LMFDB - Embedded newform 456.2.bf.d.449.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [456,2,Mod(65,456)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("456.65"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(456, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 3, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 456 = 2^{3} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	456.bf (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.64117833217$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			449.8
Root			$-0.809132 - 1.53144i$ of defining polynomial
Character	$\chi$	$=$	456.449
Dual form			456.2.bf.d.65.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.73083 + 0.0649909i) q^{3} +(3.15813 - 1.82335i) q^{5} +1.32651 q^{7} +(2.99155 + 0.224976i) q^{9} +5.22390i q^{11} +(-5.77665 - 3.33515i) q^{13} +(5.58470 - 2.95066i) q^{15} +(-4.40043 + 2.54059i) q^{17} +(-3.57090 - 2.49973i) q^{19} +(2.29596 + 0.0862108i) q^{21} +(-2.14693 - 1.23953i) q^{23} +(4.14920 - 7.18663i) q^{25} +(5.16325 + 0.583820i) q^{27} +(-0.559525 + 0.969126i) q^{29} +0.304339i q^{31} +(-0.339506 + 9.04169i) q^{33} +(4.18928 - 2.41868i) q^{35} +4.66495i q^{37} +(-9.78165 - 6.14801i) q^{39} +(-2.16072 - 3.74248i) q^{41} +(4.93321 + 8.54458i) q^{43} +(9.85793 - 4.74414i) q^{45} +(7.04877 + 4.06961i) q^{47} -5.24038 q^{49} +(-7.78151 + 4.11134i) q^{51} +(-0.391014 + 0.677256i) q^{53} +(9.52499 + 16.4978i) q^{55} +(-6.01817 - 4.55869i) q^{57} +(-2.58526 - 4.47781i) q^{59} +(7.21726 - 12.5007i) q^{61} +(3.96831 + 0.298433i) q^{63} -24.3246 q^{65} +(3.10845 + 1.79467i) q^{67} +(-3.63541 - 2.28495i) q^{69} +(-2.10867 - 3.65233i) q^{71} +(-4.88122 - 8.45453i) q^{73} +(7.64863 - 12.1692i) q^{75} +6.92954i q^{77} +(4.31234 - 2.48973i) q^{79} +(8.89877 + 1.34606i) q^{81} +5.31583i q^{83} +(-9.26476 + 16.0470i) q^{85} +(-1.03143 + 1.64103i) q^{87} +(-0.227250 + 0.393608i) q^{89} +(-7.66276 - 4.42410i) q^{91} +(-0.0197792 + 0.526759i) q^{93} +(-15.8353 - 1.38348i) q^{95} +(9.45642 - 5.45967i) q^{97} +(-1.17525 + 15.6276i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + q^{3} + 3 q^{5} - 5 q^{9} - 3 q^{13} + 12 q^{15} - 3 q^{17} + 11 q^{19} - 12 q^{21} - 3 q^{23} + 11 q^{25} + 4 q^{27} + 5 q^{29} + 14 q^{33} + 24 q^{35} - 9 q^{39} + 6 q^{41} + 13 q^{43} + 33 q^{45}+ \cdots - 20 q^{99}+O(q^{100}) $ 16 * q + q^3 + 3 * q^5 - 5 * q^9 - 3 * q^13 + 12 * q^15 - 3 * q^17 + 11 * q^19 - 12 * q^21 - 3 * q^23 + 11 * q^25 + 4 * q^27 + 5 * q^29 + 14 * q^33 + 24 * q^35 - 9 * q^39 + 6 * q^41 + 13 * q^43 + 33 * q^45 + 27 * q^47 + 8 * q^49 - 18 * q^51 - 7 * q^53 - 12 * q^55 - 36 * q^57 - 10 * q^59 - q^61 - 26 * q^63 - 30 * q^65 - 24 * q^67 - 41 * q^69 + 27 * q^71 + 2 * q^73 + 21 * q^75 - 21 * q^79 - 13 * q^81 - 5 * q^85 - 23 * q^87 + 25 * q^89 - 78 * q^91 + 22 * q^93 + 13 * q^95 - 60 * q^97 - 20 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/456\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$343$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$	$1$

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
$3$	1.73083	+	0.0649909i	0.999296	+	0.0375225i
$3$	1.73083	+	0.0649909i	0.999296	+	0.0375225i
$4$		0			0
$5$	3.15813	−	1.82335i	1.41236	−	0.815426i	0.416750	−	0.909021i	$-0.363169\pi$
$5$	3.15813	−	1.82335i	1.41236	−	0.815426i	0.995610	+	0.0935948i	$0.0298358\pi$
$6$		0			0
$7$	1.32651			0.501372			0.250686	−	0.968068i	$-0.419344\pi$
$7$	1.32651			0.501372			0.250686	+	0.968068i	$0.419344\pi$
$8$		0			0
$9$	2.99155	+	0.224976i	0.997184	+	0.0749921i
$10$		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
$15$	5.58470	−	2.95066i	1.44196	−	0.761857i
$16$		0			0
$17$	−4.40043	+	2.54059i	−1.06726	+	0.616183i	−0.927432	−	0.373992i	$-0.877989\pi$
$17$	−4.40043	+	2.54059i	−1.06726	+	0.616183i	−0.139829	+	0.990176i	$0.544655\pi$
$18$		0			0
$19$	−3.57090	−	2.49973i	−0.819221	−	0.573478i
$19$	−3.57090	−	2.49973i	−0.819221	−	0.573478i
$20$		0			0
$21$	2.29596	+	0.0862108i	0.501019	+	0.0188127i
$22$		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	−0.913289	−	0.407313i	$-0.866466\pi$
