LMFDB - Embedded newform 6041.2.a.d.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6041, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6041 = 7 \cdot 863 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6041.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.2376278611$
Analytic rank:	$1$
Dimension:	$101$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	6041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.08521 q^{2} +1.06538 q^{3} +2.34812 q^{4} +1.41345 q^{5} -2.22154 q^{6} -1.00000 q^{7} -0.725898 q^{8} -1.86497 q^{9} +O(q^{10})$	\(q-2.08521 q^{2} +1.06538 q^{3} +2.34812 q^{4} +1.41345 q^{5} -2.22154 q^{6} -1.00000 q^{7} -0.725898 q^{8} -1.86497 q^{9} -2.94734 q^{10} -2.56823 q^{11} +2.50163 q^{12} -0.702470 q^{13} +2.08521 q^{14} +1.50586 q^{15} -3.18258 q^{16} -0.506110 q^{17} +3.88887 q^{18} +2.60507 q^{19} +3.31894 q^{20} -1.06538 q^{21} +5.35531 q^{22} +3.89651 q^{23} -0.773355 q^{24} -3.00216 q^{25} +1.46480 q^{26} -5.18303 q^{27} -2.34812 q^{28} -4.32102 q^{29} -3.14003 q^{30} +7.63327 q^{31} +8.08816 q^{32} -2.73613 q^{33} +1.05535 q^{34} -1.41345 q^{35} -4.37917 q^{36} -2.73741 q^{37} -5.43213 q^{38} -0.748395 q^{39} -1.02602 q^{40} +1.03359 q^{41} +2.22154 q^{42} +5.67789 q^{43} -6.03050 q^{44} -2.63604 q^{45} -8.12505 q^{46} +7.52204 q^{47} -3.39065 q^{48} +1.00000 q^{49} +6.26015 q^{50} -0.539198 q^{51} -1.64948 q^{52} +4.89251 q^{53} +10.8077 q^{54} -3.63006 q^{55} +0.725898 q^{56} +2.77538 q^{57} +9.01024 q^{58} -5.27894 q^{59} +3.53593 q^{60} -1.46140 q^{61} -15.9170 q^{62} +1.86497 q^{63} -10.5004 q^{64} -0.992905 q^{65} +5.70542 q^{66} -3.22218 q^{67} -1.18841 q^{68} +4.15125 q^{69} +2.94734 q^{70} +10.7730 q^{71} +1.35378 q^{72} +3.40721 q^{73} +5.70808 q^{74} -3.19843 q^{75} +6.11701 q^{76} +2.56823 q^{77} +1.56056 q^{78} +5.28101 q^{79} -4.49842 q^{80} +0.0730368 q^{81} -2.15527 q^{82} -13.7858 q^{83} -2.50163 q^{84} -0.715361 q^{85} -11.8396 q^{86} -4.60351 q^{87} +1.86427 q^{88} -2.41002 q^{89} +5.49671 q^{90} +0.702470 q^{91} +9.14946 q^{92} +8.13231 q^{93} -15.6851 q^{94} +3.68213 q^{95} +8.61694 q^{96} +4.45340 q^{97} -2.08521 q^{98} +4.78968 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 101 q + 3 q^{2} - 17 q^{3} + 85 q^{4} - 12 q^{5} - 17 q^{6} - 101 q^{7} - 3 q^{8} + 88 q^{9}+O(q^{10}) $ 101 * q + 3 * q^2 - 17 * q^3 + 85 * q^4 - 12 * q^5 - 17 * q^6 - 101 * q^7 - 3 * q^8 + 88 * q^9	\( 101 q + 3 q^{2} - 17 q^{3} + 85 q^{4} - 12 q^{5} - 17 q^{6} - 101 q^{7} - 3 q^{8} + 88 q^{9} - 23 q^{10} - 13 q^{11} - 31 q^{12} - 35 q^{13} - 3 q^{14} - 20 q^{15} + 45 q^{16} - 19 q^{17} + 3 q^{18} - 59 q^{19} - 31 q^{20} + 17 q^{21} - 13 q^{22} - 29 q^{23} - 59 q^{24} + 103 q^{25} - 18 q^{26} - 47 q^{27} - 85 q^{28} - 26 q^{29} - 8 q^{30} - 125 q^{31} + 12 q^{32} - 18 q^{33} - 66 q^{34} + 12 q^{35} + 40 q^{36} + 22 q^{37} - 31 q^{38} - 94 q^{39} - 79 q^{40} - 39 q^{41} + 17 q^{42} - 5 q^{43} - 53 q^{44} - 50 q^{45} - 37 q^{46} - 47 q^{47} - 81 q^{48} + 101 q^{49} + 2 q^{50} - 23 q^{51} - 56 q^{52} - 5 q^{53} - 77 q^{54} - 155 q^{55} + 3 q^{56} + 61 q^{57} - 31 q^{58} - 33 q^{59} - 48 q^{60} - 96 q^{61} - 38 q^{62} - 88 q^{63} - 33 q^{64} - 8 q^{65} - 91 q^{66} + 8 q^{67} - 41 q^{68} - 91 q^{69} + 23 q^{70} - 116 q^{71} - 5 q^{72} - 62 q^{73} - 23 q^{74} - 94 q^{75} - 112 q^{76} + 13 q^{77} + 17 q^{78} - 127 q^{79} - 87 q^{80} + 37 q^{81} - 118 q^{82} - 58 q^{83} + 31 q^{84} - 6 q^{85} - 26 q^{86} - 82 q^{87} - 40 q^{88} - 57 q^{89} - 123 q^{90} + 35 q^{91} - 28 q^{92} - 10 q^{93} - 107 q^{94} - 70 q^{95} - 76 q^{96} - 69 q^{97} + 3 q^{98} - 67 q^{99}+O(q^{100}) \) 101 * q + 3 * q^2 - 17 * q^3 + 85 * q^4 - 12 * q^5 - 17 * q^6 - 101 * q^7 - 3 * q^8 + 88 * q^9 - 23 * q^10 - 13 * q^11 - 31 * q^12 - 35 * q^13 - 3 * q^14 - 20 * q^15 + 45 * q^16 - 19 * q^17 + 3 * q^18 - 59 * q^19 - 31 * q^20 + 17 * q^21 - 13 * q^22 - 29 * q^23 - 59 * q^24 + 103 * q^25 - 18 * q^26 - 47 * q^27 - 85 * q^28 - 26 * q^29 - 8 * q^30 - 125 * q^31 + 12 * q^32 - 18 * q^33 - 66 * q^34 + 12 * q^35 + 40 * q^36 + 22 * q^37 - 31 * q^38 - 94 * q^39 - 79 * q^40 - 39 * q^41 + 17 * q^42 - 5 * q^43 - 53 * q^44 - 50 * q^45 - 37 * q^46 - 47 * q^47 - 81 * q^48 + 101 * q^49 + 2 * q^50 - 23 * q^51 - 56 * q^52 - 5 * q^53 - 77 * q^54 - 155 * q^55 + 3 * q^56 + 61 * q^57 - 31 * q^58 - 33 * q^59 - 48 * q^60 - 96 * q^61 - 38 * q^62 - 88 * q^63 - 33 * q^64 - 8 * q^65 - 91 * q^66 + 8 * q^67 - 41 * q^68 - 91 * q^69 + 23 * q^70 - 116 * q^71 - 5 * q^72 - 62 * q^73 - 23 * q^74 - 94 * q^75 - 112 * q^76 + 13 * q^77 + 17 * q^78 - 127 * q^79 - 87 * q^80 + 37 * q^81 - 118 * q^82 - 58 * q^83 + 31 * q^84 - 6 * q^85 - 26 * q^86 - 82 * q^87 - 40 * q^88 - 57 * q^89 - 123 * q^90 + 35 * q^91 - 28 * q^92 - 10 * q^93 - 107 * q^94 - 70 * q^95 - 76 * q^96 - 69 * q^97 + 3 * q^98 - 67 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.08521	−1.47447	−0.737234	−	0.675637i	$-0.763869\pi$
$2$	−2.08521	−1.47447	−0.737234	+	0.675637i	$0.763869\pi$
$3$	1.06538	0.615096	0.307548	−	0.951533i	$-0.400492\pi$
$3$	1.06538	0.615096	0.307548	+	0.951533i	$0.400492\pi$
$4$	2.34812	1.17406
$5$	1.41345	0.632114	0.316057	−	0.948740i	$-0.397641\pi$
$5$	1.41345	0.632114	0.316057	+	0.948740i	$0.397641\pi$
$6$	−2.22154	−0.906939
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−0.725898	−0.256644
$9$	−1.86497	−0.621657
$10$	−2.94734	−0.932032
$11$	−2.56823	−0.774350	−0.387175	−	0.922006i	$-0.626549\pi$
$11$	−2.56823	−0.774350	−0.387175	+	0.922006i	$0.626549\pi$
$12$	2.50163	0.722158
$13$	−0.702470	−0.194830	−0.0974150	−	0.995244i	$-0.531057\pi$
$13$	−0.702470	−0.194830	−0.0974150	+	0.995244i	$0.531057\pi$
$14$	2.08521	0.557297
$15$	1.50586	0.388810
$16$	−3.18258	−0.795645
$17$	−0.506110	−0.122750	−0.0613749	−	0.998115i	$-0.519549\pi$
$17$	−0.506110	−0.122750	−0.0613749	+	0.998115i	$0.519549\pi$
$18$	3.88887	0.916614
$19$	2.60507	0.597644	0.298822	−	0.954309i	$-0.403406\pi$
$19$	2.60507	0.597644	0.298822	+	0.954309i	$0.403406\pi$
$20$	3.31894	0.742138
$21$	−1.06538	−0.232484
$22$	5.35531	1.14176
$23$	3.89651	0.812478	0.406239	−	0.913767i	$-0.366840\pi$
$23$	3.89651	0.812478	0.406239	+	0.913767i	$0.366840\pi$
$24$	−0.773355	−0.157860
$25$	−3.00216	−0.600432
$26$	1.46480	0.287271
$27$	−5.18303	−0.997474
