LMFDB - Embedded newform 1815.2.a.x.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:	4.4.725.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 3x^{2} + x + 1 $ x^4 - x^3 - 3*x^2 + x + 1
Coefficient ring:	$\Z[a_1, a_2]$
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			$-1.35567$ 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)

$f(q)$	$=$	$q+1.16215 q^{2} +1.00000 q^{3} -0.649414 q^{4} -1.00000 q^{5} +1.16215 q^{6} -4.28684 q^{7} -3.07901 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.16215 q^{2} +1.00000 q^{3} -0.649414 q^{4} -1.00000 q^{5} +1.16215 q^{6} -4.28684 q^{7} -3.07901 q^{8} +1.00000 q^{9} -1.16215 q^{10} -0.649414 q^{12} +5.16724 q^{13} -4.98194 q^{14} -1.00000 q^{15} -2.27943 q^{16} +5.00000 q^{17} +1.16215 q^{18} +5.59998 q^{19} +0.649414 q^{20} -4.28684 q^{21} -0.219819 q^{23} -3.07901 q^{24} +1.00000 q^{25} +6.00509 q^{26} +1.00000 q^{27} +2.78393 q^{28} +6.41843 q^{29} -1.16215 q^{30} -2.83095 q^{31} +3.50898 q^{32} +5.81074 q^{34} +4.28684 q^{35} -0.649414 q^{36} +3.92802 q^{37} +6.50800 q^{38} +5.16724 q^{39} +3.07901 q^{40} +5.86100 q^{41} -4.98194 q^{42} -8.90173 q^{43} -1.00000 q^{45} -0.255462 q^{46} -0.237878 q^{47} -2.27943 q^{48} +11.3770 q^{49} +1.16215 q^{50} +5.00000 q^{51} -3.35567 q^{52} +2.53671 q^{53} +1.16215 q^{54} +13.1992 q^{56} +5.59998 q^{57} +7.45917 q^{58} -7.87035 q^{59} +0.649414 q^{60} -4.85807 q^{61} -3.28999 q^{62} -4.28684 q^{63} +8.63682 q^{64} -5.16724 q^{65} +12.1280 q^{67} -3.24707 q^{68} -0.219819 q^{69} +4.98194 q^{70} -9.98194 q^{71} -3.07901 q^{72} +14.5625 q^{73} +4.56494 q^{74} +1.00000 q^{75} -3.63670 q^{76} +6.00509 q^{78} +8.00194 q^{79} +2.27943 q^{80} +1.00000 q^{81} +6.81134 q^{82} +12.5530 q^{83} +2.78393 q^{84} -5.00000 q^{85} -10.3451 q^{86} +6.41843 q^{87} -2.56545 q^{89} -1.16215 q^{90} -22.1511 q^{91} +0.142753 q^{92} -2.83095 q^{93} -0.276449 q^{94} -5.59998 q^{95} +3.50898 q^{96} +2.01199 q^{97} +13.2218 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 5 q^{2} + 4 q^{3} + 9 q^{4} - 4 q^{5} + 5 q^{6} - 2 q^{7} + 15 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q + 5 * q^2 + 4 * q^3 + 9 * q^4 - 4 * q^5 + 5 * q^6 - 2 * q^7 + 15 * q^8 + 4 * q^9	$ 4 q + 5 q^{2} + 4 q^{3} + 9 q^{4} - 4 q^{5} + 5 q^{6} - 2 q^{7} + 15 q^{8} + 4 q^{9} - 5 q^{10} + 9 q^{12} + 3 q^{13} - 5 q^{14} - 4 q^{15} + 15 q^{16} + 20 q^{17} + 5 q^{18} + 3 q^{19} - 9 q^{20} - 2 q^{21} - 5 q^{23} + 15 q^{24} + 4 q^{25} + 6 q^{26} + 4 q^{27} + 3 q^{28} + 5 q^{29} - 5 q^{30} - q^{31} + 30 q^{32} + 25 q^{34} + 2 q^{35} + 9 q^{36} - 7 q^{37} + q^{38} + 3 q^{39} - 15 q^{40} + 20 q^{41} - 5 q^{42} - 2 q^{43} - 4 q^{45} + 7 q^{46} - 20 q^{47} + 15 q^{48} + 8 q^{49} + 5 q^{50} + 20 q^{51} - 7 q^{52} + 6 q^{53} + 5 q^{54} + 10 q^{56} + 3 q^{57} - 21 q^{58} - 5 q^{59} - 9 q^{60} - 7 q^{61} - 12 q^{62} - 2 q^{63} + 49 q^{64} - 3 q^{65} - 13 q^{67} + 45 q^{68} - 5 q^{69} + 5 q^{70} - 25 q^{71} + 15 q^{72} + 23 q^{73} - 7 q^{74} + 4 q^{75} - 7 q^{76} + 6 q^{78} - 15 q^{80} + 4 q^{81} + 11 q^{82} + 33 q^{83} + 3 q^{84} - 20 q^{85} - 12 q^{86} + 5 q^{87} + 16 q^{89} - 5 q^{90} - 24 q^{91} - q^{93} - 17 q^{94} - 3 q^{95} + 30 q^{96} + 25 q^{98}+O(q^{100}) $ 4 * q + 5 * q^2 + 4 * q^3 + 9 * q^4 - 4 * q^5 + 5 * q^6 - 2 * q^7 + 15 * q^8 + 4 * q^9 - 5 * q^10 + 9 * q^12 + 3 * q^13 - 5 * q^14 - 4 * q^15 + 15 * q^16 + 20 * q^17 + 5 * q^18 + 3 * q^19 - 9 * q^20 - 2 * q^21 - 5 * q^23 + 15 * q^24 + 4 * q^25 + 6 * q^26 + 4 * q^27 + 3 * q^28 + 5 * q^29 - 5 * q^30 - q^31 + 30 * q^32 + 25 * q^34 + 2 * q^35 + 9 * q^36 - 7 * q^37 + q^38 + 3 * q^39 - 15 * q^40 + 20 * q^41 - 5 * q^42 - 2 * q^43 - 4 * q^45 + 7 * q^46 - 20 * q^47 + 15 * q^48 + 8 * q^49 + 5 * q^50 + 20 * q^51 - 7 * q^52 + 6 * q^53 + 5 * q^54 + 10 * q^56 + 3 * q^57 - 21 * q^58 - 5 * q^59 - 9 * q^60 - 7 * q^61 - 12 * q^62 - 2 * q^63 + 49 * q^64 - 3 * q^65 - 13 * q^67 + 45 * q^68 - 5 * q^69 + 5 * q^70 - 25 * q^71 + 15 * q^72 + 23 * q^73 - 7 * q^74 + 4 * q^75 - 7 * q^76 + 6 * q^78 - 15 * q^80 + 4 * q^81 + 11 * q^82 + 33 * q^83 + 3 * q^84 - 20 * q^85 - 12 * q^86 + 5 * q^87 + 16 * q^89 - 5 * q^90 - 24 * q^91 - q^93 - 17 * q^94 - 3 * q^95 + 30 * q^96 + 25 * 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 $

$2$	1.16215	0.821762	0.410881	−	0.911689i	$-0.365221\pi$
$2$	1.16215	0.821762	0.410881	+	0.911689i	$0.365221\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.649414	−0.324707
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	1.16215	0.474445
$7$	−4.28684	−1.62027	−0.810137	−	0.586241i	$-0.800607\pi$
$7$	−4.28684	−1.62027	−0.810137	+	0.586241i	$0.800607\pi$
$8$	−3.07901	−1.08859
$9$	1.00000	0.333333
$10$	−1.16215	−0.367503
$11$	0	0
$11$	0	0
$12$	−0.649414	−0.187470
$13$	5.16724	1.43313	0.716567	−	0.697519i	$-0.245713\pi$
$13$	5.16724	1.43313	0.716567	+	0.697519i	$0.245713\pi$
$14$	−4.98194	−1.33148
$15$	−1.00000	−0.258199
$16$	−2.27943	−0.569858
$17$	5.00000	1.21268	0.606339	−	0.795206i	$-0.292637\pi$
$17$	5.00000	1.21268	0.606339	+	0.795206i	$0.292637\pi$
$18$	1.16215	0.273921
$19$	5.59998	1.28472	0.642361	−	0.766402i	$-0.277955\pi$
$19$	5.59998	1.28472	0.642361	+	0.766402i	$0.277955\pi$
$20$	0.649414	0.145213
$21$	−4.28684	−0.935466
$22$	0	0
$23$	−0.219819	−0.0458354	−0.0229177	−	0.999737i	$-0.507296\pi$
$23$	−0.219819	−0.0458354	−0.0229177	+	0.999737i	$0.507296\pi$
$24$	−3.07901	−0.628500
$25$	1.00000	0.200000
$26$	6.00509	1.17769
$27$	1.00000	0.192450
$28$	2.78393	0.526114
$29$	6.41843	1.19187	0.595937	−	0.803031i	$-0.296781\pi$
$29$	6.41843	1.19187	0.595937	+	0.803031i	$0.296781\pi$
$30$	−1.16215	−0.212178
$31$	−2.83095	−0.508455	−0.254227	−	0.967145i	$-0.581821\pi$
$31$	−2.83095	−0.508455	−0.254227	+	0.967145i	$0.581821\pi$
$32$	3.50898	0.620306
$33$	0	0
$34$	5.81074	0.996533
$35$	4.28684	0.724608
$36$	−0.649414	−0.108236
$37$	3.92802	0.645763	0.322881	−	0.946439i	$-0.395348\pi$
$37$	3.92802	0.645763	0.322881	+	0.946439i	$0.395348\pi$
$38$	6.50800	1.05574
$39$	5.16724	0.827420
$40$	3.07901	0.486834
