LMFDB - Embedded newform 720.2.bd.e.307.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [720,2,Mod(307,720)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(720, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0, 1]))

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

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

chi := DirichletCharacter("720.307");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 720 = 2^{4} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	720.bd (of order $4$, degree $2$, 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:	$5.74922894553$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(i)$
Coefficient field:	6.0.399424.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 3x^{4} - 6x^{3} + 6x^{2} - 8x + 8 $ x^6 - 2x^5 + 3x^4 - 6x^3 + 6x^2 - 8*x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 240)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			307.1
Root			$-0.671462 - 1.24464i$ of defining polynomial
Character	$\chi$	$=$	720.307
Dual form			720.2.bd.e.523.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.671462 + 1.24464i) q^{2} +(-1.09828 - 1.67146i) q^{4} +(-2.00000 + 1.00000i) q^{5} +(0.146365 + 0.146365i) q^{7} +(2.81783 - 0.244644i) q^{8} +(0.0982788 - 3.16075i) q^{10} +(-0.146365 - 0.146365i) q^{11} +(-0.280452 + 0.0838942i) q^{14} +(-1.58757 + 3.67146i) q^{16} +(-3.68585 - 3.68585i) q^{17} +(-2.83221 - 2.83221i) q^{19} +(3.86802 + 2.24464i) q^{20} +(0.280452 - 0.0838942i) q^{22} +(2.83221 - 2.83221i) q^{23} +(3.00000 - 4.00000i) q^{25} +(0.0838942 - 0.405394i) q^{28} +(-1.00000 + 1.00000i) q^{29} -0.292731i q^{31} +(-3.50367 - 4.44120i) q^{32} +(7.06247 - 2.11266i) q^{34} +(-0.439096 - 0.146365i) q^{35} +9.37169 q^{37} +(5.42682 - 1.62337i) q^{38} +(-5.39101 + 3.30712i) q^{40} -4.00000i q^{41} +9.66442 q^{43} +(-0.0838942 + 0.405394i) q^{44} +(1.62337 + 5.42682i) q^{46} +(7.12494 - 7.12494i) q^{47} -6.95715i q^{49} +(2.96419 + 6.41978i) q^{50} -11.9572i q^{53} +(0.439096 + 0.146365i) q^{55} +(0.448240 + 0.376625i) q^{56} +(-0.573183 - 1.91611i) q^{58} +(-9.51806 + 9.51806i) q^{59} +(1.68585 + 1.68585i) q^{61} +(0.364346 + 0.196558i) q^{62} +(7.88030 - 1.37873i) q^{64} -13.0790 q^{67} +(-2.11266 + 10.2088i) q^{68} +(0.477009 - 0.448240i) q^{70} +4.58546 q^{71} +(-6.37169 - 6.37169i) q^{73} +(-6.29273 + 11.6644i) q^{74} +(-1.62337 + 7.84449i) q^{76} -0.0428457i q^{77} -4.58546 q^{79} +(-0.496327 - 8.93049i) q^{80} +(4.97858 + 2.68585i) q^{82} -8.58546i q^{83} +(11.0575 + 3.68585i) q^{85} +(-6.48929 + 12.0288i) q^{86} +(-0.448240 - 0.376625i) q^{88} +3.37169 q^{89} +(-7.84449 - 1.62337i) q^{92} +(4.08389 + 13.6521i) q^{94} +(8.49663 + 2.83221i) q^{95} +(-3.58546 - 3.58546i) q^{97} +(8.65918 + 4.67146i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 2 q^{2} - 2 q^{4} - 12 q^{5} - 2 q^{7} + 8 q^{8} - 4 q^{10} + 2 q^{11} - 6 q^{14} + 10 q^{16} + 2 q^{17} + 10 q^{19} + 8 q^{20} + 6 q^{22} - 10 q^{23} + 18 q^{25} + 14 q^{28} - 6 q^{29} + 12 q^{32}+ \cdots + 56 q^{98}+O(q^{100}) $ 6 * q + 2 * q^2 - 2 * q^4 - 12 * q^5 - 2 * q^7 + 8 * q^8 - 4 * q^10 + 2 * q^11 - 6 * q^14 + 10 * q^16 + 2 * q^17 + 10 * q^19 + 8 * q^20 + 6 * q^22 - 10 * q^23 + 18 * q^25 + 14 * q^28 - 6 * q^29 + 12 * q^32 + 26 * q^34 + 6 * q^35 + 8 * q^37 + 34 * q^38 - 22 * q^40 + 4 * q^43 - 14 * q^44 + 2 * q^46 + 10 * q^47 + 6 * q^50 - 6 * q^55 + 34 * q^56 - 2 * q^58 - 6 * q^59 - 14 * q^61 + 20 * q^62 + 22 * q^64 - 36 * q^67 + 10 * q^68 - 2 * q^70 + 16 * q^71 + 10 * q^73 - 32 * q^74 - 2 * q^76 - 16 * q^79 - 36 * q^80 - 6 * q^85 - 24 * q^86 - 34 * q^88 - 28 * q^89 - 10 * q^92 + 38 * q^94 - 30 * q^95 - 10 * q^97 + 56 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/720\mathbb{Z}\right)^\times$.

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.671462	+	1.24464i	−0.474795	+	0.880096i
$2$	−0.671462	+	1.24464i	−0.474795	+	0.880096i
$3$		0			0
$3$		0			0
$4$	−1.09828	−	1.67146i	−0.549139	−	0.835731i
$5$	−2.00000	+	1.00000i	−0.894427	+	0.447214i
$5$	−2.00000	+	1.00000i	−0.894427	+	0.447214i
$6$		0			0
$7$	0.146365	+	0.146365i	0.0553210	+	0.0553210i	0.734226	−	0.678905i	$-0.237545\pi$
$7$	0.146365	+	0.146365i	0.0553210	+	0.0553210i	−0.678905	+	0.734226i	$0.737545\pi$
$8$	2.81783	−	0.244644i	0.996252	−	0.0864948i
$9$		0			0
$10$	0.0982788	−	3.16075i	0.0310785	−	0.999517i
$11$	−0.146365	−	0.146365i	−0.0441309	−	0.0441309i	0.684697	−	0.728828i	$-0.259935\pi$
$11$	−0.146365	−	0.146365i	−0.0441309	−	0.0441309i	−0.728828	+	0.684697i	$0.759935\pi$
$12$		0			0
$13$		0			0			−	1.00000i	$-0.5\pi$
$13$		0			0				1.00000i	$0.5\pi$
$14$	−0.280452	+	0.0838942i	−0.0749539	+	0.0224217i
$15$		0			0
$16$	−1.58757	+	3.67146i	−0.396892	+	0.917865i
$17$	−3.68585	−	3.68585i	−0.893949	−	0.893949i	0.100943	−	0.994892i	$-0.467814\pi$
$17$	−3.68585	−	3.68585i	−0.893949	−	0.893949i	−0.994892	+	0.100943i	$0.967814\pi$
$18$		0			0
$19$	−2.83221	−	2.83221i	−0.649754	−	0.649754i	0.303180	−	0.952933i	$-0.401952\pi$
$19$	−2.83221	−	2.83221i	−0.649754	−	0.649754i	−0.952933	+	0.303180i	$0.901952\pi$
$20$	3.86802	+	2.24464i	0.864915	+	0.501918i
$21$		0			0
$22$	0.280452	−	0.0838942i	0.0597925	−	0.0178863i
$23$	2.83221	−	2.83221i	0.590557	−	0.590557i	−0.347225	−	0.937782i	$-0.612876\pi$
$23$	2.83221	−	2.83221i	0.590557	−	0.590557i	0.937782	+	0.347225i	$0.112876\pi$
$24$		0			0
$25$	3.00000	−	4.00000i	0.600000	−	0.800000i
$26$		0			0
$27$		0			0
$28$	0.0838942	−	0.405394i	0.0158545	−	0.0766123i
$29$	−1.00000	+	1.00000i	−0.185695	+	0.185695i	−0.793832	−	0.608137i	$-0.791917\pi$
$29$	−1.00000	+	1.00000i	−0.185695	+	0.185695i	0.608137	+	0.793832i	$0.291917\pi$
$30$		0			0
$31$		−	0.292731i		−	0.0525760i	−0.999654	−	0.0262880i	$-0.991631\pi$
$31$		−	0.292731i		−	0.0525760i	0.999654	−	0.0262880i	$-0.00836870\pi$
$32$	−3.50367	−	4.44120i	−0.619368	−	0.785101i
$33$		0			0
$34$	7.06247	−	2.11266i	1.21120	−	0.362319i
$35$	−0.439096	−	0.146365i	−0.0742208	−	0.0247403i
$36$		0			0
$37$	9.37169			1.54070			0.770348	−	0.637623i	$-0.220082\pi$
$37$	9.37169			1.54070			0.770348	+	0.637623i	$0.220082\pi$
$38$	5.42682	−	1.62337i	0.880346	−	0.263346i
$39$		0			0
$40$	−5.39101	+	3.30712i	−0.852393	+	0.522901i
$41$		−	4.00000i		−	0.624695i	−0.949968	−	0.312348i	$-0.898885\pi$
$41$		−	4.00000i		−	0.624695i	0.949968	−	0.312348i	$-0.101115\pi$
$42$		0			0
$43$	9.66442			1.47381			0.736905	−	0.675996i	$-0.236286\pi$
$43$	9.66442			1.47381			0.736905	+	0.675996i	$0.236286\pi$
$44$	−0.0838942	+	0.405394i	−0.0126475	+	0.0611155i
$45$		0			0
$46$	1.62337	+	5.42682i	0.239354	+	0.800141i
$47$	7.12494	−	7.12494i	1.03928	−	1.03928i	0.0400834	−	0.999196i	$-0.487238\pi$
$47$	7.12494	−	7.12494i	1.03928	−	1.03928i	0.999196	−	0.0400834i	$-0.0127623\pi$
$48$		0			0
$49$		−	6.95715i		−	0.993879i
$50$	2.96419	+	6.41978i	0.419200	+	0.907894i
$51$		0			0
$52$		0			0
$53$		−	11.9572i		−	1.64244i	−0.570611	−	0.821221i	$-0.693293\pi$
$53$		−	11.9572i		−	1.64244i	0.570611	−	0.821221i	$-0.306707\pi$
$54$		0			0
$55$	0.439096	+	0.146365i	0.0592078	+	0.0197359i
$56$	0.448240	+	0.376625i	0.0598986	+	0.0503287i
$57$		0			0
$58$	−0.573183	−	1.91611i	−0.0752626	−	0.251597i
$59$	−9.51806	+	9.51806i	−1.23915	+	1.23915i	−0.278795	+	0.960351i	$0.589935\pi$
$59$	−9.51806	+	9.51806i	−1.23915	+	1.23915i	−0.960351	+	0.278795i	$0.910065\pi$
$60$		0			0
