LMFDB - Embedded newform 912.2.bn.o.449.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,2,Mod(65,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 3, 1]))

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

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

chi := DirichletCharacter("912.65");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	912.bn (of order $6$, 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:	$7.28235666434$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} - 6 x^{14} + 5 x^{13} + 21 x^{12} - 4 x^{11} - 94 x^{10} - 6 x^{9} + 364 x^{8} + \cdots + 6561 $ x^16 - x^15 - 6x^14 + 5x^13 + 21x^12 - 4x^11 - 94x^10 - 6x^9 + 364x^8 - 18x^7 - 846x^6 - 108x^5 + 1701x^4 + 1215x^3 - 4374x^2 - 2187x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 456)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			449.4
Root			$-0.809132 - 1.53144i$ of defining polynomial
Character	$\chi$	$=$	912.449
Dual form			912.2.bn.o.65.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809132 + 1.53144i) q^{3} +(-3.15813 + 1.82335i) q^{5} -1.32651 q^{7} +(-1.69061 - 2.47827i) q^{9} +O(q^{10})$	\(q+(-0.809132 + 1.53144i) q^{3} +(-3.15813 + 1.82335i) q^{5} -1.32651 q^{7} +(-1.69061 - 2.47827i) q^{9} +5.22390i q^{11} +(-5.77665 - 3.33515i) q^{13} +(-0.237002 - 6.31182i) q^{15} +(4.40043 - 2.54059i) q^{17} +(3.57090 + 2.49973i) q^{19} +(1.07332 - 2.03146i) q^{21} +(-2.14693 - 1.23953i) q^{23} +(4.14920 - 7.18663i) q^{25} +(5.16325 - 0.583820i) q^{27} +(0.559525 - 0.969126i) q^{29} -0.304339i q^{31} +(-8.00009 - 4.22682i) q^{33} +(4.18928 - 2.41868i) q^{35} +4.66495i q^{37} +(9.78165 - 6.14801i) q^{39} +(2.16072 + 3.74248i) q^{41} +(-4.93321 - 8.54458i) q^{43} +(9.85793 + 4.74414i) q^{45} +(7.04877 + 4.06961i) q^{47} -5.24038 q^{49} +(0.330230 + 8.79466i) q^{51} +(0.391014 - 0.677256i) q^{53} +(-9.52499 - 16.4978i) q^{55} +(-6.71752 + 3.44601i) q^{57} +(-2.58526 - 4.47781i) q^{59} +(7.21726 - 12.5007i) q^{61} +(2.24261 + 3.28744i) q^{63} +24.3246 q^{65} +(-3.10845 - 1.79467i) q^{67} +(3.63541 - 2.28495i) q^{69} +(-2.10867 - 3.65233i) q^{71} +(-4.88122 - 8.45453i) q^{73} +(7.64863 + 12.1692i) q^{75} -6.92954i q^{77} +(-4.31234 + 2.48973i) q^{79} +(-3.28367 + 8.37959i) q^{81} +5.31583i q^{83} +(-9.26476 + 16.0470i) q^{85} +(1.03143 + 1.64103i) q^{87} +(0.227250 - 0.393608i) q^{89} +(7.66276 + 4.42410i) q^{91} +(0.466076 + 0.246250i) q^{93} +(-15.8353 - 1.38348i) q^{95} +(9.45642 - 5.45967i) q^{97} +(12.9462 - 8.83159i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + q^{3} - 3 q^{5} + 13 q^{9}+O(q^{10}) $ 16 * q + q^3 - 3 * q^5 + 13 * q^9	$ 16 q + q^{3} - 3 q^{5} + 13 q^{9} - 3 q^{13} - 15 q^{15} + 3 q^{17} - 11 q^{19} - 6 q^{21} - 3 q^{23} + 11 q^{25} + 4 q^{27} - 5 q^{29} + q^{33} + 24 q^{35} + 9 q^{39} - 6 q^{41} - 13 q^{43} + 33 q^{45} + 27 q^{47} + 8 q^{49} - 15 q^{51} + 7 q^{53} + 12 q^{55} + 23 q^{57} - 10 q^{59} - q^{61} + 8 q^{63} + 30 q^{65} + 24 q^{67} + 41 q^{69} + 27 q^{71} + 2 q^{73} + 21 q^{75} + 21 q^{79} - 7 q^{81} - 5 q^{85} + 23 q^{87} - 25 q^{89} + 78 q^{91} - 56 q^{93} + 13 q^{95} - 60 q^{97} + 35 q^{99}+O(q^{100}) $ 16 * q + q^3 - 3 * q^5 + 13 * q^9 - 3 * q^13 - 15 * q^15 + 3 * q^17 - 11 * q^19 - 6 * q^21 - 3 * q^23 + 11 * q^25 + 4 * q^27 - 5 * q^29 + q^33 + 24 * q^35 + 9 * q^39 - 6 * q^41 - 13 * q^43 + 33 * q^45 + 27 * q^47 + 8 * q^49 - 15 * q^51 + 7 * q^53 + 12 * q^55 + 23 * q^57 - 10 * q^59 - q^61 + 8 * q^63 + 30 * q^65 + 24 * q^67 + 41 * q^69 + 27 * q^71 + 2 * q^73 + 21 * q^75 + 21 * q^79 - 7 * q^81 - 5 * q^85 + 23 * q^87 - 25 * q^89 + 78 * q^91 - 56 * q^93 + 13 * q^95 - 60 * q^97 + 35 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.809132	+	1.53144i	−0.467152	+	0.884177i
$3$	−0.809132	+	1.53144i	−0.467152	+	0.884177i
$4$		0			0
$5$	−3.15813	+	1.82335i	−1.41236	+	0.815426i	−0.995610	−	0.0935948i	$-0.970164\pi$
$5$	−3.15813	+	1.82335i	−1.41236	+	0.815426i	−0.416750	+	0.909021i	$0.636831\pi$
$6$		0			0
$7$	−1.32651			−0.501372			−0.250686	−	0.968068i	$-0.580656\pi$
$7$	−1.32651			−0.501372			−0.250686	+	0.968068i	$0.580656\pi$
$8$		0			0
$9$	−1.69061	−	2.47827i	−0.563537	−	0.826091i
$10$		0			0
$11$			5.22390i			1.57507i	0.616273	+	0.787533i	$0.288642\pi$
$11$			5.22390i			1.57507i	−0.616273	+	0.787533i	$0.711358\pi$
$12$		0			0
$13$	−5.77665	−	3.33515i	−1.60215	−	0.925004i	−0.991056	−	0.133450i	$-0.957394\pi$
$13$	−5.77665	−	3.33515i	−1.60215	−	0.925004i	−0.611099	−	0.791554i	$-0.709272\pi$
$14$		0			0
$15$	−0.237002	−	6.31182i	−0.0611937	−	1.62970i
$16$		0			0
$17$	4.40043	−	2.54059i	1.06726	−	0.616183i	0.139829	−	0.990176i	$-0.455345\pi$
$17$	4.40043	−	2.54059i	1.06726	−	0.616183i	0.927432	+	0.373992i	$0.122011\pi$
$18$		0			0
$19$	3.57090	+	2.49973i	0.819221	+	0.573478i
$19$	3.57090	+	2.49973i	0.819221	+	0.573478i
$20$		0			0
$21$	1.07332	−	2.03146i	0.234217	−	0.443302i
$22$		0			0
$23$	−2.14693	−	1.23953i	−0.447665	−	0.258460i	0.259178	−	0.965829i	$-0.416548\pi$
$23$	−2.14693	−	1.23953i	−0.447665	−	0.258460i	−0.706844	+	0.707370i	$0.749882\pi$
$24$		0			0
$25$	4.14920	−	7.18663i	0.829841	−	1.43733i
$26$		0			0
$27$	5.16325	−	0.583820i	0.993668	−	0.112356i
$28$		0			0
$29$	0.559525	−	0.969126i	0.103901	−	0.179962i	−0.809388	−	0.587275i	$-0.800201\pi$
$29$	0.559525	−	0.969126i	0.103901	−	0.179962i	0.913289	+	0.407313i	$0.133534\pi$
$30$		0			0
$31$		−	0.304339i		−	0.0546608i	−0.999626	−	0.0273304i	$-0.991299\pi$
$31$		−	0.304339i		−	0.0546608i	0.999626	−	0.0273304i	$-0.00870062\pi$
$32$		0			0
$33$	−8.00009	−	4.22682i	−1.39264	−	0.735796i
$34$		0			0
$35$	4.18928	−	2.41868i	0.708118	−	0.408832i
$36$		0			0
$37$			4.66495i			0.766913i	0.923559	+	0.383456i	$0.125266\pi$
$37$			4.66495i			0.766913i	−0.923559	+	0.383456i	$0.874734\pi$
$38$		0			0
$39$	9.78165	−	6.14801i	1.56632	−	0.984470i
$40$		0			0
$41$	2.16072	+	3.74248i	0.337448	+	0.584477i	0.983952	−	0.178434i	$-0.0571030\pi$
$41$	2.16072	+	3.74248i	0.337448	+	0.584477i	−0.646504	+	0.762911i	$0.723770\pi$
$42$		0			0
$43$	−4.93321	−	8.54458i	−0.752308	−	1.30304i	−0.946701	−	0.322112i	$-0.895607\pi$
$43$	−4.93321	−	8.54458i	−0.752308	−	1.30304i	0.194393	−	0.980924i	$-0.437726\pi$
$44$		0			0
$45$	9.85793	+	4.74414i	1.46953	+	0.707214i
$46$		0			0
$47$	7.04877	+	4.06961i	1.02817	+	0.593614i	0.916460	−	0.400127i	$-0.131034\pi$
$47$	7.04877	+	4.06961i	1.02817	+	0.593614i	0.111710	+	0.993741i	$0.464367\pi$
$48$		0			0
$49$	−5.24038			−0.748626
$50$		0			0
$51$	0.330230	+	8.79466i	0.0462415	+	1.23150i
$52$		0			0
$53$	0.391014	−	0.677256i	0.0537099	−	0.0930282i	−0.837920	−	0.545792i	$-0.816229\pi$
$53$	0.391014	−	0.677256i	0.0537099	−	0.0930282i	0.891630	+	0.452764i	$0.149562\pi$
$54$		0			0
$55$	−9.52499	−	16.4978i	−1.28435	−	2.22456i
$56$		0			0
$57$	−6.71752	+	3.44601i	−0.889757	+	0.456435i
$58$		0			0
