LMFDB - Embedded newform 6031.2.a.c.1.5

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			1.5
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)

$f(q)$	$=$	$q-2.64482 q^{2} -1.59347 q^{3} +4.99505 q^{4} -2.42826 q^{5} +4.21443 q^{6} +4.09769 q^{7} -7.92136 q^{8} -0.460856 q^{9} +O(q^{10})$	\(q-2.64482 q^{2} -1.59347 q^{3} +4.99505 q^{4} -2.42826 q^{5} +4.21443 q^{6} +4.09769 q^{7} -7.92136 q^{8} -0.460856 q^{9} +6.42231 q^{10} -4.19783 q^{11} -7.95946 q^{12} +0.451356 q^{13} -10.8376 q^{14} +3.86936 q^{15} +10.9604 q^{16} -1.32793 q^{17} +1.21888 q^{18} -1.26340 q^{19} -12.1293 q^{20} -6.52954 q^{21} +11.1025 q^{22} -5.19021 q^{23} +12.6224 q^{24} +0.896456 q^{25} -1.19375 q^{26} +5.51477 q^{27} +20.4682 q^{28} +2.44271 q^{29} -10.2337 q^{30} +3.58766 q^{31} -13.1456 q^{32} +6.68912 q^{33} +3.51212 q^{34} -9.95026 q^{35} -2.30200 q^{36} -1.00000 q^{37} +3.34146 q^{38} -0.719221 q^{39} +19.2351 q^{40} +1.66171 q^{41} +17.2694 q^{42} +0.860978 q^{43} -20.9684 q^{44} +1.11908 q^{45} +13.7272 q^{46} -1.49633 q^{47} -17.4651 q^{48} +9.79103 q^{49} -2.37096 q^{50} +2.11601 q^{51} +2.25455 q^{52} +3.05894 q^{53} -14.5855 q^{54} +10.1934 q^{55} -32.4593 q^{56} +2.01319 q^{57} -6.46052 q^{58} +11.6539 q^{59} +19.3277 q^{60} +0.639544 q^{61} -9.48870 q^{62} -1.88844 q^{63} +12.8469 q^{64} -1.09601 q^{65} -17.6915 q^{66} -3.68363 q^{67} -6.63306 q^{68} +8.27045 q^{69} +26.3166 q^{70} -1.88435 q^{71} +3.65061 q^{72} +8.18194 q^{73} +2.64482 q^{74} -1.42848 q^{75} -6.31076 q^{76} -17.2014 q^{77} +1.90221 q^{78} -2.50563 q^{79} -26.6148 q^{80} -7.40504 q^{81} -4.39492 q^{82} +5.88336 q^{83} -32.6154 q^{84} +3.22455 q^{85} -2.27713 q^{86} -3.89238 q^{87} +33.2526 q^{88} -2.06005 q^{89} -2.95976 q^{90} +1.84951 q^{91} -25.9254 q^{92} -5.71682 q^{93} +3.95753 q^{94} +3.06787 q^{95} +20.9472 q^{96} -14.7769 q^{97} -25.8955 q^{98} +1.93460 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.64482	−1.87017	−0.935084	−	0.354427i	$-0.884676\pi$
$2$	−2.64482	−1.87017	−0.935084	+	0.354427i	$0.884676\pi$
$3$	−1.59347	−0.919990	−0.459995	−	0.887922i	$-0.652149\pi$
$3$	−1.59347	−0.919990	−0.459995	+	0.887922i	$0.652149\pi$
$4$	4.99505	2.49753
$5$	−2.42826	−1.08595	−0.542976	−	0.839748i	$-0.682703\pi$
$5$	−2.42826	−1.08595	−0.542976	+	0.839748i	$0.682703\pi$
$6$	4.21443	1.72054
$7$	4.09769	1.54878	0.774390	−	0.632709i	$-0.218057\pi$
$7$	4.09769	1.54878	0.774390	+	0.632709i	$0.218057\pi$
$8$	−7.92136	−2.80062
$9$	−0.460856	−0.153619
$10$	6.42231	2.03091
$11$	−4.19783	−1.26569	−0.632847	−	0.774277i	$-0.718114\pi$
$11$	−4.19783	−1.26569	−0.632847	+	0.774277i	$0.718114\pi$
$12$	−7.95946	−2.29770
$13$	0.451356	0.125184	0.0625918	−	0.998039i	$-0.480063\pi$
$13$	0.451356	0.125184	0.0625918	+	0.998039i	$0.480063\pi$
$14$	−10.8376	−2.89648
$15$	3.86936	0.999065
$16$	10.9604	2.74011
$17$	−1.32793	−0.322069	−0.161035	−	0.986949i	$-0.551483\pi$
$17$	−1.32793	−0.322069	−0.161035	+	0.986949i	$0.551483\pi$
$18$	1.21888	0.287293
$19$	−1.26340	−0.289844	−0.144922	−	0.989443i	$-0.546293\pi$
$19$	−1.26340	−0.289844	−0.144922	+	0.989443i	$0.546293\pi$
$20$	−12.1293	−2.71219
$21$	−6.52954	−1.42486
$22$	11.1025	2.36706
$23$	−5.19021	−1.08223	−0.541117	−	0.840947i	$-0.681998\pi$
$23$	−5.19021	−1.08223	−0.541117	+	0.840947i	$0.681998\pi$
$24$	12.6224	2.57655
$25$	0.896456	0.179291
$26$	−1.19375	−0.234114
$27$	5.51477	1.06132
$28$	20.4682	3.86812
$29$	2.44271	0.453600	0.226800	−	0.973941i	$-0.427174\pi$
$29$	2.44271	0.453600	0.226800	+	0.973941i	$0.427174\pi$
$30$	−10.2337	−1.86842
$31$	3.58766	0.644363	0.322181	−	0.946678i	$-0.395584\pi$
$31$	3.58766	0.644363	0.322181	+	0.946678i	$0.395584\pi$
$32$	−13.1456	−2.32384
$33$	6.68912	1.16443
$34$	3.51212	0.602324
$35$	−9.95026	−1.68190
$36$	−2.30200	−0.383667
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	3.34146	0.542057
$39$	−0.719221	−0.115168
$40$	19.2351	3.04134
$41$	1.66171	0.259516	0.129758	−	0.991546i	$-0.458580\pi$
$41$	1.66171	0.259516	0.129758	+	0.991546i	$0.458580\pi$
$42$	17.2694	2.66473
$43$	0.860978	0.131298	0.0656490	−	0.997843i	$-0.479088\pi$
$43$	0.860978	0.131298	0.0656490	+	0.997843i	$0.479088\pi$
$44$	−20.9684	−3.16111
$45$	1.11908	0.166823
$46$	13.7272	2.02396
$47$	−1.49633	−0.218263	−0.109131	−	0.994027i	$-0.534807\pi$
$47$	−1.49633	−0.218263	−0.109131	+	0.994027i	$0.534807\pi$
$48$	−17.4651	−2.52087
$49$	9.79103	1.39872
$50$	−2.37096	−0.335305
$51$	2.11601	0.296301
$52$	2.25455	0.312649
$53$	3.05894	0.420178	0.210089	−	0.977682i	$-0.432625\pi$
$53$	3.05894	0.420178	0.210089	+	0.977682i	$0.432625\pi$
$54$	−14.5855	−1.98484
$55$	10.1934	1.37448
$56$	−32.4593	−4.33755
$57$	2.01319	0.266654
$58$	−6.46052	−0.848308
$59$	11.6539	1.51721	0.758607	−	0.651548i	$-0.225880\pi$
$59$	11.6539	1.51721	0.758607	+	0.651548i	$0.225880\pi$
$60$	19.3277	2.49519
$61$	0.639544	0.0818852	0.0409426	−	0.999161i	$-0.486964\pi$
$61$	0.639544	0.0818852	0.0409426	+	0.999161i	$0.486964\pi$
$62$	−9.48870	−1.20507
$63$	−1.88844	−0.237922
$64$	12.8469	1.60586
$65$	−1.09601	−0.135943
$66$	−17.6915	−2.17767
$67$	−3.68363	−0.450028	−0.225014	−	0.974356i	$-0.572243\pi$
$67$	−3.68363	−0.450028	−0.225014	+	0.974356i	$0.572243\pi$
$68$	−6.63306	−0.804377
$69$	8.27045	0.995645
$70$	26.3166	3.14544
$71$	−1.88435	−0.223631	−0.111815	−	0.993729i	$-0.535667\pi$
$71$	−1.88435	−0.223631	−0.111815	+	0.993729i	$0.535667\pi$
$72$	3.65061	0.430228
$73$	8.18194	0.957623	0.478812	−	0.877918i	$-0.341068\pi$
$73$	8.18194	0.957623	0.478812	+	0.877918i	$0.341068\pi$
$74$	2.64482	0.307454
