LMFDB - Embedded newform 1815.2.a.r.1.2

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:	$0$
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			1.2
Root			$-2.48008$ 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)

$f(q)$	$=$	$q-1.86205 q^{2} -1.00000 q^{3} +1.46722 q^{4} -1.00000 q^{5} +1.86205 q^{6} -2.63089 q^{7} +0.992053 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.86205 q^{2} -1.00000 q^{3} +1.46722 q^{4} -1.00000 q^{5} +1.86205 q^{6} -2.63089 q^{7} +0.992053 q^{8} +1.00000 q^{9} +1.86205 q^{10} -1.46722 q^{12} +6.48008 q^{13} +4.89885 q^{14} +1.00000 q^{15} -4.78170 q^{16} +4.72410 q^{17} -1.86205 q^{18} -0.532775 q^{19} -1.46722 q^{20} +2.63089 q^{21} -4.54563 q^{23} -0.992053 q^{24} +1.00000 q^{25} -12.0662 q^{26} -1.00000 q^{27} -3.86011 q^{28} -10.6229 q^{29} -1.86205 q^{30} +0.190644 q^{31} +6.91965 q^{32} -8.79650 q^{34} +2.63089 q^{35} +1.46722 q^{36} -4.22812 q^{37} +0.992053 q^{38} -6.48008 q^{39} -0.992053 q^{40} +0.605176 q^{41} -4.89885 q^{42} +9.24893 q^{43} -1.00000 q^{45} +8.46419 q^{46} -8.82712 q^{47} +4.78170 q^{48} -0.0784084 q^{49} -1.86205 q^{50} -4.72410 q^{51} +9.50774 q^{52} +6.69644 q^{53} +1.86205 q^{54} -2.60999 q^{56} +0.532775 q^{57} +19.7804 q^{58} -5.92760 q^{59} +1.46722 q^{60} +3.21636 q^{61} -0.354989 q^{62} -2.63089 q^{63} -3.32133 q^{64} -6.48008 q^{65} +5.22812 q^{67} +6.93131 q^{68} +4.54563 q^{69} -4.89885 q^{70} -2.74381 q^{71} +0.992053 q^{72} +15.6756 q^{73} +7.87297 q^{74} -1.00000 q^{75} -0.781701 q^{76} +12.0662 q^{78} -1.21103 q^{79} +4.78170 q^{80} +1.00000 q^{81} -1.12687 q^{82} -4.66278 q^{83} +3.86011 q^{84} -4.72410 q^{85} -17.2219 q^{86} +10.6229 q^{87} +6.40768 q^{89} +1.86205 q^{90} -17.0484 q^{91} -6.66947 q^{92} -0.190644 q^{93} +16.4365 q^{94} +0.532775 q^{95} -6.91965 q^{96} -7.32927 q^{97} +0.146000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.86205	−1.31667	−0.658334	−	0.752726i	$-0.728738\pi$
$2$	−1.86205	−1.31667	−0.658334	+	0.752726i	$0.728738\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.46722	0.733612
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	1.86205	0.760178
$7$	−2.63089	−0.994384	−0.497192	−	0.867641i	$-0.665635\pi$
$7$	−2.63089	−0.994384	−0.497192	+	0.867641i	$0.665635\pi$
$8$	0.992053	0.350744
$9$	1.00000	0.333333
$10$	1.86205	0.588831
$11$	0	0
$11$	0	0
$12$	−1.46722	−0.423551
$13$	6.48008	1.79725	0.898626	−	0.438716i	$-0.144567\pi$
$13$	6.48008	1.79725	0.898626	+	0.438716i	$0.144567\pi$
$14$	4.89885	1.30927
$15$	1.00000	0.258199
$16$	−4.78170	−1.19543
$17$	4.72410	1.14576	0.572881	−	0.819639i	$-0.305826\pi$
$17$	4.72410	1.14576	0.572881	+	0.819639i	$0.305826\pi$
$18$	−1.86205	−0.438889
$19$	−0.532775	−0.122227	−0.0611135	−	0.998131i	$-0.519465\pi$
$19$	−0.532775	−0.122227	−0.0611135	+	0.998131i	$0.519465\pi$
$20$	−1.46722	−0.328081
$21$	2.63089	0.574108
$22$	0	0
$23$	−4.54563	−0.947830	−0.473915	−	0.880571i	$-0.657160\pi$
$23$	−4.54563	−0.947830	−0.473915	+	0.880571i	$0.657160\pi$
$24$	−0.992053	−0.202502
$25$	1.00000	0.200000
$26$	−12.0662	−2.36638
$27$	−1.00000	−0.192450
$28$	−3.86011	−0.729492
$29$	−10.6229	−1.97263	−0.986316	−	0.164868i	$-0.947280\pi$
$29$	−10.6229	−1.97263	−0.986316	+	0.164868i	$0.947280\pi$
$30$	−1.86205	−0.339962
$31$	0.190644	0.0342407	0.0171204	−	0.999853i	$-0.494550\pi$
$31$	0.190644	0.0342407	0.0171204	+	0.999853i	$0.494550\pi$
$32$	6.91965	1.22323
$33$	0	0
$34$	−8.79650	−1.50859
$35$	2.63089	0.444702
$36$	1.46722	0.244537
$37$	−4.22812	−0.695099	−0.347549	−	0.937662i	$-0.612986\pi$
$37$	−4.22812	−0.695099	−0.347549	+	0.937662i	$0.612986\pi$
$38$	0.992053	0.160932
$39$	−6.48008	−1.03764
$40$	−0.992053	−0.156857
$41$	0.605176	0.0945126	0.0472563	−	0.998883i	$-0.484952\pi$
$41$	0.605176	0.0945126	0.0472563	+	0.998883i	$0.484952\pi$
$42$	−4.89885	−0.755909
$43$	9.24893	1.41045	0.705224	−	0.708985i	$-0.250846\pi$
$43$	9.24893	1.41045	0.705224	+	0.708985i	$0.250846\pi$
$44$	0	0
$45$	−1.00000	−0.149071
$46$	8.46419	1.24798
$47$	−8.82712	−1.28757	−0.643784	−	0.765207i	$-0.722637\pi$
$47$	−8.82712	−1.28757	−0.643784	+	0.765207i	$0.722637\pi$
$48$	4.78170	0.690179
$49$	−0.0784084	−0.0112012
$50$	−1.86205	−0.263333
$51$	−4.72410	−0.661506
$52$	9.50774	1.31849
$53$	6.69644	0.919827	0.459914	−	0.887964i	$-0.347880\pi$
$53$	6.69644	0.919827	0.459914	+	0.887964i	$0.347880\pi$
$54$	1.86205	0.253393
$55$	0	0
$56$	−2.60999	−0.348774
$57$	0.532775	0.0705678
$58$	19.7804	2.59730
$59$	−5.92760	−0.771708	−0.385854	−	0.922560i	$-0.626093\pi$
$59$	−5.92760	−0.771708	−0.385854	+	0.922560i	$0.626093\pi$
$60$	1.46722	0.189418
$61$	3.21636	0.411813	0.205906	−	0.978572i	$-0.433986\pi$
$61$	3.21636	0.411813	0.205906	+	0.978572i	$0.433986\pi$
$62$	−0.354989	−0.0450836
$63$	−2.63089	−0.331461
$64$	−3.32133	−0.415166
$65$	−6.48008	−0.803755
$66$	0	0
$67$	5.22812	0.638717	0.319358	−	0.947634i	$-0.396533\pi$
$67$	5.22812	0.638717	0.319358	+	0.947634i	$0.396533\pi$
$68$	6.93131	0.840545
$69$	4.54563	0.547230
$70$	−4.89885	−0.585524
$71$	−2.74381	−0.325630	−0.162815	−	0.986657i	$-0.552057\pi$
$71$	−2.74381	−0.325630	−0.162815	+	0.986657i	$0.552057\pi$
$72$	0.992053	0.116915
$73$	15.6756	1.83469	0.917347	−	0.398088i	$-0.130326\pi$
$73$	15.6756	1.83469	0.917347	+	0.398088i	$0.130326\pi$
$74$	7.87297	0.915214
$75$	−1.00000	−0.115470
$76$	−0.781701	−0.0896673
$77$	0	0
$78$	12.0662	1.36623
$79$	−1.21103	−0.136252	−0.0681258	−	0.997677i	$-0.521702\pi$
$79$	−1.21103	−0.136252	−0.0681258	+	0.997677i	$0.521702\pi$