$59$	−2.58526	−	4.47781i	−0.336573	−	0.582961i	0.647213	−	0.762309i	$-0.275934\pi$
$59$	−2.58526	−	4.47781i	−0.336573	−	0.582961i	−0.983786	+	0.179348i	$0.942601\pi$
$60$		0			0
$61$	7.21726	−	12.5007i	0.924076	−	1.60055i	0.131035	−	0.991378i	$-0.458170\pi$
$61$	7.21726	−	12.5007i	0.924076	−	1.60055i	0.793041	−	0.609169i	$-0.208497\pi$
$62$		0			0
$63$	2.24261	+	3.28744i	0.282542	+	0.414179i
$64$		0			0
$65$	24.3246			3.01709
$66$		0			0
$67$	−3.10845	−	1.79467i	−0.379758	−	0.219253i	0.297955	−	0.954580i	$-0.403695\pi$
$67$	−3.10845	−	1.79467i	−0.379758	−	0.219253i	−0.677713	+	0.735327i	$0.737029\pi$
$68$		0			0
$69$	3.63541	−	2.28495i	0.437652	−	0.275075i
$70$		0			0
$71$	−2.10867	−	3.65233i	−0.250253	−	0.433451i	0.713342	−	0.700816i	$-0.247181\pi$
$71$	−2.10867	−	3.65233i	−0.250253	−	0.433451i	−0.963595	+	0.267364i	$0.913847\pi$
$72$		0			0
$73$	−4.88122	−	8.45453i	−0.571304	−	0.989527i	−0.996432	−	0.0843944i	$-0.973104\pi$
$73$	−4.88122	−	8.45453i	−0.571304	−	0.989527i	0.425128	−	0.905133i	$-0.360229\pi$
$74$		0			0
$75$	7.64863	+	12.1692i	0.883188	+	1.40518i
$76$		0			0
$77$		−	6.92954i		−	0.789694i
$78$		0			0
$79$	−4.31234	+	2.48973i	−0.485176	+	0.280117i	−0.722571	−	0.691297i	$-0.757040\pi$
$79$	−4.31234	+	2.48973i	−0.485176	+	0.280117i	0.237395	+	0.971413i	$0.423706\pi$
$80$		0			0
$81$	−3.28367	+	8.37959i	−0.364852	+	0.931066i
$82$		0			0
$83$			5.31583i			0.583488i	0.956496	+	0.291744i	$0.0942356\pi$
$83$			5.31583i			0.583488i	−0.956496	+	0.291744i	$0.905764\pi$
$84$		0			0
$85$	−9.26476	+	16.0470i	−1.00490	+	1.74055i
$86$		0			0
$87$	1.03143	+	1.64103i	0.110581	+	0.175937i
$88$		0			0
$89$	0.227250	−	0.393608i	0.0240884	−	0.0417224i	−0.853730	−	0.520716i	$-0.825665\pi$
$89$	0.227250	−	0.393608i	0.0240884	−	0.0417224i	0.877818	+	0.478994i	$0.158998\pi$
$90$		0			0
$91$	7.66276	+	4.42410i	0.803276	+	0.463772i
$92$		0			0
$93$	0.466076	+	0.246250i	0.0483298	+	0.0255349i
$94$		0			0
$95$	−15.8353	−	1.38348i	−1.62466	−	0.141942i
$96$		0			0
$97$	9.45642	−	5.45967i	0.960154	−	0.554345i	0.0639336	−	0.997954i	$-0.479635\pi$
$97$	9.45642	−	5.45967i	0.960154	−	0.554345i	0.896220	+	0.443609i	$0.146302\pi$
$98$		0			0
$99$	12.9462	−	8.83159i	1.30115	−	0.887608i
$100$		0			0
$101$	−2.03309	−	1.17381i	−0.202300	−	0.116798i	0.395428	−	0.918497i	$-0.370596\pi$
$101$	−2.03309	−	1.17381i	−0.202300	−	0.116798i	−0.597728	+	0.801699i	$0.703930\pi$
$102$		0			0
$103$			0.991616i			0.0977068i	0.998806	+	0.0488534i	$0.0155567\pi$
$103$			0.991616i			0.0977068i	−0.998806	+	0.0488534i	$0.984443\pi$
$104$		0			0
$105$	0.314385	+	8.37267i	0.0306808	+	0.817089i
$106$		0			0
$107$	−17.3827			−1.68045			−0.840224	−	0.542239i	$-0.817577\pi$
$107$	−17.3827			−1.68045			−0.840224	+	0.542239i	$0.817577\pi$
$108$		0			0
$109$	−0.553359	+	0.319482i	−0.0530021	+	0.0306008i	−0.526267	−	0.850319i	$-0.676409\pi$
$109$	−0.553359	+	0.319482i	−0.0530021	+	0.0306008i	0.473265	+	0.880920i	$0.343075\pi$
$110$		0			0
$111$	−7.14408	−	3.77456i	−0.678086	−	0.358265i
$112$		0			0
$113$	0.180146			0.0169467			0.00847334	−	0.999964i	$-0.497303\pi$
$113$	0.180146			0.0169467			0.00847334	+	0.999964i	$0.497303\pi$
$114$		0			0
$115$	9.04038			0.843020
$116$		0			0
$117$	1.50066	+	19.9546i	0.138736	+	1.84480i
$118$		0			0
$119$	−5.83720	+	3.37011i	−0.535095	+	0.308937i
$120$		0			0
$121$	−16.2891			−1.48083
$122$		0			0
$123$	−7.47969	+	0.280854i	−0.674421	+	0.0253238i
$124$		0			0
$125$			12.0283i			1.07584i
$126$		0			0
$127$	−11.6355	−	6.71777i	−1.03249	−	0.596106i	−0.114790	−	0.993390i	$-0.536619\pi$
$127$	−11.6355	−	6.71777i	−1.03249	−	0.596106i	−0.917696	+	0.397284i	$0.869953\pi$
$128$		0			0
$129$	17.0771	−	0.641228i	1.50356	−	0.0564570i
$130$		0			0
$131$	−6.84055	+	3.94939i	−0.597661	+	0.345060i	−0.768121	−	0.640305i	$-0.778808\pi$
$131$	−6.84055	+	3.94939i	−0.597661	+	0.345060i	0.170460	+	0.985365i	$0.445475\pi$
$132$		0			0
$133$	−4.73683	−	3.31591i	−0.410735	−	0.287526i
$134$		0			0
$135$	−15.2417	+	11.2582i	−1.31180	+	0.968951i
$136$		0			0
$137$	−13.4033	−	7.73838i	−1.14512	−	0.661135i	−0.197426	−	0.980318i	$-0.563258\pi$
$137$	−13.4033	−	7.73838i	−1.14512	−	0.661135i	−0.947693	+	0.319183i	$0.896592\pi$
$138$		0			0
$139$	4.38454	−	7.59424i	0.371892	−	0.644135i	−0.617965	−	0.786206i	$-0.712043\pi$
$139$	4.38454	−	7.59424i	0.371892	−	0.644135i	0.989857	+	0.142070i	$0.0453759\pi$
$140$		0			0
$141$	−11.9358	+	7.50192i	−1.00517	+	0.631775i
$142$		0			0
$143$	17.4225	−	30.1766i	1.45694	−	2.52350i
$144$		0			0
$145$			4.08084i			0.338895i
$146$		0			0
$147$	4.24016	−	8.02532i	0.349722	−	0.661918i
$148$		0			0
$149$	−5.20172	+	3.00321i	−0.426141	+	0.246033i	−0.697701	−	0.716389i	$-0.745794\pi$
$149$	−5.20172	+	3.00321i	−0.426141	+	0.246033i	0.271560	+	0.962421i	$0.412460\pi$
$150$		0			0
$151$		−	0.321176i		−	0.0261369i	−0.999915	−	0.0130685i	$-0.995840\pi$
$151$		−	0.321176i		−	0.0261369i	0.999915	−	0.0130685i	$-0.00415994\pi$
$152$		0			0
$153$	−13.7357	−	6.61031i	−1.11046	−	0.534412i
$154$		0			0
$155$	0.554915	+	0.961142i	0.0445719	+	0.0772008i
$156$		0			0
$157$	0.746362	+	1.29274i	0.0595662	+	0.103172i	0.894271	−	0.447526i	$-0.147695\pi$
$157$	0.746362	+	1.29274i	0.0595662	+	0.103172i	−0.834705	+	0.550698i	$0.814362\pi$
$158$		0			0
$159$	0.720794	+	1.14680i	0.0571627	+	0.0909474i
$160$		0			0
$161$	2.84791	+	1.64424i	0.224447	+	0.129585i
$162$		0			0
$163$	15.8647			1.24262			0.621311	−	0.783564i	$-0.286600\pi$
$163$	15.8647			1.24262			0.621311	+	0.783564i	$0.286600\pi$
$164$		0			0
$165$	32.9723	−	1.23808i	2.56689	−	0.0963840i
$166$		0			0
$167$	−4.05882	+	7.03008i	−0.314081	+	0.544004i	−0.979242	−	0.202696i	$-0.935030\pi$
$167$	−4.05882	+	7.03008i	−0.314081	+	0.544004i	0.665161	+	0.746700i	$0.268363\pi$
$168$		0			0
$169$	15.7465	+	27.2737i	1.21127	+	2.09797i
$170$		0			0
$171$	0.158007	−	13.0757i	0.0120831	−	0.999927i
$172$		0			0
$173$	1.21215	+	2.09950i	0.0921579	+	0.159622i	0.908419	−	0.418061i	$-0.137290\pi$
$173$	1.21215	+	2.09950i	0.0921579	+	0.159622i	−0.816261	+	0.577683i	$0.803957\pi$
$174$		0			0
$175$	−5.50395	+	9.53311i	−0.416059	+	0.720636i
$176$		0			0
$177$	8.94931	−	0.336037i	0.672671	−	0.0252581i
$178$		0			0
$179$	3.79105			0.283357			0.141678	−	0.989913i	$-0.454750\pi$
$179$	3.79105			0.283357			0.141678	+	0.989913i	$0.454750\pi$
$180$		0			0
$181$	−16.0677	−	9.27671i	−1.19431	−	0.689533i	−0.235026	−	0.971989i	$-0.575517\pi$
$181$	−16.0677	−	9.27671i	−1.19431	−	0.689533i	−0.959280	+	0.282456i	$0.908851\pi$
$182$		0			0
$183$	13.3043	+	21.1675i	0.983482	+	1.56475i
$184$		0			0
$185$	−8.50583	−	14.7325i	−0.625361	−	1.08316i
$186$		0			0
$187$	13.2718	+	22.9874i	0.970529	+	1.68101i
$188$		0			0
$189$	−6.84909	+	0.774441i	−0.498198	+	0.0563323i
$190$		0			0
$191$		−	3.59262i		−	0.259953i	−0.991517	−	0.129976i	$-0.958510\pi$
