LMFDB - Embedded newform 6031.2.a.d.1.16

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:	$0$
Dimension:	$133$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
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)

$f(q)$	$=$	$q-2.27893 q^{2} +2.16909 q^{3} +3.19353 q^{4} +2.05388 q^{5} -4.94321 q^{6} -4.20533 q^{7} -2.71998 q^{8} +1.70495 q^{9} +O(q^{10})$	\(q-2.27893 q^{2} +2.16909 q^{3} +3.19353 q^{4} +2.05388 q^{5} -4.94321 q^{6} -4.20533 q^{7} -2.71998 q^{8} +1.70495 q^{9} -4.68065 q^{10} +4.59267 q^{11} +6.92706 q^{12} -5.82463 q^{13} +9.58365 q^{14} +4.45505 q^{15} -0.188418 q^{16} +0.108379 q^{17} -3.88547 q^{18} +7.39501 q^{19} +6.55913 q^{20} -9.12173 q^{21} -10.4664 q^{22} -6.46256 q^{23} -5.89988 q^{24} -0.781579 q^{25} +13.2739 q^{26} -2.80908 q^{27} -13.4298 q^{28} -2.52187 q^{29} -10.1528 q^{30} +6.98897 q^{31} +5.86935 q^{32} +9.96192 q^{33} -0.246987 q^{34} -8.63724 q^{35} +5.44482 q^{36} -1.00000 q^{37} -16.8527 q^{38} -12.6341 q^{39} -5.58651 q^{40} +3.22113 q^{41} +20.7878 q^{42} +8.71497 q^{43} +14.6668 q^{44} +3.50177 q^{45} +14.7277 q^{46} -1.83441 q^{47} -0.408696 q^{48} +10.6848 q^{49} +1.78116 q^{50} +0.235083 q^{51} -18.6011 q^{52} -6.34346 q^{53} +6.40169 q^{54} +9.43280 q^{55} +11.4384 q^{56} +16.0404 q^{57} +5.74717 q^{58} +3.43767 q^{59} +14.2273 q^{60} -7.08449 q^{61} -15.9274 q^{62} -7.16988 q^{63} -12.9990 q^{64} -11.9631 q^{65} -22.7025 q^{66} +14.7522 q^{67} +0.346110 q^{68} -14.0179 q^{69} +19.6837 q^{70} +8.21120 q^{71} -4.63743 q^{72} +10.5250 q^{73} +2.27893 q^{74} -1.69531 q^{75} +23.6162 q^{76} -19.3137 q^{77} +28.7924 q^{78} +13.3156 q^{79} -0.386988 q^{80} -11.2080 q^{81} -7.34073 q^{82} +16.1527 q^{83} -29.1305 q^{84} +0.222597 q^{85} -19.8608 q^{86} -5.47016 q^{87} -12.4920 q^{88} -6.53385 q^{89} -7.98029 q^{90} +24.4945 q^{91} -20.6384 q^{92} +15.1597 q^{93} +4.18050 q^{94} +15.1885 q^{95} +12.7311 q^{96} -15.9586 q^{97} -24.3499 q^{98} +7.83029 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 133 q + 14 q^{2} + 8 q^{3} + 142 q^{4} + 34 q^{5} + 20 q^{6} + 8 q^{7} + 42 q^{8} + 177 q^{9}+O(q^{10}) $ 133 * q + 14 * q^2 + 8 * q^3 + 142 * q^4 + 34 * q^5 + 20 * q^6 + 8 * q^7 + 42 * q^8 + 177 * q^9	\( 133 q + 14 q^{2} + 8 q^{3} + 142 q^{4} + 34 q^{5} + 20 q^{6} + 8 q^{7} + 42 q^{8} + 177 q^{9} + 9 q^{10} + 23 q^{11} + 24 q^{12} + 23 q^{13} + 31 q^{14} + 9 q^{15} + 168 q^{16} + 98 q^{17} + 38 q^{18} + 29 q^{19} + 83 q^{20} + 26 q^{21} + 2 q^{22} + 34 q^{23} + 75 q^{24} + 177 q^{25} + 67 q^{26} + 32 q^{27} + 32 q^{28} + 91 q^{29} + 12 q^{30} + 24 q^{31} + 88 q^{32} + 27 q^{33} + 23 q^{34} + 66 q^{35} + 232 q^{36} - 133 q^{37} + 26 q^{38} + 28 q^{39} + 41 q^{40} + 132 q^{41} + 13 q^{42} + 11 q^{43} + 65 q^{44} + 107 q^{45} + 20 q^{46} + 10 q^{47} + 27 q^{48} + 229 q^{49} + 78 q^{50} + 19 q^{51} + 71 q^{52} + 7 q^{53} + 43 q^{54} + 41 q^{55} + 67 q^{56} + 45 q^{57} + 25 q^{58} + 97 q^{59} - 42 q^{60} + 65 q^{61} + 24 q^{62} + 39 q^{63} + 200 q^{64} + 60 q^{65} + 35 q^{66} + 25 q^{67} + 227 q^{68} + 120 q^{69} + 37 q^{70} + 26 q^{71} + 93 q^{72} + 55 q^{73} - 14 q^{74} + 5 q^{75} + 34 q^{76} + 21 q^{77} - 2 q^{78} + 50 q^{79} + 162 q^{80} + 341 q^{81} + 66 q^{82} + 30 q^{83} - 89 q^{84} + 30 q^{85} - 12 q^{86} + 80 q^{87} - 85 q^{88} + 225 q^{89} - 86 q^{90} + q^{91} + 82 q^{92} + 42 q^{93} - 17 q^{94} + 70 q^{95} + 55 q^{96} + 12 q^{97} + 90 q^{98} + 17 q^{99}+O(q^{100}) \) 133 * q + 14 * q^2 + 8 * q^3 + 142 * q^4 + 34 * q^5 + 20 * q^6 + 8 * q^7 + 42 * q^8 + 177 * q^9 + 9 * q^10 + 23 * q^11 + 24 * q^12 + 23 * q^13 + 31 * q^14 + 9 * q^15 + 168 * q^16 + 98 * q^17 + 38 * q^18 + 29 * q^19 + 83 * q^20 + 26 * q^21 + 2 * q^22 + 34 * q^23 + 75 * q^24 + 177 * q^25 + 67 * q^26 + 32 * q^27 + 32 * q^28 + 91 * q^29 + 12 * q^30 + 24 * q^31 + 88 * q^32 + 27 * q^33 + 23 * q^34 + 66 * q^35 + 232 * q^36 - 133 * q^37 + 26 * q^38 + 28 * q^39 + 41 * q^40 + 132 * q^41 + 13 * q^42 + 11 * q^43 + 65 * q^44 + 107 * q^45 + 20 * q^46 + 10 * q^47 + 27 * q^48 + 229 * q^49 + 78 * q^50 + 19 * q^51 + 71 * q^52 + 7 * q^53 + 43 * q^54 + 41 * q^55 + 67 * q^56 + 45 * q^57 + 25 * q^58 + 97 * q^59 - 42 * q^60 + 65 * q^61 + 24 * q^62 + 39 * q^63 + 200 * q^64 + 60 * q^65 + 35 * q^66 + 25 * q^67 + 227 * q^68 + 120 * q^69 + 37 * q^70 + 26 * q^71 + 93 * q^72 + 55 * q^73 - 14 * q^74 + 5 * q^75 + 34 * q^76 + 21 * q^77 - 2 * q^78 + 50 * q^79 + 162 * q^80 + 341 * q^81 + 66 * q^82 + 30 * q^83 - 89 * q^84 + 30 * q^85 - 12 * q^86 + 80 * q^87 - 85 * q^88 + 225 * q^89 - 86 * q^90 + q^91 + 82 * q^92 + 42 * q^93 - 17 * q^94 + 70 * q^95 + 55 * q^96 + 12 * q^97 + 90 * q^98 + 17 * 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 $

$2$	−2.27893	−1.61145	−0.805724	−	0.592291i	$-0.798224\pi$
$2$	−2.27893	−1.61145	−0.805724	+	0.592291i	$0.798224\pi$
$3$	2.16909	1.25232	0.626162	−	0.779693i	$-0.284625\pi$
$3$	2.16909	1.25232	0.626162	+	0.779693i	$0.284625\pi$
$4$	3.19353	1.59677
$5$	2.05388	0.918523	0.459261	−	0.888301i	$-0.348114\pi$
$5$	2.05388	0.918523	0.459261	+	0.888301i	$0.348114\pi$
$6$	−4.94321	−2.01806
$7$	−4.20533	−1.58946	−0.794732	−	0.606960i	$-0.792389\pi$
$7$	−4.20533	−1.58946	−0.794732	+	0.606960i	$0.792389\pi$
$8$	−2.71998	−0.961657
$9$	1.70495	0.568317
$10$	−4.68065	−1.48015
$11$	4.59267	1.38474	0.692372	−	0.721541i	$-0.256566\pi$
$11$	4.59267	1.38474	0.692372	+	0.721541i	$0.256566\pi$
$12$	6.92706	1.99967
$13$	−5.82463	−1.61546	−0.807731	−	0.589551i	$-0.799305\pi$
$13$	−5.82463	−1.61546	−0.807731	+	0.589551i	$0.799305\pi$
$14$	9.58365	2.56134
$15$	4.45505	1.15029
$16$	−0.188418	−0.0471046
$17$	0.108379	0.0262857	0.0131428	−	0.999914i	$-0.495816\pi$
$17$	0.108379	0.0262857	0.0131428	+	0.999914i	$0.495816\pi$
$18$	−3.88547	−0.915814
$19$	7.39501	1.69653	0.848266	−	0.529571i	$-0.177647\pi$
$19$	7.39501	1.69653	0.848266	+	0.529571i	$0.177647\pi$
$20$	6.55913	1.46667
$21$	−9.12173	−1.99053
$22$	−10.4664	−2.23144
$23$	−6.46256	−1.34754	−0.673768	−	0.738943i	$-0.735325\pi$
$23$	−6.46256	−1.34754	−0.673768	+	0.738943i	$0.735325\pi$
$24$	−5.89988	−1.20431
$25$	−0.781579	−0.156316
$26$	13.2739	2.60323
$27$	−2.80908	−0.540607
$28$	−13.4298	−2.53800
