LMFDB - Embedded newform 1323.2.f.h.442.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(442,1323)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1323, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("1323.442");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.f (of order $3$, degree $2$, not 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:	$10.5642081874$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 441)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			442.10
Character	$\chi$	$=$	1323.442
Dual form			1323.2.f.h.883.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.649936 + 1.12572i) q^{2} +(0.155166 - 0.268756i) q^{4} +(1.76292 - 3.05347i) q^{5} +3.00314 q^{8} +O(q^{10})$	\(q+(0.649936 + 1.12572i) q^{2} +(0.155166 - 0.268756i) q^{4} +(1.76292 - 3.05347i) q^{5} +3.00314 q^{8} +4.58314 q^{10} +(0.589267 + 1.02064i) q^{11} +(1.61030 - 2.78913i) q^{13} +(1.64151 + 2.84319i) q^{16} +4.90317 q^{17} -6.86637 q^{19} +(-0.547092 - 0.947591i) q^{20} +(-0.765972 + 1.32670i) q^{22} +(-2.14994 + 3.72380i) q^{23} +(-3.71578 - 6.43592i) q^{25} +4.18637 q^{26} +(-1.36140 - 2.35802i) q^{29} +(0.960401 - 1.66346i) q^{31} +(0.869378 - 1.50581i) q^{32} +(3.18675 + 5.51961i) q^{34} -9.76457 q^{37} +(-4.46270 - 7.72962i) q^{38} +(5.29429 - 9.16998i) q^{40} +(3.32673 - 5.76206i) q^{41} +(4.83441 + 8.37344i) q^{43} +0.365738 q^{44} -5.58928 q^{46} +(0.316609 + 0.548383i) q^{47} +(4.83004 - 8.36587i) q^{50} +(-0.499729 - 0.865557i) q^{52} +2.22756 q^{53} +4.15533 q^{55} +(1.76965 - 3.06512i) q^{58} +(4.10652 - 7.11270i) q^{59} +(4.82958 + 8.36508i) q^{61} +2.49680 q^{62} +8.82622 q^{64} +(-5.67767 - 9.83402i) q^{65} +(-2.66651 + 4.61852i) q^{67} +(0.760807 - 1.31776i) q^{68} +3.27719 q^{71} +1.03807 q^{73} +(-6.34635 - 10.9922i) q^{74} +(-1.06543 + 1.84538i) q^{76} +(-0.502039 - 0.869557i) q^{79} +11.5754 q^{80} +8.64864 q^{82} +(3.65598 + 6.33234i) q^{83} +(8.64391 - 14.9717i) q^{85} +(-6.28411 + 10.8844i) q^{86} +(1.76965 + 3.06512i) q^{88} -12.0429 q^{89} +(0.667195 + 1.15562i) q^{92} +(-0.411551 + 0.712828i) q^{94} +(-12.1049 + 20.9662i) q^{95} +(-5.46454 - 9.46487i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{2} - 12 q^{4} + 24 q^{8}+O(q^{10}) $ 24 * q - 4 * q^2 - 12 * q^4 + 24 * q^8	$ 24 q - 4 q^{2} - 12 q^{4} + 24 q^{8} - 20 q^{11} - 12 q^{16} - 32 q^{23} - 12 q^{25} - 16 q^{29} - 48 q^{32} + 24 q^{37} + 112 q^{44} - 48 q^{46} + 4 q^{50} + 64 q^{53} + 96 q^{64} - 60 q^{65} - 12 q^{67} + 112 q^{71} - 68 q^{74} + 12 q^{79} + 12 q^{85} - 76 q^{86} - 16 q^{92} - 64 q^{95}+O(q^{100}) $ 24 * q - 4 * q^2 - 12 * q^4 + 24 * q^8 - 20 * q^11 - 12 * q^16 - 32 * q^23 - 12 * q^25 - 16 * q^29 - 48 * q^32 + 24 * q^37 + 112 * q^44 - 48 * q^46 + 4 * q^50 + 64 * q^53 + 96 * q^64 - 60 * q^65 - 12 * q^67 + 112 * q^71 - 68 * q^74 + 12 * q^79 + 12 * q^85 - 76 * q^86 - 16 * q^92 - 64 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	0.649936	+	1.12572i	0.459574	+	0.796006i	0.998938	−	0.0460668i	$-0.0146687\pi$
$2$	0.649936	+	1.12572i	0.459574	+	0.796006i	−0.539364	+	0.842073i	$0.681335\pi$
$3$		0			0
$3$		0			0
$4$	0.155166	−	0.268756i	0.0775831	−	0.134378i
$5$	1.76292	−	3.05347i	0.788402	−	1.36555i	−0.138543	−	0.990356i	$-0.544242\pi$
$5$	1.76292	−	3.05347i	0.788402	−	1.36555i	0.926945	−	0.375196i	$-0.122425\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	3.00314			1.06177
$9$		0			0
$10$	4.58314			1.44932
$11$	0.589267	+	1.02064i	0.177671	+	0.307735i	0.941082	−	0.338178i	$-0.109810\pi$
$11$	0.589267	+	1.02064i	0.177671	+	0.307735i	−0.763412	+	0.645912i	$0.776477\pi$
$12$		0			0
$13$	1.61030	−	2.78913i	0.446618	−	0.773564i	−0.551546	−	0.834145i	$-0.685962\pi$
$13$	1.61030	−	2.78913i	0.446618	−	0.773564i	0.998163	+	0.0605803i	$0.0192951\pi$
$14$		0			0
$15$		0			0
$16$	1.64151	+	2.84319i	0.410379	+	0.710797i
$17$	4.90317			1.18919			0.594597	−	0.804024i	$-0.297312\pi$
$17$	4.90317			1.18919			0.594597	+	0.804024i	$0.297312\pi$
$18$		0			0
$19$	−6.86637			−1.57525			−0.787627	−	0.616153i	$-0.788690\pi$
$19$	−6.86637			−1.57525			−0.787627	+	0.616153i	$0.788690\pi$
$20$	−0.547092	−	0.947591i	−0.122333	−	0.211888i
$21$		0			0
$22$	−0.765972	+	1.32670i	−0.163306	+	0.282854i
$23$	−2.14994	+	3.72380i	−0.448293	+	0.776466i	−0.998275	−	0.0587106i	$-0.981301\pi$
$23$	−2.14994	+	3.72380i	−0.448293	+	0.776466i	0.549982	+	0.835176i	$0.314634\pi$
$24$		0			0
$25$	−3.71578	−	6.43592i	−0.743156	−	1.28718i
$26$	4.18637			0.821016
$27$		0			0
$28$		0			0
$29$	−1.36140	−	2.35802i	−0.252806	−	0.437873i	0.711491	−	0.702695i	$-0.248020\pi$
$29$	−1.36140	−	2.35802i	−0.252806	−	0.437873i	−0.964297	+	0.264822i	$0.914687\pi$
$30$		0			0
$31$	0.960401	−	1.66346i	0.172493	−	0.298767i	−0.766798	−	0.641889i	$-0.778151\pi$
$31$	0.960401	−	1.66346i	0.172493	−	0.298767i	0.939291	+	0.343122i	$0.111484\pi$
$32$	0.869378	−	1.50581i	0.153686	−	0.266192i
$33$		0			0
$34$	3.18675	+	5.51961i	0.546523	+	0.946606i
$35$		0			0
$36$		0			0
$37$	−9.76457			−1.60529			−0.802643	−	0.596460i	$-0.796573\pi$
$37$	−9.76457			−1.60529			−0.802643	+	0.596460i	$0.796573\pi$
$38$	−4.46270	−	7.72962i	−0.723946	−	1.25391i
$39$		0			0
$40$	5.29429	−	9.16998i	0.837101	−	1.44990i
$41$	3.32673	−	5.76206i	0.519547	−	0.899883i	−0.480194	−	0.877162i	$-0.659434\pi$
$41$	3.32673	−	5.76206i	0.519547	−	0.899883i	0.999742	−	0.0227205i	$-0.00723278\pi$
$42$		0			0
$43$	4.83441	+	8.37344i	0.737240	+	1.27694i	0.953734	+	0.300653i	$0.0972047\pi$
$43$	4.83441	+	8.37344i	0.737240	+	1.27694i	−0.216493	+	0.976284i	$0.569462\pi$
$44$	0.365738			0.0551370
$45$		0			0
$46$	−5.58928			−0.824095
$47$	0.316609	+	0.548383i	0.0461822	+	0.0799899i	0.888192	−	0.459472i	$-0.151961\pi$
$47$	0.316609	+	0.548383i	0.0461822	+	0.0799899i	−0.842010	+	0.539461i	$0.818628\pi$
$48$		0			0
$49$		0			0
$50$	4.83004	−	8.36587i	0.683071	−	1.18311i
$51$		0			0
$52$	−0.499729	−	0.865557i	−0.0693000	−	0.120031i
$53$	2.22756			0.305978			0.152989	−	0.988228i	$-0.451110\pi$
$53$	2.22756			0.305978			0.152989	+	0.988228i	$0.451110\pi$
$54$		0			0
$55$	4.15533			0.560304
$56$		0			0
$57$		0			0
$58$	1.76965	−	3.06512i	0.232366	−	0.402471i
$59$	4.10652	−	7.11270i	0.534623	−	0.925995i	−0.464558	−	0.885543i	$-0.653787\pi$
$59$	4.10652	−	7.11270i	0.534623	−	0.925995i	0.999181	−	0.0404521i	$-0.0128798\pi$
$60$		0			0
$61$	4.82958	+	8.36508i	0.618364	+	1.07104i	0.989784	+	0.142573i	$0.0455376\pi$
$61$	4.82958	+	8.36508i	0.618364	+	1.07104i	−0.371420	+	0.928465i	$0.621129\pi$
$62$	2.49680			0.317093
$63$		0			0
$64$	8.82622			1.10328
$65$	−5.67767	−	9.83402i	−0.704229	−	1.21976i
$66$		0			0
$67$	−2.66651	+	4.61852i	−0.325766	+	0.564242i	−0.981667	−	0.190604i	$-0.938955\pi$
$67$	−2.66651	+	4.61852i	−0.325766	+	0.564242i	0.655901	+	0.754847i	$0.272289\pi$
$68$	0.760807	−	1.31776i	0.0922614	−	0.159801i
$69$		0			0
$70$		0			0
$71$	3.27719			0.388931			0.194466	−	0.980909i	$-0.437703\pi$