$75$	−1.42848	−0.164946
$76$	−6.31076	−0.723894
$77$	−17.2014	−1.96028
$78$	1.90221	0.215383
$79$	−2.50563	−0.281906	−0.140953	−	0.990016i	$-0.545017\pi$
$79$	−2.50563	−0.281906	−0.140953	+	0.990016i	$0.545017\pi$
$80$	−26.6148	−2.97563
$81$	−7.40504	−0.822783
$82$	−4.39492	−0.485338
$83$	5.88336	0.645783	0.322892	−	0.946436i	$-0.395345\pi$
$83$	5.88336	0.645783	0.322892	+	0.946436i	$0.395345\pi$
$84$	−32.6154	−3.55863
$85$	3.22455	0.349752
$86$	−2.27713	−0.245549
$87$	−3.89238	−0.417307
$88$	33.2526	3.54474
$89$	−2.06005	−0.218365	−0.109183	−	0.994022i	$-0.534823\pi$
$89$	−2.06005	−0.218365	−0.109183	+	0.994022i	$0.534823\pi$
$90$	−2.95976	−0.311986
$91$	1.84951	0.193882
$92$	−25.9254	−2.70291
$93$	−5.71682	−0.592807
$94$	3.95753	0.408188
$95$	3.06787	0.314757
$96$	20.9472	2.13791
$97$	−14.7769	−1.50037	−0.750186	−	0.661227i	$-0.770036\pi$
$97$	−14.7769	−1.50037	−0.750186	+	0.661227i	$0.770036\pi$
$98$	−25.8955	−2.61584
$99$	1.93460	0.194434
$100$	4.47785	0.447785
$101$	14.7750	1.47017	0.735084	−	0.677976i	$-0.237143\pi$
$101$	14.7750	1.47017	0.735084	+	0.677976i	$0.237143\pi$
$102$	−5.59645	−0.554132
$103$	−0.714811	−0.0704324	−0.0352162	−	0.999380i	$-0.511212\pi$
$103$	−0.714811	−0.0704324	−0.0352162	+	0.999380i	$0.511212\pi$
$104$	−3.57535	−0.350592
$105$	15.8554	1.54733
$106$	−8.09035	−0.785804
$107$	−0.0661049	−0.00639060	−0.00319530	−	0.999995i	$-0.501017\pi$
$107$	−0.0661049	−0.00639060	−0.00319530	+	0.999995i	$0.501017\pi$
$108$	27.5466	2.65067
$109$	−15.9303	−1.52584	−0.762922	−	0.646490i	$-0.776236\pi$
$109$	−15.9303	−1.52584	−0.762922	+	0.646490i	$0.776236\pi$
$110$	−26.9598	−2.57051
$111$	1.59347	0.151245
$112$	44.9125	4.24383
$113$	−12.4697	−1.17305	−0.586526	−	0.809930i	$-0.699505\pi$
$113$	−12.4697	−1.17305	−0.586526	+	0.809930i	$0.699505\pi$
$114$	−5.32452	−0.498687
$115$	12.6032	1.17525
$116$	12.2015	1.13288
$117$	−0.208010	−0.0192305
$118$	−30.8226	−2.83745
$119$	−5.44142	−0.498815
$120$	−30.6506	−2.79801
$121$	6.62182	0.601984
$122$	−1.69148	−0.153139
$123$	−2.64789	−0.238752
$124$	17.9205	1.60931
$125$	9.96448	0.891250
$126$	4.99459	0.444953
$127$	5.09300	0.451931	0.225965	−	0.974135i	$-0.427446\pi$
$127$	5.09300	0.451931	0.225965	+	0.974135i	$0.427446\pi$
$128$	−7.68642	−0.679390
$129$	−1.37194	−0.120793
$130$	2.89874	0.254237
$131$	6.98303	0.610110	0.305055	−	0.952335i	$-0.401325\pi$
$131$	6.98303	0.610110	0.305055	+	0.952335i	$0.401325\pi$
$132$	33.4125	2.90819
$133$	−5.17702	−0.448905
$134$	9.74254	0.841627
$135$	−13.3913	−1.15254
$136$	10.5190	0.901995
$137$	11.3192	0.967063	0.483532	−	0.875327i	$-0.339354\pi$
$137$	11.3192	0.967063	0.483532	+	0.875327i	$0.339354\pi$
$138$	−21.8738	−1.86202
$139$	−2.19054	−0.185799	−0.0928995	−	0.995675i	$-0.529614\pi$
$139$	−2.19054	−0.185799	−0.0928995	+	0.995675i	$0.529614\pi$
$140$	−49.7021	−4.20059
$141$	2.38436	0.200800
$142$	4.98375	0.418227
$143$	−1.89472	−0.158444
$144$	−5.05119	−0.420932
$145$	−5.93154	−0.492588
$146$	−21.6397	−1.79092
$147$	−15.6017	−1.28681
$148$	−4.99505	−0.410591
$149$	1.38823	0.113728	0.0568642	−	0.998382i	$-0.481890\pi$
$149$	1.38823	0.113728	0.0568642	+	0.998382i	$0.481890\pi$
$150$	3.77806	0.308477
$151$	−11.3126	−0.920608	−0.460304	−	0.887761i	$-0.652260\pi$
$151$	−11.3126	−0.920608	−0.460304	+	0.887761i	$0.652260\pi$
$152$	10.0079	0.811745
$153$	0.611983	0.0494759
$154$	45.4946	3.66606
$155$	−8.71178	−0.699747
$156$	−3.59255	−0.287634
$157$	9.28929	0.741366	0.370683	−	0.928759i	$-0.379124\pi$
$157$	9.28929	0.741366	0.370683	+	0.928759i	$0.379124\pi$
$158$	6.62694	0.527211
$159$	−4.87433	−0.386560
$160$	31.9210	2.52358
$161$	−21.2679	−1.67614
$162$	19.5850	1.53874
$163$	−1.00000	−0.0783260
$163$	−1.00000	−0.0783260
$164$	8.30034	0.648147
$165$	−16.2429	−1.26451
$166$	−15.5604	−1.20772
$167$	1.66275	0.128668	0.0643338	−	0.997928i	$-0.479508\pi$
$167$	1.66275	0.128668	0.0643338	+	0.997928i	$0.479508\pi$
$168$	51.7228	3.99050
$169$	−12.7963	−0.984329
$170$	−8.52835	−0.654094
$171$	0.582247	0.0445255
$172$	4.30063	0.327920
$173$	2.88456	0.219309	0.109655	−	0.993970i	$-0.465026\pi$
$173$	2.88456	0.219309	0.109655	+	0.993970i	$0.465026\pi$
$174$	10.2946	0.780435
$175$	3.67340	0.277683
$176$	−46.0101	−3.46814
$177$	−18.5702	−1.39582
$178$	5.44846	0.408380
$179$	−9.41387	−0.703626	−0.351813	−	0.936070i	$-0.614435\pi$
$179$	−9.41387	−0.703626	−0.351813	+	0.936070i	$0.614435\pi$
$180$	5.58986	0.416644
$181$	−0.622418	−0.0462640	−0.0231320	−	0.999732i	$-0.507364\pi$
$181$	−0.622418	−0.0462640	−0.0231320	+	0.999732i	$0.507364\pi$
$182$	−4.89162	−0.362591
$183$	−1.01909	−0.0753336
$184$	41.1136	3.03093
$185$	2.42826	0.178529
$186$	15.1199	1.10865
$187$	5.57441	0.407642
$188$	−7.47427	−0.545117
$189$	22.5978	1.64375
$190$	−8.11395	−0.588648
$191$	17.5599	1.27059	0.635296	−	0.772269i	$-0.280878\pi$
$191$	17.5599	1.27059	0.635296	+	0.772269i	$0.280878\pi$
$192$	−20.4711	−1.47738
$193$	1.04544	0.0752526	0.0376263	−	0.999292i	$-0.488020\pi$
$193$	1.04544	0.0752526	0.0376263	+	0.999292i	$0.488020\pi$
$194$	39.0823	2.80595
$195$	1.74646	0.125066
$196$	48.9067	3.49334
$197$	8.47990	0.604168	0.302084	−	0.953281i	$-0.402318\pi$
$197$	8.47990	0.604168	0.302084	+	0.953281i	$0.402318\pi$
$198$	−5.11666	−0.363625
$199$	7.21519	0.511472	0.255736	−	0.966747i	$-0.417682\pi$
$199$	7.21519	0.511472	0.255736	+	0.966747i	$0.417682\pi$
$200$	−7.10116	−0.502128
$201$	5.86976	0.414021
$202$	−39.0772	−2.74946
$203$	10.0095	0.702527
$204$	10.5696	0.740018
$205$	−4.03507	−0.281822
$206$	1.89054	0.131720
