LMFDB - Embedded newform 387.2.bc.a.233.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [387,2,Mod(26,387)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(387, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([21, 17]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("387.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 387 = 3^{2} \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	387.bc (of order $42$, degree $12$, minimal)

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:	no
Analytic conductor:	$3.09021055822$
Analytic rank:	$0$
Dimension:	$168$
Relative dimension:	$14$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			233.6
Character	$\chi$	$=$	387.233
Dual form			387.2.bc.a.98.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.761035 - 0.366495i) q^{2} +(-0.802124 - 1.00583i) q^{4} +(1.87440 - 1.73919i) q^{5} +(3.43303 + 1.98206i) q^{7} +(0.617732 + 2.70646i) q^{8} +O(q^{10})$	\(q+(-0.761035 - 0.366495i) q^{2} +(-0.802124 - 1.00583i) q^{4} +(1.87440 - 1.73919i) q^{5} +(3.43303 + 1.98206i) q^{7} +(0.617732 + 2.70646i) q^{8} +(-2.06389 + 0.636626i) q^{10} +(-2.73143 - 2.17824i) q^{11} +(4.94040 + 1.52391i) q^{13} +(-1.88624 - 2.76661i) q^{14} +(-0.0507596 + 0.222393i) q^{16} +(1.07126 - 1.15454i) q^{17} +(-1.13205 - 0.444295i) q^{19} +(-3.25283 - 0.490286i) q^{20} +(1.28040 + 2.65878i) q^{22} +(0.829132 - 5.50093i) q^{23} +(0.114947 - 1.53387i) q^{25} +(-3.20131 - 2.97038i) q^{26} +(-0.760095 - 5.04290i) q^{28} +(-2.39492 + 1.63283i) q^{29} +(-0.484250 - 6.46186i) q^{31} +(3.58183 - 4.49147i) q^{32} +(-1.23840 + 0.486036i) q^{34} +(9.88205 - 2.25551i) q^{35} +(2.81825 - 1.62712i) q^{37} +(0.698694 + 0.753013i) q^{38} +(5.86493 + 3.99864i) q^{40} +(-3.35111 + 6.95865i) q^{41} +(-0.707326 - 6.51918i) q^{43} +4.49458i q^{44} +(-2.64706 + 3.88253i) q^{46} +(5.52286 - 4.40433i) q^{47} +(4.35712 + 7.54675i) q^{49} +(-0.649634 + 1.12520i) q^{50} +(-2.43001 - 6.19158i) q^{52} +(2.63759 + 8.55086i) q^{53} +(-8.90818 + 0.667576i) q^{55} +(-3.24368 + 10.5157i) q^{56} +(2.42104 - 0.364914i) q^{58} +(3.33064 + 0.760198i) q^{59} +(-11.4848 - 0.860664i) q^{61} +(-1.99971 + 5.09518i) q^{62} +(-3.96096 + 1.90750i) q^{64} +(11.9107 - 5.73588i) q^{65} +(-5.34188 + 13.6109i) q^{67} +(-2.02056 - 0.151420i) q^{68} +(-8.34722 - 1.90520i) q^{70} +(-10.0748 + 1.51853i) q^{71} +(-0.861270 + 2.79217i) q^{73} +(-2.74112 + 0.205419i) q^{74} +(0.461154 + 1.49503i) q^{76} +(-5.05967 - 12.8918i) q^{77} +(6.64919 - 11.5167i) q^{79} +(0.291639 + 0.505134i) q^{80} +(5.10063 - 4.06761i) q^{82} +(-2.08343 + 3.05583i) q^{83} -4.02720i q^{85} +(-1.85095 + 5.22056i) q^{86} +(4.20804 - 8.73809i) q^{88} +(-1.44507 - 0.985233i) q^{89} +(13.9400 + 15.0238i) q^{91} +(-6.19807 + 3.57846i) q^{92} +(-5.81726 + 1.32775i) q^{94} +(-2.89462 + 1.13606i) q^{95} +(-12.1832 + 15.2773i) q^{97} +(-0.550072 - 7.34020i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q - 24 q^{4} - 6 q^{7}+O(q^{10}) $ 168 * q - 24 * q^4 - 6 * q^7	$ 168 q - 24 q^{4} - 6 q^{7} + 8 q^{10} + 26 q^{13} - 8 q^{16} + 24 q^{19} + 14 q^{25} + 32 q^{31} - 48 q^{34} - 78 q^{37} - 244 q^{40} - 32 q^{43} - 92 q^{46} + 54 q^{49} + 76 q^{52} - 96 q^{55} - 20 q^{58} - 96 q^{64} - 18 q^{67} + 140 q^{70} + 10 q^{73} - 16 q^{76} - 168 q^{88} - 38 q^{91} - 112 q^{94} - 40 q^{97}+O(q^{100}) $ 168 * q - 24 * q^4 - 6 * q^7 + 8 * q^10 + 26 * q^13 - 8 * q^16 + 24 * q^19 + 14 * q^25 + 32 * q^31 - 48 * q^34 - 78 * q^37 - 244 * q^40 - 32 * q^43 - 92 * q^46 + 54 * q^49 + 76 * q^52 - 96 * q^55 - 20 * q^58 - 96 * q^64 - 18 * q^67 + 140 * q^70 + 10 * q^73 - 16 * q^76 - 168 * q^88 - 38 * q^91 - 112 * q^94 - 40 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/387\mathbb{Z}\right)^\times$.

$n$	$46$	$173$
$\chi(n)$	$e\left(\frac{29}{42}\right)$	$-1$

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 $

$2$	−0.761035	−	0.366495i	−0.538133	−	0.259151i	0.145017	−	0.989429i	$-0.453676\pi$
$2$	−0.761035	−	0.366495i	−0.538133	−	0.259151i	−0.683150	+	0.730278i	$0.739391\pi$
$3$		0			0
$3$		0			0
$4$	−0.802124	−	1.00583i	−0.401062	−	0.502916i
$5$	1.87440	−	1.73919i	0.838258	−	0.777790i	−0.138899	−	0.990306i	$-0.544356\pi$
$5$	1.87440	−	1.73919i	0.838258	−	0.777790i	0.977157	+	0.212517i	$0.0681660\pi$
$6$		0			0
$7$	3.43303	+	1.98206i	1.29756	+	0.749148i	0.979982	−	0.199084i	$-0.0637966\pi$
$7$	3.43303	+	1.98206i	1.29756	+	0.749148i	0.317580	+	0.948232i	$0.397130\pi$
$8$	0.617732	+	2.70646i	0.218401	+	0.956879i
$9$		0			0
$10$	−2.06389	+	0.636626i	−0.652660	+	0.201319i
$11$	−2.73143	−	2.17824i	−0.823557	−	0.656765i	0.118225	−	0.992987i	$-0.462279\pi$
$11$	−2.73143	−	2.17824i	−0.823557	−	0.656765i	−0.941783	+	0.336222i	$0.890851\pi$
$12$		0			0
$13$	4.94040	+	1.52391i	1.37022	+	0.422657i	0.890587	−	0.454812i	$-0.150294\pi$
$13$	4.94040	+	1.52391i	1.37022	+	0.422657i	0.479633	+	0.877469i	$0.340770\pi$
$14$	−1.88624	−	2.76661i	−0.504119	−	0.739406i
$15$		0			0
$16$	−0.0507596	+	0.222393i	−0.0126899	+	0.0555981i
$17$	1.07126	−	1.15454i	0.259818	−	0.280018i	−0.589648	−	0.807660i	$-0.700734\pi$
$17$	1.07126	−	1.15454i	0.259818	−	0.280018i	0.849466	+	0.527643i	$0.176924\pi$
$18$		0			0
$19$	−1.13205	−	0.444295i	−0.259709	−	0.101928i	0.231914	−	0.972736i	$-0.425501\pi$
$19$	−1.13205	−	0.444295i	−0.259709	−	0.101928i	−0.491623	+	0.870808i	$0.663596\pi$
$20$	−3.25283	−	0.490286i	−0.727356	−	0.109631i
$21$		0			0
$22$	1.28040	+	2.65878i	0.272982	+	0.566853i
$23$	0.829132	−	5.50093i	0.172886	−	1.14702i	−0.719082	−	0.694925i	$-0.755438\pi$
$23$	0.829132	−	5.50093i	0.172886	−	1.14702i	0.891968	−	0.452098i	$-0.149324\pi$
$24$		0			0
$25$	0.114947	−	1.53387i	0.0229895	−	0.306773i
$26$	−3.20131	−	2.97038i	−0.627829	−	0.582540i
$27$		0			0
$28$	−0.760095	−	5.04290i	−0.143644	−	0.953019i
$29$	−2.39492	+	1.63283i	−0.444726	+	0.303209i	−0.764899	−	0.644150i	$-0.777211\pi$
$29$	−2.39492	+	1.63283i	−0.444726	+	0.303209i	0.320173	+	0.947359i	$0.396259\pi$
$30$		0			0
$31$	−0.484250	−	6.46186i	−0.0869738	−	1.16059i	−0.854459	−	0.519519i	$-0.826111\pi$
$31$	−0.484250	−	6.46186i	−0.0869738	−	1.16059i	0.767485	−	0.641067i	$-0.221508\pi$
$32$	3.58183	−	4.49147i	0.633184	−	0.793988i
$33$		0			0
$34$	−1.23840	+	0.486036i	−0.212384	+	0.0833545i
$35$	9.88205	−	2.25551i	1.67037	−	0.381251i
$36$		0			0
$37$	2.81825	−	1.62712i	0.463318	−	0.267497i	−0.250120	−	0.968215i	$-0.580470\pi$
$37$	2.81825	−	1.62712i	0.463318	−	0.267497i	0.713438	+	0.700718i	$0.247137\pi$
$38$	0.698694	+	0.753013i	0.113343	+	0.122155i
$39$		0			0
$40$	5.86493	+	3.99864i	0.927327	+	0.632241i
$41$	−3.35111	+	6.95865i	−0.523356	+	1.08676i	0.456990	+	0.889472i	$0.348927\pi$
$41$	−3.35111	+	6.95865i	−0.523356	+	1.08676i	−0.980346	+	0.197287i	$0.936787\pi$
$42$		0			0
$43$	−0.707326	−	6.51918i	−0.107866	−	0.994165i
$43$	−0.707326	−	6.51918i	−0.107866	−	0.994165i
$44$			4.49458i			0.677583i
$45$		0			0
$46$	−2.64706	+	3.88253i	−0.390288	+	0.572448i
$47$	5.52286	−	4.40433i	0.805591	−	0.642438i	−0.131581	−	0.991305i	$-0.542005\pi$
$47$	5.52286	−	4.40433i	0.805591	−	0.642438i	0.937172	+	0.348868i	$0.113434\pi$
$48$		0			0
$49$	4.35712	+	7.54675i	0.622445	+	1.07811i
$50$	−0.649634	+	1.12520i	−0.0918721	+	0.159127i
$51$		0			0
$52$	−2.43001	−	6.19158i	−0.336982	−	0.858617i
$53$	2.63759	+	8.55086i	0.362301	+	1.17455i	0.934959	+	0.354756i	$0.115436\pi$
$53$	2.63759	+	8.55086i	0.362301	+	1.17455i	−0.572658	+	0.819794i	$0.694088\pi$
$54$		0			0
$55$	−8.90818	+	0.667576i	−1.20118	+	0.0900159i
$56$	−3.24368	+	10.5157i	−0.433454	+	1.40522i
$57$		0			0
$58$	2.42104	−	0.364914i	0.317899	−	0.0479155i
$59$	3.33064	+	0.760198i	0.433613	+	0.0989693i	0.433755	−	0.901031i	$-0.357188\pi$
$59$	3.33064	+	0.760198i	0.433613	+	0.0989693i	−0.000142440		1.00000i	$0.500045\pi$
$60$		0			0
$61$	−11.4848	−	0.860664i	−1.47047	−	0.110197i	−0.684752	−	0.728776i	$-0.740089\pi$