$191$		−	3.59262i		−	0.259953i	0.991517	−	0.129976i	$-0.0414902\pi$
$192$		0			0
$193$	6.33759	−	3.65901i	0.456189	−	0.263381i	−0.254251	−	0.967138i	$-0.581829\pi$
$193$	6.33759	−	3.65901i	0.456189	−	0.263381i	0.710441	+	0.703757i	$0.248496\pi$
$194$		0			0
$195$	−19.6818	+	37.2516i	−1.40944	+	2.66764i
$196$		0			0
$197$		−	21.3146i		−	1.51860i	−0.650741	−	0.759300i	$-0.725542\pi$
$197$		−	21.3146i		−	1.51860i	0.650741	−	0.759300i	$-0.274458\pi$
$198$		0			0
$199$	−5.93321	+	10.2766i	−0.420594	+	0.728491i	−0.995998	−	0.0893789i	$-0.971512\pi$
$199$	−5.93321	+	10.2766i	−0.420594	+	0.728491i	0.575403	+	0.817870i	$0.304845\pi$
$200$		0			0
$201$	5.26357	−	3.30829i	0.371264	−	0.233348i
$202$		0			0
$203$	−0.742214	+	1.28555i	−0.0520932	+	0.0902280i
$204$		0			0
$205$	−13.6477	−	7.87950i	−0.953196	−	0.550328i
$206$		0			0
$207$	0.557730	+	7.41623i	0.0387649	+	0.515464i
$208$		0			0
$209$	−13.0583	+	18.6540i	−0.903265	+	1.29033i
$210$		0			0
$211$	−6.26479	+	3.61698i	−0.431286	+	0.249003i	−0.699894	−	0.714246i	$-0.746770\pi$
$211$	−6.26479	+	3.61698i	−0.431286	+	0.249003i	0.268608	+	0.963250i	$0.413436\pi$
$212$		0			0
$213$	7.29951	−	0.274089i	0.500154	−	0.0187803i
$214$		0			0
$215$	31.1595	+	17.9899i	2.12506	+	1.22690i
$216$		0			0
$217$			0.403707i			0.0274054i
$218$		0			0
$219$	16.8971	−	0.634470i	1.14180	−	0.0428735i
$220$		0			0
$221$	−33.8930			−2.27989
$222$		0			0
$223$	−14.7806	+	8.53358i	−0.989782	+	0.571451i	−0.905209	−	0.424966i	$-0.860286\pi$
$223$	−14.7806	+	8.53358i	−0.989782	+	0.571451i	−0.0845731	+	0.996417i	$0.526953\pi$
$224$		0			0
$225$	−24.8251	+	1.86695i	−1.65501	+	0.124463i
$226$		0			0
$227$	−10.7482			−0.713381			−0.356690	−	0.934223i	$-0.616095\pi$
$227$	−10.7482			−0.713381			−0.356690	+	0.934223i	$0.616095\pi$
$228$		0			0
$229$	16.9808			1.12212			0.561061	−	0.827775i	$-0.310393\pi$
$229$	16.9808			1.12212			0.561061	+	0.827775i	$0.310393\pi$
$230$		0			0
$231$	10.6122	+	5.60691i	0.698229	+	0.368908i
$232$		0			0
$233$	−14.1267	+	8.15608i	−0.925474	+	0.534322i	−0.885377	−	0.464873i	$-0.846100\pi$
$233$	−14.1267	+	8.15608i	−0.925474	+	0.534322i	−0.0400964	+	0.999196i	$0.512767\pi$
$234$		0			0
$235$	−29.6813			−1.93619
$236$		0			0
$237$	−0.323619	−	8.61861i	−0.0210213	−	0.559839i
$238$		0			0
$239$		−	0.792303i		−	0.0512498i	−0.999672	−	0.0256249i	$-0.991842\pi$
$239$		−	0.792303i		−	0.0512498i	0.999672	−	0.0256249i	$-0.00815755\pi$
$240$		0			0
$241$	5.78713	+	3.34120i	0.372782	+	0.215226i	0.674673	−	0.738117i	$-0.264285\pi$
$241$	5.78713	+	3.34120i	0.372782	+	0.215226i	−0.301891	+	0.953342i	$0.597618\pi$
$242$		0			0
$243$	−10.1759	−	11.8089i	−0.652785	−	0.757543i
$244$		0			0
$245$	16.5498	−	9.55504i	1.05733	−	0.610449i
$246$		0			0
$247$	−12.2909	−	26.3496i	−0.782050	−	1.67658i
$248$		0			0
$249$	−8.14087	−	4.30121i	−0.515907	−	0.272578i
$250$		0			0
$251$	−0.609130	−	0.351681i	−0.0384479	−	0.0221979i	0.480653	−	0.876911i	$-0.340400\pi$
$251$	−0.609130	−	0.351681i	−0.0384479	−	0.0221979i	−0.519101	+	0.854713i	$0.673733\pi$
$252$		0			0
$253$	6.47518	−	11.2153i	0.407091	−	0.705102i
$254$		0			0
$255$	−17.0786	−	27.1726i	−1.06951	−	1.70161i
$256$		0			0
$257$	10.5433	−	18.2615i	0.657672	−	1.13912i	−0.323545	−	0.946213i	$-0.604875\pi$
$257$	10.5433	−	18.2615i	0.657672	−	1.13912i	0.981217	−	0.192908i	$-0.0617918\pi$
$258$		0			0
$259$		−	6.18808i		−	0.384509i
$260$		0			0
$261$	−3.34770	+	0.251760i	−0.207217	+	0.0155835i
$262$		0			0
$263$	2.53267	−	1.46224i	0.156171	−	0.0901655i	−0.419878	−	0.907581i	$-0.637927\pi$
$263$	2.53267	−	1.46224i	0.156171	−	0.0901655i	0.576049	+	0.817415i	$0.304594\pi$
$264$		0			0
$265$			2.85182i			0.175186i
$266$		0			0
$267$	0.418912	+	0.666500i	0.0256370	+	0.0407892i
$268$		0			0
$269$	10.4795	+	18.1511i	0.638948	+	1.10669i	0.985664	+	0.168721i	$0.0539635\pi$
$269$	10.4795	+	18.1511i	0.638948	+	1.10669i	−0.346716	+	0.937970i	$0.612703\pi$
$270$		0			0
$271$	6.71324	+	11.6277i	0.407800	+	0.706330i	0.994643	−	0.103370i	$-0.0329627\pi$
$271$	6.71324	+	11.6277i	0.407800	+	0.706330i	−0.586843	+	0.809701i	$0.699629\pi$
$272$		0			0
$273$	−12.9754	+	8.15538i	−0.785308	+	0.493586i
$274$		0			0
$275$	37.5422	+	21.6750i	2.26388	+	1.30705i
$276$		0			0
$277$	5.81486			0.349381			0.174691	−	0.984623i	$-0.444107\pi$
$277$	5.81486			0.349381			0.174691	+	0.984623i	$0.444107\pi$
$278$		0			0
$279$	−0.754234	+	0.514518i	−0.0451548	+	0.0308034i
$280$		0			0
$281$	−13.6509	+	23.6440i	−0.814342	+	1.41048i	0.0954570	+	0.995434i	$0.469569\pi$
$281$	−13.6509	+	23.6440i	−0.814342	+	1.41048i	−0.909799	+	0.415049i	$0.863765\pi$
$282$		0			0
$283$	1.45532	+	2.52070i	0.0865100	+	0.149840i	0.906034	−	0.423206i	$-0.139095\pi$
$283$	1.45532	+	2.52070i	0.0865100	+	0.149840i	−0.819524	+	0.573045i	$0.805762\pi$
$284$		0			0
$285$	14.9315	−	23.1313i	0.884468	−	1.37018i
$286$		0			0
$287$	−2.86621	−	4.96442i	−0.169187	−	0.293041i
$288$		0			0
$289$	4.40918	−	7.63693i	0.259364	−	0.449231i
$290$		0			0
$291$	0.709657	+	18.8995i	0.0416008	+	1.10791i
$292$		0			0
$293$	−10.4657			−0.611416			−0.305708	−	0.952125i	$-0.598893\pi$
$293$	−10.4657			−0.611416			−0.305708	+	0.952125i	$0.598893\pi$
$294$		0			0
$295$	16.3292	+	9.42768i	0.950724	+	0.548901i
$296$		0			0
$297$	3.04982	+	26.9723i	0.176968	+	1.56509i
$298$		0			0
$299$	8.26803	+	14.3207i	0.478153	+	0.828185i
$300$		0			0
$301$	6.54394	+	11.3344i	0.377187	+	0.653306i
$302$		0			0
$303$	3.44265	−	2.16379i	0.197775	−	0.124307i
$304$		0			0
$305$			52.6384i			3.01406i
$306$		0			0
$307$	8.49577	−	4.90503i	0.484879	−	0.279945i	−0.237568	−	0.971371i	$-0.576350\pi$
$307$	8.49577	−	4.90503i	0.484879	−	0.279945i	0.722448	+	0.691426i	$0.243017\pi$
$308$		0			0
$309$	−1.51860	−	0.802348i	−0.0863901	−	0.0456440i
$310$		0			0
$311$		−	9.42922i		−	0.534682i	−0.963602	−	0.267341i	$-0.913855\pi$
$311$		−	9.42922i		−	0.534682i	0.963602	−	0.267341i	$-0.0861450\pi$
$312$		0			0
$313$	11.1942	−	19.3890i	0.632736	−	1.09593i	−0.354254	−	0.935149i	$-0.615265\pi$
$313$	11.1942	−	19.3890i	0.632736	−	1.09593i	0.986990	−	0.160782i	$-0.0514016\pi$
$314$		0			0
$315$	−13.0766	−	6.29313i	−0.736784	−	0.354578i
$316$		0			0
$317$	9.24221	−	16.0080i	0.519094	−	0.899098i	−0.480659	−	0.876907i	$-0.659603\pi$
$317$	9.24221	−	16.0080i	0.519094	−	0.899098i	0.999754	−	0.0221905i	$-0.00706403\pi$
$318$		0			0
$319$	5.06262	+	2.92290i	0.283452	+	0.163651i
$320$		0			0
$321$	14.0649	−	26.6205i	0.785026	−	1.48581i
$322$		0			0
$323$	22.0643	+	1.92770i	1.22769	+	0.107260i
$324$		0			0
$325$	−47.9370	+	27.6764i	−2.65907	+	1.53521i
$326$		0			0
$327$	−0.0415268	−	1.10594i	−0.00229644	−	0.0611585i
$328$		0			0
$329$	−9.35025	−	5.39837i	−0.515496	−	0.297622i
$330$		0			0
$331$		−	13.3307i		−	0.732723i	−0.930473	−	0.366361i	$-0.880603\pi$
