LMFDB - Embedded newform 720.2.z.e.163.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [720,2,Mod(163,720)]

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, 3]))

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

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

chi := DirichletCharacter("720.163");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 720 = 2^{4} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	720.z (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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 240)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			163.3
Root			$-0.671462 + 1.24464i$ of defining polynomial
Character	$\chi$	$=$	720.163
Dual form			720.2.z.e.667.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.24464 + 0.671462i) q^{2} +(1.09828 + 1.67146i) q^{4} +(-1.00000 + 2.00000i) q^{5} +(0.146365 - 0.146365i) q^{7} +(0.244644 + 2.81783i) q^{8} +(-2.58757 + 1.81783i) q^{10} +(-0.146365 - 0.146365i) q^{11} +(0.280452 - 0.0838942i) q^{14} +(-1.58757 + 3.67146i) q^{16} +(-3.68585 + 3.68585i) q^{17} +(2.83221 + 2.83221i) q^{19} +(-4.44120 + 0.525096i) q^{20} +(-0.0838942 - 0.280452i) q^{22} +(2.83221 + 2.83221i) q^{23} +(-3.00000 - 4.00000i) q^{25} +(0.405394 + 0.0838942i) q^{28} +(1.00000 - 1.00000i) q^{29} -0.292731i q^{31} +(-4.44120 + 3.50367i) q^{32} +(-7.06247 + 2.11266i) q^{34} +(0.146365 + 0.439096i) q^{35} -9.37169i q^{37} +(1.62337 + 5.42682i) q^{38} +(-5.88030 - 2.32854i) q^{40} -4.00000i q^{41} +9.66442i q^{43} +(0.0838942 - 0.405394i) q^{44} +(1.62337 + 5.42682i) q^{46} +(-7.12494 - 7.12494i) q^{47} +6.95715i q^{49} +(-1.04809 - 6.99296i) q^{50} +11.9572 q^{53} +(0.439096 - 0.146365i) q^{55} +(0.448240 + 0.376625i) q^{56} +(1.91611 - 0.573183i) q^{58} +(9.51806 - 9.51806i) q^{59} +(1.68585 + 1.68585i) q^{61} +(0.196558 - 0.364346i) q^{62} +(-7.88030 + 1.37873i) q^{64} +13.0790i q^{67} +(-10.2088 - 2.11266i) q^{68} +(-0.112663 + 0.644798i) q^{70} +4.58546 q^{71} +(6.37169 - 6.37169i) q^{73} +(6.29273 - 11.6644i) q^{74} +(-1.62337 + 7.84449i) q^{76} -0.0428457 q^{77} +4.58546 q^{79} +(-5.75536 - 6.84660i) q^{80} +(2.68585 - 4.97858i) q^{82} +8.58546 q^{83} +(-3.68585 - 11.0575i) q^{85} +(-6.48929 + 12.0288i) q^{86} +(0.376625 - 0.448240i) q^{88} -3.37169 q^{89} +(-1.62337 + 7.84449i) q^{92} +(-4.08389 - 13.6521i) q^{94} +(-8.49663 + 2.83221i) q^{95} +(-3.58546 + 3.58546i) q^{97} +(-4.67146 + 8.65918i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 2 q^{4} - 6 q^{5} - 2 q^{7} - 6 q^{8} + 4 q^{10} + 2 q^{11} + 6 q^{14} + 10 q^{16} + 2 q^{17} - 10 q^{19} - 10 q^{20} - 14 q^{22} - 10 q^{23} - 18 q^{25} - 26 q^{28} + 6 q^{29} - 10 q^{32} - 26 q^{34}+ \cdots - 22 q^{98}+O(q^{100}) $ 6 * q + 2 * q^4 - 6 * q^5 - 2 * q^7 - 6 * q^8 + 4 * q^10 + 2 * q^11 + 6 * q^14 + 10 * q^16 + 2 * q^17 - 10 * q^19 - 10 * q^20 - 14 * q^22 - 10 * q^23 - 18 * q^25 - 26 * q^28 + 6 * q^29 - 10 * q^32 - 26 * q^34 - 2 * q^35 + 2 * q^38 - 10 * q^40 + 14 * q^44 + 2 * q^46 - 10 * q^47 - 8 * q^50 + 12 * q^53 - 6 * q^55 + 34 * q^56 - 2 * q^58 + 6 * q^59 - 14 * q^61 - 8 * q^62 - 22 * q^64 - 42 * q^68 + 22 * q^70 + 16 * q^71 - 10 * q^73 + 32 * q^74 - 2 * q^76 - 60 * q^77 + 16 * q^79 - 42 * q^80 - 8 * q^82 + 40 * q^83 + 2 * q^85 - 24 * q^86 + 10 * q^88 + 28 * q^89 - 2 * q^92 - 38 * q^94 + 30 * q^95 - 10 * q^97 - 22 * q^98

Character values

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

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

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 $

$2$	1.24464	+	0.671462i	0.880096	+	0.474795i
$2$	1.24464	+	0.671462i	0.880096	+	0.474795i
$3$		0			0
$3$		0			0
$4$	1.09828	+	1.67146i	0.549139	+	0.835731i
$5$	−1.00000	+	2.00000i	−0.447214	+	0.894427i
$5$	−1.00000	+	2.00000i	−0.447214	+	0.894427i
$6$		0			0
$7$	0.146365	−	0.146365i	0.0553210	−	0.0553210i	−0.678905	−	0.734226i	$-0.737545\pi$
$7$	0.146365	−	0.146365i	0.0553210	−	0.0553210i	0.734226	+	0.678905i	$0.237545\pi$
$8$	0.244644	+	2.81783i	0.0864948	+	0.996252i
$9$		0			0
$10$	−2.58757	+	1.81783i	−0.818261	+	0.574847i
$11$	−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		1.00000			$0$
$13$		0			0		−1.00000			$\pi$
$14$	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	−0.994892	−	0.100943i	$-0.967814\pi$
$17$	−3.68585	+	3.68585i	−0.893949	+	0.893949i	0.100943	+	0.994892i	$0.467814\pi$
$18$		0			0
$19$	2.83221	+	2.83221i	0.649754	+	0.649754i	0.952933	−	0.303180i	$-0.0980482\pi$
$19$	2.83221	+	2.83221i	0.649754	+	0.649754i	−0.303180	+	0.952933i	$0.598048\pi$
$20$	−4.44120	+	0.525096i	−0.993083	+	0.117415i
$21$		0			0
$22$	−0.0838942	−	0.280452i	−0.0178863	−	0.0597925i
$23$	2.83221	+	2.83221i	0.590557	+	0.590557i	0.937782	−	0.347225i	$-0.112876\pi$
$23$	2.83221	+	2.83221i	0.590557	+	0.590557i	−0.347225	+	0.937782i	$0.612876\pi$
$24$		0			0
$25$	−3.00000	−	4.00000i	−0.600000	−	0.800000i
$26$		0			0
$27$		0			0
$28$	0.405394	+	0.0838942i	0.0766123	+	0.0158545i
$29$	1.00000	−	1.00000i	0.185695	−	0.185695i	−0.608137	−	0.793832i	$-0.708083\pi$
$29$	1.00000	−	1.00000i	0.185695	−	0.185695i	0.793832	+	0.608137i	$0.208083\pi$
$30$		0			0
$31$		−	0.292731i		−	0.0525760i	−0.999654	−	0.0262880i	$-0.991631\pi$
$31$		−	0.292731i		−	0.0525760i	0.999654	−	0.0262880i	$-0.00836870\pi$
$32$	−4.44120	+	3.50367i	−0.785101	+	0.619368i
$33$		0			0
$34$	−7.06247	+	2.11266i	−1.21120	+	0.362319i
$35$	0.146365	+	0.439096i	0.0247403	+	0.0742208i
$36$		0			0
$37$		−	9.37169i		−	1.54070i	−0.637623	−	0.770348i	$-0.720082\pi$
$37$		−	9.37169i		−	1.54070i	0.637623	−	0.770348i	$-0.279918\pi$
$38$	1.62337	+	5.42682i	0.263346	+	0.880346i
$39$		0			0
$40$	−5.88030	−	2.32854i	−0.929757	−	0.368174i
$41$		−	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
$43$			9.66442i			1.47381i	0.675996	+	0.736905i	$0.263714\pi$
$43$			9.66442i			1.47381i	−0.675996	+	0.736905i	$0.736286\pi$
$44$	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	−0.999196	−	0.0400834i	$-0.987238\pi$
$47$	−7.12494	−	7.12494i	−1.03928	−	1.03928i	−0.0400834	−	0.999196i	$-0.512762\pi$
$48$		0			0
$49$			6.95715i			0.993879i
$50$	−1.04809	−	6.99296i	−0.148222	−	0.988954i
$51$		0			0
$52$		0			0