$61$	−11.4848	−	0.860664i	−1.47047	−	0.110197i	−0.785722	+	0.618580i	$0.787708\pi$
$62$	−1.99971	+	5.09518i	−0.253964	+	0.647089i
$63$		0			0
$64$	−3.96096	+	1.90750i	−0.495120	+	0.238437i
$65$	11.9107	−	5.73588i	1.47734	−	0.711448i
$66$		0			0
$67$	−5.34188	+	13.6109i	−0.652615	+	1.66283i	0.0923466	+	0.995727i	$0.470563\pi$
$67$	−5.34188	+	13.6109i	−0.652615	+	1.66283i	−0.744961	+	0.667108i	$0.767532\pi$
$68$	−2.02056	−	0.151420i	−0.245028	−	0.0183623i
$69$		0			0
$70$	−8.34722	−	1.90520i	−0.997684	−	0.227715i
$71$	−10.0748	+	1.51853i	−1.19566	+	0.180217i	−0.716548	−	0.697538i	$-0.754279\pi$
$71$	−10.0748	+	1.51853i	−1.19566	+	0.180217i	−0.479111	+	0.877754i	$0.659041\pi$
$72$		0			0
$73$	−0.861270	+	2.79217i	−0.100804	+	0.326799i	−0.991901	−	0.127015i	$-0.959461\pi$
$73$	−0.861270	+	2.79217i	−0.100804	+	0.326799i	0.891097	+	0.453813i	$0.149937\pi$
$74$	−2.74112	+	0.205419i	−0.318649	+	0.0238794i
$75$		0			0
$76$	0.461154	+	1.49503i	0.0528980	+	0.171491i
$77$	−5.05967	−	12.8918i	−0.576603	−	1.46916i
$78$		0			0
$79$	6.64919	−	11.5167i	0.748092	−	1.29573i	−0.200644	−	0.979664i	$-0.564303\pi$
$79$	6.64919	−	11.5167i	0.748092	−	1.29573i	0.948736	−	0.316070i	$-0.102363\pi$
$80$	0.291639	+	0.505134i	0.0326062	+	0.0564757i
$81$		0			0
$82$	5.10063	−	4.06761i	0.563270	−	0.449193i
$83$	−2.08343	+	3.05583i	−0.228686	+	0.335421i	−0.923382	−	0.383883i	$-0.874587\pi$
$83$	−2.08343	+	3.05583i	−0.228686	+	0.335421i	0.694696	+	0.719304i	$0.255539\pi$
$84$		0			0
$85$		−	4.02720i		−	0.436811i
$86$	−1.85095	+	5.22056i	−0.199593	+	0.562947i
$87$		0			0
$88$	4.20804	−	8.73809i	0.448579	−	0.931483i
$89$	−1.44507	−	0.985233i	−0.153177	−	0.104434i	0.484306	−	0.874899i	$-0.339072\pi$
$89$	−1.44507	−	0.985233i	−0.153177	−	0.104434i	−0.637483	+	0.770464i	$0.720025\pi$
$90$		0			0
$91$	13.9400	+	15.0238i	1.46131	+	1.57492i
$92$	−6.19807	+	3.57846i	−0.646194	+	0.373080i
$93$		0			0
$94$	−5.81726	+	1.32775i	−0.600004	+	0.136947i
$95$	−2.89462	+	1.13606i	−0.296982	+	0.116557i
$96$		0			0
$97$	−12.1832	+	15.2773i	−1.23702	+	1.55117i	−0.519887	+	0.854235i	$0.674026\pi$
$97$	−12.1832	+	15.2773i	−1.23702	+	1.55117i	−0.717132	+	0.696938i	$0.754545\pi$
$98$	−0.550072	−	7.34020i	−0.0555657	−	0.741472i
$99$		0			0
$100$	−1.63501	+	1.11473i	−0.163501	+	0.111473i
$101$	−0.381632	−	2.53196i	−0.0379738	−	0.251940i	0.961787	−	0.273798i	$-0.0882799\pi$
$101$	−0.381632	−	2.53196i	−0.0379738	−	0.251940i	−0.999761	+	0.0218580i	$0.993042\pi$
$102$		0			0
$103$	−0.211865	−	0.196582i	−0.0208757	−	0.0193698i	0.669666	−	0.742662i	$-0.266437\pi$
$103$	−0.211865	−	0.196582i	−0.0208757	−	0.0193698i	−0.690542	+	0.723293i	$0.742628\pi$
$104$	−1.07256	+	14.3124i	−0.105174	+	1.40344i
$105$		0			0
$106$	1.12655	−	7.47417i	0.109420	−	0.725955i
$107$	6.63145	+	13.7703i	0.641086	+	1.33123i	0.927751	+	0.373199i	$0.121739\pi$
$107$	6.63145	+	13.7703i	0.641086	+	1.33123i	−0.286665	+	0.958031i	$0.592547\pi$
$108$		0			0
$109$	14.9495	+	2.25327i	1.43190	+	0.215825i	0.818755	−	0.574144i	$-0.194665\pi$
$109$	14.9495	+	2.25327i	1.43190	+	0.215825i	0.613148	+	0.789968i	$0.289903\pi$
$110$	7.02410	+	2.75676i	0.669722	+	0.262847i
$111$		0			0
$112$	−0.615054	+	0.662871i	−0.0581172	+	0.0626354i
$113$	−4.29981	+	18.8387i	−0.404492	+	1.77220i	0.204342	+	0.978900i	$0.434495\pi$
$113$	−4.29981	+	18.8387i	−0.404492	+	1.77220i	−0.608834	+	0.793297i	$0.708363\pi$
$114$		0			0
$115$	−8.01304	−	11.7530i	−0.747220	−	1.09597i
$116$	3.56337	+	1.09916i	0.330851	+	0.102054i
$117$		0			0
$118$	−2.25613	−	1.79920i	−0.207694	−	0.165630i
$119$	5.96603	−	1.84028i	0.546905	−	0.168698i
$120$		0			0
$121$	0.268240	+	1.17524i	0.0243854	+	0.106840i
$122$	8.42489	+	4.86411i	0.762753	+	0.440376i
$123$		0			0
$124$	−6.11112	+	5.67029i	−0.548795	+	0.509207i
$125$	5.51904	+	6.92066i	0.493638	+	0.619002i
$126$		0			0
$127$	5.63321	+	2.71281i	0.499867	+	0.240723i	0.666789	−	0.745247i	$-0.267668\pi$
$127$	5.63321	+	2.71281i	0.499867	+	0.240723i	−0.166922	+	0.985970i	$0.553383\pi$
$128$	−7.77610			−0.687317
$129$		0			0
$130$	−11.1666			−0.979377
$131$	1.98573	+	0.956280i	0.173494	+	0.0835505i	0.518615	−	0.855008i	$-0.326448\pi$
$131$	1.98573	+	0.956280i	0.173494	+	0.0835505i	−0.345121	+	0.938558i	$0.612162\pi$
$132$		0			0
$133$	−3.00572	−	3.76906i	−0.260629	−	0.326819i
$134$	9.05369	−	8.40059i	0.782119	−	0.725701i
$135$		0			0
$136$	3.78648	+	2.18612i	0.324688	+	0.187459i
$137$	−2.60090	−	11.3953i	−0.222210	−	0.973567i	−0.955810	−	0.293985i	$-0.905018\pi$
$137$	−2.60090	−	11.3953i	−0.222210	−	0.973567i	0.733600	−	0.679582i	$-0.237839\pi$
$138$		0			0
$139$	4.50790	−	1.39050i	0.382355	−	0.117941i	−0.0976184	−	0.995224i	$-0.531122\pi$
$139$	4.50790	−	1.39050i	0.382355	−	0.117941i	0.479974	+	0.877283i	$0.340646\pi$
$140$	−10.1953	−	8.13047i	−0.861660	−	0.687151i
$141$		0			0
$142$	8.22382	+	2.53671i	0.690127	+	0.212876i
$143$	−10.1749	−	14.9239i	−0.850869	−	1.24800i
$144$		0			0
$145$	−1.64924	+	7.22580i	−0.136962	+	0.600070i
$146$	1.67877	−	1.80929i	0.138936	−	0.149738i
$147$		0			0
$148$	−3.89720	−	1.52954i	−0.320347	−	0.125727i
$149$	16.3577	+	2.46553i	1.34008	+	0.201984i	0.779649	−	0.626217i	$-0.215398\pi$
$149$	16.3577	+	2.46553i	1.34008	+	0.201984i	0.560430	+	0.828202i	$0.310636\pi$
$150$		0			0
$151$	−6.03613	−	12.5341i	−0.491213	−	1.02001i	−0.988330	−	0.152331i	$-0.951322\pi$
$151$	−6.03613	−	12.5341i	−0.491213	−	1.02001i	0.497117	−	0.867684i	$-0.334392\pi$
$152$	0.503167	−	3.33829i	0.0408122	−	0.270771i
$153$		0			0
$154$	−0.874207	+	11.6655i	−0.0704456	+	0.940031i
$155$	−12.1461	−	11.2699i	−0.975598	−	0.905223i
$156$		0			0
$157$	0.681509	+	4.52152i	0.0543903	+	0.360856i	0.999426	+	0.0338880i	$0.0107890\pi$
$157$	0.681509	+	4.52152i	0.0543903	+	0.360856i	−0.945035	+	0.326968i	$0.893973\pi$
$158$	−9.28110	+	6.32774i	−0.738364	+	0.503408i
$159$		0			0
$160$	−1.09774	−	14.6483i	−0.0867839	−	1.15805i
$161$	13.7496	−	17.2415i	1.08362	−	1.35882i
$162$		0			0
$163$	8.61724	−	3.38202i	0.674954	−	0.264900i	−0.00300956	−	0.999995i	$-0.500958\pi$
$163$	8.61724	−	3.38202i	0.674954	−	0.264900i	0.677963	+	0.735096i	$0.262863\pi$
$164$	9.68723	−	2.21105i	0.756446	−	0.172654i
$165$		0			0
$166$	2.70551	−	1.56203i	0.209989	−	0.121237i
$167$	−13.3706	−	14.4101i	−1.03465	−	1.11509i	−0.993256	−	0.115943i	$-0.963011\pi$
$167$	−13.3706	−	14.4101i	−1.03465	−	1.11509i	−0.0413931	−	0.999143i	$-0.513180\pi$
$168$		0			0
$169$	11.3441	+	7.73431i	0.872627	+	0.594947i
$170$	−1.47595	+	3.06484i	−0.113200	+	0.235063i
$171$		0			0
$172$	−5.98983	+	5.94064i	−0.456720	+	0.452969i
$173$			0.439156i			0.0333884i	0.999861	+	0.0166942i	$0.00531418\pi$
$173$			0.439156i			0.0333884i	−0.999861	+	0.0166942i	$0.994686\pi$
$174$		0			0
$175$	3.43483	−	5.03797i	0.259649	−	0.380835i
$176$	0.623071	−	0.496883i	0.0469658	−	0.0374540i
$177$		0			0
$178$	0.738667	+	1.27941i	0.0553654	+	0.0958958i
$179$	−8.54835	+	14.8062i	−0.638934	+	1.10667i	0.346733	+	0.937964i	$0.387291\pi$
$179$	−8.54835	+	14.8062i	−0.638934	+	1.10667i	−0.985667	+	0.168702i	$0.946042\pi$
$180$		0			0
$181$	−3.23375	−	8.23945i	−0.240363	−	0.612434i	0.758885	−	0.651225i	$-0.225745\pi$
$181$	−3.23375	−	8.23945i	−0.240363	−	0.612434i	−0.999247	+	0.0387911i	$0.987649\pi$
$182$	−5.10272	−	16.5426i	−0.378239	−	1.22622i
$183$		0			0
$184$	15.4002	−	1.15409i	1.13532	−	0.0850805i
$185$	2.45267	−	7.95136i	0.180324	−	0.584595i
$186$		0			0
$187$	−5.44094	+	0.820090i	−0.397881	+	0.0599709i
$188$	−8.86003	−	2.02224i	−0.646184	−	0.147487i
$189$		0			0
$190$	2.61927	+	0.196287i	0.190022	+	0.0142402i
$191$	−6.67776	+	17.0146i	−0.483186	+	1.23114i	0.456692	+	0.889625i	$0.349034\pi$
$191$	−6.67776	+	17.0146i	−0.483186	+	1.23114i	−0.939878	+	0.341512i	$0.889061\pi$
$192$		0			0
$193$	−3.39302	+	1.63399i	−0.244235	+	0.117617i	−0.551997	−	0.833846i	$-0.686134\pi$
$193$	−3.39302	+	1.63399i	−0.244235	+	0.117617i	0.307762	+	0.951463i	$0.400420\pi$