$207$	2.39194	0.166252
$208$	4.94706	0.343017
$209$	5.30355	0.366854
$210$	−41.9347	−2.89377
$211$	−12.2219	−0.841389	−0.420695	−	0.907202i	$-0.638214\pi$
$211$	−12.2219	−0.841389	−0.420695	+	0.907202i	$0.638214\pi$
$212$	15.2796	1.04941
$213$	3.00265	0.205738
$214$	0.174835	0.0119515
$215$	−2.09068	−0.142583
$216$	−43.6845	−2.97235
$217$	14.7011	0.997976
$218$	42.1327	2.85359
$219$	−13.0377	−0.881004
$220$	50.9168	3.43281
$221$	−0.599367	−0.0403178
$222$	−4.21443	−0.282854
$223$	16.2606	1.08889	0.544445	−	0.838796i	$-0.316740\pi$
$223$	16.2606	1.08889	0.544445	+	0.838796i	$0.316740\pi$
$224$	−53.8667	−3.59912
$225$	−0.413138	−0.0275425
$226$	32.9801	2.19380
$227$	19.1290	1.26964	0.634819	−	0.772661i	$-0.281075\pi$
$227$	19.1290	1.26964	0.634819	+	0.772661i	$0.281075\pi$
$228$	10.0560	0.665975
$229$	16.5468	1.09344	0.546721	−	0.837315i	$-0.315876\pi$
$229$	16.5468	1.09344	0.546721	+	0.837315i	$0.315876\pi$
$230$	−33.3331	−2.19792
$231$	27.4099	1.80344
$232$	−19.3496	−1.27036
$233$	23.2982	1.52632	0.763159	−	0.646211i	$-0.223647\pi$
$233$	23.2982	1.52632	0.763159	+	0.646211i	$0.223647\pi$
$234$	0.550148	0.0359643
$235$	3.63349	0.237023
$236$	58.2121	3.78928
$237$	3.99265	0.259351
$238$	14.3916	0.932867
$239$	−20.7401	−1.34156	−0.670782	−	0.741654i	$-0.734041\pi$
$239$	−20.7401	−1.34156	−0.670782	+	0.741654i	$0.734041\pi$
$240$	42.4099	2.73755
$241$	16.3316	1.05201	0.526004	−	0.850482i	$-0.323690\pi$
$241$	16.3316	1.05201	0.526004	+	0.850482i	$0.323690\pi$
$242$	−17.5135	−1.12581
$243$	−4.74460	−0.304366
$244$	3.19456	0.204511
$245$	−23.7752	−1.51894
$246$	7.00317	0.446506
$247$	−0.570243	−0.0362837
$248$	−28.4191	−1.80462
$249$	−9.37496	−0.594114
$250$	−26.3542	−1.66679
$251$	5.70778	0.360272	0.180136	−	0.983642i	$-0.442346\pi$
$251$	5.70778	0.360272	0.180136	+	0.983642i	$0.442346\pi$
$252$	−9.43288	−0.594215
$253$	21.7877	1.36978
$254$	−13.4700	−0.845186
$255$	−5.13822	−0.321768
$256$	−5.36464	−0.335290
$257$	−10.1664	−0.634164	−0.317082	−	0.948398i	$-0.602703\pi$
$257$	−10.1664	−0.634164	−0.317082	+	0.948398i	$0.602703\pi$
$258$	3.62854	0.225903
$259$	−4.09769	−0.254618
$260$	−5.47463	−0.339522
$261$	−1.12574	−0.0696815
$262$	−18.4688	−1.14101
$263$	−10.5706	−0.651812	−0.325906	−	0.945402i	$-0.605669\pi$
$263$	−10.5706	−0.651812	−0.325906	+	0.945402i	$0.605669\pi$
$264$	−52.9870	−3.26112
$265$	−7.42792	−0.456293
$266$	13.6923	0.839527
$267$	3.28263	0.200894
$268$	−18.3999	−1.12396
$269$	12.6905	0.773752	0.386876	−	0.922132i	$-0.373554\pi$
$269$	12.6905	0.773752	0.386876	+	0.922132i	$0.373554\pi$
$270$	35.4175	2.15544
$271$	−9.12691	−0.554420	−0.277210	−	0.960809i	$-0.589410\pi$
$271$	−9.12691	−0.554420	−0.277210	+	0.960809i	$0.589410\pi$
$272$	−14.5547	−0.882506
$273$	−2.94714	−0.178369
$274$	−29.9372	−1.80857
$275$	−3.76318	−0.226928
$276$	41.3113	2.48665
$277$	−0.574626	−0.0345259	−0.0172630	−	0.999851i	$-0.505495\pi$
$277$	−0.574626	−0.0345259	−0.0172630	+	0.999851i	$0.505495\pi$
$278$	5.79357	0.347475
$279$	−1.65339	−0.0989862
$280$	78.8196	4.71037
$281$	−23.9569	−1.42915	−0.714575	−	0.699559i	$-0.753380\pi$
$281$	−23.9569	−1.42915	−0.714575	+	0.699559i	$0.753380\pi$
$282$	−6.30620	−0.375529
$283$	2.94484	0.175052	0.0875262	−	0.996162i	$-0.472104\pi$
$283$	2.94484	0.175052	0.0875262	+	0.996162i	$0.472104\pi$
$284$	−9.41241	−0.558524
$285$	−4.88856	−0.289573
$286$	5.01118	0.296317
$287$	6.80917	0.401933
$288$	6.05825	0.356986
$289$	−15.2366	−0.896271
$290$	15.6878	0.921222
$291$	23.5466	1.38033
$292$	40.8692	2.39169
$293$	3.15296	0.184198	0.0920988	−	0.995750i	$-0.470642\pi$
$293$	3.15296	0.184198	0.0920988	+	0.995750i	$0.470642\pi$
$294$	41.2637	2.40654
$295$	−28.2988	−1.64762
$296$	7.92136	0.460420
$297$	−23.1501	−1.34330
$298$	−3.67162	−0.212691
$299$	−2.34263	−0.135478
$300$	−7.13531	−0.411957
$301$	3.52802	0.203352
$302$	29.9198	1.72169
$303$	−23.5435	−1.35254
$304$	−13.8474	−0.794205
$305$	−1.55298	−0.0889234
$306$	−1.61858	−0.0925282
$307$	7.44483	0.424899	0.212449	−	0.977172i	$-0.431856\pi$
$307$	7.44483	0.424899	0.212449	+	0.977172i	$0.431856\pi$
$308$	−85.9220	−4.89586
$309$	1.13903	0.0647971
$310$	23.0410	1.30864
$311$	6.41063	0.363514	0.181757	−	0.983344i	$-0.441822\pi$
$311$	6.41063	0.363514	0.181757	+	0.983344i	$0.441822\pi$
$312$	5.69721	0.322541
$313$	−19.7593	−1.11686	−0.558431	−	0.829551i	$-0.688596\pi$
$313$	−19.7593	−1.11686	−0.558431	+	0.829551i	$0.688596\pi$
$314$	−24.5685	−1.38648
$315$	4.58564	0.258371
$316$	−12.5158	−0.704068
$317$	28.3905	1.59457	0.797286	−	0.603602i	$-0.206269\pi$
$317$	28.3905	1.59457	0.797286	+	0.603602i	$0.206269\pi$
$318$	12.8917	0.722932
$319$	−10.2541	−0.574119
$320$	−31.1956	−1.74389
$321$	0.105336	0.00587929
$322$	56.2496	3.13467
$323$	1.67770	0.0933499
$324$	−36.9886	−2.05492
$325$	0.404621	0.0224443
$326$	2.64482	0.146483
$327$	25.3844	1.40376
$328$	−13.1630	−0.726806
$329$	−6.13151	−0.338041
$330$	42.9596	2.36485
$331$	−13.2464	−0.728089	−0.364044	−	0.931382i	$-0.618604\pi$
$331$	−13.2464	−0.728089	−0.364044	+	0.931382i	$0.618604\pi$
$332$	29.3877	1.61286
$333$	0.460856	0.0252548
$334$	−4.39767	−0.240630
$335$	8.94483	0.488708
$336$	−71.5666	−3.90428
$337$	23.4433	1.27704	0.638519	−	0.769606i	$-0.279548\pi$
$337$	23.4433	1.27704	0.638519	+	0.769606i	$0.279548\pi$
$338$	33.8438	1.84086
$339$	19.8701	1.07920
$340$	16.1068	0.873514
$341$	−15.0604	−0.815566
$342$	−1.53993	−0.0832701
$343$	11.4368	0.617528
$344$	−6.82012	−0.367716
$345$	−20.0828	−1.08122
$346$	−7.62914	−0.410145