$71$	3.27719			0.388931			0.194466	+	0.980909i	$0.437703\pi$
$72$		0			0
$73$	1.03807			0.121497			0.0607486	−	0.998153i	$-0.480651\pi$
$73$	1.03807			0.121497			0.0607486	+	0.998153i	$0.480651\pi$
$74$	−6.34635	−	10.9922i	−0.737748	−	1.27782i
$75$		0			0
$76$	−1.06543	+	1.84538i	−0.122213	+	0.211679i
$77$		0			0
$78$		0			0
$79$	−0.502039	−	0.869557i	−0.0564838	−	0.0978328i	0.836401	−	0.548118i	$-0.184656\pi$
$79$	−0.502039	−	0.869557i	−0.0564838	−	0.0978328i	−0.892885	+	0.450285i	$0.851322\pi$
$80$	11.5754			1.29417
$81$		0			0
$82$	8.64864			0.955082
$83$	3.65598	+	6.33234i	0.401296	+	0.695064i	0.993883	−	0.110442i	$-0.0352267\pi$
$83$	3.65598	+	6.33234i	0.401296	+	0.695064i	−0.592587	+	0.805506i	$0.701893\pi$
$84$		0			0
$85$	8.64391	−	14.9717i	0.937563	−	1.62391i
$86$	−6.28411	+	10.8844i	−0.677633	+	1.17369i
$87$		0			0
$88$	1.76965	+	3.06512i	0.188645	+	0.326743i
$89$	−12.0429			−1.27654			−0.638271	−	0.769812i	$-0.720350\pi$
$89$	−12.0429			−1.27654			−0.638271	+	0.769812i	$0.720350\pi$
$90$		0			0
$91$		0			0
$92$	0.667195	+	1.15562i	0.0695599	+	0.120481i
$93$		0			0
$94$	−0.411551	+	0.712828i	−0.0424483	+	0.0735226i
$95$	−12.1049	+	20.9662i	−1.24193	+	2.15109i
$96$		0			0
$97$	−5.46454	−	9.46487i	−0.554840	−	0.961012i	−0.997916	−	0.0645275i	$-0.979446\pi$
$97$	−5.46454	−	9.46487i	−0.554840	−	0.961012i	0.443076	−	0.896484i	$-0.353887\pi$
$98$		0			0
$99$		0			0
$100$	−2.30626			−0.230626
$101$	−0.797546	−	1.38139i	−0.0793588	−	0.137453i	0.823615	−	0.567150i	$-0.191954\pi$
$101$	−0.797546	−	1.38139i	−0.0793588	−	0.137453i	−0.902973	+	0.429696i	$0.858621\pi$
$102$		0			0
$103$	−1.16778	+	2.02265i	−0.115065	+	0.199298i	−0.917806	−	0.397030i	$-0.870041\pi$
$103$	−1.16778	+	2.02265i	−0.115065	+	0.199298i	0.802741	+	0.596328i	$0.203374\pi$
$104$	4.83596	−	8.37613i	0.474205	−	0.821347i
$105$		0			0
$106$	1.44777	+	2.50761i	0.140620	+	0.243561i
$107$	2.22362			0.214966			0.107483	−	0.994207i	$-0.465721\pi$
$107$	2.22362			0.214966			0.107483	+	0.994207i	$0.465721\pi$
$108$		0			0
$109$	−0.919564			−0.0880782			−0.0440391	−	0.999030i	$-0.514023\pi$
$109$	−0.919564			−0.0880782			−0.0440391	+	0.999030i	$0.514023\pi$
$110$	2.70070	+	4.67774i	0.257501	+	0.446005i
$111$		0			0
$112$		0			0
$113$	−1.19327	+	2.06681i	−0.112254	+	0.194429i	−0.916679	−	0.399625i	$-0.869140\pi$
$113$	−1.19327	+	2.06681i	−0.112254	+	0.194429i	0.804425	+	0.594054i	$0.202474\pi$
$114$		0			0
$115$	7.58033	+	13.1295i	0.706870	+	1.22433i
$116$	−0.844976			−0.0784540
$117$		0			0
$118$	10.6759			0.982796
$119$		0			0
$120$		0			0
$121$	4.80553	−	8.32342i	0.436866	−	0.756674i
$122$	−6.27783	+	10.8735i	−0.568368	+	0.984443i
$123$		0			0
$124$	−0.298044	−	0.516227i	−0.0267651	−	0.0463585i
$125$	−8.57330			−0.766819
$126$		0			0
$127$	−3.04170			−0.269907			−0.134954	−	0.990852i	$-0.543089\pi$
$127$	−3.04170			−0.269907			−0.134954	+	0.990852i	$0.543089\pi$
$128$	3.99772	+	6.92426i	0.353352	+	0.612024i
$129$		0			0
$130$	7.38025	−	12.7830i	0.647291	−	1.12114i
$131$	−1.63088	+	2.82476i	−0.142490	+	0.246801i	−0.928434	−	0.371498i	$-0.878844\pi$
$131$	−1.63088	+	2.82476i	−0.142490	+	0.246801i	0.785943	+	0.618298i	$0.212178\pi$
$132$		0			0
$133$		0			0
$134$	−6.93223			−0.598854
$135$		0			0
$136$	14.7249			1.26265
$137$	10.4669	+	18.1292i	0.894246	+	1.54888i	0.834734	+	0.550653i	$0.185621\pi$
$137$	10.4669	+	18.1292i	0.894246	+	1.54888i	0.0595120	+	0.998228i	$0.481046\pi$
$138$		0			0
$139$	−8.31195	+	14.3967i	−0.705010	+	1.22111i	0.261677	+	0.965155i	$0.415724\pi$
$139$	−8.31195	+	14.3967i	−0.705010	+	1.22111i	−0.966688	+	0.255958i	$0.917609\pi$
$140$		0			0
$141$		0			0
$142$	2.12997	+	3.68921i	0.178743	+	0.309592i
$143$	3.79559			0.317404
$144$		0			0
$145$	−9.60019			−0.797252
$146$	0.674681	+	1.16858i	0.0558370	+	0.0967124i
$147$		0			0
$148$	−1.51513	+	2.62429i	−0.124543	+	0.215715i
$149$	0.564221	−	0.977260i	0.0462228	−	0.0800602i	−0.841988	−	0.539496i	$-0.818615\pi$
$149$	0.564221	−	0.977260i	0.0462228	−	0.0800602i	0.888211	+	0.459435i	$0.151948\pi$
$150$		0			0
$151$	9.81476	+	16.9997i	0.798714	+	1.38341i	0.920454	+	0.390851i	$0.127819\pi$
$151$	9.81476	+	16.9997i	0.798714	+	1.38341i	−0.121740	+	0.992562i	$0.538847\pi$
$152$	−20.6206			−1.67256
$153$		0			0
$154$		0			0
$155$	−3.38622	−	5.86511i	−0.271988	−	0.471097i
$156$		0			0
$157$	−4.66619	+	8.08207i	−0.372402	+	0.645020i	−0.989935	−	0.141526i	$-0.954799\pi$
$157$	−4.66619	+	8.08207i	−0.372402	+	0.645020i	0.617532	+	0.786545i	$0.288132\pi$
$158$	0.652586	−	1.13031i	0.0519170	−	0.0899228i
$159$		0			0
$160$	−3.06529	−	5.30924i	−0.242332	−	0.419732i
$161$		0			0
$162$		0			0
$163$	16.9011			1.32380			0.661899	−	0.749593i	$-0.269751\pi$
$163$	16.9011			1.32380			0.661899	+	0.749593i	$0.269751\pi$
$164$	−1.03239	−	1.78815i	−0.0806162	−	0.139631i
$165$		0			0
$166$	−4.75230	+	8.23123i	−0.368850	+	0.638867i
$167$	−2.57319	+	4.45689i	−0.199119	+	0.344885i	−0.948243	−	0.317545i	$-0.897141\pi$
$167$	−2.57319	+	4.45689i	−0.199119	+	0.344885i	0.749124	+	0.662430i	$0.230475\pi$
$168$		0			0
$169$	1.31385	+	2.27566i	0.101066	+	0.175051i
$170$	22.4719			1.72352
$171$		0			0
$172$	3.00055			0.228790
$173$	4.86834	+	8.43222i	0.370133	+	0.641090i	0.989586	−	0.143945i	$-0.0459787\pi$
$173$	4.86834	+	8.43222i	0.370133	+	0.641090i	−0.619453	+	0.785034i	$0.712645\pi$
$174$		0			0
$175$		0			0
$176$	−1.93458	+	3.35079i	−0.145825	+	0.252576i
$177$		0			0
$178$	−7.82710	−	13.5569i	−0.586666	−	1.01613i
$179$	−1.37598			−0.102846			−0.0514228	−	0.998677i	$-0.516376\pi$
$179$	−1.37598			−0.102846			−0.0514228	+	0.998677i	$0.516376\pi$
$180$		0			0
$181$	−5.66560			−0.421120			−0.210560	−	0.977581i	$-0.567529\pi$
$181$	−5.66560			−0.421120			−0.210560	+	0.977581i	$0.567529\pi$
$182$		0			0
$183$		0			0
$184$	−6.45655	+	11.1831i	−0.475983	+	0.824427i
$185$	−17.2142	+	29.8158i	−1.26561	+	2.19210i
$186$		0			0
$187$	2.88928	+	5.00438i	0.211285	+	0.365956i
$188$	0.196508			0.0143318
$189$		0			0
$190$	−31.4696			−2.28304
$191$	−12.5065	−	21.6618i	−0.904936	−	1.56740i	−0.821003	−	0.570925i	$-0.806585\pi$
$191$	−12.5065	−	21.6618i	−0.904936	−	1.56740i	−0.0839339	−	0.996471i	$-0.526748\pi$
$192$		0			0
$193$	−8.76688	+	15.1847i	−0.631054	+	1.09302i	0.356282	+	0.934378i	$0.384044\pi$
$193$	−8.76688	+	15.1847i	−0.631054	+	1.09302i	−0.987337	+	0.158640i	$0.949289\pi$
$194$	7.10321	−	12.3031i	0.509981	−	0.883312i
$195$		0			0
$196$		0			0
$197$	19.7540			1.40741			0.703707	−	0.710490i	$-0.251527\pi$
$197$	19.7540			1.40741			0.703707	+	0.710490i	$0.251527\pi$
$198$		0			0
$199$	−19.0222			−1.34845			−0.674224	−	0.738527i	$-0.735522\pi$
$199$	−19.0222			−1.34845			−0.674224	+	0.738527i	$0.735522\pi$
$200$	−11.1590	−	19.3279i	−0.789060	−	1.36669i
$201$		0			0
$202$	1.03671	−	1.79563i	0.0729425	−	0.126340i
$203$		0			0
$204$		0			0
$205$	−11.7295	−	20.3161i	−0.819225	−	1.41894i
$206$	−3.03593			−0.211523
