LMFDB - Embedded newform 1323.2.g.h.361.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(361,1323)]

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, 4]))

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

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

chi := DirichletCharacter("1323.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.g (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			361.9
Character	$\chi$	$=$	1323.361
Dual form			1323.2.g.h.667.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.649936 - 1.12572i) q^{2} +(0.155166 + 0.268756i) q^{4} +3.52584 q^{5} +3.00314 q^{8} +O(q^{10})$	\(q+(0.649936 - 1.12572i) q^{2} +(0.155166 + 0.268756i) q^{4} +3.52584 q^{5} +3.00314 q^{8} +(2.29157 - 3.96912i) q^{10} -1.17853 q^{11} +(-1.61030 + 2.78913i) q^{13} +(1.64151 - 2.84319i) q^{16} +(2.45159 - 4.24627i) q^{17} +(-3.43318 - 5.94645i) q^{19} +(0.547092 + 0.947591i) q^{20} +(-0.765972 + 1.32670i) q^{22} +4.29987 q^{23} +7.43156 q^{25} +(2.09319 + 3.62551i) q^{26} +(-1.36140 - 2.35802i) q^{29} +(-0.960401 - 1.66346i) q^{31} +(0.869378 + 1.50581i) q^{32} +(-3.18675 - 5.51961i) q^{34} +(4.88229 + 8.45637i) q^{37} -8.92540 q^{38} +10.5886 q^{40} +(-3.32673 + 5.76206i) q^{41} +(4.83441 + 8.37344i) q^{43} +(-0.182869 - 0.316738i) q^{44} +(2.79464 - 4.84046i) q^{46} +(-0.316609 + 0.548383i) q^{47} +(4.83004 - 8.36587i) q^{50} -0.999459 q^{52} +(-1.11378 + 1.92912i) q^{53} -4.15533 q^{55} -3.53930 q^{58} +(-4.10652 - 7.11270i) q^{59} +(-4.82958 + 8.36508i) q^{61} -2.49680 q^{62} +8.82622 q^{64} +(-5.67767 + 9.83402i) q^{65} +(-2.66651 - 4.61852i) q^{67} +1.52161 q^{68} +3.27719 q^{71} +(0.519036 - 0.898997i) q^{73} +12.6927 q^{74} +(1.06543 - 1.84538i) q^{76} +(-0.502039 + 0.869557i) q^{79} +(5.78772 - 10.0246i) q^{80} +(4.32432 + 7.48994i) q^{82} +(-3.65598 - 6.33234i) q^{83} +(8.64391 - 14.9717i) q^{85} +12.5682 q^{86} -3.53930 q^{88} +(-6.02144 - 10.4294i) q^{89} +(0.667195 + 1.15562i) q^{92} +(0.411551 + 0.712828i) q^{94} +(-12.1049 - 20.9662i) q^{95} +(5.46454 + 9.46487i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} + 40 q^{11} - 12 q^{16} + 64 q^{23} + 24 q^{25} - 16 q^{29} - 48 q^{32} - 12 q^{37} - 56 q^{44} + 24 q^{46} + 4 q^{50} - 32 q^{53} + 96 q^{64} - 60 q^{65} - 12 q^{67} + 112 q^{71} + 136 q^{74} + 12 q^{79} + 12 q^{85} + 152 q^{86} - 16 q^{92} - 64 q^{95}+O(q^{100}) $ 24 * q - 4 * q^2 - 12 * q^4 + 24 * q^8 + 40 * q^11 - 12 * q^16 + 64 * q^23 + 24 * q^25 - 16 * q^29 - 48 * q^32 - 12 * q^37 - 56 * q^44 + 24 * q^46 + 4 * q^50 - 32 * q^53 + 96 * q^64 - 60 * q^65 - 12 * q^67 + 112 * q^71 + 136 * q^74 + 12 * q^79 + 12 * q^85 + 152 * q^86 - 16 * q^92 - 64 * q^95

Display 100 coefficients 10 coefficients

Character values

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

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.649936	−	1.12572i	0.459574	−	0.796006i	−0.539364	−	0.842073i	$-0.681335\pi$
$2$	0.649936	−	1.12572i	0.459574	−	0.796006i	0.998938	+	0.0460668i	$0.0146687\pi$
$3$		0			0
$3$		0			0
$4$	0.155166	+	0.268756i	0.0775831	+	0.134378i
$5$	3.52584			1.57680			0.788402	−	0.615160i	$-0.210909\pi$
$5$	3.52584			1.57680			0.788402	+	0.615160i	$0.210909\pi$
$6$		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
$11$	−1.17853			−0.355342			−0.177671	−	0.984090i	$-0.556856\pi$
$11$	−1.17853			−0.355342			−0.177671	+	0.984090i	$0.556856\pi$
$12$		0			0
$13$	−1.61030	+	2.78913i	−0.446618	+	0.773564i	−0.998163	−	0.0605803i	$-0.980705\pi$
$13$	−1.61030	+	2.78913i	−0.446618	+	0.773564i	0.551546	+	0.834145i	$0.314038\pi$
$14$		0			0
$15$		0			0
$16$	1.64151	−	2.84319i	0.410379	−	0.710797i
$17$	2.45159	−	4.24627i	0.594597	−	1.02987i	−0.399006	−	0.916948i	$-0.630645\pi$
$17$	2.45159	−	4.24627i	0.594597	−	1.02987i	0.993604	−	0.112924i	$-0.0360218\pi$
$18$		0			0
$19$	−3.43318	−	5.94645i	−0.787627	−	1.36421i	−0.927417	−	0.374028i	$-0.877976\pi$
$19$	−3.43318	−	5.94645i	−0.787627	−	1.36421i	0.139791	−	0.990181i	$-0.455357\pi$
$20$	0.547092	+	0.947591i	0.122333	+	0.211888i
$21$		0			0
$22$	−0.765972	+	1.32670i	−0.163306	+	0.282854i
$23$	4.29987			0.896585			0.448293	−	0.893887i	$-0.352032\pi$
$23$	4.29987			0.896585			0.448293	+	0.893887i	$0.352032\pi$
$24$		0			0
$25$	7.43156			1.48631
$26$	2.09319	+	3.62551i	0.410508	+	0.711020i
$27$		0			0
$28$		0			0
$29$	−1.36140	−	2.35802i	−0.252806	−	0.437873i	0.711491	−	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	$-0.221849\pi$
$31$	−0.960401	−	1.66346i	−0.172493	−	0.298767i	−0.939291	+	0.343122i	$0.888516\pi$
$32$	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
$37$	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	$0.536760\pi$
$38$	−8.92540			−1.44789
$39$		0			0
$40$	10.5886			1.67420
$41$	−3.32673	+	5.76206i	−0.519547	+	0.899883i	0.480194	+	0.877162i	$0.340566\pi$
$41$	−3.32673	+	5.76206i	−0.519547	+	0.899883i	−0.999742	+	0.0227205i	$0.992767\pi$
$42$		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	$0.569462\pi$