$347$	28.7235	1.54196	0.770979	−	0.636860i	$-0.219767\pi$
$347$	28.7235	1.54196	0.770979	+	0.636860i	$0.219767\pi$
$348$	−19.4427	−1.04224
$349$	2.72074	0.145638	0.0728189	−	0.997345i	$-0.476800\pi$
$349$	2.72074	0.145638	0.0728189	+	0.997345i	$0.476800\pi$
$350$	−9.71546	−0.519313
$351$	2.48912	0.132859
$352$	55.1832	2.94128
$353$	13.5807	0.722826	0.361413	−	0.932406i	$-0.382294\pi$
$353$	13.5807	0.722826	0.361413	+	0.932406i	$0.382294\pi$
$354$	49.1148	2.61042
$355$	4.57569	0.242852
$356$	−10.2901	−0.545373
$357$	8.67074	0.458904
$358$	24.8980	1.31590
$359$	−14.5498	−0.767909	−0.383954	−	0.923352i	$-0.625438\pi$
$359$	−14.5498	−0.767909	−0.383954	+	0.923352i	$0.625438\pi$
$360$	−8.86464	−0.467207
$361$	−17.4038	−0.915990
$362$	1.64618	0.0865214
$363$	−10.5517	−0.553819
$364$	9.23842	0.484225
$365$	−19.8679	−1.03993
$366$	2.69532	0.140886
$367$	−3.76162	−0.196355	−0.0981775	−	0.995169i	$-0.531301\pi$
$367$	−3.76162	−0.196355	−0.0981775	+	0.995169i	$0.531301\pi$
$368$	−56.8871	−2.96544
$369$	−0.765810	−0.0398665
$370$	−6.42231	−0.333880
$371$	12.5346	0.650764
$372$	−28.5558	−1.48055
$373$	26.7953	1.38741	0.693704	−	0.720260i	$-0.255978\pi$
$373$	26.7953	1.38741	0.693704	+	0.720260i	$0.255978\pi$
$374$	−14.7433	−0.762358
$375$	−15.8781	−0.819941
$376$	11.8530	0.611272
$377$	1.10253	0.0567832
$378$	−59.7670	−3.07408
$379$	−8.60375	−0.441945	−0.220972	−	0.975280i	$-0.570923\pi$
$379$	−8.60375	−0.441945	−0.220972	+	0.975280i	$0.570923\pi$
$380$	15.3242	0.786113
$381$	−8.11554	−0.415772
$382$	−46.4428	−2.37622
$383$	−17.4315	−0.890707	−0.445353	−	0.895355i	$-0.646922\pi$
$383$	−17.4315	−0.890707	−0.445353	+	0.895355i	$0.646922\pi$
$384$	12.2481	0.625032
$385$	41.7695	2.12877
$386$	−2.76500	−0.140735
$387$	−0.396787	−0.0201698
$388$	−73.8116	−3.74722
$389$	−4.87977	−0.247414	−0.123707	−	0.992319i	$-0.539478\pi$
$389$	−4.87977	−0.247414	−0.123707	+	0.992319i	$0.539478\pi$
$390$	−4.61906	−0.233895
$391$	6.89222	0.348555
$392$	−77.5583	−3.91729
$393$	−11.1272	−0.561295
$394$	−22.4278	−1.12990
$395$	6.08434	0.306136
$396$	9.66342	0.485605
$397$	13.7370	0.689439	0.344720	−	0.938706i	$-0.387974\pi$
$397$	13.7370	0.689439	0.344720	+	0.938706i	$0.387974\pi$
$398$	−19.0829	−0.956537
$399$	8.24943	0.412988
$400$	9.82556	0.491278
$401$	−23.3445	−1.16577	−0.582885	−	0.812555i	$-0.698076\pi$
$401$	−23.3445	−1.16577	−0.582885	+	0.812555i	$0.698076\pi$
$402$	−15.5244	−0.774288
$403$	1.61931	0.0806636
$404$	73.8020	3.67179
$405$	17.9814	0.893502
$406$	−26.4732	−1.31384
$407$	4.19783	0.208079
$408$	−16.7617	−0.829827
$409$	3.48381	0.172263	0.0861316	−	0.996284i	$-0.472549\pi$
$409$	3.48381	0.172263	0.0861316	+	0.996284i	$0.472549\pi$
$410$	10.6720	0.527054
$411$	−18.0368	−0.889688
$412$	−3.57052	−0.175907
$413$	47.7542	2.34983
$414$	−6.32625	−0.310918
$415$	−14.2863	−0.701289
$416$	−5.93336	−0.290907
$417$	3.49055	0.170933
$418$	−14.0269	−0.686079
$419$	−22.6904	−1.10850	−0.554249	−	0.832351i	$-0.686994\pi$
$419$	−22.6904	−1.10850	−0.554249	+	0.832351i	$0.686994\pi$
$420$	79.1987	3.86450
$421$	9.56041	0.465946	0.232973	−	0.972483i	$-0.425155\pi$
$421$	9.56041	0.465946	0.232973	+	0.972483i	$0.425155\pi$
$422$	32.3246	1.57354
$423$	0.689595	0.0335293
$424$	−24.2310	−1.17676
$425$	−1.19043	−0.0577442
$426$	−7.94145	−0.384765
$427$	2.62065	0.126822
$428$	−0.330197	−0.0159607
$429$	3.01917	0.145767
$430$	5.52947	0.266655
$431$	1.61268	0.0776802	0.0388401	−	0.999245i	$-0.487634\pi$
$431$	1.61268	0.0776802	0.0388401	+	0.999245i	$0.487634\pi$
$432$	60.4443	2.90813
$433$	2.85999	0.137442	0.0687212	−	0.997636i	$-0.478108\pi$
$433$	2.85999	0.137442	0.0687212	+	0.997636i	$0.478108\pi$
$434$	−38.8817	−1.86638
$435$	9.45173	0.453176
$436$	−79.5726	−3.81084
$437$	6.55733	0.313679
$438$	34.4822	1.64762
$439$	−31.4003	−1.49865	−0.749327	−	0.662201i	$-0.769623\pi$
$439$	−31.4003	−1.49865	−0.749327	+	0.662201i	$0.769623\pi$
$440$	−80.7460	−3.84941
$441$	−4.51226	−0.214869
$442$	1.58522	0.0754010
$443$	6.99669	0.332423	0.166211	−	0.986090i	$-0.446847\pi$
$443$	6.99669	0.332423	0.166211	+	0.986090i	$0.446847\pi$
$444$	7.95946	0.377739
$445$	5.00235	0.237134
$446$	−43.0063	−2.03641
$447$	−2.21211	−0.104629
$448$	52.6426	2.48713
$449$	10.4171	0.491614	0.245807	−	0.969319i	$-0.420947\pi$
$449$	10.4171	0.491614	0.245807	+	0.969319i	$0.420947\pi$
$450$	1.09267	0.0515091
$451$	−6.97559	−0.328468
$452$	−62.2869	−2.92973
$453$	18.0263	0.846950
$454$	−50.5927	−2.37444
$455$	−4.49110	−0.210546
$456$	−15.9472	−0.746797
$457$	4.88992	0.228741	0.114370	−	0.993438i	$-0.463515\pi$
$457$	4.88992	0.228741	0.114370	+	0.993438i	$0.463515\pi$
$458$	−43.7632	−2.04492
$459$	−7.32320	−0.341818
$460$	62.9536	2.93523
$461$	−10.4381	−0.486149	−0.243075	−	0.970008i	$-0.578156\pi$
$461$	−10.4381	−0.486149	−0.243075	+	0.970008i	$0.578156\pi$
$462$	−72.4942	−3.37273
$463$	21.8844	1.01705	0.508527	−	0.861046i	$-0.330190\pi$
$463$	21.8844	1.01705	0.508527	+	0.861046i	$0.330190\pi$
$464$	26.7732	1.24291
$465$	13.8819	0.643760
$466$	−61.6195	−2.85447
$467$	5.06756	0.234499	0.117249	−	0.993103i	$-0.462592\pi$
$467$	5.06756	0.234499	0.117249	+	0.993103i	$0.462592\pi$
$468$	−1.03902	−0.0480288
$469$	−15.0944	−0.696994
$470$	−9.60992	−0.443273
$471$	−14.8022	−0.682049
$472$	−92.3152	−4.24915
$473$	−3.61425	−0.166183
$474$	−10.5598	−0.485029
$475$	−1.13258	−0.0519665
$476$	−27.1802	−1.24580
$477$	−1.40973	−0.0645473
$478$	54.8537	2.50895
$479$	−28.3057	−1.29332	−0.646660	−	0.762779i	$-0.723835\pi$
$479$	−28.3057	−1.29332	−0.646660	+	0.762779i	$0.723835\pi$