$194$	14.8709	−	7.16145i	1.06767	−	0.514162i
$195$		0			0
$196$	4.09581	−	10.4359i	0.292558	−	0.745425i
$197$	15.0355	+	1.12676i	1.07124	+	0.0802781i	0.598654	−	0.801008i	$-0.295703\pi$
$197$	15.0355	+	1.12676i	1.07124	+	0.0802781i	0.472583	+	0.881286i	$0.343322\pi$
$198$		0			0
$199$	−7.23051	−	1.65032i	−0.512558	−	0.116988i	−0.0415836	−	0.999135i	$-0.513240\pi$
$199$	−7.23051	−	1.65032i	−0.512558	−	0.116988i	−0.470974	+	0.882147i	$0.656097\pi$
$200$	4.22236	−	0.636418i	0.298566	−	0.0450016i
$201$		0			0
$202$	−0.637518	+	2.06678i	−0.0448556	+	0.145418i
$203$	−11.4582	+	0.858673i	−0.804207	+	0.0602670i
$204$		0			0
$205$	5.82110	+	18.8715i	0.406563	+	1.31804i
$206$	0.0891903	+	0.227253i	0.00621418	+	0.0158335i
$207$		0			0
$208$	−0.589680	+	1.02135i	−0.0408869	+	0.0708182i
$209$	2.12432	+	3.67943i	0.146942	+	0.254512i
$210$		0			0
$211$	−1.21373	+	0.967917i	−0.0835565	+	0.0666341i	−0.664377	−	0.747397i	$-0.731303\pi$
$211$	−1.21373	+	0.967917i	−0.0835565	+	0.0666341i	0.580821	+	0.814032i	$0.302732\pi$
$212$	6.48505	−	9.51181i	0.445395	−	0.653274i
$213$		0			0
$214$		−	12.9101i		−	0.882517i
$215$	−12.6639	−	10.9894i	−0.863671	−	0.749470i
$216$		0			0
$217$	11.1454	−	23.1436i	0.756596	−	1.57109i
$218$	−10.5513	−	7.19374i	−0.714623	−	0.487222i
$219$		0			0
$220$	7.81693	+	8.42465i	0.527017	+	0.567990i
$221$	7.05187	−	4.07140i	0.474360	−	0.273872i
$222$		0			0
$223$	12.7815	−	2.91730i	0.855916	−	0.195357i	0.228022	−	0.973656i	$-0.426774\pi$
$223$	12.7815	−	2.91730i	0.855916	−	0.195357i	0.627894	+	0.778299i	$0.283917\pi$
$224$	21.1989	−	8.31995i	1.41641	−	0.555900i
$225$		0			0
$226$	10.1766	−	12.7611i	0.676938	−	0.848853i
$227$	0.703855	+	9.39229i	0.0467165	+	0.623388i	0.970597	+	0.240708i	$0.0773798\pi$
$227$	0.703855	+	9.39229i	0.0467165	+	0.623388i	−0.923881	+	0.382680i	$0.875001\pi$
$228$		0			0
$229$	−10.7122	+	7.30342i	−0.707879	+	0.482624i	−0.862956	−	0.505279i	$-0.831390\pi$
$229$	−10.7122	+	7.30342i	−0.707879	+	0.482624i	0.155077	+	0.987902i	$0.450437\pi$
$230$	1.79080	+	11.8812i	0.118082	+	0.783421i
$231$		0			0
$232$	−5.89861	−	5.47311i	−0.387263	−	0.359327i
$233$	1.33533	−	17.8187i	0.0874802	−	1.16734i	−0.764804	−	0.644263i	$-0.777164\pi$
$233$	1.33533	−	17.8187i	0.0874802	−	1.16734i	0.852284	−	0.523079i	$-0.175217\pi$
$234$		0			0
$235$	2.69208	−	17.8608i	0.175612	−	1.16511i
$236$	−1.90696	−	3.95984i	−0.124132	−	0.257764i
$237$		0			0
$238$	−5.21481	−	0.786006i	−0.338026	−	0.0509492i
$239$	−8.42416	−	3.30624i	−0.544914	−	0.213863i	0.0768849	−	0.997040i	$-0.475503\pi$
$239$	−8.42416	−	3.30624i	−0.544914	−	0.213863i	−0.621799	+	0.783177i	$0.713598\pi$
$240$		0			0
$241$	−7.40318	+	7.97874i	−0.476881	+	0.513956i	−0.924973	−	0.380032i	$-0.875913\pi$
$241$	−7.40318	+	7.97874i	−0.476881	+	0.513956i	0.448092	+	0.893987i	$0.352104\pi$
$242$	0.226578	−	0.992705i	0.0145650	−	0.0638135i
$243$		0			0
$244$	8.34652	+	12.2421i	0.534331	+	0.783720i
$245$	21.2922	+	6.56778i	1.36031	+	0.419600i
$246$		0			0
$247$	−4.91569	−	3.92013i	−0.312778	−	0.249432i
$248$	17.1897	−	5.30231i	1.09154	−	0.336697i
$249$		0			0
$250$	−1.66380	−	7.28956i	−0.105228	−	0.461033i
$251$	−8.31895	−	4.80295i	−0.525087	−	0.303159i	0.213926	−	0.976850i	$-0.431375\pi$
$251$	−8.31895	−	4.80295i	−0.525087	−	0.303159i	−0.739014	+	0.673690i	$0.764708\pi$
$252$		0			0
$253$	−14.2471	+	13.2194i	−0.895706	+	0.831094i
$254$	−3.29284	−	4.12909i	−0.206611	−	0.259082i
$255$		0			0
$256$	13.8398	+	6.66490i	0.864988	+	0.416556i
$257$	−27.0889			−1.68976			−0.844878	−	0.534958i	$-0.820327\pi$
$257$	−27.0889			−1.68976			−0.844878	+	0.534958i	$0.820327\pi$
$258$		0			0
$259$	12.9002			0.801579
$260$	−15.3232	−	7.37924i	−0.950302	−	0.457641i
$261$		0			0
$262$	−1.16074	−	1.45552i	−0.0717109	−	0.0899226i
$263$	−19.2271	+	17.8402i	−1.18560	+	1.10007i	−0.192679	+	0.981262i	$0.561718\pi$
$263$	−19.2271	+	17.8402i	−1.18560	+	1.10007i	−0.992917	+	0.118810i	$0.962092\pi$
$264$		0			0
$265$	19.8155	+	11.4405i	1.21725	+	0.702782i
$266$	0.906119	+	3.96997i	0.0555577	+	0.243414i
$267$		0			0
$268$	17.9751	−	5.54459i	1.09800	−	0.338689i
$269$	19.8300	+	15.8139i	1.20906	+	0.964191i	0.999906	−	0.0136920i	$-0.00435844\pi$
$269$	19.8300	+	15.8139i	1.20906	+	0.964191i	0.209151	+	0.977883i	$0.432930\pi$
$270$		0			0
$271$	−26.3786	−	8.13672i	−1.60239	−	0.494271i	−0.640555	−	0.767913i	$-0.721295\pi$
$271$	−26.3786	−	8.13672i	−1.60239	−	0.494271i	−0.961832	+	0.273642i	$0.911772\pi$
$272$	0.202385	+	0.296844i	0.0122714	+	0.0179988i
$273$		0			0
$274$	−2.19695	+	9.62545i	−0.132722	+	0.581495i
$275$	−3.65511	+	3.93927i	−0.220411	+	0.237547i
$276$		0			0
$277$	−24.7686	−	9.72096i	−1.48820	−	0.584076i	−0.524583	−	0.851359i	$-0.675779\pi$
$277$	−24.7686	−	9.72096i	−1.48820	−	0.584076i	−0.963618	+	0.267283i	$0.913874\pi$
$278$	−3.94028	−	0.593902i	−0.236323	−	0.0356199i
$279$		0			0
$280$	12.2089	+	25.3521i	0.729623	+	1.51508i
$281$	0.725027	−	4.81024i	0.0432515	−	0.286955i	−0.956741	−	0.290942i	$-0.906031\pi$
$281$	0.725027	−	4.81024i	0.0432515	−	0.286955i	0.999992	+	0.00398766i	$0.00126931\pi$
$282$		0			0
$283$	−1.66687	+	22.2428i	−0.0990851	+	1.32220i	0.697025	+	0.717047i	$0.254507\pi$
$283$	−1.66687	+	22.2428i	−0.0990851	+	1.32220i	−0.796110	+	0.605152i	$0.793112\pi$
$284$	9.60862	+	8.91550i	0.570167	+	0.529038i
$285$		0			0
$286$	2.27394	+	15.0866i	0.134461	+	0.892092i
$287$	−25.2969	+	17.2471i	−1.49323	+	1.01807i
$288$		0			0
$289$	1.08504	+	14.4788i	0.0638258	+	0.851696i
$290$	3.90335	−	4.89465i	0.229213	−	0.287424i
$291$		0			0
$292$	3.49930	−	1.37337i	0.204781	−	0.0803706i
$293$	14.5963	−	3.33152i	0.852726	−	0.194629i	0.226250	−	0.974069i	$-0.427354\pi$
$293$	14.5963	−	3.33152i	0.852726	−	0.194629i	0.626477	+	0.779440i	$0.284496\pi$
$294$		0			0
$295$	7.56510	−	4.36771i	0.440457	−	0.254298i
$296$	6.14466	+	6.62237i	0.357151	+	0.384918i
$297$		0			0
$298$	−11.5452	−	7.87140i	−0.668797	−	0.455978i
$299$	12.4792	−	25.9133i	0.721689	−	1.49860i
$300$		0			0
$301$	10.4931	−	23.7825i	0.604814	−	1.37080i
$302$			11.7511i			0.676202i
$303$		0			0
$304$	0.156270	−	0.229206i	0.00896270	−	0.0131459i
$305$	−23.0239	+	18.3610i	−1.31835	+	1.05135i
$306$		0			0
$307$	−8.96894	−	15.5347i	−0.511884	−	0.886610i	−0.999905	−	0.0137777i	$-0.995614\pi$
$307$	−8.96894	−	15.5347i	−0.511884	−	0.886610i	0.488021	−	0.872832i	$-0.337719\pi$
$308$	−8.90852	+	15.4300i	−0.507610	+	0.879206i
$309$		0			0
$310$	5.11323	+	13.0283i	0.290412	+	0.739958i
$311$	−6.04505	−	19.5976i	−0.342783	−	1.11128i	−0.948814	−	0.315835i	$-0.897715\pi$
$311$	−6.04505	−	19.5976i	−0.342783	−	1.11128i	0.606031	−	0.795441i	$-0.292761\pi$
$312$		0			0
$313$	−6.61183	+	0.495488i	−0.373723	+	0.0280067i	−0.260268	−	0.965536i	$-0.583811\pi$
$313$	−6.61183	+	0.495488i	−0.373723	+	0.0280067i	−0.113455	+	0.993543i	$0.536192\pi$
$314$	1.13846	−	3.69080i	0.0642471	−	0.208284i
$315$		0			0
$316$	−16.9174	+	2.54988i	−0.951676	+	0.143442i
$317$	3.60808	+	0.823521i	0.202650	+	0.0462536i	0.322641	−	0.946521i	$-0.395429\pi$
$317$	3.60808	+	0.823521i	0.202650	+	0.0462536i	−0.119991	+	0.992775i	$0.538287\pi$
$318$		0			0
$319$	10.0983	+	0.756760i	0.565394	+	0.0423704i
$320$	−4.10693	+	10.4643i	−0.229584	+	0.584971i
$321$		0			0
$322$	−16.7828	+	8.08219i	−0.935271	+	0.450403i
$323$	−1.72567	+	0.831039i	−0.0960189	+	0.0462403i
$324$		0			0
$325$	2.90536	−	7.40275i	0.161161	−	0.410630i
$326$	−7.79751	−	0.584343i	−0.431864	−	0.0323638i
$327$		0			0
$328$	−20.9034	−	4.77107i	−1.15420	−	0.263438i
$329$	27.6898	−	4.17356i	1.52659	−	0.230096i
$330$		0			0
$331$	−1.84119	+	5.96899i	−0.101201	+	0.328085i	−0.991987	−	0.126337i	$-0.959678\pi$
$331$	−1.84119	+	5.96899i	−0.101201	+	0.328085i	0.890787	+	0.454422i	$0.150154\pi$
$332$	4.74482	−	0.355575i	0.260406	−	0.0195147i
$333$		0			0
$334$	4.89428	+	15.8669i	0.267803	+	0.868196i
$335$	13.6591	+	34.8028i	0.746277	+	1.90148i
$336$		0			0