$41$	5.86100	0.915334	0.457667	−	0.889124i	$-0.348685\pi$
$41$	5.86100	0.915334	0.457667	+	0.889124i	$0.348685\pi$
$42$	−4.98194	−0.768730
$43$	−8.90173	−1.35750	−0.678751	−	0.734369i	$-0.737478\pi$
$43$	−8.90173	−1.35750	−0.678751	+	0.734369i	$0.737478\pi$
$44$	0	0
$45$	−1.00000	−0.149071
$46$	−0.255462	−0.0376658
$47$	−0.237878	−0.0346980	−0.0173490	−	0.999849i	$-0.505523\pi$
$47$	−0.237878	−0.0346980	−0.0173490	+	0.999849i	$0.505523\pi$
$48$	−2.27943	−0.329008
$49$	11.3770	1.62529
$50$	1.16215	0.164352
$51$	5.00000	0.700140
$52$	−3.35567	−0.465348
$53$	2.53671	0.348443	0.174222	−	0.984706i	$-0.444259\pi$
$53$	2.53671	0.348443	0.174222	+	0.984706i	$0.444259\pi$
$54$	1.16215	0.158148
$55$	0	0
$56$	13.1992	1.76382
$57$	5.59998	0.741735
$58$	7.45917	0.979436
$59$	−7.87035	−1.02463	−0.512316	−	0.858797i	$-0.671212\pi$
$59$	−7.87035	−1.02463	−0.512316	+	0.858797i	$0.671212\pi$
$60$	0.649414	0.0838390
$61$	−4.85807	−0.622012	−0.311006	−	0.950408i	$-0.600666\pi$
$61$	−4.85807	−0.622012	−0.311006	+	0.950408i	$0.600666\pi$
$62$	−3.28999	−0.417829
$63$	−4.28684	−0.540091
$64$	8.63682	1.07960
$65$	−5.16724	−0.640917
$66$	0	0
$67$	12.1280	1.48167	0.740834	−	0.671688i	$-0.234431\pi$
$67$	12.1280	1.48167	0.740834	+	0.671688i	$0.234431\pi$
$68$	−3.24707	−0.393765
$69$	−0.219819	−0.0264631
$70$	4.98194	0.595456
$71$	−9.98194	−1.18464	−0.592319	−	0.805703i	$-0.701788\pi$
$71$	−9.98194	−1.18464	−0.592319	+	0.805703i	$0.701788\pi$
$72$	−3.07901	−0.362865
$73$	14.5625	1.70441	0.852207	−	0.523205i	$-0.175264\pi$
$73$	14.5625	1.70441	0.852207	+	0.523205i	$0.175264\pi$
$74$	4.56494	0.530664
$75$	1.00000	0.115470
$76$	−3.63670	−0.417158
$77$	0	0
$78$	6.00509	0.679942
$79$	8.00194	0.900289	0.450144	−	0.892956i	$-0.351372\pi$
$79$	8.00194	0.900289	0.450144	+	0.892956i	$0.351372\pi$
$80$	2.27943	0.254848
$81$	1.00000	0.111111
$82$	6.81134	0.752187
$83$	12.5530	1.37787	0.688933	−	0.724825i	$-0.258079\pi$
$83$	12.5530	1.37787	0.688933	+	0.724825i	$0.258079\pi$
$84$	2.78393	0.303752
$85$	−5.00000	−0.542326
$86$	−10.3451	−1.11554
$87$	6.41843	0.688128
$88$	0	0
$89$	−2.56545	−0.271937	−0.135969	−	0.990713i	$-0.543415\pi$
$89$	−2.56545	−0.271937	−0.135969	+	0.990713i	$0.543415\pi$
$90$	−1.16215	−0.122501
$91$	−22.1511	−2.32207
$92$	0.142753	0.0148831
$93$	−2.83095	−0.293556
$94$	−0.276449	−0.0285135
$95$	−5.59998	−0.574545
$96$	3.50898	0.358134
$97$	2.01199	0.204286	0.102143	−	0.994770i	$-0.467430\pi$
$97$	2.01199	0.204286	0.102143	+	0.994770i	$0.467430\pi$
$98$	13.2218	1.33560
$99$	0	0
$100$	−0.649414	−0.0649414
$101$	−7.58484	−0.754720	−0.377360	−	0.926067i	$-0.623168\pi$
$101$	−7.58484	−0.754720	−0.377360	+	0.926067i	$0.623168\pi$
$102$	5.81074	0.575349
$103$	−16.8685	−1.66211	−0.831053	−	0.556193i	$-0.812262\pi$
$103$	−16.8685	−1.66211	−0.831053	+	0.556193i	$0.812262\pi$
$104$	−15.9100	−1.56010
$105$	4.28684	0.418353
$106$	2.94803	0.286338
$107$	7.76161	0.750343	0.375172	−	0.926955i	$-0.377584\pi$
$107$	7.76161	0.750343	0.375172	+	0.926955i	$0.377584\pi$
$108$	−0.649414	−0.0624899
$109$	4.45671	0.426876	0.213438	−	0.976957i	$-0.431534\pi$
$109$	4.45671	0.426876	0.213438	+	0.976957i	$0.431534\pi$
$110$	0	0
$111$	3.92802	0.372831
$112$	9.77157	0.923327
$113$	−7.71247	−0.725528	−0.362764	−	0.931881i	$-0.618167\pi$
$113$	−7.71247	−0.725528	−0.362764	+	0.931881i	$0.618167\pi$
$114$	6.50800	0.609530
$115$	0.219819	0.0204982
$116$	−4.16822	−0.387010
$117$	5.16724	0.477711
$118$	−9.14651	−0.842004
$119$	−21.4342	−1.96487
$120$	3.07901	0.281074
$121$	0	0
$122$	−5.64579	−0.511146
$123$	5.86100	0.528469
$124$	1.83846	0.165099
$125$	−1.00000	−0.0894427
$126$	−4.98194	−0.443827
$127$	1.53114	0.135867	0.0679335	−	0.997690i	$-0.478359\pi$
$127$	1.53114	0.135867	0.0679335	+	0.997690i	$0.478359\pi$
$128$	3.01930	0.266871
$129$	−8.90173	−0.783754
$130$	−6.00509	−0.526681
$131$	2.66108	0.232500	0.116250	−	0.993220i	$-0.462913\pi$
$131$	2.66108	0.232500	0.116250	+	0.993220i	$0.462913\pi$
$132$	0	0
$133$	−24.0062	−2.08160
$134$	14.0945	1.21758
$135$	−1.00000	−0.0860663
$136$	−15.3950	−1.32011
$137$	10.2555	0.876183	0.438092	−	0.898930i	$-0.355655\pi$
$137$	10.2555	0.876183	0.438092	+	0.898930i	$0.355655\pi$
$138$	−0.255462	−0.0217464
$139$	−5.29507	−0.449122	−0.224561	−	0.974460i	$-0.572095\pi$
$139$	−5.29507	−0.449122	−0.224561	+	0.974460i	$0.572095\pi$
$140$	−2.78393	−0.235285
$141$	−0.237878	−0.0200329
$142$	−11.6005	−0.973491
$143$	0	0
$144$	−2.27943	−0.189953
$145$	−6.41843	−0.533022
$146$	16.9238	1.40062
$147$	11.3770	0.938360
$148$	−2.55091	−0.209684
$149$	3.78841	0.310359	0.155179	−	0.987886i	$-0.450404\pi$
$149$	3.78841	0.310359	0.155179	+	0.987886i	$0.450404\pi$
$150$	1.16215	0.0948889
$151$	−5.92001	−0.481763	−0.240882	−	0.970554i	$-0.577437\pi$
$151$	−5.92001	−0.481763	−0.240882	+	0.970554i	$0.577437\pi$
$152$	−17.2424	−1.39854
$153$	5.00000	0.404226
$154$	0	0
$155$	2.83095	0.227388
$156$	−3.35567	−0.268669
$157$	−7.42909	−0.592906	−0.296453	−	0.955048i	$-0.595804\pi$
$157$	−7.42909	−0.592906	−0.296453	+	0.955048i	$0.595804\pi$
$158$	9.29944	0.739823
$159$	2.53671	0.201174
$160$	−3.50898	−0.277409
$161$	0.942328	0.0742659
$162$	1.16215	0.0913069
$163$	5.32086	0.416762	0.208381	−	0.978048i	$-0.433181\pi$
$163$	5.32086	0.416762	0.208381	+	0.978048i	$0.433181\pi$
$164$	−3.80621	−0.297215
$165$	0	0
$166$	14.5884	1.13228
$167$	−1.97139	−0.152551	−0.0762753	−	0.997087i	$-0.524303\pi$
$167$	−1.97139	−0.152551	−0.0762753	+	0.997087i	$0.524303\pi$
$168$	13.1992	1.01834
$169$	13.7003	1.05387
$170$	−5.81074	−0.445663
$171$	5.59998	0.428241
$172$	5.78091	0.440790
$173$	−1.97504	−0.150160	−0.0750799	−	0.997178i	$-0.523921\pi$
$173$	−1.97504	−0.150160	−0.0750799	+	0.997178i	$0.523921\pi$
$174$	7.45917	0.565478
$175$	−4.28684	−0.324055
$176$	0	0
$177$	−7.87035	−0.591572
$178$	−2.98143	−0.223468
$179$	−2.02315	−0.151217	−0.0756086	−	0.997138i	$-0.524090\pi$
$179$	−2.02315	−0.151217	−0.0756086	+	0.997138i	$0.524090\pi$
$180$	0.649414	0.0484045
$181$	20.1380	1.49685	0.748423	−	0.663221i	$-0.230811\pi$