$29$	−2.52187	−0.468299	−0.234150	−	0.972201i	$-0.575231\pi$
$29$	−2.52187	−0.468299	−0.234150	+	0.972201i	$0.575231\pi$
$30$	−10.1528	−1.85363
$31$	6.98897	1.25526	0.627628	−	0.778514i	$-0.284026\pi$
$31$	6.98897	1.25526	0.627628	+	0.778514i	$0.284026\pi$
$32$	5.86935	1.03756
$33$	9.96192	1.73415
$34$	−0.246987	−0.0423580
$35$	−8.63724	−1.45996
$36$	5.44482	0.907470
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	−16.8527	−2.73387
$39$	−12.6341	−2.02308
$40$	−5.58651	−0.883304
$41$	3.22113	0.503056	0.251528	−	0.967850i	$-0.419067\pi$
$41$	3.22113	0.503056	0.251528	+	0.967850i	$0.419067\pi$
$42$	20.7878	3.20763
$43$	8.71497	1.32902	0.664510	−	0.747279i	$-0.268640\pi$
$43$	8.71497	1.32902	0.664510	+	0.747279i	$0.268640\pi$
$44$	14.6668	2.21111
$45$	3.50177	0.522012
$46$	14.7277	2.17149
$47$	−1.83441	−0.267576	−0.133788	−	0.991010i	$-0.542714\pi$
$47$	−1.83441	−0.267576	−0.133788	+	0.991010i	$0.542714\pi$
$48$	−0.408696	−0.0589902
$49$	10.6848	1.52640
$50$	1.78116	0.251895
$51$	0.235083	0.0329182
$52$	−18.6011	−2.57951
$53$	−6.34346	−0.871341	−0.435671	−	0.900106i	$-0.643489\pi$
$53$	−6.34346	−0.871341	−0.435671	+	0.900106i	$0.643489\pi$
$54$	6.40169	0.871160
$55$	9.43280	1.27192
$56$	11.4384	1.52852
$57$	16.0404	2.12461
$58$	5.74717	0.754640
$59$	3.43767	0.447546	0.223773	−	0.974641i	$-0.428163\pi$
$59$	3.43767	0.447546	0.223773	+	0.974641i	$0.428163\pi$
$60$	14.2273	1.83674
$61$	−7.08449	−0.907076	−0.453538	−	0.891237i	$-0.649838\pi$
$61$	−7.08449	−0.907076	−0.453538	+	0.891237i	$0.649838\pi$
$62$	−15.9274	−2.02278
$63$	−7.16988	−0.903320
$64$	−12.9990	−1.62488
$65$	−11.9631	−1.48384
$66$	−22.7025	−2.79449
$67$	14.7522	1.80227	0.901134	−	0.433541i	$-0.142736\pi$
$67$	14.7522	1.80227	0.901134	+	0.433541i	$0.142736\pi$
$68$	0.346110	0.0419721
$69$	−14.0179	−1.68755
$70$	19.6837	2.35265
$71$	8.21120	0.974490	0.487245	−	0.873265i	$-0.338002\pi$
$71$	8.21120	0.974490	0.487245	+	0.873265i	$0.338002\pi$
$72$	−4.63743	−0.546527
$73$	10.5250	1.23186	0.615928	−	0.787802i	$-0.288781\pi$
$73$	10.5250	1.23186	0.615928	+	0.787802i	$0.288781\pi$
$74$	2.27893	0.264920
$75$	−1.69531	−0.195758
$76$	23.6162	2.70896
$77$	−19.3137	−2.20100
$78$	28.7924	3.26009
$79$	13.3156	1.49812	0.749059	−	0.662503i	$-0.230506\pi$
$79$	13.3156	1.49812	0.749059	+	0.662503i	$0.230506\pi$
$80$	−0.386988	−0.0432666
$81$	−11.2080	−1.24533
$82$	−7.34073	−0.810649
$83$	16.1527	1.77299	0.886494	−	0.462739i	$-0.153133\pi$
$83$	16.1527	1.77299	0.886494	+	0.462739i	$0.153133\pi$
$84$	−29.1305	−3.17840
$85$	0.222597	0.0241440
$86$	−19.8608	−2.14165
$87$	−5.47016	−0.586463
$88$	−12.4920	−1.33165
$89$	−6.53385	−0.692587	−0.346293	−	0.938126i	$-0.612560\pi$
$89$	−6.53385	−0.692587	−0.346293	+	0.938126i	$0.612560\pi$
$90$	−7.98029	−0.841196
$91$	24.4945	2.56772
$92$	−20.6384	−2.15170
$93$	15.1597	1.57199
$94$	4.18050	0.431185
$95$	15.1885	1.55830
$96$	12.7311	1.29937
$97$	−15.9586	−1.62035	−0.810174	−	0.586190i	$-0.800627\pi$
$97$	−15.9586	−1.62035	−0.810174	+	0.586190i	$0.800627\pi$
$98$	−24.3499	−2.45971
$99$	7.83029	0.786973
$100$	−2.49600	−0.249600
$101$	−3.23571	−0.321965	−0.160983	−	0.986957i	$-0.551466\pi$
$101$	−3.23571	−0.321965	−0.160983	+	0.986957i	$0.551466\pi$
$102$	−0.535738	−0.0530460
$103$	−15.5334	−1.53055	−0.765274	−	0.643704i	$-0.777397\pi$
$103$	−15.5334	−1.53055	−0.765274	+	0.643704i	$0.777397\pi$
$104$	15.8429	1.55352
$105$	−18.7349	−1.82834
$106$	14.4563	1.40412
$107$	−7.79363	−0.753438	−0.376719	−	0.926328i	$-0.622948\pi$
$107$	−7.79363	−0.753438	−0.376719	+	0.926328i	$0.622948\pi$
$108$	−8.97087	−0.863223
$109$	8.37928	0.802590	0.401295	−	0.915949i	$-0.368560\pi$
$109$	8.37928	0.802590	0.401295	+	0.915949i	$0.368560\pi$
$110$	−21.4967	−2.04963
$111$	−2.16909	−0.205881
$112$	0.792360	0.0748710
$113$	8.71776	0.820098	0.410049	−	0.912064i	$-0.365512\pi$
$113$	8.71776	0.820098	0.410049	+	0.912064i	$0.365512\pi$
$114$	−36.5551	−3.42370
$115$	−13.2733	−1.23774
$116$	−8.05367	−0.747765
$117$	−9.93071	−0.918095
$118$	−7.83421	−0.721197
$119$	−0.455767	−0.0417801
$120$	−12.1176	−1.10618
$121$	10.0927	0.917514
$122$	16.1451	1.46171
$123$	6.98692	0.629989
$124$	22.3195	2.00435
$125$	−11.8747	−1.06210
$126$	16.3397	1.45565
$127$	19.2005	1.70377	0.851887	−	0.523726i	$-0.175459\pi$
$127$	19.2005	1.70377	0.851887	+	0.523726i	$0.175459\pi$
$128$	17.8852	1.58084
$129$	18.9036	1.66437
$130$	27.2631	2.39113
$131$	4.08012	0.356482	0.178241	−	0.983987i	$-0.442959\pi$
$131$	4.08012	0.356482	0.178241	+	0.983987i	$0.442959\pi$
$132$	31.8137	2.76903
$133$	−31.0984	−2.69658
$134$	−33.6193	−2.90426
$135$	−5.76950	−0.496560
$136$	−0.294787	−0.0252778
$137$	−2.97414	−0.254098	−0.127049	−	0.991896i	$-0.540551\pi$
$137$	−2.97414	−0.254098	−0.127049	+	0.991896i	$0.540551\pi$
$138$	31.9458	2.71941
$139$	1.02746	0.0871476	0.0435738	−	0.999050i	$-0.486126\pi$
$139$	1.02746	0.0871476	0.0435738	+	0.999050i	$0.486126\pi$
$140$	−27.5833	−2.33121
$141$	−3.97900	−0.335092
$142$	−18.7128	−1.57034
$143$	−26.7506	−2.23700
$144$	−0.321244	−0.0267703
$145$	−5.17962	−0.430144
$146$	−23.9857	−1.98507
$147$	23.1762	1.91154
$148$	−3.19353	−0.262507
$149$	20.8668	1.70948	0.854738	−	0.519060i	$-0.173718\pi$
$149$	20.8668	1.70948	0.854738	+	0.519060i	$0.173718\pi$
$150$	3.86351	0.315454
$151$	−4.60859	−0.375042	−0.187521	−	0.982261i	$-0.560045\pi$
$151$	−4.60859	−0.375042	−0.187521	+	0.982261i	$0.560045\pi$
$152$	−20.1143	−1.63148
$153$	0.184780	0.0149386
$154$	44.0146	3.54680
$155$	14.3545	1.15298
$156$	−40.3476	−3.23039
$157$	−2.45217	−0.195704	−0.0978522	−	0.995201i	$-0.531197\pi$
$157$	−2.45217	−0.195704	−0.0978522	+	0.995201i	$0.531197\pi$
$158$	−30.3453	−2.41414
$159$	−13.7595	−1.09120
$160$	12.0549	0.953026
$161$	27.1772	2.14186
$162$	25.5423	2.00679
$163$	1.00000	0.0783260
$163$	1.00000	0.0783260
$164$	10.2868	0.803262
$165$	20.4606	1.59285
$166$	−36.8109	−2.85708
$167$	18.8280	1.45696	0.728478	−	0.685069i	$-0.240228\pi$
$167$	18.8280	1.45696	0.728478	+	0.685069i	$0.240228\pi$
$168$	24.8109	1.91420
$169$	20.9263	1.60972
$170$	−0.507282	−0.0389068
$171$	12.6081	0.964168
$172$	27.8315	2.12213
$173$	13.0528	0.992385	0.496193	−	0.868212i	$-0.334731\pi$