$337$	−3.41427	+	5.91370i	−0.185987	+	0.322140i	−0.943909	−	0.330206i	$-0.892882\pi$
$337$	−3.41427	+	5.91370i	−0.185987	+	0.322140i	0.757921	+	0.652346i	$0.226215\pi$
$338$	−5.79871	−	10.0437i	−0.315408	−	0.546303i
$339$		0			0
$340$	−4.05068	+	3.23031i	−0.219679	+	0.175188i
$341$	−12.7528	+	18.7050i	−0.690604	+	1.01293i
$342$		0			0
$343$			6.79541i			0.366918i
$344$	17.2070	−	5.94146i	0.927738	−	0.320342i
$345$		0			0
$346$	0.160949	−	0.334214i	0.00865266	−	0.0179674i
$347$	9.79552	+	6.67847i	0.525851	+	0.358519i	0.796962	−	0.604029i	$-0.206439\pi$
$347$	9.79552	+	6.67847i	0.525851	+	0.358519i	−0.271112	+	0.962548i	$0.587391\pi$
$348$		0			0
$349$	−7.67621	−	8.27299i	−0.410898	−	0.442843i	0.493362	−	0.869824i	$-0.335768\pi$
$349$	−7.67621	−	8.27299i	−0.410898	−	0.442843i	−0.904261	+	0.426981i	$0.859577\pi$
$350$	−4.46042	+	2.57523i	−0.238420	+	0.137652i
$351$		0			0
$352$	−19.5670	+	4.46605i	−1.04293	+	0.238041i
$353$	1.33559	−	0.524180i	0.0710862	−	0.0278993i	−0.329532	−	0.944145i	$-0.606891\pi$
$353$	1.33559	−	0.524180i	0.0710862	−	0.0278993i	0.400618	+	0.916245i	$0.368796\pi$
$354$		0			0
$355$	−16.2432	+	20.3683i	−0.862100	+	1.08104i
$356$	0.168148	+	2.24378i	0.00891182	+	0.118920i
$357$		0			0
$358$	11.9320	−	8.13509i	0.630625	−	0.429953i
$359$	−1.97717	−	13.1177i	−0.104351	−	0.692324i	−0.978436	−	0.206551i	$-0.933776\pi$
$359$	−1.97717	−	13.1177i	−0.104351	−	0.692324i	0.874085	−	0.485773i	$-0.161462\pi$
$360$		0			0
$361$	−12.8439	−	11.9174i	−0.675992	−	0.627229i
$362$	−0.558725	+	7.45567i	−0.0293659	+	0.391861i
$363$		0			0
$364$	3.92976	−	26.0723i	0.205976	−	1.36656i
$365$	3.24175	+	6.73156i	0.169681	+	0.352346i
$366$		0			0
$367$	6.12400	+	0.923045i	0.319670	+	0.0481825i	0.306917	−	0.951736i	$-0.400702\pi$
$367$	6.12400	+	0.923045i	0.319670	+	0.0481825i	0.0127528	+	0.999919i	$0.495941\pi$
$368$	1.18128	+	0.463618i	0.0615784	+	0.0241678i
$369$		0			0
$370$	−4.78070	+	5.15237i	−0.248537	+	0.267859i
$371$	−7.89338	+	34.5832i	−0.409804	+	1.79547i
$372$		0			0
$373$	−5.99610	−	8.79466i	−0.310466	−	0.455370i	0.639015	−	0.769194i	$-0.279342\pi$
$373$	−5.99610	−	8.79466i	−0.310466	−	0.455370i	−0.949481	+	0.313824i	$0.898390\pi$
$374$	4.44131	+	1.36996i	0.229655	+	0.0708391i
$375$		0			0
$376$	15.3318	+	12.2267i	0.790677	+	0.630544i
$377$	−14.3202	+	4.41718i	−0.737526	+	0.227497i
$378$		0			0
$379$	−1.00477	−	4.40218i	−0.0516115	−	0.226125i	0.942544	−	0.334082i	$-0.108426\pi$
$379$	−1.00477	−	4.40218i	−0.0516115	−	0.226125i	−0.994156	+	0.107957i	$0.965569\pi$
$380$	3.46452	+	2.00024i	0.177726	+	0.102610i
$381$		0			0
$382$	11.3178	−	10.5014i	0.579069	−	0.537297i
$383$	2.08167	+	2.61033i	0.106368	+	0.133382i	0.832166	−	0.554526i	$-0.187101\pi$
$383$	2.08167	+	2.61033i	0.106368	+	0.133382i	−0.725798	+	0.687908i	$0.758529\pi$
$384$		0			0
$385$	−31.9052	−	15.3647i	−1.62604	−	0.783059i
$386$	3.18106			0.161912
$387$		0			0
$388$	25.1388			1.27623
$389$	28.1449	+	13.5539i	1.42700	+	0.687209i	0.978438	−	0.206540i	$-0.0662204\pi$
$389$	28.1449	+	13.5539i	1.42700	+	0.687209i	0.448567	+	0.893749i	$0.351935\pi$
$390$		0			0
$391$	−5.46284	−	6.85019i	−0.276268	−	0.346429i
$392$	−17.7335	+	16.4542i	−0.895675	+	0.831065i
$393$		0			0
$394$	−11.0296	−	6.36795i	−0.555664	−	0.320813i
$395$	−7.56654	−	33.1512i	−0.380714	−	1.66802i
$396$		0			0
$397$	37.2305	−	11.4841i	1.86854	−	0.576369i	0.872383	−	0.488824i	$-0.162574\pi$
$397$	37.2305	−	11.4841i	1.86854	−	0.576369i	0.996161	−	0.0875457i	$-0.0279024\pi$
$398$	4.89784	+	3.90590i	0.245507	+	0.195785i
$399$		0			0
$400$	0.335286	+	0.103422i	0.0167643	+	0.00517110i
$401$	−15.3455	−	22.5077i	−0.766318	−	1.12398i	−0.988829	−	0.149052i	$-0.952378\pi$
$401$	−15.3455	−	22.5077i	−0.766318	−	1.12398i	0.222511	−	0.974930i	$-0.428575\pi$
$402$		0			0
$403$	7.45492	−	32.6622i	0.371356	−	1.62702i
$404$	−2.24061	+	2.41481i	−0.111475	+	0.120141i
$405$		0			0
$406$	9.03479	+	3.54589i	0.448389	+	0.175980i
$407$	−11.2421	−	1.69448i	−0.557252	−	0.0839922i
$408$		0			0
$409$	3.97837	+	8.26117i	0.196718	+	0.408489i	0.975872	−	0.218344i	$-0.0700654\pi$
$409$	3.97837	+	8.26117i	0.196718	+	0.408489i	−0.779154	+	0.626832i	$0.784351\pi$
$410$	2.48627	−	16.4953i	0.122788	−	0.814645i
$411$		0			0
$412$	−0.0277864	+	0.370783i	−0.00136894	+	0.0182672i
$413$	9.92743	+	9.21131i	0.488497	+	0.453259i
$414$		0			0
$415$	1.40949	+	9.35135i	0.0691891	+	0.459040i
$416$	24.5403	−	16.7313i	1.20319	−	0.820319i
$417$		0			0
$418$	−0.268189	−	3.57873i	−0.0131175	−	0.175041i
$419$	−11.6403	+	14.5965i	−0.568667	+	0.713086i	−0.980134	−	0.198339i	$-0.936445\pi$
$419$	−11.6403	+	14.5965i	−0.568667	+	0.713086i	0.411466	+	0.911425i	$0.365017\pi$
$420$		0			0
$421$	−10.3786	+	4.07329i	−0.505821	+	0.198520i	−0.604509	−	0.796598i	$-0.706631\pi$
$421$	−10.3786	+	4.07329i	−0.505821	+	0.198520i	0.0986882	+	0.995118i	$0.468535\pi$
$422$	1.27843	−	0.291793i	0.0622329	−	0.0142042i
$423$		0			0
$424$	−21.5132	+	12.4207i	−1.04478	+	0.603201i
$425$	−1.64778	−	1.77588i	−0.0799288	−	0.0861428i
$426$		0			0
$427$	−37.7216	−	25.7182i	−1.82548	−	1.24459i
$428$	8.53140	−	17.7156i	0.412381	−	0.856318i
$429$		0			0
$430$	5.61012	+	13.0046i	0.270544	+	0.627136i
$431$			10.0607i			0.484607i	0.970201	+	0.242303i	$0.0779029\pi$
$431$			10.0607i			0.484607i	−0.970201	+	0.242303i	$0.922097\pi$
$432$		0			0
$433$	18.1933	−	26.6847i	0.874316	−	1.28239i	−0.0839384	−	0.996471i	$-0.526750\pi$
$433$	18.1933	−	26.6847i	0.874316	−	1.28239i	0.958255	−	0.285916i	$-0.0922977\pi$
$434$	−16.9640	+	13.5284i	−0.814299	+	0.649382i
$435$		0			0
$436$	−9.72493	−	16.8441i	−0.465740	−	0.806685i
$437$	−3.38265	+	5.85892i	−0.161814	+	0.280270i
$438$		0			0
$439$	11.5575	+	29.4480i	0.551609	+	1.40548i	0.886283	+	0.463143i	$0.153278\pi$
$439$	11.5575	+	29.4480i	0.551609	+	1.40548i	−0.334674	+	0.942334i	$0.608626\pi$
$440$	−7.30964	−	23.6973i	−0.348473	−	1.12972i
$441$		0			0
$442$	−6.85887	+	0.514001i	−0.326243	+	0.0244485i
$443$	2.80018	−	9.07797i	0.133041	−	0.431308i	−0.864400	−	0.502805i	$-0.832301\pi$
$443$	2.80018	−	9.07797i	0.133041	−	0.431308i	0.997441	+	0.0714971i	$0.0227777\pi$
$444$		0			0
$445$	−4.42215	+	0.666532i	−0.209630	+	0.0315967i
$446$	−10.7964	−	2.46420i	−0.511224	−	0.116683i
$447$		0			0
$448$	−17.3789	−	1.30237i	−0.821074	−	0.0615310i
$449$	−7.63394	+	19.4510i	−0.360268	+	0.917948i	0.629723	+	0.776819i	$0.283168\pi$
$449$	−7.63394	+	19.4510i	−0.360268	+	0.917948i	−0.989991	+	0.141128i	$0.954927\pi$
$450$		0			0
$451$	24.3110	−	11.7075i	1.14476	−	0.551287i
$452$	22.3975	−	10.7861i	1.05349	−	0.507335i
$453$		0			0
$454$	2.90657	−	7.40583i	0.136412	−	0.347573i
$455$	52.2585	+	3.91623i	2.44992	+	0.183596i
$456$		0			0
$457$	2.24528	+	0.512470i	0.105030	+	0.0239723i	0.274713	−	0.961526i	$-0.411417\pi$
$457$	2.24528	+	0.512470i	0.105030	+	0.0239723i	−0.169683	+	0.985499i	$0.554274\pi$
$458$	10.8290	−	1.63221i	0.506006	−	0.0762681i
$459$		0			0
$460$	−5.39406	+	17.4871i	−0.251499	+	0.815340i
$461$	−22.4339	+	1.68119i	−1.04485	+	0.0783008i	−0.586080	−	0.810254i	$-0.699329\pi$
$461$	−22.4339	+	1.68119i	−1.04485	+	0.0783008i	−0.458772	+	0.888554i	$0.651710\pi$
$462$		0			0
$463$	8.07554	+	26.1803i	0.375302	+	1.21670i	0.924556	+	0.381045i	$0.124436\pi$
$463$	8.07554	+	26.1803i	0.375302	+	1.21670i	−0.549254	+	0.835655i	$0.685088\pi$
$464$	−0.241564	−	0.615494i	−0.0112143	−	0.0285736i
$465$		0			0
$466$	−7.54671	+	13.0713i	−0.349594	+	0.605515i
$467$	3.47707	+	6.02247i	0.160900	+	0.278686i	0.935192	−	0.354142i	$-0.115227\pi$
$467$	3.47707	+	6.02247i	0.160900	+	0.278686i	−0.774292	+	0.632829i	$0.781894\pi$
$468$		0			0
$469$	−45.3164	+	36.1386i	−2.09252	+	1.66873i
$470$	−8.59466	+	12.6061i	−0.396442	+	0.581474i
$471$		0			0
$472$			9.48386i			0.436530i
$473$	−12.2683	+	19.3474i	−0.564099	+	0.889595i
$474$		0			0
$475$	−0.811615	+	1.68534i	−0.0372394	+	0.0773285i
$476$	−6.63650	−	4.52469i	−0.304184	−	0.207389i