$207$		0			0
$208$	10.5733			0.733129
$209$	−4.04613	−	7.00810i	−0.279876	−	0.484760i
$210$		0			0
$211$	3.71809	−	6.43993i	0.255964	−	0.443343i	−0.709193	−	0.705015i	$-0.750940\pi$
$211$	3.71809	−	6.43993i	0.255964	−	0.443343i	0.965157	+	0.261672i	$0.0842738\pi$
$212$	0.345642	−	0.598669i	0.0237388	−	0.0411168i
$213$		0			0
$214$	1.44521	+	2.50318i	0.0987927	+	0.171114i
$215$	34.0907			2.32497
$216$		0			0
$217$		0			0
$218$	−0.597658	−	1.03517i	−0.0404785	−	0.0701108i
$219$		0			0
$220$	0.644767	−	1.11677i	0.0434702	−	0.0752925i
$221$	7.89559	−	13.6756i	0.531115	−	0.919918i
$222$		0			0
$223$	1.64565	+	2.85034i	0.110201	+	0.190873i	0.915851	−	0.401518i	$-0.131517\pi$
$223$	1.64565	+	2.85034i	0.110201	+	0.190873i	−0.805650	+	0.592391i	$0.798184\pi$
$224$		0			0
$225$		0			0
$226$	−3.10221			−0.206356
$227$	−9.00847	−	15.6031i	−0.597913	−	1.03562i	−0.993129	−	0.117028i	$-0.962663\pi$
$227$	−9.00847	−	15.6031i	−0.597913	−	1.03562i	0.395215	−	0.918589i	$-0.370670\pi$
$228$		0			0
$229$	−2.12746	+	3.68486i	−0.140586	+	0.243503i	−0.927718	−	0.373283i	$-0.878232\pi$
$229$	−2.12746	+	3.68486i	−0.140586	+	0.243503i	0.787131	+	0.616785i	$0.211565\pi$
$230$	−9.85347	+	17.0667i	−0.649718	+	1.12535i
$231$		0			0
$232$	−4.08848	−	7.08146i	−0.268422	−	0.464920i
$233$	14.7055			0.963390			0.481695	−	0.876339i	$-0.340021\pi$
$233$	14.7055			0.963390			0.481695	+	0.876339i	$0.340021\pi$
$234$		0			0
$235$	2.23263			0.145641
$236$	−1.27439	−	2.20730i	−0.0829555	−	0.143683i
$237$		0			0
$238$		0			0
$239$	−7.08187	+	12.2662i	−0.458088	+	0.793432i	−0.998860	−	0.0477377i	$-0.984799\pi$
$239$	−7.08187	+	12.2662i	−0.458088	+	0.793432i	0.540772	+	0.841169i	$0.318132\pi$
$240$		0			0
$241$	−3.96752	−	6.87194i	−0.255570	−	0.442661i	0.709480	−	0.704726i	$-0.248930\pi$
$241$	−3.96752	−	6.87194i	−0.255570	−	0.442661i	−0.965050	+	0.262065i	$0.915597\pi$
$242$	12.4931			0.803090
$243$		0			0
$244$	2.99755			0.191899
$245$		0			0
$246$		0			0
$247$	−11.0569	+	19.1512i	−0.703536	+	1.21856i
$248$	2.88422	−	4.99561i	0.183148	−	0.317221i
$249$		0			0
$250$	−5.57210	−	9.65115i	−0.352410	−	0.610392i
$251$	−8.05097			−0.508173			−0.254087	−	0.967181i	$-0.581775\pi$
$251$	−8.05097			−0.508173			−0.254087	+	0.967181i	$0.581775\pi$
$252$		0			0
$253$	−5.06755			−0.318594
$254$	−1.97691	−	3.42411i	−0.124042	−	0.214848i
$255$		0			0
$256$	3.62969	−	6.28681i	0.226856	−	0.392926i
$257$	−8.77687	+	15.2020i	−0.547486	+	0.948273i	0.450960	+	0.892544i	$0.351082\pi$
$257$	−8.77687	+	15.2020i	−0.547486	+	0.948273i	−0.998446	+	0.0557293i	$0.982252\pi$
$258$		0			0
$259$		0			0
$260$	−3.52393			−0.218545
$261$		0			0
$262$	−4.23986			−0.261940
$263$	−11.6743	−	20.2205i	−0.719867	−	1.24685i	−0.961052	−	0.276367i	$-0.910869\pi$
$263$	−11.6743	−	20.2205i	−0.719867	−	1.24685i	0.241185	−	0.970479i	$-0.422464\pi$
$264$		0			0
$265$	3.92701	−	6.80177i	0.241234	−	0.417830i
$266$		0			0
$267$		0			0
$268$	0.827504	+	1.43328i	0.0505478	+	0.0875514i
$269$	−0.538488			−0.0328322			−0.0164161	−	0.999865i	$-0.505226\pi$
$269$	−0.538488			−0.0328322			−0.0164161	+	0.999865i	$0.505226\pi$
$270$		0			0
$271$	−14.4150			−0.875648			−0.437824	−	0.899061i	$-0.644251\pi$
$271$	−14.4150			−0.875648			−0.437824	+	0.899061i	$0.644251\pi$
$272$	8.04863	+	13.9406i	0.488020	+	0.845275i
$273$		0			0
$274$	−13.6056	+	23.5656i	−0.821945	+	1.42365i
$275$	4.37918	−	7.58495i	0.264074	−	0.457390i
$276$		0			0
$277$	−10.9533	−	18.9717i	−0.658121	−	1.13990i	−0.981101	−	0.193494i	$-0.938018\pi$
$277$	−10.9533	−	18.9717i	−0.658121	−	1.13990i	0.322980	−	0.946406i	$-0.395315\pi$
$278$	−21.6089			−1.29602
$279$		0			0
$280$		0			0
$281$	0.776622	+	1.34515i	0.0463294	+	0.0802449i	0.888260	−	0.459341i	$-0.151914\pi$
$281$	0.776622	+	1.34515i	0.0463294	+	0.0802449i	−0.841931	+	0.539586i	$0.818581\pi$
$282$		0			0
$283$	1.32571	−	2.29619i	0.0788051	−	0.136495i	−0.823930	−	0.566692i	$-0.808223\pi$
$283$	1.32571	−	2.29619i	0.0788051	−	0.136495i	0.902735	+	0.430198i	$0.141556\pi$
$284$	0.508510	−	0.880765i	0.0301745	−	0.0522638i
$285$		0			0
$286$	2.46689	+	4.27279i	0.145870	+	0.252655i
$287$		0			0
$288$		0			0
$289$	7.04111			0.414183
$290$	−6.23951	−	10.8071i	−0.366396	−	0.634617i
$291$		0			0
$292$	0.161074	−	0.278988i	0.00942613	−	0.0163265i
$293$	5.19314	−	8.99478i	0.303386	−	0.525481i	−0.673514	−	0.739174i	$-0.735216\pi$
$293$	5.19314	−	8.99478i	0.303386	−	0.525481i	0.976901	+	0.213694i	$0.0685494\pi$
$294$		0			0
$295$	−14.4789	−	25.0783i	−0.842996	−	1.46011i
$296$	−29.3243			−1.70444
$297$		0			0
$298$	1.46683			0.0849712
$299$	6.92409	+	11.9929i	0.400431	+	0.693566i
$300$		0			0
$301$		0			0
$302$	−12.7579	+	22.0974i	−0.734137	+	1.27156i
$303$		0			0
$304$	−11.2712	−	19.5224i	−0.646450	−	1.11968i
$305$	34.0567			1.95008
$306$		0			0
$307$	−10.6425			−0.607400			−0.303700	−	0.952768i	$-0.598222\pi$
$307$	−10.6425			−0.607400			−0.303700	+	0.952768i	$0.598222\pi$
$308$		0			0
$309$		0			0
$310$	4.40165	−	7.62389i	0.249997	−	0.433008i
$311$	−6.85479	+	11.8728i	−0.388699	+	0.673247i	−0.992275	−	0.124059i	$-0.960409\pi$
$311$	−6.85479	+	11.8728i	−0.388699	+	0.673247i	0.603576	+	0.797306i	$0.293742\pi$
$312$		0			0
$313$	−10.6090	−	18.3752i	−0.599653	−	1.03863i	−0.992872	−	0.119185i	$-0.961972\pi$
$313$	−10.6090	−	18.3752i	−0.599653	−	1.03863i	0.393219	−	0.919445i	$-0.371362\pi$
$314$	−12.1309			−0.684586
$315$		0			0
$316$	−0.311598			−0.0175288
$317$	1.78521	+	3.09208i	0.100268	+	0.173669i	0.911795	−	0.410646i	$-0.134697\pi$
$317$	1.78521	+	3.09208i	0.100268	+	0.173669i	−0.811527	+	0.584315i	$0.801363\pi$
$318$		0			0
$319$	1.60446	−	2.77901i	0.0898326	−	0.155595i
$320$	15.5599	−	26.9506i	0.869826	−	1.50658i
$321$		0			0
$322$		0			0
$323$	−33.6670			−1.87328
$324$		0			0
$325$	−23.9341			−1.32763
$326$	10.9846	+	19.0260i	0.608383	+	1.05375i
$327$		0			0
$328$	9.99062	−	17.3043i	0.551639	−	0.955468i
$329$		0			0
$330$		0			0
$331$	11.9728	+	20.7375i	0.658085	+	1.13984i	0.981111	+	0.193446i	$0.0619666\pi$
$331$	11.9728	+	20.7375i	0.658085	+	1.13984i	−0.323026	+	0.946390i	$0.604700\pi$
$332$	2.26914			0.124535
$333$		0			0
$334$	−6.68963			−0.366040
$335$	9.40168	+	16.2842i	0.513669	+	0.889700i
$336$		0			0
$337$	−13.7468	+	23.8102i	−0.748838	+	1.29703i	0.199542	+	0.979889i	$0.436055\pi$
$337$	−13.7468	+	23.8102i	−0.748838	+	1.29703i	−0.948380	+	0.317137i	$0.897279\pi$
$338$	−1.70784	+	2.95806i	−0.0928942	+	0.160897i
$339$		0			0
$340$	−2.68249	−	4.64620i	−0.145478	−	0.251976i
$341$	2.26373			0.122588
$342$		0			0
$343$		0			0
$344$	14.5184	+	25.1466i	0.782779	+	1.35581i
$345$		0			0
$346$	−6.32822	+	10.9608i	−0.340207	+	0.589256i
$347$	−2.56412	+	4.44119i	−0.137649	+	0.238416i	−0.926606	−	0.376033i	$-0.877288\pi$
$347$	−2.56412	+	4.44119i	−0.137649	+	0.238416i	0.788957	+	0.614448i	$0.210621\pi$
$348$		0			0
$349$	−7.56980	−	13.1113i	−0.405202	−	0.701830i	0.589143	−	0.808029i	$-0.299465\pi$
