LMFDB - Embedded newform 360.2.m.c.179.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(179,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1, 1]))

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

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

chi := DirichletCharacter("360.179");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.m (of order $2$, degree $1$, 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:	$2.87461447277$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 17x^{12} - 104x^{10} + 713x^{8} + 238x^{6} + 1004x^{4} - 152x^{2} + 64 $ x^16 - 17x^12 - 104x^10 + 713x^8 + 238x^6 + 1004x^4 - 152x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			179.12
Root			$0.645096 - 0.854135i$ of defining polynomial
Character	$\chi$	$=$	360.179
Dual form			360.2.m.c.179.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.927153 + 1.06789i) q^{2} +(-0.280776 + 1.98019i) q^{4} +(2.18650 + 0.468213i) q^{5} +3.02045 q^{7} +(-2.37495 + 1.53610i) q^{8} +O(q^{10})$	\(q+(0.927153 + 1.06789i) q^{2} +(-0.280776 + 1.98019i) q^{4} +(2.18650 + 0.468213i) q^{5} +3.02045 q^{7} +(-2.37495 + 1.53610i) q^{8} +(1.52722 + 2.76904i) q^{10} -3.62258i q^{11} -1.69614 q^{13} +(2.80042 + 3.22550i) q^{14} +(-3.84233 - 1.11198i) q^{16} -6.60421 q^{17} +5.12311 q^{19} +(-1.54107 + 4.19823i) q^{20} +(3.86852 - 3.35869i) q^{22} +6.67026i q^{23} +(4.56155 + 2.04750i) q^{25} +(-1.57258 - 1.81129i) q^{26} +(-0.848071 + 5.98107i) q^{28} -6.82867 q^{29} -1.73642i q^{31} +(-2.37495 - 5.13416i) q^{32} +(-6.12311 - 7.05256i) q^{34} +(6.60421 + 1.41421i) q^{35} -0.371834 q^{37} +(4.74990 + 5.47091i) q^{38} +(-5.91205 + 2.24670i) q^{40} -5.83095i q^{41} -5.24477i q^{43} +(7.17341 + 1.01714i) q^{44} +(-7.12311 + 6.18435i) q^{46} +0.525853i q^{47} +2.12311 q^{49} +(2.04276 + 6.76958i) q^{50} +(0.476236 - 3.35869i) q^{52} -10.0054i q^{53} +(1.69614 - 7.92077i) q^{55} +(-7.17341 + 4.63972i) q^{56} +(-6.33122 - 7.29226i) q^{58} -4.86270i q^{59} +(1.85431 - 1.60993i) q^{62} +(3.28078 - 7.29634i) q^{64} +(-3.70861 - 0.794156i) q^{65} -13.4347i q^{67} +(1.85431 - 13.0776i) q^{68} +(4.61288 + 8.36375i) q^{70} +2.45567 q^{71} +14.5845i q^{73} +(-0.344747 - 0.397078i) q^{74} +(-1.43845 + 10.1447i) q^{76} -10.9418i q^{77} +14.1051i q^{79} +(-7.88060 - 4.23038i) q^{80} +(6.22681 - 5.40618i) q^{82} +5.79119 q^{83} +(-14.4401 - 3.09218i) q^{85} +(5.60083 - 4.86270i) q^{86} +(5.56466 + 8.60345i) q^{88} +10.2477i q^{89} -5.12311 q^{91} +(-13.2084 - 1.87285i) q^{92} +(-0.561553 + 0.487546i) q^{94} +(11.2017 + 2.39871i) q^{95} -9.33976i q^{97} +(1.96844 + 2.26724i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 12 q^{4}+O(q^{10}) $ 16 * q + 12 * q^4	$ 16 q + 12 q^{4} - 8 q^{10} - 12 q^{16} + 16 q^{19} + 40 q^{25} - 32 q^{34} - 28 q^{40} - 48 q^{46} - 32 q^{49} + 36 q^{64} + 32 q^{70} - 56 q^{76} - 16 q^{91} + 24 q^{94}+O(q^{100}) $ 16 * q + 12 * q^4 - 8 * q^10 - 12 * q^16 + 16 * q^19 + 40 * q^25 - 32 * q^34 - 28 * q^40 - 48 * q^46 - 32 * q^49 + 36 * q^64 + 32 * q^70 - 56 * q^76 - 16 * q^91 + 24 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$-1$	$-1$	$-1$

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 $

$2$	0.927153	+	1.06789i	0.655596	+	0.755112i
$2$	0.927153	+	1.06789i	0.655596	+	0.755112i
$3$		0			0
$3$		0			0
$4$	−0.280776	+	1.98019i	−0.140388	+	0.990097i
$5$	2.18650	+	0.468213i	0.977832	+	0.209391i
$5$	2.18650	+	0.468213i	0.977832	+	0.209391i
$6$		0			0
$7$	3.02045			1.14162			0.570811	−	0.821081i	$-0.306629\pi$
$7$	3.02045			1.14162			0.570811	+	0.821081i	$0.306629\pi$
$8$	−2.37495	+	1.53610i	−0.839672	+	0.543094i
$9$		0			0
$10$	1.52722	+	2.76904i	0.482949	+	0.875649i
$11$		−	3.62258i		−	1.09225i	−0.837704	−	0.546125i	$-0.816102\pi$
$11$		−	3.62258i		−	1.09225i	0.837704	−	0.546125i	$-0.183898\pi$
$12$		0			0
$13$	−1.69614			−0.470425			−0.235212	−	0.971944i	$-0.575579\pi$
$13$	−1.69614			−0.470425			−0.235212	+	0.971944i	$0.575579\pi$
$14$	2.80042	+	3.22550i	0.748443	+	0.862052i
$15$		0			0
$16$	−3.84233	−	1.11198i	−0.960582	−	0.277996i
$17$	−6.60421			−1.60176			−0.800878	−	0.598828i	$-0.795633\pi$
$17$	−6.60421			−1.60176			−0.800878	+	0.598828i	$0.795633\pi$
$18$		0			0
$19$	5.12311			1.17532			0.587661	−	0.809108i	$-0.300049\pi$
$19$	5.12311			1.17532			0.587661	+	0.809108i	$0.300049\pi$
$20$	−1.54107	+	4.19823i	−0.344594	+	0.938752i
$21$		0			0
$22$	3.86852	−	3.35869i	0.824771	−	0.716074i
$23$			6.67026i			1.39085i	0.718601	+	0.695423i	$0.244783\pi$
$23$			6.67026i			1.39085i	−0.718601	+	0.695423i	$0.755217\pi$
$24$		0			0
$25$	4.56155	+	2.04750i	0.912311	+	0.409499i
$26$	−1.57258	−	1.81129i	−0.308409	−	0.355223i
$27$		0			0
$28$	−0.848071	+	5.98107i	−0.160270	+	1.13032i
$29$	−6.82867			−1.26805			−0.634026	−	0.773312i	$-0.718599\pi$
$29$	−6.82867			−1.26805			−0.634026	+	0.773312i	$0.718599\pi$
$30$		0			0
$31$		−	1.73642i		−	0.311870i	−0.987767	−	0.155935i	$-0.950161\pi$
$31$		−	1.73642i		−	0.311870i	0.987767	−	0.155935i	$-0.0498391\pi$
$32$	−2.37495	−	5.13416i	−0.419836	−	0.907600i
$33$		0			0
$34$	−6.12311	−	7.05256i	−1.05010	−	1.20950i
$35$	6.60421	+	1.41421i	1.11631	+	0.239046i
$36$		0			0
$37$	−0.371834			−0.0611292			−0.0305646	−	0.999533i	$-0.509731\pi$
$37$	−0.371834			−0.0611292			−0.0305646	+	0.999533i	$0.509731\pi$
$38$	4.74990	+	5.47091i	0.770536	+	0.887499i
$39$		0			0
$40$	−5.91205	+	2.24670i	−0.934777	+	0.355235i
$41$		−	5.83095i		−	0.910642i	−0.890327	−	0.455321i	$-0.849525\pi$
$41$		−	5.83095i		−	0.910642i	0.890327	−	0.455321i	$-0.150475\pi$
$42$		0			0
$43$		−	5.24477i		−	0.799819i	−0.916555	−	0.399910i	$-0.869041\pi$
$43$		−	5.24477i		−	0.799819i	0.916555	−	0.399910i	$-0.130959\pi$
$44$	7.17341	+	1.01714i	1.08143	+	0.153339i
$45$		0			0
$46$	−7.12311	+	6.18435i	−1.05024	+	0.911833i
$47$			0.525853i			0.0767035i	0.999264	+	0.0383518i	$0.0122107\pi$
$47$			0.525853i			0.0767035i	−0.999264	+	0.0383518i	$0.987789\pi$
$48$		0			0
$49$	2.12311			0.303301
$50$	2.04276	+	6.76958i	0.288889	+	0.957362i
$51$		0			0
$52$	0.476236	−	3.35869i	0.0660421	−	0.465766i
$53$		−	10.0054i		−	1.37435i	−0.726493	−	0.687173i	$-0.758851\pi$
$53$		−	10.0054i		−	1.37435i	0.726493	−	0.687173i	$-0.241149\pi$
$54$		0			0
$55$	1.69614	−	7.92077i	0.228708	−	1.06804i
$56$	−7.17341	+	4.63972i	−0.958588	+	0.620008i
$57$		0			0
$58$	−6.33122	−	7.29226i	−0.831329	−	0.957521i
$59$		−	4.86270i		−	0.633069i	−0.948581	−	0.316535i	$-0.897481\pi$
$59$		−	4.86270i		−	0.633069i	0.948581	−	0.316535i	$-0.102519\pi$
$60$		0			0
$61$		0			0		1.00000			$0$
$61$		0			0		−1.00000			$\pi$
$62$	1.85431	−	1.60993i	0.235497	−	0.204461i
$63$		0			0
$64$	3.28078	−	7.29634i	0.410097	−	0.912042i
$65$	−3.70861	−	0.794156i	−0.459996	−	0.0985029i
$66$		0			0
$67$		−	13.4347i		−	1.64132i	−0.571420	−	0.820658i	$-0.693607\pi$
$67$		−	13.4347i		−	1.64132i	0.571420	−	0.820658i	$-0.306393\pi$
$68$	1.85431	−	13.0776i	0.224868	−	1.58589i
$69$		0			0
