-0.737470\pi$
$467$	−29.3351	−1.35747	−0.678733	+	0.734386i	$0.737470\pi$
$468$	−18.3064	−0.846215
$469$	−12.5436	−0.579210
$470$	63.9281	2.94878
$471$	48.7362	2.24564
$472$	−0.298643	−0.0137462
$473$	2.01953	0.0928579
$474$	−3.85860	−0.177231
$475$	18.2358	0.836717
$476$	−9.81634	−0.449931
$477$	4.66561	0.213624
$478$	−40.1180	−1.83495
$479$	22.2183	1.01518	0.507589	−	0.861599i	$-0.330537\pi$
$479$	22.2183	1.01518	0.507589	+	0.861599i	$0.330537\pi$
$480$	52.9065	2.41484
$481$	31.5142	1.43692
$482$	−53.6840	−2.44524
$483$	9.99276	0.454686
$484$	−21.0480	−0.956728
$485$	8.26682	0.375377
$486$	27.9887	1.26959
$487$	−33.5502	−1.52030	−0.760151	−	0.649746i	$-0.774875\pi$
$487$	−33.5502	−1.52030	−0.760151	+	0.649746i	$0.774875\pi$
$488$	−0.270833	−0.0122601
$489$	−34.8094	−1.57414
$490$	−6.26760	−0.283141
$491$	−37.3624	−1.68614	−0.843071	−	0.537802i	$-0.819255\pi$
$491$	−37.3624	−1.68614	−0.843071	+	0.537802i	$0.819255\pi$
$492$	−50.9138	−2.29537
$493$	−18.2630	−0.822524
$494$	47.7562	2.14865
$495$	−3.50475	−0.157527
$496$	4.78858	0.215014
$497$	3.96749	0.177966
$498$	−66.7368	−2.99055
$499$	−31.5294	−1.41145	−0.705726	−	0.708485i	$-0.749379\pi$
$499$	−31.5294	−1.41145	−0.705726	+	0.708485i	$0.749379\pi$
$500$	−1.48489	−0.0664061
$501$	−10.3342	−0.461698
$502$	−3.58682	−0.160088
$503$	33.2354	1.48189	0.740947	−	0.671564i	$-0.234377\pi$
$503$	33.2354	1.48189	0.740947	+	0.671564i	$0.234377\pi$
$504$	0.0664522	0.00296002
$505$	7.88849	0.351033
$506$	−7.32183	−0.325495
$507$	54.2637	2.40994
$508$	23.9710	1.06354
$509$	28.7793	1.27562	0.637810	−	0.770194i	$-0.279841\pi$
$509$	28.7793	1.27562	0.637810	+	0.770194i	$0.279841\pi$
$510$	−64.1959	−2.84264
$511$	9.41914	0.416678
$512$	−32.0785	−1.41768
$513$	−12.4825	−0.551114
$514$	−13.0399	−0.575164
$515$	−7.93250	−0.349548
$516$	−11.1822	−0.492267
$517$	7.86441	0.345876
$518$	−10.1591	−0.446366
$519$	−24.9196	−1.09385
$520$	0.888213	0.0389507
$521$	10.3918	0.455273	0.227636	−	0.973746i	$-0.426900\pi$
$521$	10.3918	0.455273	0.227636	+	0.973746i	$0.426900\pi$
$522$	10.9793	0.480552
$523$	34.7629	1.52008	0.760038	−	0.649879i	$-0.225180\pi$
$523$	34.7629	1.52008	0.760038	+	0.649879i	$0.225180\pi$
$524$	16.4573	0.718938
$525$	−10.0572	−0.438930
$526$	20.8889	0.910801
$527$	−5.87732	−0.256020
$528$	6.43441	0.280022
$529$	−0.583798	−0.0253825
$530$	−20.1033	−0.873230
$531$	9.50887	0.412650
$532$	−7.74110	−0.335619
$533$	74.1986	3.21390
$534$	79.1559	3.42541
$535$	−59.0820	−2.55434
$536$	−0.573046	−0.0247518
$537$	−6.04391	−0.260814
$538$	25.5200	1.10025
$539$	−0.771038	−0.0332109
$540$	−20.6173	−0.887228
$541$	14.2876	0.614273	0.307136	−	0.951666i	$-0.400629\pi$
$541$	14.2876	0.614273	0.307136	+	0.951666i	$0.400629\pi$
$542$	47.2841	2.03103
$543$	9.46773	0.406299
$544$	38.9286	1.66905
$545$	−8.73671	−0.374240
$546$	−26.3378	−1.12715
$547$	−3.80023	−0.162486	−0.0812430	−	0.996694i	$-0.525889\pi$
$547$	−3.80023	−0.162486	−0.0812430	+	0.996694i	$0.525889\pi$
$548$	11.2386	0.480090
$549$	8.62340	0.368038
$550$	7.36902	0.314216
$551$	−14.4021	−0.613548
$552$	0.456512	0.0194304
$553$	−0.911513	−0.0387615
$554$	−29.6100	−1.25801
