LMFDB - Embedded newform 1815.2.a.v.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1815,2,Mod(1,1815)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1815, 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("1815.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1815 = 3 \cdot 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1815.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:	$14.4928479669$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.5725.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 8x^{2} + 6x + 11 $ x^4 - x^3 - 8x^2 + 6x + 11
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 165)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.86205$ of defining polynomial
Character	$\chi$	$=$	1815.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.48008 q^{2} -1.00000 q^{3} +4.15081 q^{4} -1.00000 q^{5} +2.48008 q^{6} -4.39482 q^{7} -5.33418 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.48008 q^{2} -1.00000 q^{3} +4.15081 q^{4} -1.00000 q^{5} +2.48008 q^{6} -4.39482 q^{7} -5.33418 q^{8} +1.00000 q^{9} +2.48008 q^{10} -4.15081 q^{12} -2.13795 q^{13} +10.8995 q^{14} +1.00000 q^{15} +4.92760 q^{16} +3.96017 q^{17} -2.48008 q^{18} -2.15081 q^{19} -4.15081 q^{20} +4.39482 q^{21} +5.16367 q^{23} +5.33418 q^{24} +1.00000 q^{25} +5.30230 q^{26} -1.00000 q^{27} -18.2421 q^{28} +7.93936 q^{29} -2.48008 q^{30} +6.19132 q^{31} -1.55248 q^{32} -9.82154 q^{34} +4.39482 q^{35} +4.15081 q^{36} -8.57025 q^{37} +5.33418 q^{38} +2.13795 q^{39} +5.33418 q^{40} -7.63089 q^{41} -10.8995 q^{42} -2.22321 q^{43} -1.00000 q^{45} -12.8063 q^{46} +6.88285 q^{47} -4.92760 q^{48} +12.3145 q^{49} -2.48008 q^{50} -3.96017 q^{51} -8.87423 q^{52} -5.69644 q^{53} +2.48008 q^{54} +23.4428 q^{56} +2.15081 q^{57} -19.6903 q^{58} +3.78170 q^{59} +4.15081 q^{60} +4.83439 q^{61} -15.3550 q^{62} -4.39482 q^{63} -6.00491 q^{64} +2.13795 q^{65} +9.57025 q^{67} +16.4379 q^{68} -5.16367 q^{69} -10.8995 q^{70} -2.11030 q^{71} -5.33418 q^{72} -14.6506 q^{73} +21.2549 q^{74} -1.00000 q^{75} -8.92760 q^{76} -5.30230 q^{78} +3.26111 q^{79} -4.92760 q^{80} +1.00000 q^{81} +18.9252 q^{82} +10.6635 q^{83} +18.2421 q^{84} -3.96017 q^{85} +5.51374 q^{86} -7.93936 q^{87} -7.64375 q^{89} +2.48008 q^{90} +9.39592 q^{91} +21.4334 q^{92} -6.19132 q^{93} -17.0700 q^{94} +2.15081 q^{95} +1.55248 q^{96} -5.67073 q^{97} -30.5409 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} - 4 q^{3} + 9 q^{4} - 4 q^{5} - q^{6} - 8 q^{7} + 3 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q + q^2 - 4 * q^3 + 9 * q^4 - 4 * q^5 - q^6 - 8 * q^7 + 3 * q^8 + 4 * q^9	$ 4 q + q^{2} - 4 q^{3} + 9 q^{4} - 4 q^{5} - q^{6} - 8 q^{7} + 3 q^{8} + 4 q^{9} - q^{10} - 9 q^{12} - 15 q^{13} + 7 q^{14} + 4 q^{15} + 7 q^{16} - 6 q^{17} + q^{18} - q^{19} - 9 q^{20} + 8 q^{21} - q^{23} - 3 q^{24} + 4 q^{25} - 18 q^{26} - 4 q^{27} - 31 q^{28} + 17 q^{29} + q^{30} + 15 q^{31} - 8 q^{32} - 35 q^{34} + 8 q^{35} + 9 q^{36} - q^{37} - 3 q^{38} + 15 q^{39} - 3 q^{40} - 12 q^{41} - 7 q^{42} - 14 q^{43} - 4 q^{45} - 9 q^{46} + 14 q^{47} - 7 q^{48} + 20 q^{49} + q^{50} + 6 q^{51} - 39 q^{52} + 2 q^{53} - q^{54} - 12 q^{56} + q^{57} - 11 q^{58} - 11 q^{59} + 9 q^{60} + q^{61} - 30 q^{62} - 8 q^{63} - 3 q^{64} + 15 q^{65} + 5 q^{67} - 19 q^{68} + q^{69} - 7 q^{70} - 3 q^{71} + 3 q^{72} - 45 q^{73} + 29 q^{74} - 4 q^{75} - 23 q^{76} + 18 q^{78} - 7 q^{80} + 4 q^{81} + 11 q^{82} + 15 q^{83} + 31 q^{84} + 6 q^{85} - 10 q^{86} - 17 q^{87} + 2 q^{89} - q^{90} + 16 q^{91} + 34 q^{92} - 15 q^{93} - 29 q^{94} + q^{95} + 8 q^{96} - 26 q^{97} - q^{98}+O(q^{100}) $ 4 * q + q^2 - 4 * q^3 + 9 * q^4 - 4 * q^5 - q^6 - 8 * q^7 + 3 * q^8 + 4 * q^9 - q^10 - 9 * q^12 - 15 * q^13 + 7 * q^14 + 4 * q^15 + 7 * q^16 - 6 * q^17 + q^18 - q^19 - 9 * q^20 + 8 * q^21 - q^23 - 3 * q^24 + 4 * q^25 - 18 * q^26 - 4 * q^27 - 31 * q^28 + 17 * q^29 + q^30 + 15 * q^31 - 8 * q^32 - 35 * q^34 + 8 * q^35 + 9 * q^36 - q^37 - 3 * q^38 + 15 * q^39 - 3 * q^40 - 12 * q^41 - 7 * q^42 - 14 * q^43 - 4 * q^45 - 9 * q^46 + 14 * q^47 - 7 * q^48 + 20 * q^49 + q^50 + 6 * q^51 - 39 * q^52 + 2 * q^53 - q^54 - 12 * q^56 + q^57 - 11 * q^58 - 11 * q^59 + 9 * q^60 + q^61 - 30 * q^62 - 8 * q^63 - 3 * q^64 + 15 * q^65 + 5 * q^67 - 19 * q^68 + q^69 - 7 * q^70 - 3 * q^71 + 3 * q^72 - 45 * q^73 + 29 * q^74 - 4 * q^75 - 23 * q^76 + 18 * q^78 - 7 * q^80 + 4 * q^81 + 11 * q^82 + 15 * q^83 + 31 * q^84 + 6 * q^85 - 10 * q^86 - 17 * q^87 + 2 * q^89 - q^90 + 16 * q^91 + 34 * q^92 - 15 * q^93 - 29 * q^94 + q^95 + 8 * q^96 - 26 * q^97 - q^98

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 $

$2$	−2.48008	−1.75368	−0.876842	−	0.480779i	$-0.840354\pi$
$2$	−2.48008	−1.75368	−0.876842	+	0.480779i	$0.840354\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.15081	2.07540
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	2.48008	1.01249
$7$	−4.39482	−1.66109	−0.830544	−	0.556954i	$-0.811970\pi$
$7$	−4.39482	−1.66109	−0.830544	+	0.556954i	$0.811970\pi$
$8$	−5.33418	−1.88592
$9$	1.00000	0.333333
$10$	2.48008	0.784271
$11$	0	0
$11$	0	0
$12$	−4.15081	−1.19824
$13$	−2.13795	−0.592961	−0.296481	−	0.955039i	$-0.595813\pi$
$13$	−2.13795	−0.592961	−0.296481	+	0.955039i	$0.595813\pi$
$14$	10.8995	2.91302
$15$	1.00000	0.258199
$16$	4.92760	1.23190
$17$	3.96017	0.960481	0.480241	−	0.877137i	$-0.340549\pi$
$17$	3.96017	0.960481	0.480241	+	0.877137i	$0.340549\pi$
$18$	−2.48008	−0.584561
$19$	−2.15081	−0.493429	−0.246715	−	0.969088i	$-0.579351\pi$
$19$	−2.15081	−0.493429	−0.246715	+	0.969088i	$0.579351\pi$
$20$	−4.15081	−0.928149
$21$	4.39482	0.959029
$22$	0	0
$23$	5.16367	1.07670	0.538350	−	0.842722i	$-0.319048\pi$
$23$	5.16367	1.07670	0.538350	+	0.842722i	$0.319048\pi$
$24$	5.33418	1.08884
$25$	1.00000	0.200000
$26$	5.30230	1.03987
$27$	−1.00000	−0.192450
$28$	−18.2421	−3.44743
$29$	7.93936	1.47430	0.737151	−	0.675728i	$-0.236171\pi$
$29$	7.93936	1.47430	0.737151	+	0.675728i	$0.236171\pi$
$30$	−2.48008	−0.452799
$31$	6.19132	1.11199	0.555997	−	0.831184i	$-0.312337\pi$
