LMFDB - Embedded newform 1323.2.h.h.802.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(226,1323)]

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, 2]))

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

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

chi := DirichletCharacter("1323.226");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.h (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			802.3
Character	$\chi$	$=$	1323.802
Dual form			1323.2.h.h.226.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.29987 q^{2} -0.310333 q^{4} +(1.76292 - 3.05347i) q^{5} +3.00314 q^{8} +O(q^{10})$	\(q-1.29987 q^{2} -0.310333 q^{4} +(1.76292 - 3.05347i) q^{5} +3.00314 q^{8} +(-2.29157 + 3.96912i) q^{10} +(0.589267 + 1.02064i) q^{11} +(1.61030 + 2.78913i) q^{13} -3.28303 q^{16} +(-2.45159 + 4.24627i) q^{17} +(3.43318 + 5.94645i) q^{19} +(-0.547092 + 0.947591i) q^{20} +(-0.765972 - 1.32670i) q^{22} +(-2.14994 + 3.72380i) q^{23} +(-3.71578 - 6.43592i) q^{25} +(-2.09319 - 3.62551i) q^{26} +(-1.36140 + 2.35802i) q^{29} -1.92080 q^{31} -1.73876 q^{32} +(3.18675 - 5.51961i) q^{34} +(4.88229 + 8.45637i) q^{37} +(-4.46270 - 7.72962i) q^{38} +(5.29429 - 9.16998i) q^{40} +(3.32673 + 5.76206i) q^{41} +(4.83441 - 8.37344i) q^{43} +(-0.182869 - 0.316738i) q^{44} +(2.79464 - 4.84046i) q^{46} -0.633218 q^{47} +(4.83004 + 8.36587i) q^{50} +(-0.499729 - 0.865557i) q^{52} +(-1.11378 + 1.92912i) q^{53} +4.15533 q^{55} +(1.76965 - 3.06512i) q^{58} -8.21304 q^{59} -9.65916 q^{61} +2.49680 q^{62} +8.82622 q^{64} +11.3553 q^{65} +5.33301 q^{67} +(0.760807 - 1.31776i) q^{68} +3.27719 q^{71} +(-0.519036 + 0.898997i) q^{73} +(-6.34635 - 10.9922i) q^{74} +(-1.06543 - 1.84538i) q^{76} +1.00408 q^{79} +(-5.78772 + 10.0246i) q^{80} +(-4.32432 - 7.48994i) q^{82} +(3.65598 - 6.33234i) q^{83} +(8.64391 + 14.9717i) q^{85} +(-6.28411 + 10.8844i) q^{86} +(1.76965 + 3.06512i) q^{88} +(6.02144 + 10.4294i) q^{89} +(0.667195 - 1.15562i) q^{92} +0.823103 q^{94} +24.2097 q^{95} +(-5.46454 + 9.46487i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8 q^{2} + 24 q^{4} + 24 q^{8}+O(q^{10}) $ 24 * q + 8 * q^2 + 24 * q^4 + 24 * q^8	$ 24 q + 8 q^{2} + 24 q^{4} + 24 q^{8} - 20 q^{11} + 24 q^{16} - 32 q^{23} - 12 q^{25} - 16 q^{29} + 96 q^{32} - 12 q^{37} - 56 q^{44} + 24 q^{46} + 4 q^{50} - 32 q^{53} + 96 q^{64} + 120 q^{65} + 24 q^{67} + 112 q^{71} - 68 q^{74} - 24 q^{79} + 12 q^{85} - 76 q^{86} - 16 q^{92} + 128 q^{95}+O(q^{100}) $ 24 * q + 8 * q^2 + 24 * q^4 + 24 * q^8 - 20 * q^11 + 24 * q^16 - 32 * q^23 - 12 * q^25 - 16 * q^29 + 96 * q^32 - 12 * q^37 - 56 * q^44 + 24 * q^46 + 4 * q^50 - 32 * q^53 + 96 * q^64 + 120 * q^65 + 24 * q^67 + 112 * q^71 - 68 * q^74 - 24 * q^79 + 12 * q^85 - 76 * q^86 - 16 * q^92 + 128 * q^95

Display 100 coefficients 10 coefficients

Character values

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

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.29987			−0.919148			−0.459574	−	0.888139i	$-0.651998\pi$
$2$	−1.29987			−0.919148			−0.459574	+	0.888139i	$0.651998\pi$
$3$		0			0
$3$		0			0
$4$	−0.310333			−0.155166
$5$	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
$10$	−2.29157	+	3.96912i	−0.724659	+	1.25515i
$11$	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	0.998163	−	0.0605803i	$-0.0192951\pi$
$13$	1.61030	+	2.78913i	0.446618	+	0.773564i	−0.551546	+	0.834145i	$0.685962\pi$
$14$		0			0
$15$		0			0
$16$	−3.28303			−0.820757
$17$	−2.45159	+	4.24627i	−0.594597	+	1.02987i	0.399006	+	0.916948i	$0.369355\pi$
$17$	−2.45159	+	4.24627i	−0.594597	+	1.02987i	−0.993604	+	0.112924i	$0.963978\pi$
$18$		0			0
$19$	3.43318	+	5.94645i	0.787627	+	1.36421i	0.927417	+	0.374028i	$0.122024\pi$
$19$	3.43318	+	5.94645i	0.787627	+	1.36421i	−0.139791	+	0.990181i	$0.544643\pi$
$20$	−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
$26$	−2.09319	−	3.62551i	−0.410508	−	0.711020i
$27$		0			0
$28$		0			0
$29$	−1.36140	+	2.35802i	−0.252806	+	0.437873i	−0.964297	−	0.264822i	$-0.914687\pi$
$29$	−1.36140	+	2.35802i	−0.252806	+	0.437873i	0.711491	+	0.702695i	$0.248020\pi$
$30$		0			0
$31$	−1.92080			−0.344986			−0.172493	−	0.985011i	$-0.555182\pi$
$31$	−1.92080			−0.344986			−0.172493	+	0.985011i	$0.555182\pi$
$32$	−1.73876			−0.307372
$33$		0			0
$34$	3.18675	−	5.51961i	0.546523	−	0.946606i
$35$		0			0
$36$		0			0
$37$	4.88229	+	8.45637i	0.802643	+	1.39022i	0.917871	+	0.396879i	$0.129907\pi$
$37$	4.88229	+	8.45637i	0.802643	+	1.39022i	−0.115228	+	0.993339i	$0.536760\pi$
$38$	−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	0.999742	+	0.0227205i	$0.00723278\pi$
$41$	3.32673	+	5.76206i	0.519547	+	0.899883i	−0.480194	+	0.877162i	$0.659434\pi$
$42$		0			0
$43$	4.83441	−	8.37344i	0.737240	−	1.27694i	−0.216493	−	0.976284i	$-0.569462\pi$
$43$	4.83441	−	8.37344i	0.737240	−	1.27694i	0.953734	−	0.300653i	$-0.0972047\pi$
$44$	−0.182869	−	0.316738i	−0.0275685	−	0.0477501i
$45$		0			0
$46$	2.79464	−	4.84046i	0.412047	−	0.713687i
$47$	−0.633218			−0.0923644			−0.0461822	−	0.998933i	$-0.514705\pi$
$47$	−0.633218			−0.0923644			−0.0461822	+	0.998933i	$0.514705\pi$