$53$	11.9572			1.64244			0.821221	−	0.570611i	$-0.193293\pi$
$53$	11.9572			1.64244			0.821221	+	0.570611i	$0.193293\pi$
$54$		0			0
$55$	0.439096	−	0.146365i	0.0592078	−	0.0197359i
$56$	0.448240	+	0.376625i	0.0598986	+	0.0503287i
$57$		0			0
$58$	1.91611	−	0.573183i	0.251597	−	0.0752626i
$59$	9.51806	−	9.51806i	1.23915	−	1.23915i	0.278795	−	0.960351i	$-0.410065\pi$
$59$	9.51806	−	9.51806i	1.23915	−	1.23915i	0.960351	−	0.278795i	$-0.0899350\pi$
$60$		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	$0.701226\pi$
$62$	0.196558	−	0.364346i	0.0249628	−	0.0462720i
$63$		0			0
$64$	−7.88030	+	1.37873i	−0.985037	+	0.172341i
$65$		0			0
$66$		0			0
$67$			13.0790i			1.59785i	0.601431	+	0.798925i	$0.294597\pi$
$67$			13.0790i			1.59785i	−0.601431	+	0.798925i	$0.705403\pi$
$68$	−10.2088	−	2.11266i	−1.23800	−	0.256198i
$69$		0			0
$70$	−0.112663	+	0.644798i	−0.0134659	+	0.0770681i
$71$	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	$-0.573195\pi$
$73$	6.37169	−	6.37169i	0.745750	−	0.745750i	0.973678	+	0.227928i	$0.0731950\pi$
$74$	6.29273	−	11.6644i	0.731515	−	1.35596i
$75$		0			0
$76$	−1.62337	+	7.84449i	−0.186214	+	0.899825i
$77$	−0.0428457			−0.00488272
$78$		0			0
$79$	4.58546			0.515905			0.257952	−	0.966158i	$-0.416952\pi$
$79$	4.58546			0.515905			0.257952	+	0.966158i	$0.416952\pi$
$80$	−5.75536	−	6.84660i	−0.643468	−	0.765473i
$81$		0			0
$82$	2.68585	−	4.97858i	0.296602	−	0.549792i
$83$	8.58546			0.942377			0.471188	−	0.882033i	$-0.343825\pi$
$83$	8.58546			0.942377			0.471188	+	0.882033i	$0.343825\pi$
$84$		0			0
$85$	−3.68585	−	11.0575i	−0.399786	−	1.19936i
$86$	−6.48929	+	12.0288i	−0.699758	+	1.29710i
$87$		0			0
$88$	0.376625	−	0.448240i	0.0401484	−	0.0477826i
$89$	−3.37169			−0.357399			−0.178699	−	0.983904i	$-0.557189\pi$
$89$	−3.37169			−0.357399			−0.178699	+	0.983904i	$0.557189\pi$
$90$		0			0
$91$		0			0
$92$	−1.62337	+	7.84449i	−0.169249	+	0.817845i
$93$		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	−0.865301	−	0.501253i	$-0.832873\pi$
$97$	−3.58546	+	3.58546i	−0.364049	+	0.364049i	0.501253	+	0.865301i	$0.332873\pi$
$98$	−4.67146	+	8.65918i	−0.471889	+	0.874710i
$99$		0			0
$100$	3.39101	−	9.40750i	0.339101	−	0.940750i
$101$	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	0.380904	−	0.924615i	$-0.375613\pi$
$103$	−5.51806	−	5.51806i	−0.543710	−	0.543710i	−0.924615	+	0.380904i	$0.875613\pi$
$104$		0			0
$105$		0			0
$106$	14.8824	+	8.02877i	1.44551	+	0.779823i
$107$	11.3288			1.09520			0.547600	−	0.836740i	$-0.315541\pi$
$107$	11.3288			1.09520			0.547600	+	0.836740i	$0.315541\pi$
$108$		0			0
$109$	10.2713	−	10.2713i	0.983813	−	0.983813i	−0.0160582	−	0.999871i	$-0.505112\pi$
$109$	10.2713	−	10.2713i	0.983813	−	0.983813i	0.999871	+	0.0160582i	$0.00511169\pi$
$110$	0.644798	+	0.112663i	0.0614790	+	0.0107420i
$111$		0			0
$112$	0.305010	+	0.769740i	0.0288208	+	0.0727336i
$113$	1.68585	+	1.68585i	0.158591	+	0.158591i	0.781942	−	0.623351i	$-0.214229\pi$
$113$	1.68585	+	1.68585i	0.158591	+	0.158591i	−0.623351	+	0.781942i	$0.714229\pi$
$114$		0			0
$115$	−8.49663	+	2.83221i	−0.792315	+	0.264105i
$116$	2.76974	+	0.573183i	0.257164	+	0.0532187i
$117$		0			0
$118$	18.2376	−	5.45559i	1.67891	−	0.502227i
$119$			1.07896i			0.0989082i
$120$		0			0
$121$		−	10.9572i		−	0.996105i
$122$	0.966298	+	3.23026i	0.0874845	+	0.292454i
$123$		0			0
$124$	0.489289	−	0.321500i	0.0439394	−	0.0288716i
$125$	11.0000	−	2.00000i	0.983870	−	0.178885i
$126$		0			0
$127$	3.85363	+	3.85363i	0.341955	+	0.341955i	0.857102	−	0.515147i	$-0.172263\pi$
$127$	3.85363	+	3.85363i	0.341955	+	0.341955i	−0.515147	+	0.857102i	$0.672263\pi$
$128$	−10.7339	−	3.57529i	−0.948755	−	0.316014i
$129$		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
$133$	0.829076			0.0718900
$134$	−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	−0.998767	−	0.0496415i	$-0.984192\pi$
$137$	−12.2713	−	12.2713i	−1.04841	−	1.04841i	−0.0496415	−	0.998767i	$-0.515808\pi$
$138$		0			0
$139$	6.53948	−	6.53948i	0.554672	−	0.554672i	−0.373114	−	0.927786i	$-0.621710\pi$
$139$	6.53948	−	6.53948i	0.554672	−	0.554672i	0.927786	+	0.373114i	$0.121710\pi$
$140$	−0.573183	+	0.726895i	−0.0484428	+	0.0614338i
$141$		0			0
$142$	5.70727	+	3.07896i	0.478943	+	0.258381i
$143$		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
$148$	15.6644	−	10.2927i	1.28761	−	0.846057i
$149$	−8.37169	−	8.37169i	−0.685836	−	0.685836i	0.275473	−	0.961309i	$-0.411166\pi$
$149$	−8.37169	−	8.37169i	−0.685836	−	0.685836i	−0.961309	+	0.275473i	$0.911166\pi$
$150$		0			0
$151$		0			0			−	1.00000i	$-0.5\pi$
$151$		0			0				1.00000i	$0.5\pi$
$152$	−7.28780	+	8.67357i	−0.591118	+	0.703519i
$153$		0			0
$154$	−0.0533277	−	0.0287692i	−0.00429727	−	0.00231829i
$155$	0.585462	+	0.292731i	0.0470254	+	0.0235127i
$156$		0			0
$157$	−24.7434			−1.97474			−0.987369	−	0.158440i	$-0.949353\pi$
$157$	−24.7434			−1.97474			−0.987369	+	0.158440i	$0.949353\pi$
$158$	5.70727	+	3.07896i	0.454046	+	0.244949i
$159$		0			0
$160$	−2.56614	−	12.3861i	−0.202872	−	0.979205i
$161$	0.829076			0.0653403
$162$		0			0
$163$	−7.41454			−0.580751			−0.290376	−	0.956913i	$-0.593780\pi$
$163$	−7.41454			−0.580751			−0.290376	+	0.956913i	$0.593780\pi$
$164$	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	−0.998532	−	0.0541655i	$-0.982750\pi$
$167$	−12.2039	+	12.2039i	−0.944366	+	0.944366i	0.0541655	+	0.998532i	$0.482750\pi$
$168$		0			0
$169$	13.0000			1.00000
$170$	2.83714	−	16.2376i	0.217599	−	1.24537i
$171$		0			0
$172$	−16.1537	+	10.6142i	−1.23171	+	0.809328i
$173$		−	14.7434i		−	1.12092i	−0.828182	−	0.560459i	$-0.810625\pi$
$173$		−	14.7434i		−	1.12092i	0.828182	−	0.560459i	$-0.189375\pi$
$174$		0			0
$175$	−1.02456	−	0.146365i	−0.0774493	−	0.0110642i
$176$	0.769740	−	0.305010i	0.0580214	−	0.0229910i
$177$		0			0
$178$	−4.19656	−	2.26396i	−0.314545	−	0.169691i
$179$	9.22533	+	9.22533i	0.689533	+	0.689533i	0.962129	−	0.272595i	$-0.0878821\pi$
$179$	9.22533	+	9.22533i	0.689533	+	0.689533i	−0.272595	+	0.962129i	$0.587882\pi$
$180$		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
$187$	1.07896			0.0789015
$188$	4.08389	−	19.7342i	0.297849	−	1.43927i
$189$		0			0