$349$	−7.56980	−	13.1113i	−0.405202	−	0.701830i	−0.994345	+	0.106198i	$0.966132\pi$
$350$		0			0
$351$		0			0
$352$	2.04918			0.109222
$353$	16.4878	+	28.5578i	0.877559	+	1.51998i	0.854011	+	0.520254i	$0.174163\pi$
$353$	16.4878	+	28.5578i	0.877559	+	1.51998i	0.0235477	+	0.999723i	$0.492504\pi$
$354$		0			0
$355$	5.77743	−	10.0068i	0.306634	−	0.531106i
$356$	−1.86865	+	3.23659i	−0.0990381	+	0.171539i
$357$		0			0
$358$	−0.894299	−	1.54897i	−0.0472651	−	0.0818656i
$359$	24.0355			1.26855			0.634274	−	0.773109i	$-0.281299\pi$
$359$	24.0355			1.26855			0.634274	+	0.773109i	$0.281299\pi$
$360$		0			0
$361$	28.1470			1.48142
$362$	−3.68227	−	6.37789i	−0.193536	−	0.335214i
$363$		0			0
$364$		0			0
$365$	1.83004	−	3.16972i	0.0957886	−	0.165911i
$366$		0			0
$367$	1.32751	+	2.29931i	0.0692952	+	0.120023i	0.898591	−	0.438787i	$-0.144592\pi$
$367$	1.32751	+	2.29931i	0.0692952	+	0.120023i	−0.829296	+	0.558810i	$0.811258\pi$
$368$	−14.1166			−0.735879
$369$		0			0
$370$	−44.7524			−2.32657
$371$		0			0
$372$		0			0
$373$	15.9592	−	27.6421i	0.826334	−	1.43125i	−0.0745621	−	0.997216i	$-0.523756\pi$
$373$	15.9592	−	27.6421i	0.826334	−	1.43125i	0.900896	−	0.434036i	$-0.142911\pi$
$374$	−3.75569	+	6.50505i	−0.194202	+	0.336368i
$375$		0			0
$376$	0.950821	+	1.64687i	0.0490348	+	0.0849308i
$377$	−8.76909			−0.451631
$378$		0			0
$379$	30.2681			1.55477			0.777384	−	0.629027i	$-0.216546\pi$
$379$	30.2681			1.55477			0.777384	+	0.629027i	$0.216546\pi$
$380$	3.75653	+	6.50651i	0.192706	+	0.333777i
$381$		0			0
$382$	16.2568	−	28.1576i	0.831771	−	1.44067i
$383$	0.866526	−	1.50087i	0.0442774	−	0.0766907i	−0.843037	−	0.537855i	$-0.819235\pi$
$383$	0.866526	−	1.50087i	0.0442774	−	0.0766907i	0.887315	+	0.461164i	$0.152568\pi$
$384$		0			0
$385$		0			0
$386$	−22.7917			−1.16006
$387$		0			0
$388$	−3.39165			−0.172185
$389$	−5.54175	−	9.59859i	−0.280978	−	0.486668i	0.690648	−	0.723191i	$-0.257325\pi$
$389$	−5.54175	−	9.59859i	−0.280978	−	0.486668i	−0.971626	+	0.236523i	$0.923992\pi$
$390$		0			0
$391$	−10.5415	+	18.2584i	−0.533107	+	0.923368i
$392$		0			0
$393$		0			0
$394$	12.8388	+	22.2375i	0.646811	+	1.12031i
$395$	−3.54022			−0.178128
$396$		0			0
$397$	25.3391			1.27173			0.635867	−	0.771799i	$-0.280643\pi$
$397$	25.3391			1.27173			0.635867	+	0.771799i	$0.280643\pi$
$398$	−12.3632	−	21.4137i	−0.619712	−	1.07337i
$399$		0			0
$400$	12.1990	−	21.1293i	0.609951	−	1.05647i
$401$	−17.4122	+	30.1588i	−0.869524	+	1.50606i	−0.00704089	+	0.999975i	$0.502241\pi$
$401$	−17.4122	+	30.1588i	−0.869524	+	1.50606i	−0.862483	+	0.506085i	$0.831092\pi$
$402$		0			0
$403$	−3.09307	−	5.35736i	−0.154077	−	0.266869i
$404$	−0.495009			−0.0246276
$405$		0			0
$406$		0			0
$407$	−5.75394	−	9.96612i	−0.285212	−	0.494002i
$408$		0			0
$409$	9.12308	−	15.8016i	0.451107	−	0.781341i	−0.547348	−	0.836905i	$-0.684362\pi$
$409$	9.12308	−	15.8016i	0.451107	−	0.781341i	0.998455	+	0.0555643i	$0.0176958\pi$
$410$	15.2469	−	26.4083i	0.752989	−	1.30422i
$411$		0			0
$412$	0.362400	+	0.627695i	0.0178541	+	0.0309243i
$413$		0			0
$414$		0			0
$415$	25.7808			1.26553
$416$	−2.79992	−	4.84961i	−0.137278	−	0.237772i
$417$		0			0
$418$	5.25945	−	9.10963i	0.257248	−	0.445567i
$419$	4.20719	−	7.28708i	0.205535	−	0.355997i	−0.744768	−	0.667323i	$-0.767440\pi$
$419$	4.20719	−	7.28708i	0.205535	−	0.355997i	0.950303	+	0.311326i	$0.100773\pi$
$420$		0			0
$421$	0.144291	+	0.249919i	0.00703230	+	0.0121803i	0.869520	−	0.493897i	$-0.164428\pi$
$421$	0.144291	+	0.249919i	0.00703230	+	0.0121803i	−0.862488	+	0.506078i	$0.831095\pi$
$422$	9.66609			0.470538
$423$		0			0
$424$	6.68966			0.324878
$425$	−18.2191	−	31.5564i	−0.883757	−	1.53071i
$426$		0			0
$427$		0			0
$428$	0.345031	−	0.597612i	0.0166777	−	0.0288866i
$429$		0			0
$430$	22.1568	+	38.3767i	1.06849	+	1.85069i
$431$	13.4959			0.650075			0.325037	−	0.945701i	$-0.394623\pi$
$431$	13.4959			0.650075			0.325037	+	0.945701i	$0.394623\pi$
$432$		0			0
$433$	−4.85211			−0.233177			−0.116589	−	0.993180i	$-0.537196\pi$
$433$	−4.85211			−0.233177			−0.116589	+	0.993180i	$0.537196\pi$
$434$		0			0
$435$		0			0
$436$	−0.142685	+	0.247138i	−0.00683339	+	0.0118358i
$437$	14.7623	−	25.5690i	0.706174	−	1.22313i
$438$		0			0
$439$	−1.27397	−	2.20657i	−0.0608031	−	0.105314i	0.834022	−	0.551732i	$-0.186033\pi$
$439$	−1.27397	−	2.20657i	−0.0608031	−	0.105314i	−0.894825	+	0.446418i	$0.852699\pi$
$440$	12.4790			0.594914
$441$		0			0
$442$	20.5265			0.976347
$443$	−0.322753	−	0.559025i	−0.0153345	−	0.0265601i	0.858256	−	0.513221i	$-0.171548\pi$
$443$	−0.322753	−	0.559025i	−0.0153345	−	0.0265601i	−0.873591	+	0.486661i	$0.838215\pi$
$444$		0			0
$445$	−21.2306	+	36.7725i	−1.00643	+	1.74319i
$446$	−2.13913	+	3.70508i	−0.101291	+	0.175441i
$447$		0			0
$448$		0			0
$449$	5.22658			0.246658			0.123329	−	0.992366i	$-0.460643\pi$
$449$	5.22658			0.246658			0.123329	+	0.992366i	$0.460643\pi$
$450$		0			0
$451$	7.84133			0.369234
$452$	0.370312	+	0.641399i	0.0174180	+	0.0301689i
$453$		0			0
$454$	11.7099	−	20.2821i	0.549571	−	0.951885i
$455$		0			0
$456$		0			0
$457$	1.43037	+	2.47748i	0.0669101	+	0.115892i	0.897540	−	0.440934i	$-0.145353\pi$
$457$	1.43037	+	2.47748i	0.0669101	+	0.115892i	−0.830630	+	0.556825i	$0.812019\pi$
$458$	−5.53084			−0.258439
$459$		0			0
$460$	4.70485			0.219365
$461$	−1.82624	−	3.16314i	−0.0850566	−	0.147322i	0.820359	−	0.571849i	$-0.193774\pi$
$461$	−1.82624	−	3.16314i	−0.0850566	−	0.147322i	−0.905415	+	0.424527i	$0.860440\pi$
$462$		0			0
$463$	−15.4052	+	26.6825i	−0.715939	+	1.24004i	0.246657	+	0.969103i	$0.420668\pi$
$463$	−15.4052	+	26.6825i	−0.715939	+	1.24004i	−0.962596	+	0.270940i	$0.912666\pi$
$464$	4.46953	−	7.74145i	0.207493	−	0.359388i
$465$		0			0
$466$	9.55764	+	16.5543i	0.442749	+	0.766864i
$467$	−20.5770			−0.952191			−0.476096	−	0.879393i	$-0.657948\pi$
$467$	−20.5770			−0.952191			−0.476096	+	0.879393i	$0.657948\pi$
$468$		0			0
$469$		0			0
$470$	1.45107	+	2.51332i	0.0669327	+	0.115931i
$471$		0			0
$472$	12.3324	−	21.3604i	0.567647	−	0.983193i
$473$	−5.69752	+	9.86839i	−0.261972	+	0.453749i
$474$		0			0
$475$	25.5139	+	44.1914i	1.17066	+	2.02764i
$476$		0			0
$477$		0			0
$478$	−18.4110			−0.842102
$479$	12.5916	+	21.8093i	0.575325	+	0.996492i	0.996006	+	0.0892833i	$0.0284577\pi$
$479$	12.5916	+	21.8093i	0.575325	+	0.996492i	−0.420682	+	0.907208i	$0.638209\pi$
$480$		0			0
$481$	−15.7239	+	27.2346i	−0.716949	+	1.24179i
$482$	5.15726	−	8.93264i	0.234907	−	0.406871i
$483$		0			0
$484$	−1.49131	−	2.58303i	−0.0677869	−	0.117410i
$485$	−38.5342			−1.74975
$486$		0			0
$487$	−32.7615			−1.48456			−0.742282	−	0.670088i	$-0.766256\pi$
$487$	−32.7615			−1.48456			−0.742282	+	0.670088i	$0.766256\pi$
$488$	14.5039	+	25.1215i	0.656560	+	1.13720i
$489$		0			0
$490$		0			0
$491$	−1.76000	+	3.04841i	−0.0794278	+	0.137573i	−0.903003	−	0.429634i	$-0.858643\pi$