$477$		0			0
$478$	5.19936	+	5.60358i	0.237813	+	0.256302i
$479$	23.8571	−	13.7739i	1.09006	−	0.629344i	0.156465	−	0.987683i	$-0.449990\pi$
$479$	23.8571	−	13.7739i	1.09006	−	0.629344i	0.933592	+	0.358339i	$0.116657\pi$
$480$		0			0
$481$	16.4029	−	3.74385i	0.747907	−	0.170705i
$482$	8.55825	−	3.35887i	0.389818	−	0.152992i
$483$		0			0
$484$	0.966927	−	1.21249i	0.0439512	−	0.0551131i
$485$	3.73385	+	49.8247i	0.169545	+	2.26242i
$486$		0			0
$487$	19.3773	−	13.2112i	0.878067	−	0.598656i	−0.0381795	−	0.999271i	$-0.512156\pi$
$487$	19.3773	−	13.2112i	0.878067	−	0.598656i	0.916247	+	0.400615i	$0.131203\pi$
$488$	−4.76516	−	31.6148i	−0.215709	−	1.43113i
$489$		0			0
$490$	−13.7971	−	12.8018i	−0.623288	−	0.578327i
$491$	0.326618	−	4.35841i	0.0147400	−	0.196692i	−0.984972	−	0.172712i	$-0.944747\pi$
$491$	0.326618	−	4.35841i	0.0147400	−	0.196692i	0.999712	−	0.0239803i	$-0.00763391\pi$
$492$		0			0
$493$	−0.680409	+	4.51422i	−0.0306441	+	0.203310i
$494$	2.30430	+	4.78494i	0.103676	+	0.215284i
$495$		0			0
$496$	1.46165	+	0.220308i	0.0656301	+	0.00989214i
$497$	−37.5969	−	14.7557i	−1.68645	−	0.661883i
$498$		0			0
$499$	−7.52528	+	8.11032i	−0.336878	+	0.363068i	−0.878657	−	0.477453i	$-0.841560\pi$
$499$	−7.52528	+	8.11032i	−0.336878	+	0.363068i	0.541780	+	0.840520i	$0.317751\pi$
$500$	2.53406	−	11.1024i	0.113327	−	0.496516i
$501$		0			0
$502$	4.57076	+	6.70407i	0.204003	+	0.299217i
$503$	10.3608	+	3.19588i	0.461965	+	0.142497i	0.516997	−	0.855987i	$-0.327050\pi$
$503$	10.3608	+	3.19588i	0.461965	+	0.142497i	−0.0550317	+	0.998485i	$0.517526\pi$
$504$		0			0
$505$	−5.11890	−	4.08219i	−0.227788	−	0.181655i
$506$	15.6874	−	4.83891i	0.697388	−	0.215116i
$507$		0			0
$508$	−1.78990	−	7.84207i	−0.0794141	−	0.347936i
$509$	−11.2874	−	6.51677i	−0.500304	−	0.288851i	0.228535	−	0.973536i	$-0.426606\pi$
$509$	−11.2874	−	6.51677i	−0.500304	−	0.288851i	−0.728839	+	0.684685i	$0.759940\pi$
$510$		0			0
$511$	−8.49101	+	7.87851i	−0.375620	+	0.348525i
$512$	1.60671	+	2.01475i	0.0710073	+	0.0890403i
$513$		0			0
$514$	20.6156	+	9.92794i	0.909314	+	0.437903i
$515$	−0.739013			−0.0325648
$516$		0			0
$517$	−24.6790			−1.08538
$518$	−9.81750	−	4.72786i	−0.431356	−	0.207730i
$519$		0			0
$520$	22.8815	+	28.6925i	1.00342	+	1.25825i
$521$	25.6550	−	23.8044i	1.12397	−	1.04289i	0.125255	−	0.992125i	$-0.460025\pi$
$521$	25.6550	−	23.8044i	1.12397	−	1.04289i	0.998711	−	0.0507630i	$-0.0161653\pi$
$522$		0			0
$523$	−14.3802	−	8.30244i	−0.628804	−	0.363040i	0.151485	−	0.988460i	$-0.451595\pi$
$523$	−14.3802	−	8.30244i	−0.628804	−	0.363040i	−0.780289	+	0.625419i	$0.784928\pi$
$524$	−0.630949	−	2.76437i	−0.0275631	−	0.120762i
$525$		0			0
$526$	21.1709	−	6.53035i	0.923094	−	0.284737i
$527$	−7.97925	−	6.36324i	−0.347582	−	0.277187i
$528$		0			0
$529$	−7.59460	−	2.34262i	−0.330200	−	0.101853i
$530$	−10.8874	−	15.9689i	−0.472918	−	0.693644i
$531$		0			0
$532$	−1.38007	+	6.04650i	−0.0598338	+	0.262149i
$533$	−27.1602	+	29.2717i	−1.17644	+	1.26790i
$534$		0			0
$535$	36.3793	+	14.2778i	1.57281	+	0.617283i
$536$	−40.1372	−	6.04971i	−1.73366	−	0.261308i
$537$		0			0
$538$	−9.29562	−	19.3026i	−0.400763	−	0.832192i
$539$	4.53749	−	30.1043i	0.195443	−	1.29668i
$540$		0			0
$541$	0.468773	−	6.25535i	0.0201541	−	0.268938i	−0.978019	−	0.208517i	$-0.933136\pi$
$541$	0.468773	−	6.25535i	0.0201541	−	0.268938i	0.998173	−	0.0604216i	$-0.0192445\pi$
$542$	17.0930	+	15.8600i	0.734206	+	0.681244i
$543$		0			0
$544$	−1.34853	−	8.94691i	−0.0578177	−	0.383595i
$545$	31.9402	−	21.7765i	1.36817	−	0.932802i
$546$		0			0
$547$	−0.836138	−	11.1575i	−0.0357507	−	0.477060i	−0.986131	−	0.165969i	$-0.946925\pi$
$547$	−0.836138	−	11.1575i	−0.0357507	−	0.477060i	0.950380	−	0.311091i	$-0.100694\pi$
$548$	−9.37551	+	11.7565i	−0.400502	+	0.502214i
$549$		0			0
$550$	4.22539	−	1.65834i	0.180171	−	0.0707119i
$551$	3.43662	−	0.784385i	0.146405	−	0.0334159i
$552$		0			0
$553$	45.6537	−	26.3582i	1.94139	−	1.12086i
$554$	15.2871	+	16.4756i	0.649486	+	0.699980i
$555$		0			0
$556$	−5.01451	−	3.41883i	−0.212662	−	0.144991i
$557$	18.3699	−	38.1455i	0.778357	−	1.61627i	−0.00914138	−	0.999958i	$-0.502910\pi$
$557$	18.3699	−	38.1455i	0.778357	−	1.61627i	0.787498	−	0.616317i	$-0.211376\pi$
$558$		0			0
$559$	6.44018	−	33.2853i	0.272391	−	1.40782i
$560$			2.31218i			0.0977076i
$561$		0			0
$562$	−2.31470	+	3.39504i	−0.0976397	+	0.143211i
$563$	−17.6774	+	14.0973i	−0.745015	+	0.594130i	−0.920679	−	0.390320i	$-0.872364\pi$
$563$	−17.6774	+	14.0973i	−0.745015	+	0.594130i	0.175664	+	0.984450i	$0.443793\pi$
$564$		0			0
$565$	24.7045	+	42.7895i	1.03933	+	1.80017i
$566$	9.42043	−	16.3167i	0.395970	−	0.685841i
$567$		0			0
$568$	−10.3334	−	26.3290i	−0.433579	−	1.10474i
$569$	−13.2662	−	43.0079i	−0.556148	−	1.80299i	−0.594980	−	0.803741i	$-0.702840\pi$
$569$	−13.2662	−	43.0079i	−0.556148	−	1.80299i	0.0388323	−	0.999246i	$-0.487636\pi$
$570$		0			0
$571$	11.6993	−	0.876739i	0.489599	−	0.0366904i	0.172356	−	0.985035i	$-0.444862\pi$
$571$	11.6993	−	0.876739i	0.489599	−	0.0366904i	0.317243	+	0.948344i	$0.397243\pi$
$572$	−6.84934	+	22.2050i	−0.286385	+	0.928439i
$573$		0			0
$574$	25.5728	−	3.85449i	1.06739	−	0.160883i
$575$	−8.34239	−	1.90409i	−0.347902	−	0.0794063i
$576$		0			0
$577$	27.7034	+	2.07609i	1.15331	+	0.0864286i	0.637623	−	0.770349i	$-0.279918\pi$
$577$	27.7034	+	2.07609i	1.15331	+	0.0864286i	0.515687	+	0.856777i	$0.327537\pi$
$578$	4.48067	−	11.4166i	0.186371	−	0.474867i
$579$		0			0
$580$	8.59083	−	4.13713i	0.356715	−	0.171785i
$581$	−13.2093	+	6.36127i	−0.548015	+	0.263910i
$582$		0			0
$583$	11.4215	−	29.1014i	0.473028	−	1.20526i
$584$	−8.08894	−	0.606182i	−0.334723	−	0.0250840i
$585$		0			0
$586$	−12.3293	−	2.81408i	−0.509319	−	0.116249i
$587$	−17.6128	+	2.65470i	−0.726958	+	0.109571i	−0.502087	−	0.864817i	$-0.667434\pi$
$587$	−17.6128	+	2.65470i	−0.726958	+	0.109571i	−0.224871	+	0.974388i	$0.572196\pi$
$588$		0			0
$589$	−2.32278	+	7.53027i	−0.0957085	+	0.310279i
$590$	−7.35805	+	0.551410i	−0.302926	+	0.0227012i
$591$		0			0
$592$	0.218806	+	0.709350i	0.00899286	+	0.0291541i
$593$	−3.52723	−	8.98725i	−0.144846	−	0.369062i	0.839977	−	0.542622i	$-0.182568\pi$
$593$	−3.52723	−	8.98725i	−0.144846	−	0.369062i	−0.984823	+	0.173560i	$0.944473\pi$
$594$		0			0
$595$	7.98215	−	13.8255i	0.327236	−	0.566790i
$596$	−10.6410	−	18.4308i	−0.435873	−	0.754955i
$597$		0			0
$598$	−18.9942	+	15.1474i	−0.776730	+	0.619422i
$599$	−1.60402	+	2.35266i	−0.0655384	+	0.0961272i	−0.857609	−	0.514303i	$-0.828051\pi$
$599$	−1.60402	+	2.35266i	−0.0655384	+	0.0961272i	0.792070	+	0.610430i	$0.209003\pi$
$600$		0			0
$601$			35.9354i			1.46584i	0.680316	+	0.732919i	$0.261842\pi$
$601$			35.9354i			1.46584i	−0.680316	+	0.732919i	$0.738158\pi$
$602$	−16.7018	+	14.2536i	−0.680715	+	0.580934i
$603$		0			0
$604$	−7.76552	+	16.1253i	−0.315974	+	0.656128i
$605$	2.54675	+	1.73634i	0.103540	+	0.0705924i
$606$		0			0
$607$	−7.03112	−	7.57775i	−0.285385	−	0.307571i	0.574047	−	0.818822i	$-0.305373\pi$
$607$	−7.03112	−	7.57775i	−0.285385	−	0.307571i	−0.859431	+	0.511251i	$0.829182\pi$
$608$	−6.05033	+	3.49316i	−0.245373	+	0.141666i
$609$		0			0
$610$	24.2512	−	5.53519i	0.981904	−	0.224113i
$611$	33.9969	−	13.3428i	1.37537	−	0.539792i
$612$		0			0
$613$	3.67926	−	4.61364i	0.148604	−	0.186343i	−0.701958	−	0.712218i	$-0.747691\pi$
$613$	3.67926	−	4.61364i	0.148604	−	0.186343i	0.850562	+	0.525875i	$0.176262\pi$
$614$	1.13230	+	15.1095i	0.0456959	+	0.609770i
$615$		0			0
$616$	31.7657	−	21.6575i	1.27988	−	0.872606i
$617$	−4.94222	−	32.7895i	−0.198966	−	1.32005i	−0.835792	−	0.549047i	$-0.814991\pi$
$617$	−4.94222	−	32.7895i	−0.198966	−	1.32005i	0.636826	−	0.771008i	$-0.280247\pi$
$618$		0			0
$619$	18.0912	+	16.7862i	0.727146	+	0.674693i	0.954193	−	0.299191i	$-0.0967168\pi$
$619$	18.0912	+	16.7862i	0.727146	+	0.674693i	−0.227048	+	0.973884i	$0.572907\pi$
