LMFDB - Embedded newform 6015.2.a.c.1.4

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:	$28$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
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)

$f(q)$	$=$	$q-2.11452 q^{2} +1.00000 q^{3} +2.47118 q^{4} -1.00000 q^{5} -2.11452 q^{6} +1.95178 q^{7} -0.996316 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.11452 q^{2} +1.00000 q^{3} +2.47118 q^{4} -1.00000 q^{5} -2.11452 q^{6} +1.95178 q^{7} -0.996316 q^{8} +1.00000 q^{9} +2.11452 q^{10} +3.41248 q^{11} +2.47118 q^{12} +1.95829 q^{13} -4.12706 q^{14} -1.00000 q^{15} -2.83563 q^{16} +4.10617 q^{17} -2.11452 q^{18} -4.15330 q^{19} -2.47118 q^{20} +1.95178 q^{21} -7.21574 q^{22} -0.493681 q^{23} -0.996316 q^{24} +1.00000 q^{25} -4.14083 q^{26} +1.00000 q^{27} +4.82319 q^{28} -8.18368 q^{29} +2.11452 q^{30} -7.47845 q^{31} +7.98862 q^{32} +3.41248 q^{33} -8.68256 q^{34} -1.95178 q^{35} +2.47118 q^{36} +4.80496 q^{37} +8.78222 q^{38} +1.95829 q^{39} +0.996316 q^{40} +0.363555 q^{41} -4.12706 q^{42} -9.21615 q^{43} +8.43285 q^{44} -1.00000 q^{45} +1.04390 q^{46} -7.84581 q^{47} -2.83563 q^{48} -3.19057 q^{49} -2.11452 q^{50} +4.10617 q^{51} +4.83928 q^{52} -3.70069 q^{53} -2.11452 q^{54} -3.41248 q^{55} -1.94459 q^{56} -4.15330 q^{57} +17.3045 q^{58} -2.52456 q^{59} -2.47118 q^{60} -14.6750 q^{61} +15.8133 q^{62} +1.95178 q^{63} -11.2208 q^{64} -1.95829 q^{65} -7.21574 q^{66} -9.55602 q^{67} +10.1471 q^{68} -0.493681 q^{69} +4.12706 q^{70} +5.03149 q^{71} -0.996316 q^{72} -13.4150 q^{73} -10.1602 q^{74} +1.00000 q^{75} -10.2635 q^{76} +6.66039 q^{77} -4.14083 q^{78} +5.98271 q^{79} +2.83563 q^{80} +1.00000 q^{81} -0.768744 q^{82} -2.79997 q^{83} +4.82319 q^{84} -4.10617 q^{85} +19.4877 q^{86} -8.18368 q^{87} -3.39991 q^{88} -10.7510 q^{89} +2.11452 q^{90} +3.82214 q^{91} -1.21997 q^{92} -7.47845 q^{93} +16.5901 q^{94} +4.15330 q^{95} +7.98862 q^{96} -3.84446 q^{97} +6.74651 q^{98} +3.41248 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - q^{2} + 28 q^{3} + 21 q^{4} - 28 q^{5} - q^{6} - 20 q^{7} + 28 q^{9}+O(q^{10}) $ 28 * q - q^2 + 28 * q^3 + 21 * q^4 - 28 * q^5 - q^6 - 20 * q^7 + 28 * q^9	\( 28 q - q^{2} + 28 q^{3} + 21 q^{4} - 28 q^{5} - q^{6} - 20 q^{7} + 28 q^{9} + q^{10} - q^{11} + 21 q^{12} - 18 q^{13} - 4 q^{14} - 28 q^{15} - q^{16} - 28 q^{17} - q^{18} - 19 q^{19} - 21 q^{20} - 20 q^{21} - 35 q^{22} + 2 q^{23} + 28 q^{25} - 20 q^{26} + 28 q^{27} - 54 q^{28} + 9 q^{29} + q^{30} - 19 q^{31} - 6 q^{32} - q^{33} - 16 q^{34} + 20 q^{35} + 21 q^{36} - 32 q^{37} - 2 q^{38} - 18 q^{39} - 27 q^{41} - 4 q^{42} - 77 q^{43} + q^{44} - 28 q^{45} - 19 q^{46} + 10 q^{47} - q^{48} - 4 q^{49} - q^{50} - 28 q^{51} - 34 q^{52} - 21 q^{53} - q^{54} + q^{55} - 9 q^{56} - 19 q^{57} - 46 q^{58} - 7 q^{59} - 21 q^{60} - 31 q^{61} - 7 q^{62} - 20 q^{63} - 46 q^{64} + 18 q^{65} - 35 q^{66} - 50 q^{67} - 68 q^{68} + 2 q^{69} + 4 q^{70} - 4 q^{71} - 87 q^{73} + 4 q^{74} + 28 q^{75} - 40 q^{76} - 8 q^{77} - 20 q^{78} - 65 q^{79} + q^{80} + 28 q^{81} - 41 q^{82} + 13 q^{83} - 54 q^{84} + 28 q^{85} - 17 q^{86} + 9 q^{87} - 117 q^{88} - 33 q^{89} + q^{90} - 33 q^{91} + 3 q^{92} - 19 q^{93} - 60 q^{94} + 19 q^{95} - 6 q^{96} - 75 q^{97} - 18 q^{98} - q^{99}+O(q^{100}) \) 28 * q - q^2 + 28 * q^3 + 21 * q^4 - 28 * q^5 - q^6 - 20 * q^7 + 28 * q^9 + q^10 - q^11 + 21 * q^12 - 18 * q^13 - 4 * q^14 - 28 * q^15 - q^16 - 28 * q^17 - q^18 - 19 * q^19 - 21 * q^20 - 20 * q^21 - 35 * q^22 + 2 * q^23 + 28 * q^25 - 20 * q^26 + 28 * q^27 - 54 * q^28 + 9 * q^29 + q^30 - 19 * q^31 - 6 * q^32 - q^33 - 16 * q^34 + 20 * q^35 + 21 * q^36 - 32 * q^37 - 2 * q^38 - 18 * q^39 - 27 * q^41 - 4 * q^42 - 77 * q^43 + q^44 - 28 * q^45 - 19 * q^46 + 10 * q^47 - q^48 - 4 * q^49 - q^50 - 28 * q^51 - 34 * q^52 - 21 * q^53 - q^54 + q^55 - 9 * q^56 - 19 * q^57 - 46 * q^58 - 7 * q^59 - 21 * q^60 - 31 * q^61 - 7 * q^62 - 20 * q^63 - 46 * q^64 + 18 * q^65 - 35 * q^66 - 50 * q^67 - 68 * q^68 + 2 * q^69 + 4 * q^70 - 4 * q^71 - 87 * q^73 + 4 * q^74 + 28 * q^75 - 40 * q^76 - 8 * q^77 - 20 * q^78 - 65 * q^79 + q^80 + 28 * q^81 - 41 * q^82 + 13 * q^83 - 54 * q^84 + 28 * q^85 - 17 * q^86 + 9 * q^87 - 117 * q^88 - 33 * q^89 + q^90 - 33 * q^91 + 3 * q^92 - 19 * q^93 - 60 * q^94 + 19 * q^95 - 6 * q^96 - 75 * q^97 - 18 * 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 $

$2$	−2.11452	−1.49519	−0.747594	−	0.664156i	$-0.768791\pi$
$2$	−2.11452	−1.49519	−0.747594	+	0.664156i	$0.768791\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.47118	1.23559
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−2.11452	−0.863248
$7$	1.95178	0.737702	0.368851	−	0.929489i	$-0.379751\pi$
$7$	1.95178	0.737702	0.368851	+	0.929489i	$0.379751\pi$
$8$	−0.996316	−0.352251
$9$	1.00000	0.333333
$10$	2.11452	0.668669
$11$	3.41248	1.02890	0.514450	−	0.857520i	$-0.327996\pi$
$11$	3.41248	1.02890	0.514450	+	0.857520i	$0.327996\pi$
$12$	2.47118	0.713368
$13$	1.95829	0.543132	0.271566	−	0.962420i	$-0.412459\pi$
$13$	1.95829	0.543132	0.271566	+	0.962420i	$0.412459\pi$
$14$	−4.12706	−1.10300
$15$	−1.00000	−0.258199
$16$	−2.83563	−0.708908
$17$	4.10617	0.995892	0.497946	−	0.867208i	$-0.334088\pi$
$17$	4.10617	0.995892	0.497946	+	0.867208i	$0.334088\pi$
$18$	−2.11452	−0.498396
$19$	−4.15330	−0.952832	−0.476416	−	0.879220i	$-0.658064\pi$
$19$	−4.15330	−0.952832	−0.476416	+	0.879220i	$0.658064\pi$
$20$	−2.47118	−0.552572
$21$	1.95178	0.425913
$22$	−7.21574	−1.53840
$23$	−0.493681	−0.102940	−0.0514698	−	0.998675i	$-0.516391\pi$
$23$	−0.493681	−0.102940	−0.0514698	+	0.998675i	$0.516391\pi$
$24$	−0.996316	−0.203372
$25$	1.00000	0.200000
$26$	−4.14083	−0.812084
$27$	1.00000	0.192450
$28$	4.82319	0.911497
$29$	−8.18368	−1.51967	−0.759836	−	0.650115i	$-0.774721\pi$
$29$	−8.18368	−1.51967	−0.759836	+	0.650115i	$0.774721\pi$
$30$	2.11452	0.386056
$31$	−7.47845	−1.34317	−0.671585	−	0.740928i	$-0.734386\pi$
$31$	−7.47845	−1.34317	−0.671585	+	0.740928i	$0.734386\pi$
$32$	7.98862	1.41220
$33$	3.41248	0.594036
$34$	−8.68256	−1.48905
$35$	−1.95178	−0.329910
$36$	2.47118	0.411863
$37$	4.80496	0.789930	0.394965	−	0.918696i	$-0.370757\pi$