$181$	20.1380	1.49685	0.748423	+	0.663221i	$0.230811\pi$
$182$	−25.7429	−1.90819
$183$	−4.85807	−0.359119
$184$	0.676824	0.0498961
$185$	−3.92802	−0.288794
$186$	−3.28999	−0.241234
$187$	0	0
$188$	0.154481	0.0112667
$189$	−4.28684	−0.311822
$190$	−6.50800	−0.472140
$191$	12.6652	0.916418	0.458209	−	0.888844i	$-0.348491\pi$
$191$	12.6652	0.916418	0.458209	+	0.888844i	$0.348491\pi$
$192$	8.63682	0.623309
$193$	−13.9321	−1.00286	−0.501428	−	0.865199i	$-0.667192\pi$
$193$	−13.9321	−1.00286	−0.501428	+	0.865199i	$0.667192\pi$
$194$	2.33822	0.167875
$195$	−5.16724	−0.370033
$196$	−7.38839	−0.527742
$197$	14.6060	1.04064	0.520319	−	0.853972i	$-0.325813\pi$
$197$	14.6060	1.04064	0.520319	+	0.853972i	$0.325813\pi$
$198$	0	0
$199$	−11.8748	−0.841784	−0.420892	−	0.907111i	$-0.638283\pi$
$199$	−11.8748	−0.841784	−0.420892	+	0.907111i	$0.638283\pi$
$200$	−3.07901	−0.217719
$201$	12.1280	0.855441
$202$	−8.81471	−0.620201
$203$	−27.5148	−1.93116
$204$	−3.24707	−0.227340
$205$	−5.86100	−0.409350
$206$	−19.6037	−1.36586
$207$	−0.219819	−0.0152785
$208$	−11.7784	−0.816683
$209$	0	0
$210$	4.98194	0.343787
$211$	−22.3518	−1.53876	−0.769382	−	0.638789i	$-0.779436\pi$
$211$	−22.3518	−1.53876	−0.769382	+	0.638789i	$0.779436\pi$
$212$	−1.64737	−0.113142
$213$	−9.98194	−0.683951
$214$	9.02014	0.616604
$215$	8.90173	0.607093
$216$	−3.07901	−0.209500
$217$	12.1359	0.823836
$218$	5.17936	0.350790
$219$	14.5625	0.984044
$220$	0	0
$221$	25.8362	1.73793
$222$	4.56494	0.306379
$223$	−19.1583	−1.28294	−0.641468	−	0.767150i	$-0.721674\pi$
$223$	−19.1583	−1.28294	−0.641468	+	0.767150i	$0.721674\pi$
$224$	−15.0424	−1.00507
$225$	1.00000	0.0666667
$226$	−8.96302	−0.596211
$227$	15.3759	1.02053	0.510267	−	0.860016i	$-0.329547\pi$
$227$	15.3759	1.02053	0.510267	+	0.860016i	$0.329547\pi$
$228$	−3.63670	−0.240846
$229$	8.90126	0.588212	0.294106	−	0.955773i	$-0.404978\pi$
$229$	8.90126	0.588212	0.294106	+	0.955773i	$0.404978\pi$
$230$	0.255462	0.0168447
$231$	0	0
$232$	−19.7624	−1.29747
$233$	22.8362	1.49605	0.748024	−	0.663672i	$-0.231003\pi$
$233$	22.8362	1.49605	0.748024	+	0.663672i	$0.231003\pi$
$234$	6.00509	0.392565
$235$	0.237878	0.0155174
$236$	5.11112	0.332705
$237$	8.00194	0.519782
$238$	−24.9097	−1.61466
$239$	16.8605	1.09062	0.545308	−	0.838236i	$-0.316413\pi$
$239$	16.8605	1.09062	0.545308	+	0.838236i	$0.316413\pi$
$240$	2.27943	0.147137
$241$	−11.9607	−0.770459	−0.385229	−	0.922821i	$-0.625878\pi$
$241$	−11.9607	−0.770459	−0.385229	+	0.922821i	$0.625878\pi$
$242$	0	0
$243$	1.00000	0.0641500
$244$	3.15490	0.201972
$245$	−11.3770	−0.726851
$246$	6.81134	0.434275
$247$	28.9364	1.84118
$248$	8.71654	0.553501
$249$	12.5530	0.795511
$250$	−1.16215	−0.0735006
$251$	16.0034	1.01013	0.505063	−	0.863082i	$-0.331469\pi$
$251$	16.0034	1.01013	0.505063	+	0.863082i	$0.331469\pi$
$252$	2.78393	0.175371
$253$	0	0
$254$	1.77941	0.111650
$255$	−5.00000	−0.313112
$256$	−13.7648	−0.860298
$257$	5.47446	0.341487	0.170744	−	0.985315i	$-0.445383\pi$
$257$	5.47446	0.341487	0.170744	+	0.985315i	$0.445383\pi$
$258$	−10.3451	−0.644059
$259$	−16.8388	−1.04631
$260$	3.35567	0.208110
$261$	6.41843	0.397291
$262$	3.09257	0.191060
$263$	11.9841	0.738971	0.369486	−	0.929236i	$-0.379534\pi$
$263$	11.9841	0.738971	0.369486	+	0.929236i	$0.379534\pi$
$264$	0	0
$265$	−2.53671	−0.155829
$266$	−27.8987	−1.71058
$267$	−2.56545	−0.157003
$268$	−7.87607	−0.481108
$269$	13.6465	0.832041	0.416020	−	0.909355i	$-0.363424\pi$
$269$	13.6465	0.832041	0.416020	+	0.909355i	$0.363424\pi$
$270$	−1.16215	−0.0707260
$271$	11.8379	0.719098	0.359549	−	0.933126i	$-0.382930\pi$
$271$	11.8379	0.719098	0.359549	+	0.933126i	$0.382930\pi$
$272$	−11.3972	−0.691055
$273$	−22.1511	−1.34065
$274$	11.9184	0.720014
$275$	0	0
$276$	0.142753	0.00859274
$277$	10.2638	0.616694	0.308347	−	0.951274i	$-0.400224\pi$
$277$	10.2638	0.616694	0.308347	+	0.951274i	$0.400224\pi$
$278$	−6.15366	−0.369072
$279$	−2.83095	−0.169485
$280$	−13.1992	−0.788804
$281$	−2.93889	−0.175319	−0.0876597	−	0.996150i	$-0.527939\pi$
$281$	−2.93889	−0.175319	−0.0876597	+	0.996150i	$0.527939\pi$
$282$	−0.276449	−0.0164623
$283$	21.8279	1.29754	0.648768	−	0.760986i	$-0.275284\pi$
$283$	21.8279	1.29754	0.648768	+	0.760986i	$0.275284\pi$
$284$	6.48241	0.384660
$285$	−5.59998	−0.331714
$286$	0	0
$287$	−25.1252	−1.48309
$288$	3.50898	0.206769
$289$	8.00000	0.470588
$290$	−7.45917	−0.438017
$291$	2.01199	0.117945
$292$	−9.45710	−0.553435
$293$	−24.7665	−1.44688	−0.723438	−	0.690390i	$-0.757439\pi$
$293$	−24.7665	−1.44688	−0.723438	+	0.690390i	$0.757439\pi$
$294$	13.2218	0.771109
$295$	7.87035	0.458230
$296$	−12.0944	−0.702974
$297$	0	0
$298$	4.40269	0.255041
$299$	−1.13586	−0.0656882
$300$	−0.649414	−0.0374939
$301$	38.1603	2.19952
$302$	−6.87992	−0.395895
$303$	−7.58484	−0.435738
$304$	−12.7648	−0.732110
$305$	4.85807	0.278172
$306$	5.81074	0.332178
$307$	−4.94023	−0.281954	−0.140977	−	0.990013i	$-0.545024\pi$
$307$	−4.94023	−0.281954	−0.140977	+	0.990013i	$0.545024\pi$
$308$	0	0
$309$	−16.8685	−0.959618
$310$	3.28999	0.186859
$311$	−13.8096	−0.783070	−0.391535	−	0.920163i	$-0.628056\pi$
$311$	−13.8096	−0.783070	−0.391535	+	0.920163i	$0.628056\pi$
$312$	−15.9100	−0.900724
$313$	−4.06934	−0.230013	−0.115006	−	0.993365i	$-0.536689\pi$
$313$	−4.06934	−0.230013	−0.115006	+	0.993365i	$0.536689\pi$
$314$	−8.63369	−0.487227
$315$	4.28684	0.241536
$316$	−5.19657	−0.292330
$317$	25.8199	1.45019	0.725096	−	0.688648i	$-0.241795\pi$
$317$	25.8199	1.45019	0.725096	+	0.688648i	$0.241795\pi$
$318$	2.94803	0.165317
$319$	0	0
$320$	−8.63682	−0.482813
$321$	7.76161	0.433211
$322$	1.09512	0.0610289
$323$	27.9999	1.55795
$324$	−0.649414	−0.0360785
$325$	5.16724	0.286627
$326$	6.18362	0.342479
$327$	4.45671	0.246457
$328$	−18.0461	−0.996428
$329$	1.01974	0.0562203
$330$	0	0
$331$	−3.35008	−0.184137	−0.0920684	−	0.995753i	$-0.529348\pi$
$331$	−3.35008	−0.184137	−0.0920684	+	0.995753i	$0.529348\pi$
$332$	−8.15206	−0.447403
$333$	3.92802	0.215254
$334$	−2.29104	−0.125360
$335$	−12.1280	−0.662622
$336$	9.77157	0.533083