$29$	−0.559525	+	0.969126i	−0.103901	+	0.179962i	0.809388	+	0.587275i	$0.199799\pi$
$30$		0			0
$31$			0.304339i			0.0546608i	0.999626	+	0.0273304i	$0.00870062\pi$
$31$			0.304339i			0.0546608i	−0.999626	+	0.0273304i	$0.991299\pi$
$32$		0			0
$33$	−0.339506	+	9.04169i	−0.0591004	+	1.57396i
$34$		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	0.646504	−	0.762911i	$-0.276230\pi$
$41$	−2.16072	−	3.74248i	−0.337448	−	0.584477i	−0.983952	+	0.178434i	$0.942897\pi$
$42$		0			0
$43$	4.93321	+	8.54458i	0.752308	+	1.30304i	0.946701	+	0.322112i	$0.104393\pi$
$43$	4.93321	+	8.54458i	0.752308	+	1.30304i	−0.194393	+	0.980924i	$0.562274\pi$
$44$		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
$51$	−7.78151	+	4.11134i	−1.08963	+	0.575703i
$52$		0			0
$53$	−0.391014	+	0.677256i	−0.0537099	+	0.0930282i	−0.891630	−	0.452764i	$-0.850438\pi$
$53$	−0.391014	+	0.677256i	−0.0537099	+	0.0930282i	0.837920	+	0.545792i	$0.183771\pi$
$54$		0			0
$55$	9.52499	+	16.4978i	1.28435	+	2.22456i
$56$		0			0
$57$	−6.01817	−	4.55869i	−0.797126	−	0.603813i
$58$		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
$63$	3.96831	+	0.298433i	0.499961	+	0.0375990i
$64$		0			0
$65$	−24.3246			−3.01709
$66$		0			0
$67$	3.10845	+	1.79467i	0.379758	+	0.219253i	0.677713	−	0.735327i	$-0.262971\pi$
$67$	3.10845	+	1.79467i	0.379758	+	0.219253i	−0.297955	+	0.954580i	$0.596305\pi$
$68$		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	−0.237395	−	0.971413i	$-0.576294\pi$
$79$	4.31234	−	2.48973i	0.485176	−	0.280117i	0.722571	+	0.691297i	$0.242960\pi$
$80$		0			0
$81$	8.89877	+	1.34606i	0.988752	+	0.149562i
$82$		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	−0.877818	−	0.478994i	$-0.841002\pi$
$89$	−0.227250	+	0.393608i	−0.0240884	+	0.0417224i	0.853730	+	0.520716i	$0.174335\pi$
$90$		0			0
$91$	−7.66276	−	4.42410i	−0.803276	−	0.463772i
$92$		0			0
$93$	−0.0197792	+	0.526759i	−0.00205101	+	0.0546223i
$94$		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
$99$	−1.17525	+	15.6276i	−0.118118	+	1.57063i
$100$		0			0
$101$	2.03309	+	1.17381i	0.202300	+	0.116798i	0.597728	−	0.801699i	$-0.296070\pi$
$101$	2.03309	+	1.17381i	0.202300	+	0.116798i	−0.395428	+	0.918497i	$0.629404\pi$
$102$		0			0
$103$		−	0.991616i		−	0.0977068i	−0.998806	−	0.0488534i	$-0.984443\pi$
$103$		−	0.991616i		−	0.0977068i	0.998806	−	0.0488534i	$-0.0155567\pi$
$104$		0			0
$105$	7.40814	−	3.91407i	0.722960	−	0.381974i
$106$		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
$111$	−0.303179	+	8.07424i	−0.0287765	+	0.766373i
$112$		0			0
$113$	−0.180146			−0.0169467			−0.00847334	−	0.999964i	$-0.502697\pi$
$113$	−0.180146			−0.0169467			−0.00847334	+	0.999964i	$0.502697\pi$
$114$		0			0
$115$	−9.04038			−0.843020
$116$		0			0
$117$	−16.5308	−	11.2769i	−1.52828	−	1.04255i
$118$		0			0
$119$	−5.83720	+	3.37011i	−0.535095	+	0.308937i
$120$		0			0
$121$	−16.2891			−1.48083
$122$		0			0
$123$	−3.49662	−	6.61803i	−0.315279	−	0.596727i
$124$		0			0
$125$		−	12.0283i		−	1.07584i
$126$		0			0
$127$	11.6355	+	6.71777i	1.03249	+	0.596106i	0.917696	−	0.397284i	$-0.130047\pi$
$127$	11.6355	+	6.71777i	1.03249	+	0.596106i	0.114790	+	0.993390i	$0.463381\pi$
$128$		0			0
$129$	7.98324	+	15.1098i	0.702885	+	1.33035i
$130$		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
$135$	17.3707	−	7.57063i	1.49504	−	0.651576i
$136$		0			0
$137$	13.4033	+	7.73838i	1.14512	+	0.661135i	0.947693	−	0.319183i	$-0.103408\pi$
$137$	13.4033	+	7.73838i	1.14512	+	0.661135i	0.197426	+	0.980318i	$0.436742\pi$
$138$		0			0
$139$	−4.38454	+	7.59424i	−0.371892	+	0.644135i	−0.989857	−	0.142070i	$-0.954624\pi$
$139$	−4.38454	+	7.59424i	−0.371892	+	0.644135i	0.617965	+	0.786206i	$0.287957\pi$
$140$		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
$147$	−9.07021	−	0.340577i	−0.748099	−	0.0280903i
$148$		0			0
$149$	5.20172	−	3.00321i	0.426141	−	0.246033i	−0.271560	−	0.962421i	$-0.587540\pi$
$149$	5.20172	−	3.00321i	0.426141	−	0.246033i	0.697701	+	0.716389i	$0.254206\pi$
$150$		0			0
$151$			0.321176i			0.0261369i	0.999915	+	0.0130685i	$0.00415994\pi$
$151$			0.321176i			0.0261369i	−0.999915	+	0.0130685i	$0.995840\pi$