$37$	4.80496	0.789930	0.394965	+	0.918696i	$0.370757\pi$
$38$	8.78222	1.42466
$39$	1.95829	0.313577
$40$	0.996316	0.157531
$41$	0.363555	0.0567778	0.0283889	−	0.999597i	$-0.490962\pi$
$41$	0.363555	0.0567778	0.0283889	+	0.999597i	$0.490962\pi$
$42$	−4.12706	−0.636820
$43$	−9.21615	−1.40545	−0.702725	−	0.711462i	$-0.748033\pi$
$43$	−9.21615	−1.40545	−0.702725	+	0.711462i	$0.748033\pi$
$44$	8.43285	1.27130
$45$	−1.00000	−0.149071
$46$	1.04390	0.153914
$47$	−7.84581	−1.14443	−0.572215	−	0.820104i	$-0.693916\pi$
$47$	−7.84581	−1.14443	−0.572215	+	0.820104i	$0.693916\pi$
$48$	−2.83563	−0.409288
$49$	−3.19057	−0.455796
$50$	−2.11452	−0.299038
$51$	4.10617	0.574978
$52$	4.83928	0.671088
$53$	−3.70069	−0.508328	−0.254164	−	0.967161i	$-0.581800\pi$
$53$	−3.70069	−0.508328	−0.254164	+	0.967161i	$0.581800\pi$
$54$	−2.11452	−0.287749
$55$	−3.41248	−0.460138
$56$	−1.94459	−0.259856
$57$	−4.15330	−0.550118
$58$	17.3045	2.27220
$59$	−2.52456	−0.328670	−0.164335	−	0.986405i	$-0.552548\pi$
$59$	−2.52456	−0.328670	−0.164335	+	0.986405i	$0.552548\pi$
$60$	−2.47118	−0.319028
$61$	−14.6750	−1.87895	−0.939473	−	0.342624i	$-0.888684\pi$
$61$	−14.6750	−1.87895	−0.939473	+	0.342624i	$0.888684\pi$
$62$	15.8133	2.00829
$63$	1.95178	0.245901
$64$	−11.2208	−1.40260
$65$	−1.95829	−0.242896
$66$	−7.21574	−0.888196
$67$	−9.55602	−1.16745	−0.583727	−	0.811950i	$-0.698406\pi$
$67$	−9.55602	−1.16745	−0.583727	+	0.811950i	$0.698406\pi$
$68$	10.1471	1.23051
$69$	−0.493681	−0.0594322
$70$	4.12706	0.493278
$71$	5.03149	0.597128	0.298564	−	0.954390i	$-0.403492\pi$
$71$	5.03149	0.597128	0.298564	+	0.954390i	$0.403492\pi$
$72$	−0.996316	−0.117417
$73$	−13.4150	−1.57011	−0.785056	−	0.619425i	$-0.787366\pi$
$73$	−13.4150	−1.57011	−0.785056	+	0.619425i	$0.787366\pi$
$74$	−10.1602	−1.18109
$75$	1.00000	0.115470
$76$	−10.2635	−1.17731
$77$	6.66039	0.759022
$78$	−4.14083	−0.468857
$79$	5.98271	0.673107	0.336554	−	0.941664i	$-0.390739\pi$
$79$	5.98271	0.673107	0.336554	+	0.941664i	$0.390739\pi$
$80$	2.83563	0.317033
$81$	1.00000	0.111111
$82$	−0.768744	−0.0848936
$83$	−2.79997	−0.307336	−0.153668	−	0.988123i	$-0.549109\pi$
$83$	−2.79997	−0.307336	−0.153668	+	0.988123i	$0.549109\pi$
$84$	4.82319	0.526253
$85$	−4.10617	−0.445376
$86$	19.4877	2.10141
$87$	−8.18368	−0.877383
$88$	−3.39991	−0.362431
$89$	−10.7510	−1.13960	−0.569801	−	0.821783i	$-0.692980\pi$
$89$	−10.7510	−1.13960	−0.569801	+	0.821783i	$0.692980\pi$
$90$	2.11452	0.222890
$91$	3.82214	0.400669
$92$	−1.21997	−0.127191
$93$	−7.47845	−0.775479
$94$	16.5901	1.71114
$95$	4.15330	0.426119
$96$	7.98862	0.815335
$97$	−3.84446	−0.390346	−0.195173	−	0.980769i	$-0.562527\pi$
$97$	−3.84446	−0.390346	−0.195173	+	0.980769i	$0.562527\pi$
$98$	6.74651	0.681500
$99$	3.41248	0.342967
$100$	2.47118	0.247118
$101$	−10.4163	−1.03646	−0.518230	−	0.855241i	$-0.673409\pi$
$101$	−10.4163	−1.03646	−0.518230	+	0.855241i	$0.673409\pi$
$102$	−8.68256	−0.859701
$103$	−15.9001	−1.56668	−0.783341	−	0.621592i	$-0.786486\pi$
$103$	−15.9001	−1.56668	−0.783341	+	0.621592i	$0.786486\pi$
$104$	−1.95107	−0.191319
$105$	−1.95178	−0.190474
$106$	7.82516	0.760047
$107$	−3.98989	−0.385718	−0.192859	−	0.981227i	$-0.561776\pi$
$107$	−3.98989	−0.385718	−0.192859	+	0.981227i	$0.561776\pi$
$108$	2.47118	0.237789
$109$	9.55855	0.915543	0.457771	−	0.889070i	$-0.348648\pi$
$109$	9.55855	0.915543	0.457771	+	0.889070i	$0.348648\pi$
$110$	7.21574	0.687994
$111$	4.80496	0.456066
$112$	−5.53452	−0.522963
$113$	7.60478	0.715397	0.357699	−	0.933837i	$-0.383562\pi$
$113$	7.60478	0.715397	0.357699	+	0.933837i	$0.383562\pi$
$114$	8.78222	0.822530
$115$	0.493681	0.0460360
$116$	−20.2233	−1.87769
$117$	1.95829	0.181044
$118$	5.33823	0.491424
$119$	8.01432	0.734671
$120$	0.996316	0.0909508
$121$	0.645009	0.0586372
$122$	31.0306	2.80938
$123$	0.363555	0.0327807
$124$	−18.4806	−1.65961
$125$	−1.00000	−0.0894427
$126$	−4.12706	−0.367668
$127$	−12.8047	−1.13623	−0.568116	−	0.822948i	$-0.692328\pi$
$127$	−12.8047	−1.13623	−0.568116	+	0.822948i	$0.692328\pi$
$128$	7.74933	0.684951
$129$	−9.21615	−0.811437
$130$	4.14083	0.363175
$131$	14.3164	1.25083	0.625414	−	0.780293i	$-0.284930\pi$
$131$	14.3164	1.25083	0.625414	+	0.780293i	$0.284930\pi$
$132$	8.43285	0.733985
$133$	−8.10631	−0.702906
$134$	20.2064	1.74556
$135$	−1.00000	−0.0860663
$136$	−4.09104	−0.350804
$137$	−2.48669	−0.212452	−0.106226	−	0.994342i	$-0.533877\pi$
$137$	−2.48669	−0.212452	−0.106226	+	0.994342i	$0.533877\pi$
$138$	1.04390	0.0888623
$139$	5.30880	0.450287	0.225143	−	0.974326i	$-0.427715\pi$
$139$	5.30880	0.450287	0.225143	+	0.974326i	$0.427715\pi$
$140$	−4.82319	−0.407634
$141$	−7.84581	−0.660737
$142$	−10.6392	−0.892819
$143$	6.68262	0.558829
$144$	−2.83563	−0.236303
$145$	8.18368	0.679618
$146$	28.3663	2.34761
$147$	−3.19057	−0.263154
$148$	11.8739	0.976029
$149$	11.4948	0.941689	0.470845	−	0.882216i	$-0.343949\pi$
$149$	11.4948	0.941689	0.470845	+	0.882216i	$0.343949\pi$
$150$	−2.11452	−0.172650
$151$	3.52848	0.287143	0.143572	−	0.989640i	$-0.454141\pi$
$151$	3.52848	0.287143	0.143572	+	0.989640i	$0.454141\pi$
$152$	4.13800	0.335636
$153$	4.10617	0.331964
$154$	−14.0835	−1.13488
$155$	7.47845	0.600684
$156$	4.83928	0.387453
$157$	22.4822	1.79427	0.897136	−	0.441754i	$-0.145643\pi$
$157$	22.4822	1.79427	0.897136	+	0.441754i	$0.145643\pi$
$158$	−12.6505	−1.00642
$159$	−3.70069	−0.293483
$160$	−7.98862	−0.631556
$161$	−0.963554	−0.0759387
$162$	−2.11452	−0.166132
$163$	−13.9501	−1.09265	−0.546326	−	0.837572i	$-0.683974\pi$
$163$	−13.9501	−1.09265	−0.546326	+	0.837572i	$0.683974\pi$
$164$	0.898411	0.0701541
$165$	−3.41248	−0.265661
$166$	5.92058	0.459526
$167$	9.86964	0.763736	0.381868	−	0.924217i	$-0.375281\pi$
$167$	9.86964	0.763736	0.381868	+	0.924217i	$0.375281\pi$
$168$	−1.94459	−0.150028
$169$	−9.16510	−0.705008
$170$	8.68256	0.665922
$171$	−4.15330	−0.317611
$172$	−22.7748	−1.73656
$173$	−3.63566	−0.276414	−0.138207	−	0.990403i	$-0.544134\pi$
$173$	−3.63566	−0.276414	−0.138207	+	0.990403i	$0.544134\pi$
$174$	17.3045	1.31185
$175$	1.95178	0.147540
$176$	−9.67653	−0.729396
$177$	−2.52456	−0.189758
$178$	22.7331	1.70392