$337$	−27.3998	−1.49256	−0.746282	−	0.665630i	$-0.768163\pi$
$337$	−27.3998	−1.49256	−0.746282	+	0.665630i	$0.768163\pi$
$338$	15.9218	0.866031
$339$	−7.71247	−0.418884
$340$	3.24707	0.176097
$341$	0	0
$342$	6.50800	0.351912
$343$	−18.7636	−1.01314
$344$	27.4085	1.47777
$345$	0.219819	0.0118346
$346$	−2.29529	−0.123396
$347$	15.8265	0.849610	0.424805	−	0.905285i	$-0.360343\pi$
$347$	15.8265	0.849610	0.424805	+	0.905285i	$0.360343\pi$
$348$	−4.16822	−0.223440
$349$	−3.65930	−0.195878	−0.0979388	−	0.995192i	$-0.531225\pi$
$349$	−3.65930	−0.195878	−0.0979388	+	0.995192i	$0.531225\pi$
$350$	−4.98194	−0.266296
$351$	5.16724	0.275807
$352$	0	0
$353$	−27.4937	−1.46334	−0.731671	−	0.681658i	$-0.761259\pi$
$353$	−27.4937	−1.46334	−0.731671	+	0.681658i	$0.761259\pi$
$354$	−9.14651	−0.486131
$355$	9.98194	0.529786
$356$	1.66604	0.0882999
$357$	−21.4342	−1.13442
$358$	−2.35119	−0.124265
$359$	0.478740	0.0252670	0.0126335	−	0.999920i	$-0.495979\pi$
$359$	0.478740	0.0252670	0.0126335	+	0.999920i	$0.495979\pi$
$360$	3.07901	0.162278
$361$	12.3597	0.650512
$362$	23.4033	1.23005
$363$	0	0
$364$	14.3852	0.753992
$365$	−14.5625	−0.762237
$366$	−5.64579	−0.295110
$367$	−25.4582	−1.32891	−0.664453	−	0.747330i	$-0.731335\pi$
$367$	−25.4582	−1.32891	−0.664453	+	0.747330i	$0.731335\pi$
$368$	0.501062	0.0261197
$369$	5.86100	0.305111
$370$	−4.56494	−0.237320
$371$	−10.8745	−0.564574
$372$	1.83846	0.0953198
$373$	−2.75967	−0.142890	−0.0714451	−	0.997445i	$-0.522761\pi$
$373$	−2.75967	−0.142890	−0.0714451	+	0.997445i	$0.522761\pi$
$374$	0	0
$375$	−1.00000	−0.0516398
$376$	0.732428	0.0377721
$377$	33.1656	1.70811
$378$	−4.98194	−0.256243
$379$	−21.6535	−1.11227	−0.556133	−	0.831093i	$-0.687716\pi$
$379$	−21.6535	−1.11227	−0.556133	+	0.831093i	$0.687716\pi$
$380$	3.63670	0.186559
$381$	1.53114	0.0784428
$382$	14.7188	0.753078
$383$	16.2295	0.829287	0.414643	−	0.909984i	$-0.363906\pi$
$383$	16.2295	0.829287	0.414643	+	0.909984i	$0.363906\pi$
$384$	3.01930	0.154078
$385$	0	0
$386$	−16.1912	−0.824109
$387$	−8.90173	−0.452500
$388$	−1.30661	−0.0663332
$389$	−16.2916	−0.826019	−0.413009	−	0.910727i	$-0.635522\pi$
$389$	−16.2916	−0.826019	−0.413009	+	0.910727i	$0.635522\pi$
$390$	−6.00509	−0.304079
$391$	−1.09909	−0.0555836
$392$	−35.0299	−1.76928
$393$	2.66108	0.134234
$394$	16.9744	0.855157
$395$	−8.00194	−0.402621
$396$	0	0
$397$	−19.9673	−1.00213	−0.501064	−	0.865410i	$-0.667058\pi$
$397$	−19.9673	−1.00213	−0.501064	+	0.865410i	$0.667058\pi$
$398$	−13.8003	−0.691747
$399$	−24.0062	−1.20181
$400$	−2.27943	−0.113972
$401$	−27.3269	−1.36464	−0.682320	−	0.731053i	$-0.739029\pi$
$401$	−27.3269	−1.36464	−0.682320	+	0.731053i	$0.739029\pi$
$402$	14.0945	0.702969
$403$	−14.6282	−0.728683
$404$	4.92570	0.245063
$405$	−1.00000	−0.0496904
$406$	−31.9763	−1.58696
$407$	0	0
$408$	−15.3950	−0.762168
$409$	24.9380	1.23310	0.616552	−	0.787314i	$-0.288529\pi$
$409$	24.9380	1.23310	0.616552	+	0.787314i	$0.288529\pi$
$410$	−6.81134	−0.336388
$411$	10.2555	0.505865
$412$	10.9547	0.539698
$413$	33.7389	1.66019
$414$	−0.255462	−0.0125553
$415$	−12.5530	−0.616200
$416$	18.1317	0.888981
$417$	−5.29507	−0.259301
$418$	0	0
$419$	16.8256	0.821986	0.410993	−	0.911639i	$-0.365182\pi$
$419$	16.8256	0.821986	0.410993	+	0.911639i	$0.365182\pi$
$420$	−2.78393	−0.135842
$421$	23.6006	1.15022	0.575112	−	0.818074i	$-0.304958\pi$
$421$	23.6006	1.15022	0.575112	+	0.818074i	$0.304958\pi$
$422$	−25.9761	−1.26450
$423$	−0.237878	−0.0115660
$424$	−7.81054	−0.379313
$425$	5.00000	0.242536
$426$	−11.6005	−0.562045
$427$	20.8258	1.00783
$428$	−5.04050	−0.243642
$429$	0	0
$430$	10.3451	0.498886
$431$	−37.6556	−1.81381	−0.906903	−	0.421339i	$-0.861560\pi$
$431$	−37.6556	−1.81381	−0.906903	+	0.421339i	$0.861560\pi$
$432$	−2.27943	−0.109669
$433$	−30.9752	−1.48857	−0.744286	−	0.667861i	$-0.767210\pi$
$433$	−30.9752	−1.48857	−0.744286	+	0.667861i	$0.767210\pi$
$434$	14.1037	0.676997
$435$	−6.41843	−0.307740
$436$	−2.89425	−0.138609
$437$	−1.23098	−0.0588858
$438$	16.9238	0.808650
$439$	−28.2131	−1.34654	−0.673268	−	0.739399i	$-0.735110\pi$
$439$	−28.2131	−1.34654	−0.673268	+	0.739399i	$0.735110\pi$
$440$	0	0
$441$	11.3770	0.541762
$442$	30.0254	1.42816
$443$	14.6420	0.695663	0.347831	−	0.937557i	$-0.386918\pi$
$443$	14.6420	0.695663	0.347831	+	0.937557i	$0.386918\pi$
$444$	−2.55091	−0.121061
$445$	2.56545	0.121614
$446$	−22.2648	−1.05427
$447$	3.78841	0.179186
$448$	−37.0247	−1.74925
$449$	11.9977	0.566206	0.283103	−	0.959090i	$-0.408636\pi$
$449$	11.9977	0.566206	0.283103	+	0.959090i	$0.408636\pi$
$450$	1.16215	0.0547841
$451$	0	0
$452$	5.00858	0.235584
$453$	−5.92001	−0.278146
$454$	17.8691	0.838636
$455$	22.1511	1.03846
$456$	−17.2424	−0.807448
$457$	10.0437	0.469824	0.234912	−	0.972017i	$-0.424520\pi$
$457$	10.0437	0.469824	0.234912	+	0.972017i	$0.424520\pi$
$458$	10.3446	0.483370
$459$	5.00000	0.233380
$460$	−0.142753	−0.00665591
$461$	−13.4491	−0.626386	−0.313193	−	0.949689i	$-0.601399\pi$
$461$	−13.4491	−0.626386	−0.313193	+	0.949689i	$0.601399\pi$
$462$	0	0
$463$	18.7836	0.872946	0.436473	−	0.899717i	$-0.356227\pi$
$463$	18.7836	0.872946	0.436473	+	0.899717i	$0.356227\pi$
$464$	−14.6304	−0.679199
$465$	2.83095	0.131282
$466$	26.5390	1.22940
$467$	26.5510	1.22863	0.614316	−	0.789060i	$-0.289432\pi$
$467$	26.5510	1.22863	0.614316	+	0.789060i	$0.289432\pi$
$468$	−3.35567	−0.155116
$469$	−51.9907	−2.40071
$470$	0.276449	0.0127516
$471$	−7.42909	−0.342314
$472$	24.2329	1.11541
$473$	0	0
$474$	9.29944	0.427137
$475$	5.59998	0.256944
$476$	13.9197	0.638007
$477$	2.53671	0.116148
$478$	19.5944	0.896228
$479$	10.7830	0.492689	0.246345	−	0.969182i	$-0.420771\pi$
$479$	10.7830	0.492689	0.246345	+	0.969182i	$0.420771\pi$
$480$	−3.50898	−0.160162
$481$	20.2970	0.925464
$482$	−13.9001	−0.633134
$483$	0.942328	0.0428774
$484$	0	0
$485$	−2.01199	−0.0913596
$486$	1.16215	0.0527161
$487$	6.81095	0.308634	0.154317	−	0.988021i	$-0.450682\pi$
$487$	6.81095	0.308634	0.154317	+	0.988021i	$0.450682\pi$
$488$	14.9580	0.677119
$489$	5.32086	0.240617