$44$	−0.182869	−	0.316738i	−0.0275685	−	0.0477501i
$45$		0			0
$46$	2.79464	−	4.84046i	0.412047	−	0.713687i
$47$	−0.316609	+	0.548383i	−0.0461822	+	0.0799899i	−0.888192	−	0.459472i	$-0.848039\pi$
$47$	−0.316609	+	0.548383i	−0.0461822	+	0.0799899i	0.842010	+	0.539461i	$0.181372\pi$
$48$		0			0
$49$		0			0
$50$	4.83004	−	8.36587i	0.683071	−	1.18311i
$51$		0			0
$52$	−0.999459			−0.138600
$53$	−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
$58$	−3.53930			−0.464733
$59$	−4.10652	−	7.11270i	−0.534623	−	0.925995i	−0.999181	−	0.0404521i	$-0.987120\pi$
$59$	−4.10652	−	7.11270i	−0.534623	−	0.925995i	0.464558	−	0.885543i	$-0.346213\pi$
$60$		0			0
$61$	−4.82958	+	8.36508i	−0.618364	+	1.07104i	0.371420	+	0.928465i	$0.378871\pi$
$61$	−4.82958	+	8.36508i	−0.618364	+	1.07104i	−0.989784	+	0.142573i	$0.954462\pi$
$62$	−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	0.655901	−	0.754847i	$-0.272289\pi$
$67$	−2.66651	−	4.61852i	−0.325766	−	0.564242i	−0.981667	+	0.190604i	$0.938955\pi$
$68$	1.52161			0.184523
$69$		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	−0.834052	−	0.551686i	$-0.813985\pi$
$73$	0.519036	−	0.898997i	0.0607486	−	0.105220i	0.894800	+	0.446467i	$0.147318\pi$
$74$	12.6927			1.47550
$75$		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	−0.892885	−	0.450285i	$-0.851322\pi$
$79$	−0.502039	+	0.869557i	−0.0564838	+	0.0978328i	0.836401	+	0.548118i	$0.184656\pi$
$80$	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	$-0.298107\pi$
$83$	−3.65598	−	6.33234i	−0.401296	−	0.695064i	−0.993883	+	0.110442i	$0.964773\pi$
$84$		0			0
$85$	8.64391	−	14.9717i	0.937563	−	1.62391i
$86$	12.5682			1.35527
$87$		0			0
$88$	−3.53930			−0.377291
$89$	−6.02144	−	10.4294i	−0.638271	−	1.10552i	−0.985812	−	0.167853i	$-0.946317\pi$
$89$	−6.02144	−	10.4294i	−0.638271	−	1.10552i	0.347541	−	0.937665i	$-0.387017\pi$
$90$		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	$0.0205540\pi$
$97$	5.46454	+	9.46487i	0.554840	+	0.961012i	−0.443076	+	0.896484i	$0.646113\pi$
$98$		0			0
$99$		0			0
$100$	1.15313	+	1.99728i	0.115313	+	0.199728i
$101$	−1.59509			−0.158718			−0.0793588	−	0.996846i	$-0.525287\pi$
$101$	−1.59509			−0.158718			−0.0793588	+	0.996846i	$0.525287\pi$
$102$		0			0
$103$	−2.33556			−0.230129			−0.115065	−	0.993358i	$-0.536708\pi$
$103$	−2.33556			−0.230129			−0.115065	+	0.993358i	$0.536708\pi$
$104$	−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	$0.152644\pi$
$110$	−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
$115$	15.1607			1.41374
$116$	0.422488	−	0.731770i	0.0392270	−	0.0679432i
$117$		0			0
$118$	−10.6759			−0.982796
$119$		0			0
$120$		0			0
$121$	−9.61106			−0.873732
$122$	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
$131$	−3.26176			−0.284981			−0.142490	−	0.989796i	$-0.545511\pi$
$131$	−3.26176			−0.284981			−0.142490	+	0.989796i	$0.545511\pi$
$132$		0			0
$133$		0			0
$134$	−6.93223			−0.598854
$135$		0			0
$136$	7.36245	−	12.7521i	0.631325	−	1.09349i
$137$	−20.9338			−1.78849			−0.894246	−	0.447575i	$-0.852288\pi$
$137$	−20.9338			−1.78849			−0.894246	+	0.447575i	$0.852288\pi$
$138$		0			0
$139$	8.31195	−	14.3967i	0.705010	−	1.22111i	−0.261677	−	0.965155i	$-0.584276\pi$
$139$	8.31195	−	14.3967i	0.705010	−	1.22111i	0.966688	−	0.255958i	$-0.0823910\pi$
$140$		0			0
$141$		0			0
$142$	2.12997	−	3.68921i	0.178743	−	0.309592i
$143$	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
$149$	−1.12844			−0.0924456			−0.0462228	−	0.998931i	$-0.514718\pi$
$149$	−1.12844			−0.0924456			−0.0462228	+	0.998931i	$0.514718\pi$
$150$		0			0
$151$	−19.6295			−1.59743			−0.798714	−	0.601711i	$-0.794486\pi$
$151$	−19.6295			−1.59743			−0.798714	+	0.601711i	$0.794486\pi$
$152$	−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
$157$	4.66619	+	8.08207i	0.372402	+	0.645020i	0.989935	−	0.141526i	$-0.0452009\pi$
$157$	4.66619	+	8.08207i	0.372402	+	0.645020i	−0.617532	+	0.786545i	$0.711868\pi$
$158$	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
$163$	−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	$-0.396916\pi$
$164$	−2.06478			−0.161232
$165$		0			0
$166$	−9.50460			−0.737700
$167$	2.57319	−	4.45689i	0.199119	−	0.344885i	−0.749124	−	0.662430i	$-0.769525\pi$
$167$	2.57319	−	4.45689i	0.199119	−	0.344885i	0.948243	+	0.317545i	$0.102859\pi$
$168$		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
$173$	−4.86834	+	8.43222i	−0.370133	+	0.641090i	−0.989586	−	0.143945i	$-0.954021\pi$
$173$	−4.86834	+	8.43222i	−0.370133	+	0.641090i	0.619453	+	0.785034i	$0.287355\pi$
$174$		0			0
$175$		0			0
$176$	−1.93458	+	3.35079i	−0.145825	+	0.252576i
$177$		0			0
$178$	−15.6542			−1.17333
$179$	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	$-0.432471\pi$
$181$	5.66560			0.421120			0.210560	+	0.977581i	$0.432471\pi$
$182$		0			0
$183$		0			0
$184$	12.9131			0.951967
$185$	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	−0.0839339	+	0.996471i	$0.526748\pi$