$31$	6.19132	1.11199	0.555997	+	0.831184i	$0.312337\pi$
$32$	−1.55248	−0.274443
$33$	0	0
$34$	−9.82154	−1.68438
$35$	4.39482	0.742861
$36$	4.15081	0.691802
$37$	−8.57025	−1.40894	−0.704470	−	0.709733i	$-0.748815\pi$
$37$	−8.57025	−1.40894	−0.704470	+	0.709733i	$0.748815\pi$
$38$	5.33418	0.865319
$39$	2.13795	0.342346
$40$	5.33418	0.843409
$41$	−7.63089	−1.19175	−0.595873	−	0.803079i	$-0.703194\pi$
$41$	−7.63089	−1.19175	−0.595873	+	0.803079i	$0.703194\pi$
$42$	−10.8995	−1.68183
$43$	−2.22321	−0.339036	−0.169518	−	0.985527i	$-0.554221\pi$
$43$	−2.22321	−0.339036	−0.169518	+	0.985527i	$0.554221\pi$
$44$	0	0
$45$	−1.00000	−0.149071
$46$	−12.8063	−1.88819
$47$	6.88285	1.00397	0.501984	−	0.864877i	$-0.332604\pi$
$47$	6.88285	1.00397	0.501984	+	0.864877i	$0.332604\pi$
$48$	−4.92760	−0.711238
$49$	12.3145	1.75921
$50$	−2.48008	−0.350737
$51$	−3.96017	−0.554534
$52$	−8.87423	−1.23063
$53$	−5.69644	−0.782467	−0.391233	−	0.920292i	$-0.627951\pi$
$53$	−5.69644	−0.782467	−0.391233	+	0.920292i	$0.627951\pi$
$54$	2.48008	0.337496
$55$	0	0
$56$	23.4428	3.13268
$57$	2.15081	0.284882
$58$	−19.6903	−2.58546
$59$	3.78170	0.492336	0.246168	−	0.969227i	$-0.420829\pi$
$59$	3.78170	0.492336	0.246168	+	0.969227i	$0.420829\pi$
$60$	4.15081	0.535867
$61$	4.83439	0.618981	0.309490	−	0.950903i	$-0.399842\pi$
$61$	4.83439	0.618981	0.309490	+	0.950903i	$0.399842\pi$
$62$	−15.3550	−1.95009
$63$	−4.39482	−0.553696
$64$	−6.00491	−0.750614
$65$	2.13795	0.265180
$66$	0	0
$67$	9.57025	1.16919	0.584596	−	0.811324i	$-0.301253\pi$
$67$	9.57025	1.16919	0.584596	+	0.811324i	$0.301253\pi$
$68$	16.4379	1.99339
$69$	−5.16367	−0.621632
$70$	−10.8995	−1.30274
$71$	−2.11030	−0.250446	−0.125223	−	0.992129i	$-0.539965\pi$
$71$	−2.11030	−0.250446	−0.125223	+	0.992129i	$0.539965\pi$
$72$	−5.33418	−0.628640
$73$	−14.6506	−1.71472	−0.857362	−	0.514715i	$-0.827898\pi$
$73$	−14.6506	−1.71472	−0.857362	+	0.514715i	$0.827898\pi$
$74$	21.2549	2.47084
$75$	−1.00000	−0.115470
$76$	−8.92760	−1.02407
$77$	0	0
$78$	−5.30230	−0.600367
$79$	3.26111	0.366903	0.183452	−	0.983029i	$-0.441273\pi$
$79$	3.26111	0.366903	0.183452	+	0.983029i	$0.441273\pi$
$80$	−4.92760	−0.550922
$81$	1.00000	0.111111
$82$	18.9252	2.08994
$83$	10.6635	1.17047	0.585233	−	0.810865i	$-0.301003\pi$
$83$	10.6635	1.17047	0.585233	+	0.810865i	$0.301003\pi$
$84$	18.2421	1.99037
$85$	−3.96017	−0.429540
$86$	5.51374	0.594562
$87$	−7.93936	−0.851189
$88$	0	0
$89$	−7.64375	−0.810236	−0.405118	−	0.914264i	$-0.632770\pi$
$89$	−7.64375	−0.810236	−0.405118	+	0.914264i	$0.632770\pi$
$90$	2.48008	0.261424
$91$	9.39592	0.984960
$92$	21.4334	2.23459
$93$	−6.19132	−0.642010
$94$	−17.0700	−1.76064
$95$	2.15081	0.220668
$96$	1.55248	0.158450
$97$	−5.67073	−0.575775	−0.287888	−	0.957664i	$-0.592953\pi$
$97$	−5.67073	−0.575775	−0.287888	+	0.957664i	$0.592953\pi$
$98$	−30.5409	−3.08510
$99$	0	0
$100$	4.15081	0.415081
$101$	−7.03366	−0.699876	−0.349938	−	0.936773i	$-0.613797\pi$
$101$	−7.03366	−0.699876	−0.349938	+	0.936773i	$0.613797\pi$
$102$	9.82154	0.972477
$103$	0.622945	0.0613806	0.0306903	−	0.999529i	$-0.490229\pi$
$103$	0.622945	0.0613806	0.0306903	+	0.999529i	$0.490229\pi$
$104$	11.4042	1.11828
$105$	−4.39482	−0.428891
$106$	14.1276	1.37220
$107$	17.8847	1.72898	0.864491	−	0.502648i	$-0.167641\pi$
$107$	17.8847	1.72898	0.864491	+	0.502648i	$0.167641\pi$
$108$	−4.15081	−0.399412
$109$	13.1041	1.25515	0.627574	−	0.778557i	$-0.284048\pi$
$109$	13.1041	1.25515	0.627574	+	0.778557i	$0.284048\pi$
$110$	0	0
$111$	8.57025	0.813452
$112$	−21.6559	−2.04629
$113$	−8.38755	−0.789035	−0.394517	−	0.918888i	$-0.629088\pi$
$113$	−8.38755	−0.789035	−0.394517	+	0.918888i	$0.629088\pi$
$114$	−5.33418	−0.499592
$115$	−5.16367	−0.481514
$116$	32.9548	3.05977
$117$	−2.13795	−0.197654
$118$	−9.37893	−0.863401
$119$	−17.4042	−1.59544
$120$	−5.33418	−0.486942
$121$	0	0
$122$	−11.9897	−1.08550
$123$	7.63089	0.688054
$124$	25.6990	2.30784
$125$	−1.00000	−0.0894427
$126$	10.8995	0.971007
$127$	10.9828	0.974570	0.487285	−	0.873243i	$-0.337987\pi$
$127$	10.9828	0.974570	0.487285	+	0.873243i	$0.337987\pi$
$128$	17.9976	1.59078
$129$	2.22321	0.195743
$130$	−5.30230	−0.465042
$131$	−7.33115	−0.640525	−0.320263	−	0.947329i	$-0.603771\pi$
$131$	−7.33115	−0.640525	−0.320263	+	0.947329i	$0.603771\pi$
$132$	0	0
$133$	9.45243	0.819629
$134$	−23.7350	−2.05039
$135$	1.00000	0.0860663
$136$	−21.1243	−1.81139
$137$	−16.6774	−1.42485	−0.712424	−	0.701750i	$-0.752403\pi$
$137$	−16.6774	−1.42485	−0.712424	+	0.701750i	$0.752403\pi$
$138$	12.8063	1.09015
$139$	−11.0386	−0.936280	−0.468140	−	0.883654i	$-0.655076\pi$
$139$	−11.0386	−0.936280	−0.468140	+	0.883654i	$0.655076\pi$
$140$	18.2421	1.54174
$141$	−6.88285	−0.579641
$142$	5.23371	0.439203
$143$	0	0
$144$	4.92760	0.410633
$145$	−7.93936	−0.659328
$146$	36.3347	3.00708
$147$	−12.3145	−1.01568
$148$	−35.5735	−2.92412
$149$	4.61118	0.377763	0.188881	−	0.982000i	$-0.439514\pi$
$149$	4.61118	0.377763	0.188881	+	0.982000i	$0.439514\pi$
$150$	2.48008	0.202498
$151$	−9.00914	−0.733154	−0.366577	−	0.930388i	$-0.619470\pi$
$151$	−9.00914	−0.733154	−0.366577	+	0.930388i	$0.619470\pi$
$152$	11.4728	0.930568
$153$	3.96017	0.320160
$154$	0	0
$155$	−6.19132	−0.497299
$156$	8.87423	0.710507
$157$	2.98902	0.238550	0.119275	−	0.992861i	$-0.461943\pi$
$157$	2.98902	0.238550	0.119275	+	0.992861i	$0.461943\pi$
$158$	−8.08781	−0.643432
$159$	5.69644	0.451757
$160$	1.55248	0.122735
$161$	−22.6934	−1.78849
$162$	−2.48008	−0.194854
$163$	−2.89571	−0.226810	−0.113405	−	0.993549i	$-0.536176\pi$
$163$	−2.89571	−0.226810	−0.113405	+	0.993549i	$0.536176\pi$
$164$	−31.6744	−2.47335
$165$	0	0
$166$	−26.4463	−2.05263
$167$	−3.80512	−0.294449	−0.147225	−	0.989103i	$-0.547034\pi$
$167$	−3.80512	−0.294449	−0.147225	+	0.989103i	$0.547034\pi$
$168$	−23.4428	−1.80865
$169$	−8.42916	−0.648397
$170$	9.82154	0.753277
$171$	−2.15081	−0.164476
$172$	−9.22812	−0.703638
$173$	−1.11291	−0.0846132	−0.0423066	−	0.999105i	$-0.513471\pi$
$173$	−1.11291	−0.0846132	−0.0423066	+	0.999105i	$0.513471\pi$
$174$	19.6903	1.49272