$152$		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	$-0.713400\pi$
$163$	−15.8647			−1.24262			−0.621311	+	0.783564i	$0.713400\pi$
$164$		0			0
$165$	15.4140	+	29.1739i	1.19997	+	2.27118i
$166$		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
$171$	−10.1202	−	8.28145i	−0.773908	−	0.633298i
$172$		0			0
$173$	−1.21215	−	2.09950i	−0.0921579	−	0.159622i	0.816261	−	0.577683i	$-0.196043\pi$
$173$	−1.21215	−	2.09950i	−0.0921579	−	0.159622i	−0.908419	+	0.418061i	$0.862710\pi$
$174$		0			0
$175$	5.50395	−	9.53311i	0.416059	−	0.720636i
$176$		0			0
$177$	−4.18364	−	7.91835i	−0.314462	−	0.595180i
$178$		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
$195$	−42.1017	−	1.58088i	−3.01497	−	0.113209i
$196$		0			0
$197$			21.3146i			1.51860i	0.650741	+	0.759300i	$0.274458\pi$
$197$			21.3146i			1.51860i	−0.650741	+	0.759300i	$0.725542\pi$
$198$		0			0
$199$	5.93321	−	10.2766i	0.420594	−	0.728491i	−0.575403	−	0.817870i	$-0.695155\pi$
$199$	5.93321	−	10.2766i	0.420594	−	0.728491i	0.995998	+	0.0893789i	$0.0284882\pi$
$200$		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
$207$	−6.14378	−	4.19112i	−0.427022	−	0.291303i
$208$		0			0
$209$	13.0583	−	18.6540i	0.903265	−	1.29033i
$210$		0			0
$211$	6.26479	−	3.61698i	0.431286	−	0.249003i	−0.268608	−	0.963250i	$-0.586564\pi$
$211$	6.26479	−	3.61698i	0.431286	−	0.249003i	0.699894	+	0.714246i	$0.253230\pi$
$212$		0			0
$213$	−3.41239	−	6.45861i	−0.233813	−	0.442536i
$214$		0			0
$215$	31.1595	+	17.9899i	2.12506	+	1.22690i
$216$		0			0
$217$			0.403707i			0.0274054i
$218$		0			0
$219$	−7.89911	−	14.9506i	−0.533772	−	1.01027i
$220$		0			0
$221$	33.8930			2.27989
$222$		0			0
$223$	14.7806	−	8.53358i	0.989782	−	0.571451i	0.0845731	−	0.996417i	$-0.473047\pi$
$223$	14.7806	−	8.53358i	0.989782	−	0.571451i	0.905209	+	0.424966i	$0.139714\pi$
$224$		0			0
$225$	14.0294	−	20.5657i	0.935292	−	1.37105i
$226$		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
$231$	−0.450357	+	11.9939i	−0.0296313	+	0.789138i
$232$		0			0
$233$	14.1267	−	8.15608i	0.925474	−	0.534322i	0.0400964	−	0.999196i	$-0.487233\pi$
$233$	14.1267	−	8.15608i	0.925474	−	0.534322i	0.885377	+	0.464873i	$0.153900\pi$
$234$		0			0
$235$	29.6813			1.93619
$236$		0			0
$237$	7.62574	−	4.02904i	0.495345	−	0.261714i
$238$		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
$243$	15.3148	+	2.90814i	0.982444	+	0.186557i
$244$		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
$249$	−0.345480	+	9.20081i	−0.0218939	+	0.583077i
$250$		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	$0.395125\pi$
$257$	−10.5433	+	18.2615i	−0.657672	+	1.13912i	−0.981217	+	0.192908i	$0.938208\pi$
$258$		0			0
$259$			6.18808i			0.384509i
$260$		0			0
$261$	−1.89188	+	2.77331i	−0.117104	+	0.171664i
$262$		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	$-0.946036\pi$
$269$	−10.4795	−	18.1511i	−0.638948	−	1.10669i	0.346716	−	0.937970i	$-0.387297\pi$
$270$		0			0
$271$	−6.71324	−	11.6277i	−0.407800	−	0.706330i	0.586843	−	0.809701i	$-0.300371\pi$
$271$	−6.71324	−	11.6277i	−0.407800	−	0.706330i	−0.994643	+	0.103370i	$0.967037\pi$
$272$		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
$279$	−0.0684690	+	0.910445i	−0.00409913	+	0.0545069i
$280$		0			0
$281$	13.6509	−	23.6440i	0.814342	−	1.41048i	−0.0954570	−	0.995434i	$-0.530431\pi$
$281$	13.6509	−	23.6440i	0.814342	−	1.41048i	0.909799	−	0.415049i	$-0.136235\pi$
$282$		0			0
$283$	−1.45532	−	2.52070i	−0.0865100	−	0.149840i	0.819524	−	0.573045i	$-0.194238\pi$
$283$	−1.45532	−	2.52070i	−0.0865100	−	0.149840i	−0.906034	+	0.423206i	$0.860905\pi$
$284$		0			0
$285$	−27.3183	−	3.42372i	−1.61819	−	0.202804i
$286$		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
$291$	16.7223	−	8.83518i	0.980278	−	0.517927i
$292$		0			0
$293$	10.4657			0.611416			0.305708	−	0.952125i	$-0.401107\pi$
$293$	10.4657			0.611416			0.305708	+	0.952125i	$0.401107\pi$
$294$		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	−0.722448	−	0.691426i	$-0.756983\pi$
$307$	−8.49577	+	4.90503i	−0.484879	+	0.279945i	0.237568	+	0.971371i	$0.423650\pi$
$308$		0			0