$48$		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
$53$	−1.11378	+	1.92912i	−0.152989	+	0.264985i	−0.932325	−	0.361621i	$-0.882223\pi$
$53$	−1.11378	+	1.92912i	−0.152989	+	0.264985i	0.779336	+	0.626606i	$0.215557\pi$
$54$		0			0
$55$	4.15533			0.560304
$56$		0			0
$57$		0			0
$58$	1.76965	−	3.06512i	0.232366	−	0.402471i
$59$	−8.21304			−1.06925			−0.534623	−	0.845091i	$-0.679546\pi$
$59$	−8.21304			−1.06925			−0.534623	+	0.845091i	$0.679546\pi$
$60$		0			0
$61$	−9.65916			−1.23673			−0.618364	−	0.785892i	$-0.712204\pi$
$61$	−9.65916			−1.23673			−0.618364	+	0.785892i	$0.712204\pi$
$62$	2.49680			0.317093
$63$		0			0
$64$	8.82622			1.10328
$65$	11.3553			1.40846
$66$		0			0
$67$	5.33301			0.651531			0.325766	−	0.945451i	$-0.394378\pi$
$67$	5.33301			0.651531			0.325766	+	0.945451i	$0.394378\pi$
$68$	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
$73$	−0.519036	+	0.898997i	−0.0607486	+	0.105220i	−0.894800	−	0.446467i	$-0.852682\pi$
$73$	−0.519036	+	0.898997i	−0.0607486	+	0.105220i	0.834052	+	0.551686i	$0.186015\pi$
$74$	−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
$79$	1.00408			0.112968			0.0564838	−	0.998404i	$-0.482011\pi$
$79$	1.00408			0.112968			0.0564838	+	0.998404i	$0.482011\pi$
$80$	−5.78772	+	10.0246i	−0.647087	+	1.12079i
$81$		0			0
$82$	−4.32432	−	7.48994i	−0.477541	−	0.827126i
$83$	3.65598	−	6.33234i	0.401296	−	0.695064i	−0.592587	−	0.805506i	$-0.701893\pi$
$83$	3.65598	−	6.33234i	0.401296	−	0.695064i	0.993883	+	0.110442i	$0.0352267\pi$
$84$		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
$89$	6.02144	+	10.4294i	0.638271	+	1.10552i	0.985812	+	0.167853i	$0.0536834\pi$
$89$	6.02144	+	10.4294i	0.638271	+	1.10552i	−0.347541	+	0.937665i	$0.612983\pi$
$90$		0			0
$91$		0			0
$92$	0.667195	−	1.15562i	0.0695599	−	0.120481i
$93$		0			0
$94$	0.823103			0.0848966
$95$	24.2097			2.48387
$96$		0			0
$97$	−5.46454	+	9.46487i	−0.554840	+	0.961012i	0.443076	+	0.896484i	$0.353887\pi$
$97$	−5.46454	+	9.46487i	−0.554840	+	0.961012i	−0.997916	+	0.0645275i	$0.979446\pi$
$98$		0			0
$99$		0			0
$100$	1.15313	+	1.99728i	0.115313	+	0.199728i
$101$	−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
$107$	−1.11181	−	1.92571i	−0.107483	−	0.186166i	0.807267	−	0.590186i	$-0.200946\pi$
$107$	−1.11181	−	1.92571i	−0.107483	−	0.186166i	−0.914750	+	0.404021i	$0.867612\pi$
$108$		0			0
$109$	0.459782	−	0.796366i	0.0440391	−	0.0762780i	−0.843166	−	0.537654i	$-0.819311\pi$
$109$	0.459782	−	0.796366i	0.0440391	−	0.0762780i	0.887205	+	0.461376i	$0.152644\pi$
$110$	−5.40139			−0.515003
$111$		0			0
$112$		0			0
$113$	−1.19327	−	2.06681i	−0.112254	−	0.194429i	0.804425	−	0.594054i	$-0.202474\pi$
$113$	−1.19327	−	2.06681i	−0.112254	−	0.194429i	−0.916679	+	0.399625i	$0.869140\pi$
$114$		0			0
$115$	7.58033	+	13.1295i	0.706870	+	1.22433i
$116$	0.422488	−	0.731770i	0.0392270	−	0.0679432i
$117$		0			0
$118$	10.6759			0.982796
$119$		0			0
$120$		0			0
$121$	4.80553	−	8.32342i	0.436866	−	0.756674i
$122$	12.5557			1.13674
$123$		0			0
$124$	0.596087			0.0535302
$125$	−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	$0.543089\pi$
$128$	−7.99544			−0.706704
$129$		0			0
$130$	−14.7605			−1.29458
$131$	−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
$136$	−7.36245	+	12.7521i	−0.631325	+	1.09349i
$137$	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	−0.966688	−	0.255958i	$-0.917609\pi$
$139$	−8.31195	−	14.3967i	−0.705010	−	1.22111i	0.261677	−	0.965155i	$-0.415724\pi$
$140$		0			0
$141$		0			0
$142$	−4.25993			−0.357486
$143$	−1.89780	+	3.28708i	−0.158702	+	0.274880i
$144$		0			0
$145$	4.80009	+	8.31401i	0.398626	+	0.690441i
$146$	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	$0.538847\pi$
$152$	10.3103	+	17.8580i	0.836278	+	1.44848i
$153$		0			0
$154$		0			0
$155$	−3.38622	+	5.86511i	−0.271988	+	0.471097i
$156$		0			0
$157$	9.33237			0.744804			0.372402	−	0.928071i	$-0.378534\pi$
$157$	9.33237			0.744804			0.372402	+	0.928071i	$0.378534\pi$
$158$	−1.30517			−0.103834
$159$		0			0
$160$	−3.06529	+	5.30924i	−0.242332	+	0.419732i
$161$		0			0
$162$		0			0
$163$	−8.45056	−	14.6368i	−0.661899	−	1.14644i	−0.980116	−	0.198425i	$-0.936417\pi$
$163$	−8.45056	−	14.6368i	−0.661899	−	1.14644i	0.318217	−	0.948018i	$-0.396916\pi$
$164$	−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	0.749124	−	0.662430i	$-0.230475\pi$
$167$	−2.57319	−	4.45689i	−0.199119	−	0.344885i	−0.948243	+	0.317545i	$0.897141\pi$
$168$		0			0
$169$	1.31385	−	2.27566i	0.101066	−	0.175051i
$170$	−11.2360	−	19.4613i	−0.861760	−	1.49261i
$171$		0			0
$172$	−1.50027	+	2.59855i	−0.114395	+	0.198138i
$173$	−9.73669			−0.740266			−0.370133	−	0.928979i	$-0.620688\pi$
$173$	−9.73669			−0.740266			−0.370133	+	0.928979i	$0.620688\pi$
$174$		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
$179$	0.687990	−	1.19163i	0.0514228	−	0.0890668i	−0.839168	−	0.543872i	$-0.816958\pi$
$179$	0.687990	−	1.19163i	0.0514228	−	0.0890668i	0.890591	+	0.454805i	$0.150291\pi$
$180$		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
$185$	34.4283			2.53122
$186$		0			0
$187$	−5.77856			−0.422570
$188$	0.196508			0.0143318