$175$	−4.39482	−0.332217
$176$	0	0
$177$	−3.78170	−0.284250
$178$	18.9571	1.42090
$179$	−4.81918	−0.360202	−0.180101	−	0.983648i	$-0.557643\pi$
$179$	−4.81918	−0.360202	−0.180101	+	0.983648i	$0.557643\pi$
$180$	−4.15081	−0.309383
$181$	−21.4623	−1.59528	−0.797638	−	0.603136i	$-0.793918\pi$
$181$	−21.4623	−1.59528	−0.797638	+	0.603136i	$0.793918\pi$
$182$	−23.3027	−1.72731
$183$	−4.83439	−0.357369
$184$	−27.5440	−2.03057
$185$	8.57025	0.630097
$186$	15.3550	1.12588
$187$	0	0
$188$	28.5694	2.08364
$189$	4.39482	0.319676
$190$	−5.33418	−0.386982
$191$	−9.36184	−0.677399	−0.338699	−	0.940895i	$-0.609987\pi$
$191$	−9.36184	−0.677399	−0.338699	+	0.940895i	$0.609987\pi$
$192$	6.00491	0.433367
$193$	−18.4088	−1.32509	−0.662546	−	0.749021i	$-0.730524\pi$
$193$	−18.4088	−1.32509	−0.662546	+	0.749021i	$0.730524\pi$
$194$	14.0639	1.00973
$195$	−2.13795	−0.153102
$196$	51.1150	3.65107
$197$	−4.67182	−0.332854	−0.166427	−	0.986054i	$-0.553223\pi$
$197$	−4.67182	−0.332854	−0.166427	+	0.986054i	$0.553223\pi$
$198$	0	0
$199$	−16.2018	−1.14852	−0.574258	−	0.818674i	$-0.694710\pi$
$199$	−16.2018	−1.14852	−0.574258	+	0.818674i	$0.694710\pi$
$200$	−5.33418	−0.377184
$201$	−9.57025	−0.675034
$202$	17.4441	1.22736
$203$	−34.8921	−2.44894
$204$	−16.4379	−1.15088
$205$	7.63089	0.532965
$206$	−1.54496	−0.107642
$207$	5.16367	0.358900
$208$	−10.5350	−0.730469
$209$	0	0
$210$	10.8995	0.752139
$211$	−6.40465	−0.440914	−0.220457	−	0.975397i	$-0.570755\pi$
$211$	−6.40465	−0.440914	−0.220457	+	0.975397i	$0.570755\pi$
$212$	−23.6448	−1.62393
$213$	2.11030	0.144595
$214$	−44.3556	−3.03209
$215$	2.22321	0.151622
$216$	5.33418	0.362945
$217$	−27.2098	−1.84712
$218$	−32.4993	−2.20113
$219$	14.6506	0.989996
$220$	0	0
$221$	−8.46664	−0.569528
$222$	−21.2549	−1.42654
$223$	−14.3520	−0.961078	−0.480539	−	0.876973i	$-0.659559\pi$
$223$	−14.3520	−0.961078	−0.480539	+	0.876973i	$0.659559\pi$
$224$	6.82289	0.455874
$225$	1.00000	0.0666667
$226$	20.8018	1.38372
$227$	18.3113	1.21537	0.607683	−	0.794180i	$-0.292099\pi$
$227$	18.3113	1.21537	0.607683	+	0.794180i	$0.292099\pi$
$228$	8.92760	0.591245
$229$	−18.9191	−1.25021	−0.625104	−	0.780542i	$-0.714943\pi$
$229$	−18.9191	−1.25021	−0.625104	+	0.780542i	$0.714943\pi$
$230$	12.8063	0.844424
$231$	0	0
$232$	−42.3500	−2.78041
$233$	−6.35813	−0.416535	−0.208267	−	0.978072i	$-0.566782\pi$
$233$	−6.35813	−0.416535	−0.208267	+	0.978072i	$0.566782\pi$
$234$	5.30230	0.346622
$235$	−6.88285	−0.448988
$236$	15.6971	1.02180
$237$	−3.26111	−0.211832
$238$	43.1639	2.79790
$239$	−13.6150	−0.880681	−0.440341	−	0.897831i	$-0.645142\pi$
$239$	−13.6150	−0.880681	−0.440341	+	0.897831i	$0.645142\pi$
$240$	4.92760	0.318075
$241$	10.1564	0.654231	0.327116	−	0.944984i	$-0.393923\pi$
$241$	10.1564	0.654231	0.327116	+	0.944984i	$0.393923\pi$
$242$	0	0
$243$	−1.00000	−0.0641500
$244$	20.0666	1.28464
$245$	−12.3145	−0.786743
$246$	−18.9252	−1.20663
$247$	4.59833	0.292584
$248$	−33.0257	−2.09713
$249$	−10.6635	−0.675769
$250$	2.48008	0.156854
$251$	15.7579	0.994627	0.497314	−	0.867571i	$-0.334320\pi$
$251$	15.7579	0.994627	0.497314	+	0.867571i	$0.334320\pi$
$252$	−18.2421	−1.14914
$253$	0	0
$254$	−27.2384	−1.70909
$255$	3.96017	0.247995
$256$	−32.6258	−2.03911
$257$	−1.36335	−0.0850437	−0.0425218	−	0.999096i	$-0.513539\pi$
$257$	−1.36335	−0.0850437	−0.0425218	+	0.999096i	$0.513539\pi$
$258$	−5.51374	−0.343271
$259$	37.6647	2.34037
$260$	8.87423	0.550356
$261$	7.93936	0.491434
$262$	18.1819	1.12328
$263$	−8.12002	−0.500702	−0.250351	−	0.968155i	$-0.580546\pi$
$263$	−8.12002	−0.500702	−0.250351	+	0.968155i	$0.580546\pi$
$264$	0	0
$265$	5.69644	0.349930
$266$	−23.4428	−1.43737
$267$	7.64375	0.467790
$268$	39.7243	2.42655
$269$	−11.7112	−0.714047	−0.357023	−	0.934095i	$-0.616208\pi$
$269$	−11.7112	−0.714047	−0.357023	+	0.934095i	$0.616208\pi$
$270$	−2.48008	−0.150933
$271$	2.18651	0.132821	0.0664106	−	0.997792i	$-0.478845\pi$
$271$	2.18651	0.132821	0.0664106	+	0.997792i	$0.478845\pi$
$272$	19.5141	1.18322
$273$	−9.39592	−0.568667
$274$	41.3614	2.49873
$275$	0	0
$276$	−21.4334	−1.29014
$277$	10.6733	0.641295	0.320648	−	0.947199i	$-0.396099\pi$
$277$	10.6733	0.641295	0.320648	+	0.947199i	$0.396099\pi$
$278$	27.3766	1.64194
$279$	6.19132	0.370665
$280$	−23.4428	−1.40098
$281$	5.43272	0.324089	0.162044	−	0.986783i	$-0.448191\pi$
$281$	5.43272	0.324089	0.162044	+	0.986783i	$0.448191\pi$
$282$	17.0700	1.01651
$283$	18.2401	1.08426	0.542132	−	0.840293i	$-0.317617\pi$
$283$	18.2401	1.08426	0.542132	+	0.840293i	$0.317617\pi$
$284$	−8.75944	−0.519777
$285$	−2.15081	−0.127403
$286$	0	0
$287$	33.5364	1.97959
$288$	−1.55248	−0.0914810
$289$	−1.31709	−0.0774761
$290$	19.6903	1.15625
$291$	5.67073	0.332424
$292$	−60.8118	−3.55874
$293$	−15.8594	−0.926518	−0.463259	−	0.886223i	$-0.653320\pi$
$293$	−15.8594	−0.926518	−0.463259	+	0.886223i	$0.653320\pi$
$294$	30.5409	1.78118
$295$	−3.78170	−0.220179
$296$	45.7153	2.65715
$297$	0	0
$298$	−11.4361	−0.662476
$299$	−11.0397	−0.638441
$300$	−4.15081	−0.239647
$301$	9.77062	0.563169
$302$	22.3434	1.28572
$303$	7.03366	0.404073
$304$	−10.5983	−0.607856
$305$	−4.83439	−0.276817
$306$	−9.82154	−0.561460
$307$	−18.1026	−1.03317	−0.516585	−	0.856236i	$-0.672797\pi$
$307$	−18.1026	−1.03317	−0.516585	+	0.856236i	$0.672797\pi$
$308$	0	0
$309$	−0.622945	−0.0354381
$310$	15.3550	0.872105
$311$	−18.3391	−1.03991	−0.519957	−	0.854192i	$-0.674052\pi$
$311$	−18.3391	−1.03991	−0.519957	+	0.854192i	$0.674052\pi$
$312$	−11.4042	−0.645637
$313$	30.2483	1.70974	0.854869	−	0.518844i	$-0.173638\pi$
$313$	30.2483	1.70974	0.854869	+	0.518844i	$0.173638\pi$
$314$	−7.41301	−0.418340
$315$	4.39482	0.247620
$316$	13.5362	0.761472
$317$	30.5985	1.71858	0.859292	−	0.511485i	$-0.170904\pi$
$317$	30.5985	1.71858	0.859292	+	0.511485i	$0.170904\pi$
$318$	−14.1276	−0.792239
$319$	0	0
$320$	6.00491	0.335685
$321$	−17.8847	−0.998228
$322$	56.2815	3.13645
$323$	−8.51756	−0.473930
$324$	4.15081	0.230601
$325$	−2.13795	−0.118592
$326$	7.18160	0.397752
$327$	−13.1041	−0.724660
$328$	40.7046	2.24753
$329$	−30.2489	−1.66768