$555$	−33.4069	−1.41804
$556$	−31.1358	−1.32045
$557$	−30.8589	−1.30753	−0.653767	−	0.756696i	$-0.726812\pi$
$557$	−30.8589	−1.30753	−0.653767	+	0.756696i	$0.726812\pi$
$558$	3.53333	0.149578
$559$	16.2962	0.689256
$560$	12.3557	0.522123
$561$	−7.89735	−0.333427
$562$	25.9653	1.09528
$563$	20.5576	0.866400	0.433200	−	0.901298i	$-0.357384\pi$
$563$	20.5576	0.866400	0.433200	+	0.901298i	$0.357384\pi$
$564$	−43.5455	−1.83359
$565$	−48.6383	−2.04623
$566$	25.7075	1.08057
$567$	11.2479	0.472369
$568$	0.181252	0.00760515
$569$	37.6443	1.57813	0.789066	−	0.614308i	$-0.210565\pi$
$569$	37.6443	1.57813	0.789066	+	0.614308i	$0.210565\pi$
$570$	−50.6244	−2.12042
$571$	19.5213	0.816940	0.408470	−	0.912772i	$-0.366062\pi$
$571$	19.5213	0.816940	0.408470	+	0.912772i	$0.366062\pi$
$572$	9.70368	0.405731
$573$	40.9774	1.71186
$574$	−23.9192	−0.998367
$575$	−22.5607	−0.940845
$576$	−11.9003	−0.495846
$577$	−1.42268	−0.0592271	−0.0296136	−	0.999561i	$-0.509428\pi$
$577$	−1.42268	−0.0592271	−0.0296136	+	0.999561i	$0.509428\pi$
$578$	−13.1386	−0.546494
$579$	4.97563	0.206780
$580$	−23.7879	−0.987739
$581$	−15.7651	−0.654048
$582$	−11.1987	−0.464201
$583$	−2.47310	−0.102425
$584$	0.430307	0.0178062
$585$	−28.2809	−1.16927
$586$	3.46240	0.143030
$587$	−37.1012	−1.53133	−0.765665	−	0.643239i	$-0.777590\pi$
$587$	−37.1012	−1.53133	−0.765665	+	0.643239i	$0.777590\pi$
$588$	4.26926	0.176061
$589$	−4.63481	−0.190974
$590$	−40.9720	−1.68679
$591$	−47.6013	−1.95805
$592$	20.0273	0.823116
$593$	47.0251	1.93109	0.965545	−	0.260238i	$-0.0838010\pi$
$593$	47.0251	1.93109	0.965545	+	0.260238i	$0.0838010\pi$
$594$	−5.04411	−0.206962
$595$	−15.1649	−0.621701
$596$	8.12514	0.332819
$597$	−52.5592	−2.15111
$598$	−59.0822	−2.41605
$599$	32.2442	1.31746	0.658731	−	0.752379i	$-0.271094\pi$
$599$	32.2442	1.31746	0.658731	+	0.752379i	$0.271094\pi$
$600$	−0.459454	−0.0187571
$601$	10.9228	0.445548	0.222774	−	0.974870i	$-0.428489\pi$
$601$	10.9228	0.445548	0.222774	+	0.974870i	$0.428489\pi$
$602$	−5.25335	−0.214111
$603$	18.2459	0.743031
$604$	7.27833	0.296151
$605$	−32.5163	−1.32198
$606$	−10.6862	−0.434097
$607$	32.6210	1.32404	0.662022	−	0.749484i	$-0.269699\pi$
$607$	32.6210	1.32404	0.662022	+	0.749484i	$0.269699\pi$
$608$	30.6988	1.24500
$609$	7.94281	0.321859
$610$	−37.1567	−1.50443
$611$	63.4604	2.56733
$612$	14.2788	0.577187
$613$	22.8135	0.921427	0.460713	−	0.887549i	$-0.347594\pi$
$613$	22.8135	0.921427	0.460713	+	0.887549i	$0.347594\pi$
$614$	−52.7758	−2.12986
$615$	−78.6549	−3.17167
$616$	−0.0352243	−0.00141923
$617$	−20.2908	−0.816876	−0.408438	−	0.912786i	$-0.633926\pi$
$617$	−20.2908	−0.816876	−0.408438	+	0.912786i	$0.633926\pi$
$618$	10.7458	0.432260
$619$	−1.58983	−0.0639007	−0.0319504	−	0.999489i	$-0.510172\pi$
$619$	−1.58983	−0.0639007	−0.0319504	+	0.999489i	$0.510172\pi$
$620$	−7.65533	−0.307446
$621$	15.4428	0.619699
$622$	18.4890	0.741343
$623$	18.6989	0.749156
$624$	51.9213	2.07851
$625$	−26.1194	−1.04478
$626$	−6.27089	−0.250635
$627$	−6.22779	−0.248714
$628$	46.7084	1.86387
$629$	−24.5807	−0.980098
$630$	9.11683	0.363223