$189$		0			0
$190$	−31.4696			−2.28304
$191$	25.0129			1.80987			0.904936	−	0.425547i	$-0.139918\pi$
$191$	25.0129			1.80987			0.904936	+	0.425547i	$0.139918\pi$
$192$		0			0
$193$	17.5338			1.26211			0.631054	−	0.775739i	$-0.282623\pi$
$193$	17.5338			1.26211			0.631054	+	0.775739i	$0.282623\pi$
$194$	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
$199$	9.51110	−	16.4737i	0.674224	−	1.16779i	−0.302471	−	0.953158i	$-0.597812\pi$
$199$	9.51110	−	16.4737i	0.674224	−	1.16779i	0.976695	−	0.214631i	$-0.0688550\pi$
$200$	−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
$205$	23.4590			1.63845
$206$	1.51796	−	2.62919i	0.105761	−	0.183184i
$207$		0			0
$208$	−5.28667	−	9.15678i	−0.366565	−	0.634908i
$209$	−4.04613	+	7.00810i	−0.279876	+	0.484760i
$210$		0			0
$211$	3.71809	+	6.43993i	0.255964	+	0.443343i	0.965157	−	0.261672i	$-0.0842738\pi$
$211$	3.71809	+	6.43993i	0.255964	+	0.443343i	−0.709193	+	0.705015i	$0.750940\pi$
$212$	0.345642	−	0.598669i	0.0237388	−	0.0411168i
$213$		0			0
$214$	1.44521	+	2.50318i	0.0987927	+	0.171114i
$215$	−17.0454	−	29.5234i	−1.16248	−	2.01348i
$216$		0			0
$217$		0			0
$218$	−0.597658	+	1.03517i	−0.0404785	+	0.0701108i
$219$		0			0
$220$	−1.28953			−0.0869403
$221$	−15.7912			−1.06223
$222$		0			0
$223$	1.64565	−	2.85034i	0.110201	−	0.190873i	−0.805650	−	0.592391i	$-0.798184\pi$
$223$	1.64565	−	2.85034i	0.110201	−	0.190873i	0.915851	+	0.401518i	$0.131517\pi$
$224$		0			0
$225$		0			0
$226$	1.55110	+	2.68659i	0.103178	+	0.178709i
$227$	−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
$233$	−7.35275	−	12.7353i	−0.481695	−	0.834320i	0.518084	−	0.855330i	$-0.326645\pi$
$233$	−7.35275	−	12.7353i	−0.481695	−	0.834320i	−0.999779	+	0.0210095i	$0.993312\pi$
$234$		0			0
$235$	−1.11631	+	1.93351i	−0.0728203	+	0.126128i
$236$	2.54877			0.165911
$237$		0			0
$238$		0			0
$239$	−7.08187	−	12.2662i	−0.458088	−	0.793432i	0.540772	−	0.841169i	$-0.318132\pi$
$239$	−7.08187	−	12.2662i	−0.458088	−	0.793432i	−0.998860	+	0.0477377i	$0.984799\pi$
$240$		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	$0.915597\pi$
$242$	−6.24657	+	10.8194i	−0.401545	+	0.695496i
$243$		0			0
$244$	2.99755			0.191899
$245$		0			0
$246$		0			0
$247$	−11.0569	+	19.1512i	−0.703536	+	1.21856i
$248$	−5.76843			−0.366296
$249$		0			0
$250$	11.1442			0.704821
$251$	−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
$254$	3.95382			0.248085
$255$		0			0
$256$	−7.25938			−0.453712
$257$	−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
$262$	2.11993	−	3.67183i	0.130970	−	0.226846i
$263$	−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
$268$	−1.65501			−0.101096
$269$	0.269244	−	0.466344i	0.0164161	−	0.0284335i	−0.857701	−	0.514149i	$-0.828108\pi$
$269$	0.269244	−	0.466344i	0.0164161	−	0.0284335i	0.874117	+	0.485716i	$0.161441\pi$
$270$		0			0
$271$	7.20749	+	12.4837i	0.437824	+	0.758334i	0.997521	−	0.0703635i	$-0.0224159\pi$
$271$	7.20749	+	12.4837i	0.437824	+	0.758334i	−0.559697	+	0.828697i	$0.689083\pi$
$272$	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	$-0.395315\pi$
$278$	10.8045	+	18.7139i	0.648009	+	1.12238i
$279$		0			0
$280$		0			0
$281$	0.776622	−	1.34515i	0.0463294	−	0.0802449i	−0.841931	−	0.539586i	$-0.818581\pi$
$281$	0.776622	−	1.34515i	0.0463294	−	0.0802449i	0.888260	+	0.459341i	$0.151914\pi$
$282$		0			0
$283$	−2.65142			−0.157610			−0.0788051	−	0.996890i	$-0.525110\pi$
$283$	−2.65142			−0.157610			−0.0788051	+	0.996890i	$0.525110\pi$
$284$	−1.01702			−0.0603490
$285$		0			0
$286$	2.46689	−	4.27279i	0.145870	−	0.252655i
$287$		0			0
$288$		0			0
$289$	−3.52056	−	6.09778i	−0.207091	−	0.358693i
$290$	−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	0.976901	−	0.213694i	$-0.0685494\pi$
$293$	5.19314	+	8.99478i	0.303386	+	0.525481i	−0.673514	+	0.739174i	$0.735216\pi$
$294$		0			0
$295$	−14.4789	+	25.0783i	−0.842996	+	1.46011i
$296$	14.6622	+	25.3956i	0.852221	+	1.47609i
$297$		0			0
$298$	−0.733415	+	1.27031i	−0.0424856	+	0.0735872i
$299$	−13.8482			−0.800861
$300$		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
$305$	−17.0283	+	29.4939i	−0.975039	+	1.68882i
$306$		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
$311$	13.7096			0.777399			0.388699	−	0.921365i	$-0.372925\pi$
$311$	13.7096			0.777399			0.388699	+	0.921365i	$0.372925\pi$
$312$		0			0
$313$	21.2179			1.19931			0.599653	−	0.800260i	$-0.295305\pi$
$313$	21.2179			1.19931			0.599653	+	0.800260i	$0.295305\pi$
$314$	−12.1309			−0.684586
$315$		0			0
$316$	−0.311598			−0.0175288
$317$	−3.57043			−0.200535			−0.100268	−	0.994961i	$-0.531970\pi$
$317$	−3.57043			−0.200535			−0.100268	+	0.994961i	$0.531970\pi$
$318$		0			0
$319$	−3.20892			−0.179665
$320$	15.5599	−	26.9506i	0.869826	−	1.50658i
$321$		0			0
$322$		0			0
$323$	−33.6670			−1.87328
$324$		0			0
$325$	11.9671	−	20.7276i	0.663813	−	1.14976i
$326$	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
$331$	−23.9456			−1.31617			−0.658085	−	0.752944i	$-0.728633\pi$
$331$	−23.9456			−1.31617			−0.658085	+	0.752944i	$0.728633\pi$
$332$	−1.13457	+	1.96513i	−0.0622675	+	0.107851i
$333$		0			0