$330$	0	0
$331$	−1.09362	−0.0601110	−0.0300555	−	0.999548i	$-0.509568\pi$
$331$	−1.09362	−0.0601110	−0.0300555	+	0.999548i	$0.509568\pi$
$332$	44.2620	2.42919
$333$	−8.57025	−0.469647
$334$	9.43702	0.516371
$335$	−9.57025	−0.522879
$336$	21.6559	1.18143
$337$	16.2674	0.886140	0.443070	−	0.896487i	$-0.353889\pi$
$337$	16.2674	0.886140	0.443070	+	0.896487i	$0.353889\pi$
$338$	20.9050	1.13708
$339$	8.38755	0.455549
$340$	−16.4379	−0.891470
$341$	0	0
$342$	5.33418	0.288440
$343$	−23.3562	−1.26112
$344$	11.8590	0.639395
$345$	5.16367	0.278002
$346$	2.76012	0.148385
$347$	7.88599	0.423342	0.211671	−	0.977341i	$-0.432109\pi$
$347$	7.88599	0.423342	0.211671	+	0.977341i	$0.432109\pi$
$348$	−32.9548	−1.76656
$349$	−12.4119	−0.664395	−0.332197	−	0.943210i	$-0.607790\pi$
$349$	−12.4119	−0.664395	−0.332197	+	0.943210i	$0.607790\pi$
$350$	10.8995	0.582604
$351$	2.13795	0.114115
$352$	0	0
$353$	−13.7984	−0.734413	−0.367207	−	0.930139i	$-0.619686\pi$
$353$	−13.7984	−0.734413	−0.367207	+	0.930139i	$0.619686\pi$
$354$	9.37893	0.498485
$355$	2.11030	0.112003
$356$	−31.7277	−1.68157
$357$	17.4042	0.921129
$358$	11.9520	0.631681
$359$	−21.6248	−1.14131	−0.570657	−	0.821188i	$-0.693311\pi$
$359$	−21.6248	−1.14131	−0.570657	+	0.821188i	$0.693311\pi$
$360$	5.33418	0.281136
$361$	−14.3740	−0.756527
$362$	53.2282	2.79761
$363$	0	0
$364$	39.0007	2.04419
$365$	14.6506	0.766847
$366$	11.9897	0.626711
$367$	23.1283	1.20729	0.603644	−	0.797254i	$-0.293715\pi$
$367$	23.1283	1.20729	0.603644	+	0.797254i	$0.293715\pi$
$368$	25.4445	1.32639
$369$	−7.63089	−0.397248
$370$	−21.2549	−1.10499
$371$	25.0349	1.29975
$372$	−25.6990	−1.33243
$373$	−23.7304	−1.22871	−0.614356	−	0.789029i	$-0.710584\pi$
$373$	−23.7304	−1.22871	−0.614356	+	0.789029i	$0.710584\pi$
$374$	0	0
$375$	1.00000	0.0516398
$376$	−36.7144	−1.89340
$377$	−16.9740	−0.874204
$378$	−10.8995	−0.560611
$379$	−33.0484	−1.69758	−0.848791	−	0.528728i	$-0.822669\pi$
$379$	−33.0484	−1.69758	−0.848791	+	0.528728i	$0.822669\pi$
$380$	8.92760	0.457976
$381$	−10.9828	−0.562668
$382$	23.2181	1.18794
$383$	−7.97370	−0.407437	−0.203719	−	0.979029i	$-0.565303\pi$
$383$	−7.97370	−0.407437	−0.203719	+	0.979029i	$0.565303\pi$
$384$	−17.9976	−0.918438
$385$	0	0
$386$	45.6553	2.32379
$387$	−2.22321	−0.113012
$388$	−23.5381	−1.19497
$389$	4.28766	0.217393	0.108697	−	0.994075i	$-0.465332\pi$
$389$	4.28766	0.217393	0.108697	+	0.994075i	$0.465332\pi$
$390$	5.30230	0.268492
$391$	20.4490	1.03415
$392$	−65.6877	−3.31773
$393$	7.33115	0.369808
$394$	11.5865	0.583720
$395$	−3.26111	−0.164084
$396$	0	0
$397$	−2.21087	−0.110961	−0.0554803	−	0.998460i	$-0.517669\pi$
$397$	−2.21087	−0.110961	−0.0554803	+	0.998460i	$0.517669\pi$
$398$	40.1819	2.01413
$399$	−9.45243	−0.473213
$400$	4.92760	0.246380
$401$	12.1478	0.606631	0.303315	−	0.952890i	$-0.401906\pi$
$401$	12.1478	0.606631	0.303315	+	0.952890i	$0.401906\pi$
$402$	23.7350	1.18379
$403$	−13.2367	−0.659369
$404$	−29.1954	−1.45252
$405$	−1.00000	−0.0496904
$406$	86.5353	4.29467
$407$	0	0
$408$	21.1243	1.04581
$409$	33.8603	1.67428	0.837142	−	0.546985i	$-0.184225\pi$
$409$	33.8603	1.67428	0.837142	+	0.546985i	$0.184225\pi$
$410$	−18.9252	−0.934651
$411$	16.6774	0.822636
$412$	2.58573	0.127390
$413$	−16.6199	−0.817812
$414$	−12.8063	−0.629396
$415$	−10.6635	−0.523449
$416$	3.31913	0.162734
$417$	11.0386	0.540561
$418$	0	0
$419$	18.1583	0.887093	0.443546	−	0.896251i	$-0.353720\pi$
$419$	18.1583	0.887093	0.443546	+	0.896251i	$0.353720\pi$
$420$	−18.2421	−0.890122
$421$	39.1558	1.90834	0.954169	−	0.299269i	$-0.0967428\pi$
$421$	39.1558	1.90834	0.954169	+	0.299269i	$0.0967428\pi$
$422$	15.8841	0.773224
$423$	6.88285	0.334656
$424$	30.3859	1.47567
$425$	3.96017	0.192096
$426$	−5.23371	−0.253574
$427$	−21.2463	−1.02818
$428$	74.2361	3.58834
$429$	0	0
$430$	−5.51374	−0.265896
$431$	22.8319	1.09978	0.549888	−	0.835239i	$-0.314670\pi$
$431$	22.8319	1.09978	0.549888	+	0.835239i	$0.314670\pi$
$432$	−4.92760	−0.237079
$433$	5.89190	0.283146	0.141573	−	0.989928i	$-0.454784\pi$
$433$	5.89190	0.283146	0.141573	+	0.989928i	$0.454784\pi$
$434$	67.4825	3.23926
$435$	7.93936	0.380663
$436$	54.3927	2.60494
$437$	−11.1061	−0.531275
$438$	−36.3347	−1.73614
$439$	5.46570	0.260864	0.130432	−	0.991457i	$-0.458364\pi$
$439$	5.46570	0.260864	0.130432	+	0.991457i	$0.458364\pi$
$440$	0	0
$441$	12.3145	0.586404
$442$	20.9980	0.998771
$443$	25.2148	1.19799	0.598995	−	0.800753i	$-0.295567\pi$
$443$	25.2148	1.19799	0.598995	+	0.800753i	$0.295567\pi$
$444$	35.5735	1.68824
$445$	7.64375	0.362348
$446$	35.5940	1.68543
$447$	−4.61118	−0.218102
$448$	26.3905	1.24684
$449$	14.8612	0.701344	0.350672	−	0.936498i	$-0.385953\pi$
$449$	14.8612	0.701344	0.350672	+	0.936498i	$0.385953\pi$
$450$	−2.48008	−0.116912
$451$	0	0
$452$	−34.8151	−1.63757
$453$	9.00914	0.423287
$454$	−45.4136	−2.13137
$455$	−9.39592	−0.440488
$456$	−11.4728	−0.537264
$457$	−38.6831	−1.80952	−0.904760	−	0.425923i	$-0.859950\pi$
$457$	−38.6831	−1.80952	−0.904760	+	0.425923i	$0.859950\pi$
$458$	46.9209	2.19247
$459$	−3.96017	−0.184845
$460$	−21.4334	−0.999337
$461$	−4.32624	−0.201493	−0.100746	−	0.994912i	$-0.532123\pi$
$461$	−4.32624	−0.201493	−0.100746	+	0.994912i	$0.532123\pi$
$462$	0	0
$463$	0.723001	0.0336007	0.0168003	−	0.999859i	$-0.494652\pi$
$463$	0.723001	0.0336007	0.0168003	+	0.999859i	$0.494652\pi$
$464$	39.1220	1.81619
$465$	6.19132	0.287116
$466$	15.7687	0.730470
$467$	−19.8965	−0.920700	−0.460350	−	0.887738i	$-0.652276\pi$
$467$	−19.8965	−0.920700	−0.460350	+	0.887738i	$0.652276\pi$
$468$	−8.87423	−0.410211
$469$	−42.0596	−1.94213
$470$	17.0700	0.787382
$471$	−2.98902	−0.137727
$472$	−20.1723	−0.928505
$473$	0	0
$474$	8.08781	0.371486
$475$	−2.15081	−0.0986859
$476$	−72.2416	−3.31119
$477$	−5.69644	−0.260822
$478$	33.7663	1.54444
$479$	−18.7395	−0.856230	−0.428115	−	0.903724i	$-0.640822\pi$
$479$	−18.7395	−0.856230	−0.428115	+	0.903724i	$0.640822\pi$
$480$	−1.55248	−0.0708608
$481$	18.3228	0.835447
$482$	−25.1887	−1.14731
$483$	22.6934	1.03259
$484$	0	0
$485$	5.67073	0.257494