$179$	21.2192	1.58600	0.792998	−	0.609224i	$-0.208519\pi$
$179$	21.2192	1.58600	0.792998	+	0.609224i	$0.208519\pi$
$180$	−2.47118	−0.184191
$181$	−8.23754	−0.612292	−0.306146	−	0.951985i	$-0.599040\pi$
$181$	−8.23754	−0.612292	−0.306146	+	0.951985i	$0.599040\pi$
$182$	−8.08198	−0.599076
$183$	−14.6750	−1.08481
$184$	0.491862	0.0362605
$185$	−4.80496	−0.353267
$186$	15.8133	1.15949
$187$	14.0122	1.02467
$188$	−19.3884	−1.41405
$189$	1.95178	0.141971
$190$	−8.78222	−0.637129
$191$	13.4596	0.973900	0.486950	−	0.873430i	$-0.338109\pi$
$191$	13.4596	0.973900	0.486950	+	0.873430i	$0.338109\pi$
$192$	−11.2208	−0.809792
$193$	5.80206	0.417642	0.208821	−	0.977954i	$-0.433037\pi$
$193$	5.80206	0.417642	0.208821	+	0.977954i	$0.433037\pi$
$194$	8.12918	0.583641
$195$	−1.95829	−0.140236
$196$	−7.88447	−0.563176
$197$	−21.8719	−1.55831	−0.779153	−	0.626834i	$-0.784350\pi$
$197$	−21.8719	−1.55831	−0.779153	+	0.626834i	$0.784350\pi$
$198$	−7.21574	−0.512800
$199$	23.1298	1.63963	0.819815	−	0.572628i	$-0.194076\pi$
$199$	23.1298	1.63963	0.819815	+	0.572628i	$0.194076\pi$
$200$	−0.996316	−0.0704502
$201$	−9.55602	−0.674030
$202$	22.0254	1.54970
$203$	−15.9727	−1.12106
$204$	10.1471	0.710437
$205$	−0.363555	−0.0253918
$206$	33.6210	2.34249
$207$	−0.493681	−0.0343132
$208$	−5.55299	−0.385030
$209$	−14.1730	−0.980370
$210$	4.12706	0.284794
$211$	−19.8208	−1.36452	−0.682260	−	0.731109i	$-0.739003\pi$
$211$	−19.8208	−1.36452	−0.682260	+	0.731109i	$0.739003\pi$
$212$	−9.14506	−0.628085
$213$	5.03149	0.344752
$214$	8.43670	0.576721
$215$	9.21615	0.628536
$216$	−0.996316	−0.0677907
$217$	−14.5963	−0.990859
$218$	−20.2117	−1.36891
$219$	−13.4150	−0.906504
$220$	−8.43285	−0.568542
$221$	8.04106	0.540900
$222$	−10.1602	−0.681905
$223$	−9.82070	−0.657643	−0.328821	−	0.944392i	$-0.606651\pi$
$223$	−9.82070	−0.657643	−0.328821	+	0.944392i	$0.606651\pi$
$224$	15.5920	1.04178
$225$	1.00000	0.0666667
$226$	−16.0804	−1.06965
$227$	9.65893	0.641085	0.320543	−	0.947234i	$-0.396135\pi$
$227$	9.65893	0.641085	0.320543	+	0.947234i	$0.396135\pi$
$228$	−10.2635	−0.679720
$229$	−10.5286	−0.695751	−0.347875	−	0.937541i	$-0.613097\pi$
$229$	−10.5286	−0.695751	−0.347875	+	0.937541i	$0.613097\pi$
$230$	−1.04390	−0.0688325
$231$	6.66039	0.438222
$232$	8.15353	0.535306
$233$	5.23745	0.343117	0.171558	−	0.985174i	$-0.445120\pi$
$233$	5.23745	0.343117	0.171558	+	0.985174i	$0.445120\pi$
$234$	−4.14083	−0.270695
$235$	7.84581	0.511804
$236$	−6.23864	−0.406101
$237$	5.98271	0.388619
$238$	−16.9464	−1.09847
$239$	−1.71203	−0.110742	−0.0553710	−	0.998466i	$-0.517634\pi$
$239$	−1.71203	−0.110742	−0.0553710	+	0.998466i	$0.517634\pi$
$240$	2.83563	0.183039
$241$	−22.8884	−1.47437	−0.737184	−	0.675692i	$-0.763845\pi$
$241$	−22.8884	−1.47437	−0.737184	+	0.675692i	$0.763845\pi$
$242$	−1.36388	−0.0876736
$243$	1.00000	0.0641500
$244$	−36.2646	−2.32161
$245$	3.19057	0.203838
$246$	−0.768744	−0.0490133
$247$	−8.13336	−0.517513
$248$	7.45090	0.473132
$249$	−2.79997	−0.177441
$250$	2.11452	0.133734
$251$	−8.30509	−0.524212	−0.262106	−	0.965039i	$-0.584417\pi$
$251$	−8.30509	−0.524212	−0.262106	+	0.965039i	$0.584417\pi$
$252$	4.82319	0.303832
$253$	−1.68467	−0.105915
$254$	27.0757	1.69888
$255$	−4.10617	−0.257138
$256$	6.05552	0.378470
$257$	7.11327	0.443714	0.221857	−	0.975079i	$-0.428788\pi$
$257$	7.11327	0.443714	0.221857	+	0.975079i	$0.428788\pi$
$258$	19.4877	1.21325
$259$	9.37820	0.582733
$260$	−4.83928	−0.300120
$261$	−8.18368	−0.506557
$262$	−30.2722	−1.87022
$263$	3.49641	0.215598	0.107799	−	0.994173i	$-0.465620\pi$
$263$	3.49641	0.215598	0.107799	+	0.994173i	$0.465620\pi$
$264$	−3.39991	−0.209250
$265$	3.70069	0.227331
$266$	17.1409	1.05098
$267$	−10.7510	−0.657950
$268$	−23.6146	−1.44249
$269$	9.58718	0.584541	0.292270	−	0.956336i	$-0.405589\pi$
$269$	9.58718	0.584541	0.292270	+	0.956336i	$0.405589\pi$
$270$	2.11452	0.128685
$271$	−0.300592	−0.0182597	−0.00912984	−	0.999958i	$-0.502906\pi$
$271$	−0.300592	−0.0182597	−0.00912984	+	0.999958i	$0.502906\pi$
$272$	−11.6436	−0.705996
$273$	3.82214	0.231327
$274$	5.25815	0.317657
$275$	3.41248	0.205780
$276$	−1.21997	−0.0734338
$277$	12.6493	0.760025	0.380012	−	0.924981i	$-0.375920\pi$
$277$	12.6493	0.760025	0.380012	+	0.924981i	$0.375920\pi$
$278$	−11.2255	−0.673264
$279$	−7.47845	−0.447723
$280$	1.94459	0.116211
$281$	15.7296	0.938351	0.469175	−	0.883105i	$-0.344551\pi$
$281$	15.7296	0.938351	0.469175	+	0.883105i	$0.344551\pi$
$282$	16.5901	0.987926
$283$	−10.1684	−0.604448	−0.302224	−	0.953237i	$-0.597729\pi$
$283$	−10.1684	−0.604448	−0.302224	+	0.953237i	$0.597729\pi$
$284$	12.4337	0.737805
$285$	4.15330	0.246020
$286$	−14.1305	−0.835555
$287$	0.709579	0.0418851
$288$	7.98862	0.470734
$289$	−0.139395	−0.00819973
$290$	−17.3045	−1.01616
$291$	−3.84446	−0.225366
$292$	−33.1510	−1.94001
$293$	−6.38960	−0.373284	−0.186642	−	0.982428i	$-0.559760\pi$
$293$	−6.38960	−0.373284	−0.186642	+	0.982428i	$0.559760\pi$
$294$	6.74651	0.393464
$295$	2.52456	0.146986
$296$	−4.78725	−0.278253
$297$	3.41248	0.198012
$298$	−24.3059	−1.40800
$299$	−0.966770	−0.0559097
$300$	2.47118	0.142674
$301$	−17.9879	−1.03680
$302$	−7.46102	−0.429334
$303$	−10.4163	−0.598400
$304$	11.7772	0.675470
$305$	14.6750	0.840290
$306$	−8.68256	−0.496349
$307$	21.1895	1.20935	0.604676	−	0.796472i	$-0.293303\pi$
$307$	21.1895	1.20935	0.604676	+	0.796472i	$0.293303\pi$
$308$	16.4590	0.937840
$309$	−15.9001	−0.904525
$310$	−15.8133	−0.898135
$311$	0.0605377	0.00343278	0.00171639	−	0.999999i	$-0.499454\pi$
$311$	0.0605377	0.00343278	0.00171639	+	0.999999i	$0.499454\pi$
$312$	−1.95107	−0.110458
$313$	−9.93472	−0.561544	−0.280772	−	0.959775i	$-0.590590\pi$
$313$	−9.93472	−0.561544	−0.280772	+	0.959775i	$0.590590\pi$
$314$	−47.5389	−2.68278
$315$	−1.95178	−0.109970
$316$	14.7843	0.831684
$317$	3.05749	0.171726	0.0858630	−	0.996307i	$-0.472635\pi$
$317$	3.05749	0.171726	0.0858630	+	0.996307i	$0.472635\pi$
$318$	7.82516	0.438813
$319$	−27.9266	−1.56359
$320$	11.2208	0.627262
$321$	−3.98989	−0.222694
$322$	2.03745	0.113543
$323$	−17.0541	−0.948917
$324$	2.47118	0.137288
$325$	1.95829	0.108626