$309$	0.0644460	−	1.71632i	0.00366620	−	0.0976380i
$310$		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	$0.340397\pi$
$317$	−9.24221	+	16.0080i	−0.519094	+	0.899098i	−0.999754	+	0.0221905i	$0.992936\pi$
$318$		0			0
$319$	−5.06262	−	2.92290i	−0.283452	−	0.163651i
$320$		0			0
$321$	−30.0865	−	1.12972i	−1.67927	−	0.0630546i
$322$		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
$327$	−0.978534	+	0.517006i	−0.0541130	+	0.0285905i
$328$		0			0
$329$	9.35025	+	5.39837i	0.515496	+	0.297622i
$330$		0			0
$331$			13.3307i			0.732723i	0.930473	+	0.366361i	$0.119397\pi$
$331$			13.3307i			0.732723i	−0.930473	+	0.366361i	$0.880603\pi$
$332$		0			0
$333$	−1.04950	+	13.9554i	−0.0575124	+	0.764753i
$334$		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
$339$	−0.311802	−	0.0117078i	−0.0169347	−	0.000635882i
$340$		0			0
$341$	−1.58983			−0.0860944
$342$		0			0
$343$	−16.2369			−0.876713
$344$		0			0
$345$	−15.6474	−	0.587542i	−0.842426	−	0.0316322i
$346$		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
$351$	−27.8792	−	20.5927i	−1.48808	−	1.09916i
$352$		0			0
$353$			18.2589i			0.971822i	0.874008	+	0.485911i	$0.161512\pi$
$353$			18.2589i			0.971822i	−0.874008	+	0.485911i	$0.838488\pi$
$354$		0			0
$355$	−13.3189	−	7.68969i	−0.706896	−	0.408126i
$356$		0			0
$357$	−10.3222	+	5.45372i	−0.546310	+	0.288642i
$358$		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
$363$	−28.1937	−	1.05865i	−1.47979	−	0.0555645i
$364$		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	$0.537176\pi$
$367$	−17.5938	+	30.4734i	−0.918389	+	1.59070i	−0.801862	+	0.597510i	$0.796157\pi$
$368$		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
$375$	0.781729	−	20.8189i	0.0403683	−	1.07509i
$376$		0			0
$377$	6.46436	−	3.73220i	0.332932	−	0.192218i
$378$		0			0
$379$		−	5.67816i		−	0.291668i	−0.989309	−	0.145834i	$-0.953414\pi$
$379$		−	5.67816i		−	0.291668i	0.989309	−	0.145834i	$-0.0465865\pi$
$380$		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	0.585338	−	0.810790i	$-0.300962\pi$
$389$	3.46815	+	2.00234i	0.175842	+	0.101523i	−0.409495	+	0.912312i	$0.634295\pi$
$390$		0			0
$391$	12.5965			0.637034
$392$		0			0
$393$	−12.0965	+	6.39116i	−0.610188	+	0.322391i
$394$		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
$399$	−7.98314	−	6.04713i	−0.399657	−	0.302735i
$400$		0			0
$401$	4.34004	+	7.51717i	0.216731	+	0.375390i	0.953807	−	0.300421i	$-0.0971271\pi$
$401$	4.34004	+	7.51717i	0.216731	+	0.375390i	−0.737075	+	0.675810i	$0.763794\pi$
$402$		0			0
$403$	1.01501	−	1.75806i	0.0505615	−	0.0875751i
$404$		0			0
$405$	30.5578	−	11.9745i	1.51843	−	0.595020i
$406$		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
$423$	20.1712	+	13.7603i	0.980758	+	0.669047i
$424$		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
$435$	−0.265217	+	7.06324i	−0.0127162	+	0.338656i
$436$		0			0
$437$	4.56798	+	9.79298i	0.218516	+	0.468462i
$438$		0			0
$439$	−10.1428	+	5.85597i	−0.484091	+	0.279490i	−0.722120	−	0.691768i	$-0.756832\pi$
$439$	−10.1428	+	5.85597i	−0.484091	+	0.279490i	0.238029	+	0.971258i	$0.423499\pi$
$440$		0			0
$441$	−15.6769	−	1.17896i	−0.746518	−	0.0561410i
$442$		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
$447$	9.19848	−	4.85999i	0.435073	−	0.229870i
$448$		0			0
$449$	23.4658			1.10742			0.553709	−	0.832710i	$-0.313212\pi$
$449$	23.4658			1.10742			0.553709	+	0.832710i	$0.313212\pi$
$450$		0			0
$451$	19.5503	−	11.2874i	0.920589	−	0.531503i
$452$		0			0
$453$	−0.0208735	+	0.555901i	−0.000980722	+	0.0261185i
$454$		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
$459$	−24.2038	+	10.5486i	−1.12973	+	0.492368i
$460$		0			0
$461$	−15.9430	+	9.20470i	−0.742540	+	0.428706i	−0.822992	−	0.568053i	$-0.807697\pi$
$461$	−15.9430	+	9.20470i	−0.742540	+	0.428706i	0.0804520	+	0.996758i	$0.474364\pi$
$462$		0			0
$463$	19.1970			0.892162			0.446081	−	0.894992i	$-0.352819\pi$
$463$	19.1970			0.892162			0.446081	+	0.894992i	$0.352819\pi$
$464$		0			0
$465$	0.897999	+	1.69964i	0.0416437	+	0.0788188i
$466$		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
$471$	1.20781	+	2.28602i	0.0556530	+	0.105334i