$28$	−2.34812	−0.443752
$29$	−4.32102	−0.802392	−0.401196	−	0.915992i	$-0.631405\pi$
$29$	−4.32102	−0.802392	−0.401196	+	0.915992i	$0.631405\pi$
$30$	−3.14003	−0.573289
$31$	7.63327	1.37098	0.685488	−	0.728084i	$-0.259589\pi$
$31$	7.63327	1.37098	0.685488	+	0.728084i	$0.259589\pi$
$32$	8.08816	1.42980
$33$	−2.73613	−0.476300
$34$	1.05535	0.180991
$35$	−1.41345	−0.238917
$36$	−4.37917	−0.729862
$37$	−2.73741	−0.450027	−0.225013	−	0.974356i	$-0.572243\pi$
$37$	−2.73741	−0.450027	−0.225013	+	0.974356i	$0.572243\pi$
$38$	−5.43213	−0.881207
$39$	−0.748395	−0.119839
$40$	−1.02602	−0.162228
$41$	1.03359	0.161420	0.0807102	−	0.996738i	$-0.474281\pi$
$41$	1.03359	0.161420	0.0807102	+	0.996738i	$0.474281\pi$
$42$	2.22154	0.342791
$43$	5.67789	0.865870	0.432935	−	0.901425i	$-0.357478\pi$
$43$	5.67789	0.865870	0.432935	+	0.901425i	$0.357478\pi$
$44$	−6.03050	−0.909133
$45$	−2.63604	−0.392958
$46$	−8.12505	−1.19797
$47$	7.52204	1.09720	0.548601	−	0.836084i	$-0.315161\pi$
$47$	7.52204	1.09720	0.548601	+	0.836084i	$0.315161\pi$
$48$	−3.39065	−0.489398
$49$	1.00000	0.142857
$50$	6.26015	0.885319
$51$	−0.539198	−0.0755028
$52$	−1.64948	−0.228742
$53$	4.89251	0.672038	0.336019	−	0.941855i	$-0.390919\pi$
$53$	4.89251	0.672038	0.336019	+	0.941855i	$0.390919\pi$
$54$	10.8077	1.47074
$55$	−3.63006	−0.489477
$56$	0.725898	0.0970022
$57$	2.77538	0.367608
$58$	9.01024	1.18310
$59$	−5.27894	−0.687259	−0.343630	−	0.939105i	$-0.611656\pi$
$59$	−5.27894	−0.687259	−0.343630	+	0.939105i	$0.611656\pi$
$60$	3.53593	0.456486
$61$	−1.46140	−0.187113	−0.0935564	−	0.995614i	$-0.529824\pi$
$61$	−1.46140	−0.187113	−0.0935564	+	0.995614i	$0.529824\pi$
$62$	−15.9170	−2.02146
$63$	1.86497	0.234964
$64$	−10.5004	−1.31255
$65$	−0.992905	−0.123155
$66$	5.70542	0.702289
$67$	−3.22218	−0.393652	−0.196826	−	0.980438i	$-0.563063\pi$
$67$	−3.22218	−0.393652	−0.196826	+	0.980438i	$0.563063\pi$
$68$	−1.18841	−0.144115
$69$	4.15125	0.499752
$70$	2.94734	0.352275
$71$	10.7730	1.27852	0.639261	−	0.768990i	$-0.279240\pi$
$71$	10.7730	1.27852	0.639261	+	0.768990i	$0.279240\pi$
$72$	1.35378	0.159544
$73$	3.40721	0.398784	0.199392	−	0.979920i	$-0.436103\pi$
$73$	3.40721	0.398784	0.199392	+	0.979920i	$0.436103\pi$
$74$	5.70808	0.663550
$75$	−3.19843	−0.369323
$76$	6.11701	0.701669
$77$	2.56823	0.292677
$78$	1.56056	0.176699
$79$	5.28101	0.594160	0.297080	−	0.954853i	$-0.403987\pi$
$79$	5.28101	0.594160	0.297080	+	0.954853i	$0.403987\pi$
$80$	−4.49842	−0.502938
$81$	0.0730368	0.00811520
$82$	−2.15527	−0.238009
$83$	−13.7858	−1.51319	−0.756593	−	0.653886i	$-0.773137\pi$
$83$	−13.7858	−1.51319	−0.756593	+	0.653886i	$0.773137\pi$
$84$	−2.50163	−0.272950
$85$	−0.715361	−0.0775918
$86$	−11.8396	−1.27670
$87$	−4.60351	−0.493548
$88$	1.86427	0.198732
$89$	−2.41002	−0.255462	−0.127731	−	0.991809i	$-0.540769\pi$
$89$	−2.41002	−0.255462	−0.127731	+	0.991809i	$0.540769\pi$
$90$	5.49671	0.579404
$91$	0.702470	0.0736388
$92$	9.14946	0.953897
$93$	8.13231	0.843281
$94$	−15.6851	−1.61779
$95$	3.68213	0.377779
$96$	8.61694	0.879462
$97$	4.45340	0.452174	0.226087	−	0.974107i	$-0.427407\pi$
$97$	4.45340	0.452174	0.226087	+	0.974107i	$0.427407\pi$
$98$	−2.08521	−0.210638
$99$	4.78968	0.481381
$100$	−7.04943	−0.704943
$101$	8.12510	0.808478	0.404239	−	0.914653i	$-0.367536\pi$
$101$	8.12510	0.808478	0.404239	+	0.914653i	$0.367536\pi$
$102$	1.12434	0.111327
$103$	−0.978839	−0.0964479	−0.0482239	−	0.998837i	$-0.515356\pi$
$103$	−0.978839	−0.0964479	−0.0482239	+	0.998837i	$0.515356\pi$
$104$	0.509921	0.0500019
$105$	−1.50586	−0.146957
$106$	−10.2019	−0.990900
$107$	−5.19868	−0.502575	−0.251288	−	0.967912i	$-0.580854\pi$
$107$	−5.19868	−0.502575	−0.251288	+	0.967912i	$0.580854\pi$
$108$	−12.1704	−1.17109
$109$	−0.109949	−0.0105312	−0.00526562	−	0.999986i	$-0.501676\pi$
$109$	−0.109949	−0.0105312	−0.00526562	+	0.999986i	$0.501676\pi$
$110$	7.56946	0.721719
$111$	−2.91637	−0.276809
$112$	3.18258	0.300726
$113$	−19.1596	−1.80238	−0.901191	−	0.433421i	$-0.857306\pi$
$113$	−19.1596	−1.80238	−0.901191	+	0.433421i	$0.857306\pi$
$114$	−5.78726	−0.542027
$115$	5.50752	0.513579
$116$	−10.1462	−0.942056
$117$	1.31009	0.121118
$118$	11.0077	1.01334
$119$	0.506110	0.0463950
$120$	−1.09310	−0.0997857
$121$	−4.40420	−0.400381
$122$	3.04733	0.275892
$123$	1.10117	0.0992890
$124$	17.9238	1.60961
$125$	−11.3106	−1.01166
$126$	−3.88887	−0.346448
$127$	−4.90980	−0.435674	−0.217837	−	0.975985i	$-0.569900\pi$
$127$	−4.90980	−0.435674	−0.217837	+	0.975985i	$0.569900\pi$
$128$	5.71922	0.505512
$129$	6.04909	0.532593
$130$	2.07042	0.181588
$131$	−8.91338	−0.778766	−0.389383	−	0.921076i	$-0.627312\pi$
$131$	−8.91338	−0.778766	−0.389383	+	0.921076i	$0.627312\pi$
$132$	−6.42476	−0.559204
$133$	−2.60507	−0.225888
$134$	6.71893	0.580427
$135$	−7.32595	−0.630517
$136$	0.367384	0.0315030
$137$	−12.9924	−1.11002	−0.555009	−	0.831844i	$-0.687285\pi$
$137$	−12.9924	−1.11002	−0.555009	+	0.831844i	$0.687285\pi$
$138$	−8.65625	−0.736869
$139$	8.67861	0.736110	0.368055	−	0.929804i	$-0.380024\pi$
$139$	8.67861	0.736110	0.368055	+	0.929804i	$0.380024\pi$
$140$	−3.31894	−0.280502
$141$	8.01381	0.674884
$142$	−22.4641	−1.88514
$143$	1.80410	0.150867
$144$	5.93542	0.494619
$145$	−6.10754	−0.507203
$146$	−7.10477	−0.587995
$147$	1.06538	0.0878708
$148$	−6.42775	−0.528358
$149$	−8.10623	−0.664089	−0.332044	−	0.943264i	$-0.607738\pi$
$149$	−8.10623	−0.664089	−0.332044	+	0.943264i	$0.607738\pi$
$150$	6.66942	0.544556
$151$	−22.6975	−1.84709	−0.923546	−	0.383487i	$-0.874723\pi$
$151$	−22.6975	−1.84709	−0.923546	+	0.383487i	$0.874723\pi$
$152$	−1.89101	−0.153382
$153$	0.943881	0.0763083
$154$	−5.35531	−0.431543
$155$	10.7892	0.866612
$156$	−1.75732	−0.140698
$157$	−20.9314	−1.67051	−0.835255	−	0.549863i	$-0.814680\pi$
$157$	−20.9314	−1.67051	−0.835255	+	0.549863i	$0.814680\pi$
$158$	−11.0120	−0.876071
$159$	5.21237	0.413368
$160$	11.4322	0.903795
$161$	−3.89651	−0.307088
$162$	−0.152297	−0.0119656
$163$	−22.6152	−1.77136	−0.885681	−	0.464293i	$-0.846308\pi$
$163$	−22.6152	−1.77136	−0.885681	+	0.464293i	$0.846308\pi$
$164$	2.42700	0.189517
$165$	−3.86738	−0.301075
$166$	28.7463	2.23114
$167$	−6.39966	−0.495221	−0.247610	−	0.968860i	$-0.579645\pi$
$167$	−6.39966	−0.495221	−0.247610	+	0.968860i	$0.579645\pi$
