LMFDB - Embedded newform 6015.2.a.f.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6015,2,Mod(1,6015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6015, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("6015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6015 = 3 \cdot 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6015.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:	$48.0300168158$
Analytic rank:	$1$
Dimension:	$36$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	6015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.46470 q^{2} -1.00000 q^{3} +0.145344 q^{4} -1.00000 q^{5} +1.46470 q^{6} +1.42914 q^{7} +2.71651 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.46470 q^{2} -1.00000 q^{3} +0.145344 q^{4} -1.00000 q^{5} +1.46470 q^{6} +1.42914 q^{7} +2.71651 q^{8} +1.00000 q^{9} +1.46470 q^{10} +0.0549321 q^{11} -0.145344 q^{12} +7.07979 q^{13} -2.09326 q^{14} +1.00000 q^{15} -4.26956 q^{16} +1.64656 q^{17} -1.46470 q^{18} +1.50699 q^{19} -0.145344 q^{20} -1.42914 q^{21} -0.0804590 q^{22} -5.68165 q^{23} -2.71651 q^{24} +1.00000 q^{25} -10.3698 q^{26} -1.00000 q^{27} +0.207717 q^{28} -4.59597 q^{29} -1.46470 q^{30} +0.146218 q^{31} +0.820597 q^{32} -0.0549321 q^{33} -2.41172 q^{34} -1.42914 q^{35} +0.145344 q^{36} +3.10073 q^{37} -2.20729 q^{38} -7.07979 q^{39} -2.71651 q^{40} -9.34634 q^{41} +2.09326 q^{42} +1.78612 q^{43} +0.00798402 q^{44} -1.00000 q^{45} +8.32190 q^{46} +4.88902 q^{47} +4.26956 q^{48} -4.95755 q^{49} -1.46470 q^{50} -1.64656 q^{51} +1.02900 q^{52} -4.64763 q^{53} +1.46470 q^{54} -0.0549321 q^{55} +3.88229 q^{56} -1.50699 q^{57} +6.73172 q^{58} -10.6253 q^{59} +0.145344 q^{60} -4.83346 q^{61} -0.214166 q^{62} +1.42914 q^{63} +7.33720 q^{64} -7.07979 q^{65} +0.0804590 q^{66} -8.85753 q^{67} +0.239317 q^{68} +5.68165 q^{69} +2.09326 q^{70} +2.43588 q^{71} +2.71651 q^{72} -7.67502 q^{73} -4.54164 q^{74} -1.00000 q^{75} +0.219031 q^{76} +0.0785058 q^{77} +10.3698 q^{78} -4.23997 q^{79} +4.26956 q^{80} +1.00000 q^{81} +13.6896 q^{82} -4.13606 q^{83} -0.207717 q^{84} -1.64656 q^{85} -2.61613 q^{86} +4.59597 q^{87} +0.149224 q^{88} +16.1143 q^{89} +1.46470 q^{90} +10.1180 q^{91} -0.825790 q^{92} -0.146218 q^{93} -7.16095 q^{94} -1.50699 q^{95} -0.820597 q^{96} -1.82733 q^{97} +7.26132 q^{98} +0.0549321 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 7 q^{2} - 36 q^{3} + 45 q^{4} - 36 q^{5} + 7 q^{6} + 2 q^{7} - 24 q^{8} + 36 q^{9}+O(q^{10}) $ 36 * q - 7 * q^2 - 36 * q^3 + 45 * q^4 - 36 * q^5 + 7 * q^6 + 2 * q^7 - 24 * q^8 + 36 * q^9	\( 36 q - 7 q^{2} - 36 q^{3} + 45 q^{4} - 36 q^{5} + 7 q^{6} + 2 q^{7} - 24 q^{8} + 36 q^{9} + 7 q^{10} - q^{11} - 45 q^{12} - 8 q^{13} - 4 q^{14} + 36 q^{15} + 63 q^{16} - 50 q^{17} - 7 q^{18} + 15 q^{19} - 45 q^{20} - 2 q^{21} + 7 q^{22} - 32 q^{23} + 24 q^{24} + 36 q^{25} - 12 q^{26} - 36 q^{27} - 10 q^{28} + 7 q^{29} - 7 q^{30} + 7 q^{31} - 50 q^{32} + q^{33} + 8 q^{34} - 2 q^{35} + 45 q^{36} - 10 q^{37} - 48 q^{38} + 8 q^{39} + 24 q^{40} - 31 q^{41} + 4 q^{42} + 27 q^{43} - 9 q^{44} - 36 q^{45} + 23 q^{46} - 46 q^{47} - 63 q^{48} + 48 q^{49} - 7 q^{50} + 50 q^{51} - 14 q^{52} - 39 q^{53} + 7 q^{54} + q^{55} - 29 q^{56} - 15 q^{57} - 26 q^{58} - 9 q^{59} + 45 q^{60} + 5 q^{61} - 65 q^{62} + 2 q^{63} + 90 q^{64} + 8 q^{65} - 7 q^{66} + 18 q^{67} - 128 q^{68} + 32 q^{69} + 4 q^{70} + 4 q^{71} - 24 q^{72} - 45 q^{73} - 22 q^{74} - 36 q^{75} + 26 q^{76} - 38 q^{77} + 12 q^{78} + 25 q^{79} - 63 q^{80} + 36 q^{81} - 5 q^{82} - 71 q^{83} + 10 q^{84} + 50 q^{85} + 3 q^{86} - 7 q^{87} - 9 q^{88} - 39 q^{89} + 7 q^{90} + 19 q^{91} - 95 q^{92} - 7 q^{93} + 16 q^{94} - 15 q^{95} + 50 q^{96} - 61 q^{97} - 76 q^{98} - q^{99}+O(q^{100}) \) 36 * q - 7 * q^2 - 36 * q^3 + 45 * q^4 - 36 * q^5 + 7 * q^6 + 2 * q^7 - 24 * q^8 + 36 * q^9 + 7 * q^10 - q^11 - 45 * q^12 - 8 * q^13 - 4 * q^14 + 36 * q^15 + 63 * q^16 - 50 * q^17 - 7 * q^18 + 15 * q^19 - 45 * q^20 - 2 * q^21 + 7 * q^22 - 32 * q^23 + 24 * q^24 + 36 * q^25 - 12 * q^26 - 36 * q^27 - 10 * q^28 + 7 * q^29 - 7 * q^30 + 7 * q^31 - 50 * q^32 + q^33 + 8 * q^34 - 2 * q^35 + 45 * q^36 - 10 * q^37 - 48 * q^38 + 8 * q^39 + 24 * q^40 - 31 * q^41 + 4 * q^42 + 27 * q^43 - 9 * q^44 - 36 * q^45 + 23 * q^46 - 46 * q^47 - 63 * q^48 + 48 * q^49 - 7 * q^50 + 50 * q^51 - 14 * q^52 - 39 * q^53 + 7 * q^54 + q^55 - 29 * q^56 - 15 * q^57 - 26 * q^58 - 9 * q^59 + 45 * q^60 + 5 * q^61 - 65 * q^62 + 2 * q^63 + 90 * q^64 + 8 * q^65 - 7 * q^66 + 18 * q^67 - 128 * q^68 + 32 * q^69 + 4 * q^70 + 4 * q^71 - 24 * q^72 - 45 * q^73 - 22 * q^74 - 36 * q^75 + 26 * q^76 - 38 * q^77 + 12 * q^78 + 25 * q^79 - 63 * q^80 + 36 * q^81 - 5 * q^82 - 71 * q^83 + 10 * q^84 + 50 * q^85 + 3 * q^86 - 7 * q^87 - 9 * q^88 - 39 * q^89 + 7 * q^90 + 19 * q^91 - 95 * q^92 - 7 * q^93 + 16 * q^94 - 15 * q^95 + 50 * q^96 - 61 * q^97 - 76 * q^98 - 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 $

$2$	−1.46470	−1.03570	−0.517849	−	0.855472i	$-0.673267\pi$
$2$	−1.46470	−1.03570	−0.517849	+	0.855472i	$0.673267\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.145344	0.0726718
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	1.46470	0.597961
$7$	1.42914	0.540165	0.270083	−	0.962837i	$-0.412949\pi$
$7$	1.42914	0.540165	0.270083	+	0.962837i	$0.412949\pi$
$8$	2.71651	0.960433
$9$	1.00000	0.333333
$10$	1.46470	0.463179
$11$	0.0549321	0.0165626	0.00828132	−	0.999966i	$-0.497364\pi$
$11$	0.0549321	0.0165626	0.00828132	+	0.999966i	$0.497364\pi$
$12$	−0.145344	−0.0419571
$13$	7.07979	1.96358	0.981790	−	0.189968i	$-0.0608383\pi$
$13$	7.07979	1.96358	0.981790	+	0.189968i	$0.0608383\pi$
$14$	−2.09326	−0.559449
$15$	1.00000	0.258199
$16$	−4.26956	−1.06739
$17$	1.64656	0.399350	0.199675	−	0.979862i	$-0.436011\pi$
$17$	1.64656	0.399350	0.199675	+	0.979862i	$0.436011\pi$
$18$	−1.46470	−0.345233
$19$	1.50699	0.345727	0.172864	−	0.984946i	$-0.444698\pi$
$19$	1.50699	0.345727	0.172864	+	0.984946i	$0.444698\pi$
$20$	−0.145344	−0.0324998
$21$	−1.42914	−0.311865
$22$	−0.0804590	−0.0171539
$23$	−5.68165	−1.18471	−0.592353	−	0.805679i	$-0.701801\pi$
$23$	−5.68165	−1.18471	−0.592353	+	0.805679i	$0.701801\pi$
$24$	−2.71651	−0.554506
$25$	1.00000	0.200000
$26$	−10.3698	−2.03368
$27$	−1.00000	−0.192450
$28$	0.207717	0.0392548