$173$	13.0528	0.992385	0.496193	+	0.868212i	$0.334731\pi$
$174$	12.4661	0.945055
$175$	3.28679	0.248458
$176$	−0.865343	−0.0652277
$177$	7.45661	0.560473
$178$	14.8902	1.11607
$179$	19.7553	1.47658	0.738291	−	0.674482i	$-0.235633\pi$
$179$	19.7553	1.47658	0.738291	+	0.674482i	$0.235633\pi$
$180$	11.1830	0.833532
$181$	−2.40263	−0.178586	−0.0892930	−	0.996005i	$-0.528461\pi$
$181$	−2.40263	−0.178586	−0.0892930	+	0.996005i	$0.528461\pi$
$182$	−55.8212	−4.13775
$183$	−15.3669	−1.13595
$184$	17.5780	1.29587
$185$	−2.05388	−0.151004
$186$	−34.5479	−2.53318
$187$	0.497747	0.0363989
$188$	−5.85825	−0.427257
$189$	11.8131	0.859275
$190$	−34.6135	−2.51112
$191$	−8.02052	−0.580344	−0.290172	−	0.956974i	$-0.593713\pi$
$191$	−8.02052	−0.580344	−0.290172	+	0.956974i	$0.593713\pi$
$192$	−28.1960	−2.03487
$193$	18.4999	1.33165	0.665825	−	0.746108i	$-0.268080\pi$
$193$	18.4999	1.33165	0.665825	+	0.746108i	$0.268080\pi$
$194$	36.3685	2.61111
$195$	−25.9490	−1.85825
$196$	34.1222	2.43730
$197$	−8.83344	−0.629356	−0.314678	−	0.949198i	$-0.601897\pi$
$197$	−8.83344	−0.629356	−0.314678	+	0.949198i	$0.601897\pi$
$198$	−17.8447	−1.26817
$199$	7.49780	0.531505	0.265752	−	0.964041i	$-0.414380\pi$
$199$	7.49780	0.531505	0.265752	+	0.964041i	$0.414380\pi$
$200$	2.12588	0.150322
$201$	31.9989	2.25702
$202$	7.37396	0.518830
$203$	10.6053	0.744345
$204$	0.750745	0.0525626
$205$	6.61581	0.462068
$206$	35.3995	2.46640
$207$	−11.0184	−0.765828
$208$	1.09747	0.0760956
$209$	33.9629	2.34926
$210$	42.6957	2.94628
$211$	−3.69343	−0.254266	−0.127133	−	0.991886i	$-0.540578\pi$
$211$	−3.69343	−0.254266	−0.127133	+	0.991886i	$0.540578\pi$
$212$	−20.2580	−1.39133
$213$	17.8108	1.22038
$214$	17.7611	1.21413
$215$	17.8995	1.22074
$216$	7.64063	0.519879
$217$	−29.3909	−1.99518
$218$	−19.0958	−1.29333
$219$	22.8296	1.54268
$220$	30.1239	2.03096
$221$	−0.631265	−0.0424635
$222$	4.94321	0.331766
$223$	14.1857	0.949945	0.474973	−	0.880001i	$-0.342458\pi$
$223$	14.1857	0.949945	0.474973	+	0.880001i	$0.342458\pi$
$224$	−24.6825	−1.64917
$225$	−1.33255	−0.0888369
$226$	−19.8672	−1.32154
$227$	23.2879	1.54567	0.772837	−	0.634605i	$-0.218837\pi$
$227$	23.2879	1.54567	0.772837	+	0.634605i	$0.218837\pi$
$228$	51.2256	3.39250
$229$	19.5275	1.29041	0.645207	−	0.764008i	$-0.276771\pi$
$229$	19.5275	1.29041	0.645207	+	0.764008i	$0.276771\pi$
$230$	30.2490	1.99456
$231$	−41.8931	−2.75637
$232$	6.85943	0.450344
$233$	−9.33242	−0.611387	−0.305694	−	0.952130i	$-0.598888\pi$
$233$	−9.33242	−0.611387	−0.305694	+	0.952130i	$0.598888\pi$
$234$	22.6314	1.47946
$235$	−3.76766	−0.245775
$236$	10.9783	0.714626
$237$	28.8827	1.87613
$238$	1.03866	0.0673265
$239$	10.8003	0.698615	0.349307	−	0.937008i	$-0.386417\pi$
$239$	10.8003	0.698615	0.349307	+	0.937008i	$0.386417\pi$
$240$	−0.839413	−0.0541838
$241$	18.4174	1.18637	0.593184	−	0.805067i	$-0.297871\pi$
$241$	18.4174	1.18637	0.593184	+	0.805067i	$0.297871\pi$
$242$	−23.0005	−1.47853
$243$	−15.8839	−1.01895
$244$	−22.6245	−1.44839
$245$	21.9452	1.40203
$246$	−15.9227	−1.01520
$247$	−43.0732	−2.74068
$248$	−19.0098	−1.20713
$249$	35.0367	2.22036
$250$	27.0616	1.71152
$251$	−14.3379	−0.904998	−0.452499	−	0.891765i	$-0.649467\pi$
$251$	−14.3379	−0.904998	−0.452499	+	0.891765i	$0.649467\pi$
$252$	−22.8972	−1.44239
$253$	−29.6804	−1.86599
$254$	−43.7567	−2.74554
$255$	0.482832	0.0302361
$256$	−14.7611	−0.922566
$257$	13.2502	0.826525	0.413262	−	0.910612i	$-0.364389\pi$
$257$	13.2502	0.826525	0.413262	+	0.910612i	$0.364389\pi$
$258$	−43.0799	−2.68204
$259$	4.20533	0.261306
$260$	−38.2045	−2.36934
$261$	−4.29967	−0.266143
$262$	−9.29832	−0.574452
$263$	0.765699	0.0472150	0.0236075	−	0.999721i	$-0.492485\pi$
$263$	0.765699	0.0472150	0.0236075	+	0.999721i	$0.492485\pi$
$264$	−27.0962	−1.66766
$265$	−13.0287	−0.800347
$266$	70.8712	4.34539
$267$	−14.1725	−0.867343
$268$	47.1116	2.87780
$269$	−13.2097	−0.805412	−0.402706	−	0.915329i	$-0.631930\pi$
$269$	−13.2097	−0.805412	−0.402706	+	0.915329i	$0.631930\pi$
$270$	13.1483	0.800181
$271$	−3.24964	−0.197401	−0.0987006	−	0.995117i	$-0.531469\pi$
$271$	−3.24964	−0.197401	−0.0987006	+	0.995117i	$0.531469\pi$
$272$	−0.0204205	−0.00123817
$273$	53.1307	3.21562
$274$	6.77787	0.409466
$275$	−3.58954	−0.216457
$276$	−44.7665	−2.69463
$277$	3.24333	0.194873	0.0974365	−	0.995242i	$-0.468936\pi$
$277$	3.24333	0.194873	0.0974365	+	0.995242i	$0.468936\pi$
$278$	−2.34150	−0.140434
$279$	11.9158	0.713383
$280$	23.4931	1.40398
$281$	−12.0682	−0.719927	−0.359963	−	0.932966i	$-0.617211\pi$
$281$	−12.0682	−0.719927	−0.359963	+	0.932966i	$0.617211\pi$
$282$	9.06787	0.539984
$283$	−26.7246	−1.58861	−0.794306	−	0.607518i	$-0.792165\pi$
$283$	−26.7246	−1.58861	−0.794306	+	0.607518i	$0.792165\pi$
$284$	26.2227	1.55603
$285$	32.9451	1.95150
$286$	60.9629	3.60481
$287$	−13.5459	−0.799589
$288$	10.0070	0.589666
$289$	−16.9883	−0.999309
$290$	11.8040	0.693154
$291$	−34.6156	−2.02920
$292$	33.6119	1.96699
$293$	−29.3029	−1.71189	−0.855947	−	0.517063i	$-0.827025\pi$
$293$	−29.3029	−1.71189	−0.855947	+	0.517063i	$0.827025\pi$
$294$	−52.8171	−3.08035
$295$	7.06055	0.411081
$296$	2.71998	0.158096
$297$	−12.9012	−0.748602
$298$	−47.5540	−2.75473
$299$	37.6420	2.17689
$300$	−5.41404	−0.312580
$301$	−36.6493	−2.11243
$302$	10.5027	0.604360
$303$	−7.01855	−0.403205
$304$	−1.39335	−0.0799143
$305$	−14.5507	−0.833170
$306$	−0.421102	−0.0240728
$307$	−11.0948	−0.633211	−0.316606	−	0.948557i	$-0.602543\pi$
$307$	−11.0948	−0.633211	−0.316606	+	0.948557i	$0.602543\pi$
$308$	−61.6789	−3.51448
$309$	−33.6933	−1.91674
$310$	−32.7129	−1.85797
$311$	14.6518	0.830827	0.415413	−	0.909633i	$-0.363637\pi$
$311$	14.6518	0.830827	0.415413	+	0.909633i	$0.363637\pi$
$312$	34.3646	1.94551
$313$	19.2674	1.08906	0.544529	−	0.838742i	$-0.316708\pi$
$313$	19.2674	1.08906	0.544529	+	0.838742i	$0.316708\pi$
$314$	5.58833	0.315367
$315$	−14.7261	−0.829720
$316$	42.5237	2.39215
$317$	−14.9657	−0.840555	−0.420277	−	0.907396i	$-0.638067\pi$
$317$	−14.9657	−0.840555	−0.420277	+	0.907396i	$0.638067\pi$
$318$	31.3570	1.75842
$319$	−11.5821	−0.648474
$320$	−26.6984	−1.49249
$321$	−16.9051	−0.943550
$322$	−61.9349	−3.45150