$491$	−1.76000	+	3.04841i	−0.0794278	+	0.137573i	0.823575	+	0.567207i	$0.191976\pi$
$492$		0			0
$493$	−6.67520	−	11.5618i	−0.300636	−	0.520716i
$494$	−28.7452			−1.29331
$495$		0			0
$496$	6.30605			0.283150
$497$		0			0
$498$		0			0
$499$	−7.82082	+	13.5461i	−0.350108	+	0.606405i	−0.986268	−	0.165152i	$-0.947188\pi$
$499$	−7.82082	+	13.5461i	−0.350108	+	0.606405i	0.636160	+	0.771557i	$0.280522\pi$
$500$	−1.33029	+	2.30412i	−0.0594922	+	0.103044i
$501$		0			0
$502$	−5.23262	−	9.06316i	−0.233543	−	0.404509i
$503$	36.5427			1.62936			0.814678	−	0.579913i	$-0.196914\pi$
$503$	36.5427			1.62936			0.814678	+	0.579913i	$0.196914\pi$
$504$		0			0
$505$	−5.62404			−0.250267
$506$	−3.29358	−	5.70465i	−0.146418	−	0.253603i
$507$		0			0
$508$	−0.471969	+	0.817474i	−0.0209402	+	0.0362696i
$509$	−18.8229	+	32.6023i	−0.834311	+	1.44507i	0.0602789	+	0.998182i	$0.480801\pi$
$509$	−18.8229	+	32.6023i	−0.834311	+	1.44507i	−0.894590	+	0.446888i	$0.852532\pi$
$510$		0			0
$511$		0			0
$512$	25.4272			1.12373
$513$		0			0
$514$	−22.8176			−1.00644
$515$	4.11740	+	7.13155i	0.181434	+	0.314254i
$516$		0			0
$517$	−0.373135	+	0.646289i	−0.0164105	+	0.0284237i
$518$		0			0
$519$		0			0
$520$	−17.0508	−	29.5329i	−0.747728	−	1.29510i
$521$	14.3423			0.628347			0.314174	−	0.949366i	$-0.398273\pi$
$521$	14.3423			0.628347			0.314174	+	0.949366i	$0.398273\pi$
$522$		0			0
$523$	10.4844			0.458453			0.229226	−	0.973373i	$-0.426380\pi$
$523$	10.4844			0.458453			0.229226	+	0.973373i	$0.426380\pi$
$524$	0.506114	+	0.876616i	0.0221097	+	0.0382951i
$525$		0			0
$526$	15.1751	−	26.2840i	0.661665	−	1.14604i
$527$	4.70901	−	8.15625i	0.205128	−	0.355292i
$528$		0			0
$529$	2.25555	+	3.90673i	0.0980674	+	0.169858i
$530$	10.2092			0.443460
$531$		0			0
$532$		0			0
$533$	−10.7141	−	18.5573i	−0.464078	−	0.803807i
$534$		0			0
$535$	3.92007	−	6.78976i	0.169479	−	0.293547i
$536$	−8.00788	+	13.8701i	−0.345888	+	0.599095i
$537$		0			0
$538$	−0.349983	−	0.606188i	−0.0150888	−	0.0261346i
$539$		0			0
$540$		0			0
$541$	−46.0922			−1.98166			−0.990830	−	0.135118i	$-0.956859\pi$
$541$	−46.0922			−1.98166			−0.990830	+	0.135118i	$0.956859\pi$
$542$	−9.36882	−	16.2273i	−0.402425	−	0.697021i
$543$		0			0
$544$	4.26271	−	7.38323i	0.182762	−	0.316554i
$545$	−1.62112	+	2.80786i	−0.0694411	+	0.120275i
$546$		0			0
$547$	−12.1793	−	21.0951i	−0.520747	−	0.901961i	−0.999709	−	0.0241250i	$-0.992320\pi$
$547$	−12.1793	−	21.0951i	−0.520747	−	0.901961i	0.478962	−	0.877836i	$-0.341013\pi$
$548$	6.49643			0.277514
$549$		0			0
$550$	11.3847			0.485447
$551$	9.34790	+	16.1910i	0.398234	+	0.689761i
$552$		0			0
$553$		0			0
$554$	14.2379	−	24.6608i	0.604911	−	1.04774i
$555$		0			0
$556$	2.57947	+	4.46777i	0.109394	+	0.189476i
$557$	−30.5775			−1.29561			−0.647806	−	0.761805i	$-0.724313\pi$
$557$	−30.5775			−1.29561			−0.647806	+	0.761805i	$0.724313\pi$
$558$		0			0
$559$	31.1394			1.31706
$560$		0			0
$561$		0			0
$562$	−1.00951	+	1.74852i	−0.0425836	+	0.0737570i
$563$	4.41357	−	7.64452i	0.186010	−	0.322178i	−0.757907	−	0.652363i	$-0.773778\pi$
$563$	4.41357	−	7.64452i	0.186010	−	0.322178i	0.943916	+	0.330185i	$0.107111\pi$
$564$		0			0
$565$	4.20730	+	7.28725i	0.177002	+	0.306577i
$566$	3.44650			0.144867
$567$		0			0
$568$	9.84186			0.412955
$569$	3.56027	+	6.16658i	0.149254	+	0.258516i	0.930952	−	0.365141i	$-0.118979\pi$
$569$	3.56027	+	6.16658i	0.149254	+	0.258516i	−0.781698	+	0.623658i	$0.785646\pi$
$570$		0			0
$571$	−3.33181	+	5.77086i	−0.139432	+	0.241503i	−0.927282	−	0.374364i	$-0.877861\pi$
$571$	−3.33181	+	5.77086i	−0.139432	+	0.241503i	0.787850	+	0.615867i	$0.211194\pi$
$572$	0.588948	−	1.02009i	0.0246252	−	0.0426520i
$573$		0			0
$574$		0			0
$575$	31.9548			1.33261
$576$		0			0
$577$	7.91259			0.329405			0.164703	−	0.986343i	$-0.447334\pi$
$577$	7.91259			0.329405			0.164703	+	0.986343i	$0.447334\pi$
$578$	4.57627	+	7.92633i	0.190348	+	0.329692i
$579$		0			0
$580$	−1.48963	+	2.58011i	−0.0618533	+	0.107133i
$581$		0			0
$582$		0			0
$583$	1.31263	+	2.27354i	0.0543634	+	0.0941602i
$584$	3.11747			0.129002
$585$		0			0
$586$	13.5008			0.557714
$587$	9.13891	+	15.8291i	0.377203	+	0.653335i	0.990654	−	0.136398i	$-0.0435525\pi$
$587$	9.13891	+	15.8291i	0.377203	+	0.653335i	−0.613451	+	0.789733i	$0.710219\pi$
$588$		0			0
$589$	−6.59447	+	11.4220i	−0.271720	+	0.470633i
$590$	18.8208	−	32.5985i	0.774839	−	1.34206i
$591$		0			0
$592$	−16.0287	−	27.7625i	−0.658775	−	1.14103i
$593$	28.3816			1.16549			0.582745	−	0.812655i	$-0.301978\pi$
$593$	28.3816			1.16549			0.582745	+	0.812655i	$0.301978\pi$
$594$		0			0
$595$		0			0
$596$	−0.175096	−	0.303275i	−0.00717222	−	0.0124226i
$597$		0			0
$598$	−9.00044	+	15.5892i	−0.368055	+	0.637490i
$599$	4.69451	−	8.13113i	0.191813	−	0.332229i	−0.754038	−	0.656830i	$-0.771897\pi$
$599$	4.69451	−	8.13113i	0.191813	−	0.332229i	0.945851	+	0.324601i	$0.105230\pi$
$600$		0			0
$601$	−6.31432	−	10.9367i	−0.257566	−	0.446118i	0.708023	−	0.706189i	$-0.249587\pi$
$601$	−6.31432	−	10.9367i	−0.257566	−	0.446118i	−0.965589	+	0.260071i	$0.916254\pi$
$602$		0			0
$603$		0			0
$604$	6.09168			0.247867
$605$	−16.9435	−	29.3471i	−0.688853	−	1.19313i
$606$		0			0
$607$	−12.0133	+	20.8076i	−0.487604	+	0.844554i	−0.999898	−	0.0142555i	$-0.995462\pi$
$607$	−12.0133	+	20.8076i	−0.487604	+	0.844554i	0.512295	+	0.858810i	$0.328796\pi$
$608$	−5.96947	+	10.3394i	−0.242094	+	0.419319i
$609$		0			0
$610$	22.1347	+	38.3383i	0.896206	+	1.55227i
$611$	2.03935			0.0825031
$612$		0			0
$613$	−28.5415			−1.15278			−0.576390	−	0.817175i	$-0.695539\pi$
$613$	−28.5415			−1.15278			−0.576390	+	0.817175i	$0.695539\pi$
$614$	−6.91695	−	11.9805i	−0.279145	−	0.483494i
$615$		0			0
$616$		0			0
$617$	6.05549	−	10.4884i	0.243785	−	0.422248i	−0.718004	−	0.696039i	$-0.754944\pi$
$617$	6.05549	−	10.4884i	0.243785	−	0.422248i	0.961789	+	0.273791i	$0.0882776\pi$
$618$		0			0
$619$	13.2870	+	23.0137i	0.534048	+	0.924998i	0.999209	+	0.0397721i	$0.0126632\pi$
$619$	13.2870	+	23.0137i	0.534048	+	0.924998i	−0.465161	+	0.885226i	$0.654003\pi$
$620$	−2.10171			−0.0844067
$621$		0			0
$622$	−17.8207			−0.714545
$623$		0			0
$624$		0			0
$625$	3.46486	−	6.00131i	0.138594	−	0.240052i
$626$	13.7903	−	23.8855i	0.551170	−	0.954655i
$627$		0			0
$628$	1.44807	+	2.50813i	0.0577843	+	0.100085i
$629$	−47.8774			−1.90900
$630$		0			0
$631$	3.30962			0.131754			0.0658770	−	0.997828i	$-0.479015\pi$
$631$	3.30962			0.131754			0.0658770	+	0.997828i	$0.479015\pi$
$632$	−1.50769	−	2.61140i	−0.0599727	−	0.103876i
$633$		0			0
$634$	−2.32055	+	4.01931i	−0.0921608	+	0.159627i
$635$	−5.36227	+	9.28773i	−0.212795	+	0.368572i
$636$		0			0
$637$		0			0
$638$	4.17119			0.165139
$639$		0			0
$640$	28.1907			1.11433
$641$	16.2922	+	28.2189i	0.643503	+	1.11458i	0.984645	+	0.174568i	$0.0558530\pi$
$641$	16.2922	+	28.2189i	0.643503	+	1.11458i	−0.341142	+	0.940012i	$0.610814\pi$
$642$		0			0