$70$	4.61288	+	8.36375i	0.551345	+	0.999660i
$71$	2.45567			0.291434			0.145717	−	0.989326i	$-0.453451\pi$
$71$	2.45567			0.291434			0.145717	+	0.989326i	$0.453451\pi$
$72$		0			0
$73$			14.5845i			1.70699i	0.521102	+	0.853495i	$0.325521\pi$
$73$			14.5845i			1.70699i	−0.521102	+	0.853495i	$0.674479\pi$
$74$	−0.344747	−	0.397078i	−0.0400760	−	0.0461594i
$75$		0			0
$76$	−1.43845	+	10.1447i	−0.165001	+	1.16368i
$77$		−	10.9418i		−	1.24694i
$78$		0			0
$79$			14.1051i			1.58695i	0.608603	+	0.793475i	$0.291730\pi$
$79$			14.1051i			1.58695i	−0.608603	+	0.793475i	$0.708270\pi$
$80$	−7.88060	−	4.23038i	−0.881078	−	0.472971i
$81$		0			0
$82$	6.22681	−	5.40618i	0.687636	−	0.597013i
$83$	5.79119			0.635666			0.317833	−	0.948147i	$-0.397045\pi$
$83$	5.79119			0.635666			0.317833	+	0.948147i	$0.397045\pi$
$84$		0			0
$85$	−14.4401	−	3.09218i	−1.56625	−	0.335394i
$86$	5.60083	−	4.86270i	0.603953	−	0.524358i
$87$		0			0
$88$	5.56466	+	8.60345i	0.593195	+	0.917131i
$89$			10.2477i			1.08625i	0.839651	+	0.543126i	$0.182760\pi$
$89$			10.2477i			1.08625i	−0.839651	+	0.543126i	$0.817240\pi$
$90$		0			0
$91$	−5.12311			−0.537047
$92$	−13.2084	−	1.87285i	−1.37707	−	0.195258i
$93$		0			0
$94$	−0.561553	+	0.487546i	−0.0579198	+	0.0502865i
$95$	11.2017	+	2.39871i	1.14927	+	0.246102i
$96$		0			0
$97$		−	9.33976i		−	0.948309i	−0.880442	−	0.474154i	$-0.842754\pi$
$97$		−	9.33976i		−	0.948309i	0.880442	−	0.474154i	$-0.157246\pi$
$98$	1.96844	+	2.26724i	0.198843	+	0.229026i
$99$		0			0
$100$	−5.33521	+	8.45787i	−0.533521	+	0.845787i
$101$	4.37300			0.435129			0.217565	−	0.976046i	$-0.430189\pi$
$101$	4.37300			0.435129			0.217565	+	0.976046i	$0.430189\pi$
$102$		0			0
$103$	−8.31768			−0.819565			−0.409782	−	0.912183i	$-0.634395\pi$
$103$	−8.31768			−0.819565			−0.409782	+	0.912183i	$0.634395\pi$
$104$	4.02825	−	2.60545i	0.395002	−	0.255485i
$105$		0			0
$106$	10.6847	−	9.27653i	1.03779	−	0.901016i
$107$	7.41722			0.717050			0.358525	−	0.933520i	$-0.383280\pi$
$107$	7.41722			0.717050			0.358525	+	0.933520i	$0.383280\pi$
$108$		0			0
$109$			9.65719i			0.924991i	0.886622	+	0.462496i	$0.153046\pi$
$109$			9.65719i			0.924991i	−0.886622	+	0.462496i	$0.846954\pi$
$110$	10.0311	−	5.53247i	0.956427	−	0.527501i
$111$		0			0
$112$	−11.6056	−	3.35869i	−1.09662	−	0.317366i
$113$	0.813015			0.0764820			0.0382410	−	0.999269i	$-0.487825\pi$
$113$	0.813015			0.0764820			0.0382410	+	0.999269i	$0.487825\pi$
$114$		0			0
$115$	−3.12311	+	14.5845i	−0.291231	+	1.36001i
$116$	1.91733	−	13.5221i	0.178019	−	1.25549i
$117$		0			0
$118$	5.19283	−	4.50846i	0.478038	−	0.415038i
$119$	−19.9477			−1.82860
$120$		0			0
$121$	−2.12311			−0.193010
$122$		0			0
$123$		0			0
$124$	3.43845	+	0.487546i	0.308782	+	0.0437829i
$125$	9.01516	+	6.61262i	0.806341	+	0.591451i
$126$		0			0
$127$	15.1022			1.34011			0.670054	−	0.742313i	$-0.266271\pi$
$127$	15.1022			1.34011			0.670054	+	0.742313i	$0.266271\pi$
$128$	10.8335	−	3.26131i	0.957552	−	0.288262i
$129$		0			0
$130$	−2.59038	−	4.69669i	−0.227191	−	0.411927i
$131$			6.45101i			0.563627i	0.959469	+	0.281814i	$0.0909360\pi$
$131$			6.45101i			0.563627i	−0.959469	+	0.281814i	$0.909064\pi$
$132$		0			0
$133$	15.4741			1.34177
$134$	14.3468	−	12.4561i	1.23938	−	1.07604i
$135$		0			0
$136$	15.6847	−	10.1447i	1.34495	−	0.869904i
$137$	−6.60421			−0.564235			−0.282118	−	0.959380i	$-0.591037\pi$
$137$	−6.60421			−0.564235			−0.282118	+	0.959380i	$0.591037\pi$
$138$		0			0
$139$	−12.0000			−1.01783			−0.508913	−	0.860818i	$-0.669953\pi$
$139$	−12.0000			−1.01783			−0.508913	+	0.860818i	$0.669953\pi$
$140$	−4.65472	+	12.6805i	−0.393396	+	1.07170i
$141$		0			0
$142$	2.27678	+	2.62238i	0.191063	+	0.220066i
$143$			6.14441i			0.513821i
$144$		0			0
$145$	−14.9309	−	3.19727i	−1.23994	−	0.265519i
$146$	−15.5747	+	13.5221i	−1.28897	+	1.11910i
$147$		0			0
$148$	0.104402	−	0.736303i	0.00858181	−	0.0605238i
$149$	−15.5747			−1.27593			−0.637963	−	0.770067i	$-0.720223\pi$
$149$	−15.5747			−1.27593			−0.637963	+	0.770067i	$0.720223\pi$
$150$		0			0
$151$		−	10.6323i		−	0.865243i	−0.901576	−	0.432622i	$-0.857589\pi$
$151$		−	10.6323i		−	0.865243i	0.901576	−	0.432622i	$-0.142411\pi$
$152$	−12.1671	+	7.86962i	−0.986884	+	0.638310i
$153$		0			0
$154$	11.6847	−	10.1447i	0.941577	−	0.817486i
$155$	0.813015	−	3.79668i	0.0653029	−	0.304957i
$156$		0			0
$157$	−9.06134			−0.723174			−0.361587	−	0.932338i	$-0.617765\pi$
$157$	−9.06134			−0.723174			−0.361587	+	0.932338i	$0.617765\pi$
$158$	−15.0627	+	13.0776i	−1.19833	+	1.04040i
$159$		0			0
$160$	−2.78894	−	12.3378i	−0.220485	−	0.975390i
$161$			20.1472i			1.58782i
$162$		0			0
$163$		−	10.4895i		−	0.821604i	−0.911725	−	0.410802i	$-0.865249\pi$
$163$		−	10.4895i		−	0.821604i	0.911725	−	0.410802i	$-0.134751\pi$
$164$	11.5464	+	1.63719i	0.901623	+	0.127843i
$165$		0			0
$166$	5.36932	+	6.18435i	0.416740	+	0.479999i
$167$		−	4.79741i		−	0.371235i	−0.982622	−	0.185617i	$-0.940571\pi$
$167$		−	4.79741i		−	0.371235i	0.982622	−	0.185617i	$-0.0594285\pi$
$168$		0			0
$169$	−10.1231			−0.778700
$170$	−10.0861	−	18.2873i	−0.773565	−	1.40257i
$171$		0			0
$172$	10.3857	+	1.47261i	0.791898	+	0.112285i
$173$			3.33513i			0.253565i	0.991931	+	0.126783i	$0.0404651\pi$
$173$			3.33513i			0.253565i	−0.991931	+	0.126783i	$0.959535\pi$
$174$		0			0
$175$	13.7779	+	6.18435i	1.04151	+	0.467493i
$176$	−4.02825	+	13.9192i	−0.303641	+	1.04920i
$177$		0			0
$178$	−10.9434	+	9.50117i	−0.820243	+	0.712143i
$179$			20.9413i			1.56523i	0.622506	+	0.782615i	$0.286114\pi$
$179$			20.9413i			1.56523i	−0.622506	+	0.782615i	$0.713886\pi$
$180$		0			0
$181$		−	6.18435i		−	0.459679i	−0.973229	−	0.229840i	$-0.926180\pi$
$181$		−	6.18435i		−	0.459679i	0.973229	−	0.229840i	$-0.0738202\pi$
$182$	−4.74990	−	5.47091i	−0.352086	−	0.405531i
$183$		0			0
$184$	−10.2462	−	15.8415i	−0.755361	−	1.16785i
$185$	−0.813015	−	0.174098i	−0.0597740	−	0.0127999i
$186$		0			0
$187$			23.9243i			1.74952i
$188$	−1.04129	−	0.147647i	−0.0759439	−	0.0107683i
$189$		0			0
$190$	7.82410	+	14.1861i	0.567620	+	1.02917i
$191$	17.4920			1.26568			0.632838	−	0.774284i	$-0.281890\pi$
$191$	17.4920			1.26568			0.632838	+	0.774284i	$0.281890\pi$
$192$		0			0
$193$			15.7343i			1.13258i	0.824206	+	0.566290i	$0.191622\pi$
$193$			15.7343i			1.13258i	−0.824206	+	0.566290i	$0.808378\pi$
$194$	9.97383	−	8.65938i	0.716079	−	0.621707i
$195$		0			0
$196$	−0.596118	+	4.20416i	−0.0425799	+	0.300297i
$197$			24.6929i			1.75930i	0.475623	+	0.879649i	$0.342223\pi$
$197$			24.6929i			1.75930i	−0.475623	+	0.879649i	$0.657777\pi$
$198$		0			0
$199$		−	10.6323i		−	0.753703i	−0.926274	−	0.376851i	$-0.877007\pi$
$199$		−	10.6323i		−	0.753703i	0.926274	−	0.376851i	$-0.122993\pi$
$200$	−13.9786	+	2.14432i	−0.988438	+	0.151626i
$201$		0			0
$202$	4.05444	+	4.66988i	0.285269	+	0.328571i
$203$	−20.6256			−1.44764
$204$		0			0
$205$	2.73013	−	12.7494i	0.190680	−	0.890455i