$29$	−4.59597	−0.853451	−0.426725	−	0.904381i	$-0.640333\pi$
$29$	−4.59597	−0.853451	−0.426725	+	0.904381i	$0.640333\pi$
$30$	−1.46470	−0.267416
$31$	0.146218	0.0262616	0.0131308	−	0.999914i	$-0.495820\pi$
$31$	0.146218	0.0262616	0.0131308	+	0.999914i	$0.495820\pi$
$32$	0.820597	0.145062
$33$	−0.0549321	−0.00956245
$34$	−2.41172	−0.413606
$35$	−1.42914	−0.241569
$36$	0.145344	0.0242239
$37$	3.10073	0.509757	0.254879	−	0.966973i	$-0.417965\pi$
$37$	3.10073	0.509757	0.254879	+	0.966973i	$0.417965\pi$
$38$	−2.20729	−0.358069
$39$	−7.07979	−1.13367
$40$	−2.71651	−0.429519
$41$	−9.34634	−1.45965	−0.729827	−	0.683632i	$-0.760399\pi$
$41$	−9.34634	−1.45965	−0.729827	+	0.683632i	$0.760399\pi$
$42$	2.09326	0.322998
$43$	1.78612	0.272381	0.136191	−	0.990683i	$-0.456514\pi$
$43$	1.78612	0.272381	0.136191	+	0.990683i	$0.456514\pi$
$44$	0.00798402	0.00120364
$45$	−1.00000	−0.149071
$46$	8.32190	1.22700
$47$	4.88902	0.713137	0.356569	−	0.934269i	$-0.383947\pi$
$47$	4.88902	0.713137	0.356569	+	0.934269i	$0.383947\pi$
$48$	4.26956	0.616258
$49$	−4.95755	−0.708221
$50$	−1.46470	−0.207140
$51$	−1.64656	−0.230565
$52$	1.02900	0.142697
$53$	−4.64763	−0.638401	−0.319200	−	0.947687i	$-0.603414\pi$
$53$	−4.64763	−0.638401	−0.319200	+	0.947687i	$0.603414\pi$
$54$	1.46470	0.199320
$55$	−0.0549321	−0.00740704
$56$	3.88229	0.518792
$57$	−1.50699	−0.199606
$58$	6.73172	0.883918
$59$	−10.6253	−1.38329	−0.691646	−	0.722236i	$-0.743114\pi$
$59$	−10.6253	−1.38329	−0.691646	+	0.722236i	$0.743114\pi$
$60$	0.145344	0.0187638
$61$	−4.83346	−0.618862	−0.309431	−	0.950922i	$-0.600139\pi$
$61$	−4.83346	−0.618862	−0.309431	+	0.950922i	$0.600139\pi$
$62$	−0.214166	−0.0271991
$63$	1.42914	0.180055
$64$	7.33720	0.917150
$65$	−7.07979	−0.878140
$66$	0.0804590	0.00990381
$67$	−8.85753	−1.08212	−0.541060	−	0.840984i	$-0.681977\pi$
$67$	−8.85753	−1.08212	−0.541060	+	0.840984i	$0.681977\pi$
$68$	0.239317	0.0290215
$69$	5.68165	0.683990
$70$	2.09326	0.250193
$71$	2.43588	0.289085	0.144543	−	0.989499i	$-0.453829\pi$
$71$	2.43588	0.289085	0.144543	+	0.989499i	$0.453829\pi$
$72$	2.71651	0.320144
$73$	−7.67502	−0.898293	−0.449147	−	0.893458i	$-0.648272\pi$
$73$	−7.67502	−0.898293	−0.449147	+	0.893458i	$0.648272\pi$
$74$	−4.54164	−0.527955
$75$	−1.00000	−0.115470
$76$	0.219031	0.0251246
$77$	0.0785058	0.00894657
$78$	10.3698	1.17414
$79$	−4.23997	−0.477033	−0.238517	−	0.971138i	$-0.576661\pi$
$79$	−4.23997	−0.477033	−0.238517	+	0.971138i	$0.576661\pi$
$80$	4.26956	0.477352
$81$	1.00000	0.111111
$82$	13.6896	1.51176
$83$	−4.13606	−0.453992	−0.226996	−	0.973896i	$-0.572890\pi$
$83$	−4.13606	−0.453992	−0.226996	+	0.973896i	$0.572890\pi$
$84$	−0.207717	−0.0226638
$85$	−1.64656	−0.178595
$86$	−2.61613	−0.282105
$87$	4.59597	0.492740
$88$	0.149224	0.0159073
$89$	16.1143	1.70811	0.854054	−	0.520185i	$-0.174137\pi$
$89$	16.1143	1.70811	0.854054	+	0.520185i	$0.174137\pi$
$90$	1.46470	0.154393
$91$	10.1180	1.06066
$92$	−0.825790	−0.0860946
$93$	−0.146218	−0.0151621
$94$	−7.16095	−0.738595
$95$	−1.50699	−0.154614
$96$	−0.820597	−0.0837518
$97$	−1.82733	−0.185537	−0.0927685	−	0.995688i	$-0.529572\pi$
$97$	−1.82733	−0.185537	−0.0927685	+	0.995688i	$0.529572\pi$
$98$	7.26132	0.733504
$99$	0.0549321	0.00552088
$100$	0.145344	0.0145344
$101$	4.44051	0.441847	0.220924	−	0.975291i	$-0.429093\pi$
$101$	4.44051	0.441847	0.220924	+	0.975291i	$0.429093\pi$
$102$	2.41172	0.238796
$103$	−9.44731	−0.930871	−0.465436	−	0.885082i	$-0.654102\pi$
$103$	−9.44731	−0.930871	−0.465436	+	0.885082i	$0.654102\pi$
$104$	19.2323	1.88589
$105$	1.42914	0.139470
$106$	6.80738	0.661191
$107$	9.20766	0.890138	0.445069	−	0.895496i	$-0.353179\pi$
$107$	9.20766	0.890138	0.445069	+	0.895496i	$0.353179\pi$
$108$	−0.145344	−0.0139857
$109$	−1.84010	−0.176250	−0.0881248	−	0.996109i	$-0.528087\pi$
$109$	−1.84010	−0.176250	−0.0881248	+	0.996109i	$0.528087\pi$
$110$	0.0804590	0.00767146
$111$	−3.10073	−0.294308
$112$	−6.10182	−0.576567
$113$	−6.85890	−0.645231	−0.322615	−	0.946530i	$-0.604562\pi$
$113$	−6.85890	−0.645231	−0.322615	+	0.946530i	$0.604562\pi$
$114$	2.20729	0.206731
$115$	5.68165	0.529816
$116$	−0.667995	−0.0620218
$117$	7.07979	0.654527
$118$	15.5628	1.43267
$119$	2.35317	0.215715
$120$	2.71651	0.247983
$121$	−10.9970	−0.999726
$122$	7.07957	0.640954
$123$	9.34634	0.842731
$124$	0.0212519	0.00190848
$125$	−1.00000	−0.0894427
$126$	−2.09326	−0.186483
$127$	−1.40518	−0.124689	−0.0623447	−	0.998055i	$-0.519858\pi$
$127$	−1.40518	−0.124689	−0.0623447	+	0.998055i	$0.519858\pi$
$128$	−12.3880	−1.09495
$129$	−1.78612	−0.157259
$130$	10.3698	0.909488
$131$	12.2964	1.07435	0.537173	−	0.843472i	$-0.319492\pi$
$131$	12.2964	1.07435	0.537173	+	0.843472i	$0.319492\pi$
$132$	−0.00798402	−0.000694920 0
$133$	2.15371	0.186750
$134$	12.9736	1.12075
$135$	1.00000	0.0860663
$136$	4.47291	0.383549
$137$	−3.66845	−0.313417	−0.156708	−	0.987645i	$-0.550088\pi$
$137$	−3.66845	−0.313417	−0.156708	+	0.987645i	$0.550088\pi$
$138$	−8.32190	−0.708407
$139$	3.07742	0.261023	0.130512	−	0.991447i	$-0.458338\pi$
$139$	3.07742	0.261023	0.130512	+	0.991447i	$0.458338\pi$
$140$	−0.207717	−0.0175553
$141$	−4.88902	−0.411730
$142$	−3.56783	−0.299405
$143$	0.388908	0.0325221
$144$	−4.26956	−0.355797
$145$	4.59597	0.381675
$146$	11.2416	0.930361
$147$	4.95755	0.408892
$148$	0.450671	0.0370449
$149$	−12.7538	−1.04483	−0.522417	−	0.852690i	$-0.674970\pi$
$149$	−12.7538	−1.04483	−0.522417	+	0.852690i	$0.674970\pi$
$150$	1.46470	0.119592
$151$	19.5351	1.58975	0.794873	−	0.606776i	$-0.207537\pi$
$151$	19.5351	1.58975	0.794873	+	0.606776i	$0.207537\pi$
$152$	4.09376	0.332048
$153$	1.64656	0.133117
$154$	−0.114987	−0.00926595
$155$	−0.146218	−0.0117445
$156$	−1.02900	−0.0823861
$157$	18.4050	1.46888	0.734440	−	0.678674i	$-0.237445\pi$
$157$	18.4050	1.46888	0.734440	+	0.678674i	$0.237445\pi$
$158$	6.21027	0.494063
$159$	4.64763	0.368581
$160$	−0.820597	−0.0648739
$161$	−8.11989	−0.639937
$162$	−1.46470	−0.115078
$163$	10.7119	0.839024	0.419512	−	0.907750i	$-0.362201\pi$
$163$	10.7119	0.839024	0.419512	+	0.907750i	$0.362201\pi$
$164$	−1.35843	−0.106076
$165$	0.0549321	0.00427646
$166$	6.05808	0.470198
$167$	−6.01593	−0.465526	−0.232763	−	0.972533i	$-0.574777\pi$
$167$	−6.01593	−0.465526	−0.232763	+	0.972533i	$0.574777\pi$
$168$	−3.88229	−0.299525