$80$	4.78170	0.534610
$81$	1.00000	0.111111
$82$	−1.12687	−0.124442
$83$	−4.66278	−0.511807	−0.255903	−	0.966702i	$-0.582373\pi$
$83$	−4.66278	−0.511807	−0.255903	+	0.966702i	$0.582373\pi$
$84$	3.86011	0.421172
$85$	−4.72410	−0.512400
$86$	−17.2219	−1.85709
$87$	10.6229	1.13890
$88$	0	0
$89$	6.40768	0.679213	0.339606	−	0.940568i	$-0.389706\pi$
$89$	6.40768	0.679213	0.339606	+	0.940568i	$0.389706\pi$
$90$	1.86205	0.196277
$91$	−17.0484	−1.78716
$92$	−6.66947	−0.695340
$93$	−0.190644	−0.0197689
$94$	16.4365	1.69530
$95$	0.532775	0.0546616
$96$	−6.91965	−0.706234
$97$	−7.32927	−0.744175	−0.372087	−	0.928198i	$-0.621358\pi$
$97$	−7.32927	−0.744175	−0.372087	+	0.928198i	$0.621358\pi$
$98$	0.146000	0.0147482
$99$	0	0
$100$	1.46722	0.146722
$101$	−11.3599	−1.13035	−0.565176	−	0.824970i	$-0.691192\pi$
$101$	−11.3599	−1.13035	−0.565176	+	0.824970i	$0.691192\pi$
$102$	8.79650	0.870983
$103$	−2.06064	−0.203041	−0.101520	−	0.994833i	$-0.532371\pi$
$103$	−2.06064	−0.203041	−0.101520	+	0.994833i	$0.532371\pi$
$104$	6.42859	0.630375
$105$	−2.63089	−0.256749
$106$	−12.4691	−1.21111
$107$	−1.14971	−0.111147	−0.0555735	−	0.998455i	$-0.517699\pi$
$107$	−1.14971	−0.111147	−0.0555735	+	0.998455i	$0.517699\pi$
$108$	−1.46722	−0.141184
$109$	13.3402	1.27776	0.638879	−	0.769307i	$-0.279398\pi$
$109$	13.3402	1.27776	0.638879	+	0.769307i	$0.279398\pi$
$110$	0	0
$111$	4.22812	0.401316
$112$	12.5801	1.18871
$113$	6.29738	0.592408	0.296204	−	0.955125i	$-0.404279\pi$
$113$	6.29738	0.592408	0.296204	+	0.955125i	$0.404279\pi$
$114$	−0.992053	−0.0929143
$115$	4.54563	0.423882
$116$	−15.5862	−1.44715
$117$	6.48008	0.599084
$118$	11.0375	1.01608
$119$	−12.4286	−1.13933
$120$	0.992053	0.0905617
$121$	0	0
$122$	−5.98902	−0.542220
$123$	−0.605176	−0.0545669
$124$	0.279718	0.0251194
$125$	−1.00000	−0.0894427
$126$	4.89885	0.436424
$127$	10.0943	0.895724	0.447862	−	0.894103i	$-0.352186\pi$
$127$	10.0943	0.895724	0.447862	+	0.894103i	$0.352186\pi$
$128$	−7.65483	−0.676598
$129$	−9.24893	−0.814323
$130$	12.0662	1.05828
$131$	4.64756	0.406060	0.203030	−	0.979173i	$-0.434921\pi$
$131$	4.64756	0.406060	0.203030	+	0.979173i	$0.434921\pi$
$132$	0	0
$133$	1.40167	0.121541
$134$	−9.73502	−0.840977
$135$	1.00000	0.0860663
$136$	4.68656	0.401869
$137$	15.7676	1.34712	0.673558	−	0.739135i	$-0.264765\pi$
$137$	15.7676	1.34712	0.673558	+	0.739135i	$0.264765\pi$
$138$	−8.46419	−0.720520
$139$	−10.0386	−0.851461	−0.425730	−	0.904850i	$-0.639983\pi$
$139$	−10.0386	−0.851461	−0.425730	+	0.904850i	$0.639983\pi$
$140$	3.86011	0.326239
$141$	8.82712	0.743378
$142$	5.10910	0.428746
$143$	0	0
$144$	−4.78170	−0.398475
$145$	10.6229	0.882188
$146$	−29.1888	−2.41568
$147$	0.0784084	0.00646701
$148$	−6.20360	−0.509933
$149$	10.4653	0.857350	0.428675	−	0.903459i	$-0.358981\pi$
$149$	10.4653	0.857350	0.428675	+	0.903459i	$0.358981\pi$
$150$	1.86205	0.152036
$151$	15.6433	1.27304	0.636518	−	0.771262i	$-0.280374\pi$
$151$	15.6433	1.27304	0.636518	+	0.771262i	$0.280374\pi$
$152$	−0.528542	−0.0428704
$153$	4.72410	0.381921
$154$	0	0
$155$	−0.190644	−0.0153129
$156$	−9.50774	−0.761228
$157$	8.98970	0.717456	0.358728	−	0.933442i	$-0.383211\pi$
$157$	8.98970	0.717456	0.358728	+	0.933442i	$0.383211\pi$
$158$	2.25500	0.179398
$159$	−6.69644	−0.531062
$160$	−6.91965	−0.547047
$161$	11.9591	0.942507
$162$	−1.86205	−0.146296
$163$	19.8400	1.55399	0.776994	−	0.629508i	$-0.216744\pi$
$163$	19.8400	1.55399	0.776994	+	0.629508i	$0.216744\pi$
$164$	0.887929	0.0693356
$165$	0	0
$166$	8.68232	0.673879
$167$	−11.5133	−0.890928	−0.445464	−	0.895300i	$-0.646961\pi$
$167$	−11.5133	−0.890928	−0.445464	+	0.895300i	$0.646961\pi$
$168$	2.60999	0.201365
$169$	28.9915	2.23011
$170$	8.79650	0.674661
$171$	−0.532775	−0.0407423
$172$	13.5703	1.03472
$173$	7.50512	0.570604	0.285302	−	0.958438i	$-0.407906\pi$
$173$	7.50512	0.570604	0.285302	+	0.958438i	$0.407906\pi$
$174$	−19.7804	−1.49955
$175$	−2.63089	−0.198877
$176$	0	0
$177$	5.92760	0.445546
$178$	−11.9314	−0.894297
$179$	6.54867	0.489470	0.244735	−	0.969590i	$-0.421299\pi$
$179$	6.54867	0.489470	0.244735	+	0.969590i	$0.421299\pi$
$180$	−1.46722	−0.109360
$181$	−8.04433	−0.597930	−0.298965	−	0.954264i	$-0.596641\pi$
$181$	−8.04433	−0.597930	−0.298965	+	0.954264i	$0.596641\pi$
$182$	31.7449	2.35309
$183$	−3.21636	−0.237760
$184$	−4.50951	−0.332446
$185$	4.22812	0.310858
$186$	0.354989	0.0260290
$187$	0	0
$188$	−12.9514	−0.944576
$189$	2.63089	0.191369
$190$	−0.992053	−0.0719711
$191$	−8.72833	−0.631560	−0.315780	−	0.948832i	$-0.602266\pi$
$191$	−8.72833	−0.631560	−0.315780	+	0.948832i	$0.602266\pi$
$192$	3.32133	0.239696
$193$	−15.0613	−1.08413	−0.542066	−	0.840336i	$-0.682358\pi$
$193$	−15.0613	−1.08413	−0.542066	+	0.840336i	$0.682358\pi$
$194$	13.6475	0.979831
$195$	6.48008	0.464048
$196$	−0.115043	−0.00821734
$197$	−13.0882	−0.932498	−0.466249	−	0.884654i	$-0.654395\pi$
$197$	−13.0882	−0.932498	−0.466249	+	0.884654i	$0.654395\pi$
$198$	0	0
$199$	7.16738	0.508082	0.254041	−	0.967193i	$-0.418240\pi$
$199$	7.16738	0.508082	0.254041	+	0.967193i	$0.418240\pi$
$200$	0.992053	0.0701488
$201$	−5.22812	−0.368763
$202$	21.1527	1.48830
$203$	27.9478	1.96155
$204$	−6.93131	−0.485289
$205$	−0.605176	−0.0422673
$206$	3.83701	0.267337
$207$	−4.54563	−0.315943
$208$	−30.9858	−2.14848
$209$	0	0
$210$	4.89885	0.338053
$211$	−5.98824	−0.412247	−0.206124	−	0.978526i	$-0.566085\pi$
$211$	−5.98824	−0.412247	−0.206124	+	0.978526i	$0.566085\pi$
$212$	9.82519	0.674797
$213$	2.74381	0.188002