$620$	−1.59298	+	21.2568i	−0.0639755	+	0.853694i
$621$		0			0
$622$	−2.58192	+	17.1299i	−0.103526	+	0.686847i
$623$	−3.00818	−	6.24655i	−0.120520	−	0.250263i
$624$		0			0
$625$	29.9862	+	4.51969i	1.19945	+	0.180788i
$626$	5.21343	+	2.04612i	0.208371	+	0.0817795i
$627$		0			0
$628$	4.00123	−	4.31230i	0.159666	−	0.172079i
$629$	1.14050	−	4.99686i	0.0454747	−	0.199238i
$630$		0			0
$631$	−1.81952	−	2.66875i	−0.0724341	−	0.106241i	0.788312	−	0.615275i	$-0.210955\pi$
$631$	−1.81952	−	2.66875i	−0.0724341	−	0.106241i	−0.860746	+	0.509034i	$0.830003\pi$
$632$	35.2770	+	10.8815i	1.40324	+	0.432844i
$633$		0			0
$634$	−2.44406	−	1.94907i	−0.0970661	−	0.0774076i
$635$	15.2770	−	4.71233i	0.606249	−	0.187003i
$636$		0			0
$637$	10.0253	+	43.9238i	0.397218	+	1.74032i
$638$	−7.40778	−	4.27689i	−0.293277	−	0.169324i
$639$		0			0
$640$	−14.5755	+	13.5241i	−0.576149	+	0.534588i
$641$	4.91684	+	6.16552i	0.194203	+	0.243523i	0.869393	−	0.494121i	$-0.164510\pi$
$641$	4.91684	+	6.16552i	0.194203	+	0.243523i	−0.675190	+	0.737644i	$0.735938\pi$
$642$		0			0
$643$	−19.8154	−	9.54259i	−0.781442	−	0.376323i	0.000239626	−	1.00000i	$-0.499924\pi$
$643$	−19.8154	−	9.54259i	−0.781442	−	0.376323i	−0.781682	+	0.623677i	$0.785638\pi$
$644$	−28.3709			−1.11797
$645$		0			0
$646$	1.61787			0.0636542
$647$	−17.6633	−	8.50618i	−0.694415	−	0.334413i	0.0531638	−	0.998586i	$-0.483069\pi$
$647$	−17.6633	−	8.50618i	−0.694415	−	0.334413i	−0.747579	+	0.664173i	$0.768784\pi$
$648$		0			0
$649$	−7.44153	−	9.33138i	−0.292106	−	0.366289i
$650$	−4.92416	+	4.56895i	−0.193141	+	0.179209i
$651$		0			0
$652$	−10.3138	−	5.95469i	−0.403921	−	0.233204i
$653$	0.808457	+	3.54208i	0.0316374	+	0.138612i	0.988280	−	0.152652i	$-0.0487813\pi$
$653$	0.808457	+	3.54208i	0.0316374	+	0.138612i	−0.956643	+	0.291264i	$0.905924\pi$
$654$		0			0
$655$	5.38522	−	1.66112i	0.210418	−	0.0649053i
$656$	−1.37745	−	1.09848i	−0.0537804	−	0.0428885i
$657$		0			0
$658$	−22.6025	−	6.97194i	−0.881136	−	0.271794i
$659$	−17.7579	−	26.0461i	−0.691750	−	1.01461i	−0.998034	−	0.0626709i	$-0.980038\pi$
$659$	−17.7579	−	26.0461i	−0.691750	−	1.01461i	0.306284	−	0.951940i	$-0.400914\pi$
$660$		0			0
$661$	−4.52860	+	19.8411i	−0.176142	+	0.771728i	0.807246	+	0.590215i	$0.200957\pi$
$661$	−4.52860	+	19.8411i	−0.176142	+	0.771728i	−0.983388	+	0.181514i	$0.941900\pi$
$662$	3.58881	−	3.86782i	0.139483	−	0.150327i
$663$		0			0
$664$	−9.55750	−	3.75104i	−0.370903	−	0.145569i
$665$	−12.1890	−	1.83720i	−0.472671	−	0.0712437i
$666$		0			0
$667$	6.99638	+	14.5281i	0.270901	+	0.562531i
$668$	−3.76924	+	25.0073i	−0.145836	+	0.967560i
$669$		0			0
$670$	2.36001	−	31.4922i	0.0911752	−	1.21665i
$671$	29.4951	+	27.3675i	1.13865	+	1.05651i
$672$		0			0
$673$	−0.125135	−	0.830217i	−0.00482360	−	0.0320025i	0.986290	−	0.165024i	$-0.0527702\pi$
$673$	−0.125135	−	0.830217i	−0.00482360	−	0.0320025i	−0.991113	+	0.133021i	$0.957532\pi$
$674$	4.76572	−	3.24922i	0.183569	−	0.125155i
$675$		0			0
$676$	−1.32000	−	17.6142i	−0.0507692	−	0.677468i
$677$	29.0200	−	36.3899i	1.11533	−	1.39858i	0.208015	−	0.978126i	$-0.433300\pi$
$677$	29.0200	−	36.3899i	1.11533	−	1.39858i	0.907314	−	0.420453i	$-0.138129\pi$
$678$		0			0
$679$	−72.1058	+	28.2994i	−2.76717	+	1.08603i
$680$	10.8995	−	2.48773i	0.417975	−	0.0954001i
$681$		0			0
$682$	16.5606	−	9.56128i	0.634139	−	0.366120i
$683$	−33.6287	−	36.2431i	−1.28677	−	1.38680i	−0.881204	−	0.472736i	$-0.843266\pi$
$683$	−33.6287	−	36.2431i	−1.28677	−	1.38680i	−0.405562	−	0.914068i	$-0.632924\pi$
$684$		0			0
$685$	−24.6938	−	16.8359i	−0.943500	−	0.643267i
$686$	2.49049	−	5.17155i	0.0950872	−	0.197451i
$687$		0			0
$688$	1.48572	+	0.173607i	0.0566426	+	0.00661871i
$689$			46.2641i			1.76252i
$690$		0			0
$691$	−20.9284	+	30.6963i	−0.796154	+	1.16774i	0.186529	+	0.982449i	$0.440276\pi$
$691$	−20.9284	+	30.6963i	−0.796154	+	1.16774i	−0.982683	+	0.185294i	$0.940676\pi$
$692$	0.441717	−	0.352258i	0.0167916	−	0.0133908i
$693$		0			0
$694$	−5.00711	−	8.67256i	−0.190067	−	0.329206i
$695$	6.03127	−	10.4465i	0.228779	−	0.396257i
$696$		0			0
$697$	4.44415	+	11.3235i	0.168334	+	0.428909i
$698$	2.80986	+	9.10933i	0.106355	+	0.344793i
$699$		0			0
$700$	−7.82251	+	0.586216i	−0.295663	+	0.0221569i
$701$	−0.314717	+	1.02029i	−0.0118867	+	0.0385357i	−0.961322	−	0.275427i	$-0.911181\pi$
$701$	−0.314717	+	1.02029i	−0.0118867	+	0.0385357i	0.949435	+	0.313963i	$0.101657\pi$
$702$		0			0
$703$	−3.91331	+	0.589837i	−0.147593	+	0.0222461i
$704$	14.9741	+	3.41774i	0.564357	+	0.128811i
$705$		0			0
$706$	−1.20854	−	0.0905675i	−0.0454840	−	0.00340855i
$707$	3.70835	−	9.44872i	0.139467	−	0.355356i
$708$		0			0
$709$	−8.83979	+	4.25702i	−0.331985	+	0.159876i	−0.592449	−	0.805608i	$-0.701839\pi$
$709$	−8.83979	+	4.25702i	−0.331985	+	0.159876i	0.260464	+	0.965484i	$0.416125\pi$
$710$	19.8266	−	9.54797i	0.744078	−	0.358329i
$711$		0			0
$712$	1.77383	−	4.51964i	0.0664770	−	0.169381i
$713$	−35.9478	−	2.69391i	−1.34625	−	0.100888i
$714$		0			0
$715$	−45.0273	−	10.2772i	−1.68393	−	0.384345i
$716$	21.7493	−	3.27819i	0.812811	−	0.122512i
$717$		0			0
$718$	−3.30287	+	10.7076i	−0.123262	+	0.399605i
$719$	36.7307	−	2.75258i	1.36982	−	0.102654i	0.630597	−	0.776111i	$-0.282810\pi$
$719$	36.7307	−	2.75258i	1.36982	−	0.102654i	0.739227	+	0.673457i	$0.235191\pi$
$720$		0			0
$721$	−0.337701	−	1.09480i	−0.0125766	−	0.0407724i
$722$	5.40697	+	13.7767i	0.201227	+	0.512717i
$723$		0			0
$724$	−5.69363	+	9.86166i	−0.211602	+	0.366506i
$725$	2.22925	+	3.86118i	0.0827924	+	0.143401i
$726$		0			0
$727$	−5.46092	+	4.35494i	−0.202534	+	0.161516i	−0.719505	−	0.694488i	$-0.755631\pi$
$727$	−5.46092	+	4.35494i	−0.202534	+	0.161516i	0.516970	+	0.856003i	$0.327060\pi$
$728$	−32.0501	+	47.0089i	−1.18786	+	1.74227i
$729$		0			0
$730$		−	6.31104i		−	0.233582i
$731$	−8.28440	−	6.16709i	−0.306409	−	0.228098i
$732$		0			0
$733$	−18.2249	+	37.8445i	−0.673153	+	1.39782i	0.231993	+	0.972717i	$0.425475\pi$
$733$	−18.2249	+	37.8445i	−0.673153	+	1.39782i	−0.905146	+	0.425100i	$0.860239\pi$
$734$	−4.32229	−	2.94689i	−0.159539	−	0.108772i
$735$		0			0
$736$	−21.7375	−	23.4274i	−0.801254	−	0.863546i
$737$	44.2388	−	25.5413i	1.62956	−	0.940825i
$738$		0			0
$739$	37.9351	−	8.65844i	1.39546	−	0.318506i	0.542316	−	0.840174i	$-0.317547\pi$
$739$	37.9351	−	8.65844i	1.39546	−	0.318506i	0.853148	+	0.521669i	$0.174690\pi$
$740$	−9.96507	+	3.91100i	−0.366323	+	0.143771i
$741$		0			0
$742$	18.6817	−	23.4261i	0.685827	−	0.860000i
$743$	0.831510	+	11.0957i	0.0305051	+	0.407063i	0.991465	+	0.130374i	$0.0416179\pi$
$743$	0.831510	+	11.0957i	0.0305051	+	0.407063i	−0.960960	+	0.276688i	$0.910763\pi$
$744$		0			0
$745$	34.9490	−	23.8278i	1.28043	−	0.872985i
$746$	1.34004	+	8.89059i	0.0490624	+	0.325508i
$747$		0			0
$748$	5.18918	+	4.81486i	0.189735	+	0.176049i
$749$	−4.52769	+	60.4179i	−0.165438	+	2.20762i
$750$		0			0
$751$	4.04471	−	26.8349i	0.147593	−	0.979218i	−0.785313	−	0.619099i	$-0.787498\pi$
$751$	4.04471	−	26.8349i	0.147593	−	0.979218i	0.932906	−	0.360119i	$-0.117264\pi$
$752$	0.699152	+	1.45180i	0.0254955	+	0.0529418i
$753$		0			0
$754$	12.5170	+	1.88664i	0.455843	+	0.0687073i
$755$	−33.1134	−	12.9961i	−1.20512	−	0.472975i
$756$		0			0
$757$	−4.89898	+	5.27984i	−0.178056	+	0.191899i	−0.815773	−	0.578372i	$-0.803688\pi$
$757$	−4.89898	+	5.27984i	−0.178056	+	0.191899i	0.637717	+	0.770271i	$0.279879\pi$
$758$	−0.848714	+	3.71846i	−0.0308267	+	0.135060i
$759$		0			0
$760$	−4.86279	−	7.13241i	−0.176392	−	0.258720i
$761$	18.6710	+	5.75924i	0.676823	+	0.208772i	0.614064	−	0.789256i	$-0.289534\pi$
$761$	18.6710	+	5.75924i	0.676823	+	0.208772i	0.0627595	+	0.998029i	$0.480010\pi$
$762$		0			0
$763$	46.8559	+	37.3663i	1.69630	+	1.35275i
$764$	22.4703	−	6.93115i	0.812945	−	0.250760i
$765$		0			0
$766$	−0.627550	−	2.74948i	−0.0226743	−	0.0993427i
$767$	15.2962	+	8.83129i	0.552315	+	0.318879i
$768$		0			0