$169$	37.1234	2.85565
$170$	2.41172	0.184970
$171$	1.50699	0.115242
$172$	0.259602	0.0197944
$173$	−19.6427	−1.49340	−0.746702	−	0.665159i	$-0.768364\pi$
$173$	−19.6427	−1.49340	−0.746702	+	0.665159i	$0.768364\pi$
$174$	−6.73172	−0.510330
$175$	1.42914	0.108033
$176$	−0.234536	−0.0176788
$177$	10.6253	0.798644
$178$	−23.6025	−1.76908
$179$	−22.4561	−1.67845	−0.839223	−	0.543788i	$-0.816990\pi$
$179$	−22.4561	−1.67845	−0.839223	+	0.543788i	$0.816990\pi$
$180$	−0.145344	−0.0108333
$181$	−15.7709	−1.17224	−0.586121	−	0.810223i	$-0.699346\pi$
$181$	−15.7709	−1.17224	−0.586121	+	0.810223i	$0.699346\pi$
$182$	−14.8199	−1.09852
$183$	4.83346	0.357300
$184$	−15.4343	−1.13783
$185$	−3.10073	−0.227970
$186$	0.214166	0.0157034
$187$	0.0904491	0.00661429
$188$	0.710588	0.0518249
$189$	−1.42914	−0.103955
$190$	2.20729	0.160134
$191$	−4.28716	−0.310208	−0.155104	−	0.987898i	$-0.549571\pi$
$191$	−4.28716	−0.310208	−0.155104	+	0.987898i	$0.549571\pi$
$192$	−7.33720	−0.529517
$193$	−8.40967	−0.605341	−0.302671	−	0.953095i	$-0.597878\pi$
$193$	−8.40967	−0.605341	−0.302671	+	0.953095i	$0.597878\pi$
$194$	2.67649	0.192160
$195$	7.07979	0.506994
$196$	−0.720548	−0.0514677
$197$	−17.5258	−1.24866	−0.624329	−	0.781161i	$-0.714628\pi$
$197$	−17.5258	−1.24866	−0.624329	+	0.781161i	$0.714628\pi$
$198$	−0.0804590	−0.00571797
$199$	8.75287	0.620475	0.310237	−	0.950659i	$-0.399591\pi$
$199$	8.75287	0.620475	0.310237	+	0.950659i	$0.399591\pi$
$200$	2.71651	0.192087
$201$	8.85753	0.624762
$202$	−6.50401	−0.457621
$203$	−6.56830	−0.461005
$204$	−0.239317	−0.0167556
$205$	9.34634	0.652777
$206$	13.8375	0.964102
$207$	−5.68165	−0.394902
$208$	−30.2276	−2.09591
$209$	0.0827821	0.00572616
$210$	−2.09326	−0.144449
$211$	17.1227	1.17878	0.589388	−	0.807850i	$-0.299369\pi$
$211$	17.1227	1.17878	0.589388	+	0.807850i	$0.299369\pi$
$212$	−0.675503	−0.0463937
$213$	−2.43588	−0.166904
$214$	−13.4864	−0.921915
$215$	−1.78612	−0.121813
$216$	−2.71651	−0.184835
$217$	0.208967	0.0141856
$218$	2.69519	0.182541
$219$	7.67502	0.518630
$220$	−0.00798402	−0.000538283 0
$221$	11.6573	0.784156
$222$	4.54164	0.304815
$223$	11.1199	0.744645	0.372322	−	0.928103i	$-0.378562\pi$
$223$	11.1199	0.744645	0.372322	+	0.928103i	$0.378562\pi$
$224$	1.17275	0.0783577
$225$	1.00000	0.0666667
$226$	10.0462	0.668264
$227$	−17.4315	−1.15697	−0.578484	−	0.815694i	$-0.696355\pi$
$227$	−17.4315	−1.15697	−0.578484	+	0.815694i	$0.696355\pi$
$228$	−0.219031	−0.0145057
$229$	−26.1006	−1.72478	−0.862390	−	0.506245i	$-0.831033\pi$
$229$	−26.1006	−1.72478	−0.862390	+	0.506245i	$0.831033\pi$
$230$	−8.32190	−0.548730
$231$	−0.0785058	−0.00516530
$232$	−12.4850	−0.819682
$233$	−12.2161	−0.800303	−0.400152	−	0.916449i	$-0.631043\pi$
$233$	−12.2161	−0.800303	−0.400152	+	0.916449i	$0.631043\pi$
$234$	−10.3698	−0.677893
$235$	−4.88902	−0.318925
$236$	−1.54431	−0.100526
$237$	4.23997	0.275415
$238$	−3.44669	−0.223416
$239$	3.09490	0.200192	0.100096	−	0.994978i	$-0.468085\pi$
$239$	3.09490	0.200192	0.100096	+	0.994978i	$0.468085\pi$
$240$	−4.26956	−0.275599
$241$	4.36271	0.281027	0.140513	−	0.990079i	$-0.455125\pi$
$241$	4.36271	0.281027	0.140513	+	0.990079i	$0.455125\pi$
$242$	16.1073	1.03541
$243$	−1.00000	−0.0641500
$244$	−0.702513	−0.0449738
$245$	4.95755	0.316726
$246$	−13.6896	−0.872816
$247$	10.6692	0.678864
$248$	0.397204	0.0252225
$249$	4.13606	0.262112
$250$	1.46470	0.0926357
$251$	6.59969	0.416569	0.208284	−	0.978068i	$-0.433212\pi$
$251$	6.59969	0.416569	0.208284	+	0.978068i	$0.433212\pi$
$252$	0.207717	0.0130849
$253$	−0.312105	−0.0196218
$254$	2.05816	0.129141
$255$	1.64656	0.103112
$256$	3.47027	0.216892
$257$	11.2646	0.702666	0.351333	−	0.936251i	$-0.385728\pi$
$257$	11.2646	0.702666	0.351333	+	0.936251i	$0.385728\pi$
$258$	2.61613	0.162873
$259$	4.43139	0.275353
$260$	−1.02900	−0.0638160
$261$	−4.59597	−0.284484
$262$	−18.0106	−1.11270
$263$	−2.82495	−0.174194	−0.0870970	−	0.996200i	$-0.527759\pi$
$263$	−2.82495	−0.174194	−0.0870970	+	0.996200i	$0.527759\pi$
$264$	−0.149224	−0.00918409
$265$	4.64763	0.285502
$266$	−3.15453	−0.193417
$267$	−16.1143	−0.986176
$268$	−1.28738	−0.0786395
$269$	3.98764	0.243130	0.121565	−	0.992583i	$-0.461209\pi$
$269$	3.98764	0.243130	0.121565	+	0.992583i	$0.461209\pi$
$270$	−1.46470	−0.0891388
$271$	24.2363	1.47225	0.736125	−	0.676845i	$-0.236653\pi$
$271$	24.2363	1.47225	0.736125	+	0.676845i	$0.236653\pi$
$272$	−7.03010	−0.426263
$273$	−10.1180	−0.612371
$274$	5.37317	0.324605
$275$	0.0549321	0.00331253
$276$	0.825790	0.0497067
$277$	−17.2421	−1.03598	−0.517988	−	0.855388i	$-0.673319\pi$
$277$	−17.2421	−1.03598	−0.517988	+	0.855388i	$0.673319\pi$
$278$	−4.50749	−0.270341
$279$	0.146218	0.00875387
$280$	−3.88229	−0.232011
$281$	−12.7112	−0.758284	−0.379142	−	0.925338i	$-0.623781\pi$
$281$	−12.7112	−0.758284	−0.379142	+	0.925338i	$0.623781\pi$
$282$	7.16095	0.426428
$283$	−20.7960	−1.23619	−0.618097	−	0.786102i	$-0.712096\pi$
$283$	−20.7960	−1.23619	−0.618097	+	0.786102i	$0.712096\pi$
$284$	0.354039	0.0210084
$285$	1.50699	0.0892664
$286$	−0.569633	−0.0336831
$287$	−13.3573	−0.788454
$288$	0.820597	0.0483541
$289$	−14.2888	−0.840519
$290$	−6.73172	−0.395300
$291$	1.82733	0.107120
$292$	−1.11551	−0.0652806
$293$	19.3389	1.12979	0.564894	−	0.825163i	$-0.308917\pi$
$293$	19.3389	1.12979	0.564894	+	0.825163i	$0.308917\pi$
$294$	−7.26132	−0.423489
$295$	10.6253	0.618627
$296$	8.42318	0.489587
$297$	−0.0549321	−0.00318748
$298$	18.6805	1.08213
$299$	−40.2249	−2.32626
$300$	−0.145344	−0.00839141
$301$	2.55263	0.147131
$302$	−28.6131	−1.64650
$303$	−4.44051	−0.255101
$304$	−6.43419	−0.369026
$305$	4.83346	0.276763
$306$	−2.41172	−0.137869
$307$	26.3791	1.50554	0.752769	−	0.658285i	$-0.228718\pi$
$307$	26.3791	1.50554	0.752769	+	0.658285i	$0.228718\pi$
$308$	0.0114103	0.000650163 0
$309$	9.44731	0.537439
$310$	0.214166	0.0121638
$311$	21.8027	1.23632	0.618160	−	0.786052i	$-0.287878\pi$
$311$	21.8027	1.23632	0.618160	+	0.786052i	$0.287878\pi$
$312$	−19.2323	−1.08882
$313$	13.2384	0.748279	0.374139	−	0.927373i	$-0.377938\pi$
$313$	13.2384	0.748279	0.374139	+	0.927373i	$0.377938\pi$
$314$	−26.9578	−1.52132
$315$	−1.42914	−0.0805231
$316$	−0.616252	−0.0346669
$317$	−2.97521	−0.167104	−0.0835522	−	0.996503i	$-0.526627\pi$
$317$	−2.97521	−0.167104	−0.0835522	+	0.996503i	$0.526627\pi$