$190$	−12.4770	−	2.18007i	−0.905177	−	0.158159i
$191$			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	0.721869	−	0.692030i	$-0.243283\pi$
$193$	0.414538	+	0.414538i	0.0298391	+	0.0298391i	−0.692030	+	0.721869i	$0.743283\pi$
$194$	−6.87012	+	2.05512i	−0.493246	+	0.147549i
$195$		0			0
$196$	−11.6286	+	7.64090i	−0.830615	+	0.545778i
$197$		−	8.78623i		−	0.625993i	−0.949754	−	0.312996i	$-0.898667\pi$
$197$		−	8.78623i		−	0.625993i	0.949754	−	0.312996i	$-0.101333\pi$
$198$		0			0
$199$		−	11.7073i		−	0.829906i	−0.909843	−	0.414953i	$-0.863798\pi$
$199$		−	11.7073i		−	0.829906i	0.909843	−	0.414953i	$-0.136202\pi$
$200$	10.5374	−	9.43206i	0.745105	−	0.666947i
$201$		0			0
$202$	19.8733	−	5.94488i	1.39828	−	0.418280i
$203$		−	0.292731i		−	0.0205457i
$204$		0			0
$205$	8.00000	+	4.00000i	0.558744	+	0.279372i
$206$	−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	$0.0418411\pi$
$212$	13.1323	+	19.9859i	0.901929	+	1.37264i
$213$		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
$218$	19.6809	−	5.88734i	1.33296	−	0.398741i
$219$		0			0
$220$	0.726895	+	0.573183i	0.0490072	+	0.0386440i
$221$		0			0
$222$		0			0
$223$	−17.2253	+	17.2253i	−1.15349	+	1.15349i	−0.167646	+	0.985847i	$0.553617\pi$
$223$	−17.2253	+	17.2253i	−1.15349	+	1.15349i	−0.985847	+	0.167646i	$0.946383\pi$
$224$	−0.137222	+	1.16286i	−0.00916852	+	0.0776966i
$225$		0			0
$226$	0.966298	+	3.23026i	0.0642772	+	0.214874i
$227$			8.29273i			0.550408i	0.961386	+	0.275204i	$0.0887454\pi$
$227$			8.29273i			0.550408i	−0.961386	+	0.275204i	$0.911255\pi$
$228$		0			0
$229$	10.2713	+	10.2713i	0.678747	+	0.678747i	0.959717	−	0.280970i	$-0.0906560\pi$
$229$	10.2713	+	10.2713i	0.678747	+	0.678747i	−0.280970	+	0.959717i	$0.590656\pi$
$230$	−12.4770	−	2.18007i	−0.822710	−	0.143749i
$231$		0			0
$232$	3.06247	+	2.57318i	0.201061	+	0.168938i
$233$	−8.27131	+	8.27131i	−0.541871	+	0.541871i	−0.924077	−	0.382206i	$-0.875165\pi$
$233$	−8.27131	+	8.27131i	−0.541871	+	0.541871i	0.382206	+	0.924077i	$0.375165\pi$
$234$		0			0
$235$	21.3748	−	7.12494i	1.39434	−	0.464780i
$236$	26.3625	+	5.45559i	1.71606	+	0.355128i
$237$		0			0
$238$	−0.724481	+	1.34292i	−0.0469611	+	0.0870488i
$239$	3.41454			0.220868			0.110434	−	0.993883i	$-0.464776\pi$
$239$	3.41454			0.220868			0.110434	+	0.993883i	$0.464776\pi$
$240$		0			0
$241$	3.17092			0.204257			0.102129	−	0.994771i	$-0.467435\pi$
$241$	3.17092			0.204257			0.102129	+	0.994771i	$0.467435\pi$
$242$	7.35731	−	13.6378i	0.472946	−	0.876668i
$243$		0			0
$244$	−0.966298	+	4.66936i	−0.0618609	+	0.298925i
$245$	−13.9143	−	6.95715i	−0.888953	−	0.444476i
$246$		0			0
$247$		0			0
$248$	0.824865	−	0.0716150i	0.0523790	−	0.00454755i
$249$		0			0
$250$	15.0340	+	4.89679i	0.950834	+	0.309700i
$251$	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
$253$		−	0.829076i		−	0.0521236i
$254$	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	−0.464458	+	0.885595i	$0.653751\pi$
$257$	−21.6430	+	21.6430i	−1.35005	+	1.35005i	−0.885595	+	0.464458i	$0.846249\pi$
$258$		0			0
$259$	−1.37169	−	1.37169i	−0.0852328	−	0.0852328i
$260$		0			0
$261$		0			0
$262$	−25.3411	+	7.58053i	−1.56558	+	0.468327i
$263$	14.2467	+	14.2467i	0.878492	+	0.878492i	0.993379	−	0.114886i	$-0.0366504\pi$
$263$	14.2467	+	14.2467i	0.878492	+	0.878492i	−0.114886	+	0.993379i	$0.536650\pi$
$264$		0			0
$265$	−11.9572	+	23.9143i	−0.734522	+	1.46904i
$266$	1.03190	+	0.556693i	0.0632701	+	0.0341330i
$267$		0			0
$268$	−21.8610	+	14.3643i	−1.33537	+	0.877442i
$269$	−11.7862	+	11.7862i	−0.718619	+	0.718619i	−0.968322	−	0.249703i	$-0.919667\pi$
$269$	−11.7862	+	11.7862i	−0.718619	+	0.718619i	0.249703	+	0.968322i	$0.419667\pi$
$270$		0			0
$271$		−	11.7073i		−	0.711166i	−0.934645	−	0.355583i	$-0.884282\pi$
$271$		−	11.7073i		−	0.711166i	0.934645	−	0.355583i	$-0.115718\pi$
$272$	−7.68091	−	19.3840i	−0.465724	−	1.17533i
$273$		0			0
$274$	−7.03370	−	23.5131i	−0.424921	−	1.42048i
$275$	−0.146365	+	1.02456i	−0.00882617	+	0.0617832i
$276$		0			0
$277$		−	18.5426i		−	1.11412i	−0.830473	−	0.557059i	$-0.811930\pi$
$277$		−	18.5426i		−	1.11412i	0.830473	−	0.557059i	$-0.188070\pi$
$278$	12.5303	−	3.74832i	0.751520	−	0.224809i
$279$		0			0
$280$	−1.20149	+	0.519855i	−0.0718028	+	0.0310673i
$281$			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
$283$			22.2499i			1.32262i	0.750113	+	0.661309i	$0.229999\pi$
$283$			22.2499i			1.32262i	−0.750113	+	0.661309i	$0.770001\pi$
$284$	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
$290$	−0.769740	+	4.40539i	−0.0452007	+	0.258694i
$291$		0			0
$292$	17.6479	+	3.65214i	1.03277	+	0.213726i
$293$	−21.9143			−1.28025			−0.640124	−	0.768272i	$-0.721117\pi$
$293$	−21.9143			−1.28025			−0.640124	+	0.768272i	$0.721117\pi$
$294$		0			0
$295$	9.51806	+	28.5542i	0.554163	+	1.66249i
$296$	26.4078	−	2.29273i	1.53492	−	0.133262i
$297$		0			0
$298$	−4.79851	−	16.0410i	−0.277970	−	0.929233i
$299$		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
$307$		−	6.33558i		−	0.361590i	−0.983521	−	0.180795i	$-0.942133\pi$
$307$		−	6.33558i		−	0.361590i	0.983521	−	0.180795i	$-0.0578671\pi$
$308$	−0.0470565	−	0.0716150i	−0.00268130	−	0.00408064i
$309$		0			0
$310$	0.532134	+	0.757461i	0.0302232	+	0.0430209i
$311$	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	$-0.788259\pi$
$313$	−3.00000	+	3.00000i	−0.169570	+	0.169570i	0.617220	+	0.786790i	$0.288259\pi$
$314$	−30.7967	−	16.6142i	−1.73796	−	0.937595i
$315$		0			0
$316$	5.03612	+	7.66442i	0.283304	+	0.431157i
$317$	19.9572			1.12091			0.560453	−	0.828186i	$-0.310627\pi$
$317$	19.9572			1.12091			0.560453	+	0.828186i	$0.310627\pi$
$318$		0			0
$319$	−0.292731			−0.0163898
$320$	5.12284	−	17.1393i	0.286375	−	0.958118i
$321$		0			0
$322$	1.03190	+	0.556693i	0.0575058	+	0.0310233i
$323$	−20.8782			−1.16169
$324$		0			0
$325$		0			0
$326$	−9.22846	−	4.97858i	−0.511117	−	0.275738i
$327$		0			0
$328$	11.2713	−	0.978577i	0.622354	−	0.0540329i
$329$	−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	$0.911434\pi$
$332$	9.42923	+	14.3503i	0.517496	+	0.787573i
$333$		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	−0.990008	−	0.141013i	$-0.954964\pi$