$191$	−12.5065	+	21.6618i	−0.904936	+	1.56740i	−0.821003	+	0.570925i	$0.806585\pi$
$192$		0			0
$193$	−8.76688	−	15.1847i	−0.631054	−	1.09302i	−0.987337	−	0.158640i	$-0.949289\pi$
$193$	−8.76688	−	15.1847i	−0.631054	−	1.09302i	0.356282	−	0.934378i	$-0.384044\pi$
$194$	14.2064			1.01996
$195$		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	$0.402188\pi$
$199$	−9.51110	+	16.4737i	−0.674224	+	1.16779i	−0.976695	+	0.214631i	$0.931145\pi$
$200$	22.3180			1.57812
$201$		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
$206$	−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	−0.709193	−	0.705015i	$-0.750940\pi$
$211$	3.71809	−	6.43993i	0.255964	−	0.443343i	0.965157	+	0.261672i	$0.0842738\pi$
$212$	−0.691283			−0.0474775
$213$		0			0
$214$	−2.89043			−0.197585
$215$	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
$220$	−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	0.805650	−	0.592391i	$-0.201816\pi$
$223$	−1.64565	−	2.85034i	−0.110201	−	0.190873i	−0.915851	+	0.401518i	$0.868483\pi$
$224$		0			0
$225$		0			0
$226$	1.55110	+	2.68659i	0.103178	+	0.178709i
$227$	−18.0169			−1.19583			−0.597913	−	0.801561i	$-0.704003\pi$
$227$	−18.0169			−1.19583			−0.597913	+	0.801561i	$0.704003\pi$
$228$		0			0
$229$	−4.25491			−0.281173			−0.140586	−	0.990068i	$-0.544899\pi$
$229$	−4.25491			−0.281173			−0.140586	+	0.990068i	$0.544899\pi$
$230$	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
$236$	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
$241$	−7.93503			−0.511140			−0.255570	−	0.966791i	$-0.582263\pi$
$241$	−7.93503			−0.511140			−0.255570	+	0.966791i	$0.582263\pi$
$242$	−6.24657	+	10.8194i	−0.401545	+	0.695496i
$243$		0			0
$244$	−2.99755			−0.191899
$245$		0			0
$246$		0			0
$247$	22.1139			1.40707
$248$	−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	$-0.418225\pi$
$251$	8.05097			0.508173			0.254087	+	0.967181i	$0.418225\pi$
$252$		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
$257$	−17.5537			−1.09497			−0.547486	−	0.836815i	$-0.684415\pi$
$257$	−17.5537			−1.09497			−0.547486	+	0.836815i	$0.684415\pi$
$258$		0			0
$259$		0			0
$260$	−3.52393			−0.218545
$261$		0			0
$262$	−2.11993	+	3.67183i	−0.130970	+	0.226846i
$263$	23.3486			1.43973			0.719867	−	0.694112i	$-0.244203\pi$
$263$	23.3486			1.43973			0.719867	+	0.694112i	$0.244203\pi$
$264$		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
$269$	−0.269244	+	0.466344i	−0.0164161	+	0.0284335i	−0.874117	−	0.485716i	$-0.838559\pi$
$269$	−0.269244	+	0.466344i	−0.0164161	+	0.0284335i	0.857701	+	0.514149i	$0.171892\pi$
$270$		0			0
$271$	−7.20749	−	12.4837i	−0.437824	−	0.758334i	0.559697	−	0.828697i	$-0.310917\pi$
$271$	−7.20749	−	12.4837i	−0.437824	−	0.758334i	−0.997521	+	0.0703635i	$0.977584\pi$
$272$	−8.04863	−	13.9406i	−0.488020	−	0.845275i
$273$		0			0
$274$	−13.6056	+	23.5656i	−0.821945	+	1.42365i
$275$	−8.75835			−0.528148
$276$		0			0
$277$	21.9066			1.31624			0.658121	−	0.752912i	$-0.271351\pi$
$277$	21.9066			1.31624			0.658121	+	0.752912i	$0.271351\pi$
$278$	−10.8045	−	18.7139i	−0.648009	−	1.12238i
$279$		0			0
$280$		0			0
$281$	0.776622	+	1.34515i	0.0463294	+	0.0802449i	0.888260	−	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	$-0.191777\pi$
$283$	−1.32571	−	2.29619i	−0.0788051	−	0.136495i	−0.902735	+	0.430198i	$0.858444\pi$
$284$	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
$289$	−3.52056	−	6.09778i	−0.207091	−	0.358693i
$290$	−12.4790			−0.732793
$291$		0			0
$292$	0.322148			0.0188523
$293$	−5.19314	+	8.99478i	−0.303386	+	0.525481i	−0.976901	−	0.213694i	$-0.931451\pi$
$293$	−5.19314	+	8.99478i	−0.303386	+	0.525481i	0.673514	+	0.739174i	$0.264784\pi$
$294$		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
$299$	−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
$304$	−22.5425			−1.29290
$305$	−17.0283	+	29.4939i	−0.975039	+	1.68882i
$306$		0			0
$307$	10.6425			0.607400			0.303700	−	0.952768i	$-0.401778\pi$
$307$	10.6425			0.607400			0.303700	+	0.952768i	$0.401778\pi$
$308$		0			0
$309$		0			0
$310$	−8.80331			−0.499994
$311$	6.85479	+	11.8728i	0.388699	+	0.673247i	0.992275	−	0.124059i	$-0.0395912\pi$
$311$	6.85479	+	11.8728i	0.388699	+	0.673247i	−0.603576	+	0.797306i	$0.706258\pi$
$312$		0			0
$313$	10.6090	−	18.3752i	0.599653	−	1.03863i	−0.393219	−	0.919445i	$-0.628638\pi$
$313$	10.6090	−	18.3752i	0.599653	−	1.03863i	0.992872	−	0.119185i	$-0.0380282\pi$
$314$	12.1309			0.684586
$315$		0			0
$316$	−0.311598			−0.0175288
$317$	1.78521	−	3.09208i	0.100268	−	0.173669i	−0.811527	−	0.584315i	$-0.801363\pi$
$317$	1.78521	−	3.09208i	0.100268	−	0.173669i	0.911795	+	0.410646i	$0.134697\pi$
$318$		0			0
$319$	1.60446	+	2.77901i	0.0898326	+	0.155595i
$320$	31.1198			1.73965
$321$		0			0
$322$		0			0
$323$	−33.6670			−1.87328
$324$		0			0
$325$	−11.9671	+	20.7276i	−0.663813	+	1.14976i
$326$	−21.9693			−1.21677
$327$		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	−0.323026	−	0.946390i	$-0.604700\pi$