$490$	−13.2218	−0.597298
$491$	26.0954	1.17767	0.588834	−	0.808254i	$-0.299587\pi$
$491$	26.0954	1.17767	0.588834	+	0.808254i	$0.299587\pi$
$492$	−3.80621	−0.171597
$493$	32.0922	1.44536
$494$	33.6283	1.51301
$495$	0	0
$496$	6.45297	0.289747
$497$	42.7910	1.91944
$498$	14.5884	0.653721
$499$	19.3834	0.867719	0.433860	−	0.900981i	$-0.357151\pi$
$499$	19.3834	0.867719	0.433860	+	0.900981i	$0.357151\pi$
$500$	0.649414	0.0290427
$501$	−1.97139	−0.0880751
$502$	18.5983	0.830084
$503$	18.8422	0.840134	0.420067	−	0.907493i	$-0.362007\pi$
$503$	18.8422	0.840134	0.420067	+	0.907493i	$0.362007\pi$
$504$	13.1992	0.587940
$505$	7.58484	0.337521
$506$	0	0
$507$	13.7003	0.608453
$508$	−0.994345	−0.0441169
$509$	−5.15120	−0.228323	−0.114162	−	0.993462i	$-0.536418\pi$
$509$	−5.15120	−0.228323	−0.114162	+	0.993462i	$0.536418\pi$
$510$	−5.81074	−0.257304
$511$	−62.4272	−2.76162
$512$	−22.0353	−0.973831
$513$	5.59998	0.247245
$514$	6.36212	0.280621
$515$	16.8685	0.743317
$516$	5.78091	0.254490
$517$	0	0
$518$	−19.5692	−0.859820
$519$	−1.97504	−0.0866948
$520$	15.9100	0.697698
$521$	−41.5022	−1.81824	−0.909121	−	0.416532i	$-0.863246\pi$
$521$	−41.5022	−1.81824	−0.909121	+	0.416532i	$0.863246\pi$
$522$	7.45917	0.326479
$523$	−6.92280	−0.302713	−0.151356	−	0.988479i	$-0.548364\pi$
$523$	−6.92280	−0.302713	−0.151356	+	0.988479i	$0.548364\pi$
$524$	−1.72815	−0.0754944
$525$	−4.28684	−0.187093
$526$	13.9273	0.607259
$527$	−14.1548	−0.616592
$528$	0	0
$529$	−22.9517	−0.997899
$530$	−2.94803	−0.128054
$531$	−7.87035	−0.341544
$532$	15.5900	0.675911
$533$	30.2852	1.31180
$534$	−2.98143	−0.129019
$535$	−7.76161	−0.335564
$536$	−37.3421	−1.61293
$537$	−2.02315	−0.0873052
$538$	15.8592	0.683740
$539$	0	0
$540$	0.649414	0.0279463
$541$	−28.4183	−1.22180	−0.610899	−	0.791709i	$-0.709192\pi$
$541$	−28.4183	−1.22180	−0.610899	+	0.791709i	$0.709192\pi$
$542$	13.7573	0.590928
$543$	20.1380	0.864205
$544$	17.5449	0.752231
$545$	−4.45671	−0.190905
$546$	−25.7429	−1.10169
$547$	25.8592	1.10566	0.552829	−	0.833295i	$-0.313548\pi$
$547$	25.8592	1.10566	0.552829	+	0.833295i	$0.313548\pi$
$548$	−6.66004	−0.284503
$549$	−4.85807	−0.207337
$550$	0	0
$551$	35.9431	1.53123
$552$	0.676824	0.0288075
$553$	−34.3031	−1.45871
$554$	11.9281	0.506776
$555$	−3.92802	−0.166735
$556$	3.43869	0.145833
$557$	−8.06409	−0.341687	−0.170843	−	0.985298i	$-0.554649\pi$
$557$	−8.06409	−0.341687	−0.170843	+	0.985298i	$0.554649\pi$
$558$	−3.28999	−0.139276
$559$	−45.9973	−1.94548
$560$	−9.77157	−0.412924
$561$	0	0
$562$	−3.41542	−0.144071
$563$	29.6516	1.24966	0.624832	−	0.780759i	$-0.285167\pi$
$563$	29.6516	1.24966	0.624832	+	0.780759i	$0.285167\pi$
$564$	0.154481	0.00650483
$565$	7.71247	0.324466
$566$	25.3673	1.06627
$567$	−4.28684	−0.180030
$568$	30.7345	1.28959
$569$	−42.1026	−1.76503	−0.882517	−	0.470280i	$-0.844153\pi$
$569$	−42.1026	−1.76503	−0.882517	+	0.470280i	$0.844153\pi$
$570$	−6.50800	−0.272590
$571$	−26.6823	−1.11662	−0.558311	−	0.829632i	$-0.688550\pi$
$571$	−26.6823	−1.11662	−0.558311	+	0.829632i	$0.688550\pi$
$572$	0	0
$573$	12.6652	0.529094
$574$	−29.1992	−1.21875
$575$	−0.219819	−0.00916708
$576$	8.63682	0.359867
$577$	−3.30818	−0.137721	−0.0688606	−	0.997626i	$-0.521936\pi$
$577$	−3.30818	−0.137721	−0.0688606	+	0.997626i	$0.521936\pi$
$578$	9.29718	0.386712
$579$	−13.9321	−0.578999
$580$	4.16822	0.173076
$581$	−53.8125	−2.23252
$582$	2.33822	0.0969225
$583$	0	0
$584$	−44.8381	−1.85542
$585$	−5.16724	−0.213639
$586$	−28.7823	−1.18899
$587$	−8.52770	−0.351976	−0.175988	−	0.984392i	$-0.556312\pi$
$587$	−8.52770	−0.351976	−0.175988	+	0.984392i	$0.556312\pi$
$588$	−7.38839	−0.304692
$589$	−15.8533	−0.653223
$590$	9.14651	0.376556
$591$	14.6060	0.600813
$592$	−8.95367	−0.367993
$593$	−23.4343	−0.962333	−0.481167	−	0.876629i	$-0.659787\pi$
$593$	−23.4343	−0.962333	−0.481167	+	0.876629i	$0.659787\pi$
$594$	0	0
$595$	21.4342	0.878717
$596$	−2.46025	−0.100776
$597$	−11.8748	−0.486004
$598$	−1.32003	−0.0539801
$599$	18.8344	0.769555	0.384777	−	0.923009i	$-0.374278\pi$
$599$	18.8344	0.769555	0.384777	+	0.923009i	$0.374278\pi$
$600$	−3.07901	−0.125700
$601$	−37.6585	−1.53612	−0.768062	−	0.640376i	$-0.778779\pi$
$601$	−37.6585	−1.53612	−0.768062	+	0.640376i	$0.778779\pi$
$602$	44.3479	1.80749
$603$	12.1280	0.493889
$604$	3.84453	0.156432
$605$	0	0
$606$	−8.81471	−0.358073
$607$	−29.3680	−1.19201	−0.596004	−	0.802981i	$-0.703246\pi$
$607$	−29.3680	−1.19201	−0.596004	+	0.802981i	$0.703246\pi$
$608$	19.6502	0.796921
$609$	−27.5148	−1.11496
$610$	5.64579	0.228592
$611$	−1.22917	−0.0497269
$612$	−3.24707	−0.131255
$613$	−12.9111	−0.521474	−0.260737	−	0.965410i	$-0.583965\pi$
$613$	−12.9111	−0.521474	−0.260737	+	0.965410i	$0.583965\pi$
$614$	−5.74127	−0.231699
$615$	−5.86100	−0.236338
$616$	0	0
$617$	41.6041	1.67492	0.837459	−	0.546500i	$-0.184040\pi$
$617$	41.6041	1.67492	0.837459	+	0.546500i	$0.184040\pi$
$618$	−19.6037	−0.788578
$619$	4.27117	0.171673	0.0858363	−	0.996309i	$-0.472644\pi$
$619$	4.27117	0.171673	0.0858363	+	0.996309i	$0.472644\pi$
$620$	−1.83846	−0.0738344
$621$	−0.219819	−0.00882102
$622$	−16.0488	−0.643497
$623$	10.9977	0.440613
$624$	−11.7784	−0.471512
$625$	1.00000	0.0400000
$626$	−4.72918	−0.189016
$627$	0	0
$628$	4.82455	0.192521
$629$	19.6401	0.783103
$630$	4.98194	0.198485
$631$	−27.5510	−1.09679	−0.548393	−	0.836221i	$-0.684760\pi$
$631$	−27.5510	−1.09679	−0.548393	+	0.836221i	$0.684760\pi$
$632$	−24.6381	−0.980049
$633$	−22.3518	−0.888406
$634$	30.0066	1.19171
$635$	−1.53114	−0.0607615
$636$	−1.64737	−0.0653225
$637$	58.7877	2.32925
$638$	0	0
$639$	−9.98194	−0.394879
$640$	−3.01930	−0.119348
$641$	9.16806	0.362117	0.181058	−	0.983472i	$-0.442048\pi$
$641$	9.16806	0.362117	0.181058	+	0.983472i	$0.442048\pi$
$642$	9.02014	0.355996
$643$	−3.40908	−0.134441	−0.0672206	−	0.997738i	$-0.521413\pi$
$643$	−3.40908	−0.134441	−0.0672206	+	0.997738i	$0.521413\pi$
$644$	−0.611961	−0.0241146
$645$	8.90173	0.350505
$646$	32.5400	1.28027
$647$	22.3608	0.879092	0.439546	−	0.898220i	$-0.355139\pi$