$61$	1.68585	+	1.68585i	0.215850	+	0.215850i	0.806747	−	0.590897i	$-0.201226\pi$
$61$	1.68585	+	1.68585i	0.215850	+	0.215850i	−0.590897	+	0.806747i	$0.701226\pi$
$62$	0.364346	+	0.196558i	0.0462720	+	0.0249628i
$63$		0			0
$64$	7.88030	−	1.37873i	0.985037	−	0.172341i
$65$		0			0
$66$		0			0
$67$	−13.0790			−1.59785			−0.798925	−	0.601431i	$-0.794597\pi$
$67$	−13.0790			−1.59785			−0.798925	+	0.601431i	$0.794597\pi$
$68$	−2.11266	+	10.2088i	−0.256198	+	1.23800i
$69$		0			0
$70$	0.477009	−	0.448240i	0.0570135	−	0.0535749i
$71$	4.58546			0.544194			0.272097	−	0.962270i	$-0.412283\pi$
$71$	4.58546			0.544194			0.272097	+	0.962270i	$0.412283\pi$
$72$		0			0
$73$	−6.37169	−	6.37169i	−0.745750	−	0.745750i	0.227928	−	0.973678i	$-0.426805\pi$
$73$	−6.37169	−	6.37169i	−0.745750	−	0.745750i	−0.973678	+	0.227928i	$0.926805\pi$
$74$	−6.29273	+	11.6644i	−0.731515	+	1.35596i
$75$		0			0
$76$	−1.62337	+	7.84449i	−0.186214	+	0.899825i
$77$		−	0.0428457i		−	0.00488272i
$78$		0			0
$79$	−4.58546			−0.515905			−0.257952	−	0.966158i	$-0.583048\pi$
$79$	−4.58546			−0.515905			−0.257952	+	0.966158i	$0.583048\pi$
$80$	−0.496327	−	8.93049i	−0.0554910	−	0.998459i
$81$		0			0
$82$	4.97858	+	2.68585i	0.549792	+	0.296602i
$83$		−	8.58546i		−	0.942377i	−0.882033	−	0.471188i	$-0.843825\pi$
$83$		−	8.58546i		−	0.942377i	0.882033	−	0.471188i	$-0.156175\pi$
$84$		0			0
$85$	11.0575	+	3.68585i	1.19936	+	0.399786i
$86$	−6.48929	+	12.0288i	−0.699758	+	1.29710i
$87$		0			0
$88$	−0.448240	−	0.376625i	−0.0477826	−	0.0401484i
$89$	3.37169			0.357399			0.178699	−	0.983904i	$-0.442811\pi$
$89$	3.37169			0.357399			0.178699	+	0.983904i	$0.442811\pi$
$90$		0			0
$91$		0			0
$92$	−7.84449	−	1.62337i	−0.817845	−	0.169249i
$93$		0			0
$94$	4.08389	+	13.6521i	0.421222	+	1.40811i
$95$	8.49663	+	2.83221i	0.871736	+	0.290579i
$96$		0			0
$97$	−3.58546	−	3.58546i	−0.364049	−	0.364049i	0.501253	−	0.865301i	$-0.332873\pi$
$97$	−3.58546	−	3.58546i	−0.364049	−	0.364049i	−0.865301	+	0.501253i	$0.832873\pi$
$98$	8.65918	+	4.67146i	0.874710	+	0.471889i
$99$		0			0
$100$	−9.98068	−	0.621269i	−0.998068	−	0.0621269i
$101$	10.3717	−	10.3717i	1.03202	−	1.03202i	0.0325519	−	0.999470i	$-0.489637\pi$
$101$	10.3717	−	10.3717i	1.03202	−	1.03202i	0.999470	−	0.0325519i	$-0.0103634\pi$
$102$		0			0
$103$	−5.51806	+	5.51806i	−0.543710	+	0.543710i	−0.924615	−	0.380904i	$-0.875613\pi$
$103$	−5.51806	+	5.51806i	−0.543710	+	0.543710i	0.380904	+	0.924615i	$0.375613\pi$
$104$		0			0
$105$		0			0
$106$	14.8824	+	8.02877i	1.44551	+	0.779823i
$107$			11.3288i			1.09520i	0.836740	+	0.547600i	$0.184459\pi$
$107$			11.3288i			1.09520i	−0.836740	+	0.547600i	$0.815541\pi$
$108$		0			0
$109$	−10.2713	+	10.2713i	−0.983813	+	0.983813i	−0.999871	−	0.0160582i	$-0.994888\pi$
$109$	−10.2713	+	10.2713i	−0.983813	+	0.983813i	0.0160582	+	0.999871i	$0.494888\pi$
$110$	−0.477009	+	0.448240i	−0.0454811	+	0.0427380i
$111$		0			0
$112$	−0.769740	+	0.305010i	−0.0727336	+	0.0288208i
$113$	1.68585	−	1.68585i	0.158591	−	0.158591i	−0.623351	−	0.781942i	$-0.714229\pi$
$113$	1.68585	−	1.68585i	0.158591	−	0.158591i	0.781942	+	0.623351i	$0.214229\pi$
$114$		0			0
$115$	−2.83221	+	8.49663i	−0.264105	+	0.792315i
$116$	2.76974	+	0.573183i	0.257164	+	0.0532187i
$117$		0			0
$118$	−5.45559	−	18.2376i	−0.502227	−	1.67891i
$119$		−	1.07896i		−	0.0989082i
$120$		0			0
$121$		−	10.9572i		−	0.996105i
$122$	−3.23026	+	0.966298i	−0.292454	+	0.0874845i
$123$		0			0
$124$	−0.489289	+	0.321500i	−0.0439394	+	0.0288716i
$125$	−2.00000	+	11.0000i	−0.178885	+	0.983870i
$126$		0			0
$127$	−3.85363	+	3.85363i	−0.341955	+	0.341955i	−0.857102	−	0.515147i	$-0.827737\pi$
$127$	−3.85363	+	3.85363i	−0.341955	+	0.341955i	0.515147	+	0.857102i	$0.327737\pi$
$128$	−3.57529	+	10.7339i	−0.316014	+	0.948755i
$129$		0			0
$130$		0			0
$131$	−13.2253	+	13.2253i	−1.15550	+	1.15550i	−0.170070	+	0.985432i	$0.554399\pi$
$131$	−13.2253	+	13.2253i	−1.15550	+	1.15550i	−0.985432	+	0.170070i	$0.945601\pi$
$132$		0			0
$133$		−	0.829076i		−	0.0718900i
$134$	8.78202	−	16.2787i	0.758651	−	1.40626i
$135$		0			0
$136$	−11.2878	−	9.48436i	−0.967921	−	0.813277i
$137$	12.2713	−	12.2713i	1.04841	−	1.04841i	0.0496415	−	0.998767i	$-0.484192\pi$
$137$	12.2713	−	12.2713i	1.04841	−	1.04841i	0.998767	−	0.0496415i	$-0.0158079\pi$
$138$		0			0
$139$	−6.53948	+	6.53948i	−0.554672	+	0.554672i	−0.927786	−	0.373114i	$-0.878290\pi$
$139$	−6.53948	+	6.53948i	−0.554672	+	0.554672i	0.373114	+	0.927786i	$0.378290\pi$
$140$	0.237606	+	0.894683i	0.0200814	+	0.0756145i
$141$		0			0
$142$	−3.07896	+	5.70727i	−0.258381	+	0.478943i
$143$		0			0
$144$		0			0
$145$	1.00000	−	3.00000i	0.0830455	−	0.249136i
$146$	12.2088	−	3.65214i	1.01041	−	0.302254i
$147$		0			0
$148$	−10.2927	−	15.6644i	−0.846057	−	1.28761i
$149$	8.37169	+	8.37169i	0.685836	+	0.685836i	0.961309	−	0.275473i	$-0.0888345\pi$
$149$	8.37169	+	8.37169i	0.685836	+	0.685836i	−0.275473	+	0.961309i	$0.588834\pi$
$150$		0			0
$151$		0			0			−	1.00000i	$-0.5\pi$
$151$		0			0				1.00000i	$0.5\pi$
$152$	−8.67357	−	7.28780i	−0.703519	−	0.591118i
$153$		0			0
$154$	0.0533277	+	0.0287692i	0.00429727	+	0.00231829i
$155$	0.292731	+	0.585462i	0.0235127	+	0.0470254i
$156$		0			0
$157$		−	24.7434i		−	1.97474i	−0.158440	−	0.987369i	$-0.550647\pi$
$157$		−	24.7434i		−	1.97474i	0.158440	−	0.987369i	$-0.449353\pi$
$158$	3.07896	−	5.70727i	0.244949	−	0.454046i
$159$		0			0
$160$	11.4485	+	5.37873i	0.905087	+	0.425226i
$161$	0.829076			0.0653403
$162$		0			0
$163$			7.41454i			0.580751i	0.956913	+	0.290376i	$0.0937803\pi$
$163$			7.41454i			0.580751i	−0.956913	+	0.290376i	$0.906220\pi$
$164$	−6.68585	+	4.39312i	−0.522077	+	0.343045i
$165$		0			0
$166$	10.6858	+	5.76481i	0.829383	+	0.447436i
$167$	−12.2039	−	12.2039i	−0.944366	−	0.944366i	0.0541655	−	0.998532i	$-0.482750\pi$
$167$	−12.2039	−	12.2039i	−0.944366	−	0.944366i	−0.998532	+	0.0541655i	$0.982750\pi$
$168$		0			0
$169$	−13.0000			−1.00000
$170$	−12.0123	+	11.2878i	−0.921300	+	0.865735i
$171$		0			0
$172$	−10.6142	−	16.1537i	−0.809328	−	1.23171i
$173$	−14.7434			−1.12092			−0.560459	−	0.828182i	$-0.689375\pi$
$173$	−14.7434			−1.12092			−0.560459	+	0.828182i	$0.689375\pi$
$174$		0			0
$175$	1.02456	−	0.146365i	0.0774493	−	0.0110642i
$176$	0.769740	−	0.305010i	0.0580214	−	0.0229910i
$177$		0			0
$178$	−2.26396	+	4.19656i	−0.169691	+	0.314545i
$179$	−9.22533	−	9.22533i	−0.689533	−	0.689533i	0.272595	−	0.962129i	$-0.412118\pi$
$179$	−9.22533	−	9.22533i	−0.689533	−	0.689533i	−0.962129	+	0.272595i	$0.912118\pi$
$180$		0			0
$181$	−3.68585	+	3.68585i	−0.273967	+	0.273967i	−0.830695	−	0.556728i	$-0.812057\pi$
$181$	−3.68585	+	3.68585i	−0.273967	+	0.273967i	0.556728	+	0.830695i	$0.312057\pi$
$182$		0			0
$183$		0			0
$184$	7.28780	−	8.67357i	0.537264	−	0.639424i
$185$	−18.7434	+	9.37169i	−1.37804	+	0.689021i
$186$		0			0
$187$			1.07896i			0.0789015i
$188$	−19.7342	−	4.08389i	−1.43927	−	0.297849i
$189$		0			0
$190$	−9.23026	+	8.67357i	−0.669633	+	0.629247i
$191$			6.33558i			0.458426i	0.973376	+	0.229213i	$0.0736153\pi$
$191$			6.33558i			0.458426i	−0.973376	+	0.229213i	$0.926385\pi$
$192$		0			0
$193$	0.414538	−	0.414538i	0.0298391	−	0.0298391i	−0.692030	−	0.721869i	$-0.743283\pi$
$193$	0.414538	−	0.414538i	0.0298391	−	0.0298391i	0.721869	+	0.692030i	$0.243283\pi$
$194$	6.87012	−	2.05512i	0.493246	−	0.147549i
$195$		0			0