$331$	11.9728	−	20.7375i	0.658085	−	1.13984i	0.981111	−	0.193446i	$-0.0619666\pi$
$332$	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	0.199542	+	0.979889i	$0.436055\pi$
$337$	−13.7468	+	23.8102i	−0.748838	+	1.29703i	−0.948380	+	0.317137i	$0.897279\pi$
$338$	3.41568			0.185788
$339$		0			0
$340$	5.36497			0.290956
$341$	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
$346$	6.32822	+	10.9608i	0.340207	+	0.589256i
$347$	−2.56412	−	4.44119i	−0.137649	−	0.238416i	0.788957	−	0.614448i	$-0.210621\pi$
$347$	−2.56412	−	4.44119i	−0.137649	−	0.238416i	−0.926606	+	0.376033i	$0.877288\pi$
$348$		0			0
$349$	7.56980	+	13.1113i	0.405202	+	0.701830i	0.994345	−	0.106198i	$-0.0338679\pi$
$349$	7.56980	+	13.1113i	0.405202	+	0.701830i	−0.589143	+	0.808029i	$0.700535\pi$
$350$		0			0
$351$		0			0
$352$	−1.02459	−	1.77465i	−0.0546110	−	0.0945889i
$353$	32.9757			1.75512			0.877559	−	0.479468i	$-0.159171\pi$
$353$	32.9757			1.75512			0.877559	+	0.479468i	$0.159171\pi$
$354$		0			0
$355$	11.5549			0.613269
$356$	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
$362$	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
$367$	2.65501			0.138590			0.0692952	−	0.997596i	$-0.477925\pi$
$367$	2.65501			0.138590			0.0692952	+	0.997596i	$0.477925\pi$
$368$	7.05830	−	12.2253i	0.367939	−	0.637290i
$369$		0			0
$370$	44.7524			2.32657
$371$		0			0
$372$		0			0
$373$	−31.9183			−1.65267			−0.826334	−	0.563181i	$-0.809577\pi$
$373$	−31.9183			−1.65267			−0.826334	+	0.563181i	$0.809577\pi$
$374$	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
$383$	1.73305			0.0885548			0.0442774	−	0.999019i	$-0.485901\pi$
$383$	1.73305			0.0885548			0.0442774	+	0.999019i	$0.485901\pi$
$384$		0			0
$385$		0			0
$386$	−22.7917			−1.16006
$387$		0			0
$388$	−1.69583	+	2.93726i	−0.0860925	+	0.149117i
$389$	11.0835			0.561956			0.280978	−	0.959714i	$-0.409341\pi$
$389$	11.0835			0.561956			0.280978	+	0.959714i	$0.409341\pi$
$390$		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
$395$	−1.77011	+	3.06592i	−0.0890639	+	0.154263i
$396$		0			0
$397$	12.6696	+	21.9443i	0.635867	+	1.10135i	0.986331	+	0.164777i	$0.0526905\pi$
$397$	12.6696	+	21.9443i	0.635867	+	1.10135i	−0.350464	+	0.936576i	$0.613976\pi$
$398$	12.3632	+	21.4137i	0.619712	+	1.07337i
$399$		0			0
$400$	12.1990	−	21.1293i	0.609951	−	1.05647i
$401$	34.8244			1.73905			0.869524	−	0.493890i	$-0.164425\pi$
$401$	34.8244			1.73905			0.869524	+	0.493890i	$0.164425\pi$
$402$		0			0
$403$	6.18614			0.308154
$404$	−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
$409$	−9.12308	−	15.8016i	−0.451107	−	0.781341i	0.547348	−	0.836905i	$-0.315638\pi$
$409$	−9.12308	−	15.8016i	−0.451107	−	0.781341i	−0.998455	+	0.0555643i	$0.982304\pi$
$410$	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
$415$	−12.8904	−	22.3268i	−0.632765	−	1.09598i
$416$	−5.59985			−0.274555
$417$		0			0
$418$	10.5189			0.514496
$419$	−4.20719	+	7.28708i	−0.205535	+	0.355997i	−0.950303	−	0.311326i	$-0.899227\pi$
$419$	−4.20719	+	7.28708i	−0.205535	+	0.355997i	0.744768	+	0.667323i	$0.232560\pi$
$420$		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	$0.831095\pi$
$422$	−4.83304	−	8.37108i	−0.235269	−	0.407498i
$423$		0			0
$424$	−3.34483	+	5.79341i	−0.162439	+	0.281353i
$425$	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
$430$	44.3136			2.13699
$431$	−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	$-0.462804\pi$
$433$	4.85211			0.233177			0.116589	+	0.993180i	$0.462804\pi$
$434$		0			0
$435$		0			0
$436$	0.285371			0.0136668
$437$	−14.7623	−	25.5690i	−0.706174	−	1.22313i
$438$		0			0
$439$	1.27397	−	2.20657i	0.0608031	−	0.105314i	−0.834022	−	0.551732i	$-0.813967\pi$
$439$	1.27397	−	2.20657i	0.0608031	−	0.105314i	0.894825	+	0.446418i	$0.147301\pi$
$440$	−12.4790			−0.594914
$441$		0			0
$442$	20.5265			0.976347
$443$	−0.322753	+	0.559025i	−0.0153345	+	0.0265601i	−0.873591	−	0.486661i	$-0.838215\pi$
$443$	−0.322753	+	0.559025i	−0.0153345	+	0.0265601i	0.858256	+	0.513221i	$0.171548\pi$
$444$		0			0
$445$	−21.2306	−	36.7725i	−1.00643	−	1.74319i
$446$	−4.27826			−0.202581
$447$		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
$452$	−0.740624			−0.0348360
$453$		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	−0.830630	−	0.556825i	$-0.812019\pi$
$457$	1.43037	−	2.47748i	0.0669101	−	0.115892i	0.897540	+	0.440934i	$0.145353\pi$
$458$	−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	$-0.139560\pi$
$461$	1.82624	+	3.16314i	0.0850566	+	0.147322i	−0.820359	+	0.571849i	$0.806226\pi$
$462$		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	$0.912666\pi$
$464$	−8.93905			−0.414985
$465$		0			0
$466$	−19.1153			−0.885498
$467$	−10.2885	−	17.8202i	−0.476096	−	0.824622i	0.523529	−	0.852008i	$-0.324615\pi$
$467$	−10.2885	−	17.8202i	−0.476096	−	0.824622i	−0.999625	+	0.0273858i	$0.991282\pi$
$468$		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
