LMFDB - Embedded newform 8049.2.a.b.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8049,2,Mod(1,8049)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8049, 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("8049.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8049 = 3 \cdot 2683 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8049.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:	$64.2715885869$
Analytic rank:	$1$
Dimension:	$104$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	8049.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.13514 q^{2} -1.00000 q^{3} +2.55881 q^{4} +1.37673 q^{5} +2.13514 q^{6} -0.308813 q^{7} -1.19313 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.13514 q^{2} -1.00000 q^{3} +2.55881 q^{4} +1.37673 q^{5} +2.13514 q^{6} -0.308813 q^{7} -1.19313 q^{8} +1.00000 q^{9} -2.93951 q^{10} +2.00359 q^{11} -2.55881 q^{12} -4.09348 q^{13} +0.659358 q^{14} -1.37673 q^{15} -2.57012 q^{16} +3.92196 q^{17} -2.13514 q^{18} +2.13376 q^{19} +3.52279 q^{20} +0.308813 q^{21} -4.27795 q^{22} +4.17261 q^{23} +1.19313 q^{24} -3.10461 q^{25} +8.74014 q^{26} -1.00000 q^{27} -0.790194 q^{28} -1.92647 q^{29} +2.93951 q^{30} -3.04138 q^{31} +7.87381 q^{32} -2.00359 q^{33} -8.37391 q^{34} -0.425153 q^{35} +2.55881 q^{36} +6.26002 q^{37} -4.55587 q^{38} +4.09348 q^{39} -1.64262 q^{40} -5.96411 q^{41} -0.659358 q^{42} -2.91296 q^{43} +5.12681 q^{44} +1.37673 q^{45} -8.90909 q^{46} +0.325333 q^{47} +2.57012 q^{48} -6.90463 q^{49} +6.62876 q^{50} -3.92196 q^{51} -10.4744 q^{52} -6.61089 q^{53} +2.13514 q^{54} +2.75841 q^{55} +0.368455 q^{56} -2.13376 q^{57} +4.11328 q^{58} -2.38100 q^{59} -3.52279 q^{60} -0.283001 q^{61} +6.49377 q^{62} -0.308813 q^{63} -11.6714 q^{64} -5.63563 q^{65} +4.27795 q^{66} -1.23940 q^{67} +10.0355 q^{68} -4.17261 q^{69} +0.907760 q^{70} +15.3132 q^{71} -1.19313 q^{72} +10.5389 q^{73} -13.3660 q^{74} +3.10461 q^{75} +5.45988 q^{76} -0.618736 q^{77} -8.74014 q^{78} +12.2497 q^{79} -3.53836 q^{80} +1.00000 q^{81} +12.7342 q^{82} -7.21929 q^{83} +0.790194 q^{84} +5.39949 q^{85} +6.21956 q^{86} +1.92647 q^{87} -2.39055 q^{88} -1.03107 q^{89} -2.93951 q^{90} +1.26412 q^{91} +10.6769 q^{92} +3.04138 q^{93} -0.694630 q^{94} +2.93762 q^{95} -7.87381 q^{96} +0.581466 q^{97} +14.7423 q^{98} +2.00359 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 104 q - 9 q^{2} - 104 q^{3} + 87 q^{4} - 15 q^{5} + 9 q^{6} - 10 q^{7} - 27 q^{8} + 104 q^{9}+O(q^{10}) $ 104 * q - 9 * q^2 - 104 * q^3 + 87 * q^4 - 15 * q^5 + 9 * q^6 - 10 * q^7 - 27 * q^8 + 104 * q^9	\( 104 q - 9 q^{2} - 104 q^{3} + 87 q^{4} - 15 q^{5} + 9 q^{6} - 10 q^{7} - 27 q^{8} + 104 q^{9} + 8 q^{10} - 52 q^{11} - 87 q^{12} + 35 q^{13} - 23 q^{14} + 15 q^{15} + 53 q^{16} - 19 q^{17} - 9 q^{18} - 22 q^{19} - 35 q^{20} + 10 q^{21} - q^{22} - 70 q^{23} + 27 q^{24} + 79 q^{25} - 39 q^{26} - 104 q^{27} - 9 q^{28} - 37 q^{29} - 8 q^{30} - 47 q^{31} - 53 q^{32} + 52 q^{33} - 17 q^{34} - 54 q^{35} + 87 q^{36} + 65 q^{37} - 33 q^{38} - 35 q^{39} + 14 q^{40} - 47 q^{41} + 23 q^{42} - 30 q^{43} - 122 q^{44} - 15 q^{45} - 6 q^{46} - 101 q^{47} - 53 q^{48} + 78 q^{49} - 64 q^{50} + 19 q^{51} + 41 q^{52} - 48 q^{53} + 9 q^{54} - 29 q^{55} - 71 q^{56} + 22 q^{57} - 2 q^{58} - 86 q^{59} + 35 q^{60} + 34 q^{61} - 36 q^{62} - 10 q^{63} - 15 q^{64} - 64 q^{65} + q^{66} - 38 q^{67} - 33 q^{68} + 70 q^{69} - 29 q^{70} - 176 q^{71} - 27 q^{72} + 69 q^{73} - 86 q^{74} - 79 q^{75} - 54 q^{76} - 45 q^{77} + 39 q^{78} - 101 q^{79} - 76 q^{80} + 104 q^{81} + 38 q^{82} - 67 q^{83} + 9 q^{84} + 3 q^{85} - 90 q^{86} + 37 q^{87} + 7 q^{88} - 91 q^{89} + 8 q^{90} - 47 q^{91} - 136 q^{92} + 47 q^{93} - 20 q^{94} - 130 q^{95} + 53 q^{96} + 86 q^{97} - 44 q^{98} - 52 q^{99}+O(q^{100}) \) 104 * q - 9 * q^2 - 104 * q^3 + 87 * q^4 - 15 * q^5 + 9 * q^6 - 10 * q^7 - 27 * q^8 + 104 * q^9 + 8 * q^10 - 52 * q^11 - 87 * q^12 + 35 * q^13 - 23 * q^14 + 15 * q^15 + 53 * q^16 - 19 * q^17 - 9 * q^18 - 22 * q^19 - 35 * q^20 + 10 * q^21 - q^22 - 70 * q^23 + 27 * q^24 + 79 * q^25 - 39 * q^26 - 104 * q^27 - 9 * q^28 - 37 * q^29 - 8 * q^30 - 47 * q^31 - 53 * q^32 + 52 * q^33 - 17 * q^34 - 54 * q^35 + 87 * q^36 + 65 * q^37 - 33 * q^38 - 35 * q^39 + 14 * q^40 - 47 * q^41 + 23 * q^42 - 30 * q^43 - 122 * q^44 - 15 * q^45 - 6 * q^46 - 101 * q^47 - 53 * q^48 + 78 * q^49 - 64 * q^50 + 19 * q^51 + 41 * q^52 - 48 * q^53 + 9 * q^54 - 29 * q^55 - 71 * q^56 + 22 * q^57 - 2 * q^58 - 86 * q^59 + 35 * q^60 + 34 * q^61 - 36 * q^62 - 10 * q^63 - 15 * q^64 - 64 * q^65 + q^66 - 38 * q^67 - 33 * q^68 + 70 * q^69 - 29 * q^70 - 176 * q^71 - 27 * q^72 + 69 * q^73 - 86 * q^74 - 79 * q^75 - 54 * q^76 - 45 * q^77 + 39 * q^78 - 101 * q^79 - 76 * q^80 + 104 * q^81 + 38 * q^82 - 67 * q^83 + 9 * q^84 + 3 * q^85 - 90 * q^86 + 37 * q^87 + 7 * q^88 - 91 * q^89 + 8 * q^90 - 47 * q^91 - 136 * q^92 + 47 * q^93 - 20 * q^94 - 130 * q^95 + 53 * q^96 + 86 * q^97 - 44 * q^98 - 52 * 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 $

$2$	−2.13514	−1.50977	−0.754885	−	0.655857i	$-0.772307\pi$
$2$	−2.13514	−1.50977	−0.754885	+	0.655857i	$0.772307\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	2.55881	1.27940
$5$	1.37673	0.615694	0.307847	−	0.951436i	$-0.400392\pi$
$5$	1.37673	0.615694	0.307847	+	0.951436i	$0.400392\pi$
$6$	2.13514	0.871666
$7$	−0.308813	−0.116720	−0.0583602	−	0.998296i	$-0.518587\pi$
$7$	−0.308813	−0.116720	−0.0583602	+	0.998296i	$0.518587\pi$
$8$	−1.19313	−0.421836
$9$	1.00000	0.333333
$10$	−2.93951	−0.929555
$11$	2.00359	0.604106	0.302053	−	0.953291i	$-0.402328\pi$
$11$	2.00359	0.604106	0.302053	+	0.953291i	$0.402328\pi$
$12$	−2.55881	−0.738664
$13$	−4.09348	−1.13533	−0.567664	−	0.823260i	$-0.692153\pi$
$13$	−4.09348	−1.13533	−0.567664	+	0.823260i	$0.692153\pi$
$14$	0.659358	0.176221
$15$	−1.37673	−0.355471
$16$	−2.57012	−0.642529
$17$	3.92196	0.951214	0.475607	−	0.879658i	$-0.342228\pi$
$17$	3.92196	0.951214	0.475607	+	0.879658i	$0.342228\pi$
$18$	−2.13514	−0.503257
$19$	2.13376	0.489518	0.244759	−	0.969584i	$-0.421291\pi$
$19$	2.13376	0.489518	0.244759	+	0.969584i	$0.421291\pi$
$20$	3.52279	0.787721
$21$	0.308813	0.0673885
$22$	−4.27795	−0.912061
$23$	4.17261	0.870050	0.435025	−	0.900418i	$-0.356740\pi$
$23$	4.17261	0.870050	0.435025	+	0.900418i	$0.356740\pi$