$331$		−	13.3307i		−	0.732723i	0.930473	−	0.366361i	$-0.119397\pi$
$332$		0			0
$333$	11.5610	−	7.88661i	0.633539	−	0.432184i
$334$		0			0
$335$	13.0892			0.715140
$336$		0			0
$337$	25.8098	−	14.9013i	1.40595	−	0.811725i	0.410954	−	0.911656i	$-0.365196\pi$
$337$	25.8098	−	14.9013i	1.40595	−	0.811725i	0.994994	+	0.0999311i	$0.0318622\pi$
$338$		0			0
$339$	−0.145762	+	0.275882i	−0.00791668	+	0.0149839i
$340$		0			0
$341$	1.58983			0.0860944
$342$		0			0
$343$	16.2369			0.876713
$344$		0			0
$345$	−7.31486	+	13.8448i	−0.393819	+	0.745378i
$346$		0			0
$347$	−22.9416	+	13.2454i	−1.23157	+	0.711048i	−0.967357	−	0.253416i	$-0.918446\pi$
$347$	−22.9416	+	13.2454i	−1.23157	+	0.711048i	−0.264214	+	0.964464i	$0.585112\pi$
$348$		0			0
$349$	−15.1446			−0.810673			−0.405337	−	0.914168i	$-0.632846\pi$
$349$	−15.1446			−0.810673			−0.405337	+	0.914168i	$0.632846\pi$
$350$		0			0
$351$	−31.7734	−	13.8477i	−1.69594	−	0.739135i
$352$		0			0
$353$		−	18.2589i		−	0.971822i	−0.874008	−	0.485911i	$-0.838488\pi$
$353$		−	18.2589i		−	0.971822i	0.874008	−	0.485911i	$-0.161512\pi$
$354$		0			0
$355$	13.3189	+	7.68969i	0.706896	+	0.408126i
$356$		0			0
$357$	−0.438052	−	11.6662i	−0.0231842	−	0.617439i
$358$		0			0
$359$	−15.7764	+	9.10850i	−0.832645	+	0.480728i	−0.854758	−	0.519027i	$-0.826294\pi$
$359$	−15.7764	+	9.10850i	−0.832645	+	0.480728i	0.0221122	+	0.999755i	$0.492961\pi$
$360$		0			0
$361$	6.50269	+	17.8526i	0.342247	+	0.939610i
$362$		0			0
$363$	13.1801	−	24.9458i	0.691774	−	1.30932i
$364$		0			0
$365$	30.8311	+	17.8003i	1.61377	+	0.931713i
$366$		0			0
$367$	17.5938	−	30.4734i	0.918389	−	1.59070i	0.116528	−	0.993187i	$-0.462824\pi$
$367$	17.5938	−	30.4734i	0.918389	−	1.59070i	0.801862	−	0.597510i	$-0.203843\pi$
$368$		0			0
$369$	5.62194	−	11.6819i	0.292667	−	0.608137i
$370$		0			0
$371$	−0.518682	+	0.898384i	−0.0269286	+	0.0466418i
$372$		0			0
$373$		−	16.7168i		−	0.865561i	−0.901499	−	0.432781i	$-0.857532\pi$
$373$		−	16.7168i		−	0.865561i	0.901499	−	0.432781i	$-0.142468\pi$
$374$		0			0
$375$	−18.4206	−	9.73247i	−0.951235	−	0.502583i
$376$		0			0
$377$	−6.46436	+	3.73220i	−0.332932	+	0.192218i
$378$		0			0
$379$			5.67816i			0.291668i	0.989309	+	0.145834i	$0.0465865\pi$
$379$			5.67816i			0.291668i	−0.989309	+	0.145834i	$0.953414\pi$
$380$		0			0
$381$	19.7025	−	12.3835i	1.00939	−	0.634427i
$382$		0			0
$383$	−14.7085	−	25.4760i	−0.751572	−	1.30176i	−0.947061	−	0.321055i	$-0.895963\pi$
$383$	−14.7085	−	25.4760i	−0.751572	−	1.30176i	0.195489	−	0.980706i	$-0.437371\pi$
$384$		0			0
$385$	12.6350	+	21.8844i	0.643938	+	1.11533i
$386$		0			0
$387$	−12.8356	+	26.6714i	−0.652472	+	1.35578i
$388$		0			0
$389$	−3.46815	−	2.00234i	−0.175842	−	0.101523i	0.409495	−	0.912312i	$-0.365705\pi$
$389$	−3.46815	−	2.00234i	−0.175842	−	0.101523i	−0.585338	+	0.810790i	$0.699038\pi$
$390$		0			0
$391$	−12.5965			−0.637034
$392$		0			0
$393$	−0.513349	−	13.6715i	−0.0258950	−	0.689634i
$394$		0			0
$395$	9.07929	−	15.7258i	0.456829	−	0.791251i
$396$		0			0
$397$	1.81538	+	3.14434i	0.0911115	+	0.157810i	0.907979	−	0.419015i	$-0.137625\pi$
$397$	1.81538	+	3.14434i	0.0911115	+	0.157810i	−0.816868	+	0.576825i	$0.804291\pi$
$398$		0			0
$399$	8.91083	−	4.57115i	0.446100	−	0.228844i
$400$		0			0
$401$	−4.34004	−	7.51717i	−0.216731	−	0.375390i	0.737075	−	0.675810i	$-0.236206\pi$
$401$	−4.34004	−	7.51717i	−0.216731	−	0.375390i	−0.953807	+	0.300421i	$0.902873\pi$
$402$		0			0
$403$	−1.01501	+	1.75806i	−0.0505615	+	0.0875751i
$404$		0			0
$405$	−4.90866	−	32.4511i	−0.243914	−	1.61251i
$406$		0			0
$407$	−24.3692			−1.20794
$408$		0			0
$409$	−29.6462	−	17.1162i	−1.46591	−	0.846344i	−0.466636	−	0.884449i	$-0.654534\pi$
$409$	−29.6462	−	17.1162i	−1.46591	−	0.846344i	−0.999274	+	0.0381058i	$0.987868\pi$
$410$		0			0
$411$	22.6959	−	14.2649i	1.11951	−	0.703637i
$412$		0			0
$413$	3.42937	+	5.93984i	0.168748	+	0.292281i
$414$		0			0
$415$	−9.69262	−	16.7881i	−0.475792	−	0.824096i
$416$		0			0
$417$	8.08245	+	12.8594i	0.395799	+	0.629727i
$418$		0			0
$419$		−	15.5987i		−	0.762048i	−0.924565	−	0.381024i	$-0.875571\pi$
$419$		−	15.5987i		−	0.762048i	0.924565	−	0.381024i	$-0.124429\pi$
$420$		0			0
$421$	−10.8879	+	6.28611i	−0.530642	+	0.306366i	−0.741278	−	0.671198i	$-0.765780\pi$
$421$	−10.8879	+	6.28611i	−0.530642	+	0.306366i	0.210636	+	0.977565i	$0.432447\pi$
$422$		0			0
$423$	−1.83113	−	24.3489i	−0.0890327	−	1.18388i
$424$		0			0
$425$		−	42.1657i		−	2.04534i
$426$		0			0
$427$	−9.57375	+	16.5822i	−0.463306	+	0.802470i
$428$		0			0
$429$	32.1166	+	51.0984i	1.55060	+	2.46705i
$430$		0			0
$431$	10.2769	−	17.8001i	0.495022	−	0.857403i	−0.504962	−	0.863142i	$-0.668493\pi$
$431$	10.2769	−	17.8001i	0.495022	−	0.857403i	0.999984	+	0.00573880i	$0.00182673\pi$
$432$		0			0
$433$	−1.74254	−	1.00605i	−0.0837410	−	0.0483479i	0.457545	−	0.889187i	$-0.348729\pi$
$433$	−1.74254	−	1.00605i	−0.0837410	−	0.0483479i	−0.541286	+	0.840839i	$0.682062\pi$
$434$		0			0
$435$	−6.24955	−	3.30194i	−0.299643	−	0.158316i
$436$		0			0
$437$	−4.56798	−	9.79298i	−0.218516	−	0.468462i
$438$		0			0
$439$	10.1428	−	5.85597i	0.484091	−	0.279490i	−0.238029	−	0.971258i	$-0.576501\pi$
$439$	10.1428	−	5.85597i	0.484091	−	0.279490i	0.722120	+	0.691768i	$0.243168\pi$
$440$		0			0
$441$	8.85945	+	12.9871i	0.421878	+	0.618433i
$442$		0			0
$443$	−2.76113	−	1.59414i	−0.131185	−	0.0757397i	0.432971	−	0.901408i	$-0.357465\pi$
$443$	−2.76113	−	1.59414i	−0.131185	−	0.0757397i	−0.564156	+	0.825668i	$0.690798\pi$
$444$		0			0
$445$			1.65742i			0.0785694i
$446$		0			0
$447$	−0.390363	−	10.3961i	−0.0184635	−	0.491719i
$448$		0			0
$449$	−23.4658			−1.10742			−0.553709	−	0.832710i	$-0.686788\pi$
$449$	−23.4658			−1.10742			−0.553709	+	0.832710i	$0.686788\pi$
$450$		0			0
$451$	−19.5503	+	11.2874i	−0.920589	+	0.531503i
$452$		0			0
$453$	0.491861	+	0.259874i	0.0231096	+	0.0122099i
$454$		0			0
$455$	−32.2667			−1.51269
$456$		0			0
$457$	3.31468			0.155054			0.0775270	−	0.996990i	$-0.475298\pi$
$457$	3.31468			0.155054			0.0775270	+	0.996990i	$0.475298\pi$
$458$		0			0
$459$	21.2373	−	15.6868i	0.991271	−	0.732195i
$460$		0			0
$461$	15.9430	−	9.20470i	0.742540	−	0.428706i	−0.0804520	−	0.996758i	$-0.525636\pi$
$461$	15.9430	−	9.20470i	0.742540	−	0.428706i	0.822992	+	0.568053i	$0.192303\pi$
$462$		0			0
$463$	−19.1970			−0.892162			−0.446081	−	0.894992i	$-0.647181\pi$
$463$	−19.1970			−0.892162			−0.446081	+	0.894992i	$0.647181\pi$
$464$		0			0
$465$	−1.92093	+	0.0721289i	−0.0890810	+	0.00334490i
$466$		0			0
$467$		−	17.3740i		−	0.803972i	−0.915646	−	0.401986i	$-0.868320\pi$
$467$		−	17.3740i		−	0.803972i	0.915646	−	0.401986i	$-0.131680\pi$
$468$		0			0
$469$	4.12338	+	2.38064i	0.190400	+	0.109928i
$470$		0			0
$471$	−2.58365	+	0.0970135i	−0.119049	+	0.00447014i
$472$		0			0
$473$	44.6360	−	25.7706i	2.05237	−	1.18493i
$474$		0			0