$214$	2.14082	0.146344
$215$	−9.24893	−0.630772
$216$	−0.992053	−0.0675007
$217$	−0.501564	−0.0340484
$218$	−24.8401	−1.68238
$219$	−15.6756	−1.05926
$220$	0	0
$221$	30.6125	2.05922
$222$	−7.87297	−0.528399
$223$	−0.300522	−0.0201245	−0.0100622	−	0.999949i	$-0.503203\pi$
$223$	−0.300522	−0.0201245	−0.0100622	+	0.999949i	$0.503203\pi$
$224$	−18.2049	−1.21636
$225$	1.00000	0.0666667
$226$	−11.7260	−0.780004
$227$	22.8179	1.51448	0.757239	−	0.653138i	$-0.226548\pi$
$227$	22.8179	1.51448	0.757239	+	0.653138i	$0.226548\pi$
$228$	0.781701	0.0517694
$229$	28.2109	1.86423	0.932113	−	0.362167i	$-0.117963\pi$
$229$	28.2109	1.86423	0.932113	+	0.362167i	$0.117963\pi$
$230$	−8.46419	−0.558112
$231$	0	0
$232$	−10.5385	−0.691888
$233$	19.3845	1.26992	0.634961	−	0.772544i	$-0.281016\pi$
$233$	19.3845	1.26992	0.634961	+	0.772544i	$0.281016\pi$
$234$	−12.0662	−0.788794
$235$	8.82712	0.575818
$236$	−8.69712	−0.566134
$237$	1.21103	0.0786648
$238$	23.1426	1.50011
$239$	15.2735	0.987964	0.493982	−	0.869472i	$-0.335541\pi$
$239$	15.2735	0.987964	0.493982	+	0.869472i	$0.335541\pi$
$240$	−4.78170	−0.308657
$241$	7.21213	0.464574	0.232287	−	0.972647i	$-0.425379\pi$
$241$	7.21213	0.464574	0.232287	+	0.972647i	$0.425379\pi$
$242$	0	0
$243$	−1.00000	−0.0641500
$244$	4.71912	0.302111
$245$	0.0784084	0.00500933
$246$	1.12687	0.0718464
$247$	−3.45243	−0.219673
$248$	0.189129	0.0120097
$249$	4.66278	0.295492
$250$	1.86205	0.117766
$251$	19.0750	1.20400	0.602000	−	0.798496i	$-0.294371\pi$
$251$	19.0750	1.20400	0.602000	+	0.798496i	$0.294371\pi$
$252$	−3.86011	−0.243164
$253$	0	0
$254$	−18.7961	−1.17937
$255$	4.72410	0.295834
$256$	20.8963	1.30602
$257$	26.1060	1.62845	0.814224	−	0.580551i	$-0.197163\pi$
$257$	26.1060	1.62845	0.814224	+	0.580551i	$0.197163\pi$
$258$	17.2219	1.07219
$259$	11.1237	0.691195
$260$	−9.50774	−0.589645
$261$	−10.6229	−0.657544
$262$	−8.65399	−0.534645
$263$	−27.0086	−1.66542	−0.832710	−	0.553710i	$-0.813212\pi$
$263$	−27.0086	−1.66542	−0.832710	+	0.553710i	$0.813212\pi$
$264$	0	0
$265$	−6.69644	−0.411359
$266$	−2.60999	−0.160028
$267$	−6.40768	−0.392144
$268$	7.67083	0.468570
$269$	−10.0527	−0.612923	−0.306462	−	0.951883i	$-0.599145\pi$
$269$	−10.0527	−0.612923	−0.306462	+	0.951883i	$0.599145\pi$
$270$	−1.86205	−0.113321
$271$	−29.2643	−1.77768	−0.888841	−	0.458216i	$-0.848489\pi$
$271$	−29.2643	−1.77768	−0.888841	+	0.458216i	$0.848489\pi$
$272$	−22.5892	−1.36967
$273$	17.0484	1.03182
$274$	−29.3600	−1.77370
$275$	0	0
$276$	6.66947	0.401455
$277$	0.694566	0.0417325	0.0208662	−	0.999782i	$-0.493358\pi$
$277$	0.694566	0.0417325	0.0208662	+	0.999782i	$0.493358\pi$
$278$	18.6923	1.12109
$279$	0.190644	0.0114136
$280$	2.60999	0.155976
$281$	10.6688	0.636447	0.318223	−	0.948016i	$-0.396914\pi$
$281$	10.6688	0.636447	0.318223	+	0.948016i	$0.396914\pi$
$282$	−16.4365	−0.978781
$283$	21.6221	1.28530	0.642650	−	0.766160i	$-0.277835\pi$
$283$	21.6221	1.28530	0.642650	+	0.766160i	$0.277835\pi$
$284$	−4.02578	−0.238886
$285$	−0.532775	−0.0315589
$286$	0	0
$287$	−1.59215	−0.0939818
$288$	6.91965	0.407744
$289$	5.31709	0.312770
$290$	−19.7804	−1.16155
$291$	7.32927	0.429650
$292$	22.9997	1.34595
$293$	5.75860	0.336421	0.168211	−	0.985751i	$-0.446201\pi$
$293$	5.75860	0.336421	0.168211	+	0.985751i	$0.446201\pi$
$294$	−0.146000	−0.00851491
$295$	5.92760	0.345118
$296$	−4.19452	−0.243802
$297$	0	0
$298$	−19.4869	−1.12884
$299$	−29.4561	−1.70349
$300$	−1.46722	−0.0847103
$301$	−24.3329	−1.40253
$302$	−29.1286	−1.67616
$303$	11.3599	0.652609
$304$	2.54757	0.146113
$305$	−3.21636	−0.184168
$306$	−8.79650	−0.502862
$307$	18.4941	1.05552	0.527758	−	0.849395i	$-0.323033\pi$
$307$	18.4941	1.05552	0.527758	+	0.849395i	$0.323033\pi$
$308$	0	0
$309$	2.06064	0.117226
$310$	0.354989	0.0201620
$311$	−11.3134	−0.641523	−0.320761	−	0.947160i	$-0.603939\pi$
$311$	−11.3134	−0.641523	−0.320761	+	0.947160i	$0.603939\pi$
$312$	−6.42859	−0.363947
$313$	−18.5401	−1.04795	−0.523975	−	0.851733i	$-0.675552\pi$
$313$	−18.5401	−1.04795	−0.523975	+	0.851733i	$0.675552\pi$
$314$	−16.7392	−0.944651
$315$	2.63089	0.148234
$316$	−1.77685	−0.0999558
$317$	−0.821434	−0.0461363	−0.0230682	−	0.999734i	$-0.507343\pi$
$317$	−0.821434	−0.0461363	−0.0230682	+	0.999734i	$0.507343\pi$
$318$	12.4691	0.699232
$319$	0	0
$320$	3.32133	0.185668
$321$	1.14971	0.0641707
$322$	−22.2684	−1.24097
$323$	−2.51688	−0.140043
$324$	1.46722	0.0815125
$325$	6.48008	0.359450
$326$	−36.9430	−2.04608
$327$	−13.3402	−0.737714
$328$	0.600367	0.0331497
$329$	23.2232	1.28034
$330$	0	0
$331$	7.98217	0.438740	0.219370	−	0.975642i	$-0.429600\pi$
$331$	7.98217	0.438740	0.219370	+	0.975642i	$0.429600\pi$
$332$	−6.84135	−0.375468
$333$	−4.22812	−0.231700
$334$	21.4384	1.17306
$335$	−5.22812	−0.285643
$336$	−12.5801	−0.686303
$337$	12.4690	0.679230	0.339615	−	0.940565i	$-0.389703\pi$
$337$	12.4690	0.679230	0.339615	+	0.940565i	$0.389703\pi$
$338$	−53.9835	−2.93632
$339$	−6.29738	−0.342027
$340$	−6.93131	−0.375903
$341$	0	0
$342$	0.992053	0.0536441
$343$	18.6225	1.00552
$344$	9.17543	0.494706
$345$	−4.54563	−0.244729
$346$	−13.9749	−0.751295
$347$	−20.9124	−1.12264	−0.561318	−	0.827600i	$-0.689705\pi$
$347$	−20.9124	−1.12264	−0.561318	+	0.827600i	$0.689705\pi$
$348$	15.5862	0.835511
$349$	7.67825	0.411008	0.205504	−	0.978656i	$-0.434117\pi$
$349$	7.67825	0.411008	0.205504	+	0.978656i	$0.434117\pi$
$350$	4.89885	0.261854
$351$	−6.48008	−0.345881
$352$	0	0
$353$	−13.7984	−0.734413	−0.367207	−	0.930139i	$-0.619686\pi$