$643$	21.5327	−	37.2957i	0.849166	−	1.47080i	−0.0327873	−	0.999462i	$-0.510438\pi$
$643$	21.5327	−	37.2957i	0.849166	−	1.47080i	0.881953	−	0.471337i	$-0.156228\pi$
$644$		0			0
$645$		0			0
$646$	−21.8814	−	37.8997i	−0.860912	−	1.49114i
$647$	−46.1975			−1.81621			−0.908106	−	0.418739i	$-0.862472\pi$
$647$	−46.1975			−1.81621			−0.908106	+	0.418739i	$0.862472\pi$
$648$		0			0
$649$	9.67935			0.379948
$650$	−15.5556	−	26.9432i	−0.610143	−	1.05680i
$651$		0			0
$652$	2.62248	−	4.54228i	0.102704	−	0.177889i
$653$	16.0002	−	27.7132i	0.626138	−	1.08450i	−0.362182	−	0.932107i	$-0.617968\pi$
$653$	16.0002	−	27.7132i	0.626138	−	1.08450i	0.988320	−	0.152395i	$-0.0486985\pi$
$654$		0			0
$655$	5.75022	+	9.95967i	0.224680	+	0.389156i
$656$	21.8435			0.852845
$657$		0			0
$658$		0			0
$659$	−19.2070	−	33.2674i	−0.748197	−	1.29591i	−0.948686	−	0.316219i	$-0.897587\pi$
$659$	−19.2070	−	33.2674i	−0.748197	−	1.29591i	0.200490	−	0.979696i	$-0.435747\pi$
$660$		0			0
$661$	−14.0130	+	24.2712i	−0.545043	+	0.944042i	0.453561	+	0.891225i	$0.350153\pi$
$661$	−14.0130	+	24.2712i	−0.545043	+	0.944042i	−0.998604	+	0.0528170i	$0.983180\pi$
$662$	−15.5631	+	26.9561i	−0.604878	+	1.04768i
$663$		0			0
$664$	10.9794	+	19.0169i	0.426083	+	0.737998i
$665$		0			0
$666$		0			0
$667$	11.7077			0.453325
$668$	0.798544	+	1.38312i	0.0308966	+	0.0535145i
$669$		0			0
$670$	−12.2210	+	21.1674i	−0.472138	+	0.817766i
$671$	−5.69183	+	9.85853i	−0.219730	+	0.380584i
$672$		0			0
$673$	0.796281	+	1.37920i	0.0306944	+	0.0531642i	0.880965	−	0.473182i	$-0.156895\pi$
$673$	0.796281	+	1.37920i	0.0306944	+	0.0531642i	−0.850270	+	0.526347i	$0.823561\pi$
$674$	−35.7383			−1.37659
$675$		0			0
$676$	0.815462			0.0313639
$677$	−21.0167	−	36.4020i	−0.807737	−	1.39904i	−0.914428	−	0.404749i	$-0.867359\pi$
$677$	−21.0167	−	36.4020i	−0.807737	−	1.39904i	0.106691	−	0.994292i	$-0.465975\pi$
$678$		0			0
$679$		0			0
$680$	25.9588	−	44.9620i	0.995476	−	1.72421i
$681$		0			0
$682$	1.47128	+	2.54833i	0.0563382	+	0.0975807i
$683$	−35.7289			−1.36713			−0.683565	−	0.729890i	$-0.739571\pi$
$683$	−35.7289			−1.36713			−0.683565	+	0.729890i	$0.739571\pi$
$684$		0			0
$685$	73.8092			2.82010
$686$		0			0
$687$		0			0
$688$	−15.8715	+	27.4902i	−0.605095	+	1.04806i
$689$	3.58704	−	6.21294i	0.136655	−	0.236694i
$690$		0			0
$691$	25.5675	+	44.2841i	0.972632	+	1.68465i	0.687538	+	0.726149i	$0.258692\pi$
$691$	25.5675	+	44.2841i	0.972632	+	1.68465i	0.285094	+	0.958499i	$0.407975\pi$
$692$	3.02161			0.114864
$693$		0			0
$694$	−6.66606			−0.253040
$695$	29.3066	+	50.7606i	1.11166	+	1.92546i
$696$		0			0
$697$	16.3115	−	28.2524i	0.617843	−	1.07014i
$698$	9.83977	−	17.0430i	0.372441	−	0.645086i
$699$		0			0
$700$		0			0
$701$	24.5761			0.928226			0.464113	−	0.885776i	$-0.346373\pi$
$701$	24.5761			0.928226			0.464113	+	0.885776i	$0.346373\pi$
$702$		0			0
$703$	67.0472			2.52873
$704$	5.20100	+	9.00840i	0.196020	+	0.339517i
$705$		0			0
$706$	−21.4321	+	37.1215i	−0.806607	+	1.39708i
$707$		0			0
$708$		0			0
$709$	−15.4488	−	26.7581i	−0.580192	−	1.00492i	−0.995456	−	0.0952206i	$-0.969644\pi$
$709$	−15.4488	−	26.7581i	−0.580192	−	1.00492i	0.415265	−	0.909701i	$-0.363689\pi$
$710$	15.0198			0.563685
$711$		0			0
$712$	−36.1664			−1.35539
$713$	4.12960	+	7.15268i	0.154655	+	0.267870i
$714$		0			0
$715$	6.69133	−	11.5897i	0.250242	−	0.433431i
$716$	−0.213506	+	0.369803i	−0.00797908	+	0.0138202i
$717$		0			0
$718$	15.6216	+	27.0573i	0.582992	+	1.00977i
$719$	6.11380			0.228006			0.114003	−	0.993480i	$-0.463633\pi$
$719$	6.11380			0.228006			0.114003	+	0.993480i	$0.463633\pi$
$720$		0			0
$721$		0			0
$722$	18.2938	+	31.6857i	0.680823	+	1.17922i
$723$		0			0
$724$	−0.879109	+	1.52266i	−0.0326718	+	0.0565893i
$725$	−10.1174	+	17.5238i	−0.375749	+	0.650816i
$726$		0			0
$727$	−22.2492	−	38.5367i	−0.825176	−	1.42925i	−0.901785	−	0.432186i	$-0.857743\pi$
$727$	−22.2492	−	38.5367i	−0.825176	−	1.42925i	0.0766087	−	0.997061i	$-0.475591\pi$
$728$		0			0
$729$		0			0
$730$	4.75763			0.176088
$731$	23.7039	+	41.0564i	0.876722	+	1.51853i
$732$		0			0
$733$	4.91854	−	8.51916i	0.181670	−	0.314662i	−0.760779	−	0.649011i	$-0.775183\pi$
$733$	4.91854	−	8.51916i	0.181670	−	0.314662i	0.942449	+	0.334349i	$0.108516\pi$
$734$	−1.72559	+	2.98881i	−0.0636926	+	0.110319i
$735$		0			0
$736$	3.73821	+	6.47478i	0.137792	+	0.238663i
$737$	−6.28514			−0.231516
$738$		0			0
$739$	14.8493			0.546239			0.273120	−	0.961980i	$-0.411944\pi$
$739$	14.8493			0.546239			0.273120	+	0.961980i	$0.411944\pi$
$740$	5.34212	+	9.25282i	0.196380	+	0.340140i
$741$		0			0
$742$		0			0
$743$	3.04201	−	5.26892i	0.111601	−	0.193298i	−0.804815	−	0.593525i	$-0.797736\pi$
$743$	3.04201	−	5.26892i	0.111601	−	0.193298i	0.916416	+	0.400228i	$0.131069\pi$
$744$		0			0
$745$	−1.98935	−	3.44566i	−0.0728843	−	0.126239i
$746$	41.4897			1.51905
$747$		0			0
$748$	1.79328			0.0655686
$749$		0			0
$750$		0			0
$751$	−11.1005	+	19.2266i	−0.405063	+	0.701590i	−0.994329	−	0.106349i	$-0.966084\pi$
$751$	−11.1005	+	19.2266i	−0.405063	+	0.701590i	0.589266	+	0.807939i	$0.299417\pi$
$752$	−1.03944	+	1.80036i	−0.0379044	+	0.0656523i
$753$		0			0
$754$	−5.69934	−	9.87156i	−0.207558	−	0.359501i
$755$	69.2106			2.51883
$756$		0			0
$757$	25.0464			0.910329			0.455164	−	0.890407i	$-0.349581\pi$
$757$	25.0464			0.910329			0.455164	+	0.890407i	$0.349581\pi$
$758$	19.6723	+	34.0735i	0.714531	+	1.23760i
$759$		0			0
$760$	−36.3526	+	62.9645i	−1.31865	+	2.28396i
$761$	−3.37632	+	5.84796i	−0.122392	+	0.211988i	−0.920710	−	0.390247i	$-0.872390\pi$
$761$	−3.37632	+	5.84796i	−0.122392	+	0.211988i	0.798319	+	0.602235i	$0.205723\pi$
$762$		0			0
$763$		0			0
$764$	−7.76233			−0.280831
$765$		0			0
$766$	2.25275			0.0813950
$767$	−13.2255	−	22.9072i	−0.477544	−	0.827131i
$768$		0			0
$769$	−21.0805	+	36.5125i	−0.760182	+	1.31667i	0.182575	+	0.983192i	$0.441557\pi$
$769$	−21.0805	+	36.5125i	−0.760182	+	1.31667i	−0.942757	+	0.333482i	$0.891776\pi$
$770$		0			0
$771$		0			0
$772$	2.72065	+	4.71230i	0.0979183	+	0.169600i
$773$	3.29852			0.118639			0.0593197	−	0.998239i	$-0.481107\pi$
$773$	3.29852			0.118639			0.0593197	+	0.998239i	$0.481107\pi$
$774$		0			0
$775$	−14.2746			−0.512757
$776$	−16.4108	−	28.4243i	−0.589112	−	1.02037i
$777$		0			0
$778$	7.20356	−	12.4769i	0.258260	−	0.447320i
$779$	−22.8425	+	39.5644i	−0.818419	+	1.41754i
$780$		0			0
$781$	1.93114	+	3.34484i	0.0691017	+	0.119688i
$782$	−27.4052			−0.980009
$783$		0			0
$784$		0			0
$785$	16.4522	+	28.4961i	0.587205	+	1.01707i
$786$		0			0
$787$	3.36455	−	5.82757i	0.119933	−	0.207731i	−0.799808	−	0.600256i	$-0.795065\pi$
$787$	3.36455	−	5.82757i	0.119933	−	0.207731i	0.919741	+	0.392526i	$0.128399\pi$
$788$	3.06515	−	5.30900i	0.109192	−	0.189125i
$789$		0			0
$790$	−2.30092	−	3.98530i	−0.0818629	−	0.141791i
$791$		0			0
$792$		0			0
$793$	31.1083			1.10469
$794$	16.4688	+	28.5248i	0.584456	+	1.01231i
$795$		0			0