$480$	−50.8652	−2.32167
$481$	−0.451356	−0.0205800
$482$	−43.1940	−1.96743
$483$	33.8897	1.54203
$484$	33.0763	1.50347
$485$	35.8823	1.62933
$486$	12.5486	0.569215
$487$	−1.85474	−0.0840464	−0.0420232	−	0.999117i	$-0.513380\pi$
$487$	−1.85474	−0.0840464	−0.0420232	+	0.999117i	$0.513380\pi$
$488$	−5.06606	−0.229330
$489$	1.59347	0.0720592
$490$	62.8810	2.84067
$491$	−35.1252	−1.58518	−0.792589	−	0.609756i	$-0.791267\pi$
$491$	−35.1252	−1.58518	−0.792589	+	0.609756i	$0.791267\pi$
$492$	−13.2263	−0.596289
$493$	−3.24374	−0.146091
$494$	1.50819	0.0678566
$495$	−4.69771	−0.211146
$496$	39.3223	1.76563
$497$	−7.72146	−0.346355
$498$	24.7950	1.11109
$499$	−3.28203	−0.146924	−0.0734619	−	0.997298i	$-0.523405\pi$
$499$	−3.28203	−0.146924	−0.0734619	+	0.997298i	$0.523405\pi$
$500$	49.7731	2.22592
$501$	−2.64954	−0.118373
$502$	−15.0960	−0.673769
$503$	−17.8321	−0.795093	−0.397547	−	0.917582i	$-0.630138\pi$
$503$	−17.8321	−0.795093	−0.397547	+	0.917582i	$0.630138\pi$
$504$	14.9591	0.666329
$505$	−35.8776	−1.59653
$506$	−57.6244	−2.56172
$507$	20.3905	0.905573
$508$	25.4398	1.12871
$509$	−26.2592	−1.16392	−0.581960	−	0.813217i	$-0.697714\pi$
$509$	−26.2592	−1.16392	−0.581960	+	0.813217i	$0.697714\pi$
$510$	13.5897	0.601760
$511$	33.5270	1.48315
$512$	29.5613	1.30644
$513$	−6.96737	−0.307617
$514$	26.8883	1.18599
$515$	1.73575	0.0764862
$516$	−6.85293	−0.301683
$517$	6.28137	0.276254
$518$	10.8376	0.476178
$519$	−4.59646	−0.201762
$520$	8.68189	0.380726
$521$	16.1966	0.709585	0.354793	−	0.934945i	$-0.384552\pi$
$521$	16.1966	0.709585	0.354793	+	0.934945i	$0.384552\pi$
$522$	2.97737	0.130316
$523$	−8.72900	−0.381693	−0.190846	−	0.981620i	$-0.561123\pi$
$523$	−8.72900	−0.381693	−0.190846	+	0.981620i	$0.561123\pi$
$524$	34.8806	1.52377
$525$	−5.85345	−0.255465
$526$	27.9573	1.21900
$527$	−4.76414	−0.207529
$528$	73.3157	3.19066
$529$	3.93832	0.171231
$530$	19.6455	0.853345
$531$	−5.37079	−0.233073
$532$	−25.8595	−1.12115
$533$	0.750023	0.0324871
$534$	−8.68196	−0.375705
$535$	0.160520	0.00693989
$536$	29.1794	1.26036
$537$	15.0007	0.647329
$538$	−33.5640	−1.44705
$539$	−41.1011	−1.77035
$540$	−66.8903	−2.87850
$541$	−39.3361	−1.69119	−0.845596	−	0.533824i	$-0.820754\pi$
$541$	−39.3361	−1.69119	−0.845596	+	0.533824i	$0.820754\pi$
$542$	24.1390	1.03686
$543$	0.991804	0.0425624
$544$	17.4564	0.748438
$545$	38.6829	1.65699
$546$	7.79465	0.333580
$547$	2.95512	0.126352	0.0631759	−	0.998002i	$-0.479877\pi$
$547$	2.95512	0.126352	0.0631759	+	0.998002i	$0.479877\pi$
$548$	56.5399	2.41527
$549$	−0.294738	−0.0125791
$550$	9.95291	0.424393
$551$	−3.08612	−0.131473
$552$	−65.5132	−2.78843
$553$	−10.2673	−0.436610
$554$	1.51978	0.0645693
$555$	−3.86936	−0.164245
$556$	−10.9419	−0.464038
$557$	19.9539	0.845475	0.422738	−	0.906252i	$-0.361069\pi$
$557$	19.9539	0.845475	0.422738	+	0.906252i	$0.361069\pi$
$558$	4.37293	0.185121
$559$	0.388607	0.0164363
$560$	−109.059	−4.60859
$561$	−8.88266	−0.375026
$562$	63.3616	2.67275
$563$	−29.3676	−1.23769	−0.618847	−	0.785511i	$-0.712400\pi$
$563$	−29.3676	−1.23769	−0.618847	+	0.785511i	$0.712400\pi$
$564$	11.9100	0.501502
$565$	30.2797	1.27388
$566$	−7.78856	−0.327377
$567$	−30.3435	−1.27431
$568$	14.9266	0.626306
$569$	−33.0244	−1.38446	−0.692228	−	0.721679i	$-0.743371\pi$
$569$	−33.0244	−1.38446	−0.692228	+	0.721679i	$0.743371\pi$
$570$	12.9293	0.541550
$571$	20.5223	0.858831	0.429416	−	0.903107i	$-0.358720\pi$
$571$	20.5223	0.858831	0.429416	+	0.903107i	$0.358720\pi$
$572$	−9.46421	−0.395718
$573$	−27.9812	−1.16893
$574$	−18.0090	−0.751682
$575$	−4.65280	−0.194035
$576$	−5.92057	−0.246691
$577$	−20.1986	−0.840879	−0.420440	−	0.907320i	$-0.638124\pi$
$577$	−20.1986	−0.840879	−0.420440	+	0.907320i	$0.638124\pi$
$578$	40.2980	1.67618
$579$	−1.66588	−0.0692317
$580$	−29.6284	−1.23025
$581$	24.1082	1.00018
$582$	−62.2764	−2.58144
$583$	−12.8409	−0.531818
$584$	−64.8121	−2.68194
$585$	0.505103	0.0208834
$586$	−8.33899	−0.344480
$587$	−38.1060	−1.57280	−0.786402	−	0.617715i	$-0.788059\pi$
$587$	−38.1060	−1.57280	−0.786402	+	0.617715i	$0.788059\pi$
$588$	−77.9314	−3.21383
$589$	−4.53265	−0.186765
$590$	74.8452	3.08133
$591$	−13.5125	−0.555828
$592$	−10.9604	−0.450472
$593$	17.0410	0.699789	0.349895	−	0.936789i	$-0.386217\pi$
$593$	17.0410	0.699789	0.349895	+	0.936789i	$0.386217\pi$
$594$	61.2277	2.51220
$595$	13.2132	0.541689
$596$	6.93430	0.284040
$597$	−11.4972	−0.470549
$598$	6.19583	0.253366
$599$	13.2896	0.542997	0.271498	−	0.962439i	$-0.412481\pi$
$599$	13.2896	0.542997	0.271498	+	0.962439i	$0.412481\pi$
$600$	11.3155	0.461952
$601$	18.1724	0.741266	0.370633	−	0.928779i	$-0.379141\pi$
$601$	18.1724	0.741266	0.370633	+	0.928779i	$0.379141\pi$
$602$	−9.33096	−0.380302
$603$	1.69763	0.0691327
$604$	−56.5071	−2.29924
$605$	−16.0795	−0.653725
$606$	62.2683	2.52948
$607$	27.1896	1.10359	0.551795	−	0.833979i	$-0.313943\pi$
$607$	27.1896	1.10359	0.551795	+	0.833979i	$0.313943\pi$
$608$	16.6082	0.673552
$609$	−15.9498	−0.646317
$610$	4.10735	0.166302
$611$	−0.675379	−0.0273229
$612$	3.05689	0.123567
$613$	−1.56321	−0.0631375	−0.0315687	−	0.999502i	$-0.510050\pi$
$613$	−1.56321	−0.0631375	−0.0315687	+	0.999502i	$0.510050\pi$
$614$	−19.6902	−0.794632
$615$	6.42976	0.259273
$616$	136.259	5.49002
$617$	−20.8189	−0.838135	−0.419068	−	0.907955i	$-0.637643\pi$
$617$	−20.8189	−0.838135	−0.419068	+	0.907955i	$0.637643\pi$
$618$	−3.01252	−0.121181
$619$	−44.0831	−1.77185	−0.885924	−	0.463831i	$-0.846475\pi$
$619$	−44.0831	−1.77185	−0.885924	+	0.463831i	$0.846475\pi$
$620$	−43.5158	−1.74764