$353$	−13.7984	−0.734413	−0.367207	+	0.930139i	$0.619686\pi$
$354$	−11.0375	−0.586635
$355$	2.74381	0.145626
$356$	9.40151	0.498279
$357$	12.4286	0.657791
$358$	−12.1939	−0.644470
$359$	17.9162	0.945581	0.472790	−	0.881175i	$-0.343247\pi$
$359$	17.9162	0.945581	0.472790	+	0.881175i	$0.343247\pi$
$360$	−0.992053	−0.0522858
$361$	−18.7162	−0.985061
$362$	14.9789	0.787275
$363$	0	0
$364$	−25.0138	−1.31108
$365$	−15.6756	−0.820500
$366$	5.98902	0.313051
$367$	9.46842	0.494248	0.247124	−	0.968984i	$-0.420515\pi$
$367$	9.46842	0.494248	0.247124	+	0.968984i	$0.420515\pi$
$368$	21.7359	1.13306
$369$	0.605176	0.0315042
$370$	−7.87297	−0.409296
$371$	−17.6176	−0.914661
$372$	−0.279718	−0.0145027
$373$	−11.6402	−0.602706	−0.301353	−	0.953513i	$-0.597438\pi$
$373$	−11.6402	−0.602706	−0.301353	+	0.953513i	$0.597438\pi$
$374$	0	0
$375$	1.00000	0.0516398
$376$	−8.75698	−0.451607
$377$	−68.8376	−3.54531
$378$	−4.89885	−0.251970
$379$	−6.60408	−0.339229	−0.169614	−	0.985511i	$-0.554252\pi$
$379$	−6.60408	−0.339229	−0.169614	+	0.985511i	$0.554252\pi$
$380$	0.781701	0.0401004
$381$	−10.0943	−0.517147
$382$	16.2526	0.831554
$383$	19.7376	1.00855	0.504273	−	0.863544i	$-0.331761\pi$
$383$	19.7376	1.00855	0.504273	+	0.863544i	$0.331761\pi$
$384$	7.65483	0.390634
$385$	0	0
$386$	28.0448	1.42744
$387$	9.24893	0.470149
$388$	−10.7537	−0.545936
$389$	25.3648	1.28605	0.643023	−	0.765846i	$-0.277680\pi$
$389$	25.3648	1.28605	0.643023	+	0.765846i	$0.277680\pi$
$390$	−12.0662	−0.610997
$391$	−21.4740	−1.08599
$392$	−0.0777853	−0.00392875
$393$	−4.64756	−0.234439
$394$	24.3709	1.22779
$395$	1.21103	0.0609335
$396$	0	0
$397$	−39.2400	−1.96940	−0.984699	−	0.174264i	$-0.944245\pi$
$397$	−39.2400	−1.96940	−0.984699	+	0.174264i	$0.944245\pi$
$398$	−13.3460	−0.668975
$399$	−1.40167	−0.0701715
$400$	−4.78170	−0.239085
$401$	11.1227	0.555443	0.277721	−	0.960662i	$-0.410421\pi$
$401$	11.1227	0.555443	0.277721	+	0.960662i	$0.410421\pi$
$402$	9.73502	0.485538
$403$	1.23539	0.0615392
$404$	−16.6675	−0.829240
$405$	−1.00000	−0.0496904
$406$	−52.0402	−2.58271
$407$	0	0
$408$	−4.68656	−0.232019
$409$	11.6111	0.574131	0.287066	−	0.957911i	$-0.407320\pi$
$409$	11.6111	0.574131	0.287066	+	0.957911i	$0.407320\pi$
$410$	1.12687	0.0556520
$411$	−15.7676	−0.777757
$412$	−3.02342	−0.148953
$413$	15.5949	0.767373
$414$	8.46419	0.415992
$415$	4.66278	0.228887
$416$	44.8399	2.19846
$417$	10.0386	0.491591
$418$	0	0
$419$	18.5499	0.906220	0.453110	−	0.891455i	$-0.350314\pi$
$419$	18.5499	0.906220	0.453110	+	0.891455i	$0.350314\pi$
$420$	−3.86011	−0.188354
$421$	−19.9755	−0.973545	−0.486773	−	0.873529i	$-0.661826\pi$
$421$	−19.9755	−0.973545	−0.486773	+	0.873529i	$0.661826\pi$
$422$	11.1504	0.542793
$423$	−8.82712	−0.429189
$424$	6.64323	0.322624
$425$	4.72410	0.229152
$426$	−5.10910	−0.247537
$427$	−8.46189	−0.409500
$428$	−1.68689	−0.0815388
$429$	0	0
$430$	17.2219	0.830516
$431$	25.9565	1.25028	0.625141	−	0.780512i	$-0.285041\pi$
$431$	25.9565	1.25028	0.625141	+	0.780512i	$0.285041\pi$
$432$	4.78170	0.230060
$433$	−33.5788	−1.61369	−0.806847	−	0.590760i	$-0.798828\pi$
$433$	−33.5788	−1.61369	−0.806847	+	0.590760i	$0.798828\pi$
$434$	0.933937	0.0448304
$435$	−10.6229	−0.509331
$436$	19.5731	0.937380
$437$	2.42180	0.115850
$438$	29.1888	1.39469
$439$	17.0280	0.812703	0.406351	−	0.913717i	$-0.366801\pi$
$439$	17.0280	0.812703	0.406351	+	0.913717i	$0.366801\pi$
$440$	0	0
$441$	−0.0784084	−0.00373373
$442$	−57.0020	−2.71131
$443$	25.2148	1.19799	0.598995	−	0.800753i	$-0.295567\pi$
$443$	25.2148	1.19799	0.598995	+	0.800753i	$0.295567\pi$
$444$	6.20360	0.294410
$445$	−6.40768	−0.303753
$446$	0.559587	0.0264972
$447$	−10.4653	−0.494991
$448$	8.73805	0.412834
$449$	−26.6596	−1.25814	−0.629072	−	0.777347i	$-0.716565\pi$
$449$	−26.6596	−1.25814	−0.629072	+	0.777347i	$0.716565\pi$
$450$	−1.86205	−0.0877778
$451$	0	0
$452$	9.23968	0.434598
$453$	−15.6433	−0.734988
$454$	−42.4881	−1.99406
$455$	17.0484	0.799241
$456$	0.528542	0.0247512
$457$	21.9481	1.02669	0.513344	−	0.858183i	$-0.328406\pi$
$457$	21.9481	1.02669	0.513344	+	0.858183i	$0.328406\pi$
$458$	−52.5300	−2.45457
$459$	−4.72410	−0.220502
$460$	6.66947	0.310965
$461$	4.32624	0.201493	0.100746	−	0.994912i	$-0.467877\pi$
$461$	4.32624	0.201493	0.100746	+	0.994912i	$0.467877\pi$
$462$	0	0
$463$	11.4573	0.532468	0.266234	−	0.963908i	$-0.414221\pi$
$463$	11.4573	0.532468	0.266234	+	0.963908i	$0.414221\pi$
$464$	50.7957	2.35813
$465$	0.190644	0.00884092
$466$	−36.0949	−1.67206
$467$	−15.5544	−0.719770	−0.359885	−	0.932997i	$-0.617184\pi$
$467$	−15.5544	−0.719770	−0.359885	+	0.932997i	$0.617184\pi$
$468$	9.50774	0.439495
$469$	−13.7546	−0.635129
$470$	−16.4365	−0.758161
$471$	−8.98970	−0.414223
$472$	−5.88050	−0.270672
$473$	0	0
$474$	−2.25500	−0.103575
$475$	−0.532775	−0.0244454
$476$	−18.2355	−0.835824
$477$	6.69644	0.306609
$478$	−28.4401	−1.30082
$479$	−9.99686	−0.456768	−0.228384	−	0.973571i	$-0.573344\pi$
$479$	−9.99686	−0.456768	−0.228384	+	0.973571i	$0.573344\pi$
$480$	6.91965	0.315837
$481$	−27.3986	−1.24927
$482$	−13.4293	−0.611689
$483$	−11.9591	−0.544156
$484$	0	0
$485$	7.32927	0.332805
$486$	1.86205	0.0844642
$487$	39.5800	1.79354	0.896770	−	0.442497i	$-0.145907\pi$
$487$	39.5800	1.79354	0.896770	+	0.442497i	$0.145907\pi$
$488$	3.19080	0.144441
$489$	−19.8400	−0.897195
$490$	−0.146000	−0.00659562
$491$	9.29053	0.419276	0.209638	−	0.977779i	$-0.432771\pi$
$491$	9.29053	0.419276	0.209638	+	0.977779i	$0.432771\pi$