$196$	−11.6286	+	7.64090i	−0.830615	+	0.545778i
$197$	8.78623			0.625993			0.312996	−	0.949754i	$-0.398667\pi$
$197$	8.78623			0.625993			0.312996	+	0.949754i	$0.398667\pi$
$198$		0			0
$199$			11.7073i			0.829906i	0.909843	+	0.414953i	$0.136202\pi$
$199$			11.7073i			0.829906i	−0.909843	+	0.414953i	$0.863798\pi$
$200$	7.47490	−	12.0052i	0.528556	−	0.848899i
$201$		0			0
$202$	5.94488	+	19.8733i	0.418280	+	1.39828i
$203$	−0.292731			−0.0205457
$204$		0			0
$205$	4.00000	+	8.00000i	0.279372	+	0.558744i
$206$	−3.16286	−	10.5732i	−0.220367	−	0.736669i
$207$		0			0
$208$		0			0
$209$			0.829076i			0.0573484i
$210$		0			0
$211$	12.4966	−	12.4966i	0.860304	−	0.860304i	−0.131069	−	0.991373i	$-0.541841\pi$
$211$	12.4966	−	12.4966i	0.860304	−	0.860304i	0.991373	+	0.131069i	$0.0418411\pi$
$212$	−19.9859	+	13.1323i	−1.37264	+	0.901929i
$213$		0			0
$214$	−14.1004	−	7.60688i	−0.963882	−	0.519996i
$215$	−19.3288	+	9.66442i	−1.31822	+	0.659108i
$216$		0			0
$217$	0.0428457	−	0.0428457i	0.00290856	−	0.00290856i
$218$	−5.88734	−	19.6809i	−0.398741	−	1.33296i
$219$		0			0
$220$	−0.237606	−	0.894683i	−0.0160194	−	0.0603195i
$221$		0			0
$222$		0			0
$223$	17.2253	+	17.2253i	1.15349	+	1.15349i	0.985847	+	0.167646i	$0.0536165\pi$
$223$	17.2253	+	17.2253i	1.15349	+	1.15349i	0.167646	+	0.985847i	$0.446383\pi$
$224$	0.137222	−	1.16286i	0.00916852	−	0.0776966i
$225$		0			0
$226$	0.966298	+	3.23026i	0.0642772	+	0.214874i
$227$	−8.29273			−0.550408			−0.275204	−	0.961386i	$-0.588745\pi$
$227$	−8.29273			−0.550408			−0.275204	+	0.961386i	$0.588745\pi$
$228$		0			0
$229$	−10.2713	−	10.2713i	−0.678747	−	0.678747i	0.280970	−	0.959717i	$-0.409344\pi$
$229$	−10.2713	−	10.2713i	−0.678747	−	0.678747i	−0.959717	+	0.280970i	$0.909344\pi$
$230$	−8.67357	−	9.23026i	−0.571918	−	0.608625i
$231$		0			0
$232$	−2.57318	+	3.06247i	−0.168938	+	0.201061i
$233$	8.27131	+	8.27131i	0.541871	+	0.541871i	0.924077	−	0.382206i	$-0.124835\pi$
$233$	8.27131	+	8.27131i	0.541871	+	0.541871i	−0.382206	+	0.924077i	$0.624835\pi$
$234$		0			0
$235$	−7.12494	+	21.3748i	−0.464780	+	1.39434i
$236$	26.3625	+	5.45559i	1.71606	+	0.355128i
$237$		0			0
$238$	1.34292	+	0.724481i	0.0870488	+	0.0469611i
$239$	−3.41454			−0.220868			−0.110434	−	0.993883i	$-0.535224\pi$
$239$	−3.41454			−0.220868			−0.110434	+	0.993883i	$0.535224\pi$
$240$		0			0
$241$	3.17092			0.204257			0.102129	−	0.994771i	$-0.467435\pi$
$241$	3.17092			0.204257			0.102129	+	0.994771i	$0.467435\pi$
$242$	13.6378	+	7.35731i	0.876668	+	0.472946i
$243$		0			0
$244$	0.966298	−	4.66936i	0.0618609	−	0.298925i
$245$	6.95715	+	13.9143i	0.444476	+	0.888953i
$246$		0			0
$247$		0			0
$248$	−0.0716150	−	0.824865i	−0.00454755	−	0.0523790i
$249$		0			0
$250$	−12.3482	−	9.87537i	−0.780966	−	0.624573i
$251$	3.85363	+	3.85363i	0.243239	+	0.243239i	0.818189	−	0.574950i	$-0.194978\pi$
$251$	3.85363	+	3.85363i	0.243239	+	0.243239i	−0.574950	+	0.818189i	$0.694978\pi$
$252$		0			0
$253$	−0.829076			−0.0521236
$254$	−2.20884	−	7.38397i	−0.138595	−	0.463312i
$255$		0			0
$256$	−10.9593	−	11.6574i	−0.684954	−	0.728587i
$257$	−21.6430	−	21.6430i	−1.35005	−	1.35005i	−0.885595	−	0.464458i	$-0.846249\pi$
$257$	−21.6430	−	21.6430i	−1.35005	−	1.35005i	−0.464458	−	0.885595i	$-0.653751\pi$
$258$		0			0
$259$	1.37169	+	1.37169i	0.0852328	+	0.0852328i
$260$		0			0
$261$		0			0
$262$	−7.58053	−	25.3411i	−0.468327	−	1.56558i
$263$	14.2467	−	14.2467i	0.878492	−	0.878492i	−0.114886	−	0.993379i	$-0.536650\pi$
$263$	14.2467	−	14.2467i	0.878492	−	0.878492i	0.993379	+	0.114886i	$0.0366504\pi$
$264$		0			0
$265$	11.9572	+	23.9143i	0.734522	+	1.46904i
$266$	1.03190	+	0.556693i	0.0632701	+	0.0341330i
$267$		0			0
$268$	14.3643	+	21.8610i	0.877442	+	1.33537i
$269$	11.7862	−	11.7862i	0.718619	−	0.718619i	−0.249703	−	0.968322i	$-0.580333\pi$
$269$	11.7862	−	11.7862i	0.718619	−	0.718619i	0.968322	+	0.249703i	$0.0803331\pi$
$270$		0			0
$271$		−	11.7073i		−	0.711166i	−0.934645	−	0.355583i	$-0.884282\pi$
$271$		−	11.7073i		−	0.711166i	0.934645	−	0.355583i	$-0.115718\pi$
$272$	19.3840	−	7.68091i	1.17533	−	0.465724i
$273$		0			0
$274$	7.03370	+	23.5131i	0.424921	+	1.42048i
$275$	−1.02456	+	0.146365i	−0.0617832	+	0.00882617i
$276$		0			0
$277$	18.5426			1.11412			0.557059	−	0.830473i	$-0.311930\pi$
$277$	18.5426			1.11412			0.557059	+	0.830473i	$0.311930\pi$
$278$	−3.74832	−	12.5303i	−0.224809	−	0.751520i
$279$		0			0
$280$	−1.27311	−	0.305010i	−0.0760826	−	0.0182278i
$281$			2.62831i			0.156792i	0.996922	+	0.0783958i	$0.0249798\pi$
$281$			2.62831i			0.156792i	−0.996922	+	0.0783958i	$0.975020\pi$
$282$		0			0
$283$	22.2499			1.32262			0.661309	−	0.750113i	$-0.270001\pi$
$283$	22.2499			1.32262			0.661309	+	0.750113i	$0.270001\pi$
$284$	−5.03612	−	7.66442i	−0.298838	−	0.454800i
$285$		0			0
$286$		0			0
$287$	0.585462	−	0.585462i	0.0345587	−	0.0345587i
$288$		0			0
$289$			10.1709i			0.598290i
$290$	3.06247	+	3.25903i	0.179835	+	0.191377i
$291$		0			0
$292$	−3.65214	+	17.6479i	−0.213726	+	1.03277i
$293$			21.9143i			1.28025i	0.768272	+	0.640124i	$0.221117\pi$
$293$			21.9143i			1.28025i	−0.768272	+	0.640124i	$0.778883\pi$
$294$		0			0
$295$	9.51806	−	28.5542i	0.554163	−	1.66249i
$296$	26.4078	−	2.29273i	1.53492	−	0.133262i
$297$		0			0
$298$	−16.0410	+	4.79851i	−0.929233	+	0.277970i
$299$		0			0
$300$		0			0
$301$	1.41454	+	1.41454i	0.0815326	+	0.0815326i
$302$		0			0
$303$		0			0
$304$	14.8947	−	5.90203i	0.854269	−	0.338505i
$305$	−5.05754	−	1.68585i	−0.289594	−	0.0965313i
$306$		0			0
$307$	6.33558			0.361590			0.180795	−	0.983521i	$-0.442133\pi$
$307$	6.33558			0.361590			0.180795	+	0.983521i	$0.442133\pi$
$308$	−0.0716150	+	0.0470565i	−0.00408064	+	0.00268130i
$309$		0			0
$310$	−0.925249	−	0.0287692i	−0.0525506	−	0.00163398i
$311$	7.32885			0.415581			0.207790	−	0.978173i	$-0.433373\pi$
$311$	7.32885			0.415581			0.207790	+	0.978173i	$0.433373\pi$
$312$		0			0
$313$	3.00000	+	3.00000i	0.169570	+	0.169570i	0.786790	−	0.617220i	$-0.211741\pi$
$313$	3.00000	+	3.00000i	0.169570	+	0.169570i	−0.617220	+	0.786790i	$0.711741\pi$
$314$	30.7967	+	16.6142i	1.73796	+	0.937595i
$315$		0			0
$316$	5.03612	+	7.66442i	0.283304	+	0.431157i
$317$			19.9572i			1.12091i	0.828186	+	0.560453i	$0.189373\pi$
$317$			19.9572i			1.12091i	−0.828186	+	0.560453i	$0.810627\pi$
$318$		0			0
$319$	0.292731			0.0163898
$320$	−14.3819	+	10.6378i	−0.803971	+	0.594669i
$321$		0			0
$322$	−0.556693	+	1.03190i	−0.0310233	+	0.0575058i
$323$			20.8782i			1.16169i
$324$		0			0
$325$		0			0
$326$	−9.22846	−	4.97858i	−0.511117	−	0.275738i
$327$		0			0
$328$	−0.978577	−	11.2713i	−0.0540329	−	0.622354i
$329$	2.08569			0.114988
$330$		0			0
$331$	−12.4966	−	12.4966i	−0.686877	−	0.686877i	0.274663	−	0.961540i	$-0.411434\pi$
$331$	−12.4966	−	12.4966i	−0.686877	−	0.686877i	−0.961540	+	0.274663i	$0.911434\pi$
$332$	−14.3503	+	9.42923i	−0.787573	+	0.517496i
$333$		0			0
$334$	23.3840	−	6.99507i	1.27951	−	0.382753i
$335$	26.1579	−	13.0790i	1.42916	−	0.714580i
$336$		0			0
$337$	−15.5855	−	15.5855i	−0.848994	−	0.848994i	0.141013	−	0.990008i	$-0.454964\pi$
$337$	−15.5855	−	15.5855i	−0.848994	−	0.848994i	−0.990008	+	0.141013i	$0.954964\pi$
$338$	8.72900	−	16.1804i	0.474795	−	0.880096i
$339$		0			0
$340$	−5.98351	−	22.5303i	−0.324501	−	1.22188i
$341$	−0.0428457	+	0.0428457i	−0.00232023	+	0.00232023i
$342$		0			0
$343$	2.04285	−	2.04285i	0.110303	−	0.110303i