$472$		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
$477$	−1.32210	+	1.93808i	−0.0605350	+	0.0887384i
$478$		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	$-0.950214\pi$
$487$		−	6.87512i		−	0.311541i	0.987793	−	0.155771i	$-0.0497861\pi$
$488$		0			0
$489$	−27.4592	−	1.03106i	−1.24175	−	0.0466263i
$490$		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	0.848135	−	0.529780i	$-0.177725\pi$
$499$	−0.775921	−	1.34393i	−0.0347350	−	0.0601628i	−0.882870	+	0.469617i	$0.844392\pi$
$500$		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
$507$	25.4819	+	48.2295i	1.13169	+	2.14195i
$508$		0			0
$509$	12.5606	−	21.7555i	0.556737	−	0.964296i	−0.441029	−	0.897493i	$-0.645387\pi$
$509$	12.5606	−	21.7555i	0.556737	−	0.964296i	0.997766	−	0.0668036i	$-0.0212801\pi$
$510$		0			0
$511$	−6.47497	−	11.2150i	−0.286436	−	0.496122i
$512$		0			0
$513$	−16.9781	−	14.9915i	−0.749600	−	0.661891i
$514$		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
$519$	−1.96157	−	3.71266i	−0.0861036	−	0.162968i
$520$		0			0
$521$	−27.8194			−1.21879			−0.609395	−	0.792867i	$-0.708587\pi$
$521$	−27.8194			−1.21879			−0.609395	+	0.792867i	$0.708587\pi$
$522$		0			0
$523$	28.3513	+	16.3686i	1.23972	+	0.715750i	0.969036	−	0.246920i	$-0.0794184\pi$
$523$	28.3513	+	16.3686i	1.23972	+	0.715750i	0.270679	+	0.962670i	$0.412752\pi$
$524$		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
$537$	6.56167	+	0.246384i	0.283157	+	0.0106322i
$538$		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	0.845138	−	0.534548i	$-0.179518\pi$
$547$	18.8221	+	10.8669i	0.804774	+	0.464637i	−0.0403636	+	0.999185i	$0.512852\pi$
$548$		0			0
$549$	24.4032	−	35.7727i	1.04150	−	1.52674i
$550$		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
$555$	13.7647	+	26.0523i	0.584278	+	1.10586i
$556$		0			0
$557$	−34.5030	−	19.9203i	−1.46194	−	0.844051i	−0.462838	−	0.886443i	$-0.653169\pi$
$557$	−34.5030	−	19.9203i	−1.46194	−	0.844051i	−0.999101	+	0.0423915i	$0.986502\pi$
$558$		0			0
$559$		−	65.8121i		−	2.78355i
$560$		0			0
$561$	−21.4772	−	40.6499i	−0.906770	−	1.71624i
$562$		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
$567$	11.8043	+	1.78555i	0.495733	+	0.0749862i
$568$		0			0
$569$	27.5093			1.15325			0.576625	−	0.817009i	$-0.304369\pi$
$569$	27.5093			1.15325			0.576625	+	0.817009i	$0.304369\pi$
$570$		0			0
$571$	23.6597			0.990128			0.495064	−	0.868856i	$-0.335145\pi$
$571$	23.6597			0.990128			0.495064	+	0.868856i	$0.335145\pi$
$572$		0			0
$573$	0.233487	−	6.21822i	0.00975408	−	0.259770i
$574$		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
$579$	11.2071	−	5.92124i	0.465751	−	0.246078i
$580$		0			0
$581$			7.05149i			0.292545i
$582$		0			0
$583$	−3.53792	−	2.04262i	−0.146526	−	0.0845965i
$584$		0			0
$585$	−72.7682	−	5.47246i	−3.00860	−	0.226258i
$586$		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
$591$	−1.38525	+	36.8919i	−0.0569817	+	1.51753i
$592$		0			0
$593$	9.01249	+	5.20336i	0.370099	+	0.213677i	0.673502	−	0.739186i	$-0.264789\pi$
$593$	9.01249	+	5.20336i	0.370099	+	0.213677i	−0.303403	+	0.952862i	$0.598123\pi$
$594$		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
$603$	8.89534	+	6.06817i	0.362246	+	0.247115i
$604$		0			0
$605$	−51.4433	+	29.7008i	−2.09147	+	1.20751i
$606$		0			0
$607$		−	25.8372i		−	1.04870i	−0.851503	−	0.524350i	$-0.824308\pi$
$607$		−	25.8372i		−	1.04870i	0.851503	−	0.524350i	$-0.175692\pi$
$608$		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	0.640462	−	0.767990i	$-0.278743\pi$
$617$	7.34239	+	4.23913i	0.295594	+	0.170661i	−0.344868	+	0.938651i	$0.612076\pi$
$618$		0			0
$619$	−22.4134			−0.900872			−0.450436	−	0.892809i	$-0.648731\pi$
$619$	−22.4134			−0.900872			−0.450436	+	0.892809i	$0.648731\pi$
$620$		0			0
$621$	−10.3615	−	7.65342i	−0.415791	−	0.307121i
$622$		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
$627$	23.8141	−	31.4383i	0.951045	−	1.25553i
$628$		0			0
$629$	−11.8517	−	20.5278i	−0.472559	−	0.818496i
$630$		0			0
$631$	−8.49576	+	14.7151i	−0.338211	+	0.585798i	−0.984096	−	0.177636i	$-0.943155\pi$