$24$	1.19313	0.243547
$25$	−3.10461	−0.620921
$26$	8.74014	1.71408
$27$	−1.00000	−0.192450
$28$	−0.790194	−0.149333
$29$	−1.92647	−0.357737	−0.178869	−	0.983873i	$-0.557244\pi$
$29$	−1.92647	−0.357737	−0.178869	+	0.983873i	$0.557244\pi$
$30$	2.93951	0.536679
$31$	−3.04138	−0.546249	−0.273124	−	0.961979i	$-0.588057\pi$
$31$	−3.04138	−0.546249	−0.273124	+	0.961979i	$0.588057\pi$
$32$	7.87381	1.39191
$33$	−2.00359	−0.348781
$34$	−8.37391	−1.43611
$35$	−0.425153	−0.0718640
$36$	2.55881	0.426468
$37$	6.26002	1.02914	0.514570	−	0.857448i	$-0.327951\pi$
$37$	6.26002	1.02914	0.514570	+	0.857448i	$0.327951\pi$
$38$	−4.55587	−0.739059
$39$	4.09348	0.655482
$40$	−1.64262	−0.259722
$41$	−5.96411	−0.931437	−0.465719	−	0.884933i	$-0.654204\pi$
$41$	−5.96411	−0.931437	−0.465719	+	0.884933i	$0.654204\pi$
$42$	−0.659358	−0.101741
$43$	−2.91296	−0.444222	−0.222111	−	0.975021i	$-0.571295\pi$
$43$	−2.91296	−0.444222	−0.222111	+	0.975021i	$0.571295\pi$
$44$	5.12681	0.772896
$45$	1.37673	0.205231
$46$	−8.90909	−1.31357
$47$	0.325333	0.0474547	0.0237273	−	0.999718i	$-0.492447\pi$
$47$	0.325333	0.0474547	0.0237273	+	0.999718i	$0.492447\pi$
$48$	2.57012	0.370964
$49$	−6.90463	−0.986376
$50$	6.62876	0.937448
$51$	−3.92196	−0.549184
$52$	−10.4744	−1.45254
$53$	−6.61089	−0.908075	−0.454037	−	0.890983i	$-0.650017\pi$
$53$	−6.61089	−0.908075	−0.454037	+	0.890983i	$0.650017\pi$
$54$	2.13514	0.290555
$55$	2.75841	0.371944
$56$	0.368455	0.0492368
$57$	−2.13376	−0.282623
$58$	4.11328	0.540101
$59$	−2.38100	−0.309980	−0.154990	−	0.987916i	$-0.549535\pi$
$59$	−2.38100	−0.309980	−0.154990	+	0.987916i	$0.549535\pi$
$60$	−3.52279	−0.454791
$61$	−0.283001	−0.0362346	−0.0181173	−	0.999836i	$-0.505767\pi$
$61$	−0.283001	−0.0362346	−0.0181173	+	0.999836i	$0.505767\pi$
$62$	6.49377	0.824710
$63$	−0.308813	−0.0389068
$64$	−11.6714	−1.45893
$65$	−5.63563	−0.699014
$66$	4.27795	0.526579
$67$	−1.23940	−0.151417	−0.0757084	−	0.997130i	$-0.524122\pi$
$67$	−1.23940	−0.151417	−0.0757084	+	0.997130i	$0.524122\pi$
$68$	10.0355	1.21699
$69$	−4.17261	−0.502323
$70$	0.907760	0.108498
$71$	15.3132	1.81734	0.908669	−	0.417517i	$-0.137100\pi$
$71$	15.3132	1.81734	0.908669	+	0.417517i	$0.137100\pi$
$72$	−1.19313	−0.140612
$73$	10.5389	1.23348	0.616741	−	0.787166i	$-0.288452\pi$
$73$	10.5389	1.23348	0.616741	+	0.787166i	$0.288452\pi$
$74$	−13.3660	−1.55376
$75$	3.10461	0.358489
$76$	5.45988	0.626291
$77$	−0.618736	−0.0705115
$78$	−8.74014	−0.989627
$79$	12.2497	1.37820	0.689102	−	0.724665i	$-0.258005\pi$
$79$	12.2497	1.37820	0.689102	+	0.724665i	$0.258005\pi$
$80$	−3.53836	−0.395601
$81$	1.00000	0.111111
$82$	12.7342	1.40626
$83$	−7.21929	−0.792421	−0.396210	−	0.918160i	$-0.629675\pi$
$83$	−7.21929	−0.792421	−0.396210	+	0.918160i	$0.629675\pi$
$84$	0.790194	0.0862172
$85$	5.39949	0.585657
$86$	6.21956	0.670673
$87$	1.92647	0.206540
$88$	−2.39055	−0.254834
$89$	−1.03107	−0.109293	−0.0546467	−	0.998506i	$-0.517403\pi$
$89$	−1.03107	−0.109293	−0.0546467	+	0.998506i	$0.517403\pi$
$90$	−2.93951	−0.309852
$91$	1.26412	0.132516
$92$	10.6769	1.11314
$93$	3.04138	0.315377
$94$	−0.694630	−0.0716457
$95$	2.93762	0.301393
$96$	−7.87381	−0.803618
$97$	0.581466	0.0590389	0.0295195	−	0.999564i	$-0.490602\pi$
$97$	0.581466	0.0590389	0.0295195	+	0.999564i	$0.490602\pi$
$98$	14.7423	1.48920
$99$	2.00359	0.201369
$100$	−7.94409	−0.794409
$101$	−11.5340	−1.14767	−0.573836	−	0.818970i	$-0.694545\pi$
$101$	−11.5340	−1.14767	−0.573836	+	0.818970i	$0.694545\pi$
$102$	8.37391	0.829141
$103$	−4.69245	−0.462361	−0.231180	−	0.972911i	$-0.574259\pi$
$103$	−4.69245	−0.462361	−0.231180	+	0.972911i	$0.574259\pi$
$104$	4.88406	0.478922
$105$	0.425153	0.0414907
$106$	14.1151	1.37098
$107$	−9.59344	−0.927433	−0.463717	−	0.885984i	$-0.653484\pi$
$107$	−9.59344	−0.927433	−0.463717	+	0.885984i	$0.653484\pi$
$108$	−2.55881	−0.246221
$109$	−0.147265	−0.0141054	−0.00705272	−	0.999975i	$-0.502245\pi$
$109$	−0.147265	−0.0141054	−0.00705272	+	0.999975i	$0.502245\pi$
$110$	−5.88959	−0.561550
$111$	−6.26002	−0.594174
$112$	0.793686	0.0749963
$113$	−12.2610	−1.15342	−0.576708	−	0.816950i	$-0.695663\pi$
$113$	−12.2610	−1.15342	−0.576708	+	0.816950i	$0.695663\pi$
$114$	4.55587	0.426696
$115$	5.74457	0.535684
$116$	−4.92948	−0.457690
$117$	−4.09348	−0.378443
$118$	5.08377	0.467999
$119$	−1.21115	−0.111026
$120$	1.64262	0.149950
$121$	−6.98561	−0.635056
$122$	0.604247	0.0547059
$123$	5.96411	0.537766
$124$	−7.78232	−0.698873
$125$	−11.1579	−0.997991
$126$	0.659358	0.0587403
$127$	−11.5365	−1.02370	−0.511850	−	0.859075i	$-0.671040\pi$
$127$	−11.5365	−1.02370	−0.511850	+	0.859075i	$0.671040\pi$
$128$	9.17248	0.810740
$129$	2.91296	0.256472
$130$	12.0328	1.05535
$131$	−14.2224	−1.24262	−0.621310	−	0.783565i	$-0.713399\pi$
$131$	−14.2224	−1.24262	−0.621310	+	0.783565i	$0.713399\pi$
$132$	−5.12681	−0.446232
$133$	−0.658933	−0.0571367
$134$	2.64629	0.228605
$135$	−1.37673	−0.118490
$136$	−4.67941	−0.401256
$137$	−22.1929	−1.89607	−0.948035	−	0.318166i	$-0.896933\pi$
$137$	−22.1929	−1.89607	−0.948035	+	0.318166i	$0.896933\pi$
$138$	8.90909	0.758392
$139$	−12.8255	−1.08784	−0.543920	−	0.839137i	$-0.683061\pi$
$139$	−12.8255	−1.08784	−0.543920	+	0.839137i	$0.683061\pi$
$140$	−1.08789	−0.0919431
$141$	−0.325333	−0.0273980
$142$	−32.6957	−2.74376
$143$	−8.20168	−0.685859
$144$	−2.57012	−0.214176
$145$	−2.65224	−0.220256
$146$	−22.5020	−1.86227
$147$	6.90463	0.569485
$148$	16.0182	1.31669
$149$	10.4309	0.854533	0.427267	−	0.904126i	$-0.359477\pi$
$149$	10.4309	0.854533	0.427267	+	0.904126i	$0.359477\pi$
$150$	−6.62876	−0.541236
$151$	5.65576	0.460259	0.230130	−	0.973160i	$-0.426085\pi$
$151$	5.65576	0.460259	0.230130	+	0.973160i	$0.426085\pi$
$152$	−2.54586	−0.206496
$153$	3.92196	0.317071
$154$	1.32109	0.106456
$155$	−4.18717	−0.336322
$156$	10.4744	0.838626
$157$	−2.78274	−0.222087	−0.111043	−	0.993816i	$-0.535419\pi$
$157$	−2.78274	−0.222087	−0.111043	+	0.993816i	$0.535419\pi$
$158$	−26.1549	−2.08077
$159$	6.61089	0.524277
$160$	10.8401	0.856988
$161$	−1.28856	−0.101553
$162$	−2.13514	−0.167752
$163$	14.4402	1.13104	0.565522	−	0.824733i	$-0.308675\pi$
$163$	14.4402	1.13104	0.565522	+	0.824733i	$0.308675\pi$
$164$	−15.2610	−1.19168
$165$	−2.75841	−0.214742
$166$	15.4142	1.19637
$167$	0.406222	0.0314344	0.0157172	−	0.999876i	$-0.494997\pi$