$631$	−9.73763	−0.387649	−0.193824	−	0.981036i	$-0.562089\pi$
$631$	−9.73763	−0.387649	−0.193824	+	0.981036i	$0.562089\pi$
$632$	−0.0416418	−0.00165642
$633$	−43.7337	−1.73826
$634$	−32.4344	−1.28813
$635$	37.0319	1.46957
$636$	13.6936	0.542987
$637$	−6.22175	−0.246515
$638$	−5.81981	−0.230408
$639$	−5.77110	−0.228301
$640$	1.14200	0.0451416
$641$	22.9252	0.905491	0.452746	−	0.891640i	$-0.350445\pi$
$641$	22.9252	0.905491	0.452746	+	0.891640i	$0.350445\pi$
$642$	80.0359	3.15876
$643$	−6.54388	−0.258066	−0.129033	−	0.991640i	$-0.541187\pi$
$643$	−6.54388	−0.258066	−0.129033	+	0.991640i	$0.541187\pi$
$644$	9.57699	0.377386
$645$	−17.2749	−0.680199
$646$	−37.2494	−1.46556
$647$	−31.3315	−1.23177	−0.615883	−	0.787837i	$-0.711201\pi$
$647$	−31.3315	−1.23177	−0.615883	+	0.787837i	$0.711201\pi$
$648$	0.513854	0.0201861
$649$	−5.04036	−0.197852
$650$	59.4630	2.33233
$651$	2.55613	0.100182
$652$	−33.3611	−1.30652
$653$	−33.3938	−1.30680	−0.653399	−	0.757013i	$-0.726658\pi$
$653$	−33.3938	−1.30680	−0.653399	+	0.757013i	$0.726658\pi$
$654$	11.8352	0.462795
$655$	25.4242	0.993406
$656$	47.1533	1.84103
$657$	−13.7011	−0.534529
$658$	−20.4575	−0.797518
$659$	10.9148	0.425180	0.212590	−	0.977141i	$-0.431810\pi$
$659$	10.9148	0.425180	0.212590	+	0.977141i	$0.431810\pi$
$660$	−10.2865	−0.400400
$661$	−29.0490	−1.12988	−0.564939	−	0.825133i	$-0.691100\pi$
$661$	−29.0490	−1.12988	−0.564939	+	0.825133i	$0.691100\pi$
$662$	−35.3250	−1.37295
$663$	−63.7263	−2.47492
$664$	−0.720219	−0.0279499
$665$	−11.9589	−0.463747
$666$	14.7774	0.572614
$667$	17.8177	0.689903
$668$	−9.90424	−0.383206
$669$	−14.4092	−0.557092
$670$	−78.6183	−3.03729
$671$	−4.57100	−0.176462
$672$	−16.9305	−0.653110
$673$	−7.82489	−0.301627	−0.150814	−	0.988562i	$-0.548189\pi$
$673$	−7.82489	−0.301627	−0.150814	+	0.988562i	$0.548189\pi$
$674$	−71.5913	−2.75759
$675$	−15.5424	−0.598225
$676$	52.0060	2.00023
$677$	−0.818047	−0.0314401	−0.0157201	−	0.999876i	$-0.505004\pi$
$677$	−0.818047	−0.0314401	−0.0157201	+	0.999876i	$0.505004\pi$
$678$	65.8881	2.53042
$679$	−2.64546	−0.101523
$680$	−0.692798	−0.0265676
$681$	41.6532	1.59615
$682$	−1.87291	−0.0717174
$683$	−48.9035	−1.87124	−0.935620	−	0.353008i	$-0.885159\pi$
$683$	−48.9035	−1.87124	−0.935620	+	0.353008i	$0.885159\pi$
$684$	11.2602	0.430544
$685$	17.3621	0.663373
$686$	2.00569	0.0765775
$687$	−38.3683	−1.46384
$688$	10.3562	0.394828
$689$	−19.9562	−0.760271
$690$	62.6306	2.38430
$691$	25.7238	0.978581	0.489290	−	0.872121i	$-0.337256\pi$
$691$	25.7238	0.978581	0.489290	+	0.872121i	$0.337256\pi$
$692$	−23.8828	−0.907889
$693$	1.12155	0.0426041
$694$	55.0741	2.09059
$695$	−48.1005	−1.82456
$696$	0.362862	0.0137542
$697$	−57.8742	−2.19214
$698$	60.6724	2.29648
$699$	51.7927	1.95898
$700$	−9.63871	−0.364309
$701$	−20.6324	−0.779276	−0.389638	−	0.920968i	$-0.627400\pi$
$701$	−20.6324	−0.779276	−0.389638	+	0.920968i	$0.627400\pi$
$702$	−40.7025	−1.53622
$703$	−19.3842	−0.731088
$704$	6.30799	0.237741
$705$	−67.2718	−2.53360
$706$	−30.8193	−1.15990
$707$	−2.52439	−0.0949394
$708$	27.9086	1.04887
$709$	−30.3997	−1.14169	−0.570843	−	0.821059i	$-0.693384\pi$