$323$	0.801460	0.0445944
$324$	−35.7931	−1.98850
$325$	4.55241	0.252522
$326$	−2.27893	−0.126218
$327$	18.1754	1.00510
$328$	−8.76140	−0.483767
$329$	7.71430	0.425303
$330$	−46.6283	−2.56680
$331$	0.991384	0.0544914	0.0272457	−	0.999629i	$-0.491326\pi$
$331$	0.991384	0.0544914	0.0272457	+	0.999629i	$0.491326\pi$
$332$	51.5841	2.83105
$333$	−1.70495	−0.0934308
$334$	−42.9078	−2.34781
$335$	30.2992	1.65542
$336$	1.71870	0.0937628
$337$	−0.879684	−0.0479194	−0.0239597	−	0.999713i	$-0.507627\pi$
$337$	−0.879684	−0.0479194	−0.0239597	+	0.999713i	$0.507627\pi$
$338$	−47.6897	−2.59398
$339$	18.9096	1.02703
$340$	0.710869	0.0385523
$341$	32.0980	1.73821
$342$	−28.7331	−1.55371
$343$	−15.4957	−0.836688
$344$	−23.7045	−1.27806
$345$	−28.7910	−1.55006
$346$	−29.7464	−1.59918
$347$	22.1730	1.19031	0.595156	−	0.803610i	$-0.297090\pi$
$347$	22.1730	1.19031	0.595156	+	0.803610i	$0.297090\pi$
$348$	−17.4691	−0.936444
$349$	−14.3541	−0.768358	−0.384179	−	0.923259i	$-0.625516\pi$
$349$	−14.3541	−0.768358	−0.384179	+	0.923259i	$0.625516\pi$
$350$	−7.49038	−0.400378
$351$	16.3618	0.873330
$352$	26.9560	1.43676
$353$	−1.41109	−0.0751046	−0.0375523	−	0.999295i	$-0.511956\pi$
$353$	−1.41109	−0.0751046	−0.0375523	+	0.999295i	$0.511956\pi$
$354$	−16.9931	−0.903173
$355$	16.8648	0.895091
$356$	−20.8661	−1.10590
$357$	−0.988600	−0.0523223
$358$	−45.0210	−2.37944
$359$	−0.422995	−0.0223248	−0.0111624	−	0.999938i	$-0.503553\pi$
$359$	−0.422995	−0.0223248	−0.0111624	+	0.999938i	$0.503553\pi$
$360$	−9.52473	−0.501997
$361$	35.6861	1.87822
$362$	5.47543	0.287782
$363$	21.8919	1.14903
$364$	78.2239	4.10005
$365$	21.6170	1.13149
$366$	35.0201	1.83053
$367$	9.63825	0.503113	0.251556	−	0.967843i	$-0.419058\pi$
$367$	9.63825	0.503113	0.251556	+	0.967843i	$0.419058\pi$
$368$	1.21766	0.0634751
$369$	5.49187	0.285895
$370$	4.68065	0.243336
$371$	26.6763	1.38497
$372$	48.4130	2.51010
$373$	−29.3435	−1.51935	−0.759674	−	0.650304i	$-0.774641\pi$
$373$	−29.3435	−1.51935	−0.759674	+	0.650304i	$0.774641\pi$
$374$	−1.13433	−0.0586549
$375$	−25.7572	−1.33010
$376$	4.98956	0.257317
$377$	14.6890	0.756520
$378$	−26.9212	−1.38468
$379$	3.41769	0.175555	0.0877774	−	0.996140i	$-0.472024\pi$
$379$	3.41769	0.175555	0.0877774	+	0.996140i	$0.472024\pi$
$380$	48.5048	2.48824
$381$	41.6477	2.13368
$382$	18.2782	0.935195
$383$	17.5086	0.894649	0.447324	−	0.894372i	$-0.352377\pi$
$383$	17.5086	0.894649	0.447324	+	0.894372i	$0.352377\pi$
$384$	38.7945	1.97973
$385$	−39.6680	−2.02167
$386$	−42.1599	−2.14588
$387$	14.8586	0.755305
$388$	−50.9642	−2.58732
$389$	−21.4604	−1.08809	−0.544043	−	0.839058i	$-0.683107\pi$
$389$	−21.4604	−1.08809	−0.544043	+	0.839058i	$0.683107\pi$
$390$	59.1361	2.99447
$391$	−0.700403	−0.0354209
$392$	−29.0624	−1.46787
$393$	8.85016	0.446431
$394$	20.1308	1.01418
$395$	27.3486	1.37606
$396$	25.0063	1.25661
$397$	21.1800	1.06300	0.531498	−	0.847060i	$-0.321629\pi$
$397$	21.1800	1.06300	0.531498	+	0.847060i	$0.321629\pi$
$398$	−17.0870	−0.856493
$399$	−67.4553	−3.37699
$400$	0.147264	0.00736318
$401$	23.5552	1.17629	0.588145	−	0.808756i	$-0.299858\pi$
$401$	23.5552	1.17629	0.588145	+	0.808756i	$0.299858\pi$
$402$	−72.9232	−3.63708
$403$	−40.7081	−2.02782
$404$	−10.3333	−0.514103
$405$	−23.0199	−1.14387
$406$	−24.1687	−1.19947
$407$	−4.59267	−0.227650
$408$	−0.639420	−0.0316560
$409$	−4.62663	−0.228772	−0.114386	−	0.993436i	$-0.536490\pi$
$409$	−4.62663	−0.228772	−0.114386	+	0.993436i	$0.536490\pi$
$410$	−15.0770	−0.744599
$411$	−6.45118	−0.318213
$412$	−49.6063	−2.44393
$413$	−14.4565	−0.711358
$414$	25.1101	1.23409
$415$	33.1757	1.62853
$416$	−34.1868	−1.67615
$417$	2.22864	0.109137
$418$	−77.3990	−3.78571
$419$	−20.9541	−1.02368	−0.511838	−	0.859082i	$-0.671035\pi$
$419$	−20.9541	−1.02368	−0.511838	+	0.859082i	$0.671035\pi$
$420$	−59.8306	−2.91944
$421$	−11.8492	−0.577493	−0.288746	−	0.957406i	$-0.593238\pi$
$421$	−11.8492	−0.577493	−0.288746	+	0.957406i	$0.593238\pi$
$422$	8.41708	0.409737
$423$	−3.12758	−0.152068
$424$	17.2541	0.837932
$425$	−0.0847064	−0.00410886
$426$	−40.5897	−1.96658
$427$	29.7926	1.44176
$428$	−24.8892	−1.20306
$429$	−58.0245	−2.80145
$430$	−40.7917	−1.96715
$431$	23.6766	1.14046	0.570230	−	0.821485i	$-0.306854\pi$
$431$	23.6766	1.14046	0.570230	+	0.821485i	$0.306854\pi$
$432$	0.529281	0.0254651
$433$	−37.2537	−1.79030	−0.895149	−	0.445766i	$-0.852931\pi$
$433$	−37.2537	−1.79030	−0.895149	+	0.445766i	$0.852931\pi$
$434$	66.9798	3.21513
$435$	−11.2351	−0.538680
$436$	26.7595	1.28155
$437$	−47.7907	−2.28614
$438$	−52.0272	−2.48596
$439$	30.6492	1.46281	0.731403	−	0.681946i	$-0.238866\pi$
$439$	30.6492	1.46281	0.731403	+	0.681946i	$0.238866\pi$
$440$	−25.6570	−1.22315
$441$	18.2170	0.867477
$442$	1.43861	0.0684277
$443$	−4.11907	−0.195703	−0.0978514	−	0.995201i	$-0.531197\pi$
$443$	−4.11907	−0.195703	−0.0978514	+	0.995201i	$0.531197\pi$
$444$	−6.92706	−0.328744
$445$	−13.4197	−0.636157
$446$	−32.3283	−1.53079
$447$	45.2620	2.14082
$448$	54.6651	2.58268
$449$	−5.74593	−0.271167	−0.135584	−	0.990766i	$-0.543291\pi$
$449$	−5.74593	−0.271167	−0.135584	+	0.990766i	$0.543291\pi$
$450$	3.03680	0.143156
$451$	14.7936	0.696603
$452$	27.8404	1.30950
$453$	−9.99645	−0.469674
$454$	−53.0716	−2.49077
$455$	50.3087	2.35851
$456$	−43.6296	−2.04315
$457$	−7.10168	−0.332203	−0.166101	−	0.986109i	$-0.553118\pi$
$457$	−7.10168	−0.332203	−0.166101	+	0.986109i	$0.553118\pi$
$458$	−44.5019	−2.07944
$459$	−0.304444	−0.0142102
$460$	−42.3888	−1.97639
$461$	30.0886	1.40137	0.700684	−	0.713472i	$-0.252878\pi$
$461$	30.0886	1.40137	0.700684	+	0.713472i	$0.252878\pi$
$462$	95.4716	4.44174
$463$	−23.9992	−1.11534	−0.557668	−	0.830064i	$-0.688304\pi$
$463$	−23.9992	−1.11534	−0.557668	+	0.830064i	$0.688304\pi$
$464$	0.475166	0.0220590
$465$	31.1362	1.44391
$466$	21.2680	0.985219
$467$	1.22602	0.0567334	0.0283667	−	0.999598i	$-0.490969\pi$
$467$	1.22602	0.0567334	0.0283667	+	0.999598i	$0.490969\pi$
$468$	−31.7141	−1.46598
$469$	−62.0378	−2.86464
$470$	8.58624	0.396054
$471$	−5.31897	−0.245085
$472$	−9.35037	−0.430386
$473$	40.0250	1.84035
$474$	−65.8217	−3.02329
$475$	−5.77978	−0.265195
$476$	−1.45551	−0.0667131
$477$	−10.8153	−0.495198