$486$	2.48008	0.112499
$487$	−0.524245	−0.0237558	−0.0118779	−	0.999929i	$-0.503781\pi$
$487$	−0.524245	−0.0237558	−0.0118779	+	0.999929i	$0.503781\pi$
$488$	−25.7875	−1.16735
$489$	2.89571	0.130949
$490$	30.5409	1.37970
$491$	20.4709	0.923838	0.461919	−	0.886922i	$-0.347161\pi$
$491$	20.4709	0.923838	0.461919	+	0.886922i	$0.347161\pi$
$492$	31.6744	1.42799
$493$	31.4412	1.41604
$494$	−11.4042	−0.513100
$495$	0	0
$496$	30.5084	1.36987
$497$	9.27438	0.416013
$498$	26.4463	1.18509
$499$	−4.56237	−0.204240	−0.102120	−	0.994772i	$-0.532563\pi$
$499$	−4.56237	−0.204240	−0.102120	+	0.994772i	$0.532563\pi$
$500$	−4.15081	−0.185630
$501$	3.80512	0.170000
$502$	−39.0808	−1.74426
$503$	−23.4683	−1.04640	−0.523199	−	0.852211i	$-0.675262\pi$
$503$	−23.4683	−1.04640	−0.523199	+	0.852211i	$0.675262\pi$
$504$	23.4428	1.04423
$505$	7.03366	0.312994
$506$	0	0
$507$	8.42916	0.374352
$508$	45.5877	2.02263
$509$	4.74119	0.210149	0.105075	−	0.994464i	$-0.466492\pi$
$509$	4.74119	0.210149	0.105075	+	0.994464i	$0.466492\pi$
$510$	−9.82154	−0.434905
$511$	64.3868	2.84830
$512$	44.9194	1.98518
$513$	2.15081	0.0949605
$514$	3.38123	0.149140
$515$	−0.622945	−0.0274502
$516$	9.22812	0.406245
$517$	0	0
$518$	−93.4117	−4.10427
$519$	1.11291	0.0488515
$520$	−11.4042	−0.500108
$521$	−33.8092	−1.48121	−0.740604	−	0.671942i	$-0.765460\pi$
$521$	−33.8092	−1.48121	−0.740604	+	0.671942i	$0.765460\pi$
$522$	−19.6903	−0.861820
$523$	−28.1112	−1.22922	−0.614609	−	0.788832i	$-0.710686\pi$
$523$	−28.1112	−1.22922	−0.614609	+	0.788832i	$0.710686\pi$
$524$	−30.4302	−1.32935
$525$	4.39482	0.191806
$526$	20.1383	0.878072
$527$	24.5187	1.06805
$528$	0	0
$529$	3.66346	0.159281
$530$	−14.1276	−0.613666
$531$	3.78170	0.164112
$532$	39.2352	1.70106
$533$	16.3145	0.706658
$534$	−18.9571	−0.820355
$535$	−17.8847	−0.773224
$536$	−51.0495	−2.20500
$537$	4.81918	0.207963
$538$	29.0448	1.25221
$539$	0	0
$540$	4.15081	0.178622
$541$	14.1474	0.608242	0.304121	−	0.952633i	$-0.401637\pi$
$541$	14.1474	0.608242	0.304121	+	0.952633i	$0.401637\pi$
$542$	−5.42273	−0.232926
$543$	21.4623	0.921033
$544$	−6.14809	−0.263597
$545$	−13.1041	−0.561319
$546$	23.3027	0.997262
$547$	−31.6553	−1.35348	−0.676742	−	0.736220i	$-0.736609\pi$
$547$	−31.6553	−1.35348	−0.676742	+	0.736220i	$0.736609\pi$
$548$	−69.2248	−2.95713
$549$	4.83439	0.206327
$550$	0	0
$551$	−17.0761	−0.727464
$552$	27.5440	1.17235
$553$	−14.3320	−0.609458
$554$	−26.4706	−1.12463
$555$	−8.57025	−0.363787
$556$	−45.8190	−1.94316
$557$	−27.1124	−1.14879	−0.574395	−	0.818578i	$-0.694763\pi$
$557$	−27.1124	−1.14879	−0.574395	+	0.818578i	$0.694763\pi$
$558$	−15.3550	−0.650029
$559$	4.75312	0.201035
$560$	21.6559	0.915130
$561$	0	0
$562$	−13.4736	−0.568349
$563$	−24.0556	−1.01382	−0.506911	−	0.861999i	$-0.669213\pi$
$563$	−24.0556	−1.01382	−0.506911	+	0.861999i	$0.669213\pi$
$564$	−28.5694	−1.20299
$565$	8.38755	0.352867
$566$	−45.2370	−1.90145
$567$	−4.39482	−0.184565
$568$	11.2567	0.472321
$569$	27.8406	1.16714	0.583569	−	0.812063i	$-0.301656\pi$
$569$	27.8406	1.16714	0.583569	+	0.812063i	$0.301656\pi$
$570$	5.33418	0.223424
$571$	−33.5792	−1.40525	−0.702624	−	0.711562i	$-0.747988\pi$
$571$	−33.5792	−1.40525	−0.702624	+	0.711562i	$0.747988\pi$
$572$	0	0
$573$	9.36184	0.391096
$574$	−83.1731	−3.47158
$575$	5.16367	0.215340
$576$	−6.00491	−0.250205
$577$	−19.1012	−0.795191	−0.397596	−	0.917561i	$-0.630155\pi$
$577$	−19.1012	−0.795191	−0.397596	+	0.917561i	$0.630155\pi$
$578$	3.26650	0.135868
$579$	18.4088	0.765043
$580$	−32.9548	−1.36837
$581$	−46.8640	−1.94425
$582$	−14.0639	−0.582966
$583$	0	0
$584$	78.1490	3.23383
$585$	2.13795	0.0883934
$586$	39.3327	1.62482
$587$	−21.3648	−0.881820	−0.440910	−	0.897551i	$-0.645344\pi$
$587$	−21.3648	−0.881820	−0.440910	+	0.897551i	$0.645344\pi$
$588$	−51.1150	−2.10795
$589$	−13.3164	−0.548691
$590$	9.37893	0.386124
$591$	4.67182	0.192173
$592$	−42.2308	−1.73567
$593$	−9.16002	−0.376157	−0.188078	−	0.982154i	$-0.560226\pi$
$593$	−9.16002	−0.376157	−0.188078	+	0.982154i	$0.560226\pi$
$594$	0	0
$595$	17.4042	0.713504
$596$	19.1401	0.784011
$597$	16.2018	0.663096
$598$	27.3793	1.11962
$599$	−3.39567	−0.138743	−0.0693716	−	0.997591i	$-0.522099\pi$
$599$	−3.39567	−0.138743	−0.0693716	+	0.997591i	$0.522099\pi$
$600$	5.33418	0.217767
$601$	−14.4385	−0.588958	−0.294479	−	0.955658i	$-0.595146\pi$
$601$	−14.4385	−0.588958	−0.294479	+	0.955658i	$0.595146\pi$
$602$	−24.2319	−0.987620
$603$	9.57025	0.389731
$604$	−37.3952	−1.52159
$605$	0	0
$606$	−17.4441	−0.708617
$607$	1.37689	0.0558862	0.0279431	−	0.999610i	$-0.491104\pi$
$607$	1.37689	0.0558862	0.0279431	+	0.999610i	$0.491104\pi$
$608$	3.33910	0.135418
$609$	34.8921	1.41390
$610$	11.9897	0.485449
$611$	−14.7152	−0.595313
$612$	16.4379	0.664462
$613$	1.19074	0.0480934	0.0240467	−	0.999711i	$-0.492345\pi$
$613$	1.19074	0.0480934	0.0240467	+	0.999711i	$0.492345\pi$
$614$	44.8960	1.81185
$615$	−7.63089	−0.307707
$616$	0	0
$617$	−10.9076	−0.439122	−0.219561	−	0.975599i	$-0.570463\pi$
$617$	−10.9076	−0.439122	−0.219561	+	0.975599i	$0.570463\pi$
$618$	1.54496	0.0621472
$619$	−28.7339	−1.15491	−0.577457	−	0.816421i	$-0.695955\pi$
$619$	−28.7339	−1.15491	−0.577457	+	0.816421i	$0.695955\pi$
$620$	−25.6990	−1.03210
$621$	−5.16367	−0.207211
$622$	45.4825	1.82368
$623$	33.5929	1.34587
$624$	10.5350	0.421736
$625$	1.00000	0.0400000
$626$	−75.0184	−2.99834
$627$	0	0
$628$	12.4068	0.495087
$629$	−33.9396	−1.35326
$630$	−10.8995	−0.434247
$631$	33.7376	1.34307	0.671536	−	0.740972i	$-0.265635\pi$
$631$	33.7376	1.34307	0.671536	+	0.740972i	$0.265635\pi$
$632$	−17.3953	−0.691950
$633$	6.40465	0.254562
$634$	−75.8869	−3.01385
$635$	−10.9828	−0.435841
$636$	23.6448	0.937579
$637$	−26.3278	−1.04314
$638$	0	0
$639$	−2.11030	−0.0834821
$640$	−17.9976	−0.711419
$641$	−17.5210	−0.692036	−0.346018	−	0.938228i	$-0.612466\pi$
$641$	−17.5210	−0.692036	−0.346018	+	0.938228i	$0.612466\pi$
$642$	44.3556	1.75058
$643$	−0.699059	−0.0275682	−0.0137841	−	0.999905i	$-0.504388\pi$
$643$	−0.699059	−0.0275682	−0.0137841	+	0.999905i	$0.504388\pi$