$206$	−7.71175	−	8.88236i	−0.537303	−	0.618863i
$207$		0			0
$208$	6.51713	+	1.88608i	0.451882	+	0.130776i
$209$		−	18.5589i		−	1.28374i
$210$		0			0
$211$	4.00000			0.275371			0.137686	−	0.990476i	$-0.456034\pi$
$211$	4.00000			0.275371			0.137686	+	0.990476i	$0.456034\pi$
$212$	19.8126	+	2.80928i	1.36074	+	0.192942i
$213$		0			0
$214$	6.87689	+	7.92077i	0.470095	+	0.541453i
$215$	2.45567	−	11.4677i	0.167475	−	0.782089i
$216$		0			0
$217$		−	5.24477i		−	0.356038i
$218$	−10.3128	+	8.95369i	−0.698472	+	0.606420i
$219$		0			0
$220$	15.2084	+	5.58265i	1.02535	+	0.376382i
$221$	11.2017			0.753505
$222$		0			0
$223$	−28.6714			−1.91998			−0.959988	−	0.280040i	$-0.909652\pi$
$223$	−28.6714			−1.91998			−0.959988	+	0.280040i	$0.909652\pi$
$224$	−7.17341	−	15.5075i	−0.479294	−	1.03614i
$225$		0			0
$226$	0.753789	+	0.868210i	0.0501413	+	0.0577525i
$227$	−13.2084			−0.876673			−0.438337	−	0.898811i	$-0.644432\pi$
$227$	−13.2084			−0.876673			−0.438337	+	0.898811i	$0.644432\pi$
$228$		0			0
$229$			22.0259i			1.45551i	0.685836	+	0.727756i	$0.259437\pi$
$229$			22.0259i			1.45551i	−0.685836	+	0.727756i	$0.740563\pi$
$230$	−18.4703	+	10.1869i	−1.21789	+	0.671707i
$231$		0			0
$232$	16.2177	−	10.4895i	1.06475	−	0.688672i
$233$	21.4386			1.40449			0.702246	−	0.711934i	$-0.252181\pi$
$233$	21.4386			1.40449			0.702246	+	0.711934i	$0.252181\pi$
$234$		0			0
$235$	−0.246211	+	1.14978i	−0.0160611	+	0.0750032i
$236$	9.62908	+	1.36533i	0.626800	+	0.0888755i
$237$		0			0
$238$	−18.4945	−	21.3019i	−1.19882	−	1.38080i
$239$	−4.91134			−0.317688			−0.158844	−	0.987304i	$-0.550777\pi$
$239$	−4.91134			−0.317688			−0.158844	+	0.987304i	$0.550777\pi$
$240$		0			0
$241$	−4.00000			−0.257663			−0.128831	−	0.991667i	$-0.541123\pi$
$241$	−4.00000			−0.257663			−0.128831	+	0.991667i	$0.541123\pi$
$242$	−1.96844	−	2.26724i	−0.126536	−	0.145744i
$243$		0			0
$244$		0			0
$245$	4.64217	+	0.994066i	0.296577	+	0.0635086i
$246$		0			0
$247$	−8.68951			−0.552900
$248$	2.66732	+	4.12391i	0.169375	+	0.261869i
$249$		0			0
$250$	1.29688	+	15.7581i	0.0820219	+	0.996631i
$251$			9.27944i			0.585713i	0.956156	+	0.292856i	$0.0946058\pi$
$251$			9.27944i			0.585713i	−0.956156	+	0.292856i	$0.905394\pi$
$252$		0			0
$253$	24.1636			1.51915
$254$	14.0021	+	16.1275i	0.878569	+	1.01193i
$255$		0			0
$256$	13.5270	+	8.54521i	0.845437	+	0.534076i
$257$	12.3954			0.773204			0.386602	−	0.922247i	$-0.373649\pi$
$257$	12.3954			0.773204			0.386602	+	0.922247i	$0.373649\pi$
$258$		0			0
$259$	−1.12311			−0.0697864
$260$	2.61387	−	7.12078i	0.162105	−	0.441612i
$261$		0			0
$262$	−6.88897	+	5.98107i	−0.425602	+	0.369512i
$263$			12.2888i			0.757761i	0.925446	+	0.378881i	$0.123691\pi$
$263$			12.2888i			0.757761i	−0.925446	+	0.378881i	$0.876309\pi$
$264$		0			0
$265$	4.68466	−	21.8768i	0.287776	−	1.34388i
$266$	14.3468	+	16.5246i	0.879660	+	1.01319i
$267$		0			0
$268$	26.6034	+	3.77216i	1.62506	+	0.230421i
$269$	−1.91733			−0.116902			−0.0584508	−	0.998290i	$-0.518616\pi$
$269$	−1.91733			−0.116902			−0.0584508	+	0.998290i	$0.518616\pi$
$270$		0			0
$271$			26.4738i			1.60817i	0.594514	+	0.804085i	$0.297344\pi$
$271$			26.4738i			1.60817i	−0.594514	+	0.804085i	$0.702656\pi$
$272$	25.3755	+	7.34376i	1.53862	+	0.445281i
$273$		0			0
$274$	−6.12311	−	7.05256i	−0.369910	−	0.426061i
$275$	7.41722	−	16.5246i	0.447275	−	0.996471i
$276$		0			0
$277$	11.8730			0.713379			0.356689	−	0.934223i	$-0.383905\pi$
$277$	11.8730			0.713379			0.356689	+	0.934223i	$0.383905\pi$
$278$	−11.1258	−	12.8147i	−0.667283	−	0.768573i
$279$		0			0
$280$	−17.8570	+	6.78605i	−1.06716	+	0.405544i
$281$		−	8.65938i		−	0.516575i	−0.966068	−	0.258288i	$-0.916842\pi$
$281$		−	8.65938i		−	0.516575i	0.966068	−	0.258288i	$-0.0831582\pi$
$282$		0			0
$283$		−	15.7343i		−	0.935307i	−0.883912	−	0.467654i	$-0.845100\pi$
$283$		−	15.7343i		−	0.935307i	0.883912	−	0.467654i	$-0.154900\pi$
$284$	−0.689494	+	4.86270i	−0.0409139	+	0.288548i
$285$		0			0
$286$	−6.56155	+	5.69681i	−0.387993	+	0.336859i
$287$		−	17.6121i		−	1.03961i
$288$		0			0
$289$	26.6155			1.56562
$290$	−10.4289	−	18.9089i	−0.612404	−	1.11037i
$291$		0			0
$292$	−28.8802	−	4.09499i	−1.69008	−	0.239641i
$293$		−	16.9710i		−	0.991454i	−0.868478	−	0.495727i	$-0.834902\pi$
$293$		−	16.9710i		−	0.991454i	0.868478	−	0.495727i	$-0.165098\pi$
$294$		0			0
$295$	2.27678	−	10.6323i	0.132559	−	0.619036i
$296$	0.883088	−	0.571175i	0.0513284	−	0.0331989i
$297$		0			0
$298$	−14.4401	−	16.6320i	−0.836492	−	0.963467i
$299$		−	11.3137i		−	0.654289i
$300$		0			0
$301$		−	15.8415i		−	0.913091i
$302$	11.3541	−	9.85775i	0.653355	−	0.567250i
$303$		0			0
$304$	−19.6847	−	5.69681i	−1.12899	−	0.326734i
$305$		0			0
$306$		0			0
$307$			18.6795i			1.06610i	0.846085	+	0.533048i	$0.178954\pi$
$307$			18.6795i			1.06610i	−0.846085	+	0.533048i	$0.821046\pi$
$308$	21.6669	+	3.07221i	1.23459	+	0.175055i
$309$		0			0
$310$	4.80822	−	2.65189i	0.273089	−	0.150617i
$311$	−22.4033			−1.27038			−0.635188	−	0.772358i	$-0.719077\pi$
$311$	−22.4033			−1.27038			−0.635188	+	0.772358i	$0.719077\pi$
$312$		0			0
$313$		−	21.6247i		−	1.22230i	−0.791514	−	0.611151i	$-0.790707\pi$
$313$		−	21.6247i		−	1.22230i	0.791514	−	0.611151i	$-0.209293\pi$
$314$	−8.40125	−	9.67651i	−0.474110	−	0.546077i
$315$		0			0
$316$	−27.9309	−	3.96039i	−1.57123	−	0.222789i
$317$			0.115279i			0.00647473i	0.999995	+	0.00323737i	$0.00103049\pi$
$317$			0.115279i			0.00647473i	−0.999995	+	0.00323737i	$0.998970\pi$
$318$		0			0
$319$			24.7374i			1.38503i
$320$	10.5897	−	14.4173i	0.591980	−	0.805953i
$321$		0			0
$322$	−21.5150	+	18.6795i	−1.19898	+	1.04097i
$323$	−33.8340			−1.88258
$324$		0			0
$325$	−7.73704	−	3.47284i	−0.429174	−	0.192639i
$326$	11.2017	−	9.72540i	0.620403	−	0.538640i
$327$		0			0
$328$	8.95694	+	13.8482i	0.494564	+	0.764640i
$329$			1.58831i			0.0875664i
$330$		0			0
$331$	23.3693			1.28449			0.642247	−	0.766498i	$-0.278002\pi$
$331$	23.3693			1.28449			0.642247	+	0.766498i	$0.278002\pi$
$332$	−1.62603	+	11.4677i	−0.0892400	+	0.629370i
$333$		0			0
$334$	5.12311	−	4.44793i	0.280324	−	0.243380i
$335$	6.29033	−	29.3751i	0.343677	−	1.60493i
$336$		0			0
$337$			12.2850i			0.669205i	0.942359	+	0.334602i	$0.108602\pi$
$337$			12.2850i			0.669205i	−0.942359	+	0.334602i	$0.891398\pi$
$338$	−9.38566	−	10.8104i	−0.510513	−	0.588006i
$339$		0			0
$340$	10.1775	−	27.7259i	0.551955	−	1.50365i
$341$	−6.29033			−0.340640
$342$		0			0
$343$	−14.7304			−0.795367
$344$	8.05650	+	12.4561i	0.434377	+	0.671586i
$345$		0			0
$346$	−3.56155	+	3.09218i	−0.191470	+	0.166236i
$347$	5.79119			0.310887			0.155444	−	0.987845i	$-0.450319\pi$
$347$	5.79119			0.310887			0.155444	+	0.987845i	$0.450319\pi$
$348$		0			0
$349$		−	6.94568i		−	0.371794i	−0.982569	−	0.185897i	$-0.940481\pi$
$349$		−	6.94568i		−	0.371794i	0.982569	−	0.185897i	$-0.0595190\pi$
$350$	6.17004	+	20.4471i	0.329802	+	1.09295i
$351$		0			0
$352$	−18.5989	+	8.60345i	−0.991326	+	0.458566i