$337$	−15.5855	+	15.5855i	−0.848994	+	0.848994i	0.141013	+	0.990008i	$0.454964\pi$
$338$	16.1804	+	8.72900i	0.880096	+	0.474795i
$339$		0			0
$340$	14.4342	−	18.3050i	0.782802	−	0.992729i
$341$	−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
$347$	14.7434			0.791466			0.395733	−	0.918366i	$-0.370491\pi$
$347$	14.7434			0.791466			0.395733	+	0.918366i	$0.370491\pi$
$348$		0			0
$349$	3.64300	−	3.64300i	0.195005	−	0.195005i	−0.602850	−	0.797855i	$-0.705968\pi$
$349$	3.64300	−	3.64300i	0.195005	−	0.195005i	0.797855	+	0.602850i	$0.205968\pi$
$350$	−1.17693	−	0.870125i	−0.0629097	−	0.0465101i
$351$		0			0
$352$	1.16286	+	0.137222i	0.0619804	+	0.00731395i
$353$	−3.68585	−	3.68585i	−0.196178	−	0.196178i	0.602181	−	0.798359i	$-0.294298\pi$
$353$	−3.68585	−	3.68585i	−0.196178	−	0.196178i	−0.798359	+	0.602181i	$0.794298\pi$
$354$		0			0
$355$	−4.58546	+	9.17092i	−0.243371	+	0.486742i
$356$	−3.70306	−	5.63565i	−0.196262	−	0.298689i
$357$		0			0
$358$	5.28780	+	17.6767i	0.279469	+	0.934243i
$359$		−	32.9933i		−	1.74132i	−0.491887	−	0.870659i	$-0.663693\pi$
$359$		−	32.9933i		−	1.74132i	0.491887	−	0.870659i	$-0.336307\pi$
$360$		0			0
$361$		−	2.95715i		−	0.155640i
$362$	−7.06247	+	2.11266i	−0.371195	+	0.111039i
$363$		0			0
$364$		0			0
$365$	6.37169	+	19.1151i	0.333510	+	1.00053i
$366$		0			0
$367$	−18.1035	−	18.1035i	−0.944996	−	0.944996i	0.0535682	−	0.998564i	$-0.482941\pi$
$367$	−18.1035	−	18.1035i	−0.944996	−	0.944996i	−0.998564	+	0.0535682i	$0.982941\pi$
$368$	−14.8947	+	5.90203i	−0.776439	+	0.307665i
$369$		0			0
$370$	17.0361	+	24.2499i	0.885665	+	1.26069i
$371$	1.75011	−	1.75011i	0.0908614	−	0.0908614i
$372$		0			0
$373$	13.9143			0.720456			0.360228	−	0.932864i	$-0.382699\pi$
$373$	13.9143			0.720456			0.360228	+	0.932864i	$0.382699\pi$
$374$	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	−0.480783	−	0.876840i	$-0.659647\pi$
$379$	7.71040	−	7.71040i	0.396057	−	0.396057i	0.876840	+	0.480783i	$0.159647\pi$
$380$	−14.0656	−	11.0912i	−0.721550	−	0.568969i
$381$		0			0
$382$	−4.25410	+	7.88554i	−0.217658	+	0.403459i
$383$	−14.8322	+	14.8322i	−0.757891	+	0.757891i	−0.975938	−	0.218048i	$-0.930031\pi$
$383$	−14.8322	+	14.8322i	−0.757891	+	0.757891i	0.218048	+	0.975938i	$0.430031\pi$
$384$		0			0
$385$	0.0428457	−	0.0856914i	0.00218362	−	0.00436724i
$386$	0.237606	+	0.794299i	0.0120938	+	0.0404287i
$387$		0			0
$388$	−9.93080	−	2.05512i	−0.504160	−	0.104333i
$389$	−16.3717	−	16.3717i	−0.830078	−	0.830078i	0.157449	−	0.987527i	$-0.449673\pi$
$389$	−16.3717	−	16.3717i	−0.830078	−	0.830078i	−0.987527	+	0.157449i	$0.949673\pi$
$390$		0			0
$391$	−20.8782			−1.05586
$392$	−19.6041	+	1.70203i	−0.990154	+	0.0859654i
$393$		0			0
$394$	5.89962	−	10.9357i	0.297218	−	0.550934i
$395$	−4.58546	+	9.17092i	−0.230720	+	0.461439i
$396$		0			0
$397$	0.628308			0.0315339			0.0157669	−	0.999876i	$-0.494981\pi$
$397$	0.628308			0.0315339			0.0157669	+	0.999876i	$0.494981\pi$
$398$	7.86098	−	14.5714i	0.394035	−	0.730398i
$399$		0			0
$400$	19.4485	−	4.66412i	0.972427	−	0.233206i
$401$	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	$-0.906106\pi$
$409$	−38.7005			−1.91362			−0.956809	+	0.290716i	$0.906106\pi$
$410$	7.27131	+	10.3503i	0.359104	+	0.511163i
$411$		0			0
$412$	3.16286	−	15.2836i	0.155823	−	0.752968i
$413$		−	2.78623i		−	0.137101i
$414$		0			0
$415$	−8.58546	+	17.1709i	−0.421444	+	0.842888i
$416$		0			0
$417$		0			0
$418$	0.556693	−	1.03190i	0.0272287	−	0.0504721i
$419$	9.81079	+	9.81079i	0.479288	+	0.479288i	0.904904	−	0.425616i	$-0.139942\pi$
$419$	9.81079	+	9.81079i	0.479288	+	0.479288i	−0.425616	+	0.904904i	$0.639942\pi$
$420$		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	$0.496191\pi$
$422$	23.9449	−	7.16286i	1.16562	−	0.348682i
$423$		0			0
$424$	2.92525	+	33.6932i	0.142063	+	1.63629i
$425$	25.8009	+	3.68585i	1.25153	+	0.178790i
$426$		0			0
$427$	0.493499			0.0238821
$428$	12.4422	+	18.9357i	0.601418	+	0.915293i
$429$		0			0
$430$	−17.5682	−	25.0073i	−0.847216	−	1.20596i
$431$		−	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	0.458329	−	0.888783i	$-0.348448\pi$
$433$	−8.95715	−	8.95715i	−0.430453	−	0.430453i	−0.888783	+	0.458329i	$0.848448\pi$
$434$	−0.0245584	−	0.0820969i	−0.00117884	−	0.00394078i
$435$		0			0
$436$	28.4489	+	5.88734i	1.36245	+	0.281952i
$437$			16.0428i			0.767433i
$438$		0			0
$439$			7.03612i			0.335815i	0.985803	+	0.167908i	$0.0537011\pi$
$439$			7.03612i			0.335815i	−0.985803	+	0.167908i	$0.946299\pi$
$440$	0.519855	+	1.20149i	0.0247831	+	0.0572788i
$441$		0			0
$442$		0			0
$443$			33.8652i			1.60898i	0.593964	+	0.804492i	$0.297562\pi$
$443$			33.8652i			1.60898i	−0.593964	+	0.804492i	$0.702438\pi$
$444$		0			0
$445$	3.37169	−	6.74338i	0.159834	−	0.319667i
$446$	−33.0055	+	9.87326i	−1.56286	+	0.467512i
$447$		0			0
$448$	−0.951605	+	1.35520i	−0.0449591	+	0.0640273i
$449$			32.1151i			1.51560i	0.652484	+	0.757802i	$0.273727\pi$
$449$			32.1151i			1.51560i	−0.652484	+	0.757802i	$0.726273\pi$
$450$		0			0
$451$	−0.585462	+	0.585462i	−0.0275683	+	0.0275683i
$452$	−0.966298	+	4.66936i	−0.0454508	+	0.219628i
$453$		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	$-0.203354\pi$
$457$	4.41454	+	4.41454i	0.206503	+	0.206503i	−0.596276	+	0.802779i	$0.703354\pi$
$458$	5.88734	+	19.6809i	0.275097	+	0.919629i
$459$		0			0
$460$	−14.0656	−	11.0912i	−0.655812	−	0.517132i
$461$	−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	$-0.720936\pi$
$463$	2.77467	−	2.77467i	0.128950	−	0.128950i	0.768636	+	0.639686i	$0.220936\pi$
$464$	2.08389	+	5.25903i	0.0967424	+	0.244144i
$465$		0			0
$466$	−15.8487	+	4.74097i	−0.734177	+	0.219621i
$467$		−	23.0361i		−	1.06598i	−0.846120	−	0.532992i	$-0.821068\pi$
$467$		−	23.0361i		−	1.06598i	0.846120	−	0.532992i	$-0.178932\pi$
$468$		0			0
$469$	1.91431	+	1.91431i	0.0883946	+	0.0883946i
$470$	31.3882	+	5.48436i	1.44783	+	0.252974i
$471$		0			0
$472$	29.1488	+	24.4917i	1.34168	+	1.12732i
$473$	1.41454	−	1.41454i	0.0650405	−	0.0650405i
$474$		0			0
$475$	2.83221	−	19.8255i	0.129951	−	0.909655i
$476$	−1.80344	+	1.18500i	−0.0826606	+	0.0543144i
$477$		0			0
$478$	4.24989	+	2.29273i	0.194385	+	0.104867i