$167$	0.406222	0.0314344	0.0157172	+	0.999876i	$0.494997\pi$
$168$	−0.368455	−0.0284269
$169$	3.75660	0.288969
$170$	−11.5286	−0.884206
$171$	2.13376	0.163173
$172$	−7.45370	−0.568339
$173$	10.8584	0.825546	0.412773	−	0.910834i	$-0.364560\pi$
$173$	10.8584	0.825546	0.412773	+	0.910834i	$0.364560\pi$
$174$	−4.11328	−0.311827
$175$	0.958743	0.0724742
$176$	−5.14947	−0.388156
$177$	2.38100	0.178967
$178$	2.20148	0.165008
$179$	19.4376	1.45284	0.726418	−	0.687254i	$-0.241184\pi$
$179$	19.4376	1.45284	0.726418	+	0.687254i	$0.241184\pi$
$180$	3.52279	0.262574
$181$	4.39036	0.326333	0.163166	−	0.986599i	$-0.447829\pi$
$181$	4.39036	0.326333	0.163166	+	0.986599i	$0.447829\pi$
$182$	−2.69907	−0.200068
$183$	0.283001	0.0209201
$184$	−4.97847	−0.367018
$185$	8.61837	0.633635
$186$	−6.49377	−0.476146
$187$	7.85801	0.574634
$188$	0.832465	0.0607137
$189$	0.308813	0.0224628
$190$	−6.27221	−0.455034
$191$	−19.7323	−1.42778	−0.713888	−	0.700260i	$-0.753068\pi$
$191$	−19.7323	−1.42778	−0.713888	+	0.700260i	$0.753068\pi$
$192$	11.6714	0.842313
$193$	13.3235	0.959049	0.479525	−	0.877528i	$-0.340809\pi$
$193$	13.3235	0.959049	0.479525	+	0.877528i	$0.340809\pi$
$194$	−1.24151	−0.0891352
$195$	5.63563	0.403576
$196$	−17.6676	−1.26197
$197$	−9.12609	−0.650207	−0.325103	−	0.945678i	$-0.605399\pi$
$197$	−9.12609	−0.650207	−0.325103	+	0.945678i	$0.605399\pi$
$198$	−4.27795	−0.304020
$199$	−3.61446	−0.256222	−0.128111	−	0.991760i	$-0.540891\pi$
$199$	−3.61446	−0.256222	−0.128111	+	0.991760i	$0.540891\pi$
$200$	3.70421	0.261927
$201$	1.23940	0.0874205
$202$	24.6266	1.73272
$203$	0.594920	0.0417552
$204$	−10.0355	−0.702628
$205$	−8.21098	−0.573480
$206$	10.0190	0.698058
$207$	4.17261	0.290017
$208$	10.5207	0.729481
$209$	4.27519	0.295721
$210$	−0.907760	−0.0626414
$211$	−4.13922	−0.284956	−0.142478	−	0.989798i	$-0.545507\pi$
$211$	−4.13922	−0.284956	−0.142478	+	0.989798i	$0.545507\pi$
$212$	−16.9160	−1.16179
$213$	−15.3132	−1.04924
$214$	20.4833	1.40021
$215$	−4.01036	−0.273504
$216$	1.19313	0.0811823
$217$	0.939219	0.0637584
$218$	0.314431	0.0212960
$219$	−10.5389	−0.712152
$220$	7.05825	0.475867
$221$	−16.0545	−1.07994
$222$	13.3660	0.897067
$223$	−9.38598	−0.628532	−0.314266	−	0.949335i	$-0.601758\pi$
$223$	−9.38598	−0.628532	−0.314266	+	0.949335i	$0.601758\pi$
$224$	−2.43154	−0.162464
$225$	−3.10461	−0.206974
$226$	26.1789	1.74139
$227$	25.3246	1.68085	0.840426	−	0.541926i	$-0.182305\pi$
$227$	25.3246	1.68085	0.840426	+	0.541926i	$0.182305\pi$
$228$	−5.45988	−0.361589
$229$	27.1789	1.79603	0.898016	−	0.439963i	$-0.145009\pi$
$229$	27.1789	1.79603	0.898016	+	0.439963i	$0.145009\pi$
$230$	−12.2654	−0.808759
$231$	0.618736	0.0407098
$232$	2.29854	0.150906
$233$	24.2908	1.59134	0.795672	−	0.605727i	$-0.207118\pi$
$233$	24.2908	1.59134	0.795672	+	0.605727i	$0.207118\pi$
$234$	8.74014	0.571361
$235$	0.447897	0.0292176
$236$	−6.09253	−0.396590
$237$	−12.2497	−0.795706
$238$	2.58597	0.167624
$239$	−1.41138	−0.0912946	−0.0456473	−	0.998958i	$-0.514535\pi$
$239$	−1.41138	−0.0912946	−0.0456473	+	0.998958i	$0.514535\pi$
$240$	3.53836	0.228400
$241$	−9.27036	−0.597157	−0.298578	−	0.954385i	$-0.596512\pi$
$241$	−9.27036	−0.597157	−0.298578	+	0.954385i	$0.596512\pi$
$242$	14.9152	0.958788
$243$	−1.00000	−0.0641500
$244$	−0.724146	−0.0463587
$245$	−9.50584	−0.607306
$246$	−12.7342	−0.811902
$247$	−8.73451	−0.555763
$248$	3.62877	0.230427
$249$	7.21929	0.457504
$250$	23.8236	1.50674
$251$	−9.50798	−0.600138	−0.300069	−	0.953917i	$-0.597010\pi$
$251$	−9.50798	−0.600138	−0.300069	+	0.953917i	$0.597010\pi$
$252$	−0.790194	−0.0497775
$253$	8.36022	0.525602
$254$	24.6320	1.54555
$255$	−5.39949	−0.338129
$256$	3.75838	0.234898
$257$	−30.7585	−1.91866	−0.959331	−	0.282284i	$-0.908908\pi$
$257$	−30.7585	−1.91866	−0.959331	+	0.282284i	$0.908908\pi$
$258$	−6.21956	−0.387213
$259$	−1.93318	−0.120122
$260$	−14.4205	−0.894321
$261$	−1.92647	−0.119246
$262$	30.3668	1.87607
$263$	−23.3711	−1.44112	−0.720562	−	0.693390i	$-0.756116\pi$
$263$	−23.3711	−1.44112	−0.720562	+	0.693390i	$0.756116\pi$
$264$	2.39055	0.147128
$265$	−9.10142	−0.559096
$266$	1.40691	0.0862633
$267$	1.03107	0.0631005
$268$	−3.17139	−0.193723
$269$	19.4500	1.18589	0.592943	−	0.805244i	$-0.297966\pi$
$269$	19.4500	1.18589	0.592943	+	0.805244i	$0.297966\pi$
$270$	2.93951	0.178893
$271$	−10.1684	−0.617684	−0.308842	−	0.951113i	$-0.599941\pi$
$271$	−10.1684	−0.617684	−0.308842	+	0.951113i	$0.599941\pi$
$272$	−10.0799	−0.611183
$273$	−1.26412	−0.0765081
$274$	47.3849	2.86263
$275$	−6.22037	−0.375103
$276$	−10.6769	−0.642675
$277$	7.84628	0.471437	0.235719	−	0.971821i	$-0.424256\pi$
$277$	7.84628	0.471437	0.235719	+	0.971821i	$0.424256\pi$
$278$	27.3841	1.64239
$279$	−3.04138	−0.182083
$280$	0.507264	0.0303148
$281$	−17.2396	−1.02843	−0.514214	−	0.857662i	$-0.671916\pi$
$281$	−17.2396	−1.02843	−0.514214	+	0.857662i	$0.671916\pi$
$282$	0.694630	0.0413646
$283$	−20.5460	−1.22133	−0.610667	−	0.791888i	$-0.709098\pi$
$283$	−20.5460	−1.22133	−0.610667	+	0.791888i	$0.709098\pi$
$284$	39.1834	2.32511
$285$	−2.93762	−0.174009
$286$	17.5117	1.03549
$287$	1.84180	0.108718
$288$	7.87381	0.463969
$289$	−1.61825	−0.0951912
$290$	5.66289	0.332537
$291$	−0.581466	−0.0340862
$292$	26.9670	1.57812
$293$	17.0917	0.998506	0.499253	−	0.866456i	$-0.333608\pi$
$293$	17.0917	0.998506	0.499253	+	0.866456i	$0.333608\pi$
$294$	−14.7423	−0.859791
$295$	−3.27801	−0.190853
$296$	−7.46902	−0.434128
$297$	−2.00359	−0.116260
$298$	−22.2714	−1.29015
$299$	−17.0805	−0.987791
$300$	7.94409	0.458653
$301$	0.899559	0.0518497
$302$	−12.0758	−0.694885
$303$	11.5340	0.662609
$304$	−5.48401	−0.314530
$305$	−0.389617	−0.0223094
$306$	−8.37391	−0.478705
$307$	6.64901	0.379479	0.189740	−	0.981834i	$-0.439236\pi$
$307$	6.64901	0.379479	0.189740	+	0.981834i	$0.439236\pi$
$308$	−1.58323	−0.0902127
$309$	4.69245	0.266944
$310$	8.94019	0.507768
$311$	20.0869	1.13902	0.569511	−	0.821984i	$-0.307133\pi$
$311$	20.0869	1.13902	0.569511	+	0.821984i	$0.307133\pi$
$312$	−4.88406	−0.276506
$313$	14.3321	0.810098	0.405049	−	0.914295i	$-0.367254\pi$
$313$	14.3321	0.810098	0.405049	+	0.914295i	$0.367254\pi$
$314$	5.94153	0.335300
$315$	−0.425153	−0.0239547
$316$	31.3447	1.76328
$317$	24.6226	1.38295	0.691473	−	0.722403i	$-0.256962\pi$