$326$	29.4976	1.63372
$327$	9.55855	0.528589
$328$	−0.362216	−0.0200000
$329$	−15.3133	−0.844248
$330$	7.21574	0.397213
$331$	7.85919	0.431980	0.215990	−	0.976396i	$-0.430702\pi$
$331$	7.85919	0.431980	0.215990	+	0.976396i	$0.430702\pi$
$332$	−6.91922	−0.379741
$333$	4.80496	0.263310
$334$	−20.8695	−1.14193
$335$	9.55602	0.522101
$336$	−5.53452	−0.301933
$337$	13.7295	0.747892	0.373946	−	0.927450i	$-0.378005\pi$
$337$	13.7295	0.747892	0.373946	+	0.927450i	$0.378005\pi$
$338$	19.3798	1.05412
$339$	7.60478	0.413035
$340$	−10.1471	−0.550302
$341$	−25.5201	−1.38199
$342$	8.78222	0.474888
$343$	−19.8897	−1.07394
$344$	9.18219	0.495071
$345$	0.493681	0.0265789
$346$	7.68767	0.413292
$347$	11.8597	0.636664	0.318332	−	0.947979i	$-0.396877\pi$
$347$	11.8597	0.636664	0.318332	+	0.947979i	$0.396877\pi$
$348$	−20.2233	−1.08408
$349$	19.4559	1.04145	0.520724	−	0.853725i	$-0.325662\pi$
$349$	19.4559	1.04145	0.520724	+	0.853725i	$0.325662\pi$
$350$	−4.12706	−0.220601
$351$	1.95829	0.104526
$352$	27.2610	1.45302
$353$	−19.8920	−1.05874	−0.529371	−	0.848390i	$-0.677572\pi$
$353$	−19.8920	−1.05874	−0.529371	+	0.848390i	$0.677572\pi$
$354$	5.33823	0.283724
$355$	−5.03149	−0.267044
$356$	−26.5676	−1.40808
$357$	8.01432	0.424163
$358$	−44.8683	−2.37136
$359$	23.1150	1.21996	0.609981	−	0.792416i	$-0.291177\pi$
$359$	23.1150	1.21996	0.609981	+	0.792416i	$0.291177\pi$
$360$	0.996316	0.0525105
$361$	−1.75012	−0.0921114
$362$	17.4184	0.915492
$363$	0.645009	0.0338542
$364$	9.44520	0.495063
$365$	13.4150	0.702175
$366$	31.0306	1.62200
$367$	36.4938	1.90496	0.952480	−	0.304601i	$-0.0985231\pi$
$367$	36.4938	1.90496	0.952480	+	0.304601i	$0.0985231\pi$
$368$	1.39990	0.0729747
$369$	0.363555	0.0189259
$370$	10.1602	0.528201
$371$	−7.22291	−0.374995
$372$	−18.4806	−0.958174
$373$	32.9919	1.70826	0.854128	−	0.520063i	$-0.174091\pi$
$373$	32.9919	1.70826	0.854128	+	0.520063i	$0.174091\pi$
$374$	−29.6290	−1.53208
$375$	−1.00000	−0.0516398
$376$	7.81691	0.403126
$377$	−16.0260	−0.825382
$378$	−4.12706	−0.212273
$379$	25.9122	1.33102	0.665511	−	0.746388i	$-0.268214\pi$
$379$	25.9122	1.33102	0.665511	+	0.746388i	$0.268214\pi$
$380$	10.2635	0.526509
$381$	−12.8047	−0.656004
$382$	−28.4605	−1.45616
$383$	−3.36526	−0.171957	−0.0859783	−	0.996297i	$-0.527402\pi$
$383$	−3.36526	−0.171957	−0.0859783	+	0.996297i	$0.527402\pi$
$384$	7.74933	0.395457
$385$	−6.66039	−0.339445
$386$	−12.2686	−0.624453
$387$	−9.21615	−0.468483
$388$	−9.50035	−0.482307
$389$	28.6255	1.45137	0.725686	−	0.688026i	$-0.241522\pi$
$389$	28.6255	1.45137	0.725686	+	0.688026i	$0.241522\pi$
$390$	4.14083	0.209679
$391$	−2.02714	−0.102517
$392$	3.17881	0.160554
$393$	14.3164	0.722166
$394$	46.2484	2.32996
$395$	−5.98271	−0.301023
$396$	8.43285	0.423766
$397$	−36.5454	−1.83416	−0.917081	−	0.398700i	$-0.869462\pi$
$397$	−36.5454	−1.83416	−0.917081	+	0.398700i	$0.869462\pi$
$398$	−48.9084	−2.45156
$399$	−8.10631	−0.405823
$400$	−2.83563	−0.141782
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	20.2064	1.00780
$403$	−14.6450	−0.729518
$404$	−25.7405	−1.28064
$405$	−1.00000	−0.0496904
$406$	33.7746	1.67620
$407$	16.3968	0.812760
$408$	−4.09104	−0.202537
$409$	31.8229	1.57354	0.786772	−	0.617244i	$-0.211751\pi$
$409$	31.8229	1.57354	0.786772	+	0.617244i	$0.211751\pi$
$410$	0.768744	0.0379656
$411$	−2.48669	−0.122659
$412$	−39.2920	−1.93578
$413$	−4.92738	−0.242460
$414$	1.04390	0.0513047
$415$	2.79997	0.137445
$416$	15.6440	0.767012
$417$	5.30880	0.259973
$418$	29.9691	1.46584
$419$	−19.9777	−0.975973	−0.487986	−	0.872851i	$-0.662268\pi$
$419$	−19.9777	−0.975973	−0.487986	+	0.872851i	$0.662268\pi$
$420$	−4.82319	−0.235348
$421$	11.8697	0.578494	0.289247	−	0.957254i	$-0.406595\pi$
$421$	11.8697	0.578494	0.289247	+	0.957254i	$0.406595\pi$
$422$	41.9114	2.04022
$423$	−7.84581	−0.381477
$424$	3.68705	0.179059
$425$	4.10617	0.199178
$426$	−10.6392	−0.515470
$427$	−28.6424	−1.38610
$428$	−9.85974	−0.476589
$429$	6.68262	0.322640
$430$	−19.4877	−0.939780
$431$	−19.8812	−0.957646	−0.478823	−	0.877911i	$-0.658936\pi$
$431$	−19.8812	−0.957646	−0.478823	+	0.877911i	$0.658936\pi$
$432$	−2.83563	−0.136429
$433$	−28.9710	−1.39226	−0.696129	−	0.717917i	$-0.745096\pi$
$433$	−28.9710	−1.39226	−0.696129	+	0.717917i	$0.745096\pi$
$434$	30.8640	1.48152
$435$	8.18368	0.392378
$436$	23.6209	1.13124
$437$	2.05040	0.0980841
$438$	28.3663	1.35540
$439$	0.713170	0.0340378	0.0170189	−	0.999855i	$-0.494582\pi$
$439$	0.713170	0.0340378	0.0170189	+	0.999855i	$0.494582\pi$
$440$	3.39991	0.162084
$441$	−3.19057	−0.151932
$442$	−17.0030	−0.808748
$443$	−2.89921	−0.137746	−0.0688728	−	0.997625i	$-0.521940\pi$
$443$	−2.89921	−0.137746	−0.0688728	+	0.997625i	$0.521940\pi$
$444$	11.8739	0.563511
$445$	10.7510	0.509646
$446$	20.7660	0.983300
$447$	11.4948	0.543685
$448$	−21.9005	−1.03470
$449$	−12.0787	−0.570031	−0.285016	−	0.958523i	$-0.591999\pi$
$449$	−12.0787	−0.570031	−0.285016	+	0.958523i	$0.591999\pi$
$450$	−2.11452	−0.0996793
$451$	1.24063	0.0584188
$452$	18.7928	0.883937
$453$	3.52848	0.165782
$454$	−20.4240	−0.958544
$455$	−3.82214	−0.179185
$456$	4.13800	0.193779
$457$	1.26201	0.0590343	0.0295172	−	0.999564i	$-0.490603\pi$
$457$	1.26201	0.0590343	0.0295172	+	0.999564i	$0.490603\pi$
$458$	22.2629	1.04028
$459$	4.10617	0.191659
$460$	1.21997	0.0568816
$461$	−25.7287	−1.19830	−0.599152	−	0.800635i	$-0.704495\pi$
$461$	−25.7287	−1.19830	−0.599152	+	0.800635i	$0.704495\pi$
$462$	−14.0835	−0.655224
$463$	−0.0405140	−0.00188285	−0.000941423	−	1.00000i	$-0.500300\pi$
$463$	−0.0405140	−0.00188285	−0.000941423		1.00000i	$0.500300\pi$
$464$	23.2059	1.07731
$465$	7.47845	0.346805
$466$	−11.0747	−0.513024
$467$	−13.7127	−0.634547	−0.317274	−	0.948334i	$-0.602767\pi$
$467$	−13.7127	−0.634547	−0.317274	+	0.948334i	$0.602767\pi$
$468$	4.83928	0.223696
$469$	−18.6512	−0.861233
$470$	−16.5901	−0.765244
$471$	22.4822	1.03592
$472$	2.51526	0.115774
$473$	−31.4499	−1.44607
$474$	−12.6505	−0.581058
$475$	−4.15330	−0.190566
$476$	19.8048	0.907752
$477$	−3.70069	−0.169443
$478$	3.62011	0.165580
$479$	−14.6382	−0.668838	−0.334419	−	0.942424i	$-0.608540\pi$