$796$	−2.95160	+	5.11233i	−0.104617	+	0.181202i
$797$	8.86302	−	15.3512i	0.313944	−	0.543767i	−0.665268	−	0.746604i	$-0.731683\pi$
$797$	8.86302	−	15.3512i	0.313944	−	0.543767i	0.979213	+	0.202837i	$0.0650162\pi$
$798$		0			0
$799$	1.55239	+	2.68882i	0.0549196	+	0.0951235i
$800$	−12.9217			−0.456850
$801$		0			0
$802$	−45.2673			−1.59844
$803$	0.611702	+	1.05950i	0.0215865	+	0.0373889i
$804$		0			0
$805$		0			0
$806$	4.02060	−	6.96388i	0.141620	−	0.245292i
$807$		0			0
$808$	−2.39514	−	4.14850i	−0.0842607	−	0.145944i
$809$	−39.0857			−1.37418			−0.687089	−	0.726573i	$-0.741112\pi$
$809$	−39.0857			−1.37418			−0.687089	+	0.726573i	$0.741112\pi$
$810$		0			0
$811$	−13.9559			−0.490058			−0.245029	−	0.969516i	$-0.578797\pi$
$811$	−13.9559			−0.490058			−0.245029	+	0.969516i	$0.578797\pi$
$812$		0			0
$813$		0			0
$814$	7.47939	−	12.9547i	0.262152	−	0.454061i
$815$	29.7953	−	51.6070i	1.04369	−	1.80772i
$816$		0			0
$817$	−33.1948	−	57.4951i	−1.16134	−	2.01150i
$818$	23.7177			0.829269
$819$		0			0
$820$	−7.28010			−0.254232
$821$	−22.4983	−	38.9682i	−0.785196	−	1.36000i	−0.928882	−	0.370376i	$-0.879229\pi$
$821$	−22.4983	−	38.9682i	−0.785196	−	1.36000i	0.143685	−	0.989623i	$-0.454105\pi$
$822$		0			0
$823$	27.6232	−	47.8449i	0.962886	−	1.66777i	0.247694	−	0.968838i	$-0.420327\pi$
$823$	27.6232	−	47.8449i	0.962886	−	1.66777i	0.715191	−	0.698929i	$-0.246340\pi$
$824$	−3.50700	+	6.07430i	−0.122172	+	0.211608i
$825$		0			0
$826$		0			0
$827$	13.8901			0.483005			0.241502	−	0.970400i	$-0.422360\pi$
$827$	13.8901			0.483005			0.241502	+	0.970400i	$0.422360\pi$
$828$		0			0
$829$	38.9792			1.35381			0.676903	−	0.736073i	$-0.263322\pi$
$829$	38.9792			1.35381			0.676903	+	0.736073i	$0.263322\pi$
$830$	16.7559	+	29.0220i	0.581605	+	1.00737i
$831$		0			0
$832$	14.2129	−	24.6174i	0.492743	−	0.853456i
$833$		0			0
$834$		0			0
$835$	9.07266	+	15.7143i	0.313972	+	0.543816i
$836$	−2.51129			−0.0868548
$837$		0			0
$838$	10.9376			0.377834
$839$	−19.4708	−	33.7244i	−0.672206	−	1.16429i	−0.977277	−	0.211965i	$-0.932014\pi$
$839$	−19.4708	−	33.7244i	−0.672206	−	1.16429i	0.305072	−	0.952329i	$-0.401320\pi$
$840$		0			0
$841$	10.7932	−	18.6943i	0.372178	−	0.644631i
$842$	−0.187560	+	0.324863i	−0.00646373	+	0.0111955i
$843$		0			0
$844$	−1.15385	−	1.99852i	−0.0397170	−	0.0687918i
$845$	9.26487			0.318721
$846$		0			0
$847$		0			0
$848$	3.65657	+	6.33336i	0.125567	+	0.217488i
$849$		0			0
$850$	23.6825	−	41.0193i	0.812304	−	1.40695i
$851$	20.9932	−	36.3613i	0.719638	−	1.24645i
$852$		0			0
$853$	3.83890	+	6.64916i	0.131441	+	0.227663i	0.924232	−	0.381830i	$-0.124706\pi$
$853$	3.83890	+	6.64916i	0.131441	+	0.227663i	−0.792791	+	0.609493i	$0.791373\pi$
$854$		0			0
$855$		0			0
$856$	6.67784			0.228244
$857$	7.98194	+	13.8251i	0.272658	+	0.472258i	0.969542	−	0.244927i	$-0.0787639\pi$
$857$	7.98194	+	13.8251i	0.272658	+	0.472258i	−0.696884	+	0.717184i	$0.745431\pi$
$858$		0			0
$859$	24.1645	−	41.8542i	0.824483	−	1.42805i	−0.0778308	−	0.996967i	$-0.524799\pi$
$859$	24.1645	−	41.8542i	0.824483	−	1.42805i	0.902314	−	0.431080i	$-0.141867\pi$
$860$	5.28973	−	9.16208i	0.180378	−	0.312424i
$861$		0			0
$862$	8.77148	+	15.1926i	0.298758	+	0.517463i
$863$	34.3052			1.16776			0.583881	−	0.811839i	$-0.301533\pi$
$863$	34.3052			1.16776			0.583881	+	0.811839i	$0.301533\pi$
$864$		0			0
$865$	34.3300			1.16726
$866$	−3.15356	−	5.46212i	−0.107162	−	0.185611i
$867$		0			0
$868$		0			0
$869$	0.591670	−	1.02480i	0.0200710	−	0.0347640i
$870$		0			0
$871$	8.58776	+	14.8744i	0.290985	+	0.504001i
$872$	−2.76158			−0.0935188
$873$		0			0
$874$	38.3781			1.29816
$875$		0			0
$876$		0			0
$877$	−7.09076	+	12.2816i	−0.239438	+	0.414719i	−0.960553	−	0.278097i	$-0.910296\pi$
$877$	−7.09076	+	12.2816i	−0.239438	+	0.414719i	0.721115	+	0.692815i	$0.243630\pi$
$878$	1.65599	−	2.86826i	0.0558870	−	0.0967992i
$879$		0			0
$880$	6.82103	+	11.8144i	0.229937	+	0.398262i
$881$	−46.2822			−1.55929			−0.779643	−	0.626224i	$-0.784600\pi$
$881$	−46.2822			−1.55929			−0.779643	+	0.626224i	$0.784600\pi$
$882$		0			0
$883$	−4.37483			−0.147225			−0.0736124	−	0.997287i	$-0.523453\pi$
$883$	−4.37483			−0.147225			−0.0736124	+	0.997287i	$0.523453\pi$
$884$	−2.45026	−	4.24397i	−0.0824111	−	0.142740i
$885$		0			0
$886$	0.419538	−	0.726661i	0.0140946	−	0.0244126i
$887$	9.57208	−	16.5793i	0.321399	−	0.556679i	−0.659378	−	0.751812i	$-0.729180\pi$
$887$	9.57208	−	16.5793i	0.321399	−	0.556679i	0.980777	+	0.195132i	$0.0625136\pi$
$888$		0			0
$889$		0			0
$890$	−55.1942			−1.85011
$891$		0			0
$892$	1.02139			0.0341988
$893$	−2.17396	−	3.76540i	−0.0727486	−	0.126004i
$894$		0			0
$895$	−2.42574	+	4.20151i	−0.0810836	+	0.140441i
$896$		0			0
$897$		0			0
$898$	3.39694	+	5.88368i	0.113358	+	0.196341i
$899$	−5.22997			−0.174429
$900$		0			0
$901$	10.9221			0.363868
$902$	5.09636	+	8.82715i	0.169690	+	0.293912i
$903$		0			0
$904$	−3.58357	+	6.20692i	−0.119188	+	0.206439i
$905$	−9.98800	+	17.2997i	−0.332012	+	0.575062i
$906$		0			0
$907$	−19.9225	−	34.5068i	−0.661515	−	1.14578i	−0.980218	−	0.197923i	$-0.936580\pi$
$907$	−19.9225	−	34.5068i	−0.661515	−	1.14578i	0.318702	−	0.947855i	$-0.396753\pi$
$908$	−5.59124			−0.185552
$909$		0			0
$910$		0			0
$911$	−14.3727	−	24.8942i	−0.476189	−	0.824783i	0.523439	−	0.852063i	$-0.324649\pi$
$911$	−14.3727	−	24.8942i	−0.476189	−	0.824783i	−0.999628	+	0.0272803i	$0.991315\pi$
$912$		0			0
$913$	−4.30870	+	7.46288i	−0.142597	+	0.246985i
$914$	−1.85930	+	3.22041i	−0.0615003	+	0.106522i
$915$		0			0
$916$	0.660219	+	1.14353i	0.0218142	+	0.0377834i
$917$		0			0
$918$		0			0
$919$	−16.0269			−0.528680			−0.264340	−	0.964430i	$-0.585154\pi$
$919$	−16.0269			−0.528680			−0.264340	+	0.964430i	$0.585154\pi$
$920$	22.7648	+	39.4298i	0.750533	+	1.29996i
$921$		0			0
$922$	2.37388	−	4.11168i	0.0781796	−	0.135411i
$923$	5.27727	−	9.14050i	0.173704	−	0.300863i
$924$		0			0
$925$	36.2830	+	62.8440i	1.19298	+	2.06630i
$926$	−40.0495			−1.31611
$927$		0			0
$928$	−4.73430			−0.155411
$929$	−7.00796	−	12.1381i	−0.229924	−	0.398239i	0.727862	−	0.685724i	$-0.240514\pi$
$929$	−7.00796	−	12.1381i	−0.229924	−	0.398239i	−0.957785	+	0.287485i	$0.907181\pi$
$930$		0			0
$931$		0			0
$932$	2.28180	−	3.95219i	0.0747428	−	0.129458i
$933$		0			0
$934$	−13.3738	−	23.1640i	−0.437603	−	0.757950i
$935$	20.3743			0.666310
$936$		0			0
$937$	−51.5307			−1.68344			−0.841718	−	0.539918i	$-0.818455\pi$
$937$	−51.5307			−1.68344			−0.841718	+	0.539918i	$0.818455\pi$
$938$		0			0
$939$		0			0
$940$	0.346429	−	0.600032i	0.0112993	−	0.0195709i
$941$	23.1564	−	40.1081i	0.754877	−	1.30749i	−0.190558	−	0.981676i	$-0.561030\pi$
$941$	23.1564	−	40.1081i	0.754877	−	1.30749i	0.945435	−	0.325809i	$-0.105637\pi$
$942$		0			0
$943$	14.3045	+	24.7761i	0.465819	+	0.806821i
$944$	26.9636			0.877592
$945$		0			0
$946$	−14.8121			−0.481582
$947$	10.0041	+	17.3277i	0.325091	+	0.563073i	0.981531	−	0.191305i	$-0.0612719\pi$