$479$	20.5855			0.940574			0.470287	−	0.882514i	$-0.344150\pi$
$479$	20.5855			0.940574			0.470287	+	0.882514i	$0.344150\pi$
$480$		0			0
$481$		0			0
$482$	3.94667	+	2.12915i	0.179766	+	0.0969803i
$483$		0			0
$484$	18.3145	−	12.0340i	0.832476	−	0.547000i
$485$	−3.58546	−	10.7564i	−0.162807	−	0.488422i
$486$		0			0
$487$	5.31729	−	5.31729i	0.240949	−	0.240949i	−0.576293	−	0.817243i	$-0.695501\pi$
$487$	5.31729	−	5.31729i	0.240949	−	0.240949i	0.817243	+	0.576293i	$0.195501\pi$
$488$	−4.33799	+	5.16286i	−0.196372	+	0.233711i
$489$		0			0
$490$	−12.6469	−	18.0021i	−0.571329	−	0.813252i
$491$	−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
$493$			7.37169i			0.332004i
$494$		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	0.767653	−	0.640866i	$-0.221424\pi$
$499$	2.83221	+	2.83221i	0.126787	+	0.126787i	−0.640866	+	0.767653i	$0.721424\pi$
$500$	15.4240	+	16.1895i	0.689782	+	0.724017i
$501$		0			0
$502$	2.20884	+	7.38397i	0.0985852	+	0.329563i
$503$	−7.32571	−	7.32571i	−0.326637	−	0.326637i	0.524669	−	0.851306i	$-0.324189\pi$
$503$	−7.32571	−	7.32571i	−0.326637	−	0.326637i	−0.851306	+	0.524669i	$0.824189\pi$
$504$		0			0
$505$	10.3717	+	31.1151i	0.461534	+	1.38460i
$506$	0.556693	−	1.03190i	0.0247480	−	0.0458738i
$507$		0			0
$508$	−2.20884	+	10.6736i	−0.0980013	+	0.473563i
$509$	10.1709	−	10.1709i	0.450818	−	0.450818i	−0.444808	−	0.895626i	$-0.646728\pi$
$509$	10.1709	−	10.1709i	0.450818	−	0.450818i	0.895626	+	0.444808i	$0.146728\pi$
$510$		0			0
$511$		−	1.86519i		−	0.0825112i
$512$	−5.81289	−	21.8680i	−0.256896	−	0.966439i
$513$		0			0
$514$	−41.4703	+	12.4054i	−1.82918	+	0.547178i
$515$	16.5542	−	5.51806i	0.729464	−	0.243155i
$516$		0			0
$517$			2.08569i			0.0917286i
$518$	−0.786230	−	2.62831i	−0.0345450	−	0.115481i
$519$		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
$523$			5.07896i			0.222087i	0.993816	+	0.111044i	$0.0354194\pi$
$523$			5.07896i			0.222087i	−0.993816	+	0.111044i	$0.964581\pi$
$524$	−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
$530$	−30.9399	+	21.7360i	−1.34395	+	0.944153i
$531$		0			0
$532$	0.910557	+	1.38577i	0.0394776	+	0.0600807i
$533$		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
$538$	−22.5837	+	6.75566i	−0.973651	+	0.291257i
$539$	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	$0.453679\pi$
$542$	7.86098	−	14.5714i	0.337658	−	0.625895i
$543$		0			0
$544$	3.45559	−	29.2836i	0.148157	−	1.25552i
$545$	10.2713	+	30.8139i	0.439974	+	1.31992i
$546$		0			0
$547$			33.6644i			1.43939i	0.694292	+	0.719693i	$0.255718\pi$
$547$			33.6644i			1.43939i	−0.694292	+	0.719693i	$0.744282\pi$
$548$	7.03370	−	33.9883i	0.300465	−	1.45191i
$549$		0			0
$550$	−0.870125	+	1.17693i	−0.0371022	+	0.0501845i
$551$	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
$557$	−8.82908			−0.374100			−0.187050	−	0.982350i	$-0.559893\pi$
$557$	−8.82908			−0.374100			−0.187050	+	0.982350i	$0.559893\pi$
$558$		0			0
$559$		0			0
$560$	−1.84449	−	0.159720i	−0.0779440	−	0.00674940i
$561$		0			0
$562$	−1.76481	+	3.27131i	−0.0744439	+	0.137992i
$563$	−6.74338			−0.284200			−0.142100	−	0.989852i	$-0.545385\pi$
$563$	−6.74338			−0.284200			−0.142100	+	0.989852i	$0.545385\pi$
$564$		0			0
$565$	−5.05754	+	1.68585i	−0.212772	+	0.0709241i
$566$	−14.9399	+	27.6932i	−0.627973	+	1.16403i
$567$		0			0
$568$	1.12181	+	12.9210i	0.0470700	+	0.542155i
$569$	23.3717			0.979792			0.489896	−	0.871781i	$-0.337035\pi$
$569$	23.3717			0.979792			0.489896	+	0.871781i	$0.337035\pi$
$570$		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	−0.0966991	−	0.995314i	$-0.530828\pi$
$577$	21.5855	−	21.5855i	0.898615	−	0.898615i	0.995314	+	0.0966991i	$0.0308285\pi$
$578$	6.82938	−	12.6592i	0.284065	−	0.526553i
$579$		0			0
$580$	−3.91611	+	4.96630i	−0.162607	+	0.206214i
$581$	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
$587$	16.5855			0.684555			0.342278	−	0.939599i	$-0.388802\pi$
$587$	16.5855			0.684555			0.342278	+	0.939599i	$0.388802\pi$
$588$		0			0
$589$	0.829076	−	0.829076i	0.0341615	−	0.0341615i
$590$	−7.32643	+	41.9308i	−0.301624	+	1.72626i
$591$		0			0
$592$	34.4078	+	14.8782i	1.41415	+	0.611490i
$593$	−8.85677	−	8.85677i	−0.363704	−	0.363704i	0.501471	−	0.865175i	$-0.332793\pi$
$593$	−8.85677	−	8.85677i	−0.363704	−	0.363704i	−0.865175	+	0.501471i	$0.832793\pi$
$594$		0			0
$595$	−2.15792	−	1.07896i	−0.0884662	−	0.0442331i
$596$	4.79851	−	23.1874i	0.196555	−	0.949793i
$597$		0			0
$598$		0			0
$599$		−	24.9933i		−	1.02120i	−0.859819	−	0.510599i	$-0.829424\pi$
$599$		−	24.9933i		−	1.02120i	0.859819	−	0.510599i	$-0.170576\pi$
$600$		0			0
$601$		−	39.8286i		−	1.62464i	−0.583210	−	0.812322i	$-0.698203\pi$
$601$		−	39.8286i		−	1.62464i	0.583210	−	0.812322i	$-0.301797\pi$
$602$	0.810789	+	2.71040i	0.0330453	+	0.110468i
$603$		0			0
$604$		0			0
$605$	21.9143	+	10.9572i	0.890943	+	0.445472i
$606$		0			0
$607$	−16.8469	−	16.8469i	−0.683795	−	0.683795i	0.277058	−	0.960853i	$-0.410640\pi$
$607$	−16.8469	−	16.8469i	−0.683795	−	0.683795i	−0.960853	+	0.277058i	$0.910640\pi$
$608$	−22.5016	−	2.65528i	−0.912559	−	0.107686i
$609$		0			0
$610$	−7.42682	−	1.29766i	−0.300703	−	0.0525409i
$611$		0			0
$612$		0			0
$613$	8.62831			0.348494			0.174247	−	0.984702i	$-0.444251\pi$
$613$	8.62831			0.348494			0.174247	+	0.984702i	$0.444251\pi$
$614$	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	$-0.351520\pi$
$617$	−11.0147	−	11.0147i	−0.443435	−	0.443435i	−0.893165	+	0.449730i	$0.851520\pi$
$618$		0			0
$619$	6.53948	−	6.53948i	0.262844	−	0.262844i	−0.563365	−	0.826208i	$-0.690493\pi$
$619$	6.53948	−	6.53948i	0.262844	−	0.262844i	0.826208	+	0.563365i	$0.190493\pi$
$620$	0.153712	+	1.30008i	0.00617322	+	0.0522124i
$621$		0			0
$622$	9.12181	+	4.92104i	0.365751	+	0.197316i
$623$	−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
$628$	−27.1751	−	41.3576i	−1.08441	−	1.65035i
$629$	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	$0.184054\pi$
$632$	1.12181	+	12.9210i	0.0446231	+	0.513971i
$633$		0			0
$634$	24.8396	+	13.4005i	0.986505	+	0.532200i
$635$	−11.5609	+	3.85363i	−0.458780	+	0.152927i
$636$		0			0
$637$		0			0
$638$	−0.364346	−	0.196558i	−0.0144246	−	0.00778179i
$639$		0			0