$479$	−14.6382	−0.668838	−0.334419	+	0.942424i	$0.608540\pi$
$480$	−7.98862	−0.364629
$481$	9.40949	0.429036
$482$	48.3978	2.20446
$483$	−0.963554	−0.0438432
$484$	1.59393	0.0724515
$485$	3.84446	0.174568
$486$	−2.11452	−0.0959164
$487$	−8.11686	−0.367810	−0.183905	−	0.982944i	$-0.558874\pi$
$487$	−8.11686	−0.367810	−0.183905	+	0.982944i	$0.558874\pi$
$488$	14.6210	0.661860
$489$	−13.9501	−0.630843
$490$	−6.74651	−0.304776
$491$	37.6948	1.70114	0.850571	−	0.525861i	$-0.176257\pi$
$491$	37.6948	1.70114	0.850571	+	0.525861i	$0.176257\pi$
$492$	0.898411	0.0405035
$493$	−33.6036	−1.51343
$494$	17.1981	0.773780
$495$	−3.41248	−0.153379
$496$	21.2061	0.952184
$497$	9.82035	0.440503
$498$	5.92058	0.265307
$499$	−15.7431	−0.704760	−0.352380	−	0.935857i	$-0.614627\pi$
$499$	−15.7431	−0.704760	−0.352380	+	0.935857i	$0.614627\pi$
$500$	−2.47118	−0.110514
$501$	9.86964	0.440943
$502$	17.5612	0.783797
$503$	−24.8738	−1.10907	−0.554534	−	0.832161i	$-0.687104\pi$
$503$	−24.8738	−1.10907	−0.554534	+	0.832161i	$0.687104\pi$
$504$	−1.94459	−0.0866187
$505$	10.4163	0.463519
$506$	3.56227	0.158362
$507$	−9.16510	−0.407037
$508$	−31.6427	−1.40392
$509$	37.7935	1.67517	0.837583	−	0.546310i	$-0.183968\pi$
$509$	37.7935	1.67517	0.837583	+	0.546310i	$0.183968\pi$
$510$	8.68256	0.384470
$511$	−26.1832	−1.15827
$512$	−28.3032	−1.25083
$513$	−4.15330	−0.183373
$514$	−15.0411	−0.663436
$515$	15.9001	0.700642
$516$	−22.7748	−1.00260
$517$	−26.7737	−1.17750
$518$	−19.8304	−0.871296
$519$	−3.63566	−0.159588
$520$	1.95107	0.0855603
$521$	−13.3600	−0.585312	−0.292656	−	0.956218i	$-0.594539\pi$
$521$	−13.3600	−0.585312	−0.292656	+	0.956218i	$0.594539\pi$
$522$	17.3045	0.757399
$523$	28.4512	1.24408	0.622042	−	0.782984i	$-0.286303\pi$
$523$	28.4512	1.24408	0.622042	+	0.782984i	$0.286303\pi$
$524$	35.3783	1.54551
$525$	1.95178	0.0851825
$526$	−7.39323	−0.322360
$527$	−30.7078	−1.33765
$528$	−9.67653	−0.421117
$529$	−22.7563	−0.989403
$530$	−7.82516	−0.339903
$531$	−2.52456	−0.109557
$532$	−20.0321	−0.868503
$533$	0.711947	0.0308378
$534$	22.7331	0.983759
$535$	3.98989	0.172498
$536$	9.52082	0.411237
$537$	21.2192	0.915676
$538$	−20.2723	−0.873999
$539$	−10.8877	−0.468969
$540$	−2.47118	−0.106343
$541$	44.0839	1.89532	0.947658	−	0.319287i	$-0.103443\pi$
$541$	44.0839	1.89532	0.947658	+	0.319287i	$0.103443\pi$
$542$	0.635607	0.0273017
$543$	−8.23754	−0.353507
$544$	32.8026	1.40640
$545$	−9.55855	−0.409443
$546$	−8.08198	−0.345877
$547$	3.11580	0.133222	0.0666109	−	0.997779i	$-0.478781\pi$
$547$	3.11580	0.133222	0.0666109	+	0.997779i	$0.478781\pi$
$548$	−6.14506	−0.262504
$549$	−14.6750	−0.626315
$550$	−7.21574	−0.307680
$551$	33.9893	1.44799
$552$	0.491862	0.0209350
$553$	11.6769	0.496553
$554$	−26.7472	−1.13638
$555$	−4.80496	−0.203959
$556$	13.1190	0.556370
$557$	10.4601	0.443208	0.221604	−	0.975137i	$-0.428871\pi$
$557$	10.4601	0.443208	0.221604	+	0.975137i	$0.428871\pi$
$558$	15.8133	0.669431
$559$	−18.0479	−0.763344
$560$	5.53452	0.233876
$561$	14.0122	0.591596
$562$	−33.2605	−1.40301
$563$	−38.9365	−1.64098	−0.820489	−	0.571662i	$-0.806299\pi$
$563$	−38.9365	−1.64098	−0.820489	+	0.571662i	$0.806299\pi$
$564$	−19.3884	−0.816399
$565$	−7.60478	−0.319935
$566$	21.5012	0.903764
$567$	1.95178	0.0819669
$568$	−5.01295	−0.210339
$569$	−16.6706	−0.698867	−0.349433	−	0.936961i	$-0.613626\pi$
$569$	−16.6706	−0.698867	−0.349433	+	0.936961i	$0.613626\pi$
$570$	−8.78222	−0.367847
$571$	−10.8424	−0.453740	−0.226870	−	0.973925i	$-0.572849\pi$
$571$	−10.8424	−0.453740	−0.226870	+	0.973925i	$0.572849\pi$
$572$	16.5140	0.690483
$573$	13.4596	0.562281
$574$	−1.50042	−0.0626262
$575$	−0.493681	−0.0205879
$576$	−11.2208	−0.467534
$577$	11.9705	0.498337	0.249169	−	0.968460i	$-0.419843\pi$
$577$	11.9705	0.498337	0.249169	+	0.968460i	$0.419843\pi$
$578$	0.294754	0.0122601
$579$	5.80206	0.241126
$580$	20.2233	0.839729
$581$	−5.46491	−0.226723
$582$	8.12918	0.336965
$583$	−12.6285	−0.523019
$584$	13.3656	0.553073
$585$	−1.95829	−0.0809653
$586$	13.5109	0.558130
$587$	20.3680	0.840676	0.420338	−	0.907368i	$-0.361912\pi$
$587$	20.3680	0.840676	0.420338	+	0.907368i	$0.361912\pi$
$588$	−7.88447	−0.325150
$589$	31.0602	1.27981
$590$	−5.33823	−0.219771
$591$	−21.8719	−0.899688
$592$	−13.6251	−0.559988
$593$	−5.00900	−0.205695	−0.102848	−	0.994697i	$-0.532795\pi$
$593$	−5.00900	−0.205695	−0.102848	+	0.994697i	$0.532795\pi$
$594$	−7.21574	−0.296065
$595$	−8.01432	−0.328555
$596$	28.4057	1.16354
$597$	23.1298	0.946641
$598$	2.04425	0.0835956
$599$	4.36343	0.178285	0.0891425	−	0.996019i	$-0.471587\pi$
$599$	4.36343	0.178285	0.0891425	+	0.996019i	$0.471587\pi$
$600$	−0.996316	−0.0406744
$601$	−13.3416	−0.544214	−0.272107	−	0.962267i	$-0.587720\pi$
$601$	−13.3416	−0.544214	−0.272107	+	0.962267i	$0.587720\pi$
$602$	38.0356	1.55022
$603$	−9.55602	−0.389151
$604$	8.71950	0.354791
$605$	−0.645009	−0.0262233
$606$	22.0254	0.894721
$607$	39.2130	1.59161	0.795803	−	0.605556i	$-0.207049\pi$
$607$	39.2130	1.59161	0.795803	+	0.605556i	$0.207049\pi$
$608$	−33.1791	−1.34559
$609$	−15.9727	−0.647247
$610$	−31.0306	−1.25639
$611$	−15.3644	−0.621576
$612$	10.1471	0.410171
$613$	21.1847	0.855644	0.427822	−	0.903863i	$-0.359281\pi$
$613$	21.1847	0.855644	0.427822	+	0.903863i	$0.359281\pi$
$614$	−44.8056	−1.80821
$615$	−0.363555	−0.0146600
$616$	−6.63586	−0.267366
$617$	−6.32059	−0.254457	−0.127229	−	0.991873i	$-0.540608\pi$
$617$	−6.32059	−0.254457	−0.127229	+	0.991873i	$0.540608\pi$
$618$	33.6210	1.35244
$619$	−22.2333	−0.893630	−0.446815	−	0.894626i	$-0.647442\pi$
$619$	−22.2333	−0.893630	−0.446815	+	0.894626i	$0.647442\pi$
$620$	18.4806	0.742198
$621$	−0.493681	−0.0198107
$622$	−0.128008	−0.00513265
$623$	−20.9835	−0.840687
$624$	−5.55299	−0.222297
$625$	1.00000	0.0400000
$626$	21.0071	0.839614
$627$	−14.1730	−0.566017
$628$	55.5575	2.21698
$629$	19.7299	0.786685
$630$	4.12706	0.164426
$631$	−12.0794	−0.480872	−0.240436	−	0.970665i	$-0.577290\pi$
$631$	−12.0794	−0.480872	−0.240436	+	0.970665i	$0.577290\pi$
$632$	−5.96067	−0.237103
$633$	−19.8208	−0.787806
$634$	−6.46512	−0.256763
$635$	12.8047	0.508138
$636$	−9.14506	−0.362625
