LMFDB - Embedded newform 1155.2.a.v.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1155,2,Mod(1,1155)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1155, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("1155.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1155 = 3 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1155.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:	$9.22272143346$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.7232.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 5x^{2} + 4x + 4 $ x^4 - 2x^3 - 5x^2 + 4*x + 4
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$3.06644$ of defining polynomial
Character	$\chi$	$=$	1155.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.65222 q^{2} -1.00000 q^{3} +0.729840 q^{4} +1.00000 q^{5} -1.65222 q^{6} +1.00000 q^{7} -2.09859 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.65222 q^{2} -1.00000 q^{3} +0.729840 q^{4} +1.00000 q^{5} -1.65222 q^{6} +1.00000 q^{7} -2.09859 q^{8} +1.00000 q^{9} +1.65222 q^{10} +1.00000 q^{11} -0.729840 q^{12} +5.75081 q^{13} +1.65222 q^{14} -1.00000 q^{15} -4.92701 q^{16} -1.57461 q^{17} +1.65222 q^{18} -2.27016 q^{19} +0.729840 q^{20} -1.00000 q^{21} +1.65222 q^{22} +7.38669 q^{23} +2.09859 q^{24} +1.00000 q^{25} +9.50162 q^{26} -1.00000 q^{27} +0.729840 q^{28} +9.32541 q^{29} -1.65222 q^{30} +5.05526 q^{31} -3.94335 q^{32} -1.00000 q^{33} -2.60160 q^{34} +1.00000 q^{35} +0.729840 q^{36} -2.51494 q^{37} -3.75081 q^{38} -5.75081 q^{39} -2.09859 q^{40} +6.29113 q^{41} -1.65222 q^{42} -5.83306 q^{43} +0.729840 q^{44} +1.00000 q^{45} +12.2045 q^{46} -8.86734 q^{47} +4.92701 q^{48} +1.00000 q^{49} +1.65222 q^{50} +1.57461 q^{51} +4.19717 q^{52} +5.03429 q^{53} -1.65222 q^{54} +1.00000 q^{55} -2.09859 q^{56} +2.27016 q^{57} +15.4077 q^{58} -8.08954 q^{59} -0.729840 q^{60} -1.03429 q^{61} +8.35241 q^{62} +1.00000 q^{63} +3.33873 q^{64} +5.75081 q^{65} -1.65222 q^{66} +14.4629 q^{67} -1.14921 q^{68} -7.38669 q^{69} +1.65222 q^{70} +9.59557 q^{71} -2.09859 q^{72} +7.30445 q^{73} -4.15524 q^{74} -1.00000 q^{75} -1.65685 q^{76} +1.00000 q^{77} -9.50162 q^{78} -10.3597 q^{79} -4.92701 q^{80} +1.00000 q^{81} +10.3943 q^{82} +6.08225 q^{83} -0.729840 q^{84} -1.57461 q^{85} -9.63751 q^{86} -9.32541 q^{87} -2.09859 q^{88} -14.9823 q^{89} +1.65222 q^{90} +5.75081 q^{91} +5.39111 q^{92} -5.05526 q^{93} -14.6508 q^{94} -2.27016 q^{95} +3.94335 q^{96} -7.48065 q^{97} +1.65222 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 4 q^{3} + 6 q^{4} + 4 q^{5} - 2 q^{6} + 4 q^{7} + 6 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 - 4 * q^3 + 6 * q^4 + 4 * q^5 - 2 * q^6 + 4 * q^7 + 6 * q^8 + 4 * q^9	\( 4 q + 2 q^{2} - 4 q^{3} + 6 q^{4} + 4 q^{5} - 2 q^{6} + 4 q^{7} + 6 q^{8} + 4 q^{9} + 2 q^{10} + 4 q^{11} - 6 q^{12} + 4 q^{13} + 2 q^{14} - 4 q^{15} + 6 q^{16} + 6 q^{17} + 2 q^{18} - 6 q^{19} + 6 q^{20} - 4 q^{21} + 2 q^{22} + 10 q^{23} - 6 q^{24} + 4 q^{25} - 4 q^{27} + 6 q^{28} + 6 q^{29} - 2 q^{30} - 8 q^{31} + 14 q^{32} - 4 q^{33} - 16 q^{34} + 4 q^{35} + 6 q^{36} + 12 q^{37} + 4 q^{38} - 4 q^{39} + 6 q^{40} - 2 q^{42} + 6 q^{43} + 6 q^{44} + 4 q^{45} - 4 q^{46} - 6 q^{48} + 4 q^{49} + 2 q^{50} - 6 q^{51} - 12 q^{52} + 14 q^{53} - 2 q^{54} + 4 q^{55} + 6 q^{56} + 6 q^{57} + 20 q^{58} + 2 q^{59} - 6 q^{60} + 2 q^{61} + 20 q^{62} + 4 q^{63} - 2 q^{64} + 4 q^{65} - 2 q^{66} - 12 q^{67} + 20 q^{68} - 10 q^{69} + 2 q^{70} + 4 q^{71} + 6 q^{72} + 20 q^{73} - 32 q^{74} - 4 q^{75} + 16 q^{76} + 4 q^{77} - 4 q^{79} + 6 q^{80} + 4 q^{81} - 16 q^{82} + 14 q^{83} - 6 q^{84} + 6 q^{85} + 40 q^{86} - 6 q^{87} + 6 q^{88} - 6 q^{89} + 2 q^{90} + 4 q^{91} + 40 q^{92} + 8 q^{93} + 4 q^{94} - 6 q^{95} - 14 q^{96} - 14 q^{97} + 2 q^{98} + 4 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - 4 * q^3 + 6 * q^4 + 4 * q^5 - 2 * q^6 + 4 * q^7 + 6 * q^8 + 4 * q^9 + 2 * q^10 + 4 * q^11 - 6 * q^12 + 4 * q^13 + 2 * q^14 - 4 * q^15 + 6 * q^16 + 6 * q^17 + 2 * q^18 - 6 * q^19 + 6 * q^20 - 4 * q^21 + 2 * q^22 + 10 * q^23 - 6 * q^24 + 4 * q^25 - 4 * q^27 + 6 * q^28 + 6 * q^29 - 2 * q^30 - 8 * q^31 + 14 * q^32 - 4 * q^33 - 16 * q^34 + 4 * q^35 + 6 * q^36 + 12 * q^37 + 4 * q^38 - 4 * q^39 + 6 * q^40 - 2 * q^42 + 6 * q^43 + 6 * q^44 + 4 * q^45 - 4 * q^46 - 6 * q^48 + 4 * q^49 + 2 * q^50 - 6 * q^51 - 12 * q^52 + 14 * q^53 - 2 * q^54 + 4 * q^55 + 6 * q^56 + 6 * q^57 + 20 * q^58 + 2 * q^59 - 6 * q^60 + 2 * q^61 + 20 * q^62 + 4 * q^63 - 2 * q^64 + 4 * q^65 - 2 * q^66 - 12 * q^67 + 20 * q^68 - 10 * q^69 + 2 * q^70 + 4 * q^71 + 6 * q^72 + 20 * q^73 - 32 * q^74 - 4 * q^75 + 16 * q^76 + 4 * q^77 - 4 * q^79 + 6 * q^80 + 4 * q^81 - 16 * q^82 + 14 * q^83 - 6 * q^84 + 6 * q^85 + 40 * q^86 - 6 * q^87 + 6 * q^88 - 6 * q^89 + 2 * q^90 + 4 * q^91 + 40 * q^92 + 8 * q^93 + 4 * q^94 - 6 * q^95 - 14 * q^96 - 14 * q^97 + 2 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.65222	1.16830	0.584149	−	0.811646i	$-0.301428\pi$
$2$	1.65222	1.16830	0.584149	+	0.811646i	$0.301428\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.729840	0.364920
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.65222	−0.674517
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−2.09859	−0.741962
$9$	1.00000	0.333333
$10$	1.65222	0.522479
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−0.729840	−0.210687
$13$	5.75081	1.59499	0.797494	−	0.603327i	$-0.206159\pi$
$13$	5.75081	1.59499	0.797494	+	0.603327i	$0.206159\pi$
$14$	1.65222	0.441575
$15$	−1.00000	−0.258199
$16$	−4.92701	−1.23175
$17$	−1.57461	−0.381898	−0.190949	−	0.981600i	$-0.561156\pi$
$17$	−1.57461	−0.381898	−0.190949	+	0.981600i	$0.561156\pi$
$18$	1.65222	0.389433
$19$	−2.27016	−0.520810	−0.260405	−	0.965499i	$-0.583856\pi$
$19$	−2.27016	−0.520810	−0.260405	+	0.965499i	$0.583856\pi$
$20$	0.729840	0.163197
$21$	−1.00000	−0.218218
$22$	1.65222	0.352255
$23$	7.38669	1.54023	0.770116	−	0.637904i	$-0.220198\pi$
$23$	7.38669	1.54023	0.770116	+	0.637904i	$0.220198\pi$
$24$	2.09859	0.428372
$25$	1.00000	0.200000
$26$	9.50162	1.86342
$27$	−1.00000	−0.192450
$28$	0.729840	0.137927
$29$	9.32541	1.73169	0.865843	−	0.500316i	$-0.166783\pi$
$29$	9.32541	1.73169	0.865843	+	0.500316i	$0.166783\pi$
$30$	−1.65222	−0.301653