$709$	−30.3997	−1.14169	−0.570843	+	0.821059i	$0.693384\pi$
$710$	24.8666	0.933227
$711$	1.32588	0.0497245
$712$	0.854246	0.0320142
$713$	5.73402	0.214741
$714$	20.5432	0.768811
$715$	14.9909	0.560626
$716$	−5.79244	−0.216474
$717$	42.2163	1.57660
$718$	−8.87652	−0.331269
$719$	−9.55706	−0.356418	−0.178209	−	0.983993i	$-0.557030\pi$
$719$	−9.55706	−0.356418	−0.178209	+	0.983993i	$0.557030\pi$
$720$	−17.9725	−0.669797
$721$	2.53847	0.0945375
$722$	8.73346	0.325026
$723$	56.4919	2.10095
$724$	9.07381	0.337226
$725$	−17.9325	−0.665997
$726$	44.0484	1.63479
$727$	−34.8975	−1.29428	−0.647139	−	0.762372i	$-0.724035\pi$
$727$	−34.8975	−1.29428	−0.647139	+	0.762372i	$0.724035\pi$
$728$	−0.284236	−0.0105345
$729$	4.29122	0.158934
$730$	59.0354	2.18500
$731$	−12.7109	−0.470129
$732$	25.3098	0.935476
$733$	−51.5991	−1.90586	−0.952928	−	0.303195i	$-0.901946\pi$
$733$	−51.5991	−1.90586	−0.952928	+	0.303195i	$0.901946\pi$
$734$	56.1481	2.07246
$735$	6.59542	0.243276
$736$	−37.9794	−1.39994
$737$	−9.67160	−0.356258
$738$	34.7928	1.28074
$739$	−14.0327	−0.516200	−0.258100	−	0.966118i	$-0.583096\pi$
$739$	−14.0327	−0.516200	−0.258100	+	0.966118i	$0.583096\pi$
$740$	−32.0169	−1.17697
$741$	−50.2541	−1.84613
$742$	6.43322	0.236171
$743$	25.0857	0.920304	0.460152	−	0.887840i	$-0.347795\pi$
$743$	25.0857	0.920304	0.460152	+	0.887840i	$0.347795\pi$
$744$	0.116775	0.00428117
$745$	12.5522	0.459878
$746$	−56.0948	−2.05378
$747$	22.9319	0.839036
$748$	−7.56877	−0.276742
$749$	18.9068	0.690838
$750$	3.10751	0.113470
$751$	−26.2269	−0.957032	−0.478516	−	0.878079i	$-0.658825\pi$
$751$	−26.2269	−0.957032	−0.478516	+	0.878079i	$0.658825\pi$
$752$	40.3291	1.47065
$753$	3.77443	0.137548
$754$	−46.9619	−1.71025
$755$	11.2440	0.409212
$756$	6.59772	0.239957
$757$	36.5058	1.32682	0.663412	−	0.748254i	$-0.269108\pi$
$757$	36.5058	1.32682	0.663412	+	0.748254i	$0.269108\pi$
$758$	−39.3994	−1.43105
$759$	7.70479	0.279666
$760$	−0.546335	−0.0198177
$761$	−17.6604	−0.640189	−0.320094	−	0.947386i	$-0.603715\pi$
$761$	−17.6604	−0.640189	−0.320094	+	0.947386i	$0.603715\pi$
$762$	−50.1656	−1.81731
$763$	2.79582	0.101216
$764$	39.2725	1.42083
$765$	22.0588	0.797539
$766$	−11.3913	−0.411584
$767$	−40.6723	−1.46859
$768$	32.9872	1.19032
$769$	25.9721	0.936579	0.468289	−	0.883575i	$-0.344870\pi$
$769$	25.9721	0.936579	0.468289	+	0.883575i	$0.344870\pi$
$770$	−4.83255	−0.174153
$771$	13.7219	0.494182
$772$	4.76861	0.171626
$773$	26.9368	0.968851	0.484425	−	0.874833i	$-0.339029\pi$
$773$	26.9368	0.968851	0.484425	+	0.874833i	$0.339029\pi$
$774$	7.64151	0.274669
$775$	−5.77097	−0.207299
$776$	−0.120856	−0.00433847
$777$	10.6905	0.383519
$778$	−44.2799	−1.58751
$779$	−45.6392	−1.63519
$780$	−83.0048	−2.97205
$781$	3.05908	0.109463
$782$	46.0835	1.64794
$783$	12.2748	0.438667
$784$	−3.95393	−0.141212
$785$	72.1581	2.57543
$786$	−34.4411	−1.22847
$787$	−49.4886	−1.76408	−0.882039	−	0.471177i	$-0.843829\pi$
$787$	−49.4886	−1.76408	−0.882039	+	0.471177i	$0.843829\pi$
$788$	−45.6207	−1.62517
$789$	−21.9815	−0.782563
$790$	−5.71299	−0.203259
$791$	15.5647	0.553416
$792$	0.0512372	0.00182063
$793$	−36.8849	−1.30982
$794$	45.4552	1.61315