$353$	33.0210			1.75753			0.878766	−	0.477253i	$-0.158367\pi$
$353$	33.0210			1.75753			0.878766	+	0.477253i	$0.158367\pi$
$354$		0			0
$355$	5.36932	+	1.14978i	0.284974	+	0.0610238i
$356$	−20.2924	−	2.87731i	−1.07550	−	0.152497i
$357$		0			0
$358$	−22.3630	+	19.4158i	−1.18192	+	1.02616i
$359$	−19.9477			−1.05280			−0.526399	−	0.850238i	$-0.676458\pi$
$359$	−19.9477			−1.05280			−0.526399	+	0.850238i	$0.676458\pi$
$360$		0			0
$361$	7.24621			0.381380
$362$	6.60421	−	5.73384i	0.347109	−	0.301364i
$363$		0			0
$364$	1.43845	−	10.1447i	0.0753951	−	0.531729i
$365$	−6.82867	+	31.8890i	−0.357429	+	1.66915i
$366$		0			0
$367$	−19.9819			−1.04304			−0.521522	−	0.853238i	$-0.674636\pi$
$367$	−19.9819			−1.04304			−0.521522	+	0.853238i	$0.674636\pi$
$368$	7.41722	−	25.6294i	0.386649	−	1.33602i
$369$		0			0
$370$	−0.567872	−	1.02963i	−0.0295222	−	0.0535277i
$371$		−	30.2208i		−	1.56898i
$372$		0			0
$373$	5.66906			0.293533			0.146766	−	0.989171i	$-0.453113\pi$
$373$	5.66906			0.293533			0.146766	+	0.989171i	$0.453113\pi$
$374$	−25.5485	+	22.1815i	−1.32108	+	1.14698i
$375$		0			0
$376$	−0.807764	−	1.24887i	−0.0416573	−	0.0644058i
$377$	11.5824			0.596523
$378$		0			0
$379$	16.4924			0.847159			0.423579	−	0.905859i	$-0.360773\pi$
$379$	16.4924			0.847159			0.423579	+	0.905859i	$0.360773\pi$
$380$	−7.89506	+	21.5080i	−0.405008	+	1.10333i
$381$		0			0
$382$	16.2177	+	18.6795i	0.829772	+	0.955727i
$383$		−	14.6875i		−	0.750498i	−0.926924	−	0.375249i	$-0.877557\pi$
$383$		−	14.6875i		−	0.750498i	0.926924	−	0.375249i	$-0.122443\pi$
$384$		0			0
$385$	5.12311	−	23.9243i	0.261098	−	1.21929i
$386$	−16.8025	+	14.5881i	−0.855224	+	0.742515i
$387$		0			0
$388$	18.4945	+	2.62238i	0.938917	+	0.133131i
$389$	13.1190			0.665159			0.332580	−	0.943075i	$-0.392081\pi$
$389$	13.1190			0.665159			0.332580	+	0.943075i	$0.392081\pi$
$390$		0			0
$391$		−	44.0518i		−	2.22779i
$392$	−5.04227	+	3.26131i	−0.254673	+	0.164721i
$393$		0			0
$394$	−26.3693	+	22.8941i	−1.32847	+	1.15339i
$395$	−6.60421	+	30.8408i	−0.332294	+	1.55177i
$396$		0			0
$397$	−33.2249			−1.66751			−0.833756	−	0.552134i	$-0.813814\pi$
$397$	−33.2249			−1.66751			−0.833756	+	0.552134i	$0.813814\pi$
$398$	11.3541	−	9.85775i	0.569130	−	0.494124i
$399$		0			0
$400$	−15.2502	−	12.9395i	−0.762510	−	0.646976i
$401$		−	34.4634i		−	1.72102i	−0.509433	−	0.860510i	$-0.670145\pi$
$401$		−	34.4634i		−	1.72102i	0.509433	−	0.860510i	$-0.329855\pi$
$402$		0			0
$403$			2.94521i			0.146712i
$404$	−1.22783	+	8.65938i	−0.0610870	+	0.430820i
$405$		0			0
$406$	−19.1231	−	22.0259i	−0.949064	−	1.09313i
$407$			1.34700i			0.0667683i
$408$		0			0
$409$	−5.12311			−0.253321			−0.126661	−	0.991946i	$-0.540426\pi$
$409$	−5.12311			−0.253321			−0.126661	+	0.991946i	$0.540426\pi$
$410$	16.1462	−	8.90513i	0.797402	−	0.439793i
$411$		0			0
$412$	2.33541	−	16.4706i	0.115057	−	0.811448i
$413$		−	14.6875i		−	0.722726i
$414$		0			0
$415$	12.6624	+	2.71151i	0.621574	+	0.133103i
$416$	4.02825	+	8.70826i	0.197501	+	0.426958i
$417$		0			0
$418$	19.8188	−	17.2069i	0.969371	−	0.841617i
$419$		−	8.38752i		−	0.409757i	−0.978787	−	0.204878i	$-0.934320\pi$
$419$		−	8.38752i		−	0.409757i	0.978787	−	0.204878i	$-0.0656799\pi$
$420$		0			0
$421$			15.0802i			0.734965i	0.930030	+	0.367482i	$0.119780\pi$
$421$			15.0802i			0.734965i	−0.930030	+	0.367482i	$0.880220\pi$
$422$	3.70861	+	4.27156i	0.180532	+	0.207936i
$423$		0			0
$424$	15.3693	+	23.7623i	0.746400	+	1.15400i
$425$	−30.1254	−	13.5221i	−1.46130	−	0.655917i
$426$		0			0
$427$		0			0
$428$	−2.08258	+	14.6875i	−0.100665	+	0.709948i
$429$		0			0
$430$	14.5230	−	8.00990i	0.700361	−	0.386272i
$431$	19.9477			0.960845			0.480422	−	0.877037i	$-0.340483\pi$
$431$	19.9477			0.960845			0.480422	+	0.877037i	$0.340483\pi$
$432$		0			0
$433$			10.4895i			0.504095i	0.967715	+	0.252047i	$0.0811039\pi$
$433$			10.4895i			0.504095i	−0.967715	+	0.252047i	$0.918896\pi$
$434$	5.60083	−	4.86270i	0.268849	−	0.233417i
$435$		0			0
$436$	−19.1231	−	2.71151i	−0.915831	−	0.129858i
$437$			34.1725i			1.63469i
$438$		0			0
$439$		−	23.0010i		−	1.09778i	−0.835895	−	0.548889i	$-0.815051\pi$
$439$		−	23.0010i		−	1.09778i	0.835895	−	0.548889i	$-0.184949\pi$
$440$	8.13887	+	21.4169i	0.388005	+	1.02101i
$441$		0			0
$442$	10.3857	+	11.9621i	0.493995	+	0.568981i
$443$	−1.62603			−0.0772550			−0.0386275	−	0.999254i	$-0.512299\pi$
$443$	−1.62603			−0.0772550			−0.0386275	+	0.999254i	$0.512299\pi$
$444$		0			0
$445$	−4.79810	+	22.4066i	−0.227452	+	1.06217i
$446$	−26.5827	−	30.6179i	−1.25873	−	1.44980i
$447$		0			0
$448$	9.90941	−	22.0382i	0.468176	−	1.04121i
$449$			9.89949i			0.467186i	0.972334	+	0.233593i	$0.0750483\pi$
$449$			9.89949i			0.467186i	−0.972334	+	0.233593i	$0.924952\pi$
$450$		0			0
$451$	−21.1231			−0.994648
$452$	−0.228275	+	1.60993i	−0.0107372	+	0.0757246i
$453$		0			0
$454$	−12.2462	−	14.1051i	−0.574743	−	0.661986i
$455$	−11.2017	−	2.39871i	−0.525142	−	0.112453i
$456$		0			0
$457$		−	19.8293i		−	0.927575i	−0.885946	−	0.463788i	$-0.846490\pi$
$457$		−	19.8293i		−	0.927575i	0.885946	−	0.463788i	$-0.153510\pi$
$458$	−23.5212	+	20.4214i	−1.09907	+	0.954228i
$459$		0			0
$460$	−28.0033	−	10.2793i	−1.30566	−	0.479277i
$461$	−15.5747			−0.725384			−0.362692	−	0.931909i	$-0.618142\pi$
$461$	−15.5747			−0.725384			−0.362692	+	0.931909i	$0.618142\pi$
$462$		0			0
$463$	17.7509			0.824952			0.412476	−	0.910968i	$-0.364664\pi$
$463$	17.7509			0.824952			0.412476	+	0.910968i	$0.364664\pi$
$464$	26.2380	+	7.59336i	1.21807	+	0.352513i
$465$		0			0
$466$	19.8769	+	22.8941i	0.920779	+	1.06055i
$467$	28.0429			1.29767			0.648834	−	0.760930i	$-0.275257\pi$
$467$	28.0429			1.29767			0.648834	+	0.760930i	$0.275257\pi$
$468$		0			0
$469$		−	40.5790i		−	1.87376i
$470$	−1.45611	+	0.803092i	−0.0671653	+	0.0370439i
$471$		0			0
$472$	7.46960	+	11.5487i	0.343816	+	0.531570i
$473$	−18.9996			−0.873603
$474$		0			0
$475$	23.3693	+	10.4895i	1.07226	+	0.481293i
$476$	5.60083	−	39.5002i	0.256714	−	1.81049i
$477$		0			0
$478$	−4.55356	−	5.24477i	−0.208275	−	0.239890i
$479$	37.4396			1.71066			0.855331	−	0.518083i	$-0.173354\pi$
$479$	37.4396			1.71066			0.855331	+	0.518083i	$0.173354\pi$
$480$		0			0
$481$	0.630683			0.0287567
$482$	−3.70861	−	4.27156i	−0.168923	−	0.194564i
$483$		0			0
$484$	0.596118	−	4.20416i	0.0270963	−	0.191098i
$485$	4.37300	−	20.4214i	0.198568	−	0.927286i
$486$		0			0
$487$	4.50778			0.204267			0.102134	−	0.994771i	$-0.467433\pi$
$487$	4.50778			0.204267			0.102134	+	0.994771i	$0.467433\pi$
$488$		0			0
$489$		0			0
$490$	3.24244	+	5.87897i	0.146479	+	0.265585i
$491$			10.5196i			0.474741i	0.971419	+	0.237370i	$0.0762855\pi$
$491$			10.5196i			0.474741i	−0.971419	+	0.237370i	$0.923714\pi$
$492$		0			0
$493$	45.0979			2.03111
$494$	−8.05650	−	9.27944i	−0.362479	−	0.417502i
$495$		0			0
$496$	−1.93087	+	6.67190i	−0.0866986	+	0.299577i
$497$	7.41722			0.332708
$498$		0			0