$168$	0.773355	0.0596656
$169$	−12.5065	−0.962041
$170$	1.49168	0.114407
$171$	−4.85838	−0.371530
$172$	13.3324	1.01658
$173$	11.1285	0.846081	0.423040	−	0.906111i	$-0.360963\pi$
$173$	11.1285	0.846081	0.423040	+	0.906111i	$0.360963\pi$
$174$	9.59930	0.727721
$175$	3.00216	0.226942
$176$	8.17360	0.616108
$177$	−5.62406	−0.422730
$178$	5.02541	0.376670
$179$	−7.81127	−0.583841	−0.291921	−	0.956443i	$-0.594294\pi$
$179$	−7.81127	−0.583841	−0.291921	+	0.956443i	$0.594294\pi$
$180$	−6.18974	−0.461356
$181$	−10.5479	−0.784018	−0.392009	−	0.919961i	$-0.628220\pi$
$181$	−10.5479	−0.784018	−0.392009	+	0.919961i	$0.628220\pi$
$182$	−1.46480	−0.108578
$183$	−1.55694	−0.115092
$184$	−2.82847	−0.208517
$185$	−3.86918	−0.284468
$186$	−16.9576	−1.24339
$187$	1.29981	0.0950513
$188$	17.6626	1.28818
$189$	5.18303	0.377010
$190$	−7.67803	−0.557023
$191$	8.47296	0.613082	0.306541	−	0.951857i	$-0.400828\pi$
$191$	8.47296	0.613082	0.306541	+	0.951857i	$0.400828\pi$
$192$	−11.1869	−0.807342
$193$	−8.85661	−0.637512	−0.318756	−	0.947837i	$-0.603265\pi$
$193$	−8.85661	−0.637512	−0.318756	+	0.947837i	$0.603265\pi$
$194$	−9.28629	−0.666717
$195$	−1.05782	−0.0757519
$196$	2.34812	0.167723
$197$	−3.61356	−0.257456	−0.128728	−	0.991680i	$-0.541089\pi$
$197$	−3.61356	−0.257456	−0.128728	+	0.991680i	$0.541089\pi$
$198$	−9.98750	−0.709781
$199$	0.494543	0.0350572	0.0175286	−	0.999846i	$-0.494420\pi$
$199$	0.494543	0.0350572	0.0175286	+	0.999846i	$0.494420\pi$
$200$	2.17926	0.154097
$201$	−3.43283	−0.242133
$202$	−16.9426	−1.19208
$203$	4.32102	0.303276
$204$	−1.26610	−0.0886447
$205$	1.46093	0.102036
$206$	2.04109	0.142209
$207$	−7.26688	−0.505083
$208$	2.23567	0.155016
$209$	−6.69042	−0.462786
$210$	3.14003	0.216683
$211$	24.2858	1.67190	0.835950	−	0.548805i	$-0.184917\pi$
$211$	24.2858	1.67190	0.835950	+	0.548805i	$0.184917\pi$
$212$	11.4882	0.789012
$213$	11.4773	0.786413
$214$	10.8404	0.741032
$215$	8.02541	0.547329
$216$	3.76235	0.255996
$217$	−7.63327	−0.518180
$218$	0.229268	0.0155280
$219$	3.62997	0.245290
$220$	−8.52381	−0.574675
$221$	0.355527	0.0239153
$222$	6.08125	0.408147
$223$	−14.8744	−0.996061	−0.498030	−	0.867160i	$-0.665943\pi$
$223$	−14.8744	−0.996061	−0.498030	+	0.867160i	$0.665943\pi$
$224$	−8.08816	−0.540413
$225$	5.59895	0.373263
$226$	39.9518	2.65756
$227$	4.14581	0.275167	0.137584	−	0.990490i	$-0.456066\pi$
$227$	4.14581	0.275167	0.137584	+	0.990490i	$0.456066\pi$
$228$	6.51692	0.431593
$229$	−12.8755	−0.850836	−0.425418	−	0.904997i	$-0.639873\pi$
$229$	−12.8755	−0.850836	−0.425418	+	0.904997i	$0.639873\pi$
$230$	−11.4844	−0.757256
$231$	2.73613	0.180024
$232$	3.13662	0.205929
$233$	−6.90493	−0.452357	−0.226178	−	0.974086i	$-0.572623\pi$
$233$	−6.90493	−0.452357	−0.226178	+	0.974086i	$0.572623\pi$
$234$	−2.73181	−0.178584
$235$	10.6320	0.693556
$236$	−12.3956	−0.806882
$237$	5.62627	0.365465
$238$	−1.05535	−0.0684080
$239$	19.6522	1.27120	0.635599	−	0.772020i	$-0.280753\pi$
$239$	19.6522	1.27120	0.635599	+	0.772020i	$0.280753\pi$
$240$	−4.79251	−0.309355
$241$	−26.3524	−1.69751	−0.848755	−	0.528786i	$-0.822647\pi$
$241$	−26.3524	−1.69751	−0.848755	+	0.528786i	$0.822647\pi$
$242$	9.18369	0.590350
$243$	15.6269	1.00247
$244$	−3.43153	−0.219681
$245$	1.41345	0.0903020
$246$	−2.29617	−0.146399
$247$	−1.82998	−0.116439
$248$	−5.54097	−0.351852
$249$	−14.6870	−0.930754
$250$	23.5851	1.49165
$251$	−4.75852	−0.300355	−0.150178	−	0.988659i	$-0.547985\pi$
$251$	−4.75852	−0.300355	−0.150178	+	0.988659i	$0.547985\pi$
$252$	4.37917	0.275862
$253$	−10.0071	−0.629143
$254$	10.2380	0.642388
$255$	−0.762129	−0.0477264
$256$	9.07496	0.567185
$257$	20.0040	1.24782	0.623908	−	0.781498i	$-0.285544\pi$
$257$	20.0040	1.24782	0.623908	+	0.781498i	$0.285544\pi$
$258$	−12.6137	−0.785292
$259$	2.73741	0.170094
$260$	−2.33146	−0.144591
$261$	8.05857	0.498813
$262$	18.5863	1.14827
$263$	−7.02520	−0.433192	−0.216596	−	0.976261i	$-0.569496\pi$
$263$	−7.02520	−0.433192	−0.216596	+	0.976261i	$0.569496\pi$
$264$	1.98615	0.122239
$265$	6.91532	0.424805
$266$	5.43213	0.333065
$267$	−2.56758	−0.157133
$268$	−7.56605	−0.462170
$269$	−9.99193	−0.609219	−0.304609	−	0.952477i	$-0.598526\pi$
$269$	−9.99193	−0.609219	−0.304609	+	0.952477i	$0.598526\pi$
$270$	15.2762	0.929678
$271$	−3.65004	−0.221724	−0.110862	−	0.993836i	$-0.535361\pi$
$271$	−3.65004	−0.221724	−0.110862	+	0.993836i	$0.535361\pi$
$272$	1.61074	0.0976653
$273$	0.748395	0.0452949
$274$	27.0920	1.63669
$275$	7.71024	0.464945
$276$	9.74762	0.586738
$277$	−7.15557	−0.429936	−0.214968	−	0.976621i	$-0.568965\pi$
$277$	−7.15557	−0.429936	−0.214968	+	0.976621i	$0.568965\pi$
$278$	−18.0968	−1.08537
$279$	−14.2358	−0.852277
$280$	1.02602	0.0613164
$281$	−13.7845	−0.822316	−0.411158	−	0.911564i	$-0.634875\pi$
$281$	−13.7845	−0.822316	−0.411158	+	0.911564i	$0.634875\pi$
$282$	−16.7105	−0.995096
$283$	−1.45068	−0.0862338	−0.0431169	−	0.999070i	$-0.513729\pi$
$283$	−1.45068	−0.0862338	−0.0431169	+	0.999070i	$0.513729\pi$
$284$	25.2963	1.50106
$285$	3.92286	0.232370
$286$	−3.76194	−0.222448
$287$	−1.03359	−0.0610112
$288$	−15.0842	−0.888844
$289$	−16.7439	−0.984932
$290$	12.7355	0.747855
$291$	4.74455	0.278130
$292$	8.00053	0.468196
$293$	14.7134	0.859566	0.429783	−	0.902932i	$-0.358590\pi$
$293$	14.7134	0.859566	0.429783	+	0.902932i	$0.358590\pi$
$294$	−2.22154	−0.129563
$295$	−7.46151	−0.434426
$296$	1.98708	0.115497
$297$	13.3112	0.772395
$298$	16.9032	0.979178
$299$	−2.73718	−0.158295
$300$	−7.51030	−0.433607
$301$	−5.67789	−0.327268
$302$	47.3290	2.72348
$303$	8.65629	0.497291
$304$	−8.29084	−0.475512
$305$	−2.06561	−0.118277
$306$	−1.96819	−0.112514
$307$	−12.3380	−0.704168	−0.352084	−	0.935968i	$-0.614527\pi$
$307$	−12.3380	−0.704168	−0.352084	+	0.935968i	$0.614527\pi$
$308$	6.03050	0.343620
$309$	−1.04283	−0.0593247
$310$	−22.4979	−1.27779
$311$	27.6476	1.56775	0.783875	−	0.620918i	$-0.213240\pi$
$311$	27.6476	1.56775	0.783875	+	0.620918i	$0.213240\pi$
$312$	0.543259	0.0307560
$313$	21.5701	1.21921	0.609606	−	0.792705i	$-0.291328\pi$
$313$	21.5701	1.21921	0.609606	+	0.792705i	$0.291328\pi$
$314$	43.6465	2.46312
$315$	2.63604	0.148524
$316$	12.4004	0.697579
$317$	−5.48197	−0.307898	−0.153949	−	0.988079i	$-0.549199\pi$