$317$	24.6226	1.38295	0.691473	+	0.722403i	$0.256962\pi$
$318$	−14.1151	−0.791538
$319$	−3.85987	−0.216111
$320$	−16.0684	−0.898253
$321$	9.59344	0.535454
$322$	2.75125	0.153321
$323$	8.36851	0.465637
$324$	2.55881	0.142156
$325$	12.7087	0.704949
$326$	−30.8318	−1.70761
$327$	0.147265	0.00814378
$328$	7.11597	0.392914
$329$	−0.100467	−0.00553893
$330$	5.88959	0.324211
$331$	−0.698485	−0.0383922	−0.0191961	−	0.999816i	$-0.506111\pi$
$331$	−0.698485	−0.0383922	−0.0191961	+	0.999816i	$0.506111\pi$
$332$	−18.4728	−1.01383
$333$	6.26002	0.343047
$334$	−0.867340	−0.0474587
$335$	−1.70632	−0.0932264
$336$	−0.793686	−0.0432991
$337$	−1.59325	−0.0867897	−0.0433949	−	0.999058i	$-0.513817\pi$
$337$	−1.59325	−0.0867897	−0.0433949	+	0.999058i	$0.513817\pi$
$338$	−8.02086	−0.436277
$339$	12.2610	0.665925
$340$	13.8162	0.749291
$341$	−6.09370	−0.329992
$342$	−4.55587	−0.246353
$343$	4.29393	0.231851
$344$	3.47554	0.187389
$345$	−5.74457	−0.309277
$346$	−23.1841	−1.24638
$347$	−29.3293	−1.57448	−0.787239	−	0.616647i	$-0.788490\pi$
$347$	−29.3293	−1.57448	−0.787239	+	0.616647i	$0.788490\pi$
$348$	4.92948	0.264248
$349$	9.08756	0.486446	0.243223	−	0.969970i	$-0.421795\pi$
$349$	9.08756	0.486446	0.243223	+	0.969970i	$0.421795\pi$
$350$	−2.04705	−0.109419
$351$	4.09348	0.218494
$352$	15.7759	0.840860
$353$	30.4569	1.62106	0.810529	−	0.585699i	$-0.199180\pi$
$353$	30.4569	1.62106	0.810529	+	0.585699i	$0.199180\pi$
$354$	−5.08377	−0.270199
$355$	21.0821	1.11892
$356$	−2.63831	−0.139830
$357$	1.21115	0.0641010
$358$	−41.5020	−2.19345
$359$	−10.2294	−0.539888	−0.269944	−	0.962876i	$-0.587005\pi$
$359$	−10.2294	−0.539888	−0.269944	+	0.962876i	$0.587005\pi$
$360$	−1.64262	−0.0865739
$361$	−14.4471	−0.760372
$362$	−9.37402	−0.492687
$363$	6.98561	0.366650
$364$	3.23464	0.169541
$365$	14.5092	0.759447
$366$	−0.604247	−0.0315845
$367$	17.1344	0.894407	0.447204	−	0.894432i	$-0.352420\pi$
$367$	17.1344	0.894407	0.447204	+	0.894432i	$0.352420\pi$
$368$	−10.7241	−0.559032
$369$	−5.96411	−0.310479
$370$	−18.4014	−0.956643
$371$	2.04153	0.105991
$372$	7.78232	0.403494
$373$	8.16083	0.422552	0.211276	−	0.977426i	$-0.432238\pi$
$373$	8.16083	0.422552	0.211276	+	0.977426i	$0.432238\pi$
$374$	−16.7779	−0.867566
$375$	11.1579	0.576190
$376$	−0.388165	−0.0200181
$377$	7.88599	0.406149
$378$	−0.659358	−0.0339137
$379$	−27.1337	−1.39377	−0.696883	−	0.717185i	$-0.745430\pi$
$379$	−27.1337	−1.39377	−0.696883	+	0.717185i	$0.745430\pi$
$380$	7.51680	0.385604
$381$	11.5365	0.591033
$382$	42.1311	2.15561
$383$	6.90402	0.352779	0.176390	−	0.984320i	$-0.443558\pi$
$383$	6.90402	0.352779	0.176390	+	0.984320i	$0.443558\pi$
$384$	−9.17248	−0.468081
$385$	−0.851834	−0.0434135
$386$	−28.4476	−1.44794
$387$	−2.91296	−0.148074
$388$	1.48786	0.0755347
$389$	−35.9779	−1.82415	−0.912077	−	0.410019i	$-0.865522\pi$
$389$	−35.9779	−1.82415	−0.912077	+	0.410019i	$0.865522\pi$
$390$	−12.0328	−0.609307
$391$	16.3648	0.827604
$392$	8.23814	0.416089
$393$	14.2224	0.717427
$394$	19.4854	0.981663
$395$	16.8646	0.848551
$396$	5.12681	0.257632
$397$	7.20228	0.361472	0.180736	−	0.983532i	$-0.442152\pi$
$397$	7.20228	0.361472	0.180736	+	0.983532i	$0.442152\pi$
$398$	7.71736	0.386836
$399$	0.658933	0.0329879
$400$	7.97920	0.398960
$401$	6.20135	0.309681	0.154840	−	0.987940i	$-0.450514\pi$
$401$	6.20135	0.309681	0.154840	+	0.987940i	$0.450514\pi$
$402$	−2.64629	−0.131985
$403$	12.4499	0.620171
$404$	−29.5132	−1.46834
$405$	1.37673	0.0684104
$406$	−1.27024	−0.0630408
$407$	12.5425	0.621710
$408$	4.67941	0.231665
$409$	−11.9641	−0.591589	−0.295794	−	0.955252i	$-0.595584\pi$
$409$	−11.9641	−0.591589	−0.295794	+	0.955252i	$0.595584\pi$
$410$	17.5316	0.865823
$411$	22.1929	1.09470
$412$	−12.0071	−0.591546
$413$	0.735285	0.0361810
$414$	−8.90909	−0.437858
$415$	−9.93904	−0.487888
$416$	−32.2313	−1.58027
$417$	12.8255	0.628065
$418$	−9.12811	−0.446470
$419$	−4.60936	−0.225182	−0.112591	−	0.993641i	$-0.535915\pi$
$419$	−4.60936	−0.225182	−0.112591	+	0.993641i	$0.535915\pi$
$420$	1.08789	0.0530834
$421$	12.8948	0.628452	0.314226	−	0.949348i	$-0.398255\pi$
$421$	12.8948	0.628452	0.314226	+	0.949348i	$0.398255\pi$
$422$	8.83780	0.430217
$423$	0.325333	0.0158182
$424$	7.88766	0.383058
$425$	−12.1761	−0.590629
$426$	32.6957	1.58411
$427$	0.0873945	0.00422932
$428$	−24.5478	−1.18656
$429$	8.20168	0.395981
$430$	8.56267	0.412929
$431$	−5.91975	−0.285144	−0.142572	−	0.989784i	$-0.545537\pi$
$431$	−5.91975	−0.285144	−0.142572	+	0.989784i	$0.545537\pi$
$432$	2.57012	0.123655
$433$	17.5619	0.843970	0.421985	−	0.906603i	$-0.361333\pi$
$433$	17.5619	0.843970	0.421985	+	0.906603i	$0.361333\pi$
$434$	−2.00536	−0.0962604
$435$	2.65224	0.127165
$436$	−0.376823	−0.0180466
$437$	8.90335	0.425905
$438$	22.5020	1.07518
$439$	13.3693	0.638081	0.319041	−	0.947741i	$-0.396639\pi$
$439$	13.3693	0.638081	0.319041	+	0.947741i	$0.396639\pi$
$440$	−3.29115	−0.156899
$441$	−6.90463	−0.328792
$442$	34.2785	1.63046
$443$	21.3114	1.01253	0.506267	−	0.862377i	$-0.331025\pi$
$443$	21.3114	1.01253	0.506267	+	0.862377i	$0.331025\pi$
$444$	−16.0182	−0.760189
$445$	−1.41951	−0.0672912
$446$	20.0403	0.948938
$447$	−10.4309	−0.493365
$448$	3.60429	0.170287
$449$	−41.3482	−1.95134	−0.975672	−	0.219235i	$-0.929644\pi$
$449$	−41.3482	−1.95134	−0.975672	+	0.219235i	$0.929644\pi$
$450$	6.62876	0.312483
$451$	−11.9497	−0.562687
$452$	−31.3735	−1.47569
$453$	−5.65576	−0.265731
$454$	−54.0715	−2.53770
$455$	1.74036	0.0815892
$456$	2.54586	0.119221
$457$	37.0896	1.73498	0.867490	−	0.497455i	$-0.165732\pi$
$457$	37.0896	1.73498	0.867490	+	0.497455i	$0.165732\pi$
$458$	−58.0306	−2.71159
$459$	−3.92196	−0.183061
$460$	14.6993	0.685356
$461$	8.89356	0.414214	0.207107	−	0.978318i	$-0.433595\pi$
$461$	8.89356	0.414214	0.207107	+	0.978318i	$0.433595\pi$
$462$	−1.32109	−0.0614625
$463$	18.9213	0.879346	0.439673	−	0.898158i	$-0.355094\pi$
$463$	18.9213	0.879346	0.439673	+	0.898158i	$0.355094\pi$
$464$	4.95126	0.229857
$465$	4.18717	0.194175
$466$	−51.8642	−2.40256
$467$	31.4887	1.45712	0.728561	−	0.684981i	$-0.240189\pi$
$467$	31.4887	1.45712	0.728561	+	0.684981i	$0.240189\pi$
$468$	−10.4744	−0.484181
$469$	0.382743	0.0176734
$470$	−0.956320	−0.0441118
$471$	2.78274	0.128222
$472$	2.84085	0.130761
$473$	−5.83638	−0.268357
$474$	26.1549	1.20133