$478$	−24.6132	−1.12578
$479$	−9.69163	−0.442822	−0.221411	−	0.975181i	$-0.571066\pi$
$479$	−9.69163	−0.442822	−0.221411	+	0.975181i	$0.571066\pi$
$480$	26.1482	1.19350
$481$	5.82463	0.265580
$482$	−41.9719	−1.91177
$483$	58.9497	2.68231
$484$	32.2312	1.46505
$485$	−32.7770	−1.48833
$486$	36.1984	1.64199
$487$	−17.9547	−0.813604	−0.406802	−	0.913516i	$-0.633356\pi$
$487$	−17.9547	−0.813604	−0.406802	+	0.913516i	$0.633356\pi$
$488$	19.2697	0.872296
$489$	2.16909	0.0980896
$490$	−50.0117	−2.25930
$491$	−13.1073	−0.591523	−0.295762	−	0.955262i	$-0.595573\pi$
$491$	−13.1073	−0.591523	−0.295762	+	0.955262i	$0.595573\pi$
$492$	22.3129	1.00595
$493$	−0.273317	−0.0123096
$494$	98.1609	4.41647
$495$	16.0825	0.722853
$496$	−1.31685	−0.0591282
$497$	−34.5308	−1.54892
$498$	−79.8462	−3.57799
$499$	8.33773	0.373248	0.186624	−	0.982431i	$-0.440245\pi$
$499$	8.33773	0.373248	0.186624	+	0.982431i	$0.440245\pi$
$500$	−37.9221	−1.69593
$501$	40.8397	1.82458
$502$	32.6750	1.45836
$503$	7.30103	0.325537	0.162769	−	0.986664i	$-0.447958\pi$
$503$	7.30103	0.325537	0.162769	+	0.986664i	$0.447958\pi$
$504$	19.5019	0.868684
$505$	−6.64576	−0.295732
$506$	67.6397	3.00695
$507$	45.3911	2.01589
$508$	61.3176	2.72053
$509$	−3.14249	−0.139289	−0.0696443	−	0.997572i	$-0.522186\pi$
$509$	−3.14249	−0.139289	−0.0696443	+	0.997572i	$0.522186\pi$
$510$	−1.10034	−0.0487239
$511$	−44.2610	−1.95799
$512$	−2.13088	−0.0941724
$513$	−20.7731	−0.917157
$514$	−30.1963	−1.33190
$515$	−31.9037	−1.40584
$516$	60.3691	2.65760
$517$	−8.42485	−0.370524
$518$	−9.58365	−0.421082
$519$	28.3127	1.24279
$520$	32.5393	1.42694
$521$	29.7982	1.30548	0.652742	−	0.757580i	$-0.273619\pi$
$521$	29.7982	1.30548	0.652742	+	0.757580i	$0.273619\pi$
$522$	9.79865	0.428875
$523$	−11.6955	−0.511407	−0.255704	−	0.966755i	$-0.582307\pi$
$523$	−11.6955	−0.511407	−0.255704	+	0.966755i	$0.582307\pi$
$524$	13.0300	0.569218
$525$	7.12935	0.311150
$526$	−1.74498	−0.0760846
$527$	0.757454	0.0329952
$528$	−1.87701	−0.0816863
$529$	18.7647	0.815855
$530$	29.6915	1.28972
$531$	5.86105	0.254348
$532$	−99.3138	−4.30580
$533$	−18.7619	−0.812667
$534$	32.2982	1.39768
$535$	−16.0072	−0.692050
$536$	−40.1257	−1.73316
$537$	42.8511	1.84916
$538$	30.1041	1.29788
$539$	49.0717	2.11367
$540$	−18.4251	−0.792890
$541$	1.79676	0.0772486	0.0386243	−	0.999254i	$-0.487702\pi$
$541$	1.79676	0.0772486	0.0386243	+	0.999254i	$0.487702\pi$
$542$	7.40570	0.318102
$543$	−5.21152	−0.223648
$544$	0.636112	0.0272731
$545$	17.2100	0.737197
$546$	−121.081	−5.18180
$547$	−39.0950	−1.67158	−0.835792	−	0.549047i	$-0.814991\pi$
$547$	−39.0950	−1.67158	−0.835792	+	0.549047i	$0.814991\pi$
$548$	−9.49801	−0.405735
$549$	−12.0787	−0.515507
$550$	8.18031	0.348810
$551$	−18.6492	−0.794485
$552$	38.1283	1.62285
$553$	−55.9963	−2.38121
$554$	−7.39134	−0.314028
$555$	−4.45505	−0.189106
$556$	3.28121	0.139154
$557$	−2.13218	−0.0903434	−0.0451717	−	0.998979i	$-0.514383\pi$
$557$	−2.13218	−0.0903434	−0.0451717	+	0.998979i	$0.514383\pi$
$558$	−27.1554	−1.14958
$559$	−50.7615	−2.14698
$560$	1.62741	0.0687707
$561$	1.07966	0.0455832
$562$	27.5025	1.16012
$563$	−0.583463	−0.0245900	−0.0122950	−	0.999924i	$-0.503914\pi$
$563$	−0.583463	−0.0245900	−0.0122950	+	0.999924i	$0.503914\pi$
$564$	−12.7071	−0.535064
$565$	17.9052	0.753278
$566$	60.9035	2.55997
$567$	47.1333	1.97941
$568$	−22.3343	−0.937125
$569$	24.5130	1.02764	0.513820	−	0.857898i	$-0.328230\pi$
$569$	24.5130	1.02764	0.513820	+	0.857898i	$0.328230\pi$
$570$	−75.0797	−3.14474
$571$	−11.4186	−0.477855	−0.238928	−	0.971037i	$-0.576796\pi$
$571$	−11.4186	−0.477855	−0.238928	+	0.971037i	$0.576796\pi$
$572$	−85.4290	−3.57196
$573$	−17.3972	−0.726780
$574$	30.8702	1.28850
$575$	5.05100	0.210641
$576$	−22.1627	−0.923445
$577$	42.1839	1.75614	0.878068	−	0.478535i	$-0.158832\pi$
$577$	42.1839	1.75614	0.878068	+	0.478535i	$0.158832\pi$
$578$	38.7151	1.61033
$579$	40.1279	1.66766
$580$	−16.5413	−0.686839
$581$	−67.9274	−2.81810
$582$	78.8865	3.26995
$583$	−29.1334	−1.20658
$584$	−28.6277	−1.18462
$585$	−20.3965	−0.843291
$586$	66.7794	2.75863
$587$	−29.9323	−1.23544	−0.617719	−	0.786399i	$-0.711943\pi$
$587$	−29.9323	−1.23544	−0.617719	+	0.786399i	$0.711943\pi$
$588$	74.0141	3.05229
$589$	51.6835	2.12958
$590$	−16.0905	−0.662436
$591$	−19.1605	−0.788159
$592$	0.188418	0.00774394
$593$	−14.4682	−0.594137	−0.297069	−	0.954856i	$-0.596009\pi$
$593$	−14.4682	−0.594137	−0.297069	+	0.954856i	$0.596009\pi$
$594$	29.4009	1.20633
$595$	−0.936091	−0.0383760
$596$	66.6388	2.72963
$597$	16.2634	0.665617
$598$	−85.7836	−3.50795
$599$	42.9934	1.75666	0.878331	−	0.478053i	$-0.158657\pi$
$599$	42.9934	1.75666	0.878331	+	0.478053i	$0.158657\pi$
$600$	4.61122	0.188252
$601$	−23.9128	−0.975422	−0.487711	−	0.873005i	$-0.662168\pi$
$601$	−23.9128	−0.975422	−0.487711	+	0.873005i	$0.662168\pi$
$602$	83.5213	3.40407
$603$	25.1518	1.02426
$604$	−14.7177	−0.598854
$605$	20.7291	0.842757
$606$	15.9948	0.649744
$607$	37.8974	1.53821	0.769104	−	0.639123i	$-0.220703\pi$
$607$	37.8974	1.53821	0.769104	+	0.639123i	$0.220703\pi$
$608$	43.4039	1.76026
$609$	23.0038	0.932162
$610$	33.1600	1.34261
$611$	10.6848	0.432259
$612$	0.590102	0.0238534
$613$	31.1097	1.25651	0.628255	−	0.778008i	$-0.283770\pi$
$613$	31.1097	1.25651	0.628255	+	0.778008i	$0.283770\pi$
$614$	25.2842	1.02039
$615$	14.3503	0.578660
$616$	52.5328	2.11661
$617$	24.6801	0.993583	0.496792	−	0.867870i	$-0.334511\pi$
$617$	24.6801	0.993583	0.496792	+	0.867870i	$0.334511\pi$
$618$	76.7847	3.08873
$619$	−11.3523	−0.456287	−0.228144	−	0.973627i	$-0.573266\pi$
$619$	−11.3523	−0.456287	−0.228144	+	0.973627i	$0.573266\pi$
$620$	45.8415	1.84104
$621$	18.1538	0.728488
$622$	−33.3904	−1.33883
$623$	27.4770	1.10084
$624$	2.38050	0.0952964
$625$	−20.4812	−0.819250
$626$	−43.9091	−1.75496
$627$	73.6685	2.94204
$628$	−7.83108	−0.312494
$629$	−0.108379	−0.00432134
$630$	33.5597	1.33705
$631$	−17.0749	−0.679741	−0.339870	−	0.940472i	$-0.610383\pi$
$631$	−17.0749	−0.679741	−0.339870	+	0.940472i	$0.610383\pi$
$632$	−36.2181	−1.44068
$633$	−8.01139	−0.318424
$634$	34.1057	1.35451
$635$	39.4356	1.56495
$636$	−43.9415	−1.74239