$644$	−94.1960	−3.71184
$645$	−2.22321	−0.0875388
$646$	21.1243	0.831123
$647$	45.4242	1.78581	0.892905	−	0.450246i	$-0.148664\pi$
$647$	45.4242	1.78581	0.892905	+	0.450246i	$0.148664\pi$
$648$	−5.33418	−0.209547
$649$	0	0
$650$	5.30230	0.207973
$651$	27.2098	1.06643
$652$	−12.0195	−0.470722
$653$	37.1061	1.45207	0.726036	−	0.687656i	$-0.241360\pi$
$653$	37.1061	1.45207	0.726036	+	0.687656i	$0.241360\pi$
$654$	32.4993	1.27082
$655$	7.33115	0.286452
$656$	−37.6020	−1.46811
$657$	−14.6506	−0.571574
$658$	75.0198	2.92458
$659$	16.0716	0.626061	0.313031	−	0.949743i	$-0.398656\pi$
$659$	16.0716	0.626061	0.313031	+	0.949743i	$0.398656\pi$
$660$	0	0
$661$	42.1478	1.63936	0.819680	−	0.572822i	$-0.194151\pi$
$661$	42.1478	1.63936	0.819680	+	0.572822i	$0.194151\pi$
$662$	2.71228	0.105416
$663$	8.46664	0.328817
$664$	−56.8809	−2.20741
$665$	−9.45243	−0.366549
$666$	21.2549	0.823612
$667$	40.9962	1.58738
$668$	−15.7943	−0.611101
$669$	14.3520	0.554879
$670$	23.7350	0.916964
$671$	0	0
$672$	−6.82289	−0.263199
$673$	−38.9658	−1.50202	−0.751010	−	0.660291i	$-0.770433\pi$
$673$	−38.9658	−1.50202	−0.751010	+	0.660291i	$0.770433\pi$
$674$	−40.3444	−1.55401
$675$	−1.00000	−0.0384900
$676$	−34.9879	−1.34569
$677$	−1.42510	−0.0547709	−0.0273854	−	0.999625i	$-0.508718\pi$
$677$	−1.42510	−0.0547709	−0.0273854	+	0.999625i	$0.508718\pi$
$678$	−20.8018	−0.798889
$679$	24.9218	0.956413
$680$	21.1243	0.810078
$681$	−18.3113	−0.701692
$682$	0	0
$683$	−21.1490	−0.809245	−0.404623	−	0.914484i	$-0.632597\pi$
$683$	−21.1490	−0.809245	−0.404623	+	0.914484i	$0.632597\pi$
$684$	−8.92760	−0.341355
$685$	16.6774	0.637211
$686$	57.9253	2.21160
$687$	18.9191	0.721807
$688$	−10.9551	−0.417659
$689$	12.1787	0.463972
$690$	−12.8063	−0.487528
$691$	27.8197	1.05831	0.529155	−	0.848525i	$-0.322509\pi$
$691$	27.8197	1.05831	0.529155	+	0.848525i	$0.322509\pi$
$692$	−4.61949	−0.175607
$693$	0	0
$694$	−19.5579	−0.742408
$695$	11.0386	0.418717
$696$	42.3500	1.60527
$697$	−30.2196	−1.14465
$698$	30.7826	1.16514
$699$	6.35813	0.240486
$700$	−18.2421	−0.689486
$701$	1.45437	0.0549307	0.0274653	−	0.999623i	$-0.491256\pi$
$701$	1.45437	0.0549307	0.0274653	+	0.999623i	$0.491256\pi$
$702$	−5.30230	−0.200122
$703$	18.4330	0.695213
$704$	0	0
$705$	6.88285	0.259223
$706$	34.2211	1.28793
$707$	30.9117	1.16255
$708$	−15.6971	−0.589934
$709$	−12.3696	−0.464551	−0.232275	−	0.972650i	$-0.574617\pi$
$709$	−12.3696	−0.464551	−0.232275	+	0.972650i	$0.574617\pi$
$710$	−5.23371	−0.196418
$711$	3.26111	0.122301
$712$	40.7732	1.52804
$713$	31.9699	1.19728
$714$	−43.1639	−1.61537
$715$	0	0
$716$	−20.0035	−0.747566
$717$	13.6150	0.508461
$718$	53.6313	2.00150
$719$	30.4067	1.13398	0.566989	−	0.823725i	$-0.308108\pi$
$719$	30.4067	1.13398	0.566989	+	0.823725i	$0.308108\pi$
$720$	−4.92760	−0.183641
$721$	−2.73773	−0.101959
$722$	35.6488	1.32671
$723$	−10.1564	−0.377721
$724$	−89.0857	−3.31084
$725$	7.93936	0.294860
$726$	0	0
$727$	36.7184	1.36181	0.680906	−	0.732371i	$-0.261586\pi$
$727$	36.7184	1.36181	0.680906	+	0.732371i	$0.261586\pi$
$728$	−50.1196	−1.85755
$729$	1.00000	0.0370370
$730$	−36.3347	−1.34481
$731$	−8.80428	−0.325638
$732$	−20.0666	−0.741685
$733$	42.8001	1.58086	0.790429	−	0.612554i	$-0.209858\pi$
$733$	42.8001	1.58086	0.790429	+	0.612554i	$0.209858\pi$
$734$	−57.3602	−2.11720
$735$	12.3145	0.454226
$736$	−8.01651	−0.295492
$737$	0	0
$738$	18.9252	0.696648
$739$	−32.2616	−1.18676	−0.593381	−	0.804921i	$-0.702207\pi$
$739$	−32.2616	−1.18676	−0.593381	+	0.804921i	$0.702207\pi$
$740$	35.5735	1.30771
$741$	−4.59833	−0.168924
$742$	−62.0885	−2.27934
$743$	40.5472	1.48753	0.743767	−	0.668439i	$-0.233037\pi$
$743$	40.5472	1.48753	0.743767	+	0.668439i	$0.233037\pi$
$744$	33.0257	1.21078
$745$	−4.61118	−0.168941
$746$	58.8533	2.15477
$747$	10.6635	0.390156
$748$	0	0
$749$	−78.6002	−2.87199
$750$	−2.48008	−0.0905598
$751$	−33.5276	−1.22344	−0.611720	−	0.791074i	$-0.709522\pi$
$751$	−33.5276	−1.22344	−0.611720	+	0.791074i	$0.709522\pi$
$752$	33.9159	1.23679
$753$	−15.7579	−0.574248
$754$	42.0968	1.53308
$755$	9.00914	0.327876
$756$	18.2421	0.663458
$757$	10.8866	0.395679	0.197839	−	0.980234i	$-0.436608\pi$
$757$	10.8866	0.395679	0.197839	+	0.980234i	$0.436608\pi$
$758$	81.9627	2.97702
$759$	0	0
$760$	−11.4728	−0.416163
$761$	−21.7351	−0.787896	−0.393948	−	0.919133i	$-0.628891\pi$
$761$	−21.7351	−0.787896	−0.393948	+	0.919133i	$0.628891\pi$
$762$	27.2384	0.986742
$763$	−57.5903	−2.08491
$764$	−38.8592	−1.40588
$765$	−3.96017	−0.143180
$766$	19.7754	0.714516
$767$	−8.08509	−0.291936
$768$	32.6258	1.17728
$769$	−38.6384	−1.39333	−0.696667	−	0.717394i	$-0.745335\pi$
$769$	−38.6384	−1.39333	−0.696667	+	0.717394i	$0.745335\pi$
$770$	0	0
$771$	1.36335	0.0491000
$772$	−76.4113	−2.75010
$773$	−7.50909	−0.270083	−0.135042	−	0.990840i	$-0.543117\pi$
$773$	−7.50909	−0.270083	−0.135042	+	0.990840i	$0.543117\pi$
$774$	5.51374	0.198187
$775$	6.19132	0.222399
$776$	30.2487	1.08587
$777$	−37.6647	−1.35122
$778$	−10.6338	−0.381239
$779$	16.4126	0.588042
$780$	−8.87423	−0.317748
$781$	0	0
$782$	−50.7151	−1.81357
$783$	−7.93936	−0.283730
$784$	60.6808	2.16717
$785$	−2.98902	−0.106683
$786$	−18.1819	−0.648525
$787$	−37.4105	−1.33354	−0.666770	−	0.745264i	$-0.732324\pi$
$787$	−37.4105	−1.33354	−0.666770	+	0.745264i	$0.732324\pi$
$788$	−19.3918	−0.690806
$789$	8.12002	0.289080
$790$	8.08781	0.287751
$791$	36.8618	1.31066
$792$	0	0
$793$	−10.3357	−0.367031
$794$	5.48315	0.194590
$795$	−5.69644	−0.202032
$796$	−67.2507	−2.38364
$797$	10.7695	0.381476	0.190738	−	0.981641i	$-0.438912\pi$
$797$	10.7695	0.381476	0.190738	+	0.981641i	$0.438912\pi$
$798$	23.4428	0.829866
$799$	27.2572	0.964292
$800$	−1.55248	−0.0548886
$801$	−7.64375	−0.270079
$802$	−30.1275	−1.06384
$803$	0	0
$804$	−39.7243	−1.40097
$805$	22.6934	0.799838
$806$	32.8282	1.15632
$807$	11.7112	0.412255
$808$	37.5189	1.31991
$809$	20.1705	0.709155	0.354578	−	0.935027i	$-0.384625\pi$
$809$	20.1705	0.709155	0.354578	+	0.935027i	$0.384625\pi$
$810$	2.48008	0.0871412