$621$	−28.6228	−1.14859
$622$	−16.9549	−0.679831
$623$	−8.44146	−0.338200
$624$	−7.88299	−0.315572
$625$	−28.6786	−1.14715
$626$	52.2597	2.08872
$627$	−8.45105	−0.337502
$628$	46.4005	1.85158
$629$	1.32793	0.0529479
$630$	−12.1282	−0.483198
$631$	14.1638	0.563852	0.281926	−	0.959436i	$-0.409027\pi$
$631$	14.1638	0.563852	0.281926	+	0.959436i	$0.409027\pi$
$632$	19.8480	0.789513
$633$	19.4752	0.774069
$634$	−75.0877	−2.98211
$635$	−12.3671	−0.490775
$636$	−24.3476	−0.965443
$637$	4.41924	0.175097
$638$	27.1202	1.07370
$639$	0.868413	0.0343539
$640$	18.6646	0.737784
$641$	30.2711	1.19564	0.597819	−	0.801631i	$-0.296034\pi$
$641$	30.2711	1.19564	0.597819	+	0.801631i	$0.296034\pi$
$642$	−0.278595	−0.0109953
$643$	8.94120	0.352607	0.176303	−	0.984336i	$-0.443586\pi$
$643$	8.94120	0.352607	0.176303	+	0.984336i	$0.443586\pi$
$644$	−106.234	−4.18621
$645$	3.33144	0.131175
$646$	−4.43722	−0.174580
$647$	−31.9305	−1.25532	−0.627658	−	0.778489i	$-0.715986\pi$
$647$	−31.9305	−1.25532	−0.627658	+	0.778489i	$0.715986\pi$
$648$	58.6580	2.30431
$649$	−48.9214	−1.92033
$650$	−1.07015	−0.0419746
$651$	−23.4257	−0.918127
$652$	−4.99505	−0.195621
$653$	−43.8405	−1.71561	−0.857805	−	0.513975i	$-0.828172\pi$
$653$	−43.8405	−1.71561	−0.857805	+	0.513975i	$0.828172\pi$
$654$	−67.1371	−2.62527
$655$	−16.9566	−0.662550
$656$	18.2131	0.711102
$657$	−3.77070	−0.147109
$658$	16.2167	0.632193
$659$	18.7837	0.731708	0.365854	−	0.930672i	$-0.380777\pi$
$659$	18.7837	0.731708	0.365854	+	0.930672i	$0.380777\pi$
$660$	−81.1343	−3.15815
$661$	−9.00625	−0.350303	−0.175151	−	0.984542i	$-0.556041\pi$
$661$	−9.00625	−0.350303	−0.175151	+	0.984542i	$0.556041\pi$
$662$	35.0343	1.36165
$663$	0.955073	0.0370919
$664$	−46.6043	−1.80860
$665$	12.5712	0.487489
$666$	−1.21888	−0.0472306
$667$	−12.6782	−0.490902
$668$	8.30553	0.321351
$669$	−25.9108	−1.00177
$670$	−23.6574	−0.913966
$671$	−2.68470	−0.103642
$672$	85.8349	3.31115
$673$	−48.5736	−1.87237	−0.936187	−	0.351503i	$-0.885671\pi$
$673$	−48.5736	−1.87237	−0.936187	+	0.351503i	$0.885671\pi$
$674$	−62.0032	−2.38827
$675$	4.94375	0.190285
$676$	−63.9181	−2.45839
$677$	12.5490	0.482297	0.241149	−	0.970488i	$-0.422476\pi$
$677$	12.5490	0.482297	0.241149	+	0.970488i	$0.422476\pi$
$678$	−52.5528	−2.01828
$679$	−60.5513	−2.32375
$680$	−25.5428	−0.979524
$681$	−30.4815	−1.16805
$682$	39.8320	1.52525
$683$	−15.6135	−0.597435	−0.298717	−	0.954342i	$-0.596559\pi$
$683$	−15.6135	−0.597435	−0.298717	+	0.954342i	$0.596559\pi$
$684$	2.90835	0.111204
$685$	−27.4860	−1.05018
$686$	−30.2482	−1.15488
$687$	−26.3668	−1.00596
$688$	9.43671	0.359771
$689$	1.38067	0.0525994
$690$	53.1153	2.02207
$691$	19.4960	0.741664	0.370832	−	0.928700i	$-0.379073\pi$
$691$	19.4960	0.741664	0.370832	+	0.928700i	$0.379073\pi$
$692$	14.4085	0.547731
$693$	7.92738	0.301136
$694$	−75.9684	−2.88372
$695$	5.31920	0.201769
$696$	30.8330	1.16872
$697$	−2.20663	−0.0835821
$698$	−7.19585	−0.272367
$699$	−37.1250	−1.40420
$700$	18.3488	0.693520
$701$	−1.14255	−0.0431536	−0.0215768	−	0.999767i	$-0.506869\pi$
$701$	−1.14255	−0.0431536	−0.0215768	+	0.999767i	$0.506869\pi$
$702$	−6.58327	−0.248469
$703$	1.26340	0.0476501
$704$	−53.9292	−2.03253
$705$	−5.78986	−0.218059
$706$	−35.9184	−1.35181
$707$	60.5434	2.27697
$708$	−92.7592	−3.48610
$709$	−12.9079	−0.484765	−0.242382	−	0.970181i	$-0.577929\pi$
$709$	−12.9079	−0.484765	−0.242382	+	0.970181i	$0.577929\pi$
$710$	−12.1018	−0.454174
$711$	1.15474	0.0433060
$712$	16.3184	0.611559
$713$	−18.6207	−0.697351
$714$	−22.9325	−0.858228
$715$	4.60087	0.172063
$716$	−47.0228	−1.75732
$717$	33.0487	1.23423
$718$	38.4815	1.43612
$719$	−46.5638	−1.73654	−0.868269	−	0.496093i	$-0.834767\pi$
$719$	−46.5638	−1.73654	−0.868269	+	0.496093i	$0.834767\pi$
$720$	12.2656	0.457112
$721$	−2.92907	−0.109084
$722$	46.0299	1.71306
$723$	−26.0238	−0.967836
$724$	−3.10901	−0.115546
$725$	2.18978	0.0813265
$726$	27.9072	1.03573
$727$	2.75509	0.102180	0.0510902	−	0.998694i	$-0.483730\pi$
$727$	2.75509	0.102180	0.0510902	+	0.998694i	$0.483730\pi$
$728$	−14.6507	−0.542990
$729$	29.7755	1.10280
$730$	52.5469	1.94485
$731$	−1.14332	−0.0422871
$732$	−5.09043	−0.188148
$733$	−41.3046	−1.52562	−0.762811	−	0.646622i	$-0.776181\pi$
$733$	−41.3046	−1.52562	−0.762811	+	0.646622i	$0.776181\pi$
$734$	9.94880	0.367217
$735$	37.8850	1.39741
$736$	68.2287	2.51494
$737$	15.4633	0.569598
$738$	2.02543	0.0745570
$739$	34.2721	1.26072	0.630359	−	0.776304i	$-0.282908\pi$
$739$	34.2721	1.26072	0.630359	+	0.776304i	$0.282908\pi$
$740$	12.1293	0.445882
$741$	0.908665	0.0333807
$742$	−33.1517	−1.21704
$743$	1.33557	0.0489975	0.0244987	−	0.999700i	$-0.492201\pi$
$743$	1.33557	0.0489975	0.0244987	+	0.999700i	$0.492201\pi$
$744$	45.2850	1.66023
$745$	−3.37099	−0.123504
$746$	−70.8687	−2.59469
$747$	−2.71139	−0.0992044
$748$	27.8445	1.01810
$749$	−0.270877	−0.00989764
$750$	41.9946	1.53343
$751$	−36.5137	−1.33241	−0.666203	−	0.745771i	$-0.732081\pi$
$751$	−36.5137	−1.33241	−0.666203	+	0.745771i	$0.732081\pi$
$752$	−16.4005	−0.598064
$753$	−9.09517	−0.331446
$754$	−2.91599	−0.106194
$755$	27.4700	0.999736
$756$	112.877	4.10530
$757$	−40.1879	−1.46065	−0.730327	−	0.683098i	$-0.760632\pi$
$757$	−40.1879	−1.46065	−0.730327	+	0.683098i	$0.760632\pi$
$758$	22.7553	0.826511
$759$	−34.7180	−1.26018
$760$	−24.3017	−0.881516
$761$	1.50876	0.0546924	0.0273462	−	0.999626i	$-0.491294\pi$
$761$	1.50876	0.0546924	0.0273462	+	0.999626i	$0.491294\pi$
$762$	21.4641	0.777563
$763$	−65.2773	−2.36320
$764$	87.7127	3.17334