$318$	−6.80738	−0.381739
$319$	−0.252466	−0.0141354
$320$	−7.33720	−0.410162
$321$	−9.20766	−0.513921
$322$	11.8932	0.662782
$323$	2.48136	0.138066
$324$	0.145344	0.00807464
$325$	7.07979	0.392716
$326$	−15.6898	−0.868976
$327$	1.84010	0.101758
$328$	−25.3895	−1.40190
$329$	6.98711	0.385212
$330$	−0.0804590	−0.00442912
$331$	5.65071	0.310591	0.155295	−	0.987868i	$-0.450367\pi$
$331$	5.65071	0.310591	0.155295	+	0.987868i	$0.450367\pi$
$332$	−0.601150	−0.0329924
$333$	3.10073	0.169919
$334$	8.81152	0.482145
$335$	8.85753	0.483939
$336$	6.10182	0.332881
$337$	6.16439	0.335796	0.167898	−	0.985804i	$-0.446302\pi$
$337$	6.16439	0.335796	0.167898	+	0.985804i	$0.446302\pi$
$338$	−54.3747	−2.95759
$339$	6.85890	0.372524
$340$	−0.239317	−0.0129788
$341$	0.00803208	0.000434962 0
$342$	−2.20729	−0.119356
$343$	−17.0891	−0.922722
$344$	4.85203	0.261604
$345$	−5.68165	−0.305890
$346$	28.7706	1.54672
$347$	−3.88868	−0.208755	−0.104378	−	0.994538i	$-0.533285\pi$
$347$	−3.88868	−0.208755	−0.104378	+	0.994538i	$0.533285\pi$
$348$	0.667995	0.0358083
$349$	0.987266	0.0528472	0.0264236	−	0.999651i	$-0.491588\pi$
$349$	0.987266	0.0528472	0.0264236	+	0.999651i	$0.491588\pi$
$350$	−2.09326	−0.111890
$351$	−7.07979	−0.377891
$352$	0.0450771	0.00240262
$353$	9.10261	0.484483	0.242241	−	0.970216i	$-0.422117\pi$
$353$	9.10261	0.484483	0.242241	+	0.970216i	$0.422117\pi$
$354$	−15.5628	−0.827155
$355$	−2.43588	−0.129283
$356$	2.34210	0.124131
$357$	−2.35317	−0.124543
$358$	32.8914	1.73836
$359$	−20.5229	−1.08316	−0.541578	−	0.840650i	$-0.682173\pi$
$359$	−20.5229	−1.08316	−0.541578	+	0.840650i	$0.682173\pi$
$360$	−2.71651	−0.143173
$361$	−16.7290	−0.880473
$362$	23.0996	1.21409
$363$	10.9970	0.577192
$364$	1.47059	0.0770799
$365$	7.67502	0.401729
$366$	−7.07957	−0.370055
$367$	−29.1881	−1.52361	−0.761804	−	0.647807i	$-0.775686\pi$
$367$	−29.1881	−1.52361	−0.761804	+	0.647807i	$0.775686\pi$
$368$	24.2581	1.26454
$369$	−9.34634	−0.486551
$370$	4.54164	0.236109
$371$	−6.64213	−0.344842
$372$	−0.0212519	−0.00110186
$373$	−34.6850	−1.79592	−0.897962	−	0.440074i	$-0.854952\pi$
$373$	−34.6850	−1.79592	−0.897962	+	0.440074i	$0.854952\pi$
$374$	−0.132481	−0.00685042
$375$	1.00000	0.0516398
$376$	13.2811	0.684920
$377$	−32.5385	−1.67582
$378$	2.09326	0.107666
$379$	−17.0102	−0.873754	−0.436877	−	0.899521i	$-0.643916\pi$
$379$	−17.0102	−0.873754	−0.436877	+	0.899521i	$0.643916\pi$
$380$	−0.219031	−0.0112361
$381$	1.40518	0.0719894
$382$	6.27940	0.321282
$383$	−15.2996	−0.781772	−0.390886	−	0.920439i	$-0.627831\pi$
$383$	−15.2996	−0.781772	−0.390886	+	0.920439i	$0.627831\pi$
$384$	12.3880	0.632171
$385$	−0.0785058	−0.00400103
$386$	12.3176	0.626951
$387$	1.78612	0.0907938
$388$	−0.265590	−0.0134833
$389$	−12.7251	−0.645189	−0.322595	−	0.946537i	$-0.604555\pi$
$389$	−12.7251	−0.645189	−0.322595	+	0.946537i	$0.604555\pi$
$390$	−10.3698	−0.525093
$391$	−9.35519	−0.473112
$392$	−13.4673	−0.680199
$393$	−12.2964	−0.620273
$394$	25.6700	1.29323
$395$	4.23997	0.213336
$396$	0.00798402	0.000401212 0
$397$	−27.8768	−1.39910	−0.699548	−	0.714586i	$-0.746615\pi$
$397$	−27.8768	−1.39910	−0.699548	+	0.714586i	$0.746615\pi$
$398$	−12.8203	−0.642625
$399$	−2.15371	−0.107820
$400$	−4.26956	−0.213478
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	−12.9736	−0.647065
$403$	1.03520	0.0515668
$404$	0.645399	0.0321098
$405$	−1.00000	−0.0496904
$406$	9.62059	0.477462
$407$	0.170330	0.00844293
$408$	−4.47291	−0.221442
$409$	−1.80698	−0.0893494	−0.0446747	−	0.999002i	$-0.514225\pi$
$409$	−1.80698	−0.0893494	−0.0446747	+	0.999002i	$0.514225\pi$
$410$	−13.6896	−0.676080
$411$	3.66845	0.180951
$412$	−1.37311	−0.0676481
$413$	−15.1850	−0.747207
$414$	8.32190	0.408999
$415$	4.13606	0.203031
$416$	5.80965	0.284842
$417$	−3.07742	−0.150702
$418$	−0.121251	−0.00593058
$419$	13.2541	0.647503	0.323751	−	0.946142i	$-0.395056\pi$
$419$	13.2541	0.647503	0.323751	+	0.946142i	$0.395056\pi$
$420$	0.207717	0.0101355
$421$	29.3761	1.43170	0.715851	−	0.698253i	$-0.246039\pi$
$421$	29.3761	1.43170	0.715851	+	0.698253i	$0.246039\pi$
$422$	−25.0796	−1.22086
$423$	4.88902	0.237712
$424$	−12.6253	−0.613141
$425$	1.64656	0.0798700
$426$	3.56783	0.172862
$427$	−6.90771	−0.334288
$428$	1.33827	0.0646879
$429$	−0.388908	−0.0187766
$430$	2.61613	0.126161
$431$	−30.8381	−1.48542	−0.742709	−	0.669614i	$-0.766460\pi$
$431$	−30.8381	−1.48542	−0.742709	+	0.669614i	$0.766460\pi$
$432$	4.26956	0.205419
$433$	14.5761	0.700483	0.350242	−	0.936659i	$-0.386099\pi$
$433$	14.5761	0.700483	0.350242	+	0.936659i	$0.386099\pi$
$434$	−0.306074	−0.0146920
$435$	−4.59597	−0.220360
$436$	−0.267446	−0.0128084
$437$	−8.56219	−0.409585
$438$	−11.2416	−0.537144
$439$	37.7365	1.80106	0.900531	−	0.434791i	$-0.143178\pi$
$439$	37.7365	1.80106	0.900531	+	0.434791i	$0.143178\pi$
$440$	−0.149224	−0.00711396
$441$	−4.95755	−0.236074
$442$	−17.0745	−0.812150
$443$	31.0902	1.47714	0.738569	−	0.674178i	$-0.235502\pi$
$443$	31.0902	1.47714	0.738569	+	0.674178i	$0.235502\pi$
$444$	−0.450671	−0.0213879
$445$	−16.1143	−0.763889
$446$	−16.2873	−0.771228
$447$	12.7538	0.603235
$448$	10.4859	0.495412
$449$	−23.5822	−1.11291	−0.556455	−	0.830878i	$-0.687839\pi$
$449$	−23.5822	−1.11291	−0.556455	+	0.830878i	$0.687839\pi$
$450$	−1.46470	−0.0690466
$451$	−0.513414	−0.0241757
$452$	−0.996896	−0.0468900
$453$	−19.5351	−0.917841
$454$	25.5319	1.19827
$455$	−10.1180	−0.474341
$456$	−4.09376	−0.191708
$457$	14.6482	0.685214	0.342607	−	0.939479i	$-0.388690\pi$
$457$	14.6482	0.685214	0.342607	+	0.939479i	$0.388690\pi$
$458$	38.2296	1.78635
$459$	−1.64656	−0.0768550
$460$	0.825790	0.0385027
$461$	22.8503	1.06425	0.532123	−	0.846667i	$-0.321395\pi$
$461$	22.8503	1.06425	0.532123	+	0.846667i	$0.321395\pi$
$462$	0.114987	0.00534970
$463$	16.0391	0.745399	0.372700	−	0.927952i	$-0.378432\pi$
$463$	16.0391	0.745399	0.372700	+	0.927952i	$0.378432\pi$
$464$	19.6228	0.910966
$465$	0.146218	0.00678072
$466$	17.8929	0.828873
$467$	7.60222	0.351789	0.175894	−	0.984409i	$-0.443718\pi$
$467$	7.60222	0.351789	0.175894	+	0.984409i	$0.443718\pi$
$468$	1.02900	0.0475656
$469$	−12.6587	−0.584523
$470$	7.16095	0.330310
$471$	−18.4050	−0.848058
$472$	−28.8637	−1.32856
$473$	0.0981155	0.00451136
$474$	−6.21027	−0.285247
$475$	1.50699	0.0691455