$795$	21.1547	0.750281
$796$	−50.3724	−1.78540
$797$	3.52698	0.124932	0.0624661	−	0.998047i	$-0.480103\pi$
$797$	3.52698	0.124932	0.0624661	+	0.998047i	$0.480103\pi$
$798$	16.2002	0.573482
$799$	−49.4985	−1.75113
$800$	38.2241	1.35143
$801$	−27.1994	−0.961043
$802$	−61.3939	−2.16790
$803$	7.26251	0.256289
$804$	53.5519	1.88863
$805$	14.7951	0.521460
$806$	−15.1131	−0.532336
$807$	−26.8548	−0.945335
$808$	−0.115325	−0.00405711
$809$	−43.7581	−1.53845	−0.769227	−	0.638976i	$-0.779358\pi$
$809$	−43.7581	−1.53845	−0.769227	+	0.638976i	$0.779358\pi$
$810$	70.4975	2.47703
$811$	15.4346	0.541982	0.270991	−	0.962582i	$-0.412649\pi$
$811$	15.4346	0.541982	0.270991	+	0.962582i	$0.412649\pi$
$812$	7.61234	0.267141
$813$	−49.7573	−1.74506
$814$	−7.83307	−0.274549
$815$	−51.5384	−1.80531
$816$	−40.4981	−1.41772
$817$	−10.0237	−0.350685
$818$	−34.3696	−1.20170
$819$	9.05014	0.316238
$820$	−75.3823	−2.63246
$821$	−31.2879	−1.09195	−0.545977	−	0.837800i	$-0.683841\pi$
$821$	−31.2879	−1.09195	−0.545977	+	0.837800i	$0.683841\pi$
$822$	−23.5197	−0.820345
$823$	−5.90418	−0.205807	−0.102903	−	0.994691i	$-0.532813\pi$
$823$	−5.90418	−0.205807	−0.102903	+	0.994691i	$0.532813\pi$
$824$	0.115968	0.00403994
$825$	−7.75445	−0.269975
$826$	13.1114	0.456204
$827$	1.64856	0.0573262	0.0286631	−	0.999589i	$-0.490875\pi$
$827$	1.64856	0.0573262	0.0286631	+	0.999589i	$0.490875\pi$
$828$	−13.9307	−0.484124
$829$	31.5871	1.09707	0.548533	−	0.836129i	$-0.315187\pi$
$829$	31.5871	1.09707	0.548533	+	0.836129i	$0.315187\pi$
$830$	−98.8096	−3.42973
$831$	31.1587	1.08088
$832$	50.9012	1.76468
$833$	4.85290	0.168143
$834$	65.1597	2.25630
$835$	−15.3007	−0.529502
$836$	−5.96868	−0.206431
$837$	3.95024	0.136540
$838$	−34.5692	−1.19417
$839$	48.0463	1.65874	0.829370	−	0.558699i	$-0.188699\pi$
$839$	48.0463	1.65874	0.829370	+	0.558699i	$0.188699\pi$
$840$	0.301307	0.0103961
$841$	−14.8375	−0.511637
$842$	38.2775	1.31913
$843$	−27.3234	−0.941067
$844$	−41.9141	−1.44274
$845$	80.3421	2.76385
$846$	29.7575	1.02308
$847$	10.4055	0.357537
$848$	−12.6822	−0.435508
$849$	−27.0522	−0.928427
$850$	−46.3805	−1.59084
$851$	23.9814	0.822071
$852$	−16.9382	−0.580294
$853$	−0.685587	−0.0234740	−0.0117370	−	0.999931i	$-0.503736\pi$
$853$	−0.685587	−0.0234740	−0.0117370	+	0.999931i	$0.503736\pi$
$854$	11.8905	0.406883
$855$	17.3954	0.594911
$856$	0.863742	0.0295221
$857$	22.7996	0.778819	0.389410	−	0.921065i	$-0.372679\pi$
$857$	22.7996	0.778819	0.389410	+	0.921065i	$0.372679\pi$
$858$	−20.3075	−0.693285
$859$	49.4475	1.68713	0.843563	−	0.537031i	$-0.180454\pi$
$859$	49.4475	1.68713	0.843563	+	0.537031i	$0.180454\pi$
$860$	−16.5562	−0.564561
$861$	25.1702	0.857800
$862$	26.4664	0.901449
$863$	−1.00000	−0.0340404
$863$	−1.00000	−0.0340404
$864$	−26.1645	−0.890135
$865$	−36.8957	−1.25449
$866$	46.6267	1.58444
$867$	13.8258	0.469549
$868$	2.44977	0.0831508
$869$	−0.702811	−0.0238412
$870$	49.7824	1.68778
$871$	−78.0433	−2.64440
$872$	0.127725	0.00432532
$873$	3.84807	0.130238
$874$	36.3411	1.22926
$875$	0.734082	0.0248165
$876$	−40.2127	−1.35866
$877$	−23.9116	−0.807439	−0.403719	−	0.914883i	$-0.632283\pi$