$765$	−1.48605	−0.0537284
$766$	46.1031	1.66577
$767$	5.26008	0.189930
$768$	8.54839	0.308463
$769$	48.5479	1.75068	0.875342	−	0.483505i	$-0.160636\pi$
$769$	48.5479	1.75068	0.875342	+	0.483505i	$0.160636\pi$
$770$	−110.473	−3.98116
$771$	16.1999	0.583425
$772$	5.22204	0.187945
$773$	−13.2954	−0.478201	−0.239100	−	0.970995i	$-0.576852\pi$
$773$	−13.2954	−0.478201	−0.239100	+	0.970995i	$0.576852\pi$
$774$	1.04943	0.0377210
$775$	3.21618	0.115529
$776$	117.054	4.20198
$777$	6.52954	0.234246
$778$	12.9061	0.462706
$779$	−2.09941	−0.0752191
$780$	8.72365	0.312357
$781$	7.91017	0.283048
$782$	−18.2287	−0.651855
$783$	13.4710	0.481414
$784$	107.314	3.83265
$785$	−22.5568	−0.805088
$786$	29.4295	1.04972
$787$	37.1193	1.32316	0.661580	−	0.749875i	$-0.269886\pi$
$787$	37.1193	1.32316	0.661580	+	0.749875i	$0.269886\pi$
$788$	42.3576	1.50893
$789$	16.8439	0.599660
$790$	−16.0920	−0.572526
$791$	−51.0970	−1.81680
$792$	−15.3247	−0.544538
$793$	0.288662	0.0102507
$794$	−36.3318	−1.28937
$795$	11.8362	0.419785
$796$	36.0403	1.27741
$797$	13.6434	0.483274	0.241637	−	0.970367i	$-0.422316\pi$
$797$	13.6434	0.483274	0.241637	+	0.970367i	$0.422316\pi$
$798$	−21.8182	−0.772357
$799$	1.98702	0.0702958
$800$	−11.7845	−0.416645
$801$	0.949389	0.0335450
$802$	61.7420	2.18019
$803$	−34.3464	−1.21206
$804$	29.3197	1.03403
$805$	51.6440	1.82021
$806$	−4.28278	−0.150854
$807$	−20.2219	−0.711844
$808$	−117.038	−4.11739
$809$	−31.2891	−1.10007	−0.550033	−	0.835143i	$-0.685385\pi$
$809$	−31.2891	−1.10007	−0.550033	+	0.835143i	$0.685385\pi$
$810$	−47.5575	−1.67100
$811$	28.5214	1.00152	0.500761	−	0.865586i	$-0.333054\pi$
$811$	28.5214	1.00152	0.500761	+	0.865586i	$0.333054\pi$
$812$	49.9978	1.75458
$813$	14.5434	0.510061
$814$	−11.1025	−0.389142
$815$	2.42826	0.0850583
$816$	23.1924	0.811896
$817$	−1.08776	−0.0380560
$818$	−9.21404	−0.322161
$819$	−0.852360	−0.0297839
$820$	−20.1554	−0.703857
$821$	20.0055	0.698197	0.349099	−	0.937086i	$-0.386488\pi$
$821$	20.0055	0.698197	0.349099	+	0.937086i	$0.386488\pi$
$822$	47.7040	1.66387
$823$	54.6493	1.90495	0.952477	−	0.304609i	$-0.0985259\pi$
$823$	54.6493	1.90495	0.952477	+	0.304609i	$0.0985259\pi$
$824$	5.66228	0.197255
$825$	5.99651	0.208772
$826$	−126.301	−4.39458
$827$	−17.9459	−0.624042	−0.312021	−	0.950075i	$-0.601006\pi$
$827$	−17.9459	−0.624042	−0.312021	+	0.950075i	$0.601006\pi$
$828$	11.9479	0.415218
$829$	−17.8440	−0.619746	−0.309873	−	0.950778i	$-0.600287\pi$
$829$	−17.8440	−0.619746	−0.309873	+	0.950778i	$0.600287\pi$
$830$	37.7848	1.31153
$831$	0.915649	0.0317635
$832$	5.79852	0.201028
$833$	−13.0018	−0.450485
$834$	−9.23188	−0.319674
$835$	−4.03760	−0.139727
$836$	26.4915	0.916228
$837$	19.7851	0.683873
$838$	60.0119	2.07308
$839$	−39.1534	−1.35173	−0.675863	−	0.737027i	$-0.736229\pi$
$839$	−39.1534	−1.35173	−0.675863	+	0.737027i	$0.736229\pi$
$840$	−125.597	−4.33349
$841$	−23.0332	−0.794247
$842$	−25.2855	−0.871397
$843$	38.1746	1.31480
$844$	−61.0489	−2.10139
$845$	31.0727	1.06893
$846$	−1.82385	−0.0627053
$847$	27.1341	0.932340
$848$	33.5274	1.15134
$849$	−4.69251	−0.161046
$850$	3.14846	0.107991
$851$	5.19021	0.177918
$852$	14.9984	0.513836
$853$	−49.5096	−1.69518	−0.847588	−	0.530654i	$-0.821946\pi$
$853$	−49.5096	−1.69518	−0.847588	+	0.530654i	$0.821946\pi$
$854$	−6.93114	−0.237179
$855$	−1.41385	−0.0483525
$856$	0.523641	0.0178977
$857$	5.82225	0.198884	0.0994421	−	0.995043i	$-0.468294\pi$
$857$	5.82225	0.198884	0.0994421	+	0.995043i	$0.468294\pi$
$858$	−7.98516	−0.272609
$859$	0.558961	0.0190715	0.00953575	−	0.999955i	$-0.496965\pi$
$859$	0.558961	0.0190715	0.00953575	+	0.999955i	$0.496965\pi$
$860$	−10.4431	−0.356106
$861$	−10.8502	−0.369774
$862$	−4.26525	−0.145275
$863$	−40.7438	−1.38694	−0.693468	−	0.720487i	$-0.743918\pi$
$863$	−40.7438	−1.38694	−0.693468	+	0.720487i	$0.743918\pi$
$864$	−72.4951	−2.46633
$865$	−7.00447	−0.238159
$866$	−7.56415	−0.257040
$867$	24.2791	0.824560
$868$	73.4328	2.49247
$869$	10.5182	0.356807
$870$	−24.9981	−0.847514
$871$	−1.66263	−0.0563360
$872$	126.190	4.27332
$873$	6.81005	0.230485
$874$	−17.3429	−0.586633
$875$	40.8313	1.38035
$876$	−65.1238	−2.20033
$877$	−5.94045	−0.200595	−0.100297	−	0.994958i	$-0.531979\pi$
$877$	−5.94045	−0.200595	−0.100297	+	0.994958i	$0.531979\pi$
$878$	83.0479	2.80273
$879$	−5.02414	−0.169460
$880$	111.725	3.76624
$881$	−45.9886	−1.54940	−0.774698	−	0.632331i	$-0.782098\pi$
$881$	−45.9886	−1.54940	−0.774698	+	0.632331i	$0.782098\pi$
$882$	11.9341	0.401842
$883$	−37.8161	−1.27261	−0.636307	−	0.771436i	$-0.719539\pi$
$883$	−37.8161	−1.27261	−0.636307	+	0.771436i	$0.719539\pi$
$884$	−2.99387	−0.100695
$885$	45.0933	1.51580
$886$	−18.5050	−0.621686
$887$	−31.2196	−1.04825	−0.524126	−	0.851641i	$-0.675608\pi$
$887$	−31.2196	−1.04825	−0.524126	+	0.851641i	$0.675608\pi$
$888$	−12.6224	−0.423582
$889$	20.8695	0.699941
$890$	−13.2303	−0.443481
$891$	31.0851	1.04139
$892$	81.2226	2.71953
$893$	1.89047	0.0632622
$894$	5.85061	0.195674
$895$	22.8593	0.764104
$896$	−31.4965	−1.05223
$897$	3.73291	0.124638
$898$	−27.5514	−0.919401
$899$	8.76361	0.292283
$900$	−2.06364	−0.0687881
$901$	−4.06205	−0.135327
$902$	18.4492	0.614290
$903$	−5.62179	−0.187081
$904$	98.7772	3.28528
$905$	1.51139	0.0502405
$906$	−47.6763	−1.58394
$907$	27.3347	0.907633	0.453816	−	0.891095i	$-0.350062\pi$
$907$	27.3347	0.907633	0.453816	+	0.891095i	$0.350062\pi$
$908$	95.5505	3.17095
$909$	−6.80916	−0.225845
$910$	11.8781	0.393757
$911$	19.9021	0.659386	0.329693	−	0.944088i	$-0.393055\pi$