$476$	0.342019	0.0156764
$477$	−4.64763	−0.212800
$478$	−4.53309	−0.207339
$479$	−22.6815	−1.03634	−0.518172	−	0.855277i	$-0.673387\pi$
$479$	−22.6815	−1.03634	−0.518172	+	0.855277i	$0.673387\pi$
$480$	0.820597	0.0374549
$481$	21.9525	1.00095
$482$	−6.39005	−0.291059
$483$	8.11989	0.369468
$484$	−1.59834	−0.0726518
$485$	1.82733	0.0829747
$486$	1.46470	0.0664401
$487$	−18.1380	−0.821910	−0.410955	−	0.911656i	$-0.634805\pi$
$487$	−18.1380	−0.821910	−0.410955	+	0.911656i	$0.634805\pi$
$488$	−13.1302	−0.594375
$489$	−10.7119	−0.484411
$490$	−7.26132	−0.328033
$491$	22.3881	1.01036	0.505180	−	0.863014i	$-0.331426\pi$
$491$	22.3881	1.01036	0.505180	+	0.863014i	$0.331426\pi$
$492$	1.35843	0.0612428
$493$	−7.56756	−0.340826
$494$	−15.6271	−0.703098
$495$	−0.0549321	−0.00246901
$496$	−0.624289	−0.0280314
$497$	3.48122	0.156154
$498$	−6.05808	−0.271469
$499$	28.3358	1.26848	0.634241	−	0.773135i	$-0.281313\pi$
$499$	28.3358	1.26848	0.634241	+	0.773135i	$0.281313\pi$
$500$	−0.145344	−0.00649996
$501$	6.01593	0.268772
$502$	−9.66656	−0.431440
$503$	6.87525	0.306552	0.153276	−	0.988183i	$-0.451018\pi$
$503$	6.87525	0.306552	0.153276	+	0.988183i	$0.451018\pi$
$504$	3.88229	0.172931
$505$	−4.44051	−0.197600
$506$	0.457139	0.0203223
$507$	−37.1234	−1.64871
$508$	−0.204233	−0.00906139
$509$	−26.7645	−1.18631	−0.593157	−	0.805087i	$-0.702119\pi$
$509$	−26.7645	−1.18631	−0.593157	+	0.805087i	$0.702119\pi$
$510$	−2.41172	−0.106793
$511$	−10.9687	−0.485227
$512$	19.6931	0.870319
$513$	−1.50699	−0.0665353
$514$	−16.4992	−0.727750
$515$	9.44731	0.416298
$516$	−0.259602	−0.0114283
$517$	0.268564	0.0118114
$518$	−6.49065	−0.285183
$519$	19.6427	0.862217
$520$	−19.2323	−0.843394
$521$	−1.51692	−0.0664574	−0.0332287	−	0.999448i	$-0.510579\pi$
$521$	−1.51692	−0.0664574	−0.0332287	+	0.999448i	$0.510579\pi$
$522$	6.73172	0.294639
$523$	−41.0089	−1.79320	−0.896598	−	0.442846i	$-0.853969\pi$
$523$	−41.0089	−1.79320	−0.896598	+	0.442846i	$0.853969\pi$
$524$	1.78721	0.0780746
$525$	−1.42914	−0.0623729
$526$	4.13770	0.180412
$527$	0.240758	0.0104876
$528$	0.234536	0.0102069
$529$	9.28110	0.403526
$530$	−6.80738	−0.295694
$531$	−10.6253	−0.461097
$532$	0.313027	0.0135715
$533$	−66.1701	−2.86615
$534$	23.6025	1.02138
$535$	−9.20766	−0.398082
$536$	−24.0616	−1.03930
$537$	22.4561	0.969051
$538$	−5.84069	−0.251810
$539$	−0.272329	−0.0117300
$540$	0.145344	0.00625459
$541$	−24.5931	−1.05734	−0.528671	−	0.848827i	$-0.677309\pi$
$541$	−24.5931	−1.05734	−0.528671	+	0.848827i	$0.677309\pi$
$542$	−35.4989	−1.52481
$543$	15.7709	0.676794
$544$	1.35116	0.0579307
$545$	1.84010	0.0788212
$546$	14.8199	0.634232
$547$	−28.0748	−1.20039	−0.600195	−	0.799854i	$-0.704910\pi$
$547$	−28.0748	−1.20039	−0.600195	+	0.799854i	$0.704910\pi$
$548$	−0.533185	−0.0227765
$549$	−4.83346	−0.206287
$550$	−0.0804590	−0.00343078
$551$	−6.92609	−0.295061
$552$	15.4343	0.656926
$553$	−6.05952	−0.257677
$554$	25.2545	1.07296
$555$	3.10073	0.131619
$556$	0.447283	0.0189690
$557$	−40.6558	−1.72264	−0.861322	−	0.508060i	$-0.830363\pi$
$557$	−40.6558	−1.72264	−0.861322	+	0.508060i	$0.830363\pi$
$558$	−0.214166	−0.00906637
$559$	12.6454	0.534843
$560$	6.10182	0.257849
$561$	−0.0904491	−0.00381876
$562$	18.6180	0.785354
$563$	−29.0396	−1.22387	−0.611936	−	0.790907i	$-0.709609\pi$
$563$	−29.0396	−1.22387	−0.611936	+	0.790907i	$0.709609\pi$
$564$	−0.710588	−0.0299211
$565$	6.85890	0.288556
$566$	30.4599	1.28032
$567$	1.42914	0.0600184
$568$	6.61709	0.277647
$569$	−10.8508	−0.454888	−0.227444	−	0.973791i	$-0.573037\pi$
$569$	−10.8508	−0.454888	−0.227444	+	0.973791i	$0.573037\pi$
$570$	−2.20729	−0.0924531
$571$	3.38018	0.141456	0.0707281	−	0.997496i	$-0.477468\pi$
$571$	3.38018	0.141456	0.0707281	+	0.997496i	$0.477468\pi$
$572$	0.0565252	0.00236344
$573$	4.28716	0.179099
$574$	19.5644	0.816601
$575$	−5.68165	−0.236941
$576$	7.33720	0.305717
$577$	36.3669	1.51397	0.756986	−	0.653431i	$-0.226671\pi$
$577$	36.3669	1.51397	0.756986	+	0.653431i	$0.226671\pi$
$578$	20.9288	0.870525
$579$	8.40967	0.349494
$580$	0.667995	0.0277370
$581$	−5.91102	−0.245230
$582$	−2.67649	−0.110944
$583$	−0.255304	−0.0105736
$584$	−20.8493	−0.862750
$585$	−7.07979	−0.292713
$586$	−28.3256	−1.17012
$587$	−15.2421	−0.629111	−0.314555	−	0.949239i	$-0.601855\pi$
$587$	−15.2421	−0.629111	−0.314555	+	0.949239i	$0.601855\pi$
$588$	0.720548	0.0297149
$589$	0.220350	0.00907936
$590$	−15.5628	−0.640711
$591$	17.5258	0.720913
$592$	−13.2388	−0.544110
$593$	12.9796	0.533006	0.266503	−	0.963834i	$-0.414132\pi$
$593$	12.9796	0.533006	0.266503	+	0.963834i	$0.414132\pi$
$594$	0.0804590	0.00330127
$595$	−2.35317	−0.0964707
$596$	−1.85369	−0.0759299
$597$	−8.75287	−0.358231
$598$	58.9173	2.40931
$599$	30.3047	1.23822	0.619108	−	0.785305i	$-0.287494\pi$
$599$	30.3047	1.23822	0.619108	+	0.785305i	$0.287494\pi$
$600$	−2.71651	−0.110901
$601$	−13.4553	−0.548851	−0.274426	−	0.961608i	$-0.588488\pi$
$601$	−13.4553	−0.548851	−0.274426	+	0.961608i	$0.588488\pi$
$602$	−3.73883	−0.152383
$603$	−8.85753	−0.360707
$604$	2.83931	0.115530
$605$	10.9970	0.447091
$606$	6.50401	0.264207
$607$	7.54767	0.306350	0.153175	−	0.988199i	$-0.451050\pi$
$607$	7.54767	0.306350	0.153175	+	0.988199i	$0.451050\pi$
$608$	1.23663	0.0501520
$609$	6.56830	0.266161
$610$	−7.07957	−0.286643
$611$	34.6133	1.40030
$612$	0.239317	0.00967383
$613$	20.3912	0.823594	0.411797	−	0.911276i	$-0.364901\pi$
$613$	20.3912	0.823594	0.411797	+	0.911276i	$0.364901\pi$
$614$	−38.6375	−1.55928
$615$	−9.34634	−0.376881
$616$	0.213262	0.00859258
$617$	−13.5530	−0.545621	−0.272811	−	0.962068i	$-0.587953\pi$
$617$	−13.5530	−0.545621	−0.272811	+	0.962068i	$0.587953\pi$
$618$	−13.8375	−0.556625
$619$	−8.77000	−0.352496	−0.176248	−	0.984346i	$-0.556396\pi$
$619$	−8.77000	−0.352496	−0.176248	+	0.984346i	$0.556396\pi$
$620$	−0.0212519	−0.000853497 0
$621$	5.68165	0.227997
$622$	−31.9345	−1.28046
$623$	23.0296	0.922660
$624$	30.2276	1.21007
$625$	1.00000	0.0400000
$626$	−19.3903	−0.774991
$627$	−0.0827821	−0.00330600
$628$	2.67505	0.106746
$629$	5.10555	0.203572
$630$	2.09326	0.0833977
$631$	5.16270	0.205524	0.102762	−	0.994706i	$-0.467232\pi$
$631$	5.16270	0.205524	0.102762	+	0.994706i	$0.467232\pi$
$632$	−11.5179	−0.458159
$633$	−17.1227	−0.680567
$634$	4.35779	0.173070