$877$	−23.9116	−0.807439	−0.403719	+	0.914883i	$0.632283\pi$
$878$	30.2941	1.02238
$879$	−3.64349	−0.122892
$880$	9.52670	0.321145
$881$	1.56623	0.0527678	0.0263839	−	0.999652i	$-0.491601\pi$
$881$	1.56623	0.0527678	0.0263839	+	0.999652i	$0.491601\pi$
$882$	−2.91747	−0.0982362
$883$	9.54769	0.321306	0.160653	−	0.987011i	$-0.448640\pi$
$883$	9.54769	0.321306	0.160653	+	0.987011i	$0.448640\pi$
$884$	−61.0748	−2.05417
$885$	43.1150	1.44930
$886$	−15.8269	−0.531716
$887$	37.9066	1.27278	0.636389	−	0.771368i	$-0.280427\pi$
$887$	37.9066	1.27278	0.636389	+	0.771368i	$0.280427\pi$
$888$	0.488387	0.0163892
$889$	−11.8505	−0.397455
$890$	117.197	3.92846
$891$	8.67259	0.290543
$892$	−13.8097	−0.462382
$893$	−39.0342	−1.30623
$894$	−17.0040	−0.568697
$895$	−8.94853	−0.299116
$896$	−0.365450	−0.0122088
$897$	62.1724	2.07588
$898$	75.1472	2.50769
$899$	4.55773	0.152009
$900$	14.0204	0.467348
$901$	15.5656	0.518567
$902$	−18.4426	−0.614071
$903$	5.52812	0.183964
$904$	0.711061	0.0236495
$905$	14.0178	0.465967
$906$	−15.2318	−0.506042
$907$	11.6803	0.387839	0.193919	−	0.981017i	$-0.437880\pi$
$907$	11.6803	0.387839	0.193919	+	0.981017i	$0.437880\pi$
$908$	39.9202	1.32480
$909$	3.67197	0.121791
$910$	−38.9954	−1.29269
$911$	−49.9377	−1.65451	−0.827256	−	0.561826i	$-0.810099\pi$
$911$	−49.9377	−1.65451	−0.827256	+	0.561826i	$0.810099\pi$
$912$	−31.9365	−1.05752
$913$	−12.1555	−0.402289
$914$	−43.3262	−1.43310
$915$	39.1001	1.29261
$916$	−36.7720	−1.21498
$917$	−8.13597	−0.268673
$918$	31.7476	1.04783
$919$	−18.3232	−0.604428	−0.302214	−	0.953240i	$-0.597726\pi$
$919$	−18.3232	−0.604428	−0.302214	+	0.953240i	$0.597726\pi$
$920$	0.675905	0.0222839
$921$	55.5362	1.82998
$922$	15.4520	0.508885
$923$	24.6847	0.812507
$924$	3.29176	0.108291
$925$	−24.1359	−0.793585
$926$	−33.6246	−1.10497
$927$	−3.69245	−0.121276
$928$	−30.1882	−0.990975
$929$	31.8893	1.04625	0.523127	−	0.852255i	$-0.324766\pi$
$929$	31.8893	1.04625	0.523127	+	0.852255i	$0.324766\pi$
$930$	16.0208	0.525342
$931$	3.82696	0.125424
$932$	49.6378	1.62594
$933$	−19.4561	−0.636964
$934$	58.8369	1.92520
$935$	−11.6927	−0.382393
$936$	0.413449	0.0135140
$937$	−8.99858	−0.293971	−0.146985	−	0.989139i	$-0.546957\pi$
$937$	−8.99858	−0.293971	−0.146985	+	0.989139i	$0.546957\pi$
$938$	25.1586	0.821456
$939$	6.59888	0.215346
$940$	−64.4728	−2.10287
$941$	−22.5364	−0.734667	−0.367333	−	0.930089i	$-0.619729\pi$
$941$	−22.5364	−0.734667	−0.367333	+	0.930089i	$0.619729\pi$
$942$	−97.7495	−3.18485
$943$	56.4630	1.83869
$944$	−25.8473	−0.841257
$945$	10.1926	0.331565
$946$	−4.05053	−0.131694
$947$	−31.6262	−1.02771	−0.513856	−	0.857876i	$-0.671784\pi$
$947$	−31.6262	−1.02771	−0.513856	+	0.857876i	$0.671784\pi$
$948$	3.89148	0.126389
$949$	58.6036	1.90235
$950$	−36.5753	−1.18666
$951$	34.1308	1.10677
$952$	0.221701	0.00718538
$953$	47.4234	1.53620	0.768098	−	0.640333i	$-0.221204\pi$
$953$	47.4234	1.53620	0.768098	+	0.640333i	$0.221204\pi$
$954$	−9.35775	−0.302968
$955$	60.6706	1.96325
$956$	40.4598	1.30856
$957$	6.12421	0.197968
$958$	−44.5628	−1.43976
$959$	−5.55604	−0.179414
$960$	−53.9582	−1.74149