$475$	−6.62449	−0.303952
$476$	−3.09911	−0.142047
$477$	−6.61089	−0.302692
$478$	3.01349	0.137834
$479$	−12.6046	−0.575918	−0.287959	−	0.957643i	$-0.592977\pi$
$479$	−12.6046	−0.575918	−0.287959	+	0.957643i	$0.592977\pi$
$480$	−10.8401	−0.494782
$481$	−25.6253	−1.16841
$482$	19.7935	0.901569
$483$	1.28856	0.0586314
$484$	−17.8748	−0.812493
$485$	0.800523	0.0363499
$486$	2.13514	0.0968518
$487$	17.5394	0.794788	0.397394	−	0.917648i	$-0.369915\pi$
$487$	17.5394	0.794788	0.397394	+	0.917648i	$0.369915\pi$
$488$	0.337658	0.0152851
$489$	−14.4402	−0.653008
$490$	20.2963	0.916891
$491$	−34.8401	−1.57231	−0.786156	−	0.618028i	$-0.787932\pi$
$491$	−34.8401	−1.57231	−0.786156	+	0.618028i	$0.787932\pi$
$492$	15.2610	0.688020
$493$	−7.55555	−0.340285
$494$	18.6494	0.839075
$495$	2.75841	0.123981
$496$	7.81671	0.350981
$497$	−4.72891	−0.212120
$498$	−15.4142	−0.690726
$499$	−19.8113	−0.886875	−0.443437	−	0.896305i	$-0.646241\pi$
$499$	−19.8113	−0.886875	−0.443437	+	0.896305i	$0.646241\pi$
$500$	−28.5509	−1.27683
$501$	−0.406222	−0.0181487
$502$	20.3008	0.906071
$503$	−5.48597	−0.244607	−0.122304	−	0.992493i	$-0.539028\pi$
$503$	−5.48597	−0.244607	−0.122304	+	0.992493i	$0.539028\pi$
$504$	0.368455	0.0164123
$505$	−15.8792	−0.706615
$506$	−17.8502	−0.793538
$507$	−3.75660	−0.166837
$508$	−29.5197	−1.30973
$509$	−8.02698	−0.355790	−0.177895	−	0.984050i	$-0.556929\pi$
$509$	−8.02698	−0.355790	−0.177895	+	0.984050i	$0.556929\pi$
$510$	11.5286	0.510497
$511$	−3.25454	−0.143973
$512$	−26.3696	−1.16538
$513$	−2.13376	−0.0942078
$514$	65.6736	2.89674
$515$	−6.46025	−0.284672
$516$	7.45370	0.328131
$517$	0.651835	0.0286677
$518$	4.12759	0.181356
$519$	−10.8584	−0.476629
$520$	6.72405	0.294869
$521$	−34.8039	−1.52479	−0.762394	−	0.647113i	$-0.775976\pi$
$521$	−34.8039	−1.52479	−0.762394	+	0.647113i	$0.775976\pi$
$522$	4.11328	0.180034
$523$	−15.6521	−0.684420	−0.342210	−	0.939623i	$-0.611175\pi$
$523$	−15.6521	−0.684420	−0.342210	+	0.939623i	$0.611175\pi$
$524$	−36.3925	−1.58981
$525$	−0.958743	−0.0418430
$526$	49.9005	2.17577
$527$	−11.9282	−0.519600
$528$	5.14947	0.224102
$529$	−5.58932	−0.243014
$530$	19.4328	0.844106
$531$	−2.38100	−0.103327
$532$	−1.68608	−0.0731010
$533$	24.4140	1.05749
$534$	−2.20148	−0.0952673
$535$	−13.2076	−0.571015
$536$	1.47877	0.0638730
$537$	−19.4376	−0.838795
$538$	−41.5284	−1.79042
$539$	−13.8341	−0.595876
$540$	−3.52279	−0.151597
$541$	−3.21337	−0.138153	−0.0690767	−	0.997611i	$-0.522005\pi$
$541$	−3.21337	−0.138153	−0.0690767	+	0.997611i	$0.522005\pi$
$542$	21.7108	0.932560
$543$	−4.39036	−0.188408
$544$	30.8808	1.32400
$545$	−0.202745	−0.00868463
$546$	2.69907	0.115510
$547$	−35.3064	−1.50959	−0.754796	−	0.655959i	$-0.772264\pi$
$547$	−35.3064	−1.50959	−0.754796	+	0.655959i	$0.772264\pi$
$548$	−56.7875	−2.42584
$549$	−0.283001	−0.0120782
$550$	13.2813	0.566318
$551$	−4.11063	−0.175119
$552$	4.97847	0.211898
$553$	−3.78288	−0.160864
$554$	−16.7529	−0.711762
$555$	−8.61837	−0.365829
$556$	−32.8179	−1.39179
$557$	36.2107	1.53430	0.767148	−	0.641470i	$-0.221675\pi$
$557$	36.2107	1.53430	0.767148	+	0.641470i	$0.221675\pi$
$558$	6.49377	0.274903
$559$	11.9241	0.504337
$560$	1.09269	0.0461747
$561$	−7.85801	−0.331765
$562$	36.8089	1.55269
$563$	37.9504	1.59942	0.799709	−	0.600388i	$-0.204987\pi$
$563$	37.9504	1.59942	0.799709	+	0.600388i	$0.204987\pi$
$564$	−0.832465	−0.0350531
$565$	−16.8801	−0.710151
$566$	43.8685	1.84393
$567$	−0.308813	−0.0129689
$568$	−18.2706	−0.766618
$569$	−2.52775	−0.105969	−0.0529845	−	0.998595i	$-0.516873\pi$
$569$	−2.52775	−0.105969	−0.0529845	+	0.998595i	$0.516873\pi$
$570$	6.27221	0.262714
$571$	−24.0482	−1.00638	−0.503192	−	0.864175i	$-0.667841\pi$
$571$	−24.0482	−1.00638	−0.503192	+	0.864175i	$0.667841\pi$
$572$	−20.9865	−0.877490
$573$	19.7323	0.824327
$574$	−3.93248	−0.164139
$575$	−12.9543	−0.540232
$576$	−11.6714	−0.486310
$577$	7.28980	0.303478	0.151739	−	0.988421i	$-0.451513\pi$
$577$	7.28980	0.303478	0.151739	+	0.988421i	$0.451513\pi$
$578$	3.45519	0.143717
$579$	−13.3235	−0.553707
$580$	−6.78657	−0.281797
$581$	2.22941	0.0924916
$582$	1.24151	0.0514622
$583$	−13.2455	−0.548574
$584$	−12.5743	−0.520327
$585$	−5.63563	−0.233005
$586$	−36.4931	−1.50751
$587$	−12.6617	−0.522604	−0.261302	−	0.965257i	$-0.584152\pi$
$587$	−12.6617	−0.522604	−0.261302	+	0.965257i	$0.584152\pi$
$588$	17.6676	0.728601
$589$	−6.48958	−0.267399
$590$	6.99899	0.288144
$591$	9.12609	0.375397
$592$	−16.0890	−0.661253
$593$	3.50739	0.144031	0.0720156	−	0.997404i	$-0.477057\pi$
$593$	3.50739	0.144031	0.0720156	+	0.997404i	$0.477057\pi$
$594$	4.27795	0.175526
$595$	−1.66743	−0.0683581
$596$	26.6907	1.09329
$597$	3.61446	0.147930
$598$	36.4692	1.49134
$599$	−13.5055	−0.551819	−0.275910	−	0.961184i	$-0.588979\pi$
$599$	−13.5055	−0.551819	−0.275910	+	0.961184i	$0.588979\pi$
$600$	−3.70421	−0.151224
$601$	14.3314	0.584592	0.292296	−	0.956328i	$-0.405581\pi$
$601$	14.3314	0.584592	0.292296	+	0.956328i	$0.405581\pi$
$602$	−1.92068	−0.0782812
$603$	−1.23940	−0.0504723
$604$	14.4720	0.588857
$605$	−9.61732	−0.391000
$606$	−24.6266	−1.00039
$607$	−6.46650	−0.262467	−0.131234	−	0.991351i	$-0.541894\pi$
$607$	−6.46650	−0.262467	−0.131234	+	0.991351i	$0.541894\pi$
$608$	16.8008	0.681363
$609$	−0.594920	−0.0241074
$610$	0.831886	0.0336821
$611$	−1.33175	−0.0538766
$612$	10.0355	0.405663
$613$	−9.53844	−0.385254	−0.192627	−	0.981272i	$-0.561701\pi$
$613$	−9.53844	−0.385254	−0.192627	+	0.981272i	$0.561701\pi$
$614$	−14.1965	−0.572926
$615$	8.21098	0.331099
$616$	0.738234	0.0297443
$617$	−24.1933	−0.973986	−0.486993	−	0.873406i	$-0.661906\pi$
$617$	−24.1933	−0.973986	−0.486993	+	0.873406i	$0.661906\pi$
$618$	−10.0190	−0.403024
$619$	−25.5704	−1.02776	−0.513880	−	0.857862i	$-0.671792\pi$
$619$	−25.5704	−1.02776	−0.513880	+	0.857862i	$0.671792\pi$
$620$	−10.7142	−0.430292
$621$	−4.17261	−0.167441
$622$	−42.8882	−1.71966
$623$	0.318408	0.0127568
$624$	−10.5207	−0.421166
$625$	0.161624	0.00646496
$626$	−30.6010	−1.22306
$627$	−4.27519	−0.170735
$628$	−7.12049	−0.284139
$629$	24.5515	0.978933
$630$	0.907760	0.0361660
$631$	−13.1488	−0.523447	−0.261723	−	0.965143i	$-0.584291\pi$
$631$	−13.1488	−0.523447	−0.261723	+	0.965143i	$0.584291\pi$
$632$	−14.6156	−0.581376
$633$	4.13922	0.164519
$634$	−52.5727	−2.08793