$334$	3.34482	+	5.79339i	0.183020	+	0.317000i
$335$	9.40168	−	16.2842i	0.513669	−	0.889700i
$336$		0			0
$337$	−13.7468	−	23.8102i	−0.748838	−	1.29703i	−0.948380	−	0.317137i	$-0.897279\pi$
$337$	−13.7468	−	23.8102i	−0.748838	−	1.29703i	0.199542	−	0.979889i	$-0.436055\pi$
$338$	−1.70784	+	2.95806i	−0.0928942	+	0.160897i
$339$		0			0
$340$	−2.68249	−	4.64620i	−0.145478	−	0.251976i
$341$	−1.13187	−	1.96045i	−0.0612940	−	0.106164i
$342$		0			0
$343$		0			0
$344$	14.5184	−	25.1466i	0.782779	−	1.35581i
$345$		0			0
$346$	12.6564			0.680415
$347$	5.12824			0.275299			0.137649	−	0.990481i	$-0.456045\pi$
$347$	5.12824			0.275299			0.137649	+	0.990481i	$0.456045\pi$
$348$		0			0
$349$	−7.56980	+	13.1113i	−0.405202	+	0.701830i	−0.994345	−	0.106198i	$-0.966132\pi$
$349$	−7.56980	+	13.1113i	−0.405202	+	0.701830i	0.589143	+	0.808029i	$0.299465\pi$
$350$		0			0
$351$		0			0
$352$	−1.02459	−	1.77465i	−0.0546110	−	0.0945889i
$353$	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
$359$	−12.0178	−	20.8154i	−0.634274	−	1.09859i	−0.986669	−	0.162743i	$-0.947966\pi$
$359$	−12.0178	−	20.8154i	−0.634274	−	1.09859i	0.352395	−	0.935851i	$-0.385367\pi$
$360$		0			0
$361$	−14.0735	+	24.3760i	−0.740711	+	1.28295i
$362$	7.36455			0.387072
$363$		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	$0.811258\pi$
$368$	7.05830	−	12.2253i	0.367939	−	0.637290i
$369$		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	$-0.142911\pi$
$374$	7.51139			0.388405
$375$		0			0
$376$	−1.90164			−0.0980697
$377$	−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	$0.216546\pi$
$380$	−7.51307			−0.385412
$381$		0			0
$382$	−32.5136			−1.66354
$383$	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
$388$	1.69583	−	2.93726i	0.0860925	−	0.149117i
$389$	−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
$394$	−25.6777			−1.29362
$395$	1.77011	−	3.06592i	0.0890639	−	0.154263i
$396$		0			0
$397$	−12.6696	−	21.9443i	−0.635867	−	1.10135i	−0.986331	−	0.164777i	$-0.947310\pi$
$397$	−12.6696	−	21.9443i	−0.635867	−	1.10135i	0.350464	−	0.936576i	$-0.386024\pi$
$398$	−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
$404$	0.247505	+	0.428690i	0.0123138	+	0.0213281i
$405$		0			0
$406$		0			0
$407$	−5.75394	+	9.96612i	−0.285212	+	0.494002i
$408$		0			0
$409$	−18.2462			−0.902215			−0.451107	−	0.892470i	$-0.648971\pi$
$409$	−18.2462			−0.902215			−0.451107	+	0.892470i	$0.648971\pi$
$410$	−30.4937			−1.50598
$411$		0			0
$412$	0.362400	−	0.627695i	0.0178541	−	0.0309243i
$413$		0			0
$414$		0			0
$415$	−12.8904	−	22.3268i	−0.632765	−	1.09598i
$416$	−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	0.950303	−	0.311326i	$-0.100773\pi$
$419$	4.20719	+	7.28708i	0.205535	+	0.355997i	−0.744768	+	0.667323i	$0.767440\pi$
$420$		0			0
$421$	0.144291	−	0.249919i	0.00703230	−	0.0121803i	−0.862488	−	0.506078i	$-0.831095\pi$
$421$	0.144291	−	0.249919i	0.00703230	−	0.0121803i	0.869520	+	0.493897i	$0.164428\pi$
$422$	−4.83304	−	8.37108i	−0.235269	−	0.407498i
$423$		0			0
$424$	−3.34483	+	5.79341i	−0.162439	+	0.281353i
$425$	36.4382			1.76751
$426$		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
$431$	−6.74795	+	11.6878i	−0.325037	+	0.562981i	−0.981520	−	0.191360i	$-0.938710\pi$
$431$	−6.74795	+	11.6878i	−0.325037	+	0.562981i	0.656482	+	0.754341i	$0.272044\pi$
$432$		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
$437$	−29.5245			−1.41235
$438$		0			0
$439$	2.54793			0.121606			0.0608031	−	0.998150i	$-0.480634\pi$
$439$	2.54793			0.121606			0.0608031	+	0.998150i	$0.480634\pi$
$440$	12.4790			0.594914
$441$		0			0
$442$	20.5265			0.976347
$443$	0.645506			0.0306689			0.0153345	−	0.999882i	$-0.495119\pi$
$443$	0.645506			0.0306689			0.0153345	+	0.999882i	$0.495119\pi$
$444$		0			0
$445$	42.4613			2.01286
$446$	−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
$451$	−3.92066	+	6.79079i	−0.184617	+	0.319766i
$452$	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
$457$	−2.86075			−0.133820			−0.0669101	−	0.997759i	$-0.521314\pi$
$457$	−2.86075			−0.133820			−0.0669101	+	0.997759i	$0.521314\pi$
$458$	2.76542	−	4.78985i	0.129220	−	0.223815i
$459$		0			0
$460$	−2.35242	−	4.07452i	−0.109682	−	0.189975i
$461$	−1.82624	+	3.16314i	−0.0850566	+	0.147322i	−0.905415	−	0.424527i	$-0.860440\pi$
$461$	−1.82624	+	3.16314i	−0.0850566	+	0.147322i	0.820359	+	0.571849i	$0.193774\pi$
$462$		0			0
$463$	−15.4052	−	26.6825i	−0.715939	−	1.24004i	−0.962596	−	0.270940i	$-0.912666\pi$
$463$	−15.4052	−	26.6825i	−0.715939	−	1.24004i	0.246657	−	0.969103i	$-0.420668\pi$
$464$	4.46953	−	7.74145i	0.207493	−	0.359388i
$465$		0			0
$466$	9.55764	+	16.5543i	0.442749	+	0.766864i
$467$	10.2885	+	17.8202i	0.476096	+	0.824622i	0.999625	−	0.0273858i	$-0.00871825\pi$
$467$	10.2885	+	17.8202i	0.476096	+	0.824622i	−0.523529	+	0.852008i	$0.675385\pi$
$468$		0			0
$469$		0			0
$470$	1.45107	−	2.51332i	0.0669327	−	0.115931i
$471$		0			0
$472$	−24.6649			−1.13529
$473$	11.3950			0.523944
$474$		0			0
$475$	25.5139	−	44.1914i	1.17066	−	2.02764i
$476$		0			0
$477$		0			0
$478$	9.20552	+	15.9444i	0.421051	+	0.729281i