$31$	5.05526	0.907951	0.453975	−	0.891014i	$-0.350005\pi$
$31$	5.05526	0.907951	0.453975	+	0.891014i	$0.350005\pi$
$32$	−3.94335	−0.697093
$33$	−1.00000	−0.174078
$34$	−2.60160	−0.446171
$35$	1.00000	0.169031
$36$	0.729840	0.121640
$37$	−2.51494	−0.413453	−0.206726	−	0.978399i	$-0.566281\pi$
$37$	−2.51494	−0.413453	−0.206726	+	0.978399i	$0.566281\pi$
$38$	−3.75081	−0.608462
$39$	−5.75081	−0.920867
$40$	−2.09859	−0.331816
$41$	6.29113	0.982509	0.491255	−	0.871016i	$-0.336538\pi$
$41$	6.29113	0.982509	0.491255	+	0.871016i	$0.336538\pi$
$42$	−1.65222	−0.254944
$43$	−5.83306	−0.889533	−0.444767	−	0.895647i	$-0.646713\pi$
$43$	−5.83306	−0.889533	−0.444767	+	0.895647i	$0.646713\pi$
$44$	0.729840	0.110028
$45$	1.00000	0.149071
$46$	12.2045	1.79945
$47$	−8.86734	−1.29344	−0.646718	−	0.762730i	$-0.723859\pi$
$47$	−8.86734	−1.29344	−0.646718	+	0.762730i	$0.723859\pi$
$48$	4.92701	0.711153
$49$	1.00000	0.142857
$50$	1.65222	0.233660
$51$	1.57461	0.220489
$52$	4.19717	0.582043
$53$	5.03429	0.691512	0.345756	−	0.938324i	$-0.387622\pi$
$53$	5.03429	0.691512	0.345756	+	0.938324i	$0.387622\pi$
$54$	−1.65222	−0.224839
$55$	1.00000	0.134840
$56$	−2.09859	−0.280435
$57$	2.27016	0.300690
$58$	15.4077	2.02313
$59$	−8.08954	−1.05317	−0.526584	−	0.850123i	$-0.676528\pi$
$59$	−8.08954	−1.05317	−0.526584	+	0.850123i	$0.676528\pi$
$60$	−0.729840	−0.0942220
$61$	−1.03429	−0.132427	−0.0662134	−	0.997805i	$-0.521092\pi$
$61$	−1.03429	−0.132427	−0.0662134	+	0.997805i	$0.521092\pi$
$62$	8.35241	1.06076
$63$	1.00000	0.125988
$64$	3.33873	0.417341
$65$	5.75081	0.713300
$66$	−1.65222	−0.203375
$67$	14.4629	1.76693	0.883463	−	0.468500i	$-0.155205\pi$
$67$	14.4629	1.76693	0.883463	+	0.468500i	$0.155205\pi$
$68$	−1.14921	−0.139362
$69$	−7.38669	−0.889254
$70$	1.65222	0.197478
$71$	9.59557	1.13879	0.569393	−	0.822066i	$-0.307178\pi$
$71$	9.59557	1.13879	0.569393	+	0.822066i	$0.307178\pi$
$72$	−2.09859	−0.247321
$73$	7.30445	0.854921	0.427460	−	0.904034i	$-0.359408\pi$
$73$	7.30445	0.854921	0.427460	+	0.904034i	$0.359408\pi$
$74$	−4.15524	−0.483036
$75$	−1.00000	−0.115470
$76$	−1.65685	−0.190054
$77$	1.00000	0.113961
$78$	−9.50162	−1.07585
$79$	−10.3597	−1.16556	−0.582779	−	0.812631i	$-0.698035\pi$
$79$	−10.3597	−1.16556	−0.582779	+	0.812631i	$0.698035\pi$
$80$	−4.92701	−0.550857
$81$	1.00000	0.111111
$82$	10.3943	1.14786
$83$	6.08225	0.667614	0.333807	−	0.942642i	$-0.391667\pi$
$83$	6.08225	0.667614	0.333807	+	0.942642i	$0.391667\pi$
$84$	−0.729840	−0.0796321
$85$	−1.57461	−0.170790
$86$	−9.63751	−1.03924
$87$	−9.32541	−0.999789
$88$	−2.09859	−0.223710
$89$	−14.9823	−1.58812	−0.794059	−	0.607841i	$-0.792036\pi$
$89$	−14.9823	−1.58812	−0.794059	+	0.607841i	$0.792036\pi$
$90$	1.65222	0.174160
$91$	5.75081	0.602849
$92$	5.39111	0.562062
$93$	−5.05526	−0.524206
$94$	−14.6508	−1.51112
$95$	−2.27016	−0.232913
$96$	3.94335	0.402467
$97$	−7.48065	−0.759545	−0.379772	−	0.925080i	$-0.623998\pi$
$97$	−7.48065	−0.759545	−0.379772	+	0.925080i	$0.623998\pi$
$98$	1.65222	0.166900
$99$	1.00000	0.100504
$100$	0.729840	0.0729840
$101$	−11.3464	−1.12901	−0.564504	−	0.825431i	$-0.690932\pi$
$101$	−11.3464	−1.12901	−0.564504	+	0.825431i	$0.690932\pi$
$102$	2.60160	0.257597
$103$	−12.9403	−1.27505	−0.637524	−	0.770430i	$-0.720041\pi$
$103$	−12.9403	−1.27505	−0.637524	+	0.770430i	$0.720041\pi$
$104$	−12.0686	−1.18342
$105$	−1.00000	−0.0975900
$106$	8.31776	0.807893
$107$	−1.81938	−0.175886	−0.0879431	−	0.996125i	$-0.528029\pi$
$107$	−1.81938	−0.175886	−0.0879431	+	0.996125i	$0.528029\pi$
$108$	−0.729840	−0.0702289
$109$	−7.78349	−0.745523	−0.372761	−	0.927927i	$-0.621589\pi$
$109$	−7.78349	−0.745523	−0.372761	+	0.927927i	$0.621589\pi$
$110$	1.65222	0.157533
$111$	2.51494	0.238707
$112$	−4.92701	−0.465559
$113$	17.2641	1.62407	0.812037	−	0.583607i	$-0.198359\pi$
$113$	17.2641	1.62407	0.812037	+	0.583607i	$0.198359\pi$
$114$	3.75081	0.351296
$115$	7.38669	0.688813
$116$	6.80606	0.631927
$117$	5.75081	0.531663
$118$	−13.3657	−1.23041
$119$	−1.57461	−0.144344
$120$	2.09859	0.191574
$121$	1.00000	0.0909091
$122$	−1.70887	−0.154714
$123$	−6.29113	−0.567252
$124$	3.68953	0.331330
$125$	1.00000	0.0894427
$126$	1.65222	0.147192
$127$	−4.08954	−0.362888	−0.181444	−	0.983401i	$-0.558077\pi$
$127$	−4.08954	−0.362888	−0.181444	+	0.983401i	$0.558077\pi$
$128$	13.4030	1.18467
$129$	5.83306	0.513572
$130$	9.50162	0.833347
$131$	−7.97462	−0.696746	−0.348373	−	0.937356i	$-0.613266\pi$
$131$	−7.97462	−0.696746	−0.348373	+	0.937356i	$0.613266\pi$
$132$	−0.729840	−0.0635245
$133$	−2.27016	−0.196848
$134$	23.8960	2.06430
$135$	−1.00000	−0.0860663
$136$	3.30445	0.283354
$137$	−19.0718	−1.62941	−0.814707	−	0.579872i	$-0.803102\pi$
$137$	−19.0718	−1.62941	−0.814707	+	0.579872i	$0.803102\pi$
$138$	−12.2045	−1.03891
$139$	−2.88346	−0.244572	−0.122286	−	0.992495i	$-0.539023\pi$
$139$	−2.88346	−0.244572	−0.122286	+	0.992495i	$0.539023\pi$
$140$	0.729840	0.0616828
$141$	8.86734	0.746765
$142$	15.8540	1.33044
$143$	5.75081	0.480907
$144$	−4.92701	−0.410584
$145$	9.32541	0.774434
$146$	12.0686	0.998802
$147$	−1.00000	−0.0824786
$148$	−1.83550	−0.150877
$149$	−6.45366	−0.528704	−0.264352	−	0.964426i	$-0.585158\pi$
$149$	−6.45366	−0.528704	−0.264352	+	0.964426i	$0.585158\pi$
$150$	−1.65222	−0.134903
$151$	−19.7254	−1.60523	−0.802616	−	0.596496i	$-0.796559\pi$
$151$	−19.7254	−1.60523	−0.802616	+	0.596496i	$0.796559\pi$
$152$	4.76413	0.386422
$153$	−1.57461	−0.127299
$154$	1.65222	0.133140
$155$	5.05526	0.406048
$156$	−4.19717	−0.336043
$157$	−14.4420	−1.15259	−0.576297	−	0.817241i	$-0.695503\pi$
$157$	−14.4420	−1.15259	−0.576297	+	0.817241i	$0.695503\pi$
$158$	−17.1165	−1.36172
$159$	−5.03429	−0.399245
$160$	−3.94335	−0.311749
$161$	7.38669	0.582153
$162$	1.65222	0.129811
$163$	−19.1658	−1.50118	−0.750589	−	0.660769i	$-0.770230\pi$
$163$	−19.1658	−1.50118	−0.750589	+	0.660769i	$0.770230\pi$
$164$	4.59152	0.358537
$165$	−1.00000	−0.0778499
$166$	10.0492	0.779972
$167$	−2.19717	−0.170022	−0.0850112	−	0.996380i	$-0.527093\pi$
$167$	−2.19717	−0.170022	−0.0850112	+	0.996380i	$0.527093\pi$
$168$	2.09859	0.161909
$169$	20.0718	1.54399
$170$	−2.60160	−0.199534
$171$	−2.27016	−0.173603
$172$	−4.25720	−0.324609