$635$	−15.8827	−0.630285
$636$	16.9160	0.670763
$637$	28.2640	1.11986
$638$	8.24135	0.326278
$639$	15.3132	0.605779
$640$	12.6281	0.499168
$641$	1.91627	0.0756880	0.0378440	−	0.999284i	$-0.487951\pi$
$641$	1.91627	0.0756880	0.0378440	+	0.999284i	$0.487951\pi$
$642$	−20.4833	−0.808412
$643$	11.5310	0.454740	0.227370	−	0.973808i	$-0.426987\pi$
$643$	11.5310	0.454740	0.227370	+	0.973808i	$0.426987\pi$
$644$	−3.29717	−0.129927
$645$	4.01036	0.157908
$646$	−17.8679	−0.703004
$647$	−40.0954	−1.57631	−0.788157	−	0.615474i	$-0.788965\pi$
$647$	−40.0954	−1.57631	−0.788157	+	0.615474i	$0.788965\pi$
$648$	−1.19313	−0.0468706
$649$	−4.77056	−0.187261
$650$	−27.1347	−1.06431
$651$	−0.939219	−0.0368109
$652$	36.9497	1.44706
$653$	5.34692	0.209241	0.104620	−	0.994512i	$-0.466637\pi$
$653$	5.34692	0.209241	0.104620	+	0.994512i	$0.466637\pi$
$654$	−0.314431	−0.0122952
$655$	−19.5805	−0.765073
$656$	15.3285	0.598476
$657$	10.5389	0.411161
$658$	0.214511	0.00836251
$659$	−42.0226	−1.63697	−0.818484	−	0.574529i	$-0.805185\pi$
$659$	−42.0226	−1.63697	−0.818484	+	0.574529i	$0.805185\pi$
$660$	−7.05825	−0.274742
$661$	−9.80468	−0.381358	−0.190679	−	0.981652i	$-0.561069\pi$
$661$	−9.80468	−0.381358	−0.190679	+	0.981652i	$0.561069\pi$
$662$	1.49136	0.0579634
$663$	16.0545	0.623504
$664$	8.61357	0.334271
$665$	−0.907174	−0.0351787
$666$	−13.3660	−0.517922
$667$	−8.03843	−0.311249
$668$	1.03945	0.0402173
$669$	9.38598	0.362883
$670$	3.64323	0.140750
$671$	−0.567020	−0.0218896
$672$	2.43154	0.0937986
$673$	−17.3979	−0.670640	−0.335320	−	0.942104i	$-0.608844\pi$
$673$	−17.3979	−0.670640	−0.335320	+	0.942104i	$0.608844\pi$
$674$	3.40180	0.131033
$675$	3.10461	0.119496
$676$	9.61242	0.369709
$677$	19.2485	0.739781	0.369890	−	0.929075i	$-0.379395\pi$
$677$	19.2485	0.739781	0.369890	+	0.929075i	$0.379395\pi$
$678$	−26.1789	−1.00539
$679$	−0.179564	−0.00689105
$680$	−6.44230	−0.247051
$681$	−25.3246	−0.970441
$682$	13.0109	0.498212
$683$	11.6111	0.444285	0.222143	−	0.975014i	$-0.428695\pi$
$683$	11.6111	0.444285	0.222143	+	0.975014i	$0.428695\pi$
$684$	5.45988	0.208764
$685$	−30.5537	−1.16740
$686$	−9.16813	−0.350041
$687$	−27.1789	−1.03694
$688$	7.48664	0.285426
$689$	27.0615	1.03096
$690$	12.2654	0.466937
$691$	−26.8732	−1.02231	−0.511153	−	0.859490i	$-0.670781\pi$
$691$	−26.8732	−1.02231	−0.511153	+	0.859490i	$0.670781\pi$
$692$	27.7845	1.05621
$693$	−0.618736	−0.0235038
$694$	62.6220	2.37710
$695$	−17.6572	−0.669777
$696$	−2.29854	−0.0871258
$697$	−23.3910	−0.885997
$698$	−19.4032	−0.734421
$699$	−24.2908	−0.918763
$700$	2.45324	0.0927238
$701$	0.507118	0.0191536	0.00957679	−	0.999954i	$-0.496952\pi$
$701$	0.507118	0.0191536	0.00957679	+	0.999954i	$0.496952\pi$
$702$	−8.74014	−0.329876
$703$	13.3574	0.503783
$704$	−23.3848	−0.881348
$705$	−0.447897	−0.0168688
$706$	−65.0297	−2.44742
$707$	3.56184	0.133957
$708$	6.09253	0.228971
$709$	16.8612	0.633236	0.316618	−	0.948553i	$-0.397453\pi$
$709$	16.8612	0.633236	0.316618	+	0.948553i	$0.397453\pi$
$710$	−45.0132	−1.68932
$711$	12.2497	0.459401
$712$	1.23020	0.0461038
$713$	−12.6905	−0.475263
$714$	−2.58597	−0.0967777
$715$	−11.2915	−0.422279
$716$	49.7371	1.85876
$717$	1.41138	0.0527090
$718$	21.8412	0.815107
$719$	−7.20366	−0.268651	−0.134326	−	0.990937i	$-0.542887\pi$
$719$	−7.20366	−0.268651	−0.134326	+	0.990937i	$0.542887\pi$
$720$	−3.53836	−0.131867
$721$	1.44909	0.0539669
$722$	30.8465	1.14799
$723$	9.27036	0.344769
$724$	11.2341	0.417512
$725$	5.98094	0.222127
$726$	−14.9152	−0.553556
$727$	−2.01194	−0.0746188	−0.0373094	−	0.999304i	$-0.511879\pi$
$727$	−2.01194	−0.0746188	−0.0373094	+	0.999304i	$0.511879\pi$
$728$	−1.50826	−0.0558999
$729$	1.00000	0.0370370
$730$	−30.9792	−1.14659
$731$	−11.4245	−0.422550
$732$	0.724146	0.0267652
$733$	−24.1778	−0.893029	−0.446515	−	0.894776i	$-0.647335\pi$
$733$	−24.1778	−0.893029	−0.446515	+	0.894776i	$0.647335\pi$
$734$	−36.5842	−1.35035
$735$	9.50584	0.350628
$736$	32.8544	1.21103
$737$	−2.48325	−0.0914718
$738$	12.7342	0.468752
$739$	−34.0903	−1.25403	−0.627015	−	0.779007i	$-0.715724\pi$
$739$	−34.0903	−1.25403	−0.627015	+	0.779007i	$0.715724\pi$
$740$	22.0528	0.810675
$741$	8.73451	0.320870
$742$	−4.35894	−0.160022
$743$	−29.9403	−1.09840	−0.549201	−	0.835690i	$-0.685068\pi$
$743$	−29.9403	−1.09840	−0.549201	+	0.835690i	$0.685068\pi$
$744$	−3.62877	−0.133037
$745$	14.3606	0.526131
$746$	−17.4245	−0.637956
$747$	−7.21929	−0.264140
$748$	20.1071	0.735190
$749$	2.96258	0.108250
$750$	−23.8236	−0.869915
$751$	12.9498	0.472546	0.236273	−	0.971687i	$-0.424074\pi$
$751$	12.9498	0.472546	0.236273	+	0.971687i	$0.424074\pi$
$752$	−0.836144	−0.0304910
$753$	9.50798	0.346490
$754$	−16.8377	−0.613191
$755$	7.78647	0.283379
$756$	0.790194	0.0287391
$757$	−17.3956	−0.632255	−0.316128	−	0.948717i	$-0.602383\pi$
$757$	−17.3956	−0.632255	−0.316128	+	0.948717i	$0.602383\pi$
$758$	57.9342	2.10427
$759$	−8.36022	−0.303457
$760$	−3.50496	−0.127138
$761$	4.87864	0.176851	0.0884253	−	0.996083i	$-0.471817\pi$
$761$	4.87864	0.176851	0.0884253	+	0.996083i	$0.471817\pi$
$762$	−24.6320	−0.892324
$763$	0.0454774	0.00164639
$764$	−50.4911	−1.82670
$765$	5.39949	0.195219
$766$	−14.7410	−0.532615
$767$	9.74660	0.351929
$768$	−3.75838	−0.135619
$769$	−23.2371	−0.837953	−0.418977	−	0.907997i	$-0.637611\pi$
$769$	−23.2371	−0.837953	−0.418977	+	0.907997i	$0.637611\pi$
$770$	1.81878	0.0655443
$771$	30.7585	1.10774
$772$	34.0924	1.22701
$773$	−24.5397	−0.882633	−0.441316	−	0.897352i	$-0.645488\pi$
$773$	−24.5397	−0.882633	−0.441316	+	0.897352i	$0.645488\pi$
$774$	6.21956	0.223558
$775$	9.44230	0.339178
$776$	−0.693766	−0.0249047
$777$	1.93318	0.0693523
$778$	76.8178	2.75405
$779$	−12.7260	−0.455955
$780$	14.4205	0.516337
$781$	30.6814	1.09787
$782$	−34.9411	−1.24949
$783$	1.92647	0.0688466
$784$	17.7457	0.633776
$785$	−3.83109	−0.136737
$786$	−30.3668	−1.08315
$787$	−17.7915	−0.634198	−0.317099	−	0.948392i	$-0.602709\pi$
$787$	−17.7915	−0.634198	−0.317099	+	0.948392i	$0.602709\pi$
$788$	−23.3519	−0.831877
$789$	23.3711	0.832034
$790$	−36.0083	−1.28112
$791$	3.78635	0.134627
$792$	−2.39055	−0.0849445
$793$	1.15846	0.0411382
$794$	−15.3779	−0.545739
$795$	9.10142	0.322794
$796$	−9.24870	−0.327812
$797$	−48.2504	−1.70912	−0.854559	−	0.519354i	$-0.826172\pi$