$479$	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
$485$	19.2671	+	33.3716i	0.874875	+	1.51533i
$486$		0			0
$487$	16.3807	−	28.3723i	0.742282	−	1.28567i	−0.209173	−	0.977879i	$-0.567077\pi$
$487$	16.3807	−	28.3723i	0.742282	−	1.28567i	0.951454	−	0.307791i	$-0.0995896\pi$
$488$	−29.0078			−1.31312
$489$		0			0
$490$		0			0
$491$	−1.76000	−	3.04841i	−0.0794278	−	0.137573i	0.823575	−	0.567207i	$-0.191976\pi$
$491$	−1.76000	−	3.04841i	−0.0794278	−	0.137573i	−0.903003	+	0.429634i	$0.858643\pi$
$492$		0			0
$493$	−6.67520	−	11.5618i	−0.300636	−	0.520716i
$494$	14.3726	−	24.8941i	0.646654	−	1.12004i
$495$		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	$0.280522\pi$
$500$	2.66057			0.118984
$501$		0			0
$502$	10.4652			0.467086
$503$	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
$506$	6.58716			0.292835
$507$		0			0
$508$	0.943938			0.0418805
$509$	−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
$514$	11.4088	−	19.7606i	0.503221	−	0.871604i
$515$	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
$520$	34.1017			1.49546
$521$	−7.17115	+	12.4208i	−0.314174	+	0.544165i	−0.979262	−	0.202600i	$-0.935061\pi$
$521$	−7.17115	+	12.4208i	−0.314174	+	0.544165i	0.665088	+	0.746765i	$0.268394\pi$
$522$		0			0
$523$	−5.24222	−	9.07980i	−0.229226	−	0.397032i	0.728353	−	0.685202i	$-0.240286\pi$
$523$	−5.24222	−	9.07980i	−0.229226	−	0.397032i	−0.957579	+	0.288171i	$0.906953\pi$
$524$	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
$530$	−5.10461	−	8.84144i	−0.221730	−	0.384047i
$531$		0			0
$532$		0			0
$533$	−10.7141	+	18.5573i	−0.464078	+	0.803807i
$534$		0			0
$535$	−7.84014			−0.338959
$536$	16.0158			0.691776
$537$		0			0
$538$	−0.349983	+	0.606188i	−0.0150888	+	0.0261346i
$539$		0			0
$540$		0			0
$541$	23.0461	+	39.9170i	0.990830	+	1.71617i	0.612430	+	0.790524i	$0.290192\pi$
$541$	23.0461	+	39.9170i	0.990830	+	1.71617i	0.378399	+	0.925643i	$0.376475\pi$
$542$	−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	0.478962	+	0.877836i	$0.341013\pi$
$547$	−12.1793	+	21.0951i	−0.520747	+	0.901961i	−0.999709	+	0.0241250i	$0.992320\pi$
$548$	−3.24822	−	5.62607i	−0.138757	−	0.240334i
$549$		0			0
$550$	−5.69237	+	9.85947i	−0.242723	+	0.420409i
$551$	−18.6958			−0.796468
$552$		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
$557$	15.2888	−	26.4809i	0.647806	−	1.12203i	−0.335840	−	0.941919i	$-0.609020\pi$
$557$	15.2888	−	26.4809i	0.647806	−	1.12203i	0.983646	−	0.180114i	$-0.0576466\pi$
$558$		0			0
$559$	31.1394			1.31706
$560$		0			0
$561$		0			0
$562$	−1.00951	+	1.74852i	−0.0425836	+	0.0737570i
$563$	−8.82714			−0.372019			−0.186010	−	0.982548i	$-0.559556\pi$
$563$	−8.82714			−0.372019			−0.186010	+	0.982548i	$0.559556\pi$
$564$		0			0
$565$	−8.41459			−0.354005
$566$	3.44650			0.144867
$567$		0			0
$568$	9.84186			0.412955
$569$	−7.12055			−0.298509			−0.149254	−	0.988799i	$-0.547687\pi$
$569$	−7.12055			−0.298509			−0.149254	+	0.988799i	$0.547687\pi$
$570$		0			0
$571$	6.66361			0.278863			0.139432	−	0.990232i	$-0.455472\pi$
$571$	6.66361			0.278863			0.139432	+	0.990232i	$0.455472\pi$
$572$	0.588948	−	1.02009i	0.0246252	−	0.0426520i
$573$		0			0
$574$		0			0
$575$	31.9548			1.33261
$576$		0			0
$577$	−3.95629	+	6.85250i	−0.164703	+	0.285273i	−0.936550	−	0.350535i	$-0.886000\pi$
$577$	−3.95629	+	6.85250i	−0.164703	+	0.285273i	0.771847	+	0.635808i	$0.219333\pi$
$578$	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
$583$	−2.62525			−0.108727
$584$	−1.55874	+	2.69981i	−0.0645010	+	0.111719i
$585$		0			0
$586$	−6.75042	−	11.6921i	−0.278857	−	0.482995i
$587$	9.13891	−	15.8291i	0.377203	−	0.653335i	−0.613451	−	0.789733i	$-0.710219\pi$
$587$	9.13891	−	15.8291i	0.377203	−	0.653335i	0.990654	+	0.136398i	$0.0435525\pi$
$588$		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
$593$	−14.1908	−	24.5792i	−0.582745	−	1.00934i	−0.995152	−	0.0983450i	$-0.968645\pi$
$593$	−14.1908	−	24.5792i	−0.582745	−	1.00934i	0.412407	−	0.911000i	$-0.364688\pi$
$594$		0			0
$595$		0			0
$596$	−0.175096	+	0.303275i	−0.00717222	+	0.0124226i
$597$		0			0
$598$	18.0009			0.736111
$599$	−9.38902			−0.383625			−0.191813	−	0.981432i	$-0.561437\pi$
$599$	−9.38902			−0.383625			−0.191813	+	0.981432i	$0.561437\pi$
$600$		0			0
$601$	−6.31432	+	10.9367i	−0.257566	+	0.446118i	−0.965589	−	0.260071i	$-0.916254\pi$
$601$	−6.31432	+	10.9367i	−0.257566	+	0.446118i	0.708023	+	0.706189i	$0.249587\pi$
$602$		0			0
$603$		0			0
$604$	−3.04584	−	5.27555i	−0.123934	−	0.214659i
$605$	−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
$611$	−1.01967	−	1.76613i	−0.0412516	−	0.0714498i
$612$		0			0
$613$	14.2708	−	24.7177i	0.576390	−	0.998337i	−0.419499	−	0.907756i	$-0.637794\pi$
$613$	14.2708	−	24.7177i	0.576390	−	0.998337i	0.995889	−	0.0905814i	$-0.0288725\pi$
$614$	13.8339			0.558291
$615$		0			0
$616$		0			0
$617$	6.05549	+	10.4884i	0.243785	+	0.422248i	0.961789	−	0.273791i	$-0.0882776\pi$
$617$	6.05549	+	10.4884i	0.243785	+	0.422248i	−0.718004	+	0.696039i	$0.754944\pi$
$618$		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	$0.654003\pi$
$620$	1.05085	−	1.82013i	0.0422033	−	0.0730983i
$621$		0			0