$344$	27.2327	−	2.36435i	1.46829	−	0.127477i
$345$		0			0
$346$	9.89962	−	18.3503i	0.532207	−	0.986517i
$347$			14.7434i			0.791466i	0.918366	+	0.395733i	$0.129509\pi$
$347$			14.7434i			0.791466i	−0.918366	+	0.395733i	$0.870491\pi$
$348$		0			0
$349$	−3.64300	+	3.64300i	−0.195005	+	0.195005i	−0.797855	−	0.602850i	$-0.794032\pi$
$349$	−3.64300	+	3.64300i	−0.195005	+	0.195005i	0.602850	+	0.797855i	$0.294032\pi$
$350$	−0.505779	+	1.37349i	−0.0270350	+	0.0734161i
$351$		0			0
$352$	−0.137222	+	1.16286i	−0.00731395	+	0.0619804i
$353$	−3.68585	+	3.68585i	−0.196178	+	0.196178i	−0.798359	−	0.602181i	$-0.794298\pi$
$353$	−3.68585	+	3.68585i	−0.196178	+	0.196178i	0.602181	+	0.798359i	$0.294298\pi$
$354$		0			0
$355$	−9.17092	+	4.58546i	−0.486742	+	0.243371i
$356$	−3.70306	−	5.63565i	−0.196262	−	0.298689i
$357$		0			0
$358$	17.6767	−	5.28780i	0.934243	−	0.279469i
$359$			32.9933i			1.74132i	0.491887	+	0.870659i	$0.336307\pi$
$359$			32.9933i			1.74132i	−0.491887	+	0.870659i	$0.663693\pi$
$360$		0			0
$361$		−	2.95715i		−	0.155640i
$362$	−2.11266	−	7.06247i	−0.111039	−	0.371195i
$363$		0			0
$364$		0			0
$365$	19.1151	+	6.37169i	1.00053	+	0.333510i
$366$		0			0
$367$	18.1035	−	18.1035i	0.944996	−	0.944996i	−0.0535682	−	0.998564i	$-0.517059\pi$
$367$	18.1035	−	18.1035i	0.944996	−	0.944996i	0.998564	+	0.0535682i	$0.0170594\pi$
$368$	5.90203	+	14.8947i	0.307665	+	0.776439i
$369$		0			0
$370$	0.921039	−	29.6216i	0.0478825	−	1.53995i
$371$	1.75011	−	1.75011i	0.0908614	−	0.0908614i
$372$		0			0
$373$		−	13.9143i		−	0.720456i	−0.932864	−	0.360228i	$-0.882699\pi$
$373$		−	13.9143i		−	0.720456i	0.932864	−	0.360228i	$-0.117301\pi$
$374$	−1.34292	−	0.724481i	−0.0694409	−	0.0374620i
$375$		0			0
$376$	18.3338	−	21.8199i	0.945492	−	1.12528i
$377$		0			0
$378$		0			0
$379$	−7.71040	+	7.71040i	−0.396057	+	0.396057i	−0.876840	−	0.480783i	$-0.840353\pi$
$379$	−7.71040	+	7.71040i	−0.396057	+	0.396057i	0.480783	+	0.876840i	$0.340353\pi$
$380$	−4.59774	−	17.3124i	−0.235859	−	0.888105i
$381$		0			0
$382$	−7.88554	−	4.25410i	−0.403459	−	0.217658i
$383$	14.8322	+	14.8322i	0.757891	+	0.757891i	0.975938	−	0.218048i	$-0.0699688\pi$
$383$	14.8322	+	14.8322i	0.757891	+	0.757891i	−0.218048	+	0.975938i	$0.569969\pi$
$384$		0			0
$385$	0.0428457	+	0.0856914i	0.00218362	+	0.00436724i
$386$	0.237606	+	0.794299i	0.0120938	+	0.0404287i
$387$		0			0
$388$	−2.05512	+	9.93080i	−0.104333	+	0.504160i
$389$	16.3717	+	16.3717i	0.830078	+	0.830078i	0.987527	−	0.157449i	$-0.0503271\pi$
$389$	16.3717	+	16.3717i	0.830078	+	0.830078i	−0.157449	+	0.987527i	$0.550327\pi$
$390$		0			0
$391$	−20.8782			−1.05586
$392$	−1.70203	−	19.6041i	−0.0859654	−	0.990154i
$393$		0			0
$394$	−5.89962	+	10.9357i	−0.297218	+	0.550934i
$395$	9.17092	−	4.58546i	0.461439	−	0.230720i
$396$		0			0
$397$			0.628308i			0.0315339i	0.999876	+	0.0157669i	$0.00501898\pi$
$397$			0.628308i			0.0315339i	−0.999876	+	0.0157669i	$0.994981\pi$
$398$	−14.5714	−	7.86098i	−0.730398	−	0.394035i
$399$		0			0
$400$	9.92314	+	17.3647i	0.496157	+	0.868233i
$401$	8.54262			0.426598			0.213299	−	0.976987i	$-0.431579\pi$
$401$	8.54262			0.426598			0.213299	+	0.976987i	$0.431579\pi$
$402$		0			0
$403$		0			0
$404$	−28.7269	−	5.94488i	−1.42922	−	0.295769i
$405$		0			0
$406$	0.196558	−	0.364346i	0.00975499	−	0.0180822i
$407$	−1.37169	−	1.37169i	−0.0679923	−	0.0679923i
$408$		0			0
$409$	38.7005			1.91362			0.956809	−	0.290716i	$-0.0938936\pi$
$409$	38.7005			1.91362			0.956809	+	0.290716i	$0.0938936\pi$
$410$	−12.6430	−	0.393115i	−0.624393	−	0.0194146i
$411$		0			0
$412$	15.2836	+	3.16286i	0.752968	+	0.155823i
$413$	−2.78623			−0.137101
$414$		0			0
$415$	8.58546	+	17.1709i	0.421444	+	0.842888i
$416$		0			0
$417$		0			0
$418$	−1.03190	−	0.556693i	−0.0504721	−	0.0272287i
$419$	−9.81079	−	9.81079i	−0.479288	−	0.479288i	0.425616	−	0.904904i	$-0.360058\pi$
$419$	−9.81079	−	9.81079i	−0.479288	−	0.479288i	−0.904904	+	0.425616i	$0.860058\pi$
$420$		0			0
$421$	−20.2713	+	20.2713i	−0.987963	+	0.987963i	−0.999928	−	0.0119653i	$-0.996191\pi$
$421$	−20.2713	+	20.2713i	−0.987963	+	0.987963i	0.0119653	+	0.999928i	$0.496191\pi$
$422$	7.16286	+	23.9449i	0.348682	+	1.16562i
$423$		0			0
$424$	−2.92525	−	33.6932i	−0.142063	−	1.63629i
$425$	−25.8009	+	3.68585i	−1.25153	+	0.178790i
$426$		0			0
$427$			0.493499i			0.0238821i
$428$	18.9357	−	12.4422i	0.915293	−	0.601418i
$429$		0			0
$430$	0.949808	−	30.5468i	0.0458038	−	1.47310i
$431$		−	29.0790i		−	1.40068i	−0.713807	−	0.700342i	$-0.753031\pi$
$431$		−	29.0790i		−	1.40068i	0.713807	−	0.700342i	$-0.246969\pi$
$432$		0			0
$433$	−8.95715	+	8.95715i	−0.430453	+	0.430453i	−0.888783	−	0.458329i	$-0.848448\pi$
$433$	−8.95715	+	8.95715i	−0.430453	+	0.430453i	0.458329	+	0.888783i	$0.348448\pi$
$434$	0.0245584	+	0.0820969i	0.00117884	+	0.00394078i
$435$		0			0
$436$	28.4489	+	5.88734i	1.36245	+	0.281952i
$437$	−16.0428			−0.767433
$438$		0			0
$439$		−	7.03612i		−	0.335815i	−0.985803	−	0.167908i	$-0.946299\pi$
$439$		−	7.03612i		−	0.335815i	0.985803	−	0.167908i	$-0.0537011\pi$
$440$	1.27311	+	0.305010i	0.0606929	+	0.0145408i
$441$		0			0
$442$		0			0
$443$	33.8652			1.60898			0.804492	−	0.593964i	$-0.202438\pi$
$443$	33.8652			1.60898			0.804492	+	0.593964i	$0.202438\pi$
$444$		0			0
$445$	−6.74338	+	3.37169i	−0.319667	+	0.159834i
$446$	−33.0055	+	9.87326i	−1.56286	+	0.467512i
$447$		0			0
$448$	1.35520	+	0.951605i	0.0640273	+	0.0449591i
$449$		−	32.1151i		−	1.51560i	−0.652484	−	0.757802i	$-0.726273\pi$
$449$		−	32.1151i		−	1.51560i	0.652484	−	0.757802i	$-0.273727\pi$
$450$		0			0
$451$	−0.585462	+	0.585462i	−0.0275683	+	0.0275683i
$452$	−4.66936	−	0.966298i	−0.219628	−	0.0454508i
$453$		0			0
$454$	5.56825	−	10.3215i	0.261331	−	0.484412i
$455$		0			0
$456$		0			0
$457$	−4.41454	+	4.41454i	−0.206503	+	0.206503i	−0.802779	−	0.596276i	$-0.796646\pi$
$457$	−4.41454	+	4.41454i	−0.206503	+	0.206503i	0.596276	+	0.802779i	$0.296646\pi$
$458$	19.6809	−	5.88734i	0.919629	−	0.275097i
$459$		0			0
$460$	17.3124	−	4.59774i	0.807193	−	0.214371i
$461$	−4.95715	−	4.95715i	−0.230878	−	0.230878i	0.582181	−	0.813059i	$-0.302199\pi$
$461$	−4.95715	−	4.95715i	−0.230878	−	0.230878i	−0.813059	+	0.582181i	$0.802199\pi$
$462$		0			0
$463$	−2.77467	−	2.77467i	−0.128950	−	0.128950i	0.639686	−	0.768636i	$-0.279064\pi$
$463$	−2.77467	−	2.77467i	−0.128950	−	0.128950i	−0.768636	+	0.639686i	$0.779064\pi$
$464$	−2.08389	−	5.25903i	−0.0967424	−	0.244144i
$465$		0			0
$466$	−15.8487	+	4.74097i	−0.734177	+	0.219621i
$467$	23.0361			1.06598			0.532992	−	0.846120i	$-0.321068\pi$
$467$	23.0361			1.06598			0.532992	+	0.846120i	$0.321068\pi$
$468$		0			0
$469$	−1.91431	−	1.91431i	−0.0883946	−	0.0883946i
$470$	−21.8199	−	23.2204i	−1.00648	−	1.07108i
$471$		0			0
$472$	−24.4917	+	29.1488i	−1.12732	+	1.34168i
$473$	−1.41454	−	1.41454i	−0.0650405	−	0.0650405i
$474$		0			0
$475$	−19.8255	+	2.83221i	−0.909655	+	0.129951i
$476$	−1.80344	+	1.18500i	−0.0826606	+	0.0543144i
$477$		0			0
$478$	2.29273	−	4.24989i	0.104867	−	0.194385i
$479$	−20.5855			−0.940574			−0.470287	−	0.882514i	$-0.655850\pi$
$479$	−20.5855			−0.940574			−0.470287	+	0.882514i	$0.655850\pi$
$480$		0			0
$481$		0			0
$482$	−2.12915	+	3.94667i	−0.0969803	+	0.179766i
$483$		0			0
$484$	−18.3145	+	12.0340i	−0.832476	+	0.547000i
$485$	10.7564	+	3.58546i	0.488422	+	0.162807i