$492$	−0.887929	−0.0400310
$493$	−50.1838	−2.26017
$494$	6.42859	0.289236
$495$	0	0
$496$	−0.911604	−0.0409322
$497$	7.21865	0.323801
$498$	−8.68232	−0.389064
$499$	−23.3475	−1.04518	−0.522588	−	0.852585i	$-0.675033\pi$
$499$	−23.3475	−1.04518	−0.522588	+	0.852585i	$0.675033\pi$
$500$	−1.46722	−0.0656163
$501$	11.5133	0.514377
$502$	−35.5185	−1.58527
$503$	−12.0518	−0.537365	−0.268683	−	0.963229i	$-0.586588\pi$
$503$	−12.0518	−0.537365	−0.268683	+	0.963229i	$0.586588\pi$
$504$	−2.60999	−0.116258
$505$	11.3599	0.505509
$506$	0	0
$507$	−28.9915	−1.28756
$508$	14.8106	0.657114
$509$	−1.65102	−0.0731801	−0.0365901	−	0.999330i	$-0.511650\pi$
$509$	−1.65102	−0.0731801	−0.0365901	+	0.999330i	$0.511650\pi$
$510$	−8.79650	−0.389515
$511$	−41.2409	−1.82439
$512$	−23.6003	−1.04300
$513$	0.532775	0.0235226
$514$	−48.6106	−2.14412
$515$	2.06064	0.0908026
$516$	−13.5703	−0.597397
$517$	0	0
$518$	−20.7129	−0.910074
$519$	−7.50512	−0.329438
$520$	−6.42859	−0.281912
$521$	21.3715	0.936302	0.468151	−	0.883648i	$-0.344920\pi$
$521$	21.3715	0.936302	0.468151	+	0.883648i	$0.344920\pi$
$522$	19.7804	0.865766
$523$	12.1593	0.531688	0.265844	−	0.964016i	$-0.414349\pi$
$523$	12.1593	0.531688	0.265844	+	0.964016i	$0.414349\pi$
$524$	6.81902	0.297890
$525$	2.63089	0.114822
$526$	50.2913	2.19280
$527$	0.900622	0.0392317
$528$	0	0
$529$	−2.33722	−0.101618
$530$	12.4691	0.541623
$531$	−5.92760	−0.257236
$532$	2.05657	0.0891637
$533$	3.92159	0.169863
$534$	11.9314	0.516323
$535$	1.14971	0.0497064
$536$	5.18658	0.224026
$537$	−6.54867	−0.282596
$538$	18.7186	0.807016
$539$	0	0
$540$	1.46722	0.0631393
$541$	−20.5396	−0.883065	−0.441532	−	0.897245i	$-0.645565\pi$
$541$	−20.5396	−0.883065	−0.441532	+	0.897245i	$0.645565\pi$
$542$	54.4916	2.34062
$543$	8.04433	0.345215
$544$	32.6891	1.40153
$545$	−13.3402	−0.571431
$546$	−31.7449	−1.35856
$547$	−19.1832	−0.820215	−0.410107	−	0.912037i	$-0.634509\pi$
$547$	−19.1832	−0.820215	−0.410107	+	0.912037i	$0.634509\pi$
$548$	23.1346	0.988261
$549$	3.21636	0.137271
$550$	0	0
$551$	5.65964	0.241109
$552$	4.50951	0.191938
$553$	3.18609	0.135486
$554$	−1.29332	−0.0549477
$555$	−4.22812	−0.179474
$556$	−14.7288	−0.624642
$557$	22.1368	0.937966	0.468983	−	0.883207i	$-0.344621\pi$
$557$	22.1368	0.937966	0.468983	+	0.883207i	$0.344621\pi$
$558$	−0.354989	−0.0150279
$559$	59.9338	2.53493
$560$	−12.5801	−0.531608
$561$	0	0
$562$	−19.8658	−0.837988
$563$	−25.1244	−1.05887	−0.529435	−	0.848351i	$-0.677596\pi$
$563$	−25.1244	−1.05887	−0.529435	+	0.848351i	$0.677596\pi$
$564$	12.9514	0.545351
$565$	−6.29738	−0.264933
$566$	−40.2614	−1.69231
$567$	−2.63089	−0.110487
$568$	−2.72200	−0.114213
$569$	25.6815	1.07663	0.538313	−	0.842745i	$-0.319062\pi$
$569$	25.6815	1.07663	0.538313	+	0.842745i	$0.319062\pi$
$570$	0.992053	0.0415525
$571$	−13.3087	−0.556953	−0.278476	−	0.960443i	$-0.589829\pi$
$571$	−13.3087	−0.556953	−0.278476	+	0.960443i	$0.589829\pi$
$572$	0	0
$573$	8.72833	0.364631
$574$	2.96467	0.123743
$575$	−4.54563	−0.189566
$576$	−3.32133	−0.138389
$577$	−13.1005	−0.545380	−0.272690	−	0.962102i	$-0.587913\pi$
$577$	−13.1005	−0.545380	−0.272690	+	0.962102i	$0.587913\pi$
$578$	−9.90069	−0.411814
$579$	15.0613	0.625924
$580$	15.5862	0.647184
$581$	12.2673	0.508932
$582$	−13.6475	−0.565706
$583$	0	0
$584$	15.5511	0.643508
$585$	−6.48008	−0.267918
$586$	−10.7228	−0.442955
$587$	−0.287665	−0.0118732	−0.00593659	−	0.999982i	$-0.501890\pi$
$587$	−0.287665	−0.0118732	−0.00593659	+	0.999982i	$0.501890\pi$
$588$	0.115043	0.00474428
$589$	−0.101571	−0.00418514
$590$	−11.0375	−0.454406
$591$	13.0882	0.538378
$592$	20.2176	0.830939
$593$	31.8957	1.30980	0.654900	−	0.755716i	$-0.272711\pi$
$593$	31.8957	1.30980	0.654900	+	0.755716i	$0.272711\pi$
$594$	0	0
$595$	12.4286	0.509522
$596$	15.3549	0.628962
$597$	−7.16738	−0.293341
$598$	54.8486	2.24293
$599$	−33.5486	−1.37076	−0.685379	−	0.728186i	$-0.740364\pi$
$599$	−33.5486	−1.37076	−0.685379	+	0.728186i	$0.740364\pi$
$600$	−0.992053	−0.0405004
$601$	32.8320	1.33925	0.669623	−	0.742701i	$-0.266456\pi$
$601$	32.8320	1.33925	0.669623	+	0.742701i	$0.266456\pi$
$602$	45.3091	1.84666
$603$	5.22812	0.212906
$604$	22.9523	0.933915
$605$	0	0
$606$	−21.1527	−0.859269
$607$	45.1195	1.83135	0.915673	−	0.401925i	$-0.131659\pi$
$607$	45.1195	1.83135	0.915673	+	0.401925i	$0.131659\pi$
$608$	−3.68662	−0.149512
$609$	−27.9478	−1.13250
$610$	5.98902	0.242488
$611$	−57.2005	−2.31408
$612$	6.93131	0.280182
$613$	46.5727	1.88105	0.940527	−	0.339719i	$-0.110332\pi$
$613$	46.5727	1.88105	0.940527	+	0.339719i	$0.110332\pi$
$614$	−34.4370	−1.38976
$615$	0.605176	0.0244031
$616$	0	0
$617$	−30.9597	−1.24639	−0.623195	−	0.782067i	$-0.714166\pi$
$617$	−30.9597	−1.24639	−0.623195	+	0.782067i	$0.714166\pi$
$618$	−3.83701	−0.154347
$619$	−14.6825	−0.590139	−0.295070	−	0.955476i	$-0.595343\pi$
$619$	−14.6825	−0.590139	−0.295070	+	0.955476i	$0.595343\pi$
$620$	−0.279718	−0.0112337
$621$	4.54563	0.182410
$622$	21.0661	0.844672
$623$	−16.8579	−0.675398
$624$	30.9858	1.24043
$625$	1.00000	0.0400000
$626$	34.5226	1.37980
$627$	0	0
$628$	13.1899	0.526334
$629$	−19.9741	−0.796418
$630$	−4.89885	−0.195175
$631$	−12.7589	−0.507922	−0.253961	−	0.967214i	$-0.581733\pi$
$631$	−12.7589	−0.507922	−0.253961	+	0.967214i	$0.581733\pi$
$632$	−1.20141	−0.0477894
$633$	5.98824	0.238011
$634$	1.52955	0.0607462
$635$	−10.0943	−0.400580
$636$	−9.82519	−0.389594
$637$	−0.508093	−0.0201314
$638$	0	0
$639$	−2.74381	−0.108543
$640$	7.65483	0.302584