$640$	17.8845	−	17.8926i	0.706947	−	0.707266i
$641$	−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
$643$	38.0722			1.50142			0.750711	−	0.660631i	$-0.229711\pi$
$643$	38.0722			1.50142			0.750711	+	0.660631i	$0.229711\pi$
$644$	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	−0.679693	−	0.733497i	$-0.737887\pi$
$647$	1.36856	−	1.36856i	0.0538035	−	0.0538035i	0.733497	+	0.679693i	$0.237887\pi$
$648$		0			0
$649$	−2.78623			−0.109369
$650$		0			0
$651$		0			0
$652$	−8.14323	−	12.3931i	−0.318913	−	0.485352i
$653$		−	17.9572i		−	0.702718i	−0.936241	−	0.351359i	$-0.885720\pi$
$653$		−	17.9572i		−	0.702718i	0.936241	−	0.351359i	$-0.114280\pi$
$654$		0			0
$655$	−13.2253	−	39.6760i	−0.516756	−	1.55027i
$656$	14.6858	+	6.35027i	0.573386	+	0.247936i
$657$		0			0
$658$	−2.59594	−	1.40046i	−0.101200	−	0.0545957i
$659$	11.1825	+	11.1825i	0.435608	+	0.435608i	0.890531	−	0.454923i	$-0.150333\pi$
$659$	11.1825	+	11.1825i	0.435608	+	0.435608i	−0.454923	+	0.890531i	$0.650333\pi$
$660$		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	$0.276423\pi$
$662$	−7.16286	−	23.9449i	−0.278392	−	0.930644i
$663$		0			0
$664$	2.10038	+	24.1923i	0.0815107	+	0.938845i
$665$	−0.829076	+	1.65815i	−0.0321502	+	0.0643004i
$666$		0			0
$667$	5.66442			0.219327
$668$	−33.8016	−	6.99507i	−1.30782	−	0.270647i
$669$		0			0
$670$	−23.7753	−	33.8427i	−0.918520	−	1.30746i
$671$		−	0.493499i		−	0.0190513i
$672$		0			0
$673$	−12.5725	−	12.5725i	−0.484633	−	0.484633i	0.421975	−	0.906608i	$-0.361337\pi$
$673$	−12.5725	−	12.5725i	−0.484633	−	0.484633i	−0.906608	+	0.421975i	$0.861337\pi$
$674$	−29.8634	+	8.93332i	−1.15029	+	0.344099i
$675$		0			0
$676$	14.2776	+	21.7290i	0.549139	+	0.835731i
$677$		−	16.7862i		−	0.645147i	−0.946544	−	0.322574i	$-0.895452\pi$
$677$		−	16.7862i		−	0.645147i	0.946544	−	0.322574i	$-0.104548\pi$
$678$		0			0
$679$			1.04958i			0.0402790i
$680$	30.2565	−	13.0912i	1.16028	−	0.502026i
$681$		0			0
$682$	−0.0820969	+	0.0245584i	−0.00314365	+	0.000940391i
$683$		−	0.378422i		−	0.0144799i	−0.999974	−	0.00723997i	$-0.997695\pi$
$683$		−	0.378422i		−	0.0144799i	0.999974	−	0.00723997i	$-0.00230457\pi$
$684$		0			0
$685$	36.8139	−	12.2713i	1.40659	−	0.468863i
$686$	1.17092	+	3.91431i	0.0447061	+	0.149449i
$687$		0			0
$688$	−35.4826	−	15.3429i	−1.35276	−	0.584943i
$689$		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	$0.182747\pi$
$692$	24.6430	−	16.1923i	0.936786	−	0.615541i
$693$		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
$698$	6.98037	−	2.08810i	0.264211	−	0.0790359i
$699$		0			0
$700$	−0.880607	−	1.87326i	−0.0332838	−	0.0708026i
$701$	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
$707$		−	3.03612i		−	0.114185i
$708$		0			0
$709$	21.6858	+	21.6858i	0.814429	+	0.814429i	0.985294	−	0.170865i	$-0.0546563\pi$
$709$	21.6858	+	21.6858i	0.814429	+	0.814429i	−0.170865	+	0.985294i	$0.554656\pi$
$710$	−11.8652	+	8.33558i	−0.445293	+	0.312829i
$711$		0			0
$712$	−0.824865	−	9.50085i	−0.0309131	−	0.356059i
$713$	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
$718$	22.1537	−	41.0649i	0.826769	−	1.53253i
$719$	8.00000			0.298350			0.149175	−	0.988811i	$-0.452338\pi$
$719$	8.00000			0.298350			0.149175	+	0.988811i	$0.452338\pi$
$720$		0			0
$721$	−1.61531			−0.0601572
$722$	1.98562	−	3.68061i	0.0738970	−	0.136978i
$723$		0			0
$724$	−10.2088	−	2.11266i	−0.379408	−	0.0785165i
$725$	−7.00000	−	1.00000i	−0.259973	−	0.0371391i
$726$		0			0
$727$	33.6331	−	33.6331i	1.24738	−	1.24738i	0.290513	−	0.956871i	$-0.406174\pi$
$727$	33.6331	−	33.6331i	1.24738	−	1.24738i	0.956871	−	0.290513i	$-0.0938259\pi$
$728$		0			0
$729$		0			0
$730$	−4.90455	+	28.0698i	−0.181525	+	1.03891i
$731$	−35.6216	−	35.6216i	−1.31751	−	1.31751i
$732$		0			0
$733$		−	20.1151i		−	0.742967i	−0.928439	−	0.371484i	$-0.878849\pi$
$733$		−	20.1151i		−	0.742967i	0.928439	−	0.371484i	$-0.121151\pi$
$734$	−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	0.300666	−	0.953730i	$-0.402791\pi$
$739$	−17.7533	−	17.7533i	−0.653064	−	0.653064i	−0.953730	+	0.300666i	$0.902791\pi$
$740$	4.92104	+	41.6216i	0.180901	+	1.53004i
$741$		0			0
$742$	3.35341	−	1.00314i	0.123107	−	0.0368263i
$743$	0.203904	+	0.203904i	0.00748051	+	0.00748051i	0.710837	−	0.703357i	$-0.248316\pi$
$743$	0.203904	+	0.203904i	0.00748051	+	0.00748051i	−0.703357	+	0.710837i	$0.748316\pi$
$744$		0			0
$745$	25.1151	−	8.37169i	0.920145	−	0.306715i
$746$	17.3184	+	9.34292i	0.634070	+	0.342069i
$747$		0			0
$748$	1.18500	+	1.80344i	0.0433279	+	0.0659404i
$749$	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	$0.985763\pi$
$752$	37.4703	−	14.8476i	1.36640	−	0.541437i
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$		−	37.2860i		−	1.35518i	−0.735439	−	0.677591i	$-0.763024\pi$
$757$		−	37.2860i		−	1.35518i	0.735439	−	0.677591i	$-0.236976\pi$
$758$	14.7740	−	4.41947i	0.536614	−	0.160522i
$759$		0			0
$760$	−10.0593	−	23.2492i	−0.364890	−	0.843336i
$761$			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
$763$		−	3.00673i		−	0.108851i
$764$	−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	$-0.981545\pi$
$769$		−	3.21377i		−	0.115891i	0.998320	−	0.0579457i	$-0.0184550\pi$
$770$	0.110866	−	0.0778861i	0.00399534	−	0.00280682i
$771$		0			0
$772$	−0.237606	+	1.14816i	−0.00855163	+	0.0413233i
$773$	42.6148			1.53275			0.766375	−	0.642394i	$-0.222059\pi$
$773$	42.6148			1.53275			0.766375	+	0.642394i	$0.222059\pi$
$774$		0			0
$775$	−1.17092	+	0.878193i	−0.0420608	+	0.0315456i
$776$	−10.9804	−	9.22605i	−0.394172	−	0.331196i
$777$		0			0
$778$	−9.38397	−	31.3699i	−0.336432	−	1.12467i
$779$	11.3288	−	11.3288i	0.405898	−	0.405898i
$780$		0			0
$781$	−0.671153	−	0.671153i	−0.0240158	−	0.0240158i
$782$	−25.9859	−	14.0189i	−0.929255	−	0.501315i
$783$		0			0
$784$	−25.5429	−	11.0450i	−0.912247	−	0.394463i
$785$	24.7434	−	49.4868i	0.883129	−	1.76626i
$786$		0			0
$787$		−	47.2369i		−	1.68381i	−0.539623	−	0.841907i	$-0.681433\pi$
$787$		−	47.2369i		−	1.68381i	0.539623	−	0.841907i	$-0.318567\pi$
$788$	14.6858	−	9.64973i	0.523162	−	0.343757i
$789$		0			0
$790$	−11.8652	+	8.33558i	−0.422145	+	0.296567i
$791$	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