$486$		0			0
$487$	5.31729	+	5.31729i	0.240949	+	0.240949i	0.817243	−	0.576293i	$-0.195501\pi$
$487$	5.31729	+	5.31729i	0.240949	+	0.240949i	−0.576293	+	0.817243i	$0.695501\pi$
$488$	5.16286	+	4.33799i	0.233711	+	0.196372i
$489$		0			0
$490$	−21.9898	−	0.683741i	−0.993399	−	0.0308883i
$491$	−21.5181	−	21.5181i	−0.971096	−	0.971096i	0.0284975	−	0.999594i	$-0.490928\pi$
$491$	−21.5181	−	21.5181i	−0.971096	−	0.971096i	−0.999594	+	0.0284975i	$0.990928\pi$
$492$		0			0
$493$	7.37169			0.332004
$494$		0			0
$495$		0			0
$496$	1.07475	+	0.464730i	0.0482577	+	0.0208670i
$497$	0.671153	+	0.671153i	0.0301053	+	0.0301053i
$498$		0			0
$499$	−2.83221	−	2.83221i	−0.126787	−	0.126787i	0.640866	−	0.767653i	$-0.278576\pi$
$499$	−2.83221	−	2.83221i	−0.126787	−	0.126787i	−0.767653	+	0.640866i	$0.778576\pi$
$500$	20.5826	−	8.73814i	0.920483	−	0.390782i
$501$		0			0
$502$	−7.38397	+	2.20884i	−0.329563	+	0.0985852i
$503$	−7.32571	+	7.32571i	−0.326637	+	0.326637i	−0.851306	−	0.524669i	$-0.824189\pi$
$503$	−7.32571	+	7.32571i	−0.326637	+	0.326637i	0.524669	+	0.851306i	$0.324189\pi$
$504$		0			0
$505$	−10.3717	+	31.1151i	−0.461534	+	1.38460i
$506$	0.556693	−	1.03190i	0.0247480	−	0.0458738i
$507$		0			0
$508$	10.6736	+	2.20884i	0.473563	+	0.0980013i
$509$	−10.1709	+	10.1709i	−0.450818	+	0.450818i	−0.895626	−	0.444808i	$-0.853272\pi$
$509$	−10.1709	+	10.1709i	−0.450818	+	0.450818i	0.444808	+	0.895626i	$0.353272\pi$
$510$		0			0
$511$		−	1.86519i		−	0.0825112i
$512$	21.8680	−	5.81289i	0.966439	−	0.256896i
$513$		0			0
$514$	41.4703	−	12.4054i	1.82918	−	0.547178i
$515$	5.51806	−	16.5542i	0.243155	−	0.729464i
$516$		0			0
$517$	−2.08569			−0.0917286
$518$	−2.62831	+	0.786230i	−0.115481	+	0.0345450i
$519$		0			0
$520$		0			0
$521$			8.11508i			0.355528i	0.984073	+	0.177764i	$0.0568864\pi$
$521$			8.11508i			0.355528i	−0.984073	+	0.177764i	$0.943114\pi$
$522$		0			0
$523$	5.07896			0.222087			0.111044	−	0.993816i	$-0.464581\pi$
$523$	5.07896			0.222087			0.111044	+	0.993816i	$0.464581\pi$
$524$	36.6307	+	7.58053i	1.60022	+	0.331157i
$525$		0			0
$526$	8.16599	+	27.2983i	0.356054	+	1.19026i
$527$	−1.07896	+	1.07896i	−0.0470003	+	0.0470003i
$528$		0			0
$529$			6.95715i			0.302485i
$530$	−37.7936	−	1.17513i	−1.64165	−	0.0510446i
$531$		0			0
$532$	−1.38577	+	0.910557i	−0.0600807	+	0.0394776i
$533$		0			0
$534$		0			0
$535$	−11.3288	−	22.6577i	−0.489789	−	0.979578i
$536$	−36.8543	+	3.19969i	−1.59186	+	0.138206i
$537$		0			0
$538$	6.75566	+	22.5837i	0.291257	+	0.973651i
$539$	−1.01829	+	1.01829i	−0.0438607	+	0.0438607i
$540$		0			0
$541$	26.3864	+	26.3864i	1.13444	+	1.13444i	0.989430	+	0.145009i	$0.0463211\pi$
$541$	26.3864	+	26.3864i	1.13444	+	1.13444i	0.145009	+	0.989430i	$0.453679\pi$
$542$	14.5714	+	7.86098i	0.625895	+	0.337658i
$543$		0			0
$544$	−3.45559	+	29.2836i	−0.148157	+	1.25552i
$545$	10.2713	−	30.8139i	0.439974	−	1.31992i
$546$		0			0
$547$	−33.6644			−1.43939			−0.719693	−	0.694292i	$-0.755718\pi$
$547$	−33.6644			−1.43939			−0.719693	+	0.694292i	$0.755718\pi$
$548$	−33.9883	−	7.03370i	−1.45191	−	0.300465i
$549$		0			0
$550$	0.505779	−	1.37349i	0.0215665	−	0.0585658i
$551$	5.66442			0.241313
$552$		0			0
$553$	−0.671153	−	0.671153i	−0.0285403	−	0.0285403i
$554$	−12.4507	+	23.0790i	−0.528978	+	0.980531i
$555$		0			0
$556$	18.1127	+	3.74832i	0.768148	+	0.158964i
$557$		−	8.82908i		−	0.374100i	−0.982350	−	0.187050i	$-0.940107\pi$
$557$		−	8.82908i		−	0.374100i	0.982350	−	0.187050i	$-0.0598926\pi$
$558$		0			0
$559$		0			0
$560$	1.23447	−	1.37976i	0.0521659	−	0.0583055i
$561$		0			0
$562$	−3.27131	−	1.76481i	−0.137992	−	0.0744439i
$563$			6.74338i			0.284200i	0.989852	+	0.142100i	$0.0453854\pi$
$563$			6.74338i			0.284200i	−0.989852	+	0.142100i	$0.954615\pi$
$564$		0			0
$565$	−1.68585	+	5.05754i	−0.0709241	+	0.212772i
$566$	−14.9399	+	27.6932i	−0.627973	+	1.16403i
$567$		0			0
$568$	12.9210	−	1.12181i	0.542155	−	0.0470700i
$569$	−23.3717			−0.979792			−0.489896	−	0.871781i	$-0.662965\pi$
$569$	−23.3717			−0.979792			−0.489896	+	0.871781i	$0.662965\pi$
$570$		0			0
$571$	−22.5395	−	22.5395i	−0.943248	−	0.943248i	0.0552260	−	0.998474i	$-0.482412\pi$
$571$	−22.5395	−	22.5395i	−0.943248	−	0.943248i	−0.998474	+	0.0552260i	$0.982412\pi$
$572$		0			0
$573$		0			0
$574$	0.335577	+	1.12181i	0.0140067	+	0.0468233i
$575$	−2.83221	−	19.8255i	−0.118111	−	0.826780i
$576$		0			0
$577$	21.5855	+	21.5855i	0.898615	+	0.898615i	0.995314	−	0.0966991i	$-0.0308285\pi$
$577$	21.5855	+	21.5855i	0.898615	+	0.898615i	−0.0966991	+	0.995314i	$0.530828\pi$
$578$	−12.6592	−	6.82938i	−0.526553	−	0.284065i
$579$		0			0
$580$	−6.11266	+	1.62337i	−0.253815	+	0.0674070i
$581$	1.25662	−	1.25662i	0.0521332	−	0.0521332i
$582$		0			0
$583$	−1.75011	+	1.75011i	−0.0724823	+	0.0724823i
$584$	−19.5131	−	16.3955i	−0.807459	−	0.678452i
$585$		0			0
$586$	−27.2755	−	14.7146i	−1.12674	−	0.607855i
$587$			16.5855i			0.684555i	0.939599	+	0.342278i	$0.111198\pi$
$587$			16.5855i			0.684555i	−0.939599	+	0.342278i	$0.888802\pi$
$588$		0			0
$589$	−0.829076	+	0.829076i	−0.0341615	+	0.0341615i
$590$	29.1488	+	31.0196i	1.20004	+	1.27706i
$591$		0			0
$592$	−14.8782	+	34.4078i	−0.611490	+	1.41415i
$593$	−8.85677	+	8.85677i	−0.363704	+	0.363704i	−0.865175	−	0.501471i	$-0.832793\pi$
$593$	−8.85677	+	8.85677i	−0.363704	+	0.363704i	0.501471	+	0.865175i	$0.332793\pi$
$594$		0			0
$595$	1.07896	+	2.15792i	0.0442331	+	0.0884662i
$596$	4.79851	−	23.1874i	0.196555	−	0.949793i
$597$		0			0
$598$		0			0
$599$			24.9933i			1.02120i	0.859819	+	0.510599i	$0.170576\pi$
$599$			24.9933i			1.02120i	−0.859819	+	0.510599i	$0.829424\pi$
$600$		0			0
$601$		−	39.8286i		−	1.62464i	−0.583210	−	0.812322i	$-0.698203\pi$
$601$		−	39.8286i		−	1.62464i	0.583210	−	0.812322i	$-0.301797\pi$
$602$	−2.71040	+	0.810789i	−0.110468	+	0.0330453i
$603$		0			0
$604$		0			0
$605$	10.9572	+	21.9143i	0.445472	+	0.890943i
$606$		0			0
$607$	16.8469	−	16.8469i	0.683795	−	0.683795i	−0.277058	−	0.960853i	$-0.589360\pi$
$607$	16.8469	−	16.8469i	0.683795	−	0.683795i	0.960853	+	0.277058i	$0.0893595\pi$
$608$	−2.65528	+	22.5016i	−0.107686	+	0.912559i
$609$		0			0
$610$	5.49422	−	5.16286i	0.222455	−	0.209038i
$611$		0			0
$612$		0			0
$613$		−	8.62831i		−	0.348494i	−0.984702	−	0.174247i	$-0.944251\pi$
$613$		−	8.62831i		−	0.348494i	0.984702	−	0.174247i	$-0.0557491\pi$
$614$	−4.25410	+	7.88554i	−0.171681	+	0.318234i
$615$		0			0
$616$	−0.0104820	−	0.120732i	−0.000422330	−	0.00486442i
$617$	11.0147	−	11.0147i	0.443435	−	0.443435i	−0.449730	−	0.893165i	$-0.648480\pi$
$617$	11.0147	−	11.0147i	0.443435	−	0.443435i	0.893165	+	0.449730i	$0.148480\pi$
$618$		0			0
$619$	−6.53948	+	6.53948i	−0.262844	+	0.262844i	−0.826208	−	0.563365i	$-0.809507\pi$
$619$	−6.53948	+	6.53948i	−0.262844	+	0.262844i	0.563365	+	0.826208i	$0.309507\pi$
$620$	0.657077	−	1.13229i	0.0263888	−	0.0454738i
$621$		0			0
$622$	−4.92104	+	9.12181i	−0.197316	+	0.365751i
$623$	0.493499	+	0.493499i	0.0197716	+	0.0197716i
$624$		0			0
$625$	−7.00000	−	24.0000i	−0.280000	−	0.960000i
$626$	−5.74832	+	1.71955i	−0.229749	+	0.0687270i
$627$		0			0
$628$	−41.3576	+	27.1751i	−1.65035	+	1.08441i
$629$	−34.5426	−	34.5426i	−1.37730	−	1.37730i
$630$		0			0
$631$	42.0722			1.67487			0.837435	−	0.546538i	$-0.184054\pi$
$631$	42.0722			1.67487			0.837435	+	0.546538i	$0.184054\pi$
$632$	−12.9210	+	1.12181i	−0.513971	+	0.0446231i