$641$	16.3406	0.645415	0.322708	−	0.946499i	$-0.395407\pi$
$641$	16.3406	0.645415	0.322708	+	0.946499i	$0.395407\pi$
$642$	−2.14082	−0.0844915
$643$	5.93513	0.234059	0.117029	−	0.993128i	$-0.462663\pi$
$643$	5.93513	0.234059	0.117029	+	0.993128i	$0.462663\pi$
$644$	17.5466	0.691435
$645$	9.24893	0.364176
$646$	4.68656	0.184390
$647$	−8.09795	−0.318363	−0.159182	−	0.987249i	$-0.550886\pi$
$647$	−8.09795	−0.318363	−0.159182	+	0.987249i	$0.550886\pi$
$648$	0.992053	0.0389715
$649$	0	0
$650$	−12.0662	−0.473276
$651$	0.501564	0.0196579
$652$	29.1097	1.14002
$653$	28.4218	1.11223	0.556116	−	0.831105i	$-0.312291\pi$
$653$	28.4218	1.11223	0.556116	+	0.831105i	$0.312291\pi$
$654$	24.8401	0.971324
$655$	−4.64756	−0.181595
$656$	−2.89377	−0.112983
$657$	15.6756	0.611565
$658$	−43.2427	−1.68578
$659$	−7.38736	−0.287771	−0.143885	−	0.989594i	$-0.545960\pi$
$659$	−7.38736	−0.287771	−0.143885	+	0.989594i	$0.545960\pi$
$660$	0	0
$661$	−31.4264	−1.22235	−0.611174	−	0.791497i	$-0.709302\pi$
$661$	−31.4264	−1.22235	−0.611174	+	0.791497i	$0.709302\pi$
$662$	−14.8632	−0.577674
$663$	−30.6125	−1.18889
$664$	−4.62573	−0.179513
$665$	−1.40167	−0.0543546
$666$	7.87297	0.305071
$667$	48.2880	1.86972
$668$	−16.8926	−0.653596
$669$	0.300522	0.0116189
$670$	9.73502	0.376096
$671$	0	0
$672$	18.2049	0.702268
$673$	15.5966	0.601203	0.300601	−	0.953750i	$-0.402813\pi$
$673$	15.5966	0.601203	0.300601	+	0.953750i	$0.402813\pi$
$674$	−23.2179	−0.894319
$675$	−1.00000	−0.0384900
$676$	42.5370	1.63604
$677$	3.86670	0.148609	0.0743047	−	0.997236i	$-0.476326\pi$
$677$	3.86670	0.148609	0.0743047	+	0.997236i	$0.476326\pi$
$678$	11.7260	0.450336
$679$	19.2825	0.739995
$680$	−4.68656	−0.179721
$681$	−22.8179	−0.874384
$682$	0	0
$683$	34.2736	1.31144	0.655722	−	0.755002i	$-0.272364\pi$
$683$	34.2736	1.31144	0.655722	+	0.755002i	$0.272364\pi$
$684$	−0.781701	−0.0298891
$685$	−15.7676	−0.602448
$686$	−34.6760	−1.32394
$687$	−28.2109	−1.07631
$688$	−44.2256	−1.68609
$689$	43.3935	1.65316
$690$	8.46419	0.322226
$691$	−44.7295	−1.70159	−0.850796	−	0.525497i	$-0.823879\pi$
$691$	−44.7295	−1.70159	−0.850796	+	0.525497i	$0.823879\pi$
$692$	11.0117	0.418602
$693$	0	0
$694$	38.9399	1.47814
$695$	10.0386	0.380785
$696$	10.5385	0.399462
$697$	2.85891	0.108289
$698$	−14.2973	−0.541160
$699$	−19.3845	−0.733190
$700$	−3.86011	−0.145898
$701$	−11.1637	−0.421646	−0.210823	−	0.977524i	$-0.567614\pi$
$701$	−11.1637	−0.421646	−0.210823	+	0.977524i	$0.567614\pi$
$702$	12.0662	0.455410
$703$	2.25264	0.0849599
$704$	0	0
$705$	−8.82712	−0.332449
$706$	25.6932	0.966978
$707$	29.8867	1.12400
$708$	8.69712	0.326858
$709$	41.7860	1.56931	0.784654	−	0.619934i	$-0.212841\pi$
$709$	41.7860	1.56931	0.784654	+	0.619934i	$0.212841\pi$
$710$	−5.10910	−0.191741
$711$	−1.21103	−0.0454172
$712$	6.35676	0.238230
$713$	−0.866599	−0.0324544
$714$	−23.1426	−0.866091
$715$	0	0
$716$	9.60837	0.359082
$717$	−15.2735	−0.570401
$718$	−33.3608	−1.24502
$719$	−17.9903	−0.670924	−0.335462	−	0.942054i	$-0.608892\pi$
$719$	−17.9903	−0.670924	−0.335462	+	0.942054i	$0.608892\pi$
$720$	4.78170	0.178203
$721$	5.42132	0.201900
$722$	34.8504	1.29700
$723$	−7.21213	−0.268222
$724$	−11.8028	−0.438649
$725$	−10.6229	−0.394526
$726$	0	0
$727$	23.9340	0.887664	0.443832	−	0.896110i	$-0.353619\pi$
$727$	23.9340	0.887664	0.443832	+	0.896110i	$0.353619\pi$
$728$	−16.9129	−0.626835
$729$	1.00000	0.0370370
$730$	29.1888	1.08033
$731$	43.6928	1.61604
$732$	−4.71912	−0.174424
$733$	7.40496	0.273509	0.136754	−	0.990605i	$-0.456333\pi$
$733$	7.40496	0.273509	0.136754	+	0.990605i	$0.456333\pi$
$734$	−17.6307	−0.650760
$735$	−0.0784084	−0.00289214
$736$	−31.4542	−1.15942
$737$	0	0
$738$	−1.12687	−0.0414806
$739$	−30.9698	−1.13924	−0.569622	−	0.821907i	$-0.692910\pi$
$739$	−30.9698	−1.13924	−0.569622	+	0.821907i	$0.692910\pi$
$740$	6.20360	0.228049
$741$	3.45243	0.126828
$742$	32.8049	1.20430
$743$	49.7620	1.82559	0.912796	−	0.408416i	$-0.133919\pi$
$743$	49.7620	1.82559	0.912796	+	0.408416i	$0.133919\pi$
$744$	−0.189129	−0.00693382
$745$	−10.4653	−0.383418
$746$	21.6746	0.793564
$747$	−4.66278	−0.170602
$748$	0	0
$749$	3.02477	0.110523
$750$	−1.86205	−0.0679924
$751$	34.4375	1.25664	0.628320	−	0.777955i	$-0.283743\pi$
$751$	34.4375	1.25664	0.628320	+	0.777955i	$0.283743\pi$
$752$	42.2087	1.53919
$753$	−19.0750	−0.695130
$754$	128.179	4.66800
$755$	−15.6433	−0.569319
$756$	3.86011	0.140391
$757$	−18.4833	−0.671787	−0.335894	−	0.941900i	$-0.609038\pi$
$757$	−18.4833	−0.671787	−0.335894	+	0.941900i	$0.609038\pi$
$758$	12.2971	0.446651
$759$	0	0
$760$	0.528542	0.0191722
$761$	7.05014	0.255567	0.127784	−	0.991802i	$-0.459214\pi$
$761$	7.05014	0.255567	0.127784	+	0.991802i	$0.459214\pi$
$762$	18.7961	0.680910
$763$	−35.0966	−1.27058
$764$	−12.8064	−0.463320
$765$	−4.72410	−0.170800
$766$	−36.7524	−1.32792
$767$	−38.4113	−1.38695
$768$	−20.8963	−0.754031
$769$	15.9027	0.573465	0.286732	−	0.958011i	$-0.407431\pi$
$769$	15.9027	0.573465	0.286732	+	0.958011i	$0.407431\pi$
$770$	0	0
$771$	−26.1060	−0.940185
$772$	−22.0982	−0.795333
$773$	17.1271	0.616020	0.308010	−	0.951383i	$-0.400337\pi$
$773$	17.1271	0.616020	0.308010	+	0.951383i	$0.400337\pi$
$774$	−17.2219	−0.619030
$775$	0.190644	0.00684814
$776$	−7.27103	−0.261015
$777$	−11.1237	−0.399062
$778$	−47.2305	−1.69330
$779$	−0.322423	−0.0115520
$780$	9.50774	0.340432
$781$	0	0
$782$	39.9857	1.42988
$783$	10.6229	0.379633
$784$	0.374925	0.0133902
$785$	−8.98970	−0.320856
$786$	8.65399	0.308678