$475$	32.7810	−	15.2909i	1.50410	−	0.701593i
$476$		0			0
$477$	−2.33948	+	0.175938i	−0.107117	+	0.00805564i
$478$		0			0
$479$	21.1329	+	12.2011i	0.965589	+	0.557483i	0.897889	−	0.440223i	$-0.145100\pi$
$479$	21.1329	+	12.2011i	0.965589	+	0.557483i	0.0677004	+	0.997706i	$0.478434\pi$
$480$		0			0
$481$	15.5583	−	26.9478i	0.709398	−	1.22871i
$482$		0			0
$483$	−4.82240	+	3.03100i	−0.219427	+	0.137915i
$484$		0			0
$485$	−19.9098	+	34.4847i	−0.904055	+	1.56587i
$486$		0			0
$487$			6.87512i			0.311541i	0.987793	+	0.155771i	$0.0497861\pi$
$487$			6.87512i			0.311541i	−0.987793	+	0.155771i	$0.950214\pi$
$488$		0			0
$489$	−12.8367	+	24.2959i	−0.580494	+	1.09870i
$490$		0			0
$491$	4.89360	−	2.82532i	0.220845	−	0.127505i	−0.385496	−	0.922709i	$-0.625970\pi$
$491$	4.89360	−	2.82532i	0.220845	−	0.127505i	0.606342	+	0.795204i	$0.292636\pi$
$492$		0			0
$493$		−	5.68609i		−	0.256089i
$494$		0			0
$495$	−24.7829	+	51.4969i	−1.11391	+	2.31461i
$496$		0			0
$497$	2.79717	+	4.84484i	0.125470	+	0.217321i
$498$		0			0
$499$	0.775921	+	1.34393i	0.0347350	+	0.0601628i	0.882870	−	0.469617i	$-0.155608\pi$
$499$	0.775921	+	1.34393i	0.0347350	+	0.0601628i	−0.848135	+	0.529780i	$0.822275\pi$
$500$		0			0
$501$	−7.48202	−	11.9041i	−0.334272	−	0.531836i
$502$		0			0
$503$	34.2917	+	19.7983i	1.52899	+	0.882765i	0.999404	+	0.0345100i	$0.0109871\pi$
$503$	34.2917	+	19.7983i	1.52899	+	0.882765i	0.529589	+	0.848255i	$0.322346\pi$
$504$		0			0
$505$	8.56104			0.380961
$506$		0			0
$507$	−54.5089	+	2.04675i	−2.42083	+	0.0908995i
$508$		0			0
$509$	−12.5606	+	21.7555i	−0.556737	+	0.964296i	0.441029	+	0.897493i	$0.354613\pi$
$509$	−12.5606	+	21.7555i	−0.556737	+	0.964296i	−0.997766	+	0.0668036i	$0.978720\pi$
$510$		0			0
$511$	6.47497	+	11.2150i	0.286436	+	0.496122i
$512$		0			0
$513$	19.8969	+	10.8220i	0.878468	+	0.477802i
$514$		0			0
$515$	−1.80806	−	3.13165i	−0.0796727	−	0.137997i
$516$		0			0
$517$	−21.2592	+	36.8221i	−0.934981	+	1.61943i
$518$		0			0
$519$	−4.19605	+	0.157557i	−0.184186	+	0.00691599i
$520$		0			0
$521$	27.8194			1.21879			0.609395	−	0.792867i	$-0.291413\pi$
$521$	27.8194			1.21879			0.609395	+	0.792867i	$0.291413\pi$
$522$		0			0
$523$	−28.3513	−	16.3686i	−1.23972	−	0.715750i	−0.270679	−	0.962670i	$-0.587248\pi$
$523$	−28.3513	−	16.3686i	−1.23972	−	0.715750i	−0.969036	+	0.246920i	$0.920582\pi$
$524$		0			0
$525$	−10.1460	−	16.1425i	−0.442806	−	0.704517i
$526$		0			0
$527$	−0.773199	−	1.33922i	−0.0336811	−	0.0583373i
$528$		0			0
$529$	−8.42713	−	14.5962i	−0.366397	−	0.634618i
$530$		0			0
$531$	−6.72655	+	13.9772i	−0.291907	+	0.606560i
$532$		0			0
$533$		−	28.8253i		−	1.24856i
$534$		0			0
$535$	54.8969	−	31.6947i	2.37340	−	1.37028i
$536$		0			0
$537$	−3.06746	+	5.80577i	−0.132371	+	0.250537i
$538$		0			0
$539$		−	27.3752i		−	1.17913i
$540$		0			0
$541$	6.11682	−	10.5946i	0.262982	−	0.455499i	−0.704051	−	0.710150i	$-0.748627\pi$
$541$	6.11682	−	10.5946i	0.262982	−	0.455499i	0.967033	+	0.254651i	$0.0819605\pi$
$542$		0			0
$543$	27.2076	−	17.1007i	1.16759	−	0.733861i
$544$		0			0
$545$	1.16505	−	2.01793i	0.0499054	−	0.0864387i
$546$		0			0
$547$	−18.8221	−	10.8669i	−0.804774	−	0.464637i	0.0403636	−	0.999185i	$-0.487148\pi$
$547$	−18.8221	−	10.8669i	−0.804774	−	0.464637i	−0.845138	+	0.534548i	$0.820482\pi$
$548$		0			0
$549$	−43.1816	+	3.24743i	−1.84295	+	0.138597i
$550$		0			0
$551$	4.42056	−	2.06199i	0.188322	−	0.0878438i
$552$		0			0
$553$	5.72035	−	3.30264i	0.243254	−	0.140443i
$554$		0			0
$555$	29.4443	−	1.10560i	1.24984	−	0.0469302i
$556$		0			0
$557$	34.5030	+	19.9203i	1.46194	+	0.844051i	0.999101	−	0.0423915i	$-0.0134977\pi$
$557$	34.5030	+	19.9203i	1.46194	+	0.844051i	0.462838	+	0.886443i	$0.346831\pi$
$558$		0			0
$559$			65.8121i			2.78355i
$560$		0			0
$561$	−45.9424	+	1.72509i	−1.93969	+	0.0728333i
$562$		0			0
$563$	−19.8969			−0.838554			−0.419277	−	0.907858i	$-0.637716\pi$
$563$	−19.8969			−0.838554			−0.419277	+	0.907858i	$0.637716\pi$
$564$		0			0
$565$	−0.568924	+	0.328468i	−0.0239348	+	0.0138188i
$566$		0			0
$567$	4.35580	−	11.1156i	0.182927	−	0.466811i
$568$		0			0
$569$	−27.5093			−1.15325			−0.576625	−	0.817009i	$-0.695631\pi$
$569$	−27.5093			−1.15325			−0.576625	+	0.817009i	$0.695631\pi$
$570$		0			0
$571$	−23.6597			−0.990128			−0.495064	−	0.868856i	$-0.664855\pi$
$571$	−23.6597			−0.990128			−0.495064	+	0.868856i	$0.664855\pi$
$572$		0			0
$573$	5.50188	+	2.90690i	0.229844	+	0.121438i
$574$		0			0
$575$	−17.8161	+	10.2861i	−0.742982	+	0.428961i
$576$		0			0
$577$	33.6172			1.39950			0.699751	−	0.714387i	$-0.253294\pi$
$577$	33.6172			1.39950			0.699751	+	0.714387i	$0.253294\pi$
$578$		0			0
$579$	0.475604	+	12.6662i	0.0197654	+	0.526391i
$580$		0			0
$581$		−	7.05149i		−	0.292545i
$582$		0			0
$583$	3.53792	+	2.04262i	0.146526	+	0.0845965i
$584$		0			0
$585$	−41.1234	−	60.2829i	−1.70024	−	2.49239i
$586$		0			0
$587$	−10.2731	+	5.93120i	−0.424018	+	0.244807i	−0.696795	−	0.717271i	$-0.745391\pi$
$587$	−10.2731	+	5.93120i	−0.424018	+	0.244807i	0.272777	+	0.962077i	$0.412058\pi$
$588$		0			0
$589$	0.760765	−	1.08676i	0.0313468	−	0.0447793i
$590$		0			0
$591$	32.6420	+	17.2463i	1.34271	+	0.709418i
$592$		0			0
$593$	−9.01249	−	5.20336i	−0.370099	−	0.213677i	0.303403	−	0.952862i	$-0.401877\pi$
$593$	−9.01249	−	5.20336i	−0.370099	−	0.213677i	−0.673502	+	0.739186i	$0.735211\pi$
$594$		0			0
$595$	12.2898	−	21.2865i	0.503831	−	0.872661i
$596$		0			0
$597$	−10.9373	−	17.4015i	−0.447633	−	0.712196i
$598$		0			0
$599$	−18.0611	+	31.2828i	−0.737958	+	1.27818i	0.215455	+	0.976514i	$0.430877\pi$
$599$	−18.0611	+	31.2828i	−0.737958	+	1.27818i	−0.953413	+	0.301668i	$0.902457\pi$
$600$		0			0
$601$			32.2619i			1.31599i	0.753021	+	0.657996i	$0.228596\pi$
$601$			32.2619i			1.31599i	−0.753021	+	0.657996i	$0.771404\pi$
$602$		0			0
$603$	0.807515	+	10.7377i	0.0328846	+	0.437272i
$604$		0			0
$605$	51.4433	−	29.7008i	2.09147	−	1.20751i
$606$		0			0
$607$			25.8372i			1.04870i	0.851503	+	0.524350i	$0.175692\pi$
$607$			25.8372i			1.04870i	−0.851503	+	0.524350i	$0.824308\pi$
$608$		0			0
$609$	−1.36820	−	2.17684i	−0.0554421	−	0.0882098i
$610$		0			0
$611$	−27.1455	−	47.0174i	−1.09819	−	1.90212i
$612$		0			0
$613$	3.88258	+	6.72483i	0.156816	+	0.271613i	0.933719	−	0.358007i	$-0.116544\pi$
$613$	3.88258	+	6.72483i	0.156816	+	0.271613i	−0.776903	+	0.629621i	$0.783210\pi$
$614$		0			0
$615$	23.1098	−	14.5251i	0.931875	−	0.585707i
$616$		0			0
$617$	−7.34239	−	4.23913i	−0.295594	−	0.170661i	0.344868	−	0.938651i	$-0.387924\pi$
$617$	−7.34239	−	4.23913i	−0.295594	−	0.170661i	−0.640462	+	0.767990i	$0.721257\pi$
$618$		0			0
$619$	22.4134			0.900872			0.450436	−	0.892809i	$-0.351269\pi$
$619$	22.4134			0.900872			0.450436	+	0.892809i	$0.351269\pi$
$620$		0			0
$621$	−11.8088	−	5.14658i	−0.473870	−	0.206525i
$622$		0			0