$797$	−19.8715			−0.703883			−0.351942	−	0.936022i	$-0.614478\pi$
$797$	−19.8715			−0.703883			−0.351942	+	0.936022i	$0.614478\pi$
$798$		0			0
$799$	52.5229			1.85813
$800$	27.3383	+	7.25379i	0.966555	+	0.256460i
$801$		0			0
$802$	10.6325	+	5.73604i	0.375447	+	0.202547i
$803$	−1.86519			−0.0658212
$804$		0			0
$805$	−0.829076	+	1.65815i	−0.0292211	+	0.0584422i
$806$		0			0
$807$		0			0
$808$	31.7630	+	26.6883i	1.11742	+	0.938890i
$809$	−38.3158			−1.34711			−0.673557	−	0.739136i	$-0.735234\pi$
$809$	−38.3158			−1.34711			−0.673557	+	0.739136i	$0.735234\pi$
$810$		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	$0.690348\pi$
$812$	0.489289	−	0.321500i	0.0171707	−	0.0112824i
$813$		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
$818$	−48.1684	−	25.9859i	−1.68417	−	0.908577i
$819$		0			0
$820$	2.10038	+	17.7648i	0.0733486	+	0.620374i
$821$	−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	−0.997054	−	0.0767084i	$-0.975559\pi$
$823$	−30.8041	−	30.8041i	−1.07376	−	1.07376i	−0.0767084	−	0.997054i	$-0.524441\pi$
$824$	14.1990	−	16.8989i	0.494645	−	0.588701i
$825$		0			0
$826$	1.87085	−	3.46787i	0.0650951	−	0.120662i
$827$	23.9143			0.831582			0.415791	−	0.909460i	$-0.363505\pi$
$827$	23.9143			0.831582			0.415791	+	0.909460i	$0.363505\pi$
$828$		0			0
$829$	−8.47208	+	8.47208i	−0.294247	+	0.294247i	−0.838756	−	0.544508i	$-0.816716\pi$
$829$	−8.47208	+	8.47208i	−0.294247	+	0.294247i	0.544508	+	0.838756i	$0.316716\pi$
$830$	−22.2155	+	15.6069i	−0.771110	+	0.541723i
$831$		0			0
$832$		0			0
$833$	−25.6430	−	25.6430i	−0.888477	−	0.888477i
$834$		0			0
$835$	−12.2039	−	36.6117i	−0.422334	−	1.26700i
$836$	1.38577	−	0.910557i	0.0479278	−	0.0314923i
$837$		0			0
$838$	5.62337	+	18.7985i	0.194256	+	0.649384i
$839$			49.5787i			1.71165i	0.517267	+	0.855824i	$0.326949\pi$
$839$			49.5787i			1.71165i	−0.517267	+	0.855824i	$0.673051\pi$
$840$		0			0
$841$			27.0000i			0.931034i
$842$	−38.8420	+	11.6192i	−1.33858	+	0.400423i
$843$		0			0
$844$	34.6124	+	7.16286i	1.19141	+	0.246556i
$845$	−13.0000	+	26.0000i	−0.447214	+	0.894427i
$846$		0			0
$847$	−1.60375	−	1.60375i	−0.0551055	−	0.0551055i
$848$	−18.9828	+	43.9002i	−0.651872	+	1.50754i
$849$		0			0
$850$	29.6381	+	21.9119i	1.01658	+	0.751572i
$851$	26.5426	−	26.5426i	0.909869	−	0.909869i
$852$		0			0
$853$	−28.6283			−0.980215			−0.490107	−	0.871662i	$-0.663042\pi$
$853$	−28.6283			−0.980215			−0.490107	+	0.871662i	$0.663042\pi$
$854$	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	$-0.243083\pi$
$857$	0.899616	+	0.899616i	0.0307303	+	0.0307303i	−0.691575	+	0.722305i	$0.743083\pi$
$858$		0			0
$859$	−38.0754	+	38.0754i	−1.29911	+	1.29911i	−0.370138	+	0.928977i	$0.620690\pi$
$859$	−38.0754	+	38.0754i	−1.29911	+	1.29911i	−0.928977	+	0.370138i	$0.879310\pi$
$860$	−5.07475	−	42.9217i	−0.173048	−	1.46362i
$861$		0			0
$862$	19.5254	−	36.1930i	0.665038	−	1.23274i
$863$	3.12494	−	3.12494i	0.106374	−	0.106374i	−0.651916	−	0.758291i	$-0.726035\pi$
$863$	3.12494	−	3.12494i	0.106374	−	0.106374i	0.758291	+	0.651916i	$0.226035\pi$
$864$		0			0
$865$	29.4868	+	14.7434i	1.00258	+	0.501290i
$866$	−5.13409	−	17.1629i	−0.174463	−	0.583218i
$867$		0			0
$868$	0.0245584	−	0.118671i	0.000833567	−	0.00402797i
$869$	−0.671153	−	0.671153i	−0.0227673	−	0.0227673i
$870$		0			0
$871$		0			0
$872$	31.4556	+	26.4300i	1.06522	+	0.895031i
$873$		0			0
$874$	−10.7722	+	19.9676i	−0.364374	+	0.675415i
$875$	1.31729	−	1.90275i	0.0445325	−	0.0643247i
$876$		0			0
$877$	−0.743385			−0.0251023			−0.0125512	−	0.999921i	$-0.503995\pi$
$877$	−0.743385			−0.0251023			−0.0125512	+	0.999921i	$0.503995\pi$
$878$	−4.72448	+	8.75746i	−0.159444	+	0.295550i
$879$		0			0
$880$	−0.159720	+	1.84449i	−0.00538416	+	0.0621778i
$881$	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
$883$	32.9870			1.11010			0.555050	−	0.831817i	$-0.312699\pi$
$883$	32.9870			1.11010			0.555050	+	0.831817i	$0.312699\pi$
$884$		0			0
$885$		0			0
$886$	−22.7392	+	42.1501i	−0.763937	+	1.41606i
$887$	5.16779	−	5.16779i	0.173517	−	0.173517i	−0.615005	−	0.788523i	$-0.710846\pi$
$887$	5.16779	−	5.16779i	0.173517	−	0.173517i	0.788523	+	0.615005i	$0.210846\pi$
$888$		0			0
$889$	1.12808			0.0378345
$890$	8.72448	−	6.12915i	0.292445	−	0.205450i
$891$		0			0
$892$	−47.7097	−	9.87326i	−1.59744	−	0.330581i
$893$		−	40.3587i		−	1.35055i
$894$		0			0
$895$	−27.6760	+	9.22533i	−0.925106	+	0.308369i
$896$	−2.09438	+	1.04778i	−0.0699682	+	0.0350038i
$897$		0			0
$898$	−21.5640	+	39.9718i	−0.719601	+	1.33388i
$899$	−0.292731	−	0.292731i	−0.00976312	−	0.00976312i
$900$		0			0
$901$	−44.0722	+	44.0722i	−1.46826	+	1.46826i
$902$	−1.12181	+	0.335577i	−0.0373521	+	0.0111735i
$903$		0			0
$904$	−4.33799	+	5.16286i	−0.144279	+	0.171714i
$905$	−3.68585	−	11.0575i	−0.122522	−	0.367565i
$906$		0			0
$907$	−6.74338			−0.223910			−0.111955	−	0.993713i	$-0.535711\pi$
$907$	−6.74338			−0.223910			−0.111955	+	0.993713i	$0.535711\pi$
$908$	−13.8610	+	9.10773i	−0.459993	+	0.302251i
$909$		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
$917$			3.87146i			0.127847i
$918$		0			0
$919$		−	25.8652i		−	0.853214i	−0.904437	−	0.426607i	$-0.859709\pi$
$919$		−	25.8652i		−	0.853214i	0.904437	−	0.426607i	$-0.140291\pi$
$920$	−10.0593	−	23.2492i	−0.331646	−	0.766502i
$921$		0			0
$922$	−2.84136	−	9.49843i	−0.0935751	−	0.312814i
$923$		0			0
$924$		0			0
$925$	−37.4868	+	28.1151i	−1.23256	+	0.924418i
$926$	5.31657	−	1.59039i	0.174713	−	0.0522636i
$927$		0			0
$928$	−0.937529	+	7.94488i	−0.0307759	+	0.260803i
$929$		−	37.2003i		−	1.22050i	−0.792208	−	0.610251i	$-0.791068\pi$
$929$		−	37.2003i		−	1.22050i	0.792208	−	0.610251i	$-0.208932\pi$
$930$		0			0
$931$	−19.7041	+	19.7041i	−0.645777	+	0.645777i
$932$	−22.9094	−	4.74097i	−0.750422	−	0.155296i
$933$		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	$-0.0895020\pi$
$937$	20.9143	+	20.9143i	0.683241	+	0.683241i	−0.277488	+	0.960729i	$0.589502\pi$
$938$	1.09725	+	3.66802i	0.0358264	+	0.119765i
$939$		0			0
$940$	35.3846	+	27.9020i	1.15412	+	0.910064i
$941$	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
$947$		−	20.7925i		−	0.675666i	−0.941206	−	0.337833i	$-0.890306\pi$