$797$	−48.2504	−1.70912	−0.854559	+	0.519354i	$0.826172\pi$
$798$	−1.40691	−0.0498041
$799$	1.27594	0.0451396
$800$	−24.4451	−0.864265
$801$	−1.03107	−0.0364311
$802$	−13.2407	−0.467546
$803$	21.1156	0.745155
$804$	3.17139	0.111846
$805$	−1.77400	−0.0625252
$806$	−26.5821	−0.936316
$807$	−19.4500	−0.684672
$808$	13.7615	0.484129
$809$	−25.5660	−0.898851	−0.449426	−	0.893318i	$-0.648371\pi$
$809$	−25.5660	−0.898851	−0.449426	+	0.893318i	$0.648371\pi$
$810$	−2.93951	−0.103284
$811$	53.9381	1.89402	0.947012	−	0.321198i	$-0.104085\pi$
$811$	53.9381	1.89402	0.947012	+	0.321198i	$0.104085\pi$
$812$	1.52229	0.0534218
$813$	10.1684	0.356620
$814$	−26.7800	−0.938639
$815$	19.8803	0.696376
$816$	10.0799	0.352867
$817$	−6.21555	−0.217455
$818$	25.5451	0.893163
$819$	1.26412	0.0441720
$820$	−21.0103	−0.733713
$821$	1.19394	0.0416687	0.0208344	−	0.999783i	$-0.493368\pi$
$821$	1.19394	0.0416687	0.0208344	+	0.999783i	$0.493368\pi$
$822$	−47.3849	−1.65274
$823$	−50.8764	−1.77344	−0.886721	−	0.462306i	$-0.847022\pi$
$823$	−50.8764	−1.77344	−0.886721	+	0.462306i	$0.847022\pi$
$824$	5.59871	0.195040
$825$	6.22037	0.216566
$826$	−1.56993	−0.0546250
$827$	42.0396	1.46186	0.730931	−	0.682452i	$-0.239086\pi$
$827$	42.0396	1.46186	0.730931	+	0.682452i	$0.239086\pi$
$828$	10.6769	0.371048
$829$	−30.1170	−1.04601	−0.523004	−	0.852330i	$-0.675189\pi$
$829$	−30.1170	−1.04601	−0.523004	+	0.852330i	$0.675189\pi$
$830$	21.2212	0.736599
$831$	−7.84628	−0.272185
$832$	47.7768	1.65636
$833$	−27.0797	−0.938255
$834$	−27.3841	−0.948234
$835$	0.559260	0.0193540
$836$	10.9394	0.378346
$837$	3.04138	0.105126
$838$	9.84161	0.339973
$839$	−3.00936	−0.103895	−0.0519474	−	0.998650i	$-0.516543\pi$
$839$	−3.00936	−0.103895	−0.0519474	+	0.998650i	$0.516543\pi$
$840$	−0.507264	−0.0175023
$841$	−25.2887	−0.872024
$842$	−27.5321	−0.948817
$843$	17.2396	0.593763
$844$	−10.5915	−0.364573
$845$	5.17184	0.177917
$846$	−0.694630	−0.0238819
$847$	2.15725	0.0741239
$848$	16.9907	0.583465
$849$	20.5460	0.705137
$850$	25.9977	0.891714
$851$	26.1206	0.895403
$852$	−39.1834	−1.34240
$853$	−7.69253	−0.263387	−0.131694	−	0.991290i	$-0.542041\pi$
$853$	−7.69253	−0.263387	−0.131694	+	0.991290i	$0.542041\pi$
$854$	−0.186599	−0.00638530
$855$	2.93762	0.100464
$856$	11.4462	0.391224
$857$	13.8482	0.473047	0.236524	−	0.971626i	$-0.423992\pi$
$857$	13.8482	0.473047	0.236524	+	0.971626i	$0.423992\pi$
$858$	−17.5117	−0.597840
$859$	48.9201	1.66913	0.834565	−	0.550909i	$-0.185719\pi$
$859$	48.9201	1.66913	0.834565	+	0.550909i	$0.185719\pi$
$860$	−10.2617	−0.349923
$861$	−1.84180	−0.0627682
$862$	12.6395	0.430502
$863$	−27.0243	−0.919916	−0.459958	−	0.887941i	$-0.652136\pi$
$863$	−27.0243	−0.919916	−0.459958	+	0.887941i	$0.652136\pi$
$864$	−7.87381	−0.267873
$865$	14.9491	0.508284
$866$	−37.4970	−1.27420
$867$	1.61825	0.0549587
$868$	2.40328	0.0815727
$869$	24.5435	0.832581
$870$	−5.66289	−0.191990
$871$	5.07346	0.171908
$872$	0.175707	0.00595018
$873$	0.581466	0.0196796
$874$	−19.0099	−0.643018
$875$	3.44570	0.116486
$876$	−26.9670	−0.911130
$877$	−7.53690	−0.254503	−0.127252	−	0.991870i	$-0.540616\pi$
$877$	−7.53690	−0.254503	−0.127252	+	0.991870i	$0.540616\pi$
$878$	−28.5452	−0.963355
$879$	−17.0917	−0.576488
$880$	−7.08944	−0.238985
$881$	0.419302	0.0141266	0.00706332	−	0.999975i	$-0.497752\pi$
$881$	0.419302	0.0141266	0.00706332	+	0.999975i	$0.497752\pi$
$882$	14.7423	0.496400
$883$	−12.4730	−0.419750	−0.209875	−	0.977728i	$-0.567306\pi$
$883$	−12.4730	−0.419750	−0.209875	+	0.977728i	$0.567306\pi$
$884$	−41.0803	−1.38168
$885$	3.27801	0.110189
$886$	−45.5027	−1.52869
$887$	−47.9947	−1.61150	−0.805752	−	0.592254i	$-0.798238\pi$
$887$	−47.9947	−1.61150	−0.805752	+	0.592254i	$0.798238\pi$
$888$	7.46902	0.250644
$889$	3.56263	0.119487
$890$	3.03085	0.101594
$891$	2.00359	0.0671229
$892$	−24.0169	−0.804146
$893$	0.694182	0.0232299
$894$	22.2714	0.744868
$895$	26.7604	0.894501
$896$	−2.83258	−0.0946299
$897$	17.0805	0.570302
$898$	88.2841	2.94608
$899$	5.85915	0.195414
$900$	−7.94409	−0.264803
$901$	−25.9276	−0.863774
$902$	25.5141	0.849528
$903$	−0.899559	−0.0299355
$904$	14.6290	0.486552
$905$	6.04435	0.200921
$906$	12.0758	0.401192
$907$	9.93047	0.329736	0.164868	−	0.986316i	$-0.447280\pi$
$907$	9.93047	0.329736	0.164868	+	0.986316i	$0.447280\pi$
$908$	64.8008	2.15049
$909$	−11.5340	−0.382558
$910$	−3.71590	−0.123181
$911$	29.6088	0.980984	0.490492	−	0.871446i	$-0.336817\pi$
$911$	29.6088	0.980984	0.490492	+	0.871446i	$0.336817\pi$
$912$	5.48401	0.181594
$913$	−14.4645	−0.478706
$914$	−79.1914	−2.61942
$915$	0.389617	0.0128803
$916$	69.5456	2.29785
$917$	4.39207	0.145039
$918$	8.37391	0.276380
$919$	−12.1648	−0.401279	−0.200639	−	0.979665i	$-0.564302\pi$
$919$	−12.1648	−0.401279	−0.200639	+	0.979665i	$0.564302\pi$
$920$	−6.85403	−0.225971
$921$	−6.64901	−0.219092
$922$	−18.9890	−0.625368
$923$	−62.6842	−2.06327
$924$	1.58323	0.0520843
$925$	−19.4349	−0.639015
$926$	−40.3995	−1.32761
$927$	−4.69245	−0.154120
$928$	−15.1687	−0.497937
$929$	−32.1068	−1.05339	−0.526695	−	0.850054i	$-0.676569\pi$
$929$	−32.1068	−1.05339	−0.526695	+	0.850054i	$0.676569\pi$
$930$	−8.94019	−0.293160
$931$	−14.7328	−0.482849
$932$	62.1556	2.03597
$933$	−20.0869	−0.657615
$934$	−67.2326	−2.19992
$935$	10.8184	0.353799
$936$	4.88406	0.159641
$937$	35.0612	1.14540	0.572699	−	0.819766i	$-0.305896\pi$
$937$	35.0612	1.14540	0.572699	+	0.819766i	$0.305896\pi$
$938$	−0.817209	−0.0266828
$939$	−14.3321	−0.467710
$940$	1.14608	0.0373811
$941$	−49.2106	−1.60422	−0.802109	−	0.597177i	$-0.796289\pi$
$941$	−49.2106	−1.60422	−0.802109	+	0.597177i	$0.796289\pi$
$942$	−5.94153	−0.193585
$943$	−24.8859	−0.810397
$944$	6.11946	0.199171
$945$	0.425153	0.0138302
$946$	12.4615	0.405157
$947$	−10.2736	−0.333847	−0.166923	−	0.985970i	$-0.553383\pi$
$947$	−10.2736	−0.333847	−0.166923	+	0.985970i	$0.553383\pi$
$948$	−31.3447	−1.01803
$949$	−43.1407	−1.40041
$950$	14.1442	0.458898
$951$	−24.6226	−0.798444
$952$	1.44506	0.0468348
$953$	42.2179	1.36757	0.683786	−	0.729682i	$-0.260332\pi$
$953$	42.2179	1.36757	0.683786	+	0.729682i	$0.260332\pi$
$954$	14.1151	0.456995
$955$	−27.1660	−0.879073
$956$	−3.61145	−0.116803
$957$	3.85987	0.124772
$958$	26.9125	0.869504
$959$	6.85347	0.221310
$960$	16.0684	0.518607
$961$	−21.7500	−0.701612