$769$	20.6753	−	19.1839i	0.745570	−	0.691788i	−0.212870	−	0.977080i	$-0.568281\pi$
$769$	20.6753	−	19.1839i	0.745570	−	0.691788i	0.958440	+	0.285293i	$0.0920907\pi$
$770$	18.6499	+	23.3862i	0.672095	+	0.842780i
$771$		0			0
$772$	4.36514	+	2.10214i	0.157105	+	0.0756577i
$773$	23.0054			0.827445			0.413723	−	0.910403i	$-0.364228\pi$
$773$	23.0054			0.827445			0.413723	+	0.910403i	$0.364228\pi$
$774$		0			0
$775$	−9.96730			−0.358036
$776$	−48.8734	−	23.5362i	−1.75445	−	0.844899i
$777$		0			0
$778$	−16.4519	−	20.6300i	−0.589828	−	0.739620i
$779$	6.88530	−	6.38863i	0.246692	−	0.228896i
$780$		0			0
$781$	30.8264	+	17.7976i	1.10305	+	0.636848i
$782$	1.64685	+	7.21534i	0.0588914	+	0.258020i
$783$		0			0
$784$	−1.89951	+	0.585920i	−0.0678395	+	0.0209257i
$785$	9.14120	+	7.28987i	0.326264	+	0.260186i
$786$		0			0
$787$	8.21425	+	2.53376i	0.292806	+	0.0903188i	0.437678	−	0.899132i	$-0.355801\pi$
$787$	8.21425	+	2.53376i	0.292806	+	0.0903188i	−0.144872	+	0.989450i	$0.546277\pi$
$788$	−10.9270	−	16.0270i	−0.389259	−	0.570938i
$789$		0			0
$790$	−6.39135	+	28.0023i	−0.227394	+	0.996278i
$791$	−52.1008	+	56.1513i	−1.85249	+	1.99651i
$792$		0			0
$793$	−55.4278	−	21.7538i	−1.96830	−	0.772500i
$794$	−32.5426	−	4.90500i	−1.15489	−	0.174072i
$795$		0			0
$796$	4.13983	+	8.59644i	0.146732	+	0.304693i
$797$	5.28380	−	35.0557i	0.187162	−	1.24174i	−0.676035	−	0.736870i	$-0.736303\pi$
$797$	5.28380	−	35.0557i	0.187162	−	1.24174i	0.863197	−	0.504868i	$-0.168459\pi$
$798$		0			0
$799$	0.831421	−	11.0945i	0.0294136	−	0.392497i
$800$	−6.47760	−	6.01033i	−0.229018	−	0.212497i
$801$		0			0
$802$	3.42950	+	22.7532i	0.121100	+	0.803444i
$803$	8.43453	−	5.75056i	0.297648	−	0.202933i
$804$		0			0
$805$	−4.21390	−	56.2306i	−0.148520	−	1.98187i
$806$	−17.6440	+	22.1249i	−0.621483	+	0.779315i
$807$		0			0
$808$	6.61692	−	2.59695i	0.232782	−	0.0913604i
$809$	−1.81522	+	0.414313i	−0.0638199	+	0.0145665i	−0.254312	−	0.967122i	$-0.581849\pi$
$809$	−1.81522	+	0.414313i	−0.0638199	+	0.0145665i	0.190492	+	0.981689i	$0.438992\pi$
$810$		0			0
$811$	11.7856	−	6.80439i	0.413847	−	0.238935i	−0.278594	−	0.960409i	$-0.589869\pi$
$811$	11.7856	−	6.80439i	0.413847	−	0.238935i	0.692441	+	0.721474i	$0.256535\pi$
$812$	10.0546	+	10.8362i	0.352846	+	0.380278i
$813$		0			0
$814$	7.93464	+	5.40974i	0.278109	+	0.189611i
$815$	10.2702	−	21.3263i	0.359749	−	0.747027i
$816$		0			0
$817$	−2.09571	+	7.69427i	−0.0733197	+	0.269188i
$818$		−	7.74510i		−	0.270801i
$819$		0			0
$820$	14.3123	−	20.9923i	0.499808	−	0.733084i
$821$	16.0700	−	12.8154i	0.560845	−	0.447259i	−0.301582	−	0.953440i	$-0.597515\pi$
$821$	16.0700	−	12.8154i	0.560845	−	0.447259i	0.862427	+	0.506181i	$0.168943\pi$
$822$		0			0
$823$	−20.6352	−	35.7413i	−0.719299	−	1.24586i	−0.961278	−	0.275582i	$-0.911130\pi$
$823$	−20.6352	−	35.7413i	−0.719299	−	1.24586i	0.241978	−	0.970282i	$-0.422204\pi$
$824$	0.401166	−	0.694839i	0.0139753	−	0.0242059i
$825$		0			0
$826$	−4.17923	−	10.6485i	−0.145414	−	0.370508i
$827$	13.6761	+	44.3368i	0.475564	+	1.54174i	0.802474	+	0.596687i	$0.203516\pi$
$827$	13.6761	+	44.3368i	0.475564	+	1.54174i	−0.326910	+	0.945055i	$0.606007\pi$
$828$		0			0
$829$	−9.17568	+	0.687622i	−0.318685	+	0.0238821i	−0.233112	−	0.972450i	$-0.574891\pi$
$829$	−9.17568	+	0.687622i	−0.318685	+	0.0238821i	−0.0855724	+	0.996332i	$0.527272\pi$
$830$	2.35455	−	7.63328i	0.0817278	−	0.264955i
$831$		0			0
$832$	−22.4756	+	3.38765i	−0.779201	+	0.117446i
$833$	13.3806	+	3.05404i	0.463611	+	0.105816i
$834$		0			0
$835$	−50.1238	−	3.75626i	−1.73461	−	0.129991i
$836$	1.99692	−	5.08807i	0.0690649	−	0.175974i
$837$		0			0
$838$	14.2083	−	6.84234i	0.490816	−	0.236365i
$839$	33.8069	−	16.2805i	1.16714	−	0.562066i	0.253003	−	0.967466i	$-0.418582\pi$
$839$	33.8069	−	16.2805i	1.16714	−	0.562066i	0.914140	+	0.405399i	$0.132868\pi$
$840$		0			0
$841$	−7.52538	+	19.1743i	−0.259496	+	0.661184i
$842$	9.39130	+	0.703781i	0.323646	+	0.0242539i
$843$		0			0
$844$	1.94712	+	0.444418i	0.0670227	+	0.0152975i
$845$	34.7149	−	5.23243i	1.19423	−	0.180001i
$846$		0			0
$847$	−1.40851	+	4.56628i	−0.0483970	+	0.156899i
$848$	−2.03553	+	0.152542i	−0.0699004	+	0.00523831i
$849$		0			0
$850$	0.603164	+	1.95541i	0.0206883	+	0.0670700i
$851$	−6.61397	−	16.8521i	−0.226724	−	0.577683i
$852$		0			0
$853$	0.197287	−	0.341712i	0.00675499	−	0.0117000i	−0.862628	−	0.505839i	$-0.831183\pi$
$853$	0.197287	−	0.341712i	0.00675499	−	0.0117000i	0.869383	+	0.494139i	$0.164516\pi$
$854$	19.2819	+	33.3972i	0.659813	+	1.14283i
$855$		0			0
$856$	−33.1725	+	26.4542i	−1.13381	+	0.904184i
$857$	−6.00750	+	8.81139i	−0.205212	+	0.300991i	−0.915023	−	0.403401i	$-0.867828\pi$
$857$	−6.00750	+	8.81139i	−0.205212	+	0.300991i	0.709811	+	0.704392i	$0.248780\pi$
$858$		0			0
$859$		−	49.0986i		−	1.67522i	−0.546266	−	0.837612i	$-0.683951\pi$
$859$		−	49.0986i		−	1.67522i	0.546266	−	0.837612i	$-0.316049\pi$
$860$	−0.895447	+	21.5526i	−0.0305345	+	0.734938i
$861$		0			0
$862$	3.68720	−	7.65654i	0.125586	−	0.260783i
$863$	0.738118	+	0.503240i	0.0251258	+	0.0171305i	0.575818	−	0.817578i	$-0.304684\pi$
$863$	0.738118	+	0.503240i	0.0251258	+	0.0171305i	−0.550692	+	0.834709i	$0.685636\pi$
$864$		0			0
$865$	0.763777	+	0.823156i	0.0259692	+	0.0279881i
$866$	−23.6256	+	13.6403i	−0.802831	+	0.463515i
$867$		0			0
$868$	−32.2185	+	7.35366i	−1.09357	+	0.249599i
$869$	−43.2481	+	16.9736i	−1.46709	+	0.575790i
$870$		0			0
$871$	−47.1328	+	59.1027i	−1.59703	+	2.00262i
$872$	3.13639	+	41.8522i	0.106211	+	1.41729i
$873$		0			0
$874$	4.72158	−	3.21912i	0.159710	−	0.108888i
$875$	5.22986	+	34.6979i	0.176802	+	1.17300i
$876$		0			0
$877$	−2.73723	−	2.53978i	−0.0924296	−	0.0857621i	0.632605	−	0.774475i	$-0.281986\pi$
$877$	−2.73723	−	2.53978i	−0.0924296	−	0.0857621i	−0.725034	+	0.688713i	$0.758176\pi$
$878$	1.99690	−	26.6467i	0.0673920	−	0.899284i
$879$		0			0
$880$	0.303712	−	2.01500i	0.0102381	−	0.0679256i
$881$	15.8736	+	32.9618i	0.534794	+	1.11051i	0.976929	+	0.213562i	$0.0685067\pi$
$881$	15.8736	+	32.9618i	0.534794	+	1.11051i	−0.442136	+	0.896948i	$0.645779\pi$
$882$		0			0
$883$	4.75887	+	0.717284i	0.160149	+	0.0241385i	0.228627	−	0.973514i	$-0.426576\pi$
$883$	4.75887	+	0.717284i	0.160149	+	0.0241385i	−0.0684784	+	0.997653i	$0.521814\pi$
$884$	−9.75161	−	3.82722i	−0.327982	−	0.128723i
$885$		0			0
$886$	−5.45807	+	5.88240i	−0.183368	+	0.197623i
$887$	−7.92622	+	34.7270i	−0.266136	+	1.16602i	0.648331	+	0.761359i	$0.275467\pi$
$887$	−7.92622	+	34.7270i	−0.266136	+	1.16602i	−0.914467	+	0.404661i	$0.867390\pi$
$888$		0			0
$889$	13.9620	+	20.4785i	0.468271	+	0.686828i
$890$	3.60970	+	1.11344i	0.120997	+	0.0373227i
$891$		0			0
$892$	−13.1867	−	10.5160i	−0.441523	−	0.352103i
$893$	−8.20895	+	2.53212i	−0.274702	+	0.0847343i
$894$		0			0
$895$	9.72772	+	42.6199i	0.325162	+	1.42463i
$896$	−26.6956	−	15.4127i	−0.891836	−	0.514902i
$897$		0			0
$898$	12.9384	−	12.0051i	0.431760	−	0.400614i
$899$	11.7109	+	14.6850i	0.390579	+	0.489771i
$900$		0			0
$901$	12.6979	+	6.11497i	0.423027	+	0.203719i
$902$	−22.7923			−0.758899
$903$		0			0
$904$	−53.6424			−1.78412
$905$	−20.3913	−	9.81994i	−0.677831	−	0.326426i
$906$		0			0
$907$	23.6746	+	29.6870i	0.786101	+	0.985739i	0.999961	+	0.00887508i	$0.00282506\pi$
$907$	23.6746	+	29.6870i	0.786101	+	0.985739i	−0.213860	+	0.976864i	$0.568604\pi$
$908$	8.88248	−	8.24174i	0.294776	−	0.273512i
$909$		0			0
$910$	−38.3353	−	22.1329i	−1.27080	−	0.733698i
$911$	−1.17984	−	5.16922i	−0.0390899	−	0.171264i	0.951615	−	0.307293i	$-0.0994231\pi$
$911$	−1.17984	−	5.16922i	−0.0390899	−	0.171264i	−0.990705	+	0.136029i	$0.956566\pi$
$912$		0			0
$913$	12.3471	−	3.80858i	0.408629	−	0.126045i
$914$	−1.52092	−	1.21289i	−0.0503075	−	0.0401189i
$915$		0			0
$916$	15.9385	+	4.91637i	0.526622	+	0.162441i
$917$	4.92168	+	7.21878i	0.162528	+	0.238385i
$918$		0			0
$919$	−0.0379559	+	0.166296i	−0.00125205	+	0.00548559i	−0.975550	−	0.219777i	$-0.929467\pi$