$635$	1.40518	0.0557628
$636$	0.675503	0.0267854
$637$	−35.0984	−1.39065
$638$	0.369787	0.0146400
$639$	2.43588	0.0963618
$640$	12.3880	0.489678
$641$	−20.2870	−0.801289	−0.400645	−	0.916234i	$-0.631214\pi$
$641$	−20.2870	−0.801289	−0.400645	+	0.916234i	$0.631214\pi$
$642$	13.4864	0.532268
$643$	−29.6424	−1.16898	−0.584492	−	0.811399i	$-0.698706\pi$
$643$	−29.6424	−1.16898	−0.584492	+	0.811399i	$0.698706\pi$
$644$	−1.18017	−0.0465053
$645$	1.78612	0.0703286
$646$	−3.63444	−0.142995
$647$	−38.1024	−1.49796	−0.748979	−	0.662594i	$-0.769456\pi$
$647$	−38.1024	−1.49796	−0.748979	+	0.662594i	$0.769456\pi$
$648$	2.71651	0.106715
$649$	−0.583668	−0.0229110
$650$	−10.3698	−0.406736
$651$	−0.208967	−0.00819006
$652$	1.55691	0.0609734
$653$	21.8475	0.854960	0.427480	−	0.904025i	$-0.359401\pi$
$653$	21.8475	0.854960	0.427480	+	0.904025i	$0.359401\pi$
$654$	−2.69519	−0.105390
$655$	−12.2964	−0.480462
$656$	39.9048	1.55802
$657$	−7.67502	−0.299431
$658$	−10.2340	−0.398964
$659$	22.7051	0.884464	0.442232	−	0.896901i	$-0.354187\pi$
$659$	22.7051	0.884464	0.442232	+	0.896901i	$0.354187\pi$
$660$	0.00798402	0.000310778 0
$661$	24.9090	0.968848	0.484424	−	0.874833i	$-0.339029\pi$
$661$	24.9090	0.968848	0.484424	+	0.874833i	$0.339029\pi$
$662$	−8.27658	−0.321679
$663$	−11.6573	−0.452733
$664$	−11.2357	−0.436028
$665$	−2.15371	−0.0835171
$666$	−4.54164	−0.175985
$667$	26.1127	1.01109
$668$	−0.874376	−0.0338306
$669$	−11.1199	−0.429921
$670$	−12.9736	−0.501215
$671$	−0.265512	−0.0102500
$672$	−1.17275	−0.0452398
$673$	−41.8364	−1.61267	−0.806337	−	0.591456i	$-0.798553\pi$
$673$	−41.8364	−1.61267	−0.806337	+	0.591456i	$0.798553\pi$
$674$	−9.02898	−0.347783
$675$	−1.00000	−0.0384900
$676$	5.39565	0.207525
$677$	35.2883	1.35624	0.678120	−	0.734952i	$-0.262795\pi$
$677$	35.2883	1.35624	0.678120	+	0.734952i	$0.262795\pi$
$678$	−10.0462	−0.385823
$679$	−2.61151	−0.100221
$680$	−4.47291	−0.171528
$681$	17.4315	0.667976
$682$	−0.0117646	−0.000450489 0
$683$	−25.3580	−0.970299	−0.485149	−	0.874431i	$-0.661235\pi$
$683$	−25.3580	−0.970299	−0.485149	+	0.874431i	$0.661235\pi$
$684$	0.219031	0.00837487
$685$	3.66845	0.140164
$686$	25.0303	0.955662
$687$	26.1006	0.995802
$688$	−7.62597	−0.290737
$689$	−32.9042	−1.25355
$690$	8.32190	0.316809
$691$	25.4235	0.967155	0.483578	−	0.875301i	$-0.339337\pi$
$691$	25.4235	0.967155	0.483578	+	0.875301i	$0.339337\pi$
$692$	−2.85493	−0.108528
$693$	0.0785058	0.00298219
$694$	5.69574	0.216207
$695$	−3.07742	−0.116733
$696$	12.4850	0.473244
$697$	−15.3893	−0.582913
$698$	−1.44605	−0.0547337
$699$	12.2161	0.462055
$700$	0.207717	0.00785095
$701$	21.8212	0.824175	0.412087	−	0.911144i	$-0.364800\pi$
$701$	21.8212	0.824175	0.412087	+	0.911144i	$0.364800\pi$
$702$	10.3698	0.391382
$703$	4.67277	0.176237
$704$	0.403048	0.0151904
$705$	4.88902	0.184131
$706$	−13.3326	−0.501778
$707$	6.34612	0.238671
$708$	1.54431	0.0580389
$709$	41.6137	1.56284	0.781418	−	0.624008i	$-0.214497\pi$
$709$	41.6137	1.56284	0.781418	+	0.624008i	$0.214497\pi$
$710$	3.56783	0.133898
$711$	−4.23997	−0.159011
$712$	43.7746	1.64052
$713$	−0.830761	−0.0311123
$714$	3.44669	0.128989
$715$	−0.388908	−0.0145443
$716$	−3.26384	−0.121976
$717$	−3.09490	−0.115581
$718$	30.0599	1.12182
$719$	−44.2353	−1.64970	−0.824849	−	0.565354i	$-0.808740\pi$
$719$	−44.2353	−1.64970	−0.824849	+	0.565354i	$0.808740\pi$
$720$	4.26956	0.159117
$721$	−13.5016	−0.502824
$722$	24.5029	0.911904
$723$	−4.36271	−0.162251
$724$	−2.29220	−0.0851889
$725$	−4.59597	−0.170690
$726$	−16.1073	−0.597797
$727$	19.3116	0.716229	0.358114	−	0.933678i	$-0.383420\pi$
$727$	19.3116	0.716229	0.358114	+	0.933678i	$0.383420\pi$
$728$	27.4858	1.01869
$729$	1.00000	0.0370370
$730$	−11.2416	−0.416070
$731$	2.94096	0.108776
$732$	0.702513	0.0259656
$733$	−46.5904	−1.72085	−0.860427	−	0.509573i	$-0.829803\pi$
$733$	−46.5904	−1.72085	−0.860427	+	0.509573i	$0.829803\pi$
$734$	42.7519	1.57800
$735$	−4.95755	−0.182862
$736$	−4.66234	−0.171856
$737$	−0.486563	−0.0179228
$738$	13.6896	0.503920
$739$	35.1128	1.29165	0.645823	−	0.763487i	$-0.276514\pi$
$739$	35.1128	1.29165	0.645823	+	0.763487i	$0.276514\pi$
$740$	−0.450671	−0.0165670
$741$	−10.6692	−0.391942
$742$	9.72872	0.357152
$743$	−7.76181	−0.284753	−0.142377	−	0.989813i	$-0.545474\pi$
$743$	−7.76181	−0.284753	−0.142377	+	0.989813i	$0.545474\pi$
$744$	−0.397204	−0.0145622
$745$	12.7538	0.467264
$746$	50.8031	1.86004
$747$	−4.13606	−0.151331
$748$	0.0131462	0.000480672 0
$749$	13.1591	0.480822
$750$	−1.46470	−0.0534833
$751$	8.47961	0.309425	0.154713	−	0.987960i	$-0.450555\pi$
$751$	8.47961	0.309425	0.154713	+	0.987960i	$0.450555\pi$
$752$	−20.8740	−0.761196
$753$	−6.59969	−0.240506
$754$	47.6592	1.73564
$755$	−19.5351	−0.710956
$756$	−0.207717	−0.00755458
$757$	23.6882	0.860963	0.430481	−	0.902599i	$-0.358344\pi$
$757$	23.6882	0.860963	0.430481	+	0.902599i	$0.358344\pi$
$758$	24.9148	0.904946
$759$	0.312105	0.0113287
$760$	−4.09376	−0.148496
$761$	−14.0304	−0.508603	−0.254301	−	0.967125i	$-0.581846\pi$
$761$	−14.0304	−0.508603	−0.254301	+	0.967125i	$0.581846\pi$
$762$	−2.05816	−0.0745594
$763$	−2.62976	−0.0952039
$764$	−0.623111	−0.0225434
$765$	−1.64656	−0.0595316
$766$	22.4093	0.809680
$767$	−75.2247	−2.71621
$768$	−3.47027	−0.125223
$769$	−19.1571	−0.690823	−0.345412	−	0.938451i	$-0.612261\pi$
$769$	−19.1571	−0.690823	−0.345412	+	0.938451i	$0.612261\pi$
$770$	0.114987	0.00414386
$771$	−11.2646	−0.405685
$772$	−1.22229	−0.0439912
$773$	−7.77114	−0.279508	−0.139754	−	0.990186i	$-0.544631\pi$
$773$	−7.77114	−0.279508	−0.139754	+	0.990186i	$0.544631\pi$
$774$	−2.61613	−0.0940350
$775$	0.146218	0.00525232
$776$	−4.96396	−0.178196
$777$	−4.43139	−0.158975
$778$	18.6385	0.668222
$779$	−14.0849	−0.504642
$780$	1.02900	0.0368442
$781$	0.133808	0.00478802
$782$	13.7025	0.490002
$783$	4.59597	0.164247
$784$	21.1666	0.755949
$785$	−18.4050	−0.656903
$786$	18.0106	0.642416
$787$	−14.8345	−0.528792	−0.264396	−	0.964414i	$-0.585173\pi$
$787$	−14.8345	−0.528792	−0.264396	+	0.964414i	$0.585173\pi$
$788$	−2.54726	−0.0907422
$789$	2.82495	0.100571
$790$	−6.21027	−0.220952
$791$	−9.80234	−0.348531
$792$	0.149224	0.00530244
$793$	−34.2199	−1.21519
$794$	40.8311	1.44904
$795$	−4.64763	−0.164834
$796$	1.27217	0.0450910
$797$	−34.4534	−1.22040	−0.610201	−	0.792247i	$-0.708911\pi$