$317$	−5.48197	−0.307898	−0.153949	+	0.988079i	$0.549199\pi$
$318$	−10.8689	−0.609498
$319$	11.0974	0.621333
$320$	−14.8417	−0.829679
$321$	−5.53855	−0.309132
$322$	8.12505	0.452792
$323$	−1.31845	−0.0733606
$324$	0.171499	0.00952772
$325$	2.10893	0.116982
$326$	47.1576	2.61182
$327$	−0.117137	−0.00647771
$328$	−0.750285	−0.0414275
$329$	−7.52204	−0.414703
$330$	8.06432	0.443926
$331$	12.8765	0.707758	0.353879	−	0.935291i	$-0.384862\pi$
$331$	12.8765	0.707758	0.353879	+	0.935291i	$0.384862\pi$
$332$	−32.3706	−1.77657
$333$	5.10518	0.279762
$334$	13.3447	0.730188
$335$	−4.55438	−0.248833
$336$	3.39065	0.184975
$337$	−28.0562	−1.52832	−0.764159	−	0.645028i	$-0.776846\pi$
$337$	−28.0562	−1.52832	−0.764159	+	0.645028i	$0.776846\pi$
$338$	26.0788	1.41850
$339$	−20.4122	−1.10864
$340$	−1.67975	−0.0910973
$341$	−19.6040	−1.06162
$342$	10.1308	0.547809
$343$	−1.00000	−0.0539949
$344$	−4.12157	−0.222220
$345$	5.86758	0.315900
$346$	−23.2052	−1.24752
$347$	−36.5381	−1.96147	−0.980733	−	0.195353i	$-0.937415\pi$
$347$	−36.5381	−1.96147	−0.980733	+	0.195353i	$0.937415\pi$
$348$	−10.8096	−0.579454
$349$	−10.1059	−0.540958	−0.270479	−	0.962726i	$-0.587182\pi$
$349$	−10.1059	−0.540958	−0.270479	+	0.962726i	$0.587182\pi$
$350$	−6.26015	−0.334619
$351$	3.64092	0.194338
$352$	−20.7722	−1.10716
$353$	20.2893	1.07989	0.539945	−	0.841700i	$-0.318445\pi$
$353$	20.2893	1.07989	0.539945	+	0.841700i	$0.318445\pi$
$354$	11.7274	0.623302
$355$	15.2271	0.808171
$356$	−5.65901	−0.299927
$357$	0.539198	0.0285374
$358$	16.2882	0.860856
$359$	4.26981	0.225352	0.112676	−	0.993632i	$-0.464058\pi$
$359$	4.26981	0.225352	0.112676	+	0.993632i	$0.464058\pi$
$360$	1.91350	0.100850
$361$	−12.2136	−0.642822
$362$	21.9946	1.15601
$363$	−4.69213	−0.246273
$364$	1.64948	0.0864563
$365$	4.81592	0.252077
$366$	3.24655	0.169700
$367$	−18.0848	−0.944017	−0.472008	−	0.881594i	$-0.656471\pi$
$367$	−18.0848	−0.944017	−0.472008	+	0.881594i	$0.656471\pi$
$368$	−12.4010	−0.646444
$369$	−1.92763	−0.100348
$370$	8.06808	0.419439
$371$	−4.89251	−0.254007
$372$	19.0956	0.990061
$373$	16.0926	0.833242	0.416621	−	0.909080i	$-0.363214\pi$
$373$	16.0926	0.833242	0.416621	+	0.909080i	$0.363214\pi$
$374$	−2.71038	−0.140150
$375$	−12.0501	−0.622265
$376$	−5.46023	−0.281590
$377$	3.03538	0.156330
$378$	−10.8077	−0.555889
$379$	−35.1115	−1.80355	−0.901777	−	0.432201i	$-0.857737\pi$
$379$	−35.1115	−1.80355	−0.901777	+	0.432201i	$0.857737\pi$
$380$	8.64608	0.443534
$381$	−5.23079	−0.267981
$382$	−17.6679	−0.903970
$383$	−1.87811	−0.0959670	−0.0479835	−	0.998848i	$-0.515279\pi$
$383$	−1.87811	−0.0959670	−0.0479835	+	0.998848i	$0.515279\pi$
$384$	6.09312	0.310938
$385$	3.63006	0.185005
$386$	18.4679	0.939992
$387$	−10.5891	−0.538275
$388$	10.4571	0.530879
$389$	37.0362	1.87781	0.938906	−	0.344173i	$-0.111841\pi$
$389$	37.0362	1.87781	0.938906	+	0.344173i	$0.111841\pi$
$390$	2.20578	0.111694
$391$	−1.97206	−0.0997315
$392$	−0.725898	−0.0366634
$393$	−9.49611	−0.479015
$394$	7.53505	0.379610
$395$	7.46444	0.375577
$396$	11.2467	0.565169
$397$	30.6607	1.53882	0.769408	−	0.638757i	$-0.220551\pi$
$397$	30.6607	1.53882	0.769408	+	0.638757i	$0.220551\pi$
$398$	−1.03123	−0.0516908
$399$	−2.77538	−0.138943
$400$	9.55462	0.477731
$401$	−32.6588	−1.63090	−0.815451	−	0.578826i	$-0.803511\pi$
$401$	−32.6588	−1.63090	−0.815451	+	0.578826i	$0.803511\pi$
$402$	7.15819	0.357018
$403$	−5.36214	−0.267107
$404$	19.0787	0.949200
$405$	0.103234	0.00512973
$406$	−9.01024	−0.447171
$407$	7.03029	0.348478
$408$	0.391403	0.0193773
$409$	−10.3403	−0.511293	−0.255646	−	0.966770i	$-0.582288\pi$
$409$	−10.3403	−0.511293	−0.255646	+	0.966770i	$0.582288\pi$
$410$	−3.04636	−0.150449
$411$	−13.8418	−0.682767
$412$	−2.29843	−0.113235
$413$	5.27894	0.259760
$414$	15.1530	0.744729
$415$	−19.4855	−0.956505
$416$	−5.68169	−0.278568
$417$	9.24599	0.452778
$418$	13.9509	0.682363
$419$	8.33316	0.407102	0.203551	−	0.979064i	$-0.434752\pi$
$419$	8.33316	0.407102	0.203551	+	0.979064i	$0.434752\pi$
$420$	−3.53593	−0.172536
$421$	15.8152	0.770786	0.385393	−	0.922753i	$-0.374066\pi$
$421$	15.8152	0.770786	0.385393	+	0.922753i	$0.374066\pi$
$422$	−50.6410	−2.46517
$423$	−14.0284	−0.682084
$424$	−3.55147	−0.172474
$425$	1.51942	0.0737029
$426$	−23.9327	−1.15954
$427$	1.46140	0.0707220
$428$	−12.2071	−0.590053
$429$	1.92205	0.0927975
$430$	−16.7347	−0.807019
$431$	−3.44136	−0.165765	−0.0828823	−	0.996559i	$-0.526413\pi$
$431$	−3.44136	−0.165765	−0.0828823	+	0.996559i	$0.526413\pi$
$432$	16.4954	0.793636
$433$	13.8122	0.663771	0.331885	−	0.943320i	$-0.392315\pi$
$433$	13.8122	0.663771	0.331885	+	0.943320i	$0.392315\pi$
$434$	15.9170	0.764040
$435$	−6.50683	−0.311978
$436$	−0.258174	−0.0123643
$437$	10.1507	0.485573
$438$	−7.56925	−0.361673
$439$	27.0903	1.29295	0.646476	−	0.762935i	$-0.276242\pi$
$439$	27.0903	1.29295	0.646476	+	0.762935i	$0.276242\pi$
$440$	2.63506	0.125621
$441$	−1.86497	−0.0888082
$442$	−0.741350	−0.0352624
$443$	27.2779	1.29601	0.648007	−	0.761635i	$-0.275603\pi$
$443$	27.2779	1.29601	0.648007	+	0.761635i	$0.275603\pi$
$444$	−6.84797	−0.324990
$445$	−3.40644	−0.161481
$446$	31.0162	1.46866
$447$	−8.63619	−0.408478
$448$	10.5004	0.496096
$449$	−18.7095	−0.882954	−0.441477	−	0.897272i	$-0.645545\pi$
$449$	−18.7095	−0.882954	−0.441477	+	0.897272i	$0.645545\pi$
$450$	−11.6750	−0.550365
$451$	−2.65451	−0.124996
$452$	−44.9890	−2.11610
$453$	−24.1813	−1.13614
$454$	−8.64490	−0.405725
$455$	0.992905	0.0465481
$456$	−2.01464	−0.0943443
$457$	20.8421	0.974954	0.487477	−	0.873136i	$-0.337917\pi$
$457$	20.8421	0.974954	0.487477	+	0.873136i	$0.337917\pi$
$458$	26.8481	1.25453
$459$	2.62318	0.122440
$460$	12.9323	0.602971
$461$	20.4860	0.954130	0.477065	−	0.878868i	$-0.341701\pi$
$461$	20.4860	0.954130	0.477065	+	0.878868i	$0.341701\pi$
$462$	−5.70542	−0.265440
$463$	2.73920	0.127302	0.0636508	−	0.997972i	$-0.479726\pi$
$463$	2.73920	0.127302	0.0636508	+	0.997972i	$0.479726\pi$
$464$	13.7520	0.638420
$465$	11.4946	0.533049
$466$	14.3982	0.666986
$467$	1.19675	0.0553791	0.0276896	−	0.999617i	$-0.491185\pi$
$467$	1.19675	0.0553791	0.0276896	+	0.999617i	$0.491185\pi$
$468$	3.07624	0.142199
$469$	3.22218	0.148786
$470$	−22.1700	−1.02263
$471$	−22.2999	−1.02752
$472$	3.83197	0.176381
$473$	−14.5821	−0.670487