$173$	0.379043	0.0288181	0.0144090	−	0.999896i	$-0.495413\pi$
$173$	0.379043	0.0288181	0.0144090	+	0.999896i	$0.495413\pi$
$174$	−15.4077	−1.16805
$175$	1.00000	0.0755929
$176$	−4.92701	−0.371388
$177$	8.08954	0.608047
$178$	−24.7540	−1.85539
$179$	16.9093	1.26386	0.631930	−	0.775026i	$-0.282263\pi$
$179$	16.9093	1.26386	0.631930	+	0.775026i	$0.282263\pi$
$180$	0.729840	0.0543991
$181$	−3.08064	−0.228982	−0.114491	−	0.993424i	$-0.536524\pi$
$181$	−3.08064	−0.228982	−0.114491	+	0.993424i	$0.536524\pi$
$182$	9.50162	0.704307
$183$	1.03429	0.0764566
$184$	−15.5016	−1.14279
$185$	−2.51494	−0.184902
$186$	−8.35241	−0.612428
$187$	−1.57461	−0.115147
$188$	−6.47175	−0.472001
$189$	−1.00000	−0.0727393
$190$	−3.75081	−0.272112
$191$	3.68953	0.266965	0.133483	−	0.991051i	$-0.457384\pi$
$191$	3.68953	0.266965	0.133483	+	0.991051i	$0.457384\pi$
$192$	−3.33873	−0.240952
$193$	23.1585	1.66698	0.833492	−	0.552532i	$-0.186338\pi$
$193$	23.1585	1.66698	0.833492	+	0.552532i	$0.186338\pi$
$194$	−12.3597	−0.887375
$195$	−5.75081	−0.411824
$196$	0.729840	0.0521315
$197$	15.4330	1.09956	0.549780	−	0.835310i	$-0.314712\pi$
$197$	15.4330	1.09956	0.549780	+	0.835310i	$0.314712\pi$
$198$	1.65222	0.117418
$199$	−23.0032	−1.63066	−0.815328	−	0.578999i	$-0.803443\pi$
$199$	−23.0032	−1.63066	−0.815328	+	0.578999i	$0.803443\pi$
$200$	−2.09859	−0.148392
$201$	−14.4629	−1.02014
$202$	−18.7468	−1.31902
$203$	9.32541	0.654516
$204$	1.14921	0.0804608
$205$	6.29113	0.439391
$206$	−21.3803	−1.48964
$207$	7.38669	0.513411
$208$	−28.3343	−1.96463
$209$	−2.27016	−0.157030
$210$	−1.65222	−0.114014
$211$	14.5222	0.999751	0.499876	−	0.866097i	$-0.333379\pi$
$211$	14.5222	0.999751	0.499876	+	0.866097i	$0.333379\pi$
$212$	3.67423	0.252347
$213$	−9.59557	−0.657478
$214$	−3.00602	−0.205488
$215$	−5.83306	−0.397811
$216$	2.09859	0.142791
$217$	5.05526	0.343173
$218$	−12.8601	−0.870993
$219$	−7.30445	−0.493589
$220$	0.729840	0.0492058
$221$	−9.05526	−0.609122
$222$	4.15524	0.278881
$223$	−17.4807	−1.17059	−0.585295	−	0.810820i	$-0.699021\pi$
$223$	−17.4807	−1.17059	−0.585295	+	0.810820i	$0.699021\pi$
$224$	−3.94335	−0.263476
$225$	1.00000	0.0666667
$226$	28.5242	1.89740
$227$	6.81048	0.452027	0.226014	−	0.974124i	$-0.427431\pi$
$227$	6.81048	0.452027	0.226014	+	0.974124i	$0.427431\pi$
$228$	1.65685	0.109728
$229$	19.4077	1.28249	0.641247	−	0.767334i	$-0.278417\pi$
$229$	19.4077	1.28249	0.641247	+	0.767334i	$0.278417\pi$
$230$	12.2045	0.804739
$231$	−1.00000	−0.0657952
$232$	−19.5702	−1.28485
$233$	26.2464	1.71946	0.859730	−	0.510750i	$-0.170632\pi$
$233$	26.2464	1.71946	0.859730	+	0.510750i	$0.170632\pi$
$234$	9.50162	0.621140
$235$	−8.86734	−0.578442
$236$	−5.90407	−0.384323
$237$	10.3597	0.672935
$238$	−2.60160	−0.168637
$239$	−24.4839	−1.58373	−0.791866	−	0.610695i	$-0.790890\pi$
$239$	−24.4839	−1.58373	−0.791866	+	0.610695i	$0.790890\pi$
$240$	4.92701	0.318037
$241$	−11.0387	−0.711065	−0.355533	−	0.934664i	$-0.615700\pi$
$241$	−11.0387	−0.711065	−0.355533	+	0.934664i	$0.615700\pi$
$242$	1.65222	0.106209
$243$	−1.00000	−0.0641500
$244$	−0.754864	−0.0483252
$245$	1.00000	0.0638877
$246$	−10.3943	−0.662719
$247$	−13.0553	−0.830686
$248$	−10.6089	−0.673665
$249$	−6.08225	−0.385447
$250$	1.65222	0.104496
$251$	−13.7855	−0.870130	−0.435065	−	0.900399i	$-0.643275\pi$
$251$	−13.7855	−0.870130	−0.435065	+	0.900399i	$0.643275\pi$
$252$	0.729840	0.0459756
$253$	7.38669	0.464398
$254$	−6.75683	−0.423961
$255$	1.57461	0.0986056
$256$	15.4673	0.966708
$257$	30.1811	1.88264	0.941321	−	0.337512i	$-0.109585\pi$
$257$	30.1811	1.88264	0.941321	+	0.337512i	$0.109585\pi$
$258$	9.63751	0.600005
$259$	−2.51494	−0.156271
$260$	4.19717	0.260298
$261$	9.32541	0.577229
$262$	−13.1758	−0.814006
$263$	5.98191	0.368860	0.184430	−	0.982846i	$-0.440956\pi$
$263$	5.98191	0.368860	0.184430	+	0.982846i	$0.440956\pi$
$264$	2.09859	0.129159
$265$	5.03429	0.309254
$266$	−3.75081	−0.229977
$267$	14.9823	0.916900
$268$	10.5556	0.644787
$269$	−6.56451	−0.400245	−0.200123	−	0.979771i	$-0.564134\pi$
$269$	−6.56451	−0.400245	−0.200123	+	0.979771i	$0.564134\pi$
$270$	−1.65222	−0.100551
$271$	11.9629	0.726695	0.363348	−	0.931654i	$-0.381634\pi$
$271$	11.9629	0.726695	0.363348	+	0.931654i	$0.381634\pi$
$272$	7.75810	0.470404
$273$	−5.75081	−0.348055
$274$	−31.5109	−1.90364
$275$	1.00000	0.0603023
$276$	−5.39111	−0.324507
$277$	−6.30768	−0.378992	−0.189496	−	0.981881i	$-0.560685\pi$
$277$	−6.30768	−0.378992	−0.189496	+	0.981881i	$0.560685\pi$
$278$	−4.76413	−0.285733
$279$	5.05526	0.302650
$280$	−2.09859	−0.125415
$281$	−15.6988	−0.936511	−0.468256	−	0.883593i	$-0.655117\pi$
$281$	−15.6988	−0.936511	−0.468256	+	0.883593i	$0.655117\pi$
$282$	14.6508	0.872444
$283$	−9.05526	−0.538279	−0.269140	−	0.963101i	$-0.586739\pi$
$283$	−9.05526	−0.538279	−0.269140	+	0.963101i	$0.586739\pi$
$284$	7.00324	0.415566
$285$	2.27016	0.134473
$286$	9.50162	0.561843
$287$	6.29113	0.371354
$288$	−3.94335	−0.232364
$289$	−14.5206	−0.854154
$290$	15.4077	0.904769
$291$	7.48065	0.438523
$292$	5.33108	0.311978
$293$	−13.0528	−0.762553	−0.381277	−	0.924461i	$-0.624515\pi$
$293$	−13.0528	−0.762553	−0.381277	+	0.924461i	$0.624515\pi$
$294$	−1.65222	−0.0963596
$295$	−8.08954	−0.470991
$296$	5.27781	0.306767
$297$	−1.00000	−0.0580259
$298$	−10.6629	−0.617684
$299$	42.4795	2.45665
$300$	−0.729840	−0.0421374
$301$	−5.83306	−0.336212
$302$	−32.5908	−1.87539
$303$	11.3464	0.651833
$304$	11.1851	0.641510
$305$	−1.03429	−0.0592231
$306$	−2.60160	−0.148724
$307$	−2.11934	−0.120957	−0.0604785	−	0.998169i	$-0.519263\pi$
$307$	−2.11934	−0.120957	−0.0604785	+	0.998169i	$0.519263\pi$
$308$	0.729840	0.0415865
$309$	12.9403	0.736150
$310$	8.35241	0.474385
$311$	15.1258	0.857705	0.428853	−	0.903374i	$-0.358918\pi$
$311$	15.1258	0.857705	0.428853	+	0.903374i	$0.358918\pi$
$312$	12.0686	0.683248
$313$	−5.90163	−0.333580	−0.166790	−	0.985992i	$-0.553340\pi$
$313$	−5.90163	−0.333580	−0.166790	+	0.985992i	$0.553340\pi$
$314$	−23.8613	−1.34657
$315$	1.00000	0.0563436
$316$	−7.56093	−0.425335
$317$	7.88066	0.442622	0.221311	−	0.975203i	$-0.428966\pi$
$317$	7.88066	0.442622	0.221311	+	0.975203i	$0.428966\pi$
$318$	−8.31776	−0.466437
$319$	9.32541	0.522123
$320$	3.33873	0.186641
$321$	1.81938	0.101548