$637$	−62.2349	−2.46584
$638$	26.3949	1.04498
$639$	13.9997	0.553819
$640$	36.7340	1.45204
$641$	−9.00725	−0.355765	−0.177882	−	0.984052i	$-0.556925\pi$
$641$	−9.00725	−0.355765	−0.177882	+	0.984052i	$0.556925\pi$
$642$	38.5255	1.52048
$643$	40.7261	1.60608	0.803041	−	0.595924i	$-0.203214\pi$
$643$	40.7261	1.60608	0.803041	+	0.595924i	$0.203214\pi$
$644$	86.7912	3.42005
$645$	38.8256	1.52876
$646$	−1.82647	−0.0718616
$647$	20.6018	0.809942	0.404971	−	0.914330i	$-0.367282\pi$
$647$	20.6018	0.809942	0.404971	+	0.914330i	$0.367282\pi$
$648$	30.4855	1.19758
$649$	15.7881	0.619736
$650$	−10.3746	−0.406926
$651$	−63.7515	−2.49862
$652$	3.19353	0.125068
$653$	3.23934	0.126765	0.0633826	−	0.997989i	$-0.479811\pi$
$653$	3.23934	0.126765	0.0633826	+	0.997989i	$0.479811\pi$
$654$	−41.4205	−1.61967
$655$	8.38008	0.327437
$656$	−0.606919	−0.0236962
$657$	17.9446	0.700085
$658$	−17.5804	−0.685354
$659$	−35.1331	−1.36859	−0.684295	−	0.729205i	$-0.739890\pi$
$659$	−35.1331	−1.36859	−0.684295	+	0.729205i	$0.739890\pi$
$660$	65.3415	2.54342
$661$	−13.4660	−0.523766	−0.261883	−	0.965100i	$-0.584343\pi$
$661$	−13.4660	−0.523766	−0.261883	+	0.965100i	$0.584343\pi$
$662$	−2.25930	−0.0878100
$663$	−1.36927	−0.0531781
$664$	−43.9350	−1.70501
$665$	−63.8724	−2.47687
$666$	3.88547	0.150559
$667$	16.2977	0.631051
$668$	60.1279	2.32642
$669$	30.7701	1.18964
$670$	−69.0499	−2.66763
$671$	−32.5368	−1.25607
$672$	−53.5386	−2.06530
$673$	13.4884	0.519938	0.259969	−	0.965617i	$-0.416288\pi$
$673$	13.4884	0.519938	0.259969	+	0.965617i	$0.416288\pi$
$674$	2.00474	0.0772197
$675$	2.19551	0.0845054
$676$	66.8289	2.57034
$677$	24.5875	0.944975	0.472488	−	0.881337i	$-0.343356\pi$
$677$	24.5875	0.944975	0.472488	+	0.881337i	$0.343356\pi$
$678$	−43.0937	−1.65500
$679$	67.1110	2.57548
$680$	−0.605458	−0.0232182
$681$	50.5136	1.93569
$682$	−73.1492	−2.80103
$683$	−33.8075	−1.29361	−0.646805	−	0.762656i	$-0.723895\pi$
$683$	−33.8075	−1.29361	−0.646805	+	0.762656i	$0.723895\pi$
$684$	40.2645	1.53955
$685$	−6.10853	−0.233395
$686$	35.3136	1.34828
$687$	42.3569	1.61602
$688$	−1.64206	−0.0626029
$689$	36.9483	1.40762
$690$	65.6128	2.49784
$691$	7.97835	0.303511	0.151755	−	0.988418i	$-0.451507\pi$
$691$	7.97835	0.303511	0.151755	+	0.988418i	$0.451507\pi$
$692$	41.6845	1.58461
$693$	−32.9289	−1.25087
$694$	−50.5309	−1.91813
$695$	2.11027	0.0800471
$696$	14.8787	0.563976
$697$	0.349101	0.0132232
$698$	32.7121	1.23817
$699$	−20.2429	−0.765656
$700$	10.4965	0.396730
$701$	−4.98654	−0.188339	−0.0941696	−	0.995556i	$-0.530020\pi$
$701$	−4.98654	−0.188339	−0.0941696	+	0.995556i	$0.530020\pi$
$702$	−37.2875	−1.40733
$703$	−7.39501	−0.278908
$704$	−59.7002	−2.25004
$705$	−8.17239	−0.307790
$706$	3.21577	0.121027
$707$	13.6072	0.511752
$708$	23.8129	0.894944
$709$	−35.1957	−1.32180	−0.660902	−	0.750472i	$-0.729826\pi$
$709$	−35.1957	−1.32180	−0.660902	+	0.750472i	$0.729826\pi$
$710$	−38.4338	−1.44239
$711$	22.7024	0.851407
$712$	17.7719	0.666031
$713$	−45.1666	−1.69150
$714$	2.25295	0.0843147
$715$	−54.9426	−2.05474
$716$	63.0892	2.35776
$717$	23.4269	0.874893
$718$	0.963977	0.0359753
$719$	2.52041	0.0939953	0.0469976	−	0.998895i	$-0.485035\pi$
$719$	2.52041	0.0939953	0.0469976	+	0.998895i	$0.485035\pi$
$720$	−0.659796	−0.0245892
$721$	65.3229	2.43275
$722$	−81.3263	−3.02665
$723$	39.9489	1.48572
$724$	−7.67287	−0.285160
$725$	1.97104	0.0732026
$726$	−49.8901	−1.85159
$727$	39.7612	1.47466	0.737330	−	0.675532i	$-0.236086\pi$
$727$	39.7612	1.47466	0.737330	+	0.675532i	$0.236086\pi$
$728$	−66.6244	−2.46927
$729$	−0.829673	−0.0307286
$730$	−49.2638	−1.82333
$731$	0.944516	0.0349342
$732$	−49.0747	−1.81385
$733$	16.5173	0.610081	0.305041	−	0.952339i	$-0.401330\pi$
$733$	16.5173	0.610081	0.305041	+	0.952339i	$0.401330\pi$
$734$	−21.9649	−0.810740
$735$	47.6012	1.75580
$736$	−37.9310	−1.39816
$737$	67.7520	2.49568
$738$	−12.5156	−0.460706
$739$	34.4225	1.26625	0.633127	−	0.774048i	$-0.281771\pi$
$739$	34.4225	1.26625	0.633127	+	0.774048i	$0.281771\pi$
$740$	−6.55913	−0.241118
$741$	−93.4296	−3.43222
$742$	−60.7935	−2.23180
$743$	−24.4142	−0.895672	−0.447836	−	0.894116i	$-0.647805\pi$
$743$	−24.4142	−0.895672	−0.447836	+	0.894116i	$0.647805\pi$
$744$	−41.2340	−1.51171
$745$	42.8579	1.57019
$746$	66.8718	2.44835
$747$	27.5396	1.00762
$748$	1.58957	0.0581205
$749$	32.7748	1.19756
$750$	58.6990	2.14338
$751$	4.19723	0.153159	0.0765795	−	0.997063i	$-0.475600\pi$
$751$	4.19723	0.153159	0.0765795	+	0.997063i	$0.475600\pi$
$752$	0.345636	0.0126041
$753$	−31.1001	−1.13335
$754$	−33.4751	−1.21909
$755$	−9.46549	−0.344484
$756$	37.7255	1.37206
$757$	22.2342	0.808116	0.404058	−	0.914733i	$-0.367599\pi$
$757$	22.2342	0.808116	0.404058	+	0.914733i	$0.367599\pi$
$758$	−7.78868	−0.282898
$759$	−64.3795	−2.33683
$760$	−41.3123	−1.49855
$761$	−3.63986	−0.131945	−0.0659724	−	0.997821i	$-0.521015\pi$
$761$	−3.63986	−0.131945	−0.0659724	+	0.997821i	$0.521015\pi$
$762$	−94.9123	−3.43831
$763$	−35.2376	−1.27569
$764$	−25.6138	−0.926674
$765$	0.379516	0.0137214
$766$	−39.9010	−1.44168
$767$	−20.0231	−0.722993
$768$	−32.0181	−1.15535
$769$	−29.4726	−1.06281	−0.531404	−	0.847119i	$-0.678335\pi$
$769$	−29.4726	−1.06281	−0.531404	+	0.847119i	$0.678335\pi$
$770$	90.4007	3.25781
$771$	28.7409	1.03508
$772$	59.0799	2.12633
$773$	7.67941	0.276209	0.138105	−	0.990418i	$-0.455899\pi$
$773$	7.67941	0.276209	0.138105	+	0.990418i	$0.455899\pi$
$774$	−33.8617	−1.21714
$775$	−5.46243	−0.196216
$776$	43.4070	1.55822
$777$	9.12173	0.327240
$778$	48.9068	1.75339
$779$	23.8203	0.853450
$780$	−82.8690	−2.96719
$781$	37.7113	1.34942
$782$	1.59617	0.0570789
$783$	7.08412	0.253166
$784$	−2.01321	−0.0719002
$785$	−5.03646	−0.179759
$786$	−20.1689	−0.719401
$787$	−42.3843	−1.51084	−0.755419	−	0.655242i	$-0.772566\pi$
$787$	−42.3843	−1.51084	−0.755419	+	0.655242i	$0.772566\pi$
$788$	−28.2099	−1.00493
$789$	1.66087	0.0591286
$790$	−62.3256	−2.21744
$791$	−36.6610	−1.30352
$792$	−21.2982	−0.756799
$793$	41.2645	1.46535
$794$	−48.2679	−1.71296
$795$	−28.2604	−1.00229
$796$	23.9445	0.848689
$797$	27.4066	0.970793	0.485397	−	0.874294i	$-0.338675\pi$
$797$	27.4066	0.970793	0.485397	+	0.874294i	$0.338675\pi$