$474$	−11.7320	−0.538867
$475$	−7.82084	−0.358845
$476$	1.18841	0.0544705
$477$	−9.12440	−0.417778
$478$	−40.9791	−1.87434
$479$	−2.93839	−0.134259	−0.0671293	−	0.997744i	$-0.521384\pi$
$479$	−2.93839	−0.134259	−0.0671293	+	0.997744i	$0.521384\pi$
$480$	12.1796	0.555920
$481$	1.92294	0.0876787
$482$	54.9505	2.50293
$483$	−4.15125	−0.188888
$484$	−10.3416	−0.470071
$485$	6.29465	0.285825
$486$	−32.5854	−1.47810
$487$	14.1821	0.642654	0.321327	−	0.946968i	$-0.395871\pi$
$487$	14.1821	0.642654	0.321327	+	0.946968i	$0.395871\pi$
$488$	1.06083	0.0480213
$489$	−24.0938	−1.08956
$490$	−2.94734	−0.133147
$491$	−39.8967	−1.80051	−0.900256	−	0.435360i	$-0.856621\pi$
$491$	−39.8967	−1.80051	−0.900256	+	0.435360i	$0.856621\pi$
$492$	2.58567	0.116571
$493$	2.18691	0.0984935
$494$	3.81590	0.171686
$495$	6.76996	0.304287
$496$	−24.2935	−1.09081
$497$	−10.7730	−0.483236
$498$	30.6256	1.37237
$499$	−0.343762	−0.0153889	−0.00769446	−	0.999970i	$-0.502449\pi$
$499$	−0.343762	−0.0153889	−0.00769446	+	0.999970i	$0.502449\pi$
$500$	−26.5587	−1.18774
$501$	−6.81805	−0.304608
$502$	9.92253	0.442864
$503$	−19.5465	−0.871535	−0.435767	−	0.900059i	$-0.643523\pi$
$503$	−19.5465	−0.871535	−0.435767	+	0.900059i	$0.643523\pi$
$504$	−1.35378	−0.0603021
$505$	11.4844	0.511050
$506$	20.8670	0.927652
$507$	−13.3242	−0.591747
$508$	−11.5288	−0.511507
$509$	40.8493	1.81062	0.905308	−	0.424757i	$-0.139640\pi$
$509$	40.8493	1.81062	0.905308	+	0.424757i	$0.139640\pi$
$510$	1.58920	0.0703711
$511$	−3.40721	−0.150726
$512$	−30.3617	−1.34181
$513$	−13.5021	−0.596134
$514$	−41.7126	−1.83986
$515$	−1.38354	−0.0609660
$516$	14.2040	0.625295
$517$	−19.3183	−0.849619
$518$	−5.70808	−0.250798
$519$	11.8560	0.520421
$520$	0.720748	0.0316069
$521$	−21.5877	−0.945775	−0.472888	−	0.881123i	$-0.656788\pi$
$521$	−21.5877	−0.945775	−0.472888	+	0.881123i	$0.656788\pi$
$522$	−16.8038	−0.735484
$523$	14.0534	0.614512	0.307256	−	0.951627i	$-0.400589\pi$
$523$	14.0534	0.614512	0.307256	+	0.951627i	$0.400589\pi$
$524$	−20.9297	−0.914317
$525$	3.19843	0.139591
$526$	14.6490	0.638729
$527$	−3.86327	−0.168287
$528$	8.70796	0.378965
$529$	−7.81722	−0.339879
$530$	−14.4199	−0.626361
$531$	9.84507	0.427240
$532$	−6.11701	−0.265206
$533$	−0.726069	−0.0314495
$534$	5.35395	0.231688
$535$	−7.34807	−0.317685
$536$	2.33897	0.101028
$537$	−8.32194	−0.359118
$538$	20.8353	0.898274
$539$	−2.56823	−0.110621
$540$	−17.2022	−0.740264
$541$	8.89486	0.382420	0.191210	−	0.981549i	$-0.438759\pi$
$541$	8.89486	0.382420	0.191210	+	0.981549i	$0.438759\pi$
$542$	7.61112	0.326925
$543$	−11.2375	−0.482246
$544$	−4.09350	−0.175507
$545$	−0.155408	−0.00665693
$546$	−1.56056	−0.0667860
$547$	29.0659	1.24277	0.621384	−	0.783506i	$-0.286571\pi$
$547$	29.0659	1.24277	0.621384	+	0.783506i	$0.286571\pi$
$548$	−30.5077	−1.30323
$549$	2.72547	0.116320
$550$	−16.0775	−0.685547
$551$	−11.2565	−0.479545
$552$	−3.01339	−0.128258
$553$	−5.28101	−0.224571
$554$	14.9209	0.633928
$555$	−4.12214	−0.174975
$556$	20.3784	0.864237
$557$	8.37417	0.354825	0.177412	−	0.984137i	$-0.443227\pi$
$557$	8.37417	0.354825	0.177412	+	0.984137i	$0.443227\pi$
$558$	29.6848	1.25666
$559$	−3.98855	−0.168698
$560$	4.49842	0.190093
$561$	1.38478	0.0584657
$562$	28.7437	1.21248
$563$	46.6652	1.96670	0.983352	−	0.181712i	$-0.0581638\pi$
$563$	46.6652	1.96670	0.983352	+	0.181712i	$0.0581638\pi$
$564$	18.8174	0.792353
$565$	−27.0811	−1.13931
$566$	3.02497	0.127149
$567$	−0.0730368	−0.00306726
$568$	−7.82012	−0.328125
$569$	12.8077	0.536928	0.268464	−	0.963290i	$-0.413484\pi$
$569$	12.8077	0.536928	0.268464	+	0.963290i	$0.413484\pi$
$570$	−8.18000	−0.342622
$571$	−43.3333	−1.81344	−0.906721	−	0.421732i	$-0.861422\pi$
$571$	−43.3333	−1.81344	−0.906721	+	0.421732i	$0.861422\pi$
$572$	4.23625	0.177126
$573$	9.02689	0.377104
$574$	2.15527	0.0899591
$575$	−11.6979	−0.487838
$576$	19.5829	0.815955
$577$	−30.1402	−1.25475	−0.627377	−	0.778716i	$-0.715871\pi$
$577$	−30.1402	−1.25475	−0.627377	+	0.778716i	$0.715871\pi$
$578$	34.9145	1.45225
$579$	−9.43562	−0.392131
$580$	−14.3412	−0.595486
$581$	13.7858	0.571930
$582$	−9.89340	−0.410095
$583$	−12.5651	−0.520393
$584$	−2.47329	−0.102345
$585$	1.85174	0.0765600
$586$	−30.6806	−1.26740
$587$	−32.0772	−1.32397	−0.661984	−	0.749518i	$-0.730285\pi$
$587$	−32.0772	−1.32397	−0.661984	+	0.749518i	$0.730285\pi$
$588$	2.50163	0.103165
$589$	19.8852	0.819355
$590$	15.5588	0.640547
$591$	−3.84981	−0.158360
$592$	8.71201	0.358062
$593$	−3.93413	−0.161555	−0.0807776	−	0.996732i	$-0.525740\pi$
$593$	−3.93413	−0.161555	−0.0807776	+	0.996732i	$0.525740\pi$
$594$	−27.7567	−1.13887
$595$	0.715361	0.0293269
$596$	−19.0344	−0.779679
$597$	0.526875	0.0215635
$598$	5.70760	0.233401
$599$	−8.19812	−0.334966	−0.167483	−	0.985875i	$-0.553564\pi$
$599$	−8.19812	−0.334966	−0.167483	+	0.985875i	$0.553564\pi$
$600$	2.32174	0.0947845
$601$	−13.3043	−0.542695	−0.271348	−	0.962481i	$-0.587469\pi$
$601$	−13.3043	−0.542695	−0.271348	+	0.962481i	$0.587469\pi$
$602$	11.8396	0.482547
$603$	6.00927	0.244716
$604$	−53.2963	−2.16859
$605$	−6.22511	−0.253087
$606$	−18.0502	−0.733240
$607$	−10.8886	−0.441956	−0.220978	−	0.975279i	$-0.570925\pi$
$607$	−10.8886	−0.441956	−0.220978	+	0.975279i	$0.570925\pi$
$608$	21.0702	0.854510
$609$	4.60351	0.186544
$610$	4.30724	0.174395
$611$	−5.28400	−0.213768
$612$	2.21634	0.0895904
$613$	−15.1349	−0.611295	−0.305647	−	0.952145i	$-0.598873\pi$
$613$	−15.1349	−0.611295	−0.305647	+	0.952145i	$0.598873\pi$
$614$	25.7274	1.03827
$615$	1.55645	0.0627619
$616$	−1.86427	−0.0751137
$617$	−20.1274	−0.810299	−0.405149	−	0.914251i	$-0.632780\pi$
$617$	−20.1274	−0.810299	−0.405149	+	0.914251i	$0.632780\pi$
$618$	2.17453	0.0874724
$619$	−39.4558	−1.58586	−0.792931	−	0.609311i	$-0.791446\pi$
$619$	−39.4558	−1.58586	−0.792931	+	0.609311i	$0.791446\pi$
$620$	25.3344	1.01745
$621$	−20.1957	−0.810426
$622$	−57.6511	−2.31160
$623$	2.41002	0.0965554
$624$	2.38183	0.0953494
$625$	−0.976217	−0.0390487
$626$	−44.9782	−1.79769
$627$	−7.12781	−0.284657
$628$	−49.1495	−1.96128
$629$	1.38543	0.0552407
$630$	−5.49671	−0.218994
$631$	−18.9594	−0.754760	−0.377380	−	0.926058i	$-0.623175\pi$
$631$	−18.9594	−0.754760	−0.377380	+	0.926058i	$0.623175\pi$
$632$	−3.83348	−0.152488
$633$	25.8735	1.02838