$622$	−17.8207			−0.714545
$623$		0			0
$624$		0			0
$625$	3.46486	−	6.00131i	0.138594	−	0.240052i
$626$	−27.5806			−1.10234
$627$		0			0
$628$	−2.89614			−0.115569
$629$	−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	$0.479015\pi$
$632$	3.01538			0.119945
$633$		0			0
$634$	4.64110			0.184322
$635$	−5.36227	+	9.28773i	−0.212795	+	0.368572i
$636$		0			0
$637$		0			0
$638$	4.17119			0.165139
$639$		0			0
$640$	−14.0953	+	24.4138i	−0.557167	+	0.965041i
$641$	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	0.881953	+	0.471337i	$0.156228\pi$
$643$	21.5327	+	37.2957i	0.849166	+	1.47080i	−0.0327873	+	0.999462i	$0.510438\pi$
$644$		0			0
$645$		0			0
$646$	43.7628			1.72182
$647$	23.0988	−	40.0082i	0.908106	−	1.57289i	0.0914143	−	0.995813i	$-0.470861\pi$
$647$	23.0988	−	40.0082i	0.908106	−	1.57289i	0.816692	−	0.577074i	$-0.195805\pi$
$648$		0			0
$649$	−4.83968	−	8.38256i	−0.189974	−	0.329044i
$650$	−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
$656$	−10.9217	−	18.9170i	−0.426422	−	0.738585i
$657$		0			0
$658$		0			0
$659$	−19.2070	+	33.2674i	−0.748197	+	1.29591i	0.200490	+	0.979696i	$0.435747\pi$
$659$	−19.2070	+	33.2674i	−0.748197	+	1.29591i	−0.948686	+	0.316219i	$0.897587\pi$
$660$		0			0
$661$	28.0260			1.09009			0.545043	−	0.838408i	$-0.316513\pi$
$661$	28.0260			1.09009			0.545043	+	0.838408i	$0.316513\pi$
$662$	31.1262			1.20976
$663$		0			0
$664$	10.9794	−	19.0169i	0.426083	−	0.737998i
$665$		0			0
$666$		0			0
$667$	−5.85386	−	10.1392i	−0.226662	−	0.392591i
$668$	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	−0.850270	−	0.526347i	$-0.823561\pi$
$673$	0.796281	−	1.37920i	0.0306944	−	0.0531642i	0.880965	+	0.473182i	$0.156895\pi$
$674$	17.8691	+	30.9503i	0.688293	+	1.19216i
$675$		0			0
$676$	−0.407731	+	0.706211i	−0.0156820	+	0.0271619i
$677$	42.0334			1.61547			0.807737	−	0.589543i	$-0.200692\pi$
$677$	42.0334			1.61547			0.807737	+	0.589543i	$0.200692\pi$
$678$		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
$683$	17.8645	−	30.9422i	0.683565	−	1.18397i	−0.290321	−	0.956929i	$-0.593762\pi$
$683$	17.8645	−	30.9422i	0.683565	−	1.18397i	0.973886	−	0.227039i	$-0.0729046\pi$
$684$		0			0
$685$	73.8092			2.82010
$686$		0			0
$687$		0			0
$688$	−15.8715	+	27.4902i	−0.605095	+	1.04806i
$689$	−7.17408			−0.273311
$690$		0			0
$691$	−51.1349			−1.94526			−0.972632	−	0.232351i	$-0.925358\pi$
$691$	−51.1349			−1.94526			−0.972632	+	0.232351i	$0.925358\pi$
$692$	3.02161			0.114864
$693$		0			0
$694$	−6.66606			−0.253040
$695$	−58.6132			−2.22333
$696$		0			0
$697$	−32.6230			−1.23569
$698$	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
$703$	−33.5236	+	58.0645i	−1.26437	+	2.18995i
$704$	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
$709$	30.8976			1.16038			0.580192	−	0.814480i	$-0.302978\pi$
$709$	30.8976			1.16038			0.580192	+	0.814480i	$0.302978\pi$
$710$	−7.50992	+	13.0076i	−0.281842	+	0.488165i
$711$		0			0
$712$	18.0832	+	31.3210i	0.677697	+	1.17380i
$713$	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
$719$	−3.05690	−	5.29471i	−0.114003	−	0.197459i	0.803378	−	0.595470i	$-0.203034\pi$
$719$	−3.05690	−	5.29471i	−0.114003	−	0.197459i	−0.917381	+	0.398011i	$0.869701\pi$
$720$		0			0
$721$		0			0
$722$	18.2938	−	31.6857i	0.680823	−	1.17922i
$723$		0			0
$724$	1.75822			0.0653437
$725$	20.2347			0.751498
$726$		0			0
$727$	−22.2492	+	38.5367i	−0.825176	+	1.42925i	0.0766087	+	0.997061i	$0.475591\pi$
$727$	−22.2492	+	38.5367i	−0.825176	+	1.42925i	−0.901785	+	0.432186i	$0.857743\pi$
$728$		0			0
$729$		0			0
$730$	−2.37882	−	4.12023i	−0.0880440	−	0.152497i
$731$	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
$737$	3.14257	+	5.44309i	0.115758	+	0.200499i
$738$		0			0
$739$	−7.42464	+	12.8598i	−0.273120	+	0.473057i	−0.969659	−	0.244461i	$-0.921389\pi$
$739$	−7.42464	+	12.8598i	−0.273120	+	0.473057i	0.696539	+	0.717519i	$0.254722\pi$
$740$	−10.6842			−0.392760
$741$		0			0
$742$		0			0
$743$	3.04201	+	5.26892i	0.111601	+	0.193298i	0.916416	−	0.400228i	$-0.131069\pi$
$743$	3.04201	+	5.26892i	0.111601	+	0.193298i	−0.804815	+	0.593525i	$0.797736\pi$
$744$		0			0
$745$	−1.98935	−	3.44566i	−0.0728843	−	0.126239i
$746$	−20.7449	+	35.9311i	−0.759523	+	1.31553i
$747$		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	$0.299417\pi$
$752$	2.07887			0.0758087
$753$		0			0
$754$	11.3987			0.415116
$755$	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	$0.349581\pi$
$758$	−39.3446			−1.42906
$759$		0			0
$760$	72.7051			2.63729
$761$	−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
$766$	−1.12637	+	1.95094i	−0.0406975	+	0.0704902i
$767$	−13.2255	−	22.9072i	−0.477544	−	0.827131i
$768$		0			0
$769$	−21.0805	−	36.5125i	−0.760182	−	1.31667i	−0.942757	−	0.333482i	$-0.891776\pi$
$769$	−21.0805	−	36.5125i	−0.760182	−	1.31667i	0.182575	−	0.983192i	$-0.441557\pi$
$770$		0			0
$771$		0			0
$772$	−5.44130			−0.195837
$773$	−1.64926	+	2.85660i	−0.0593197	+	0.102745i	−0.894160	−	0.447747i	$-0.852226\pi$
$773$	−1.64926	+	2.85660i	−0.0593197	+	0.102745i	0.834841	+	0.550492i	$0.185560\pi$
$774$		0			0
$775$	7.13728	+	12.3621i	0.256379	+	0.444061i