$811$	4.33664	0.152280	0.0761399	−	0.997097i	$-0.475740\pi$
$811$	4.33664	0.152280	0.0761399	+	0.997097i	$0.475740\pi$
$812$	−144.830	−5.08255
$813$	−2.18651	−0.0766843
$814$	0	0
$815$	2.89571	0.101432
$816$	−19.5141	−0.683130
$817$	4.78170	0.167291
$818$	−83.9764	−2.93616
$819$	9.39592	0.328320
$820$	31.6744	1.10612
$821$	44.7129	1.56049	0.780246	−	0.625472i	$-0.215094\pi$
$821$	44.7129	1.56049	0.780246	+	0.625472i	$0.215094\pi$
$822$	−41.3614	−1.44264
$823$	−23.8721	−0.832130	−0.416065	−	0.909335i	$-0.636591\pi$
$823$	−23.8721	−0.832130	−0.416065	+	0.909335i	$0.636591\pi$
$824$	−3.32290	−0.115759
$825$	0	0
$826$	41.2187	1.43418
$827$	3.43278	0.119370	0.0596848	−	0.998217i	$-0.480990\pi$
$827$	3.43278	0.119370	0.0596848	+	0.998217i	$0.480990\pi$
$828$	21.4334	0.744862
$829$	23.8429	0.828097	0.414048	−	0.910255i	$-0.364114\pi$
$829$	23.8429	0.828097	0.414048	+	0.910255i	$0.364114\pi$
$830$	26.4463	0.917963
$831$	−10.6733	−0.370252
$832$	12.8382	0.445085
$833$	48.7674	1.68969
$834$	−27.3766	−0.947973
$835$	3.80512	0.131682
$836$	0	0
$837$	−6.19132	−0.214003
$838$	−45.0342	−1.55568
$839$	−16.6444	−0.574629	−0.287315	−	0.957836i	$-0.592763\pi$
$839$	−16.6444	−0.574629	−0.287315	+	0.957836i	$0.592763\pi$
$840$	23.4428	0.808853
$841$	34.0334	1.17357
$842$	−97.1096	−3.34662
$843$	−5.43272	−0.187113
$844$	−26.5845	−0.915075
$845$	8.42916	0.289972
$846$	−17.0700	−0.586880
$847$	0	0
$848$	−28.0698	−0.963920
$849$	−18.2401	−0.626000
$850$	−9.82154	−0.336876
$851$	−44.2539	−1.51701
$852$	8.75944	0.300093
$853$	4.76800	0.163253	0.0816266	−	0.996663i	$-0.473989\pi$
$853$	4.76800	0.163253	0.0816266	+	0.996663i	$0.473989\pi$
$854$	52.6926	1.80310
$855$	2.15081	0.0735561
$856$	−95.4004	−3.26072
$857$	−27.8195	−0.950296	−0.475148	−	0.879906i	$-0.657605\pi$
$857$	−27.8195	−0.950296	−0.475148	+	0.879906i	$0.657605\pi$
$858$	0	0
$859$	−25.1802	−0.859139	−0.429569	−	0.903034i	$-0.641335\pi$
$859$	−25.1802	−0.859139	−0.429569	+	0.903034i	$0.641335\pi$
$860$	9.22812	0.314676
$861$	−33.5364	−1.14292
$862$	−56.6251	−1.92866
$863$	21.9684	0.747812	0.373906	−	0.927467i	$-0.378018\pi$
$863$	21.9684	0.747812	0.373906	+	0.927467i	$0.378018\pi$
$864$	1.55248	0.0528166
$865$	1.11291	0.0378402
$866$	−14.6124	−0.496549
$867$	1.31709	0.0447308
$868$	−112.943	−3.83352
$869$	0	0
$870$	−19.6903	−0.667563
$871$	−20.4607	−0.693286
$872$	−69.8998	−2.36711
$873$	−5.67073	−0.191925
$874$	27.5440	0.931688
$875$	4.39482	0.148572
$876$	60.8118	2.05464
$877$	33.0169	1.11490	0.557451	−	0.830210i	$-0.311779\pi$
$877$	33.0169	1.11490	0.557451	+	0.830210i	$0.311779\pi$
$878$	−13.5554	−0.457473
$879$	15.8594	0.534925
$880$	0	0
$881$	2.26357	0.0762615	0.0381307	−	0.999273i	$-0.487860\pi$
$881$	2.26357	0.0762615	0.0381307	+	0.999273i	$0.487860\pi$
$882$	−30.5409	−1.02837
$883$	−28.9534	−0.974360	−0.487180	−	0.873302i	$-0.661974\pi$
$883$	−28.9534	−0.974360	−0.487180	+	0.873302i	$0.661974\pi$
$884$	−35.1434	−1.18200
$885$	3.78170	0.127120
$886$	−62.5347	−2.10090
$887$	36.6047	1.22907	0.614533	−	0.788891i	$-0.289345\pi$
$887$	36.6047	1.22907	0.614533	+	0.788891i	$0.289345\pi$
$888$	−45.7153	−1.53411
$889$	−48.2677	−1.61885
$890$	−18.9571	−0.635444
$891$	0	0
$892$	−59.5722	−1.99463
$893$	−14.8037	−0.495387
$894$	11.4361	0.382481
$895$	4.81918	0.161087
$896$	−79.0965	−2.64243
$897$	11.0397	0.368604
$898$	−36.8570	−1.22993
$899$	49.1551	1.63942
$900$	4.15081	0.138360
$901$	−22.5589	−0.751544
$902$	0	0
$903$	−9.77062	−0.325146
$904$	44.7408	1.48806
$905$	21.4623	0.713429
$906$	−22.3434	−0.742311
$907$	23.2651	0.772506	0.386253	−	0.922393i	$-0.373769\pi$
$907$	23.2651	0.772506	0.386253	+	0.922393i	$0.373769\pi$
$908$	76.0069	2.52238
$909$	−7.03366	−0.233292
$910$	23.3027	0.772476
$911$	32.5851	1.07959	0.539796	−	0.841796i	$-0.318501\pi$
$911$	32.5851	1.07959	0.539796	+	0.841796i	$0.318501\pi$
$912$	10.5983	0.350946
$913$	0	0
$914$	95.9373	3.17332
$915$	4.83439	0.159820
$916$	−78.5294	−2.59469
$917$	32.2191	1.06397
$918$	9.82154	0.324159
$919$	4.19869	0.138502	0.0692511	−	0.997599i	$-0.477939\pi$
$919$	4.19869	0.138502	0.0692511	+	0.997599i	$0.477939\pi$
$920$	27.5440	0.908097
$921$	18.1026	0.596501
$922$	10.7294	0.353355
$923$	4.51171	0.148505
$924$	0	0
$925$	−8.57025	−0.281788
$926$	−1.79310	−0.0589250
$927$	0.622945	0.0204602
$928$	−12.3257	−0.404612
$929$	−35.9774	−1.18038	−0.590189	−	0.807265i	$-0.700947\pi$
$929$	−35.9774	−1.18038	−0.590189	+	0.807265i	$0.700947\pi$
$930$	−15.3550	−0.503510
$931$	−26.4861	−0.868047
$932$	−26.3914	−0.864478
$933$	18.3391	0.600395
$934$	49.3449	1.61462
$935$	0	0
$936$	11.4042	0.372759
$937$	20.6219	0.673689	0.336845	−	0.941560i	$-0.390640\pi$
$937$	20.6219	0.673689	0.336845	+	0.941560i	$0.390640\pi$
$938$	104.311	3.40588
$939$	−30.2483	−0.987117
$940$	−28.5694	−0.931831
$941$	−37.4439	−1.22064	−0.610318	−	0.792156i	$-0.708958\pi$
$941$	−37.4439	−1.22064	−0.610318	+	0.792156i	$0.708958\pi$
$942$	7.41301	0.241529
$943$	−39.4034	−1.28315
$944$	18.6347	0.606508
$945$	−4.39482	−0.142964
$946$	0	0
$947$	46.3928	1.50756	0.753781	−	0.657126i	$-0.228228\pi$
$947$	46.3928	1.50756	0.753781	+	0.657126i	$0.228228\pi$
$948$	−13.5362	−0.439636
$949$	31.3223	1.01676
$950$	5.33418	0.173064
$951$	−30.5985	−0.992225
$952$	92.8374	3.00888
$953$	−44.0854	−1.42806	−0.714032	−	0.700113i	$-0.753133\pi$
$953$	−44.0854	−1.42806	−0.714032	+	0.700113i	$0.753133\pi$
$954$	14.1276	0.457399
$955$	9.36184	0.302942
$956$	−56.5133	−1.82777
$957$	0	0
$958$	46.4755	1.50156
$959$	73.2943	2.36680
$960$	−6.00491	−0.193808
$961$	7.33247	0.236531
$962$	−45.4420	−1.46511
$963$	17.8847	0.576327
$964$	42.1573	1.35779
$965$	18.4088	0.592600
$966$	−56.2815	−1.81083
$967$	18.7661	0.603476	0.301738	−	0.953391i	$-0.402433\pi$
$967$	18.7661	0.603476	0.301738	+	0.953391i	$0.402433\pi$
$968$	0	0
$969$	8.51756	0.273623
$970$	−14.0639	−0.451564
$971$	−48.7690	−1.56507	−0.782536	−	0.622605i	$-0.786074\pi$
$971$	−48.7690	−1.56507	−0.782536	+	0.622605i	$0.786074\pi$
$972$	−4.15081	−0.133137
$973$	48.5126	1.55524
$974$	1.30017	0.0416601
$975$	2.13795	0.0684692