$322$	12.2045	0.680128
$323$	3.57461	0.198896
$324$	0.729840	0.0405467
$325$	5.75081	0.318998
$326$	−31.6661	−1.75382
$327$	7.78349	0.430428
$328$	−13.2025	−0.728985
$329$	−8.86734	−0.488873
$330$	−1.65222	−0.0909519
$331$	−21.2674	−1.16896	−0.584480	−	0.811408i	$-0.698701\pi$
$331$	−21.2674	−1.16896	−0.584480	+	0.811408i	$0.698701\pi$
$332$	4.43907	0.243626
$333$	−2.51494	−0.137818
$334$	−3.63022	−0.198637
$335$	14.4629	0.790194
$336$	4.92701	0.268791
$337$	13.4714	0.733833	0.366917	−	0.930254i	$-0.380413\pi$
$337$	13.4714	0.733833	0.366917	+	0.930254i	$0.380413\pi$
$338$	33.1631	1.80384
$339$	−17.2641	−0.937659
$340$	−1.14921	−0.0623247
$341$	5.05526	0.273757
$342$	−3.75081	−0.202821
$343$	1.00000	0.0539949
$344$	12.2412	0.660000
$345$	−7.38669	−0.397686
$346$	0.626263	0.0336681
$347$	14.5496	0.781062	0.390531	−	0.920590i	$-0.372291\pi$
$347$	14.5496	0.781062	0.390531	+	0.920590i	$0.372291\pi$
$348$	−6.80606	−0.364843
$349$	−15.8077	−0.846165	−0.423083	−	0.906091i	$-0.639052\pi$
$349$	−15.8077	−0.846165	−0.423083	+	0.906091i	$0.639052\pi$
$350$	1.65222	0.0883150
$351$	−5.75081	−0.306956
$352$	−3.94335	−0.210181
$353$	19.0299	1.01286	0.506429	−	0.862282i	$-0.330965\pi$
$353$	19.0299	1.01286	0.506429	+	0.862282i	$0.330965\pi$
$354$	13.3657	0.710380
$355$	9.59557	0.509280
$356$	−10.9347	−0.579536
$357$	1.57461	0.0833370
$358$	27.9379	1.47656
$359$	−33.9169	−1.79007	−0.895034	−	0.445999i	$-0.852849\pi$
$359$	−33.9169	−1.79007	−0.895034	+	0.445999i	$0.852849\pi$
$360$	−2.09859	−0.110605
$361$	−13.8464	−0.728757
$362$	−5.08990	−0.267519
$363$	−1.00000	−0.0524864
$364$	4.19717	0.219992
$365$	7.30445	0.382332
$366$	1.70887	0.0893241
$367$	9.33468	0.487266	0.243633	−	0.969867i	$-0.421661\pi$
$367$	9.33468	0.487266	0.243633	+	0.969867i	$0.421661\pi$
$368$	−36.3943	−1.89719
$369$	6.29113	0.327503
$370$	−4.15524	−0.216020
$371$	5.03429	0.261367
$372$	−3.68953	−0.191293
$373$	−15.0835	−0.780995	−0.390497	−	0.920604i	$-0.627697\pi$
$373$	−15.0835	−0.780995	−0.390497	+	0.920604i	$0.627697\pi$
$374$	−2.60160	−0.134525
$375$	−1.00000	−0.0516398
$376$	18.6089	0.959680
$377$	53.6287	2.76202
$378$	−1.65222	−0.0849812
$379$	−12.3448	−0.634108	−0.317054	−	0.948407i	$-0.602694\pi$
$379$	−12.3448	−0.634108	−0.317054	+	0.948407i	$0.602694\pi$
$380$	−1.65685	−0.0849948
$381$	4.08954	0.209514
$382$	6.09593	0.311895
$383$	28.1537	1.43859	0.719293	−	0.694706i	$-0.244466\pi$
$383$	28.1537	1.43859	0.719293	+	0.694706i	$0.244466\pi$
$384$	−13.4030	−0.683971
$385$	1.00000	0.0509647
$386$	38.2630	1.94753
$387$	−5.83306	−0.296511
$388$	−5.45968	−0.277173
$389$	−21.2077	−1.07527	−0.537637	−	0.843177i	$-0.680683\pi$
$389$	−21.2077	−1.07527	−0.537637	+	0.843177i	$0.680683\pi$
$390$	−9.50162	−0.481133
$391$	−11.6311	−0.588211
$392$	−2.09859	−0.105995
$393$	7.97462	0.402266
$394$	25.4988	1.28461
$395$	−10.3597	−0.521253
$396$	0.729840	0.0366759
$397$	27.3969	1.37501	0.687505	−	0.726180i	$-0.258706\pi$
$397$	27.3969	1.37501	0.687505	+	0.726180i	$0.258706\pi$
$398$	−38.0065	−1.90509
$399$	2.27016	0.113650
$400$	−4.92701	−0.246351
$401$	4.89398	0.244394	0.122197	−	0.992506i	$-0.461006\pi$
$401$	4.89398	0.244394	0.122197	+	0.992506i	$0.461006\pi$
$402$	−23.8960	−1.19182
$403$	29.0718	1.44817
$404$	−8.28105	−0.411998
$405$	1.00000	0.0496904
$406$	15.4077	0.764670
$407$	−2.51494	−0.124661
$408$	−3.30445	−0.163594
$409$	10.7282	0.530477	0.265238	−	0.964183i	$-0.414549\pi$
$409$	10.7282	0.530477	0.265238	+	0.964183i	$0.414549\pi$
$410$	10.3943	0.513340
$411$	19.0718	0.940743
$412$	−9.44438	−0.465291
$413$	−8.08954	−0.398060
$414$	12.2045	0.599817
$415$	6.08225	0.298566
$416$	−22.6775	−1.11185
$417$	2.88346	0.141204
$418$	−3.75081	−0.183458
$419$	21.1614	1.03380	0.516900	−	0.856046i	$-0.327086\pi$
$419$	21.1614	1.03380	0.516900	+	0.856046i	$0.327086\pi$
$420$	−0.729840	−0.0356126
$421$	35.0077	1.70617	0.853084	−	0.521773i	$-0.174729\pi$
$421$	35.0077	1.70617	0.853084	+	0.521773i	$0.174729\pi$
$422$	23.9940	1.16801
$423$	−8.86734	−0.431145
$424$	−10.5649	−0.513076
$425$	−1.57461	−0.0763796
$426$	−15.8540	−0.768130
$427$	−1.03429	−0.0500526
$428$	−1.32786	−0.0641845
$429$	−5.75081	−0.277652
$430$	−9.63751	−0.464762
$431$	8.58226	0.413393	0.206696	−	0.978405i	$-0.433729\pi$
$431$	8.58226	0.413393	0.206696	+	0.978405i	$0.433729\pi$
$432$	4.92701	0.237051
$433$	−18.1879	−0.874055	−0.437028	−	0.899448i	$-0.643969\pi$
$433$	−18.1879	−0.874055	−0.437028	+	0.899448i	$0.643969\pi$
$434$	8.35241	0.400928
$435$	−9.32541	−0.447119
$436$	−5.68070	−0.272056
$437$	−16.7690	−0.802169
$438$	−12.0686	−0.576659
$439$	−18.4581	−0.880956	−0.440478	−	0.897763i	$-0.645191\pi$
$439$	−18.4581	−0.880956	−0.440478	+	0.897763i	$0.645191\pi$
$440$	−2.09859	−0.100046
$441$	1.00000	0.0476190
$442$	−14.9613	−0.711636
$443$	25.4476	1.20905	0.604527	−	0.796585i	$-0.293362\pi$
$443$	25.4476	1.20905	0.604527	+	0.796585i	$0.293362\pi$
$444$	1.83550	0.0871091
$445$	−14.9823	−0.710228
$446$	−28.8819	−1.36760
$447$	6.45366	0.305247
$448$	3.33873	0.157740
$449$	21.8521	1.03126	0.515631	−	0.856811i	$-0.327557\pi$
$449$	21.8521	1.03126	0.515631	+	0.856811i	$0.327557\pi$
$450$	1.65222	0.0778865
$451$	6.29113	0.296238
$452$	12.6001	0.592657
$453$	19.7254	0.926781
$454$	11.2524	0.528103
$455$	5.75081	0.269602
$456$	−4.76413	−0.223101
$457$	−17.2746	−0.808074	−0.404037	−	0.914743i	$-0.632393\pi$
$457$	−17.2746	−0.808074	−0.404037	+	0.914743i	$0.632393\pi$
$458$	32.0658	1.49834
$459$	1.57461	0.0734963
$460$	5.39111	0.251362
$461$	15.9166	0.741308	0.370654	−	0.928771i	$-0.379134\pi$
$461$	15.9166	0.741308	0.370654	+	0.928771i	$0.379134\pi$
$462$	−1.65222	−0.0768684
$463$	25.9645	1.20667	0.603337	−	0.797486i	$-0.293837\pi$
$463$	25.9645	1.20667	0.603337	+	0.797486i	$0.293837\pi$
$464$	−45.9464	−2.13301
$465$	−5.05526	−0.234432
$466$	43.3649	2.00884
$467$	−16.2718	−0.752969	−0.376484	−	0.926423i	$-0.622867\pi$
$467$	−16.2718	−0.752969	−0.376484	+	0.926423i	$0.622867\pi$
$468$	4.19717	0.194014
$469$	14.4629	0.667836
$470$	−14.6508	−0.675792
$471$	14.4420	0.665450
$472$	16.9766	0.781412
$473$	−5.83306	−0.268204
$474$	17.1165	0.786188
$475$	−2.27016	−0.104162
$476$	−1.14921	−0.0526740
$477$	5.03429	0.230504
$478$	−40.4528	−1.85027