$776$	−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
$782$	13.7026	+	23.7336i	0.490004	+	0.848713i
$783$		0			0
$784$		0			0
$785$	16.4522	−	28.4961i	0.587205	−	1.01707i
$786$		0			0
$787$	−6.72910			−0.239867			−0.119933	−	0.992782i	$-0.538268\pi$
$787$	−6.72910			−0.239867			−0.119933	+	0.992782i	$0.538268\pi$
$788$	−6.13031			−0.218383
$789$		0			0
$790$	−2.30092	+	3.98530i	−0.0818629	+	0.141791i
$791$		0			0
$792$		0			0
$793$	−15.5542	−	26.9406i	−0.552345	−	0.956689i
$794$	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	0.979213	−	0.202837i	$-0.0650162\pi$
$797$	8.86302	+	15.3512i	0.313944	+	0.543767i	−0.665268	+	0.746604i	$0.731683\pi$
$798$		0			0
$799$	1.55239	−	2.68882i	0.0549196	−	0.0951235i
$800$	6.46084	+	11.1905i	0.228425	+	0.395644i
$801$		0			0
$802$	22.6336	−	39.2026i	0.799222	−	1.38429i
$803$	−1.22340			−0.0431730
$804$		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
$809$	19.5428	−	33.8492i	0.687089	−	1.19007i	−0.285686	−	0.958323i	$-0.592221\pi$
$809$	19.5428	−	33.8492i	0.687089	−	1.19007i	0.972775	−	0.231751i	$-0.0744453\pi$
$810$		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
$815$	−59.5907			−2.08737
$816$		0			0
$817$	66.3896			2.32268
$818$	23.7177			0.829269
$819$		0			0
$820$	−7.28010			−0.254232
$821$	44.9966			1.57039			0.785196	−	0.619247i	$-0.212562\pi$
$821$	44.9966			1.57039			0.785196	+	0.619247i	$0.212562\pi$
$822$		0			0
$823$	−55.2465			−1.92577			−0.962886	−	0.269909i	$-0.913006\pi$
$823$	−55.2465			−1.92577			−0.962886	+	0.269909i	$0.913006\pi$
$824$	−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
$829$	−19.4896	+	33.7570i	−0.676903	+	1.17243i	0.299006	+	0.954251i	$0.403345\pi$
$829$	−19.4896	+	33.7570i	−0.676903	+	1.17243i	−0.975909	+	0.218179i	$0.929988\pi$
$830$	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
$835$	−18.1453			−0.627944
$836$	1.25564	−	2.17484i	0.0434274	−	0.0752184i
$837$		0			0
$838$	−5.46882	−	9.47227i	−0.188917	−	0.327214i
$839$	−19.4708	+	33.7244i	−0.672206	+	1.16429i	0.305072	+	0.952329i	$0.401320\pi$
$839$	−19.4708	+	33.7244i	−0.672206	+	1.16429i	−0.977277	+	0.211965i	$0.932014\pi$
$840$		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
$845$	−4.63243	−	8.02361i	−0.159361	−	0.276021i
$846$		0			0
$847$		0			0
$848$	3.65657	−	6.33336i	0.125567	−	0.217488i
$849$		0			0
$850$	−47.3650			−1.62461
$851$	−41.9864			−1.43928
$852$		0			0
$853$	3.83890	−	6.64916i	0.131441	−	0.227663i	−0.792791	−	0.609493i	$-0.791373\pi$
$853$	3.83890	−	6.64916i	0.131441	−	0.227663i	0.924232	+	0.381830i	$0.124706\pi$
$854$		0			0
$855$		0			0
$856$	−3.33892	−	5.78318i	−0.114122	−	0.197665i
$857$	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
$863$	−17.1526	−	29.7092i	−0.583881	−	1.01131i	−0.995014	−	0.0997366i	$-0.968200\pi$
$863$	−17.1526	−	29.7092i	−0.583881	−	1.01131i	0.411133	−	0.911576i	$-0.365133\pi$
$864$		0			0
$865$	−17.1650	+	29.7307i	−0.583628	+	1.01087i
$866$	6.30712			0.214325
$867$		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
$872$	1.38079	−	2.39159i	0.0467594	−	0.0809896i
$873$		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	$0.243630\pi$
$878$	−3.31198			−0.111774
$879$		0			0
$880$	−13.6421			−0.459874
$881$	−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	$0.523453\pi$
$884$	4.90052			0.164822
$885$		0			0
$886$	−0.839076			−0.0281893
$887$	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
$892$	−0.510697	+	0.884554i	−0.0170994	+	0.0296171i
$893$	−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
$898$	−6.79389			−0.226715
$899$	2.61499	−	4.52929i	0.0872147	−	0.151060i
$900$		0			0
$901$	−5.46105	−	9.45881i	−0.181934	−	0.315119i
$902$	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	$-0.396753\pi$
$908$	2.79562	+	4.84216i	0.0927760	+	0.160693i
$909$		0			0
$910$		0			0
$911$	−14.3727	+	24.8942i	−0.476189	+	0.824783i	−0.999628	−	0.0272803i	$-0.991315\pi$
$911$	−14.3727	+	24.8942i	−0.476189	+	0.824783i	0.523439	+	0.852063i	$0.324649\pi$
$912$		0			0
$913$	8.61739			0.285194
$914$	3.71861			0.123001
$915$		0			0
$916$	0.660219	−	1.14353i	0.0218142	−	0.0377834i
$917$		0			0
$918$		0			0
$919$	8.01347	+	13.8797i	0.264340	+	0.457850i	0.967390	−	0.253290i	$-0.0815126\pi$
$919$	8.01347	+	13.8797i	0.264340	+	0.457850i	−0.703051	+	0.711140i	$0.748179\pi$
$920$	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
$926$	20.0247	+	34.6839i	0.658054	+	1.13978i
$927$		0			0
$928$	2.36715	−	4.10002i	0.0777055	−	0.134590i
$929$	14.0159			0.459847			0.229924	−	0.973209i	$-0.426152\pi$
$929$	14.0159			0.459847			0.229924	+	0.973209i	$0.426152\pi$
$930$		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
$935$	−10.1871	+	17.6447i	−0.333155	+	0.577042i
$936$		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
$941$	−46.3128			−1.50975			−0.754877	−	0.655866i	$-0.772303\pi$
$941$	−46.3128			−1.50975			−0.754877	+	0.655866i	$0.772303\pi$
$942$		0			0
$943$	−28.6090			−0.931637
$944$	26.9636			0.877592
$945$		0			0
$946$	−14.8121			−0.481582
$947$	−20.0083			−0.650181			−0.325091	−	0.945683i	$-0.605395\pi$