$631$	−8.49576	+	14.7151i	−0.338211	+	0.585798i	0.645885	+	0.763434i	$0.276488\pi$
$632$		0			0
$633$	11.0784	−	5.85323i	0.440326	−	0.232645i
$634$		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	0.964079	−	0.265617i	$-0.0855757\pi$
$641$	6.38034	+	11.0511i	0.252008	+	0.436491i	−0.712070	+	0.702108i	$0.752242\pi$
$642$		0			0
$643$	18.3192	+	31.7298i	0.722438	+	1.25130i	0.960020	+	0.279932i	$0.0903118\pi$
$643$	18.3192	+	31.7298i	0.722438	+	1.25130i	−0.237582	+	0.971368i	$0.576355\pi$
$644$		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
$651$	−0.0262373	+	0.698749i	−0.00102832	+	0.0273861i
$652$		0			0
$653$			8.60841i			0.336873i	0.985713	+	0.168436i	$0.0538718\pi$
$653$			8.60841i			0.336873i	−0.985713	+	0.168436i	$0.946128\pi$
$654$		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
$663$	58.6630	+	2.20273i	2.27828	+	0.0855471i
$664$		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
$669$	26.1373	−	13.8096i	1.01053	−	0.533910i
$670$		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
$675$	25.6191	−	34.6840i	0.986078	−	1.33499i
$676$		0			0
$677$	31.8988			1.22597			0.612985	−	0.790095i	$-0.289969\pi$
$677$	31.8988			1.22597			0.612985	+	0.790095i	$0.289969\pi$
$678$		0			0
$679$	12.5440	−	7.24228i	0.481395	−	0.277933i
$680$		0			0
$681$	−18.6033	−	0.698533i	−0.712879	−	0.0267678i
$682$		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
$687$	29.3909	+	1.10360i	1.12133	+	0.0421048i
$688$		0			0
$689$	4.51750	−	2.60818i	0.172103	−	0.0993637i
$690$		0			0
$691$	−11.0315			−0.419658			−0.209829	−	0.977738i	$-0.567291\pi$
$691$	−11.0315			−0.419658			−0.209829	+	0.977738i	$0.567291\pi$
$692$		0			0
$693$	−1.55898	+	20.7301i	−0.0592209	+	0.787471i
$694$		0			0
$695$			31.9782i			1.21300i
$696$		0			0
$697$	19.0162	+	10.9790i	0.720290	+	0.415860i
$698$		0			0
$699$	24.9811	−	13.1987i	0.944871	−	0.499220i
$700$		0			0
$701$	39.0004	−	22.5169i	1.47302	−	0.850451i	0.473485	−	0.880802i	$-0.342996\pi$
$701$	39.0004	−	22.5169i	1.47302	−	0.850451i	0.999539	+	0.0303510i	$0.00966249\pi$
$702$		0			0
$703$	11.6611	−	16.6581i	0.439807	−	0.628271i
$704$		0			0
$705$	51.3733	+	1.92901i	1.93483	+	0.0726508i
$706$		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
$717$	0.0514924	−	1.37134i	0.00192302	−	0.0512137i
$718$		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	$-0.869246\pi$
$727$	−21.6844	−	37.5584i	−0.804228	−	1.39296i	0.112583	−	0.993642i	$-0.464088\pi$
$728$		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
$735$	−29.2659	+	15.4626i	−1.07949	+	0.570346i
$736$		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	$-0.991566\pi$
$739$	−14.2112	−	24.6146i	−0.522768	−	0.905461i	0.476881	−	0.878968i	$-0.341767\pi$
$740$		0			0
$741$	19.5609	+	46.4055i	0.718589	+	1.70475i
$742$		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
$747$	−1.19594	+	15.9026i	−0.0437570	+	0.581845i
$748$		0			0
$749$	−23.0583			−0.842530
$750$		0			0
$751$	16.5106	+	9.53241i	0.602481	+	0.347843i	0.770017	−	0.638023i	$-0.220248\pi$
$751$	16.5106	+	9.53241i	0.602481	+	0.347843i	−0.167536	+	0.985866i	$0.553581\pi$
$752$		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	$-0.846420\pi$
$761$		−	25.5990i		−	0.927964i	0.885845	−	0.463982i	$-0.153580\pi$
$762$		0			0
$763$	−0.734034	+	0.423795i	−0.0265738	+	0.0153424i
$764$		0			0
$765$	−31.3262	+	45.9212i	−1.13260	+	1.66028i
$766$		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	−0.537299	−	0.843392i	$-0.680555\pi$
$773$	12.8380	−	22.2360i	0.461749	−	0.799774i	0.999048	+	0.0436184i	$0.0138886\pi$
$774$		0			0
$775$	2.18717	+	1.26276i	0.0785654	+	0.0453598i
$776$		0			0
$777$	−0.402169	+	10.7105i	−0.0144277	+	0.384238i
$778$		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
$783$	−3.45476	+	4.67718i	−0.123463	+	0.167149i
$784$		0			0
$785$	4.71422	+	2.72176i	0.168258	+	0.0971437i
$786$		0			0
$787$			48.3999i			1.72527i	0.505827	+	0.862635i	$0.331187\pi$
$787$			48.3999i			1.72527i	−0.505827	+	0.862635i	$0.668813\pi$
$788$		0			0
$789$	4.47866	−	2.36629i	0.159444	−	0.0842421i
$790$		0			0
$791$	−0.238964			−0.00849659
$792$		0			0
$793$	−83.3832	+	48.1413i	−2.96102	+	1.70955i