$798$	153.726	5.44184
$799$	−0.198811	−0.00703342
$800$	−4.58736	−0.162188
$801$	−11.1399	−0.393609
$802$	−53.6807	−1.89553
$803$	48.3378	1.70580
$804$	102.189	3.60394
$805$	55.8186	1.96735
$806$	92.7711	3.26772
$807$	−28.6531	−1.00864
$808$	8.80106	0.309620
$809$	−22.8533	−0.803479	−0.401740	−	0.915754i	$-0.631594\pi$
$809$	−22.8533	−0.803479	−0.401740	+	0.915754i	$0.631594\pi$
$810$	52.4607	1.84328
$811$	44.3589	1.55765	0.778827	−	0.627239i	$-0.215815\pi$
$811$	44.3589	1.55765	0.778827	+	0.627239i	$0.215815\pi$
$812$	33.8683	1.18854
$813$	−7.04875	−0.247210
$814$	10.4664	0.366847
$815$	2.05388	0.0719443
$816$	−0.0442939	−0.00155060
$817$	64.4473	2.25472
$818$	10.5438	0.368655
$819$	41.7619	1.45928
$820$	21.1278	0.737815
$821$	−32.2162	−1.12435	−0.562177	−	0.827017i	$-0.690036\pi$
$821$	−32.2162	−1.12435	−0.562177	+	0.827017i	$0.690036\pi$
$822$	14.7018	0.512784
$823$	4.50826	0.157148	0.0785740	−	0.996908i	$-0.474963\pi$
$823$	4.50826	0.157148	0.0785740	+	0.996908i	$0.474963\pi$
$824$	42.2504	1.47186
$825$	−7.78603	−0.271075
$826$	32.9454	1.14632
$827$	23.3468	0.811849	0.405924	−	0.913907i	$-0.366950\pi$
$827$	23.3468	0.811849	0.405924	+	0.913907i	$0.366950\pi$
$828$	−35.1875	−1.22285
$829$	−31.7389	−1.10234	−0.551168	−	0.834394i	$-0.685818\pi$
$829$	−31.7389	−1.10234	−0.551168	+	0.834394i	$0.685818\pi$
$830$	−75.6052	−2.62429
$831$	7.03508	0.244044
$832$	75.7144	2.62493
$833$	1.15800	0.0401223
$834$	−5.07893	−0.175869
$835$	38.6705	1.33825
$836$	108.461	3.75122
$837$	−19.6325	−0.678600
$838$	47.7530	1.64960
$839$	35.2819	1.21807	0.609033	−	0.793145i	$-0.291558\pi$
$839$	35.2819	1.21807	0.609033	+	0.793145i	$0.291558\pi$
$840$	50.9586	1.75824
$841$	−22.6402	−0.780696
$842$	27.0034	0.930600
$843$	−26.1769	−0.901582
$844$	−11.7951	−0.406004
$845$	42.9801	1.47856
$846$	7.12755	0.245050
$847$	−42.4429	−1.45836
$848$	1.19522	0.0410441
$849$	−57.9681	−1.98946
$850$	0.193040	0.00662122
$851$	6.46256	0.221534
$852$	56.8794	1.94866
$853$	27.8440	0.953361	0.476681	−	0.879077i	$-0.341840\pi$
$853$	27.8440	0.953361	0.476681	+	0.879077i	$0.341840\pi$
$854$	−67.8953	−2.32333
$855$	25.8956	0.885610
$856$	21.1985	0.724550
$857$	15.7519	0.538075	0.269038	−	0.963130i	$-0.413294\pi$
$857$	15.7519	0.538075	0.269038	+	0.963130i	$0.413294\pi$
$858$	132.234	4.51439
$859$	−39.2892	−1.34053	−0.670266	−	0.742121i	$-0.733820\pi$
$859$	−39.2892	−1.34053	−0.670266	+	0.742121i	$0.733820\pi$
$860$	57.1626	1.94923
$861$	−29.3823	−1.00135
$862$	−53.9573	−1.83779
$863$	−12.8863	−0.438654	−0.219327	−	0.975651i	$-0.570386\pi$
$863$	−12.8863	−0.438654	−0.219327	+	0.975651i	$0.570386\pi$
$864$	−16.4874	−0.560914
$865$	26.8089	0.911529
$866$	84.8987	2.88497
$867$	−36.8491	−1.25146
$868$	−93.8607	−3.18584
$869$	61.1541	2.07451
$870$	25.6039	0.868054
$871$	−85.9261	−2.91150
$872$	−22.7915	−0.771816
$873$	−27.2086	−0.920871
$874$	108.912	3.68399
$875$	49.9369	1.68817
$876$	72.9072	2.46331
$877$	15.1718	0.512316	0.256158	−	0.966635i	$-0.417543\pi$
$877$	15.1718	0.512316	0.256158	+	0.966635i	$0.417543\pi$
$878$	−69.8474	−2.35724
$879$	−63.5607	−2.14385
$880$	−1.77731	−0.0599131
$881$	−46.8022	−1.57681	−0.788404	−	0.615158i	$-0.789092\pi$
$881$	−46.8022	−1.57681	−0.788404	+	0.615158i	$0.789092\pi$
$882$	−41.5154	−1.39790
$883$	7.68630	0.258665	0.129332	−	0.991601i	$-0.458717\pi$
$883$	7.68630	0.258665	0.129332	+	0.991601i	$0.458717\pi$
$884$	−2.01597	−0.0678042
$885$	15.3150	0.514807
$886$	9.38708	0.315365
$887$	14.4641	0.485657	0.242829	−	0.970069i	$-0.421925\pi$
$887$	14.4641	0.485657	0.242829	+	0.970069i	$0.421925\pi$
$888$	5.89988	0.197987
$889$	−80.7446	−2.70809
$890$	30.5827	1.02513
$891$	−51.4747	−1.72447
$892$	45.3025	1.51684
$893$	−13.5655	−0.453951
$894$	−103.149	−3.44982
$895$	40.5750	1.35627
$896$	−75.2130	−2.51269
$897$	81.6489	2.72618
$898$	13.0946	0.436972
$899$	−17.6253	−0.587835
$900$	−4.25555	−0.141852
$901$	−0.687495	−0.0229038
$902$	−33.7136	−1.12254
$903$	−79.4956	−2.64545
$904$	−23.7121	−0.788653
$905$	−4.93471	−0.164035
$906$	22.7812	0.756855
$907$	−16.7664	−0.556719	−0.278360	−	0.960477i	$-0.589791\pi$
$907$	−16.7664	−0.556719	−0.278360	+	0.960477i	$0.589791\pi$
$908$	74.3707	2.46808
$909$	−5.51673	−0.182978
$910$	−114.650	−3.80061
$911$	−19.3773	−0.642000	−0.321000	−	0.947079i	$-0.604019\pi$
$911$	−19.3773	−0.642000	−0.321000	+	0.947079i	$0.604019\pi$
$912$	−3.02231	−0.100079
$913$	74.1841	2.45513
$914$	16.1842	0.535327
$915$	−31.5618	−1.04340
$916$	62.3617	2.06049
$917$	−17.1583	−0.566615
$918$	0.693806	0.0228990
$919$	−43.4662	−1.43382	−0.716909	−	0.697166i	$-0.754444\pi$
$919$	−43.4662	−1.43382	−0.716909	+	0.697166i	$0.754444\pi$
$920$	36.1031	1.19029
$921$	−24.0655	−0.792986
$922$	−68.5699	−2.25823
$923$	−47.8272	−1.57425
$924$	−133.787	−4.40127
$925$	0.781579	0.0256981
$926$	54.6925	1.79731
$927$	−26.4837	−0.869837
$928$	−14.8017	−0.485891
$929$	1.64859	0.0540886	0.0270443	−	0.999634i	$-0.491390\pi$
$929$	1.64859	0.0540886	0.0270443	+	0.999634i	$0.491390\pi$
$930$	−70.9573	−2.32678
$931$	79.0140	2.58958
$932$	−29.8034	−0.976243
$933$	31.7810	1.04046
$934$	−2.79401	−0.0914229
$935$	1.02231	0.0334332
$936$	27.0113	0.882893
$937$	−39.1738	−1.27975	−0.639876	−	0.768478i	$-0.721014\pi$
$937$	−39.1738	−1.27975	−0.639876	+	0.768478i	$0.721014\pi$
$938$	141.380	4.61622
$939$	41.7928	1.36385
$940$	−12.0321	−0.392445
$941$	9.62466	0.313755	0.156878	−	0.987618i	$-0.449857\pi$
$941$	9.62466	0.313755	0.156878	+	0.987618i	$0.449857\pi$
$942$	12.1216	0.394943
$943$	−20.8167	−0.677886
$944$	−0.647719	−0.0210815
$945$	24.2627	0.789264
$946$	−91.2143	−2.96563
$947$	−0.374898	−0.0121825	−0.00609127	−	0.999981i	$-0.501939\pi$
$947$	−0.374898	−0.0121825	−0.00609127	+	0.999981i	$0.501939\pi$
$948$	92.2377	2.99574
$949$	−61.3041	−1.99002
$950$	13.1717	0.427347
$951$	−32.4618	−1.05265
$952$	1.23968	0.0401782
$953$	−53.8917	−1.74572	−0.872862	−	0.487967i	$-0.837739\pi$
$953$	−53.8917	−1.74572	−0.872862	+	0.487967i	$0.837739\pi$
$954$	24.6473	0.797986
$955$	−16.4732	−0.533060
$956$	34.4912	1.11552
$957$	−25.1227	−0.812101
$958$	22.0866	0.713585
$959$	12.5072	0.403880
$960$	−57.9112	−1.86908