$499$	25.1231			1.12466			0.562332	−	0.826911i	$-0.309904\pi$
$499$	25.1231			1.12466			0.562332	+	0.826911i	$0.309904\pi$
$500$	−15.6255	+	15.9951i	−0.698794	+	0.715323i
$501$		0			0
$502$	−9.90941	+	8.60345i	−0.442279	+	0.383991i
$503$			16.5604i			0.738391i	0.929352	+	0.369195i	$0.120367\pi$
$503$			16.5604i			0.738391i	−0.929352	+	0.369195i	$0.879633\pi$
$504$		0			0
$505$	9.56155	+	2.04750i	0.425484	+	0.0911123i
$506$	22.4033	+	25.8040i	0.995949	+	1.14713i
$507$		0			0
$508$	−4.24035	+	29.9054i	−0.188135	+	1.32684i
$509$	4.37300			0.193830			0.0969148	−	0.995293i	$-0.469103\pi$
$509$	4.37300			0.193830			0.0969148	+	0.995293i	$0.469103\pi$
$510$		0			0
$511$			44.0518i			1.94874i
$512$	3.41624	+	22.3680i	0.150978	+	0.988537i
$513$		0			0
$514$	11.4924	+	13.2369i	0.506909	+	0.583855i
$515$	−18.1866	−	3.89445i	−0.801397	−	0.171610i
$516$		0			0
$517$	1.90495			0.0837794
$518$	−1.04129	−	1.19935i	−0.0457517	−	0.0526965i
$519$		0			0
$520$	10.0277	−	3.81073i	0.439742	−	0.167111i
$521$			14.3162i			0.627206i	0.949554	+	0.313603i	$0.101536\pi$
$521$			14.3162i			0.627206i	−0.949554	+	0.313603i	$0.898464\pi$
$522$		0			0
$523$		−	18.6795i		−	0.816798i	−0.912803	−	0.408399i	$-0.866087\pi$
$523$		−	18.6795i		−	0.816798i	0.912803	−	0.408399i	$-0.133913\pi$
$524$	−12.7742	−	1.81129i	−0.558045	−	0.0791266i
$525$		0			0
$526$	−13.1231	+	11.3936i	−0.572195	+	0.496785i
$527$			11.4677i			0.499540i
$528$		0			0
$529$	−21.4924			−0.934453
$530$	27.7054	−	15.2804i	1.20344	−	0.663739i
$531$		0			0
$532$	−4.34475	+	30.6417i	−0.188369	+	1.32848i
$533$			9.89012i			0.428389i
$534$		0			0
$535$	16.2177	+	3.47284i	0.701154	+	0.150144i
$536$	20.6372	+	31.9069i	0.891389	+	1.37817i
$537$		0			0
$538$	−1.77766	−	2.04750i	−0.0766402	−	0.0882738i
$539$		−	7.69113i		−	0.331280i
$540$		0			0
$541$			37.8674i			1.62805i	0.580831	+	0.814024i	$0.302728\pi$
$541$			37.8674i			1.62805i	−0.580831	+	0.814024i	$0.697272\pi$
$542$	−28.2711	+	24.5453i	−1.21435	+	1.05431i
$543$		0			0
$544$	15.6847	+	33.9071i	0.672474	+	1.45375i
$545$	−4.52162	+	21.1154i	−0.193685	+	0.904486i
$546$		0			0
$547$			32.1143i			1.37311i	0.727079	+	0.686553i	$0.240877\pi$
$547$			32.1143i			1.37311i	−0.727079	+	0.686553i	$0.759123\pi$
$548$	1.85431	−	13.0776i	0.0792120	−	0.558647i
$549$		0			0
$550$	24.5233	−	7.40005i	1.04568	−	0.315539i
$551$	−34.9840			−1.49037
$552$		0			0
$553$			42.6038i			1.81170i
$554$	11.0081	+	12.6790i	0.467688	+	0.538681i
$555$		0			0
$556$	3.36932	−	23.7623i	0.142891	−	1.00775i
$557$		−	9.18425i		−	0.389149i	−0.980888	−	0.194575i	$-0.937667\pi$
$557$		−	9.18425i		−	0.389149i	0.980888	−	0.194575i	$-0.0623326\pi$
$558$		0			0
$559$			8.89586i			0.376255i
$560$	−23.8029	−	12.7776i	−1.00586	−	0.539954i
$561$		0			0
$562$	9.24726	−	8.02857i	0.390072	−	0.338665i
$563$	−5.79119			−0.244070			−0.122035	−	0.992526i	$-0.538942\pi$
$563$	−5.79119			−0.244070			−0.122035	+	0.992526i	$0.538942\pi$
$564$		0			0
$565$	1.77766	+	0.380664i	0.0747865	+	0.0160147i
$566$	16.8025	−	14.5881i	0.706262	−	0.613183i
$567$		0			0
$568$	−5.83209	+	3.77216i	−0.244709	+	0.158276i
$569$			6.72287i			0.281837i	0.990021	+	0.140919i	$0.0450056\pi$
$569$			6.72287i			0.281837i	−0.990021	+	0.140919i	$0.954994\pi$
$570$		0			0
$571$	−23.8617			−0.998583			−0.499291	−	0.866434i	$-0.666406\pi$
$571$	−23.8617			−0.998583			−0.499291	+	0.866434i	$0.666406\pi$
$572$	−12.1671	−	1.72521i	−0.508733	−	0.0721345i
$573$		0			0
$574$	18.8078	−	16.3291i	0.785021	−	0.681563i
$575$	−13.6573	+	30.4268i	−0.569550	+	1.26888i
$576$		0			0
$577$			5.24477i			0.218342i	0.994023	+	0.109171i	$0.0348197\pi$
$577$			5.24477i			0.218342i	−0.994023	+	0.109171i	$0.965180\pi$
$578$	24.6767	+	28.4224i	1.02641	+	1.18222i
$579$		0			0
$580$	10.5235	−	28.6683i	0.436963	−	1.19039i
$581$	17.4920			0.725690
$582$		0			0
$583$	−36.2454			−1.50113
$584$	−22.4033	−	34.6375i	−0.927056	−	1.43331i
$585$		0			0
$586$	18.1231	−	15.7347i	0.748659	−	0.649993i
$587$	−7.41722			−0.306141			−0.153071	−	0.988215i	$-0.548916\pi$
$587$	−7.41722			−0.306141			−0.153071	+	0.988215i	$0.548916\pi$
$588$		0			0
$589$		−	8.89586i		−	0.366548i
$590$	13.4650	−	7.42640i	0.554346	−	0.305740i
$591$		0			0
$592$	1.42871	+	0.413473i	0.0587196	+	0.0169936i
$593$	−23.9778			−0.984649			−0.492325	−	0.870412i	$-0.663853\pi$
$593$	−23.9778			−0.984649			−0.492325	+	0.870412i	$0.663853\pi$
$594$		0			0
$595$	−43.6155	−	9.33976i	−1.78806	−	0.382893i
$596$	4.37300	−	30.8408i	0.179125	−	1.26329i
$597$		0			0
$598$	12.0818	−	10.4895i	0.494061	−	0.428949i
$599$	29.7703			1.21638			0.608191	−	0.793790i	$-0.291895\pi$
$599$	29.7703			1.21638			0.608191	+	0.793790i	$0.291895\pi$
$600$		0			0
$601$	1.36932			0.0558556			0.0279278	−	0.999610i	$-0.491109\pi$
$601$	1.36932			0.0558556			0.0279278	+	0.999610i	$0.491109\pi$
$602$	16.9170	−	14.6875i	0.689486	−	0.598619i
$603$		0			0
$604$	21.0540	+	2.98529i	0.856674	+	0.121470i
$605$	−4.64217	−	0.994066i	−0.188731	−	0.0404145i
$606$		0			0
$607$	43.4018			1.76162			0.880812	−	0.473467i	$-0.156998\pi$
$607$	43.4018			1.76162			0.880812	+	0.473467i	$0.156998\pi$
$608$	−12.1671	−	26.3029i	−0.493442	−	1.06672i
$609$		0			0
$610$		0			0
$611$		−	0.891921i		−	0.0360832i
$612$		0			0
$613$	−22.6305			−0.914036			−0.457018	−	0.889457i	$-0.651083\pi$
$613$	−22.6305			−0.914036			−0.457018	+	0.889457i	$0.651083\pi$
$614$	−19.9477	+	17.3188i	−0.805022	+	0.698928i
$615$		0			0
$616$	16.8078	+	25.9863i	0.677204	+	1.04702i
$617$	−12.3954			−0.499020			−0.249510	−	0.968372i	$-0.580270\pi$
$617$	−12.3954			−0.499020			−0.249510	+	0.968372i	$0.580270\pi$
$618$		0			0
$619$	−30.7386			−1.23549			−0.617745	−	0.786378i	$-0.711954\pi$
$619$	−30.7386			−1.23549			−0.617745	+	0.786378i	$0.711954\pi$
$620$	7.28988	+	2.67594i	0.292769	+	0.107469i
$621$		0			0
$622$	−20.7713	−	23.9243i	−0.832853	−	0.959276i
$623$			30.9526i			1.24009i
$624$		0			0
$625$	16.6155	+	18.6795i	0.664621	+	0.747181i
$626$	23.0928	−	20.0494i	0.922975	−	0.801336i
$627$		0			0
$628$	2.54421	−	17.9432i	0.101525	−	0.716012i
$629$	2.45567			0.0979139
$630$		0			0
$631$		−	10.6323i		−	0.423265i	−0.977349	−	0.211632i	$-0.932122\pi$
$631$		−	10.6323i		−	0.423265i	0.977349	−	0.211632i	$-0.0678779\pi$
$632$	−21.6669	−	33.4990i	−0.861864	−	1.33252i
$633$		0			0
$634$	−0.123106	+	0.106882i	−0.00488915	+	0.00424481i
$635$	33.0210	+	7.07107i	1.31040	+	0.280607i
$636$		0			0
$637$	−3.60109			−0.142680
$638$	−26.4168	+	22.9354i	−1.04585	+	0.908019i
$639$		0			0
$640$	25.2143	−	2.05848i	0.996684	−	0.0813685i
$641$			7.07107i			0.279290i	0.990202	+	0.139645i	$0.0445962\pi$
$641$			7.07107i			0.279290i	−0.990202	+	0.139645i	$0.955404\pi$
$642$		0			0
$643$		−	37.3590i		−	1.47330i	−0.676276	−	0.736648i	$-0.736407\pi$
$643$		−	37.3590i		−	1.47330i	0.676276	−	0.736648i	$-0.263593\pi$
$644$	−39.8953	−	5.65685i	−1.57210	−	0.222911i
$645$		0			0
$646$	−31.3693	−	36.1310i	−1.23421	−	1.42156i