$797$	−34.4534	−1.22040	−0.610201	+	0.792247i	$0.708911\pi$
$798$	3.15453	0.111669
$799$	8.05008	0.284791
$800$	0.820597	0.0290125
$801$	16.1143	0.569369
$802$	1.46470	0.0517203
$803$	−0.421605	−0.0148781
$804$	1.28738	0.0454026
$805$	8.11989	0.286188
$806$	−1.51625	−0.0534076
$807$	−3.98764	−0.140371
$808$	12.0627	0.424364
$809$	24.8251	0.872803	0.436401	−	0.899752i	$-0.356253\pi$
$809$	24.8251	0.872803	0.436401	+	0.899752i	$0.356253\pi$
$810$	1.46470	0.0514643
$811$	25.8041	0.906105	0.453052	−	0.891484i	$-0.350335\pi$
$811$	25.8041	0.906105	0.453052	+	0.891484i	$0.350335\pi$
$812$	−0.954661	−0.0335020
$813$	−24.2363	−0.850004
$814$	−0.249482	−0.00874433
$815$	−10.7119	−0.375223
$816$	7.03010	0.246103
$817$	2.69167	0.0941697
$818$	2.64668	0.0925391
$819$	10.1180	0.353553
$820$	1.35843	0.0474384
$821$	27.7427	0.968228	0.484114	−	0.875005i	$-0.339142\pi$
$821$	27.7427	0.968228	0.484114	+	0.875005i	$0.339142\pi$
$822$	−5.37317	−0.187411
$823$	−29.7640	−1.03751	−0.518754	−	0.854923i	$-0.673604\pi$
$823$	−29.7640	−1.03751	−0.518754	+	0.854923i	$0.673604\pi$
$824$	−25.6638	−0.894039
$825$	−0.0549321	−0.00191249
$826$	22.2415	0.773881
$827$	25.0215	0.870083	0.435041	−	0.900410i	$-0.356734\pi$
$827$	25.0215	0.870083	0.435041	+	0.900410i	$0.356734\pi$
$828$	−0.825790	−0.0286982
$829$	−50.1569	−1.74202	−0.871010	−	0.491265i	$-0.836535\pi$
$829$	−50.1569	−1.74202	−0.871010	+	0.491265i	$0.836535\pi$
$830$	−6.05808	−0.210279
$831$	17.2421	0.598121
$832$	51.9458	1.80090
$833$	−8.16292	−0.282828
$834$	4.50749	0.156082
$835$	6.01593	0.208190
$836$	0.0120319	0.000416130 0
$837$	−0.146218	−0.00505405
$838$	−19.4132	−0.670618
$839$	−7.67649	−0.265022	−0.132511	−	0.991182i	$-0.542304\pi$
$839$	−7.67649	−0.265022	−0.132511	+	0.991182i	$0.542304\pi$
$840$	3.88229	0.133952
$841$	−7.87702	−0.271621
$842$	−43.0271	−1.48281
$843$	12.7112	0.437796
$844$	2.48868	0.0856638
$845$	−37.1234	−1.27709
$846$	−7.16095	−0.246198
$847$	−15.7163	−0.540017
$848$	19.8433	0.681423
$849$	20.7960	0.713717
$850$	−2.41172	−0.0827213
$851$	−17.6173	−0.603912
$852$	−0.354039	−0.0121292
$853$	−18.3915	−0.629714	−0.314857	−	0.949139i	$-0.601957\pi$
$853$	−18.3915	−0.629714	−0.314857	+	0.949139i	$0.601957\pi$
$854$	10.1177	0.346221
$855$	−1.50699	−0.0515380
$856$	25.0127	0.854917
$857$	38.7658	1.32421	0.662107	−	0.749409i	$-0.269662\pi$
$857$	38.7658	1.32421	0.662107	+	0.749409i	$0.269662\pi$
$858$	0.569633	0.0194469
$859$	22.3358	0.762089	0.381045	−	0.924557i	$-0.375564\pi$
$859$	22.3358	0.762089	0.381045	+	0.924557i	$0.375564\pi$
$860$	−0.259602	−0.00885234
$861$	13.3573	0.455214
$862$	45.1685	1.53845
$863$	28.5162	0.970704	0.485352	−	0.874319i	$-0.338691\pi$
$863$	28.5162	0.970704	0.485352	+	0.874319i	$0.338691\pi$
$864$	−0.820597	−0.0279173
$865$	19.6427	0.667870
$866$	−21.3496	−0.725490
$867$	14.2888	0.485274
$868$	0.0303720	0.00103089
$869$	−0.232910	−0.00790094
$870$	6.73172	0.228227
$871$	−62.7095	−2.12483
$872$	−4.99865	−0.169276
$873$	−1.82733	−0.0618457
$874$	12.5410	0.424207
$875$	−1.42914	−0.0483139
$876$	1.11551	0.0376898
$877$	−21.3354	−0.720447	−0.360223	−	0.932866i	$-0.617299\pi$
$877$	−21.3354	−0.720447	−0.360223	+	0.932866i	$0.617299\pi$
$878$	−55.2726	−1.86536
$879$	−19.3389	−0.652284
$880$	0.234536	0.00790621
$881$	46.9480	1.58172	0.790858	−	0.611999i	$-0.209634\pi$
$881$	46.9480	1.58172	0.790858	+	0.611999i	$0.209634\pi$
$882$	7.26132	0.244501
$883$	−13.0392	−0.438803	−0.219401	−	0.975635i	$-0.570410\pi$
$883$	−13.0392	−0.438803	−0.219401	+	0.975635i	$0.570410\pi$
$884$	1.69432	0.0569860
$885$	−10.6253	−0.357165
$886$	−45.5377	−1.52987
$887$	−41.6701	−1.39914	−0.699572	−	0.714562i	$-0.746626\pi$
$887$	−41.6701	−1.39914	−0.699572	+	0.714562i	$0.746626\pi$
$888$	−8.42318	−0.282663
$889$	−2.00820	−0.0673529
$890$	23.6025	0.791159
$891$	0.0549321	0.00184029
$892$	1.61621	0.0541147
$893$	7.36771	0.246551
$894$	−18.6805	−0.624770
$895$	22.4561	0.750624
$896$	−17.7042	−0.591456
$897$	40.2249	1.34307
$898$	34.5408	1.15264
$899$	−0.672016	−0.0224130
$900$	0.145344	0.00484478
$901$	−7.65261	−0.254945
$902$	0.751997	0.0250388
$903$	−2.55263	−0.0849461
$904$	−18.6323	−0.619701
$905$	15.7709	0.524243
$906$	28.6131	0.950606
$907$	−16.4722	−0.546951	−0.273475	−	0.961879i	$-0.588173\pi$
$907$	−16.4722	−0.546951	−0.273475	+	0.961879i	$0.588173\pi$
$908$	−2.53355	−0.0840789
$909$	4.44051	0.147282
$910$	14.8199	0.491274
$911$	−0.603573	−0.0199973	−0.00999863	−	0.999950i	$-0.503183\pi$
$911$	−0.603573	−0.0199973	−0.00999863	+	0.999950i	$0.503183\pi$
$912$	6.43419	0.213057
$913$	−0.227202	−0.00751930
$914$	−21.4552	−0.709675
$915$	−4.83346	−0.159789
$916$	−3.79356	−0.125343
$917$	17.5734	0.580324
$918$	2.41172	0.0795986
$919$	40.8493	1.34749	0.673747	−	0.738962i	$-0.264684\pi$
$919$	40.8493	1.34749	0.673747	+	0.738962i	$0.264684\pi$
$920$	15.4343	0.508853
$921$	−26.3791	−0.869222
$922$	−33.4688	−1.10224
$923$	17.2455	0.567643
$924$	−0.0114103	−0.000375372 0
$925$	3.10073	0.101951
$926$	−23.4924	−0.772009
$927$	−9.44731	−0.310290
$928$	−3.77144	−0.123804
$929$	−59.3173	−1.94614	−0.973070	−	0.230512i	$-0.925960\pi$
$929$	−59.3173	−1.94614	−0.973070	+	0.230512i	$0.925960\pi$
$930$	−0.214166	−0.00702278
$931$	−7.47098	−0.244852
$932$	−1.77553	−0.0581594
$933$	−21.8027	−0.713790
$934$	−11.1350	−0.364347
$935$	−0.0904491	−0.00295800
$936$	19.2323	0.628629
$937$	0.603090	0.0197021	0.00985105	−	0.999951i	$-0.496864\pi$
$937$	0.603090	0.0197021	0.00985105	+	0.999951i	$0.496864\pi$
$938$	18.5412	0.605390
$939$	−13.2384	−0.432019
$940$	−0.710588	−0.0231768
$941$	−4.25171	−0.138602	−0.0693009	−	0.997596i	$-0.522077\pi$
$941$	−4.25171	−0.138602	−0.0693009	+	0.997596i	$0.522077\pi$
$942$	26.9578	0.878332
$943$	53.1026	1.72926
$944$	45.3653	1.47651
$945$	1.42914	0.0464900
$946$	−0.143710	−0.00467240
$947$	7.84791	0.255023	0.127511	−	0.991837i	$-0.459301\pi$
$947$	7.84791	0.255023	0.127511	+	0.991837i	$0.459301\pi$
$948$	0.616252	0.0200149
$949$	−54.3376	−1.76387
$950$	−2.20729	−0.0716139
$951$	2.97521	0.0964778
$952$	6.39243	0.207180
$953$	21.7988	0.706132	0.353066	−	0.935599i	$-0.385139\pi$
$953$	21.7988	0.706132	0.353066	+	0.935599i	$0.385139\pi$
$954$	6.80738	0.220397
$955$	4.28716	0.138729
$956$	0.449823	0.0145483
$957$	0.252466	0.00816108