$911$	19.9021	0.659386	0.329693	+	0.944088i	$0.393055\pi$
$912$	22.0655	0.730661
$913$	−24.6974	−0.817364
$914$	−12.9329	−0.427784
$915$	2.47463	0.0818086
$916$	82.6520	2.73090
$917$	28.6142	0.944926
$918$	19.3685	0.639257
$919$	−28.4703	−0.939147	−0.469574	−	0.882893i	$-0.655592\pi$
$919$	−28.4703	−0.939147	−0.469574	+	0.882893i	$0.655592\pi$
$920$	−99.8345	−3.29145
$921$	−11.8631	−0.390903
$922$	27.6068	0.909181
$923$	−0.850510	−0.0279949
$924$	136.914	4.50414
$925$	−0.896456	−0.0294753
$926$	−57.8802	−1.90206
$927$	0.329425	0.0108197
$928$	−32.1110	−1.05409
$929$	27.2542	0.894181	0.447091	−	0.894489i	$-0.352460\pi$
$929$	27.2542	0.894181	0.447091	+	0.894489i	$0.352460\pi$
$930$	−36.7152	−1.20394
$931$	−12.3700	−0.405411
$932$	116.376	3.81202
$933$	−10.2151	−0.334429
$934$	−13.4028	−0.438552
$935$	−13.5361	−0.442679
$936$	1.64772	0.0538575
$937$	20.9485	0.684356	0.342178	−	0.939635i	$-0.388835\pi$
$937$	20.9485	0.684356	0.342178	+	0.939635i	$0.388835\pi$
$938$	39.9219	1.30349
$939$	31.4858	1.02750
$940$	18.1495	0.591971
$941$	−12.2319	−0.398748	−0.199374	−	0.979923i	$-0.563891\pi$
$941$	−12.2319	−0.398748	−0.199374	+	0.979923i	$0.563891\pi$
$942$	39.1491	1.27555
$943$	−8.62464	−0.280857
$944$	127.732	4.15734
$945$	−54.8733	−1.78503
$946$	9.55902	0.310790
$947$	31.7141	1.03057	0.515285	−	0.857019i	$-0.327686\pi$
$947$	31.7141	1.03057	0.515285	+	0.857019i	$0.327686\pi$
$948$	19.9435	0.647735
$949$	3.69296	0.119879
$950$	2.99548	0.0971861
$951$	−45.2394	−1.46699
$952$	43.1035	1.39699
$953$	17.6304	0.571103	0.285552	−	0.958363i	$-0.407823\pi$
$953$	17.6304	0.571103	0.285552	+	0.958363i	$0.407823\pi$
$954$	3.72849	0.120714
$955$	−42.6401	−1.37980
$956$	−103.598	−3.35059
$957$	16.3396	0.528184
$958$	74.8633	2.41872
$959$	46.3825	1.49777
$960$	49.7093	1.60436
$961$	−18.1287	−0.584797
$962$	1.19375	0.0384881
$963$	0.0304649	0.000981716 0
$964$	81.5770	2.62742
$965$	−2.53861	−0.0817207
$966$	−89.6320	−2.88386
$967$	−46.1469	−1.48398	−0.741992	−	0.670409i	$-0.766119\pi$
$967$	−46.1469	−1.48398	−0.741992	+	0.670409i	$0.766119\pi$
$968$	−52.4538	−1.68593
$969$	−2.67337	−0.0858810
$970$	−94.9021	−3.04712
$971$	22.8662	0.733810	0.366905	−	0.930258i	$-0.380417\pi$
$971$	22.8662	0.733810	0.366905	+	0.930258i	$0.380417\pi$
$972$	−23.6995	−0.760162
$973$	−8.97614	−0.287762
$974$	4.90545	0.157181
$975$	−0.644751	−0.0206485
$976$	7.00969	0.224375
$977$	10.3648	0.331598	0.165799	−	0.986160i	$-0.446980\pi$
$977$	10.3648	0.331598	0.165799	+	0.986160i	$0.446980\pi$
$978$	−4.21443	−0.134763
$979$	8.64777	0.276384
$980$	−118.758	−3.79360
$981$	7.34157	0.234398
$982$	92.8997	2.96455
$983$	−11.5619	−0.368768	−0.184384	−	0.982854i	$-0.559029\pi$
$983$	−11.5619	−0.368768	−0.184384	+	0.982854i	$0.559029\pi$
$984$	20.9749	0.668654
$985$	−20.5914	−0.656097
$986$	8.57909	0.273214
$987$	9.77037	0.310994
$988$	−2.84840	−0.0906195
$989$	−4.46866	−0.142095
$990$	12.4246	0.394879
$991$	−15.3641	−0.488058	−0.244029	−	0.969768i	$-0.578469\pi$
$991$	−15.3641	−0.488058	−0.244029	+	0.969768i	$0.578469\pi$
$992$	−47.1621	−1.49740
$993$	21.1078	0.669834
$994$	20.4218	0.647741
$995$	−17.5204	−0.555433
$996$	−46.8284	−1.48382
$997$	−6.03877	−0.191250	−0.0956249	−	0.995417i	$-0.530485\pi$
$997$	−6.03877	−0.191250	−0.0956249	+	0.995417i	$0.530485\pi$
$998$	8.68037	0.274772
$999$	−5.51477	−0.174480

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6031.2.a.c.1.5	✓	110

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6031.2.a.c.1.5	✓	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)

\(f(q)\)	\(=\)	\(q-2.64482 q^{2} -1.59347 q^{3} +4.99505 q^{4} -2.42826 q^{5} +4.21443 q^{6} +4.09769 q^{7} -7.92136 q^{8} -0.460856 q^{9} +O(q^{10})\)	\(q-2.64482 q^{2} -1.59347 q^{3} +4.99505 q^{4} -2.42826 q^{5} +4.21443 q^{6} +4.09769 q^{7} -7.92136 q^{8} -0.460856 q^{9} +6.42231 q^{10} -4.19783 q^{11} -7.95946 q^{12} +0.451356 q^{13} -10.8376 q^{14} +3.86936 q^{15} +10.9604 q^{16} -1.32793 q^{17} +1.21888 q^{18} -1.26340 q^{19} -12.1293 q^{20} -6.52954 q^{21} +11.1025 q^{22} -5.19021 q^{23} +12.6224 q^{24} +0.896456 q^{25} -1.19375 q^{26} +5.51477 q^{27} +20.4682 q^{28} +2.44271 q^{29} -10.2337 q^{30} +3.58766 q^{31} -13.1456 q^{32} +6.68912 q^{33} +3.51212 q^{34} -9.95026 q^{35} -2.30200 q^{36} -1.00000 q^{37} +3.34146 q^{38} -0.719221 q^{39} +19.2351 q^{40} +1.66171 q^{41} +17.2694 q^{42} +0.860978 q^{43} -20.9684 q^{44} +1.11908 q^{45} +13.7272 q^{46} -1.49633 q^{47} -17.4651 q^{48} +9.79103 q^{49} -2.37096 q^{50} +2.11601 q^{51} +2.25455 q^{52} +3.05894 q^{53} -14.5855 q^{54} +10.1934 q^{55} -32.4593 q^{56} +2.01319 q^{57} -6.46052 q^{58} +11.6539 q^{59} +19.3277 q^{60} +0.639544 q^{61} -9.48870 q^{62} -1.88844 q^{63} +12.8469 q^{64} -1.09601 q^{65} -17.6915 q^{66} -3.68363 q^{67} -6.63306 q^{68} +8.27045 q^{69} +26.3166 q^{70} -1.88435 q^{71} +3.65061 q^{72} +8.18194 q^{73} +2.64482 q^{74} -1.42848 q^{75} -6.31076 q^{76} -17.2014 q^{77} +1.90221 q^{78} -2.50563 q^{79} -26.6148 q^{80} -7.40504 q^{81} -4.39492 q^{82} +5.88336 q^{83} -32.6154 q^{84} +3.22455 q^{85} -2.27713 q^{86} -3.89238 q^{87} +33.2526 q^{88} -2.06005 q^{89} -2.95976 q^{90} +1.84951 q^{91} -25.9254 q^{92} -5.71682 q^{93} +3.95753 q^{94} +3.06787 q^{95} +20.9472 q^{96} -14.7769 q^{97} -25.8955 q^{98} +1.93460 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 110 q - 9 q^{2} + 97 q^{4} - 26 q^{5} - 26 q^{6} - 4 q^{7} - 27 q^{8} + 62 q^{9}+O(q^{10}) \) 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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