$647$			4.27156i			0.167932i	0.996469	+	0.0839661i	$0.0267588\pi$
$647$			4.27156i			0.167932i	−0.996469	+	0.0839661i	$0.973241\pi$
$648$		0			0
$649$	−17.6155			−0.691470
$650$	−3.46480	−	11.4822i	−0.135901	−	0.450367i
$651$		0			0
$652$	20.7713	+	2.94521i	0.813467	+	0.115343i
$653$		−	10.5312i		−	0.412120i	−0.978539	−	0.206060i	$-0.933936\pi$
$653$		−	10.5312i		−	0.412120i	0.978539	−	0.206060i	$-0.0660641\pi$
$654$		0			0
$655$	−3.02045	+	14.1051i	−0.118019	+	0.551133i
$656$	−6.48392	+	22.4044i	−0.253155	+	0.874746i
$657$		0			0
$658$	−1.69614	+	1.47261i	−0.0661225	+	0.0574082i
$659$			27.4901i			1.07086i	0.844579	+	0.535431i	$0.179851\pi$
$659$			27.4901i			1.07086i	−0.844579	+	0.535431i	$0.820149\pi$
$660$		0			0
$661$		−	33.6333i		−	1.30818i	−0.756416	−	0.654091i	$-0.773051\pi$
$661$		−	33.6333i		−	1.30818i	0.756416	−	0.654091i	$-0.226949\pi$
$662$	21.6669	+	24.9559i	0.842109	+	0.969937i
$663$		0			0
$664$	−13.7538	+	8.89586i	−0.533751	+	0.345226i
$665$	33.8340	+	7.24517i	1.31203	+	0.280955i
$666$		0			0
$667$		−	45.5490i		−	1.76366i
$668$	9.49980	+	1.34700i	0.367558	+	0.0521170i
$669$		0			0
$670$	37.2014	−	20.5178i	1.43722	−	0.792671i
$671$		0			0
$672$		0			0
$673$		0			0		1.00000			$0$
$673$		0			0		−1.00000			$\pi$
$674$	−13.1190	+	11.3900i	−0.505325	+	0.438728i
$675$		0			0
$676$	2.84233	−	20.0457i	0.109320	−	0.770989i
$677$		−	44.7037i		−	1.71810i	−0.511889	−	0.859052i	$-0.671054\pi$
$677$		−	44.7037i		−	1.71810i	0.511889	−	0.859052i	$-0.328946\pi$
$678$		0			0
$679$		−	28.2102i		−	1.08261i
$680$	39.0444	−	14.8377i	1.49728	−	0.569000i
$681$		0			0
$682$	−5.83209	−	6.71737i	−0.223322	−	0.257222i
$683$	32.2080			1.23241			0.616203	−	0.787588i	$-0.288670\pi$
$683$	32.2080			1.23241			0.616203	+	0.787588i	$0.288670\pi$
$684$		0			0
$685$	−14.4401	−	3.09218i	−0.551727	−	0.118146i
$686$	−13.6573	−	15.7304i	−0.521439	−	0.600591i
$687$		0			0
$688$	−5.83209	+	20.1521i	−0.222346	+	0.768292i
$689$			16.9706i			0.646527i
$690$		0			0
$691$	−14.8769			−0.565944			−0.282972	−	0.959128i	$-0.591320\pi$
$691$	−14.8769			−0.565944			−0.282972	+	0.959128i	$0.591320\pi$
$692$	−6.60421	−	0.936426i	−0.251054	−	0.0355976i
$693$		0			0
$694$	5.36932	+	6.18435i	0.203816	+	0.234755i
$695$	−26.2380	−	5.61856i	−0.995263	−	0.213124i
$696$		0			0
$697$			38.5088i			1.45862i
$698$	7.41722	−	6.43971i	0.280746	−	0.243746i
$699$		0			0
$700$	−16.1147	+	25.5465i	−0.609080	+	0.965569i
$701$	−9.28434			−0.350665			−0.175332	−	0.984509i	$-0.556100\pi$
$701$	−9.28434			−0.350665			−0.175332	+	0.984509i	$0.556100\pi$
$702$		0			0
$703$	−1.90495			−0.0718464
$704$	−26.4316	−	11.8849i	−0.996178	−	0.447928i
$705$		0			0
$706$	30.6155	+	35.2628i	1.15223	+	1.32713i
$707$	13.2084			0.496753
$708$		0			0
$709$			15.0802i			0.566349i	0.959068	+	0.283175i	$0.0913876\pi$
$709$			15.0802i			0.566349i	−0.959068	+	0.283175i	$0.908612\pi$
$710$	3.75034	+	6.79986i	0.140748	+	0.255194i
$711$		0			0
$712$	−15.7415	−	24.3378i	−0.589938	−	0.912096i
$713$	11.5824			0.433764
$714$		0			0
$715$	−2.87689	+	13.4347i	−0.107590	+	0.502431i
$716$	−41.4679	−	5.87983i	−1.54973	−	0.219740i
$717$		0			0
$718$	−18.4945	−	21.3019i	−0.690209	−	0.794980i
$719$	47.2623			1.76259			0.881294	−	0.472569i	$-0.156673\pi$
$719$	47.2623			1.76259			0.881294	+	0.472569i	$0.156673\pi$
$720$		0			0
$721$	−25.1231			−0.935633
$722$	6.71834	+	7.73815i	0.250031	+	0.287984i
$723$		0			0
$724$	12.2462	+	1.73642i	0.455127	+	0.0645335i
$725$	−31.1493	−	13.9817i	−1.15686	−	0.519266i
$726$		0			0
$727$	−5.66906			−0.210254			−0.105127	−	0.994459i	$-0.533525\pi$
$727$	−5.66906			−0.210254			−0.105127	+	0.994459i	$0.533525\pi$
$728$	12.1671	−	7.86962i	0.450943	−	0.291667i
$729$		0			0
$730$	−40.3852	+	22.2737i	−1.49472	+	0.824388i
$731$			34.6375i			1.28111i
$732$		0			0
$733$	−23.9548			−0.884790			−0.442395	−	0.896820i	$-0.645871\pi$
$733$	−23.9548			−0.884790			−0.442395	+	0.896820i	$0.645871\pi$
$734$	−18.5262	−	21.3384i	−0.683816	−	0.787615i
$735$		0			0
$736$	34.2462	−	15.8415i	1.26233	−	0.583927i
$737$	−48.6685			−1.79273
$738$		0			0
$739$	−5.61553			−0.206571			−0.103285	−	0.994652i	$-0.532935\pi$
$739$	−5.61553			−0.206571			−0.103285	+	0.994652i	$0.532935\pi$
$740$	0.573022	−	1.56104i	0.0210647	−	0.0573851i
$741$		0			0
$742$	32.2725	−	28.0193i	1.18476	−	1.02862i
$743$		−	14.6875i		−	0.538833i	−0.963024	−	0.269417i	$-0.913169\pi$
$743$		−	14.6875i		−	0.538833i	0.963024	−	0.269417i	$-0.0868308\pi$
$744$		0			0
$745$	−34.0540	−	7.29226i	−1.24764	−	0.267168i
$746$	5.25608	+	6.05393i	0.192439	+	0.221650i
$747$		0			0
$748$	−47.3747	−	6.71737i	−1.73219	−	0.245611i
$749$	22.4033			0.818600
$750$		0			0
$751$		−	8.68210i		−	0.316814i	−0.987374	−	0.158407i	$-0.949364\pi$
$751$		−	8.68210i		−	0.316814i	0.987374	−	0.158407i	$-0.0506359\pi$
$752$	0.584739	−	2.02050i	0.0213233	−	0.0736800i
$753$		0			0
$754$	10.7386	+	12.3687i	0.391078	+	0.450442i
$755$	4.97818	−	23.2475i	0.181174	−	0.846062i
$756$		0			0
$757$	−1.69614			−0.0616473			−0.0308236	−	0.999525i	$-0.509813\pi$
$757$	−1.69614			−0.0616473			−0.0308236	+	0.999525i	$0.509813\pi$
$758$	15.2910	+	17.6121i	0.555394	+	0.639700i
$759$		0			0
$760$	−30.2881	+	11.5101i	−1.09866	+	0.417515i
$761$			32.3314i			1.17201i	0.810307	+	0.586006i	$0.199300\pi$
$761$			32.3314i			1.17201i	−0.810307	+	0.586006i	$0.800700\pi$
$762$		0			0
$763$			29.1690i			1.05599i
$764$	−4.91134	+	34.6375i	−0.177686	+	1.25314i
$765$		0			0
$766$	15.6847	−	13.6176i	0.566710	−	0.492023i
$767$			8.24782i			0.297812i
$768$		0			0
$769$	−15.6155			−0.563110			−0.281555	−	0.959545i	$-0.590850\pi$
$769$	−15.6155			−0.563110			−0.281555	+	0.959545i	$0.590850\pi$
$770$	30.2984	−	16.7105i	1.09188	−	0.602206i
$771$		0			0
$772$	−31.1570	−	4.41782i	−1.12136	−	0.159001i
$773$		−	16.1498i		−	0.580868i	−0.956895	−	0.290434i	$-0.906200\pi$
$773$		−	16.1498i		−	0.580868i	0.956895	−	0.290434i	$-0.0937997\pi$
$774$		0			0
$775$	3.55531	−	7.92077i	0.127711	−	0.284523i
$776$	14.3468	+	22.1815i	0.515021	+	0.796268i
$777$		0			0
$778$	12.1633	+	14.0096i	0.436076	+	0.502270i
$779$		−	29.8726i		−	1.07030i
$780$		0			0
$781$		−	8.89586i		−	0.318319i
$782$	47.0425	−	40.8427i	1.68223	−	1.46053i
$783$		0			0
$784$	−8.15767	−	2.36086i	−0.291345	−	0.0843163i
$785$	−19.8126	−	4.24264i	−0.707143	−	0.151426i
$786$		0			0
$787$		−	8.18998i		−	0.291941i	−0.989289	−	0.145971i	$-0.953369\pi$
$787$		−	8.18998i		−	0.291941i	0.989289	−	0.145971i	$-0.0466305\pi$
$788$	−48.8968	−	6.93319i	−1.74187	−	0.246985i
$789$		0			0
$790$	−39.0577	+	21.5416i	−1.38961	+	0.766416i
$791$	2.45567			0.0873135
$792$		0			0
$793$		0			0
$794$	−30.8046	−	35.4806i	−1.09321	−	1.25916i
$795$		0			0
$796$	21.0540	+	2.98529i	0.746238	+	0.105811i
$797$		−	24.1671i		−	0.856042i	−0.903769	−	0.428021i	$-0.859211\pi$
$797$		−	24.1671i		−	0.856042i	0.903769	−	0.428021i	$-0.140789\pi$
$798$		0			0
$799$		−	3.47284i		−	0.122860i