$637$	−6.24806	−0.247557
$638$	59.0513	2.33786
$639$	5.03149	0.199043
$640$	−7.74933	−0.306319
$641$	−7.35993	−0.290700	−0.145350	−	0.989380i	$-0.546431\pi$
$641$	−7.35993	−0.290700	−0.145350	+	0.989380i	$0.546431\pi$
$642$	8.43670	0.332970
$643$	26.6180	1.04971	0.524856	−	0.851191i	$-0.324119\pi$
$643$	26.6180	1.04971	0.524856	+	0.851191i	$0.324119\pi$
$644$	−2.38112	−0.0938291
$645$	9.21615	0.362886
$646$	36.0612	1.41881
$647$	30.6644	1.20554	0.602771	−	0.797914i	$-0.294063\pi$
$647$	30.6644	1.20554	0.602771	+	0.797914i	$0.294063\pi$
$648$	−0.996316	−0.0391390
$649$	−8.61501	−0.338169
$650$	−4.14083	−0.162417
$651$	−14.5963	−0.572073
$652$	−34.4731	−1.35007
$653$	−31.0219	−1.21398	−0.606990	−	0.794709i	$-0.707623\pi$
$653$	−31.0219	−1.21398	−0.606990	+	0.794709i	$0.707623\pi$
$654$	−20.2117	−0.790340
$655$	−14.3164	−0.559387
$656$	−1.03091	−0.0402503
$657$	−13.4150	−0.523371
$658$	32.3802	1.26231
$659$	−28.3331	−1.10370	−0.551851	−	0.833943i	$-0.686078\pi$
$659$	−28.3331	−1.10370	−0.551851	+	0.833943i	$0.686078\pi$
$660$	−8.43285	−0.328248
$661$	−6.70406	−0.260758	−0.130379	−	0.991464i	$-0.541619\pi$
$661$	−6.70406	−0.260758	−0.130379	+	0.991464i	$0.541619\pi$
$662$	−16.6184	−0.645892
$663$	8.04106	0.312289
$664$	2.78965	0.108259
$665$	8.10631	0.314349
$666$	−10.1602	−0.393698
$667$	4.04013	0.156434
$668$	24.3896	0.943664
$669$	−9.82070	−0.379690
$670$	−20.2064	−0.780640
$671$	−50.0782	−1.93325
$672$	15.5920	0.601475
$673$	7.23012	0.278701	0.139350	−	0.990243i	$-0.455499\pi$
$673$	7.23012	0.278701	0.139350	+	0.990243i	$0.455499\pi$
$674$	−29.0312	−1.11824
$675$	1.00000	0.0384900
$676$	−22.6486	−0.871100
$677$	32.5956	1.25275	0.626376	−	0.779521i	$-0.284537\pi$
$677$	32.5956	1.25275	0.626376	+	0.779521i	$0.284537\pi$
$678$	−16.0804	−0.617565
$679$	−7.50353	−0.287959
$680$	4.09104	0.156884
$681$	9.65893	0.370131
$682$	53.9626	2.06633
$683$	−22.3591	−0.855547	−0.427774	−	0.903886i	$-0.640702\pi$
$683$	−22.3591	−0.855547	−0.427774	+	0.903886i	$0.640702\pi$
$684$	−10.2635	−0.392436
$685$	2.48669	0.0950116
$686$	42.0571	1.60575
$687$	−10.5286	−0.401692
$688$	26.1336	0.996335
$689$	−7.24701	−0.276089
$690$	−1.04390	−0.0397404
$691$	−0.134280	−0.00510826	−0.00255413	−	0.999997i	$-0.500813\pi$
$691$	−0.134280	−0.00510826	−0.00255413	+	0.999997i	$0.500813\pi$
$692$	−8.98437	−0.341535
$693$	6.66039	0.253007
$694$	−25.0776	−0.951933
$695$	−5.30880	−0.201374
$696$	8.15353	0.309059
$697$	1.49282	0.0565446
$698$	−41.1398	−1.55716
$699$	5.23745	0.198098
$700$	4.82319	0.182299
$701$	−13.5042	−0.510045	−0.255022	−	0.966935i	$-0.582083\pi$
$701$	−13.5042	−0.510045	−0.255022	+	0.966935i	$0.582083\pi$
$702$	−4.14083	−0.156286
$703$	−19.9564	−0.752670
$704$	−38.2908	−1.44314
$705$	7.84581	0.295490
$706$	42.0619	1.58302
$707$	−20.3303	−0.764598
$708$	−6.23864	−0.234463
$709$	28.4896	1.06995	0.534976	−	0.844868i	$-0.320321\pi$
$709$	28.4896	1.06995	0.534976	+	0.844868i	$0.320321\pi$
$710$	10.6392	0.399281
$711$	5.98271	0.224369
$712$	10.7114	0.401426
$713$	3.69197	0.138265
$714$	−16.9464	−0.634203
$715$	−6.68262	−0.249916
$716$	52.4364	1.95964
$717$	−1.71203	−0.0639369
$718$	−48.8770	−1.82407
$719$	21.7472	0.811035	0.405518	−	0.914087i	$-0.367091\pi$
$719$	21.7472	0.811035	0.405518	+	0.914087i	$0.367091\pi$
$720$	2.83563	0.105678
$721$	−31.0334	−1.15575
$722$	3.70065	0.137724
$723$	−22.8884	−0.851227
$724$	−20.3564	−0.756541
$725$	−8.18368	−0.303934
$726$	−1.36388	−0.0506184
$727$	−31.2569	−1.15925	−0.579626	−	0.814882i	$-0.696801\pi$
$727$	−31.2569	−1.15925	−0.579626	+	0.814882i	$0.696801\pi$
$728$	−3.80806	−0.141136
$729$	1.00000	0.0370370
$730$	−28.3663	−1.04988
$731$	−37.8430	−1.39968
$732$	−36.2646	−1.34038
$733$	25.0370	0.924762	0.462381	−	0.886681i	$-0.346995\pi$
$733$	25.0370	0.924762	0.462381	+	0.886681i	$0.346995\pi$
$734$	−77.1667	−2.84827
$735$	3.19057	0.117686
$736$	−3.94383	−0.145371
$737$	−32.6097	−1.20119
$738$	−0.768744	−0.0282979
$739$	−33.9104	−1.24741	−0.623707	−	0.781659i	$-0.714374\pi$
$739$	−33.9104	−1.24741	−0.623707	+	0.781659i	$0.714374\pi$
$740$	−11.8739	−0.436493
$741$	−8.13336	−0.298786
$742$	15.2730	0.560688
$743$	−3.74004	−0.137209	−0.0686044	−	0.997644i	$-0.521855\pi$
$743$	−3.74004	−0.137209	−0.0686044	+	0.997644i	$0.521855\pi$
$744$	7.45090	0.273163
$745$	−11.4948	−0.421136
$746$	−69.7619	−2.55417
$747$	−2.79997	−0.102445
$748$	34.6267	1.26608
$749$	−7.78738	−0.284545
$750$	2.11452	0.0772112
$751$	−27.9897	−1.02136	−0.510679	−	0.859771i	$-0.670606\pi$
$751$	−27.9897	−1.02136	−0.510679	+	0.859771i	$0.670606\pi$
$752$	22.2478	0.811295
$753$	−8.30509	−0.302654
$754$	33.8873	1.23410
$755$	−3.52848	−0.128414
$756$	4.82319	0.175418
$757$	31.2126	1.13444	0.567220	−	0.823566i	$-0.308019\pi$
$757$	31.2126	1.13444	0.567220	+	0.823566i	$0.308019\pi$
$758$	−54.7918	−1.99013
$759$	−1.68467	−0.0611498
$760$	−4.13800	−0.150101
$761$	42.7652	1.55024	0.775120	−	0.631815i	$-0.217690\pi$
$761$	42.7652	1.55024	0.775120	+	0.631815i	$0.217690\pi$
$762$	27.0757	0.980850
$763$	18.6561	0.675398
$764$	33.2610	1.20334
$765$	−4.10617	−0.148459
$766$	7.11589	0.257108
$767$	−4.94382	−0.178511
$768$	6.05552	0.218510
$769$	2.76910	0.0998564	0.0499282	−	0.998753i	$-0.484101\pi$
$769$	2.76910	0.0998564	0.0499282	+	0.998753i	$0.484101\pi$
$770$	14.0835	0.507535
$771$	7.11327	0.256178
$772$	14.3379	0.516034
$773$	−34.5040	−1.24102	−0.620511	−	0.784198i	$-0.713075\pi$
$773$	−34.5040	−1.24102	−0.620511	+	0.784198i	$0.713075\pi$
$774$	19.4877	0.700471
$775$	−7.47845	−0.268634
$776$	3.83030	0.137500
$777$	9.37820	0.336441
$778$	−60.5292	−2.17008
$779$	−1.50995	−0.0540997
$780$	−4.83928	−0.173274
$781$	17.1699	0.614386
$782$	4.28641	0.153282
$783$	−8.18368	−0.292461
$784$	9.04728	0.323117
$785$	−22.4822	−0.802423
$786$	−30.2722	−1.07977
$787$	−28.6087	−1.01979	−0.509895	−	0.860237i	$-0.670316\pi$
$787$	−28.6087	−1.01979	−0.509895	+	0.860237i	$0.670316\pi$
$788$	−54.0493	−1.92543
$789$	3.49641	0.124476
$790$	12.6505	0.450086
$791$	14.8428	0.527750
$792$	−3.39991	−0.120810
$793$	−28.7380	−1.02051
$794$	77.2759	2.74242
$795$	3.70069	0.131250
$796$	57.1579	2.02591