$479$	34.8553	1.59258	0.796290	−	0.604916i	$-0.206793\pi$
$479$	34.8553	1.59258	0.796290	+	0.604916i	$0.206793\pi$
$480$	3.94335	0.179989
$481$	−14.4629	−0.659452
$482$	−18.2384	−0.830736
$483$	−7.38669	−0.336106
$484$	0.729840	0.0331746
$485$	−7.48065	−0.339679
$486$	−1.65222	−0.0749464
$487$	−17.4330	−0.789967	−0.394983	−	0.918688i	$-0.629250\pi$
$487$	−17.4330	−0.789967	−0.394983	+	0.918688i	$0.629250\pi$
$488$	2.17054	0.0982557
$489$	19.1658	0.866706
$490$	1.65222	0.0746398
$491$	−30.2420	−1.36480	−0.682401	−	0.730978i	$-0.739064\pi$
$491$	−30.2420	−1.36480	−0.682401	+	0.730978i	$0.739064\pi$
$492$	−4.59152	−0.207002
$493$	−14.6838	−0.661327
$494$	−21.5702	−0.970489
$495$	1.00000	0.0449467
$496$	−24.9073	−1.11837
$497$	9.59557	0.430420
$498$	−10.0492	−0.450317
$499$	−31.7537	−1.42149	−0.710745	−	0.703450i	$-0.751642\pi$
$499$	−31.7537	−1.42149	−0.710745	+	0.703450i	$0.751642\pi$
$500$	0.729840	0.0326395
$501$	2.19717	0.0981625
$502$	−22.7766	−1.01657
$503$	6.39272	0.285037	0.142519	−	0.989792i	$-0.454480\pi$
$503$	6.39272	0.285037	0.142519	+	0.989792i	$0.454480\pi$
$504$	−2.09859	−0.0934785
$505$	−11.3464	−0.504907
$506$	12.2045	0.542555
$507$	−20.0718	−0.891420
$508$	−2.98471	−0.132425
$509$	18.0895	0.801805	0.400902	−	0.916121i	$-0.368697\pi$
$509$	18.0895	0.801805	0.400902	+	0.916121i	$0.368697\pi$
$510$	2.60160	0.115201
$511$	7.30445	0.323130
$512$	−1.25058	−0.0552685
$513$	2.27016	0.100230
$514$	49.8658	2.19949
$515$	−12.9403	−0.570219
$516$	4.25720	0.187413
$517$	−8.86734	−0.389985
$518$	−4.15524	−0.182571
$519$	−0.379043	−0.0166381
$520$	−12.0686	−0.529242
$521$	−22.1549	−0.970623	−0.485312	−	0.874341i	$-0.661294\pi$
$521$	−22.1549	−0.970623	−0.485312	+	0.874341i	$0.661294\pi$
$522$	15.4077	0.674375
$523$	−22.4395	−0.981211	−0.490606	−	0.871382i	$-0.663224\pi$
$523$	−22.4395	−0.981211	−0.490606	+	0.871382i	$0.663224\pi$
$524$	−5.82020	−0.254257
$525$	−1.00000	−0.0436436
$526$	9.88345	0.430939
$527$	−7.96003	−0.346744
$528$	4.92701	0.214421
$529$	31.5633	1.37232
$530$	8.31776	0.361301
$531$	−8.08954	−0.351056
$532$	−1.65685	−0.0718337
$533$	36.1791	1.56709
$534$	24.7540	1.07121
$535$	−1.81938	−0.0786587
$536$	−30.3517	−1.31099
$537$	−16.9093	−0.729689
$538$	−10.8460	−0.467606
$539$	1.00000	0.0430730
$540$	−0.729840	−0.0314073
$541$	−4.16575	−0.179100	−0.0895498	−	0.995982i	$-0.528543\pi$
$541$	−4.16575	−0.179100	−0.0895498	+	0.995982i	$0.528543\pi$
$542$	19.7654	0.848996
$543$	3.08064	0.132203
$544$	6.20922	0.266218
$545$	−7.78349	−0.333408
$546$	−9.50162	−0.406632
$547$	9.29274	0.397329	0.198664	−	0.980068i	$-0.436340\pi$
$547$	9.29274	0.397329	0.198664	+	0.980068i	$0.436340\pi$
$548$	−13.9194	−0.594606
$549$	−1.03429	−0.0441423
$550$	1.65222	0.0704510
$551$	−21.1702	−0.901880
$552$	15.5016	0.659793
$553$	−10.3597	−0.440539
$554$	−10.4217	−0.442776
$555$	2.51494	0.106753
$556$	−2.10447	−0.0892494
$557$	16.8153	0.712488	0.356244	−	0.934393i	$-0.384057\pi$
$557$	16.8153	0.712488	0.356244	+	0.934393i	$0.384057\pi$
$558$	8.35241	0.353586
$559$	−33.5448	−1.41879
$560$	−4.92701	−0.208204
$561$	1.57461	0.0664799
$562$	−25.9379	−1.09412
$563$	3.38185	0.142528	0.0712639	−	0.997457i	$-0.477297\pi$
$563$	3.38185	0.142528	0.0712639	+	0.997457i	$0.477297\pi$
$564$	6.47175	0.272510
$565$	17.2641	0.726308
$566$	−14.9613	−0.628870
$567$	1.00000	0.0419961
$568$	−20.1371	−0.844936
$569$	38.7916	1.62623	0.813114	−	0.582105i	$-0.197771\pi$
$569$	38.7916	1.62623	0.813114	+	0.582105i	$0.197771\pi$
$570$	3.75081	0.157104
$571$	−17.7960	−0.744738	−0.372369	−	0.928085i	$-0.621454\pi$
$571$	−17.7960	−0.744738	−0.372369	+	0.928085i	$0.621454\pi$
$572$	4.19717	0.175493
$573$	−3.68953	−0.154132
$574$	10.3943	0.433852
$575$	7.38669	0.308046
$576$	3.33873	0.139114
$577$	−30.4597	−1.26805	−0.634027	−	0.773311i	$-0.718599\pi$
$577$	−30.4597	−1.26805	−0.634027	+	0.773311i	$0.718599\pi$
$578$	−23.9913	−0.997906
$579$	−23.1585	−0.962433
$580$	6.80606	0.282606
$581$	6.08225	0.252334
$582$	12.3597	0.512326
$583$	5.03429	0.208499
$584$	−15.3290	−0.634319
$585$	5.75081	0.237767
$586$	−21.5662	−0.890890
$587$	−2.02860	−0.0837295	−0.0418647	−	0.999123i	$-0.513330\pi$
$587$	−2.02860	−0.0837295	−0.0418647	+	0.999123i	$0.513330\pi$
$588$	−0.729840	−0.0300981
$589$	−11.4762	−0.472870
$590$	−13.3657	−0.550258
$591$	−15.4330	−0.634831
$592$	12.3911	0.509272
$593$	3.17584	0.130416	0.0652082	−	0.997872i	$-0.479229\pi$
$593$	3.17584	0.130416	0.0652082	+	0.997872i	$0.479229\pi$
$594$	−1.65222	−0.0677915
$595$	−1.57461	−0.0645525
$596$	−4.71014	−0.192935
$597$	23.0032	0.941460
$598$	70.1856	2.87010
$599$	−2.63230	−0.107553	−0.0537765	−	0.998553i	$-0.517126\pi$
$599$	−2.63230	−0.107553	−0.0537765	+	0.998553i	$0.517126\pi$
$600$	2.09859	0.0856744
$601$	−7.46409	−0.304467	−0.152233	−	0.988345i	$-0.548647\pi$
$601$	−7.46409	−0.304467	−0.152233	+	0.988345i	$0.548647\pi$
$602$	−9.63751	−0.392796
$603$	14.4629	0.588976
$604$	−14.3964	−0.585782
$605$	1.00000	0.0406558
$606$	18.7468	0.761535
$607$	45.0331	1.82784	0.913919	−	0.405896i	$-0.133041\pi$
$607$	45.0331	1.82784	0.913919	+	0.405896i	$0.133041\pi$
$608$	8.95204	0.363053
$609$	−9.32541	−0.377885
$610$	−1.70887	−0.0691902
$611$	−50.9944	−2.06301
$612$	−1.14921	−0.0464541
$613$	31.4182	1.26897	0.634484	−	0.772936i	$-0.281213\pi$
$613$	31.4182	1.26897	0.634484	+	0.772936i	$0.281213\pi$
$614$	−3.50162	−0.141314
$615$	−6.29113	−0.253683
$616$	−2.09859	−0.0845545
$617$	−5.09844	−0.205256	−0.102628	−	0.994720i	$-0.532725\pi$
$617$	−5.09844	−0.205256	−0.102628	+	0.994720i	$0.532725\pi$
$618$	21.3803	0.860042
$619$	−11.8540	−0.476454	−0.238227	−	0.971210i	$-0.576566\pi$
$619$	−11.8540	−0.476454	−0.238227	+	0.971210i	$0.576566\pi$
$620$	3.68953	0.148175
$621$	−7.38669	−0.296418
$622$	24.9912	1.00206
$623$	−14.9823	−0.600252
$624$	28.3343	1.13428
$625$	1.00000	0.0400000
$626$	−9.75081	−0.389721
$627$	2.27016	0.0906614
$628$	−10.5403	−0.420605
$629$	3.96003	0.157897
$630$	1.65222	0.0658261
$631$	−7.43746	−0.296081	−0.148040	−	0.988981i	$-0.547297\pi$
$631$	−7.43746	−0.296081	−0.148040	+	0.988981i	$0.547297\pi$
$632$	21.7407	0.864800
$633$	−14.5222	−0.577207
$634$	13.0206	0.517114
$635$	−4.08954	−0.162289
$636$	−3.67423	−0.145693