$947$	−20.0083			−0.650181			−0.325091	+	0.945683i	$0.605395\pi$
$948$		0			0
$949$	−3.34322			−0.108526
$950$	−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
$955$	44.0958	−	76.3762i	1.42691	−	2.47148i
$956$	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
$961$	−27.3105			−0.880985
$962$	20.4391	−	35.4015i	0.658982	−	1.14139i
$963$		0			0
$964$	1.23125	+	2.13259i	0.0396559	+	0.0686860i
$965$	30.9106	−	53.5388i	0.995049	−	1.72348i
$966$		0			0
$967$	16.5721	+	28.7037i	0.532923	+	0.923050i	0.999261	+	0.0384431i	$0.0122398\pi$
$967$	16.5721	+	28.7037i	0.532923	+	0.923050i	−0.466338	+	0.884607i	$0.654427\pi$
$968$	14.4317	−	24.9964i	0.463851	−	0.803414i
$969$		0			0
$970$	−25.0448	−	43.3788i	−0.804140	−	1.39281i
$971$	−20.8234	−	36.0672i	−0.668256	−	1.15745i	−0.978392	−	0.206761i	$-0.933708\pi$
$971$	−20.8234	−	36.0672i	−0.668256	−	1.15745i	0.310136	−	0.950692i	$-0.399625\pi$
$972$		0			0
$973$		0			0
$974$	−21.2928	+	36.8803i	−0.682267	+	1.18172i
$975$		0			0
$976$	31.7113			1.01505
$977$	−37.5181			−1.20031			−0.600154	−	0.799884i	$-0.704894\pi$
$977$	−37.5181			−1.20031			−0.600154	+	0.799884i	$0.704894\pi$
$978$		0			0
$979$	−7.09647	+	12.2914i	−0.226804	+	0.392836i
$980$		0			0
$981$		0			0
$982$	2.28778	+	3.96255i	0.0730059	+	0.126450i
$983$	−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
$989$	20.7873	+	36.0047i	0.660999	+	1.14488i
$990$		0			0
$991$	17.0643	−	29.5562i	0.542065	−	0.938884i	−0.456720	−	0.889610i	$-0.650976\pi$
$991$	17.0643	−	29.5562i	0.542065	−	0.938884i	0.998785	−	0.0492737i	$-0.0156907\pi$
$992$	3.33981			0.106039
$993$		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	$-0.412618\pi$
$998$	10.1661	−	17.6081i	0.321801	−	0.557376i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.f.h.148.3	✓	24	63.59	even	6
441.2.f.h.148.4	yes	24	63.32	odd	6
441.2.f.h.295.3	yes	24	21.17	even	6
441.2.f.h.295.4	yes	24	21.11	odd	6
441.2.g.h.67.3		24	9.5	odd	6
441.2.g.h.67.4		24	63.41	even	6
441.2.g.h.79.3		24	21.2	odd	6
441.2.g.h.79.4		24	21.5	even	6
441.2.h.h.214.9		24	21.20	even	2
441.2.h.h.214.10		24	3.2	odd	2
441.2.h.h.373.9		24	63.5	even	6
441.2.h.h.373.10		24	63.23	odd	6
1323.2.f.h.442.9		24	63.31	odd	6
1323.2.f.h.442.10		24	63.4	even	3
1323.2.f.h.883.9		24	7.3	odd	6
1323.2.f.h.883.10		24	7.4	even	3
1323.2.g.h.361.9		24	63.13	odd	6
1323.2.g.h.361.10		24	9.4	even	3
1323.2.g.h.667.9		24	7.5	odd	6
1323.2.g.h.667.10		24	7.2	even	3
1323.2.h.h.226.3		24	63.58	even	3	inner
1323.2.h.h.226.4		24	63.40	odd	6	inner
1323.2.h.h.802.3		24	1.1	even	1	trivial
1323.2.h.h.802.4		24	7.6	odd	2	inner
3969.2.a.bh.1.9		12	63.38	even	6
3969.2.a.bh.1.10		12	63.11	odd	6
3969.2.a.bi.1.3		12	63.25	even	3
3969.2.a.bi.1.4		12	63.52	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.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.29987 q^{2} -0.310333 q^{4} +(1.76292 - 3.05347i) q^{5} +3.00314 q^{8} +O(q^{10})\)	\(q-1.29987 q^{2} -0.310333 q^{4} +(1.76292 - 3.05347i) q^{5} +3.00314 q^{8} +(-2.29157 + 3.96912i) q^{10} +(0.589267 + 1.02064i) q^{11} +(1.61030 + 2.78913i) q^{13} -3.28303 q^{16} +(-2.45159 + 4.24627i) q^{17} +(3.43318 + 5.94645i) q^{19} +(-0.547092 + 0.947591i) q^{20} +(-0.765972 - 1.32670i) q^{22} +(-2.14994 + 3.72380i) q^{23} +(-3.71578 - 6.43592i) q^{25} +(-2.09319 - 3.62551i) q^{26} +(-1.36140 + 2.35802i) q^{29} -1.92080 q^{31} -1.73876 q^{32} +(3.18675 - 5.51961i) q^{34} +(4.88229 + 8.45637i) q^{37} +(-4.46270 - 7.72962i) q^{38} +(5.29429 - 9.16998i) q^{40} +(3.32673 + 5.76206i) q^{41} +(4.83441 - 8.37344i) q^{43} +(-0.182869 - 0.316738i) q^{44} +(2.79464 - 4.84046i) q^{46} -0.633218 q^{47} +(4.83004 + 8.36587i) q^{50} +(-0.499729 - 0.865557i) q^{52} +(-1.11378 + 1.92912i) q^{53} +4.15533 q^{55} +(1.76965 - 3.06512i) q^{58} -8.21304 q^{59} -9.65916 q^{61} +2.49680 q^{62} +8.82622 q^{64} +11.3553 q^{65} +5.33301 q^{67} +(0.760807 - 1.31776i) q^{68} +3.27719 q^{71} +(-0.519036 + 0.898997i) q^{73} +(-6.34635 - 10.9922i) q^{74} +(-1.06543 - 1.84538i) q^{76} +1.00408 q^{79} +(-5.78772 + 10.0246i) q^{80} +(-4.32432 - 7.48994i) q^{82} +(3.65598 - 6.33234i) q^{83} +(8.64391 + 14.9717i) q^{85} +(-6.28411 + 10.8844i) q^{86} +(1.76965 + 3.06512i) q^{88} +(6.02144 + 10.4294i) q^{89} +(0.667195 - 1.15562i) q^{92} +0.823103 q^{94} +24.2097 q^{95} +(-5.46454 + 9.46487i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{2} + 24 q^{4} + 24 q^{8}+O(q^{10}) \) 24 * q + 8 * q^2 + 24 * q^4 + 24 * q^8	\( 24 q + 8 q^{2} + 24 q^{4} + 24 q^{8} - 20 q^{11} + 24 q^{16} - 32 q^{23} - 12 q^{25} - 16 q^{29} + 96 q^{32} - 12 q^{37} - 56 q^{44} + 24 q^{46} + 4 q^{50} - 32 q^{53} + 96 q^{64} + 120 q^{65} + 24 q^{67} + 112 q^{71} - 68 q^{74} - 24 q^{79} + 12 q^{85} - 76 q^{86} - 16 q^{92} + 128 q^{95}+O(q^{100}) \) 24 * q + 8 * q^2 + 24 * q^4 + 24 * q^8 - 20 * q^11 + 24 * q^16 - 32 * q^23 - 12 * q^25 - 16 * q^29 + 96 * q^32 - 12 * q^37 - 56 * q^44 + 24 * q^46 + 4 * q^50 - 32 * q^53 + 96 * q^64 + 120 * q^65 + 24 * q^67 + 112 * q^71 - 68 * q^74 - 24 * q^79 + 12 * q^85 - 76 * q^86 - 16 * q^92 + 128 * q^95

Introduction

L-functions

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