$623$	−0.301448	+	0.522124i	−0.0120773	+	0.0209185i
$624$		0			0
$625$	−1.18576	−	2.05379i	−0.0474302	−	0.0821516i
$626$		0			0
$627$	−18.0016	−	35.0916i	−0.718915	−	1.40143i
$628$		0			0
$629$	11.8517	+	20.5278i	0.472559	+	0.818496i
$630$		0			0
$631$	8.49576	−	14.7151i	0.338211	−	0.585798i	−0.645885	−	0.763434i	$-0.723512\pi$
$631$	8.49576	−	14.7151i	0.338211	−	0.585798i	0.984096	+	0.177636i	$0.0568450\pi$
$632$		0			0
$633$	−0.470141	−	12.5208i	−0.0186864	−	0.497656i
$634$		0			0
$635$	48.9954			1.94432
$636$		0			0
$637$	30.2718	+	17.4775i	1.19941	+	0.692482i
$638$		0			0
$639$	−5.48651	+	11.4005i	−0.217043	+	0.450998i
$640$		0			0
$641$	−6.38034	−	11.0511i	−0.252008	−	0.436491i	0.712070	−	0.702108i	$-0.247758\pi$
$641$	−6.38034	−	11.0511i	−0.252008	−	0.436491i	−0.964079	+	0.265617i	$0.914424\pi$
$642$		0			0
$643$	−18.3192	−	31.7298i	−0.722438	−	1.25130i	−0.960020	−	0.279932i	$-0.909688\pi$
$643$	−18.3192	−	31.7298i	−0.722438	−	1.25130i	0.237582	−	0.971368i	$-0.423645\pi$
$644$		0			0
$645$	−52.7626	+	33.1626i	−2.07753	+	1.30578i
$646$		0			0
$647$			8.57536i			0.337132i	0.985690	+	0.168566i	$0.0539137\pi$
$647$			8.57536i			0.337132i	−0.985690	+	0.168566i	$0.946086\pi$
$648$		0			0
$649$	23.3916	−	13.5052i	0.918202	−	0.530124i
$650$		0			0
$651$	−0.618253	−	0.326652i	−0.0242312	−	0.0128025i
$652$		0			0
$653$		−	8.60841i		−	0.336873i	−0.985713	−	0.168436i	$-0.946128\pi$
$653$		−	8.60841i		−	0.336873i	0.985713	−	0.168436i	$-0.0538718\pi$
$654$		0			0
$655$	14.4022	−	24.9454i	0.562742	−	0.974698i
$656$		0			0
$657$	−12.7004	+	26.3903i	−0.495488	+	1.02958i
$658$		0			0
$659$	−14.6656	+	25.4016i	−0.571292	+	0.989507i	0.425142	+	0.905127i	$0.360224\pi$
$659$	−14.6656	+	25.4016i	−0.571292	+	0.989507i	−0.996434	+	0.0843799i	$0.973109\pi$
$660$		0			0
$661$	−21.6602	−	12.5055i	−0.842484	−	0.486408i	0.0156237	−	0.999878i	$-0.495027\pi$
$661$	−21.6602	−	12.5055i	−0.842484	−	0.486408i	−0.858108	+	0.513469i	$0.828360\pi$
$662$		0			0
$663$	27.4239	−	51.9050i	1.06506	−	2.01582i
$664$		0			0
$665$	21.0056	+	1.83520i	0.814562	+	0.0711660i
$666$		0			0
$667$	−2.40252	+	1.38710i	−0.0930259	+	0.0537085i
$668$		0			0
$669$	−1.10921	−	29.5404i	−0.0428845	−	1.14210i
$670$		0			0
$671$	65.3022	+	37.7023i	2.52097	+	1.45548i
$672$		0			0
$673$			35.5191i			1.36916i	0.728938	+	0.684580i	$0.240014\pi$
$673$			35.5191i			1.36916i	−0.728938	+	0.684580i	$0.759986\pi$
$674$		0			0
$675$	17.2277	−	39.5288i	0.663094	−	1.52146i
$676$		0			0
$677$	−31.8988			−1.22597			−0.612985	−	0.790095i	$-0.710031\pi$
$677$	−31.8988			−1.22597			−0.612985	+	0.790095i	$0.710031\pi$
$678$		0			0
$679$	−12.5440	+	7.24228i	−0.481395	+	0.277933i
$680$		0			0
$681$	8.69668	−	16.4602i	0.333258	−	0.630755i
$682$		0			0
$683$	−4.68720			−0.179351			−0.0896753	−	0.995971i	$-0.528583\pi$
$683$	−4.68720			−0.179351			−0.0896753	+	0.995971i	$0.528583\pi$
$684$		0			0
$685$	56.4391			2.15643
$686$		0			0
$687$	−13.7397	+	26.0050i	−0.524202	+	0.992154i
$688$		0			0
$689$	−4.51750	+	2.60818i	−0.172103	+	0.0993637i
$690$		0			0
$691$	11.0315			0.419658			0.209829	−	0.977738i	$-0.432709\pi$
$691$	11.0315			0.419658			0.209829	+	0.977738i	$0.432709\pi$
$692$		0			0
$693$	−17.1733	+	11.7152i	−0.652359	+	0.445022i
$694$		0			0
$695$			31.9782i			1.21300i
$696$		0			0
$697$	19.0162	+	10.9790i	0.720290	+	0.415860i
$698$		0			0
$699$	−1.06014	−	28.2336i	−0.0400982	−	1.06789i
$700$		0			0
$701$	−39.0004	+	22.5169i	−1.47302	+	0.850451i	−0.999539	−	0.0303510i	$-0.990338\pi$
$701$	−39.0004	+	22.5169i	−1.47302	+	0.850451i	−0.473485	+	0.880802i	$0.657004\pi$
$702$		0			0
$703$	−11.6611	+	16.6581i	−0.439807	+	0.628271i
$704$		0			0
$705$	24.0161	−	45.4551i	0.904498	−	1.71194i
$706$		0			0
$707$	2.69691	+	1.55706i	0.101428	+	0.0585594i
$708$		0			0
$709$	1.35288	−	2.34326i	0.0508085	−	0.0880028i	−0.839503	−	0.543356i	$-0.817154\pi$
$709$	1.35288	−	2.34326i	0.0508085	−	0.0880028i	0.890311	+	0.455353i	$0.150487\pi$
$710$		0			0
$711$	13.4607	+	6.47798i	0.504816	+	0.242943i
$712$		0			0
$713$	−0.377237	+	0.653393i	−0.0141276	+	0.0244698i
$714$		0			0
$715$			127.069i			4.75212i
$716$		0			0
$717$	1.21336	+	0.641077i	0.0453139	+	0.0239415i
$718$		0			0
$719$	26.3955	−	15.2394i	0.984385	−	0.568335i	0.0807942	−	0.996731i	$-0.474254\pi$
$719$	26.3955	−	15.2394i	0.984385	−	0.568335i	0.903591	+	0.428396i	$0.140921\pi$
$720$		0			0
$721$		−	1.31538i		−	0.0489875i
$722$		0			0
$723$	−9.79939	+	6.15916i	−0.364443	+	0.229062i
$724$		0			0
$725$	−4.64317	−	8.04220i	−0.172443	−	0.298680i
$726$		0			0
$727$	21.6844	+	37.5584i	0.804228	+	1.39296i	0.916811	+	0.399322i	$0.130754\pi$
$727$	21.6844	+	37.5584i	0.804228	+	1.39296i	−0.112583	+	0.993642i	$0.535912\pi$
$728$		0			0
$729$	26.3183	−	6.02881i	0.974752	−	0.223289i
$730$		0			0
$731$	−43.4165	−	25.0665i	−1.60582	−	0.927119i
$732$		0			0
$733$	−50.9747			−1.88279			−0.941396	−	0.337302i	$-0.890486\pi$
$733$	−50.9747			−1.88279			−0.941396	+	0.337302i	$0.890486\pi$
$734$		0			0
$735$	1.24198	+	33.0763i	0.0458112	+	1.22004i
$736$		0			0
$737$	9.37516	−	16.2383i	0.345338	−	0.598144i
$738$		0			0
$739$	14.2112	+	24.6146i	0.522768	+	0.905461i	0.999649	+	0.0264934i	$0.00843409\pi$
$739$	14.2112	+	24.6146i	0.522768	+	0.905461i	−0.476881	+	0.878968i	$0.658233\pi$
$740$		0			0
$741$	50.2977	+	2.49755i	1.84773	+	0.0917499i
$742$		0			0
$743$	−26.1097	−	45.2234i	−0.957873	−	1.65908i	−0.727652	−	0.685947i	$-0.759388\pi$
$743$	−26.1097	−	45.2234i	−0.957873	−	1.65908i	−0.230221	−	0.973138i	$-0.573945\pi$
$744$		0			0
$745$	10.9518	−	18.9691i	0.401243	−	0.694974i
$746$		0			0
$747$	13.1741	−	8.98701i	0.482014	−	0.328817i
$748$		0			0
$749$	23.0583			0.842530
$750$		0			0
$751$	−16.5106	−	9.53241i	−0.602481	−	0.347843i	0.167536	−	0.985866i	$-0.446419\pi$
$751$	−16.5106	−	9.53241i	−0.602481	−	0.347843i	−0.770017	+	0.638023i	$0.779752\pi$
$752$		0			0
$753$	1.03144	−	0.648288i	0.0375879	−	0.0236249i
$754$		0			0
$755$	0.585615	+	1.01432i	0.0213127	+	0.0369147i
$756$		0			0
$757$	−8.96773	−	15.5326i	−0.325938	−	0.564541i	0.655764	−	0.754966i	$-0.272347\pi$
$757$	−8.96773	−	15.5326i	−0.325938	−	0.564541i	−0.981702	+	0.190425i	$0.939013\pi$
$758$		0			0
$759$	11.9363	+	18.9910i	0.433261	+	0.689331i
$760$		0			0
$761$			25.5990i			0.927964i	0.885845	+	0.463982i	$0.153580\pi$
$761$			25.5990i			0.927964i	−0.885845	+	0.463982i	$0.846420\pi$
$762$		0			0
$763$	0.734034	−	0.423795i	0.0265738	−	0.0153424i
$764$		0			0
$765$	55.4320	−	4.16870i	2.00415	−	0.150720i
$766$		0			0
$767$			34.4890i			1.24532i
$768$		0			0
$769$	11.7113	−	20.2845i	0.422319	−	0.731478i	−0.573847	−	0.818963i	$-0.694550\pi$
$769$	11.7113	−	20.2845i	0.422319	−	0.731478i	0.996166	+	0.0874846i	$0.0278828\pi$
$770$		0			0
$771$	19.4355	+	30.9223i	0.699951	+	1.11364i
$772$		0			0