$962$	54.7135	1.76403
$963$	−9.59344	−0.309144
$964$	−23.7211	−0.764005
$965$	18.3429	0.590480
$966$	−2.75125	−0.0885199
$967$	29.7677	0.957264	0.478632	−	0.878015i	$-0.341133\pi$
$967$	29.7677	0.957264	0.478632	+	0.878015i	$0.341133\pi$
$968$	8.33476	0.267889
$969$	−8.36851	−0.268835
$970$	−1.70923	−0.0548800
$971$	−23.7623	−0.762568	−0.381284	−	0.924458i	$-0.624518\pi$
$971$	−23.7623	−0.762568	−0.381284	+	0.924458i	$0.624518\pi$
$972$	−2.55881	−0.0820738
$973$	3.96067	0.126973
$974$	−37.4491	−1.19995
$975$	−12.7087	−0.407003
$976$	0.727347	0.0232818
$977$	41.6793	1.33344	0.666719	−	0.745309i	$-0.267698\pi$
$977$	41.6793	1.33344	0.666719	+	0.745309i	$0.267698\pi$
$978$	30.8318	0.985892
$979$	−2.06585	−0.0660248
$980$	−24.3236	−0.776989
$981$	−0.147265	−0.00470181
$982$	74.3884	2.37383
$983$	−2.14191	−0.0683162	−0.0341581	−	0.999416i	$-0.510875\pi$
$983$	−2.14191	−0.0683162	−0.0341581	+	0.999416i	$0.510875\pi$
$984$	−7.11597	−0.226849
$985$	−12.5642	−0.400328
$986$	16.1321	0.513752
$987$	0.100467	0.00319790
$988$	−22.3499	−0.711046
$989$	−12.1546	−0.386495
$990$	−5.88959	−0.187183
$991$	−56.4156	−1.79210	−0.896051	−	0.443952i	$-0.853576\pi$
$991$	−56.4156	−1.79210	−0.896051	+	0.443952i	$0.853576\pi$
$992$	−23.9473	−0.760327
$993$	0.698485	0.0221657
$994$	10.0969	0.320253
$995$	−4.97614	−0.157754
$996$	18.4728	0.585333
$997$	−3.32423	−0.105279	−0.0526397	−	0.998614i	$-0.516763\pi$
$997$	−3.32423	−0.105279	−0.0526397	+	0.998614i	$0.516763\pi$
$998$	42.2998	1.33898
$999$	−6.26002	−0.198058

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8049.2.a.b.1.15	✓	104

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8049.2.a.b.1.15	✓	104	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:	\( N \)	\(=\)	\( 8049 = 3 \cdot 2683 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8049.a (trivial)

\(f(q)\)	\(=\)	\(q-2.13514 q^{2} -1.00000 q^{3} +2.55881 q^{4} +1.37673 q^{5} +2.13514 q^{6} -0.308813 q^{7} -1.19313 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.13514 q^{2} -1.00000 q^{3} +2.55881 q^{4} +1.37673 q^{5} +2.13514 q^{6} -0.308813 q^{7} -1.19313 q^{8} +1.00000 q^{9} -2.93951 q^{10} +2.00359 q^{11} -2.55881 q^{12} -4.09348 q^{13} +0.659358 q^{14} -1.37673 q^{15} -2.57012 q^{16} +3.92196 q^{17} -2.13514 q^{18} +2.13376 q^{19} +3.52279 q^{20} +0.308813 q^{21} -4.27795 q^{22} +4.17261 q^{23} +1.19313 q^{24} -3.10461 q^{25} +8.74014 q^{26} -1.00000 q^{27} -0.790194 q^{28} -1.92647 q^{29} +2.93951 q^{30} -3.04138 q^{31} +7.87381 q^{32} -2.00359 q^{33} -8.37391 q^{34} -0.425153 q^{35} +2.55881 q^{36} +6.26002 q^{37} -4.55587 q^{38} +4.09348 q^{39} -1.64262 q^{40} -5.96411 q^{41} -0.659358 q^{42} -2.91296 q^{43} +5.12681 q^{44} +1.37673 q^{45} -8.90909 q^{46} +0.325333 q^{47} +2.57012 q^{48} -6.90463 q^{49} +6.62876 q^{50} -3.92196 q^{51} -10.4744 q^{52} -6.61089 q^{53} +2.13514 q^{54} +2.75841 q^{55} +0.368455 q^{56} -2.13376 q^{57} +4.11328 q^{58} -2.38100 q^{59} -3.52279 q^{60} -0.283001 q^{61} +6.49377 q^{62} -0.308813 q^{63} -11.6714 q^{64} -5.63563 q^{65} +4.27795 q^{66} -1.23940 q^{67} +10.0355 q^{68} -4.17261 q^{69} +0.907760 q^{70} +15.3132 q^{71} -1.19313 q^{72} +10.5389 q^{73} -13.3660 q^{74} +3.10461 q^{75} +5.45988 q^{76} -0.618736 q^{77} -8.74014 q^{78} +12.2497 q^{79} -3.53836 q^{80} +1.00000 q^{81} +12.7342 q^{82} -7.21929 q^{83} +0.790194 q^{84} +5.39949 q^{85} +6.21956 q^{86} +1.92647 q^{87} -2.39055 q^{88} -1.03107 q^{89} -2.93951 q^{90} +1.26412 q^{91} +10.6769 q^{92} +3.04138 q^{93} -0.694630 q^{94} +2.93762 q^{95} -7.87381 q^{96} +0.581466 q^{97} +14.7423 q^{98} +2.00359 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 104 q - 9 q^{2} - 104 q^{3} + 87 q^{4} - 15 q^{5} + 9 q^{6} - 10 q^{7} - 27 q^{8} + 104 q^{9}+O(q^{10}) \) 104 * q - 9 * q^2 - 104 * q^3 + 87 * q^4 - 15 * q^5 + 9 * q^6 - 10 * q^7 - 27 * q^8 + 104 * q^9	\( 104 q - 9 q^{2} - 104 q^{3} + 87 q^{4} - 15 q^{5} + 9 q^{6} - 10 q^{7} - 27 q^{8} + 104 q^{9} + 8 q^{10} - 52 q^{11} - 87 q^{12} + 35 q^{13} - 23 q^{14} + 15 q^{15} + 53 q^{16} - 19 q^{17} - 9 q^{18} - 22 q^{19} - 35 q^{20} + 10 q^{21} - q^{22} - 70 q^{23} + 27 q^{24} + 79 q^{25} - 39 q^{26} - 104 q^{27} - 9 q^{28} - 37 q^{29} - 8 q^{30} - 47 q^{31} - 53 q^{32} + 52 q^{33} - 17 q^{34} - 54 q^{35} + 87 q^{36} + 65 q^{37} - 33 q^{38} - 35 q^{39} + 14 q^{40} - 47 q^{41} + 23 q^{42} - 30 q^{43} - 122 q^{44} - 15 q^{45} - 6 q^{46} - 101 q^{47} - 53 q^{48} + 78 q^{49} - 64 q^{50} + 19 q^{51} + 41 q^{52} - 48 q^{53} + 9 q^{54} - 29 q^{55} - 71 q^{56} + 22 q^{57} - 2 q^{58} - 86 q^{59} + 35 q^{60} + 34 q^{61} - 36 q^{62} - 10 q^{63} - 15 q^{64} - 64 q^{65} + q^{66} - 38 q^{67} - 33 q^{68} + 70 q^{69} - 29 q^{70} - 176 q^{71} - 27 q^{72} + 69 q^{73} - 86 q^{74} - 79 q^{75} - 54 q^{76} - 45 q^{77} + 39 q^{78} - 101 q^{79} - 76 q^{80} + 104 q^{81} + 38 q^{82} - 67 q^{83} + 9 q^{84} + 3 q^{85} - 90 q^{86} + 37 q^{87} + 7 q^{88} - 91 q^{89} + 8 q^{90} - 47 q^{91} - 136 q^{92} + 47 q^{93} - 20 q^{94} - 130 q^{95} + 53 q^{96} + 86 q^{97} - 44 q^{98} - 52 q^{99}+O(q^{100}) \) 104 * q - 9 * q^2 - 104 * q^3 + 87 * q^4 - 15 * q^5 + 9 * q^6 - 10 * q^7 - 27 * q^8 + 104 * q^9 + 8 * q^10 - 52 * q^11 - 87 * q^12 + 35 * q^13 - 23 * q^14 + 15 * q^15 + 53 * q^16 - 19 * q^17 - 9 * q^18 - 22 * q^19 - 35 * q^20 + 10 * q^21 - q^22 - 70 * q^23 + 27 * q^24 + 79 * q^25 - 39 * q^26 - 104 * q^27 - 9 * q^28 - 37 * q^29 - 8 * q^30 - 47 * q^31 - 53 * q^32 + 52 * q^33 - 17 * q^34 - 54 * q^35 + 87 * q^36 + 65 * q^37 - 33 * q^38 - 35 * q^39 + 14 * q^40 - 47 * q^41 + 23 * q^42 - 30 * q^43 - 122 * q^44 - 15 * q^45 - 6 * q^46 - 101 * q^47 - 53 * q^48 + 78 * q^49 - 64 * q^50 + 19 * q^51 + 41 * q^52 - 48 * q^53 + 9 * q^54 - 29 * q^55 - 71 * q^56 + 22 * q^57 - 2 * q^58 - 86 * q^59 + 35 * q^60 + 34 * q^61 - 36 * q^62 - 10 * q^63 - 15 * q^64 - 64 * q^65 + q^66 - 38 * q^67 - 33 * q^68 + 70 * q^69 - 29 * q^70 - 176 * q^71 - 27 * q^72 + 69 * q^73 - 86 * q^74 - 79 * q^75 - 54 * q^76 - 45 * q^77 + 39 * q^78 - 101 * q^79 - 76 * q^80 + 104 * q^81 + 38 * q^82 - 67 * q^83 + 9 * q^84 + 3 * q^85 - 90 * q^86 + 37 * q^87 + 7 * q^88 - 91 * q^89 + 8 * q^90 - 47 * q^91 - 136 * q^92 + 47 * q^93 - 20 * q^94 - 130 * q^95 + 53 * q^96 + 86 * q^97 - 44 * q^98 - 52 * q^99

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