$961$	−29.5333	−0.952685
$962$	−63.2075	−2.03789
$963$	−27.5017	−0.886231
$964$	54.1414	1.74378
$965$	7.36685	0.237147
$966$	−20.0423	−0.644851
$967$	−19.0756	−0.613429	−0.306714	−	0.951802i	$-0.599230\pi$
$967$	−19.0756	−0.613429	−0.306714	+	0.951802i	$0.599230\pi$
$968$	0.475368	0.0152789
$969$	39.1977	1.25921
$970$	−16.5806	−0.532372
$971$	10.5446	0.338393	0.169197	−	0.985582i	$-0.445883\pi$
$971$	10.5446	0.338393	0.169197	+	0.985582i	$0.445883\pi$
$972$	−28.2272	−0.905387
$973$	15.3926	0.493464
$974$	67.2911	2.15615
$975$	−62.5731	−2.00394
$976$	−23.4404	−0.750308
$977$	26.1152	0.835500	0.417750	−	0.908562i	$-0.362819\pi$
$977$	26.1152	0.835500	0.417750	+	0.908562i	$0.362819\pi$
$978$	69.8168	2.23249
$979$	14.4176	0.460787
$980$	6.32101	0.201917
$981$	−4.06680	−0.129843
$982$	74.9373	2.39134
$983$	−21.4184	−0.683142	−0.341571	−	0.939856i	$-0.610959\pi$
$983$	−21.4184	−0.683142	−0.341571	+	0.939856i	$0.610959\pi$
$984$	1.14988	0.0366570
$985$	−70.4778	−2.24561
$986$	36.6298	1.16653
$987$	21.5276	0.685230
$988$	−48.1632	−1.53227
$989$	12.4009	0.394327
$990$	7.02942	0.223410
$991$	−58.4750	−1.85752	−0.928760	−	0.370683i	$-0.879124\pi$
$991$	−58.4750	−1.85752	−0.928760	+	0.370683i	$0.879124\pi$
$992$	−9.71504	−0.308453
$993$	37.1726	1.17964
$994$	−7.95753	−0.252398
$995$	−77.8185	−2.46701
$996$	67.3055	2.13266
$997$	1.58953	0.0503409	0.0251705	−	0.999683i	$-0.491987\pi$
$997$	1.58953	0.0503409	0.0251705	+	0.999683i	$0.491987\pi$
$998$	63.2382	2.00177
$999$	16.5211	0.522705

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6041.2.a.d.1.16	✓	101

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6041.2.a.d.1.16	✓	101	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:	\( N \)	\(=\)	\( 6041 = 7 \cdot 863 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6041.a (trivial)

\(f(q)\)	\(=\)	\(q-2.00569 q^{2} +2.11059 q^{3} +2.02278 q^{4} +3.12491 q^{5} -4.23318 q^{6} -1.00000 q^{7} -0.0456843 q^{8} +1.45460 q^{9} +O(q^{10})\)	\(q-2.00569 q^{2} +2.11059 q^{3} +2.02278 q^{4} +3.12491 q^{5} -4.23318 q^{6} -1.00000 q^{7} -0.0456843 q^{8} +1.45460 q^{9} -6.26760 q^{10} -0.771038 q^{11} +4.26926 q^{12} -6.22175 q^{13} +2.00569 q^{14} +6.59542 q^{15} -3.95393 q^{16} +4.85290 q^{17} -2.91747 q^{18} +3.82696 q^{19} +6.32101 q^{20} -2.11059 q^{21} +1.54646 q^{22} -4.73458 q^{23} -0.0964208 q^{24} +4.76509 q^{25} +12.4789 q^{26} -3.26171 q^{27} -2.02278 q^{28} -3.76331 q^{29} -13.2283 q^{30} -1.21109 q^{31} +8.02170 q^{32} -1.62735 q^{33} -9.73340 q^{34} -3.12491 q^{35} +2.94233 q^{36} -5.06516 q^{37} -7.67569 q^{38} -13.1316 q^{39} -0.142759 q^{40} -11.9257 q^{41} +4.23318 q^{42} -2.61923 q^{43} -1.55964 q^{44} +4.54549 q^{45} +9.49607 q^{46} -10.1998 q^{47} -8.34512 q^{48} +1.00000 q^{49} -9.55727 q^{50} +10.2425 q^{51} -12.5852 q^{52} +3.20749 q^{53} +6.54197 q^{54} -2.40943 q^{55} +0.0456843 q^{56} +8.07716 q^{57} +7.54802 q^{58} +6.53712 q^{59} +13.3411 q^{60} +5.92838 q^{61} +2.42908 q^{62} -1.45460 q^{63} -8.18117 q^{64} -19.4424 q^{65} +3.26395 q^{66} +12.5436 q^{67} +9.81634 q^{68} -9.99276 q^{69} +6.26760 q^{70} -3.96749 q^{71} -0.0664522 