$773$	−12.8380	+	22.2360i	−0.461749	+	0.799774i	−0.999048	−	0.0436184i	$-0.986111\pi$
$773$	−12.8380	+	22.2360i	−0.461749	+	0.799774i	0.537299	+	0.843392i	$0.319445\pi$
$774$		0			0
$775$	−2.18717	−	1.26276i	−0.0785654	−	0.0453598i
$776$		0			0
$777$	9.47667	+	5.00698i	0.339974	+	0.179624i
$778$		0			0
$779$	−1.63947	+	18.7652i	−0.0587400	+	0.672335i
$780$		0			0
$781$	19.0794	−	11.0155i	0.682714	−	0.394165i
$782$		0			0
$783$	2.32317	−	5.33050i	0.0830234	−	0.190497i
$784$		0			0
$785$	−4.71422	−	2.72176i	−0.168258	−	0.0971437i
$786$		0			0
$787$		−	48.3999i		−	1.72527i	−0.505827	−	0.862635i	$-0.668813\pi$
$787$		−	48.3999i		−	1.72527i	0.505827	−	0.862635i	$-0.331187\pi$
$788$		0			0
$789$	0.190064	+	5.06178i	0.00676647	+	0.180204i
$790$		0			0
$791$	−0.238964			−0.00849659
$792$		0			0
$793$	−83.3832	+	48.1413i	−2.96102	+	1.70955i
$794$		0			0
$795$	−4.36739	−	2.30750i	−0.154895	−	0.0818385i
$796$		0			0
$797$	28.2387			1.00027			0.500133	−	0.865949i	$-0.333284\pi$
$797$	28.2387			1.00027			0.500133	+	0.865949i	$0.333284\pi$
$798$		0			0
$799$	41.3568			1.46310
$800$		0			0
$801$	−1.35966	+	0.102252i	−0.0480412	+	0.00361289i
$802$		0			0
$803$	44.1656	−	25.4990i	1.55857	−	0.899841i
$804$		0			0
$805$	−11.9921			−0.422667
$806$		0			0
$807$	−36.2766	+	1.36215i	−1.27700	+	0.0479499i
$808$		0			0
$809$		−	21.6359i		−	0.760679i	−0.924847	−	0.380340i	$-0.875807\pi$
$809$		−	21.6359i		−	0.760679i	0.924847	−	0.380340i	$-0.124193\pi$
$810$		0			0
$811$	−20.8163	−	12.0183i	−0.730958	−	0.422019i	0.0878147	−	0.996137i	$-0.472012\pi$
$811$	−20.8163	−	12.0183i	−0.730958	−	0.422019i	−0.818772	+	0.574118i	$0.805345\pi$
$812$		0			0
$813$	−23.2390	+	0.872598i	−0.815026	+	0.0306033i
$814$		0			0
$815$	−50.1030	+	28.9270i	−1.75503	+	1.01327i
$816$		0			0
$817$	3.74312	−	42.8436i	0.130955	−	1.49891i
$818$		0			0
$819$	−1.99064	−	26.4699i	−0.0695585	−	0.924931i
$820$		0			0
$821$	26.0781	+	15.0562i	0.910134	+	0.525466i	0.880474	−	0.474094i	$-0.157224\pi$
$821$	26.0781	+	15.0562i	0.910134	+	0.525466i	0.0296595	+	0.999560i	$0.490558\pi$
$822$		0			0
$823$	−25.7676	+	44.6309i	−0.898204	+	1.55573i	−0.0684145	+	0.997657i	$0.521794\pi$
$823$	−25.7676	+	44.6309i	−0.898204	+	1.55573i	−0.829789	+	0.558077i	$0.811539\pi$
$824$		0			0
$825$	−63.5706	+	39.9557i	−2.21324	+	1.39108i
$826$		0			0
$827$	−27.8954	+	48.3162i	−0.970017	+	1.68012i	−0.274531	+	0.961578i	$0.588523\pi$
$827$	−27.8954	+	48.3162i	−0.970017	+	1.68012i	−0.695485	+	0.718540i	$0.744811\pi$
$828$		0			0
$829$		−	14.7161i		−	0.511111i	−0.966794	−	0.255556i	$-0.917742\pi$
$829$		−	14.7161i		−	0.511111i	0.966794	−	0.255556i	$-0.0822584\pi$
$830$		0			0
$831$	−4.70499	+	8.90511i	−0.163214	+	0.308915i
$832$		0			0
$833$	−23.0599	+	13.3137i	−0.798979	+	0.461291i
$834$		0			0
$835$		−	29.6026i		−	1.02444i
$836$		0			0
$837$	−0.177679	−	1.57138i	−0.00614148	−	0.0543147i
$838$		0			0
$839$	5.71764	+	9.90324i	0.197395	+	0.341898i	0.947683	−	0.319213i	$-0.103419\pi$
$839$	5.71764	+	9.90324i	0.197395	+	0.341898i	−0.750288	+	0.661111i	$0.770085\pi$
$840$		0			0
$841$	13.8739	+	24.0302i	0.478409	+	0.828629i
$842$		0			0
$843$	−25.1640	−	40.0366i	−0.866694	−	1.37893i
$844$		0			0
$845$	−99.4588	−	57.4226i	−3.42149	−	1.97540i
$846$		0			0
$847$	21.6077			0.742448
$848$		0			0
$849$	−5.03784	+	0.189166i	−0.172898	+	0.00649214i
$850$		0			0
$851$	5.78234	−	10.0153i	0.198216	−	0.343320i
$852$		0			0
$853$	7.10018	+	12.2979i	0.243105	+	0.421071i	0.961597	−	0.274464i	$-0.0885006\pi$
$853$	7.10018	+	12.2979i	0.243105	+	0.421071i	−0.718492	+	0.695535i	$0.755167\pi$
$854$		0			0
$855$	23.3426	+	41.5830i	0.798301	+	1.42211i
$856$		0			0
$857$	26.7454	+	46.3243i	0.913604	+	1.58241i	0.808933	+	0.587902i	$0.200046\pi$
$857$	26.7454	+	46.3243i	0.913604	+	1.58241i	0.104671	+	0.994507i	$0.466621\pi$
$858$		0			0
$859$	2.59167	−	4.48890i	0.0884266	−	0.153159i	−0.818420	−	0.574621i	$-0.805149\pi$
$859$	2.59167	−	4.48890i	0.0884266	−	0.153159i	0.906846	+	0.421462i	$0.138483\pi$
$860$		0			0
$861$	9.92185	−	0.372555i	0.338136	−	0.0126966i
$862$		0			0
$863$	−38.4263			−1.30804			−0.654022	−	0.756475i	$-0.726920\pi$
$863$	−38.4263			−1.30804			−0.654022	+	0.756475i	$0.726920\pi$
$864$		0			0
$865$	−7.65625	−	4.42034i	−0.260320	−	0.150296i
$866$		0			0
$867$	8.12788	+	12.9317i	0.276037	+	0.439183i
$868$		0			0
$869$	−13.0061	−	22.5272i	−0.441202	−	0.764184i
$870$		0			0
$871$	11.9710	+	20.7343i	0.405621	+	0.702556i
$872$		0			0
$873$	−29.5177	−	14.2054i	−0.999022	−	0.480780i
$874$		0			0
$875$		−	15.9556i		−	0.539398i
$876$		0			0
$877$	−43.3245	+	25.0134i	−1.46296	+	0.844642i	−0.999147	−	0.0412898i	$-0.986853\pi$
$877$	−43.3245	+	25.0134i	−1.46296	+	0.844642i	−0.463816	+	0.885932i	$0.653520\pi$
$878$		0			0
$879$	8.46817	−	16.0277i	0.285624	−	0.540599i
$880$		0			0
$881$			22.3822i			0.754076i	0.926198	+	0.377038i	$0.123057\pi$
$881$			22.3822i			0.754076i	−0.926198	+	0.377038i	$0.876943\pi$
$882$		0			0
$883$	2.38436	−	4.12984i	0.0802402	−	0.138980i	−0.823113	−	0.567878i	$-0.807765\pi$
$883$	2.38436	−	4.12984i	0.0802402	−	0.138980i	0.903353	+	0.428898i	$0.141098\pi$
$884$		0			0
$885$	−27.6504	+	17.3790i	−0.929458	+	0.584188i
$886$		0			0
$887$	1.96367	−	3.40117i	0.0659335	−	0.114200i	−0.831174	−	0.556012i	$-0.812331\pi$
$887$	1.96367	−	3.40117i	0.0659335	−	0.114200i	0.897108	+	0.441812i	$0.145664\pi$
$888$		0			0
$889$	15.4346	+	8.91117i	0.517660	+	0.298871i
$890$		0			0
$891$	−43.7742	−	17.1535i	−1.46649	−	0.574665i
$892$		0			0
$893$	14.9975	+	32.1522i	0.501874	+	1.07593i
$894$		0			0
$895$	−11.9727	+	6.91241i	−0.400202	+	0.231056i
$896$		0			0
$897$	−28.6211	+	1.07469i	−0.955632	+	0.0358830i
$898$		0			0
$899$	−0.294942	−	0.170285i	−0.00983688	−	0.00567932i
$900$		0			0
$901$		−	3.97362i		−	0.132380i
$902$		0			0
$903$	−22.6529	+	0.850593i	−0.753842	+	0.0283060i
$904$		0			0
$905$	67.6588			2.24905
$906$		0			0
$907$	28.4180	−	16.4072i	0.943605	−	0.544791i	0.0525167	−	0.998620i	$-0.483276\pi$
$907$	28.4180	−	16.4072i	0.943605	−	0.544791i	0.891089	+	0.453829i	$0.149942\pi$
$908$		0			0
$909$	0.528158	+	7.02301i	0.0175179	+	0.232938i
$910$		0			0
$911$	−51.8536			−1.71799			−0.858993	−	0.511988i	$-0.828909\pi$
$911$	−51.8536			−1.71799			−0.858993	+	0.511988i	$0.828909\pi$
$912$		0			0
$913$	−27.7694			−0.919032
$914$		0			0
$915$	−80.6124	−	42.5914i	−2.66497	−	1.40803i
$916$		0			0
$917$	9.07403	−	5.23889i	0.299651	−	0.173004i
$918$		0			0
$919$	−39.8042			−1.31302			−0.656510	−	0.754317i	$-0.727968\pi$
$919$	−39.8042			−1.31302			−0.656510	+	0.754317i	$0.727968\pi$
$920$		0			0
$921$	0.637565	+	16.9796i	0.0210085	+	0.559496i
$922$		0			0
$923$			28.1310i			0.925942i
$924$		0			0
$925$	33.5253	+	19.3558i	1.10230	+	0.636415i
$926$		0			0
$927$	2.45749	−	1.67644i	0.0807147	−	0.0550614i
$928$		0			0