$976$	23.8220	0.762522
$977$	18.6971	0.598174	0.299087	−	0.954226i	$-0.403318\pi$
$977$	18.6971	0.598174	0.299087	+	0.954226i	$0.403318\pi$
$978$	−7.18160	−0.229642
$979$	0	0
$980$	−51.1150	−1.63281
$981$	13.1041	0.418382
$982$	−50.7695	−1.62012
$983$	−39.6527	−1.26473	−0.632363	−	0.774672i	$-0.717915\pi$
$983$	−39.6527	−1.26473	−0.632363	+	0.774672i	$0.717915\pi$
$984$	−40.7046	−1.29761
$985$	4.67182	0.148857
$986$	−77.9767	−2.48328
$987$	30.2489	0.962834
$988$	19.0868	0.607231
$989$	−11.4799	−0.365040
$990$	0	0
$991$	−15.4204	−0.489846	−0.244923	−	0.969542i	$-0.578763\pi$
$991$	−15.4204	−0.489846	−0.244923	+	0.969542i	$0.578763\pi$
$992$	−9.61192	−0.305179
$993$	1.09362	0.0347051
$994$	−23.0012	−0.729555
$995$	16.2018	0.513632
$996$	−44.2620	−1.40249
$997$	15.3415	0.485869	0.242934	−	0.970043i	$-0.421890\pi$
$997$	15.3415	0.485869	0.242934	+	0.970043i	$0.421890\pi$
$998$	11.3151	0.358172
$999$	8.57025	0.271151

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1815.2.a.v.1.1		4
3.2	odd	2		5445.2.a.bk.1.4		4
5.4	even	2		9075.2.a.cq.1.4		4
11.5	even	5		165.2.m.b.91.2	✓	8
11.9	even	5		165.2.m.b.136.2	yes	8
11.10	odd	2		1815.2.a.r.1.4		4
33.5	odd	10		495.2.n.b.91.1		8
33.20	odd	10		495.2.n.b.136.1		8
33.32	even	2		5445.2.a.br.1.1		4
55.9	even	10		825.2.n.i.301.1		8
55.27	odd	20		825.2.bx.g.124.4		16
55.38	odd	20		825.2.bx.g.124.1		16
55.42	odd	20		825.2.bx.g.499.1		16
55.49	even	10		825.2.n.i.751.1		8
55.53	odd	20		825.2.bx.g.499.4		16
55.54	odd	2		9075.2.a.dg.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.m.b.91.2	✓	8	11.5	even	5
165.2.m.b.136.2	yes	8	11.9	even	5
495.2.n.b.91.1		8	33.5	odd	10
495.2.n.b.136.1		8	33.20	odd	10
825.2.n.i.301.1		8	55.9	even	10
825.2.n.i.751.1		8	55.49	even	10
825.2.bx.g.124.1		16	55.38	odd	20
825.2.bx.g.124.4		16	55.27	odd	20
825.2.bx.g.499.1		16	55.42	odd	20
825.2.bx.g.499.4		16	55.53	odd	20
1815.2.a.r.1.4		4	11.10	odd	2
1815.2.a.v.1.1		4	1.1	even	1	trivial
5445.2.a.bk.1.4		4	3.2	odd	2
5445.2.a.br.1.1		4	33.32	even	2
9075.2.a.cq.1.4		4	5.4	even	2
9075.2.a.dg.1.1		4	55.54	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:	\( N \)	\(=\)	\( 1815 = 3 \cdot 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1815.a (trivial)

\(f(q)\)	\(=\)	\(q-2.48008 q^{2} -1.00000 q^{3} +4.15081 q^{4} -1.00000 q^{5} +2.48008 q^{6} -4.39482 q^{7} -5.33418 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.48008 q^{2} -1.00000 q^{3} +4.15081 q^{4} -1.00000 q^{5} +2.48008 q^{6} -4.39482 q^{7} -5.33418 q^{8} +1.00000 q^{9} +2.48008 q^{10} -4.15081 q^{12} -2.13795 q^{13} +10.8995 q^{14} +1.00000 q^{15} +4.92760 q^{16} +3.96017 q^{17} -2.48008 q^{18} -2.15081 q^{19} -4.15081 q^{20} +4.39482 q^{21} +5.16367 q^{23} +5.33418 q^{24} +1.00000 q^{25} +5.30230 q^{26} -1.00000 q^{27} -18.2421 q^{28} +7.93936 q^{29} -2.48008 q^{30} +6.19132 q^{31} -1.55248 q^{32} -9.82154 q^{34} +4.39482 q^{35} +4.15081 q^{36} -8.57025 q^{37} +5.33418 q^{38} +2.13795 q^{39} +5.33418 q^{40} -7.63089 q^{41} -10.8995 q^{42} -2.22321 q^{43} -1.00000 q^{45} -12.8063 q^{46} +6.88285 q^{47} -4.92760 q^{48} +12.3145 q^{49} -2.48008 q^{50} -3.96017 q^{51} -8.87423 q^{52} -5.69644 q^{53} +2.48008 q^{54} +23.4428 q^{56} +2.15081 q^{57} -19.6903 q^{58} +3.78170 q^{59} +4.15081 q^{60} +4.83439 q^{61} -15.3550 q^{62} -4.39482 q^{63} -6.00491 q^{64} +2.13795 q^{65} +9.57025 q^{67} +16.4379 q^{68} -5.16367 q^{69} -10.8995 q^{70} -2.11030 q^{71} -5.33418 q^{72} -14.6506 q^{73} +21.2549 q^{74} -1.00000 q^{75} -8.92760 q^{76} -5.30230 q^{78} +3.26111 q^{79} -4.92760 q^{80} +1.00000 q^{81} +18.9252 q^{82} +10.6635 q^{83} +18.2421 q^{84} -3.96017 q^{85} +5.51374 q^{86} -7.93936 q^{87} -7.64375 q^{89} +2.48008 q^{90} +9.39592 q^{91} +21.4334 q^{92} -6.19132 q^{93} -17.0700 q^{94} +2.15081 q^{95} +1.55248 q^{96} -5.67073 q^{97} -30.5409 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} - 4 q^{3} + 9 q^{4} - 4 q^{5} - q^{6} - 8 q^{7} + 3 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + q^2 - 4 * q^3 + 9 * q^4 - 4 * q^5 - q^6 - 8 * q^7 + 3 * q^8 + 4 * q^9	\( 4 q + q^{2} - 4 q^{3} + 9 q^{4} - 4 q^{5} - q^{6} - 8 q^{7} + 3 q^{8} + 4 q^{9} - q^{10} - 9 q^{12} - 15 q^{13} + 7 q^{14} + 4 q^{15} + 7 q^{16} - 6 q^{17} + q^{18} - q^{19} - 9 q^{20} + 8 q^{21} - q^{23} - 3 q^{24} + 4 q^{25} - 18 q^{26} - 4 q^{27} - 31 q^{28} + 17 q^{29} + q^{30} + 15 q^{31} - 8 q^{32} - 35 q^{34} + 8 q^{35} + 9 q^{36} - q^{37} - 3 q^{38} + 15 q^{39} - 3 q^{40} - 12 q^{41} - 7 q^{42} - 14 q^{43} - 4 q^{45} - 9 q^{46} + 14 q^{47} - 7 q^{48} + 20 q^{49} + q^{50} + 6 q^{51} - 39 q^{52} + 2 q^{53} - q^{54} - 12 q^{56} + q^{57} - 11 q^{58} - 11 q^{59} + 9 q^{60} + q^{61} - 30 q^{62} - 8 q^{63} - 3 q^{64} + 15 q^{65} + 5 q^{67} - 19 q^{68} + q^{69} - 7 q^{70} - 3 q^{71} + 3 q^{72} - 45 q^{73} + 29 q^{74} - 4 q^{75} - 23 q^{76} + 18 q^{78} - 7 q^{80} + 4 q^{81} + 11 q^{82} + 15 q^{83} + 31 q^{84} + 6 q^{85} - 10 q^{86} - 17 q^{87} + 2 q^{89} - q^{90} + 16 q^{91} + 34 q^{92} - 15 q^{93} - 29 q^{94} + q^{95} + 8 q^{96} - 26 q^{97} - q^{98}+O(q^{100}) \) 4 * q + q^2 - 4 * q^3 + 9 * q^4 - 4 * q^5 - q^6 - 8 * q^7 + 3 * q^8 + 4 * q^9 - q^10 - 9 * q^12 - 15 * q^13 + 7 * q^14 + 4 * q^15 + 7 * q^16 - 6 * q^17 + q^18 - q^19 - 9 * q^20 + 8 * q^21 - q^23 - 3 * q^24 + 4 * q^25 - 18 * q^26 - 4 * q^27 - 31 * q^28 + 17 * q^29 + q^30 + 15 * q^31 - 8 * q^32 - 35 * q^34 + 8 * q^35 + 9 * q^36 - q^37 - 3 * q^38 + 15 * q^39 - 3 * q^40 - 12 * q^41 - 7 * q^42 - 14 * q^43 - 4 * q^45 - 9 * q^46 + 14 * q^47 - 7 * q^48 + 20 * q^49 + q^50 + 6 * q^51 - 39 * q^52 + 2 * q^53 - q^54 - 12 * q^56 + q^57 - 11 * q^58 - 11 * q^59 + 9 * q^60 + q^61 - 30 * q^62 - 8 * q^63 - 3 * q^64 + 15 * q^65 + 5 * q^67 - 19 * q^68 + q^69 - 7 * q^70 - 3 * q^71 + 3 * q^72 - 45 * q^73 + 29 * q^74 - 4 * q^75 - 23 * q^76 + 18 * q^78 - 7 * q^80 + 4 * q^81 + 11 * q^82 + 15 * q^83 + 31 * q^84 + 6 * q^85 - 10 * q^86 - 17 * q^87 + 2 * q^89 - q^90 + 16 * q^91 + 34 * q^92 - 15 * q^93 - 29 * q^94 + q^95 + 8 * q^96 - 26 * q^97 - q^98

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