$634$	11.4311	0.453986
$635$	−6.93975	−0.275396
$636$	12.2393	0.485318
$637$	−0.702470	−0.0278329
$638$	−23.1404	−0.916136
$639$	−20.0914	−0.794803
$640$	8.08382	0.319541
$641$	−35.0022	−1.38250	−0.691252	−	0.722613i	$-0.742941\pi$
$641$	−35.0022	−1.38250	−0.691252	+	0.722613i	$0.742941\pi$
$642$	11.5491	0.455805
$643$	41.2139	1.62532	0.812658	−	0.582741i	$-0.198020\pi$
$643$	41.2139	1.62532	0.812658	+	0.582741i	$0.198020\pi$
$644$	−9.14946	−0.360539
$645$	8.55009	0.336659
$646$	2.74925	0.108168
$647$	−12.1397	−0.477263	−0.238631	−	0.971110i	$-0.576699\pi$
$647$	−12.1397	−0.477263	−0.238631	+	0.971110i	$0.576699\pi$
$648$	−0.0530173	−0.00208272
$649$	13.5575	0.532179
$650$	−4.39756	−0.172487
$651$	−8.13231	−0.318730
$652$	−53.1032	−2.07968
$653$	22.6731	0.887265	0.443633	−	0.896209i	$-0.353689\pi$
$653$	22.6731	0.887265	0.443633	+	0.896209i	$0.353689\pi$
$654$	0.244257	0.00955119
$655$	−12.5986	−0.492269
$656$	−3.28950	−0.128433
$657$	−6.35436	−0.247907
$658$	15.6851	0.611467
$659$	41.4499	1.61466	0.807329	−	0.590102i	$-0.200912\pi$
$659$	41.4499	1.61466	0.807329	+	0.590102i	$0.200912\pi$
$660$	−9.08107	−0.353480
$661$	−32.9221	−1.28052	−0.640260	−	0.768158i	$-0.721173\pi$
$661$	−32.9221	−1.28052	−0.640260	+	0.768158i	$0.721173\pi$
$662$	−26.8503	−1.04357
$663$	0.378770	0.0147102
$664$	10.0071	0.388350
$665$	−3.68213	−0.142787
$666$	−10.6454	−0.412501
$667$	−16.8369	−0.651926
$668$	−15.0272	−0.581418
$669$	−15.8468	−0.612673
$670$	9.49686	0.366896
$671$	3.75321	0.144891
$672$	−8.61694	−0.332406
$673$	23.4868	0.905350	0.452675	−	0.891676i	$-0.350470\pi$
$673$	23.4868	0.905350	0.452675	+	0.891676i	$0.350470\pi$
$674$	58.5031	2.25346
$675$	15.5603	0.598916
$676$	−29.3668	−1.12949
$677$	27.8418	1.07005	0.535023	−	0.844837i	$-0.320303\pi$
$677$	27.8418	1.07005	0.535023	+	0.844837i	$0.320303\pi$
$678$	42.5638	1.63465
$679$	−4.45340	−0.170906
$680$	0.519279	0.0199134
$681$	4.41685	0.169254
$682$	40.8785	1.56532
$683$	−47.0118	−1.79886	−0.899428	−	0.437069i	$-0.856017\pi$
$683$	−47.0118	−1.79886	−0.899428	+	0.437069i	$0.856017\pi$
$684$	−11.4080	−0.436198
$685$	−18.3641	−0.701658
$686$	2.08521	0.0796138
$687$	−13.7172	−0.523346
$688$	−18.0704	−0.688926
$689$	−3.43684	−0.130933
$690$	−12.2352	−0.465785
$691$	25.0579	0.953249	0.476624	−	0.879107i	$-0.341860\pi$
$691$	25.0579	0.953249	0.476624	+	0.879107i	$0.341860\pi$
$692$	26.1309	0.993349
$693$	−4.78968	−0.181945
$694$	76.1897	2.89212
$695$	12.2668	0.465305
$696$	3.34168	0.126666
$697$	−0.523113	−0.0198143
$698$	21.0730	0.797626
$699$	−7.35635	−0.278243
$700$	7.04943	0.266443
$701$	31.2912	1.18185	0.590926	−	0.806726i	$-0.298763\pi$
$701$	31.2912	1.18185	0.590926	+	0.806726i	$0.298763\pi$
$702$	−7.59210	−0.286545
$703$	−7.13113	−0.268956
$704$	26.9674	1.01637
$705$	11.3271	0.426603
$706$	−42.3075	−1.59227
$707$	−8.12510	−0.305576
$708$	−13.2059	−0.496310
$709$	45.5967	1.71242	0.856211	−	0.516627i	$-0.172813\pi$
$709$	45.5967	1.71242	0.856211	+	0.516627i	$0.172813\pi$
$710$	−31.7518	−1.19162
$711$	−9.84894	−0.369364
$712$	1.74943	0.0655626
$713$	29.7431	1.11389
$714$	−1.12434	−0.0420775
$715$	2.55001	0.0953649
$716$	−18.3418	−0.685464
$717$	20.9370	0.781908
$718$	−8.90346	−0.332274
$719$	−7.83200	−0.292084	−0.146042	−	0.989278i	$-0.546654\pi$
$719$	−7.83200	−0.292084	−0.146042	+	0.989278i	$0.546654\pi$
$720$	8.38942	0.312655
$721$	0.978839	0.0364539
$722$	25.4680	0.947821
$723$	−28.0753	−1.04413
$724$	−24.7677	−0.920483
$725$	12.9724	0.481782
$726$	9.78409	0.363122
$727$	−22.0184	−0.816617	−0.408309	−	0.912844i	$-0.633881\pi$
$727$	−22.0184	−0.816617	−0.408309	+	0.912844i	$0.633881\pi$
$728$	−0.509921	−0.0188989
$729$	16.4294	0.608497
$730$	−10.0422	−0.371679
$731$	−2.87364	−0.106285
$732$	−3.65588	−0.135125
$733$	44.5046	1.64382	0.821908	−	0.569621i	$-0.192910\pi$
$733$	44.5046	1.64382	0.821908	+	0.569621i	$0.192910\pi$
$734$	37.7106	1.39192
$735$	1.50586	0.0555443
$736$	31.5156	1.16168
$737$	8.27529	0.304824
$738$	4.01951	0.147960
$739$	−48.8238	−1.79601	−0.898006	−	0.439984i	$-0.854984\pi$
$739$	−48.8238	−1.79601	−0.898006	+	0.439984i	$0.854984\pi$
$740$	−9.08530	−0.333982
$741$	−1.94962	−0.0716211
$742$	10.2019	0.374525
$743$	−25.8681	−0.949010	−0.474505	−	0.880253i	$-0.657373\pi$
$743$	−25.8681	−0.949010	−0.474505	+	0.880253i	$0.657373\pi$
$744$	−5.90323	−0.216423
$745$	−11.4577	−0.419779
$746$	−33.5565	−1.22859
$747$	25.7101	0.940683
$748$	3.05210	0.111596
$749$	5.19868	0.189956
$750$	25.1270	0.917510
$751$	−6.30271	−0.229989	−0.114995	−	0.993366i	$-0.536685\pi$
$751$	−6.30271	−0.229989	−0.114995	+	0.993366i	$0.536685\pi$
$752$	−23.9395	−0.872983
$753$	−5.06962	−0.184747
$754$	−6.32942	−0.230504
$755$	−32.0817	−1.16757
$756$	12.1704	0.442632
$757$	−52.6326	−1.91296	−0.956482	−	0.291792i	$-0.905748\pi$
$757$	−52.6326	−1.91296	−0.956482	+	0.291792i	$0.905748\pi$
$758$	73.2149	2.65929
$759$	−10.6614	−0.386983
$760$	−2.67285	−0.0969546
$761$	21.6987	0.786577	0.393288	−	0.919415i	$-0.371337\pi$
$761$	21.6987	0.786577	0.393288	+	0.919415i	$0.371337\pi$
$762$	10.9073	0.395130
$763$	0.109949	0.00398043
$764$	19.8955	0.719794
$765$	1.33413	0.0482355
$766$	3.91626	0.141500
$767$	3.70829	0.133899
$768$	9.66826	0.348873
$769$	−11.1569	−0.402330	−0.201165	−	0.979557i	$-0.564473\pi$
$769$	−11.1569	−0.402330	−0.201165	+	0.979557i	$0.564473\pi$
$770$	−7.56946	−0.272784
$771$	21.3118	0.767526
$772$	−20.7963	−0.748477
$773$	5.30657	0.190864	0.0954320	−	0.995436i	$-0.469577\pi$
$773$	5.30657	0.190864	0.0954320	+	0.995436i	$0.469577\pi$
$774$	22.0806	0.793669
$775$	−22.9163	−0.823178
$776$	−3.23271	−0.116048
$777$	2.91637	0.104624
$778$	−77.2285	−2.76878
$779$	2.69259	0.0964719
$780$	−2.48388	−0.0889372
$781$	−27.6676	−0.990024
$782$	4.11217	0.147051
$783$	22.3959	0.800366
$784$	−3.18258	−0.113664
$785$	−29.5855	−1.05595
$786$	19.8014	0.706293
$787$	−6.80601	−0.242608	−0.121304	−	0.992615i	$-0.538708\pi$
$787$	−6.80601	−0.242608	−0.121304	+	0.992615i	$0.538708\pi$
$788$	−8.48507	−0.302268
$789$	−7.48449	−0.266455
$790$	−15.5650	−0.553776
$791$	19.1596	0.681237
$792$	−3.47682	−0.123543
$793$	1.02659	0.0364552
$794$	−63.9341	−2.26894
$795$	7.36742	0.261295
$796$	1.16124	0.0411592
$797$	−2.00953	−0.0711812	−0.0355906	−	0.999366i	$-0.511331\pi$