q^{72} -9.41914 q^{73} +10.1591 q^{74} +10.0572 q^{75} +7.74110 q^{76} +0.771038 q^{77} +26.3378 q^{78} +0.911513 q^{79} -12.3557 q^{80} -11.2479 q^{81} +23.9192 q^{82} +15.7651 q^{83} -4.26926 q^{84} +15.1649 q^{85} +5.25335 q^{86} -7.94281 q^{87} +0.0352243 q^{88} -18.6989 q^{89} -9.11683 q^{90} +6.22175 q^{91} -9.57699 q^{92} -2.55613 q^{93} +20.4575 q^{94} +11.9589 q^{95} +16.9305 q^{96} +2.64546 q^{97} -2.00569 q^{98} -1.12155 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 101 q + 3 q^{2} - 17 q^{3} + 85 q^{4} - 12 q^{5} - 17 q^{6} - 101 q^{7} - 3 q^{8} + 88 q^{9}+O(q^{10}) \) 101 * q + 3 * q^2 - 17 * q^3 + 85 * q^4 - 12 * q^5 - 17 * q^6 - 101 * q^7 - 3 * q^8 + 88 * q^9	\( 101 q + 3 q^{2} - 17 q^{3} + 85 q^{4} - 12 q^{5} - 17 q^{6} - 101 q^{7} - 3 q^{8} + 88 q^{9} - 23 q^{10} - 13 q^{11} - 31 q^{12} - 35 q^{13} - 3 q^{14} - 20 q^{15} + 45 q^{16} - 19 q^{17} + 3 q^{18} - 59 q^{19} - 31 q^{20} + 17 q^{21} - 13 q^{22} - 29 q^{23} - 59 q^{24} + 103 q^{25} - 18 q^{26} - 47 q^{27} - 85 q^{28} - 26 q^{29} - 8 q^{30} - 125 q^{31} + 12 q^{32} - 18 q^{33} - 66 q^{34} + 12 q^{35} + 40 q^{36} + 22 q^{37} - 31 q^{38} - 94 q^{39} - 79 q^{40} - 39 q^{41} + 17 q^{42} - 5 q^{43} - 53 q^{44} - 50 q^{45} - 37 q^{46} - 47 q^{47} - 81 q^{48} + 101 q^{49} + 2 q^{50} - 23 q^{51} - 56 q^{52} - 5 q^{53} - 77 q^{54} - 155 q^{55} + 3 q^{56} + 61 q^{57} - 31 q^{58} - 33 q^{59} - 48 q^{60} - 96 q^{61} - 38 q^{62} - 88 q^{63} - 33 q^{64} - 8 q^{65} - 91 q^{66} + 8 q^{67} - 41 q^{68} - 91 q^{69} + 23 q^{70} - 116 q^{71} - 5 q^{72} - 62 q^{73} - 23 q^{74} - 94 q^{75} - 112 q^{76} + 13 q^{77} + 17 q^{78} - 127 q^{79} - 87 q^{80} + 37 q^{81} - 118 q^{82} - 58 q^{83} + 31 q^{84} - 6 q^{85} - 26 q^{86} - 82 q^{87} - 40 q^{88} - 57 q^{89} - 123 q^{90} + 35 q^{91} - 28 q^{92} - 10 q^{93} - 107 q^{94} - 70 q^{95} - 76 q^{96} - 69 q^{97} + 3 q^{98} - 67 q^{99}+O(q^{100}) \) 101 * q + 3 * q^2 - 17 * q^3 + 85 * q^4 - 12 * q^5 - 17 * q^6 - 101 * q^7 - 3 * q^8 + 88 * q^9 - 23 * q^10 - 13 * q^11 - 31 * q^12 - 35 * q^13 - 3 * q^14 - 20 * q^15 + 45 * q^16 - 19 * q^17 + 3 * q^18 - 59 * q^19 - 31 * q^20 + 17 * q^21 - 13 * q^22 - 29 * q^23 - 59 * q^24 + 103 * q^25 - 18 * q^26 - 47 * q^27 - 85 * q^28 - 26 * q^29 - 8 * q^30 - 125 * q^31 + 12 * q^32 - 18 * q^33 - 66 * q^34 + 12 * q^35 + 40 * q^36 + 22 * q^37 - 31 * q^38 - 94 * q^39 - 79 * q^40 - 39 * q^41 + 17 * q^42 - 5 * q^43 - 53 * q^44 - 50 * q^45 - 37 * q^46 - 47 * q^47 - 81 * q^48 + 101 * q^49 + 2 * q^50 - 23 * q^51 - 56 * q^52 - 5 * q^53 - 77 * q^54 - 155 * q^55 + 3 * q^56 + 61 * q^57 - 31 * q^58 - 33 * q^59 - 48 * q^60 - 96 * q^61 - 38 * q^62 - 88 * q^63 - 33 * q^64 - 8 * q^65 - 91 * q^66 + 8 * q^67 - 41 * q^68 - 91 * q^69 + 23 * q^70 - 116 * q^71 - 5 * q^72 - 62 * q^73 - 23 * q^74 - 94 * q^75 - 112 * q^76 + 13 * q^77 + 17 * q^78 - 127 * q^79 - 87 * q^80 + 37 * q^81 - 118 * q^82 - 58 * q^83 + 31 * q^84 - 6 * q^85 - 26 * q^86 - 82 * q^87 - 40 * q^88 - 57 * q^89 - 123 * q^90 + 35 * q^91 - 28 * q^92 - 10 * q^93 - 107 * q^94 - 70 * q^95 - 76 * q^96 - 69 * q^97 + 3 * q^98 - 67 * q^99

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