$478$	9.20552	+	15.9444i	0.421051	+	0.729281i
$479$	25.1832			1.15065			0.575325	−	0.817925i	$-0.304876\pi$
$479$	25.1832			1.15065			0.575325	+	0.817925i	$0.304876\pi$
$480$		0			0
$481$	−31.4478			−1.43390
$482$	−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	$-0.0995896\pi$
$488$	−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
$493$	−13.3504			−0.601272
$494$	14.3726	−	24.8941i	0.646654	−	1.12004i
$495$		0			0
$496$	−6.30605			−0.283150
$497$		0			0
$498$		0			0
$499$	15.6416			0.700216			0.350108	−	0.936709i	$-0.386145\pi$
$499$	15.6416			0.700216			0.350108	+	0.936709i	$0.386145\pi$
$500$	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	$-0.803086\pi$
$503$	−36.5427			−1.62936			−0.814678	+	0.579913i	$0.803086\pi$
$504$		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
$509$	−37.6458			−1.66862			−0.834311	−	0.551294i	$-0.814134\pi$
$509$	−37.6458			−1.66862			−0.834311	+	0.551294i	$0.814134\pi$
$510$		0			0
$511$		0			0
$512$	25.4272			1.12373
$513$		0			0
$514$	−11.4088	+	19.7606i	−0.503221	+	0.871604i
$515$	−8.23480			−0.362869
$516$		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
$521$	7.17115	−	12.4208i	0.314174	−	0.544165i	−0.665088	−	0.746765i	$-0.731606\pi$
$521$	7.17115	−	12.4208i	0.314174	−	0.544165i	0.979262	+	0.202600i	$0.0649392\pi$
$522$		0			0
$523$	5.24222	+	9.07980i	0.229226	+	0.397032i	0.957579	−	0.288171i	$-0.0930471\pi$
$523$	5.24222	+	9.07980i	0.229226	+	0.397032i	−0.728353	+	0.685202i	$0.759714\pi$
$524$	−0.506114	−	0.876616i	−0.0221097	−	0.0382951i
$525$		0			0
$526$	15.1751	−	26.2840i	0.661665	−	1.14604i
$527$	−9.41802			−0.410256
$528$		0			0
$529$	−4.51110			−0.196135
$530$	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
$535$	−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
$541$	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	$0.376475\pi$
$542$	−18.7376			−0.804851
$543$		0			0
$544$	8.52542			0.365525
$545$	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	$-0.341013\pi$
$548$	−3.24822	−	5.62607i	−0.138757	−	0.240334i
$549$		0			0
$550$	−5.69237	+	9.85947i	−0.242723	+	0.420409i
$551$	−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
$556$	5.15894			0.218788
$557$	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
$562$	2.01902			0.0851672
$563$	−4.41357	−	7.64452i	−0.186010	−	0.322178i	0.757907	−	0.652363i	$-0.226222\pi$
$563$	−4.41357	−	7.64452i	−0.186010	−	0.322178i	−0.943916	+	0.330185i	$0.892889\pi$
$564$		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	−0.781698	−	0.623658i	$-0.785646\pi$
$569$	3.56027	−	6.16658i	0.149254	−	0.258516i	0.930952	+	0.365141i	$0.118979\pi$
$570$		0			0
$571$	−3.33181	−	5.77086i	−0.139432	−	0.241503i	0.787850	−	0.615867i	$-0.211194\pi$
$571$	−3.33181	−	5.77086i	−0.139432	−	0.241503i	−0.927282	+	0.374364i	$0.877861\pi$
$572$	1.17790			0.0492503
$573$		0			0
$574$		0			0
$575$	31.9548			1.33261
$576$		0			0
$577$	3.95629	−	6.85250i	0.164703	−	0.285273i	−0.771847	−	0.635808i	$-0.780667\pi$
$577$	3.95629	−	6.85250i	0.164703	−	0.285273i	0.936550	+	0.350535i	$0.114000\pi$
$578$	−9.15254			−0.380696
$579$		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
$584$	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	$-0.289781\pi$
$587$	−9.13891	−	15.8291i	−0.377203	−	0.653335i	−0.990654	+	0.136398i	$0.956447\pi$
$588$		0			0
$589$	−6.59447	+	11.4220i	−0.271720	+	0.470633i
$590$	−37.6415			−1.54968
$591$		0			0
$592$	32.0574			1.31755
$593$	14.1908	+	24.5792i	0.582745	+	1.00934i	0.995152	+	0.0983450i	$0.0313549\pi$
$593$	14.1908	+	24.5792i	0.582745	+	1.00934i	−0.412407	+	0.911000i	$0.635312\pi$
$594$		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	0.945851	−	0.324601i	$-0.105230\pi$
$599$	4.69451	+	8.13113i	0.191813	+	0.332229i	−0.754038	+	0.656830i	$0.771897\pi$
$600$		0			0
$601$	6.31432	+	10.9367i	0.257566	+	0.446118i	0.965589	−	0.260071i	$-0.0837460\pi$
$601$	6.31432	+	10.9367i	0.257566	+	0.446118i	−0.708023	+	0.706189i	$0.750413\pi$
$602$		0			0
$603$		0			0
$604$	−3.04584	−	5.27555i	−0.123934	−	0.214659i
$605$	−33.8871			−1.37771
$606$		0			0
$607$	−24.0265			−0.975207			−0.487604	−	0.873065i	$-0.662129\pi$
$607$	−24.0265			−0.975207			−0.487604	+	0.873065i	$0.662129\pi$
$608$	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	$-0.0288725\pi$
$614$	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
$619$	26.5739			1.06810			0.534048	−	0.845454i	$-0.320670\pi$
$619$	26.5739			1.06810			0.534048	+	0.845454i	$0.320670\pi$
$620$	1.05085	−	1.82013i	0.0422033	−	0.0730983i
$621$		0			0
$622$	17.8207			0.714545
$623$		0			0
$624$		0			0
$625$	−6.92971			−0.277188
$626$	−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
$635$	−10.7245			−0.425591
$636$		0			0
$637$		0			0
$638$	4.17119			0.165139
$639$		0			0
$640$	14.0953	−	24.4138i	0.557167	−	0.965041i
$641$	−32.5844			−1.28701			−0.643503	−	0.765443i	$-0.722520\pi$
$641$	−32.5844			−1.28701			−0.643503	+	0.765443i	$0.722520\pi$
$642$		0			0