$797$	−2.00953	−0.0711812	−0.0355906	+	0.999366i	$0.511331\pi$
$798$	5.78726	0.204867
$799$	−3.80698	−0.134681
$800$	−24.2820	−0.858497
$801$	4.49462	0.158810
$802$	68.1006	2.40472
$803$	−8.75050	−0.308799
$804$	−8.06069	−0.284279
$805$	−5.50752	−0.194114
$806$	11.1812	0.393841
$807$	−10.6452	−0.374728
$808$	−5.89800	−0.207491
$809$	−19.8187	−0.696789	−0.348395	−	0.937348i	$-0.613273\pi$
$809$	−19.8187	−0.696789	−0.348395	+	0.937348i	$0.613273\pi$
$810$	−0.215265	−0.00756363
$811$	−17.4997	−0.614497	−0.307248	−	0.951629i	$-0.599408\pi$
$811$	−17.4997	−0.614497	−0.307248	+	0.951629i	$0.599408\pi$
$812$	10.1462	0.356064
$813$	−3.88867	−0.136382
$814$	−14.6597	−0.513821
$815$	−31.9655	−1.11970
$816$	1.71604	0.0600735
$817$	14.7913	0.517482
$818$	21.5616	0.753885
$819$	−1.31009	−0.0457781
$820$	3.43044	0.119796
$821$	−10.7808	−0.376252	−0.188126	−	0.982145i	$-0.560241\pi$
$821$	−10.7808	−0.376252	−0.188126	+	0.982145i	$0.560241\pi$
$822$	28.8632	1.00672
$823$	−47.7265	−1.66364	−0.831821	−	0.555045i	$-0.812701\pi$
$823$	−47.7265	−1.66364	−0.831821	+	0.555045i	$0.812701\pi$
$824$	0.710537	0.0247527
$825$	8.21431	0.285986
$826$	−11.0077	−0.383007
$827$	22.8929	0.796065	0.398033	−	0.917371i	$-0.369693\pi$
$827$	22.8929	0.796065	0.398033	+	0.917371i	$0.369693\pi$
$828$	−17.0635	−0.592997
$829$	−49.1528	−1.70715	−0.853574	−	0.520971i	$-0.825570\pi$
$829$	−49.1528	−1.70715	−0.853574	+	0.520971i	$0.825570\pi$
$830$	40.6314	1.41034
$831$	−7.62338	−0.264452
$832$	7.37620	0.255724
$833$	−0.506110	−0.0175357
$834$	−19.2799	−0.667607
$835$	−9.04560	−0.313036
$836$	−15.7099	−0.543337
$837$	−39.5634	−1.36751
$838$	−17.3764	−0.600258
$839$	22.6936	0.783468	0.391734	−	0.920078i	$-0.371875\pi$
$839$	22.6936	0.783468	0.391734	+	0.920078i	$0.371875\pi$
$840$	1.09310	0.0377155
$841$	−10.3288	−0.356166
$842$	−32.9781	−1.13650
$843$	−14.6857	−0.505803
$844$	57.0258	1.96291
$845$	−17.6774	−0.608119
$846$	29.2522	1.00571
$847$	4.40420	0.151330
$848$	−15.5708	−0.534704
$849$	−1.54552	−0.0530421
$850$	−3.16833	−0.108673
$851$	−10.6663	−0.365637
$852$	26.9501	0.923295
$853$	−38.3085	−1.31166	−0.655829	−	0.754909i	$-0.727681\pi$
$853$	−38.3085	−1.31166	−0.655829	+	0.754909i	$0.727681\pi$
$854$	−3.04733	−0.104277
$855$	−6.86707	−0.234849
$856$	3.77371	0.128983
$857$	−19.5713	−0.668543	−0.334272	−	0.942477i	$-0.608490\pi$
$857$	−19.5713	−0.668543	−0.334272	+	0.942477i	$0.608490\pi$
$858$	−4.00789	−0.136827
$859$	−49.2275	−1.67962	−0.839811	−	0.542879i	$-0.817334\pi$
$859$	−49.2275	−1.67962	−0.839811	+	0.542879i	$0.817334\pi$
$860$	18.8446	0.642596
$861$	−1.10117	−0.0375277
$862$	7.17597	0.244415
$863$	−1.00000	−0.0340404
$863$	−1.00000	−0.0340404
$864$	−41.9212	−1.42619
$865$	15.7295	0.534819
$866$	−28.8013	−0.978710
$867$	−17.8385	−0.605828
$868$	−17.9238	−0.608374
$869$	−13.5629	−0.460088
$870$	13.5681	0.460003
$871$	2.26348	0.0766952
$872$	0.0798120	0.00270277
$873$	−8.30546	−0.281097
$874$	−21.1663	−0.715962
$875$	11.3106	0.382370
$876$	8.52358	0.287985
$877$	−12.2999	−0.415337	−0.207669	−	0.978199i	$-0.566588\pi$
$877$	−12.2999	−0.415337	−0.207669	+	0.978199i	$0.566588\pi$
$878$	−56.4892	−1.90642
$879$	15.6753	0.528715
$880$	11.5530	0.389450
$881$	37.5016	1.26346	0.631731	−	0.775188i	$-0.282345\pi$
$881$	37.5016	1.26346	0.631731	+	0.775188i	$0.282345\pi$
$882$	3.88887	0.130945
$883$	23.3283	0.785061	0.392530	−	0.919739i	$-0.371600\pi$
$883$	23.3283	0.785061	0.392530	+	0.919739i	$0.371600\pi$
$884$	0.834819	0.0280780
$885$	−7.94932	−0.267213
$886$	−56.8803	−1.91093
$887$	−48.5401	−1.62982	−0.814908	−	0.579590i	$-0.803213\pi$
$887$	−48.5401	−1.62982	−0.814908	+	0.579590i	$0.803213\pi$
$888$	2.11699	0.0710414
$889$	4.90980	0.164669
$890$	7.10316	0.238098
$891$	−0.187575	−0.00628401
$892$	−34.9267	−1.16943
$893$	19.5954	0.655736
$894$	18.0083	0.602288
$895$	−11.0408	−0.369054
$896$	−5.71922	−0.191066
$897$	−2.91613	−0.0973667
$898$	39.0132	1.30189
$899$	−32.9835	−1.10006
$900$	13.1470	0.438233
$901$	−2.47615	−0.0824925
$902$	5.53522	0.184303
$903$	−6.04909	−0.201301
$904$	13.9079	0.462570
$905$	−14.9089	−0.495589
$906$	50.4233	1.67520
$907$	−32.6909	−1.08548	−0.542741	−	0.839900i	$-0.682614\pi$
$907$	−32.6909	−1.08548	−0.542741	+	0.839900i	$0.682614\pi$
$908$	9.73485	0.323062
$909$	−15.1531	−0.502596
$910$	−2.07042	−0.0686337
$911$	−32.0684	−1.06247	−0.531237	−	0.847223i	$-0.678273\pi$
$911$	−32.0684	−1.06247	−0.531237	+	0.847223i	$0.678273\pi$
$912$	−8.83287	−0.292486
$913$	35.4050	1.17174
$914$	−43.4603	−1.43754
$915$	−2.20065	−0.0727514
$916$	−30.2332	−0.998932
$917$	8.91338	0.294346
$918$	−5.46990	−0.180534
$919$	0.745903	0.0246051	0.0123025	−	0.999924i	$-0.496084\pi$
$919$	0.745903	0.0246051	0.0123025	+	0.999924i	$0.496084\pi$
$920$	−3.99790	−0.131807
$921$	−13.1446	−0.433130
$922$	−42.7178	−1.40683
$923$	−7.56772	−0.249095
$924$	6.42476	0.211359
$925$	8.21813	0.270211
$926$	−5.71182	−0.187702
$927$	1.82551	0.0599575
$928$	−34.9491	−1.14726
$929$	−12.1326	−0.398058	−0.199029	−	0.979994i	$-0.563779\pi$
$929$	−12.1326	−0.398058	−0.199029	+	0.979994i	$0.563779\pi$
$930$	−23.9687	−0.785965
$931$	2.60507	0.0853777
$932$	−16.2136	−0.531093
$933$	29.4551	0.964317
$934$	−2.49549	−0.0816548
$935$	1.83721	0.0600832
$936$	−0.950989	−0.0310841
$937$	−30.3604	−0.991832	−0.495916	−	0.868370i	$-0.665168\pi$
$937$	−30.3604	−0.991832	−0.495916	+	0.868370i	$0.665168\pi$
$938$	−6.71893	−0.219381
$939$	22.9802	0.749932
$940$	24.9652	0.814276
$941$	59.6972	1.94607	0.973037	−	0.230648i	$-0.0740845\pi$
$941$	59.6972	1.94607	0.973037	+	0.230648i	$0.0740845\pi$
$942$	46.5000	1.51505
$943$	4.02741	0.131151
$944$	16.8006	0.546814
$945$	7.32595	0.238313
$946$	30.4069	0.988612
$947$	21.5142	0.699118	0.349559	−	0.936914i	$-0.386331\pi$
$947$	21.5142	0.699118	0.349559	+	0.936914i	$0.386331\pi$
$948$	13.2111	0.429078
$949$	−2.39346	−0.0776951
$950$	16.3081	0.529105
$951$	−5.84037	−0.189387
$952$	−0.367384	−0.0119070
$953$	−9.07175	−0.293863	−0.146931	−	0.989147i	$-0.546940\pi$
$953$	−9.07175	−0.293863	−0.146931	+	0.989147i	$0.546940\pi$
$954$	19.0263	0.616000
$955$	11.9761	0.387537
$956$	46.1457	1.49246
$957$	11.8229	0.382179
$958$	6.12718	0.197960
$959$	12.9924	0.419548
$960$	−15.8121	−0.510332