$637$	5.75081	0.227855
$638$	15.4077	0.609995
$639$	9.59557	0.379595
$640$	13.4030	0.529801
$641$	−17.7613	−0.701530	−0.350765	−	0.936463i	$-0.614078\pi$
$641$	−17.7613	−0.701530	−0.350765	+	0.936463i	$0.614078\pi$
$642$	3.00602	0.118638
$643$	13.8331	0.545523	0.272761	−	0.962082i	$-0.412063\pi$
$643$	13.8331	0.545523	0.272761	+	0.962082i	$0.412063\pi$
$644$	5.39111	0.212439
$645$	5.83306	0.229676
$646$	5.90604	0.232370
$647$	−31.5016	−1.23846	−0.619228	−	0.785211i	$-0.712554\pi$
$647$	−31.5016	−1.23846	−0.619228	+	0.785211i	$0.712554\pi$
$648$	−2.09859	−0.0824403
$649$	−8.08954	−0.317542
$650$	9.50162	0.372684
$651$	−5.05526	−0.198131
$652$	−13.9880	−0.547810
$653$	−22.2521	−0.870791	−0.435395	−	0.900239i	$-0.643391\pi$
$653$	−22.2521	−0.870791	−0.435395	+	0.900239i	$0.643391\pi$
$654$	12.8601	0.502868
$655$	−7.97462	−0.311594
$656$	−30.9965	−1.21021
$657$	7.30445	0.284974
$658$	−14.6508	−0.571149
$659$	20.8597	0.812579	0.406289	−	0.913744i	$-0.366822\pi$
$659$	20.8597	0.812579	0.406289	+	0.913744i	$0.366822\pi$
$660$	−0.729840	−0.0284090
$661$	17.7061	0.688687	0.344343	−	0.938844i	$-0.388102\pi$
$661$	17.7061	0.688687	0.344343	+	0.938844i	$0.388102\pi$
$662$	−35.1384	−1.36569
$663$	9.05526	0.351677
$664$	−12.7641	−0.495344
$665$	−2.27016	−0.0880330
$666$	−4.15524	−0.161012
$667$	68.8840	2.66720
$668$	−1.60359	−0.0620446
$669$	17.4807	0.675841
$670$	23.8960	0.923182
$671$	−1.03429	−0.0399282
$672$	3.94335	0.152118
$673$	−7.95283	−0.306559	−0.153280	−	0.988183i	$-0.548984\pi$
$673$	−7.95283	−0.306559	−0.153280	+	0.988183i	$0.548984\pi$
$674$	22.2577	0.857336
$675$	−1.00000	−0.0384900
$676$	14.6492	0.563432
$677$	28.0375	1.07757	0.538785	−	0.842443i	$-0.318884\pi$
$677$	28.0375	1.07757	0.538785	+	0.842443i	$0.318884\pi$
$678$	−28.5242	−1.09547
$679$	−7.48065	−0.287081
$680$	3.30445	0.126720
$681$	−6.81048	−0.260978
$682$	8.35241	0.319830
$683$	−18.3823	−0.703379	−0.351690	−	0.936117i	$-0.614393\pi$
$683$	−18.3823	−0.703379	−0.351690	+	0.936117i	$0.614393\pi$
$684$	−1.65685	−0.0633514
$685$	−19.0718	−0.728696
$686$	1.65222	0.0630822
$687$	−19.4077	−0.740449
$688$	28.7396	1.09569
$689$	28.9512	1.10295
$690$	−12.2045	−0.464616
$691$	36.7613	1.39847	0.699234	−	0.714893i	$-0.253525\pi$
$691$	36.7613	1.39847	0.699234	+	0.714893i	$0.253525\pi$
$692$	0.276641	0.0105163
$693$	1.00000	0.0379869
$694$	24.0392	0.912514
$695$	−2.88346	−0.109376
$696$	19.5702	0.741806
$697$	−9.90604	−0.375218
$698$	−26.1178	−0.988573
$699$	−26.2464	−0.992730
$700$	0.729840	0.0275854
$701$	4.83586	0.182648	0.0913240	−	0.995821i	$-0.470890\pi$
$701$	4.83586	0.182648	0.0913240	+	0.995821i	$0.470890\pi$
$702$	−9.50162	−0.358616
$703$	5.70931	0.215331
$704$	3.33873	0.125833
$705$	8.86734	0.333964
$706$	31.4416	1.18332
$707$	−11.3464	−0.426725
$708$	5.90407	0.221889
$709$	−23.0077	−0.864071	−0.432035	−	0.901857i	$-0.642204\pi$
$709$	−23.0077	−0.864071	−0.432035	+	0.901857i	$0.642204\pi$
$710$	15.8540	0.594991
$711$	−10.3597	−0.388519
$712$	31.4416	1.17832
$713$	37.3416	1.39845
$714$	2.60160	0.0973624
$715$	5.75081	0.215068
$716$	12.3411	0.461208
$717$	24.4839	0.914368
$718$	−56.0383	−2.09133
$719$	−20.7944	−0.775499	−0.387749	−	0.921765i	$-0.626747\pi$
$719$	−20.7944	−0.775499	−0.387749	+	0.921765i	$0.626747\pi$
$720$	−4.92701	−0.183619
$721$	−12.9403	−0.481923
$722$	−22.8773	−0.851405
$723$	11.0387	0.410534
$724$	−2.24837	−0.0835602
$725$	9.32541	0.346337
$726$	−1.65222	−0.0613197
$727$	−43.1201	−1.59924	−0.799619	−	0.600508i	$-0.794965\pi$
$727$	−43.1201	−1.59924	−0.799619	+	0.600508i	$0.794965\pi$
$728$	−12.0686	−0.447291
$729$	1.00000	0.0370370
$730$	12.0686	0.446678
$731$	9.18476	0.339711
$732$	0.754864	0.0279006
$733$	1.63022	0.0602136	0.0301068	−	0.999547i	$-0.490415\pi$
$733$	1.63022	0.0602136	0.0301068	+	0.999547i	$0.490415\pi$
$734$	15.4230	0.569272
$735$	−1.00000	−0.0368856
$736$	−29.1283	−1.07368
$737$	14.4629	0.532748
$738$	10.3943	0.382621
$739$	10.7609	0.395846	0.197923	−	0.980218i	$-0.436580\pi$
$739$	10.7609	0.395846	0.197923	+	0.980218i	$0.436580\pi$
$740$	−1.83550	−0.0674744
$741$	13.0553	0.479597
$742$	8.31776	0.305355
$743$	23.7947	0.872944	0.436472	−	0.899718i	$-0.356228\pi$
$743$	23.7947	0.872944	0.436472	+	0.899718i	$0.356228\pi$
$744$	10.6089	0.388941
$745$	−6.45366	−0.236444
$746$	−24.9213	−0.912435
$747$	6.08225	0.222538
$748$	−1.14921	−0.0420193
$749$	−1.81938	−0.0664788
$750$	−1.65222	−0.0603306
$751$	−33.7271	−1.23072	−0.615359	−	0.788247i	$-0.710989\pi$
$751$	−33.7271	−1.23072	−0.615359	+	0.788247i	$0.710989\pi$
$752$	43.6895	1.59319
$753$	13.7855	0.502370
$754$	88.6065	3.22686
$755$	−19.7254	−0.717882
$756$	−0.729840	−0.0265440
$757$	−2.58226	−0.0938537	−0.0469269	−	0.998898i	$-0.514943\pi$
$757$	−2.58226	−0.0938537	−0.0469269	+	0.998898i	$0.514943\pi$
$758$	−20.3963	−0.740828
$759$	−7.38669	−0.268120
$760$	4.76413	0.172813
$761$	−37.5980	−1.36293	−0.681463	−	0.731853i	$-0.738656\pi$
$761$	−37.5980	−1.36293	−0.681463	+	0.731853i	$0.738656\pi$
$762$	6.75683	0.244774
$763$	−7.78349	−0.281781
$764$	2.69277	0.0974209
$765$	−1.57461	−0.0569300
$766$	46.5162	1.68070
$767$	−46.5214	−1.67979
$768$	−15.4673	−0.558129
$769$	−26.7391	−0.964237	−0.482119	−	0.876106i	$-0.660133\pi$
$769$	−26.7391	−0.964237	−0.482119	+	0.876106i	$0.660133\pi$
$770$	1.65222	0.0595420
$771$	−30.1811	−1.08694
$772$	16.9020	0.608316
$773$	21.3283	0.767125	0.383563	−	0.923515i	$-0.374697\pi$
$773$	21.3283	0.767125	0.383563	+	0.923515i	$0.374697\pi$
$774$	−9.63751	−0.346413
$775$	5.05526	0.181590
$776$	15.6988	0.563554
$777$	2.51494	0.0902228
$778$	−35.0399	−1.25624
$779$	−14.2819	−0.511701
$780$	−4.19717	−0.150283
$781$	9.59557	0.343357
$782$	−19.2172	−0.687206
$783$	−9.32541	−0.333263
$784$	−4.92701	−0.175965
$785$	−14.4420	−0.515455
$786$	13.1758	0.469967
$787$	−4.54915	−0.162160	−0.0810798	−	0.996708i	$-0.525837\pi$
$787$	−4.54915	−0.162160	−0.0810798	+	0.996708i	$0.525837\pi$
$788$	11.2637	0.401251
$789$	−5.98191	−0.212962
$790$	−17.1165	−0.608979
$791$	17.2641	0.613842
$792$	−2.09859	−0.0745700
$793$	−5.94798	−0.211219
$794$	45.2657	1.60642
$795$	−5.03429	−0.178548
$796$	−16.7887	−0.595059
$797$	−35.7347	−1.26579	−0.632894	−	0.774239i	$-0.718133\pi$