$797$	−31.8009	−1.12645	−0.563223	−	0.826305i	$-0.690439\pi$
$797$	−31.8009	−1.12645	−0.563223	+	0.826305i	$0.690439\pi$
$798$	17.1409	0.606782
$799$	−32.2162	−1.13973
$800$	7.98862	0.282440
$801$	−10.7510	−0.379867
$802$	−2.11452	−0.0746662
$803$	−45.7785	−1.61549
$804$	−23.6146	−0.832824
$805$	0.963554	0.0339608
$806$	30.9670	1.09077
$807$	9.58718	0.337485
$808$	10.3779	0.365094
$809$	54.4169	1.91320	0.956598	−	0.291412i	$-0.0941250\pi$
$809$	54.4169	1.91320	0.956598	+	0.291412i	$0.0941250\pi$
$810$	2.11452	0.0742965
$811$	−1.87611	−0.0658792	−0.0329396	−	0.999457i	$-0.510487\pi$
$811$	−1.87611	−0.0658792	−0.0329396	+	0.999457i	$0.510487\pi$
$812$	−39.4714	−1.38518
$813$	−0.300592	−0.0105422
$814$	−34.6713	−1.21523
$815$	13.9501	0.488649
$816$	−11.6436	−0.407607
$817$	38.2774	1.33916
$818$	−67.2901	−2.35274
$819$	3.82214	0.133556
$820$	−0.898411	−0.0313739
$821$	3.25705	0.113672	0.0568359	−	0.998384i	$-0.481899\pi$
$821$	3.25705	0.113672	0.0568359	+	0.998384i	$0.481899\pi$
$822$	5.25815	0.183399
$823$	−26.0229	−0.907102	−0.453551	−	0.891230i	$-0.649843\pi$
$823$	−26.0229	−0.907102	−0.453551	+	0.891230i	$0.649843\pi$
$824$	15.8415	0.551865
$825$	3.41248	0.118807
$826$	10.4190	0.362524
$827$	3.24617	0.112881	0.0564403	−	0.998406i	$-0.482025\pi$
$827$	3.24617	0.112881	0.0564403	+	0.998406i	$0.482025\pi$
$828$	−1.21997	−0.0423970
$829$	−30.5157	−1.05985	−0.529927	−	0.848043i	$-0.677781\pi$
$829$	−30.5157	−1.05985	−0.529927	+	0.848043i	$0.677781\pi$
$830$	−5.92058	−0.205506
$831$	12.6493	0.438801
$832$	−21.9736	−0.761797
$833$	−13.1010	−0.453923
$834$	−11.2255	−0.388709
$835$	−9.86964	−0.341553
$836$	−35.0241	−1.21133
$837$	−7.47845	−0.258493
$838$	42.2431	1.45926
$839$	−6.54644	−0.226008	−0.113004	−	0.993595i	$-0.536047\pi$
$839$	−6.54644	−0.226008	−0.113004	+	0.993595i	$0.536047\pi$
$840$	1.94459	0.0670946
$841$	37.9726	1.30940
$842$	−25.0987	−0.864958
$843$	15.7296	0.541757
$844$	−48.9808	−1.68599
$845$	9.16510	0.315289
$846$	16.5901	0.570379
$847$	1.25891	0.0432568
$848$	10.4938	0.360358
$849$	−10.1684	−0.348978
$850$	−8.68256	−0.297809
$851$	−2.37211	−0.0813150
$852$	12.4337	0.425972
$853$	−45.2096	−1.54795	−0.773974	−	0.633217i	$-0.781734\pi$
$853$	−45.2096	−1.54795	−0.773974	+	0.633217i	$0.781734\pi$
$854$	60.5648	2.07248
$855$	4.15330	0.142040
$856$	3.97520	0.135869
$857$	−42.2577	−1.44350	−0.721749	−	0.692155i	$-0.756661\pi$
$857$	−42.2577	−1.44350	−0.721749	+	0.692155i	$0.756661\pi$
$858$	−14.1305	−0.482408
$859$	−7.35830	−0.251062	−0.125531	−	0.992090i	$-0.540063\pi$
$859$	−7.35830	−0.251062	−0.125531	+	0.992090i	$0.540063\pi$
$860$	22.7748	0.776613
$861$	0.709579	0.0241824
$862$	42.0392	1.43186
$863$	10.6197	0.361498	0.180749	−	0.983529i	$-0.442148\pi$
$863$	10.6197	0.361498	0.180749	+	0.983529i	$0.442148\pi$
$864$	7.98862	0.271778
$865$	3.63566	0.123616
$866$	61.2597	2.08169
$867$	−0.139395	−0.00473412
$868$	−36.0700	−1.22429
$869$	20.4159	0.692561
$870$	−17.3045	−0.586678
$871$	−18.7135	−0.634081
$872$	−9.52333	−0.322501
$873$	−3.84446	−0.130115
$874$	−4.33561	−0.146654
$875$	−1.95178	−0.0659821
$876$	−33.1510	−1.12007
$877$	−8.07124	−0.272546	−0.136273	−	0.990671i	$-0.543513\pi$
$877$	−8.07124	−0.272546	−0.136273	+	0.990671i	$0.543513\pi$
$878$	−1.50801	−0.0508929
$879$	−6.38960	−0.215516
$880$	9.67653	0.326196
$881$	4.27297	0.143960	0.0719800	−	0.997406i	$-0.477068\pi$
$881$	4.27297	0.143960	0.0719800	+	0.997406i	$0.477068\pi$
$882$	6.74651	0.227167
$883$	−0.137106	−0.00461397	−0.00230699	−	0.999997i	$-0.500734\pi$
$883$	−0.137106	−0.00461397	−0.00230699	+	0.999997i	$0.500734\pi$
$884$	19.8709	0.668331
$885$	2.52456	0.0848622
$886$	6.13042	0.205956
$887$	−38.9342	−1.30728	−0.653641	−	0.756805i	$-0.726759\pi$
$887$	−38.9342	−1.30728	−0.653641	+	0.756805i	$0.726759\pi$
$888$	−4.78725	−0.160650
$889$	−24.9919	−0.838201
$890$	−22.7331	−0.762017
$891$	3.41248	0.114322
$892$	−24.2687	−0.812576
$893$	32.5860	1.09045
$894$	−24.3059	−0.812911
$895$	−21.2192	−0.709279
$896$	15.1250	0.505290
$897$	−0.966770	−0.0322795
$898$	25.5407	0.852305
$899$	61.2013	2.04118
$900$	2.47118	0.0823726
$901$	−15.1956	−0.506240
$902$	−2.62332	−0.0873471
$903$	−17.9879	−0.598599
$904$	−7.57676	−0.251999
$905$	8.23754	0.273825
$906$	−7.46102	−0.247876
$907$	−51.7593	−1.71864	−0.859319	−	0.511439i	$-0.829113\pi$
$907$	−51.7593	−1.71864	−0.859319	+	0.511439i	$0.829113\pi$
$908$	23.8689	0.792118
$909$	−10.4163	−0.345487
$910$	8.08198	0.267915
$911$	−20.7915	−0.688855	−0.344427	−	0.938813i	$-0.611927\pi$
$911$	−20.7915	−0.688855	−0.344427	+	0.938813i	$0.611927\pi$
$912$	11.7772	0.389983
$913$	−9.55483	−0.316219
$914$	−2.66854	−0.0882675
$915$	14.6750	0.485142
$916$	−26.0181	−0.859662
$917$	27.9424	0.922738
$918$	−8.68256	−0.286567
$919$	−9.26248	−0.305541	−0.152771	−	0.988262i	$-0.548820\pi$
$919$	−9.26248	−0.305541	−0.152771	+	0.988262i	$0.548820\pi$
$920$	−0.491862	−0.0162162
$921$	21.1895	0.698219
$922$	54.4037	1.79169
$923$	9.85312	0.324319
$924$	16.4590	0.541462
$925$	4.80496	0.157986
$926$	0.0856675	0.00281521
$927$	−15.9001	−0.522228
$928$	−65.3763	−2.14608
$929$	−49.9760	−1.63966	−0.819830	−	0.572607i	$-0.805932\pi$
$929$	−49.9760	−1.63966	−0.819830	+	0.572607i	$0.805932\pi$
$930$	−15.8133	−0.518539
$931$	13.2514	0.434297
$932$	12.9427	0.423951
$933$	0.0605377	0.00198191
$934$	28.9957	0.948768
$935$	−14.0122	−0.458248
$936$	−1.95107	−0.0637729
$937$	−16.7743	−0.547993	−0.273997	−	0.961731i	$-0.588346\pi$
$937$	−16.7743	−0.547993	−0.273997	+	0.961731i	$0.588346\pi$
$938$	39.4383	1.28771
$939$	−9.93472	−0.324207
$940$	19.3884	0.632380
$941$	22.1879	0.723306	0.361653	−	0.932313i	$-0.382213\pi$
$941$	22.1879	0.723306	0.361653	+	0.932313i	$0.382213\pi$
$942$	−47.5389	−1.54890
$943$	−0.179480	−0.00584468
$944$	7.15873	0.232997
$945$	−1.95178	−0.0634913
$946$	66.5013	2.16215
$947$	15.9872	0.519513	0.259757	−	0.965674i	$-0.416358\pi$
$947$	15.9872	0.519513	0.259757	+	0.965674i	$0.416358\pi$
$948$	14.7843	0.480173
$949$	−26.2705	−0.852777
$950$	8.78222	0.284933
$951$	3.05749	0.0991460
$952$	−7.98479	−0.258789
$953$	−37.4704	−1.21378	−0.606892	−	0.794784i	$-0.707584\pi$