$961$	27.2668	0.879573
$962$	−4.00975	−0.129280
$963$	9.69539	0.312430
$964$	−61.8786	−1.99298
$965$	−12.5184	−0.402980
$966$	8.65625	0.278510
$967$	19.8922	0.639690	0.319845	−	0.947470i	$-0.396369\pi$
$967$	19.8922	0.639690	0.319845	+	0.947470i	$0.396369\pi$
$968$	3.19700	0.102755
$969$	−1.40465	−0.0451238
$970$	−13.1257	−0.421441
$971$	15.8409	0.508360	0.254180	−	0.967157i	$-0.418194\pi$
$971$	15.8409	0.508360	0.254180	+	0.967157i	$0.418194\pi$
$972$	36.6938	1.17695
$973$	−8.67861	−0.278224
$974$	−29.5728	−0.947574
$975$	2.24680	0.0719553
$976$	4.65102	0.148875
$977$	4.88390	0.156250	0.0781248	−	0.996944i	$-0.475107\pi$
$977$	4.88390	0.156250	0.0781248	+	0.996944i	$0.475107\pi$
$978$	50.2406	1.60652
$979$	6.18948	0.197817
$980$	3.31894	0.106020
$981$	0.205052	0.00654682
$982$	83.1932	2.65480
$983$	9.19229	0.293189	0.146594	−	0.989197i	$-0.453169\pi$
$983$	9.19229	0.293189	0.146594	+	0.989197i	$0.453169\pi$
$984$	−0.799336	−0.0254819
$985$	−5.10759	−0.162741
$986$	−4.56017	−0.145226
$987$	−8.01381	−0.255082
$988$	−4.29701	−0.136706
$989$	22.1240	0.703501
$990$	−14.1168	−0.448662
$991$	36.8820	1.17160	0.585798	−	0.810457i	$-0.300781\pi$
$991$	36.8820	1.17160	0.585798	+	0.810457i	$0.300781\pi$
$992$	61.7391	1.96022
$993$	13.7184	0.435339
$994$	22.4641	0.712516
$995$	0.699011	0.0221601
$996$	−34.4869	−1.09276
$997$	−24.1562	−0.765034	−0.382517	−	0.923949i	$-0.624943\pi$
$997$	−24.1562	−0.765034	−0.382517	+	0.923949i	$0.624943\pi$
$998$	0.716818	0.0226905
$999$	14.1881	0.448890

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6041.2.a.d.1.15	✓	101

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6041.2.a.d.1.15	✓	101	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6041 = 7 \cdot 863 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6041.a (trivial)

\(f(q)\)	\(=\)	\(q-2.08521 q^{2} +1.06538 q^{3} +2.34812 q^{4} +1.41345 q^{5} -2.22154 q^{6} -1.00000 q^{7} -0.725898 q^{8} -1.86497 q^{9} +O(q^{10})\)	\(q-2.08521 q^{2} +1.06538 q^{3} +2.34812 q^{4} +1.41345 q^{5} -2.22154 q^{6} -1.00000 q^{7} -0.725898 q^{8} -1.86497 q^{9} -2.94734 q^{10} -2.56823 q^{11} +2.50163 q^{12} -0.702470 q^{13} +2.08521 q^{14} +1.50586 q^{15} -3.18258 q^{16} -0.506110 q^{17} +3.88887 q^{18} +2.60507 q^{19} +3.31894 q^{20} -1.06538 q^{21} +5.35531 q^{22} +3.89651 q^{23} -0.773355 q^{24} -3.00216 q^{25} +1.46480 q^{26} -5.18303 q^{27} -2.34812 q^{28} -4.32102 q^{29} -3.14003 q^{30} +7.63327 q^{31} +8.08816 q^{32} -2.73613 q^{33} +1.05535 q^{34} -1.41345 q^{35} -4.37917 q^{36} -2.73741 q^{37} -5.43213 q^{38} -0.748395 q^{39} -1.02602 q^{40} +1.03359 q^{41} +2.22154 q^{42} +5.67789 q^{43} -6.03050 q^{44} -2.63604 q^{45} -8.12505 q^{46} +7.52204 q^{47} -3.39065 q^{48} +1.00000 q^{49} +6.26015 q^{50} -0.539198 q^{51} -1.64948 q^{52} +4.89251 q^{53} +10.8077 q^{54} -3.63006 q^{55} +0.725898 q^{56} +2.77538 q^{57} +9.01024 q^{58} -5.27894 q^{59} +3.53593 q^{60} -1.46140 q^{61} -15.9170 q^{62} +1.86497 q^{63} -10.5004 q^{64} -0.992905 q^{65} +5.70542 q^{66} -3.22218 q^{67} -1.18841 q^{68} +4.15125 q^{69} +2.94734 q^{70} +10.7730 q^{71} +1.35378 q^{72} +3.40721 q^{73} +5.70808 q^{74} -3.19843 q^{75} +6.11701 q^{76} +2.56823 q^{77} +1.56056 q^{78} +5.28101 q^{79} -4.49842 q^{80} +0.0730368 q^{81} -2.15527 q^{82} -13.7858 q^{83} -2.50163 q^{84} -0.715361 q^{85} -11.8396 q^{86} -4.60351 q^{87} +1.86427 q^{88} -2.41002 q^{89} +5.49671 q^{90} +0.702470 q^{91} +9.14946 q^{92} +8.13231 q^{93} -15.6851 q^{94} +3.68213 q^{95} +8.61694 q^{96} +4.45340 q^{97} -2.08521 q^{98} +4.78968 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 101 q + 3 q^{2} - 17 q^{3} + 85 q^{4} - 12 q^{5} - 17 q^{6} - 101 q^{7} - 3 q^{8} + 88 q^{9}+O(q^{10}) \) 101 * q + 3 * q^2 - 17 * q^3 + 85 * q^4 - 12 * q^5 - 17 * q^6 - 101 * q^7 - 3 * q^8 + 88 * q^9	\( 101 q + 3 q^{2} - 17 q^{3} + 85 q^{4} - 12 q^{5} - 17 q^{6} - 101 q^{7} - 3 q^{8} + 88 q^{9} - 23 q^{10} - 13 q^{11} - 31 q^{12} - 35 q^{13} - 3 q^{14} - 20 q^{15} + 45 q^{16} - 19 q^{17} + 3 q^{18} - 59 q^{19} - 31 q^{20} + 17 q^{21} - 13 q^{22} - 29 q^{23} - 59 q^{24} + 103 q^{25} - 18 q^{26} - 47 q^{27} - 85 q^{28} - 26 q^{29} - 8 q^{30} - 125 q^{31} + 12 q^{32} - 18 q^{33} - 66 q^{34} + 12 q^{35} + 40 q^{36} + 22 q^{37} - 31 q^{38} - 94 q^{39} - 79 q^{40} - 39 q^{41} + 17 q^{42} - 5 q^{43} - 53 q^{44} - 50 q^{45} - 37 q^{46} - 47 q^{47} - 81 q^{48} + 101 q^{49} + 2 q^{50} - 23 q^{51} - 56 q^{52} - 5 q^{53} - 77 q^{54} - 155 q^{55} + 3 q^{56} + 61 q^{57} - 31 q^{58} - 33 q^{59} - 48 q^{60} - 96 q^{61} - 38 q^{62} - 88 q^{63} - 33 q^{64} - 8 q^{65} - 91 q^{66} + 8 q^{67} - 41 q^{68} - 91 q^{69} + 23 q^{70} - 116 q^{71} - 5 q^{72} - 62 q^{73} - 23 q^{74} - 94 q^{75} - 112 q^{76} + 13 q^{77} + 17 q^{78} - 127 q^{79} - 87 q^{80} + 37 q^{81} - 118 q^{82} - 58 q^{83} + 31 q^{84} - 6 q^{85} - 26 q^{86} - 82 q^{87} - 40 q^{88} - 57 q^{89} - 123 q^{90} + 35 q^{91} - 28 q^{92} - 10 q^{93} - 107 q^{94} - 70 q^{95} - 76 q^{96} - 69 q^{97} + 3 q^{98} - 67 q^{99}+O(q^{100}) \) 101 * q + 3 * q^2 - 17 * q^3 + 85 * q^4 - 12 * q^5 - 17 * q^6 - 101 * q^7 - 3 * q^8 + 88 * q^9 - 23 * q^10 - 13 * q^11 - 31 * q^12 - 35 * q^13 - 3 * q^14 - 20 * q^15 + 45 * q^16 - 19 * q^17 + 3 * q^18 - 59 * q^19 - 31 * q^20 + 17 * q^21 - 13 * q^22 - 29 * q^23 - 59 * q^24 + 103 * q^25 - 18 * q^26 - 47 * q^27 - 85 * q^28 - 26 * q^29 - 8 * q^30 - 125 * q^31 + 12 * q^32 - 18 * q^33 - 66 * q^34 + 12 * q^35 + 40 * q^36 + 22 * q^37 - 31 * q^38 - 94 * q^39 - 79 * q^40 - 39 * q^41 + 17 * q^42 - 5 * q^43 - 53 * q^44 - 50 * q^45 - 37 * q^46 - 47 * q^47 - 81 * q^48 + 101 * q^49 + 2 * q^50 - 23 * q^51 - 56 * q^52 - 5 * q^53 - 77 * q^54 - 155 * q^55 + 3 * q^56 + 61 * q^57 - 31 * q^58 - 33 * q^59 - 48 * q^60 - 96 * q^61 - 38 * q^62 - 88 * q^63 - 33 * q^64 - 8 * q^65 - 91 * q^66 + 8 * q^67 - 41 * q^68 - 91 * q^69 + 23 * q^70 - 116 * q^71 - 5 * q^72 - 62 * q^73 - 23 * q^74 - 94 * q^75 - 112 * q^76 + 13 * q^77 + 17 * q^78 - 127 * q^79 - 87 * q^80 + 37 * q^81 - 118 * q^82 - 58 * q^83 + 31 * q^84 - 6 * q^85 - 26 * q^86 - 82 * q^87 - 40 * q^88 - 57 * q^89 - 123 * q^90 + 35 * q^91 - 28 * q^92 - 10 * q^93 - 107 * q^94 - 70 * q^95 - 76 * q^96 - 69 * q^97 + 3 * q^98 - 67 * q^99

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