$647$	22.3608	0.879092	0.439546	+	0.898220i	$0.355139\pi$
$648$	−3.07901	−0.120955
$649$	0	0
$650$	6.00509	0.235539
$651$	12.1359	0.475642
$652$	−3.45544	−0.135325
$653$	−14.7957	−0.578999	−0.289500	−	0.957178i	$-0.593489\pi$
$653$	−14.7957	−0.578999	−0.289500	+	0.957178i	$0.593489\pi$
$654$	5.17936	0.202529
$655$	−2.66108	−0.103977
$656$	−13.3598	−0.521611
$657$	14.5625	0.568138
$658$	1.18509	0.0461997
$659$	−47.4724	−1.84926	−0.924631	−	0.380864i	$-0.875627\pi$
$659$	−47.4724	−1.84926	−0.924631	+	0.380864i	$0.875627\pi$
$660$	0	0
$661$	−21.6525	−0.842184	−0.421092	−	0.907018i	$-0.638353\pi$
$661$	−21.6525	−0.842184	−0.421092	+	0.907018i	$0.638353\pi$
$662$	−3.89328	−0.151317
$663$	25.8362	1.00339
$664$	−38.6507	−1.49994
$665$	24.0062	0.930921
$666$	4.56494	0.176888
$667$	−1.41089	−0.0546300
$668$	1.28025	0.0495342
$669$	−19.1583	−0.740703
$670$	−14.0945	−0.544518
$671$	0	0
$672$	−15.0424	−0.580275
$673$	−38.3923	−1.47991	−0.739957	−	0.672654i	$-0.765154\pi$
$673$	−38.3923	−1.47991	−0.739957	+	0.672654i	$0.765154\pi$
$674$	−31.8426	−1.22653
$675$	1.00000	0.0384900
$676$	−8.89718	−0.342199
$677$	−22.9333	−0.881398	−0.440699	−	0.897655i	$-0.645269\pi$
$677$	−22.9333	−0.881398	−0.440699	+	0.897655i	$0.645269\pi$
$678$	−8.96302	−0.344223
$679$	−8.62507	−0.331000
$680$	15.3950	0.590373
$681$	15.3759	0.589206
$682$	0	0
$683$	25.9084	0.991359	0.495680	−	0.868505i	$-0.334919\pi$
$683$	25.9084	0.991359	0.495680	+	0.868505i	$0.334919\pi$
$684$	−3.63670	−0.139053
$685$	−10.2555	−0.391841
$686$	−21.8060	−0.832557
$687$	8.90126	0.339604
$688$	20.2909	0.773584
$689$	13.1078	0.499366
$690$	0.255462	0.00972526
$691$	14.8155	0.563608	0.281804	−	0.959472i	$-0.409067\pi$
$691$	14.8155	0.563608	0.281804	+	0.959472i	$0.409067\pi$
$692$	1.28262	0.0487579
$693$	0	0
$694$	18.3927	0.698177
$695$	5.29507	0.200854
$696$	−19.7624	−0.749092
$697$	29.3050	1.11001
$698$	−4.25264	−0.160965
$699$	22.8362	0.863744
$700$	2.78393	0.105223
$701$	5.50632	0.207971	0.103985	−	0.994579i	$-0.466840\pi$
$701$	5.50632	0.207971	0.103985	+	0.994579i	$0.466840\pi$
$702$	6.00509	0.226647
$703$	21.9968	0.829626
$704$	0	0
$705$	0.237878	0.00895899
$706$	−31.9517	−1.20252
$707$	32.5150	1.22285
$708$	5.11112	0.192087
$709$	−17.9007	−0.672274	−0.336137	−	0.941813i	$-0.609120\pi$
$709$	−17.9007	−0.672274	−0.336137	+	0.941813i	$0.609120\pi$
$710$	11.6005	0.435358
$711$	8.00194	0.300096
$712$	7.89905	0.296029
$713$	0.622297	0.0233052
$714$	−24.9097	−0.932222
$715$	0	0
$716$	1.31386	0.0491012
$717$	16.8605	0.629668
$718$	0.556367	0.0207634
$719$	32.5918	1.21547	0.607734	−	0.794141i	$-0.292079\pi$
$719$	32.5918	1.21547	0.607734	+	0.794141i	$0.292079\pi$
$720$	2.27943	0.0849495
$721$	72.3128	2.69307
$722$	14.3638	0.534566
$723$	−11.9607	−0.444825
$724$	−13.0779	−0.486037
$725$	6.41843	0.238375
$726$	0	0
$727$	−43.0199	−1.59552	−0.797759	−	0.602976i	$-0.793982\pi$
$727$	−43.0199	−1.59552	−0.797759	+	0.602976i	$0.793982\pi$
$728$	68.2035	2.52779
$729$	1.00000	0.0370370
$730$	−16.9238	−0.626378
$731$	−44.5087	−1.64621
$732$	3.15490	0.116608
$733$	40.7066	1.50353	0.751766	−	0.659429i	$-0.229202\pi$
$733$	40.7066	1.50353	0.751766	+	0.659429i	$0.229202\pi$
$734$	−29.5862	−1.09204
$735$	−11.3770	−0.419647
$736$	−0.771340	−0.0284320
$737$	0	0
$738$	6.81134	0.250729
$739$	38.1240	1.40241	0.701207	−	0.712958i	$-0.252645\pi$
$739$	38.1240	1.40241	0.701207	+	0.712958i	$0.252645\pi$
$740$	2.55091	0.0937734
$741$	28.9364	1.06300
$742$	−12.6377	−0.463945
$743$	−18.0381	−0.661754	−0.330877	−	0.943674i	$-0.607345\pi$
$743$	−18.0381	−0.661754	−0.330877	+	0.943674i	$0.607345\pi$
$744$	8.71654	0.319564
$745$	−3.78841	−0.138797
$746$	−3.20714	−0.117422
$747$	12.5530	0.459289
$748$	0	0
$749$	−33.2728	−1.21576
$750$	−1.16215	−0.0424356
$751$	−17.5349	−0.639859	−0.319929	−	0.947441i	$-0.603659\pi$
$751$	−17.5349	−0.639859	−0.319929	+	0.947441i	$0.603659\pi$
$752$	0.542227	0.0197730
$753$	16.0034	0.583197
$754$	38.5433	1.40366
$755$	5.92001	0.215451
$756$	2.78393	0.101251
$757$	−25.9609	−0.943565	−0.471782	−	0.881715i	$-0.656389\pi$
$757$	−25.9609	−0.943565	−0.471782	+	0.881715i	$0.656389\pi$
$758$	−25.1646	−0.914019
$759$	0	0
$760$	17.2424	0.625447
$761$	28.0059	1.01521	0.507607	−	0.861589i	$-0.330530\pi$
$761$	28.0059	1.01521	0.507607	+	0.861589i	$0.330530\pi$
$762$	1.77941	0.0644613
$763$	−19.1052	−0.691655
$764$	−8.22493	−0.297567
$765$	−5.00000	−0.180775
$766$	18.8610	0.681477
$767$	−40.6680	−1.46843
$768$	−13.7648	−0.496693
$769$	22.9537	0.827732	0.413866	−	0.910338i	$-0.364178\pi$
$769$	22.9537	0.827732	0.413866	+	0.910338i	$0.364178\pi$
$770$	0	0
$771$	5.47446	0.197158
$772$	9.04772	0.325634
$773$	−23.5282	−0.846251	−0.423126	−	0.906071i	$-0.639067\pi$
$773$	−23.5282	−0.846251	−0.423126	+	0.906071i	$0.639067\pi$
$774$	−10.3451	−0.371848
$775$	−2.83095	−0.101691
$776$	−6.19492	−0.222385
$777$	−16.8388	−0.604089
$778$	−18.9333	−0.678791
$779$	32.8215	1.17595
$780$	3.35567	0.120152
$781$	0	0
$782$	−1.27731	−0.0456765
$783$	6.41843	0.229376
$784$	−25.9331	−0.926184
$785$	7.42909	0.265155
$786$	3.09257	0.110308
$787$	−25.2725	−0.900869	−0.450434	−	0.892810i	$-0.648731\pi$
$787$	−25.2725	−0.900869	−0.450434	+	0.892810i	$0.648731\pi$
$788$	−9.48537	−0.337902
$789$	11.9841	0.426645
$790$	−9.29944	−0.330859
$791$	33.0621	1.17555
$792$	0	0
$793$	−25.1028	−0.891427
$794$	−23.2049	−0.823511
$795$	−2.53671	−0.0899677
$796$	7.71168	0.273333
$797$	8.65645	0.306627	0.153314	−	0.988178i	$-0.451006\pi$
$797$	8.65645	0.306627	0.153314	+	0.988178i	$0.451006\pi$
$798$	−27.8987	−0.987605
$799$	−1.18939	−0.0420775
$800$	3.50898	0.124061
$801$	−2.56545	−0.0906457
$802$	−31.7579	−1.12141
$803$	0	0
$804$	−7.87607	−0.277768
$805$	−0.942328	−0.0332127
$806$	−17.0001	−0.598804
$807$	13.6465	0.480379
$808$	23.3538	0.821584
$809$	−10.2124	−0.359050	−0.179525	−	0.983753i	$-0.557456\pi$
$809$	−10.2124	−0.359050	−0.179525	+	0.983753i	$0.557456\pi$
$810$	−1.16215	−0.0408337
$811$	−47.6224	−1.67225	−0.836124	−	0.548540i	$-0.815184\pi$