$787$	−46.2646	−1.64915	−0.824577	−	0.565749i	$-0.808587\pi$
$787$	−46.2646	−1.64915	−0.824577	+	0.565749i	$0.808587\pi$
$788$	−19.2034	−0.684092
$789$	27.0086	0.961530
$790$	−2.25500	−0.0802292
$791$	−16.5677	−0.589081
$792$	0	0
$793$	20.8423	0.740131
$794$	73.0667	2.59304
$795$	6.69644	0.237498
$796$	10.5162	0.372735
$797$	−3.91542	−0.138691	−0.0693456	−	0.997593i	$-0.522091\pi$
$797$	−3.91542	−0.138691	−0.0693456	+	0.997593i	$0.522091\pi$
$798$	2.60999	0.0923925
$799$	−41.7002	−1.47525
$800$	6.91965	0.244647
$801$	6.40768	0.226404
$802$	−20.7111	−0.731333
$803$	0	0
$804$	−7.67083	−0.270529
$805$	−11.9591	−0.421502
$806$	−2.30036	−0.0810266
$807$	10.0527	0.353872
$808$	−11.2696	−0.396464
$809$	−6.75253	−0.237406	−0.118703	−	0.992930i	$-0.537874\pi$
$809$	−6.75253	−0.237406	−0.118703	+	0.992930i	$0.537874\pi$
$810$	1.86205	0.0654257
$811$	43.4268	1.52492	0.762461	−	0.647035i	$-0.223991\pi$
$811$	43.4268	1.52492	0.762461	+	0.647035i	$0.223991\pi$
$812$	41.0057	1.43902
$813$	29.2643	1.02635
$814$	0	0
$815$	−19.8400	−0.694964
$816$	22.5892	0.790781
$817$	−4.92760	−0.172395
$818$	−21.6204	−0.755939
$819$	−17.0484	−0.595719
$820$	−0.887929	−0.0310078
$821$	7.15064	0.249559	0.124780	−	0.992184i	$-0.460178\pi$
$821$	7.15064	0.249559	0.124780	+	0.992184i	$0.460178\pi$
$822$	29.3600	1.02405
$823$	−9.57872	−0.333893	−0.166947	−	0.985966i	$-0.553391\pi$
$823$	−9.57872	−0.333893	−0.166947	+	0.985966i	$0.553391\pi$
$824$	−2.04426	−0.0712153
$825$	0	0
$826$	−29.0384	−1.01038
$827$	−6.11637	−0.212687	−0.106343	−	0.994329i	$-0.533914\pi$
$827$	−6.11637	−0.212687	−0.106343	+	0.994329i	$0.533914\pi$
$828$	−6.66947	−0.231780
$829$	34.4276	1.19572	0.597861	−	0.801600i	$-0.296018\pi$
$829$	34.4276	1.19572	0.597861	+	0.801600i	$0.296018\pi$
$830$	−8.68232	−0.301368
$831$	−0.694566	−0.0240942
$832$	−21.5225	−0.746157
$833$	−0.370409	−0.0128339
$834$	−18.6923	−0.647262
$835$	11.5133	0.398435
$836$	0	0
$837$	−0.190644	−0.00658963
$838$	−34.5408	−1.19319
$839$	9.40836	0.324813	0.162406	−	0.986724i	$-0.448074\pi$
$839$	9.40836	0.324813	0.162406	+	0.986724i	$0.448074\pi$
$840$	−2.60999	−0.0900530
$841$	83.8470	2.89127
$842$	37.1953	1.28183
$843$	−10.6688	−0.367453
$844$	−8.78609	−0.302430
$845$	−28.9915	−0.997337
$846$	16.4365	0.565100
$847$	0	0
$848$	−32.0204	−1.09958
$849$	−21.6221	−0.742069
$850$	−8.79650	−0.301717
$851$	19.2195	0.658836
$852$	4.02578	0.137921
$853$	35.0942	1.20160	0.600802	−	0.799398i	$-0.294848\pi$
$853$	35.0942	1.20160	0.600802	+	0.799398i	$0.294848\pi$
$854$	15.7565	0.539175
$855$	0.532775	0.0182205
$856$	−1.14058	−0.0389841
$857$	−21.3605	−0.729661	−0.364831	−	0.931074i	$-0.618873\pi$
$857$	−21.3605	−0.729661	−0.364831	+	0.931074i	$0.618873\pi$
$858$	0	0
$859$	5.21468	0.177923	0.0889613	−	0.996035i	$-0.471645\pi$
$859$	5.21468	0.177923	0.0889613	+	0.996035i	$0.471645\pi$
$860$	−13.5703	−0.462742
$861$	1.59215	0.0542604
$862$	−48.3323	−1.64621
$863$	4.35787	0.148344	0.0741718	−	0.997245i	$-0.476369\pi$
$863$	4.35787	0.148344	0.0741718	+	0.997245i	$0.476369\pi$
$864$	−6.91965	−0.235411
$865$	−7.50512	−0.255182
$866$	62.5254	2.12470
$867$	−5.31709	−0.180578
$868$	−0.735908	−0.0249783
$869$	0	0
$870$	19.7804	0.670620
$871$	33.8787	1.14793
$872$	13.2342	0.448166
$873$	−7.32927	−0.248058
$874$	−4.50951	−0.152536
$875$	2.63089	0.0889404
$876$	−22.9997	−0.777087
$877$	13.8710	0.468391	0.234196	−	0.972189i	$-0.424754\pi$
$877$	13.8710	0.468391	0.234196	+	0.972189i	$0.424754\pi$
$878$	−31.7070	−1.07006
$879$	−5.75860	−0.194233
$880$	0	0
$881$	40.9512	1.37968	0.689841	−	0.723961i	$-0.257681\pi$
$881$	40.9512	1.37968	0.689841	+	0.723961i	$0.257681\pi$
$882$	0.146000	0.00491608
$883$	−35.5876	−1.19762	−0.598809	−	0.800892i	$-0.704359\pi$
$883$	−35.5876	−1.19762	−0.598809	+	0.800892i	$0.704359\pi$
$884$	44.9155	1.51067
$885$	−5.92760	−0.199254
$886$	−46.9511	−1.57735
$887$	−32.2626	−1.08327	−0.541635	−	0.840614i	$-0.682195\pi$
$887$	−32.2626	−1.08327	−0.541635	+	0.840614i	$0.682195\pi$
$888$	4.19452	0.140759
$889$	−26.5570	−0.890694
$890$	11.9314	0.399942
$891$	0	0
$892$	−0.440934	−0.0147636
$893$	4.70287	0.157376
$894$	19.4869	0.651738
$895$	−6.54867	−0.218898
$896$	20.1390	0.672798
$897$	29.4561	0.983510
$898$	49.6414	1.65656
$899$	−2.02520	−0.0675443
$900$	1.46722	0.0489075
$901$	31.6346	1.05390
$902$	0	0
$903$	24.3329	0.809749
$904$	6.24734	0.207784
$905$	8.04433	0.267402
$906$	29.1286	0.967734
$907$	14.5809	0.484149	0.242075	−	0.970258i	$-0.422172\pi$
$907$	14.5809	0.484149	0.242075	+	0.970258i	$0.422172\pi$
$908$	33.4790	1.11104
$909$	−11.3599	−0.376784
$910$	−31.7449	−1.05233
$911$	−33.5719	−1.11229	−0.556144	−	0.831086i	$-0.687720\pi$
$911$	−33.5719	−1.11229	−0.556144	+	0.831086i	$0.687720\pi$
$912$	−2.54757	−0.0843585
$913$	0	0
$914$	−40.8684	−1.35181
$915$	3.21636	0.106330
$916$	41.3917	1.36762
$917$	−12.2272	−0.403779
$918$	8.79650	0.290328
$919$	−36.2522	−1.19585	−0.597924	−	0.801553i	$-0.704008\pi$
$919$	−36.2522	−1.19585	−0.597924	+	0.801553i	$0.704008\pi$
$920$	4.50951	0.148674
$921$	−18.4941	−0.609403
$922$	−8.05566	−0.265299
$923$	−17.7801	−0.585239
$924$	0	0
$925$	−4.22812	−0.139020
$926$	−21.3341	−0.701083
$927$	−2.06064	−0.0676803
$928$	−73.5071	−2.41299
$929$	24.1790	0.793286	0.396643	−	0.917973i	$-0.370175\pi$
$929$	24.1790	0.793286	0.396643	+	0.917973i	$0.370175\pi$
$930$	−0.354989	−0.0116405
$931$	0.0417740	0.00136909
$932$	28.4414	0.931631
$933$	11.3134	0.370383
$934$	28.9630	0.947697
$935$	0	0
$936$	6.42859	0.210125