$643$	−21.5327	+	37.2957i	−0.849166	+	1.47080i	0.0327873	+	0.999462i	$0.489562\pi$
$643$	−21.5327	+	37.2957i	−0.849166	+	1.47080i	−0.881953	+	0.471337i	$0.843772\pi$
$644$		0			0
$645$		0			0
$646$	−21.8814	+	37.8997i	−0.860912	+	1.49114i
$647$	−23.0988	+	40.0082i	−0.908106	+	1.57289i	−0.0914143	+	0.995813i	$0.529139\pi$
$647$	−23.0988	+	40.0082i	−0.908106	+	1.57289i	−0.816692	+	0.577074i	$0.804195\pi$
$648$		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
$653$	−32.0005			−1.25228			−0.626138	−	0.779713i	$-0.715365\pi$
$653$	−32.0005			−1.25228			−0.626138	+	0.779713i	$0.715365\pi$
$654$		0			0
$655$	−11.5004			−0.449359
$656$	10.9217	+	18.9170i	0.426422	+	0.738585i
$657$		0			0
$658$		0			0
$659$	−19.2070	−	33.2674i	−0.748197	−	1.29591i	−0.948686	−	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	0.998604	+	0.0528170i	$0.0168200\pi$
$661$	14.0130	+	24.2712i	0.545043	+	0.944042i	−0.453561	+	0.891225i	$0.649847\pi$
$662$	−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
$667$	−5.85386	−	10.1392i	−0.226662	−	0.392591i
$668$	1.59709			0.0617932
$669$		0			0
$670$	−24.4420			−0.944275
$671$	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	$0.823561\pi$
$674$	17.8691	+	30.9503i	0.688293	+	1.19216i
$675$		0			0
$676$	−0.407731	+	0.706211i	−0.0156820	+	0.0271619i
$677$	21.0167	−	36.4020i	0.807737	−	1.39904i	−0.106691	−	0.994292i	$-0.534025\pi$
$677$	21.0167	−	36.4020i	0.807737	−	1.39904i	0.914428	−	0.404749i	$-0.132641\pi$
$678$		0			0
$679$		0			0
$680$	25.9588	−	44.9620i	0.995476	−	1.72421i
$681$		0			0
$682$	2.94256			0.112676
$683$	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
$688$	31.7430			1.21019
$689$	−3.58704	−	6.21294i	−0.136655	−	0.236694i
$690$		0			0
$691$	−25.5675	+	44.2841i	−0.972632	+	1.68465i	−0.285094	+	0.958499i	$0.592025\pi$
$691$	−25.5675	+	44.2841i	−0.972632	+	1.68465i	−0.687538	+	0.726149i	$0.741308\pi$
$692$	−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
$698$	19.6795			0.744881
$699$		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
$704$	−10.4020			−0.392040
$705$		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	0.415265	+	0.909701i	$0.363689\pi$
$709$	−15.4488	+	26.7581i	−0.580192	+	1.00492i	−0.995456	+	0.0952206i	$0.969644\pi$
$710$	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
$716$	0.427011			0.0159582
$717$		0			0
$718$	−31.2431			−1.16598
$719$	3.05690	+	5.29471i	0.114003	+	0.197459i	0.917381	−	0.398011i	$-0.130299\pi$
$719$	3.05690	+	5.29471i	0.114003	+	0.197459i	−0.803378	+	0.595470i	$0.796966\pi$
$720$		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	$0.142257\pi$
$727$	22.2492	+	38.5367i	0.825176	+	1.42925i	−0.0766087	+	0.997061i	$0.524409\pi$
$728$		0			0
$729$		0			0
$730$	−2.37882	−	4.12023i	−0.0880440	−	0.152497i
$731$	47.4079			1.75344
$732$		0			0
$733$	9.83708			0.363341			0.181670	−	0.983359i	$-0.441850\pi$
$733$	9.83708			0.363341			0.181670	+	0.983359i	$0.441850\pi$
$734$	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	$0.254722\pi$
$740$	−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
$745$	−3.97871			−0.145769
$746$	−20.7449	+	35.9311i	−0.759523	+	1.31553i
$747$		0			0
$748$	−1.79328			−0.0655686
$749$		0			0
$750$		0			0
$751$	22.2010			0.810127			0.405063	−	0.914289i	$-0.367249\pi$
$751$	22.2010			0.810127			0.405063	+	0.914289i	$0.367249\pi$
$752$	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
$761$	−6.75264			−0.244783			−0.122392	−	0.992482i	$-0.539056\pi$
$761$	−6.75264			−0.244783			−0.122392	+	0.992482i	$0.539056\pi$
$762$		0			0
$763$		0			0
$764$	−7.76233			−0.280831
$765$		0			0
$766$	1.12637	−	1.95094i	0.0406975	−	0.0704902i
$767$	26.4510			0.955089
$768$		0			0
$769$	21.0805	−	36.5125i	0.760182	−	1.31667i	−0.182575	−	0.983192i	$-0.558443\pi$
$769$	21.0805	−	36.5125i	0.760182	−	1.31667i	0.942757	−	0.333482i	$-0.108224\pi$
$770$		0			0
$771$		0			0
$772$	2.72065	−	4.71230i	0.0979183	−	0.169600i
$773$	1.64926	−	2.85660i	0.0593197	−	0.102745i	−0.834841	−	0.550492i	$-0.814440\pi$
$773$	1.64926	−	2.85660i	0.0593197	−	0.102745i	0.894160	+	0.447747i	$0.147774\pi$
$774$		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
$779$	45.6851			1.63684
$780$		0			0
$781$	−3.86229			−0.138203
$782$	−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
$787$	−3.36455	−	5.82757i	−0.119933	−	0.207731i	0.799808	−	0.600256i	$-0.204935\pi$
$787$	−3.36455	−	5.82757i	−0.119933	−	0.207731i	−0.919741	+	0.392526i	$0.871601\pi$
$788$	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
$793$	−15.5542	−	26.9406i	−0.552345	−	0.956689i
$794$	32.9376			1.16891
$795$		0			0
$796$	−5.90321			−0.209234
$797$	−8.86302	+	15.3512i	−0.313944	+	0.543767i	−0.979213	−	0.202837i	$-0.934984\pi$
$797$	−8.86302	+	15.3512i	−0.313944	+	0.543767i	0.665268	+	0.746604i	$0.268317\pi$
$798$		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
$803$	−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
$808$	−4.79028			−0.168521