$811$	−47.6224	−1.67225	−0.836124	+	0.548540i	$0.815184\pi$
$812$	17.8685	0.627061
$813$	11.8379	0.415172
$814$	0	0
$815$	−5.32086	−0.186381
$816$	−11.3972	−0.398981
$817$	−49.8495	−1.74401
$818$	28.9816	1.01332
$819$	−22.1511	−0.774023
$820$	3.80621	0.132919
$821$	−47.5598	−1.65985	−0.829925	−	0.557875i	$-0.811617\pi$
$821$	−47.5598	−1.65985	−0.829925	+	0.557875i	$0.811617\pi$
$822$	11.9184	0.415700
$823$	−24.7360	−0.862242	−0.431121	−	0.902294i	$-0.641882\pi$
$823$	−24.7360	−0.862242	−0.431121	+	0.902294i	$0.641882\pi$
$824$	51.9384	1.80936
$825$	0	0
$826$	39.2096	1.36428
$827$	−1.56166	−0.0543043	−0.0271522	−	0.999631i	$-0.508644\pi$
$827$	−1.56166	−0.0543043	−0.0271522	+	0.999631i	$0.508644\pi$
$828$	0.142753	0.00496102
$829$	42.1950	1.46549	0.732747	−	0.680501i	$-0.238238\pi$
$829$	42.1950	1.46549	0.732747	+	0.680501i	$0.238238\pi$
$830$	−14.5884	−0.506370
$831$	10.2638	0.356048
$832$	44.6285	1.54721
$833$	56.8851	1.97095
$834$	−6.15366	−0.213084
$835$	1.97139	0.0682227
$836$	0	0
$837$	−2.83095	−0.0978521
$838$	19.5539	0.675477
$839$	−6.29451	−0.217311	−0.108655	−	0.994079i	$-0.534654\pi$
$839$	−6.29451	−0.217311	−0.108655	+	0.994079i	$0.534654\pi$
$840$	−13.1992	−0.455416
$841$	12.1963	0.420562
$842$	27.4274	0.945211
$843$	−2.93889	−0.101221
$844$	14.5156	0.499647
$845$	−13.7003	−0.471305
$846$	−0.276449	−0.00950451
$847$	0	0
$848$	−5.78225	−0.198563
$849$	21.8279	0.749133
$850$	5.81074	0.199307
$851$	−0.863453	−0.0295988
$852$	6.48241	0.222084
$853$	−7.27120	−0.248961	−0.124481	−	0.992222i	$-0.539726\pi$
$853$	−7.27120	−0.248961	−0.124481	+	0.992222i	$0.539726\pi$
$854$	24.2026	0.828197
$855$	−5.59998	−0.191515
$856$	−23.8981	−0.816819
$857$	39.8590	1.36156	0.680779	−	0.732489i	$-0.261641\pi$
$857$	39.8590	1.36156	0.680779	+	0.732489i	$0.261641\pi$
$858$	0	0
$859$	13.5278	0.461564	0.230782	−	0.973006i	$-0.425872\pi$
$859$	13.5278	0.461564	0.230782	+	0.973006i	$0.425872\pi$
$860$	−5.78091	−0.197127
$861$	−25.1252	−0.856264
$862$	−43.7613	−1.49052
$863$	50.3117	1.71263	0.856316	−	0.516453i	$-0.172748\pi$
$863$	50.3117	1.71263	0.856316	+	0.516453i	$0.172748\pi$
$864$	3.50898	0.119378
$865$	1.97504	0.0671535
$866$	−35.9977	−1.22325
$867$	8.00000	0.271694
$868$	−7.88119	−0.267505
$869$	0	0
$870$	−7.45917	−0.252889
$871$	62.6681	2.12343
$872$	−13.7223	−0.464694
$873$	2.01199	0.0680954
$874$	−1.43058	−0.0483901
$875$	4.28684	0.144922
$876$	−9.45710	−0.319526
$877$	−1.20736	−0.0407696	−0.0203848	−	0.999792i	$-0.506489\pi$
$877$	−1.20736	−0.0407696	−0.0203848	+	0.999792i	$0.506489\pi$
$878$	−32.7877	−1.10653
$879$	−24.7665	−0.835354
$880$	0	0
$881$	1.91816	0.0646245	0.0323123	−	0.999478i	$-0.489713\pi$
$881$	1.91816	0.0646245	0.0323123	+	0.999478i	$0.489713\pi$
$882$	13.2218	0.445200
$883$	58.0890	1.95485	0.977425	−	0.211281i	$-0.0677634\pi$
$883$	58.0890	1.95485	0.977425	+	0.211281i	$0.0677634\pi$
$884$	−16.7784	−0.564318
$885$	7.87035	0.264559
$886$	17.0162	0.571669
$887$	30.2427	1.01545	0.507725	−	0.861519i	$-0.330487\pi$
$887$	30.2427	1.01545	0.507725	+	0.861519i	$0.330487\pi$
$888$	−12.0944	−0.405862
$889$	−6.56377	−0.220142
$890$	2.98143	0.0999378
$891$	0	0
$892$	12.4417	0.416578
$893$	−1.33211	−0.0445773
$894$	4.40269	0.147248
$895$	2.02315	0.0676263
$896$	−12.9432	−0.432403
$897$	−1.13586	−0.0379251
$898$	13.9431	0.465286
$899$	−18.1703	−0.606013
$900$	−0.649414	−0.0216471
$901$	12.6835	0.422550
$902$	0	0
$903$	38.1603	1.26990
$904$	23.7468	0.789805
$905$	−20.1380	−0.669410
$906$	−6.87992	−0.228570
$907$	−31.9669	−1.06144	−0.530721	−	0.847547i	$-0.678079\pi$
$907$	−31.9669	−1.06144	−0.530721	+	0.847547i	$0.678079\pi$
$908$	−9.98532	−0.331374
$909$	−7.58484	−0.251573
$910$	25.7429	0.853368
$911$	−51.8454	−1.71771	−0.858857	−	0.512216i	$-0.828825\pi$
$911$	−51.8454	−1.71771	−0.858857	+	0.512216i	$0.828825\pi$
$912$	−12.7648	−0.422684
$913$	0	0
$914$	11.6722	0.386083
$915$	4.85807	0.160603
$916$	−5.78060	−0.190996
$917$	−11.4076	−0.376714
$918$	5.81074	0.191783
$919$	−34.2084	−1.12843	−0.564215	−	0.825628i	$-0.690821\pi$
$919$	−34.2084	−1.12843	−0.564215	+	0.825628i	$0.690821\pi$
$920$	−0.676824	−0.0223142
$921$	−4.94023	−0.162786
$922$	−15.6298	−0.514741
$923$	−51.5790	−1.69774
$924$	0	0
$925$	3.92802	0.129153
$926$	21.8293	0.717354
$927$	−16.8685	−0.554036
$928$	22.5222	0.739326
$929$	18.3482	0.601984	0.300992	−	0.953627i	$-0.402682\pi$
$929$	18.3482	0.601984	0.300992	+	0.953627i	$0.402682\pi$
$930$	3.28999	0.107883
$931$	63.7110	2.08804
$932$	−14.8301	−0.485777
$933$	−13.8096	−0.452106
$934$	30.8561	1.00964
$935$	0	0
$936$	−15.9100	−0.520033
$937$	3.38415	0.110555	0.0552777	−	0.998471i	$-0.482396\pi$
$937$	3.38415	0.110555	0.0552777	+	0.998471i	$0.482396\pi$
$938$	−60.4208	−1.97281
$939$	−4.06934	−0.132798
$940$	−0.154481	−0.00503862
$941$	−35.1002	−1.14423	−0.572116	−	0.820172i	$-0.693877\pi$
$941$	−35.1002	−1.14423	−0.572116	+	0.820172i	$0.693877\pi$
$942$	−8.63369	−0.281301
$943$	−1.28836	−0.0419547
$944$	17.9399	0.583895
$945$	4.28684	0.139451
$946$	0	0
$947$	−39.0512	−1.26899	−0.634497	−	0.772925i	$-0.718793\pi$
$947$	−39.0512	−1.26899	−0.634497	+	0.772925i	$0.718793\pi$
$948$	−5.19657	−0.168777
$949$	75.2480	2.44265
$950$	6.50800	0.211147
$951$	25.8199	0.837269
$952$	65.9961	2.13895
$953$	24.6783	0.799409	0.399705	−	0.916644i	$-0.369113\pi$
$953$	24.6783	0.799409	0.399705	+	0.916644i	$0.369113\pi$
$954$	2.94803	0.0954458
$955$	−12.6652	−0.409835
$956$	−10.9495	−0.354131
$957$	0	0
$958$	12.5315	0.404873
$959$	−43.9635	−1.41966
$960$	−8.63682	−0.278752
$961$	−22.9857	−0.741474
$962$	23.5881	0.760512
$963$	7.76161	0.250114
$964$	7.76747	0.250173
$965$	13.9321	0.448491
$966$	1.09512	0.0352350
$967$	1.20724	0.0388222	0.0194111	−	0.999812i	$-0.493821\pi$
$967$	1.20724	0.0388222	0.0194111	+	0.999812i	$0.493821\pi$
$968$	0	0
$969$	27.9999	0.899486
$970$	−2.33822	−0.0750758
$971$	50.3821	1.61684	0.808418	−	0.588608i	$-0.200324\pi$
$971$	50.3821	1.61684	0.808418	+	0.588608i	$0.200324\pi$
$972$	−0.649414	−0.0208300
$973$	22.6991	0.727701
$974$	7.91533	0.253624