$633$		0			0
$634$	−24.8396	−	13.4005i	−0.986505	−	0.532200i
$635$	3.85363	−	11.5609i	0.152927	−	0.458780i
$636$		0			0
$637$		0			0
$638$	−0.196558	+	0.364346i	−0.00778179	+	0.0144246i
$639$		0			0
$640$	−3.58336	−	25.0432i	−0.141645	−	0.989918i
$641$	−16.8291			−0.664709			−0.332354	−	0.943155i	$-0.607843\pi$
$641$	−16.8291			−0.664709			−0.332354	+	0.943155i	$0.607843\pi$
$642$		0			0
$643$		−	38.0722i		−	1.50142i	−0.660631	−	0.750711i	$-0.729711\pi$
$643$		−	38.0722i		−	1.50142i	0.660631	−	0.750711i	$-0.270289\pi$
$644$	−0.910557	−	1.38577i	−0.0358810	−	0.0546069i
$645$		0			0
$646$	−25.9859	−	14.0189i	−1.02240	−	0.551566i
$647$	1.36856	+	1.36856i	0.0538035	+	0.0538035i	0.733497	−	0.679693i	$-0.237887\pi$
$647$	1.36856	+	1.36856i	0.0538035	+	0.0538035i	−0.679693	+	0.733497i	$0.737887\pi$
$648$		0			0
$649$	2.78623			0.109369
$650$		0			0
$651$		0			0
$652$	12.3931	−	8.14323i	0.485352	−	0.318913i
$653$	−17.9572			−0.702718			−0.351359	−	0.936241i	$-0.614280\pi$
$653$	−17.9572			−0.702718			−0.351359	+	0.936241i	$0.614280\pi$
$654$		0			0
$655$	13.2253	−	39.6760i	0.516756	−	1.55027i
$656$	14.6858	+	6.35027i	0.573386	+	0.247936i
$657$		0			0
$658$	−1.40046	+	2.59594i	−0.0545957	+	0.101200i
$659$	−11.1825	−	11.1825i	−0.435608	−	0.435608i	0.454923	−	0.890531i	$-0.349667\pi$
$659$	−11.1825	−	11.1825i	−0.435608	−	0.435608i	−0.890531	+	0.454923i	$0.849667\pi$
$660$		0			0
$661$	−3.01469	+	3.01469i	−0.117258	+	0.117258i	−0.763301	−	0.646043i	$-0.776423\pi$
$661$	−3.01469	+	3.01469i	−0.117258	+	0.117258i	0.646043	+	0.763301i	$0.276423\pi$
$662$	23.9449	−	7.16286i	0.930644	−	0.278392i
$663$		0			0
$664$	−2.10038	−	24.1923i	−0.0815107	−	0.938845i
$665$	0.829076	+	1.65815i	0.0321502	+	0.0643004i
$666$		0			0
$667$			5.66442i			0.219327i
$668$	−6.99507	+	33.8016i	−0.270647	+	1.30782i
$669$		0			0
$670$	−1.28538	+	41.3393i	−0.0496587	+	1.59708i
$671$		−	0.493499i		−	0.0190513i
$672$		0			0
$673$	−12.5725	+	12.5725i	−0.484633	+	0.484633i	−0.906608	−	0.421975i	$-0.861337\pi$
$673$	−12.5725	+	12.5725i	−0.484633	+	0.484633i	0.421975	+	0.906608i	$0.361337\pi$
$674$	29.8634	−	8.93332i	1.15029	−	0.344099i
$675$		0			0
$676$	14.2776	+	21.7290i	0.549139	+	0.835731i
$677$	16.7862			0.645147			0.322574	−	0.946544i	$-0.395452\pi$
$677$	16.7862			0.645147			0.322574	+	0.946544i	$0.395452\pi$
$678$		0			0
$679$		−	1.04958i		−	0.0402790i
$680$	32.0600	+	7.68091i	1.22944	+	0.294550i
$681$		0			0
$682$	−0.0245584	−	0.0820969i	−0.000940391	−	0.00314365i
$683$	−0.378422			−0.0144799			−0.00723997	−	0.999974i	$-0.502305\pi$
$683$	−0.378422			−0.0144799			−0.00723997	+	0.999974i	$0.502305\pi$
$684$		0			0
$685$	−12.2713	+	36.8139i	−0.468863	+	1.40659i
$686$	1.17092	+	3.91431i	0.0447061	+	0.149449i
$687$		0			0
$688$	−15.3429	+	35.4826i	−0.584943	+	1.35276i
$689$		0			0
$690$		0			0
$691$	7.79610	−	7.79610i	0.296577	−	0.296577i	−0.543094	−	0.839672i	$-0.682747\pi$
$691$	7.79610	−	7.79610i	0.296577	−	0.296577i	0.839672	+	0.543094i	$0.182747\pi$
$692$	16.1923	+	24.6430i	0.615541	+	0.936786i
$693$		0			0
$694$	−18.3503	−	9.89962i	−0.696567	−	0.375784i
$695$	6.53948	−	19.6184i	0.248057	−	0.744170i
$696$		0			0
$697$	−14.7434	+	14.7434i	−0.558446	+	0.558446i
$698$	−2.08810	−	6.98037i	−0.0790359	−	0.264211i
$699$		0			0
$700$	−1.36990	−	1.55176i	−0.0517772	−	0.0586510i
$701$	1.78623	+	1.78623i	0.0674650	+	0.0674650i	0.740034	−	0.672569i	$-0.234809\pi$
$701$	1.78623	+	1.78623i	0.0674650	+	0.0674650i	−0.672569	+	0.740034i	$0.734809\pi$
$702$		0			0
$703$	−26.5426	−	26.5426i	−1.00107	−	1.00107i
$704$	−1.35520	−	0.951605i	−0.0510761	−	0.0358650i
$705$		0			0
$706$	−2.11266	−	7.06247i	−0.0795111	−	0.265800i
$707$	3.03612			0.114185
$708$		0			0
$709$	−21.6858	−	21.6858i	−0.814429	−	0.814429i	0.170865	−	0.985294i	$-0.445344\pi$
$709$	−21.6858	−	21.6858i	−0.814429	−	0.814429i	−0.985294	+	0.170865i	$0.945344\pi$
$710$	0.450654	−	14.4935i	0.0169127	−	0.543931i
$711$		0			0
$712$	9.50085	−	0.824865i	0.356059	−	0.0309131i
$713$	−0.829076	−	0.829076i	−0.0310491	−	0.0310491i
$714$		0			0
$715$		0			0
$716$	−5.28780	+	25.5518i	−0.197614	+	0.954914i
$717$		0			0
$718$	−41.0649	−	22.1537i	−1.53253	−	0.826769i
$719$	−8.00000			−0.298350			−0.149175	−	0.988811i	$-0.547662\pi$
$719$	−8.00000			−0.298350			−0.149175	+	0.988811i	$0.547662\pi$
$720$		0			0
$721$	−1.61531			−0.0601572
$722$	3.68061	+	1.98562i	0.136978	+	0.0738970i
$723$		0			0
$724$	10.2088	+	2.11266i	0.379408	+	0.0785165i
$725$	1.00000	+	7.00000i	0.0371391	+	0.259973i
$726$		0			0
$727$	33.6331	+	33.6331i	1.24738	+	1.24738i	0.956871	+	0.290513i	$0.0938259\pi$
$727$	33.6331	+	33.6331i	1.24738	+	1.24738i	0.290513	+	0.956871i	$0.406174\pi$
$728$		0			0
$729$		0			0
$730$	−20.7655	+	19.5131i	−0.768567	+	0.722213i
$731$	−35.6216	−	35.6216i	−1.31751	−	1.31751i
$732$		0			0
$733$	−20.1151			−0.742967			−0.371484	−	0.928439i	$-0.621151\pi$
$733$	−20.1151			−0.742967			−0.371484	+	0.928439i	$0.621151\pi$
$734$	10.3766	+	34.6883i	0.383008	+	1.28037i
$735$		0			0
$736$	−22.5016	−	2.65528i	−0.829419	−	0.0978749i
$737$	1.91431	+	1.91431i	0.0705145	+	0.0705145i
$738$		0			0
$739$	17.7533	+	17.7533i	0.653064	+	0.653064i	0.953730	−	0.300666i	$-0.0972088\pi$
$739$	17.7533	+	17.7533i	0.653064	+	0.653064i	−0.300666	+	0.953730i	$0.597209\pi$
$740$	36.2499	+	21.0361i	1.33257	+	0.773303i
$741$		0			0
$742$	1.00314	+	3.35341i	0.0368263	+	0.123107i
$743$	0.203904	−	0.203904i	0.00748051	−	0.00748051i	−0.703357	−	0.710837i	$-0.748316\pi$
$743$	0.203904	−	0.203904i	0.00748051	−	0.00748051i	0.710837	+	0.703357i	$0.248316\pi$
$744$		0			0
$745$	−25.1151	−	8.37169i	−0.920145	−	0.306715i
$746$	17.3184	+	9.34292i	0.634070	+	0.342069i
$747$		0			0
$748$	1.80344	−	1.18500i	0.0659404	−	0.0433279i
$749$	−1.65815	+	1.65815i	−0.0605876	+	0.0605876i
$750$		0			0
$751$			2.45065i			0.0894256i	0.999000	+	0.0447128i	$0.0142373\pi$
$751$			2.45065i			0.0894256i	−0.999000	+	0.0447128i	$0.985763\pi$
$752$	14.8476	+	37.4703i	0.541437	+	1.36640i
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	37.2860			1.35518			0.677591	−	0.735439i	$-0.263024\pi$
$757$	37.2860			1.35518			0.677591	+	0.735439i	$0.263024\pi$
$758$	−4.41947	−	14.7740i	−0.160522	−	0.536614i
$759$		0			0
$760$	24.6349	+	5.90203i	0.893603	+	0.214089i
$761$			12.2008i			0.442278i	0.975242	+	0.221139i	$0.0709774\pi$
$761$			12.2008i			0.442278i	−0.975242	+	0.221139i	$0.929023\pi$
$762$		0			0
$763$	−3.00673			−0.108851
$764$	10.5897	−	6.95823i	0.383121	−	0.251740i
$765$		0			0
$766$	−28.4201	+	8.50157i	−1.02686	+	0.307174i
$767$		0			0
$768$		0			0
$769$			3.21377i			0.115891i	0.998320	+	0.0579457i	$0.0184550\pi$
$769$			3.21377i			0.115891i	−0.998320	+	0.0579457i	$0.981545\pi$
$770$	−0.135425	−	0.00421083i	−0.00488036	−	0.000151748i
$771$		0			0
$772$	−1.14816	−	0.237606i	−0.0413233	−	0.00855163i
$773$		−	42.6148i		−	1.53275i	−0.642394	−	0.766375i	$-0.722059\pi$
$773$		−	42.6148i		−	1.53275i	0.642394	−	0.766375i	$-0.277941\pi$
$774$		0			0
$775$	−1.17092	−	0.878193i	−0.0420608	−	0.0315456i
$776$	−10.9804	−	9.22605i	−0.394172	−	0.331196i
$777$		0			0
$778$	−31.3699	+	9.38397i	−1.12467	+	0.336432i
$779$	−11.3288	+	11.3288i	−0.405898	+	0.405898i
$780$		0			0
$781$	−0.671153	−	0.671153i	−0.0240158	−	0.0240158i
$782$	14.0189	−	25.9859i	0.501315	−	0.929255i
$783$		0			0