$958$	33.2216	1.07334
$959$	−5.24274	−0.169297
$960$	7.33720	0.236807
$961$	−30.9786	−0.999310
$962$	−32.1538	−1.03668
$963$	9.20766	0.296713
$964$	0.634091	0.0204227
$965$	8.40967	0.270717
$966$	−11.8932	−0.382657
$967$	−5.81559	−0.187017	−0.0935084	−	0.995618i	$-0.529808\pi$
$967$	−5.81559	−0.187017	−0.0935084	+	0.995618i	$0.529808\pi$
$968$	−29.8735	−0.960169
$969$	−2.48136	−0.0797126
$970$	−2.67649	−0.0859368
$971$	38.3271	1.22997	0.614987	−	0.788537i	$-0.289161\pi$
$971$	38.3271	1.22997	0.614987	+	0.788537i	$0.289161\pi$
$972$	−0.145344	−0.00466190
$973$	4.39807	0.140996
$974$	26.5667	0.851251
$975$	−7.07979	−0.226735
$976$	20.6368	0.660567
$977$	−45.5086	−1.45595	−0.727974	−	0.685604i	$-0.759538\pi$
$977$	−45.5086	−1.45595	−0.727974	+	0.685604i	$0.759538\pi$
$978$	15.6898	0.501704
$979$	0.885189	0.0282908
$980$	0.720548	0.0230171
$981$	−1.84010	−0.0587498
$982$	−32.7918	−1.04643
$983$	−38.8279	−1.23842	−0.619209	−	0.785226i	$-0.712547\pi$
$983$	−38.8279	−1.23842	−0.619209	+	0.785226i	$0.712547\pi$
$984$	25.3895	0.809387
$985$	17.5258	0.558417
$986$	11.0842	0.352993
$987$	−6.98711	−0.222402
$988$	1.55070	0.0493342
$989$	−10.1481	−0.322692
$990$	0.0804590	0.00255715
$991$	30.8279	0.979280	0.489640	−	0.871925i	$-0.337128\pi$
$991$	30.8279	0.979280	0.489640	+	0.871925i	$0.337128\pi$
$992$	0.119986	0.00380957
$993$	−5.65071	−0.179320
$994$	−5.09894	−0.161728
$995$	−8.75287	−0.277485
$996$	0.601150	0.0190482
$997$	3.56493	0.112903	0.0564513	−	0.998405i	$-0.482021\pi$
$997$	3.56493	0.112903	0.0564513	+	0.998405i	$0.482021\pi$
$998$	−41.5034	−1.31377
$999$	−3.10073	−0.0981028

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6015.2.a.f.1.12	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6015.2.a.f.1.12	✓	36	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:	\( N \)	\(=\)	\( 6015 = 3 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6015.a (trivial)

\(f(q)\)	\(=\)	\(q-1.46470 q^{2} -1.00000 q^{3} +0.145344 q^{4} -1.00000 q^{5} +1.46470 q^{6} +1.42914 q^{7} +2.71651 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.46470 q^{2} -1.00000 q^{3} +0.145344 q^{4} -1.00000 q^{5} +1.46470 q^{6} +1.42914 q^{7} +2.71651 q^{8} +1.00000 q^{9} +1.46470 q^{10} +0.0549321 q^{11} -0.145344 q^{12} +7.07979 q^{13} -2.09326 q^{14} +1.00000 q^{15} -4.26956 q^{16} +1.64656 q^{17} -1.46470 q^{18} +1.50699 q^{19} -0.145344 q^{20} -1.42914 q^{21} -0.0804590 q^{22} -5.68165 q^{23} -2.71651 q^{24} +1.00000 q^{25} -10.3698 q^{26} -1.00000 q^{27} +0.207717 q^{28} -4.59597 q^{29} -1.46470 q^{30} +0.146218 q^{31} +0.820597 q^{32} -0.0549321 q^{33} -2.41172 q^{34} -1.42914 q^{35} +0.145344 q^{36} +3.10073 q^{37} -2.20729 q^{38} -7.07979 q^{39} -2.71651 q^{40} -9.34634 q^{41} +2.09326 q^{42} +1.78612 q^{43} +0.00798402 q^{44} -1.00000 q^{45} +8.32190 q^{46} +4.88902 q^{47} +4.26956 q^{48} -4.95755 q^{49} -1.46470 q^{50} -1.64656 q^{51} +1.02900 q^{52} -4.64763 q^{53} +1.46470 q^{54} -0.0549321 q^{55} +3.88229 q^{56} -1.50699 q^{57} +6.73172 q^{58} -10.6253 q^{59} +0.145344 q^{60} -4.83346 q^{61} -0.214166 q^{62} +1.42914 q^{63} +7.33720 q^{64} -7.07979 q^{65} +0.0804590 q^{66} -8.85753 q^{67} +0.239317 q^{68} +5.68165 q^{69} +2.09326 q^{70} +2.43588 q^{71} +2.71651 q^{72} -7.67502 q^{73} -4.54164 q^{74} -1.00000 q^{75} +0.219031 q^{76} +0.0785058 q^{77} +10.3698 q^{78} -4.23997 q^{79} +4.26956 q^{80} +1.00000 q^{81} +13.6896 q^{82} -4.13606 q^{83} -0.207717 q^{84} -1.64656 q^{85} -2.61613 q^{86} +4.59597 q^{87} +0.149224 q^{88} +16.1143 q^{89} +1.46470 q^{90} +10.1180 q^{91} -0.825790 q^{92} -0.146218 q^{93} -7.16095 q^{94} -1.50699 q^{95} -0.820597 q^{96} -1.82733 q^{97} +7.26132 q^{98} +0.0549321 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 7 q^{2} - 36 q^{3} + 45 q^{4} - 36 q^{5} + 7 q^{6} + 2 q^{7} - 24 q^{8} + 36 q^{9}+O(q^{10}) \) 36 * q - 7 * q^2 - 36 * q^3 + 45 * q^4 - 36 * q^5 + 7 * q^6 + 2 * q^7 - 24 * q^8 + 36 * q^9	\( 36 q - 7 q^{2} - 36 q^{3} + 45 q^{4} - 36 q^{5} + 7 q^{6} + 2 q^{7} - 24 q^{8} + 36 q^{9} + 7 q^{10} - q^{11} - 45 q^{12} - 8 q^{13} - 4 q^{14} + 36 q^{15} + 63 q^{16} - 50 q^{17} - 7 q^{18} + 15 q^{19} - 45 q^{20} - 2 q^{21} + 7 q^{22} - 32 q^{23} + 24 q^{24} + 36 q^{25} - 12 q^{26} - 36 q^{27} - 10 q^{28} + 7 q^{29} - 7 q^{30} + 7 q^{31} - 50 q^{32} + q^{33} + 8 q^{34} - 2 q^{35} + 45 q^{36} - 10 q^{37} - 48 q^{38} + 8 q^{39} + 24 q^{40} - 31 q^{41} + 4 q^{42} + 27 q^{43} - 9 q^{44} - 36 q^{45} + 23 q^{46} - 46 q^{47} - 63 q^{48} + 48 q^{49} - 7 q^{50} + 50 q^{51} - 14 q^{52} - 39 q^{53} + 7 q^{54} + q^{55} - 29 q^{56} - 15 q^{57} - 26 q^{58} - 9 q^{59} + 45 q^{60} + 5 q^{61} - 65 q^{62} + 2 q^{63} + 90 q^{64} + 8 q^{65} - 7 q^{66} + 18 q^{67} - 128 q^{68} + 32 q^{69} + 4 q^{70} + 4 q^{71} - 24 q^{72} - 45 q^{73} - 22 q^{74} - 36 q^{75} + 26 q^{76} - 38 q^{77} + 12 q^{78} + 25 q^{79} - 63 q^{80} + 36 q^{81} - 5 q^{82} - 71 q^{83} + 10 q^{84} + 50 q^{85} + 3 q^{86} - 7 q^{87} - 9 q^{88} - 39 q^{89} + 7 q^{90} + 19 q^{91} - 95 q^{92} - 7 q^{93} + 16 q^{94} - 15 q^{95} + 50 q^{96} - 61 q^{97} - 76 q^{98} - q^{99}+O(q^{100}) \) 36 * q - 7 * q^2 - 36 * q^3 + 45 * q^4 - 36 * q^5 + 7 * q^6 + 2 * q^7 - 24 * q^8 + 36 * q^9 + 7 * q^10 - q^11 - 45 * q^12 - 8 * q^13 - 4 * q^14 + 36 * q^15 + 63 * q^16 - 50 * q^17 - 7 * q^18 + 15 * q^19 - 45 * q^20 - 2 * q^21 + 7 * q^22 - 32 * q^23 + 24 * q^24 + 36 * q^25 - 12 * q^26 - 36 * q^27 - 10 * q^28 + 7 * q^29 - 7 * q^30 + 7 * q^31 - 50 * q^32 + q^33 + 8 * q^34 - 2 * q^35 + 45 * q^36 - 10 * q^37 - 48 * q^38 + 8 * q^39 + 24 * q^40 - 31 * q^41 + 4 * q^42 + 27 * q^43 - 9 * q^44 - 36 * q^45 + 23 * q^46 - 46 * q^47 - 63 * q^48 + 48 * q^49 - 7 * q^50 + 50 * q^51 - 14 * q^52 - 39 * q^53 + 7 * q^54 + q^55 - 29 * q^56 - 15 * q^57 - 26 * q^58 - 9 * q^59 + 45 * q^60 + 5 * q^61 - 65 * q^62 + 2 * q^63 + 90 * q^64 + 8 * q^65 - 7 * q^66 + 18 * q^67 - 128 * q^68 + 32 * q^69 + 4 * q^70 + 4 * q^71 - 24 * q^72 - 45 * q^73 - 22 * q^74 - 36 * q^75 + 26 * q^76 - 38 * q^77 + 12 * q^78 + 25 * q^79 - 63 * q^80 + 36 * q^81 - 5 * q^82 - 71 * q^83 + 10 * q^84 + 50 * q^85 + 3 * q^86 - 7 * q^87 - 9 * q^88 - 39 * q^89 + 7 * q^90 + 19 * q^91 - 95 * q^92 - 7 * q^93 + 16 * q^94 - 15 * q^95 + 50 * q^96 - 61 * q^97 - 76 * q^98 - q^99

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