$947$		−	20.7925i		−	0.675666i	0.941206	−	0.337833i	$-0.109694\pi$
$948$		0			0
$949$		0			0
$950$	16.8371	−	22.7740i	0.546269	−	0.738885i
$951$		0			0
$952$	−3.04033	+	0.263962i	−0.0985375	+	0.00855505i
$953$	16.3142	−	16.3142i	0.528467	−	0.528467i	−0.391648	−	0.920115i	$-0.628095\pi$
$953$	16.3142	−	16.3142i	0.528467	−	0.528467i	0.920115	+	0.391648i	$0.128095\pi$
$954$		0			0
$955$	−12.6712	−	6.33558i	−0.410029	−	0.205014i
$956$	3.75011	+	5.70727i	0.121287	+	0.184586i
$957$		0			0
$958$	25.6216	+	13.8223i	0.827796	+	0.446580i
$959$	−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
$965$	−1.24361	+	0.414538i	−0.0400334	+	0.0133445i
$966$		0			0
$967$	−19.5672	+	19.5672i	−0.629238	+	0.629238i	−0.947876	−	0.318638i	$-0.896774\pi$
$967$	−19.5672	+	19.5672i	−0.629238	+	0.629238i	0.318638	+	0.947876i	$0.396774\pi$
$968$	30.8754	−	2.68061i	0.992372	−	0.0861579i
$969$		0			0
$970$	2.75987	−	15.7954i	0.0886142	−	0.507159i
$971$	−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
$973$		−	1.91431i		−	0.0613699i
$974$	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	−0.109598	−	0.993976i	$-0.534956\pi$
$977$	27.6430	−	27.6430i	0.884378	−	0.884378i	0.993976	+	0.109598i	$0.0349564\pi$
$978$		0			0
$979$	0.493499	+	0.493499i	0.0157723	+	0.0157723i
$980$	−3.65317	−	30.8981i	−0.116696	−	0.987004i
$981$		0			0
$982$	−12.3338	−	41.2309i	−0.393587	−	1.31573i
$983$	22.1611	+	22.1611i	0.706828	+	0.706828i	0.965867	−	0.259039i	$-0.0834058\pi$
$983$	22.1611	+	22.1611i	0.706828	+	0.706828i	−0.259039	+	0.965867i	$0.583406\pi$
$984$		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	$0.699876\pi$
$992$	1.02563	+	1.30008i	0.0325639	+	0.0412775i
$993$		0			0
$994$	1.28600	−	0.384694i	0.0407895	−	0.0122017i
$995$	23.4145	+	11.7073i	0.742291	+	0.371145i
$996$		0			0
$997$			19.9143i			0.630692i	0.948977	+	0.315346i	$0.102121\pi$
$997$			19.9143i			0.630692i	−0.948977	+	0.315346i	$0.897879\pi$
$998$	1.62337	+	5.42682i	0.0513870	+	0.171783i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.z.e.163.3		6
3.2	odd	2		240.2.y.d.163.1	✓	6
5.2	odd	4		720.2.bd.e.307.1		6
12.11	even	2		960.2.y.d.943.2		6
15.2	even	4		240.2.bc.d.67.3	yes	6
16.11	odd	4		720.2.bd.e.523.1		6
24.5	odd	2		1920.2.y.g.223.2		6
24.11	even	2		1920.2.y.h.223.2		6
48.5	odd	4		960.2.bc.d.463.2		6
48.11	even	4		240.2.bc.d.43.3	yes	6
48.29	odd	4		1920.2.bc.h.1183.2		6
48.35	even	4		1920.2.bc.g.1183.2		6
60.47	odd	4		960.2.bc.d.367.2		6
80.27	even	4	inner	720.2.z.e.667.3		6
120.77	even	4		1920.2.bc.g.607.2		6
120.107	odd	4		1920.2.bc.h.607.2		6
240.77	even	4		1920.2.y.h.1567.2		6
240.107	odd	4		240.2.y.d.187.1	yes	6
240.197	even	4		960.2.y.d.847.2		6
240.227	odd	4		1920.2.y.g.1567.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.y.d.163.1	✓	6	3.2	odd	2
240.2.y.d.187.1	yes	6	240.107	odd	4
240.2.bc.d.43.3	yes	6	48.11	even	4
240.2.bc.d.67.3	yes	6	15.2	even	4
720.2.z.e.163.3		6	1.1	even	1	trivial
720.2.z.e.667.3		6	80.27	even	4	inner
720.2.bd.e.307.1		6	5.2	odd	4
720.2.bd.e.523.1		6	16.11	odd	4
960.2.y.d.847.2		6	240.197	even	4
960.2.y.d.943.2		6	12.11	even	2
960.2.bc.d.367.2		6	60.47	odd	4
960.2.bc.d.463.2		6	48.5	odd	4
1920.2.y.g.223.2		6	24.5	odd	2
1920.2.y.g.1567.2		6	240.227	odd	4
1920.2.y.h.223.2		6	24.11	even	2
1920.2.y.h.1567.2		6	240.77	even	4
1920.2.bc.g.607.2		6	120.77	even	4
1920.2.bc.g.1183.2		6	48.35	even	4
1920.2.bc.h.607.2		6	120.107	odd	4
1920.2.bc.h.1183.2		6	48.29	odd	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.z (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.24464 + 0.671462i) q^{2} +(1.09828 + 1.67146i) q^{4} +(-1.00000 + 2.00000i) q^{5} +(0.146365 - 0.146365i) q^{7} +(0.244644 + 2.81783i) q^{8} +(-2.58757 + 1.81783i) q^{10} +(-0.146365 - 0.146365i) q^{11} +(0.280452 - 0.0838942i) q^{14} +(-1.58757 + 3.67146i) q^{16} +(-3.68585 + 3.68585i) q^{17} +(2.83221 + 2.83221i) q^{19} +(-4.44120 + 0.525096i) q^{20} +(-0.0838942 - 0.280452i) q^{22} +(2.83221 + 2.83221i) q^{23} +(-3.00000 - 4.00000i) q^{25} +(0.405394 + 0.0838942i) q^{28} +(1.00000 - 1.00000i) q^{29} -0.292731i q^{31} +(-4.44120 + 3.50367i) q^{32} +(-7.06247 + 2.11266i) q^{34} +(0.146365 + 0.439096i) q^{35} -9.37169i q^{37} +(1.62337 + 5.42682i) q^{38} +(-5.88030 - 2.32854i) q^{40} -4.00000i q^{41} +9.66442i q^{43} +(0.0838942 - 0.405394i) q^{44} +(1.62337 + 5.42682i) q^{46} +(-7.12494 - 7.12494i) q^{47} +6.95715i q^{49} +(-1.04809 - 6.99296i) q^{50} +11.9572 q^{53} +(0.439096 - 0.146365i) q^{55} +(0.448240 + 0.376625i) q^{56} +(1.91611 - 0.573183i) q^{58} +(9.51806 - 9.51806i) q^{59} +(1.68585 + 1.68585i) q^{61} +(0.196558 - 0.364346i) q^{62} +(-7.88030 + 1.37873i) q^{64} +13.0790i q^{67} +(-10.2088 - 2.11266i) q^{68} +(-0.112663 + 0.644798i) q^{70} +4.58546 q^{71} +(6.37169 - 6.37169i) q^{73} +(6.29273 - 11.6644i) q^{74} +(-1.62337 + 7.84449i) q^{76} -0.0428457 q^{77} +4.58546 q^{79} +(-5.75536 - 6.84660i) q^{80} +(2.68585 - 4.97858i) q^{82} +8.58546 q^{83} +(-3.68585 - 11.0575i) q^{85} +(-6.48929 + 12.0288i) q^{86} +(0.376625 - 0.448240i) q^{88} -3.37169 q^{89} +(-1.62337 + 7.84449i) q^{92} +(-4.08389 - 13.6521i) q^{94} +(-8.49663 + 2.83221i) q^{95} +(-3.58546 + 3.58546i) q^{97} +(-4.67146 + 8.65918i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{4} - 6 q^{5} - 2 q^{7} - 6 q^{8} + 4 q^{10} + 2 q^{11} + 6 q^{14} + 10 q^{16} + 2 q^{17} - 10 q^{19} - 10 q^{20} - 14 q^{22} - 10 q^{23} - 18 q^{25} - 26 q^{28} + 6 q^{29} - 10 q^{32} - 26 q^{34}+ \cdots - 22 q^{98}+O(q^{100}) \) 6 * q + 2 * q^4 - 6 * q^5 - 2 * q^7 - 6 * q^8 + 4 * q^10 + 2 * q^11 + 6 * q^14 + 10 * q^16 + 2 * q^17 - 10 * q^19 - 10 * q^20 - 14 * q^22 - 10 * q^23 - 18 * q^25 - 26 * q^28 + 6 * q^29 - 10 * q^32 - 26 * q^34 - 2 * q^35 + 2 * q^38 - 10 * q^40 + 14 * q^44 + 2 * q^46 - 10 * q^47 - 8 * q^50 + 12 * q^53 - 6 * q^55 + 34 * q^56 - 2 * q^58 + 6 * q^59 - 14 * q^61 - 8 * q^62 - 22 * q^64 - 42 * q^68 + 22 * q^70 + 16 * q^71 - 10 * q^73 + 32 * q^74 - 2 * q^76 - 60 * q^77 + 16 * q^79 - 42 * q^80 - 8 * q^82 + 40 * q^83 + 2 * q^85 - 24 * q^86 + 10 * q^88 + 28 * q^89 - 2 * q^92 - 38 * q^94 + 30 * q^95 - 10 * q^97 - 22 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more