$784$	25.5429	+	11.0450i	0.912247	+	0.394463i
$785$	24.7434	+	49.4868i	0.883129	+	1.76626i
$786$		0			0
$787$	47.2369			1.68381			0.841907	−	0.539623i	$-0.181433\pi$
$787$	47.2369			1.68381			0.841907	+	0.539623i	$0.181433\pi$
$788$	−9.64973	−	14.6858i	−0.343757	−	0.523162i
$789$		0			0
$790$	−0.450654	+	14.4935i	−0.0160335	+	0.515656i
$791$	0.493499			0.0175468
$792$		0			0
$793$		0			0
$794$	−0.782020	−	0.421884i	−0.0277528	−	0.0149721i
$795$		0			0
$796$	19.5682	−	12.8578i	0.693578	−	0.455734i
$797$		−	19.8715i		−	0.703883i	−0.936022	−	0.351942i	$-0.885522\pi$
$797$		−	19.8715i		−	0.703883i	0.936022	−	0.351942i	$-0.114478\pi$
$798$		0			0
$799$	−52.5229			−1.85813
$800$	−28.2758	+	0.691087i	−0.999701	+	0.0244336i
$801$		0			0
$802$	−5.73604	+	10.6325i	−0.202547	+	0.375447i
$803$			1.86519i			0.0658212i
$804$		0			0
$805$	−1.65815	+	0.829076i	−0.0584422	+	0.0292211i
$806$		0			0
$807$		0			0
$808$	26.6883	−	31.7630i	0.938890	−	1.11742i
$809$	38.3158			1.34711			0.673557	−	0.739136i	$-0.264766\pi$
$809$	38.3158			1.34711			0.673557	+	0.739136i	$0.264766\pi$
$810$		0			0
$811$	7.50337	+	7.50337i	0.263479	+	0.263479i	0.826466	−	0.562987i	$-0.190348\pi$
$811$	7.50337	+	7.50337i	0.263479	+	0.263479i	−0.562987	+	0.826466i	$0.690348\pi$
$812$	0.321500	+	0.489289i	0.0112824	+	0.0171707i
$813$		0			0
$814$	2.62831	−	0.786230i	0.0921221	−	0.0275574i
$815$	−7.41454	−	14.8291i	−0.259720	−	0.519440i
$816$		0			0
$817$	−27.3717	−	27.3717i	−0.957614	−	0.957614i
$818$	−25.9859	+	48.1684i	−0.908577	+	1.68417i
$819$		0			0
$820$	8.97858	−	15.4721i	0.313546	−	0.540308i
$821$	−35.1151	+	35.1151i	−1.22552	+	1.22552i	−0.259885	+	0.965640i	$0.583685\pi$
$821$	−35.1151	+	35.1151i	−1.22552	+	1.22552i	−0.965640	+	0.259885i	$0.916315\pi$
$822$		0			0
$823$	−30.8041	+	30.8041i	−1.07376	+	1.07376i	−0.0767084	+	0.997054i	$0.524441\pi$
$823$	−30.8041	+	30.8041i	−1.07376	+	1.07376i	−0.997054	+	0.0767084i	$0.975559\pi$
$824$	−14.1990	+	16.8989i	−0.494645	+	0.588701i
$825$		0			0
$826$	1.87085	−	3.46787i	0.0650951	−	0.120662i
$827$			23.9143i			0.831582i	0.909460	+	0.415791i	$0.136495\pi$
$827$			23.9143i			0.831582i	−0.909460	+	0.415791i	$0.863505\pi$
$828$		0			0
$829$	8.47208	−	8.47208i	0.294247	−	0.294247i	−0.544508	−	0.838756i	$-0.683284\pi$
$829$	8.47208	−	8.47208i	0.294247	−	0.294247i	0.838756	+	0.544508i	$0.183284\pi$
$830$	−27.1365	−	0.843769i	−0.941922	−	0.0292876i
$831$		0			0
$832$		0			0
$833$	−25.6430	+	25.6430i	−0.888477	+	0.888477i
$834$		0			0
$835$	36.6117	+	12.2039i	1.26700	+	0.422334i
$836$	1.38577	−	0.910557i	0.0479278	−	0.0314923i
$837$		0			0
$838$	18.7985	−	5.62337i	0.649384	−	0.194256i
$839$		−	49.5787i		−	1.71165i	−0.517267	−	0.855824i	$-0.673051\pi$
$839$		−	49.5787i		−	1.71165i	0.517267	−	0.855824i	$-0.326949\pi$
$840$		0			0
$841$			27.0000i			0.931034i
$842$	−11.6192	−	38.8420i	−0.400423	−	1.33858i
$843$		0			0
$844$	−34.6124	−	7.16286i	−1.19141	−	0.246556i
$845$	26.0000	−	13.0000i	0.894427	−	0.447214i
$846$		0			0
$847$	1.60375	−	1.60375i	0.0551055	−	0.0551055i
$848$	43.9002	+	18.9828i	1.50754	+	0.651872i
$849$		0			0
$850$	12.7368	−	34.5879i	0.436867	−	1.18635i
$851$	26.5426	−	26.5426i	0.909869	−	0.909869i
$852$		0			0
$853$			28.6283i			0.980215i	0.871662	+	0.490107i	$0.163042\pi$
$853$			28.6283i			0.980215i	−0.871662	+	0.490107i	$0.836958\pi$
$854$	−0.614231	−	0.331366i	−0.0210186	−	0.0113391i
$855$		0			0
$856$	2.77154	+	31.9227i	0.0947292	+	1.09110i
$857$	−0.899616	+	0.899616i	−0.0307303	+	0.0307303i	−0.722305	−	0.691575i	$-0.756917\pi$
$857$	−0.899616	+	0.899616i	−0.0307303	+	0.0307303i	0.691575	+	0.722305i	$0.256917\pi$
$858$		0			0
$859$	38.0754	−	38.0754i	1.29911	−	1.29911i	0.370138	−	0.928977i	$-0.379310\pi$
$859$	38.0754	−	38.0754i	1.29911	−	1.29911i	0.928977	−	0.370138i	$-0.120690\pi$
$860$	37.3822	+	21.6932i	1.27472	+	0.739732i
$861$		0			0
$862$	36.1930	+	19.5254i	1.23274	+	0.665038i
$863$	−3.12494	−	3.12494i	−0.106374	−	0.106374i	0.651916	−	0.758291i	$-0.273965\pi$
$863$	−3.12494	−	3.12494i	−0.106374	−	0.106374i	−0.758291	+	0.651916i	$0.773965\pi$
$864$		0			0
$865$	29.4868	−	14.7434i	1.00258	−	0.501290i
$866$	−5.13409	−	17.1629i	−0.174463	−	0.583218i
$867$		0			0
$868$	−0.118671	−	0.0245584i	−0.00402797	−	0.000833567i
$869$	0.671153	+	0.671153i	0.0227673	+	0.0227673i
$870$		0			0
$871$		0			0
$872$	−26.4300	+	31.4556i	−0.895031	+	1.06522i
$873$		0			0
$874$	10.7722	−	19.9676i	0.364374	−	0.675415i
$875$	−1.90275	+	1.31729i	−0.0643247	+	0.0445325i
$876$		0			0
$877$		−	0.743385i		−	0.0251023i	−0.999921	−	0.0125512i	$-0.996005\pi$
$877$		−	0.743385i		−	0.0251023i	0.999921	−	0.0125512i	$-0.00399526\pi$
$878$	8.75746	+	4.72448i	0.295550	+	0.159444i
$879$		0			0
$880$	−1.23447	+	1.37976i	−0.0416140	+	0.0465117i
$881$	35.2860			1.18882			0.594408	−	0.804164i	$-0.297387\pi$
$881$	35.2860			1.18882			0.594408	+	0.804164i	$0.297387\pi$
$882$		0			0
$883$		−	32.9870i		−	1.11010i	−0.831817	−	0.555050i	$-0.812699\pi$
$883$		−	32.9870i		−	1.11010i	0.831817	−	0.555050i	$-0.187301\pi$
$884$		0			0
$885$		0			0
$886$	−22.7392	+	42.1501i	−0.763937	+	1.41606i
$887$	5.16779	+	5.16779i	0.173517	+	0.173517i	0.788523	−	0.615005i	$-0.210846\pi$
$887$	5.16779	+	5.16779i	0.173517	+	0.173517i	−0.615005	+	0.788523i	$0.710846\pi$
$888$		0			0
$889$	−1.12808			−0.0378345
$890$	0.331366	−	10.6571i	0.0111074	−	0.357226i
$891$		0			0
$892$	9.87326	−	47.7097i	0.330581	−	1.59744i
$893$	−40.3587			−1.35055
$894$		0			0
$895$	27.6760	+	9.22533i	0.925106	+	0.308369i
$896$	−2.09438	+	1.04778i	−0.0699682	+	0.0350038i
$897$		0			0
$898$	39.9718	+	21.5640i	1.33388	+	0.719601i
$899$	0.292731	+	0.292731i	0.00976312	+	0.00976312i
$900$		0			0
$901$	−44.0722	+	44.0722i	−1.46826	+	1.46826i
$902$	−0.335577	−	1.12181i	−0.0111735	−	0.0373521i
$903$		0			0
$904$	4.33799	−	5.16286i	0.144279	−	0.171714i
$905$	3.68585	−	11.0575i	0.122522	−	0.367565i
$906$		0			0
$907$		−	6.74338i		−	0.223910i	−0.993713	−	0.111955i	$-0.964289\pi$
$907$		−	6.74338i		−	0.223910i	0.993713	−	0.111955i	$-0.0357113\pi$
$908$	9.10773	+	13.8610i	0.302251	+	0.459993i
$909$		0			0
$910$		0			0
$911$		−	1.16465i		−	0.0385867i	−0.999814	−	0.0192933i	$-0.993858\pi$
$911$		−	1.16465i		−	0.0385867i	0.999814	−	0.0192933i	$-0.00614164\pi$
$912$		0			0
$913$	−1.25662	+	1.25662i	−0.0415879	+	0.0415879i
$914$	−2.53034	−	8.45872i	−0.0836961	−	0.279790i
$915$		0			0
$916$	−5.88734	+	28.4489i	−0.194523	+	0.939977i
$917$	−3.87146			−0.127847
$918$		0			0
$919$			25.8652i			0.853214i	0.904437	+	0.426607i	$0.140291\pi$
$919$			25.8652i			0.853214i	−0.904437	+	0.426607i	$0.859709\pi$
$920$	−5.90203	+	24.6349i	−0.194584	+	0.812190i
$921$		0			0
$922$	9.49843	−	2.84136i	0.312814	−	0.0935751i
$923$		0			0
$924$		0			0
$925$	28.1151	−	37.4868i	0.924418	−	1.23256i
$926$	5.31657	−	1.59039i	0.174713	−	0.0522636i
$927$		0			0
$928$	7.94488	+	0.937529i	0.260803	+	0.0307759i
$929$			37.2003i			1.22050i	0.792208	+	0.610251i	$0.208932\pi$
$929$			37.2003i			1.22050i	−0.792208	+	0.610251i	$0.791068\pi$
$930$		0			0
$931$	−19.7041	+	19.7041i	−0.645777	+	0.645777i
$932$	4.74097	−	22.9094i	0.155296	−	0.750422i
$933$		0			0
$934$	−15.4679	+	28.6718i	−0.506124	+	0.938169i
$935$	−1.07896	−	2.15792i	−0.0352858	−	0.0705716i
$936$		0			0
$937$	−20.9143	+	20.9143i	−0.683241	+	0.683241i	−0.960729	−	0.277488i	$-0.910498\pi$