$953$	−37.4704	−1.21378	−0.606892	+	0.794784i	$0.707584\pi$
$954$	7.82516	0.253349
$955$	−13.4596	−0.435541
$956$	−4.23073	−0.136832
$957$	−27.9266	−0.902740
$958$	30.9528	1.00004
$959$	−4.85347	−0.156727
$960$	11.2208	0.362150
$961$	24.9272	0.804104
$962$	−19.8965	−0.641490
$963$	−3.98989	−0.128573
$964$	−56.5612	−1.82171
$965$	−5.80206	−0.186775
$966$	2.03745	0.0655539
$967$	−34.7117	−1.11625	−0.558127	−	0.829756i	$-0.688480\pi$
$967$	−34.7117	−1.11625	−0.558127	+	0.829756i	$0.688480\pi$
$968$	−0.642633	−0.0206550
$969$	−17.0541	−0.547858
$970$	−8.12918	−0.261012
$971$	29.0205	0.931312	0.465656	−	0.884966i	$-0.345818\pi$
$971$	29.0205	0.931312	0.465656	+	0.884966i	$0.345818\pi$
$972$	2.47118	0.0792631
$973$	10.3616	0.332177
$974$	17.1632	0.549946
$975$	1.95829	0.0627155
$976$	41.6130	1.33200
$977$	11.9889	0.383560	0.191780	−	0.981438i	$-0.438574\pi$
$977$	11.9889	0.383560	0.191780	+	0.981438i	$0.438574\pi$
$978$	29.4976	0.943230
$979$	−36.6875	−1.17254
$980$	7.88447	0.251860
$981$	9.55855	0.305181
$982$	−79.7062	−2.54353
$983$	32.6702	1.04202	0.521009	−	0.853551i	$-0.325556\pi$
$983$	32.6702	1.04202	0.521009	+	0.853551i	$0.325556\pi$
$984$	−0.362216	−0.0115470
$985$	21.8719	0.696895
$986$	71.0553	2.26286
$987$	−15.3133	−0.487427
$988$	−20.0990	−0.639434
$989$	4.54984	0.144676
$990$	7.21574	0.229331
$991$	60.9047	1.93470	0.967351	−	0.253440i	$-0.0815622\pi$
$991$	60.9047	1.93470	0.967351	+	0.253440i	$0.0815622\pi$
$992$	−59.7425	−1.89683
$993$	7.85919	0.249404
$994$	−20.7653	−0.658635
$995$	−23.1298	−0.733265
$996$	−6.91922	−0.219244
$997$	−20.7594	−0.657455	−0.328728	−	0.944425i	$-0.606620\pi$
$997$	−20.7594	−0.657455	−0.328728	+	0.944425i	$0.606620\pi$
$998$	33.2891	1.05375
$999$	4.80496	0.152022

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6015.2.a.c.1.4	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6015.2.a.c.1.4	✓	28	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)

\(f(q)\)	\(=\)	\(q-2.11452 q^{2} +1.00000 q^{3} +2.47118 q^{4} -1.00000 q^{5} -2.11452 q^{6} +1.95178 q^{7} -0.996316 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.11452 q^{2} +1.00000 q^{3} +2.47118 q^{4} -1.00000 q^{5} -2.11452 q^{6} +1.95178 q^{7} -0.996316 q^{8} +1.00000 q^{9} +2.11452 q^{10} +3.41248 q^{11} +2.47118 q^{12} +1.95829 q^{13} -4.12706 q^{14} -1.00000 q^{15} -2.83563 q^{16} +4.10617 q^{17} -2.11452 q^{18} -4.15330 q^{19} -2.47118 q^{20} +1.95178 q^{21} -7.21574 q^{22} -0.493681 q^{23} -0.996316 q^{24} +1.00000 q^{25} -4.14083 q^{26} +1.00000 q^{27} +4.82319 q^{28} -8.18368 q^{29} +2.11452 q^{30} -7.47845 q^{31} +7.98862 q^{32} +3.41248 q^{33} -8.68256 q^{34} -1.95178 q^{35} +2.47118 q^{36} +4.80496 q^{37} +8.78222 q^{38} +1.95829 q^{39} +0.996316 q^{40} +0.363555 q^{41} -4.12706 q^{42} -9.21615 q^{43} +8.43285 q^{44} -1.00000 q^{45} +1.04390 q^{46} -7.84581 q^{47} -2.83563 q^{48} -3.19057 q^{49} -2.11452 q^{50} +4.10617 q^{51} +4.83928 q^{52} -3.70069 q^{53} -2.11452 q^{54} -3.41248 q^{55} -1.94459 q^{56} -4.15330 q^{57} +17.3045 q^{58} -2.52456 q^{59} -2.47118 q^{60} -14.6750 q^{61} +15.8133 q^{62} +1.95178 q^{63} -11.2208 q^{64} -1.95829 q^{65} -7.21574 q^{66} -9.55602 q^{67} +10.1471 q^{68} -0.493681 q^{69} +4.12706 q^{70} +5.03149 q^{71} -0.996316 q^{72} -13.4150 q^{73} -10.1602 q^{74} +1.00000 q^{75} -10.2635 q^{76} +6.66039 q^{77} -4.14083 q^{78} +5.98271 q^{79} +2.83563 q^{80} +1.00000 q^{81} -0.768744 q^{82} -2.79997 q^{83} +4.82319 q^{84} -4.10617 q^{85} +19.4877 q^{86} -8.18368 q^{87} -3.39991 q^{88} -10.7510 q^{89} +2.11452 q^{90} +3.82214 q^{91} -1.21997 q^{92} -7.47845 q^{93} +16.5901 q^{94} +4.15330 q^{95} +7.98862 q^{96} -3.84446 q^{97} +6.74651 q^{98} +3.41248 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - q^{2} + 28 q^{3} + 21 q^{4} - 28 q^{5} - q^{6} - 20 q^{7} + 28 q^{9}+O(q^{10}) \) 28 * q - q^2 + 28 * q^3 + 21 * q^4 - 28 * q^5 - q^6 - 20 * q^7 + 28 * q^9	\( 28 q - q^{2} + 28 q^{3} + 21 q^{4} - 28 q^{5} - q^{6} - 20 q^{7} + 28 q^{9} + q^{10} - q^{11} + 21 q^{12} - 18 q^{13} - 4 q^{14} - 28 q^{15} - q^{16} - 28 q^{17} - q^{18} - 19 q^{19} - 21 q^{20} - 20 q^{21} - 35 q^{22} + 2 q^{23} + 28 q^{25} - 20 q^{26} + 28 q^{27} - 54 q^{28} + 9 q^{29} + q^{30} - 19 q^{31} - 6 q^{32} - q^{33} - 16 q^{34} + 20 q^{35} + 21 q^{36} - 32 q^{37} - 2 q^{38} - 18 q^{39} - 27 q^{41} - 4 q^{42} - 77 q^{43} + q^{44} - 28 q^{45} - 19 q^{46} + 10 q^{47} - q^{48} - 4 q^{49} - q^{50} - 28 q^{51} - 34 q^{52} - 21 q^{53} - q^{54} + q^{55} - 9 q^{56} - 19 q^{57} - 46 q^{58} - 7 q^{59} - 21 q^{60} - 31 q^{61} - 7 q^{62} - 20 q^{63} - 46 q^{64} + 18 q^{65} - 35 q^{66} - 50 q^{67} - 68 q^{68} + 2 q^{69} + 4 q^{70} - 4 q^{71} - 87 q^{73} + 4 q^{74} + 28 q^{75} - 40 q^{76} - 8 q^{77} - 20 q^{78} - 65 q^{79} + q^{80} + 28 q^{81} - 41 q^{82} + 13 q^{83} - 54 q^{84} + 28 q^{85} - 17 q^{86} + 9 q^{87} - 117 q^{88} - 33 q^{89} + q^{90} - 33 q^{91} + 3 q^{92} - 19 q^{93} - 60 q^{94} + 19 q^{95} - 6 q^{96} - 75 q^{97} - 18 q^{98} - q^{99}+O(q^{100}) \) 28 * q - q^2 + 28 * q^3 + 21 * q^4 - 28 * q^5 - q^6 - 20 * q^7 + 28 * q^9 + q^10 - q^11 + 21 * q^12 - 18 * q^13 - 4 * q^14 - 28 * q^15 - q^16 - 28 * q^17 - q^18 - 19 * q^19 - 21 * q^20 - 20 * q^21 - 35 * q^22 + 2 * q^23 + 28 * q^25 - 20 * q^26 + 28 * q^27 - 54 * q^28 + 9 * q^29 + q^30 - 19 * q^31 - 6 * q^32 - q^33 - 16 * q^34 + 20 * q^35 + 21 * q^36 - 32 * q^37 - 2 * q^38 - 18 * q^39 - 27 * q^41 - 4 * q^42 - 77 * q^43 + q^44 - 28 * q^45 - 19 * q^46 + 10 * q^47 - q^48 - 4 * q^49 - q^50 - 28 * q^51 - 34 * q^52 - 21 * q^53 - q^54 + q^55 - 9 * q^56 - 19 * q^57 - 46 * q^58 - 7 * q^59 - 21 * q^60 - 31 * q^61 - 7 * q^62 - 20 * q^63 - 46 * q^64 + 18 * q^65 - 35 * q^66 - 50 * q^67 - 68 * q^68 + 2 * q^69 + 4 * q^70 - 4 * q^71 - 87 * q^73 + 4 * q^74 + 28 * q^75 - 40 * q^76 - 8 * q^77 - 20 * q^78 - 65 * q^79 + q^80 + 28 * q^81 - 41 * q^82 + 13 * q^83 - 54 * q^84 + 28 * q^85 - 17 * q^86 + 9 * q^87 - 117 * q^88 - 33 * q^89 + q^90 - 33 * q^91 + 3 * q^92 - 19 * q^93 - 60 * q^94 + 19 * q^95 - 6 * q^96 - 75 * q^97 - 18 * q^98 - q^99

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