$797$	−35.7347	−1.26579	−0.632894	+	0.774239i	$0.718133\pi$
$798$	3.75081	0.132777
$799$	13.9626	0.493960
$800$	−3.94335	−0.139419
$801$	−14.9823	−0.529372
$802$	8.08594	0.285525
$803$	7.30445	0.257768
$804$	−10.5556	−0.372268
$805$	7.38669	0.260347
$806$	48.0331	1.69189
$807$	6.56451	0.231082
$808$	23.8114	0.837681
$809$	20.8239	0.732128	0.366064	−	0.930590i	$-0.380705\pi$
$809$	20.8239	0.732128	0.366064	+	0.930590i	$0.380705\pi$
$810$	1.65222	0.0580532
$811$	−4.71336	−0.165508	−0.0827542	−	0.996570i	$-0.526372\pi$
$811$	−4.71336	−0.165508	−0.0827542	+	0.996570i	$0.526372\pi$
$812$	6.80606	0.238846
$813$	−11.9629	−0.419558
$814$	−4.15524	−0.145641
$815$	−19.1658	−0.671348
$816$	−7.75810	−0.271588
$817$	13.2420	0.463278
$818$	17.7254	0.619755
$819$	5.75081	0.200950
$820$	4.59152	0.160343
$821$	3.06010	0.106798	0.0533992	−	0.998573i	$-0.482994\pi$
$821$	3.06010	0.106798	0.0533992	+	0.998573i	$0.482994\pi$
$822$	31.5109	1.09907
$823$	−21.7601	−0.758508	−0.379254	−	0.925293i	$-0.623819\pi$
$823$	−21.7601	−0.758508	−0.379254	+	0.925293i	$0.623819\pi$
$824$	27.1564	0.946038
$825$	−1.00000	−0.0348155
$826$	−13.3657	−0.465053
$827$	−36.6747	−1.27530	−0.637652	−	0.770325i	$-0.720094\pi$
$827$	−36.6747	−1.27530	−0.637652	+	0.770325i	$0.720094\pi$
$828$	5.39111	0.187354
$829$	1.19115	0.0413703	0.0206852	−	0.999786i	$-0.493415\pi$
$829$	1.19115	0.0413703	0.0206852	+	0.999786i	$0.493415\pi$
$830$	10.0492	0.348814
$831$	6.30768	0.218811
$832$	19.2004	0.665655
$833$	−1.57461	−0.0545568
$834$	4.76413	0.164968
$835$	−2.19717	−0.0760363
$836$	−1.65685	−0.0573035
$837$	−5.05526	−0.174735
$838$	34.9633	1.20779
$839$	−18.2420	−0.629783	−0.314892	−	0.949128i	$-0.601968\pi$
$839$	−18.2420	−0.629783	−0.314892	+	0.949128i	$0.601968\pi$
$840$	2.09859	0.0724081
$841$	57.9634	1.99874
$842$	57.8404	1.99331
$843$	15.6988	0.540695
$844$	10.5989	0.364830
$845$	20.0718	0.690491
$846$	−14.6508	−0.503706
$847$	1.00000	0.0343604
$848$	−24.8040	−0.851773
$849$	9.05526	0.310776
$850$	−2.60160	−0.0892341
$851$	−18.5771	−0.636814
$852$	−7.00324	−0.239927
$853$	14.9774	0.512817	0.256409	−	0.966568i	$-0.417461\pi$
$853$	14.9774	0.512817	0.256409	+	0.966568i	$0.417461\pi$
$854$	−1.70887	−0.0584764
$855$	−2.27016	−0.0776378
$856$	3.81813	0.130501
$857$	18.5315	0.633024	0.316512	−	0.948589i	$-0.397488\pi$
$857$	18.5315	0.633024	0.316512	+	0.948589i	$0.397488\pi$
$858$	−9.50162	−0.324380
$859$	−10.5835	−0.361105	−0.180552	−	0.983565i	$-0.557789\pi$
$859$	−10.5835	−0.361105	−0.180552	+	0.983565i	$0.557789\pi$
$860$	−4.25720	−0.145169
$861$	−6.29113	−0.214401
$862$	14.1798	0.482966
$863$	47.1182	1.60392	0.801960	−	0.597377i	$-0.203790\pi$
$863$	47.1182	1.60392	0.801960	+	0.597377i	$0.203790\pi$
$864$	3.94335	0.134156
$865$	0.379043	0.0128878
$866$	−30.0505	−1.02116
$867$	14.5206	0.493146
$868$	3.68953	0.125231
$869$	−10.3597	−0.351429
$870$	−15.4077	−0.522369
$871$	83.1735	2.81823
$872$	16.3343	0.553150
$873$	−7.48065	−0.253182
$874$	−27.7061	−0.937172
$875$	1.00000	0.0338062
$876$	−5.33108	−0.180120
$877$	49.3585	1.66672	0.833359	−	0.552731i	$-0.186414\pi$
$877$	49.3585	1.66672	0.833359	+	0.552731i	$0.186414\pi$
$878$	−30.4968	−1.02922
$879$	13.0528	0.440260
$880$	−4.92701	−0.166090
$881$	−56.5436	−1.90500	−0.952502	−	0.304533i	$-0.901500\pi$
$881$	−56.5436	−1.90500	−0.952502	+	0.304533i	$0.901500\pi$
$882$	1.65222	0.0556332
$883$	42.3315	1.42457	0.712285	−	0.701891i	$-0.247660\pi$
$883$	42.3315	1.42457	0.712285	+	0.701891i	$0.247660\pi$
$884$	−6.60889	−0.222281
$885$	8.08954	0.271927
$886$	42.0452	1.41253
$887$	−31.7984	−1.06769	−0.533843	−	0.845584i	$-0.679253\pi$
$887$	−31.7984	−1.06769	−0.533843	+	0.845584i	$0.679253\pi$
$888$	−5.27781	−0.177112
$889$	−4.08954	−0.137159
$890$	−24.7540	−0.829758
$891$	1.00000	0.0335013
$892$	−12.7581	−0.427172
$893$	20.1303	0.673634
$894$	10.6629	0.356620
$895$	16.9093	0.565215
$896$	13.4030	0.447764
$897$	−42.4795	−1.41835
$898$	36.1045	1.20482
$899$	47.1424	1.57229
$900$	0.729840	0.0243280
$901$	−7.92701	−0.264087
$902$	10.3943	0.346094
$903$	5.83306	0.194112
$904$	−36.2303	−1.20500
$905$	−3.08064	−0.102404
$906$	32.5908	1.08276
$907$	−47.8521	−1.58890	−0.794451	−	0.607329i	$-0.792241\pi$
$907$	−47.8521	−1.58890	−0.794451	+	0.607329i	$0.792241\pi$
$908$	4.97056	0.164954
$909$	−11.3464	−0.376336
$910$	9.50162	0.314976
$911$	7.77591	0.257627	0.128814	−	0.991669i	$-0.458883\pi$
$911$	7.77591	0.257627	0.128814	+	0.991669i	$0.458883\pi$
$912$	−11.1851	−0.370376
$913$	6.08225	0.201293
$914$	−28.5416	−0.944071
$915$	1.03429	0.0341924
$916$	14.1645	0.468008
$917$	−7.97462	−0.263345
$918$	2.60160	0.0858656
$919$	−18.2690	−0.602638	−0.301319	−	0.953523i	$-0.597427\pi$
$919$	−18.2690	−0.602638	−0.301319	+	0.953523i	$0.597427\pi$
$920$	−15.5016	−0.511073
$921$	2.11934	0.0698346
$922$	26.2977	0.866069
$923$	55.1823	1.81635
$924$	−0.729840	−0.0240100
$925$	−2.51494	−0.0826906
$926$	42.8992	1.40976
$927$	−12.9403	−0.425016
$928$	−36.7734	−1.20715
$929$	−43.1049	−1.41423	−0.707113	−	0.707100i	$-0.750003\pi$
$929$	−43.1049	−1.41423	−0.707113	+	0.707100i	$0.750003\pi$
$930$	−8.35241	−0.273886
$931$	−2.27016	−0.0744015
$932$	19.1557	0.627465
$933$	−15.1258	−0.495196
$934$	−26.8846	−0.879692
$935$	−1.57461	−0.0514951
$936$	−12.0686	−0.394474
$937$	55.4767	1.81234	0.906172	−	0.422909i	$-0.138991\pi$
$937$	55.4767	1.81234	0.906172	+	0.422909i	$0.138991\pi$
$938$	23.8960	0.780231
$939$	5.90163	0.192592
$940$	−6.47175	−0.211085
$941$	−50.4887	−1.64589	−0.822943	−	0.568124i	$-0.807669\pi$
$941$	−50.4887	−1.64589	−0.822943	+	0.568124i	$0.807669\pi$
$942$	23.8613	0.777444
$943$	46.4706	1.51329
$944$	39.8573	1.29724
$945$	−1.00000	−0.0325300
$946$	−9.63751	−0.313343
$947$	1.43185	0.0465290	0.0232645	−	0.999729i	$-0.492594\pi$
$947$	1.43185	0.0465290	0.0232645	+	0.999729i	$0.492594\pi$
$948$	7.56093	0.245568
$949$	42.0065	1.36359
$950$	−3.75081	−0.121692
$951$	−7.88066	−0.255548
$952$	3.30445	0.107098
$953$	−46.3582	−1.50169	−0.750844	−	0.660479i	$-0.770353\pi$
$953$	−46.3582	−1.50169	−0.750844	+	0.660479i	$0.770353\pi$
$954$	8.31776	0.269298
$955$	3.68953	0.119390
$956$	−17.8693	−0.577935
$957$	−9.32541	−0.301448
$958$	57.5887	1.86061
$959$	−19.0718	−0.615861
$960$	−3.33873	−0.107757