$961$	17.8456	0.575666
$962$	−13.2739	−0.427969
$963$	−13.2878	−0.428192
$964$	58.8165	1.89435
$965$	37.9965	1.22315
$966$	−134.342	−4.32240
$967$	26.1449	0.840762	0.420381	−	0.907348i	$-0.361896\pi$
$967$	26.1449	0.840762	0.420381	+	0.907348i	$0.361896\pi$
$968$	−27.4518	−0.882334
$969$	1.73844	0.0558467
$970$	74.6965	2.39836
$971$	15.9611	0.512215	0.256108	−	0.966648i	$-0.417560\pi$
$971$	15.9611	0.512215	0.256108	+	0.966648i	$0.417560\pi$
$972$	−50.7258	−1.62703
$973$	−4.32079	−0.138518
$974$	40.9175	1.31108
$975$	9.87458	0.316240
$976$	1.33485	0.0427274
$977$	55.6769	1.78126	0.890631	−	0.454728i	$-0.150263\pi$
$977$	55.6769	1.78126	0.890631	+	0.454728i	$0.150263\pi$
$978$	−4.94321	−0.158066
$979$	−30.0078	−0.959055
$980$	70.0828	2.23871
$981$	14.2863	0.456126
$982$	29.8706	0.953209
$983$	11.9908	0.382446	0.191223	−	0.981547i	$-0.438755\pi$
$983$	11.9908	0.382446	0.191223	+	0.981547i	$0.438755\pi$
$984$	−19.0043	−0.605834
$985$	−18.1428	−0.578078
$986$	0.622870	0.0198362
$987$	16.7330	0.532617
$988$	−137.556	−4.37623
$989$	−56.3210	−1.79090
$990$	−36.6509	−1.16484
$991$	56.7964	1.80420	0.902098	−	0.431532i	$-0.142027\pi$
$991$	56.7964	1.80420	0.902098	+	0.431532i	$0.142027\pi$
$992$	41.0207	1.30241
$993$	2.15040	0.0682409
$994$	78.6933	2.49600
$995$	15.3996	0.488199
$996$	111.891	3.54539
$997$	−3.68949	−0.116847	−0.0584236	−	0.998292i	$-0.518607\pi$
$997$	−3.68949	−0.116847	−0.0584236	+	0.998292i	$0.518607\pi$
$998$	−19.0011	−0.601470
$999$	2.80908	0.0888752

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6031.2.a.d.1.16	✓	133

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6031.2.a.d.1.16	✓	133	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)

\(f(q)\)	\(=\)	\(q-2.27893 q^{2} +2.16909 q^{3} +3.19353 q^{4} +2.05388 q^{5} -4.94321 q^{6} -4.20533 q^{7} -2.71998 q^{8} +1.70495 q^{9} +O(q^{10})\)	\(q-2.27893 q^{2} +2.16909 q^{3} +3.19353 q^{4} +2.05388 q^{5} -4.94321 q^{6} -4.20533 q^{7} -2.71998 q^{8} +1.70495 q^{9} -4.68065 q^{10} +4.59267 q^{11} +6.92706 q^{12} -5.82463 q^{13} +9.58365 q^{14} +4.45505 q^{15} -0.188418 q^{16} +0.108379 q^{17} -3.88547 q^{18} +7.39501 q^{19} +6.55913 q^{20} -9.12173 q^{21} -10.4664 q^{22} -6.46256 q^{23} -5.89988 q^{24} -0.781579 q^{25} +13.2739 q^{26} -2.80908 q^{27} -13.4298 q^{28} -2.52187 q^{29} -10.1528 q^{30} +6.98897 q^{31} +5.86935 q^{32} +9.96192 q^{33} -0.246987 q^{34} -8.63724 q^{35} +5.44482 q^{36} -1.00000 q^{37} -16.8527 q^{38} -12.6341 q^{39} -5.58651 q^{40} +3.22113 q^{41} +20.7878 q^{42} +8.71497 q^{43} +14.6668 q^{44} +3.50177 q^{45} +14.7277 q^{46} -1.83441 q^{47} -0.408696 q^{48} +10.6848 q^{49} +1.78116 q^{50} +0.235083 q^{51} -18.6011 q^{52} -6.34346 q^{53} +6.40169 q^{54} +9.43280 q^{55} +11.4384 q^{56} +16.0404 q^{57} +5.74717 q^{58} +3.43767 q^{59} +14.2273 q^{60} -7.08449 q^{61} -15.9274 q^{62} -7.16988 q^{63} -12.9990 q^{64} -11.9631 q^{65} -22.7025 q^{66} +14.7522 q^{67} +0.346110 q^{68} -14.0179 q^{69} +19.6837 q^{70} +8.21120 q^{71} -4.63743 q^{72} +10.5250 q^{73} +2.27893 q^{74} -1.69531 q^{75} +23.6162 q^{76} -19.3137 q^{77} +28.7924 q^{78} +13.3156 q^{79} -0.386988 q^{80} -11.2080 q^{81} -7.34073 q^{82} +16.1527 q^{83} -29.1305 q^{84} +0.222597 q^{85} -19.8608 q^{86} -5.47016 q^{87} -12.4920 q^{88} -6.53385 q^{89} -7.98029 q^{90} +24.4945 q^{91} -20.6384 q^{92} +15.1597 q^{93} +4.18050 q^{94} +15.1885 q^{95} +12.7311 q^{96} -15.9586 q^{97} -24.3499 q^{98} +7.83029 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 133 q + 14 q^{2} + 8 q^{3} + 142 q^{4} + 34 q^{5} + 20 q^{6} + 8 q^{7} + 42 q^{8} + 177 q^{9}+O(q^{10}) \) 133 * q + 14 * q^2 + 8 * q^3 + 142 * q^4 + 34 * q^5 + 20 * q^6 + 8 * q^7 + 42 * q^8 + 177 * q^9	\( 133 q + 14 q^{2} + 8 q^{3} + 142 q^{4} + 34 q^{5} + 20 q^{6} + 8 q^{7} + 42 q^{8} + 177 q^{9} + 9 q^{10} + 23 q^{11} + 24 q^{12} + 23 q^{13} + 31 q^{14} + 9 q^{15} + 168 q^{16} + 98 q^{17} + 38 q^{18} + 29 q^{19} + 83 q^{20} + 26 q^{21} + 2 q^{22} + 34 q^{23} + 75 q^{24} + 177 q^{25} + 67 q^{26} + 32 q^{27} + 32 q^{28} + 91 q^{29} + 12 q^{30} + 24 q^{31} + 88 q^{32} + 27 q^{33} + 23 q^{34} + 66 q^{35} + 232 q^{36} - 133 q^{37} + 26 q^{38} + 28 q^{39} + 41 q^{40} + 132 q^{41} + 13 q^{42} + 11 q^{43} + 65 q^{44} + 107 q^{45} + 20 q^{46} + 10 q^{47} + 27 q^{48} + 229 q^{49} + 78 q^{50} + 19 q^{51} + 71 q^{52} + 7 q^{53} + 43 q^{54} + 41 q^{55} + 67 q^{56} + 45 q^{57} + 25 q^{58} + 97 q^{59} - 42 q^{60} + 65 q^{61} + 24 q^{62} + 39 q^{63} + 200 q^{64} + 60 q^{65} + 35 q^{66} + 25 q^{67} + 227 q^{68} + 120 q^{69} + 37 q^{70} + 26 q^{71} + 93 q^{72} + 55 q^{73} - 14 q^{74} + 5 q^{75} + 34 q^{76} + 21 q^{77} - 2 q^{78} + 50 q^{79} + 162 q^{80} + 341 q^{81} + 66 q^{82} + 30 q^{83} - 89 q^{84} + 30 q^{85} - 12 q^{86} + 80 q^{87} - 85 q^{88} + 225 q^{89} - 86 q^{90} + q^{91} + 82 q^{92} + 42 q^{93} - 17 q^{94} + 70 q^{95} + 55 q^{96} + 12 q^{97} + 90 q^{98} + 17 q^{99}+O(q^{100}) \) 133 * q + 14 * q^2 + 8 * q^3 + 142 * q^4 + 34 * q^5 + 20 * q^6 + 8 * q^7 + 42 * q^8 + 177 * q^9 + 9 * q^10 + 23 * q^11 + 24 * q^12 + 23 * q^13 + 31 * q^14 + 9 * q^15 + 168 * q^16 + 98 * q^17 + 38 * q^18 + 29 * q^19 + 83 * q^20 + 26 * q^21 + 2 * q^22 + 34 * q^23 + 75 * q^24 + 177 * q^25 + 67 * q^26 + 32 * q^27 + 32 * q^28 + 91 * q^29 + 12 * q^30 + 24 * q^31 + 88 * q^32 + 27 * q^33 + 23 * q^34 + 66 * q^35 + 232 * q^36 - 133 * q^37 + 26 * q^38 + 28 * q^39 + 41 * q^40 + 132 * q^41 + 13 * q^42 + 11 * q^43 + 65 * q^44 + 107 * q^45 + 20 * q^46 + 10 * q^47 + 27 * q^48 + 229 * q^49 + 78 * q^50 + 19 * q^51 + 71 * q^52 + 7 * q^53 + 43 * q^54 + 41 * q^55 + 67 * q^56 + 45 * q^57 + 25 * q^58 + 97 * q^59 - 42 * q^60 + 65 * q^61 + 24 * q^62 + 39 * q^63 + 200 * q^64 + 60 * q^65 + 35 * q^66 + 25 * q^67 + 227 * q^68 + 120 * q^69 + 37 * q^70 + 26 * q^71 + 93 * q^72 + 55 * q^73 - 14 * q^74 + 5 * q^75 + 34 * q^76 + 21 * q^77 - 2 * q^78 + 50 * q^79 + 162 * q^80 + 341 * q^81 + 66 * q^82 + 30 * q^83 - 89 * q^84 + 30 * q^85 - 12 * q^86 + 80 * q^87 - 85 * q^88 + 225 * q^89 - 86 * q^90 + q^91 + 82 * q^92 + 42 * q^93 - 17 * q^94 + 70 * q^95 + 55 * q^96 + 12 * q^97 + 90 * q^98 + 17 * q^99

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