$947$	10.0041	+	17.3277i	0.325091	+	0.563073i	−0.656440	+	0.754378i	$0.727939\pi$
$948$		0			0
$949$	1.67161	−	2.89531i	0.0542628	−	0.0939859i
$950$	−33.1648	+	57.4432i	−1.07601	+	1.86370i
$951$		0			0
$952$		0			0
$953$	−30.0109			−0.972148			−0.486074	−	0.873918i	$-0.661571\pi$
$953$	−30.0109			−0.972148			−0.486074	+	0.873918i	$0.661571\pi$
$954$		0			0
$955$	−88.1917			−2.85382
$956$	2.19773	+	3.80659i	0.0710798	+	0.123114i
$957$		0			0
$958$	−16.3675	+	28.3493i	−0.528809	+	0.915924i
$959$		0			0
$960$		0			0
$961$	13.6553	+	23.6516i	0.440492	+	0.762955i
$962$	−40.8782			−1.31796
$963$		0			0
$964$	−2.46250			−0.0793117
$965$	30.9106	+	53.5388i	0.995049	+	1.72348i
$966$		0			0
$967$	16.5721	−	28.7037i	0.532923	−	0.923050i	−0.466338	−	0.884607i	$-0.654427\pi$
$967$	16.5721	−	28.7037i	0.532923	−	0.923050i	0.999261	−	0.0384431i	$-0.0122398\pi$
$968$	14.4317	−	24.9964i	0.463851	−	0.803414i
$969$		0			0
$970$	−25.0448	−	43.3788i	−0.804140	−	1.39281i
$971$	41.6469			1.33651			0.668256	−	0.743932i	$-0.267041\pi$
$971$	41.6469			1.33651			0.668256	+	0.743932i	$0.267041\pi$
$972$		0			0
$973$		0			0
$974$	−21.2928	−	36.8803i	−0.682267	−	1.18172i
$975$		0			0
$976$	−15.8556	+	27.4628i	−0.507527	+	0.879062i
$977$	18.7590	−	32.4916i	0.600154	−	1.03950i	−0.392643	−	0.919691i	$-0.628439\pi$
$977$	18.7590	−	32.4916i	0.600154	−	1.03950i	0.992797	−	0.119807i	$-0.0382276\pi$
$978$		0			0
$979$	−7.09647	−	12.2914i	−0.226804	−	0.392836i
$980$		0			0
$981$		0			0
$982$	−4.57556			−0.146012
$983$	−24.0379	−	41.6349i	−0.766690	−	1.32795i	−0.939348	−	0.342964i	$-0.888569\pi$
$983$	−24.0379	−	41.6349i	−0.766690	−	1.32795i	0.172658	−	0.984982i	$-0.444764\pi$
$984$		0			0
$985$	34.8247	−	60.3182i	1.10961	−	1.92190i
$986$	8.67690	−	15.0288i	0.276329	−	0.478616i
$987$		0			0
$988$	3.43133	+	5.94323i	0.109165	+	0.189079i
$989$	−41.5747			−1.32200
$990$		0			0
$991$	−34.1286			−1.08413			−0.542065	−	0.840337i	$-0.682357\pi$
$991$	−34.1286			−1.08413			−0.542065	+	0.840337i	$0.682357\pi$
$992$	−1.66990	−	2.89236i	−0.0530195	−	0.0918324i
$993$		0			0
$994$		0			0
$995$	−33.5346	+	58.0837i	−1.06312	+	1.84138i
$996$		0			0
$997$	−22.0413	−	38.1767i	−0.698056	−	1.20907i	−0.969140	−	0.246512i	$-0.920715\pi$
$997$	−22.0413	−	38.1767i	−0.698056	−	1.20907i	0.271084	−	0.962556i	$-0.412618\pi$
$998$	−20.3321			−0.643602
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1323.2.f.h.442.10		24
3.2	odd	2		441.2.f.h.148.4	yes	24
7.2	even	3		1323.2.g.h.361.10		24
7.3	odd	6		1323.2.h.h.226.4		24
7.4	even	3		1323.2.h.h.226.3		24
7.5	odd	6		1323.2.g.h.361.9		24
7.6	odd	2	inner	1323.2.f.h.442.9		24
9.2	odd	6		441.2.f.h.295.4	yes	24
9.4	even	3		3969.2.a.bi.1.3		12
9.5	odd	6		3969.2.a.bh.1.10		12
9.7	even	3	inner	1323.2.f.h.883.10		24
21.2	odd	6		441.2.g.h.67.3		24
21.5	even	6		441.2.g.h.67.4		24
21.11	odd	6		441.2.h.h.373.10		24
21.17	even	6		441.2.h.h.373.9		24
21.20	even	2		441.2.f.h.148.3	✓	24
63.2	odd	6		441.2.h.h.214.10		24
63.11	odd	6		441.2.g.h.79.3		24
63.13	odd	6		3969.2.a.bi.1.4		12
63.16	even	3		1323.2.h.h.802.3		24
63.20	even	6		441.2.f.h.295.3	yes	24
63.25	even	3		1323.2.g.h.667.10		24
63.34	odd	6	inner	1323.2.f.h.883.9		24
63.38	even	6		441.2.g.h.79.4		24
63.41	even	6		3969.2.a.bh.1.9		12
63.47	even	6		441.2.h.h.214.9		24
63.52	odd	6		1323.2.g.h.667.9		24
63.61	odd	6		1323.2.h.h.802.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.f.h.148.3	✓	24	21.20	even	2
441.2.f.h.148.4	yes	24	3.2	odd	2
441.2.f.h.295.3	yes	24	63.20	even	6
441.2.f.h.295.4	yes	24	9.2	odd	6
441.2.g.h.67.3		24	21.2	odd	6
441.2.g.h.67.4		24	21.5	even	6
441.2.g.h.79.3		24	63.11	odd	6
441.2.g.h.79.4		24	63.38	even	6
441.2.h.h.214.9		24	63.47	even	6
441.2.h.h.214.10		24	63.2	odd	6
441.2.h.h.373.9		24	21.17	even	6
441.2.h.h.373.10		24	21.11	odd	6
1323.2.f.h.442.9		24	7.6	odd	2	inner
1323.2.f.h.442.10		24	1.1	even	1	trivial
1323.2.f.h.883.9		24	63.34	odd	6	inner
1323.2.f.h.883.10		24	9.7	even	3	inner
1323.2.g.h.361.9		24	7.5	odd	6
1323.2.g.h.361.10		24	7.2	even	3
1323.2.g.h.667.9		24	63.52	odd	6
1323.2.g.h.667.10		24	63.25	even	3
1323.2.h.h.226.3		24	7.4	even	3
1323.2.h.h.226.4		24	7.3	odd	6
1323.2.h.h.802.3		24	63.16	even	3
1323.2.h.h.802.4		24	63.61	odd	6
3969.2.a.bh.1.9		12	63.41	even	6
3969.2.a.bh.1.10		12	9.5	odd	6
3969.2.a.bi.1.3		12	9.4	even	3
3969.2.a.bi.1.4		12	63.13	odd	6

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:	\( N \)	\(=\)	\( 1323 = 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1323.f (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.649936 + 1.12572i) q^{2} +(0.155166 - 0.268756i) q^{4} +(1.76292 - 3.05347i) q^{5} +3.00314 q^{8} +O(q^{10})\)	\(q+(0.649936 + 1.12572i) q^{2} +(0.155166 - 0.268756i) q^{4} +(1.76292 - 3.05347i) q^{5} +3.00314 q^{8} +4.58314 q^{10} +(0.589267 + 1.02064i) q^{11} +(1.61030 - 2.78913i) q^{13} +(1.64151 + 2.84319i) q^{16} +4.90317 q^{17} -6.86637 q^{19} +(-0.547092 - 0.947591i) q^{20} +(-0.765972 + 1.32670i) q^{22} +(-2.14994 + 3.72380i) q^{23} +(-3.71578 - 6.43592i) q^{25} +4.18637 q^{26} +(-1.36140 - 2.35802i) q^{29} +(0.960401 - 1.66346i) q^{31} +(0.869378 - 1.50581i) q^{32} +(3.18675 + 5.51961i) q^{34} -9.76457 q^{37} +(-4.46270 - 7.72962i) q^{38} +(5.29429 - 9.16998i) q^{40} +(3.32673 - 5.76206i) q^{41} +(4.83441 + 8.37344i) q^{43} +0.365738 q^{44} -5.58928 q^{46} +(0.316609 + 0.548383i) q^{47} +(4.83004 - 8.36587i) q^{50} +(-0.499729 - 0.865557i) q^{52} +2.22756 q^{53} +4.15533 q^{55} +(1.76965 - 3.06512i) q^{58} +(4.10652 - 7.11270i) q^{59} +(4.82958 + 8.36508i) q^{61} +2.49680 q^{62} +8.82622 q^{64} +(-5.67767 - 9.83402i) q^{65} +(-2.66651 + 4.61852i) q^{67} +(0.760807 - 1.31776i) q^{68} +3.27719 q^{71} +1.03807 q^{73} +(-6.34635 - 10.9922i) q^{74} +(-1.06543 + 1.84538i) q^{76} +(-0.502039 - 0.869557i) q^{79} +11.5754 q^{80} +8.64864 q^{82} +(3.65598 + 6.33234i) q^{83} +(8.64391 - 14.9717i) q^{85} +(-6.28411 + 10.8844i) q^{86} +(1.76965 + 3.06512i) q^{88} -12.0429 q^{89} +(0.667195 + 1.15562i) q^{92} +(-0.411551 + 0.712828i) q^{94} +(-12.1049 + 20.9662i) q^{95} +(-5.46454 - 9.46487i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{2} - 12 q^{4} + 24 q^{8}+O(q^{10}) \) 24 * q - 4 * q^2 - 12 * q^4 + 24 * q^8	\( 24 q - 4 q^{2} - 12 q^{4} + 24 q^{8} - 20 q^{11} - 12 q^{16} - 32 q^{23} - 12 q^{25} - 16 q^{29} - 48 q^{32} + 24 q^{37} + 112 q^{44} - 48 q^{46} + 4 q^{50} + 64 q^{53} + 96 q^{64} - 60 q^{65} - 12 q^{67} + 112 q^{71} - 68 q^{74} + 12 q^{79} + 12 q^{85} - 76 q^{86} - 16 q^{92} - 64 q^{95}+O(q^{100}) \) 24 * q - 4 * q^2 - 12 * q^4 + 24 * q^8 - 20 * q^11 - 12 * q^16 - 32 * q^23 - 12 * q^25 - 16 * q^29 - 48 * q^32 + 24 * q^37 + 112 * q^44 - 48 * q^46 + 4 * q^50 + 64 * q^53 + 96 * q^64 - 60 * q^65 - 12 * q^67 + 112 * q^71 - 68 * q^74 + 12 * q^79 + 12 * q^85 - 76 * q^86 - 16 * q^92 - 64 * q^95

Introduction

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