$800$	−0.321291	−	28.2824i	−0.0113593	−	0.999935i
$801$		0			0
$802$	36.8031	−	31.9528i	1.29956	−	1.12829i
$803$	52.8336			1.86446
$804$		0			0
$805$	−9.43318	+	44.0518i	−0.332476	+	1.55262i
$806$	−3.14516	+	2.73066i	−0.110784	+	0.0961835i
$807$		0			0
$808$	−10.3857	+	6.71737i	−0.365366	+	0.236316i
$809$		−	37.6400i		−	1.32335i	−0.749789	−	0.661677i	$-0.769845\pi$
$809$		−	37.6400i		−	1.32335i	0.749789	−	0.661677i	$-0.230155\pi$
$810$		0			0
$811$	49.4773			1.73738			0.868691	−	0.495354i	$-0.164962\pi$
$811$	49.4773			1.73738			0.868691	+	0.495354i	$0.164962\pi$
$812$	5.79119	−	40.8427i	0.203231	−	1.43330i
$813$		0			0
$814$	−1.43845	+	1.24887i	−0.0504175	+	0.0437730i
$815$	4.91134	−	22.9354i	0.172037	−	0.803390i
$816$		0			0
$817$		−	26.8695i		−	0.940045i
$818$	−4.74990	−	5.47091i	−0.166076	−	0.191286i
$819$		0			0
$820$	24.4797	+	8.98590i	0.854867	+	0.313801i
$821$	−37.9780			−1.32544			−0.662720	−	0.748867i	$-0.730598\pi$
$821$	−37.9780			−1.32544			−0.662720	+	0.748867i	$0.730598\pi$
$822$		0			0
$823$	32.0636			1.11767			0.558834	−	0.829279i	$-0.311249\pi$
$823$	32.0636			1.11767			0.558834	+	0.829279i	$0.311249\pi$
$824$	19.7541	−	12.7768i	0.688165	−	0.445101i
$825$		0			0
$826$	15.6847	−	13.6176i	0.545739	−	0.473816i
$827$	−4.16516			−0.144837			−0.0724184	−	0.997374i	$-0.523072\pi$
$827$	−4.16516			−0.144837			−0.0724184	+	0.997374i	$0.523072\pi$
$828$		0			0
$829$		−	6.18435i		−	0.214791i	−0.994216	−	0.107396i	$-0.965749\pi$
$829$		−	6.18435i		−	0.214791i	0.994216	−	0.107396i	$-0.0342512\pi$
$830$	8.84441	+	16.0361i	0.306994	+	0.556620i
$831$		0			0
$832$	−5.56466	+	12.3756i	−0.192920	+	0.429047i
$833$	−14.0214			−0.485814
$834$		0			0
$835$	2.24621	−	10.4895i	0.0777333	−	0.363005i
$836$	36.7502	+	5.21089i	1.27103	+	0.180223i
$837$		0			0
$838$	8.95694	−	7.77651i	0.309412	−	0.268635i
$839$	−15.0363			−0.519111			−0.259556	−	0.965728i	$-0.583576\pi$
$839$	−15.0363			−0.519111			−0.259556	+	0.965728i	$0.583576\pi$
$840$		0			0
$841$	17.6307			0.607955
$842$	−16.1040	+	13.9817i	−0.554981	+	0.481840i
$843$		0			0
$844$	−1.12311	+	7.92077i	−0.0386589	+	0.272644i
$845$	−22.1342	−	4.73977i	−0.761438	−	0.163053i
$846$		0			0
$847$	−6.41273			−0.220344
$848$	−11.1258	+	38.4440i	−0.382063	+	1.32017i
$849$		0			0
$850$	−13.4908	−	44.7077i	−0.462730	−	1.53346i
$851$		−	2.48023i		−	0.0850213i
$852$		0			0
$853$	−22.3044			−0.763689			−0.381844	−	0.924227i	$-0.624711\pi$
$853$	−22.3044			−0.763689			−0.381844	+	0.924227i	$0.624711\pi$
$854$		0			0
$855$		0			0
$856$	−17.6155	+	11.3936i	−0.602086	+	0.389426i
$857$	−10.7694			−0.367875			−0.183937	−	0.982938i	$-0.558884\pi$
$857$	−10.7694			−0.367875			−0.183937	+	0.982938i	$0.558884\pi$
$858$		0			0
$859$	−50.2462			−1.71438			−0.857189	−	0.515001i	$-0.827791\pi$
$859$	−50.2462			−1.71438			−0.857189	+	0.515001i	$0.827791\pi$
$860$	22.0187	+	8.08255i	0.750832	+	0.275613i
$861$		0			0
$862$	18.4945	+	21.3019i	0.629926	+	0.725545i
$863$		−	6.43971i		−	0.219210i	−0.993975	−	0.109605i	$-0.965041\pi$
$863$		−	6.43971i		−	0.219210i	0.993975	−	0.109605i	$-0.0349586\pi$
$864$		0			0
$865$	−1.56155	+	7.29226i	−0.0530944	+	0.247944i
$866$	−11.2017	+	9.72540i	−0.380648	+	0.330482i
$867$		0			0
$868$	10.3857	+	1.47261i	0.352512	+	0.0499835i
$869$	51.0970			1.73335
$870$		0			0
$871$			22.7872i			0.772116i
$872$	−14.8344	−	22.9354i	−0.502358	−	0.776689i
$873$		0			0
$874$	−36.4924	+	31.6831i	−1.23437	+	1.07170i
$875$	27.2298	+	19.9731i	0.920536	+	0.675214i
$876$		0			0
$877$	0.789443			0.0266576			0.0133288	−	0.999911i	$-0.495757\pi$
$877$	0.789443			0.0266576			0.0133288	+	0.999911i	$0.495757\pi$
$878$	24.5625	−	21.3254i	0.828945	−	0.719698i
$879$		0			0
$880$	−15.3249	+	28.5481i	−0.516602	+	0.962357i
$881$			5.83095i			0.196450i	0.995164	+	0.0982249i	$0.0313164\pi$
$881$			5.83095i			0.196450i	−0.995164	+	0.0982249i	$0.968684\pi$
$882$		0			0
$883$		0			0		1.00000			$0$
$883$		0			0		−1.00000			$\pi$
$884$	−3.14516	+	22.1815i	−0.105783	+	0.746043i
$885$		0			0
$886$	−1.50758	−	1.73642i	−0.0506481	−	0.0583362i
$887$			18.1379i			0.609012i	0.952510	+	0.304506i	$0.0984914\pi$
$887$			18.1379i			0.609012i	−0.952510	+	0.304506i	$0.901509\pi$
$888$		0			0
$889$	45.6155			1.52990
$890$	−28.3763	+	15.6505i	−0.951176	+	0.524604i
$891$		0			0
$892$	8.05024	−	56.7748i	0.269542	−	1.90096i
$893$			2.69400i			0.0901513i
$894$		0			0
$895$	−9.80501	+	45.7882i	−0.327745	+	1.53053i
$896$	32.7219	−	9.85061i	1.09316	−	0.329086i
$897$		0			0
$898$	−10.5716	+	9.17834i	−0.352778	+	0.306285i
$899$			11.8574i			0.395468i
$900$		0			0
$901$			66.0777i			2.20137i
$902$	−19.5843	−	22.5571i	−0.652087	−	0.751071i
$903$		0			0
$904$	−1.93087	+	1.24887i	−0.0642198	+	0.0415369i
$905$	2.89560	−	13.5221i	0.0962528	−	0.449489i
$906$		0			0
$907$		−	32.1143i		−	1.06634i	−0.846009	−	0.533168i	$-0.821001\pi$
$907$		−	32.1143i		−	1.06634i	0.846009	−	0.533168i	$-0.178999\pi$
$908$	3.70861	−	26.1552i	0.123075	−	0.867991i
$909$		0			0
$910$	−7.82410	−	14.1861i	−0.259366	−	0.470265i
$911$	12.5807			0.416816			0.208408	−	0.978042i	$-0.433172\pi$
$911$	12.5807			0.416816			0.208408	+	0.978042i	$0.433172\pi$
$912$		0			0
$913$		−	20.9791i		−	0.694306i
$914$	21.1755	−	18.3848i	0.700423	−	0.608114i
$915$		0			0
$916$	−43.6155	−	6.18435i	−1.44110	−	0.204337i
$917$			19.4849i			0.643449i
$918$		0			0
$919$		−	49.2611i		−	1.62497i	−0.582981	−	0.812486i	$-0.698114\pi$
$919$		−	49.2611i		−	1.62497i	0.582981	−	0.812486i	$-0.301886\pi$
$920$	−14.9861	−	39.4349i	−0.494077	−	1.30013i
$921$		0			0
$922$	−14.4401	−	16.6320i	−0.475559	−	0.547746i
$923$	−4.16516			−0.137098
$924$		0			0
$925$	−1.69614	−	0.761329i	−0.0557688	−	0.0250323i
$926$	16.4577	+	18.9560i	0.540835	+	0.622931i
$927$		0			0
$928$	16.2177	+	35.0595i	0.532373	+	1.15088i
$929$			8.65938i			0.284105i	0.989859	+	0.142053i	$0.0453702\pi$
$929$			8.65938i			0.284105i	−0.989859	+	0.142053i	$0.954630\pi$
$930$		0			0
$931$	10.8769			0.356476
$932$	−6.01947	+	42.4527i	−0.197174	+	1.39058i
$933$		0			0
$934$	26.0000	+	29.9467i	0.850746	+	0.979885i
$935$	−11.2017	+	52.3104i	−0.366334	+	1.71073i
$936$		0			0
$937$		0			0		1.00000			$0$
$937$		0			0		−1.00000			$\pi$
$938$	43.3338	−	37.6229i	1.41490	−	1.22843i
$939$		0			0
$940$	−2.20765	−	0.810376i	−0.0720056	−	0.0264315i
$941$	−4.37300			−0.142556			−0.0712778	−	0.997457i	$-0.522708\pi$
$941$	−4.37300			−0.142556			−0.0712778	+	0.997457i	$0.522708\pi$
$942$		0			0
$943$	38.8940			1.26656
$944$	−5.40724	+	18.6841i	−0.175991	+	0.608115i
$945$		0			0
$946$	−17.6155	−	20.2895i	−0.572730	−	0.659668i
$947$	−22.2517			−0.723082			−0.361541	−	0.932356i	$-0.617749\pi$
$947$	−22.2517			−0.723082			−0.361541	+	0.932356i	$0.617749\pi$
$948$		0			0
$949$		−	24.7374i		−	0.803010i
$950$	10.4653	+	34.6812i	0.339538	+	1.12521i
$951$		0			0
$952$	47.3747	−	30.6417i	1.53542	−	0.993102i
$953$	−0.813015			−0.0263361			−0.0131681	−	0.999913i	$-0.504192\pi$