$975$	5.16724	0.165484
$976$	11.0737	0.354459
$977$	−5.88330	−0.188223	−0.0941117	−	0.995562i	$-0.530001\pi$
$977$	−5.88330	−0.188223	−0.0941117	+	0.995562i	$0.530001\pi$
$978$	6.18362	0.197730
$979$	0	0
$980$	7.38839	0.236013
$981$	4.45671	0.142292
$982$	30.3267	0.967763
$983$	36.4899	1.16385	0.581924	−	0.813243i	$-0.302300\pi$
$983$	36.4899	1.16385	0.581924	+	0.813243i	$0.302300\pi$
$984$	−18.0461	−0.575288
$985$	−14.6060	−0.465387
$986$	37.2958	1.18774
$987$	1.01974	0.0324588
$988$	−18.7917	−0.597843
$989$	1.95677	0.0622216
$990$	0	0
$991$	−36.8404	−1.17027	−0.585137	−	0.810934i	$-0.698959\pi$
$991$	−36.8404	−1.17027	−0.585137	+	0.810934i	$0.698959\pi$
$992$	−9.93376	−0.315397
$993$	−3.35008	−0.106311
$994$	49.7294	1.57732
$995$	11.8748	0.376457
$996$	−8.15206	−0.258308
$997$	34.8694	1.10432	0.552162	−	0.833737i	$-0.313803\pi$
$997$	34.8694	1.10432	0.552162	+	0.833737i	$0.313803\pi$
$998$	22.5263	0.713059
$999$	3.92802	0.124277

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1815.2.a.x.1.2		4
3.2	odd	2		5445.2.a.be.1.3		4
5.4	even	2		9075.2.a.cl.1.3		4
11.3	even	5		165.2.m.a.31.1	yes	8
11.4	even	5		165.2.m.a.16.1	✓	8
11.10	odd	2		1815.2.a.o.1.3		4
33.14	odd	10		495.2.n.d.361.2		8
33.26	odd	10		495.2.n.d.181.2		8
33.32	even	2		5445.2.a.bv.1.2		4
55.3	odd	20		825.2.bx.h.724.2		16
55.4	even	10		825.2.n.k.676.2		8
55.14	even	10		825.2.n.k.526.2		8
55.37	odd	20		825.2.bx.h.49.2		16
55.47	odd	20		825.2.bx.h.724.3		16
55.48	odd	20		825.2.bx.h.49.3		16
55.54	odd	2		9075.2.a.dj.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.m.a.16.1	✓	8	11.4	even	5
165.2.m.a.31.1	yes	8	11.3	even	5
495.2.n.d.181.2		8	33.26	odd	10
495.2.n.d.361.2		8	33.14	odd	10
825.2.n.k.526.2		8	55.14	even	10
825.2.n.k.676.2		8	55.4	even	10
825.2.bx.h.49.2		16	55.37	odd	20
825.2.bx.h.49.3		16	55.48	odd	20
825.2.bx.h.724.2		16	55.3	odd	20
825.2.bx.h.724.3		16	55.47	odd	20
1815.2.a.o.1.3		4	11.10	odd	2
1815.2.a.x.1.2		4	1.1	even	1	trivial
5445.2.a.be.1.3		4	3.2	odd	2
5445.2.a.bv.1.2		4	33.32	even	2
9075.2.a.cl.1.3		4	5.4	even	2
9075.2.a.dj.1.2		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)

\(f(q)\)	\(=\)	\(q+1.16215 q^{2} +1.00000 q^{3} -0.649414 q^{4} -1.00000 q^{5} +1.16215 q^{6} -4.28684 q^{7} -3.07901 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.16215 q^{2} +1.00000 q^{3} -0.649414 q^{4} -1.00000 q^{5} +1.16215 q^{6} -4.28684 q^{7} -3.07901 q^{8} +1.00000 q^{9} -1.16215 q^{10} -0.649414 q^{12} +5.16724 q^{13} -4.98194 q^{14} -1.00000 q^{15} -2.27943 q^{16} +5.00000 q^{17} +1.16215 q^{18} +5.59998 q^{19} +0.649414 q^{20} -4.28684 q^{21} -0.219819 q^{23} -3.07901 q^{24} +1.00000 q^{25} +6.00509 q^{26} +1.00000 q^{27} +2.78393 q^{28} +6.41843 q^{29} -1.16215 q^{30} -2.83095 q^{31} +3.50898 q^{32} +5.81074 q^{34} +4.28684 q^{35} -0.649414 q^{36} +3.92802 q^{37} +6.50800 q^{38} +5.16724 q^{39} +3.07901 q^{40} +5.86100 q^{41} -4.98194 q^{42} -8.90173 q^{43} -1.00000 q^{45} -0.255462 q^{46} -0.237878 q^{47} -2.27943 q^{48} +11.3770 q^{49} +1.16215 q^{50} +5.00000 q^{51} -3.35567 q^{52} +2.53671 q^{53} +1.16215 q^{54} +13.1992 q^{56} +5.59998 q^{57} +7.45917 q^{58} -7.87035 q^{59} +0.649414 q^{60} -4.85807 q^{61} -3.28999 q^{62} -4.28684 q^{63} +8.63682 q^{64} -5.16724 q^{65} +12.1280 q^{67} -3.24707 q^{68} -0.219819 q^{69} +4.98194 q^{70} -9.98194 q^{71} -3.07901 q^{72} +14.5625 q^{73} +4.56494 q^{74} +1.00000 q^{75} -3.63670 q^{76} +6.00509 q^{78} +8.00194 q^{79} +2.27943 q^{80} +1.00000 q^{81} +6.81134 q^{82} +12.5530 q^{83} +2.78393 q^{84} -5.00000 q^{85} -10.3451 q^{86} +6.41843 q^{87} -2.56545 q^{89} -1.16215 q^{90} -22.1511 q^{91} +0.142753 q^{92} -2.83095 q^{93} -0.276449 q^{94} -5.59998 q^{95} +3.50898 q^{96} +2.01199 q^{97} +13.2218 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 5 q^{2} + 4 q^{3} + 9 q^{4} - 4 q^{5} + 5 q^{6} - 2 q^{7} + 15 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + 5 * q^2 + 4 * q^3 + 9 * q^4 - 4 * q^5 + 5 * q^6 - 2 * q^7 + 15 * q^8 + 4 * q^9	\( 4 q + 5 q^{2} + 4 q^{3} + 9 q^{4} - 4 q^{5} + 5 q^{6} - 2 q^{7} + 15 q^{8} + 4 q^{9} - 5 q^{10} + 9 q^{12} + 3 q^{13} - 5 q^{14} - 4 q^{15} + 15 q^{16} + 20 q^{17} + 5 q^{18} + 3 q^{19} - 9 q^{20} - 2 q^{21} - 5 q^{23} + 15 q^{24} + 4 q^{25} + 6 q^{26} + 4 q^{27} + 3 q^{28} + 5 q^{29} - 5 q^{30} - q^{31} + 30 q^{32} + 25 q^{34} + 2 q^{35} + 9 q^{36} - 7 q^{37} + q^{38} + 3 q^{39} - 15 q^{40} + 20 q^{41} - 5 q^{42} - 2 q^{43} - 4 q^{45} + 7 q^{46} - 20 q^{47} + 15 q^{48} + 8 q^{49} + 5 q^{50} + 20 q^{51} - 7 q^{52} + 6 q^{53} + 5 q^{54} + 10 q^{56} + 3 q^{57} - 21 q^{58} - 5 q^{59} - 9 q^{60} - 7 q^{61} - 12 q^{62} - 2 q^{63} + 49 q^{64} - 3 q^{65} - 13 q^{67} + 45 q^{68} - 5 q^{69} + 5 q^{70} - 25 q^{71} + 15 q^{72} + 23 q^{73} - 7 q^{74} + 4 q^{75} - 7 q^{76} + 6 q^{78} - 15 q^{80} + 4 q^{81} + 11 q^{82} + 33 q^{83} + 3 q^{84} - 20 q^{85} - 12 q^{86} + 5 q^{87} + 16 q^{89} - 5 q^{90} - 24 q^{91} - q^{93} - 17 q^{94} - 3 q^{95} + 30 q^{96} + 25 q^{98}+O(q^{100}) \) 4 * q + 5 * q^2 + 4 * q^3 + 9 * q^4 - 4 * q^5 + 5 * q^6 - 2 * q^7 + 15 * q^8 + 4 * q^9 - 5 * q^10 + 9 * q^12 + 3 * q^13 - 5 * q^14 - 4 * q^15 + 15 * q^16 + 20 * q^17 + 5 * q^18 + 3 * q^19 - 9 * q^20 - 2 * q^21 - 5 * q^23 + 15 * q^24 + 4 * q^25 + 6 * q^26 + 4 * q^27 + 3 * q^28 + 5 * q^29 - 5 * q^30 - q^31 + 30 * q^32 + 25 * q^34 + 2 * q^35 + 9 * q^36 - 7 * q^37 + q^38 + 3 * q^39 - 15 * q^40 + 20 * q^41 - 5 * q^42 - 2 * q^43 - 4 * q^45 + 7 * q^46 - 20 * q^47 + 15 * q^48 + 8 * q^49 + 5 * q^50 + 20 * q^51 - 7 * q^52 + 6 * q^53 + 5 * q^54 + 10 * q^56 + 3 * q^57 - 21 * q^58 - 5 * q^59 - 9 * q^60 - 7 * q^61 - 12 * q^62 - 2 * q^63 + 49 * q^64 - 3 * q^65 - 13 * q^67 + 45 * q^68 - 5 * q^69 + 5 * q^70 - 25 * q^71 + 15 * q^72 + 23 * q^73 - 7 * q^74 + 4 * q^75 - 7 * q^76 + 6 * q^78 - 15 * q^80 + 4 * q^81 + 11 * q^82 + 33 * q^83 + 3 * q^84 - 20 * q^85 - 12 * q^86 + 5 * q^87 + 16 * q^89 - 5 * q^90 - 24 * q^91 - q^93 - 17 * q^94 - 3 * q^95 + 30 * q^96 + 25 * q^98

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