$961$	−5.44439	−0.175626
$962$	−23.8960	−0.770437
$963$	−1.81938	−0.0586288
$964$	−8.05649	−0.259482
$965$	23.1585	0.745498
$966$	−12.2045	−0.392672
$967$	−7.67178	−0.246708	−0.123354	−	0.992363i	$-0.539365\pi$
$967$	−7.67178	−0.246708	−0.123354	+	0.992363i	$0.539365\pi$
$968$	−2.09859	−0.0674511
$969$	−3.57461	−0.114833
$970$	−12.3597	−0.396846
$971$	−36.3048	−1.16508	−0.582538	−	0.812803i	$-0.697940\pi$
$971$	−36.3048	−1.16508	−0.582538	+	0.812803i	$0.697940\pi$
$972$	−0.729840	−0.0234096
$973$	−2.88346	−0.0924396
$974$	−28.8033	−0.922917
$975$	−5.75081	−0.184173
$976$	5.09594	0.163117
$977$	−50.1900	−1.60572	−0.802860	−	0.596168i	$-0.796689\pi$
$977$	−50.1900	−1.60572	−0.802860	+	0.596168i	$0.796689\pi$
$978$	31.6661	1.01257
$979$	−14.9823	−0.478835
$980$	0.729840	0.0233139
$981$	−7.78349	−0.248508
$982$	−49.9665	−1.59450
$983$	−55.2541	−1.76233	−0.881166	−	0.472806i	$-0.843241\pi$
$983$	−55.2541	−1.76233	−0.881166	+	0.472806i	$0.843241\pi$
$984$	13.2025	0.420880
$985$	15.4330	0.491738
$986$	−24.2610	−0.772627
$987$	8.86734	0.282251
$988$	−9.52825	−0.303134
$989$	−43.0870	−1.37009
$990$	1.65222	0.0525111
$991$	−52.5150	−1.66819	−0.834097	−	0.551617i	$-0.814011\pi$
$991$	−52.5150	−1.66819	−0.834097	+	0.551617i	$0.814011\pi$
$992$	−19.9346	−0.632926
$993$	21.2674	0.674899
$994$	15.8540	0.502859
$995$	−23.0032	−0.729252
$996$	−4.43907	−0.140657
$997$	−38.9891	−1.23480	−0.617398	−	0.786651i	$-0.711813\pi$
$997$	−38.9891	−1.23480	−0.617398	+	0.786651i	$0.711813\pi$
$998$	−52.4642	−1.66072
$999$	2.51494	0.0795691

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.a.v.1.3	✓	4
3.2	odd	2		3465.2.a.bj.1.2		4
5.4	even	2		5775.2.a.by.1.2		4
7.6	odd	2		8085.2.a.bq.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.a.v.1.3	✓	4	1.1	even	1	trivial
3465.2.a.bj.1.2		4	3.2	odd	2
5775.2.a.by.1.2		4	5.4	even	2
8085.2.a.bq.1.3		4	7.6	odd	2

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:	\( N \)	\(=\)	\( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1155.a (trivial)

\(f(q)\)	\(=\)	\(q+1.65222 q^{2} -1.00000 q^{3} +0.729840 q^{4} +1.00000 q^{5} -1.65222 q^{6} +1.00000 q^{7} -2.09859 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.65222 q^{2} -1.00000 q^{3} +0.729840 q^{4} +1.00000 q^{5} -1.65222 q^{6} +1.00000 q^{7} -2.09859 q^{8} +1.00000 q^{9} +1.65222 q^{10} +1.00000 q^{11} -0.729840 q^{12} +5.75081 q^{13} +1.65222 q^{14} -1.00000 q^{15} -4.92701 q^{16} -1.57461 q^{17} +1.65222 q^{18} -2.27016 q^{19} +0.729840 q^{20} -1.00000 q^{21} +1.65222 q^{22} +7.38669 q^{23} +2.09859 q^{24} +1.00000 q^{25} +9.50162 q^{26} -1.00000 q^{27} +0.729840 q^{28} +9.32541 q^{29} -1.65222 q^{30} +5.05526 q^{31} -3.94335 q^{32} -1.00000 q^{33} -2.60160 q^{34} +1.00000 q^{35} +0.729840 q^{36} -2.51494 q^{37} -3.75081 q^{38} -5.75081 q^{39} -2.09859 q^{40} +6.29113 q^{41} -1.65222 q^{42} -5.83306 q^{43} +0.729840 q^{44} +1.00000 q^{45} +12.2045 q^{46} -8.86734 q^{47} +4.92701 q^{48} +1.00000 q^{49} +1.65222 q^{50} +1.57461 q^{51} +4.19717 q^{52} +5.03429 q^{53} -1.65222 q^{54} +1.00000 q^{55} -2.09859 q^{56} +2.27016 q^{57} +15.4077 q^{58} -8.08954 q^{59} -0.729840 q^{60} -1.03429 q^{61} +8.35241 q^{62} +1.00000 q^{63} +3.33873 q^{64} +5.75081 q^{65} -1.65222 q^{66} +14.4629 q^{67} -1.14921 q^{68} -7.38669 q^{69} +1.65222 q^{70} +9.59557 q^{71} -2.09859 q^{72} +7.30445 q^{73} -4.15524 q^{74} -1.00000 q^{75} -1.65685 q^{76} +1.00000 q^{77} -9.50162 q^{78} -10.3597 q^{79} -4.92701 q^{80} +1.00000 q^{81} +10.3943 q^{82} +6.08225 q^{83} -0.729840 q^{84} -1.57461 q^{85} -9.63751 q^{86} -9.32541 q^{87} -2.09859 q^{88} -14.9823 q^{89} +1.65222 q^{90} +5.75081 q^{91} +5.39111 q^{92} -5.05526 q^{93} -14.6508 q^{94} -2.27016 q^{95} +3.94335 q^{96} -7.48065 q^{97} +1.65222 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 4 q^{3} + 6 q^{4} + 4 q^{5} - 2 q^{6} + 4 q^{7} + 6 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 - 4 * q^3 + 6 * q^4 + 4 * q^5 - 2 * q^6 + 4 * q^7 + 6 * q^8 + 4 * q^9	\( 4 q + 2 q^{2} - 4 q^{3} + 6 q^{4} + 4 q^{5} - 2 q^{6} + 4 q^{7} + 6 q^{8} + 4 q^{9} + 2 q^{10} + 4 q^{11} - 6 q^{12} + 4 q^{13} + 2 q^{14} - 4 q^{15} + 6 q^{16} + 6 q^{17} + 2 q^{18} - 6 q^{19} + 6 q^{20} - 4 q^{21} + 2 q^{22} + 10 q^{23} - 6 q^{24} + 4 q^{25} - 4 q^{27} + 6 q^{28} + 6 q^{29} - 2 q^{30} - 8 q^{31} + 14 q^{32} - 4 q^{33} - 16 q^{34} + 4 q^{35} + 6 q^{36} + 12 q^{37} + 4 q^{38} - 4 q^{39} + 6 q^{40} - 2 q^{42} + 6 q^{43} + 6 q^{44} + 4 q^{45} - 4 q^{46} - 6 q^{48} + 4 q^{49} + 2 q^{50} - 6 q^{51} - 12 q^{52} + 14 q^{53} - 2 q^{54} + 4 q^{55} + 6 q^{56} + 6 q^{57} + 20 q^{58} + 2 q^{59} - 6 q^{60} + 2 q^{61} + 20 q^{62} + 4 q^{63} - 2 q^{64} + 4 q^{65} - 2 q^{66} - 12 q^{67} + 20 q^{68} - 10 q^{69} + 2 q^{70} + 4 q^{71} + 6 q^{72} + 20 q^{73} - 32 q^{74} - 4 q^{75} + 16 q^{76} + 4 q^{77} - 4 q^{79} + 6 q^{80} + 4 q^{81} - 16 q^{82} + 14 q^{83} - 6 q^{84} + 6 q^{85} + 40 q^{86} - 6 q^{87} + 6 q^{88} - 6 q^{89} + 2 q^{90} + 4 q^{91} + 40 q^{92} + 8 q^{93} + 4 q^{94} - 6 q^{95} - 14 q^{96} - 14 q^{97} + 2 q^{98} + 4 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - 4 * q^3 + 6 * q^4 + 4 * q^5 - 2 * q^6 + 4 * q^7 + 6 * q^8 + 4 * q^9 + 2 * q^10 + 4 * q^11 - 6 * q^12 + 4 * q^13 + 2 * q^14 - 4 * q^15 + 6 * q^16 + 6 * q^17 + 2 * q^18 - 6 * q^19 + 6 * q^20 - 4 * q^21 + 2 * q^22 + 10 * q^23 - 6 * q^24 + 4 * q^25 - 4 * q^27 + 6 * q^28 + 6 * q^29 - 2 * q^30 - 8 * q^31 + 14 * q^32 - 4 * q^33 - 16 * q^34 + 4 * q^35 + 6 * q^36 + 12 * q^37 + 4 * q^38 - 4 * q^39 + 6 * q^40 - 2 * q^42 + 6 * q^43 + 6 * q^44 + 4 * q^45 - 4 * q^46 - 6 * q^48 + 4 * q^49 + 2 * q^50 - 6 * q^51 - 12 * q^52 + 14 * q^53 - 2 * q^54 + 4 * q^55 + 6 * q^56 + 6 * q^57 + 20 * q^58 + 2 * q^59 - 6 * q^60 + 2 * q^61 + 20 * q^62 + 4 * q^63 - 2 * q^64 + 4 * q^65 - 2 * q^66 - 12 * q^67 + 20 * q^68 - 10 * q^69 + 2 * q^70 + 4 * q^71 + 6 * q^72 + 20 * q^73 - 32 * q^74 - 4 * q^75 + 16 * q^76 + 4 * q^77 - 4 * q^79 + 6 * q^80 + 4 * q^81 - 16 * q^82 + 14 * q^83 - 6 * q^84 + 6 * q^85 + 40 * q^86 - 6 * q^87 + 6 * q^88 - 6 * q^89 + 2 * q^90 + 4 * q^91 + 40 * q^92 + 8 * q^93 + 4 * q^94 - 6 * q^95 - 14 * q^96 - 14 * q^97 + 2 * q^98 + 4 * q^99

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