$794$		0			0
$795$	−0.185342	+	4.93601i	−0.00657341	+	0.175062i
$796$		0			0
$797$	−28.2387			−1.00027			−0.500133	−	0.865949i	$-0.666716\pi$
$797$	−28.2387			−1.00027			−0.500133	+	0.865949i	$0.666716\pi$
$798$		0			0
$799$	−41.3568			−1.46310
$800$		0			0
$801$	−0.768382	+	1.12637i	−0.0271495	+	0.0397985i
$802$		0			0
$803$	44.1656	−	25.4990i	1.55857	−	0.899841i
$804$		0			0
$805$	−11.9921			−0.422667
$806$		0			0
$807$	−16.9586	−	32.0975i	−0.596972	−	1.12989i
$808$		0			0
$809$			21.6359i			0.760679i	0.924847	+	0.380340i	$0.124193\pi$
$809$			21.6359i			0.760679i	−0.924847	+	0.380340i	$0.875807\pi$
$810$		0			0
$811$	20.8163	+	12.0183i	0.730958	+	0.422019i	0.818772	−	0.574118i	$-0.194655\pi$
$811$	20.8163	+	12.0183i	0.730958	+	0.422019i	−0.0878147	+	0.996137i	$0.527988\pi$
$812$		0			0
$813$	−10.8638	−	20.5618i	−0.381010	−	0.721135i
$814$		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
$819$	−21.9282	−	14.9589i	−0.766235	−	0.522705i
$820$		0			0
$821$	−26.0781	−	15.0562i	−0.910134	−	0.525466i	−0.0296595	−	0.999560i	$-0.509442\pi$
$821$	−26.0781	−	15.0562i	−0.910134	−	0.525466i	−0.880474	+	0.474094i	$0.842776\pi$
$822$		0			0
$823$	25.7676	−	44.6309i	0.898204	−	1.55573i	0.0684145	−	0.997657i	$-0.478206\pi$
$823$	25.7676	−	44.6309i	0.898204	−	1.55573i	0.829789	−	0.558077i	$-0.188461\pi$
$824$		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
$831$	10.0645	+	0.377913i	0.349135	+	0.0131097i
$832$		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
$849$	−2.35510	−	4.45748i	−0.0808267	−	0.152980i
$850$		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
$855$	−47.0608	−	7.70133i	−1.60944	−	0.263380i
$856$		0			0
$857$	−26.7454	−	46.3243i	−0.913604	−	1.58241i	−0.808933	−	0.587902i	$-0.799954\pi$
$857$	−26.7454	−	46.3243i	−0.913604	−	1.58241i	−0.104671	−	0.994507i	$-0.533379\pi$
$858$		0			0
$859$	−2.59167	+	4.48890i	−0.0884266	+	0.153159i	−0.906846	−	0.421462i	$-0.861517\pi$
$859$	−2.59167	+	4.48890i	−0.0884266	+	0.153159i	0.818420	+	0.574621i	$0.194851\pi$
$860$		0			0
$861$	−4.63828	−	8.77886i	−0.158072	−	0.299183i
$862$		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
$879$	18.1144	+	0.680178i	0.610985	+	0.0229418i
$880$		0			0
$881$		−	22.3822i		−	0.754076i	−0.926198	−	0.377038i	$-0.876943\pi$
$881$		−	22.3822i		−	0.754076i	0.926198	−	0.377038i	$-0.123057\pi$
$882$		0			0
$883$	−2.38436	+	4.12984i	−0.0802402	+	0.138980i	−0.903353	−	0.428898i	$-0.858902\pi$
$883$	−2.38436	+	4.12984i	−0.0802402	+	0.138980i	0.823113	+	0.567878i	$0.192235\pi$
$884$		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
$891$	−7.03167	+	46.4863i	−0.235570	+	1.55735i
$892$		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
$897$	13.3799	+	25.3240i	0.446740	+	0.845543i
$898$		0			0
$899$	−0.294942	−	0.170285i	−0.00983688	−	0.00567932i
$900$		0			0
$901$		−	3.97362i		−	0.132380i
$902$		0			0
$903$	10.5898	+	20.0433i	0.352407	+	0.666999i
$904$		0			0
$905$	−67.6588			−2.24905
$906$		0			0
$907$	−28.4180	+	16.4072i	−0.943605	+	0.544791i	−0.891089	−	0.453829i	$-0.850058\pi$
$907$	−28.4180	+	16.4072i	−0.943605	+	0.544791i	−0.0525167	+	0.998620i	$0.516724\pi$
$908$		0			0
$909$	5.81803	+	3.96890i	0.192972	+	0.131640i
$910$		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
$915$	3.42101	−	91.1081i	0.113095	−	3.01194i
$916$		0			0
$917$	−9.07403	+	5.23889i	−0.299651	+	0.173004i
$918$		0			0
$919$	39.8042			1.31302			0.656510	−	0.754317i	$-0.272032\pi$
$919$	39.8042			1.31302			0.656510	+	0.754317i	$0.272032\pi$
$920$		0			0
$921$	−15.0235	+	7.93764i	−0.495042	+	0.261554i
$922$		0			0
$923$			28.1310i			0.925942i
$924$		0			0
$925$	33.5253	+	19.3558i	1.10230	+	0.636415i
$926$		0			0
$927$	0.223090	−	2.96647i	0.00732724	−	0.0974317i
$928$		0			0
$929$	9.94317	−	5.74069i	0.326225	−	0.188346i	−0.327939	−	0.944699i	$-0.606354\pi$
$929$	9.94317	−	5.74069i	0.326225	−	0.188346i	0.654164	+	0.756353i	$0.273021\pi$
$930$		0			0
$931$	18.7129	+	13.0995i	0.613290	+	0.429320i
$932$		0			0
$933$	0.612813	−	16.3204i	0.0200626	−	0.534305i
$934$		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	−0.714178	−	0.699964i	$-0.753199\pi$