$919$	−0.0379559	+	0.166296i	−0.00125205	+	0.00548559i	0.974298	+	0.225263i	$0.0723241\pi$
$920$	26.8591	−	28.9472i	0.885517	−	0.954360i
$921$		0			0
$922$	17.6891	+	6.94248i	0.582561	+	0.228638i
$923$	−52.0877	−	7.85095i	−1.71449	−	0.258417i
$924$		0			0
$925$	−2.17183	−	4.50986i	−0.0714094	−	0.148283i
$926$	3.44917	−	22.8838i	0.113347	−	0.752007i
$927$		0			0
$928$	−1.24439	+	16.6052i	−0.0408491	+	0.545094i
$929$	0.290549	+	0.269590i	0.00953259	+	0.00884495i	0.684925	−	0.728614i	$-0.259835\pi$
$929$	0.290549	+	0.269590i	0.00953259	+	0.00884495i	−0.675392	+	0.737459i	$0.736026\pi$
$930$		0			0
$931$	−1.57947	−	10.4791i	−0.0517651	−	0.343439i
$932$	−18.9937	+	12.9497i	−0.622160	+	0.424181i
$933$		0			0
$934$	−0.438969	−	5.85764i	−0.0143635	−	0.191668i
$935$	−8.77222	+	11.0000i	−0.286882	+	0.359739i
$936$		0			0
$937$	11.7203	−	4.59988i	0.382886	−	0.150272i	−0.166088	−	0.986111i	$-0.553114\pi$
$937$	11.7203	−	4.59988i	0.382886	−	0.150272i	0.548974	+	0.835839i	$0.315018\pi$
$938$	47.7320	−	10.8945i	1.55851	−	0.355719i
$939$		0			0
$940$	−20.1243	+	11.6188i	−0.656383	+	0.378963i
$941$	25.0328	+	26.9789i	0.816046	+	0.879488i	0.994530	−	0.104455i	$-0.0333098\pi$
$941$	25.0328	+	26.9789i	0.816046	+	0.879488i	−0.178484	+	0.983943i	$0.557119\pi$
$942$		0			0
$943$	35.5005	+	24.2039i	1.15606	+	0.788186i
$944$	−0.338125	+	0.702123i	−0.0110050	+	0.0228522i
$945$		0			0
$946$	16.4274	−	10.2278i	0.534100	−	0.332534i
$947$			22.6844i			0.737144i	0.929599	+	0.368572i	$0.120153\pi$
$947$			22.6844i			0.737144i	−0.929599	+	0.368572i	$0.879847\pi$
$948$		0			0
$949$	−8.51004	+	12.4819i	−0.276248	+	0.405181i
$950$	1.23534	−	0.985147i	0.0400796	−	0.0319624i
$951$		0			0
$952$	8.66605	+	15.0100i	0.280868	+	0.486478i
$953$	8.59556	−	14.8879i	0.278438	−	0.482268i	−0.692559	−	0.721361i	$-0.743517\pi$
$953$	8.59556	−	14.8879i	0.278438	−	0.482268i	0.970997	+	0.239093i	$0.0768501\pi$
$954$		0			0
$955$	17.0749	+	43.5062i	0.552531	+	1.40783i
$956$	3.43170	+	11.1253i	0.110989	+	0.359818i
$957$		0			0
$958$	−23.2041	+	1.73891i	−0.749691	+	0.0561816i
$959$	13.6572	−	44.2755i	0.441014	−	1.42973i
$960$		0			0
$961$	−10.8674	+	1.63800i	−0.350563	+	0.0528388i
$962$	−13.8553	−	3.16238i	−0.446712	−	0.101959i
$963$		0			0
$964$	13.9635	+	1.04642i	0.449735	+	0.0337030i
$965$	−3.51806	+	8.96386i	−0.113250	+	0.288557i
$966$		0			0
$967$	−14.5026	+	6.98408i	−0.466372	+	0.224593i	−0.652286	−	0.757973i	$-0.726190\pi$
$967$	−14.5026	+	6.98408i	−0.466372	+	0.224593i	0.185914	+	0.982566i	$0.440476\pi$
$968$	−3.01503	+	1.45196i	−0.0969068	+	0.0466678i
$969$		0			0
$970$	15.4189	−	39.2868i	0.495072	−	1.26142i
$971$	17.8911	+	1.34075i	0.574153	+	0.0430268i	0.358643	−	0.933475i	$-0.383240\pi$
$971$	17.8911	+	1.34075i	0.574153	+	0.0430268i	0.215510	+	0.976502i	$0.430859\pi$
$972$		0			0
$973$	18.2318	+	4.16129i	0.584485	+	0.133405i
$974$	−19.5886	+	2.95251i	−0.627660	+	0.0946045i
$975$		0			0
$976$	0.774368	−	2.51044i	0.0247869	−	0.0803572i
$977$	−53.7689	+	4.02943i	−1.72022	+	0.128913i	−0.897925	−	0.440148i	$-0.854926\pi$
$977$	−53.7689	+	4.02943i	−1.72022	+	0.128913i	−0.822296	+	0.569061i	$0.807307\pi$
$978$		0			0
$979$	1.80104	+	5.83881i	0.0575613	+	0.186609i
$980$	−10.4729	−	26.6845i	−0.334545	−	0.852407i
$981$		0			0
$982$	−1.84590	+	3.19720i	−0.0589052	+	0.102027i
$983$	−11.0766	−	19.1852i	−0.353289	−	0.611914i	0.633535	−	0.773714i	$-0.281603\pi$
$983$	−11.0766	−	19.1852i	−0.353289	−	0.611914i	−0.986824	+	0.161800i	$0.948270\pi$
$984$		0			0
$985$	30.1423	−	24.0377i	0.960413	−	0.765903i
$986$	2.17226	−	3.18611i	0.0691787	−	0.101467i
$987$		0			0
$988$			8.08879i			0.257339i
$989$	−36.4480	−	1.51431i	−1.15898	−	0.0481522i
$990$		0			0
$991$	7.69070	−	15.9699i	0.244303	−	0.507301i	−0.742375	−	0.669984i	$-0.766301\pi$
$991$	7.69070	−	15.9699i	0.244303	−	0.507301i	0.986678	+	0.162684i	$0.0520150\pi$
$992$	−30.7578	−	20.9703i	−0.976561	−	0.665808i
$993$		0			0
$994$	23.2047	+	25.0087i	0.736007	+	0.793227i
$995$	−16.4231	+	9.48188i	−0.520647	+	0.300596i
$996$		0			0
$997$	48.0221	−	10.9607i	1.52088	−	0.347130i	0.621187	−	0.783662i	$-0.286651\pi$
$997$	48.0221	−	10.9607i	1.52088	−	0.347130i	0.899689	+	0.436532i	$0.143793\pi$
$998$	8.69939	−	3.41426i	0.275374	−	0.108077i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	387.2.bc.a.233.6	yes	168
3.2	odd	2	inner	387.2.bc.a.233.9	yes	168
43.12	odd	42	inner	387.2.bc.a.98.9	yes	168
129.98	even	42	inner	387.2.bc.a.98.6	✓	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
387.2.bc.a.98.6	✓	168	129.98	even	42	inner
387.2.bc.a.98.9	yes	168	43.12	odd	42	inner
387.2.bc.a.233.6	yes	168	1.1	even	1	trivial
387.2.bc.a.233.9	yes	168	3.2	odd	2	inner

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:	\( N \)	\(=\)	\( 387 = 3^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	387.bc (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.761035 - 0.366495i) q^{2} +(-0.802124 - 1.00583i) q^{4} +(1.87440 - 1.73919i) q^{5} +(3.43303 + 1.98206i) q^{7} +(0.617732 + 2.70646i) q^{8} +O(q^{10})\)	\(q+(-0.761035 - 0.366495i) q^{2} +(-0.802124 - 1.00583i) q^{4} +(1.87440 - 1.73919i) q^{5} +(3.43303 + 1.98206i) q^{7} +(0.617732 + 2.70646i) q^{8} +(-2.06389 + 0.636626i) q^{10} +(-2.73143 - 2.17824i) q^{11} +(4.94040 + 1.52391i) q^{13} +(-1.88624 - 2.76661i) q^{14} +(-0.0507596 + 0.222393i) q^{16} +(1.07126 - 1.15454i) q^{17} +(-1.13205 - 0.444295i) q^{19} +(-3.25283 - 0.490286i) q^{20} +(1.28040 + 2.65878i) q^{22} +(0.829132 - 5.50093i) q^{23} +(0.114947 - 1.53387i) q^{25} +(-3.20131 - 2.97038i) q^{26} +(-0.760095 - 5.04290i) q^{28} +(-2.39492 + 1.63283i) q^{29} +(-0.484250 - 6.46186i) q^{31} +(3.58183 - 4.49147i) q^{32} +(-1.23840 + 0.486036i) q^{34} +(9.88205 - 2.25551i) q^{35} +(2.81825 - 1.62712i) q^{37} +(0.698694 + 0.753013i) q^{38} +(5.86493 + 3.99864i) q^{40} +(-3.35111 + 6.95865i) q^{41} +(-0.707326 - 6.51918i) q^{43} +4.49458i q^{44} +(-2.64706 + 3.88253i) q^{46} +(5.52286 - 4.40433i) q^{47} +(4.35712 + 7.54675i) q^{49} +(-0.649634 + 1.12520i) q^{50} +(-2.43001 - 6.19158i) q^{52} +(2.63759 + 8.55086i) q^{53} +(-8.90818 + 0.667576i) q^{55} +(-3.24368 + 10.5157i) q^{56} +(2.42104 - 0.364914i) q^{58} +(3.33064 + 0.760198i) q^{59} +(-11.4848 - 0.860664i) q^{61} +(-1.99971 + 5.09518i) q^{62} +(-3.96096 + 1.90750i) q^{64} +(11.9107 - 5.73588i) q^{65} +(-5.34188 + 13.6109i) q^{67} +(-2.02056 - 0.151420i) q^{68} +(-8.34722 - 1.90520i) q^{70} +(-10.0748 + 1.51853i) q^{71} +(-0.861270 + 2.79217i) q^{73} +(-2.74112 + 0.205419i) q^{74} +(0.461154 + 1.49503i) q^{76} +(-5.05967 - 12.8918i) q^{77} +(6.64919 - 11.5167i) q^{79} +(0.291639 + 0.505134i) q^{80} +(5.10063 - 4.06761i) q^{82} +(-2.08343 + 3.05583i) q^{83} -4.02720i q^{85} +(-1.85095 + 5.22056i) q^{86} +(4.20804 - 8.73809i) q^{88} +(-1.44507 - 0.985233i) q^{89} +(13.9400 + 15.0238i) q^{91} +(-6.19807 + 3.57846i) q^{92} +(-5.81726 + 1.32775i) q^{94} +(-2.89462 + 1.13606i) q^{95} +(-12.1832 + 15.2773i) q^{97} +(-0.550072 - 7.34020i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q - 24 q^{4} - 6 q^{7}+O(q^{10}) \) 168 * q - 24 * q^4 - 6 * q^7	\( 168 q - 24 q^{4} - 6 q^{7} + 8 q^{10} + 26 q^{13} - 8 q^{16} + 24 q^{19} + 14 q^{25} + 32 q^{31} - 48 q^{34} - 78 q^{37} - 244 q^{40} - 32 q^{43} - 92 q^{46} + 54 q^{49} + 76 q^{52} - 96 q^{55} - 20 q^{58} - 96 q^{64} - 18 q^{67} + 140 q^{70} + 10 q^{73} - 16 q^{76} - 168 q^{88} - 38 q^{91} - 112 q^{94} - 40 q^{97}+O(q^{100}) \) 168 * q - 24 * q^4 - 6 * q^7 + 8 * q^10 + 26 * q^13 - 8 * q^16 + 24 * q^19 + 14 * q^25 + 32 * q^31 - 48 * q^34 - 78 * q^37 - 244 * q^40 - 32 * q^43 - 92 * q^46 + 54 * q^49 + 76 * q^52 - 96 * q^55 - 20 * q^58 - 96 * q^64 - 18 * q^67 + 140 * q^70 + 10 * q^73 - 16 * q^76 - 168 * q^88 - 38 * q^91 - 112 * q^94 - 40 * q^97

Introduction

L-functions

Modular forms

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