$809$	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	$-0.421203\pi$
$811$	13.9559			0.490058			0.245029	+	0.969516i	$0.421203\pi$
$812$		0			0
$813$		0			0
$814$	−14.9588			−0.524305
$815$	−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	0.143685	+	0.989623i	$0.454105\pi$
$821$	−22.4983	+	38.9682i	−0.785196	+	1.36000i	−0.928882	+	0.370376i	$0.879229\pi$
$822$		0			0
$823$	27.6232	+	47.8449i	0.962886	+	1.66777i	0.715191	+	0.698929i	$0.246340\pi$
$823$	27.6232	+	47.8449i	0.962886	+	1.66777i	0.247694	+	0.968838i	$0.420327\pi$
$824$	−7.01400			−0.244344
$825$		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	$-0.596655\pi$
$829$	19.4896	−	33.7570i	0.676903	−	1.17243i	0.975909	−	0.218179i	$-0.0700115\pi$
$830$	−33.5117			−1.16321
$831$		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
$836$	−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	0.977277	+	0.211965i	$0.0679862\pi$
$839$	19.4708	+	33.7244i	0.672206	+	1.16429i	−0.305072	+	0.952329i	$0.598680\pi$
$840$		0			0
$841$	10.7932	−	18.6943i	0.372178	−	0.644631i
$842$	0.375119			0.0129275
$843$		0			0
$844$	2.30769			0.0794340
$845$	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
$850$	−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	0.792791	−	0.609493i	$-0.208627\pi$
$853$	−3.83890	−	6.64916i	−0.131441	−	0.227663i	−0.924232	+	0.381830i	$0.875294\pi$
$854$		0			0
$855$		0			0
$856$	−3.33892	−	5.78318i	−0.114122	−	0.197665i
$857$	15.9639			0.545316			0.272658	−	0.962111i	$-0.412097\pi$
$857$	15.9639			0.545316			0.272658	+	0.962111i	$0.412097\pi$
$858$		0			0
$859$	48.3291			1.64897			0.824483	−	0.565887i	$-0.191466\pi$
$859$	48.3291			1.64897			0.824483	+	0.565887i	$0.191466\pi$
$860$	−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
$866$	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
$871$	17.1755			0.581970
$872$	1.38079	−	2.39159i	0.0467594	−	0.0809896i
$873$		0			0
$874$	−38.3781			−1.29816
$875$		0			0
$876$		0			0
$877$	14.1815			0.478876			0.239438	−	0.970912i	$-0.423037\pi$
$877$	14.1815			0.478876			0.239438	+	0.970912i	$0.423037\pi$
$878$	−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	$-0.215400\pi$
$881$	46.2822			1.55929			0.779643	+	0.626224i	$0.215400\pi$
$882$		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
$887$	19.1442			0.642798			0.321399	−	0.946944i	$-0.395847\pi$
$887$	19.1442			0.642798			0.321399	+	0.946944i	$0.395847\pi$
$888$		0			0
$889$		0			0
$890$	−55.1942			−1.85011
$891$		0			0
$892$	0.510697	−	0.884554i	0.0170994	−	0.0296171i
$893$	4.34791			0.145497
$894$		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
$899$	−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
$905$	19.9760			0.664024
$906$		0			0
$907$	39.8450			1.32303			0.661515	−	0.749932i	$-0.269914\pi$
$907$	39.8450			1.32303			0.661515	+	0.749932i	$0.269914\pi$
$908$	−2.79562	−	4.84216i	−0.0927760	−	0.160693i
$909$		0			0
$910$		0			0
$911$	−14.3727	−	24.8942i	−0.476189	−	0.824783i	0.523439	−	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
$919$	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	$0.748179\pi$
$920$	45.5296			1.50107
$921$		0			0
$922$	4.74776			0.156359
$923$	−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
$929$	7.00796	−	12.1381i	0.229924	−	0.398239i	−0.727862	−	0.685724i	$-0.759486\pi$
$929$	7.00796	−	12.1381i	0.229924	−	0.398239i	0.957785	+	0.287485i	$0.0928190\pi$
$930$		0			0
$931$		0			0
$932$	2.28180	−	3.95219i	0.0747428	−	0.129458i
$933$		0			0
$934$	−26.7475			−0.875205
$935$	−10.1871	+	17.6447i	−0.333155	+	0.577042i
$936$		0			0
$937$	51.5307			1.68344			0.841718	−	0.539918i	$-0.181545\pi$
$937$	51.5307			1.68344			0.841718	+	0.539918i	$0.181545\pi$
$938$		0			0
$939$		0			0
$940$	−0.692857			−0.0225985
$941$	−23.1564	−	40.1081i	−0.754877	−	1.30749i	−0.945435	−	0.325809i	$-0.894363\pi$
$941$	−23.1564	−	40.1081i	−0.754877	−	1.30749i	0.190558	−	0.981676i	$-0.438970\pi$
$942$		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	−0.656440	−	0.754378i	$-0.727939\pi$
$947$	10.0041	−	17.3277i	0.325091	−	0.563073i	0.981531	+	0.191305i	$0.0612719\pi$
$948$		0			0
$949$	1.67161	+	2.89531i	0.0542628	+	0.0939859i
$950$	−66.3297			−2.15202
$951$		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
$956$	−4.39547			−0.142160
$957$		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
$962$	−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	−0.466338	−	0.884607i	$-0.654427\pi$
$967$	16.5721	−	28.7037i	0.532923	−	0.923050i	0.999261	−	0.0384431i	$-0.0122398\pi$
$968$	−28.8633			−0.927702
$969$		0			0
$970$	50.0896			1.60828
$971$	20.8234	+	36.0672i	0.668256	+	1.15745i	0.978392	+	0.206761i	$0.0662921\pi$
$971$	20.8234	+	36.0672i	0.668256	+	1.15745i	−0.310136	+	0.950692i	$0.600375\pi$
$972$		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	0.992797	+	0.119807i	$0.0382276\pi$
$977$	18.7590	+	32.4916i	0.600154	+	1.03950i	−0.392643	+	0.919691i	$0.628439\pi$