$941$	7.64125	−	13.2350i	0.249098	−	0.431450i	0.963276	+	0.268514i	$0.0865326\pi$
$942$		0			0
$943$			10.7131i			0.348867i
$944$		0			0
$945$	23.0424	−	10.0425i	0.749569	−	0.326682i
$946$		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	$0.0652673\pi$
$953$	20.5555	+	35.6031i	0.665857	+	1.15330i	−0.313195	+	0.949689i	$0.601399\pi$
$954$		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
$963$	−52.0012	−	3.91070i	−1.67572	−	0.126020i
$964$		0			0
$965$	13.3433	−	23.1113i	0.429536	−	0.743978i
$966$		0			0
$967$	5.21929	+	9.04007i	0.167841	+	0.290709i	0.937661	−	0.347552i	$-0.112987\pi$
$967$	5.21929	+	9.04007i	0.167841	+	0.290709i	−0.769820	+	0.638262i	$0.779654\pi$
$968$		0			0
$969$	38.0643	+	4.77049i	1.22280	+	0.153250i
$970$		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
$975$	−84.7695	+	44.7878i	−2.71480	+	1.43436i
$976$		0			0
$977$	−29.5411			−0.945102			−0.472551	−	0.881303i	$-0.656667\pi$
$977$	−29.5411			−0.945102			−0.472551	+	0.881303i	$0.656667\pi$
$978$		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	−0.939879	−	0.341508i	$-0.889062\pi$
$991$	−35.0709	+	20.2482i	−1.11406	+	0.643205i	−0.174185	+	0.984713i	$0.555729\pi$
$992$		0			0
$993$	−0.866375	+	23.0732i	−0.0274936	+	0.732207i
$994$		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	456.2.bf.d.449.8	yes	16
3.2	odd	2		456.2.bf.c.449.5	yes	16
4.3	odd	2		912.2.bn.n.449.1		16
12.11	even	2		912.2.bn.o.449.4		16
19.8	odd	6		456.2.bf.c.65.5	✓	16
57.8	even	6	inner	456.2.bf.d.65.8	yes	16
76.27	even	6		912.2.bn.o.65.4		16
228.179	odd	6		912.2.bn.n.65.1		16

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

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 456 = 2^{3} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	456.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.73083 + 0.0649909i) q^{3} +(3.15813 - 1.82335i) q^{5} +1.32651 q^{7} +(2.99155 + 0.224976i) q^{9} +5.22390i q^{11} +(-5.77665 - 3.33515i) q^{13} +(5.58470 - 2.95066i) q^{15} +(-4.40043 + 2.54059i) q^{17} +(-3.57090 - 2.49973i) q^{19} +(2.29596 + 0.0862108i) q^{21} +(-2.14693 - 1.23953i) q^{23} +(4.14920 - 7.18663i) q^{25} +(5.16325 + 0.583820i) q^{27} +(-0.559525 + 0.969126i) q^{29} +0.304339i q^{31} +(-0.339506 + 9.04169i) q^{33} +(4.18928 - 2.41868i) q^{35} +4.66495i q^{37} +(-9.78165 - 6.14801i) q^{39} +(-2.16072 - 3.74248i) q^{41} +(4.93321 + 8.54458i) q^{43} +(9.85793 - 4.74414i) q^{45} +(7.04877 + 4.06961i) q^{47} -5.24038 q^{49} +(-7.78151 + 4.11134i) q^{51} +(-0.391014 + 0.677256i) q^{53} +(9.52499 + 16.4978i) q^{55} +(-6.01817 - 4.55869i) q^{57} +(-2.58526 - 4.47781i) q^{59} +(7.21726 - 12.5007i) q^{61} +(3.96831 + 0.298433i) q^{63} -24.3246 q^{65} +(3.10845 + 1.79467i) q^{67} +(-3.63541 - 2.28495i) q^{69} +(-2.10867 - 3.65233i) q^{71} +(-4.88122 - 8.45453i) q^{73} +(7.64863 - 12.1692i) q^{75} +6.92954i q^{77} +(4.31234 - 2.48973i) q^{79} +(8.89877 + 1.34606i) q^{81} +5.31583i q^{83} +(-9.26476 + 16.0470i) q^{85} +(-1.03143 + 1.64103i) q^{87} +(-0.227250 + 0.393608i) q^{89} +(-7.66276 - 4.42410i) q^{91} +(-0.0197792 + 0.526759i) q^{93} +(-15.8353 - 1.38348i) q^{95} +(9.45642 - 5.45967i) q^{97} +(-1.17525 + 15.6276i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + q^{3} + 3 q^{5} - 5 q^{9} - 3 q^{13} + 12 q^{15} - 3 q^{17} + 11 q^{19} - 12 q^{21} - 3 q^{23} + 11 q^{25} + 4 q^{27} + 5 q^{29} + 14 q^{33} + 24 q^{35} - 9 q^{39} + 6 q^{41} + 13 q^{43} + 33 q^{45}+ \cdots - 20 q^{99}+O(q^{100}) \) 16 * q + q^3 + 3 * q^5 - 5 * q^9 - 3 * q^13 + 12 * q^15 - 3 * q^17 + 11 * q^19 - 12 * q^21 - 3 * q^23 + 11 * q^25 + 4 * q^27 + 5 * q^29 + 14 * q^33 + 24 * q^35 - 9 * q^39 + 6 * q^41 + 13 * q^43 + 33 * q^45 + 27 * q^47 + 8 * q^49 - 18 * q^51 - 7 * q^53 - 12 * q^55 - 36 * q^57 - 10 * q^59 - q^61 - 26 * q^63 - 30 * q^65 - 24 * q^67 - 41 * q^69 + 27 * q^71 + 2 * q^73 + 21 * q^75 - 21 * q^79 - 13 * q^81 - 5 * q^85 - 23 * q^87 + 25 * q^89 - 78 * q^91 + 22 * q^93 + 13 * q^95 - 60 * q^97 - 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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