$937$	16.4072	0.535999	0.267999	−	0.963419i	$-0.413638\pi$
$937$	16.4072	0.535999	0.267999	+	0.963419i	$0.413638\pi$
$938$	25.6118	0.836254
$939$	18.5401	0.605035
$940$	12.9514	0.422427
$941$	−8.02749	−0.261689	−0.130844	−	0.991403i	$-0.541769\pi$
$941$	−8.02749	−0.261689	−0.130844	+	0.991403i	$0.541769\pi$
$942$	16.7392	0.545394
$943$	−2.75091	−0.0895819
$944$	28.3440	0.922519
$945$	−2.63089	−0.0855829
$946$	0	0
$947$	36.0500	1.17147	0.585733	−	0.810504i	$-0.300807\pi$
$947$	36.0500	1.17147	0.585733	+	0.810504i	$0.300807\pi$
$948$	1.77685	0.0577095
$949$	101.579	3.29741
$950$	0.992053	0.0321865
$951$	0.821434	0.0266368
$952$	−12.3298	−0.399612
$953$	−6.99518	−0.226596	−0.113298	−	0.993561i	$-0.536142\pi$
$953$	−6.99518	−0.226596	−0.113298	+	0.993561i	$0.536142\pi$
$954$	−12.4691	−0.403702
$955$	8.72833	0.282442
$956$	22.4097	0.724782
$957$	0	0
$958$	18.6146	0.601412
$959$	−41.4828	−1.33955
$960$	−3.32133	−0.107195
$961$	−30.9637	−0.998828
$962$	51.0175	1.64487
$963$	−1.14971	−0.0370490
$964$	10.5818	0.340817
$965$	15.0613	0.484839
$966$	22.2684	0.716473
$967$	−13.1569	−0.423098	−0.211549	−	0.977367i	$-0.567851\pi$
$967$	−13.1569	−0.423098	−0.211549	+	0.977367i	$0.567851\pi$
$968$	0	0
$969$	2.51688	0.0808539
$970$	−13.6475	−0.438194
$971$	−22.7163	−0.728999	−0.364500	−	0.931204i	$-0.618760\pi$
$971$	−22.7163	−0.728999	−0.364500	+	0.931204i	$0.618760\pi$
$972$	−1.46722	−0.0470613
$973$	26.4104	0.846679
$974$	−73.6998	−2.36149
$975$	−6.48008	−0.207529
$976$	−15.3797	−0.492291
$977$	−5.69712	−0.182267	−0.0911335	−	0.995839i	$-0.529049\pi$
$977$	−5.69712	−0.182267	−0.0911335	+	0.995839i	$0.529049\pi$
$978$	36.9430	1.18131
$979$	0	0
$980$	0.115043	0.00367490
$981$	13.3402	0.425920
$982$	−17.2994	−0.552047
$983$	16.9445	0.540446	0.270223	−	0.962798i	$-0.412903\pi$
$983$	16.9445	0.540446	0.270223	+	0.962798i	$0.412903\pi$
$984$	−0.600367	−0.0191390
$985$	13.0882	0.417026
$986$	93.4447	2.97589
$987$	−23.2232	−0.739203
$988$	−5.06549	−0.161155
$989$	−42.0422	−1.33686
$990$	0	0
$991$	36.0516	1.14522	0.572609	−	0.819829i	$-0.305931\pi$
$991$	36.0516	1.14522	0.572609	+	0.819829i	$0.305931\pi$
$992$	1.31919	0.0418844
$993$	−7.98217	−0.253306
$994$	−13.4415	−0.426338
$995$	−7.16738	−0.227221
$996$	6.84135	0.216776
$997$	−18.6585	−0.590922	−0.295461	−	0.955355i	$-0.595473\pi$
$997$	−18.6585	−0.590922	−0.295461	+	0.955355i	$0.595473\pi$
$998$	43.4741	1.37615
$999$	4.22812	0.133772

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1815.2.a.r.1.2		4
3.2	odd	2		5445.2.a.br.1.3		4
5.4	even	2		9075.2.a.dg.1.3		4
11.2	odd	10		165.2.m.b.136.1	yes	8
11.6	odd	10		165.2.m.b.91.1	✓	8
11.10	odd	2		1815.2.a.v.1.3		4
33.2	even	10		495.2.n.b.136.2		8
33.17	even	10		495.2.n.b.91.2		8
33.32	even	2		5445.2.a.bk.1.2		4
55.2	even	20		825.2.bx.g.499.3		16
55.13	even	20		825.2.bx.g.499.2		16
55.17	even	20		825.2.bx.g.124.2		16
55.24	odd	10		825.2.n.i.301.2		8
55.28	even	20		825.2.bx.g.124.3		16
55.39	odd	10		825.2.n.i.751.2		8
55.54	odd	2		9075.2.a.cq.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.m.b.91.1	✓	8	11.6	odd	10
165.2.m.b.136.1	yes	8	11.2	odd	10
495.2.n.b.91.2		8	33.17	even	10
495.2.n.b.136.2		8	33.2	even	10
825.2.n.i.301.2		8	55.24	odd	10
825.2.n.i.751.2		8	55.39	odd	10
825.2.bx.g.124.2		16	55.17	even	20
825.2.bx.g.124.3		16	55.28	even	20
825.2.bx.g.499.2		16	55.13	even	20
825.2.bx.g.499.3		16	55.2	even	20
1815.2.a.r.1.2		4	1.1	even	1	trivial
1815.2.a.v.1.3		4	11.10	odd	2
5445.2.a.bk.1.2		4	33.32	even	2
5445.2.a.br.1.3		4	3.2	odd	2
9075.2.a.cq.1.2		4	55.54	odd	2
9075.2.a.dg.1.3		4	5.4	even	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)

\(f(q)\)	\(=\)	\(q-1.86205 q^{2} -1.00000 q^{3} +1.46722 q^{4} -1.00000 q^{5} +1.86205 q^{6} -2.63089 q^{7} +0.992053 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.86205 q^{2} -1.00000 q^{3} +1.46722 q^{4} -1.00000 q^{5} +1.86205 q^{6} -2.63089 q^{7} +0.992053 q^{8} +1.00000 q^{9} +1.86205 q^{10} -1.46722 q^{12} +6.48008 q^{13} +4.89885 q^{14} +1.00000 q^{15} -4.78170 q^{16} +4.72410 q^{17} -1.86205 q^{18} -0.532775 q^{19} -1.46722 q^{20} +2.63089 q^{21} -4.54563 q^{23} -0.992053 q^{24} +1.00000 q^{25} -12.0662 q^{26} -1.00000 q^{27} -3.86011 q^{28} -10.6229 q^{29} -1.86205 q^{30} +0.190644 q^{31} +6.91965 q^{32} -8.79650 q^{34} +2.63089 q^{35} +1.46722 q^{36} -4.22812 q^{37} +0.992053 q^{38} -6.48008 q^{39} -0.992053 q^{40} +0.605176 q^{41} -4.89885 q^{42} +9.24893 q^{43} -1.00000 q^{45} +8.46419 q^{46} -8.82712 q^{47} +4.78170 q^{48} -0.0784084 q^{49} -1.86205 q^{50} -4.72410 q^{51} +9.50774 q^{52} +6.69644 q^{53} +1.86205 q^{54} -2.60999 q^{56} +0.532775 q^{57} +19.7804 q^{58} -5.92760 q^{59} +1.46722 q^{60} +3.21636 q^{61} -0.354989 q^{62} -2.63089 q^{63} -3.32133 q^{64} -6.48008 q^{65} +5.22812 q^{67} +6.93131 q^{68} +4.54563 q^{69} -4.89885 q^{70} -2.74381 q^{71} +0.992053 q^{72} +15.6756 q^{73} +7.87297 q^{74} -1.00000 q^{75} -0.781701 q^{76} +12.0662 q^{78} -1.21103 q^{79} +4.78170 q^{80} +1.00000 q^{81} -1.12687 q^{82} -4.66278 q^{83} +3.86011 q^{84} -4.72410 q^{85} -17.2219 q^{86} +10.6229 q^{87} +6.40768 q^{89} +1.86205 q^{90} -17.0484 q^{91} -6.66947 q^{92} -0.190644 q^{93} +16.4365 q^{94} +0.532775 q^{95} -6.91965 q^{96} -7.32927 q^{97} +0.146000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} - 4 q^{3} + 9 q^{4} - 4 q^{5} + q^{6} + 8 q^{7} - 3 q^{8} + 4 q^{9}+O(q^{10}) \) 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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