$978$		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
$983$	−48.0758			−1.53338			−0.766690	−	0.642017i	$-0.778098\pi$
$983$	−48.0758			−1.53338			−0.766690	+	0.642017i	$0.778098\pi$
$984$		0			0
$985$	69.6495			2.21922
$986$	−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	$-0.0156907\pi$
$992$	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
$997$	−44.0827			−1.39611			−0.698056	−	0.716043i	$-0.745951\pi$
$997$	−44.0827			−1.39611			−0.698056	+	0.716043i	$0.745951\pi$
$998$	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.g.h.361.9		24
3.2	odd	2		441.2.g.h.67.4		24
7.2	even	3		1323.2.h.h.226.4		24
7.3	odd	6		1323.2.f.h.442.10		24
7.4	even	3		1323.2.f.h.442.9		24
7.5	odd	6		1323.2.h.h.226.3		24
7.6	odd	2	inner	1323.2.g.h.361.10		24
9.2	odd	6		441.2.h.h.214.9		24
9.7	even	3		1323.2.h.h.802.4		24
21.2	odd	6		441.2.h.h.373.9		24
21.5	even	6		441.2.h.h.373.10		24
21.11	odd	6		441.2.f.h.148.3	✓	24
21.17	even	6		441.2.f.h.148.4	yes	24
21.20	even	2		441.2.g.h.67.3		24
63.2	odd	6		441.2.g.h.79.4		24
63.4	even	3		3969.2.a.bi.1.4		12
63.11	odd	6		441.2.f.h.295.3	yes	24
63.16	even	3	inner	1323.2.g.h.667.9		24
63.20	even	6		441.2.h.h.214.10		24
63.25	even	3		1323.2.f.h.883.9		24
63.31	odd	6		3969.2.a.bi.1.3		12
63.32	odd	6		3969.2.a.bh.1.9		12
63.34	odd	6		1323.2.h.h.802.3		24
63.38	even	6		441.2.f.h.295.4	yes	24
63.47	even	6		441.2.g.h.79.3		24
63.52	odd	6		1323.2.f.h.883.10		24
63.59	even	6		3969.2.a.bh.1.10		12
63.61	odd	6	inner	1323.2.g.h.667.10		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.f.h.148.3	✓	24	21.11	odd	6
441.2.f.h.148.4	yes	24	21.17	even	6
441.2.f.h.295.3	yes	24	63.11	odd	6
441.2.f.h.295.4	yes	24	63.38	even	6
441.2.g.h.67.3		24	21.20	even	2
441.2.g.h.67.4		24	3.2	odd	2
441.2.g.h.79.3		24	63.47	even	6
441.2.g.h.79.4		24	63.2	odd	6
441.2.h.h.214.9		24	9.2	odd	6
441.2.h.h.214.10		24	63.20	even	6
441.2.h.h.373.9		24	21.2	odd	6
441.2.h.h.373.10		24	21.5	even	6
1323.2.f.h.442.9		24	7.4	even	3
1323.2.f.h.442.10		24	7.3	odd	6
1323.2.f.h.883.9		24	63.25	even	3
1323.2.f.h.883.10		24	63.52	odd	6
1323.2.g.h.361.9		24	1.1	even	1	trivial
1323.2.g.h.361.10		24	7.6	odd	2	inner
1323.2.g.h.667.9		24	63.16	even	3	inner
1323.2.g.h.667.10		24	63.61	odd	6	inner
1323.2.h.h.226.3		24	7.5	odd	6
1323.2.h.h.226.4		24	7.2	even	3
1323.2.h.h.802.3		24	63.34	odd	6
1323.2.h.h.802.4		24	9.7	even	3
3969.2.a.bh.1.9		12	63.32	odd	6
3969.2.a.bh.1.10		12	63.59	even	6
3969.2.a.bi.1.3		12	63.31	odd	6
3969.2.a.bi.1.4		12	63.4	even	3

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.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.649936 - 1.12572i) q^{2} +(0.155166 + 0.268756i) q^{4} +3.52584 q^{5} +3.00314 q^{8} +O(q^{10})\)	\(q+(0.649936 - 1.12572i) q^{2} +(0.155166 + 0.268756i) q^{4} +3.52584 q^{5} +3.00314 q^{8} +(2.29157 - 3.96912i) q^{10} -1.17853 q^{11} +(-1.61030 + 2.78913i) q^{13} +(1.64151 - 2.84319i) q^{16} +(2.45159 - 4.24627i) q^{17} +(-3.43318 - 5.94645i) q^{19} +(0.547092 + 0.947591i) q^{20} +(-0.765972 + 1.32670i) q^{22} +4.29987 q^{23} +7.43156 q^{25} +(2.09319 + 3.62551i) q^{26} +(-1.36140 - 2.35802i) q^{29} +(-0.960401 - 1.66346i) q^{31} +(0.869378 + 1.50581i) q^{32} +(-3.18675 - 5.51961i) q^{34} +(4.88229 + 8.45637i) q^{37} -8.92540 q^{38} +10.5886 q^{40} +(-3.32673 + 5.76206i) q^{41} +(4.83441 + 8.37344i) q^{43} +(-0.182869 - 0.316738i) q^{44} +(2.79464 - 4.84046i) q^{46} +(-0.316609 + 0.548383i) q^{47} +(4.83004 - 8.36587i) q^{50} -0.999459 q^{52} +(-1.11378 + 1.92912i) q^{53} -4.15533 q^{55} -3.53930 q^{58} +(-4.10652 - 7.11270i) q^{59} +(-4.82958 + 8.36508i) q^{61} -2.49680 q^{62} +8.82622 q^{64} +(-5.67767 + 9.83402i) q^{65} +(-2.66651 - 4.61852i) q^{67} +1.52161 q^{68} +3.27719 q^{71} +(0.519036 - 0.898997i) q^{73} +12.6927 q^{74} +(1.06543 - 1.84538i) q^{76} +(-0.502039 + 0.869557i) q^{79} +(5.78772 - 10.0246i) q^{80} +(4.32432 + 7.48994i) q^{82} +(-3.65598 - 6.33234i) q^{83} +(8.64391 - 14.9717i) q^{85} +12.5682 q^{86} -3.53930 q^{88} +(-6.02144 - 10.4294i) q^{89} +(0.667195 + 1.15562i) q^{92} +(0.411551 + 0.712828i) q^{94} +(-12.1049 - 20.9662i) q^{95} +(5.46454 + 9.46487i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{2} - 12 q^{4} + 24 q^{8}+O(q^{10}) \) 24 * q - 4 * q^2 - 12 * q^4 + 24 * q^8	\( 24 q - 4 q^{2} - 12 q^{4} + 24 q^{8} + 40 q^{11} - 12 q^{16} + 64 q^{23} + 24 q^{25} - 16 q^{29} - 48 q^{32} - 12 q^{37} - 56 q^{44} + 24 q^{46} + 4 q^{50} - 32 q^{53} + 96 q^{64} - 60 q^{65} - 12 q^{67} + 112 q^{71} + 136 q^{74} + 12 q^{79} + 12 q^{85} + 152 q^{86} - 16 q^{92} - 64 q^{95}+O(q^{100}) \) 24 * q - 4 * q^2 - 12 * q^4 + 24 * q^8 + 40 * q^11 - 12 * q^16 + 64 * q^23 + 24 * q^25 - 16 * q^29 - 48 * q^32 - 12 * q^37 - 56 * q^44 + 24 * q^46 + 4 * q^50 - 32 * q^53 + 96 * q^64 - 60 * q^65 - 12 * q^67 + 112 * q^71 + 136 * q^74 + 12 * q^79 + 12 * q^85 + 152 * q^86 - 16 * q^92 - 64 * q^95

Introduction

L-functions

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