$937$	−20.9143	+	20.9143i	−0.683241	+	0.683241i	0.277488	+	0.960729i	$0.410498\pi$
$938$	3.66802	−	1.09725i	0.119765	−	0.0358264i
$939$		0			0
$940$	43.5524	−	11.5665i	1.42052	−	0.377256i
$941$	5.58546	+	5.58546i	0.182081	+	0.182081i	0.792262	−	0.610181i	$-0.208903\pi$
$941$	5.58546	+	5.58546i	0.182081	+	0.182081i	−0.610181	+	0.792262i	$0.708903\pi$
$942$		0			0
$943$	−11.3288	−	11.3288i	−0.368918	−	0.368918i
$944$	−19.8346	−	50.0557i	−0.645562	−	1.62918i
$945$		0			0
$946$	2.71040	−	0.810789i	0.0881229	−	0.0263610i
$947$	20.7925			0.675666			0.337833	−	0.941206i	$-0.390306\pi$
$947$	20.7925			0.675666			0.337833	+	0.941206i	$0.390306\pi$
$948$		0			0
$949$		0			0
$950$	9.78695	−	26.5774i	0.317531	−	0.862285i
$951$		0			0
$952$	−0.263962	−	3.04033i	−0.00855505	−	0.0985375i
$953$	−16.3142	−	16.3142i	−0.528467	−	0.528467i	0.391648	−	0.920115i	$-0.371905\pi$
$953$	−16.3142	−	16.3142i	−0.528467	−	0.528467i	−0.920115	+	0.391648i	$0.871905\pi$
$954$		0			0
$955$	−6.33558	−	12.6712i	−0.205014	−	0.410029i
$956$	3.75011	+	5.70727i	0.121287	+	0.184586i
$957$		0			0
$958$	13.8223	−	25.6216i	0.446580	−	0.827796i
$959$	3.59219			0.115998
$960$		0			0
$961$	30.9143			0.997236
$962$		0			0
$963$		0			0
$964$	−3.48256	−	5.30008i	−0.112166	−	0.170704i
$965$	−0.414538	+	1.24361i	−0.0133445	+	0.0400334i
$966$		0			0
$967$	−19.5672	−	19.5672i	−0.629238	−	0.629238i	0.318638	−	0.947876i	$-0.396774\pi$
$967$	−19.5672	−	19.5672i	−0.629238	−	0.629238i	−0.947876	+	0.318638i	$0.896774\pi$
$968$	−2.68061	−	30.8754i	−0.0861579	−	0.992372i
$969$		0			0
$970$	−11.6851	+	10.9804i	−0.375187	+	0.352559i
$971$	−12.8469	−	12.8469i	−0.412277	−	0.412277i	0.470254	−	0.882531i	$-0.344162\pi$
$971$	−12.8469	−	12.8469i	−0.412277	−	0.412277i	−0.882531	+	0.470254i	$0.844162\pi$
$972$		0			0
$973$	−1.91431			−0.0613699
$974$	−10.1885	+	3.04778i	−0.326460	+	0.0976571i
$975$		0			0
$976$	−8.86591	+	3.51313i	−0.283791	+	0.112452i
$977$	27.6430	+	27.6430i	0.884378	+	0.884378i	0.993976	−	0.109598i	$-0.0349564\pi$
$977$	27.6430	+	27.6430i	0.884378	+	0.884378i	−0.109598	+	0.993976i	$0.534956\pi$
$978$		0			0
$979$	−0.493499	−	0.493499i	−0.0157723	−	0.0157723i
$980$	15.6163	−	26.9104i	0.498846	−	0.859621i
$981$		0			0
$982$	41.2309	−	12.3338i	1.31573	−	0.393587i
$983$	22.1611	−	22.1611i	0.706828	−	0.706828i	−0.259039	−	0.965867i	$-0.583406\pi$
$983$	22.1611	−	22.1611i	0.706828	−	0.706828i	0.965867	+	0.259039i	$0.0834058\pi$
$984$		0			0
$985$	−17.5725	+	8.78623i	−0.559905	+	0.279953i
$986$	−4.94981	+	9.17513i	−0.157634	+	0.292196i
$987$		0			0
$988$		0			0
$989$	27.3717	−	27.3717i	0.870369	−	0.870369i
$990$		0			0
$991$			50.9504i			1.61849i	0.587469	+	0.809247i	$0.300124\pi$
$991$			50.9504i			1.61849i	−0.587469	+	0.809247i	$0.699876\pi$
$992$	−1.30008	+	1.02563i	−0.0412775	+	0.0325639i
$993$		0			0
$994$	−1.28600	+	0.384694i	−0.0407895	+	0.0122017i
$995$	−11.7073	−	23.4145i	−0.371145	−	0.742291i
$996$		0			0
$997$	−19.9143			−0.630692			−0.315346	−	0.948977i	$-0.602121\pi$
$997$	−19.9143			−0.630692			−0.315346	+	0.948977i	$0.602121\pi$
$998$	5.42682	−	1.62337i	0.171783	−	0.0513870i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.bd.e.307.1		6
3.2	odd	2		240.2.bc.d.67.3	yes	6
5.3	odd	4		720.2.z.e.163.3		6
12.11	even	2		960.2.bc.d.367.2		6
15.8	even	4		240.2.y.d.163.1	✓	6
16.11	odd	4		720.2.z.e.667.3		6
24.5	odd	2		1920.2.bc.g.607.2		6
24.11	even	2		1920.2.bc.h.607.2		6
48.5	odd	4		960.2.y.d.847.2		6
48.11	even	4		240.2.y.d.187.1	yes	6
48.29	odd	4		1920.2.y.h.1567.2		6
48.35	even	4		1920.2.y.g.1567.2		6
60.23	odd	4		960.2.y.d.943.2		6
80.43	even	4	inner	720.2.bd.e.523.1		6
120.53	even	4		1920.2.y.g.223.2		6
120.83	odd	4		1920.2.y.h.223.2		6
240.53	even	4		960.2.bc.d.463.2		6
240.83	odd	4		1920.2.bc.g.1183.2		6
240.173	even	4		1920.2.bc.h.1183.2		6
240.203	odd	4		240.2.bc.d.43.3	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.y.d.163.1	✓	6	15.8	even	4
240.2.y.d.187.1	yes	6	48.11	even	4
240.2.bc.d.43.3	yes	6	240.203	odd	4
240.2.bc.d.67.3	yes	6	3.2	odd	2
720.2.z.e.163.3		6	5.3	odd	4
720.2.z.e.667.3		6	16.11	odd	4
720.2.bd.e.307.1		6	1.1	even	1	trivial
720.2.bd.e.523.1		6	80.43	even	4	inner
960.2.y.d.847.2		6	48.5	odd	4
960.2.y.d.943.2		6	60.23	odd	4
960.2.bc.d.367.2		6	12.11	even	2
960.2.bc.d.463.2		6	240.53	even	4
1920.2.y.g.223.2		6	120.53	even	4
1920.2.y.g.1567.2		6	48.35	even	4
1920.2.y.h.223.2		6	120.83	odd	4
1920.2.y.h.1567.2		6	48.29	odd	4
1920.2.bc.g.607.2		6	24.5	odd	2
1920.2.bc.g.1183.2		6	240.83	odd	4
1920.2.bc.h.607.2		6	24.11	even	2
1920.2.bc.h.1183.2		6	240.173	even	4

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:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	720.bd (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.671462 + 1.24464i) q^{2} +(-1.09828 - 1.67146i) q^{4} +(-2.00000 + 1.00000i) q^{5} +(0.146365 + 0.146365i) q^{7} +(2.81783 - 0.244644i) q^{8} +(0.0982788 - 3.16075i) q^{10} +(-0.146365 - 0.146365i) q^{11} +(-0.280452 + 0.0838942i) q^{14} +(-1.58757 + 3.67146i) q^{16} +(-3.68585 - 3.68585i) q^{17} +(-2.83221 - 2.83221i) q^{19} +(3.86802 + 2.24464i) q^{20} +(0.280452 - 0.0838942i) q^{22} +(2.83221 - 2.83221i) q^{23} +(3.00000 - 4.00000i) q^{25} +(0.0838942 - 0.405394i) q^{28} +(-1.00000 + 1.00000i) q^{29} -0.292731i q^{31} +(-3.50367 - 4.44120i) q^{32} +(7.06247 - 2.11266i) q^{34} +(-0.439096 - 0.146365i) q^{35} +9.37169 q^{37} +(5.42682 - 1.62337i) q^{38} +(-5.39101 + 3.30712i) q^{40} -4.00000i q^{41} +9.66442 q^{43} +(-0.0838942 + 0.405394i) q^{44} +(1.62337 + 5.42682i) q^{46} +(7.12494 - 7.12494i) q^{47} -6.95715i q^{49} +(2.96419 + 6.41978i) q^{50} -11.9572i q^{53} +(0.439096 + 0.146365i) q^{55} +(0.448240 + 0.376625i) q^{56} +(-0.573183 - 1.91611i) q^{58} +(-9.51806 + 9.51806i) q^{59} +(1.68585 + 1.68585i) q^{61} +(0.364346 + 0.196558i) q^{62} +(7.88030 - 1.37873i) q^{64} -13.0790 q^{67} +(-2.11266 + 10.2088i) q^{68} +(0.477009 - 0.448240i) q^{70} +4.58546 q^{71} +(-6.37169 - 6.37169i) q^{73} +(-6.29273 + 11.6644i) q^{74} +(-1.62337 + 7.84449i) q^{76} -0.0428457i q^{77} -4.58546 q^{79} +(-0.496327 - 8.93049i) q^{80} +(4.97858 + 2.68585i) q^{82} -8.58546i q^{83} +(11.0575 + 3.68585i) q^{85} +(-6.48929 + 12.0288i) q^{86} +(-0.448240 - 0.376625i) q^{88} +3.37169 q^{89} +(-7.84449 - 1.62337i) q^{92} +(4.08389 + 13.6521i) q^{94} +(8.49663 + 2.83221i) q^{95} +(-3.58546 - 3.58546i) q^{97} +(8.65918 + 4.67146i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{2} - 2 q^{4} - 12 q^{5} - 2 q^{7} + 8 q^{8} - 4 q^{10} + 2 q^{11} - 6 q^{14} + 10 q^{16} + 2 q^{17} + 10 q^{19} + 8 q^{20} + 6 q^{22} - 10 q^{23} + 18 q^{25} + 14 q^{28} - 6 q^{29} + 12 q^{32}+ \cdots + 56 q^{98}+O(q^{100}) \) 6 * q + 2 * q^2 - 2 * q^4 - 12 * q^5 - 2 * q^7 + 8 * q^8 - 4 * q^10 + 2 * q^11 - 6 * q^14 + 10 * q^16 + 2 * q^17 + 10 * q^19 + 8 * q^20 + 6 * q^22 - 10 * q^23 + 18 * q^25 + 14 * q^28 - 6 * q^29 + 12 * q^32 + 26 * q^34 + 6 * q^35 + 8 * q^37 + 34 * q^38 - 22 * q^40 + 4 * q^43 - 14 * q^44 + 2 * q^46 + 10 * q^47 + 6 * q^50 - 6 * q^55 + 34 * q^56 - 2 * q^58 - 6 * q^59 - 14 * q^61 + 20 * q^62 + 22 * q^64 - 36 * q^67 + 10 * q^68 - 2 * q^70 + 16 * q^71 + 10 * q^73 - 32 * q^74 - 2 * q^76 - 16 * q^79 - 36 * q^80 - 6 * q^85 - 24 * q^86 - 34 * q^88 - 28 * q^89 - 10 * q^92 + 38 * q^94 - 30 * q^95 - 10 * q^97 + 56 * q^98

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