$929$	−9.94317	+	5.74069i	−0.326225	+	0.188346i	−0.654164	−	0.756353i	$-0.726979\pi$
$929$	−9.94317	+	5.74069i	−0.326225	+	0.188346i	0.327939	+	0.944699i	$0.393646\pi$
$930$		0			0
$931$	−18.7129	−	13.0995i	−0.613290	−	0.429320i
$932$		0			0
$933$	14.4403	+	7.62948i	0.472753	+	0.249778i
$934$		0			0
$935$	−83.8281	−	48.3982i	−2.74147	−	1.58279i
$936$		0			0
$937$	−15.0634	+	26.0906i	−0.492101	+	0.852344i	−0.999959	−	0.00909679i	$-0.997104\pi$
$937$	−15.0634	+	26.0906i	−0.492101	+	0.852344i	0.507857	+	0.861441i	$0.330438\pi$
$938$		0			0
$939$	20.6355	+	32.8316i	0.673413	+	1.07142i
$940$		0			0
$941$	−7.64125	+	13.2350i	−0.249098	+	0.431450i	−0.963276	−	0.268514i	$-0.913467\pi$
$941$	−7.64125	+	13.2350i	−0.249098	+	0.431450i	0.714178	+	0.699964i	$0.246801\pi$
$942$		0			0
$943$		−	10.7131i		−	0.348867i
$944$		0			0
$945$	20.2182	−	14.9341i	0.657700	−	0.485805i
$946$		0			0
$947$	−16.8743	+	9.74235i	−0.548340	+	0.316584i	−0.748452	−	0.663189i	$-0.769203\pi$
$947$	−16.8743	+	9.74235i	−0.548340	+	0.316584i	0.200112	+	0.979773i	$0.435869\pi$
$948$		0			0
$949$			65.1185i			2.11383i
$950$		0			0
$951$	17.0371	+	27.1065i	0.552465	+	0.878987i
$952$		0			0
$953$	−20.5555	−	35.6031i	−0.665857	−	1.15330i	−0.979052	−	0.203610i	$-0.934733\pi$
$953$	−20.5555	−	35.6031i	−0.665857	−	1.15330i	0.313195	−	0.949689i	$-0.398601\pi$
$954$		0			0
$955$	6.55060	+	11.3460i	0.211972	+	0.367147i
$956$		0			0
$957$	−8.57257	+	5.38808i	−0.277112	+	0.174172i
$958$		0			0
$959$	17.7795	+	10.2650i	0.574131	+	0.331475i
$960$		0			0
$961$	30.9074			0.997012
$962$		0			0
$963$	29.3874	+	43.0791i	0.946995	+	1.38820i
$964$		0			0
$965$	−13.3433	+	23.1113i	−0.429536	+	0.743978i
$966$		0			0
$967$	−5.21929	−	9.04007i	−0.167841	−	0.290709i	0.769820	−	0.638262i	$-0.220346\pi$
$967$	−5.21929	−	9.04007i	−0.167841	−	0.290709i	−0.937661	+	0.347552i	$0.887013\pi$
$968$		0			0
$969$	−20.8051	+	32.2304i	−0.668355	+	1.03539i
$970$		0			0
$971$	17.3621	+	30.0720i	0.557176	+	0.965057i	0.997731	+	0.0673314i	$0.0214485\pi$
$971$	17.3621	+	30.0720i	0.557176	+	0.965057i	−0.440555	+	0.897726i	$0.645218\pi$
$972$		0			0
$973$	−5.81612	+	10.0738i	−0.186456	+	0.322952i
$974$		0			0
$975$	−3.59743	−	95.8065i	−0.115210	−	3.06826i
$976$		0			0
$977$	29.5411			0.945102			0.472551	−	0.881303i	$-0.343333\pi$
$977$	29.5411			0.945102			0.472551	+	0.881303i	$0.343333\pi$
$978$		0			0
$979$	2.05617	+	1.18713i	0.0657155	+	0.0379409i
$980$		0			0
$981$	1.72728	+	0.831254i	0.0551477	+	0.0265399i
$982$		0			0
$983$	−6.08349	−	10.5369i	−0.194033	−	0.336075i	0.752550	−	0.658535i	$-0.228824\pi$
$983$	−6.08349	−	10.5369i	−0.194033	−	0.336075i	−0.946583	+	0.322460i	$0.895490\pi$
$984$		0			0
$985$	38.8639	+	67.3142i	1.23831	+	2.14481i
$986$		0			0
$987$	15.8329	−	9.95134i	0.503965	−	0.316755i
$988$		0			0
$989$			24.4595i			0.777765i
$990$		0			0
$991$	35.0709	−	20.2482i	1.11406	−	0.643205i	0.174185	−	0.984713i	$-0.444271\pi$
$991$	35.0709	−	20.2482i	1.11406	−	0.643205i	0.939879	+	0.341508i	$0.110938\pi$
$992$		0			0
$993$	20.4152	+	10.7863i	0.647857	+	0.342293i
$994$		0			0
$995$		−	43.2733i		−	1.37186i
$996$		0			0
$997$	0.0891873	−	0.154477i	0.00282459	−	0.00489233i	−0.864610	−	0.502444i	$-0.832434\pi$
$997$	0.0891873	−	0.154477i	0.00282459	−	0.00489233i	0.867434	+	0.497552i	$0.165768\pi$
$998$		0			0
$999$	2.72349	+	24.0863i	0.0861674	+	0.762057i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.bn.o.449.4		16
3.2	odd	2		912.2.bn.n.449.1		16
4.3	odd	2		456.2.bf.c.449.5	yes	16
12.11	even	2		456.2.bf.d.449.8	yes	16
19.8	odd	6		912.2.bn.n.65.1		16
57.8	even	6	inner	912.2.bn.o.65.4		16
76.27	even	6		456.2.bf.d.65.8	yes	16
228.179	odd	6		456.2.bf.c.65.5	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.2.bf.c.65.5	✓	16	228.179	odd	6
456.2.bf.c.449.5	yes	16	4.3	odd	2
456.2.bf.d.65.8	yes	16	76.27	even	6
456.2.bf.d.449.8	yes	16	12.11	even	2
912.2.bn.n.65.1		16	19.8	odd	6
912.2.bn.n.449.1		16	3.2	odd	2
912.2.bn.o.65.4		16	57.8	even	6	inner
912.2.bn.o.449.4		16	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.bn (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.809132 + 1.53144i) q^{3} +(-3.15813 + 1.82335i) q^{5} -1.32651 q^{7} +(-1.69061 - 2.47827i) q^{9} +O(q^{10})\)	\(q+(-0.809132 + 1.53144i) q^{3} +(-3.15813 + 1.82335i) q^{5} -1.32651 q^{7} +(-1.69061 - 2.47827i) q^{9} +5.22390i q^{11} +(-5.77665 - 3.33515i) q^{13} +(-0.237002 - 6.31182i) q^{15} +(4.40043 - 2.54059i) q^{17} +(3.57090 + 2.49973i) q^{19} +(1.07332 - 2.03146i) q^{21} +(-2.14693 - 1.23953i) q^{23} +(4.14920 - 7.18663i) q^{25} +(5.16325 - 0.583820i) q^{27} +(0.559525 - 0.969126i) q^{29} -0.304339i q^{31} +(-8.00009 - 4.22682i) q^{33} +(4.18928 - 2.41868i) q^{35} +4.66495i q^{37} +(9.78165 - 6.14801i) q^{39} +(2.16072 + 3.74248i) q^{41} +(-4.93321 - 8.54458i) q^{43} +(9.85793 + 4.74414i) q^{45} +(7.04877 + 4.06961i) q^{47} -5.24038 q^{49} +(0.330230 + 8.79466i) q^{51} +(0.391014 - 0.677256i) q^{53} +(-9.52499 - 16.4978i) q^{55} +(-6.71752 + 3.44601i) q^{57} +(-2.58526 - 4.47781i) q^{59} +(7.21726 - 12.5007i) q^{61} +(2.24261 + 3.28744i) q^{63} +24.3246 q^{65} +(-3.10845 - 1.79467i) q^{67} +(3.63541 - 2.28495i) q^{69} +(-2.10867 - 3.65233i) q^{71} +(-4.88122 - 8.45453i) q^{73} +(7.64863 + 12.1692i) q^{75} -6.92954i q^{77} +(-4.31234 + 2.48973i) q^{79} +(-3.28367 + 8.37959i) q^{81} +5.31583i q^{83} +(-9.26476 + 16.0470i) q^{85} +(1.03143 + 1.64103i) q^{87} +(0.227250 - 0.393608i) q^{89} +(7.66276 + 4.42410i) q^{91} +(0.466076 + 0.246250i) q^{93} +(-15.8353 - 1.38348i) q^{95} +(9.45642 - 5.45967i) q^{97} +(12.9462 - 8.83159i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + q^{3} - 3 q^{5} + 13 q^{9}+O(q^{10}) \) 16 * q + q^3 - 3 * q^5 + 13 * q^9	\( 16 q + q^{3} - 3 q^{5} + 13 q^{9} - 3 q^{13} - 15 q^{15} + 3 q^{17} - 11 q^{19} - 6 q^{21} - 3 q^{23} + 11 q^{25} + 4 q^{27} - 5 q^{29} + q^{33} + 24 q^{35} + 9 q^{39} - 6 q^{41} - 13 q^{43} + 33 q^{45} + 27 q^{47} + 8 q^{49} - 15 q^{51} + 7 q^{53} + 12 q^{55} + 23 q^{57} - 10 q^{59} - q^{61} + 8 q^{63} + 30 q^{65} + 24 q^{67} + 41 q^{69} + 27 q^{71} + 2 q^{73} + 21 q^{75} + 21 q^{79} - 7 q^{81} - 5 q^{85} + 23 q^{87} - 25 q^{89} + 78 q^{91} - 56 q^{93} + 13 q^{95} - 60 q^{97} + 35 q^{99}+O(q^{100}) \) 16 * q + q^3 - 3 * q^5 + 13 * q^9 - 3 * q^13 - 15 * q^15 + 3 * q^17 - 11 * q^19 - 6 * q^21 - 3 * q^23 + 11 * q^25 + 4 * q^27 - 5 * q^29 + q^33 + 24 * q^35 + 9 * q^39 - 6 * q^41 - 13 * q^43 + 33 * q^45 + 27 * q^47 + 8 * q^49 - 15 * q^51 + 7 * q^53 + 12 * q^55 + 23 * q^57 - 10 * q^59 - q^61 + 8 * q^63 + 30 * q^65 + 24 * q^67 + 41 * q^69 + 27 * q^71 + 2 * q^73 + 21 * q^75 + 21 * q^79 - 7 * q^81 - 5 * q^85 + 23 * q^87 - 25 * q^89 + 78 * q^91 - 56 * q^93 + 13 * q^95 - 60 * q^97 + 35 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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