$953$	−0.813015			−0.0263361			−0.0131681	+	0.999913i	$0.504192\pi$
$954$		0			0
$955$	38.2462	+	8.18998i	1.23762	+	0.265022i
$956$	1.37899	−	9.72540i	0.0445997	−	0.314542i
$957$		0			0
$958$	34.7123	+	39.9814i	1.12150	+	1.29174i
$959$	−19.9477			−0.644143
$960$		0			0
$961$	27.9848			0.902737
$962$	0.584739	+	0.673500i	0.0188528	+	0.0217145i
$963$		0			0
$964$	1.12311	−	7.92077i	0.0361728	−	0.255111i
$965$	−7.36701	+	34.4030i	−0.237152	+	1.10747i
$966$		0			0
$967$	23.7917			0.765091			0.382546	−	0.923937i	$-0.375048\pi$
$967$	23.7917			0.765091			0.382546	+	0.923937i	$0.375048\pi$
$968$	5.04227	−	3.26131i	0.162065	−	0.104822i
$969$		0			0
$970$	25.8622	−	14.2638i	0.830385	−	0.457984i
$971$		−	32.6032i		−	1.04629i	−0.852244	−	0.523144i	$-0.824759\pi$
$971$		−	32.6032i		−	1.04629i	0.852244	−	0.523144i	$-0.175241\pi$
$972$		0			0
$973$	−36.2454			−1.16197
$974$	4.17940	+	4.81382i	0.133917	+	0.154245i
$975$		0			0
$976$		0			0
$977$	2.43904			0.0780319			0.0390160	−	0.999239i	$-0.487578\pi$
$977$	2.43904			0.0780319			0.0390160	+	0.999239i	$0.487578\pi$
$978$		0			0
$979$	37.1231			1.18646
$980$	−3.27185	+	8.91328i	−0.104516	+	0.284724i
$981$		0			0
$982$	−11.2337	+	9.75323i	−0.358482	+	0.311238i
$983$			12.5841i			0.401371i	0.979656	+	0.200685i	$0.0643169\pi$
$983$			12.5841i			0.401371i	−0.979656	+	0.200685i	$0.935683\pi$
$984$		0			0
$985$	−11.5616	+	53.9910i	−0.368382	+	1.72030i
$986$	41.8126	+	48.1596i	1.33159	+	1.53371i
$987$		0			0
$988$	2.43981	−	17.2069i	0.0776207	−	0.547425i
$989$	34.9840			1.11243
$990$		0			0
$991$			10.6323i			0.337746i	0.985638	+	0.168873i	$0.0540127\pi$
$991$			10.6323i			0.337746i	−0.985638	+	0.168873i	$0.945987\pi$
$992$	−8.91506	+	4.12391i	−0.283053	+	0.130934i
$993$		0			0
$994$	6.87689	+	7.92077i	0.218122	+	0.251232i
$995$	4.97818	−	23.2475i	0.157819	−	0.736995i
$996$		0			0
$997$	32.4813			1.02869			0.514346	−	0.857583i	$-0.328035\pi$
$997$	32.4813			1.02869			0.514346	+	0.857583i	$0.328035\pi$
$998$	23.2930	+	26.8287i	0.737325	+	0.849248i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.m.c.179.12	yes	16
3.2	odd	2	inner	360.2.m.c.179.5	✓	16
4.3	odd	2		1440.2.m.c.719.15		16
5.2	odd	4		1800.2.b.g.251.4		16
5.3	odd	4		1800.2.b.g.251.13		16
5.4	even	2	inner	360.2.m.c.179.6	yes	16
8.3	odd	2	inner	360.2.m.c.179.9	yes	16
8.5	even	2		1440.2.m.c.719.2		16
12.11	even	2		1440.2.m.c.719.1		16
15.2	even	4		1800.2.b.g.251.14		16
15.8	even	4		1800.2.b.g.251.3		16
15.14	odd	2	inner	360.2.m.c.179.11	yes	16
20.3	even	4		7200.2.b.i.4751.16		16
20.7	even	4		7200.2.b.i.4751.3		16
20.19	odd	2		1440.2.m.c.719.14		16
24.5	odd	2		1440.2.m.c.719.16		16
24.11	even	2	inner	360.2.m.c.179.8	yes	16
40.3	even	4		1800.2.b.g.251.2		16
40.13	odd	4		7200.2.b.i.4751.4		16
40.19	odd	2	inner	360.2.m.c.179.7	yes	16
40.27	even	4		1800.2.b.g.251.15		16
40.29	even	2		1440.2.m.c.719.3		16
40.37	odd	4		7200.2.b.i.4751.15		16
60.23	odd	4		7200.2.b.i.4751.13		16
60.47	odd	4		7200.2.b.i.4751.2		16
60.59	even	2		1440.2.m.c.719.4		16
120.29	odd	2		1440.2.m.c.719.13		16
120.53	even	4		7200.2.b.i.4751.1		16
120.59	even	2	inner	360.2.m.c.179.10	yes	16
120.77	even	4		7200.2.b.i.4751.14		16
120.83	odd	4		1800.2.b.g.251.16		16
120.107	odd	4		1800.2.b.g.251.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.m.c.179.5	✓	16	3.2	odd	2	inner
360.2.m.c.179.6	yes	16	5.4	even	2	inner
360.2.m.c.179.7	yes	16	40.19	odd	2	inner
360.2.m.c.179.8	yes	16	24.11	even	2	inner
360.2.m.c.179.9	yes	16	8.3	odd	2	inner
360.2.m.c.179.10	yes	16	120.59	even	2	inner
360.2.m.c.179.11	yes	16	15.14	odd	2	inner
360.2.m.c.179.12	yes	16	1.1	even	1	trivial
1440.2.m.c.719.1		16	12.11	even	2
1440.2.m.c.719.2		16	8.5	even	2
1440.2.m.c.719.3		16	40.29	even	2
1440.2.m.c.719.4		16	60.59	even	2
1440.2.m.c.719.13		16	120.29	odd	2
1440.2.m.c.719.14		16	20.19	odd	2
1440.2.m.c.719.15		16	4.3	odd	2
1440.2.m.c.719.16		16	24.5	odd	2
1800.2.b.g.251.1		16	120.107	odd	4
1800.2.b.g.251.2		16	40.3	even	4
1800.2.b.g.251.3		16	15.8	even	4
1800.2.b.g.251.4		16	5.2	odd	4
1800.2.b.g.251.13		16	5.3	odd	4
1800.2.b.g.251.14		16	15.2	even	4
1800.2.b.g.251.15		16	40.27	even	4
1800.2.b.g.251.16		16	120.83	odd	4
7200.2.b.i.4751.1		16	120.53	even	4
7200.2.b.i.4751.2		16	60.47	odd	4
7200.2.b.i.4751.3		16	20.7	even	4
7200.2.b.i.4751.4		16	40.13	odd	4
7200.2.b.i.4751.13		16	60.23	odd	4
7200.2.b.i.4751.14		16	120.77	even	4
7200.2.b.i.4751.15		16	40.37	odd	4
7200.2.b.i.4751.16		16	20.3	even	4

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:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.m (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.927153 + 1.06789i) q^{2} +(-0.280776 + 1.98019i) q^{4} +(2.18650 + 0.468213i) q^{5} +3.02045 q^{7} +(-2.37495 + 1.53610i) q^{8} +O(q^{10})\)	\(q+(0.927153 + 1.06789i) q^{2} +(-0.280776 + 1.98019i) q^{4} +(2.18650 + 0.468213i) q^{5} +3.02045 q^{7} +(-2.37495 + 1.53610i) q^{8} +(1.52722 + 2.76904i) q^{10} -3.62258i q^{11} -1.69614 q^{13} +(2.80042 + 3.22550i) q^{14} +(-3.84233 - 1.11198i) q^{16} -6.60421 q^{17} +5.12311 q^{19} +(-1.54107 + 4.19823i) q^{20} +(3.86852 - 3.35869i) q^{22} +6.67026i q^{23} +(4.56155 + 2.04750i) q^{25} +(-1.57258 - 1.81129i) q^{26} +(-0.848071 + 5.98107i) q^{28} -6.82867 q^{29} -1.73642i q^{31} +(-2.37495 - 5.13416i) q^{32} +(-6.12311 - 7.05256i) q^{34} +(6.60421 + 1.41421i) q^{35} -0.371834 q^{37} +(4.74990 + 5.47091i) q^{38} +(-5.91205 + 2.24670i) q^{40} -5.83095i q^{41} -5.24477i q^{43} +(7.17341 + 1.01714i) q^{44} +(-7.12311 + 6.18435i) q^{46} +0.525853i q^{47} +2.12311 q^{49} +(2.04276 + 6.76958i) q^{50} +(0.476236 - 3.35869i) q^{52} -10.0054i q^{53} +(1.69614 - 7.92077i) q^{55} +(-7.17341 + 4.63972i) q^{56} +(-6.33122 - 7.29226i) q^{58} -4.86270i q^{59} +(1.85431 - 1.60993i) q^{62} +(3.28078 - 7.29634i) q^{64} +(-3.70861 - 0.794156i) q^{65} -13.4347i q^{67} +(1.85431 - 13.0776i) q^{68} +(4.61288 + 8.36375i) q^{70} +2.45567 q^{71} +14.5845i q^{73} +(-0.344747 - 0.397078i) q^{74} +(-1.43845 + 10.1447i) q^{76} -10.9418i q^{77} +14.1051i q^{79} +(-7.88060 - 4.23038i) q^{80} +(6.22681 - 5.40618i) q^{82} +5.79119 q^{83} +(-14.4401 - 3.09218i) q^{85} +(5.60083 - 4.86270i) q^{86} +(5.56466 + 8.60345i) q^{88} +10.2477i q^{89} -5.12311 q^{91} +(-13.2084 - 1.87285i) q^{92} +(-0.561553 + 0.487546i) q^{94} +(11.2017 + 2.39871i) q^{95} -9.33976i q^{97} +(1.96844 + 2.26724i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{4}+O(q^{10}) \) 16 * q + 12 * q^4	\( 16 q + 12 q^{4} - 8 q^{10} - 12 q^{16} + 16 q^{19} + 40 q^{25} - 32 q^{34} - 28 q^{40} - 48 q^{46} - 32 q^{49} + 36 q^{64} + 32 q^{70} - 56 q^{76} - 16 q^{91} + 24 q^{94}+O(q^{100}) \) 16 * q + 12 * q^4 - 8 * q^10 - 12 * q^16 + 16 * q^19 + 40 * q^25 - 32 * q^34 - 28 * q^40 - 48 * q^46 - 32 * q^49 + 36 * q^64 + 32 * q^70 - 56 * q^76 - 16 * q^91 + 24 * q^94

Introduction

L-functions

Modular forms

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